Properties

Label 84.12.i.b.37.5
Level $84$
Weight $12$
Character 84.37
Analytic conductor $64.541$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 84.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(64.5408271670\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 581500324 x^{14} - 481772282104 x^{13} + 132272376701859942 x^{12} + \)\(18\!\cdots\!08\)\( x^{11} - \)\(14\!\cdots\!08\)\( x^{10} - \)\(25\!\cdots\!56\)\( x^{9} + \)\(80\!\cdots\!79\)\( x^{8} + \)\(11\!\cdots\!68\)\( x^{7} - \)\(19\!\cdots\!68\)\( x^{6} + \)\(59\!\cdots\!08\)\( x^{5} + \)\(21\!\cdots\!06\)\( x^{4} - \)\(37\!\cdots\!04\)\( x^{3} - \)\(31\!\cdots\!28\)\( x^{2} + \)\(25\!\cdots\!24\)\( x + \)\(79\!\cdots\!77\)\(\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{42}\cdot 3^{15}\cdot 7^{9} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 37.5
Root \(-438.744 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 84.37
Dual form 84.12.i.b.25.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-121.500 - 210.444i) q^{3} +(84.6221 - 146.570i) q^{5} +(-9851.70 - 43362.1i) q^{7} +(-29524.5 + 51137.9i) q^{9} +O(q^{10})\) \(q+(-121.500 - 210.444i) q^{3} +(84.6221 - 146.570i) q^{5} +(-9851.70 - 43362.1i) q^{7} +(-29524.5 + 51137.9i) q^{9} +(-143939. - 249309. i) q^{11} +2.48841e6 q^{13} -41126.3 q^{15} +(-3.58228e6 - 6.20469e6i) q^{17} +(-1.63429e6 + 2.83067e6i) q^{19} +(-7.92832e6 + 7.34173e6i) q^{21} +(1.56616e7 - 2.71268e7i) q^{23} +(2.43997e7 + 4.22616e7i) q^{25} +1.43489e7 q^{27} +5.63075e7 q^{29} +(-8.04560e7 - 1.39354e8i) q^{31} +(-3.49771e7 + 6.05821e7i) q^{33} +(-7.18924e6 - 2.22543e6i) q^{35} +(1.48880e8 - 2.57868e8i) q^{37} +(-3.02342e8 - 5.23672e8i) q^{39} +1.39570e9 q^{41} -4.76296e8 q^{43} +(4.99685e6 + 8.65480e6i) q^{45} +(-1.19265e9 + 2.06573e9i) q^{47} +(-1.78321e9 + 8.54381e8i) q^{49} +(-8.70493e8 + 1.50774e9i) q^{51} +(-2.34079e9 - 4.05437e9i) q^{53} -4.87215e7 q^{55} +7.94263e8 q^{57} +(-8.21849e8 - 1.42348e9i) q^{59} +(-1.55428e9 + 2.69209e9i) q^{61} +(2.50831e9 + 7.76448e8i) q^{63} +(2.10575e8 - 3.64726e8i) q^{65} +(-5.33960e9 - 9.24846e9i) q^{67} -7.61156e9 q^{69} -2.59617e10 q^{71} +(-2.45048e8 - 4.24435e8i) q^{73} +(5.92914e9 - 1.02696e10i) q^{75} +(-9.39252e9 + 8.69760e9i) q^{77} +(-4.61089e9 + 7.98630e9i) q^{79} +(-1.74339e9 - 3.01964e9i) q^{81} -3.48255e10 q^{83} -1.21256e9 q^{85} +(-6.84136e9 - 1.18496e10i) q^{87} +(1.81904e10 - 3.15067e10i) q^{89} +(-2.45151e10 - 1.07903e11i) q^{91} +(-1.95508e10 + 3.38630e10i) q^{93} +(2.76593e8 + 4.79074e8i) q^{95} -1.51725e11 q^{97} +1.69989e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 1944 q^{3} - 2156 q^{5} + 50512 q^{7} - 472392 q^{9} + O(q^{10}) \) \( 16 q - 1944 q^{3} - 2156 q^{5} + 50512 q^{7} - 472392 q^{9} - 222796 q^{11} + 2703176 q^{13} + 1047816 q^{15} + 5114600 q^{17} + 6910556 q^{19} - 18340668 q^{21} - 51387712 q^{23} - 191456372 q^{25} + 229582512 q^{27} + 118854616 q^{29} + 164659160 q^{31} - 54139428 q^{33} + 55239344 q^{35} + 75658364 q^{37} - 328435884 q^{39} - 1815568608 q^{41} + 10754408 q^{43} - 127309644 q^{45} - 1034359464 q^{47} + 4123496848 q^{49} + 1242847800 q^{51} - 665159988 q^{53} - 1264543896 q^{55} - 3358530216 q^{57} + 1040514580 q^{59} - 14391208024 q^{61} + 1474099236 q^{63} - 20938150200 q^{65} - 33307097284 q^{67} + 24974428032 q^{69} + 65848902896 q^{71} + 17709749204 q^{73} - 46523898396 q^{75} + 8594484604 q^{77} - 26626784032 q^{79} - 27894275208 q^{81} - 210306955048 q^{83} - 25867402032 q^{85} - 14440835844 q^{87} - 55951560072 q^{89} + 66078280292 q^{91} + 40012175880 q^{93} + 106810047392 q^{95} - 156216030712 q^{97} + 26311762008 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(43\) \(73\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) −121.500 210.444i −0.288675 0.500000i
\(4\) 0 0
\(5\) 84.6221 146.570i 0.0121101 0.0209754i −0.859907 0.510451i \(-0.829478\pi\)
0.872017 + 0.489476i \(0.162812\pi\)
\(6\) 0 0
\(7\) −9851.70 43362.1i −0.221550 0.975149i
\(8\) 0 0
\(9\) −29524.5 + 51137.9i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −143939. 249309.i −0.269474 0.466743i 0.699252 0.714875i \(-0.253517\pi\)
−0.968726 + 0.248132i \(0.920183\pi\)
\(12\) 0 0
\(13\) 2.48841e6 1.85881 0.929404 0.369065i \(-0.120322\pi\)
0.929404 + 0.369065i \(0.120322\pi\)
\(14\) 0 0
\(15\) −41126.3 −0.0139836
\(16\) 0 0
\(17\) −3.58228e6 6.20469e6i −0.611914 1.05987i −0.990918 0.134470i \(-0.957067\pi\)
0.379004 0.925395i \(-0.376267\pi\)
\(18\) 0 0
\(19\) −1.63429e6 + 2.83067e6i −0.151420 + 0.262267i −0.931750 0.363101i \(-0.881718\pi\)
0.780330 + 0.625368i \(0.215051\pi\)
\(20\) 0 0
\(21\) −7.92832e6 + 7.34173e6i −0.423618 + 0.392276i
\(22\) 0 0
\(23\) 1.56616e7 2.71268e7i 0.507381 0.878810i −0.492582 0.870266i \(-0.663947\pi\)
0.999963 0.00854416i \(-0.00271972\pi\)
\(24\) 0 0
\(25\) 2.43997e7 + 4.22616e7i 0.499707 + 0.865517i
\(26\) 0 0
\(27\) 1.43489e7 0.192450
\(28\) 0 0
\(29\) 5.63075e7 0.509773 0.254887 0.966971i \(-0.417962\pi\)
0.254887 + 0.966971i \(0.417962\pi\)
\(30\) 0 0
\(31\) −8.04560e7 1.39354e8i −0.504742 0.874238i −0.999985 0.00548373i \(-0.998254\pi\)
0.495243 0.868754i \(-0.335079\pi\)
\(32\) 0 0
\(33\) −3.49771e7 + 6.05821e7i −0.155581 + 0.269474i
\(34\) 0 0
\(35\) −7.18924e6 2.22543e6i −0.0231371 0.00716208i
\(36\) 0 0
\(37\) 1.48880e8 2.57868e8i 0.352962 0.611348i −0.633805 0.773493i \(-0.718508\pi\)
0.986767 + 0.162145i \(0.0518413\pi\)
\(38\) 0 0
\(39\) −3.02342e8 5.23672e8i −0.536591 0.929404i
\(40\) 0 0
\(41\) 1.39570e9 1.88140 0.940702 0.339235i \(-0.110168\pi\)
0.940702 + 0.339235i \(0.110168\pi\)
\(42\) 0 0
\(43\) −4.76296e8 −0.494083 −0.247042 0.969005i \(-0.579458\pi\)
−0.247042 + 0.969005i \(0.579458\pi\)
\(44\) 0 0
\(45\) 4.99685e6 + 8.65480e6i 0.00403671 + 0.00699178i
\(46\) 0 0
\(47\) −1.19265e9 + 2.06573e9i −0.758533 + 1.31382i 0.185066 + 0.982726i \(0.440750\pi\)
−0.943599 + 0.331091i \(0.892583\pi\)
\(48\) 0 0
\(49\) −1.78321e9 + 8.54381e8i −0.901831 + 0.432089i
\(50\) 0 0
\(51\) −8.70493e8 + 1.50774e9i −0.353288 + 0.611914i
\(52\) 0 0
\(53\) −2.34079e9 4.05437e9i −0.768856 1.33170i −0.938183 0.346139i \(-0.887493\pi\)
0.169327 0.985560i \(-0.445841\pi\)
\(54\) 0 0
\(55\) −4.87215e7 −0.0130535
\(56\) 0 0
\(57\) 7.94263e8 0.174845
\(58\) 0 0
\(59\) −8.21849e8 1.42348e9i −0.149660 0.259219i 0.781442 0.623978i \(-0.214485\pi\)
−0.931102 + 0.364759i \(0.881151\pi\)
\(60\) 0 0
\(61\) −1.55428e9 + 2.69209e9i −0.235621 + 0.408108i −0.959453 0.281868i \(-0.909046\pi\)
0.723832 + 0.689977i \(0.242379\pi\)
\(62\) 0 0
\(63\) 2.50831e9 + 7.76448e8i 0.318426 + 0.0985688i
\(64\) 0 0
\(65\) 2.10575e8 3.64726e8i 0.0225104 0.0389891i
\(66\) 0 0
\(67\) −5.33960e9 9.24846e9i −0.483167 0.836870i 0.516646 0.856199i \(-0.327180\pi\)
−0.999813 + 0.0193290i \(0.993847\pi\)
\(68\) 0 0
\(69\) −7.61156e9 −0.585873
\(70\) 0 0
\(71\) −2.59617e10 −1.70770 −0.853852 0.520516i \(-0.825739\pi\)
−0.853852 + 0.520516i \(0.825739\pi\)
\(72\) 0 0
\(73\) −2.45048e8 4.24435e8i −0.0138349 0.0239627i 0.859025 0.511933i \(-0.171071\pi\)
−0.872860 + 0.487971i \(0.837737\pi\)
\(74\) 0 0
\(75\) 5.92914e9 1.02696e10i 0.288506 0.499707i
\(76\) 0 0
\(77\) −9.39252e9 + 8.69760e9i −0.395442 + 0.366185i
\(78\) 0 0
\(79\) −4.61089e9 + 7.98630e9i −0.168592 + 0.292009i −0.937925 0.346838i \(-0.887255\pi\)
0.769333 + 0.638848i \(0.220589\pi\)
\(80\) 0 0
\(81\) −1.74339e9 3.01964e9i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −3.48255e10 −0.970437 −0.485219 0.874393i \(-0.661260\pi\)
−0.485219 + 0.874393i \(0.661260\pi\)
\(84\) 0 0
\(85\) −1.21256e9 −0.0296414
\(86\) 0 0
\(87\) −6.84136e9 1.18496e10i −0.147159 0.254887i
\(88\) 0 0
\(89\) 1.81904e10 3.15067e10i 0.345301 0.598078i −0.640108 0.768285i \(-0.721110\pi\)
0.985408 + 0.170207i \(0.0544437\pi\)
\(90\) 0 0
\(91\) −2.45151e10 1.07903e11i −0.411819 1.81261i
\(92\) 0 0
\(93\) −1.95508e10 + 3.38630e10i −0.291413 + 0.504742i
\(94\) 0 0
\(95\) 2.76593e8 + 4.79074e8i 0.00366743 + 0.00635218i
\(96\) 0 0
\(97\) −1.51725e11 −1.79396 −0.896978 0.442076i \(-0.854242\pi\)
−0.896978 + 0.442076i \(0.854242\pi\)
\(98\) 0 0
\(99\) 1.69989e10 0.179650
\(100\) 0 0
\(101\) −7.68508e10 1.33110e11i −0.727581 1.26021i −0.957903 0.287092i \(-0.907311\pi\)
0.230322 0.973114i \(-0.426022\pi\)
\(102\) 0 0
\(103\) −8.88312e10 + 1.53860e11i −0.755024 + 1.30774i 0.190338 + 0.981719i \(0.439042\pi\)
−0.945362 + 0.326022i \(0.894292\pi\)
\(104\) 0 0
\(105\) 4.05164e8 + 1.78332e9i 0.00309806 + 0.0136361i
\(106\) 0 0
\(107\) −1.46571e9 + 2.53868e9i −0.0101027 + 0.0174984i −0.871033 0.491225i \(-0.836549\pi\)
0.860930 + 0.508724i \(0.169883\pi\)
\(108\) 0 0
\(109\) 1.37623e10 + 2.38371e10i 0.0856734 + 0.148391i 0.905678 0.423966i \(-0.139362\pi\)
−0.820005 + 0.572357i \(0.806029\pi\)
\(110\) 0 0
\(111\) −7.23558e10 −0.407565
\(112\) 0 0
\(113\) −7.29842e10 −0.372647 −0.186323 0.982488i \(-0.559657\pi\)
−0.186323 + 0.982488i \(0.559657\pi\)
\(114\) 0 0
\(115\) −2.65064e9 4.59105e9i −0.0122889 0.0212850i
\(116\) 0 0
\(117\) −7.34692e10 + 1.27252e11i −0.309801 + 0.536591i
\(118\) 0 0
\(119\) −2.33757e11 + 2.16462e11i −0.897957 + 0.831520i
\(120\) 0 0
\(121\) 1.01219e11 1.75317e11i 0.354767 0.614475i
\(122\) 0 0
\(123\) −1.69578e11 2.93718e11i −0.543114 0.940702i
\(124\) 0 0
\(125\) 1.65229e10 0.0484263
\(126\) 0 0
\(127\) −4.83730e11 −1.29922 −0.649610 0.760268i \(-0.725068\pi\)
−0.649610 + 0.760268i \(0.725068\pi\)
\(128\) 0 0
\(129\) 5.78699e10 + 1.00234e11i 0.142630 + 0.247042i
\(130\) 0 0
\(131\) 1.84860e11 3.20188e11i 0.418651 0.725124i −0.577153 0.816636i \(-0.695836\pi\)
0.995804 + 0.0915115i \(0.0291698\pi\)
\(132\) 0 0
\(133\) 1.38844e11 + 4.29792e10i 0.289297 + 0.0895517i
\(134\) 0 0
\(135\) 1.21423e9 2.10312e9i 0.00233059 0.00403671i
\(136\) 0 0
\(137\) 3.08974e11 + 5.35159e11i 0.546964 + 0.947370i 0.998480 + 0.0551072i \(0.0175501\pi\)
−0.451516 + 0.892263i \(0.649117\pi\)
\(138\) 0 0
\(139\) 8.57532e11 1.40175 0.700873 0.713287i \(-0.252794\pi\)
0.700873 + 0.713287i \(0.252794\pi\)
\(140\) 0 0
\(141\) 5.79627e11 0.875878
\(142\) 0 0
\(143\) −3.58179e11 6.20384e11i −0.500901 0.867586i
\(144\) 0 0
\(145\) 4.76485e9 8.25297e9i 0.00617342 0.0106927i
\(146\) 0 0
\(147\) 3.96460e11 + 2.71460e11i 0.476381 + 0.326182i
\(148\) 0 0
\(149\) 3.33560e11 5.77744e11i 0.372092 0.644482i −0.617795 0.786339i \(-0.711974\pi\)
0.989887 + 0.141857i \(0.0453073\pi\)
\(150\) 0 0
\(151\) −2.61750e11 4.53365e11i −0.271340 0.469975i 0.697865 0.716229i \(-0.254134\pi\)
−0.969205 + 0.246254i \(0.920800\pi\)
\(152\) 0 0
\(153\) 4.23060e11 0.407942
\(154\) 0 0
\(155\) −2.72334e10 −0.0244499
\(156\) 0 0
\(157\) 8.68955e11 + 1.50507e12i 0.727024 + 1.25924i 0.958135 + 0.286316i \(0.0924307\pi\)
−0.231111 + 0.972927i \(0.574236\pi\)
\(158\) 0 0
\(159\) −5.68812e11 + 9.85211e11i −0.443899 + 0.768856i
\(160\) 0 0
\(161\) −1.33057e12 4.11877e11i −0.969381 0.300072i
\(162\) 0 0
\(163\) −6.47918e11 + 1.12223e12i −0.441050 + 0.763922i −0.997768 0.0667802i \(-0.978727\pi\)
0.556717 + 0.830702i \(0.312061\pi\)
\(164\) 0 0
\(165\) 5.91967e9 + 1.02532e10i 0.00376821 + 0.00652674i
\(166\) 0 0
\(167\) 2.54401e12 1.51558 0.757789 0.652500i \(-0.226280\pi\)
0.757789 + 0.652500i \(0.226280\pi\)
\(168\) 0 0
\(169\) 4.40005e12 2.45516
\(170\) 0 0
\(171\) −9.65030e10 1.67148e11i −0.0504733 0.0874224i
\(172\) 0 0
\(173\) 6.74851e11 1.16888e12i 0.331096 0.573476i −0.651631 0.758536i \(-0.725915\pi\)
0.982727 + 0.185061i \(0.0592482\pi\)
\(174\) 0 0
\(175\) 1.59217e12 1.47437e12i 0.733298 0.679044i
\(176\) 0 0
\(177\) −1.99709e11 + 3.45907e11i −0.0864063 + 0.149660i
\(178\) 0 0
\(179\) 1.63584e12 + 2.83337e12i 0.665350 + 1.15242i 0.979190 + 0.202945i \(0.0650512\pi\)
−0.313840 + 0.949476i \(0.601615\pi\)
\(180\) 0 0
\(181\) −4.17692e12 −1.59817 −0.799087 0.601216i \(-0.794683\pi\)
−0.799087 + 0.601216i \(0.794683\pi\)
\(182\) 0 0
\(183\) 7.55379e11 0.272072
\(184\) 0 0
\(185\) −2.51971e10 4.36427e10i −0.00854882 0.0148070i
\(186\) 0 0
\(187\) −1.03126e12 + 1.78619e12i −0.329790 + 0.571213i
\(188\) 0 0
\(189\) −1.41361e11 6.22199e11i −0.0426374 0.187668i
\(190\) 0 0
\(191\) 1.45917e12 2.52736e12i 0.415359 0.719423i −0.580107 0.814540i \(-0.696989\pi\)
0.995466 + 0.0951173i \(0.0303226\pi\)
\(192\) 0 0
\(193\) 2.76848e12 + 4.79515e12i 0.744178 + 1.28895i 0.950578 + 0.310486i \(0.100492\pi\)
−0.206400 + 0.978468i \(0.566175\pi\)
\(194\) 0 0
\(195\) −1.02339e11 −0.0259928
\(196\) 0 0
\(197\) 3.28547e11 0.0788920 0.0394460 0.999222i \(-0.487441\pi\)
0.0394460 + 0.999222i \(0.487441\pi\)
\(198\) 0 0
\(199\) −1.41328e12 2.44787e12i −0.321023 0.556027i 0.659677 0.751549i \(-0.270693\pi\)
−0.980699 + 0.195522i \(0.937360\pi\)
\(200\) 0 0
\(201\) −1.29752e12 + 2.24738e12i −0.278957 + 0.483167i
\(202\) 0 0
\(203\) −5.54724e11 2.44161e12i −0.112940 0.497105i
\(204\) 0 0
\(205\) 1.18107e11 2.04568e11i 0.0227840 0.0394631i
\(206\) 0 0
\(207\) 9.24805e11 + 1.60181e12i 0.169127 + 0.292937i
\(208\) 0 0
\(209\) 9.40947e11 0.163215
\(210\) 0 0
\(211\) 4.59968e12 0.757137 0.378568 0.925573i \(-0.376416\pi\)
0.378568 + 0.925573i \(0.376416\pi\)
\(212\) 0 0
\(213\) 3.15435e12 + 5.46349e12i 0.492972 + 0.853852i
\(214\) 0 0
\(215\) −4.03051e10 + 6.98105e10i −0.00598341 + 0.0103636i
\(216\) 0 0
\(217\) −5.25005e12 + 4.86161e12i −0.740687 + 0.685886i
\(218\) 0 0
\(219\) −5.95466e10 + 1.03138e11i −0.00798756 + 0.0138349i
\(220\) 0 0
\(221\) −8.91419e12 1.54398e13i −1.13743 1.97009i
\(222\) 0 0
\(223\) 5.12583e12 0.622426 0.311213 0.950340i \(-0.399265\pi\)
0.311213 + 0.950340i \(0.399265\pi\)
\(224\) 0 0
\(225\) −2.88156e12 −0.333138
\(226\) 0 0
\(227\) −7.71055e12 1.33551e13i −0.849069 1.47063i −0.882040 0.471175i \(-0.843830\pi\)
0.0329705 0.999456i \(-0.489503\pi\)
\(228\) 0 0
\(229\) −1.68621e12 + 2.92060e12i −0.176936 + 0.306463i −0.940830 0.338880i \(-0.889952\pi\)
0.763893 + 0.645342i \(0.223285\pi\)
\(230\) 0 0
\(231\) 2.97155e12 + 9.19842e11i 0.297247 + 0.0920127i
\(232\) 0 0
\(233\) 3.52941e12 6.11311e12i 0.336701 0.583183i −0.647109 0.762397i \(-0.724022\pi\)
0.983810 + 0.179215i \(0.0573556\pi\)
\(234\) 0 0
\(235\) 2.01849e11 + 3.49612e11i 0.0183719 + 0.0318210i
\(236\) 0 0
\(237\) 2.24089e12 0.194673
\(238\) 0 0
\(239\) −7.38390e12 −0.612487 −0.306244 0.951953i \(-0.599072\pi\)
−0.306244 + 0.951953i \(0.599072\pi\)
\(240\) 0 0
\(241\) −3.35164e12 5.80522e12i −0.265561 0.459965i 0.702149 0.712030i \(-0.252224\pi\)
−0.967710 + 0.252065i \(0.918890\pi\)
\(242\) 0 0
\(243\) −4.23644e11 + 7.33773e11i −0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) −2.56729e10 + 3.33665e11i −0.00185807 + 0.0241489i
\(246\) 0 0
\(247\) −4.06678e12 + 7.04387e12i −0.281461 + 0.487504i
\(248\) 0 0
\(249\) 4.23129e12 + 7.32882e12i 0.280141 + 0.485219i
\(250\) 0 0
\(251\) −1.93352e13 −1.22502 −0.612509 0.790464i \(-0.709840\pi\)
−0.612509 + 0.790464i \(0.709840\pi\)
\(252\) 0 0
\(253\) −9.01726e12 −0.546905
\(254\) 0 0
\(255\) 1.47326e11 + 2.55176e11i 0.00855674 + 0.0148207i
\(256\) 0 0
\(257\) −9.86761e12 + 1.70912e13i −0.549009 + 0.950912i 0.449333 + 0.893364i \(0.351662\pi\)
−0.998343 + 0.0575480i \(0.981672\pi\)
\(258\) 0 0
\(259\) −1.26484e13 3.91532e12i −0.674354 0.208746i
\(260\) 0 0
\(261\) −1.66245e12 + 2.87945e12i −0.0849622 + 0.147159i
\(262\) 0 0
\(263\) −1.57662e13 2.73078e13i −0.772627 1.33823i −0.936119 0.351685i \(-0.885609\pi\)
0.163492 0.986545i \(-0.447724\pi\)
\(264\) 0 0
\(265\) −7.92330e11 −0.0372438
\(266\) 0 0
\(267\) −8.84054e12 −0.398719
\(268\) 0 0
\(269\) −1.20365e13 2.08477e13i −0.521028 0.902447i −0.999701 0.0244535i \(-0.992215\pi\)
0.478673 0.877993i \(-0.341118\pi\)
\(270\) 0 0
\(271\) −9.29904e12 + 1.61064e13i −0.386462 + 0.669372i −0.991971 0.126467i \(-0.959636\pi\)
0.605509 + 0.795839i \(0.292970\pi\)
\(272\) 0 0
\(273\) −1.97289e13 + 1.82693e13i −0.787425 + 0.729166i
\(274\) 0 0
\(275\) 7.02413e12 1.21661e13i 0.269316 0.466470i
\(276\) 0 0
\(277\) 1.44061e13 + 2.49521e13i 0.530772 + 0.919323i 0.999355 + 0.0359041i \(0.0114311\pi\)
−0.468584 + 0.883419i \(0.655236\pi\)
\(278\) 0 0
\(279\) 9.50169e12 0.336494
\(280\) 0 0
\(281\) 3.61357e13 1.23042 0.615208 0.788365i \(-0.289072\pi\)
0.615208 + 0.788365i \(0.289072\pi\)
\(282\) 0 0
\(283\) −7.12729e11 1.23448e12i −0.0233399 0.0404259i 0.854120 0.520077i \(-0.174097\pi\)
−0.877459 + 0.479651i \(0.840763\pi\)
\(284\) 0 0
\(285\) 6.72122e10 1.16415e11i 0.00211739 0.00366743i
\(286\) 0 0
\(287\) −1.37501e13 6.05206e13i −0.416825 1.83465i
\(288\) 0 0
\(289\) −8.52946e12 + 1.47735e13i −0.248876 + 0.431066i
\(290\) 0 0
\(291\) 1.84345e13 + 3.19296e13i 0.517870 + 0.896978i
\(292\) 0 0
\(293\) −3.28945e13 −0.889922 −0.444961 0.895550i \(-0.646782\pi\)
−0.444961 + 0.895550i \(0.646782\pi\)
\(294\) 0 0
\(295\) −2.78186e11 −0.00724961
\(296\) 0 0
\(297\) −2.06536e12 3.57731e12i −0.0518604 0.0898248i
\(298\) 0 0
\(299\) 3.89727e13 6.75027e13i 0.943124 1.63354i
\(300\) 0 0
\(301\) 4.69232e12 + 2.06532e13i 0.109464 + 0.481805i
\(302\) 0 0
\(303\) −1.86748e13 + 3.23456e13i −0.420069 + 0.727581i
\(304\) 0 0
\(305\) 2.63052e11 + 4.55620e11i 0.00570681 + 0.00988448i
\(306\) 0 0
\(307\) 1.20907e13 0.253040 0.126520 0.991964i \(-0.459619\pi\)
0.126520 + 0.991964i \(0.459619\pi\)
\(308\) 0 0
\(309\) 4.31720e13 0.871827
\(310\) 0 0
\(311\) −2.99473e12 5.18703e12i −0.0583682 0.101097i 0.835365 0.549696i \(-0.185256\pi\)
−0.893733 + 0.448599i \(0.851923\pi\)
\(312\) 0 0
\(313\) 1.28228e13 2.22098e13i 0.241263 0.417879i −0.719812 0.694169i \(-0.755772\pi\)
0.961074 + 0.276290i \(0.0891052\pi\)
\(314\) 0 0
\(315\) 3.26063e11 3.01938e11i 0.00592370 0.00548542i
\(316\) 0 0
\(317\) −9.63494e12 + 1.66882e13i −0.169053 + 0.292808i −0.938087 0.346399i \(-0.887404\pi\)
0.769034 + 0.639208i \(0.220738\pi\)
\(318\) 0 0
\(319\) −8.10482e12 1.40380e13i −0.137371 0.237933i
\(320\) 0 0
\(321\) 7.12335e11 0.0116656
\(322\) 0 0
\(323\) 2.34179e13 0.370624
\(324\) 0 0
\(325\) 6.07167e13 + 1.05164e14i 0.928858 + 1.60883i
\(326\) 0 0
\(327\) 3.34425e12 5.79240e12i 0.0494636 0.0856734i
\(328\) 0 0
\(329\) 1.01324e14 + 3.13648e13i 1.44922 + 0.448606i
\(330\) 0 0
\(331\) 3.34435e13 5.79259e13i 0.462656 0.801343i −0.536437 0.843941i \(-0.680230\pi\)
0.999092 + 0.0425974i \(0.0135633\pi\)
\(332\) 0 0
\(333\) 8.79123e12 + 1.52269e13i 0.117654 + 0.203783i
\(334\) 0 0
\(335\) −1.80739e12 −0.0234049
\(336\) 0 0
\(337\) −1.48408e13 −0.185992 −0.0929958 0.995667i \(-0.529644\pi\)
−0.0929958 + 0.995667i \(0.529644\pi\)
\(338\) 0 0
\(339\) 8.86757e12 + 1.53591e13i 0.107574 + 0.186323i
\(340\) 0 0
\(341\) −2.31614e13 + 4.01168e13i −0.272030 + 0.471169i
\(342\) 0 0
\(343\) 5.46154e13 + 6.89068e13i 0.621152 + 0.783690i
\(344\) 0 0
\(345\) −6.44106e11 + 1.11562e12i −0.00709500 + 0.0122889i
\(346\) 0 0
\(347\) −6.92423e13 1.19931e14i −0.738855 1.27974i −0.953011 0.302936i \(-0.902033\pi\)
0.214156 0.976800i \(-0.431300\pi\)
\(348\) 0 0
\(349\) 1.38407e14 1.43093 0.715463 0.698651i \(-0.246216\pi\)
0.715463 + 0.698651i \(0.246216\pi\)
\(350\) 0 0
\(351\) 3.57060e13 0.357728
\(352\) 0 0
\(353\) −5.08428e13 8.80624e13i −0.493707 0.855125i 0.506267 0.862377i \(-0.331025\pi\)
−0.999974 + 0.00725175i \(0.997692\pi\)
\(354\) 0 0
\(355\) −2.19693e12 + 3.80520e12i −0.0206805 + 0.0358197i
\(356\) 0 0
\(357\) 7.39545e13 + 2.28926e13i 0.674978 + 0.208939i
\(358\) 0 0
\(359\) 4.26384e13 7.38518e13i 0.377382 0.653645i −0.613299 0.789851i \(-0.710158\pi\)
0.990680 + 0.136207i \(0.0434911\pi\)
\(360\) 0 0
\(361\) 5.29033e13 + 9.16313e13i 0.454144 + 0.786600i
\(362\) 0 0
\(363\) −4.91925e13 −0.409650
\(364\) 0 0
\(365\) −8.29458e10 −0.000670168
\(366\) 0 0
\(367\) −3.58256e13 6.20517e13i −0.280886 0.486509i 0.690717 0.723125i \(-0.257295\pi\)
−0.971603 + 0.236616i \(0.923962\pi\)
\(368\) 0 0
\(369\) −4.12074e13 + 7.13734e13i −0.313567 + 0.543114i
\(370\) 0 0
\(371\) −1.52745e14 + 1.41444e14i −1.12826 + 1.04479i
\(372\) 0 0
\(373\) −9.39443e13 + 1.62716e14i −0.673708 + 1.16690i 0.303137 + 0.952947i \(0.401966\pi\)
−0.976845 + 0.213950i \(0.931367\pi\)
\(374\) 0 0
\(375\) −2.00753e12 3.47715e12i −0.0139795 0.0242131i
\(376\) 0 0
\(377\) 1.40116e14 0.947570
\(378\) 0 0
\(379\) 1.29326e14 0.849516 0.424758 0.905307i \(-0.360359\pi\)
0.424758 + 0.905307i \(0.360359\pi\)
\(380\) 0 0
\(381\) 5.87732e13 + 1.01798e14i 0.375052 + 0.649610i
\(382\) 0 0
\(383\) 1.21897e14 2.11132e14i 0.755790 1.30907i −0.189191 0.981940i \(-0.560587\pi\)
0.944981 0.327126i \(-0.106080\pi\)
\(384\) 0 0
\(385\) 4.79990e11 + 2.11267e12i 0.00289200 + 0.0127291i
\(386\) 0 0
\(387\) 1.40624e13 2.43568e13i 0.0823472 0.142630i
\(388\) 0 0
\(389\) 1.06560e14 + 1.84568e14i 0.606559 + 1.05059i 0.991803 + 0.127776i \(0.0407839\pi\)
−0.385244 + 0.922815i \(0.625883\pi\)
\(390\) 0 0
\(391\) −2.24417e14 −1.24189
\(392\) 0 0
\(393\) −8.98422e13 −0.483416
\(394\) 0 0
\(395\) 7.80367e11 + 1.35163e12i 0.00408333 + 0.00707254i
\(396\) 0 0
\(397\) −3.57142e13 + 6.18588e13i −0.181758 + 0.314814i −0.942479 0.334265i \(-0.891512\pi\)
0.760721 + 0.649078i \(0.224845\pi\)
\(398\) 0 0
\(399\) −7.82484e12 3.44409e13i −0.0387369 0.170500i
\(400\) 0 0
\(401\) −3.73100e13 + 6.46228e13i −0.179693 + 0.311237i −0.941775 0.336243i \(-0.890844\pi\)
0.762082 + 0.647480i \(0.224177\pi\)
\(402\) 0 0
\(403\) −2.00208e14 3.46770e14i −0.938217 1.62504i
\(404\) 0 0
\(405\) −5.90118e11 −0.00269114
\(406\) 0 0
\(407\) −8.57184e13 −0.380457
\(408\) 0 0
\(409\) −7.84760e13 1.35924e14i −0.339046 0.587245i 0.645207 0.764007i \(-0.276771\pi\)
−0.984254 + 0.176762i \(0.943438\pi\)
\(410\) 0 0
\(411\) 7.50807e13 1.30044e14i 0.315790 0.546964i
\(412\) 0 0
\(413\) −5.36287e13 + 4.96609e13i −0.219620 + 0.203371i
\(414\) 0 0
\(415\) −2.94700e12 + 5.10436e12i −0.0117521 + 0.0203553i
\(416\) 0 0
\(417\) −1.04190e14 1.80463e14i −0.404649 0.700873i
\(418\) 0 0
\(419\) −5.96915e13 −0.225806 −0.112903 0.993606i \(-0.536015\pi\)
−0.112903 + 0.993606i \(0.536015\pi\)
\(420\) 0 0
\(421\) 2.52328e14 0.929853 0.464927 0.885349i \(-0.346081\pi\)
0.464927 + 0.885349i \(0.346081\pi\)
\(422\) 0 0
\(423\) −7.04247e13 1.21979e14i −0.252844 0.437939i
\(424\) 0 0
\(425\) 1.74813e14 3.02785e14i 0.611555 1.05924i
\(426\) 0 0
\(427\) 1.32047e14 + 4.08751e13i 0.450168 + 0.139349i
\(428\) 0 0
\(429\) −8.70375e13 + 1.50753e14i −0.289195 + 0.500901i
\(430\) 0 0
\(431\) 6.39033e13 + 1.10684e14i 0.206966 + 0.358475i 0.950757 0.309937i \(-0.100308\pi\)
−0.743792 + 0.668412i \(0.766974\pi\)
\(432\) 0 0
\(433\) −3.97113e14 −1.25381 −0.626903 0.779098i \(-0.715678\pi\)
−0.626903 + 0.779098i \(0.715678\pi\)
\(434\) 0 0
\(435\) −2.31572e12 −0.00712845
\(436\) 0 0
\(437\) 5.11912e13 + 8.86658e13i 0.153655 + 0.266139i
\(438\) 0 0
\(439\) 1.50834e14 2.61252e14i 0.441513 0.764723i −0.556289 0.830989i \(-0.687775\pi\)
0.997802 + 0.0662662i \(0.0211086\pi\)
\(440\) 0 0
\(441\) 8.95724e12 1.16415e14i 0.0255718 0.332351i
\(442\) 0 0
\(443\) −2.51908e14 + 4.36317e14i −0.701489 + 1.21502i 0.266454 + 0.963848i \(0.414148\pi\)
−0.967944 + 0.251168i \(0.919185\pi\)
\(444\) 0 0
\(445\) −3.07862e12 5.33232e12i −0.00836327 0.0144856i
\(446\) 0 0
\(447\) −1.62110e14 −0.429655
\(448\) 0 0
\(449\) −4.47372e14 −1.15695 −0.578474 0.815701i \(-0.696351\pi\)
−0.578474 + 0.815701i \(0.696351\pi\)
\(450\) 0 0
\(451\) −2.00896e14 3.47961e14i −0.506990 0.878133i
\(452\) 0 0
\(453\) −6.36054e13 + 1.10168e14i −0.156658 + 0.271340i
\(454\) 0 0
\(455\) −1.78898e13 5.53779e12i −0.0430074 0.0133129i
\(456\) 0 0
\(457\) −2.59567e14 + 4.49583e14i −0.609131 + 1.05505i 0.382253 + 0.924058i \(0.375148\pi\)
−0.991384 + 0.130988i \(0.958185\pi\)
\(458\) 0 0
\(459\) −5.14018e13 8.90304e13i −0.117763 0.203971i
\(460\) 0 0
\(461\) −6.55113e14 −1.46542 −0.732709 0.680543i \(-0.761744\pi\)
−0.732709 + 0.680543i \(0.761744\pi\)
\(462\) 0 0
\(463\) −1.51172e13 −0.0330199 −0.0165099 0.999864i \(-0.505256\pi\)
−0.0165099 + 0.999864i \(0.505256\pi\)
\(464\) 0 0
\(465\) 3.30886e12 + 5.73111e12i 0.00705809 + 0.0122250i
\(466\) 0 0
\(467\) −1.12796e14 + 1.95369e14i −0.234992 + 0.407017i −0.959270 0.282490i \(-0.908840\pi\)
0.724279 + 0.689507i \(0.242173\pi\)
\(468\) 0 0
\(469\) −3.48428e14 + 3.22649e14i −0.709027 + 0.656569i
\(470\) 0 0
\(471\) 2.11156e14 3.65733e14i 0.419748 0.727024i
\(472\) 0 0
\(473\) 6.85573e13 + 1.18745e14i 0.133143 + 0.230610i
\(474\) 0 0
\(475\) −1.59505e14 −0.302662
\(476\) 0 0
\(477\) 2.76443e14 0.512571
\(478\) 0 0
\(479\) −1.28941e14 2.23332e14i −0.233639 0.404674i 0.725237 0.688499i \(-0.241730\pi\)
−0.958876 + 0.283825i \(0.908397\pi\)
\(480\) 0 0
\(481\) 3.70476e14 6.41683e14i 0.656088 1.13638i
\(482\) 0 0
\(483\) 7.49869e13 + 3.30053e14i 0.129800 + 0.571314i
\(484\) 0 0
\(485\) −1.28393e13 + 2.22382e13i −0.0217250 + 0.0376289i
\(486\) 0 0
\(487\) −1.49469e14 2.58887e14i −0.247253 0.428254i 0.715510 0.698603i \(-0.246194\pi\)
−0.962763 + 0.270349i \(0.912861\pi\)
\(488\) 0 0
\(489\) 3.14888e14 0.509281
\(490\) 0 0
\(491\) 7.76606e14 1.22815 0.614076 0.789247i \(-0.289529\pi\)
0.614076 + 0.789247i \(0.289529\pi\)
\(492\) 0 0
\(493\) −2.01709e14 3.49370e14i −0.311937 0.540291i
\(494\) 0 0
\(495\) 1.43848e12 2.49152e12i 0.00217558 0.00376821i
\(496\) 0 0
\(497\) 2.55767e14 + 1.12575e15i 0.378342 + 1.66527i
\(498\) 0 0
\(499\) 6.88471e13 1.19247e14i 0.0996169 0.172541i −0.811909 0.583784i \(-0.801572\pi\)
0.911526 + 0.411242i \(0.134905\pi\)
\(500\) 0 0
\(501\) −3.09097e14 5.35372e14i −0.437510 0.757789i
\(502\) 0 0
\(503\) 7.47083e14 1.03453 0.517267 0.855824i \(-0.326949\pi\)
0.517267 + 0.855824i \(0.326949\pi\)
\(504\) 0 0
\(505\) −2.60131e13 −0.0352444
\(506\) 0 0
\(507\) −5.34606e14 9.25964e14i −0.708745 1.22758i
\(508\) 0 0
\(509\) −7.15602e14 + 1.23946e15i −0.928376 + 1.60799i −0.142337 + 0.989818i \(0.545462\pi\)
−0.786039 + 0.618176i \(0.787872\pi\)
\(510\) 0 0
\(511\) −1.59903e13 + 1.48072e13i −0.0203021 + 0.0188000i
\(512\) 0 0
\(513\) −2.34502e13 + 4.06170e13i −0.0291408 + 0.0504733i
\(514\) 0 0
\(515\) 1.50342e13 + 2.60399e13i 0.0182869 + 0.0316738i
\(516\) 0 0
\(517\) 6.86673e14 0.817621
\(518\) 0 0
\(519\) −3.27978e14 −0.382317
\(520\) 0 0
\(521\) 1.34528e14 + 2.33009e14i 0.153534 + 0.265929i 0.932524 0.361107i \(-0.117601\pi\)
−0.778990 + 0.627036i \(0.784268\pi\)
\(522\) 0 0
\(523\) 5.20397e13 9.01353e13i 0.0581534 0.100725i −0.835483 0.549516i \(-0.814812\pi\)
0.893637 + 0.448791i \(0.148145\pi\)
\(524\) 0 0
\(525\) −5.03722e14 1.55927e14i −0.551207 0.170626i
\(526\) 0 0
\(527\) −5.76431e14 + 9.98408e14i −0.617716 + 1.06992i
\(528\) 0 0
\(529\) −1.41696e13 2.45424e13i −0.0148714 0.0257580i
\(530\) 0 0
\(531\) 9.70588e13 0.0997734
\(532\) 0 0
\(533\) 3.47309e15 3.49717
\(534\) 0 0
\(535\) 2.48063e11 + 4.29657e11i 0.000244690 + 0.000423815i
\(536\) 0 0
\(537\) 3.97510e14 6.88508e14i 0.384140 0.665350i
\(538\) 0 0
\(539\) 4.69678e14 + 3.21593e14i 0.444695 + 0.304487i
\(540\) 0 0
\(541\) 4.91782e14 8.51791e14i 0.456234 0.790220i −0.542524 0.840040i \(-0.682531\pi\)
0.998758 + 0.0498200i \(0.0158648\pi\)
\(542\) 0 0
\(543\) 5.07496e14 + 8.79009e14i 0.461353 + 0.799087i
\(544\) 0 0
\(545\) 4.65839e12 0.00415006
\(546\) 0 0
\(547\) 1.61612e15 1.41105 0.705527 0.708683i \(-0.250710\pi\)
0.705527 + 0.708683i \(0.250710\pi\)
\(548\) 0 0
\(549\) −9.17786e13 1.58965e14i −0.0785404 0.136036i
\(550\) 0 0
\(551\) −9.20225e13 + 1.59388e14i −0.0771899 + 0.133697i
\(552\) 0 0
\(553\) 3.91728e14 + 1.21259e14i 0.322104 + 0.0997073i
\(554\) 0 0
\(555\) −6.12290e12 + 1.06052e13i −0.00493566 + 0.00854882i
\(556\) 0 0
\(557\) −1.67288e14 2.89751e14i −0.132209 0.228992i 0.792319 0.610107i \(-0.208874\pi\)
−0.924528 + 0.381115i \(0.875540\pi\)
\(558\) 0 0
\(559\) −1.18522e15 −0.918405
\(560\) 0 0
\(561\) 5.01190e14 0.380809
\(562\) 0 0
\(563\) −1.53096e14 2.65170e14i −0.114069 0.197573i 0.803338 0.595523i \(-0.203055\pi\)
−0.917407 + 0.397950i \(0.869722\pi\)
\(564\) 0 0
\(565\) −6.17607e12 + 1.06973e13i −0.00451280 + 0.00781639i
\(566\) 0 0
\(567\) −1.13763e14 + 1.05346e14i −0.0815254 + 0.0754936i
\(568\) 0 0
\(569\) 9.44055e13 1.63515e14i 0.0663559 0.114932i −0.830939 0.556364i \(-0.812196\pi\)
0.897295 + 0.441432i \(0.145529\pi\)
\(570\) 0 0
\(571\) 7.11167e14 + 1.23178e15i 0.490313 + 0.849247i 0.999938 0.0111499i \(-0.00354920\pi\)
−0.509625 + 0.860397i \(0.670216\pi\)
\(572\) 0 0
\(573\) −7.09159e14 −0.479615
\(574\) 0 0
\(575\) 1.52856e15 1.01417
\(576\) 0 0
\(577\) −7.83726e14 1.35745e15i −0.510149 0.883605i −0.999931 0.0117595i \(-0.996257\pi\)
0.489781 0.871845i \(-0.337077\pi\)
\(578\) 0 0
\(579\) 6.72741e14 1.16522e15i 0.429651 0.744178i
\(580\) 0 0
\(581\) 3.43090e14 + 1.51011e15i 0.215001 + 0.946321i
\(582\) 0 0
\(583\) −6.73860e14 + 1.16716e15i −0.414374 + 0.717717i
\(584\) 0 0
\(585\) 1.24342e13 + 2.15367e13i 0.00750346 + 0.0129964i
\(586\) 0 0
\(587\) −8.80723e14 −0.521591 −0.260795 0.965394i \(-0.583985\pi\)
−0.260795 + 0.965394i \(0.583985\pi\)
\(588\) 0 0
\(589\) 5.25952e14 0.305712
\(590\) 0 0
\(591\) −3.99185e13 6.91408e13i −0.0227742 0.0394460i
\(592\) 0 0
\(593\) 5.84464e14 1.01232e15i 0.327308 0.566915i −0.654668 0.755916i \(-0.727192\pi\)
0.981977 + 0.189001i \(0.0605251\pi\)
\(594\) 0 0
\(595\) 1.19458e13 + 5.25791e13i 0.00656706 + 0.0289048i
\(596\) 0 0
\(597\) −3.43426e14 + 5.94832e14i −0.185342 + 0.321023i
\(598\) 0 0
\(599\) 3.09149e14 + 5.35461e14i 0.163802 + 0.283714i 0.936229 0.351390i \(-0.114291\pi\)
−0.772427 + 0.635104i \(0.780957\pi\)
\(600\) 0 0
\(601\) 1.60739e15 0.836202 0.418101 0.908401i \(-0.362696\pi\)
0.418101 + 0.908401i \(0.362696\pi\)
\(602\) 0 0
\(603\) 6.30596e14 0.322111
\(604\) 0 0
\(605\) −1.71308e13 2.96713e13i −0.00859255 0.0148827i
\(606\) 0 0
\(607\) 7.44943e14 1.29028e15i 0.366932 0.635544i −0.622152 0.782896i \(-0.713742\pi\)
0.989084 + 0.147352i \(0.0470749\pi\)
\(608\) 0 0
\(609\) −4.46423e14 + 4.13394e14i −0.215949 + 0.199972i
\(610\) 0 0
\(611\) −2.96780e15 + 5.14039e15i −1.40997 + 2.44213i
\(612\) 0 0
\(613\) −3.20198e14 5.54599e14i −0.149412 0.258790i 0.781598 0.623782i \(-0.214405\pi\)
−0.931010 + 0.364993i \(0.881071\pi\)
\(614\) 0 0
\(615\) −5.74002e13 −0.0263087
\(616\) 0 0
\(617\) 2.78051e14 0.125186 0.0625932 0.998039i \(-0.480063\pi\)
0.0625932 + 0.998039i \(0.480063\pi\)
\(618\) 0 0
\(619\) −1.25743e15 2.17793e15i −0.556140 0.963263i −0.997814 0.0660874i \(-0.978948\pi\)
0.441674 0.897176i \(-0.354385\pi\)
\(620\) 0 0
\(621\) 2.24728e14 3.89240e14i 0.0976456 0.169127i
\(622\) 0 0
\(623\) −1.54540e15 4.78379e14i −0.659717 0.204215i
\(624\) 0 0
\(625\) −1.19000e15 + 2.06113e15i −0.499120 + 0.864502i
\(626\) 0 0
\(627\) −1.14325e14 1.98017e14i −0.0471162 0.0816076i
\(628\) 0 0
\(629\) −2.13332e15 −0.863928
\(630\) 0 0
\(631\) 3.79204e15 1.50908 0.754539 0.656256i \(-0.227861\pi\)
0.754539 + 0.656256i \(0.227861\pi\)
\(632\) 0 0
\(633\) −5.58861e14 9.67976e14i −0.218567 0.378568i
\(634\) 0 0
\(635\) −4.09342e13 + 7.09002e13i −0.0157337 + 0.0272516i
\(636\) 0 0
\(637\) −4.43738e15 + 2.12605e15i −1.67633 + 0.803170i
\(638\) 0 0
\(639\) 7.66507e14 1.32763e15i 0.284617 0.492972i
\(640\) 0 0
\(641\) −9.30652e14 1.61194e15i −0.339679 0.588341i 0.644694 0.764441i \(-0.276985\pi\)
−0.984372 + 0.176100i \(0.943652\pi\)
\(642\) 0 0
\(643\) −2.46490e15 −0.884380 −0.442190 0.896921i \(-0.645798\pi\)
−0.442190 + 0.896921i \(0.645798\pi\)
\(644\) 0 0
\(645\) 1.95883e13 0.00690905
\(646\) 0 0
\(647\) −9.99898e14 1.73187e15i −0.346723 0.600541i 0.638943 0.769254i \(-0.279372\pi\)
−0.985665 + 0.168713i \(0.946039\pi\)
\(648\) 0 0
\(649\) −2.36592e14 + 4.09789e14i −0.0806591 + 0.139706i
\(650\) 0 0
\(651\) 1.66098e15 + 5.14156e14i 0.556761 + 0.172345i
\(652\) 0 0
\(653\) 2.80003e15 4.84979e15i 0.922869 1.59846i 0.127915 0.991785i \(-0.459172\pi\)
0.794954 0.606670i \(-0.207495\pi\)
\(654\) 0 0
\(655\) −3.12866e13 5.41899e13i −0.0101398 0.0175627i
\(656\) 0 0
\(657\) 2.89397e13 0.00922325
\(658\) 0 0
\(659\) −1.96747e14 −0.0616649 −0.0308324 0.999525i \(-0.509816\pi\)
−0.0308324 + 0.999525i \(0.509816\pi\)
\(660\) 0 0
\(661\) −2.71632e15 4.70481e15i −0.837286 1.45022i −0.892156 0.451728i \(-0.850808\pi\)
0.0548702 0.998493i \(-0.482525\pi\)
\(662\) 0 0
\(663\) −2.16615e15 + 3.75188e15i −0.656695 + 1.13743i
\(664\) 0 0
\(665\) 1.80487e13 1.67134e13i 0.00538180 0.00498362i
\(666\) 0 0
\(667\) 8.81868e14 1.52744e15i 0.258649 0.447994i
\(668\) 0 0
\(669\) −6.22789e14 1.07870e15i −0.179679 0.311213i
\(670\) 0 0
\(671\) 8.94882e14 0.253976
\(672\) 0 0
\(673\) 3.16858e15 0.884672 0.442336 0.896849i \(-0.354150\pi\)
0.442336 + 0.896849i \(0.354150\pi\)
\(674\) 0 0
\(675\) 3.50110e14 + 6.06408e14i 0.0961686 + 0.166569i
\(676\) 0 0
\(677\) 1.05566e15 1.82845e15i 0.285289 0.494135i −0.687390 0.726288i \(-0.741244\pi\)
0.972679 + 0.232154i \(0.0745772\pi\)
\(678\) 0 0
\(679\) 1.49475e15 + 6.57910e15i 0.397451 + 1.74937i
\(680\) 0 0
\(681\) −1.87366e15 + 3.24528e15i −0.490210 + 0.849069i
\(682\) 0 0
\(683\) −2.33152e14 4.03831e14i −0.0600240 0.103965i 0.834452 0.551081i \(-0.185784\pi\)
−0.894476 + 0.447116i \(0.852451\pi\)
\(684\) 0 0
\(685\) 1.04584e14 0.0264952
\(686\) 0 0
\(687\) 8.19499e14 0.204308
\(688\) 0 0
\(689\) −5.82486e15 1.00889e16i −1.42916 2.47537i
\(690\) 0 0
\(691\) −2.05478e15 + 3.55899e15i −0.496177 + 0.859404i −0.999990 0.00440848i \(-0.998597\pi\)
0.503813 + 0.863813i \(0.331930\pi\)
\(692\) 0 0
\(693\) −1.67468e14 7.37106e14i −0.0398014 0.175185i
\(694\) 0 0
\(695\) 7.25662e13 1.25688e14i 0.0169753 0.0294021i
\(696\) 0 0
\(697\) −4.99980e15 8.65990e15i −1.15126 1.99403i
\(698\) 0 0
\(699\) −1.71529e15 −0.388788
\(700\) 0 0
\(701\) 1.49697e15 0.334013 0.167006 0.985956i \(-0.446590\pi\)
0.167006 + 0.985956i \(0.446590\pi\)
\(702\) 0 0
\(703\) 4.86626e14 + 8.42861e14i 0.106891 + 0.185141i
\(704\) 0 0
\(705\) 4.90493e13 8.49558e13i 0.0106070 0.0183719i
\(706\) 0 0
\(707\) −5.01480e15 + 4.64377e15i −1.06769 + 0.988698i
\(708\) 0 0
\(709\) −4.09130e15 + 7.08633e15i −0.857643 + 1.48548i 0.0165280 + 0.999863i \(0.494739\pi\)
−0.874171 + 0.485618i \(0.838595\pi\)
\(710\) 0 0
\(711\) −2.72269e14 4.71583e14i −0.0561972 0.0973364i
\(712\) 0 0
\(713\) −5.04029e15 −1.02439
\(714\) 0 0
\(715\) −1.21239e14 −0.0242639
\(716\) 0 0
\(717\) 8.97143e14 + 1.55390e15i 0.176810 + 0.306244i
\(718\) 0 0
\(719\) 4.14413e15 7.17784e15i 0.804312 1.39311i −0.112443 0.993658i \(-0.535868\pi\)
0.916755 0.399451i \(-0.130799\pi\)
\(720\) 0 0
\(721\) 7.54684e15 + 2.33612e15i 1.44252 + 0.446531i
\(722\) 0 0
\(723\) −8.14450e14 + 1.41067e15i −0.153322 + 0.265561i
\(724\) 0 0
\(725\) 1.37389e15 + 2.37964e15i 0.254737 + 0.441218i
\(726\) 0 0
\(727\) −6.11784e15 −1.11727 −0.558636 0.829413i \(-0.688675\pi\)
−0.558636 + 0.829413i \(0.688675\pi\)
\(728\) 0 0
\(729\) 2.05891e14 0.0370370
\(730\) 0 0
\(731\) 1.70622e15 + 2.95526e15i 0.302336 + 0.523662i
\(732\) 0 0
\(733\) 1.89724e15 3.28612e15i 0.331170 0.573603i −0.651571 0.758587i \(-0.725890\pi\)
0.982742 + 0.184984i \(0.0592233\pi\)
\(734\) 0 0
\(735\) 7.33371e13 3.51376e13i 0.0126108 0.00604215i
\(736\) 0 0
\(737\) −1.53715e15 + 2.66242e15i −0.260402 + 0.451030i
\(738\) 0 0
\(739\) 1.52876e15 + 2.64789e15i 0.255150 + 0.441933i 0.964936 0.262484i \(-0.0845419\pi\)
−0.709786 + 0.704417i \(0.751209\pi\)
\(740\) 0 0
\(741\) 1.97646e15 0.325003
\(742\) 0 0
\(743\) 2.20470e15 0.357199 0.178600 0.983922i \(-0.442843\pi\)
0.178600 + 0.983922i \(0.442843\pi\)
\(744\) 0 0
\(745\) −5.64532e13 9.77797e13i −0.00901216 0.0156095i
\(746\) 0 0
\(747\) 1.02820e15 1.78090e15i 0.161740 0.280141i
\(748\) 0 0
\(749\) 1.24522e14 + 3.85459e13i 0.0193018 + 0.00597486i
\(750\) 0 0
\(751\) −1.87510e15 + 3.24777e15i −0.286421 + 0.496096i −0.972953 0.231004i \(-0.925799\pi\)
0.686532 + 0.727100i \(0.259132\pi\)
\(752\) 0 0
\(753\) 2.34922e15 + 4.06897e15i 0.353632 + 0.612509i
\(754\) 0 0
\(755\) −8.85995e13 −0.0131439
\(756\) 0 0
\(757\) 3.28803e15 0.480738 0.240369 0.970682i \(-0.422731\pi\)
0.240369 + 0.970682i \(0.422731\pi\)
\(758\) 0 0
\(759\) 1.09560e15 + 1.89763e15i 0.157878 + 0.273452i
\(760\) 0 0
\(761\) 5.66595e15 9.81371e15i 0.804742 1.39385i −0.111722 0.993739i \(-0.535637\pi\)
0.916465 0.400115i \(-0.131030\pi\)
\(762\) 0 0
\(763\) 8.98042e14 8.31599e14i 0.125722 0.116420i
\(764\) 0 0
\(765\) 3.58002e13 6.20078e13i 0.00494023 0.00855674i
\(766\) 0 0
\(767\) −2.04510e15 3.54222e15i −0.278189 0.481838i
\(768\) 0 0
\(769\) −1.28420e15 −0.172201 −0.0861006 0.996286i \(-0.527441\pi\)
−0.0861006 + 0.996286i \(0.527441\pi\)
\(770\) 0 0
\(771\) 4.79566e15 0.633941
\(772\) 0 0
\(773\) −6.84876e15 1.18624e16i −0.892534 1.54591i −0.836827 0.547467i \(-0.815592\pi\)
−0.0557073 0.998447i \(-0.517741\pi\)
\(774\) 0 0
\(775\) 3.92621e15 6.80040e15i 0.504445 0.873725i
\(776\)