Properties

Label 108.5.k.a.29.5
Level 108
Weight 5
Character 108.29
Analytic conductor 11.164
Analytic rank 0
Dimension 72
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 108.k (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1639560131\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(12\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 29.5
Character \(\chi\) \(=\) 108.29
Dual form 108.5.k.a.41.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.24301 + 8.71602i) q^{3} +(-14.1660 - 16.8824i) q^{5} +(35.7790 - 13.0225i) q^{7} +(-70.9378 - 39.1002i) q^{9} +O(q^{10})\) \(q+(-2.24301 + 8.71602i) q^{3} +(-14.1660 - 16.8824i) q^{5} +(35.7790 - 13.0225i) q^{7} +(-70.9378 - 39.1002i) q^{9} +(-102.369 + 121.998i) q^{11} +(-49.7378 - 282.077i) q^{13} +(178.921 - 85.6037i) q^{15} +(492.251 - 284.201i) q^{17} +(135.673 - 234.992i) q^{19} +(33.2517 + 341.060i) q^{21} +(31.0578 - 85.3307i) q^{23} +(24.1910 - 137.194i) q^{25} +(499.912 - 530.593i) q^{27} +(-438.837 - 77.3788i) q^{29} +(1185.32 + 431.421i) q^{31} +(-833.724 - 1165.89i) q^{33} +(-726.696 - 419.558i) q^{35} +(-522.756 - 905.440i) q^{37} +(2570.15 + 199.185i) q^{39} +(-2177.54 + 383.960i) q^{41} +(-2656.90 - 2229.41i) q^{43} +(344.801 + 1751.49i) q^{45} +(-224.867 - 617.817i) q^{47} +(-728.720 + 611.469i) q^{49} +(1372.98 + 4927.94i) q^{51} +4302.32i q^{53} +3509.77 q^{55} +(1743.88 + 1709.61i) q^{57} +(-1523.19 - 1815.27i) q^{59} +(2634.33 - 958.816i) q^{61} +(-3047.27 - 475.177i) q^{63} +(-4057.54 + 4835.59i) q^{65} +(-672.010 - 3811.16i) q^{67} +(674.081 + 462.098i) q^{69} +(-2218.83 + 1281.04i) q^{71} +(2217.70 - 3841.17i) q^{73} +(1141.53 + 518.577i) q^{75} +(-2073.93 + 5698.06i) q^{77} +(-985.019 + 5586.32i) q^{79} +(3503.36 + 5547.36i) q^{81} +(3307.71 + 583.239i) q^{83} +(-11771.2 - 4284.37i) q^{85} +(1658.75 - 3651.35i) q^{87} +(-2394.32 - 1382.36i) q^{89} +(-5452.92 - 9444.73i) q^{91} +(-6418.95 + 9363.58i) q^{93} +(-5889.16 + 1038.42i) q^{95} +(5628.76 + 4723.09i) q^{97} +(12031.9 - 4651.65i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q + 9q^{5} - 102q^{9} + O(q^{10}) \) \( 72q + 9q^{5} - 102q^{9} + 18q^{11} - 225q^{15} - 282q^{21} - 1278q^{23} + 441q^{25} + 54q^{27} + 1854q^{29} - 1665q^{31} - 45q^{33} - 2673q^{35} + 6951q^{39} - 5472q^{41} + 1260q^{43} + 5553q^{45} + 5103q^{47} - 5904q^{49} + 1899q^{51} + 1107q^{57} - 10944q^{59} + 8352q^{61} - 11985q^{63} + 8757q^{65} + 378q^{67} + 5607q^{69} - 19764q^{71} + 6111q^{73} - 3453q^{75} - 5679q^{77} - 5652q^{79} - 20466q^{81} - 20061q^{83} + 26100q^{85} + 40545q^{87} + 15633q^{89} - 6039q^{91} + 40179q^{93} + 48024q^{95} - 37530q^{97} + 12177q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{1}{18}\right)\) \(1\)

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 0
\(3\) −2.24301 + 8.71602i −0.249223 + 0.968446i
\(4\) 0 0
\(5\) −14.1660 16.8824i −0.566639 0.675295i 0.404298 0.914627i \(-0.367516\pi\)
−0.970938 + 0.239333i \(0.923071\pi\)
\(6\) 0 0
\(7\) 35.7790 13.0225i 0.730184 0.265765i 0.0499412 0.998752i \(-0.484097\pi\)
0.680243 + 0.732987i \(0.261874\pi\)
\(8\) 0 0
\(9\) −70.9378 39.1002i −0.875776 0.482718i
\(10\) 0 0
\(11\) −102.369 + 121.998i −0.846021 + 1.00825i 0.153776 + 0.988106i \(0.450856\pi\)
−0.999797 + 0.0201426i \(0.993588\pi\)
\(12\) 0 0
\(13\) −49.7378 282.077i −0.294307 1.66910i −0.670008 0.742354i \(-0.733709\pi\)
0.375701 0.926741i \(-0.377402\pi\)
\(14\) 0 0
\(15\) 178.921 85.6037i 0.795206 0.380461i
\(16\) 0 0
\(17\) 492.251 284.201i 1.70329 0.983396i 0.760909 0.648858i \(-0.224753\pi\)
0.942382 0.334538i \(-0.108580\pi\)
\(18\) 0 0
\(19\) 135.673 234.992i 0.375825 0.650947i −0.614625 0.788819i \(-0.710693\pi\)
0.990450 + 0.137872i \(0.0440262\pi\)
\(20\) 0 0
\(21\) 33.2517 + 341.060i 0.0754007 + 0.773379i
\(22\) 0 0
\(23\) 31.0578 85.3307i 0.0587104 0.161306i −0.906870 0.421411i \(-0.861535\pi\)
0.965580 + 0.260105i \(0.0837573\pi\)
\(24\) 0 0
\(25\) 24.1910 137.194i 0.0387056 0.219511i
\(26\) 0 0
\(27\) 499.912 530.593i 0.685750 0.727837i
\(28\) 0 0
\(29\) −438.837 77.3788i −0.521804 0.0920081i −0.0934583 0.995623i \(-0.529792\pi\)
−0.428345 + 0.903615i \(0.640903\pi\)
\(30\) 0 0
\(31\) 1185.32 + 431.421i 1.23342 + 0.448929i 0.874768 0.484542i \(-0.161014\pi\)
0.358654 + 0.933471i \(0.383236\pi\)
\(32\) 0 0
\(33\) −833.724 1165.89i −0.765586 1.07060i
\(34\) 0 0
\(35\) −726.696 419.558i −0.593221 0.342496i
\(36\) 0 0
\(37\) −522.756 905.440i −0.381852 0.661388i 0.609475 0.792806i \(-0.291380\pi\)
−0.991327 + 0.131418i \(0.958047\pi\)
\(38\) 0 0
\(39\) 2570.15 + 199.185i 1.68978 + 0.130957i
\(40\) 0 0
\(41\) −2177.54 + 383.960i −1.29539 + 0.228412i −0.778501 0.627643i \(-0.784020\pi\)
−0.516885 + 0.856055i \(0.672909\pi\)
\(42\) 0 0
\(43\) −2656.90 2229.41i −1.43694 1.20574i −0.941463 0.337116i \(-0.890549\pi\)
−0.495478 0.868621i \(-0.665007\pi\)
\(44\) 0 0
\(45\) 344.801 + 1751.49i 0.170272 + 0.864934i
\(46\) 0 0
\(47\) −224.867 617.817i −0.101796 0.279682i 0.878331 0.478053i \(-0.158657\pi\)
−0.980127 + 0.198371i \(0.936435\pi\)
\(48\) 0 0
\(49\) −728.720 + 611.469i −0.303507 + 0.254673i
\(50\) 0 0
\(51\) 1372.98 + 4927.94i 0.527867 + 1.89463i
\(52\) 0 0
\(53\) 4302.32i 1.53162i 0.643067 + 0.765810i \(0.277662\pi\)
−0.643067 + 0.765810i \(0.722338\pi\)
\(54\) 0 0
\(55\) 3509.77 1.16025
\(56\) 0 0
\(57\) 1743.88 + 1709.61i 0.536743 + 0.526197i
\(58\) 0 0
\(59\) −1523.19 1815.27i −0.437573 0.521479i 0.501518 0.865147i \(-0.332775\pi\)
−0.939091 + 0.343668i \(0.888330\pi\)
\(60\) 0 0
\(61\) 2634.33 958.816i 0.707962 0.257677i 0.0371553 0.999310i \(-0.488170\pi\)
0.670806 + 0.741633i \(0.265948\pi\)
\(62\) 0 0
\(63\) −3047.27 475.177i −0.767767 0.119722i
\(64\) 0 0
\(65\) −4057.54 + 4835.59i −0.960365 + 1.14452i
\(66\) 0 0
\(67\) −672.010 3811.16i −0.149702 0.848999i −0.963471 0.267812i \(-0.913699\pi\)
0.813770 0.581187i \(-0.197412\pi\)
\(68\) 0 0
\(69\) 674.081 + 462.098i 0.141584 + 0.0970590i
\(70\) 0 0
\(71\) −2218.83 + 1281.04i −0.440157 + 0.254125i −0.703664 0.710533i \(-0.748454\pi\)
0.263507 + 0.964657i \(0.415121\pi\)
\(72\) 0 0
\(73\) 2217.70 3841.17i 0.416157 0.720806i −0.579392 0.815049i \(-0.696710\pi\)
0.995549 + 0.0942434i \(0.0300432\pi\)
\(74\) 0 0
\(75\) 1141.53 + 518.577i 0.202938 + 0.0921914i
\(76\) 0 0
\(77\) −2073.93 + 5698.06i −0.349793 + 0.961050i
\(78\) 0 0
\(79\) −985.019 + 5586.32i −0.157830 + 0.895100i 0.798322 + 0.602231i \(0.205721\pi\)
−0.956152 + 0.292870i \(0.905390\pi\)
\(80\) 0 0
\(81\) 3503.36 + 5547.36i 0.533967 + 0.845505i
\(82\) 0 0
\(83\) 3307.71 + 583.239i 0.480144 + 0.0846624i 0.408482 0.912767i \(-0.366058\pi\)
0.0716626 + 0.997429i \(0.477170\pi\)
\(84\) 0 0
\(85\) −11771.2 4284.37i −1.62923 0.592993i
\(86\) 0 0
\(87\) 1658.75 3651.35i 0.219150 0.482408i
\(88\) 0 0
\(89\) −2394.32 1382.36i −0.302275 0.174519i 0.341189 0.939995i \(-0.389170\pi\)
−0.643465 + 0.765476i \(0.722504\pi\)
\(90\) 0 0
\(91\) −5452.92 9444.73i −0.658485 1.14053i
\(92\) 0 0
\(93\) −6418.95 + 9363.58i −0.742161 + 1.08262i
\(94\) 0 0
\(95\) −5889.16 + 1038.42i −0.652538 + 0.115060i
\(96\) 0 0
\(97\) 5628.76 + 4723.09i 0.598231 + 0.501976i 0.890877 0.454245i \(-0.150091\pi\)
−0.292645 + 0.956221i \(0.594536\pi\)
\(98\) 0 0
\(99\) 12031.9 4651.65i 1.22762 0.474610i
\(100\) 0 0
\(101\) −3705.03 10179.5i −0.363203 0.997891i −0.977890 0.209120i \(-0.932940\pi\)
0.614687 0.788771i \(-0.289282\pi\)
\(102\) 0 0
\(103\) 12221.3 10254.9i 1.15198 0.966624i 0.152213 0.988348i \(-0.451360\pi\)
0.999764 + 0.0217238i \(0.00691543\pi\)
\(104\) 0 0
\(105\) 5286.86 5392.82i 0.479533 0.489145i
\(106\) 0 0
\(107\) 2421.06i 0.211465i 0.994395 + 0.105732i \(0.0337187\pi\)
−0.994395 + 0.105732i \(0.966281\pi\)
\(108\) 0 0
\(109\) 13754.8 1.15772 0.578859 0.815428i \(-0.303498\pi\)
0.578859 + 0.815428i \(0.303498\pi\)
\(110\) 0 0
\(111\) 9064.37 2525.44i 0.735685 0.204970i
\(112\) 0 0
\(113\) −7941.63 9464.47i −0.621946 0.741207i 0.359457 0.933162i \(-0.382962\pi\)
−0.981404 + 0.191955i \(0.938517\pi\)
\(114\) 0 0
\(115\) −1880.55 + 684.464i −0.142196 + 0.0517553i
\(116\) 0 0
\(117\) −7500.97 + 21954.7i −0.547956 + 1.60382i
\(118\) 0 0
\(119\) 13911.3 16578.8i 0.982364 1.17074i
\(120\) 0 0
\(121\) −1861.83 10558.9i −0.127165 0.721190i
\(122\) 0 0
\(123\) 1537.65 19840.7i 0.101636 1.31144i
\(124\) 0 0
\(125\) −14587.5 + 8422.08i −0.933598 + 0.539013i
\(126\) 0 0
\(127\) −8361.83 + 14483.1i −0.518434 + 0.897954i 0.481336 + 0.876536i \(0.340152\pi\)
−0.999771 + 0.0214185i \(0.993182\pi\)
\(128\) 0 0
\(129\) 25391.0 18157.0i 1.52581 1.09110i
\(130\) 0 0
\(131\) −730.630 + 2007.39i −0.0425750 + 0.116974i −0.959158 0.282870i \(-0.908713\pi\)
0.916583 + 0.399844i \(0.130936\pi\)
\(132\) 0 0
\(133\) 1794.05 10174.6i 0.101422 0.575192i
\(134\) 0 0
\(135\) −16039.4 923.310i −0.880078 0.0506617i
\(136\) 0 0
\(137\) 12532.9 + 2209.88i 0.667743 + 0.117741i 0.497236 0.867615i \(-0.334348\pi\)
0.170507 + 0.985356i \(0.445459\pi\)
\(138\) 0 0
\(139\) −11446.2 4166.09i −0.592425 0.215625i 0.0283707 0.999597i \(-0.490968\pi\)
−0.620796 + 0.783972i \(0.713190\pi\)
\(140\) 0 0
\(141\) 5889.28 574.177i 0.296227 0.0288807i
\(142\) 0 0
\(143\) 39504.4 + 22807.9i 1.93185 + 1.11536i
\(144\) 0 0
\(145\) 4910.22 + 8504.75i 0.233542 + 0.404507i
\(146\) 0 0
\(147\) −3695.05 7723.07i −0.170996 0.357400i
\(148\) 0 0
\(149\) −5612.04 + 989.554i −0.252783 + 0.0445725i −0.298604 0.954377i \(-0.596521\pi\)
0.0458206 + 0.998950i \(0.485410\pi\)
\(150\) 0 0
\(151\) 13097.9 + 10990.5i 0.574445 + 0.482017i 0.883118 0.469152i \(-0.155440\pi\)
−0.308672 + 0.951168i \(0.599885\pi\)
\(152\) 0 0
\(153\) −46031.6 + 913.534i −1.96640 + 0.0390249i
\(154\) 0 0
\(155\) −9507.81 26122.5i −0.395746 1.08730i
\(156\) 0 0
\(157\) −24837.2 + 20840.9i −1.00763 + 0.845505i −0.988024 0.154303i \(-0.950687\pi\)
−0.0196102 + 0.999808i \(0.506243\pi\)
\(158\) 0 0
\(159\) −37499.1 9650.13i −1.48329 0.381715i
\(160\) 0 0
\(161\) 3457.50i 0.133386i
\(162\) 0 0
\(163\) 35016.5 1.31794 0.658972 0.752167i \(-0.270991\pi\)
0.658972 + 0.752167i \(0.270991\pi\)
\(164\) 0 0
\(165\) −7872.43 + 30591.2i −0.289162 + 1.12364i
\(166\) 0 0
\(167\) 13360.2 + 15922.1i 0.479050 + 0.570910i 0.950398 0.311038i \(-0.100677\pi\)
−0.471347 + 0.881948i \(0.656232\pi\)
\(168\) 0 0
\(169\) −50255.1 + 18291.4i −1.75957 + 0.640431i
\(170\) 0 0
\(171\) −18812.6 + 11365.0i −0.643362 + 0.388667i
\(172\) 0 0
\(173\) 11971.0 14266.5i 0.399979 0.476677i −0.528034 0.849223i \(-0.677071\pi\)
0.928014 + 0.372546i \(0.121515\pi\)
\(174\) 0 0
\(175\) −921.079 5223.70i −0.0300760 0.170570i
\(176\) 0 0
\(177\) 19238.4 9204.50i 0.614077 0.293801i
\(178\) 0 0
\(179\) 21872.3 12628.0i 0.682634 0.394119i −0.118213 0.992988i \(-0.537717\pi\)
0.800847 + 0.598870i \(0.204383\pi\)
\(180\) 0 0
\(181\) 12185.2 21105.4i 0.371942 0.644223i −0.617922 0.786240i \(-0.712025\pi\)
0.989864 + 0.142016i \(0.0453585\pi\)
\(182\) 0 0
\(183\) 2448.25 + 25111.5i 0.0731060 + 0.749842i
\(184\) 0 0
\(185\) −7880.61 + 21651.8i −0.230259 + 0.632631i
\(186\) 0 0
\(187\) −15719.0 + 89147.0i −0.449513 + 2.54931i
\(188\) 0 0
\(189\) 10976.7 25494.2i 0.307290 0.713704i
\(190\) 0 0
\(191\) 11663.4 + 2056.58i 0.319712 + 0.0563739i 0.331201 0.943560i \(-0.392546\pi\)
−0.0114892 + 0.999934i \(0.503657\pi\)
\(192\) 0 0
\(193\) 11024.1 + 4012.45i 0.295957 + 0.107720i 0.485731 0.874108i \(-0.338553\pi\)
−0.189774 + 0.981828i \(0.560776\pi\)
\(194\) 0 0
\(195\) −33046.0 46211.9i −0.869060 1.21530i
\(196\) 0 0
\(197\) 17211.6 + 9937.10i 0.443494 + 0.256051i 0.705079 0.709129i \(-0.250912\pi\)
−0.261584 + 0.965181i \(0.584245\pi\)
\(198\) 0 0
\(199\) 3015.26 + 5222.58i 0.0761410 + 0.131880i 0.901582 0.432608i \(-0.142407\pi\)
−0.825441 + 0.564489i \(0.809073\pi\)
\(200\) 0 0
\(201\) 34725.4 + 2691.20i 0.859519 + 0.0666123i
\(202\) 0 0
\(203\) −16708.8 + 2946.21i −0.405465 + 0.0714944i
\(204\) 0 0
\(205\) 37329.2 + 31322.9i 0.888262 + 0.745340i
\(206\) 0 0
\(207\) −5539.62 + 4838.81i −0.129282 + 0.112927i
\(208\) 0 0
\(209\) 14780.0 + 40607.6i 0.338361 + 0.929639i
\(210\) 0 0
\(211\) −46442.0 + 38969.5i −1.04315 + 0.875305i −0.992357 0.123404i \(-0.960619\pi\)
−0.0507916 + 0.998709i \(0.516174\pi\)
\(212\) 0 0
\(213\) −6188.73 22212.7i −0.136409 0.489602i
\(214\) 0 0
\(215\) 76436.6i 1.65358i
\(216\) 0 0
\(217\) 48027.7 1.01993
\(218\) 0 0
\(219\) 28505.4 + 27945.3i 0.594346 + 0.582667i
\(220\) 0 0
\(221\) −104650. 124717.i −2.14267 2.55354i
\(222\) 0 0
\(223\) −33001.8 + 12011.7i −0.663633 + 0.241543i −0.651804 0.758387i \(-0.725988\pi\)
−0.0118291 + 0.999930i \(0.503765\pi\)
\(224\) 0 0
\(225\) −7080.37 + 8786.38i −0.139859 + 0.173558i
\(226\) 0 0
\(227\) 58153.6 69304.8i 1.12856 1.34497i 0.197415 0.980320i \(-0.436745\pi\)
0.931146 0.364647i \(-0.118810\pi\)
\(228\) 0 0
\(229\) −8477.62 48079.0i −0.161660 0.916820i −0.952442 0.304721i \(-0.901437\pi\)
0.790781 0.612099i \(-0.209674\pi\)
\(230\) 0 0
\(231\) −45012.6 30857.2i −0.843548 0.578272i
\(232\) 0 0
\(233\) 79883.9 46121.0i 1.47146 0.849546i 0.471971 0.881614i \(-0.343543\pi\)
0.999486 + 0.0320679i \(0.0102093\pi\)
\(234\) 0 0
\(235\) −7244.75 + 12548.3i −0.131186 + 0.227221i
\(236\) 0 0
\(237\) −46481.1 21115.6i −0.827522 0.375930i
\(238\) 0 0
\(239\) 11892.0 32673.0i 0.208189 0.571996i −0.791018 0.611792i \(-0.790449\pi\)
0.999208 + 0.0397967i \(0.0126710\pi\)
\(240\) 0 0
\(241\) −3822.86 + 21680.5i −0.0658194 + 0.373281i 0.934050 + 0.357141i \(0.116249\pi\)
−0.999870 + 0.0161391i \(0.994863\pi\)
\(242\) 0 0
\(243\) −56208.9 + 18092.5i −0.951903 + 0.306399i
\(244\) 0 0
\(245\) 20646.1 + 3640.46i 0.343958 + 0.0606491i
\(246\) 0 0
\(247\) −73033.9 26582.2i −1.19710 0.435709i
\(248\) 0 0
\(249\) −12502.7 + 27521.9i −0.201654 + 0.443894i
\(250\) 0 0
\(251\) 18993.5 + 10965.9i 0.301480 + 0.174060i 0.643108 0.765776i \(-0.277645\pi\)
−0.341628 + 0.939835i \(0.610978\pi\)
\(252\) 0 0
\(253\) 7230.83 + 12524.2i 0.112966 + 0.195663i
\(254\) 0 0
\(255\) 63745.6 92988.2i 0.980324 1.43004i
\(256\) 0 0
\(257\) −3220.03 + 567.778i −0.0487522 + 0.00859632i −0.197971 0.980208i \(-0.563435\pi\)
0.149219 + 0.988804i \(0.452324\pi\)
\(258\) 0 0
\(259\) −30494.8 25588.2i −0.454596 0.381452i
\(260\) 0 0
\(261\) 28104.6 + 22647.7i 0.412569 + 0.332462i
\(262\) 0 0
\(263\) −8965.93 24633.7i −0.129624 0.356138i 0.857855 0.513892i \(-0.171797\pi\)
−0.987478 + 0.157754i \(0.949575\pi\)
\(264\) 0 0
\(265\) 72633.3 60946.6i 1.03429 0.867876i
\(266\) 0 0
\(267\) 17419.2 17768.3i 0.244346 0.249243i
\(268\) 0 0
\(269\) 107301.i 1.48286i 0.671030 + 0.741430i \(0.265852\pi\)
−0.671030 + 0.741430i \(0.734148\pi\)
\(270\) 0 0
\(271\) 17327.7 0.235940 0.117970 0.993017i \(-0.462361\pi\)
0.117970 + 0.993017i \(0.462361\pi\)
\(272\) 0 0
\(273\) 94551.3 26343.1i 1.26865 0.353461i
\(274\) 0 0
\(275\) 14261.0 + 16995.6i 0.188575 + 0.224735i
\(276\) 0 0
\(277\) 95578.4 34787.7i 1.24566 0.453384i 0.366729 0.930328i \(-0.380478\pi\)
0.878934 + 0.476944i \(0.158256\pi\)
\(278\) 0 0
\(279\) −67215.3 76950.2i −0.863495 0.988556i
\(280\) 0 0
\(281\) 53939.1 64282.1i 0.683111 0.814100i −0.307393 0.951583i \(-0.599457\pi\)
0.990504 + 0.137483i \(0.0439012\pi\)
\(282\) 0 0
\(283\) 11342.7 + 64327.8i 0.141626 + 0.803203i 0.970014 + 0.243048i \(0.0781474\pi\)
−0.828388 + 0.560155i \(0.810742\pi\)
\(284\) 0 0
\(285\) 4158.56 53659.2i 0.0511980 0.660624i
\(286\) 0 0
\(287\) −72910.3 + 42094.8i −0.885166 + 0.511051i
\(288\) 0 0
\(289\) 119780. 207466.i 1.43414 2.48399i
\(290\) 0 0
\(291\) −53791.9 + 38466.4i −0.635229 + 0.454251i
\(292\) 0 0
\(293\) −58005.3 + 159368.i −0.675667 + 1.85638i −0.191250 + 0.981541i \(0.561254\pi\)
−0.484417 + 0.874837i \(0.660968\pi\)
\(294\) 0 0
\(295\) −9068.52 + 51430.1i −0.104206 + 0.590981i
\(296\) 0 0
\(297\) 13556.2 + 115304.i 0.153682 + 1.30717i
\(298\) 0 0
\(299\) −25614.6 4516.54i −0.286513 0.0505200i
\(300\) 0 0
\(301\) −124094. 45166.5i −1.36967 0.498521i
\(302\) 0 0
\(303\) 97035.0 9460.45i 1.05692 0.103045i
\(304\) 0 0
\(305\) −53504.9 30891.1i −0.575167 0.332073i
\(306\) 0 0
\(307\) 25634.2 + 44399.7i 0.271984 + 0.471090i 0.969370 0.245606i \(-0.0789870\pi\)
−0.697386 + 0.716696i \(0.745654\pi\)
\(308\) 0 0
\(309\) 61969.5 + 129523.i 0.649024 + 1.35653i
\(310\) 0 0
\(311\) 64464.1 11366.8i 0.666495 0.117521i 0.169844 0.985471i \(-0.445674\pi\)
0.496652 + 0.867950i \(0.334563\pi\)
\(312\) 0 0
\(313\) −52415.3 43981.7i −0.535019 0.448935i 0.334811 0.942285i \(-0.391327\pi\)
−0.869830 + 0.493351i \(0.835772\pi\)
\(314\) 0 0
\(315\) 35145.4 + 58176.4i 0.354199 + 0.586308i
\(316\) 0 0
\(317\) −43526.9 119589.i −0.433150 1.19007i −0.943868 0.330323i \(-0.892842\pi\)
0.510718 0.859749i \(-0.329380\pi\)
\(318\) 0 0
\(319\) 54363.1 45616.1i 0.534224 0.448267i
\(320\) 0 0
\(321\) −21102.0 5430.46i −0.204792 0.0527019i
\(322\) 0 0
\(323\) 154233.i 1.47834i
\(324\) 0 0
\(325\) −39902.5 −0.377775
\(326\) 0 0
\(327\) −30852.2 + 119887.i −0.288530 + 1.12119i
\(328\) 0 0
\(329\) −16091.0 19176.6i −0.148659 0.177165i
\(330\) 0 0
\(331\) −48971.0 + 17824.0i −0.446975 + 0.162685i −0.555694 0.831387i \(-0.687547\pi\)
0.108719 + 0.994073i \(0.465325\pi\)
\(332\) 0 0
\(333\) 1680.34 + 84669.8i 0.0151534 + 0.763554i
\(334\) 0 0
\(335\) −54821.7 + 65333.9i −0.488498 + 0.582169i
\(336\) 0 0
\(337\) −33649.8 190837.i −0.296293 1.68036i −0.661898 0.749594i \(-0.730249\pi\)
0.365605 0.930770i \(-0.380862\pi\)
\(338\) 0 0
\(339\) 100306. 47990.5i 0.872822 0.417596i
\(340\) 0 0
\(341\) −173972. + 100443.i −1.49613 + 0.863792i
\(342\) 0 0
\(343\) −63819.4 + 110538.i −0.542456 + 0.939561i
\(344\) 0 0
\(345\) −1747.71 17926.1i −0.0146836 0.150608i
\(346\) 0 0
\(347\) −71892.7 + 197524.i −0.597071 + 1.64044i 0.160008 + 0.987116i \(0.448848\pi\)
−0.757079 + 0.653324i \(0.773374\pi\)
\(348\) 0 0
\(349\) −9455.56 + 53625.2i −0.0776312 + 0.440269i 0.921074 + 0.389389i \(0.127314\pi\)
−0.998705 + 0.0508800i \(0.983797\pi\)
\(350\) 0 0
\(351\) −174533. 114623.i −1.41665 0.930374i
\(352\) 0 0
\(353\) −157085. 27698.4i −1.26062 0.222282i −0.496891 0.867813i \(-0.665525\pi\)
−0.763734 + 0.645531i \(0.776636\pi\)
\(354\) 0 0
\(355\) 53058.9 + 19311.9i 0.421019 + 0.153238i
\(356\) 0 0
\(357\) 113298. + 158437.i 0.888967 + 1.24314i
\(358\) 0 0
\(359\) 126427. + 72992.7i 0.980960 + 0.566358i 0.902560 0.430564i \(-0.141685\pi\)
0.0784002 + 0.996922i \(0.475019\pi\)
\(360\) 0 0
\(361\) 28346.3 + 49097.3i 0.217512 + 0.376741i
\(362\) 0 0
\(363\) 96208.0 + 7456.07i 0.730126 + 0.0565844i
\(364\) 0 0
\(365\) −96264.0 + 16973.9i −0.722567 + 0.127408i
\(366\) 0 0
\(367\) 90808.8 + 76197.6i 0.674211 + 0.565730i 0.914308 0.405019i \(-0.132735\pi\)
−0.240097 + 0.970749i \(0.577179\pi\)
\(368\) 0 0
\(369\) 169483. + 57905.0i 1.24473 + 0.425269i
\(370\) 0 0
\(371\) 56026.9 + 153933.i 0.407051 + 1.11836i
\(372\) 0 0
\(373\) −82341.3 + 69092.6i −0.591834 + 0.496608i −0.888809 0.458277i \(-0.848467\pi\)
0.296975 + 0.954885i \(0.404022\pi\)
\(374\) 0 0
\(375\) −40687.2 146035.i −0.289331 1.03847i
\(376\) 0 0
\(377\) 127634.i 0.898018i
\(378\) 0 0
\(379\) −184493. −1.28440 −0.642200 0.766537i \(-0.721978\pi\)
−0.642200 + 0.766537i \(0.721978\pi\)
\(380\) 0 0
\(381\) −107479. 105368.i −0.740415 0.725866i
\(382\) 0 0
\(383\) −141634. 168793.i −0.965540 1.15069i −0.988541 0.150950i \(-0.951767\pi\)
0.0230014 0.999735i \(-0.492678\pi\)
\(384\) 0 0
\(385\) 125576. 45705.9i 0.847198 0.308355i
\(386\) 0 0
\(387\) 101305. + 262035.i 0.676407 + 1.74959i
\(388\) 0 0
\(389\) −76519.9 + 91192.9i −0.505680 + 0.602645i −0.957133 0.289649i \(-0.906461\pi\)
0.451453 + 0.892295i \(0.350906\pi\)
\(390\) 0 0
\(391\) −8962.84 50830.8i −0.0586263 0.332486i
\(392\) 0 0
\(393\) −15857.6 10870.8i −0.102672 0.0703842i
\(394\) 0 0
\(395\) 108264. 62506.3i 0.693889 0.400617i
\(396\) 0 0
\(397\) −4558.39 + 7895.36i −0.0289221 + 0.0500946i −0.880124 0.474744i \(-0.842541\pi\)
0.851202 + 0.524838i \(0.175874\pi\)
\(398\) 0 0
\(399\) 84657.7 + 38458.6i 0.531766 + 0.241573i
\(400\) 0 0
\(401\) 38160.2 104844.i 0.237313 0.652013i −0.762673 0.646784i \(-0.776113\pi\)
0.999986 0.00522863i \(-0.00166433\pi\)
\(402\) 0 0
\(403\) 62738.8 355809.i 0.386301 2.19082i
\(404\) 0 0
\(405\) 44024.1 137729.i 0.268399 0.839682i
\(406\) 0 0
\(407\) 163976. + 28913.3i 0.989898 + 0.174546i
\(408\) 0 0
\(409\) 206181. + 75043.7i 1.23254 + 0.448609i 0.874468 0.485084i \(-0.161211\pi\)
0.358075 + 0.933693i \(0.383433\pi\)
\(410\) 0 0
\(411\) −47372.7 + 104280.i −0.280443 + 0.617329i
\(412\) 0 0
\(413\) −78137.6 45112.8i −0.458100 0.264484i
\(414\) 0 0
\(415\) −37010.6 64104.2i −0.214897 0.372212i
\(416\) 0 0
\(417\) 61985.7 90421.1i 0.356467 0.519993i
\(418\) 0 0
\(419\) 163579. 28843.3i 0.931749 0.164292i 0.312885 0.949791i \(-0.398704\pi\)
0.618864 + 0.785499i \(0.287593\pi\)
\(420\) 0 0
\(421\) −49836.8 41818.0i −0.281181 0.235939i 0.491279 0.871002i \(-0.336530\pi\)
−0.772460 + 0.635063i \(0.780974\pi\)
\(422\) 0 0
\(423\) −8205.16 + 52619.0i −0.0458571 + 0.294077i
\(424\) 0 0
\(425\) −27082.7 74409.1i −0.149939 0.411954i
\(426\) 0 0
\(427\) 81767.4 68611.0i 0.448461 0.376303i
\(428\) 0 0
\(429\) −287403. + 293163.i −1.56162 + 1.59292i
\(430\) 0 0
\(431\) 175223.i 0.943271i −0.881793 0.471636i \(-0.843664\pi\)
0.881793 0.471636i \(-0.156336\pi\)
\(432\) 0 0
\(433\) 23396.7 0.124790 0.0623950 0.998052i \(-0.480126\pi\)
0.0623950 + 0.998052i \(0.480126\pi\)
\(434\) 0 0
\(435\) −85141.2 + 23721.3i −0.449947 + 0.125361i
\(436\) 0 0
\(437\) −15838.3 18875.4i −0.0829366 0.0988400i
\(438\) 0 0
\(439\) −169001. + 61511.3i −0.876920 + 0.319173i −0.740966 0.671542i \(-0.765632\pi\)
−0.135954 + 0.990715i \(0.543410\pi\)
\(440\) 0 0
\(441\) 75602.4 14883.2i 0.388739 0.0765278i
\(442\) 0 0
\(443\) −92863.7 + 110671.i −0.473193 + 0.563930i −0.948861 0.315696i \(-0.897762\pi\)
0.475667 + 0.879625i \(0.342207\pi\)
\(444\) 0 0
\(445\) 10580.4 + 60004.3i 0.0534295 + 0.303014i
\(446\) 0 0
\(447\) 3962.87 51134.2i 0.0198333 0.255915i
\(448\) 0 0
\(449\) −199330. + 115083.i −0.988737 + 0.570848i −0.904896 0.425632i \(-0.860052\pi\)
−0.0838404 + 0.996479i \(0.526719\pi\)
\(450\) 0 0
\(451\) 176070. 304961.i 0.865628 1.49931i
\(452\) 0 0
\(453\) −125172. + 89510.1i −0.609972 + 0.436190i
\(454\) 0 0
\(455\) −82203.4 + 225852.i −0.397070 + 1.09094i
\(456\) 0 0
\(457\) 1722.66 9769.66i 0.00824833 0.0467786i −0.980406 0.196988i \(-0.936884\pi\)
0.988654 + 0.150210i \(0.0479949\pi\)
\(458\) 0 0
\(459\) 95286.7 403261.i 0.452280 1.91408i
\(460\) 0 0
\(461\) 226367. + 39914.6i 1.06515 + 0.187815i 0.678641 0.734470i \(-0.262569\pi\)
0.386511 + 0.922285i \(0.373680\pi\)
\(462\) 0 0
\(463\) 33865.3 + 12326.0i 0.157977 + 0.0574988i 0.419798 0.907618i \(-0.362101\pi\)
−0.261821 + 0.965116i \(0.584323\pi\)
\(464\) 0 0
\(465\) 249010. 24277.3i 1.15162 0.112278i
\(466\) 0 0
\(467\) −67234.9 38818.1i −0.308291 0.177992i 0.337871 0.941193i \(-0.390293\pi\)
−0.646161 + 0.763201i \(0.723627\pi\)
\(468\) 0 0
\(469\) −73674.7 127608.i −0.334944 0.580140i
\(470\) 0 0
\(471\) −125939. 263227.i −0.567701 1.18656i
\(472\) 0 0
\(473\) 543967. 95916.0i 2.43136 0.428715i
\(474\) 0 0
\(475\) −28957.5 24298.2i −0.128343 0.107693i
\(476\) 0 0
\(477\) 168221. 305197.i 0.739340 1.34136i
\(478\) 0 0
\(479\) −68424.0 187994.i −0.298221 0.819355i −0.994797 0.101872i \(-0.967517\pi\)
0.696577 0.717482i \(-0.254706\pi\)
\(480\) 0 0
\(481\) −229403. + 192492.i −0.991537 + 0.831999i
\(482\) 0 0
\(483\) 30135.6 + 7755.19i 0.129177 + 0.0332428i
\(484\) 0 0
\(485\) 161934.i 0.688422i
\(486\) 0 0
\(487\) 156064. 0.658027 0.329013 0.944325i \(-0.393284\pi\)
0.329013 + 0.944325i \(0.393284\pi\)
\(488\) 0 0
\(489\) −78542.1 + 305204.i −0.328462 + 1.27636i
\(490\) 0 0
\(491\) −128201. 152784.i −0.531775 0.633745i 0.431547 0.902090i \(-0.357968\pi\)
−0.963323 + 0.268345i \(0.913523\pi\)
\(492\) 0 0
\(493\) −238009. + 86628.2i −0.979264 + 0.356423i
\(494\) 0 0
\(495\) −248975. 137232.i −1.01612 0.560075i
\(496\) 0 0
\(497\) −62705.2 + 74729.1i −0.253858 + 0.302536i
\(498\) 0 0
\(499\) 82436.2 + 467519.i 0.331068 + 1.87758i 0.463059 + 0.886328i \(0.346752\pi\)
−0.131991 + 0.991251i \(0.542137\pi\)
\(500\) 0 0
\(501\) −168744. + 80734.6i −0.672286 + 0.321651i
\(502\) 0 0
\(503\) 390878. 225674.i 1.54492 0.891959i 0.546402 0.837523i \(-0.315997\pi\)
0.998517 0.0544361i \(-0.0173361\pi\)
\(504\) 0 0
\(505\) −119368. + 206752.i −0.468065 + 0.810713i
\(506\) 0 0
\(507\) −46705.2 479052.i −0.181698 1.86366i
\(508\) 0 0
\(509\) 28313.2 77789.8i 0.109283 0.300253i −0.872981 0.487754i \(-0.837816\pi\)
0.982264 + 0.187501i \(0.0600387\pi\)
\(510\) 0 0
\(511\) 29325.5 166313.i 0.112306 0.636921i
\(512\) 0 0
\(513\) −56860.9 189462.i −0.216062 0.719926i
\(514\) 0 0
\(515\) −346254. 61054.0i −1.30551 0.230197i
\(516\) 0 0
\(517\) 98391.8 + 35811.7i 0.368110 + 0.133981i
\(518\) 0 0
\(519\) 97495.6 + 136339.i 0.361952 + 0.506157i
\(520\) 0 0
\(521\) −184540. 106544.i −0.679852 0.392513i 0.119947 0.992780i \(-0.461727\pi\)
−0.799799 + 0.600267i \(0.795061\pi\)
\(522\) 0 0
\(523\) 182766. + 316561.i 0.668179 + 1.15732i 0.978413 + 0.206660i \(0.0662595\pi\)
−0.310233 + 0.950660i \(0.600407\pi\)
\(524\) 0 0
\(525\) 47595.8 + 3688.65i 0.172683 + 0.0133829i
\(526\) 0 0
\(527\) 706085. 124502.i 2.54235 0.448285i
\(528\) 0 0
\(529\) 208054. + 174578.i 0.743472 + 0.623847i
\(530\) 0 0
\(531\) 37074.6 + 188328.i 0.131488 + 0.667923i
\(532\) 0 0
\(533\) 216612. + 595138.i 0.762481 + 2.09490i
\(534\) 0 0
\(535\) 40873.3 34296.7i 0.142801 0.119824i
\(536\) 0 0
\(537\) 61005.8 + 218964.i 0.211555 + 0.759317i
\(538\) 0 0
\(539\) 151498.i 0.521469i
\(540\) 0 0
\(541\) −329733. −1.12660 −0.563298 0.826254i \(-0.690468\pi\)
−0.563298 + 0.826254i \(0.690468\pi\)
\(542\) 0 0
\(543\) 156623. + 153546.i 0.531199 + 0.520761i
\(544\) 0 0
\(545\) −194851. 232214.i −0.656008 0.781800i
\(546\) 0 0
\(547\) 432146. 157288.i 1.44429 0.525680i 0.503302 0.864111i \(-0.332118\pi\)
0.940991 + 0.338431i \(0.109896\pi\)
\(548\) 0 0
\(549\) −224363. 34986.2i −0.744401 0.116079i
\(550\) 0 0
\(551\) −77721.6 + 92625.0i −0.255999 + 0.305088i
\(552\) 0 0
\(553\) 37504.8 + 212700.i 0.122641 + 0.695534i
\(554\) 0 0
\(555\) −171041. 117253.i −0.555283 0.380660i
\(556\) 0 0
\(557\) 390948. 225714.i 1.26011 0.727524i 0.287014 0.957926i \(-0.407337\pi\)
0.973096 + 0.230402i \(0.0740041\pi\)
\(558\) 0 0
\(559\) −496716. + 860338.i −1.58959 + 2.75325i
\(560\) 0 0
\(561\) −741748. 336964.i −2.35684 1.07068i
\(562\) 0 0
\(563\) −160569. + 441159.i −0.506576 + 1.39180i 0.378172 + 0.925735i \(0.376553\pi\)
−0.884748 + 0.466070i \(0.845670\pi\)
\(564\) 0 0
\(565\) −47281.6 + 268147.i −0.148114 + 0.839994i
\(566\) 0 0
\(567\) 197587. + 152857.i 0.614600 + 0.475465i
\(568\) 0 0
\(569\) 153331. + 27036.4i 0.473592 + 0.0835071i 0.405350 0.914162i \(-0.367150\pi\)
0.0682426 + 0.997669i \(0.478261\pi\)
\(570\) 0 0
\(571\) 71327.1 + 25960.9i 0.218767 + 0.0796247i 0.449079 0.893492i \(-0.351752\pi\)
−0.230312 + 0.973117i \(0.573975\pi\)
\(572\) 0 0
\(573\) −44086.3 + 97045.6i −0.134275 + 0.295574i
\(574\) 0 0
\(575\) −10955.5 6325.19i −0.0331359 0.0191310i
\(576\) 0 0
\(577\) −216466. 374930.i −0.650186 1.12615i −0.983078 0.183190i \(-0.941358\pi\)
0.332892 0.942965i \(-0.391976\pi\)
\(578\) 0 0
\(579\) −59699.7 + 87086.4i −0.178080 + 0.259772i
\(580\) 0 0
\(581\) 125942. 22207.0i 0.373094 0.0657865i
\(582\) 0 0
\(583\) −524875. 440422.i −1.54425 1.29578i
\(584\) 0 0
\(585\) 476906. 184376.i 1.39354 0.538756i
\(586\) 0 0
\(587\) −42558.1 116928.i −0.123511 0.339344i 0.862492 0.506071i \(-0.168903\pi\)
−0.986003 + 0.166726i \(0.946680\pi\)
\(588\) 0 0
\(589\) 262196. 220008.i 0.755780 0.634174i
\(590\) 0 0
\(591\) −125218. + 127727.i −0.358501 + 0.365686i
\(592\) 0 0
\(593\) 257653.i 0.732699i 0.930477 + 0.366349i \(0.119393\pi\)
−0.930477 + 0.366349i \(0.880607\pi\)
\(594\) 0 0
\(595\) −476956. −1.34724
\(596\) 0 0
\(597\) −52283.4 + 14566.8i −0.146695 + 0.0408709i
\(598\) 0 0
\(599\) 194068. + 231281.i 0.540880 + 0.644595i 0.965385 0.260830i \(-0.0839963\pi\)
−0.424505 + 0.905426i \(0.639552\pi\)
\(600\) 0 0
\(601\) 224736. 81797.4i 0.622192 0.226459i −0.0116373 0.999932i \(-0.503704\pi\)
0.633829 + 0.773473i \(0.281482\pi\)
\(602\) 0 0
\(603\) −101346. + 296631.i −0.278722 + 0.815797i
\(604\) 0 0
\(605\) −151885. + 181010.i −0.414959 + 0.494529i
\(606\) 0 0
\(607\) 87821.0 + 498057.i 0.238353 + 1.35177i 0.835436 + 0.549588i \(0.185215\pi\)
−0.597083 + 0.802180i \(0.703674\pi\)
\(608\) 0 0
\(609\) 11798.7 152243.i 0.0318127 0.410489i
\(610\) 0 0
\(611\) −163088. + 94158.7i −0.436856 + 0.252219i
\(612\) 0 0
\(613\) −215234. + 372796.i −0.572783 + 0.992090i 0.423495 + 0.905898i \(0.360803\pi\)
−0.996279 + 0.0861913i \(0.972530\pi\)
\(614\) 0 0
\(615\) −356741. + 255104.i −0.943197 + 0.674478i
\(616\) 0 0
\(617\) −22270.7 + 61188.3i −0.0585010 + 0.160730i −0.965500 0.260402i \(-0.916145\pi\)
0.906999 + 0.421132i \(0.138367\pi\)
\(618\) 0 0
\(619\) 45353.3 257211.i 0.118366 0.671287i −0.866662 0.498895i \(-0.833739\pi\)
0.985028 0.172392i \(-0.0551497\pi\)
\(620\) 0 0
\(621\) −29749.7 59136.9i −0.0771436 0.153347i
\(622\) 0 0
\(623\) −103668. 18279.5i −0.267098 0.0470965i
\(624\) 0 0
\(625\) 267012. + 97184.5i 0.683551 + 0.248792i
\(626\) 0 0
\(627\) −387088. + 37739.2i −0.984633 + 0.0959970i
\(628\) 0 0
\(629\) −514655. 297136.i −1.30081 0.751024i
\(630\) 0 0
\(631\) 14823.3 + 25674.8i 0.0372295 + 0.0644834i 0.884040 0.467412i \(-0.154813\pi\)
−0.846810 + 0.531895i \(0.821480\pi\)
\(632\) 0 0
\(633\) −235489. 492198.i −0.587709 1.22838i
\(634\) 0 0
\(635\) 362963. 64000.1i 0.900149 0.158721i
\(636\) 0 0
\(637\) 208726. + 175142.i 0.514397 + 0.431630i
\(638\) 0 0
\(639\) 207488. 4117.77i 0.508149 0.0100846i
\(640\) 0 0
\(641\) −19746.3 54252.5i −0.0480584 0.132040i 0.913341 0.407195i \(-0.133493\pi\)
−0.961400 + 0.275155i \(0.911271\pi\)
\(642\) 0 0
\(643\) 414021. 347405.i 1.00138 0.840261i 0.0142090 0.999899i \(-0.495477\pi\)
0.987176 + 0.159638i \(0.0510326\pi\)
\(644\) 0 0
\(645\) −666222. 171448.i −1.60140 0.412109i
\(646\) 0 0
\(647\) 235395.i 0.562326i −0.959660 0.281163i \(-0.909280\pi\)
0.959660 0.281163i \(-0.0907202\pi\)
\(648\) 0 0
\(649\) 377386. 0.895976
\(650\) 0 0
\(651\) −107726. + 418610.i −0.254191 + 0.987752i
\(652\) 0 0
\(653\) 79303.1 + 94509.8i 0.185979 + 0.221641i 0.850976 0.525205i \(-0.176011\pi\)
−0.664997 + 0.746846i \(0.731567\pi\)
\(654\) 0 0
\(655\) 44239.6 16101.9i 0.103117 0.0375314i
\(656\) 0 0
\(657\) −307510. + 185772.i −0.712407 + 0.430378i
\(658\) 0 0
\(659\) 222560. 265236.i 0.512479 0.610749i −0.446306 0.894880i \(-0.647261\pi\)
0.958785 + 0.284132i \(0.0917053\pi\)
\(660\) 0 0
\(661\) −16127.3 91462.5i −0.0369113 0.209334i 0.960774 0.277332i \(-0.0894501\pi\)
−0.997685 + 0.0679976i \(0.978339\pi\)
\(662\) 0 0
\(663\) 1.32177e6 632391.i 3.00697 1.43866i
\(664\) 0 0
\(665\) −197185. + 113845.i −0.445894 + 0.257437i
\(666\) 0 0
\(667\) −20232.1 + 35043.0i −0.0454767 + 0.0787680i
\(668\) 0 0
\(669\) −30670.7 314587.i −0.0685285 0.702891i
\(670\) 0 0
\(671\) −152698. + 419535.i −0.339148 + 0.931801i
\(672\) 0 0
\(673\) 18591.2 105436.i 0.0410465 0.232786i −0.957382 0.288824i \(-0.906736\pi\)
0.998429 + 0.0560379i \(0.0178468\pi\)
\(674\) 0 0
\(675\) −60700.9 81420.5i −0.133226 0.178701i
\(676\) 0 0
\(677\) 410730. + 72422.8i 0.896147 + 0.158015i 0.602707 0.797963i \(-0.294089\pi\)
0.293440 + 0.955978i \(0.405200\pi\)
\(678\) 0 0
\(679\) 262898. + 95687.0i 0.570227 + 0.207545i
\(680\) 0 0
\(681\) 473623. + 662319.i 1.02126 + 1.42815i
\(682\) 0 0
\(683\) −31295.1 18068.2i −0.0670864 0.0387324i 0.466082 0.884742i \(-0.345665\pi\)
−0.533168 + 0.846009i \(0.678999\pi\)
\(684\) 0 0
\(685\) −140232. 242890.i −0.298860 0.517640i
\(686\) 0 0
\(687\) 438072. + 33950.4i 0.928180 + 0.0719335i
\(688\) 0 0
\(689\) 1.21359e6 213988.i 2.55642 0.450766i
\(690\) 0 0
\(691\) −293104. 245944.i −0.613855 0.515086i 0.282010 0.959411i \(-0.408999\pi\)
−0.895865 + 0.444326i \(0.853443\pi\)
\(692\) 0 0
\(693\) 369915. 323117.i 0.770257 0.672812i
\(694\) 0 0
\(695\) 91813.8 + 252256.i 0.190081 + 0.522243i
\(696\) 0 0
\(697\) −962777. + 807866.i −1.98180 + 1.66293i
\(698\) 0 0
\(699\) 222811. + 799719.i 0.456019 + 1.63675i
\(700\) 0 0
\(701\) 780717.i 1.58876i −0.607423 0.794379i \(-0.707797\pi\)
0.607423 0.794379i \(-0.292203\pi\)
\(702\) 0 0
\(703\) −283695. −0.574038
\(704\) 0 0
\(705\) −93121.0 91291.2i −0.187357 0.183675i
\(706\) 0 0
\(707\) −265125. 315963.i −0.530409 0.632117i
\(708\) 0 0
\(709\) 341740. 124383.i 0.679834 0.247439i 0.0210578 0.999778i \(-0.493297\pi\)
0.658776 + 0.752339i \(0.271074\pi\)
\(710\) 0 0
\(711\) 288301. 357767.i 0.570305 0.707720i
\(712\) 0 0
\(713\) 73626.8 87745.1i 0.144830 0.172601i
\(714\) 0 0
\(715\) −174568. 990025.i −0.341470 1.93657i
\(716\) 0 0
\(717\) 258104. + 176936.i 0.502061 + 0.344175i
\(718\) 0 0
\(719\) −437833. + 252783.i −0.846936 + 0.488979i −0.859616 0.510941i \(-0.829297\pi\)
0.0126796 + 0.999920i \(0.495964\pi\)
\(720\) 0 0
\(721\) 303723. 526063.i 0.584260 1.01197i
\(722\) 0 0
\(723\) −180393. 81949.6i −0.345098 0.156773i
\(724\) 0 0
\(725\) −21231.8 + 58334.0i −0.0403935 + 0.110980i
\(726\) 0 0
\(727\) 11474.5 65075.1i 0.0217102 0.123125i −0.972027 0.234871i \(-0.924533\pi\)
0.993737 + 0.111746i \(0.0356443\pi\)
\(728\) 0 0
\(729\) −31617.8 530500.i −0.0594945 0.998229i
\(730\) 0 0
\(731\) −1.94147e6 342333.i −3.63325 0.640639i
\(732\) 0 0
\(733\) −617502. 224752.i −1.14929 0.418308i −0.304031 0.952662i \(-0.598333\pi\)
−0.845261 + 0.534354i \(0.820555\pi\)
\(734\) 0 0
\(735\) −78039.6 + 171786.i −0.144458 + 0.317990i
\(736\) 0 0
\(737\) 533747. + 308159.i 0.982653 + 0.567335i
\(738\) 0 0
\(739\) 8202.93 + 14207.9i 0.0150204 + 0.0260160i 0.873438 0.486936i \(-0.161885\pi\)
−0.858418 + 0.512952i \(0.828552\pi\)
\(740\) 0 0
\(741\) 395506. 576941.i 0.720306 1.05074i
\(742\) 0 0
\(743\) −380166. + 67033.5i −0.688646 + 0.121427i −0.507011 0.861939i \(-0.669250\pi\)
−0.181634 + 0.983366i \(0.558139\pi\)
\(744\) 0 0
\(745\) 96206.1 + 80726.5i 0.173336 + 0.145447i
\(746\) 0 0
\(747\) −211837. 170706.i −0.379631 0.305920i
\(748\) 0 0
\(749\) 31528.3 + 86623.2i 0.0562000 + 0.154408i
\(750\) 0 0
\(751\) 252123. 211557.i 0.447026 0.375100i −0.391305 0.920261i \(-0.627976\pi\)
0.838331 + 0.545162i \(0.183532\pi\)
\(752\) 0 0
\(753\) −138182. + 140951.i −0.243703 + 0.248587i
\(754\) 0 0
\(755\) 376815.i 0.661050i
\(756\) 0 0
\(757\) 1.06844e6 1.86448 0.932240 0.361841i \(-0.117852\pi\)
0.932240 + 0.361841i \(0.117852\pi\)
\(758\) 0 0
\(759\) −125380. + 34932.3i −0.217642 + 0.0606377i
\(760\) 0 0
\(761\) −655835. 781594.i −1.13247 1.34962i −0.928800 0.370580i \(-0.879159\pi\)
−0.203666 0.979040i \(-0.565286\pi\)
\(762\) 0 0
\(763\) 492135. 179122.i 0.845347 0.307681i
\(764\) 0 0
\(765\) 667505. + 764181.i 1.14060 + 1.30579i
\(766\) 0 0
\(767\) −436285. + 519945.i −0.741617 + 0.883825i
\(768\) 0 0
\(769\) −24137.7 136892.i −0.0408172 0.231486i 0.957574 0.288188i \(-0.0930527\pi\)
−0.998391 + 0.0567019i \(0.981942\pi\)
\(770\) 0 0
\(771\) 2273.79 29339.4i 0.00382508 0.0493562i
\(772\) 0 0
\(773\) −615069. + 355110.i −1.02935 + 0.594298i −0.916800 0.399347i \(-0.869237\pi\)
−0.112555 + 0.993646i \(0.535903\pi\)
\(774\) 0 0
\(775\) 87862.5 152182.i 0.146285 0.253373i
\(776\) 0 0
\(777\) 291427. 208399.i 0.482711 0.345186i
\(778\) 0 0
\(779\) −205206. + 563798.i −0.338154 + 0.929071i
\(780\) 0 0