Properties

Label 76.5.j.a.21.6
Level $76$
Weight $5$
Character 76.21
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 21.6
Character \(\chi\) \(=\) 76.21
Dual form 76.5.j.a.29.6

$q$-expansion

\(f(q)\) \(=\) \(q+(9.11558 - 10.8635i) q^{3} +(31.4208 - 11.4362i) q^{5} +(39.9854 + 69.2568i) q^{7} +(-20.8569 - 118.285i) q^{9} +O(q^{10})\) \(q+(9.11558 - 10.8635i) q^{3} +(31.4208 - 11.4362i) q^{5} +(39.9854 + 69.2568i) q^{7} +(-20.8569 - 118.285i) q^{9} +(-10.1615 + 17.6003i) q^{11} +(-101.104 - 120.492i) q^{13} +(162.181 - 445.589i) q^{15} +(-64.2649 + 364.464i) q^{17} +(-169.897 - 318.521i) q^{19} +(1116.86 + 196.933i) q^{21} +(-341.165 - 124.174i) q^{23} +(377.702 - 316.930i) q^{25} +(-480.325 - 277.316i) q^{27} +(-681.081 + 120.093i) q^{29} +(889.421 - 513.507i) q^{31} +(98.5730 + 270.827i) q^{33} +(2048.41 + 1718.82i) q^{35} +694.298i q^{37} -2230.59 q^{39} +(-1060.01 + 1263.27i) q^{41} +(-3223.73 + 1173.34i) q^{43} +(-2008.08 - 3478.10i) q^{45} +(-468.777 - 2658.57i) q^{47} +(-1997.17 + 3459.20i) q^{49} +(3373.56 + 4020.45i) q^{51} +(-767.791 + 2109.49i) q^{53} +(-118.003 + 669.226i) q^{55} +(-5008.98 - 1057.82i) q^{57} +(6503.10 + 1146.67i) q^{59} +(5819.67 + 2118.19i) q^{61} +(7358.09 - 6174.17i) q^{63} +(-4554.75 - 2629.69i) q^{65} +(6482.83 - 1143.10i) q^{67} +(-4458.88 + 2574.34i) q^{69} +(-1833.99 - 5038.85i) q^{71} +(-2417.99 - 2028.93i) q^{73} -6992.18i q^{75} -1625.26 q^{77} +(-1721.85 + 2052.02i) q^{79} +(1751.11 - 637.353i) q^{81} +(1760.24 + 3048.83i) q^{83} +(2148.85 + 12186.7i) q^{85} +(-4903.82 + 8493.66i) q^{87} +(-6598.36 - 7863.62i) q^{89} +(4302.16 - 11820.1i) q^{91} +(2529.09 - 14343.2i) q^{93} +(-8981.00 - 8065.22i) q^{95} +(11690.2 + 2061.29i) q^{97} +(2293.80 + 834.873i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} + O(q^{10}) \) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} - 45q^{11} + 33q^{13} - 393q^{15} + 909q^{17} + 1242q^{19} + 1107q^{21} - 360q^{23} - 810q^{25} - 7056q^{27} - 2889q^{29} + 2808q^{31} + 10875q^{33} + 6741q^{35} - 3480q^{39} - 3060q^{41} - 8079q^{43} - 4320q^{45} - 2655q^{47} - 474q^{49} - 12222q^{51} - 6705q^{53} + 4623q^{55} - 8022q^{57} + 24309q^{59} + 7104q^{61} + 12063q^{63} + 25245q^{65} + 15573q^{67} - 10881q^{69} - 25506q^{71} + 3036q^{73} + 12924q^{77} - 16839q^{79} - 2208q^{81} - 6363q^{83} - 37890q^{85} - 21924q^{87} - 22644q^{89} + 17418q^{91} + 8184q^{93} - 82413q^{95} + 13383q^{97} + 23565q^{99} + O(q^{100}) \)

Character values

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

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

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
\(3\) 9.11558 10.8635i 1.01284 1.20706i 0.0346409 0.999400i \(-0.488971\pi\)
0.978201 0.207659i \(-0.0665843\pi\)
\(4\) 0 0
\(5\) 31.4208 11.4362i 1.25683 0.457450i 0.374128 0.927377i \(-0.377942\pi\)
0.882705 + 0.469927i \(0.155720\pi\)
\(6\) 0 0
\(7\) 39.9854 + 69.2568i 0.816029 + 1.41340i 0.908586 + 0.417697i \(0.137163\pi\)
−0.0925569 + 0.995707i \(0.529504\pi\)
\(8\) 0 0
\(9\) −20.8569 118.285i −0.257492 1.46031i
\(10\) 0 0
\(11\) −10.1615 + 17.6003i −0.0839797 + 0.145457i −0.904956 0.425505i \(-0.860096\pi\)
0.820976 + 0.570962i \(0.193430\pi\)
\(12\) 0 0
\(13\) −101.104 120.492i −0.598251 0.712968i 0.378918 0.925430i \(-0.376296\pi\)
−0.977169 + 0.212463i \(0.931852\pi\)
\(14\) 0 0
\(15\) 162.181 445.589i 0.720805 1.98039i
\(16\) 0 0
\(17\) −64.2649 + 364.464i −0.222370 + 1.26112i 0.645280 + 0.763947i \(0.276741\pi\)
−0.867650 + 0.497176i \(0.834370\pi\)
\(18\) 0 0
\(19\) −169.897 318.521i −0.470630 0.882331i
\(20\) 0 0
\(21\) 1116.86 + 196.933i 2.53257 + 0.446561i
\(22\) 0 0
\(23\) −341.165 124.174i −0.644924 0.234733i −0.00121023 0.999999i \(-0.500385\pi\)
−0.643714 + 0.765266i \(0.722607\pi\)
\(24\) 0 0
\(25\) 377.702 316.930i 0.604324 0.507088i
\(26\) 0 0
\(27\) −480.325 277.316i −0.658882 0.380406i
\(28\) 0 0
\(29\) −681.081 + 120.093i −0.809847 + 0.142798i −0.563214 0.826311i \(-0.690435\pi\)
−0.246633 + 0.969109i \(0.579324\pi\)
\(30\) 0 0
\(31\) 889.421 513.507i 0.925516 0.534347i 0.0401254 0.999195i \(-0.487224\pi\)
0.885391 + 0.464848i \(0.153891\pi\)
\(32\) 0 0
\(33\) 98.5730 + 270.827i 0.0905170 + 0.248693i
\(34\) 0 0
\(35\) 2048.41 + 1718.82i 1.67217 + 1.40312i
\(36\) 0 0
\(37\) 694.298i 0.507157i 0.967315 + 0.253578i \(0.0816076\pi\)
−0.967315 + 0.253578i \(0.918392\pi\)
\(38\) 0 0
\(39\) −2230.59 −1.46653
\(40\) 0 0
\(41\) −1060.01 + 1263.27i −0.630584 + 0.751501i −0.982852 0.184399i \(-0.940966\pi\)
0.352268 + 0.935899i \(0.385411\pi\)
\(42\) 0 0
\(43\) −3223.73 + 1173.34i −1.74350 + 0.634581i −0.999438 0.0335306i \(-0.989325\pi\)
−0.744061 + 0.668112i \(0.767103\pi\)
\(44\) 0 0
\(45\) −2008.08 3478.10i −0.991644 1.71758i
\(46\) 0 0
\(47\) −468.777 2658.57i −0.212212 1.20352i −0.885679 0.464298i \(-0.846307\pi\)
0.673466 0.739218i \(-0.264805\pi\)
\(48\) 0 0
\(49\) −1997.17 + 3459.20i −0.831808 + 1.44073i
\(50\) 0 0
\(51\) 3373.56 + 4020.45i 1.29702 + 1.54573i
\(52\) 0 0
\(53\) −767.791 + 2109.49i −0.273333 + 0.750975i 0.724746 + 0.689016i \(0.241957\pi\)
−0.998079 + 0.0619591i \(0.980265\pi\)
\(54\) 0 0
\(55\) −118.003 + 669.226i −0.0390091 + 0.221232i
\(56\) 0 0
\(57\) −5008.98 1057.82i −1.54170 0.325584i
\(58\) 0 0
\(59\) 6503.10 + 1146.67i 1.86817 + 0.329409i 0.989096 0.147273i \(-0.0470497\pi\)
0.879076 + 0.476683i \(0.158161\pi\)
\(60\) 0 0
\(61\) 5819.67 + 2118.19i 1.56401 + 0.569252i 0.971650 0.236424i \(-0.0759754\pi\)
0.592357 + 0.805676i \(0.298198\pi\)
\(62\) 0 0
\(63\) 7358.09 6174.17i 1.85389 1.55560i
\(64\) 0 0
\(65\) −4554.75 2629.69i −1.07805 0.622411i
\(66\) 0 0
\(67\) 6482.83 1143.10i 1.44416 0.254644i 0.603999 0.796985i \(-0.293573\pi\)
0.840159 + 0.542341i \(0.182462\pi\)
\(68\) 0 0
\(69\) −4458.88 + 2574.34i −0.936544 + 0.540714i
\(70\) 0 0
\(71\) −1833.99 5038.85i −0.363815 0.999574i −0.977668 0.210154i \(-0.932603\pi\)
0.613853 0.789420i \(-0.289619\pi\)
\(72\) 0 0
\(73\) −2417.99 2028.93i −0.453741 0.380734i 0.387081 0.922046i \(-0.373483\pi\)
−0.840822 + 0.541312i \(0.817928\pi\)
\(74\) 0 0
\(75\) 6992.18i 1.24305i
\(76\) 0 0
\(77\) −1625.26 −0.274120
\(78\) 0 0
\(79\) −1721.85 + 2052.02i −0.275893 + 0.328796i −0.886142 0.463413i \(-0.846625\pi\)
0.610250 + 0.792209i \(0.291069\pi\)
\(80\) 0 0
\(81\) 1751.11 637.353i 0.266897 0.0971427i
\(82\) 0 0
\(83\) 1760.24 + 3048.83i 0.255515 + 0.442564i 0.965035 0.262120i \(-0.0844218\pi\)
−0.709521 + 0.704685i \(0.751088\pi\)
\(84\) 0 0
\(85\) 2148.85 + 12186.7i 0.297418 + 1.68674i
\(86\) 0 0
\(87\) −4903.82 + 8493.66i −0.647882 + 1.12216i
\(88\) 0 0
\(89\) −6598.36 7863.62i −0.833021 0.992756i −0.999977 0.00679184i \(-0.997838\pi\)
0.166956 0.985964i \(-0.446606\pi\)
\(90\) 0 0
\(91\) 4302.16 11820.1i 0.519521 1.42737i
\(92\) 0 0
\(93\) 2529.09 14343.2i 0.292414 1.65836i
\(94\) 0 0
\(95\) −8981.00 8065.22i −0.995125 0.893653i
\(96\) 0 0
\(97\) 11690.2 + 2061.29i 1.24245 + 0.219077i 0.755964 0.654613i \(-0.227168\pi\)
0.486483 + 0.873690i \(0.338280\pi\)
\(98\) 0 0
\(99\) 2293.80 + 834.873i 0.234037 + 0.0851824i
\(100\) 0 0
\(101\) −11664.3 + 9787.51i −1.14345 + 0.959466i −0.999546 0.0301266i \(-0.990409\pi\)
−0.143900 + 0.989592i \(0.545965\pi\)
\(102\) 0 0
\(103\) 6416.27 + 3704.43i 0.604795 + 0.349178i 0.770925 0.636925i \(-0.219794\pi\)
−0.166131 + 0.986104i \(0.553127\pi\)
\(104\) 0 0
\(105\) 37344.9 6584.92i 3.38730 0.597272i
\(106\) 0 0
\(107\) −1560.12 + 900.738i −0.136267 + 0.0786739i −0.566584 0.824004i \(-0.691735\pi\)
0.430317 + 0.902678i \(0.358402\pi\)
\(108\) 0 0
\(109\) −404.983 1112.68i −0.0340866 0.0936523i 0.921482 0.388421i \(-0.126979\pi\)
−0.955569 + 0.294769i \(0.904757\pi\)
\(110\) 0 0
\(111\) 7542.52 + 6328.93i 0.612168 + 0.513670i
\(112\) 0 0
\(113\) 11311.2i 0.885831i −0.896563 0.442915i \(-0.853944\pi\)
0.896563 0.442915i \(-0.146056\pi\)
\(114\) 0 0
\(115\) −12139.8 −0.917941
\(116\) 0 0
\(117\) −12143.6 + 14472.2i −0.887110 + 1.05722i
\(118\) 0 0
\(119\) −27811.3 + 10122.5i −1.96394 + 0.714815i
\(120\) 0 0
\(121\) 7113.99 + 12321.8i 0.485895 + 0.841595i
\(122\) 0 0
\(123\) 4060.97 + 23030.9i 0.268423 + 1.52230i
\(124\) 0 0
\(125\) −2205.94 + 3820.80i −0.141180 + 0.244531i
\(126\) 0 0
\(127\) −15879.3 18924.2i −0.984516 1.17330i −0.984869 0.173301i \(-0.944557\pi\)
0.000352700 1.00000i \(-0.499888\pi\)
\(128\) 0 0
\(129\) −16639.5 + 45716.7i −0.999912 + 2.74724i
\(130\) 0 0
\(131\) 2841.19 16113.2i 0.165561 0.938942i −0.782924 0.622118i \(-0.786273\pi\)
0.948484 0.316824i \(-0.102616\pi\)
\(132\) 0 0
\(133\) 15266.4 24502.8i 0.863043 1.38520i
\(134\) 0 0
\(135\) −18263.7 3220.38i −1.00212 0.176701i
\(136\) 0 0
\(137\) −1624.05 591.107i −0.0865285 0.0314938i 0.298393 0.954443i \(-0.403549\pi\)
−0.384922 + 0.922949i \(0.625772\pi\)
\(138\) 0 0
\(139\) 2634.82 2210.87i 0.136371 0.114429i −0.572051 0.820218i \(-0.693852\pi\)
0.708422 + 0.705790i \(0.249408\pi\)
\(140\) 0 0
\(141\) −33154.6 19141.8i −1.66765 0.962819i
\(142\) 0 0
\(143\) 3148.06 555.089i 0.153947 0.0271450i
\(144\) 0 0
\(145\) −20026.7 + 11562.4i −0.952519 + 0.549937i
\(146\) 0 0
\(147\) 19373.8 + 53229.0i 0.896560 + 2.46328i
\(148\) 0 0
\(149\) −10888.8 9136.81i −0.490466 0.411550i 0.363727 0.931505i \(-0.381504\pi\)
−0.854193 + 0.519956i \(0.825948\pi\)
\(150\) 0 0
\(151\) 13297.5i 0.583199i −0.956540 0.291600i \(-0.905813\pi\)
0.956540 0.291600i \(-0.0941875\pi\)
\(152\) 0 0
\(153\) 44451.1 1.89889
\(154\) 0 0
\(155\) 22073.7 26306.5i 0.918782 1.09496i
\(156\) 0 0
\(157\) −3071.50 + 1117.94i −0.124610 + 0.0453542i −0.403572 0.914948i \(-0.632232\pi\)
0.278963 + 0.960302i \(0.410009\pi\)
\(158\) 0 0
\(159\) 15917.6 + 27570.1i 0.629628 + 1.09055i
\(160\) 0 0
\(161\) −5041.74 28593.2i −0.194504 1.10309i
\(162\) 0 0
\(163\) −1349.50 + 2337.40i −0.0507923 + 0.0879749i −0.890304 0.455367i \(-0.849508\pi\)
0.839511 + 0.543342i \(0.182841\pi\)
\(164\) 0 0
\(165\) 6194.49 + 7382.31i 0.227530 + 0.271159i
\(166\) 0 0
\(167\) 3277.80 9005.69i 0.117530 0.322912i −0.866953 0.498390i \(-0.833925\pi\)
0.984483 + 0.175478i \(0.0561470\pi\)
\(168\) 0 0
\(169\) 663.458 3762.65i 0.0232295 0.131741i
\(170\) 0 0
\(171\) −34132.9 + 26739.7i −1.16729 + 0.914460i
\(172\) 0 0
\(173\) −10425.9 1838.36i −0.348354 0.0614241i −0.00326608 0.999995i \(-0.501040\pi\)
−0.345087 + 0.938571i \(0.612151\pi\)
\(174\) 0 0
\(175\) 37052.2 + 13485.9i 1.20987 + 0.440355i
\(176\) 0 0
\(177\) 71736.5 60194.1i 2.28978 1.92135i
\(178\) 0 0
\(179\) −26213.8 15134.5i −0.818132 0.472349i 0.0316398 0.999499i \(-0.489927\pi\)
−0.849772 + 0.527150i \(0.823260\pi\)
\(180\) 0 0
\(181\) −22735.5 + 4008.87i −0.693979 + 0.122367i −0.509502 0.860469i \(-0.670170\pi\)
−0.184477 + 0.982837i \(0.559059\pi\)
\(182\) 0 0
\(183\) 76060.6 43913.6i 2.27121 1.31129i
\(184\) 0 0
\(185\) 7940.16 + 21815.4i 0.231999 + 0.637411i
\(186\) 0 0
\(187\) −5761.66 4834.60i −0.164765 0.138254i
\(188\) 0 0
\(189\) 44354.4i 1.24169i
\(190\) 0 0
\(191\) −21072.9 −0.577641 −0.288821 0.957383i \(-0.593263\pi\)
−0.288821 + 0.957383i \(0.593263\pi\)
\(192\) 0 0
\(193\) 2698.18 3215.56i 0.0724362 0.0863261i −0.728609 0.684929i \(-0.759833\pi\)
0.801046 + 0.598603i \(0.204277\pi\)
\(194\) 0 0
\(195\) −70086.9 + 25509.5i −1.84318 + 0.670862i
\(196\) 0 0
\(197\) 13290.6 + 23019.9i 0.342461 + 0.593159i 0.984889 0.173186i \(-0.0554063\pi\)
−0.642428 + 0.766346i \(0.722073\pi\)
\(198\) 0 0
\(199\) −3824.40 21689.2i −0.0965732 0.547694i −0.994254 0.107047i \(-0.965860\pi\)
0.897681 0.440647i \(-0.145251\pi\)
\(200\) 0 0
\(201\) 46676.7 80846.3i 1.15533 2.00110i
\(202\) 0 0
\(203\) −35550.6 42367.6i −0.862690 1.02811i
\(204\) 0 0
\(205\) −18859.3 + 51815.6i −0.448765 + 1.23297i
\(206\) 0 0
\(207\) −7572.31 + 42944.7i −0.176721 + 1.00223i
\(208\) 0 0
\(209\) 7332.49 + 246.424i 0.167865 + 0.00564145i
\(210\) 0 0
\(211\) 79876.0 + 14084.3i 1.79412 + 0.316352i 0.968713 0.248185i \(-0.0798342\pi\)
0.825408 + 0.564537i \(0.190945\pi\)
\(212\) 0 0
\(213\) −71457.6 26008.5i −1.57503 0.573265i
\(214\) 0 0
\(215\) −87873.6 + 73734.7i −1.90100 + 1.59513i
\(216\) 0 0
\(217\) 71127.8 + 41065.6i 1.51050 + 0.872086i
\(218\) 0 0
\(219\) −44082.7 + 7772.97i −0.919136 + 0.162069i
\(220\) 0 0
\(221\) 50412.3 29105.6i 1.03217 0.595925i
\(222\) 0 0
\(223\) 12288.9 + 33763.5i 0.247118 + 0.678950i 0.999789 + 0.0205533i \(0.00654279\pi\)
−0.752671 + 0.658397i \(0.771235\pi\)
\(224\) 0 0
\(225\) −45365.8 38066.5i −0.896115 0.751930i
\(226\) 0 0
\(227\) 12563.2i 0.243808i 0.992542 + 0.121904i \(0.0389000\pi\)
−0.992542 + 0.121904i \(0.961100\pi\)
\(228\) 0 0
\(229\) 35829.1 0.683228 0.341614 0.939840i \(-0.389027\pi\)
0.341614 + 0.939840i \(0.389027\pi\)
\(230\) 0 0
\(231\) −14815.1 + 17656.0i −0.277640 + 0.330878i
\(232\) 0 0
\(233\) −50070.9 + 18224.3i −0.922303 + 0.335691i −0.759154 0.650911i \(-0.774387\pi\)
−0.163149 + 0.986602i \(0.552165\pi\)
\(234\) 0 0
\(235\) −45133.4 78173.3i −0.817264 1.41554i
\(236\) 0 0
\(237\) 6596.50 + 37410.6i 0.117440 + 0.666037i
\(238\) 0 0
\(239\) 50961.0 88267.0i 0.892158 1.54526i 0.0548758 0.998493i \(-0.482524\pi\)
0.837283 0.546770i \(-0.184143\pi\)
\(240\) 0 0
\(241\) 17732.2 + 21132.4i 0.305301 + 0.363843i 0.896780 0.442477i \(-0.145900\pi\)
−0.591479 + 0.806320i \(0.701456\pi\)
\(242\) 0 0
\(243\) 24403.8 67049.0i 0.413281 1.13548i
\(244\) 0 0
\(245\) −23192.5 + 131531.i −0.386380 + 2.19127i
\(246\) 0 0
\(247\) −21201.8 + 52675.1i −0.347519 + 0.863399i
\(248\) 0 0
\(249\) 49166.6 + 8669.40i 0.792997 + 0.139827i
\(250\) 0 0
\(251\) 18177.2 + 6615.95i 0.288522 + 0.105013i 0.482227 0.876046i \(-0.339828\pi\)
−0.193705 + 0.981060i \(0.562050\pi\)
\(252\) 0 0
\(253\) 5652.26 4742.81i 0.0883042 0.0740960i
\(254\) 0 0
\(255\) 151979. + 87745.0i 2.33724 + 1.34940i
\(256\) 0 0
\(257\) −8736.84 + 1540.54i −0.132278 + 0.0233242i −0.239395 0.970922i \(-0.576949\pi\)
0.107117 + 0.994246i \(0.465838\pi\)
\(258\) 0 0
\(259\) −48084.8 + 27761.8i −0.716818 + 0.413855i
\(260\) 0 0
\(261\) 28410.5 + 78057.1i 0.417059 + 1.14586i
\(262\) 0 0
\(263\) −64278.6 53936.1i −0.929298 0.779773i 0.0463935 0.998923i \(-0.485227\pi\)
−0.975691 + 0.219150i \(0.929672\pi\)
\(264\) 0 0
\(265\) 75062.5i 1.06889i
\(266\) 0 0
\(267\) −145575. −2.04203
\(268\) 0 0
\(269\) 30336.6 36153.7i 0.419239 0.499630i −0.514547 0.857462i \(-0.672040\pi\)
0.933786 + 0.357833i \(0.116484\pi\)
\(270\) 0 0
\(271\) 34101.1 12411.8i 0.464333 0.169003i −0.0992505 0.995062i \(-0.531645\pi\)
0.563584 + 0.826059i \(0.309422\pi\)
\(272\) 0 0
\(273\) −89191.0 154483.i −1.19673 2.07280i
\(274\) 0 0
\(275\) 1740.03 + 9868.17i 0.0230086 + 0.130488i
\(276\) 0 0
\(277\) 1499.37 2596.99i 0.0195412 0.0338463i −0.856089 0.516828i \(-0.827113\pi\)
0.875631 + 0.482981i \(0.160446\pi\)
\(278\) 0 0
\(279\) −79290.9 94495.2i −1.01863 1.21395i
\(280\) 0 0
\(281\) −37837.4 + 103957.i −0.479191 + 1.31657i 0.430991 + 0.902356i \(0.358164\pi\)
−0.910182 + 0.414209i \(0.864058\pi\)
\(282\) 0 0
\(283\) −21586.7 + 122424.i −0.269534 + 1.52860i 0.486272 + 0.873807i \(0.338356\pi\)
−0.755806 + 0.654796i \(0.772755\pi\)
\(284\) 0 0
\(285\) −169484. + 24046.2i −2.08660 + 0.296044i
\(286\) 0 0
\(287\) −129875. 22900.5i −1.57675 0.278023i
\(288\) 0 0
\(289\) −50220.3 18278.7i −0.601290 0.218852i
\(290\) 0 0
\(291\) 128956. 108207.i 1.52284 1.27782i
\(292\) 0 0
\(293\) −595.018 343.534i −0.00693098 0.00400160i 0.496531 0.868019i \(-0.334607\pi\)
−0.503461 + 0.864018i \(0.667940\pi\)
\(294\) 0 0
\(295\) 217446. 38341.7i 2.49867 0.440582i
\(296\) 0 0
\(297\) 9761.69 5635.91i 0.110665 0.0638927i
\(298\) 0 0
\(299\) 19531.4 + 53662.0i 0.218469 + 0.600240i
\(300\) 0 0
\(301\) −210164. 176349.i −2.31967 1.94643i
\(302\) 0 0
\(303\) 215934.i 2.35199i
\(304\) 0 0
\(305\) 207083. 2.22610
\(306\) 0 0
\(307\) 3439.79 4099.38i 0.0364968 0.0434953i −0.747487 0.664276i \(-0.768740\pi\)
0.783984 + 0.620781i \(0.213184\pi\)
\(308\) 0 0
\(309\) 98731.2 35935.2i 1.03404 0.376360i
\(310\) 0 0
\(311\) 66863.5 + 115811.i 0.691303 + 1.19737i 0.971411 + 0.237404i \(0.0762964\pi\)
−0.280108 + 0.959968i \(0.590370\pi\)
\(312\) 0 0
\(313\) 44.4220 + 251.930i 0.000453430 + 0.00257153i 0.985034 0.172362i \(-0.0551400\pi\)
−0.984580 + 0.174934i \(0.944029\pi\)
\(314\) 0 0
\(315\) 160588. 278146.i 1.61842 2.80319i
\(316\) 0 0
\(317\) 47164.2 + 56208.1i 0.469347 + 0.559346i 0.947840 0.318745i \(-0.103261\pi\)
−0.478493 + 0.878091i \(0.658817\pi\)
\(318\) 0 0
\(319\) 4807.16 13207.6i 0.0472397 0.129790i
\(320\) 0 0
\(321\) −4436.25 + 25159.2i −0.0430532 + 0.244167i
\(322\) 0 0
\(323\) 127008. 41451.8i 1.21738 0.397318i
\(324\) 0 0
\(325\) −76374.7 13466.9i −0.723074 0.127498i
\(326\) 0 0
\(327\) −15779.3 5743.20i −0.147568 0.0537104i
\(328\) 0 0
\(329\) 165380. 138770.i 1.52788 1.28205i
\(330\) 0 0
\(331\) 49342.1 + 28487.7i 0.450362 + 0.260016i 0.707983 0.706230i \(-0.249605\pi\)
−0.257621 + 0.966246i \(0.582939\pi\)
\(332\) 0 0
\(333\) 82125.2 14480.9i 0.740607 0.130589i
\(334\) 0 0
\(335\) 190623. 110056.i 1.69858 0.980675i
\(336\) 0 0
\(337\) −32311.1 88774.1i −0.284507 0.781675i −0.996811 0.0798043i \(-0.974570\pi\)
0.712304 0.701871i \(-0.247652\pi\)
\(338\) 0 0
\(339\) −122879. 103108.i −1.06925 0.897207i
\(340\) 0 0
\(341\) 20872.1i 0.179497i
\(342\) 0 0
\(343\) −127421. −1.08306
\(344\) 0 0
\(345\) −110661. + 131881.i −0.929729 + 1.10801i
\(346\) 0 0
\(347\) 38153.7 13886.8i 0.316867 0.115330i −0.178690 0.983905i \(-0.557186\pi\)
0.495557 + 0.868575i \(0.334964\pi\)
\(348\) 0 0
\(349\) −117786. 204011.i −0.967036 1.67495i −0.704043 0.710157i \(-0.748624\pi\)
−0.262992 0.964798i \(-0.584709\pi\)
\(350\) 0 0
\(351\) 15148.8 + 85913.0i 0.122960 + 0.697340i
\(352\) 0 0
\(353\) −45139.8 + 78184.5i −0.362252 + 0.627439i −0.988331 0.152321i \(-0.951325\pi\)
0.626079 + 0.779759i \(0.284659\pi\)
\(354\) 0 0
\(355\) −115251. 137351.i −0.914510 1.08987i
\(356\) 0 0
\(357\) −143550. + 394401.i −1.12634 + 3.09458i
\(358\) 0 0
\(359\) 31253.9 177250.i 0.242502 1.37530i −0.583721 0.811954i \(-0.698404\pi\)
0.826223 0.563343i \(-0.190485\pi\)
\(360\) 0 0
\(361\) −72590.8 + 108232.i −0.557015 + 0.830502i
\(362\) 0 0
\(363\) 198706. + 35037.3i 1.50799 + 0.265899i
\(364\) 0 0
\(365\) −99178.4 36098.0i −0.744443 0.270955i
\(366\) 0 0
\(367\) −16101.2 + 13510.5i −0.119543 + 0.100309i −0.700600 0.713555i \(-0.747084\pi\)
0.581056 + 0.813863i \(0.302640\pi\)
\(368\) 0 0
\(369\) 171535. + 99035.8i 1.25980 + 0.727344i
\(370\) 0 0
\(371\) −176797. + 31174.1i −1.28448 + 0.226488i
\(372\) 0 0
\(373\) 108749. 62786.3i 0.781642 0.451281i −0.0553697 0.998466i \(-0.517634\pi\)
0.837012 + 0.547185i \(0.184300\pi\)
\(374\) 0 0
\(375\) 21398.9 + 58793.0i 0.152170 + 0.418084i
\(376\) 0 0
\(377\) 83330.5 + 69922.6i 0.586302 + 0.491966i
\(378\) 0 0
\(379\) 67710.3i 0.471385i 0.971828 + 0.235693i \(0.0757359\pi\)
−0.971828 + 0.235693i \(0.924264\pi\)
\(380\) 0 0
\(381\) −350332. −2.41340
\(382\) 0 0
\(383\) −70745.6 + 84311.4i −0.482283 + 0.574763i −0.951237 0.308460i \(-0.900186\pi\)
0.468954 + 0.883223i \(0.344631\pi\)
\(384\) 0 0
\(385\) −51066.8 + 18586.8i −0.344522 + 0.125396i
\(386\) 0 0
\(387\) 206026. + 356847.i 1.37562 + 2.38265i
\(388\) 0 0
\(389\) −35032.5 198679.i −0.231511 1.31296i −0.849838 0.527043i \(-0.823301\pi\)
0.618327 0.785921i \(-0.287811\pi\)
\(390\) 0 0
\(391\) 67181.9 116363.i 0.439439 0.761131i
\(392\) 0 0
\(393\) −149147. 177746.i −0.965670 1.15084i
\(394\) 0 0
\(395\) −30634.5 + 84167.5i −0.196343 + 0.539449i
\(396\) 0 0
\(397\) 2992.49 16971.2i 0.0189868 0.107679i −0.973842 0.227228i \(-0.927034\pi\)
0.992828 + 0.119549i \(0.0381448\pi\)
\(398\) 0 0
\(399\) −127025. 389203.i −0.797889 2.44473i
\(400\) 0 0
\(401\) −35490.2 6257.89i −0.220709 0.0389170i 0.0622000 0.998064i \(-0.480188\pi\)
−0.282909 + 0.959147i \(0.591299\pi\)
\(402\) 0 0
\(403\) −151798. 55249.8i −0.934663 0.340189i
\(404\) 0 0
\(405\) 47732.5 40052.3i 0.291007 0.244184i
\(406\) 0 0
\(407\) −12219.9 7055.13i −0.0737695 0.0425909i
\(408\) 0 0
\(409\) 164991. 29092.3i 0.986309 0.173913i 0.342847 0.939391i \(-0.388609\pi\)
0.643462 + 0.765478i \(0.277498\pi\)
\(410\) 0 0
\(411\) −21225.7 + 12254.7i −0.125655 + 0.0725467i
\(412\) 0 0
\(413\) 180615. + 496235.i 1.05889 + 2.90929i
\(414\) 0 0
\(415\) 90175.3 + 75666.1i 0.523590 + 0.439344i
\(416\) 0 0
\(417\) 48776.8i 0.280505i
\(418\) 0 0
\(419\) 287217. 1.63599 0.817997 0.575222i \(-0.195084\pi\)
0.817997 + 0.575222i \(0.195084\pi\)
\(420\) 0 0
\(421\) −1143.71 + 1363.01i −0.00645283 + 0.00769018i −0.769261 0.638934i \(-0.779376\pi\)
0.762808 + 0.646625i \(0.223820\pi\)
\(422\) 0 0
\(423\) −304692. + 110899.i −1.70287 + 0.619793i
\(424\) 0 0
\(425\) 91236.7 + 158027.i 0.505117 + 0.874888i
\(426\) 0 0
\(427\) 86003.2 + 487748.i 0.471692 + 2.67510i
\(428\) 0 0
\(429\) 22666.2 39259.0i 0.123158 0.213317i
\(430\) 0 0
\(431\) −180287. 214857.i −0.970530 1.15663i −0.987634 0.156779i \(-0.949889\pi\)
0.0171038 0.999854i \(-0.494555\pi\)
\(432\) 0 0
\(433\) 106300. 292057.i 0.566968 1.55773i −0.242245 0.970215i \(-0.577884\pi\)
0.809213 0.587516i \(-0.199894\pi\)
\(434\) 0 0
\(435\) −56946.4 + 322959.i −0.300945 + 1.70675i
\(436\) 0 0
\(437\) 18411.0 + 129765.i 0.0964082 + 0.679509i
\(438\) 0 0
\(439\) 13886.1 + 2448.49i 0.0720528 + 0.0127049i 0.209558 0.977796i \(-0.432797\pi\)
−0.137506 + 0.990501i \(0.543908\pi\)
\(440\) 0 0
\(441\) 450827. + 164088.i 2.31811 + 0.843721i
\(442\) 0 0
\(443\) −121549. + 101992.i −0.619363 + 0.519708i −0.897603 0.440804i \(-0.854693\pi\)
0.278240 + 0.960512i \(0.410249\pi\)
\(444\) 0 0
\(445\) −297256. 171621.i −1.50110 0.866663i
\(446\) 0 0
\(447\) −198516. + 35003.7i −0.993529 + 0.175186i
\(448\) 0 0
\(449\) −112147. + 64748.0i −0.556281 + 0.321169i −0.751652 0.659560i \(-0.770742\pi\)
0.195370 + 0.980730i \(0.437409\pi\)
\(450\) 0 0
\(451\) −11462.6 31493.3i −0.0563549 0.154834i
\(452\) 0 0
\(453\) −144458. 121215.i −0.703956 0.590689i
\(454\) 0 0
\(455\) 420597.i 2.03162i
\(456\) 0 0
\(457\) 150128. 0.718836 0.359418 0.933177i \(-0.382975\pi\)
0.359418 + 0.933177i \(0.382975\pi\)
\(458\) 0 0
\(459\) 131940. 157240.i 0.626254 0.746341i
\(460\) 0 0
\(461\) −344288. + 125310.i −1.62002 + 0.589638i −0.983385 0.181531i \(-0.941895\pi\)
−0.636631 + 0.771168i \(0.719673\pi\)
\(462\) 0 0
\(463\) −75550.3 130857.i −0.352431 0.610428i 0.634244 0.773133i \(-0.281312\pi\)
−0.986675 + 0.162705i \(0.947978\pi\)
\(464\) 0 0
\(465\) −84565.9 479597.i −0.391102 2.21805i
\(466\) 0 0
\(467\) 54139.2 93771.8i 0.248243 0.429970i −0.714795 0.699334i \(-0.753480\pi\)
0.963039 + 0.269364i \(0.0868134\pi\)
\(468\) 0 0
\(469\) 338386. + 403273.i 1.53839 + 1.83338i
\(470\) 0 0
\(471\) −15853.8 + 43558.0i −0.0714647 + 0.196348i
\(472\) 0 0
\(473\) 12106.9 68661.6i 0.0541141 0.306896i
\(474\) 0 0
\(475\) −165120. 66460.8i −0.731832 0.294563i
\(476\) 0 0
\(477\) 265535. + 46821.0i 1.16704 + 0.205780i
\(478\) 0 0
\(479\) 3460.44 + 1259.50i 0.0150820 + 0.00548941i 0.349550 0.936918i \(-0.386334\pi\)
−0.334468 + 0.942407i \(0.608557\pi\)
\(480\) 0 0
\(481\) 83657.0 70196.5i 0.361586 0.303407i
\(482\) 0 0
\(483\) −356581. 205872.i −1.52849 0.882477i
\(484\) 0 0
\(485\) 390889. 68924.2i 1.66176 0.293014i
\(486\) 0 0
\(487\) −226072. + 130523.i −0.953212 + 0.550337i −0.894077 0.447913i \(-0.852168\pi\)
−0.0591348 + 0.998250i \(0.518834\pi\)
\(488\) 0 0
\(489\) 13091.0 + 35967.1i 0.0547462 + 0.150414i
\(490\) 0 0
\(491\) 186984. + 156898.i 0.775607 + 0.650812i 0.942138 0.335224i \(-0.108812\pi\)
−0.166531 + 0.986036i \(0.553257\pi\)
\(492\) 0 0
\(493\) 255948.i 1.05307i
\(494\) 0 0
\(495\) 81620.7 0.333112
\(496\) 0 0
\(497\) 275642. 328497.i 1.11592 1.32990i
\(498\) 0 0
\(499\) −273900. + 99691.6i −1.10000 + 0.400366i −0.827315 0.561738i \(-0.810133\pi\)
−0.272682 + 0.962104i \(0.587911\pi\)
\(500\) 0 0
\(501\) −67954.5 117701.i −0.270734 0.468925i
\(502\) 0 0
\(503\) 28729.7 + 162934.i 0.113552 + 0.643986i 0.987457 + 0.157889i \(0.0504689\pi\)
−0.873905 + 0.486097i \(0.838420\pi\)
\(504\) 0 0
\(505\) −254569. + 440927.i −0.998214 + 1.72896i
\(506\) 0 0
\(507\) −34827.9 41506.3i −0.135491 0.161472i
\(508\) 0 0
\(509\) 55300.2 151936.i 0.213448 0.586443i −0.786049 0.618164i \(-0.787877\pi\)
0.999497 + 0.0317215i \(0.0100990\pi\)
\(510\) 0 0
\(511\) 43833.1 248590.i 0.167865 0.952010i
\(512\) 0 0
\(513\) −6725.09 + 200109.i −0.0255543 + 0.760383i
\(514\) 0 0
\(515\) 243969. + 43018.3i 0.919857 + 0.162196i
\(516\) 0 0
\(517\) 51555.1 + 18764.5i 0.192881 + 0.0702031i
\(518\) 0 0
\(519\) −115009. + 96504.0i −0.426970 + 0.358270i
\(520\) 0 0
\(521\) −92452.8 53377.6i −0.340600 0.196645i 0.319937 0.947439i \(-0.396338\pi\)
−0.660537 + 0.750793i \(0.729671\pi\)
\(522\) 0 0
\(523\) 522060. 92053.2i 1.90861 0.336539i 0.911419 0.411478i \(-0.134987\pi\)
0.997188 + 0.0749394i \(0.0238763\pi\)
\(524\) 0 0
\(525\) 484256. 279585.i 1.75694 1.01437i
\(526\) 0 0
\(527\) 129997. + 357163.i 0.468070 + 1.28601i
\(528\) 0 0
\(529\) −113396. 95150.7i −0.405217 0.340017i
\(530\) 0 0
\(531\) 793137.i 2.81293i
\(532\) 0 0
\(533\) 259385. 0.913043
\(534\) 0 0
\(535\) −38719.3 + 46143.9i −0.135276 + 0.161215i
\(536\) 0 0
\(537\) −403368. + 146814.i −1.39879 + 0.509118i
\(538\) 0 0
\(539\) −40588.7 70301.7i −0.139710 0.241985i
\(540\) 0 0
\(541\) 32808.2 + 186064.i 0.112095 + 0.635724i 0.988147 + 0.153508i \(0.0490570\pi\)
−0.876052 + 0.482216i \(0.839832\pi\)
\(542\) 0 0
\(543\) −163696. + 283530.i −0.555187 + 0.961612i
\(544\) 0 0
\(545\) −25449.8 30329.9i −0.0856824 0.102112i
\(546\) 0 0
\(547\) −54831.0 + 150647.i −0.183253 + 0.503484i −0.996971 0.0777765i \(-0.975218\pi\)
0.813718 + 0.581260i \(0.197440\pi\)
\(548\) 0 0
\(549\) 129170. 732560.i 0.428566 2.43052i
\(550\) 0 0
\(551\) 153966. + 196536.i 0.507133 + 0.647348i
\(552\) 0 0
\(553\) −210965. 37198.8i −0.689858 0.121641i
\(554\) 0 0
\(555\) 309371. + 112602.i 1.00437 + 0.365561i
\(556\) 0 0
\(557\) 107255. 89997.5i 0.345706 0.290082i −0.453357 0.891329i \(-0.649774\pi\)
0.799063 + 0.601247i \(0.205329\pi\)
\(558\) 0 0
\(559\) 467311. + 269802.i 1.49549 + 0.863419i
\(560\) 0 0
\(561\) −105042. + 18521.7i −0.333761 + 0.0588511i
\(562\) 0 0
\(563\) −121704. + 70266.1i −0.383963 + 0.221681i −0.679541 0.733637i \(-0.737821\pi\)
0.295578 + 0.955319i \(0.404488\pi\)
\(564\) 0 0
\(565\) −129357. 355406.i −0.405223 1.11334i
\(566\) 0 0
\(567\) 114160. + 95791.7i 0.355098 + 0.297963i
\(568\) 0 0
\(569\) 250293.i 0.773080i −0.922273 0.386540i \(-0.873670\pi\)
0.922273 0.386540i \(-0.126330\pi\)
\(570\) 0 0
\(571\) 199899. 0.613111 0.306555 0.951853i \(-0.400824\pi\)
0.306555 + 0.951853i \(0.400824\pi\)
\(572\) 0 0
\(573\) −192092. + 228926.i −0.585059 + 0.697247i
\(574\) 0 0
\(575\) −168213. + 61224.6i −0.508774 + 0.185178i
\(576\) 0 0
\(577\) −55103.4 95442.0i −0.165511 0.286674i 0.771326 0.636441i \(-0.219594\pi\)
−0.936837 + 0.349767i \(0.886261\pi\)
\(578\) 0 0
\(579\) −10336.9 58623.4i −0.0308342 0.174869i
\(580\) 0 0
\(581\) −140768. + 243817.i −0.417015 + 0.722291i
\(582\) 0 0
\(583\) −29325.7 34949.0i −0.0862803 0.102825i
\(584\) 0 0
\(585\) −216055. + 593607.i −0.631325 + 1.73455i
\(586\) 0 0
\(587\) −87834.7 + 498135.i −0.254912 + 1.44568i 0.541387 + 0.840773i \(0.317899\pi\)
−0.796299 + 0.604903i \(0.793212\pi\)
\(588\) 0 0
\(589\) −314673. 196056.i −0.907046 0.565132i
\(590\) 0 0
\(591\) 371229. + 65457.6i 1.06284 + 0.187407i
\(592\) 0 0
\(593\) −187637. 68294.1i −0.533591 0.194211i 0.0611503 0.998129i \(-0.480523\pi\)
−0.594741 + 0.803917i \(0.702745\pi\)
\(594\) 0 0
\(595\) −758091. + 636114.i −2.14135 + 1.79680i
\(596\) 0 0
\(597\) −270483. 156164.i −0.758912 0.438158i
\(598\) 0 0
\(599\) −641784. + 113164.i −1.78869 + 0.315395i −0.967046 0.254604i \(-0.918055\pi\)
−0.821646 + 0.569998i \(0.806944\pi\)
\(600\) 0 0
\(601\) −372533. + 215082.i −1.03137 + 0.595464i −0.917378 0.398018i \(-0.869698\pi\)
−0.113996 + 0.993481i \(0.536365\pi\)
\(602\) 0 0
\(603\) −270423. 742981.i −0.743719 2.04335i
\(604\) 0 0
\(605\) 364442. + 305803.i 0.995676 + 0.835471i
\(606\) 0 0
\(607\) 157443.i 0.427314i −0.976909 0.213657i \(-0.931463\pi\)
0.976909 0.213657i \(-0.0685374\pi\)
\(608\) 0 0
\(609\) −784325. −2.11476
\(610\) 0 0
\(611\) −272939. + 325276.i −0.731112 + 0.871305i
\(612\) 0 0
\(613\) 410211. 149305.i 1.09166 0.397331i 0.267423 0.963579i \(-0.413828\pi\)
0.824235 + 0.566248i \(0.191606\pi\)
\(614\) 0 0
\(615\) 390986. + 677208.i 1.03374 + 1.79049i
\(616\) 0 0
\(617\) 102238. + 579819.i 0.268560 + 1.52308i 0.758703 + 0.651437i \(0.225833\pi\)
−0.490143 + 0.871642i \(0.663056\pi\)
\(618\) 0 0
\(619\) 205858. 356557.i 0.537263 0.930568i −0.461787 0.886991i \(-0.652791\pi\)
0.999050 0.0435765i \(-0.0138752\pi\)
\(620\) 0 0
\(621\) 129435. + 154254.i 0.335635 + 0.399995i
\(622\) 0 0
\(623\) 280771. 771412.i 0.723396 1.98751i
\(624\) 0 0
\(625\) −79128.2 + 448758.i −0.202568 + 1.14882i
\(626\) 0 0
\(627\) 69517.0 77410.4i 0.176830 0.196908i
\(628\) 0 0
\(629\) −253047. 44619.0i −0.639587 0.112776i
\(630\) 0 0
\(631\) 63143.6 + 22982.4i 0.158588 + 0.0577214i 0.420094 0.907480i \(-0.361997\pi\)
−0.261506 + 0.965202i \(0.584219\pi\)
\(632\) 0 0
\(633\) 881122. 739349.i 2.19902 1.84519i
\(634\) 0 0
\(635\) −715361. 413014.i −1.77410 1.02428i
\(636\) 0 0
\(637\) 618727. 109098.i 1.52483 0.268868i
\(638\) 0 0
\(639\) −557771. + 322029.i −1.36601 + 0.788667i
\(640\) 0 0
\(641\) −7873.10 21631.2i −0.0191615 0.0526458i 0.929743 0.368209i \(-0.120029\pi\)
−0.948905 + 0.315563i \(0.897807\pi\)
\(642\) 0 0
\(643\) 41981.6 + 35226.7i 0.101540 + 0.0852021i 0.692144 0.721759i \(-0.256666\pi\)
−0.590604 + 0.806961i \(0.701111\pi\)
\(644\) 0 0
\(645\) 1.62675e6i 3.91022i
\(646\) 0 0
\(647\) −485981. −1.16094 −0.580471 0.814281i \(-0.697132\pi\)
−0.580471 + 0.814281i \(0.697132\pi\)
\(648\) 0 0
\(649\) −86263.4 + 102805.i −0.204803 + 0.244075i
\(650\) 0 0
\(651\) 1.09449e6 398361.i 2.58255 0.939972i
\(652\) 0 0
\(653\) 243189. + 421215.i 0.570318 + 0.987819i 0.996533 + 0.0831976i \(0.0265133\pi\)
−0.426215 + 0.904622i \(0.640153\pi\)
\(654\) 0 0
\(655\) −95001.7 538782.i −0.221436 1.25583i
\(656\) 0 0
\(657\) −189561. + 328329.i −0.439155 + 0.760640i
\(658\) 0 0
\(659\) −158420. 188797.i −0.364786 0.434735i 0.552165 0.833735i \(-0.313802\pi\)
−0.916951 + 0.399000i \(0.869357\pi\)
\(660\) 0 0
\(661\) 239119. 656975.i 0.547283 1.50365i −0.290082 0.957002i \(-0.593683\pi\)
0.837365 0.546645i \(-0.184095\pi\)
\(662\) 0 0
\(663\) 143349. 812970.i 0.326112 1.84947i
\(664\) 0 0
\(665\) 199462. 944487.i 0.451042 2.13576i
\(666\) 0 0
\(667\) 247274. + 43601.0i 0.555810 + 0.0980042i
\(668\) 0 0
\(669\) 478811. + 174273.i 1.06982 + 0.389384i
\(670\) 0 0
\(671\) −96417.5 + 80903.9i −0.214147 + 0.179690i
\(672\) 0 0
\(673\) 600361. + 346618.i 1.32551 + 0.765282i 0.984601 0.174815i \(-0.0559328\pi\)
0.340906 + 0.940097i \(0.389266\pi\)
\(674\) 0 0
\(675\) −269310. + 47486.6i −0.591078 + 0.104223i
\(676\) 0 0
\(677\) 205564. 118683.i 0.448508 0.258946i −0.258692 0.965960i \(-0.583291\pi\)
0.707200 + 0.707013i \(0.249958\pi\)
\(678\) 0 0
\(679\) 324678. + 892047.i 0.704229 + 1.93485i
\(680\) 0 0
\(681\) 136480. + 114521.i 0.294290 + 0.246939i
\(682\) 0 0
\(683\) 561678.i 1.20405i 0.798476 + 0.602027i \(0.205640\pi\)
−0.798476 + 0.602027i \(0.794360\pi\)
\(684\) 0 0
\(685\) −57789.1 −0.123159
\(686\) 0 0
\(687\) 326603. 389231.i 0.692002 0.824696i
\(688\) 0 0
\(689\) 331803. 120766.i 0.698942 0.254394i
\(690\) 0 0
\(691\) −145381. 251808.i −0.304475 0.527367i 0.672669 0.739944i \(-0.265148\pi\)
−0.977144 + 0.212577i \(0.931814\pi\)
\(692\) 0 0
\(693\) 33897.8 + 192244.i 0.0705837 + 0.400300i
\(694\) 0 0
\(695\) 57504.0 99599.9i 0.119050 0.206200i
\(696\) 0 0
\(697\) −392296. 467521.i −0.807512 0.962355i
\(698\) 0 0
\(699\) −258445. + 710072.i −0.528949 + 1.45328i
\(700\) 0 0
\(701\) 99320.0 563272.i 0.202116 1.14626i −0.699798 0.714341i \(-0.746727\pi\)
0.901914 0.431916i \(-0.142162\pi\)
\(702\) 0 0
\(703\) 221149. 117959.i 0.447480 0.238683i
\(704\) 0 0
\(705\) −1.26065e6 222287.i −2.53640 0.447236i
\(706\) 0 0
\(707\) −1.14425e6 416474.i −2.28920 0.833200i
\(708\) 0 0
\(709\) −75386.6 + 63256.9i −0.149969 + 0.125839i −0.714685 0.699446i \(-0.753430\pi\)
0.564716 + 0.825285i \(0.308986\pi\)
\(710\) 0 0
\(711\) 278636. + 160870.i 0.551185 + 0.318227i
\(712\) 0 0
\(713\) −367204. + 64747.9i −0.722317 + 0.127364i
\(714\) 0 0
\(715\) 92566.6 53443.4i 0.181068 0.104540i
\(716\) 0 0
\(717\) −494352. 1.35822e6i −0.961608 2.64200i
\(718\) 0 0
\(719\) −179686. 150775.i −0.347582 0.291656i 0.452236 0.891898i \(-0.350626\pi\)
−0.799818 + 0.600242i \(0.795071\pi\)
\(720\) 0 0
\(721\) 592494.i 1.13976i
\(722\) 0 0
\(723\) 391211. 0.748402
\(724\) 0 0
\(725\) −219185. + 261214.i −0.416999 + 0.496960i
\(726\) 0 0
\(727\) 378526. 137772.i 0.716188 0.260671i 0.0418813 0.999123i \(-0.486665\pi\)
0.674307 + 0.738452i \(0.264443\pi\)
\(728\) 0 0
\(729\) −430462. 745581.i −0.809989 1.40294i
\(730\) 0 0
\(731\) −220469. 1.25034e6i −0.412584 2.33988i
\(732\) 0 0
\(733\) −13781.4 + 23870.1i −0.0256499 + 0.0444269i −0.878565 0.477622i \(-0.841499\pi\)
0.852916 + 0.522049i \(0.174832\pi\)
\(734\) 0 0
\(735\) 1.21748e6 + 1.45093e6i 2.25365 + 2.68580i
\(736\) 0 0
\(737\) −45756.6 + 125715.i −0.0842402 + 0.231448i
\(738\) 0 0
\(739\) −50633.3 + 287155.i −0.0927144 + 0.525809i 0.902709 + 0.430251i \(0.141575\pi\)
−0.995424 + 0.0955586i \(0.969536\pi\)
\(740\) 0 0
\(741\) 378971. + 710490.i 0.690191 + 1.29396i
\(742\) 0 0
\(743\) 96689.8 + 17049.0i 0.175147 + 0.0308832i 0.260534 0.965465i \(-0.416101\pi\)
−0.0853867 + 0.996348i \(0.527213\pi\)
\(744\) 0 0
\(745\) −446627. 162559.i −0.804697 0.292886i
\(746\) 0 0
\(747\) 323918. 271799.i 0.580489 0.487088i
\(748\) 0 0
\(749\) −124764. 72032.8i −0.222396 0.128401i
\(750\) 0 0
\(751\) 153713. 27103.8i 0.272541 0.0480563i −0.0357074 0.999362i \(-0.511368\pi\)
0.308248 + 0.951306i \(0.400257\pi\)
\(752\) 0 0
\(753\) 237568. 137160.i 0.418984 0.241901i
\(754\) 0 0
\(755\) −152074. 417819.i −0.266784 0.732984i
\(756\) 0 0
\(757\) 208986. + 175360.i 0.364690 + 0.306012i 0.806657 0.591020i \(-0.201275\pi\)
−0.441966 + 0.897032i \(0.645719\pi\)
\(758\) 0 0
\(759\) 104637.i 0.181636i
\(760\) 0 0
\(761\) −51387.1 −0.0887330 −0.0443665 0.999015i \(-0.514127\pi\)
−0.0443665 + 0.999015i \(0.514127\pi\)
\(762\) 0 0
\(763\) 60867.4 72539.0i 0.104553 0.124601i
\(764\) 0 0
\(765\) 1.39669e6 508354.i 2.38659 0.868647i
\(766\) 0 0
\(767\) −519328. 899503.i −0.882777 1.52901i
\(768\) 0 0
\(769\) 129377. + 733731.i 0.218778 + 1.24075i 0.874229 + 0.485513i \(0.161367\pi\)
−0.655452 + 0.755237i \(0.727522\pi\)
\(770\) 0 0
\(771\) −62905.7 + 108956.i −0.105823 + 0.183291i
\(772\) 0 0
\(773\) 29794.7 + 35507.9i 0.0498632 + 0.0594246i 0.790400 0.612592i \(-0.209873\pi\)
−0.740536 + 0.672016i \(0.765429\pi\)
\(774\) 0 0
\(775\) 173191. 475837.i 0.288351 0.792237i
\(776\) 0 0
\(777\) −136730. + 775436.i −0.226476 + 1.28441i
\(778\) 0 0
\(779\) 582472. + 123010.i 0.959844 + 0.202705i
\(780\) 0 0
\(781\) 107322. + 18923.7i 0.175948 + 0.0310244i
\(782\) 0 0
\(783\) 360444. + 131191.i 0.587915 + 0.213984i
\(784\) 0 0
\(785\) −83724.1 + 70252.9i −0.135866 + 0.114005i
\(786\) 0 0
\(787\) 499855. + 288591.i 0.807039 + 0.465944i 0.845927 0.533299i \(-0.179048\pi\)
−0.0388875 + 0.999244i \(0.512381\pi\)
\(788\) 0 0
\(789\) −1.17187e6 + 206633.i −1.88246 + 0.331929i
\(790\) 0 0
\(791\) 783376. 452282.i 1.25204 0.722864i
\(792\) 0 0