Properties

Label 99.8.j.a.8.13
Level $99$
Weight $8$
Character 99.8
Analytic conductor $30.926$
Analytic rank $0$
Dimension $112$
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] = [99,8,Mod(8,99)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(99, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 3]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("99.8");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 99.j (of order \(10\), degree \(4\), 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: \(30.9261175229\)
Analytic rank: \(0\)
Dimension: \(112\)
Relative dimension: \(28\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 8.13
Character \(\chi\) \(=\) 99.8
Dual form 99.8.j.a.62.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.14320 + 2.28367i) q^{2} +(-34.8896 + 107.379i) q^{4} +(310.082 - 426.791i) q^{5} +(354.776 + 115.274i) q^{7} +(-289.230 - 890.158i) q^{8} +O(q^{10})\) \(q+(-3.14320 + 2.28367i) q^{2} +(-34.8896 + 107.379i) q^{4} +(310.082 - 426.791i) q^{5} +(354.776 + 115.274i) q^{7} +(-289.230 - 890.158i) q^{8} +2049.61i q^{10} +(2328.18 - 3750.57i) q^{11} +(2521.31 + 3470.28i) q^{13} +(-1378.38 + 447.862i) q^{14} +(-8749.86 - 6357.15i) q^{16} +(-24357.4 - 17696.7i) q^{17} +(-22078.8 + 7173.85i) q^{19} +(35009.8 + 48186.8i) q^{20} +(1247.12 + 17105.6i) q^{22} +86557.4i q^{23} +(-61857.7 - 190378. i) q^{25} +(-15850.0 - 5149.97i) q^{26} +(-24756.0 + 34073.7i) q^{28} +(27351.6 - 84179.6i) q^{29} +(79761.4 - 57950.0i) q^{31} +161824. q^{32} +116974. q^{34} +(159207. - 115671. i) q^{35} +(10690.5 - 32901.9i) q^{37} +(53015.6 - 72969.7i) q^{38} +(-469596. - 152581. i) q^{40} +(-215040. - 661825. i) q^{41} -181019. i q^{43} +(321503. + 380854. i) q^{44} +(-197669. - 272068. i) q^{46} +(343217. - 111518. i) q^{47} +(-553683. - 402274. i) q^{49} +(629193. + 457136. i) q^{50} +(-460604. + 149659. i) q^{52} +(-453428. - 624090. i) q^{53} +(-878782. - 2.15663e6i) q^{55} -349147. i q^{56} +(106267. + 327056. i) q^{58} +(-19782.6 - 6427.77i) q^{59} +(1.36304e6 - 1.87607e6i) q^{61} +(-118367. + 364297. i) q^{62} +(611336. - 444162. i) q^{64} +2.26290e6 q^{65} -1.71436e6 q^{67} +(2.75007e6 - 1.99805e6i) q^{68} +(-236266. + 727153. i) q^{70} +(1.42865e6 - 1.96636e6i) q^{71} +(6.09802e6 + 1.98137e6i) q^{73} +(41534.7 + 127831. i) q^{74} -2.62110e6i q^{76} +(1.25832e6 - 1.06223e6i) q^{77} +(-1.35884e6 - 1.87028e6i) q^{79} +(-5.42634e6 + 1.76312e6i) q^{80} +(2.18730e6 + 1.58917e6i) q^{82} +(-2.33431e6 - 1.69598e6i) q^{83} +(-1.51056e7 + 4.90809e6i) q^{85} +(413389. + 568981. i) q^{86} +(-4.01198e6 - 987671. i) q^{88} +1.13938e7i q^{89} +(494467. + 1.52181e6i) q^{91} +(-9.29446e6 - 3.01995e6i) q^{92} +(-824131. + 1.13432e6i) q^{94} +(-3.78451e6 + 1.16475e7i) q^{95} +(2.89080e6 - 2.10029e6i) q^{97} +2.65900e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 112 q - 1792 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 112 q - 1792 q^{4} - 134096 q^{16} + 401484 q^{22} - 68552 q^{25} + 1493020 q^{28} - 398144 q^{31} - 729944 q^{34} + 685476 q^{37} - 399360 q^{40} - 1410880 q^{46} + 2923872 q^{49} + 6472520 q^{52} + 1445488 q^{55} + 13215936 q^{58} - 7843440 q^{61} - 12806712 q^{64} + 1864032 q^{67} - 1233728 q^{70} + 53841940 q^{73} - 53845440 q^{79} - 36360204 q^{82} + 41703500 q^{85} + 21474024 q^{88} + 27611736 q^{91} - 94707560 q^{94} - 27695460 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{3}{10}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.14320 + 2.28367i −0.277823 + 0.201850i −0.717967 0.696077i \(-0.754927\pi\)
0.440145 + 0.897927i \(0.354927\pi\)
\(3\) 0 0
\(4\) −34.8896 + 107.379i −0.272575 + 0.838900i
\(5\) 310.082 426.791i 1.10938 1.52693i 0.287057 0.957914i \(-0.407323\pi\)
0.822324 0.569019i \(-0.192677\pi\)
\(6\) 0 0
\(7\) 354.776 + 115.274i 0.390940 + 0.127024i 0.497890 0.867240i \(-0.334108\pi\)
−0.106950 + 0.994264i \(0.534108\pi\)
\(8\) −289.230 890.158i −0.199723 0.614684i
\(9\) 0 0
\(10\) 2049.61i 0.648145i
\(11\) 2328.18 3750.57i 0.527402 0.849616i
\(12\) 0 0
\(13\) 2521.31 + 3470.28i 0.318291 + 0.438090i 0.937944 0.346786i \(-0.112727\pi\)
−0.619653 + 0.784876i \(0.712727\pi\)
\(14\) −1378.38 + 447.862i −0.134252 + 0.0436211i
\(15\) 0 0
\(16\) −8749.86 6357.15i −0.534049 0.388009i
\(17\) −24357.4 17696.7i −1.20243 0.873616i −0.207908 0.978148i \(-0.566665\pi\)
−0.994521 + 0.104533i \(0.966665\pi\)
\(18\) 0 0
\(19\) −22078.8 + 7173.85i −0.738480 + 0.239947i −0.654017 0.756480i \(-0.726917\pi\)
−0.0844630 + 0.996427i \(0.526917\pi\)
\(20\) 35009.8 + 48186.8i 0.978553 + 1.34686i
\(21\) 0 0
\(22\) 1247.12 + 17105.6i 0.0249706 + 0.342499i
\(23\) 86557.4i 1.48340i 0.670734 + 0.741698i \(0.265979\pi\)
−0.670734 + 0.741698i \(0.734021\pi\)
\(24\) 0 0
\(25\) −61857.7 190378.i −0.791779 2.43684i
\(26\) −15850.0 5149.97i −0.176857 0.0574643i
\(27\) 0 0
\(28\) −24756.0 + 34073.7i −0.213121 + 0.293336i
\(29\) 27351.6 84179.6i 0.208252 0.640935i −0.791312 0.611413i \(-0.790602\pi\)
0.999564 0.0295219i \(-0.00939847\pi\)
\(30\) 0 0
\(31\) 79761.4 57950.0i 0.480869 0.349372i −0.320793 0.947149i \(-0.603949\pi\)
0.801662 + 0.597778i \(0.203949\pi\)
\(32\) 161824. 0.873008
\(33\) 0 0
\(34\) 116974. 0.510401
\(35\) 159207. 115671.i 0.627659 0.456021i
\(36\) 0 0
\(37\) 10690.5 32901.9i 0.0346969 0.106786i −0.932208 0.361923i \(-0.882120\pi\)
0.966905 + 0.255137i \(0.0821204\pi\)
\(38\) 53015.6 72969.7i 0.156733 0.215725i
\(39\) 0 0
\(40\) −469596. 152581.i −1.16015 0.376956i
\(41\) −215040. 661825.i −0.487276 1.49968i −0.828657 0.559757i \(-0.810894\pi\)
0.341380 0.939925i \(-0.389106\pi\)
\(42\) 0 0
\(43\) 181019.i 0.347205i −0.984816 0.173602i \(-0.944459\pi\)
0.984816 0.173602i \(-0.0555407\pi\)
\(44\) 321503. + 380854.i 0.568986 + 0.674022i
\(45\) 0 0
\(46\) −197669. 272068.i −0.299423 0.412121i
\(47\) 343217. 111518.i 0.482199 0.156676i −0.0578230 0.998327i \(-0.518416\pi\)
0.540022 + 0.841651i \(0.318416\pi\)
\(48\) 0 0
\(49\) −553683. 402274.i −0.672318 0.488467i
\(50\) 629193. + 457136.i 0.711851 + 0.517190i
\(51\) 0 0
\(52\) −460604. + 149659.i −0.454272 + 0.147602i
\(53\) −453428. 624090.i −0.418353 0.575813i 0.546878 0.837212i \(-0.315816\pi\)
−0.965231 + 0.261399i \(0.915816\pi\)
\(54\) 0 0
\(55\) −878782. 2.15663e6i −0.712216 1.74786i
\(56\) 349147.i 0.265675i
\(57\) 0 0
\(58\) 106267. + 327056.i 0.0715154 + 0.220102i
\(59\) −19782.6 6427.77i −0.0125401 0.00407453i 0.302740 0.953073i \(-0.402099\pi\)
−0.315280 + 0.948999i \(0.602099\pi\)
\(60\) 0 0
\(61\) 1.36304e6 1.87607e6i 0.768875 1.05827i −0.227549 0.973767i \(-0.573071\pi\)
0.996424 0.0844989i \(-0.0269289\pi\)
\(62\) −118367. + 364297.i −0.0630756 + 0.194127i
\(63\) 0 0
\(64\) 611336. 444162.i 0.291508 0.211793i
\(65\) 2.26290e6 1.02204
\(66\) 0 0
\(67\) −1.71436e6 −0.696371 −0.348186 0.937426i \(-0.613202\pi\)
−0.348186 + 0.937426i \(0.613202\pi\)
\(68\) 2.75007e6 1.99805e6i 1.06063 0.770591i
\(69\) 0 0
\(70\) −236266. + 727153.i −0.0823301 + 0.253386i
\(71\) 1.42865e6 1.96636e6i 0.473718 0.652017i −0.503564 0.863958i \(-0.667978\pi\)
0.977283 + 0.211940i \(0.0679783\pi\)
\(72\) 0 0
\(73\) 6.09802e6 + 1.98137e6i 1.83467 + 0.596122i 0.998892 + 0.0470593i \(0.0149850\pi\)
0.835781 + 0.549062i \(0.185015\pi\)
\(74\) 41534.7 + 127831.i 0.0119152 + 0.0366711i
\(75\) 0 0
\(76\) 2.62110e6i 0.684914i
\(77\) 1.25832e6 1.06223e6i 0.314105 0.265156i
\(78\) 0 0
\(79\) −1.35884e6 1.87028e6i −0.310079 0.426787i 0.625327 0.780363i \(-0.284966\pi\)
−0.935406 + 0.353576i \(0.884966\pi\)
\(80\) −5.42634e6 + 1.76312e6i −1.18493 + 0.385006i
\(81\) 0 0
\(82\) 2.18730e6 + 1.58917e6i 0.438087 + 0.318289i
\(83\) −2.33431e6 1.69598e6i −0.448111 0.325572i 0.340739 0.940158i \(-0.389323\pi\)
−0.788849 + 0.614586i \(0.789323\pi\)
\(84\) 0 0
\(85\) −1.51056e7 + 4.90809e6i −2.66790 + 0.866855i
\(86\) 413389. + 568981.i 0.0700832 + 0.0964613i
\(87\) 0 0
\(88\) −4.01198e6 987671.i −0.627580 0.154498i
\(89\) 1.13938e7i 1.71319i 0.515991 + 0.856594i \(0.327424\pi\)
−0.515991 + 0.856594i \(0.672576\pi\)
\(90\) 0 0
\(91\) 494467. + 1.52181e6i 0.0687848 + 0.211698i
\(92\) −9.29446e6 3.01995e6i −1.24442 0.404336i
\(93\) 0 0
\(94\) −824131. + 1.13432e6i −0.102341 + 0.140860i
\(95\) −3.78451e6 + 1.16475e7i −0.452873 + 1.39380i
\(96\) 0 0
\(97\) 2.89080e6 2.10029e6i 0.321600 0.233656i −0.415258 0.909704i \(-0.636309\pi\)
0.736858 + 0.676048i \(0.236309\pi\)
\(98\) 2.65900e6 0.285382
\(99\) 0 0
\(100\) 2.26009e7 2.26009
\(101\) −7.25016e6 + 5.26755e6i −0.700201 + 0.508726i −0.879998 0.474978i \(-0.842456\pi\)
0.179796 + 0.983704i \(0.442456\pi\)
\(102\) 0 0
\(103\) −6.72939e6 + 2.07109e7i −0.606800 + 1.86754i −0.122891 + 0.992420i \(0.539216\pi\)
−0.483909 + 0.875118i \(0.660784\pi\)
\(104\) 2.35986e6 3.24807e6i 0.205717 0.283145i
\(105\) 0 0
\(106\) 2.85043e6 + 926161.i 0.232456 + 0.0755294i
\(107\) −5.34161e6 1.64398e7i −0.421531 1.29734i −0.906278 0.422683i \(-0.861088\pi\)
0.484747 0.874654i \(-0.338912\pi\)
\(108\) 0 0
\(109\) 1.48134e6i 0.109563i −0.998498 0.0547813i \(-0.982554\pi\)
0.998498 0.0547813i \(-0.0174462\pi\)
\(110\) 7.68721e6 + 4.77187e6i 0.550674 + 0.341833i
\(111\) 0 0
\(112\) −2.37143e6 3.26399e6i −0.159495 0.219526i
\(113\) 1.40373e7 4.56100e6i 0.915186 0.297362i 0.186695 0.982418i \(-0.440222\pi\)
0.728490 + 0.685056i \(0.240222\pi\)
\(114\) 0 0
\(115\) 3.69419e7 + 2.68399e7i 2.26504 + 1.64565i
\(116\) 8.08484e6 + 5.87398e6i 0.480915 + 0.349406i
\(117\) 0 0
\(118\) 76859.7 24973.2i 0.00430637 0.00139923i
\(119\) −6.60145e6 9.08611e6i −0.359108 0.494269i
\(120\) 0 0
\(121\) −8.64634e6 1.74640e7i −0.443694 0.896178i
\(122\) 9.00962e6i 0.449207i
\(123\) 0 0
\(124\) 3.43978e6 + 1.05866e7i 0.162015 + 0.498631i
\(125\) −6.12356e7 1.98967e7i −2.80426 0.911161i
\(126\) 0 0
\(127\) 7.61102e6 1.04757e7i 0.329708 0.453804i −0.611692 0.791096i \(-0.709511\pi\)
0.941400 + 0.337292i \(0.109511\pi\)
\(128\) −7.30805e6 + 2.24919e7i −0.308011 + 0.947962i
\(129\) 0 0
\(130\) −7.11274e6 + 5.16771e6i −0.283946 + 0.206299i
\(131\) 3.09516e7 1.20291 0.601455 0.798907i \(-0.294588\pi\)
0.601455 + 0.798907i \(0.294588\pi\)
\(132\) 0 0
\(133\) −8.65999e6 −0.319181
\(134\) 5.38859e6 3.91504e6i 0.193468 0.140563i
\(135\) 0 0
\(136\) −8.70796e6 + 2.68003e7i −0.296845 + 0.913596i
\(137\) −6.29149e6 + 8.65949e6i −0.209041 + 0.287720i −0.900644 0.434558i \(-0.856905\pi\)
0.691603 + 0.722278i \(0.256905\pi\)
\(138\) 0 0
\(139\) 2.15723e7 + 7.00928e6i 0.681311 + 0.221371i 0.629169 0.777268i \(-0.283395\pi\)
0.0521419 + 0.998640i \(0.483395\pi\)
\(140\) 6.86595e6 + 2.11312e7i 0.211472 + 0.650843i
\(141\) 0 0
\(142\) 9.44323e6i 0.276765i
\(143\) 1.88856e7 1.37690e6i 0.540075 0.0393754i
\(144\) 0 0
\(145\) −2.74458e7 3.77759e7i −0.747633 1.02903i
\(146\) −2.36921e7 + 7.69803e6i −0.630041 + 0.204713i
\(147\) 0 0
\(148\) 3.15999e6 + 2.29587e6i 0.0801253 + 0.0582144i
\(149\) −4.08790e7 2.97004e7i −1.01239 0.735546i −0.0476824 0.998863i \(-0.515184\pi\)
−0.964709 + 0.263317i \(0.915184\pi\)
\(150\) 0 0
\(151\) −6.95470e7 + 2.25972e7i −1.64384 + 0.534115i −0.977391 0.211438i \(-0.932185\pi\)
−0.666446 + 0.745553i \(0.732185\pi\)
\(152\) 1.27717e7 + 1.75788e7i 0.294983 + 0.406009i
\(153\) 0 0
\(154\) −1.52937e6 + 6.21241e6i −0.0337436 + 0.137068i
\(155\) 5.20106e7i 1.12184i
\(156\) 0 0
\(157\) −6.14636e6 1.89165e7i −0.126756 0.390115i 0.867461 0.497506i \(-0.165751\pi\)
−0.994217 + 0.107390i \(0.965751\pi\)
\(158\) 8.54219e6 + 2.77553e6i 0.172294 + 0.0559816i
\(159\) 0 0
\(160\) 5.01787e7 6.90650e7i 0.968499 1.33302i
\(161\) −9.97778e6 + 3.07085e7i −0.188427 + 0.579919i
\(162\) 0 0
\(163\) −7.10890e6 + 5.16492e6i −0.128572 + 0.0934129i −0.650213 0.759752i \(-0.725320\pi\)
0.521641 + 0.853165i \(0.325320\pi\)
\(164\) 7.85688e7 1.39090
\(165\) 0 0
\(166\) 1.12103e7 0.190212
\(167\) 6.74149e7 4.89798e7i 1.12008 0.813784i 0.135857 0.990728i \(-0.456621\pi\)
0.984221 + 0.176944i \(0.0566211\pi\)
\(168\) 0 0
\(169\) 1.37045e7 4.21781e7i 0.218403 0.672176i
\(170\) 3.62714e7 4.99232e7i 0.566230 0.779348i
\(171\) 0 0
\(172\) 1.94377e7 + 6.31569e6i 0.291270 + 0.0946393i
\(173\) 6.52355e6 + 2.00774e7i 0.0957905 + 0.294813i 0.987459 0.157876i \(-0.0504647\pi\)
−0.891668 + 0.452689i \(0.850465\pi\)
\(174\) 0 0
\(175\) 7.46722e7i 1.05324i
\(176\) −4.42141e7 + 1.80164e7i −0.611317 + 0.249099i
\(177\) 0 0
\(178\) −2.60198e7 3.58132e7i −0.345807 0.475962i
\(179\) 5.64000e7 1.83255e7i 0.735010 0.238819i 0.0824915 0.996592i \(-0.473712\pi\)
0.652519 + 0.757772i \(0.273712\pi\)
\(180\) 0 0
\(181\) −2.52202e7 1.83236e7i −0.316136 0.229686i 0.418389 0.908268i \(-0.362595\pi\)
−0.734525 + 0.678582i \(0.762595\pi\)
\(182\) −5.02953e6 3.65417e6i −0.0618411 0.0449302i
\(183\) 0 0
\(184\) 7.70498e7 2.50350e7i 0.911820 0.296268i
\(185\) −1.07273e7 1.47649e7i −0.124563 0.171446i
\(186\) 0 0
\(187\) −1.23081e8 + 5.01530e7i −1.37640 + 0.560856i
\(188\) 4.07452e7i 0.447223i
\(189\) 0 0
\(190\) −1.47036e7 4.52531e7i −0.155520 0.478642i
\(191\) 1.11707e8 + 3.62958e7i 1.16001 + 0.376912i 0.824907 0.565268i \(-0.191227\pi\)
0.335108 + 0.942180i \(0.391227\pi\)
\(192\) 0 0
\(193\) −2.80266e7 + 3.85753e7i −0.280620 + 0.386241i −0.925939 0.377672i \(-0.876725\pi\)
0.645319 + 0.763913i \(0.276725\pi\)
\(194\) −4.29000e6 + 1.32033e7i −0.0421843 + 0.129830i
\(195\) 0 0
\(196\) 6.25136e7 4.54188e7i 0.593032 0.430863i
\(197\) −2.13761e7 −0.199203 −0.0996016 0.995027i \(-0.531757\pi\)
−0.0996016 + 0.995027i \(0.531757\pi\)
\(198\) 0 0
\(199\) −9.65698e7 −0.868671 −0.434336 0.900751i \(-0.643017\pi\)
−0.434336 + 0.900751i \(0.643017\pi\)
\(200\) −1.51576e8 + 1.10126e8i −1.33975 + 0.973388i
\(201\) 0 0
\(202\) 1.07594e7 3.31140e7i 0.0918454 0.282671i
\(203\) 1.94074e7 2.67119e7i 0.162828 0.224114i
\(204\) 0 0
\(205\) −3.49140e8 1.13443e8i −2.83049 0.919682i
\(206\) −2.61451e7 8.04664e7i −0.208380 0.641327i
\(207\) 0 0
\(208\) 4.63928e7i 0.357461i
\(209\) −2.44975e7 + 9.95102e7i −0.185613 + 0.753972i
\(210\) 0 0
\(211\) 1.18687e8 + 1.63358e8i 0.869788 + 1.19716i 0.979146 + 0.203159i \(0.0651207\pi\)
−0.109357 + 0.994003i \(0.534879\pi\)
\(212\) 8.28342e7 2.69144e7i 0.597082 0.194004i
\(213\) 0 0
\(214\) 5.43328e7 + 3.94751e7i 0.378978 + 0.275344i
\(215\) −7.72574e7 5.61308e7i −0.530158 0.385182i
\(216\) 0 0
\(217\) 3.49775e7 1.13649e7i 0.232370 0.0755015i
\(218\) 3.38289e6 + 4.65615e6i 0.0221152 + 0.0304389i
\(219\) 0 0
\(220\) 2.62237e8 1.91190e7i 1.66041 0.121056i
\(221\) 1.29146e8i 0.804836i
\(222\) 0 0
\(223\) 6.18020e7 + 1.90207e8i 0.373195 + 1.14858i 0.944688 + 0.327969i \(0.106364\pi\)
−0.571493 + 0.820607i \(0.693636\pi\)
\(224\) 5.74112e7 + 1.86540e7i 0.341294 + 0.110893i
\(225\) 0 0
\(226\) −3.37063e7 + 4.63927e7i −0.194237 + 0.267344i
\(227\) 9.42468e7 2.90062e8i 0.534781 1.64589i −0.209340 0.977843i \(-0.567131\pi\)
0.744121 0.668045i \(-0.232869\pi\)
\(228\) 0 0
\(229\) 4.68538e7 3.40413e7i 0.257822 0.187319i −0.451364 0.892340i \(-0.649062\pi\)
0.709186 + 0.705021i \(0.249062\pi\)
\(230\) −1.77409e8 −0.961455
\(231\) 0 0
\(232\) −8.28440e7 −0.435565
\(233\) 1.25442e8 9.11386e7i 0.649674 0.472016i −0.213486 0.976946i \(-0.568482\pi\)
0.863160 + 0.504930i \(0.168482\pi\)
\(234\) 0 0
\(235\) 5.88304e7 1.81061e8i 0.295709 0.910099i
\(236\) 1.38042e6 1.89998e6i 0.00683625 0.00940929i
\(237\) 0 0
\(238\) 4.14994e7 + 1.34840e7i 0.199536 + 0.0648333i
\(239\) 4.29001e7 + 1.32033e8i 0.203266 + 0.625589i 0.999780 + 0.0209690i \(0.00667514\pi\)
−0.796514 + 0.604620i \(0.793325\pi\)
\(240\) 0 0
\(241\) 3.55899e8i 1.63782i 0.573919 + 0.818912i \(0.305422\pi\)
−0.573919 + 0.818912i \(0.694578\pi\)
\(242\) 6.70592e7 + 3.51475e7i 0.304162 + 0.159419i
\(243\) 0 0
\(244\) 1.53895e8 + 2.11818e8i 0.678203 + 0.933466i
\(245\) −3.43373e8 + 1.11569e8i −1.49171 + 0.484687i
\(246\) 0 0
\(247\) −8.05629e7 5.85324e7i −0.340170 0.247148i
\(248\) −7.46541e7 5.42394e7i −0.310794 0.225805i
\(249\) 0 0
\(250\) 2.37913e8 7.73027e7i 0.963006 0.312900i
\(251\) 2.19931e8 + 3.02709e8i 0.877865 + 1.20828i 0.977008 + 0.213205i \(0.0683901\pi\)
−0.0991422 + 0.995073i \(0.531610\pi\)
\(252\) 0 0
\(253\) 3.24639e8 + 2.01521e8i 1.26032 + 0.782346i
\(254\) 5.03082e7i 0.192629i
\(255\) 0 0
\(256\) 1.49588e6 + 4.60386e6i 0.00557260 + 0.0171507i
\(257\) −9.16055e6 2.97644e6i −0.0336632 0.0109378i 0.292137 0.956376i \(-0.405634\pi\)
−0.325800 + 0.945439i \(0.605634\pi\)
\(258\) 0 0
\(259\) 7.58543e6 1.04405e7i 0.0271288 0.0373396i
\(260\) −7.89515e7 + 2.42988e8i −0.278583 + 0.857389i
\(261\) 0 0
\(262\) −9.72871e7 + 7.06832e7i −0.334196 + 0.242807i
\(263\) −3.38201e8 −1.14638 −0.573192 0.819421i \(-0.694295\pi\)
−0.573192 + 0.819421i \(0.694295\pi\)
\(264\) 0 0
\(265\) −4.06955e8 −1.34334
\(266\) 2.72201e7 1.97766e7i 0.0886756 0.0644266i
\(267\) 0 0
\(268\) 5.98134e7 1.84087e8i 0.189813 0.584186i
\(269\) −5.56045e7 + 7.65330e7i −0.174171 + 0.239726i −0.887174 0.461435i \(-0.847335\pi\)
0.713003 + 0.701161i \(0.247335\pi\)
\(270\) 0 0
\(271\) −1.31023e8 4.25721e7i −0.399905 0.129937i 0.102158 0.994768i \(-0.467425\pi\)
−0.502063 + 0.864831i \(0.667425\pi\)
\(272\) 1.00623e8 + 3.09687e8i 0.303185 + 0.933107i
\(273\) 0 0
\(274\) 4.15862e7i 0.122130i
\(275\) −8.58043e8 2.11234e8i −2.48797 0.612489i
\(276\) 0 0
\(277\) 1.25606e8 + 1.72882e8i 0.355084 + 0.488731i 0.948771 0.315965i \(-0.102328\pi\)
−0.593687 + 0.804696i \(0.702328\pi\)
\(278\) −8.38132e7 + 2.72325e7i −0.233967 + 0.0760206i
\(279\) 0 0
\(280\) −1.49013e8 1.08264e8i −0.405667 0.294735i
\(281\) 3.18286e8 + 2.31248e8i 0.855747 + 0.621737i 0.926725 0.375741i \(-0.122612\pi\)
−0.0709774 + 0.997478i \(0.522612\pi\)
\(282\) 0 0
\(283\) −7.93685e7 + 2.57884e7i −0.208159 + 0.0676351i −0.411241 0.911527i \(-0.634904\pi\)
0.203081 + 0.979162i \(0.434904\pi\)
\(284\) 1.61301e8 + 2.22012e8i 0.417853 + 0.575126i
\(285\) 0 0
\(286\) −5.62169e7 + 4.74563e7i −0.142097 + 0.119954i
\(287\) 2.59588e8i 0.648182i
\(288\) 0 0
\(289\) 1.53308e8 + 4.71834e8i 0.373614 + 1.14987i
\(290\) 1.72536e8 + 5.60602e7i 0.415418 + 0.134978i
\(291\) 0 0
\(292\) −4.25515e8 + 5.85671e8i −1.00017 + 1.37662i
\(293\) 5.28032e7 1.62512e8i 0.122638 0.377440i −0.870826 0.491592i \(-0.836415\pi\)
0.993463 + 0.114152i \(0.0364151\pi\)
\(294\) 0 0
\(295\) −8.87754e6 + 6.44991e6i −0.0201333 + 0.0146277i
\(296\) −3.23799e7 −0.0725695
\(297\) 0 0
\(298\) 1.96317e8 0.429735
\(299\) −3.00379e8 + 2.18238e8i −0.649861 + 0.472151i
\(300\) 0 0
\(301\) 2.08667e7 6.42212e7i 0.0441034 0.135736i
\(302\) 1.66996e8 2.29850e8i 0.348884 0.480198i
\(303\) 0 0
\(304\) 2.38792e8 + 7.75882e7i 0.487486 + 0.158394i
\(305\) −3.78034e8 1.16347e9i −0.762925 2.34804i
\(306\) 0 0
\(307\) 7.56242e8i 1.49168i −0.666124 0.745841i \(-0.732048\pi\)
0.666124 0.745841i \(-0.267952\pi\)
\(308\) 7.01592e7 + 1.72178e8i 0.136822 + 0.335777i
\(309\) 0 0
\(310\) 1.18775e8 + 1.63480e8i 0.226443 + 0.311673i
\(311\) 6.12391e8 1.98978e8i 1.15443 0.375097i 0.331619 0.943413i \(-0.392405\pi\)
0.822810 + 0.568317i \(0.192405\pi\)
\(312\) 0 0
\(313\) 3.14228e8 + 2.28300e8i 0.579216 + 0.420825i 0.838441 0.544992i \(-0.183467\pi\)
−0.259226 + 0.965817i \(0.583467\pi\)
\(314\) 6.25184e7 + 4.54223e7i 0.113960 + 0.0827971i
\(315\) 0 0
\(316\) 2.48238e8 8.06574e7i 0.442551 0.143794i
\(317\) 2.74272e8 + 3.77503e8i 0.483587 + 0.665600i 0.979189 0.202950i \(-0.0650527\pi\)
−0.495603 + 0.868549i \(0.665053\pi\)
\(318\) 0 0
\(319\) −2.52042e8 2.98569e8i −0.434715 0.514965i
\(320\) 3.98639e8i 0.680072i
\(321\) 0 0
\(322\) −3.87658e7 1.19309e8i −0.0647073 0.199149i
\(323\) 6.64736e8 + 2.15986e8i 1.09759 + 0.356629i
\(324\) 0 0
\(325\) 5.04705e8 6.94667e8i 0.815541 1.12250i
\(326\) 1.05497e7 3.24688e7i 0.0168648 0.0519044i
\(327\) 0 0
\(328\) −5.26933e8 + 3.82839e8i −0.824511 + 0.599043i
\(329\) 1.34620e8 0.208413
\(330\) 0 0
\(331\) 4.60801e7 0.0698418 0.0349209 0.999390i \(-0.488882\pi\)
0.0349209 + 0.999390i \(0.488882\pi\)
\(332\) 2.63556e8 1.91484e8i 0.395266 0.287177i
\(333\) 0 0
\(334\) −1.00045e8 + 3.07907e8i −0.146921 + 0.452175i
\(335\) −5.31592e8 + 7.31674e8i −0.772542 + 1.06331i
\(336\) 0 0
\(337\) −7.00493e8 2.27604e8i −0.997008 0.323948i −0.235339 0.971913i \(-0.575620\pi\)
−0.761670 + 0.647966i \(0.775620\pi\)
\(338\) 5.32448e7 + 1.63871e8i 0.0750014 + 0.230830i
\(339\) 0 0
\(340\) 1.79326e9i 2.47439i
\(341\) −3.16467e7 4.34068e8i −0.0432204 0.592813i
\(342\) 0 0
\(343\) −3.30634e8 4.55079e8i −0.442403 0.608916i
\(344\) −1.61136e8 + 5.23562e7i −0.213421 + 0.0693448i
\(345\) 0 0
\(346\) −6.63550e7 4.82098e7i −0.0861207 0.0625704i
\(347\) 1.11513e8 + 8.10191e7i 0.143276 + 0.104096i 0.657114 0.753791i \(-0.271777\pi\)
−0.513838 + 0.857887i \(0.671777\pi\)
\(348\) 0 0
\(349\) −1.88812e8 + 6.13487e7i −0.237761 + 0.0772532i −0.425474 0.904971i \(-0.639893\pi\)
0.187713 + 0.982224i \(0.439893\pi\)
\(350\) 1.70527e8 + 2.34710e8i 0.212596 + 0.292613i
\(351\) 0 0
\(352\) 3.76755e8 6.06932e8i 0.460426 0.741721i
\(353\) 1.12234e9i 1.35805i 0.734117 + 0.679023i \(0.237596\pi\)
−0.734117 + 0.679023i \(0.762404\pi\)
\(354\) 0 0
\(355\) −3.96228e8 1.21946e9i −0.470052 1.44667i
\(356\) −1.22346e9 3.97526e8i −1.43719 0.466972i
\(357\) 0 0
\(358\) −1.35427e8 + 1.86400e8i −0.155997 + 0.214711i
\(359\) −1.51042e8 + 4.64859e8i −0.172293 + 0.530262i −0.999499 0.0316352i \(-0.989929\pi\)
0.827207 + 0.561898i \(0.189929\pi\)
\(360\) 0 0
\(361\) −2.87146e8 + 2.08624e8i −0.321239 + 0.233394i
\(362\) 1.21117e8 0.134192
\(363\) 0 0
\(364\) −1.80663e8 −0.196342
\(365\) 2.73651e9 1.98819e9i 2.94559 2.14010i
\(366\) 0 0
\(367\) −5.29655e8 + 1.63011e9i −0.559322 + 1.72141i 0.124927 + 0.992166i \(0.460130\pi\)
−0.684249 + 0.729249i \(0.739870\pi\)
\(368\) 5.50258e8 7.57365e8i 0.575571 0.792206i
\(369\) 0 0
\(370\) 6.74361e7 + 2.19113e7i 0.0692128 + 0.0224886i
\(371\) −8.89241e7 2.73680e8i −0.0904088 0.278250i
\(372\) 0 0
\(373\) 3.33188e8i 0.332436i 0.986089 + 0.166218i \(0.0531556\pi\)
−0.986089 + 0.166218i \(0.946844\pi\)
\(374\) 2.72335e8 4.38717e8i 0.269187 0.433645i
\(375\) 0 0
\(376\) −1.98537e8 2.73263e8i −0.192613 0.265108i
\(377\) 3.61089e8 1.17325e8i 0.347072 0.112770i
\(378\) 0 0
\(379\) 1.41932e9 + 1.03119e9i 1.33919 + 0.972977i 0.999473 + 0.0324490i \(0.0103307\pi\)
0.339715 + 0.940528i \(0.389669\pi\)
\(380\) −1.11866e9 8.12755e8i −1.04582 0.759831i
\(381\) 0 0
\(382\) −4.34005e8 + 1.41017e8i −0.398358 + 0.129434i
\(383\) 6.71577e8 + 9.24347e8i 0.610802 + 0.840696i 0.996643 0.0818688i \(-0.0260888\pi\)
−0.385842 + 0.922565i \(0.626089\pi\)
\(384\) 0 0
\(385\) −6.31682e7 8.66419e8i −0.0564139 0.773776i
\(386\) 1.85253e8i 0.163950i
\(387\) 0 0
\(388\) 1.24668e8 + 3.83689e8i 0.108354 + 0.333479i
\(389\) −7.62537e8 2.47763e8i −0.656806 0.213409i −0.0383935 0.999263i \(-0.512224\pi\)
−0.618413 + 0.785853i \(0.712224\pi\)
\(390\) 0 0
\(391\) 1.53178e9 2.10831e9i 1.29592 1.78368i
\(392\) −1.97946e8 + 6.09215e8i −0.165976 + 0.510822i
\(393\) 0 0
\(394\) 6.71894e7 4.88159e7i 0.0553432 0.0402092i
\(395\) −1.21957e9 −0.995670
\(396\) 0 0
\(397\) 1.42395e8 0.114216 0.0571081 0.998368i \(-0.481812\pi\)
0.0571081 + 0.998368i \(0.481812\pi\)
\(398\) 3.03539e8 2.20534e8i 0.241337 0.175341i
\(399\) 0 0
\(400\) −6.69017e8 + 2.05902e9i −0.522670 + 1.60861i
\(401\) −3.07368e8 + 4.23055e8i −0.238042 + 0.327636i −0.911278 0.411791i \(-0.864903\pi\)
0.673237 + 0.739427i \(0.264903\pi\)
\(402\) 0 0
\(403\) 4.02206e8 + 1.30685e8i 0.306112 + 0.0994620i
\(404\) −3.12670e8 9.62299e8i −0.235913 0.726065i
\(405\) 0 0
\(406\) 1.28281e8i 0.0951309i
\(407\) −9.85113e7 1.16697e8i −0.0724279 0.0857982i
\(408\) 0 0
\(409\) 7.23607e7 + 9.95960e7i 0.0522963 + 0.0719797i 0.834364 0.551213i \(-0.185835\pi\)
−0.782068 + 0.623193i \(0.785835\pi\)
\(410\) 1.35648e9 4.40749e8i 0.972012 0.315826i
\(411\) 0 0
\(412\) −1.98914e9 1.44519e9i −1.40128 1.01809i
\(413\) −6.27744e6 4.56083e6i −0.00438488 0.00318580i
\(414\) 0 0
\(415\) −1.44765e9 + 4.70371e8i −0.994252 + 0.323052i
\(416\) 4.08009e8 + 5.61576e8i 0.277871 + 0.382456i
\(417\) 0 0
\(418\) −1.50248e8 3.68725e8i −0.100622 0.246937i
\(419\) 1.48703e8i 0.0987577i 0.998780 + 0.0493788i \(0.0157242\pi\)
−0.998780 + 0.0493788i \(0.984276\pi\)
\(420\) 0 0
\(421\) 7.82892e8 + 2.40949e9i 0.511346 + 1.57376i 0.789834 + 0.613320i \(0.210167\pi\)
−0.278489 + 0.960440i \(0.589833\pi\)
\(422\) −7.46113e8 2.42427e8i −0.483294 0.157032i
\(423\) 0 0
\(424\) −4.24394e8 + 5.84128e8i −0.270389 + 0.372158i
\(425\) −1.86237e9 + 5.73180e9i −1.17681 + 3.62184i
\(426\) 0 0
\(427\) 6.99836e8 5.08461e8i 0.435010 0.316053i
\(428\) 1.95166e9 1.20323
\(429\) 0 0
\(430\) 3.71020e8 0.225039
\(431\) −3.25922e8 + 2.36796e8i −0.196084 + 0.142464i −0.681495 0.731823i \(-0.738670\pi\)
0.485411 + 0.874286i \(0.338670\pi\)
\(432\) 0 0
\(433\) 5.25971e8 1.61877e9i 0.311354 0.958248i −0.665876 0.746062i \(-0.731942\pi\)
0.977229 0.212185i \(-0.0680580\pi\)
\(434\) −8.39877e7 + 1.15599e8i −0.0493176 + 0.0678798i
\(435\) 0 0
\(436\) 1.59065e8 + 5.16834e7i 0.0919120 + 0.0298640i
\(437\) −6.20950e8 1.91109e9i −0.355936 1.09546i
\(438\) 0 0
\(439\) 2.18972e9i 1.23527i −0.786463 0.617637i \(-0.788090\pi\)
0.786463 0.617637i \(-0.211910\pi\)
\(440\) −1.66557e9 + 1.40602e9i −0.932134 + 0.786875i
\(441\) 0 0
\(442\) 2.94927e8 + 4.05932e8i 0.162456 + 0.223602i
\(443\) −7.00222e8 + 2.27516e8i −0.382668 + 0.124336i −0.494033 0.869443i \(-0.664478\pi\)
0.111365 + 0.993780i \(0.464478\pi\)
\(444\) 0 0
\(445\) 4.86278e9 + 3.53302e9i 2.61592 + 1.90058i
\(446\) −6.28627e8 4.56724e8i −0.335522 0.243771i
\(447\) 0 0
\(448\) 2.68087e8 8.71068e7i 0.140865 0.0457698i
\(449\) 7.16181e8 + 9.85739e8i 0.373388 + 0.513925i 0.953818 0.300386i \(-0.0971153\pi\)
−0.580430 + 0.814310i \(0.697115\pi\)
\(450\) 0 0
\(451\) −2.98287e9 7.34325e8i −1.53114 0.376938i
\(452\) 1.66645e9i 0.848802i
\(453\) 0 0
\(454\) 3.66169e8 + 1.12695e9i 0.183648 + 0.565210i
\(455\) 8.02820e8 + 2.60852e8i 0.399557 + 0.129824i
\(456\) 0 0
\(457\) 2.17390e8 2.99212e8i 0.106545 0.146647i −0.752415 0.658690i \(-0.771111\pi\)
0.858960 + 0.512043i \(0.171111\pi\)
\(458\) −6.95319e7 + 2.13997e8i −0.0338186 + 0.104083i
\(459\) 0 0
\(460\) −4.17093e9 + 3.03036e9i −1.99793 + 1.45158i
\(461\) −2.38448e9 −1.13355 −0.566774 0.823874i \(-0.691809\pi\)
−0.566774 + 0.823874i \(0.691809\pi\)
\(462\) 0 0
\(463\) 3.45661e9 1.61852 0.809259 0.587452i \(-0.199869\pi\)
0.809259 + 0.587452i \(0.199869\pi\)
\(464\) −7.74464e8 + 5.62681e8i −0.359906 + 0.261487i
\(465\) 0 0
\(466\) −1.86158e8 + 5.72935e8i −0.0852178 + 0.262273i
\(467\) 1.48596e9 2.04525e9i 0.675148 0.929261i −0.324715 0.945812i \(-0.605268\pi\)
0.999863 + 0.0165506i \(0.00526846\pi\)
\(468\) 0 0
\(469\) −6.08214e8 1.97621e8i −0.272240 0.0884561i
\(470\) 2.28569e8 + 7.03462e8i 0.101549 + 0.312535i
\(471\) 0 0
\(472\) 1.94688e7i 0.00852200i
\(473\) −6.78925e8 4.21445e8i −0.294990 0.183116i
\(474\) 0 0
\(475\) 2.73149e9 + 3.75958e9i 1.16943 + 1.60958i
\(476\) 1.20598e9 3.91847e8i 0.512526 0.166530i
\(477\) 0 0
\(478\) −4.36363e8 3.17036e8i −0.182747 0.132774i
\(479\) −2.35717e9 1.71259e9i −0.979980 0.711997i −0.0222762 0.999752i \(-0.507091\pi\)
−0.957704 + 0.287754i \(0.907091\pi\)
\(480\) 0 0
\(481\) 1.41133e8 4.58568e7i 0.0578256 0.0187887i
\(482\) −8.12757e8 1.11866e9i −0.330595 0.455025i
\(483\) 0 0
\(484\) 2.17693e9 3.19125e8i 0.872744 0.127939i
\(485\) 1.88502e9i 0.750276i
\(486\) 0 0
\(487\) 2.91945e8 + 8.98515e8i 0.114538 + 0.352512i 0.991850 0.127408i \(-0.0406657\pi\)
−0.877312 + 0.479920i \(0.840666\pi\)
\(488\) −2.06423e9 6.70710e8i −0.804062 0.261255i
\(489\) 0 0
\(490\) 8.24506e8 1.13484e9i 0.316598 0.435759i
\(491\) 5.94128e8 1.82854e9i 0.226514 0.697138i −0.771621 0.636083i \(-0.780554\pi\)
0.998134 0.0610547i \(-0.0194464\pi\)
\(492\) 0 0
\(493\) −2.15591e9 + 1.56636e9i −0.810339 + 0.588746i
\(494\) 3.86894e8 0.144394
\(495\) 0 0
\(496\) −1.06630e9 −0.392367
\(497\) 7.33518e8 5.32932e8i 0.268018 0.194726i
\(498\) 0 0
\(499\) 1.15343e9 3.54989e9i 0.415565 1.27898i −0.496180 0.868220i \(-0.665264\pi\)
0.911745 0.410757i \(-0.134736\pi\)
\(500\) 4.27297e9 5.88124e9i 1.52874 2.10414i
\(501\) 0 0
\(502\) −1.38257e9 4.49226e8i −0.487782 0.158490i
\(503\) 4.71396e8 + 1.45081e9i 0.165157 + 0.508302i 0.999048 0.0436281i \(-0.0138917\pi\)
−0.833891 + 0.551930i \(0.813892\pi\)
\(504\) 0 0
\(505\) 4.72767e9i 1.63353i
\(506\) −1.48062e9 + 1.07948e8i −0.508061 + 0.0370413i
\(507\) 0 0
\(508\) 8.59323e8 + 1.18276e9i 0.290826 + 0.400288i
\(509\) −2.90555e9 + 9.44069e8i −0.976597 + 0.317316i −0.753476 0.657475i \(-0.771624\pi\)
−0.223121 + 0.974791i \(0.571624\pi\)
\(510\) 0 0
\(511\) 1.93503e9 + 1.40588e9i 0.641526 + 0.466096i
\(512\) −2.46421e9 1.79035e9i −0.811394 0.589513i
\(513\) 0 0
\(514\) 3.55907e7 1.15641e7i 0.0115602 0.00375614i
\(515\) 6.75257e9 + 9.29412e9i 2.17843 + 2.99835i
\(516\) 0 0
\(517\) 3.80815e8 1.54689e9i 0.121198 0.492315i
\(518\) 5.01391e7i 0.0158497i
\(519\) 0 0
\(520\) −6.54497e8 2.01434e9i −0.204125 0.628232i
\(521\) 2.51651e9 + 8.17664e8i 0.779591 + 0.253305i 0.671666 0.740854i \(-0.265579\pi\)
0.107926 + 0.994159i \(0.465579\pi\)
\(522\) 0 0
\(523\) 2.12165e9 2.92020e9i 0.648512 0.892601i −0.350521 0.936555i \(-0.613996\pi\)
0.999034 + 0.0439541i \(0.0139955\pi\)
\(524\) −1.07989e9 + 3.32355e9i −0.327883 + 1.00912i
\(525\) 0 0
\(526\) 1.06303e9 7.72340e8i 0.318491 0.231397i
\(527\) −2.96830e9 −0.883427
\(528\) 0 0
\(529\) −4.08736e9 −1.20046
\(530\) 1.27914e9 9.29352e8i 0.373210 0.271153i
\(531\) 0 0
\(532\) 3.02144e8 9.29902e8i 0.0870007 0.267761i
\(533\) 1.75454e9 2.41491e9i 0.501900 0.690806i
\(534\) 0 0
\(535\) −8.67268e9 2.81793e9i −2.44858 0.795593i
\(536\) 4.95845e8 + 1.52605e9i 0.139081 + 0.428049i
\(537\) 0 0
\(538\) 3.67541e8i 0.101758i
\(539\) −2.79783e9 + 1.14006e9i −0.769591 + 0.313593i
\(540\) 0 0
\(541\) −1.12750e9 1.55188e9i −0.306146 0.421373i 0.628029 0.778190i \(-0.283862\pi\)
−0.934174 + 0.356817i \(0.883862\pi\)
\(542\) 5.09054e8 1.65402e8i 0.137330 0.0446213i
\(543\) 0 0
\(544\) −3.94161e9 2.86375e9i −1.04973 0.762674i
\(545\) −6.32222e8 4.59336e8i −0.167295 0.121547i
\(546\) 0 0
\(547\) 5.01230e9 1.62860e9i 1.30943 0.425459i 0.430576 0.902554i \(-0.358310\pi\)
0.878851 + 0.477096i \(0.158310\pi\)
\(548\) −7.10341e8 9.77701e8i −0.184389 0.253790i
\(549\) 0 0
\(550\) 3.17939e9 1.29554e9i 0.814844 0.332033i
\(551\) 2.05480e9i 0.523287i
\(552\) 0 0
\(553\) −2.66488e8 8.20166e8i −0.0670101 0.206236i
\(554\) −7.89610e8 2.56560e8i −0.197301 0.0641069i
\(555\) 0 0
\(556\) −1.50530e9 + 2.07187e9i −0.371417 + 0.511211i
\(557\) −4.08785e8 + 1.25811e9i −0.100231 + 0.308479i −0.988582 0.150687i \(-0.951852\pi\)
0.888351 + 0.459166i \(0.151852\pi\)
\(558\) 0 0
\(559\) 6.28189e8 4.56406e8i 0.152107 0.110512i
\(560\) −2.12837e9 −0.512141
\(561\) 0 0
\(562\) −1.52853e9 −0.363243
\(563\) 4.65486e9 3.38196e9i 1.09933 0.798709i 0.118378 0.992969i \(-0.462230\pi\)
0.980950 + 0.194260i \(0.0622305\pi\)
\(564\) 0 0
\(565\) 2.40612e9 7.40527e9i 0.561238 1.72731i
\(566\) 1.90579e8 2.62310e8i 0.0441792 0.0608075i
\(567\) 0 0
\(568\) −2.16358e9 7.02990e8i −0.495397 0.160964i
\(569\) 7.69196e8 + 2.36734e9i 0.175043 + 0.538726i 0.999635 0.0270008i \(-0.00859568\pi\)
−0.824593 + 0.565727i \(0.808596\pi\)
\(570\) 0 0
\(571\) 4.73666e9i 1.06475i 0.846510 + 0.532373i \(0.178700\pi\)
−0.846510 + 0.532373i \(0.821300\pi\)
\(572\) −5.11061e8 + 2.07596e9i −0.114179 + 0.463802i
\(573\) 0 0
\(574\) 5.92813e8 + 8.15937e8i 0.130836 + 0.180080i
\(575\) 1.64787e10 5.35424e9i 3.61480 1.17452i
\(576\) 0 0
\(577\) 6.93876e8 + 5.04131e8i 0.150372 + 0.109252i 0.660427 0.750890i \(-0.270375\pi\)
−0.510055 + 0.860142i \(0.670375\pi\)
\(578\) −1.55939e9 1.13297e9i −0.335899 0.244045i
\(579\) 0 0
\(580\) 5.01392e9 1.62912e9i 1.06704 0.346701i
\(581\) −6.32656e8 8.70776e8i −0.133829 0.184200i
\(582\) 0 0
\(583\) −3.39635e9 + 2.47619e8i −0.709860 + 0.0517539i
\(584\) 6.00127e9i 1.24680i
\(585\) 0 0
\(586\) 2.05152e8 + 6.31392e8i 0.0421147 + 0.129616i
\(587\) 3.05840e9 + 9.93735e8i 0.624110 + 0.202786i 0.603964 0.797011i \(-0.293587\pi\)
0.0201459 + 0.999797i \(0.493587\pi\)
\(588\) 0 0
\(589\) −1.34531e9 + 1.85167e9i −0.271281 + 0.373387i
\(590\) 1.31744e7 4.05467e7i 0.00264089 0.00812782i
\(591\) 0 0
\(592\) −3.02702e8 + 2.19926e8i −0.0599638 + 0.0435663i
\(593\) −7.27783e9 −1.43321 −0.716606 0.697478i \(-0.754306\pi\)
−0.716606 + 0.697478i \(0.754306\pi\)
\(594\) 0 0
\(595\) −5.92485e9 −1.15310
\(596\) 4.61545e9 3.35332e9i 0.893002 0.648804i
\(597\) 0 0
\(598\) 4.45768e8 1.37193e9i 0.0852422 0.262349i
\(599\) 4.53979e9 6.24849e9i 0.863062 1.18790i −0.117769 0.993041i \(-0.537574\pi\)
0.980831 0.194862i \(-0.0624258\pi\)
\(600\) 0 0
\(601\) −7.42131e9 2.41133e9i −1.39450 0.453102i −0.487095 0.873349i \(-0.661943\pi\)
−0.907410 + 0.420247i \(0.861943\pi\)
\(602\) 8.10718e7 + 2.49513e8i 0.0151454 + 0.0466129i
\(603\) 0 0
\(604\) 8.25630e9i 1.52460i
\(605\) −1.01345e10 1.72508e9i −1.86063 0.316713i
\(606\) 0 0
\(607\) 2.56171e9 + 3.52590e9i 0.464911 + 0.639896i 0.975518 0.219919i \(-0.0705792\pi\)
−0.510607 + 0.859814i \(0.670579\pi\)
\(608\) −3.57289e9 + 1.16090e9i −0.644699 + 0.209475i
\(609\) 0 0
\(610\) 3.84522e9 + 2.79372e9i 0.685909 + 0.498342i
\(611\) 1.25236e9 + 9.09889e8i 0.222118 + 0.161378i
\(612\) 0 0
\(613\) 7.24210e9 2.35310e9i 1.26985 0.412599i 0.404856 0.914380i \(-0.367322\pi\)
0.864995 + 0.501781i \(0.167322\pi\)
\(614\) 1.72701e9 + 2.37702e9i 0.301096 + 0.414423i
\(615\) 0 0
\(616\) −1.30950e9 8.12877e8i −0.225721 0.140117i
\(617\) 6.09475e9i 1.04462i 0.852756 + 0.522309i \(0.174929\pi\)
−0.852756 + 0.522309i \(0.825071\pi\)
\(618\) 0 0
\(619\) −3.40123e7 1.04679e8i −0.00576393 0.0177395i 0.948133 0.317873i \(-0.102969\pi\)
−0.953897 + 0.300134i \(0.902969\pi\)
\(620\) 5.58486e9 + 1.81463e9i 0.941112 + 0.305786i
\(621\) 0 0
\(622\) −1.47047e9 + 2.02393e9i −0.245013 + 0.337232i
\(623\) −1.31341e9 + 4.04226e9i −0.217616 + 0.669754i
\(624\) 0 0
\(625\) −1.48277e10 + 1.07730e10i −2.42938 + 1.76505i
\(626\) −1.50905e9 −0.245863
\(627\) 0 0
\(628\) 2.24569e9 0.361818
\(629\) −8.42645e8 + 6.12218e8i −0.135011 + 0.0980909i
\(630\) 0 0
\(631\) 1.26911e9 3.90593e9i 0.201093 0.618901i −0.798758 0.601652i \(-0.794509\pi\)
0.999851 0.0172489i \(-0.00549077\pi\)
\(632\) −1.27183e9 + 1.75052e9i −0.200409 + 0.275840i
\(633\) 0 0
\(634\) −1.72419e9 5.60222e8i −0.268703 0.0873068i
\(635\) −2.11088e9 6.49662e9i −0.327156 1.00688i
\(636\) 0 0
\(637\) 2.93569e9i 0.450010i
\(638\) 1.47405e9 + 3.62883e8i 0.224719 + 0.0553216i
\(639\) 0 0
\(640\) 7.33323e9 + 1.00933e10i 1.10577 + 1.52196i
\(641\) −6.08661e9 + 1.97766e9i −0.912793 + 0.296585i −0.727507 0.686100i \(-0.759321\pi\)
−0.185286 + 0.982685i \(0.559321\pi\)
\(642\) 0 0
\(643\) −6.34491e9 4.60985e9i −0.941211 0.683830i 0.00750082 0.999972i \(-0.497612\pi\)
−0.948712 + 0.316142i \(0.897612\pi\)
\(644\) −2.94933e9 2.14281e9i −0.435133 0.316143i
\(645\) 0 0
\(646\) −2.58264e9 + 8.39151e8i −0.376921 + 0.122469i
\(647\) 9.14002e7 + 1.25802e8i 0.0132673 + 0.0182609i 0.815599 0.578617i \(-0.196408\pi\)
−0.802332 + 0.596878i \(0.796408\pi\)
\(648\) 0 0
\(649\) −7.01653e7 + 5.92311e7i −0.0100755 + 0.00850537i
\(650\) 3.33606e9i 0.476472i
\(651\) 0 0
\(652\) −3.06578e8 9.43549e8i −0.0433186 0.133321i
\(653\) 4.17017e9 + 1.35497e9i 0.586082 + 0.190429i 0.587023 0.809570i \(-0.300300\pi\)
−0.000941570 1.00000i \(0.500300\pi\)
\(654\) 0 0
\(655\) 9.59751e9 1.32098e10i 1.33449 1.83676i
\(656\) −2.32575e9 + 7.15791e9i −0.321661 + 0.989972i
\(657\) 0 0
\(658\) −4.23138e8 + 3.07428e8i −0.0579018 + 0.0420681i
\(659\) −1.44304e9 −0.196417 −0.0982085 0.995166i \(-0.531311\pi\)
−0.0982085 + 0.995166i \(0.531311\pi\)
\(660\) 0 0
\(661\) 7.50617e9 1.01091 0.505456 0.862853i \(-0.331324\pi\)
0.505456 + 0.862853i \(0.331324\pi\)
\(662\) −1.44839e8 + 1.05232e8i −0.0194036 + 0.0140976i
\(663\) 0 0
\(664\) −8.34535e8 + 2.56843e9i −0.110626 + 0.340471i
\(665\) −2.68530e9 + 3.69600e9i −0.354093 + 0.487367i
\(666\) 0 0
\(667\) 7.28637e9 + 2.36748e9i 0.950759 + 0.308920i
\(668\) 2.90733e9 + 8.94784e9i 0.377378 + 1.16145i
\(669\) 0 0
\(670\) 3.51378e9i 0.451350i
\(671\) −3.86292e9 9.48002e9i −0.493613 1.21138i
\(672\) 0 0
\(673\) 3.92485e9 + 5.40209e9i 0.496329 + 0.683139i 0.981540 0.191259i \(-0.0612570\pi\)
−0.485210 + 0.874397i \(0.661257\pi\)
\(674\) 2.72156e9 8.84289e8i 0.342380 0.111246i
\(675\) 0 0
\(676\) 4.05090e9 + 2.94315e9i 0.504357 + 0.366437i
\(677\) −9.81606e9 7.13178e9i −1.21584 0.883360i −0.220093 0.975479i \(-0.570636\pi\)
−0.995748 + 0.0921190i \(0.970636\pi\)
\(678\) 0 0
\(679\) 1.26769e9 4.11898e8i 0.155407 0.0504946i
\(680\) 8.73795e9 + 1.20268e10i 1.06568 + 1.46679i
\(681\) 0 0
\(682\) 1.09074e9 + 1.29209e9i 0.131667 + 0.155973i
\(683\) 5.56126e9i 0.667884i −0.942594 0.333942i \(-0.891621\pi\)
0.942594 0.333942i \(-0.108379\pi\)
\(684\) 0 0
\(685\) 1.74491e9 + 5.37030e9i 0.207423 + 0.638383i
\(686\) 2.07850e9 + 6.75346e8i 0.245819 + 0.0798715i
\(687\) 0 0
\(688\) −1.15077e9 + 1.58389e9i −0.134719 + 0.185424i
\(689\) 1.02254e9 3.14705e9i 0.119100 0.366552i
\(690\) 0 0
\(691\) −6.78846e9 + 4.93210e9i −0.782705 + 0.568668i −0.905790 0.423728i \(-0.860721\pi\)
0.123085 + 0.992396i \(0.460721\pi\)
\(692\) −2.38350e9 −0.273428
\(693\) 0 0
\(694\) −5.35530e8 −0.0608170
\(695\) 9.68068e9 7.03343e9i 1.09385 0.794731i
\(696\) 0 0
\(697\) −6.47429e9 + 1.99258e10i −0.724231 + 2.22895i
\(698\) 4.53374e8 6.24015e8i 0.0504618 0.0694547i
\(699\) 0 0
\(700\) 8.01824e9 + 2.60528e9i 0.883559 + 0.287086i
\(701\) −5.10031e9 1.56972e10i −0.559221 1.72111i −0.684526 0.728988i \(-0.739991\pi\)
0.125305 0.992118i \(-0.460009\pi\)
\(702\) 0 0
\(703\) 8.03127e8i 0.0871847i
\(704\) −2.42558e8 3.32694e9i −0.0262006 0.359370i
\(705\) 0 0
\(706\) −2.56306e9 3.52776e9i −0.274121 0.377296i
\(707\) −3.17939e9 + 1.03305e9i −0.338358 + 0.109939i
\(708\) 0 0
\(709\) 9.07886e9 + 6.59617e9i 0.956686 + 0.695073i 0.952379 0.304918i \(-0.0986290\pi\)
0.00430709 + 0.999991i \(0.498629\pi\)
\(710\) 4.03028e9 + 2.92817e9i 0.422602 + 0.307038i
\(711\) 0 0
\(712\) 1.01423e10 3.29544e9i 1.05307 0.342163i
\(713\) 5.01600e9 + 6.90394e9i 0.518256 + 0.713319i
\(714\) 0 0
\(715\) 5.26843e9 8.48714e9i 0.539026 0.868341i
\(716\) 6.69555e9i 0.681696i
\(717\) 0 0
\(718\) −5.86830e8 1.80608e9i −0.0591666 0.182096i
\(719\) −1.50105e10 4.87721e9i −1.50607 0.489351i −0.564287 0.825579i \(-0.690849\pi\)
−0.941781 + 0.336228i \(0.890849\pi\)
\(720\) 0 0
\(721\) −4.77485e9 + 6.57201e9i −0.474445 + 0.653018i
\(722\) 4.26131e8 1.31150e9i 0.0421369 0.129684i
\(723\) 0 0
\(724\) 2.84749e9 2.06883e9i 0.278855 0.202600i
\(725\) −1.77179e10 −1.72675
\(726\) 0 0
\(727\) 4.96655e9 0.479384 0.239692 0.970849i \(-0.422953\pi\)
0.239692 + 0.970849i \(0.422953\pi\)
\(728\) 1.21164e9 8.80307e8i 0.116389 0.0845619i
\(729\) 0 0
\(730\) −4.06104e9 + 1.24986e10i −0.386373 + 1.18913i
\(731\) −3.20344e9 + 4.40916e9i −0.303323 + 0.417489i
\(732\) 0 0
\(733\) 5.26982e9 + 1.71227e9i 0.494233 + 0.160586i 0.545520 0.838098i \(-0.316332\pi\)
−0.0512867 + 0.998684i \(0.516332\pi\)
\(734\) −2.05782e9 6.33332e9i −0.192075 0.591147i
\(735\) 0 0
\(736\) 1.40071e10i 1.29502i
\(737\) −3.99134e9 + 6.42983e9i −0.367268 + 0.591648i
\(738\) 0 0
\(739\) −9.17761e9 1.26319e10i −0.836516 1.15137i −0.986675 0.162703i \(-0.947979\pi\)
0.150159 0.988662i \(-0.452021\pi\)
\(740\) 1.95971e9 6.36748e8i 0.177779 0.0577639i
\(741\) 0 0
\(742\) 9.04502e8 + 6.57159e8i 0.0812822 + 0.0590550i
\(743\) 9.14165e9 + 6.64180e9i 0.817643 + 0.594053i 0.916036 0.401095i \(-0.131370\pi\)
−0.0983931 + 0.995148i \(0.531370\pi\)
\(744\) 0 0
\(745\) −2.53517e10 + 8.23725e9i −2.24626 + 0.729853i
\(746\) −7.60892e8 1.04728e9i −0.0671023 0.0923584i
\(747\) 0 0
\(748\) −1.09114e9 1.49661e10i −0.0953290 1.30754i
\(749\) 6.44818e9i 0.560726i
\(750\) 0 0
\(751\) 2.35142e9 + 7.23692e9i 0.202577 + 0.623468i 0.999804 + 0.0197886i \(0.00629932\pi\)
−0.797227 + 0.603679i \(0.793701\pi\)
\(752\) −3.71204e9 1.20611e9i −0.318310 0.103425i
\(753\) 0 0
\(754\) −8.67044e8 + 1.19338e9i −0.0736617 + 0.101387i
\(755\) −1.19210e10 + 3.66890e10i −1.00808 + 3.10257i
\(756\) 0 0
\(757\) −8.04486e9 + 5.84493e9i −0.674036 + 0.489716i −0.871374 0.490620i \(-0.836770\pi\)
0.197338 + 0.980336i \(0.436770\pi\)
\(758\) −6.81610e9 −0.568452
\(759\) 0 0
\(760\) 1.14627e10 0.947197
\(761\) 6.05726e9 4.40086e9i 0.498230 0.361985i −0.310110 0.950701i \(-0.600366\pi\)
0.808341 + 0.588715i \(0.200366\pi\)
\(762\) 0 0
\(763\) 1.70759e8 5.25543e8i 0.0139171 0.0428324i
\(764\) −7.79483e9 + 1.07287e10i −0.632382 + 0.870399i
\(765\) 0 0
\(766\) −4.22181e9 1.37175e9i −0.339389 0.110274i
\(767\) −2.75719e7 8.48577e7i −0.00220640 0.00679059i
\(768\) 0 0
\(769\) 2.02351e10i 1.60459i −0.596930 0.802293i \(-0.703613\pi\)
0.596930 0.802293i \(-0.296387\pi\)
\(770\) 2.17717e9 + 2.57907e9i 0.171860 + 0.203585i
\(771\) 0 0
\(772\) −3.16434e9 4.35534e9i −0.247527 0.340692i
\(773\) 2.18448e10 7.09781e9i 1.70106 0.552708i 0.712256 0.701920i \(-0.247674\pi\)
0.988805 +