Properties

Label 320.6.l.a.81.12
Level 320
Weight 6
Character 320.81
Analytic conductor 51.323
Analytic rank 0
Dimension 80
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 320.l (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(51.3228223402\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(40\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 80)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 81.12
Character \(\chi\) \(=\) 320.81
Dual form 320.6.l.a.241.12

$q$-expansion

\(f(q)\) \(=\) \(q+(-9.77316 - 9.77316i) q^{3} +(17.6777 - 17.6777i) q^{5} +103.649i q^{7} -51.9707i q^{9} +O(q^{10})\) \(q+(-9.77316 - 9.77316i) q^{3} +(17.6777 - 17.6777i) q^{5} +103.649i q^{7} -51.9707i q^{9} +(-1.18069 + 1.18069i) q^{11} +(-196.412 - 196.412i) q^{13} -345.533 q^{15} +274.760 q^{17} +(464.105 + 464.105i) q^{19} +(1012.98 - 1012.98i) q^{21} +3172.08i q^{23} -625.000i q^{25} +(-2882.80 + 2882.80i) q^{27} +(-3615.12 - 3615.12i) q^{29} -8594.55 q^{31} +23.0781 q^{33} +(1832.27 + 1832.27i) q^{35} +(5380.92 - 5380.92i) q^{37} +3839.13i q^{39} +12794.9i q^{41} +(-2059.02 + 2059.02i) q^{43} +(-918.721 - 918.721i) q^{45} +19.2201 q^{47} +6063.86 q^{49} +(-2685.27 - 2685.27i) q^{51} +(2845.02 - 2845.02i) q^{53} +41.7437i q^{55} -9071.55i q^{57} +(16076.8 - 16076.8i) q^{59} +(28235.3 + 28235.3i) q^{61} +5386.72 q^{63} -6944.22 q^{65} +(41683.6 + 41683.6i) q^{67} +(31001.2 - 31001.2i) q^{69} +25386.5i q^{71} +24731.7i q^{73} +(-6108.22 + 6108.22i) q^{75} +(-122.377 - 122.377i) q^{77} -8180.40 q^{79} +43719.2 q^{81} +(73736.2 + 73736.2i) q^{83} +(4857.11 - 4857.11i) q^{85} +70662.3i q^{87} +31074.5i q^{89} +(20357.9 - 20357.9i) q^{91} +(83995.9 + 83995.9i) q^{93} +16408.6 q^{95} +48319.6 q^{97} +(61.3613 + 61.3613i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q + O(q^{10}) \) \( 80q - 1208q^{11} + 1800q^{15} - 2360q^{19} + 7464q^{27} - 8144q^{29} + 21296q^{37} - 32072q^{43} + 88360q^{47} - 192080q^{49} + 5920q^{51} - 49456q^{53} - 44984q^{59} + 48080q^{61} - 158760q^{63} - 61160q^{67} - 22320q^{69} - 14896q^{77} - 177680q^{79} - 524880q^{81} + 329240q^{83} + 132400q^{85} - 364832q^{91} - 362352q^{93} - 288800q^{95} - 659000q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(257\) \(261\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) −9.77316 9.77316i −0.626948 0.626948i 0.320351 0.947299i \(-0.396199\pi\)
−0.947299 + 0.320351i \(0.896199\pi\)
\(4\) 0 0
\(5\) 17.6777 17.6777i 0.316228 0.316228i
\(6\) 0 0
\(7\) 103.649i 0.799504i 0.916623 + 0.399752i \(0.130904\pi\)
−0.916623 + 0.399752i \(0.869096\pi\)
\(8\) 0 0
\(9\) 51.9707i 0.213871i
\(10\) 0 0
\(11\) −1.18069 + 1.18069i −0.00294208 + 0.00294208i −0.708576 0.705634i \(-0.750662\pi\)
0.705634 + 0.708576i \(0.250662\pi\)
\(12\) 0 0
\(13\) −196.412 196.412i −0.322337 0.322337i 0.527326 0.849663i \(-0.323195\pi\)
−0.849663 + 0.527326i \(0.823195\pi\)
\(14\) 0 0
\(15\) −345.533 −0.396517
\(16\) 0 0
\(17\) 274.760 0.230585 0.115292 0.993332i \(-0.463219\pi\)
0.115292 + 0.993332i \(0.463219\pi\)
\(18\) 0 0
\(19\) 464.105 + 464.105i 0.294939 + 0.294939i 0.839028 0.544089i \(-0.183124\pi\)
−0.544089 + 0.839028i \(0.683124\pi\)
\(20\) 0 0
\(21\) 1012.98 1012.98i 0.501248 0.501248i
\(22\) 0 0
\(23\) 3172.08i 1.25033i 0.780493 + 0.625164i \(0.214968\pi\)
−0.780493 + 0.625164i \(0.785032\pi\)
\(24\) 0 0
\(25\) 625.000i 0.200000i
\(26\) 0 0
\(27\) −2882.80 + 2882.80i −0.761035 + 0.761035i
\(28\) 0 0
\(29\) −3615.12 3615.12i −0.798229 0.798229i 0.184587 0.982816i \(-0.440905\pi\)
−0.982816 + 0.184587i \(0.940905\pi\)
\(30\) 0 0
\(31\) −8594.55 −1.60627 −0.803135 0.595797i \(-0.796836\pi\)
−0.803135 + 0.595797i \(0.796836\pi\)
\(32\) 0 0
\(33\) 23.0781 0.00368906
\(34\) 0 0
\(35\) 1832.27 + 1832.27i 0.252825 + 0.252825i
\(36\) 0 0
\(37\) 5380.92 5380.92i 0.646178 0.646178i −0.305889 0.952067i \(-0.598954\pi\)
0.952067 + 0.305889i \(0.0989538\pi\)
\(38\) 0 0
\(39\) 3839.13i 0.404177i
\(40\) 0 0
\(41\) 12794.9i 1.18871i 0.804203 + 0.594355i \(0.202593\pi\)
−0.804203 + 0.594355i \(0.797407\pi\)
\(42\) 0 0
\(43\) −2059.02 + 2059.02i −0.169820 + 0.169820i −0.786900 0.617080i \(-0.788315\pi\)
0.617080 + 0.786900i \(0.288315\pi\)
\(44\) 0 0
\(45\) −918.721 918.721i −0.0676320 0.0676320i
\(46\) 0 0
\(47\) 19.2201 0.00126914 0.000634572 1.00000i \(-0.499798\pi\)
0.000634572 1.00000i \(0.499798\pi\)
\(48\) 0 0
\(49\) 6063.86 0.360794
\(50\) 0 0
\(51\) −2685.27 2685.27i −0.144565 0.144565i
\(52\) 0 0
\(53\) 2845.02 2845.02i 0.139122 0.139122i −0.634116 0.773238i \(-0.718636\pi\)
0.773238 + 0.634116i \(0.218636\pi\)
\(54\) 0 0
\(55\) 41.7437i 0.00186073i
\(56\) 0 0
\(57\) 9071.55i 0.369823i
\(58\) 0 0
\(59\) 16076.8 16076.8i 0.601268 0.601268i −0.339381 0.940649i \(-0.610218\pi\)
0.940649 + 0.339381i \(0.110218\pi\)
\(60\) 0 0
\(61\) 28235.3 + 28235.3i 0.971557 + 0.971557i 0.999607 0.0280491i \(-0.00892948\pi\)
−0.0280491 + 0.999607i \(0.508929\pi\)
\(62\) 0 0
\(63\) 5386.72 0.170991
\(64\) 0 0
\(65\) −6944.22 −0.203864
\(66\) 0 0
\(67\) 41683.6 + 41683.6i 1.13443 + 1.13443i 0.989432 + 0.145000i \(0.0463182\pi\)
0.145000 + 0.989432i \(0.453682\pi\)
\(68\) 0 0
\(69\) 31001.2 31001.2i 0.783891 0.783891i
\(70\) 0 0
\(71\) 25386.5i 0.597663i 0.954306 + 0.298832i \(0.0965969\pi\)
−0.954306 + 0.298832i \(0.903403\pi\)
\(72\) 0 0
\(73\) 24731.7i 0.543184i 0.962412 + 0.271592i \(0.0875502\pi\)
−0.962412 + 0.271592i \(0.912450\pi\)
\(74\) 0 0
\(75\) −6108.22 + 6108.22i −0.125390 + 0.125390i
\(76\) 0 0
\(77\) −122.377 122.377i −0.00235220 0.00235220i
\(78\) 0 0
\(79\) −8180.40 −0.147471 −0.0737355 0.997278i \(-0.523492\pi\)
−0.0737355 + 0.997278i \(0.523492\pi\)
\(80\) 0 0
\(81\) 43719.2 0.740388
\(82\) 0 0
\(83\) 73736.2 + 73736.2i 1.17486 + 1.17486i 0.981037 + 0.193822i \(0.0620885\pi\)
0.193822 + 0.981037i \(0.437912\pi\)
\(84\) 0 0
\(85\) 4857.11 4857.11i 0.0729173 0.0729173i
\(86\) 0 0
\(87\) 70662.3i 1.00090i
\(88\) 0 0
\(89\) 31074.5i 0.415842i 0.978146 + 0.207921i \(0.0666698\pi\)
−0.978146 + 0.207921i \(0.933330\pi\)
\(90\) 0 0
\(91\) 20357.9 20357.9i 0.257709 0.257709i
\(92\) 0 0
\(93\) 83995.9 + 83995.9i 1.00705 + 1.00705i
\(94\) 0 0
\(95\) 16408.6 0.186536
\(96\) 0 0
\(97\) 48319.6 0.521427 0.260714 0.965416i \(-0.416042\pi\)
0.260714 + 0.965416i \(0.416042\pi\)
\(98\) 0 0
\(99\) 61.3613 + 61.3613i 0.000629225 + 0.000629225i
\(100\) 0 0
\(101\) −83227.2 + 83227.2i −0.811824 + 0.811824i −0.984907 0.173083i \(-0.944627\pi\)
0.173083 + 0.984907i \(0.444627\pi\)
\(102\) 0 0
\(103\) 24932.4i 0.231564i −0.993275 0.115782i \(-0.963063\pi\)
0.993275 0.115782i \(-0.0369374\pi\)
\(104\) 0 0
\(105\) 35814.2i 0.317017i
\(106\) 0 0
\(107\) 86761.1 86761.1i 0.732598 0.732598i −0.238536 0.971134i \(-0.576668\pi\)
0.971134 + 0.238536i \(0.0766675\pi\)
\(108\) 0 0
\(109\) 108586. + 108586.i 0.875399 + 0.875399i 0.993054 0.117656i \(-0.0375379\pi\)
−0.117656 + 0.993054i \(0.537538\pi\)
\(110\) 0 0
\(111\) −105177. −0.810240
\(112\) 0 0
\(113\) −96237.1 −0.709000 −0.354500 0.935056i \(-0.615349\pi\)
−0.354500 + 0.935056i \(0.615349\pi\)
\(114\) 0 0
\(115\) 56074.9 + 56074.9i 0.395388 + 0.395388i
\(116\) 0 0
\(117\) −10207.7 + 10207.7i −0.0689385 + 0.0689385i
\(118\) 0 0
\(119\) 28478.6i 0.184353i
\(120\) 0 0
\(121\) 161048.i 0.999983i
\(122\) 0 0
\(123\) 125046. 125046.i 0.745260 0.745260i
\(124\) 0 0
\(125\) −11048.5 11048.5i −0.0632456 0.0632456i
\(126\) 0 0
\(127\) 83496.0 0.459363 0.229682 0.973266i \(-0.426232\pi\)
0.229682 + 0.973266i \(0.426232\pi\)
\(128\) 0 0
\(129\) 40246.3 0.212937
\(130\) 0 0
\(131\) −4990.15 4990.15i −0.0254059 0.0254059i 0.694290 0.719696i \(-0.255719\pi\)
−0.719696 + 0.694290i \(0.755719\pi\)
\(132\) 0 0
\(133\) −48104.1 + 48104.1i −0.235805 + 0.235805i
\(134\) 0 0
\(135\) 101922.i 0.481321i
\(136\) 0 0
\(137\) 319403.i 1.45391i −0.686686 0.726954i \(-0.740935\pi\)
0.686686 0.726954i \(-0.259065\pi\)
\(138\) 0 0
\(139\) 126010. 126010.i 0.553182 0.553182i −0.374176 0.927358i \(-0.622074\pi\)
0.927358 + 0.374176i \(0.122074\pi\)
\(140\) 0 0
\(141\) −187.841 187.841i −0.000795689 0.000795689i
\(142\) 0 0
\(143\) 463.803 0.00189668
\(144\) 0 0
\(145\) −127814. −0.504845
\(146\) 0 0
\(147\) −59263.1 59263.1i −0.226199 0.226199i
\(148\) 0 0
\(149\) −127764. + 127764.i −0.471456 + 0.471456i −0.902386 0.430929i \(-0.858186\pi\)
0.430929 + 0.902386i \(0.358186\pi\)
\(150\) 0 0
\(151\) 313476.i 1.11882i 0.828890 + 0.559412i \(0.188973\pi\)
−0.828890 + 0.559412i \(0.811027\pi\)
\(152\) 0 0
\(153\) 14279.5i 0.0493154i
\(154\) 0 0
\(155\) −151932. + 151932.i −0.507947 + 0.507947i
\(156\) 0 0
\(157\) 252249. + 252249.i 0.816734 + 0.816734i 0.985633 0.168899i \(-0.0540212\pi\)
−0.168899 + 0.985633i \(0.554021\pi\)
\(158\) 0 0
\(159\) −55609.7 −0.174445
\(160\) 0 0
\(161\) −328783. −0.999642
\(162\) 0 0
\(163\) −282574. 282574.i −0.833035 0.833035i 0.154896 0.987931i \(-0.450496\pi\)
−0.987931 + 0.154896i \(0.950496\pi\)
\(164\) 0 0
\(165\) 407.968 407.968i 0.00116658 0.00116658i
\(166\) 0 0
\(167\) 52609.2i 0.145972i −0.997333 0.0729861i \(-0.976747\pi\)
0.997333 0.0729861i \(-0.0232529\pi\)
\(168\) 0 0
\(169\) 294138.i 0.792198i
\(170\) 0 0
\(171\) 24119.9 24119.9i 0.0630790 0.0630790i
\(172\) 0 0
\(173\) 538675. + 538675.i 1.36839 + 1.36839i 0.862731 + 0.505663i \(0.168752\pi\)
0.505663 + 0.862731i \(0.331248\pi\)
\(174\) 0 0
\(175\) 64780.7 0.159901
\(176\) 0 0
\(177\) −314241. −0.753928
\(178\) 0 0
\(179\) 194994. + 194994.i 0.454871 + 0.454871i 0.896967 0.442097i \(-0.145765\pi\)
−0.442097 + 0.896967i \(0.645765\pi\)
\(180\) 0 0
\(181\) −417889. + 417889.i −0.948123 + 0.948123i −0.998719 0.0505962i \(-0.983888\pi\)
0.0505962 + 0.998719i \(0.483888\pi\)
\(182\) 0 0
\(183\) 551897.i 1.21823i
\(184\) 0 0
\(185\) 190244.i 0.408679i
\(186\) 0 0
\(187\) −324.406 + 324.406i −0.000678398 + 0.000678398i
\(188\) 0 0
\(189\) −298799. 298799.i −0.608450 0.608450i
\(190\) 0 0
\(191\) −497076. −0.985915 −0.492957 0.870053i \(-0.664084\pi\)
−0.492957 + 0.870053i \(0.664084\pi\)
\(192\) 0 0
\(193\) 462532. 0.893817 0.446908 0.894580i \(-0.352525\pi\)
0.446908 + 0.894580i \(0.352525\pi\)
\(194\) 0 0
\(195\) 67866.9 + 67866.9i 0.127812 + 0.127812i
\(196\) 0 0
\(197\) 286303. 286303.i 0.525606 0.525606i −0.393653 0.919259i \(-0.628789\pi\)
0.919259 + 0.393653i \(0.128789\pi\)
\(198\) 0 0
\(199\) 1.00987e6i 1.80772i 0.427828 + 0.903860i \(0.359279\pi\)
−0.427828 + 0.903860i \(0.640721\pi\)
\(200\) 0 0
\(201\) 814761.i 1.42246i
\(202\) 0 0
\(203\) 374704. 374704.i 0.638187 0.638187i
\(204\) 0 0
\(205\) 226183. + 226183.i 0.375903 + 0.375903i
\(206\) 0 0
\(207\) 164855. 0.267409
\(208\) 0 0
\(209\) −1095.93 −0.00173547
\(210\) 0 0
\(211\) −277285. 277285.i −0.428765 0.428765i 0.459442 0.888208i \(-0.348049\pi\)
−0.888208 + 0.459442i \(0.848049\pi\)
\(212\) 0 0
\(213\) 248106. 248106.i 0.374704 0.374704i
\(214\) 0 0
\(215\) 72797.4i 0.107404i
\(216\) 0 0
\(217\) 890817.i 1.28422i
\(218\) 0 0
\(219\) 241707. 241707.i 0.340549 0.340549i
\(220\) 0 0
\(221\) −53966.1 53966.1i −0.0743259 0.0743259i
\(222\) 0 0
\(223\) −912396. −1.22863 −0.614315 0.789061i \(-0.710568\pi\)
−0.614315 + 0.789061i \(0.710568\pi\)
\(224\) 0 0
\(225\) −32481.7 −0.0427742
\(226\) 0 0
\(227\) −173993. 173993.i −0.224113 0.224113i 0.586115 0.810228i \(-0.300657\pi\)
−0.810228 + 0.586115i \(0.800657\pi\)
\(228\) 0 0
\(229\) 845428. 845428.i 1.06534 1.06534i 0.0676288 0.997711i \(-0.478457\pi\)
0.997711 0.0676288i \(-0.0215434\pi\)
\(230\) 0 0
\(231\) 2392.03i 0.00294942i
\(232\) 0 0
\(233\) 33744.0i 0.0407199i −0.999793 0.0203599i \(-0.993519\pi\)
0.999793 0.0203599i \(-0.00648122\pi\)
\(234\) 0 0
\(235\) 339.767 339.767i 0.000401339 0.000401339i
\(236\) 0 0
\(237\) 79948.3 + 79948.3i 0.0924567 + 0.0924567i
\(238\) 0 0
\(239\) −1.42903e6 −1.61825 −0.809125 0.587637i \(-0.800058\pi\)
−0.809125 + 0.587637i \(0.800058\pi\)
\(240\) 0 0
\(241\) −387370. −0.429619 −0.214809 0.976656i \(-0.568913\pi\)
−0.214809 + 0.976656i \(0.568913\pi\)
\(242\) 0 0
\(243\) 273245. + 273245.i 0.296850 + 0.296850i
\(244\) 0 0
\(245\) 107195. 107195.i 0.114093 0.114093i
\(246\) 0 0
\(247\) 182312.i 0.190140i
\(248\) 0 0
\(249\) 1.44127e6i 1.47315i
\(250\) 0 0
\(251\) 151092. 151092.i 0.151376 0.151376i −0.627356 0.778732i \(-0.715863\pi\)
0.778732 + 0.627356i \(0.215863\pi\)
\(252\) 0 0
\(253\) −3745.24 3745.24i −0.00367856 0.00367856i
\(254\) 0 0
\(255\) −94938.6 −0.0914308
\(256\) 0 0
\(257\) −1.10772e6 −1.04616 −0.523081 0.852283i \(-0.675218\pi\)
−0.523081 + 0.852283i \(0.675218\pi\)
\(258\) 0 0
\(259\) 557727. + 557727.i 0.516621 + 0.516621i
\(260\) 0 0
\(261\) −187880. + 187880.i −0.170718 + 0.170718i
\(262\) 0 0
\(263\) 166218.i 0.148179i 0.997252 + 0.0740897i \(0.0236051\pi\)
−0.997252 + 0.0740897i \(0.976395\pi\)
\(264\) 0 0
\(265\) 100587.i 0.0879884i
\(266\) 0 0
\(267\) 303696. 303696.i 0.260712 0.260712i
\(268\) 0 0
\(269\) −1.20947e6 1.20947e6i −1.01910 1.01910i −0.999814 0.0192827i \(-0.993862\pi\)
−0.0192827 0.999814i \(-0.506138\pi\)
\(270\) 0 0
\(271\) −1.78497e6 −1.47641 −0.738207 0.674574i \(-0.764327\pi\)
−0.738207 + 0.674574i \(0.764327\pi\)
\(272\) 0 0
\(273\) −397923. −0.323141
\(274\) 0 0
\(275\) 737.931 + 737.931i 0.000588415 + 0.000588415i
\(276\) 0 0
\(277\) −1.21139e6 + 1.21139e6i −0.948602 + 0.948602i −0.998742 0.0501403i \(-0.984033\pi\)
0.0501403 + 0.998742i \(0.484033\pi\)
\(278\) 0 0
\(279\) 446665.i 0.343535i
\(280\) 0 0
\(281\) 2.33417e6i 1.76347i 0.471748 + 0.881734i \(0.343623\pi\)
−0.471748 + 0.881734i \(0.656377\pi\)
\(282\) 0 0
\(283\) 1.45993e6 1.45993e6i 1.08359 1.08359i 0.0874233 0.996171i \(-0.472137\pi\)
0.996171 0.0874233i \(-0.0278633\pi\)
\(284\) 0 0
\(285\) −160364. 160364.i −0.116948 0.116948i
\(286\) 0 0
\(287\) −1.32618e6 −0.950378
\(288\) 0 0
\(289\) −1.34436e6 −0.946831
\(290\) 0 0
\(291\) −472235. 472235.i −0.326908 0.326908i
\(292\) 0 0
\(293\) −268466. + 268466.i −0.182692 + 0.182692i −0.792528 0.609836i \(-0.791235\pi\)
0.609836 + 0.792528i \(0.291235\pi\)
\(294\) 0 0
\(295\) 568399.i 0.380275i
\(296\) 0 0
\(297\) 6807.37i 0.00447804i
\(298\) 0 0
\(299\) 623034. 623034.i 0.403027 0.403027i
\(300\) 0 0
\(301\) −213416. 213416.i −0.135772 0.135772i
\(302\) 0 0
\(303\) 1.62679e6 1.01794
\(304\) 0 0
\(305\) 998270. 0.614467
\(306\) 0 0
\(307\) −1.30877e6 1.30877e6i −0.792534 0.792534i 0.189372 0.981905i \(-0.439355\pi\)
−0.981905 + 0.189372i \(0.939355\pi\)
\(308\) 0 0
\(309\) −243668. + 243668.i −0.145179 + 0.145179i
\(310\) 0 0
\(311\) 3.06774e6i 1.79853i −0.437406 0.899264i \(-0.644103\pi\)
0.437406 0.899264i \(-0.355897\pi\)
\(312\) 0 0
\(313\) 2.27439e6i 1.31221i 0.754669 + 0.656105i \(0.227797\pi\)
−0.754669 + 0.656105i \(0.772203\pi\)
\(314\) 0 0
\(315\) 95224.6 95224.6i 0.0540720 0.0540720i
\(316\) 0 0
\(317\) 2.44805e6 + 2.44805e6i 1.36827 + 1.36827i 0.862909 + 0.505360i \(0.168640\pi\)
0.505360 + 0.862909i \(0.331360\pi\)
\(318\) 0 0
\(319\) 8536.67 0.00469690
\(320\) 0 0
\(321\) −1.69586e6 −0.918602
\(322\) 0 0
\(323\) 127517. + 127517.i 0.0680085 + 0.0680085i
\(324\) 0 0
\(325\) −122758. + 122758.i −0.0644673 + 0.0644673i
\(326\) 0 0
\(327\) 2.12245e6i 1.09766i
\(328\) 0 0
\(329\) 1992.15i 0.00101469i
\(330\) 0 0
\(331\) −786844. + 786844.i −0.394747 + 0.394747i −0.876376 0.481628i \(-0.840045\pi\)
0.481628 + 0.876376i \(0.340045\pi\)
\(332\) 0 0
\(333\) −279650. 279650.i −0.138199 0.138199i
\(334\) 0 0
\(335\) 1.47374e6 0.717478
\(336\) 0 0
\(337\) −1.52615e6 −0.732021 −0.366010 0.930611i \(-0.619276\pi\)
−0.366010 + 0.930611i \(0.619276\pi\)
\(338\) 0 0
\(339\) 940541. + 940541.i 0.444507 + 0.444507i
\(340\) 0 0
\(341\) 10147.5 10147.5i 0.00472577 0.00472577i
\(342\) 0 0
\(343\) 2.37054e6i 1.08796i
\(344\) 0 0
\(345\) 1.09606e6i 0.495776i
\(346\) 0 0
\(347\) −2.37371e6 + 2.37371e6i −1.05829 + 1.05829i −0.0600956 + 0.998193i \(0.519141\pi\)
−0.998193 + 0.0600956i \(0.980859\pi\)
\(348\) 0 0
\(349\) −1.11045e6 1.11045e6i −0.488017 0.488017i 0.419663 0.907680i \(-0.362148\pi\)
−0.907680 + 0.419663i \(0.862148\pi\)
\(350\) 0 0
\(351\) 1.13243e6 0.490619
\(352\) 0 0
\(353\) 4.02943e6 1.72110 0.860551 0.509365i \(-0.170120\pi\)
0.860551 + 0.509365i \(0.170120\pi\)
\(354\) 0 0
\(355\) 448774. + 448774.i 0.188998 + 0.188998i
\(356\) 0 0
\(357\) 278326. 278326.i 0.115580 0.115580i
\(358\) 0 0
\(359\) 2.88668e6i 1.18212i 0.806626 + 0.591062i \(0.201291\pi\)
−0.806626 + 0.591062i \(0.798709\pi\)
\(360\) 0 0
\(361\) 2.04531e6i 0.826022i
\(362\) 0 0
\(363\) 1.57395e6 1.57395e6i 0.626938 0.626938i
\(364\) 0 0
\(365\) 437199. + 437199.i 0.171770 + 0.171770i
\(366\) 0 0
\(367\) 1.53810e6 0.596100 0.298050 0.954550i \(-0.403664\pi\)
0.298050 + 0.954550i \(0.403664\pi\)
\(368\) 0 0
\(369\) 664958. 0.254231
\(370\) 0 0
\(371\) 294884. + 294884.i 0.111228 + 0.111228i
\(372\) 0 0
\(373\) 665688. 665688.i 0.247741 0.247741i −0.572302 0.820043i \(-0.693949\pi\)
0.820043 + 0.572302i \(0.193949\pi\)
\(374\) 0 0
\(375\) 215958.i 0.0793034i
\(376\) 0 0
\(377\) 1.42011e6i 0.514597i
\(378\) 0 0
\(379\) −733269. + 733269.i −0.262220 + 0.262220i −0.825955 0.563736i \(-0.809364\pi\)
0.563736 + 0.825955i \(0.309364\pi\)
\(380\) 0 0
\(381\) −816019. 816019.i −0.287997 0.287997i
\(382\) 0 0
\(383\) 2.45123e6 0.853863 0.426931 0.904284i \(-0.359595\pi\)
0.426931 + 0.904284i \(0.359595\pi\)
\(384\) 0 0
\(385\) −4326.70 −0.00148766
\(386\) 0 0
\(387\) 107009. + 107009.i 0.0363197 + 0.0363197i
\(388\) 0 0
\(389\) 1.54868e6 1.54868e6i 0.518906 0.518906i −0.398334 0.917240i \(-0.630412\pi\)
0.917240 + 0.398334i \(0.130412\pi\)
\(390\) 0 0
\(391\) 871558.i 0.288307i
\(392\) 0 0
\(393\) 97539.1i 0.0318564i
\(394\) 0 0
\(395\) −144610. + 144610.i −0.0466344 + 0.0466344i
\(396\) 0 0
\(397\) 552320. + 552320.i 0.175879 + 0.175879i 0.789557 0.613678i \(-0.210311\pi\)
−0.613678 + 0.789557i \(0.710311\pi\)
\(398\) 0 0
\(399\) 940258. 0.295675
\(400\) 0 0
\(401\) 4.92193e6 1.52853 0.764266 0.644901i \(-0.223101\pi\)
0.764266 + 0.644901i \(0.223101\pi\)
\(402\) 0 0
\(403\) 1.68807e6 + 1.68807e6i 0.517760 + 0.517760i
\(404\) 0 0
\(405\) 772853. 772853.i 0.234131 0.234131i
\(406\) 0 0
\(407\) 12706.4i 0.00380221i
\(408\) 0 0
\(409\) 5.16304e6i 1.52615i 0.646311 + 0.763074i \(0.276311\pi\)
−0.646311 + 0.763074i \(0.723689\pi\)
\(410\) 0 0
\(411\) −3.12157e6 + 3.12157e6i −0.911526 + 0.911526i
\(412\) 0 0
\(413\) 1.66634e6 + 1.66634e6i 0.480716 + 0.480716i
\(414\) 0 0
\(415\) 2.60697e6 0.743046
\(416\) 0 0
\(417\) −2.46303e6 −0.693633
\(418\) 0 0
\(419\) −1.56043e6 1.56043e6i −0.434219 0.434219i 0.455842 0.890061i \(-0.349338\pi\)
−0.890061 + 0.455842i \(0.849338\pi\)
\(420\) 0 0
\(421\) −905154. + 905154.i −0.248896 + 0.248896i −0.820517 0.571622i \(-0.806315\pi\)
0.571622 + 0.820517i \(0.306315\pi\)
\(422\) 0 0
\(423\) 998.883i 0.000271434i
\(424\) 0 0
\(425\) 171725.i 0.0461170i
\(426\) 0 0
\(427\) −2.92657e6 + 2.92657e6i −0.776764 + 0.776764i
\(428\) 0 0
\(429\) −4532.82 4532.82i −0.00118912 0.00118912i
\(430\) 0 0
\(431\) 1.58952e6 0.412168 0.206084 0.978534i \(-0.433928\pi\)
0.206084 + 0.978534i \(0.433928\pi\)
\(432\) 0 0
\(433\) 6.53092e6 1.67400 0.836998 0.547205i \(-0.184308\pi\)
0.836998 + 0.547205i \(0.184308\pi\)
\(434\) 0 0
\(435\) 1.24914e6 + 1.24914e6i 0.316512 + 0.316512i
\(436\) 0 0
\(437\) −1.47218e6 + 1.47218e6i −0.368771 + 0.368771i
\(438\) 0 0
\(439\) 2.38268e6i 0.590071i 0.955486 + 0.295036i \(0.0953315\pi\)
−0.955486 + 0.295036i \(0.904669\pi\)
\(440\) 0 0
\(441\) 315143.i 0.0771634i
\(442\) 0 0
\(443\) 32077.4 32077.4i 0.00776586 0.00776586i −0.703213 0.710979i \(-0.748252\pi\)
0.710979 + 0.703213i \(0.248252\pi\)
\(444\) 0 0
\(445\) 549324. + 549324.i 0.131501 + 0.131501i
\(446\) 0 0
\(447\) 2.49731e6 0.591158
\(448\) 0 0
\(449\) 4.51574e6 1.05709 0.528547 0.848904i \(-0.322737\pi\)
0.528547 + 0.848904i \(0.322737\pi\)
\(450\) 0 0
\(451\) −15106.8 15106.8i −0.00349728 0.00349728i
\(452\) 0 0
\(453\) 3.06365e6 3.06365e6i 0.701445 0.701445i
\(454\) 0 0
\(455\) 719762.i 0.162990i
\(456\) 0 0
\(457\) 1.27748e6i 0.286131i −0.989713 0.143065i \(-0.954304\pi\)
0.989713 0.143065i \(-0.0456959\pi\)
\(458\) 0 0
\(459\) −792076. + 792076.i −0.175483 + 0.175483i
\(460\) 0 0
\(461\) −4.40915e6 4.40915e6i −0.966279 0.966279i 0.0331708 0.999450i \(-0.489439\pi\)
−0.999450 + 0.0331708i \(0.989439\pi\)
\(462\) 0 0
\(463\) 4.01094e6 0.869548 0.434774 0.900540i \(-0.356828\pi\)
0.434774 + 0.900540i \(0.356828\pi\)
\(464\) 0 0
\(465\) 2.96970e6 0.636914
\(466\) 0 0
\(467\) −2.22576e6 2.22576e6i −0.472266 0.472266i 0.430381 0.902647i \(-0.358379\pi\)
−0.902647 + 0.430381i \(0.858379\pi\)
\(468\) 0 0
\(469\) −4.32047e6 + 4.32047e6i −0.906982 + 0.906982i
\(470\) 0 0
\(471\) 4.93054e6i 1.02410i
\(472\) 0 0
\(473\) 4862.13i 0.000999249i
\(474\) 0 0
\(475\) 290066. 290066.i 0.0589878 0.0589878i
\(476\) 0 0
\(477\) −147858. 147858.i −0.0297542 0.0297542i
\(478\) 0 0
\(479\) −2.87342e6 −0.572216 −0.286108 0.958197i \(-0.592362\pi\)
−0.286108 + 0.958197i \(0.592362\pi\)
\(480\) 0 0
\(481\) −2.11375e6 −0.416574
\(482\) 0 0
\(483\) 3.21325e6 + 3.21325e6i 0.626724 + 0.626724i
\(484\) 0 0
\(485\) 854178. 854178.i 0.164890 0.164890i
\(486\) 0 0
\(487\) 9.71226e6i 1.85566i 0.373007 + 0.927829i \(0.378327\pi\)
−0.373007 + 0.927829i \(0.621673\pi\)
\(488\) 0 0
\(489\) 5.52328e6i 1.04454i
\(490\) 0 0
\(491\) −941766. + 941766.i −0.176295 + 0.176295i −0.789738 0.613444i \(-0.789784\pi\)
0.613444 + 0.789738i \(0.289784\pi\)
\(492\) 0 0
\(493\) −993289. 993289.i −0.184060 0.184060i
\(494\) 0 0
\(495\) 2169.45 0.000397957
\(496\) 0 0
\(497\) −2.63129e6 −0.477834
\(498\) 0 0
\(499\) −1.63368e6 1.63368e6i −0.293708 0.293708i 0.544835 0.838543i \(-0.316592\pi\)
−0.838543 + 0.544835i \(0.816592\pi\)
\(500\) 0 0
\(501\) −514158. + 514158.i −0.0915171 + 0.0915171i
\(502\) 0 0
\(503\) 3.45939e6i 0.609649i −0.952409 0.304825i \(-0.901402\pi\)
0.952409 0.304825i \(-0.0985978\pi\)
\(504\) 0 0
\(505\) 2.94253e6i 0.513443i
\(506\) 0 0
\(507\) −2.87465e6 + 2.87465e6i −0.496667 + 0.496667i
\(508\) 0 0
\(509\) 4.00462e6 + 4.00462e6i 0.685120 + 0.685120i 0.961149 0.276029i \(-0.0890186\pi\)
−0.276029 + 0.961149i \(0.589019\pi\)
\(510\) 0 0
\(511\) −2.56342e6 −0.434278
\(512\) 0 0
\(513\) −2.67584e6 −0.448918
\(514\) 0 0
\(515\) −440747. 440747.i −0.0732270 0.0732270i
\(516\) 0 0
\(517\) −22.6930 + 22.6930i −3.73392e−6 + 3.73392e-6i
\(518\) 0 0
\(519\) 1.05291e7i 1.71583i
\(520\) 0 0
\(521\) 3.26819e6i 0.527489i 0.964593 + 0.263744i \(0.0849575\pi\)
−0.964593 + 0.263744i \(0.915042\pi\)
\(522\) 0 0
\(523\) −2.30613e6 + 2.30613e6i −0.368662 + 0.368662i −0.866989 0.498327i \(-0.833948\pi\)
0.498327 + 0.866989i \(0.333948\pi\)
\(524\) 0 0
\(525\) −633112. 633112.i −0.100250 0.100250i
\(526\) 0 0
\(527\) −2.36143e6 −0.370382
\(528\) 0 0
\(529\) −3.62572e6 −0.563320
\(530\) 0 0
\(531\) −835520. 835520.i −0.128594 0.128594i
\(532\) 0 0
\(533\) 2.51306e6 2.51306e6i 0.383165 0.383165i
\(534\) 0 0
\(535\) 3.06747e6i 0.463335i
\(536\) 0 0
\(537\) 3.81141e6i 0.570361i
\(538\) 0 0
\(539\) −7159.53 + 7159.53i −0.00106148 + 0.00106148i
\(540\) 0 0
\(541\) −8.57389e6 8.57389e6i −1.25946 1.25946i −0.951350 0.308111i \(-0.900303\pi\)
−0.308111 0.951350i \(-0.599697\pi\)
\(542\) 0 0
\(543\) 8.16820e6 1.18885
\(544\) 0 0
\(545\) 3.83908e6 0.553651
\(546\) 0 0
\(547\) 552021. + 552021.i 0.0788837 + 0.0788837i 0.745448 0.666564i \(-0.232236\pi\)
−0.666564 + 0.745448i \(0.732236\pi\)
\(548\) 0 0
\(549\) 1.46741e6 1.46741e6i 0.207788 0.207788i
\(550\) 0 0
\(551\) 3.35559e6i 0.470858i
\(552\) 0 0
\(553\) 847891.i 0.117904i
\(554\) 0 0
\(555\) −1.85929e6 + 1.85929e6i −0.256220 + 0.256220i
\(556\) 0 0
\(557\) −8.78654e6 8.78654e6i −1.20000 1.20000i −0.974167 0.225829i \(-0.927491\pi\)
−0.225829 0.974167i \(-0.572509\pi\)
\(558\) 0 0
\(559\) 808833. 0.109479
\(560\) 0 0
\(561\) 6340.94 0.000850641
\(562\) 0 0
\(563\) −971504. 971504.i −0.129174 0.129174i 0.639564 0.768738i \(-0.279115\pi\)
−0.768738 + 0.639564i \(0.779115\pi\)
\(564\) 0 0
\(565\) −1.70125e6 + 1.70125e6i −0.224206 + 0.224206i
\(566\) 0 0
\(567\) 4.53145e6i 0.591943i
\(568\) 0 0
\(569\) 2.27634e6i 0.294752i 0.989081 + 0.147376i \(0.0470828\pi\)
−0.989081 + 0.147376i \(0.952917\pi\)
\(570\) 0 0
\(571\) −8.52439e6 + 8.52439e6i −1.09414 + 1.09414i −0.0990592 + 0.995082i \(0.531583\pi\)
−0.995082 + 0.0990592i \(0.968417\pi\)
\(572\) 0 0
\(573\) 4.85800e6 + 4.85800e6i 0.618118 + 0.618118i
\(574\) 0 0
\(575\) 1.98255e6 0.250066
\(576\) 0 0
\(577\) −1.05005e7 −1.31301 −0.656506 0.754321i \(-0.727966\pi\)
−0.656506 + 0.754321i \(0.727966\pi\)
\(578\) 0 0
\(579\) −4.52040e6 4.52040e6i −0.560377 0.560377i
\(580\) 0 0
\(581\) −7.64270e6 + 7.64270e6i −0.939304 + 0.939304i
\(582\) 0 0
\(583\) 6718.17i 0.000818615i
\(584\) 0 0
\(585\) 360896.i 0.0436006i
\(586\) 0 0
\(587\) 8.30426e6 8.30426e6i 0.994731 0.994731i −0.00525489 0.999986i \(-0.501673\pi\)
0.999986 + 0.00525489i \(0.00167269\pi\)
\(588\) 0 0
\(589\) −3.98877e6 3.98877e6i −0.473752 0.473752i
\(590\) 0 0
\(591\) −5.59617e6 −0.659056
\(592\) 0 0
\(593\) 1.25153e7 1.46152 0.730759 0.682635i \(-0.239166\pi\)
0.730759 + 0.682635i \(0.239166\pi\)
\(594\) 0 0
\(595\) 503435. + 503435.i 0.0582977 + 0.0582977i
\(596\) 0 0
\(597\) 9.86958e6 9.86958e6i 1.13335 1.13335i
\(598\) 0 0
\(599\) 6.70362e6i 0.763383i −0.924290 0.381691i \(-0.875342\pi\)
0.924290 0.381691i \(-0.124658\pi\)
\(600\) 0 0
\(601\) 5.33668e6i 0.602677i 0.953517 + 0.301339i \(0.0974335\pi\)
−0.953517 + 0.301339i \(0.902567\pi\)
\(602\) 0 0
\(603\) 2.16633e6 2.16633e6i 0.242622 0.242622i
\(604\) 0 0
\(605\) 2.84696e6 + 2.84696e6i 0.316222 + 0.316222i
\(606\) 0 0
\(607\) −871941. −0.0960540 −0.0480270 0.998846i \(-0.515293\pi\)
−0.0480270 + 0.998846i \(0.515293\pi\)
\(608\) 0 0
\(609\) −7.32408e6 −0.800221
\(610\) 0 0
\(611\) −3775.06 3775.06i −0.000409092 0.000409092i
\(612\) 0 0
\(613\) 7.72342e6 7.72342e6i 0.830154 0.830154i −0.157384 0.987537i \(-0.550306\pi\)
0.987537 + 0.157384i \(0.0503060\pi\)
\(614\) 0 0
\(615\) 4.42105e6i 0.471344i
\(616\) 0 0
\(617\) 644309.i 0.0681367i 0.999420 + 0.0340684i \(0.0108464\pi\)
−0.999420 + 0.0340684i \(0.989154\pi\)
\(618\) 0 0
\(619\) 1.08770e7 1.08770e7i 1.14099 1.14099i 0.152725 0.988269i \(-0.451195\pi\)
0.988269 0.152725i \(-0.0488048\pi\)
\(620\) 0 0
\(621\) −9.14445e6 9.14445e6i −0.951543 0.951543i
\(622\) 0 0
\(623\) −3.22084e6 −0.332468
\(624\) 0 0
\(625\) −390625. −0.0400000
\(626\) 0 0
\(627\) 10710.7 + 10710.7i 0.00108805 + 0.00108805i
\(628\) 0 0
\(629\) 1.47846e6 1.47846e6i 0.148999 0.148999i
\(630\) 0 0
\(631\) 1.93042e6i 0.193010i −0.995333 0.0965048i \(-0.969234\pi\)
0.995333 0.0965048i \(-0.0307663\pi\)
\(632\) 0 0
\(633\) 5.41990e6i 0.537628i
\(634\) 0 0
\(635\) 1.47601e6 1.47601e6i 0.145263 0.145263i
\(636\) 0 0
\(637\) −1.19102e6 1.19102e6i −0.116297 0.116297i
\(638\) 0 0
\(639\) 1.31935e6 0.127823
\(640\) 0 0
\(641\) 4.63206e6 0.445275 0.222638 0.974901i \(-0.428533\pi\)
0.222638 + 0.974901i \(0.428533\pi\)
\(642\) 0 0
\(643\) 8.05489e6 + 8.05489e6i 0.768303 + 0.768303i 0.977808 0.209505i \(-0.0671852\pi\)
−0.209505 + 0.977808i \(0.567185\pi\)
\(644\) 0 0
\(645\) 711460. 711460.i 0.0673366 0.0673366i
\(646\) 0 0
\(647\) 5.33268e6i 0.500824i −0.968139 0.250412i \(-0.919434\pi\)
0.968139 0.250412i \(-0.0805660\pi\)
\(648\) 0 0
\(649\) 37963.3i 0.00353795i
\(650\) 0 0
\(651\) −8.70610e6 + 8.70610e6i −0.805139 + 0.805139i
\(652\) 0 0
\(653\) 316713. + 316713.i 0.0290659 + 0.0290659i 0.721490 0.692424i \(-0.243457\pi\)
−0.692424 + 0.721490i \(0.743457\pi\)
\(654\) 0 0
\(655\) −176428. −0.0160681
\(656\) 0 0
\(657\) 1.28532e6 0.116171
\(658\) 0 0
\(659\) −1.13480e7 1.13480e7i −1.01790 1.01790i −0.999837 0.0180657i \(-0.994249\pi\)
−0.0180657 0.999837i \(-0.505751\pi\)
\(660\) 0 0
\(661\) −8.40738e6 + 8.40738e6i −0.748440 + 0.748440i −0.974186 0.225746i \(-0.927518\pi\)
0.225746 + 0.974186i \(0.427518\pi\)
\(662\) 0 0
\(663\) 1.05484e6i 0.0931971i
\(664\) 0 0
\(665\) 1.70074e6i 0.149136i
\(666\) 0 0
\(667\) 1.14674e7 1.14674e7i 0.998048 0.998048i
\(668\) 0 0
\(669\) 8.91699e6 + 8.91699e6i 0.770288 + 0.770288i
\(670\) 0 0
\(671\) −66674.3 −0.00571679
\(672\) 0 0
\(673\) −1.83364e7 −1.56054 −0.780272 0.625440i \(-0.784920\pi\)
−0.780272 + 0.625440i \(0.784920\pi\)
\(674\) 0 0
\(675\) 1.80175e6 + 1.80175e6i 0.152207 + 0.152207i
\(676\) 0 0
\(677\) −1.19331e6 + 1.19331e6i −0.100065 + 0.100065i −0.755367 0.655302i \(-0.772541\pi\)
0.655302 + 0.755367i \(0.272541\pi\)
\(678\) 0 0
\(679\) 5.00828e6i 0.416883i
\(680\) 0 0
\(681\) 3.40092e6i 0.281015i
\(682\) 0 0
\(683\) 2.57827e6 2.57827e6i 0.211483 0.211483i −0.593414 0.804897i \(-0.702220\pi\)
0.804897 + 0.593414i \(0.202220\pi\)
\(684\) 0 0
\(685\) −5.64629e6 5.64629e6i −0.459766 0.459766i
\(686\) 0 0
\(687\) −1.65250e7 −1.33583
\(688\) 0 0
\(689\) −1.11759e6 −0.0896882
\(690\) 0 0
\(691\) −2.88279e6 2.88279e6i −0.229678 0.229678i 0.582880 0.812558i \(-0.301926\pi\)
−0.812558 + 0.582880i \(0.801926\pi\)
\(692\) 0 0
\(693\) −6360.04 + 6360.04i −0.000503068 + 0.000503068i
\(694\) 0 0
\(695\) 4.45513e6i 0.349863i
\(696\) 0 0
\(697\) 3.51551e6i 0.274098i
\(698\) 0 0
\(699\) −329785. + 329785.i −0.0255293 + 0.0255293i
\(700\) 0 0
\(701\) −5.60275e6 5.60275e6i −0.430632 0.430632i 0.458211 0.888843i \(-0.348490\pi\)
−0.888843 + 0.458211i \(0.848490\pi\)
\(702\) 0 0
\(703\) 4.99462e6 0.381166
\(704\) 0 0
\(705\) −6641.19 −0.000503238
\(706\) 0 0
\(707\) −8.62643e6 8.62643e6i −0.649056 0.649056i
\(708\) 0 0
\(709\) −1.35415e6 + 1.35415e6i −0.101170 + 0.101170i −0.755880 0.654710i \(-0.772791\pi\)
0.654710 + 0.755880i \(0.272791\pi\)
\(710\) 0 0
\(711\) 425141.i 0.0315398i
\(712\) 0 0
\(713\) 2.72625e7i 2.00836i
\(714\) 0 0
\(715\) 8198.96 8198.96i 0.000599782 0.000599782i
\(716\) 0 0
\(717\) 1.39661e7 + 1.39661e7i 1.01456 + 1.01456i
\(718\) 0 0
\(719\) −2.32962e6 −0.168059 −0.0840297 0.996463i \(-0.526779\pi\)
−0.0840297 + 0.996463i \(0.526779\pi\)
\(720\) 0 0
\(721\) 2.58422e6 0.185136
\(722\) 0 0
\(723\) 3.78583e6 + 3.78583e6i 0.269349 + 0.269349i
\(724\) 0 0
\(725\) −2.25945e6 + 2.25945e6i −0.159646 + 0.159646i
\(726\) 0 0
\(727\) 7.09851e6i 0.498117i 0.968488 + 0.249058i \(0.0801211\pi\)
−0.968488 + 0.249058i \(0.919879\pi\)
\(728\) 0 0
\(729\) 1.59647e7i 1.11261i
\(730\) 0 0
\(731\) −565736. + 565736.i −0.0391580 + 0.0391580i
\(732\) 0 0
\(733\) −4.97014e6 4.97014e6i −0.341672 0.341672i 0.515324 0.856995i \(-0.327672\pi\)
−0.856995 + 0.515324i \(0.827672\pi\)
\(734\) 0 0
\(735\) −2.09527e6 −0.143061
\(736\) 0 0
\(737\) −98430.8 −0.00667517
\(738\) 0 0
\(739\) 3.33606e6 + 3.33606e6i 0.224710 + 0.224710i 0.810478 0.585768i \(-0.199207\pi\)
−0.585768 + 0.810478i \(0.699207\pi\)
\(740\) 0 0
\(741\) −1.78176e6 + 1.78176e6i −0.119208 + 0.119208i
\(742\) 0 0
\(743\) 1.56473e7i 1.03985i 0.854213 + 0.519923i \(0.174039\pi\)
−0.854213 + 0.519923i \(0.825961\pi\)
\(744\) 0 0
\(745\) 4.51713e6i 0.298175i
\(746\) 0 0
\(747\) 3.83212e6 3.83212e6i 0.251268 0.251268i
\(748\) 0 0
\(749\) 8.99271e6 + 8.99271e6i 0.585714 + 0.585714i
\(750\) 0 0
\(751\) −2.63215e7 −1.70298 −0.851491 0.524369i \(-0.824301\pi\)
−0.851491 + 0.524369i \(0.824301\pi\)
\(752\) 0 0
\(753\) −2.95330e6 −0.189810
\(754\) 0 0
\(755\) 5.54152e6 + 5.54152e6i 0.353803 + 0.353803i
\(756\) 0 0
\(757\) −6.68400e6 + 6.68400e6i −0.423932 + 0.423932i −0.886555 0.462623i \(-0.846908\pi\)
0.462623 + 0.886555i \(0.346908\pi\)
\(758\) 0 0
\(759\) 73205.6i 0.00461254i
\(760\) 0 0
\(761\) 2.40574e7i 1.50587i −0.658096 0.752934i \(-0.728638\pi\)
0.658096 0.752934i \(-0.271362\pi\)
\(762\) 0 0
\(763\) −1.12548e7 + 1.12548e7i −0.699885 + 0.699885i
\(764\) 0 0
\(765\) −252427. 252427.i −0.0155949 0.0155949i
\(766\) 0 0
\(767\) −6.31534e6 −0.387622
\(768\) 0 0
\(769\) −4.66056e6 −0.284199 −0.142099 0.989852i \(-0.545385\pi\)
−0.142099 + 0.989852i \(0.545385\pi\)
\(770\) 0 0
\(771\) 1.08260e7 + 1.08260e7i 0.655890 + 0.655890i
\(772\) 0 0
\(773\) 5.41580e6 5.41580e6i 0.325997 0.325997i −0.525065 0.851062i \(-0.675959\pi\)
0.851062 + 0.525065i \(0.175959\pi\)
\(774\) 0 0
\(775\) 5.37159e6i 0.321254i
\(776\) 0 0
\(777\) 1.09015e7i 0.647790i
\(778\) 0 0
\(779\) −5.93816e6 + 5.93816e6i −0.350597 + 0.350597i
\(780\) 0 0
\(781\) −29973.5 29973.5i −0.00175837 0.00175837i
\(782\) 0 0
\(783\) 2.08433e7 1.21496
\(784\) 0 0
\(785\) 8.91836e6 0.516548
\(786\) 0 0 <