Properties

Label 147.6.e.m.79.1
Level $147$
Weight $6$
Character 147.79
Analytic conductor $23.576$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 79.1
Root \(-3.22311 + 5.58259i\) of defining polynomial
Character \(\chi\) \(=\) 147.79
Dual form 147.6.e.m.67.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.72311 + 4.71657i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(1.16933 + 2.02534i) q^{4} +(18.0000 - 31.1769i) q^{5} +49.0160 q^{6} -187.016 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\) \(q+(-2.72311 + 4.71657i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(1.16933 + 2.02534i) q^{4} +(18.0000 - 31.1769i) q^{5} +49.0160 q^{6} -187.016 q^{8} +(-40.5000 + 70.1481i) q^{9} +(98.0320 + 169.796i) q^{10} +(-92.2151 - 159.721i) q^{11} +(10.5240 - 18.2281i) q^{12} -147.872 q^{13} -324.000 q^{15} +(471.847 - 817.262i) q^{16} +(984.192 + 1704.67i) q^{17} +(-220.572 - 382.042i) q^{18} +(946.256 - 1638.96i) q^{19} +84.1920 q^{20} +1004.45 q^{22} +(-68.4942 + 118.635i) q^{23} +(841.572 + 1457.65i) q^{24} +(914.500 + 1583.96i) q^{25} +(402.672 - 697.448i) q^{26} +729.000 q^{27} -1259.58 q^{29} +(882.288 - 1528.17i) q^{30} +(4484.51 + 7767.40i) q^{31} +(-422.474 - 731.747i) q^{32} +(-829.936 + 1437.49i) q^{33} -10720.3 q^{34} -189.432 q^{36} +(-6448.61 + 11169.3i) q^{37} +(5153.52 + 8926.16i) q^{38} +(665.424 + 1152.55i) q^{39} +(-3366.29 + 5830.58i) q^{40} -8975.62 q^{41} +13538.9 q^{43} +(215.660 - 373.535i) q^{44} +(1458.00 + 2525.33i) q^{45} +(-373.035 - 646.115i) q^{46} +(-10023.1 + 17360.5i) q^{47} -8493.24 q^{48} -9961.14 q^{50} +(8857.73 - 15342.0i) q^{51} +(-172.912 - 299.492i) q^{52} +(-4667.16 - 8083.76i) q^{53} +(-1985.15 + 3438.38i) q^{54} -6639.49 q^{55} -17032.6 q^{57} +(3429.98 - 5940.90i) q^{58} +(4433.23 + 7678.58i) q^{59} +(-378.864 - 656.212i) q^{60} +(-20574.2 + 35635.5i) q^{61} -48847.3 q^{62} +34800.0 q^{64} +(-2661.70 + 4610.19i) q^{65} +(-4520.02 - 7828.90i) q^{66} +(27675.8 + 47935.8i) q^{67} +(-2301.70 + 3986.65i) q^{68} +1232.90 q^{69} -63866.8 q^{71} +(7574.15 - 13118.8i) q^{72} +(20649.7 + 35766.3i) q^{73} +(-35120.5 - 60830.6i) q^{74} +(8230.50 - 14255.6i) q^{75} +4425.95 q^{76} -7248.09 q^{78} +(-8481.76 + 14690.8i) q^{79} +(-16986.5 - 29421.4i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(24441.6 - 42334.1i) q^{82} +101693. q^{83} +70861.8 q^{85} +(-36868.0 + 63857.3i) q^{86} +(5668.12 + 9817.47i) q^{87} +(17245.7 + 29870.4i) q^{88} +(43551.3 - 75433.0i) q^{89} -15881.2 q^{90} -320.370 q^{92} +(40360.6 - 69906.6i) q^{93} +(-54587.9 - 94549.0i) q^{94} +(-34065.2 - 59002.7i) q^{95} +(-3802.27 + 6585.72i) q^{96} +118107. q^{97} +14938.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 3 q^{2} - 18 q^{3} - 37 q^{4} + 72 q^{5} - 54 q^{6} - 498 q^{8} - 162 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 3 q^{2} - 18 q^{3} - 37 q^{4} + 72 q^{5} - 54 q^{6} - 498 q^{8} - 162 q^{9} - 108 q^{10} - 480 q^{11} - 333 q^{12} - 2592 q^{13} - 1296 q^{15} + 1679 q^{16} + 936 q^{17} + 243 q^{18} - 216 q^{19} - 2664 q^{20} - 2984 q^{22} + 504 q^{23} + 2241 q^{24} + 3658 q^{25} - 8892 q^{26} + 2916 q^{27} + 12744 q^{29} - 972 q^{30} + 9936 q^{31} - 9039 q^{32} - 4320 q^{33} - 38880 q^{34} + 5994 q^{36} - 11124 q^{37} + 28116 q^{38} + 11664 q^{39} - 8964 q^{40} - 41904 q^{41} - 12528 q^{43} - 11196 q^{44} + 5832 q^{45} - 6160 q^{46} + 7920 q^{47} - 30222 q^{48} + 10974 q^{50} + 8424 q^{51} + 44820 q^{52} - 2220 q^{53} + 2187 q^{54} - 34560 q^{55} + 3888 q^{57} + 71318 q^{58} + 29736 q^{59} + 11988 q^{60} - 17280 q^{61} - 81360 q^{62} - 21758 q^{64} - 46656 q^{65} + 13428 q^{66} + 20680 q^{67} - 45216 q^{68} - 9072 q^{69} - 184560 q^{71} + 20169 q^{72} + 56592 q^{73} - 85218 q^{74} + 32922 q^{75} + 174744 q^{76} + 160056 q^{78} + 56096 q^{79} - 60444 q^{80} - 13122 q^{81} - 52272 q^{82} + 142704 q^{83} + 67392 q^{85} - 240996 q^{86} - 57348 q^{87} + 52812 q^{88} + 123192 q^{89} + 17496 q^{90} - 51072 q^{92} + 89424 q^{93} - 345384 q^{94} + 7776 q^{95} - 81351 q^{96} - 71712 q^{97} + 77760 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.72311 + 4.71657i −0.481383 + 0.833779i −0.999772 0.0213658i \(-0.993199\pi\)
0.518389 + 0.855145i \(0.326532\pi\)
\(3\) −4.50000 7.79423i −0.288675 0.500000i
\(4\) 1.16933 + 2.02534i 0.0365417 + 0.0632920i
\(5\) 18.0000 31.1769i 0.321994 0.557710i −0.658906 0.752226i \(-0.728980\pi\)
0.980899 + 0.194516i \(0.0623136\pi\)
\(6\) 49.0160 0.555853
\(7\) 0 0
\(8\) −187.016 −1.03313
\(9\) −40.5000 + 70.1481i −0.166667 + 0.288675i
\(10\) 98.0320 + 169.796i 0.310004 + 0.536943i
\(11\) −92.2151 159.721i −0.229784 0.397998i 0.727960 0.685620i \(-0.240469\pi\)
−0.957744 + 0.287622i \(0.907135\pi\)
\(12\) 10.5240 18.2281i 0.0210973 0.0365417i
\(13\) −147.872 −0.242676 −0.121338 0.992611i \(-0.538719\pi\)
−0.121338 + 0.992611i \(0.538719\pi\)
\(14\) 0 0
\(15\) −324.000 −0.371806
\(16\) 471.847 817.262i 0.460788 0.798108i
\(17\) 984.192 + 1704.67i 0.825957 + 1.43060i 0.901186 + 0.433433i \(0.142698\pi\)
−0.0752284 + 0.997166i \(0.523969\pi\)
\(18\) −220.572 382.042i −0.160461 0.277926i
\(19\) 946.256 1638.96i 0.601346 1.04156i −0.391271 0.920275i \(-0.627965\pi\)
0.992617 0.121287i \(-0.0387021\pi\)
\(20\) 84.1920 0.0470647
\(21\) 0 0
\(22\) 1004.45 0.442457
\(23\) −68.4942 + 118.635i −0.0269982 + 0.0467622i −0.879209 0.476437i \(-0.841928\pi\)
0.852211 + 0.523199i \(0.175261\pi\)
\(24\) 841.572 + 1457.65i 0.298238 + 0.516564i
\(25\) 914.500 + 1583.96i 0.292640 + 0.506867i
\(26\) 402.672 697.448i 0.116820 0.202339i
\(27\) 729.000 0.192450
\(28\) 0 0
\(29\) −1259.58 −0.278120 −0.139060 0.990284i \(-0.544408\pi\)
−0.139060 + 0.990284i \(0.544408\pi\)
\(30\) 882.288 1528.17i 0.178981 0.310004i
\(31\) 4484.51 + 7767.40i 0.838129 + 1.45168i 0.891457 + 0.453105i \(0.149684\pi\)
−0.0533279 + 0.998577i \(0.516983\pi\)
\(32\) −422.474 731.747i −0.0729332 0.126324i
\(33\) −829.936 + 1437.49i −0.132666 + 0.229784i
\(34\) −10720.3 −1.59041
\(35\) 0 0
\(36\) −189.432 −0.0243611
\(37\) −6448.61 + 11169.3i −0.774393 + 1.34129i 0.160742 + 0.986996i \(0.448611\pi\)
−0.935135 + 0.354292i \(0.884722\pi\)
\(38\) 5153.52 + 8926.16i 0.578955 + 1.00278i
\(39\) 665.424 + 1152.55i 0.0700547 + 0.121338i
\(40\) −3366.29 + 5830.58i −0.332661 + 0.576185i
\(41\) −8975.62 −0.833882 −0.416941 0.908934i \(-0.636898\pi\)
−0.416941 + 0.908934i \(0.636898\pi\)
\(42\) 0 0
\(43\) 13538.9 1.11664 0.558320 0.829626i \(-0.311446\pi\)
0.558320 + 0.829626i \(0.311446\pi\)
\(44\) 215.660 373.535i 0.0167934 0.0290870i
\(45\) 1458.00 + 2525.33i 0.107331 + 0.185903i
\(46\) −373.035 646.115i −0.0259929 0.0450210i
\(47\) −10023.1 + 17360.5i −0.661845 + 1.14635i 0.318286 + 0.947995i \(0.396893\pi\)
−0.980130 + 0.198354i \(0.936440\pi\)
\(48\) −8493.24 −0.532072
\(49\) 0 0
\(50\) −9961.14 −0.563487
\(51\) 8857.73 15342.0i 0.476867 0.825957i
\(52\) −172.912 299.492i −0.00886780 0.0153595i
\(53\) −4667.16 8083.76i −0.228225 0.395297i 0.729057 0.684453i \(-0.239959\pi\)
−0.957282 + 0.289155i \(0.906626\pi\)
\(54\) −1985.15 + 3438.38i −0.0926421 + 0.160461i
\(55\) −6639.49 −0.295956
\(56\) 0 0
\(57\) −17032.6 −0.694375
\(58\) 3429.98 5940.90i 0.133882 0.231890i
\(59\) 4433.23 + 7678.58i 0.165802 + 0.287178i 0.936940 0.349491i \(-0.113645\pi\)
−0.771138 + 0.636668i \(0.780312\pi\)
\(60\) −378.864 656.212i −0.0135864 0.0235324i
\(61\) −20574.2 + 35635.5i −0.707942 + 1.22619i 0.257678 + 0.966231i \(0.417043\pi\)
−0.965619 + 0.259960i \(0.916291\pi\)
\(62\) −48847.3 −1.61384
\(63\) 0 0
\(64\) 34800.0 1.06201
\(65\) −2661.70 + 4610.19i −0.0781403 + 0.135343i
\(66\) −4520.02 7828.90i −0.127726 0.221228i
\(67\) 27675.8 + 47935.8i 0.753204 + 1.30459i 0.946262 + 0.323400i \(0.104826\pi\)
−0.193058 + 0.981187i \(0.561841\pi\)
\(68\) −2301.70 + 3986.65i −0.0603637 + 0.104553i
\(69\) 1232.90 0.0311748
\(70\) 0 0
\(71\) −63866.8 −1.50359 −0.751794 0.659398i \(-0.770811\pi\)
−0.751794 + 0.659398i \(0.770811\pi\)
\(72\) 7574.15 13118.8i 0.172188 0.298238i
\(73\) 20649.7 + 35766.3i 0.453530 + 0.785537i 0.998602 0.0528522i \(-0.0168312\pi\)
−0.545073 + 0.838389i \(0.683498\pi\)
\(74\) −35120.5 60830.6i −0.745559 1.29135i
\(75\) 8230.50 14255.6i 0.168956 0.292640i
\(76\) 4425.95 0.0878968
\(77\) 0 0
\(78\) −7248.09 −0.134892
\(79\) −8481.76 + 14690.8i −0.152904 + 0.264837i −0.932294 0.361702i \(-0.882196\pi\)
0.779390 + 0.626539i \(0.215529\pi\)
\(80\) −16986.5 29421.4i −0.296742 0.513972i
\(81\) −3280.50 5681.99i −0.0555556 0.0962250i
\(82\) 24441.6 42334.1i 0.401416 0.695273i
\(83\) 101693. 1.62030 0.810150 0.586223i \(-0.199386\pi\)
0.810150 + 0.586223i \(0.199386\pi\)
\(84\) 0 0
\(85\) 70861.8 1.06381
\(86\) −36868.0 + 63857.3i −0.537531 + 0.931031i
\(87\) 5668.12 + 9817.47i 0.0802862 + 0.139060i
\(88\) 17245.7 + 29870.4i 0.237396 + 0.411183i
\(89\) 43551.3 75433.0i 0.582808 1.00945i −0.412336 0.911032i \(-0.635287\pi\)
0.995145 0.0984220i \(-0.0313795\pi\)
\(90\) −15881.2 −0.206670
\(91\) 0 0
\(92\) −320.370 −0.00394623
\(93\) 40360.6 69906.6i 0.483894 0.838129i
\(94\) −54587.9 94549.0i −0.637201 1.10366i
\(95\) −34065.2 59002.7i −0.387260 0.670753i
\(96\) −3802.27 + 6585.72i −0.0421080 + 0.0729332i
\(97\) 118107. 1.27452 0.637258 0.770650i \(-0.280068\pi\)
0.637258 + 0.770650i \(0.280068\pi\)
\(98\) 0 0
\(99\) 14938.8 0.153190
\(100\) −2138.71 + 3704.35i −0.0213871 + 0.0370435i
\(101\) 11116.4 + 19254.1i 0.108432 + 0.187811i 0.915135 0.403147i \(-0.132084\pi\)
−0.806703 + 0.590957i \(0.798750\pi\)
\(102\) 48241.2 + 83556.1i 0.459111 + 0.795203i
\(103\) 67965.3 117719.i 0.631239 1.09334i −0.356059 0.934463i \(-0.615880\pi\)
0.987299 0.158875i \(-0.0507868\pi\)
\(104\) 27654.4 0.250716
\(105\) 0 0
\(106\) 50836.8 0.439454
\(107\) −58813.1 + 101867.i −0.496609 + 0.860152i −0.999992 0.00391112i \(-0.998755\pi\)
0.503383 + 0.864063i \(0.332088\pi\)
\(108\) 852.444 + 1476.48i 0.00703244 + 0.0121806i
\(109\) 17332.1 + 30020.1i 0.139729 + 0.242017i 0.927394 0.374086i \(-0.122044\pi\)
−0.787665 + 0.616103i \(0.788710\pi\)
\(110\) 18080.1 31315.6i 0.142468 0.246762i
\(111\) 116075. 0.894192
\(112\) 0 0
\(113\) −26584.5 −0.195854 −0.0979269 0.995194i \(-0.531221\pi\)
−0.0979269 + 0.995194i \(0.531221\pi\)
\(114\) 46381.7 80335.4i 0.334260 0.578955i
\(115\) 2465.79 + 4270.88i 0.0173865 + 0.0301143i
\(116\) −1472.87 2551.09i −0.0101629 0.0176027i
\(117\) 5988.82 10372.9i 0.0404461 0.0700547i
\(118\) −48288.7 −0.319257
\(119\) 0 0
\(120\) 60593.2 0.384123
\(121\) 63518.2 110017.i 0.394398 0.683118i
\(122\) −112051. 194079.i −0.681582 1.18053i
\(123\) 40390.3 + 69958.0i 0.240721 + 0.416941i
\(124\) −10487.8 + 18165.4i −0.0612533 + 0.106094i
\(125\) 178344. 1.02090
\(126\) 0 0
\(127\) −137111. −0.754334 −0.377167 0.926145i \(-0.623102\pi\)
−0.377167 + 0.926145i \(0.623102\pi\)
\(128\) −81245.0 + 140720.i −0.438300 + 0.759158i
\(129\) −60925.2 105526.i −0.322346 0.558320i
\(130\) −14496.2 25108.1i −0.0752308 0.130304i
\(131\) −27044.6 + 46842.6i −0.137690 + 0.238486i −0.926622 0.375995i \(-0.877301\pi\)
0.788932 + 0.614481i \(0.210634\pi\)
\(132\) −3881.89 −0.0193913
\(133\) 0 0
\(134\) −301457. −1.45032
\(135\) 13122.0 22728.0i 0.0619677 0.107331i
\(136\) −184060. 318801.i −0.853319 1.47799i
\(137\) −211424. 366198.i −0.962395 1.66692i −0.716456 0.697632i \(-0.754237\pi\)
−0.245939 0.969285i \(-0.579096\pi\)
\(138\) −3357.31 + 5815.04i −0.0150070 + 0.0259929i
\(139\) 9913.38 0.0435196 0.0217598 0.999763i \(-0.493073\pi\)
0.0217598 + 0.999763i \(0.493073\pi\)
\(140\) 0 0
\(141\) 180415. 0.764233
\(142\) 173916. 301232.i 0.723801 1.25366i
\(143\) 13636.0 + 23618.3i 0.0557632 + 0.0965848i
\(144\) 38219.6 + 66198.3i 0.153596 + 0.266036i
\(145\) −22672.5 + 39269.9i −0.0895528 + 0.155110i
\(146\) −224925. −0.873285
\(147\) 0 0
\(148\) −30162.3 −0.113190
\(149\) −252731. + 437743.i −0.932595 + 1.61530i −0.153727 + 0.988113i \(0.549128\pi\)
−0.778868 + 0.627188i \(0.784206\pi\)
\(150\) 44825.1 + 77639.4i 0.162665 + 0.281744i
\(151\) 96551.4 + 167232.i 0.344601 + 0.596866i 0.985281 0.170942i \(-0.0546810\pi\)
−0.640680 + 0.767808i \(0.721348\pi\)
\(152\) −176965. + 306512.i −0.621267 + 1.07607i
\(153\) −159439. −0.550638
\(154\) 0 0
\(155\) 322885. 1.07949
\(156\) −1556.20 + 2695.43i −0.00511983 + 0.00886780i
\(157\) 132462. + 229430.i 0.428885 + 0.742850i 0.996774 0.0802545i \(-0.0255733\pi\)
−0.567890 + 0.823105i \(0.692240\pi\)
\(158\) −46193.5 80009.6i −0.147210 0.254976i
\(159\) −42004.5 + 72753.9i −0.131766 + 0.228225i
\(160\) −30418.1 −0.0939362
\(161\) 0 0
\(162\) 35732.7 0.106974
\(163\) 269546. 466868.i 0.794629 1.37634i −0.128446 0.991717i \(-0.540999\pi\)
0.923075 0.384621i \(-0.125668\pi\)
\(164\) −10495.5 18178.7i −0.0304714 0.0527781i
\(165\) 29877.7 + 51749.7i 0.0854353 + 0.147978i
\(166\) −276921. + 479641.i −0.779984 + 1.35097i
\(167\) −218748. −0.606949 −0.303475 0.952840i \(-0.598147\pi\)
−0.303475 + 0.952840i \(0.598147\pi\)
\(168\) 0 0
\(169\) −349427. −0.941108
\(170\) −192965. + 334225.i −0.512101 + 0.886984i
\(171\) 76646.7 + 132756.i 0.200449 + 0.347187i
\(172\) 15831.5 + 27421.0i 0.0408039 + 0.0706744i
\(173\) 295101. 511129.i 0.749644 1.29842i −0.198350 0.980131i \(-0.563558\pi\)
0.947994 0.318289i \(-0.103108\pi\)
\(174\) −61739.7 −0.154593
\(175\) 0 0
\(176\) −174046. −0.423527
\(177\) 39899.1 69107.2i 0.0957260 0.165802i
\(178\) 237190. + 410825.i 0.561108 + 0.971867i
\(179\) 108676. + 188232.i 0.253513 + 0.439098i 0.964491 0.264117i \(-0.0850805\pi\)
−0.710977 + 0.703215i \(0.751747\pi\)
\(180\) −3409.78 + 5905.90i −0.00784412 + 0.0135864i
\(181\) −188109. −0.426790 −0.213395 0.976966i \(-0.568452\pi\)
−0.213395 + 0.976966i \(0.568452\pi\)
\(182\) 0 0
\(183\) 370335. 0.817461
\(184\) 12809.5 22186.7i 0.0278925 0.0483113i
\(185\) 232150. + 402095.i 0.498700 + 0.863773i
\(186\) 219813. + 380727.i 0.465876 + 0.806922i
\(187\) 181515. 314393.i 0.379584 0.657459i
\(188\) −46881.2 −0.0967396
\(189\) 0 0
\(190\) 371053. 0.745680
\(191\) −86761.3 + 150275.i −0.172085 + 0.298060i −0.939149 0.343511i \(-0.888384\pi\)
0.767064 + 0.641571i \(0.221717\pi\)
\(192\) −156600. 271239.i −0.306576 0.531005i
\(193\) −58890.7 102002.i −0.113803 0.197113i 0.803498 0.595308i \(-0.202970\pi\)
−0.917301 + 0.398195i \(0.869637\pi\)
\(194\) −321618. + 557059.i −0.613530 + 1.06267i
\(195\) 47910.5 0.0902287
\(196\) 0 0
\(197\) 224734. 0.412575 0.206288 0.978491i \(-0.433862\pi\)
0.206288 + 0.978491i \(0.433862\pi\)
\(198\) −40680.1 + 70460.1i −0.0737428 + 0.127726i
\(199\) 370137. + 641096.i 0.662567 + 1.14760i 0.979939 + 0.199298i \(0.0638661\pi\)
−0.317372 + 0.948301i \(0.602801\pi\)
\(200\) −171026. 296226.i −0.302334 0.523658i
\(201\) 249082. 431422.i 0.434862 0.753204i
\(202\) −121084. −0.208790
\(203\) 0 0
\(204\) 41430.5 0.0697020
\(205\) −161561. + 279832.i −0.268505 + 0.465064i
\(206\) 370154. + 641126.i 0.607735 + 1.05263i
\(207\) −5548.03 9609.47i −0.00899939 0.0155874i
\(208\) −69772.9 + 120850.i −0.111822 + 0.193682i
\(209\) −349036. −0.552720
\(210\) 0 0
\(211\) −705896. −1.09153 −0.545763 0.837939i \(-0.683760\pi\)
−0.545763 + 0.837939i \(0.683760\pi\)
\(212\) 10914.9 18905.2i 0.0166794 0.0288896i
\(213\) 287400. + 497792.i 0.434049 + 0.751794i
\(214\) −320309. 554792.i −0.478118 0.828124i
\(215\) 243701. 422102.i 0.359551 0.622761i
\(216\) −136335. −0.198825
\(217\) 0 0
\(218\) −188789. −0.269052
\(219\) 185847. 321896.i 0.261846 0.453530i
\(220\) −7763.77 13447.2i −0.0108147 0.0187317i
\(221\) −145534. 252073.i −0.200440 0.347173i
\(222\) −316085. + 547475.i −0.430449 + 0.745559i
\(223\) −42214.3 −0.0568456 −0.0284228 0.999596i \(-0.509048\pi\)
−0.0284228 + 0.999596i \(0.509048\pi\)
\(224\) 0 0
\(225\) −148149. −0.195093
\(226\) 72392.5 125387.i 0.0942806 0.163299i
\(227\) 371201. + 642940.i 0.478129 + 0.828144i 0.999686 0.0250731i \(-0.00798184\pi\)
−0.521557 + 0.853217i \(0.674649\pi\)
\(228\) −19916.8 34496.9i −0.0253736 0.0439484i
\(229\) 470618. 815134.i 0.593034 1.02717i −0.400787 0.916171i \(-0.631263\pi\)
0.993821 0.110994i \(-0.0354035\pi\)
\(230\) −26858.5 −0.0334782
\(231\) 0 0
\(232\) 235562. 0.287333
\(233\) 256166. 443692.i 0.309123 0.535416i −0.669048 0.743219i \(-0.733298\pi\)
0.978171 + 0.207803i \(0.0666313\pi\)
\(234\) 32616.4 + 56493.3i 0.0389401 + 0.0674462i
\(235\) 360831. + 624977.i 0.426220 + 0.738234i
\(236\) −10367.8 + 17957.6i −0.0121174 + 0.0209879i
\(237\) 152672. 0.176558
\(238\) 0 0
\(239\) −115323. −0.130593 −0.0652966 0.997866i \(-0.520799\pi\)
−0.0652966 + 0.997866i \(0.520799\pi\)
\(240\) −152878. + 264793.i −0.171324 + 0.296742i
\(241\) −454932. 787965.i −0.504549 0.873905i −0.999986 0.00526118i \(-0.998325\pi\)
0.495437 0.868644i \(-0.335008\pi\)
\(242\) 345934. + 599176.i 0.379713 + 0.657682i
\(243\) −29524.5 + 51137.9i −0.0320750 + 0.0555556i
\(244\) −96232.2 −0.103477
\(245\) 0 0
\(246\) −439949. −0.463516
\(247\) −139925. + 242357.i −0.145933 + 0.252763i
\(248\) −838675. 1.45263e6i −0.865894 1.49977i
\(249\) −457618. 792618.i −0.467740 0.810150i
\(250\) −485651. + 841171.i −0.491444 + 0.851206i
\(251\) 321264. 0.321868 0.160934 0.986965i \(-0.448549\pi\)
0.160934 + 0.986965i \(0.448549\pi\)
\(252\) 0 0
\(253\) 25264.8 0.0248150
\(254\) 373369. 646694.i 0.363123 0.628948i
\(255\) −318878. 552313.i −0.307096 0.531906i
\(256\) 114321. + 198010.i 0.109025 + 0.188837i
\(257\) −278246. + 481936.i −0.262782 + 0.455152i −0.966980 0.254851i \(-0.917973\pi\)
0.704198 + 0.710004i \(0.251307\pi\)
\(258\) 663624. 0.620688
\(259\) 0 0
\(260\) −12449.6 −0.0114215
\(261\) 51013.1 88357.2i 0.0463533 0.0802862i
\(262\) −147291. 255115.i −0.132563 0.229606i
\(263\) 116690. + 202112.i 0.104026 + 0.180179i 0.913340 0.407198i \(-0.133494\pi\)
−0.809314 + 0.587377i \(0.800161\pi\)
\(264\) 155211. 268834.i 0.137061 0.237396i
\(265\) −336036. −0.293948
\(266\) 0 0
\(267\) −783923. −0.672969
\(268\) −64724.4 + 112106.i −0.0550466 + 0.0953436i
\(269\) −739286. 1.28048e6i −0.622919 1.07893i −0.988939 0.148321i \(-0.952613\pi\)
0.366020 0.930607i \(-0.380720\pi\)
\(270\) 71465.3 + 123782.i 0.0596604 + 0.103335i
\(271\) 88880.8 153946.i 0.0735165 0.127334i −0.826924 0.562314i \(-0.809911\pi\)
0.900440 + 0.434980i \(0.143245\pi\)
\(272\) 1.85755e6 1.52236
\(273\) 0 0
\(274\) 2.30293e6 1.85312
\(275\) 168661. 292130.i 0.134488 0.232940i
\(276\) 1441.67 + 2497.04i 0.00113918 + 0.00197312i
\(277\) 611259. + 1.05873e6i 0.478659 + 0.829062i 0.999701 0.0244697i \(-0.00778972\pi\)
−0.521042 + 0.853531i \(0.674456\pi\)
\(278\) −26995.2 + 46757.1i −0.0209496 + 0.0362857i
\(279\) −726491. −0.558753
\(280\) 0 0
\(281\) 177799. 0.134327 0.0671636 0.997742i \(-0.478605\pi\)
0.0671636 + 0.997742i \(0.478605\pi\)
\(282\) −491291. + 850941.i −0.367888 + 0.637201i
\(283\) −545259. 944416.i −0.404703 0.700966i 0.589584 0.807707i \(-0.299292\pi\)
−0.994287 + 0.106741i \(0.965958\pi\)
\(284\) −74681.5 129352.i −0.0549436 0.0951651i
\(285\) −306587. + 531024.i −0.223584 + 0.387260i
\(286\) −148530. −0.107374
\(287\) 0 0
\(288\) 68440.8 0.0486221
\(289\) −1.22734e6 + 2.12581e6i −0.864410 + 1.49720i
\(290\) −123479. 213872.i −0.0862183 0.149334i
\(291\) −531481. 920551.i −0.367921 0.637258i
\(292\) −48292.7 + 83645.4i −0.0331455 + 0.0574096i
\(293\) −545742. −0.371380 −0.185690 0.982608i \(-0.559452\pi\)
−0.185690 + 0.982608i \(0.559452\pi\)
\(294\) 0 0
\(295\) 319193. 0.213549
\(296\) 1.20599e6 2.08884e6i 0.800047 1.38572i
\(297\) −67224.8 116437.i −0.0442220 0.0765948i
\(298\) −1.37643e6 2.38405e6i −0.897870 1.55516i
\(299\) 10128.4 17542.9i 0.00655182 0.0113481i
\(300\) 38496.8 0.0246957
\(301\) 0 0
\(302\) −1.05168e6 −0.663539
\(303\) 100047. 173287.i 0.0626035 0.108432i
\(304\) −892975. 1.54668e6i −0.554186 0.959878i
\(305\) 740670. + 1.28288e6i 0.455906 + 0.789652i
\(306\) 434170. 752005.i 0.265068 0.459111i
\(307\) 3.29000e6 1.99228 0.996138 0.0878052i \(-0.0279853\pi\)
0.996138 + 0.0878052i \(0.0279853\pi\)
\(308\) 0 0
\(309\) −1.22338e6 −0.728892
\(310\) −879251. + 1.52291e6i −0.519647 + 0.900056i
\(311\) −349856. 605968.i −0.205111 0.355262i 0.745057 0.667000i \(-0.232422\pi\)
−0.950168 + 0.311738i \(0.899089\pi\)
\(312\) −124445. 215545.i −0.0723754 0.125358i
\(313\) 311609. 539723.i 0.179783 0.311394i −0.762023 0.647550i \(-0.775794\pi\)
0.941806 + 0.336156i \(0.109127\pi\)
\(314\) −1.44283e6 −0.825831
\(315\) 0 0
\(316\) −39672.0 −0.0223494
\(317\) 319622. 553601.i 0.178644 0.309420i −0.762772 0.646667i \(-0.776162\pi\)
0.941416 + 0.337247i \(0.109496\pi\)
\(318\) −228766. 396234.i −0.126860 0.219727i
\(319\) 116153. + 201182.i 0.0639075 + 0.110691i
\(320\) 626399. 1.08496e6i 0.341961 0.592294i
\(321\) 1.05864e6 0.573435
\(322\) 0 0
\(323\) 3.72519e6 1.98675
\(324\) 7671.99 13288.3i 0.00406018 0.00703244i
\(325\) −135229. 234223.i −0.0710168 0.123005i
\(326\) 1.46801e6 + 2.54267e6i 0.765041 + 1.32509i
\(327\) 155989. 270181.i 0.0806724 0.139729i
\(328\) 1.67858e6 0.861506
\(329\) 0 0
\(330\) −325441. −0.164508
\(331\) −704817. + 1.22078e6i −0.353595 + 0.612445i −0.986876 0.161477i \(-0.948374\pi\)
0.633281 + 0.773922i \(0.281708\pi\)
\(332\) 118913. + 205963.i 0.0592084 + 0.102552i
\(333\) −522337. 904714.i −0.258131 0.447096i
\(334\) 595674. 1.03174e6i 0.292175 0.506062i
\(335\) 1.99265e6 0.970108
\(336\) 0 0
\(337\) −1.55677e6 −0.746704 −0.373352 0.927690i \(-0.621792\pi\)
−0.373352 + 0.927690i \(0.621792\pi\)
\(338\) 951528. 1.64810e6i 0.453033 0.784676i
\(339\) 119630. + 207205.i 0.0565381 + 0.0979269i
\(340\) 82861.1 + 143520.i 0.0388735 + 0.0673308i
\(341\) 827080. 1.43254e6i 0.385178 0.667148i
\(342\) −834870. −0.385970
\(343\) 0 0
\(344\) −2.53200e6 −1.15363
\(345\) 22192.1 38437.9i 0.0100381 0.0173865i
\(346\) 1.60718e6 + 2.78372e6i 0.721731 + 1.25007i
\(347\) −124148. 215031.i −0.0553500 0.0958690i 0.837023 0.547168i \(-0.184294\pi\)
−0.892373 + 0.451299i \(0.850961\pi\)
\(348\) −13255.8 + 22959.8i −0.00586758 + 0.0101629i
\(349\) −1.86169e6 −0.818171 −0.409086 0.912496i \(-0.634152\pi\)
−0.409086 + 0.912496i \(0.634152\pi\)
\(350\) 0 0
\(351\) −107799. −0.0467031
\(352\) −77917.0 + 134956.i −0.0335178 + 0.0580546i
\(353\) 885642. + 1.53398e6i 0.378287 + 0.655212i 0.990813 0.135238i \(-0.0431799\pi\)
−0.612526 + 0.790450i \(0.709847\pi\)
\(354\) 217299. + 376373.i 0.0921616 + 0.159629i
\(355\) −1.14960e6 + 1.99117e6i −0.484146 + 0.838566i
\(356\) 203704. 0.0851871
\(357\) 0 0
\(358\) −1.18375e6 −0.488147
\(359\) 2.23780e6 3.87599e6i 0.916401 1.58725i 0.111563 0.993757i \(-0.464414\pi\)
0.804837 0.593495i \(-0.202253\pi\)
\(360\) −272669. 472277.i −0.110887 0.192062i
\(361\) −552751. 957393.i −0.223235 0.386654i
\(362\) 512243. 887230.i 0.205449 0.355848i
\(363\) −1.14333e6 −0.455412
\(364\) 0 0
\(365\) 1.48678e6 0.584135
\(366\) −1.00846e6 + 1.74671e6i −0.393511 + 0.681582i
\(367\) 1.58548e6 + 2.74614e6i 0.614465 + 1.06428i 0.990478 + 0.137670i \(0.0439613\pi\)
−0.376014 + 0.926614i \(0.622705\pi\)
\(368\) 64637.5 + 111955.i 0.0248809 + 0.0430949i
\(369\) 363512. 629622.i 0.138980 0.240721i
\(370\) −2.52868e6 −0.960261
\(371\) 0 0
\(372\) 188780. 0.0707292
\(373\) 1.15590e6 2.00207e6i 0.430177 0.745088i −0.566712 0.823916i \(-0.691785\pi\)
0.996888 + 0.0788285i \(0.0251179\pi\)
\(374\) 988570. + 1.71225e6i 0.365450 + 0.632978i
\(375\) −802548. 1.39005e6i −0.294709 0.510450i
\(376\) 1.87447e6 3.24669e6i 0.683770 1.18432i
\(377\) 186257. 0.0674931
\(378\) 0 0
\(379\) −591840. −0.211644 −0.105822 0.994385i \(-0.533747\pi\)
−0.105822 + 0.994385i \(0.533747\pi\)
\(380\) 79667.2 137988.i 0.0283022 0.0490209i
\(381\) 617000. + 1.06868e6i 0.217757 + 0.377167i
\(382\) −472521. 818431.i −0.165677 0.286961i
\(383\) −1.79883e6 + 3.11567e6i −0.626605 + 1.08531i 0.361623 + 0.932324i \(0.382223\pi\)
−0.988228 + 0.152987i \(0.951111\pi\)
\(384\) 1.46241e6 0.506105
\(385\) 0 0
\(386\) 641464. 0.219131
\(387\) −548327. + 949730.i −0.186107 + 0.322346i
\(388\) 138106. + 239207.i 0.0465730 + 0.0806667i
\(389\) 1.12373e6 + 1.94636e6i 0.376520 + 0.652152i 0.990553 0.137128i \(-0.0437873\pi\)
−0.614033 + 0.789280i \(0.710454\pi\)
\(390\) −130466. + 225973.i −0.0434345 + 0.0752308i
\(391\) −269646. −0.0891973
\(392\) 0 0
\(393\) 486803. 0.158991
\(394\) −611976. + 1.05997e6i −0.198607 + 0.343997i
\(395\) 305343. + 528870.i 0.0984681 + 0.170552i
\(396\) 17468.5 + 30256.3i 0.00559780 + 0.00969567i
\(397\) −2.29335e6 + 3.97220e6i −0.730288 + 1.26490i 0.226471 + 0.974018i \(0.427281\pi\)
−0.956760 + 0.290879i \(0.906052\pi\)
\(398\) −4.03169e6 −1.27579
\(399\) 0 0
\(400\) 1.72602e6 0.539380
\(401\) −3.00216e6 + 5.19990e6i −0.932338 + 1.61486i −0.153023 + 0.988223i \(0.548901\pi\)
−0.779314 + 0.626633i \(0.784432\pi\)
\(402\) 1.35655e6 + 2.34962e6i 0.418670 + 0.725158i
\(403\) −663134. 1.14858e6i −0.203394 0.352289i
\(404\) −25997.5 + 45028.9i −0.00792461 + 0.0137258i
\(405\) −236196. −0.0715542
\(406\) 0 0
\(407\) 2.37864e6 0.711774
\(408\) −1.65654e6 + 2.86921e6i −0.492664 + 0.853319i
\(409\) −1.77670e6 3.07733e6i −0.525177 0.909633i −0.999570 0.0293196i \(-0.990666\pi\)
0.474393 0.880313i \(-0.342667\pi\)
\(410\) −879898. 1.52403e6i −0.258507 0.447747i
\(411\) −1.90282e6 + 3.29578e6i −0.555639 + 0.962395i
\(412\) 317896. 0.0922661
\(413\) 0 0
\(414\) 60431.6 0.0173286
\(415\) 1.83047e6 3.17047e6i 0.521726 0.903657i
\(416\) 62472.1 + 108205.i 0.0176992 + 0.0306559i
\(417\) −44610.2 77267.1i −0.0125630 0.0217598i
\(418\) 950465. 1.64625e6i 0.266070 0.460846i
\(419\) −2.01375e6 −0.560365 −0.280182 0.959947i \(-0.590395\pi\)
−0.280182 + 0.959947i \(0.590395\pi\)
\(420\) 0 0
\(421\) −5.89987e6 −1.62232 −0.811161 0.584823i \(-0.801164\pi\)
−0.811161 + 0.584823i \(0.801164\pi\)
\(422\) 1.92223e6 3.32940e6i 0.525442 0.910092i
\(423\) −811869. 1.40620e6i −0.220615 0.382116i
\(424\) 872834. + 1.51179e6i 0.235786 + 0.408392i
\(425\) −1.80009e6 + 3.11784e6i −0.483416 + 0.837301i
\(426\) −3.13049e6 −0.835774
\(427\) 0 0
\(428\) −275088. −0.0725877
\(429\) 122724. 212565.i 0.0321949 0.0557632i
\(430\) 1.32725e6 + 2.29886e6i 0.346163 + 0.599573i
\(431\) 1.90524e6 + 3.29997e6i 0.494033 + 0.855690i 0.999976 0.00687645i \(-0.00218886\pi\)
−0.505943 + 0.862567i \(0.668856\pi\)
\(432\) 343976. 595784.i 0.0886786 0.153596i
\(433\) −6.59449e6 −1.69029 −0.845146 0.534536i \(-0.820487\pi\)
−0.845146 + 0.534536i \(0.820487\pi\)
\(434\) 0 0
\(435\) 408105. 0.103407
\(436\) −40534.0 + 70207.0i −0.0102118 + 0.0176874i
\(437\) 129626. + 224519.i 0.0324705 + 0.0562406i
\(438\) 1.01216e6 + 1.75312e6i 0.252096 + 0.436643i
\(439\) −2.27514e6 + 3.94065e6i −0.563438 + 0.975904i 0.433755 + 0.901031i \(0.357188\pi\)
−0.997193 + 0.0748729i \(0.976145\pi\)
\(440\) 1.24169e6 0.305761
\(441\) 0 0
\(442\) 1.58523e6 0.385954
\(443\) −2.55769e6 + 4.43004e6i −0.619210 + 1.07250i 0.370420 + 0.928864i \(0.379214\pi\)
−0.989630 + 0.143639i \(0.954120\pi\)
\(444\) 135730. + 235092.i 0.0326753 + 0.0565952i
\(445\) −1.56785e6 2.71559e6i −0.375321 0.650076i
\(446\) 114954. 199106.i 0.0273645 0.0473967i
\(447\) 4.54916e6 1.07687
\(448\) 0 0
\(449\) 5.95600e6 1.39424 0.697122 0.716953i \(-0.254464\pi\)
0.697122 + 0.716953i \(0.254464\pi\)
\(450\) 403426. 698755.i 0.0939145 0.162665i
\(451\) 827687. + 1.43360e6i 0.191613 + 0.331883i
\(452\) −31086.1 53842.7i −0.00715682 0.0123960i
\(453\) 868962. 1.50509e6i 0.198955 0.344601i
\(454\) −4.04329e6 −0.920652
\(455\) 0 0
\(456\) 3.18537e6 0.717378
\(457\) 1.29917e6 2.25022e6i 0.290988 0.504006i −0.683056 0.730366i \(-0.739349\pi\)
0.974044 + 0.226361i \(0.0726828\pi\)
\(458\) 2.56309e6 + 4.43940e6i 0.570953 + 0.988919i
\(459\) 717476. + 1.24270e6i 0.158956 + 0.275319i
\(460\) −5766.66 + 9988.15i −0.00127066 + 0.00220085i
\(461\) −4.51513e6 −0.989505 −0.494752 0.869034i \(-0.664741\pi\)
−0.494752 + 0.869034i \(0.664741\pi\)
\(462\) 0 0
\(463\) −5.55129e6 −1.20349 −0.601744 0.798689i \(-0.705527\pi\)
−0.601744 + 0.798689i \(0.705527\pi\)
\(464\) −594330. + 1.02941e6i −0.128154 + 0.221969i
\(465\) −1.45298e6 2.51664e6i −0.311622 0.539745i
\(466\) 1.39513e6 + 2.41644e6i 0.297613 + 0.515480i
\(467\) −3.97675e6 + 6.88794e6i −0.843794 + 1.46149i 0.0428708 + 0.999081i \(0.486350\pi\)
−0.886665 + 0.462413i \(0.846984\pi\)
\(468\) 28011.7 0.00591187
\(469\) 0 0
\(470\) −3.93033e6 −0.820699
\(471\) 1.19215e6 2.06487e6i 0.247617 0.428885i
\(472\) −829085. 1.43602e6i −0.171295 0.296691i
\(473\) −1.24849e6 2.16246e6i −0.256586 0.444421i
\(474\) −415742. + 720086.i −0.0849920 + 0.147210i
\(475\) 3.46140e6 0.703912
\(476\) 0 0
\(477\) 756080. 0.152150
\(478\) 314037. 543928.i 0.0628653 0.108886i
\(479\) −3.28185e6 5.68433e6i −0.653552 1.13199i −0.982255 0.187552i \(-0.939945\pi\)
0.328703 0.944433i \(-0.393389\pi\)
\(480\) 136882. + 237086.i 0.0271170 + 0.0469681i
\(481\) 953568. 1.65163e6i 0.187927 0.325499i
\(482\) 4.95532e6 0.971525
\(483\) 0 0
\(484\) 297096. 0.0576479
\(485\) 2.12592e6 3.68221e6i 0.410387 0.710810i
\(486\) −160797. 278509.i −0.0308807 0.0534870i
\(487\) −2.33185e6 4.03888e6i −0.445531 0.771683i 0.552558 0.833475i \(-0.313652\pi\)
−0.998089 + 0.0617918i \(0.980319\pi\)
\(488\) 3.84770e6 6.66441e6i 0.731394 1.26681i
\(489\) −4.85183e6 −0.917558
\(490\) 0 0
\(491\) −917227. −0.171701 −0.0858506 0.996308i \(-0.527361\pi\)
−0.0858506 + 0.996308i \(0.527361\pi\)
\(492\) −94459.4 + 163608.i −0.0175927 + 0.0304714i
\(493\) −1.23967e6 2.14717e6i −0.229715 0.397878i
\(494\) −762061. 1.31993e6i −0.140499 0.243351i
\(495\) 268899. 465747.i 0.0493261 0.0854353i
\(496\) 8.46401e6 1.54480
\(497\) 0 0
\(498\) 4.98458e6 0.900648
\(499\) −156718. + 271443.i −0.0281752 + 0.0488009i −0.879769 0.475401i \(-0.842303\pi\)
0.851594 + 0.524202i \(0.175636\pi\)
\(500\) 208544. + 361208.i 0.0373054 + 0.0646148i
\(501\) 984365. + 1.70497e6i 0.175211 + 0.303475i
\(502\) −874837. + 1.51526e6i −0.154942 + 0.268367i
\(503\) 3.74110e6 0.659294 0.329647 0.944104i \(-0.393070\pi\)
0.329647 + 0.944104i \(0.393070\pi\)
\(504\) 0 0
\(505\) 800378. 0.139658
\(506\) −68798.9 + 119163.i −0.0119455 + 0.0206902i
\(507\) 1.57242e6 + 2.72351e6i 0.271675 + 0.470554i
\(508\) −160329. 277697.i −0.0275646 0.0477433i
\(509\) 5.15085e6 8.92153e6i 0.881220 1.52632i 0.0312337 0.999512i \(-0.490056\pi\)
0.849986 0.526805i \(-0.176610\pi\)
\(510\) 3.47336e6 0.591323
\(511\) 0 0
\(512\) −6.44492e6 −1.08653
\(513\) 689821. 1.19480e6i 0.115729 0.200449i
\(514\) −1.51539e6 2.62473e6i −0.252998 0.438205i
\(515\) −2.44675e6 4.23790e6i −0.406510 0.704096i
\(516\) 142484. 246789.i 0.0235581 0.0408039i
\(517\) 3.69711e6 0.608326
\(518\) 0 0
\(519\) −5.31181e6 −0.865614
\(520\) 497780. 862180.i 0.0807289 0.139827i
\(521\) −3.28663e6 5.69260e6i −0.530464 0.918791i −0.999368 0.0355415i \(-0.988684\pi\)
0.468904 0.883249i \(-0.344649\pi\)
\(522\) 277829. + 481213.i 0.0446273 + 0.0772967i
\(523\) 4.18266e6 7.24458e6i 0.668650 1.15814i −0.309632 0.950856i \(-0.600206\pi\)
0.978282 0.207279i \(-0.0664607\pi\)
\(524\) −126497. −0.0201257
\(525\) 0 0
\(526\) −1.27103e6 −0.200306
\(527\) −8.82724e6 + 1.52892e7i −1.38452 + 2.39805i
\(528\) 783205. + 1.35655e6i 0.122262 + 0.211764i
\(529\) 3.20879e6 + 5.55778e6i 0.498542 + 0.863500i
\(530\) 915063. 1.58494e6i 0.141502 0.245088i
\(531\) −718184. −0.110535
\(532\) 0 0
\(533\) 1.32724e6 0.202364
\(534\) 2.13471e6 3.69742e6i 0.323956 0.561108i
\(535\) 2.11727e6 + 3.66722e6i 0.319810 + 0.553927i
\(536\) −5.17581e6 8.96477e6i −0.778155 1.34780i
\(537\) 978083. 1.69409e6i 0.146366 0.253513i
\(538\) 8.05263e6 1.19945
\(539\) 0 0
\(540\) 61376.0 0.00905761
\(541\) 4.03311e6 6.98556e6i 0.592444 1.02614i −0.401458 0.915877i \(-0.631496\pi\)
0.993902 0.110266i \(-0.0351702\pi\)
\(542\) 484064. + 838424.i 0.0707791 + 0.122593i
\(543\) 846492. + 1.46617e6i 0.123204 + 0.213395i
\(544\) 831592. 1.44036e6i 0.120479 0.208676i
\(545\) 1.24791e6 0.179967
\(546\) 0 0
\(547\) 3.90775e6 0.558416 0.279208 0.960231i \(-0.409928\pi\)
0.279208 + 0.960231i \(0.409928\pi\)
\(548\) 494451. 856414.i 0.0703350 0.121824i
\(549\) −1.66651e6 2.88647e6i −0.235981 0.408730i
\(550\) 918568. + 1.59101e6i 0.129481 + 0.224267i
\(551\) −1.19189e6 + 2.06441e6i −0.167246 + 0.289679i
\(552\) −230571. −0.0322075
\(553\) 0 0
\(554\) −6.65811e6 −0.921672
\(555\) 2.08935e6 3.61886e6i 0.287924 0.498700i
\(556\) 11592.0 + 20078.0i 0.00159028 + 0.00275444i
\(557\) 5.79311e6 + 1.00340e7i 0.791177 + 1.37036i 0.925239 + 0.379385i \(0.123864\pi\)
−0.134062 + 0.990973i \(0.542802\pi\)
\(558\) 1.97832e6 3.42654e6i 0.268974 0.465876i
\(559\) −2.00203e6 −0.270982
\(560\) 0 0
\(561\) −3.26727e6 −0.438306
\(562\) −484167. + 838602.i −0.0646628 + 0.111999i
\(563\) 955879. + 1.65563e6i 0.127096 + 0.220137i 0.922550 0.385877i \(-0.126101\pi\)
−0.795454 + 0.606014i \(0.792768\pi\)
\(564\) 210966. + 365403.i 0.0279263 + 0.0483698i
\(565\) −478520. + 828822.i −0.0630637 + 0.109230i
\(566\) 5.93920e6 0.779268
\(567\) 0 0
\(568\) 1.19441e7 1.55340
\(569\) −4.08409e6 + 7.07385e6i −0.528828 + 0.915957i 0.470607 + 0.882343i \(0.344035\pi\)
−0.999435 + 0.0336138i \(0.989298\pi\)
\(570\) −1.66974e6 2.89208e6i −0.215259 0.372840i
\(571\) 3.73297e6 + 6.46569e6i 0.479141 + 0.829897i 0.999714 0.0239203i \(-0.00761479\pi\)
−0.520573 + 0.853817i \(0.674281\pi\)
\(572\) −31890.1 + 55235.3i −0.00407536 + 0.00705873i
\(573\) 1.56170e6 0.198706
\(574\) 0 0
\(575\) −250552. −0.0316030
\(576\) −1.40940e6 + 2.44115e6i −0.177002 + 0.306576i
\(577\) −3.44219e6 5.96205e6i −0.430423 0.745514i 0.566487 0.824071i \(-0.308302\pi\)
−0.996910 + 0.0785568i \(0.974969\pi\)
\(578\) −6.68436e6 1.15777e7i −0.832224 1.44145i
\(579\) −530017. + 918016.i −0.0657042 + 0.113803i
\(580\) −106047. −0.0130896
\(581\) 0 0
\(582\) 5.78912e6 0.708444
\(583\) −860766. + 1.49089e6i −0.104885 + 0.181666i
\(584\) −3.86182e6 6.68886e6i −0.468554 0.811559i
\(585\) −215597. 373426.i −0.0260468 0.0451143i
\(586\) 1.48612e6 2.57403e6i 0.178776 0.309649i
\(587\) 8.91086e6 1.06739 0.533696 0.845676i \(-0.320803\pi\)
0.533696 + 0.845676i \(0.320803\pi\)
\(588\) 0 0
\(589\) 1.69740e7 2.01602
\(590\) −869197. + 1.50549e6i −0.102799 + 0.178053i
\(591\) −1.01130e6 1.75163e6i −0.119100 0.206288i
\(592\) 6.08551e6 + 1.05404e7i 0.713662 + 1.23610i
\(593\) 6.17151e6 1.06894e7i 0.720700 1.24829i −0.240019 0.970768i \(-0.577154\pi\)
0.960720 0.277521i \(-0.0895128\pi\)
\(594\) 732243. 0.0851508
\(595\) 0 0
\(596\) −1.18211e6 −0.136314
\(597\) 3.33123e6 5.76986e6i 0.382533 0.662567i
\(598\) 55161.4 + 95542.3i 0.00630786 + 0.0109255i
\(599\) −4.52866e6 7.84387e6i −0.515707 0.893230i −0.999834 0.0182325i \(-0.994196\pi\)
0.484127 0.874998i \(-0.339137\pi\)
\(600\) −1.53924e6 + 2.66603e6i −0.174553 + 0.302334i
\(601\) −7.41700e6 −0.837611 −0.418805 0.908076i \(-0.637551\pi\)
−0.418805 + 0.908076i \(0.637551\pi\)
\(602\) 0 0
\(603\) −4.48347e6 −0.502136
\(604\) −225801. + 391100.i −0.0251846 + 0.0436209i
\(605\) −2.28666e6 3.96061e6i −0.253988 0.439919i
\(606\) 544880. + 943760.i 0.0602725 + 0.104395i
\(607\) −2.88907e6 + 5.00401e6i −0.318263 + 0.551247i −0.980126 0.198378i \(-0.936433\pi\)
0.661863 + 0.749625i \(0.269766\pi\)
\(608\) −1.59908e6 −0.175432
\(609\) 0 0
\(610\) −8.06770e6 −0.877860
\(611\) 1.48213e6 2.56713e6i 0.160614 0.278192i
\(612\) −186437. 322919.i −0.0201212 0.0348510i
\(613\) −3.14632e6 5.44959e6i −0.338183 0.585750i 0.645908 0.763415i \(-0.276479\pi\)
−0.984091 + 0.177665i \(0.943146\pi\)
\(614\) −8.95902e6 + 1.55175e7i −0.959047 + 1.66112i
\(615\) 2.90810e6 0.310043
\(616\) 0 0
\(617\) −9.79133e6 −1.03545 −0.517725 0.855547i \(-0.673221\pi\)
−0.517725 + 0.855547i \(0.673221\pi\)
\(618\) 3.33139e6 5.77013e6i 0.350876 0.607735i
\(619\) −6.63386e6 1.14902e7i −0.695889 1.20531i −0.969880 0.243583i \(-0.921677\pi\)
0.273991 0.961732i \(-0.411656\pi\)
\(620\) 377560. + 653953.i 0.0394463 + 0.0683231i
\(621\) −49932.3 + 86485.3i −0.00519580 + 0.00899939i
\(622\) 3.81079e6 0.394947
\(623\) 0 0
\(624\) 1.25591e6 0.129121
\(625\) 352380. 610339.i 0.0360837 0.0624987i
\(626\) 1.69709e6 + 2.93945e6i 0.173089 + 0.299799i
\(627\) 1.57066e6 + 2.72047e6i 0.159556 + 0.276360i
\(628\) −309783. + 536560.i −0.0313443 + 0.0542900i
\(629\) −2.53867e7 −2.55846
\(630\) 0 0
\(631\) 4.41233e6 0.441158 0.220579 0.975369i \(-0.429205\pi\)
0.220579 + 0.975369i \(0.429205\pi\)
\(632\) 1.58622e6 2.74742e6i 0.157969 0.273610i
\(633\) 3.17653e6 + 5.50191e6i 0.315097 + 0.545763i
\(634\) 1.74073e6 + 3.01504e6i 0.171992 + 0.297899i
\(635\) −2.46800e6 + 4.27470e6i −0.242891 + 0.420699i
\(636\) −196469. −0.0192598
\(637\) 0 0
\(638\) −1.26518e6 −0.123056
\(639\) 2.58660e6 4.48013e6i 0.250598 0.434049i
\(640\) 2.92482e6 + 5.06594e6i 0.282260 + 0.488888i
\(641\) −4.06518e6 7.04109e6i −0.390782 0.676854i 0.601771 0.798669i \(-0.294462\pi\)
−0.992553 + 0.121815i \(0.961129\pi\)
\(642\) −2.88278e6 + 4.99313e6i −0.276041 + 0.478118i
\(643\) 3.12961e6 0.298513 0.149256 0.988799i \(-0.452312\pi\)
0.149256 + 0.988799i \(0.452312\pi\)
\(644\) 0 0
\(645\) −4.38661e6 −0.415174
\(646\) −1.01441e7 + 1.75701e7i −0.956384 + 1.65651i
\(647\) 6.73300e6 + 1.16619e7i 0.632336 + 1.09524i 0.987073 + 0.160271i \(0.0512370\pi\)
−0.354737 + 0.934966i \(0.615430\pi\)
\(648\) 613506. + 1.06262e6i 0.0573960 + 0.0994127i
\(649\) 817622. 1.41616e6i 0.0761975 0.131978i
\(650\) 1.47297e6 0.136745
\(651\) 0 0
\(652\) 1.26076e6 0.116148
\(653\) −7.23861e6 + 1.25376e7i −0.664312 + 1.15062i 0.315159 + 0.949039i \(0.397942\pi\)
−0.979471 + 0.201584i \(0.935391\pi\)
\(654\) 849551. + 1.47147e6i 0.0776685 + 0.134526i
\(655\) 973605. + 1.68633e6i 0.0886706 + 0.153582i
\(656\) −4.23511e6 + 7.33543e6i −0.384243 + 0.665528i
\(657\) −3.34525e6 −0.302353
\(658\) 0 0
\(659\) 432708. 0.0388134 0.0194067 0.999812i \(-0.493822\pi\)
0.0194067 + 0.999812i \(0.493822\pi\)
\(660\) −69874.0 + 121025.i −0.00624389 + 0.0108147i
\(661\) −14982.6 25950.6i −0.00133378 0.00231017i 0.865358 0.501155i \(-0.167091\pi\)
−0.866692 + 0.498844i \(0.833758\pi\)
\(662\) −3.83859e6 6.64863e6i −0.340429 0.589640i
\(663\) −1.30981e6 + 2.26866e6i −0.115724 + 0.200440i
\(664\) −1.90182e7 −1.67398
\(665\) 0 0
\(666\) 5.68953e6 0.497039
\(667\) 86274.1 149431.i 0.00750872 0.0130055i
\(668\) −255789. 443039.i −0.0221789 0.0384150i
\(669\) 189964. + 329028.i 0.0164099 + 0.0284228i
\(670\) −5.42622e6 + 9.39849e6i −0.466993 + 0.808856i
\(671\) 7.58899e6 0.650696
\(672\) 0 0
\(673\) −6.71329e6 −0.571344 −0.285672 0.958327i \(-0.592217\pi\)
−0.285672 + 0.958327i \(0.592217\pi\)
\(674\) 4.23925e6 7.34259e6i 0.359450 0.622586i
\(675\) 666670. + 1.15471e6i 0.0563186 + 0.0975467i
\(676\) −408596. 707710.i −0.0343897 0.0595646i
\(677\) −2.22965e6 + 3.86186e6i −0.186967 + 0.323836i −0.944237 0.329265i \(-0.893199\pi\)
0.757271 + 0.653101i \(0.226532\pi\)
\(678\) −1.30306e6 −0.108866
\(679\) 0 0
\(680\) −1.32523e7 −1.09905
\(681\) 3.34081e6 5.78646e6i 0.276048 0.478129i
\(682\) 4.50446e6 + 7.80195e6i 0.370836 + 0.642306i
\(683\) 8.99196e6 + 1.55745e7i 0.737569 + 1.27751i 0.953587 + 0.301117i \(0.0973596\pi\)
−0.216018 + 0.976389i \(0.569307\pi\)
\(684\) −179251. + 310472.i −0.0146495 + 0.0253736i
\(685\) −1.52225e7 −1.23954
\(686\) 0 0
\(687\) −8.47112e6 −0.684777
\(688\) 6.38830e6 1.10649e7i 0.514534 0.891199i
\(689\) 690143. + 1.19536e6i 0.0553848 + 0.0959294i
\(690\) 120863. + 209341.i 0.00966432 + 0.0167391i
\(691\) 1.25468e6 2.17316e6i 0.0999624 0.173140i −0.811706 0.584066i \(-0.801461\pi\)
0.911669 + 0.410926i \(0.134794\pi\)
\(692\) 1.38028e6 0.109573
\(693\) 0 0
\(694\) 1.35228e6 0.106578
\(695\) 178441. 309069.i 0.0140130 0.0242713i
\(696\) −1.06003e6 1.83602e6i −0.0829458 0.143666i
\(697\) −8.83373e6 1.53005e7i −0.688751 1.19295i
\(698\) 5.06959e6 8.78079e6i 0.393853 0.682174i
\(699\) −4.61098e6 −0.356944
\(700\) 0 0
\(701\) 9.68649e6 0.744512 0.372256 0.928130i \(-0.378584\pi\)
0.372256 + 0.928130i \(0.378584\pi\)
\(702\) 293548. 508440.i 0.0224821 0.0389401i
\(703\) 1.22041e7 + 2.11381e7i 0.931357 + 1.61316i
\(704\) −3.20908e6 5.55829e6i −0.244033 0.422678i
\(705\) 3.24748e6 5.62479e6i 0.246078 0.426220i
\(706\) −9.64681e6 −0.728403
\(707\) 0 0
\(708\) 186621. 0.0139919
\(709\) 4.76360e6 8.25079e6i 0.355893 0.616425i −0.631377 0.775476i \(-0.717510\pi\)
0.987270 + 0.159051i \(0.0508434\pi\)
\(710\) −6.26099e6 1.08443e7i −0.466119 0.807342i
\(711\) −687023. 1.18996e6i −0.0509679 0.0882790i
\(712\) −8.14478e6 + 1.41072e7i −0.602115 + 1.04289i
\(713\) −1.22865e6 −0.0905118
\(714\) 0 0
\(715\) 981794. 0.0718217
\(716\) −254157. + 440212.i −0.0185276 + 0.0320907i
\(717\) 518953. + 898853.i 0.0376990 + 0.0652966i
\(718\) 1.21876e7 + 2.11095e7i 0.882279 + 1.52815i
\(719\) 378588. 655734.i 0.0273114 0.0473048i −0.852047 0.523466i \(-0.824639\pi\)
0.879358 + 0.476161i \(0.157972\pi\)
\(720\) 2.75181e6 0.197828
\(721\) 0 0
\(722\) 6.02081e6 0.429845
\(723\) −4.09439e6 + 7.09169e6i −0.291302 + 0.504549i
\(724\) −219962. 380986.i −0.0155956 0.0270124i
\(725\) −1.15189e6 1.99513e6i −0.0813889 0.140970i
\(726\) 3.11341e6 5.39258e6i 0.219227 0.379713i
\(727\) 2.66570e7 1.87058 0.935288 0.353888i \(-0.115141\pi\)
0.935288 + 0.353888i \(0.115141\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) −4.04866e6 + 7.01248e6i −0.281192 + 0.487040i
\(731\) 1.33249e7 + 2.30794e7i 0.922297 + 1.59747i
\(732\) 433045. + 750056.i 0.0298714 + 0.0517387i
\(733\) 1.35429e7 2.34569e7i 0.931001 1.61254i 0.149387 0.988779i \(-0.452270\pi\)
0.781614 0.623762i \(-0.214397\pi\)
\(734\) −1.72698e7 −1.18317
\(735\) 0 0
\(736\) 115748. 0.00787625
\(737\) 5.10425e6 8.84081e6i 0.346149 0.599547i
\(738\) 1.97977e6 + 3.42906e6i 0.133805 + 0.231758i
\(739\) −1.09753e7 1.90098e7i −0.739276 1.28046i −0.952822 0.303531i \(-0.901834\pi\)
0.213545 0.976933i \(-0.431499\pi\)
\(740\) −542921. + 940366.i −0.0364466 + 0.0631274i
\(741\) 2.51865e6 0.168508
\(742\) 0 0
\(743\) 5.77370e6 0.383691 0.191846 0.981425i \(-0.438553\pi\)
0.191846 + 0.981425i \(0.438553\pi\)
\(744\) −7.54808e6 + 1.30737e7i −0.499924 + 0.865894i
\(745\) 9.09832e6 + 1.57587e7i 0.600579 + 1.04023i
\(746\) 6.29527e6 + 1.09037e7i 0.414159 + 0.717345i
\(747\) −4.11856e6 + 7.13356e6i −0.270050 + 0.467740i
\(748\) 849005. 0.0554825
\(749\) 0 0
\(750\) 8.74171e6 0.567470
\(751\) 4.18875e6 7.25512e6i 0.271009 0.469402i −0.698111 0.715989i \(-0.745976\pi\)
0.969121 + 0.246587i \(0.0793093\pi\)
\(752\) 9.45871e6 + 1.63830e7i 0.609940 + 1.05645i
\(753\) −1.44569e6 2.50400e6i −0.0929153 0.160934i
\(754\) −507198. + 878493.i −0.0324900 + 0.0562743i
\(755\) 6.95170e6 0.443837
\(756\) 0 0
\(757\) 1.18828e7 0.753665 0.376833 0.926281i \(-0.377013\pi\)
0.376833 + 0.926281i \(0.377013\pi\)
\(758\) 1.61165e6 2.79145e6i 0.101882 0.176465i
\(759\) −113692. 196920.i −0.00716348 0.0124075i
\(760\) 6.37074e6 + 1.10344e7i 0.400088 + 0.692973i
\(761\) 8.84701e6 1.53235e7i 0.553777 0.959170i −0.444221 0.895917i \(-0.646519\pi\)
0.997998 0.0632523i \(-0.0201473\pi\)
\(762\) −6.72064e6 −0.419298
\(763\) 0 0
\(764\) −405811. −0.0251531
\(765\) −2.86990e6 + 4.97082e6i −0.177302 + 0.307096i
\(766\) −9.79684e6 1.69686e7i −0.603273 1.04490i
\(767\) −655551. 1.13545e6i −0.0402363 0.0696913i
\(768\) 1.02889e6 1.78209e6i 0.0629457 0.109025i
\(769\) 4.12006e6 0.251239 0.125620 0.992078i \(-0.459908\pi\)
0.125620 + 0.992078i \(0.459908\pi\)
\(770\) 0 0
\(771\) 5.00843e6 0.303435
\(772\) 137726. 238548.i 0.00831710 0.0144056i
\(773\) 6.34320e6 + 1.09868e7i 0.381821 + 0.661334i 0.991323