Properties

Label 128.5.f.b.95.5
Level $128$
Weight $5$
Character 128.95
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 95.5
Root \(2.79265 + 0.448449i\) of defining polynomial
Character \(\chi\) \(=\) 128.95
Dual form 128.5.f.b.31.5

$q$-expansion

\(f(q)\) \(=\) \(q+(4.63552 - 4.63552i) q^{3} +(29.2002 - 29.2002i) q^{5} +59.6196 q^{7} +38.0239i q^{9} +O(q^{10})\) \(q+(4.63552 - 4.63552i) q^{3} +(29.2002 - 29.2002i) q^{5} +59.6196 q^{7} +38.0239i q^{9} +(18.0837 + 18.0837i) q^{11} +(-50.7721 - 50.7721i) q^{13} -270.716i q^{15} -223.769 q^{17} +(-14.7360 + 14.7360i) q^{19} +(276.368 - 276.368i) q^{21} +739.082 q^{23} -1080.30i q^{25} +(551.738 + 551.738i) q^{27} +(-938.904 - 938.904i) q^{29} +938.741i q^{31} +167.655 q^{33} +(1740.90 - 1740.90i) q^{35} +(-263.837 + 263.837i) q^{37} -470.710 q^{39} -248.841i q^{41} +(-1035.00 - 1035.00i) q^{43} +(1110.31 + 1110.31i) q^{45} -2018.46i q^{47} +1153.50 q^{49} +(-1037.29 + 1037.29i) q^{51} +(-833.240 + 833.240i) q^{53} +1056.09 q^{55} +136.618i q^{57} +(2223.17 + 2223.17i) q^{59} +(341.374 + 341.374i) q^{61} +2266.97i q^{63} -2965.11 q^{65} +(-4845.43 + 4845.43i) q^{67} +(3426.03 - 3426.03i) q^{69} -4180.93 q^{71} +9071.36i q^{73} +(-5007.74 - 5007.74i) q^{75} +(1078.14 + 1078.14i) q^{77} -735.536i q^{79} +2035.24 q^{81} +(-1441.90 + 1441.90i) q^{83} +(-6534.10 + 6534.10i) q^{85} -8704.61 q^{87} +5071.77i q^{89} +(-3027.01 - 3027.01i) q^{91} +(4351.55 + 4351.55i) q^{93} +860.586i q^{95} -2523.85 q^{97} +(-687.613 + 687.613i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 2q^{3} + 2q^{5} - 4q^{7} + O(q^{10}) \) \( 14q + 2q^{3} + 2q^{5} - 4q^{7} - 94q^{11} + 2q^{13} - 4q^{17} + 706q^{19} + 164q^{21} + 1148q^{23} + 1664q^{27} - 862q^{29} - 4q^{33} - 1340q^{35} + 1826q^{37} + 2684q^{39} - 1694q^{43} - 1410q^{45} + 682q^{49} + 3012q^{51} + 482q^{53} - 11780q^{55} + 2786q^{59} + 3778q^{61} - 2020q^{65} - 7998q^{67} - 9628q^{69} + 19964q^{71} - 17570q^{75} + 9508q^{77} + 1454q^{81} + 17282q^{83} - 9948q^{85} - 49284q^{87} + 28036q^{91} - 8896q^{93} - 4q^{97} - 49214q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 4.63552 4.63552i 0.515058 0.515058i −0.401014 0.916072i \(-0.631342\pi\)
0.916072 + 0.401014i \(0.131342\pi\)
\(4\) 0 0
\(5\) 29.2002 29.2002i 1.16801 1.16801i 0.185330 0.982676i \(-0.440665\pi\)
0.982676 0.185330i \(-0.0593353\pi\)
\(6\) 0 0
\(7\) 59.6196 1.21673 0.608363 0.793659i \(-0.291826\pi\)
0.608363 + 0.793659i \(0.291826\pi\)
\(8\) 0 0
\(9\) 38.0239i 0.469431i
\(10\) 0 0
\(11\) 18.0837 + 18.0837i 0.149452 + 0.149452i 0.777873 0.628421i \(-0.216299\pi\)
−0.628421 + 0.777873i \(0.716299\pi\)
\(12\) 0 0
\(13\) −50.7721 50.7721i −0.300427 0.300427i 0.540754 0.841181i \(-0.318139\pi\)
−0.841181 + 0.540754i \(0.818139\pi\)
\(14\) 0 0
\(15\) 270.716i 1.20318i
\(16\) 0 0
\(17\) −223.769 −0.774289 −0.387144 0.922019i \(-0.626538\pi\)
−0.387144 + 0.922019i \(0.626538\pi\)
\(18\) 0 0
\(19\) −14.7360 + 14.7360i −0.0408199 + 0.0408199i −0.727222 0.686402i \(-0.759189\pi\)
0.686402 + 0.727222i \(0.259189\pi\)
\(20\) 0 0
\(21\) 276.368 276.368i 0.626684 0.626684i
\(22\) 0 0
\(23\) 739.082 1.39713 0.698565 0.715547i \(-0.253822\pi\)
0.698565 + 0.715547i \(0.253822\pi\)
\(24\) 0 0
\(25\) 1080.30i 1.72848i
\(26\) 0 0
\(27\) 551.738 + 551.738i 0.756842 + 0.756842i
\(28\) 0 0
\(29\) −938.904 938.904i −1.11641 1.11641i −0.992263 0.124150i \(-0.960380\pi\)
−0.124150 0.992263i \(-0.539620\pi\)
\(30\) 0 0
\(31\) 938.741i 0.976838i 0.872609 + 0.488419i \(0.162426\pi\)
−0.872609 + 0.488419i \(0.837574\pi\)
\(32\) 0 0
\(33\) 167.655 0.153953
\(34\) 0 0
\(35\) 1740.90 1740.90i 1.42114 1.42114i
\(36\) 0 0
\(37\) −263.837 + 263.837i −0.192722 + 0.192722i −0.796871 0.604149i \(-0.793513\pi\)
0.604149 + 0.796871i \(0.293513\pi\)
\(38\) 0 0
\(39\) −470.710 −0.309474
\(40\) 0 0
\(41\) 248.841i 0.148031i −0.997257 0.0740157i \(-0.976418\pi\)
0.997257 0.0740157i \(-0.0235815\pi\)
\(42\) 0 0
\(43\) −1035.00 1035.00i −0.559765 0.559765i 0.369476 0.929240i \(-0.379537\pi\)
−0.929240 + 0.369476i \(0.879537\pi\)
\(44\) 0 0
\(45\) 1110.31 + 1110.31i 0.548299 + 0.548299i
\(46\) 0 0
\(47\) 2018.46i 0.913746i −0.889532 0.456873i \(-0.848969\pi\)
0.889532 0.456873i \(-0.151031\pi\)
\(48\) 0 0
\(49\) 1153.50 0.480424
\(50\) 0 0
\(51\) −1037.29 + 1037.29i −0.398803 + 0.398803i
\(52\) 0 0
\(53\) −833.240 + 833.240i −0.296632 + 0.296632i −0.839693 0.543061i \(-0.817265\pi\)
0.543061 + 0.839693i \(0.317265\pi\)
\(54\) 0 0
\(55\) 1056.09 0.349122
\(56\) 0 0
\(57\) 136.618i 0.0420492i
\(58\) 0 0
\(59\) 2223.17 + 2223.17i 0.638660 + 0.638660i 0.950225 0.311565i \(-0.100853\pi\)
−0.311565 + 0.950225i \(0.600853\pi\)
\(60\) 0 0
\(61\) 341.374 + 341.374i 0.0917425 + 0.0917425i 0.751489 0.659746i \(-0.229336\pi\)
−0.659746 + 0.751489i \(0.729336\pi\)
\(62\) 0 0
\(63\) 2266.97i 0.571170i
\(64\) 0 0
\(65\) −2965.11 −0.701800
\(66\) 0 0
\(67\) −4845.43 + 4845.43i −1.07940 + 1.07940i −0.0828379 + 0.996563i \(0.526398\pi\)
−0.996563 + 0.0828379i \(0.973602\pi\)
\(68\) 0 0
\(69\) 3426.03 3426.03i 0.719602 0.719602i
\(70\) 0 0
\(71\) −4180.93 −0.829386 −0.414693 0.909961i \(-0.636111\pi\)
−0.414693 + 0.909961i \(0.636111\pi\)
\(72\) 0 0
\(73\) 9071.36i 1.70226i 0.524953 + 0.851131i \(0.324083\pi\)
−0.524953 + 0.851131i \(0.675917\pi\)
\(74\) 0 0
\(75\) −5007.74 5007.74i −0.890265 0.890265i
\(76\) 0 0
\(77\) 1078.14 + 1078.14i 0.181842 + 0.181842i
\(78\) 0 0
\(79\) 735.536i 0.117855i −0.998262 0.0589277i \(-0.981232\pi\)
0.998262 0.0589277i \(-0.0187682\pi\)
\(80\) 0 0
\(81\) 2035.24 0.310203
\(82\) 0 0
\(83\) −1441.90 + 1441.90i −0.209305 + 0.209305i −0.803972 0.594667i \(-0.797284\pi\)
0.594667 + 0.803972i \(0.297284\pi\)
\(84\) 0 0
\(85\) −6534.10 + 6534.10i −0.904374 + 0.904374i
\(86\) 0 0
\(87\) −8704.61 −1.15003
\(88\) 0 0
\(89\) 5071.77i 0.640294i 0.947368 + 0.320147i \(0.103732\pi\)
−0.947368 + 0.320147i \(0.896268\pi\)
\(90\) 0 0
\(91\) −3027.01 3027.01i −0.365537 0.365537i
\(92\) 0 0
\(93\) 4351.55 + 4351.55i 0.503128 + 0.503128i
\(94\) 0 0
\(95\) 860.586i 0.0953558i
\(96\) 0 0
\(97\) −2523.85 −0.268238 −0.134119 0.990965i \(-0.542820\pi\)
−0.134119 + 0.990965i \(0.542820\pi\)
\(98\) 0 0
\(99\) −687.613 + 687.613i −0.0701575 + 0.0701575i
\(100\) 0 0
\(101\) −425.990 + 425.990i −0.0417596 + 0.0417596i −0.727678 0.685919i \(-0.759401\pi\)
0.685919 + 0.727678i \(0.259401\pi\)
\(102\) 0 0
\(103\) 13178.6 1.24221 0.621103 0.783729i \(-0.286685\pi\)
0.621103 + 0.783729i \(0.286685\pi\)
\(104\) 0 0
\(105\) 16140.0i 1.46394i
\(106\) 0 0
\(107\) 10821.5 + 10821.5i 0.945190 + 0.945190i 0.998574 0.0533845i \(-0.0170009\pi\)
−0.0533845 + 0.998574i \(0.517001\pi\)
\(108\) 0 0
\(109\) 1428.57 + 1428.57i 0.120240 + 0.120240i 0.764666 0.644426i \(-0.222904\pi\)
−0.644426 + 0.764666i \(0.722904\pi\)
\(110\) 0 0
\(111\) 2446.04i 0.198526i
\(112\) 0 0
\(113\) 20121.5 1.57581 0.787904 0.615798i \(-0.211166\pi\)
0.787904 + 0.615798i \(0.211166\pi\)
\(114\) 0 0
\(115\) 21581.3 21581.3i 1.63186 1.63186i
\(116\) 0 0
\(117\) 1930.56 1930.56i 0.141030 0.141030i
\(118\) 0 0
\(119\) −13341.0 −0.942098
\(120\) 0 0
\(121\) 13987.0i 0.955328i
\(122\) 0 0
\(123\) −1153.51 1153.51i −0.0762447 0.0762447i
\(124\) 0 0
\(125\) −13294.8 13294.8i −0.850865 0.850865i
\(126\) 0 0
\(127\) 2630.54i 0.163094i −0.996669 0.0815470i \(-0.974014\pi\)
0.996669 0.0815470i \(-0.0259861\pi\)
\(128\) 0 0
\(129\) −9595.57 −0.576622
\(130\) 0 0
\(131\) −12437.0 + 12437.0i −0.724722 + 0.724722i −0.969563 0.244841i \(-0.921264\pi\)
0.244841 + 0.969563i \(0.421264\pi\)
\(132\) 0 0
\(133\) −878.554 + 878.554i −0.0496667 + 0.0496667i
\(134\) 0 0
\(135\) 32221.6 1.76799
\(136\) 0 0
\(137\) 15392.0i 0.820078i 0.912068 + 0.410039i \(0.134485\pi\)
−0.912068 + 0.410039i \(0.865515\pi\)
\(138\) 0 0
\(139\) −12151.3 12151.3i −0.628915 0.628915i 0.318880 0.947795i \(-0.396693\pi\)
−0.947795 + 0.318880i \(0.896693\pi\)
\(140\) 0 0
\(141\) −9356.63 9356.63i −0.470632 0.470632i
\(142\) 0 0
\(143\) 1836.29i 0.0897987i
\(144\) 0 0
\(145\) −54832.3 −2.60796
\(146\) 0 0
\(147\) 5347.06 5347.06i 0.247446 0.247446i
\(148\) 0 0
\(149\) 20803.7 20803.7i 0.937062 0.937062i −0.0610710 0.998133i \(-0.519452\pi\)
0.998133 + 0.0610710i \(0.0194516\pi\)
\(150\) 0 0
\(151\) −7756.67 −0.340190 −0.170095 0.985428i \(-0.554407\pi\)
−0.170095 + 0.985428i \(0.554407\pi\)
\(152\) 0 0
\(153\) 8508.60i 0.363475i
\(154\) 0 0
\(155\) 27411.4 + 27411.4i 1.14095 + 1.14095i
\(156\) 0 0
\(157\) −7040.20 7040.20i −0.285618 0.285618i 0.549727 0.835345i \(-0.314732\pi\)
−0.835345 + 0.549727i \(0.814732\pi\)
\(158\) 0 0
\(159\) 7725.00i 0.305565i
\(160\) 0 0
\(161\) 44063.8 1.69993
\(162\) 0 0
\(163\) −7273.43 + 7273.43i −0.273756 + 0.273756i −0.830610 0.556854i \(-0.812008\pi\)
0.556854 + 0.830610i \(0.312008\pi\)
\(164\) 0 0
\(165\) 4895.54 4895.54i 0.179818 0.179818i
\(166\) 0 0
\(167\) 30069.6 1.07819 0.539095 0.842245i \(-0.318766\pi\)
0.539095 + 0.842245i \(0.318766\pi\)
\(168\) 0 0
\(169\) 23405.4i 0.819488i
\(170\) 0 0
\(171\) −560.320 560.320i −0.0191621 0.0191621i
\(172\) 0 0
\(173\) 8329.72 + 8329.72i 0.278316 + 0.278316i 0.832436 0.554121i \(-0.186945\pi\)
−0.554121 + 0.832436i \(0.686945\pi\)
\(174\) 0 0
\(175\) 64406.9i 2.10308i
\(176\) 0 0
\(177\) 20611.1 0.657893
\(178\) 0 0
\(179\) 7537.56 7537.56i 0.235247 0.235247i −0.579632 0.814879i \(-0.696803\pi\)
0.814879 + 0.579632i \(0.196803\pi\)
\(180\) 0 0
\(181\) −3802.64 + 3802.64i −0.116072 + 0.116072i −0.762757 0.646685i \(-0.776155\pi\)
0.646685 + 0.762757i \(0.276155\pi\)
\(182\) 0 0
\(183\) 3164.89 0.0945054
\(184\) 0 0
\(185\) 15408.2i 0.450202i
\(186\) 0 0
\(187\) −4046.58 4046.58i −0.115719 0.115719i
\(188\) 0 0
\(189\) 32894.4 + 32894.4i 0.920869 + 0.920869i
\(190\) 0 0
\(191\) 52248.1i 1.43220i 0.697997 + 0.716100i \(0.254075\pi\)
−0.697997 + 0.716100i \(0.745925\pi\)
\(192\) 0 0
\(193\) −24380.0 −0.654514 −0.327257 0.944935i \(-0.606124\pi\)
−0.327257 + 0.944935i \(0.606124\pi\)
\(194\) 0 0
\(195\) −13744.8 + 13744.8i −0.361468 + 0.361468i
\(196\) 0 0
\(197\) −31537.9 + 31537.9i −0.812644 + 0.812644i −0.985030 0.172386i \(-0.944852\pi\)
0.172386 + 0.985030i \(0.444852\pi\)
\(198\) 0 0
\(199\) −71129.4 −1.79615 −0.898076 0.439841i \(-0.855035\pi\)
−0.898076 + 0.439841i \(0.855035\pi\)
\(200\) 0 0
\(201\) 44922.2i 1.11191i
\(202\) 0 0
\(203\) −55977.1 55977.1i −1.35837 1.35837i
\(204\) 0 0
\(205\) −7266.19 7266.19i −0.172902 0.172902i
\(206\) 0 0
\(207\) 28102.8i 0.655857i
\(208\) 0 0
\(209\) −532.962 −0.0122012
\(210\) 0 0
\(211\) 13393.4 13393.4i 0.300833 0.300833i −0.540507 0.841340i \(-0.681767\pi\)
0.841340 + 0.540507i \(0.181767\pi\)
\(212\) 0 0
\(213\) −19380.8 + 19380.8i −0.427181 + 0.427181i
\(214\) 0 0
\(215\) −60444.6 −1.30762
\(216\) 0 0
\(217\) 55967.4i 1.18854i
\(218\) 0 0
\(219\) 42050.4 + 42050.4i 0.876763 + 0.876763i
\(220\) 0 0
\(221\) 11361.2 + 11361.2i 0.232617 + 0.232617i
\(222\) 0 0
\(223\) 54266.9i 1.09125i 0.838029 + 0.545626i \(0.183708\pi\)
−0.838029 + 0.545626i \(0.816292\pi\)
\(224\) 0 0
\(225\) 41077.2 0.811401
\(226\) 0 0
\(227\) −14529.0 + 14529.0i −0.281957 + 0.281957i −0.833889 0.551932i \(-0.813891\pi\)
0.551932 + 0.833889i \(0.313891\pi\)
\(228\) 0 0
\(229\) −21618.1 + 21618.1i −0.412237 + 0.412237i −0.882517 0.470280i \(-0.844153\pi\)
0.470280 + 0.882517i \(0.344153\pi\)
\(230\) 0 0
\(231\) 9995.50 0.187318
\(232\) 0 0
\(233\) 92103.6i 1.69654i −0.529562 0.848271i \(-0.677644\pi\)
0.529562 0.848271i \(-0.322356\pi\)
\(234\) 0 0
\(235\) −58939.5 58939.5i −1.06726 1.06726i
\(236\) 0 0
\(237\) −3409.59 3409.59i −0.0607024 0.0607024i
\(238\) 0 0
\(239\) 70411.0i 1.23266i −0.787487 0.616332i \(-0.788618\pi\)
0.787487 0.616332i \(-0.211382\pi\)
\(240\) 0 0
\(241\) 22402.6 0.385714 0.192857 0.981227i \(-0.438225\pi\)
0.192857 + 0.981227i \(0.438225\pi\)
\(242\) 0 0
\(243\) −35256.4 + 35256.4i −0.597070 + 0.597070i
\(244\) 0 0
\(245\) 33682.3 33682.3i 0.561138 0.561138i
\(246\) 0 0
\(247\) 1496.35 0.0245268
\(248\) 0 0
\(249\) 13367.9i 0.215608i
\(250\) 0 0
\(251\) 72407.6 + 72407.6i 1.14931 + 1.14931i 0.986689 + 0.162621i \(0.0519947\pi\)
0.162621 + 0.986689i \(0.448005\pi\)
\(252\) 0 0
\(253\) 13365.3 + 13365.3i 0.208804 + 0.208804i
\(254\) 0 0
\(255\) 60577.9i 0.931609i
\(256\) 0 0
\(257\) −56466.3 −0.854916 −0.427458 0.904035i \(-0.640591\pi\)
−0.427458 + 0.904035i \(0.640591\pi\)
\(258\) 0 0
\(259\) −15729.9 + 15729.9i −0.234490 + 0.234490i
\(260\) 0 0
\(261\) 35700.8 35700.8i 0.524080 0.524080i
\(262\) 0 0
\(263\) 76515.5 1.10621 0.553105 0.833111i \(-0.313443\pi\)
0.553105 + 0.833111i \(0.313443\pi\)
\(264\) 0 0
\(265\) 48661.5i 0.692937i
\(266\) 0 0
\(267\) 23510.3 + 23510.3i 0.329788 + 0.329788i
\(268\) 0 0
\(269\) −1928.97 1928.97i −0.0266576 0.0266576i 0.693652 0.720310i \(-0.256000\pi\)
−0.720310 + 0.693652i \(0.756000\pi\)
\(270\) 0 0
\(271\) 128685.i 1.75222i −0.482109 0.876111i \(-0.660129\pi\)
0.482109 0.876111i \(-0.339871\pi\)
\(272\) 0 0
\(273\) −28063.5 −0.376545
\(274\) 0 0
\(275\) 19535.8 19535.8i 0.258324 0.258324i
\(276\) 0 0
\(277\) −56674.5 + 56674.5i −0.738632 + 0.738632i −0.972313 0.233681i \(-0.924923\pi\)
0.233681 + 0.972313i \(0.424923\pi\)
\(278\) 0 0
\(279\) −35694.6 −0.458558
\(280\) 0 0
\(281\) 10599.7i 0.134240i 0.997745 + 0.0671200i \(0.0213810\pi\)
−0.997745 + 0.0671200i \(0.978619\pi\)
\(282\) 0 0
\(283\) −63293.6 63293.6i −0.790291 0.790291i 0.191251 0.981541i \(-0.438746\pi\)
−0.981541 + 0.191251i \(0.938746\pi\)
\(284\) 0 0
\(285\) 3989.26 + 3989.26i 0.0491137 + 0.0491137i
\(286\) 0 0
\(287\) 14835.8i 0.180114i
\(288\) 0 0
\(289\) −33448.2 −0.400477
\(290\) 0 0
\(291\) −11699.3 + 11699.3i −0.138158 + 0.138158i
\(292\) 0 0
\(293\) 89072.9 89072.9i 1.03755 1.03755i 0.0382867 0.999267i \(-0.487810\pi\)
0.999267 0.0382867i \(-0.0121900\pi\)
\(294\) 0 0
\(295\) 129834. 1.49192
\(296\) 0 0
\(297\) 19954.9i 0.226223i
\(298\) 0 0
\(299\) −37524.7 37524.7i −0.419735 0.419735i
\(300\) 0 0
\(301\) −61706.6 61706.6i −0.681080 0.681080i
\(302\) 0 0
\(303\) 3949.36i 0.0430172i
\(304\) 0 0
\(305\) 19936.3 0.214312
\(306\) 0 0
\(307\) 124227. 124227.i 1.31807 1.31807i 0.402769 0.915302i \(-0.368048\pi\)
0.915302 0.402769i \(-0.131952\pi\)
\(308\) 0 0
\(309\) 61089.5 61089.5i 0.639808 0.639808i
\(310\) 0 0
\(311\) 15733.9 0.162673 0.0813364 0.996687i \(-0.474081\pi\)
0.0813364 + 0.996687i \(0.474081\pi\)
\(312\) 0 0
\(313\) 104554.i 1.06721i −0.845733 0.533606i \(-0.820837\pi\)
0.845733 0.533606i \(-0.179163\pi\)
\(314\) 0 0
\(315\) 66196.0 + 66196.0i 0.667130 + 0.667130i
\(316\) 0 0
\(317\) −45847.9 45847.9i −0.456248 0.456248i 0.441174 0.897422i \(-0.354562\pi\)
−0.897422 + 0.441174i \(0.854562\pi\)
\(318\) 0 0
\(319\) 33957.7i 0.333700i
\(320\) 0 0
\(321\) 100326. 0.973654
\(322\) 0 0
\(323\) 3297.46 3297.46i 0.0316064 0.0316064i
\(324\) 0 0
\(325\) −54849.0 + 54849.0i −0.519281 + 0.519281i
\(326\) 0 0
\(327\) 13244.3 0.123861
\(328\) 0 0
\(329\) 120340.i 1.11178i
\(330\) 0 0
\(331\) 137545. + 137545.i 1.25542 + 1.25542i 0.953258 + 0.302159i \(0.0977073\pi\)
0.302159 + 0.953258i \(0.402293\pi\)
\(332\) 0 0
\(333\) −10032.1 10032.1i −0.0904700 0.0904700i
\(334\) 0 0
\(335\) 282975.i 2.52149i
\(336\) 0 0
\(337\) −40849.6 −0.359690 −0.179845 0.983695i \(-0.557560\pi\)
−0.179845 + 0.983695i \(0.557560\pi\)
\(338\) 0 0
\(339\) 93273.5 93273.5i 0.811632 0.811632i
\(340\) 0 0
\(341\) −16975.9 + 16975.9i −0.145990 + 0.145990i
\(342\) 0 0
\(343\) −74375.6 −0.632182
\(344\) 0 0
\(345\) 200081.i 1.68100i
\(346\) 0 0
\(347\) −21361.1 21361.1i −0.177404 0.177404i 0.612819 0.790223i \(-0.290035\pi\)
−0.790223 + 0.612819i \(0.790035\pi\)
\(348\) 0 0
\(349\) −139275. 139275.i −1.14347 1.14347i −0.987812 0.155654i \(-0.950252\pi\)
−0.155654 0.987812i \(-0.549748\pi\)
\(350\) 0 0
\(351\) 56025.8i 0.454751i
\(352\) 0 0
\(353\) −100461. −0.806209 −0.403105 0.915154i \(-0.632069\pi\)
−0.403105 + 0.915154i \(0.632069\pi\)
\(354\) 0 0
\(355\) −122084. + 122084.i −0.968728 + 0.968728i
\(356\) 0 0
\(357\) −61842.6 + 61842.6i −0.485234 + 0.485234i
\(358\) 0 0
\(359\) 96352.7 0.747609 0.373805 0.927507i \(-0.378053\pi\)
0.373805 + 0.927507i \(0.378053\pi\)
\(360\) 0 0
\(361\) 129887.i 0.996667i
\(362\) 0 0
\(363\) −64836.8 64836.8i −0.492049 0.492049i
\(364\) 0 0
\(365\) 264885. + 264885.i 1.98825 + 1.98825i
\(366\) 0 0
\(367\) 190661.i 1.41557i −0.706429 0.707784i \(-0.749695\pi\)
0.706429 0.707784i \(-0.250305\pi\)
\(368\) 0 0
\(369\) 9461.91 0.0694906
\(370\) 0 0
\(371\) −49677.5 + 49677.5i −0.360920 + 0.360920i
\(372\) 0 0
\(373\) −51771.9 + 51771.9i −0.372114 + 0.372114i −0.868247 0.496133i \(-0.834753\pi\)
0.496133 + 0.868247i \(0.334753\pi\)
\(374\) 0 0
\(375\) −123256. −0.876489
\(376\) 0 0
\(377\) 95340.2i 0.670801i
\(378\) 0 0
\(379\) −121232. 121232.i −0.843990 0.843990i 0.145385 0.989375i \(-0.453558\pi\)
−0.989375 + 0.145385i \(0.953558\pi\)
\(380\) 0 0
\(381\) −12193.9 12193.9i −0.0840028 0.0840028i
\(382\) 0 0
\(383\) 8262.20i 0.0563246i 0.999603 + 0.0281623i \(0.00896552\pi\)
−0.999603 + 0.0281623i \(0.991034\pi\)
\(384\) 0 0
\(385\) 62963.9 0.424786
\(386\) 0 0
\(387\) 39355.0 39355.0i 0.262771 0.262771i
\(388\) 0 0
\(389\) −43964.9 + 43964.9i −0.290541 + 0.290541i −0.837294 0.546753i \(-0.815864\pi\)
0.546753 + 0.837294i \(0.315864\pi\)
\(390\) 0 0
\(391\) −165384. −1.08178
\(392\) 0 0
\(393\) 115303.i 0.746547i
\(394\) 0 0
\(395\) −21477.8 21477.8i −0.137656 0.137656i
\(396\) 0 0
\(397\) −72864.3 72864.3i −0.462311 0.462311i 0.437101 0.899412i \(-0.356005\pi\)
−0.899412 + 0.437101i \(0.856005\pi\)
\(398\) 0 0
\(399\) 8145.10i 0.0511624i
\(400\) 0 0
\(401\) 237249. 1.47542 0.737711 0.675116i \(-0.235907\pi\)
0.737711 + 0.675116i \(0.235907\pi\)
\(402\) 0 0
\(403\) 47661.9 47661.9i 0.293468 0.293468i
\(404\) 0 0
\(405\) 59429.3 59429.3i 0.362319 0.362319i
\(406\) 0 0
\(407\) −9542.29 −0.0576055
\(408\) 0 0
\(409\) 150042.i 0.896945i 0.893797 + 0.448473i \(0.148032\pi\)
−0.893797 + 0.448473i \(0.851968\pi\)
\(410\) 0 0
\(411\) 71350.1 + 71350.1i 0.422387 + 0.422387i
\(412\) 0 0
\(413\) 132545. + 132545.i 0.777074 + 0.777074i
\(414\) 0 0
\(415\) 84207.5i 0.488939i
\(416\) 0 0
\(417\) −112655. −0.647855
\(418\) 0 0
\(419\) −71760.1 + 71760.1i −0.408747 + 0.408747i −0.881302 0.472554i \(-0.843332\pi\)
0.472554 + 0.881302i \(0.343332\pi\)
\(420\) 0 0
\(421\) 209821. 209821.i 1.18382 1.18382i 0.205070 0.978747i \(-0.434258\pi\)
0.978747 0.205070i \(-0.0657424\pi\)
\(422\) 0 0
\(423\) 76750.0 0.428941
\(424\) 0 0
\(425\) 241738.i 1.33834i
\(426\) 0 0
\(427\) 20352.6 + 20352.6i 0.111626 + 0.111626i
\(428\) 0 0
\(429\) −8512.18 8512.18i −0.0462515 0.0462515i
\(430\) 0 0
\(431\) 123853.i 0.666731i 0.942798 + 0.333366i \(0.108184\pi\)
−0.942798 + 0.333366i \(0.891816\pi\)
\(432\) 0 0
\(433\) −265114. −1.41402 −0.707012 0.707202i \(-0.749957\pi\)
−0.707012 + 0.707202i \(0.749957\pi\)
\(434\) 0 0
\(435\) −254176. + 254176.i −1.34325 + 1.34325i
\(436\) 0 0
\(437\) −10891.1 + 10891.1i −0.0570307 + 0.0570307i
\(438\) 0 0
\(439\) 186089. 0.965590 0.482795 0.875734i \(-0.339622\pi\)
0.482795 + 0.875734i \(0.339622\pi\)
\(440\) 0 0
\(441\) 43860.5i 0.225526i
\(442\) 0 0
\(443\) −25618.8 25618.8i −0.130542 0.130542i 0.638817 0.769359i \(-0.279424\pi\)
−0.769359 + 0.638817i \(0.779424\pi\)
\(444\) 0 0
\(445\) 148096. + 148096.i 0.747867 + 0.747867i
\(446\) 0 0
\(447\) 192872.i 0.965282i
\(448\) 0 0
\(449\) −2307.59 −0.0114463 −0.00572316 0.999984i \(-0.501822\pi\)
−0.00572316 + 0.999984i \(0.501822\pi\)
\(450\) 0 0
\(451\) 4499.96 4499.96i 0.0221236 0.0221236i
\(452\) 0 0
\(453\) −35956.2 + 35956.2i −0.175217 + 0.175217i
\(454\) 0 0
\(455\) −176778. −0.853899
\(456\) 0 0
\(457\) 262378.i 1.25631i −0.778090 0.628153i \(-0.783811\pi\)
0.778090 0.628153i \(-0.216189\pi\)
\(458\) 0 0
\(459\) −123462. 123462.i −0.586014 0.586014i
\(460\) 0 0
\(461\) −136771. 136771.i −0.643564 0.643564i 0.307866 0.951430i \(-0.400385\pi\)
−0.951430 + 0.307866i \(0.900385\pi\)
\(462\) 0 0
\(463\) 22250.8i 0.103797i −0.998652 0.0518983i \(-0.983473\pi\)
0.998652 0.0518983i \(-0.0165272\pi\)
\(464\) 0 0
\(465\) 254132. 1.17531
\(466\) 0 0
\(467\) −175541. + 175541.i −0.804906 + 0.804906i −0.983858 0.178952i \(-0.942729\pi\)
0.178952 + 0.983858i \(0.442729\pi\)
\(468\) 0 0
\(469\) −288883. + 288883.i −1.31334 + 1.31334i
\(470\) 0 0
\(471\) −65269.9 −0.294219
\(472\) 0 0
\(473\) 37433.4i 0.167316i
\(474\) 0 0
\(475\) 15919.3 + 15919.3i 0.0705563 + 0.0705563i
\(476\) 0 0
\(477\) −31683.1 31683.1i −0.139249 0.139249i
\(478\) 0 0
\(479\) 117920.i 0.513945i −0.966419 0.256973i \(-0.917275\pi\)
0.966419 0.256973i \(-0.0827250\pi\)
\(480\) 0 0
\(481\) 26791.1 0.115798
\(482\) 0 0
\(483\) 204258. 204258.i 0.875559 0.875559i
\(484\) 0 0
\(485\) −73696.7 + 73696.7i −0.313303 + 0.313303i
\(486\) 0 0
\(487\) −449942. −1.89714 −0.948568 0.316574i \(-0.897467\pi\)
−0.948568 + 0.316574i \(0.897467\pi\)
\(488\) 0 0
\(489\) 67432.3i 0.282001i
\(490\) 0 0
\(491\) 122509. + 122509.i 0.508166 + 0.508166i 0.913963 0.405797i \(-0.133006\pi\)
−0.405797 + 0.913963i \(0.633006\pi\)
\(492\) 0 0
\(493\) 210098. + 210098.i 0.864426 + 0.864426i
\(494\) 0 0
\(495\) 40156.8i 0.163889i
\(496\) 0 0
\(497\) −249266. −1.00914
\(498\) 0 0
\(499\) 44886.9 44886.9i 0.180268 0.180268i −0.611205 0.791473i \(-0.709315\pi\)
0.791473 + 0.611205i \(0.209315\pi\)
\(500\) 0 0
\(501\) 139388. 139388.i 0.555330 0.555330i
\(502\) 0 0
\(503\) 235778. 0.931896 0.465948 0.884812i \(-0.345713\pi\)
0.465948 + 0.884812i \(0.345713\pi\)
\(504\) 0 0
\(505\) 24877.9i 0.0975509i
\(506\) 0 0
\(507\) −108496. 108496.i −0.422083 0.422083i
\(508\) 0 0
\(509\) −227812. 227812.i −0.879308 0.879308i 0.114155 0.993463i \(-0.463584\pi\)
−0.993463 + 0.114155i \(0.963584\pi\)
\(510\) 0 0
\(511\) 540831.i 2.07119i
\(512\) 0 0
\(513\) −16260.8 −0.0617884
\(514\) 0 0
\(515\) 384816. 384816.i 1.45090 1.45090i
\(516\) 0 0
\(517\) 36501.3 36501.3i 0.136561 0.136561i
\(518\) 0 0
\(519\) 77225.1 0.286697
\(520\) 0 0
\(521\) 539683.i 1.98822i −0.108395 0.994108i \(-0.534571\pi\)
0.108395 0.994108i \(-0.465429\pi\)
\(522\) 0 0
\(523\) 175071. + 175071.i 0.640044 + 0.640044i 0.950566 0.310522i \(-0.100504\pi\)
−0.310522 + 0.950566i \(0.600504\pi\)
\(524\) 0 0
\(525\) −298560. 298560.i −1.08321 1.08321i
\(526\) 0 0
\(527\) 210062.i 0.756354i
\(528\) 0 0
\(529\) 266401. 0.951972
\(530\) 0 0
\(531\) −84533.9 + 84533.9i −0.299807 + 0.299807i
\(532\) 0 0
\(533\) −12634.2 + 12634.2i −0.0444726 + 0.0444726i
\(534\) 0 0
\(535\) 631977. 2.20797
\(536\) 0 0
\(537\) 69880.9i 0.242332i
\(538\) 0 0
\(539\) 20859.5 + 20859.5i 0.0718003 + 0.0718003i
\(540\) 0 0
\(541\) 142203. + 142203.i 0.485863 + 0.485863i 0.906998 0.421135i \(-0.138368\pi\)
−0.421135 + 0.906998i \(0.638368\pi\)
\(542\) 0 0
\(543\) 35254.4i 0.119568i
\(544\) 0 0
\(545\) 83428.9 0.280882
\(546\) 0 0
\(547\) 265412. 265412.i 0.887045 0.887045i −0.107193 0.994238i \(-0.534186\pi\)
0.994238 + 0.107193i \(0.0341862\pi\)
\(548\) 0 0
\(549\) −12980.4 + 12980.4i −0.0430668 + 0.0430668i
\(550\) 0 0
\(551\) 27671.3 0.0911438
\(552\) 0 0
\(553\) 43852.4i 0.143398i
\(554\) 0 0
\(555\) 71424.8 + 71424.8i 0.231880 + 0.231880i
\(556\) 0 0
\(557\) −168105. 168105.i −0.541837 0.541837i 0.382230 0.924067i \(-0.375156\pi\)
−0.924067 + 0.382230i \(0.875156\pi\)
\(558\) 0 0
\(559\) 105099.i 0.336336i
\(560\) 0 0
\(561\) −37516.0 −0.119204
\(562\) 0 0
\(563\) 181113. 181113.i 0.571389 0.571389i −0.361127 0.932517i \(-0.617608\pi\)
0.932517 + 0.361127i \(0.117608\pi\)
\(564\) 0 0
\(565\) 587551. 587551.i 1.84055 1.84055i
\(566\) 0 0
\(567\) 121340. 0.377432
\(568\) 0 0
\(569\) 124083.i 0.383254i 0.981468 + 0.191627i \(0.0613765\pi\)
−0.981468 + 0.191627i \(0.938624\pi\)
\(570\) 0 0
\(571\) 92801.0 + 92801.0i 0.284630 + 0.284630i 0.834952 0.550322i \(-0.185495\pi\)
−0.550322 + 0.834952i \(0.685495\pi\)
\(572\) 0 0
\(573\) 242197. + 242197.i 0.737666 + 0.737666i
\(574\) 0 0
\(575\) 798429.i 2.41491i
\(576\) 0 0
\(577\) 182478. 0.548098 0.274049 0.961716i \(-0.411637\pi\)
0.274049 + 0.961716i \(0.411637\pi\)
\(578\) 0 0
\(579\) −113014. + 113014.i −0.337112 + 0.337112i
\(580\) 0 0
\(581\) −85965.6 + 85965.6i −0.254667 + 0.254667i
\(582\) 0 0
\(583\) −30136.1 −0.0886646
\(584\) 0 0
\(585\) 112745.i 0.329447i
\(586\) 0 0
\(587\) −197015. 197015.i −0.571772 0.571772i 0.360851 0.932623i \(-0.382486\pi\)
−0.932623 + 0.360851i \(0.882486\pi\)
\(588\) 0 0
\(589\) −13833.3 13833.3i −0.0398744 0.0398744i
\(590\) 0 0
\(591\) 292389.i 0.837116i
\(592\) 0 0
\(593\) −478257. −1.36004 −0.680020 0.733194i \(-0.738029\pi\)
−0.680020 + 0.733194i \(0.738029\pi\)
\(594\) 0 0
\(595\) −389561. + 389561.i −1.10038 + 1.10038i
\(596\) 0 0
\(597\) −329722. + 329722.i −0.925121 + 0.925121i
\(598\) 0 0
\(599\) −141800. −0.395206 −0.197603 0.980282i \(-0.563316\pi\)
−0.197603 + 0.980282i \(0.563316\pi\)
\(600\) 0 0
\(601\) 50813.1i 0.140678i −0.997523 0.0703391i \(-0.977592\pi\)
0.997523 0.0703391i \(-0.0224081\pi\)
\(602\) 0 0
\(603\) −184242. 184242.i −0.506705 0.506705i
\(604\) 0 0
\(605\) −408421. 408421.i −1.11583 1.11583i
\(606\) 0 0
\(607\) 448023.i 1.21597i −0.793948 0.607985i \(-0.791978\pi\)
0.793948 0.607985i \(-0.208022\pi\)
\(608\) 0 0
\(609\) −518965. −1.39928
\(610\) 0 0
\(611\) −102482. + 102482.i −0.274514 + 0.274514i
\(612\) 0 0
\(613\) −8742.04 + 8742.04i −0.0232644 + 0.0232644i −0.718643 0.695379i \(-0.755237\pi\)
0.695379 + 0.718643i \(0.255237\pi\)
\(614\) 0 0
\(615\) −67365.1 −0.178109
\(616\) 0 0
\(617\) 488336.i 1.28277i 0.767220 + 0.641384i \(0.221639\pi\)
−0.767220 + 0.641384i \(0.778361\pi\)
\(618\) 0 0
\(619\) 416206. + 416206.i 1.08624 + 1.08624i 0.995912 + 0.0903309i \(0.0287925\pi\)
0.0903309 + 0.995912i \(0.471208\pi\)
\(620\) 0 0
\(621\) 407779. + 407779.i 1.05741 + 1.05741i
\(622\) 0 0
\(623\) 302377.i 0.779062i
\(624\) 0 0
\(625\) −101233. −0.259155
\(626\) 0 0
\(627\) −2470.56 + 2470.56i −0.00628434 + 0.00628434i
\(628\) 0 0
\(629\) 59038.6 59038.6i 0.149223 0.149223i
\(630\) 0 0
\(631\) 77166.0 0.193806 0.0969030 0.995294i \(-0.469106\pi\)
0.0969030 + 0.995294i \(0.469106\pi\)
\(632\) 0 0
\(633\) 124171.i 0.309893i
\(634\) 0 0
\(635\) −76812.3 76812.3i −0.190495 0.190495i
\(636\) 0 0
\(637\) −58565.5 58565.5i −0.144332 0.144332i
\(638\) 0 0
\(639\) 158976.i 0.389340i
\(640\) 0 0
\(641\) 692532. 1.68548 0.842740 0.538321i \(-0.180941\pi\)
0.842740 + 0.538321i \(0.180941\pi\)
\(642\) 0 0
\(643\) −515879. + 515879.i −1.24774 + 1.24774i −0.291031 + 0.956714i \(0.593998\pi\)
−0.956714 + 0.291031i \(0.906002\pi\)
\(644\) 0 0
\(645\) −280192. + 280192.i −0.673498 + 0.673498i
\(646\) 0 0
\(647\) −187947. −0.448980 −0.224490 0.974476i \(-0.572072\pi\)
−0.224490 + 0.974476i \(0.572072\pi\)
\(648\) 0 0
\(649\) 80406.4i 0.190898i
\(650\) 0 0
\(651\) 259438. + 259438.i 0.612169 + 0.612169i
\(652\) 0 0
\(653\) −363478. 363478.i −0.852415 0.852415i 0.138015 0.990430i \(-0.455928\pi\)
−0.990430 + 0.138015i \(0.955928\pi\)
\(654\) 0 0
\(655\) 726322.i 1.69296i
\(656\) 0 0
\(657\) −344929. −0.799096
\(658\) 0 0
\(659\) 59401.3 59401.3i 0.136781 0.136781i −0.635401 0.772182i \(-0.719165\pi\)
0.772182 + 0.635401i \(0.219165\pi\)
\(660\) 0 0
\(661\) 352242. 352242.i 0.806191 0.806191i −0.177864 0.984055i \(-0.556919\pi\)
0.984055 + 0.177864i \(0.0569187\pi\)
\(662\) 0 0
\(663\) 105331. 0.239622
\(664\) 0 0
\(665\) 51307.8i 0.116022i
\(666\) 0 0
\(667\) −693927. 693927.i −1.55977 1.55977i
\(668\) 0 0
\(669\) 251555. + 251555.i 0.562058 + 0.562058i
\(670\) 0 0
\(671\) 12346.6i 0.0274222i
\(672\) 0 0
\(673\) 678354. 1.49771 0.748853 0.662736i \(-0.230605\pi\)
0.748853 + 0.662736i \(0.230605\pi\)
\(674\) 0 0
\(675\) 596041. 596041.i 1.30818 1.30818i
\(676\) 0 0
\(677\) 348304. 348304.i 0.759943 0.759943i −0.216369 0.976312i \(-0.569421\pi\)
0.976312 + 0.216369i \(0.0694214\pi\)
\(678\) 0 0
\(679\) −150471. −0.326372
\(680\) 0 0
\(681\) 134699.i 0.290448i
\(682\) 0 0
\(683\) 218970. + 218970.i 0.469401 + 0.469401i 0.901721 0.432319i \(-0.142305\pi\)
−0.432319 + 0.901721i \(0.642305\pi\)
\(684\) 0 0
\(685\) 449450. + 449450.i 0.957856 + 0.957856i
\(686\) 0 0
\(687\) 200422.i 0.424652i
\(688\) 0 0
\(689\) 84610.7 0.178233
\(690\) 0 0
\(691\) −166441. + 166441.i −0.348581 + 0.348581i −0.859581 0.511000i \(-0.829275\pi\)
0.511000 + 0.859581i \(0.329275\pi\)
\(692\) 0 0
\(693\) −40995.2 + 40995.2i −0.0853625 + 0.0853625i
\(694\) 0 0
\(695\) −709638. −1.46915
\(696\) 0 0
\(697\) 55683.0i 0.114619i
\(698\) 0 0
\(699\) −426948. 426948.i −0.873817 0.873817i
\(700\) 0 0
\(701\) 606601. + 606601.i 1.23443 + 1.23443i 0.962244 + 0.272188i \(0.0877473\pi\)
0.272188 + 0.962244i \(0.412253\pi\)
\(702\) 0 0
\(703\) 7775.80i 0.0157338i
\(704\) 0 0
\(705\) −546430. −1.09940
\(706\) 0 0
\(707\) −25397.3 + 25397.3i −0.0508100 + 0.0508100i
\(708\) 0 0
\(709\) −590171. + 590171.i −1.17405 + 1.17405i −0.192811 + 0.981236i \(0.561760\pi\)
−0.981236 + 0.192811i \(0.938240\pi\)
\(710\) 0 0
\(711\) 27968.0 0.0553251
\(712\) 0 0
\(713\) 693806.i 1.36477i
\(714\) 0 0
\(715\) −53620.1 53620.1i −0.104885 0.104885i
\(716\) 0 0
\(717\) −326391. 326391.i −0.634893 0.634893i
\(718\) 0 0
\(719\) 319294.i 0.617637i −0.951121 0.308819i \(-0.900066\pi\)
0.951121 0.308819i \(-0.0999336\pi\)
\(720\) 0 0
\(721\) 785701. 1.51143
\(722\) 0 0
\(723\) 103848. 103848.i 0.198665 0.198665i
\(724\) 0 0
\(725\) −1.01430e6 + 1.01430e6i −1.92969 + 1.92969i
\(726\) 0 0
\(727\) −295780. −0.559628 −0.279814 0.960054i \(-0.590273\pi\)
−0.279814 + 0.960054i \(0.590273\pi\)
\(728\) 0 0
\(729\) 491717.i 0.925253i
\(730\) 0 0
\(731\) 231602. + 231602.i 0.433419 + 0.433419i
\(732\) 0 0
\(733\) −353645. 353645.i −0.658203 0.658203i 0.296752 0.954955i \(-0.404097\pi\)
−0.954955 + 0.296752i \(0.904097\pi\)
\(734\) 0 0
\(735\) 312270.i 0.578036i
\(736\) 0 0
\(737\) −175247. −0.322637
\(738\) 0 0
\(739\) 23782.9 23782.9i 0.0435488 0.0435488i −0.684997 0.728546i \(-0.740197\pi\)
0.728546 + 0.684997i \(0.240197\pi\)
\(740\) 0 0
\(741\) 6936.38 6936.38i 0.0126327 0.0126327i
\(742\) 0 0
\(743\) −912931. −1.65371 −0.826857 0.562412i \(-0.809873\pi\)
−0.826857 + 0.562412i \(0.809873\pi\)
\(744\) 0 0
\(745\) 1.21494e6i 2.18899i
\(746\) 0 0
\(747\) −54826.8 54826.8i −0.0982543 0.0982543i
\(748\) 0 0
\(749\) 645172. + 645172.i 1.15004 + 1.15004i
\(750\) 0 0
\(751\) 799005.i 1.41667i 0.705875 + 0.708336i \(0.250554\pi\)
−0.705875 + 0.708336i \(0.749446\pi\)
\(752\) 0 0
\(753\) 671294. 1.18392
\(754\) 0 0
\(755\) −226496. + 226496.i −0.397344 + 0.397344i
\(756\) 0 0
\(757\) 24122.0 24122.0i 0.0420940 0.0420940i −0.685746 0.727841i \(-0.740524\pi\)
0.727841 + 0.685746i \(0.240524\pi\)
\(758\) 0 0
\(759\) 123910. 0.215092
\(760\) 0 0
\(761\) 97444.6i 0.168263i −0.996455 0.0841315i \(-0.973188\pi\)
0.996455 0.0841315i \(-0.0268116\pi\)
\(762\) 0 0
\(763\) 85170.8 + 85170.8i 0.146299 + 0.146299i
\(764\) 0 0
\(765\) −248452. 248452.i −0.424542 0.424542i
\(766\) 0 0
\(767\) 225750.i 0.383741i
\(768\) 0 0
\(769\) −747937. −1.26477 −0.632386 0.774653i \(-0.717924\pi\)
−0.632386 + 0.774653i \(0.717924\pi\)
\(770\) 0 0
\(771\) −261751. + 261751.i −0.440331 + 0.440331i
\(772\) 0 0
\(773\) 328529. 328529.i 0.549813 0.549813i −0.376574 0.926387i \(-0.622898\pi\)
0.926387 + 0.376574i \(0.122898\pi\)
\(774\) 0 0
\(775\) 1.01412e6 1.68844
\(776\) 0 0
\(777\) 145832.i 0.241552i
\(778\) 0 0
\(779\) 3666.92 + 3666.92i 0.00604263 + 0.00604263i
\(780\) 0 0
\(781\) −75606.7 75606.7i −0.123953 0.123953i
\(782\) 0 0
\(783\) 1.03606e6i 1.68990i
\(784\) 0 0
\(785\) −411150. −0.667207
\(786\) 0 0
\(787\) 76254.3 76254.3i 0.123116 0.123116i −0.642864 0.765980i \(-0.722254\pi\)
0.765980 + 0.642864i \(0.222254\pi\)
\(788\) 0 0
\(789\) 354689. 354689.i 0.569762 0.569762i
\(790\) 0 0
\(791\) 1.19964e6 1.91733
\(792\) 0 0
\(793\) 34664.5i 0.0551238i
\(794\) 0 0
\(795\) 225571. + 225571.i 0.356902 + 0.356902i
\(796\) 0 0