Properties

Label 160.6.n.b.127.5
Level 160
Weight 6
Character 160.127
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 127.5
Root \(4.57273 - 4.57273i\) of defining polynomial
Character \(\chi\) \(=\) 160.127
Dual form 160.6.n.b.63.5

$q$-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 \(\left(\mathbb{Z}/160\mathbb{Z}\right)^\times\).

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

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
\(3\) 9.28112 + 9.28112i 0.595384 + 0.595384i 0.939081 0.343697i \(-0.111679\pi\)
−0.343697 + 0.939081i \(0.611679\pi\)
\(4\) 0 0
\(5\) 42.6946 36.0856i 0.763744 0.645519i
\(6\) 0 0
\(7\) −105.819 + 105.819i −0.816242 + 0.816242i −0.985561 0.169319i \(-0.945843\pi\)
0.169319 + 0.985561i \(0.445843\pi\)
\(8\) 0 0
\(9\) 70.7216i 0.291035i
\(10\) 0 0
\(11\) 344.770i 0.859108i −0.903041 0.429554i \(-0.858671\pi\)
0.903041 0.429554i \(-0.141329\pi\)
\(12\) 0 0
\(13\) 707.360 707.360i 1.16087 1.16087i 0.176579 0.984286i \(-0.443497\pi\)
0.984286 0.176579i \(-0.0565031\pi\)
\(14\) 0 0
\(15\) 731.169 + 61.3385i 0.839053 + 0.0703891i
\(16\) 0 0
\(17\) 1263.06 + 1263.06i 1.05999 + 1.05999i 0.998082 + 0.0619108i \(0.0197194\pi\)
0.0619108 + 0.998082i \(0.480281\pi\)
\(18\) 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 0.280725 0.959788i \(-0.409425\pi\)
−0.959788 + 0.280725i \(0.909425\pi\)
\(24\) 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 \(-0.910514\pi\)
0.960743 0.277441i \(-0.0894862\pi\)
\(30\) 0 0
\(31\) 7145.63i 1.33548i 0.744396 + 0.667739i \(0.232738\pi\)
−0.744396 + 0.667739i \(0.767262\pi\)
\(32\) 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 0.475873 0.879514i \(-0.342132\pi\)
−0.879514 + 0.475873i \(0.842132\pi\)
\(38\) 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 0.890695 + 0.454602i \(0.150219\pi\)
0.454602 + 0.890695i \(0.349781\pi\)
\(44\) 0 0
\(45\) −2552.03 3019.43i −0.187869 0.222277i
\(46\) 0 0
\(47\) 13020.0 13020.0i 0.859740 0.859740i −0.131567 0.991307i \(-0.542001\pi\)
0.991307 + 0.131567i \(0.0420008\pi\)
\(48\) 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 −0.0203564 0.999793i \(-0.506480\pi\)
0.999793 + 0.0203564i \(0.00648008\pi\)
\(54\) 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 −0.701703 0.712470i \(-0.747577\pi\)
0.712470 + 0.701703i \(0.247577\pi\)
\(68\) 0 0
\(69\) 31978.6i 0.808606i
\(70\) 0 0
\(71\) 40844.5i 0.961585i −0.876834 0.480793i \(-0.840349\pi\)
0.876834 0.480793i \(-0.159651\pi\)
\(72\) 0 0
\(73\) −45689.8 + 45689.8i −1.00349 + 1.00349i −0.00349408 + 0.999994i \(0.501112\pi\)
−0.999994 + 0.00349408i \(0.998888\pi\)
\(74\) 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 0.888234 0.459391i \(-0.151932\pi\)
−0.459391 + 0.888234i \(0.651932\pi\)
\(84\) 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 \(-0.863978\pi\)
0.910077 0.414439i \(-0.136022\pi\)
\(90\) 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 0.644692 0.764442i \(-0.276986\pi\)
−0.764442 + 0.644692i \(0.776986\pi\)
\(98\) 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 0.00684431 0.999977i \(-0.497821\pi\)
−0.999977 + 0.00684431i \(0.997821\pi\)
\(104\) 0 0
\(105\) −83862.4 + 70880.8i −0.742325 + 0.627416i
\(106\) 0 0
\(107\) −19347.9 + 19347.9i −0.163371 + 0.163371i −0.784058 0.620687i \(-0.786854\pi\)
0.620687 + 0.784058i \(0.286854\pi\)
\(108\) 0 0
\(109\) 155519.i 1.25376i 0.779114 + 0.626882i \(0.215669\pi\)
−0.779114 + 0.626882i \(0.784331\pi\)
\(110\) 0 0
\(111\) 62392.1i 0.480643i
\(112\) 0 0
\(113\) −88859.9 + 88859.9i −0.654651 + 0.654651i −0.954109 0.299459i \(-0.903194\pi\)
0.299459 + 0.954109i \(0.403194\pi\)
\(114\) 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 −0.171186 0.985239i \(-0.554760\pi\)
0.985239 + 0.171186i \(0.0547600\pi\)
\(128\) 0 0
\(129\) 302775.i 1.60194i
\(130\) 0 0
\(131\) 103447.i 0.526670i 0.964704 + 0.263335i \(0.0848225\pi\)
−0.964704 + 0.263335i \(0.915178\pi\)
\(132\) 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 0.952843 0.303463i \(-0.0981430\pi\)
−0.303463 + 0.952843i \(0.598143\pi\)
\(138\) 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 \(0.195723\pi\)
−0.816842 + 0.576861i \(0.804277\pi\)
\(150\) 0 0
\(151\) 91450.6i 0.326396i 0.986593 + 0.163198i \(0.0521809\pi\)
−0.986593 + 0.163198i \(0.947819\pi\)
\(152\) 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 0.266467 0.963844i \(-0.414144\pi\)
−0.963844 + 0.266467i \(0.914144\pi\)
\(158\) 0 0
\(159\) 371789. 1.16628
\(160\) 0 0
\(161\) 364606. 1.10856
\(162\) 0 0
\(163\) −419280. 419280.i −1.23605 1.23605i −0.961603 0.274444i \(-0.911506\pi\)
−0.274444 0.961603i \(1.41151\pi\)
\(164\) 0 0
\(165\) 21147.7 252085.i 0.0604718 0.720837i
\(166\) 0 0
\(167\) −396893. + 396893.i −1.10124 + 1.10124i −0.106978 + 0.994261i \(0.534117\pi\)
−0.994261 + 0.106978i \(0.965883\pi\)
\(168\) 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 −0.763285 0.646062i \(-0.776415\pi\)
0.646062 + 0.763285i \(0.276415\pi\)
\(174\) 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 \(0.156031\pi\)
−0.882246 + 0.470789i \(0.843969\pi\)
\(192\) 0 0
\(193\) −345560. + 345560.i −0.667776 + 0.667776i −0.957201 0.289425i \(-0.906536\pi\)
0.289425 + 0.957201i \(0.406536\pi\)
\(194\) 0 0
\(195\) 560588. 473811.i 1.05574 0.892315i
\(196\) 0 0
\(197\) −458847. 458847.i −0.842370 0.842370i 0.146797 0.989167i \(-0.453104\pi\)
−0.989167 + 0.146797i \(0.953104\pi\)
\(198\) 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 \(0.255798\pi\)
−0.694111 + 0.719868i \(0.744202\pi\)
\(212\) 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 0.963827 0.266528i \(-0.0858765\pi\)
−0.266528 + 0.963827i \(0.585877\pi\)
\(224\) 0 0
\(225\) −217916. 36821.6i −0.286968 0.0484893i
\(226\) 0 0
\(227\) −62975.3 + 62975.3i −0.0811158 + 0.0811158i −0.746501 0.665385i \(-0.768268\pi\)
0.665385 + 0.746501i \(0.268268\pi\)
\(228\) 0 0
\(229\) 300417.i 0.378560i −0.981923 0.189280i \(-0.939385\pi\)
0.981923 0.189280i \(-0.0606155\pi\)
\(230\) 0 0
\(231\) 677211.i 0.835014i
\(232\) 0 0
\(233\) 488904. 488904.i 0.589975 0.589975i −0.347649 0.937625i \(-0.613020\pi\)
0.937625 + 0.347649i \(0.113020\pi\)
\(234\) 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 \(-0.922152\pi\)
0.970242 0.242136i \(-0.0778481\pi\)
\(252\) 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 0.812891 0.582416i \(-0.197893\pi\)
−0.582416 + 0.812891i \(0.697893\pi\)
\(258\) 0 0
\(259\) 711366. 0.658937
\(260\) 0 0
\(261\) −177724. −0.161490
\(262\) 0 0
\(263\) −660423. 660423.i −0.588752 0.588752i 0.348541 0.937293i \(-0.386677\pi\)
−0.937293 + 0.348541i \(0.886677\pi\)
\(264\) 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 \(0.150601\pi\)
−0.890148 + 0.455672i \(0.849399\pi\)
\(270\) 0 0
\(271\) 343393.i 0.284032i −0.989864 0.142016i \(-0.954642\pi\)
0.989864 0.142016i \(-0.0453585\pi\)
\(272\) 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 0.826258 0.563292i \(-0.190465\pi\)
−0.563292 + 0.826258i \(0.690465\pi\)
\(278\) 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 0.0248326 0.999692i \(-0.492095\pi\)
−0.999692 + 0.0248326i \(0.992095\pi\)
\(284\) 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 −0.956869 0.290520i \(-0.906172\pi\)
0.290520 + 0.956869i \(0.406172\pi\)
\(294\) 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 −0.153058 0.988217i \(-0.548912\pi\)
0.988217 + 0.153058i \(0.0489122\pi\)
\(308\) 0 0
\(309\) 1.98486e6i 1.18259i
\(310\) 0 0
\(311\) 3.40266e6i 1.99488i 0.0714984 + 0.997441i \(0.477222\pi\)
−0.0714984 + 0.997441i \(0.522778\pi\)
\(312\) 0 0
\(313\) −1.12834e6 + 1.12834e6i −0.650997 + 0.650997i −0.953233 0.302236i \(-0.902267\pi\)
0.302236 + 0.953233i \(0.402267\pi\)
\(314\) 0 0
\(315\) 589567. + 49459.4i 0.334778 + 0.0280849i
\(316\) 0 0
\(317\) 2.46256e6 + 2.46256e6i 1.37638 + 1.37638i 0.850657 + 0.525722i \(0.176205\pi\)
0.525722 + 0.850657i \(0.323795\pi\)
\(318\) 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 \(0.415782\pi\)
−0.261503 + 0.965203i \(0.584218\pi\)
\(332\) 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 0.999531 + 0.0306217i \(0.00974872\pi\)
0.0306217 + 0.999531i \(0.490251\pi\)
\(338\) 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 0.0953396 0.995445i \(-0.469606\pi\)
0.995445 0.0953396i \(-0.0303937\pi\)
\(348\) 0 0
\(349\) 3.21607e6i 1.41339i 0.707519 + 0.706694i \(0.249814\pi\)
−0.707519 + 0.706694i \(0.750186\pi\)
\(350\) 0 0
\(351\) 4.11922e6i 1.78463i
\(352\) 0 0
\(353\) 1.20920e6 1.20920e6i 0.516490 0.516490i −0.400017 0.916508i \(-0.630996\pi\)
0.916508 + 0.400017i \(0.130996\pi\)
\(354\) 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 −0.411111 0.911585i \(-0.634859\pi\)
0.911585 + 0.411111i \(0.134859\pi\)
\(368\) 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 −0.710825 0.703369i \(-0.751678\pi\)
0.703369 + 0.710825i \(0.251678\pi\)
\(374\) 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 0.414567 0.910019i \(-0.363933\pi\)
−0.910019 + 0.414567i \(0.863933\pi\)
\(384\) 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 \(-0.828311\pi\)
0.858029 0.513602i \(-0.171689\pi\)
\(390\) 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 0.996569 0.0827685i \(-0.0263762\pi\)
−0.0827685 + 0.996569i \(0.526376\pi\)
\(398\) 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 \(-0.661145\pi\)
0.484902 0.874569i \(-0.338855\pi\)
\(410\) 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 \(-0.980593\pi\)
0.998142 0.0609325i \(-0.0194074\pi\)
\(432\) 0 0
\(433\) 630785. 630785.i 0.161682 0.161682i −0.621629 0.783311i \(-0.713529\pi\)
0.783311 + 0.621629i \(0.213529\pi\)
\(434\) 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 0.993216 0.116282i \(-0.0370977\pi\)
−0.116282 + 0.993216i \(0.537098\pi\)
\(444\) 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 \(0.341915\pi\)
−0.476474 + 0.879188i \(0.658085\pi\)
\(450\) 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 0.586929 0.809638i \(-0.300337\pi\)
−0.809638 + 0.586929i \(0.800337\pi\)
\(458\) 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 0.943279 0.332000i \(-0.107723\pi\)
−0.332000 + 0.943279i \(0.607723\pi\)
\(464\) 0 0
\(465\) −438303. + 5.22466e6i −0.0940030 + 1.12054i
\(466\) 0 0
\(467\) −5.53855e6 + 5.53855e6i −1.17518 + 1.17518i −0.194221 + 0.980958i \(0.562218\pi\)
−0.980958 + 0.194221i \(0.937782\pi\)
\(468\) 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 −0.545115 0.838361i \(-0.683514\pi\)
0.838361 + 0.545115i \(0.183514\pi\)
\(488\) 0 0
\(489\) 7.78278e6i 1.47185i
\(490\) 0 0
\(491\) 4.17663e6i 0.781848i 0.920423 + 0.390924i \(0.127844\pi\)
−0.920423 + 0.390924i \(0.872156\pi\)
\(492\) 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 −0.995222 0.0976412i \(-0.968870\pi\)
−0.0976412 0.995222i \(1.46887\pi\)
\(504\) 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 \(0.0293265\pi\)
−0.995759 + 0.0920015i \(0.970674\pi\)
\(510\) 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 0.565275 0.824902i \(-0.308770\pi\)
−0.824902 + 0.565275i \(0.808770\pi\)
\(524\) 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 0.0129482 0.999916i \(-0.495878\pi\)
0.999916 0.0129482i \(-0.00412164\pi\)
\(548\) 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 0.985165 + 0.171612i \(0.0548975\pi\)
0.171612 + 0.985165i \(0.445102\pi\)
\(558\) 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 0.452131 0.891952i \(-0.350664\pi\)
−0.891952 + 0.452131i \(0.850664\pi\)
\(564\) 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 \(0.117651\pi\)
−0.932468 + 0.361252i \(0.882349\pi\)
\(570\) 0 0
\(571\) 119122.i 0.0152898i 0.999971 + 0.00764491i \(0.00243348\pi\)
−0.999971 + 0.00764491i \(0.997567\pi\)
\(572\) 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 0.249579 0.968354i \(-0.419708\pi\)
−0.968354 + 0.249579i \(0.919708\pi\)
\(578\) 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 −0.765258 0.643724i \(-0.777389\pi\)
0.643724 + 0.765258i \(0.277389\pi\)
\(588\) 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 −0.957363 0.288887i \(-0.906715\pi\)
0.288887 + 0.957363i \(0.406715\pi\)
\(594\) 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 −0.0400449 + 0.999198i \(0.512750\pi\)
−0.999198 + 0.0400449i \(0.987250\pi\)
\(608\) 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 −0.384252 0.923228i \(-0.625541\pi\)
0.923228 + 0.384252i \(0.125541\pi\)
\(614\) 0 0
\(615\) 5.09612e6 + 427519.i 0.543316 + 0.0455793i
\(616\) 0 0
\(617\) 4.22945e6 + 4.22945e6i 0.447272 + 0.447272i 0.894446 0.447175i \(-0.147570\pi\)
−0.447175 + 0.894446i \(0.647570\pi\)
\(618\) 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 \(0.0413598\pi\)
−0.991570 + 0.129570i \(0.958640\pi\)
\(632\) 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 0.746106 0.665827i \(-0.231921\pi\)
−0.665827 + 0.746106i \(0.731921\pi\)
\(644\) 0 0
\(645\) 1.09258e7 + 1.29268e7i 1.03408 + 1.22347i
\(646\) 0 0
\(647\) −1.18127e7 + 1.18127e7i −1.10940 + 1.10940i −0.116170 + 0.993229i \(0.537062\pi\)
−0.993229 + 0.116170i \(0.962938\pi\)
\(648\) 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 −0.648478 0.761233i \(-0.724594\pi\)
0.761233 + 0.648478i \(0.224594\pi\)
\(654\) 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 −0.930390 0.366571i \(-0.880532\pi\)
0.366571 + 0.930390i \(0.380532\pi\)
\(674\) 0 0
\(675\) −7.45586e6 1.04878e7i −0.629852 0.885985i
\(676\) 0 0
\(677\) 5.62424e6 + 5.62424e6i 0.471620 + 0.471620i 0.902438 0.430819i \(-0.141775\pi\)
−0.430819 + 0.902438i \(0.641775\pi\)
\(678\) 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 0.931499 0.363745i \(-0.118502\pi\)
−0.363745 + 0.931499i \(0.618502\pi\)
\(684\) 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 \(-0.876472\pi\)
0.925639 0.378407i \(-0.123528\pi\)
\(692\) 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 \(-0.965494\pi\)
0.994130 0.108191i \(-0.0345057\pi\)
\(710\) 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 0.248536 0.968623i \(-0.420051\pi\)
0.968623 0.248536i \(-0.0799494\pi\)
\(728\) 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 −0.152766 0.988262i \(-0.548818\pi\)
0.988262 + 0.152766i \(0.0488181\pi\)
\(734\) 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 0.817616 0.575764i \(-0.195295\pi\)
−0.575764 + 0.817616i \(0.695295\pi\)
\(744\) 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 \(0.00208143\pi\)
−0.999979 + 0.00653897i \(0.997919\pi\)
\(752\) 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 0.373579 0.927599i \(-0.378131\pi\)
−0.927599 + 0.373579i \(0.878131\pi\)
\(758\) 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 \(-0.943130\pi\)
0.984082 0.177715i \(-0.0568705\pi\)
\(770\) 0 0
\(771\) 4.52986e6i 0.274441i
\(772\) 0 0
\(773\) −3.64656e6 + 3.64656e6i −0.219500 + 0.219500i −0.808288 0.588788i \(-0.799605\pi\)
0.588788 + 0.808288i \(0.299605\pi\)
\(774\) 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 −0.944507 0.328491i \(-0.893460\pi\)
0.328491 + 0.944507i \(0.393460\pi\)
\(788\) 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