Properties

Label 84.9.m.b.73.5
Level $84$
Weight $9$
Character 84.73
Analytic conductor $34.220$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 84.m (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(34.2198032451\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \( x^{12} - 3 x^{11} + 148097 x^{10} + 46071824 x^{9} + 21578502553 x^{8} + 3561445462121 x^{7} + 576413321817541 x^{6} + \cdots + 45\!\cdots\!96 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{20}\cdot 3^{10}\cdot 7^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 73.5
Root \(221.993 - 384.503i\) of defining polynomial
Character \(\chi\) \(=\) 84.73
Dual form 84.9.m.b.61.5

$q$-expansion

\(f(q)\) \(=\) \(q+(40.5000 + 23.3827i) q^{3} +(632.551 - 365.204i) q^{5} +(984.437 - 2189.91i) q^{7} +(1093.50 + 1894.00i) q^{9} +O(q^{10})\) \(q+(40.5000 + 23.3827i) q^{3} +(632.551 - 365.204i) q^{5} +(984.437 - 2189.91i) q^{7} +(1093.50 + 1894.00i) q^{9} +(6353.95 - 11005.4i) q^{11} -21176.4i q^{13} +34157.8 q^{15} +(-82551.9 - 47661.3i) q^{17} +(-133336. + 76981.8i) q^{19} +(91075.6 - 65672.4i) q^{21} +(-47111.5 - 81599.5i) q^{23} +(71435.0 - 123729. i) q^{25} +102276. i q^{27} +541664. q^{29} +(-185730. - 107231. i) q^{31} +(514670. - 297145. i) q^{33} +(-177055. - 1.74475e6i) q^{35} +(-370376. - 641510. i) q^{37} +(495160. - 857643. i) q^{39} +782599. i q^{41} -221324. q^{43} +(1.38339e6 + 798700. i) q^{45} +(7.13230e6 - 4.11784e6i) q^{47} +(-3.82657e6 - 4.31165e6i) q^{49} +(-2.22890e6 - 3.86057e6i) q^{51} +(659083. - 1.14157e6i) q^{53} -9.28194e6i q^{55} -7.20016e6 q^{57} +(-7.52865e6 - 4.34667e6i) q^{59} +(1.31192e7 - 7.57439e6i) q^{61} +(5.22416e6 - 530140. i) q^{63} +(-7.73369e6 - 1.33951e7i) q^{65} +(1.99100e7 - 3.44851e7i) q^{67} -4.40638e6i q^{69} -9.34713e6 q^{71} +(2.94520e7 + 1.70041e7i) q^{73} +(5.78623e6 - 3.34068e6i) q^{75} +(-1.78456e7 - 2.47486e7i) q^{77} +(2.26450e7 + 3.92223e7i) q^{79} +(-2.39148e6 + 4.14217e6i) q^{81} +6.58893e7i q^{83} -6.96244e7 q^{85} +(2.19374e7 + 1.26656e7i) q^{87} +(-1.09902e7 + 6.34517e6i) q^{89} +(-4.63742e7 - 2.08468e7i) q^{91} +(-5.01470e6 - 8.68571e6i) q^{93} +(-5.62280e7 + 9.73898e7i) q^{95} +6.15780e6i q^{97} +2.77922e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 486 q^{3} + 285 q^{5} + 198 q^{7} + 13122 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 486 q^{3} + 285 q^{5} + 198 q^{7} + 13122 q^{9} - 17919 q^{11} + 15390 q^{15} - 205782 q^{17} + 74313 q^{19} - 39609 q^{21} - 62832 q^{23} + 878679 q^{25} - 575454 q^{29} + 1442952 q^{31} - 1451439 q^{33} - 3989514 q^{35} - 2058621 q^{37} - 930933 q^{39} + 7721322 q^{43} + 623295 q^{45} + 12088194 q^{47} - 16964694 q^{49} - 5556114 q^{51} - 5506743 q^{53} + 4012902 q^{57} + 7511901 q^{59} - 37215576 q^{61} - 3641355 q^{63} + 5047122 q^{65} - 36824553 q^{67} - 30011556 q^{71} + 95080185 q^{73} + 71172999 q^{75} - 38333727 q^{77} + 8514456 q^{79} - 28697814 q^{81} + 20121540 q^{85} - 23305887 q^{87} + 83038554 q^{89} - 198538635 q^{91} + 38959704 q^{93} - 221605224 q^{95} - 78377706 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(29\) \(43\) \(73\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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
\(3\) 40.5000 + 23.3827i 0.500000 + 0.288675i
\(4\) 0 0
\(5\) 632.551 365.204i 1.01208 0.584326i 0.100282 0.994959i \(-0.468026\pi\)
0.911801 + 0.410633i \(0.134692\pi\)
\(6\) 0 0
\(7\) 984.437 2189.91i 0.410011 0.912080i
\(8\) 0 0
\(9\) 1093.50 + 1894.00i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) 6353.95 11005.4i 0.433983 0.751681i −0.563229 0.826301i \(-0.690441\pi\)
0.997212 + 0.0746198i \(0.0237743\pi\)
\(12\) 0 0
\(13\) 21176.4i 0.741444i −0.928744 0.370722i \(-0.879110\pi\)
0.928744 0.370722i \(-0.120890\pi\)
\(14\) 0 0
\(15\) 34157.8 0.674721
\(16\) 0 0
\(17\) −82551.9 47661.3i −0.988397 0.570651i −0.0836020 0.996499i \(-0.526642\pi\)
−0.904795 + 0.425848i \(0.859976\pi\)
\(18\) 0 0
\(19\) −133336. + 76981.8i −1.02314 + 0.590709i −0.915011 0.403428i \(-0.867818\pi\)
−0.108126 + 0.994137i \(0.534485\pi\)
\(20\) 0 0
\(21\) 91075.6 65672.4i 0.468301 0.337680i
\(22\) 0 0
\(23\) −47111.5 81599.5i −0.168351 0.291593i 0.769489 0.638660i \(-0.220511\pi\)
−0.937840 + 0.347067i \(0.887178\pi\)
\(24\) 0 0
\(25\) 71435.0 123729.i 0.182874 0.316746i
\(26\) 0 0
\(27\) 102276.i 0.192450i
\(28\) 0 0
\(29\) 541664. 0.765840 0.382920 0.923782i \(-0.374919\pi\)
0.382920 + 0.923782i \(0.374919\pi\)
\(30\) 0 0
\(31\) −185730. 107231.i −0.201110 0.116111i 0.396063 0.918223i \(-0.370376\pi\)
−0.597173 + 0.802112i \(0.703710\pi\)
\(32\) 0 0
\(33\) 514670. 297145.i 0.433983 0.250560i
\(34\) 0 0
\(35\) −177055. 1.74475e6i −0.117987 1.16268i
\(36\) 0 0
\(37\) −370376. 641510.i −0.197622 0.342292i 0.750135 0.661285i \(-0.229989\pi\)
−0.947757 + 0.318993i \(0.896655\pi\)
\(38\) 0 0
\(39\) 495160. 857643.i 0.214036 0.370722i
\(40\) 0 0
\(41\) 782599.i 0.276952i 0.990366 + 0.138476i \(0.0442203\pi\)
−0.990366 + 0.138476i \(0.955780\pi\)
\(42\) 0 0
\(43\) −221324. −0.0647373 −0.0323687 0.999476i \(-0.510305\pi\)
−0.0323687 + 0.999476i \(0.510305\pi\)
\(44\) 0 0
\(45\) 1.38339e6 + 798700.i 0.337361 + 0.194775i
\(46\) 0 0
\(47\) 7.13230e6 4.11784e6i 1.46163 0.843874i 0.462546 0.886595i \(-0.346936\pi\)
0.999087 + 0.0427209i \(0.0136026\pi\)
\(48\) 0 0
\(49\) −3.82657e6 4.31165e6i −0.663782 0.747926i
\(50\) 0 0
\(51\) −2.22890e6 3.86057e6i −0.329466 0.570651i
\(52\) 0 0
\(53\) 659083. 1.14157e6i 0.0835289 0.144676i −0.821235 0.570591i \(-0.806714\pi\)
0.904763 + 0.425915i \(0.140048\pi\)
\(54\) 0 0
\(55\) 9.28194e6i 1.01435i
\(56\) 0 0
\(57\) −7.20016e6 −0.682092
\(58\) 0 0
\(59\) −7.52865e6 4.34667e6i −0.621311 0.358714i 0.156068 0.987746i \(-0.450118\pi\)
−0.777379 + 0.629032i \(0.783451\pi\)
\(60\) 0 0
\(61\) 1.31192e7 7.57439e6i 0.947521 0.547052i 0.0552112 0.998475i \(-0.482417\pi\)
0.892310 + 0.451423i \(0.149083\pi\)
\(62\) 0 0
\(63\) 5.22416e6 530140.i 0.331630 0.0336534i
\(64\) 0 0
\(65\) −7.73369e6 1.33951e7i −0.433245 0.750402i
\(66\) 0 0
\(67\) 1.99100e7 3.44851e7i 0.988033 1.71132i 0.360436 0.932784i \(-0.382628\pi\)
0.627596 0.778539i \(-0.284039\pi\)
\(68\) 0 0
\(69\) 4.40638e6i 0.194395i
\(70\) 0 0
\(71\) −9.34713e6 −0.367828 −0.183914 0.982942i \(-0.558877\pi\)
−0.183914 + 0.982942i \(0.558877\pi\)
\(72\) 0 0
\(73\) 2.94520e7 + 1.70041e7i 1.03711 + 0.598774i 0.919012 0.394229i \(-0.128988\pi\)
0.118094 + 0.993002i \(0.462321\pi\)
\(74\) 0 0
\(75\) 5.78623e6 3.34068e6i 0.182874 0.105582i
\(76\) 0 0
\(77\) −1.78456e7 2.47486e7i −0.507656 0.704025i
\(78\) 0 0
\(79\) 2.26450e7 + 3.92223e7i 0.581385 + 1.00699i 0.995316 + 0.0966799i \(0.0308223\pi\)
−0.413931 + 0.910308i \(0.635844\pi\)
\(80\) 0 0
\(81\) −2.39148e6 + 4.14217e6i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 6.58893e7i 1.38836i 0.719801 + 0.694180i \(0.244233\pi\)
−0.719801 + 0.694180i \(0.755767\pi\)
\(84\) 0 0
\(85\) −6.96244e7 −1.33378
\(86\) 0 0
\(87\) 2.19374e7 + 1.26656e7i 0.382920 + 0.221079i
\(88\) 0 0
\(89\) −1.09902e7 + 6.34517e6i −0.175164 + 0.101131i −0.585018 0.811020i \(-0.698913\pi\)
0.409855 + 0.912151i \(0.365579\pi\)
\(90\) 0 0
\(91\) −4.63742e7 2.08468e7i −0.676256 0.304000i
\(92\) 0 0
\(93\) −5.01470e6 8.68571e6i −0.0670368 0.116111i
\(94\) 0 0
\(95\) −5.62280e7 + 9.73898e7i −0.690333 + 1.19569i
\(96\) 0 0
\(97\) 6.15780e6i 0.0695566i 0.999395 + 0.0347783i \(0.0110725\pi\)
−0.999395 + 0.0347783i \(0.988927\pi\)
\(98\) 0 0
\(99\) 2.77922e7 0.289322
\(100\) 0 0
\(101\) 1.15329e8 + 6.65855e7i 1.10829 + 0.639874i 0.938387 0.345587i \(-0.112320\pi\)
0.169907 + 0.985460i \(0.445653\pi\)
\(102\) 0 0
\(103\) 4.81925e7 2.78240e7i 0.428184 0.247212i −0.270389 0.962751i \(-0.587152\pi\)
0.698573 + 0.715539i \(0.253819\pi\)
\(104\) 0 0
\(105\) 3.36262e7 7.48023e7i 0.276643 0.615400i
\(106\) 0 0
\(107\) 7.23667e6 + 1.25343e7i 0.0552082 + 0.0956234i 0.892309 0.451426i \(-0.149084\pi\)
−0.837101 + 0.547049i \(0.815751\pi\)
\(108\) 0 0
\(109\) −9.01793e7 + 1.56195e8i −0.638853 + 1.10653i 0.346832 + 0.937927i \(0.387257\pi\)
−0.985685 + 0.168598i \(0.946076\pi\)
\(110\) 0 0
\(111\) 3.46415e7i 0.228195i
\(112\) 0 0
\(113\) −2.21791e7 −0.136028 −0.0680142 0.997684i \(-0.521666\pi\)
−0.0680142 + 0.997684i \(0.521666\pi\)
\(114\) 0 0
\(115\) −5.96009e7 3.44106e7i −0.340770 0.196744i
\(116\) 0 0
\(117\) 4.01080e7 2.31564e7i 0.214036 0.123574i
\(118\) 0 0
\(119\) −1.85641e8 + 1.33861e8i −0.925733 + 0.667524i
\(120\) 0 0
\(121\) 2.64341e7 + 4.57852e7i 0.123317 + 0.213591i
\(122\) 0 0
\(123\) −1.82993e7 + 3.16953e7i −0.0799490 + 0.138476i
\(124\) 0 0
\(125\) 1.80962e8i 0.741221i
\(126\) 0 0
\(127\) 1.77711e8 0.683123 0.341561 0.939859i \(-0.389044\pi\)
0.341561 + 0.939859i \(0.389044\pi\)
\(128\) 0 0
\(129\) −8.96362e6 5.17515e6i −0.0323687 0.0186881i
\(130\) 0 0
\(131\) −4.83164e8 + 2.78955e8i −1.64062 + 0.947215i −0.660012 + 0.751255i \(0.729449\pi\)
−0.980612 + 0.195960i \(0.937218\pi\)
\(132\) 0 0
\(133\) 3.73216e7 + 3.67778e8i 0.119276 + 1.17538i
\(134\) 0 0
\(135\) 3.73515e7 + 6.46947e7i 0.112454 + 0.194775i
\(136\) 0 0
\(137\) −1.96914e8 + 3.41064e8i −0.558977 + 0.968176i 0.438606 + 0.898680i \(0.355472\pi\)
−0.997582 + 0.0694962i \(0.977861\pi\)
\(138\) 0 0
\(139\) 4.85677e8i 1.30103i −0.759492 0.650516i \(-0.774553\pi\)
0.759492 0.650516i \(-0.225447\pi\)
\(140\) 0 0
\(141\) 3.85144e8 0.974422
\(142\) 0 0
\(143\) −2.33054e8 1.34554e8i −0.557329 0.321774i
\(144\) 0 0
\(145\) 3.42630e8 1.97818e8i 0.775093 0.447500i
\(146\) 0 0
\(147\) −5.41582e7 2.64097e8i −0.115983 0.565580i
\(148\) 0 0
\(149\) 1.60563e8 + 2.78103e8i 0.325762 + 0.564236i 0.981666 0.190608i \(-0.0610459\pi\)
−0.655905 + 0.754844i \(0.727713\pi\)
\(150\) 0 0
\(151\) 4.12702e8 7.14822e8i 0.793833 1.37496i −0.129744 0.991547i \(-0.541416\pi\)
0.923577 0.383412i \(-0.125251\pi\)
\(152\) 0 0
\(153\) 2.08471e8i 0.380434i
\(154\) 0 0
\(155\) −1.56645e8 −0.271387
\(156\) 0 0
\(157\) 9.15549e8 + 5.28592e8i 1.50689 + 0.870006i 0.999968 + 0.00801653i \(0.00255177\pi\)
0.506926 + 0.861989i \(0.330782\pi\)
\(158\) 0 0
\(159\) 5.33857e7 3.08223e7i 0.0835289 0.0482254i
\(160\) 0 0
\(161\) −2.25074e8 + 2.28402e7i −0.334982 + 0.0339935i
\(162\) 0 0
\(163\) −5.67831e8 9.83512e8i −0.804394 1.39325i −0.916699 0.399577i \(-0.869157\pi\)
0.112306 0.993674i \(-0.464176\pi\)
\(164\) 0 0
\(165\) 2.17037e8 3.75919e8i 0.292818 0.507175i
\(166\) 0 0
\(167\) 1.00076e9i 1.28666i −0.765591 0.643328i \(-0.777553\pi\)
0.765591 0.643328i \(-0.222447\pi\)
\(168\) 0 0
\(169\) 3.67292e8 0.450261
\(170\) 0 0
\(171\) −2.91606e8 1.68359e8i −0.341046 0.196903i
\(172\) 0 0
\(173\) −5.46649e8 + 3.15608e8i −0.610273 + 0.352341i −0.773072 0.634318i \(-0.781281\pi\)
0.162799 + 0.986659i \(0.447948\pi\)
\(174\) 0 0
\(175\) −2.00632e8 2.78239e8i −0.213918 0.296665i
\(176\) 0 0
\(177\) −2.03274e8 3.52080e8i −0.207104 0.358714i
\(178\) 0 0
\(179\) −5.77342e8 + 9.99986e8i −0.562369 + 0.974052i 0.434920 + 0.900469i \(0.356777\pi\)
−0.997289 + 0.0735826i \(0.976557\pi\)
\(180\) 0 0
\(181\) 1.42212e9i 1.32502i −0.749052 0.662511i \(-0.769491\pi\)
0.749052 0.662511i \(-0.230509\pi\)
\(182\) 0 0
\(183\) 7.08438e8 0.631681
\(184\) 0 0
\(185\) −4.68564e8 2.70525e8i −0.400020 0.230952i
\(186\) 0 0
\(187\) −1.04906e9 + 6.05676e8i −0.857895 + 0.495306i
\(188\) 0 0
\(189\) 2.23974e8 + 1.00684e8i 0.175530 + 0.0789067i
\(190\) 0 0
\(191\) 3.05844e8 + 5.29737e8i 0.229809 + 0.398040i 0.957751 0.287598i \(-0.0928566\pi\)
−0.727943 + 0.685638i \(0.759523\pi\)
\(192\) 0 0
\(193\) 9.49542e8 1.64465e9i 0.684360 1.18535i −0.289277 0.957245i \(-0.593415\pi\)
0.973637 0.228101i \(-0.0732518\pi\)
\(194\) 0 0
\(195\) 7.23338e8i 0.500268i
\(196\) 0 0
\(197\) 1.00843e9 0.669544 0.334772 0.942299i \(-0.391341\pi\)
0.334772 + 0.942299i \(0.391341\pi\)
\(198\) 0 0
\(199\) 2.76255e8 + 1.59496e8i 0.176156 + 0.101704i 0.585485 0.810683i \(-0.300904\pi\)
−0.409329 + 0.912387i \(0.634237\pi\)
\(200\) 0 0
\(201\) 1.61271e9 9.31097e8i 0.988033 0.570441i
\(202\) 0 0
\(203\) 5.33234e8 1.18619e9i 0.314003 0.698507i
\(204\) 0 0
\(205\) 2.85808e8 + 4.95034e8i 0.161830 + 0.280298i
\(206\) 0 0
\(207\) 1.03033e8 1.78458e8i 0.0561170 0.0971975i
\(208\) 0 0
\(209\) 1.95655e9i 1.02543i
\(210\) 0 0
\(211\) −1.39969e9 −0.706160 −0.353080 0.935593i \(-0.614866\pi\)
−0.353080 + 0.935593i \(0.614866\pi\)
\(212\) 0 0
\(213\) −3.78559e8 2.18561e8i −0.183914 0.106183i
\(214\) 0 0
\(215\) −1.39999e8 + 8.08283e7i −0.0655195 + 0.0378277i
\(216\) 0 0
\(217\) −4.17665e8 + 3.01168e8i −0.188360 + 0.135822i
\(218\) 0 0
\(219\) 7.95204e8 + 1.37733e9i 0.345702 + 0.598774i
\(220\) 0 0
\(221\) −1.00929e9 + 1.74815e9i −0.423106 + 0.732840i
\(222\) 0 0
\(223\) 3.09118e9i 1.24999i 0.780630 + 0.624993i \(0.214898\pi\)
−0.780630 + 0.624993i \(0.785102\pi\)
\(224\) 0 0
\(225\) 3.12457e8 0.121916
\(226\) 0 0
\(227\) −3.27805e9 1.89258e9i −1.23456 0.712774i −0.266583 0.963812i \(-0.585895\pi\)
−0.967977 + 0.251038i \(0.919228\pi\)
\(228\) 0 0
\(229\) −2.74391e9 + 1.58420e9i −0.997763 + 0.576059i −0.907586 0.419867i \(-0.862077\pi\)
−0.0901773 + 0.995926i \(0.528743\pi\)
\(230\) 0 0
\(231\) −1.44059e8 1.41960e9i −0.0505932 0.498560i
\(232\) 0 0
\(233\) 2.76314e9 + 4.78590e9i 0.937518 + 1.62383i 0.770081 + 0.637946i \(0.220216\pi\)
0.167437 + 0.985883i \(0.446451\pi\)
\(234\) 0 0
\(235\) 3.00770e9 5.20949e9i 0.986195 1.70814i
\(236\) 0 0
\(237\) 2.11800e9i 0.671326i
\(238\) 0 0
\(239\) −3.93530e9 −1.20611 −0.603054 0.797701i \(-0.706049\pi\)
−0.603054 + 0.797701i \(0.706049\pi\)
\(240\) 0 0
\(241\) 5.76301e9 + 3.32727e9i 1.70837 + 0.986326i 0.936586 + 0.350437i \(0.113967\pi\)
0.771780 + 0.635889i \(0.219367\pi\)
\(242\) 0 0
\(243\) −1.93710e8 + 1.11839e8i −0.0555556 + 0.0320750i
\(244\) 0 0
\(245\) −3.99513e9 1.32986e9i −1.10883 0.369098i
\(246\) 0 0
\(247\) 1.63019e9 + 2.82358e9i 0.437977 + 0.758599i
\(248\) 0 0
\(249\) −1.54067e9 + 2.66852e9i −0.400785 + 0.694180i
\(250\) 0 0
\(251\) 4.25680e9i 1.07248i 0.844066 + 0.536239i \(0.180155\pi\)
−0.844066 + 0.536239i \(0.819845\pi\)
\(252\) 0 0
\(253\) −1.19738e9 −0.292246
\(254\) 0 0
\(255\) −2.81979e9 1.62801e9i −0.666892 0.385031i
\(256\) 0 0
\(257\) −2.63398e9 + 1.52073e9i −0.603782 + 0.348593i −0.770528 0.637406i \(-0.780007\pi\)
0.166746 + 0.986000i \(0.446674\pi\)
\(258\) 0 0
\(259\) −1.76946e9 + 1.79562e8i −0.393225 + 0.0399039i
\(260\) 0 0
\(261\) 5.92309e8 + 1.02591e9i 0.127640 + 0.221079i
\(262\) 0 0
\(263\) 4.20815e9 7.28873e9i 0.879566 1.52345i 0.0277486 0.999615i \(-0.491166\pi\)
0.851818 0.523838i \(-0.175500\pi\)
\(264\) 0 0
\(265\) 9.62798e8i 0.195232i
\(266\) 0 0
\(267\) −5.93468e8 −0.116776
\(268\) 0 0
\(269\) 6.40038e9 + 3.69526e9i 1.22235 + 0.705726i 0.965419 0.260703i \(-0.0839542\pi\)
0.256934 + 0.966429i \(0.417288\pi\)
\(270\) 0 0
\(271\) −3.72934e9 + 2.15314e9i −0.691441 + 0.399204i −0.804152 0.594424i \(-0.797380\pi\)
0.112711 + 0.993628i \(0.464047\pi\)
\(272\) 0 0
\(273\) −1.39070e9 1.92865e9i −0.250371 0.347218i
\(274\) 0 0
\(275\) −9.07789e8 1.57234e9i −0.158728 0.274925i
\(276\) 0 0
\(277\) −2.54312e7 + 4.40481e7i −0.00431964 + 0.00748183i −0.868177 0.496254i \(-0.834708\pi\)
0.863858 + 0.503736i \(0.168042\pi\)
\(278\) 0 0
\(279\) 4.69028e8i 0.0774074i
\(280\) 0 0
\(281\) 1.03421e10 1.65877 0.829383 0.558680i \(-0.188692\pi\)
0.829383 + 0.558680i \(0.188692\pi\)
\(282\) 0 0
\(283\) −2.55984e9 1.47792e9i −0.399086 0.230412i 0.287003 0.957930i \(-0.407341\pi\)
−0.686090 + 0.727517i \(0.740674\pi\)
\(284\) 0 0
\(285\) −4.55447e9 + 2.62953e9i −0.690333 + 0.398564i
\(286\) 0 0
\(287\) 1.71382e9 + 7.70419e8i 0.252602 + 0.113553i
\(288\) 0 0
\(289\) 1.05533e9 + 1.82788e9i 0.151285 + 0.262034i
\(290\) 0 0
\(291\) −1.43986e8 + 2.49391e8i −0.0200793 + 0.0347783i
\(292\) 0 0
\(293\) 4.22563e9i 0.573351i −0.958028 0.286676i \(-0.907450\pi\)
0.958028 0.286676i \(-0.0925502\pi\)
\(294\) 0 0
\(295\) −6.34968e9 −0.838424
\(296\) 0 0
\(297\) 1.12558e9 + 6.49856e8i 0.144661 + 0.0835201i
\(298\) 0 0
\(299\) −1.72798e9 + 9.97651e8i −0.216199 + 0.124823i
\(300\) 0 0
\(301\) −2.17880e8 + 4.84679e8i −0.0265430 + 0.0590456i
\(302\) 0 0
\(303\) 3.11390e9 + 5.39343e9i 0.369431 + 0.639874i
\(304\) 0 0
\(305\) 5.53239e9 9.58238e9i 0.639313 1.10732i
\(306\) 0 0
\(307\) 2.96070e9i 0.333304i 0.986016 + 0.166652i \(0.0532956\pi\)
−0.986016 + 0.166652i \(0.946704\pi\)
\(308\) 0 0
\(309\) 2.60240e9 0.285456
\(310\) 0 0
\(311\) −7.74956e9 4.47421e9i −0.828391 0.478272i 0.0249101 0.999690i \(-0.492070\pi\)
−0.853302 + 0.521418i \(0.825403\pi\)
\(312\) 0 0
\(313\) −5.04664e9 + 2.91368e9i −0.525806 + 0.303574i −0.739307 0.673369i \(-0.764847\pi\)
0.213501 + 0.976943i \(0.431513\pi\)
\(314\) 0 0
\(315\) 3.11094e9 2.24322e9i 0.315972 0.227840i
\(316\) 0 0
\(317\) 2.50614e9 + 4.34076e9i 0.248181 + 0.429861i 0.963021 0.269426i \(-0.0868340\pi\)
−0.714840 + 0.699288i \(0.753501\pi\)
\(318\) 0 0
\(319\) 3.44171e9 5.96121e9i 0.332362 0.575667i
\(320\) 0 0
\(321\) 6.76851e8i 0.0637489i
\(322\) 0 0
\(323\) 1.46762e10 1.34835
\(324\) 0 0
\(325\) −2.62013e9 1.51273e9i −0.234850 0.135590i
\(326\) 0 0
\(327\) −7.30452e9 + 4.21727e9i −0.638853 + 0.368842i
\(328\) 0 0
\(329\) −1.99637e9 1.96728e10i −0.170395 1.67912i
\(330\) 0 0
\(331\) 4.78357e9 + 8.28539e9i 0.398511 + 0.690242i 0.993542 0.113461i \(-0.0361937\pi\)
−0.595031 + 0.803703i \(0.702860\pi\)
\(332\) 0 0
\(333\) 8.10012e8 1.40298e9i 0.0658741 0.114097i
\(334\) 0 0
\(335\) 2.90848e10i 2.30933i
\(336\) 0 0
\(337\) 2.32884e9 0.180560 0.0902798 0.995916i \(-0.471224\pi\)
0.0902798 + 0.995916i \(0.471224\pi\)
\(338\) 0 0
\(339\) −8.98252e8 5.18606e8i −0.0680142 0.0392680i
\(340\) 0 0
\(341\) −2.36023e9 + 1.36268e9i −0.174557 + 0.100781i
\(342\) 0 0
\(343\) −1.32091e10 + 4.13528e9i −0.954327 + 0.298764i
\(344\) 0 0
\(345\) −1.60922e9 2.78726e9i −0.113590 0.196744i
\(346\) 0 0
\(347\) 1.04233e10 1.80536e10i 0.718928 1.24522i −0.242497 0.970152i \(-0.577966\pi\)
0.961425 0.275068i \(-0.0887002\pi\)
\(348\) 0 0
\(349\) 2.91490e10i 1.96482i −0.186745 0.982409i \(-0.559794\pi\)
0.186745 0.982409i \(-0.440206\pi\)
\(350\) 0 0
\(351\) 2.16583e9 0.142691
\(352\) 0 0
\(353\) 9.78829e8 + 5.65127e8i 0.0630388 + 0.0363955i 0.531188 0.847254i \(-0.321746\pi\)
−0.468149 + 0.883649i \(0.655079\pi\)
\(354\) 0 0
\(355\) −5.91254e9 + 3.41361e9i −0.372272 + 0.214932i
\(356\) 0 0
\(357\) −1.06485e10 + 1.08059e9i −0.655564 + 0.0665258i
\(358\) 0 0
\(359\) 5.49405e9 + 9.51597e9i 0.330761 + 0.572896i 0.982661 0.185409i \(-0.0593611\pi\)
−0.651900 + 0.758305i \(0.726028\pi\)
\(360\) 0 0
\(361\) 3.36060e9 5.82073e9i 0.197874 0.342727i
\(362\) 0 0
\(363\) 2.47240e9i 0.142394i
\(364\) 0 0
\(365\) 2.48399e10 1.39952
\(366\) 0 0
\(367\) −2.47539e9 1.42917e9i −0.136452 0.0787805i 0.430220 0.902724i \(-0.358436\pi\)
−0.566672 + 0.823944i \(0.691769\pi\)
\(368\) 0 0
\(369\) −1.48224e9 + 8.55772e8i −0.0799490 + 0.0461586i
\(370\) 0 0
\(371\) −1.85109e9 2.56713e9i −0.0977086 0.135504i
\(372\) 0 0
\(373\) 8.91785e9 + 1.54462e10i 0.460707 + 0.797968i 0.998996 0.0447919i \(-0.0142625\pi\)
−0.538289 + 0.842760i \(0.680929\pi\)
\(374\) 0 0
\(375\) −4.23138e9 + 7.32897e9i −0.213972 + 0.370610i
\(376\) 0 0
\(377\) 1.14705e10i 0.567827i
\(378\) 0 0
\(379\) 3.25934e10 1.57969 0.789847 0.613303i \(-0.210160\pi\)
0.789847 + 0.613303i \(0.210160\pi\)
\(380\) 0 0
\(381\) 7.19729e9 + 4.15536e9i 0.341561 + 0.197201i
\(382\) 0 0
\(383\) −1.90349e10 + 1.09898e10i −0.884619 + 0.510735i −0.872179 0.489187i \(-0.837293\pi\)
−0.0124407 + 0.999923i \(0.503960\pi\)
\(384\) 0 0
\(385\) −2.03266e10 9.13749e9i −0.925170 0.415895i
\(386\) 0 0
\(387\) −2.42018e8 4.19187e8i −0.0107896 0.0186881i
\(388\) 0 0
\(389\) −1.09555e10 + 1.89755e10i −0.478448 + 0.828695i −0.999695 0.0247103i \(-0.992134\pi\)
0.521247 + 0.853406i \(0.325467\pi\)
\(390\) 0 0
\(391\) 8.98159e9i 0.384279i
\(392\) 0 0
\(393\) −2.60908e10 −1.09375
\(394\) 0 0
\(395\) 2.86482e10 + 1.65401e10i 1.17682 + 0.679437i
\(396\) 0 0
\(397\) −4.10594e10 + 2.37057e10i −1.65292 + 0.954312i −0.677052 + 0.735936i \(0.736743\pi\)
−0.975865 + 0.218376i \(0.929924\pi\)
\(398\) 0 0
\(399\) −7.08810e9 + 1.57677e10i −0.279665 + 0.622123i
\(400\) 0 0
\(401\) 6.47336e8 + 1.12122e9i 0.0250353 + 0.0433623i 0.878272 0.478162i \(-0.158697\pi\)
−0.853236 + 0.521524i \(0.825364\pi\)
\(402\) 0 0
\(403\) −2.27076e9 + 3.93308e9i −0.0860898 + 0.149112i
\(404\) 0 0
\(405\) 3.49352e9i 0.129850i
\(406\) 0 0
\(407\) −9.41340e9 −0.343059
\(408\) 0 0
\(409\) 1.05517e10 + 6.09204e9i 0.377077 + 0.217705i 0.676546 0.736401i \(-0.263476\pi\)
−0.299469 + 0.954106i \(0.596809\pi\)
\(410\) 0 0
\(411\) −1.59500e10 + 9.20874e9i −0.558977 + 0.322725i
\(412\) 0 0
\(413\) −1.69303e10 + 1.22080e10i −0.581921 + 0.419609i
\(414\) 0 0
\(415\) 2.40630e10 + 4.16783e10i 0.811255 + 1.40514i
\(416\) 0 0
\(417\) 1.13564e10 1.96699e10i 0.375576 0.650516i
\(418\) 0 0
\(419\) 2.83249e9i 0.0918992i 0.998944 + 0.0459496i \(0.0146314\pi\)
−0.998944 + 0.0459496i \(0.985369\pi\)
\(420\) 0 0
\(421\) 1.47344e10 0.469033 0.234517 0.972112i \(-0.424649\pi\)
0.234517 + 0.972112i \(0.424649\pi\)
\(422\) 0 0
\(423\) 1.55983e10 + 9.00571e9i 0.487211 + 0.281291i
\(424\) 0 0
\(425\) −1.17942e10 + 6.80938e9i −0.361503 + 0.208714i
\(426\) 0 0
\(427\) −3.67214e9 3.61864e10i −0.110461 1.08851i
\(428\) 0 0
\(429\) −6.29245e9 1.08988e10i −0.185776 0.321774i
\(430\) 0 0
\(431\) 1.99404e10 3.45377e10i 0.577862 1.00089i −0.417862 0.908510i \(-0.637220\pi\)
0.995724 0.0923761i \(-0.0294462\pi\)
\(432\) 0 0
\(433\) 3.77901e10i 1.07505i 0.843249 + 0.537523i \(0.180640\pi\)
−0.843249 + 0.537523i \(0.819360\pi\)
\(434\) 0 0
\(435\) 1.85020e10 0.516729
\(436\) 0 0
\(437\) 1.25634e10 + 7.25345e9i 0.344493 + 0.198893i
\(438\) 0 0
\(439\) 7.02545e9 4.05614e9i 0.189154 0.109208i −0.402432 0.915450i \(-0.631835\pi\)
0.591587 + 0.806242i \(0.298502\pi\)
\(440\) 0 0
\(441\) 3.98190e9 1.19623e10i 0.105277 0.316272i
\(442\) 0 0
\(443\) 2.85877e10 + 4.95154e10i 0.742274 + 1.28566i 0.951457 + 0.307780i \(0.0995861\pi\)
−0.209183 + 0.977876i \(0.567081\pi\)
\(444\) 0 0
\(445\) −4.63456e9 + 8.02729e9i −0.118187 + 0.204705i
\(446\) 0 0
\(447\) 1.50176e10i 0.376157i
\(448\) 0 0
\(449\) −6.27811e10 −1.54470 −0.772349 0.635199i \(-0.780918\pi\)
−0.772349 + 0.635199i \(0.780918\pi\)
\(450\) 0 0
\(451\) 8.61279e9 + 4.97259e9i 0.208179 + 0.120192i
\(452\) 0 0
\(453\) 3.34289e10 1.93002e10i 0.793833 0.458320i
\(454\) 0 0
\(455\) −3.69474e10 + 3.74937e9i −0.862062 + 0.0874809i
\(456\) 0 0
\(457\) −8.34859e9 1.44602e10i −0.191403 0.331519i 0.754313 0.656515i \(-0.227970\pi\)
−0.945715 + 0.324996i \(0.894637\pi\)
\(458\) 0 0
\(459\) 4.87461e9 8.44306e9i 0.109822 0.190217i
\(460\) 0 0
\(461\) 1.39906e10i 0.309766i 0.987933 + 0.154883i \(0.0495001\pi\)
−0.987933 + 0.154883i \(0.950500\pi\)
\(462\) 0 0
\(463\) −2.56476e10 −0.558114 −0.279057 0.960274i \(-0.590022\pi\)
−0.279057 + 0.960274i \(0.590022\pi\)
\(464\) 0 0
\(465\) −6.34411e9 3.66277e9i −0.135693 0.0783426i
\(466\) 0 0
\(467\) −3.36726e10 + 1.94409e10i −0.707960 + 0.408741i −0.810305 0.586008i \(-0.800699\pi\)
0.102345 + 0.994749i \(0.467365\pi\)
\(468\) 0 0
\(469\) −5.59189e10 7.75493e10i −1.15576 1.60283i
\(470\) 0 0
\(471\) 2.47198e10 + 4.28160e10i 0.502298 + 0.870006i
\(472\) 0 0
\(473\) −1.40628e9 + 2.43575e9i −0.0280949 + 0.0486618i
\(474\) 0 0
\(475\) 2.19968e10i 0.432100i
\(476\) 0 0
\(477\) 2.88283e9 0.0556859
\(478\) 0 0
\(479\) 6.40797e9 + 3.69965e9i 0.121725 + 0.0702778i 0.559626 0.828745i \(-0.310945\pi\)
−0.437901 + 0.899023i \(0.644278\pi\)
\(480\) 0 0
\(481\) −1.35849e10 + 7.84322e9i −0.253790 + 0.146526i
\(482\) 0 0
\(483\) −9.64954e9 4.33780e9i −0.177304 0.0797041i
\(484\) 0 0
\(485\) 2.24885e9 + 3.89512e9i 0.0406437 + 0.0703970i
\(486\) 0 0
\(487\) −1.11183e10 + 1.92575e10i −0.197662 + 0.342361i −0.947770 0.318954i \(-0.896668\pi\)
0.750108 + 0.661316i \(0.230002\pi\)
\(488\) 0 0
\(489\) 5.31097e10i 0.928834i
\(490\) 0 0
\(491\) 3.62576e10 0.623839 0.311920 0.950109i \(-0.399028\pi\)
0.311920 + 0.950109i \(0.399028\pi\)
\(492\) 0 0
\(493\) −4.47154e10 2.58164e10i −0.756953 0.437027i
\(494\) 0 0
\(495\) 1.75800e10 1.01498e10i 0.292818 0.169058i
\(496\) 0 0
\(497\) −9.20166e9 + 2.04693e10i −0.150814 + 0.335489i
\(498\) 0 0
\(499\) 3.67859e10 + 6.37151e10i 0.593307 + 1.02764i 0.993783 + 0.111331i \(0.0355114\pi\)
−0.400476 + 0.916307i \(0.631155\pi\)
\(500\) 0 0
\(501\) 2.34004e10 4.05306e10i 0.371425 0.643328i
\(502\) 0 0
\(503\) 5.49729e10i 0.858770i −0.903122 0.429385i \(-0.858730\pi\)
0.903122 0.429385i \(-0.141270\pi\)
\(504\) 0 0
\(505\) 9.72691e10 1.49558
\(506\) 0 0
\(507\) 1.48753e10 + 8.58827e9i 0.225131 + 0.129979i
\(508\) 0 0
\(509\) −5.64437e10 + 3.25878e10i −0.840900 + 0.485494i −0.857570 0.514367i \(-0.828027\pi\)
0.0166697 + 0.999861i \(0.494694\pi\)
\(510\) 0 0
\(511\) 6.62311e10 4.77576e10i 0.971355 0.700421i
\(512\) 0 0
\(513\) −7.87338e9 1.36371e10i −0.113682 0.196903i
\(514\) 0 0
\(515\) 2.03228e10 3.52002e10i 0.288905 0.500398i
\(516\) 0 0
\(517\) 1.04658e11i 1.46491i
\(518\) 0 0
\(519\) −2.95190e10 −0.406849
\(520\) 0 0
\(521\) 6.65862e9 + 3.84435e9i 0.0903718 + 0.0521762i 0.544505 0.838758i \(-0.316718\pi\)
−0.454133 + 0.890934i \(0.650051\pi\)
\(522\) 0 0
\(523\) 1.07896e11 6.22937e10i 1.44211 0.832602i 0.444119 0.895968i \(-0.353517\pi\)
0.997990 + 0.0633652i \(0.0201833\pi\)
\(524\) 0 0
\(525\) −1.61960e9 1.59600e10i −0.0213192 0.210085i
\(526\) 0 0
\(527\) 1.02215e10 + 1.77042e10i 0.132518 + 0.229528i
\(528\) 0 0
\(529\) 3.47165e10 6.01307e10i 0.443316 0.767846i
\(530\) 0 0
\(531\) 1.90123e10i 0.239143i
\(532\) 0 0
\(533\) 1.65726e10 0.205344
\(534\) 0 0
\(535\) 9.15513e9 + 5.28572e9i 0.111750 + 0.0645191i
\(536\) 0 0
\(537\) −4.67647e10 + 2.69996e10i −0.562369 + 0.324684i
\(538\) 0 0
\(539\) −7.17651e10 + 1.47168e10i −0.850272 + 0.174365i
\(540\) 0 0
\(541\) −4.97811e10 8.62233e10i −0.581132 1.00655i −0.995346 0.0963708i \(-0.969277\pi\)
0.414213 0.910180i \(-0.364057\pi\)
\(542\) 0 0
\(543\) 3.32531e10 5.75960e10i 0.382501 0.662511i
\(544\) 0 0
\(545\) 1.31735e11i 1.49319i
\(546\) 0 0
\(547\) −2.34938e10 −0.262424 −0.131212 0.991354i \(-0.541887\pi\)
−0.131212 + 0.991354i \(0.541887\pi\)
\(548\) 0 0
\(549\) 2.86918e10 + 1.65652e10i 0.315840 + 0.182351i
\(550\) 0 0
\(551\) −7.22235e10 + 4.16982e10i −0.783559 + 0.452388i
\(552\) 0 0
\(553\) 1.08186e11 1.09785e10i 1.15683 0.117393i
\(554\) 0 0
\(555\) −1.26512e10 2.19126e10i −0.133340 0.230952i
\(556\) 0 0
\(557\) 1.24108e10 2.14962e10i 0.128938 0.223327i −0.794328 0.607490i \(-0.792177\pi\)
0.923265 + 0.384163i \(0.125510\pi\)
\(558\) 0 0
\(559\) 4.68684e9i 0.0479991i
\(560\) 0 0
\(561\) −5.66493e10 −0.571930
\(562\) 0 0
\(563\) −1.47632e11 8.52355e10i −1.46942 0.848373i −0.470013 0.882660i \(-0.655751\pi\)
−0.999412 + 0.0342868i \(0.989084\pi\)
\(564\) 0 0
\(565\) −1.40294e10 + 8.09988e9i −0.137672 + 0.0794849i
\(566\) 0 0
\(567\) 6.71670e9 + 9.31483e9i 0.0649866 + 0.0901245i
\(568\) 0 0
\(569\) −2.03247e10 3.52033e10i −0.193898 0.335842i 0.752640 0.658432i \(-0.228780\pi\)
−0.946539 + 0.322590i \(0.895447\pi\)
\(570\) 0 0
\(571\) 4.24414e9 7.35107e9i 0.0399250 0.0691522i −0.845372 0.534177i \(-0.820621\pi\)
0.885297 + 0.465025i \(0.153955\pi\)
\(572\) 0 0
\(573\) 2.86058e10i 0.265360i
\(574\) 0 0
\(575\) −1.34616e10 −0.123148
\(576\) 0 0
\(577\) −5.94782e10 3.43397e10i −0.536604 0.309809i 0.207097 0.978320i \(-0.433598\pi\)
−0.743702 + 0.668512i \(0.766932\pi\)
\(578\) 0 0
\(579\) 7.69129e10 4.44057e10i 0.684360 0.395116i
\(580\) 0 0
\(581\) 1.44291e11 + 6.48638e10i 1.26630 + 0.569243i
\(582\) 0 0
\(583\) −8.37556e9 1.45069e10i −0.0725003 0.125574i
\(584\) 0 0
\(585\) 1.69136e10 2.92952e10i 0.144415 0.250134i
\(586\) 0 0
\(587\) 1.43383e11i 1.20766i −0.797114 0.603829i \(-0.793641\pi\)
0.797114 0.603829i \(-0.206359\pi\)
\(588\) 0 0
\(589\) 3.30193e10 0.274351
\(590\) 0 0
\(591\) 4.08413e10 + 2.35797e10i 0.334772 + 0.193281i
\(592\) 0 0
\(593\) −1.30721e11 + 7.54720e10i −1.05713 + 0.610333i −0.924636 0.380851i \(-0.875631\pi\)
−0.132491 + 0.991184i \(0.542298\pi\)
\(594\) 0 0
\(595\) −6.85408e10 + 1.52471e11i −0.546867 + 1.21652i
\(596\) 0 0
\(597\) 7.45888e9 + 1.29192e10i 0.0587187 + 0.101704i
\(598\) 0 0
\(599\) −8.29322e10 + 1.43643e11i −0.644193 + 1.11577i 0.340294 + 0.940319i \(0.389473\pi\)
−0.984487 + 0.175456i \(0.943860\pi\)
\(600\) 0 0
\(601\) 7.04035e10i 0.539630i 0.962912 + 0.269815i \(0.0869625\pi\)
−0.962912 + 0.269815i \(0.913037\pi\)
\(602\) 0 0
\(603\) 8.70862e10 0.658688
\(604\) 0 0
\(605\) 3.34418e10 + 1.93076e10i 0.249614 + 0.144115i
\(606\) 0 0
\(607\) −5.15559e10 + 2.97658e10i −0.379773 + 0.219262i −0.677719 0.735321i \(-0.737032\pi\)
0.297947 + 0.954583i \(0.403698\pi\)
\(608\) 0 0
\(609\) 4.93323e10 3.55724e10i 0.358643 0.258609i
\(610\) 0 0
\(611\) −8.72009e10 1.51036e11i −0.625685 1.08372i
\(612\) 0 0
\(613\) 1.14654e11 1.98587e11i 0.811986 1.40640i −0.0994852 0.995039i \(-0.531720\pi\)
0.911472 0.411363i \(-0.134947\pi\)
\(614\) 0 0
\(615\) 2.67318e10i 0.186865i
\(616\) 0 0
\(617\) 1.93904e11 1.33797 0.668986 0.743275i \(-0.266728\pi\)
0.668986 + 0.743275i \(0.266728\pi\)
\(618\) 0 0
\(619\) 1.77090e10 + 1.02243e10i 0.120623 + 0.0696418i 0.559098 0.829102i \(-0.311148\pi\)
−0.438474 + 0.898744i \(0.644481\pi\)
\(620\) 0 0
\(621\) 8.34566e9 4.81837e9i 0.0561170 0.0323992i
\(622\) 0 0
\(623\) 3.07621e9 + 3.03138e10i 0.0204203 + 0.201228i
\(624\) 0 0
\(625\) 9.39923e10 + 1.62799e11i 0.615988 + 1.06692i
\(626\) 0 0
\(627\) −4.57495e10 + 7.92404e10i −0.296016 + 0.512716i
\(628\) 0 0
\(629\) 7.06105e10i 0.451094i
\(630\) 0 0
\(631\) −1.43159e11 −0.903030 −0.451515 0.892263i \(-0.649116\pi\)
−0.451515 + 0.892263i \(0.649116\pi\)
\(632\) 0 0
\(633\) −5.66876e10 3.27286e10i −0.353080 0.203851i
\(634\) 0 0
\(635\) 1.12411e11 6.49006e10i 0.691377 0.399166i
\(636\) 0 0
\(637\) −9.13050e10 + 8.10328e10i −0.554545 + 0.492157i
\(638\) 0 0
\(639\) −1.02211e10 1.77034e10i −0.0613047 0.106183i
\(640\) 0 0
\(641\) −1.32450e11 + 2.29411e11i −0.784551 + 1.35888i 0.144716 + 0.989473i \(0.453773\pi\)
−0.929267 + 0.369409i \(0.879560\pi\)
\(642\) 0 0
\(643\) 1.18901e9i 0.00695572i −0.999994 0.00347786i \(-0.998893\pi\)
0.999994 0.00347786i \(-0.00110704\pi\)
\(644\) 0 0
\(645\) −7.55994e9 −0.0436797
\(646\) 0 0
\(647\) −8.24205e10 4.75855e10i −0.470347 0.271555i 0.246038 0.969260i \(-0.420871\pi\)
−0.716385 + 0.697705i \(0.754204\pi\)
\(648\) 0 0
\(649\) −9.56733e10 + 5.52370e10i −0.539277 + 0.311352i
\(650\) 0 0
\(651\) −2.39575e10 + 2.43118e9i −0.133388 + 0.0135361i
\(652\) 0 0
\(653\) 1.66756e11 + 2.88829e11i 0.917124 + 1.58850i 0.803762 + 0.594951i \(0.202829\pi\)
0.113362 + 0.993554i \(0.463838\pi\)
\(654\) 0 0
\(655\) −2.03751e11 + 3.52906e11i −1.10696 + 1.91732i
\(656\) 0 0
\(657\) 7.43760e10i 0.399183i
\(658\) 0 0
\(659\) 1.17025e11 0.620493 0.310246 0.950656i \(-0.399588\pi\)
0.310246 + 0.950656i \(0.399588\pi\)
\(660\) 0 0
\(661\) 2.68769e10 + 1.55174e10i 0.140791 + 0.0812855i 0.568741 0.822517i \(-0.307431\pi\)
−0.427950 + 0.903802i \(0.640764\pi\)
\(662\) 0 0
\(663\) −8.17528e10 + 4.72000e10i −0.423106 + 0.244280i
\(664\) 0 0
\(665\) 1.57922e11 + 2.19008e11i 0.807523 + 1.11989i
\(666\) 0 0
\(667\) −2.55186e10 4.41995e10i −0.128930 0.223313i
\(668\) 0 0
\(669\) −7.22801e10 + 1.25193e11i −0.360840 + 0.624993i
\(670\) 0 0
\(671\) 1.92509e11i 0.949645i
\(672\) 0 0
\(673\) −2.12193e11 −1.03436 −0.517179 0.855877i \(-0.673018\pi\)
−0.517179 + 0.855877i \(0.673018\pi\)
\(674\) 0 0
\(675\) 1.26545e10 + 7.30608e9i 0.0609579 + 0.0351940i
\(676\) 0 0
\(677\) 9.30441e10 5.37191e10i 0.442929 0.255725i −0.261910 0.965092i \(-0.584352\pi\)
0.704839 + 0.709367i \(0.251019\pi\)
\(678\) 0 0
\(679\) 1.34850e10 + 6.06196e9i 0.0634412 + 0.0285190i
\(680\) 0 0
\(681\) −8.85074e10 1.53299e11i −0.411520 0.712774i
\(682\) 0 0
\(683\) 5.88995e10 1.02017e11i 0.270663 0.468802i −0.698369 0.715738i \(-0.746091\pi\)
0.969032 + 0.246936i \(0.0794238\pi\)
\(684\) 0 0
\(685\) 2.87654e11i 1.30650i
\(686\) 0 0
\(687\) −1.48171e11 −0.665175
\(688\) 0 0
\(689\) −2.41742e10 1.39570e10i −0.107269 0.0619320i
\(690\) 0 0
\(691\) 2.96618e11 1.71253e11i 1.30103 0.751148i 0.320446 0.947267i \(-0.396167\pi\)
0.980580 + 0.196119i \(0.0628339\pi\)
\(692\) 0 0
\(693\) 2.73596e10 6.08622e10i 0.118625 0.263885i
\(694\) 0 0
\(695\) −1.77371e11 3.07215e11i −0.760227 1.31675i
\(696\) 0 0
\(697\) 3.72997e10 6.46050e10i 0.158043 0.273738i
\(698\) 0 0
\(699\) 2.58439e11i 1.08255i
\(700\) 0 0
\(701\) −1.15900e11 −0.479967 −0.239984 0.970777i \(-0.577142\pi\)
−0.239984 + 0.970777i \(0.577142\pi\)
\(702\) 0 0
\(703\) 9.87691e10 + 5.70244e10i 0.404390 + 0.233474i
\(704\) 0 0
\(705\) 2.43624e11 1.40656e11i 0.986195 0.569380i
\(706\) 0 0
\(707\) 2.59351e11 1.87011e11i 1.03803 0.748498i
\(708\) 0 0
\(709\) −7.71407e10 1.33612e11i −0.305280 0.528761i 0.672044 0.740512i \(-0.265417\pi\)
−0.977324 + 0.211751i \(0.932083\pi\)
\(710\) 0 0
\(711\) −4.95246e10 + 8.57791e10i −0.193795 + 0.335663i
\(712\) 0 0
\(713\) 2.02073e10i 0.0781897i
\(714\) 0 0
\(715\) −1.96558e11 −0.752084
\(716\) 0 0
\(717\) −1.59380e11 9.20178e10i −0.603054 0.348173i
\(718\) 0 0
\(719\) 1.82639e11 1.05447e11i 0.683404 0.394564i −0.117732 0.993045i \(-0.537562\pi\)
0.801136 + 0.598482i \(0.204229\pi\)
\(720\) 0 0
\(721\) −1.34893e10 1.32928e11i −0.0499172 0.491898i
\(722\) 0 0
\(723\) 1.55601e11 + 2.69509e11i 0.569456 + 0.986326i
\(724\) 0 0
\(725\) 3.86938e10 6.70195e10i 0.140052 0.242577i
\(726\) 0 0
\(727\) 2.28475e10i 0.0817900i 0.999163 + 0.0408950i \(0.0130209\pi\)
−0.999163 + 0.0408950i \(0.986979\pi\)
\(728\) 0 0
\(729\) −1.04604e10 −0.0370370
\(730\) 0 0
\(731\) 1.82707e10 + 1.05486e10i 0.0639861 + 0.0369424i
\(732\) 0 0
\(733\) 3.90685e11 2.25562e11i 1.35335 0.781358i 0.364634 0.931151i \(-0.381194\pi\)
0.988717 + 0.149793i \(0.0478609\pi\)
\(734\) 0 0
\(735\) −1.30707e11 1.47276e11i −0.447868 0.504642i
\(736\) 0 0
\(737\) −2.53014e11 4.38233e11i −0.857579 1.48537i
\(738\) 0 0
\(739\) 8.06607e10 1.39708e11i 0.270448 0.468430i −0.698528 0.715582i \(-0.746161\pi\)
0.968977 + 0.247152i \(0.0794948\pi\)
\(740\) 0 0
\(741\) 1.52473e11i 0.505733i
\(742\) 0 0
\(743\) −2.11855e11 −0.695159 −0.347579 0.937651i \(-0.612996\pi\)
−0.347579 + 0.937651i \(0.612996\pi\)
\(744\) 0 0
\(745\) 2.03129e11 + 1.17276e11i 0.659395 + 0.380702i
\(746\) 0 0
\(747\) −1.24794e11 + 7.20499e10i −0.400785 + 0.231393i
\(748\) 0 0
\(749\) 3.45729e10 3.50841e9i 0.109852 0.0111477i
\(750\) 0 0
\(751\) −2.80633e11 4.86071e11i −0.882224 1.52806i −0.848862 0.528614i \(-0.822712\pi\)
−0.0333617 0.999443i \(-0.510621\pi\)
\(752\) 0 0
\(753\) −9.95354e10 + 1.72400e11i −0.309598 + 0.536239i
\(754\) 0 0
\(755\) 6.02882e11i 1.85543i
\(756\) 0 0
\(757\) −2.12454e11 −0.646967 −0.323483 0.946234i \(-0.604854\pi\)
−0.323483 + 0.946234i \(0.604854\pi\)
\(758\) 0 0
\(759\) −4.84938e10 2.79979e10i −0.146123 0.0843642i
\(760\) 0 0
\(761\) 3.11683e11 1.79950e11i 0.929338 0.536554i 0.0427362 0.999086i \(-0.486393\pi\)
0.886602 + 0.462533i \(0.153059\pi\)
\(762\) 0 0
\(763\) 2.53277e11 + 3.51248e11i 0.747304 + 1.03637i
\(764\) 0 0
\(765\) −7.61343e10 1.31868e11i −0.222297 0.385031i
\(766\) 0 0
\(767\) −9.20467e10 + 1.59429e11i −0.265966 + 0.460667i
\(768\) 0 0
\(769\) 1.74232e11i 0.498222i 0.968475 + 0.249111i \(0.0801385\pi\)
−0.968475 + 0.249111i \(0.919862\pi\)
\(770\) 0 0
\(771\) −1.42235e11 −0.402521
\(772\) 0 0
\(773\) 2.44377e11 + 1.41091e11i 0.684450 + 0.395168i 0.801530 0.597955i \(-0.204020\pi\)
−0.117079 + 0.993123i \(0.537353\pi\)
\(774\) 0 0
\(775\) −2.65352e10 + 1.53201e10i −0.0735555 + 0.0424673i
\(776\) 0 0
\(777\) −7.58617e10 3.41024e10i −0.208132 0.0935623i
\(778\) 0 0
\(779\) −6.02458e10 1.04349e11i −0.163598 0.283360i
\(780\) 0 0
\(781\) −5.93912e10 + 1.02869e11i −0.159631