Properties

Label 84.12.i.b.25.5
Level $84$
Weight $12$
Character 84.25
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 25.5
Root \(-438.744 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 84.25
Dual form 84.12.i.b.37.5

$q$-expansion

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

Character values

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

\(n\) \(29\) \(43\) \(73\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 0.872017 0.489476i \(-0.162812\pi\)
−0.859907 + 0.510451i \(0.829478\pi\)
\(6\) 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 −0.968726 0.248132i \(-0.920183\pi\)
0.699252 + 0.714875i \(0.253517\pi\)
\(12\) 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 0.379004 + 0.925395i \(0.376267\pi\)
−0.990918 + 0.134470i \(0.957067\pi\)
\(18\) 0 0
\(19\) −1.63429e6 2.83067e6i −0.151420 0.262267i 0.780330 0.625368i \(-0.215051\pi\)
−0.931750 + 0.363101i \(0.881718\pi\)
\(20\) 0 0
\(21\) −7.92832e6 7.34173e6i −0.423618 0.392276i
\(22\) 0 0
\(23\) 1.56616e7 + 2.71268e7i 0.507381 + 0.878810i 0.999963 + 0.00854416i \(0.00271972\pi\)
−0.492582 + 0.870266i \(0.663947\pi\)
\(24\) 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 0.495243 + 0.868754i \(0.335079\pi\)
−0.999985 + 0.00548373i \(0.998254\pi\)
\(32\) 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 0.986767 0.162145i \(-0.0518413\pi\)
−0.633805 + 0.773493i \(0.718508\pi\)
\(38\) 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 −0.943599 0.331091i \(-0.892583\pi\)
0.185066 0.982726i \(-0.440750\pi\)
\(48\) 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 0.169327 + 0.985560i \(0.445841\pi\)
−0.938183 + 0.346139i \(0.887493\pi\)
\(54\) 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 −0.931102 0.364759i \(-0.881151\pi\)
0.781442 + 0.623978i \(0.214485\pi\)
\(60\) 0 0
\(61\) −1.55428e9 2.69209e9i −0.235621 0.408108i 0.723832 0.689977i \(-0.242379\pi\)
−0.959453 + 0.281868i \(0.909046\pi\)
\(62\) 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 −0.999813 0.0193290i \(-0.993847\pi\)
0.516646 + 0.856199i \(0.327180\pi\)
\(68\) 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 −0.872860 0.487971i \(-0.837737\pi\)
0.859025 + 0.511933i \(0.171071\pi\)
\(74\) 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 0.769333 0.638848i \(-0.220589\pi\)
−0.937925 + 0.346838i \(0.887255\pi\)
\(80\) 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 0.985408 0.170207i \(-0.0544437\pi\)
−0.640108 + 0.768285i \(0.721110\pi\)
\(90\) 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 0.230322 + 0.973114i \(0.426022\pi\)
−0.957903 + 0.287092i \(0.907311\pi\)
\(102\) 0 0
\(103\) −8.88312e10 1.53860e11i −0.755024 1.30774i −0.945362 0.326022i \(-0.894292\pi\)
0.190338 0.981719i \(-0.439042\pi\)
\(104\) 0 0
\(105\) 4.05164e8 1.78332e9i 0.00309806 0.0136361i
\(106\) 0 0
\(107\) −1.46571e9 2.53868e9i −0.0101027 0.0174984i 0.860930 0.508724i \(-0.169883\pi\)
−0.871033 + 0.491225i \(0.836549\pi\)
\(108\) 0 0
\(109\) 1.37623e10 2.38371e10i 0.0856734 0.148391i −0.820005 0.572357i \(-0.806029\pi\)
0.905678 + 0.423966i \(0.139362\pi\)
\(110\) 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 0.995804 0.0915115i \(-0.0291698\pi\)
−0.577153 + 0.816636i \(0.695836\pi\)
\(132\) 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 −0.451516 0.892263i \(-0.649117\pi\)
0.998480 0.0551072i \(-0.0175501\pi\)
\(138\) 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 0.989887 0.141857i \(-0.0453073\pi\)
−0.617795 + 0.786339i \(0.711974\pi\)
\(150\) 0 0
\(151\) −2.61750e11 + 4.53365e11i −0.271340 + 0.469975i −0.969205 0.246254i \(-0.920800\pi\)
0.697865 + 0.716229i \(0.254134\pi\)
\(152\) 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 −0.231111 0.972927i \(-0.574236\pi\)
0.958135 0.286316i \(-0.0924307\pi\)
\(158\) 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 0.556717 0.830702i \(-0.312061\pi\)
−0.997768 + 0.0667802i \(0.978727\pi\)
\(164\) 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 0.982727 0.185061i \(-0.0592482\pi\)
−0.651631 + 0.758536i \(0.725915\pi\)
\(174\) 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 −0.313840 0.949476i \(-0.601615\pi\)
0.979190 0.202945i \(-0.0650512\pi\)
\(180\) 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 0.995466 0.0951173i \(-0.0303226\pi\)
−0.580107 + 0.814540i \(0.696989\pi\)
\(192\) 0 0
\(193\) 2.76848e12 4.79515e12i 0.744178 1.28895i −0.206400 0.978468i \(-0.566175\pi\)
0.950578 0.310486i \(-0.100492\pi\)
\(194\) 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 −0.980699 0.195522i \(-0.937360\pi\)
0.659677 + 0.751549i \(0.270693\pi\)
\(200\) 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 0.0329705 + 0.999456i \(0.489503\pi\)
−0.882040 + 0.471175i \(0.843830\pi\)
\(228\) 0 0
\(229\) −1.68621e12 2.92060e12i −0.176936 0.306463i 0.763893 0.645342i \(-0.223285\pi\)
−0.940830 + 0.338880i \(0.889952\pi\)
\(230\) 0 0
\(231\) 2.97155e12 9.19842e11i 0.297247 0.0920127i
\(232\) 0 0
\(233\) 3.52941e12 + 6.11311e12i 0.336701 + 0.583183i 0.983810 0.179215i \(-0.0573556\pi\)
−0.647109 + 0.762397i \(0.724022\pi\)
\(234\) 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 −0.967710 0.252065i \(-0.918890\pi\)
0.702149 + 0.712030i \(0.252224\pi\)
\(242\) 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 −0.998343 0.0575480i \(-0.981672\pi\)
0.449333 0.893364i \(-0.351662\pi\)
\(258\) 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 0.163492 + 0.986545i \(0.447724\pi\)
−0.936119 + 0.351685i \(0.885609\pi\)
\(264\) 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 0.478673 + 0.877993i \(0.341118\pi\)
−0.999701 + 0.0244535i \(0.992215\pi\)
\(270\) 0 0
\(271\) −9.29904e12 1.61064e13i −0.386462 0.669372i 0.605509 0.795839i \(-0.292970\pi\)
−0.991971 + 0.126467i \(0.959636\pi\)
\(272\) 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 −0.468584 0.883419i \(-0.655236\pi\)
0.999355 0.0359041i \(-0.0114311\pi\)
\(278\) 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 −0.877459 0.479651i \(-0.840763\pi\)
0.854120 + 0.520077i \(0.174097\pi\)
\(284\) 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 −0.893733 0.448599i \(-0.851923\pi\)
0.835365 + 0.549696i \(0.185256\pi\)
\(312\) 0 0
\(313\) 1.28228e13 + 2.22098e13i 0.241263 + 0.417879i 0.961074 0.276290i \(-0.0891052\pi\)
−0.719812 + 0.694169i \(0.755772\pi\)
\(314\) 0 0
\(315\) 3.26063e11 + 3.01938e11i 0.00592370 + 0.00548542i
\(316\) 0 0
\(317\) −9.63494e12 1.66882e13i −0.169053 0.292808i 0.769034 0.639208i \(-0.220738\pi\)
−0.938087 + 0.346399i \(0.887404\pi\)
\(318\) 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 0.999092 0.0425974i \(-0.0135633\pi\)
−0.536437 + 0.843941i \(0.680230\pi\)
\(332\) 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 0.214156 + 0.976800i \(0.431300\pi\)
−0.953011 + 0.302936i \(0.902033\pi\)
\(348\) 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 −0.999974 0.00725175i \(-0.997692\pi\)
0.506267 + 0.862377i \(0.331025\pi\)
\(354\) 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 0.990680 0.136207i \(-0.0434911\pi\)
−0.613299 + 0.789851i \(0.710158\pi\)
\(360\) 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 −0.971603 0.236616i \(-0.923962\pi\)
0.690717 + 0.723125i \(0.257295\pi\)
\(368\) 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 −0.976845 0.213950i \(-0.931367\pi\)
0.303137 0.952947i \(-0.401966\pi\)
\(374\) 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 0.944981 + 0.327126i \(0.106080\pi\)
−0.189191 + 0.981940i \(0.560587\pi\)
\(384\) 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 −0.385244 0.922815i \(-0.625883\pi\)
0.991803 0.127776i \(-0.0407839\pi\)
\(390\) 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 0.760721 0.649078i \(-0.224845\pi\)
−0.942479 + 0.334265i \(0.891512\pi\)
\(398\) 0 0
\(399\) −7.82484e12 + 3.44409e13i −0.0387369 + 0.170500i
\(400\) 0 0
\(401\) −3.73100e13 6.46228e13i −0.179693 0.311237i 0.762082 0.647480i \(-0.224177\pi\)
−0.941775 + 0.336243i \(0.890844\pi\)
\(402\) 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 −0.984254 0.176762i \(-0.943438\pi\)
0.645207 + 0.764007i \(0.276771\pi\)
\(410\) 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 −0.743792 0.668412i \(-0.766974\pi\)
0.950757 + 0.309937i \(0.100308\pi\)
\(432\) 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 0.997802 0.0662662i \(-0.0211086\pi\)
−0.556289 + 0.830989i \(0.687775\pi\)
\(440\) 0 0
\(441\) 8.95724e12 + 1.16415e14i 0.0255718 + 0.332351i
\(442\) 0 0
\(443\) −2.51908e14 4.36317e14i −0.701489 1.21502i −0.967944 0.251168i \(-0.919185\pi\)
0.266454 0.963848i \(-0.414148\pi\)
\(444\) 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 −0.991384 0.130988i \(-0.958185\pi\)
0.382253 0.924058i \(-0.375148\pi\)
\(458\) 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 0.724279 0.689507i \(-0.242173\pi\)
−0.959270 + 0.282490i \(0.908840\pi\)
\(468\) 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 −0.958876 0.283825i \(-0.908397\pi\)
0.725237 + 0.688499i \(0.241730\pi\)
\(480\) 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 −0.962763 0.270349i \(-0.912861\pi\)
0.715510 + 0.698603i \(0.246194\pi\)
\(488\) 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 0.911526 0.411242i \(-0.134905\pi\)
−0.811909 + 0.583784i \(0.801572\pi\)
\(500\) 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 −0.786039 0.618176i \(-0.787872\pi\)
−0.142337 0.989818i \(-0.545462\pi\)
\(510\) 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 −0.778990 0.627036i \(-0.784268\pi\)
0.932524 + 0.361107i \(0.117601\pi\)
\(522\) 0 0
\(523\) 5.20397e13 + 9.01353e13i 0.0581534 + 0.100725i 0.893637 0.448791i \(-0.148145\pi\)
−0.835483 + 0.549516i \(0.814812\pi\)
\(524\) 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 0.998758 0.0498200i \(-0.0158648\pi\)
−0.542524 + 0.840040i \(0.682531\pi\)
\(542\) 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 −0.924528 0.381115i \(-0.875540\pi\)
0.792319 + 0.610107i \(0.208874\pi\)
\(558\) 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 −0.917407 0.397950i \(-0.869722\pi\)
0.803338 + 0.595523i \(0.203055\pi\)
\(564\) 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 0.897295 0.441432i \(-0.145529\pi\)
−0.830939 + 0.556364i \(0.812196\pi\)
\(570\) 0 0
\(571\) 7.11167e14 1.23178e15i 0.490313 0.849247i −0.509625 0.860397i \(-0.670216\pi\)
0.999938 + 0.0111499i \(0.00354920\pi\)
\(572\) 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 0.489781 + 0.871845i \(0.337077\pi\)
−0.999931 + 0.0117595i \(0.996257\pi\)
\(578\) 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 0.981977 0.189001i \(-0.0605251\pi\)
−0.654668 + 0.755916i \(0.727192\pi\)
\(594\) 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 −0.772427 0.635104i \(-0.780957\pi\)
0.936229 + 0.351390i \(0.114291\pi\)
\(600\) 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 0.989084 0.147352i \(-0.0470749\pi\)
−0.622152 + 0.782896i \(0.713742\pi\)
\(608\) 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 −0.931010 0.364993i \(-0.881071\pi\)
0.781598 + 0.623782i \(0.214405\pi\)
\(614\) 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 0.441674 + 0.897176i \(0.354385\pi\)
−0.997814 + 0.0660874i \(0.978948\pi\)
\(620\) 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 −0.984372 0.176100i \(-0.943652\pi\)
0.644694 + 0.764441i \(0.276985\pi\)
\(642\) 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 −0.985665 0.168713i \(-0.946039\pi\)
0.638943 + 0.769254i \(0.279372\pi\)
\(648\) 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 0.794954 + 0.606670i \(0.207495\pi\)
0.127915 + 0.991785i \(0.459172\pi\)
\(654\) 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 0.0548702 + 0.998493i \(0.482525\pi\)
−0.892156 + 0.451728i \(0.850808\pi\)
\(662\) 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 0.972679 0.232154i \(-0.0745772\pi\)
−0.687390 + 0.726288i \(0.741244\pi\)
\(678\) 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 −0.894476 0.447116i \(-0.852451\pi\)
0.834452 + 0.551081i \(0.185784\pi\)
\(684\) 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 0.503813 0.863813i \(-0.331930\pi\)
−0.999990 + 0.00440848i \(0.998597\pi\)
\(692\) 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 −0.874171 0.485618i \(-0.838595\pi\)
0.0165280 0.999863i \(-0.494739\pi\)
\(710\) 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 0.916755 + 0.399451i \(0.130799\pi\)
−0.112443 + 0.993658i \(0.535868\pi\)
\(720\) 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 0.982742 0.184984i \(-0.0592233\pi\)
−0.651571 + 0.758587i \(0.725890\pi\)
\(734\) 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 −0.709786 0.704417i \(-0.751209\pi\)
0.964936 + 0.262484i \(0.0845419\pi\)
\(740\) 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 0.686532 0.727100i \(-0.259132\pi\)
−0.972953 + 0.231004i \(0.925799\pi\)
\(752\) 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 0.916465 + 0.400115i \(0.131030\pi\)
−0.111722 + 0.993739i \(0.535637\pi\)
\(762\) 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 −0.0557073 + 0.998447i \(0.517741\pi\)
−0.836827 + 0.547467i \(0.815592\pi\)
\(774\) 0 0
\(775\) 3.92621e15 + 6.80040e15i 0.504445 + 0.873725i
\(776\) 0