Properties

Label 76.6.e.a.45.8
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 45.8
Root \(-10.9539 + 18.9727i\) of defining polynomial
Character \(\chi\) \(=\) 76.45
Dual form 76.6.e.a.49.8

$q$-expansion

\(f(q)\) \(=\) \(q+(10.4539 + 18.1067i) q^{3} +(50.5928 + 87.6293i) q^{5} +95.5451 q^{7} +(-97.0688 + 168.128i) q^{9} +O(q^{10})\) \(q+(10.4539 + 18.1067i) q^{3} +(50.5928 + 87.6293i) q^{5} +95.5451 q^{7} +(-97.0688 + 168.128i) q^{9} -119.504 q^{11} +(297.428 - 515.161i) q^{13} +(-1057.79 + 1832.14i) q^{15} +(-459.911 - 796.589i) q^{17} +(-806.703 + 1351.05i) q^{19} +(998.821 + 1730.01i) q^{21} +(2124.58 - 3679.89i) q^{23} +(-3556.76 + 6160.48i) q^{25} +1021.61 q^{27} +(-2214.69 + 3835.95i) q^{29} -4955.30 q^{31} +(-1249.29 - 2163.83i) q^{33} +(4833.89 + 8372.55i) q^{35} +7651.95 q^{37} +12437.2 q^{39} +(2006.97 + 3476.18i) q^{41} +(-5228.80 - 9056.55i) q^{43} -19643.9 q^{45} +(4318.48 - 7479.83i) q^{47} -7678.13 q^{49} +(9615.75 - 16655.0i) q^{51} +(18534.0 - 32101.9i) q^{53} +(-6046.06 - 10472.1i) q^{55} +(-32896.2 - 482.998i) q^{57} +(-20727.5 - 35901.1i) q^{59} +(-2244.12 + 3886.93i) q^{61} +(-9274.45 + 16063.8i) q^{63} +60190.9 q^{65} +(18484.7 - 32016.5i) q^{67} +88840.9 q^{69} +(23408.1 + 40543.9i) q^{71} +(40666.6 + 70436.6i) q^{73} -148728. q^{75} -11418.1 q^{77} +(6656.35 + 11529.1i) q^{79} +(34267.5 + 59353.1i) q^{81} -18380.7 q^{83} +(46536.4 - 80603.3i) q^{85} -92608.6 q^{87} +(-7307.86 + 12657.6i) q^{89} +(28417.8 - 49221.1i) q^{91} +(-51802.3 - 89724.2i) q^{93} +(-159205. - 2337.52i) q^{95} +(61844.5 + 107118. i) q^{97} +(11600.1 - 20092.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q - 11q^{3} + 11q^{5} + 336q^{7} - 902q^{9} + O(q^{10}) \) \( 18q - 11q^{3} + 11q^{5} + 336q^{7} - 902q^{9} - 320q^{11} + 227q^{13} - 101q^{15} + 179q^{17} - 868q^{19} - 5700q^{21} - 3425q^{23} - 7054q^{25} + 14722q^{27} - 7349q^{29} - 9960q^{31} - 2998q^{33} + 15888q^{35} + 26444q^{37} - 30246q^{39} - 7311q^{41} - 8283q^{43} - 62164q^{45} + 37603q^{47} + 124738q^{49} + 47227q^{51} - 20337q^{53} + 716q^{55} - 57555q^{57} - 74455q^{59} - 7569q^{61} - 52544q^{63} + 188998q^{65} - 26177q^{67} + 116282q^{69} - 53463q^{71} - 14103q^{73} + 120912q^{75} - 31960q^{77} + 31825q^{79} - 21137q^{81} + 82600q^{83} - 50787q^{85} - 339766q^{87} - 155197q^{89} - 2800q^{91} - 46460q^{93} + 49315q^{95} + 111241q^{97} - 193544q^{99} + O(q^{100}) \)

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
\(3\) 10.4539 + 18.1067i 0.670619 + 1.16155i 0.977729 + 0.209872i \(0.0673048\pi\)
−0.307110 + 0.951674i \(0.599362\pi\)
\(4\) 0 0
\(5\) 50.5928 + 87.6293i 0.905031 + 1.56756i 0.820876 + 0.571107i \(0.193486\pi\)
0.0841554 + 0.996453i \(0.473181\pi\)
\(6\) 0 0
\(7\) 95.5451 0.736993 0.368497 0.929629i \(-0.379873\pi\)
0.368497 + 0.929629i \(0.379873\pi\)
\(8\) 0 0
\(9\) −97.0688 + 168.128i −0.399460 + 0.691885i
\(10\) 0 0
\(11\) −119.504 −0.297784 −0.148892 0.988853i \(-0.547571\pi\)
−0.148892 + 0.988853i \(0.547571\pi\)
\(12\) 0 0
\(13\) 297.428 515.161i 0.488117 0.845443i −0.511790 0.859111i \(-0.671017\pi\)
0.999907 + 0.0136677i \(0.00435069\pi\)
\(14\) 0 0
\(15\) −1057.79 + 1832.14i −1.21386 + 2.10247i
\(16\) 0 0
\(17\) −459.911 796.589i −0.385968 0.668517i 0.605935 0.795514i \(-0.292799\pi\)
−0.991903 + 0.126998i \(0.959466\pi\)
\(18\) 0 0
\(19\) −806.703 + 1351.05i −0.512660 + 0.858592i
\(20\) 0 0
\(21\) 998.821 + 1730.01i 0.494242 + 0.856052i
\(22\) 0 0
\(23\) 2124.58 3679.89i 0.837441 1.45049i −0.0545863 0.998509i \(-0.517384\pi\)
0.892027 0.451981i \(-0.149283\pi\)
\(24\) 0 0
\(25\) −3556.76 + 6160.48i −1.13816 + 1.97135i
\(26\) 0 0
\(27\) 1021.61 0.269696
\(28\) 0 0
\(29\) −2214.69 + 3835.95i −0.489009 + 0.846989i −0.999920 0.0126447i \(-0.995975\pi\)
0.510911 + 0.859634i \(0.329308\pi\)
\(30\) 0 0
\(31\) −4955.30 −0.926116 −0.463058 0.886328i \(-0.653248\pi\)
−0.463058 + 0.886328i \(0.653248\pi\)
\(32\) 0 0
\(33\) −1249.29 2163.83i −0.199700 0.345890i
\(34\) 0 0
\(35\) 4833.89 + 8372.55i 0.667002 + 1.15528i
\(36\) 0 0
\(37\) 7651.95 0.918900 0.459450 0.888204i \(-0.348047\pi\)
0.459450 + 0.888204i \(0.348047\pi\)
\(38\) 0 0
\(39\) 12437.2 1.30936
\(40\) 0 0
\(41\) 2006.97 + 3476.18i 0.186458 + 0.322955i 0.944067 0.329754i \(-0.106966\pi\)
−0.757609 + 0.652709i \(0.773632\pi\)
\(42\) 0 0
\(43\) −5228.80 9056.55i −0.431252 0.746950i 0.565729 0.824591i \(-0.308595\pi\)
−0.996981 + 0.0776405i \(0.975261\pi\)
\(44\) 0 0
\(45\) −19643.9 −1.44610
\(46\) 0 0
\(47\) 4318.48 7479.83i 0.285159 0.493909i −0.687489 0.726195i \(-0.741287\pi\)
0.972648 + 0.232286i \(0.0746204\pi\)
\(48\) 0 0
\(49\) −7678.13 −0.456841
\(50\) 0 0
\(51\) 9615.75 16655.0i 0.517675 0.896640i
\(52\) 0 0
\(53\) 18534.0 32101.9i 0.906318 1.56979i 0.0871791 0.996193i \(-0.472215\pi\)
0.819139 0.573596i \(-0.194452\pi\)
\(54\) 0 0
\(55\) −6046.06 10472.1i −0.269504 0.466795i
\(56\) 0 0
\(57\) −32896.2 482.998i −1.34109 0.0196906i
\(58\) 0 0
\(59\) −20727.5 35901.1i −0.775207 1.34270i −0.934678 0.355495i \(-0.884312\pi\)
0.159472 0.987203i \(-0.449021\pi\)
\(60\) 0 0
\(61\) −2244.12 + 3886.93i −0.0772186 + 0.133747i −0.902049 0.431634i \(-0.857937\pi\)
0.824830 + 0.565380i \(0.191271\pi\)
\(62\) 0 0
\(63\) −9274.45 + 16063.8i −0.294399 + 0.509915i
\(64\) 0 0
\(65\) 60190.9 1.76704
\(66\) 0 0
\(67\) 18484.7 32016.5i 0.503067 0.871338i −0.496927 0.867793i \(-0.665538\pi\)
0.999994 0.00354526i \(-0.00112849\pi\)
\(68\) 0 0
\(69\) 88840.9 2.24642
\(70\) 0 0
\(71\) 23408.1 + 40543.9i 0.551086 + 0.954509i 0.998197 + 0.0600303i \(0.0191197\pi\)
−0.447110 + 0.894479i \(0.647547\pi\)
\(72\) 0 0
\(73\) 40666.6 + 70436.6i 0.893163 + 1.54700i 0.836062 + 0.548635i \(0.184852\pi\)
0.0571012 + 0.998368i \(0.481814\pi\)
\(74\) 0 0
\(75\) −148728. −3.05309
\(76\) 0 0
\(77\) −11418.1 −0.219465
\(78\) 0 0
\(79\) 6656.35 + 11529.1i 0.119996 + 0.207840i 0.919766 0.392467i \(-0.128378\pi\)
−0.799770 + 0.600307i \(0.795045\pi\)
\(80\) 0 0
\(81\) 34267.5 + 59353.1i 0.580323 + 1.00515i
\(82\) 0 0
\(83\) −18380.7 −0.292864 −0.146432 0.989221i \(-0.546779\pi\)
−0.146432 + 0.989221i \(0.546779\pi\)
\(84\) 0 0
\(85\) 46536.4 80603.3i 0.698627 1.21006i
\(86\) 0 0
\(87\) −92608.6 −1.31176
\(88\) 0 0
\(89\) −7307.86 + 12657.6i −0.0977946 + 0.169385i −0.910772 0.412911i \(-0.864512\pi\)
0.812977 + 0.582296i \(0.197846\pi\)
\(90\) 0 0
\(91\) 28417.8 49221.1i 0.359739 0.623086i
\(92\) 0 0
\(93\) −51802.3 89724.2i −0.621071 1.07573i
\(94\) 0 0
\(95\) −159205. 2337.52i −1.80987 0.0265733i
\(96\) 0 0
\(97\) 61844.5 + 107118.i 0.667378 + 1.15593i 0.978635 + 0.205606i \(0.0659166\pi\)
−0.311257 + 0.950326i \(0.600750\pi\)
\(98\) 0 0
\(99\) 11600.1 20092.0i 0.118953 0.206033i
\(100\) 0 0
\(101\) −24891.8 + 43113.9i −0.242803 + 0.420546i −0.961511 0.274765i \(-0.911400\pi\)
0.718709 + 0.695311i \(0.244733\pi\)
\(102\) 0 0
\(103\) −102447. −0.951496 −0.475748 0.879582i \(-0.657823\pi\)
−0.475748 + 0.879582i \(0.657823\pi\)
\(104\) 0 0
\(105\) −101066. + 175052.i −0.894608 + 1.54951i
\(106\) 0 0
\(107\) 45310.9 0.382598 0.191299 0.981532i \(-0.438730\pi\)
0.191299 + 0.981532i \(0.438730\pi\)
\(108\) 0 0
\(109\) 75259.9 + 130354.i 0.606733 + 1.05089i 0.991775 + 0.127993i \(0.0408535\pi\)
−0.385042 + 0.922899i \(0.625813\pi\)
\(110\) 0 0
\(111\) 79992.9 + 138552.i 0.616232 + 1.06734i
\(112\) 0 0
\(113\) 71068.5 0.523577 0.261789 0.965125i \(-0.415688\pi\)
0.261789 + 0.965125i \(0.415688\pi\)
\(114\) 0 0
\(115\) 429954. 3.03164
\(116\) 0 0
\(117\) 57742.0 + 100012.i 0.389966 + 0.675442i
\(118\) 0 0
\(119\) −43942.3 76110.2i −0.284456 0.492692i
\(120\) 0 0
\(121\) −146770. −0.911324
\(122\) 0 0
\(123\) −41961.5 + 72679.4i −0.250085 + 0.433160i
\(124\) 0 0
\(125\) −403580. −2.31023
\(126\) 0 0
\(127\) 65658.5 113724.i 0.361228 0.625666i −0.626935 0.779071i \(-0.715691\pi\)
0.988163 + 0.153406i \(0.0490242\pi\)
\(128\) 0 0
\(129\) 109323. 189353.i 0.578412 1.00184i
\(130\) 0 0
\(131\) −100412. 173920.i −0.511222 0.885462i −0.999915 0.0130067i \(-0.995860\pi\)
0.488694 0.872456i \(-0.337474\pi\)
\(132\) 0 0
\(133\) −77076.5 + 129086.i −0.377827 + 0.632776i
\(134\) 0 0
\(135\) 51685.9 + 89522.6i 0.244083 + 0.422764i
\(136\) 0 0
\(137\) 181520. 314402.i 0.826272 1.43114i −0.0746720 0.997208i \(-0.523791\pi\)
0.900944 0.433936i \(-0.142876\pi\)
\(138\) 0 0
\(139\) 190140. 329331.i 0.834710 1.44576i −0.0595567 0.998225i \(-0.518969\pi\)
0.894266 0.447535i \(-0.147698\pi\)
\(140\) 0 0
\(141\) 180580. 0.764931
\(142\) 0 0
\(143\) −35544.0 + 61563.9i −0.145354 + 0.251760i
\(144\) 0 0
\(145\) −448188. −1.77027
\(146\) 0 0
\(147\) −80266.5 139026.i −0.306366 0.530642i
\(148\) 0 0
\(149\) −21911.4 37951.7i −0.0808546 0.140044i 0.822763 0.568385i \(-0.192432\pi\)
−0.903617 + 0.428341i \(0.859098\pi\)
\(150\) 0 0
\(151\) −131110. −0.467942 −0.233971 0.972244i \(-0.575172\pi\)
−0.233971 + 0.972244i \(0.575172\pi\)
\(152\) 0 0
\(153\) 178572. 0.616716
\(154\) 0 0
\(155\) −250702. 434229.i −0.838164 1.45174i
\(156\) 0 0
\(157\) 239102. + 414137.i 0.774166 + 1.34089i 0.935262 + 0.353956i \(0.115164\pi\)
−0.161096 + 0.986939i \(0.551503\pi\)
\(158\) 0 0
\(159\) 775013. 2.43118
\(160\) 0 0
\(161\) 202994. 351595.i 0.617188 1.06900i
\(162\) 0 0
\(163\) −389081. −1.14702 −0.573509 0.819199i \(-0.694418\pi\)
−0.573509 + 0.819199i \(0.694418\pi\)
\(164\) 0 0
\(165\) 126410. 218948.i 0.361469 0.626083i
\(166\) 0 0
\(167\) −261490. + 452914.i −0.725544 + 1.25668i 0.233206 + 0.972427i \(0.425078\pi\)
−0.958750 + 0.284252i \(0.908255\pi\)
\(168\) 0 0
\(169\) 8719.47 + 15102.6i 0.0234841 + 0.0406756i
\(170\) 0 0
\(171\) −148843. 266774.i −0.389260 0.697675i
\(172\) 0 0
\(173\) −228433. 395658.i −0.580289 1.00509i −0.995445 0.0953400i \(-0.969606\pi\)
0.415156 0.909750i \(-0.363727\pi\)
\(174\) 0 0
\(175\) −339831. + 588604.i −0.838818 + 1.45288i
\(176\) 0 0
\(177\) 433368. 750615.i 1.03974 1.80088i
\(178\) 0 0
\(179\) 380329. 0.887211 0.443606 0.896222i \(-0.353699\pi\)
0.443606 + 0.896222i \(0.353699\pi\)
\(180\) 0 0
\(181\) −172037. + 297977.i −0.390325 + 0.676062i −0.992492 0.122308i \(-0.960971\pi\)
0.602168 + 0.798370i \(0.294304\pi\)
\(182\) 0 0
\(183\) −93839.5 −0.207137
\(184\) 0 0
\(185\) 387134. + 670535.i 0.831633 + 1.44043i
\(186\) 0 0
\(187\) 54961.4 + 95195.9i 0.114935 + 0.199074i
\(188\) 0 0
\(189\) 97609.5 0.198764
\(190\) 0 0
\(191\) −699156. −1.38673 −0.693363 0.720588i \(-0.743872\pi\)
−0.693363 + 0.720588i \(0.743872\pi\)
\(192\) 0 0
\(193\) 27621.7 + 47842.2i 0.0533774 + 0.0924524i 0.891480 0.453061i \(-0.149668\pi\)
−0.838102 + 0.545513i \(0.816335\pi\)
\(194\) 0 0
\(195\) 629230. + 1.08986e6i 1.18501 + 2.05250i
\(196\) 0 0
\(197\) −1.00021e6 −1.83623 −0.918113 0.396318i \(-0.870288\pi\)
−0.918113 + 0.396318i \(0.870288\pi\)
\(198\) 0 0
\(199\) 246676. 427255.i 0.441564 0.764811i −0.556242 0.831020i \(-0.687757\pi\)
0.997806 + 0.0662094i \(0.0210905\pi\)
\(200\) 0 0
\(201\) 772951. 1.34947
\(202\) 0 0
\(203\) −211602. + 366506.i −0.360397 + 0.624225i
\(204\) 0 0
\(205\) −203077. + 351739.i −0.337501 + 0.584569i
\(206\) 0 0
\(207\) 412462. + 714405.i 0.669049 + 1.15883i
\(208\) 0 0
\(209\) 96404.5 161456.i 0.152662 0.255675i
\(210\) 0 0
\(211\) −309293. 535711.i −0.478259 0.828369i 0.521430 0.853294i \(-0.325399\pi\)
−0.999689 + 0.0249246i \(0.992065\pi\)
\(212\) 0 0
\(213\) −489412. + 847686.i −0.739138 + 1.28022i
\(214\) 0 0
\(215\) 529079. 916392.i 0.780593 1.35203i
\(216\) 0 0
\(217\) −473455. −0.682541
\(218\) 0 0
\(219\) −850251. + 1.47268e6i −1.19794 + 2.07490i
\(220\) 0 0
\(221\) −547162. −0.753590
\(222\) 0 0
\(223\) −75025.2 129947.i −0.101029 0.174987i 0.811080 0.584935i \(-0.198880\pi\)
−0.912109 + 0.409948i \(0.865547\pi\)
\(224\) 0 0
\(225\) −690500. 1.19598e6i −0.909301 1.57496i
\(226\) 0 0
\(227\) 1.05214e6 1.35522 0.677610 0.735421i \(-0.263016\pi\)
0.677610 + 0.735421i \(0.263016\pi\)
\(228\) 0 0
\(229\) 766814. 0.966276 0.483138 0.875544i \(-0.339497\pi\)
0.483138 + 0.875544i \(0.339497\pi\)
\(230\) 0 0
\(231\) −119363. 206744.i −0.147177 0.254919i
\(232\) 0 0
\(233\) −722964. 1.25221e6i −0.872423 1.51108i −0.859483 0.511165i \(-0.829214\pi\)
−0.0129403 0.999916i \(-0.504119\pi\)
\(234\) 0 0
\(235\) 873936. 1.03231
\(236\) 0 0
\(237\) −139170. + 241049.i −0.160944 + 0.278763i
\(238\) 0 0
\(239\) −749353. −0.848578 −0.424289 0.905527i \(-0.639476\pi\)
−0.424289 + 0.905527i \(0.639476\pi\)
\(240\) 0 0
\(241\) −459395. + 795696.i −0.509499 + 0.882479i 0.490440 + 0.871475i \(0.336836\pi\)
−0.999939 + 0.0110040i \(0.996497\pi\)
\(242\) 0 0
\(243\) −592334. + 1.02595e6i −0.643504 + 1.11458i
\(244\) 0 0
\(245\) −388458. 672829.i −0.413455 0.716126i
\(246\) 0 0
\(247\) 456071. + 817421.i 0.475652 + 0.852518i
\(248\) 0 0
\(249\) −192150. 332814.i −0.196400 0.340176i
\(250\) 0 0
\(251\) 158549. 274616.i 0.158848 0.275132i −0.775606 0.631218i \(-0.782556\pi\)
0.934453 + 0.356086i \(0.115889\pi\)
\(252\) 0 0
\(253\) −253897. + 439762.i −0.249377 + 0.431933i
\(254\) 0 0
\(255\) 1.94595e6 1.87405
\(256\) 0 0
\(257\) −293395. + 508174.i −0.277089 + 0.479932i −0.970660 0.240456i \(-0.922703\pi\)
0.693571 + 0.720388i \(0.256036\pi\)
\(258\) 0 0
\(259\) 731107. 0.677223
\(260\) 0 0
\(261\) −429954. 744702.i −0.390680 0.676677i
\(262\) 0 0
\(263\) −602410. 1.04341e6i −0.537036 0.930173i −0.999062 0.0433068i \(-0.986211\pi\)
0.462026 0.886866i \(-0.347123\pi\)
\(264\) 0 0
\(265\) 3.75075e6 3.28098
\(266\) 0 0
\(267\) −305583. −0.262332
\(268\) 0 0
\(269\) 154072. + 266860.i 0.129820 + 0.224855i 0.923607 0.383341i \(-0.125227\pi\)
−0.793787 + 0.608196i \(0.791893\pi\)
\(270\) 0 0
\(271\) 476222. + 824840.i 0.393900 + 0.682255i 0.992960 0.118449i \(-0.0377923\pi\)
−0.599060 + 0.800704i \(0.704459\pi\)
\(272\) 0 0
\(273\) 1.18831e6 0.964991
\(274\) 0 0
\(275\) 425048. 736205.i 0.338927 0.587039i
\(276\) 0 0
\(277\) −575120. −0.450359 −0.225179 0.974317i \(-0.572297\pi\)
−0.225179 + 0.974317i \(0.572297\pi\)
\(278\) 0 0
\(279\) 481005. 833125.i 0.369947 0.640766i
\(280\) 0 0
\(281\) −917605. + 1.58934e6i −0.693250 + 1.20074i 0.277517 + 0.960721i \(0.410488\pi\)
−0.970767 + 0.240023i \(0.922845\pi\)
\(282\) 0 0
\(283\) −615501. 1.06608e6i −0.456838 0.791267i 0.541954 0.840408i \(-0.317685\pi\)
−0.998792 + 0.0491413i \(0.984352\pi\)
\(284\) 0 0
\(285\) −1.62199e6 2.90711e6i −1.18287 2.12007i
\(286\) 0 0
\(287\) 191757. + 332132.i 0.137419 + 0.238016i
\(288\) 0 0
\(289\) 286892. 496912.i 0.202057 0.349973i
\(290\) 0 0
\(291\) −1.29303e6 + 2.23960e6i −0.895113 + 1.55038i
\(292\) 0 0
\(293\) −923293. −0.628305 −0.314153 0.949373i \(-0.601720\pi\)
−0.314153 + 0.949373i \(0.601720\pi\)
\(294\) 0 0
\(295\) 2.09733e6 3.63268e6i 1.40317 2.43037i
\(296\) 0 0
\(297\) −122086. −0.0803112
\(298\) 0 0
\(299\) −1.26382e6 2.18900e6i −0.817538 1.41602i
\(300\) 0 0
\(301\) −499587. 865310.i −0.317830 0.550497i
\(302\) 0 0
\(303\) −1.04087e6 −0.651312
\(304\) 0 0
\(305\) −454145. −0.279541
\(306\) 0 0
\(307\) 843091. + 1.46028e6i 0.510539 + 0.884279i 0.999925 + 0.0122119i \(0.00388726\pi\)
−0.489387 + 0.872067i \(0.662779\pi\)
\(308\) 0 0
\(309\) −1.07097e6 1.85498e6i −0.638091 1.10521i
\(310\) 0 0
\(311\) −1.06080e6 −0.621915 −0.310957 0.950424i \(-0.600650\pi\)
−0.310957 + 0.950424i \(0.600650\pi\)
\(312\) 0 0
\(313\) 8090.23 14012.7i 0.00466767 0.00808464i −0.863682 0.504037i \(-0.831848\pi\)
0.868350 + 0.495952i \(0.165181\pi\)
\(314\) 0 0
\(315\) −1.87688e6 −1.06576
\(316\) 0 0
\(317\) 1.27571e6 2.20960e6i 0.713024 1.23499i −0.250693 0.968067i \(-0.580658\pi\)
0.963717 0.266927i \(-0.0860082\pi\)
\(318\) 0 0
\(319\) 264665. 458413.i 0.145619 0.252220i
\(320\) 0 0
\(321\) 473676. + 820431.i 0.256578 + 0.444406i
\(322\) 0 0
\(323\) 1.44724e6 + 21249.1i 0.771853 + 0.0113327i
\(324\) 0 0
\(325\) 2.11576e6 + 3.66460e6i 1.11111 + 1.92450i
\(326\) 0 0
\(327\) −1.57352e6 + 2.72542e6i −0.813773 + 1.40950i
\(328\) 0 0
\(329\) 412610. 714661.i 0.210160 0.364008i
\(330\) 0 0
\(331\) 1.14830e6 0.576082 0.288041 0.957618i \(-0.406996\pi\)
0.288041 + 0.957618i \(0.406996\pi\)
\(332\) 0 0
\(333\) −742766. + 1.28651e6i −0.367064 + 0.635773i
\(334\) 0 0
\(335\) 3.74077e6 1.82117
\(336\) 0 0
\(337\) −742181. 1.28549e6i −0.355988 0.616589i 0.631299 0.775540i \(-0.282522\pi\)
−0.987286 + 0.158951i \(0.949189\pi\)
\(338\) 0 0
\(339\) 742944. + 1.28682e6i 0.351121 + 0.608160i
\(340\) 0 0
\(341\) 592180. 0.275783
\(342\) 0 0
\(343\) −2.33943e6 −1.07368
\(344\) 0 0
\(345\) 4.49471e6 + 7.78506e6i 2.03308 + 3.52139i
\(346\) 0 0
\(347\) 1.09955e6 + 1.90448e6i 0.490222 + 0.849089i 0.999937 0.0112544i \(-0.00358245\pi\)
−0.509715 + 0.860343i \(0.670249\pi\)
\(348\) 0 0
\(349\) −3.81500e6 −1.67660 −0.838302 0.545206i \(-0.816451\pi\)
−0.838302 + 0.545206i \(0.816451\pi\)
\(350\) 0 0
\(351\) 303855. 526292.i 0.131643 0.228012i
\(352\) 0 0
\(353\) 550982. 0.235342 0.117671 0.993053i \(-0.462457\pi\)
0.117671 + 0.993053i \(0.462457\pi\)
\(354\) 0 0
\(355\) −2.36856e6 + 4.10246e6i −0.997500 + 1.72772i
\(356\) 0 0
\(357\) 918738. 1.59130e6i 0.381523 0.660818i
\(358\) 0 0
\(359\) −110651. 191653.i −0.0453126 0.0784838i 0.842480 0.538728i \(-0.181095\pi\)
−0.887792 + 0.460245i \(0.847762\pi\)
\(360\) 0 0
\(361\) −1.17456e6 2.17979e6i −0.474359 0.880331i
\(362\) 0 0
\(363\) −1.53432e6 2.65752e6i −0.611152 1.05855i
\(364\) 0 0
\(365\) −4.11487e6 + 7.12717e6i −1.61668 + 2.80017i
\(366\) 0 0
\(367\) −680360. + 1.17842e6i −0.263678 + 0.456704i −0.967216 0.253954i \(-0.918269\pi\)
0.703538 + 0.710657i \(0.251602\pi\)
\(368\) 0 0
\(369\) −779258. −0.297931
\(370\) 0 0
\(371\) 1.77084e6 3.06718e6i 0.667950 1.15692i
\(372\) 0 0
\(373\) 4.37071e6 1.62660 0.813298 0.581848i \(-0.197670\pi\)
0.813298 + 0.581848i \(0.197670\pi\)
\(374\) 0 0
\(375\) −4.21899e6 7.30751e6i −1.54928 2.68344i
\(376\) 0 0
\(377\) 1.31742e6 + 2.28184e6i 0.477387 + 0.826859i
\(378\) 0 0
\(379\) −3.26062e6 −1.16601 −0.583005 0.812469i \(-0.698123\pi\)
−0.583005 + 0.812469i \(0.698123\pi\)
\(380\) 0 0
\(381\) 2.74555e6 0.968986
\(382\) 0 0
\(383\) 1.11542e6 + 1.93197e6i 0.388546 + 0.672981i 0.992254 0.124224i \(-0.0396441\pi\)
−0.603708 + 0.797205i \(0.706311\pi\)
\(384\) 0 0
\(385\) −577671. 1.00056e6i −0.198623 0.344025i
\(386\) 0 0
\(387\) 2.03021e6 0.689072
\(388\) 0 0
\(389\) 520809. 902068.i 0.174504 0.302249i −0.765486 0.643453i \(-0.777501\pi\)
0.939989 + 0.341204i \(0.110835\pi\)
\(390\) 0 0
\(391\) −3.90848e6 −1.29290
\(392\) 0 0
\(393\) 2.09941e6 3.63628e6i 0.685670 1.18762i
\(394\) 0 0
\(395\) −673527. + 1.16658e6i −0.217201 + 0.376203i
\(396\) 0 0
\(397\) −2.19687e6 3.80509e6i −0.699565 1.21168i −0.968618 0.248556i \(-0.920044\pi\)
0.269053 0.963125i \(-0.413289\pi\)
\(398\) 0 0
\(399\) −3.14308e6 46148.1i −0.988377 0.0145118i
\(400\) 0 0
\(401\) 393217. + 681071.i 0.122116 + 0.211510i 0.920602 0.390503i \(-0.127699\pi\)
−0.798486 + 0.602013i \(0.794365\pi\)
\(402\) 0 0
\(403\) −1.47385e6 + 2.55277e6i −0.452053 + 0.782979i
\(404\) 0 0
\(405\) −3.46738e6 + 6.00567e6i −1.05042 + 1.81938i
\(406\) 0 0
\(407\) −914442. −0.273634
\(408\) 0 0
\(409\) −584641. + 1.01263e6i −0.172815 + 0.299324i −0.939403 0.342815i \(-0.888620\pi\)
0.766588 + 0.642139i \(0.221953\pi\)
\(410\) 0 0
\(411\) 7.59038e6 2.21645
\(412\) 0 0
\(413\) −1.98041e6 3.43018e6i −0.571322 0.989559i
\(414\) 0 0
\(415\) −929930. 1.61069e6i −0.265051 0.459082i
\(416\) 0 0
\(417\) 7.95081e6 2.23909
\(418\) 0 0
\(419\) −4.14739e6 −1.15409 −0.577045 0.816712i \(-0.695794\pi\)
−0.577045 + 0.816712i \(0.695794\pi\)
\(420\) 0 0
\(421\) 1.59962e6 + 2.77063e6i 0.439858 + 0.761857i 0.997678 0.0681052i \(-0.0216954\pi\)
−0.557820 + 0.829962i \(0.688362\pi\)
\(422\) 0 0
\(423\) 838380. + 1.45212e6i 0.227819 + 0.394594i
\(424\) 0 0
\(425\) 6.54317e6 1.75718
\(426\) 0 0
\(427\) −214415. + 371378.i −0.0569096 + 0.0985703i
\(428\) 0 0
\(429\) −1.48629e6 −0.389908
\(430\) 0 0
\(431\) 2.91306e6 5.04557e6i 0.755364 1.30833i −0.189830 0.981817i \(-0.560794\pi\)
0.945193 0.326511i \(-0.105873\pi\)
\(432\) 0 0
\(433\) 1.29561e6 2.24407e6i 0.332090 0.575196i −0.650832 0.759222i \(-0.725580\pi\)
0.982921 + 0.184026i \(0.0589130\pi\)
\(434\) 0 0
\(435\) −4.68533e6 8.11522e6i −1.18718 2.05626i
\(436\) 0 0
\(437\) 3.25779e6 + 5.83899e6i 0.816056 + 1.46263i
\(438\) 0 0
\(439\) 986761. + 1.70912e6i 0.244372 + 0.423264i 0.961955 0.273209i \(-0.0880850\pi\)
−0.717583 + 0.696473i \(0.754752\pi\)
\(440\) 0 0
\(441\) 745307. 1.29091e6i 0.182490 0.316082i
\(442\) 0 0
\(443\) 73870.7 127948.i 0.0178839 0.0309759i −0.856945 0.515408i \(-0.827640\pi\)
0.874829 + 0.484432i \(0.160974\pi\)
\(444\) 0 0
\(445\) −1.47890e6 −0.354029
\(446\) 0 0
\(447\) 458120. 793487.i 0.108445 0.187833i
\(448\) 0 0
\(449\) −6.33075e6 −1.48197 −0.740985 0.671522i \(-0.765641\pi\)
−0.740985 + 0.671522i \(0.765641\pi\)
\(450\) 0 0
\(451\) −239842. 415419.i −0.0555244 0.0961711i
\(452\) 0 0
\(453\) −1.37061e6 2.37396e6i −0.313811 0.543536i
\(454\) 0 0
\(455\) 5.75094e6 1.30230
\(456\) 0 0
\(457\) −175313. −0.0392667 −0.0196334 0.999807i \(-0.506250\pi\)
−0.0196334 + 0.999807i \(0.506250\pi\)
\(458\) 0 0
\(459\) −469848. 813801.i −0.104094 0.180296i
\(460\) 0 0
\(461\) −3.20957e6 5.55914e6i −0.703388 1.21830i −0.967270 0.253749i \(-0.918336\pi\)
0.263882 0.964555i \(-0.414997\pi\)
\(462\) 0 0
\(463\) 2.17798e6 0.472174 0.236087 0.971732i \(-0.424135\pi\)
0.236087 + 0.971732i \(0.424135\pi\)
\(464\) 0 0
\(465\) 5.24164e6 9.07879e6i 1.12418 1.94713i
\(466\) 0 0
\(467\) 742392. 0.157522 0.0787610 0.996894i \(-0.474904\pi\)
0.0787610 + 0.996894i \(0.474904\pi\)
\(468\) 0 0
\(469\) 1.76613e6 3.05902e6i 0.370757 0.642170i
\(470\) 0 0
\(471\) −4.99910e6 + 8.65870e6i −1.03834 + 1.79846i
\(472\) 0 0
\(473\) 624865. + 1.08230e6i 0.128420 + 0.222430i
\(474\) 0 0
\(475\) −5.45386e6 9.77503e6i −1.10910 1.98785i
\(476\) 0 0
\(477\) 3.59815e6 + 6.23219e6i 0.724076 + 1.25414i
\(478\) 0 0
\(479\) −2.42943e6 + 4.20789e6i −0.483799 + 0.837965i −0.999827 0.0186069i \(-0.994077\pi\)
0.516028 + 0.856572i \(0.327410\pi\)
\(480\) 0 0
\(481\) 2.27591e6 3.94199e6i 0.448530 0.776877i
\(482\) 0 0
\(483\) 8.48832e6 1.65559
\(484\) 0 0
\(485\) −6.25777e6 + 1.08388e7i −1.20800 + 2.09231i
\(486\) 0 0
\(487\) 3.50290e6 0.669275 0.334638 0.942347i \(-0.391386\pi\)
0.334638 + 0.942347i \(0.391386\pi\)
\(488\) 0 0
\(489\) −4.06742e6 7.04497e6i −0.769213 1.33232i
\(490\) 0 0
\(491\) 368324. + 637956.i 0.0689488 + 0.119423i 0.898439 0.439099i \(-0.144702\pi\)
−0.829490 + 0.558521i \(0.811369\pi\)
\(492\) 0 0
\(493\) 4.07424e6 0.754968
\(494\) 0 0
\(495\) 2.34753e6 0.430625
\(496\) 0 0
\(497\) 2.23653e6 + 3.87378e6i 0.406147 + 0.703467i
\(498\) 0 0
\(499\) 9216.83 + 15964.0i 0.00165703 + 0.00287006i 0.866853 0.498564i \(-0.166139\pi\)
−0.865196 + 0.501434i \(0.832806\pi\)
\(500\) 0 0
\(501\) −1.09344e7 −1.94625
\(502\) 0 0
\(503\) 249975. 432970.i 0.0440532 0.0763024i −0.843158 0.537666i \(-0.819306\pi\)
0.887211 + 0.461363i \(0.152640\pi\)
\(504\) 0 0
\(505\) −5.03738e6 −0.878975
\(506\) 0 0
\(507\) −182305. + 315762.i −0.0314977 + 0.0545557i
\(508\) 0 0
\(509\) −2.32529e6 + 4.02752e6i −0.397816 + 0.689038i −0.993456 0.114213i \(-0.963565\pi\)
0.595640 + 0.803252i \(0.296899\pi\)
\(510\) 0 0
\(511\) 3.88550e6 + 6.72988e6i 0.658255 + 1.14013i
\(512\) 0 0
\(513\) −824133. + 1.38024e6i −0.138262 + 0.231559i
\(514\) 0 0
\(515\) −5.18309e6 8.97737e6i −0.861133 1.49153i
\(516\) 0 0
\(517\) −516077. + 893872.i −0.0849158 + 0.147078i
\(518\) 0 0
\(519\) 4.77605e6 8.27236e6i 0.778306 1.34807i
\(520\) 0 0
\(521\) 7.64507e6 1.23392 0.616960 0.786994i \(-0.288364\pi\)
0.616960 + 0.786994i \(0.288364\pi\)
\(522\) 0 0
\(523\) 794941. 1.37688e6i 0.127081 0.220111i −0.795463 0.606002i \(-0.792773\pi\)
0.922544 + 0.385891i \(0.126106\pi\)
\(524\) 0 0
\(525\) −1.42103e7 −2.25011
\(526\) 0 0
\(527\) 2.27900e6 + 3.94734e6i 0.357451 + 0.619124i
\(528\) 0 0
\(529\) −5.80954e6 1.00624e7i −0.902615 1.56338i
\(530\) 0 0
\(531\) 8.04799e6 1.23866
\(532\) 0 0
\(533\) 2.38772e6 0.364054
\(534\) 0 0
\(535\) 2.29240e6 + 3.97056e6i 0.346263 + 0.599746i
\(536\) 0 0
\(537\) 3.97593e6 + 6.88651e6i 0.594981 + 1.03054i
\(538\) 0 0
\(539\) 917570. 0.136040
\(540\) 0 0
\(541\) −2.63644e6 + 4.56645e6i −0.387280 + 0.670789i −0.992083 0.125587i \(-0.959919\pi\)
0.604803 + 0.796375i \(0.293252\pi\)
\(542\) 0 0
\(543\) −7.19385e6 −1.04704
\(544\) 0 0
\(545\) −7.61521e6 + 1.31899e7i −1.09822 + 1.90218i
\(546\) 0 0
\(547\) −1.94792e6 + 3.37389e6i −0.278357 + 0.482128i −0.970977 0.239175i \(-0.923123\pi\)
0.692620 + 0.721303i \(0.256456\pi\)
\(548\) 0 0
\(549\) −435669. 754600.i −0.0616915 0.106853i
\(550\) 0 0
\(551\) −3.39596e6 6.08662e6i −0.476522 0.854077i
\(552\) 0 0
\(553\) 635982. + 1.10155e6i 0.0884366 + 0.153177i
\(554\) 0 0
\(555\) −8.09413e6 + 1.40194e7i −1.11542 + 1.93196i
\(556\) 0 0
\(557\) 3.90618e6 6.76570e6i 0.533475 0.924006i −0.465761 0.884911i \(-0.654219\pi\)
0.999235 0.0390950i \(-0.0124475\pi\)
\(558\) 0 0
\(559\) −6.22077e6 −0.842005
\(560\) 0 0
\(561\) −1.14912e6 + 1.99034e6i −0.154156 + 0.267005i
\(562\) 0 0
\(563\) 7.01256e6 0.932407 0.466204 0.884677i \(-0.345621\pi\)
0.466204 + 0.884677i \(0.345621\pi\)
\(564\) 0 0
\(565\) 3.59555e6 + 6.22768e6i 0.473854 + 0.820739i
\(566\) 0 0
\(567\) 3.27409e6 + 5.67090e6i 0.427694 + 0.740788i
\(568\) 0 0
\(569\) 6.70622e6 0.868355 0.434177 0.900827i \(-0.357039\pi\)
0.434177 + 0.900827i \(0.357039\pi\)
\(570\) 0 0
\(571\) 5.59306e6 0.717893 0.358946 0.933358i \(-0.383136\pi\)
0.358946 + 0.933358i \(0.383136\pi\)
\(572\) 0 0
\(573\) −7.30892e6 1.26594e7i −0.929965 1.61075i
\(574\) 0 0
\(575\) 1.51133e7 + 2.61769e7i 1.90629 + 3.30179i
\(576\) 0 0
\(577\) 1.19869e7 1.49888 0.749442 0.662070i \(-0.230322\pi\)
0.749442 + 0.662070i \(0.230322\pi\)
\(578\) 0 0
\(579\) −577510. + 1.00028e6i −0.0715918 + 0.124001i
\(580\) 0 0
\(581\) −1.75619e6 −0.215839
\(582\) 0 0
\(583\) −2.21490e6 + 3.83632e6i −0.269887 + 0.467458i
\(584\) 0 0
\(585\) −5.84266e6 + 1.01198e7i −0.705863 + 1.22259i
\(586\) 0 0
\(587\) 7.13321e6 + 1.23551e7i 0.854456 + 1.47996i 0.877149 + 0.480219i \(0.159443\pi\)
−0.0226925 + 0.999742i \(0.507224\pi\)
\(588\) 0 0
\(589\) 3.99745e6 6.69484e6i 0.474783 0.795156i
\(590\) 0 0
\(591\) −1.04561e7 1.81105e7i −1.23141 2.13286i
\(592\) 0 0
\(593\) 3.81201e6 6.60260e6i 0.445161 0.771042i −0.552902 0.833246i \(-0.686480\pi\)
0.998063 + 0.0622043i \(0.0198130\pi\)
\(594\) 0 0
\(595\) 4.44632e6 7.70126e6i 0.514883 0.891803i
\(596\) 0 0
\(597\) 1.03149e7 1.18448
\(598\) 0 0
\(599\) −5.20469e6 + 9.01479e6i −0.592691 + 1.02657i 0.401178 + 0.916000i \(0.368601\pi\)
−0.993868 + 0.110570i \(0.964732\pi\)
\(600\) 0 0
\(601\) 1.96843e6 0.222297 0.111149 0.993804i \(-0.464547\pi\)
0.111149 + 0.993804i \(0.464547\pi\)
\(602\) 0 0
\(603\) 3.58858e6 + 6.21560e6i 0.401911 + 0.696129i
\(604\) 0 0
\(605\) −7.42549e6 1.28613e7i −0.824777 1.42856i
\(606\) 0 0
\(607\) −1.79114e7 −1.97314 −0.986569 0.163347i \(-0.947771\pi\)
−0.986569 + 0.163347i \(0.947771\pi\)
\(608\) 0 0
\(609\) −8.84830e6 −0.966755
\(610\) 0 0
\(611\) −2.56888e6 4.44942e6i −0.278381 0.482171i
\(612\) 0 0
\(613\) −206107. 356988.i −0.0221535 0.0383709i 0.854736 0.519063i \(-0.173719\pi\)
−0.876890 + 0.480692i \(0.840386\pi\)
\(614\) 0 0
\(615\) −8.49179e6 −0.905339
\(616\) 0 0
\(617\) 6.97181e6 1.20755e7i 0.737281 1.27701i −0.216435 0.976297i \(-0.569443\pi\)
0.953715 0.300711i \(-0.0972238\pi\)
\(618\) 0 0
\(619\) −1.59596e7 −1.67415 −0.837075 0.547088i \(-0.815736\pi\)
−0.837075 + 0.547088i \(0.815736\pi\)
\(620\) 0 0
\(621\) 2.17049e6 3.75940e6i 0.225854 0.391191i
\(622\) 0 0
\(623\) −698230. + 1.20937e6i −0.0720740 + 0.124836i
\(624\) 0 0
\(625\) −9.30336e6 1.61139e7i −0.952664 1.65006i
\(626\) 0 0
\(627\) 3.93124e6 + 57720.4i 0.399357 + 0.00586354i
\(628\) 0 0
\(629\) −3.51922e6 6.09547e6i −0.354666 0.614300i
\(630\) 0 0
\(631\) 3.10790e6 5.38304e6i 0.310737 0.538213i −0.667785 0.744354i \(-0.732757\pi\)
0.978522 + 0.206141i \(0.0660907\pi\)
\(632\) 0 0
\(633\) 6.46664e6 1.12005e7i 0.641460 1.11104i
\(634\) 0 0
\(635\) 1.32874e7 1.30769
\(636\) 0 0
\(637\) −2.28369e6 + 3.95547e6i −0.222992 + 0.386233i
\(638\) 0 0
\(639\) −9.08877e6 −0.880548
\(640\) 0 0
\(641\) 4.32033e6 + 7.48302e6i 0.415309 + 0.719337i 0.995461 0.0951719i \(-0.0303401\pi\)
−0.580152 + 0.814508i \(0.697007\pi\)
\(642\) 0 0
\(643\) −8.07254e6 1.39820e7i −0.769985 1.33365i −0.937570 0.347796i \(-0.886930\pi\)
0.167585 0.985858i \(-0.446403\pi\)
\(644\) 0 0
\(645\) 2.21238e7 2.09392
\(646\) 0 0
\(647\) 8.16344e6 0.766677 0.383338 0.923608i \(-0.374774\pi\)
0.383338 + 0.923608i \(0.374774\pi\)
\(648\) 0 0
\(649\) 2.47703e6 + 4.29034e6i 0.230844 + 0.399834i
\(650\) 0 0
\(651\) −4.94946e6 8.57271e6i −0.457725 0.792803i
\(652\) 0 0
\(653\) 1.08567e7 0.996359 0.498179 0.867074i \(-0.334002\pi\)
0.498179 + 0.867074i \(0.334002\pi\)
\(654\) 0 0
\(655\) 1.01603e7 1.75981e7i 0.925343 1.60274i
\(656\) 0 0
\(657\) −1.57898e7 −1.42713
\(658\) 0 0
\(659\) 2.49623e6 4.32359e6i 0.223908 0.387821i −0.732083 0.681215i \(-0.761452\pi\)
0.955991 + 0.293395i \(0.0947850\pi\)
\(660\) 0 0
\(661\) −7.54002e6 + 1.30597e7i −0.671226 + 1.16260i 0.306330 + 0.951925i \(0.400899\pi\)
−0.977557 + 0.210673i \(0.932435\pi\)
\(662\) 0 0
\(663\) −5.71999e6 9.90731e6i −0.505372 0.875330i
\(664\) 0 0
\(665\) −1.52112e7 223338.i −1.33386 0.0195844i
\(666\) 0 0
\(667\) 9.41057e6 + 1.62996e7i 0.819033 + 1.41861i
\(668\) 0 0
\(669\) 1.56862e6 2.71692e6i 0.135504 0.234699i
\(670\) 0 0
\(671\) 268182. 464505.i 0.0229945 0.0398276i
\(672\) 0 0
\(673\) −1.89452e7 −1.61236 −0.806180 0.591671i \(-0.798469\pi\)
−0.806180 + 0.591671i \(0.798469\pi\)
\(674\) 0 0
\(675\) −3.63361e6 + 6.29359e6i −0.306958 + 0.531666i
\(676\) 0 0
\(677\) −4.05825e6 −0.340304 −0.170152 0.985418i \(-0.554426\pi\)
−0.170152 + 0.985418i \(0.554426\pi\)
\(678\) 0 0
\(679\) 5.90894e6 + 1.02346e7i 0.491853 + 0.851914i
\(680\) 0 0
\(681\) 1.09990e7 + 1.90508e7i 0.908836 + 1.57415i
\(682\) 0 0
\(683\) 2.85503e6 0.234185 0.117092 0.993121i \(-0.462643\pi\)
0.117092 + 0.993121i \(0.462643\pi\)
\(684\) 0 0
\(685\) 3.67344e7 2.99121
\(686\) 0 0
\(687\) 8.01621e6 + 1.38845e7i 0.648003 + 1.12237i
\(688\) 0 0
\(689\) −1.10251e7 1.90960e7i −0.884778 1.53248i
\(690\) 0 0
\(691\) 4.38220e6 0.349138 0.174569 0.984645i \(-0.444147\pi\)
0.174569 + 0.984645i \(0.444147\pi\)
\(692\) 0 0
\(693\) 1.10834e6 1.91970e6i 0.0876675 0.151845i
\(694\) 0 0
\(695\) 3.84788e7 3.02175
\(696\) 0 0
\(697\) 1.84606e6 3.19747e6i 0.143934 0.249301i
\(698\) 0 0
\(699\) 1.51156e7 2.61810e7i 1.17013 2.02672i
\(700\) 0 0
\(701\) −2.33852e6 4.05044e6i −0.179741 0.311320i 0.762051 0.647517i \(-0.224193\pi\)
−0.941792 + 0.336197i \(0.890859\pi\)
\(702\) 0 0
\(703\) −6.17285e6 + 1.03382e7i −0.471083 + 0.788959i
\(704\) 0 0
\(705\) 9.13605e6 + 1.58241e7i 0.692287 + 1.19908i
\(706\) 0 0
\(707\) −2.37829e6 + 4.11932e6i −0.178944 + 0.309940i
\(708\) 0 0
\(709\) −177992. + 308291.i −0.0132980 + 0.0230328i −0.872598 0.488439i \(-0.837566\pi\)
0.859300 + 0.511472i \(0.170900\pi\)
\(710\) 0 0
\(711\) −2.58450e6 −0.191735
\(712\) 0 0
\(713\) −1.05279e7 + 1.82349e7i −0.775568 + 1.34332i
\(714\) 0 0
\(715\) −7.19307e6 −0.526198
\(716\) 0 0
\(717\) −7.83368e6 1.35683e7i −0.569073 0.985663i
\(718\) 0 0
\(719\) −705747. 1.22239e6i −0.0509128 0.0881835i 0.839446 0.543443i \(-0.182880\pi\)
−0.890359 + 0.455260i \(0.849546\pi\)
\(720\) 0 0
\(721\) −9.78833e6 −0.701246
\(722\) 0 0
\(723\) −1.92099e7 −1.36672
\(724\) 0 0
\(725\) −1.57542e7 2.72871e7i −1.11314 1.92802i
\(726\) 0 0
\(727\) 6.82049e6 + 1.18134e7i 0.478608 + 0.828973i 0.999699 0.0245278i \(-0.00780822\pi\)
−0.521091 + 0.853501i \(0.674475\pi\)
\(728\) 0 0
\(729\) −8.11485e6 −0.565538
\(730\) 0 0
\(731\) −4.80957e6 + 8.33042e6i −0.332899 + 0.576598i
\(732\) 0 0
\(733\) −2.66079e7 −1.82915 −0.914577 0.404412i \(-0.867476\pi\)
−0.914577 + 0.404412i \(0.867476\pi\)
\(734\) 0 0
\(735\) 8.12181e6 1.40674e7i 0.554542 0.960495i
\(736\) 0 0
\(737\) −2.20900e6 + 3.82611e6i −0.149806 + 0.259471i
\(738\) 0 0
\(739\) 4.22169e6 + 7.31218e6i 0.284364 + 0.492533i 0.972455 0.233091i \(-0.0748842\pi\)
−0.688091 + 0.725625i \(0.741551\pi\)
\(740\) 0 0
\(741\) −1.00331e7 + 1.68032e7i −0.671258 + 1.12421i
\(742\) 0 0
\(743\) −2.70095e6 4.67819e6i −0.179492 0.310889i 0.762215 0.647324i \(-0.224112\pi\)
−0.941707 + 0.336435i \(0.890779\pi\)
\(744\) 0 0
\(745\) 2.21712e6 3.84016e6i 0.146352 0.253489i
\(746\) 0 0
\(747\) 1.78419e6 3.09031e6i 0.116988 0.202629i
\(748\) 0 0
\(749\) 4.32923e6 0.281972
\(750\) 0 0
\(751\) 6.66101e6 1.15372e7i 0.430963 0.746450i −0.565994 0.824410i \(-0.691507\pi\)
0.996956 + 0.0779599i \(0.0248406\pi\)
\(752\) 0 0
\(753\) 6.62985e6 0.426105
\(754\) 0 0
\(755\) −6.63319e6 1.14890e7i −0.423502 0.733527i
\(756\) 0 0
\(757\) 1.61706e6 + 2.80083e6i 0.102562 + 0.177642i 0.912739 0.408542i \(-0.133963\pi\)
−0.810178 + 0.586185i \(0.800629\pi\)
\(758\) 0 0
\(759\) −1.06169e7 −0.668948
\(760\) 0 0
\(761\) 602035. 0.0376843 0.0188421 0.999822i \(-0.494002\pi\)
0.0188421 + 0.999822i \(0.494002\pi\)
\(762\) 0 0
\(763\) 7.19072e6 + 1.24547e7i 0.447158 + 0.774500i
\(764\) 0 0
\(765\) 9.03446e6 + 1.56481e7i 0.558147 + 0.966739i
\(766\) 0 0
\(767\) −2.46598e7 −1.51357
\(768\) 0 0
\(769\) −9.81675e6 + 1.70031e7i −0.598621 + 1.03684i 0.394404 + 0.918937i \(0.370951\pi\)
−0.993025 + 0.117904i \(0.962382\pi\)
\(770\) 0 0
\(771\) −1.22685e7 −0.743285
\(772\) 0 0
\(773\) 2.03679e6 3.52782e6i 0.122602 0.212353i −0.798191 0.602404i \(-0.794210\pi\)
0.920793 + 0.390052i \(0.127543\pi\)
\(774\) 0 0
\(775\) 1.76248e7 3.05270e7i 1.05407 1.82570i
\(776\) 0 0
\(777\) 7.64293e6 + 1.32379e7i 0.454159 + 0.786626i
\(778\) 0 0
\(779\) −6.31552e6 92727.4i −0.372877 0.00547475i
\(780\) 0 0
\(781\) −2.79736e6 4.84518e6i −0.164105 0.284238i
\(782\) 0 0
\(783\) −2.26254e6 + 3.91883e6i −0.131884 + 0.228429i
\(784\) 0 0
\(785\) −2.41937e7 + 4.19047e7i −1.40129 + 2.42710i
\(786\) 0 0
\(787\) 4.13033e6 0.237710 0.118855 0.992912i \(-0.462078\pi\)
0.118855 + 0.992912i \(0.462078\pi\)
\(788\) 0 0
\(789\) 1.25951e7 2.18154e7i 0.720293