Properties

Label 245.4.e.q.226.2
Level $245$
Weight $4$
Character 245.226
Analytic conductor $14.455$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 245.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.4554679514\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \( x^{12} - 2 x^{11} + 27 x^{10} + 22 x^{9} + 399 x^{8} + 492 x^{7} + 4046 x^{6} + 8784 x^{5} + 22536 x^{4} + 22736 x^{3} + 18792 x^{2} + 4256 x + 784 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2}\cdot 7^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.2
Root \(-0.120924 - 0.209447i\) of defining polynomial
Character \(\chi\) \(=\) 245.226
Dual form 245.4.e.q.116.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.828031 + 1.43419i) q^{2} +(-0.166444 - 0.288289i) q^{3} +(2.62873 + 4.55309i) q^{4} +(-2.50000 + 4.33013i) q^{5} +0.551283 q^{6} -21.9552 q^{8} +(13.4446 - 23.2867i) q^{9} +O(q^{10})\) \(q+(-0.828031 + 1.43419i) q^{2} +(-0.166444 - 0.288289i) q^{3} +(2.62873 + 4.55309i) q^{4} +(-2.50000 + 4.33013i) q^{5} +0.551283 q^{6} -21.9552 q^{8} +(13.4446 - 23.2867i) q^{9} +(-4.14016 - 7.17096i) q^{10} +(-34.7863 - 60.2517i) q^{11} +(0.875071 - 1.51567i) q^{12} -68.4326 q^{13} +1.66444 q^{15} +(-2.85026 + 4.93680i) q^{16} +(52.1659 + 90.3539i) q^{17} +(22.2651 + 38.5643i) q^{18} +(35.9465 - 62.2611i) q^{19} -26.2873 q^{20} +115.217 q^{22} +(50.5154 - 87.4952i) q^{23} +(3.65430 + 6.32944i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(56.6643 - 98.1454i) q^{26} -17.9390 q^{27} -114.661 q^{29} +(-1.37821 + 2.38712i) q^{30} +(-36.8252 - 63.7832i) q^{31} +(-92.5409 - 160.286i) q^{32} +(-11.5799 + 20.0570i) q^{33} -172.780 q^{34} +141.369 q^{36} +(100.467 - 174.013i) q^{37} +(59.5296 + 103.108i) q^{38} +(11.3902 + 19.7284i) q^{39} +(54.8879 - 95.0687i) q^{40} -417.308 q^{41} +311.175 q^{43} +(182.888 - 316.771i) q^{44} +(67.2230 + 116.434i) q^{45} +(83.6566 + 144.897i) q^{46} +(74.8485 - 129.641i) q^{47} +1.89763 q^{48} +41.4016 q^{50} +(17.3654 - 30.0777i) q^{51} +(-179.891 - 311.580i) q^{52} +(-135.737 - 235.104i) q^{53} +(14.8541 - 25.7280i) q^{54} +347.863 q^{55} -23.9323 q^{57} +(94.9425 - 164.445i) q^{58} +(-259.014 - 448.625i) q^{59} +(4.37536 + 7.57834i) q^{60} +(-109.963 + 190.461i) q^{61} +121.970 q^{62} +260.903 q^{64} +(171.081 - 296.322i) q^{65} +(-19.1771 - 33.2157i) q^{66} +(-40.3475 - 69.8839i) q^{67} +(-274.260 + 475.032i) q^{68} -33.6319 q^{69} -91.0463 q^{71} +(-295.178 + 511.264i) q^{72} +(441.141 + 764.078i) q^{73} +(166.379 + 288.177i) q^{74} +(-4.16110 + 7.20723i) q^{75} +377.974 q^{76} -37.7257 q^{78} +(-299.939 + 519.509i) q^{79} +(-14.2513 - 24.6840i) q^{80} +(-360.018 - 623.570i) q^{81} +(345.544 - 598.499i) q^{82} -70.8820 q^{83} -521.659 q^{85} +(-257.662 + 446.284i) q^{86} +(19.0845 + 33.0554i) q^{87} +(763.740 + 1322.84i) q^{88} +(401.296 - 695.065i) q^{89} -222.651 q^{90} +531.165 q^{92} +(-12.2587 + 21.2326i) q^{93} +(123.954 + 214.694i) q^{94} +(179.732 + 311.305i) q^{95} +(-30.8057 + 53.3571i) q^{96} -145.648 q^{97} -1870.75 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{2} + 16 q^{3} - 14 q^{4} - 30 q^{5} - 48 q^{6} - 132 q^{8} - 70 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{2} + 16 q^{3} - 14 q^{4} - 30 q^{5} - 48 q^{6} - 132 q^{8} - 70 q^{9} + 10 q^{10} + 16 q^{11} + 160 q^{12} - 336 q^{13} - 160 q^{15} - 298 q^{16} - 4 q^{17} - 354 q^{18} + 308 q^{19} + 140 q^{20} - 472 q^{22} + 336 q^{23} - 92 q^{24} - 150 q^{25} + 56 q^{26} - 1928 q^{27} + 352 q^{29} + 120 q^{30} + 392 q^{31} + 770 q^{32} + 188 q^{33} - 1624 q^{34} + 460 q^{36} + 140 q^{37} + 20 q^{38} - 140 q^{39} + 330 q^{40} - 1312 q^{41} - 776 q^{43} + 160 q^{44} - 350 q^{45} + 388 q^{46} + 628 q^{47} - 2792 q^{48} - 100 q^{50} - 744 q^{51} + 1520 q^{52} + 676 q^{53} + 2284 q^{54} - 160 q^{55} + 2936 q^{57} + 2012 q^{58} + 996 q^{59} + 800 q^{60} + 740 q^{61} + 728 q^{62} + 2852 q^{64} + 840 q^{65} - 3620 q^{66} - 1768 q^{67} - 2940 q^{68} + 2096 q^{69} - 448 q^{71} - 2858 q^{72} + 2640 q^{73} - 928 q^{74} + 400 q^{75} + 2680 q^{76} + 16 q^{78} - 1636 q^{79} - 1490 q^{80} - 4442 q^{81} - 1756 q^{82} - 280 q^{83} + 40 q^{85} - 1180 q^{86} + 1940 q^{87} + 5652 q^{88} - 1904 q^{89} + 3540 q^{90} - 3904 q^{92} + 1592 q^{93} - 3332 q^{94} + 1540 q^{95} - 6460 q^{96} - 1032 q^{97} - 5608 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.828031 + 1.43419i −0.292753 + 0.507063i −0.974460 0.224562i \(-0.927905\pi\)
0.681707 + 0.731626i \(0.261238\pi\)
\(3\) −0.166444 0.288289i −0.0320321 0.0554813i 0.849565 0.527484i \(-0.176865\pi\)
−0.881597 + 0.472003i \(0.843531\pi\)
\(4\) 2.62873 + 4.55309i 0.328591 + 0.569137i
\(5\) −2.50000 + 4.33013i −0.223607 + 0.387298i
\(6\) 0.551283 0.0375100
\(7\) 0 0
\(8\) −21.9552 −0.970291
\(9\) 13.4446 23.2867i 0.497948 0.862471i
\(10\) −4.14016 7.17096i −0.130923 0.226766i
\(11\) −34.7863 60.2517i −0.953497 1.65151i −0.737770 0.675052i \(-0.764121\pi\)
−0.215727 0.976454i \(-0.569212\pi\)
\(12\) 0.875071 1.51567i 0.0210509 0.0364613i
\(13\) −68.4326 −1.45998 −0.729991 0.683456i \(-0.760476\pi\)
−0.729991 + 0.683456i \(0.760476\pi\)
\(14\) 0 0
\(15\) 1.66444 0.0286504
\(16\) −2.85026 + 4.93680i −0.0445354 + 0.0771375i
\(17\) 52.1659 + 90.3539i 0.744240 + 1.28906i 0.950549 + 0.310574i \(0.100521\pi\)
−0.206309 + 0.978487i \(0.566145\pi\)
\(18\) 22.2651 + 38.5643i 0.291552 + 0.504982i
\(19\) 35.9465 62.2611i 0.434036 0.751772i −0.563180 0.826334i \(-0.690422\pi\)
0.997216 + 0.0745616i \(0.0237557\pi\)
\(20\) −26.2873 −0.293901
\(21\) 0 0
\(22\) 115.217 1.11656
\(23\) 50.5154 87.4952i 0.457964 0.793218i −0.540889 0.841094i \(-0.681912\pi\)
0.998853 + 0.0478764i \(0.0152453\pi\)
\(24\) 3.65430 + 6.32944i 0.0310805 + 0.0538330i
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) 56.6643 98.1454i 0.427415 0.740304i
\(27\) −17.9390 −0.127866
\(28\) 0 0
\(29\) −114.661 −0.734205 −0.367102 0.930181i \(-0.619650\pi\)
−0.367102 + 0.930181i \(0.619650\pi\)
\(30\) −1.37821 + 2.38712i −0.00838750 + 0.0145276i
\(31\) −36.8252 63.7832i −0.213355 0.369542i 0.739407 0.673258i \(-0.235106\pi\)
−0.952762 + 0.303716i \(0.901772\pi\)
\(32\) −92.5409 160.286i −0.511221 0.885461i
\(33\) −11.5799 + 20.0570i −0.0610851 + 0.105802i
\(34\) −172.780 −0.871514
\(35\) 0 0
\(36\) 141.369 0.654485
\(37\) 100.467 174.013i 0.446395 0.773178i −0.551753 0.834007i \(-0.686041\pi\)
0.998148 + 0.0608289i \(0.0193744\pi\)
\(38\) 59.5296 + 103.108i 0.254131 + 0.440168i
\(39\) 11.3902 + 19.7284i 0.0467663 + 0.0810017i
\(40\) 54.8879 95.0687i 0.216964 0.375792i
\(41\) −417.308 −1.58957 −0.794786 0.606889i \(-0.792417\pi\)
−0.794786 + 0.606889i \(0.792417\pi\)
\(42\) 0 0
\(43\) 311.175 1.10357 0.551787 0.833985i \(-0.313946\pi\)
0.551787 + 0.833985i \(0.313946\pi\)
\(44\) 182.888 316.771i 0.626621 1.08534i
\(45\) 67.2230 + 116.434i 0.222689 + 0.385709i
\(46\) 83.6566 + 144.897i 0.268141 + 0.464434i
\(47\) 74.8485 129.641i 0.232293 0.402344i −0.726189 0.687495i \(-0.758710\pi\)
0.958483 + 0.285151i \(0.0920438\pi\)
\(48\) 1.89763 0.00570625
\(49\) 0 0
\(50\) 41.4016 0.117101
\(51\) 17.3654 30.0777i 0.0476792 0.0825827i
\(52\) −179.891 311.580i −0.479737 0.830929i
\(53\) −135.737 235.104i −0.351791 0.609320i 0.634772 0.772699i \(-0.281094\pi\)
−0.986563 + 0.163379i \(0.947761\pi\)
\(54\) 14.8541 25.7280i 0.0374331 0.0648360i
\(55\) 347.863 0.852834
\(56\) 0 0
\(57\) −23.9323 −0.0556124
\(58\) 94.9425 164.445i 0.214941 0.372288i
\(59\) −259.014 448.625i −0.571538 0.989933i −0.996408 0.0846788i \(-0.973014\pi\)
0.424870 0.905254i \(-0.360320\pi\)
\(60\) 4.37536 + 7.57834i 0.00941427 + 0.0163060i
\(61\) −109.963 + 190.461i −0.230808 + 0.399771i −0.958046 0.286614i \(-0.907470\pi\)
0.727238 + 0.686385i \(0.240804\pi\)
\(62\) 121.970 0.249842
\(63\) 0 0
\(64\) 260.903 0.509576
\(65\) 171.081 296.322i 0.326462 0.565449i
\(66\) −19.1771 33.2157i −0.0357657 0.0619480i
\(67\) −40.3475 69.8839i −0.0735706 0.127428i 0.826893 0.562359i \(-0.190106\pi\)
−0.900464 + 0.434931i \(0.856773\pi\)
\(68\) −274.260 + 475.032i −0.489101 + 0.847148i
\(69\) −33.6319 −0.0586783
\(70\) 0 0
\(71\) −91.0463 −0.152186 −0.0760930 0.997101i \(-0.524245\pi\)
−0.0760930 + 0.997101i \(0.524245\pi\)
\(72\) −295.178 + 511.264i −0.483154 + 0.836848i
\(73\) 441.141 + 764.078i 0.707283 + 1.22505i 0.965861 + 0.259059i \(0.0834125\pi\)
−0.258579 + 0.965990i \(0.583254\pi\)
\(74\) 166.379 + 288.177i 0.261367 + 0.452701i
\(75\) −4.16110 + 7.20723i −0.00640643 + 0.0110963i
\(76\) 377.974 0.570481
\(77\) 0 0
\(78\) −37.7257 −0.0547640
\(79\) −299.939 + 519.509i −0.427161 + 0.739865i −0.996620 0.0821553i \(-0.973820\pi\)
0.569458 + 0.822020i \(0.307153\pi\)
\(80\) −14.2513 24.6840i −0.0199168 0.0344969i
\(81\) −360.018 623.570i −0.493852 0.855377i
\(82\) 345.544 598.499i 0.465353 0.806014i
\(83\) −70.8820 −0.0937387 −0.0468694 0.998901i \(-0.514924\pi\)
−0.0468694 + 0.998901i \(0.514924\pi\)
\(84\) 0 0
\(85\) −521.659 −0.665668
\(86\) −257.662 + 446.284i −0.323075 + 0.559582i
\(87\) 19.0845 + 33.0554i 0.0235181 + 0.0407346i
\(88\) 763.740 + 1322.84i 0.925170 + 1.60244i
\(89\) 401.296 695.065i 0.477947 0.827828i −0.521733 0.853109i \(-0.674714\pi\)
0.999680 + 0.0252802i \(0.00804778\pi\)
\(90\) −222.651 −0.260772
\(91\) 0 0
\(92\) 531.165 0.601932
\(93\) −12.2587 + 21.2326i −0.0136684 + 0.0236744i
\(94\) 123.954 + 214.694i 0.136009 + 0.235575i
\(95\) 179.732 + 311.305i 0.194107 + 0.336203i
\(96\) −30.8057 + 53.3571i −0.0327510 + 0.0567264i
\(97\) −145.648 −0.152457 −0.0762283 0.997090i \(-0.524288\pi\)
−0.0762283 + 0.997090i \(0.524288\pi\)
\(98\) 0 0
\(99\) −1870.75 −1.89917
\(100\) 65.7182 113.827i 0.0657182 0.113827i
\(101\) −309.718 536.447i −0.305129 0.528499i 0.672161 0.740405i \(-0.265366\pi\)
−0.977290 + 0.211906i \(0.932033\pi\)
\(102\) 28.7581 + 49.8105i 0.0279165 + 0.0483527i
\(103\) −911.040 + 1577.97i −0.871528 + 1.50953i −0.0111125 + 0.999938i \(0.503537\pi\)
−0.860416 + 0.509593i \(0.829796\pi\)
\(104\) 1502.45 1.41661
\(105\) 0 0
\(106\) 449.578 0.411952
\(107\) −544.851 + 943.709i −0.492268 + 0.852634i −0.999960 0.00890504i \(-0.997165\pi\)
0.507692 + 0.861539i \(0.330499\pi\)
\(108\) −47.1569 81.6781i −0.0420155 0.0727730i
\(109\) −294.833 510.666i −0.259082 0.448743i 0.706914 0.707299i \(-0.250087\pi\)
−0.965996 + 0.258556i \(0.916753\pi\)
\(110\) −288.042 + 498.903i −0.249670 + 0.432441i
\(111\) −66.8882 −0.0571959
\(112\) 0 0
\(113\) −900.358 −0.749544 −0.374772 0.927117i \(-0.622279\pi\)
−0.374772 + 0.927117i \(0.622279\pi\)
\(114\) 19.8167 34.3235i 0.0162807 0.0281990i
\(115\) 252.577 + 437.476i 0.204808 + 0.354738i
\(116\) −301.412 522.060i −0.241253 0.417863i
\(117\) −920.048 + 1593.57i −0.726995 + 1.25919i
\(118\) 857.887 0.669279
\(119\) 0 0
\(120\) −36.5430 −0.0277992
\(121\) −1754.68 + 3039.19i −1.31831 + 2.28339i
\(122\) −182.105 315.415i −0.135140 0.234069i
\(123\) 69.4583 + 120.305i 0.0509174 + 0.0881915i
\(124\) 193.607 335.337i 0.140213 0.242856i
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −1755.75 −1.22676 −0.613378 0.789790i \(-0.710190\pi\)
−0.613378 + 0.789790i \(0.710190\pi\)
\(128\) 524.292 908.100i 0.362041 0.627074i
\(129\) −51.7931 89.7083i −0.0353498 0.0612277i
\(130\) 283.321 + 490.727i 0.191146 + 0.331074i
\(131\) 904.549 1566.72i 0.603289 1.04493i −0.389031 0.921225i \(-0.627190\pi\)
0.992319 0.123702i \(-0.0394766\pi\)
\(132\) −121.762 −0.0802881
\(133\) 0 0
\(134\) 133.636 0.0861521
\(135\) 44.8476 77.6783i 0.0285916 0.0495221i
\(136\) −1145.31 1983.74i −0.722129 1.25076i
\(137\) 9.25670 + 16.0331i 0.00577265 + 0.00999852i 0.868897 0.494992i \(-0.164829\pi\)
−0.863125 + 0.504991i \(0.831496\pi\)
\(138\) 27.8482 48.2346i 0.0171783 0.0297536i
\(139\) 625.608 0.381751 0.190875 0.981614i \(-0.438867\pi\)
0.190875 + 0.981614i \(0.438867\pi\)
\(140\) 0 0
\(141\) −49.8323 −0.0297634
\(142\) 75.3892 130.578i 0.0445530 0.0771680i
\(143\) 2380.52 + 4123.18i 1.39209 + 2.41117i
\(144\) 76.6413 + 132.747i 0.0443526 + 0.0768209i
\(145\) 286.651 496.495i 0.164173 0.284356i
\(146\) −1461.11 −0.828237
\(147\) 0 0
\(148\) 1056.40 0.586725
\(149\) 514.317 890.823i 0.282782 0.489792i −0.689287 0.724488i \(-0.742076\pi\)
0.972069 + 0.234696i \(0.0754095\pi\)
\(150\) −6.89103 11.9356i −0.00375100 0.00649693i
\(151\) −35.5037 61.4942i −0.0191341 0.0331412i 0.856300 0.516479i \(-0.172758\pi\)
−0.875434 + 0.483338i \(0.839424\pi\)
\(152\) −789.211 + 1366.95i −0.421141 + 0.729438i
\(153\) 2805.39 1.48237
\(154\) 0 0
\(155\) 368.252 0.190831
\(156\) −59.8834 + 103.721i −0.0307340 + 0.0532329i
\(157\) −1030.66 1785.16i −0.523922 0.907459i −0.999612 0.0278461i \(-0.991135\pi\)
0.475691 0.879613i \(-0.342198\pi\)
\(158\) −496.717 860.339i −0.250106 0.433196i
\(159\) −45.1852 + 78.2631i −0.0225372 + 0.0390356i
\(160\) 925.409 0.457250
\(161\) 0 0
\(162\) 1192.42 0.578307
\(163\) 981.899 1700.70i 0.471830 0.817234i −0.527651 0.849462i \(-0.676927\pi\)
0.999481 + 0.0322280i \(0.0102603\pi\)
\(164\) −1096.99 1900.04i −0.522320 0.904684i
\(165\) −57.8997 100.285i −0.0273181 0.0473163i
\(166\) 58.6925 101.658i 0.0274423 0.0475315i
\(167\) −2855.04 −1.32293 −0.661467 0.749974i \(-0.730066\pi\)
−0.661467 + 0.749974i \(0.730066\pi\)
\(168\) 0 0
\(169\) 2486.01 1.13155
\(170\) 431.950 748.158i 0.194877 0.337536i
\(171\) −966.571 1674.15i −0.432255 0.748687i
\(172\) 817.994 + 1416.81i 0.362625 + 0.628084i
\(173\) −776.603 + 1345.12i −0.341295 + 0.591140i −0.984673 0.174408i \(-0.944199\pi\)
0.643378 + 0.765548i \(0.277532\pi\)
\(174\) −63.2104 −0.0275400
\(175\) 0 0
\(176\) 396.601 0.169857
\(177\) −86.2226 + 149.342i −0.0366152 + 0.0634193i
\(178\) 664.571 + 1151.07i 0.279841 + 0.484699i
\(179\) −134.920 233.689i −0.0563376 0.0975795i 0.836481 0.547996i \(-0.184609\pi\)
−0.892819 + 0.450416i \(0.851276\pi\)
\(180\) −353.422 + 612.145i −0.146347 + 0.253481i
\(181\) −2229.61 −0.915613 −0.457806 0.889052i \(-0.651365\pi\)
−0.457806 + 0.889052i \(0.651365\pi\)
\(182\) 0 0
\(183\) 73.2105 0.0295731
\(184\) −1109.07 + 1920.97i −0.444359 + 0.769652i
\(185\) 502.333 + 870.066i 0.199634 + 0.345776i
\(186\) −20.3011 35.1626i −0.00800296 0.0138615i
\(187\) 3629.32 6286.16i 1.41926 2.45823i
\(188\) 787.026 0.305318
\(189\) 0 0
\(190\) −595.296 −0.227302
\(191\) 232.960 403.498i 0.0882533 0.152859i −0.818520 0.574479i \(-0.805205\pi\)
0.906773 + 0.421619i \(0.138538\pi\)
\(192\) −43.4257 75.2154i −0.0163228 0.0282719i
\(193\) 2207.23 + 3823.04i 0.823212 + 1.42585i 0.903278 + 0.429056i \(0.141154\pi\)
−0.0800657 + 0.996790i \(0.525513\pi\)
\(194\) 120.601 208.887i 0.0446321 0.0773051i
\(195\) −113.902 −0.0418291
\(196\) 0 0
\(197\) −289.812 −0.104814 −0.0524068 0.998626i \(-0.516689\pi\)
−0.0524068 + 0.998626i \(0.516689\pi\)
\(198\) 1549.04 2683.02i 0.555987 0.962998i
\(199\) 2408.87 + 4172.28i 0.858091 + 1.48626i 0.873748 + 0.486380i \(0.161683\pi\)
−0.0156567 + 0.999877i \(0.504984\pi\)
\(200\) 274.440 + 475.343i 0.0970291 + 0.168059i
\(201\) −13.4312 + 23.2635i −0.00471324 + 0.00816358i
\(202\) 1025.82 0.357310
\(203\) 0 0
\(204\) 182.595 0.0626678
\(205\) 1043.27 1806.99i 0.355439 0.615639i
\(206\) −1508.74 2613.21i −0.510285 0.883840i
\(207\) −1358.32 2352.67i −0.456085 0.789962i
\(208\) 195.051 337.838i 0.0650209 0.112619i
\(209\) −5001.78 −1.65541
\(210\) 0 0
\(211\) 2022.01 0.659719 0.329859 0.944030i \(-0.392999\pi\)
0.329859 + 0.944030i \(0.392999\pi\)
\(212\) 713.632 1236.05i 0.231191 0.400434i
\(213\) 15.1541 + 26.2477i 0.00487484 + 0.00844347i
\(214\) −902.306 1562.84i −0.288226 0.499222i
\(215\) −777.937 + 1347.43i −0.246767 + 0.427412i
\(216\) 393.855 0.124067
\(217\) 0 0
\(218\) 976.525 0.303388
\(219\) 146.850 254.352i 0.0453115 0.0784819i
\(220\) 914.438 + 1583.85i 0.280234 + 0.485379i
\(221\) −3569.84 6183.15i −1.08658 1.88201i
\(222\) 55.3855 95.9305i 0.0167443 0.0290019i
\(223\) −4343.86 −1.30442 −0.652211 0.758037i \(-0.726158\pi\)
−0.652211 + 0.758037i \(0.726158\pi\)
\(224\) 0 0
\(225\) −672.230 −0.199179
\(226\) 745.524 1291.29i 0.219432 0.380067i
\(227\) −1323.80 2292.88i −0.387064 0.670414i 0.604989 0.796234i \(-0.293177\pi\)
−0.992053 + 0.125819i \(0.959844\pi\)
\(228\) −62.9114 108.966i −0.0182737 0.0316510i
\(229\) −722.545 + 1251.49i −0.208503 + 0.361137i −0.951243 0.308442i \(-0.900192\pi\)
0.742740 + 0.669580i \(0.233526\pi\)
\(230\) −836.566 −0.239833
\(231\) 0 0
\(232\) 2517.39 0.712392
\(233\) 3122.96 5409.12i 0.878076 1.52087i 0.0246255 0.999697i \(-0.492161\pi\)
0.853450 0.521175i \(-0.174506\pi\)
\(234\) −1523.66 2639.05i −0.425660 0.737265i
\(235\) 374.243 + 648.207i 0.103885 + 0.179934i
\(236\) 1361.76 2358.63i 0.375605 0.650566i
\(237\) 199.692 0.0547315
\(238\) 0 0
\(239\) 1340.24 0.362731 0.181366 0.983416i \(-0.441948\pi\)
0.181366 + 0.983416i \(0.441948\pi\)
\(240\) −4.74409 + 8.21700i −0.00127596 + 0.00221002i
\(241\) 1684.96 + 2918.44i 0.450364 + 0.780054i 0.998409 0.0563953i \(-0.0179607\pi\)
−0.548044 + 0.836449i \(0.684627\pi\)
\(242\) −2905.85 5033.08i −0.771881 1.33694i
\(243\) −362.023 + 627.042i −0.0955710 + 0.165534i
\(244\) −1156.25 −0.303366
\(245\) 0 0
\(246\) −230.054 −0.0596249
\(247\) −2459.91 + 4260.69i −0.633685 + 1.09757i
\(248\) 808.504 + 1400.37i 0.207016 + 0.358563i
\(249\) 11.7979 + 20.4345i 0.00300265 + 0.00520074i
\(250\) −103.504 + 179.274i −0.0261846 + 0.0453531i
\(251\) 3592.64 0.903449 0.451724 0.892158i \(-0.350809\pi\)
0.451724 + 0.892158i \(0.350809\pi\)
\(252\) 0 0
\(253\) −7028.97 −1.74667
\(254\) 1453.82 2518.09i 0.359137 0.622043i
\(255\) 86.8268 + 150.388i 0.0213228 + 0.0369321i
\(256\) 1911.87 + 3311.46i 0.466765 + 0.808461i
\(257\) −1.42381 + 2.46612i −0.000345584 + 0.000598569i −0.866198 0.499701i \(-0.833443\pi\)
0.865853 + 0.500299i \(0.166777\pi\)
\(258\) 171.545 0.0413951
\(259\) 0 0
\(260\) 1798.91 0.429090
\(261\) −1541.56 + 2670.07i −0.365596 + 0.633230i
\(262\) 1497.99 + 2594.59i 0.353229 + 0.611811i
\(263\) 1408.54 + 2439.66i 0.330244 + 0.571999i 0.982560 0.185948i \(-0.0595357\pi\)
−0.652316 + 0.757947i \(0.726202\pi\)
\(264\) 254.239 440.356i 0.0592703 0.102659i
\(265\) 1357.37 0.314652
\(266\) 0 0
\(267\) −267.173 −0.0612386
\(268\) 212.125 367.412i 0.0483493 0.0837434i
\(269\) −723.716 1253.51i −0.164036 0.284119i 0.772276 0.635287i \(-0.219118\pi\)
−0.936313 + 0.351168i \(0.885785\pi\)
\(270\) 74.2704 + 128.640i 0.0167406 + 0.0289955i
\(271\) 4027.25 6975.40i 0.902724 1.56356i 0.0787797 0.996892i \(-0.474898\pi\)
0.823944 0.566671i \(-0.191769\pi\)
\(272\) −594.746 −0.132580
\(273\) 0 0
\(274\) −30.6593 −0.00675985
\(275\) −869.658 + 1506.29i −0.190699 + 0.330301i
\(276\) −88.4091 153.129i −0.0192812 0.0333960i
\(277\) 285.650 + 494.760i 0.0619604 + 0.107319i 0.895342 0.445380i \(-0.146931\pi\)
−0.833381 + 0.552699i \(0.813598\pi\)
\(278\) −518.023 + 897.242i −0.111759 + 0.193572i
\(279\) −1980.40 −0.424959
\(280\) 0 0
\(281\) −1784.48 −0.378837 −0.189418 0.981896i \(-0.560660\pi\)
−0.189418 + 0.981896i \(0.560660\pi\)
\(282\) 41.2627 71.4691i 0.00871333 0.0150919i
\(283\) 1660.52 + 2876.11i 0.348791 + 0.604124i 0.986035 0.166538i \(-0.0532590\pi\)
−0.637244 + 0.770662i \(0.719926\pi\)
\(284\) −239.336 414.542i −0.0500070 0.0866146i
\(285\) 59.8307 103.630i 0.0124353 0.0215386i
\(286\) −7884.57 −1.63015
\(287\) 0 0
\(288\) −4976.70 −1.01825
\(289\) −2986.05 + 5172.00i −0.607786 + 1.05272i
\(290\) 474.713 + 822.226i 0.0961244 + 0.166492i
\(291\) 24.2422 + 41.9887i 0.00488351 + 0.00845848i
\(292\) −2319.28 + 4017.11i −0.464814 + 0.805081i
\(293\) 5049.54 1.00682 0.503408 0.864049i \(-0.332079\pi\)
0.503408 + 0.864049i \(0.332079\pi\)
\(294\) 0 0
\(295\) 2590.14 0.511199
\(296\) −2205.76 + 3820.49i −0.433133 + 0.750208i
\(297\) 624.033 + 1080.86i 0.121919 + 0.211171i
\(298\) 851.740 + 1475.26i 0.165570 + 0.286776i
\(299\) −3456.90 + 5987.52i −0.668620 + 1.15808i
\(300\) −43.7536 −0.00842038
\(301\) 0 0
\(302\) 117.593 0.0224063
\(303\) −103.101 + 178.576i −0.0195479 + 0.0338579i
\(304\) 204.914 + 354.921i 0.0386599 + 0.0669609i
\(305\) −549.814 952.305i −0.103220 0.178783i
\(306\) −2322.95 + 4023.47i −0.433969 + 0.751656i
\(307\) 1535.73 0.285500 0.142750 0.989759i \(-0.454405\pi\)
0.142750 + 0.989759i \(0.454405\pi\)
\(308\) 0 0
\(309\) 606.548 0.111668
\(310\) −304.924 + 528.145i −0.0558663 + 0.0967632i
\(311\) −4641.52 8039.35i −0.846291 1.46582i −0.884495 0.466550i \(-0.845497\pi\)
0.0382037 0.999270i \(-0.487836\pi\)
\(312\) −250.073 433.140i −0.0453770 0.0785952i
\(313\) 3012.72 5218.18i 0.544054 0.942329i −0.454612 0.890690i \(-0.650222\pi\)
0.998666 0.0516393i \(-0.0164446\pi\)
\(314\) 3413.68 0.613519
\(315\) 0 0
\(316\) −3153.83 −0.561445
\(317\) 3488.79 6042.76i 0.618139 1.07065i −0.371686 0.928358i \(-0.621220\pi\)
0.989825 0.142289i \(-0.0454464\pi\)
\(318\) −74.8295 129.609i −0.0131957 0.0228556i
\(319\) 3988.62 + 6908.49i 0.700062 + 1.21254i
\(320\) −652.257 + 1129.74i −0.113945 + 0.197358i
\(321\) 362.748 0.0630736
\(322\) 0 0
\(323\) 7500.71 1.29211
\(324\) 1892.78 3278.39i 0.324551 0.562139i
\(325\) 855.407 + 1481.61i 0.145998 + 0.252876i
\(326\) 1626.09 + 2816.46i 0.276259 + 0.478495i
\(327\) −98.1464 + 169.995i −0.0165979 + 0.0287484i
\(328\) 9162.06 1.54235
\(329\) 0 0
\(330\) 191.771 0.0319898
\(331\) −492.439 + 852.930i −0.0817731 + 0.141635i −0.904012 0.427508i \(-0.859392\pi\)
0.822239 + 0.569143i \(0.192725\pi\)
\(332\) −186.330 322.732i −0.0308017 0.0533501i
\(333\) −2701.46 4679.07i −0.444563 0.770005i
\(334\) 2364.07 4094.68i 0.387293 0.670812i
\(335\) 403.475 0.0658035
\(336\) 0 0
\(337\) 51.9653 0.00839979 0.00419990 0.999991i \(-0.498663\pi\)
0.00419990 + 0.999991i \(0.498663\pi\)
\(338\) −2058.50 + 3565.42i −0.331265 + 0.573767i
\(339\) 149.859 + 259.563i 0.0240095 + 0.0415857i
\(340\) −1371.30 2375.16i −0.218733 0.378856i
\(341\) −2562.03 + 4437.56i −0.406867 + 0.704714i
\(342\) 3201.40 0.506176
\(343\) 0 0
\(344\) −6831.89 −1.07079
\(345\) 84.0797 145.630i 0.0131209 0.0227260i
\(346\) −1286.10 2227.60i −0.199830 0.346116i
\(347\) 5650.24 + 9786.50i 0.874123 + 1.51403i 0.857694 + 0.514161i \(0.171897\pi\)
0.0164299 + 0.999865i \(0.494770\pi\)
\(348\) −100.336 + 173.787i −0.0154557 + 0.0267701i
\(349\) 2016.91 0.309349 0.154674 0.987966i \(-0.450567\pi\)
0.154674 + 0.987966i \(0.450567\pi\)
\(350\) 0 0
\(351\) 1227.61 0.186682
\(352\) −6438.31 + 11151.5i −0.974896 + 1.68857i
\(353\) −3794.71 6572.62i −0.572158 0.991007i −0.996344 0.0854319i \(-0.972773\pi\)
0.424186 0.905575i \(-0.360560\pi\)
\(354\) −142.790 247.319i −0.0214384 0.0371324i
\(355\) 227.616 394.242i 0.0340298 0.0589414i
\(356\) 4219.59 0.628196
\(357\) 0 0
\(358\) 446.873 0.0659720
\(359\) −4367.12 + 7564.08i −0.642027 + 1.11202i 0.342952 + 0.939353i \(0.388573\pi\)
−0.984980 + 0.172671i \(0.944760\pi\)
\(360\) −1475.89 2556.32i −0.216073 0.374250i
\(361\) 845.204 + 1463.94i 0.123226 + 0.213433i
\(362\) 1846.19 3197.69i 0.268049 0.464274i
\(363\) 1168.22 0.168914
\(364\) 0 0
\(365\) −4411.41 −0.632613
\(366\) −60.6206 + 104.998i −0.00865762 + 0.0149954i
\(367\) −945.271 1637.26i −0.134449 0.232872i 0.790938 0.611896i \(-0.209593\pi\)
−0.925387 + 0.379024i \(0.876260\pi\)
\(368\) 287.964 + 498.769i 0.0407912 + 0.0706525i
\(369\) −5610.53 + 9717.72i −0.791524 + 1.37096i
\(370\) −1663.79 −0.233774
\(371\) 0 0
\(372\) −128.899 −0.0179653
\(373\) −1356.94 + 2350.29i −0.188364 + 0.326256i −0.944705 0.327922i \(-0.893652\pi\)
0.756341 + 0.654178i \(0.226985\pi\)
\(374\) 6010.37 + 10410.3i 0.830987 + 1.43931i
\(375\) −20.8055 36.0361i −0.00286504 0.00496240i
\(376\) −1643.31 + 2846.30i −0.225392 + 0.390390i
\(377\) 7846.52 1.07193
\(378\) 0 0
\(379\) 8941.19 1.21182 0.605908 0.795535i \(-0.292810\pi\)
0.605908 + 0.795535i \(0.292810\pi\)
\(380\) −944.935 + 1636.68i −0.127564 + 0.220947i
\(381\) 292.234 + 506.165i 0.0392956 + 0.0680620i
\(382\) 385.796 + 668.218i 0.0516729 + 0.0895001i
\(383\) −4646.94 + 8048.74i −0.619968 + 1.07382i 0.369524 + 0.929221i \(0.379521\pi\)
−0.989491 + 0.144594i \(0.953812\pi\)
\(384\) −349.060 −0.0463878
\(385\) 0 0
\(386\) −7310.62 −0.963992
\(387\) 4183.62 7246.24i 0.549522 0.951801i
\(388\) −382.868 663.147i −0.0500959 0.0867686i
\(389\) −5227.38 9054.08i −0.681333 1.18010i −0.974574 0.224065i \(-0.928067\pi\)
0.293242 0.956038i \(-0.405266\pi\)
\(390\) 94.3142 163.357i 0.0122456 0.0212100i
\(391\) 10540.7 1.36334
\(392\) 0 0
\(393\) −602.226 −0.0772985
\(394\) 239.974 415.646i 0.0306845 0.0531471i
\(395\) −1499.69 2597.54i −0.191032 0.330878i
\(396\) −4917.70 8517.70i −0.624050 1.08089i
\(397\) −1813.01 + 3140.23i −0.229200 + 0.396987i −0.957571 0.288196i \(-0.906944\pi\)
0.728371 + 0.685183i \(0.240278\pi\)
\(398\) −7978.47 −1.00484
\(399\) 0 0
\(400\) 142.513 0.0178141
\(401\) 4211.26 7294.12i 0.524440 0.908356i −0.475156 0.879902i \(-0.657608\pi\)
0.999595 0.0284542i \(-0.00905846\pi\)
\(402\) −22.2429 38.5258i −0.00275963 0.00477983i
\(403\) 2520.04 + 4364.85i 0.311495 + 0.539525i
\(404\) 1628.33 2820.35i 0.200526 0.347320i
\(405\) 3600.18 0.441715
\(406\) 0 0
\(407\) −13979.5 −1.70254
\(408\) −381.260 + 660.361i −0.0462627 + 0.0801293i
\(409\) −7290.34 12627.2i −0.881379 1.52659i −0.849808 0.527092i \(-0.823282\pi\)
−0.0315714 0.999502i \(-0.510051\pi\)
\(410\) 1727.72 + 2992.50i 0.208112 + 0.360461i
\(411\) 3.08144 5.33721i 0.000369820 0.000640548i
\(412\) −9579.51 −1.14551
\(413\) 0 0
\(414\) 4498.92 0.534081
\(415\) 177.205 306.928i 0.0209606 0.0363049i
\(416\) 6332.81 + 10968.8i 0.746374 + 1.29276i
\(417\) −104.129 180.356i −0.0122283 0.0211800i
\(418\) 4141.63 7173.51i 0.484626 0.839397i
\(419\) 2537.53 0.295863 0.147931 0.988998i \(-0.452739\pi\)
0.147931 + 0.988998i \(0.452739\pi\)
\(420\) 0 0
\(421\) 9649.52 1.11708 0.558538 0.829479i \(-0.311363\pi\)
0.558538 + 0.829479i \(0.311363\pi\)
\(422\) −1674.28 + 2899.94i −0.193135 + 0.334519i
\(423\) −2012.62 3485.95i −0.231340 0.400692i
\(424\) 2980.13 + 5161.74i 0.341340 + 0.591218i
\(425\) 1304.15 2258.85i 0.148848 0.257812i
\(426\) −50.1922 −0.00570850
\(427\) 0 0
\(428\) −5729.06 −0.647020
\(429\) 792.444 1372.55i 0.0891832 0.154470i
\(430\) −1288.31 2231.42i −0.144483 0.250253i
\(431\) 3631.28 + 6289.57i 0.405830 + 0.702918i 0.994418 0.105515i \(-0.0336492\pi\)
−0.588588 + 0.808433i \(0.700316\pi\)
\(432\) 51.1310 88.5615i 0.00569454 0.00986323i
\(433\) −11345.0 −1.25914 −0.629570 0.776944i \(-0.716769\pi\)
−0.629570 + 0.776944i \(0.716769\pi\)
\(434\) 0 0
\(435\) −190.845 −0.0210353
\(436\) 1550.07 2684.81i 0.170264 0.294906i
\(437\) −3631.70 6290.28i −0.397546 0.688570i
\(438\) 243.193 + 421.223i 0.0265302 + 0.0459516i
\(439\) 5852.94 10137.6i 0.636323 1.10214i −0.349911 0.936783i \(-0.613788\pi\)
0.986233 0.165360i \(-0.0528786\pi\)
\(440\) −7637.40 −0.827497
\(441\) 0 0
\(442\) 11823.8 1.27240
\(443\) −7538.99 + 13057.9i −0.808551 + 1.40045i 0.105316 + 0.994439i \(0.466415\pi\)
−0.913867 + 0.406013i \(0.866919\pi\)
\(444\) −175.831 304.548i −0.0187941 0.0325523i
\(445\) 2006.48 + 3475.32i 0.213744 + 0.370216i
\(446\) 3596.85 6229.92i 0.381874 0.661425i
\(447\) −342.419 −0.0362324
\(448\) 0 0
\(449\) 1075.45 0.113037 0.0565185 0.998402i \(-0.482000\pi\)
0.0565185 + 0.998402i \(0.482000\pi\)
\(450\) 556.627 964.106i 0.0583103 0.100996i
\(451\) 14516.6 + 25143.5i 1.51565 + 2.62519i
\(452\) −2366.80 4099.41i −0.246294 0.426593i
\(453\) −11.8187 + 20.4706i −0.00122581 + 0.00212317i
\(454\) 4384.58 0.453257
\(455\) 0 0
\(456\) 525.437 0.0539602
\(457\) 5368.47 9298.47i 0.549511 0.951781i −0.448797 0.893634i \(-0.648147\pi\)
0.998308 0.0581472i \(-0.0185193\pi\)
\(458\) −1196.58 2072.54i −0.122080 0.211448i
\(459\) −935.805 1620.86i −0.0951627 0.164827i
\(460\) −1327.91 + 2300.01i −0.134596 + 0.233127i
\(461\) −452.568 −0.0457228 −0.0228614 0.999739i \(-0.507278\pi\)
−0.0228614 + 0.999739i \(0.507278\pi\)
\(462\) 0 0
\(463\) 7118.15 0.714489 0.357244 0.934011i \(-0.383716\pi\)
0.357244 + 0.934011i \(0.383716\pi\)
\(464\) 326.813 566.057i 0.0326981 0.0566347i
\(465\) −61.2933 106.163i −0.00611271 0.0105875i
\(466\) 5171.81 + 8957.83i 0.514119 + 0.890480i
\(467\) 486.900 843.335i 0.0482463 0.0835651i −0.840894 0.541200i \(-0.817970\pi\)
0.889140 + 0.457635i \(0.151303\pi\)
\(468\) −9674.23 −0.955537
\(469\) 0 0
\(470\) −1239.54 −0.121650
\(471\) −343.094 + 594.257i −0.0335646 + 0.0581357i
\(472\) 5686.70 + 9849.65i 0.554558 + 0.960523i
\(473\) −10824.6 18748.8i −1.05225 1.82256i
\(474\) −165.351 + 286.396i −0.0160228 + 0.0277524i
\(475\) −1797.32 −0.173614
\(476\) 0 0
\(477\) −7299.72 −0.700695
\(478\) −1109.76 + 1922.16i −0.106191 + 0.183928i
\(479\) 4857.00 + 8412.57i 0.463303 + 0.802464i 0.999123 0.0418680i \(-0.0133309\pi\)
−0.535820 + 0.844332i \(0.679998\pi\)
\(480\) −154.029 266.785i −0.0146467 0.0253688i
\(481\) −6875.19 + 11908.2i −0.651729 + 1.12883i
\(482\) −5580.80 −0.527383
\(483\) 0 0
\(484\) −18450.3 −1.73274
\(485\) 364.119 630.673i 0.0340903 0.0590462i
\(486\) −599.532 1038.42i −0.0559575 0.0969212i
\(487\) −461.694 799.678i −0.0429597 0.0744084i 0.843746 0.536743i \(-0.180345\pi\)
−0.886706 + 0.462334i \(0.847012\pi\)
\(488\) 2414.25 4181.61i 0.223951 0.387894i
\(489\) −653.724 −0.0604549
\(490\) 0 0
\(491\) 1289.11 0.118486 0.0592430 0.998244i \(-0.481131\pi\)
0.0592430 + 0.998244i \(0.481131\pi\)
\(492\) −365.174 + 632.500i −0.0334620 + 0.0579579i
\(493\) −5981.37 10360.0i −0.546424 0.946435i
\(494\) −4073.76 7055.96i −0.371027 0.642637i
\(495\) 4676.88 8100.59i 0.424667 0.735544i
\(496\) 419.846 0.0380074
\(497\) 0 0
\(498\) −39.0760 −0.00351614
\(499\) 9669.15 16747.5i 0.867436 1.50244i 0.00282829 0.999996i \(-0.499100\pi\)
0.864608 0.502447i \(-0.167567\pi\)
\(500\) 328.591 + 569.137i 0.0293901 + 0.0509051i
\(501\) 475.205 + 823.078i 0.0423764 + 0.0733981i
\(502\) −2974.82 + 5152.54i −0.264488 + 0.458106i
\(503\) 1772.84 0.157151 0.0785757 0.996908i \(-0.474963\pi\)
0.0785757 + 0.996908i \(0.474963\pi\)
\(504\) 0 0
\(505\) 3097.18 0.272916
\(506\) 5820.21 10080.9i 0.511344 0.885673i
\(507\) −413.782 716.691i −0.0362459 0.0627798i
\(508\) −4615.40 7994.11i −0.403101 0.698192i
\(509\) 1575.88 2729.50i 0.137229 0.237687i −0.789218 0.614113i \(-0.789514\pi\)
0.926447 + 0.376426i \(0.122847\pi\)
\(510\) −287.581 −0.0249692
\(511\) 0 0
\(512\) 2056.31 0.177494
\(513\) −644.845 + 1116.90i −0.0554983 + 0.0961258i
\(514\) −2.35792 4.08404i −0.000202341 0.000350466i
\(515\) −4555.20 7889.83i −0.389759 0.675083i
\(516\) 272.300 471.637i 0.0232313 0.0402377i
\(517\) −10414.8 −0.885964
\(518\) 0 0
\(519\) 517.043 0.0437296
\(520\) −3756.12 + 6505.79i −0.316763 + 0.548650i
\(521\) −5514.69 9551.72i −0.463729 0.803202i 0.535414 0.844590i \(-0.320156\pi\)
−0.999143 + 0.0413875i \(0.986822\pi\)
\(522\) −2552.93 4421.80i −0.214059 0.370760i
\(523\) 7224.21 12512.7i 0.604002 1.04616i −0.388207 0.921572i \(-0.626905\pi\)
0.992208 0.124589i \(-0.0397613\pi\)
\(524\) 9511.26 0.792941
\(525\) 0 0
\(526\) −4665.25 −0.386720
\(527\) 3842.04 6654.61i 0.317575 0.550056i
\(528\) −66.0117 114.336i −0.00544089 0.00942390i
\(529\) 979.894 + 1697.23i 0.0805371 + 0.139494i
\(530\) −1123.95 + 1946.73i −0.0921153 + 0.159548i
\(531\) −13929.4 −1.13838
\(532\) 0 0
\(533\) 28557.4 2.32075
\(534\) 221.227 383.177i 0.0179278 0.0310519i
\(535\) −2724.25 4718.54i −0.220149 0.381309i
\(536\) 885.836 + 1534.31i 0.0713849 + 0.123642i
\(537\) −44.9133 + 77.7922i −0.00360922 + 0.00625136i
\(538\) 2397.04 0.192089
\(539\) 0 0
\(540\) 471.569 0.0375798
\(541\) 11137.4 19290.5i 0.885091 1.53302i 0.0394817 0.999220i \(-0.487429\pi\)
0.845609 0.533802i \(-0.179237\pi\)
\(542\) 6669.38 + 11551.7i 0.528551 + 0.915476i
\(543\) 371.105 + 642.773i 0.0293290 + 0.0507994i
\(544\) 9654.95 16722.9i 0.760942 1.31799i
\(545\) 2948.33 0.231730
\(546\) 0 0
\(547\) 18642.6 1.45722 0.728609 0.684930i \(-0.240167\pi\)
0.728609 + 0.684930i \(0.240167\pi\)
\(548\) −48.6667 + 84.2932i −0.00379368 + 0.00657085i
\(549\) 2956.81 + 5121.34i 0.229861 + 0.398130i
\(550\) −1440.21 2494.51i −0.111656 0.193393i
\(551\) −4121.64 + 7138.89i −0.318671 + 0.551955i
\(552\) 738.394 0.0569350
\(553\) 0 0
\(554\) −946.108 −0.0725565
\(555\) 167.220 289.634i 0.0127894 0.0221519i
\(556\) 1644.55 + 2848.45i 0.125440 + 0.217268i
\(557\) 10715.9 + 18560.5i 0.815165 + 1.41191i 0.909209 + 0.416339i \(0.136687\pi\)
−0.0940446 + 0.995568i \(0.529980\pi\)
\(558\) 1639.83 2840.28i 0.124408 0.215481i
\(559\) −21294.5 −1.61120
\(560\) 0 0
\(561\) −2416.31 −0.181848
\(562\) 1477.60 2559.29i 0.110906 0.192094i
\(563\) −3077.43 5330.26i −0.230370 0.399012i 0.727547 0.686057i \(-0.240660\pi\)
−0.957917 + 0.287046i \(0.907327\pi\)
\(564\) −130.996 226.891i −0.00977998 0.0169394i
\(565\) 2250.89 3898.66i 0.167603 0.290297i
\(566\) −5499.86 −0.408439
\(567\) 0 0
\(568\) 1998.94 0.147665
\(569\) 4194.99 7265.94i 0.309074 0.535333i −0.669086 0.743185i \(-0.733314\pi\)
0.978160 + 0.207853i \(0.0666475\pi\)
\(570\) 99.0833 + 171.617i 0.00728095 + 0.0126110i
\(571\) 300.251 + 520.050i 0.0220055 + 0.0381146i 0.876818 0.480822i \(-0.159662\pi\)
−0.854813 + 0.518936i \(0.826328\pi\)
\(572\) −12515.5 + 21677.4i −0.914856 + 1.58458i
\(573\) −155.099 −0.0113078
\(574\) 0 0
\(575\) −2525.77 −0.183186
\(576\) 3507.73 6075.57i 0.253742 0.439494i
\(577\) 2031.17 + 3518.10i 0.146549 + 0.253831i 0.929950 0.367686i \(-0.119850\pi\)
−0.783401 + 0.621517i \(0.786517\pi\)
\(578\) −4945.09 8565.15i −0.355863 0.616372i
\(579\) 734.760 1272.64i 0.0527385 0.0913457i
\(580\) 3014.12 0.215783
\(581\) 0 0
\(582\) −80.2931 −0.00571865
\(583\) −9443.59 + 16356.8i −0.670864 + 1.16197i
\(584\) −9685.32 16775.5i −0.686270 1.18865i
\(585\) −4600.24 7967.85i −0.325122 0.563128i
\(586\) −4181.18 + 7242.01i −0.294749 + 0.510520i
\(587\) 8387.50 0.589760 0.294880 0.955534i \(-0.404720\pi\)
0.294880 + 0.955534i \(0.404720\pi\)
\(588\) 0 0
\(589\) −5294.95 −0.370415
\(590\) −2144.72 + 3714.76i −0.149655 + 0.259210i
\(591\) 48.2375 + 83.5497i 0.00335740 + 0.00581519i
\(592\) 572.713 + 991.967i 0.0397607 + 0.0688676i
\(593\) −7671.31 + 13287.1i −0.531236 + 0.920128i 0.468099 + 0.883676i \(0.344939\pi\)
−0.999335 + 0.0364520i \(0.988394\pi\)
\(594\) −2066.88 −0.142769
\(595\) 0 0
\(596\) 5408.00 0.371678
\(597\) 801.882 1388.90i 0.0549730 0.0952159i
\(598\) −5724.83 9915.70i −0.391481 0.678066i
\(599\) 9854.23 + 17068.0i 0.672175 + 1.16424i 0.977286 + 0.211925i \(0.0679731\pi\)
−0.305111 + 0.952317i \(0.598694\pi\)
\(600\) 91.3576 158.236i 0.00621610 0.0107666i
\(601\) 19002.5 1.28973 0.644866 0.764295i \(-0.276913\pi\)
0.644866 + 0.764295i \(0.276913\pi\)
\(602\) 0 0
\(603\) −2169.82 −0.146537
\(604\) 186.659 323.303i 0.0125746 0.0217798i
\(605\) −8773.38 15195.9i −0.589568 1.02116i
\(606\) −170.742 295.734i −0.0114454 0.0198240i
\(607\) 14726.6 25507.1i 0.984732 1.70561i 0.341612 0.939841i \(-0.389027\pi\)
0.643121 0.765765i \(-0.277639\pi\)
\(608\) −13306.1 −0.887553
\(609\) 0 0
\(610\) 1821.05 0.120873
\(611\) −5122.08 + 8871.70i −0.339144 + 0.587415i
\(612\) 7374.62 + 12773.2i 0.487094 + 0.843671i
\(613\) −4993.63 8649.23i −0.329023 0.569884i 0.653295 0.757103i \(-0.273386\pi\)
−0.982318 + 0.187219i \(0.940053\pi\)
\(614\) −1271.63 + 2202.53i −0.0835811 + 0.144767i
\(615\) −694.583 −0.0455419
\(616\) 0 0
\(617\) −21076.1 −1.37519 −0.687593 0.726096i \(-0.741333\pi\)
−0.687593 + 0.726096i \(0.741333\pi\)
\(618\) −502.240 + 869.906i −0.0326910 + 0.0566226i
\(619\) −157.334 272.511i −0.0102161 0.0176949i 0.860872 0.508821i \(-0.169919\pi\)
−0.871088 + 0.491126i \(0.836585\pi\)
\(620\) 968.036 + 1676.69i 0.0627052 + 0.108609i
\(621\) −906.197 + 1569.58i −0.0585579 + 0.101425i
\(622\) 15373.3 0.991018
\(623\) 0 0
\(624\) −129.860 −0.00833103
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) 4989.25 + 8641.63i 0.318547 + 0.551740i
\(627\) 832.515 + 1441.96i 0.0530262 + 0.0918442i
\(628\) 5418.66 9385.39i 0.344312 0.596366i
\(629\) 20963.7 1.32890
\(630\) 0 0
\(631\) 3314.96 0.209138 0.104569 0.994518i \(-0.466654\pi\)
0.104569 + 0.994518i \(0.466654\pi\)
\(632\) 6585.21 11405.9i 0.414471 0.717884i
\(633\) −336.550 582.922i −0.0211322 0.0366020i
\(634\) 5777.65 + 10007.2i 0.361924 + 0.626871i
\(635\) 4389.39 7602.64i 0.274311 0.475121i
\(636\) −475.119 −0.0296221
\(637\) 0 0
\(638\) −13210.8 −0.819782
\(639\) −1224.08 + 2120.17i −0.0757807 + 0.131256i
\(640\) 2621.46 + 4540.50i 0.161910 + 0.280436i
\(641\) −1502.56 2602.51i −0.0925858 0.160363i 0.816013 0.578034i \(-0.196180\pi\)
−0.908598 + 0.417671i \(0.862847\pi\)
\(642\) −300.367 + 520.250i −0.0184650 + 0.0319823i
\(643\) −21225.7 −1.30180 −0.650902 0.759162i \(-0.725609\pi\)
−0.650902 + 0.759162i \(0.725609\pi\)
\(644\) 0 0
\(645\) 517.931 0.0316178
\(646\) −6210.82 + 10757.5i −0.378269 + 0.655180i
\(647\) −1370.18 2373.21i −0.0832568 0.144205i 0.821390 0.570367i \(-0.193199\pi\)
−0.904647 + 0.426162i \(0.859866\pi\)
\(648\) 7904.26 + 13690.6i 0.479180 + 0.829964i
\(649\) −18020.3 + 31212.1i −1.08992 + 1.88780i
\(650\) −2833.21 −0.170966
\(651\) 0 0
\(652\) 10324.6 0.620157
\(653\) −11395.3 + 19737.3i −0.682900 + 1.18282i 0.291191 + 0.956665i \(0.405948\pi\)
−0.974092 + 0.226153i \(0.927385\pi\)
\(654\) −162.536 281.521i −0.00971817 0.0168324i
\(655\) 4522.74 + 7833.62i 0.269799 + 0.467305i
\(656\) 1189.44 2060.16i 0.0707922 0.122616i
\(657\) 23723.8 1.40876
\(658\) 0 0
\(659\) 19405.1 1.14706 0.573532 0.819183i \(-0.305573\pi\)
0.573532 + 0.819183i \(0.305573\pi\)
\(660\) 304.405 527.245i 0.0179530 0.0310954i
\(661\) 7818.63 + 13542.3i 0.460075 + 0.796873i 0.998964 0.0455035i \(-0.0144892\pi\)
−0.538889 + 0.842377i \(0.681156\pi\)
\(662\) −815.510 1412.50i −0.0478787 0.0829283i
\(663\) −1188.36 + 2058.29i −0.0696108 + 0.120569i
\(664\) 1556.23 0.0909538
\(665\) 0 0
\(666\) 8947.59 0.520589
\(667\) −5792.12 + 10032.3i −0.336240 + 0.582384i
\(668\) −7505.14 12999.3i −0.434704 0.752930i
\(669\) 723.008 + 1252.29i 0.0417834 + 0.0723710i
\(670\) −334.090 + 578.660i −0.0192642 + 0.0333666i
\(671\) 15300.8 0.880299
\(672\) 0 0
\(673\) −2579.54 −0.147747 −0.0738735 0.997268i \(-0.523536\pi\)
−0.0738735 + 0.997268i \(0.523536\pi\)
\(674\) −43.0289 + 74.5282i −0.00245907 + 0.00425923i
\(675\) 224.238 + 388.392i 0.0127866 + 0.0221470i
\(676\) 6535.06 + 11319.1i 0.371817 + 0.644006i
\(677\) 4079.78 7066.39i 0.231608 0.401157i −0.726673 0.686983i \(-0.758935\pi\)
0.958282 + 0.285826i \(0.0922680\pi\)
\(678\) −496.351 −0.0281154
\(679\) 0 0
\(680\) 11453.1 0.645892
\(681\) −440.676 + 763.272i −0.0247969 + 0.0429496i
\(682\) −4242.88 7348.88i −0.238223 0.412615i
\(683\) 10264.6 + 17778.9i 0.575059 + 0.996032i 0.996035 + 0.0889598i \(0.0283543\pi\)
−0.420976 + 0.907072i \(0.638312\pi\)
\(684\) 5081.71 8801.77i 0.284070 0.492024i
\(685\) −92.5670 −0.00516321
\(686\) 0 0
\(687\) 481.053 0.0267151
\(688\) −886.930 + 1536.21i −0.0491481 + 0.0851270i
\(689\) 9288.84 + 16088.7i 0.513609 + 0.889597i
\(690\) 139.241 + 241.173i 0.00768235 + 0.0133062i
\(691\) −458.647 + 794.401i −0.0252500 + 0.0437343i −0.878374 0.477973i \(-0.841372\pi\)
0.853124 + 0.521708i \(0.174705\pi\)
\(692\) −8165.92 −0.448586
\(693\) 0 0
\(694\) −18714.3 −1.02361
\(695\) −1564.02 + 2708.96i −0.0853621 + 0.147851i
\(696\) −419.005 725.737i −0.0228194 0.0395244i
\(697\) −21769.2 37705.4i −1.18302 2.04906i
\(698\) −1670.06 + 2892.63i −0.0905628 + 0.156859i
\(699\) −2079.19 −0.112507
\(700\) 0 0
\(701\) −10491.3 −0.565266 −0.282633 0.959228i \(-0.591208\pi\)
−0.282633 + 0.959228i \(0.591208\pi\)
\(702\) −1016.50 + 1760.63i −0.0546516 + 0.0946594i
\(703\) −7222.84 12510.3i −0.387503 0.671175i
\(704\) −9075.85 15719.8i −0.485879 0.841567i
\(705\) 124.581 215.780i 0.00665530 0.0115273i
\(706\) 12568.5 0.670005
\(707\) 0 0
\(708\) −906.623 −0.0481257
\(709\) −11918.8 + 20643.9i −0.631339 + 1.09351i 0.355939 + 0.934509i \(0.384161\pi\)
−0.987278 + 0.159002i \(0.949172\pi\)
\(710\) 376.946 + 652.889i 0.0199247 + 0.0345106i
\(711\) 8065.11 + 13969.2i 0.425408 + 0.736828i
\(712\) −8810.52 + 15260.3i −0.463748 + 0.803234i
\(713\) −7440.96 −0.390836
\(714\) 0 0
\(715\) −23805.2 −1.24512
\(716\) 709.338 1228.61i 0.0370240 0.0641275i
\(717\) −223.074 386.376i −0.0116190 0.0201248i
\(718\) −7232.22 12526.6i −0.375911 0.651097i
\(719\) −1963.10 + 3400.18i −0.101824 + 0.176364i −0.912436 0.409219i \(-0.865801\pi\)
0.810612 + 0.585583i \(0.199134\pi\)
\(720\) −766.413 −0.0396702
\(721\) 0 0
\(722\) −2799.42 −0.144299
\(723\) 560.902 971.512i 0.0288523 0.0499736i
\(724\) −5861.05 10151.6i −0.300862 0.521109i
\(725\) 1433.26 + 2482.47i 0.0734205 + 0.127168i
\(726\) −967.322 + 1675.45i −0.0494500 + 0.0856499i
\(727\) 21071.2 1.07495 0.537474 0.843281i \(-0.319379\pi\)
0.537474 + 0.843281i \(0.319379\pi\)
\(728\) 0 0
\(729\) −19200.0 −0.975459
\(730\) 3652.78 6326.81i 0.185199 0.320775i
\(731\) 16232.7 + 28115.8i 0.821324 + 1.42257i
\(732\) 192.451 + 333.334i 0.00971745 + 0.0168311i
\(733\) −11420.3 + 19780.6i −0.575470 + 0.996744i 0.420520 + 0.907283i \(0.361848\pi\)
−0.995990 + 0.0894605i \(0.971486\pi\)
\(734\) 3130.86 0.157441
\(735\) 0 0
\(736\) −18699.0 −0.936485
\(737\) −2807.08 + 4862.01i −0.140299 + 0.243004i
\(738\) −9291.39 16093.2i −0.463443 0.802706i
\(739\) −5418.67 9385.42i −0.269728 0.467183i 0.699063 0.715060i \(-0.253600\pi\)
−0.968792 + 0.247877i \(0.920267\pi\)
\(740\) −2640.99 + 4574.34i −0.131196 + 0.227238i
\(741\) 1637.75 0.0811931
\(742\) 0 0
\(743\) −21631.9 −1.06810 −0.534050 0.845453i \(-0.679331\pi\)
−0.534050 + 0.845453i \(0.679331\pi\)
\(744\) 269.141 466.166i 0.0132624 0.0229711i
\(745\) 2571.58 + 4454.11i 0.126464 + 0.219042i
\(746\) −2247.18 3892.23i −0.110288 0.191025i
\(747\) −952.980 + 1650.61i −0.0466770 + 0.0808469i
\(748\) 38161.9 1.86543
\(749\) 0 0
\(750\) 68.9103 0.00335500
\(751\) 8089.58 14011.6i 0.393067 0.680812i −0.599786 0.800161i \(-0.704747\pi\)
0.992852 + 0.119349i \(0.0380808\pi\)
\(752\) 426.676 + 739.025i 0.0206905 + 0.0358370i
\(753\) −597.973 1035.72i −0.0289394 0.0501245i
\(754\) −6497.16 + 11253.4i −0.313810 + 0.543535i
\(755\) 355.037 0.0171140
\(756\) 0 0
\(757\) −40930.9 −1.96520 −0.982601 0.185727i \(-0.940536\pi\)
−0.982601 + 0.185727i \(0.940536\pi\)
\(758\) −7403.59 + 12823.4i −0.354763 + 0.614467i
\(759\) 1169.93 + 2026.38i 0.0559496 + 0.0969075i
\(760\) −3946.05 6834.77i −0.188340 0.326215i
\(761\) 1591.99 2757.40i 0.0758337 0.131348i −0.825615 0.564234i \(-0.809172\pi\)
0.901449 + 0.432886i \(0.142505\pi\)
\(762\) −967.917 −0.0460157
\(763\) 0 0
\(764\) 2449.55 0.115997
\(765\) −7013.49 + 12147.7i −0.331468 + 0.574120i
\(766\) −7695.62 13329.2i −0.362995 0.628726i
\(767\) 17725.0 + 30700.6i 0.834436 + 1.44529i
\(768\) 636.438 1102.34i 0.0299030 0.0517935i
\(769\) −33595.8 −1.57542 −0.787708 0.616048i \(-0.788733\pi\)
−0.787708 + 0.616048i \(0.788733\pi\)
\(770\) 0 0
\(771\) 0.947940 4.42791e−5
\(772\) −11604.4 + 20099.5i −0.541000 + 0.937040i
\(773\) 17193.0 + 29779.1i 0.799986 + 1.38562i 0.919624 + 0.392799i \(0.128493\pi\)
−0.119638 + 0.992818i \(0.538174\pi\)
\(774\) 6928.33 + 12000.2i 0.321749 + 0.557285i
\(775\) −920.631 + 1594.58i −0.0426710 + 0.0739084i
\(776\) 3197.72 0.147927