Properties

Label 245.4.e.p.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.p.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 0.881597 0.472003i \(-0.156469\pi\)
−0.849565 + 0.527484i \(0.823135\pi\)
\(4\) 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 \(-0.239524\pi\)
0.729991 + 0.683456i \(0.239524\pi\)
\(14\) 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 \(-0.899479\pi\)
0.206309 0.978487i \(-0.433855\pi\)
\(18\) 22.2651 + 38.5643i 0.291552 + 0.504982i
\(19\) −35.9465 + 62.2611i −0.434036 + 0.751772i −0.997216 0.0745616i \(-0.976244\pi\)
0.563180 + 0.826334i \(0.309578\pi\)
\(20\) 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 0.952762 0.303716i \(-0.0982275\pi\)
−0.739407 + 0.673258i \(0.764894\pi\)
\(32\) −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 \(-0.207583\pi\)
0.794786 + 0.606889i \(0.207583\pi\)
\(42\) 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 −0.958483 0.285151i \(-0.907956\pi\)
0.726189 + 0.687495i \(0.241290\pi\)
\(48\) −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 \(0.0269864\pi\)
−0.424870 + 0.905254i \(0.639680\pi\)
\(60\) 4.37536 + 7.57834i 0.00941427 + 0.0163060i
\(61\) 109.963 190.461i 0.230808 0.399771i −0.727238 0.686385i \(-0.759196\pi\)
0.958046 + 0.286614i \(0.0925297\pi\)
\(62\) −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 \(-0.916588\pi\)
0.258579 0.965990i \(-0.416746\pi\)
\(74\) 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 \(-0.485076\pi\)
0.0468694 + 0.998901i \(0.485076\pi\)
\(84\) 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 −0.999680 0.0252802i \(-0.991952\pi\)
0.521733 + 0.853109i \(0.325286\pi\)
\(90\) 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 \(-0.475712\pi\)
0.0762283 + 0.997090i \(0.475712\pi\)
\(98\) 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 0.977290 0.211906i \(-0.0679670\pi\)
−0.672161 + 0.740405i \(0.734634\pi\)
\(102\) 28.7581 + 49.8105i 0.0279165 + 0.0483527i
\(103\) 911.040 1577.97i 0.871528 1.50953i 0.0111125 0.999938i \(-0.496463\pi\)
0.860416 0.509593i \(-0.170204\pi\)
\(104\) −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 \(0.372810\pi\)
−0.992319 + 0.123702i \(0.960523\pi\)
\(132\) 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 \(-0.561133\pi\)
−0.190875 + 0.981614i \(0.561133\pi\)
\(140\) 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 \(0.00886484\pi\)
−0.475691 + 0.879613i \(0.657802\pi\)
\(158\) −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 \(-0.269934\pi\)
0.661467 + 0.749974i \(0.269934\pi\)
\(168\) 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 −0.643378 0.765548i \(-0.722468\pi\)
0.984673 + 0.174408i \(0.0558011\pi\)
\(174\) 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 \(-0.348635\pi\)
0.457806 + 0.889052i \(0.348635\pi\)
\(182\) 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 \(-0.838317\pi\)
0.0156567 0.999877i \(-0.495016\pi\)
\(200\) 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 \(-0.273842\pi\)
0.652211 + 0.758037i \(0.273842\pi\)
\(224\) 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 0.992053 0.125819i \(-0.0401560\pi\)
−0.604989 + 0.796234i \(0.706823\pi\)
\(228\) −62.9114 108.966i −0.0182737 0.0316510i
\(229\) 722.545 1251.49i 0.208503 0.361137i −0.742740 0.669580i \(-0.766474\pi\)
0.951243 + 0.308442i \(0.0998076\pi\)
\(230\) 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 0.548044 0.836449i \(-0.315373\pi\)
−0.998409 + 0.0563953i \(0.982039\pi\)
\(242\) −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 \(-0.649191\pi\)
−0.451724 + 0.892158i \(0.649191\pi\)
\(252\) 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 −0.865853 0.500299i \(-0.833223\pi\)
0.866198 + 0.499701i \(0.166557\pi\)
\(258\) −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 0.936313 0.351168i \(-0.114215\pi\)
−0.772276 + 0.635287i \(0.780882\pi\)
\(270\) 74.2704 + 128.640i 0.0167406 + 0.0289955i
\(271\) −4027.25 + 6975.40i −0.902724 + 1.56356i −0.0787797 + 0.996892i \(0.525102\pi\)
−0.823944 + 0.566671i \(0.808231\pi\)
\(272\) 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 0.637244 0.770662i \(-0.280074\pi\)
−0.986035 + 0.166538i \(0.946741\pi\)
\(284\) −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 \(-0.667921\pi\)
−0.503408 + 0.864049i \(0.667921\pi\)
\(294\) 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 \(-0.545595\pi\)
−0.142750 + 0.989759i \(0.545595\pi\)
\(308\) 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 \(0.154503\pi\)
−0.0382037 + 0.999270i \(0.512164\pi\)
\(312\) −250.073 433.140i −0.0453770 0.0785952i
\(313\) −3012.72 + 5218.18i −0.544054 + 0.942329i 0.454612 + 0.890690i \(0.349778\pi\)
−0.998666 + 0.0516393i \(0.983555\pi\)
\(314\) −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 \(-0.549433\pi\)
−0.154674 + 0.987966i \(0.549433\pi\)
\(350\) 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 \(0.0272270\pi\)
−0.424186 + 0.905575i \(0.639440\pi\)
\(354\) −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 0.925387 0.379024i \(-0.123740\pi\)
−0.790938 + 0.611896i \(0.790407\pi\)
\(368\) 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 \(-0.620479\pi\)
0.989491 0.144594i \(-0.0461876\pi\)
\(384\) 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 −0.728371 0.685183i \(-0.759722\pi\)
0.957571 + 0.288196i \(0.0930556\pi\)
\(398\) 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 \(0.176718\pi\)
0.0315714 + 0.999502i \(0.489949\pi\)
\(410\) 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 \(-0.547261\pi\)
−0.147931 + 0.988998i \(0.547261\pi\)
\(420\) 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 \(-0.283231\pi\)
0.629570 + 0.776944i \(0.283231\pi\)
\(434\) 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 \(0.386212\pi\)
−0.986233 + 0.165360i \(0.947121\pi\)
\(440\) 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 \(-0.492722\pi\)
0.0228614 + 0.999739i \(0.492722\pi\)
\(462\) 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 −0.889140 0.457635i \(-0.848697\pi\)
0.840894 + 0.541200i \(0.182030\pi\)
\(468\) 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 0.535820 0.844332i \(-0.320002\pi\)
−0.999123 + 0.0418680i \(0.986669\pi\)
\(480\) −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 \(-0.525037\pi\)
−0.0785757 + 0.996908i \(0.525037\pi\)
\(504\) 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 −0.926447 0.376426i \(-0.877153\pi\)
0.789218 + 0.614113i \(0.210486\pi\)
\(510\) 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 0.999143 0.0413875i \(-0.0131778\pi\)
−0.535414 + 0.844590i \(0.679844\pi\)
\(522\) −2552.93 4421.80i −0.214059 0.370760i
\(523\) −7224.21 + 12512.7i −0.604002 + 1.04616i 0.388207 + 0.921572i \(0.373095\pi\)
−0.992208 + 0.124589i \(0.960239\pi\)
\(524\) −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 0.957917 0.287046i \(-0.0926732\pi\)
−0.727547 + 0.686057i \(0.759340\pi\)
\(564\) −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 0.783401 0.621517i \(-0.213483\pi\)
−0.929950 + 0.367686i \(0.880150\pi\)
\(578\) −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 \(-0.595280\pi\)
−0.294880 + 0.955534i \(0.595280\pi\)
\(588\) 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 \(-0.655061\pi\)
0.999335 0.0364520i \(-0.0116056\pi\)
\(594\) 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 \(-0.723087\pi\)
−0.644866 + 0.764295i \(0.723087\pi\)
\(602\) 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 \(0.610973\pi\)
−0.643121 + 0.765765i \(0.722361\pi\)
\(608\) 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 0.871088 0.491126i \(-0.163415\pi\)
−0.860872 + 0.508821i \(0.830081\pi\)
\(620\) 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 \(-0.274391\pi\)
0.650902 + 0.759162i \(0.274391\pi\)
\(644\) 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 0.904647 0.426162i \(-0.140134\pi\)
−0.821390 + 0.570367i \(0.806801\pi\)
\(648\) 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 0.538889 0.842377i \(-0.318844\pi\)
−0.998964 + 0.0455035i \(0.985511\pi\)
\(662\) −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 −0.958282 0.285826i \(-0.907732\pi\)
0.726673 + 0.686983i \(0.241065\pi\)
\(678\) 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 −0.853124 0.521708i \(-0.825295\pi\)
0.878374 + 0.477973i \(0.158628\pi\)
\(692\) 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 −0.810612 0.585583i \(-0.800866\pi\)
0.912436 + 0.409219i \(0.134199\pi\)
\(720\) 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 \(-0.680621\pi\)
−0.537474 + 0.843281i \(0.680621\pi\)
\(728\) 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 \(-0.638152\pi\)
0.995990 0.0894605i \(-0.0285143\pi\)
\(734\) −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 −0.901449 0.432886i \(-0.857495\pi\)
0.825615 + 0.564234i \(0.190828\pi\)
\(762\) 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 \(-0.211267\pi\)
0.787708 + 0.616048i \(0.211267\pi\)
\(770\) 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 \(-0.871507\pi\)
0.119638 0.992818i \(-0.461826\pi\)
\(774\) 6928.33 + 12000.2i 0.321749 + 0.557285i
\(775\) 920.631 1594.58i 0.0426710 0.0739084i
\(776\) −3197.72 −0.147927