Properties

Label 76.5.j.a.13.1
Level $76$
Weight $5$
Character 76.13
Analytic conductor $7.856$
Analytic rank $0$
Dimension $42$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 76.j (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.85611719437\)
Analytic rank: \(0\)
Dimension: \(42\)
Relative dimension: \(7\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 13.1
Character \(\chi\) \(=\) 76.13
Dual form 76.5.j.a.41.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.65644 + 12.7935i) q^{3} +(6.59099 + 37.3793i) q^{5} +(5.00284 - 8.66518i) q^{7} +(-79.9406 - 67.0781i) q^{9} +O(q^{10})\) \(q+(-4.65644 + 12.7935i) q^{3} +(6.59099 + 37.3793i) q^{5} +(5.00284 - 8.66518i) q^{7} +(-79.9406 - 67.0781i) q^{9} +(-7.63671 - 13.2272i) q^{11} +(-22.1718 - 60.9166i) q^{13} +(-508.902 - 89.7331i) q^{15} +(-348.579 + 292.493i) q^{17} +(281.167 - 226.421i) q^{19} +(87.5622 + 104.353i) q^{21} +(49.2696 - 279.422i) q^{23} +(-766.467 + 278.971i) q^{25} +(275.368 - 158.984i) q^{27} +(-472.367 + 562.945i) q^{29} +(1430.40 + 825.841i) q^{31} +(204.781 - 36.1084i) q^{33} +(356.872 + 129.891i) q^{35} -1474.16i q^{37} +882.576 q^{39} +(-842.731 + 2315.38i) q^{41} +(-329.577 - 1869.12i) q^{43} +(1980.45 - 3430.24i) q^{45} +(985.584 + 827.003i) q^{47} +(1150.44 + 1992.63i) q^{49} +(-2118.86 - 5821.51i) q^{51} +(3118.81 + 549.931i) q^{53} +(444.089 - 372.635i) q^{55} +(1587.47 + 4651.41i) q^{57} +(938.249 + 1118.16i) q^{59} +(-920.289 + 5219.22i) q^{61} +(-981.174 + 357.118i) q^{63} +(2130.89 - 1230.27i) q^{65} +(-4064.52 + 4843.91i) q^{67} +(3345.35 + 1931.44i) q^{69} +(-9089.14 + 1602.66i) q^{71} +(-3636.99 - 1323.76i) q^{73} -11104.8i q^{75} -152.821 q^{77} +(-1439.36 + 3954.62i) q^{79} +(-716.087 - 4061.13i) q^{81} +(6219.89 - 10773.2i) q^{83} +(-13230.7 - 11101.8i) q^{85} +(-5002.47 - 8664.53i) q^{87} +(4134.29 + 11358.9i) q^{89} +(-638.775 - 112.633i) q^{91} +(-17225.9 + 14454.3i) q^{93} +(10316.6 + 9017.49i) q^{95} +(-1907.80 - 2273.62i) q^{97} +(-276.771 + 1569.64i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} + O(q^{10}) \) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} - 45q^{11} + 33q^{13} - 393q^{15} + 909q^{17} + 1242q^{19} + 1107q^{21} - 360q^{23} - 810q^{25} - 7056q^{27} - 2889q^{29} + 2808q^{31} + 10875q^{33} + 6741q^{35} - 3480q^{39} - 3060q^{41} - 8079q^{43} - 4320q^{45} - 2655q^{47} - 474q^{49} - 12222q^{51} - 6705q^{53} + 4623q^{55} - 8022q^{57} + 24309q^{59} + 7104q^{61} + 12063q^{63} + 25245q^{65} + 15573q^{67} - 10881q^{69} - 25506q^{71} + 3036q^{73} + 12924q^{77} - 16839q^{79} - 2208q^{81} - 6363q^{83} - 37890q^{85} - 21924q^{87} - 22644q^{89} + 17418q^{91} + 8184q^{93} - 82413q^{95} + 13383q^{97} + 23565q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(1\)

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
\(3\) −4.65644 + 12.7935i −0.517382 + 1.42150i 0.356012 + 0.934481i \(0.384136\pi\)
−0.873394 + 0.487014i \(0.838086\pi\)
\(4\) 0 0
\(5\) 6.59099 + 37.3793i 0.263640 + 1.49517i 0.772881 + 0.634551i \(0.218815\pi\)
−0.509242 + 0.860623i \(0.670074\pi\)
\(6\) 0 0
\(7\) 5.00284 8.66518i 0.102099 0.176840i −0.810450 0.585807i \(-0.800778\pi\)
0.912549 + 0.408967i \(0.134111\pi\)
\(8\) 0 0
\(9\) −79.9406 67.0781i −0.986921 0.828125i
\(10\) 0 0
\(11\) −7.63671 13.2272i −0.0631133 0.109315i 0.832742 0.553661i \(-0.186770\pi\)
−0.895856 + 0.444345i \(0.853436\pi\)
\(12\) 0 0
\(13\) −22.1718 60.9166i −0.131194 0.360453i 0.856650 0.515897i \(-0.172541\pi\)
−0.987845 + 0.155444i \(0.950319\pi\)
\(14\) 0 0
\(15\) −508.902 89.7331i −2.26179 0.398814i
\(16\) 0 0
\(17\) −348.579 + 292.493i −1.20616 + 1.01209i −0.206724 + 0.978399i \(0.566280\pi\)
−0.999432 + 0.0336857i \(0.989275\pi\)
\(18\) 0 0
\(19\) 281.167 226.421i 0.778855 0.627204i
\(20\) 0 0
\(21\) 87.5622 + 104.353i 0.198554 + 0.236627i
\(22\) 0 0
\(23\) 49.2696 279.422i 0.0931372 0.528207i −0.902165 0.431391i \(-0.858023\pi\)
0.995302 0.0968164i \(-0.0308660\pi\)
\(24\) 0 0
\(25\) −766.467 + 278.971i −1.22635 + 0.446354i
\(26\) 0 0
\(27\) 275.368 158.984i 0.377734 0.218085i
\(28\) 0 0
\(29\) −472.367 + 562.945i −0.561673 + 0.669376i −0.969900 0.243505i \(-0.921703\pi\)
0.408227 + 0.912881i \(0.366147\pi\)
\(30\) 0 0
\(31\) 1430.40 + 825.841i 1.48845 + 0.859356i 0.999913 0.0131887i \(-0.00419821\pi\)
0.488535 + 0.872544i \(0.337532\pi\)
\(32\) 0 0
\(33\) 204.781 36.1084i 0.188045 0.0331574i
\(34\) 0 0
\(35\) 356.872 + 129.891i 0.291324 + 0.106033i
\(36\) 0 0
\(37\) 1474.16i 1.07681i −0.842685 0.538407i \(-0.819026\pi\)
0.842685 0.538407i \(-0.180974\pi\)
\(38\) 0 0
\(39\) 882.576 0.580260
\(40\) 0 0
\(41\) −842.731 + 2315.38i −0.501327 + 1.37739i 0.388652 + 0.921385i \(0.372941\pi\)
−0.889979 + 0.456001i \(0.849281\pi\)
\(42\) 0 0
\(43\) −329.577 1869.12i −0.178246 1.01088i −0.934330 0.356409i \(-0.884001\pi\)
0.756084 0.654474i \(-0.227110\pi\)
\(44\) 0 0
\(45\) 1980.45 3430.24i 0.978000 1.69395i
\(46\) 0 0
\(47\) 985.584 + 827.003i 0.446167 + 0.374379i 0.838011 0.545653i \(-0.183718\pi\)
−0.391844 + 0.920032i \(0.628163\pi\)
\(48\) 0 0
\(49\) 1150.44 + 1992.63i 0.479152 + 0.829915i
\(50\) 0 0
\(51\) −2118.86 5821.51i −0.814631 2.23818i
\(52\) 0 0
\(53\) 3118.81 + 549.931i 1.11029 + 0.195775i 0.698575 0.715537i \(-0.253818\pi\)
0.411718 + 0.911311i \(0.364929\pi\)
\(54\) 0 0
\(55\) 444.089 372.635i 0.146806 0.123185i
\(56\) 0 0
\(57\) 1587.47 + 4651.41i 0.488603 + 1.43164i
\(58\) 0 0
\(59\) 938.249 + 1118.16i 0.269534 + 0.321218i 0.883786 0.467892i \(-0.154986\pi\)
−0.614251 + 0.789110i \(0.710542\pi\)
\(60\) 0 0
\(61\) −920.289 + 5219.22i −0.247323 + 1.40264i 0.567712 + 0.823227i \(0.307829\pi\)
−0.815035 + 0.579411i \(0.803283\pi\)
\(62\) 0 0
\(63\) −981.174 + 357.118i −0.247209 + 0.0899769i
\(64\) 0 0
\(65\) 2130.89 1230.27i 0.504352 0.291188i
\(66\) 0 0
\(67\) −4064.52 + 4843.91i −0.905441 + 1.07906i 0.0910906 + 0.995843i \(0.470965\pi\)
−0.996531 + 0.0832195i \(0.973480\pi\)
\(68\) 0 0
\(69\) 3345.35 + 1931.44i 0.702657 + 0.405679i
\(70\) 0 0
\(71\) −9089.14 + 1602.66i −1.80304 + 0.317925i −0.971411 0.237402i \(-0.923704\pi\)
−0.831632 + 0.555328i \(0.812593\pi\)
\(72\) 0 0
\(73\) −3636.99 1323.76i −0.682491 0.248406i −0.0225741 0.999745i \(-0.507186\pi\)
−0.659917 + 0.751339i \(0.729408\pi\)
\(74\) 0 0
\(75\) 11104.8i 1.97418i
\(76\) 0 0
\(77\) −152.821 −0.0257752
\(78\) 0 0
\(79\) −1439.36 + 3954.62i −0.230630 + 0.633652i −0.999987 0.00516827i \(-0.998355\pi\)
0.769356 + 0.638820i \(0.220577\pi\)
\(80\) 0 0
\(81\) −716.087 4061.13i −0.109143 0.618980i
\(82\) 0 0
\(83\) 6219.89 10773.2i 0.902873 1.56382i 0.0791251 0.996865i \(-0.474787\pi\)
0.823748 0.566957i \(-0.191879\pi\)
\(84\) 0 0
\(85\) −13230.7 11101.8i −1.83123 1.53659i
\(86\) 0 0
\(87\) −5002.47 8664.53i −0.660915 1.14474i
\(88\) 0 0
\(89\) 4134.29 + 11358.9i 0.521940 + 1.43402i 0.868358 + 0.495938i \(0.165176\pi\)
−0.346418 + 0.938080i \(0.612602\pi\)
\(90\) 0 0
\(91\) −638.775 112.633i −0.0771374 0.0136014i
\(92\) 0 0
\(93\) −17225.9 + 14454.3i −1.99167 + 1.67121i
\(94\) 0 0
\(95\) 10316.6 + 9017.49i 1.14312 + 0.999168i
\(96\) 0 0
\(97\) −1907.80 2273.62i −0.202763 0.241643i 0.655075 0.755564i \(-0.272637\pi\)
−0.857838 + 0.513920i \(0.828193\pi\)
\(98\) 0 0
\(99\) −276.771 + 1569.64i −0.0282390 + 0.160151i
\(100\) 0 0
\(101\) 830.282 302.198i 0.0813923 0.0296244i −0.301003 0.953623i \(-0.597321\pi\)
0.382395 + 0.923999i \(0.375099\pi\)
\(102\) 0 0
\(103\) −1371.68 + 791.938i −0.129294 + 0.0746477i −0.563252 0.826285i \(-0.690450\pi\)
0.433958 + 0.900933i \(0.357117\pi\)
\(104\) 0 0
\(105\) −3323.51 + 3960.80i −0.301452 + 0.359256i
\(106\) 0 0
\(107\) 10273.8 + 5931.59i 0.897355 + 0.518088i 0.876341 0.481691i \(-0.159977\pi\)
0.0210141 + 0.999779i \(0.493311\pi\)
\(108\) 0 0
\(109\) 6748.93 1190.02i 0.568044 0.100161i 0.117752 0.993043i \(-0.462431\pi\)
0.450292 + 0.892882i \(0.351320\pi\)
\(110\) 0 0
\(111\) 18859.6 + 6864.33i 1.53069 + 0.557124i
\(112\) 0 0
\(113\) 353.475i 0.0276823i −0.999904 0.0138412i \(-0.995594\pi\)
0.999904 0.0138412i \(-0.00440592\pi\)
\(114\) 0 0
\(115\) 10769.3 0.814317
\(116\) 0 0
\(117\) −2313.74 + 6356.96i −0.169022 + 0.464384i
\(118\) 0 0
\(119\) 790.614 + 4483.79i 0.0558304 + 0.316630i
\(120\) 0 0
\(121\) 7203.86 12477.5i 0.492033 0.852227i
\(122\) 0 0
\(123\) −25697.7 21562.9i −1.69857 1.42527i
\(124\) 0 0
\(125\) −3618.28 6267.05i −0.231570 0.401091i
\(126\) 0 0
\(127\) 761.552 + 2092.35i 0.0472163 + 0.129726i 0.961060 0.276341i \(-0.0891221\pi\)
−0.913843 + 0.406067i \(0.866900\pi\)
\(128\) 0 0
\(129\) 25447.2 + 4487.03i 1.52919 + 0.269637i
\(130\) 0 0
\(131\) 20343.3 17070.1i 1.18544 0.994700i 0.185510 0.982642i \(-0.440606\pi\)
0.999927 0.0120581i \(-0.00383830\pi\)
\(132\) 0 0
\(133\) −555.343 3569.11i −0.0313948 0.201770i
\(134\) 0 0
\(135\) 7757.67 + 9245.23i 0.425661 + 0.507283i
\(136\) 0 0
\(137\) 612.283 3472.43i 0.0326221 0.185009i −0.964143 0.265385i \(-0.914501\pi\)
0.996765 + 0.0803760i \(0.0256121\pi\)
\(138\) 0 0
\(139\) 13225.7 4813.75i 0.684522 0.249146i 0.0237343 0.999718i \(-0.492444\pi\)
0.660788 + 0.750573i \(0.270222\pi\)
\(140\) 0 0
\(141\) −15169.5 + 8758.14i −0.763017 + 0.440528i
\(142\) 0 0
\(143\) −636.434 + 758.472i −0.0311230 + 0.0370909i
\(144\) 0 0
\(145\) −24155.9 13946.4i −1.14891 0.663325i
\(146\) 0 0
\(147\) −30849.6 + 5439.61i −1.42763 + 0.251729i
\(148\) 0 0
\(149\) 33951.2 + 12357.2i 1.52927 + 0.556607i 0.963442 0.267918i \(-0.0863357\pi\)
0.565825 + 0.824526i \(0.308558\pi\)
\(150\) 0 0
\(151\) 22405.3i 0.982644i −0.870978 0.491322i \(-0.836514\pi\)
0.870978 0.491322i \(-0.163486\pi\)
\(152\) 0 0
\(153\) 47485.5 2.02851
\(154\) 0 0
\(155\) −21441.7 + 58910.5i −0.892473 + 2.45205i
\(156\) 0 0
\(157\) −8341.26 47305.7i −0.338402 1.91917i −0.390654 0.920538i \(-0.627751\pi\)
0.0522519 0.998634i \(-0.483360\pi\)
\(158\) 0 0
\(159\) −21558.1 + 37339.7i −0.852738 + 1.47699i
\(160\) 0 0
\(161\) −2174.75 1824.83i −0.0838992 0.0703998i
\(162\) 0 0
\(163\) 5852.63 + 10137.0i 0.220280 + 0.381537i 0.954893 0.296950i \(-0.0959695\pi\)
−0.734613 + 0.678487i \(0.762636\pi\)
\(164\) 0 0
\(165\) 2699.42 + 7416.59i 0.0991522 + 0.272418i
\(166\) 0 0
\(167\) 11805.3 + 2081.60i 0.423297 + 0.0746387i 0.381239 0.924476i \(-0.375497\pi\)
0.0420580 + 0.999115i \(0.486609\pi\)
\(168\) 0 0
\(169\) 18659.8 15657.4i 0.653330 0.548209i
\(170\) 0 0
\(171\) −37664.5 759.921i −1.28807 0.0259882i
\(172\) 0 0
\(173\) −12729.2 15170.1i −0.425315 0.506870i 0.510250 0.860026i \(-0.329553\pi\)
−0.935564 + 0.353156i \(0.885108\pi\)
\(174\) 0 0
\(175\) −1417.18 + 8037.22i −0.0462752 + 0.262440i
\(176\) 0 0
\(177\) −18674.1 + 6796.80i −0.596063 + 0.216949i
\(178\) 0 0
\(179\) 12656.1 7306.98i 0.394996 0.228051i −0.289327 0.957230i \(-0.593431\pi\)
0.684322 + 0.729179i \(0.260098\pi\)
\(180\) 0 0
\(181\) −19336.0 + 23043.8i −0.590215 + 0.703391i −0.975647 0.219345i \(-0.929608\pi\)
0.385432 + 0.922736i \(0.374052\pi\)
\(182\) 0 0
\(183\) −62486.6 36076.6i −1.86588 1.07727i
\(184\) 0 0
\(185\) 55103.1 9716.16i 1.61002 0.283891i
\(186\) 0 0
\(187\) 6530.84 + 2377.03i 0.186761 + 0.0679754i
\(188\) 0 0
\(189\) 3181.49i 0.0890649i
\(190\) 0 0
\(191\) −26426.2 −0.724383 −0.362191 0.932104i \(-0.617971\pi\)
−0.362191 + 0.932104i \(0.617971\pi\)
\(192\) 0 0
\(193\) −11007.9 + 30243.9i −0.295521 + 0.811938i 0.699713 + 0.714424i \(0.253311\pi\)
−0.995234 + 0.0975137i \(0.968911\pi\)
\(194\) 0 0
\(195\) 5817.05 + 32990.1i 0.152980 + 0.867590i
\(196\) 0 0
\(197\) −22446.5 + 38878.6i −0.578385 + 1.00179i 0.417280 + 0.908778i \(0.362984\pi\)
−0.995665 + 0.0930142i \(0.970350\pi\)
\(198\) 0 0
\(199\) −4917.74 4126.47i −0.124182 0.104201i 0.578582 0.815625i \(-0.303606\pi\)
−0.702764 + 0.711423i \(0.748051\pi\)
\(200\) 0 0
\(201\) −43044.2 74554.7i −1.06542 1.84537i
\(202\) 0 0
\(203\) 2514.84 + 6909.47i 0.0610265 + 0.167669i
\(204\) 0 0
\(205\) −92102.0 16240.1i −2.19160 0.386438i
\(206\) 0 0
\(207\) −22681.7 + 19032.2i −0.529341 + 0.444170i
\(208\) 0 0
\(209\) −5142.09 1989.93i −0.117719 0.0455559i
\(210\) 0 0
\(211\) 32561.2 + 38804.9i 0.731367 + 0.871609i 0.995682 0.0928271i \(-0.0295904\pi\)
−0.264315 + 0.964436i \(0.585146\pi\)
\(212\) 0 0
\(213\) 21819.5 123744.i 0.480933 2.72751i
\(214\) 0 0
\(215\) 67694.4 24638.7i 1.46445 0.533018i
\(216\) 0 0
\(217\) 14312.1 8263.10i 0.303937 0.175478i
\(218\) 0 0
\(219\) 33870.9 40365.7i 0.706217 0.841637i
\(220\) 0 0
\(221\) 25546.3 + 14749.2i 0.523050 + 0.301983i
\(222\) 0 0
\(223\) 2412.23 425.340i 0.0485074 0.00855317i −0.149342 0.988786i \(-0.547715\pi\)
0.197849 + 0.980232i \(0.436604\pi\)
\(224\) 0 0
\(225\) 79984.7 + 29112.0i 1.57994 + 0.575053i
\(226\) 0 0
\(227\) 35918.6i 0.697056i 0.937298 + 0.348528i \(0.113318\pi\)
−0.937298 + 0.348528i \(0.886682\pi\)
\(228\) 0 0
\(229\) −33051.1 −0.630253 −0.315126 0.949050i \(-0.602047\pi\)
−0.315126 + 0.949050i \(0.602047\pi\)
\(230\) 0 0
\(231\) 711.601 1955.11i 0.0133356 0.0366393i
\(232\) 0 0
\(233\) −3363.41 19074.9i −0.0619539 0.351358i −0.999988 0.00481606i \(-0.998467\pi\)
0.938035 0.346542i \(-0.112644\pi\)
\(234\) 0 0
\(235\) −24416.9 + 42291.2i −0.442134 + 0.765799i
\(236\) 0 0
\(237\) −43891.0 36828.9i −0.781409 0.655680i
\(238\) 0 0
\(239\) 28728.8 + 49759.7i 0.502946 + 0.871127i 0.999994 + 0.00340461i \(0.00108372\pi\)
−0.497049 + 0.867723i \(0.665583\pi\)
\(240\) 0 0
\(241\) 19044.5 + 52324.4i 0.327896 + 0.900887i 0.988644 + 0.150279i \(0.0480171\pi\)
−0.660748 + 0.750608i \(0.729761\pi\)
\(242\) 0 0
\(243\) 80654.5 + 14221.6i 1.36589 + 0.240843i
\(244\) 0 0
\(245\) −66900.5 + 56136.2i −1.11454 + 0.935213i
\(246\) 0 0
\(247\) −20026.8 12107.5i −0.328259 0.198455i
\(248\) 0 0
\(249\) 108864. + 129739.i 1.75584 + 2.09252i
\(250\) 0 0
\(251\) −2649.04 + 15023.4i −0.0420476 + 0.238464i −0.998587 0.0531390i \(-0.983077\pi\)
0.956540 + 0.291603i \(0.0941885\pi\)
\(252\) 0 0
\(253\) −4072.21 + 1482.16i −0.0636194 + 0.0231556i
\(254\) 0 0
\(255\) 203639. 117571.i 3.13170 1.80809i
\(256\) 0 0
\(257\) −6421.48 + 7652.82i −0.0972230 + 0.115866i −0.812462 0.583014i \(-0.801873\pi\)
0.715239 + 0.698880i \(0.246318\pi\)
\(258\) 0 0
\(259\) −12773.8 7374.98i −0.190424 0.109941i
\(260\) 0 0
\(261\) 75522.6 13316.7i 1.10865 0.195486i
\(262\) 0 0
\(263\) −33819.4 12309.2i −0.488938 0.177959i 0.0857740 0.996315i \(-0.472664\pi\)
−0.574712 + 0.818356i \(0.694886\pi\)
\(264\) 0 0
\(265\) 120204.i 1.71169i
\(266\) 0 0
\(267\) −164570. −2.30849
\(268\) 0 0
\(269\) 43070.1 118334.i 0.595211 1.63533i −0.165478 0.986214i \(-0.552917\pi\)
0.760689 0.649116i \(-0.224861\pi\)
\(270\) 0 0
\(271\) −12760.4 72368.0i −0.173751 0.985389i −0.939576 0.342340i \(-0.888780\pi\)
0.765825 0.643049i \(-0.222331\pi\)
\(272\) 0 0
\(273\) 4415.39 7647.67i 0.0592439 0.102613i
\(274\) 0 0
\(275\) 9543.28 + 8007.76i 0.126192 + 0.105888i
\(276\) 0 0
\(277\) −3268.44 5661.10i −0.0425971 0.0737804i 0.843941 0.536436i \(-0.180230\pi\)
−0.886538 + 0.462656i \(0.846897\pi\)
\(278\) 0 0
\(279\) −58951.1 161967.i −0.757327 2.08074i
\(280\) 0 0
\(281\) 23883.9 + 4211.38i 0.302477 + 0.0533349i 0.322827 0.946458i \(-0.395367\pi\)
−0.0203497 + 0.999793i \(0.506478\pi\)
\(282\) 0 0
\(283\) 50567.4 42431.1i 0.631390 0.529799i −0.269970 0.962869i \(-0.587014\pi\)
0.901361 + 0.433069i \(0.142569\pi\)
\(284\) 0 0
\(285\) −163404. + 89996.0i −2.01174 + 1.10798i
\(286\) 0 0
\(287\) 15847.2 + 18885.9i 0.192392 + 0.229284i
\(288\) 0 0
\(289\) 21452.2 121661.i 0.256848 1.45666i
\(290\) 0 0
\(291\) 37971.1 13820.3i 0.448401 0.163205i
\(292\) 0 0
\(293\) 94398.8 54501.2i 1.09959 0.634849i 0.163478 0.986547i \(-0.447729\pi\)
0.936114 + 0.351698i \(0.114396\pi\)
\(294\) 0 0
\(295\) −35612.2 + 42440.9i −0.409218 + 0.487686i
\(296\) 0 0
\(297\) −4205.82 2428.23i −0.0476801 0.0275281i
\(298\) 0 0
\(299\) −18113.8 + 3193.95i −0.202613 + 0.0357262i
\(300\) 0 0
\(301\) −17845.1 6495.09i −0.196964 0.0716889i
\(302\) 0 0
\(303\) 12029.4i 0.131026i
\(304\) 0 0
\(305\) −201157. −2.16239
\(306\) 0 0
\(307\) −33364.0 + 91666.9i −0.353999 + 0.972603i 0.627073 + 0.778960i \(0.284253\pi\)
−0.981072 + 0.193643i \(0.937970\pi\)
\(308\) 0 0
\(309\) −3744.50 21236.1i −0.0392172 0.222412i
\(310\) 0 0
\(311\) −28528.3 + 49412.5i −0.294955 + 0.510876i −0.974974 0.222317i \(-0.928638\pi\)
0.680020 + 0.733194i \(0.261971\pi\)
\(312\) 0 0
\(313\) 126121. + 105828.i 1.28735 + 1.08022i 0.992185 + 0.124772i \(0.0398201\pi\)
0.295168 + 0.955445i \(0.404624\pi\)
\(314\) 0 0
\(315\) −19815.8 34321.9i −0.199705 0.345900i
\(316\) 0 0
\(317\) −1581.86 4346.13i −0.0157416 0.0432498i 0.931573 0.363554i \(-0.118437\pi\)
−0.947315 + 0.320305i \(0.896215\pi\)
\(318\) 0 0
\(319\) 11053.5 + 1949.03i 0.108622 + 0.0191530i
\(320\) 0 0
\(321\) −123725. + 103818.i −1.20074 + 1.00754i
\(322\) 0 0
\(323\) −31782.4 + 161165.i −0.304636 + 1.54477i
\(324\) 0 0
\(325\) 33987.9 + 40505.2i 0.321779 + 0.383482i
\(326\) 0 0
\(327\) −16201.5 + 91883.4i −0.151517 + 0.859293i
\(328\) 0 0
\(329\) 12096.8 4402.89i 0.111758 0.0406767i
\(330\) 0 0
\(331\) 153760. 88773.4i 1.40342 0.810264i 0.408677 0.912679i \(-0.365990\pi\)
0.994742 + 0.102415i \(0.0326570\pi\)
\(332\) 0 0
\(333\) −98883.8 + 117845.i −0.891737 + 1.06273i
\(334\) 0 0
\(335\) −207851. 120003.i −1.85210 1.06931i
\(336\) 0 0
\(337\) 81386.6 14350.7i 0.716627 0.126361i 0.196567 0.980490i \(-0.437021\pi\)
0.520060 + 0.854130i \(0.325910\pi\)
\(338\) 0 0
\(339\) 4522.17 + 1645.94i 0.0393503 + 0.0143223i
\(340\) 0 0
\(341\) 25226.8i 0.216947i
\(342\) 0 0
\(343\) 47045.6 0.399881
\(344\) 0 0
\(345\) −50146.8 + 137777.i −0.421313 + 1.15755i
\(346\) 0 0
\(347\) −27172.5 154103.i −0.225668 1.27983i −0.861404 0.507921i \(-0.830414\pi\)
0.635735 0.771907i \(-0.280697\pi\)
\(348\) 0 0
\(349\) −53851.5 + 93273.5i −0.442127 + 0.765786i −0.997847 0.0655833i \(-0.979109\pi\)
0.555720 + 0.831369i \(0.312443\pi\)
\(350\) 0 0
\(351\) −15790.2 13249.5i −0.128166 0.107544i
\(352\) 0 0
\(353\) −38337.3 66402.2i −0.307661 0.532884i 0.670189 0.742190i \(-0.266213\pi\)
−0.977850 + 0.209306i \(0.932880\pi\)
\(354\) 0 0
\(355\) −119813. 329183.i −0.950707 2.61205i
\(356\) 0 0
\(357\) −61044.7 10763.8i −0.478973 0.0844559i
\(358\) 0 0
\(359\) −34087.3 + 28602.6i −0.264486 + 0.221931i −0.765380 0.643578i \(-0.777449\pi\)
0.500894 + 0.865509i \(0.333005\pi\)
\(360\) 0 0
\(361\) 27788.3 127324.i 0.213230 0.977002i
\(362\) 0 0
\(363\) 126085. + 150263.i 0.956868 + 1.14035i
\(364\) 0 0
\(365\) 25509.8 144673.i 0.191479 1.08593i
\(366\) 0 0
\(367\) −105525. + 38408.0i −0.783473 + 0.285161i −0.702620 0.711565i \(-0.747987\pi\)
−0.0808531 + 0.996726i \(0.525764\pi\)
\(368\) 0 0
\(369\) 222680. 128564.i 1.63542 0.944209i
\(370\) 0 0
\(371\) 20368.2 24273.8i 0.147980 0.176356i
\(372\) 0 0
\(373\) 135345. + 78141.6i 0.972804 + 0.561649i 0.900090 0.435704i \(-0.143501\pi\)
0.0727141 + 0.997353i \(0.476834\pi\)
\(374\) 0 0
\(375\) 97025.6 17108.2i 0.689960 0.121659i
\(376\) 0 0
\(377\) 44765.9 + 16293.5i 0.314967 + 0.114639i
\(378\) 0 0
\(379\) 180715.i 1.25810i −0.777364 0.629051i \(-0.783443\pi\)
0.777364 0.629051i \(-0.216557\pi\)
\(380\) 0 0
\(381\) −30314.5 −0.208834
\(382\) 0 0
\(383\) 11888.3 32662.7i 0.0810439 0.222666i −0.892552 0.450944i \(-0.851087\pi\)
0.973596 + 0.228278i \(0.0733095\pi\)
\(384\) 0 0
\(385\) −1007.24 5712.35i −0.00679535 0.0385383i
\(386\) 0 0
\(387\) −99030.7 + 171526.i −0.661223 + 1.14527i
\(388\) 0 0
\(389\) −179821. 150888.i −1.18834 0.997137i −0.999887 0.0150555i \(-0.995208\pi\)
−0.188455 0.982082i \(-0.560348\pi\)
\(390\) 0 0
\(391\) 64554.4 + 111812.i 0.422253 + 0.731363i
\(392\) 0 0
\(393\) 123658. + 339747.i 0.800638 + 2.19973i
\(394\) 0 0
\(395\) −157308. 27737.6i −1.00822 0.177777i
\(396\) 0 0
\(397\) −164819. + 138300.i −1.04575 + 0.877487i −0.992640 0.121102i \(-0.961357\pi\)
−0.0531080 + 0.998589i \(0.516913\pi\)
\(398\) 0 0
\(399\) 48247.1 + 9514.56i 0.303058 + 0.0597644i
\(400\) 0 0
\(401\) 118155. + 140811.i 0.734789 + 0.875688i 0.995978 0.0895999i \(-0.0285588\pi\)
−0.261188 + 0.965288i \(0.584114\pi\)
\(402\) 0 0
\(403\) 18592.9 105445.i 0.114482 0.649258i
\(404\) 0 0
\(405\) 147083. 53533.7i 0.896709 0.326375i
\(406\) 0 0
\(407\) −19498.9 + 11257.7i −0.117712 + 0.0679612i
\(408\) 0 0
\(409\) 161880. 192921.i 0.967714 1.15328i −0.0204371 0.999791i \(-0.506506\pi\)
0.988151 0.153485i \(-0.0490498\pi\)
\(410\) 0 0
\(411\) 41573.4 + 24002.4i 0.246111 + 0.142092i
\(412\) 0 0
\(413\) 14383.0 2536.11i 0.0843235 0.0148685i
\(414\) 0 0
\(415\) 443689. + 161490.i 2.57622 + 0.937667i
\(416\) 0 0
\(417\) 191617.i 1.10195i
\(418\) 0 0
\(419\) 155593. 0.886261 0.443130 0.896457i \(-0.353868\pi\)
0.443130 + 0.896457i \(0.353868\pi\)
\(420\) 0 0
\(421\) −113197. + 311006.i −0.638661 + 1.75471i 0.0172286 + 0.999852i \(0.494516\pi\)
−0.655890 + 0.754856i \(0.727707\pi\)
\(422\) 0 0
\(423\) −23314.4 132222.i −0.130299 0.738965i
\(424\) 0 0
\(425\) 185577. 321429.i 1.02742 1.77954i
\(426\) 0 0
\(427\) 40621.4 + 34085.4i 0.222792 + 0.186944i
\(428\) 0 0
\(429\) −6739.97 11674.0i −0.0366221 0.0634314i
\(430\) 0 0
\(431\) 11427.4 + 31396.5i 0.0615166 + 0.169016i 0.966643 0.256127i \(-0.0824464\pi\)
−0.905127 + 0.425142i \(0.860224\pi\)
\(432\) 0 0
\(433\) −87468.3 15423.0i −0.466525 0.0822609i −0.0645556 0.997914i \(-0.520563\pi\)
−0.401969 + 0.915653i \(0.631674\pi\)
\(434\) 0 0
\(435\) 290903. 244097.i 1.53734 1.28998i
\(436\) 0 0
\(437\) −49413.9 89719.7i −0.258754 0.469813i
\(438\) 0 0
\(439\) −11796.9 14059.0i −0.0612124 0.0729501i 0.734569 0.678534i \(-0.237384\pi\)
−0.795782 + 0.605583i \(0.792940\pi\)
\(440\) 0 0
\(441\) 41694.5 236461.i 0.214389 1.21586i
\(442\) 0 0
\(443\) −5871.78 + 2137.15i −0.0299201 + 0.0108900i −0.356937 0.934129i \(-0.616179\pi\)
0.327017 + 0.945019i \(0.393957\pi\)
\(444\) 0 0
\(445\) −397338. + 229403.i −2.00650 + 1.15846i
\(446\) 0 0
\(447\) −316184. + 376813.i −1.58243 + 1.88587i
\(448\) 0 0
\(449\) −86468.3 49922.5i −0.428908 0.247630i 0.269973 0.962868i \(-0.412985\pi\)
−0.698881 + 0.715238i \(0.746319\pi\)
\(450\) 0 0
\(451\) 37061.7 6534.97i 0.182210 0.0321285i
\(452\) 0 0
\(453\) 286641. + 104329.i 1.39682 + 0.508402i
\(454\) 0 0
\(455\) 24619.4i 0.118920i
\(456\) 0 0
\(457\) 304377. 1.45740 0.728700 0.684833i \(-0.240125\pi\)
0.728700 + 0.684833i \(0.240125\pi\)
\(458\) 0 0
\(459\) −49486.0 + 135962.i −0.234886 + 0.645344i
\(460\) 0 0
\(461\) 8793.03 + 49867.7i 0.0413749 + 0.234648i 0.998482 0.0550872i \(-0.0175437\pi\)
−0.957107 + 0.289736i \(0.906433\pi\)
\(462\) 0 0
\(463\) −38991.0 + 67534.3i −0.181887 + 0.315038i −0.942523 0.334141i \(-0.891554\pi\)
0.760636 + 0.649179i \(0.224887\pi\)
\(464\) 0 0
\(465\) −653827. 548626.i −3.02383 2.53729i
\(466\) 0 0
\(467\) −187480. 324725.i −0.859649 1.48896i −0.872264 0.489035i \(-0.837349\pi\)
0.0126152 0.999920i \(-0.495984\pi\)
\(468\) 0 0
\(469\) 21639.2 + 59453.1i 0.0983773 + 0.270289i
\(470\) 0 0
\(471\) 644044. + 113562.i 2.90318 + 0.511908i
\(472\) 0 0
\(473\) −22206.3 + 18633.3i −0.0992554 + 0.0832852i
\(474\) 0 0
\(475\) −152340. + 251981.i −0.675191 + 1.11681i
\(476\) 0 0
\(477\) −212431. 253166.i −0.933646 1.11268i
\(478\) 0 0
\(479\) −45381.3 + 257370.i −0.197791 + 1.12173i 0.710597 + 0.703599i \(0.248425\pi\)
−0.908388 + 0.418128i \(0.862686\pi\)
\(480\) 0 0
\(481\) −89800.7 + 32684.8i −0.388141 + 0.141272i
\(482\) 0 0
\(483\) 33472.5 19325.4i 0.143481 0.0828387i
\(484\) 0 0
\(485\) 72412.3 86297.6i 0.307843 0.366873i
\(486\) 0 0
\(487\) −276196. 159462.i −1.16455 0.672355i −0.212162 0.977235i \(-0.568050\pi\)
−0.952391 + 0.304880i \(0.901384\pi\)
\(488\) 0 0
\(489\) −156940. + 27672.8i −0.656322 + 0.115727i
\(490\) 0 0
\(491\) −370318. 134785.i −1.53607 0.559085i −0.570973 0.820969i \(-0.693434\pi\)
−0.965099 + 0.261884i \(0.915656\pi\)
\(492\) 0 0
\(493\) 334395.i 1.37583i
\(494\) 0 0
\(495\) −60496.5 −0.246899
\(496\) 0 0
\(497\) −31584.2 + 86776.9i −0.127867 + 0.351310i
\(498\) 0 0
\(499\) −13867.0 78643.7i −0.0556906 0.315837i 0.944219 0.329320i \(-0.106819\pi\)
−0.999909 + 0.0134826i \(0.995708\pi\)
\(500\) 0 0
\(501\) −81601.7 + 141338.i −0.325105 + 0.563098i
\(502\) 0 0
\(503\) 86261.9 + 72382.4i 0.340944 + 0.286086i 0.797142 0.603793i \(-0.206344\pi\)
−0.456197 + 0.889879i \(0.650789\pi\)
\(504\) 0 0
\(505\) 16768.3 + 29043.6i 0.0657518 + 0.113885i
\(506\) 0 0
\(507\) 113424. + 311631.i 0.441255 + 1.21234i
\(508\) 0 0
\(509\) 161578. + 28490.6i 0.623658 + 0.109968i 0.476542 0.879151i \(-0.341890\pi\)
0.147116 + 0.989119i \(0.453001\pi\)
\(510\) 0 0
\(511\) −29665.9 + 24892.6i −0.113610 + 0.0953299i
\(512\) 0 0
\(513\) 41427.1 107050.i 0.157416 0.406773i
\(514\) 0 0
\(515\) −38642.8 46052.7i −0.145698 0.173636i
\(516\) 0 0
\(517\) 3412.29 19352.1i 0.0127663 0.0724012i
\(518\) 0 0
\(519\) 253351. 92212.3i 0.940564 0.342337i
\(520\) 0 0
\(521\) −165547. + 95578.7i −0.609883 + 0.352116i −0.772919 0.634504i \(-0.781204\pi\)
0.163037 + 0.986620i \(0.447871\pi\)
\(522\) 0 0
\(523\) 53445.8 63694.2i 0.195393 0.232861i −0.659448 0.751750i \(-0.729210\pi\)
0.854841 + 0.518889i \(0.173654\pi\)
\(524\) 0 0
\(525\) −96224.8 55555.4i −0.349115 0.201562i
\(526\) 0 0
\(527\) −740159. + 130510.i −2.66504 + 0.469919i
\(528\) 0 0
\(529\) 187316. + 68177.3i 0.669364 + 0.243629i
\(530\) 0 0
\(531\) 152323.i 0.540225i
\(532\) 0 0
\(533\) 159730. 0.562254
\(534\) 0 0
\(535\) −154004. + 423124.i −0.538054 + 1.47829i
\(536\) 0 0
\(537\) 34549.4 + 195939.i 0.119810 + 0.679474i
\(538\) 0 0
\(539\) 17571.2 30434.2i 0.0604817 0.104757i
\(540\) 0 0
\(541\) −47919.3 40209.1i −0.163725 0.137382i 0.557244 0.830349i \(-0.311859\pi\)
−0.720969 + 0.692967i \(0.756303\pi\)
\(542\) 0 0
\(543\) −204773. 354677.i −0.694500 1.20291i
\(544\) 0 0
\(545\) 88964.2 + 244427.i 0.299518 + 0.822918i
\(546\) 0 0
\(547\) 36797.9 + 6488.47i 0.122984 + 0.0216854i 0.234801 0.972043i \(-0.424556\pi\)
−0.111817 + 0.993729i \(0.535667\pi\)
\(548\) 0 0
\(549\) 423664. 355496.i 1.40565 1.17948i
\(550\) 0 0
\(551\) −5351.39 + 265235.i −0.0176264 + 0.873630i
\(552\) 0 0
\(553\) 27066.6 + 32256.7i 0.0885081 + 0.105480i
\(554\) 0 0
\(555\) −132281. + 750202.i −0.429448 + 2.43552i
\(556\) 0 0
\(557\) 449858. 163735.i 1.44999 0.527753i 0.507402 0.861709i \(-0.330606\pi\)
0.942589 + 0.333956i \(0.108384\pi\)
\(558\) 0 0
\(559\) −106553. + 61518.6i −0.340991 + 0.196871i
\(560\) 0 0
\(561\) −60820.9 + 72483.6i −0.193254 + 0.230311i
\(562\) 0 0
\(563\) 158180. + 91325.4i 0.499040 + 0.288121i 0.728317 0.685240i \(-0.240303\pi\)
−0.229277 + 0.973361i \(0.573636\pi\)
\(564\) 0 0
\(565\) 13212.7 2329.75i 0.0413899 0.00729815i
\(566\) 0 0
\(567\) −38772.9 14112.2i −0.120604 0.0438963i
\(568\) 0 0
\(569\) 307756.i 0.950565i −0.879833 0.475283i \(-0.842346\pi\)
0.879833 0.475283i \(-0.157654\pi\)
\(570\) 0 0
\(571\) 474577. 1.45557 0.727787 0.685803i \(-0.240549\pi\)
0.727787 + 0.685803i \(0.240549\pi\)
\(572\) 0 0
\(573\) 123052. 338083.i 0.374783 1.02971i
\(574\) 0 0
\(575\) 40187.1 + 227912.i 0.121549 + 0.689338i
\(576\) 0 0
\(577\) −15494.2 + 26836.7i −0.0465390 + 0.0806078i −0.888357 0.459154i \(-0.848152\pi\)
0.841818 + 0.539762i \(0.181486\pi\)
\(578\) 0 0
\(579\) −335666. 281657.i −1.00127 0.840164i
\(580\) 0 0
\(581\) −62234.2 107793.i −0.184364 0.319329i
\(582\) 0 0
\(583\) −16543.4 45452.7i −0.0486730 0.133728i
\(584\) 0 0
\(585\) −252869. 44587.6i −0.738896 0.130287i
\(586\) 0 0
\(587\) −355861. + 298603.i −1.03277 + 0.866598i −0.991178 0.132536i \(-0.957688\pi\)
−0.0415934 + 0.999135i \(0.513243\pi\)
\(588\) 0 0
\(589\) 589168. 91673.0i 1.69828 0.264247i
\(590\) 0 0
\(591\) −392870. 468205.i −1.12480 1.34048i
\(592\) 0 0
\(593\) −483.474 + 2741.92i −0.00137488 + 0.00779731i −0.985487 0.169748i \(-0.945705\pi\)
0.984113 + 0.177545i \(0.0568157\pi\)
\(594\) 0 0
\(595\) −162390. + 59105.3i −0.458697 + 0.166952i
\(596\) 0 0
\(597\) 75691.0 43700.2i 0.212371 0.122613i
\(598\) 0 0
\(599\) −18966.7 + 22603.6i −0.0528613 + 0.0629976i −0.791827 0.610745i \(-0.790870\pi\)
0.738966 + 0.673743i \(0.235314\pi\)
\(600\) 0 0
\(601\) −20074.7 11590.2i −0.0555777 0.0320878i 0.471954 0.881623i \(-0.343549\pi\)
−0.527531 + 0.849536i \(0.676882\pi\)
\(602\) 0 0
\(603\) 649841. 114585.i 1.78720 0.315131i
\(604\) 0 0
\(605\) 513880. + 187037.i 1.40395 + 0.510995i
\(606\) 0 0
\(607\) 199091.i 0.540350i −0.962811 0.270175i \(-0.912918\pi\)
0.962811 0.270175i \(-0.0870815\pi\)
\(608\) 0 0
\(609\) −100106. −0.269915
\(610\) 0 0
\(611\) 28526.0 78374.6i 0.0764115 0.209939i
\(612\) 0 0
\(613\) −73960.7 419452.i −0.196825 1.11625i −0.909796 0.415056i \(-0.863762\pi\)
0.712971 0.701194i \(-0.247349\pi\)
\(614\) 0 0
\(615\) 636634. 1.10268e6i 1.68322 2.91541i
\(616\) 0 0
\(617\) −5407.03 4537.04i −0.0142033 0.0119180i 0.635658 0.771971i \(-0.280729\pi\)
−0.649862 + 0.760053i \(0.725173\pi\)
\(618\) 0 0
\(619\) 267202. + 462808.i 0.697362 + 1.20787i 0.969378 + 0.245574i \(0.0789765\pi\)
−0.272015 + 0.962293i \(0.587690\pi\)
\(620\) 0 0
\(621\) −30856.3 84777.0i −0.0800130 0.219834i
\(622\) 0 0
\(623\) 119110. + 21002.3i 0.306882 + 0.0541115i
\(624\) 0 0
\(625\) −180108. + 151129.i −0.461077 + 0.386889i
\(626\) 0 0
\(627\) 49401.9 56519.2i 0.125663 0.143767i
\(628\) 0 0
\(629\) 431180. + 513861.i 1.08983 + 1.29881i
\(630\) 0 0
\(631\) 130960. 742708.i 0.328911 1.86535i −0.151720 0.988424i \(-0.548481\pi\)
0.480631 0.876923i \(-0.340408\pi\)
\(632\) 0 0
\(633\) −648068. + 235878.i −1.61738 + 0.588680i
\(634\) 0 0
\(635\) −73191.2 + 42257.0i −0.181515 + 0.104797i
\(636\) 0 0
\(637\) 95876.6 114261.i 0.236284 0.281592i
\(638\) 0 0
\(639\) 834095. + 481565.i 2.04274 + 1.17938i
\(640\) 0 0
\(641\) −45355.0 + 7997.30i −0.110385 + 0.0194638i −0.228568 0.973528i \(-0.573404\pi\)
0.118183 + 0.992992i \(0.462293\pi\)
\(642\) 0 0
\(643\) −610909. 222353.i −1.47759 0.537800i −0.527442 0.849591i \(-0.676849\pi\)
−0.950151 + 0.311791i \(0.899071\pi\)
\(644\) 0 0
\(645\) 980774.i 2.35749i
\(646\) 0 0
\(647\) −156389. −0.373592 −0.186796 0.982399i \(-0.559810\pi\)
−0.186796 + 0.982399i \(0.559810\pi\)
\(648\) 0 0
\(649\) 7624.97 20949.4i 0.0181029 0.0497374i
\(650\) 0 0
\(651\) 39070.2 + 221578.i 0.0921900 + 0.522835i
\(652\) 0 0
\(653\) −161708. + 280086.i −0.379232 + 0.656849i −0.990951 0.134226i \(-0.957145\pi\)
0.611719 + 0.791075i \(0.290478\pi\)
\(654\) 0 0
\(655\) 772150. + 647911.i 1.79978 + 1.51019i
\(656\) 0 0
\(657\) 201948. + 349785.i 0.467853 + 0.810345i
\(658\) 0 0
\(659\) 23712.1 + 65148.5i 0.0546009 + 0.150015i 0.963995 0.265922i \(-0.0856762\pi\)
−0.909394 + 0.415936i \(0.863454\pi\)
\(660\) 0 0
\(661\) −730123. 128740.i −1.67106 0.294653i −0.743616 0.668607i \(-0.766891\pi\)
−0.927447 + 0.373954i \(0.878002\pi\)
\(662\) 0 0
\(663\) −307647. + 258147.i −0.699884 + 0.587273i
\(664\) 0 0
\(665\) 129751. 44282.3i 0.293404 0.100135i
\(666\) 0 0
\(667\) 134026. + 159726.i 0.301257 + 0.359024i
\(668\) 0 0
\(669\) −5790.80 + 32841.3i −0.0129386 + 0.0733783i
\(670\) 0 0
\(671\) 76063.4 27684.8i 0.168939 0.0614889i
\(672\) 0 0
\(673\) −555858. + 320925.i −1.22725 + 0.708554i −0.966454 0.256839i \(-0.917319\pi\)
−0.260798 + 0.965393i \(0.583986\pi\)
\(674\) 0 0
\(675\) −166709. + 198676.i −0.365890 + 0.436051i
\(676\) 0 0
\(677\) 276698. + 159752.i 0.603711 + 0.348552i 0.770500 0.637440i \(-0.220007\pi\)
−0.166789 + 0.985993i \(0.553340\pi\)
\(678\) 0 0
\(679\) −29245.8 + 5156.82i −0.0634342 + 0.0111852i
\(680\) 0 0
\(681\) −459523. 167253.i −0.990862 0.360644i
\(682\) 0 0
\(683\) 368384.i 0.789694i −0.918747 0.394847i \(-0.870798\pi\)
0.918747 0.394847i \(-0.129202\pi\)
\(684\) 0 0
\(685\) 133833. 0.285221
\(686\) 0 0
\(687\) 153900. 422838.i 0.326081 0.895902i
\(688\) 0 0
\(689\) −35649.9 202180.i −0.0750964 0.425893i
\(690\) 0 0
\(691\) 165830. 287226.i 0.347302 0.601544i −0.638467 0.769649i \(-0.720431\pi\)
0.985769 + 0.168105i \(0.0537647\pi\)
\(692\) 0 0
\(693\) 12216.6 + 10250.9i 0.0254381 + 0.0213451i
\(694\) 0 0
\(695\) 267105. + 462639.i 0.552983 + 0.957795i
\(696\) 0 0
\(697\) −383474. 1.05359e6i −0.789352 2.16873i
\(698\) 0 0
\(699\) 259695. + 45791.3i 0.531508 + 0.0937191i
\(700\) 0 0
\(701\) 24515.3 20570.8i 0.0498885 0.0418615i −0.617502 0.786569i \(-0.711855\pi\)
0.667391 + 0.744707i \(0.267411\pi\)
\(702\) 0 0
\(703\) −333780. 414484.i −0.675382 0.838682i
\(704\) 0 0
\(705\) −427356. 509303.i −0.859827 1.02470i
\(706\) 0 0
\(707\) 1535.17 8706.39i 0.00307127 0.0174180i
\(708\) 0 0
\(709\) −867795. + 315852.i −1.72633 + 0.628334i −0.998359 0.0572695i \(-0.981761\pi\)
−0.727975 + 0.685604i \(0.759538\pi\)
\(710\) 0 0
\(711\) 380332. 219585.i 0.752357 0.434373i
\(712\) 0 0
\(713\) 301233. 358996.i 0.592548 0.706171i
\(714\) 0 0
\(715\) −32545.9 18790.4i −0.0636626 0.0367556i
\(716\) 0 0
\(717\) −770372. + 135837.i −1.49852 + 0.264229i
\(718\) 0 0
\(719\) −656850. 239074.i −1.27060 0.462460i −0.383287 0.923629i \(-0.625208\pi\)
−0.887312 + 0.461169i \(0.847430\pi\)
\(720\) 0 0
\(721\) 15847.8i 0.0304858i
\(722\) 0 0
\(723\) −758090. −1.45025
\(724\) 0 0
\(725\) 205008. 563255.i 0.390027 1.07159i
\(726\) 0 0
\(727\) −97044.7 550368.i −0.183613 1.04132i −0.927725 0.373265i \(-0.878238\pi\)
0.744112 0.668055i \(-0.232873\pi\)
\(728\) 0 0
\(729\) −390492. + 676353.i −0.734780 + 1.27268i
\(730\) 0 0
\(731\) 661588. + 555138.i 1.23809 + 1.03888i
\(732\) 0 0
\(733\) 93102.8 + 161259.i 0.173283 + 0.300134i 0.939566 0.342369i \(-0.111229\pi\)
−0.766283 + 0.642503i \(0.777896\pi\)
\(734\) 0 0
\(735\) −406658. 1.11728e6i −0.752757 2.06818i
\(736\) 0 0
\(737\) 95110.8 + 16770.6i 0.175103 + 0.0308755i
\(738\) 0 0
\(739\) 620269. 520467.i 1.13577 0.953025i 0.136479 0.990643i \(-0.456421\pi\)
0.999292 + 0.0376175i \(0.0119769\pi\)
\(740\) 0 0
\(741\) 248151. 199833.i 0.451938 0.363942i
\(742\) 0 0
\(743\) −315238. 375686.i −0.571032 0.680530i 0.400810 0.916161i \(-0.368729\pi\)
−0.971842 + 0.235631i \(0.924284\pi\)
\(744\) 0 0
\(745\) −238133. + 1.35052e6i −0.429050 + 2.43326i
\(746\) 0 0
\(747\) −1.21987e6 + 443995.i −2.18610 + 0.795677i
\(748\) 0 0
\(749\) 102797. 59349.6i 0.183238 0.105792i
\(750\) 0 0
\(751\) −374067. + 445796.i −0.663239 + 0.790418i −0.987847 0.155431i \(-0.950323\pi\)
0.324608 + 0.945849i \(0.394768\pi\)
\(752\) 0 0
\(753\) −179867. 103846.i −0.317220 0.183147i
\(754\) 0 0
\(755\) 837494. 147673.i 1.46922 0.259064i
\(756\) 0 0
\(757\) 186518. + 67886.8i 0.325483 + 0.118466i 0.499593 0.866260i \(-0.333483\pi\)
−0.174111 + 0.984726i \(0.555705\pi\)
\(758\) 0 0
\(759\) 58999.3i 0.102415i
\(760\) 0 0
\(761\) −325873. −0.562703 −0.281352 0.959605i \(-0.590783\pi\)
−0.281352 + 0.959605i \(0.590783\pi\)
\(762\) 0 0
\(763\) 23452.1 64434.1i 0.0402840 0.110679i
\(764\) 0 0
\(765\) 312976. + 1.77498e6i 0.534797 + 3.03298i
\(766\) 0 0
\(767\) 47311.9 81946.6i 0.0804229 0.139296i
\(768\) 0 0
\(769\) 512619. + 430138.i 0.866845 + 0.727370i 0.963431 0.267955i \(-0.0863478\pi\)
−0.0965860 + 0.995325i \(0.530792\pi\)
\(770\) 0 0
\(771\) −68004.9 117788.i −0.114401 0.198149i
\(772\) 0 0
\(773\) 156644. + 430375.i 0.262152 + 0.720257i 0.999022 + 0.0442223i \(0.0140810\pi\)
−0.736870 + 0.676035i \(0.763697\pi\)
\(774\) 0 0
\(775\) −1.32674e6 233940.i −2.20893 0.389494i
\(776\) 0 0
\(777\) 153832. 129080.i 0.254803 0.213805i
\(778\) 0 0
\(779\) 287303. + 841821.i 0.473441 + 1.38722i
\(780\) 0 0
\(781\) 90609.7 + 107984.i 0.148550 + 0.177035i
\(782\) 0 0
\(783\) −40575.7 + 230116.i −0.0661824 + 0.375339i
\(784\) 0 0
\(785\) 1.71328e6 623582.i 2.78028 1.01194i
\(786\) 0 0
\(787\) 405172. 233926.i 0.654169 0.377685i −0.135883 0.990725i \(-0.543387\pi\)
0.790052 + 0.613040i \(0.210054\pi\)
\(788\) 0 0
\(789\) 314955. 375349.i 0.505936 0.602950i
\(790\) 0 0
\(791\) −3062.93 1768.38i −0.00489535 0.00282633i
\(792\) 0