Properties

Label 76.5.j.a.29.6
Level $76$
Weight $5$
Character 76.29
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 29.6
Character \(\chi\) \(=\) 76.29
Dual form 76.5.j.a.21.6

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

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{17}{18}\right)\) \(1\)

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 0.978201 + 0.207659i \(0.0665843\pi\)
0.0346409 + 0.999400i \(0.488971\pi\)
\(4\) 0 0
\(5\) 31.4208 + 11.4362i 1.25683 + 0.457450i 0.882705 0.469927i \(-0.155720\pi\)
0.374128 + 0.927377i \(0.377942\pi\)
\(6\) 0 0
\(7\) 39.9854 69.2568i 0.816029 1.41340i −0.0925569 0.995707i \(-0.529504\pi\)
0.908586 0.417697i \(-0.137163\pi\)
\(8\) 0 0
\(9\) −20.8569 + 118.285i −0.257492 + 1.46031i
\(10\) 0 0
\(11\) −10.1615 17.6003i −0.0839797 0.145457i 0.820976 0.570962i \(-0.193430\pi\)
−0.904956 + 0.425505i \(0.860096\pi\)
\(12\) 0 0
\(13\) −101.104 + 120.492i −0.598251 + 0.712968i −0.977169 0.212463i \(-0.931852\pi\)
0.378918 + 0.925430i \(0.376296\pi\)
\(14\) 0 0
\(15\) 162.181 + 445.589i 0.720805 + 1.98039i
\(16\) 0 0
\(17\) −64.2649 364.464i −0.222370 1.26112i −0.867650 0.497176i \(-0.834370\pi\)
0.645280 0.763947i \(-0.276741\pi\)
\(18\) 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 −0.643714 0.765266i \(-0.722607\pi\)
−0.00121023 + 0.999999i \(0.500385\pi\)
\(24\) 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 −0.246633 0.969109i \(-0.579324\pi\)
−0.563214 + 0.826311i \(0.690435\pi\)
\(30\) 0 0
\(31\) 889.421 + 513.507i 0.925516 + 0.534347i 0.885391 0.464848i \(-0.153891\pi\)
0.0401254 + 0.999195i \(0.487224\pi\)
\(32\) 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 \(-0.918392\pi\)
0.967315 0.253578i \(-0.0816076\pi\)
\(38\) 0 0
\(39\) −2230.59 −1.46653
\(40\) 0 0
\(41\) −1060.01 1263.27i −0.630584 0.751501i 0.352268 0.935899i \(-0.385411\pi\)
−0.982852 + 0.184399i \(0.940966\pi\)
\(42\) 0 0
\(43\) −3223.73 1173.34i −1.74350 0.634581i −0.744061 0.668112i \(-0.767103\pi\)
−0.999438 + 0.0335306i \(0.989325\pi\)
\(44\) 0 0
\(45\) −2008.08 + 3478.10i −0.991644 + 1.71758i
\(46\) 0 0
\(47\) −468.777 + 2658.57i −0.212212 + 1.20352i 0.673466 + 0.739218i \(0.264805\pi\)
−0.885679 + 0.464298i \(0.846307\pi\)
\(48\) 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 −0.998079 0.0619591i \(-0.980265\pi\)
0.724746 0.689016i \(-0.241957\pi\)
\(54\) 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 0.879076 0.476683i \(-0.158161\pi\)
0.989096 + 0.147273i \(0.0470497\pi\)
\(60\) 0 0
\(61\) 5819.67 2118.19i 1.56401 0.569252i 0.592357 0.805676i \(-0.298198\pi\)
0.971650 + 0.236424i \(0.0759754\pi\)
\(62\) 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 0.840159 0.542341i \(-0.182462\pi\)
0.603999 + 0.796985i \(0.293573\pi\)
\(68\) 0 0
\(69\) −4458.88 2574.34i −0.936544 0.540714i
\(70\) 0 0
\(71\) −1833.99 + 5038.85i −0.363815 + 0.999574i 0.613853 + 0.789420i \(0.289619\pi\)
−0.977668 + 0.210154i \(0.932603\pi\)
\(72\) 0 0
\(73\) −2417.99 + 2028.93i −0.453741 + 0.380734i −0.840822 0.541312i \(-0.817928\pi\)
0.387081 + 0.922046i \(0.373483\pi\)
\(74\) 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 0.610250 0.792209i \(-0.291069\pi\)
−0.886142 + 0.463413i \(0.846625\pi\)
\(80\) 0 0
\(81\) 1751.11 + 637.353i 0.266897 + 0.0971427i
\(82\) 0 0
\(83\) 1760.24 3048.83i 0.255515 0.442564i −0.709521 0.704685i \(-0.751088\pi\)
0.965035 + 0.262120i \(0.0844218\pi\)
\(84\) 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 0.166956 + 0.985964i \(0.446606\pi\)
−0.999977 + 0.00679184i \(0.997838\pi\)
\(90\) 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 0.486483 0.873690i \(-0.338280\pi\)
0.755964 + 0.654613i \(0.227168\pi\)
\(98\) 0 0
\(99\) 2293.80 834.873i 0.234037 0.0851824i
\(100\) 0 0
\(101\) −11664.3 9787.51i −1.14345 0.959466i −0.143900 0.989592i \(-0.545965\pi\)
−0.999546 + 0.0301266i \(0.990409\pi\)
\(102\) 0 0
\(103\) 6416.27 3704.43i 0.604795 0.349178i −0.166131 0.986104i \(-0.553127\pi\)
0.770925 + 0.636925i \(0.219794\pi\)
\(104\) 0 0
\(105\) 37344.9 + 6584.92i 3.38730 + 0.597272i
\(106\) 0 0
\(107\) −1560.12 900.738i −0.136267 0.0786739i 0.430317 0.902678i \(-0.358402\pi\)
−0.566584 + 0.824004i \(0.691735\pi\)
\(108\) 0 0
\(109\) −404.983 + 1112.68i −0.0340866 + 0.0936523i −0.955569 0.294769i \(-0.904757\pi\)
0.921482 + 0.388421i \(0.126979\pi\)
\(110\) 0 0
\(111\) 7542.52 6328.93i 0.612168 0.513670i
\(112\) 0 0
\(113\) 11311.2i 0.885831i 0.896563 + 0.442915i \(0.146056\pi\)
−0.896563 + 0.442915i \(0.853944\pi\)
\(114\) 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 0.000352700 1.00000i \(0.499888\pi\)
−0.984869 + 0.173301i \(0.944557\pi\)
\(128\) 0 0
\(129\) −16639.5 45716.7i −0.999912 2.74724i
\(130\) 0 0
\(131\) 2841.19 + 16113.2i 0.165561 + 0.938942i 0.948484 + 0.316824i \(0.102616\pi\)
−0.782924 + 0.622118i \(0.786273\pi\)
\(132\) 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 −0.384922 0.922949i \(-0.625772\pi\)
0.298393 + 0.954443i \(0.403549\pi\)
\(138\) 0 0
\(139\) 2634.82 + 2210.87i 0.136371 + 0.114429i 0.708422 0.705790i \(-0.249408\pi\)
−0.572051 + 0.820218i \(0.693852\pi\)
\(140\) 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 −0.854193 0.519956i \(-0.825948\pi\)
0.363727 + 0.931505i \(0.381504\pi\)
\(150\) 0 0
\(151\) 13297.5i 0.583199i 0.956540 + 0.291600i \(0.0941875\pi\)
−0.956540 + 0.291600i \(0.905813\pi\)
\(152\) 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 0.278963 0.960302i \(-0.410009\pi\)
−0.403572 + 0.914948i \(0.632232\pi\)
\(158\) 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 0.839511 0.543342i \(-0.182841\pi\)
−0.890304 + 0.455367i \(0.849508\pi\)
\(164\) 0 0
\(165\) 6194.49 7382.31i 0.227530 0.271159i
\(166\) 0 0
\(167\) 3277.80 + 9005.69i 0.117530 + 0.322912i 0.984483 0.175478i \(-0.0561470\pi\)
−0.866953 + 0.498390i \(0.833925\pi\)
\(168\) 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 −0.345087 0.938571i \(-0.612151\pi\)
−0.00326608 + 0.999995i \(0.501040\pi\)
\(174\) 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 −0.849772 0.527150i \(-0.823260\pi\)
0.0316398 + 0.999499i \(0.489927\pi\)
\(180\) 0 0
\(181\) −22735.5 4008.87i −0.693979 0.122367i −0.184477 0.982837i \(-0.559059\pi\)
−0.509502 + 0.860469i \(0.670170\pi\)
\(182\) 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 0.801046 0.598603i \(-0.204277\pi\)
−0.728609 + 0.684929i \(0.759833\pi\)
\(194\) 0 0
\(195\) −70086.9 25509.5i −1.84318 0.670862i
\(196\) 0 0
\(197\) 13290.6 23019.9i 0.342461 0.593159i −0.642428 0.766346i \(-0.722073\pi\)
0.984889 + 0.173186i \(0.0554063\pi\)
\(198\) 0 0
\(199\) −3824.40 + 21689.2i −0.0965732 + 0.547694i 0.897681 + 0.440647i \(0.145251\pi\)
−0.994254 + 0.107047i \(0.965860\pi\)
\(200\) 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 0.825408 0.564537i \(-0.190945\pi\)
0.968713 + 0.248185i \(0.0798342\pi\)
\(212\) 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 −0.752671 0.658397i \(-0.771235\pi\)
0.999789 0.0205533i \(-0.00654279\pi\)
\(224\) 0 0
\(225\) −45365.8 + 38066.5i −0.896115 + 0.751930i
\(226\) 0 0
\(227\) 12563.2i 0.243808i −0.992542 0.121904i \(-0.961100\pi\)
0.992542 0.121904i \(-0.0389000\pi\)
\(228\) 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 −0.163149 0.986602i \(-0.552165\pi\)
−0.759154 + 0.650911i \(0.774387\pi\)
\(234\) 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 0.837283 + 0.546770i \(0.184143\pi\)
0.0548758 + 0.998493i \(0.482524\pi\)
\(240\) 0 0
\(241\) 17732.2 21132.4i 0.305301 0.363843i −0.591479 0.806320i \(-0.701456\pi\)
0.896780 + 0.442477i \(0.145900\pi\)
\(242\) 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 −0.193705 0.981060i \(-0.562050\pi\)
0.482227 + 0.876046i \(0.339828\pi\)
\(252\) 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 0.107117 0.994246i \(-0.465838\pi\)
−0.239395 + 0.970922i \(0.576949\pi\)
\(258\) 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 −0.975691 0.219150i \(-0.929672\pi\)
0.0463935 + 0.998923i \(0.485227\pi\)
\(264\) 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 0.933786 0.357833i \(-0.116484\pi\)
−0.514547 + 0.857462i \(0.672040\pi\)
\(270\) 0 0
\(271\) 34101.1 + 12411.8i 0.464333 + 0.169003i 0.563584 0.826059i \(-0.309422\pi\)
−0.0992505 + 0.995062i \(0.531645\pi\)
\(272\) 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 0.875631 0.482981i \(-0.160446\pi\)
−0.856089 + 0.516828i \(0.827113\pi\)
\(278\) 0 0
\(279\) −79290.9 + 94495.2i −1.01863 + 1.21395i
\(280\) 0 0
\(281\) −37837.4 103957.i −0.479191 1.31657i −0.910182 0.414209i \(-0.864058\pi\)
0.430991 0.902356i \(-0.358164\pi\)
\(282\) 0 0
\(283\) −21586.7 122424.i −0.269534 1.52860i −0.755806 0.654796i \(-0.772755\pi\)
0.486272 0.873807i \(-0.338356\pi\)
\(284\) 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 −0.503461 0.864018i \(-0.667940\pi\)
0.496531 + 0.868019i \(0.334607\pi\)
\(294\) 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 0.783984 0.620781i \(-0.213184\pi\)
−0.747487 + 0.664276i \(0.768740\pi\)
\(308\) 0 0
\(309\) 98731.2 + 35935.2i 1.03404 + 0.376360i
\(310\) 0 0
\(311\) 66863.5 115811.i 0.691303 1.19737i −0.280108 0.959968i \(-0.590370\pi\)
0.971411 0.237404i \(-0.0762964\pi\)
\(312\) 0 0
\(313\) 44.4220 251.930i 0.000453430 0.00257153i −0.984580 0.174934i \(-0.944029\pi\)
0.985034 + 0.172362i \(0.0551400\pi\)
\(314\) 0 0
\(315\) 160588. + 278146.i 1.61842 + 2.80319i
\(316\) 0 0
\(317\) 47164.2 56208.1i 0.469347 0.559346i −0.478493 0.878091i \(-0.658817\pi\)
0.947840 + 0.318745i \(0.103261\pi\)
\(318\) 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 −0.257621 0.966246i \(-0.582939\pi\)
0.707983 + 0.706230i \(0.249605\pi\)
\(332\) 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 0.712304 + 0.701871i \(0.247652\pi\)
−0.996811 + 0.0798043i \(0.974570\pi\)
\(338\) 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 0.495557 0.868575i \(-0.334964\pi\)
−0.178690 + 0.983905i \(0.557186\pi\)
\(348\) 0 0
\(349\) −117786. + 204011.i −0.967036 + 1.67495i −0.262992 + 0.964798i \(0.584709\pi\)
−0.704043 + 0.710157i \(0.748624\pi\)
\(350\) 0 0
\(351\) 15148.8 85913.0i 0.122960 0.697340i
\(352\) 0 0
\(353\) −45139.8 78184.5i −0.362252 0.627439i 0.626079 0.779759i \(-0.284659\pi\)
−0.988331 + 0.152321i \(0.951325\pi\)
\(354\) 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 0.826223 + 0.563343i \(0.190485\pi\)
−0.583721 + 0.811954i \(0.698404\pi\)
\(360\) 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 0.581056 0.813863i \(-0.302640\pi\)
−0.700600 + 0.713555i \(0.747084\pi\)
\(368\) 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 0.837012 0.547185i \(-0.184300\pi\)
−0.0553697 + 0.998466i \(0.517634\pi\)
\(374\) 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 \(-0.924264\pi\)
0.971828 0.235693i \(-0.0757359\pi\)
\(380\) 0 0
\(381\) −350332. −2.41340
\(382\) 0 0
\(383\) −70745.6 84311.4i −0.482283 0.574763i 0.468954 0.883223i \(-0.344631\pi\)
−0.951237 + 0.308460i \(0.900186\pi\)
\(384\) 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 0.618327 + 0.785921i \(0.287811\pi\)
−0.849838 + 0.527043i \(0.823301\pi\)
\(390\) 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 0.992828 0.119549i \(-0.0381448\pi\)
−0.973842 + 0.227228i \(0.927034\pi\)
\(398\) 0 0
\(399\) −127025. + 389203.i −0.797889 + 2.44473i
\(400\) 0 0
\(401\) −35490.2 + 6257.89i −0.220709 + 0.0389170i −0.282909 0.959147i \(-0.591299\pi\)
0.0622000 + 0.998064i \(0.480188\pi\)
\(402\) 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 0.643462 0.765478i \(-0.277498\pi\)
0.342847 + 0.939391i \(0.388609\pi\)
\(410\) 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 0.762808 0.646625i \(-0.223820\pi\)
−0.769261 + 0.638934i \(0.779376\pi\)
\(422\) 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 0.0171038 + 0.999854i \(0.494555\pi\)
−0.987634 + 0.156779i \(0.949889\pi\)
\(432\) 0 0
\(433\) 106300. + 292057.i 0.566968 + 1.55773i 0.809213 + 0.587516i \(0.199894\pi\)
−0.242245 + 0.970215i \(0.577884\pi\)
\(434\) 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 −0.137506 0.990501i \(-0.543908\pi\)
0.209558 + 0.977796i \(0.432797\pi\)
\(440\) 0 0
\(441\) 450827. 164088.i 2.31811 0.843721i
\(442\) 0 0
\(443\) −121549. 101992.i −0.619363 0.519708i 0.278240 0.960512i \(-0.410249\pi\)
−0.897603 + 0.440804i \(0.854693\pi\)
\(444\) 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 0.195370 0.980730i \(-0.437409\pi\)
−0.751652 + 0.659560i \(0.770742\pi\)
\(450\) 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 −0.636631 0.771168i \(-0.719673\pi\)
−0.983385 + 0.181531i \(0.941895\pi\)
\(462\) 0 0
\(463\) −75550.3 + 130857.i −0.352431 + 0.610428i −0.986675 0.162705i \(-0.947978\pi\)
0.634244 + 0.773133i \(0.281312\pi\)
\(464\) 0 0
\(465\) −84565.9 + 479597.i −0.391102 + 2.21805i
\(466\) 0 0
\(467\) 54139.2 + 93771.8i 0.248243 + 0.429970i 0.963039 0.269364i \(-0.0868134\pi\)
−0.714795 + 0.699334i \(0.753480\pi\)
\(468\) 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 −0.334468 0.942407i \(-0.608557\pi\)
0.349550 + 0.936918i \(0.386334\pi\)
\(480\) 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 −0.0591348 0.998250i \(-0.518834\pi\)
−0.894077 + 0.447913i \(0.852168\pi\)
\(488\) 0 0
\(489\) 13091.0 35967.1i 0.0547462 0.150414i
\(490\) 0 0
\(491\) 186984. 156898.i 0.775607 0.650812i −0.166531 0.986036i \(-0.553257\pi\)
0.942138 + 0.335224i \(0.108812\pi\)
\(492\) 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 −0.272682 0.962104i \(-0.587911\pi\)
−0.827315 + 0.561738i \(0.810133\pi\)
\(500\) 0 0
\(501\) −67954.5 + 117701.i −0.270734 + 0.468925i
\(502\) 0 0
\(503\) 28729.7 162934.i 0.113552 0.643986i −0.873905 0.486097i \(-0.838420\pi\)
0.987457 0.157889i \(-0.0504689\pi\)
\(504\) 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 0.999497 0.0317215i \(-0.0100990\pi\)
−0.786049 + 0.618164i \(0.787877\pi\)
\(510\) 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 −0.660537 0.750793i \(-0.729671\pi\)
0.319937 + 0.947439i \(0.396338\pi\)
\(522\) 0 0
\(523\) 522060. + 92053.2i 1.90861 + 0.336539i 0.997188 0.0749394i \(-0.0238763\pi\)
0.911419 + 0.411478i \(0.134987\pi\)
\(524\) 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 −0.876052 0.482216i \(-0.839832\pi\)
0.988147 0.153508i \(-0.0490570\pi\)
\(542\) 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 0.813718 0.581260i \(-0.197440\pi\)
−0.996971 + 0.0777765i \(0.975218\pi\)
\(548\) 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 0.799063 0.601247i \(-0.205329\pi\)
−0.453357 + 0.891329i \(0.649774\pi\)
\(558\) 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 0.295578 0.955319i \(-0.404488\pi\)
−0.679541 + 0.733637i \(0.737821\pi\)
\(564\) 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 \(0.126330\pi\)
−0.922273 + 0.386540i \(0.873670\pi\)
\(570\) 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 −0.936837 0.349767i \(-0.886261\pi\)
0.771326 + 0.636441i \(0.219594\pi\)
\(578\) 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 −0.796299 0.604903i \(-0.793212\pi\)
0.541387 0.840773i \(-0.317899\pi\)
\(588\) 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 −0.594741 0.803917i \(-0.702745\pi\)
0.0611503 + 0.998129i \(0.480523\pi\)
\(594\) 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 −0.821646 0.569998i \(-0.806944\pi\)
−0.967046 + 0.254604i \(0.918055\pi\)
\(600\) 0 0
\(601\) −372533. 215082.i −1.03137 0.595464i −0.113996 0.993481i \(-0.536365\pi\)
−0.917378 + 0.398018i \(0.869698\pi\)
\(602\) 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 \(0.0685374\pi\)
−0.976909 + 0.213657i \(0.931463\pi\)
\(608\) 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 0.824235 0.566248i \(-0.191606\pi\)
0.267423 + 0.963579i \(0.413828\pi\)
\(614\) 0 0
\(615\) 390986. 677208.i 1.03374 1.79049i
\(616\) 0 0
\(617\) 102238. 579819.i 0.268560 1.52308i −0.490143 0.871642i \(-0.663056\pi\)
0.758703 0.651437i \(-0.225833\pi\)
\(618\) 0 0
\(619\) 205858. + 356557.i 0.537263 + 0.930568i 0.999050 + 0.0435765i \(0.0138752\pi\)
−0.461787 + 0.886991i \(0.652791\pi\)
\(620\) 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 −0.261506 0.965202i \(-0.584219\pi\)
0.420094 + 0.907480i \(0.361997\pi\)
\(632\) 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 −0.948905 0.315563i \(-0.897807\pi\)
0.929743 + 0.368209i \(0.120029\pi\)
\(642\) 0 0
\(643\) 41981.6 35226.7i 0.101540 0.0852021i −0.590604 0.806961i \(-0.701111\pi\)
0.692144 + 0.721759i \(0.256666\pi\)
\(644\) 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 −0.426215 0.904622i \(-0.640153\pi\)
0.996533 0.0831976i \(-0.0265133\pi\)
\(654\) 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 −0.916951 0.399000i \(-0.869357\pi\)
0.552165 + 0.833735i \(0.313802\pi\)
\(660\) 0 0
\(661\) 239119. + 656975.i 0.547283 + 1.50365i 0.837365 + 0.546645i \(0.184095\pi\)
−0.290082 + 0.957002i \(0.593683\pi\)
\(662\) 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 0.340906 0.940097i \(-0.389266\pi\)
0.984601 + 0.174815i \(0.0559328\pi\)
\(674\) 0 0
\(675\) −269310. 47486.6i −0.591078 0.104223i
\(676\) 0 0
\(677\) 205564. + 118683.i 0.448508 + 0.258946i 0.707200 0.707013i \(-0.249958\pi\)
−0.258692 + 0.965960i \(0.583291\pi\)
\(678\) 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 \(-0.794360\pi\)
0.798476 0.602027i \(-0.205640\pi\)
\(684\) 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 −0.977144 0.212577i \(-0.931814\pi\)
0.672669 + 0.739944i \(0.265148\pi\)
\(692\) 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 0.901914 + 0.431916i \(0.142162\pi\)
−0.699798 + 0.714341i \(0.746727\pi\)
\(702\) 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 0.564716 0.825285i \(-0.308986\pi\)
−0.714685 + 0.699446i \(0.753430\pi\)
\(710\) 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 −0.799818 0.600242i \(-0.795071\pi\)
0.452236 + 0.891898i \(0.350626\pi\)
\(720\) 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 0.674307 0.738452i \(-0.264443\pi\)
0.0418813 + 0.999123i \(0.486665\pi\)
\(728\) 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 0.852916 0.522049i \(-0.174832\pi\)
−0.878565 + 0.477622i \(0.841499\pi\)
\(734\) 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 −0.995424 0.0955586i \(-0.969536\pi\)
0.902709 0.430251i \(-0.141575\pi\)
\(740\) 0 0
\(741\) 378971. 710490.i 0.690191 1.29396i
\(742\) 0 0
\(743\) 96689.8 17049.0i 0.175147 0.0308832i −0.0853867 0.996348i \(-0.527213\pi\)
0.260534 + 0.965465i \(0.416101\pi\)
\(744\) 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 0.308248 0.951306i \(-0.400257\pi\)
−0.0357074 + 0.999362i \(0.511368\pi\)
\(752\) 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 −0.441966 0.897032i \(-0.645719\pi\)
0.806657 + 0.591020i \(0.201275\pi\)
\(758\) 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 −0.655452 0.755237i \(-0.727522\pi\)
0.874229 0.485513i \(-0.161367\pi\)
\(770\) 0 0
\(771\) −62905.7 108956.i −0.105823 0.183291i
\(772\) 0 0
\(773\) 29794.7 35507.9i 0.0498632 0.0594246i −0.740536 0.672016i \(-0.765429\pi\)
0.790400 + 0.612592i \(0.209873\pi\)
\(774\) 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 −0.0388875 0.999244i \(-0.512381\pi\)
0.845927 + 0.533299i \(0.179048\pi\)
\(788\) 0 0
\(789\) −1.17187e6 206633.i −1.88246 0.331929i
\(790\) 0 0
\(791\) 783376. + 452282.i 1.25204 + 0.722864i
\(792\) 0