Properties

Label 76.6.e.a.45.4
Level $76$
Weight $6$
Character 76.45
Analytic conductor $12.189$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 76.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.1891703058\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(9\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Defining polynomial: \(x^{18} - 2 x^{17} + 1540 x^{16} - 768 x^{15} + 1608492 x^{14} - 1027368 x^{13} + 897054160 x^{12} - 1275481376 x^{11} + 361098181456 x^{10} - 863969476320 x^{9} + 79755165392064 x^{8} - 375077568148992 x^{7} + 12736924096193536 x^{6} - 57314532742553600 x^{5} + 977121800205220864 x^{4} - 4977732006498379776 x^{3} + 53672321824823513088 x^{2} - 185653809995679793152 x + 804303742853852430336\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{16}\cdot 3^{3}\cdot 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 45.4
Root \(3.49628 - 6.05573i\) of defining polynomial
Character \(\chi\) \(=\) 76.45
Dual form 76.6.e.a.49.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.99628 - 6.92176i) q^{3} +(31.6056 + 54.7425i) q^{5} -80.2775 q^{7} +(89.5595 - 155.122i) q^{9} +O(q^{10})\) \(q+(-3.99628 - 6.92176i) q^{3} +(31.6056 + 54.7425i) q^{5} -80.2775 q^{7} +(89.5595 - 155.122i) q^{9} -475.169 q^{11} +(-337.473 + 584.520i) q^{13} +(252.609 - 437.532i) q^{15} +(866.499 + 1500.82i) q^{17} +(-574.366 + 1464.99i) q^{19} +(320.811 + 555.661i) q^{21} +(-2424.72 + 4199.73i) q^{23} +(-435.326 + 754.007i) q^{25} -3373.81 q^{27} +(2394.08 - 4146.67i) q^{29} -127.218 q^{31} +(1898.91 + 3289.01i) q^{33} +(-2537.22 - 4394.59i) q^{35} -13949.4 q^{37} +5394.54 q^{39} +(7883.24 + 13654.2i) q^{41} +(964.112 + 1669.89i) q^{43} +11322.3 q^{45} +(8099.51 - 14028.8i) q^{47} -10362.5 q^{49} +(6925.54 - 11995.4i) q^{51} +(8925.98 - 15460.3i) q^{53} +(-15018.0 - 26011.9i) q^{55} +(12435.6 - 1878.90i) q^{57} +(8424.75 + 14592.1i) q^{59} +(11641.7 - 20164.0i) q^{61} +(-7189.61 + 12452.8i) q^{63} -42664.1 q^{65} +(13618.4 - 23587.8i) q^{67} +38759.3 q^{69} +(-37449.3 - 64864.1i) q^{71} +(34900.9 + 60450.1i) q^{73} +6958.73 q^{75} +38145.4 q^{77} +(11408.5 + 19760.1i) q^{79} +(-8280.29 - 14341.9i) q^{81} -58008.8 q^{83} +(-54772.4 + 94868.6i) q^{85} -38269.6 q^{87} +(8203.84 - 14209.5i) q^{89} +(27091.5 - 46923.8i) q^{91} +(508.400 + 880.575i) q^{93} +(-98350.5 + 14859.7i) q^{95} +(65710.8 + 113814. i) q^{97} +(-42555.9 + 73709.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q - 11q^{3} + 11q^{5} + 336q^{7} - 902q^{9} + O(q^{10}) \) \( 18q - 11q^{3} + 11q^{5} + 336q^{7} - 902q^{9} - 320q^{11} + 227q^{13} - 101q^{15} + 179q^{17} - 868q^{19} - 5700q^{21} - 3425q^{23} - 7054q^{25} + 14722q^{27} - 7349q^{29} - 9960q^{31} - 2998q^{33} + 15888q^{35} + 26444q^{37} - 30246q^{39} - 7311q^{41} - 8283q^{43} - 62164q^{45} + 37603q^{47} + 124738q^{49} + 47227q^{51} - 20337q^{53} + 716q^{55} - 57555q^{57} - 74455q^{59} - 7569q^{61} - 52544q^{63} + 188998q^{65} - 26177q^{67} + 116282q^{69} - 53463q^{71} - 14103q^{73} + 120912q^{75} - 31960q^{77} + 31825q^{79} - 21137q^{81} + 82600q^{83} - 50787q^{85} - 339766q^{87} - 155197q^{89} - 2800q^{91} - 46460q^{93} + 49315q^{95} + 111241q^{97} - 193544q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) −3.99628 6.92176i −0.256361 0.444031i 0.708903 0.705306i \(-0.249190\pi\)
−0.965264 + 0.261275i \(0.915857\pi\)
\(4\) 0 0
\(5\) 31.6056 + 54.7425i 0.565378 + 0.979263i 0.997014 + 0.0772156i \(0.0246030\pi\)
−0.431637 + 0.902048i \(0.642064\pi\)
\(6\) 0 0
\(7\) −80.2775 −0.619225 −0.309613 0.950863i \(-0.600199\pi\)
−0.309613 + 0.950863i \(0.600199\pi\)
\(8\) 0 0
\(9\) 89.5595 155.122i 0.368558 0.638361i
\(10\) 0 0
\(11\) −475.169 −1.18404 −0.592020 0.805923i \(-0.701669\pi\)
−0.592020 + 0.805923i \(0.701669\pi\)
\(12\) 0 0
\(13\) −337.473 + 584.520i −0.553835 + 0.959270i 0.444158 + 0.895948i \(0.353503\pi\)
−0.997993 + 0.0633218i \(0.979831\pi\)
\(14\) 0 0
\(15\) 252.609 437.532i 0.289882 0.502090i
\(16\) 0 0
\(17\) 866.499 + 1500.82i 0.727186 + 1.25952i 0.958068 + 0.286542i \(0.0925058\pi\)
−0.230881 + 0.972982i \(0.574161\pi\)
\(18\) 0 0
\(19\) −574.366 + 1464.99i −0.365010 + 0.931004i
\(20\) 0 0
\(21\) 320.811 + 555.661i 0.158745 + 0.274955i
\(22\) 0 0
\(23\) −2424.72 + 4199.73i −0.955743 + 1.65540i −0.223085 + 0.974799i \(0.571613\pi\)
−0.732658 + 0.680597i \(0.761721\pi\)
\(24\) 0 0
\(25\) −435.326 + 754.007i −0.139304 + 0.241282i
\(26\) 0 0
\(27\) −3373.81 −0.890658
\(28\) 0 0
\(29\) 2394.08 4146.67i 0.528620 0.915597i −0.470823 0.882228i \(-0.656043\pi\)
0.999443 0.0333693i \(-0.0106237\pi\)
\(30\) 0 0
\(31\) −127.218 −0.0237764 −0.0118882 0.999929i \(-0.503784\pi\)
−0.0118882 + 0.999929i \(0.503784\pi\)
\(32\) 0 0
\(33\) 1898.91 + 3289.01i 0.303542 + 0.525751i
\(34\) 0 0
\(35\) −2537.22 4394.59i −0.350096 0.606384i
\(36\) 0 0
\(37\) −13949.4 −1.67514 −0.837570 0.546331i \(-0.816024\pi\)
−0.837570 + 0.546331i \(0.816024\pi\)
\(38\) 0 0
\(39\) 5394.54 0.567927
\(40\) 0 0
\(41\) 7883.24 + 13654.2i 0.732394 + 1.26854i 0.955857 + 0.293831i \(0.0949304\pi\)
−0.223463 + 0.974712i \(0.571736\pi\)
\(42\) 0 0
\(43\) 964.112 + 1669.89i 0.0795163 + 0.137726i 0.903041 0.429554i \(-0.141329\pi\)
−0.823525 + 0.567280i \(0.807996\pi\)
\(44\) 0 0
\(45\) 11322.3 0.833498
\(46\) 0 0
\(47\) 8099.51 14028.8i 0.534828 0.926349i −0.464344 0.885655i \(-0.653710\pi\)
0.999172 0.0406941i \(-0.0129569\pi\)
\(48\) 0 0
\(49\) −10362.5 −0.616560
\(50\) 0 0
\(51\) 6925.54 11995.4i 0.372845 0.645786i
\(52\) 0 0
\(53\) 8925.98 15460.3i 0.436482 0.756009i −0.560933 0.827861i \(-0.689558\pi\)
0.997415 + 0.0718520i \(0.0228909\pi\)
\(54\) 0 0
\(55\) −15018.0 26011.9i −0.669430 1.15949i
\(56\) 0 0
\(57\) 12435.6 1878.90i 0.506969 0.0765978i
\(58\) 0 0
\(59\) 8424.75 + 14592.1i 0.315084 + 0.545742i 0.979455 0.201661i \(-0.0646339\pi\)
−0.664371 + 0.747403i \(0.731301\pi\)
\(60\) 0 0
\(61\) 11641.7 20164.0i 0.400583 0.693830i −0.593214 0.805045i \(-0.702141\pi\)
0.993796 + 0.111215i \(0.0354743\pi\)
\(62\) 0 0
\(63\) −7189.61 + 12452.8i −0.228220 + 0.395289i
\(64\) 0 0
\(65\) −42664.1 −1.25250
\(66\) 0 0
\(67\) 13618.4 23587.8i 0.370630 0.641950i −0.619033 0.785365i \(-0.712475\pi\)
0.989663 + 0.143415i \(0.0458085\pi\)
\(68\) 0 0
\(69\) 38759.3 0.980062
\(70\) 0 0
\(71\) −37449.3 64864.1i −0.881654 1.52707i −0.849501 0.527586i \(-0.823097\pi\)
−0.0321524 0.999483i \(-0.510236\pi\)
\(72\) 0 0
\(73\) 34900.9 + 60450.1i 0.766530 + 1.32767i 0.939434 + 0.342731i \(0.111352\pi\)
−0.172903 + 0.984939i \(0.555315\pi\)
\(74\) 0 0
\(75\) 6958.73 0.142849
\(76\) 0 0
\(77\) 38145.4 0.733188
\(78\) 0 0
\(79\) 11408.5 + 19760.1i 0.205665 + 0.356222i 0.950344 0.311200i \(-0.100731\pi\)
−0.744680 + 0.667422i \(0.767398\pi\)
\(80\) 0 0
\(81\) −8280.29 14341.9i −0.140227 0.242881i
\(82\) 0 0
\(83\) −58008.8 −0.924270 −0.462135 0.886810i \(-0.652916\pi\)
−0.462135 + 0.886810i \(0.652916\pi\)
\(84\) 0 0
\(85\) −54772.4 + 94868.6i −0.822270 + 1.42421i
\(86\) 0 0
\(87\) −38269.6 −0.542071
\(88\) 0 0
\(89\) 8203.84 14209.5i 0.109785 0.190153i −0.805898 0.592054i \(-0.798317\pi\)
0.915683 + 0.401901i \(0.131651\pi\)
\(90\) 0 0
\(91\) 27091.5 46923.8i 0.342948 0.594004i
\(92\) 0 0
\(93\) 508.400 + 880.575i 0.00609535 + 0.0105575i
\(94\) 0 0
\(95\) −98350.5 + 14859.7i −1.11807 + 0.168928i
\(96\) 0 0
\(97\) 65710.8 + 113814.i 0.709100 + 1.22820i 0.965191 + 0.261544i \(0.0842318\pi\)
−0.256092 + 0.966653i \(0.582435\pi\)
\(98\) 0 0
\(99\) −42555.9 + 73709.0i −0.436387 + 0.755845i
\(100\) 0 0
\(101\) −46068.0 + 79792.2i −0.449362 + 0.778318i −0.998345 0.0575159i \(-0.981682\pi\)
0.548983 + 0.835834i \(0.315015\pi\)
\(102\) 0 0
\(103\) 149801. 1.39130 0.695651 0.718380i \(-0.255116\pi\)
0.695651 + 0.718380i \(0.255116\pi\)
\(104\) 0 0
\(105\) −20278.8 + 35124.0i −0.179502 + 0.310907i
\(106\) 0 0
\(107\) 62370.7 0.526649 0.263324 0.964707i \(-0.415181\pi\)
0.263324 + 0.964707i \(0.415181\pi\)
\(108\) 0 0
\(109\) −27370.0 47406.1i −0.220652 0.382180i 0.734354 0.678767i \(-0.237485\pi\)
−0.955006 + 0.296586i \(0.904152\pi\)
\(110\) 0 0
\(111\) 55745.6 + 96554.3i 0.429441 + 0.743813i
\(112\) 0 0
\(113\) −84395.3 −0.621759 −0.310879 0.950449i \(-0.600624\pi\)
−0.310879 + 0.950449i \(0.600624\pi\)
\(114\) 0 0
\(115\) −306538. −2.16142
\(116\) 0 0
\(117\) 60447.8 + 104699.i 0.408240 + 0.707093i
\(118\) 0 0
\(119\) −69560.4 120482.i −0.450292 0.779929i
\(120\) 0 0
\(121\) 64734.8 0.401952
\(122\) 0 0
\(123\) 63007.2 109132.i 0.375515 0.650411i
\(124\) 0 0
\(125\) 142500. 0.815717
\(126\) 0 0
\(127\) 59200.7 102539.i 0.325700 0.564128i −0.655954 0.754801i \(-0.727734\pi\)
0.981654 + 0.190672i \(0.0610668\pi\)
\(128\) 0 0
\(129\) 7705.72 13346.7i 0.0407698 0.0706154i
\(130\) 0 0
\(131\) −37228.3 64481.4i −0.189538 0.328289i 0.755559 0.655081i \(-0.227366\pi\)
−0.945096 + 0.326792i \(0.894032\pi\)
\(132\) 0 0
\(133\) 46108.6 117606.i 0.226023 0.576501i
\(134\) 0 0
\(135\) −106631. 184691.i −0.503559 0.872189i
\(136\) 0 0
\(137\) −70227.1 + 121637.i −0.319671 + 0.553686i −0.980419 0.196921i \(-0.936906\pi\)
0.660748 + 0.750607i \(0.270239\pi\)
\(138\) 0 0
\(139\) −112322. + 194548.i −0.493093 + 0.854061i −0.999968 0.00795774i \(-0.997467\pi\)
0.506876 + 0.862019i \(0.330800\pi\)
\(140\) 0 0
\(141\) −129472. −0.548437
\(142\) 0 0
\(143\) 160357. 277746.i 0.655763 1.13581i
\(144\) 0 0
\(145\) 302665. 1.19548
\(146\) 0 0
\(147\) 41411.5 + 71726.9i 0.158062 + 0.273772i
\(148\) 0 0
\(149\) −146994. 254601.i −0.542417 0.939494i −0.998765 0.0496923i \(-0.984176\pi\)
0.456347 0.889802i \(-0.349157\pi\)
\(150\) 0 0
\(151\) 366703. 1.30880 0.654398 0.756150i \(-0.272922\pi\)
0.654398 + 0.756150i \(0.272922\pi\)
\(152\) 0 0
\(153\) 310413. 1.07204
\(154\) 0 0
\(155\) −4020.81 6964.26i −0.0134426 0.0232833i
\(156\) 0 0
\(157\) 14338.2 + 24834.5i 0.0464243 + 0.0804093i 0.888304 0.459256i \(-0.151884\pi\)
−0.841880 + 0.539666i \(0.818551\pi\)
\(158\) 0 0
\(159\) −142683. −0.447588
\(160\) 0 0
\(161\) 194650. 337144.i 0.591820 1.02506i
\(162\) 0 0
\(163\) 12767.3 0.0376383 0.0188192 0.999823i \(-0.494009\pi\)
0.0188192 + 0.999823i \(0.494009\pi\)
\(164\) 0 0
\(165\) −120032. + 207902.i −0.343232 + 0.594495i
\(166\) 0 0
\(167\) −121547. + 210526.i −0.337252 + 0.584138i −0.983915 0.178638i \(-0.942831\pi\)
0.646663 + 0.762776i \(0.276164\pi\)
\(168\) 0 0
\(169\) −42129.2 72969.8i −0.113466 0.196529i
\(170\) 0 0
\(171\) 175812. + 220301.i 0.459789 + 0.576137i
\(172\) 0 0
\(173\) −213672. 370091.i −0.542792 0.940143i −0.998742 0.0501376i \(-0.984034\pi\)
0.455951 0.890005i \(-0.349299\pi\)
\(174\) 0 0
\(175\) 34946.9 60529.7i 0.0862607 0.149408i
\(176\) 0 0
\(177\) 67335.2 116628.i 0.161551 0.279814i
\(178\) 0 0
\(179\) 41174.1 0.0960488 0.0480244 0.998846i \(-0.484707\pi\)
0.0480244 + 0.998846i \(0.484707\pi\)
\(180\) 0 0
\(181\) −241411. + 418136.i −0.547723 + 0.948684i 0.450707 + 0.892672i \(0.351172\pi\)
−0.998430 + 0.0560122i \(0.982161\pi\)
\(182\) 0 0
\(183\) −186094. −0.410776
\(184\) 0 0
\(185\) −440879. 763624.i −0.947087 1.64040i
\(186\) 0 0
\(187\) −411734. 713144.i −0.861018 1.49133i
\(188\) 0 0
\(189\) 270841. 0.551518
\(190\) 0 0
\(191\) 218201. 0.432786 0.216393 0.976306i \(-0.430571\pi\)
0.216393 + 0.976306i \(0.430571\pi\)
\(192\) 0 0
\(193\) 357570. + 619329.i 0.690983 + 1.19682i 0.971516 + 0.236973i \(0.0761554\pi\)
−0.280533 + 0.959844i \(0.590511\pi\)
\(194\) 0 0
\(195\) 170498. + 295310.i 0.321094 + 0.556150i
\(196\) 0 0
\(197\) 17740.5 0.0325686 0.0162843 0.999867i \(-0.494816\pi\)
0.0162843 + 0.999867i \(0.494816\pi\)
\(198\) 0 0
\(199\) −290101. + 502469.i −0.519297 + 0.899449i 0.480451 + 0.877021i \(0.340473\pi\)
−0.999748 + 0.0224275i \(0.992861\pi\)
\(200\) 0 0
\(201\) −217692. −0.380061
\(202\) 0 0
\(203\) −192191. + 332884.i −0.327335 + 0.566961i
\(204\) 0 0
\(205\) −498309. + 863096.i −0.828159 + 1.43441i
\(206\) 0 0
\(207\) 434313. + 752252.i 0.704493 + 1.22022i
\(208\) 0 0
\(209\) 272921. 696119.i 0.432186 1.10235i
\(210\) 0 0
\(211\) 418159. + 724272.i 0.646599 + 1.11994i 0.983930 + 0.178556i \(0.0571427\pi\)
−0.337330 + 0.941386i \(0.609524\pi\)
\(212\) 0 0
\(213\) −299316. + 518430.i −0.452044 + 0.782963i
\(214\) 0 0
\(215\) −60942.6 + 105556.i −0.0899135 + 0.155735i
\(216\) 0 0
\(217\) 10212.8 0.0147229
\(218\) 0 0
\(219\) 278947. 483151.i 0.393017 0.680726i
\(220\) 0 0
\(221\) −1.16968e6 −1.61096
\(222\) 0 0
\(223\) 349535. + 605413.i 0.470684 + 0.815248i 0.999438 0.0335271i \(-0.0106740\pi\)
−0.528754 + 0.848775i \(0.677341\pi\)
\(224\) 0 0
\(225\) 77975.2 + 135057.i 0.102683 + 0.177853i
\(226\) 0 0
\(227\) 813403. 1.04771 0.523855 0.851808i \(-0.324493\pi\)
0.523855 + 0.851808i \(0.324493\pi\)
\(228\) 0 0
\(229\) −1.18902e6 −1.49830 −0.749151 0.662399i \(-0.769538\pi\)
−0.749151 + 0.662399i \(0.769538\pi\)
\(230\) 0 0
\(231\) −152440. 264033.i −0.187961 0.325558i
\(232\) 0 0
\(233\) −106736. 184872.i −0.128801 0.223091i 0.794411 0.607381i \(-0.207780\pi\)
−0.923212 + 0.384290i \(0.874446\pi\)
\(234\) 0 0
\(235\) 1.02396e6 1.20952
\(236\) 0 0
\(237\) 91182.9 157933.i 0.105449 0.182643i
\(238\) 0 0
\(239\) −965775. −1.09366 −0.546829 0.837245i \(-0.684165\pi\)
−0.546829 + 0.837245i \(0.684165\pi\)
\(240\) 0 0
\(241\) 391235. 677639.i 0.433906 0.751547i −0.563300 0.826252i \(-0.690468\pi\)
0.997206 + 0.0747059i \(0.0238018\pi\)
\(242\) 0 0
\(243\) −476099. + 824627.i −0.517227 + 0.895863i
\(244\) 0 0
\(245\) −327514. 567270.i −0.348590 0.603775i
\(246\) 0 0
\(247\) −662485. 830123.i −0.690929 0.865765i
\(248\) 0 0
\(249\) 231819. + 401523.i 0.236947 + 0.410404i
\(250\) 0 0
\(251\) −448780. + 777310.i −0.449624 + 0.778771i −0.998361 0.0572236i \(-0.981775\pi\)
0.548738 + 0.835995i \(0.315109\pi\)
\(252\) 0 0
\(253\) 1.15215e6 1.99558e6i 1.13164 1.96006i
\(254\) 0 0
\(255\) 875543. 0.843193
\(256\) 0 0
\(257\) −552328. + 956660.i −0.521632 + 0.903493i 0.478051 + 0.878332i \(0.341343\pi\)
−0.999683 + 0.0251612i \(0.991990\pi\)
\(258\) 0 0
\(259\) 1.11982e6 1.03729
\(260\) 0 0
\(261\) −428825. 742747.i −0.389654 0.674901i
\(262\) 0 0
\(263\) −306009. 530023.i −0.272800 0.472504i 0.696778 0.717287i \(-0.254616\pi\)
−0.969578 + 0.244783i \(0.921283\pi\)
\(264\) 0 0
\(265\) 1.12844e6 0.987109
\(266\) 0 0
\(267\) −131139. −0.112578
\(268\) 0 0
\(269\) −248820. 430969.i −0.209655 0.363133i 0.741951 0.670454i \(-0.233901\pi\)
−0.951606 + 0.307321i \(0.900567\pi\)
\(270\) 0 0
\(271\) 724980. + 1.25570e6i 0.599657 + 1.03864i 0.992871 + 0.119190i \(0.0380297\pi\)
−0.393214 + 0.919447i \(0.628637\pi\)
\(272\) 0 0
\(273\) −433060. −0.351675
\(274\) 0 0
\(275\) 206853. 358281.i 0.164942 0.285688i
\(276\) 0 0
\(277\) −87028.2 −0.0681492 −0.0340746 0.999419i \(-0.510848\pi\)
−0.0340746 + 0.999419i \(0.510848\pi\)
\(278\) 0 0
\(279\) −11393.6 + 19734.3i −0.00876297 + 0.0151779i
\(280\) 0 0
\(281\) 949563. 1.64469e6i 0.717394 1.24256i −0.244635 0.969615i \(-0.578668\pi\)
0.962029 0.272948i \(-0.0879987\pi\)
\(282\) 0 0
\(283\) −727473. 1.26002e6i −0.539946 0.935214i −0.998906 0.0467574i \(-0.985111\pi\)
0.458960 0.888457i \(-0.348222\pi\)
\(284\) 0 0
\(285\) 495891. + 621374.i 0.361638 + 0.453149i
\(286\) 0 0
\(287\) −632846. 1.09612e6i −0.453517 0.785514i
\(288\) 0 0
\(289\) −791713. + 1.37129e6i −0.557600 + 0.965792i
\(290\) 0 0
\(291\) 525197. 909668.i 0.363572 0.629724i
\(292\) 0 0
\(293\) 795288. 0.541197 0.270598 0.962692i \(-0.412778\pi\)
0.270598 + 0.962692i \(0.412778\pi\)
\(294\) 0 0
\(295\) −532538. + 922383.i −0.356283 + 0.617101i
\(296\) 0 0
\(297\) 1.60313e6 1.05458
\(298\) 0 0
\(299\) −1.63655e6 2.83459e6i −1.05865 1.83363i
\(300\) 0 0
\(301\) −77396.5 134055.i −0.0492385 0.0852836i
\(302\) 0 0
\(303\) 736403. 0.460796
\(304\) 0 0
\(305\) 1.47177e6 0.905923
\(306\) 0 0
\(307\) 964887. + 1.67123e6i 0.584293 + 1.01202i 0.994963 + 0.100241i \(0.0319613\pi\)
−0.410670 + 0.911784i \(0.634705\pi\)
\(308\) 0 0
\(309\) −598646. 1.03689e6i −0.356676 0.617781i
\(310\) 0 0
\(311\) 1.42463e6 0.835220 0.417610 0.908626i \(-0.362868\pi\)
0.417610 + 0.908626i \(0.362868\pi\)
\(312\) 0 0
\(313\) 1.12004e6 1.93997e6i 0.646209 1.11927i −0.337812 0.941214i \(-0.609687\pi\)
0.984021 0.178053i \(-0.0569800\pi\)
\(314\) 0 0
\(315\) −908928. −0.516123
\(316\) 0 0
\(317\) −278493. + 482363.i −0.155656 + 0.269604i −0.933298 0.359104i \(-0.883082\pi\)
0.777642 + 0.628708i \(0.216416\pi\)
\(318\) 0 0
\(319\) −1.13759e6 + 1.97037e6i −0.625908 + 1.08410i
\(320\) 0 0
\(321\) −249251. 431715.i −0.135012 0.233848i
\(322\) 0 0
\(323\) −2.69638e6 + 407395.i −1.43805 + 0.217275i
\(324\) 0 0
\(325\) −293821. 508913.i −0.154303 0.267261i
\(326\) 0 0
\(327\) −218756. + 378896.i −0.113133 + 0.195953i
\(328\) 0 0
\(329\) −650208. + 1.12619e6i −0.331179 + 0.573619i
\(330\) 0 0
\(331\) −1.85079e6 −0.928511 −0.464256 0.885701i \(-0.653678\pi\)
−0.464256 + 0.885701i \(0.653678\pi\)
\(332\) 0 0
\(333\) −1.24930e6 + 2.16385e6i −0.617386 + 1.06934i
\(334\) 0 0
\(335\) 1.72168e6 0.838184
\(336\) 0 0
\(337\) 1.16626e6 + 2.02003e6i 0.559399 + 0.968907i 0.997547 + 0.0700041i \(0.0223013\pi\)
−0.438148 + 0.898903i \(0.644365\pi\)
\(338\) 0 0
\(339\) 337267. + 584163.i 0.159395 + 0.276080i
\(340\) 0 0
\(341\) 60450.3 0.0281522
\(342\) 0 0
\(343\) 2.18110e6 1.00101
\(344\) 0 0
\(345\) 1.22501e6 + 2.12178e6i 0.554106 + 0.959739i
\(346\) 0 0
\(347\) 1.33391e6 + 2.31041e6i 0.594708 + 1.03006i 0.993588 + 0.113062i \(0.0360657\pi\)
−0.398880 + 0.917003i \(0.630601\pi\)
\(348\) 0 0
\(349\) −2.33528e6 −1.02630 −0.513152 0.858298i \(-0.671522\pi\)
−0.513152 + 0.858298i \(0.671522\pi\)
\(350\) 0 0
\(351\) 1.13857e6 1.97206e6i 0.493278 0.854382i
\(352\) 0 0
\(353\) −2.57168e6 −1.09845 −0.549225 0.835675i \(-0.685077\pi\)
−0.549225 + 0.835675i \(0.685077\pi\)
\(354\) 0 0
\(355\) 2.36722e6 4.10014e6i 0.996935 1.72674i
\(356\) 0 0
\(357\) −555965. + 962960.i −0.230875 + 0.399887i
\(358\) 0 0
\(359\) −2.06014e6 3.56826e6i −0.843645 1.46124i −0.886793 0.462168i \(-0.847072\pi\)
0.0431473 0.999069i \(-0.486262\pi\)
\(360\) 0 0
\(361\) −1.81631e6 1.68288e6i −0.733536 0.679651i
\(362\) 0 0
\(363\) −258698. 448078.i −0.103045 0.178479i
\(364\) 0 0
\(365\) −2.20613e6 + 3.82112e6i −0.866759 + 1.50127i
\(366\) 0 0
\(367\) −1.76851e6 + 3.06315e6i −0.685398 + 1.18714i 0.287914 + 0.957656i \(0.407038\pi\)
−0.973312 + 0.229487i \(0.926295\pi\)
\(368\) 0 0
\(369\) 2.82408e6 1.07972
\(370\) 0 0
\(371\) −716555. + 1.24111e6i −0.270281 + 0.468140i
\(372\) 0 0
\(373\) −3.14142e6 −1.16910 −0.584552 0.811356i \(-0.698730\pi\)
−0.584552 + 0.811356i \(0.698730\pi\)
\(374\) 0 0
\(375\) −569469. 986350.i −0.209118 0.362204i
\(376\) 0 0
\(377\) 1.61587e6 + 2.79878e6i 0.585537 + 1.01418i
\(378\) 0 0
\(379\) 1.24166e6 0.444021 0.222011 0.975044i \(-0.428738\pi\)
0.222011 + 0.975044i \(0.428738\pi\)
\(380\) 0 0
\(381\) −946329. −0.333987
\(382\) 0 0
\(383\) 1.41220e6 + 2.44600e6i 0.491924 + 0.852038i 0.999957 0.00929990i \(-0.00296029\pi\)
−0.508032 + 0.861338i \(0.669627\pi\)
\(384\) 0 0
\(385\) 1.20561e6 + 2.08817e6i 0.414528 + 0.717984i
\(386\) 0 0
\(387\) 345382. 0.117225
\(388\) 0 0
\(389\) 2.26664e6 3.92593e6i 0.759465 1.31543i −0.183658 0.982990i \(-0.558794\pi\)
0.943124 0.332442i \(-0.107873\pi\)
\(390\) 0 0
\(391\) −8.40405e6 −2.78001
\(392\) 0 0
\(393\) −297550. + 515371.i −0.0971802 + 0.168321i
\(394\) 0 0
\(395\) −721143. + 1.24906e6i −0.232557 + 0.402800i
\(396\) 0 0
\(397\) 968813. + 1.67803e6i 0.308506 + 0.534348i 0.978036 0.208437i \(-0.0668377\pi\)
−0.669530 + 0.742785i \(0.733504\pi\)
\(398\) 0 0
\(399\) −998302. + 150833.i −0.313928 + 0.0474313i
\(400\) 0 0
\(401\) 2.21857e6 + 3.84268e6i 0.688990 + 1.19336i 0.972165 + 0.234297i \(0.0752788\pi\)
−0.283176 + 0.959068i \(0.591388\pi\)
\(402\) 0 0
\(403\) 42932.8 74361.7i 0.0131682 0.0228080i
\(404\) 0 0
\(405\) 523407. 906567.i 0.158563 0.274639i
\(406\) 0 0
\(407\) 6.62832e6 1.98343
\(408\) 0 0
\(409\) 3.20721e6 5.55506e6i 0.948025 1.64203i 0.198446 0.980112i \(-0.436411\pi\)
0.749579 0.661915i \(-0.230256\pi\)
\(410\) 0 0
\(411\) 1.12259e6 0.327805
\(412\) 0 0
\(413\) −676317. 1.17142e6i −0.195108 0.337937i
\(414\) 0 0
\(415\) −1.83340e6 3.17555e6i −0.522562 0.905103i
\(416\) 0 0
\(417\) 1.79548e6 0.505639
\(418\) 0 0
\(419\) 2.16492e6 0.602429 0.301215 0.953556i \(-0.402608\pi\)
0.301215 + 0.953556i \(0.402608\pi\)
\(420\) 0 0
\(421\) 3.39931e6 + 5.88777e6i 0.934727 + 1.61900i 0.775119 + 0.631815i \(0.217690\pi\)
0.159608 + 0.987180i \(0.448977\pi\)
\(422\) 0 0
\(423\) −1.45078e6 2.51282e6i −0.394230 0.682826i
\(424\) 0 0
\(425\) −1.50884e6 −0.405201
\(426\) 0 0
\(427\) −934567. + 1.61872e6i −0.248051 + 0.429637i
\(428\) 0 0
\(429\) −2.56332e6 −0.672449
\(430\) 0 0
\(431\) 101699. 176148.i 0.0263708 0.0456756i −0.852539 0.522664i \(-0.824938\pi\)
0.878910 + 0.476988i \(0.158272\pi\)
\(432\) 0 0
\(433\) 487850. 844981.i 0.125045 0.216584i −0.796705 0.604368i \(-0.793426\pi\)
0.921751 + 0.387783i \(0.126759\pi\)
\(434\) 0 0
\(435\) −1.20953e6 2.09497e6i −0.306475 0.530830i
\(436\) 0 0
\(437\) −4.75990e6 5.96437e6i −1.19232 1.49404i
\(438\) 0 0
\(439\) −1.96789e6 3.40848e6i −0.487348 0.844111i 0.512546 0.858660i \(-0.328702\pi\)
−0.999894 + 0.0145483i \(0.995369\pi\)
\(440\) 0 0
\(441\) −928063. + 1.60745e6i −0.227238 + 0.393588i
\(442\) 0 0
\(443\) 1.39091e6 2.40913e6i 0.336737 0.583246i −0.647080 0.762422i \(-0.724010\pi\)
0.983817 + 0.179176i \(0.0573433\pi\)
\(444\) 0 0
\(445\) 1.03715e6 0.248279
\(446\) 0 0
\(447\) −1.17486e6 + 2.03491e6i −0.278110 + 0.481700i
\(448\) 0 0
\(449\) 6.91764e6 1.61936 0.809678 0.586875i \(-0.199642\pi\)
0.809678 + 0.586875i \(0.199642\pi\)
\(450\) 0 0
\(451\) −3.74587e6 6.48804e6i −0.867184 1.50201i
\(452\) 0 0
\(453\) −1.46545e6 2.53823e6i −0.335525 0.581146i
\(454\) 0 0
\(455\) 3.42497e6 0.775582
\(456\) 0 0
\(457\) 6.44928e6 1.44451 0.722256 0.691626i \(-0.243105\pi\)
0.722256 + 0.691626i \(0.243105\pi\)
\(458\) 0 0
\(459\) −2.92340e6 5.06348e6i −0.647675 1.12181i
\(460\) 0 0
\(461\) 610341. + 1.05714e6i 0.133758 + 0.231676i 0.925122 0.379669i \(-0.123962\pi\)
−0.791364 + 0.611345i \(0.790629\pi\)
\(462\) 0 0
\(463\) 847245. 0.183678 0.0918388 0.995774i \(-0.470726\pi\)
0.0918388 + 0.995774i \(0.470726\pi\)
\(464\) 0 0
\(465\) −32136.6 + 55662.2i −0.00689235 + 0.0119379i
\(466\) 0 0
\(467\) −76212.7 −0.0161709 −0.00808547 0.999967i \(-0.502574\pi\)
−0.00808547 + 0.999967i \(0.502574\pi\)
\(468\) 0 0
\(469\) −1.09325e6 + 1.89357e6i −0.229503 + 0.397512i
\(470\) 0 0
\(471\) 114599. 198491.i 0.0238028 0.0412276i
\(472\) 0 0
\(473\) −458116. 793481.i −0.0941505 0.163074i
\(474\) 0 0
\(475\) −854578. 1.07082e6i −0.173787 0.217763i
\(476\) 0 0
\(477\) −1.59881e6 2.76923e6i −0.321738 0.557266i
\(478\) 0 0
\(479\) −1.33045e6 + 2.30441e6i −0.264947 + 0.458902i −0.967550 0.252680i \(-0.918688\pi\)
0.702602 + 0.711583i \(0.252021\pi\)
\(480\) 0 0
\(481\) 4.70754e6 8.15370e6i 0.927750 1.60691i
\(482\) 0 0
\(483\) −3.11150e6 −0.606879
\(484\) 0 0
\(485\) −4.15366e6 + 7.19434e6i −0.801819 + 1.38879i
\(486\) 0 0
\(487\) 5.81426e6 1.11089 0.555446 0.831552i \(-0.312547\pi\)
0.555446 + 0.831552i \(0.312547\pi\)
\(488\) 0 0
\(489\) −51021.7 88372.2i −0.00964901 0.0167126i
\(490\) 0 0
\(491\) 2.27968e6 + 3.94853e6i 0.426747 + 0.739148i 0.996582 0.0826113i \(-0.0263260\pi\)
−0.569834 + 0.821760i \(0.692993\pi\)
\(492\) 0 0
\(493\) 8.29787e6 1.53762
\(494\) 0 0
\(495\) −5.38002e6 −0.986895
\(496\) 0 0
\(497\) 3.00634e6 + 5.20713e6i 0.545942 + 0.945600i
\(498\) 0 0
\(499\) 3.38613e6 + 5.86495e6i 0.608769 + 1.05442i 0.991444 + 0.130536i \(0.0416697\pi\)
−0.382675 + 0.923883i \(0.624997\pi\)
\(500\) 0 0
\(501\) 1.94295e6 0.345833
\(502\) 0 0
\(503\) 2.62169e6 4.54089e6i 0.462020 0.800242i −0.537042 0.843556i \(-0.680458\pi\)
0.999062 + 0.0433140i \(0.0137916\pi\)
\(504\) 0 0
\(505\) −5.82403e6 −1.01624
\(506\) 0 0
\(507\) −336720. + 583215.i −0.0581766 + 0.100765i
\(508\) 0 0
\(509\) −4.68578e6 + 8.11601e6i −0.801655 + 1.38851i 0.116872 + 0.993147i \(0.462713\pi\)
−0.918526 + 0.395360i \(0.870620\pi\)
\(510\) 0 0
\(511\) −2.80175e6 4.85278e6i −0.474655 0.822126i
\(512\) 0 0
\(513\) 1.93780e6 4.94261e6i 0.325099 0.829206i
\(514\) 0 0
\(515\) 4.73455e6 + 8.20047e6i 0.786611 + 1.36245i
\(516\) 0 0
\(517\) −3.84864e6 + 6.66604e6i −0.633258 + 1.09683i
\(518\) 0 0
\(519\) −1.70779e6 + 2.95798e6i −0.278302 + 0.482032i
\(520\) 0 0
\(521\) 244496. 0.0394619 0.0197309 0.999805i \(-0.493719\pi\)
0.0197309 + 0.999805i \(0.493719\pi\)
\(522\) 0 0
\(523\) −2.04939e6 + 3.54964e6i −0.327619 + 0.567453i −0.982039 0.188678i \(-0.939580\pi\)
0.654420 + 0.756131i \(0.272913\pi\)
\(524\) 0 0
\(525\) −558630. −0.0884557
\(526\) 0 0
\(527\) −110235. 190932.i −0.0172899 0.0299469i
\(528\) 0 0
\(529\) −8.54032e6 1.47923e7i −1.32689 2.29824i
\(530\) 0 0
\(531\) 3.01807e6 0.464507
\(532\) 0 0
\(533\) −1.06415e7 −1.62250
\(534\) 0 0
\(535\) 1.97126e6 + 3.41433e6i 0.297756 + 0.515728i
\(536\) 0 0
\(537\) −164543. 284997.i −0.0246232 0.0426486i
\(538\) 0 0
\(539\) 4.92395e6 0.730032
\(540\) 0 0
\(541\) 227501. 394043.i 0.0334187 0.0578829i −0.848832 0.528662i \(-0.822694\pi\)
0.882251 + 0.470779i \(0.156027\pi\)
\(542\) 0 0
\(543\) 3.85898e6 0.561660
\(544\) 0 0
\(545\) 1.73009e6 2.99660e6i 0.249503 0.432153i
\(546\) 0 0
\(547\) −4.19066e6 + 7.25843e6i −0.598844 + 1.03723i 0.394148 + 0.919047i \(0.371040\pi\)
−0.992992 + 0.118182i \(0.962293\pi\)
\(548\) 0 0
\(549\) −2.08525e6 3.61176e6i −0.295276 0.511433i
\(550\) 0 0
\(551\) 4.69976e6 + 5.88901e6i 0.659473 + 0.826349i
\(552\) 0 0
\(553\) −915844. 1.58629e6i −0.127353 0.220582i
\(554\) 0 0
\(555\) −3.52375e6 + 6.10331e6i −0.485593 + 0.841071i
\(556\) 0 0
\(557\) −2.14702e6 + 3.71874e6i −0.293222 + 0.507876i −0.974570 0.224084i \(-0.928061\pi\)
0.681347 + 0.731960i \(0.261394\pi\)
\(558\) 0 0
\(559\) −1.30145e6 −0.176156
\(560\) 0 0
\(561\) −3.29080e6 + 5.69984e6i −0.441464 + 0.764637i
\(562\) 0 0
\(563\) −5.43360e6 −0.722465 −0.361232 0.932476i \(-0.617644\pi\)
−0.361232 + 0.932476i \(0.617644\pi\)
\(564\) 0 0
\(565\) −2.66736e6 4.62001e6i −0.351529 0.608866i
\(566\) 0 0
\(567\) 664720. + 1.15133e6i 0.0868323 + 0.150398i
\(568\) 0 0
\(569\) 4.53732e6 0.587514 0.293757 0.955880i \(-0.405094\pi\)
0.293757 + 0.955880i \(0.405094\pi\)
\(570\) 0 0
\(571\) −1.75132e6 −0.224789 −0.112395 0.993664i \(-0.535852\pi\)
−0.112395 + 0.993664i \(0.535852\pi\)
\(572\) 0 0
\(573\) −871992. 1.51033e6i −0.110950 0.192170i
\(574\) 0 0
\(575\) −2.11108e6 3.65650e6i −0.266278 0.461208i
\(576\) 0 0
\(577\) 2.69353e6 0.336808 0.168404 0.985718i \(-0.446139\pi\)
0.168404 + 0.985718i \(0.446139\pi\)
\(578\) 0 0
\(579\) 2.85790e6 4.95002e6i 0.354283 0.613636i
\(580\) 0 0
\(581\) 4.65680e6 0.572331
\(582\) 0 0
\(583\) −4.24135e6 + 7.34624e6i −0.516812 + 0.895145i
\(584\) 0 0
\(585\) −3.82098e6 + 6.61812e6i −0.461620 + 0.799549i
\(586\) 0 0
\(587\) 1.95802e6 + 3.39138e6i 0.234542 + 0.406239i 0.959140 0.282934i \(-0.0913076\pi\)
−0.724597 + 0.689172i \(0.757974\pi\)
\(588\) 0 0
\(589\) 73069.9 186374.i 0.00867862 0.0221359i
\(590\) 0 0
\(591\) −70895.9 122795.i −0.00834934 0.0144615i
\(592\) 0 0
\(593\) −5.66866e6 + 9.81841e6i −0.661978 + 1.14658i 0.318117 + 0.948051i \(0.396950\pi\)
−0.980095 + 0.198528i \(0.936384\pi\)
\(594\) 0 0
\(595\) 4.39699e6 7.61581e6i 0.509170 0.881909i
\(596\) 0 0
\(597\) 4.63729e6 0.532511
\(598\) 0 0
\(599\) 3.86543e6 6.69512e6i 0.440180 0.762414i −0.557522 0.830162i \(-0.688248\pi\)
0.997702 + 0.0677475i \(0.0215812\pi\)
\(600\) 0 0
\(601\) −6.87953e6 −0.776913 −0.388457 0.921467i \(-0.626992\pi\)
−0.388457 + 0.921467i \(0.626992\pi\)
\(602\) 0 0
\(603\) −2.43932e6 4.22503e6i −0.273197 0.473191i
\(604\) 0 0
\(605\) 2.04598e6 + 3.54374e6i 0.227255 + 0.393617i
\(606\) 0 0
\(607\) 1.19598e7 1.31750 0.658750 0.752362i \(-0.271085\pi\)
0.658750 + 0.752362i \(0.271085\pi\)
\(608\) 0 0
\(609\) 3.07219e6 0.335664
\(610\) 0 0
\(611\) 5.46673e6 + 9.46865e6i 0.592413 + 1.02609i
\(612\) 0 0
\(613\) 1.49181e6 + 2.58389e6i 0.160347 + 0.277730i 0.934993 0.354666i \(-0.115405\pi\)
−0.774646 + 0.632395i \(0.782072\pi\)
\(614\) 0 0
\(615\) 7.96552e6 0.849232
\(616\) 0 0
\(617\) −2.62649e6 + 4.54922e6i −0.277756 + 0.481087i −0.970827 0.239782i \(-0.922924\pi\)
0.693071 + 0.720869i \(0.256257\pi\)
\(618\) 0 0
\(619\) −1.09695e7 −1.15069 −0.575346 0.817910i \(-0.695133\pi\)
−0.575346 + 0.817910i \(0.695133\pi\)
\(620\) 0 0
\(621\) 8.18053e6 1.41691e7i 0.851241 1.47439i
\(622\) 0 0
\(623\) −658583. + 1.14070e6i −0.0679815 + 0.117747i
\(624\) 0 0
\(625\) 5.86419e6 + 1.01571e7i 0.600493 + 1.04008i
\(626\) 0 0
\(627\) −5.90904e6 + 892794.i −0.600272 + 0.0906949i
\(628\) 0 0
\(629\) −1.20871e7 2.09355e7i −1.21814 2.10988i
\(630\) 0 0
\(631\) −3.73436e6 + 6.46811e6i −0.373373 + 0.646701i −0.990082 0.140490i \(-0.955132\pi\)
0.616709 + 0.787191i \(0.288466\pi\)
\(632\) 0 0
\(633\) 3.34216e6 5.78879e6i 0.331526 0.574220i
\(634\) 0 0
\(635\) 7.48429e6 0.736573
\(636\) 0 0
\(637\) 3.49707e6 6.05710e6i 0.341473 0.591448i
\(638\) 0 0
\(639\) −1.34158e7 −1.29976
\(640\) 0 0
\(641\) −8.26419e6 1.43140e7i −0.794430 1.37599i −0.923201 0.384318i \(-0.874437\pi\)
0.128771 0.991674i \(-0.458897\pi\)
\(642\) 0 0
\(643\) −6.29383e6 1.09012e7i −0.600326 1.03980i −0.992771 0.120020i \(-0.961704\pi\)
0.392445 0.919775i \(-0.371629\pi\)
\(644\) 0 0
\(645\) 974175. 0.0922014
\(646\) 0 0
\(647\) 1.21912e7 1.14494 0.572472 0.819924i \(-0.305985\pi\)
0.572472 + 0.819924i \(0.305985\pi\)
\(648\) 0 0
\(649\) −4.00318e6 6.93371e6i −0.373073 0.646181i
\(650\) 0 0
\(651\) −40813.1 70690.4i −0.00377439 0.00653744i
\(652\) 0 0
\(653\) −7.52249e6 −0.690365 −0.345182 0.938536i \(-0.612183\pi\)
−0.345182 + 0.938536i \(0.612183\pi\)
\(654\) 0 0
\(655\) 2.35325e6 4.07594e6i 0.214321 0.371214i
\(656\) 0 0
\(657\) 1.25028e7 1.13004
\(658\) 0 0
\(659\) 8.02028e6 1.38915e7i 0.719409 1.24605i −0.241825 0.970320i \(-0.577746\pi\)
0.961234 0.275733i \(-0.0889206\pi\)
\(660\) 0 0
\(661\) 6.26368e6 1.08490e7i 0.557604 0.965798i −0.440092 0.897953i \(-0.645054\pi\)
0.997696 0.0678454i \(-0.0216125\pi\)
\(662\) 0 0
\(663\) 4.67436e6 + 8.09623e6i 0.412989 + 0.715318i
\(664\) 0 0
\(665\) 7.89533e6 1.19290e6i 0.692335 0.104605i
\(666\) 0 0
\(667\) 1.16099e7 + 2.01090e7i 1.01045 + 1.75015i
\(668\) 0 0
\(669\) 2.79368e6 4.83880e6i 0.241330 0.417996i
\(670\) 0 0
\(671\) −5.53178e6 + 9.58133e6i −0.474306 + 0.821523i
\(672\) 0 0
\(673\) −7.50054e6 −0.638344 −0.319172 0.947697i \(-0.603405\pi\)
−0.319172 + 0.947697i \(0.603405\pi\)
\(674\) 0 0
\(675\) 1.46871e6 2.54388e6i 0.124073 0.214900i
\(676\) 0 0
\(677\) 1.19677e7 1.00355 0.501777 0.864997i \(-0.332680\pi\)
0.501777 + 0.864997i \(0.332680\pi\)
\(678\) 0 0
\(679\) −5.27510e6 9.13673e6i −0.439092 0.760530i
\(680\) 0 0
\(681\) −3.25058e6 5.63017e6i −0.268592 0.465215i
\(682\) 0 0
\(683\) 8.11577e6 0.665699 0.332850 0.942980i \(-0.391990\pi\)
0.332850 + 0.942980i \(0.391990\pi\)
\(684\) 0 0
\(685\) −8.87827e6 −0.722939
\(686\) 0 0
\(687\) 4.75164e6 + 8.23009e6i 0.384107 + 0.665293i
\(688\) 0 0
\(689\) 6.02455e6 + 1.04348e7i 0.483478 + 0.837408i
\(690\) 0 0
\(691\) −1.23034e7 −0.980235 −0.490117 0.871657i \(-0.663046\pi\)
−0.490117 + 0.871657i \(0.663046\pi\)
\(692\) 0 0
\(693\) 3.41628e6 5.91717e6i 0.270222 0.468038i
\(694\) 0 0
\(695\) −1.42000e7 −1.11513
\(696\) 0 0
\(697\) −1.36616e7 + 2.36626e7i −1.06517 + 1.84494i
\(698\) 0 0
\(699\) −853093. + 1.47760e6i −0.0660394 + 0.114384i
\(700\) 0 0
\(701\) −7.04732e6 1.22063e7i −0.541663 0.938188i −0.998809 0.0487959i \(-0.984462\pi\)
0.457146 0.889392i \(-0.348872\pi\)
\(702\) 0 0
\(703\) 8.01205e6 2.04358e7i 0.611442 1.55956i
\(704\) 0 0
\(705\) −4.09202e6 7.08759e6i −0.310074 0.537064i
\(706\) 0 0
\(707\) 3.69823e6 6.40552e6i 0.278256 0.481954i
\(708\) 0 0
\(709\) −2.13108e6 + 3.69113e6i −0.159215 + 0.275768i −0.934586 0.355738i \(-0.884230\pi\)
0.775371 + 0.631506i \(0.217563\pi\)
\(710\) 0 0
\(711\) 4.08695e6 0.303197
\(712\) 0 0
\(713\) 308469. 534283.i 0.0227241 0.0393593i
\(714\) 0 0
\(715\) 2.02727e7 1.48302
\(716\) 0 0
\(717\) 3.85950e6 + 6.68486e6i 0.280371 + 0.485617i
\(718\) 0 0
\(719\) 6.85763e6 + 1.18778e7i 0.494711 + 0.856865i 0.999981 0.00609644i \(-0.00194057\pi\)
−0.505270 + 0.862961i \(0.668607\pi\)
\(720\) 0 0
\(721\) −1.20256e7 −0.861529
\(722\) 0 0
\(723\) −6.25394e6 −0.444946
\(724\) 0 0
\(725\) 2.08441e6 + 3.61031e6i 0.147278 + 0.255093i
\(726\) 0 0
\(727\) −1.05919e7 1.83457e7i −0.743256 1.28736i −0.951005 0.309175i \(-0.899947\pi\)
0.207749 0.978182i \(-0.433386\pi\)
\(728\) 0 0
\(729\) 3.58627e6 0.249933
\(730\) 0 0
\(731\) −1.67080e6 + 2.89392e6i −0.115646 + 0.200305i
\(732\) 0 0
\(733\) 6.01308e6 0.413368 0.206684 0.978408i \(-0.433733\pi\)
0.206684 + 0.978408i \(0.433733\pi\)
\(734\) 0 0
\(735\) −2.61767e6 + 4.53394e6i −0.178730 + 0.309569i
\(736\) 0 0
\(737\) −6.47107e6 + 1.12082e7i −0.438841 + 0.760095i
\(738\) 0 0
\(739\) −8.41424e6 1.45739e7i −0.566766 0.981667i −0.996883 0.0788942i \(-0.974861\pi\)
0.430117 0.902773i \(-0.358472\pi\)
\(740\) 0 0
\(741\) −3.09844e6 + 7.90296e6i −0.207299 + 0.528742i
\(742\) 0 0
\(743\) −2.01935e6 3.49762e6i −0.134196 0.232434i 0.791094 0.611695i \(-0.209512\pi\)
−0.925290 + 0.379260i \(0.876179\pi\)
\(744\) 0 0
\(745\) 9.29165e6 1.60936e7i 0.613341 1.06234i
\(746\) 0 0
\(747\) −5.19524e6 + 8.99842e6i −0.340647 + 0.590018i
\(748\) 0 0
\(749\) −5.00696e6 −0.326114
\(750\) 0 0
\(751\) −351347. + 608550.i −0.0227319 + 0.0393728i −0.877168 0.480184i \(-0.840570\pi\)
0.854436 + 0.519557i \(0.173903\pi\)
\(752\) 0 0
\(753\) 7.17380e6 0.461064
\(754\) 0 0
\(755\) 1.15899e7 + 2.00742e7i 0.739964 + 1.28166i
\(756\) 0 0
\(757\) 1.19882e7 + 2.07642e7i 0.760354 + 1.31697i 0.942668 + 0.333731i \(0.108308\pi\)
−0.182314 + 0.983240i \(0.558359\pi\)
\(758\) 0 0
\(759\) −1.84172e7 −1.16043
\(760\) 0 0
\(761\) −1.29063e7 −0.807869 −0.403934 0.914788i \(-0.632358\pi\)
−0.403934 + 0.914788i \(0.632358\pi\)
\(762\) 0 0
\(763\) 2.19719e6 + 3.80565e6i 0.136633 + 0.236656i
\(764\) 0 0
\(765\) 9.81078e6 + 1.69928e7i 0.606108 + 1.04981i
\(766\) 0 0
\(767\) −1.13725e7 −0.698019
\(768\) 0 0
\(769\) −1.05367e7 + 1.82501e7i −0.642524 + 1.11288i 0.342343 + 0.939575i \(0.388779\pi\)
−0.984867 + 0.173310i \(0.944554\pi\)
\(770\) 0 0
\(771\) 8.82902e6 0.534905
\(772\) 0 0
\(773\) 4.35234e6 7.53848e6i 0.261984 0.453769i −0.704785 0.709421i \(-0.748957\pi\)
0.966769 + 0.255652i \(0.0822900\pi\)
\(774\) 0 0
\(775\) 55381.5 95923.6i 0.00331215 0.00573682i
\(776\) 0 0
\(777\) −4.47512e6 7.75113e6i −0.265921 0.460588i
\(778\) 0 0
\(779\) −2.45311e7 + 3.70640e6i −1.44835 + 0.218831i
\(780\) 0 0
\(781\) 1.77948e7 + 3.08214e7i 1.04391 + 1.80811i
\(782\) 0 0
\(783\) −8.07717e6 + 1.39901e7i −0.470820 + 0.815484i
\(784\) 0 0
\(785\) −906334. + 1.56982e6i −0.0524946 + 0.0909232i
\(786\) 0 0
\(787\) −2.69329e6 −0.155005 −0.0775026 0.996992i \(-0.524695\pi\)
−0.0775026 + 0.996992i \(0.524695\pi\)
\(788\) 0 0
\(789\) −2.44579e6 + 4.23624e6i −0.139871 +