Properties

Label 76.6.e.a.49.5
Level $76$
Weight $6$
Character 76.49
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 49.5
Root \(2.80322 + 4.85531i\) of defining polynomial
Character \(\chi\) \(=\) 76.49
Dual form 76.6.e.a.45.5

$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 −0.952310 0.305133i \(-0.901299\pi\)
0.740408 + 0.672158i \(0.234632\pi\)
\(4\) 0 0
\(5\) 12.6095 21.8402i 0.225565 0.390690i −0.730924 0.682459i \(-0.760911\pi\)
0.956489 + 0.291769i \(0.0942439\pi\)
\(6\) 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 0.823144 0.567833i \(-0.192218\pi\)
−0.903329 + 0.428947i \(0.858885\pi\)
\(14\) 0 0
\(15\) 83.3036 + 144.286i 0.0955951 + 0.165575i
\(16\) 0 0
\(17\) −1057.36 + 1831.41i −0.887365 + 1.53696i −0.0443869 + 0.999014i \(0.514133\pi\)
−0.842978 + 0.537947i \(0.819200\pi\)
\(18\) 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 0.993722 + 0.111875i \(0.0356856\pi\)
−0.399975 + 0.916526i \(0.630981\pi\)
\(24\) 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 0.801863 0.597507i \(-0.203842\pi\)
−0.918388 + 0.395680i \(0.870509\pi\)
\(30\) 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 −0.855124 0.518424i \(-0.826519\pi\)
0.876530 + 0.481347i \(0.159852\pi\)
\(42\) 0 0
\(43\) −188.582 + 326.633i −0.0155535 + 0.0269395i −0.873697 0.486470i \(-0.838284\pi\)
0.858144 + 0.513409i \(0.171618\pi\)
\(44\) 0 0
\(45\) 5027.52 0.370103
\(46\) 0 0
\(47\) −8354.76 14470.9i −0.551682 0.955542i −0.998153 0.0607440i \(-0.980653\pi\)
0.446471 0.894798i \(-0.352681\pi\)
\(48\) 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 0.965152 0.261689i \(-0.0842795\pi\)
−0.709206 + 0.705002i \(0.750946\pi\)
\(54\) 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 0.0449408 0.998990i \(-0.485690\pi\)
0.842680 0.538415i \(-0.180977\pi\)
\(60\) 0 0
\(61\) −13715.7 23756.3i −0.471948 0.817438i 0.527537 0.849532i \(-0.323116\pi\)
−0.999485 + 0.0320943i \(0.989782\pi\)
\(62\) 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 0.999367 0.0355811i \(-0.0113282\pi\)
−0.530498 + 0.847686i \(0.677995\pi\)
\(68\) 0 0
\(69\) −19903.0 −0.503264
\(70\) 0 0
\(71\) 1879.84 3255.97i 0.0442562 0.0766541i −0.843049 0.537837i \(-0.819242\pi\)
0.887305 + 0.461183i \(0.152575\pi\)
\(72\) 0 0
\(73\) 6145.42 10644.2i 0.134972 0.233779i −0.790615 0.612314i \(-0.790239\pi\)
0.925587 + 0.378535i \(0.123572\pi\)
\(74\) 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 −0.518139 0.855297i \(-0.673375\pi\)
0.999778 + 0.0210731i \(0.00670827\pi\)
\(80\) 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 0.971068 + 0.238801i \(0.0767545\pi\)
−0.278726 + 0.960371i \(0.589912\pi\)
\(90\) 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 0.424488 + 0.905434i \(0.360454\pi\)
−0.996372 + 0.0850998i \(0.972879\pi\)
\(98\) 0 0
\(99\) 32378.5 + 56081.1i 0.332023 + 0.575081i
\(100\) 0 0
\(101\) −34282.4 59378.8i −0.334401 0.579200i 0.648969 0.760815i \(-0.275201\pi\)
−0.983370 + 0.181616i \(0.941867\pi\)
\(102\) 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 −0.00601921 + 0.999982i \(0.501916\pi\)
−0.863000 + 0.505204i \(0.831417\pi\)
\(110\) 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 0.655452 0.755237i \(-0.272478\pi\)
−0.981780 + 0.190020i \(0.939145\pi\)
\(128\) 0 0
\(129\) −1245.85 2157.88i −0.00659163 0.0114170i
\(130\) 0 0
\(131\) −27739.5 + 48046.2i −0.141228 + 0.244614i −0.927959 0.372682i \(-0.878438\pi\)
0.786731 + 0.617295i \(0.211772\pi\)
\(132\) 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 −0.957797 0.287447i \(-0.907193\pi\)
0.229962 0.973200i \(-0.426140\pi\)
\(138\) 0 0
\(139\) −105811. 183269.i −0.464506 0.804549i 0.534673 0.845059i \(-0.320435\pi\)
−0.999179 + 0.0405104i \(0.987102\pi\)
\(140\) 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 −0.791809 0.610769i \(-0.790860\pi\)
0.924846 + 0.380342i \(0.124194\pi\)
\(150\) 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 0.482267 + 0.876024i \(0.339814\pi\)
−0.999793 + 0.0203568i \(0.993520\pi\)
\(158\) 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 0.574815 0.818284i \(-0.305074\pi\)
−0.996062 + 0.0886623i \(0.971741\pi\)
\(168\) 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 −0.0592118 0.998245i \(-0.518859\pi\)
0.894112 0.447844i \(-0.147808\pi\)
\(174\) 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 0.938933 0.344099i \(-0.111816\pi\)
−0.767465 + 0.641090i \(0.778482\pi\)
\(182\) 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 −0.826551 0.562862i \(-0.809700\pi\)
0.900728 + 0.434384i \(0.143034\pi\)
\(194\) 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 0.931056 0.364876i \(-0.118889\pi\)
−0.781520 + 0.623880i \(0.785555\pi\)
\(200\) 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 0.440733 + 0.897638i \(0.354719\pi\)
−0.997744 + 0.0671336i \(0.978615\pi\)
\(212\) 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 −0.0980458 + 0.995182i \(0.531259\pi\)
−0.812830 + 0.582501i \(0.802074\pi\)
\(224\) 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 −0.394821 0.918758i \(-0.629193\pi\)
0.993078 0.117454i \(-0.0374733\pi\)
\(234\) 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 0.556166 0.831072i \(-0.312272\pi\)
−0.997812 + 0.0661177i \(0.978939\pi\)
\(242\) 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 0.681357 0.731951i \(-0.261390\pi\)
−0.974567 + 0.224097i \(0.928057\pi\)
\(252\) 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 0.582606 0.812754i \(-0.302033\pi\)
−0.995169 + 0.0981747i \(0.968700\pi\)
\(258\) 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 −0.793060 0.609144i \(-0.791513\pi\)
0.924064 + 0.382238i \(0.124847\pi\)
\(264\) 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 0.318440 0.947943i \(-0.396841\pi\)
0.661722 0.749749i \(-0.269826\pi\)
\(270\) 0 0
\(271\) 130705. 226387.i 0.108111 0.187253i −0.806894 0.590696i \(-0.798853\pi\)
0.915005 + 0.403443i \(0.132187\pi\)
\(272\) 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 0.627113 0.778929i \(-0.284237\pi\)
−0.988128 + 0.153631i \(0.950903\pi\)
\(282\) 0 0
\(283\) 172840. 299368.i 0.128286 0.222197i −0.794727 0.606967i \(-0.792386\pi\)
0.923013 + 0.384770i \(0.125719\pi\)
\(284\) 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 −0.910411 0.413705i \(-0.864234\pi\)
0.813485 + 0.581586i \(0.197568\pi\)
\(308\) 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 0.997754 + 0.0669807i \(0.0213366\pi\)
−0.440870 + 0.897571i \(0.645330\pi\)
\(314\) 0 0
\(315\) −204709. −0.116241
\(316\) 0 0
\(317\) 757768. + 1.31249e6i 0.423534 + 0.733582i 0.996282 0.0861494i \(-0.0274562\pi\)
−0.572749 + 0.819731i \(0.694123\pi\)
\(318\) 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 0.173889 + 0.984765i \(0.444367\pi\)
−0.939776 + 0.341791i \(0.888967\pi\)
\(338\) 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 −0.761309 0.648390i \(-0.775443\pi\)
0.942176 + 0.335118i \(0.108776\pi\)
\(348\) 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 0.441879 + 0.897075i \(0.354312\pi\)
−0.997829 + 0.0658593i \(0.979021\pi\)
\(360\) 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 0.999858 + 0.0168222i \(0.00535492\pi\)
−0.485361 + 0.874314i \(0.661312\pi\)
\(368\) 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 −0.506229 0.862399i \(-0.668961\pi\)
0.999974 + 0.00720770i \(0.00229430\pi\)
\(384\) 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 0.999288 0.0377363i \(-0.0120147\pi\)
−0.532324 + 0.846540i \(0.678681\pi\)
\(390\) 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 0.405745 + 0.913986i \(0.367012\pi\)
−0.994408 + 0.105607i \(0.966321\pi\)
\(398\) 0 0
\(399\) 423242. 6075.26i 0.133093 0.00191044i
\(400\) 0 0
\(401\) −2.13618e6 + 3.69998e6i −0.663404 + 1.14905i 0.316312 + 0.948655i \(0.397555\pi\)
−0.979715 + 0.200394i \(0.935778\pi\)
\(402\) 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 −0.876454 0.481485i \(-0.840098\pi\)
0.0212492 0.999774i \(-0.493236\pi\)
\(410\) 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 −0.333418 0.942779i \(-0.608202\pi\)
0.983180 0.182641i \(-0.0584646\pi\)
\(422\) 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 0.892256 0.451530i \(-0.149122\pi\)
−0.837164 + 0.546951i \(0.815788\pi\)
\(432\) 0 0
\(433\) −3.10444e6 5.37705e6i −0.795726 1.37824i −0.922377 0.386291i \(-0.873756\pi\)
0.126651 0.991947i \(-0.459577\pi\)
\(434\) 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 −0.00544290 0.999985i \(-0.501733\pi\)
0.868734 0.495279i \(-0.164934\pi\)
\(440\) 0 0
\(441\) −1.51002e6 2.61543e6i −0.369732 0.640394i
\(442\) 0 0
\(443\) −1.32950e6 2.30277e6i −0.321870 0.557495i 0.659004 0.752139i \(-0.270978\pi\)
−0.980874 + 0.194645i \(0.937645\pi\)
\(444\) 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 −0.582640 0.812730i \(-0.697980\pi\)
0.995165 + 0.0982159i \(0.0313136\pi\)
\(462\) 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 −0.719578 0.694412i \(-0.755665\pi\)
−0.241589 0.970379i \(-0.577669\pi\)
\(480\) 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 0.334395 + 0.942433i \(0.391468\pi\)
−0.983368 + 0.181622i \(0.941865\pi\)
\(492\) 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 −0.840502 0.541809i \(-0.817740\pi\)
0.889471 + 0.456991i \(0.151073\pi\)
\(500\) 0 0
\(501\) 2.00597e6 0.357052
\(502\) 0 0
\(503\) 3.01810e6 + 5.22751e6i 0.531880 + 0.921244i 0.999307 + 0.0372121i \(0.0118477\pi\)
−0.467427 + 0.884032i \(0.654819\pi\)
\(504\) 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 0.889943 0.456071i \(-0.150744\pi\)
−0.839941 + 0.542678i \(0.817410\pi\)
\(510\) 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 0.983323 0.181870i \(-0.0582151\pi\)
−0.649166 + 0.760647i \(0.724882\pi\)
\(524\) 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 0.985688 0.168582i \(-0.0539187\pi\)
−0.638840 + 0.769340i \(0.720585\pi\)
\(542\) 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 0.618882 0.785484i \(-0.287586\pi\)
−0.989690 + 0.143225i \(0.954253\pi\)
\(548\) 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 0.999871 0.0160563i \(-0.00511109\pi\)
−0.513841 + 0.857886i \(0.671778\pi\)
\(558\) 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 0.00311341 + 0.999995i \(0.499009\pi\)
−0.867578 + 0.497301i \(0.834324\pi\)
\(588\) 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 0.558764 0.829327i \(-0.311276\pi\)
−0.997600 + 0.0692407i \(0.977942\pi\)
\(594\) 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 −0.796538 0.604589i \(-0.793337\pi\)
−0.125321 0.992116i \(-0.539996\pi\)
\(600\) 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 −0.322129 0.946696i \(-0.604398\pi\)
0.980927 0.194376i \(-0.0622683\pi\)
\(614\) 0 0
\(615\) 76777.6 0.00818553
\(616\) 0 0
\(617\) −3.89936e6 6.75389e6i −0.412364 0.714235i 0.582784 0.812627i \(-0.301963\pi\)
−0.995148 + 0.0983924i \(0.968630\pi\)
\(618\) 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 0.900021 0.435846i \(-0.143551\pi\)
−0.827465 + 0.561518i \(0.810218\pi\)
\(632\) 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 −0.994200 0.107545i \(-0.965701\pi\)
0.590237 + 0.807230i \(0.299034\pi\)
\(642\) 0 0
\(643\) 2.07760e6 3.59850e6i 0.198168 0.343237i −0.749766 0.661703i \(-0.769834\pi\)
0.947934 + 0.318465i \(0.103167\pi\)
\(644\) 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 0.903219 0.429179i \(-0.141197\pi\)
−0.823290 + 0.567621i \(0.807864\pi\)
\(660\) 0 0
\(661\) −8.15028e6 1.41167e7i −0.725553 1.25669i −0.958746 0.284264i \(-0.908251\pi\)
0.233193 0.972430i \(-0.425083\pi\)
\(662\) 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 −0.368661 0.929564i \(-0.620184\pi\)
0.989356 0.145513i \(-0.0464831\pi\)
\(702\) 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 0.966640 0.256141i \(-0.0824510\pi\)
−0.705144 + 0.709064i \(0.749118\pi\)
\(710\) 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 −0.526879 0.849940i \(-0.676638\pi\)
0.999509 + 0.0313203i \(0.00997121\pi\)
\(720\) 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 0.498021 + 0.867165i \(0.334060\pi\)
−0.999997 + 0.00228403i \(0.999273\pi\)
\(728\) 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 −0.738316 0.674455i \(-0.764379\pi\)
0.953253 + 0.302173i \(0.0977122\pi\)
\(740\) 0 0
\(741\) 520506. + 872382.i 0.0348241 + 0.0583661i
\(742\) 0 0
\(743\) −401987. + 696262.i −0.0267141 + 0.0462701i −0.879073 0.476686i \(-0.841838\pi\)
0.852359 + 0.522957i \(0.175171\pi\)
\(744\) 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 0.925918 + 0.377725i \(0.123294\pi\)
−0.135839 + 0.990731i \(0.543373\pi\)
\(752\) 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 −0.255570 + 0.966790i \(0.582263\pi\)
−0.709480 + 0.704726i \(0.751070\pi\)
\(758\) 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 0.971726 0.236112i \(-0.0758734\pi\)
−0.690342 + 0.723483i \(0.742540\pi\)
\(770\) 0 0
\(771\) 5.77192e6 0.349691
\(772\) 0 0
\(773\) −2207.17 3822.92i −0.000132858 0.000230116i 0.865959 0.500115i \(-0.166709\pi\)
−0.866092 + 0.499885i \(0.833376\pi\)
\(774\) 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 +