Properties

Label 147.4.c.a.146.9
Level $147$
Weight $4$
Character 147.146
Analytic conductor $8.673$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 147.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.67328077084\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - x^{11} - 29 x^{9} + 6 x^{8} - 49 x^{7} + 1564 x^{6} - 441 x^{5} + 486 x^{4} - 21141 x^{3} - 59049 x + 531441\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{3} \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 146.9
Root \(-2.59957 - 1.49740i\) of defining polynomial
Character \(\chi\) \(=\) 147.146
Dual form 147.4.c.a.146.3

$q$-expansion

\(f(q)\) \(=\) \(q+2.58741i q^{2} +(-2.60257 + 4.49740i) q^{3} +1.30532 q^{4} -16.1181 q^{5} +(-11.6366 - 6.73392i) q^{6} +24.0767i q^{8} +(-13.4532 - 23.4096i) q^{9} +O(q^{10})\) \(q+2.58741i q^{2} +(-2.60257 + 4.49740i) q^{3} +1.30532 q^{4} -16.1181 q^{5} +(-11.6366 - 6.73392i) q^{6} +24.0767i q^{8} +(-13.4532 - 23.4096i) q^{9} -41.7042i q^{10} -35.5990i q^{11} +(-3.39719 + 5.87054i) q^{12} +7.40831i q^{13} +(41.9486 - 72.4897i) q^{15} -51.8536 q^{16} -28.9202 q^{17} +(60.5703 - 34.8090i) q^{18} -35.1698i q^{19} -21.0393 q^{20} +92.1090 q^{22} +55.4275i q^{23} +(-108.282 - 62.6613i) q^{24} +134.794 q^{25} -19.1683 q^{26} +(140.295 + 0.420792i) q^{27} -68.1510i q^{29} +(187.560 + 108.538i) q^{30} -178.671i q^{31} +58.4469i q^{32} +(160.103 + 92.6489i) q^{33} -74.8285i q^{34} +(-17.5608 - 30.5571i) q^{36} -233.676 q^{37} +90.9987 q^{38} +(-33.3181 - 19.2807i) q^{39} -388.071i q^{40} -370.068 q^{41} -187.068 q^{43} -46.4680i q^{44} +(216.841 + 377.320i) q^{45} -143.414 q^{46} -174.745 q^{47} +(134.953 - 233.206i) q^{48} +348.768i q^{50} +(75.2671 - 130.066i) q^{51} +9.67022i q^{52} +272.180i q^{53} +(-1.08876 + 363.002i) q^{54} +573.789i q^{55} +(158.173 + 91.5321i) q^{57} +176.334 q^{58} -96.8709 q^{59} +(54.7564 - 94.6222i) q^{60} +385.534i q^{61} +462.295 q^{62} -566.055 q^{64} -119.408i q^{65} +(-239.721 + 414.251i) q^{66} -1018.02 q^{67} -37.7502 q^{68} +(-249.280 - 144.254i) q^{69} -125.333i q^{71} +(563.626 - 323.909i) q^{72} +225.566i q^{73} -604.616i q^{74} +(-350.812 + 606.223i) q^{75} -45.9079i q^{76} +(49.8870 - 86.2076i) q^{78} -1064.31 q^{79} +835.783 q^{80} +(-367.022 + 629.870i) q^{81} -957.517i q^{82} +601.040 q^{83} +466.140 q^{85} -484.021i q^{86} +(306.502 + 177.368i) q^{87} +857.104 q^{88} +1505.21 q^{89} +(-976.280 + 561.055i) q^{90} +72.3506i q^{92} +(803.556 + 465.005i) q^{93} -452.137i q^{94} +566.872i q^{95} +(-262.859 - 152.112i) q^{96} -327.463i q^{97} +(-833.358 + 478.920i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 28 q^{4} + 6 q^{9} + O(q^{10}) \) \( 12 q - 28 q^{4} + 6 q^{9} + 6 q^{15} - 268 q^{16} - 132 q^{18} - 268 q^{22} + 84 q^{25} + 1644 q^{30} + 852 q^{36} - 1528 q^{37} + 852 q^{39} - 1012 q^{43} - 1216 q^{46} + 2682 q^{51} + 270 q^{57} - 5740 q^{58} + 1836 q^{60} - 548 q^{64} - 1584 q^{67} + 5424 q^{72} + 4296 q^{78} - 3348 q^{79} - 1674 q^{81} + 348 q^{85} + 1108 q^{88} + 2958 q^{93} - 3354 q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(50\) \(52\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.58741i 0.914787i 0.889264 + 0.457393i \(0.151217\pi\)
−0.889264 + 0.457393i \(0.848783\pi\)
\(3\) −2.60257 + 4.49740i −0.500866 + 0.865525i
\(4\) 1.30532 0.163165
\(5\) −16.1181 −1.44165 −0.720825 0.693117i \(-0.756237\pi\)
−0.720825 + 0.693117i \(0.756237\pi\)
\(6\) −11.6366 6.73392i −0.791771 0.458185i
\(7\) 0 0
\(8\) 24.0767i 1.06405i
\(9\) −13.4532 23.4096i −0.498267 0.867023i
\(10\) 41.7042i 1.31880i
\(11\) 35.5990i 0.975772i −0.872907 0.487886i \(-0.837768\pi\)
0.872907 0.487886i \(-0.162232\pi\)
\(12\) −3.39719 + 5.87054i −0.0817237 + 0.141223i
\(13\) 7.40831i 0.158054i 0.996872 + 0.0790268i \(0.0251813\pi\)
−0.996872 + 0.0790268i \(0.974819\pi\)
\(14\) 0 0
\(15\) 41.9486 72.4897i 0.722073 1.24778i
\(16\) −51.8536 −0.810212
\(17\) −28.9202 −0.412599 −0.206300 0.978489i \(-0.566142\pi\)
−0.206300 + 0.978489i \(0.566142\pi\)
\(18\) 60.5703 34.8090i 0.793142 0.455808i
\(19\) 35.1698i 0.424659i −0.977198 0.212329i \(-0.931895\pi\)
0.977198 0.212329i \(-0.0681050\pi\)
\(20\) −21.0393 −0.235227
\(21\) 0 0
\(22\) 92.1090 0.892623
\(23\) 55.4275i 0.502497i 0.967923 + 0.251249i \(0.0808412\pi\)
−0.967923 + 0.251249i \(0.919159\pi\)
\(24\) −108.282 62.6613i −0.920960 0.532945i
\(25\) 134.794 1.07835
\(26\) −19.1683 −0.144585
\(27\) 140.295 + 0.420792i 0.999996 + 0.00299931i
\(28\) 0 0
\(29\) 68.1510i 0.436390i −0.975905 0.218195i \(-0.929983\pi\)
0.975905 0.218195i \(-0.0700169\pi\)
\(30\) 187.560 + 108.538i 1.14146 + 0.660543i
\(31\) 178.671i 1.03517i −0.855632 0.517585i \(-0.826831\pi\)
0.855632 0.517585i \(-0.173169\pi\)
\(32\) 58.4469i 0.322877i
\(33\) 160.103 + 92.6489i 0.844555 + 0.488730i
\(34\) 74.8285i 0.377440i
\(35\) 0 0
\(36\) −17.5608 30.5571i −0.0812998 0.141468i
\(37\) −233.676 −1.03827 −0.519137 0.854691i \(-0.673747\pi\)
−0.519137 + 0.854691i \(0.673747\pi\)
\(38\) 90.9987 0.388472
\(39\) −33.3181 19.2807i −0.136799 0.0791636i
\(40\) 388.071i 1.53398i
\(41\) −370.068 −1.40963 −0.704816 0.709390i \(-0.748970\pi\)
−0.704816 + 0.709390i \(0.748970\pi\)
\(42\) 0 0
\(43\) −187.068 −0.663432 −0.331716 0.943379i \(-0.607628\pi\)
−0.331716 + 0.943379i \(0.607628\pi\)
\(44\) 46.4680i 0.159212i
\(45\) 216.841 + 377.320i 0.718327 + 1.24994i
\(46\) −143.414 −0.459678
\(47\) −174.745 −0.542324 −0.271162 0.962534i \(-0.587408\pi\)
−0.271162 + 0.962534i \(0.587408\pi\)
\(48\) 134.953 233.206i 0.405807 0.701259i
\(49\) 0 0
\(50\) 348.768i 0.986464i
\(51\) 75.2671 130.066i 0.206657 0.357115i
\(52\) 9.67022i 0.0257888i
\(53\) 272.180i 0.705412i 0.935734 + 0.352706i \(0.114738\pi\)
−0.935734 + 0.352706i \(0.885262\pi\)
\(54\) −1.08876 + 363.002i −0.00274373 + 0.914783i
\(55\) 573.789i 1.40672i
\(56\) 0 0
\(57\) 158.173 + 91.5321i 0.367553 + 0.212697i
\(58\) 176.334 0.399204
\(59\) −96.8709 −0.213754 −0.106877 0.994272i \(-0.534085\pi\)
−0.106877 + 0.994272i \(0.534085\pi\)
\(60\) 54.7564 94.6222i 0.117817 0.203595i
\(61\) 385.534i 0.809223i 0.914489 + 0.404611i \(0.132593\pi\)
−0.914489 + 0.404611i \(0.867407\pi\)
\(62\) 462.295 0.946960
\(63\) 0 0
\(64\) −566.055 −1.10558
\(65\) 119.408i 0.227858i
\(66\) −239.721 + 414.251i −0.447084 + 0.772588i
\(67\) −1018.02 −1.85628 −0.928140 0.372231i \(-0.878593\pi\)
−0.928140 + 0.372231i \(0.878593\pi\)
\(68\) −37.7502 −0.0673218
\(69\) −249.280 144.254i −0.434924 0.251684i
\(70\) 0 0
\(71\) 125.333i 0.209497i −0.994499 0.104749i \(-0.966596\pi\)
0.994499 0.104749i \(-0.0334038\pi\)
\(72\) 563.626 323.909i 0.922555 0.530180i
\(73\) 225.566i 0.361651i 0.983515 + 0.180825i \(0.0578768\pi\)
−0.983515 + 0.180825i \(0.942123\pi\)
\(74\) 604.616i 0.949800i
\(75\) −350.812 + 606.223i −0.540110 + 0.933342i
\(76\) 45.9079i 0.0692894i
\(77\) 0 0
\(78\) 49.8870 86.2076i 0.0724178 0.125142i
\(79\) −1064.31 −1.51575 −0.757874 0.652401i \(-0.773762\pi\)
−0.757874 + 0.652401i \(0.773762\pi\)
\(80\) 835.783 1.16804
\(81\) −367.022 + 629.870i −0.503459 + 0.864019i
\(82\) 957.517i 1.28951i
\(83\) 601.040 0.794852 0.397426 0.917634i \(-0.369904\pi\)
0.397426 + 0.917634i \(0.369904\pi\)
\(84\) 0 0
\(85\) 466.140 0.594824
\(86\) 484.021i 0.606899i
\(87\) 306.502 + 177.368i 0.377707 + 0.218573i
\(88\) 857.104 1.03827
\(89\) 1505.21 1.79272 0.896360 0.443327i \(-0.146202\pi\)
0.896360 + 0.443327i \(0.146202\pi\)
\(90\) −976.280 + 561.055i −1.14343 + 0.657116i
\(91\) 0 0
\(92\) 72.3506i 0.0819900i
\(93\) 803.556 + 465.005i 0.895966 + 0.518481i
\(94\) 452.137i 0.496111i
\(95\) 566.872i 0.612209i
\(96\) −262.859 152.112i −0.279458 0.161718i
\(97\) 327.463i 0.342771i −0.985204 0.171386i \(-0.945176\pi\)
0.985204 0.171386i \(-0.0548244\pi\)
\(98\) 0 0
\(99\) −833.358 + 478.920i −0.846017 + 0.486195i
\(100\) 175.949 0.175949
\(101\) −1095.69 −1.07946 −0.539729 0.841839i \(-0.681473\pi\)
−0.539729 + 0.841839i \(0.681473\pi\)
\(102\) 336.534 + 194.747i 0.326684 + 0.189047i
\(103\) 207.670i 0.198664i −0.995054 0.0993318i \(-0.968329\pi\)
0.995054 0.0993318i \(-0.0316705\pi\)
\(104\) −178.367 −0.168177
\(105\) 0 0
\(106\) −704.242 −0.645302
\(107\) 1802.78i 1.62880i 0.580305 + 0.814399i \(0.302933\pi\)
−0.580305 + 0.814399i \(0.697067\pi\)
\(108\) 183.130 + 0.549267i 0.163164 + 0.000489382i
\(109\) 283.649 0.249254 0.124627 0.992204i \(-0.460227\pi\)
0.124627 + 0.992204i \(0.460227\pi\)
\(110\) −1484.63 −1.28685
\(111\) 608.160 1050.94i 0.520036 0.898652i
\(112\) 0 0
\(113\) 1037.39i 0.863627i −0.901963 0.431814i \(-0.857874\pi\)
0.901963 0.431814i \(-0.142126\pi\)
\(114\) −236.831 + 409.258i −0.194572 + 0.336232i
\(115\) 893.388i 0.724425i
\(116\) 88.9588i 0.0712036i
\(117\) 173.426 99.6657i 0.137036 0.0787529i
\(118\) 250.644i 0.195540i
\(119\) 0 0
\(120\) 1745.31 + 1009.98i 1.32770 + 0.768320i
\(121\) 63.7146 0.0478697
\(122\) −997.534 −0.740266
\(123\) 963.129 1664.34i 0.706036 1.22007i
\(124\) 233.223i 0.168904i
\(125\) −157.864 −0.112958
\(126\) 0 0
\(127\) 1645.81 1.14994 0.574968 0.818176i \(-0.305015\pi\)
0.574968 + 0.818176i \(0.305015\pi\)
\(128\) 997.039i 0.688489i
\(129\) 486.858 841.319i 0.332290 0.574217i
\(130\) 308.958 0.208441
\(131\) 628.369 0.419091 0.209545 0.977799i \(-0.432802\pi\)
0.209545 + 0.977799i \(0.432802\pi\)
\(132\) 208.985 + 120.936i 0.137802 + 0.0797437i
\(133\) 0 0
\(134\) 2634.03i 1.69810i
\(135\) −2261.30 6.78237i −1.44164 0.00432395i
\(136\) 696.303i 0.439026i
\(137\) 498.922i 0.311137i −0.987825 0.155569i \(-0.950279\pi\)
0.987825 0.155569i \(-0.0497209\pi\)
\(138\) 373.245 644.989i 0.230237 0.397863i
\(139\) 1216.65i 0.742410i 0.928551 + 0.371205i \(0.121055\pi\)
−0.928551 + 0.371205i \(0.878945\pi\)
\(140\) 0 0
\(141\) 454.788 785.900i 0.271631 0.469395i
\(142\) 324.288 0.191645
\(143\) 263.728 0.154224
\(144\) 697.598 + 1213.87i 0.403702 + 0.702473i
\(145\) 1098.47i 0.629122i
\(146\) −583.631 −0.330833
\(147\) 0 0
\(148\) −305.022 −0.169410
\(149\) 2321.16i 1.27622i −0.769945 0.638111i \(-0.779716\pi\)
0.769945 0.638111i \(-0.220284\pi\)
\(150\) −1568.55 907.693i −0.853809 0.494086i
\(151\) 977.451 0.526780 0.263390 0.964689i \(-0.415159\pi\)
0.263390 + 0.964689i \(0.415159\pi\)
\(152\) 846.772 0.451857
\(153\) 389.070 + 677.012i 0.205585 + 0.357733i
\(154\) 0 0
\(155\) 2879.85i 1.49235i
\(156\) −43.4908 25.1675i −0.0223209 0.0129167i
\(157\) 165.990i 0.0843786i −0.999110 0.0421893i \(-0.986567\pi\)
0.999110 0.0421893i \(-0.0134333\pi\)
\(158\) 2753.80i 1.38659i
\(159\) −1224.10 708.369i −0.610552 0.353317i
\(160\) 942.055i 0.465475i
\(161\) 0 0
\(162\) −1629.73 949.635i −0.790393 0.460558i
\(163\) 977.023 0.469487 0.234743 0.972057i \(-0.424575\pi\)
0.234743 + 0.972057i \(0.424575\pi\)
\(164\) −483.057 −0.230002
\(165\) −2580.56 1493.33i −1.21755 0.704578i
\(166\) 1555.14i 0.727120i
\(167\) −1.00709 −0.000466651 −0.000233326 1.00000i \(-0.500074\pi\)
−0.000233326 1.00000i \(0.500074\pi\)
\(168\) 0 0
\(169\) 2142.12 0.975019
\(170\) 1206.10i 0.544137i
\(171\) −823.313 + 473.148i −0.368189 + 0.211594i
\(172\) −244.183 −0.108249
\(173\) −3956.55 −1.73879 −0.869395 0.494117i \(-0.835491\pi\)
−0.869395 + 0.494117i \(0.835491\pi\)
\(174\) −458.923 + 793.046i −0.199948 + 0.345521i
\(175\) 0 0
\(176\) 1845.93i 0.790582i
\(177\) 252.114 435.667i 0.107062 0.185010i
\(178\) 3894.60i 1.63996i
\(179\) 2798.47i 1.16853i 0.811562 + 0.584266i \(0.198617\pi\)
−0.811562 + 0.584266i \(0.801383\pi\)
\(180\) 283.046 + 492.523i 0.117206 + 0.203947i
\(181\) 1506.74i 0.618758i −0.950939 0.309379i \(-0.899879\pi\)
0.950939 0.309379i \(-0.100121\pi\)
\(182\) 0 0
\(183\) −1733.90 1003.38i −0.700403 0.405312i
\(184\) −1334.51 −0.534681
\(185\) 3766.43 1.49683
\(186\) −1203.16 + 2079.13i −0.474300 + 0.819618i
\(187\) 1029.53i 0.402603i
\(188\) −228.098 −0.0884882
\(189\) 0 0
\(190\) −1466.73 −0.560041
\(191\) 3677.16i 1.39304i 0.717539 + 0.696518i \(0.245268\pi\)
−0.717539 + 0.696518i \(0.754732\pi\)
\(192\) 1473.20 2545.77i 0.553745 0.956903i
\(193\) −129.467 −0.0482862 −0.0241431 0.999709i \(-0.507686\pi\)
−0.0241431 + 0.999709i \(0.507686\pi\)
\(194\) 847.280 0.313563
\(195\) 537.026 + 310.769i 0.197217 + 0.114126i
\(196\) 0 0
\(197\) 3044.81i 1.10119i 0.834774 + 0.550593i \(0.185598\pi\)
−0.834774 + 0.550593i \(0.814402\pi\)
\(198\) −1239.16 2156.24i −0.444765 0.773925i
\(199\) 3993.29i 1.42250i 0.702941 + 0.711248i \(0.251870\pi\)
−0.702941 + 0.711248i \(0.748130\pi\)
\(200\) 3245.39i 1.14742i
\(201\) 2649.47 4578.44i 0.929747 1.60666i
\(202\) 2835.00i 0.987473i
\(203\) 0 0
\(204\) 98.2476 169.778i 0.0337191 0.0582687i
\(205\) 5964.80 2.03219
\(206\) 537.327 0.181735
\(207\) 1297.54 745.679i 0.435677 0.250378i
\(208\) 384.148i 0.128057i
\(209\) −1252.01 −0.414370
\(210\) 0 0
\(211\) −4383.67 −1.43026 −0.715129 0.698992i \(-0.753632\pi\)
−0.715129 + 0.698992i \(0.753632\pi\)
\(212\) 355.282i 0.115099i
\(213\) 563.673 + 326.188i 0.181325 + 0.104930i
\(214\) −4664.53 −1.49000
\(215\) 3015.19 0.956437
\(216\) −10.1313 + 3377.85i −0.00319141 + 1.06404i
\(217\) 0 0
\(218\) 733.916i 0.228014i
\(219\) −1014.46 587.052i −0.313018 0.181138i
\(220\) 748.978i 0.229528i
\(221\) 214.250i 0.0652128i
\(222\) 2719.20 + 1573.56i 0.822076 + 0.475722i
\(223\) 4851.53i 1.45687i 0.685114 + 0.728436i \(0.259753\pi\)
−0.685114 + 0.728436i \(0.740247\pi\)
\(224\) 0 0
\(225\) −1813.42 3155.48i −0.537308 0.934958i
\(226\) 2684.16 0.790035
\(227\) −2368.10 −0.692407 −0.346203 0.938159i \(-0.612529\pi\)
−0.346203 + 0.938159i \(0.612529\pi\)
\(228\) 206.466 + 119.479i 0.0599717 + 0.0347047i
\(229\) 4315.43i 1.24529i 0.782504 + 0.622646i \(0.213942\pi\)
−0.782504 + 0.622646i \(0.786058\pi\)
\(230\) 2311.56 0.662695
\(231\) 0 0
\(232\) 1640.85 0.464340
\(233\) 5573.72i 1.56715i −0.621296 0.783576i \(-0.713393\pi\)
0.621296 0.783576i \(-0.286607\pi\)
\(234\) 257.876 + 448.724i 0.0720421 + 0.125359i
\(235\) 2816.57 0.781841
\(236\) −126.447 −0.0348772
\(237\) 2769.94 4786.62i 0.759186 1.31192i
\(238\) 0 0
\(239\) 4683.70i 1.26763i −0.773485 0.633814i \(-0.781488\pi\)
0.773485 0.633814i \(-0.218512\pi\)
\(240\) −2175.19 + 3758.85i −0.585032 + 1.01097i
\(241\) 2190.20i 0.585407i −0.956203 0.292703i \(-0.905445\pi\)
0.956203 0.292703i \(-0.0945549\pi\)
\(242\) 164.856i 0.0437906i
\(243\) −1877.58 3289.93i −0.495665 0.868514i
\(244\) 503.245i 0.132037i
\(245\) 0 0
\(246\) 4306.34 + 2492.01i 1.11611 + 0.645872i
\(247\) 260.549 0.0671188
\(248\) 4301.80 1.10147
\(249\) −1564.25 + 2703.12i −0.398114 + 0.687964i
\(250\) 408.458i 0.103333i
\(251\) −2240.70 −0.563473 −0.281736 0.959492i \(-0.590910\pi\)
−0.281736 + 0.959492i \(0.590910\pi\)
\(252\) 0 0
\(253\) 1973.16 0.490323
\(254\) 4258.38i 1.05195i
\(255\) −1213.16 + 2096.42i −0.297927 + 0.514835i
\(256\) −1948.69 −0.475754
\(257\) −1111.57 −0.269797 −0.134898 0.990859i \(-0.543071\pi\)
−0.134898 + 0.990859i \(0.543071\pi\)
\(258\) 2176.84 + 1259.70i 0.525287 + 0.303975i
\(259\) 0 0
\(260\) 155.866i 0.0371784i
\(261\) −1595.39 + 916.850i −0.378361 + 0.217439i
\(262\) 1625.85i 0.383379i
\(263\) 2058.67i 0.482673i −0.970441 0.241337i \(-0.922414\pi\)
0.970441 0.241337i \(-0.0775858\pi\)
\(264\) −2230.68 + 3854.74i −0.520033 + 0.898647i
\(265\) 4387.04i 1.01696i
\(266\) 0 0
\(267\) −3917.42 + 6769.54i −0.897912 + 1.55164i
\(268\) −1328.84 −0.302880
\(269\) −4829.24 −1.09459 −0.547294 0.836941i \(-0.684342\pi\)
−0.547294 + 0.836941i \(0.684342\pi\)
\(270\) 17.5488 5850.91i 0.00395550 1.31880i
\(271\) 221.440i 0.0496366i 0.999692 + 0.0248183i \(0.00790072\pi\)
−0.999692 + 0.0248183i \(0.992099\pi\)
\(272\) 1499.62 0.334293
\(273\) 0 0
\(274\) 1290.91 0.284624
\(275\) 4798.53i 1.05223i
\(276\) −325.390 188.298i −0.0709644 0.0410660i
\(277\) 2467.15 0.535151 0.267576 0.963537i \(-0.413777\pi\)
0.267576 + 0.963537i \(0.413777\pi\)
\(278\) −3147.97 −0.679147
\(279\) −4182.63 + 2403.70i −0.897517 + 0.515792i
\(280\) 0 0
\(281\) 4174.76i 0.886282i −0.896452 0.443141i \(-0.853864\pi\)
0.896452 0.443141i \(-0.146136\pi\)
\(282\) 2033.44 + 1176.72i 0.429396 + 0.248485i
\(283\) 6499.11i 1.36513i −0.730825 0.682565i \(-0.760864\pi\)
0.730825 0.682565i \(-0.239136\pi\)
\(284\) 163.600i 0.0341826i
\(285\) −2549.45 1475.33i −0.529882 0.306634i
\(286\) 682.372i 0.141082i
\(287\) 0 0
\(288\) 1368.22 786.299i 0.279942 0.160879i
\(289\) −4076.62 −0.829762
\(290\) −2842.18 −0.575512
\(291\) 1472.73 + 852.247i 0.296677 + 0.171682i
\(292\) 294.436i 0.0590087i
\(293\) −5637.32 −1.12401 −0.562007 0.827133i \(-0.689970\pi\)
−0.562007 + 0.827133i \(0.689970\pi\)
\(294\) 0 0
\(295\) 1561.38 0.308159
\(296\) 5626.15i 1.10477i
\(297\) 14.9797 4994.37i 0.00292664 0.975767i
\(298\) 6005.79 1.16747
\(299\) −410.625 −0.0794215
\(300\) −457.922 + 791.315i −0.0881270 + 0.152289i
\(301\) 0 0
\(302\) 2529.06i 0.481892i
\(303\) 2851.61 4927.75i 0.540663 0.934297i
\(304\) 1823.68i 0.344064i
\(305\) 6214.09i 1.16662i
\(306\) −1751.71 + 1006.68i −0.327250 + 0.188066i
\(307\) 3442.95i 0.640064i 0.947407 + 0.320032i \(0.103694\pi\)
−0.947407 + 0.320032i \(0.896306\pi\)
\(308\) 0 0
\(309\) 933.976 + 540.477i 0.171948 + 0.0995037i
\(310\) −7451.33 −1.36519
\(311\) −151.465 −0.0276166 −0.0138083 0.999905i \(-0.504395\pi\)
−0.0138083 + 0.999905i \(0.504395\pi\)
\(312\) 464.214 802.190i 0.0842339 0.145561i
\(313\) 9624.79i 1.73810i −0.494724 0.869050i \(-0.664731\pi\)
0.494724 0.869050i \(-0.335269\pi\)
\(314\) 429.484 0.0771885
\(315\) 0 0
\(316\) −1389.26 −0.247317
\(317\) 9083.95i 1.60948i 0.593627 + 0.804741i \(0.297696\pi\)
−0.593627 + 0.804741i \(0.702304\pi\)
\(318\) 1832.84 3167.26i 0.323209 0.558525i
\(319\) −2426.10 −0.425817
\(320\) 9123.74 1.59385
\(321\) −8107.83 4691.87i −1.40977 0.815809i
\(322\) 0 0
\(323\) 1017.12i 0.175214i
\(324\) −479.081 + 822.181i −0.0821469 + 0.140978i
\(325\) 998.597i 0.170438i
\(326\) 2527.96i 0.429480i
\(327\) −738.218 + 1275.68i −0.124843 + 0.215735i
\(328\) 8910.00i 1.49992i
\(329\) 0 0
\(330\) 3863.85 6676.95i 0.644539 1.11380i
\(331\) −1405.58 −0.233406 −0.116703 0.993167i \(-0.537233\pi\)
−0.116703 + 0.993167i \(0.537233\pi\)
\(332\) 784.549 0.129692
\(333\) 3143.70 + 5470.28i 0.517338 + 0.900208i
\(334\) 2.60575i 0.000426887i
\(335\) 16408.6 2.67611
\(336\) 0 0
\(337\) 7983.35 1.29045 0.645223 0.763994i \(-0.276764\pi\)
0.645223 + 0.763994i \(0.276764\pi\)
\(338\) 5542.53i 0.891935i
\(339\) 4665.58 + 2699.90i 0.747491 + 0.432561i
\(340\) 608.462 0.0970544
\(341\) −6360.51 −1.01009
\(342\) −1224.23 2130.25i −0.193563 0.336815i
\(343\) 0 0
\(344\) 4503.97i 0.705924i
\(345\) 4017.92 + 2325.11i 0.627008 + 0.362840i
\(346\) 10237.2i 1.59062i
\(347\) 2619.33i 0.405225i −0.979259 0.202612i \(-0.935057\pi\)
0.979259 0.202612i \(-0.0649432\pi\)
\(348\) 400.083 + 231.522i 0.0616285 + 0.0356634i
\(349\) 6032.33i 0.925224i 0.886561 + 0.462612i \(0.153088\pi\)
−0.886561 + 0.462612i \(0.846912\pi\)
\(350\) 0 0
\(351\) −3.11736 + 1039.35i −0.000474052 + 0.158053i
\(352\) 2080.65 0.315054
\(353\) −5316.31 −0.801582 −0.400791 0.916170i \(-0.631265\pi\)
−0.400791 + 0.916170i \(0.631265\pi\)
\(354\) 1127.25 + 652.321i 0.169245 + 0.0979392i
\(355\) 2020.13i 0.302021i
\(356\) 1964.78 0.292509
\(357\) 0 0
\(358\) −7240.77 −1.06896
\(359\) 1861.96i 0.273735i 0.990589 + 0.136867i \(0.0437034\pi\)
−0.990589 + 0.136867i \(0.956297\pi\)
\(360\) −9084.59 + 5220.80i −1.33000 + 0.764334i
\(361\) 5622.08 0.819665
\(362\) 3898.55 0.566032
\(363\) −165.822 + 286.550i −0.0239763 + 0.0414325i
\(364\) 0 0
\(365\) 3635.70i 0.521373i
\(366\) 2596.16 4486.31i 0.370774 0.640719i
\(367\) 1935.15i 0.275242i −0.990485 0.137621i \(-0.956054\pi\)
0.990485 0.137621i \(-0.0439456\pi\)
\(368\) 2874.12i 0.407130i
\(369\) 4978.60 + 8663.15i 0.702373 + 1.22218i
\(370\) 9745.28i 1.36928i
\(371\) 0 0
\(372\) 1048.90 + 606.980i 0.146190 + 0.0845980i
\(373\) 7742.08 1.07472 0.537359 0.843354i \(-0.319422\pi\)
0.537359 + 0.843354i \(0.319422\pi\)
\(374\) −2663.81 −0.368296
\(375\) 410.852 709.977i 0.0565768 0.0977681i
\(376\) 4207.28i 0.577059i
\(377\) 504.884 0.0689730
\(378\) 0 0
\(379\) −3722.15 −0.504470 −0.252235 0.967666i \(-0.581166\pi\)
−0.252235 + 0.967666i \(0.581166\pi\)
\(380\) 739.949i 0.0998911i
\(381\) −4283.34 + 7401.86i −0.575963 + 0.995298i
\(382\) −9514.31 −1.27433
\(383\) 7093.46 0.946368 0.473184 0.880964i \(-0.343105\pi\)
0.473184 + 0.880964i \(0.343105\pi\)
\(384\) 4484.08 + 2594.87i 0.595905 + 0.344841i
\(385\) 0 0
\(386\) 334.984i 0.0441716i
\(387\) 2516.67 + 4379.19i 0.330567 + 0.575212i
\(388\) 427.444i 0.0559283i
\(389\) 7128.11i 0.929073i 0.885554 + 0.464537i \(0.153779\pi\)
−0.885554 + 0.464537i \(0.846221\pi\)
\(390\) −804.085 + 1389.51i −0.104401 + 0.180411i
\(391\) 1602.98i 0.207330i
\(392\) 0 0
\(393\) −1635.38 + 2826.03i −0.209908 + 0.362733i
\(394\) −7878.16 −1.00735
\(395\) 17154.7 2.18518
\(396\) −1087.80 + 625.144i −0.138040 + 0.0793300i
\(397\) 8936.22i 1.12971i −0.825189 0.564857i \(-0.808932\pi\)
0.825189 0.564857i \(-0.191068\pi\)
\(398\) −10332.3 −1.30128
\(399\) 0 0
\(400\) −6989.56 −0.873695
\(401\) 8913.83i 1.11006i −0.831829 0.555032i \(-0.812706\pi\)
0.831829 0.555032i \(-0.187294\pi\)
\(402\) 11846.3 + 6855.26i 1.46975 + 0.850520i
\(403\) 1323.65 0.163612
\(404\) −1430.22 −0.176130
\(405\) 5915.71 10152.3i 0.725812 1.24561i
\(406\) 0 0
\(407\) 8318.63i 1.01312i
\(408\) 3131.55 + 1812.18i 0.379988 + 0.219893i
\(409\) 3094.75i 0.374145i −0.982346 0.187073i \(-0.940100\pi\)
0.982346 0.187073i \(-0.0599000\pi\)
\(410\) 15433.4i 1.85903i
\(411\) 2243.85 + 1298.48i 0.269297 + 0.155838i
\(412\) 271.076i 0.0324149i
\(413\) 0 0
\(414\) 1929.38 + 3357.26i 0.229043 + 0.398552i
\(415\) −9687.64 −1.14590
\(416\) −432.993 −0.0510318
\(417\) −5471.77 3166.42i −0.642574 0.371848i
\(418\) 3239.46i 0.379060i
\(419\) −7234.25 −0.843476 −0.421738 0.906718i \(-0.638580\pi\)
−0.421738 + 0.906718i \(0.638580\pi\)
\(420\) 0 0
\(421\) 406.124 0.0470148 0.0235074 0.999724i \(-0.492517\pi\)
0.0235074 + 0.999724i \(0.492517\pi\)
\(422\) 11342.4i 1.30838i
\(423\) 2350.89 + 4090.72i 0.270222 + 0.470208i
\(424\) −6553.19 −0.750592
\(425\) −3898.28 −0.444928
\(426\) −843.982 + 1458.45i −0.0959885 + 0.165874i
\(427\) 0 0
\(428\) 2353.21i 0.265763i
\(429\) −686.372 + 1186.09i −0.0772456 + 0.133485i
\(430\) 7801.52i 0.874936i
\(431\) 12228.7i 1.36668i −0.730102 0.683338i \(-0.760528\pi\)
0.730102 0.683338i \(-0.239472\pi\)
\(432\) −7274.82 21.8196i −0.810209 0.00243008i
\(433\) 3252.79i 0.361014i 0.983574 + 0.180507i \(0.0577738\pi\)
−0.983574 + 0.180507i \(0.942226\pi\)
\(434\) 0 0
\(435\) −4940.24 2858.84i −0.544521 0.315105i
\(436\) 370.253 0.0406695
\(437\) 1949.38 0.213390
\(438\) 1518.94 2624.82i 0.165703 0.286344i
\(439\) 15053.6i 1.63661i 0.574787 + 0.818303i \(0.305085\pi\)
−0.574787 + 0.818303i \(0.694915\pi\)
\(440\) −13814.9 −1.49682
\(441\) 0 0
\(442\) 554.353 0.0596558
\(443\) 235.990i 0.0253098i 0.999920 + 0.0126549i \(0.00402828\pi\)
−0.999920 + 0.0126549i \(0.995972\pi\)
\(444\) 793.843 1371.81i 0.0848516 0.146629i
\(445\) −24261.2 −2.58447
\(446\) −12552.9 −1.33273
\(447\) 10439.2 + 6040.99i 1.10460 + 0.639215i
\(448\) 0 0
\(449\) 5874.66i 0.617466i 0.951149 + 0.308733i \(0.0999049\pi\)
−0.951149 + 0.308733i \(0.900095\pi\)
\(450\) 8164.52 4692.05i 0.855287 0.491523i
\(451\) 13174.0i 1.37548i
\(452\) 1354.13i 0.140914i
\(453\) −2543.89 + 4395.99i −0.263846 + 0.455942i
\(454\) 6127.24i 0.633405i
\(455\) 0 0
\(456\) −2203.79 + 3808.27i −0.226320 + 0.391094i
\(457\) 307.766 0.0315026 0.0157513 0.999876i \(-0.494986\pi\)
0.0157513 + 0.999876i \(0.494986\pi\)
\(458\) −11165.8 −1.13918
\(459\) −4057.38 12.1694i −0.412597 0.00123751i
\(460\) 1166.16i 0.118201i
\(461\) 4752.26 0.480119 0.240060 0.970758i \(-0.422833\pi\)
0.240060 + 0.970758i \(0.422833\pi\)
\(462\) 0 0
\(463\) −9529.43 −0.956523 −0.478261 0.878218i \(-0.658733\pi\)
−0.478261 + 0.878218i \(0.658733\pi\)
\(464\) 3533.87i 0.353569i
\(465\) −12951.8 7495.01i −1.29167 0.747468i
\(466\) 14421.5 1.43361
\(467\) −6538.56 −0.647899 −0.323949 0.946074i \(-0.605011\pi\)
−0.323949 + 0.946074i \(0.605011\pi\)
\(468\) 226.376 130.096i 0.0223595 0.0128497i
\(469\) 0 0
\(470\) 7287.61i 0.715218i
\(471\) 746.524 + 432.001i 0.0730318 + 0.0422624i
\(472\) 2332.33i 0.227445i
\(473\) 6659.42i 0.647359i
\(474\) 12384.9 + 7166.97i 1.20013 + 0.694493i
\(475\) 4740.69i 0.457932i
\(476\) 0 0
\(477\) 6371.64 3661.70i 0.611609 0.351484i
\(478\) 12118.6 1.15961
\(479\) 7342.57 0.700398 0.350199 0.936675i \(-0.386114\pi\)
0.350199 + 0.936675i \(0.386114\pi\)
\(480\) 4236.80 + 2451.77i 0.402880 + 0.233140i
\(481\) 1731.15i 0.164103i
\(482\) 5666.94 0.535523
\(483\) 0 0
\(484\) 83.1680 0.00781066
\(485\) 5278.09i 0.494156i
\(486\) 8512.38 4858.05i 0.794505 0.453428i
\(487\) 7017.57 0.652970 0.326485 0.945202i \(-0.394136\pi\)
0.326485 + 0.945202i \(0.394136\pi\)
\(488\) −9282.37 −0.861052
\(489\) −2542.77 + 4394.06i −0.235150 + 0.406352i
\(490\) 0 0
\(491\) 224.222i 0.0206089i 0.999947 + 0.0103045i \(0.00328007\pi\)
−0.999947 + 0.0103045i \(0.996720\pi\)
\(492\) 1257.19 2172.50i 0.115200 0.199073i
\(493\) 1970.94i 0.180054i
\(494\) 674.147i 0.0613994i
\(495\) 13432.2 7719.30i 1.21966 0.700923i
\(496\) 9264.74i 0.838708i
\(497\) 0 0
\(498\) −6994.07 4047.36i −0.629341 0.364189i
\(499\) −20792.2 −1.86530 −0.932651 0.360780i \(-0.882510\pi\)
−0.932651 + 0.360780i \(0.882510\pi\)
\(500\) −206.063 −0.0184308
\(501\) 2.62102 4.52928i 0.000233730 0.000403898i
\(502\) 5797.60i 0.515458i
\(503\) 7341.52 0.650780 0.325390 0.945580i \(-0.394504\pi\)
0.325390 + 0.945580i \(0.394504\pi\)
\(504\) 0 0
\(505\) 17660.5 1.55620
\(506\) 5105.38i 0.448541i
\(507\) −5575.02 + 9633.96i −0.488353 + 0.843903i
\(508\) 2148.31 0.187629
\(509\) 19912.2 1.73398 0.866988 0.498330i \(-0.166053\pi\)
0.866988 + 0.498330i \(0.166053\pi\)
\(510\) −5424.29 3138.95i −0.470964 0.272539i
\(511\) 0 0
\(512\) 13018.4i 1.12370i
\(513\) 14.7992 4934.17i 0.00127368 0.424657i
\(514\) 2876.08i 0.246807i
\(515\) 3347.25i 0.286403i
\(516\) 635.506 1098.19i 0.0542182 0.0936922i
\(517\) 6220.75i 0.529184i
\(518\) 0 0
\(519\) 10297.2 17794.2i 0.870900 1.50497i
\(520\) 2874.95 0.242452
\(521\) 7491.80 0.629984 0.314992 0.949094i \(-0.397998\pi\)
0.314992 + 0.949094i \(0.397998\pi\)
\(522\) −2372.26 4127.92i −0.198910 0.346119i
\(523\) 288.115i 0.0240887i −0.999927 0.0120444i \(-0.996166\pi\)
0.999927 0.0120444i \(-0.00383393\pi\)
\(524\) 820.223 0.0683809
\(525\) 0 0
\(526\) 5326.62 0.441543
\(527\) 5167.21i 0.427111i
\(528\) −8301.90 4804.18i −0.684269 0.395975i
\(529\) 9094.79 0.747496
\(530\) 11351.1 0.930299
\(531\) 1303.23 + 2267.71i 0.106507 + 0.185330i
\(532\) 0 0
\(533\) 2741.58i 0.222797i
\(534\) −17515.6 10136.0i −1.41942 0.821398i
\(535\) 29057.5i 2.34816i
\(536\) 24510.5i 1.97517i
\(537\) −12585.8 7283.21i −1.01139 0.585277i
\(538\) 12495.2i 1.00131i
\(539\) 0 0
\(540\) −2951.72 8.85317i −0.235226 0.000705518i
\(541\) 14801.7 1.17630 0.588149 0.808753i \(-0.299857\pi\)
0.588149 + 0.808753i \(0.299857\pi\)
\(542\) −572.955 −0.0454069
\(543\) 6776.42 + 3921.40i 0.535550 + 0.309915i
\(544\) 1690.30i 0.133219i
\(545\) −4571.90 −0.359337
\(546\) 0 0
\(547\) −4036.80 −0.315541 −0.157771 0.987476i \(-0.550431\pi\)
−0.157771 + 0.987476i \(0.550431\pi\)
\(548\) 651.253i 0.0507667i
\(549\) 9025.21 5186.68i 0.701615 0.403209i
\(550\) 12415.8 0.962563
\(551\) −2396.86 −0.185317
\(552\) 3473.16 6001.82i 0.267803 0.462780i
\(553\) 0 0
\(554\) 6383.53i 0.489549i
\(555\) −9802.40 + 16939.1i −0.749709 + 1.29554i
\(556\) 1588.12i 0.121135i
\(557\) 17194.7i 1.30801i 0.756489 + 0.654007i \(0.226913\pi\)
−0.756489 + 0.654007i \(0.773087\pi\)
\(558\) −6219.36 10822.2i −0.471839 0.821037i
\(559\) 1385.86i 0.104858i
\(560\) 0 0
\(561\) −4630.21 2679.43i −0.348463 0.201650i
\(562\) 10801.8 0.810759
\(563\) −18907.3 −1.41536 −0.707678 0.706535i \(-0.750257\pi\)
−0.707678 + 0.706535i \(0.750257\pi\)
\(564\) 593.643 1025.85i 0.0443207 0.0765888i
\(565\) 16720.9i 1.24505i
\(566\) 16815.8 1.24880
\(567\) 0 0
\(568\) 3017.60 0.222915
\(569\) 7223.31i 0.532191i 0.963947 + 0.266096i \(0.0857337\pi\)
−0.963947 + 0.266096i \(0.914266\pi\)
\(570\) 3817.27 6596.47i 0.280505 0.484729i
\(571\) −9930.34 −0.727797 −0.363898 0.931439i \(-0.618554\pi\)
−0.363898 + 0.931439i \(0.618554\pi\)
\(572\) 344.250 0.0251640
\(573\) −16537.7 9570.08i −1.20571 0.697724i
\(574\) 0 0
\(575\) 7471.31i 0.541870i
\(576\) 7615.26 + 13251.1i 0.550872 + 0.958560i
\(577\) 8376.39i 0.604356i 0.953251 + 0.302178i \(0.0977137\pi\)
−0.953251 + 0.302178i \(0.902286\pi\)
\(578\) 10547.9i 0.759055i
\(579\) 336.947 582.265i 0.0241849 0.0417929i
\(580\) 1433.85i 0.102651i
\(581\) 0 0
\(582\) −2205.11 + 3810.56i −0.157053 + 0.271397i
\(583\) 9689.33 0.688321
\(584\) −5430.87 −0.384814
\(585\) −2795.30 + 1606.42i −0.197558 + 0.113534i
\(586\) 14586.1i 1.02823i
\(587\) −21277.2 −1.49609 −0.748043 0.663650i \(-0.769006\pi\)
−0.748043 + 0.663650i \(0.769006\pi\)
\(588\) 0 0
\(589\) −6283.84 −0.439594
\(590\) 4039.92i 0.281900i
\(591\) −13693.7 7924.34i −0.953104 0.551546i
\(592\) 12117.0 0.841223
\(593\) 2848.98 0.197291 0.0986454 0.995123i \(-0.468549\pi\)
0.0986454 + 0.995123i \(0.468549\pi\)
\(594\) 12922.5 + 38.7587i 0.892619 + 0.00267725i
\(595\) 0 0
\(596\) 3029.86i 0.208235i
\(597\) −17959.4 10392.8i −1.23121 0.712479i
\(598\) 1062.45i 0.0726537i
\(599\) 4439.14i 0.302802i 0.988472 + 0.151401i \(0.0483784\pi\)
−0.988472 + 0.151401i \(0.951622\pi\)
\(600\) −14595.8 8446.38i −0.993121 0.574703i
\(601\) 7868.29i 0.534033i −0.963692 0.267017i \(-0.913962\pi\)
0.963692 0.267017i \(-0.0860379\pi\)
\(602\) 0 0
\(603\) 13695.6 + 23831.4i 0.924924 + 1.60944i
\(604\) 1275.89 0.0859521
\(605\) −1026.96 −0.0690114
\(606\) 12750.1 + 7378.28i 0.854683 + 0.494591i
\(607\) 17487.8i 1.16937i 0.811259 + 0.584686i \(0.198782\pi\)
−0.811259 + 0.584686i \(0.801218\pi\)
\(608\) 2055.57 0.137112
\(609\) 0 0
\(610\) 16078.4 1.06720
\(611\) 1294.57i 0.0857162i
\(612\) 507.861 + 883.717i 0.0335442 + 0.0583695i
\(613\) 12844.1 0.846280 0.423140 0.906064i \(-0.360928\pi\)
0.423140 + 0.906064i \(0.360928\pi\)
\(614\) −8908.32 −0.585522
\(615\) −15523.8 + 26826.1i −1.01786 + 1.75892i
\(616\) 0 0
\(617\) 23625.5i 1.54153i −0.637117 0.770767i \(-0.719873\pi\)
0.637117 0.770767i \(-0.280127\pi\)
\(618\) −1398.43 + 2416.58i −0.0910247 + 0.157296i
\(619\) 19086.1i 1.23931i 0.784873 + 0.619657i \(0.212728\pi\)
−0.784873 + 0.619657i \(0.787272\pi\)
\(620\) 3759.12i 0.243500i
\(621\) −23.3234 + 7776.23i −0.00150715 + 0.502495i
\(622\) 391.901i 0.0252633i
\(623\) 0 0
\(624\) 1727.67 + 999.772i 0.110836 + 0.0641393i
\(625\) −14304.8 −0.915507
\(626\) 24903.3 1.58999
\(627\) 3258.45 5630.79i 0.207544 0.358648i
\(628\) 216.670i 0.0137676i
\(629\) 6757.98 0.428391
\(630\) 0 0
\(631\) 32.3893 0.00204342 0.00102171 0.999999i \(-0.499675\pi\)
0.00102171 + 0.999999i \(0.499675\pi\)
\(632\) 25625.0i 1.61283i
\(633\) 11408.8 19715.1i 0.716367 1.23792i
\(634\) −23503.9 −1.47233
\(635\) −26527.3 −1.65780
\(636\) −1597.85 924.648i −0.0996207 0.0576489i
\(637\) 0 0
\(638\) 6277.32i 0.389532i
\(639\) −2934.00 + 1686.13i −0.181639 + 0.104386i
\(640\) 16070.4i 0.992560i
\(641\) 21642.2i 1.33357i −0.745251 0.666784i \(-0.767670\pi\)
0.745251 0.666784i \(-0.232330\pi\)
\(642\) 12139.8 20978.3i 0.746291 1.28964i
\(643\) 19867.3i 1.21849i −0.792982 0.609246i \(-0.791472\pi\)
0.792982 0.609246i \(-0.208528\pi\)
\(644\) 0 0
\(645\) −7847.24 + 13560.5i −0.479046 + 0.827820i
\(646\) −2631.71 −0.160283
\(647\) −22424.4 −1.36259 −0.681294 0.732010i \(-0.738582\pi\)
−0.681294 + 0.732010i \(0.738582\pi\)
\(648\) −15165.2 8836.66i −0.919358 0.535705i
\(649\) 3448.50i 0.208576i
\(650\) −2583.78 −0.155914
\(651\) 0 0
\(652\) 1275.33 0.0766038
\(653\) 20043.8i 1.20119i −0.799554 0.600594i \(-0.794931\pi\)
0.799554 0.600594i \(-0.205069\pi\)
\(654\) −3300.72 1910.07i −0.197352 0.114204i
\(655\) −10128.1 −0.604182
\(656\) 19189.3 1.14210
\(657\) 5280.41 3034.59i 0.313559 0.180199i
\(658\) 0 0
\(659\) 13217.9i 0.781327i −0.920533 0.390664i \(-0.872246\pi\)
0.920533 0.390664i \(-0.127754\pi\)
\(660\) −3368.45 1949.27i −0.198662 0.114962i
\(661\) 9781.36i 0.575568i 0.957695 + 0.287784i \(0.0929186\pi\)
−0.957695 + 0.287784i \(0.907081\pi\)
\(662\) 3636.80i 0.213517i
\(663\) 963.569 + 557.602i 0.0564433 + 0.0326628i
\(664\) 14471.0i 0.845761i
\(665\) 0 0
\(666\) −14153.8 + 8134.03i −0.823499 + 0.473254i
\(667\) 3777.44 0.219285
\(668\) −1.31457 −7.61411e−5
\(669\) −21819.3 12626.5i −1.26096 0.729697i
\(670\) 42455.6i 2.44807i
\(671\) 13724.6 0.789617
\(672\) 0 0
\(673\) −4670.73 −0.267524 −0.133762 0.991014i \(-0.542706\pi\)
−0.133762 + 0.991014i \(0.542706\pi\)
\(674\) 20656.2i 1.18048i
\(675\) 18911.0 + 56.7203i 1.07835 + 0.00323432i
\(676\) 2796.15 0.159089
\(677\) 27042.0 1.53517 0.767584 0.640948i \(-0.221459\pi\)
0.767584 + 0.640948i \(0.221459\pi\)
\(678\) −6985.73 + 12071.8i −0.395701 + 0.683795i
\(679\) 0 0
\(680\) 11223.1i 0.632921i
\(681\) 6163.16 10650.3i 0.346803 0.599295i
\(682\) 16457.2i 0.924017i
\(683\) 13390.9i 0.750203i 0.926984 + 0.375101i \(0.122392\pi\)
−0.926984 + 0.375101i \(0.877608\pi\)
\(684\) −1074.69 + 617.609i −0.0600756 + 0.0345247i
\(685\) 8041.69i 0.448551i
\(686\) 0 0
\(687\) −19408.2 11231.2i −1.07783 0.623724i
\(688\) 9700.14 0.537521
\(689\) −2016.40 −0.111493
\(690\) −6016.01 + 10396.0i −0.331921 + 0.573579i
\(691\) 30989.1i 1.70605i −0.521870 0.853025i \(-0.674765\pi\)
0.521870 0.853025i \(-0.325235\pi\)
\(692\) −5164.56 −0.283710
\(693\) 0 0
\(694\) 6777.28 0.370694
\(695\) 19610.1i 1.07029i
\(696\) −4270.43 + 7379.55i −0.232572 + 0.401898i
\(697\) 10702.5 0.581613
\(698\) −15608.1 −0.846383
\(699\) 25067.3 + 14506.0i 1.35641 + 0.784933i
\(700\) 0 0
\(701\) 2892.67i 0.155855i −0.996959 0.0779277i \(-0.975170\pi\)
0.996959 0.0779277i \(-0.0248303\pi\)
\(702\) −2689.23 8.06587i −0.144585 0.000433656i
\(703\) 8218.36i 0.440912i
\(704\) 20151.0i 1.07879i
\(705\) −7330.33 + 12667.2i −0.391597 + 0.676703i
\(706\) 13755.5i 0.733277i
\(707\) 0 0
\(708\) 329.089 568.685i 0.0174688 0.0301871i
\(709\) 15930.4 0.843833 0.421917 0.906635i \(-0.361357\pi\)
0.421917 + 0.906635i \(0.361357\pi\)
\(710\) −5226.91 −0.276285
\(711\) 14318.4 + 24915.1i 0.755248 + 1.31419i
\(712\) 36240.5i 1.90754i
\(713\) 9903.30 0.520171
\(714\) 0 0
\(715\) −4250.81 −0.222337
\(716\) 3652.89i 0.190663i
\(717\) 21064.5 + 12189.7i 1.09716 + 0.634911i
\(718\) −4817.66 −0.250409
\(719\) 11877.7 0.616085 0.308042 0.951373i \(-0.400326\pi\)
0.308042 + 0.951373i \(0.400326\pi\)
\(720\) −11244.0 19565.4i −0.581997 1.01272i
\(721\) 0 0
\(722\) 14546.6i 0.749819i
\(723\) 9850.20 + 5700.15i 0.506684 + 0.293210i
\(724\) 1966.78i 0.100960i
\(725\) 9186.35i 0.470583i
\(726\) −741.422 429.049i −0.0379019 0.0219332i
\(727\) 16795.8i 0.856839i 0.903580 + 0.428419i \(0.140929\pi\)
−0.903580 + 0.428419i \(0.859071\pi\)
\(728\) 0 0
\(729\) 19682.6 + 118.070i 0.999982 + 0.00599859i
\(730\) 9407.04 0.476945
\(731\) 5410.05 0.273732
\(732\) −2263.30 1309.73i −0.114281 0.0661327i
\(733\) 25459.3i 1.28289i −0.767167 0.641447i \(-0.778334\pi\)
0.767167 0.641447i \(-0.221666\pi\)
\(734\) 5007.02 0.251788
\(735\) 0 0
\(736\) −3239.57 −0.162245
\(737\) 36240.4i 1.81131i
\(738\) −22415.1 + 12881.7i −1.11804 + 0.642522i
\(739\) −18639.0 −0.927801 −0.463901 0.885887i \(-0.653551\pi\)
−0.463901 + 0.885887i \(0.653551\pi\)
\(740\) 4916.39 0.244230
\(741\) −678.099 + 1171.79i −0.0336175 + 0.0580930i
\(742\) 0 0
\(743\) 14043.3i 0.693401i 0.937976 + 0.346700i \(0.112698\pi\)
−0.937976 + 0.346700i \(0.887302\pi\)
\(744\) −11195.8 + 19346.9i −0.551689 + 0.953351i
\(745\) 37412.8i 1.83986i
\(746\) 20031.9i 0.983137i
\(747\) −8085.92 14070.1i −0.396049 0.689155i
\(748\) 1343.87i 0.0656907i
\(749\) 0 0
\(750\) 1837.00 + 1063.04i 0.0894370 + 0.0517557i
\(751\) 16230.3 0.788616 0.394308 0.918978i \(-0.370984\pi\)
0.394308 + 0.918978i \(0.370984\pi\)
\(752\) 9061.17 0.439397
\(753\) 5831.59 10077.3i 0.282224 0.487700i
\(754\) 1306.34i 0.0630956i
\(755\) −15754.7 −0.759433
\(756\) 0 0
\(757\) −33345.7 −1.60102 −0.800508 0.599322i \(-0.795437\pi\)
−0.800508 + 0.599322i \(0.795437\pi\)
\(758\) 9630.72i 0.461482i
\(759\) −5135.30 + 8874.10i −0.245586 + 0.424387i
\(760\) −13648.4 −0.651420
\(761\) −10788.0 −0.513884 −0.256942 0.966427i \(-0.582715\pi\)
−0.256942 + 0.966427i \(0.582715\pi\)
\(762\) −19151.6 11082.7i −0.910486 0.526884i
\(763\) 0 0
\(764\) 4799.87i 0.227295i
\(765\) −6271.09 10912.2i −0.296381 0.515726i
\(766\) 18353.7i 0.865725i
\(767\) 717.650i 0.0337847i
\(768\) 5071.61 8764.04i 0.238289 0.411777i
\(769\) 35799.6i 1.67876i −0.543543 0.839381i \(-0.682918\pi\)
0.543543 0.839381i \(-0.317082\pi\)
\(770\) 0 0
\(771\) 2892.94 4999.17i 0.135132 0.233516i
\(772\) −168.996 −0.00787862
\(773\) 36612.6 1.70358 0.851788 0.523887i \(-0.175519\pi\)
0.851788 + 0.523887i \(0.175519\pi\)
\(774\) −11330.8 + 6511.64i −0.526196 + 0.302398i
\(775\) 24083.8i 1.11628i
\(776\) 7884.22 0.364725
\(777\) 0 0
\(778\) −18443.3 −0.849904
\(779\) 13015.2i 0.598612i
\(780\) 700.991 + 405.652i 0.0321789 + 0.0186214i
\(781\) −4461.72 −0.204421
\(782\) 4147.56 0.189663
\(783\) 28.6773 9561.27i 0.00130887 0.436388i
\(784\) 0 0
\(785\) 2675.45i 0.121644i
\(786\) −7312.09 4231.39i −0.331824 0.192021i
\(787\)