Properties

Label 84.12.i.b.37.2
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 37.2
Root \(10810.2 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 84.37
Dual form 84.12.i.b.25.2

$q$-expansion

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

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
\(5\) −5539.86 + 9595.32i −0.792801 + 1.37317i 0.131426 + 0.991326i \(0.458044\pi\)
−0.924226 + 0.381845i \(0.875289\pi\)
\(6\) 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 0.884794 + 0.465982i \(0.154299\pi\)
−0.0388451 + 0.999245i \(0.512368\pi\)
\(12\) 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 0.994723 0.102599i \(-0.0327160\pi\)
−0.586215 + 0.810155i \(0.699383\pi\)
\(18\) 0 0
\(19\) −2.25438e6 + 3.90470e6i −0.208873 + 0.361779i −0.951360 0.308082i \(-0.900313\pi\)
0.742487 + 0.669861i \(0.233646\pi\)
\(20\) 0 0
\(21\) −2.60260e6 + 1.04874e7i −0.139060 + 0.560353i
\(22\) 0 0
\(23\) −2.38885e7 + 4.13761e7i −0.773901 + 1.34044i 0.161509 + 0.986871i \(0.448364\pi\)
−0.935410 + 0.353565i \(0.884969\pi\)
\(24\) 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 0.758338 0.651862i \(-0.226012\pi\)
−0.943698 + 0.330809i \(0.892678\pi\)
\(32\) 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 −0.708217 0.705995i \(-0.750500\pi\)
0.965518 + 0.260337i \(0.0838335\pi\)
\(38\) 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 −0.887222 0.461342i \(-0.847368\pi\)
0.843145 + 0.537686i \(0.180702\pi\)
\(48\) 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 0.937758 + 0.347290i \(0.112898\pi\)
−0.168117 + 0.985767i \(0.553768\pi\)
\(54\) 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 −0.906706 0.421763i \(-0.861412\pi\)
0.0880959 0.996112i \(-0.471922\pi\)
\(60\) 0 0
\(61\) −1.08443e8 + 1.87828e8i −0.0164394 + 0.0284739i −0.874128 0.485695i \(-0.838566\pi\)
0.857689 + 0.514169i \(0.171900\pi\)
\(62\) 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 −0.930840 0.365426i \(-0.880923\pi\)
0.148952 0.988844i \(-0.452410\pi\)
\(68\) 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 0.665715 0.746206i \(-0.268127\pi\)
−0.979091 + 0.203424i \(0.934793\pi\)
\(74\) 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 −0.824176 0.566333i \(-0.808361\pi\)
0.902547 + 0.430591i \(0.141695\pi\)
\(80\) 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 −0.935618 0.353013i \(-0.885157\pi\)
0.773527 + 0.633763i \(0.218490\pi\)
\(90\) 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 −0.954099 0.299490i \(-0.903183\pi\)
0.217683 0.976019i \(-0.430150\pi\)
\(102\) 0 0
\(103\) 6.88269e10 1.19212e11i 0.584997 1.01324i −0.409879 0.912140i \(-0.634429\pi\)
0.994876 0.101105i \(-0.0322377\pi\)
\(104\) 0 0
\(105\) −8.62119e10 8.30716e10i −0.659214 0.635201i
\(106\) 0 0
\(107\) −9.51994e10 + 1.64890e11i −0.656181 + 1.13654i 0.325416 + 0.945571i \(0.394496\pi\)
−0.981596 + 0.190967i \(0.938838\pi\)
\(108\) 0 0
\(109\) −9.45648e10 1.63791e11i −0.588686 1.01963i −0.994405 0.105636i \(-0.966312\pi\)
0.405719 0.913998i \(-0.367021\pi\)
\(110\) 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 −0.881207 0.472730i \(-0.843269\pi\)
0.850000 + 0.526783i \(0.176602\pi\)
\(132\) 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 0.969997 0.243116i \(-0.0781694\pi\)
−0.695543 + 0.718485i \(0.744836\pi\)
\(138\) 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 −0.715870 0.698234i \(-0.753970\pi\)
0.962623 + 0.270845i \(0.0873030\pi\)
\(150\) 0 0
\(151\) 8.75046e11 + 1.51562e12i 0.907105 + 1.57115i 0.818066 + 0.575124i \(0.195046\pi\)
0.0890393 + 0.996028i \(0.471620\pi\)
\(152\) 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 −0.995015 0.0997250i \(-0.968204\pi\)
0.411143 0.911571i \(-0.365130\pi\)
\(158\) 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 −0.534062 0.845445i \(-0.679335\pi\)
0.999208 + 0.0397888i \(0.0126685\pi\)
\(164\) 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 −0.947165 0.320747i \(-0.896066\pi\)
0.751357 + 0.659896i \(0.229400\pi\)
\(174\) 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 0.935641 0.352954i \(-0.114823\pi\)
−0.773488 + 0.633811i \(0.781490\pi\)
\(180\) 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 −0.999334 0.0364981i \(-0.988380\pi\)
0.531275 + 0.847199i \(0.321713\pi\)
\(192\) 0 0
\(193\) −1.74782e12 3.02731e12i −0.469819 0.813750i 0.529586 0.848257i \(-0.322347\pi\)
−0.999404 + 0.0345062i \(0.989014\pi\)
\(194\) 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 0.990704 + 0.136035i \(0.0434359\pi\)
−0.377542 + 0.925992i \(0.623231\pi\)
\(200\) 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 −0.940901 0.338682i \(-0.890019\pi\)
0.177144 0.984185i \(-0.443314\pi\)
\(228\) 0 0
\(229\) −2.91500e12 + 5.04892e12i −0.305874 + 0.529790i −0.977456 0.211141i \(-0.932282\pi\)
0.671581 + 0.740931i \(0.265615\pi\)
\(230\) 0 0
\(231\) −9.38392e12 + 2.70192e12i −0.938682 + 0.270276i
\(232\) 0 0
\(233\) 7.68712e12 1.33145e13i 0.733341 1.27018i −0.222107 0.975022i \(-0.571293\pi\)
0.955447 0.295161i \(-0.0953734\pi\)
\(234\) 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 0.928382 0.371628i \(-0.121200\pi\)
−0.786030 + 0.618188i \(0.787867\pi\)
\(242\) 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 −0.701986 0.712191i \(-0.747703\pi\)
0.967768 + 0.251842i \(0.0810362\pi\)
\(258\) 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 −0.922036 0.387103i \(-0.873476\pi\)
0.125777 0.992059i \(-0.459858\pi\)
\(264\) 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 0.961137 0.276070i \(-0.0890322\pi\)
−0.719653 + 0.694334i \(0.755699\pi\)
\(270\) 0 0
\(271\) −6.81340e12 + 1.18012e13i −0.283161 + 0.490449i −0.972161 0.234312i \(-0.924716\pi\)
0.689001 + 0.724761i \(0.258050\pi\)
\(272\) 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 0.996217 0.0869014i \(-0.0276965\pi\)
−0.573367 + 0.819298i \(0.694363\pi\)
\(278\) 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 −0.935563 0.353161i \(-0.885107\pi\)
0.161935 0.986801i \(-0.448226\pi\)
\(284\) 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 −0.840811 0.541329i \(-0.817922\pi\)
−0.0483988 0.998828i \(-0.515412\pi\)
\(312\) 0 0
\(313\) −1.75443e13 + 3.03876e13i −0.330097 + 0.571745i −0.982531 0.186101i \(-0.940415\pi\)
0.652433 + 0.757846i \(0.273748\pi\)
\(314\) 0 0
\(315\) −7.00718e12 + 2.82360e13i −0.127302 + 0.512974i
\(316\) 0 0
\(317\) −3.71054e13 + 6.42684e13i −0.651045 + 1.12764i 0.331825 + 0.943341i \(0.392336\pi\)
−0.982870 + 0.184301i \(0.940998\pi\)
\(318\) 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 −0.899324 0.437283i \(-0.855941\pi\)
0.828360 + 0.560196i \(0.189274\pi\)
\(332\) 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 −0.982415 0.186712i \(-0.940217\pi\)
0.329510 0.944152i \(-0.393116\pi\)
\(348\) 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 0.956256 0.292533i \(-0.0944980\pi\)
−0.731468 + 0.681875i \(0.761165\pi\)
\(354\) 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 0.00740641 + 0.999973i \(0.497642\pi\)
−0.869705 + 0.493572i \(0.835691\pi\)
\(360\) 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 −0.992231 0.124406i \(-0.960298\pi\)
0.388377 0.921501i \(-0.373036\pi\)
\(368\) 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 0.467104 + 0.884203i \(0.345297\pi\)
−0.999294 + 0.0375776i \(0.988036\pi\)
\(374\) 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 −0.785241 0.619190i \(-0.787461\pi\)
0.928855 + 0.370444i \(0.120794\pi\)
\(384\) 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 0.856995 0.515325i \(-0.172329\pi\)
−0.874782 + 0.484517i \(0.838995\pi\)
\(390\) 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 −0.962379 0.271710i \(-0.912411\pi\)
0.716497 + 0.697590i \(0.245744\pi\)
\(398\) 0 0
\(399\) −3.50829e13 3.38050e13i −0.173678 0.167352i
\(400\) 0 0
\(401\) −6.00607e13 + 1.04028e14i −0.289265 + 0.501022i −0.973635 0.228113i \(-0.926744\pi\)
0.684369 + 0.729136i \(0.260078\pi\)
\(402\) 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 0.539911 0.841722i \(-0.318458\pi\)
−0.998908 + 0.0467150i \(0.985125\pi\)
\(410\) 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 0.802835 0.596202i \(-0.203324\pi\)
−0.917743 + 0.397174i \(0.869991\pi\)
\(432\) 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 −0.439583 0.898202i \(-0.644874\pi\)
0.997657 0.0684109i \(-0.0217929\pi\)
\(440\) 0 0
\(441\) −1.03212e14 5.45891e13i −0.294658 0.155845i
\(442\) 0 0
\(443\) 6.88095e13 1.19182e14i 0.191614 0.331886i −0.754171 0.656678i \(-0.771961\pi\)
0.945785 + 0.324792i \(0.105294\pi\)
\(444\) 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 −0.0355355 0.999368i \(-0.511314\pi\)
0.883246 0.468910i \(-0.155353\pi\)
\(458\) 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 0.218033 + 0.975941i \(0.430036\pi\)
−0.954207 + 0.299148i \(0.903298\pi\)
\(468\) 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 0.927792 0.373098i \(-0.121705\pi\)
−0.787008 + 0.616942i \(0.788371\pi\)
\(480\) 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 0.693812 0.720156i \(-0.255930\pi\)
−0.970579 + 0.240781i \(0.922596\pi\)
\(488\) 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 −0.526868 0.849947i \(-0.676634\pi\)
0.999510 + 0.0313069i \(0.00996694\pi\)
\(500\) 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 −0.301686 0.953407i \(-0.597549\pi\)
0.976518 0.215436i \(-0.0691172\pi\)
\(510\) 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 0.758231 + 0.651986i \(0.226064\pi\)
0.185522 + 0.982640i \(0.440603\pi\)
\(522\) 0 0
\(523\) −2.37190e14 + 4.10824e14i −0.265055 + 0.459089i −0.967578 0.252572i \(-0.918724\pi\)
0.702523 + 0.711661i \(0.252057\pi\)
\(524\) 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 −0.960273 0.279062i \(-0.909977\pi\)
0.721811 + 0.692090i \(0.243310\pi\)
\(542\) 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 0.872124 + 0.489285i \(0.162742\pi\)
−0.0123289 + 0.999924i \(0.503925\pi\)
\(558\) 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 0.651023 0.759058i \(-0.274340\pi\)
−0.982875 + 0.184273i \(0.941007\pi\)
\(564\) 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 −0.0260291 + 0.999661i \(0.508286\pi\)
−0.852717 + 0.522372i \(0.825047\pi\)
\(570\) 0 0
\(571\) 1.20063e15 + 2.07955e15i 0.827773 + 1.43374i 0.899782 + 0.436341i \(0.143726\pi\)
−0.0720088 + 0.997404i \(0.522941\pi\)
\(572\) 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 −0.999674 0.0255249i \(-0.991874\pi\)
0.477732 0.878506i \(-0.341459\pi\)
\(578\) 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 −0.995580 0.0939186i \(-0.970061\pi\)
0.579126 + 0.815238i \(0.303394\pi\)
\(594\) 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 0.691357 0.722513i \(-0.257013\pi\)
−0.971393 + 0.237477i \(0.923680\pi\)
\(600\) 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 −0.999342 0.0362702i \(-0.988452\pi\)
0.531082 + 0.847320i \(0.321786\pi\)
\(608\) 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 0.730158 0.683279i \(-0.239447\pi\)
−0.956816 + 0.290696i \(0.906113\pi\)
\(614\) 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 −0.970564 0.240844i \(-0.922576\pi\)
0.276705 0.960955i \(-0.410758\pi\)
\(620\) 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 0.761618 0.648026i \(-0.224405\pi\)
−0.942016 + 0.335568i \(0.891072\pi\)
\(642\) 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 −0.999914 0.0130960i \(-0.995831\pi\)
0.488616 0.872499i \(-0.337502\pi\)
\(648\) 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 −0.603486 0.797374i \(-0.706222\pi\)
0.992289 + 0.123947i \(0.0395553\pi\)
\(654\) 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 0.959831 0.280577i \(-0.0905259\pi\)
−0.722903 + 0.690950i \(0.757193\pi\)
\(662\) 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 −0.582228 0.813025i \(-0.697819\pi\)
0.995215 + 0.0977120i \(0.0311524\pi\)
\(678\) 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 0.660447 0.750872i \(-0.270367\pi\)
−0.980498 + 0.196528i \(0.937033\pi\)
\(684\) 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 −0.573145 0.819454i \(-0.694277\pi\)
0.996240 + 0.0866310i \(0.0276101\pi\)
\(692\) 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 0.438155 + 0.898900i \(0.355632\pi\)
−0.997547 + 0.0699967i \(0.977701\pi\)
\(710\) 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 −0.680968 0.732313i \(-0.738441\pi\)
0.974686 + 0.223579i \(0.0717740\pi\)
\(720\) 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 −0.991551 0.129719i \(-0.958593\pi\)
0.608115 + 0.793849i \(0.291926\pi\)
\(734\) 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 0.772834 0.634609i \(-0.218839\pi\)
−0.936004 + 0.351989i \(0.885505\pi\)
\(740\) 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 0.200427 + 0.979709i \(0.435767\pi\)
−0.948666 + 0.316279i \(0.897566\pi\)
\(752\) 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 −0.438882 0.898545i \(-0.644625\pi\)
0.997604 0.0691896i \(-0.0220413\pi\)
\(762\) 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 0.953963 0.299925i \(-0.0969618\pi\)
−0.736724 + 0.676193i \(0.763628\pi\)
\(774\) 0 0
\(775\) −2.18443e15 + 3.78355e15i −0.280659 + 0.486116i
\(776\) 0