Properties

Label 84.12.i.b.25.2
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 25.2
Root \(10810.2 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 84.25
Dual form 84.12.i.b.37.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-121.500 + 210.444i) q^{3} +(-5539.86 - 9595.32i) q^{5} +(-32020.8 + 30854.4i) q^{7} +(-29524.5 - 51137.9i) q^{9} +O(q^{10})\) \(q+(-121.500 + 210.444i) q^{3} +(-5539.86 - 9595.32i) q^{5} +(-32020.8 + 30854.4i) q^{7} +(-29524.5 - 51137.9i) q^{9} +(451860. - 782645. i) q^{11} -761355. q^{13} +2.69237e6 q^{15} +(2.39149e6 - 4.14219e6i) q^{17} +(-2.25438e6 - 3.90470e6i) q^{19} +(-2.60260e6 - 1.04874e7i) q^{21} +(-2.38885e7 - 4.13761e7i) q^{23} +(-3.69661e7 + 6.40271e7i) q^{25} +1.43489e7 q^{27} +1.65205e8 q^{29} +(-2.95464e7 + 5.11759e7i) q^{31} +(1.09802e8 + 1.90183e8i) q^{33} +(4.73449e8 + 1.36321e8i) q^{35} +(1.08530e8 + 1.87980e8i) q^{37} +(9.25047e7 - 1.60223e8i) q^{39} -5.52269e8 q^{41} -1.04028e9 q^{43} +(-3.27123e8 + 5.66594e8i) q^{45} +(-6.93035e7 - 1.20037e8i) q^{47} +(7.33368e7 - 1.97597e9i) q^{49} +(5.81133e8 + 1.00655e9i) q^{51} +(2.34318e9 - 4.05851e9i) q^{53} -1.00130e10 q^{55} +1.09563e9 q^{57} +(-4.49535e9 + 7.78617e9i) q^{59} +(-1.08443e8 - 1.87828e8i) q^{61} +(2.52323e9 + 7.26517e8i) q^{63} +(4.21780e9 + 7.30545e9i) q^{65} +(-8.64085e9 + 1.49664e10i) q^{67} +1.16098e10 q^{69} -5.28267e9 q^{71} +(-5.55061e9 + 9.61394e9i) q^{73} +(-8.98276e9 - 1.55586e10i) q^{75} +(9.67912e9 + 3.90028e10i) q^{77} +(2.14340e9 + 3.71248e9i) q^{79} +(-1.74339e9 + 3.01964e9i) q^{81} -4.61200e10 q^{83} -5.29942e10 q^{85} +(-2.00724e10 + 3.47665e10i) q^{87} +(-8.53894e9 - 1.47899e10i) q^{89} +(2.43792e10 - 2.34912e10i) q^{91} +(-7.17979e9 - 1.24358e10i) q^{93} +(-2.49779e10 + 4.32631e10i) q^{95} +1.57413e11 q^{97} -5.33638e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 1944q^{3} - 2156q^{5} + 50512q^{7} - 472392q^{9} + O(q^{10}) \) \( 16q - 1944q^{3} - 2156q^{5} + 50512q^{7} - 472392q^{9} - 222796q^{11} + 2703176q^{13} + 1047816q^{15} + 5114600q^{17} + 6910556q^{19} - 18340668q^{21} - 51387712q^{23} - 191456372q^{25} + 229582512q^{27} + 118854616q^{29} + 164659160q^{31} - 54139428q^{33} + 55239344q^{35} + 75658364q^{37} - 328435884q^{39} - 1815568608q^{41} + 10754408q^{43} - 127309644q^{45} - 1034359464q^{47} + 4123496848q^{49} + 1242847800q^{51} - 665159988q^{53} - 1264543896q^{55} - 3358530216q^{57} + 1040514580q^{59} - 14391208024q^{61} + 1474099236q^{63} - 20938150200q^{65} - 33307097284q^{67} + 24974428032q^{69} + 65848902896q^{71} + 17709749204q^{73} - 46523898396q^{75} + 8594484604q^{77} - 26626784032q^{79} - 27894275208q^{81} - 210306955048q^{83} - 25867402032q^{85} - 14440835844q^{87} - 55951560072q^{89} + 66078280292q^{91} + 40012175880q^{93} + 106810047392q^{95} - 156216030712q^{97} + 26311762008q^{99} + O(q^{100}) \)

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
\(5\) −5539.86 9595.32i −0.792801 1.37317i −0.924226 0.381845i \(-0.875289\pi\)
0.131426 0.991326i \(-0.458044\pi\)
\(6\) 0 0
\(7\) −32020.8 + 30854.4i −0.720100 + 0.693870i
\(8\) 0 0
\(9\) −29524.5 51137.9i −0.166667 0.288675i
\(10\) 0 0
\(11\) 451860. 782645.i 0.845949 1.46523i −0.0388451 0.999245i \(-0.512368\pi\)
0.884794 0.465982i \(-0.154299\pi\)
\(12\) 0 0
\(13\) −761355. −0.568721 −0.284360 0.958717i \(-0.591781\pi\)
−0.284360 + 0.958717i \(0.591781\pi\)
\(14\) 0 0
\(15\) 2.69237e6 0.915447
\(16\) 0 0
\(17\) 2.39149e6 4.14219e6i 0.408508 0.707556i −0.586215 0.810155i \(-0.699383\pi\)
0.994723 + 0.102599i \(0.0327160\pi\)
\(18\) 0 0
\(19\) −2.25438e6 3.90470e6i −0.208873 0.361779i 0.742487 0.669861i \(-0.233646\pi\)
−0.951360 + 0.308082i \(0.900313\pi\)
\(20\) 0 0
\(21\) −2.60260e6 1.04874e7i −0.139060 0.560353i
\(22\) 0 0
\(23\) −2.38885e7 4.13761e7i −0.773901 1.34044i −0.935410 0.353565i \(-0.884969\pi\)
0.161509 0.986871i \(-0.448364\pi\)
\(24\) 0 0
\(25\) −3.69661e7 + 6.40271e7i −0.757065 + 1.31128i
\(26\) 0 0
\(27\) 1.43489e7 0.192450
\(28\) 0 0
\(29\) 1.65205e8 1.49567 0.747833 0.663887i \(-0.231095\pi\)
0.747833 + 0.663887i \(0.231095\pi\)
\(30\) 0 0
\(31\) −2.95464e7 + 5.11759e7i −0.185360 + 0.321053i −0.943698 0.330809i \(-0.892678\pi\)
0.758338 + 0.651862i \(0.226012\pi\)
\(32\) 0 0
\(33\) 1.09802e8 + 1.90183e8i 0.488409 + 0.845949i
\(34\) 0 0
\(35\) 4.73449e8 + 1.36321e8i 1.52370 + 0.438720i
\(36\) 0 0
\(37\) 1.08530e8 + 1.87980e8i 0.257301 + 0.445658i 0.965518 0.260337i \(-0.0838335\pi\)
−0.708217 + 0.705995i \(0.750500\pi\)
\(38\) 0 0
\(39\) 9.25047e7 1.60223e8i 0.164176 0.284360i
\(40\) 0 0
\(41\) −5.52269e8 −0.744456 −0.372228 0.928141i \(-0.621406\pi\)
−0.372228 + 0.928141i \(0.621406\pi\)
\(42\) 0 0
\(43\) −1.04028e9 −1.07913 −0.539563 0.841945i \(-0.681411\pi\)
−0.539563 + 0.841945i \(0.681411\pi\)
\(44\) 0 0
\(45\) −3.27123e8 + 5.66594e8i −0.264267 + 0.457724i
\(46\) 0 0
\(47\) −6.93035e7 1.20037e8i −0.0440775 0.0763445i 0.843145 0.537686i \(-0.180702\pi\)
−0.887222 + 0.461342i \(0.847368\pi\)
\(48\) 0 0
\(49\) 7.33368e7 1.97597e9i 0.0370889 0.999312i
\(50\) 0 0
\(51\) 5.81133e8 + 1.00655e9i 0.235852 + 0.408508i
\(52\) 0 0
\(53\) 2.34318e9 4.05851e9i 0.769641 1.33306i −0.168117 0.985767i \(-0.553768\pi\)
0.937758 0.347290i \(-0.112898\pi\)
\(54\) 0 0
\(55\) −1.00130e10 −2.68268
\(56\) 0 0
\(57\) 1.09563e9 0.241186
\(58\) 0 0
\(59\) −4.49535e9 + 7.78617e9i −0.818610 + 1.41787i 0.0880959 + 0.996112i \(0.471922\pi\)
−0.906706 + 0.421763i \(0.861412\pi\)
\(60\) 0 0
\(61\) −1.08443e8 1.87828e8i −0.0164394 0.0284739i 0.857689 0.514169i \(-0.171900\pi\)
−0.874128 + 0.485695i \(0.838566\pi\)
\(62\) 0 0
\(63\) 2.52323e9 + 7.26517e8i 0.320320 + 0.0922301i
\(64\) 0 0
\(65\) 4.21780e9 + 7.30545e9i 0.450882 + 0.780951i
\(66\) 0 0
\(67\) −8.64085e9 + 1.49664e10i −0.781889 + 1.35427i 0.148952 + 0.988844i \(0.452410\pi\)
−0.930840 + 0.365426i \(0.880923\pi\)
\(68\) 0 0
\(69\) 1.16098e10 0.893624
\(70\) 0 0
\(71\) −5.28267e9 −0.347482 −0.173741 0.984791i \(-0.555586\pi\)
−0.173741 + 0.984791i \(0.555586\pi\)
\(72\) 0 0
\(73\) −5.55061e9 + 9.61394e9i −0.313375 + 0.542782i −0.979091 0.203424i \(-0.934793\pi\)
0.665715 + 0.746206i \(0.268127\pi\)
\(74\) 0 0
\(75\) −8.98276e9 1.55586e10i −0.437092 0.757065i
\(76\) 0 0
\(77\) 9.67912e9 + 3.90028e10i 0.407509 + 1.64209i
\(78\) 0 0
\(79\) 2.14340e9 + 3.71248e9i 0.0783709 + 0.135742i 0.902547 0.430591i \(-0.141695\pi\)
−0.824176 + 0.566333i \(0.808361\pi\)
\(80\) 0 0
\(81\) −1.74339e9 + 3.01964e9i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) −4.61200e10 −1.28517 −0.642584 0.766216i \(-0.722137\pi\)
−0.642584 + 0.766216i \(0.722137\pi\)
\(84\) 0 0
\(85\) −5.29942e10 −1.29546
\(86\) 0 0
\(87\) −2.00724e10 + 3.47665e10i −0.431761 + 0.747833i
\(88\) 0 0
\(89\) −8.53894e9 1.47899e10i −0.162091 0.280750i 0.773527 0.633763i \(-0.218490\pi\)
−0.935618 + 0.353013i \(0.885157\pi\)
\(90\) 0 0
\(91\) 2.43792e10 2.34912e10i 0.409536 0.394618i
\(92\) 0 0
\(93\) −7.17979e9 1.24358e10i −0.107018 0.185360i
\(94\) 0 0
\(95\) −2.49779e10 + 4.32631e10i −0.331190 + 0.573637i
\(96\) 0 0
\(97\) 1.57413e11 1.86121 0.930605 0.366026i \(-0.119282\pi\)
0.930605 + 0.366026i \(0.119282\pi\)
\(98\) 0 0
\(99\) −5.33638e10 −0.563966
\(100\) 0 0
\(101\) −7.77841e10 + 1.34726e11i −0.736416 + 1.27551i 0.217683 + 0.976019i \(0.430150\pi\)
−0.954099 + 0.299490i \(0.903183\pi\)
\(102\) 0 0
\(103\) 6.88269e10 + 1.19212e11i 0.584997 + 1.01324i 0.994876 + 0.101105i \(0.0322377\pi\)
−0.409879 + 0.912140i \(0.634429\pi\)
\(104\) 0 0
\(105\) −8.62119e10 + 8.30716e10i −0.659214 + 0.635201i
\(106\) 0 0
\(107\) −9.51994e10 1.64890e11i −0.656181 1.13654i −0.981596 0.190967i \(-0.938838\pi\)
0.325416 0.945571i \(-0.394496\pi\)
\(108\) 0 0
\(109\) −9.45648e10 + 1.63791e11i −0.588686 + 1.01963i 0.405719 + 0.913998i \(0.367021\pi\)
−0.994405 + 0.105636i \(0.966312\pi\)
\(110\) 0 0
\(111\) −5.27457e10 −0.297106
\(112\) 0 0
\(113\) −1.29301e11 −0.660190 −0.330095 0.943948i \(-0.607081\pi\)
−0.330095 + 0.943948i \(0.607081\pi\)
\(114\) 0 0
\(115\) −2.64678e11 + 4.58436e11i −1.22710 + 2.12540i
\(116\) 0 0
\(117\) 2.24786e10 + 3.89341e10i 0.0947868 + 0.164176i
\(118\) 0 0
\(119\) 5.12273e10 + 2.06424e11i 0.196785 + 0.792962i
\(120\) 0 0
\(121\) −2.65699e11 4.60205e11i −0.931260 1.61299i
\(122\) 0 0
\(123\) 6.71007e10 1.16222e11i 0.214906 0.372228i
\(124\) 0 0
\(125\) 2.78146e11 0.815206
\(126\) 0 0
\(127\) 1.94863e10 0.0523369 0.0261685 0.999658i \(-0.491669\pi\)
0.0261685 + 0.999658i \(0.491669\pi\)
\(128\) 0 0
\(129\) 1.26394e11 2.18920e11i 0.311517 0.539563i
\(130\) 0 0
\(131\) −1.37802e10 2.38680e10i −0.0312078 0.0540535i 0.850000 0.526783i \(-0.176602\pi\)
−0.881207 + 0.472730i \(0.843269\pi\)
\(132\) 0 0
\(133\) 1.92665e11 + 5.54741e10i 0.401437 + 0.115586i
\(134\) 0 0
\(135\) −7.94910e10 1.37682e11i −0.152575 0.264267i
\(136\) 0 0
\(137\) 1.55036e11 2.68531e11i 0.274454 0.475369i −0.695543 0.718485i \(-0.744836\pi\)
0.969997 + 0.243116i \(0.0781694\pi\)
\(138\) 0 0
\(139\) 5.28928e11 0.864600 0.432300 0.901730i \(-0.357702\pi\)
0.432300 + 0.901730i \(0.357702\pi\)
\(140\) 0 0
\(141\) 3.36815e10 0.0508963
\(142\) 0 0
\(143\) −3.44026e11 + 5.95871e11i −0.481109 + 0.833305i
\(144\) 0 0
\(145\) −9.15213e11 1.58520e12i −1.18576 2.05380i
\(146\) 0 0
\(147\) 4.06920e11 + 2.55513e11i 0.488949 + 0.307021i
\(148\) 0 0
\(149\) 2.21201e11 + 3.83131e11i 0.246753 + 0.427389i 0.962623 0.270845i \(-0.0873030\pi\)
−0.715870 + 0.698234i \(0.753970\pi\)
\(150\) 0 0
\(151\) 8.75046e11 1.51562e12i 0.907105 1.57115i 0.0890393 0.996028i \(-0.471620\pi\)
0.818066 0.575124i \(-0.195046\pi\)
\(152\) 0 0
\(153\) −2.82431e11 −0.272338
\(154\) 0 0
\(155\) 6.54733e11 0.587814
\(156\) 0 0
\(157\) −6.97856e11 + 1.20872e12i −0.583872 + 1.01130i 0.411143 + 0.911571i \(0.365130\pi\)
−0.995015 + 0.0997250i \(0.968204\pi\)
\(158\) 0 0
\(159\) 5.69393e11 + 9.86217e11i 0.444353 + 0.769641i
\(160\) 0 0
\(161\) 2.04156e12 + 5.87830e11i 1.48738 + 0.428262i
\(162\) 0 0
\(163\) 6.83315e11 + 1.18354e12i 0.465146 + 0.805656i 0.999208 0.0397888i \(-0.0126685\pi\)
−0.534062 + 0.845445i \(0.679335\pi\)
\(164\) 0 0
\(165\) 1.21658e12 2.10717e12i 0.774422 1.34134i
\(166\) 0 0
\(167\) 6.20052e11 0.369392 0.184696 0.982796i \(-0.440870\pi\)
0.184696 + 0.982796i \(0.440870\pi\)
\(168\) 0 0
\(169\) −1.21250e12 −0.676557
\(170\) 0 0
\(171\) −1.33119e11 + 2.30569e11i −0.0696244 + 0.120593i
\(172\) 0 0
\(173\) −3.99102e11 6.91264e11i −0.195808 0.339149i 0.751357 0.659896i \(-0.229400\pi\)
−0.947165 + 0.320747i \(0.896066\pi\)
\(174\) 0 0
\(175\) −7.91836e11 3.19077e12i −0.364692 1.46955i
\(176\) 0 0
\(177\) −1.09237e12 1.89204e12i −0.472625 0.818610i
\(178\) 0 0
\(179\) 3.98673e11 6.90522e11i 0.162153 0.280857i −0.773488 0.633811i \(-0.781490\pi\)
0.935641 + 0.352954i \(0.114823\pi\)
\(180\) 0 0
\(181\) 3.89173e12 1.48906 0.744528 0.667591i \(-0.232675\pi\)
0.744528 + 0.667591i \(0.232675\pi\)
\(182\) 0 0
\(183\) 5.27032e10 0.0189826
\(184\) 0 0
\(185\) 1.20249e12 2.08277e12i 0.407977 0.706636i
\(186\) 0 0
\(187\) −2.16124e12 3.74338e12i −0.691153 1.19711i
\(188\) 0 0
\(189\) −4.59464e11 + 4.42727e11i −0.138583 + 0.133535i
\(190\) 0 0
\(191\) −1.64431e12 2.84803e12i −0.468059 0.810701i 0.531275 0.847199i \(-0.321713\pi\)
−0.999334 + 0.0364981i \(0.988380\pi\)
\(192\) 0 0
\(193\) −1.74782e12 + 3.02731e12i −0.469819 + 0.813750i −0.999404 0.0345062i \(-0.989014\pi\)
0.529586 + 0.848257i \(0.322347\pi\)
\(194\) 0 0
\(195\) −2.04985e12 −0.520634
\(196\) 0 0
\(197\) 5.58940e12 1.34215 0.671074 0.741390i \(-0.265833\pi\)
0.671074 + 0.741390i \(0.265833\pi\)
\(198\) 0 0
\(199\) 2.69940e12 4.67549e12i 0.613162 1.06203i −0.377542 0.925992i \(-0.623231\pi\)
0.990704 0.136035i \(-0.0434359\pi\)
\(200\) 0 0
\(201\) −2.09973e12 3.63683e12i −0.451424 0.781889i
\(202\) 0 0
\(203\) −5.29000e12 + 5.09731e12i −1.07703 + 1.03780i
\(204\) 0 0
\(205\) 3.05949e12 + 5.29920e12i 0.590205 + 1.02227i
\(206\) 0 0
\(207\) −1.41059e12 + 2.44322e12i −0.257967 + 0.446812i
\(208\) 0 0
\(209\) −4.07466e12 −0.706785
\(210\) 0 0
\(211\) 8.02377e12 1.32076 0.660381 0.750930i \(-0.270395\pi\)
0.660381 + 0.750930i \(0.270395\pi\)
\(212\) 0 0
\(213\) 6.41845e11 1.11171e12i 0.100310 0.173741i
\(214\) 0 0
\(215\) 5.76299e12 + 9.98179e12i 0.855532 + 1.48182i
\(216\) 0 0
\(217\) −6.32903e11 2.55033e12i −0.0892912 0.359806i
\(218\) 0 0
\(219\) −1.34880e12 2.33619e12i −0.180927 0.313375i
\(220\) 0 0
\(221\) −1.82078e12 + 3.15368e12i −0.232327 + 0.402402i
\(222\) 0 0
\(223\) 2.85492e10 0.00346671 0.00173336 0.999998i \(-0.499448\pi\)
0.00173336 + 0.999998i \(0.499448\pi\)
\(224\) 0 0
\(225\) 4.36562e12 0.504710
\(226\) 0 0
\(227\) −6.93582e12 + 1.20132e13i −0.763757 + 1.32287i 0.177144 + 0.984185i \(0.443314\pi\)
−0.940901 + 0.338682i \(0.890019\pi\)
\(228\) 0 0
\(229\) −2.91500e12 5.04892e12i −0.305874 0.529790i 0.671581 0.740931i \(-0.265615\pi\)
−0.977456 + 0.211141i \(0.932282\pi\)
\(230\) 0 0
\(231\) −9.38392e12 2.70192e12i −0.938682 0.270276i
\(232\) 0 0
\(233\) 7.68712e12 + 1.33145e13i 0.733341 + 1.27018i 0.955447 + 0.295161i \(0.0953734\pi\)
−0.222107 + 0.975022i \(0.571293\pi\)
\(234\) 0 0
\(235\) −7.67864e11 + 1.32998e12i −0.0698893 + 0.121052i
\(236\) 0 0
\(237\) −1.04169e12 −0.0904950
\(238\) 0 0
\(239\) 1.72983e13 1.43488 0.717438 0.696622i \(-0.245314\pi\)
0.717438 + 0.696622i \(0.245314\pi\)
\(240\) 0 0
\(241\) 1.79662e12 3.11184e12i 0.142352 0.246560i −0.786030 0.618188i \(-0.787867\pi\)
0.928382 + 0.371628i \(0.121200\pi\)
\(242\) 0 0
\(243\) −4.23644e11 7.33773e11i −0.0320750 0.0555556i
\(244\) 0 0
\(245\) −1.93663e13 + 1.02429e13i −1.40163 + 0.741326i
\(246\) 0 0
\(247\) 1.71639e12 + 2.97287e12i 0.118791 + 0.205751i
\(248\) 0 0
\(249\) 5.60358e12 9.70568e12i 0.370996 0.642584i
\(250\) 0 0
\(251\) −2.07857e12 −0.131692 −0.0658461 0.997830i \(-0.520975\pi\)
−0.0658461 + 0.997830i \(0.520975\pi\)
\(252\) 0 0
\(253\) −4.31770e13 −2.61872
\(254\) 0 0
\(255\) 6.43879e12 1.11523e13i 0.373967 0.647730i
\(256\) 0 0
\(257\) 4.77704e12 + 8.27408e12i 0.265783 + 0.460350i 0.967768 0.251842i \(-0.0810362\pi\)
−0.701986 + 0.712191i \(0.747703\pi\)
\(258\) 0 0
\(259\) −9.27524e12 2.67063e12i −0.494511 0.142385i
\(260\) 0 0
\(261\) −4.87760e12 8.44825e12i −0.249278 0.431761i
\(262\) 0 0
\(263\) −1.62484e13 + 2.81431e13i −0.796259 + 1.37916i 0.125777 + 0.992059i \(0.459858\pi\)
−0.922036 + 0.387103i \(0.873476\pi\)
\(264\) 0 0
\(265\) −5.19236e13 −2.44069
\(266\) 0 0
\(267\) 4.14992e12 0.187167
\(268\) 0 0
\(269\) 5.57863e12 9.66247e12i 0.241485 0.418264i −0.719653 0.694334i \(-0.755699\pi\)
0.961137 + 0.276070i \(0.0890322\pi\)
\(270\) 0 0
\(271\) −6.81340e12 1.18012e13i −0.283161 0.490449i 0.689001 0.724761i \(-0.258050\pi\)
−0.972161 + 0.234312i \(0.924716\pi\)
\(272\) 0 0
\(273\) 1.98151e12 + 7.98464e12i 0.0790863 + 0.318684i
\(274\) 0 0
\(275\) 3.34070e13 + 5.78626e13i 1.28088 + 2.21855i
\(276\) 0 0
\(277\) 1.14769e13 1.98786e13i 0.422850 0.732397i −0.573367 0.819298i \(-0.694363\pi\)
0.996217 + 0.0869014i \(0.0276965\pi\)
\(278\) 0 0
\(279\) 3.48938e12 0.123573
\(280\) 0 0
\(281\) −1.32538e13 −0.451291 −0.225645 0.974210i \(-0.572449\pi\)
−0.225645 + 0.974210i \(0.572449\pi\)
\(282\) 0 0
\(283\) −2.36242e13 + 4.09183e13i −0.773627 + 1.33996i 0.161935 + 0.986801i \(0.448226\pi\)
−0.935563 + 0.353161i \(0.885107\pi\)
\(284\) 0 0
\(285\) −6.06964e12 1.05129e13i −0.191212 0.331190i
\(286\) 0 0
\(287\) 1.76841e13 1.70399e13i 0.536083 0.516556i
\(288\) 0 0
\(289\) 5.69746e12 + 9.86829e12i 0.166243 + 0.287941i
\(290\) 0 0
\(291\) −1.91256e13 + 3.31266e13i −0.537285 + 0.930605i
\(292\) 0 0
\(293\) 4.50335e13 1.21833 0.609164 0.793045i \(-0.291505\pi\)
0.609164 + 0.793045i \(0.291505\pi\)
\(294\) 0 0
\(295\) 9.96144e13 2.59598
\(296\) 0 0
\(297\) 6.48370e12 1.12301e13i 0.162803 0.281983i
\(298\) 0 0
\(299\) 1.81876e13 + 3.15019e13i 0.440134 + 0.762334i
\(300\) 0 0
\(301\) 3.33105e13 3.20971e13i 0.777079 0.748773i
\(302\) 0 0
\(303\) −1.89015e13 3.27384e13i −0.425170 0.736416i
\(304\) 0 0
\(305\) −1.20152e12 + 2.08109e12i −0.0260664 + 0.0451483i
\(306\) 0 0
\(307\) −8.11886e13 −1.69916 −0.849580 0.527460i \(-0.823144\pi\)
−0.849580 + 0.527460i \(0.823144\pi\)
\(308\) 0 0
\(309\) −3.34499e13 −0.675496
\(310\) 0 0
\(311\) −4.56233e13 + 7.90218e13i −0.889210 + 1.54016i −0.0483988 + 0.998828i \(0.515412\pi\)
−0.840811 + 0.541329i \(0.817922\pi\)
\(312\) 0 0
\(313\) −1.75443e13 3.03876e13i −0.330097 0.571745i 0.652433 0.757846i \(-0.273748\pi\)
−0.982531 + 0.186101i \(0.940415\pi\)
\(314\) 0 0
\(315\) −7.00718e12 2.82360e13i −0.127302 0.512974i
\(316\) 0 0
\(317\) −3.71054e13 6.42684e13i −0.651045 1.12764i −0.982870 0.184301i \(-0.940998\pi\)
0.331825 0.943341i \(-0.392336\pi\)
\(318\) 0 0
\(319\) 7.46496e13 1.29297e14i 1.26526 2.19149i
\(320\) 0 0
\(321\) 4.62669e13 0.757692
\(322\) 0 0
\(323\) −2.15654e13 −0.341305
\(324\) 0 0
\(325\) 2.81443e13 4.87474e13i 0.430559 0.745750i
\(326\) 0 0
\(327\) −2.29792e13 3.98012e13i −0.339878 0.588686i
\(328\) 0 0
\(329\) 5.92283e12 + 1.70537e12i 0.0847133 + 0.0243916i
\(330\) 0 0
\(331\) −5.12968e12 8.88487e12i −0.0709637 0.122913i 0.828360 0.560196i \(-0.189274\pi\)
−0.899324 + 0.437283i \(0.855941\pi\)
\(332\) 0 0
\(333\) 6.40860e12 1.11000e13i 0.0857670 0.148553i
\(334\) 0 0
\(335\) 1.91476e14 2.47953
\(336\) 0 0
\(337\) 5.27820e13 0.661487 0.330743 0.943721i \(-0.392701\pi\)
0.330743 + 0.943721i \(0.392701\pi\)
\(338\) 0 0
\(339\) 1.57100e13 2.72105e13i 0.190580 0.330095i
\(340\) 0 0
\(341\) 2.67017e13 + 4.62487e13i 0.313610 + 0.543189i
\(342\) 0 0
\(343\) 5.86190e13 + 6.55348e13i 0.666685 + 0.745340i
\(344\) 0 0
\(345\) −6.43167e13 1.11400e14i −0.708466 1.22710i
\(346\) 0 0
\(347\) −6.11874e13 + 1.05980e14i −0.652905 + 1.13086i 0.329510 + 0.944152i \(0.393116\pi\)
−0.982415 + 0.186712i \(0.940217\pi\)
\(348\) 0 0
\(349\) 2.45906e13 0.254232 0.127116 0.991888i \(-0.459428\pi\)
0.127116 + 0.991888i \(0.459428\pi\)
\(350\) 0 0
\(351\) −1.09246e13 −0.109450
\(352\) 0 0
\(353\) 2.31490e13 4.00952e13i 0.224787 0.389343i −0.731468 0.681875i \(-0.761165\pi\)
0.956256 + 0.292533i \(0.0944980\pi\)
\(354\) 0 0
\(355\) 2.92653e13 + 5.06889e13i 0.275484 + 0.477153i
\(356\) 0 0
\(357\) −4.96649e13 1.43001e13i −0.453288 0.130516i
\(358\) 0 0
\(359\) −9.74265e13 1.68748e14i −0.862298 1.49354i −0.869705 0.493572i \(-0.835691\pi\)
0.00740641 0.999973i \(-0.497642\pi\)
\(360\) 0 0
\(361\) 4.80807e13 8.32781e13i 0.412744 0.714893i
\(362\) 0 0
\(363\) 1.29130e14 1.07533
\(364\) 0 0
\(365\) 1.22998e14 0.993777
\(366\) 0 0
\(367\) −7.70186e13 + 1.33400e14i −0.603854 + 1.04591i 0.388377 + 0.921501i \(0.373036\pi\)
−0.992231 + 0.124406i \(0.960298\pi\)
\(368\) 0 0
\(369\) 1.63055e13 + 2.82419e13i 0.124076 + 0.214906i
\(370\) 0 0
\(371\) 5.01923e13 + 2.02254e14i 0.370750 + 1.49397i
\(372\) 0 0
\(373\) −7.42105e13 1.28536e14i −0.532190 0.921780i −0.999294 0.0375776i \(-0.988036\pi\)
0.467104 0.884203i \(-0.345297\pi\)
\(374\) 0 0
\(375\) −3.37947e13 + 5.85342e13i −0.235330 + 0.407603i
\(376\) 0 0
\(377\) −1.25780e14 −0.850616
\(378\) 0 0
\(379\) −2.63905e14 −1.73353 −0.866766 0.498715i \(-0.833805\pi\)
−0.866766 + 0.498715i \(0.833805\pi\)
\(380\) 0 0
\(381\) −2.36758e12 + 4.10077e12i −0.0151084 + 0.0261685i
\(382\) 0 0
\(383\) 2.31627e13 + 4.01190e13i 0.143614 + 0.248746i 0.928855 0.370444i \(-0.120794\pi\)
−0.785241 + 0.619190i \(0.787461\pi\)
\(384\) 0 0
\(385\) 3.20623e14 3.08944e14i 1.93180 1.86143i
\(386\) 0 0
\(387\) 3.07136e13 + 5.31976e13i 0.179854 + 0.311517i
\(388\) 0 0
\(389\) −3.12486e12 + 5.41242e12i −0.0177872 + 0.0308084i −0.874782 0.484517i \(-0.838995\pi\)
0.856995 + 0.515325i \(0.172329\pi\)
\(390\) 0 0
\(391\) −2.28517e14 −1.26458
\(392\) 0 0
\(393\) 6.69717e12 0.0360356
\(394\) 0 0
\(395\) 2.37483e13 4.11333e13i 0.124265 0.215233i
\(396\) 0 0
\(397\) −4.83142e13 8.36827e13i −0.245882 0.425880i 0.716497 0.697590i \(-0.245744\pi\)
−0.962379 + 0.271710i \(0.912411\pi\)
\(398\) 0 0
\(399\) −3.50829e13 + 3.38050e13i −0.173678 + 0.167352i
\(400\) 0 0
\(401\) −6.00607e13 1.04028e14i −0.289265 0.501022i 0.684369 0.729136i \(-0.260078\pi\)
−0.973635 + 0.228113i \(0.926744\pi\)
\(402\) 0 0
\(403\) 2.24953e13 3.89631e13i 0.105418 0.182589i
\(404\) 0 0
\(405\) 3.86326e13 0.176178
\(406\) 0 0
\(407\) 1.96162e14 0.870654
\(408\) 0 0
\(409\) −1.06240e14 + 1.84013e14i −0.458998 + 0.795007i −0.998908 0.0467150i \(-0.985125\pi\)
0.539911 + 0.841722i \(0.318458\pi\)
\(410\) 0 0
\(411\) 3.76738e13 + 6.52530e13i 0.158456 + 0.274454i
\(412\) 0 0
\(413\) −9.62931e13 3.88021e14i −0.394339 1.58902i
\(414\) 0 0
\(415\) 2.55498e14 + 4.42536e14i 1.01888 + 1.76475i
\(416\) 0 0
\(417\) −6.42647e13 + 1.11310e14i −0.249588 + 0.432300i
\(418\) 0 0
\(419\) 7.70399e13 0.291433 0.145716 0.989326i \(-0.453451\pi\)
0.145716 + 0.989326i \(0.453451\pi\)
\(420\) 0 0
\(421\) −3.49104e14 −1.28648 −0.643241 0.765664i \(-0.722411\pi\)
−0.643241 + 0.765664i \(0.722411\pi\)
\(422\) 0 0
\(423\) −4.09230e12 + 7.08807e12i −0.0146925 + 0.0254482i
\(424\) 0 0
\(425\) 1.76808e14 + 3.06241e14i 0.618534 + 1.07133i
\(426\) 0 0
\(427\) 9.26776e12 + 2.66848e12i 0.0315952 + 0.00909726i
\(428\) 0 0
\(429\) −8.35984e13 1.44797e14i −0.277768 0.481109i
\(430\) 0 0
\(431\) −3.54794e13 + 6.14522e13i −0.114908 + 0.199027i −0.917743 0.397174i \(-0.869991\pi\)
0.802835 + 0.596202i \(0.203324\pi\)
\(432\) 0 0
\(433\) −5.57341e14 −1.75969 −0.879847 0.475256i \(-0.842355\pi\)
−0.879847 + 0.475256i \(0.842355\pi\)
\(434\) 0 0
\(435\) 4.44794e14 1.36920
\(436\) 0 0
\(437\) −1.07708e14 + 1.86555e14i −0.323295 + 0.559963i
\(438\) 0 0
\(439\) 1.90654e14 + 3.30223e14i 0.558074 + 0.966613i 0.997657 + 0.0684109i \(0.0217929\pi\)
−0.439583 + 0.898202i \(0.644874\pi\)
\(440\) 0 0
\(441\) −1.03212e14 + 5.45891e13i −0.294658 + 0.155845i
\(442\) 0 0
\(443\) 6.88095e13 + 1.19182e14i 0.191614 + 0.331886i 0.945785 0.324792i \(-0.105294\pi\)
−0.754171 + 0.656678i \(0.771961\pi\)
\(444\) 0 0
\(445\) −9.46091e13 + 1.63868e14i −0.257012 + 0.445157i
\(446\) 0 0
\(447\) −1.07504e14 −0.284926
\(448\) 0 0
\(449\) −1.91960e14 −0.496429 −0.248214 0.968705i \(-0.579844\pi\)
−0.248214 + 0.968705i \(0.579844\pi\)
\(450\) 0 0
\(451\) −2.49548e14 + 4.32230e14i −0.629772 + 1.09080i
\(452\) 0 0
\(453\) 2.12636e14 + 3.68297e14i 0.523717 + 0.907105i
\(454\) 0 0
\(455\) −3.60463e14 1.03789e14i −0.866558 0.249509i
\(456\) 0 0
\(457\) 3.61232e14 + 6.25673e14i 0.847711 + 1.46828i 0.883246 + 0.468910i \(0.155353\pi\)
−0.0355355 + 0.999368i \(0.511314\pi\)
\(458\) 0 0
\(459\) 3.43153e13 5.94359e13i 0.0786173 0.136169i
\(460\) 0 0
\(461\) −4.28898e14 −0.959398 −0.479699 0.877433i \(-0.659254\pi\)
−0.479699 + 0.877433i \(0.659254\pi\)
\(462\) 0 0
\(463\) 6.20134e14 1.35453 0.677267 0.735737i \(-0.263164\pi\)
0.677267 + 0.735737i \(0.263164\pi\)
\(464\) 0 0
\(465\) −7.95501e13 + 1.37785e14i −0.169687 + 0.293907i
\(466\) 0 0
\(467\) −3.53364e14 6.12045e14i −0.736173 1.27509i −0.954207 0.299148i \(-0.903298\pi\)
0.218033 0.975941i \(-0.430036\pi\)
\(468\) 0 0
\(469\) −1.85092e14 7.45844e14i −0.376650 1.51774i
\(470\) 0 0
\(471\) −1.69579e14 2.93719e14i −0.337099 0.583872i
\(472\) 0 0
\(473\) −4.70059e14 + 8.14167e14i −0.912886 + 1.58116i
\(474\) 0 0
\(475\) 3.33343e14 0.632523
\(476\) 0 0
\(477\) −2.76725e14 −0.513094
\(478\) 0 0
\(479\) 7.76957e13 1.34573e14i 0.140783 0.243844i −0.787008 0.616942i \(-0.788371\pi\)
0.927792 + 0.373098i \(0.121705\pi\)
\(480\) 0 0
\(481\) −8.26301e13 1.43120e14i −0.146332 0.253455i
\(482\) 0 0
\(483\) −3.71755e14 + 3.58214e14i −0.643499 + 0.620059i
\(484\) 0 0
\(485\) −8.72045e14 1.51043e15i −1.47557 2.55576i
\(486\) 0 0
\(487\) −1.67311e14 + 2.89791e14i −0.276767 + 0.479375i −0.970579 0.240781i \(-0.922596\pi\)
0.693812 + 0.720156i \(0.255930\pi\)
\(488\) 0 0
\(489\) −3.32091e14 −0.537104
\(490\) 0 0
\(491\) 5.46129e14 0.863668 0.431834 0.901953i \(-0.357867\pi\)
0.431834 + 0.901953i \(0.357867\pi\)
\(492\) 0 0
\(493\) 3.95087e14 6.84311e14i 0.610991 1.05827i
\(494\) 0 0
\(495\) 2.95628e14 + 5.12043e14i 0.447113 + 0.774422i
\(496\) 0 0
\(497\) 1.69155e14 1.62994e14i 0.250222 0.241108i
\(498\) 0 0
\(499\) 3.26652e14 + 5.65778e14i 0.472642 + 0.818640i 0.999510 0.0313069i \(-0.00996694\pi\)
−0.526868 + 0.849947i \(0.676634\pi\)
\(500\) 0 0
\(501\) −7.53363e13 + 1.30486e14i −0.106634 + 0.184696i
\(502\) 0 0
\(503\) −1.29756e15 −1.79682 −0.898409 0.439161i \(-0.855276\pi\)
−0.898409 + 0.439161i \(0.855276\pi\)
\(504\) 0 0
\(505\) 1.72365e15 2.33532
\(506\) 0 0
\(507\) 1.47319e14 2.55163e14i 0.195305 0.338278i
\(508\) 0 0
\(509\) 5.20168e14 + 9.00957e14i 0.674832 + 1.16884i 0.976518 + 0.215436i \(0.0691172\pi\)
−0.301686 + 0.953407i \(0.597549\pi\)
\(510\) 0 0
\(511\) −1.18897e14 4.79107e14i −0.150959 0.608300i
\(512\) 0 0
\(513\) −3.23479e13 5.60282e13i −0.0401977 0.0696244i
\(514\) 0 0
\(515\) 7.62583e14 1.32083e15i 0.927572 1.60660i
\(516\) 0 0
\(517\) −1.25262e14 −0.149149
\(518\) 0 0
\(519\) 1.93963e14 0.226099
\(520\) 0 0
\(521\) 8.26924e14 1.43227e15i 0.943752 1.63463i 0.185522 0.982640i \(-0.440603\pi\)
0.758231 0.651986i \(-0.226064\pi\)
\(522\) 0 0
\(523\) −2.37190e14 4.10824e14i −0.265055 0.459089i 0.702523 0.711661i \(-0.252057\pi\)
−0.967578 + 0.252572i \(0.918724\pi\)
\(524\) 0 0
\(525\) 7.67686e14 + 2.21041e14i 0.840055 + 0.241878i
\(526\) 0 0
\(527\) 1.41320e14 + 2.44774e14i 0.151442 + 0.262305i
\(528\) 0 0
\(529\) −6.64915e14 + 1.15167e15i −0.697847 + 1.20871i
\(530\) 0 0
\(531\) 5.30892e14 0.545740
\(532\) 0 0
\(533\) 4.20473e14 0.423388
\(534\) 0 0
\(535\) −1.05478e15 + 1.82694e15i −1.04044 + 1.80210i
\(536\) 0 0
\(537\) 9.68775e13 + 1.67797e14i 0.0936191 + 0.162153i
\(538\) 0 0
\(539\) −1.51334e15 9.50257e14i −1.43284 0.899711i
\(540\) 0 0
\(541\) −2.57042e14 4.45210e14i −0.238462 0.413028i 0.721811 0.692090i \(-0.243310\pi\)
−0.960273 + 0.279062i \(0.909977\pi\)
\(542\) 0 0
\(543\) −4.72846e14 + 8.18993e14i −0.429853 + 0.744528i
\(544\) 0 0
\(545\) 2.09550e15 1.86684
\(546\) 0 0
\(547\) 4.36242e14 0.380888 0.190444 0.981698i \(-0.439007\pi\)
0.190444 + 0.981698i \(0.439007\pi\)
\(548\) 0 0
\(549\) −6.40344e12 + 1.10911e13i −0.00547981 + 0.00949131i
\(550\) 0 0
\(551\) −3.72435e14 6.45077e14i −0.312404 0.541100i
\(552\) 0 0
\(553\) −1.83180e14 5.27433e13i −0.150623 0.0433689i
\(554\) 0 0
\(555\) 2.92204e14 + 5.06112e14i 0.235545 + 0.407977i
\(556\) 0 0
\(557\) 1.08792e15 1.88434e15i 0.859795 1.48921i −0.0123289 0.999924i \(-0.503925\pi\)
0.872124 0.489285i \(-0.162742\pi\)
\(558\) 0 0
\(559\) 7.92020e14 0.613721
\(560\) 0 0
\(561\) 1.05036e15 0.798075
\(562\) 0 0
\(563\) −4.45391e14 + 7.71439e14i −0.331852 + 0.574785i −0.982875 0.184273i \(-0.941007\pi\)
0.651023 + 0.759058i \(0.274340\pi\)
\(564\) 0 0
\(565\) 7.16307e14 + 1.24068e15i 0.523399 + 0.906554i
\(566\) 0 0
\(567\) −3.73445e13 1.50483e14i −0.0267621 0.107840i
\(568\) 0 0
\(569\) −1.25020e15 2.16542e15i −0.878747 1.52203i −0.852717 0.522372i \(-0.825047\pi\)
−0.0260291 0.999661i \(-0.508286\pi\)
\(570\) 0 0
\(571\) 1.20063e15 2.07955e15i 0.827773 1.43374i −0.0720088 0.997404i \(-0.522941\pi\)
0.899782 0.436341i \(-0.143726\pi\)
\(572\) 0 0
\(573\) 7.99135e14 0.540467
\(574\) 0 0
\(575\) 3.53226e15 2.34358
\(576\) 0 0
\(577\) −8.01843e14 + 1.38883e15i −0.521942 + 0.904031i 0.477732 + 0.878506i \(0.341459\pi\)
−0.999674 + 0.0255249i \(0.991874\pi\)
\(578\) 0 0
\(579\) −4.24719e14 7.35635e14i −0.271250 0.469819i
\(580\) 0 0
\(581\) 1.47680e15 1.42301e15i 0.925449 0.891739i
\(582\) 0 0
\(583\) −2.11758e15 3.66775e15i −1.30215 2.25540i
\(584\) 0 0
\(585\) 2.49057e14 4.31380e14i 0.150294 0.260317i
\(586\) 0 0
\(587\) −2.58598e15 −1.53150 −0.765749 0.643140i \(-0.777631\pi\)
−0.765749 + 0.643140i \(0.777631\pi\)
\(588\) 0 0
\(589\) 2.66436e14 0.154867
\(590\) 0 0
\(591\) −6.79112e14 + 1.17626e15i −0.387445 + 0.671074i
\(592\) 0 0
\(593\) −7.43649e14 1.28804e15i −0.416454 0.721320i 0.579126 0.815238i \(-0.303394\pi\)
−0.995580 + 0.0939186i \(0.970061\pi\)
\(594\) 0 0
\(595\) 1.69692e15 1.63510e15i 0.932861 0.898881i
\(596\) 0 0
\(597\) 6.55954e14 + 1.13615e15i 0.354009 + 0.613162i
\(598\) 0 0
\(599\) −5.28520e14 + 9.15423e14i −0.280036 + 0.485036i −0.971393 0.237477i \(-0.923680\pi\)
0.691357 + 0.722513i \(0.257013\pi\)
\(600\) 0 0
\(601\) −2.15911e15 −1.12322 −0.561610 0.827402i \(-0.689818\pi\)
−0.561610 + 0.827402i \(0.689818\pi\)
\(602\) 0 0
\(603\) 1.02047e15 0.521259
\(604\) 0 0
\(605\) −2.94388e15 + 5.09894e15i −1.47661 + 2.55756i
\(606\) 0 0
\(607\) −9.50659e14 1.64659e15i −0.468260 0.811050i 0.531082 0.847320i \(-0.321786\pi\)
−0.999342 + 0.0362702i \(0.988452\pi\)
\(608\) 0 0
\(609\) −4.29964e14 1.73257e15i −0.207987 0.838101i
\(610\) 0 0
\(611\) 5.27646e13 + 9.13909e13i 0.0250678 + 0.0434187i
\(612\) 0 0
\(613\) −4.85740e14 + 8.41326e14i −0.226658 + 0.392583i −0.956816 0.290696i \(-0.906113\pi\)
0.730158 + 0.683279i \(0.239447\pi\)
\(614\) 0 0
\(615\) −1.48691e15 −0.681511
\(616\) 0 0
\(617\) −1.39104e15 −0.626282 −0.313141 0.949707i \(-0.601381\pi\)
−0.313141 + 0.949707i \(0.601381\pi\)
\(618\) 0 0
\(619\) −1.56881e15 + 2.71726e15i −0.693859 + 1.20180i 0.276705 + 0.960955i \(0.410758\pi\)
−0.970564 + 0.240844i \(0.922576\pi\)
\(620\) 0 0
\(621\) −3.42774e14 5.93701e14i −0.148937 0.257967i
\(622\) 0 0
\(623\) 7.29757e14 + 2.10120e14i 0.311526 + 0.0896979i
\(624\) 0 0
\(625\) 2.64095e14 + 4.57426e14i 0.110769 + 0.191858i
\(626\) 0 0
\(627\) 4.95071e14 8.57489e14i 0.204031 0.353392i
\(628\) 0 0
\(629\) 1.03820e15 0.420438
\(630\) 0 0
\(631\) 4.42265e15 1.76003 0.880017 0.474942i \(-0.157531\pi\)
0.880017 + 0.474942i \(0.157531\pi\)
\(632\) 0 0
\(633\) −9.74888e14 + 1.68855e15i −0.381271 + 0.660381i
\(634\) 0 0
\(635\) −1.07951e14 1.86977e14i −0.0414927 0.0718675i
\(636\) 0 0
\(637\) −5.58354e13 + 1.50441e15i −0.0210932 + 0.568329i
\(638\) 0 0
\(639\) 1.55968e14 + 2.70145e14i 0.0579137 + 0.100310i
\(640\) 0 0
\(641\) −4.94254e14 + 8.56073e14i −0.180398 + 0.312458i −0.942016 0.335568i \(-0.891072\pi\)
0.761618 + 0.648026i \(0.224405\pi\)
\(642\) 0 0
\(643\) 2.69033e15 0.965262 0.482631 0.875824i \(-0.339681\pi\)
0.482631 + 0.875824i \(0.339681\pi\)
\(644\) 0 0
\(645\) −2.80081e15 −0.987883
\(646\) 0 0
\(647\) −1.47451e15 + 2.55393e15i −0.511299 + 0.885595i 0.488616 + 0.872499i \(0.337502\pi\)
−0.999914 + 0.0130960i \(0.995831\pi\)
\(648\) 0 0
\(649\) 4.06254e15 + 7.03652e15i 1.38501 + 2.39890i
\(650\) 0 0
\(651\) 6.13600e14 + 1.76675e14i 0.205679 + 0.0592214i
\(652\) 0 0
\(653\) 1.17965e15 + 2.04321e15i 0.388803 + 0.673427i 0.992289 0.123947i \(-0.0395553\pi\)
−0.603486 + 0.797374i \(0.706222\pi\)
\(654\) 0 0
\(655\) −1.52681e14 + 2.64451e14i −0.0494831 + 0.0857072i
\(656\) 0 0
\(657\) 6.55516e14 0.208917
\(658\) 0 0
\(659\) −4.40458e14 −0.138050 −0.0690248 0.997615i \(-0.521989\pi\)
−0.0690248 + 0.997615i \(0.521989\pi\)
\(660\) 0 0
\(661\) 7.68645e14 1.33133e15i 0.236929 0.410373i −0.722903 0.690950i \(-0.757193\pi\)
0.959831 + 0.280577i \(0.0905259\pi\)
\(662\) 0 0
\(663\) −4.42449e14 7.66344e14i −0.134134 0.232327i
\(664\) 0 0
\(665\) −5.35043e14 2.15600e15i −0.159540 0.642879i
\(666\) 0 0
\(667\) −3.94650e15 6.83554e15i −1.15750 2.00484i
\(668\) 0 0
\(669\) −3.46873e12 + 6.00802e12i −0.00100075 + 0.00173336i
\(670\) 0 0
\(671\) −1.96004e14 −0.0556277
\(672\) 0 0
\(673\) −3.83410e14 −0.107048 −0.0535242 0.998567i \(-0.517045\pi\)
−0.0535242 + 0.998567i \(0.517045\pi\)
\(674\) 0 0
\(675\) −5.30423e14 + 9.18719e14i −0.145697 + 0.252355i
\(676\) 0 0
\(677\) 1.52818e15 + 2.64688e15i 0.412986 + 0.715313i 0.995215 0.0977120i \(-0.0311524\pi\)
−0.582228 + 0.813025i \(0.697819\pi\)
\(678\) 0 0
\(679\) −5.04048e15 + 4.85688e15i −1.34026 + 1.29144i
\(680\) 0 0
\(681\) −1.68540e15 2.91920e15i −0.440956 0.763757i
\(682\) 0 0
\(683\) −1.24318e15 + 2.15324e15i −0.320051 + 0.554344i −0.980498 0.196528i \(-0.937033\pi\)
0.660447 + 0.750872i \(0.270367\pi\)
\(684\) 0 0
\(685\) −3.43552e15 −0.870350
\(686\) 0 0
\(687\) 1.41669e15 0.353193
\(688\) 0 0
\(689\) −1.78399e15 + 3.08997e15i −0.437711 + 0.758137i
\(690\) 0 0
\(691\) 1.75214e15 + 3.03479e15i 0.423096 + 0.732823i 0.996240 0.0866310i \(-0.0276101\pi\)
−0.573145 + 0.819454i \(0.694277\pi\)
\(692\) 0 0
\(693\) 1.70875e15 1.64651e15i 0.406112 0.391319i
\(694\) 0 0
\(695\) −2.93019e15 5.07523e15i −0.685455 1.18724i
\(696\) 0 0
\(697\) −1.32075e15 + 2.28760e15i −0.304116 + 0.526745i
\(698\) 0 0
\(699\) −3.73594e15 −0.846789
\(700\) 0 0
\(701\) 5.93387e15 1.32400 0.662001 0.749503i \(-0.269707\pi\)
0.662001 + 0.749503i \(0.269707\pi\)
\(702\) 0 0
\(703\) 4.89337e14 8.47557e14i 0.107487 0.186172i
\(704\) 0 0
\(705\) −1.86591e14 3.23185e14i −0.0403506 0.0698893i
\(706\) 0 0
\(707\) −1.66618e15 6.71402e15i −0.354745 1.42947i
\(708\) 0 0
\(709\) −2.66852e15 4.62202e15i −0.559393 0.968896i −0.997547 0.0699967i \(-0.977701\pi\)
0.438155 0.898900i \(-0.355632\pi\)
\(710\) 0 0
\(711\) 1.26566e14 2.19219e14i 0.0261236 0.0452475i
\(712\) 0 0
\(713\) 2.82328e15 0.573801
\(714\) 0 0
\(715\) 7.62343e15 1.52569
\(716\) 0 0
\(717\) −2.10174e15 + 3.64032e15i −0.414213 + 0.717438i
\(718\) 0 0
\(719\) 1.51335e15 + 2.62120e15i 0.293718 + 0.508735i 0.974686 0.223579i \(-0.0717740\pi\)
−0.680968 + 0.732313i \(0.738441\pi\)
\(720\) 0 0
\(721\) −5.88210e15 1.69364e15i −1.12432 0.323726i
\(722\) 0 0
\(723\) 4.36579e14 + 7.56176e14i 0.0821868 + 0.142352i
\(724\) 0 0
\(725\) −6.10699e15 + 1.05776e16i −1.13232 + 1.96123i
\(726\) 0 0
\(727\) −1.66738e15 −0.304506 −0.152253 0.988342i \(-0.548653\pi\)
−0.152253 + 0.988342i \(0.548653\pi\)
\(728\) 0 0
\(729\) 2.05891e14 0.0370370
\(730\) 0 0
\(731\) −2.48781e15 + 4.30902e15i −0.440831 + 0.763542i
\(732\) 0 0
\(733\) −2.19667e15 3.80474e15i −0.383436 0.664130i 0.608115 0.793849i \(-0.291926\pi\)
−0.991551 + 0.129719i \(0.958593\pi\)
\(734\) 0 0
\(735\) 1.97450e14 5.32004e15i 0.0339529 0.914817i
\(736\) 0 0
\(737\) 7.80891e15 + 1.35254e16i 1.32288 + 2.29129i
\(738\) 0 0
\(739\) −9.77656e14 + 1.69335e15i −0.163170 + 0.282620i −0.936004 0.351989i \(-0.885505\pi\)
0.772834 + 0.634609i \(0.218839\pi\)
\(740\) 0 0
\(741\) −8.34164e14 −0.137167
\(742\) 0 0
\(743\) 7.66464e15 1.24180 0.620902 0.783888i \(-0.286766\pi\)
0.620902 + 0.783888i \(0.286766\pi\)
\(744\) 0 0
\(745\) 2.45085e15 4.24499e15i 0.391252 0.677668i
\(746\) 0 0
\(747\) 1.36167e15 + 2.35848e15i 0.214195 + 0.370996i
\(748\) 0 0
\(749\) 8.13595e15 + 2.34259e15i 1.26113 + 0.363117i
\(750\) 0 0
\(751\) −4.89846e15 8.48439e15i −0.748239 1.29599i −0.948666 0.316279i \(-0.897566\pi\)
0.200427 0.979709i \(-0.435767\pi\)
\(752\) 0 0
\(753\) 2.52547e14 4.37424e14i 0.0380163 0.0658461i
\(754\) 0 0
\(755\) −1.93905e16 −2.87661
\(756\) 0 0
\(757\) 1.58148e15 0.231226 0.115613 0.993294i \(-0.463117\pi\)
0.115613 + 0.993294i \(0.463117\pi\)
\(758\) 0 0
\(759\) 5.24601e15 9.08635e15i 0.755961 1.30936i
\(760\) 0 0
\(761\) 3.93379e15 + 6.81352e15i 0.558722 + 0.967734i 0.997604 + 0.0691896i \(0.0220413\pi\)
−0.438882 + 0.898545i \(0.644625\pi\)
\(762\) 0 0
\(763\) −2.02564e15 8.16246e15i −0.283580 1.14271i
\(764\) 0 0
\(765\) 1.56463e15 + 2.71001e15i 0.215910 + 0.373967i
\(766\) 0 0
\(767\) 3.42256e15 5.92804e15i 0.465561 0.806375i
\(768\) 0 0
\(769\) 6.27927e15 0.842005 0.421002 0.907060i \(-0.361678\pi\)
0.421002 + 0.907060i \(0.361678\pi\)
\(770\) 0 0
\(771\) −2.32164e15 −0.306900
\(772\) 0 0
\(773\) 1.66695e15 2.88725e15i 0.217238 0.376268i −0.736724 0.676193i \(-0.763628\pi\)
0.953963 + 0.299925i \(0.0969618\pi\)
\(774\) 0 0
\(775\) −2.18443e15 3.78355e15i −0.280659 0.486116i
\(776\) 0 0