Properties

Label 76.6.e.a.45.1
Level $76$
Weight $6$
Character 76.45
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 45.1
Root \(14.2764 - 24.7275i\) of defining polynomial
Character \(\chi\) \(=\) 76.45
Dual form 76.6.e.a.49.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-14.7764 - 25.5935i) q^{3} +(35.6401 + 61.7304i) q^{5} +252.315 q^{7} +(-315.186 + 545.918i) q^{9} +O(q^{10})\) \(q+(-14.7764 - 25.5935i) q^{3} +(35.6401 + 61.7304i) q^{5} +252.315 q^{7} +(-315.186 + 545.918i) q^{9} +88.0323 q^{11} +(307.862 - 533.232i) q^{13} +(1053.27 - 1824.31i) q^{15} +(285.543 + 494.575i) q^{17} +(361.524 - 1531.47i) q^{19} +(-3728.32 - 6457.64i) q^{21} +(-1214.28 + 2103.20i) q^{23} +(-977.931 + 1693.83i) q^{25} +11447.9 q^{27} +(1142.82 - 1979.43i) q^{29} +3684.20 q^{31} +(-1300.80 - 2253.06i) q^{33} +(8992.54 + 15575.5i) q^{35} +3064.28 q^{37} -18196.4 q^{39} +(-1246.89 - 2159.67i) q^{41} +(-2450.11 - 4243.71i) q^{43} -44933.0 q^{45} +(8786.51 - 15218.7i) q^{47} +46856.0 q^{49} +(8438.61 - 14616.1i) q^{51} +(-12713.9 + 22021.1i) q^{53} +(3137.48 + 5434.27i) q^{55} +(-44537.7 + 13377.0i) q^{57} +(-11756.9 - 20363.5i) q^{59} +(9886.00 - 17123.1i) q^{61} +(-79526.2 + 137743. i) q^{63} +43888.8 q^{65} +(-13694.3 + 23719.2i) q^{67} +71771.0 q^{69} +(-16750.0 - 29011.9i) q^{71} +(-8986.08 - 15564.3i) q^{73} +57801.3 q^{75} +22211.9 q^{77} +(41242.9 + 71434.8i) q^{79} +(-92569.6 - 160335. i) q^{81} +40274.4 q^{83} +(-20353.5 + 35253.4i) q^{85} -67547.4 q^{87} +(-27641.5 + 47876.5i) q^{89} +(77678.2 - 134543. i) q^{91} +(-54439.3 - 94291.7i) q^{93} +(107423. - 32264.7i) q^{95} +(13348.8 + 23120.7i) q^{97} +(-27746.6 + 48058.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q - 11q^{3} + 11q^{5} + 336q^{7} - 902q^{9} + O(q^{10}) \) \( 18q - 11q^{3} + 11q^{5} + 336q^{7} - 902q^{9} - 320q^{11} + 227q^{13} - 101q^{15} + 179q^{17} - 868q^{19} - 5700q^{21} - 3425q^{23} - 7054q^{25} + 14722q^{27} - 7349q^{29} - 9960q^{31} - 2998q^{33} + 15888q^{35} + 26444q^{37} - 30246q^{39} - 7311q^{41} - 8283q^{43} - 62164q^{45} + 37603q^{47} + 124738q^{49} + 47227q^{51} - 20337q^{53} + 716q^{55} - 57555q^{57} - 74455q^{59} - 7569q^{61} - 52544q^{63} + 188998q^{65} - 26177q^{67} + 116282q^{69} - 53463q^{71} - 14103q^{73} + 120912q^{75} - 31960q^{77} + 31825q^{79} - 21137q^{81} + 82600q^{83} - 50787q^{85} - 339766q^{87} - 155197q^{89} - 2800q^{91} - 46460q^{93} + 49315q^{95} + 111241q^{97} - 193544q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −14.7764 25.5935i −0.947909 1.64183i −0.749820 0.661642i \(-0.769860\pi\)
−0.198088 0.980184i \(-0.563473\pi\)
\(4\) 0 0
\(5\) 35.6401 + 61.7304i 0.637549 + 1.10427i 0.985969 + 0.166929i \(0.0533850\pi\)
−0.348420 + 0.937339i \(0.613282\pi\)
\(6\) 0 0
\(7\) 252.315 1.94625 0.973125 0.230279i \(-0.0739637\pi\)
0.973125 + 0.230279i \(0.0739637\pi\)
\(8\) 0 0
\(9\) −315.186 + 545.918i −1.29706 + 2.24658i
\(10\) 0 0
\(11\) 88.0323 0.219362 0.109681 0.993967i \(-0.465017\pi\)
0.109681 + 0.993967i \(0.465017\pi\)
\(12\) 0 0
\(13\) 307.862 533.232i 0.505239 0.875100i −0.494742 0.869040i \(-0.664738\pi\)
0.999982 0.00606030i \(-0.00192907\pi\)
\(14\) 0 0
\(15\) 1053.27 1824.31i 1.20868 2.09349i
\(16\) 0 0
\(17\) 285.543 + 494.575i 0.239634 + 0.415059i 0.960609 0.277902i \(-0.0896391\pi\)
−0.720975 + 0.692961i \(0.756306\pi\)
\(18\) 0 0
\(19\) 361.524 1531.47i 0.229748 0.973250i
\(20\) 0 0
\(21\) −3728.32 6457.64i −1.84487 3.19540i
\(22\) 0 0
\(23\) −1214.28 + 2103.20i −0.478630 + 0.829011i −0.999700 0.0245027i \(-0.992200\pi\)
0.521070 + 0.853514i \(0.325533\pi\)
\(24\) 0 0
\(25\) −977.931 + 1693.83i −0.312938 + 0.542024i
\(26\) 0 0
\(27\) 11447.9 3.02216
\(28\) 0 0
\(29\) 1142.82 1979.43i 0.252339 0.437064i −0.711830 0.702351i \(-0.752134\pi\)
0.964169 + 0.265288i \(0.0854669\pi\)
\(30\) 0 0
\(31\) 3684.20 0.688555 0.344278 0.938868i \(-0.388124\pi\)
0.344278 + 0.938868i \(0.388124\pi\)
\(32\) 0 0
\(33\) −1300.80 2253.06i −0.207935 0.360153i
\(34\) 0 0
\(35\) 8992.54 + 15575.5i 1.24083 + 2.14918i
\(36\) 0 0
\(37\) 3064.28 0.367980 0.183990 0.982928i \(-0.441099\pi\)
0.183990 + 0.982928i \(0.441099\pi\)
\(38\) 0 0
\(39\) −18196.4 −1.91568
\(40\) 0 0
\(41\) −1246.89 2159.67i −0.115842 0.200645i 0.802274 0.596956i \(-0.203623\pi\)
−0.918116 + 0.396311i \(0.870290\pi\)
\(42\) 0 0
\(43\) −2450.11 4243.71i −0.202075 0.350005i 0.747122 0.664687i \(-0.231435\pi\)
−0.949197 + 0.314682i \(0.898102\pi\)
\(44\) 0 0
\(45\) −44933.0 −3.30776
\(46\) 0 0
\(47\) 8786.51 15218.7i 0.580192 1.00492i −0.415264 0.909701i \(-0.636311\pi\)
0.995456 0.0952210i \(-0.0303558\pi\)
\(48\) 0 0
\(49\) 46856.0 2.78789
\(50\) 0 0
\(51\) 8438.61 14616.1i 0.454303 0.786876i
\(52\) 0 0
\(53\) −12713.9 + 22021.1i −0.621712 + 1.07684i 0.367455 + 0.930041i \(0.380229\pi\)
−0.989167 + 0.146795i \(0.953104\pi\)
\(54\) 0 0
\(55\) 3137.48 + 5434.27i 0.139854 + 0.242234i
\(56\) 0 0
\(57\) −44537.7 + 13377.0i −1.81569 + 0.545345i
\(58\) 0 0
\(59\) −11756.9 20363.5i −0.439706 0.761592i 0.557961 0.829867i \(-0.311584\pi\)
−0.997667 + 0.0682748i \(0.978251\pi\)
\(60\) 0 0
\(61\) 9886.00 17123.1i 0.340170 0.589192i −0.644294 0.764778i \(-0.722849\pi\)
0.984464 + 0.175586i \(0.0561820\pi\)
\(62\) 0 0
\(63\) −79526.2 + 137743.i −2.52440 + 4.37240i
\(64\) 0 0
\(65\) 43888.8 1.28846
\(66\) 0 0
\(67\) −13694.3 + 23719.2i −0.372694 + 0.645525i −0.989979 0.141214i \(-0.954899\pi\)
0.617285 + 0.786740i \(0.288233\pi\)
\(68\) 0 0
\(69\) 71771.0 1.81479
\(70\) 0 0
\(71\) −16750.0 29011.9i −0.394339 0.683014i 0.598678 0.800990i \(-0.295693\pi\)
−0.993017 + 0.117975i \(0.962360\pi\)
\(72\) 0 0
\(73\) −8986.08 15564.3i −0.197362 0.341841i 0.750310 0.661086i \(-0.229904\pi\)
−0.947672 + 0.319245i \(0.896571\pi\)
\(74\) 0 0
\(75\) 57801.3 1.18655
\(76\) 0 0
\(77\) 22211.9 0.426932
\(78\) 0 0
\(79\) 41242.9 + 71434.8i 0.743501 + 1.28778i 0.950892 + 0.309523i \(0.100169\pi\)
−0.207391 + 0.978258i \(0.566497\pi\)
\(80\) 0 0
\(81\) −92569.6 160335.i −1.56767 2.71529i
\(82\) 0 0
\(83\) 40274.4 0.641702 0.320851 0.947130i \(-0.396031\pi\)
0.320851 + 0.947130i \(0.396031\pi\)
\(84\) 0 0
\(85\) −20353.5 + 35253.4i −0.305557 + 0.529241i
\(86\) 0 0
\(87\) −67547.4 −0.956777
\(88\) 0 0
\(89\) −27641.5 + 47876.5i −0.369902 + 0.640689i −0.989550 0.144191i \(-0.953942\pi\)
0.619648 + 0.784880i \(0.287275\pi\)
\(90\) 0 0
\(91\) 77678.2 134543.i 0.983322 1.70316i
\(92\) 0 0
\(93\) −54439.3 94291.7i −0.652688 1.13049i
\(94\) 0 0
\(95\) 107423. 32264.7i 1.22120 0.366791i
\(96\) 0 0
\(97\) 13348.8 + 23120.7i 0.144049 + 0.249501i 0.929018 0.370035i \(-0.120654\pi\)
−0.784968 + 0.619536i \(0.787321\pi\)
\(98\) 0 0
\(99\) −27746.6 + 48058.4i −0.284525 + 0.492812i
\(100\) 0 0
\(101\) −60668.2 + 105080.i −0.591777 + 1.02499i 0.402216 + 0.915545i \(0.368240\pi\)
−0.993993 + 0.109443i \(0.965093\pi\)
\(102\) 0 0
\(103\) −123258. −1.14478 −0.572392 0.819980i \(-0.693985\pi\)
−0.572392 + 0.819980i \(0.693985\pi\)
\(104\) 0 0
\(105\) 265755. 460302.i 2.35239 4.07445i
\(106\) 0 0
\(107\) 225615. 1.90506 0.952529 0.304449i \(-0.0984722\pi\)
0.952529 + 0.304449i \(0.0984722\pi\)
\(108\) 0 0
\(109\) −25583.8 44312.5i −0.206253 0.357240i 0.744279 0.667869i \(-0.232793\pi\)
−0.950531 + 0.310629i \(0.899460\pi\)
\(110\) 0 0
\(111\) −45279.2 78425.8i −0.348812 0.604160i
\(112\) 0 0
\(113\) −113870. −0.838909 −0.419454 0.907776i \(-0.637779\pi\)
−0.419454 + 0.907776i \(0.637779\pi\)
\(114\) 0 0
\(115\) −173108. −1.22060
\(116\) 0 0
\(117\) 194067. + 336134.i 1.31065 + 2.27012i
\(118\) 0 0
\(119\) 72046.9 + 124789.i 0.466388 + 0.807808i
\(120\) 0 0
\(121\) −153301. −0.951881
\(122\) 0 0
\(123\) −36849.1 + 63824.5i −0.219616 + 0.380386i
\(124\) 0 0
\(125\) 83336.4 0.477045
\(126\) 0 0
\(127\) −23234.7 + 40243.6i −0.127828 + 0.221405i −0.922835 0.385196i \(-0.874134\pi\)
0.795007 + 0.606601i \(0.207467\pi\)
\(128\) 0 0
\(129\) −72407.6 + 125414.i −0.383098 + 0.663546i
\(130\) 0 0
\(131\) 142237. + 246361.i 0.724157 + 1.25428i 0.959320 + 0.282321i \(0.0911044\pi\)
−0.235163 + 0.971956i \(0.575562\pi\)
\(132\) 0 0
\(133\) 91217.9 386413.i 0.447148 1.89419i
\(134\) 0 0
\(135\) 408006. + 706687.i 1.92678 + 3.33728i
\(136\) 0 0
\(137\) −143955. + 249337.i −0.655277 + 1.13497i 0.326547 + 0.945181i \(0.394115\pi\)
−0.981824 + 0.189792i \(0.939219\pi\)
\(138\) 0 0
\(139\) 88821.1 153843.i 0.389923 0.675367i −0.602515 0.798107i \(-0.705835\pi\)
0.992439 + 0.122740i \(0.0391681\pi\)
\(140\) 0 0
\(141\) −519333. −2.19988
\(142\) 0 0
\(143\) 27101.8 46941.6i 0.110830 0.191963i
\(144\) 0 0
\(145\) 162921. 0.643514
\(146\) 0 0
\(147\) −692365. 1.19921e6i −2.64266 4.57723i
\(148\) 0 0
\(149\) −81129.1 140520.i −0.299372 0.518527i 0.676621 0.736332i \(-0.263444\pi\)
−0.975992 + 0.217805i \(0.930110\pi\)
\(150\) 0 0
\(151\) −449650. −1.60484 −0.802420 0.596760i \(-0.796455\pi\)
−0.802420 + 0.596760i \(0.796455\pi\)
\(152\) 0 0
\(153\) −359996. −1.24328
\(154\) 0 0
\(155\) 131305. + 227427.i 0.438988 + 0.760349i
\(156\) 0 0
\(157\) −27389.5 47440.1i −0.0886820 0.153602i 0.818272 0.574831i \(-0.194932\pi\)
−0.906954 + 0.421229i \(0.861599\pi\)
\(158\) 0 0
\(159\) 751464. 2.35730
\(160\) 0 0
\(161\) −306382. + 530669.i −0.931533 + 1.61346i
\(162\) 0 0
\(163\) 207755. 0.612467 0.306233 0.951956i \(-0.400931\pi\)
0.306233 + 0.951956i \(0.400931\pi\)
\(164\) 0 0
\(165\) 92721.5 160598.i 0.265137 0.459231i
\(166\) 0 0
\(167\) −136696. + 236765.i −0.379284 + 0.656940i −0.990958 0.134170i \(-0.957163\pi\)
0.611674 + 0.791110i \(0.290496\pi\)
\(168\) 0 0
\(169\) −3910.94 6773.94i −0.0105333 0.0182442i
\(170\) 0 0
\(171\) 722110. + 680060.i 1.88848 + 1.77851i
\(172\) 0 0
\(173\) −262508. 454677.i −0.666848 1.15501i −0.978781 0.204910i \(-0.934310\pi\)
0.311933 0.950104i \(-0.399024\pi\)
\(174\) 0 0
\(175\) −246747. + 427378.i −0.609055 + 1.05491i
\(176\) 0 0
\(177\) −347449. + 601800.i −0.833601 + 1.44384i
\(178\) 0 0
\(179\) −13590.9 −0.0317041 −0.0158520 0.999874i \(-0.505046\pi\)
−0.0158520 + 0.999874i \(0.505046\pi\)
\(180\) 0 0
\(181\) −36970.5 + 64034.9i −0.0838802 + 0.145285i −0.904913 0.425596i \(-0.860065\pi\)
0.821033 + 0.570880i \(0.193398\pi\)
\(182\) 0 0
\(183\) −584319. −1.28980
\(184\) 0 0
\(185\) 109211. + 189160.i 0.234606 + 0.406349i
\(186\) 0 0
\(187\) 25137.0 + 43538.6i 0.0525666 + 0.0910480i
\(188\) 0 0
\(189\) 2.88849e6 5.88189
\(190\) 0 0
\(191\) −522570. −1.03648 −0.518240 0.855235i \(-0.673413\pi\)
−0.518240 + 0.855235i \(0.673413\pi\)
\(192\) 0 0
\(193\) 12411.0 + 21496.6i 0.0239836 + 0.0415409i 0.877768 0.479086i \(-0.159032\pi\)
−0.853784 + 0.520627i \(0.825698\pi\)
\(194\) 0 0
\(195\) −648520. 1.12327e6i −1.22134 2.11543i
\(196\) 0 0
\(197\) −363318. −0.666993 −0.333496 0.942751i \(-0.608228\pi\)
−0.333496 + 0.942751i \(0.608228\pi\)
\(198\) 0 0
\(199\) 40673.4 70448.5i 0.0728078 0.126107i −0.827323 0.561726i \(-0.810137\pi\)
0.900131 + 0.435620i \(0.143471\pi\)
\(200\) 0 0
\(201\) 809411. 1.41312
\(202\) 0 0
\(203\) 288352. 499440.i 0.491114 0.850635i
\(204\) 0 0
\(205\) 88878.3 153942.i 0.147710 0.255842i
\(206\) 0 0
\(207\) −765449. 1.32580e6i −1.24162 2.15056i
\(208\) 0 0
\(209\) 31825.8 134819.i 0.0503980 0.213494i
\(210\) 0 0
\(211\) −235569. 408017.i −0.364260 0.630917i 0.624397 0.781107i \(-0.285345\pi\)
−0.988657 + 0.150190i \(0.952011\pi\)
\(212\) 0 0
\(213\) −495011. + 857384.i −0.747594 + 1.29487i
\(214\) 0 0
\(215\) 174644. 302492.i 0.257666 0.446291i
\(216\) 0 0
\(217\) 929580. 1.34010
\(218\) 0 0
\(219\) −265564. + 459971.i −0.374162 + 0.648068i
\(220\) 0 0
\(221\) 351631. 0.484291
\(222\) 0 0
\(223\) −650115. 1.12603e6i −0.875443 1.51631i −0.856290 0.516495i \(-0.827236\pi\)
−0.0191530 0.999817i \(-0.506097\pi\)
\(224\) 0 0
\(225\) −616460. 1.06774e6i −0.811799 1.40608i
\(226\) 0 0
\(227\) −73342.4 −0.0944692 −0.0472346 0.998884i \(-0.515041\pi\)
−0.0472346 + 0.998884i \(0.515041\pi\)
\(228\) 0 0
\(229\) −1.25234e6 −1.57809 −0.789046 0.614335i \(-0.789424\pi\)
−0.789046 + 0.614335i \(0.789424\pi\)
\(230\) 0 0
\(231\) −328213. 568481.i −0.404693 0.700949i
\(232\) 0 0
\(233\) 544644. + 943351.i 0.657238 + 1.13837i 0.981328 + 0.192344i \(0.0616089\pi\)
−0.324089 + 0.946027i \(0.605058\pi\)
\(234\) 0 0
\(235\) 1.25261e6 1.47960
\(236\) 0 0
\(237\) 1.21885e6 2.11110e6i 1.40954 2.44140i
\(238\) 0 0
\(239\) 928359. 1.05129 0.525644 0.850705i \(-0.323825\pi\)
0.525644 + 0.850705i \(0.323825\pi\)
\(240\) 0 0
\(241\) −49744.9 + 86160.6i −0.0551703 + 0.0955578i −0.892292 0.451460i \(-0.850904\pi\)
0.837121 + 0.547017i \(0.184237\pi\)
\(242\) 0 0
\(243\) −1.34477e6 + 2.32921e6i −1.46094 + 2.53043i
\(244\) 0 0
\(245\) 1.66995e6 + 2.89244e6i 1.77742 + 3.07857i
\(246\) 0 0
\(247\) −705329. 664256.i −0.735613 0.692777i
\(248\) 0 0
\(249\) −595112. 1.03076e6i −0.608275 1.05356i
\(250\) 0 0
\(251\) −190030. + 329141.i −0.190387 + 0.329760i −0.945379 0.325975i \(-0.894308\pi\)
0.754992 + 0.655735i \(0.227641\pi\)
\(252\) 0 0
\(253\) −106896. + 185149.i −0.104993 + 0.181853i
\(254\) 0 0
\(255\) 1.20301e6 1.15856
\(256\) 0 0
\(257\) −552645. + 957209.i −0.521931 + 0.904012i 0.477743 + 0.878500i \(0.341455\pi\)
−0.999675 + 0.0255121i \(0.991878\pi\)
\(258\) 0 0
\(259\) 773166. 0.716182
\(260\) 0 0
\(261\) 720404. + 1.24778e6i 0.654598 + 1.13380i
\(262\) 0 0
\(263\) −276003. 478051.i −0.246050 0.426172i 0.716376 0.697714i \(-0.245800\pi\)
−0.962426 + 0.271543i \(0.912466\pi\)
\(264\) 0 0
\(265\) −1.81250e6 −1.58549
\(266\) 0 0
\(267\) 1.63377e6 1.40253
\(268\) 0 0
\(269\) 859906. + 1.48940e6i 0.724553 + 1.25496i 0.959158 + 0.282872i \(0.0912872\pi\)
−0.234604 + 0.972091i \(0.575379\pi\)
\(270\) 0 0
\(271\) 451795. + 782532.i 0.373696 + 0.647260i 0.990131 0.140146i \(-0.0447571\pi\)
−0.616435 + 0.787406i \(0.711424\pi\)
\(272\) 0 0
\(273\) −4.59123e6 −3.72840
\(274\) 0 0
\(275\) −86089.5 + 149111.i −0.0686465 + 0.118899i
\(276\) 0 0
\(277\) −1.04518e6 −0.818447 −0.409223 0.912434i \(-0.634200\pi\)
−0.409223 + 0.912434i \(0.634200\pi\)
\(278\) 0 0
\(279\) −1.16121e6 + 2.01127e6i −0.893099 + 1.54689i
\(280\) 0 0
\(281\) −213159. + 369202.i −0.161041 + 0.278932i −0.935242 0.354008i \(-0.884819\pi\)
0.774201 + 0.632940i \(0.218152\pi\)
\(282\) 0 0
\(283\) −29882.7 51758.4i −0.0221796 0.0384162i 0.854723 0.519085i \(-0.173727\pi\)
−0.876902 + 0.480669i \(0.840394\pi\)
\(284\) 0 0
\(285\) −2.41310e6 2.27258e6i −1.75980 1.65732i
\(286\) 0 0
\(287\) −314609. 544918.i −0.225458 0.390505i
\(288\) 0 0
\(289\) 546859. 947188.i 0.385151 0.667101i
\(290\) 0 0
\(291\) 394494. 683284.i 0.273092 0.473008i
\(292\) 0 0
\(293\) 1.17326e6 0.798410 0.399205 0.916862i \(-0.369286\pi\)
0.399205 + 0.916862i \(0.369286\pi\)
\(294\) 0 0
\(295\) 838032. 1.45151e6i 0.560668 0.971105i
\(296\) 0 0
\(297\) 1.00779e6 0.662947
\(298\) 0 0
\(299\) 747661. + 1.29499e6i 0.483645 + 0.837698i
\(300\) 0 0
\(301\) −618199. 1.07075e6i −0.393289 0.681197i
\(302\) 0 0
\(303\) 3.58584e6 2.24380
\(304\) 0 0
\(305\) 1.40935e6 0.867501
\(306\) 0 0
\(307\) −252040. 436545.i −0.152624 0.264353i 0.779567 0.626318i \(-0.215439\pi\)
−0.932191 + 0.361966i \(0.882106\pi\)
\(308\) 0 0
\(309\) 1.82132e6 + 3.15462e6i 1.08515 + 1.87954i
\(310\) 0 0
\(311\) 2.39525e6 1.40426 0.702132 0.712046i \(-0.252231\pi\)
0.702132 + 0.712046i \(0.252231\pi\)
\(312\) 0 0
\(313\) −1.06455e6 + 1.84385e6i −0.614193 + 1.06381i 0.376332 + 0.926485i \(0.377185\pi\)
−0.990525 + 0.137329i \(0.956148\pi\)
\(314\) 0 0
\(315\) −1.13373e7 −6.43773
\(316\) 0 0
\(317\) −399285. + 691581.i −0.223169 + 0.386541i −0.955769 0.294120i \(-0.904974\pi\)
0.732599 + 0.680660i \(0.238307\pi\)
\(318\) 0 0
\(319\) 100605. 174254.i 0.0553535 0.0958750i
\(320\) 0 0
\(321\) −3.33378e6 5.77428e6i −1.80582 3.12777i
\(322\) 0 0
\(323\) 860657. 258500.i 0.459012 0.137865i
\(324\) 0 0
\(325\) 602135. + 1.04293e6i 0.316217 + 0.547704i
\(326\) 0 0
\(327\) −756075. + 1.30956e6i −0.391017 + 0.677261i
\(328\) 0 0
\(329\) 2.21697e6 3.83991e6i 1.12920 1.95583i
\(330\) 0 0
\(331\) −224790. −0.112773 −0.0563867 0.998409i \(-0.517958\pi\)
−0.0563867 + 0.998409i \(0.517958\pi\)
\(332\) 0 0
\(333\) −965819. + 1.67285e6i −0.477293 + 0.826696i
\(334\) 0 0
\(335\) −1.95226e6 −0.950444
\(336\) 0 0
\(337\) 1.02795e6 + 1.78046e6i 0.493056 + 0.853998i 0.999968 0.00799964i \(-0.00254639\pi\)
−0.506912 + 0.861998i \(0.669213\pi\)
\(338\) 0 0
\(339\) 1.68260e6 + 2.91435e6i 0.795209 + 1.37734i
\(340\) 0 0
\(341\) 324329. 0.151043
\(342\) 0 0
\(343\) 7.58183e6 3.47967
\(344\) 0 0
\(345\) 2.55792e6 + 4.43046e6i 1.15702 + 2.00401i
\(346\) 0 0
\(347\) −1.48248e6 2.56773e6i −0.660946 1.14479i −0.980368 0.197179i \(-0.936822\pi\)
0.319422 0.947613i \(-0.396511\pi\)
\(348\) 0 0
\(349\) 2.25013e6 0.988883 0.494441 0.869211i \(-0.335373\pi\)
0.494441 + 0.869211i \(0.335373\pi\)
\(350\) 0 0
\(351\) 3.52438e6 6.10441e6i 1.52692 2.64470i
\(352\) 0 0
\(353\) −1.72711e6 −0.737706 −0.368853 0.929488i \(-0.620249\pi\)
−0.368853 + 0.929488i \(0.620249\pi\)
\(354\) 0 0
\(355\) 1.19394e6 2.06797e6i 0.502820 0.870910i
\(356\) 0 0
\(357\) 2.12919e6 3.68787e6i 0.884187 1.53146i
\(358\) 0 0
\(359\) −526967. 912734.i −0.215798 0.373773i 0.737721 0.675106i \(-0.235902\pi\)
−0.953519 + 0.301332i \(0.902569\pi\)
\(360\) 0 0
\(361\) −2.21470e6 1.10732e6i −0.894431 0.447205i
\(362\) 0 0
\(363\) 2.26525e6 + 3.92352e6i 0.902296 + 1.56282i
\(364\) 0 0
\(365\) 640529. 1.10943e6i 0.251656 0.435881i
\(366\) 0 0
\(367\) −1.90021e6 + 3.29126e6i −0.736438 + 1.27555i 0.217651 + 0.976027i \(0.430160\pi\)
−0.954089 + 0.299522i \(0.903173\pi\)
\(368\) 0 0
\(369\) 1.57200e6 0.601018
\(370\) 0 0
\(371\) −3.20791e6 + 5.55627e6i −1.21001 + 2.09579i
\(372\) 0 0
\(373\) −1.16264e6 −0.432685 −0.216342 0.976318i \(-0.569413\pi\)
−0.216342 + 0.976318i \(0.569413\pi\)
\(374\) 0 0
\(375\) −1.23141e6 2.13287e6i −0.452195 0.783225i
\(376\) 0 0
\(377\) −703663. 1.21878e6i −0.254983 0.441643i
\(378\) 0 0
\(379\) −1.49509e6 −0.534648 −0.267324 0.963607i \(-0.586139\pi\)
−0.267324 + 0.963607i \(0.586139\pi\)
\(380\) 0 0
\(381\) 1.37330e6 0.484678
\(382\) 0 0
\(383\) −2.52086e6 4.36626e6i −0.878115 1.52094i −0.853407 0.521246i \(-0.825467\pi\)
−0.0247088 0.999695i \(-0.507866\pi\)
\(384\) 0 0
\(385\) 791634. + 1.37115e6i 0.272190 + 0.471448i
\(386\) 0 0
\(387\) 3.08895e6 1.04842
\(388\) 0 0
\(389\) 612495. 1.06087e6i 0.205224 0.355459i −0.744980 0.667087i \(-0.767541\pi\)
0.950204 + 0.311628i \(0.100874\pi\)
\(390\) 0 0
\(391\) −1.38692e6 −0.458785
\(392\) 0 0
\(393\) 4.20350e6 7.28067e6i 1.37287 2.37788i
\(394\) 0 0
\(395\) −2.93980e6 + 5.09188e6i −0.948036 + 1.64205i
\(396\) 0 0
\(397\) −639677. 1.10795e6i −0.203697 0.352813i 0.746020 0.665924i \(-0.231962\pi\)
−0.949717 + 0.313110i \(0.898629\pi\)
\(398\) 0 0
\(399\) −1.12376e7 + 3.37522e6i −3.53378 + 1.06138i
\(400\) 0 0
\(401\) −473386. 819928.i −0.147013 0.254633i 0.783109 0.621884i \(-0.213632\pi\)
−0.930122 + 0.367251i \(0.880299\pi\)
\(402\) 0 0
\(403\) 1.13422e6 1.96453e6i 0.347885 0.602555i
\(404\) 0 0
\(405\) 6.59838e6 1.14287e7i 1.99894 3.46226i
\(406\) 0 0
\(407\) 269756. 0.0807208
\(408\) 0 0
\(409\) −1.78713e6 + 3.09540e6i −0.528260 + 0.914974i 0.471197 + 0.882028i \(0.343822\pi\)
−0.999457 + 0.0329456i \(0.989511\pi\)
\(410\) 0 0
\(411\) 8.50856e6 2.48457
\(412\) 0 0
\(413\) −2.96644e6 5.13803e6i −0.855777 1.48225i
\(414\) 0 0
\(415\) 1.43538e6 + 2.48616e6i 0.409117 + 0.708611i
\(416\) 0 0
\(417\) −5.24984e6 −1.47845
\(418\) 0 0
\(419\) −4.64582e6 −1.29279 −0.646395 0.763003i \(-0.723724\pi\)
−0.646395 + 0.763003i \(0.723724\pi\)
\(420\) 0 0
\(421\) 1.59986e6 + 2.77104e6i 0.439923 + 0.761970i 0.997683 0.0680329i \(-0.0216723\pi\)
−0.557760 + 0.830002i \(0.688339\pi\)
\(422\) 0 0
\(423\) 5.53877e6 + 9.59342e6i 1.50509 + 2.60689i
\(424\) 0 0
\(425\) −1.11697e6 −0.299963
\(426\) 0 0
\(427\) 2.49439e6 4.32041e6i 0.662056 1.14671i
\(428\) 0 0
\(429\) −1.60187e6 −0.420227
\(430\) 0 0
\(431\) 2.46054e6 4.26178e6i 0.638025 1.10509i −0.347841 0.937553i \(-0.613085\pi\)
0.985866 0.167537i \(-0.0535815\pi\)
\(432\) 0 0
\(433\) 1.48931e6 2.57956e6i 0.381738 0.661189i −0.609573 0.792730i \(-0.708659\pi\)
0.991311 + 0.131541i \(0.0419924\pi\)
\(434\) 0 0
\(435\) −2.40740e6 4.16973e6i −0.609992 1.05654i
\(436\) 0 0
\(437\) 2.78199e6 + 2.61999e6i 0.696871 + 0.656291i
\(438\) 0 0
\(439\) 1.08758e6 + 1.88374e6i 0.269339 + 0.466509i 0.968691 0.248268i \(-0.0798614\pi\)
−0.699352 + 0.714777i \(0.746528\pi\)
\(440\) 0 0
\(441\) −1.47684e7 + 2.55795e7i −3.61606 + 6.26320i
\(442\) 0 0
\(443\) −189407. + 328062.i −0.0458549 + 0.0794231i −0.888042 0.459763i \(-0.847935\pi\)
0.842187 + 0.539186i \(0.181268\pi\)
\(444\) 0 0
\(445\) −3.94058e6 −0.943323
\(446\) 0 0
\(447\) −2.39760e6 + 4.15276e6i −0.567554 + 0.983032i
\(448\) 0 0
\(449\) −5.64067e6 −1.32043 −0.660214 0.751077i \(-0.729534\pi\)
−0.660214 + 0.751077i \(0.729534\pi\)
\(450\) 0 0
\(451\) −109766. 190121.i −0.0254114 0.0440138i
\(452\) 0 0
\(453\) 6.64422e6 + 1.15081e7i 1.52124 + 2.63487i
\(454\) 0 0
\(455\) 1.10738e7 2.50766
\(456\) 0 0
\(457\) −317551. −0.0711252 −0.0355626 0.999367i \(-0.511322\pi\)
−0.0355626 + 0.999367i \(0.511322\pi\)
\(458\) 0 0
\(459\) 3.26888e6 + 5.66187e6i 0.724215 + 1.25438i
\(460\) 0 0
\(461\) 1.63141e6 + 2.82569e6i 0.357529 + 0.619259i 0.987547 0.157322i \(-0.0502859\pi\)
−0.630018 + 0.776580i \(0.716953\pi\)
\(462\) 0 0
\(463\) −7.65368e6 −1.65927 −0.829636 0.558305i \(-0.811452\pi\)
−0.829636 + 0.558305i \(0.811452\pi\)
\(464\) 0 0
\(465\) 3.88044e6 6.72113e6i 0.832241 1.44148i
\(466\) 0 0
\(467\) 885237. 0.187831 0.0939155 0.995580i \(-0.470062\pi\)
0.0939155 + 0.995580i \(0.470062\pi\)
\(468\) 0 0
\(469\) −3.45528e6 + 5.98472e6i −0.725356 + 1.25635i
\(470\) 0 0
\(471\) −809439. + 1.40199e6i −0.168125 + 0.291201i
\(472\) 0 0
\(473\) −215689. 373583.i −0.0443276 0.0767777i
\(474\) 0 0
\(475\) 2.24050e6 + 2.11003e6i 0.455628 + 0.429096i
\(476\) 0 0
\(477\) −8.01448e6 1.38815e7i −1.61280 2.79345i
\(478\) 0 0
\(479\) 2.58332e6 4.47445e6i 0.514447 0.891047i −0.485413 0.874285i \(-0.661331\pi\)
0.999859 0.0167625i \(-0.00533592\pi\)
\(480\) 0 0
\(481\) 943375. 1.63397e6i 0.185918 0.322020i
\(482\) 0 0
\(483\) 1.81089e7 3.53203
\(484\) 0 0
\(485\) −951502. + 1.64805e6i −0.183677 + 0.318138i
\(486\) 0 0
\(487\) −4.53740e6 −0.866931 −0.433465 0.901170i \(-0.642709\pi\)
−0.433465 + 0.901170i \(0.642709\pi\)
\(488\) 0 0
\(489\) −3.06988e6 5.31719e6i −0.580563 1.00556i
\(490\) 0 0
\(491\) −4.58323e6 7.93839e6i −0.857963 1.48603i −0.873869 0.486161i \(-0.838397\pi\)
0.0159066 0.999873i \(-0.494937\pi\)
\(492\) 0 0
\(493\) 1.30530e6 0.241876
\(494\) 0 0
\(495\) −3.95556e6 −0.725596
\(496\) 0 0
\(497\) −4.22628e6 7.32014e6i −0.767481 1.32932i
\(498\) 0 0
\(499\) −4.86531e6 8.42697e6i −0.874700 1.51503i −0.857081 0.515181i \(-0.827725\pi\)
−0.0176190 0.999845i \(-0.505609\pi\)
\(500\) 0 0
\(501\) 8.07952e6 1.43811
\(502\) 0 0
\(503\) −5.37084e6 + 9.30257e6i −0.946503 + 1.63939i −0.193791 + 0.981043i \(0.562078\pi\)
−0.752713 + 0.658349i \(0.771255\pi\)
\(504\) 0 0
\(505\) −8.64888e6 −1.50915
\(506\) 0 0
\(507\) −115579. + 200189.i −0.0199692 + 0.0345876i
\(508\) 0 0
\(509\) −2.77946e6 + 4.81416e6i −0.475516 + 0.823618i −0.999607 0.0280444i \(-0.991072\pi\)
0.524090 + 0.851663i \(0.324405\pi\)
\(510\) 0 0
\(511\) −2.26733e6 3.92712e6i −0.384115 0.665307i
\(512\) 0 0
\(513\) 4.13870e6 1.75322e7i 0.694338 2.94132i
\(514\) 0 0
\(515\) −4.39294e6 7.60880e6i −0.729856 1.26415i
\(516\) 0 0
\(517\) 773497. 1.33974e6i 0.127272 0.220441i
\(518\) 0 0
\(519\) −7.75785e6 + 1.34370e7i −1.26422 + 2.18970i
\(520\) 0 0
\(521\) −2.44377e6 −0.394427 −0.197213 0.980361i \(-0.563189\pi\)
−0.197213 + 0.980361i \(0.563189\pi\)
\(522\) 0 0
\(523\) 2.06842e6 3.58260e6i 0.330662 0.572723i −0.651980 0.758236i \(-0.726061\pi\)
0.982642 + 0.185513i \(0.0593948\pi\)
\(524\) 0 0
\(525\) 1.45842e7 2.30931
\(526\) 0 0
\(527\) 1.05200e6 + 1.82211e6i 0.165002 + 0.285791i
\(528\) 0 0
\(529\) 269211. + 466288.i 0.0418268 + 0.0724461i
\(530\) 0 0
\(531\) 1.48224e7 2.28130
\(532\) 0 0
\(533\) −1.53547e6 −0.234112
\(534\) 0 0
\(535\) 8.04093e6 + 1.39273e7i 1.21457 + 2.10369i
\(536\) 0 0
\(537\) 200825. + 347839.i 0.0300526 + 0.0520526i
\(538\) 0 0
\(539\) 4.12485e6 0.611555
\(540\) 0 0
\(541\) 332076. 575172.i 0.0487803 0.0844899i −0.840604 0.541650i \(-0.817800\pi\)
0.889385 + 0.457160i \(0.151133\pi\)
\(542\) 0 0
\(543\) 2.18517e6 0.318043
\(544\) 0 0
\(545\) 1.82362e6 3.15860e6i 0.262992 0.455516i
\(546\) 0 0
\(547\) −2.27290e6 + 3.93678e6i −0.324797 + 0.562565i −0.981471 0.191609i \(-0.938629\pi\)
0.656674 + 0.754174i \(0.271963\pi\)
\(548\) 0 0
\(549\) 6.23186e6 + 1.07939e7i 0.882443 + 1.52844i
\(550\) 0 0
\(551\) −2.61828e6 2.46581e6i −0.367398 0.346004i
\(552\) 0 0
\(553\) 1.04062e7 + 1.80241e7i 1.44704 + 2.50634i
\(554\) 0 0
\(555\) 3.22751e6 5.59021e6i 0.444769 0.770363i
\(556\) 0 0
\(557\) 4.10469e6 7.10954e6i 0.560586 0.970964i −0.436859 0.899530i \(-0.643909\pi\)
0.997445 0.0714342i \(-0.0227576\pi\)
\(558\) 0 0
\(559\) −3.01717e6 −0.408386
\(560\) 0 0
\(561\) 742871. 1.28669e6i 0.0996566 0.172610i
\(562\) 0 0
\(563\) −1.32458e7 −1.76119 −0.880597 0.473866i \(-0.842858\pi\)
−0.880597 + 0.473866i \(0.842858\pi\)
\(564\) 0 0
\(565\) −4.05835e6 7.02927e6i −0.534846 0.926380i
\(566\) 0 0
\(567\) −2.33567e7 4.04550e7i −3.05109 5.28464i
\(568\) 0 0
\(569\) 1.11112e7 1.43873 0.719365 0.694632i \(-0.244433\pi\)
0.719365 + 0.694632i \(0.244433\pi\)
\(570\) 0 0
\(571\) 1.44176e7 1.85055 0.925277 0.379291i \(-0.123832\pi\)
0.925277 + 0.379291i \(0.123832\pi\)
\(572\) 0 0
\(573\) 7.72172e6 + 1.33744e7i 0.982489 + 1.70172i
\(574\) 0 0
\(575\) −2.37497e6 4.11356e6i −0.299563 0.518858i
\(576\) 0 0
\(577\) −4.63470e6 −0.579538 −0.289769 0.957097i \(-0.593578\pi\)
−0.289769 + 0.957097i \(0.593578\pi\)
\(578\) 0 0
\(579\) 366782. 635285.i 0.0454686 0.0787539i
\(580\) 0 0
\(581\) 1.01618e7 1.24891
\(582\) 0 0
\(583\) −1.11923e6 + 1.93857e6i −0.136380 + 0.236217i
\(584\) 0 0
\(585\) −1.38331e7 + 2.39597e7i −1.67121 + 2.89462i
\(586\) 0 0
\(587\) −87378.3 151344.i −0.0104667 0.0181288i 0.860745 0.509037i \(-0.169998\pi\)
−0.871211 + 0.490908i \(0.836665\pi\)
\(588\) 0 0
\(589\) 1.33193e6 5.64224e6i 0.158195 0.670137i
\(590\) 0 0
\(591\) 5.36854e6 + 9.29858e6i 0.632248 + 1.09509i
\(592\) 0 0
\(593\) 63610.1 110176.i 0.00742830 0.0128662i −0.862287 0.506419i \(-0.830969\pi\)
0.869716 + 0.493553i \(0.164302\pi\)
\(594\) 0 0
\(595\) −5.13551e6 + 8.89497e6i −0.594691 + 1.03003i
\(596\) 0 0
\(597\) −2.40403e6 −0.276061
\(598\) 0 0
\(599\) 8.00216e6 1.38601e7i 0.911255 1.57834i 0.0989618 0.995091i \(-0.468448\pi\)
0.812293 0.583249i \(-0.198219\pi\)
\(600\) 0 0
\(601\) 1.52423e7 1.72134 0.860668 0.509166i \(-0.170046\pi\)
0.860668 + 0.509166i \(0.170046\pi\)
\(602\) 0 0
\(603\) −8.63250e6 1.49519e7i −0.966815 1.67457i
\(604\) 0 0
\(605\) −5.46367e6 9.46336e6i −0.606871 1.05113i
\(606\) 0 0
\(607\) 1.49576e7 1.64774 0.823870 0.566778i \(-0.191810\pi\)
0.823870 + 0.566778i \(0.191810\pi\)
\(608\) 0 0
\(609\) −1.70432e7 −1.86213
\(610\) 0 0
\(611\) −5.41005e6 9.37049e6i −0.586271 1.01545i
\(612\) 0 0
\(613\) 889245. + 1.54022e6i 0.0955807 + 0.165551i 0.909851 0.414936i \(-0.136196\pi\)
−0.814270 + 0.580486i \(0.802863\pi\)
\(614\) 0 0
\(615\) −5.25322e6 −0.560064
\(616\) 0 0
\(617\) 7.97293e6 1.38095e7i 0.843150 1.46038i −0.0440683 0.999029i \(-0.514032\pi\)
0.887218 0.461350i \(-0.152635\pi\)
\(618\) 0 0
\(619\) −1.53524e7 −1.61046 −0.805231 0.592962i \(-0.797959\pi\)
−0.805231 + 0.592962i \(0.797959\pi\)
\(620\) 0 0
\(621\) −1.39010e7 + 2.40773e7i −1.44650 + 2.50541i
\(622\) 0 0
\(623\) −6.97438e6 + 1.20800e7i −0.719922 + 1.24694i
\(624\) 0 0
\(625\) 6.02615e6 + 1.04376e7i 0.617078 + 1.06881i
\(626\) 0 0
\(627\) −3.92076e6 + 1.17761e6i −0.398292 + 0.119628i
\(628\) 0 0
\(629\) 874985. + 1.51552e6i 0.0881807 + 0.152734i
\(630\) 0 0
\(631\) 1.84277e6 3.19177e6i 0.184246 0.319123i −0.759076 0.651002i \(-0.774349\pi\)
0.943322 + 0.331879i \(0.107682\pi\)
\(632\) 0 0
\(633\) −6.96173e6 + 1.20581e7i −0.690570 + 1.19610i
\(634\) 0 0
\(635\) −3.31234e6 −0.325988
\(636\) 0 0
\(637\) 1.44252e7 2.49851e7i 1.40855 2.43968i
\(638\) 0 0
\(639\) 2.11175e7 2.04592
\(640\) 0 0
\(641\) 2.60486e6 + 4.51176e6i 0.250403 + 0.433711i 0.963637 0.267215i \(-0.0861035\pi\)
−0.713234 + 0.700926i \(0.752770\pi\)
\(642\) 0 0
\(643\) 3.62947e6 + 6.28642e6i 0.346191 + 0.599620i 0.985569 0.169272i \(-0.0541417\pi\)
−0.639379 + 0.768892i \(0.720808\pi\)
\(644\) 0 0
\(645\) −1.03225e7 −0.976976
\(646\) 0 0
\(647\) −8.49406e6 −0.797728 −0.398864 0.917010i \(-0.630595\pi\)
−0.398864 + 0.917010i \(0.630595\pi\)
\(648\) 0 0
\(649\) −1.03499e6 1.79265e6i −0.0964545 0.167064i
\(650\) 0 0
\(651\) −1.37359e7 2.37912e7i −1.27029 2.20021i
\(652\) 0 0
\(653\) −1.16393e7 −1.06818 −0.534089 0.845428i \(-0.679345\pi\)
−0.534089 + 0.845428i \(0.679345\pi\)
\(654\) 0 0
\(655\) −1.01386e7 + 1.75606e7i −0.923372 + 1.59933i
\(656\) 0 0
\(657\) 1.13291e7 1.02396
\(658\) 0 0
\(659\) −9.86735e6 + 1.70907e7i −0.885089 + 1.53302i −0.0394769 + 0.999220i \(0.512569\pi\)
−0.845612 + 0.533798i \(0.820764\pi\)
\(660\) 0 0
\(661\) 7.97821e6 1.38187e7i 0.710235 1.23016i −0.254534 0.967064i \(-0.581922\pi\)
0.964769 0.263099i \(-0.0847446\pi\)
\(662\) 0 0
\(663\) −5.19585e6 8.99947e6i −0.459063 0.795121i
\(664\) 0 0
\(665\) 2.71045e7 8.14088e6i 2.37677 0.713867i
\(666\) 0 0
\(667\) 2.77542e6 + 4.80717e6i 0.241554 + 0.418384i
\(668\) 0 0
\(669\) −1.92128e7 + 3.32775e7i −1.65968 + 2.87465i
\(670\) 0 0
\(671\) 870288. 1.50738e6i 0.0746202 0.129246i
\(672\) 0 0
\(673\) 1.18685e7 1.01008 0.505041 0.863096i \(-0.331477\pi\)
0.505041 + 0.863096i \(0.331477\pi\)
\(674\) 0 0
\(675\) −1.11953e7 + 1.93908e7i −0.945750 + 1.63809i
\(676\) 0 0
\(677\) −1.13643e7 −0.952952 −0.476476 0.879188i \(-0.658086\pi\)
−0.476476 + 0.879188i \(0.658086\pi\)
\(678\) 0 0
\(679\) 3.36810e6 + 5.83372e6i 0.280356 + 0.485591i
\(680\) 0 0
\(681\) 1.08374e6 + 1.87709e6i 0.0895482 + 0.155102i
\(682\) 0 0
\(683\) 1.33134e7 1.09204 0.546018 0.837774i \(-0.316143\pi\)
0.546018 + 0.837774i \(0.316143\pi\)
\(684\) 0 0
\(685\) −2.05223e7 −1.67109
\(686\) 0 0
\(687\) 1.85051e7 + 3.20517e7i 1.49589 + 2.59095i
\(688\) 0 0
\(689\) 7.82824e6 + 1.35589e7i 0.628226 + 1.08812i
\(690\) 0 0
\(691\) 1.77578e7 1.41480 0.707400 0.706813i \(-0.249868\pi\)
0.707400 + 0.706813i \(0.249868\pi\)
\(692\) 0 0
\(693\) −7.00088e6 + 1.21259e7i −0.553757 + 0.959136i
\(694\) 0 0
\(695\) 1.26624e7 0.994381
\(696\) 0 0
\(697\) 712079. 1.23336e6i 0.0555196 0.0961628i
\(698\) 0 0
\(699\) 1.60958e7 2.78787e7i 1.24600 2.15814i
\(700\) 0 0
\(701\) 2.58452e6 + 4.47652e6i 0.198648 + 0.344069i 0.948090 0.318001i \(-0.103012\pi\)
−0.749442 + 0.662070i \(0.769678\pi\)
\(702\) 0 0
\(703\) 1.10781e6 4.69286e6i 0.0845429 0.358137i
\(704\) 0 0
\(705\) −1.85091e7 3.20586e7i −1.40253 2.42925i
\(706\) 0 0
\(707\) −1.53075e7 + 2.65134e7i −1.15175 + 1.99488i
\(708\) 0 0
\(709\) 6.35081e6 1.09999e7i 0.474476 0.821816i −0.525097 0.851042i \(-0.675971\pi\)
0.999573 + 0.0292265i \(0.00930441\pi\)
\(710\) 0 0
\(711\) −5.19967e7 −3.85746
\(712\) 0 0
\(713\) −4.47366e6 + 7.74860e6i −0.329563 + 0.570820i
\(714\) 0 0
\(715\) 3.86364e6 0.282638
\(716\) 0 0
\(717\) −1.37178e7 2.37600e7i −0.996524 1.72603i
\(718\) 0 0
\(719\) 1.17643e7 + 2.03763e7i 0.848678 + 1.46995i 0.882388 + 0.470522i \(0.155934\pi\)
−0.0337101 + 0.999432i \(0.510732\pi\)
\(720\) 0 0
\(721\) −3.11000e7 −2.22804
\(722\) 0 0
\(723\) 2.94021e6 0.209186
\(724\) 0 0
\(725\) 2.23520e6 + 3.87149e6i 0.157933 + 0.273548i
\(726\) 0 0
\(727\) 1.08765e7 + 1.88387e7i 0.763229 + 1.32195i 0.941178 + 0.337911i \(0.109720\pi\)
−0.177949 + 0.984040i \(0.556946\pi\)
\(728\) 0 0
\(729\) 3.44949e7 2.40401
\(730\) 0 0
\(731\) 1.39922e6 2.42352e6i 0.0968485 0.167746i
\(732\) 0 0
\(733\) −9.80139e6 −0.673795 −0.336897 0.941541i \(-0.609378\pi\)
−0.336897 + 0.941541i \(0.609378\pi\)
\(734\) 0 0
\(735\) 4.93519e7 8.54800e7i 3.36965 5.83641i
\(736\) 0 0
\(737\) −1.20554e6 + 2.08806e6i −0.0817548 + 0.141603i
\(738\) 0 0
\(739\) −7.08883e6 1.22782e7i −0.477489 0.827035i 0.522178 0.852837i \(-0.325120\pi\)
−0.999667 + 0.0258011i \(0.991786\pi\)
\(740\) 0 0
\(741\) −6.57842e6 + 2.78672e7i −0.440125 + 1.86444i
\(742\) 0 0
\(743\) −3.04168e6 5.26834e6i −0.202135 0.350108i 0.747081 0.664733i \(-0.231455\pi\)
−0.949216 + 0.314625i \(0.898121\pi\)
\(744\) 0 0
\(745\) 5.78289e6 1.00163e7i 0.381728 0.661173i
\(746\) 0 0
\(747\) −1.26939e7 + 2.19865e7i −0.832327 + 1.44163i
\(748\) 0 0
\(749\) 5.69261e7 3.70772
\(750\) 0 0
\(751\) 6.05235e6 1.04830e7i 0.391584 0.678243i −0.601075 0.799193i \(-0.705261\pi\)
0.992659 + 0.120950i \(0.0385941\pi\)
\(752\) 0 0
\(753\) 1.12318e7 0.721878
\(754\) 0 0
\(755\) −1.60255e7 2.77571e7i −1.02316 1.77217i
\(756\) 0 0
\(757\) −837126. 1.44994e6i −0.0530947 0.0919627i 0.838257 0.545276i \(-0.183575\pi\)
−0.891351 + 0.453313i \(0.850242\pi\)
\(758\) 0 0
\(759\) 6.31817e6 0.398095
\(760\) 0 0
\(761\) −1.71108e7 −1.07105 −0.535525 0.844520i \(-0.679886\pi\)
−0.535525 + 0.844520i \(0.679886\pi\)
\(762\) 0 0
\(763\) −6.45519e6 1.11807e7i −0.401419 0.695278i
\(764\) 0 0
\(765\) −1.28303e7 2.22227e7i −0.792653 1.37292i
\(766\) 0 0
\(767\) −1.44780e7 −0.888626
\(768\) 0 0
\(769\) −4.88795e6 + 8.46617e6i −0.298065 + 0.516263i −0.975693 0.219141i \(-0.929674\pi\)
0.677628 + 0.735404i \(0.263008\pi\)
\(770\) 0 0
\(771\) 3.26645e7 1.97897
\(772\) 0 0
\(773\) −6.30084e6 + 1.09134e7i −0.379271 + 0.656916i −0.990956 0.134185i \(-0.957158\pi\)
0.611686 + 0.791101i \(0.290492\pi\)
\(774\) 0 0
\(775\) −3.60289e6 + 6.24039e6i −0.215475 + 0.373214i
\(776\) 0 0
\(777\) −1.14246e7 1.97880e7i −0.678875 1.17585i
\(778\) 0 0
\(779\) −3.75825e6 + 1.12880e6i −0.221892 + 0.0666457i
\(780\) 0 0
\(781\) −1.47454e6 2.55398e6i −0.0865027 0.149827i
\(782\) 0 0
\(783\) 1.30830e7 2.26604e7i 0.762610 1.32088i
\(784\) 0 0
\(785\) 1.95233e6 3.38154e6i 0.113078 0.195857i
\(786\) 0 0
\(787\) −1.91406e7 −1.10159 −0.550795 0.834641i \(-0.685675\pi\)
−0.550795 + 0.834641i \(0.685675\pi\)
\(788\) 0 0
\(789\) −8.15667e6 + 1.41278e7i