Properties

Label 160.6.n.b.127.4
Level $160$
Weight $6$
Character 160.127
Analytic conductor $25.661$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 160.n (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(25.6614111701\)
Analytic rank: \(0\)
Dimension: \(14\)
Relative dimension: \(7\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 4 x^{13} + 8 x^{12} - 4626 x^{11} + 149441 x^{10} - 2113414 x^{9} + 17958066 x^{8} - 97717112 x^{7} + 355171384 x^{6} - 910571904 x^{5} + 2428303248 x^{4} - 9166992192 x^{3} + 32237484304 x^{2} - 66916821408 x + 69451154208\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{31}\cdot 5^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 127.4
Root \(6.86993 - 6.86993i\) of defining polynomial
Character \(\chi\) \(=\) 160.127
Dual form 160.6.n.b.63.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.47740 + 1.47740i) q^{3} +(55.2474 + 8.52775i) q^{5} +(156.265 - 156.265i) q^{7} -238.635i q^{9} +O(q^{10})\) \(q+(1.47740 + 1.47740i) q^{3} +(55.2474 + 8.52775i) q^{5} +(156.265 - 156.265i) q^{7} -238.635i q^{9} -35.4820i q^{11} +(-247.384 + 247.384i) q^{13} +(69.0238 + 94.2216i) q^{15} +(-1193.47 - 1193.47i) q^{17} -1010.27 q^{19} +461.733 q^{21} +(2033.39 + 2033.39i) q^{23} +(2979.55 + 942.273i) q^{25} +(711.568 - 711.568i) q^{27} -2206.91i q^{29} -6179.11i q^{31} +(52.4213 - 52.4213i) q^{33} +(9965.84 - 7300.66i) q^{35} +(-9466.02 - 9466.02i) q^{37} -730.972 q^{39} -9004.04 q^{41} +(15902.9 + 15902.9i) q^{43} +(2035.02 - 13183.9i) q^{45} +(7193.64 - 7193.64i) q^{47} -32030.6i q^{49} -3526.47i q^{51} +(-12995.3 + 12995.3i) q^{53} +(302.582 - 1960.29i) q^{55} +(-1492.57 - 1492.57i) q^{57} +40515.4 q^{59} +29233.6 q^{61} +(-37290.3 - 37290.3i) q^{63} +(-15777.0 + 11557.7i) q^{65} +(18221.2 - 18221.2i) q^{67} +6008.26i q^{69} +26609.8i q^{71} +(36402.4 - 36402.4i) q^{73} +(3009.89 + 5794.12i) q^{75} +(-5544.61 - 5544.61i) q^{77} -5089.11 q^{79} -55885.7 q^{81} +(20395.0 + 20395.0i) q^{83} +(-55758.6 - 76113.8i) q^{85} +(3260.49 - 3260.49i) q^{87} +59348.0i q^{89} +77315.1i q^{91} +(9129.03 - 9129.03i) q^{93} +(-55814.6 - 8615.30i) q^{95} +(69542.4 + 69542.4i) q^{97} -8467.24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 10q^{3} + 42q^{5} + 66q^{7} + O(q^{10}) \) \( 14q + 10q^{3} + 42q^{5} + 66q^{7} - 414q^{13} + 278q^{15} + 1222q^{17} + 5672q^{19} + 5924q^{21} + 2902q^{23} - 4466q^{25} - 2168q^{27} - 2444q^{33} - 2618q^{35} - 1790q^{37} - 11076q^{39} + 11644q^{41} - 3982q^{43} + 14704q^{45} - 1278q^{47} + 5882q^{53} + 65608q^{55} - 14552q^{57} - 8504q^{59} + 20564q^{61} + 19422q^{63} + 40798q^{65} + 107926q^{67} - 16418q^{73} + 66586q^{75} - 13348q^{77} - 146544q^{79} + 173806q^{81} - 36398q^{83} - 66262q^{85} + 124384q^{87} - 306620q^{93} + 173768q^{95} - 60314q^{97} - 388628q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/160\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(97\) \(101\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(1\)

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
\(3\) 1.47740 + 1.47740i 0.0947754 + 0.0947754i 0.752905 0.658129i \(-0.228652\pi\)
−0.658129 + 0.752905i \(0.728652\pi\)
\(4\) 0 0
\(5\) 55.2474 + 8.52775i 0.988296 + 0.152549i
\(6\) 0 0
\(7\) 156.265 156.265i 1.20536 1.20536i 0.232848 0.972513i \(-0.425196\pi\)
0.972513 0.232848i \(-0.0748044\pi\)
\(8\) 0 0
\(9\) 238.635i 0.982035i
\(10\) 0 0
\(11\) 35.4820i 0.0884152i −0.999022 0.0442076i \(-0.985924\pi\)
0.999022 0.0442076i \(-0.0140763\pi\)
\(12\) 0 0
\(13\) −247.384 + 247.384i −0.405988 + 0.405988i −0.880337 0.474349i \(-0.842684\pi\)
0.474349 + 0.880337i \(0.342684\pi\)
\(14\) 0 0
\(15\) 69.0238 + 94.2216i 0.0792083 + 0.108124i
\(16\) 0 0
\(17\) −1193.47 1193.47i −1.00159 1.00159i −0.999999 0.00159016i \(-0.999494\pi\)
−0.00159016 0.999999i \(-0.500506\pi\)
\(18\) 0 0
\(19\) −1010.27 −0.642025 −0.321012 0.947075i \(-0.604023\pi\)
−0.321012 + 0.947075i \(0.604023\pi\)
\(20\) 0 0
\(21\) 461.733 0.228477
\(22\) 0 0
\(23\) 2033.39 + 2033.39i 0.801494 + 0.801494i 0.983329 0.181835i \(-0.0582036\pi\)
−0.181835 + 0.983329i \(0.558204\pi\)
\(24\) 0 0
\(25\) 2979.55 + 942.273i 0.953458 + 0.301527i
\(26\) 0 0
\(27\) 711.568 711.568i 0.187848 0.187848i
\(28\) 0 0
\(29\) 2206.91i 0.487291i −0.969864 0.243646i \(-0.921657\pi\)
0.969864 0.243646i \(-0.0783434\pi\)
\(30\) 0 0
\(31\) 6179.11i 1.15484i −0.816448 0.577419i \(-0.804060\pi\)
0.816448 0.577419i \(-0.195940\pi\)
\(32\) 0 0
\(33\) 52.4213 52.4213i 0.00837959 0.00837959i
\(34\) 0 0
\(35\) 9965.84 7300.66i 1.37513 1.00738i
\(36\) 0 0
\(37\) −9466.02 9466.02i −1.13674 1.13674i −0.989030 0.147715i \(-0.952808\pi\)
−0.147715 0.989030i \(-0.547192\pi\)
\(38\) 0 0
\(39\) −730.972 −0.0769554
\(40\) 0 0
\(41\) −9004.04 −0.836523 −0.418261 0.908327i \(-0.637360\pi\)
−0.418261 + 0.908327i \(0.637360\pi\)
\(42\) 0 0
\(43\) 15902.9 + 15902.9i 1.31161 + 1.31161i 0.920228 + 0.391383i \(0.128003\pi\)
0.391383 + 0.920228i \(0.371997\pi\)
\(44\) 0 0
\(45\) 2035.02 13183.9i 0.149809 0.970541i
\(46\) 0 0
\(47\) 7193.64 7193.64i 0.475011 0.475011i −0.428521 0.903532i \(-0.640965\pi\)
0.903532 + 0.428521i \(0.140965\pi\)
\(48\) 0 0
\(49\) 32030.6i 1.90579i
\(50\) 0 0
\(51\) 3526.47i 0.189852i
\(52\) 0 0
\(53\) −12995.3 + 12995.3i −0.635474 + 0.635474i −0.949436 0.313962i \(-0.898344\pi\)
0.313962 + 0.949436i \(0.398344\pi\)
\(54\) 0 0
\(55\) 302.582 1960.29i 0.0134877 0.0873804i
\(56\) 0 0
\(57\) −1492.57 1492.57i −0.0608482 0.0608482i
\(58\) 0 0
\(59\) 40515.4 1.51527 0.757636 0.652677i \(-0.226354\pi\)
0.757636 + 0.652677i \(0.226354\pi\)
\(60\) 0 0
\(61\) 29233.6 1.00591 0.502954 0.864313i \(-0.332247\pi\)
0.502954 + 0.864313i \(0.332247\pi\)
\(62\) 0 0
\(63\) −37290.3 37290.3i −1.18371 1.18371i
\(64\) 0 0
\(65\) −15777.0 + 11557.7i −0.463170 + 0.339303i
\(66\) 0 0
\(67\) 18221.2 18221.2i 0.495894 0.495894i −0.414263 0.910157i \(-0.635961\pi\)
0.910157 + 0.414263i \(0.135961\pi\)
\(68\) 0 0
\(69\) 6008.26i 0.151924i
\(70\) 0 0
\(71\) 26609.8i 0.626463i 0.949677 + 0.313232i \(0.101412\pi\)
−0.949677 + 0.313232i \(0.898588\pi\)
\(72\) 0 0
\(73\) 36402.4 36402.4i 0.799507 0.799507i −0.183511 0.983018i \(-0.558746\pi\)
0.983018 + 0.183511i \(0.0587462\pi\)
\(74\) 0 0
\(75\) 3009.89 + 5794.12i 0.0617870 + 0.118942i
\(76\) 0 0
\(77\) −5544.61 5544.61i −0.106572 0.106572i
\(78\) 0 0
\(79\) −5089.11 −0.0917432 −0.0458716 0.998947i \(-0.514607\pi\)
−0.0458716 + 0.998947i \(0.514607\pi\)
\(80\) 0 0
\(81\) −55885.7 −0.946428
\(82\) 0 0
\(83\) 20395.0 + 20395.0i 0.324958 + 0.324958i 0.850666 0.525707i \(-0.176199\pi\)
−0.525707 + 0.850666i \(0.676199\pi\)
\(84\) 0 0
\(85\) −55758.6 76113.8i −0.837075 1.14266i
\(86\) 0 0
\(87\) 3260.49 3260.49i 0.0461832 0.0461832i
\(88\) 0 0
\(89\) 59348.0i 0.794202i 0.917775 + 0.397101i \(0.129984\pi\)
−0.917775 + 0.397101i \(0.870016\pi\)
\(90\) 0 0
\(91\) 77315.1i 0.978725i
\(92\) 0 0
\(93\) 9129.03 9129.03i 0.109450 0.109450i
\(94\) 0 0
\(95\) −55814.6 8615.30i −0.634511 0.0979403i
\(96\) 0 0
\(97\) 69542.4 + 69542.4i 0.750447 + 0.750447i 0.974563 0.224115i \(-0.0719492\pi\)
−0.224115 + 0.974563i \(0.571949\pi\)
\(98\) 0 0
\(99\) −8467.24 −0.0868268
\(100\) 0 0
\(101\) 51962.3 0.506857 0.253428 0.967354i \(-0.418442\pi\)
0.253428 + 0.967354i \(0.418442\pi\)
\(102\) 0 0
\(103\) −95475.1 95475.1i −0.886742 0.886742i 0.107467 0.994209i \(-0.465726\pi\)
−0.994209 + 0.107467i \(0.965726\pi\)
\(104\) 0 0
\(105\) 25509.6 + 3937.55i 0.225803 + 0.0348540i
\(106\) 0 0
\(107\) 47628.0 47628.0i 0.402164 0.402164i −0.476831 0.878995i \(-0.658215\pi\)
0.878995 + 0.476831i \(0.158215\pi\)
\(108\) 0 0
\(109\) 207149.i 1.67000i 0.550249 + 0.835000i \(0.314533\pi\)
−0.550249 + 0.835000i \(0.685467\pi\)
\(110\) 0 0
\(111\) 27970.2i 0.215471i
\(112\) 0 0
\(113\) −69766.1 + 69766.1i −0.513983 + 0.513983i −0.915744 0.401762i \(-0.868398\pi\)
0.401762 + 0.915744i \(0.368398\pi\)
\(114\) 0 0
\(115\) 94999.2 + 129680.i 0.669846 + 0.914381i
\(116\) 0 0
\(117\) 59034.4 + 59034.4i 0.398695 + 0.398695i
\(118\) 0 0
\(119\) −372996. −2.41455
\(120\) 0 0
\(121\) 159792. 0.992183
\(122\) 0 0
\(123\) −13302.6 13302.6i −0.0792818 0.0792818i
\(124\) 0 0
\(125\) 156577. + 77467.0i 0.896301 + 0.443447i
\(126\) 0 0
\(127\) −211933. + 211933.i −1.16598 + 1.16598i −0.182831 + 0.983144i \(0.558526\pi\)
−0.983144 + 0.182831i \(0.941474\pi\)
\(128\) 0 0
\(129\) 46990.0i 0.248617i
\(130\) 0 0
\(131\) 231312.i 1.17766i 0.808258 + 0.588829i \(0.200411\pi\)
−0.808258 + 0.588829i \(0.799589\pi\)
\(132\) 0 0
\(133\) −157869. + 157869.i −0.773872 + 0.773872i
\(134\) 0 0
\(135\) 45380.4 33244.2i 0.214306 0.156994i
\(136\) 0 0
\(137\) −148753. 148753.i −0.677119 0.677119i 0.282228 0.959347i \(-0.408926\pi\)
−0.959347 + 0.282228i \(0.908926\pi\)
\(138\) 0 0
\(139\) −28622.8 −0.125653 −0.0628267 0.998024i \(-0.520012\pi\)
−0.0628267 + 0.998024i \(0.520012\pi\)
\(140\) 0 0
\(141\) 21255.8 0.0900388
\(142\) 0 0
\(143\) 8777.70 + 8777.70i 0.0358955 + 0.0358955i
\(144\) 0 0
\(145\) 18819.9 121926.i 0.0743358 0.481588i
\(146\) 0 0
\(147\) 47322.1 47322.1i 0.180622 0.180622i
\(148\) 0 0
\(149\) 168468.i 0.621658i −0.950466 0.310829i \(-0.899393\pi\)
0.950466 0.310829i \(-0.100607\pi\)
\(150\) 0 0
\(151\) 114484.i 0.408604i −0.978908 0.204302i \(-0.934508\pi\)
0.978908 0.204302i \(-0.0654924\pi\)
\(152\) 0 0
\(153\) −284803. + 284803.i −0.983596 + 0.983596i
\(154\) 0 0
\(155\) 52693.9 341380.i 0.176170 1.14132i
\(156\) 0 0
\(157\) −148793. 148793.i −0.481762 0.481762i 0.423932 0.905694i \(-0.360650\pi\)
−0.905694 + 0.423932i \(0.860650\pi\)
\(158\) 0 0
\(159\) −38398.7 −0.120455
\(160\) 0 0
\(161\) 635495. 1.93218
\(162\) 0 0
\(163\) −14195.8 14195.8i −0.0418496 0.0418496i 0.685872 0.727722i \(-0.259421\pi\)
−0.727722 + 0.685872i \(0.759421\pi\)
\(164\) 0 0
\(165\) 3343.17 2449.10i 0.00955981 0.00700321i
\(166\) 0 0
\(167\) 129380. 129380.i 0.358985 0.358985i −0.504453 0.863439i \(-0.668306\pi\)
0.863439 + 0.504453i \(0.168306\pi\)
\(168\) 0 0
\(169\) 248895.i 0.670347i
\(170\) 0 0
\(171\) 241084.i 0.630491i
\(172\) 0 0
\(173\) 152149. 152149.i 0.386505 0.386505i −0.486934 0.873439i \(-0.661885\pi\)
0.873439 + 0.486934i \(0.161885\pi\)
\(174\) 0 0
\(175\) 612845. 318356.i 1.51271 0.785811i
\(176\) 0 0
\(177\) 59857.6 + 59857.6i 0.143611 + 0.143611i
\(178\) 0 0
\(179\) −293286. −0.684161 −0.342081 0.939671i \(-0.611132\pi\)
−0.342081 + 0.939671i \(0.611132\pi\)
\(180\) 0 0
\(181\) −35244.3 −0.0799635 −0.0399818 0.999200i \(-0.512730\pi\)
−0.0399818 + 0.999200i \(0.512730\pi\)
\(182\) 0 0
\(183\) 43189.8 + 43189.8i 0.0953353 + 0.0953353i
\(184\) 0 0
\(185\) −442249. 603697.i −0.950031 1.29685i
\(186\) 0 0
\(187\) −42346.8 + 42346.8i −0.0885557 + 0.0885557i
\(188\) 0 0
\(189\) 222387.i 0.452850i
\(190\) 0 0
\(191\) 862350.i 1.71041i 0.518291 + 0.855204i \(0.326568\pi\)
−0.518291 + 0.855204i \(0.673432\pi\)
\(192\) 0 0
\(193\) −87253.9 + 87253.9i −0.168613 + 0.168613i −0.786370 0.617756i \(-0.788042\pi\)
0.617756 + 0.786370i \(0.288042\pi\)
\(194\) 0 0
\(195\) −40384.3 6233.55i −0.0760547 0.0117395i
\(196\) 0 0
\(197\) −113501. 113501.i −0.208369 0.208369i 0.595205 0.803574i \(-0.297071\pi\)
−0.803574 + 0.595205i \(0.797071\pi\)
\(198\) 0 0
\(199\) 497444. 0.890455 0.445227 0.895418i \(-0.353123\pi\)
0.445227 + 0.895418i \(0.353123\pi\)
\(200\) 0 0
\(201\) 53840.0 0.0939971
\(202\) 0 0
\(203\) −344863. 344863.i −0.587362 0.587362i
\(204\) 0 0
\(205\) −497450. 76784.2i −0.826732 0.127611i
\(206\) 0 0
\(207\) 485236. 485236.i 0.787096 0.787096i
\(208\) 0 0
\(209\) 35846.3i 0.0567648i
\(210\) 0 0
\(211\) 359007.i 0.555133i −0.960706 0.277566i \(-0.910472\pi\)
0.960706 0.277566i \(-0.0895278\pi\)
\(212\) 0 0
\(213\) −39313.4 + 39313.4i −0.0593733 + 0.0593733i
\(214\) 0 0
\(215\) 742978. + 1.01421e6i 1.09617 + 1.49634i
\(216\) 0 0
\(217\) −965579. 965579.i −1.39200 1.39200i
\(218\) 0 0
\(219\) 107562. 0.151547
\(220\) 0 0
\(221\) 590492. 0.813267
\(222\) 0 0
\(223\) −927233. 927233.i −1.24861 1.24861i −0.956334 0.292276i \(-0.905587\pi\)
−0.292276 0.956334i \(1.40559\pi\)
\(224\) 0 0
\(225\) 224859. 711025.i 0.296110 0.936329i
\(226\) 0 0
\(227\) 1.02849e6 1.02849e6i 1.32475 1.32475i 0.414871 0.909880i \(-0.363827\pi\)
0.909880 0.414871i \(-0.136173\pi\)
\(228\) 0 0
\(229\) 624395.i 0.786812i 0.919365 + 0.393406i \(0.128703\pi\)
−0.919365 + 0.393406i \(0.871297\pi\)
\(230\) 0 0
\(231\) 16383.2i 0.0202009i
\(232\) 0 0
\(233\) 73769.5 73769.5i 0.0890199 0.0890199i −0.661195 0.750214i \(-0.729950\pi\)
0.750214 + 0.661195i \(0.229950\pi\)
\(234\) 0 0
\(235\) 458776. 336084.i 0.541914 0.396989i
\(236\) 0 0
\(237\) −7518.66 7518.66i −0.00869500 0.00869500i
\(238\) 0 0
\(239\) 1.58693e6 1.79706 0.898529 0.438914i \(-0.144637\pi\)
0.898529 + 0.438914i \(0.144637\pi\)
\(240\) 0 0
\(241\) 217448. 0.241165 0.120582 0.992703i \(-0.461524\pi\)
0.120582 + 0.992703i \(0.461524\pi\)
\(242\) 0 0
\(243\) −255477. 255477.i −0.277546 0.277546i
\(244\) 0 0
\(245\) 273149. 1.76961e6i 0.290727 1.88349i
\(246\) 0 0
\(247\) 249924. 249924.i 0.260655 0.260655i
\(248\) 0 0
\(249\) 60263.1i 0.0615961i
\(250\) 0 0
\(251\) 1.84448e6i 1.84794i 0.382460 + 0.923972i \(0.375077\pi\)
−0.382460 + 0.923972i \(0.624923\pi\)
\(252\) 0 0
\(253\) 72148.7 72148.7i 0.0708643 0.0708643i
\(254\) 0 0
\(255\) 30072.9 194829.i 0.0289617 0.187630i
\(256\) 0 0
\(257\) 934464. + 934464.i 0.882531 + 0.882531i 0.993791 0.111261i \(-0.0354888\pi\)
−0.111261 + 0.993791i \(0.535489\pi\)
\(258\) 0 0
\(259\) −2.95842e6 −2.74038
\(260\) 0 0
\(261\) −526644. −0.478537
\(262\) 0 0
\(263\) 545731. + 545731.i 0.486508 + 0.486508i 0.907202 0.420695i \(-0.138214\pi\)
−0.420695 + 0.907202i \(0.638214\pi\)
\(264\) 0 0
\(265\) −828779. + 607137.i −0.724977 + 0.531095i
\(266\) 0 0
\(267\) −87680.8 + 87680.8i −0.0752708 + 0.0752708i
\(268\) 0 0
\(269\) 1.62710e6i 1.37099i 0.728078 + 0.685495i \(0.240414\pi\)
−0.728078 + 0.685495i \(0.759586\pi\)
\(270\) 0 0
\(271\) 344866.i 0.285251i 0.989777 + 0.142626i \(0.0455545\pi\)
−0.989777 + 0.142626i \(0.954446\pi\)
\(272\) 0 0
\(273\) −114225. + 114225.i −0.0927591 + 0.0927591i
\(274\) 0 0
\(275\) 33433.8 105721.i 0.0266596 0.0843001i
\(276\) 0 0
\(277\) −1.31320e6 1.31320e6i −1.02833 1.02833i −0.999587 0.0287441i \(-0.990849\pi\)
−0.0287441 0.999587i \(-0.509151\pi\)
\(278\) 0 0
\(279\) −1.47455e6 −1.13409
\(280\) 0 0
\(281\) 592433. 0.447583 0.223791 0.974637i \(-0.428157\pi\)
0.223791 + 0.974637i \(0.428157\pi\)
\(282\) 0 0
\(283\) −898854. 898854.i −0.667149 0.667149i 0.289906 0.957055i \(-0.406376\pi\)
−0.957055 + 0.289906i \(0.906376\pi\)
\(284\) 0 0
\(285\) −69732.4 95188.9i −0.0508537 0.0694183i
\(286\) 0 0
\(287\) −1.40702e6 + 1.40702e6i −1.00831 + 1.00831i
\(288\) 0 0
\(289\) 1.42889e6i 1.00636i
\(290\) 0 0
\(291\) 205484.i 0.142248i
\(292\) 0 0
\(293\) −1.69674e6 + 1.69674e6i −1.15464 + 1.15464i −0.169032 + 0.985611i \(0.554064\pi\)
−0.985611 + 0.169032i \(0.945936\pi\)
\(294\) 0 0
\(295\) 2.23837e6 + 345506.i 1.49754 + 0.231153i
\(296\) 0 0
\(297\) −25247.9 25247.9i −0.0166086 0.0166086i
\(298\) 0 0
\(299\) −1.00606e6 −0.650795
\(300\) 0 0
\(301\) 4.97014e6 3.16193
\(302\) 0 0
\(303\) 76769.3 + 76769.3i 0.0480375 + 0.0480375i
\(304\) 0 0
\(305\) 1.61508e6 + 249297.i 0.994135 + 0.153450i
\(306\) 0 0
\(307\) 149779. 149779.i 0.0906992 0.0906992i −0.660301 0.751001i \(-0.729571\pi\)
0.751001 + 0.660301i \(0.229571\pi\)
\(308\) 0 0
\(309\) 282110.i 0.168083i
\(310\) 0 0
\(311\) 384127.i 0.225203i 0.993640 + 0.112601i \(0.0359183\pi\)
−0.993640 + 0.112601i \(0.964082\pi\)
\(312\) 0 0
\(313\) −661386. + 661386.i −0.381588 + 0.381588i −0.871674 0.490086i \(-0.836965\pi\)
0.490086 + 0.871674i \(0.336965\pi\)
\(314\) 0 0
\(315\) −1.74219e6 2.37819e6i −0.989279 1.35043i
\(316\) 0 0
\(317\) 1.48199e6 + 1.48199e6i 0.828319 + 0.828319i 0.987284 0.158965i \(-0.0508159\pi\)
−0.158965 + 0.987284i \(0.550816\pi\)
\(318\) 0 0
\(319\) −78305.5 −0.0430840
\(320\) 0 0
\(321\) 140732. 0.0762305
\(322\) 0 0
\(323\) 1.20572e6 + 1.20572e6i 0.643045 + 0.643045i
\(324\) 0 0
\(325\) −970198. + 503991.i −0.509509 + 0.264676i
\(326\) 0 0
\(327\) −306042. + 306042.i −0.158275 + 0.158275i
\(328\) 0 0
\(329\) 2.24823e6i 1.14512i
\(330\) 0 0
\(331\) 1.76606e6i 0.886004i 0.896521 + 0.443002i \(0.146087\pi\)
−0.896521 + 0.443002i \(0.853913\pi\)
\(332\) 0 0
\(333\) −2.25892e6 + 2.25892e6i −1.11632 + 1.11632i
\(334\) 0 0
\(335\) 1.16206e6 851286.i 0.565738 0.414442i
\(336\) 0 0
\(337\) −239492. 239492.i −0.114872 0.114872i 0.647334 0.762206i \(-0.275884\pi\)
−0.762206 + 0.647334i \(0.775884\pi\)
\(338\) 0 0
\(339\) −206145. −0.0974258
\(340\) 0 0
\(341\) −219247. −0.102105
\(342\) 0 0
\(343\) −2.37892e6 2.37892e6i −1.09180 1.09180i
\(344\) 0 0
\(345\) −51237.0 + 331941.i −0.0231758 + 0.150146i
\(346\) 0 0
\(347\) 111547. 111547.i 0.0497316 0.0497316i −0.681804 0.731535i \(-0.738804\pi\)
0.731535 + 0.681804i \(0.238804\pi\)
\(348\) 0 0
\(349\) 726170.i 0.319135i 0.987187 + 0.159568i \(0.0510100\pi\)
−0.987187 + 0.159568i \(0.948990\pi\)
\(350\) 0 0
\(351\) 352061.i 0.152528i
\(352\) 0 0
\(353\) −254625. + 254625.i −0.108759 + 0.108759i −0.759392 0.650633i \(-0.774504\pi\)
0.650633 + 0.759392i \(0.274504\pi\)
\(354\) 0 0
\(355\) −226922. + 1.47012e6i −0.0955664 + 0.619131i
\(356\) 0 0
\(357\) −551065. 551065.i −0.228840 0.228840i
\(358\) 0 0
\(359\) −3.35115e6 −1.37233 −0.686163 0.727447i \(-0.740707\pi\)
−0.686163 + 0.727447i \(0.740707\pi\)
\(360\) 0 0
\(361\) −1.45546e6 −0.587804
\(362\) 0 0
\(363\) 236077. + 236077.i 0.0940345 + 0.0940345i
\(364\) 0 0
\(365\) 2.32157e6 1.70071e6i 0.912114 0.668186i
\(366\) 0 0
\(367\) −2.84683e6 + 2.84683e6i −1.10331 + 1.10331i −0.109299 + 0.994009i \(0.534861\pi\)
−0.994009 + 0.109299i \(0.965139\pi\)
\(368\) 0 0
\(369\) 2.14868e6i 0.821495i
\(370\) 0 0
\(371\) 4.06144e6i 1.53195i
\(372\) 0 0
\(373\) 450340. 450340.i 0.167598 0.167598i −0.618325 0.785923i \(-0.712188\pi\)
0.785923 + 0.618325i \(0.212188\pi\)
\(374\) 0 0
\(375\) 116878. + 345778.i 0.0429194 + 0.126975i
\(376\) 0 0
\(377\) 545954. + 545954.i 0.197835 + 0.197835i
\(378\) 0 0
\(379\) 3.33522e6 1.19269 0.596343 0.802729i \(-0.296620\pi\)
0.596343 + 0.802729i \(0.296620\pi\)
\(380\) 0 0
\(381\) −626221. −0.221012
\(382\) 0 0
\(383\) −1.03183e6 1.03183e6i −0.359427 0.359427i 0.504175 0.863602i \(-0.331797\pi\)
−0.863602 + 0.504175i \(0.831797\pi\)
\(384\) 0 0
\(385\) −259042. 353608.i −0.0890674 0.121582i
\(386\) 0 0
\(387\) 3.79498e6 3.79498e6i 1.28805 1.28805i
\(388\) 0 0
\(389\) 695763.i 0.233124i −0.993183 0.116562i \(-0.962813\pi\)
0.993183 0.116562i \(-0.0371874\pi\)
\(390\) 0 0
\(391\) 4.85358e6i 1.60554i
\(392\) 0 0
\(393\) −341740. + 341740.i −0.111613 + 0.111613i
\(394\) 0 0
\(395\) −281160. 43398.6i −0.0906694 0.0139953i
\(396\) 0 0
\(397\) 752665. + 752665.i 0.239677 + 0.239677i 0.816716 0.577040i \(-0.195792\pi\)
−0.577040 + 0.816716i \(0.695792\pi\)
\(398\) 0 0
\(399\) −466473. −0.146688
\(400\) 0 0
\(401\) 5.46256e6 1.69643 0.848214 0.529654i \(-0.177678\pi\)
0.848214 + 0.529654i \(0.177678\pi\)
\(402\) 0 0
\(403\) 1.52861e6 + 1.52861e6i 0.468851 + 0.468851i
\(404\) 0 0
\(405\) −3.08754e6 476579.i −0.935351 0.144377i
\(406\) 0 0
\(407\) −335874. + 335874.i −0.100506 + 0.100506i
\(408\) 0 0
\(409\) 2.57791e6i 0.762008i 0.924573 + 0.381004i \(0.124422\pi\)
−0.924573 + 0.381004i \(0.875578\pi\)
\(410\) 0 0
\(411\) 439537.i 0.128348i
\(412\) 0 0
\(413\) 6.33115e6 6.33115e6i 1.82645 1.82645i
\(414\) 0 0
\(415\) 952846. + 1.30069e6i 0.271583 + 0.370727i
\(416\) 0 0
\(417\) −42287.3 42287.3i −0.0119089 0.0119089i
\(418\) 0 0
\(419\) 1.48123e6 0.412181 0.206090 0.978533i \(-0.433926\pi\)
0.206090 + 0.978533i \(0.433926\pi\)
\(420\) 0 0
\(421\) −6.15274e6 −1.69186 −0.845928 0.533297i \(-0.820953\pi\)
−0.845928 + 0.533297i \(0.820953\pi\)
\(422\) 0 0
\(423\) −1.71665e6 1.71665e6i −0.466478 0.466478i
\(424\) 0 0
\(425\) −2.43144e6 4.68059e6i −0.652966 1.25698i
\(426\) 0 0
\(427\) 4.56820e6 4.56820e6i 1.21248 1.21248i
\(428\) 0 0
\(429\) 25936.4i 0.00680403i
\(430\) 0 0
\(431\) 3.08017e6i 0.798695i −0.916800 0.399348i \(-0.869237\pi\)
0.916800 0.399348i \(-0.130763\pi\)
\(432\) 0 0
\(433\) 1.51152e6 1.51152e6i 0.387430 0.387430i −0.486340 0.873770i \(-0.661668\pi\)
0.873770 + 0.486340i \(0.161668\pi\)
\(434\) 0 0
\(435\) 207938. 152329.i 0.0526879 0.0385975i
\(436\) 0 0
\(437\) −2.05426e6 2.05426e6i −0.514579 0.514579i
\(438\) 0 0
\(439\) 5.41400e6 1.34078 0.670389 0.742010i \(-0.266127\pi\)
0.670389 + 0.742010i \(0.266127\pi\)
\(440\) 0 0
\(441\) −7.64361e6 −1.87155
\(442\) 0 0
\(443\) 5.09102e6 + 5.09102e6i 1.23252 + 1.23252i 0.962991 + 0.269533i \(0.0868693\pi\)
0.269533 + 0.962991i \(0.413131\pi\)
\(444\) 0 0
\(445\) −506105. + 3.27882e6i −0.121155 + 0.784906i
\(446\) 0 0
\(447\) 248895. 248895.i 0.0589179 0.0589179i
\(448\) 0 0
\(449\) 3.85655e6i 0.902783i −0.892326 0.451392i \(-0.850928\pi\)
0.892326 0.451392i \(-0.149072\pi\)
\(450\) 0 0
\(451\) 319482.i 0.0739613i
\(452\) 0 0
\(453\) 169139. 169139.i 0.0387256 0.0387256i
\(454\) 0 0
\(455\) −659324. + 4.27146e6i −0.149304 + 0.967270i
\(456\) 0 0
\(457\) −5.72418e6 5.72418e6i −1.28210 1.28210i −0.939469 0.342634i \(-0.888681\pi\)
−0.342634 0.939469i \(-0.611319\pi\)
\(458\) 0 0
\(459\) −1.69847e6 −0.376293
\(460\) 0 0
\(461\) −1.28502e6 −0.281615 −0.140808 0.990037i \(-0.544970\pi\)
−0.140808 + 0.990037i \(0.544970\pi\)
\(462\) 0 0
\(463\) −3.79316e6 3.79316e6i −0.822334 0.822334i 0.164108 0.986442i \(-0.447525\pi\)
−0.986442 + 0.164108i \(0.947525\pi\)
\(464\) 0 0
\(465\) 582205. 426505.i 0.124866 0.0914728i
\(466\) 0 0
\(467\) 2.71510e6 2.71510e6i 0.576095 0.576095i −0.357730 0.933825i \(-0.616449\pi\)
0.933825 + 0.357730i \(0.116449\pi\)
\(468\) 0 0
\(469\) 5.69467e6i 1.19546i
\(470\) 0 0
\(471\) 439653.i 0.0913184i
\(472\) 0 0
\(473\) 564267. 564267.i 0.115966 0.115966i
\(474\) 0 0
\(475\) −3.01014e6 951946.i −0.612143 0.193588i
\(476\) 0 0
\(477\) 3.10113e6 + 3.10113e6i 0.624058 + 0.624058i
\(478\) 0 0
\(479\) 7.87712e6 1.56866 0.784329 0.620345i \(-0.213007\pi\)
0.784329 + 0.620345i \(0.213007\pi\)
\(480\) 0 0
\(481\) 4.68349e6 0.923010
\(482\) 0 0
\(483\) 938882. + 938882.i 0.183123 + 0.183123i
\(484\) 0 0
\(485\) 3.24900e6 + 4.43508e6i 0.627184 + 0.856144i
\(486\) 0 0
\(487\) −2.23639e6 + 2.23639e6i −0.427292 + 0.427292i −0.887705 0.460413i \(-0.847701\pi\)
0.460413 + 0.887705i \(0.347701\pi\)
\(488\) 0 0
\(489\) 41945.9i 0.00793263i
\(490\) 0 0
\(491\) 5.93940e6i 1.11183i 0.831239 + 0.555916i \(0.187632\pi\)
−0.831239 + 0.555916i \(0.812368\pi\)
\(492\) 0 0
\(493\) −2.63388e6 + 2.63388e6i −0.488066 + 0.488066i
\(494\) 0 0
\(495\) −467793. 72206.5i −0.0858106 0.0132454i
\(496\) 0 0
\(497\) 4.15818e6 + 4.15818e6i 0.755114 + 0.755114i
\(498\) 0 0
\(499\) −41191.0 −0.00740545 −0.00370272 0.999993i \(-0.501179\pi\)
−0.00370272 + 0.999993i \(0.501179\pi\)
\(500\) 0 0
\(501\) 382293. 0.0680460
\(502\) 0 0
\(503\) 1.52979e6 + 1.52979e6i 0.269596 + 0.269596i 0.828937 0.559342i \(-0.188946\pi\)
−0.559342 + 0.828937i \(0.688946\pi\)
\(504\) 0 0
\(505\) 2.87078e6 + 443122.i 0.500924 + 0.0773205i
\(506\) 0 0
\(507\) −367718. + 367718.i −0.0635324 + 0.0635324i
\(508\) 0 0
\(509\) 2.48052e6i 0.424374i −0.977229 0.212187i \(-0.931941\pi\)
0.977229 0.212187i \(-0.0680586\pi\)
\(510\) 0 0
\(511\) 1.13768e7i 1.92739i
\(512\) 0 0
\(513\) −718873. + 718873.i −0.120603 + 0.120603i
\(514\) 0 0
\(515\) −4.46057e6 6.08894e6i −0.741092 1.01163i
\(516\) 0 0
\(517\) −255245. 255245.i −0.0419982 0.0419982i
\(518\) 0 0
\(519\) 449572. 0.0732624
\(520\) 0 0
\(521\) −949964. −0.153325 −0.0766624 0.997057i \(-0.524426\pi\)
−0.0766624 + 0.997057i \(0.524426\pi\)
\(522\) 0 0
\(523\) 3.91973e6 + 3.91973e6i 0.626617 + 0.626617i 0.947215 0.320598i \(-0.103884\pi\)
−0.320598 + 0.947215i \(0.603884\pi\)
\(524\) 0 0
\(525\) 1.37576e6 + 435079.i 0.217843 + 0.0688921i
\(526\) 0 0
\(527\) −7.37458e6 + 7.37458e6i −1.15667 + 1.15667i
\(528\) 0 0
\(529\) 1.83298e6i 0.284786i
\(530\) 0 0
\(531\) 9.66839e6i 1.48805i
\(532\) 0 0
\(533\) 2.22746e6 2.22746e6i 0.339619 0.339619i
\(534\) 0 0
\(535\) 3.03749e6 2.22517e6i 0.458807 0.336107i
\(536\) 0 0
\(537\) −433301. 433301.i −0.0648416 0.0648416i
\(538\) 0 0
\(539\) −1.13651e6 −0.168501
\(540\) 0 0
\(541\) −7.07953e6 −1.03995 −0.519973 0.854182i \(-0.674058\pi\)
−0.519973 + 0.854182i \(0.674058\pi\)
\(542\) 0 0
\(543\) −52070.0 52070.0i −0.00757858 0.00757858i
\(544\) 0 0
\(545\) −1.76652e6 + 1.14444e7i −0.254757 + 1.65045i
\(546\) 0 0
\(547\) −8.01896e6 + 8.01896e6i −1.14591 + 1.14591i −0.158559 + 0.987350i \(0.550685\pi\)
−0.987350 + 0.158559i \(0.949315\pi\)
\(548\) 0 0
\(549\) 6.97616e6i 0.987837i
\(550\) 0 0
\(551\) 2.22956e6i 0.312853i
\(552\) 0 0
\(553\) −795250. + 795250.i −0.110584 + 0.110584i
\(554\) 0 0
\(555\) 238523. 1.54528e6i 0.0328699 0.212949i
\(556\) 0 0
\(557\) 687054. + 687054.i 0.0938324 + 0.0938324i 0.752465 0.658632i \(-0.228865\pi\)
−0.658632 + 0.752465i \(0.728865\pi\)
\(558\) 0 0
\(559\) −7.86825e6 −1.06500
\(560\) 0 0
\(561\) −125126. −0.0167858
\(562\) 0 0
\(563\) 7.17411e6 + 7.17411e6i 0.953888 + 0.953888i 0.998983 0.0450948i \(-0.0143590\pi\)
−0.0450948 + 0.998983i \(0.514359\pi\)
\(564\) 0 0
\(565\) −4.44935e6 + 3.25945e6i −0.586375 + 0.429559i
\(566\) 0 0
\(567\) −8.73298e6 + 8.73298e6i −1.14079 + 1.14079i
\(568\) 0 0
\(569\) 8.08487e6i 1.04687i −0.852066 0.523435i \(-0.824650\pi\)
0.852066 0.523435i \(-0.175350\pi\)
\(570\) 0 0
\(571\) 3.00555e6i 0.385774i −0.981221 0.192887i \(-0.938215\pi\)
0.981221 0.192887i \(-0.0617851\pi\)
\(572\) 0 0
\(573\) −1.27404e6 + 1.27404e6i −0.162105 + 0.162105i
\(574\) 0 0
\(575\) 4.14258e6 + 7.97459e6i 0.522518 + 1.00586i
\(576\) 0 0
\(577\) 4.07557e6 + 4.07557e6i 0.509622 + 0.509622i 0.914410 0.404788i \(-0.132655\pi\)
−0.404788 + 0.914410i \(0.632655\pi\)
\(578\) 0 0
\(579\) −257818. −0.0319608
\(580\) 0 0
\(581\) 6.37405e6 0.783384
\(582\) 0 0
\(583\) 461101. + 461101.i 0.0561855 + 0.0561855i
\(584\) 0 0
\(585\) 2.75807e6 + 3.76493e6i 0.333208 + 0.454849i
\(586\) 0 0
\(587\) 3.45341e6 3.45341e6i 0.413669 0.413669i −0.469346 0.883014i \(-0.655510\pi\)
0.883014 + 0.469346i \(0.155510\pi\)
\(588\) 0 0
\(589\) 6.24254e6i 0.741435i
\(590\) 0 0
\(591\) 335373.i 0.0394965i
\(592\) 0 0
\(593\) 4.96777e6 4.96777e6i 0.580129 0.580129i −0.354810 0.934939i \(-0.615454\pi\)
0.934939 + 0.354810i \(0.115454\pi\)
\(594\) 0 0
\(595\) −2.06071e7 3.18082e6i −2.38629 0.368338i
\(596\) 0 0
\(597\) 734926. + 734926.i 0.0843932 + 0.0843932i
\(598\) 0 0
\(599\) 8.61814e6 0.981401 0.490701 0.871328i \(-0.336741\pi\)
0.490701 + 0.871328i \(0.336741\pi\)
\(600\) 0 0
\(601\) −1.36092e7 −1.53690 −0.768451 0.639909i \(-0.778972\pi\)
−0.768451 + 0.639909i \(0.778972\pi\)
\(602\) 0 0
\(603\) −4.34820e6 4.34820e6i −0.486986 0.486986i
\(604\) 0 0
\(605\) 8.82810e6 + 1.36267e6i 0.980570 + 0.151357i
\(606\) 0 0
\(607\) 7.54202e6 7.54202e6i 0.830837 0.830837i −0.156794 0.987631i \(-0.550116\pi\)
0.987631 + 0.156794i \(0.0501159\pi\)
\(608\) 0 0
\(609\) 1.01900e6i 0.111335i
\(610\) 0 0
\(611\) 3.55918e6i 0.385698i
\(612\) 0 0
\(613\) −2.33571e6 + 2.33571e6i −0.251054 + 0.251054i −0.821403 0.570349i \(-0.806808\pi\)
0.570349 + 0.821403i \(0.306808\pi\)
\(614\) 0 0
\(615\) −621493. 848375.i −0.0662595 0.0904483i
\(616\) 0 0
\(617\) 9.52103e6 + 9.52103e6i 1.00686 + 1.00686i 0.999976 + 0.00688826i \(0.00219262\pi\)
0.00688826 + 0.999976i \(0.497807\pi\)
\(618\) 0 0
\(619\) −1.71115e7 −1.79499 −0.897494 0.441027i \(-0.854614\pi\)
−0.897494 + 0.441027i \(0.854614\pi\)
\(620\) 0 0
\(621\) 2.89379e6 0.301119
\(622\) 0 0
\(623\) 9.27402e6 + 9.27402e6i 0.957300 + 0.957300i
\(624\) 0 0
\(625\) 7.98987e6 + 5.61511e6i 0.818163 + 0.574987i
\(626\) 0 0
\(627\) −52959.4 + 52959.4i −0.00537990 + 0.00537990i
\(628\) 0 0
\(629\) 2.25948e7i 2.27710i
\(630\) 0 0
\(631\) 1.54863e7i 1.54837i −0.632958 0.774186i \(-0.718159\pi\)
0.632958 0.774186i \(-0.281841\pi\)
\(632\) 0 0
\(633\) 530398. 530398.i 0.0526129 0.0526129i
\(634\) 0 0
\(635\) −1.35161e7 + 9.90144e6i −1.33020 + 0.974460i
\(636\) 0 0
\(637\) 7.92387e6 + 7.92387e6i 0.773729 + 0.773729i
\(638\) 0 0
\(639\) 6.35001e6 0.615209
\(640\) 0 0
\(641\) −8.16308e6 −0.784709 −0.392355 0.919814i \(-0.628339\pi\)
−0.392355 + 0.919814i \(0.628339\pi\)
\(642\) 0 0
\(643\) −6.82289e6 6.82289e6i −0.650791 0.650791i 0.302393 0.953183i \(-0.402215\pi\)
−0.953183 + 0.302393i \(0.902215\pi\)
\(644\) 0 0
\(645\) −400719. + 2.59607e6i −0.0379263 + 0.245707i
\(646\) 0 0
\(647\) −1.04574e7 + 1.04574e7i −0.982113 + 0.982113i −0.999843 0.0177299i \(-0.994356\pi\)
0.0177299 + 0.999843i \(0.494356\pi\)
\(648\) 0 0
\(649\) 1.43757e6i 0.133973i
\(650\) 0 0
\(651\) 2.85310e6i 0.263854i
\(652\) 0 0
\(653\) 8.91308e6 8.91308e6i 0.817984 0.817984i −0.167831 0.985816i \(-0.553676\pi\)
0.985816 + 0.167831i \(0.0536764\pi\)
\(654\) 0 0
\(655\) −1.97257e6 + 1.27794e7i −0.179651 + 1.16387i
\(656\) 0 0
\(657\) −8.68686e6 8.68686e6i −0.785144 0.785144i
\(658\) 0 0
\(659\) 4.26560e6 0.382619 0.191310 0.981530i \(-0.438727\pi\)
0.191310 + 0.981530i \(0.438727\pi\)
\(660\) 0 0
\(661\) −5.64640e6 −0.502653 −0.251326 0.967902i \(-0.580867\pi\)
−0.251326 + 0.967902i \(0.580867\pi\)
\(662\) 0 0
\(663\) 872394. + 872394.i 0.0770777 + 0.0770777i
\(664\) 0 0
\(665\) −1.00682e7 + 7.37561e6i −0.882868 + 0.646761i
\(666\) 0 0
\(667\) 4.48749e6 4.48749e6i 0.390561 0.390561i
\(668\) 0 0
\(669\) 2.73979e6i 0.236675i
\(670\) 0 0
\(671\) 1.03727e6i 0.0889376i
\(672\) 0 0
\(673\) 6.79083e6 6.79083e6i 0.577943 0.577943i −0.356393 0.934336i \(-0.615994\pi\)
0.934336 + 0.356393i \(0.115994\pi\)
\(674\) 0 0
\(675\) 2.79065e6 1.44967e6i 0.235747 0.122464i
\(676\) 0 0
\(677\) −1.14580e7 1.14580e7i −0.960807 0.960807i 0.0384535 0.999260i \(-0.487757\pi\)
−0.999260 + 0.0384535i \(0.987757\pi\)
\(678\) 0 0
\(679\) 2.17341e7 1.80912
\(680\) 0 0
\(681\) 3.03898e6 0.251108
\(682\) 0 0
\(683\) −9.47517e6 9.47517e6i −0.777204 0.777204i 0.202150 0.979354i \(-0.435207\pi\)
−0.979354 + 0.202150i \(0.935207\pi\)
\(684\) 0 0
\(685\) −6.94970e6 9.48676e6i −0.565900 0.772488i
\(686\) 0 0
\(687\) −922483. + 922483.i −0.0745704 + 0.0745704i
\(688\) 0 0
\(689\) 6.42968e6i 0.515990i
\(690\) 0 0
\(691\) 2.19649e7i 1.74998i 0.484137 + 0.874992i \(0.339133\pi\)
−0.484137 + 0.874992i \(0.660867\pi\)
\(692\) 0 0
\(693\) −1.32314e6 + 1.32314e6i −0.104658 + 0.104658i
\(694\) 0 0
\(695\) −1.58133e6 244088.i −0.124183 0.0191683i
\(696\) 0 0
\(697\) 1.07461e7 + 1.07461e7i 0.837852 + 0.837852i
\(698\) 0 0
\(699\) 217975. 0.0168738
\(700\) 0 0
\(701\) −9.21992e6 −0.708651 −0.354325 0.935122i \(-0.615289\pi\)
−0.354325 + 0.935122i \(0.615289\pi\)
\(702\) 0 0
\(703\) 9.56320e6 + 9.56320e6i 0.729818 + 0.729818i
\(704\) 0 0
\(705\) 1.17433e6 + 181264.i 0.0889850 + 0.0137353i
\(706\) 0 0
\(707\) 8.11990e6 8.11990e6i 0.610945 0.610945i
\(708\) 0 0
\(709\) 2.13169e7i 1.59260i −0.604900 0.796301i \(-0.706787\pi\)
0.604900 0.796301i \(-0.293213\pi\)
\(710\) 0 0
\(711\) 1.21444e6i 0.0900951i
\(712\) 0 0
\(713\) 1.25645e7 1.25645e7i 0.925597 0.925597i
\(714\) 0 0
\(715\) 410091. + 559799.i 0.0299996 + 0.0409512i
\(716\) 0 0
\(717\) 2.34453e6 + 2.34453e6i 0.170317 + 0.170317i
\(718\) 0 0
\(719\) 5.27347e6 0.380430 0.190215 0.981742i \(-0.439082\pi\)
0.190215 + 0.981742i \(0.439082\pi\)
\(720\) 0 0
\(721\) −2.98389e7 −2.13769
\(722\) 0 0
\(723\) 321259. + 321259.i 0.0228565 + 0.0228565i
\(724\) 0 0
\(725\) 2.07951e6 6.57560e6i 0.146932 0.464612i
\(726\) 0 0
\(727\) 8.91293e6 8.91293e6i 0.625438 0.625438i −0.321479 0.946917i \(-0.604180\pi\)
0.946917 + 0.321479i \(0.104180\pi\)
\(728\) 0 0
\(729\) 1.28253e7i 0.893819i
\(730\) 0 0
\(731\) 3.79593e7i 2.62739i
\(732\) 0 0
\(733\) 3.62320e6 3.62320e6i 0.249076 0.249076i −0.571515 0.820591i \(-0.693644\pi\)
0.820591 + 0.571515i \(0.193644\pi\)
\(734\) 0 0
\(735\) 3.01798e6 2.21087e6i 0.206062 0.150954i
\(736\) 0 0
\(737\) −646524. 646524.i −0.0438446 0.0438446i
\(738\) 0 0
\(739\) 8.18176e6 0.551106 0.275553 0.961286i \(-0.411139\pi\)
0.275553 + 0.961286i \(0.411139\pi\)
\(740\) 0 0
\(741\) 738476. 0.0494073
\(742\) 0 0
\(743\) −1.12407e7 1.12407e7i −0.747004 0.747004i 0.226911 0.973915i \(-0.427137\pi\)
−0.973915 + 0.226911i \(0.927137\pi\)
\(744\) 0 0
\(745\) 1.43665e6 9.30742e6i 0.0948333 0.614382i
\(746\) 0 0
\(747\) 4.86694e6 4.86694e6i 0.319121 0.319121i
\(748\) 0 0
\(749\) 1.48852e7i 0.969506i
\(750\) 0 0
\(751\) 1.89630e7i 1.22689i −0.789736 0.613447i \(-0.789783\pi\)
0.789736 0.613447i \(-0.210217\pi\)
\(752\) 0 0
\(753\) −2.72503e6 + 2.72503e6i −0.175140 + 0.175140i
\(754\) 0 0
\(755\) 976291. 6.32495e6i 0.0623321 0.403822i
\(756\) 0 0
\(757\) 9.61677e6 + 9.61677e6i 0.609943 + 0.609943i 0.942931 0.332988i \(-0.108057\pi\)
−0.332988 + 0.942931i \(0.608057\pi\)
\(758\) 0 0
\(759\) 213185. 0.0134324
\(760\) 0 0
\(761\) 2.07945e7 1.30163 0.650814 0.759238i \(-0.274428\pi\)
0.650814 + 0.759238i \(0.274428\pi\)
\(762\) 0 0
\(763\) 3.23702e7 + 3.23702e7i 2.01295 + 2.01295i
\(764\) 0 0
\(765\) −1.81634e7 + 1.33059e7i −1.12213 + 0.822037i
\(766\) 0 0
\(767\) −1.00229e7 + 1.00229e7i −0.615183 + 0.615183i
\(768\) 0 0
\(769\) 1.39172e7i 0.848667i −0.905506 0.424334i \(-0.860508\pi\)
0.905506 0.424334i \(-0.139492\pi\)
\(770\) 0 0
\(771\) 2.76116e6i 0.167284i
\(772\) 0 0
\(773\) −3.19729e6 + 3.19729e6i −0.192457 + 0.192457i −0.796757 0.604300i \(-0.793453\pi\)
0.604300 + 0.796757i \(0.293453\pi\)
\(774\) 0 0
\(775\) 5.82240e6 1.84110e7i 0.348215 1.10109i
\(776\) 0 0
\(777\) −4.37077e6 4.37077e6i −0.259720 0.259720i
\(778\) 0 0
\(779\) 9.09648e6 0.537069
\(780\) 0 0
\(781\) 944170. 0.0553889
\(782\) 0 0
\(783\) −1.57036e6 1.57036e6i −0.0915368 0.0915368i
\(784\) 0 0
\(785\) −6.95154e6 9.48928e6i −0.402631 0.549616i
\(786\) 0 0
\(787\) −5.00799e6 + 5.00799e6i −0.288222 + 0.288222i −0.836377 0.548155i \(-0.815330\pi\)
0.548155 + 0.836377i \(0.315330\pi\)
\(788\) 0 0
\(789\) 1.61253e6i 0.0922179i
\(790\) 0 0
\(791\) 2.18040e7i 1.23907i
\(792\) 0 0
\(793\) −7.23194e6 + 7.23194e6i −0.408387 + 0.408387i