Properties

Label 128.5.f.b.31.3
Level $128$
Weight $5$
Character 128.31
Analytic conductor $13.231$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 128.f (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2313552747\)
Analytic rank: \(0\)
Dimension: \(14\)
Relative dimension: \(7\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + 11456 x^{6} - 19968 x^{5} + 31744 x^{4} - 139264 x^{3} + 491520 x^{2} - 1048576 x + 2097152\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{42} \)
Twist minimal: no (minimal twist has level 16)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 31.3
Root \(-2.15805 + 1.82834i\) of defining polynomial
Character \(\chi\) \(=\) 128.31
Dual form 128.5.f.b.95.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.91498 - 3.91498i) q^{3} +(-4.72348 - 4.72348i) q^{5} +45.3712 q^{7} -50.3458i q^{9} +O(q^{10})\) \(q+(-3.91498 - 3.91498i) q^{3} +(-4.72348 - 4.72348i) q^{5} +45.3712 q^{7} -50.3458i q^{9} +(-110.228 + 110.228i) q^{11} +(157.128 - 157.128i) q^{13} +36.9847i q^{15} -378.592 q^{17} +(-203.127 - 203.127i) q^{19} +(-177.627 - 177.627i) q^{21} -740.444 q^{23} -580.377i q^{25} +(-514.217 + 514.217i) q^{27} +(-82.6244 + 82.6244i) q^{29} +286.217i q^{31} +863.080 q^{33} +(-214.310 - 214.310i) q^{35} +(-1470.39 - 1470.39i) q^{37} -1230.31 q^{39} -1301.21i q^{41} +(366.979 - 366.979i) q^{43} +(-237.808 + 237.808i) q^{45} +751.307i q^{47} -342.455 q^{49} +(1482.18 + 1482.18i) q^{51} +(1929.33 + 1929.33i) q^{53} +1041.32 q^{55} +1590.48i q^{57} +(1357.57 - 1357.57i) q^{59} +(1835.78 - 1835.78i) q^{61} -2284.25i q^{63} -1484.39 q^{65} +(-2205.02 - 2205.02i) q^{67} +(2898.83 + 2898.83i) q^{69} +8970.40 q^{71} +9350.46i q^{73} +(-2272.17 + 2272.17i) q^{75} +(-5001.17 + 5001.17i) q^{77} -2860.08i q^{79} -51.7173 q^{81} +(1036.63 + 1036.63i) q^{83} +(1788.27 + 1788.27i) q^{85} +646.946 q^{87} -5171.06i q^{89} +(7129.10 - 7129.10i) q^{91} +(1120.54 - 1120.54i) q^{93} +1918.94i q^{95} +8539.92 q^{97} +(5549.51 + 5549.51i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 2q^{3} + 2q^{5} - 4q^{7} + O(q^{10}) \) \( 14q + 2q^{3} + 2q^{5} - 4q^{7} - 94q^{11} + 2q^{13} - 4q^{17} + 706q^{19} + 164q^{21} + 1148q^{23} + 1664q^{27} - 862q^{29} - 4q^{33} - 1340q^{35} + 1826q^{37} + 2684q^{39} - 1694q^{43} - 1410q^{45} + 682q^{49} + 3012q^{51} + 482q^{53} - 11780q^{55} + 2786q^{59} + 3778q^{61} - 2020q^{65} - 7998q^{67} - 9628q^{69} + 19964q^{71} - 17570q^{75} + 9508q^{77} + 1454q^{81} + 17282q^{83} - 9948q^{85} - 49284q^{87} + 28036q^{91} - 8896q^{93} - 4q^{97} - 49214q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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
\(3\) −3.91498 3.91498i −0.434998 0.434998i 0.455327 0.890324i \(-0.349523\pi\)
−0.890324 + 0.455327i \(0.849523\pi\)
\(4\) 0 0
\(5\) −4.72348 4.72348i −0.188939 0.188939i 0.606298 0.795237i \(-0.292654\pi\)
−0.795237 + 0.606298i \(0.792654\pi\)
\(6\) 0 0
\(7\) 45.3712 0.925943 0.462971 0.886373i \(-0.346783\pi\)
0.462971 + 0.886373i \(0.346783\pi\)
\(8\) 0 0
\(9\) 50.3458i 0.621554i
\(10\) 0 0
\(11\) −110.228 + 110.228i −0.910974 + 0.910974i −0.996349 0.0853752i \(-0.972791\pi\)
0.0853752 + 0.996349i \(0.472791\pi\)
\(12\) 0 0
\(13\) 157.128 157.128i 0.929754 0.929754i −0.0679357 0.997690i \(-0.521641\pi\)
0.997690 + 0.0679357i \(0.0216413\pi\)
\(14\) 0 0
\(15\) 36.9847i 0.164376i
\(16\) 0 0
\(17\) −378.592 −1.31001 −0.655003 0.755626i \(-0.727333\pi\)
−0.655003 + 0.755626i \(0.727333\pi\)
\(18\) 0 0
\(19\) −203.127 203.127i −0.562680 0.562680i 0.367388 0.930068i \(-0.380252\pi\)
−0.930068 + 0.367388i \(0.880252\pi\)
\(20\) 0 0
\(21\) −177.627 177.627i −0.402783 0.402783i
\(22\) 0 0
\(23\) −740.444 −1.39971 −0.699853 0.714287i \(-0.746751\pi\)
−0.699853 + 0.714287i \(0.746751\pi\)
\(24\) 0 0
\(25\) 580.377i 0.928604i
\(26\) 0 0
\(27\) −514.217 + 514.217i −0.705372 + 0.705372i
\(28\) 0 0
\(29\) −82.6244 + 82.6244i −0.0982455 + 0.0982455i −0.754521 0.656276i \(-0.772131\pi\)
0.656276 + 0.754521i \(0.272131\pi\)
\(30\) 0 0
\(31\) 286.217i 0.297833i 0.988850 + 0.148916i \(0.0475785\pi\)
−0.988850 + 0.148916i \(0.952421\pi\)
\(32\) 0 0
\(33\) 863.080 0.792543
\(34\) 0 0
\(35\) −214.310 214.310i −0.174947 0.174947i
\(36\) 0 0
\(37\) −1470.39 1470.39i −1.07406 1.07406i −0.997028 0.0770352i \(-0.975455\pi\)
−0.0770352 0.997028i \(-0.524545\pi\)
\(38\) 0 0
\(39\) −1230.31 −0.808882
\(40\) 0 0
\(41\) 1301.21i 0.774070i −0.922065 0.387035i \(-0.873499\pi\)
0.922065 0.387035i \(-0.126501\pi\)
\(42\) 0 0
\(43\) 366.979 366.979i 0.198474 0.198474i −0.600871 0.799346i \(-0.705180\pi\)
0.799346 + 0.600871i \(0.205180\pi\)
\(44\) 0 0
\(45\) −237.808 + 237.808i −0.117436 + 0.117436i
\(46\) 0 0
\(47\) 751.307i 0.340112i 0.985434 + 0.170056i \(0.0543948\pi\)
−0.985434 + 0.170056i \(0.945605\pi\)
\(48\) 0 0
\(49\) −342.455 −0.142630
\(50\) 0 0
\(51\) 1482.18 + 1482.18i 0.569850 + 0.569850i
\(52\) 0 0
\(53\) 1929.33 + 1929.33i 0.686838 + 0.686838i 0.961532 0.274693i \(-0.0885764\pi\)
−0.274693 + 0.961532i \(0.588576\pi\)
\(54\) 0 0
\(55\) 1041.32 0.344238
\(56\) 0 0
\(57\) 1590.48i 0.489529i
\(58\) 0 0
\(59\) 1357.57 1357.57i 0.389994 0.389994i −0.484691 0.874685i \(-0.661068\pi\)
0.874685 + 0.484691i \(0.161068\pi\)
\(60\) 0 0
\(61\) 1835.78 1835.78i 0.493356 0.493356i −0.416006 0.909362i \(-0.636570\pi\)
0.909362 + 0.416006i \(0.136570\pi\)
\(62\) 0 0
\(63\) 2284.25i 0.575523i
\(64\) 0 0
\(65\) −1484.39 −0.351334
\(66\) 0 0
\(67\) −2205.02 2205.02i −0.491204 0.491204i 0.417481 0.908686i \(-0.362913\pi\)
−0.908686 + 0.417481i \(0.862913\pi\)
\(68\) 0 0
\(69\) 2898.83 + 2898.83i 0.608869 + 0.608869i
\(70\) 0 0
\(71\) 8970.40 1.77949 0.889744 0.456460i \(-0.150883\pi\)
0.889744 + 0.456460i \(0.150883\pi\)
\(72\) 0 0
\(73\) 9350.46i 1.75464i 0.479909 + 0.877318i \(0.340670\pi\)
−0.479909 + 0.877318i \(0.659330\pi\)
\(74\) 0 0
\(75\) −2272.17 + 2272.17i −0.403941 + 0.403941i
\(76\) 0 0
\(77\) −5001.17 + 5001.17i −0.843509 + 0.843509i
\(78\) 0 0
\(79\) 2860.08i 0.458273i −0.973394 0.229137i \(-0.926410\pi\)
0.973394 0.229137i \(-0.0735903\pi\)
\(80\) 0 0
\(81\) −51.7173 −0.00788253
\(82\) 0 0
\(83\) 1036.63 + 1036.63i 0.150477 + 0.150477i 0.778331 0.627854i \(-0.216067\pi\)
−0.627854 + 0.778331i \(0.716067\pi\)
\(84\) 0 0
\(85\) 1788.27 + 1788.27i 0.247512 + 0.247512i
\(86\) 0 0
\(87\) 646.946 0.0854731
\(88\) 0 0
\(89\) 5171.06i 0.652830i −0.945227 0.326415i \(-0.894159\pi\)
0.945227 0.326415i \(-0.105841\pi\)
\(90\) 0 0
\(91\) 7129.10 7129.10i 0.860899 0.860899i
\(92\) 0 0
\(93\) 1120.54 1120.54i 0.129557 0.129557i
\(94\) 0 0
\(95\) 1918.94i 0.212625i
\(96\) 0 0
\(97\) 8539.92 0.907633 0.453817 0.891095i \(-0.350062\pi\)
0.453817 + 0.891095i \(0.350062\pi\)
\(98\) 0 0
\(99\) 5549.51 + 5549.51i 0.566219 + 0.566219i
\(100\) 0 0
\(101\) −537.642 537.642i −0.0527049 0.0527049i 0.680263 0.732968i \(-0.261866\pi\)
−0.732968 + 0.680263i \(0.761866\pi\)
\(102\) 0 0
\(103\) −5543.86 −0.522562 −0.261281 0.965263i \(-0.584145\pi\)
−0.261281 + 0.965263i \(0.584145\pi\)
\(104\) 0 0
\(105\) 1678.04i 0.152203i
\(106\) 0 0
\(107\) 2989.60 2989.60i 0.261123 0.261123i −0.564387 0.825510i \(-0.690887\pi\)
0.825510 + 0.564387i \(0.190887\pi\)
\(108\) 0 0
\(109\) 3353.83 3353.83i 0.282285 0.282285i −0.551734 0.834020i \(-0.686034\pi\)
0.834020 + 0.551734i \(0.186034\pi\)
\(110\) 0 0
\(111\) 11513.1i 0.934431i
\(112\) 0 0
\(113\) −3193.81 −0.250122 −0.125061 0.992149i \(-0.539913\pi\)
−0.125061 + 0.992149i \(0.539913\pi\)
\(114\) 0 0
\(115\) 3497.48 + 3497.48i 0.264459 + 0.264459i
\(116\) 0 0
\(117\) −7910.76 7910.76i −0.577892 0.577892i
\(118\) 0 0
\(119\) −17177.2 −1.21299
\(120\) 0 0
\(121\) 9659.34i 0.659746i
\(122\) 0 0
\(123\) −5094.22 + 5094.22i −0.336719 + 0.336719i
\(124\) 0 0
\(125\) −5693.58 + 5693.58i −0.364389 + 0.364389i
\(126\) 0 0
\(127\) 22900.5i 1.41983i −0.704287 0.709915i \(-0.748733\pi\)
0.704287 0.709915i \(-0.251267\pi\)
\(128\) 0 0
\(129\) −2873.43 −0.172672
\(130\) 0 0
\(131\) −19255.9 19255.9i −1.12207 1.12207i −0.991429 0.130644i \(-0.958296\pi\)
−0.130644 0.991429i \(-0.541704\pi\)
\(132\) 0 0
\(133\) −9216.13 9216.13i −0.521009 0.521009i
\(134\) 0 0
\(135\) 4857.79 0.266545
\(136\) 0 0
\(137\) 19938.2i 1.06229i −0.847280 0.531147i \(-0.821761\pi\)
0.847280 0.531147i \(-0.178239\pi\)
\(138\) 0 0
\(139\) −25175.4 + 25175.4i −1.30301 + 1.30301i −0.376649 + 0.926356i \(0.622924\pi\)
−0.926356 + 0.376649i \(0.877076\pi\)
\(140\) 0 0
\(141\) 2941.35 2941.35i 0.147948 0.147948i
\(142\) 0 0
\(143\) 34639.8i 1.69396i
\(144\) 0 0
\(145\) 780.550 0.0371249
\(146\) 0 0
\(147\) 1340.70 + 1340.70i 0.0620438 + 0.0620438i
\(148\) 0 0
\(149\) 3216.99 + 3216.99i 0.144903 + 0.144903i 0.775837 0.630934i \(-0.217328\pi\)
−0.630934 + 0.775837i \(0.717328\pi\)
\(150\) 0 0
\(151\) −14770.5 −0.647802 −0.323901 0.946091i \(-0.604994\pi\)
−0.323901 + 0.946091i \(0.604994\pi\)
\(152\) 0 0
\(153\) 19060.5i 0.814239i
\(154\) 0 0
\(155\) 1351.94 1351.94i 0.0562723 0.0562723i
\(156\) 0 0
\(157\) 18014.6 18014.6i 0.730845 0.730845i −0.239942 0.970787i \(-0.577128\pi\)
0.970787 + 0.239942i \(0.0771284\pi\)
\(158\) 0 0
\(159\) 15106.6i 0.597547i
\(160\) 0 0
\(161\) −33594.8 −1.29605
\(162\) 0 0
\(163\) −15083.2 15083.2i −0.567700 0.567700i 0.363784 0.931483i \(-0.381485\pi\)
−0.931483 + 0.363784i \(0.881485\pi\)
\(164\) 0 0
\(165\) −4076.74 4076.74i −0.149743 0.149743i
\(166\) 0 0
\(167\) 23733.6 0.851001 0.425501 0.904958i \(-0.360098\pi\)
0.425501 + 0.904958i \(0.360098\pi\)
\(168\) 0 0
\(169\) 20817.7i 0.728885i
\(170\) 0 0
\(171\) −10226.6 + 10226.6i −0.349736 + 0.349736i
\(172\) 0 0
\(173\) 12072.3 12072.3i 0.403363 0.403363i −0.476053 0.879416i \(-0.657933\pi\)
0.879416 + 0.476053i \(0.157933\pi\)
\(174\) 0 0
\(175\) 26332.4i 0.859834i
\(176\) 0 0
\(177\) −10629.7 −0.339293
\(178\) 0 0
\(179\) 28111.5 + 28111.5i 0.877361 + 0.877361i 0.993261 0.115900i \(-0.0369752\pi\)
−0.115900 + 0.993261i \(0.536975\pi\)
\(180\) 0 0
\(181\) 15906.7 + 15906.7i 0.485539 + 0.485539i 0.906895 0.421356i \(-0.138446\pi\)
−0.421356 + 0.906895i \(0.638446\pi\)
\(182\) 0 0
\(183\) −14374.1 −0.429218
\(184\) 0 0
\(185\) 13890.8i 0.405866i
\(186\) 0 0
\(187\) 41731.4 41731.4i 1.19338 1.19338i
\(188\) 0 0
\(189\) −23330.6 + 23330.6i −0.653134 + 0.653134i
\(190\) 0 0
\(191\) 28038.6i 0.768581i 0.923212 + 0.384290i \(0.125554\pi\)
−0.923212 + 0.384290i \(0.874446\pi\)
\(192\) 0 0
\(193\) 56713.1 1.52254 0.761270 0.648436i \(-0.224576\pi\)
0.761270 + 0.648436i \(0.224576\pi\)
\(194\) 0 0
\(195\) 5811.35 + 5811.35i 0.152830 + 0.152830i
\(196\) 0 0
\(197\) 10179.3 + 10179.3i 0.262292 + 0.262292i 0.825985 0.563692i \(-0.190620\pi\)
−0.563692 + 0.825985i \(0.690620\pi\)
\(198\) 0 0
\(199\) 31787.3 0.802689 0.401344 0.915927i \(-0.368543\pi\)
0.401344 + 0.915927i \(0.368543\pi\)
\(200\) 0 0
\(201\) 17265.2i 0.427346i
\(202\) 0 0
\(203\) −3748.77 + 3748.77i −0.0909697 + 0.0909697i
\(204\) 0 0
\(205\) −6146.25 + 6146.25i −0.146252 + 0.146252i
\(206\) 0 0
\(207\) 37278.3i 0.869992i
\(208\) 0 0
\(209\) 44780.6 1.02517
\(210\) 0 0
\(211\) 10699.8 + 10699.8i 0.240332 + 0.240332i 0.816988 0.576655i \(-0.195642\pi\)
−0.576655 + 0.816988i \(0.695642\pi\)
\(212\) 0 0
\(213\) −35118.9 35118.9i −0.774073 0.774073i
\(214\) 0 0
\(215\) −3466.84 −0.0749992
\(216\) 0 0
\(217\) 12986.0i 0.275776i
\(218\) 0 0
\(219\) 36606.9 36606.9i 0.763263 0.763263i
\(220\) 0 0
\(221\) −59487.5 + 59487.5i −1.21798 + 1.21798i
\(222\) 0 0
\(223\) 91700.4i 1.84400i −0.387187 0.922001i \(-0.626553\pi\)
0.387187 0.922001i \(-0.373447\pi\)
\(224\) 0 0
\(225\) −29219.6 −0.577177
\(226\) 0 0
\(227\) −17499.5 17499.5i −0.339605 0.339605i 0.516614 0.856218i \(-0.327192\pi\)
−0.856218 + 0.516614i \(0.827192\pi\)
\(228\) 0 0
\(229\) 63859.8 + 63859.8i 1.21775 + 1.21775i 0.968420 + 0.249326i \(0.0802091\pi\)
0.249326 + 0.968420i \(0.419791\pi\)
\(230\) 0 0
\(231\) 39159.0 0.733850
\(232\) 0 0
\(233\) 63891.7i 1.17688i 0.808540 + 0.588441i \(0.200258\pi\)
−0.808540 + 0.588441i \(0.799742\pi\)
\(234\) 0 0
\(235\) 3548.79 3548.79i 0.0642605 0.0642605i
\(236\) 0 0
\(237\) −11197.2 + 11197.2i −0.199348 + 0.199348i
\(238\) 0 0
\(239\) 12096.4i 0.211768i 0.994378 + 0.105884i \(0.0337672\pi\)
−0.994378 + 0.105884i \(0.966233\pi\)
\(240\) 0 0
\(241\) 27978.6 0.481717 0.240859 0.970560i \(-0.422571\pi\)
0.240859 + 0.970560i \(0.422571\pi\)
\(242\) 0 0
\(243\) 41854.0 + 41854.0i 0.708801 + 0.708801i
\(244\) 0 0
\(245\) 1617.58 + 1617.58i 0.0269484 + 0.0269484i
\(246\) 0 0
\(247\) −63834.2 −1.04631
\(248\) 0 0
\(249\) 8116.80i 0.130914i
\(250\) 0 0
\(251\) −1996.06 + 1996.06i −0.0316830 + 0.0316830i −0.722771 0.691088i \(-0.757132\pi\)
0.691088 + 0.722771i \(0.257132\pi\)
\(252\) 0 0
\(253\) 81617.5 81617.5i 1.27509 1.27509i
\(254\) 0 0
\(255\) 14002.1i 0.215334i
\(256\) 0 0
\(257\) −73510.4 −1.11297 −0.556484 0.830859i \(-0.687850\pi\)
−0.556484 + 0.830859i \(0.687850\pi\)
\(258\) 0 0
\(259\) −66713.5 66713.5i −0.994521 0.994521i
\(260\) 0 0
\(261\) 4159.80 + 4159.80i 0.0610648 + 0.0610648i
\(262\) 0 0
\(263\) 68109.3 0.984680 0.492340 0.870403i \(-0.336142\pi\)
0.492340 + 0.870403i \(0.336142\pi\)
\(264\) 0 0
\(265\) 18226.3i 0.259542i
\(266\) 0 0
\(267\) −20244.6 + 20244.6i −0.283980 + 0.283980i
\(268\) 0 0
\(269\) 15056.1 15056.1i 0.208069 0.208069i −0.595377 0.803446i \(-0.702997\pi\)
0.803446 + 0.595377i \(0.202997\pi\)
\(270\) 0 0
\(271\) 104320.i 1.42046i 0.703968 + 0.710232i \(0.251410\pi\)
−0.703968 + 0.710232i \(0.748590\pi\)
\(272\) 0 0
\(273\) −55820.6 −0.748979
\(274\) 0 0
\(275\) 63973.7 + 63973.7i 0.845934 + 0.845934i
\(276\) 0 0
\(277\) −2136.36 2136.36i −0.0278430 0.0278430i 0.693048 0.720891i \(-0.256267\pi\)
−0.720891 + 0.693048i \(0.756267\pi\)
\(278\) 0 0
\(279\) 14409.8 0.185119
\(280\) 0 0
\(281\) 36783.7i 0.465846i −0.972495 0.232923i \(-0.925171\pi\)
0.972495 0.232923i \(-0.0748290\pi\)
\(282\) 0 0
\(283\) −14172.0 + 14172.0i −0.176953 + 0.176953i −0.790026 0.613073i \(-0.789933\pi\)
0.613073 + 0.790026i \(0.289933\pi\)
\(284\) 0 0
\(285\) 7512.60 7512.60i 0.0924913 0.0924913i
\(286\) 0 0
\(287\) 59037.5i 0.716744i
\(288\) 0 0
\(289\) 59810.8 0.716117
\(290\) 0 0
\(291\) −33433.6 33433.6i −0.394819 0.394819i
\(292\) 0 0
\(293\) −80721.8 80721.8i −0.940276 0.940276i 0.0580384 0.998314i \(-0.481515\pi\)
−0.998314 + 0.0580384i \(0.981515\pi\)
\(294\) 0 0
\(295\) −12824.9 −0.147370
\(296\) 0 0
\(297\) 113362.i 1.28515i
\(298\) 0 0
\(299\) −116345. + 116345.i −1.30138 + 1.30138i
\(300\) 0 0
\(301\) 16650.3 16650.3i 0.183776 0.183776i
\(302\) 0 0
\(303\) 4209.72i 0.0458530i
\(304\) 0 0
\(305\) −17342.5 −0.186429
\(306\) 0 0
\(307\) −113714. 113714.i −1.20653 1.20653i −0.972143 0.234389i \(-0.924691\pi\)
−0.234389 0.972143i \(-0.575309\pi\)
\(308\) 0 0
\(309\) 21704.1 + 21704.1i 0.227313 + 0.227313i
\(310\) 0 0
\(311\) −93801.8 −0.969819 −0.484909 0.874564i \(-0.661147\pi\)
−0.484909 + 0.874564i \(0.661147\pi\)
\(312\) 0 0
\(313\) 9229.52i 0.0942086i −0.998890 0.0471043i \(-0.985001\pi\)
0.998890 0.0471043i \(-0.0149993\pi\)
\(314\) 0 0
\(315\) −10789.6 + 10789.6i −0.108739 + 0.108739i
\(316\) 0 0
\(317\) 8447.44 8447.44i 0.0840634 0.0840634i −0.663825 0.747888i \(-0.731068\pi\)
0.747888 + 0.663825i \(0.231068\pi\)
\(318\) 0 0
\(319\) 18215.0i 0.178998i
\(320\) 0 0
\(321\) −23408.5 −0.227176
\(322\) 0 0
\(323\) 76902.4 + 76902.4i 0.737114 + 0.737114i
\(324\) 0 0
\(325\) −91193.8 91193.8i −0.863373 0.863373i
\(326\) 0 0
\(327\) −26260.4 −0.245587
\(328\) 0 0
\(329\) 34087.7i 0.314924i
\(330\) 0 0
\(331\) 46092.1 46092.1i 0.420698 0.420698i −0.464746 0.885444i \(-0.653854\pi\)
0.885444 + 0.464746i \(0.153854\pi\)
\(332\) 0 0
\(333\) −74028.2 + 74028.2i −0.667588 + 0.667588i
\(334\) 0 0
\(335\) 20830.7i 0.185616i
\(336\) 0 0
\(337\) 39317.8 0.346201 0.173101 0.984904i \(-0.444621\pi\)
0.173101 + 0.984904i \(0.444621\pi\)
\(338\) 0 0
\(339\) 12503.7 + 12503.7i 0.108803 + 0.108803i
\(340\) 0 0
\(341\) −31549.1 31549.1i −0.271318 0.271318i
\(342\) 0 0
\(343\) −124474. −1.05801
\(344\) 0 0
\(345\) 27385.1i 0.230079i
\(346\) 0 0
\(347\) 67694.0 67694.0i 0.562201 0.562201i −0.367731 0.929932i \(-0.619865\pi\)
0.929932 + 0.367731i \(0.119865\pi\)
\(348\) 0 0
\(349\) 7662.83 7662.83i 0.0629127 0.0629127i −0.674950 0.737863i \(-0.735835\pi\)
0.737863 + 0.674950i \(0.235835\pi\)
\(350\) 0 0
\(351\) 161596.i 1.31165i
\(352\) 0 0
\(353\) 70618.0 0.566716 0.283358 0.959014i \(-0.408551\pi\)
0.283358 + 0.959014i \(0.408551\pi\)
\(354\) 0 0
\(355\) −42371.5 42371.5i −0.336215 0.336215i
\(356\) 0 0
\(357\) 67248.3 + 67248.3i 0.527649 + 0.527649i
\(358\) 0 0
\(359\) −168144. −1.30465 −0.652323 0.757941i \(-0.726206\pi\)
−0.652323 + 0.757941i \(0.726206\pi\)
\(360\) 0 0
\(361\) 47799.6i 0.366783i
\(362\) 0 0
\(363\) −37816.1 + 37816.1i −0.286988 + 0.286988i
\(364\) 0 0
\(365\) 44166.7 44166.7i 0.331520 0.331520i
\(366\) 0 0
\(367\) 82596.4i 0.613238i −0.951832 0.306619i \(-0.900802\pi\)
0.951832 0.306619i \(-0.0991977\pi\)
\(368\) 0 0
\(369\) −65510.6 −0.481126
\(370\) 0 0
\(371\) 87536.0 + 87536.0i 0.635973 + 0.635973i
\(372\) 0 0
\(373\) 76631.0 + 76631.0i 0.550791 + 0.550791i 0.926669 0.375878i \(-0.122659\pi\)
−0.375878 + 0.926669i \(0.622659\pi\)
\(374\) 0 0
\(375\) 44580.5 0.317017
\(376\) 0 0
\(377\) 25965.3i 0.182688i
\(378\) 0 0
\(379\) 95935.8 95935.8i 0.667886 0.667886i −0.289340 0.957226i \(-0.593436\pi\)
0.957226 + 0.289340i \(0.0934360\pi\)
\(380\) 0 0
\(381\) −89654.8 + 89654.8i −0.617623 + 0.617623i
\(382\) 0 0
\(383\) 168708.i 1.15011i −0.818116 0.575054i \(-0.804981\pi\)
0.818116 0.575054i \(-0.195019\pi\)
\(384\) 0 0
\(385\) 47245.9 0.318744
\(386\) 0 0
\(387\) −18475.9 18475.9i −0.123362 0.123362i
\(388\) 0 0
\(389\) −66490.0 66490.0i −0.439397 0.439397i 0.452412 0.891809i \(-0.350564\pi\)
−0.891809 + 0.452412i \(0.850564\pi\)
\(390\) 0 0
\(391\) 280326. 1.83362
\(392\) 0 0
\(393\) 150773.i 0.976199i
\(394\) 0 0
\(395\) −13509.6 + 13509.6i −0.0865859 + 0.0865859i
\(396\) 0 0
\(397\) −18578.8 + 18578.8i −0.117879 + 0.117879i −0.763586 0.645706i \(-0.776563\pi\)
0.645706 + 0.763586i \(0.276563\pi\)
\(398\) 0 0
\(399\) 72162.0i 0.453276i
\(400\) 0 0
\(401\) −129108. −0.802908 −0.401454 0.915879i \(-0.631495\pi\)
−0.401454 + 0.915879i \(0.631495\pi\)
\(402\) 0 0
\(403\) 44972.9 + 44972.9i 0.276911 + 0.276911i
\(404\) 0 0
\(405\) 244.286 + 244.286i 0.00148932 + 0.00148932i
\(406\) 0 0
\(407\) 324156. 1.95689
\(408\) 0 0
\(409\) 17952.4i 0.107319i −0.998559 0.0536594i \(-0.982911\pi\)
0.998559 0.0536594i \(-0.0170885\pi\)
\(410\) 0 0
\(411\) −78057.7 + 78057.7i −0.462096 + 0.462096i
\(412\) 0 0
\(413\) 61594.5 61594.5i 0.361112 0.361112i
\(414\) 0 0
\(415\) 9793.04i 0.0568619i
\(416\) 0 0
\(417\) 197122. 1.13361
\(418\) 0 0
\(419\) −56887.3 56887.3i −0.324031 0.324031i 0.526280 0.850311i \(-0.323586\pi\)
−0.850311 + 0.526280i \(0.823586\pi\)
\(420\) 0 0
\(421\) 144162. + 144162.i 0.813365 + 0.813365i 0.985137 0.171772i \(-0.0549492\pi\)
−0.171772 + 0.985137i \(0.554949\pi\)
\(422\) 0 0
\(423\) 37825.2 0.211398
\(424\) 0 0
\(425\) 219726.i 1.21648i
\(426\) 0 0
\(427\) 83291.4 83291.4i 0.456819 0.456819i
\(428\) 0 0
\(429\) 135614. 135614.i 0.736870 0.736870i
\(430\) 0 0
\(431\) 18641.5i 0.100352i 0.998740 + 0.0501760i \(0.0159782\pi\)
−0.998740 + 0.0501760i \(0.984022\pi\)
\(432\) 0 0
\(433\) 2193.97 0.0117019 0.00585094 0.999983i \(-0.498138\pi\)
0.00585094 + 0.999983i \(0.498138\pi\)
\(434\) 0 0
\(435\) −3055.84 3055.84i −0.0161492 0.0161492i
\(436\) 0 0
\(437\) 150404. + 150404.i 0.787586 + 0.787586i
\(438\) 0 0
\(439\) 118115. 0.612880 0.306440 0.951890i \(-0.400862\pi\)
0.306440 + 0.951890i \(0.400862\pi\)
\(440\) 0 0
\(441\) 17241.2i 0.0886523i
\(442\) 0 0
\(443\) −37885.8 + 37885.8i −0.193050 + 0.193050i −0.797013 0.603963i \(-0.793588\pi\)
0.603963 + 0.797013i \(0.293588\pi\)
\(444\) 0 0
\(445\) −24425.4 + 24425.4i −0.123345 + 0.123345i
\(446\) 0 0
\(447\) 25188.9i 0.126065i
\(448\) 0 0
\(449\) −85186.6 −0.422550 −0.211275 0.977427i \(-0.567762\pi\)
−0.211275 + 0.977427i \(0.567762\pi\)
\(450\) 0 0
\(451\) 143430. + 143430.i 0.705157 + 0.705157i
\(452\) 0 0
\(453\) 57826.4 + 57826.4i 0.281793 + 0.281793i
\(454\) 0 0
\(455\) −67348.4 −0.325315
\(456\) 0 0
\(457\) 96935.7i 0.464142i −0.972699 0.232071i \(-0.925450\pi\)
0.972699 0.232071i \(-0.0745502\pi\)
\(458\) 0 0
\(459\) 194678. 194678.i 0.924042 0.924042i
\(460\) 0 0
\(461\) −295014. + 295014.i −1.38816 + 1.38816i −0.558988 + 0.829176i \(0.688810\pi\)
−0.829176 + 0.558988i \(0.811190\pi\)
\(462\) 0 0
\(463\) 224348.i 1.04655i −0.852164 0.523275i \(-0.824710\pi\)
0.852164 0.523275i \(-0.175290\pi\)
\(464\) 0 0
\(465\) −10585.7 −0.0489567
\(466\) 0 0
\(467\) −189556. 189556.i −0.869168 0.869168i 0.123212 0.992380i \(-0.460680\pi\)
−0.992380 + 0.123212i \(0.960680\pi\)
\(468\) 0 0
\(469\) −100044. 100044.i −0.454827 0.454827i
\(470\) 0 0
\(471\) −141054. −0.635832
\(472\) 0 0
\(473\) 80902.6i 0.361610i
\(474\) 0 0
\(475\) −117891. + 117891.i −0.522506 + 0.522506i
\(476\) 0 0
\(477\) 97133.7 97133.7i 0.426907 0.426907i
\(478\) 0 0
\(479\) 132796.i 0.578781i 0.957211 + 0.289390i \(0.0934526\pi\)
−0.957211 + 0.289390i \(0.906547\pi\)
\(480\) 0 0
\(481\) −462081. −1.99723
\(482\) 0 0
\(483\) 131523. + 131523.i 0.563778 + 0.563778i
\(484\) 0 0
\(485\) −40338.2 40338.2i −0.171488 0.171488i
\(486\) 0 0
\(487\) −283936. −1.19719 −0.598595 0.801052i \(-0.704274\pi\)
−0.598595 + 0.801052i \(0.704274\pi\)
\(488\) 0 0
\(489\) 118101.i 0.493896i
\(490\) 0 0
\(491\) 111725. 111725.i 0.463435 0.463435i −0.436345 0.899780i \(-0.643727\pi\)
0.899780 + 0.436345i \(0.143727\pi\)
\(492\) 0 0
\(493\) 31280.9 31280.9i 0.128702 0.128702i
\(494\) 0 0
\(495\) 52426.1i 0.213962i
\(496\) 0 0
\(497\) 406998. 1.64770
\(498\) 0 0
\(499\) −61595.1 61595.1i −0.247369 0.247369i 0.572521 0.819890i \(-0.305965\pi\)
−0.819890 + 0.572521i \(0.805965\pi\)
\(500\) 0 0
\(501\) −92916.5 92916.5i −0.370184 0.370184i
\(502\) 0 0
\(503\) −70874.1 −0.280125 −0.140062 0.990143i \(-0.544730\pi\)
−0.140062 + 0.990143i \(0.544730\pi\)
\(504\) 0 0
\(505\) 5079.09i 0.0199160i
\(506\) 0 0
\(507\) −81500.9 + 81500.9i −0.317064 + 0.317064i
\(508\) 0 0
\(509\) 128181. 128181.i 0.494754 0.494754i −0.415046 0.909800i \(-0.636235\pi\)
0.909800 + 0.415046i \(0.136235\pi\)
\(510\) 0 0
\(511\) 424241.i 1.62469i
\(512\) 0 0
\(513\) 208903. 0.793797
\(514\) 0 0
\(515\) 26186.3 + 26186.3i 0.0987324 + 0.0987324i
\(516\) 0 0
\(517\) −82814.9 82814.9i −0.309833 0.309833i
\(518\) 0 0
\(519\) −94525.3 −0.350924
\(520\) 0 0
\(521\) 494250.i 1.82084i −0.413688 0.910419i \(-0.635759\pi\)
0.413688 0.910419i \(-0.364241\pi\)
\(522\) 0 0
\(523\) −179670. + 179670.i −0.656859 + 0.656859i −0.954636 0.297776i \(-0.903755\pi\)
0.297776 + 0.954636i \(0.403755\pi\)
\(524\) 0 0
\(525\) −103091. + 103091.i −0.374026 + 0.374026i
\(526\) 0 0
\(527\) 108360.i 0.390163i
\(528\) 0 0
\(529\) 268417. 0.959175
\(530\) 0 0
\(531\) −68347.9 68347.9i −0.242402 0.242402i
\(532\) 0 0
\(533\) −204457. 204457.i −0.719694 0.719694i
\(534\) 0 0
\(535\) −28242.7 −0.0986729
\(536\) 0 0
\(537\) 220112.i 0.763300i
\(538\) 0 0
\(539\) 37748.1 37748.1i 0.129932 0.129932i
\(540\) 0 0
\(541\) −300961. + 300961.i −1.02829 + 1.02829i −0.0287034 + 0.999588i \(0.509138\pi\)
−0.999588 + 0.0287034i \(0.990862\pi\)
\(542\) 0 0
\(543\) 124549.i 0.422417i
\(544\) 0 0
\(545\) −31683.6 −0.106670
\(546\) 0 0
\(547\) 159057. + 159057.i 0.531591 + 0.531591i 0.921046 0.389455i \(-0.127337\pi\)
−0.389455 + 0.921046i \(0.627337\pi\)
\(548\) 0 0
\(549\) −92423.8 92423.8i −0.306647 0.306647i
\(550\) 0 0
\(551\) 33566.6 0.110561
\(552\) 0 0
\(553\) 129765.i 0.424335i
\(554\) 0 0
\(555\) 54382.0 54382.0i 0.176551 0.176551i
\(556\) 0 0
\(557\) 394524. 394524.i 1.27164 1.27164i 0.326409 0.945229i \(-0.394161\pi\)
0.945229 0.326409i \(-0.105839\pi\)
\(558\) 0 0
\(559\) 115326.i 0.369065i
\(560\) 0 0
\(561\) −326755. −1.03824
\(562\) 0 0
\(563\) −169317. 169317.i −0.534177 0.534177i 0.387636 0.921813i \(-0.373292\pi\)
−0.921813 + 0.387636i \(0.873292\pi\)
\(564\) 0 0
\(565\) 15085.9 + 15085.9i 0.0472579 + 0.0472579i
\(566\) 0 0
\(567\) −2346.48 −0.00729877
\(568\) 0 0
\(569\) 165645.i 0.511626i −0.966726 0.255813i \(-0.917657\pi\)
0.966726 0.255813i \(-0.0823432\pi\)
\(570\) 0 0
\(571\) −335641. + 335641.i −1.02945 + 1.02945i −0.0298925 + 0.999553i \(0.509517\pi\)
−0.999553 + 0.0298925i \(0.990483\pi\)
\(572\) 0 0
\(573\) 109771. 109771.i 0.334331 0.334331i
\(574\) 0 0
\(575\) 429737.i 1.29977i
\(576\) 0 0
\(577\) −99615.9 −0.299211 −0.149605 0.988746i \(-0.547800\pi\)
−0.149605 + 0.988746i \(0.547800\pi\)
\(578\) 0 0
\(579\) −222031. 222031.i −0.662301 0.662301i
\(580\) 0 0
\(581\) 47033.3 + 47033.3i 0.139333 + 0.139333i
\(582\) 0 0
\(583\) −425331. −1.25138
\(584\) 0 0
\(585\) 74732.7i 0.218373i
\(586\) 0 0
\(587\) 45023.9 45023.9i 0.130667 0.130667i −0.638748 0.769416i \(-0.720548\pi\)
0.769416 + 0.638748i \(0.220548\pi\)
\(588\) 0 0
\(589\) 58138.5 58138.5i 0.167584 0.167584i
\(590\) 0 0
\(591\) 79703.6i 0.228193i
\(592\) 0 0
\(593\) −385101. −1.09513 −0.547564 0.836764i \(-0.684445\pi\)
−0.547564 + 0.836764i \(0.684445\pi\)
\(594\) 0 0
\(595\) 81136.1 + 81136.1i 0.229182 + 0.229182i
\(596\) 0 0
\(597\) −124447. 124447.i −0.349168 0.349168i
\(598\) 0 0
\(599\) 209331. 0.583417 0.291709 0.956507i \(-0.405776\pi\)
0.291709 + 0.956507i \(0.405776\pi\)
\(600\) 0 0
\(601\) 515555.i 1.42734i 0.700484 + 0.713668i \(0.252967\pi\)
−0.700484 + 0.713668i \(0.747033\pi\)
\(602\) 0 0
\(603\) −111013. + 111013.i −0.305310 + 0.305310i
\(604\) 0 0
\(605\) −45625.7 + 45625.7i −0.124652 + 0.124652i
\(606\) 0 0
\(607\) 30292.7i 0.0822167i 0.999155 + 0.0411084i \(0.0130889\pi\)
−0.999155 + 0.0411084i \(0.986911\pi\)
\(608\) 0 0
\(609\) 29352.7 0.0791432
\(610\) 0 0
\(611\) 118052. + 118052.i 0.316220 + 0.316220i
\(612\) 0 0
\(613\) 99803.4 + 99803.4i 0.265598 + 0.265598i 0.827324 0.561726i \(-0.189862\pi\)
−0.561726 + 0.827324i \(0.689862\pi\)
\(614\) 0 0
\(615\) 48124.9 0.127239
\(616\) 0 0
\(617\) 102196.i 0.268451i −0.990951 0.134226i \(-0.957145\pi\)
0.990951 0.134226i \(-0.0428547\pi\)
\(618\) 0 0
\(619\) 105904. 105904.i 0.276395 0.276395i −0.555273 0.831668i \(-0.687386\pi\)
0.831668 + 0.555273i \(0.187386\pi\)
\(620\) 0 0
\(621\) 380749. 380749.i 0.987314 0.987314i
\(622\) 0 0
\(623\) 234617.i 0.604483i
\(624\) 0 0
\(625\) −308949. −0.790909
\(626\) 0 0
\(627\) −175315. 175315.i −0.445948 0.445948i
\(628\) 0 0
\(629\) 556679. + 556679.i 1.40703 + 1.40703i
\(630\) 0 0
\(631\) 692480. 1.73920 0.869598 0.493760i \(-0.164378\pi\)
0.869598 + 0.493760i \(0.164378\pi\)
\(632\) 0 0
\(633\) 83779.3i 0.209088i
\(634\) 0 0
\(635\) −108170. + 108170.i −0.268262 + 0.268262i
\(636\) 0 0
\(637\) −53809.4 + 53809.4i −0.132611 + 0.132611i
\(638\) 0 0
\(639\) 451622.i 1.10605i
\(640\) 0 0
\(641\) 49519.0 0.120519 0.0602595 0.998183i \(-0.480807\pi\)
0.0602595 + 0.998183i \(0.480807\pi\)
\(642\) 0 0
\(643\) 165494. + 165494.i 0.400276 + 0.400276i 0.878330 0.478054i \(-0.158658\pi\)
−0.478054 + 0.878330i \(0.658658\pi\)
\(644\) 0 0
\(645\) 13572.6 + 13572.6i 0.0326245 + 0.0326245i
\(646\) 0 0
\(647\) −666565. −1.59233 −0.796166 0.605078i \(-0.793142\pi\)
−0.796166 + 0.605078i \(0.793142\pi\)
\(648\) 0 0
\(649\) 299284.i 0.710548i
\(650\) 0 0
\(651\) 50840.0 50840.0i 0.119962 0.119962i
\(652\) 0 0
\(653\) −461118. + 461118.i −1.08140 + 1.08140i −0.0850198 + 0.996379i \(0.527095\pi\)
−0.996379 + 0.0850198i \(0.972905\pi\)
\(654\) 0 0
\(655\) 181910.i 0.424008i
\(656\) 0 0
\(657\) 470757. 1.09060
\(658\) 0 0
\(659\) −326883. 326883.i −0.752698 0.752698i 0.222284 0.974982i \(-0.428649\pi\)
−0.974982 + 0.222284i \(0.928649\pi\)
\(660\) 0 0
\(661\) −549615. 549615.i −1.25793 1.25793i −0.952080 0.305848i \(-0.901060\pi\)
−0.305848 0.952080i \(-0.598940\pi\)
\(662\) 0 0
\(663\) 465785. 1.05964
\(664\) 0 0
\(665\) 87064.5i 0.196878i
\(666\) 0 0
\(667\) 61178.8 61178.8i 0.137515 0.137515i
\(668\) 0 0
\(669\) −359005. + 359005.i −0.802137 + 0.802137i
\(670\) 0 0
\(671\) 404708.i 0.898869i
\(672\) 0 0
\(673\) 191664. 0.423166 0.211583 0.977360i \(-0.432138\pi\)
0.211583 + 0.977360i \(0.432138\pi\)
\(674\) 0 0
\(675\) 298440. + 298440.i 0.655012 + 0.655012i
\(676\) 0 0
\(677\) 544201. + 544201.i 1.18736 + 1.18736i 0.977795 + 0.209564i \(0.0672043\pi\)
0.209564 + 0.977795i \(0.432796\pi\)
\(678\) 0 0
\(679\) 387466. 0.840416
\(680\) 0 0
\(681\) 137020.i 0.295455i
\(682\) 0 0
\(683\) 570769. 570769.i 1.22354 1.22354i 0.257179 0.966364i \(-0.417207\pi\)
0.966364 0.257179i \(-0.0827929\pi\)
\(684\) 0 0
\(685\) −94177.8 + 94177.8i −0.200709 + 0.200709i
\(686\) 0 0
\(687\) 500020.i 1.05943i
\(688\) 0 0
\(689\) 606305. 1.27718
\(690\) 0 0
\(691\) 333477. + 333477.i 0.698409 + 0.698409i 0.964067 0.265658i \(-0.0855893\pi\)
−0.265658 + 0.964067i \(0.585589\pi\)
\(692\) 0 0
\(693\) 251788. + 251788.i 0.524286 + 0.524286i
\(694\) 0 0
\(695\) 237831. 0.492378
\(696\) 0 0
\(697\) 492628.i 1.01404i
\(698\) 0 0
\(699\) 250135. 250135.i 0.511941 0.511941i
\(700\) 0 0
\(701\) −31503.2 + 31503.2i −0.0641089 + 0.0641089i −0.738434 0.674325i \(-0.764435\pi\)
0.674325 + 0.738434i \(0.264435\pi\)
\(702\) 0 0
\(703\) 597354.i 1.20871i
\(704\) 0 0
\(705\) −27786.9 −0.0559064
\(706\) 0 0
\(707\) −24393.5 24393.5i −0.0488017 0.0488017i
\(708\) 0 0
\(709\) −609708. 609708.i −1.21291 1.21291i −0.970064 0.242847i \(-0.921919\pi\)
−0.242847 0.970064i \(-0.578081\pi\)
\(710\) 0 0
\(711\) −143993. −0.284841
\(712\) 0 0
\(713\) 211928.i 0.416878i
\(714\) 0 0
\(715\) 163621. 163621.i 0.320056 0.320056i
\(716\) 0 0
\(717\) 47357.2 47357.2i 0.0921187 0.0921187i
\(718\) 0 0
\(719\) 720908.i 1.39451i −0.716823 0.697256i \(-0.754404\pi\)
0.716823 0.697256i \(-0.245596\pi\)
\(720\) 0 0
\(721\) −251531. −0.483862
\(722\) 0 0
\(723\) −109536. 109536.i −0.209546 0.209546i
\(724\) 0 0
\(725\) 47953.4 + 47953.4i 0.0912311 + 0.0912311i
\(726\) 0 0
\(727\) −279904. −0.529591 −0.264796 0.964305i \(-0.585304\pi\)
−0.264796 + 0.964305i \(0.585304\pi\)
\(728\) 0 0
\(729\) 323526.i 0.608772i
\(730\) 0 0
\(731\) −138935. + 138935.i −0.260003 + 0.260003i
\(732\) 0 0
\(733\) 266306. 266306.i 0.495648 0.495648i −0.414432 0.910080i \(-0.636020\pi\)
0.910080 + 0.414432i \(0.136020\pi\)
\(734\) 0 0
\(735\) 12665.6i 0.0234450i
\(736\) 0 0
\(737\) 486108. 0.894948
\(738\) 0 0
\(739\) 594958. + 594958.i 1.08943 + 1.08943i 0.995587 + 0.0938378i \(0.0299135\pi\)
0.0938378 + 0.995587i \(0.470086\pi\)
\(740\) 0 0
\(741\) 249910. + 249910.i 0.455142 + 0.455142i
\(742\) 0 0
\(743\) 289367. 0.524170 0.262085 0.965045i \(-0.415590\pi\)
0.262085 + 0.965045i \(0.415590\pi\)
\(744\) 0 0
\(745\) 30390.8i 0.0547557i
\(746\) 0 0
\(747\) 52190.2 52190.2i 0.0935293 0.0935293i
\(748\) 0 0
\(749\) 135642. 135642.i 0.241785 0.241785i
\(750\) 0 0
\(751\) 935795.i 1.65921i 0.558352 + 0.829604i \(0.311434\pi\)
−0.558352 + 0.829604i \(0.688566\pi\)
\(752\) 0 0
\(753\) 15629.1 0.0275641
\(754\) 0 0
\(755\) 69768.4 + 69768.4i 0.122395 + 0.122395i
\(756\) 0 0
\(757\) 626956. + 626956.i 1.09407 + 1.09407i 0.995089 + 0.0989818i \(0.0315586\pi\)
0.0989818 + 0.995089i \(0.468441\pi\)
\(758\) 0 0
\(759\) −639062. −1.10933
\(760\) 0 0
\(761\) 253505.i 0.437741i 0.975754 + 0.218871i \(0.0702372\pi\)
−0.975754 + 0.218871i \(0.929763\pi\)
\(762\) 0 0
\(763\) 152167. 152167.i 0.261380 0.261380i
\(764\) 0 0
\(765\) 90032.1 90032.1i 0.153842 0.153842i
\(766\) 0 0
\(767\) 426625.i 0.725197i
\(768\) 0 0
\(769\) −740462. −1.25213 −0.626066 0.779770i \(-0.715336\pi\)
−0.626066 + 0.779770i \(0.715336\pi\)
\(770\) 0 0
\(771\) 287792. + 287792.i 0.484138 + 0.484138i
\(772\) 0 0
\(773\) −422057. 422057.i −0.706337 0.706337i 0.259426 0.965763i \(-0.416467\pi\)
−0.965763 + 0.259426i \(0.916467\pi\)
\(774\) 0 0
\(775\) 166114. 0.276569
\(776\) 0 0
\(777\) 522364.i 0.865229i
\(778\) 0 0
\(779\) −264312. + 264312.i −0.435553 + 0.435553i
\(780\) 0 0
\(781\) −988787. + 988787.i −1.62107 + 1.62107i
\(782\) 0 0
\(783\) 84973.7i 0.138599i
\(784\) 0 0
\(785\) −170183. −0.276171
\(786\) 0 0
\(787\) −658152. 658152.i −1.06262 1.06262i −0.997904 0.0647134i \(-0.979387\pi\)
−0.0647134 0.997904i \(-0.520613\pi\)
\(788\) 0 0
\(789\) −266647. 266647.i −0.428334 0.428334i
\(790\) 0 0
\(791\) −144907. −0.231599
\(792\) 0 0
\(793\) 576906.i 0.917400i
\(794\) 0 0
\(795\) −71355.7 + 71355.7i −0.112900 + 0.112900i
\(796\) 0 0