Properties

Label 147.6.e.l.67.1
Level $147$
Weight $6$
Character 147.67
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: \(\Q(\sqrt{-3}, \sqrt{-83})\)
Defining polynomial: \( x^{4} - x^{3} - 20x^{2} - 21x + 441 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.1
Root \(4.19493 + 1.84460i\) of defining polynomial
Character \(\chi\) \(=\) 147.67
Dual form 147.6.e.l.79.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.19493 - 5.53379i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-4.41520 + 7.64735i) q^{4} +(19.3645 + 33.5404i) q^{5} +57.5088 q^{6} -148.051 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\) \(q+(-3.19493 - 5.53379i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-4.41520 + 7.64735i) q^{4} +(19.3645 + 33.5404i) q^{5} +57.5088 q^{6} -148.051 q^{8} +(-40.5000 - 70.1481i) q^{9} +(123.737 - 214.318i) q^{10} +(288.195 - 499.168i) q^{11} +(-39.7368 - 68.8262i) q^{12} -391.491 q^{13} -348.562 q^{15} +(614.298 + 1064.00i) q^{16} +(-664.850 + 1151.55i) q^{17} +(-258.790 + 448.237i) q^{18} +(471.237 + 816.206i) q^{19} -341.993 q^{20} -3683.05 q^{22} +(816.040 + 1413.42i) q^{23} +(666.228 - 1153.94i) q^{24} +(812.530 - 1407.34i) q^{25} +(1250.79 + 2166.43i) q^{26} +729.000 q^{27} -1463.54 q^{29} +(1113.63 + 1928.87i) q^{30} +(-1956.21 + 3388.25i) q^{31} +(1556.47 - 2695.89i) q^{32} +(2593.75 + 4492.51i) q^{33} +8496.61 q^{34} +715.262 q^{36} +(8150.17 + 14116.5i) q^{37} +(3011.14 - 5215.45i) q^{38} +(1761.71 - 3051.37i) q^{39} +(-2866.93 - 4965.67i) q^{40} +13103.8 q^{41} +14733.5 q^{43} +(2544.88 + 4407.86i) q^{44} +(1568.53 - 2716.77i) q^{45} +(5214.38 - 9031.58i) q^{46} +(-3407.26 - 5901.55i) q^{47} -11057.4 q^{48} -10383.9 q^{50} +(-5983.65 - 10364.0i) q^{51} +(1728.51 - 2993.87i) q^{52} +(1005.67 - 1741.87i) q^{53} +(-2329.11 - 4034.13i) q^{54} +22323.0 q^{55} -8482.26 q^{57} +(4675.93 + 8098.94i) q^{58} +(25726.6 - 44559.7i) q^{59} +(1538.97 - 2665.57i) q^{60} +(20548.9 + 35591.8i) q^{61} +24999.8 q^{62} +19423.8 q^{64} +(-7581.04 - 13130.8i) q^{65} +(16573.7 - 28706.6i) q^{66} +(-25289.1 + 43802.0i) q^{67} +(-5870.89 - 10168.7i) q^{68} -14688.7 q^{69} +39970.6 q^{71} +(5996.05 + 10385.5i) q^{72} +(-27843.3 + 48226.0i) q^{73} +(52078.5 - 90202.6i) q^{74} +(7312.77 + 12666.1i) q^{75} -8322.42 q^{76} -22514.2 q^{78} +(31575.7 + 54690.7i) q^{79} +(-23791.2 + 41207.6i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(-41865.9 - 72513.8i) q^{82} -45572.4 q^{83} -51498.1 q^{85} +(-47072.5 - 81532.0i) q^{86} +(6585.95 - 11407.2i) q^{87} +(-42667.5 + 73902.2i) q^{88} +(7843.34 + 13585.1i) q^{89} -20045.4 q^{90} -14411.9 q^{92} +(-17605.9 - 30494.3i) q^{93} +(-21771.9 + 37710.1i) q^{94} +(-18250.6 + 31610.9i) q^{95} +(14008.3 + 24263.0i) q^{96} -3128.49 q^{97} -46687.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 3 q^{2} - 18 q^{3} - 65 q^{4} - 33 q^{5} - 54 q^{6} - 750 q^{8} - 162 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 3 q^{2} - 18 q^{3} - 65 q^{4} - 33 q^{5} - 54 q^{6} - 750 q^{8} - 162 q^{9} + 921 q^{10} + 1137 q^{11} - 585 q^{12} - 1850 q^{13} + 594 q^{15} + 895 q^{16} - 324 q^{17} + 243 q^{18} + 2311 q^{19} + 7374 q^{20} + 3162 q^{22} - 1596 q^{23} + 3375 q^{24} - 395 q^{25} - 2508 q^{26} + 2916 q^{27} - 4434 q^{29} + 8289 q^{30} + 4294 q^{31} - 1017 q^{32} + 10233 q^{33} + 35880 q^{34} + 10530 q^{36} + 19109 q^{37} - 6828 q^{38} + 8325 q^{39} + 10545 q^{40} + 25716 q^{41} - 5542 q^{43} + 36579 q^{44} - 2673 q^{45} + 40740 q^{46} - 23160 q^{47} - 16110 q^{48} - 58704 q^{50} - 2916 q^{51} + 33424 q^{52} + 31653 q^{53} + 2187 q^{54} - 35778 q^{55} - 41598 q^{57} + 2277 q^{58} + 41097 q^{59} - 33183 q^{60} + 42052 q^{61} + 204114 q^{62} - 60062 q^{64} + 23106 q^{65} - 14229 q^{66} - 30763 q^{67} + 44748 q^{68} + 28728 q^{69} + 204192 q^{71} + 30375 q^{72} - 28577 q^{73} + 77784 q^{74} - 3555 q^{75} - 170384 q^{76} + 45144 q^{78} + 18464 q^{79} - 71511 q^{80} - 13122 q^{81} - 86040 q^{82} - 122358 q^{83} - 247272 q^{85} - 258510 q^{86} + 19953 q^{87} - 212565 q^{88} + 29322 q^{89} - 149202 q^{90} + 333816 q^{92} + 38646 q^{93} + 109938 q^{94} + 61662 q^{95} - 9153 q^{96} + 19582 q^{97} - 184194 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(50\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.19493 5.53379i −0.564790 0.978245i −0.997069 0.0765049i \(-0.975624\pi\)
0.432279 0.901740i \(-0.357709\pi\)
\(3\) −4.50000 + 7.79423i −0.288675 + 0.500000i
\(4\) −4.41520 + 7.64735i −0.137975 + 0.238980i
\(5\) 19.3645 + 33.5404i 0.346403 + 0.599988i 0.985608 0.169049i \(-0.0540695\pi\)
−0.639204 + 0.769037i \(0.720736\pi\)
\(6\) 57.5088 0.652163
\(7\) 0 0
\(8\) −148.051 −0.817872
\(9\) −40.5000 70.1481i −0.166667 0.288675i
\(10\) 123.737 214.318i 0.391290 0.677734i
\(11\) 288.195 499.168i 0.718133 1.24384i −0.243606 0.969874i \(-0.578330\pi\)
0.961739 0.273968i \(-0.0883362\pi\)
\(12\) −39.7368 68.8262i −0.0796599 0.137975i
\(13\) −391.491 −0.642486 −0.321243 0.946997i \(-0.604101\pi\)
−0.321243 + 0.946997i \(0.604101\pi\)
\(14\) 0 0
\(15\) −348.562 −0.399992
\(16\) 614.298 + 1064.00i 0.599901 + 1.03906i
\(17\) −664.850 + 1151.55i −0.557958 + 0.966412i 0.439709 + 0.898140i \(0.355082\pi\)
−0.997667 + 0.0682711i \(0.978252\pi\)
\(18\) −258.790 + 448.237i −0.188263 + 0.326082i
\(19\) 471.237 + 816.206i 0.299471 + 0.518699i 0.976015 0.217703i \(-0.0698564\pi\)
−0.676544 + 0.736402i \(0.736523\pi\)
\(20\) −341.993 −0.191180
\(21\) 0 0
\(22\) −3683.05 −1.62238
\(23\) 816.040 + 1413.42i 0.321656 + 0.557124i 0.980830 0.194866i \(-0.0624272\pi\)
−0.659174 + 0.751991i \(0.729094\pi\)
\(24\) 666.228 1153.94i 0.236099 0.408936i
\(25\) 812.530 1407.34i 0.260009 0.450350i
\(26\) 1250.79 + 2166.43i 0.362869 + 0.628508i
\(27\) 729.000 0.192450
\(28\) 0 0
\(29\) −1463.54 −0.323155 −0.161577 0.986860i \(-0.551658\pi\)
−0.161577 + 0.986860i \(0.551658\pi\)
\(30\) 1113.63 + 1928.87i 0.225911 + 0.391290i
\(31\) −1956.21 + 3388.25i −0.365604 + 0.633245i −0.988873 0.148763i \(-0.952471\pi\)
0.623269 + 0.782008i \(0.285804\pi\)
\(32\) 1556.47 2695.89i 0.268700 0.465401i
\(33\) 2593.75 + 4492.51i 0.414614 + 0.718133i
\(34\) 8496.61 1.26052
\(35\) 0 0
\(36\) 715.262 0.0919833
\(37\) 8150.17 + 14116.5i 0.978729 + 1.69521i 0.667038 + 0.745024i \(0.267562\pi\)
0.311691 + 0.950184i \(0.399105\pi\)
\(38\) 3011.14 5215.45i 0.338277 0.585912i
\(39\) 1761.71 3051.37i 0.185470 0.321243i
\(40\) −2866.93 4965.67i −0.283314 0.490714i
\(41\) 13103.8 1.21741 0.608707 0.793395i \(-0.291688\pi\)
0.608707 + 0.793395i \(0.291688\pi\)
\(42\) 0 0
\(43\) 14733.5 1.21516 0.607582 0.794257i \(-0.292140\pi\)
0.607582 + 0.794257i \(0.292140\pi\)
\(44\) 2544.88 + 4407.86i 0.198169 + 0.343238i
\(45\) 1568.53 2716.77i 0.115468 0.199996i
\(46\) 5214.38 9031.58i 0.363336 0.629316i
\(47\) −3407.26 5901.55i −0.224989 0.389692i 0.731327 0.682027i \(-0.238901\pi\)
−0.956316 + 0.292335i \(0.905568\pi\)
\(48\) −11057.4 −0.692706
\(49\) 0 0
\(50\) −10383.9 −0.587403
\(51\) −5983.65 10364.0i −0.322137 0.557958i
\(52\) 1728.51 2993.87i 0.0886470 0.153541i
\(53\) 1005.67 1741.87i 0.0491775 0.0851779i −0.840389 0.541984i \(-0.817673\pi\)
0.889566 + 0.456806i \(0.151007\pi\)
\(54\) −2329.11 4034.13i −0.108694 0.188263i
\(55\) 22323.0 0.995054
\(56\) 0 0
\(57\) −8482.26 −0.345800
\(58\) 4675.93 + 8098.94i 0.182515 + 0.316125i
\(59\) 25726.6 44559.7i 0.962170 1.66653i 0.245135 0.969489i \(-0.421168\pi\)
0.717035 0.697037i \(-0.245499\pi\)
\(60\) 1538.97 2665.57i 0.0551889 0.0955900i
\(61\) 20548.9 + 35591.8i 0.707073 + 1.22469i 0.965938 + 0.258773i \(0.0833181\pi\)
−0.258865 + 0.965913i \(0.583349\pi\)
\(62\) 24999.8 0.825958
\(63\) 0 0
\(64\) 19423.8 0.592766
\(65\) −7581.04 13130.8i −0.222559 0.385484i
\(66\) 16573.7 28706.6i 0.468340 0.811188i
\(67\) −25289.1 + 43802.0i −0.688250 + 1.19208i 0.284153 + 0.958779i \(0.408288\pi\)
−0.972404 + 0.233305i \(0.925046\pi\)
\(68\) −5870.89 10168.7i −0.153968 0.266681i
\(69\) −14688.7 −0.371416
\(70\) 0 0
\(71\) 39970.6 0.941012 0.470506 0.882397i \(-0.344071\pi\)
0.470506 + 0.882397i \(0.344071\pi\)
\(72\) 5996.05 + 10385.5i 0.136312 + 0.236099i
\(73\) −27843.3 + 48226.0i −0.611524 + 1.05919i 0.379459 + 0.925208i \(0.376110\pi\)
−0.990984 + 0.133983i \(0.957223\pi\)
\(74\) 52078.5 90202.6i 1.10555 1.91487i
\(75\) 7312.77 + 12666.1i 0.150117 + 0.260009i
\(76\) −8322.42 −0.165278
\(77\) 0 0
\(78\) −22514.2 −0.419006
\(79\) 31575.7 + 54690.7i 0.569226 + 0.985929i 0.996643 + 0.0818739i \(0.0260905\pi\)
−0.427416 + 0.904055i \(0.640576\pi\)
\(80\) −23791.2 + 41207.6i −0.415615 + 0.719867i
\(81\) −3280.50 + 5681.99i −0.0555556 + 0.0962250i
\(82\) −41865.9 72513.8i −0.687583 1.19093i
\(83\) −45572.4 −0.726116 −0.363058 0.931766i \(-0.618267\pi\)
−0.363058 + 0.931766i \(0.618267\pi\)
\(84\) 0 0
\(85\) −51498.1 −0.773114
\(86\) −47072.5 81532.0i −0.686312 1.18873i
\(87\) 6585.95 11407.2i 0.0932868 0.161577i
\(88\) −42667.5 + 73902.2i −0.587341 + 1.01730i
\(89\) 7843.34 + 13585.1i 0.104961 + 0.181797i 0.913722 0.406340i \(-0.133195\pi\)
−0.808762 + 0.588137i \(0.799862\pi\)
\(90\) −20045.4 −0.260860
\(91\) 0 0
\(92\) −14411.9 −0.177522
\(93\) −17605.9 30494.3i −0.211082 0.365604i
\(94\) −21771.9 + 37710.1i −0.254143 + 0.440188i
\(95\) −18250.6 + 31610.9i −0.207476 + 0.359358i
\(96\) 14008.3 + 24263.0i 0.155134 + 0.268700i
\(97\) −3128.49 −0.0337603 −0.0168801 0.999858i \(-0.505373\pi\)
−0.0168801 + 0.999858i \(0.505373\pi\)
\(98\) 0 0
\(99\) −46687.6 −0.478755
\(100\) 7174.96 + 12427.4i 0.0717496 + 0.124274i
\(101\) −84505.5 + 146368.i −0.824292 + 1.42772i 0.0781663 + 0.996940i \(0.475093\pi\)
−0.902459 + 0.430776i \(0.858240\pi\)
\(102\) −38234.7 + 66224.5i −0.363880 + 0.630258i
\(103\) 56410.1 + 97705.1i 0.523918 + 0.907453i 0.999612 + 0.0278422i \(0.00886360\pi\)
−0.475694 + 0.879611i \(0.657803\pi\)
\(104\) 57960.5 0.525471
\(105\) 0 0
\(106\) −12852.2 −0.111100
\(107\) 11154.7 + 19320.6i 0.0941890 + 0.163140i 0.909270 0.416207i \(-0.136641\pi\)
−0.815081 + 0.579347i \(0.803308\pi\)
\(108\) −3218.68 + 5574.92i −0.0265533 + 0.0459917i
\(109\) 41909.8 72589.8i 0.337869 0.585207i −0.646162 0.763200i \(-0.723627\pi\)
0.984032 + 0.177993i \(0.0569604\pi\)
\(110\) −71320.6 123531.i −0.561996 0.973406i
\(111\) −146703. −1.13014
\(112\) 0 0
\(113\) −40928.4 −0.301529 −0.150764 0.988570i \(-0.548174\pi\)
−0.150764 + 0.988570i \(0.548174\pi\)
\(114\) 27100.3 + 46939.0i 0.195304 + 0.338277i
\(115\) −31604.4 + 54740.5i −0.222845 + 0.385980i
\(116\) 6461.84 11192.2i 0.0445873 0.0772275i
\(117\) 15855.4 + 27462.3i 0.107081 + 0.185470i
\(118\) −328779. −2.17369
\(119\) 0 0
\(120\) 51604.8 0.327142
\(121\) −85587.1 148241.i −0.531429 0.920462i
\(122\) 131305. 227427.i 0.798695 1.38338i
\(123\) −58967.2 + 102134.i −0.351437 + 0.608707i
\(124\) −17274.1 29919.6i −0.100888 0.174744i
\(125\) 183965. 1.05308
\(126\) 0 0
\(127\) 83270.1 0.458120 0.229060 0.973412i \(-0.426435\pi\)
0.229060 + 0.973412i \(0.426435\pi\)
\(128\) −111865. 193756.i −0.603488 1.04527i
\(129\) −66300.7 + 114836.i −0.350788 + 0.607582i
\(130\) −48441.9 + 83903.8i −0.251398 + 0.435435i
\(131\) −83437.4 144518.i −0.424798 0.735772i 0.571603 0.820530i \(-0.306322\pi\)
−0.996402 + 0.0847580i \(0.972988\pi\)
\(132\) −45807.8 −0.228825
\(133\) 0 0
\(134\) 323188. 1.55487
\(135\) 14116.7 + 24450.9i 0.0666653 + 0.115468i
\(136\) 98431.5 170488.i 0.456338 0.790401i
\(137\) −19111.9 + 33102.9i −0.0869969 + 0.150683i −0.906240 0.422763i \(-0.861060\pi\)
0.819244 + 0.573446i \(0.194394\pi\)
\(138\) 46929.5 + 81284.2i 0.209772 + 0.363336i
\(139\) −106263. −0.466492 −0.233246 0.972418i \(-0.574935\pi\)
−0.233246 + 0.972418i \(0.574935\pi\)
\(140\) 0 0
\(141\) 61330.7 0.259795
\(142\) −127703. 221189.i −0.531474 0.920540i
\(143\) −112826. + 195420.i −0.461390 + 0.799151i
\(144\) 49758.2 86183.7i 0.199967 0.346353i
\(145\) −28340.8 49087.8i −0.111942 0.193889i
\(146\) 355830. 1.38153
\(147\) 0 0
\(148\) −143938. −0.540160
\(149\) −96277.8 166758.i −0.355271 0.615348i 0.631893 0.775056i \(-0.282278\pi\)
−0.987164 + 0.159708i \(0.948945\pi\)
\(150\) 46727.6 80934.6i 0.169569 0.293701i
\(151\) −70849.3 + 122715.i −0.252868 + 0.437980i −0.964314 0.264761i \(-0.914707\pi\)
0.711447 + 0.702740i \(0.248040\pi\)
\(152\) −69766.9 120840.i −0.244929 0.424230i
\(153\) 107706. 0.371972
\(154\) 0 0
\(155\) −151524. −0.506586
\(156\) 15556.6 + 26944.8i 0.0511804 + 0.0886470i
\(157\) 282885. 489972.i 0.915928 1.58643i 0.110392 0.993888i \(-0.464789\pi\)
0.805536 0.592546i \(-0.201877\pi\)
\(158\) 201764. 349466.i 0.642986 1.11368i
\(159\) 9051.04 + 15676.9i 0.0283926 + 0.0491775i
\(160\) 120562. 0.372314
\(161\) 0 0
\(162\) 41923.9 0.125509
\(163\) 215101. + 372565.i 0.634121 + 1.09833i 0.986701 + 0.162549i \(0.0519714\pi\)
−0.352579 + 0.935782i \(0.614695\pi\)
\(164\) −57856.0 + 100210.i −0.167973 + 0.290937i
\(165\) −100454. + 173991.i −0.287247 + 0.497527i
\(166\) 145601. + 252188.i 0.410103 + 0.710319i
\(167\) 240265. 0.666653 0.333327 0.942811i \(-0.391829\pi\)
0.333327 + 0.942811i \(0.391829\pi\)
\(168\) 0 0
\(169\) −218028. −0.587212
\(170\) 164533. + 284979.i 0.436647 + 0.756295i
\(171\) 38170.2 66112.7i 0.0998238 0.172900i
\(172\) −65051.3 + 112672.i −0.167662 + 0.290399i
\(173\) −89650.1 155279.i −0.227738 0.394454i 0.729399 0.684088i \(-0.239800\pi\)
−0.957137 + 0.289634i \(0.906466\pi\)
\(174\) −84166.7 −0.210750
\(175\) 0 0
\(176\) 708151. 1.72323
\(177\) 231539. + 401037.i 0.555509 + 0.962170i
\(178\) 50117.9 86806.8i 0.118561 0.205354i
\(179\) 287780. 498449.i 0.671317 1.16275i −0.306214 0.951963i \(-0.599062\pi\)
0.977531 0.210792i \(-0.0676043\pi\)
\(180\) 13850.7 + 23990.2i 0.0318633 + 0.0551889i
\(181\) −581006. −1.31821 −0.659105 0.752051i \(-0.729065\pi\)
−0.659105 + 0.752051i \(0.729065\pi\)
\(182\) 0 0
\(183\) −369880. −0.816458
\(184\) −120815. 209258.i −0.263073 0.455657i
\(185\) −315648. + 546719.i −0.678070 + 1.17445i
\(186\) −112499. + 194854.i −0.238433 + 0.412979i
\(187\) 383213. + 663744.i 0.801376 + 1.38802i
\(188\) 60174.9 0.124171
\(189\) 0 0
\(190\) 233237. 0.468721
\(191\) 330280. + 572062.i 0.655087 + 1.13464i 0.981872 + 0.189545i \(0.0607013\pi\)
−0.326785 + 0.945099i \(0.605965\pi\)
\(192\) −87407.0 + 151393.i −0.171117 + 0.296383i
\(193\) 278655. 482645.i 0.538485 0.932684i −0.460501 0.887659i \(-0.652330\pi\)
0.998986 0.0450243i \(-0.0143365\pi\)
\(194\) 9995.33 + 17312.4i 0.0190675 + 0.0330258i
\(195\) 136459. 0.256989
\(196\) 0 0
\(197\) −761400. −1.39781 −0.698904 0.715216i \(-0.746328\pi\)
−0.698904 + 0.715216i \(0.746328\pi\)
\(198\) 149164. + 258359.i 0.270396 + 0.468340i
\(199\) −67929.9 + 117658.i −0.121598 + 0.210615i −0.920398 0.390982i \(-0.872135\pi\)
0.798800 + 0.601597i \(0.205469\pi\)
\(200\) −120296. + 208358.i −0.212655 + 0.368328i
\(201\) −227602. 394218.i −0.397361 0.688250i
\(202\) 1.07996e6 1.86221
\(203\) 0 0
\(204\) 105676. 0.177787
\(205\) 253750. + 439507.i 0.421716 + 0.730434i
\(206\) 360453. 624323.i 0.591807 1.02504i
\(207\) 66099.2 114487.i 0.107219 0.185708i
\(208\) −240492. 416545.i −0.385428 0.667581i
\(209\) 543232. 0.860240
\(210\) 0 0
\(211\) −991157. −1.53263 −0.766313 0.642467i \(-0.777911\pi\)
−0.766313 + 0.642467i \(0.777911\pi\)
\(212\) 8880.48 + 15381.4i 0.0135705 + 0.0235048i
\(213\) −179868. + 311540.i −0.271647 + 0.470506i
\(214\) 71277.3 123456.i 0.106394 0.184280i
\(215\) 285307. + 494167.i 0.420937 + 0.729084i
\(216\) −107929. −0.157400
\(217\) 0 0
\(218\) −535596. −0.763301
\(219\) −250590. 434034.i −0.353064 0.611524i
\(220\) −98560.7 + 170712.i −0.137293 + 0.237798i
\(221\) 260283. 450823.i 0.358480 0.620906i
\(222\) 468706. + 811823.i 0.638291 + 1.10555i
\(223\) −543344. −0.731666 −0.365833 0.930681i \(-0.619216\pi\)
−0.365833 + 0.930681i \(0.619216\pi\)
\(224\) 0 0
\(225\) −131630. −0.173340
\(226\) 130764. + 226489.i 0.170300 + 0.294969i
\(227\) 8.16704 14.1457i 1.05196e−5 1.82205e-5i −0.866020 0.500009i \(-0.833330\pi\)
0.866031 + 0.499991i \(0.166663\pi\)
\(228\) 37450.9 64866.8i 0.0477117 0.0826391i
\(229\) −38689.5 67012.2i −0.0487534 0.0844433i 0.840619 0.541627i \(-0.182192\pi\)
−0.889372 + 0.457184i \(0.848858\pi\)
\(230\) 403896. 0.503443
\(231\) 0 0
\(232\) 216679. 0.264299
\(233\) 51828.6 + 89769.9i 0.0625432 + 0.108328i 0.895602 0.444857i \(-0.146746\pi\)
−0.833058 + 0.553185i \(0.813412\pi\)
\(234\) 101314. 175481.i 0.120956 0.209503i
\(235\) 131960. 228561.i 0.155874 0.269981i
\(236\) 227176. + 393480.i 0.265511 + 0.459878i
\(237\) −568362. −0.657286
\(238\) 0 0
\(239\) 689109. 0.780356 0.390178 0.920739i \(-0.372413\pi\)
0.390178 + 0.920739i \(0.372413\pi\)
\(240\) −214121. 370868.i −0.239956 0.415615i
\(241\) 110148. 190782.i 0.122161 0.211590i −0.798458 0.602050i \(-0.794351\pi\)
0.920620 + 0.390460i \(0.127684\pi\)
\(242\) −546890. + 947242.i −0.600291 + 1.03973i
\(243\) −29524.5 51137.9i −0.0320750 0.0555556i
\(244\) −362910. −0.390234
\(245\) 0 0
\(246\) 753585. 0.793953
\(247\) −184485. 319537.i −0.192406 0.333257i
\(248\) 289618. 501633.i 0.299017 0.517913i
\(249\) 205076. 355201.i 0.209612 0.363058i
\(250\) −587757. 1.01803e6i −0.594768 1.03017i
\(251\) −1.43641e6 −1.43912 −0.719558 0.694433i \(-0.755655\pi\)
−0.719558 + 0.694433i \(0.755655\pi\)
\(252\) 0 0
\(253\) 940714. 0.923966
\(254\) −266042. 460799.i −0.258742 0.448154i
\(255\) 231741. 401388.i 0.223179 0.386557i
\(256\) −404021. + 699785.i −0.385305 + 0.667367i
\(257\) −454598. 787388.i −0.429334 0.743628i 0.567480 0.823387i \(-0.307918\pi\)
−0.996814 + 0.0797589i \(0.974585\pi\)
\(258\) 847306. 0.792485
\(259\) 0 0
\(260\) 133887. 0.122830
\(261\) 59273.5 + 102665.i 0.0538592 + 0.0932868i
\(262\) −533154. + 923450.i −0.479843 + 0.831113i
\(263\) −374528. + 648702.i −0.333884 + 0.578304i −0.983270 0.182155i \(-0.941693\pi\)
0.649386 + 0.760459i \(0.275026\pi\)
\(264\) −384007. 665120.i −0.339101 0.587341i
\(265\) 77897.4 0.0681410
\(266\) 0 0
\(267\) −141180. −0.121198
\(268\) −223313. 386789.i −0.189923 0.328956i
\(269\) 334972. 580189.i 0.282246 0.488865i −0.689691 0.724104i \(-0.742254\pi\)
0.971938 + 0.235238i \(0.0755871\pi\)
\(270\) 90204.1 156238.i 0.0753038 0.130430i
\(271\) 270330. + 468225.i 0.223599 + 0.387285i 0.955898 0.293698i \(-0.0948860\pi\)
−0.732299 + 0.680983i \(0.761553\pi\)
\(272\) −1.63367e6 −1.33888
\(273\) 0 0
\(274\) 244246. 0.196540
\(275\) −468334. 811178.i −0.373443 0.646821i
\(276\) 64853.6 112330.i 0.0512462 0.0887610i
\(277\) 200955. 348064.i 0.157362 0.272558i −0.776555 0.630050i \(-0.783035\pi\)
0.933916 + 0.357491i \(0.116368\pi\)
\(278\) 339502. + 588035.i 0.263470 + 0.456343i
\(279\) 316906. 0.243736
\(280\) 0 0
\(281\) −429139. −0.324214 −0.162107 0.986773i \(-0.551829\pi\)
−0.162107 + 0.986773i \(0.551829\pi\)
\(282\) −195947. 339391.i −0.146729 0.254143i
\(283\) −170463. + 295251.i −0.126522 + 0.219142i −0.922327 0.386411i \(-0.873715\pi\)
0.795805 + 0.605553i \(0.207048\pi\)
\(284\) −176478. + 305669.i −0.129836 + 0.224883i
\(285\) −164255. 284498.i −0.119786 0.207476i
\(286\) 1.44188e6 1.04235
\(287\) 0 0
\(288\) −252149. −0.179133
\(289\) −174123. 301590.i −0.122634 0.212409i
\(290\) −181094. + 313664.i −0.126447 + 0.219013i
\(291\) 14078.2 24384.2i 0.00974575 0.0168801i
\(292\) −245868. 425855.i −0.168750 0.292284i
\(293\) 388847. 0.264612 0.132306 0.991209i \(-0.457762\pi\)
0.132306 + 0.991209i \(0.457762\pi\)
\(294\) 0 0
\(295\) 1.99273e6 1.33319
\(296\) −1.20664e6 2.08996e6i −0.800475 1.38646i
\(297\) 210094. 363894.i 0.138205 0.239378i
\(298\) −615202. + 1.06556e6i −0.401307 + 0.695085i
\(299\) −319472. 553342.i −0.206659 0.357945i
\(300\) −129149. −0.0828493
\(301\) 0 0
\(302\) 905435. 0.571268
\(303\) −760549. 1.31731e6i −0.475905 0.824292i
\(304\) −578960. + 1.00279e6i −0.359306 + 0.622336i
\(305\) −795840. + 1.37844e6i −0.489865 + 0.848471i
\(306\) −344113. 596021.i −0.210086 0.363880i
\(307\) 2.35747e6 1.42758 0.713789 0.700361i \(-0.246978\pi\)
0.713789 + 0.700361i \(0.246978\pi\)
\(308\) 0 0
\(309\) −1.01538e6 −0.604969
\(310\) 484110. + 838503.i 0.286114 + 0.495565i
\(311\) −718314. + 1.24416e6i −0.421127 + 0.729414i −0.996050 0.0887939i \(-0.971699\pi\)
0.574923 + 0.818208i \(0.305032\pi\)
\(312\) −260822. + 451758.i −0.151691 + 0.262736i
\(313\) −411400. 712566.i −0.237358 0.411116i 0.722598 0.691269i \(-0.242948\pi\)
−0.959955 + 0.280153i \(0.909615\pi\)
\(314\) −3.61520e6 −2.06923
\(315\) 0 0
\(316\) −557652. −0.314156
\(317\) 883467. + 1.53021e6i 0.493790 + 0.855269i 0.999974 0.00715584i \(-0.00227779\pi\)
−0.506184 + 0.862425i \(0.668944\pi\)
\(318\) 57835.0 100173.i 0.0320718 0.0555499i
\(319\) −421786. + 730555.i −0.232068 + 0.401954i
\(320\) 376132. + 651480.i 0.205336 + 0.355653i
\(321\) −200785. −0.108760
\(322\) 0 0
\(323\) −1.25321e6 −0.668370
\(324\) −28968.1 50174.3i −0.0153306 0.0265533i
\(325\) −318098. + 550962.i −0.167052 + 0.289343i
\(326\) 1.37446e6 2.38064e6i 0.716291 1.24065i
\(327\) 377188. + 653309.i 0.195069 + 0.337869i
\(328\) −1.94003e6 −0.995689
\(329\) 0 0
\(330\) 1.28377e6 0.648937
\(331\) 1526.14 + 2643.35i 0.000765638 + 0.00132612i 0.866408 0.499337i \(-0.166423\pi\)
−0.865642 + 0.500663i \(0.833090\pi\)
\(332\) 201211. 348508.i 0.100186 0.173527i
\(333\) 660164. 1.14344e6i 0.326243 0.565069i
\(334\) −767632. 1.32958e6i −0.376519 0.652150i
\(335\) −1.95885e6 −0.953649
\(336\) 0 0
\(337\) 2.02939e6 0.973398 0.486699 0.873570i \(-0.338201\pi\)
0.486699 + 0.873570i \(0.338201\pi\)
\(338\) 696584. + 1.20652e6i 0.331651 + 0.574437i
\(339\) 184178. 319006.i 0.0870439 0.150764i
\(340\) 227374. 393824.i 0.106670 0.184759i
\(341\) 1.12754e6 + 1.95295e6i 0.525104 + 0.909507i
\(342\) −487805. −0.225518
\(343\) 0 0
\(344\) −2.18130e6 −0.993848
\(345\) −284440. 492665.i −0.128660 0.222845i
\(346\) −572852. + 992209.i −0.257248 + 0.445567i
\(347\) −1.89109e6 + 3.27547e6i −0.843119 + 1.46033i 0.0441252 + 0.999026i \(0.485950\pi\)
−0.887245 + 0.461299i \(0.847383\pi\)
\(348\) 58156.6 + 100730.i 0.0257425 + 0.0445873i
\(349\) −291147. −0.127953 −0.0639763 0.997951i \(-0.520378\pi\)
−0.0639763 + 0.997951i \(0.520378\pi\)
\(350\) 0 0
\(351\) −285397. −0.123646
\(352\) −897136. 1.55389e6i −0.385924 0.668440i
\(353\) 192538. 333486.i 0.0822394 0.142443i −0.821972 0.569528i \(-0.807126\pi\)
0.904212 + 0.427085i \(0.140459\pi\)
\(354\) 1.47950e6 2.56257e6i 0.627491 1.08685i
\(355\) 774013. + 1.34063e6i 0.325970 + 0.564596i
\(356\) −138520. −0.0579277
\(357\) 0 0
\(358\) −3.67775e6 −1.51661
\(359\) 1.61507e6 + 2.79738e6i 0.661385 + 1.14555i 0.980252 + 0.197753i \(0.0633645\pi\)
−0.318866 + 0.947800i \(0.603302\pi\)
\(360\) −232222. + 402219.i −0.0944379 + 0.163571i
\(361\) 793921. 1.37511e6i 0.320634 0.555354i
\(362\) 1.85628e6 + 3.21517e6i 0.744511 + 1.28953i
\(363\) 1.54057e6 0.613641
\(364\) 0 0
\(365\) −2.15669e6 −0.847336
\(366\) 1.18174e6 + 2.04684e6i 0.461127 + 0.798695i
\(367\) −239779. + 415310.i −0.0929280 + 0.160956i −0.908742 0.417358i \(-0.862956\pi\)
0.815814 + 0.578314i \(0.196289\pi\)
\(368\) −1.00258e6 + 1.73653e6i −0.385923 + 0.668439i
\(369\) −530705. 919208.i −0.202902 0.351437i
\(370\) 4.03390e6 1.53187
\(371\) 0 0
\(372\) 310934. 0.116496
\(373\) −436333. 755751.i −0.162385 0.281259i 0.773339 0.633993i \(-0.218585\pi\)
−0.935724 + 0.352734i \(0.885252\pi\)
\(374\) 2.44868e6 4.24124e6i 0.905217 1.56788i
\(375\) −827844. + 1.43387e6i −0.303998 + 0.526540i
\(376\) 504447. + 873728.i 0.184012 + 0.318718i
\(377\) 572965. 0.207622
\(378\) 0 0
\(379\) −2.43493e6 −0.870742 −0.435371 0.900251i \(-0.643383\pi\)
−0.435371 + 0.900251i \(0.643383\pi\)
\(380\) −161160. 279137.i −0.0572529 0.0991650i
\(381\) −374715. + 649026.i −0.132248 + 0.229060i
\(382\) 2.11044e6 3.65540e6i 0.739973 1.28167i
\(383\) −1.80584e6 3.12781e6i −0.629047 1.08954i −0.987743 0.156087i \(-0.950112\pi\)
0.358696 0.933454i \(-0.383222\pi\)
\(384\) 2.01357e6 0.696848
\(385\) 0 0
\(386\) −3.56114e6 −1.21652
\(387\) −596707. 1.03353e6i −0.202527 0.350788i
\(388\) 13812.9 23924.7i 0.00465807 0.00806802i
\(389\) 87616.2 151756.i 0.0293569 0.0508477i −0.850974 0.525208i \(-0.823987\pi\)
0.880331 + 0.474361i \(0.157321\pi\)
\(390\) −435977. 755134.i −0.145145 0.251398i
\(391\) −2.17018e6 −0.717882
\(392\) 0 0
\(393\) 1.50187e6 0.490515
\(394\) 2.43262e6 + 4.21343e6i 0.789467 + 1.36740i
\(395\) −1.22290e6 + 2.11812e6i −0.394364 + 0.683058i
\(396\) 206135. 357036.i 0.0660562 0.114413i
\(397\) 942577. + 1.63259e6i 0.300152 + 0.519878i 0.976170 0.217007i \(-0.0696294\pi\)
−0.676019 + 0.736885i \(0.736296\pi\)
\(398\) 868126. 0.274710
\(399\) 0 0
\(400\) 1.99654e6 0.623920
\(401\) −669915. 1.16033e6i −0.208046 0.360346i 0.743053 0.669232i \(-0.233377\pi\)
−0.951099 + 0.308887i \(0.900044\pi\)
\(402\) −1.45435e6 + 2.51900e6i −0.448851 + 0.777433i
\(403\) 765839. 1.32647e6i 0.234895 0.406851i
\(404\) −746217. 1.29249e6i −0.227463 0.393978i
\(405\) −254101. −0.0769785
\(406\) 0 0
\(407\) 9.39535e6 2.81143
\(408\) 885884. + 1.53440e6i 0.263467 + 0.456338i
\(409\) 3.29314e6 5.70388e6i 0.973423 1.68602i 0.288381 0.957516i \(-0.406883\pi\)
0.685043 0.728503i \(-0.259783\pi\)
\(410\) 1.62143e6 2.80839e6i 0.476362 0.825084i
\(411\) −172008. 297926.i −0.0502277 0.0869969i
\(412\) −996247. −0.289150
\(413\) 0 0
\(414\) −844730. −0.242224
\(415\) −882487. 1.52851e6i −0.251529 0.435661i
\(416\) −609346. + 1.05542e6i −0.172636 + 0.299014i
\(417\) 478182. 828236.i 0.134665 0.233246i
\(418\) −1.73559e6 3.00613e6i −0.485855 0.841525i
\(419\) 6.96869e6 1.93917 0.969585 0.244754i \(-0.0787071\pi\)
0.969585 + 0.244754i \(0.0787071\pi\)
\(420\) 0 0
\(421\) 3.84041e6 1.05602 0.528010 0.849238i \(-0.322938\pi\)
0.528010 + 0.849238i \(0.322938\pi\)
\(422\) 3.16668e6 + 5.48485e6i 0.865612 + 1.49928i
\(423\) −275988. + 478025.i −0.0749962 + 0.129897i
\(424\) −148890. + 257886.i −0.0402209 + 0.0696647i
\(425\) 1.08042e6 + 1.87134e6i 0.290149 + 0.502552i
\(426\) 2.29866e6 0.613693
\(427\) 0 0
\(428\) −197002. −0.0519829
\(429\) −1.01543e6 1.75878e6i −0.266384 0.461390i
\(430\) 1.82308e6 3.15766e6i 0.475481 0.823558i
\(431\) −1.51818e6 + 2.62957e6i −0.393668 + 0.681854i −0.992930 0.118699i \(-0.962128\pi\)
0.599262 + 0.800553i \(0.295461\pi\)
\(432\) 447824. + 775653.i 0.115451 + 0.199967i
\(433\) 941529. 0.241332 0.120666 0.992693i \(-0.461497\pi\)
0.120666 + 0.992693i \(0.461497\pi\)
\(434\) 0 0
\(435\) 510135. 0.129259
\(436\) 370080. + 640997.i 0.0932351 + 0.161488i
\(437\) −769096. + 1.33211e6i −0.192653 + 0.333686i
\(438\) −1.60124e6 + 2.77342e6i −0.398814 + 0.690765i
\(439\) 670546. + 1.16142e6i 0.166061 + 0.287626i 0.937031 0.349245i \(-0.113562\pi\)
−0.770971 + 0.636871i \(0.780229\pi\)
\(440\) −3.30494e6 −0.813827
\(441\) 0 0
\(442\) −3.32635e6 −0.809864
\(443\) 386171. + 668867.i 0.0934910 + 0.161931i 0.908978 0.416844i \(-0.136864\pi\)
−0.815487 + 0.578776i \(0.803531\pi\)
\(444\) 647723. 1.12189e6i 0.155931 0.270080i
\(445\) −303765. + 526137.i −0.0727174 + 0.125950i
\(446\) 1.73595e6 + 3.00675e6i 0.413238 + 0.715748i
\(447\) 1.73300e6 0.410232
\(448\) 0 0
\(449\) 2.25684e6 0.528304 0.264152 0.964481i \(-0.414908\pi\)
0.264152 + 0.964481i \(0.414908\pi\)
\(450\) 420548. + 728411.i 0.0979005 + 0.169569i
\(451\) 3.77646e6 6.54101e6i 0.874265 1.51427i
\(452\) 180707. 312994.i 0.0416034 0.0720593i
\(453\) −637644. 1.10443e6i −0.145993 0.252868i
\(454\) −104.373 −2.37655e−5
\(455\) 0 0
\(456\) 1.25580e6 0.282820
\(457\) −2.14235e6 3.71066e6i −0.479844 0.831114i 0.519889 0.854234i \(-0.325973\pi\)
−0.999733 + 0.0231196i \(0.992640\pi\)
\(458\) −247221. + 428199.i −0.0550708 + 0.0953854i
\(459\) −484676. + 839483.i −0.107379 + 0.185986i
\(460\) −279080. 483381.i −0.0614942 0.106511i
\(461\) 3.10462e6 0.680387 0.340193 0.940355i \(-0.389507\pi\)
0.340193 + 0.940355i \(0.389507\pi\)
\(462\) 0 0
\(463\) −3.53386e6 −0.766121 −0.383060 0.923723i \(-0.625130\pi\)
−0.383060 + 0.923723i \(0.625130\pi\)
\(464\) −899053. 1.55721e6i −0.193861 0.335777i
\(465\) 681859. 1.18102e6i 0.146239 0.253293i
\(466\) 331178. 573617.i 0.0706475 0.122365i
\(467\) 1.36230e6 + 2.35957e6i 0.289054 + 0.500657i 0.973584 0.228328i \(-0.0733258\pi\)
−0.684530 + 0.728985i \(0.739993\pi\)
\(468\) −280019. −0.0590980
\(469\) 0 0
\(470\) −1.68641e6 −0.352143
\(471\) 2.54597e6 + 4.40975e6i 0.528812 + 0.915928i
\(472\) −3.80883e6 + 6.59709e6i −0.786932 + 1.36301i
\(473\) 4.24612e6 7.35449e6i 0.872649 1.51147i
\(474\) 1.81588e6 + 3.14520e6i 0.371228 + 0.642986i
\(475\) 1.53158e6 0.311461
\(476\) 0 0
\(477\) −162919. −0.0327850
\(478\) −2.20166e6 3.81338e6i −0.440737 0.763379i
\(479\) 489342. 847566.i 0.0974482 0.168785i −0.813180 0.582013i \(-0.802265\pi\)
0.910628 + 0.413228i \(0.135599\pi\)
\(480\) −542527. + 939685.i −0.107478 + 0.186157i
\(481\) −3.19072e6 5.52649e6i −0.628819 1.08915i
\(482\) −1.40766e6 −0.275982
\(483\) 0 0
\(484\) 1.51154e6 0.293296
\(485\) −60581.8 104931.i −0.0116947 0.0202558i
\(486\) −188658. + 326765.i −0.0362313 + 0.0627544i
\(487\) −1.96372e6 + 3.40126e6i −0.375195 + 0.649857i −0.990356 0.138544i \(-0.955758\pi\)
0.615161 + 0.788401i \(0.289091\pi\)
\(488\) −3.04228e6 5.26938e6i −0.578295 1.00164i
\(489\) −3.87181e6 −0.732220
\(490\) 0 0
\(491\) 2.63241e6 0.492777 0.246388 0.969171i \(-0.420756\pi\)
0.246388 + 0.969171i \(0.420756\pi\)
\(492\) −520704. 901886.i −0.0969791 0.167973i
\(493\) 973037. 1.68535e6i 0.180307 0.312301i
\(494\) −1.17883e6 + 2.04180e6i −0.217338 + 0.376440i
\(495\) −904083. 1.56592e6i −0.165842 0.287247i
\(496\) −4.80678e6 −0.877305
\(497\) 0 0
\(498\) −2.62081e6 −0.473546
\(499\) −1.06272e6 1.84069e6i −0.191059 0.330924i 0.754542 0.656251i \(-0.227859\pi\)
−0.945601 + 0.325327i \(0.894526\pi\)
\(500\) −812244. + 1.40685e6i −0.145299 + 0.251665i
\(501\) −1.08119e6 + 1.87268e6i −0.192446 + 0.333327i
\(502\) 4.58925e6 + 7.94881e6i 0.812798 + 1.40781i
\(503\) −2.60929e6 −0.459835 −0.229917 0.973210i \(-0.573846\pi\)
−0.229917 + 0.973210i \(0.573846\pi\)
\(504\) 0 0
\(505\) −6.54564e6 −1.14215
\(506\) −3.00552e6 5.20571e6i −0.521847 0.903865i
\(507\) 981124. 1.69936e6i 0.169513 0.293606i
\(508\) −367654. + 636795.i −0.0632092 + 0.109481i
\(509\) −5.00911e6 8.67603e6i −0.856970 1.48432i −0.874805 0.484475i \(-0.839011\pi\)
0.0178348 0.999841i \(-0.494323\pi\)
\(510\) −2.96159e6 −0.504196
\(511\) 0 0
\(512\) −1.99607e6 −0.336512
\(513\) 343532. + 595014.i 0.0576333 + 0.0998238i
\(514\) −2.90482e6 + 5.03130e6i −0.484967 + 0.839987i
\(515\) −2.18471e6 + 3.78403e6i −0.362974 + 0.628689i
\(516\) −585462. 1.01405e6i −0.0967998 0.167662i
\(517\) −3.92782e6 −0.646287
\(518\) 0 0
\(519\) 1.61370e6 0.262969
\(520\) 1.12238e6 + 1.94402e6i 0.182025 + 0.315277i
\(521\) −2.08970e6 + 3.61947e6i −0.337280 + 0.584186i −0.983920 0.178609i \(-0.942840\pi\)
0.646640 + 0.762795i \(0.276174\pi\)
\(522\) 378750. 656014.i 0.0608382 0.105375i
\(523\) 1.80263e6 + 3.12224e6i 0.288172 + 0.499128i 0.973373 0.229225i \(-0.0736193\pi\)
−0.685202 + 0.728353i \(0.740286\pi\)
\(524\) 1.47357e6 0.234446
\(525\) 0 0
\(526\) 4.78637e6 0.754297
\(527\) −2.60117e6 4.50536e6i −0.407983 0.706648i
\(528\) −3.18668e6 + 5.51949e6i −0.497455 + 0.861617i
\(529\) 1.88633e6 3.26722e6i 0.293075 0.507621i
\(530\) −248877. 431068.i −0.0384853 0.0666586i
\(531\) −4.16770e6 −0.641446
\(532\) 0 0
\(533\) −5.13003e6 −0.782172
\(534\) 451061. + 781261.i 0.0684514 + 0.118561i
\(535\) −432013. + 748268.i −0.0652547 + 0.113025i
\(536\) 3.74407e6 6.48492e6i 0.562901 0.974972i
\(537\) 2.59002e6 + 4.48604e6i 0.387585 + 0.671317i
\(538\) −4.28086e6 −0.637640
\(539\) 0 0
\(540\) −249313. −0.0367926
\(541\) 3.34083e6 + 5.78648e6i 0.490751 + 0.850005i 0.999943 0.0106475i \(-0.00338926\pi\)
−0.509193 + 0.860653i \(0.670056\pi\)
\(542\) 1.72737e6 2.99189e6i 0.252573 0.437470i
\(543\) 2.61453e6 4.52850e6i 0.380534 0.659105i
\(544\) 2.06964e6 + 3.58473e6i 0.299846 + 0.519349i
\(545\) 3.24625e6 0.468156
\(546\) 0 0
\(547\) 8.69076e6 1.24191 0.620954 0.783847i \(-0.286745\pi\)
0.620954 + 0.783847i \(0.286745\pi\)
\(548\) −168766. 292312.i −0.0240068 0.0415810i
\(549\) 1.66446e6 2.88293e6i 0.235691 0.408229i
\(550\) −2.99259e6 + 5.18332e6i −0.421833 + 0.730636i
\(551\) −689676. 1.19455e6i −0.0967756 0.167620i
\(552\) 2.17467e6 0.303771
\(553\) 0 0
\(554\) −2.56815e6 −0.355505
\(555\) −2.84084e6 4.92047e6i −0.391484 0.678070i
\(556\) 469171. 812628.i 0.0643642 0.111482i
\(557\) −3.12371e6 + 5.41042e6i −0.426612 + 0.738913i −0.996569 0.0827611i \(-0.973626\pi\)
0.569958 + 0.821674i \(0.306960\pi\)
\(558\) −1.01249e6 1.75369e6i −0.137660 0.238433i
\(559\) −5.76803e6 −0.780725
\(560\) 0 0
\(561\) −6.89783e6 −0.925349
\(562\) 1.37107e6 + 2.37476e6i 0.183113 + 0.317161i
\(563\) −5.95223e6 + 1.03096e7i −0.791423 + 1.37078i 0.133663 + 0.991027i \(0.457326\pi\)
−0.925086 + 0.379758i \(0.876007\pi\)
\(564\) −270787. + 469017.i −0.0358451 + 0.0620856i
\(565\) −792560. 1.37275e6i −0.104451 0.180914i
\(566\) 2.17848e6 0.285833
\(567\) 0 0
\(568\) −5.91768e6 −0.769627
\(569\) −10707.2 18545.4i −0.00138642 0.00240135i 0.865331 0.501200i \(-0.167108\pi\)
−0.866718 + 0.498799i \(0.833775\pi\)
\(570\) −1.04957e6 + 1.81791e6i −0.135308 + 0.234360i
\(571\) −3.55823e6 + 6.16304e6i −0.456714 + 0.791051i −0.998785 0.0492811i \(-0.984307\pi\)
0.542071 + 0.840333i \(0.317640\pi\)
\(572\) −996297. 1.72564e6i −0.127321 0.220526i
\(573\) −5.94504e6 −0.756429
\(574\) 0 0
\(575\) 2.65223e6 0.334534
\(576\) −786663. 1.36254e6i −0.0987944 0.171117i
\(577\) −5.33259e6 + 9.23632e6i −0.666805 + 1.15494i 0.311988 + 0.950086i \(0.399005\pi\)
−0.978793 + 0.204854i \(0.934328\pi\)
\(578\) −1.11262e6 + 1.92712e6i −0.138525 + 0.239932i
\(579\) 2.50790e6 + 4.34380e6i 0.310895 + 0.538485i
\(580\) 500522. 0.0617808
\(581\) 0 0
\(582\) −179916. −0.0220172
\(583\) −579659. 1.00400e6i −0.0706319 0.122338i
\(584\) 4.12222e6 7.13990e6i 0.500149 0.866283i
\(585\) −614065. + 1.06359e6i −0.0741864 + 0.128495i
\(586\) −1.24234e6 2.15180e6i −0.149450 0.258856i
\(587\) 1.30101e7 1.55843 0.779213 0.626759i \(-0.215619\pi\)
0.779213 + 0.626759i \(0.215619\pi\)
\(588\) 0 0
\(589\) −3.68735e6 −0.437952
\(590\) −6.36664e6 1.10273e7i −0.752975 1.30419i
\(591\) 3.42630e6 5.93453e6i 0.403512 0.698904i
\(592\) −1.00133e7 + 1.73435e7i −1.17428 + 2.03391i
\(593\) 2.13043e6 + 3.69002e6i 0.248789 + 0.430915i 0.963190 0.268821i \(-0.0866342\pi\)
−0.714401 + 0.699736i \(0.753301\pi\)
\(594\) −2.68495e6 −0.312226
\(595\) 0 0
\(596\) 1.70034e6 0.196074
\(597\) −611369. 1.05892e6i −0.0702049 0.121598i
\(598\) −2.04139e6 + 3.53578e6i −0.233438 + 0.404327i
\(599\) 6.89790e6 1.19475e7i 0.785507 1.36054i −0.143189 0.989695i \(-0.545736\pi\)
0.928696 0.370842i \(-0.120931\pi\)
\(600\) −1.08266e6 1.87522e6i −0.122776 0.212655i
\(601\) −4.99695e6 −0.564311 −0.282155 0.959369i \(-0.591049\pi\)
−0.282155 + 0.959369i \(0.591049\pi\)
\(602\) 0 0
\(603\) 4.09683e6 0.458833
\(604\) −625628. 1.08362e6i −0.0697788 0.120860i
\(605\) 3.31471e6 5.74125e6i 0.368177 0.637702i
\(606\) −4.85981e6 + 8.41743e6i −0.537573 + 0.931104i
\(607\) −1.52473e6 2.64091e6i −0.167966 0.290926i 0.769739 0.638359i \(-0.220387\pi\)
−0.937705 + 0.347434i \(0.887053\pi\)
\(608\) 2.93387e6 0.321871
\(609\) 0 0
\(610\) 1.01706e7 1.10668
\(611\) 1.33391e6 + 2.31040e6i 0.144552 + 0.250372i
\(612\) −475542. + 823663.i −0.0513228 + 0.0888937i
\(613\) 3.51813e6 6.09357e6i 0.378147 0.654969i −0.612646 0.790357i \(-0.709895\pi\)
0.990793 + 0.135388i \(0.0432282\pi\)
\(614\) −7.53195e6 1.30457e7i −0.806281 1.39652i
\(615\) −4.56749e6 −0.486956
\(616\) 0 0
\(617\) 1.00066e7 1.05822 0.529108 0.848554i \(-0.322527\pi\)
0.529108 + 0.848554i \(0.322527\pi\)
\(618\) 3.24408e6 + 5.61890e6i 0.341680 + 0.591807i
\(619\) −3.27533e6 + 5.67304e6i −0.343581 + 0.595099i −0.985095 0.172012i \(-0.944973\pi\)
0.641514 + 0.767111i \(0.278307\pi\)
\(620\) 669010. 1.15876e6i 0.0698962 0.121064i
\(621\) 594893. + 1.03038e6i 0.0619027 + 0.107219i
\(622\) 9.17986e6 0.951393
\(623\) 0 0
\(624\) 4.32886e6 0.445054
\(625\) 1.02325e6 + 1.77232e6i 0.104781 + 0.181485i
\(626\) −2.62879e6 + 4.55320e6i −0.268114 + 0.464388i
\(627\) −2.44455e6 + 4.23408e6i −0.248330 + 0.430120i
\(628\) 2.49799e6 + 4.32665e6i 0.252750 + 0.437777i
\(629\) −2.16746e7 −2.18436
\(630\) 0 0
\(631\) 2.22672e6 0.222635 0.111317 0.993785i \(-0.464493\pi\)
0.111317 + 0.993785i \(0.464493\pi\)
\(632\) −4.67480e6 8.09699e6i −0.465554 0.806364i
\(633\) 4.46021e6 7.72531e6i 0.442431 0.766313i
\(634\) 5.64524e6 9.77784e6i 0.557775 0.966095i
\(635\) 1.61249e6 + 2.79291e6i 0.158694 + 0.274867i
\(636\) −159849. −0.0156699
\(637\) 0 0
\(638\) 5.39031e6 0.524279
\(639\) −1.61881e6 2.80386e6i −0.156835 0.271647i
\(640\) 4.33242e6 7.50397e6i 0.418101 0.724171i
\(641\) 7.96698e6 1.37992e7i 0.765859 1.32651i −0.173932 0.984758i \(-0.555647\pi\)
0.939791 0.341749i \(-0.111019\pi\)
\(642\) 641496. + 1.11110e6i 0.0614266 + 0.106394i
\(643\) 1.49933e7 1.43011 0.715056 0.699067i \(-0.246401\pi\)
0.715056 + 0.699067i \(0.246401\pi\)
\(644\) 0 0
\(645\) −5.13553e6 −0.486056
\(646\) 4.00391e6 + 6.93498e6i 0.377488 + 0.653829i
\(647\) 6.49027e6 1.12415e7i 0.609540 1.05575i −0.381776 0.924255i \(-0.624687\pi\)
0.991316 0.131500i \(-0.0419792\pi\)
\(648\) 485680. 841223.i 0.0454373 0.0786998i
\(649\) −1.48285e7 2.56838e7i −1.38193 2.39357i
\(650\) 4.06521e6 0.377398
\(651\) 0 0
\(652\) −3.79885e6 −0.349972
\(653\) 8.27460e6 + 1.43320e7i 0.759389 + 1.31530i 0.943163 + 0.332332i \(0.107835\pi\)
−0.183774 + 0.982969i \(0.558831\pi\)
\(654\) 2.41018e6 4.17455e6i 0.220346 0.381650i
\(655\) 3.23145e6 5.59704e6i 0.294303 0.509748i
\(656\) 8.04966e6 + 1.39424e7i 0.730328 + 1.26497i
\(657\) 4.51062e6 0.407683
\(658\) 0 0
\(659\) 5.86879e6 0.526423 0.263212 0.964738i \(-0.415218\pi\)
0.263212 + 0.964738i \(0.415218\pi\)
\(660\) −887046. 1.53641e6i −0.0792659 0.137293i
\(661\) 3.63843e6 6.30195e6i 0.323900 0.561011i −0.657389 0.753551i \(-0.728339\pi\)
0.981289 + 0.192540i \(0.0616726\pi\)
\(662\) 9751.81 16890.6i 0.000864849 0.00149796i
\(663\) 2.34255e6 + 4.05741e6i 0.206969 + 0.358480i
\(664\) 6.74702e6 0.593870
\(665\) 0 0
\(666\) −8.43672e6 −0.737035
\(667\) −1.19431e6 2.06861e6i −0.103945 0.180038i
\(668\) −1.06082e6 + 1.83739e6i −0.0919815 + 0.159317i
\(669\) 2.44505e6 4.23495e6i 0.211214 0.365833i
\(670\) 6.25838e6 + 1.08398e7i 0.538611 + 0.932902i
\(671\) 2.36884e7 2.03109
\(672\) 0 0
\(673\) −1.82417e7 −1.55248 −0.776241 0.630437i \(-0.782876\pi\)
−0.776241 + 0.630437i \(0.782876\pi\)
\(674\) −6.48376e6 1.12302e7i −0.549765 0.952222i
\(675\) 592334. 1.02595e6i 0.0500388 0.0866698i
\(676\) 962636. 1.66733e6i 0.0810205 0.140332i
\(677\) −3.88203e6 6.72387e6i −0.325527 0.563829i 0.656092 0.754681i \(-0.272208\pi\)
−0.981619 + 0.190852i \(0.938875\pi\)
\(678\) −2.35374e6 −0.196646
\(679\) 0 0
\(680\) 7.62432e6 0.632308
\(681\) 73.5034 + 127.312i 6.07351e−6 + 1.05196e-5i
\(682\) 7.20482e6 1.24791e7i 0.593147 1.02736i
\(683\) −4.28162e6 + 7.41598e6i −0.351201 + 0.608299i −0.986460 0.164001i \(-0.947560\pi\)
0.635259 + 0.772299i \(0.280893\pi\)
\(684\) 337058. + 583801.i 0.0275464 + 0.0477117i
\(685\) −1.48038e6 −0.120544
\(686\) 0 0
\(687\) 696411. 0.0562955
\(688\) 9.05076e6 + 1.56764e7i 0.728978 + 1.26263i
\(689\) −393712. + 681928.i −0.0315959 + 0.0547256i
\(690\) −1.81753e6 + 3.14806e6i −0.145332 + 0.251722i
\(691\) 8.22547e6 + 1.42469e7i 0.655338 + 1.13508i 0.981809 + 0.189872i \(0.0608071\pi\)
−0.326471 + 0.945207i \(0.605860\pi\)
\(692\) 1.58329e6 0.125689
\(693\) 0 0
\(694\) 2.41677e7 1.90474
\(695\) −2.05773e6 3.56409e6i −0.161594 0.279890i
\(696\) −975054. + 1.68884e6i −0.0762967 + 0.132150i
\(697\) −8.71208e6 + 1.50898e7i −0.679266 + 1.17652i
\(698\) 930197. + 1.61115e6i 0.0722664 + 0.125169i
\(699\) −932916. −0.0722187
\(700\) 0 0
\(701\) −1.66928e7 −1.28302 −0.641512 0.767113i \(-0.721693\pi\)
−0.641512 + 0.767113i \(0.721693\pi\)
\(702\) 911825. + 1.57933e6i 0.0698343 + 0.120956i
\(703\) −7.68132e6 + 1.33044e7i −0.586202 + 1.01533i
\(704\) 5.59783e6 9.69573e6i 0.425685 0.737308i
\(705\) 1.18764e6 + 2.05705e6i 0.0899937 + 0.155874i
\(706\) −2.46059e6 −0.185792
\(707\) 0 0
\(708\) −4.08916e6 −0.306585
\(709\) −2.80890e6 4.86515e6i −0.209855 0.363480i 0.741813 0.670606i \(-0.233966\pi\)
−0.951669 + 0.307126i \(0.900633\pi\)
\(710\) 4.94584e6 8.56644e6i 0.368209 0.637756i
\(711\) 2.55763e6 4.42994e6i 0.189742 0.328643i
\(712\) −1.16121e6 2.01128e6i −0.0858443 0.148687i
\(713\) −6.38537e6 −0.470395
\(714\) 0 0
\(715\) −8.73927e6 −0.639308
\(716\) 2.54121e6 + 4.40150e6i 0.185250 + 0.320862i
\(717\) −3.10099e6 + 5.37107e6i −0.225269 + 0.390178i
\(718\) 1.03201e7 1.78749e7i 0.747087 1.29399i
\(719\) 5.18592e6 + 8.98227e6i 0.374113 + 0.647983i 0.990194 0.139700i \(-0.0446138\pi\)
−0.616081 + 0.787683i \(0.711280\pi\)
\(720\) 3.85418e6 0.277077
\(721\) 0 0
\(722\) −1.01461e7 −0.724363
\(723\) 991332. + 1.71704e6i 0.0705299 + 0.122161i
\(724\) 2.56526e6 4.44316e6i 0.181880 0.315025i
\(725\) −1.18917e6 + 2.05971e6i −0.0840233 + 0.145533i
\(726\) −4.92201e6 8.52518e6i −0.346578 0.600291i
\(727\) −1.15369e7 −0.809565 −0.404783 0.914413i \(-0.632653\pi\)
−0.404783 + 0.914413i \(0.632653\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) 6.89049e6 + 1.19347e7i 0.478567 + 0.828902i
\(731\) −9.79557e6 + 1.69664e7i −0.678010 + 1.17435i
\(732\) 1.63310e6 2.82860e6i 0.112651 0.195117i
\(733\) 7.47349e6 + 1.29445e7i 0.513764 + 0.889865i 0.999873 + 0.0159667i \(0.00508258\pi\)
−0.486109 + 0.873898i \(0.661584\pi\)
\(734\) 3.06432e6 0.209939
\(735\) 0 0
\(736\) 5.08058e6 0.345715
\(737\) 1.45764e7 + 2.52470e7i 0.988510 + 1.71215i
\(738\) −3.39113e6 + 5.87362e6i −0.229194 + 0.396976i
\(739\) −4.50682e6 + 7.80604e6i −0.303570 + 0.525799i −0.976942 0.213505i \(-0.931512\pi\)
0.673372 + 0.739304i \(0.264845\pi\)
\(740\) −2.78730e6 4.82775e6i −0.187113 0.324090i
\(741\) 3.32073e6 0.222171
\(742\) 0 0
\(743\) −2.10239e7 −1.39714 −0.698571 0.715541i \(-0.746180\pi\)
−0.698571 + 0.715541i \(0.746180\pi\)
\(744\) 2.60656e6 + 4.51470e6i 0.172638 + 0.299017i
\(745\) 3.72875e6 6.45838e6i 0.246134 0.426317i
\(746\) −2.78811e6 + 4.82915e6i −0.183427 + 0.317705i
\(747\) 1.84568e6 + 3.19681e6i 0.121019 + 0.209612i
\(748\) −6.76785e6 −0.442279
\(749\) 0 0
\(750\) 1.05796e7 0.686779
\(751\) −2.02110e6 3.50064e6i −0.130764 0.226489i 0.793207 0.608952i \(-0.208410\pi\)
−0.923971 + 0.382462i \(0.875076\pi\)
\(752\) 4.18615e6 7.25062e6i 0.269942 0.467553i
\(753\) 6.46387e6 1.11957e7i 0.415437 0.719558i
\(754\) −1.83058e6 3.17066e6i −0.117263 0.203106i
\(755\) −5.48786e6 −0.350377
\(756\) 0 0
\(757\) −1.82059e7 −1.15471 −0.577353 0.816495i \(-0.695914\pi\)
−0.577353 + 0.816495i \(0.695914\pi\)
\(758\) 7.77945e6 + 1.34744e7i 0.491786 + 0.851798i
\(759\) −4.23321e6 + 7.33214e6i −0.266726 + 0.461983i
\(760\) 2.70201e6 4.68001e6i 0.169689 0.293909i
\(761\) −9.45999e6 1.63852e7i −0.592146 1.02563i −0.993943 0.109898i \(-0.964947\pi\)
0.401797 0.915729i \(-0.368386\pi\)
\(762\) 4.78876e6 0.298769
\(763\) 0 0
\(764\) −5.83301e6 −0.361542
\(765\) 2.08567e6 + 3.61249e6i 0.128852 + 0.223179i
\(766\) −1.15391e7 + 1.99863e7i −0.710559 + 1.23072i
\(767\) −1.00717e7 + 1.74447e7i −0.618180 + 1.07072i
\(768\) −3.63619e6 6.29807e6i −0.222456 0.385305i
\(769\) 1.12831e7 0.688037 0.344019 0.938963i \(-0.388212\pi\)
0.344019 + 0.938963i \(0.388212\pi\)
\(770\) 0 0
\(771\) 8.18277e6 0.495752
\(772\) 2.46064e6 + 4.26195e6i 0.148595 + 0.257374i
\(773\) &minus