Properties

Label 98.10.c.f.67.1
Level $98$
Weight $10$
Character 98.67
Analytic conductor $50.474$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 98 = 2 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 98.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(50.4735119441\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 14)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 98.67
Dual form 98.10.c.f.79.1

$q$-expansion

\(f(q)\) \(=\) \(q+(8.00000 + 13.8564i) q^{2} +(3.00000 - 5.19615i) q^{3} +(-128.000 + 221.703i) q^{4} +(-280.000 - 484.974i) q^{5} +96.0000 q^{6} -4096.00 q^{8} +(9823.50 + 17014.8i) q^{9} +O(q^{10})\) \(q+(8.00000 + 13.8564i) q^{2} +(3.00000 - 5.19615i) q^{3} +(-128.000 + 221.703i) q^{4} +(-280.000 - 484.974i) q^{5} +96.0000 q^{6} -4096.00 q^{8} +(9823.50 + 17014.8i) q^{9} +(4480.00 - 7759.59i) q^{10} +(27076.0 - 46897.0i) q^{11} +(768.000 + 1330.22i) q^{12} -113172. q^{13} -3360.00 q^{15} +(-32768.0 - 56755.8i) q^{16} +(-3131.00 + 5423.05i) q^{17} +(-157176. + 272237. i) q^{18} +(-128539. - 222636. i) q^{19} +143360. q^{20} +866432. q^{22} +(133000. + 230363. i) q^{23} +(-12288.0 + 21283.4i) q^{24} +(819762. - 1.41987e6i) q^{25} +(-905376. - 1.56816e6i) q^{26} +235980. q^{27} +1.57471e6 q^{29} +(-26880.0 - 46557.5i) q^{30} +(2.31874e6 - 4.01618e6i) q^{31} +(524288. - 908093. i) q^{32} +(-162456. - 281382. i) q^{33} -100192. q^{34} -5.02963e6 q^{36} +(5.97312e6 + 1.03457e7i) q^{37} +(2.05662e6 - 3.56218e6i) q^{38} +(-339516. + 588059. i) q^{39} +(1.14688e6 + 1.98645e6i) q^{40} +2.19091e7 q^{41} +2.75206e7 q^{43} +(6.93146e6 + 1.20056e7i) q^{44} +(5.50116e6 - 9.52829e6i) q^{45} +(-2.12800e6 + 3.68580e6i) q^{46} +(-2.64639e7 - 4.58369e7i) q^{47} -393216. q^{48} +2.62324e7 q^{50} +(18786.0 + 32538.3i) q^{51} +(1.44860e7 - 2.50905e7i) q^{52} +(-8.11061e6 + 1.40480e7i) q^{53} +(1.88784e6 + 3.26983e6i) q^{54} -3.03251e7 q^{55} -1.54247e6 q^{57} +(1.25977e7 + 2.18199e7i) q^{58} +(7.02548e7 - 1.21685e8i) q^{59} +(430080. - 744920. i) q^{60} +(1.01482e8 + 1.75772e8i) q^{61} +7.41997e7 q^{62} +1.67772e7 q^{64} +(3.16882e7 + 5.48855e7i) q^{65} +(2.59930e6 - 4.50211e6i) q^{66} +(-7.68673e7 + 1.33138e8i) q^{67} +(-801536. - 1.38830e6i) q^{68} +1.59600e6 q^{69} +2.79656e8 q^{71} +(-4.02371e7 - 6.96926e7i) q^{72} +(2.02011e8 - 3.49894e8i) q^{73} +(-9.55699e7 + 1.65532e8i) q^{74} +(-4.91858e6 - 8.51922e6i) q^{75} +6.58120e7 q^{76} -1.08645e7 q^{78} +(6.53449e7 + 1.13181e8i) q^{79} +(-1.83501e7 + 3.17833e7i) q^{80} +(-1.92648e8 + 3.33676e8i) q^{81} +(1.75273e8 + 3.03582e8i) q^{82} +4.20134e8 q^{83} +3.50672e6 q^{85} +(2.20165e8 + 3.81337e8i) q^{86} +(4.72414e6 - 8.18245e6i) q^{87} +(-1.10903e8 + 1.92090e8i) q^{88} +(2.34771e8 + 4.06636e8i) q^{89} +1.76037e8 q^{90} -6.80960e7 q^{92} +(-1.39125e7 - 2.40971e7i) q^{93} +(4.23423e8 - 7.33390e8i) q^{94} +(-7.19818e7 + 1.24676e8i) q^{95} +(-3.14573e6 - 5.44856e6i) q^{96} -8.72502e8 q^{97} +1.06392e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 16 q^{2} + 6 q^{3} - 256 q^{4} - 560 q^{5} + 192 q^{6} - 8192 q^{8} + 19647 q^{9} + O(q^{10}) \) \( 2 q + 16 q^{2} + 6 q^{3} - 256 q^{4} - 560 q^{5} + 192 q^{6} - 8192 q^{8} + 19647 q^{9} + 8960 q^{10} + 54152 q^{11} + 1536 q^{12} - 226344 q^{13} - 6720 q^{15} - 65536 q^{16} - 6262 q^{17} - 314352 q^{18} - 257078 q^{19} + 286720 q^{20} + 1732864 q^{22} + 266000 q^{23} - 24576 q^{24} + 1639525 q^{25} - 1810752 q^{26} + 471960 q^{27} + 3149428 q^{29} - 53760 q^{30} + 4637484 q^{31} + 1048576 q^{32} - 324912 q^{33} - 200384 q^{34} - 10059264 q^{36} + 11946238 q^{37} + 4113248 q^{38} - 679032 q^{39} + 2293760 q^{40} + 43818252 q^{41} + 55041184 q^{43} + 13862912 q^{44} + 11002320 q^{45} - 4256000 q^{46} - 52927836 q^{47} - 786432 q^{48} + 52464800 q^{50} + 37572 q^{51} + 28972032 q^{52} - 16221222 q^{53} + 3775680 q^{54} - 60650240 q^{55} - 3084936 q^{57} + 25195424 q^{58} + 140509618 q^{59} + 860160 q^{60} + 202963560 q^{61} + 148399488 q^{62} + 33554432 q^{64} + 63376320 q^{65} + 5198592 q^{66} - 153734572 q^{67} - 1603072 q^{68} + 3192000 q^{69} + 559311872 q^{71} - 80474112 q^{72} + 404022830 q^{73} - 191139808 q^{74} - 9837150 q^{75} + 131623936 q^{76} - 21729024 q^{78} + 130689816 q^{79} - 36700160 q^{80} - 385296021 q^{81} + 350546016 q^{82} + 840268028 q^{83} + 7013440 q^{85} + 440329472 q^{86} + 9448284 q^{87} - 221806592 q^{88} + 469542390 q^{89} + 352074240 q^{90} - 136192000 q^{92} - 27824904 q^{93} + 846845376 q^{94} - 143963680 q^{95} - 6291456 q^{96} - 1745003380 q^{97} + 2127848688 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 8.00000 + 13.8564i 0.353553 + 0.612372i
\(3\) 3.00000 5.19615i 0.0213833 0.0370370i −0.855136 0.518404i \(-0.826526\pi\)
0.876519 + 0.481367i \(0.159860\pi\)
\(4\) −128.000 + 221.703i −0.250000 + 0.433013i
\(5\) −280.000 484.974i −0.200352 0.347019i 0.748290 0.663372i \(-0.230875\pi\)
−0.948642 + 0.316352i \(0.897542\pi\)
\(6\) 96.0000 0.0302406
\(7\) 0 0
\(8\) −4096.00 −0.353553
\(9\) 9823.50 + 17014.8i 0.499086 + 0.864441i
\(10\) 4480.00 7759.59i 0.141670 0.245380i
\(11\) 27076.0 46897.0i 0.557593 0.965780i −0.440104 0.897947i \(-0.645058\pi\)
0.997697 0.0678326i \(-0.0216084\pi\)
\(12\) 768.000 + 1330.22i 0.0106917 + 0.0185185i
\(13\) −113172. −1.09899 −0.549495 0.835497i \(-0.685180\pi\)
−0.549495 + 0.835497i \(0.685180\pi\)
\(14\) 0 0
\(15\) −3360.00 −0.0171368
\(16\) −32768.0 56755.8i −0.125000 0.216506i
\(17\) −3131.00 + 5423.05i −0.00909207 + 0.0157479i −0.870536 0.492105i \(-0.836227\pi\)
0.861444 + 0.507853i \(0.169561\pi\)
\(18\) −157176. + 272237.i −0.352907 + 0.611252i
\(19\) −128539. 222636.i −0.226279 0.391926i 0.730424 0.682994i \(-0.239323\pi\)
−0.956702 + 0.291068i \(0.905989\pi\)
\(20\) 143360. 0.200352
\(21\) 0 0
\(22\) 866432. 0.788556
\(23\) 133000. + 230363.i 0.0991006 + 0.171647i 0.911313 0.411715i \(-0.135070\pi\)
−0.812212 + 0.583362i \(0.801737\pi\)
\(24\) −12288.0 + 21283.4i −0.00756015 + 0.0130946i
\(25\) 819762. 1.41987e6i 0.419718 0.726974i
\(26\) −905376. 1.56816e6i −0.388552 0.672991i
\(27\) 235980. 0.0854552
\(28\) 0 0
\(29\) 1.57471e6 0.413438 0.206719 0.978400i \(-0.433721\pi\)
0.206719 + 0.978400i \(0.433721\pi\)
\(30\) −26880.0 46557.5i −0.00605876 0.0104941i
\(31\) 2.31874e6 4.01618e6i 0.450946 0.781062i −0.547499 0.836806i \(-0.684420\pi\)
0.998445 + 0.0557446i \(0.0177533\pi\)
\(32\) 524288. 908093.i 0.0883883 0.153093i
\(33\) −162456. 281382.i −0.0238464 0.0413032i
\(34\) −100192. −0.0128581
\(35\) 0 0
\(36\) −5.02963e6 −0.499086
\(37\) 5.97312e6 + 1.03457e7i 0.523954 + 0.907515i 0.999611 + 0.0278845i \(0.00887708\pi\)
−0.475657 + 0.879631i \(0.657790\pi\)
\(38\) 2.05662e6 3.56218e6i 0.160003 0.277134i
\(39\) −339516. + 588059.i −0.0235001 + 0.0407033i
\(40\) 1.14688e6 + 1.98645e6i 0.0708350 + 0.122690i
\(41\) 2.19091e7 1.21087 0.605435 0.795895i \(-0.292999\pi\)
0.605435 + 0.795895i \(0.292999\pi\)
\(42\) 0 0
\(43\) 2.75206e7 1.22758 0.613790 0.789469i \(-0.289644\pi\)
0.613790 + 0.789469i \(0.289644\pi\)
\(44\) 6.93146e6 + 1.20056e7i 0.278797 + 0.482890i
\(45\) 5.50116e6 9.52829e6i 0.199985 0.346385i
\(46\) −2.12800e6 + 3.68580e6i −0.0700747 + 0.121373i
\(47\) −2.64639e7 4.58369e7i −0.791068 1.37017i −0.925306 0.379221i \(-0.876192\pi\)
0.134238 0.990949i \(-0.457141\pi\)
\(48\) −393216. −0.0106917
\(49\) 0 0
\(50\) 2.62324e7 0.593571
\(51\) 18786.0 + 32538.3i 0.000388838 + 0.000673487i
\(52\) 1.44860e7 2.50905e7i 0.274748 0.475877i
\(53\) −8.11061e6 + 1.40480e7i −0.141193 + 0.244553i −0.927946 0.372715i \(-0.878427\pi\)
0.786753 + 0.617268i \(0.211760\pi\)
\(54\) 1.88784e6 + 3.26983e6i 0.0302130 + 0.0523304i
\(55\) −3.03251e7 −0.446859
\(56\) 0 0
\(57\) −1.54247e6 −0.0193544
\(58\) 1.25977e7 + 2.18199e7i 0.146173 + 0.253178i
\(59\) 7.02548e7 1.21685e8i 0.754818 1.30738i −0.190647 0.981659i \(-0.561059\pi\)
0.945465 0.325724i \(-0.105608\pi\)
\(60\) 430080. 744920.i 0.00428419 0.00742043i
\(61\) 1.01482e8 + 1.75772e8i 0.938434 + 1.62542i 0.768393 + 0.639979i \(0.221057\pi\)
0.170042 + 0.985437i \(0.445610\pi\)
\(62\) 7.41997e7 0.637734
\(63\) 0 0
\(64\) 1.67772e7 0.125000
\(65\) 3.16882e7 + 5.48855e7i 0.220185 + 0.381371i
\(66\) 2.59930e6 4.50211e6i 0.0168620 0.0292058i
\(67\) −7.68673e7 + 1.33138e8i −0.466020 + 0.807171i −0.999247 0.0388015i \(-0.987646\pi\)
0.533227 + 0.845972i \(0.320979\pi\)
\(68\) −801536. 1.38830e6i −0.00454604 0.00787397i
\(69\) 1.59600e6 0.00847641
\(70\) 0 0
\(71\) 2.79656e8 1.30606 0.653028 0.757334i \(-0.273499\pi\)
0.653028 + 0.757334i \(0.273499\pi\)
\(72\) −4.02371e7 6.96926e7i −0.176453 0.305626i
\(73\) 2.02011e8 3.49894e8i 0.832574 1.44206i −0.0634158 0.997987i \(-0.520199\pi\)
0.895990 0.444074i \(-0.146467\pi\)
\(74\) −9.55699e7 + 1.65532e8i −0.370492 + 0.641710i
\(75\) −4.91858e6 8.51922e6i −0.0179500 0.0310903i
\(76\) 6.58120e7 0.226279
\(77\) 0 0
\(78\) −1.08645e7 −0.0332341
\(79\) 6.53449e7 + 1.13181e8i 0.188751 + 0.326927i 0.944834 0.327549i \(-0.106223\pi\)
−0.756083 + 0.654476i \(0.772889\pi\)
\(80\) −1.83501e7 + 3.17833e7i −0.0500879 + 0.0867548i
\(81\) −1.92648e8 + 3.33676e8i −0.497258 + 0.861276i
\(82\) 1.75273e8 + 3.03582e8i 0.428107 + 0.741504i
\(83\) 4.20134e8 0.971709 0.485855 0.874040i \(-0.338508\pi\)
0.485855 + 0.874040i \(0.338508\pi\)
\(84\) 0 0
\(85\) 3.50672e6 0.00728645
\(86\) 2.20165e8 + 3.81337e8i 0.434015 + 0.751736i
\(87\) 4.72414e6 8.18245e6i 0.00884069 0.0153125i
\(88\) −1.10903e8 + 1.92090e8i −0.197139 + 0.341455i
\(89\) 2.34771e8 + 4.06636e8i 0.396634 + 0.686990i 0.993308 0.115493i \(-0.0368449\pi\)
−0.596674 + 0.802483i \(0.703512\pi\)
\(90\) 1.76037e8 0.282822
\(91\) 0 0
\(92\) −6.80960e7 −0.0991006
\(93\) −1.39125e7 2.40971e7i −0.0192855 0.0334034i
\(94\) 4.23423e8 7.33390e8i 0.559370 0.968856i
\(95\) −7.19818e7 + 1.24676e8i −0.0906706 + 0.157046i
\(96\) −3.14573e6 5.44856e6i −0.00378008 0.00654729i
\(97\) −8.72502e8 −1.00068 −0.500338 0.865830i \(-0.666791\pi\)
−0.500338 + 0.865830i \(0.666791\pi\)
\(98\) 0 0
\(99\) 1.06392e9 1.11315
\(100\) 2.09859e8 + 3.63487e8i 0.209859 + 0.363487i
\(101\) 6.04507e8 1.04704e9i 0.578037 1.00119i −0.417668 0.908600i \(-0.637152\pi\)
0.995704 0.0925891i \(-0.0295143\pi\)
\(102\) −300576. + 520613.i −0.000274950 + 0.000476227i
\(103\) −3.45281e8 5.98045e8i −0.302277 0.523560i 0.674374 0.738390i \(-0.264414\pi\)
−0.976651 + 0.214830i \(0.931080\pi\)
\(104\) 4.63553e8 0.388552
\(105\) 0 0
\(106\) −2.59540e8 −0.199677
\(107\) −8.97497e7 1.55451e8i −0.0661921 0.114648i 0.831030 0.556227i \(-0.187752\pi\)
−0.897222 + 0.441579i \(0.854418\pi\)
\(108\) −3.02054e7 + 5.23174e7i −0.0213638 + 0.0370032i
\(109\) 8.01804e8 1.38877e9i 0.544063 0.942345i −0.454602 0.890695i \(-0.650219\pi\)
0.998665 0.0516501i \(-0.0164480\pi\)
\(110\) −2.42601e8 4.20197e8i −0.157988 0.273644i
\(111\) 7.16774e7 0.0448156
\(112\) 0 0
\(113\) 1.42785e9 0.823815 0.411908 0.911226i \(-0.364863\pi\)
0.411908 + 0.911226i \(0.364863\pi\)
\(114\) −1.23397e7 2.13731e7i −0.00684281 0.0118521i
\(115\) 7.44800e7 1.29003e8i 0.0397100 0.0687797i
\(116\) −2.01563e8 + 3.49118e8i −0.103360 + 0.179024i
\(117\) −1.11175e9 1.92560e9i −0.548490 0.950013i
\(118\) 2.24815e9 1.06747
\(119\) 0 0
\(120\) 1.37626e7 0.00605876
\(121\) −2.87246e8 4.97524e8i −0.121820 0.210999i
\(122\) −1.62371e9 + 2.81235e9i −0.663573 + 1.14934i
\(123\) 6.57274e7 1.13843e8i 0.0258925 0.0448471i
\(124\) 5.93598e8 + 1.02814e9i 0.225473 + 0.390531i
\(125\) −2.01188e9 −0.737069
\(126\) 0 0
\(127\) −2.35873e9 −0.804565 −0.402282 0.915516i \(-0.631783\pi\)
−0.402282 + 0.915516i \(0.631783\pi\)
\(128\) 1.34218e8 + 2.32472e8i 0.0441942 + 0.0765466i
\(129\) 8.25618e7 1.43001e8i 0.0262498 0.0454659i
\(130\) −5.07011e8 + 8.78168e8i −0.155694 + 0.269670i
\(131\) −3.00833e8 5.21057e8i −0.0892492 0.154584i 0.817945 0.575297i \(-0.195113\pi\)
−0.907194 + 0.420713i \(0.861780\pi\)
\(132\) 8.31775e7 0.0238464
\(133\) 0 0
\(134\) −2.45975e9 −0.659052
\(135\) −6.60744e7 1.14444e8i −0.0171211 0.0296546i
\(136\) 1.28246e7 2.22128e7i 0.00321453 0.00556773i
\(137\) 2.58004e9 4.46877e9i 0.625726 1.08379i −0.362673 0.931916i \(-0.618136\pi\)
0.988400 0.151874i \(-0.0485307\pi\)
\(138\) 1.27680e7 + 2.21148e7i 0.00299686 + 0.00519072i
\(139\) −7.14356e9 −1.62311 −0.811556 0.584275i \(-0.801379\pi\)
−0.811556 + 0.584275i \(0.801379\pi\)
\(140\) 0 0
\(141\) −3.17567e8 −0.0676627
\(142\) 2.23725e9 + 3.87503e9i 0.461760 + 0.799792i
\(143\) −3.06425e9 + 5.30743e9i −0.612790 + 1.06138i
\(144\) 6.43793e8 1.11508e9i 0.124771 0.216110i
\(145\) −4.40920e8 7.63696e8i −0.0828331 0.143471i
\(146\) 6.46437e9 1.17744
\(147\) 0 0
\(148\) −3.05824e9 −0.523954
\(149\) −4.55212e9 7.88450e9i −0.756616 1.31050i −0.944567 0.328319i \(-0.893518\pi\)
0.187951 0.982178i \(-0.439815\pi\)
\(150\) 7.86972e7 1.36308e8i 0.0126925 0.0219841i
\(151\) 1.44716e8 2.50655e8i 0.0226527 0.0392357i −0.854477 0.519490i \(-0.826122\pi\)
0.877130 + 0.480254i \(0.159455\pi\)
\(152\) 5.26496e8 + 9.11917e8i 0.0800016 + 0.138567i
\(153\) −1.23030e8 −0.0181509
\(154\) 0 0
\(155\) −2.59699e9 −0.361391
\(156\) −8.69161e7 1.50543e8i −0.0117500 0.0203517i
\(157\) −6.95339e9 + 1.20436e10i −0.913373 + 1.58201i −0.104107 + 0.994566i \(0.533198\pi\)
−0.809266 + 0.587442i \(0.800135\pi\)
\(158\) −1.04552e9 + 1.81089e9i −0.133467 + 0.231172i
\(159\) 4.86637e7 + 8.42879e7i 0.00603834 + 0.0104587i
\(160\) −5.87203e8 −0.0708350
\(161\) 0 0
\(162\) −6.16474e9 −0.703229
\(163\) −8.31162e9 1.43962e10i −0.922235 1.59736i −0.795948 0.605364i \(-0.793027\pi\)
−0.126287 0.991994i \(-0.540306\pi\)
\(164\) −2.80437e9 + 4.85731e9i −0.302718 + 0.524322i
\(165\) −9.09754e7 + 1.57574e8i −0.00955534 + 0.0165503i
\(166\) 3.36107e9 + 5.82155e9i 0.343551 + 0.595048i
\(167\) −1.58019e10 −1.57212 −0.786061 0.618149i \(-0.787883\pi\)
−0.786061 + 0.618149i \(0.787883\pi\)
\(168\) 0 0
\(169\) 2.20340e9 0.207780
\(170\) 2.80538e7 + 4.85905e7i 0.00257615 + 0.00446202i
\(171\) 2.52541e9 4.37413e9i 0.225865 0.391209i
\(172\) −3.52264e9 + 6.10138e9i −0.306895 + 0.531558i
\(173\) −1.61562e9 2.79834e9i −0.137130 0.237516i 0.789279 0.614035i \(-0.210455\pi\)
−0.926409 + 0.376518i \(0.877121\pi\)
\(174\) 1.51173e8 0.0125026
\(175\) 0 0
\(176\) −3.54891e9 −0.278797
\(177\) −4.21529e8 7.30109e8i −0.0322810 0.0559124i
\(178\) −3.75634e9 + 6.50617e9i −0.280462 + 0.485775i
\(179\) 1.20704e10 2.09065e10i 0.878785 1.52210i 0.0261099 0.999659i \(-0.491688\pi\)
0.852675 0.522441i \(-0.174979\pi\)
\(180\) 1.40830e9 + 2.43924e9i 0.0999926 + 0.173192i
\(181\) −3.89332e9 −0.269629 −0.134814 0.990871i \(-0.543044\pi\)
−0.134814 + 0.990871i \(0.543044\pi\)
\(182\) 0 0
\(183\) 1.21778e9 0.0802674
\(184\) −5.44768e8 9.43566e8i −0.0350374 0.0606865i
\(185\) 3.34495e9 5.79362e9i 0.209950 0.363645i
\(186\) 2.22599e8 3.85553e8i 0.0136369 0.0236198i
\(187\) 1.69550e8 + 2.93669e8i 0.0101394 + 0.0175619i
\(188\) 1.35495e10 0.791068
\(189\) 0 0
\(190\) −2.30342e9 −0.128228
\(191\) 1.29494e10 + 2.24290e10i 0.704043 + 1.21944i 0.967036 + 0.254641i \(0.0819571\pi\)
−0.262993 + 0.964798i \(0.584710\pi\)
\(192\) 5.03316e7 8.71770e7i 0.00267292 0.00462963i
\(193\) −7.96837e9 + 1.38016e10i −0.413391 + 0.716015i −0.995258 0.0972694i \(-0.968989\pi\)
0.581867 + 0.813284i \(0.302323\pi\)
\(194\) −6.98001e9 1.20897e10i −0.353792 0.612786i
\(195\) 3.80258e8 0.0188331
\(196\) 0 0
\(197\) −3.34685e9 −0.158321 −0.0791604 0.996862i \(-0.525224\pi\)
−0.0791604 + 0.996862i \(0.525224\pi\)
\(198\) 8.51139e9 + 1.47422e10i 0.393557 + 0.681660i
\(199\) 6.71304e9 1.16273e10i 0.303445 0.525583i −0.673469 0.739216i \(-0.735196\pi\)
0.976914 + 0.213633i \(0.0685297\pi\)
\(200\) −3.35775e9 + 5.81579e9i −0.148393 + 0.257024i
\(201\) 4.61204e8 + 7.98828e8i 0.0199301 + 0.0345200i
\(202\) 1.93442e10 0.817467
\(203\) 0 0
\(204\) −9.61843e6 −0.000388838
\(205\) −6.13456e9 1.06254e10i −0.242600 0.420195i
\(206\) 5.52450e9 9.56872e9i 0.213742 0.370213i
\(207\) −2.61305e9 + 4.52594e9i −0.0989194 + 0.171333i
\(208\) 3.70842e9 + 6.42317e9i 0.137374 + 0.237938i
\(209\) −1.39213e10 −0.504686
\(210\) 0 0
\(211\) 3.01702e10 1.04787 0.523935 0.851759i \(-0.324464\pi\)
0.523935 + 0.851759i \(0.324464\pi\)
\(212\) −2.07632e9 3.59629e9i −0.0705963 0.122276i
\(213\) 8.38968e8 1.45313e9i 0.0279278 0.0483724i
\(214\) 1.43599e9 2.48722e9i 0.0468049 0.0810684i
\(215\) −7.70577e9 1.33468e10i −0.245948 0.425994i
\(216\) −9.66574e8 −0.0302130
\(217\) 0 0
\(218\) 2.56577e10 0.769421
\(219\) −1.21207e9 2.09936e9i −0.0356064 0.0616722i
\(220\) 3.88162e9 6.72316e9i 0.111715 0.193496i
\(221\) 3.54342e8 6.13738e8i 0.00999210 0.0173068i
\(222\) 5.73419e8 + 9.93192e8i 0.0158447 + 0.0274438i
\(223\) 5.35030e10 1.44879 0.724396 0.689384i \(-0.242119\pi\)
0.724396 + 0.689384i \(0.242119\pi\)
\(224\) 0 0
\(225\) 3.22117e10 0.837901
\(226\) 1.14228e10 + 1.97849e10i 0.291263 + 0.504482i
\(227\) 2.01352e10 3.48752e10i 0.503315 0.871766i −0.496678 0.867935i \(-0.665447\pi\)
0.999993 0.00383159i \(-0.00121964\pi\)
\(228\) 1.97436e8 3.41969e8i 0.00483860 0.00838069i
\(229\) −9.51236e9 1.64759e10i −0.228575 0.395903i 0.728811 0.684715i \(-0.240073\pi\)
−0.957386 + 0.288812i \(0.906740\pi\)
\(230\) 2.38336e9 0.0561584
\(231\) 0 0
\(232\) −6.45003e9 −0.146173
\(233\) 1.83874e10 + 3.18479e10i 0.408713 + 0.707911i 0.994746 0.102376i \(-0.0326444\pi\)
−0.586033 + 0.810287i \(0.699311\pi\)
\(234\) 1.77879e10 3.08096e10i 0.387841 0.671761i
\(235\) −1.48198e10 + 2.56686e10i −0.316984 + 0.549032i
\(236\) 1.79852e10 + 3.11513e10i 0.377409 + 0.653691i
\(237\) 7.84139e8 0.0161445
\(238\) 0 0
\(239\) 6.56110e9 0.130073 0.0650363 0.997883i \(-0.479284\pi\)
0.0650363 + 0.997883i \(0.479284\pi\)
\(240\) 1.10100e8 + 1.90700e8i 0.00214209 + 0.00371022i
\(241\) 4.48409e10 7.76667e10i 0.856244 1.48306i −0.0192424 0.999815i \(-0.506125\pi\)
0.875486 0.483243i \(-0.160541\pi\)
\(242\) 4.59593e9 7.96039e9i 0.0861399 0.149199i
\(243\) 3.47829e9 + 6.02457e9i 0.0639937 + 0.110840i
\(244\) −5.19587e10 −0.938434
\(245\) 0 0
\(246\) 2.10328e9 0.0366175
\(247\) 1.45470e10 + 2.51962e10i 0.248678 + 0.430723i
\(248\) −9.49757e9 + 1.64503e10i −0.159434 + 0.276147i
\(249\) 1.26040e9 2.18308e9i 0.0207784 0.0359892i
\(250\) −1.60951e10 2.78775e10i −0.260593 0.451360i
\(251\) 5.33703e9 0.0848727 0.0424363 0.999099i \(-0.486488\pi\)
0.0424363 + 0.999099i \(0.486488\pi\)
\(252\) 0 0
\(253\) 1.44044e10 0.221031
\(254\) −1.88698e10 3.26835e10i −0.284457 0.492693i
\(255\) 1.05202e7 1.82215e7i 0.000155809 0.000269868i
\(256\) −2.14748e9 + 3.71955e9i −0.0312500 + 0.0541266i
\(257\) 4.17788e10 + 7.23630e10i 0.597388 + 1.03471i 0.993205 + 0.116377i \(0.0371282\pi\)
−0.395817 + 0.918329i \(0.629539\pi\)
\(258\) 2.64198e9 0.0371228
\(259\) 0 0
\(260\) −1.62243e10 −0.220185
\(261\) 1.54692e10 + 2.67934e10i 0.206341 + 0.357393i
\(262\) 4.81332e9 8.33692e9i 0.0631087 0.109307i
\(263\) −5.43174e10 + 9.40806e10i −0.700065 + 1.21255i 0.268378 + 0.963314i \(0.413512\pi\)
−0.968443 + 0.249235i \(0.919821\pi\)
\(264\) 6.65420e8 + 1.15254e9i 0.00843098 + 0.0146029i
\(265\) 9.08388e9 0.113153
\(266\) 0 0
\(267\) 2.81725e9 0.0339254
\(268\) −1.96780e10 3.40833e10i −0.233010 0.403586i
\(269\) −7.07003e10 + 1.22456e11i −0.823258 + 1.42592i 0.0799860 + 0.996796i \(0.474512\pi\)
−0.903244 + 0.429128i \(0.858821\pi\)
\(270\) 1.05719e9 1.83111e9i 0.0121064 0.0209690i
\(271\) 4.54176e10 + 7.86657e10i 0.511520 + 0.885979i 0.999911 + 0.0133539i \(0.00425079\pi\)
−0.488391 + 0.872625i \(0.662416\pi\)
\(272\) 4.10386e8 0.00454604
\(273\) 0 0
\(274\) 8.25614e10 0.884911
\(275\) −4.43918e10 7.68888e10i −0.468064 0.810711i
\(276\) −2.04288e8 + 3.53837e8i −0.00211910 + 0.00367039i
\(277\) 1.32538e10 2.29562e10i 0.135263 0.234283i −0.790435 0.612546i \(-0.790145\pi\)
0.925698 + 0.378263i \(0.123479\pi\)
\(278\) −5.71485e10 9.89841e10i −0.573857 0.993949i
\(279\) 9.11126e10 0.900243
\(280\) 0 0
\(281\) −1.86968e11 −1.78891 −0.894455 0.447158i \(-0.852436\pi\)
−0.894455 + 0.447158i \(0.852436\pi\)
\(282\) −2.54054e9 4.40034e9i −0.0239224 0.0414348i
\(283\) 2.66706e9 4.61949e9i 0.0247169 0.0428110i −0.853402 0.521253i \(-0.825465\pi\)
0.878119 + 0.478442i \(0.158798\pi\)
\(284\) −3.57960e10 + 6.20004e10i −0.326514 + 0.565538i
\(285\) 4.31891e8 + 7.48057e8i 0.00387768 + 0.00671634i
\(286\) −9.80558e10 −0.866615
\(287\) 0 0
\(288\) 2.06014e10 0.176453
\(289\) 5.92743e10 + 1.02666e11i 0.499835 + 0.865739i
\(290\) 7.05472e9 1.22191e10i 0.0585718 0.101449i
\(291\) −2.61751e9 + 4.53365e9i −0.0213978 + 0.0370621i
\(292\) 5.17149e10 + 8.95729e10i 0.416287 + 0.721031i
\(293\) 7.65433e10 0.606741 0.303370 0.952873i \(-0.401888\pi\)
0.303370 + 0.952873i \(0.401888\pi\)
\(294\) 0 0
\(295\) −7.86854e10 −0.604916
\(296\) −2.44659e10 4.23762e10i −0.185246 0.320855i
\(297\) 6.38939e9 1.10668e10i 0.0476492 0.0825308i
\(298\) 7.28339e10 1.26152e11i 0.535008 0.926662i
\(299\) −1.50519e10 2.60706e10i −0.108911 0.188639i
\(300\) 2.51831e9 0.0179500
\(301\) 0 0
\(302\) 4.63091e9 0.0320358
\(303\) −3.62704e9 6.28223e9i −0.0247207 0.0428175i
\(304\) −8.42393e9 + 1.45907e10i −0.0565697 + 0.0979816i
\(305\) 5.68298e10 9.84321e10i 0.376034 0.651310i
\(306\) −9.84236e8 1.70475e9i −0.00641731 0.0111151i
\(307\) −7.51944e10 −0.483128 −0.241564 0.970385i \(-0.577660\pi\)
−0.241564 + 0.970385i \(0.577660\pi\)
\(308\) 0 0
\(309\) −4.14338e9 −0.0258548
\(310\) −2.07759e10 3.59850e10i −0.127771 0.221306i
\(311\) −1.07567e11 + 1.86311e11i −0.652014 + 1.12932i 0.330619 + 0.943764i \(0.392743\pi\)
−0.982633 + 0.185558i \(0.940591\pi\)
\(312\) 1.39066e9 2.40869e9i 0.00830854 0.0143908i
\(313\) −4.79537e10 8.30583e10i −0.282405 0.489140i 0.689571 0.724218i \(-0.257799\pi\)
−0.971977 + 0.235077i \(0.924466\pi\)
\(314\) −2.22508e11 −1.29170
\(315\) 0 0
\(316\) −3.34566e10 −0.188751
\(317\) −8.52932e10 1.47732e11i −0.474403 0.821691i 0.525167 0.850999i \(-0.324003\pi\)
−0.999570 + 0.0293083i \(0.990670\pi\)
\(318\) −7.78619e8 + 1.34861e9i −0.00426975 + 0.00739543i
\(319\) 4.26370e10 7.38494e10i 0.230530 0.399290i
\(320\) −4.69762e9 8.13652e9i −0.0250440 0.0433774i
\(321\) −1.07700e9 −0.00566163
\(322\) 0 0
\(323\) 1.60982e9 0.00822937
\(324\) −4.93179e10 8.54211e10i −0.248629 0.430638i
\(325\) −9.27742e10 + 1.60690e11i −0.461266 + 0.798937i
\(326\) 1.32986e11 2.30338e11i 0.652119 1.12950i
\(327\) −4.81083e9 8.33259e9i −0.0232678 0.0403010i
\(328\) −8.97398e10 −0.428107
\(329\) 0 0
\(330\) −2.91121e9 −0.0135133
\(331\) 6.19958e10 + 1.07380e11i 0.283881 + 0.491697i 0.972337 0.233581i \(-0.0750445\pi\)
−0.688456 + 0.725278i \(0.741711\pi\)
\(332\) −5.37772e10 + 9.31448e10i −0.242927 + 0.420763i
\(333\) −1.17354e11 + 2.03263e11i −0.522996 + 0.905856i
\(334\) −1.26416e11 2.18958e11i −0.555829 0.962724i
\(335\) 8.60914e10 0.373472
\(336\) 0 0
\(337\) −7.29335e10 −0.308030 −0.154015 0.988069i \(-0.549220\pi\)
−0.154015 + 0.988069i \(0.549220\pi\)
\(338\) 1.76272e10 + 3.05312e10i 0.0734613 + 0.127239i
\(339\) 4.28355e9 7.41933e9i 0.0176159 0.0305117i
\(340\) −4.48860e8 + 7.77449e8i −0.00182161 + 0.00315512i
\(341\) −1.25565e11 2.17484e11i −0.502889 0.871029i
\(342\) 8.08130e10 0.319421
\(343\) 0 0
\(344\) −1.12724e11 −0.434015
\(345\) −4.46880e8 7.74019e8i −0.00169826 0.00294148i
\(346\) 2.58500e10 4.47735e10i 0.0969657 0.167949i
\(347\) 7.78602e10 1.34858e11i 0.288292 0.499337i −0.685110 0.728440i \(-0.740246\pi\)
0.973402 + 0.229103i \(0.0735792\pi\)
\(348\) 1.20938e9 + 2.09471e9i 0.00442035 + 0.00765626i
\(349\) 1.08728e11 0.392310 0.196155 0.980573i \(-0.437154\pi\)
0.196155 + 0.980573i \(0.437154\pi\)
\(350\) 0 0
\(351\) −2.67063e10 −0.0939144
\(352\) −2.83912e10 4.91751e10i −0.0985695 0.170727i
\(353\) −1.62793e11 + 2.81965e11i −0.558018 + 0.966516i 0.439644 + 0.898172i \(0.355105\pi\)
−0.997662 + 0.0683436i \(0.978229\pi\)
\(354\) 6.74446e9 1.16818e10i 0.0228261 0.0395360i
\(355\) −7.83037e10 1.35626e11i −0.261670 0.453226i
\(356\) −1.20203e11 −0.396634
\(357\) 0 0
\(358\) 3.86252e11 1.24279
\(359\) 1.13775e11 + 1.97064e11i 0.361511 + 0.626155i 0.988210 0.153106i \(-0.0489277\pi\)
−0.626699 + 0.779261i \(0.715594\pi\)
\(360\) −2.25328e10 + 3.90279e10i −0.0707055 + 0.122465i
\(361\) 1.28299e11 2.22221e11i 0.397596 0.688656i
\(362\) −3.11465e10 5.39474e10i −0.0953282 0.165113i
\(363\) −3.44695e9 −0.0104197
\(364\) 0 0
\(365\) −2.26253e11 −0.667231
\(366\) 9.74225e9 + 1.68741e10i 0.0283788 + 0.0491536i
\(367\) 2.10996e11 3.65457e11i 0.607125 1.05157i −0.384587 0.923089i \(-0.625656\pi\)
0.991712 0.128482i \(-0.0410105\pi\)
\(368\) 8.71629e9 1.50971e10i 0.0247752 0.0429118i
\(369\) 2.15224e11 + 3.72779e11i 0.604328 + 1.04673i
\(370\) 1.07038e11 0.296915
\(371\) 0 0
\(372\) 7.12318e9 0.0192855
\(373\) −1.91642e11 3.31933e11i −0.512625 0.887893i −0.999893 0.0146401i \(-0.995340\pi\)
0.487268 0.873253i \(-0.337994\pi\)
\(374\) −2.71280e9 + 4.69870e9i −0.00716961 + 0.0124181i
\(375\) −6.03565e9 + 1.04541e10i −0.0157610 + 0.0272988i
\(376\) 1.08396e11 + 1.87748e11i 0.279685 + 0.484428i
\(377\) −1.78214e11 −0.454365
\(378\) 0 0
\(379\) −1.21462e11 −0.302386 −0.151193 0.988504i \(-0.548312\pi\)
−0.151193 + 0.988504i \(0.548312\pi\)
\(380\) −1.84274e10 3.19171e10i −0.0453353 0.0785231i
\(381\) −7.07618e9 + 1.22563e10i −0.0172043 + 0.0297987i
\(382\) −2.07190e11 + 3.58864e11i −0.497834 + 0.862273i
\(383\) 1.98860e11 + 3.44436e11i 0.472230 + 0.817927i 0.999495 0.0317740i \(-0.0101157\pi\)
−0.527265 + 0.849701i \(0.676782\pi\)
\(384\) 1.61061e9 0.00378008
\(385\) 0 0
\(386\) −2.54988e11 −0.584624
\(387\) 2.70349e11 + 4.68257e11i 0.612667 + 1.06117i
\(388\) 1.11680e11 1.93436e11i 0.250169 0.433305i
\(389\) −3.37731e10 + 5.84968e10i −0.0747821 + 0.129526i −0.900992 0.433837i \(-0.857159\pi\)
0.826209 + 0.563363i \(0.190493\pi\)
\(390\) 3.04206e9 + 5.26901e9i 0.00665852 + 0.0115329i
\(391\) −1.66569e9 −0.00360412
\(392\) 0 0
\(393\) −3.60999e9 −0.00763378
\(394\) −2.67748e10 4.63753e10i −0.0559748 0.0969512i
\(395\) 3.65931e10 6.33812e10i 0.0756333 0.131001i
\(396\) −1.36182e11 + 2.35875e11i −0.278287 + 0.482007i
\(397\) −6.23278e10 1.07955e11i −0.125929 0.218115i 0.796167 0.605077i \(-0.206858\pi\)
−0.922096 + 0.386962i \(0.873524\pi\)
\(398\) 2.14817e11 0.429136
\(399\) 0 0
\(400\) −1.07448e11 −0.209859
\(401\) −1.75598e11 3.04144e11i −0.339133 0.587395i 0.645137 0.764067i \(-0.276800\pi\)
−0.984270 + 0.176672i \(0.943467\pi\)
\(402\) −7.37926e9 + 1.27813e10i −0.0140927 + 0.0244093i
\(403\) −2.62417e11 + 4.54519e11i −0.495586 + 0.858380i
\(404\) 1.54754e11 + 2.68042e11i 0.289018 + 0.500594i
\(405\) 2.15766e11 0.398506
\(406\) 0 0
\(407\) 6.46913e11 1.16861
\(408\) −7.69475e7 1.33277e8i −0.000137475 0.000238114i
\(409\) 1.90978e10 3.30784e10i 0.0337465 0.0584506i −0.848659 0.528941i \(-0.822589\pi\)
0.882405 + 0.470490i \(0.155923\pi\)
\(410\) 9.81529e10 1.70006e11i 0.171544 0.297123i
\(411\) −1.54803e10 2.68126e10i −0.0267602 0.0463501i
\(412\) 1.76784e11 0.302277
\(413\) 0 0
\(414\) −8.36176e10 −0.139893
\(415\) −1.17638e11 2.03754e11i −0.194684 0.337202i
\(416\) −5.93347e10 + 1.02771e11i −0.0971379 + 0.168248i
\(417\) −2.14307e10 + 3.71190e10i −0.0347075 + 0.0601152i
\(418\) −1.11370e11 1.92899e11i −0.178433 0.309056i
\(419\) 2.15268e11 0.341205 0.170603 0.985340i \(-0.445429\pi\)
0.170603 + 0.985340i \(0.445429\pi\)
\(420\) 0 0
\(421\) 1.19933e12 1.86066 0.930332 0.366718i \(-0.119519\pi\)
0.930332 + 0.366718i \(0.119519\pi\)
\(422\) 2.41362e11 + 4.18050e11i 0.370478 + 0.641686i
\(423\) 5.19937e11 9.00557e11i 0.789621 1.36766i
\(424\) 3.32211e10 5.75406e10i 0.0499191 0.0864625i
\(425\) 5.13335e9 + 8.89123e9i 0.00763222 + 0.0132194i
\(426\) 2.68470e10 0.0394959
\(427\) 0 0
\(428\) 4.59518e10 0.0661921
\(429\) 1.83855e10 + 3.18446e10i 0.0262070 + 0.0453918i
\(430\) 1.23292e11 2.13548e11i 0.173911 0.301223i
\(431\) −3.95559e11 + 6.85128e11i −0.552158 + 0.956365i 0.445961 + 0.895052i \(0.352862\pi\)
−0.998119 + 0.0613129i \(0.980471\pi\)
\(432\) −7.73259e9 1.33932e10i −0.0106819 0.0185016i
\(433\) −1.15451e12 −1.57834 −0.789170 0.614174i \(-0.789489\pi\)
−0.789170 + 0.614174i \(0.789489\pi\)
\(434\) 0 0
\(435\) −5.29104e9 −0.00708499
\(436\) 2.05262e11 + 3.55524e11i 0.272031 + 0.471172i
\(437\) 3.41914e10 5.92212e10i 0.0448487 0.0776803i
\(438\) 1.93931e10 3.35898e10i 0.0251776 0.0436088i
\(439\) 1.06364e11 + 1.84228e11i 0.136680 + 0.236737i 0.926238 0.376939i \(-0.123023\pi\)
−0.789558 + 0.613676i \(0.789690\pi\)
\(440\) 1.24212e11 0.157988
\(441\) 0 0
\(442\) 1.13389e10 0.0141310
\(443\) 3.24150e10 + 5.61444e10i 0.0399880 + 0.0692612i 0.885327 0.464969i \(-0.153935\pi\)
−0.845339 + 0.534231i \(0.820601\pi\)
\(444\) −9.17471e9 + 1.58911e10i −0.0112039 + 0.0194057i
\(445\) 1.31472e11 2.27716e11i 0.158933 0.275279i
\(446\) 4.28024e11 + 7.41359e11i 0.512225 + 0.887200i
\(447\) −5.46255e10 −0.0647159
\(448\) 0 0
\(449\) −1.08031e12 −1.25441 −0.627207 0.778853i \(-0.715802\pi\)
−0.627207 + 0.778853i \(0.715802\pi\)
\(450\) 2.57694e11 + 4.46339e11i 0.296243 + 0.513108i
\(451\) 5.93211e11 1.02747e12i 0.675173 1.16943i
\(452\) −1.82765e11 + 3.16558e11i −0.205954 + 0.356722i
\(453\) −8.68296e8 1.50393e9i −0.000968782 0.00167798i
\(454\) 6.44326e11 0.711794
\(455\) 0 0
\(456\) 6.31795e9 0.00684281
\(457\) 3.23363e10 + 5.60081e10i 0.0346790 + 0.0600658i 0.882844 0.469666i \(-0.155626\pi\)
−0.848165 + 0.529732i \(0.822292\pi\)
\(458\) 1.52198e11 2.63614e11i 0.161627 0.279946i
\(459\) −7.38853e8 + 1.27973e9i −0.000776965 + 0.00134574i
\(460\) 1.90669e10 + 3.30248e10i 0.0198550 + 0.0343898i
\(461\) 4.29254e11 0.442649 0.221325 0.975200i \(-0.428962\pi\)
0.221325 + 0.975200i \(0.428962\pi\)
\(462\) 0 0
\(463\) 1.61883e12 1.63715 0.818574 0.574401i \(-0.194765\pi\)
0.818574 + 0.574401i \(0.194765\pi\)
\(464\) −5.16002e10 8.93742e10i −0.0516798 0.0895120i
\(465\) −7.79097e9 + 1.34944e10i −0.00772776 + 0.0133849i
\(466\) −2.94198e11 + 5.09566e11i −0.289004 + 0.500569i
\(467\) −1.63661e11 2.83468e11i −0.159228 0.275790i 0.775363 0.631516i \(-0.217567\pi\)
−0.934590 + 0.355726i \(0.884234\pi\)
\(468\) 5.69214e11 0.548490
\(469\) 0 0
\(470\) −4.74233e11 −0.448283
\(471\) 4.17203e10 + 7.22617e10i 0.0390619 + 0.0676573i
\(472\) −2.87764e11 + 4.98421e11i −0.266868 + 0.462229i
\(473\) 7.45148e11 1.29063e12i 0.684490 1.18557i
\(474\) 6.27311e9 + 1.08653e10i 0.00570795 + 0.00988647i
\(475\) −4.21486e11 −0.379893
\(476\) 0 0
\(477\) −3.18698e11 −0.281869
\(478\) 5.24888e10 + 9.09132e10i 0.0459876 + 0.0796529i
\(479\) −1.42406e11 + 2.46654e11i −0.123600 + 0.214081i −0.921185 0.389126i \(-0.872777\pi\)
0.797585 + 0.603206i \(0.206111\pi\)
\(480\) −1.76161e9 + 3.05119e9i −0.00151469 + 0.00262352i
\(481\) −6.75990e11 1.17085e12i −0.575821 0.997351i
\(482\) 1.43491e12 1.21091
\(483\) 0 0
\(484\) 1.47070e11 0.121820
\(485\) 2.44300e11 + 4.23141e11i 0.200487 + 0.347254i
\(486\) −5.56526e10 + 9.63931e10i −0.0452504 + 0.0783759i
\(487\) 3.57388e11 6.19014e11i 0.287912 0.498678i −0.685399 0.728167i \(-0.740372\pi\)
0.973311 + 0.229490i \(0.0737057\pi\)
\(488\) −4.15669e11 7.19960e11i −0.331787 0.574671i
\(489\) −9.97395e10 −0.0788819
\(490\) 0 0
\(491\) 1.01506e12 0.788176 0.394088 0.919073i \(-0.371061\pi\)
0.394088 + 0.919073i \(0.371061\pi\)
\(492\) 1.68262e10 + 2.91438e10i 0.0129462 + 0.0224235i
\(493\) −4.93043e9 + 8.53975e9i −0.00375901 + 0.00651080i
\(494\) −2.32752e11 + 4.03139e11i −0.175842 + 0.304567i
\(495\) −2.97899e11 5.15976e11i −0.223021 0.386283i
\(496\) −3.03922e11 −0.225473
\(497\) 0 0
\(498\) 4.03329e10 0.0293851
\(499\) −6.67062e11 1.15539e12i −0.481630 0.834208i 0.518148 0.855291i \(-0.326622\pi\)
−0.999778 + 0.0210833i \(0.993288\pi\)
\(500\) 2.57521e11 4.46040e11i 0.184267 0.319160i
\(501\) −4.74058e10 + 8.21093e10i −0.0336172 + 0.0582267i
\(502\) 4.26962e10 + 7.39520e10i 0.0300070 + 0.0519737i
\(503\) −5.68445e11 −0.395943 −0.197971 0.980208i \(-0.563435\pi\)
−0.197971 + 0.980208i \(0.563435\pi\)
\(504\) 0 0
\(505\) −6.77048e11 −0.463243
\(506\) 1.15235e11 + 1.99594e11i 0.0781464 + 0.135353i
\(507\) 6.61021e9 1.14492e10i 0.00444303 0.00769555i
\(508\) 3.01917e11 5.22936e11i 0.201141 0.348387i
\(509\) −1.78586e11 3.09321e11i −0.117928 0.204258i 0.801018 0.598640i \(-0.204292\pi\)
−0.918947 + 0.394382i \(0.870959\pi\)
\(510\) 3.36645e8 0.000220347
\(511\) 0 0
\(512\) −6.87195e10 −0.0441942
\(513\) −3.03326e10 5.25377e10i −0.0193367 0.0334921i
\(514\) −6.68460e11 + 1.15781e12i −0.422417 + 0.731648i
\(515\) −1.93358e11 + 3.34905e11i −0.121124 + 0.209792i
\(516\) 2.11358e10 + 3.66083e10i 0.0131249 + 0.0227330i
\(517\) −2.86615e12 −1.76438
\(518\) 0 0
\(519\) −1.93875e10 −0.0117292
\(520\) −1.29795e11 2.24811e11i −0.0778470 0.134835i
\(521\) −1.08986e12 + 1.88770e12i −0.648040 + 1.12244i 0.335550 + 0.942022i \(0.391078\pi\)
−0.983590 + 0.180416i \(0.942256\pi\)
\(522\) −2.47507e11 + 4.28695e11i −0.145905 + 0.252715i
\(523\) 7.85404e11 + 1.36036e12i 0.459024 + 0.795053i 0.998910 0.0466853i \(-0.0148658\pi\)
−0.539885 + 0.841738i \(0.681532\pi\)
\(524\) 1.54026e11 0.0892492
\(525\) 0 0
\(526\) −1.73816e12 −0.990042
\(527\) 1.45200e10 + 2.51493e10i 0.00820007 + 0.0142029i
\(528\) −1.06467e10 + 1.84407e10i −0.00596160 + 0.0103258i
\(529\) 8.65198e11 1.49857e12i 0.480358 0.832005i
\(530\) 7.26711e10 + 1.25870e11i 0.0400055 + 0.0692916i
\(531\) 2.76059e12 1.50687
\(532\) 0 0
\(533\) −2.47950e12 −1.33074
\(534\) 2.25380e10 + 3.90370e10i 0.0119945 + 0.0207750i
\(535\) −5.02598e10 + 8.70526e10i −0.0265234 + 0.0459399i
\(536\) 3.14848e11 5.45333e11i 0.164763 0.285378i
\(537\) −7.24223e10 1.25439e11i −0.0375827 0.0650952i
\(538\) −2.26241e12 −1.16426
\(539\) 0 0
\(540\) 3.38301e10 0.0171211
\(541\) −1.12272e12 1.94460e12i −0.563486 0.975986i −0.997189 0.0749302i \(-0.976127\pi\)
0.433703 0.901056i \(-0.357207\pi\)
\(542\) −7.26682e11 + 1.25865e12i −0.361699 + 0.626482i
\(543\) −1.16800e10 + 2.02303e10i −0.00576556 + 0.00998625i
\(544\) 3.28309e9 + 5.68648e9i 0.00160727 + 0.00278387i
\(545\) −8.98021e11 −0.436016
\(546\) 0 0
\(547\) −3.86062e11 −0.184380 −0.0921899 0.995741i \(-0.529387\pi\)
−0.0921899 + 0.995741i \(0.529387\pi\)
\(548\) 6.60491e11 + 1.14400e12i 0.312863 + 0.541895i
\(549\) −1.99381e12 + 3.45338e12i −0.936718 + 1.62244i
\(550\) 7.10268e11 1.23022e12i 0.330971 0.573259i
\(551\) −2.02412e11 3.50588e11i −0.0935523 0.162037i
\(552\) −6.53722e9 −0.00299686
\(553\) 0 0
\(554\) 4.24120e11 0.191291
\(555\) −2.00697e10 3.47617e10i −0.00897888 0.0155519i
\(556\) 9.14376e11 1.58375e12i 0.405778 0.702828i
\(557\) 3.97551e11 6.88578e11i 0.175003 0.303113i −0.765160 0.643841i \(-0.777340\pi\)
0.940162 + 0.340727i \(0.110673\pi\)
\(558\) 7.28901e11 + 1.26249e12i 0.318284 + 0.551284i
\(559\) −3.11456e12 −1.34910
\(560\) 0 0
\(561\) 2.03460e9 0.000867253
\(562\) −1.49574e12 2.59070e12i −0.632475 1.09548i
\(563\) 1.06834e12 1.85041e12i 0.448146 0.776212i −0.550119 0.835086i \(-0.685418\pi\)
0.998265 + 0.0588741i \(0.0187511\pi\)
\(564\) 4.06486e10 7.04054e10i 0.0169157 0.0292988i
\(565\) −3.99798e11 6.92471e11i −0.165053 0.285880i
\(566\) 8.53460e10 0.0349550
\(567\) 0 0
\(568\) −1.14547e12 −0.461760
\(569\) −1.08731e12 1.88327e12i −0.434857 0.753194i 0.562427 0.826847i \(-0.309868\pi\)
−0.997284 + 0.0736527i \(0.976534\pi\)
\(570\) −6.91026e9 + 1.19689e10i −0.00274194 + 0.00474917i
\(571\) −4.97538e11 + 8.61760e11i −0.195868 + 0.339253i −0.947185 0.320689i \(-0.896086\pi\)
0.751317 + 0.659942i \(0.229419\pi\)
\(572\) −7.84447e11 1.35870e12i −0.306395 0.530691i
\(573\) 1.55393e11 0.0602192
\(574\) 0 0
\(575\) 4.36114e11 0.166377
\(576\) 1.64811e11 + 2.85461e11i 0.0623857 + 0.108055i
\(577\) −2.15294e12 + 3.72900e12i −0.808614 + 1.40056i 0.105211 + 0.994450i \(0.466448\pi\)
−0.913824 + 0.406110i \(0.866885\pi\)
\(578\) −9.48389e11 + 1.64266e12i −0.353436 + 0.612170i
\(579\) 4.78102e10 + 8.28097e10i 0.0176794 + 0.0306216i
\(580\) 2.25751e11 0.0828331
\(581\) 0 0
\(582\) −8.37602e10 −0.0302611
\(583\) 4.39206e11 + 7.60727e11i 0.157456 + 0.272722i
\(584\) −8.27439e11 + 1.43317e12i −0.294359 + 0.509846i
\(585\) −6.22577e11 + 1.07834e12i −0.219782 + 0.380673i
\(586\) 6.12347e11 + 1.06062e12i 0.214515 + 0.371551i
\(587\) 5.05762e12 1.75822 0.879112 0.476615i \(-0.158136\pi\)
0.879112 + 0.476615i \(0.158136\pi\)
\(588\) 0 0
\(589\) −1.19220e12 −0.408158
\(590\) −6.29483e11 1.09030e12i −0.213870 0.370434i
\(591\) −1.00405e10 + 1.73907e10i −0.00338543 + 0.00586373i
\(592\) 3.91454e11 6.78019e11i 0.130989 0.226879i
\(593\) 1.40150e12 + 2.42747e12i 0.465422 + 0.806135i 0.999220 0.0394771i \(-0.0125692\pi\)
−0.533798 + 0.845612i \(0.679236\pi\)
\(594\) 2.04461e11 0.0673862
\(595\) 0 0
\(596\) 2.33069e12 0.756616
\(597\) −4.02782e10 6.97640e10i −0.0129773 0.0224774i
\(598\) 2.40830e11 4.17130e11i 0.0770114 0.133388i
\(599\) −1.60454e12 + 2.77914e12i −0.509247 + 0.882042i 0.490696 + 0.871331i \(0.336743\pi\)
−0.999943 + 0.0107108i \(0.996591\pi\)
\(600\) 2.01465e10 + 3.48947e10i 0.00634627 + 0.0109921i
\(601\) 7.49502e11 0.234335 0.117168 0.993112i \(-0.462619\pi\)
0.117168 + 0.993112i \(0.462619\pi\)
\(602\) 0 0
\(603\) −3.02042e12 −0.930336
\(604\) 3.70473e10 + 6.41678e10i 0.0113264 + 0.0196178i
\(605\) −1.60858e11 + 2.78614e11i −0.0488138 + 0.0845479i
\(606\) 5.80327e10 1.00516e11i 0.0174802 0.0302766i
\(607\) 8.70485e11 + 1.50772e12i 0.260263 + 0.450789i 0.966312 0.257375i \(-0.0828574\pi\)
−0.706049 + 0.708163i \(0.749524\pi\)
\(608\) −2.69566e11 −0.0800016
\(609\) 0 0
\(610\) 1.81855e12 0.531792
\(611\) 2.99497e12 + 5.18745e12i 0.869376 + 1.50580i
\(612\) 1.57478e10 2.72760e10i 0.00453772 0.00785956i
\(613\) 2.01989e12 3.49854e12i 0.577770 1.00073i −0.417965 0.908463i \(-0.637257\pi\)
0.995735 0.0922632i \(-0.0294101\pi\)
\(614\) −6.01555e11 1.04192e12i −0.170812 0.295855i
\(615\) −7.36147e10 −0.0207504
\(616\) 0 0
\(617\) −2.93367e12 −0.814945 −0.407472 0.913218i \(-0.633590\pi\)
−0.407472 + 0.913218i \(0.633590\pi\)
\(618\) −3.31470e10 5.74123e10i −0.00914105 0.0158328i
\(619\) 2.88846e12 5.00295e12i 0.790784 1.36968i −0.134698 0.990887i \(-0.543006\pi\)
0.925482 0.378792i \(-0.123660\pi\)
\(620\) 3.32415e11 5.75759e11i 0.0903478 0.156487i
\(621\) 3.13853e10 + 5.43610e10i 0.00846866 + 0.0146681i
\(622\) −3.44214e12 −0.922088
\(623\) 0 0
\(624\) 4.45010e10 0.0117500
\(625\) −1.03777e12 1.79747e12i −0.272045 0.471197i
\(626\) 7.67260e11 1.32893e12i 0.199691 0.345874i
\(627\) −4.17639e10 + 7.23371e10i −0.0107919 + 0.0186921i
\(628\) −1.78007e12 3.08317e12i −0.456686 0.791004i
\(629\) −7.48073e10 −0.0190553
\(630\) 0 0
\(631\) 3.99985e12 1.00441 0.502206 0.864748i \(-0.332522\pi\)
0.502206 + 0.864748i \(0.332522\pi\)
\(632\) −2.67653e11 4.63588e11i −0.0667336 0.115586i
\(633\) 9.05106e10 1.56769e11i 0.0224069 0.0388100i
\(634\) 1.36469e12 2.36372e12i 0.335454 0.581023i
\(635\) 6.60444e11 + 1.14392e12i 0.161196 + 0.279200i
\(636\) −2.49158e10 −0.00603834
\(637\) 0 0
\(638\) 1.36438e12 0.326019
\(639\) 2.74720e12 + 4.75829e12i 0.651833 + 1.12901i
\(640\) 7.51619e10 1.30184e11i 0.0177088 0.0306725i
\(641\) −2.34164e12 + 4.05584e12i −0.547846 + 0.948898i 0.450575 + 0.892738i \(0.351219\pi\)
−0.998422 + 0.0561595i \(0.982114\pi\)
\(642\) −8.61597e9 1.49233e10i −0.00200169 0.00346703i
\(643\) −1.54877e12 −0.357304 −0.178652 0.983912i \(-0.557174\pi\)
−0.178652 + 0.983912i \(0.557174\pi\)
\(644\) 0 0
\(645\) −9.24692e10 −0.0210367
\(646\) 1.28786e10 + 2.23064e10i 0.00290952 + 0.00503944i
\(647\) 4.07246e12 7.05372e12i 0.913667 1.58252i 0.104826 0.994491i \(-0.466571\pi\)
0.808841 0.588028i \(-0.200095\pi\)
\(648\) 7.89086e11 1.36674e12i 0.175807 0.304507i
\(649\) −3.80444e12 6.58948e12i −0.841762 1.45797i
\(650\) −2.96877e12 −0.652329
\(651\) 0 0
\(652\) 4.25555e12 0.922235
\(653\) 1.44463e12 + 2.50216e12i 0.310918 + 0.538526i 0.978561 0.205955i \(-0.0660302\pi\)
−0.667643 + 0.744481i \(0.732697\pi\)
\(654\) 7.69732e10 1.33322e11i 0.0164528 0.0284971i
\(655\) −1.68466e11 + 2.91792e11i −0.0357624 + 0.0619424i
\(656\) −7.17918e11 1.24347e12i −0.151359 0.262161i
\(657\) 7.93784e12 1.66210
\(658\) 0 0
\(659\) 5.20255e12 1.07456 0.537281 0.843403i \(-0.319451\pi\)
0.537281 + 0.843403i \(0.319451\pi\)
\(660\) −2.32897e10 4.03389e10i −0.00477767 0.00827517i
\(661\) −1.44486e12 + 2.50258e12i −0.294388 + 0.509896i −0.974842 0.222895i \(-0.928449\pi\)
0.680454 + 0.732791i \(0.261783\pi\)
\(662\) −9.91933e11 + 1.71808e12i −0.200734 + 0.347682i
\(663\) −2.12605e9 3.68243e9i −0.000427329 0.000740156i
\(664\) −1.72087e12 −0.343551
\(665\) 0 0
\(666\) −3.75532e12 −0.739628
\(667\) 2.09437e11 + 3.62755e11i 0.0409720 + 0.0709656i
\(668\) 2.02265e12 3.50333e12i 0.393031 0.680749i
\(669\) 1.60509e11 2.78009e11i 0.0309800 0.0536589i
\(670\) 6.88731e11 + 1.19292e12i 0.132042 + 0.228704i
\(671\) 1.09909e13 2.09306
\(672\) 0 0
\(673\) 9.46362e12 1.77824 0.889119 0.457677i \(-0.151318\pi\)
0.889119 + 0.457677i \(0.151318\pi\)
\(674\) −5.83468e11 1.01060e12i −0.108905 0.188629i
\(675\) 1.93448e11 3.35061e11i 0.0358671 0.0621236i
\(676\) −2.82035e11 + 4.88500e11i −0.0519450 + 0.0899714i
\(677\) 3.26134e12 + 5.64881e12i 0.596688 + 1.03349i 0.993306 + 0.115510i \(0.0368502\pi\)
−0.396619 + 0.917983i \(0.629817\pi\)
\(678\) 1.37074e11 0.0249127
\(679\) 0 0
\(680\) −1.43635e10 −0.00257615
\(681\) −1.20811e11 2.09251e11i −0.0215251 0.0372826i
\(682\) 2.00903e12 3.47975e12i 0.355596 0.615911i
\(683\) −2.68620e12 + 4.65264e12i −0.472330 + 0.818099i −0.999499 0.0316613i \(-0.989920\pi\)
0.527169 + 0.849761i \(0.323254\pi\)
\(684\) 6.46504e11 + 1.11978e12i 0.112932 + 0.195605i
\(685\) −2.88965e12 −0.501461
\(686\) 0 0
\(687\) −1.14148e11 −0.0195508
\(688\) −9.01795e11 1.56195e12i −0.153447 0.265779i
\(689\) 9.17894e11 1.58984e12i 0.155169 0.268761i
\(690\) 7.15008e9 1.23843e10i 0.00120085 0.00207994i
\(691\) −1.00781e12 1.74559e12i −0.168163 0.291266i 0.769611 0.638513i \(-0.220450\pi\)
−0.937774 + 0.347246i \(0.887117\pi\)
\(692\) 8.27200e11 0.137130
\(693\) 0 0
\(694\) 2.49153e12 0.407707
\(695\) 2.00020e12 + 3.46444e12i 0.325193 + 0.563251i
\(696\) −1.93501e10 + 3.35153e10i −0.00312566 + 0.00541380i
\(697\) −6.85975e10 + 1.18814e11i −0.0110093 + 0.0190687i
\(698\) 8.69828e11 + 1.50659e12i 0.138702 + 0.240240i
\(699\) 2.20649e11 0.0349586
\(700\) 0 0
\(701\) −1.06523e13 −1.66614 −0.833068 0.553171i \(-0.813418\pi\)
−0.833068 + 0.553171i \(0.813418\pi\)
\(702\) −2.13651e11 3.70054e11i −0.0332038 0.0575106i
\(703\) 1.53556e12 2.65966e12i 0.237119 0.410703i
\(704\) 4.54260e11 7.86801e11i 0.0696991 0.120722i
\(705\) 8.89188e10 + 1.54012e11i 0.0135563 + 0.0234803i
\(706\) −5.20936e12 −0.789157
\(707\) 0 0
\(708\) 2.15823e11 0.0322810
\(709\) −1.73093e12 2.99807e12i −0.257260 0.445588i 0.708247 0.705965i \(-0.249486\pi\)
−0.965507 + 0.260377i \(0.916153\pi\)
\(710\) 1.25286e12 2.17001e12i 0.185029 0.320479i
\(711\) −1.28383e12 + 2.22366e12i −0.188406 + 0.326329i
\(712\) −9.61623e11 1.66558e12i −0.140231 0.242888i
\(713\) 1.23357e12 0.178756
\(714\) 0 0
\(715\) 3.43195e12 0.491094
\(716\) 3.09002e12 + 5.35207e12i 0.439393 + 0.761050i
\(717\) 1.96833e10 3.40925e10i 0.00278139 0.00481750i
\(718\) −1.82040e12 + 3.15302e12i −0.255627 + 0.442758i
\(719\) 4.81013e12 + 8.33138e12i 0.671238 + 1.16262i 0.977553 + 0.210688i \(0.0675704\pi\)
−0.306316 + 0.951930i \(0.599096\pi\)
\(720\) −7.21048e11 −0.0999926
\(721\) 0 0
\(722\) 4.10558e12 0.562285
\(723\) −2.69045e11 4.66000e11i −0.0366187 0.0634255i
\(724\) 4.98345e11 8.63158e11i 0.0674072 0.116753i
\(725\) 1.29089e12 2.23589e12i 0.173528 0.300559i
\(726\) −2.75756e10 4.77623e10i −0.00368392 0.00638073i
\(727\) −3.13479e12 −0.416202 −0.208101 0.978107i \(-0.566728\pi\)
−0.208101 + 0.978107i \(0.566728\pi\)
\(728\) 0 0
\(729\) −7.54204e12 −0.989043
\(730\) −1.81002e12 3.13505e12i −0.235902 0.408594i
\(731\) −8.61670e10 + 1.49246e11i −0.0111612 + 0.0193318i
\(732\) −1.55876e11 + 2.69985e11i −0.0200669 + 0.0347568i
\(733\) −3.23887e12 5.60989e12i −0.414406 0.717772i 0.580960 0.813932i \(-0.302677\pi\)
−0.995366 + 0.0961599i \(0.969344\pi\)
\(734\) 6.75189e12 0.858604
\(735\) 0 0
\(736\) 2.78921e11 0.0350374
\(737\) 4.16252e12 + 7.20969e12i 0.519700 + 0.900146i
\(738\) −3.44359e12 + 5.96447e12i −0.427324 + 0.740148i
\(739\) 5.62550e11 9.74365e11i 0.0693843 0.120177i −0.829246 0.558884i \(-0.811230\pi\)
0.898630 + 0.438706i \(0.144563\pi\)
\(740\) 8.56306e11 + 1.48317e12i 0.104975 + 0.181822i
\(741\) 1.74564e11 0.0212703
\(742\) 0 0
\(743\) 1.65266e12 0.198945 0.0994725 0.995040i \(-0.468284\pi\)
0.0994725 + 0.995040i \(0.468284\pi\)
\(744\) 5.69854e10 + 9.87016e10i 0.00681845 + 0.0118099i
\(745\) −2.54919e12 + 4.41532e12i −0.303179 + 0.525121i
\(746\) 3.06626e12 5.31093e12i 0.362481 0.627835i
\(747\) 4.12719e12 + 7.14850e12i 0.484966 + 0.839986i
\(748\) −8.68096e10 −0.0101394
\(749\) 0 0
\(750\) −1.93141e11 −0.0222894
\(751\) −3.01649e12 5.22472e12i −0.346037 0.599354i 0.639505 0.768787i \(-0.279140\pi\)
−0.985542 + 0.169434i \(0.945806\pi\)
\(752\) −1.73434e12 + 3.00396e12i −0.197767 + 0.342542i
\(753\) 1.60111e10 2.77320e10i 0.00181486 0.00314343i
\(754\) −1.42571e12 2.46940e12i −0.160642 0.278240i
\(755\) −1.62082e11 −0.0181540
\(756\) 0 0
\(757\) −8.02798e12 −0.888535 −0.444268 0.895894i \(-0.646536\pi\)
−0.444268 + 0.895894i \(0.646536\pi\)
\(758\) −9.71692e11 1.68302e12i −0.106910 0.185173i
\(759\) 4.32133e10 7.48476e10i 0.00472639 0.00818634i
\(760\) 2.94838e11 5.10674e11i 0.0320569 0.0555242i
\(761\) 3.25961e12 + 5.64582e12i 0.352318 + 0.610233i 0.986655 0.162824i \(-0.0520601\pi\)
−0.634337 + 0.773057i \(0.718727\pi\)
\(762\) −2.26438e11 −0.0243305
\(763\) 0 0
\(764\) −6.63009e12 −0.704043
\(765\) 3.44483e10 + 5.96661e10i 0.00363656 + 0.00629871i
\(766\) −3.18177e12 + 5.51098e12i −0.333917 + 0.578362i
\(767\) −7.95088e12 + 1.37713e13i −0.829537 + 1.43680i
\(768\) 1.28849e10 + 2.23173e10i