Properties

Label 76.6.e.a.45.5
Level $76$
Weight $6$
Character 76.45
Analytic conductor $12.189$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 76.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.1891703058\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(9\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Defining polynomial: \(x^{18} - 2 x^{17} + 1540 x^{16} - 768 x^{15} + 1608492 x^{14} - 1027368 x^{13} + 897054160 x^{12} - 1275481376 x^{11} + 361098181456 x^{10} - 863969476320 x^{9} + 79755165392064 x^{8} - 375077568148992 x^{7} + 12736924096193536 x^{6} - 57314532742553600 x^{5} + 977121800205220864 x^{4} - 4977732006498379776 x^{3} + 53672321824823513088 x^{2} - 185653809995679793152 x + 804303742853852430336\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{16}\cdot 3^{3}\cdot 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 45.5
Root \(2.80322 - 4.85531i\) of defining polynomial
Character \(\chi\) \(=\) 76.45
Dual form 76.6.e.a.49.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.30322 - 5.72134i) q^{3} +(12.6095 + 21.8402i) q^{5} -40.7176 q^{7} +(99.6775 - 172.647i) q^{9} +O(q^{10})\) \(q+(-3.30322 - 5.72134i) q^{3} +(12.6095 + 21.8402i) q^{5} -40.7176 q^{7} +(99.6775 - 172.647i) q^{9} +324.832 q^{11} +(-48.8600 + 84.6280i) q^{13} +(83.3036 - 144.286i) q^{15} +(-1057.36 - 1831.41i) q^{17} +(806.259 - 1351.31i) q^{19} +(134.499 + 232.959i) q^{21} +(1506.33 - 2609.05i) q^{23} +(1244.50 - 2155.54i) q^{25} -2922.39 q^{27} +(-527.733 + 914.060i) q^{29} +7602.00 q^{31} +(-1072.99 - 1858.48i) q^{33} +(-513.427 - 889.282i) q^{35} -2057.16 q^{37} +645.581 q^{39} +(230.415 + 399.091i) q^{41} +(-188.582 - 326.633i) q^{43} +5027.52 q^{45} +(-8354.76 + 14470.9i) q^{47} -15149.1 q^{49} +(-6985.41 + 12099.1i) q^{51} +(5234.06 - 9065.67i) q^{53} +(4095.96 + 7094.41i) q^{55} +(-10394.6 - 149.205i) q^{57} +(23733.3 + 41107.2i) q^{59} +(-13715.7 + 23756.3i) q^{61} +(-4058.63 + 7029.76i) q^{63} -2464.39 q^{65} +(17228.2 - 29840.0i) q^{67} -19903.0 q^{69} +(1879.84 + 3255.97i) q^{71} +(6145.42 + 10644.2i) q^{73} -16443.5 q^{75} -13226.4 q^{77} +(26717.1 + 46275.4i) q^{79} +(-14568.3 - 25233.1i) q^{81} -1317.09 q^{83} +(26665.6 - 46186.2i) q^{85} +6972.87 q^{87} +(51736.4 - 89610.0i) q^{89} +(1989.46 - 3445.85i) q^{91} +(-25111.1 - 43493.7i) q^{93} +(39679.5 + 569.563i) q^{95} +(-52995.4 - 91790.7i) q^{97} +(32378.5 - 56081.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q - 11q^{3} + 11q^{5} + 336q^{7} - 902q^{9} + O(q^{10}) \) \( 18q - 11q^{3} + 11q^{5} + 336q^{7} - 902q^{9} - 320q^{11} + 227q^{13} - 101q^{15} + 179q^{17} - 868q^{19} - 5700q^{21} - 3425q^{23} - 7054q^{25} + 14722q^{27} - 7349q^{29} - 9960q^{31} - 2998q^{33} + 15888q^{35} + 26444q^{37} - 30246q^{39} - 7311q^{41} - 8283q^{43} - 62164q^{45} + 37603q^{47} + 124738q^{49} + 47227q^{51} - 20337q^{53} + 716q^{55} - 57555q^{57} - 74455q^{59} - 7569q^{61} - 52544q^{63} + 188998q^{65} - 26177q^{67} + 116282q^{69} - 53463q^{71} - 14103q^{73} + 120912q^{75} - 31960q^{77} + 31825q^{79} - 21137q^{81} + 82600q^{83} - 50787q^{85} - 339766q^{87} - 155197q^{89} - 2800q^{91} - 46460q^{93} + 49315q^{95} + 111241q^{97} - 193544q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) −3.30322 5.72134i −0.211901 0.367024i 0.740408 0.672158i \(-0.234632\pi\)
−0.952310 + 0.305133i \(0.901299\pi\)
\(4\) 0 0
\(5\) 12.6095 + 21.8402i 0.225565 + 0.390690i 0.956489 0.291769i \(-0.0942439\pi\)
−0.730924 + 0.682459i \(0.760911\pi\)
\(6\) 0 0
\(7\) −40.7176 −0.314078 −0.157039 0.987592i \(-0.550195\pi\)
−0.157039 + 0.987592i \(0.550195\pi\)
\(8\) 0 0
\(9\) 99.6775 172.647i 0.410196 0.710479i
\(10\) 0 0
\(11\) 324.832 0.809426 0.404713 0.914444i \(-0.367371\pi\)
0.404713 + 0.914444i \(0.367371\pi\)
\(12\) 0 0
\(13\) −48.8600 + 84.6280i −0.0801854 + 0.138885i −0.903329 0.428947i \(-0.858885\pi\)
0.823144 + 0.567833i \(0.192218\pi\)
\(14\) 0 0
\(15\) 83.3036 144.286i 0.0955951 0.165575i
\(16\) 0 0
\(17\) −1057.36 1831.41i −0.887365 1.53696i −0.842978 0.537947i \(-0.819200\pi\)
−0.0443869 0.999014i \(-0.514133\pi\)
\(18\) 0 0
\(19\) 806.259 1351.31i 0.512378 0.858760i
\(20\) 0 0
\(21\) 134.499 + 232.959i 0.0665536 + 0.115274i
\(22\) 0 0
\(23\) 1506.33 2609.05i 0.593748 1.02840i −0.399975 0.916526i \(-0.630981\pi\)
0.993722 0.111875i \(-0.0356856\pi\)
\(24\) 0 0
\(25\) 1244.50 2155.54i 0.398241 0.689774i
\(26\) 0 0
\(27\) −2922.39 −0.771487
\(28\) 0 0
\(29\) −527.733 + 914.060i −0.116525 + 0.201827i −0.918388 0.395680i \(-0.870509\pi\)
0.801863 + 0.597507i \(0.203842\pi\)
\(30\) 0 0
\(31\) 7602.00 1.42077 0.710385 0.703813i \(-0.248521\pi\)
0.710385 + 0.703813i \(0.248521\pi\)
\(32\) 0 0
\(33\) −1072.99 1858.48i −0.171519 0.297079i
\(34\) 0 0
\(35\) −513.427 889.282i −0.0708449 0.122707i
\(36\) 0 0
\(37\) −2057.16 −0.247037 −0.123519 0.992342i \(-0.539418\pi\)
−0.123519 + 0.992342i \(0.539418\pi\)
\(38\) 0 0
\(39\) 645.581 0.0679656
\(40\) 0 0
\(41\) 230.415 + 399.091i 0.0214068 + 0.0370777i 0.876530 0.481347i \(-0.159852\pi\)
−0.855124 + 0.518424i \(0.826519\pi\)
\(42\) 0 0
\(43\) −188.582 326.633i −0.0155535 0.0269395i 0.858144 0.513409i \(-0.171618\pi\)
−0.873697 + 0.486470i \(0.838284\pi\)
\(44\) 0 0
\(45\) 5027.52 0.370103
\(46\) 0 0
\(47\) −8354.76 + 14470.9i −0.551682 + 0.955542i 0.446471 + 0.894798i \(0.352681\pi\)
−0.998153 + 0.0607440i \(0.980653\pi\)
\(48\) 0 0
\(49\) −15149.1 −0.901355
\(50\) 0 0
\(51\) −6985.41 + 12099.1i −0.376068 + 0.651369i
\(52\) 0 0
\(53\) 5234.06 9065.67i 0.255947 0.443313i −0.709206 0.705002i \(-0.750946\pi\)
0.965152 + 0.261689i \(0.0842795\pi\)
\(54\) 0 0
\(55\) 4095.96 + 7094.41i 0.182578 + 0.316235i
\(56\) 0 0
\(57\) −10394.6 149.205i −0.423759 0.00608268i
\(58\) 0 0
\(59\) 23733.3 + 41107.2i 0.887621 + 1.53740i 0.842680 + 0.538415i \(0.180977\pi\)
0.0449408 + 0.998990i \(0.485690\pi\)
\(60\) 0 0
\(61\) −13715.7 + 23756.3i −0.471948 + 0.817438i −0.999485 0.0320943i \(-0.989782\pi\)
0.527537 + 0.849532i \(0.323116\pi\)
\(62\) 0 0
\(63\) −4058.63 + 7029.76i −0.128833 + 0.223146i
\(64\) 0 0
\(65\) −2464.39 −0.0723480
\(66\) 0 0
\(67\) 17228.2 29840.0i 0.468869 0.812105i −0.530498 0.847686i \(-0.677995\pi\)
0.999367 + 0.0355811i \(0.0113282\pi\)
\(68\) 0 0
\(69\) −19903.0 −0.503264
\(70\) 0 0
\(71\) 1879.84 + 3255.97i 0.0442562 + 0.0766541i 0.887305 0.461183i \(-0.152575\pi\)
−0.843049 + 0.537837i \(0.819242\pi\)
\(72\) 0 0
\(73\) 6145.42 + 10644.2i 0.134972 + 0.233779i 0.925587 0.378535i \(-0.123572\pi\)
−0.790615 + 0.612314i \(0.790239\pi\)
\(74\) 0 0
\(75\) −16443.5 −0.337551
\(76\) 0 0
\(77\) −13226.4 −0.254223
\(78\) 0 0
\(79\) 26717.1 + 46275.4i 0.481639 + 0.834223i 0.999778 0.0210731i \(-0.00670827\pi\)
−0.518139 + 0.855297i \(0.673375\pi\)
\(80\) 0 0
\(81\) −14568.3 25233.1i −0.246716 0.427325i
\(82\) 0 0
\(83\) −1317.09 −0.0209856 −0.0104928 0.999945i \(-0.503340\pi\)
−0.0104928 + 0.999945i \(0.503340\pi\)
\(84\) 0 0
\(85\) 26665.6 46186.2i 0.400317 0.693369i
\(86\) 0 0
\(87\) 6972.87 0.0987673
\(88\) 0 0
\(89\) 51736.4 89610.0i 0.692342 1.19917i −0.278726 0.960371i \(-0.589912\pi\)
0.971068 0.238801i \(-0.0767545\pi\)
\(90\) 0 0
\(91\) 1989.46 3445.85i 0.0251845 0.0436208i
\(92\) 0 0
\(93\) −25111.1 43493.7i −0.301063 0.521457i
\(94\) 0 0
\(95\) 39679.5 + 569.563i 0.451083 + 0.00647489i
\(96\) 0 0
\(97\) −52995.4 91790.7i −0.571885 0.990533i −0.996372 0.0850998i \(-0.972879\pi\)
0.424488 0.905434i \(-0.360454\pi\)
\(98\) 0 0
\(99\) 32378.5 56081.1i 0.332023 0.575081i
\(100\) 0 0
\(101\) −34282.4 + 59378.8i −0.334401 + 0.579200i −0.983370 0.181616i \(-0.941867\pi\)
0.648969 + 0.760815i \(0.275201\pi\)
\(102\) 0 0
\(103\) −35253.0 −0.327419 −0.163709 0.986509i \(-0.552346\pi\)
−0.163709 + 0.986509i \(0.552346\pi\)
\(104\) 0 0
\(105\) −3391.92 + 5874.98i −0.0300243 + 0.0520036i
\(106\) 0 0
\(107\) 126916. 1.07166 0.535832 0.844325i \(-0.319998\pi\)
0.535832 + 0.844325i \(0.319998\pi\)
\(108\) 0 0
\(109\) −107794. 186705.i −0.869019 1.50519i −0.863000 0.505204i \(-0.831417\pi\)
−0.00601921 0.999982i \(-0.501916\pi\)
\(110\) 0 0
\(111\) 6795.23 + 11769.7i 0.0523476 + 0.0906687i
\(112\) 0 0
\(113\) 25767.6 0.189835 0.0949177 0.995485i \(-0.469741\pi\)
0.0949177 + 0.995485i \(0.469741\pi\)
\(114\) 0 0
\(115\) 75976.3 0.535714
\(116\) 0 0
\(117\) 9740.49 + 16871.0i 0.0657834 + 0.113940i
\(118\) 0 0
\(119\) 43053.4 + 74570.6i 0.278702 + 0.482726i
\(120\) 0 0
\(121\) −55535.1 −0.344829
\(122\) 0 0
\(123\) 1522.22 2636.57i 0.00907226 0.0157136i
\(124\) 0 0
\(125\) 141579. 0.810446
\(126\) 0 0
\(127\) −59314.9 + 102736.i −0.326328 + 0.565216i −0.981780 0.190020i \(-0.939145\pi\)
0.655452 + 0.755237i \(0.272478\pi\)
\(128\) 0 0
\(129\) −1245.85 + 2157.88i −0.00659163 + 0.0114170i
\(130\) 0 0
\(131\) −27739.5 48046.2i −0.141228 0.244614i 0.786731 0.617295i \(-0.211772\pi\)
−0.927959 + 0.372682i \(0.878438\pi\)
\(132\) 0 0
\(133\) −32829.0 + 55022.2i −0.160927 + 0.269717i
\(134\) 0 0
\(135\) −36849.7 63825.6i −0.174020 0.301412i
\(136\) 0 0
\(137\) −159895. + 276946.i −0.727835 + 1.26065i 0.229962 + 0.973200i \(0.426140\pi\)
−0.957797 + 0.287447i \(0.907193\pi\)
\(138\) 0 0
\(139\) −105811. + 183269.i −0.464506 + 0.804549i −0.999179 0.0405104i \(-0.987102\pi\)
0.534673 + 0.845059i \(0.320435\pi\)
\(140\) 0 0
\(141\) 110390. 0.467609
\(142\) 0 0
\(143\) −15871.3 + 27489.9i −0.0649041 + 0.112417i
\(144\) 0 0
\(145\) −26617.7 −0.105136
\(146\) 0 0
\(147\) 50040.7 + 86673.0i 0.190998 + 0.330819i
\(148\) 0 0
\(149\) 36052.9 + 62445.4i 0.133037 + 0.230428i 0.924846 0.380342i \(-0.124194\pi\)
−0.791809 + 0.610769i \(0.790860\pi\)
\(150\) 0 0
\(151\) 265545. 0.947753 0.473877 0.880591i \(-0.342854\pi\)
0.473877 + 0.880591i \(0.342854\pi\)
\(152\) 0 0
\(153\) −421582. −1.45597
\(154\) 0 0
\(155\) 95857.2 + 166029.i 0.320476 + 0.555080i
\(156\) 0 0
\(157\) −159838. 276848.i −0.517526 0.896381i −0.999793 0.0203568i \(-0.993520\pi\)
0.482267 0.876024i \(-0.339814\pi\)
\(158\) 0 0
\(159\) −69157.0 −0.216942
\(160\) 0 0
\(161\) −61334.4 + 106234.i −0.186483 + 0.322998i
\(162\) 0 0
\(163\) −202591. −0.597244 −0.298622 0.954371i \(-0.596527\pi\)
−0.298622 + 0.954371i \(0.596527\pi\)
\(164\) 0 0
\(165\) 27059.7 46868.7i 0.0773771 0.134021i
\(166\) 0 0
\(167\) −151820. + 262959.i −0.421247 + 0.729621i −0.996062 0.0886623i \(-0.971741\pi\)
0.574815 + 0.818284i \(0.305074\pi\)
\(168\) 0 0
\(169\) 180872. + 313279.i 0.487141 + 0.843752i
\(170\) 0 0
\(171\) −152933. 273893.i −0.399956 0.716294i
\(172\) 0 0
\(173\) 328662. + 569260.i 0.834900 + 1.44609i 0.894112 + 0.447844i \(0.147808\pi\)
−0.0592118 + 0.998245i \(0.518859\pi\)
\(174\) 0 0
\(175\) −50673.2 + 87768.6i −0.125079 + 0.216643i
\(176\) 0 0
\(177\) 156792. 271572.i 0.376176 0.651557i
\(178\) 0 0
\(179\) 265873. 0.620215 0.310108 0.950701i \(-0.399635\pi\)
0.310108 + 0.950701i \(0.399635\pi\)
\(180\) 0 0
\(181\) 75575.2 130900.i 0.171468 0.296991i −0.767465 0.641090i \(-0.778482\pi\)
0.938933 + 0.344099i \(0.111816\pi\)
\(182\) 0 0
\(183\) 181224. 0.400026
\(184\) 0 0
\(185\) −25939.6 44928.7i −0.0557230 0.0965150i
\(186\) 0 0
\(187\) −343466. 594901.i −0.718257 1.24406i
\(188\) 0 0
\(189\) 118993. 0.242307
\(190\) 0 0
\(191\) −120491. −0.238986 −0.119493 0.992835i \(-0.538127\pi\)
−0.119493 + 0.992835i \(0.538127\pi\)
\(192\) 0 0
\(193\) 38385.0 + 66484.8i 0.0741769 + 0.128478i 0.900728 0.434384i \(-0.143034\pi\)
−0.826551 + 0.562862i \(0.809700\pi\)
\(194\) 0 0
\(195\) 8140.43 + 14099.6i 0.0153307 + 0.0265535i
\(196\) 0 0
\(197\) 581905. 1.06828 0.534141 0.845395i \(-0.320635\pi\)
0.534141 + 0.845395i \(0.320635\pi\)
\(198\) 0 0
\(199\) 83536.9 144690.i 0.149536 0.259004i −0.781520 0.623880i \(-0.785555\pi\)
0.931056 + 0.364876i \(0.118889\pi\)
\(200\) 0 0
\(201\) −227633. −0.397416
\(202\) 0 0
\(203\) 21488.0 37218.4i 0.0365979 0.0633895i
\(204\) 0 0
\(205\) −5810.82 + 10064.6i −0.00965724 + 0.0167268i
\(206\) 0 0
\(207\) −300295. 520127.i −0.487105 0.843691i
\(208\) 0 0
\(209\) 261899. 438950.i 0.414732 0.695103i
\(210\) 0 0
\(211\) −360222. 623923.i −0.557011 0.964772i −0.997744 0.0671336i \(-0.978615\pi\)
0.440733 0.897638i \(-0.354719\pi\)
\(212\) 0 0
\(213\) 12419.0 21510.4i 0.0187559 0.0324862i
\(214\) 0 0
\(215\) 4755.83 8237.33i 0.00701665 0.0121532i
\(216\) 0 0
\(217\) −309536. −0.446233
\(218\) 0 0
\(219\) 40599.3 70320.1i 0.0572016 0.0990761i
\(220\) 0 0
\(221\) 206651. 0.284615
\(222\) 0 0
\(223\) −676428. 1.17161e6i −0.910876 1.57768i −0.812830 0.582501i \(-0.802074\pi\)
−0.0980458 0.995182i \(-0.531259\pi\)
\(224\) 0 0
\(225\) −248098. 429718.i −0.326713 0.565884i
\(226\) 0 0
\(227\) 944144. 1.21611 0.608056 0.793894i \(-0.291950\pi\)
0.608056 + 0.793894i \(0.291950\pi\)
\(228\) 0 0
\(229\) 1.23700e6 1.55877 0.779383 0.626547i \(-0.215532\pi\)
0.779383 + 0.626547i \(0.215532\pi\)
\(230\) 0 0
\(231\) 43689.6 + 75672.7i 0.0538702 + 0.0933059i
\(232\) 0 0
\(233\) 495767. + 858694.i 0.598258 + 1.03621i 0.993078 + 0.117454i \(0.0374733\pi\)
−0.394821 + 0.918758i \(0.629193\pi\)
\(234\) 0 0
\(235\) −421396. −0.497761
\(236\) 0 0
\(237\) 176505. 305715.i 0.204120 0.353546i
\(238\) 0 0
\(239\) −256516. −0.290482 −0.145241 0.989396i \(-0.546396\pi\)
−0.145241 + 0.989396i \(0.546396\pi\)
\(240\) 0 0
\(241\) −398215. + 689728.i −0.441646 + 0.764954i −0.997812 0.0661177i \(-0.978939\pi\)
0.556166 + 0.831072i \(0.312272\pi\)
\(242\) 0 0
\(243\) −451315. + 781701.i −0.490303 + 0.849229i
\(244\) 0 0
\(245\) −191022. 330859.i −0.203314 0.352150i
\(246\) 0 0
\(247\) 74965.1 + 134257.i 0.0781838 + 0.140022i
\(248\) 0 0
\(249\) 4350.64 + 7535.53i 0.00444687 + 0.00770221i
\(250\) 0 0
\(251\) −292660. + 506902.i −0.293210 + 0.507855i −0.974567 0.224097i \(-0.928057\pi\)
0.681357 + 0.731951i \(0.261390\pi\)
\(252\) 0 0
\(253\) 489306. 847503.i 0.480595 0.832415i
\(254\) 0 0
\(255\) −352329. −0.339311
\(256\) 0 0
\(257\) −436841. + 756630.i −0.412563 + 0.714580i −0.995169 0.0981747i \(-0.968700\pi\)
0.582606 + 0.812754i \(0.302033\pi\)
\(258\) 0 0
\(259\) 83762.5 0.0775890
\(260\) 0 0
\(261\) 105206. + 182222.i 0.0955961 + 0.165577i
\(262\) 0 0
\(263\) 146951. + 254527.i 0.131004 + 0.226905i 0.924064 0.382238i \(-0.124847\pi\)
−0.793060 + 0.609144i \(0.791513\pi\)
\(264\) 0 0
\(265\) 263995. 0.230930
\(266\) 0 0
\(267\) −683586. −0.586833
\(268\) 0 0
\(269\) 1.16327e6 + 2.01484e6i 0.980163 + 1.69769i 0.661722 + 0.749749i \(0.269826\pi\)
0.318440 + 0.947943i \(0.396841\pi\)
\(270\) 0 0
\(271\) 130705. + 226387.i 0.108111 + 0.187253i 0.915005 0.403443i \(-0.132187\pi\)
−0.806894 + 0.590696i \(0.798853\pi\)
\(272\) 0 0
\(273\) −26286.5 −0.0213465
\(274\) 0 0
\(275\) 404255. 700189.i 0.322347 0.558321i
\(276\) 0 0
\(277\) −1.76335e6 −1.38083 −0.690415 0.723414i \(-0.742572\pi\)
−0.690415 + 0.723414i \(0.742572\pi\)
\(278\) 0 0
\(279\) 757749. 1.31246e6i 0.582794 1.00943i
\(280\) 0 0
\(281\) −477850. + 827661.i −0.361016 + 0.625297i −0.988128 0.153631i \(-0.950903\pi\)
0.627113 + 0.778929i \(0.284237\pi\)
\(282\) 0 0
\(283\) 172840. + 299368.i 0.128286 + 0.222197i 0.923013 0.384770i \(-0.125719\pi\)
−0.794727 + 0.606967i \(0.792386\pi\)
\(284\) 0 0
\(285\) −127811. 228901.i −0.0932088 0.166930i
\(286\) 0 0
\(287\) −9381.96 16250.0i −0.00672340 0.0116453i
\(288\) 0 0
\(289\) −1.52611e6 + 2.64330e6i −1.07483 + 1.86167i
\(290\) 0 0
\(291\) −350110. + 606409.i −0.242366 + 0.419791i
\(292\) 0 0
\(293\) 1.17269e6 0.798023 0.399011 0.916946i \(-0.369353\pi\)
0.399011 + 0.916946i \(0.369353\pi\)
\(294\) 0 0
\(295\) −598527. + 1.03668e6i −0.400432 + 0.693569i
\(296\) 0 0
\(297\) −949286. −0.624462
\(298\) 0 0
\(299\) 147199. + 254956.i 0.0952198 + 0.164925i
\(300\) 0 0
\(301\) 7678.60 + 13299.7i 0.00488501 + 0.00846109i
\(302\) 0 0
\(303\) 452969. 0.283440
\(304\) 0 0
\(305\) −691791. −0.425819
\(306\) 0 0
\(307\) −160062. 277235.i −0.0969264 0.167881i 0.813485 0.581586i \(-0.197568\pi\)
−0.910411 + 0.413705i \(0.864234\pi\)
\(308\) 0 0
\(309\) 116448. + 201695.i 0.0693805 + 0.120171i
\(310\) 0 0
\(311\) 1.45223e6 0.851400 0.425700 0.904864i \(-0.360028\pi\)
0.425700 + 0.904864i \(0.360028\pi\)
\(312\) 0 0
\(313\) 965219. 1.67181e6i 0.556884 0.964552i −0.440870 0.897571i \(-0.645330\pi\)
0.997754 0.0669807i \(-0.0213366\pi\)
\(314\) 0 0
\(315\) −204709. −0.116241
\(316\) 0 0
\(317\) 757768. 1.31249e6i 0.423534 0.733582i −0.572749 0.819731i \(-0.694123\pi\)
0.996282 + 0.0861494i \(0.0274562\pi\)
\(318\) 0 0
\(319\) −171425. + 296916.i −0.0943184 + 0.163364i
\(320\) 0 0
\(321\) −419233. 726132.i −0.227087 0.393326i
\(322\) 0 0
\(323\) −3.32732e6 47760.6i −1.77455 0.0254720i
\(324\) 0 0
\(325\) 121613. + 210640.i 0.0638662 + 0.110620i
\(326\) 0 0
\(327\) −712136. + 1.23346e6i −0.368293 + 0.637902i
\(328\) 0 0
\(329\) 340186. 589219.i 0.173271 0.300115i
\(330\) 0 0
\(331\) 3.41462e6 1.71306 0.856531 0.516096i \(-0.172615\pi\)
0.856531 + 0.516096i \(0.172615\pi\)
\(332\) 0 0
\(333\) −205052. + 355161.i −0.101334 + 0.175515i
\(334\) 0 0
\(335\) 868951. 0.423042
\(336\) 0 0
\(337\) −1.59676e6 2.76567e6i −0.765888 1.32656i −0.939776 0.341791i \(-0.888967\pi\)
0.173889 0.984765i \(-0.444367\pi\)
\(338\) 0 0
\(339\) −85115.9 147425.i −0.0402264 0.0696742i
\(340\) 0 0
\(341\) 2.46938e6 1.15001
\(342\) 0 0
\(343\) 1.30118e6 0.597174
\(344\) 0 0
\(345\) −250966. 434686.i −0.113519 0.196620i
\(346\) 0 0
\(347\) 405681. + 702659.i 0.180868 + 0.313272i 0.942176 0.335118i \(-0.108776\pi\)
−0.761309 + 0.648390i \(0.775443\pi\)
\(348\) 0 0
\(349\) −491593. −0.216044 −0.108022 0.994148i \(-0.534452\pi\)
−0.108022 + 0.994148i \(0.534452\pi\)
\(350\) 0 0
\(351\) 142788. 247316.i 0.0618620 0.107148i
\(352\) 0 0
\(353\) −1.82830e6 −0.780929 −0.390465 0.920618i \(-0.627686\pi\)
−0.390465 + 0.920618i \(0.627686\pi\)
\(354\) 0 0
\(355\) −47407.5 + 82112.2i −0.0199653 + 0.0345809i
\(356\) 0 0
\(357\) 284429. 492646.i 0.118115 0.204581i
\(358\) 0 0
\(359\) −1.35760e6 2.35143e6i −0.555950 0.962934i −0.997829 0.0658593i \(-0.979021\pi\)
0.441879 0.897075i \(-0.354312\pi\)
\(360\) 0 0
\(361\) −1.17599e6 2.17902e6i −0.474937 0.880020i
\(362\) 0 0
\(363\) 183444. + 317735.i 0.0730698 + 0.126561i
\(364\) 0 0
\(365\) −154981. + 268435.i −0.0608900 + 0.105465i
\(366\) 0 0
\(367\) 1.32754e6 2.29937e6i 0.514498 0.891136i −0.485361 0.874314i \(-0.661312\pi\)
0.999858 0.0168222i \(-0.00535492\pi\)
\(368\) 0 0
\(369\) 91868.9 0.0351239
\(370\) 0 0
\(371\) −213119. + 369132.i −0.0803872 + 0.139235i
\(372\) 0 0
\(373\) 4.33938e6 1.61494 0.807468 0.589911i \(-0.200837\pi\)
0.807468 + 0.589911i \(0.200837\pi\)
\(374\) 0 0
\(375\) −467667. 810023.i −0.171735 0.297453i
\(376\) 0 0
\(377\) −51570.1 89322.0i −0.0186872 0.0323672i
\(378\) 0 0
\(379\) 3.27824e6 1.17231 0.586155 0.810199i \(-0.300641\pi\)
0.586155 + 0.810199i \(0.300641\pi\)
\(380\) 0 0
\(381\) 783719. 0.276597
\(382\) 0 0
\(383\) 1.41742e6 + 2.45505e6i 0.493745 + 0.855191i 0.999974 0.00720770i \(-0.00229430\pi\)
−0.506229 + 0.862399i \(0.668961\pi\)
\(384\) 0 0
\(385\) −166778. 288867.i −0.0573437 0.0993223i
\(386\) 0 0
\(387\) −75189.4 −0.0255199
\(388\) 0 0
\(389\) 1.39366e6 2.41389e6i 0.466963 0.808804i −0.532324 0.846540i \(-0.678681\pi\)
0.999288 + 0.0377363i \(0.0120147\pi\)
\(390\) 0 0
\(391\) −6.37098e6 −2.10748
\(392\) 0 0
\(393\) −183259. + 317414.i −0.0598528 + 0.103668i
\(394\) 0 0
\(395\) −673777. + 1.16702e6i −0.217282 + 0.376343i
\(396\) 0 0
\(397\) −1.84860e6 3.20187e6i −0.588663 1.01959i −0.994408 0.105607i \(-0.966321\pi\)
0.405745 0.913986i \(-0.367012\pi\)
\(398\) 0 0
\(399\) 423242. + 6075.26i 0.133093 + 0.00191044i
\(400\) 0 0
\(401\) −2.13618e6 3.69998e6i −0.663404 1.14905i −0.979715 0.200394i \(-0.935778\pi\)
0.316312 0.948655i \(-0.397555\pi\)
\(402\) 0 0
\(403\) −371434. + 643343.i −0.113925 + 0.197324i
\(404\) 0 0
\(405\) 367398. 636352.i 0.111301 0.192779i
\(406\) 0 0
\(407\) −668230. −0.199959
\(408\) 0 0
\(409\) −2.89320e6 + 5.01117e6i −0.855205 + 1.48126i 0.0212492 + 0.999774i \(0.493236\pi\)
−0.876454 + 0.481485i \(0.840098\pi\)
\(410\) 0 0
\(411\) 2.11267e6 0.616917
\(412\) 0 0
\(413\) −966362. 1.67379e6i −0.278782 0.482865i
\(414\) 0 0
\(415\) −16607.8 28765.6i −0.00473361 0.00819885i
\(416\) 0 0
\(417\) 1.39806e6 0.393718
\(418\) 0 0
\(419\) 3.36575e6 0.936585 0.468293 0.883573i \(-0.344869\pi\)
0.468293 + 0.883573i \(0.344869\pi\)
\(420\) 0 0
\(421\) 2.36298e6 + 4.09279e6i 0.649761 + 1.12542i 0.983180 + 0.182641i \(0.0584646\pi\)
−0.333418 + 0.942779i \(0.608202\pi\)
\(422\) 0 0
\(423\) 1.66556e6 + 2.88484e6i 0.452595 + 0.783918i
\(424\) 0 0
\(425\) −5.26357e6 −1.41354
\(426\) 0 0
\(427\) 558472. 967301.i 0.148228 0.256739i
\(428\) 0 0
\(429\) 209705. 0.0550131
\(430\) 0 0
\(431\) 212460. 367991.i 0.0550914 0.0954211i −0.837164 0.546951i \(-0.815788\pi\)
0.892256 + 0.451530i \(0.149122\pi\)
\(432\) 0 0
\(433\) −3.10444e6 + 5.37705e6i −0.795726 + 1.37824i 0.126651 + 0.991947i \(0.459577\pi\)
−0.922377 + 0.386291i \(0.873756\pi\)
\(434\) 0 0
\(435\) 87924.1 + 152289.i 0.0222784 + 0.0385874i
\(436\) 0 0
\(437\) −2.31114e6 4.13910e6i −0.578926 1.03682i
\(438\) 0 0
\(439\) 3.48593e6 + 6.03781e6i 0.863291 + 1.49526i 0.868734 + 0.495279i \(0.164934\pi\)
−0.00544290 + 0.999985i \(0.501733\pi\)
\(440\) 0 0
\(441\) −1.51002e6 + 2.61543e6i −0.369732 + 0.640394i
\(442\) 0 0
\(443\) −1.32950e6 + 2.30277e6i −0.321870 + 0.557495i −0.980874 0.194645i \(-0.937645\pi\)
0.659004 + 0.752139i \(0.270978\pi\)
\(444\) 0 0
\(445\) 2.60947e6 0.624672
\(446\) 0 0
\(447\) 238181. 412541.i 0.0563817 0.0976559i
\(448\) 0 0
\(449\) −636809. −0.149071 −0.0745355 0.997218i \(-0.523747\pi\)
−0.0745355 + 0.997218i \(0.523747\pi\)
\(450\) 0 0
\(451\) 74846.3 + 129638.i 0.0173272 + 0.0300116i
\(452\) 0 0
\(453\) −877152. 1.51927e6i −0.200830 0.347848i
\(454\) 0 0
\(455\) 100344. 0.0227229
\(456\) 0 0
\(457\) −1.62218e6 −0.363337 −0.181668 0.983360i \(-0.558150\pi\)
−0.181668 + 0.983360i \(0.558150\pi\)
\(458\) 0 0
\(459\) 3.09003e6 + 5.35209e6i 0.684591 + 1.18575i
\(460\) 0 0
\(461\) 1.88236e6 + 3.26034e6i 0.412525 + 0.714514i 0.995165 0.0982159i \(-0.0313136\pi\)
−0.582640 + 0.812730i \(0.697980\pi\)
\(462\) 0 0
\(463\) 8.56420e6 1.85667 0.928334 0.371748i \(-0.121241\pi\)
0.928334 + 0.371748i \(0.121241\pi\)
\(464\) 0 0
\(465\) 633274. 1.09686e6i 0.135819 0.235245i
\(466\) 0 0
\(467\) −8.68072e6 −1.84189 −0.920944 0.389694i \(-0.872581\pi\)
−0.920944 + 0.389694i \(0.872581\pi\)
\(468\) 0 0
\(469\) −701489. + 1.21502e6i −0.147261 + 0.255064i
\(470\) 0 0
\(471\) −1.05596e6 + 1.82898e6i −0.219329 + 0.379889i
\(472\) 0 0
\(473\) −61257.4 106101.i −0.0125894 0.0218055i
\(474\) 0 0
\(475\) −1.90942e6 3.41964e6i −0.388300 0.695418i
\(476\) 0 0
\(477\) −1.04344e6 1.80729e6i −0.209976 0.363690i
\(478\) 0 0
\(479\) −4.82656e6 + 8.35985e6i −0.961167 + 1.66479i −0.241589 + 0.970379i \(0.577669\pi\)
−0.719578 + 0.694412i \(0.755665\pi\)
\(480\) 0 0
\(481\) 100513. 174093.i 0.0198088 0.0343098i
\(482\) 0 0
\(483\) 810403. 0.158064
\(484\) 0 0
\(485\) 1.33649e6 2.31486e6i 0.257994 0.446859i
\(486\) 0 0
\(487\) −3.07551e6 −0.587617 −0.293809 0.955864i \(-0.594923\pi\)
−0.293809 + 0.955864i \(0.594923\pi\)
\(488\) 0 0
\(489\) 669203. + 1.15909e6i 0.126557 + 0.219203i
\(490\) 0 0
\(491\) −3.46681e6 6.00470e6i −0.648973 1.12405i −0.983368 0.181622i \(-0.941865\pi\)
0.334395 0.942433i \(-0.391468\pi\)
\(492\) 0 0
\(493\) 2.23202e6 0.413601
\(494\) 0 0
\(495\) 1.63310e6 0.299571
\(496\) 0 0
\(497\) −76542.5 132576.i −0.0138999 0.0240753i
\(498\) 0 0
\(499\) 272382. + 471779.i 0.0489696 + 0.0848178i 0.889471 0.456991i \(-0.151073\pi\)
−0.840502 + 0.541809i \(0.817740\pi\)
\(500\) 0 0
\(501\) 2.00597e6 0.357052
\(502\) 0 0
\(503\) 3.01810e6 5.22751e6i 0.531880 0.921244i −0.467427 0.884032i \(-0.654819\pi\)
0.999307 0.0372121i \(-0.0118477\pi\)
\(504\) 0 0
\(505\) −1.72913e6 −0.301716
\(506\) 0 0
\(507\) 1.19492e6 2.06966e6i 0.206452 0.357585i
\(508\) 0 0
\(509\) 292272. 506231.i 0.0500027 0.0866072i −0.839941 0.542678i \(-0.817410\pi\)
0.889943 + 0.456071i \(0.150744\pi\)
\(510\) 0 0
\(511\) −250227. 433406.i −0.0423918 0.0734247i
\(512\) 0 0
\(513\) −2.35620e6 + 3.94906e6i −0.395293 + 0.662522i
\(514\) 0 0
\(515\) −444522. 769934.i −0.0738542 0.127919i
\(516\) 0 0
\(517\) −2.71389e6 + 4.70060e6i −0.446546 + 0.773441i
\(518\) 0 0
\(519\) 2.17129e6 3.76078e6i 0.353833 0.612857i
\(520\) 0 0
\(521\) 5.06982e6 0.818272 0.409136 0.912473i \(-0.365830\pi\)
0.409136 + 0.912473i \(0.365830\pi\)
\(522\) 0 0
\(523\) 2.09028e6 3.62047e6i 0.334157 0.578777i −0.649166 0.760647i \(-0.724882\pi\)
0.983323 + 0.181870i \(0.0582151\pi\)
\(524\) 0 0
\(525\) 669539. 0.106017
\(526\) 0 0
\(527\) −8.03809e6 1.39224e7i −1.26074 2.18367i
\(528\) 0 0
\(529\) −1.31992e6 2.28617e6i −0.205073 0.355196i
\(530\) 0 0
\(531\) 9.46269e6 1.45639
\(532\) 0 0
\(533\) −45032.4 −0.00686605
\(534\) 0 0
\(535\) 1.60035e6 + 2.77188e6i 0.241730 + 0.418688i
\(536\) 0 0
\(537\) −878238. 1.52115e6i −0.131425 0.227634i
\(538\) 0 0
\(539\) −4.92091e6 −0.729580
\(540\) 0 0
\(541\) 2.36120e6 4.08971e6i 0.346848 0.600758i −0.638840 0.769340i \(-0.720585\pi\)
0.985688 + 0.168582i \(0.0539187\pi\)
\(542\) 0 0
\(543\) −998565. −0.145337
\(544\) 0 0
\(545\) 2.71845e6 4.70850e6i 0.392040 0.679034i
\(546\) 0 0
\(547\) −2.59488e6 + 4.49447e6i −0.370808 + 0.642259i −0.989690 0.143225i \(-0.954253\pi\)
0.618882 + 0.785484i \(0.287586\pi\)
\(548\) 0 0
\(549\) 2.73430e6 + 4.73594e6i 0.387182 + 0.670619i
\(550\) 0 0
\(551\) 809691. + 1.45010e6i 0.113616 + 0.203479i
\(552\) 0 0
\(553\) −1.08786e6 1.88422e6i −0.151272 0.262011i
\(554\) 0 0
\(555\) −171368. + 296819.i −0.0236156 + 0.0409033i
\(556\) 0 0
\(557\) 3.55878e6 6.16399e6i 0.486030 0.841829i −0.513841 0.857886i \(-0.671778\pi\)
0.999871 + 0.0160563i \(0.00511109\pi\)
\(558\) 0 0
\(559\) 36856.4 0.00498866
\(560\) 0 0
\(561\) −2.26909e6 + 3.93017e6i −0.304399 + 0.527235i
\(562\) 0 0
\(563\) 6.55995e6 0.872227 0.436114 0.899892i \(-0.356355\pi\)
0.436114 + 0.899892i \(0.356355\pi\)
\(564\) 0 0
\(565\) 324915. + 562769.i 0.0428202 + 0.0741668i
\(566\) 0 0
\(567\) 593188. + 1.02743e6i 0.0774881 + 0.134213i
\(568\) 0 0
\(569\) 1.10777e7 1.43440 0.717200 0.696868i \(-0.245424\pi\)
0.717200 + 0.696868i \(0.245424\pi\)
\(570\) 0 0
\(571\) −5.64684e6 −0.724795 −0.362398 0.932024i \(-0.618042\pi\)
−0.362398 + 0.932024i \(0.618042\pi\)
\(572\) 0 0
\(573\) 398009. + 689372.i 0.0506415 + 0.0877136i
\(574\) 0 0
\(575\) −3.74928e6 6.49394e6i −0.472909 0.819103i
\(576\) 0 0
\(577\) 2.99850e6 0.374942 0.187471 0.982270i \(-0.439971\pi\)
0.187471 + 0.982270i \(0.439971\pi\)
\(578\) 0 0
\(579\) 253588. 439227.i 0.0314364 0.0544494i
\(580\) 0 0
\(581\) 53628.9 0.00659110
\(582\) 0 0
\(583\) 1.70019e6 2.94482e6i 0.207170 0.358829i
\(584\) 0 0
\(585\) −245645. + 425469.i −0.0296768 + 0.0514018i
\(586\) 0 0
\(587\) −7.21676e6 1.24998e7i −0.864465 1.49730i −0.867578 0.497301i \(-0.834324\pi\)
0.00311341 0.999995i \(-0.499009\pi\)
\(588\) 0 0
\(589\) 6.12919e6 1.02727e7i 0.727972 1.22010i
\(590\) 0 0
\(591\) −1.92216e6 3.32927e6i −0.226371 0.392086i
\(592\) 0 0
\(593\) −3.75784e6 + 6.50878e6i −0.438836 + 0.760086i −0.997600 0.0692407i \(-0.977942\pi\)
0.558764 + 0.829327i \(0.311276\pi\)
\(594\) 0 0
\(595\) −1.08576e6 + 1.88059e6i −0.125731 + 0.217772i
\(596\) 0 0
\(597\) −1.10376e6 −0.126748
\(598\) 0 0
\(599\) −8.09527e6 + 1.40214e7i −0.921858 + 1.59671i −0.125321 + 0.992116i \(0.539996\pi\)
−0.796538 + 0.604589i \(0.793337\pi\)
\(600\) 0 0
\(601\) 1.99094e6 0.224839 0.112419 0.993661i \(-0.464140\pi\)
0.112419 + 0.993661i \(0.464140\pi\)
\(602\) 0 0
\(603\) −3.43452e6 5.94876e6i −0.384656 0.666244i
\(604\) 0 0
\(605\) −700267. 1.21290e6i −0.0777814 0.134721i
\(606\) 0 0
\(607\) 1.47599e6 0.162596 0.0812982 0.996690i \(-0.474093\pi\)
0.0812982 + 0.996690i \(0.474093\pi\)
\(608\) 0 0
\(609\) −283919. −0.0310206
\(610\) 0 0
\(611\) −816427. 1.41409e6i −0.0884737 0.153241i
\(612\) 0 0
\(613\) 6.12920e6 + 1.06161e7i 0.658798 + 1.14107i 0.980927 + 0.194376i \(0.0622683\pi\)
−0.322129 + 0.946696i \(0.604398\pi\)
\(614\) 0 0
\(615\) 76777.6 0.00818553
\(616\) 0 0
\(617\) −3.89936e6 + 6.75389e6i −0.412364 + 0.714235i −0.995148 0.0983924i \(-0.968630\pi\)
0.582784 + 0.812627i \(0.301963\pi\)
\(618\) 0 0
\(619\) 8.39100e6 0.880212 0.440106 0.897946i \(-0.354941\pi\)
0.440106 + 0.897946i \(0.354941\pi\)
\(620\) 0 0
\(621\) −4.40210e6 + 7.62466e6i −0.458069 + 0.793398i
\(622\) 0 0
\(623\) −2.10658e6 + 3.64871e6i −0.217449 + 0.376633i
\(624\) 0 0
\(625\) −2.10384e6 3.64395e6i −0.215433 0.373141i
\(626\) 0 0
\(627\) −3.37649e6 48466.5i −0.343002 0.00492348i
\(628\) 0 0
\(629\) 2.17516e6 + 3.76749e6i 0.219212 + 0.379687i
\(630\) 0 0
\(631\) 725688. 1.25693e6i 0.0725565 0.125672i −0.827465 0.561518i \(-0.810218\pi\)
0.900021 + 0.435846i \(0.143551\pi\)
\(632\) 0 0
\(633\) −2.37978e6 + 4.12191e6i −0.236063 + 0.408873i
\(634\) 0 0
\(635\) −2.99171e6 −0.294432
\(636\) 0 0
\(637\) 740184. 1.28204e6i 0.0722755 0.125185i
\(638\) 0 0
\(639\) 749510. 0.0726148
\(640\) 0 0
\(641\) −4.20230e6 7.27859e6i −0.403963 0.699684i 0.590237 0.807230i \(-0.299034\pi\)
−0.994200 + 0.107545i \(0.965701\pi\)
\(642\) 0 0
\(643\) 2.07760e6 + 3.59850e6i 0.198168 + 0.343237i 0.947934 0.318465i \(-0.103167\pi\)
−0.749766 + 0.661703i \(0.769834\pi\)
\(644\) 0 0
\(645\) −62838.1 −0.00594736
\(646\) 0 0
\(647\) −5.48842e6 −0.515450 −0.257725 0.966218i \(-0.582973\pi\)
−0.257725 + 0.966218i \(0.582973\pi\)
\(648\) 0 0
\(649\) 7.70933e6 + 1.33529e7i 0.718464 + 1.24442i
\(650\) 0 0
\(651\) 1.02246e6 + 1.77096e6i 0.0945573 + 0.163778i
\(652\) 0 0
\(653\) 6.39658e6 0.587036 0.293518 0.955954i \(-0.405174\pi\)
0.293518 + 0.955954i \(0.405174\pi\)
\(654\) 0 0
\(655\) 699560. 1.21167e6i 0.0637120 0.110353i
\(656\) 0 0
\(657\) 2.45024e6 0.221460
\(658\) 0 0
\(659\) 891088. 1.54341e6i 0.0799295 0.138442i −0.823290 0.567621i \(-0.807864\pi\)
0.903219 + 0.429179i \(0.141197\pi\)
\(660\) 0 0
\(661\) −8.15028e6 + 1.41167e7i −0.725553 + 1.25669i 0.233193 + 0.972430i \(0.425083\pi\)
−0.958746 + 0.284264i \(0.908251\pi\)
\(662\) 0 0
\(663\) −682614. 1.18232e6i −0.0603103 0.104461i
\(664\) 0 0
\(665\) −1.61565e6 23191.2i −0.141675 0.00203362i
\(666\) 0 0
\(667\) 1.58988e6 + 2.75376e6i 0.138373 + 0.239669i
\(668\) 0 0
\(669\) −4.46877e6 + 7.74014e6i −0.386032 + 0.668627i
\(670\) 0 0
\(671\) −4.45531e6 + 7.71682e6i −0.382007 + 0.661656i
\(672\) 0 0
\(673\) 3.81795e6 0.324932 0.162466 0.986714i \(-0.448055\pi\)
0.162466 + 0.986714i \(0.448055\pi\)
\(674\) 0 0
\(675\) −3.63692e6 + 6.29934e6i −0.307238 + 0.532152i
\(676\) 0 0
\(677\) 1.93449e6 0.162216 0.0811081 0.996705i \(-0.474154\pi\)
0.0811081 + 0.996705i \(0.474154\pi\)
\(678\) 0 0
\(679\) 2.15785e6 + 3.73750e6i 0.179616 + 0.311105i
\(680\) 0 0
\(681\) −3.11871e6 5.40177e6i −0.257696 0.446342i
\(682\) 0 0
\(683\) 732465. 0.0600808 0.0300404 0.999549i \(-0.490436\pi\)
0.0300404 + 0.999549i \(0.490436\pi\)
\(684\) 0 0
\(685\) −8.06474e6 −0.656696
\(686\) 0 0
\(687\) −4.08608e6 7.07730e6i −0.330305 0.572105i
\(688\) 0 0
\(689\) 511473. + 885897.i 0.0410464 + 0.0710944i
\(690\) 0 0
\(691\) −5.91673e6 −0.471397 −0.235698 0.971826i \(-0.575738\pi\)
−0.235698 + 0.971826i \(0.575738\pi\)
\(692\) 0 0
\(693\) −1.31837e6 + 2.28349e6i −0.104281 + 0.180620i
\(694\) 0 0
\(695\) −5.33685e6 −0.419105
\(696\) 0 0
\(697\) 487266. 843969.i 0.0379913 0.0658028i
\(698\) 0 0
\(699\) 3.27525e6 5.67291e6i 0.253543 0.439150i
\(700\) 0 0
\(701\) 8.07558e6 + 1.39873e7i 0.620696 + 1.07508i 0.989356 + 0.145513i \(0.0464831\pi\)
−0.368661 + 0.929564i \(0.620184\pi\)
\(702\) 0 0
\(703\) −1.65860e6 + 2.77986e6i −0.126577 + 0.212146i
\(704\) 0 0
\(705\) 1.39196e6 + 2.41095e6i 0.105476 + 0.182690i
\(706\) 0 0
\(707\) 1.39590e6 2.41777e6i 0.105028 0.181914i
\(708\) 0 0
\(709\) 3.50009e6 6.06234e6i 0.261495 0.452923i −0.705144 0.709064i \(-0.749118\pi\)
0.966640 + 0.256141i \(0.0824510\pi\)
\(710\) 0 0
\(711\) 1.06524e7 0.790265
\(712\) 0 0
\(713\) 1.14512e7 1.98340e7i 0.843579 1.46112i
\(714\) 0 0
\(715\) −800514. −0.0585604
\(716\) 0 0
\(717\) 847328. + 1.46762e6i 0.0615536 + 0.106614i
\(718\) 0 0
\(719\) 6.55155e6 + 1.13476e7i 0.472630 + 0.818620i 0.999509 0.0313203i \(-0.00997121\pi\)
−0.526879 + 0.849940i \(0.676638\pi\)
\(720\) 0 0
\(721\) 1.43542e6 0.102835
\(722\) 0 0
\(723\) 5.26156e6 0.374342
\(724\) 0 0
\(725\) 1.31353e6 + 2.27510e6i 0.0928101 + 0.160752i
\(726\) 0 0
\(727\) −7.15352e6 1.23903e7i −0.501977 0.869449i −0.999997 0.00228403i \(-0.999273\pi\)
0.498021 0.867165i \(-0.334060\pi\)
\(728\) 0 0
\(729\) −1.11705e6 −0.0778490
\(730\) 0 0
\(731\) −398799. + 690741.i −0.0276033 + 0.0478103i
\(732\) 0 0
\(733\) −2.46017e7 −1.69124 −0.845620 0.533785i \(-0.820769\pi\)
−0.845620 + 0.533785i \(0.820769\pi\)
\(734\) 0 0
\(735\) −1.26197e6 + 2.18580e6i −0.0861651 + 0.149242i
\(736\) 0 0
\(737\) 5.59626e6 9.69300e6i 0.379515 0.657339i
\(738\) 0 0
\(739\) 3.19096e6 + 5.52691e6i 0.214937 + 0.372281i 0.953253 0.302173i \(-0.0977122\pi\)
−0.738316 + 0.674455i \(0.764379\pi\)
\(740\) 0 0
\(741\) 520506. 872382.i 0.0348241 0.0583661i
\(742\) 0 0
\(743\) −401987. 696262.i −0.0267141 0.0462701i 0.852359 0.522957i \(-0.175171\pi\)
−0.879073 + 0.476686i \(0.841838\pi\)
\(744\) 0 0
\(745\) −909214. + 1.57480e6i −0.0600172 + 0.103953i
\(746\) 0 0
\(747\) −131284. + 227391.i −0.00860819 + 0.0149098i
\(748\) 0 0
\(749\) −5.16774e6 −0.336586
\(750\) 0 0
\(751\) 1.22115e7 2.11510e7i 0.790078 1.36846i −0.135839 0.990731i \(-0.543373\pi\)
0.925918 0.377725i \(-0.123294\pi\)
\(752\) 0 0
\(753\) 3.86688e6 0.248527
\(754\) 0 0
\(755\) 3.34837e6 + 5.79956e6i 0.213780 + 0.370277i
\(756\) 0 0
\(757\) −1.52156e7 2.63542e7i −0.965050 1.67152i −0.709480 0.704726i \(-0.751070\pi\)
−0.255570 0.966790i \(-0.582263\pi\)
\(758\) 0 0
\(759\) −6.46514e6 −0.407355
\(760\) 0 0
\(761\) 6.72001e6 0.420638 0.210319 0.977633i \(-0.432550\pi\)
0.210319 + 0.977633i \(0.432550\pi\)
\(762\) 0 0
\(763\) 4.38913e6 + 7.60219e6i 0.272940 + 0.472745i
\(764\) 0 0
\(765\) −5.31592e6 9.20744e6i −0.328416 0.568834i
\(766\) 0 0
\(767\) −4.63843e6 −0.284697
\(768\) 0 0
\(769\) 4.61439e6 7.99236e6i 0.281384 0.487371i −0.690342 0.723483i \(-0.742540\pi\)
0.971726 + 0.236112i \(0.0758734\pi\)
\(770\) 0 0
\(771\) 5.77192e6 0.349691
\(772\) 0 0
\(773\) −2207.17 + 3822.92i −0.000132858 + 0.000230116i −0.866092 0.499885i \(-0.833376\pi\)
0.865959 + 0.500115i \(0.166709\pi\)
\(774\) 0 0
\(775\) 9.46072e6 1.63864e7i 0.565809 0.980010i
\(776\) 0 0
\(777\) −276686. 479234.i −0.0164412 0.0284770i
\(778\) 0 0
\(779\) 725071. + 10407.7i 0.0428092 + 0.000614487i
\(780\) 0 0
\(781\) 610632. + 1.05765e6i 0.0358222 + 0.0620458i
\(782\) 0 0
\(783\) 1.54224e6 2.67124e6i 0.0898975 0.155707i
\(784\) 0 0
\(785\) 4.03095e6 6.98181e6i 0.233471 0.404384i
\(786\) 0 0
\(787\) −1.44974e7 −0.834360 −0.417180 0.908824i \(-0.636982\pi\)
−0.417180 + 0.908824i \(0.636982\pi\)
\(788\) 0 0
\(789\) 970823. 1.68152e6i 0.0555198