Properties

Label 147.6.e.m.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: \(\Q(\sqrt{-3}, \sqrt{193})\)
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 67.1
Root \(-3.22311 - 5.58259i\) of defining polynomial
Character \(\chi\) \(=\) 147.67
Dual form 147.6.e.m.79.1

$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.72311 4.71657i −0.481383 0.833779i 0.518389 0.855145i \(-0.326532\pi\)
−0.999772 + 0.0213658i \(0.993199\pi\)
\(3\) −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 0.980899 0.194516i \(-0.0623136\pi\)
−0.658906 + 0.752226i \(0.728980\pi\)
\(6\) 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 −0.957744 0.287622i \(-0.907135\pi\)
0.727960 + 0.685620i \(0.240469\pi\)
\(12\) 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 −0.0752284 0.997166i \(-0.523969\pi\)
0.901186 0.433433i \(-0.142698\pi\)
\(18\) −220.572 + 382.042i −0.160461 + 0.277926i
\(19\) 946.256 + 1638.96i 0.601346 + 1.04156i 0.992617 + 0.121287i \(0.0387021\pi\)
−0.391271 + 0.920275i \(0.627965\pi\)
\(20\) 84.1920 0.0470647
\(21\) 0 0
\(22\) 1004.45 0.442457
\(23\) −68.4942 118.635i −0.0269982 0.0467622i 0.852211 0.523199i \(-0.175261\pi\)
−0.879209 + 0.476437i \(0.841928\pi\)
\(24\) 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 −0.0533279 0.998577i \(-0.516983\pi\)
0.891457 0.453105i \(-0.149684\pi\)
\(32\) −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 −0.935135 0.354292i \(-0.884722\pi\)
0.160742 0.986996i \(-0.448611\pi\)
\(38\) 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 −0.980130 0.198354i \(-0.936440\pi\)
0.318286 0.947995i \(-0.396893\pi\)
\(48\) −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 −0.957282 0.289155i \(-0.906626\pi\)
0.729057 + 0.684453i \(0.239959\pi\)
\(54\) −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 −0.771138 0.636668i \(-0.780312\pi\)
0.936940 + 0.349491i \(0.113645\pi\)
\(60\) −378.864 + 656.212i −0.0135864 + 0.0235324i
\(61\) −20574.2 35635.5i −0.707942 1.22619i −0.965619 0.259960i \(-0.916291\pi\)
0.257678 0.966231i \(-0.417043\pi\)
\(62\) −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 −0.193058 0.981187i \(-0.561841\pi\)
0.946262 0.323400i \(-0.104826\pi\)
\(68\) −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 −0.545073 0.838389i \(-0.683498\pi\)
0.998602 + 0.0528522i \(0.0168312\pi\)
\(74\) −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 0.779390 0.626539i \(-0.215529\pi\)
−0.932294 + 0.361702i \(0.882196\pi\)
\(80\) −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 0.995145 + 0.0984220i \(0.0313795\pi\)
−0.412336 + 0.911032i \(0.635287\pi\)
\(90\) −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 −0.806703 0.590957i \(-0.798750\pi\)
0.915135 + 0.403147i \(0.132084\pi\)
\(102\) 48241.2 83556.1i 0.459111 0.795203i
\(103\) 67965.3 + 117719.i 0.631239 + 1.09334i 0.987299 + 0.158875i \(0.0507868\pi\)
−0.356059 + 0.934463i \(0.615880\pi\)
\(104\) 27654.4 0.250716
\(105\) 0 0
\(106\) 50836.8 0.439454
\(107\) −58813.1 101867.i −0.496609 0.860152i 0.503383 0.864063i \(-0.332088\pi\)
−0.999992 + 0.00391112i \(0.998755\pi\)
\(108\) 852.444 1476.48i 0.00703244 0.0121806i
\(109\) 17332.1 30020.1i 0.139729 0.242017i −0.787665 0.616103i \(-0.788710\pi\)
0.927394 + 0.374086i \(0.122044\pi\)
\(110\) 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 0.788932 0.614481i \(-0.210634\pi\)
−0.926622 + 0.375995i \(0.877301\pi\)
\(132\) −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 −0.245939 + 0.969285i \(0.579096\pi\)
−0.716456 + 0.697632i \(0.754237\pi\)
\(138\) −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 −0.778868 0.627188i \(-0.784206\pi\)
−0.153727 0.988113i \(-0.549128\pi\)
\(150\) 44825.1 77639.4i 0.162665 0.281744i
\(151\) 96551.4 167232.i 0.344601 0.596866i −0.640680 0.767808i \(-0.721348\pi\)
0.985281 + 0.170942i \(0.0546810\pi\)
\(152\) −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 −0.567890 0.823105i \(-0.692240\pi\)
0.996774 + 0.0802545i \(0.0255733\pi\)
\(158\) −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 0.923075 + 0.384621i \(0.125668\pi\)
−0.128446 + 0.991717i \(0.540999\pi\)
\(164\) −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 0.947994 + 0.318289i \(0.103108\pi\)
−0.198350 + 0.980131i \(0.563558\pi\)
\(174\) −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 −0.710977 0.703215i \(-0.751747\pi\)
0.964491 + 0.264117i \(0.0850805\pi\)
\(180\) −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 0.767064 0.641571i \(-0.221717\pi\)
−0.939149 + 0.343511i \(0.888384\pi\)
\(192\) −156600. + 271239.i −0.306576 + 0.531005i
\(193\) −58890.7 + 102002.i −0.113803 + 0.197113i −0.917301 0.398195i \(-0.869637\pi\)
0.803498 + 0.595308i \(0.202970\pi\)
\(194\) −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 −0.317372 0.948301i \(-0.602801\pi\)
0.979939 0.199298i \(-0.0638661\pi\)
\(200\) −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 −0.521557 0.853217i \(-0.674649\pi\)
0.999686 + 0.0250731i \(0.00798184\pi\)
\(228\) −19916.8 + 34496.9i −0.0253736 + 0.0439484i
\(229\) 470618. + 815134.i 0.593034 + 1.02717i 0.993821 + 0.110994i \(0.0354035\pi\)
−0.400787 + 0.916171i \(0.631263\pi\)
\(230\) −26858.5 −0.0334782
\(231\) 0 0
\(232\) 235562. 0.287333
\(233\) 256166. + 443692.i 0.309123 + 0.535416i 0.978171 0.207803i \(-0.0666313\pi\)
−0.669048 + 0.743219i \(0.733298\pi\)
\(234\) 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 0.495437 + 0.868644i \(0.335008\pi\)
−0.999986 + 0.00526118i \(0.998325\pi\)
\(242\) 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 0.704198 0.710004i \(-0.251307\pi\)
−0.966980 + 0.254851i \(0.917973\pi\)
\(258\) 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 −0.809314 0.587377i \(-0.800161\pi\)
0.913340 + 0.407198i \(0.133494\pi\)
\(264\) 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 0.366020 + 0.930607i \(0.380720\pi\)
−0.988939 + 0.148321i \(0.952613\pi\)
\(270\) 71465.3 123782.i 0.0596604 0.103335i
\(271\) 88880.8 + 153946.i 0.0735165 + 0.127334i 0.900440 0.434980i \(-0.143245\pi\)
−0.826924 + 0.562314i \(0.809911\pi\)
\(272\) 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 −0.521042 0.853531i \(-0.674456\pi\)
0.999701 + 0.0244697i \(0.00778972\pi\)
\(278\) −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 −0.994287 0.106741i \(-0.965958\pi\)
0.589584 + 0.807707i \(0.299292\pi\)
\(284\) −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 −0.950168 0.311738i \(-0.899089\pi\)
0.745057 + 0.667000i \(0.232422\pi\)
\(312\) −124445. + 215545.i −0.0723754 + 0.125358i
\(313\) 311609. + 539723.i 0.179783 + 0.311394i 0.941806 0.336156i \(-0.109127\pi\)
−0.762023 + 0.647550i \(0.775794\pi\)
\(314\) −1.44283e6 −0.825831
\(315\) 0 0
\(316\) −39672.0 −0.0223494
\(317\) 319622. + 553601.i 0.178644 + 0.309420i 0.941416 0.337247i \(-0.109496\pi\)
−0.762772 + 0.646667i \(0.776162\pi\)
\(318\) −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 0.633281 0.773922i \(-0.281708\pi\)
−0.986876 + 0.161477i \(0.948374\pi\)
\(332\) 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 −0.892373 0.451299i \(-0.850961\pi\)
0.837023 + 0.547168i \(0.184294\pi\)
\(348\) −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 −0.612526 0.790450i \(-0.709847\pi\)
0.990813 + 0.135238i \(0.0431799\pi\)
\(354\) 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 0.804837 + 0.593495i \(0.202253\pi\)
0.111563 + 0.993757i \(0.464414\pi\)
\(360\) −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 −0.376014 0.926614i \(-0.622705\pi\)
0.990478 0.137670i \(-0.0439613\pi\)
\(368\) 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 0.996888 0.0788285i \(-0.0251179\pi\)
−0.566712 + 0.823916i \(0.691785\pi\)
\(374\) 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 −0.988228 0.152987i \(-0.951111\pi\)
0.361623 0.932324i \(-0.382223\pi\)
\(384\) 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 −0.614033 0.789280i \(-0.710454\pi\)
0.990553 + 0.137128i \(0.0437873\pi\)
\(390\) −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 −0.956760 0.290879i \(-0.906052\pi\)
0.226471 0.974018i \(-0.427281\pi\)
\(398\) −4.03169e6 −1.27579
\(399\) 0 0
\(400\) 1.72602e6 0.539380
\(401\) −3.00216e6 5.19990e6i −0.932338 1.61486i −0.779314 0.626633i \(-0.784432\pi\)
−0.153023 0.988223i \(-0.548901\pi\)
\(402\) 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 0.474393 + 0.880313i \(0.342667\pi\)
−0.999570 + 0.0293196i \(0.990666\pi\)
\(410\) −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 −0.505943 0.862567i \(-0.668856\pi\)
0.999976 + 0.00687645i \(0.00218886\pi\)
\(432\) 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 −0.997193 0.0748729i \(-0.976145\pi\)
0.433755 0.901031i \(-0.357188\pi\)
\(440\) 1.24169e6 0.305761
\(441\) 0 0
\(442\) 1.58523e6 0.385954
\(443\) −2.55769e6 4.43004e6i −0.619210 1.07250i −0.989630 0.143639i \(-0.954120\pi\)
0.370420 0.928864i \(-0.379214\pi\)
\(444\) 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 0.974044 0.226361i \(-0.0726828\pi\)
−0.683056 + 0.730366i \(0.739349\pi\)
\(458\) 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 −0.886665 0.462413i \(-0.846984\pi\)
0.0428708 0.999081i \(-0.486350\pi\)
\(468\) 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 0.328703 + 0.944433i \(0.393389\pi\)
−0.982255 + 0.187552i \(0.939945\pi\)
\(480\) 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 −0.998089 0.0617918i \(-0.980319\pi\)
0.552558 + 0.833475i \(0.313652\pi\)
\(488\) 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 0.851594 0.524202i \(-0.175636\pi\)
−0.879769 + 0.475401i \(0.842303\pi\)
\(500\) 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 0.849986 + 0.526805i \(0.176610\pi\)
0.0312337 + 0.999512i \(0.490056\pi\)
\(510\) 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 0.468904 + 0.883249i \(0.344649\pi\)
−0.999368 + 0.0355415i \(0.988684\pi\)
\(522\) 277829. 481213.i 0.0446273 0.0772967i
\(523\) 4.18266e6 + 7.24458e6i 0.668650 + 1.15814i 0.978282 + 0.207279i \(0.0664607\pi\)
−0.309632 + 0.950856i \(0.600206\pi\)
\(524\) −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 0.993902 + 0.110266i \(0.0351702\pi\)
−0.401458 + 0.915877i \(0.631496\pi\)
\(542\) 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 −0.134062 0.990973i \(-0.542802\pi\)
0.925239 0.379385i \(-0.123864\pi\)
\(558\) 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 −0.795454 0.606014i \(-0.792768\pi\)
0.922550 + 0.385877i \(0.126101\pi\)
\(564\) 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 −0.999435 0.0336138i \(-0.989298\pi\)
0.470607 0.882343i \(-0.344035\pi\)
\(570\) −1.66974e6 + 2.89208e6i −0.215259 + 0.372840i
\(571\) 3.73297e6 6.46569e6i 0.479141 0.829897i −0.520573 0.853817i \(-0.674281\pi\)
0.999714 + 0.0239203i \(0.00761479\pi\)
\(572\) −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 −0.996910 0.0785568i \(-0.974969\pi\)
0.566487 + 0.824071i \(0.308302\pi\)
\(578\) −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 0.960720 + 0.277521i \(0.0895128\pi\)
−0.240019 + 0.970768i \(0.577154\pi\)
\(594\) 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 0.484127 + 0.874998i \(0.339137\pi\)
−0.999834 + 0.0182325i \(0.994196\pi\)
\(600\) −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 0.661863 0.749625i \(-0.269766\pi\)
−0.980126 + 0.198378i \(0.936433\pi\)
\(608\) −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 −0.984091 0.177665i \(-0.943146\pi\)
0.645908 + 0.763415i \(0.276479\pi\)
\(614\) −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 0.273991 + 0.961732i \(0.411656\pi\)
−0.969880 + 0.243583i \(0.921677\pi\)
\(620\) 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 −0.992553 0.121815i \(-0.961129\pi\)
0.601771 + 0.798669i \(0.294462\pi\)
\(642\) −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 −0.354737 0.934966i \(-0.615430\pi\)
0.987073 0.160271i \(-0.0512370\pi\)
\(648\) 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 −0.979471 0.201584i \(-0.935391\pi\)
0.315159 0.949039i \(-0.397942\pi\)
\(654\) 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 −0.866692 0.498844i \(-0.833758\pi\)
0.865358 + 0.501155i \(0.167091\pi\)
\(662\) −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 0.757271 0.653101i \(-0.226532\pi\)
−0.944237 + 0.329265i \(0.893199\pi\)
\(678\) −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 −0.216018 0.976389i \(-0.569307\pi\)
0.953587 0.301117i \(-0.0973596\pi\)
\(684\) −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 0.911669 0.410926i \(-0.134794\pi\)
−0.811706 + 0.584066i \(0.801461\pi\)
\(692\) 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 0.987270 0.159051i \(-0.0508434\pi\)
−0.631377 + 0.775476i \(0.717510\pi\)
\(710\) −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 0.879358 0.476161i \(-0.157972\pi\)
−0.852047 + 0.523466i \(0.824639\pi\)
\(720\) 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 0.781614 + 0.623762i \(0.214397\pi\)
0.149387 + 0.988779i \(0.452270\pi\)
\(734\) −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 0.213545 + 0.976933i \(0.431499\pi\)
−0.952822 + 0.303531i \(0.901834\pi\)
\(740\) −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 0.969121 0.246587i \(-0.0793093\pi\)
−0.698111 + 0.715989i \(0.745976\pi\)
\(752\) 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 0.997998 + 0.0632523i \(0.0201473\pi\)
−0.444221 + 0.895917i \(0.646519\pi\)
\(762\) −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