Properties

Label 76.6.e.a.49.9
Level $76$
Weight $6$
Character 76.49
Analytic conductor $12.189$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 49.9
Root \(-12.9311 - 22.3974i\) of defining polynomial
Character \(\chi\) \(=\) 76.49
Dual form 76.6.e.a.45.9

$q$-expansion

\(f(q)\) \(=\) \(q+(12.4311 - 21.5314i) q^{3} +(-18.0963 + 31.3437i) q^{5} -208.885 q^{7} +(-187.566 - 324.875i) q^{9} +O(q^{10})\) \(q+(12.4311 - 21.5314i) q^{3} +(-18.0963 + 31.3437i) q^{5} -208.885 q^{7} +(-187.566 - 324.875i) q^{9} -204.444 q^{11} +(-146.736 - 254.155i) q^{13} +(449.916 + 779.277i) q^{15} +(-850.109 + 1472.43i) q^{17} +(1329.36 - 841.960i) q^{19} +(-2596.68 + 4497.58i) q^{21} +(-1768.22 - 3062.65i) q^{23} +(907.547 + 1571.92i) q^{25} -3285.13 q^{27} +(-3204.96 - 5551.15i) q^{29} -2731.24 q^{31} +(-2541.47 + 4401.96i) q^{33} +(3780.05 - 6547.24i) q^{35} -5427.82 q^{37} -7296.40 q^{39} +(-3692.75 + 6396.03i) q^{41} +(7870.13 - 13631.5i) q^{43} +13577.1 q^{45} +(9723.97 + 16842.4i) q^{47} +26826.0 q^{49} +(21135.7 + 36608.0i) q^{51} +(-4290.51 - 7431.39i) q^{53} +(3699.69 - 6408.05i) q^{55} +(-1603.08 - 39089.5i) q^{57} +(13969.1 - 24195.1i) q^{59} +(-15366.2 - 26615.0i) q^{61} +(39179.8 + 67861.5i) q^{63} +10621.5 q^{65} +(-24126.9 - 41788.9i) q^{67} -87924.1 q^{69} +(-3430.92 + 5942.53i) q^{71} +(19300.4 - 33429.3i) q^{73} +45127.4 q^{75} +42705.4 q^{77} +(-32155.8 + 55695.5i) q^{79} +(4740.78 - 8211.28i) q^{81} +71525.2 q^{83} +(-30767.7 - 53291.2i) q^{85} -159365. q^{87} +(-23256.6 - 40281.7i) q^{89} +(30651.0 + 53089.2i) q^{91} +(-33952.4 + 58807.3i) q^{93} +(2333.64 + 56903.5i) q^{95} +(-45206.3 + 78299.6i) q^{97} +(38346.9 + 66418.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q - 11q^{3} + 11q^{5} + 336q^{7} - 902q^{9} + O(q^{10}) \) \( 18q - 11q^{3} + 11q^{5} + 336q^{7} - 902q^{9} - 320q^{11} + 227q^{13} - 101q^{15} + 179q^{17} - 868q^{19} - 5700q^{21} - 3425q^{23} - 7054q^{25} + 14722q^{27} - 7349q^{29} - 9960q^{31} - 2998q^{33} + 15888q^{35} + 26444q^{37} - 30246q^{39} - 7311q^{41} - 8283q^{43} - 62164q^{45} + 37603q^{47} + 124738q^{49} + 47227q^{51} - 20337q^{53} + 716q^{55} - 57555q^{57} - 74455q^{59} - 7569q^{61} - 52544q^{63} + 188998q^{65} - 26177q^{67} + 116282q^{69} - 53463q^{71} - 14103q^{73} + 120912q^{75} - 31960q^{77} + 31825q^{79} - 21137q^{81} + 82600q^{83} - 50787q^{85} - 339766q^{87} - 155197q^{89} - 2800q^{91} - 46460q^{93} + 49315q^{95} + 111241q^{97} - 193544q^{99} + O(q^{100}) \)

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
\(3\) 12.4311 21.5314i 0.797458 1.38124i −0.123809 0.992306i \(-0.539511\pi\)
0.921267 0.388932i \(-0.127156\pi\)
\(4\) 0 0
\(5\) −18.0963 + 31.3437i −0.323717 + 0.560694i −0.981252 0.192730i \(-0.938266\pi\)
0.657535 + 0.753424i \(0.271599\pi\)
\(6\) 0 0
\(7\) −208.885 −1.61125 −0.805624 0.592427i \(-0.798170\pi\)
−0.805624 + 0.592427i \(0.798170\pi\)
\(8\) 0 0
\(9\) −187.566 324.875i −0.771879 1.33693i
\(10\) 0 0
\(11\) −204.444 −0.509440 −0.254720 0.967015i \(-0.581983\pi\)
−0.254720 + 0.967015i \(0.581983\pi\)
\(12\) 0 0
\(13\) −146.736 254.155i −0.240813 0.417100i 0.720133 0.693836i \(-0.244081\pi\)
−0.960946 + 0.276736i \(0.910747\pi\)
\(14\) 0 0
\(15\) 449.916 + 779.277i 0.516301 + 0.894260i
\(16\) 0 0
\(17\) −850.109 + 1472.43i −0.713432 + 1.23570i 0.250130 + 0.968212i \(0.419527\pi\)
−0.963561 + 0.267488i \(0.913807\pi\)
\(18\) 0 0
\(19\) 1329.36 841.960i 0.844810 0.535066i
\(20\) 0 0
\(21\) −2596.68 + 4497.58i −1.28490 + 2.22552i
\(22\) 0 0
\(23\) −1768.22 3062.65i −0.696975 1.20720i −0.969510 0.245051i \(-0.921195\pi\)
0.272535 0.962146i \(-0.412138\pi\)
\(24\) 0 0
\(25\) 907.547 + 1571.92i 0.290415 + 0.503013i
\(26\) 0 0
\(27\) −3285.13 −0.867247
\(28\) 0 0
\(29\) −3204.96 5551.15i −0.707664 1.22571i −0.965722 0.259580i \(-0.916416\pi\)
0.258058 0.966130i \(-0.416918\pi\)
\(30\) 0 0
\(31\) −2731.24 −0.510452 −0.255226 0.966881i \(-0.582150\pi\)
−0.255226 + 0.966881i \(0.582150\pi\)
\(32\) 0 0
\(33\) −2541.47 + 4401.96i −0.406257 + 0.703658i
\(34\) 0 0
\(35\) 3780.05 6547.24i 0.521588 0.903417i
\(36\) 0 0
\(37\) −5427.82 −0.651811 −0.325905 0.945402i \(-0.605669\pi\)
−0.325905 + 0.945402i \(0.605669\pi\)
\(38\) 0 0
\(39\) −7296.40 −0.768152
\(40\) 0 0
\(41\) −3692.75 + 6396.03i −0.343076 + 0.594225i −0.985002 0.172541i \(-0.944802\pi\)
0.641926 + 0.766766i \(0.278135\pi\)
\(42\) 0 0
\(43\) 7870.13 13631.5i 0.649099 1.12427i −0.334240 0.942488i \(-0.608480\pi\)
0.983339 0.181784i \(-0.0581871\pi\)
\(44\) 0 0
\(45\) 13577.1 0.999480
\(46\) 0 0
\(47\) 9723.97 + 16842.4i 0.642094 + 1.11214i 0.984964 + 0.172757i \(0.0552676\pi\)
−0.342870 + 0.939383i \(0.611399\pi\)
\(48\) 0 0
\(49\) 26826.0 1.59612
\(50\) 0 0
\(51\) 21135.7 + 36608.0i 1.13786 + 1.97084i
\(52\) 0 0
\(53\) −4290.51 7431.39i −0.209807 0.363396i 0.741847 0.670569i \(-0.233950\pi\)
−0.951654 + 0.307173i \(0.900617\pi\)
\(54\) 0 0
\(55\) 3699.69 6408.05i 0.164914 0.285640i
\(56\) 0 0
\(57\) −1603.08 39089.5i −0.0653532 1.59358i
\(58\) 0 0
\(59\) 13969.1 24195.1i 0.522441 0.904894i −0.477218 0.878785i \(-0.658355\pi\)
0.999659 0.0261092i \(-0.00831175\pi\)
\(60\) 0 0
\(61\) −15366.2 26615.0i −0.528739 0.915803i −0.999438 0.0335090i \(-0.989332\pi\)
0.470700 0.882294i \(-0.344002\pi\)
\(62\) 0 0
\(63\) 39179.8 + 67861.5i 1.24369 + 2.15413i
\(64\) 0 0
\(65\) 10621.5 0.311820
\(66\) 0 0
\(67\) −24126.9 41788.9i −0.656619 1.13730i −0.981485 0.191538i \(-0.938652\pi\)
0.324866 0.945760i \(-0.394681\pi\)
\(68\) 0 0
\(69\) −87924.1 −2.22323
\(70\) 0 0
\(71\) −3430.92 + 5942.53i −0.0807727 + 0.139902i −0.903582 0.428415i \(-0.859072\pi\)
0.822809 + 0.568317i \(0.192405\pi\)
\(72\) 0 0
\(73\) 19300.4 33429.3i 0.423897 0.734210i −0.572420 0.819961i \(-0.693995\pi\)
0.996317 + 0.0857501i \(0.0273287\pi\)
\(74\) 0 0
\(75\) 45127.4 0.926375
\(76\) 0 0
\(77\) 42705.4 0.820834
\(78\) 0 0
\(79\) −32155.8 + 55695.5i −0.579684 + 1.00404i 0.415831 + 0.909442i \(0.363491\pi\)
−0.995515 + 0.0946008i \(0.969843\pi\)
\(80\) 0 0
\(81\) 4740.78 8211.28i 0.0802856 0.139059i
\(82\) 0 0
\(83\) 71525.2 1.13963 0.569815 0.821773i \(-0.307015\pi\)
0.569815 + 0.821773i \(0.307015\pi\)
\(84\) 0 0
\(85\) −30767.7 53291.2i −0.461900 0.800034i
\(86\) 0 0
\(87\) −159365. −2.25733
\(88\) 0 0
\(89\) −23256.6 40281.7i −0.311223 0.539054i 0.667404 0.744696i \(-0.267405\pi\)
−0.978627 + 0.205641i \(0.934072\pi\)
\(90\) 0 0
\(91\) 30651.0 + 53089.2i 0.388009 + 0.672051i
\(92\) 0 0
\(93\) −33952.4 + 58807.3i −0.407064 + 0.705056i
\(94\) 0 0
\(95\) 2333.64 + 56903.5i 0.0265292 + 0.646890i
\(96\) 0 0
\(97\) −45206.3 + 78299.6i −0.487831 + 0.844949i −0.999902 0.0139945i \(-0.995545\pi\)
0.512071 + 0.858943i \(0.328879\pi\)
\(98\) 0 0
\(99\) 38346.9 + 66418.7i 0.393226 + 0.681087i
\(100\) 0 0
\(101\) 73036.4 + 126503.i 0.712420 + 1.23395i 0.963946 + 0.266097i \(0.0857340\pi\)
−0.251527 + 0.967850i \(0.580933\pi\)
\(102\) 0 0
\(103\) −85248.6 −0.791761 −0.395880 0.918302i \(-0.629561\pi\)
−0.395880 + 0.918302i \(0.629561\pi\)
\(104\) 0 0
\(105\) −93980.7 162779.i −0.831889 1.44087i
\(106\) 0 0
\(107\) −28226.4 −0.238339 −0.119170 0.992874i \(-0.538023\pi\)
−0.119170 + 0.992874i \(0.538023\pi\)
\(108\) 0 0
\(109\) 109018. 188825.i 0.878888 1.52228i 0.0263250 0.999653i \(-0.491620\pi\)
0.852563 0.522625i \(-0.175047\pi\)
\(110\) 0 0
\(111\) −67474.0 + 116868.i −0.519792 + 0.900305i
\(112\) 0 0
\(113\) −174546. −1.28592 −0.642958 0.765901i \(-0.722293\pi\)
−0.642958 + 0.765901i \(0.722293\pi\)
\(114\) 0 0
\(115\) 127993. 0.902490
\(116\) 0 0
\(117\) −55045.6 + 95341.8i −0.371756 + 0.643901i
\(118\) 0 0
\(119\) 177575. 307569.i 1.14952 1.99102i
\(120\) 0 0
\(121\) −119254. −0.740471
\(122\) 0 0
\(123\) 91810.2 + 159020.i 0.547177 + 0.947739i
\(124\) 0 0
\(125\) −178795. −1.02348
\(126\) 0 0
\(127\) −71846.8 124442.i −0.395274 0.684634i 0.597862 0.801599i \(-0.296017\pi\)
−0.993136 + 0.116965i \(0.962684\pi\)
\(128\) 0 0
\(129\) −195669. 338909.i −1.03526 1.79312i
\(130\) 0 0
\(131\) 2867.13 4966.01i 0.0145972 0.0252830i −0.858635 0.512588i \(-0.828687\pi\)
0.873232 + 0.487305i \(0.162020\pi\)
\(132\) 0 0
\(133\) −277684. + 175873.i −1.36120 + 0.862125i
\(134\) 0 0
\(135\) 59448.7 102968.i 0.280742 0.486260i
\(136\) 0 0
\(137\) 150187. + 260131.i 0.683645 + 1.18411i 0.973861 + 0.227146i \(0.0729394\pi\)
−0.290216 + 0.956961i \(0.593727\pi\)
\(138\) 0 0
\(139\) 218624. + 378668.i 0.959757 + 1.66235i 0.723087 + 0.690757i \(0.242723\pi\)
0.236670 + 0.971590i \(0.423944\pi\)
\(140\) 0 0
\(141\) 483520. 2.04817
\(142\) 0 0
\(143\) 29999.4 + 51960.5i 0.122680 + 0.212487i
\(144\) 0 0
\(145\) 231992. 0.916331
\(146\) 0 0
\(147\) 333478. 577600.i 1.27284 2.20462i
\(148\) 0 0
\(149\) 4540.46 7864.31i 0.0167546 0.0290198i −0.857527 0.514440i \(-0.828000\pi\)
0.874281 + 0.485420i \(0.161333\pi\)
\(150\) 0 0
\(151\) 43328.1 0.154642 0.0773209 0.997006i \(-0.475363\pi\)
0.0773209 + 0.997006i \(0.475363\pi\)
\(152\) 0 0
\(153\) 637808. 2.20273
\(154\) 0 0
\(155\) 49425.3 85607.2i 0.165242 0.286208i
\(156\) 0 0
\(157\) −50402.1 + 87299.0i −0.163192 + 0.282657i −0.936012 0.351968i \(-0.885512\pi\)
0.772820 + 0.634626i \(0.218846\pi\)
\(158\) 0 0
\(159\) −213344. −0.669248
\(160\) 0 0
\(161\) 369355. + 639742.i 1.12300 + 1.94509i
\(162\) 0 0
\(163\) −315707. −0.930712 −0.465356 0.885124i \(-0.654074\pi\)
−0.465356 + 0.885124i \(0.654074\pi\)
\(164\) 0 0
\(165\) −91982.7 159319.i −0.263024 0.455572i
\(166\) 0 0
\(167\) 280911. + 486551.i 0.779430 + 1.35001i 0.932271 + 0.361761i \(0.117824\pi\)
−0.152841 + 0.988251i \(0.548842\pi\)
\(168\) 0 0
\(169\) 142583. 246962.i 0.384019 0.665140i
\(170\) 0 0
\(171\) −522875. 273952.i −1.36744 0.716448i
\(172\) 0 0
\(173\) −323128. + 559674.i −0.820842 + 1.42174i 0.0842143 + 0.996448i \(0.473162\pi\)
−0.905056 + 0.425292i \(0.860171\pi\)
\(174\) 0 0
\(175\) −189573. 328350.i −0.467930 0.810479i
\(176\) 0 0
\(177\) −347303. 601546.i −0.833249 1.44323i
\(178\) 0 0
\(179\) 391686. 0.913704 0.456852 0.889543i \(-0.348977\pi\)
0.456852 + 0.889543i \(0.348977\pi\)
\(180\) 0 0
\(181\) −356595. 617641.i −0.809057 1.40133i −0.913518 0.406798i \(-0.866645\pi\)
0.104461 0.994529i \(-0.466688\pi\)
\(182\) 0 0
\(183\) −764076. −1.68659
\(184\) 0 0
\(185\) 98223.6 170128.i 0.211002 0.365466i
\(186\) 0 0
\(187\) 173800. 301030.i 0.363451 0.629515i
\(188\) 0 0
\(189\) 686214. 1.39735
\(190\) 0 0
\(191\) 73696.8 0.146172 0.0730862 0.997326i \(-0.476715\pi\)
0.0730862 + 0.997326i \(0.476715\pi\)
\(192\) 0 0
\(193\) −281706. + 487929.i −0.544381 + 0.942896i 0.454264 + 0.890867i \(0.349902\pi\)
−0.998646 + 0.0520289i \(0.983431\pi\)
\(194\) 0 0
\(195\) 132038. 228696.i 0.248664 0.430698i
\(196\) 0 0
\(197\) 227957. 0.418491 0.209246 0.977863i \(-0.432899\pi\)
0.209246 + 0.977863i \(0.432899\pi\)
\(198\) 0 0
\(199\) −305231. 528676.i −0.546382 0.946361i −0.998519 0.0544126i \(-0.982671\pi\)
0.452137 0.891949i \(-0.350662\pi\)
\(200\) 0 0
\(201\) −1.19970e6 −2.09451
\(202\) 0 0
\(203\) 669468. + 1.15955e6i 1.14022 + 1.97492i
\(204\) 0 0
\(205\) −133650. 231489.i −0.222119 0.384721i
\(206\) 0 0
\(207\) −663319. + 1.14890e6i −1.07596 + 1.86362i
\(208\) 0 0
\(209\) −271780. + 172134.i −0.430380 + 0.272584i
\(210\) 0 0
\(211\) −340640. + 590006.i −0.526732 + 0.912327i 0.472782 + 0.881179i \(0.343250\pi\)
−0.999515 + 0.0311480i \(0.990084\pi\)
\(212\) 0 0
\(213\) 85300.5 + 147745.i 0.128826 + 0.223133i
\(214\) 0 0
\(215\) 284841. + 493359.i 0.420248 + 0.727891i
\(216\) 0 0
\(217\) 570515. 0.822466
\(218\) 0 0
\(219\) −479853. 831129.i −0.676079 1.17100i
\(220\) 0 0
\(221\) 498968. 0.687214
\(222\) 0 0
\(223\) −464769. + 805003.i −0.625856 + 1.08402i 0.362518 + 0.931977i \(0.381917\pi\)
−0.988375 + 0.152038i \(0.951416\pi\)
\(224\) 0 0
\(225\) 340451. 589678.i 0.448330 0.776530i
\(226\) 0 0
\(227\) −836852. −1.07791 −0.538957 0.842333i \(-0.681181\pi\)
−0.538957 + 0.842333i \(0.681181\pi\)
\(228\) 0 0
\(229\) −43953.2 −0.0553862 −0.0276931 0.999616i \(-0.508816\pi\)
−0.0276931 + 0.999616i \(0.508816\pi\)
\(230\) 0 0
\(231\) 530876. 919505.i 0.654581 1.13377i
\(232\) 0 0
\(233\) 19649.6 34034.0i 0.0237117 0.0410699i −0.853926 0.520394i \(-0.825785\pi\)
0.877638 + 0.479324i \(0.159118\pi\)
\(234\) 0 0
\(235\) −703872. −0.831427
\(236\) 0 0
\(237\) 799466. + 1.38472e6i 0.924548 + 1.60136i
\(238\) 0 0
\(239\) 1.14239e6 1.29365 0.646827 0.762637i \(-0.276096\pi\)
0.646827 + 0.762637i \(0.276096\pi\)
\(240\) 0 0
\(241\) −142528. 246866.i −0.158073 0.273790i 0.776101 0.630609i \(-0.217195\pi\)
−0.934174 + 0.356819i \(0.883861\pi\)
\(242\) 0 0
\(243\) −517010. 895487.i −0.561672 0.972845i
\(244\) 0 0
\(245\) −485452. + 840827.i −0.516691 + 0.894935i
\(246\) 0 0
\(247\) −409054. 214317.i −0.426617 0.223519i
\(248\) 0 0
\(249\) 889139. 1.54003e6i 0.908806 1.57410i
\(250\) 0 0
\(251\) −787154. 1.36339e6i −0.788634 1.36595i −0.926804 0.375546i \(-0.877455\pi\)
0.138169 0.990409i \(-0.455878\pi\)
\(252\) 0 0
\(253\) 361503. + 626141.i 0.355067 + 0.614994i
\(254\) 0 0
\(255\) −1.52991e6 −1.47338
\(256\) 0 0
\(257\) 172908. + 299486.i 0.163299 + 0.282842i 0.936050 0.351867i \(-0.114453\pi\)
−0.772751 + 0.634709i \(0.781120\pi\)
\(258\) 0 0
\(259\) 1.13379e6 1.05023
\(260\) 0 0
\(261\) −1.20228e6 + 2.08242e6i −1.09246 + 1.89220i
\(262\) 0 0
\(263\) 494023. 855673.i 0.440411 0.762814i −0.557309 0.830305i \(-0.688166\pi\)
0.997720 + 0.0674913i \(0.0214995\pi\)
\(264\) 0 0
\(265\) 310570. 0.271672
\(266\) 0 0
\(267\) −1.15643e6 −0.992750
\(268\) 0 0
\(269\) 418483. 724833.i 0.352612 0.610741i −0.634094 0.773256i \(-0.718627\pi\)
0.986706 + 0.162514i \(0.0519603\pi\)
\(270\) 0 0
\(271\) 1.04254e6 1.80574e6i 0.862325 1.49359i −0.00735345 0.999973i \(-0.502341\pi\)
0.869679 0.493618i \(-0.164326\pi\)
\(272\) 0 0
\(273\) 1.52411e6 1.23768
\(274\) 0 0
\(275\) −185543. 321369.i −0.147949 0.256255i
\(276\) 0 0
\(277\) −654742. −0.512709 −0.256355 0.966583i \(-0.582521\pi\)
−0.256355 + 0.966583i \(0.582521\pi\)
\(278\) 0 0
\(279\) 512289. + 887310.i 0.394007 + 0.682441i
\(280\) 0 0
\(281\) 432664. + 749397.i 0.326878 + 0.566169i 0.981891 0.189449i \(-0.0606702\pi\)
−0.655013 + 0.755618i \(0.727337\pi\)
\(282\) 0 0
\(283\) 840551. 1.45588e6i 0.623876 1.08058i −0.364882 0.931054i \(-0.618891\pi\)
0.988757 0.149530i \(-0.0477761\pi\)
\(284\) 0 0
\(285\) 1.25422e6 + 657129.i 0.914665 + 0.479224i
\(286\) 0 0
\(287\) 771360. 1.33604e6i 0.552780 0.957444i
\(288\) 0 0
\(289\) −735443. 1.27382e6i −0.517970 0.897150i
\(290\) 0 0
\(291\) 1.12393e6 + 1.94671e6i 0.778050 + 1.34762i
\(292\) 0 0
\(293\) 495850. 0.337428 0.168714 0.985665i \(-0.446039\pi\)
0.168714 + 0.985665i \(0.446039\pi\)
\(294\) 0 0
\(295\) 505577. + 875685.i 0.338246 + 0.585859i
\(296\) 0 0
\(297\) 671625. 0.441810
\(298\) 0 0
\(299\) −518925. + 898805.i −0.335681 + 0.581416i
\(300\) 0 0
\(301\) −1.64395e6 + 2.84741e6i −1.04586 + 1.81148i
\(302\) 0 0
\(303\) 3.63170e6 2.27250
\(304\) 0 0
\(305\) 1.11228e6 0.684647
\(306\) 0 0
\(307\) 1.22956e6 2.12967e6i 0.744569 1.28963i −0.205826 0.978589i \(-0.565988\pi\)
0.950396 0.311043i \(-0.100678\pi\)
\(308\) 0 0
\(309\) −1.05974e6 + 1.83552e6i −0.631396 + 1.09361i
\(310\) 0 0
\(311\) 1.82000e6 1.06702 0.533508 0.845795i \(-0.320873\pi\)
0.533508 + 0.845795i \(0.320873\pi\)
\(312\) 0 0
\(313\) −847350. 1.46765e6i −0.488880 0.846765i 0.511038 0.859558i \(-0.329261\pi\)
−0.999918 + 0.0127931i \(0.995928\pi\)
\(314\) 0 0
\(315\) −2.83604e6 −1.61041
\(316\) 0 0
\(317\) −785090. 1.35982e6i −0.438805 0.760033i 0.558793 0.829307i \(-0.311265\pi\)
−0.997598 + 0.0692749i \(0.977931\pi\)
\(318\) 0 0
\(319\) 655235. + 1.13490e6i 0.360512 + 0.624426i
\(320\) 0 0
\(321\) −350886. + 607753.i −0.190066 + 0.329203i
\(322\) 0 0
\(323\) 109627. + 2.67315e6i 0.0584671 + 1.42567i
\(324\) 0 0
\(325\) 266340. 461315.i 0.139871 0.242264i
\(326\) 0 0
\(327\) −2.71045e6 4.69463e6i −1.40175 2.42791i
\(328\) 0 0
\(329\) −2.03119e6 3.51813e6i −1.03457 1.79193i
\(330\) 0 0
\(331\) −1.47267e6 −0.738816 −0.369408 0.929267i \(-0.620440\pi\)
−0.369408 + 0.929267i \(0.620440\pi\)
\(332\) 0 0
\(333\) 1.01808e6 + 1.76336e6i 0.503119 + 0.871427i
\(334\) 0 0
\(335\) 1.74643e6 0.850235
\(336\) 0 0
\(337\) −1.04852e6 + 1.81609e6i −0.502922 + 0.871087i 0.497072 + 0.867709i \(0.334409\pi\)
−0.999994 + 0.00337788i \(0.998925\pi\)
\(338\) 0 0
\(339\) −2.16980e6 + 3.75820e6i −1.02546 + 1.77616i
\(340\) 0 0
\(341\) 558386. 0.260045
\(342\) 0 0
\(343\) −2.09282e6 −0.960498
\(344\) 0 0
\(345\) 1.59110e6 2.75587e6i 0.719698 1.24655i
\(346\) 0 0
\(347\) −1.08983e6 + 1.88764e6i −0.485887 + 0.841582i −0.999868 0.0162199i \(-0.994837\pi\)
0.513981 + 0.857802i \(0.328170\pi\)
\(348\) 0 0
\(349\) 1.80723e6 0.794238 0.397119 0.917767i \(-0.370010\pi\)
0.397119 + 0.917767i \(0.370010\pi\)
\(350\) 0 0
\(351\) 482047. + 834931.i 0.208844 + 0.361728i
\(352\) 0 0
\(353\) −2.11807e6 −0.904696 −0.452348 0.891842i \(-0.649414\pi\)
−0.452348 + 0.891842i \(0.649414\pi\)
\(354\) 0 0
\(355\) −124174. 215076.i −0.0522950 0.0905775i
\(356\) 0 0
\(357\) −4.41492e6 7.64687e6i −1.83338 3.17551i
\(358\) 0 0
\(359\) −1.04610e6 + 1.81190e6i −0.428388 + 0.741990i −0.996730 0.0808022i \(-0.974252\pi\)
0.568342 + 0.822793i \(0.307585\pi\)
\(360\) 0 0
\(361\) 1.05830e6 2.23854e6i 0.427408 0.904059i
\(362\) 0 0
\(363\) −1.48246e6 + 2.56769e6i −0.590494 + 1.02277i
\(364\) 0 0
\(365\) 698534. + 1.20990e6i 0.274445 + 0.475352i
\(366\) 0 0
\(367\) −1.45084e6 2.51293e6i −0.562282 0.973901i −0.997297 0.0734776i \(-0.976590\pi\)
0.435015 0.900423i \(-0.356743\pi\)
\(368\) 0 0
\(369\) 2.77054e6 1.05925
\(370\) 0 0
\(371\) 896224. + 1.55231e6i 0.338051 + 0.585521i
\(372\) 0 0
\(373\) −3.15657e6 −1.17474 −0.587372 0.809317i \(-0.699837\pi\)
−0.587372 + 0.809317i \(0.699837\pi\)
\(374\) 0 0
\(375\) −2.22263e6 + 3.84970e6i −0.816184 + 1.41367i
\(376\) 0 0
\(377\) −940567. + 1.62911e6i −0.340829 + 0.590333i
\(378\) 0 0
\(379\) 3.95334e6 1.41373 0.706864 0.707350i \(-0.250109\pi\)
0.706864 + 0.707350i \(0.250109\pi\)
\(380\) 0 0
\(381\) −3.57255e6 −1.26086
\(382\) 0 0
\(383\) 1.93528e6 3.35201e6i 0.674136 1.16764i −0.302584 0.953123i \(-0.597849\pi\)
0.976720 0.214516i \(-0.0688174\pi\)
\(384\) 0 0
\(385\) −772810. + 1.33855e6i −0.265718 + 0.460237i
\(386\) 0 0
\(387\) −5.90469e6 −2.00410
\(388\) 0 0
\(389\) 1.11143e6 + 1.92505e6i 0.372399 + 0.645013i 0.989934 0.141530i \(-0.0452021\pi\)
−0.617535 + 0.786543i \(0.711869\pi\)
\(390\) 0 0
\(391\) 6.01273e6 1.98898
\(392\) 0 0
\(393\) −71283.3 123466.i −0.0232813 0.0403243i
\(394\) 0 0
\(395\) −1.16380e6 2.01577e6i −0.375307 0.650051i
\(396\) 0 0
\(397\) −207721. + 359784.i −0.0661462 + 0.114569i −0.897202 0.441621i \(-0.854404\pi\)
0.831056 + 0.556189i \(0.187737\pi\)
\(398\) 0 0
\(399\) 334859. + 8.16521e6i 0.105300 + 2.56765i
\(400\) 0 0
\(401\) 1.50770e6 2.61141e6i 0.468224 0.810988i −0.531116 0.847299i \(-0.678227\pi\)
0.999341 + 0.0363107i \(0.0115606\pi\)
\(402\) 0 0
\(403\) 400772. + 694157.i 0.122923 + 0.212910i
\(404\) 0 0
\(405\) 171581. + 297188.i 0.0519796 + 0.0900313i
\(406\) 0 0
\(407\) 1.10969e6 0.332058
\(408\) 0 0
\(409\) −1.89456e6 3.28148e6i −0.560016 0.969976i −0.997494 0.0707474i \(-0.977462\pi\)
0.437478 0.899229i \(-0.355872\pi\)
\(410\) 0 0
\(411\) 7.46797e6 2.18071
\(412\) 0 0
\(413\) −2.91793e6 + 5.05400e6i −0.841782 + 1.45801i
\(414\) 0 0
\(415\) −1.29434e6 + 2.24187e6i −0.368917 + 0.638983i
\(416\) 0 0
\(417\) 1.08710e7 3.06146
\(418\) 0 0
\(419\) 359202. 0.0999549 0.0499774 0.998750i \(-0.484085\pi\)
0.0499774 + 0.998750i \(0.484085\pi\)
\(420\) 0 0
\(421\) −272896. + 472669.i −0.0750398 + 0.129973i −0.901104 0.433604i \(-0.857242\pi\)
0.826064 + 0.563577i \(0.190575\pi\)
\(422\) 0 0
\(423\) 3.64778e6 6.31814e6i 0.991238 1.71687i
\(424\) 0 0
\(425\) −3.08606e6 −0.828765
\(426\) 0 0
\(427\) 3.20977e6 + 5.55948e6i 0.851930 + 1.47559i
\(428\) 0 0
\(429\) 1.49171e6 0.391327
\(430\) 0 0
\(431\) −1.14797e6 1.98834e6i −0.297671 0.515581i 0.677932 0.735125i \(-0.262876\pi\)
−0.975603 + 0.219544i \(0.929543\pi\)
\(432\) 0 0
\(433\) −2.52128e6 4.36698e6i −0.646251 1.11934i −0.984011 0.178107i \(-0.943003\pi\)
0.337760 0.941232i \(-0.390331\pi\)
\(434\) 0 0
\(435\) 2.88392e6 4.99510e6i 0.730735 1.26567i
\(436\) 0 0
\(437\) −4.92924e6 2.58260e6i −1.23474 0.646924i
\(438\) 0 0
\(439\) −3.91644e6 + 6.78347e6i −0.969907 + 1.67993i −0.274097 + 0.961702i \(0.588379\pi\)
−0.695810 + 0.718226i \(0.744955\pi\)
\(440\) 0 0
\(441\) −5.03166e6 8.71509e6i −1.23201 2.13391i
\(442\) 0 0
\(443\) −2.75654e6 4.77446e6i −0.667351 1.15589i −0.978642 0.205571i \(-0.934095\pi\)
0.311291 0.950315i \(-0.399239\pi\)
\(444\) 0 0
\(445\) 1.68344e6 0.402993
\(446\) 0 0
\(447\) −112886. 195525.i −0.0267222 0.0462842i
\(448\) 0 0
\(449\) 5.99055e6 1.40233 0.701166 0.712998i \(-0.252663\pi\)
0.701166 + 0.712998i \(0.252663\pi\)
\(450\) 0 0
\(451\) 754961. 1.30763e6i 0.174777 0.302722i
\(452\) 0 0
\(453\) 538617. 932913.i 0.123320 0.213597i
\(454\) 0 0
\(455\) −2.21868e6 −0.502420
\(456\) 0 0
\(457\) 289587. 0.0648617 0.0324308 0.999474i \(-0.489675\pi\)
0.0324308 + 0.999474i \(0.489675\pi\)
\(458\) 0 0
\(459\) 2.79272e6 4.83713e6i 0.618721 1.07166i
\(460\) 0 0
\(461\) −1.79574e6 + 3.11031e6i −0.393542 + 0.681635i −0.992914 0.118836i \(-0.962084\pi\)
0.599372 + 0.800471i \(0.295417\pi\)
\(462\) 0 0
\(463\) 108518. 0.0235260 0.0117630 0.999931i \(-0.496256\pi\)
0.0117630 + 0.999931i \(0.496256\pi\)
\(464\) 0 0
\(465\) −1.22883e6 2.12839e6i −0.263547 0.456477i
\(466\) 0 0
\(467\) −4.47855e6 −0.950267 −0.475133 0.879914i \(-0.657600\pi\)
−0.475133 + 0.879914i \(0.657600\pi\)
\(468\) 0 0
\(469\) 5.03974e6 + 8.72909e6i 1.05798 + 1.83247i
\(470\) 0 0
\(471\) 1.25311e6 + 2.17045e6i 0.260278 + 0.450815i
\(472\) 0 0
\(473\) −1.60900e6 + 2.78687e6i −0.330677 + 0.572749i
\(474\) 0 0
\(475\) 2.52995e6 + 1.32553e6i 0.514491 + 0.269560i
\(476\) 0 0
\(477\) −1.60951e6 + 2.78776e6i −0.323891 + 0.560995i
\(478\) 0 0
\(479\) −3.21830e6 5.57425e6i −0.640896 1.11006i −0.985233 0.171218i \(-0.945230\pi\)
0.344337 0.938846i \(-0.388104\pi\)
\(480\) 0 0
\(481\) 796459. + 1.37951e6i 0.156964 + 0.271870i
\(482\) 0 0
\(483\) 1.83660e7 3.58218
\(484\) 0 0
\(485\) −1.63614e6 2.83387e6i −0.315838 0.547048i
\(486\) 0 0
\(487\) −983792. −0.187967 −0.0939833 0.995574i \(-0.529960\pi\)
−0.0939833 + 0.995574i \(0.529960\pi\)
\(488\) 0 0
\(489\) −3.92460e6 + 6.79761e6i −0.742204 + 1.28553i
\(490\) 0 0
\(491\) 3.28089e6 5.68267e6i 0.614170 1.06377i −0.376360 0.926474i \(-0.622824\pi\)
0.990530 0.137300i \(-0.0438423\pi\)
\(492\) 0 0
\(493\) 1.08983e7 2.01948
\(494\) 0 0
\(495\) −2.77575e6 −0.509175
\(496\) 0 0
\(497\) 716668. 1.24131e6i 0.130145 0.225418i
\(498\) 0 0
\(499\) −2.23268e6 + 3.86711e6i −0.401398 + 0.695241i −0.993895 0.110331i \(-0.964809\pi\)
0.592497 + 0.805572i \(0.298142\pi\)
\(500\) 0 0
\(501\) 1.39682e7 2.48625
\(502\) 0 0
\(503\) −1.44875e6 2.50931e6i −0.255313 0.442215i 0.709667 0.704537i \(-0.248845\pi\)
−0.964981 + 0.262322i \(0.915512\pi\)
\(504\) 0 0
\(505\) −5.28676e6 −0.922489
\(506\) 0 0
\(507\) −3.54495e6 6.14003e6i −0.612477 1.06084i
\(508\) 0 0
\(509\) 3.19919e6 + 5.54116e6i 0.547325 + 0.947995i 0.998457 + 0.0555374i \(0.0176872\pi\)
−0.451131 + 0.892458i \(0.648979\pi\)
\(510\) 0 0
\(511\) −4.03157e6 + 6.98289e6i −0.683003 + 1.18300i
\(512\) 0 0
\(513\) −4.36712e6 + 2.76595e6i −0.732659 + 0.464035i
\(514\) 0 0
\(515\) 1.54269e6 2.67201e6i 0.256306 0.443936i
\(516\) 0 0
\(517\) −1.98801e6 3.44333e6i −0.327109 0.566569i
\(518\) 0 0
\(519\) 8.03370e6 + 1.39148e7i 1.30917 + 2.26756i
\(520\) 0 0
\(521\) −1.13178e7 −1.82671 −0.913353 0.407168i \(-0.866516\pi\)
−0.913353 + 0.407168i \(0.866516\pi\)
\(522\) 0 0
\(523\) −214962. 372326.i −0.0343643 0.0595208i 0.848332 0.529465i \(-0.177607\pi\)
−0.882696 + 0.469944i \(0.844274\pi\)
\(524\) 0 0
\(525\) −9.42643e6 −1.49262
\(526\) 0 0
\(527\) 2.32185e6 4.02156e6i 0.364173 0.630766i
\(528\) 0 0
\(529\) −3.03505e6 + 5.25687e6i −0.471549 + 0.816747i
\(530\) 0 0
\(531\) −1.04805e7 −1.61304
\(532\) 0 0
\(533\) 2.16744e6 0.330468
\(534\) 0 0
\(535\) 510794. 884721.i 0.0771545 0.133635i
\(536\) 0 0
\(537\) 4.86910e6 8.43354e6i 0.728641 1.26204i
\(538\) 0 0
\(539\) −5.48442e6 −0.813128
\(540\) 0 0
\(541\) 4.05574e6 + 7.02475e6i 0.595768 + 1.03190i 0.993438 + 0.114372i \(0.0364855\pi\)
−0.397670 + 0.917529i \(0.630181\pi\)
\(542\) 0 0
\(543\) −1.77315e7 −2.58075
\(544\) 0 0
\(545\) 3.94566e6 + 6.83409e6i 0.569021 + 0.985574i
\(546\) 0 0
\(547\) −4.15311e6 7.19340e6i −0.593479 1.02794i −0.993760 0.111543i \(-0.964421\pi\)
0.400281 0.916393i \(-0.368913\pi\)
\(548\) 0 0
\(549\) −5.76436e6 + 9.98416e6i −0.816244 + 1.41378i
\(550\) 0 0
\(551\) −8.93439e6 4.68103e6i −1.25368 0.656845i
\(552\) 0 0
\(553\) 6.71687e6 1.16340e7i 0.934015 1.61776i
\(554\) 0 0
\(555\) −2.44206e6 4.22978e6i −0.336531 0.582888i
\(556\) 0 0
\(557\) −1.99228e6 3.45072e6i −0.272089 0.471272i 0.697307 0.716772i \(-0.254381\pi\)
−0.969397 + 0.245500i \(0.921048\pi\)
\(558\) 0 0
\(559\) −4.61934e6 −0.625245
\(560\) 0 0
\(561\) −4.32106e6 7.48430e6i −0.579673 1.00402i
\(562\) 0 0
\(563\) 6.11824e6 0.813496 0.406748 0.913540i \(-0.366663\pi\)
0.406748 + 0.913540i \(0.366663\pi\)
\(564\) 0 0
\(565\) 3.15863e6 5.47091e6i 0.416273 0.721005i
\(566\) 0 0
\(567\) −990279. + 1.71521e6i −0.129360 + 0.224058i
\(568\) 0 0
\(569\) 908888. 0.117687 0.0588436 0.998267i \(-0.481259\pi\)
0.0588436 + 0.998267i \(0.481259\pi\)
\(570\) 0 0
\(571\) 1.83881e6 0.236019 0.118010 0.993012i \(-0.462349\pi\)
0.118010 + 0.993012i \(0.462349\pi\)
\(572\) 0 0
\(573\) 916135. 1.58679e6i 0.116566 0.201899i
\(574\) 0 0
\(575\) 3.20949e6 5.55900e6i 0.404824 0.701176i
\(576\) 0 0
\(577\) 5.44901e6 0.681362 0.340681 0.940179i \(-0.389342\pi\)
0.340681 + 0.940179i \(0.389342\pi\)
\(578\) 0 0
\(579\) 7.00386e6 + 1.21310e7i 0.868242 + 1.50384i
\(580\) 0 0
\(581\) −1.49405e7 −1.83623
\(582\) 0 0
\(583\) 877170. + 1.51930e6i 0.106884 + 0.185128i
\(584\) 0 0
\(585\) −1.99225e6 3.45067e6i −0.240687 0.416883i
\(586\) 0 0
\(587\) −1.89239e6 + 3.27772e6i −0.226681 + 0.392623i −0.956823 0.290673i \(-0.906121\pi\)
0.730141 + 0.683296i \(0.239454\pi\)
\(588\) 0 0
\(589\) −3.63080e6 + 2.29959e6i −0.431235 + 0.273126i
\(590\) 0 0
\(591\) 2.83376e6 4.90822e6i 0.333729 0.578036i
\(592\) 0 0
\(593\) 5.72339e6 + 9.91320e6i 0.668369 + 1.15765i 0.978360 + 0.206910i \(0.0663408\pi\)
−0.309990 + 0.950740i \(0.600326\pi\)
\(594\) 0 0
\(595\) 6.42691e6 + 1.11317e7i 0.744235 + 1.28905i
\(596\) 0 0
\(597\) −1.51775e7 −1.74287
\(598\) 0 0
\(599\) −3.14807e6 5.45262e6i −0.358491 0.620924i 0.629218 0.777229i \(-0.283375\pi\)
−0.987709 + 0.156305i \(0.950042\pi\)
\(600\) 0 0
\(601\) −3.03647e6 −0.342913 −0.171456 0.985192i \(-0.554847\pi\)
−0.171456 + 0.985192i \(0.554847\pi\)
\(602\) 0 0
\(603\) −9.05078e6 + 1.56764e7i −1.01366 + 1.75571i
\(604\) 0 0
\(605\) 2.15805e6 3.73785e6i 0.239703 0.415177i
\(606\) 0 0
\(607\) −1.08106e7 −1.19091 −0.595454 0.803389i \(-0.703028\pi\)
−0.595454 + 0.803389i \(0.703028\pi\)
\(608\) 0 0
\(609\) 3.32890e7 3.63712
\(610\) 0 0
\(611\) 2.85372e6 4.94279e6i 0.309249 0.535635i
\(612\) 0 0
\(613\) 4.94957e6 8.57291e6i 0.532006 0.921461i −0.467296 0.884101i \(-0.654772\pi\)
0.999302 0.0373600i \(-0.0118948\pi\)
\(614\) 0 0
\(615\) −6.64570e6 −0.708522
\(616\) 0 0
\(617\) 973579. + 1.68629e6i 0.102958 + 0.178328i 0.912902 0.408179i \(-0.133836\pi\)
−0.809944 + 0.586507i \(0.800503\pi\)
\(618\) 0 0
\(619\) 3.48976e6 0.366074 0.183037 0.983106i \(-0.441407\pi\)
0.183037 + 0.983106i \(0.441407\pi\)
\(620\) 0 0
\(621\) 5.80884e6 + 1.00612e7i 0.604450 + 1.04694i
\(622\) 0 0
\(623\) 4.85797e6 + 8.41424e6i 0.501458 + 0.868550i
\(624\) 0 0
\(625\) 399448. 691864.i 0.0409034 0.0708468i
\(626\) 0 0
\(627\) 327740. + 7.99162e6i 0.0332936 + 0.811832i
\(628\) 0 0
\(629\) 4.61424e6 7.99210e6i 0.465022 0.805442i
\(630\) 0 0
\(631\) −4.65587e6 8.06421e6i −0.465509 0.806285i 0.533716 0.845664i \(-0.320795\pi\)
−0.999224 + 0.0393793i \(0.987462\pi\)
\(632\) 0 0
\(633\) 8.46910e6 + 1.46689e7i 0.840094 + 1.45509i
\(634\) 0 0
\(635\) 5.20065e6 0.511827
\(636\) 0 0
\(637\) −3.93635e6 6.81796e6i −0.384366 0.665741i
\(638\) 0 0
\(639\) 2.57410e6 0.249387
\(640\) 0 0
\(641\) 2.98479e6 5.16981e6i 0.286925 0.496969i −0.686149 0.727461i \(-0.740700\pi\)
0.973074 + 0.230492i \(0.0740336\pi\)
\(642\) 0 0
\(643\) 9.07253e6 1.57141e7i 0.865368 1.49886i −0.00131239 0.999999i \(-0.500418\pi\)
0.866681 0.498863i \(-0.166249\pi\)
\(644\) 0 0
\(645\) 1.41636e7 1.34052
\(646\) 0 0
\(647\) 1.03554e7 0.972537 0.486269 0.873809i \(-0.338358\pi\)
0.486269 + 0.873809i \(0.338358\pi\)
\(648\) 0 0
\(649\) −2.85589e6 + 4.94655e6i −0.266152 + 0.460989i
\(650\) 0 0
\(651\) 7.09215e6 1.22840e7i 0.655882 1.13602i
\(652\) 0 0
\(653\) 4.38119e6 0.402077 0.201038 0.979583i \(-0.435568\pi\)
0.201038 + 0.979583i \(0.435568\pi\)
\(654\) 0 0
\(655\) 103769. + 179733.i 0.00945069 + 0.0163691i
\(656\) 0 0
\(657\) −1.44805e7 −1.30879
\(658\) 0 0
\(659\) −7.34358e6 1.27195e7i −0.658710 1.14092i −0.980950 0.194262i \(-0.937769\pi\)
0.322239 0.946658i \(-0.395564\pi\)
\(660\) 0 0
\(661\) −1.90277e6 3.29569e6i −0.169388 0.293388i 0.768817 0.639469i \(-0.220846\pi\)
−0.938205 + 0.346081i \(0.887512\pi\)
\(662\) 0 0
\(663\) 6.20274e6 1.07435e7i 0.548024 0.949205i
\(664\) 0 0
\(665\) −487462. 1.18863e7i −0.0427452 1.04230i
\(666\) 0 0
\(667\) −1.13342e7 + 1.96313e7i −0.986449 + 1.70858i
\(668\) 0 0
\(669\) 1.15552e7 + 2.00142e7i 0.998188 + 1.72891i
\(670\) 0 0
\(671\) 3.14153e6 + 5.44128e6i 0.269361 + 0.466547i
\(672\) 0 0
\(673\) 2.15454e7 1.83365 0.916824 0.399291i \(-0.130744\pi\)
0.916824 + 0.399291i \(0.130744\pi\)
\(674\) 0 0
\(675\) −2.98141e6 5.16395e6i −0.251861 0.436237i
\(676\) 0 0
\(677\) −182950. −0.0153412 −0.00767061 0.999971i \(-0.502442\pi\)
−0.00767061 + 0.999971i \(0.502442\pi\)
\(678\) 0 0
\(679\) 9.44293e6 1.63556e7i 0.786017 1.36142i
\(680\) 0 0
\(681\) −1.04030e7 + 1.80186e7i −0.859591 + 1.48885i
\(682\) 0 0
\(683\) −1.90678e7 −1.56404 −0.782021 0.623252i \(-0.785811\pi\)
−0.782021 + 0.623252i \(0.785811\pi\)
\(684\) 0 0
\(685\) −1.08713e7 −0.885229
\(686\) 0 0
\(687\) −546388. + 946372.i −0.0441682 + 0.0765015i
\(688\) 0 0
\(689\) −1.25915e6 + 2.18091e6i −0.101048 + 0.175021i
\(690\) 0 0
\(691\) 1.57718e7 1.25657 0.628285 0.777983i \(-0.283757\pi\)
0.628285 + 0.777983i \(0.283757\pi\)
\(692\) 0 0
\(693\) −8.01009e6 1.38739e7i −0.633584 1.09740i
\(694\) 0 0
\(695\) −1.58252e7 −1.24276
\(696\) 0 0
\(697\) −6.27848e6 1.08746e7i −0.489522 0.847878i
\(698\) 0 0
\(699\) −488533. 846164.i −0.0378182 0.0655030i
\(700\) 0 0
\(701\) −8.89878e6 + 1.54131e7i −0.683967 + 1.18467i 0.289793 + 0.957089i \(0.406414\pi\)
−0.973760 + 0.227577i \(0.926920\pi\)
\(702\) 0 0
\(703\) −7.21554e6 + 4.57001e6i −0.550656 + 0.348762i
\(704\) 0 0
\(705\) −8.74993e6 + 1.51553e7i −0.663028 + 1.14840i
\(706\) 0 0
\(707\) −1.52562e7 2.64245e7i −1.14788 1.98819i
\(708\) 0 0
\(709\) −1.02786e6 1.78031e6i −0.0767924 0.133008i 0.825072 0.565028i \(-0.191135\pi\)
−0.901864 + 0.432019i \(0.857801\pi\)
\(710\) 0 0
\(711\) 2.41254e7 1.78978
\(712\) 0 0
\(713\) 4.82944e6 + 8.36483e6i 0.355773 + 0.616217i
\(714\) 0 0
\(715\) −2.17151e6 −0.158854
\(716\) 0 0
\(717\) 1.42012e7 2.45971e7i 1.03163 1.78684i
\(718\) 0 0
\(719\) 1.09362e7 1.89420e7i 0.788940 1.36648i −0.137676 0.990477i \(-0.543963\pi\)
0.926617 0.376007i \(-0.122703\pi\)
\(720\) 0 0
\(721\) 1.78072e7 1.27572
\(722\) 0 0
\(723\) −7.08714e6 −0.504226
\(724\) 0 0
\(725\) 5.81729e6 1.00758e7i 0.411032 0.711929i
\(726\) 0 0
\(727\) 1.17837e6 2.04099e6i 0.0826884 0.143221i −0.821715 0.569898i \(-0.806983\pi\)
0.904404 + 0.426677i \(0.140316\pi\)
\(728\) 0 0
\(729\) −2.34041e7 −1.63107
\(730\) 0 0
\(731\) 1.33809e7 + 2.31765e7i 0.926175 + 1.60418i
\(732\) 0 0
\(733\) 2.16077e7 1.48541 0.742707 0.669616i \(-0.233541\pi\)
0.742707 + 0.669616i \(0.233541\pi\)
\(734\) 0 0
\(735\) 1.20694e7 + 2.09049e7i 0.824079 + 1.42735i
\(736\) 0 0
\(737\) 4.93260e6 + 8.54351e6i 0.334508 + 0.579385i
\(738\) 0 0
\(739\) −2.23082e6 + 3.86389e6i −0.150263 + 0.260264i −0.931324 0.364191i \(-0.881345\pi\)
0.781061 + 0.624455i \(0.214679\pi\)
\(740\) 0 0
\(741\) −9.69955e6 + 6.14328e6i −0.648942 + 0.411012i
\(742\) 0 0
\(743\) −7.70913e6 + 1.33526e7i −0.512311 + 0.887348i 0.487587 + 0.873074i \(0.337877\pi\)
−0.999898 + 0.0142742i \(0.995456\pi\)
\(744\) 0 0
\(745\) 164331. + 284630.i 0.0108475 + 0.0187884i
\(746\) 0 0
\(747\) −1.34157e7 2.32367e7i −0.879655 1.52361i
\(748\) 0 0
\(749\) 5.89607e6 0.384024
\(750\) 0 0
\(751\) −1.64269e6 2.84522e6i −0.106281 0.184084i 0.807980 0.589210i \(-0.200561\pi\)
−0.914261 + 0.405126i \(0.867228\pi\)
\(752\) 0 0
\(753\) −3.91409e7 −2.51561
\(754\) 0 0
\(755\) −784079. + 1.35806e6i −0.0500602 + 0.0867068i
\(756\) 0 0
\(757\) −5.40092e6 + 9.35466e6i −0.342553 + 0.593319i −0.984906 0.173090i \(-0.944625\pi\)
0.642353 + 0.766409i \(0.277958\pi\)
\(758\) 0 0
\(759\) 1.79756e7 1.13260
\(760\) 0 0
\(761\) −9.38280e6 −0.587315 −0.293657 0.955911i \(-0.594872\pi\)
−0.293657 + 0.955911i \(0.594872\pi\)
\(762\) 0 0
\(763\) −2.27723e7 + 3.94428e7i −1.41611 + 2.45277i
\(764\) 0 0
\(765\) −1.15420e7 + 1.99913e7i −0.713061 + 1.23506i
\(766\) 0 0
\(767\) −8.19907e6 −0.503241
\(768\) 0 0
\(769\) 2.58311e6 + 4.47407e6i 0.157517 + 0.272827i 0.933973 0.357345i \(-0.116318\pi\)
−0.776456 + 0.630172i \(0.782985\pi\)
\(770\) 0 0
\(771\) 8.59780e6 0.520896
\(772\) 0 0
\(773\) 2.46904e6 + 4.27650e6i 0.148621 + 0.257419i 0.930718 0.365738i \(-0.119183\pi\)
−0.782097 + 0.623156i \(0.785850\pi\)
\(774\) 0 0
\(775\) −2.47873e6 4.29328e6i −0.148243 0.256764i
\(776\) 0 0
\(777\) 1.40943e7 2.44121e7i 0.837513 1.45062i
\(778\) 0 0
\(779\) 476204. + 1.16118e7i 0.0281157 + 0.685575i
\(780\) 0 0
\(781\) 701432. 1.21492e6i 0.0411489 0.0712719i
\(782\) 0 0
\(783\) 1.05287e7 + 1.82362e7i 0.613719 + 1.06299i
\(784\) 0 0
\(785\) −1.82419e6 3.15958e6i −0.105656 0.183002i
\(786\) 0 0
\(787\) −7.65272e6 −0.440432 −0.220216 0.975451i \(-0.570676\pi\)
−0.220216 + 0.975451i \(0.570676\pi\)
\(788\) 0 0
\(789\) −1.22825e7 2.12740e7i