Properties

Label 882.3.n.e.19.2
Level $882$
Weight $3$
Character 882.19
Analytic conductor $24.033$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 882.n (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.0327593166\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.2
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 882.19
Dual form 882.3.n.e.325.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(7.24264 + 4.18154i) q^{5} -2.82843 q^{8} +O(q^{10})\) \(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(7.24264 + 4.18154i) q^{5} -2.82843 q^{8} +(10.2426 - 5.91359i) q^{10} +(3.00000 + 5.19615i) q^{11} +17.8639i q^{13} +(-2.00000 + 3.46410i) q^{16} +(-16.2426 + 9.37769i) q^{17} +(14.7426 + 8.51167i) q^{19} -16.7262i q^{20} +8.48528 q^{22} +(6.72792 - 11.6531i) q^{23} +(22.4706 + 38.9202i) q^{25} +(21.8787 + 12.6317i) q^{26} -33.9411 q^{29} +(-12.7721 + 7.37396i) q^{31} +(2.82843 + 4.89898i) q^{32} +26.5241i q^{34} +(-2.98528 + 5.17066i) q^{37} +(20.8492 - 12.0373i) q^{38} +(-20.4853 - 11.8272i) q^{40} +35.2354i q^{41} +15.4853 q^{43} +(6.00000 - 10.3923i) q^{44} +(-9.51472 - 16.4800i) q^{46} +(-28.7574 - 16.6031i) q^{47} +63.5563 q^{50} +(30.9411 - 17.8639i) q^{52} +(-17.2721 - 29.9161i) q^{53} +50.1785i q^{55} +(-24.0000 + 41.5692i) q^{58} +(23.6985 - 13.6823i) q^{59} +(34.9706 + 20.1903i) q^{61} +20.8567i q^{62} +8.00000 q^{64} +(-74.6985 + 129.382i) q^{65} +(57.1985 + 99.0707i) q^{67} +(32.4853 + 18.7554i) q^{68} -18.6030 q^{71} +(101.353 - 58.5161i) q^{73} +(4.22183 + 7.31242i) q^{74} -34.0467i q^{76} +(44.1690 - 76.5030i) q^{79} +(-28.9706 + 16.7262i) q^{80} +(43.1543 + 24.9152i) q^{82} +75.7601i q^{83} -156.853 q^{85} +(10.9497 - 18.9655i) q^{86} +(-8.48528 - 14.6969i) q^{88} +(-18.0000 - 10.3923i) q^{89} -26.9117 q^{92} +(-40.6690 + 23.4803i) q^{94} +(71.1838 + 123.294i) q^{95} -30.5826i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{4} + 12q^{5} + O(q^{10}) \) \( 4q - 4q^{4} + 12q^{5} + 24q^{10} + 12q^{11} - 8q^{16} - 48q^{17} + 42q^{19} - 24q^{23} + 22q^{25} + 96q^{26} - 102q^{31} + 22q^{37} + 24q^{38} - 48q^{40} + 28q^{43} + 24q^{44} - 72q^{46} - 132q^{47} + 192q^{50} - 12q^{52} - 120q^{53} - 96q^{58} - 24q^{59} + 72q^{61} + 32q^{64} - 180q^{65} + 110q^{67} + 96q^{68} - 312q^{71} + 66q^{73} + 48q^{74} - 10q^{79} - 48q^{80} - 48q^{82} - 288q^{85} + 24q^{86} - 72q^{89} + 96q^{92} + 24q^{94} + 132q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 1.22474i 0.353553 0.612372i
\(3\) 0 0
\(4\) −1.00000 1.73205i −0.250000 0.433013i
\(5\) 7.24264 + 4.18154i 1.44853 + 0.836308i 0.998394 0.0566528i \(-0.0180428\pi\)
0.450134 + 0.892961i \(0.351376\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −2.82843 −0.353553
\(9\) 0 0
\(10\) 10.2426 5.91359i 1.02426 0.591359i
\(11\) 3.00000 + 5.19615i 0.272727 + 0.472377i 0.969559 0.244857i \(-0.0787410\pi\)
−0.696832 + 0.717234i \(0.745408\pi\)
\(12\) 0 0
\(13\) 17.8639i 1.37414i 0.726590 + 0.687072i \(0.241104\pi\)
−0.726590 + 0.687072i \(0.758896\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) −16.2426 + 9.37769i −0.955449 + 0.551629i −0.894770 0.446528i \(-0.852660\pi\)
−0.0606799 + 0.998157i \(0.519327\pi\)
\(18\) 0 0
\(19\) 14.7426 + 8.51167i 0.775928 + 0.447983i 0.834985 0.550272i \(-0.185476\pi\)
−0.0590569 + 0.998255i \(0.518809\pi\)
\(20\) 16.7262i 0.836308i
\(21\) 0 0
\(22\) 8.48528 0.385695
\(23\) 6.72792 11.6531i 0.292518 0.506657i −0.681886 0.731458i \(-0.738840\pi\)
0.974405 + 0.224802i \(0.0721734\pi\)
\(24\) 0 0
\(25\) 22.4706 + 38.9202i 0.898823 + 1.55681i
\(26\) 21.8787 + 12.6317i 0.841488 + 0.485833i
\(27\) 0 0
\(28\) 0 0
\(29\) −33.9411 −1.17038 −0.585192 0.810895i \(-0.698981\pi\)
−0.585192 + 0.810895i \(0.698981\pi\)
\(30\) 0 0
\(31\) −12.7721 + 7.37396i −0.412003 + 0.237870i −0.691650 0.722233i \(-0.743116\pi\)
0.279647 + 0.960103i \(0.409782\pi\)
\(32\) 2.82843 + 4.89898i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 26.5241i 0.780121i
\(35\) 0 0
\(36\) 0 0
\(37\) −2.98528 + 5.17066i −0.0806833 + 0.139748i −0.903544 0.428496i \(-0.859044\pi\)
0.822860 + 0.568244i \(0.192377\pi\)
\(38\) 20.8492 12.0373i 0.548664 0.316771i
\(39\) 0 0
\(40\) −20.4853 11.8272i −0.512132 0.295680i
\(41\) 35.2354i 0.859399i 0.902972 + 0.429700i \(0.141381\pi\)
−0.902972 + 0.429700i \(0.858619\pi\)
\(42\) 0 0
\(43\) 15.4853 0.360123 0.180061 0.983655i \(-0.442370\pi\)
0.180061 + 0.983655i \(0.442370\pi\)
\(44\) 6.00000 10.3923i 0.136364 0.236189i
\(45\) 0 0
\(46\) −9.51472 16.4800i −0.206842 0.358260i
\(47\) −28.7574 16.6031i −0.611859 0.353257i 0.161834 0.986818i \(-0.448259\pi\)
−0.773693 + 0.633561i \(0.781592\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 63.5563 1.27113
\(51\) 0 0
\(52\) 30.9411 17.8639i 0.595022 0.343536i
\(53\) −17.2721 29.9161i −0.325888 0.564455i 0.655803 0.754932i \(-0.272330\pi\)
−0.981692 + 0.190477i \(0.938997\pi\)
\(54\) 0 0
\(55\) 50.1785i 0.912336i
\(56\) 0 0
\(57\) 0 0
\(58\) −24.0000 + 41.5692i −0.413793 + 0.716711i
\(59\) 23.6985 13.6823i 0.401669 0.231904i −0.285535 0.958368i \(-0.592171\pi\)
0.687204 + 0.726465i \(0.258838\pi\)
\(60\) 0 0
\(61\) 34.9706 + 20.1903i 0.573288 + 0.330988i 0.758461 0.651718i \(-0.225951\pi\)
−0.185174 + 0.982706i \(0.559285\pi\)
\(62\) 20.8567i 0.336399i
\(63\) 0 0
\(64\) 8.00000 0.125000
\(65\) −74.6985 + 129.382i −1.14921 + 1.99049i
\(66\) 0 0
\(67\) 57.1985 + 99.0707i 0.853709 + 1.47867i 0.877838 + 0.478958i \(0.158985\pi\)
−0.0241291 + 0.999709i \(0.507681\pi\)
\(68\) 32.4853 + 18.7554i 0.477725 + 0.275814i
\(69\) 0 0
\(70\) 0 0
\(71\) −18.6030 −0.262015 −0.131007 0.991381i \(-0.541821\pi\)
−0.131007 + 0.991381i \(0.541821\pi\)
\(72\) 0 0
\(73\) 101.353 58.5161i 1.38839 0.801590i 0.395260 0.918569i \(-0.370654\pi\)
0.993134 + 0.116979i \(0.0373210\pi\)
\(74\) 4.22183 + 7.31242i 0.0570517 + 0.0988164i
\(75\) 0 0
\(76\) 34.0467i 0.447983i
\(77\) 0 0
\(78\) 0 0
\(79\) 44.1690 76.5030i 0.559102 0.968393i −0.438470 0.898746i \(-0.644479\pi\)
0.997572 0.0696469i \(-0.0221873\pi\)
\(80\) −28.9706 + 16.7262i −0.362132 + 0.209077i
\(81\) 0 0
\(82\) 43.1543 + 24.9152i 0.526272 + 0.303843i
\(83\) 75.7601i 0.912772i 0.889782 + 0.456386i \(0.150856\pi\)
−0.889782 + 0.456386i \(0.849144\pi\)
\(84\) 0 0
\(85\) −156.853 −1.84533
\(86\) 10.9497 18.9655i 0.127323 0.220529i
\(87\) 0 0
\(88\) −8.48528 14.6969i −0.0964237 0.167011i
\(89\) −18.0000 10.3923i −0.202247 0.116767i 0.395456 0.918485i \(-0.370587\pi\)
−0.597703 + 0.801717i \(0.703920\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −26.9117 −0.292518
\(93\) 0 0
\(94\) −40.6690 + 23.4803i −0.432649 + 0.249790i
\(95\) 71.1838 + 123.294i 0.749303 + 1.29783i
\(96\) 0 0
\(97\) 30.5826i 0.315284i −0.987496 0.157642i \(-0.949611\pi\)
0.987496 0.157642i \(-0.0503892\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 44.9411 77.8403i 0.449411 0.778403i
\(101\) 110.823 63.9839i 1.09726 0.633504i 0.161761 0.986830i \(-0.448283\pi\)
0.935500 + 0.353326i \(0.114949\pi\)
\(102\) 0 0
\(103\) 70.1102 + 40.4781i 0.680681 + 0.392992i 0.800112 0.599851i \(-0.204774\pi\)
−0.119430 + 0.992843i \(0.538107\pi\)
\(104\) 50.5266i 0.485833i
\(105\) 0 0
\(106\) −48.8528 −0.460876
\(107\) 84.7279 146.753i 0.791850 1.37152i −0.132971 0.991120i \(-0.542452\pi\)
0.924820 0.380404i \(-0.124215\pi\)
\(108\) 0 0
\(109\) −89.4706 154.968i −0.820831 1.42172i −0.905064 0.425275i \(-0.860177\pi\)
0.0842335 0.996446i \(-0.473156\pi\)
\(110\) 61.4558 + 35.4815i 0.558689 + 0.322560i
\(111\) 0 0
\(112\) 0 0
\(113\) 17.3970 0.153955 0.0769777 0.997033i \(-0.475473\pi\)
0.0769777 + 0.997033i \(0.475473\pi\)
\(114\) 0 0
\(115\) 97.4558 56.2662i 0.847442 0.489271i
\(116\) 33.9411 + 58.7878i 0.292596 + 0.506791i
\(117\) 0 0
\(118\) 38.6995i 0.327962i
\(119\) 0 0
\(120\) 0 0
\(121\) 42.5000 73.6122i 0.351240 0.608365i
\(122\) 49.4558 28.5533i 0.405376 0.234044i
\(123\) 0 0
\(124\) 25.5442 + 14.7479i 0.206001 + 0.118935i
\(125\) 166.769i 1.33415i
\(126\) 0 0
\(127\) 167.426 1.31832 0.659159 0.752004i \(-0.270912\pi\)
0.659159 + 0.752004i \(0.270912\pi\)
\(128\) 5.65685 9.79796i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 105.640 + 182.973i 0.812612 + 1.40749i
\(131\) −1.54416 0.891519i −0.0117874 0.00680549i 0.494095 0.869408i \(-0.335500\pi\)
−0.505882 + 0.862603i \(0.668833\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 161.782 1.20733
\(135\) 0 0
\(136\) 45.9411 26.5241i 0.337802 0.195030i
\(137\) 50.4853 + 87.4431i 0.368506 + 0.638271i 0.989332 0.145677i \(-0.0465362\pi\)
−0.620826 + 0.783948i \(0.713203\pi\)
\(138\) 0 0
\(139\) 140.542i 1.01110i 0.862799 + 0.505548i \(0.168710\pi\)
−0.862799 + 0.505548i \(0.831290\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −13.1543 + 22.7840i −0.0926361 + 0.160450i
\(143\) −92.8234 + 53.5916i −0.649115 + 0.374766i
\(144\) 0 0
\(145\) −245.823 141.926i −1.69533 0.978801i
\(146\) 165.508i 1.13362i
\(147\) 0 0
\(148\) 11.9411 0.0806833
\(149\) 91.4558 158.406i 0.613798 1.06313i −0.376797 0.926296i \(-0.622974\pi\)
0.990594 0.136833i \(-0.0436922\pi\)
\(150\) 0 0
\(151\) 144.397 + 250.103i 0.956271 + 1.65631i 0.731432 + 0.681915i \(0.238852\pi\)
0.224840 + 0.974396i \(0.427814\pi\)
\(152\) −41.6985 24.0746i −0.274332 0.158386i
\(153\) 0 0
\(154\) 0 0
\(155\) −123.338 −0.795730
\(156\) 0 0
\(157\) −162.000 + 93.5307i −1.03185 + 0.595737i −0.917513 0.397705i \(-0.869807\pi\)
−0.114334 + 0.993442i \(0.536473\pi\)
\(158\) −62.4645 108.192i −0.395345 0.684757i
\(159\) 0 0
\(160\) 47.3087i 0.295680i
\(161\) 0 0
\(162\) 0 0
\(163\) −8.02944 + 13.9074i −0.0492604 + 0.0853214i −0.889604 0.456732i \(-0.849020\pi\)
0.840344 + 0.542054i \(0.182353\pi\)
\(164\) 61.0294 35.2354i 0.372131 0.214850i
\(165\) 0 0
\(166\) 92.7868 + 53.5705i 0.558957 + 0.322714i
\(167\) 176.117i 1.05459i −0.849681 0.527297i \(-0.823206\pi\)
0.849681 0.527297i \(-0.176794\pi\)
\(168\) 0 0
\(169\) −150.118 −0.888271
\(170\) −110.912 + 192.105i −0.652422 + 1.13003i
\(171\) 0 0
\(172\) −15.4853 26.8213i −0.0900307 0.155938i
\(173\) −200.184 115.576i −1.15713 0.668070i −0.206517 0.978443i \(-0.566213\pi\)
−0.950615 + 0.310373i \(0.899546\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −24.0000 −0.136364
\(177\) 0 0
\(178\) −25.4558 + 14.6969i −0.143010 + 0.0825671i
\(179\) −42.6396 73.8540i −0.238210 0.412592i 0.721991 0.691903i \(-0.243227\pi\)
−0.960201 + 0.279311i \(0.909894\pi\)
\(180\) 0 0
\(181\) 5.58655i 0.0308649i 0.999881 + 0.0154325i \(0.00491250\pi\)
−0.999881 + 0.0154325i \(0.995087\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −19.0294 + 32.9600i −0.103421 + 0.179130i
\(185\) −43.2426 + 24.9662i −0.233744 + 0.134952i
\(186\) 0 0
\(187\) −97.4558 56.2662i −0.521154 0.300889i
\(188\) 66.4123i 0.353257i
\(189\) 0 0
\(190\) 201.338 1.05967
\(191\) 92.6985 160.558i 0.485332 0.840620i −0.514526 0.857475i \(-0.672032\pi\)
0.999858 + 0.0168547i \(0.00536527\pi\)
\(192\) 0 0
\(193\) −113.897 197.275i −0.590140 1.02215i −0.994213 0.107425i \(-0.965739\pi\)
0.404073 0.914727i \(-0.367594\pi\)
\(194\) −37.4558 21.6251i −0.193071 0.111470i
\(195\) 0 0
\(196\) 0 0
\(197\) −123.161 −0.625185 −0.312593 0.949887i \(-0.601197\pi\)
−0.312593 + 0.949887i \(0.601197\pi\)
\(198\) 0 0
\(199\) −5.39697 + 3.11594i −0.0271205 + 0.0156580i −0.513499 0.858090i \(-0.671651\pi\)
0.486378 + 0.873748i \(0.338318\pi\)
\(200\) −63.5563 110.083i −0.317782 0.550414i
\(201\) 0 0
\(202\) 180.974i 0.895910i
\(203\) 0 0
\(204\) 0 0
\(205\) −147.338 + 255.197i −0.718722 + 1.24486i
\(206\) 99.1508 57.2447i 0.481314 0.277887i
\(207\) 0 0
\(208\) −61.8823 35.7277i −0.297511 0.171768i
\(209\) 102.140i 0.488708i
\(210\) 0 0
\(211\) −124.912 −0.591999 −0.295999 0.955188i \(-0.595653\pi\)
−0.295999 + 0.955188i \(0.595653\pi\)
\(212\) −34.5442 + 59.8322i −0.162944 + 0.282228i
\(213\) 0 0
\(214\) −119.823 207.540i −0.559922 0.969814i
\(215\) 112.154 + 64.7523i 0.521648 + 0.301174i
\(216\) 0 0
\(217\) 0 0
\(218\) −253.061 −1.16083
\(219\) 0 0
\(220\) 86.9117 50.1785i 0.395053 0.228084i
\(221\) −167.522 290.156i −0.758017 1.31292i
\(222\) 0 0
\(223\) 228.631i 1.02525i 0.858613 + 0.512625i \(0.171327\pi\)
−0.858613 + 0.512625i \(0.828673\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 12.3015 21.3068i 0.0544315 0.0942781i
\(227\) −146.823 + 84.7685i −0.646799 + 0.373430i −0.787229 0.616661i \(-0.788485\pi\)
0.140430 + 0.990091i \(0.455152\pi\)
\(228\) 0 0
\(229\) −30.0442 17.3460i −0.131197 0.0757467i 0.432965 0.901411i \(-0.357467\pi\)
−0.564162 + 0.825664i \(0.690801\pi\)
\(230\) 159.145i 0.691934i
\(231\) 0 0
\(232\) 96.0000 0.413793
\(233\) −127.243 + 220.391i −0.546106 + 0.945883i 0.452431 + 0.891800i \(0.350557\pi\)
−0.998536 + 0.0540833i \(0.982776\pi\)
\(234\) 0 0
\(235\) −138.853 240.500i −0.590863 1.02340i
\(236\) −47.3970 27.3647i −0.200835 0.115952i
\(237\) 0 0
\(238\) 0 0
\(239\) −197.147 −0.824884 −0.412442 0.910984i \(-0.635324\pi\)
−0.412442 + 0.910984i \(0.635324\pi\)
\(240\) 0 0
\(241\) −76.6173 + 44.2350i −0.317914 + 0.183548i −0.650462 0.759538i \(-0.725425\pi\)
0.332548 + 0.943086i \(0.392092\pi\)
\(242\) −60.1041 104.103i −0.248364 0.430179i
\(243\) 0 0
\(244\) 80.7611i 0.330988i
\(245\) 0 0
\(246\) 0 0
\(247\) −152.051 + 263.361i −0.615592 + 1.06624i
\(248\) 36.1249 20.8567i 0.145665 0.0840997i
\(249\) 0 0
\(250\) 204.250 + 117.924i 0.816999 + 0.471695i
\(251\) 215.903i 0.860172i −0.902788 0.430086i \(-0.858483\pi\)
0.902788 0.430086i \(-0.141517\pi\)
\(252\) 0 0
\(253\) 80.7351 0.319111
\(254\) 118.388 205.055i 0.466096 0.807302i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) −3.72792 2.15232i −0.0145055 0.00837477i 0.492730 0.870182i \(-0.335999\pi\)
−0.507235 + 0.861808i \(0.669332\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 298.794 1.14921
\(261\) 0 0
\(262\) −2.18377 + 1.26080i −0.00833499 + 0.00481221i
\(263\) 141.338 + 244.805i 0.537407 + 0.930817i 0.999043 + 0.0437468i \(0.0139295\pi\)
−0.461635 + 0.887070i \(0.652737\pi\)
\(264\) 0 0
\(265\) 288.896i 1.09017i
\(266\) 0 0
\(267\) 0 0
\(268\) 114.397 198.141i 0.426854 0.739333i
\(269\) −330.765 + 190.967i −1.22961 + 0.709914i −0.966948 0.254974i \(-0.917933\pi\)
−0.262660 + 0.964888i \(0.584600\pi\)
\(270\) 0 0
\(271\) 73.0294 + 42.1636i 0.269481 + 0.155585i 0.628652 0.777687i \(-0.283607\pi\)
−0.359171 + 0.933272i \(0.616940\pi\)
\(272\) 75.0215i 0.275814i
\(273\) 0 0
\(274\) 142.794 0.521146
\(275\) −134.823 + 233.521i −0.490267 + 0.849167i
\(276\) 0 0
\(277\) 68.5589 + 118.747i 0.247505 + 0.428691i 0.962833 0.270098i \(-0.0870560\pi\)
−0.715328 + 0.698789i \(0.753723\pi\)
\(278\) 172.128 + 99.3784i 0.619167 + 0.357476i
\(279\) 0 0
\(280\) 0 0
\(281\) 325.103 1.15695 0.578474 0.815701i \(-0.303648\pi\)
0.578474 + 0.815701i \(0.303648\pi\)
\(282\) 0 0
\(283\) −168.507 + 97.2876i −0.595432 + 0.343773i −0.767242 0.641357i \(-0.778372\pi\)
0.171811 + 0.985130i \(0.445038\pi\)
\(284\) 18.6030 + 32.2214i 0.0655036 + 0.113456i
\(285\) 0 0
\(286\) 151.580i 0.530000i
\(287\) 0 0
\(288\) 0 0
\(289\) 31.3823 54.3557i 0.108589 0.188082i
\(290\) −347.647 + 200.714i −1.19878 + 0.692117i
\(291\) 0 0
\(292\) −202.706 117.032i −0.694197 0.400795i
\(293\) 239.702i 0.818095i −0.912513 0.409048i \(-0.865861\pi\)
0.912513 0.409048i \(-0.134139\pi\)
\(294\) 0 0
\(295\) 228.853 0.775772
\(296\) 8.44365 14.6248i 0.0285258 0.0494082i
\(297\) 0 0
\(298\) −129.338 224.020i −0.434020 0.751745i
\(299\) 208.169 + 120.187i 0.696219 + 0.401962i
\(300\) 0 0
\(301\) 0 0
\(302\) 408.416 1.35237
\(303\) 0 0
\(304\) −58.9706 + 34.0467i −0.193982 + 0.111996i
\(305\) 168.853 + 292.462i 0.553616 + 0.958891i
\(306\) 0 0
\(307\) 540.272i 1.75984i −0.475120 0.879921i \(-0.657595\pi\)
0.475120 0.879921i \(-0.342405\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −87.2132 + 151.058i −0.281333 + 0.487283i
\(311\) 350.044 202.098i 1.12554 0.649832i 0.182732 0.983163i \(-0.441506\pi\)
0.942810 + 0.333330i \(0.108172\pi\)
\(312\) 0 0
\(313\) 113.706 + 65.6482i 0.363278 + 0.209739i 0.670518 0.741893i \(-0.266072\pi\)
−0.307240 + 0.951632i \(0.599405\pi\)
\(314\) 264.545i 0.842500i
\(315\) 0 0
\(316\) −176.676 −0.559102
\(317\) −46.9706 + 81.3554i −0.148172 + 0.256642i −0.930552 0.366160i \(-0.880672\pi\)
0.782380 + 0.622802i \(0.214006\pi\)
\(318\) 0 0
\(319\) −101.823 176.363i −0.319196 0.552863i
\(320\) 57.9411 + 33.4523i 0.181066 + 0.104539i
\(321\) 0 0
\(322\) 0 0
\(323\) −319.279 −0.988481
\(324\) 0 0
\(325\) −695.265 + 401.411i −2.13928 + 1.23511i
\(326\) 11.3553 + 19.6680i 0.0348323 + 0.0603314i
\(327\) 0 0
\(328\) 99.6607i 0.303843i
\(329\) 0 0
\(330\) 0 0
\(331\) 130.684 226.351i 0.394815 0.683840i −0.598263 0.801300i \(-0.704142\pi\)
0.993078 + 0.117460i \(0.0374754\pi\)
\(332\) 131.220 75.7601i 0.395242 0.228193i
\(333\) 0 0
\(334\) −215.698 124.534i −0.645804 0.372855i
\(335\) 956.711i 2.85585i
\(336\) 0 0
\(337\) 136.265 0.404347 0.202173 0.979350i \(-0.435200\pi\)
0.202173 + 0.979350i \(0.435200\pi\)
\(338\) −106.149 + 183.856i −0.314051 + 0.543952i
\(339\) 0 0
\(340\) 156.853 + 271.677i 0.461332 + 0.799050i
\(341\) −76.6325 44.2438i −0.224729 0.129747i
\(342\) 0 0
\(343\) 0 0
\(344\) −43.7990 −0.127323
\(345\) 0 0
\(346\) −283.103 + 163.449i −0.818216 + 0.472397i
\(347\) −161.095 279.026i −0.464252 0.804108i 0.534915 0.844906i \(-0.320343\pi\)
−0.999167 + 0.0407975i \(0.987010\pi\)
\(348\) 0 0
\(349\) 346.495i 0.992821i −0.868088 0.496411i \(-0.834651\pi\)
0.868088 0.496411i \(-0.165349\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −16.9706 + 29.3939i −0.0482118 + 0.0835053i
\(353\) −537.448 + 310.296i −1.52252 + 0.879025i −0.522869 + 0.852413i \(0.675138\pi\)
−0.999646 + 0.0266116i \(0.991528\pi\)
\(354\) 0 0
\(355\) −134.735 77.7893i −0.379535 0.219125i
\(356\) 41.5692i 0.116767i
\(357\) 0 0
\(358\) −120.603 −0.336880
\(359\) 10.1177 17.5245i 0.0281831 0.0488146i −0.851590 0.524209i \(-0.824361\pi\)
0.879773 + 0.475394i \(0.157695\pi\)
\(360\) 0 0
\(361\) −35.6030 61.6663i −0.0986234 0.170821i
\(362\) 6.84210 + 3.95029i 0.0189008 + 0.0109124i
\(363\) 0 0
\(364\) 0 0
\(365\) 978.749 2.68151
\(366\) 0 0
\(367\) 269.831 155.787i 0.735234 0.424488i −0.0850998 0.996372i \(-0.527121\pi\)
0.820334 + 0.571885i \(0.193788\pi\)
\(368\) 26.9117 + 46.6124i 0.0731296 + 0.126664i
\(369\) 0 0
\(370\) 70.6149i 0.190851i
\(371\) 0 0
\(372\) 0 0
\(373\) 340.691 590.094i 0.913380 1.58202i 0.104125 0.994564i \(-0.466796\pi\)
0.809255 0.587457i \(-0.199871\pi\)
\(374\) −137.823 + 79.5724i −0.368512 + 0.212760i
\(375\) 0 0
\(376\) 81.3381 + 46.9606i 0.216325 + 0.124895i
\(377\) 606.320i 1.60828i
\(378\) 0 0
\(379\) −624.779 −1.64849 −0.824246 0.566231i \(-0.808401\pi\)
−0.824246 + 0.566231i \(0.808401\pi\)
\(380\) 142.368 246.588i 0.374651 0.648915i
\(381\) 0 0
\(382\) −131.095 227.064i −0.343182 0.594408i
\(383\) 119.772 + 69.1502i 0.312720 + 0.180549i 0.648143 0.761519i \(-0.275546\pi\)
−0.335423 + 0.942068i \(0.608879\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −322.149 −0.834584
\(387\) 0 0
\(388\) −52.9706 + 30.5826i −0.136522 + 0.0788211i
\(389\) −281.787 488.069i −0.724388 1.25468i −0.959226 0.282642i \(-0.908789\pi\)
0.234838 0.972035i \(-0.424544\pi\)
\(390\) 0 0
\(391\) 252.370i 0.645446i
\(392\) 0 0
\(393\) 0 0
\(394\) −87.0883 + 150.841i −0.221036 + 0.382846i
\(395\) 639.801 369.389i 1.61975 0.935163i
\(396\) 0 0
\(397\) 392.603 + 226.669i 0.988923 + 0.570955i 0.904952 0.425513i \(-0.139906\pi\)
0.0839711 + 0.996468i \(0.473240\pi\)
\(398\) 8.81321i 0.0221438i
\(399\) 0 0
\(400\) −179.765 −0.449411
\(401\) −137.875 + 238.807i −0.343828 + 0.595528i −0.985140 0.171752i \(-0.945057\pi\)
0.641312 + 0.767280i \(0.278390\pi\)
\(402\) 0 0
\(403\) −131.727 228.159i −0.326867 0.566151i
\(404\) −221.647 127.968i −0.548631 0.316752i
\(405\) 0 0
\(406\) 0 0
\(407\) −35.8234 −0.0880181
\(408\) 0 0
\(409\) 377.441 217.916i 0.922839 0.532801i 0.0382993 0.999266i \(-0.487806\pi\)
0.884540 + 0.466465i \(0.154473\pi\)
\(410\) 208.368 + 360.903i 0.508213 + 0.880252i
\(411\) 0 0
\(412\) 161.913i 0.392992i
\(413\) 0 0
\(414\) 0 0
\(415\) −316.794 + 548.703i −0.763359 + 1.32218i
\(416\) −87.5147 + 50.5266i −0.210372 + 0.121458i
\(417\) 0 0
\(418\) 125.095 + 72.2239i 0.299271 + 0.172784i
\(419\) 301.257i 0.718991i −0.933147 0.359496i \(-0.882949\pi\)
0.933147 0.359496i \(-0.117051\pi\)
\(420\) 0 0
\(421\) −203.794 −0.484071 −0.242036 0.970267i \(-0.577815\pi\)
−0.242036 + 0.970267i \(0.577815\pi\)
\(422\) −88.3259 + 152.985i −0.209303 + 0.362524i
\(423\) 0 0
\(424\) 48.8528 + 84.6156i 0.115219 + 0.199565i
\(425\) −729.963 421.444i −1.71756 0.991633i
\(426\) 0 0
\(427\) 0 0
\(428\) −338.912 −0.791850
\(429\) 0 0
\(430\) 158.610 91.5736i 0.368861 0.212962i
\(431\) −197.860 342.703i −0.459072 0.795136i 0.539840 0.841767i \(-0.318485\pi\)
−0.998912 + 0.0466317i \(0.985151\pi\)
\(432\) 0 0
\(433\) 44.2685i 0.102237i 0.998693 + 0.0511184i \(0.0162786\pi\)
−0.998693 + 0.0511184i \(0.983721\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −178.941 + 309.935i −0.410415 + 0.710860i
\(437\) 198.375 114.532i 0.453947 0.262086i
\(438\) 0 0
\(439\) −344.558 198.931i −0.784871 0.453146i 0.0532827 0.998579i \(-0.483032\pi\)
−0.838154 + 0.545434i \(0.816365\pi\)
\(440\) 141.926i 0.322560i
\(441\) 0 0
\(442\) −473.823 −1.07200
\(443\) −59.2721 + 102.662i −0.133797 + 0.231743i −0.925137 0.379633i \(-0.876050\pi\)
0.791340 + 0.611376i \(0.209384\pi\)
\(444\) 0 0
\(445\) −86.9117 150.535i −0.195307 0.338282i
\(446\) 280.014 + 161.666i 0.627835 + 0.362481i
\(447\) 0 0
\(448\) 0 0
\(449\) −713.897 −1.58997 −0.794985 0.606629i \(-0.792521\pi\)
−0.794985 + 0.606629i \(0.792521\pi\)
\(450\) 0 0
\(451\) −183.088 + 105.706i −0.405961 + 0.234382i
\(452\) −17.3970 30.1324i −0.0384889 0.0666647i
\(453\) 0 0
\(454\) 239.762i 0.528109i
\(455\) 0 0
\(456\) 0 0
\(457\) 62.5883 108.406i 0.136955 0.237213i −0.789388 0.613895i \(-0.789602\pi\)
0.926342 + 0.376682i \(0.122935\pi\)
\(458\) −42.4889 + 24.5310i −0.0927704 + 0.0535610i
\(459\) 0 0
\(460\) −194.912 112.532i −0.423721 0.244635i
\(461\) 655.767i 1.42249i 0.702945 + 0.711244i \(0.251868\pi\)
−0.702945 + 0.711244i \(0.748132\pi\)
\(462\) 0 0
\(463\) 869.396 1.87775 0.938873 0.344265i \(-0.111872\pi\)
0.938873 + 0.344265i \(0.111872\pi\)
\(464\) 67.8823 117.576i 0.146298 0.253395i
\(465\) 0 0
\(466\) 179.948 + 311.680i 0.386155 + 0.668840i
\(467\) −231.551 133.686i −0.495827 0.286266i 0.231162 0.972915i \(-0.425747\pi\)
−0.726989 + 0.686649i \(0.759081\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −392.735 −0.835607
\(471\) 0 0
\(472\) −67.0294 + 38.6995i −0.142012 + 0.0819904i
\(473\) 46.4558 + 80.4639i 0.0982153 + 0.170114i
\(474\) 0 0
\(475\) 765.048i 1.61063i
\(476\) 0 0
\(477\) 0 0
\(478\) −139.404 + 241.455i −0.291640 + 0.505136i
\(479\) 235.331 135.868i 0.491296 0.283650i −0.233816 0.972281i \(-0.575121\pi\)
0.725112 + 0.688631i \(0.241788\pi\)
\(480\) 0 0
\(481\) −92.3680 53.3287i −0.192033 0.110870i
\(482\) 125.116i 0.259576i
\(483\) 0 0
\(484\) −170.000 −0.351240
\(485\) 127.882 221.499i 0.263675 0.456698i
\(486\) 0 0
\(487\) 280.757 + 486.285i 0.576503 + 0.998532i 0.995877 + 0.0907186i \(0.0289164\pi\)
−0.419374 + 0.907814i \(0.637750\pi\)
\(488\) −98.9117 57.1067i −0.202688 0.117022i
\(489\) 0 0
\(490\) 0 0
\(491\) 406.441 0.827781 0.413891 0.910327i \(-0.364170\pi\)
0.413891 + 0.910327i \(0.364170\pi\)
\(492\) 0 0
\(493\) 551.294 318.289i 1.11824 0.645618i
\(494\) 215.033 + 372.448i 0.435289 + 0.753944i
\(495\) 0 0
\(496\) 58.9917i 0.118935i
\(497\) 0 0
\(498\) 0 0
\(499\) 185.713 321.665i 0.372171 0.644619i −0.617728 0.786391i \(-0.711947\pi\)
0.989899 + 0.141773i \(0.0452802\pi\)
\(500\) 288.853 166.769i 0.577706 0.333538i
\(501\) 0 0
\(502\) −264.426 152.667i −0.526746 0.304117i
\(503\) 64.6292i 0.128488i 0.997934 + 0.0642438i \(0.0204635\pi\)
−0.997934 + 0.0642438i \(0.979536\pi\)
\(504\) 0 0
\(505\) 1070.21 2.11922
\(506\) 57.0883 98.8799i 0.112823 0.195415i
\(507\) 0 0
\(508\) −167.426 289.991i −0.329580 0.570849i
\(509\) 871.889 + 503.385i 1.71294 + 0.988969i 0.930534 + 0.366205i \(0.119343\pi\)
0.782410 + 0.622764i \(0.213990\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −22.6274 −0.0441942
\(513\) 0 0
\(514\) −5.27208 + 3.04384i −0.0102570 + 0.00592186i
\(515\) 338.522 + 586.337i 0.657324 + 1.13852i
\(516\) 0 0
\(517\) 199.237i 0.385371i
\(518\) 0 0
\(519\) 0 0
\(520\) 211.279 365.946i 0.406306 0.703743i
\(521\) −322.294 + 186.077i −0.618607 + 0.357153i −0.776327 0.630331i \(-0.782919\pi\)
0.157719 + 0.987484i \(0.449586\pi\)
\(522\) 0 0
\(523\) 551.904 + 318.642i 1.05527 + 0.609258i 0.924119 0.382105i \(-0.124801\pi\)
0.131147 + 0.991363i \(0.458134\pi\)
\(524\) 3.56608i 0.00680549i
\(525\) 0 0
\(526\) 399.765 0.760009
\(527\) 138.302 239.545i 0.262432 0.454545i
\(528\) 0 0
\(529\) 173.970 + 301.325i 0.328866 + 0.569613i
\(530\) −353.823 204.280i −0.667591 0.385434i
\(531\) 0 0
\(532\) 0 0
\(533\) −629.440 −1.18094
\(534\) 0 0
\(535\) 1227.31 708.586i 2.29403 1.32446i
\(536\) −161.782 280.214i −0.301832 0.522788i
\(537\) 0 0
\(538\) 540.136i 1.00397i
\(539\) 0 0
\(540\) 0 0
\(541\) −110.412 + 191.239i −0.204088 + 0.353491i −0.949842 0.312731i \(-0.898756\pi\)
0.745754 + 0.666222i \(0.232090\pi\)
\(542\) 103.279 59.6283i 0.190552 0.110015i
\(543\) 0 0
\(544\) −91.8823 53.0482i −0.168901 0.0975152i
\(545\) 1496.50i 2.74587i
\(546\) 0 0
\(547\) −160.676 −0.293741 −0.146870 0.989156i \(-0.546920\pi\)
−0.146870 + 0.989156i \(0.546920\pi\)
\(548\) 100.971 174.886i 0.184253 0.319135i
\(549\) 0 0
\(550\) 190.669 + 330.248i 0.346671 + 0.600452i
\(551\) −500.382 288.896i −0.908134 0.524311i
\(552\) 0 0
\(553\) 0 0
\(554\) 193.914 0.350025
\(555\) 0 0
\(556\) 243.426 140.542i 0.437817 0.252774i
\(557\) −237.177 410.802i −0.425811 0.737526i 0.570685 0.821169i \(-0.306678\pi\)
−0.996496 + 0.0836431i \(0.973344\pi\)
\(558\) 0 0
\(559\) 276.627i 0.494860i
\(560\) 0 0
\(561\) 0 0
\(562\) 229.882 398.168i 0.409043 0.708484i
\(563\) −430.301 + 248.434i −0.764300 + 0.441269i −0.830837 0.556515i \(-0.812138\pi\)
0.0665378 + 0.997784i \(0.478805\pi\)
\(564\) 0 0
\(565\) 126.000 + 72.7461i 0.223009 + 0.128754i
\(566\) 275.171i 0.486168i
\(567\) 0 0
\(568\) 52.6173 0.0926361
\(569\) 392.647 680.084i 0.690065 1.19523i −0.281752 0.959487i \(-0.590915\pi\)
0.971816 0.235740i \(-0.0757512\pi\)
\(570\) 0 0
\(571\) 357.521 + 619.245i 0.626132 + 1.08449i 0.988321 + 0.152388i \(0.0486963\pi\)
−0.362189 + 0.932105i \(0.617970\pi\)
\(572\) 185.647 + 107.183i 0.324557 + 0.187383i
\(573\) 0 0
\(574\) 0 0
\(575\) 604.721 1.05169
\(576\) 0 0
\(577\) −669.117 + 386.315i −1.15965 + 0.669524i −0.951220 0.308514i \(-0.900168\pi\)
−0.208429 + 0.978038i \(0.566835\pi\)
\(578\) −44.3812 76.8705i −0.0767841 0.132994i
\(579\) 0 0
\(580\) 567.705i 0.978801i
\(581\) 0 0
\(582\) 0 0
\(583\) 103.632 179.497i 0.177757 0.307885i
\(584\) −286.669 + 165.508i −0.490872 + 0.283405i
\(585\) 0 0
\(586\) −293.574 169.495i −0.500979 0.289240i
\(587\) 436.477i 0.743572i −0.928318 0.371786i \(-0.878746\pi\)
0.928318 0.371786i \(-0.121254\pi\)
\(588\) 0 0
\(589\) −251.059 −0.426246
\(590\) 161.823 280.286i 0.274277 0.475062i
\(591\) 0 0
\(592\) −11.9411 20.6826i −0.0201708 0.0349369i
\(593\) 722.397 + 417.076i 1.21821 + 0.703332i 0.964534 0.263958i \(-0.0850279\pi\)
0.253673 + 0.967290i \(0.418361\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −365.823 −0.613798
\(597\) 0 0
\(598\) 294.396 169.970i 0.492301 0.284230i
\(599\) 436.794 + 756.549i 0.729205 + 1.26302i 0.957220 + 0.289363i \(0.0934434\pi\)
−0.228014 + 0.973658i \(0.573223\pi\)
\(600\) 0 0
\(601\) 198.982i 0.331085i −0.986203 0.165542i \(-0.947063\pi\)
0.986203 0.165542i \(-0.0529375\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 288.794 500.206i 0.478136 0.828155i
\(605\) 615.624 355.431i 1.01756 0.587489i
\(606\) 0 0
\(607\) −137.654 79.4748i −0.226778 0.130930i 0.382307 0.924035i \(-0.375130\pi\)
−0.609085 + 0.793105i \(0.708463\pi\)
\(608\) 96.2985i 0.158386i
\(609\) 0 0
\(610\) 477.588 0.782931
\(611\) 296.595 513.718i 0.485426 0.840782i
\(612\) 0 0
\(613\) 357.368 + 618.979i 0.582981 + 1.00975i 0.995124 + 0.0986338i \(0.0314473\pi\)
−0.412143 + 0.911119i \(0.635219\pi\)
\(614\) −661.695 382.030i −1.07768 0.622198i
\(615\) 0 0
\(616\) 0 0
\(617\) 639.381 1.03627 0.518137 0.855298i \(-0.326626\pi\)
0.518137 + 0.855298i \(0.326626\pi\)
\(618\) 0 0
\(619\) −148.978 + 86.0126i −0.240676 + 0.138954i −0.615487 0.788147i \(-0.711041\pi\)
0.374812 + 0.927101i \(0.377707\pi\)
\(620\) 123.338 + 213.628i 0.198932 + 0.344561i
\(621\) 0 0
\(622\) 571.619i 0.919002i
\(623\) 0 0
\(624\) 0 0
\(625\) −135.588 + 234.846i −0.216941 + 0.375753i
\(626\) 160.805 92.8406i 0.256876 0.148308i
\(627\) 0 0
\(628\) 324.000 + 187.061i 0.515924 + 0.297869i
\(629\) 111.980i 0.178029i
\(630\) 0 0
\(631\) −1141.06 −1.80833 −0.904166 0.427180i \(-0.859507\pi\)
−0.904166 + 0.427180i \(0.859507\pi\)
\(632\) −124.929 + 216.383i −0.197672 + 0.342379i
\(633\) 0 0
\(634\) 66.4264 + 115.054i 0.104774 + 0.181473i
\(635\) 1212.61 + 700.100i 1.90962 + 1.10252i
\(636\) 0 0
\(637\) 0 0
\(638\) −288.000 −0.451411
\(639\) 0 0
\(640\) 81.9411 47.3087i 0.128033 0.0739199i
\(641\) 114.551 + 198.409i 0.178707 + 0.309530i 0.941438 0.337186i \(-0.109475\pi\)
−0.762731 + 0.646716i \(0.776142\pi\)
\(642\) 0 0
\(643\) 707.670i 1.10058i −0.834975 0.550288i \(-0.814518\pi\)
0.834975 0.550288i \(-0.185482\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −225.765 + 391.036i −0.349481 + 0.605318i
\(647\) 1021.37 589.687i 1.57862 0.911417i 0.583568 0.812064i \(-0.301656\pi\)
0.995052 0.0993530i \(-0.0316773\pi\)
\(648\) 0 0
\(649\) 142.191 + 82.0940i 0.219092 + 0.126493i
\(650\) 1135.36i 1.74671i
\(651\) 0 0
\(652\) 32.1177 0.0492604
\(653\) −77.3818 + 134.029i −0.118502 + 0.205252i −0.919174 0.393851i \(-0.871143\pi\)
0.800672 + 0.599103i \(0.204476\pi\)
\(654\) 0 0
\(655\) −7.45584 12.9139i −0.0113830 0.0197159i
\(656\) −122.059 70.4707i −0.186065 0.107425i
\(657\) 0 0
\(658\) 0 0
\(659\) −591.308 −0.897280 −0.448640 0.893712i \(-0.648092\pi\)
−0.448640 + 0.893712i \(0.648092\pi\)
\(660\) 0 0
\(661\) −140.441 + 81.0837i −0.212468 + 0.122668i −0.602458 0.798151i \(-0.705812\pi\)
0.389990 + 0.920819i \(0.372478\pi\)
\(662\) −184.815 320.109i −0.279176 0.483548i
\(663\) 0 0
\(664\) 214.282i 0.322714i
\(665\) 0 0
\(666\) 0 0
\(667\) −228.353 + 395.519i −0.342359 + 0.592983i
\(668\) −305.044 + 176.117i −0.456652 + 0.263648i
\(669\) 0 0
\(670\) 1171.73 + 676.497i 1.74885 + 1.00970i
\(671\) 242.283i 0.361078i
\(672\) 0 0
\(673\) 42.3238 0.0628883 0.0314441 0.999506i \(-0.489989\pi\)
0.0314441 + 0.999506i \(0.489989\pi\)
\(674\) 96.3539 166.890i 0.142958 0.247611i
\(675\) 0 0
\(676\) 150.118 + 260.012i 0.222068 + 0.384632i
\(677\) 430.721 + 248.677i 0.636220 + 0.367322i 0.783157 0.621824i \(-0.213608\pi\)
−0.146937 + 0.989146i \(0.546941\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 443.647 0.652422
\(681\) 0 0
\(682\) −108.375 + 62.5701i −0.158907 + 0.0917451i
\(683\) 608.080 + 1053.23i 0.890308 + 1.54206i 0.839506 + 0.543350i \(0.182844\pi\)
0.0508015 + 0.998709i \(0.483822\pi\)
\(684\) 0 0
\(685\) 844.425i 1.23274i
\(686\) 0 0
\(687\) 0 0
\(688\) −30.9706 + 53.6426i −0.0450154 + 0.0779689i
\(689\) 534.418 308.546i 0.775642 0.447817i
\(690\) 0 0
\(691\) 932.182 + 538.196i 1.34903 + 0.778865i 0.988113 0.153731i \(-0.0491290\pi\)
0.360921 + 0.932596i \(0.382462\pi\)
\(692\) 462.305i 0.668070i
\(693\) 0 0
\(694\) −455.647 −0.656552
\(695\) −587.683 + 1017.90i −0.845588 + 1.46460i
\(696\) 0 0
\(697\) −330.426 572.315i −0.474069 0.821112i
\(698\) −424.368 245.009i −0.607976 0.351015i
\(699\) 0 0
\(700\) 0 0
\(701\) 695.897 0.992720 0.496360 0.868117i \(-0.334670\pi\)
0.496360 + 0.868117i \(0.334670\pi\)
\(702\) 0 0
\(703\) −88.0219 + 50.8194i −0.125209 + 0.0722894i
\(704\) 24.0000 + 41.5692i 0.0340909 + 0.0590472i
\(705\) 0 0
\(706\) 877.649i 1.24313i
\(707\) 0 0
\(708\) 0 0
\(709\) −127.412 + 220.684i −0.179707 + 0.311261i −0.941780 0.336229i \(-0.890848\pi\)
0.762073 + 0.647491i \(0.224182\pi\)
\(710\) −190.544 + 110.011i −0.268372 + 0.154945i
\(711\) 0 0
\(712\) 50.9117 + 29.3939i 0.0715052 + 0.0412835i
\(713\) 198.446i 0.278325i
\(714\) 0 0
\(715\) −896.382 −1.25368
\(716\) −85.2792 + 147.708i −0.119105 + 0.206296i
\(717\) 0 0
\(718\) −14.3087 24.7833i −0.0199285 0.0345172i
\(719\) −964.925 557.100i −1.34204 0.774826i −0.354931 0.934892i \(-0.615496\pi\)
−0.987106 + 0.160066i \(0.948829\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −100.701 −0.139474
\(723\) 0 0
\(724\) 9.67619 5.58655i 0.0133649 0.00771623i
\(725\) −762.676 1320.99i −1.05197 1.82206i
\(726\) 0 0
\(727\) 398.345i 0.547930i 0.961740 + 0.273965i \(0.0883353\pi\)
−0.961740 + 0.273965i \(0.911665\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 692.080 1198.72i 0.948055 1.64208i
\(731\) −251.522 + 145.216i −0.344079 + 0.198654i
\(732\) 0 0
\(733\) −818.514 472.569i −1.11666 0.644706i −0.176116 0.984369i \(-0.556354\pi\)
−0.940547 + 0.339663i \(0.889687\pi\)
\(734\) 440.632i 0.600316i
\(735\) 0 0
\(736\) 76.1177 0.103421
\(737\) −343.191 + 594.424i −0.465659 + 0.806546i
\(738\) 0 0
\(739\) −96.3162 166.825i −0.130333 0.225744i 0.793472 0.608607i \(-0.208271\pi\)
−0.923805 + 0.382863i \(0.874938\pi\)
\(740\) 86.4853 + 49.9323i 0.116872 + 0.0674761i
\(741\) 0 0
\(742\) 0 0
\(743\) 911.616 1.22694 0.613470 0.789718i \(-0.289773\pi\)
0.613470 + 0.789718i \(0.289773\pi\)
\(744\) 0 0
\(745\) 1324.76 764.853i 1.77821 1.02665i
\(746\) −481.810 834.519i −0.645858 1.11866i
\(747\) 0 0
\(748\) 225.065i 0.300889i
\(749\) 0 0
\(750\) 0 0
\(751\) 195.831 339.189i 0.260760 0.451650i −0.705684 0.708527i \(-0.749360\pi\)
0.966444 + 0.256877i \(0.0826935\pi\)
\(752\) 115.029 66.4123i 0.152965 0.0883142i
\(753\) 0 0
\(754\) −742.587 428.733i −0.984863 0.568611i
\(755\) 2415.21i 3.19895i
\(756\) 0 0
\(757\) −152.823 −0.201879 −0.100940 0.994893i \(-0.532185\pi\)
−0.100940 + 0.994893i \(0.532185\pi\)
\(758\) −441.785 + 765.195i −0.582830 + 1.00949i
\(759\) 0 0
\(760\) −201.338 348.728i −0.264919 0.458852i
\(761\) −109.331 63.1223i −0.143667 0.0829465i 0.426443 0.904514i \(-0.359766\pi\)
−0.570111 + 0.821568i \(0.693100\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −370.794 −0.485332
\(765\) 0 0
\(766\) 169.383 97.7931i 0.221126 0.127667i
\(767\) 244.419 + 423.347i 0.318669 + 0.551951i
\(768\) 0 0
\(769\) 369.148i 0.480037i 0.970768 + 0.240018i \(0.0771535\pi\)
−0.970768 + 0.240018i \(0.922847\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −227.794 + 394.551i −0.295070 + 0.511076i
\(773\) −1215.65 + 701.853i −1.57263 + 0.907961i −0.576789 + 0.816893i \(0.695695\pi\)
−0.995845 + 0.0910674i \(0.970972\pi\)
\(774\) 0 0
\(775\) −573.992 331.394i −0.740634 0.427605i
\(776\) 86.5006i 0.111470i
\(777\) 0 0
\(778\) −797.013 −1.02444
\(779\) −299.912 + 519.462i −0.384996 + 0.666832i
\(780\) 0 0
\(781\) −55.8091 96.6642i −0.0714585 0.123770i
\(782\) 309.088 + 178.452i 0.395254 + 0.228200i
\(783\) 0 0
\(784\) 0 0
\(785\) −1564.41 −1.99288
\(786\) 0 0
\(787\) −196.161 + 113.253i −0.249251 + 0.143905i −0.619421 0.785059i \(-0.712633\pi\)
0.370170 + 0.928964i \(0.379299\pi\)
\(788\) 123.161 + 213.322i 0.156296 + 0.270713i
\(789\) 0 0
\(790\) 1044.79i 1.32252i
\(791\) 0 0