Properties

Label 76.6.e.a.49.7
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 49.7
Root \(-8.45017 - 14.6361i\) of defining polynomial
Character \(\chi\) \(=\) 76.49
Dual form 76.6.e.a.45.7

$q$-expansion

\(f(q)\) \(=\) \(q+(7.95017 - 13.7701i) q^{3} +(-15.4645 + 26.7852i) q^{5} +132.225 q^{7} +(-4.91049 - 8.50521i) q^{9} +O(q^{10})\) \(q+(7.95017 - 13.7701i) q^{3} +(-15.4645 + 26.7852i) q^{5} +132.225 q^{7} +(-4.91049 - 8.50521i) q^{9} +670.612 q^{11} +(-411.330 - 712.445i) q^{13} +(245.890 + 425.895i) q^{15} +(731.251 - 1266.56i) q^{17} +(-1573.26 - 30.7850i) q^{19} +(1051.21 - 1820.76i) q^{21} +(-1145.60 - 1984.23i) q^{23} +(1084.20 + 1877.89i) q^{25} +3707.63 q^{27} +(-1381.18 - 2392.27i) q^{29} +10591.8 q^{31} +(5331.48 - 9234.40i) q^{33} +(-2044.79 + 3541.69i) q^{35} +4815.22 q^{37} -13080.6 q^{39} +(-7285.18 + 12618.3i) q^{41} +(-5150.23 + 8920.46i) q^{43} +303.752 q^{45} +(-2555.09 - 4425.55i) q^{47} +676.549 q^{49} +(-11627.1 - 20138.8i) q^{51} +(-3724.23 - 6450.55i) q^{53} +(-10370.7 + 17962.5i) q^{55} +(-12931.6 + 21419.2i) q^{57} +(-17150.1 + 29704.9i) q^{59} +(20608.6 + 35695.1i) q^{61} +(-649.291 - 1124.60i) q^{63} +25444.0 q^{65} +(-19625.6 - 33992.5i) q^{67} -36430.7 q^{69} +(5848.69 - 10130.2i) q^{71} +(-13696.8 + 23723.6i) q^{73} +34478.3 q^{75} +88671.9 q^{77} +(-2583.48 + 4474.71i) q^{79} +(30669.5 - 53121.2i) q^{81} -86152.6 q^{83} +(22616.8 + 39173.5i) q^{85} -43922.4 q^{87} +(25384.0 + 43966.4i) q^{89} +(-54388.3 - 94203.3i) q^{91} +(84206.9 - 145851. i) q^{93} +(25154.2 - 41664.1i) q^{95} +(-13304.7 + 23044.5i) q^{97} +(-3293.03 - 5703.70i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q - 11q^{3} + 11q^{5} + 336q^{7} - 902q^{9} + O(q^{10}) \) \( 18q - 11q^{3} + 11q^{5} + 336q^{7} - 902q^{9} - 320q^{11} + 227q^{13} - 101q^{15} + 179q^{17} - 868q^{19} - 5700q^{21} - 3425q^{23} - 7054q^{25} + 14722q^{27} - 7349q^{29} - 9960q^{31} - 2998q^{33} + 15888q^{35} + 26444q^{37} - 30246q^{39} - 7311q^{41} - 8283q^{43} - 62164q^{45} + 37603q^{47} + 124738q^{49} + 47227q^{51} - 20337q^{53} + 716q^{55} - 57555q^{57} - 74455q^{59} - 7569q^{61} - 52544q^{63} + 188998q^{65} - 26177q^{67} + 116282q^{69} - 53463q^{71} - 14103q^{73} + 120912q^{75} - 31960q^{77} + 31825q^{79} - 21137q^{81} + 82600q^{83} - 50787q^{85} - 339766q^{87} - 155197q^{89} - 2800q^{91} - 46460q^{93} + 49315q^{95} + 111241q^{97} - 193544q^{99} + O(q^{100}) \)

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
\(3\) 7.95017 13.7701i 0.510004 0.883352i −0.489929 0.871762i \(-0.662977\pi\)
0.999933 0.0115902i \(-0.00368935\pi\)
\(4\) 0 0
\(5\) −15.4645 + 26.7852i −0.276637 + 0.479149i −0.970547 0.240913i \(-0.922553\pi\)
0.693910 + 0.720062i \(0.255887\pi\)
\(6\) 0 0
\(7\) 132.225 1.01993 0.509964 0.860196i \(-0.329659\pi\)
0.509964 + 0.860196i \(0.329659\pi\)
\(8\) 0 0
\(9\) −4.91049 8.50521i −0.0202078 0.0350009i
\(10\) 0 0
\(11\) 670.612 1.67105 0.835525 0.549452i \(-0.185163\pi\)
0.835525 + 0.549452i \(0.185163\pi\)
\(12\) 0 0
\(13\) −411.330 712.445i −0.675044 1.16921i −0.976456 0.215717i \(-0.930791\pi\)
0.301412 0.953494i \(-0.402542\pi\)
\(14\) 0 0
\(15\) 245.890 + 425.895i 0.282172 + 0.488736i
\(16\) 0 0
\(17\) 731.251 1266.56i 0.613683 1.06293i −0.376931 0.926241i \(-0.623021\pi\)
0.990614 0.136689i \(-0.0436461\pi\)
\(18\) 0 0
\(19\) −1573.26 30.7850i −0.999809 0.0195639i
\(20\) 0 0
\(21\) 1051.21 1820.76i 0.520167 0.900956i
\(22\) 0 0
\(23\) −1145.60 1984.23i −0.451556 0.782118i 0.546927 0.837180i \(-0.315798\pi\)
−0.998483 + 0.0550625i \(0.982464\pi\)
\(24\) 0 0
\(25\) 1084.20 + 1877.89i 0.346944 + 0.600925i
\(26\) 0 0
\(27\) 3707.63 0.978783
\(28\) 0 0
\(29\) −1381.18 2392.27i −0.304968 0.528221i 0.672286 0.740292i \(-0.265313\pi\)
−0.977254 + 0.212071i \(0.931979\pi\)
\(30\) 0 0
\(31\) 10591.8 1.97955 0.989776 0.142628i \(-0.0455552\pi\)
0.989776 + 0.142628i \(0.0455552\pi\)
\(32\) 0 0
\(33\) 5331.48 9234.40i 0.852242 1.47613i
\(34\) 0 0
\(35\) −2044.79 + 3541.69i −0.282150 + 0.488698i
\(36\) 0 0
\(37\) 4815.22 0.578245 0.289122 0.957292i \(-0.406637\pi\)
0.289122 + 0.957292i \(0.406637\pi\)
\(38\) 0 0
\(39\) −13080.6 −1.37710
\(40\) 0 0
\(41\) −7285.18 + 12618.3i −0.676832 + 1.17231i 0.299098 + 0.954222i \(0.403314\pi\)
−0.975930 + 0.218085i \(0.930019\pi\)
\(42\) 0 0
\(43\) −5150.23 + 8920.46i −0.424772 + 0.735726i −0.996399 0.0847874i \(-0.972979\pi\)
0.571628 + 0.820513i \(0.306312\pi\)
\(44\) 0 0
\(45\) 303.752 0.0223608
\(46\) 0 0
\(47\) −2555.09 4425.55i −0.168718 0.292228i 0.769251 0.638946i \(-0.220629\pi\)
−0.937969 + 0.346718i \(0.887296\pi\)
\(48\) 0 0
\(49\) 676.549 0.0402540
\(50\) 0 0
\(51\) −11627.1 20138.8i −0.625961 1.08420i
\(52\) 0 0
\(53\) −3724.23 6450.55i −0.182115 0.315433i 0.760485 0.649355i \(-0.224961\pi\)
−0.942601 + 0.333922i \(0.891628\pi\)
\(54\) 0 0
\(55\) −10370.7 + 17962.5i −0.462274 + 0.800682i
\(56\) 0 0
\(57\) −12931.6 + 21419.2i −0.527188 + 0.873206i
\(58\) 0 0
\(59\) −17150.1 + 29704.9i −0.641412 + 1.11096i 0.343705 + 0.939077i \(0.388318\pi\)
−0.985118 + 0.171881i \(0.945016\pi\)
\(60\) 0 0
\(61\) 20608.6 + 35695.1i 0.709126 + 1.22824i 0.965182 + 0.261580i \(0.0842434\pi\)
−0.256056 + 0.966662i \(0.582423\pi\)
\(62\) 0 0
\(63\) −649.291 1124.60i −0.0206105 0.0356984i
\(64\) 0 0
\(65\) 25444.0 0.746968
\(66\) 0 0
\(67\) −19625.6 33992.5i −0.534116 0.925116i −0.999206 0.0398521i \(-0.987311\pi\)
0.465090 0.885263i \(-0.346022\pi\)
\(68\) 0 0
\(69\) −36430.7 −0.921181
\(70\) 0 0
\(71\) 5848.69 10130.2i 0.137693 0.238492i −0.788930 0.614483i \(-0.789365\pi\)
0.926623 + 0.375992i \(0.122698\pi\)
\(72\) 0 0
\(73\) −13696.8 + 23723.6i −0.300824 + 0.521043i −0.976323 0.216318i \(-0.930595\pi\)
0.675498 + 0.737361i \(0.263928\pi\)
\(74\) 0 0
\(75\) 34478.3 0.707771
\(76\) 0 0
\(77\) 88671.9 1.70435
\(78\) 0 0
\(79\) −2583.48 + 4474.71i −0.0465733 + 0.0806673i −0.888372 0.459124i \(-0.848163\pi\)
0.841799 + 0.539791i \(0.181497\pi\)
\(80\) 0 0
\(81\) 30669.5 53121.2i 0.519391 0.899612i
\(82\) 0 0
\(83\) −86152.6 −1.37269 −0.686346 0.727275i \(-0.740786\pi\)
−0.686346 + 0.727275i \(0.740786\pi\)
\(84\) 0 0
\(85\) 22616.8 + 39173.5i 0.339535 + 0.588091i
\(86\) 0 0
\(87\) −43922.4 −0.622140
\(88\) 0 0
\(89\) 25384.0 + 43966.4i 0.339692 + 0.588364i 0.984375 0.176087i \(-0.0563438\pi\)
−0.644683 + 0.764450i \(0.723011\pi\)
\(90\) 0 0
\(91\) −54388.3 94203.3i −0.688497 1.19251i
\(92\) 0 0
\(93\) 84206.9 145851.i 1.00958 1.74864i
\(94\) 0 0
\(95\) 25154.2 41664.1i 0.285958 0.473645i
\(96\) 0 0
\(97\) −13304.7 + 23044.5i −0.143574 + 0.248678i −0.928840 0.370481i \(-0.879193\pi\)
0.785266 + 0.619159i \(0.212526\pi\)
\(98\) 0 0
\(99\) −3293.03 5703.70i −0.0337682 0.0584882i
\(100\) 0 0
\(101\) 32085.7 + 55574.0i 0.312974 + 0.542086i 0.979005 0.203838i \(-0.0653416\pi\)
−0.666031 + 0.745924i \(0.732008\pi\)
\(102\) 0 0
\(103\) 66441.0 0.617082 0.308541 0.951211i \(-0.400159\pi\)
0.308541 + 0.951211i \(0.400159\pi\)
\(104\) 0 0
\(105\) 32512.9 + 56314.1i 0.287795 + 0.498475i
\(106\) 0 0
\(107\) −187958. −1.58709 −0.793546 0.608510i \(-0.791768\pi\)
−0.793546 + 0.608510i \(0.791768\pi\)
\(108\) 0 0
\(109\) 89626.3 155237.i 0.722552 1.25150i −0.237422 0.971407i \(-0.576302\pi\)
0.959974 0.280090i \(-0.0903643\pi\)
\(110\) 0 0
\(111\) 38281.8 66306.0i 0.294907 0.510794i
\(112\) 0 0
\(113\) −59332.4 −0.437115 −0.218557 0.975824i \(-0.570135\pi\)
−0.218557 + 0.975824i \(0.570135\pi\)
\(114\) 0 0
\(115\) 70864.1 0.499668
\(116\) 0 0
\(117\) −4039.66 + 6996.90i −0.0272823 + 0.0472542i
\(118\) 0 0
\(119\) 96689.9 167472.i 0.625913 1.08411i
\(120\) 0 0
\(121\) 288669. 1.79241
\(122\) 0 0
\(123\) 115837. + 200635.i 0.690374 + 1.19576i
\(124\) 0 0
\(125\) −163719. −0.937184
\(126\) 0 0
\(127\) −33405.1 57859.3i −0.183782 0.318320i 0.759383 0.650643i \(-0.225501\pi\)
−0.943165 + 0.332324i \(0.892167\pi\)
\(128\) 0 0
\(129\) 81890.4 + 141838.i 0.433270 + 0.750446i
\(130\) 0 0
\(131\) −175425. + 303846.i −0.893129 + 1.54695i −0.0570264 + 0.998373i \(0.518162\pi\)
−0.836103 + 0.548573i \(0.815171\pi\)
\(132\) 0 0
\(133\) −208025. 4070.56i −1.01973 0.0199538i
\(134\) 0 0
\(135\) −57336.5 + 99309.7i −0.270767 + 0.468983i
\(136\) 0 0
\(137\) −124390. 215450.i −0.566219 0.980719i −0.996935 0.0782321i \(-0.975072\pi\)
0.430717 0.902487i \(-0.358261\pi\)
\(138\) 0 0
\(139\) 221518. + 383680.i 0.972459 + 1.68435i 0.688078 + 0.725637i \(0.258455\pi\)
0.284381 + 0.958711i \(0.408212\pi\)
\(140\) 0 0
\(141\) −81253.7 −0.344188
\(142\) 0 0
\(143\) −275843. 477774.i −1.12803 1.95381i
\(144\) 0 0
\(145\) 85436.8 0.337462
\(146\) 0 0
\(147\) 5378.68 9316.15i 0.0205297 0.0355585i
\(148\) 0 0
\(149\) −120138. + 208085.i −0.443317 + 0.767847i −0.997933 0.0642591i \(-0.979532\pi\)
0.554617 + 0.832106i \(0.312865\pi\)
\(150\) 0 0
\(151\) −166073. −0.592730 −0.296365 0.955075i \(-0.595774\pi\)
−0.296365 + 0.955075i \(0.595774\pi\)
\(152\) 0 0
\(153\) −14363.2 −0.0496046
\(154\) 0 0
\(155\) −163797. + 283705.i −0.547617 + 0.948501i
\(156\) 0 0
\(157\) −50926.7 + 88207.7i −0.164891 + 0.285599i −0.936617 0.350356i \(-0.886061\pi\)
0.771726 + 0.635956i \(0.219394\pi\)
\(158\) 0 0
\(159\) −118433. −0.371518
\(160\) 0 0
\(161\) −151477. 262365.i −0.460555 0.797704i
\(162\) 0 0
\(163\) −256024. −0.754764 −0.377382 0.926058i \(-0.623176\pi\)
−0.377382 + 0.926058i \(0.623176\pi\)
\(164\) 0 0
\(165\) 164897. + 285610.i 0.471523 + 0.816702i
\(166\) 0 0
\(167\) 53946.9 + 93438.8i 0.149684 + 0.259260i 0.931111 0.364737i \(-0.118841\pi\)
−0.781427 + 0.623997i \(0.785508\pi\)
\(168\) 0 0
\(169\) −152738. + 264551.i −0.411369 + 0.712512i
\(170\) 0 0
\(171\) 7463.64 + 13532.1i 0.0195191 + 0.0353895i
\(172\) 0 0
\(173\) 197251. 341649.i 0.501077 0.867890i −0.498922 0.866647i \(-0.666271\pi\)
0.999999 0.00124378i \(-0.000395908\pi\)
\(174\) 0 0
\(175\) 143359. + 248305.i 0.353858 + 0.612900i
\(176\) 0 0
\(177\) 272693. + 472318.i 0.654245 + 1.13319i
\(178\) 0 0
\(179\) −229285. −0.534863 −0.267432 0.963577i \(-0.586175\pi\)
−0.267432 + 0.963577i \(0.586175\pi\)
\(180\) 0 0
\(181\) −269882. 467449.i −0.612318 1.06057i −0.990849 0.134977i \(-0.956904\pi\)
0.378531 0.925589i \(-0.376429\pi\)
\(182\) 0 0
\(183\) 655367. 1.44663
\(184\) 0 0
\(185\) −74464.8 + 128977.i −0.159964 + 0.277065i
\(186\) 0 0
\(187\) 490386. 849373.i 1.02550 1.77621i
\(188\) 0 0
\(189\) 490242. 0.998289
\(190\) 0 0
\(191\) 448848. 0.890259 0.445129 0.895466i \(-0.353158\pi\)
0.445129 + 0.895466i \(0.353158\pi\)
\(192\) 0 0
\(193\) 23904.7 41404.2i 0.0461945 0.0800113i −0.842004 0.539472i \(-0.818624\pi\)
0.888198 + 0.459461i \(0.151957\pi\)
\(194\) 0 0
\(195\) 202284. 350366.i 0.380957 0.659836i
\(196\) 0 0
\(197\) 43802.6 0.0804145 0.0402072 0.999191i \(-0.487198\pi\)
0.0402072 + 0.999191i \(0.487198\pi\)
\(198\) 0 0
\(199\) 300067. + 519730.i 0.537137 + 0.930348i 0.999057 + 0.0434264i \(0.0138274\pi\)
−0.461920 + 0.886922i \(0.652839\pi\)
\(200\) 0 0
\(201\) −624107. −1.08960
\(202\) 0 0
\(203\) −182627. 316319.i −0.311046 0.538747i
\(204\) 0 0
\(205\) −225323. 390271.i −0.374473 0.648607i
\(206\) 0 0
\(207\) −11250.9 + 19487.1i −0.0182499 + 0.0316097i
\(208\) 0 0
\(209\) −1.05505e6 20644.8i −1.67073 0.0326923i
\(210\) 0 0
\(211\) 239624. 415040.i 0.370530 0.641777i −0.619117 0.785299i \(-0.712509\pi\)
0.989647 + 0.143522i \(0.0458427\pi\)
\(212\) 0 0
\(213\) −92996.2 161074.i −0.140448 0.243263i
\(214\) 0 0
\(215\) −159291. 275900.i −0.235015 0.407058i
\(216\) 0 0
\(217\) 1.40051e6 2.01900
\(218\) 0 0
\(219\) 217784. + 377214.i 0.306843 + 0.531468i
\(220\) 0 0
\(221\) −1.20314e6 −1.65705
\(222\) 0 0
\(223\) −93000.5 + 161082.i −0.125234 + 0.216912i −0.921824 0.387608i \(-0.873302\pi\)
0.796590 + 0.604520i \(0.206635\pi\)
\(224\) 0 0
\(225\) 10647.9 18442.7i 0.0140219 0.0242867i
\(226\) 0 0
\(227\) 131418. 0.169274 0.0846371 0.996412i \(-0.473027\pi\)
0.0846371 + 0.996412i \(0.473027\pi\)
\(228\) 0 0
\(229\) 105774. 0.133288 0.0666440 0.997777i \(-0.478771\pi\)
0.0666440 + 0.997777i \(0.478771\pi\)
\(230\) 0 0
\(231\) 704957. 1.22102e6i 0.869226 1.50554i
\(232\) 0 0
\(233\) 504870. 874460.i 0.609241 1.05524i −0.382124 0.924111i \(-0.624807\pi\)
0.991366 0.131126i \(-0.0418593\pi\)
\(234\) 0 0
\(235\) 158053. 0.186695
\(236\) 0 0
\(237\) 41078.2 + 71149.5i 0.0475051 + 0.0822813i
\(238\) 0 0
\(239\) −538983. −0.610351 −0.305176 0.952296i \(-0.598715\pi\)
−0.305176 + 0.952296i \(0.598715\pi\)
\(240\) 0 0
\(241\) 618134. + 1.07064e6i 0.685551 + 1.18741i 0.973263 + 0.229692i \(0.0737720\pi\)
−0.287712 + 0.957717i \(0.592895\pi\)
\(242\) 0 0
\(243\) −37179.3 64396.4i −0.0403911 0.0699594i
\(244\) 0 0
\(245\) −10462.5 + 18121.5i −0.0111357 + 0.0192877i
\(246\) 0 0
\(247\) 625197. + 1.13352e6i 0.652040 + 1.18219i
\(248\) 0 0
\(249\) −684928. + 1.18633e6i −0.700078 + 1.21257i
\(250\) 0 0
\(251\) −665047. 1.15190e6i −0.666298 1.15406i −0.978932 0.204188i \(-0.934545\pi\)
0.312634 0.949874i \(-0.398789\pi\)
\(252\) 0 0
\(253\) −768250. 1.33065e6i −0.754573 1.30696i
\(254\) 0 0
\(255\) 719230. 0.692656
\(256\) 0 0
\(257\) 471458. + 816590.i 0.445257 + 0.771207i 0.998070 0.0620979i \(-0.0197791\pi\)
−0.552813 + 0.833305i \(0.686446\pi\)
\(258\) 0 0
\(259\) 636694. 0.589768
\(260\) 0 0
\(261\) −13564.5 + 23494.4i −0.0123255 + 0.0213483i
\(262\) 0 0
\(263\) −848058. + 1.46888e6i −0.756025 + 1.30947i 0.188838 + 0.982008i \(0.439528\pi\)
−0.944863 + 0.327465i \(0.893806\pi\)
\(264\) 0 0
\(265\) 230373. 0.201519
\(266\) 0 0
\(267\) 807229. 0.692977
\(268\) 0 0
\(269\) 403755. 699325.i 0.340203 0.589248i −0.644268 0.764800i \(-0.722838\pi\)
0.984470 + 0.175552i \(0.0561710\pi\)
\(270\) 0 0
\(271\) −1.02987e6 + 1.78379e6i −0.851845 + 1.47544i 0.0276959 + 0.999616i \(0.491183\pi\)
−0.879541 + 0.475823i \(0.842150\pi\)
\(272\) 0 0
\(273\) −1.72958e6 −1.40454
\(274\) 0 0
\(275\) 727078. + 1.25934e6i 0.579761 + 1.00418i
\(276\) 0 0
\(277\) −1.06729e6 −0.835761 −0.417881 0.908502i \(-0.637227\pi\)
−0.417881 + 0.908502i \(0.637227\pi\)
\(278\) 0 0
\(279\) −52011.1 90085.8i −0.0400023 0.0692861i
\(280\) 0 0
\(281\) −352862. 611176.i −0.266587 0.461743i 0.701391 0.712777i \(-0.252563\pi\)
−0.967978 + 0.251034i \(0.919229\pi\)
\(282\) 0 0
\(283\) 190924. 330690.i 0.141708 0.245446i −0.786432 0.617677i \(-0.788074\pi\)
0.928140 + 0.372231i \(0.121407\pi\)
\(284\) 0 0
\(285\) −373739. 677613.i −0.272556 0.494162i
\(286\) 0 0
\(287\) −963286. + 1.66846e6i −0.690320 + 1.19567i
\(288\) 0 0
\(289\) −359527. 622720.i −0.253214 0.438579i
\(290\) 0 0
\(291\) 211550. + 366415.i 0.146447 + 0.253653i
\(292\) 0 0
\(293\) −2.08651e6 −1.41988 −0.709941 0.704261i \(-0.751278\pi\)
−0.709941 + 0.704261i \(0.751278\pi\)
\(294\) 0 0
\(295\) −530435. 918740.i −0.354876 0.614664i
\(296\) 0 0
\(297\) 2.48638e6 1.63560
\(298\) 0 0
\(299\) −942435. + 1.63235e6i −0.609640 + 1.05593i
\(300\) 0 0
\(301\) −680991. + 1.17951e6i −0.433237 + 0.750388i
\(302\) 0 0
\(303\) 1.02035e6 0.638471
\(304\) 0 0
\(305\) −1.27480e6 −0.784681
\(306\) 0 0
\(307\) 805874. 1.39582e6i 0.488002 0.845244i −0.511903 0.859043i \(-0.671059\pi\)
0.999905 + 0.0137995i \(0.00439266\pi\)
\(308\) 0 0
\(309\) 528217. 914899.i 0.314714 0.545101i
\(310\) 0 0
\(311\) 785721. 0.460646 0.230323 0.973114i \(-0.426022\pi\)
0.230323 + 0.973114i \(0.426022\pi\)
\(312\) 0 0
\(313\) 1.34106e6 + 2.32278e6i 0.773724 + 1.34013i 0.935509 + 0.353303i \(0.114942\pi\)
−0.161785 + 0.986826i \(0.551725\pi\)
\(314\) 0 0
\(315\) 40163.7 0.0228065
\(316\) 0 0
\(317\) −1.30544e6 2.26109e6i −0.729642 1.26378i −0.957034 0.289974i \(-0.906353\pi\)
0.227392 0.973803i \(-0.426980\pi\)
\(318\) 0 0
\(319\) −926235. 1.60429e6i −0.509618 0.882684i
\(320\) 0 0
\(321\) −1.49430e6 + 2.58821e6i −0.809423 + 1.40196i
\(322\) 0 0
\(323\) −1.18944e6 + 1.97012e6i −0.634361 + 1.05072i
\(324\) 0 0
\(325\) 891929. 1.54487e6i 0.468405 0.811302i
\(326\) 0 0
\(327\) −1.42509e6 2.46833e6i −0.737008 1.27654i
\(328\) 0 0
\(329\) −337848. 585170.i −0.172080 0.298052i
\(330\) 0 0
\(331\) 2.09316e6 1.05010 0.525052 0.851070i \(-0.324046\pi\)
0.525052 + 0.851070i \(0.324046\pi\)
\(332\) 0 0
\(333\) −23645.1 40954.4i −0.0116850 0.0202391i
\(334\) 0 0
\(335\) 1.21400e6 0.591024
\(336\) 0 0
\(337\) −1.63109e6 + 2.82513e6i −0.782353 + 1.35508i 0.148214 + 0.988955i \(0.452647\pi\)
−0.930568 + 0.366120i \(0.880686\pi\)
\(338\) 0 0
\(339\) −471703. + 817013.i −0.222930 + 0.386127i
\(340\) 0 0
\(341\) 7.10301e6 3.30793
\(342\) 0 0
\(343\) −2.13285e6 −0.978872
\(344\) 0 0
\(345\) 563382. 975805.i 0.254833 0.441383i
\(346\) 0 0
\(347\) 602372. 1.04334e6i 0.268560 0.465159i −0.699930 0.714211i \(-0.746786\pi\)
0.968490 + 0.249052i \(0.0801189\pi\)
\(348\) 0 0
\(349\) 2.97327e6 1.30668 0.653342 0.757063i \(-0.273366\pi\)
0.653342 + 0.757063i \(0.273366\pi\)
\(350\) 0 0
\(351\) −1.52506e6 2.64148e6i −0.660722 1.14440i
\(352\) 0 0
\(353\) 2.66290e6 1.13741 0.568706 0.822541i \(-0.307444\pi\)
0.568706 + 0.822541i \(0.307444\pi\)
\(354\) 0 0
\(355\) 180894. + 313317.i 0.0761820 + 0.131951i
\(356\) 0 0
\(357\) −1.53740e6 2.66286e6i −0.638436 1.10580i
\(358\) 0 0
\(359\) 415704. 720020.i 0.170235 0.294855i −0.768267 0.640129i \(-0.778881\pi\)
0.938502 + 0.345274i \(0.112214\pi\)
\(360\) 0 0
\(361\) 2.47420e6 + 96865.8i 0.999235 + 0.0391203i
\(362\) 0 0
\(363\) 2.29497e6 3.97501e6i 0.914136 1.58333i
\(364\) 0 0
\(365\) −423629. 733746.i −0.166438 0.288279i
\(366\) 0 0
\(367\) 543635. + 941604.i 0.210689 + 0.364925i 0.951930 0.306314i \(-0.0990958\pi\)
−0.741241 + 0.671239i \(0.765763\pi\)
\(368\) 0 0
\(369\) 143095. 0.0547090
\(370\) 0 0
\(371\) −492438. 852927.i −0.185745 0.321719i
\(372\) 0 0
\(373\) 3.00979e6 1.12012 0.560059 0.828452i \(-0.310778\pi\)
0.560059 + 0.828452i \(0.310778\pi\)
\(374\) 0 0
\(375\) −1.30160e6 + 2.25443e6i −0.477967 + 0.827863i
\(376\) 0 0
\(377\) −1.13624e6 + 1.96803e6i −0.411734 + 0.713145i
\(378\) 0 0
\(379\) −1.58924e6 −0.568317 −0.284158 0.958777i \(-0.591714\pi\)
−0.284158 + 0.958777i \(0.591714\pi\)
\(380\) 0 0
\(381\) −1.06230e6 −0.374918
\(382\) 0 0
\(383\) 1.14784e6 1.98811e6i 0.399837 0.692538i −0.593869 0.804562i \(-0.702400\pi\)
0.993705 + 0.112024i \(0.0357335\pi\)
\(384\) 0 0
\(385\) −1.37126e6 + 2.37510e6i −0.471486 + 0.816638i
\(386\) 0 0
\(387\) 101160. 0.0343347
\(388\) 0 0
\(389\) −2.12902e6 3.68757e6i −0.713355 1.23557i −0.963590 0.267383i \(-0.913841\pi\)
0.250235 0.968185i \(-0.419492\pi\)
\(390\) 0 0
\(391\) −3.35087e6 −1.10845
\(392\) 0 0
\(393\) 2.78933e6 + 4.83125e6i 0.910999 + 1.57790i
\(394\) 0 0
\(395\) −79904.2 138398.i −0.0257678 0.0446311i
\(396\) 0 0
\(397\) −173073. + 299772.i −0.0551130 + 0.0954585i −0.892266 0.451511i \(-0.850885\pi\)
0.837153 + 0.546969i \(0.184219\pi\)
\(398\) 0 0
\(399\) −1.70989e6 + 2.83216e6i −0.537694 + 0.890607i
\(400\) 0 0
\(401\) 777399. 1.34649e6i 0.241425 0.418161i −0.719695 0.694290i \(-0.755718\pi\)
0.961121 + 0.276129i \(0.0890517\pi\)
\(402\) 0 0
\(403\) −4.35674e6 7.54610e6i −1.33629 2.31451i
\(404\) 0 0
\(405\) 948576. + 1.64298e6i 0.287365 + 0.497731i
\(406\) 0 0
\(407\) 3.22914e6 0.966276
\(408\) 0 0
\(409\) −796042. 1.37878e6i −0.235303 0.407557i 0.724058 0.689739i \(-0.242275\pi\)
−0.959361 + 0.282183i \(0.908942\pi\)
\(410\) 0 0
\(411\) −3.95569e6 −1.15509
\(412\) 0 0
\(413\) −2.26768e6 + 3.92774e6i −0.654195 + 1.13310i
\(414\) 0 0
\(415\) 1.33230e6 2.30762e6i 0.379737 0.657724i
\(416\) 0 0
\(417\) 7.04441e6 1.98383
\(418\) 0 0
\(419\) −4.11283e6 −1.14447 −0.572236 0.820089i \(-0.693924\pi\)
−0.572236 + 0.820089i \(0.693924\pi\)
\(420\) 0 0
\(421\) 1.57964e6 2.73602e6i 0.434364 0.752341i −0.562879 0.826539i \(-0.690306\pi\)
0.997244 + 0.0741981i \(0.0236397\pi\)
\(422\) 0 0
\(423\) −25093.5 + 43463.2i −0.00681883 + 0.0118106i
\(424\) 0 0
\(425\) 3.17129e6 0.851655
\(426\) 0 0
\(427\) 2.72498e6 + 4.71980e6i 0.723257 + 1.25272i
\(428\) 0 0
\(429\) −8.77199e6 −2.30120
\(430\) 0 0
\(431\) 508299. + 880400.i 0.131803 + 0.228290i 0.924372 0.381493i \(-0.124590\pi\)
−0.792568 + 0.609783i \(0.791257\pi\)
\(432\) 0 0
\(433\) −1.49339e6 2.58663e6i −0.382784 0.663001i 0.608675 0.793419i \(-0.291701\pi\)
−0.991459 + 0.130419i \(0.958368\pi\)
\(434\) 0 0
\(435\) 679237. 1.17647e6i 0.172107 0.298098i
\(436\) 0 0
\(437\) 1.74124e6 + 3.15698e6i 0.436168 + 0.790802i
\(438\) 0 0
\(439\) −3.05381e6 + 5.28936e6i −0.756277 + 1.30991i 0.188459 + 0.982081i \(0.439651\pi\)
−0.944737 + 0.327830i \(0.893683\pi\)
\(440\) 0 0
\(441\) −3322.18 5754.19i −0.000813443 0.00140892i
\(442\) 0 0
\(443\) 2.29170e6 + 3.96935e6i 0.554816 + 0.960970i 0.997918 + 0.0644983i \(0.0205447\pi\)
−0.443102 + 0.896471i \(0.646122\pi\)
\(444\) 0 0
\(445\) −1.57020e6 −0.375885
\(446\) 0 0
\(447\) 1.91023e6 + 3.30862e6i 0.452186 + 0.783210i
\(448\) 0 0
\(449\) −2.65968e6 −0.622607 −0.311304 0.950310i \(-0.600766\pi\)
−0.311304 + 0.950310i \(0.600766\pi\)
\(450\) 0 0
\(451\) −4.88553e6 + 8.46199e6i −1.13102 + 1.95899i
\(452\) 0 0
\(453\) −1.32031e6 + 2.28684e6i −0.302294 + 0.523589i
\(454\) 0 0
\(455\) 3.36434e6 0.761854
\(456\) 0 0
\(457\) 5.09945e6 1.14217 0.571087 0.820889i \(-0.306522\pi\)
0.571087 + 0.820889i \(0.306522\pi\)
\(458\) 0 0
\(459\) 2.71121e6 4.69595e6i 0.600663 1.04038i
\(460\) 0 0
\(461\) 3.18373e6 5.51438e6i 0.697725 1.20849i −0.271529 0.962430i \(-0.587529\pi\)
0.969254 0.246064i \(-0.0791374\pi\)
\(462\) 0 0
\(463\) −5.07803e6 −1.10089 −0.550443 0.834873i \(-0.685541\pi\)
−0.550443 + 0.834873i \(0.685541\pi\)
\(464\) 0 0
\(465\) 2.60443e6 + 4.51101e6i 0.558574 + 0.967478i
\(466\) 0 0
\(467\) 3.58423e6 0.760507 0.380254 0.924882i \(-0.375837\pi\)
0.380254 + 0.924882i \(0.375837\pi\)
\(468\) 0 0
\(469\) −2.59500e6 4.49467e6i −0.544760 0.943552i
\(470\) 0 0
\(471\) 809753. + 1.40253e6i 0.168190 + 0.291314i
\(472\) 0 0
\(473\) −3.45381e6 + 5.98217e6i −0.709815 + 1.22944i
\(474\) 0 0
\(475\) −1.64792e6 2.98779e6i −0.335121 0.607598i
\(476\) 0 0
\(477\) −36575.5 + 63350.7i −0.00736029 + 0.0127484i
\(478\) 0 0
\(479\) −3.65416e6 6.32919e6i −0.727694 1.26040i −0.957855 0.287251i \(-0.907259\pi\)
0.230161 0.973153i \(-0.426075\pi\)
\(480\) 0 0
\(481\) −1.98064e6 3.43058e6i −0.390341 0.676090i
\(482\) 0 0
\(483\) −4.81706e6 −0.939539
\(484\) 0 0
\(485\) −411501. 712740.i −0.0794358 0.137587i
\(486\) 0 0
\(487\) 5.63917e6 1.07744 0.538719 0.842485i \(-0.318908\pi\)
0.538719 + 0.842485i \(0.318908\pi\)
\(488\) 0 0
\(489\) −2.03543e6 + 3.52547e6i −0.384932 + 0.666723i
\(490\) 0 0
\(491\) −3.98866e6 + 6.90857e6i −0.746661 + 1.29325i 0.202754 + 0.979230i \(0.435011\pi\)
−0.949415 + 0.314025i \(0.898322\pi\)
\(492\) 0 0
\(493\) −4.03995e6 −0.748616
\(494\) 0 0
\(495\) 203700. 0.0373661
\(496\) 0 0
\(497\) 773345. 1.33947e6i 0.140437 0.243244i
\(498\) 0 0
\(499\) 2.71915e6 4.70971e6i 0.488858 0.846727i −0.511060 0.859545i \(-0.670747\pi\)
0.999918 + 0.0128184i \(0.00408034\pi\)
\(500\) 0 0
\(501\) 1.71555e6 0.305358
\(502\) 0 0
\(503\) 4.08679e6 + 7.07853e6i 0.720216 + 1.24745i 0.960913 + 0.276850i \(0.0892906\pi\)
−0.240697 + 0.970600i \(0.577376\pi\)
\(504\) 0 0
\(505\) −1.98475e6 −0.346320
\(506\) 0 0
\(507\) 2.42859e6 + 4.20645e6i 0.419599 + 0.726767i
\(508\) 0 0
\(509\) −5.63560e6 9.76115e6i −0.964153 1.66996i −0.711873 0.702308i \(-0.752153\pi\)
−0.252280 0.967654i \(-0.581180\pi\)
\(510\) 0 0
\(511\) −1.81107e6 + 3.13686e6i −0.306819 + 0.531427i
\(512\) 0 0
\(513\) −5.83307e6 114139.i −0.978596 0.0191488i
\(514\) 0 0
\(515\) −1.02747e6 + 1.77964e6i −0.170708 + 0.295674i
\(516\) 0 0
\(517\) −1.71348e6 2.96783e6i −0.281937 0.488329i
\(518\) 0 0
\(519\) −3.13636e6 5.43234e6i −0.511102 0.885255i
\(520\) 0 0
\(521\) 6.41682e6 1.03568 0.517840 0.855477i \(-0.326736\pi\)
0.517840 + 0.855477i \(0.326736\pi\)
\(522\) 0 0
\(523\) −1.77525e6 3.07483e6i −0.283796 0.491549i 0.688520 0.725217i \(-0.258261\pi\)
−0.972317 + 0.233668i \(0.924927\pi\)
\(524\) 0 0
\(525\) 4.55891e6 0.721876
\(526\) 0 0
\(527\) 7.74529e6 1.34152e7i 1.21482 2.10413i
\(528\) 0 0
\(529\) 593395. 1.02779e6i 0.0921945 0.159686i
\(530\) 0 0
\(531\) 336862. 0.0518460
\(532\) 0 0
\(533\) 1.19865e7 1.82757
\(534\) 0 0
\(535\) 2.90668e6 5.03451e6i 0.439048 0.760454i
\(536\) 0 0
\(537\) −1.82285e6 + 3.15727e6i −0.272782 + 0.472473i
\(538\) 0 0
\(539\) 453702. 0.0672665
\(540\) 0 0
\(541\) 2.87812e6 + 4.98505e6i 0.422781 + 0.732279i 0.996210 0.0869765i \(-0.0277205\pi\)
−0.573429 + 0.819255i \(0.694387\pi\)
\(542\) 0 0
\(543\) −8.58242e6 −1.24914
\(544\) 0 0
\(545\) 2.77204e6 + 4.80132e6i 0.399769 + 0.692420i
\(546\) 0 0
\(547\) 561663. + 972828.i 0.0802615 + 0.139017i 0.903362 0.428878i \(-0.141091\pi\)
−0.823101 + 0.567895i \(0.807758\pi\)
\(548\) 0 0
\(549\) 202396. 350560.i 0.0286597 0.0496400i
\(550\) 0 0
\(551\) 2.09931e6 + 3.80619e6i 0.294576 + 0.534086i
\(552\) 0 0
\(553\) −341601. + 591671.i −0.0475014 + 0.0822749i
\(554\) 0 0
\(555\) 1.18402e6 + 2.05077e6i 0.163164 + 0.282609i
\(556\) 0 0
\(557\) 2.85326e6 + 4.94199e6i 0.389676 + 0.674938i 0.992406 0.123007i \(-0.0392537\pi\)
−0.602730 + 0.797945i \(0.705920\pi\)
\(558\) 0 0
\(559\) 8.47378e6 1.14696
\(560\) 0 0
\(561\) −7.79730e6 1.35053e7i −1.04601 1.81175i
\(562\) 0 0
\(563\) 1.30560e7 1.73596 0.867980 0.496599i \(-0.165418\pi\)
0.867980 + 0.496599i \(0.165418\pi\)
\(564\) 0 0
\(565\) 917543. 1.58923e6i 0.120922 0.209443i
\(566\) 0 0
\(567\) 4.05529e6 7.02397e6i 0.529742 0.917540i
\(568\) 0 0
\(569\) 8.04953e6 1.04229 0.521147 0.853467i \(-0.325504\pi\)
0.521147 + 0.853467i \(0.325504\pi\)
\(570\) 0 0
\(571\) −604331. −0.0775683 −0.0387842 0.999248i \(-0.512348\pi\)
−0.0387842 + 0.999248i \(0.512348\pi\)
\(572\) 0 0
\(573\) 3.56842e6 6.18069e6i 0.454035 0.786412i
\(574\) 0 0
\(575\) 2.48411e6 4.30260e6i 0.313329 0.542702i
\(576\) 0 0
\(577\) 3.91150e6 0.489107 0.244554 0.969636i \(-0.421359\pi\)
0.244554 + 0.969636i \(0.421359\pi\)
\(578\) 0 0
\(579\) −380093. 658341.i −0.0471188 0.0816121i
\(580\) 0 0
\(581\) −1.13916e7 −1.40005
\(582\) 0 0
\(583\) −2.49751e6 4.32582e6i −0.304324 0.527105i
\(584\) 0 0
\(585\) −124942. 216407.i −0.0150945 0.0261445i
\(586\) 0 0
\(587\) −720645. + 1.24819e6i −0.0863229 + 0.149516i −0.905954 0.423376i \(-0.860845\pi\)
0.819631 + 0.572891i \(0.194178\pi\)
\(588\) 0 0
\(589\) −1.66637e7 326070.i −1.97917 0.0387278i
\(590\) 0 0
\(591\) 348238. 603166.i 0.0410117 0.0710343i
\(592\) 0 0
\(593\) −1.01304e6 1.75464e6i −0.118302 0.204904i 0.800793 0.598941i \(-0.204412\pi\)
−0.919095 + 0.394037i \(0.871078\pi\)
\(594\) 0 0
\(595\) 2.99052e6 + 5.17973e6i 0.346301 + 0.599811i
\(596\) 0 0
\(597\) 9.54232e6 1.09577
\(598\) 0 0
\(599\) 697546. + 1.20819e6i 0.0794339 + 0.137584i 0.903006 0.429628i \(-0.141355\pi\)
−0.823572 + 0.567212i \(0.808022\pi\)
\(600\) 0 0
\(601\) −1.12873e7 −1.27469 −0.637346 0.770578i \(-0.719968\pi\)
−0.637346 + 0.770578i \(0.719968\pi\)
\(602\) 0 0
\(603\) −192742. + 333839.i −0.0215866 + 0.0373890i
\(604\) 0 0
\(605\) −4.46412e6 + 7.73208e6i −0.495847 + 0.858832i
\(606\) 0 0
\(607\) 1.45297e7 1.60061 0.800306 0.599591i \(-0.204670\pi\)
0.800306 + 0.599591i \(0.204670\pi\)
\(608\) 0 0
\(609\) −5.80766e6 −0.634538
\(610\) 0 0
\(611\) −2.10197e6 + 3.64072e6i −0.227784 + 0.394534i
\(612\) 0 0
\(613\) −7.68601e6 + 1.33126e7i −0.826133 + 1.43090i 0.0749172 + 0.997190i \(0.476131\pi\)
−0.901050 + 0.433715i \(0.857203\pi\)
\(614\) 0 0
\(615\) −7.16543e6 −0.763931
\(616\) 0 0
\(617\) 1.39641e6 + 2.41866e6i 0.147673 + 0.255777i 0.930367 0.366630i \(-0.119488\pi\)
−0.782694 + 0.622407i \(0.786155\pi\)
\(618\) 0 0
\(619\) −8.26283e6 −0.866766 −0.433383 0.901210i \(-0.642680\pi\)
−0.433383 + 0.901210i \(0.642680\pi\)
\(620\) 0 0
\(621\) −4.24744e6 7.35678e6i −0.441975 0.765524i
\(622\) 0 0
\(623\) 3.35641e6 + 5.81347e6i 0.346461 + 0.600089i
\(624\) 0 0
\(625\) −856296. + 1.48315e6i −0.0876848 + 0.151874i
\(626\) 0 0
\(627\) −8.67209e6 + 1.43640e7i −0.880958 + 1.45917i
\(628\) 0 0
\(629\) 3.52113e6 6.09878e6i 0.354859 0.614634i
\(630\) 0 0
\(631\) −329136. 570081.i −0.0329081 0.0569985i 0.849102 0.528228i \(-0.177144\pi\)
−0.882010 + 0.471230i \(0.843810\pi\)
\(632\) 0 0
\(633\) −3.81010e6 6.59929e6i −0.377944 0.654618i
\(634\) 0 0
\(635\) 2.06637e6 0.203364
\(636\) 0 0
\(637\) −278285. 482004.i −0.0271732 0.0470654i
\(638\) 0 0
\(639\) −114880. −0.0111299
\(640\) 0 0
\(641\) −626336. + 1.08485e6i −0.0602091 + 0.104285i −0.894559 0.446950i \(-0.852510\pi\)
0.834350 + 0.551236i \(0.185843\pi\)
\(642\) 0 0
\(643\) 7.69468e6 1.33276e7i 0.733945 1.27123i −0.221240 0.975219i \(-0.571010\pi\)
0.955185 0.296010i \(-0.0956562\pi\)
\(644\) 0 0
\(645\) −5.06557e6 −0.479434
\(646\) 0 0
\(647\) 1.31905e6 0.123880 0.0619398 0.998080i \(-0.480271\pi\)
0.0619398 + 0.998080i \(0.480271\pi\)
\(648\) 0 0
\(649\) −1.15011e7 + 1.99205e7i −1.07183 + 1.85647i
\(650\) 0 0
\(651\) 1.11343e7 1.92852e7i 1.02970 1.78349i
\(652\) 0 0
\(653\) −2.35430e6 −0.216062 −0.108031 0.994148i \(-0.534455\pi\)
−0.108031 + 0.994148i \(0.534455\pi\)
\(654\) 0 0
\(655\) −5.42572e6 9.39762e6i −0.494145 0.855884i
\(656\) 0 0
\(657\) 269032. 0.0243160
\(658\) 0 0
\(659\) 1.16918e6 + 2.02508e6i 0.104874 + 0.181647i 0.913687 0.406419i \(-0.133223\pi\)
−0.808813 + 0.588066i \(0.799889\pi\)
\(660\) 0 0
\(661\) 4.27183e6 + 7.39902e6i 0.380286 + 0.658674i 0.991103 0.133098i \(-0.0424924\pi\)
−0.610817 + 0.791772i \(0.709159\pi\)
\(662\) 0 0
\(663\) −9.56519e6 + 1.65674e7i −0.845103 + 1.46376i
\(664\) 0 0
\(665\) 3.32603e6 5.50905e6i 0.291657 0.483084i
\(666\) 0 0
\(667\) −3.16454e6 + 5.48115e6i −0.275421 + 0.477042i
\(668\) 0 0
\(669\) 1.47874e6 + 2.56125e6i 0.127740 + 0.221252i
\(670\) 0 0
\(671\) 1.38204e7 + 2.39376e7i 1.18498 + 2.05245i
\(672\) 0 0
\(673\) 7.81154e6 0.664813 0.332406 0.943136i \(-0.392139\pi\)
0.332406 + 0.943136i \(0.392139\pi\)
\(674\) 0 0
\(675\) 4.01981e6 + 6.96252e6i 0.339583 + 0.588175i
\(676\) 0 0
\(677\) −9.38338e6 −0.786842 −0.393421 0.919358i \(-0.628709\pi\)
−0.393421 + 0.919358i \(0.628709\pi\)
\(678\) 0 0
\(679\) −1.75922e6 + 3.04706e6i −0.146435 + 0.253634i
\(680\) 0 0
\(681\) 1.04480e6 1.80964e6i 0.0863305 0.149529i
\(682\) 0 0
\(683\) −1.64103e7 −1.34606 −0.673031 0.739614i \(-0.735008\pi\)
−0.673031 + 0.739614i \(0.735008\pi\)
\(684\) 0 0
\(685\) 7.69450e6 0.626547
\(686\) 0 0
\(687\) 840923. 1.45652e6i 0.0679774 0.117740i
\(688\) 0 0
\(689\) −3.06377e6 + 5.30661e6i −0.245872 + 0.425862i
\(690\) 0 0
\(691\) −1.44148e7 −1.14846 −0.574228 0.818695i \(-0.694698\pi\)
−0.574228 + 0.818695i \(0.694698\pi\)
\(692\) 0 0
\(693\) −435422. 754173.i −0.0344411 0.0596538i
\(694\) 0 0
\(695\) −1.37026e7 −1.07607
\(696\) 0 0
\(697\) 1.06546e7 + 1.84543e7i 0.830721 + 1.43885i
\(698\) 0 0
\(699\) −8.02760e6 1.39042e7i −0.621431 1.07635i
\(700\) 0 0
\(701\) 9.22639e6 1.59806e7i 0.709148 1.22828i −0.256025 0.966670i \(-0.582413\pi\)
0.965174 0.261610i \(-0.0842536\pi\)
\(702\) 0 0
\(703\) −7.57559e6 148237.i −0.578134 0.0113127i
\(704\) 0 0
\(705\) 1.25654e6 2.17640e6i 0.0952150 0.164917i
\(706\) 0 0
\(707\) 4.24254e6 + 7.34829e6i 0.319211 + 0.552889i
\(708\) 0 0
\(709\) 2.36759e6 + 4.10078e6i 0.176885 + 0.306373i 0.940812 0.338929i \(-0.110065\pi\)
−0.763927 + 0.645302i \(0.776731\pi\)
\(710\) 0 0
\(711\) 50744.5 0.00376457
\(712\) 0 0
\(713\) −1.21340e7 2.10166e7i −0.893879 1.54824i
\(714\) 0 0
\(715\) 1.70631e7 1.24822
\(716\) 0 0
\(717\) −4.28500e6 + 7.42185e6i −0.311282 + 0.539155i
\(718\) 0 0
\(719\) −1.63001e6 + 2.82326e6i −0.117589 + 0.203671i −0.918812 0.394696i \(-0.870850\pi\)
0.801222 + 0.598367i \(0.204183\pi\)
\(720\) 0 0
\(721\) 8.78518e6 0.629379
\(722\) 0 0
\(723\) 1.96571e7 1.39853
\(724\) 0 0
\(725\) 2.99495e6 5.18740e6i 0.211614 0.366526i
\(726\) 0 0
\(727\) 1.20435e7 2.08600e7i 0.845117 1.46379i −0.0404018 0.999184i \(-0.512864\pi\)
0.885519 0.464603i \(-0.153803\pi\)
\(728\) 0 0
\(729\) 1.37231e7 0.956384
\(730\) 0 0
\(731\) 7.53222e6 + 1.30462e7i 0.521350 + 0.903005i
\(732\) 0 0
\(733\) 8.14935e6 0.560225 0.280113 0.959967i \(-0.409628\pi\)
0.280113 + 0.959967i \(0.409628\pi\)
\(734\) 0 0
\(735\) 166357. + 288138.i 0.0113585 + 0.0196736i
\(736\) 0 0
\(737\) −1.31611e7 2.27958e7i −0.892535 1.54592i
\(738\) 0 0
\(739\) −3.07531e6 + 5.32659e6i −0.207146 + 0.358788i −0.950814 0.309761i \(-0.899751\pi\)
0.743668 + 0.668549i \(0.233084\pi\)
\(740\) 0 0
\(741\) 2.05792e7 + 402686.i 1.37684 + 0.0269415i
\(742\) 0 0
\(743\) −6.28020e6 + 1.08776e7i −0.417351 + 0.722873i −0.995672 0.0929364i \(-0.970375\pi\)
0.578321 + 0.815809i \(0.303708\pi\)
\(744\) 0 0
\(745\) −3.71573e6 6.43584e6i −0.245275 0.424829i
\(746\) 0 0
\(747\) 423051. + 732746.i 0.0277390 + 0.0480454i
\(748\) 0 0
\(749\) −2.48529e7 −1.61872
\(750\) 0 0
\(751\) −6.87642e6 1.19103e7i −0.444900 0.770590i 0.553145 0.833085i \(-0.313428\pi\)
−0.998045 + 0.0624953i \(0.980094\pi\)
\(752\) 0 0
\(753\) −2.11490e7 −1.35926
\(754\) 0 0
\(755\) 2.56823e6 4.44831e6i 0.163971 0.284006i
\(756\) 0 0
\(757\) −3.85263e6 + 6.67296e6i −0.244353 + 0.423232i −0.961950 0.273227i \(-0.911909\pi\)
0.717596 + 0.696459i \(0.245242\pi\)
\(758\) 0 0
\(759\) −2.44309e7 −1.53934
\(760\) 0 0
\(761\) −2.30446e7 −1.44247 −0.721236 0.692689i \(-0.756426\pi\)
−0.721236 + 0.692689i \(0.756426\pi\)
\(762\) 0 0
\(763\) 1.18509e7 2.05263e7i 0.736951 1.27644i
\(764\) 0 0
\(765\) 222119. 384721.i 0.0137225 0.0237680i
\(766\) 0 0
\(767\) 2.82174e7 1.73193
\(768\) 0 0
\(769\) 8.54029e6 + 1.47922e7i 0.520783 + 0.902023i 0.999708 + 0.0241667i \(0.00769325\pi\)
−0.478925 + 0.877856i \(0.658973\pi\)
\(770\) 0 0
\(771\) 1.49927e7 0.908330
\(772\) 0 0
\(773\) −7.20473e6 1.24790e7i −0.433680 0.751155i 0.563507 0.826111i \(-0.309452\pi\)
−0.997187 + 0.0749561i \(0.976118\pi\)
\(774\) 0 0
\(775\) 1.14837e7 + 1.98903e7i 0.686794 + 1.18956i
\(776\) 0 0
\(777\) 5.06183e6 8.76734e6i 0.300784 0.520973i
\(778\) 0 0
\(779\) 1.18500e7 1.96276e7i 0.699637 1.15884i
\(780\) 0 0
\(781\) 3.92220e6 6.79345e6i 0.230092 0.398532i
\(782\) 0 0
\(783\) −5.12090e6 8.86965e6i −0.298498 0.517014i
\(784\) 0 0
\(785\) −1.57511e6 2.72817e6i −0.0912298 0.158015i
\(786\) 0 0
\(787\) −2.96282e7 −1.70518 −0.852588 0.522584i \(-0.824968\pi\)
−0.852588 + 0.522584i \(0.824968\pi\)
\(788\) 0 0
\(789\) 1.34844e7 + 2.33557e7i