Properties

Label 76.5.j.a.41.1
Level $76$
Weight $5$
Character 76.41
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 41.1
Character \(\chi\) \(=\) 76.41
Dual form 76.5.j.a.13.1

$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{13}{18}\right)\) \(1\)

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 −0.873394 0.487014i \(-0.838086\pi\)
0.356012 0.934481i \(-0.384136\pi\)
\(4\) 0 0
\(5\) 6.59099 37.3793i 0.263640 1.49517i −0.509242 0.860623i \(-0.670074\pi\)
0.772881 0.634551i \(-0.218815\pi\)
\(6\) 0 0
\(7\) 5.00284 + 8.66518i 0.102099 + 0.176840i 0.912549 0.408967i \(-0.134111\pi\)
−0.810450 + 0.585807i \(0.800778\pi\)
\(8\) 0 0
\(9\) −79.9406 + 67.0781i −0.986921 + 0.828125i
\(10\) 0 0
\(11\) −7.63671 + 13.2272i −0.0631133 + 0.109315i −0.895856 0.444345i \(-0.853436\pi\)
0.832742 + 0.553661i \(0.186770\pi\)
\(12\) 0 0
\(13\) −22.1718 + 60.9166i −0.131194 + 0.360453i −0.987845 0.155444i \(-0.950319\pi\)
0.856650 + 0.515897i \(0.172541\pi\)
\(14\) 0 0
\(15\) −508.902 + 89.7331i −2.26179 + 0.398814i
\(16\) 0 0
\(17\) −348.579 292.493i −1.20616 1.01209i −0.999432 0.0336857i \(-0.989275\pi\)
−0.206724 0.978399i \(-0.566280\pi\)
\(18\) 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 0.995302 + 0.0968164i \(0.0308660\pi\)
−0.902165 + 0.431391i \(0.858023\pi\)
\(24\) 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 0.408227 0.912881i \(-0.366147\pi\)
−0.969900 + 0.243505i \(0.921703\pi\)
\(30\) 0 0
\(31\) 1430.40 825.841i 1.48845 0.859356i 0.488535 0.872544i \(-0.337532\pi\)
0.999913 + 0.0131887i \(0.00419821\pi\)
\(32\) 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 \(0.180974\pi\)
−0.842685 + 0.538407i \(0.819026\pi\)
\(38\) 0 0
\(39\) 882.576 0.580260
\(40\) 0 0
\(41\) −842.731 2315.38i −0.501327 1.37739i −0.889979 0.456001i \(-0.849281\pi\)
0.388652 0.921385i \(-0.372941\pi\)
\(42\) 0 0
\(43\) −329.577 + 1869.12i −0.178246 + 1.01088i 0.756084 + 0.654474i \(0.227110\pi\)
−0.934330 + 0.356409i \(0.884001\pi\)
\(44\) 0 0
\(45\) 1980.45 + 3430.24i 0.978000 + 1.69395i
\(46\) 0 0
\(47\) 985.584 827.003i 0.446167 0.374379i −0.391844 0.920032i \(-0.628163\pi\)
0.838011 + 0.545653i \(0.183718\pi\)
\(48\) 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 0.411718 0.911311i \(-0.364929\pi\)
0.698575 + 0.715537i \(0.253818\pi\)
\(54\) 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 −0.614251 0.789110i \(-0.710542\pi\)
0.883786 + 0.467892i \(0.154986\pi\)
\(60\) 0 0
\(61\) −920.289 5219.22i −0.247323 1.40264i −0.815035 0.579411i \(-0.803283\pi\)
0.567712 0.823227i \(-0.307829\pi\)
\(62\) 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 −0.996531 0.0832195i \(-0.973480\pi\)
0.0910906 0.995843i \(-0.470965\pi\)
\(68\) 0 0
\(69\) 3345.35 1931.44i 0.702657 0.405679i
\(70\) 0 0
\(71\) −9089.14 1602.66i −1.80304 0.317925i −0.831632 0.555328i \(-0.812593\pi\)
−0.971411 + 0.237402i \(0.923704\pi\)
\(72\) 0 0
\(73\) −3636.99 + 1323.76i −0.682491 + 0.248406i −0.659917 0.751339i \(-0.729408\pi\)
−0.0225741 + 0.999745i \(0.507186\pi\)
\(74\) 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 0.769356 0.638820i \(-0.220577\pi\)
−0.999987 + 0.00516827i \(0.998355\pi\)
\(80\) 0 0
\(81\) −716.087 + 4061.13i −0.109143 + 0.618980i
\(82\) 0 0
\(83\) 6219.89 + 10773.2i 0.902873 + 1.56382i 0.823748 + 0.566957i \(0.191879\pi\)
0.0791251 + 0.996865i \(0.474787\pi\)
\(84\) 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 −0.346418 0.938080i \(-0.612602\pi\)
0.868358 0.495938i \(-0.165176\pi\)
\(90\) 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 −0.857838 0.513920i \(-0.828193\pi\)
0.655075 + 0.755564i \(0.272637\pi\)
\(98\) 0 0
\(99\) −276.771 1569.64i −0.0282390 0.160151i
\(100\) 0 0
\(101\) 830.282 + 302.198i 0.0813923 + 0.0296244i 0.382395 0.923999i \(-0.375099\pi\)
−0.301003 + 0.953623i \(0.597321\pi\)
\(102\) 0 0
\(103\) −1371.68 791.938i −0.129294 0.0746477i 0.433958 0.900933i \(-0.357117\pi\)
−0.563252 + 0.826285i \(0.690450\pi\)
\(104\) 0 0
\(105\) −3323.51 3960.80i −0.301452 0.359256i
\(106\) 0 0
\(107\) 10273.8 5931.59i 0.897355 0.518088i 0.0210141 0.999779i \(-0.493311\pi\)
0.876341 + 0.481691i \(0.159977\pi\)
\(108\) 0 0
\(109\) 6748.93 + 1190.02i 0.568044 + 0.100161i 0.450292 0.892882i \(-0.351320\pi\)
0.117752 + 0.993043i \(0.462431\pi\)
\(110\) 0 0
\(111\) 18859.6 6864.33i 1.53069 0.557124i
\(112\) 0 0
\(113\) 353.475i 0.0276823i 0.999904 + 0.0138412i \(0.00440592\pi\)
−0.999904 + 0.0138412i \(0.995594\pi\)
\(114\) 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 −0.913843 0.406067i \(-0.866900\pi\)
0.961060 + 0.276341i \(0.0891221\pi\)
\(128\) 0 0
\(129\) 25447.2 4487.03i 1.52919 0.269637i
\(130\) 0 0
\(131\) 20343.3 + 17070.1i 1.18544 + 0.994700i 0.999927 + 0.0120581i \(0.00383830\pi\)
0.185510 + 0.982642i \(0.440606\pi\)
\(132\) 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 0.996765 0.0803760i \(-0.0256121\pi\)
−0.964143 + 0.265385i \(0.914501\pi\)
\(138\) 0 0
\(139\) 13225.7 + 4813.75i 0.684522 + 0.249146i 0.660788 0.750573i \(-0.270222\pi\)
0.0237343 + 0.999718i \(0.492444\pi\)
\(140\) 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 0.565825 0.824526i \(-0.308558\pi\)
0.963442 + 0.267918i \(0.0863357\pi\)
\(150\) 0 0
\(151\) 22405.3i 0.982644i 0.870978 + 0.491322i \(0.163486\pi\)
−0.870978 + 0.491322i \(0.836514\pi\)
\(152\) 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 0.0522519 + 0.998634i \(0.483360\pi\)
−0.390654 + 0.920538i \(0.627751\pi\)
\(158\) 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 −0.734613 0.678487i \(-0.762636\pi\)
0.954893 + 0.296950i \(0.0959695\pi\)
\(164\) 0 0
\(165\) 2699.42 7416.59i 0.0991522 0.272418i
\(166\) 0 0
\(167\) 11805.3 2081.60i 0.423297 0.0746387i 0.0420580 0.999115i \(-0.486609\pi\)
0.381239 + 0.924476i \(0.375497\pi\)
\(168\) 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 −0.935564 0.353156i \(-0.885108\pi\)
0.510250 + 0.860026i \(0.329553\pi\)
\(174\) 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 0.684322 0.729179i \(-0.260098\pi\)
−0.289327 + 0.957230i \(0.593431\pi\)
\(180\) 0 0
\(181\) −19336.0 23043.8i −0.590215 0.703391i 0.385432 0.922736i \(-0.374052\pi\)
−0.975647 + 0.219345i \(0.929608\pi\)
\(182\) 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 −0.995234 0.0975137i \(-0.968911\pi\)
0.699713 0.714424i \(-0.253311\pi\)
\(194\) 0 0
\(195\) 5817.05 32990.1i 0.152980 0.867590i
\(196\) 0 0
\(197\) −22446.5 38878.6i −0.578385 1.00179i −0.995665 0.0930142i \(-0.970350\pi\)
0.417280 0.908778i \(-0.362984\pi\)
\(198\) 0 0
\(199\) −4917.74 + 4126.47i −0.124182 + 0.104201i −0.702764 0.711423i \(-0.748051\pi\)
0.578582 + 0.815625i \(0.303606\pi\)
\(200\) 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 −0.264315 0.964436i \(-0.585146\pi\)
0.995682 + 0.0928271i \(0.0295904\pi\)
\(212\) 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 0.197849 0.980232i \(-0.436604\pi\)
−0.149342 + 0.988786i \(0.547715\pi\)
\(224\) 0 0
\(225\) 79984.7 29112.0i 1.57994 0.575053i
\(226\) 0 0
\(227\) 35918.6i 0.697056i −0.937298 0.348528i \(-0.886682\pi\)
0.937298 0.348528i \(-0.113318\pi\)
\(228\) 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 0.938035 + 0.346542i \(0.112644\pi\)
−0.999988 + 0.00481606i \(0.998467\pi\)
\(234\) 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 −0.497049 0.867723i \(-0.665583\pi\)
0.999994 0.00340461i \(-0.00108372\pi\)
\(240\) 0 0
\(241\) 19044.5 52324.4i 0.327896 0.900887i −0.660748 0.750608i \(-0.729761\pi\)
0.988644 0.150279i \(-0.0480171\pi\)
\(242\) 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 0.956540 0.291603i \(-0.0941885\pi\)
−0.998587 + 0.0531390i \(0.983077\pi\)
\(252\) 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 0.715239 0.698880i \(-0.246318\pi\)
−0.812462 + 0.583014i \(0.801873\pi\)
\(258\) 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 −0.574712 0.818356i \(-0.694886\pi\)
0.0857740 + 0.996315i \(0.472664\pi\)
\(264\) 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 0.760689 + 0.649116i \(0.224861\pi\)
−0.165478 + 0.986214i \(0.552917\pi\)
\(270\) 0 0
\(271\) −12760.4 + 72368.0i −0.173751 + 0.985389i 0.765825 + 0.643049i \(0.222331\pi\)
−0.939576 + 0.342340i \(0.888780\pi\)
\(272\) 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 −0.886538 0.462656i \(-0.846897\pi\)
0.843941 + 0.536436i \(0.180230\pi\)
\(278\) 0 0
\(279\) −58951.1 + 161967.i −0.757327 + 2.08074i
\(280\) 0 0
\(281\) 23883.9 4211.38i 0.302477 0.0533349i −0.0203497 0.999793i \(-0.506478\pi\)
0.322827 + 0.946458i \(0.395367\pi\)
\(282\) 0 0
\(283\) 50567.4 + 42431.1i 0.631390 + 0.529799i 0.901361 0.433069i \(-0.142569\pi\)
−0.269970 + 0.962869i \(0.587014\pi\)
\(284\) 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 0.936114 0.351698i \(-0.114396\pi\)
0.163478 + 0.986547i \(0.447729\pi\)
\(294\) 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 −0.981072 0.193643i \(-0.937970\pi\)
0.627073 0.778960i \(-0.284253\pi\)
\(308\) 0 0
\(309\) −3744.50 + 21236.1i −0.0392172 + 0.222412i
\(310\) 0 0
\(311\) −28528.3 49412.5i −0.294955 0.510876i 0.680020 0.733194i \(-0.261971\pi\)
−0.974974 + 0.222317i \(0.928638\pi\)
\(312\) 0 0
\(313\) 126121. 105828.i 1.28735 1.08022i 0.295168 0.955445i \(-0.404624\pi\)
0.992185 0.124772i \(-0.0398201\pi\)
\(314\) 0 0
\(315\) −19815.8 + 34321.9i −0.199705 + 0.345900i
\(316\) 0 0
\(317\) −1581.86 + 4346.13i −0.0157416 + 0.0432498i −0.947315 0.320305i \(-0.896215\pi\)
0.931573 + 0.363554i \(0.118437\pi\)
\(318\) 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 0.994742 0.102415i \(-0.0326570\pi\)
0.408677 + 0.912679i \(0.365990\pi\)
\(332\) 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 0.520060 0.854130i \(-0.325910\pi\)
0.196567 + 0.980490i \(0.437021\pi\)
\(338\) 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 0.635735 + 0.771907i \(0.280697\pi\)
−0.861404 + 0.507921i \(0.830414\pi\)
\(348\) 0 0
\(349\) −53851.5 93273.5i −0.442127 0.765786i 0.555720 0.831369i \(-0.312443\pi\)
−0.997847 + 0.0655833i \(0.979109\pi\)
\(350\) 0 0
\(351\) −15790.2 + 13249.5i −0.128166 + 0.107544i
\(352\) 0 0
\(353\) −38337.3 + 66402.2i −0.307661 + 0.532884i −0.977850 0.209306i \(-0.932880\pi\)
0.670189 + 0.742190i \(0.266213\pi\)
\(354\) 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 0.500894 0.865509i \(-0.333005\pi\)
−0.765380 + 0.643578i \(0.777449\pi\)
\(360\) 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 −0.0808531 0.996726i \(-0.525764\pi\)
−0.702620 + 0.711565i \(0.747987\pi\)
\(368\) 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 0.0727141 0.997353i \(-0.476834\pi\)
0.900090 + 0.435704i \(0.143501\pi\)
\(374\) 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 \(0.216557\pi\)
−0.777364 + 0.629051i \(0.783443\pi\)
\(380\) 0 0
\(381\) −30314.5 −0.208834
\(382\) 0 0
\(383\) 11888.3 + 32662.7i 0.0810439 + 0.222666i 0.973596 0.228278i \(-0.0733095\pi\)
−0.892552 + 0.450944i \(0.851087\pi\)
\(384\) 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 −0.188455 + 0.982082i \(0.560348\pi\)
−0.999887 + 0.0150555i \(0.995208\pi\)
\(390\) 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 −0.0531080 0.998589i \(-0.516913\pi\)
−0.992640 + 0.121102i \(0.961357\pi\)
\(398\) 0 0
\(399\) 48247.1 9514.56i 0.303058 0.0597644i
\(400\) 0 0
\(401\) 118155. 140811.i 0.734789 0.875688i −0.261188 0.965288i \(-0.584114\pi\)
0.995978 + 0.0895999i \(0.0285588\pi\)
\(402\) 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 0.988151 + 0.153485i \(0.0490498\pi\)
−0.0204371 + 0.999791i \(0.506506\pi\)
\(410\) 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 −0.655890 0.754856i \(-0.727707\pi\)
0.0172286 0.999852i \(-0.494516\pi\)
\(422\) 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 −0.905127 0.425142i \(-0.860224\pi\)
0.966643 + 0.256127i \(0.0824464\pi\)
\(432\) 0 0
\(433\) −87468.3 + 15423.0i −0.466525 + 0.0822609i −0.401969 0.915653i \(-0.631674\pi\)
−0.0645556 + 0.997914i \(0.520563\pi\)
\(434\) 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 −0.795782 0.605583i \(-0.792940\pi\)
0.734569 + 0.678534i \(0.237384\pi\)
\(440\) 0 0
\(441\) 41694.5 + 236461.i 0.214389 + 1.21586i
\(442\) 0 0
\(443\) −5871.78 2137.15i −0.0299201 0.0108900i 0.327017 0.945019i \(-0.393957\pi\)
−0.356937 + 0.934129i \(0.616179\pi\)
\(444\) 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 −0.698881 0.715238i \(-0.746319\pi\)
0.269973 + 0.962868i \(0.412985\pi\)
\(450\) 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 −0.957107 0.289736i \(-0.906433\pi\)
0.998482 + 0.0550872i \(0.0175437\pi\)
\(462\) 0 0
\(463\) −38991.0 67534.3i −0.181887 0.315038i 0.760636 0.649179i \(-0.224887\pi\)
−0.942523 + 0.334141i \(0.891554\pi\)
\(464\) 0 0
\(465\) −653827. + 548626.i −3.02383 + 2.53729i
\(466\) 0 0
\(467\) −187480. + 324725.i −0.859649 + 1.48896i 0.0126152 + 0.999920i \(0.495984\pi\)
−0.872264 + 0.489035i \(0.837349\pi\)
\(468\) 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 −0.908388 0.418128i \(-0.862686\pi\)
0.710597 0.703599i \(-0.248425\pi\)
\(480\) 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 −0.952391 0.304880i \(-0.901384\pi\)
−0.212162 + 0.977235i \(0.568050\pi\)
\(488\) 0 0
\(489\) −156940. 27672.8i −0.656322 0.115727i
\(490\) 0 0
\(491\) −370318. + 134785.i −1.53607 + 0.559085i −0.965099 0.261884i \(-0.915656\pi\)
−0.570973 + 0.820969i \(0.693434\pi\)
\(492\) 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 −0.999909 0.0134826i \(-0.995708\pi\)
0.944219 + 0.329320i \(0.106819\pi\)
\(500\) 0 0
\(501\) −81601.7 141338.i −0.325105 0.563098i
\(502\) 0 0
\(503\) 86261.9 72382.4i 0.340944 0.286086i −0.456197 0.889879i \(-0.650789\pi\)
0.797142 + 0.603793i \(0.206344\pi\)
\(504\) 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 0.147116 0.989119i \(-0.453001\pi\)
0.476542 + 0.879151i \(0.341890\pi\)
\(510\) 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 0.163037 0.986620i \(-0.447871\pi\)
−0.772919 + 0.634504i \(0.781204\pi\)
\(522\) 0 0
\(523\) 53445.8 + 63694.2i 0.195393 + 0.232861i 0.854841 0.518889i \(-0.173654\pi\)
−0.659448 + 0.751750i \(0.729210\pi\)
\(524\) 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 −0.720969 0.692967i \(-0.756303\pi\)
0.557244 + 0.830349i \(0.311859\pi\)
\(542\) 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 −0.111817 0.993729i \(-0.535667\pi\)
0.234801 + 0.972043i \(0.424556\pi\)
\(548\) 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 0.942589 0.333956i \(-0.108384\pi\)
0.507402 + 0.861709i \(0.330606\pi\)
\(558\) 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 −0.229277 0.973361i \(-0.573636\pi\)
0.728317 + 0.685240i \(0.240303\pi\)
\(564\) 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 \(0.157654\pi\)
−0.879833 + 0.475283i \(0.842346\pi\)
\(570\) 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 0.841818 0.539762i \(-0.181486\pi\)
−0.888357 + 0.459154i \(0.848152\pi\)
\(578\) 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 −0.0415934 0.999135i \(-0.513243\pi\)
−0.991178 + 0.132536i \(0.957688\pi\)
\(588\) 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 0.984113 0.177545i \(-0.0568157\pi\)
−0.985487 + 0.169748i \(0.945705\pi\)
\(594\) 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 0.738966 0.673743i \(-0.235314\pi\)
−0.791827 + 0.610745i \(0.790870\pi\)
\(600\) 0 0
\(601\) −20074.7 + 11590.2i −0.0555777 + 0.0320878i −0.527531 0.849536i \(-0.676882\pi\)
0.471954 + 0.881623i \(0.343549\pi\)
\(602\) 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 \(0.0870815\pi\)
−0.962811 + 0.270175i \(0.912918\pi\)
\(608\) 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 0.712971 + 0.701194i \(0.247349\pi\)
−0.909796 + 0.415056i \(0.863762\pi\)
\(614\) 0 0
\(615\) 636634. + 1.10268e6i 1.68322 + 2.91541i
\(616\) 0 0
\(617\) −5407.03 + 4537.04i −0.0142033 + 0.0119180i −0.649862 0.760053i \(-0.725173\pi\)
0.635658 + 0.771971i \(0.280729\pi\)
\(618\) 0 0
\(619\) 267202. 462808.i 0.697362 1.20787i −0.272015 0.962293i \(-0.587690\pi\)
0.969378 0.245574i \(-0.0789765\pi\)
\(620\) 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 0.480631 + 0.876923i \(0.340408\pi\)
−0.151720 + 0.988424i \(0.548481\pi\)
\(632\) 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 0.118183 0.992992i \(-0.462293\pi\)
−0.228568 + 0.973528i \(0.573404\pi\)
\(642\) 0 0
\(643\) −610909. + 222353.i −1.47759 + 0.537800i −0.950151 0.311791i \(-0.899071\pi\)
−0.527442 + 0.849591i \(0.676849\pi\)
\(644\) 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 0.611719 0.791075i \(-0.290478\pi\)
−0.990951 + 0.134226i \(0.957145\pi\)
\(654\) 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 −0.909394 0.415936i \(-0.863454\pi\)
0.963995 + 0.265922i \(0.0856762\pi\)
\(660\) 0 0
\(661\) −730123. + 128740.i −1.67106 + 0.294653i −0.927447 0.373954i \(-0.878002\pi\)
−0.743616 + 0.668607i \(0.766891\pi\)
\(662\) 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 −0.260798 0.965393i \(-0.583986\pi\)
−0.966454 + 0.256839i \(0.917319\pi\)
\(674\) 0 0
\(675\) −166709. 198676.i −0.365890 0.436051i
\(676\) 0 0
\(677\) 276698. 159752.i 0.603711 0.348552i −0.166789 0.985993i \(-0.553340\pi\)
0.770500 + 0.637440i \(0.220007\pi\)
\(678\) 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 \(0.129202\pi\)
−0.918747 + 0.394847i \(0.870798\pi\)
\(684\) 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 0.985769 0.168105i \(-0.0537647\pi\)
−0.638467 + 0.769649i \(0.720431\pi\)
\(692\) 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 0.667391 0.744707i \(-0.267411\pi\)
−0.617502 + 0.786569i \(0.711855\pi\)
\(702\) 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 −0.727975 0.685604i \(-0.759538\pi\)
−0.998359 + 0.0572695i \(0.981761\pi\)
\(710\) 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 −0.887312 0.461169i \(-0.847430\pi\)
−0.383287 + 0.923629i \(0.625208\pi\)
\(720\) 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 0.744112 + 0.668055i \(0.232873\pi\)
−0.927725 + 0.373265i \(0.878238\pi\)
\(728\) 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 −0.766283 0.642503i \(-0.777896\pi\)
0.939566 + 0.342369i \(0.111229\pi\)
\(734\) 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 0.999292 0.0376175i \(-0.0119769\pi\)
0.136479 + 0.990643i \(0.456421\pi\)
\(740\) 0 0
\(741\) 248151. + 199833.i 0.451938 + 0.363942i
\(742\) 0 0
\(743\) −315238. + 375686.i −0.571032 + 0.680530i −0.971842 0.235631i \(-0.924284\pi\)
0.400810 + 0.916161i \(0.368729\pi\)
\(744\) 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 0.324608 0.945849i \(-0.394768\pi\)
−0.987847 + 0.155431i \(0.950323\pi\)
\(752\) 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 −0.174111 0.984726i \(-0.555705\pi\)
0.499593 + 0.866260i \(0.333483\pi\)
\(758\) 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 −0.0965860 0.995325i \(-0.530792\pi\)
0.963431 + 0.267955i \(0.0863478\pi\)
\(770\) 0 0
\(771\) −68004.9 + 117788.i −0.114401 + 0.198149i
\(772\) 0 0
\(773\) 156644. 430375.i 0.262152 0.720257i −0.736870 0.676035i \(-0.763697\pi\)
0.999022 0.0442223i \(-0.0140810\pi\)
\(774\) 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 0.790052 0.613040i \(-0.210054\pi\)
−0.135883 + 0.990725i \(0.543387\pi\)
\(788\) 0 0
\(789\) 314955. + 375349.i 0.505936 + 0.602950i
\(790\) 0 0
\(791\) −3062.93 + 1768.38i −0.00489535 + 0.00282633i
\(792\) 0