Properties

Label 84.9.m.b.73.2
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 73.2
Root \(-72.3408 + 125.298i\) of defining polynomial
Character \(\chi\) \(=\) 84.73
Dual form 84.9.m.b.61.2

$q$-expansion

\(f(q)\) \(=\) \(q+(40.5000 + 23.3827i) q^{3} +(-225.043 + 129.928i) q^{5} +(597.275 + 2325.52i) q^{7} +(1093.50 + 1894.00i) q^{9} +O(q^{10})\) \(q+(40.5000 + 23.3827i) q^{3} +(-225.043 + 129.928i) q^{5} +(597.275 + 2325.52i) q^{7} +(1093.50 + 1894.00i) q^{9} +(9723.49 - 16841.6i) q^{11} +46381.7i q^{13} -12152.3 q^{15} +(-105886. - 61133.6i) q^{17} +(18446.7 - 10650.2i) q^{19} +(-30187.4 + 108150. i) q^{21} +(152199. + 263616. i) q^{23} +(-161550. + 279812. i) q^{25} +102276. i q^{27} +88119.4 q^{29} +(-1.54998e6 - 894884. i) q^{31} +(787602. - 454722. i) q^{33} +(-436564. - 445739. i) q^{35} +(755092. + 1.30786e6i) q^{37} +(-1.08453e6 + 1.87846e6i) q^{39} +188022. i q^{41} -123402. q^{43} +(-492168. - 284153. i) q^{45} +(-5.58909e6 + 3.22686e6i) q^{47} +(-5.05133e6 + 2.77796e6i) q^{49} +(-2.85893e6 - 4.95182e6i) q^{51} +(-6.88508e6 + 1.19253e7i) q^{53} +5.05343e6i q^{55} +996123. q^{57} +(1.00305e7 + 5.79109e6i) q^{59} +(-1.92663e7 + 1.11234e7i) q^{61} +(-3.75142e6 + 3.67420e6i) q^{63} +(-6.02630e6 - 1.04379e7i) q^{65} +(5.75873e6 - 9.97442e6i) q^{67} +1.42353e7i q^{69} -3.11345e7 q^{71} +(-1.08437e7 - 6.26059e6i) q^{73} +(-1.30855e7 + 7.55493e6i) q^{75} +(4.49731e7 + 1.25532e7i) q^{77} +(2.13222e7 + 3.69312e7i) q^{79} +(-2.39148e6 + 4.14217e6i) q^{81} -7.19982e7i q^{83} +3.17720e7 q^{85} +(3.56884e6 + 2.06047e6i) q^{87} +(4.37683e7 - 2.52696e7i) q^{89} +(-1.07862e8 + 2.77026e7i) q^{91} +(-4.18496e7 - 7.24856e7i) q^{93} +(-2.76753e6 + 4.79351e6i) q^{95} -1.16642e8i q^{97} +4.25305e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 486 q^{3} + 285 q^{5} + 198 q^{7} + 13122 q^{9}+O(q^{10}) \) 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
\(5\) −225.043 + 129.928i −0.360068 + 0.207885i −0.669111 0.743163i \(-0.733325\pi\)
0.309042 + 0.951048i \(0.399991\pi\)
\(6\) 0 0
\(7\) 597.275 + 2325.52i 0.248761 + 0.968565i
\(8\) 0 0
\(9\) 1093.50 + 1894.00i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) 9723.49 16841.6i 0.664127 1.15030i −0.315394 0.948961i \(-0.602137\pi\)
0.979521 0.201341i \(-0.0645300\pi\)
\(12\) 0 0
\(13\) 46381.7i 1.62395i 0.583690 + 0.811976i \(0.301608\pi\)
−0.583690 + 0.811976i \(0.698392\pi\)
\(14\) 0 0
\(15\) −12152.3 −0.240045
\(16\) 0 0
\(17\) −105886. 61133.6i −1.26778 0.731955i −0.293215 0.956047i \(-0.594725\pi\)
−0.974568 + 0.224092i \(0.928058\pi\)
\(18\) 0 0
\(19\) 18446.7 10650.2i 0.141548 0.0817230i −0.427553 0.903990i \(-0.640624\pi\)
0.569102 + 0.822267i \(0.307291\pi\)
\(20\) 0 0
\(21\) −30187.4 + 108150.i −0.155220 + 0.556094i
\(22\) 0 0
\(23\) 152199. + 263616.i 0.543876 + 0.942020i 0.998677 + 0.0514271i \(0.0163770\pi\)
−0.454801 + 0.890593i \(0.650290\pi\)
\(24\) 0 0
\(25\) −161550. + 279812.i −0.413567 + 0.716320i
\(26\) 0 0
\(27\) 102276.i 0.192450i
\(28\) 0 0
\(29\) 88119.4 0.124589 0.0622945 0.998058i \(-0.480158\pi\)
0.0622945 + 0.998058i \(0.480158\pi\)
\(30\) 0 0
\(31\) −1.54998e6 894884.i −1.67834 0.968991i −0.962718 0.270505i \(-0.912809\pi\)
−0.715624 0.698486i \(-0.753857\pi\)
\(32\) 0 0
\(33\) 787602. 454722.i 0.664127 0.383434i
\(34\) 0 0
\(35\) −436564. 445739.i −0.290921 0.297036i
\(36\) 0 0
\(37\) 755092. + 1.30786e6i 0.402896 + 0.697836i 0.994074 0.108705i \(-0.0346703\pi\)
−0.591178 + 0.806541i \(0.701337\pi\)
\(38\) 0 0
\(39\) −1.08453e6 + 1.87846e6i −0.468795 + 0.811976i
\(40\) 0 0
\(41\) 188022.i 0.0665385i 0.999446 + 0.0332692i \(0.0105919\pi\)
−0.999446 + 0.0332692i \(0.989408\pi\)
\(42\) 0 0
\(43\) −123402. −0.0360953 −0.0180476 0.999837i \(-0.505745\pi\)
−0.0180476 + 0.999837i \(0.505745\pi\)
\(44\) 0 0
\(45\) −492168. 284153.i −0.120023 0.0692952i
\(46\) 0 0
\(47\) −5.58909e6 + 3.22686e6i −1.14538 + 0.661285i −0.947757 0.318993i \(-0.896655\pi\)
−0.197623 + 0.980278i \(0.563322\pi\)
\(48\) 0 0
\(49\) −5.05133e6 + 2.77796e6i −0.876236 + 0.481882i
\(50\) 0 0
\(51\) −2.85893e6 4.95182e6i −0.422594 0.731955i
\(52\) 0 0
\(53\) −6.88508e6 + 1.19253e7i −0.872580 + 1.51135i −0.0132616 + 0.999912i \(0.504221\pi\)
−0.859318 + 0.511441i \(0.829112\pi\)
\(54\) 0 0
\(55\) 5.05343e6i 0.552250i
\(56\) 0 0
\(57\) 996123. 0.0943656
\(58\) 0 0
\(59\) 1.00305e7 + 5.79109e6i 0.827776 + 0.477917i 0.853090 0.521763i \(-0.174725\pi\)
−0.0253148 + 0.999680i \(0.508059\pi\)
\(60\) 0 0
\(61\) −1.92663e7 + 1.11234e7i −1.39149 + 0.803375i −0.993480 0.114007i \(-0.963631\pi\)
−0.398007 + 0.917383i \(0.630298\pi\)
\(62\) 0 0
\(63\) −3.75142e6 + 3.67420e6i −0.238140 + 0.233239i
\(64\) 0 0
\(65\) −6.02630e6 1.04379e7i −0.337596 0.584734i
\(66\) 0 0
\(67\) 5.75873e6 9.97442e6i 0.285777 0.494981i −0.687020 0.726638i \(-0.741082\pi\)
0.972797 + 0.231658i \(0.0744149\pi\)
\(68\) 0 0
\(69\) 1.42353e7i 0.628013i
\(70\) 0 0
\(71\) −3.11345e7 −1.22520 −0.612602 0.790392i \(-0.709877\pi\)
−0.612602 + 0.790392i \(0.709877\pi\)
\(72\) 0 0
\(73\) −1.08437e7 6.26059e6i −0.381843 0.220457i 0.296777 0.954947i \(-0.404088\pi\)
−0.678620 + 0.734490i \(0.737422\pi\)
\(74\) 0 0
\(75\) −1.30855e7 + 7.55493e6i −0.413567 + 0.238773i
\(76\) 0 0
\(77\) 4.49731e7 + 1.25532e7i 1.27935 + 0.357100i
\(78\) 0 0
\(79\) 2.13222e7 + 3.69312e7i 0.547424 + 0.948167i 0.998450 + 0.0556558i \(0.0177249\pi\)
−0.451026 + 0.892511i \(0.648942\pi\)
\(80\) 0 0
\(81\) −2.39148e6 + 4.14217e6i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 7.19982e7i 1.51708i −0.651625 0.758541i \(-0.725912\pi\)
0.651625 0.758541i \(-0.274088\pi\)
\(84\) 0 0
\(85\) 3.17720e7 0.608651
\(86\) 0 0
\(87\) 3.56884e6 + 2.06047e6i 0.0622945 + 0.0359657i
\(88\) 0 0
\(89\) 4.37683e7 2.52696e7i 0.697589 0.402753i −0.108860 0.994057i \(-0.534720\pi\)
0.806449 + 0.591304i \(0.201387\pi\)
\(90\) 0 0
\(91\) −1.07862e8 + 2.77026e7i −1.57290 + 0.403976i
\(92\) 0 0
\(93\) −4.18496e7 7.24856e7i −0.559447 0.968991i
\(94\) 0 0
\(95\) −2.76753e6 + 4.79351e6i −0.0339781 + 0.0588517i
\(96\) 0 0
\(97\) 1.16642e8i 1.31755i −0.752339 0.658776i \(-0.771075\pi\)
0.752339 0.658776i \(-0.228925\pi\)
\(98\) 0 0
\(99\) 4.25305e7 0.442751
\(100\) 0 0
\(101\) 9.23786e7 + 5.33348e7i 0.887740 + 0.512537i 0.873203 0.487357i \(-0.162039\pi\)
0.0145374 + 0.999894i \(0.495372\pi\)
\(102\) 0 0
\(103\) 1.77725e8 1.02609e8i 1.57906 0.911671i 0.584070 0.811703i \(-0.301459\pi\)
0.994991 0.0999675i \(-0.0318739\pi\)
\(104\) 0 0
\(105\) −7.25827e6 2.82605e7i −0.0597139 0.232500i
\(106\) 0 0
\(107\) 8.90703e7 + 1.54274e8i 0.679513 + 1.17695i 0.975128 + 0.221644i \(0.0711423\pi\)
−0.295615 + 0.955307i \(0.595524\pi\)
\(108\) 0 0
\(109\) −5.48168e7 + 9.49454e7i −0.388336 + 0.672617i −0.992226 0.124450i \(-0.960283\pi\)
0.603890 + 0.797068i \(0.293617\pi\)
\(110\) 0 0
\(111\) 7.06243e7i 0.465224i
\(112\) 0 0
\(113\) 2.74592e8 1.68413 0.842063 0.539379i \(-0.181341\pi\)
0.842063 + 0.539379i \(0.181341\pi\)
\(114\) 0 0
\(115\) −6.85024e7 3.95499e7i −0.391665 0.226128i
\(116\) 0 0
\(117\) −8.78469e7 + 5.07184e7i −0.468795 + 0.270659i
\(118\) 0 0
\(119\) 7.89243e7 2.82755e8i 0.393571 1.41001i
\(120\) 0 0
\(121\) −8.19129e7 1.41877e8i −0.382130 0.661868i
\(122\) 0 0
\(123\) −4.39645e6 + 7.61488e6i −0.0192080 + 0.0332692i
\(124\) 0 0
\(125\) 1.85466e8i 0.759669i
\(126\) 0 0
\(127\) −3.97605e7 −0.152840 −0.0764199 0.997076i \(-0.524349\pi\)
−0.0764199 + 0.997076i \(0.524349\pi\)
\(128\) 0 0
\(129\) −4.99780e6 2.88548e6i −0.0180476 0.0104198i
\(130\) 0 0
\(131\) 3.31807e7 1.91569e7i 0.112668 0.0650490i −0.442607 0.896716i \(-0.645946\pi\)
0.555275 + 0.831667i \(0.312613\pi\)
\(132\) 0 0
\(133\) 3.57851e7 + 3.65372e7i 0.114366 + 0.116769i
\(134\) 0 0
\(135\) −1.32885e7 2.30164e7i −0.0400076 0.0692952i
\(136\) 0 0
\(137\) 2.07018e8 3.58565e8i 0.587659 1.01786i −0.406879 0.913482i \(-0.633383\pi\)
0.994538 0.104374i \(-0.0332838\pi\)
\(138\) 0 0
\(139\) 2.15646e8i 0.577674i 0.957378 + 0.288837i \(0.0932686\pi\)
−0.957378 + 0.288837i \(0.906731\pi\)
\(140\) 0 0
\(141\) −3.01811e8 −0.763587
\(142\) 0 0
\(143\) 7.81141e8 + 4.50992e8i 1.86804 + 1.07851i
\(144\) 0 0
\(145\) −1.98306e7 + 1.14492e7i −0.0448605 + 0.0259002i
\(146\) 0 0
\(147\) −2.69535e8 5.60637e6i −0.577225 0.0120064i
\(148\) 0 0
\(149\) −2.59668e8 4.49759e8i −0.526834 0.912503i −0.999511 0.0312676i \(-0.990046\pi\)
0.472677 0.881236i \(-0.343288\pi\)
\(150\) 0 0
\(151\) −1.65131e8 + 2.86015e8i −0.317630 + 0.550151i −0.979993 0.199032i \(-0.936220\pi\)
0.662363 + 0.749183i \(0.269554\pi\)
\(152\) 0 0
\(153\) 2.67398e8i 0.487970i
\(154\) 0 0
\(155\) 4.65083e8 0.805757
\(156\) 0 0
\(157\) −2.58909e8 1.49481e8i −0.426137 0.246030i 0.271563 0.962421i \(-0.412460\pi\)
−0.697700 + 0.716390i \(0.745793\pi\)
\(158\) 0 0
\(159\) −5.57691e8 + 3.21983e8i −0.872580 + 0.503784i
\(160\) 0 0
\(161\) −5.22141e8 + 5.11393e8i −0.777113 + 0.761117i
\(162\) 0 0
\(163\) 2.92142e8 + 5.06004e8i 0.413850 + 0.716810i 0.995307 0.0967676i \(-0.0308504\pi\)
−0.581457 + 0.813577i \(0.697517\pi\)
\(164\) 0 0
\(165\) −1.18163e8 + 2.04664e8i −0.159421 + 0.276125i
\(166\) 0 0
\(167\) 7.46657e8i 0.959965i 0.877278 + 0.479983i \(0.159357\pi\)
−0.877278 + 0.479983i \(0.840643\pi\)
\(168\) 0 0
\(169\) −1.33553e9 −1.63722
\(170\) 0 0
\(171\) 4.03430e7 + 2.32920e7i 0.0471828 + 0.0272410i
\(172\) 0 0
\(173\) 9.08205e8 5.24352e8i 1.01391 0.585381i 0.101576 0.994828i \(-0.467612\pi\)
0.912334 + 0.409447i \(0.134278\pi\)
\(174\) 0 0
\(175\) −7.47200e8 2.08563e8i −0.796681 0.222374i
\(176\) 0 0
\(177\) 2.70822e8 + 4.69078e8i 0.275925 + 0.477917i
\(178\) 0 0
\(179\) −1.24237e8 + 2.15185e8i −0.121015 + 0.209604i −0.920168 0.391523i \(-0.871948\pi\)
0.799153 + 0.601127i \(0.205282\pi\)
\(180\) 0 0
\(181\) 4.91957e8i 0.458366i −0.973383 0.229183i \(-0.926394\pi\)
0.973383 0.229183i \(-0.0736055\pi\)
\(182\) 0 0
\(183\) −1.04038e9 −0.927658
\(184\) 0 0
\(185\) −3.39856e8 1.96216e8i −0.290140 0.167512i
\(186\) 0 0
\(187\) −2.05917e9 + 1.18886e9i −1.68394 + 0.972222i
\(188\) 0 0
\(189\) −2.37845e8 + 6.10868e7i −0.186400 + 0.0478741i
\(190\) 0 0
\(191\) 9.53669e8 + 1.65180e9i 0.716579 + 1.24115i 0.962347 + 0.271823i \(0.0876265\pi\)
−0.245768 + 0.969329i \(0.579040\pi\)
\(192\) 0 0
\(193\) −4.70293e8 + 8.14571e8i −0.338953 + 0.587083i −0.984236 0.176860i \(-0.943406\pi\)
0.645283 + 0.763943i \(0.276739\pi\)
\(194\) 0 0
\(195\) 5.63645e8i 0.389822i
\(196\) 0 0
\(197\) 1.22807e9 0.815379 0.407689 0.913121i \(-0.366335\pi\)
0.407689 + 0.913121i \(0.366335\pi\)
\(198\) 0 0
\(199\) 9.98896e7 + 5.76713e7i 0.0636954 + 0.0367745i 0.531509 0.847052i \(-0.321625\pi\)
−0.467814 + 0.883827i \(0.654958\pi\)
\(200\) 0 0
\(201\) 4.66457e8 2.69309e8i 0.285777 0.164994i
\(202\) 0 0
\(203\) 5.26315e7 + 2.04924e8i 0.0309929 + 0.120672i
\(204\) 0 0
\(205\) −2.44294e7 4.23129e7i −0.0138324 0.0239584i
\(206\) 0 0
\(207\) −3.32859e8 + 5.76528e8i −0.181292 + 0.314007i
\(208\) 0 0
\(209\) 4.14229e8i 0.217098i
\(210\) 0 0
\(211\) 2.33973e9 1.18042 0.590209 0.807250i \(-0.299045\pi\)
0.590209 + 0.807250i \(0.299045\pi\)
\(212\) 0 0
\(213\) −1.26095e9 7.28008e8i −0.612602 0.353686i
\(214\) 0 0
\(215\) 2.77708e7 1.60335e7i 0.0129968 0.00750368i
\(216\) 0 0
\(217\) 1.15531e9 4.13902e9i 0.521025 1.86663i
\(218\) 0 0
\(219\) −2.92779e8 5.07108e8i −0.127281 0.220457i
\(220\) 0 0
\(221\) 2.83548e9 4.91120e9i 1.18866 2.05882i
\(222\) 0 0
\(223\) 1.14133e9i 0.461523i 0.973010 + 0.230762i \(0.0741218\pi\)
−0.973010 + 0.230762i \(0.925878\pi\)
\(224\) 0 0
\(225\) −7.06618e8 −0.275712
\(226\) 0 0
\(227\) −1.82252e8 1.05223e8i −0.0686387 0.0396285i 0.465288 0.885159i \(-0.345951\pi\)
−0.533927 + 0.845531i \(0.679284\pi\)
\(228\) 0 0
\(229\) −3.18730e9 + 1.84019e9i −1.15899 + 0.669146i −0.951063 0.308997i \(-0.900007\pi\)
−0.207932 + 0.978143i \(0.566673\pi\)
\(230\) 0 0
\(231\) 1.52788e9 + 1.55999e9i 0.536590 + 0.547867i
\(232\) 0 0
\(233\) 1.42196e8 + 2.46291e8i 0.0482464 + 0.0835652i 0.889140 0.457635i \(-0.151303\pi\)
−0.840894 + 0.541200i \(0.817970\pi\)
\(234\) 0 0
\(235\) 8.38522e8 1.45236e9i 0.274943 0.476216i
\(236\) 0 0
\(237\) 1.99428e9i 0.632111i
\(238\) 0 0
\(239\) 2.62607e9 0.804850 0.402425 0.915453i \(-0.368167\pi\)
0.402425 + 0.915453i \(0.368167\pi\)
\(240\) 0 0
\(241\) 2.05781e8 + 1.18808e8i 0.0610011 + 0.0352190i 0.530190 0.847879i \(-0.322120\pi\)
−0.469189 + 0.883098i \(0.655454\pi\)
\(242\) 0 0
\(243\) −1.93710e8 + 1.11839e8i −0.0555556 + 0.0320750i
\(244\) 0 0
\(245\) 7.75828e8 1.28147e9i 0.215328 0.355667i
\(246\) 0 0
\(247\) 4.93976e8 + 8.55591e8i 0.132714 + 0.229868i
\(248\) 0 0
\(249\) 1.68351e9 2.91593e9i 0.437944 0.758541i
\(250\) 0 0
\(251\) 3.49203e9i 0.879797i −0.898047 0.439899i \(-0.855014\pi\)
0.898047 0.439899i \(-0.144986\pi\)
\(252\) 0 0
\(253\) 5.91961e9 1.44481
\(254\) 0 0
\(255\) 1.28676e9 + 7.42914e8i 0.304325 + 0.175702i
\(256\) 0 0
\(257\) −3.36384e9 + 1.94211e9i −0.771086 + 0.445187i −0.833262 0.552879i \(-0.813529\pi\)
0.0621759 + 0.998065i \(0.480196\pi\)
\(258\) 0 0
\(259\) −2.59046e9 + 2.53714e9i −0.575675 + 0.563825i
\(260\) 0 0
\(261\) 9.63585e7 + 1.66898e8i 0.0207648 + 0.0359657i
\(262\) 0 0
\(263\) −9.40863e8 + 1.62962e9i −0.196654 + 0.340615i −0.947442 0.319929i \(-0.896341\pi\)
0.750787 + 0.660544i \(0.229674\pi\)
\(264\) 0 0
\(265\) 3.57827e9i 0.725587i
\(266\) 0 0
\(267\) 2.36349e9 0.465059
\(268\) 0 0
\(269\) 2.78854e9 + 1.60997e9i 0.532559 + 0.307473i 0.742058 0.670336i \(-0.233850\pi\)
−0.209499 + 0.977809i \(0.567183\pi\)
\(270\) 0 0
\(271\) 4.42388e9 2.55413e9i 0.820212 0.473550i −0.0302773 0.999542i \(-0.509639\pi\)
0.850490 + 0.525992i \(0.176306\pi\)
\(272\) 0 0
\(273\) −5.01617e9 1.40014e9i −0.903070 0.252070i
\(274\) 0 0
\(275\) 3.14165e9 + 5.44150e9i 0.549323 + 0.951455i
\(276\) 0 0
\(277\) 5.20091e9 9.00825e9i 0.883406 1.53010i 0.0358772 0.999356i \(-0.488577\pi\)
0.847529 0.530749i \(-0.178089\pi\)
\(278\) 0 0
\(279\) 3.91422e9i 0.645994i
\(280\) 0 0
\(281\) −9.79146e9 −1.57044 −0.785222 0.619215i \(-0.787451\pi\)
−0.785222 + 0.619215i \(0.787451\pi\)
\(282\) 0 0
\(283\) −9.03261e8 5.21498e8i −0.140821 0.0813031i 0.427934 0.903810i \(-0.359242\pi\)
−0.568755 + 0.822507i \(0.692575\pi\)
\(284\) 0 0
\(285\) −2.24170e8 + 1.29425e8i −0.0339781 + 0.0196172i
\(286\) 0 0
\(287\) −4.37249e8 + 1.12301e8i −0.0644468 + 0.0165522i
\(288\) 0 0
\(289\) 3.98675e9 + 6.90526e9i 0.571515 + 0.989893i
\(290\) 0 0
\(291\) 2.72740e9 4.72400e9i 0.380344 0.658776i
\(292\) 0 0
\(293\) 2.83834e9i 0.385118i −0.981285 0.192559i \(-0.938321\pi\)
0.981285 0.192559i \(-0.0616787\pi\)
\(294\) 0 0
\(295\) −3.00971e9 −0.397408
\(296\) 0 0
\(297\) 1.72249e9 + 9.94478e8i 0.221376 + 0.127811i
\(298\) 0 0
\(299\) −1.22270e10 + 7.05924e9i −1.52980 + 0.883228i
\(300\) 0 0
\(301\) −7.37052e7 2.86975e8i −0.00897909 0.0349606i
\(302\) 0 0
\(303\) 2.49422e9 + 4.32012e9i 0.295913 + 0.512537i
\(304\) 0 0
\(305\) 2.89049e9 5.00648e9i 0.334020 0.578540i
\(306\) 0 0
\(307\) 1.01655e10i 1.14439i 0.820116 + 0.572197i \(0.193909\pi\)
−0.820116 + 0.572197i \(0.806091\pi\)
\(308\) 0 0
\(309\) 9.59713e9 1.05271
\(310\) 0 0
\(311\) −9.35774e9 5.40269e9i −1.00030 0.577522i −0.0919614 0.995763i \(-0.529314\pi\)
−0.908336 + 0.418240i \(0.862647\pi\)
\(312\) 0 0
\(313\) −7.81261e9 + 4.51061e9i −0.813989 + 0.469957i −0.848339 0.529453i \(-0.822397\pi\)
0.0343502 + 0.999410i \(0.489064\pi\)
\(314\) 0 0
\(315\) 3.66846e8 1.31427e9i 0.0372599 0.133488i
\(316\) 0 0
\(317\) 2.10486e9 + 3.64573e9i 0.208443 + 0.361034i 0.951224 0.308500i \(-0.0998271\pi\)
−0.742781 + 0.669534i \(0.766494\pi\)
\(318\) 0 0
\(319\) 8.56828e8 1.48407e9i 0.0827429 0.143315i
\(320\) 0 0
\(321\) 8.33081e9i 0.784634i
\(322\) 0 0
\(323\) −2.60435e9 −0.239270
\(324\) 0 0
\(325\) −1.29782e10 7.49295e9i −1.16327 0.671614i
\(326\) 0 0
\(327\) −4.44016e9 + 2.56353e9i −0.388336 + 0.224206i
\(328\) 0 0
\(329\) −1.08424e10 1.10702e10i −0.925424 0.944873i
\(330\) 0 0
\(331\) 5.98155e9 + 1.03603e10i 0.498312 + 0.863102i 0.999998 0.00194777i \(-0.000619995\pi\)
−0.501686 + 0.865050i \(0.667287\pi\)
\(332\) 0 0
\(333\) −1.65139e9 + 2.86028e9i −0.134299 + 0.232612i
\(334\) 0 0
\(335\) 2.99289e9i 0.237636i
\(336\) 0 0
\(337\) 8.47484e9 0.657070 0.328535 0.944492i \(-0.393445\pi\)
0.328535 + 0.944492i \(0.393445\pi\)
\(338\) 0 0
\(339\) 1.11210e10 + 6.42071e9i 0.842063 + 0.486165i
\(340\) 0 0
\(341\) −3.01425e10 + 1.74028e10i −2.22927 + 1.28707i
\(342\) 0 0
\(343\) −9.47723e9 1.00878e10i −0.684708 0.728818i
\(344\) 0 0
\(345\) −1.84956e9 3.20354e9i −0.130555 0.226128i
\(346\) 0 0
\(347\) −7.92809e9 + 1.37319e10i −0.546828 + 0.947134i 0.451661 + 0.892190i \(0.350832\pi\)
−0.998489 + 0.0549447i \(0.982502\pi\)
\(348\) 0 0
\(349\) 7.90260e9i 0.532682i −0.963879 0.266341i \(-0.914185\pi\)
0.963879 0.266341i \(-0.0858148\pi\)
\(350\) 0 0
\(351\) −4.74373e9 −0.312530
\(352\) 0 0
\(353\) 8.28745e9 + 4.78476e9i 0.533731 + 0.308150i 0.742534 0.669808i \(-0.233624\pi\)
−0.208804 + 0.977958i \(0.566957\pi\)
\(354\) 0 0
\(355\) 7.00658e9 4.04525e9i 0.441157 0.254702i
\(356\) 0 0
\(357\) 9.80801e9 9.60612e9i 0.603821 0.591392i
\(358\) 0 0
\(359\) 5.12021e9 + 8.86847e9i 0.308255 + 0.533914i 0.977981 0.208695i \(-0.0669216\pi\)
−0.669726 + 0.742609i \(0.733588\pi\)
\(360\) 0 0
\(361\) −8.26493e9 + 1.43153e10i −0.486643 + 0.842890i
\(362\) 0 0
\(363\) 7.66138e9i 0.441246i
\(364\) 0 0
\(365\) 3.25371e9 0.183319
\(366\) 0 0
\(367\) 2.80339e10 + 1.61854e10i 1.54532 + 0.892193i 0.998489 + 0.0549514i \(0.0175004\pi\)
0.546834 + 0.837241i \(0.315833\pi\)
\(368\) 0 0
\(369\) −3.56113e8 + 2.05602e8i −0.0192080 + 0.0110897i
\(370\) 0 0
\(371\) −3.18449e10 8.88873e9i −1.68091 0.469185i
\(372\) 0 0
\(373\) 1.25975e10 + 2.18195e10i 0.650803 + 1.12722i 0.982928 + 0.183988i \(0.0589008\pi\)
−0.332126 + 0.943235i \(0.607766\pi\)
\(374\) 0 0
\(375\) 4.33670e9 7.51138e9i 0.219298 0.379835i
\(376\) 0 0
\(377\) 4.08713e9i 0.202327i
\(378\) 0 0
\(379\) −6.03658e9 −0.292573 −0.146287 0.989242i \(-0.546732\pi\)
−0.146287 + 0.989242i \(0.546732\pi\)
\(380\) 0 0
\(381\) −1.61030e9 9.29707e8i −0.0764199 0.0441211i
\(382\) 0 0
\(383\) −9.57427e9 + 5.52771e9i −0.444949 + 0.256892i −0.705695 0.708516i \(-0.749365\pi\)
0.260745 + 0.965408i \(0.416032\pi\)
\(384\) 0 0
\(385\) −1.17519e10 + 3.01829e9i −0.534890 + 0.137378i
\(386\) 0 0
\(387\) −1.34941e8 2.33724e8i −0.00601588 0.0104198i
\(388\) 0 0
\(389\) 1.58412e10 2.74378e10i 0.691814 1.19826i −0.279428 0.960167i \(-0.590145\pi\)
0.971243 0.238091i \(-0.0765217\pi\)
\(390\) 0 0
\(391\) 3.72178e10i 1.59237i
\(392\) 0 0
\(393\) 1.79176e9 0.0751121
\(394\) 0 0
\(395\) −9.59682e9 5.54072e9i −0.394220 0.227603i
\(396\) 0 0
\(397\) −1.81623e10 + 1.04860e10i −0.731155 + 0.422132i −0.818844 0.574015i \(-0.805385\pi\)
0.0876897 + 0.996148i \(0.472052\pi\)
\(398\) 0 0
\(399\) 5.94960e8 + 2.31651e9i 0.0234745 + 0.0913992i
\(400\) 0 0
\(401\) −5.84375e9 1.01217e10i −0.226003 0.391449i 0.730617 0.682788i \(-0.239233\pi\)
−0.956620 + 0.291339i \(0.905899\pi\)
\(402\) 0 0
\(403\) 4.15062e10 7.18909e10i 1.57360 2.72555i
\(404\) 0 0
\(405\) 1.24289e9i 0.0461968i
\(406\) 0 0
\(407\) 2.93685e10 1.07030
\(408\) 0 0
\(409\) 2.98804e10 + 1.72515e10i 1.06781 + 0.616499i 0.927582 0.373620i \(-0.121884\pi\)
0.140226 + 0.990119i \(0.455217\pi\)
\(410\) 0 0
\(411\) 1.67684e10 9.68127e9i 0.587659 0.339285i
\(412\) 0 0
\(413\) −7.47637e9 + 2.67849e10i −0.256975 + 0.920642i
\(414\) 0 0
\(415\) 9.35461e9 + 1.62027e10i 0.315379 + 0.546253i
\(416\) 0 0
\(417\) −5.04239e9 + 8.73368e9i −0.166760 + 0.288837i
\(418\) 0 0
\(419\) 1.71261e10i 0.555652i −0.960631 0.277826i \(-0.910386\pi\)
0.960631 0.277826i \(-0.0896139\pi\)
\(420\) 0 0
\(421\) 3.64524e10 1.16037 0.580187 0.814484i \(-0.302980\pi\)
0.580187 + 0.814484i \(0.302980\pi\)
\(422\) 0 0
\(423\) −1.22233e10 7.05715e9i −0.381793 0.220428i
\(424\) 0 0
\(425\) 3.42119e10 1.97522e10i 1.04863 0.605425i
\(426\) 0 0
\(427\) −3.73750e10 3.81605e10i −1.12427 1.14790i
\(428\) 0 0
\(429\) 2.10908e10 + 3.65303e10i 0.622679 + 1.07851i
\(430\) 0 0
\(431\) 1.09904e10 1.90360e10i 0.318497 0.551654i −0.661677 0.749789i \(-0.730155\pi\)
0.980175 + 0.198135i \(0.0634884\pi\)
\(432\) 0 0
\(433\) 1.35544e10i 0.385593i −0.981239 0.192796i \(-0.938244\pi\)
0.981239 0.192796i \(-0.0617557\pi\)
\(434\) 0 0
\(435\) −1.07085e9 −0.0299070
\(436\) 0 0
\(437\) 5.61514e9 + 3.24190e9i 0.153969 + 0.0888943i
\(438\) 0 0
\(439\) −4.13004e10 + 2.38448e10i −1.11198 + 0.642001i −0.939341 0.342985i \(-0.888562\pi\)
−0.172637 + 0.984986i \(0.555229\pi\)
\(440\) 0 0
\(441\) −1.07851e10 6.52950e9i −0.285147 0.172634i
\(442\) 0 0
\(443\) 9.20913e9 + 1.59507e10i 0.239113 + 0.414156i 0.960460 0.278418i \(-0.0898100\pi\)
−0.721347 + 0.692574i \(0.756477\pi\)
\(444\) 0 0
\(445\) −6.56648e9 + 1.13735e10i −0.167453 + 0.290037i
\(446\) 0 0
\(447\) 2.42870e10i 0.608336i
\(448\) 0 0
\(449\) 4.72530e10 1.16264 0.581319 0.813676i \(-0.302537\pi\)
0.581319 + 0.813676i \(0.302537\pi\)
\(450\) 0 0
\(451\) 3.16658e9 + 1.82823e9i 0.0765393 + 0.0441900i
\(452\) 0 0
\(453\) −1.33756e10 + 7.72242e9i −0.317630 + 0.183384i
\(454\) 0 0
\(455\) 2.06741e10 2.02486e10i 0.482372 0.472443i
\(456\) 0 0
\(457\) 9.30524e9 + 1.61172e10i 0.213335 + 0.369508i 0.952756 0.303736i \(-0.0982340\pi\)
−0.739421 + 0.673243i \(0.764901\pi\)
\(458\) 0 0
\(459\) 6.25249e9 1.08296e10i 0.140865 0.243985i
\(460\) 0 0
\(461\) 9.20893e9i 0.203895i −0.994790 0.101947i \(-0.967493\pi\)
0.994790 0.101947i \(-0.0325073\pi\)
\(462\) 0 0
\(463\) −1.42010e10 −0.309025 −0.154513 0.987991i \(-0.549381\pi\)
−0.154513 + 0.987991i \(0.549381\pi\)
\(464\) 0 0
\(465\) 1.88359e10 + 1.08749e10i 0.402878 + 0.232602i
\(466\) 0 0
\(467\) −2.95507e10 + 1.70611e10i −0.621299 + 0.358707i −0.777374 0.629038i \(-0.783449\pi\)
0.156076 + 0.987745i \(0.450116\pi\)
\(468\) 0 0
\(469\) 2.66353e10 + 7.43460e9i 0.550511 + 0.153662i
\(470\) 0 0
\(471\) −6.99056e9 1.21080e10i −0.142046 0.246030i
\(472\) 0 0
\(473\) −1.19990e9 + 2.07829e9i −0.0239718 + 0.0415204i
\(474\) 0 0
\(475\) 6.88216e9i 0.135192i
\(476\) 0 0
\(477\) −3.01153e10 −0.581720
\(478\) 0 0
\(479\) 7.59507e9 + 4.38502e9i 0.144275 + 0.0832970i 0.570400 0.821367i \(-0.306788\pi\)
−0.426125 + 0.904664i \(0.640122\pi\)
\(480\) 0 0
\(481\) −6.06607e10 + 3.50225e10i −1.13325 + 0.654284i
\(482\) 0 0
\(483\) −3.31044e10 + 8.50236e9i −0.608272 + 0.156225i
\(484\) 0 0
\(485\) 1.51551e10 + 2.62494e10i 0.273900 + 0.474408i
\(486\) 0 0
\(487\) −6.41038e9 + 1.11031e10i −0.113964 + 0.197392i −0.917365 0.398047i \(-0.869688\pi\)
0.803401 + 0.595438i \(0.203022\pi\)
\(488\) 0 0
\(489\) 2.73242e10i 0.477873i
\(490\) 0 0
\(491\) 6.34320e10 1.09140 0.545698 0.837982i \(-0.316265\pi\)
0.545698 + 0.837982i \(0.316265\pi\)
\(492\) 0 0
\(493\) −9.33065e9 5.38705e9i −0.157952 0.0911934i
\(494\) 0 0
\(495\) −9.57118e9 + 5.52592e9i −0.159421 + 0.0920416i
\(496\) 0 0
\(497\) −1.85958e10 7.24040e10i −0.304783 1.18669i
\(498\) 0 0
\(499\) −3.36380e10 5.82628e10i −0.542536 0.939700i −0.998758 0.0498336i \(-0.984131\pi\)
0.456222 0.889866i \(-0.349202\pi\)
\(500\) 0 0
\(501\) −1.74589e10 + 3.02396e10i −0.277118 + 0.479983i
\(502\) 0 0
\(503\) 1.04697e11i 1.63554i −0.575542 0.817772i \(-0.695209\pi\)
0.575542 0.817772i \(-0.304791\pi\)
\(504\) 0 0
\(505\) −2.77188e10 −0.426196
\(506\) 0 0
\(507\) −5.40891e10 3.12283e10i −0.818611 0.472625i
\(508\) 0 0
\(509\) −4.94469e10 + 2.85482e10i −0.736662 + 0.425312i −0.820854 0.571137i \(-0.806502\pi\)
0.0841923 + 0.996450i \(0.473169\pi\)
\(510\) 0 0
\(511\) 8.08251e9 2.89565e10i 0.118539 0.424680i
\(512\) 0 0
\(513\) 1.08926e9 + 1.88666e9i 0.0157276 + 0.0272410i
\(514\) 0 0
\(515\) −2.66637e10 + 4.61830e10i −0.379046 + 0.656527i
\(516\) 0 0
\(517\) 1.25505e11i 1.75671i
\(518\) 0 0
\(519\) 4.90430e10 0.675940
\(520\) 0 0
\(521\) 7.48609e10 + 4.32210e10i 1.01602 + 0.586602i 0.912950 0.408072i \(-0.133799\pi\)
0.103074 + 0.994674i \(0.467132\pi\)
\(522\) 0 0
\(523\) 1.27623e10 7.36833e9i 0.170578 0.0984832i −0.412280 0.911057i \(-0.635268\pi\)
0.582858 + 0.812574i \(0.301934\pi\)
\(524\) 0 0
\(525\) −2.53848e10 2.59183e10i −0.334147 0.341169i
\(526\) 0 0
\(527\) 1.09415e11 + 1.89512e11i 1.41852 + 2.45694i
\(528\) 0 0
\(529\) −7.17338e9 + 1.24247e10i −0.0916012 + 0.158658i
\(530\) 0 0
\(531\) 2.53302e10i 0.318611i
\(532\) 0 0
\(533\) −8.72077e9 −0.108055
\(534\) 0 0
\(535\) −4.00892e10 2.31455e10i −0.489342 0.282522i
\(536\) 0 0
\(537\) −1.00632e10 + 5.80999e9i −0.121015 + 0.0698679i
\(538\) 0 0
\(539\) −2.33136e9 + 1.12084e11i −0.0276220 + 1.32797i
\(540\) 0 0
\(541\) −5.99660e10 1.03864e11i −0.700029 1.21249i −0.968456 0.249185i \(-0.919837\pi\)
0.268427 0.963300i \(-0.413496\pi\)
\(542\) 0 0
\(543\) 1.15033e10 1.99243e10i 0.132319 0.229183i
\(544\) 0 0
\(545\) 2.84890e10i 0.322917i
\(546\) 0 0
\(547\) −7.72241e10 −0.862588 −0.431294 0.902211i \(-0.641943\pi\)
−0.431294 + 0.902211i \(0.641943\pi\)
\(548\) 0 0
\(549\) −4.21354e10 2.43269e10i −0.463829 0.267792i
\(550\) 0 0
\(551\) 1.62551e9 9.38491e8i 0.0176354 0.0101818i
\(552\) 0 0
\(553\) −7.31491e10 + 7.16434e10i −0.782183 + 0.766083i
\(554\) 0 0
\(555\) −9.17610e9 1.58935e10i −0.0967133 0.167512i
\(556\) 0 0
\(557\) 8.89933e10 1.54141e11i 0.924564 1.60139i 0.132302 0.991209i \(-0.457763\pi\)
0.792262 0.610182i \(-0.208904\pi\)
\(558\) 0 0
\(559\) 5.72362e9i 0.0586170i
\(560\) 0 0
\(561\) −1.11195e11 −1.12263
\(562\) 0 0
\(563\) −1.36022e11 7.85323e10i −1.35386 0.781654i −0.365076 0.930978i \(-0.618957\pi\)
−0.988788 + 0.149323i \(0.952290\pi\)
\(564\) 0 0
\(565\) −6.17950e10 + 3.56774e10i −0.606400 + 0.350105i
\(566\) 0 0
\(567\) −1.10611e10 3.08744e9i −0.107020 0.0298721i
\(568\) 0 0
\(569\) −2.78668e8 4.82667e8i −0.00265851 0.00460467i 0.864693 0.502301i \(-0.167513\pi\)
−0.867352 + 0.497696i \(0.834180\pi\)
\(570\) 0 0
\(571\) 1.85718e10 3.21672e10i 0.174706 0.302600i −0.765353 0.643610i \(-0.777436\pi\)
0.940060 + 0.341010i \(0.110769\pi\)
\(572\) 0 0
\(573\) 8.91974e10i 0.827434i
\(574\) 0 0
\(575\) −9.83506e10 −0.899716
\(576\) 0 0
\(577\) 3.46036e10 + 1.99784e10i 0.312189 + 0.180243i 0.647906 0.761721i \(-0.275645\pi\)
−0.335716 + 0.941963i \(0.608978\pi\)
\(578\) 0 0
\(579\) −3.80937e10 + 2.19934e10i −0.338953 + 0.195694i
\(580\) 0 0
\(581\) 1.67434e11 4.30027e10i 1.46939 0.377391i
\(582\) 0 0
\(583\) 1.33894e11 + 2.31911e11i 1.15901 + 2.00746i
\(584\) 0 0
\(585\) 1.31795e10 2.28276e10i 0.112532 0.194911i
\(586\) 0 0
\(587\) 1.12252e11i 0.945460i 0.881207 + 0.472730i \(0.156731\pi\)
−0.881207 + 0.472730i \(0.843269\pi\)
\(588\) 0 0
\(589\) −3.81229e10 −0.316756
\(590\) 0 0
\(591\) 4.97370e10 + 2.87156e10i 0.407689 + 0.235380i
\(592\) 0 0
\(593\) 4.84487e10 2.79719e10i 0.391799 0.226205i −0.291140 0.956680i \(-0.594035\pi\)
0.682939 + 0.730475i \(0.260701\pi\)
\(594\) 0 0
\(595\) 1.89766e10 + 7.38865e10i 0.151409 + 0.589518i
\(596\) 0 0
\(597\) 2.69702e9 + 4.67137e9i 0.0212318 + 0.0367745i
\(598\) 0 0
\(599\) 1.46361e10 2.53505e10i 0.113689 0.196916i −0.803566 0.595216i \(-0.797067\pi\)
0.917255 + 0.398300i \(0.130400\pi\)
\(600\) 0 0
\(601\) 3.04406e10i 0.233322i 0.993172 + 0.116661i \(0.0372191\pi\)
−0.993172 + 0.116661i \(0.962781\pi\)
\(602\) 0 0
\(603\) 2.51887e10 0.190518
\(604\) 0 0
\(605\) 3.68678e10 + 2.12856e10i 0.275186 + 0.158879i
\(606\) 0 0
\(607\) 1.87228e11 1.08096e11i 1.37917 0.796262i 0.387107 0.922035i \(-0.373474\pi\)
0.992059 + 0.125772i \(0.0401409\pi\)
\(608\) 0 0
\(609\) −2.66009e9 + 9.53008e9i −0.0193387 + 0.0692831i
\(610\) 0 0
\(611\) −1.49667e11 2.59232e11i −1.07390 1.86004i
\(612\) 0 0
\(613\) 3.15010e10 5.45613e10i 0.223091 0.386405i −0.732654 0.680601i \(-0.761719\pi\)
0.955745 + 0.294196i \(0.0950519\pi\)
\(614\) 0 0
\(615\) 2.28490e9i 0.0159723i
\(616\) 0 0
\(617\) 2.31396e11 1.59667 0.798336 0.602213i \(-0.205714\pi\)
0.798336 + 0.602213i \(0.205714\pi\)
\(618\) 0 0
\(619\) −8.62110e10 4.97739e10i −0.587219 0.339031i 0.176778 0.984251i \(-0.443432\pi\)
−0.763997 + 0.645220i \(0.776766\pi\)
\(620\) 0 0
\(621\) −2.69615e10 + 1.55663e10i −0.181292 + 0.104669i
\(622\) 0 0
\(623\) 8.49068e10 + 8.66913e10i 0.563625 + 0.575471i
\(624\) 0 0
\(625\) −3.90080e10 6.75639e10i −0.255643 0.442787i
\(626\) 0 0
\(627\) 9.68579e9 1.67763e10i 0.0626708 0.108549i
\(628\) 0 0
\(629\) 1.84646e11i 1.17961i
\(630\) 0 0
\(631\) −3.88355e10 −0.244969 −0.122485 0.992470i \(-0.539086\pi\)
−0.122485 + 0.992470i \(0.539086\pi\)
\(632\) 0 0
\(633\) 9.47590e10 + 5.47092e10i 0.590209 + 0.340757i
\(634\) 0 0
\(635\) 8.94780e9 5.16602e9i 0.0550328 0.0317732i
\(636\) 0 0
\(637\) −1.28846e11 2.34289e11i −0.782554 1.42297i
\(638\) 0 0
\(639\) −3.40455e10 5.89686e10i −0.204201 0.353686i
\(640\) 0 0
\(641\) −1.01203e11 + 1.75289e11i −0.599462 + 1.03830i 0.393439 + 0.919351i \(0.371285\pi\)
−0.992901 + 0.118948i \(0.962048\pi\)
\(642\) 0 0
\(643\) 1.46591e11i 0.857558i −0.903409 0.428779i \(-0.858944\pi\)
0.903409 0.428779i \(-0.141056\pi\)
\(644\) 0 0
\(645\) 1.49962e9 0.00866450
\(646\) 0 0
\(647\) 2.40431e11 + 1.38813e11i 1.37206 + 0.792158i 0.991187 0.132470i \(-0.0422907\pi\)
0.380871 + 0.924628i \(0.375624\pi\)
\(648\) 0 0
\(649\) 1.95062e11 1.12619e11i 1.09950 0.634795i
\(650\) 0 0
\(651\) 1.43571e11 1.40616e11i 0.799362 0.782908i
\(652\) 0 0
\(653\) −1.35533e11 2.34750e11i −0.745406 1.29108i −0.950005 0.312236i \(-0.898922\pi\)
0.204598 0.978846i \(-0.434411\pi\)
\(654\) 0 0
\(655\) −4.97805e9 + 8.62224e9i −0.0270455 + 0.0468441i
\(656\) 0 0
\(657\) 2.73838e10i 0.146971i
\(658\) 0 0
\(659\) 8.76828e10 0.464914 0.232457 0.972607i \(-0.425324\pi\)
0.232457 + 0.972607i \(0.425324\pi\)
\(660\) 0 0
\(661\) −3.77894e10 2.18177e10i −0.197954 0.114289i 0.397747 0.917495i \(-0.369792\pi\)
−0.595701 + 0.803206i \(0.703126\pi\)
\(662\) 0 0
\(663\) 2.29674e11 1.32602e11i 1.18866 0.686273i
\(664\) 0 0
\(665\) −1.28004e10 3.57292e9i −0.0654541 0.0182699i
\(666\) 0 0
\(667\) 1.34117e10 + 2.32297e10i 0.0677609 + 0.117365i
\(668\) 0 0
\(669\) −2.66875e10 + 4.62241e10i −0.133230 + 0.230762i
\(670\) 0 0
\(671\) 4.32633e11i 2.13417i
\(672\) 0 0
\(673\) 1.88626e11 0.919480 0.459740 0.888054i \(-0.347943\pi\)
0.459740 + 0.888054i \(0.347943\pi\)
\(674\) 0 0
\(675\) −2.86180e10 1.65226e10i −0.137856 0.0795911i
\(676\) 0 0
\(677\) 3.41068e10 1.96916e10i 0.162363 0.0937401i −0.416617 0.909082i \(-0.636784\pi\)
0.578980 + 0.815342i \(0.303451\pi\)
\(678\) 0 0
\(679\) 2.71253e11 6.96673e10i 1.27613 0.327755i
\(680\) 0 0
\(681\) −4.92080e9 8.52308e9i −0.0228796 0.0396285i
\(682\) 0 0
\(683\) −1.05360e11 + 1.82490e11i −0.484167 + 0.838601i −0.999835 0.0181874i \(-0.994210\pi\)
0.515668 + 0.856788i \(0.327544\pi\)
\(684\) 0 0
\(685\) 1.07590e11i 0.488663i
\(686\) 0 0
\(687\) −1.72114e11 −0.772663
\(688\) 0 0
\(689\) −5.53116e11 3.19342e11i −2.45437 1.41703i
\(690\) 0 0
\(691\) −3.03078e10 + 1.74982e10i −0.132936 + 0.0767505i −0.564993 0.825096i \(-0.691121\pi\)
0.432057 + 0.901846i \(0.357788\pi\)
\(692\) 0 0
\(693\) 2.54024e10 + 9.89058e10i 0.110139 + 0.428834i
\(694\) 0 0
\(695\) −2.80186e10 4.85296e10i −0.120090 0.208002i
\(696\) 0 0
\(697\) 1.14944e10 1.99090e10i 0.0487031 0.0843563i
\(698\) 0 0
\(699\) 1.32997e10i 0.0557101i
\(700\) 0 0
\(701\) 8.58032e10 0.355330 0.177665 0.984091i \(-0.443146\pi\)
0.177665 + 0.984091i \(0.443146\pi\)
\(702\) 0 0
\(703\) 2.78580e10 + 1.60838e10i 0.114059 + 0.0658517i
\(704\) 0 0
\(705\) 6.79203e10 3.92138e10i 0.274943 0.158739i
\(706\) 0 0
\(707\) −6.88559e10 + 2.46684e11i −0.275590 + 0.987333i
\(708\) 0 0
\(709\) 9.74057e10 + 1.68712e11i 0.385478 + 0.667668i 0.991835 0.127525i \(-0.0407032\pi\)
−0.606357 + 0.795192i \(0.707370\pi\)
\(710\) 0 0
\(711\) −4.66317e10 + 8.07685e10i −0.182475 + 0.316056i
\(712\) 0 0
\(713\) 5.44801e11i 2.10804i
\(714\) 0 0
\(715\) −2.34387e11 −0.896827
\(716\) 0 0
\(717\) 1.06356e11 + 6.14046e10i 0.402425 + 0.232340i
\(718\) 0 0
\(719\) −2.89871e11 + 1.67357e11i −1.08465 + 0.626222i −0.932147 0.362081i \(-0.882066\pi\)
−0.152502 + 0.988303i \(0.548733\pi\)
\(720\) 0 0
\(721\) 3.44771e11 + 3.52017e11i 1.27582 + 1.30263i
\(722\) 0 0
\(723\) 5.55609e9 + 9.62343e9i 0.0203337 + 0.0352190i
\(724\) 0 0
\(725\) −1.42357e10 + 2.46569e10i −0.0515259 + 0.0892455i
\(726\) 0 0
\(727\) 9.86180e10i 0.353035i 0.984297 + 0.176518i \(0.0564833\pi\)
−0.984297 + 0.176518i \(0.943517\pi\)
\(728\) 0 0
\(729\) −1.04604e10 −0.0370370
\(730\) 0 0
\(731\) 1.30667e10 + 7.54404e9i 0.0457609 + 0.0264201i
\(732\) 0 0
\(733\) 2.61192e11 1.50799e11i 0.904782 0.522376i 0.0260337 0.999661i \(-0.491712\pi\)
0.878749 + 0.477285i \(0.158379\pi\)
\(734\) 0 0
\(735\) 6.13852e10 3.37586e10i 0.210336 0.115674i
\(736\) 0 0
\(737\) −1.11990e11 1.93972e11i −0.379585 0.657460i
\(738\) 0 0
\(739\) −1.82846e11 + 3.16698e11i −0.613065 + 1.06186i 0.377655 + 0.925946i \(0.376730\pi\)
−0.990721 + 0.135914i \(0.956603\pi\)
\(740\) 0 0
\(741\) 4.62019e10i 0.153245i
\(742\) 0 0
\(743\) −3.52082e11 −1.15528 −0.577642 0.816290i \(-0.696027\pi\)
−0.577642 + 0.816290i \(0.696027\pi\)
\(744\) 0 0
\(745\) 1.16873e11 + 6.74766e10i 0.379392 + 0.219042i
\(746\) 0 0
\(747\) 1.36364e11 7.87300e10i 0.437944 0.252847i
\(748\) 0 0
\(749\) −3.05569e11 + 2.99279e11i −0.970917 + 0.950932i
\(750\) 0 0
\(751\) −1.44039e11 2.49484e11i −0.452816 0.784300i 0.545744 0.837952i \(-0.316247\pi\)
−0.998560 + 0.0536517i \(0.982914\pi\)
\(752\) 0 0
\(753\) 8.16530e10 1.41427e11i 0.253976 0.439899i
\(754\) 0 0
\(755\) 8.58209e10i 0.264122i
\(756\) 0 0
\(757\) −5.34615e11 −1.62801 −0.814006 0.580857i \(-0.802718\pi\)
−0.814006 + 0.580857i \(0.802718\pi\)
\(758\) 0 0
\(759\) 2.39744e11 + 1.38416e11i 0.722405 + 0.417081i
\(760\) 0 0
\(761\) 2.20516e10 1.27315e10i 0.0657507 0.0379612i −0.466764 0.884382i \(-0.654580\pi\)
0.532515 + 0.846421i \(0.321247\pi\)
\(762\) 0 0
\(763\) −2.53539e11 7.07692e10i −0.748076 0.208807i
\(764\) 0 0
\(765\) 3.47426e10 + 6.01760e10i 0.101442 + 0.175702i
\(766\) 0 0
\(767\) −2.68601e11 + 4.65230e11i −0.776114 + 1.34427i
\(768\) 0 0
\(769\) 1.61134e11i 0.460768i 0.973100 + 0.230384i \(0.0739982\pi\)
−0.973100 + 0.230384i \(0.926002\pi\)
\(770\) 0 0
\(771\) −1.81647e11 −0.514057
\(772\) 0 0
\(773\) −2.00134e11 1.15547e11i −0.560535 0.323625i 0.192825 0.981233i \(-0.438235\pi\)
−0.753360 + 0.657608i \(0.771568\pi\)
\(774\) 0 0
\(775\) 5.00799e11 2.89136e11i 1.38821 0.801486i
\(776\) 0 0
\(777\) −1.64239e11 + 4.21821e10i −0.450600 + 0.115730i
\(778\) 0 0
\(779\) 2.00247e9 + 3.46839e9i 0.00543772 + 0.00941841i
\(780\) 0 0
\(781\) −3.02736e11 + 5.24353e11i −0.8136