Properties

Label 160.6.n.b.63.5
Level $160$
Weight $6$
Character 160.63
Analytic conductor $25.661$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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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 63.5
Root \(4.57273 + 4.57273i\) of defining polynomial
Character \(\chi\) \(=\) 160.63
Dual form 160.6.n.b.127.5

$q$-expansion

\(f(q)\) \(=\) \(q+(9.28112 - 9.28112i) q^{3} +(42.6946 + 36.0856i) q^{5} +(-105.819 - 105.819i) q^{7} +70.7216i q^{9} +O(q^{10})\) \(q+(9.28112 - 9.28112i) q^{3} +(42.6946 + 36.0856i) q^{5} +(-105.819 - 105.819i) q^{7} +70.7216i q^{9} +344.770i q^{11} +(707.360 + 707.360i) q^{13} +(731.169 - 61.3385i) q^{15} +(1263.06 - 1263.06i) q^{17} +438.382 q^{19} -1964.24 q^{21} +(-1722.78 + 1722.78i) q^{23} +(520.655 + 3081.32i) q^{25} +(2911.69 + 2911.69i) q^{27} +2513.02i q^{29} -7145.63i q^{31} +(3199.85 + 3199.85i) q^{33} +(-699.354 - 8336.45i) q^{35} +(-3361.24 + 3361.24i) q^{37} +13130.2 q^{39} +6969.83 q^{41} +(16311.3 - 16311.3i) q^{43} +(-2552.03 + 3019.43i) q^{45} +(13020.0 + 13020.0i) q^{47} +5588.36i q^{49} -23445.3i q^{51} +(20029.3 + 20029.3i) q^{53} +(-12441.2 + 14719.8i) q^{55} +(4068.67 - 4068.67i) q^{57} +8416.00 q^{59} -2293.72 q^{61} +(7483.70 - 7483.70i) q^{63} +(4674.91 + 55725.9i) q^{65} +(395.619 + 395.619i) q^{67} +31978.6i q^{69} +40844.5i q^{71} +(-45689.8 - 45689.8i) q^{73} +(33430.4 + 23765.9i) q^{75} +(36483.2 - 36483.2i) q^{77} -58457.5 q^{79} +36862.1 q^{81} +(26914.9 - 26914.9i) q^{83} +(99504.4 - 8347.53i) q^{85} +(23323.6 + 23323.6i) q^{87} +61939.2i q^{89} -149704. i q^{91} +(-66319.5 - 66319.5i) q^{93} +(18716.5 + 15819.3i) q^{95} +(-11097.0 + 11097.0i) q^{97} -24382.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 10q^{3} + 42q^{5} + 66q^{7} + O(q^{10}) \) \( 14q + 10q^{3} + 42q^{5} + 66q^{7} - 414q^{13} + 278q^{15} + 1222q^{17} + 5672q^{19} + 5924q^{21} + 2902q^{23} - 4466q^{25} - 2168q^{27} - 2444q^{33} - 2618q^{35} - 1790q^{37} - 11076q^{39} + 11644q^{41} - 3982q^{43} + 14704q^{45} - 1278q^{47} + 5882q^{53} + 65608q^{55} - 14552q^{57} - 8504q^{59} + 20564q^{61} + 19422q^{63} + 40798q^{65} + 107926q^{67} - 16418q^{73} + 66586q^{75} - 13348q^{77} - 146544q^{79} + 173806q^{81} - 36398q^{83} - 66262q^{85} + 124384q^{87} - 306620q^{93} + 173768q^{95} - 60314q^{97} - 388628q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(31\) \(97\) \(101\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(1\)

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
\(3\) 9.28112 9.28112i 0.595384 0.595384i −0.343697 0.939081i \(-0.611679\pi\)
0.939081 + 0.343697i \(0.111679\pi\)
\(4\) 0 0
\(5\) 42.6946 + 36.0856i 0.763744 + 0.645519i
\(6\) 0 0
\(7\) −105.819 105.819i −0.816242 0.816242i 0.169319 0.985561i \(-0.445843\pi\)
−0.985561 + 0.169319i \(0.945843\pi\)
\(8\) 0 0
\(9\) 70.7216i 0.291035i
\(10\) 0 0
\(11\) 344.770i 0.859108i 0.903041 + 0.429554i \(0.141329\pi\)
−0.903041 + 0.429554i \(0.858671\pi\)
\(12\) 0 0
\(13\) 707.360 + 707.360i 1.16087 + 1.16087i 0.984286 + 0.176579i \(0.0565031\pi\)
0.176579 + 0.984286i \(0.443497\pi\)
\(14\) 0 0
\(15\) 731.169 61.3385i 0.839053 0.0703891i
\(16\) 0 0
\(17\) 1263.06 1263.06i 1.05999 1.05999i 0.0619108 0.998082i \(-0.480281\pi\)
0.998082 0.0619108i \(-0.0197194\pi\)
\(18\) 0 0
\(19\) 438.382 0.278592 0.139296 0.990251i \(-0.455516\pi\)
0.139296 + 0.990251i \(0.455516\pi\)
\(20\) 0 0
\(21\) −1964.24 −0.971955
\(22\) 0 0
\(23\) −1722.78 + 1722.78i −0.679063 + 0.679063i −0.959788 0.280725i \(-0.909425\pi\)
0.280725 + 0.959788i \(0.409425\pi\)
\(24\) 0 0
\(25\) 520.655 + 3081.32i 0.166610 + 0.986023i
\(26\) 0 0
\(27\) 2911.69 + 2911.69i 0.768662 + 0.768662i
\(28\) 0 0
\(29\) 2513.02i 0.554881i 0.960743 + 0.277441i \(0.0894862\pi\)
−0.960743 + 0.277441i \(0.910514\pi\)
\(30\) 0 0
\(31\) 7145.63i 1.33548i −0.744396 0.667739i \(-0.767262\pi\)
0.744396 0.667739i \(-0.232738\pi\)
\(32\) 0 0
\(33\) 3199.85 + 3199.85i 0.511499 + 0.511499i
\(34\) 0 0
\(35\) −699.354 8336.45i −0.0964999 1.15030i
\(36\) 0 0
\(37\) −3361.24 + 3361.24i −0.403641 + 0.403641i −0.879514 0.475873i \(-0.842132\pi\)
0.475873 + 0.879514i \(0.342132\pi\)
\(38\) 0 0
\(39\) 13130.2 1.38232
\(40\) 0 0
\(41\) 6969.83 0.647534 0.323767 0.946137i \(-0.395051\pi\)
0.323767 + 0.946137i \(0.395051\pi\)
\(42\) 0 0
\(43\) 16311.3 16311.3i 1.34530 1.34530i 0.454602 0.890695i \(-0.349781\pi\)
0.890695 0.454602i \(-0.150219\pi\)
\(44\) 0 0
\(45\) −2552.03 + 3019.43i −0.187869 + 0.222277i
\(46\) 0 0
\(47\) 13020.0 + 13020.0i 0.859740 + 0.859740i 0.991307 0.131567i \(-0.0420008\pi\)
−0.131567 + 0.991307i \(0.542001\pi\)
\(48\) 0 0
\(49\) 5588.36i 0.332502i
\(50\) 0 0
\(51\) 23445.3i 1.26221i
\(52\) 0 0
\(53\) 20029.3 + 20029.3i 0.979436 + 0.979436i 0.999793 0.0203564i \(-0.00648008\pi\)
−0.0203564 + 0.999793i \(0.506480\pi\)
\(54\) 0 0
\(55\) −12441.2 + 14719.8i −0.554571 + 0.656138i
\(56\) 0 0
\(57\) 4068.67 4068.67i 0.165869 0.165869i
\(58\) 0 0
\(59\) 8416.00 0.314757 0.157379 0.987538i \(-0.449696\pi\)
0.157379 + 0.987538i \(0.449696\pi\)
\(60\) 0 0
\(61\) −2293.72 −0.0789254 −0.0394627 0.999221i \(-0.512565\pi\)
−0.0394627 + 0.999221i \(0.512565\pi\)
\(62\) 0 0
\(63\) 7483.70 7483.70i 0.237555 0.237555i
\(64\) 0 0
\(65\) 4674.91 + 55725.9i 0.137243 + 1.63596i
\(66\) 0 0
\(67\) 395.619 + 395.619i 0.0107669 + 0.0107669i 0.712470 0.701703i \(-0.247577\pi\)
−0.701703 + 0.712470i \(0.747577\pi\)
\(68\) 0 0
\(69\) 31978.6i 0.808606i
\(70\) 0 0
\(71\) 40844.5i 0.961585i 0.876834 + 0.480793i \(0.159651\pi\)
−0.876834 + 0.480793i \(0.840349\pi\)
\(72\) 0 0
\(73\) −45689.8 45689.8i −1.00349 1.00349i −0.999994 0.00349408i \(-0.998888\pi\)
−0.00349408 0.999994i \(-0.501112\pi\)
\(74\) 0 0
\(75\) 33430.4 + 23765.9i 0.686259 + 0.487866i
\(76\) 0 0
\(77\) 36483.2 36483.2i 0.701240 0.701240i
\(78\) 0 0
\(79\) −58457.5 −1.05383 −0.526917 0.849916i \(-0.676652\pi\)
−0.526917 + 0.849916i \(0.676652\pi\)
\(80\) 0 0
\(81\) 36862.1 0.624263
\(82\) 0 0
\(83\) 26914.9 26914.9i 0.428843 0.428843i −0.459391 0.888234i \(-0.651932\pi\)
0.888234 + 0.459391i \(0.151932\pi\)
\(84\) 0 0
\(85\) 99504.4 8347.53i 1.49381 0.125317i
\(86\) 0 0
\(87\) 23323.6 + 23323.6i 0.330368 + 0.330368i
\(88\) 0 0
\(89\) 61939.2i 0.828878i 0.910077 + 0.414439i \(0.136022\pi\)
−0.910077 + 0.414439i \(0.863978\pi\)
\(90\) 0 0
\(91\) 149704.i 1.89509i
\(92\) 0 0
\(93\) −66319.5 66319.5i −0.795122 0.795122i
\(94\) 0 0
\(95\) 18716.5 + 15819.3i 0.212773 + 0.179836i
\(96\) 0 0
\(97\) −11097.0 + 11097.0i −0.119751 + 0.119751i −0.764442 0.644692i \(-0.776986\pi\)
0.644692 + 0.764442i \(0.276986\pi\)
\(98\) 0 0
\(99\) −24382.7 −0.250031
\(100\) 0 0
\(101\) −137921. −1.34533 −0.672664 0.739948i \(-0.734850\pi\)
−0.672664 + 0.739948i \(0.734850\pi\)
\(102\) 0 0
\(103\) −106930. + 106930.i −0.993132 + 0.993132i −0.999977 0.00684431i \(-0.997821\pi\)
0.00684431 + 0.999977i \(0.497821\pi\)
\(104\) 0 0
\(105\) −83862.4 70880.8i −0.742325 0.627416i
\(106\) 0 0
\(107\) −19347.9 19347.9i −0.163371 0.163371i 0.620687 0.784058i \(-0.286854\pi\)
−0.784058 + 0.620687i \(0.786854\pi\)
\(108\) 0 0
\(109\) 155519.i 1.25376i −0.779114 0.626882i \(-0.784331\pi\)
0.779114 0.626882i \(-0.215669\pi\)
\(110\) 0 0
\(111\) 62392.1i 0.480643i
\(112\) 0 0
\(113\) −88859.9 88859.9i −0.654651 0.654651i 0.299459 0.954109i \(-0.403194\pi\)
−0.954109 + 0.299459i \(0.903194\pi\)
\(114\) 0 0
\(115\) −135721. + 11385.8i −0.956978 + 0.0802819i
\(116\) 0 0
\(117\) −50025.6 + 50025.6i −0.337853 + 0.337853i
\(118\) 0 0
\(119\) −267312. −1.73042
\(120\) 0 0
\(121\) 42184.7 0.261934
\(122\) 0 0
\(123\) 64687.9 64687.9i 0.385532 0.385532i
\(124\) 0 0
\(125\) −88962.3 + 150344.i −0.509250 + 0.860619i
\(126\) 0 0
\(127\) 147966. + 147966.i 0.814052 + 0.814052i 0.985239 0.171186i \(-0.0547600\pi\)
−0.171186 + 0.985239i \(0.554760\pi\)
\(128\) 0 0
\(129\) 302775.i 1.60194i
\(130\) 0 0
\(131\) 103447.i 0.526670i −0.964704 0.263335i \(-0.915178\pi\)
0.964704 0.263335i \(-0.0848225\pi\)
\(132\) 0 0
\(133\) −46389.1 46389.1i −0.227398 0.227398i
\(134\) 0 0
\(135\) 19243.2 + 229383.i 0.0908748 + 1.08325i
\(136\) 0 0
\(137\) 142659. 142659.i 0.649380 0.649380i −0.303463 0.952843i \(-0.598143\pi\)
0.952843 + 0.303463i \(0.0981430\pi\)
\(138\) 0 0
\(139\) −147275. −0.646534 −0.323267 0.946308i \(-0.604781\pi\)
−0.323267 + 0.946308i \(0.604781\pi\)
\(140\) 0 0
\(141\) 241681. 1.02375
\(142\) 0 0
\(143\) −243876. + 243876.i −0.997309 + 0.997309i
\(144\) 0 0
\(145\) −90683.7 + 107292.i −0.358187 + 0.423787i
\(146\) 0 0
\(147\) 51866.2 + 51866.2i 0.197966 + 0.197966i
\(148\) 0 0
\(149\) 312656.i 1.15372i −0.816842 0.576861i \(-0.804277\pi\)
0.816842 0.576861i \(-0.195723\pi\)
\(150\) 0 0
\(151\) 91450.6i 0.326396i −0.986593 0.163198i \(-0.947819\pi\)
0.986593 0.163198i \(-0.0521809\pi\)
\(152\) 0 0
\(153\) 89325.9 + 89325.9i 0.308495 + 0.308495i
\(154\) 0 0
\(155\) 257855. 305080.i 0.862076 1.01996i
\(156\) 0 0
\(157\) −215386. + 215386.i −0.697377 + 0.697377i −0.963844 0.266467i \(-0.914144\pi\)
0.266467 + 0.963844i \(0.414144\pi\)
\(158\) 0 0
\(159\) 371789. 1.16628
\(160\) 0 0
\(161\) 364606. 1.10856
\(162\) 0 0
\(163\) −419280. + 419280.i −1.23605 + 1.23605i −0.274444 + 0.961603i \(0.588494\pi\)
−0.961603 + 0.274444i \(0.911506\pi\)
\(164\) 0 0
\(165\) 21147.7 + 252085.i 0.0604718 + 0.720837i
\(166\) 0 0
\(167\) −396893. 396893.i −1.10124 1.10124i −0.994261 0.106978i \(-0.965883\pi\)
−0.106978 0.994261i \(1.46588\pi\)
\(168\) 0 0
\(169\) 629422.i 1.69522i
\(170\) 0 0
\(171\) 31003.1i 0.0810801i
\(172\) 0 0
\(173\) −46145.1 46145.1i −0.117222 0.117222i 0.646062 0.763285i \(-0.276415\pi\)
−0.763285 + 0.646062i \(0.776415\pi\)
\(174\) 0 0
\(175\) 270967. 381158.i 0.668840 0.940827i
\(176\) 0 0
\(177\) 78109.9 78109.9i 0.187401 0.187401i
\(178\) 0 0
\(179\) 18040.3 0.0420834 0.0210417 0.999779i \(-0.493302\pi\)
0.0210417 + 0.999779i \(0.493302\pi\)
\(180\) 0 0
\(181\) 125468. 0.284667 0.142333 0.989819i \(-0.454540\pi\)
0.142333 + 0.989819i \(0.454540\pi\)
\(182\) 0 0
\(183\) −21288.3 + 21288.3i −0.0469909 + 0.0469909i
\(184\) 0 0
\(185\) −264799. + 22214.3i −0.568836 + 0.0477203i
\(186\) 0 0
\(187\) 435466. + 435466.i 0.910648 + 0.910648i
\(188\) 0 0
\(189\) 616224.i 1.25483i
\(190\) 0 0
\(191\) 474723.i 0.941579i −0.882246 0.470789i \(-0.843969\pi\)
0.882246 0.470789i \(-0.156031\pi\)
\(192\) 0 0
\(193\) −345560. 345560.i −0.667776 0.667776i 0.289425 0.957201i \(-0.406536\pi\)
−0.957201 + 0.289425i \(0.906536\pi\)
\(194\) 0 0
\(195\) 560588. + 473811.i 1.05574 + 0.892315i
\(196\) 0 0
\(197\) −458847. + 458847.i −0.842370 + 0.842370i −0.989167 0.146797i \(-0.953104\pi\)
0.146797 + 0.989167i \(0.453104\pi\)
\(198\) 0 0
\(199\) 362349. 0.648627 0.324313 0.945950i \(-0.394867\pi\)
0.324313 + 0.945950i \(0.394867\pi\)
\(200\) 0 0
\(201\) 7343.57 0.0128209
\(202\) 0 0
\(203\) 265925. 265925.i 0.452917 0.452917i
\(204\) 0 0
\(205\) 297574. + 251511.i 0.494550 + 0.417996i
\(206\) 0 0
\(207\) −121838. 121838.i −0.197631 0.197631i
\(208\) 0 0
\(209\) 151141.i 0.239340i
\(210\) 0 0
\(211\) 931084.i 1.43974i −0.694111 0.719868i \(-0.744202\pi\)
0.694111 0.719868i \(-0.255798\pi\)
\(212\) 0 0
\(213\) 379083. + 379083.i 0.572513 + 0.572513i
\(214\) 0 0
\(215\) 1.28501e6 107801.i 1.89588 0.159047i
\(216\) 0 0
\(217\) −756144. + 756144.i −1.09007 + 1.09007i
\(218\) 0 0
\(219\) −848105. −1.19492
\(220\) 0 0
\(221\) 1.78688e6 2.46102
\(222\) 0 0
\(223\) 517823. 517823.i 0.697299 0.697299i −0.266528 0.963827i \(-0.585877\pi\)
0.963827 + 0.266528i \(0.0858765\pi\)
\(224\) 0 0
\(225\) −217916. + 36821.6i −0.286968 + 0.0484893i
\(226\) 0 0
\(227\) −62975.3 62975.3i −0.0811158 0.0811158i 0.665385 0.746501i \(-0.268268\pi\)
−0.746501 + 0.665385i \(0.768268\pi\)
\(228\) 0 0
\(229\) 300417.i 0.378560i 0.981923 + 0.189280i \(0.0606155\pi\)
−0.981923 + 0.189280i \(0.939385\pi\)
\(230\) 0 0
\(231\) 677211.i 0.835014i
\(232\) 0 0
\(233\) 488904. + 488904.i 0.589975 + 0.589975i 0.937625 0.347649i \(-0.113020\pi\)
−0.347649 + 0.937625i \(0.613020\pi\)
\(234\) 0 0
\(235\) 86048.8 + 1.02572e6i 0.101642 + 1.21160i
\(236\) 0 0
\(237\) −542551. + 542551.i −0.627437 + 0.627437i
\(238\) 0 0
\(239\) −1.06439e6 −1.20533 −0.602663 0.797996i \(-0.705894\pi\)
−0.602663 + 0.797996i \(0.705894\pi\)
\(240\) 0 0
\(241\) 1.37049e6 1.51996 0.759981 0.649946i \(-0.225208\pi\)
0.759981 + 0.649946i \(0.225208\pi\)
\(242\) 0 0
\(243\) −365419. + 365419.i −0.396986 + 0.396986i
\(244\) 0 0
\(245\) −201659. + 238593.i −0.214636 + 0.253946i
\(246\) 0 0
\(247\) 310093. + 310093.i 0.323408 + 0.323408i
\(248\) 0 0
\(249\) 499602.i 0.510652i
\(250\) 0 0
\(251\) 483364.i 0.484272i 0.970242 + 0.242136i \(0.0778481\pi\)
−0.970242 + 0.242136i \(0.922152\pi\)
\(252\) 0 0
\(253\) −593962. 593962.i −0.583388 0.583388i
\(254\) 0 0
\(255\) 846038. 1.00099e6i 0.814778 0.964002i
\(256\) 0 0
\(257\) 244037. 244037.i 0.230474 0.230474i −0.582416 0.812891i \(-0.697893\pi\)
0.812891 + 0.582416i \(0.197893\pi\)
\(258\) 0 0
\(259\) 711366. 0.658937
\(260\) 0 0
\(261\) −177724. −0.161490
\(262\) 0 0
\(263\) −660423. + 660423.i −0.588752 + 0.588752i −0.937293 0.348541i \(-0.886677\pi\)
0.348541 + 0.937293i \(0.386677\pi\)
\(264\) 0 0
\(265\) 132373. + 1.57791e6i 0.115793 + 1.38028i
\(266\) 0 0
\(267\) 574865. + 574865.i 0.493501 + 0.493501i
\(268\) 0 0
\(269\) 1.08159e6i 0.911344i −0.890148 0.455672i \(-0.849399\pi\)
0.890148 0.455672i \(-0.150601\pi\)
\(270\) 0 0
\(271\) 343393.i 0.284032i 0.989864 + 0.142016i \(0.0453585\pi\)
−0.989864 + 0.142016i \(0.954642\pi\)
\(272\) 0 0
\(273\) −1.38942e6 1.38942e6i −1.12831 1.12831i
\(274\) 0 0
\(275\) −1.06235e6 + 179506.i −0.847100 + 0.143136i
\(276\) 0 0
\(277\) 335813. 335813.i 0.262965 0.262965i −0.563292 0.826258i \(-0.690465\pi\)
0.826258 + 0.563292i \(0.190465\pi\)
\(278\) 0 0
\(279\) 505351. 0.388671
\(280\) 0 0
\(281\) 1.59679e6 1.20637 0.603187 0.797600i \(-0.293897\pi\)
0.603187 + 0.797600i \(0.293897\pi\)
\(282\) 0 0
\(283\) −1.31343e6 + 1.31343e6i −0.974859 + 0.974859i −0.999692 0.0248326i \(-0.992095\pi\)
0.0248326 + 0.999692i \(0.492095\pi\)
\(284\) 0 0
\(285\) 320531. 26889.7i 0.233753 0.0196098i
\(286\) 0 0
\(287\) −737541. 737541.i −0.528545 0.528545i
\(288\) 0 0
\(289\) 1.77080e6i 1.24717i
\(290\) 0 0
\(291\) 205986.i 0.142595i
\(292\) 0 0
\(293\) −979199. 979199.i −0.666350 0.666350i 0.290520 0.956869i \(-0.406172\pi\)
−0.956869 + 0.290520i \(0.906172\pi\)
\(294\) 0 0
\(295\) 359318. + 303697.i 0.240394 + 0.203182i
\(296\) 0 0
\(297\) −1.00386e6 + 1.00386e6i −0.660364 + 0.660364i
\(298\) 0 0
\(299\) −2.43725e6 −1.57660
\(300\) 0 0
\(301\) −3.45210e6 −2.19618
\(302\) 0 0
\(303\) −1.28006e6 + 1.28006e6i −0.800986 + 0.800986i
\(304\) 0 0
\(305\) −97929.6 82770.5i −0.0602788 0.0509478i
\(306\) 0 0
\(307\) 1.37916e6 + 1.37916e6i 0.835159 + 0.835159i 0.988217 0.153058i \(-0.0489122\pi\)
−0.153058 + 0.988217i \(0.548912\pi\)
\(308\) 0 0
\(309\) 1.98486e6i 1.18259i
\(310\) 0 0
\(311\) 3.40266e6i 1.99488i −0.0714984 0.997441i \(-0.522778\pi\)
0.0714984 0.997441i \(-0.477222\pi\)
\(312\) 0 0
\(313\) −1.12834e6 1.12834e6i −0.650997 0.650997i 0.302236 0.953233i \(-0.402267\pi\)
−0.953233 + 0.302236i \(0.902267\pi\)
\(314\) 0 0
\(315\) 589567. 49459.4i 0.334778 0.0280849i
\(316\) 0 0
\(317\) 2.46256e6 2.46256e6i 1.37638 1.37638i 0.525722 0.850657i \(-0.323795\pi\)
0.850657 0.525722i \(-0.176205\pi\)
\(318\) 0 0
\(319\) −866412. −0.476703
\(320\) 0 0
\(321\) −359141. −0.194537
\(322\) 0 0
\(323\) 553704. 553704.i 0.295305 0.295305i
\(324\) 0 0
\(325\) −1.81131e6 + 2.54789e6i −0.951229 + 1.33805i
\(326\) 0 0
\(327\) −1.44339e6 1.44339e6i −0.746471 0.746471i
\(328\) 0 0
\(329\) 2.75554e6i 1.40351i
\(330\) 0 0
\(331\) 3.84785e6i 1.93041i −0.261503 0.965203i \(-0.584218\pi\)
0.261503 0.965203i \(-0.415782\pi\)
\(332\) 0 0
\(333\) −237712. 237712.i −0.117474 0.117474i
\(334\) 0 0
\(335\) 2614.63 + 31166.9i 0.00127291 + 0.0151734i
\(336\) 0 0
\(337\) 2.14771e6 2.14771e6i 1.03015 1.03015i 0.0306217 0.999531i \(-0.490251\pi\)
0.999531 0.0306217i \(-0.00974872\pi\)
\(338\) 0 0
\(339\) −1.64944e6 −0.779537
\(340\) 0 0
\(341\) 2.46360e6 1.14732
\(342\) 0 0
\(343\) −1.18715e6 + 1.18715e6i −0.544840 + 0.544840i
\(344\) 0 0
\(345\) −1.15397e6 + 1.36531e6i −0.521971 + 0.617568i
\(346\) 0 0
\(347\) 2.44660e6 + 2.44660e6i 1.09078 + 1.09078i 0.995445 + 0.0953396i \(0.0303937\pi\)
0.0953396 + 0.995445i \(0.469606\pi\)
\(348\) 0 0
\(349\) 3.21607e6i 1.41339i −0.707519 0.706694i \(-0.750186\pi\)
0.707519 0.706694i \(-0.249814\pi\)
\(350\) 0 0
\(351\) 4.11922e6i 1.78463i
\(352\) 0 0
\(353\) 1.20920e6 + 1.20920e6i 0.516490 + 0.516490i 0.916508 0.400017i \(-0.130996\pi\)
−0.400017 + 0.916508i \(0.630996\pi\)
\(354\) 0 0
\(355\) −1.47390e6 + 1.74384e6i −0.620722 + 0.734405i
\(356\) 0 0
\(357\) −2.48096e6 + 2.48096e6i −1.03027 + 1.03027i
\(358\) 0 0
\(359\) 1.56580e6 0.641211 0.320606 0.947213i \(-0.396114\pi\)
0.320606 + 0.947213i \(0.396114\pi\)
\(360\) 0 0
\(361\) −2.28392e6 −0.922387
\(362\) 0 0
\(363\) 391521. 391521.i 0.155951 0.155951i
\(364\) 0 0
\(365\) −301962. 3.59945e6i −0.118637 1.41418i
\(366\) 0 0
\(367\) 1.29136e6 + 1.29136e6i 0.500475 + 0.500475i 0.911585 0.411111i \(-0.134859\pi\)
−0.411111 + 0.911585i \(0.634859\pi\)
\(368\) 0 0
\(369\) 492918.i 0.188455i
\(370\) 0 0
\(371\) 4.23897e6i 1.59891i
\(372\) 0 0
\(373\) −20034.2 20034.2i −0.00745588 0.00745588i 0.703369 0.710825i \(-0.251678\pi\)
−0.710825 + 0.703369i \(0.751678\pi\)
\(374\) 0 0
\(375\) 569690. + 2.22103e6i 0.209200 + 0.815598i
\(376\) 0 0
\(377\) −1.77761e6 + 1.77761e6i −0.644143 + 0.644143i
\(378\) 0 0
\(379\) −3.86453e6 −1.38197 −0.690985 0.722869i \(-0.742823\pi\)
−0.690985 + 0.722869i \(0.742823\pi\)
\(380\) 0 0
\(381\) 2.74658e6 0.969348
\(382\) 0 0
\(383\) −1.42232e6 + 1.42232e6i −0.495452 + 0.495452i −0.910019 0.414567i \(-0.863933\pi\)
0.414567 + 0.910019i \(0.363933\pi\)
\(384\) 0 0
\(385\) 2.87416e6 241116.i 0.988232 0.0829038i
\(386\) 0 0
\(387\) 1.15356e6 + 1.15356e6i 0.391529 + 0.391529i
\(388\) 0 0
\(389\) 3.06571e6i 1.02720i 0.858029 + 0.513602i \(0.171689\pi\)
−0.858029 + 0.513602i \(0.828311\pi\)
\(390\) 0 0
\(391\) 4.35196e6i 1.43960i
\(392\) 0 0
\(393\) −960102. 960102.i −0.313571 0.313571i
\(394\) 0 0
\(395\) −2.49582e6 2.10948e6i −0.804860 0.680271i
\(396\) 0 0
\(397\) 2.86964e6 2.86964e6i 0.913800 0.913800i −0.0827685 0.996569i \(-0.526376\pi\)
0.996569 + 0.0827685i \(0.0263762\pi\)
\(398\) 0 0
\(399\) −861086. −0.270779
\(400\) 0 0
\(401\) −1.30150e6 −0.404187 −0.202093 0.979366i \(-0.564774\pi\)
−0.202093 + 0.979366i \(0.564774\pi\)
\(402\) 0 0
\(403\) 5.05453e6 5.05453e6i 1.55031 1.55031i
\(404\) 0 0
\(405\) 1.57381e6 + 1.33019e6i 0.476777 + 0.402974i
\(406\) 0 0
\(407\) −1.15885e6 1.15885e6i −0.346771 0.346771i
\(408\) 0 0
\(409\) 5.91742e6i 1.74914i 0.484902 + 0.874569i \(0.338855\pi\)
−0.484902 + 0.874569i \(0.661145\pi\)
\(410\) 0 0
\(411\) 2.64808e6i 0.773261i
\(412\) 0 0
\(413\) −890573. 890573.i −0.256918 0.256918i
\(414\) 0 0
\(415\) 2.12036e6 177880.i 0.604352 0.0506998i
\(416\) 0 0
\(417\) −1.36687e6 + 1.36687e6i −0.384936 + 0.384936i
\(418\) 0 0
\(419\) 5.36914e6 1.49407 0.747033 0.664788i \(-0.231478\pi\)
0.747033 + 0.664788i \(0.231478\pi\)
\(420\) 0 0
\(421\) 2.11924e6 0.582740 0.291370 0.956610i \(-0.405889\pi\)
0.291370 + 0.956610i \(0.405889\pi\)
\(422\) 0 0
\(423\) −920798. + 920798.i −0.250215 + 0.250215i
\(424\) 0 0
\(425\) 4.54952e6 + 3.23428e6i 1.22178 + 0.868572i
\(426\) 0 0
\(427\) 242720. + 242720.i 0.0644222 + 0.0644222i
\(428\) 0 0
\(429\) 4.52689e6i 1.18756i
\(430\) 0 0
\(431\) 469972.i 0.121865i 0.998142 + 0.0609325i \(0.0194074\pi\)
−0.998142 + 0.0609325i \(0.980593\pi\)
\(432\) 0 0
\(433\) 630785. + 630785.i 0.161682 + 0.161682i 0.783311 0.621629i \(-0.213529\pi\)
−0.621629 + 0.783311i \(0.713529\pi\)
\(434\) 0 0
\(435\) 154145. + 1.83744e6i 0.0390576 + 0.465575i
\(436\) 0 0
\(437\) −755235. + 755235.i −0.189181 + 0.189181i
\(438\) 0 0
\(439\) 798304. 0.197700 0.0988501 0.995102i \(-0.468484\pi\)
0.0988501 + 0.995102i \(0.468484\pi\)
\(440\) 0 0
\(441\) −395218. −0.0967698
\(442\) 0 0
\(443\) 3.62223e6 3.62223e6i 0.876934 0.876934i −0.116282 0.993216i \(-0.537098\pi\)
0.993216 + 0.116282i \(0.0370977\pi\)
\(444\) 0 0
\(445\) −2.23512e6 + 2.64447e6i −0.535057 + 0.633051i
\(446\) 0 0
\(447\) −2.90180e6 2.90180e6i −0.686908 0.686908i
\(448\) 0 0
\(449\) 7.51152e6i 1.75838i −0.476474 0.879188i \(-0.658085\pi\)
0.476474 0.879188i \(-0.341915\pi\)
\(450\) 0 0
\(451\) 2.40299e6i 0.556302i
\(452\) 0 0
\(453\) −848764. 848764.i −0.194331 0.194331i
\(454\) 0 0
\(455\) 5.40217e6 6.39156e6i 1.22332 1.44737i
\(456\) 0 0
\(457\) −994327. + 994327.i −0.222710 + 0.222710i −0.809638 0.586929i \(-0.800337\pi\)
0.586929 + 0.809638i \(0.300337\pi\)
\(458\) 0 0
\(459\) 7.35529e6 1.62955
\(460\) 0 0
\(461\) 3.47063e6 0.760600 0.380300 0.924863i \(-0.375821\pi\)
0.380300 + 0.924863i \(0.375821\pi\)
\(462\) 0 0
\(463\) 2.81963e6 2.81963e6i 0.611280 0.611280i −0.332000 0.943279i \(-0.607723\pi\)
0.943279 + 0.332000i \(0.107723\pi\)
\(464\) 0 0
\(465\) −438303. 5.22466e6i −0.0940030 1.12054i
\(466\) 0 0
\(467\) −5.53855e6 5.53855e6i −1.17518 1.17518i −0.980958 0.194221i \(-0.937782\pi\)
−0.194221 0.980958i \(1.43778\pi\)
\(468\) 0 0
\(469\) 83728.0i 0.0175768i
\(470\) 0 0
\(471\) 3.99804e6i 0.830415i
\(472\) 0 0
\(473\) 5.62365e6 + 5.62365e6i 1.15575 + 1.15575i
\(474\) 0 0
\(475\) 228246. + 1.35079e6i 0.0464161 + 0.274698i
\(476\) 0 0
\(477\) −1.41650e6 + 1.41650e6i −0.285051 + 0.285051i
\(478\) 0 0
\(479\) 2.72200e6 0.542063 0.271031 0.962571i \(-0.412635\pi\)
0.271031 + 0.962571i \(0.412635\pi\)
\(480\) 0 0
\(481\) −4.75521e6 −0.937145
\(482\) 0 0
\(483\) 3.38395e6 3.38395e6i 0.660018 0.660018i
\(484\) 0 0
\(485\) −874227. + 73339.8i −0.168760 + 0.0141575i
\(486\) 0 0
\(487\) 1.53481e6 + 1.53481e6i 0.293246 + 0.293246i 0.838361 0.545115i \(-0.183514\pi\)
−0.545115 + 0.838361i \(0.683514\pi\)
\(488\) 0 0
\(489\) 7.78278e6i 1.47185i
\(490\) 0 0
\(491\) 4.17663e6i 0.781848i −0.920423 0.390924i \(-0.872156\pi\)
0.920423 0.390924i \(-0.127844\pi\)
\(492\) 0 0
\(493\) 3.17410e6 + 3.17410e6i 0.588170 + 0.588170i
\(494\) 0 0
\(495\) −1.04101e6 879865.i −0.190960 0.161400i
\(496\) 0 0
\(497\) 4.32213e6 4.32213e6i 0.784886 0.784886i
\(498\) 0 0
\(499\) −5.43895e6 −0.977830 −0.488915 0.872331i \(-0.662607\pi\)
−0.488915 + 0.872331i \(0.662607\pi\)
\(500\) 0 0
\(501\) −7.36721e6 −1.31132
\(502\) 0 0
\(503\) −6.20134e6 + 6.20134e6i −1.09286 + 1.09286i −0.0976412 + 0.995222i \(0.531130\pi\)
−0.995222 + 0.0976412i \(0.968870\pi\)
\(504\) 0 0
\(505\) −5.88849e6 4.97698e6i −1.02749 0.868435i
\(506\) 0 0
\(507\) 5.84174e6 + 5.84174e6i 1.00931 + 1.00931i
\(508\) 0 0
\(509\) 1.07552e6i 0.184003i −0.995759 0.0920015i \(-0.970674\pi\)
0.995759 0.0920015i \(-0.0293265\pi\)
\(510\) 0 0
\(511\) 9.66971e6i 1.63818i
\(512\) 0 0
\(513\) 1.27643e6 + 1.27643e6i 0.214143 + 0.214143i
\(514\) 0 0
\(515\) −8.42398e6 + 706697.i −1.39958 + 0.117413i
\(516\) 0 0
\(517\) −4.48892e6 + 4.48892e6i −0.738610 + 0.738610i
\(518\) 0 0
\(519\) −856557. −0.139585
\(520\) 0 0
\(521\) 512247. 0.0826770 0.0413385 0.999145i \(-0.486838\pi\)
0.0413385 + 0.999145i \(0.486838\pi\)
\(522\) 0 0
\(523\) −1.62407e6 + 1.62407e6i −0.259627 + 0.259627i −0.824902 0.565275i \(-0.808770\pi\)
0.565275 + 0.824902i \(0.308770\pi\)
\(524\) 0 0
\(525\) −1.02269e6 6.05245e6i −0.161937 0.958370i
\(526\) 0 0
\(527\) −9.02539e6 9.02539e6i −1.41560 1.41560i
\(528\) 0 0
\(529\) 500411.i 0.0777477i
\(530\) 0 0
\(531\) 595193.i 0.0916055i
\(532\) 0 0
\(533\) 4.93018e6 + 4.93018e6i 0.751700 + 0.751700i
\(534\) 0 0
\(535\) −127870. 1.52423e6i −0.0193145 0.230233i
\(536\) 0 0
\(537\) 167434. 167434.i 0.0250558 0.0250558i
\(538\) 0 0
\(539\) −1.92670e6 −0.285655
\(540\) 0 0
\(541\) −2.18839e6 −0.321464 −0.160732 0.986998i \(-0.551385\pi\)
−0.160732 + 0.986998i \(0.551385\pi\)
\(542\) 0 0
\(543\) 1.16448e6 1.16448e6i 0.169486 0.169486i
\(544\) 0 0
\(545\) 5.61198e6 6.63980e6i 0.809329 0.957555i
\(546\) 0 0
\(547\) 7.08793e6 + 7.08793e6i 1.01286 + 1.01286i 0.999916 + 0.0129482i \(0.00412164\pi\)
0.0129482 + 0.999916i \(0.495878\pi\)
\(548\) 0 0
\(549\) 162216.i 0.0229701i
\(550\) 0 0
\(551\) 1.10166e6i 0.154585i
\(552\) 0 0
\(553\) 6.18592e6 + 6.18592e6i 0.860184 + 0.860184i
\(554\) 0 0
\(555\) −2.25146e6 + 2.66381e6i −0.310264 + 0.367088i
\(556\) 0 0
\(557\) 8.47008e6 8.47008e6i 1.15678 1.15678i 0.171612 0.985165i \(-0.445102\pi\)
0.985165 0.171612i \(-0.0548975\pi\)
\(558\) 0 0
\(559\) 2.30759e7 3.12342
\(560\) 0 0
\(561\) 8.08323e6 1.08437
\(562\) 0 0
\(563\) −3.30786e6 + 3.30786e6i −0.439821 + 0.439821i −0.891952 0.452131i \(-0.850664\pi\)
0.452131 + 0.891952i \(0.350664\pi\)
\(564\) 0 0
\(565\) −587271. 7.00040e6i −0.0773958 0.922575i
\(566\) 0 0
\(567\) −3.90071e6 3.90071e6i −0.509550 0.509550i
\(568\) 0 0
\(569\) 5.57983e6i 0.722504i −0.932468 0.361252i \(-0.882349\pi\)
0.932468 0.361252i \(-0.117651\pi\)
\(570\) 0 0
\(571\) 119122.i 0.0152898i −0.999971 0.00764491i \(-0.997567\pi\)
0.999971 0.00764491i \(-0.00243348\pi\)
\(572\) 0 0
\(573\) −4.40596e6 4.40596e6i −0.560601 0.560601i
\(574\) 0 0
\(575\) −6.20541e6 4.41146e6i −0.782710 0.556433i
\(576\) 0 0
\(577\) −5.74821e6 + 5.74821e6i −0.718775 + 0.718775i −0.968354 0.249579i \(-0.919708\pi\)
0.249579 + 0.968354i \(0.419708\pi\)
\(578\) 0 0
\(579\) −6.41438e6 −0.795166
\(580\) 0 0
\(581\) −5.69623e6 −0.700079
\(582\) 0 0
\(583\) −6.90550e6 + 6.90550e6i −0.841442 + 0.841442i
\(584\) 0 0
\(585\) −3.94103e6 + 330617.i −0.476124 + 0.0399425i
\(586\) 0 0
\(587\) −1.01460e6 1.01460e6i −0.121535 0.121535i 0.643724 0.765258i \(-0.277389\pi\)
−0.765258 + 0.643724i \(0.777389\pi\)
\(588\) 0 0
\(589\) 3.13252e6i 0.372053i
\(590\) 0 0
\(591\) 8.51724e6i 1.00307i
\(592\) 0 0
\(593\) −5.72430e6 5.72430e6i −0.668476 0.668476i 0.288887 0.957363i \(-0.406715\pi\)
−0.957363 + 0.288887i \(0.906715\pi\)
\(594\) 0 0
\(595\) −1.14128e7 9.64614e6i −1.32160 1.11702i
\(596\) 0 0
\(597\) 3.36301e6 3.36301e6i 0.386182 0.386182i
\(598\) 0 0
\(599\) −5.13903e6 −0.585213 −0.292606 0.956233i \(-0.594523\pi\)
−0.292606 + 0.956233i \(0.594523\pi\)
\(600\) 0 0
\(601\) −1.24740e7 −1.40871 −0.704353 0.709850i \(-0.748763\pi\)
−0.704353 + 0.709850i \(0.748763\pi\)
\(602\) 0 0
\(603\) −27978.8 + 27978.8i −0.00313354 + 0.00313354i
\(604\) 0 0
\(605\) 1.80106e6 + 1.52226e6i 0.200050 + 0.169083i
\(606\) 0 0
\(607\) −9.43385e6 9.43385e6i −1.03924 1.03924i −0.999198 0.0400449i \(-0.987250\pi\)
−0.0400449 0.999198i \(1.48725\pi\)
\(608\) 0 0
\(609\) 4.93616e6i 0.539320i
\(610\) 0 0
\(611\) 1.84197e7i 1.99609i
\(612\) 0 0
\(613\) 5.01442e6 + 5.01442e6i 0.538976 + 0.538976i 0.923228 0.384252i \(-0.125541\pi\)
−0.384252 + 0.923228i \(0.625541\pi\)
\(614\) 0 0
\(615\) 5.09612e6 427519.i 0.543316 0.0455793i
\(616\) 0 0
\(617\) 4.22945e6 4.22945e6i 0.447272 0.447272i −0.447175 0.894446i \(-0.647570\pi\)
0.894446 + 0.447175i \(0.147570\pi\)
\(618\) 0 0
\(619\) −6.02116e6 −0.631617 −0.315808 0.948823i \(-0.602276\pi\)
−0.315808 + 0.948823i \(0.602276\pi\)
\(620\) 0 0
\(621\) −1.00324e7 −1.04394
\(622\) 0 0
\(623\) 6.55435e6 6.55435e6i 0.676565 0.676565i
\(624\) 0 0
\(625\) −9.22346e6 + 3.20861e6i −0.944482 + 0.328562i
\(626\) 0 0
\(627\) 1.40276e6 + 1.40276e6i 0.142499 + 0.142499i
\(628\) 0 0
\(629\) 8.49092e6i 0.855713i
\(630\) 0 0
\(631\) 2.59184e6i 0.259141i −0.991570 0.129570i \(-0.958640\pi\)
0.991570 0.129570i \(-0.0413598\pi\)
\(632\) 0 0
\(633\) −8.64150e6 8.64150e6i −0.857196 0.857196i
\(634\) 0 0
\(635\) 977900. + 1.16568e7i 0.0962410 + 1.14721i
\(636\) 0 0
\(637\) −3.95298e6 + 3.95298e6i −0.385990 + 0.385990i
\(638\) 0 0
\(639\) −2.88859e6 −0.279855
\(640\) 0 0
\(641\) −5.99741e6 −0.576526 −0.288263 0.957551i \(-0.593078\pi\)
−0.288263 + 0.957551i \(0.593078\pi\)
\(642\) 0 0
\(643\) 841642. 841642.i 0.0802786 0.0802786i −0.665827 0.746106i \(-0.731921\pi\)
0.746106 + 0.665827i \(0.231921\pi\)
\(644\) 0 0
\(645\) 1.09258e7 1.29268e7i 1.03408 1.22347i
\(646\) 0 0
\(647\) −1.18127e7 1.18127e7i −1.10940 1.10940i −0.993229 0.116170i \(-0.962938\pi\)
−0.116170 0.993229i \(1.46294\pi\)
\(648\) 0 0
\(649\) 2.90158e6i 0.270410i
\(650\) 0 0
\(651\) 1.40357e7i 1.29802i
\(652\) 0 0
\(653\) 1.22862e6 + 1.22862e6i 0.112755 + 0.112755i 0.761233 0.648478i \(-0.224594\pi\)
−0.648478 + 0.761233i \(0.724594\pi\)
\(654\) 0 0
\(655\) 3.73294e6 4.41662e6i 0.339976 0.402241i
\(656\) 0 0
\(657\) 3.23126e6 3.23126e6i 0.292051 0.292051i
\(658\) 0 0
\(659\) 4.69732e6 0.421343 0.210672 0.977557i \(-0.432435\pi\)
0.210672 + 0.977557i \(0.432435\pi\)
\(660\) 0 0
\(661\) −1.07325e7 −0.955423 −0.477712 0.878517i \(-0.658534\pi\)
−0.477712 + 0.878517i \(0.658534\pi\)
\(662\) 0 0
\(663\) 1.65842e7 1.65842e7i 1.46525 1.46525i
\(664\) 0 0
\(665\) −306584. 3.65455e6i −0.0268841 0.320464i
\(666\) 0 0
\(667\) −4.32937e6 4.32937e6i −0.376799 0.376799i
\(668\) 0 0
\(669\) 9.61195e6i 0.830322i
\(670\) 0 0
\(671\) 790807.i 0.0678054i
\(672\) 0 0
\(673\) −6.62488e6 6.62488e6i −0.563820 0.563820i 0.366571 0.930390i \(-0.380532\pi\)
−0.930390 + 0.366571i \(0.880532\pi\)
\(674\) 0 0
\(675\) −7.45586e6 + 1.04878e7i −0.629852 + 0.885985i
\(676\) 0 0
\(677\) 5.62424e6 5.62424e6i 0.471620 0.471620i −0.430819 0.902438i \(-0.641775\pi\)
0.902438 + 0.430819i \(0.141775\pi\)
\(678\) 0 0
\(679\) 2.34856e6 0.195491
\(680\) 0 0
\(681\) −1.16896e6 −0.0965902
\(682\) 0 0
\(683\) 6.92168e6 6.92168e6i 0.567754 0.567754i −0.363745 0.931499i \(-0.618502\pi\)
0.931499 + 0.363745i \(0.118502\pi\)
\(684\) 0 0
\(685\) 1.12387e7 942829.i 0.915147 0.0767727i
\(686\) 0 0
\(687\) 2.78820e6 + 2.78820e6i 0.225389 + 0.225389i
\(688\) 0 0
\(689\) 2.83358e7i 2.27399i
\(690\) 0 0
\(691\) 9.49915e6i 0.756815i 0.925639 + 0.378407i \(0.123528\pi\)
−0.925639 + 0.378407i \(0.876472\pi\)
\(692\) 0 0
\(693\) 2.58015e6 + 2.58015e6i 0.204086 + 0.204086i
\(694\) 0 0
\(695\) −6.28783e6 5.31450e6i −0.493786 0.417350i
\(696\) 0 0
\(697\) 8.80334e6 8.80334e6i 0.686381 0.686381i
\(698\) 0 0
\(699\) 9.07516e6 0.702524
\(700\) 0 0
\(701\) 1.94148e6 0.149224 0.0746120 0.997213i \(-0.476228\pi\)
0.0746120 + 0.997213i \(0.476228\pi\)
\(702\) 0 0
\(703\) −1.47351e6 + 1.47351e6i −0.112451 + 0.112451i
\(704\) 0 0
\(705\) 1.03185e7 + 8.72121e6i 0.781884 + 0.660852i
\(706\) 0 0
\(707\) 1.45947e7 + 1.45947e7i 1.09811 + 1.09811i
\(708\) 0 0
\(709\) 2.89625e6i 0.216382i 0.994130 + 0.108191i \(0.0345057\pi\)
−0.994130 + 0.108191i \(0.965494\pi\)
\(710\) 0 0
\(711\) 4.13421e6i 0.306703i
\(712\) 0 0
\(713\) 1.23103e7 + 1.23103e7i 0.906873 + 0.906873i
\(714\) 0 0
\(715\) −1.92126e7 + 1.61177e6i −1.40547 + 0.117906i
\(716\) 0 0
\(717\) −9.87870e6 + 9.87870e6i −0.717632 + 0.717632i
\(718\) 0 0
\(719\) −751266. −0.0541965 −0.0270983 0.999633i \(-0.508627\pi\)
−0.0270983 + 0.999633i \(0.508627\pi\)
\(720\) 0 0
\(721\) 2.26305e7 1.62127
\(722\) 0 0
\(723\) 1.27197e7 1.27197e7i 0.904961 0.904961i
\(724\) 0 0
\(725\) −7.74341e6 + 1.30841e6i −0.547126 + 0.0924486i
\(726\) 0 0
\(727\) 1.73454e7 + 1.73454e7i 1.21716 + 1.21716i 0.968623 + 0.248536i \(0.0799494\pi\)
0.248536 + 0.968623i \(0.420051\pi\)
\(728\) 0 0
\(729\) 1.57405e7i 1.09698i
\(730\) 0 0
\(731\) 4.12045e7i 2.85201i
\(732\) 0 0
\(733\) 1.21536e7 + 1.21536e7i 0.835496 + 0.835496i 0.988262 0.152766i \(-0.0488181\pi\)
−0.152766 + 0.988262i \(0.548818\pi\)
\(734\) 0 0
\(735\) 342782. + 4.08603e6i 0.0234045 + 0.278987i
\(736\) 0 0
\(737\) −136397. + 136397.i −0.00924991 + 0.00924991i
\(738\) 0 0
\(739\) 888631. 0.0598564 0.0299282 0.999552i \(-0.490472\pi\)
0.0299282 + 0.999552i \(0.490472\pi\)
\(740\) 0 0
\(741\) 5.75603e6 0.385104
\(742\) 0 0
\(743\) 3.63933e6 3.63933e6i 0.241852 0.241852i −0.575764 0.817616i \(-0.695295\pi\)
0.817616 + 0.575764i \(0.195295\pi\)
\(744\) 0 0
\(745\) 1.12824e7 1.33487e7i 0.744750 0.881148i
\(746\) 0 0
\(747\) 1.90347e6 + 1.90347e6i 0.124808 + 0.124808i
\(748\) 0 0
\(749\) 4.09476e6i 0.266700i
\(750\) 0 0
\(751\) 202134.i 0.0130779i −0.999979 0.00653897i \(-0.997919\pi\)
0.999979 0.00653897i \(-0.00208143\pi\)
\(752\) 0 0
\(753\) 4.48616e6 + 4.48616e6i 0.288328 + 0.288328i
\(754\) 0 0
\(755\) 3.30005e6 3.90445e6i 0.210695 0.249283i
\(756\) 0 0
\(757\) −8.73504e6 + 8.73504e6i −0.554020 + 0.554020i −0.927599 0.373579i \(-0.878131\pi\)
0.373579 + 0.927599i \(0.378131\pi\)
\(758\) 0 0
\(759\) −1.10253e7 −0.694680
\(760\) 0 0
\(761\) −1.57714e7 −0.987208 −0.493604 0.869687i \(-0.664321\pi\)
−0.493604 + 0.869687i \(0.664321\pi\)
\(762\) 0 0
\(763\) −1.64568e7 + 1.64568e7i −1.02337 + 1.02337i
\(764\) 0 0
\(765\) 590351. + 7.03711e6i 0.0364717 + 0.434751i
\(766\) 0 0
\(767\) 5.95314e6 + 5.95314e6i 0.365391 + 0.365391i
\(768\) 0 0
\(769\) 5.82867e6i 0.355430i 0.984082 + 0.177715i \(0.0568705\pi\)
−0.984082 + 0.177715i \(0.943130\pi\)
\(770\) 0 0
\(771\) 4.52986e6i 0.274441i
\(772\) 0 0
\(773\) −3.64656e6 3.64656e6i −0.219500 0.219500i 0.588788 0.808288i \(-0.299605\pi\)
−0.808288 + 0.588788i \(0.799605\pi\)
\(774\) 0 0
\(775\) 2.20180e7 3.72041e6i 1.31681 0.222503i
\(776\) 0 0
\(777\) 6.60228e6 6.60228e6i 0.392321 0.392321i
\(778\) 0 0
\(779\) 3.05545e6 0.180398
\(780\) 0 0
\(781\) −1.40820e7 −0.826105
\(782\) 0 0
\(783\) −7.31712e6 + 7.31712e6i −0.426516 + 0.426516i
\(784\) 0 0
\(785\) −1.69681e7 + 1.42348e6i −0.982788 + 0.0824472i
\(786\) 0 0
\(787\) −1.07036e7 1.07036e7i −0.616016 0.616016i 0.328491 0.944507i \(-0.393460\pi\)
−0.944507 + 0.328491i \(0.893460\pi\)
\(788\) 0 0
\(789\) 1.22589e7i 0.701068i
\(790\) 0 0
\(791\) 1.88061e7i 1.06871i
\(792\) 0 0
\(793\) −1.62249e6 1.62249e6i −0.0916217 0.0916217i