Properties

Label 84.9.p.b.65.17
Level $84$
Weight $9$
Character 84.65
Analytic conductor $34.220$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [84,9,Mod(53,84)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(84, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("84.53");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 84.p (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(34.2198032451\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 65.17
Character \(\chi\) \(=\) 84.65
Dual form 84.9.p.b.53.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(67.5468 - 44.7037i) q^{3} +(737.233 + 425.642i) q^{5} +(2359.93 + 442.194i) q^{7} +(2564.15 - 6039.19i) q^{9} +O(q^{10})\) \(q+(67.5468 - 44.7037i) q^{3} +(737.233 + 425.642i) q^{5} +(2359.93 + 442.194i) q^{7} +(2564.15 - 6039.19i) q^{9} +(5724.94 - 3305.29i) q^{11} +27957.8 q^{13} +(68825.6 - 4206.32i) q^{15} +(-99130.5 + 57233.0i) q^{17} +(-77405.2 + 134070. i) q^{19} +(179173. - 75628.8i) q^{21} +(225502. + 130194. i) q^{23} +(167030. + 289304. i) q^{25} +(-96774.1 - 522556. i) q^{27} +17129.9i q^{29} +(-405878. - 703001. i) q^{31} +(238942. - 479188. i) q^{33} +(1.55160e6 + 1.33048e6i) q^{35} +(247100. - 427990. i) q^{37} +(1.88846e6 - 1.24982e6i) q^{39} -424820. i q^{41} -4.54551e6 q^{43} +(4.46091e6 - 3.36088e6i) q^{45} +(2.85874e6 + 1.65049e6i) q^{47} +(5.37373e6 + 2.08709e6i) q^{49} +(-4.13742e6 + 8.29742e6i) q^{51} +(1.31496e7 - 7.59194e6i) q^{53} +5.62749e6 q^{55} +(764942. + 1.25163e7i) q^{57} +(5.96730e6 - 3.44522e6i) q^{59} +(1.03062e6 - 1.78509e6i) q^{61} +(8.72171e6 - 1.31182e7i) q^{63} +(2.06114e7 + 1.19000e7i) q^{65} +(1.09091e7 + 1.88951e7i) q^{67} +(2.10521e7 - 1.28661e6i) q^{69} -4.05615e7i q^{71} +(-2.19692e7 - 3.80517e7i) q^{73} +(2.42153e7 + 1.20747e7i) q^{75} +(1.49720e7 - 5.26873e6i) q^{77} +(-3.58177e7 + 6.20381e7i) q^{79} +(-2.98970e7 - 3.09708e7i) q^{81} +2.39935e7i q^{83} -9.74431e7 q^{85} +(765771. + 1.15707e6i) q^{87} +(-1.76023e7 - 1.01627e7i) q^{89} +(6.59784e7 + 1.23628e7i) q^{91} +(-5.88426e7 - 2.93413e7i) q^{93} +(-1.14131e8 + 6.58938e7i) q^{95} +271197. q^{97} +(-5.28170e6 - 4.30493e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 81 q^{3} - 34 q^{7} + 4771 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 81 q^{3} - 34 q^{7} + 4771 q^{9} - 55464 q^{13} + 68482 q^{15} + 311690 q^{19} - 172343 q^{21} + 1766792 q^{25} - 3451932 q^{27} + 31596 q^{31} + 1874885 q^{33} - 1853482 q^{37} + 11217526 q^{39} - 13372600 q^{43} - 527785 q^{45} - 12653462 q^{49} - 1103461 q^{51} + 71577224 q^{55} - 17195214 q^{57} - 21761970 q^{61} + 21945045 q^{63} - 26337350 q^{67} - 5588722 q^{69} + 41115682 q^{73} - 17971730 q^{75} - 120916932 q^{79} - 24550133 q^{81} + 139250060 q^{85} - 16321046 q^{87} + 345074940 q^{91} + 25774675 q^{93} - 707216948 q^{97} - 94510994 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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
\(3\) 67.5468 44.7037i 0.833912 0.551898i
\(4\) 0 0
\(5\) 737.233 + 425.642i 1.17957 + 0.681027i 0.955916 0.293641i \(-0.0948669\pi\)
0.223658 + 0.974668i \(0.428200\pi\)
\(6\) 0 0
\(7\) 2359.93 + 442.194i 0.982894 + 0.184171i
\(8\) 0 0
\(9\) 2564.15 6039.19i 0.390817 0.920468i
\(10\) 0 0
\(11\) 5724.94 3305.29i 0.391021 0.225756i −0.291582 0.956546i \(-0.594181\pi\)
0.682602 + 0.730790i \(0.260848\pi\)
\(12\) 0 0
\(13\) 27957.8 0.978879 0.489440 0.872037i \(-0.337201\pi\)
0.489440 + 0.872037i \(0.337201\pi\)
\(14\) 0 0
\(15\) 68825.6 4206.32i 1.35952 0.0830878i
\(16\) 0 0
\(17\) −99130.5 + 57233.0i −1.18689 + 0.685253i −0.957599 0.288104i \(-0.906975\pi\)
−0.229294 + 0.973357i \(0.573642\pi\)
\(18\) 0 0
\(19\) −77405.2 + 134070.i −0.593958 + 1.02877i 0.399735 + 0.916631i \(0.369102\pi\)
−0.993693 + 0.112135i \(0.964231\pi\)
\(20\) 0 0
\(21\) 179173. 75628.8i 0.921290 0.388875i
\(22\) 0 0
\(23\) 225502. + 130194.i 0.805821 + 0.465241i 0.845503 0.533971i \(-0.179301\pi\)
−0.0396813 + 0.999212i \(0.512634\pi\)
\(24\) 0 0
\(25\) 167030. + 289304.i 0.427596 + 0.740617i
\(26\) 0 0
\(27\) −96774.1 522556.i −0.182098 0.983280i
\(28\) 0 0
\(29\) 17129.9i 0.0242194i 0.999927 + 0.0121097i \(0.00385473\pi\)
−0.999927 + 0.0121097i \(0.996145\pi\)
\(30\) 0 0
\(31\) −405878. 703001.i −0.439490 0.761219i 0.558160 0.829733i \(-0.311507\pi\)
−0.997650 + 0.0685146i \(0.978174\pi\)
\(32\) 0 0
\(33\) 238942. 479188.i 0.201483 0.404064i
\(34\) 0 0
\(35\) 1.55160e6 + 1.33048e6i 1.03397 + 0.886620i
\(36\) 0 0
\(37\) 247100. 427990.i 0.131846 0.228364i −0.792542 0.609817i \(-0.791243\pi\)
0.924388 + 0.381453i \(0.124576\pi\)
\(38\) 0 0
\(39\) 1.88846e6 1.24982e6i 0.816299 0.540242i
\(40\) 0 0
\(41\) 424820.i 0.150338i −0.997171 0.0751691i \(-0.976050\pi\)
0.997171 0.0751691i \(-0.0239496\pi\)
\(42\) 0 0
\(43\) −4.54551e6 −1.32956 −0.664781 0.747039i \(-0.731475\pi\)
−0.664781 + 0.747039i \(0.731475\pi\)
\(44\) 0 0
\(45\) 4.46091e6 3.36088e6i 1.08786 0.819603i
\(46\) 0 0
\(47\) 2.85874e6 + 1.65049e6i 0.585845 + 0.338238i 0.763453 0.645864i \(-0.223503\pi\)
−0.177608 + 0.984101i \(0.556836\pi\)
\(48\) 0 0
\(49\) 5.37373e6 + 2.08709e6i 0.932162 + 0.362041i
\(50\) 0 0
\(51\) −4.13742e6 + 8.29742e6i −0.611574 + 1.22648i
\(52\) 0 0
\(53\) 1.31496e7 7.59194e6i 1.66652 0.962164i 0.697022 0.717049i \(-0.254508\pi\)
0.969494 0.245114i \(-0.0788255\pi\)
\(54\) 0 0
\(55\) 5.62749e6 0.614984
\(56\) 0 0
\(57\) 764942. + 1.25163e7i 0.0724651 + 1.18570i
\(58\) 0 0
\(59\) 5.96730e6 3.44522e6i 0.492459 0.284321i −0.233135 0.972444i \(-0.574898\pi\)
0.725594 + 0.688123i \(0.241565\pi\)
\(60\) 0 0
\(61\) 1.03062e6 1.78509e6i 0.0744356 0.128926i −0.826405 0.563076i \(-0.809618\pi\)
0.900841 + 0.434150i \(0.142951\pi\)
\(62\) 0 0
\(63\) 8.72171e6 1.31182e7i 0.553655 0.832746i
\(64\) 0 0
\(65\) 2.06114e7 + 1.19000e7i 1.15466 + 0.666643i
\(66\) 0 0
\(67\) 1.09091e7 + 1.88951e7i 0.541364 + 0.937671i 0.998826 + 0.0484413i \(0.0154254\pi\)
−0.457462 + 0.889229i \(0.651241\pi\)
\(68\) 0 0
\(69\) 2.10521e7 1.28661e6i 0.928749 0.0567611i
\(70\) 0 0
\(71\) 4.05615e7i 1.59618i −0.602541 0.798088i \(-0.705845\pi\)
0.602541 0.798088i \(-0.294155\pi\)
\(72\) 0 0
\(73\) −2.19692e7 3.80517e7i −0.773610 1.33993i −0.935572 0.353135i \(-0.885116\pi\)
0.161962 0.986797i \(-0.448218\pi\)
\(74\) 0 0
\(75\) 2.42153e7 + 1.20747e7i 0.765322 + 0.381620i
\(76\) 0 0
\(77\) 1.49720e7 5.26873e6i 0.425910 0.149880i
\(78\) 0 0
\(79\) −3.58177e7 + 6.20381e7i −0.919580 + 1.59276i −0.119526 + 0.992831i \(0.538138\pi\)
−0.800054 + 0.599928i \(0.795196\pi\)
\(80\) 0 0
\(81\) −2.98970e7 3.09708e7i −0.694524 0.719470i
\(82\) 0 0
\(83\) 2.39935e7i 0.505571i 0.967522 + 0.252785i \(0.0813466\pi\)
−0.967522 + 0.252785i \(0.918653\pi\)
\(84\) 0 0
\(85\) −9.74431e7 −1.86670
\(86\) 0 0
\(87\) 765771. + 1.15707e6i 0.0133666 + 0.0201968i
\(88\) 0 0
\(89\) −1.76023e7 1.01627e7i −0.280549 0.161975i 0.353123 0.935577i \(-0.385120\pi\)
−0.633672 + 0.773602i \(0.718453\pi\)
\(90\) 0 0
\(91\) 6.59784e7 + 1.23628e7i 0.962135 + 0.180281i
\(92\) 0 0
\(93\) −5.88426e7 2.93413e7i −0.786611 0.392235i
\(94\) 0 0
\(95\) −1.14131e8 + 6.58938e7i −1.40123 + 0.809003i
\(96\) 0 0
\(97\) 271197. 0.00306336 0.00153168 0.999999i \(-0.499512\pi\)
0.00153168 + 0.999999i \(0.499512\pi\)
\(98\) 0 0
\(99\) −5.28170e6 4.30493e7i −0.0549836 0.448152i
\(100\) 0 0
\(101\) −6.56327e7 + 3.78930e7i −0.630717 + 0.364145i −0.781030 0.624494i \(-0.785305\pi\)
0.150313 + 0.988639i \(0.451972\pi\)
\(102\) 0 0
\(103\) 6.78145e7 1.17458e8i 0.602523 1.04360i −0.389914 0.920851i \(-0.627495\pi\)
0.992438 0.122750i \(-0.0391713\pi\)
\(104\) 0 0
\(105\) 1.64283e8 + 2.05076e7i 1.35156 + 0.168717i
\(106\) 0 0
\(107\) −6.30545e7 3.64045e7i −0.481039 0.277728i 0.239810 0.970820i \(-0.422915\pi\)
−0.720850 + 0.693092i \(0.756248\pi\)
\(108\) 0 0
\(109\) −7.41755e6 1.28476e7i −0.0525478 0.0910155i 0.838555 0.544817i \(-0.183401\pi\)
−0.891103 + 0.453801i \(0.850068\pi\)
\(110\) 0 0
\(111\) −2.44192e6 3.99557e7i −0.0160857 0.263201i
\(112\) 0 0
\(113\) 1.42202e8i 0.872151i 0.899910 + 0.436076i \(0.143632\pi\)
−0.899910 + 0.436076i \(0.856368\pi\)
\(114\) 0 0
\(115\) 1.10832e8 + 1.91966e8i 0.633684 + 1.09757i
\(116\) 0 0
\(117\) 7.16880e7 1.68842e8i 0.382563 0.901027i
\(118\) 0 0
\(119\) −2.59249e8 + 9.12310e7i −1.29279 + 0.454940i
\(120\) 0 0
\(121\) −8.53295e7 + 1.47795e8i −0.398068 + 0.689475i
\(122\) 0 0
\(123\) −1.89910e7 2.86952e7i −0.0829713 0.125369i
\(124\) 0 0
\(125\) 4.81536e7i 0.197237i
\(126\) 0 0
\(127\) −3.99281e8 −1.53484 −0.767420 0.641144i \(-0.778460\pi\)
−0.767420 + 0.641144i \(0.778460\pi\)
\(128\) 0 0
\(129\) −3.07035e8 + 2.03201e8i −1.10874 + 0.733782i
\(130\) 0 0
\(131\) −2.81218e8 1.62361e8i −0.954900 0.551311i −0.0603000 0.998180i \(-0.519206\pi\)
−0.894600 + 0.446869i \(0.852539\pi\)
\(132\) 0 0
\(133\) −2.41956e8 + 2.82167e8i −0.773267 + 0.901778i
\(134\) 0 0
\(135\) 1.51076e8 4.26437e8i 0.454843 1.28386i
\(136\) 0 0
\(137\) 2.90779e8 1.67881e8i 0.825430 0.476562i −0.0268553 0.999639i \(-0.508549\pi\)
0.852285 + 0.523077i \(0.175216\pi\)
\(138\) 0 0
\(139\) −4.71007e8 −1.26173 −0.630867 0.775891i \(-0.717301\pi\)
−0.630867 + 0.775891i \(0.717301\pi\)
\(140\) 0 0
\(141\) 2.66882e8 1.63107e7i 0.675215 0.0412662i
\(142\) 0 0
\(143\) 1.60056e8 9.24087e7i 0.382762 0.220988i
\(144\) 0 0
\(145\) −7.29121e6 + 1.26287e7i −0.0164941 + 0.0285685i
\(146\) 0 0
\(147\) 4.56279e8 9.92493e7i 0.977151 0.212549i
\(148\) 0 0
\(149\) 4.11751e8 + 2.37725e8i 0.835391 + 0.482313i 0.855695 0.517481i \(-0.173130\pi\)
−0.0203042 + 0.999794i \(0.506463\pi\)
\(150\) 0 0
\(151\) −3.70129e8 6.41082e8i −0.711943 1.23312i −0.964127 0.265442i \(-0.914482\pi\)
0.252184 0.967679i \(-0.418851\pi\)
\(152\) 0 0
\(153\) 9.14556e7 + 7.45422e8i 0.166895 + 1.36031i
\(154\) 0 0
\(155\) 6.91035e8i 1.19722i
\(156\) 0 0
\(157\) 5.26987e8 + 9.12768e8i 0.867364 + 1.50232i 0.864681 + 0.502322i \(0.167521\pi\)
0.00268327 + 0.999996i \(0.499146\pi\)
\(158\) 0 0
\(159\) 5.48827e8 1.10065e9i 0.858711 1.72211i
\(160\) 0 0
\(161\) 4.74598e8 + 4.06963e8i 0.706353 + 0.605692i
\(162\) 0 0
\(163\) −2.09473e8 + 3.62817e8i −0.296740 + 0.513969i −0.975388 0.220494i \(-0.929233\pi\)
0.678648 + 0.734464i \(0.262566\pi\)
\(164\) 0 0
\(165\) 3.80119e8 2.51570e8i 0.512842 0.339408i
\(166\) 0 0
\(167\) 9.95285e8i 1.27962i −0.768532 0.639811i \(-0.779013\pi\)
0.768532 0.639811i \(-0.220987\pi\)
\(168\) 0 0
\(169\) −3.40936e7 −0.0417951
\(170\) 0 0
\(171\) 6.11194e8 + 8.11240e8i 0.714817 + 0.948779i
\(172\) 0 0
\(173\) 1.19011e9 + 6.87112e8i 1.32863 + 0.767084i 0.985088 0.172053i \(-0.0550402\pi\)
0.343541 + 0.939138i \(0.388374\pi\)
\(174\) 0 0
\(175\) 2.66250e8 + 7.56596e8i 0.283881 + 0.806699i
\(176\) 0 0
\(177\) 2.49058e8 4.99474e8i 0.253751 0.508886i
\(178\) 0 0
\(179\) −7.58952e8 + 4.38181e8i −0.739268 + 0.426817i −0.821803 0.569771i \(-0.807032\pi\)
0.0825349 + 0.996588i \(0.473698\pi\)
\(180\) 0 0
\(181\) −1.46390e9 −1.36395 −0.681974 0.731377i \(-0.738878\pi\)
−0.681974 + 0.731377i \(0.738878\pi\)
\(182\) 0 0
\(183\) −1.01849e7 1.66650e8i −0.00908141 0.148594i
\(184\) 0 0
\(185\) 3.64341e8 2.10353e8i 0.311044 0.179581i
\(186\) 0 0
\(187\) −3.78344e8 + 6.55311e8i −0.309400 + 0.535897i
\(188\) 0 0
\(189\) 2.69084e6 1.27599e9i 0.00210882 0.999998i
\(190\) 0 0
\(191\) 2.04023e9 + 1.17793e9i 1.53301 + 0.885086i 0.999221 + 0.0394719i \(0.0125675\pi\)
0.533794 + 0.845615i \(0.320766\pi\)
\(192\) 0 0
\(193\) 2.60745e8 + 4.51624e8i 0.187926 + 0.325498i 0.944559 0.328343i \(-0.106490\pi\)
−0.756633 + 0.653840i \(0.773157\pi\)
\(194\) 0 0
\(195\) 1.92421e9 1.17599e8i 1.33080 0.0813330i
\(196\) 0 0
\(197\) 4.28916e8i 0.284779i −0.989811 0.142389i \(-0.954521\pi\)
0.989811 0.142389i \(-0.0454785\pi\)
\(198\) 0 0
\(199\) −3.26328e8 5.65217e8i −0.208086 0.360415i 0.743026 0.669263i \(-0.233390\pi\)
−0.951111 + 0.308848i \(0.900057\pi\)
\(200\) 0 0
\(201\) 1.58156e9 + 7.88628e8i 0.968949 + 0.483157i
\(202\) 0 0
\(203\) −7.57474e6 + 4.04254e7i −0.00446050 + 0.0238051i
\(204\) 0 0
\(205\) 1.80821e8 3.13191e8i 0.102384 0.177335i
\(206\) 0 0
\(207\) 1.36448e9 1.02801e9i 0.743169 0.559909i
\(208\) 0 0
\(209\) 1.02339e9i 0.536359i
\(210\) 0 0
\(211\) −4.94462e8 −0.249461 −0.124731 0.992191i \(-0.539807\pi\)
−0.124731 + 0.992191i \(0.539807\pi\)
\(212\) 0 0
\(213\) −1.81325e9 2.73980e9i −0.880926 1.33107i
\(214\) 0 0
\(215\) −3.35110e9 1.93476e9i −1.56832 0.905467i
\(216\) 0 0
\(217\) −6.46980e8 1.83851e9i −0.291778 0.829138i
\(218\) 0 0
\(219\) −3.18500e9 1.58817e9i −1.38463 0.690431i
\(220\) 0 0
\(221\) −2.77147e9 + 1.60011e9i −1.16183 + 0.670780i
\(222\) 0 0
\(223\) −5.81279e8 −0.235053 −0.117526 0.993070i \(-0.537496\pi\)
−0.117526 + 0.993070i \(0.537496\pi\)
\(224\) 0 0
\(225\) 2.17545e9 2.66905e8i 0.848827 0.104142i
\(226\) 0 0
\(227\) −2.34115e9 + 1.35166e9i −0.881711 + 0.509056i −0.871222 0.490889i \(-0.836672\pi\)
−0.0104886 + 0.999945i \(0.503339\pi\)
\(228\) 0 0
\(229\) −2.54279e9 + 4.40424e9i −0.924632 + 1.60151i −0.132479 + 0.991186i \(0.542294\pi\)
−0.792152 + 0.610323i \(0.791039\pi\)
\(230\) 0 0
\(231\) 7.75781e8 1.02519e9i 0.272453 0.360045i
\(232\) 0 0
\(233\) 2.95404e9 + 1.70552e9i 1.00229 + 0.578672i 0.908925 0.416960i \(-0.136904\pi\)
0.0933650 + 0.995632i \(0.470238\pi\)
\(234\) 0 0
\(235\) 1.40504e9 + 2.43360e9i 0.460698 + 0.797952i
\(236\) 0 0
\(237\) 3.53961e8 + 5.79166e9i 0.112192 + 1.83573i
\(238\) 0 0
\(239\) 6.19737e9i 1.89940i −0.313164 0.949699i \(-0.601389\pi\)
0.313164 0.949699i \(-0.398611\pi\)
\(240\) 0 0
\(241\) −2.73668e9 4.74006e9i −0.811251 1.40513i −0.911989 0.410215i \(-0.865454\pi\)
0.100738 0.994913i \(-0.467880\pi\)
\(242\) 0 0
\(243\) −3.40396e9 7.55474e8i −0.976245 0.216668i
\(244\) 0 0
\(245\) 3.07334e9 + 3.82596e9i 0.852994 + 1.06188i
\(246\) 0 0
\(247\) −2.16408e9 + 3.74829e9i −0.581413 + 1.00704i
\(248\) 0 0
\(249\) 1.07260e9 + 1.62069e9i 0.279023 + 0.421601i
\(250\) 0 0
\(251\) 3.83957e9i 0.967359i −0.875245 0.483679i \(-0.839300\pi\)
0.875245 0.483679i \(-0.160700\pi\)
\(252\) 0 0
\(253\) 1.72131e9 0.420124
\(254\) 0 0
\(255\) −6.58197e9 + 4.35607e9i −1.55667 + 1.03023i
\(256\) 0 0
\(257\) −6.84207e9 3.95027e9i −1.56839 0.905513i −0.996357 0.0852853i \(-0.972820\pi\)
−0.572038 0.820227i \(-0.693847\pi\)
\(258\) 0 0
\(259\) 7.72394e8 9.00761e8i 0.171648 0.200175i
\(260\) 0 0
\(261\) 1.03451e8 + 4.39237e7i 0.0222932 + 0.00946535i
\(262\) 0 0
\(263\) −3.19117e9 + 1.84242e9i −0.667002 + 0.385094i −0.794940 0.606688i \(-0.792498\pi\)
0.127938 + 0.991782i \(0.459164\pi\)
\(264\) 0 0
\(265\) 1.29258e10 2.62104
\(266\) 0 0
\(267\) −1.64329e9 + 1.00431e8i −0.323347 + 0.0197615i
\(268\) 0 0
\(269\) −3.92677e9 + 2.26712e9i −0.749941 + 0.432978i −0.825672 0.564150i \(-0.809204\pi\)
0.0757319 + 0.997128i \(0.475871\pi\)
\(270\) 0 0
\(271\) 3.65092e9 6.32358e9i 0.676901 1.17243i −0.299009 0.954250i \(-0.596656\pi\)
0.975909 0.218176i \(-0.0700107\pi\)
\(272\) 0 0
\(273\) 5.00929e9 2.11441e9i 0.901832 0.380662i
\(274\) 0 0
\(275\) 1.91247e9 + 1.10416e9i 0.334398 + 0.193065i
\(276\) 0 0
\(277\) 9.12992e7 + 1.58135e8i 0.0155077 + 0.0268602i 0.873675 0.486510i \(-0.161730\pi\)
−0.858167 + 0.513370i \(0.828397\pi\)
\(278\) 0 0
\(279\) −5.28629e9 + 6.48573e8i −0.872438 + 0.107039i
\(280\) 0 0
\(281\) 5.03022e8i 0.0806792i 0.999186 + 0.0403396i \(0.0128440\pi\)
−0.999186 + 0.0403396i \(0.987156\pi\)
\(282\) 0 0
\(283\) −2.26060e9 3.91547e9i −0.352434 0.610434i 0.634241 0.773135i \(-0.281313\pi\)
−0.986675 + 0.162701i \(0.947979\pi\)
\(284\) 0 0
\(285\) −4.76352e9 + 9.55302e9i −0.722019 + 1.44798i
\(286\) 0 0
\(287\) 1.87853e8 1.00254e9i 0.0276879 0.147767i
\(288\) 0 0
\(289\) 3.06336e9 5.30590e9i 0.439144 0.760619i
\(290\) 0 0
\(291\) 1.83185e7 1.21235e7i 0.00255457 0.00169066i
\(292\) 0 0
\(293\) 4.43372e8i 0.0601586i −0.999548 0.0300793i \(-0.990424\pi\)
0.999548 0.0300793i \(-0.00957598\pi\)
\(294\) 0 0
\(295\) 5.86572e9 0.774521
\(296\) 0 0
\(297\) −2.28123e9 2.67173e9i −0.293185 0.343374i
\(298\) 0 0
\(299\) 6.30453e9 + 3.63992e9i 0.788802 + 0.455415i
\(300\) 0 0
\(301\) −1.07271e10 2.01000e9i −1.30682 0.244866i
\(302\) 0 0
\(303\) −2.73932e9 + 5.49358e9i −0.324992 + 0.651756i
\(304\) 0 0
\(305\) 1.51962e9 8.77352e8i 0.175604 0.101385i
\(306\) 0 0
\(307\) −9.08706e9 −1.02299 −0.511493 0.859287i \(-0.670908\pi\)
−0.511493 + 0.859287i \(0.670908\pi\)
\(308\) 0 0
\(309\) −6.70164e8 1.09655e10i −0.0735101 1.20280i
\(310\) 0 0
\(311\) 1.38439e9 7.99278e8i 0.147985 0.0854390i −0.424179 0.905578i \(-0.639437\pi\)
0.572164 + 0.820139i \(0.306104\pi\)
\(312\) 0 0
\(313\) −4.42736e9 + 7.66841e9i −0.461283 + 0.798965i −0.999025 0.0441441i \(-0.985944\pi\)
0.537743 + 0.843109i \(0.319277\pi\)
\(314\) 0 0
\(315\) 1.20136e10 5.95886e9i 1.22020 0.605231i
\(316\) 0 0
\(317\) 1.50897e10 + 8.71204e9i 1.49432 + 0.862746i 0.999979 0.00652281i \(-0.00207629\pi\)
0.494340 + 0.869268i \(0.335410\pi\)
\(318\) 0 0
\(319\) 5.66194e7 + 9.80676e7i 0.00546767 + 0.00947028i
\(320\) 0 0
\(321\) −5.88655e9 + 3.59760e8i −0.554422 + 0.0338839i
\(322\) 0 0
\(323\) 1.77205e10i 1.62805i
\(324\) 0 0
\(325\) 4.66977e9 + 8.08829e9i 0.418565 + 0.724975i
\(326\) 0 0
\(327\) −1.07537e9 5.36221e8i −0.0940515 0.0468978i
\(328\) 0 0
\(329\) 6.01658e9 + 5.15916e9i 0.513530 + 0.440347i
\(330\) 0 0
\(331\) 9.18605e9 1.59107e10i 0.765273 1.32549i −0.174828 0.984599i \(-0.555937\pi\)
0.940102 0.340894i \(-0.110730\pi\)
\(332\) 0 0
\(333\) −1.95111e9 2.58972e9i −0.158674 0.210608i
\(334\) 0 0
\(335\) 1.85735e10i 1.47474i
\(336\) 0 0
\(337\) 1.78424e10 1.38335 0.691677 0.722207i \(-0.256872\pi\)
0.691677 + 0.722207i \(0.256872\pi\)
\(338\) 0 0
\(339\) 6.35696e9 + 9.60529e9i 0.481338 + 0.727297i
\(340\) 0 0
\(341\) −4.64725e9 2.68309e9i −0.343699 0.198435i
\(342\) 0 0
\(343\) 1.17587e10 + 7.30162e9i 0.849540 + 0.527525i
\(344\) 0 0
\(345\) 1.60679e10 + 8.01211e9i 1.13418 + 0.565550i
\(346\) 0 0
\(347\) −1.52110e9 + 8.78209e8i −0.104916 + 0.0605732i −0.551540 0.834149i \(-0.685960\pi\)
0.446624 + 0.894722i \(0.352626\pi\)
\(348\) 0 0
\(349\) 1.65106e9 0.111291 0.0556457 0.998451i \(-0.482278\pi\)
0.0556457 + 0.998451i \(0.482278\pi\)
\(350\) 0 0
\(351\) −2.70559e9 1.46095e10i −0.178252 0.962513i
\(352\) 0 0
\(353\) −8.15852e9 + 4.71032e9i −0.525427 + 0.303356i −0.739152 0.673538i \(-0.764774\pi\)
0.213725 + 0.976894i \(0.431440\pi\)
\(354\) 0 0
\(355\) 1.72647e10 2.99033e10i 1.08704 1.88281i
\(356\) 0 0
\(357\) −1.34331e10 + 1.77518e10i −0.826995 + 1.09287i
\(358\) 0 0
\(359\) 1.94388e10 + 1.12230e10i 1.17029 + 0.675666i 0.953748 0.300608i \(-0.0971896\pi\)
0.216540 + 0.976274i \(0.430523\pi\)
\(360\) 0 0
\(361\) −3.49136e9 6.04721e9i −0.205573 0.356062i
\(362\) 0 0
\(363\) 8.43252e8 + 1.37976e10i 0.0485658 + 0.794654i
\(364\) 0 0
\(365\) 3.74040e10i 2.10740i
\(366\) 0 0
\(367\) 1.30340e10 + 2.25755e10i 0.718476 + 1.24444i 0.961604 + 0.274442i \(0.0884931\pi\)
−0.243128 + 0.969994i \(0.578174\pi\)
\(368\) 0 0
\(369\) −2.56557e9 1.08930e9i −0.138381 0.0587547i
\(370\) 0 0
\(371\) 3.43893e10 1.21017e10i 1.81521 0.638782i
\(372\) 0 0
\(373\) 4.96157e9 8.59369e9i 0.256321 0.443961i −0.708933 0.705276i \(-0.750823\pi\)
0.965253 + 0.261316i \(0.0841563\pi\)
\(374\) 0 0
\(375\) −2.15265e9 3.25263e9i −0.108855 0.164478i
\(376\) 0 0
\(377\) 4.78914e8i 0.0237078i
\(378\) 0 0
\(379\) −2.22862e10 −1.08014 −0.540069 0.841621i \(-0.681602\pi\)
−0.540069 + 0.841621i \(0.681602\pi\)
\(380\) 0 0
\(381\) −2.69701e10 + 1.78493e10i −1.27992 + 0.847076i
\(382\) 0 0
\(383\) −1.89715e10 1.09532e10i −0.881671 0.509033i −0.0104621 0.999945i \(-0.503330\pi\)
−0.871209 + 0.490912i \(0.836664\pi\)
\(384\) 0 0
\(385\) 1.32805e10 + 2.48844e9i 0.604464 + 0.113262i
\(386\) 0 0
\(387\) −1.16554e10 + 2.74512e10i −0.519616 + 1.22382i
\(388\) 0 0
\(389\) 7.97181e9 4.60253e9i 0.348144 0.201001i −0.315724 0.948851i \(-0.602247\pi\)
0.663867 + 0.747850i \(0.268914\pi\)
\(390\) 0 0
\(391\) −2.98055e10 −1.27523
\(392\) 0 0
\(393\) −2.62535e10 + 1.60450e9i −1.10057 + 0.0672621i
\(394\) 0 0
\(395\) −5.28120e10 + 3.04910e10i −2.16942 + 1.25252i
\(396\) 0 0
\(397\) 5.56436e9 9.63775e9i 0.224002 0.387984i −0.732017 0.681286i \(-0.761421\pi\)
0.956020 + 0.293302i \(0.0947543\pi\)
\(398\) 0 0
\(399\) −3.72942e9 + 2.98758e10i −0.147146 + 1.17877i
\(400\) 0 0
\(401\) −1.38739e10 8.01009e9i −0.536563 0.309785i 0.207122 0.978315i \(-0.433590\pi\)
−0.743685 + 0.668531i \(0.766924\pi\)
\(402\) 0 0
\(403\) −1.13474e10 1.96544e10i −0.430207 0.745141i
\(404\) 0 0
\(405\) −8.85857e9 3.55581e10i −0.329263 1.32166i
\(406\) 0 0
\(407\) 3.26696e9i 0.119060i
\(408\) 0 0
\(409\) −6.45257e9 1.11762e10i −0.230589 0.399392i 0.727392 0.686222i \(-0.240732\pi\)
−0.957982 + 0.286829i \(0.907399\pi\)
\(410\) 0 0
\(411\) 1.21363e10 2.43387e10i 0.425322 0.852964i
\(412\) 0 0
\(413\) 1.56059e10 5.49178e9i 0.536398 0.188761i
\(414\) 0 0
\(415\) −1.02127e10 + 1.76888e10i −0.344307 + 0.596358i
\(416\) 0 0
\(417\) −3.18150e10 + 2.10558e10i −1.05217 + 0.696348i
\(418\) 0 0
\(419\) 2.16778e10i 0.703331i 0.936126 + 0.351665i \(0.114385\pi\)
−0.936126 + 0.351665i \(0.885615\pi\)
\(420\) 0 0
\(421\) 1.47352e10 0.469059 0.234530 0.972109i \(-0.424645\pi\)
0.234530 + 0.972109i \(0.424645\pi\)
\(422\) 0 0
\(423\) 1.72979e10 1.30323e10i 0.540295 0.407062i
\(424\) 0 0
\(425\) −3.31155e10 1.91192e10i −1.01502 0.586023i
\(426\) 0 0
\(427\) 3.22155e9 3.75695e9i 0.0969067 0.113012i
\(428\) 0 0
\(429\) 6.68030e9 1.33970e10i 0.197227 0.395530i
\(430\) 0 0
\(431\) −1.75141e10 + 1.01118e10i −0.507550 + 0.293034i −0.731826 0.681492i \(-0.761332\pi\)
0.224276 + 0.974526i \(0.427998\pi\)
\(432\) 0 0
\(433\) 5.65884e10 1.60981 0.804907 0.593401i \(-0.202215\pi\)
0.804907 + 0.593401i \(0.202215\pi\)
\(434\) 0 0
\(435\) 7.20539e7 + 1.17898e9i 0.00201234 + 0.0329267i
\(436\) 0 0
\(437\) −3.49100e10 + 2.01553e10i −0.957248 + 0.552668i
\(438\) 0 0
\(439\) −9.27059e9 + 1.60571e10i −0.249603 + 0.432325i −0.963416 0.268012i \(-0.913633\pi\)
0.713813 + 0.700336i \(0.246967\pi\)
\(440\) 0 0
\(441\) 2.63834e10 2.71014e10i 0.697552 0.716534i
\(442\) 0 0
\(443\) −1.71616e10 9.90825e9i −0.445598 0.257266i 0.260372 0.965509i \(-0.416155\pi\)
−0.705969 + 0.708243i \(0.749488\pi\)
\(444\) 0 0
\(445\) −8.65132e9 1.49845e10i −0.220619 0.382123i
\(446\) 0 0
\(447\) 3.84397e10 2.34927e9i 0.962829 0.0588440i
\(448\) 0 0
\(449\) 5.08034e10i 1.24999i −0.780627 0.624997i \(-0.785100\pi\)
0.780627 0.624997i \(-0.214900\pi\)
\(450\) 0 0
\(451\) −1.40415e9 2.43207e9i −0.0339397 0.0587854i
\(452\) 0 0
\(453\) −5.36598e10 2.67569e10i −1.27425 0.635394i
\(454\) 0 0
\(455\) 4.33793e10 + 3.71974e10i 1.01213 + 0.867895i
\(456\) 0 0
\(457\) −2.78637e10 + 4.82613e10i −0.638813 + 1.10646i 0.346881 + 0.937909i \(0.387241\pi\)
−0.985694 + 0.168547i \(0.946092\pi\)
\(458\) 0 0
\(459\) 3.95007e10 + 4.62625e10i 0.889926 + 1.04227i
\(460\) 0 0
\(461\) 6.67468e10i 1.47784i 0.673794 + 0.738919i \(0.264664\pi\)
−0.673794 + 0.738919i \(0.735336\pi\)
\(462\) 0 0
\(463\) −4.05204e10 −0.881759 −0.440879 0.897566i \(-0.645333\pi\)
−0.440879 + 0.897566i \(0.645333\pi\)
\(464\) 0 0
\(465\) −3.08918e10 4.66772e10i −0.660742 0.998374i
\(466\) 0 0
\(467\) 2.46885e10 + 1.42539e10i 0.519072 + 0.299686i 0.736555 0.676378i \(-0.236451\pi\)
−0.217483 + 0.976064i \(0.569785\pi\)
\(468\) 0 0
\(469\) 1.73894e10 + 4.94151e10i 0.359413 + 1.02133i
\(470\) 0 0
\(471\) 7.64005e10 + 3.80963e10i 1.55243 + 0.774104i
\(472\) 0 0
\(473\) −2.60227e10 + 1.50242e10i −0.519886 + 0.300156i
\(474\) 0 0
\(475\) −5.17158e10 −1.01590
\(476\) 0 0
\(477\) −1.21315e10 9.88799e10i −0.234338 1.91001i
\(478\) 0 0
\(479\) −6.66737e10 + 3.84941e10i −1.26652 + 0.731227i −0.974328 0.225133i \(-0.927718\pi\)
−0.292193 + 0.956359i \(0.594385\pi\)
\(480\) 0 0
\(481\) 6.90838e9 1.19657e10i 0.129061 0.223541i
\(482\) 0 0
\(483\) 5.02503e10 + 6.27279e9i 0.923316 + 0.115258i
\(484\) 0 0
\(485\) 1.99935e8 + 1.15433e8i 0.00361346 + 0.00208623i
\(486\) 0 0
\(487\) 2.55719e10 + 4.42919e10i 0.454619 + 0.787423i 0.998666 0.0516314i \(-0.0164421\pi\)
−0.544047 + 0.839055i \(0.683109\pi\)
\(488\) 0 0
\(489\) 2.07007e9 + 3.38714e10i 0.0362034 + 0.592375i
\(490\) 0 0
\(491\) 3.21356e10i 0.552918i −0.961026 0.276459i \(-0.910839\pi\)
0.961026 0.276459i \(-0.0891610\pi\)
\(492\) 0 0
\(493\) −9.80396e8 1.69810e9i −0.0165964 0.0287458i
\(494\) 0 0
\(495\) 1.44297e10 3.39855e10i 0.240346 0.566073i
\(496\) 0 0
\(497\) 1.79360e10 9.57223e10i 0.293969 1.56887i
\(498\) 0 0
\(499\) −2.38782e10 + 4.13582e10i −0.385123 + 0.667052i −0.991786 0.127907i \(-0.959174\pi\)
0.606663 + 0.794959i \(0.292508\pi\)
\(500\) 0 0
\(501\) −4.44930e10 6.72284e10i −0.706221 1.06709i
\(502\) 0 0
\(503\) 4.19041e9i 0.0654613i 0.999464 + 0.0327306i \(0.0104203\pi\)
−0.999464 + 0.0327306i \(0.989580\pi\)
\(504\) 0 0
\(505\) −6.45155e10 −0.991970
\(506\) 0 0
\(507\) −2.30291e9 + 1.52411e9i −0.0348534 + 0.0230666i
\(508\) 0 0
\(509\) 5.97316e10 + 3.44860e10i 0.889883 + 0.513774i 0.873904 0.486098i \(-0.161580\pi\)
0.0159785 + 0.999872i \(0.494914\pi\)
\(510\) 0 0
\(511\) −3.50194e10 9.95140e10i −0.513601 1.45949i
\(512\) 0 0
\(513\) 7.75497e10 + 2.74740e10i 1.11972 + 0.396692i
\(514\) 0 0
\(515\) 9.99903e10 5.77294e10i 1.42144 0.820669i
\(516\) 0 0
\(517\) 2.18214e10 0.305437
\(518\) 0 0
\(519\) 1.11105e11 6.79025e9i 1.53131 0.0935871i
\(520\) 0 0
\(521\) 7.71114e10 4.45203e10i 1.04657 0.604237i 0.124882 0.992172i \(-0.460145\pi\)
0.921687 + 0.387935i \(0.126811\pi\)
\(522\) 0 0
\(523\) −3.08198e10 + 5.33814e10i −0.411929 + 0.713483i −0.995101 0.0988666i \(-0.968478\pi\)
0.583171 + 0.812349i \(0.301812\pi\)
\(524\) 0 0
\(525\) 5.18070e10 + 3.92033e10i 0.681948 + 0.516042i
\(526\) 0 0
\(527\) 8.04698e10 + 4.64593e10i 1.04325 + 0.602323i
\(528\) 0 0
\(529\) −5.25477e9 9.10153e9i −0.0671014 0.116223i
\(530\) 0 0
\(531\) −5.50530e9 4.48717e10i −0.0692473 0.564410i
\(532\) 0 0
\(533\) 1.18770e10i 0.147163i
\(534\) 0 0
\(535\) −3.09906e10 5.36772e10i −0.378281 0.655202i
\(536\) 0 0
\(537\) −3.16765e10 + 6.35257e10i −0.380925 + 0.763928i
\(538\) 0 0
\(539\) 3.76627e10 5.81328e9i 0.446228 0.0688758i
\(540\) 0 0
\(541\) 4.06098e10 7.03382e10i 0.474069 0.821111i −0.525490 0.850800i \(-0.676118\pi\)
0.999559 + 0.0296882i \(0.00945144\pi\)
\(542\) 0 0
\(543\) −9.88819e10 + 6.54419e10i −1.13741 + 0.752760i
\(544\) 0 0
\(545\) 1.26289e10i 0.143146i
\(546\) 0 0
\(547\) 8.62204e10 0.963076 0.481538 0.876425i \(-0.340078\pi\)
0.481538 + 0.876425i \(0.340078\pi\)
\(548\) 0 0
\(549\) −8.13784e9 1.08014e10i −0.0895817 0.118902i
\(550\) 0 0
\(551\) −2.29660e9 1.32594e9i −0.0249161 0.0143853i
\(552\) 0 0
\(553\) −1.11960e11 + 1.30567e11i −1.19719 + 1.39615i
\(554\) 0 0
\(555\) 1.52066e10 3.04961e10i 0.160272 0.321419i
\(556\) 0 0
\(557\) 2.48180e10 1.43287e10i 0.257838 0.148863i −0.365510 0.930807i \(-0.619105\pi\)
0.623348 + 0.781945i \(0.285772\pi\)
\(558\) 0 0
\(559\) −1.27082e11 −1.30148
\(560\) 0 0
\(561\) 3.73891e9 + 6.11776e10i 0.0377480 + 0.617648i
\(562\) 0 0
\(563\) 1.03960e11 6.00214e10i 1.03475 0.597410i 0.116405 0.993202i \(-0.462863\pi\)
0.918340 + 0.395791i \(0.129530\pi\)
\(564\) 0 0
\(565\) −6.05271e10 + 1.04836e11i −0.593959 + 1.02877i
\(566\) 0 0
\(567\) −5.68596e10 8.63092e10i −0.550138 0.835074i
\(568\) 0 0
\(569\) −1.69153e11 9.76605e10i −1.61373 0.931687i −0.988496 0.151248i \(-0.951671\pi\)
−0.625233 0.780438i \(-0.714996\pi\)
\(570\) 0 0
\(571\) 6.06566e10 + 1.05060e11i 0.570603 + 0.988313i 0.996504 + 0.0835434i \(0.0266237\pi\)
−0.425901 + 0.904770i \(0.640043\pi\)
\(572\) 0 0
\(573\) 1.90469e11 1.16407e10i 1.76688 0.107984i
\(574\) 0 0
\(575\) 8.69847e10i 0.795740i
\(576\) 0 0
\(577\) 9.93010e10 + 1.71994e11i 0.895881 + 1.55171i 0.832710 + 0.553709i \(0.186788\pi\)
0.0631706 + 0.998003i \(0.479879\pi\)
\(578\) 0 0
\(579\) 3.78018e10 + 1.88495e10i 0.336355 + 0.167720i
\(580\) 0 0
\(581\) −1.06098e10 + 5.66230e10i −0.0931113 + 0.496923i
\(582\) 0 0
\(583\) 5.01871e10 8.69267e10i 0.434428 0.752452i
\(584\) 0 0
\(585\) 1.24717e11 9.39628e10i 1.06489 0.802292i
\(586\) 0 0
\(587\) 4.82000e10i 0.405971i −0.979182 0.202985i \(-0.934936\pi\)
0.979182 0.202985i \(-0.0650644\pi\)
\(588\) 0 0
\(589\) 1.25668e11 1.04415
\(590\) 0 0
\(591\) −1.91742e10 2.89719e10i −0.157169 0.237480i
\(592\) 0 0
\(593\) −1.84197e10 1.06346e10i −0.148958 0.0860010i 0.423669 0.905817i \(-0.360742\pi\)
−0.572627 + 0.819816i \(0.694075\pi\)
\(594\) 0 0
\(595\) −2.29959e11 4.30887e10i −1.83477 0.343792i
\(596\) 0 0
\(597\) −4.73097e10 2.35905e10i −0.372437 0.185712i
\(598\) 0 0
\(599\) −5.52238e10 + 3.18835e10i −0.428962 + 0.247661i −0.698904 0.715215i \(-0.746329\pi\)
0.269942 + 0.962876i \(0.412995\pi\)
\(600\) 0 0
\(601\) −7.10722e10 −0.544756 −0.272378 0.962190i \(-0.587810\pi\)
−0.272378 + 0.962190i \(0.587810\pi\)
\(602\) 0 0
\(603\) 1.42084e11 1.74322e10i 1.07467 0.131851i
\(604\) 0 0
\(605\) −1.25816e11 + 7.26396e10i −0.939102 + 0.542191i
\(606\) 0 0
\(607\) −1.65702e9 + 2.87004e9i −0.0122060 + 0.0211414i −0.872064 0.489392i \(-0.837219\pi\)
0.859858 + 0.510533i \(0.170552\pi\)
\(608\) 0 0
\(609\) 1.29551e9 + 3.06922e9i 0.00941832 + 0.0223131i
\(610\) 0 0
\(611\) 7.99239e10 + 4.61441e10i 0.573471 + 0.331094i
\(612\) 0 0
\(613\) −2.59650e10 4.49727e10i −0.183885 0.318498i 0.759315 0.650723i \(-0.225534\pi\)
−0.943200 + 0.332225i \(0.892201\pi\)
\(614\) 0 0
\(615\) −1.78693e9 2.92385e10i −0.0124913 0.204387i
\(616\) 0 0
\(617\) 1.76641e11i 1.21885i 0.792843 + 0.609426i \(0.208600\pi\)
−0.792843 + 0.609426i \(0.791400\pi\)
\(618\) 0 0
\(619\) −1.33248e10 2.30792e10i −0.0907607 0.157202i 0.817071 0.576537i \(-0.195597\pi\)
−0.907831 + 0.419335i \(0.862263\pi\)
\(620\) 0 0
\(621\) 4.62106e10 1.30437e11i 0.310724 0.877068i
\(622\) 0 0
\(623\) −3.70462e10 3.17668e10i −0.245919 0.210873i
\(624\) 0 0
\(625\) 8.57421e10 1.48510e11i 0.561920 0.973273i
\(626\) 0 0
\(627\) 4.57493e10 + 6.91266e10i 0.296015 + 0.447276i
\(628\) 0 0
\(629\) 5.65692e10i 0.361391i
\(630\) 0 0
\(631\) 4.36815e10 0.275537 0.137768 0.990464i \(-0.456007\pi\)
0.137768 + 0.990464i \(0.456007\pi\)
\(632\) 0 0
\(633\) −3.33994e10 + 2.21043e10i −0.208029 + 0.137677i
\(634\) 0 0
\(635\) −2.94363e11 1.69951e11i −1.81046 1.04527i
\(636\) 0 0
\(637\) 1.50238e11 + 5.83505e10i 0.912474 + 0.354394i
\(638\) 0 0
\(639\) −2.44959e11 1.04006e11i −1.46923 0.623813i
\(640\) 0 0
\(641\) −9.82752e10 + 5.67392e10i −0.582119 + 0.336086i −0.761975 0.647606i \(-0.775770\pi\)
0.179856 + 0.983693i \(0.442437\pi\)
\(642\) 0 0
\(643\) −1.06840e11 −0.625017 −0.312509 0.949915i \(-0.601169\pi\)
−0.312509 + 0.949915i \(0.601169\pi\)
\(644\) 0 0
\(645\) −3.12847e11 + 1.91199e10i −1.80756 + 0.110470i
\(646\) 0 0
\(647\) −1.63667e11 + 9.44929e10i −0.933991 + 0.539240i −0.888072 0.459705i \(-0.847955\pi\)
−0.0459197 + 0.998945i \(0.514622\pi\)
\(648\) 0 0
\(649\) 2.27749e10 3.94473e10i 0.128374 0.222351i
\(650\) 0 0
\(651\) −1.25890e11 9.52631e10i −0.700917 0.530397i
\(652\) 0 0
\(653\) 1.67148e11 + 9.65027e10i 0.919279 + 0.530746i 0.883405 0.468610i \(-0.155245\pi\)
0.0358742 + 0.999356i \(0.488578\pi\)
\(654\) 0 0
\(655\) −1.38215e11 2.39396e11i −0.750916 1.30062i
\(656\) 0 0
\(657\) −2.86134e11 + 3.51057e10i −1.53571 + 0.188415i
\(658\) 0 0
\(659\) 2.01067e11i 1.06610i −0.846083 0.533051i \(-0.821045\pi\)
0.846083 0.533051i \(-0.178955\pi\)
\(660\) 0 0
\(661\) 1.75229e10 + 3.03506e10i 0.0917912 + 0.158987i 0.908265 0.418396i \(-0.137407\pi\)
−0.816474 + 0.577383i \(0.804074\pi\)
\(662\) 0 0
\(663\) −1.15673e11 + 2.31977e11i −0.598657 + 1.20058i
\(664\) 0 0
\(665\) −2.98480e11 + 1.05037e11i −1.52626 + 0.537098i
\(666\) 0 0
\(667\) −2.23020e9 + 3.86283e9i −0.0112679 + 0.0195165i
\(668\) 0 0
\(669\) −3.92635e10 + 2.59853e10i −0.196013 + 0.129725i
\(670\) 0 0
\(671\) 1.36260e10i 0.0672171i
\(672\) 0 0
\(673\) 2.00983e9 0.00979714 0.00489857 0.999988i \(-0.498441\pi\)
0.00489857 + 0.999988i \(0.498441\pi\)
\(674\) 0 0
\(675\) 1.35013e11 1.15279e11i 0.650370 0.555311i
\(676\) 0 0
\(677\) 2.07359e11 + 1.19719e11i 0.987117 + 0.569912i 0.904411 0.426662i \(-0.140311\pi\)
0.0827056 + 0.996574i \(0.473644\pi\)
\(678\) 0 0
\(679\) 6.40006e8 + 1.19922e8i 0.00301096 + 0.000564181i
\(680\) 0 0
\(681\) −9.77129e10 + 1.95959e11i −0.454322 + 0.911122i
\(682\) 0 0
\(683\) −4.23598e10 + 2.44564e10i −0.194657 + 0.112385i −0.594161 0.804346i \(-0.702516\pi\)
0.399504 + 0.916732i \(0.369182\pi\)
\(684\) 0 0
\(685\) 2.85829e11 1.29821
\(686\) 0 0
\(687\) 2.51286e10 + 4.11165e11i 0.112809 + 1.84582i
\(688\) 0 0
\(689\) 3.67634e11 2.12254e11i 1.63132 0.941842i
\(690\) 0 0
\(691\) 1.06906e10 1.85167e10i 0.0468913 0.0812180i −0.841627 0.540059i \(-0.818402\pi\)
0.888518 + 0.458841i \(0.151735\pi\)
\(692\) 0 0
\(693\) 6.57169e9 1.03929e11i 0.0284934 0.450612i
\(694\) 0 0
\(695\) −3.47242e11 2.00480e11i −1.48831 0.859275i
\(696\) 0 0
\(697\) 2.43137e10 + 4.21126e10i 0.103020 + 0.178435i
\(698\) 0 0
\(699\) 2.75779e11 1.68544e10i 1.15519 0.0706002i
\(700\) 0 0
\(701\) 1.23088e11i 0.509732i 0.966976 + 0.254866i \(0.0820314\pi\)
−0.966976 + 0.254866i \(0.917969\pi\)
\(702\) 0 0
\(703\) 3.82537e10 + 6.62574e10i 0.156622 + 0.271277i
\(704\) 0 0
\(705\) 2.03697e11 + 1.01571e11i 0.824570 + 0.411163i
\(706\) 0 0
\(707\) −1.71645e11 + 6.04025e10i −0.686993 + 0.241756i
\(708\) 0 0
\(709\) 4.18701e10 7.25211e10i 0.165699 0.286998i −0.771205 0.636587i \(-0.780345\pi\)
0.936903 + 0.349589i \(0.113679\pi\)
\(710\) 0 0
\(711\) 2.82818e11 + 3.75385e11i 1.10670 + 1.46892i
\(712\) 0 0
\(713\) 2.11371e11i 0.817875i
\(714\) 0 0
\(715\) 1.57332e11 0.601995
\(716\) 0 0
\(717\) −2.77046e11 4.18613e11i −1.04827 1.58393i
\(718\) 0 0
\(719\) 2.23400e11 + 1.28980e11i 0.835924 + 0.482621i 0.855877 0.517180i \(-0.173018\pi\)
−0.0199527 + 0.999801i \(0.506352\pi\)
\(720\) 0 0
\(721\) 2.11977e11 2.47206e11i 0.784418 0.914782i
\(722\) 0 0
\(723\) −3.96752e11 1.97837e11i −1.45200 0.724025i
\(724\) 0 0
\(725\) −4.95574e9 + 2.86120e9i −0.0179373 + 0.0103561i
\(726\) 0 0
\(727\) 9.25752e10 0.331403 0.165702 0.986176i \(-0.447011\pi\)
0.165702 + 0.986176i \(0.447011\pi\)
\(728\) 0 0
\(729\) −2.63699e11 + 1.01140e11i −0.933681 + 0.358106i
\(730\) 0 0
\(731\) 4.50598e11 2.60153e11i 1.57805 0.911086i
\(732\) 0 0
\(733\) 1.60331e11 2.77702e11i 0.555396 0.961973i −0.442477 0.896780i \(-0.645900\pi\)
0.997873 0.0651935i \(-0.0207665\pi\)
\(734\) 0 0
\(735\) 3.78629e11 + 1.21042e11i 1.29737 + 0.414749i
\(736\) 0 0
\(737\) 1.24908e11 + 7.21156e10i 0.423370 + 0.244433i
\(738\) 0 0
\(739\) 7.36210e9 + 1.27515e10i 0.0246845 + 0.0427547i 0.878104 0.478470i \(-0.158809\pi\)
−0.853419 + 0.521225i \(0.825475\pi\)
\(740\) 0 0
\(741\) 2.13861e10 + 3.49928e11i 0.0709346 + 1.16066i
\(742\) 0 0
\(743\) 2.44534e11i 0.802387i 0.915993 + 0.401194i \(0.131405\pi\)
−0.915993 + 0.401194i \(0.868595\pi\)
\(744\) 0 0
\(745\) 2.02371e11 + 3.50517e11i 0.656936 + 1.13785i
\(746\) 0 0
\(747\) 1.44902e11 + 6.15231e10i 0.465362 + 0.197586i
\(748\) 0 0
\(749\) −1.32706e11 1.13794e11i −0.421662 0.361571i
\(750\) 0 0
\(751\) −9.11817e10 + 1.57931e11i −0.286647 + 0.496488i −0.973007 0.230774i \(-0.925874\pi\)
0.686360 + 0.727262i \(0.259208\pi\)
\(752\) 0 0
\(753\) −1.71643e11 2.59351e11i −0.533883 0.806692i
\(754\) 0 0
\(755\) 6.30170e11i 1.93941i
\(756\) 0 0
\(757\) −1.11403e11 −0.339246 −0.169623 0.985509i \(-0.554255\pi\)
−0.169623 + 0.985509i \(0.554255\pi\)
\(758\) 0 0
\(759\) 1.16269e11 7.69491e10i 0.350346 0.231866i
\(760\) 0 0
\(761\) 4.50095e11 + 2.59863e11i 1.34204 + 0.774828i 0.987107 0.160063i \(-0.0511698\pi\)
0.354935 + 0.934891i \(0.384503\pi\)
\(762\) 0 0
\(763\) −1.18238e10 3.35994e10i −0.0348866 0.0991364i
\(764\) 0 0
\(765\) −2.49859e11 + 5.88478e11i −0.729540 + 1.71824i
\(766\) 0 0
\(767\) 1.66832e11 9.63207e10i 0.482058 0.278316i
\(768\) 0 0
\(769\) −1.18834e11 −0.339809 −0.169904 0.985461i \(-0.554346\pi\)
−0.169904 + 0.985461i \(0.554346\pi\)
\(770\) 0 0
\(771\) −6.38752e11 + 3.90378e10i −1.80765 + 0.110476i
\(772\) 0 0
\(773\) 5.80476e11 3.35138e11i 1.62580 0.938654i 0.640467 0.767986i \(-0.278741\pi\)
0.985329 0.170668i \(-0.0545925\pi\)
\(774\) 0 0
\(775\) 1.35587e11 2.34844e11i 0.375848 0.650987i
\(776\) 0 0
\(777\) 1.19054e10 9.53724e10i 0.0326633 0.261661i
\(778\) 0 0
\(779\) 5.69555e10 + 3.28833e10i 0.154663 + 0.0892946i
\(780\) 0 0
\(781\) −1.34068e11 2.32212e11i −0.360346 0.624138i
\(782\) 0 0
\(783\) 8.95133e9 1.65773e9i 0.0238144 0.00441029i
\(784\) 0 0
\(785\) 8.97231e11i 2.36279i
\(786\) 0 0
\(787\) −8.40529e10 1.45584e11i −0.219106 0.379503i 0.735429 0.677602i \(-0.236981\pi\)
−0.954535 + 0.298099i \(0.903647\pi\)
\(788\) 0 0
\(789\) −1.33190e11 + 2.67107e11i −0.343688 + 0.689251i
\(790\) 0 0
\(791\) −6.28808e10 + 3.35587e11i −0.160625 + 0.857232i
\(792\) 0 0
\(793\) 2.88139e10 4.99072e10i 0.0728634 0.126203i
\(794\) 0 0
\(795\) 8.73096e11 5.77831e11i 2.18571 1.44655i
\(796\) 0 0
\(797\) 5.40452e11i 1.33944i −0.742613 0.669721i \(-0.766414\pi\)
0.742613 0.669721i \(-0.233586\pi\)
\(798\) 0 0
\(799\) −3.77851e11 −0.927114
\(800\) 0 0
\(801\) −1.06509e11 + 8.02448e10i −0.258736 + 0.194934i
\(802\) 0 0
\(803\) −2.51544e11 1.45229e11i −0.604995 0.349294i
\(804\) 0 0
\(805\) 1.76669e11 + 5.02035e11i 0.420703 + 1.19550i
\(806\) 0 0
\(807\) −1.63892e11 + 3.28679e11i −0.386424 + 0.774956i
\(808\) 0 0
\(809\) 1.00440e11 5.79890e10i 0.234484 0.135379i −0.378155 0.925742i \(-0.623441\pi\)
0.612639 + 0.790363i \(0.290108\pi\)
\(810\) 0 0
\(811\) −1.67234e11 −0.386581 −0.193291 0.981142i \(-0.561916\pi\)
−0.193291 + 0.981142i \(0.561916\pi\)
\(812\) 0 0
\(813\) −3.60795e10 5.90347e11i −0.0825844 1.35128i
\(814\) 0 0
\(815\) −3.08860e11 + 1.78321e11i −0.700054 + 0.404176i
\(816\) 0 0
\(817\) 3.51846e11 6.09415e11i 0.789704 1.36781i
\(818\) 0 0
\(819\) 2.43840e11 3.66756e11i 0.541962 0.815158i
\(820\) 0 0
\(821\) 7.33030e10 + 4.23215e10i 0.161343 + 0.0931511i 0.578497 0.815684i \(-0.303639\pi\)
−0.417155 + 0.908835i \(0.636973\pi\)
\(822\) 0 0
\(823\) −1.94981e11 3.37717e11i −0.425003 0.736127i 0.571417 0.820660i \(-0.306394\pi\)
−0.996421 + 0.0845322i \(0.973060\pi\)
\(824\) 0 0
\(825\) 1.78541e11 1.09117e10i 0.385410 0.0235546i
\(826\) 0 0
\(827\) 5.78023e9i 0.0123573i 0.999981 + 0.00617865i \(0.00196674\pi\)
−0.999981 + 0.00617865i \(0.998033\pi\)
\(828\) 0 0
\(829\) 2.50699e11 + 4.34223e11i 0.530803 + 0.919378i 0.999354 + 0.0359417i \(0.0114431\pi\)
−0.468551 + 0.883437i \(0.655224\pi\)
\(830\) 0 0
\(831\) 1.32362e10 + 6.60009e9i 0.0277561 + 0.0138403i
\(832\) 0 0
\(833\) −6.52151e11 + 1.00660e11i −1.35447 + 0.209063i
\(834\) 0 0
\(835\) 4.23635e11 7.33757e11i 0.871457 1.50941i
\(836\) 0 0
\(837\) −3.28079e11 + 2.80126e11i −0.668461 + 0.570758i
\(838\) 0 0
\(839\) 8.71109e11i 1.75802i 0.476799 + 0.879012i \(0.341797\pi\)
−0.476799 + 0.879012i \(0.658203\pi\)
\(840\) 0 0
\(841\) 4.99953e11 0.999413
\(842\) 0 0
\(843\) 2.24870e10 + 3.39775e10i 0.0445267 + 0.0672793i
\(844\) 0 0
\(845\) −2.51349e10 1.45116e10i −0.0493004 0.0284636i
\(846\) 0 0
\(847\) −2.66726e11 + 3.11054e11i −0.518240 + 0.604368i
\(848\) 0 0
\(849\) −3.27733e11 1.63421e11i −0.630796 0.314540i
\(850\) 0 0
\(851\) 1.11443e11 6.43417e10i 0.212488 0.122680i
\(852\) 0 0
\(853\) −9.38766e10 −0.177321 −0.0886607 0.996062i \(-0.528259\pi\)
−0.0886607 + 0.996062i \(0.528259\pi\)
\(854\) 0 0
\(855\) 1.05295e11 + 8.58223e11i 0.197035 + 1.60596i
\(856\) 0 0
\(857\) 4.94371e11 2.85425e11i 0.916494 0.529138i 0.0339790 0.999423i \(-0.489182\pi\)
0.882515 + 0.470285i \(0.155849\pi\)
\(858\) 0 0
\(859\) 1.81322e11 3.14059e11i 0.333026 0.576818i −0.650078 0.759868i \(-0.725264\pi\)
0.983104 + 0.183050i \(0.0585970\pi\)
\(860\) 0 0
\(861\) −3.21286e10 7.61164e10i −0.0584628 0.138505i
\(862\) 0 0
\(863\) −6.17513e11 3.56521e11i −1.11328 0.642750i −0.173600 0.984816i \(-0.555540\pi\)
−0.939676 + 0.342066i \(0.888873\pi\)
\(864\) 0 0
\(865\) 5.84927e11 + 1.01312e12i 1.04481 + 1.80966i
\(866\) 0 0
\(867\) −3.02731e10 4.95340e11i −0.0535772 0.876652i
\(868\) 0 0
\(869\) 4.73552e11i 0.830403i
\(870\) 0 0
\(871\) 3.04994e11 + 5.28265e11i 0.529931 + 0.917867i
\(872\) 0 0
\(873\) 6.95390e8 1.63781e9i 0.00119721 0.00281972i
\(874\) 0 0
\(875\) 2.12932e10 1.13639e11i 0.0363253 0.193863i
\(876\) 0 0
\(877\) 3.99463e11 6.91889e11i 0.675270 1.16960i −0.301119 0.953586i \(-0.597360\pi\)
0.976390 0.216016i \(-0.0693064\pi\)
\(878\) 0 0
\(879\) −1.98204e10 2.99484e10i −0.0332014 0.0501670i
\(880\) 0 0
\(881\) 7.69821e10i 0.127787i −0.997957 0.0638934i \(-0.979648\pi\)
0.997957 0.0638934i \(-0.0203518\pi\)
\(882\) 0 0
\(883\) 1.26548e11 0.208168 0.104084 0.994569i \(-0.466809\pi\)
0.104084 + 0.994569i \(0.466809\pi\)
\(884\) 0 0
\(885\) 3.96211e11 2.62220e11i 0.645882 0.427457i
\(886\) 0 0
\(887\) −1.27221e11 7.34509e10i −0.205524 0.118659i 0.393705 0.919237i \(-0.371193\pi\)
−0.599230 + 0.800577i \(0.704526\pi\)
\(888\) 0 0
\(889\) −9.42274e11 1.76559e11i −1.50859 0.282673i
\(890\) 0 0
\(891\) −2.73526e11 7.84877e10i −0.433998 0.124535i
\(892\) 0 0
\(893\) −4.42562e11 + 2.55513e11i −0.695935 + 0.401798i
\(894\) 0 0
\(895\) −7.46033e11 −1.16270
\(896\) 0 0
\(897\) 5.88569e11 3.59708e10i 0.909134 0.0555623i
\(898\) 0 0
\(899\) 1.20423e10 6.95265e9i 0.0184362 0.0106442i
\(900\) 0 0
\(901\) −8.69019e11 + 1.50518e12i −1.31865 + 2.28397i
\(902\) 0 0
\(903\) −8.14434e11 + 3.43771e11i −1.22491 + 0.517034i
\(904\) 0 0
\(905\) −1.07924e12 6.23098e11i −1.60888 0.928885i
\(906\) 0 0
\(907\) −3.68384e11 6.38059e11i −0.544341 0.942827i −0.998648 0.0519816i \(-0.983446\pi\)
0.454307 0.890845i \(-0.349887\pi\)
\(908\) 0 0
\(909\) 6.05512e10 + 4.93532e11i 0.0886885 + 0.722869i
\(910\) 0 0
\(911\) 6.34089e11i 0.920612i 0.887760 + 0.460306i \(0.152260\pi\)
−0.887760 + 0.460306i \(0.847740\pi\)
\(912\) 0 0
\(913\) 7.93057e10 + 1.37361e11i 0.114136 + 0.197689i
\(914\) 0 0
\(915\) 6.34245e10 1.27195e11i 0.0904842 0.181462i
\(916\) 0 0
\(917\) −5.91859e11 5.07514e11i −0.837030 0.717745i
\(918\) 0 0
\(919\) 2.08020e11 3.60301e11i 0.291637 0.505131i −0.682560 0.730830i \(-0.739133\pi\)
0.974197 + 0.225699i \(0.0724666\pi\)
\(920\) 0 0
\(921\) −6.13802e11 + 4.06226e11i −0.853081 + 0.564584i
\(922\) 0 0
\(923\) 1.13401e12i 1.56246i
\(924\) 0 0
\(925\) 1.65092e11 0.225507
\(926\) 0 0
\(927\) −5.35466e11 7.10726e11i −0.725125 0.962461i
\(928\) 0 0
\(929\) 3.30922e11 + 1.91058e11i 0.444287 + 0.256509i 0.705414 0.708795i \(-0.250761\pi\)
−0.261128 + 0.965304i \(0.584094\pi\)
\(930\) 0 0
\(931\) −6.95771e11 + 5.58903e11i −0.926121 + 0.743940i
\(932\) 0 0
\(933\) 5.77805e10 1.15876e11i 0.0762526 0.152921i
\(934\) 0 0
\(935\) −5.57856e11 + 3.22078e11i −0.729920 + 0.421420i
\(936\) 0 0
\(937\) −1.02637e12 −1.33151 −0.665754 0.746171i \(-0.731890\pi\)
−0.665754 + 0.746171i \(0.731890\pi\)
\(938\) 0 0
\(939\) 4.37525e10 + 7.15896e11i 0.0562782 + 0.920847i
\(940\) 0 0
\(941\) −6.43853e11 + 3.71729e11i −0.821161 + 0.474098i −0.850817 0.525462i \(-0.823892\pi\)
0.0296554 + 0.999560i \(0.490559\pi\)
\(942\) 0 0
\(943\) 5.53088e10 9.57976e10i 0.0699435 0.121146i
\(944\) 0 0
\(945\) 5.45097e11 9.39555e11i 0.683513 1.17813i
\(946\) 0 0
\(947\) 1.10236e12 + 6.36445e11i 1.37064 + 0.791337i 0.991008 0.133803i \(-0.0427189\pi\)
0.379627 + 0.925140i \(0.376052\pi\)
\(948\) 0 0
\(949\) −6.14209e11 1.06384e12i −0.757271 1.31163i
\(950\) 0 0
\(951\) 1.40872e12 8.60950e10i 1.72228 0.105258i
\(952\) 0 0
\(953\) 1.33087e12i 1.61348i −0.590904 0.806742i \(-0.701229\pi\)
0.590904 0.806742i \(-0.298771\pi\)
\(954\) 0 0
\(955\) 1.00275e12 + 1.73682e12i 1.20554 + 2.08805i
\(956\) 0 0
\(957\) 8.20845e9 + 4.09306e9i 0.00978618 + 0.00487978i
\(958\) 0 0
\(959\) 7.60453e11 2.67607e11i 0.899079 0.316390i
\(960\) 0 0
\(961\) 9.69716e10 1.67960e11i 0.113698 0.196930i
\(962\) 0 0
\(963\) −3.81535e11 + 2.87451e11i −0.443639 + 0.334241i
\(964\) 0 0
\(965\) 4.43936e11i 0.511931i
\(966\) 0 0
\(967\) 1.91088e10 0.0218538 0.0109269 0.999940i \(-0.496522\pi\)
0.0109269 + 0.999940i \(0.496522\pi\)
\(968\) 0 0
\(969\) −7.92174e11 1.19697e12i −0.898516 1.35765i
\(970\) 0 0
\(971\) 7.06433e11 + 4.07859e11i 0.794683 + 0.458810i 0.841609 0.540088i \(-0.181609\pi\)
−0.0469256 + 0.998898i \(0.514942\pi\)
\(972\) 0 0
\(973\) −1.11154e12 2.08276e11i −1.24015 0.232374i
\(974\) 0 0
\(975\) 6.77005e11 + 3.37582e11i 0.749158 + 0.373560i
\(976\) 0 0
\(977\) 6.55698e11 3.78567e11i 0.719657 0.415494i −0.0949697 0.995480i \(-0.530275\pi\)
0.814626 + 0.579986i \(0.196942\pi\)
\(978\) 0 0
\(979\) −1.34362e11 −0.146267
\(980\) 0 0
\(981\) −9.66087e10 + 1.18529e10i −0.104313 + 0.0127982i
\(982\) 0 0
\(983\) −4.45625e11 + 2.57281e11i −0.477260 + 0.275546i −0.719274 0.694727i \(-0.755525\pi\)
0.242014 + 0.970273i \(0.422192\pi\)
\(984\) 0 0
\(985\) 1.82565e11 3.16211e11i 0.193942 0.335917i
\(986\) 0 0
\(987\) 6.37034e11 + 7.95215e10i 0.671265 + 0.0837946i
\(988\) 0 0
\(989\) −1.02502e12 5.91796e11i −1.07139 0.618567i
\(990\) 0 0
\(991\) 1.18738e11 + 2.05661e11i 0.123111 + 0.213234i 0.920993 0.389579i \(-0.127380\pi\)
−0.797882 + 0.602814i \(0.794046\pi\)
\(992\) 0 0
\(993\) −9.07793e10 1.48537e12i −0.0933662 1.52770i
\(994\) 0 0
\(995\) 5.55596e11i 0.566848i
\(996\) 0 0
\(997\) −3.37631e11 5.84795e11i −0.341713 0.591865i 0.643038 0.765835i \(-0.277674\pi\)
−0.984751 + 0.173970i \(0.944341\pi\)
\(998\) 0 0
\(999\) −2.47562e11 8.77053e10i −0.248554 0.0880570i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 84.9.p.b.65.17 yes 40
3.2 odd 2 inner 84.9.p.b.65.3 yes 40
7.4 even 3 inner 84.9.p.b.53.3 40
21.11 odd 6 inner 84.9.p.b.53.17 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.9.p.b.53.3 40 7.4 even 3 inner
84.9.p.b.53.17 yes 40 21.11 odd 6 inner
84.9.p.b.65.3 yes 40 3.2 odd 2 inner
84.9.p.b.65.17 yes 40 1.1 even 1 trivial