Properties

Label 5.9.c.a.3.2
Level $5$
Weight $9$
Character 5.3
Analytic conductor $2.037$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 5 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 5.c (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.03689305031\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
Defining polynomial: \(x^{6} - 2 x^{5} + 2 x^{4} - 30 x^{3} + 1089 x^{2} - 3168 x + 4608\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{6}\cdot 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 3.2
Root \(-4.23471 - 4.23471i\) of defining polynomial
Character \(\chi\) \(=\) 5.3
Dual form 5.9.c.a.2.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.39608 + 4.39608i) q^{2} +(75.2981 + 75.2981i) q^{3} +217.349i q^{4} +(-14.1685 - 624.839i) q^{5} -662.032 q^{6} +(730.992 - 730.992i) q^{7} +(-2080.88 - 2080.88i) q^{8} +4778.60i q^{9} +O(q^{10})\) \(q+(-4.39608 + 4.39608i) q^{2} +(75.2981 + 75.2981i) q^{3} +217.349i q^{4} +(-14.1685 - 624.839i) q^{5} -662.032 q^{6} +(730.992 - 730.992i) q^{7} +(-2080.88 - 2080.88i) q^{8} +4778.60i q^{9} +(2809.13 + 2684.56i) q^{10} +19599.8 q^{11} +(-16366.0 + 16366.0i) q^{12} +(-24915.1 - 24915.1i) q^{13} +6426.99i q^{14} +(45982.3 - 48116.1i) q^{15} -37346.0 q^{16} +(-11288.6 + 11288.6i) q^{17} +(-21007.1 - 21007.1i) q^{18} +171525. i q^{19} +(135808. - 3079.51i) q^{20} +110085. q^{21} +(-86162.2 + 86162.2i) q^{22} +(-132074. - 132074. i) q^{23} -313372. i q^{24} +(-390224. + 17706.1i) q^{25} +219057. q^{26} +(134211. - 134211. i) q^{27} +(158880. + 158880. i) q^{28} +127019. i q^{29} +(9380.00 + 413664. i) q^{30} -960715. q^{31} +(696880. - 696880. i) q^{32} +(1.47583e6 + 1.47583e6i) q^{33} -99251.5i q^{34} +(-467110. - 446396. i) q^{35} -1.03862e6 q^{36} +(-243873. + 243873. i) q^{37} +(-754036. - 754036. i) q^{38} -3.75212e6i q^{39} +(-1.27073e6 + 1.32970e6i) q^{40} +2.50747e6 q^{41} +(-483940. + 483940. i) q^{42} +(-6763.95 - 6763.95i) q^{43} +4.26000e6i q^{44} +(2.98586e6 - 67705.6i) q^{45} +1.16122e6 q^{46} +(-1.79394e6 + 1.79394e6i) q^{47} +(-2.81208e6 - 2.81208e6i) q^{48} +4.69610e6i q^{49} +(1.63761e6 - 1.79329e6i) q^{50} -1.70003e6 q^{51} +(5.41527e6 - 5.41527e6i) q^{52} +(-2.97161e6 - 2.97161e6i) q^{53} +1.18001e6i q^{54} +(-277700. - 1.22467e7i) q^{55} -3.04221e6 q^{56} +(-1.29155e7 + 1.29155e7i) q^{57} +(-558385. - 558385. i) q^{58} -313805. i q^{59} +(1.04580e7 + 9.99422e6i) q^{60} +1.76977e7 q^{61} +(4.22338e6 - 4.22338e6i) q^{62} +(3.49312e6 + 3.49312e6i) q^{63} -3.43349e6i q^{64} +(-1.52149e7 + 1.59209e7i) q^{65} -1.29757e7 q^{66} +(4.41349e6 - 4.41349e6i) q^{67} +(-2.45358e6 - 2.45358e6i) q^{68} -1.98899e7i q^{69} +(4.01584e6 - 91060.8i) q^{70} -8.89315e6 q^{71} +(9.94368e6 - 9.94368e6i) q^{72} +(1.95076e7 + 1.95076e7i) q^{73} -2.14417e6i q^{74} +(-3.07163e7 - 2.80498e7i) q^{75} -3.72808e7 q^{76} +(1.43273e7 - 1.43273e7i) q^{77} +(1.64946e7 + 1.64946e7i) q^{78} +1.11272e7i q^{79} +(529136. + 2.33352e7i) q^{80} +5.15641e7 q^{81} +(-1.10230e7 + 1.10230e7i) q^{82} +(1.58712e7 + 1.58712e7i) q^{83} +2.39268e7i q^{84} +(7.21353e6 + 6.89365e6i) q^{85} +59469.7 q^{86} +(-9.56429e6 + 9.56429e6i) q^{87} +(-4.07848e7 - 4.07848e7i) q^{88} -4.85032e7i q^{89} +(-1.28284e7 + 1.34237e7i) q^{90} -3.64255e7 q^{91} +(2.87062e7 - 2.87062e7i) q^{92} +(-7.23400e7 - 7.23400e7i) q^{93} -1.57726e7i q^{94} +(1.07176e8 - 2.43025e6i) q^{95} +1.04948e8 q^{96} +(-1.07411e8 + 1.07411e8i) q^{97} +(-2.06444e7 - 2.06444e7i) q^{98} +9.36596e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 2q^{2} - 72q^{3} + 220q^{5} + 1752q^{6} - 2352q^{7} - 8220q^{8} + O(q^{10}) \) \( 6q - 2q^{2} - 72q^{3} + 220q^{5} + 1752q^{6} - 2352q^{7} - 8220q^{8} + 30870q^{10} + 23192q^{11} - 45912q^{12} - 119142q^{13} + 241440q^{15} + 218616q^{16} - 265502q^{17} - 454062q^{18} + 412260q^{20} + 231672q^{21} - 35664q^{22} + 28888q^{23} - 340350q^{25} - 801388q^{26} + 392040q^{27} + 1305192q^{28} - 2549760q^{30} - 747648q^{31} + 3033928q^{32} + 4269096q^{33} - 4971680q^{35} - 3972804q^{36} - 454002q^{37} + 1443720q^{38} + 2683500q^{40} + 2489432q^{41} + 4223856q^{42} + 792648q^{43} + 210690q^{45} - 3149928q^{46} - 15313352q^{47} - 21677712q^{48} + 29537650q^{50} + 35567712q^{51} - 735732q^{52} - 13509122q^{53} + 4448040q^{55} - 18454800q^{56} - 34625520q^{57} - 23903520q^{58} + 13688520q^{60} + 24111192q^{61} + 53913416q^{62} + 44837688q^{63} - 30943610q^{65} - 55047936q^{66} - 32827752q^{67} + 8118692q^{68} - 44156280q^{70} - 13992928q^{71} + 82596420q^{72} + 111859638q^{73} - 126793200q^{75} - 56470800q^{76} + 26260136q^{77} + 31125576q^{78} + 23045920q^{80} + 65834226q^{81} + 38023056q^{82} - 14768432q^{83} - 19713030q^{85} - 135560008q^{86} - 133207680q^{87} - 44555040q^{88} + 135147990q^{90} + 167542032q^{91} + 69931048q^{92} - 96798024q^{93} + 239661000q^{95} + 184867872q^{96} - 186656202q^{97} - 345959698q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.39608 + 4.39608i −0.274755 + 0.274755i −0.831011 0.556256i \(-0.812237\pi\)
0.556256 + 0.831011i \(0.312237\pi\)
\(3\) 75.2981 + 75.2981i 0.929606 + 0.929606i 0.997680 0.0680745i \(-0.0216855\pi\)
−0.0680745 + 0.997680i \(0.521686\pi\)
\(4\) 217.349i 0.849020i
\(5\) −14.1685 624.839i −0.0226696 0.999743i
\(6\) −662.032 −0.510827
\(7\) 730.992 730.992i 0.304453 0.304453i −0.538300 0.842753i \(-0.680933\pi\)
0.842753 + 0.538300i \(0.180933\pi\)
\(8\) −2080.88 2080.88i −0.508027 0.508027i
\(9\) 4778.60i 0.728334i
\(10\) 2809.13 + 2684.56i 0.280913 + 0.268456i
\(11\) 19599.8 1.33869 0.669347 0.742950i \(-0.266574\pi\)
0.669347 + 0.742950i \(0.266574\pi\)
\(12\) −16366.0 + 16366.0i −0.789254 + 0.789254i
\(13\) −24915.1 24915.1i −0.872347 0.872347i 0.120381 0.992728i \(-0.461588\pi\)
−0.992728 + 0.120381i \(0.961588\pi\)
\(14\) 6426.99i 0.167300i
\(15\) 45982.3 48116.1i 0.908293 0.950441i
\(16\) −37346.0 −0.569854
\(17\) −11288.6 + 11288.6i −0.135159 + 0.135159i −0.771450 0.636290i \(-0.780468\pi\)
0.636290 + 0.771450i \(0.280468\pi\)
\(18\) −21007.1 21007.1i −0.200113 0.200113i
\(19\) 171525.i 1.31617i 0.752943 + 0.658086i \(0.228634\pi\)
−0.752943 + 0.658086i \(0.771366\pi\)
\(20\) 135808. 3079.51i 0.848802 0.0192469i
\(21\) 110085. 0.566043
\(22\) −86162.2 + 86162.2i −0.367812 + 0.367812i
\(23\) −132074. 132074.i −0.471961 0.471961i 0.430587 0.902549i \(-0.358306\pi\)
−0.902549 + 0.430587i \(0.858306\pi\)
\(24\) 313372.i 0.944529i
\(25\) −390224. + 17706.1i −0.998972 + 0.0453275i
\(26\) 219057. 0.479363
\(27\) 134211. 134211.i 0.252542 0.252542i
\(28\) 158880. + 158880.i 0.258487 + 0.258487i
\(29\) 127019.i 0.179588i 0.995960 + 0.0897939i \(0.0286208\pi\)
−0.995960 + 0.0897939i \(0.971379\pi\)
\(30\) 9380.00 + 413664.i 0.0115802 + 0.510696i
\(31\) −960715. −1.04027 −0.520137 0.854083i \(-0.674119\pi\)
−0.520137 + 0.854083i \(0.674119\pi\)
\(32\) 696880. 696880.i 0.664597 0.664597i
\(33\) 1.47583e6 + 1.47583e6i 1.24446 + 1.24446i
\(34\) 99251.5i 0.0742713i
\(35\) −467110. 446396.i −0.311277 0.297473i
\(36\) −1.03862e6 −0.618370
\(37\) −243873. + 243873.i −0.130124 + 0.130124i −0.769169 0.639045i \(-0.779330\pi\)
0.639045 + 0.769169i \(0.279330\pi\)
\(38\) −754036. 754036.i −0.361625 0.361625i
\(39\) 3.75212e6i 1.62188i
\(40\) −1.27073e6 + 1.32970e6i −0.496380 + 0.519413i
\(41\) 2.50747e6 0.887360 0.443680 0.896185i \(-0.353673\pi\)
0.443680 + 0.896185i \(0.353673\pi\)
\(42\) −483940. + 483940.i −0.155523 + 0.155523i
\(43\) −6763.95 6763.95i −0.00197846 0.00197846i 0.706117 0.708095i \(-0.250445\pi\)
−0.708095 + 0.706117i \(0.750445\pi\)
\(44\) 4.26000e6i 1.13658i
\(45\) 2.98586e6 67705.6i 0.728147 0.0165110i
\(46\) 1.16122e6 0.259347
\(47\) −1.79394e6 + 1.79394e6i −0.367635 + 0.367635i −0.866614 0.498979i \(-0.833709\pi\)
0.498979 + 0.866614i \(0.333709\pi\)
\(48\) −2.81208e6 2.81208e6i −0.529740 0.529740i
\(49\) 4.69610e6i 0.814617i
\(50\) 1.63761e6 1.79329e6i 0.262018 0.286926i
\(51\) −1.70003e6 −0.251290
\(52\) 5.41527e6 5.41527e6i 0.740640 0.740640i
\(53\) −2.97161e6 2.97161e6i −0.376608 0.376608i 0.493269 0.869877i \(-0.335802\pi\)
−0.869877 + 0.493269i \(0.835802\pi\)
\(54\) 1.18001e6i 0.138774i
\(55\) −277700. 1.22467e7i −0.0303476 1.33835i
\(56\) −3.04221e6 −0.309341
\(57\) −1.29155e7 + 1.29155e7i −1.22352 + 1.22352i
\(58\) −558385. 558385.i −0.0493426 0.0493426i
\(59\) 313805.i 0.0258972i −0.999916 0.0129486i \(-0.995878\pi\)
0.999916 0.0129486i \(-0.00412178\pi\)
\(60\) 1.04580e7 + 9.99422e6i 0.806943 + 0.771159i
\(61\) 1.76977e7 1.27820 0.639098 0.769125i \(-0.279308\pi\)
0.639098 + 0.769125i \(0.279308\pi\)
\(62\) 4.22338e6 4.22338e6i 0.285820 0.285820i
\(63\) 3.49312e6 + 3.49312e6i 0.221744 + 0.221744i
\(64\) 3.43349e6i 0.204652i
\(65\) −1.52149e7 + 1.59209e7i −0.852347 + 0.891899i
\(66\) −1.29757e7 −0.683841
\(67\) 4.41349e6 4.41349e6i 0.219020 0.219020i −0.589066 0.808085i \(-0.700504\pi\)
0.808085 + 0.589066i \(0.200504\pi\)
\(68\) −2.45358e6 2.45358e6i −0.114753 0.114753i
\(69\) 1.98899e7i 0.877476i
\(70\) 4.01584e6 91060.8i 0.167257 0.00379262i
\(71\) −8.89315e6 −0.349963 −0.174982 0.984572i \(-0.555987\pi\)
−0.174982 + 0.984572i \(0.555987\pi\)
\(72\) 9.94368e6 9.94368e6i 0.370013 0.370013i
\(73\) 1.95076e7 + 1.95076e7i 0.686928 + 0.686928i 0.961552 0.274624i \(-0.0885532\pi\)
−0.274624 + 0.961552i \(0.588553\pi\)
\(74\) 2.14417e6i 0.0715043i
\(75\) −3.07163e7 2.80498e7i −0.970787 0.886514i
\(76\) −3.72808e7 −1.11746
\(77\) 1.43273e7 1.43273e7i 0.407569 0.407569i
\(78\) 1.64946e7 + 1.64946e7i 0.445619 + 0.445619i
\(79\) 1.11272e7i 0.285680i 0.989746 + 0.142840i \(0.0456234\pi\)
−0.989746 + 0.142840i \(0.954377\pi\)
\(80\) 529136. + 2.33352e7i 0.0129184 + 0.569708i
\(81\) 5.15641e7 1.19786
\(82\) −1.10230e7 + 1.10230e7i −0.243806 + 0.243806i
\(83\) 1.58712e7 + 1.58712e7i 0.334423 + 0.334423i 0.854264 0.519840i \(-0.174008\pi\)
−0.519840 + 0.854264i \(0.674008\pi\)
\(84\) 2.39268e7i 0.480581i
\(85\) 7.21353e6 + 6.89365e6i 0.138189 + 0.132061i
\(86\) 59469.7 0.00108718
\(87\) −9.56429e6 + 9.56429e6i −0.166946 + 0.166946i
\(88\) −4.07848e7 4.07848e7i −0.680092 0.680092i
\(89\) 4.85032e7i 0.773056i −0.922278 0.386528i \(-0.873674\pi\)
0.922278 0.386528i \(-0.126326\pi\)
\(90\) −1.28284e7 + 1.34237e7i −0.195525 + 0.204598i
\(91\) −3.64255e7 −0.531178
\(92\) 2.87062e7 2.87062e7i 0.400704 0.400704i
\(93\) −7.23400e7 7.23400e7i −0.967045 0.967045i
\(94\) 1.57726e7i 0.202019i
\(95\) 1.07176e8 2.43025e6i 1.31583 0.0298371i
\(96\) 1.04948e8 1.23563
\(97\) −1.07411e8 + 1.07411e8i −1.21329 + 1.21329i −0.243348 + 0.969939i \(0.578246\pi\)
−0.969939 + 0.243348i \(0.921754\pi\)
\(98\) −2.06444e7 2.06444e7i −0.223820 0.223820i
\(99\) 9.36596e7i 0.975016i
\(100\) −3.84840e6 8.48147e7i −0.0384840 0.848147i
\(101\) −7.16023e7 −0.688084 −0.344042 0.938954i \(-0.611796\pi\)
−0.344042 + 0.938954i \(0.611796\pi\)
\(102\) 7.47344e6 7.47344e6i 0.0690431 0.0690431i
\(103\) 9.89158e7 + 9.89158e7i 0.878854 + 0.878854i 0.993416 0.114562i \(-0.0365464\pi\)
−0.114562 + 0.993416i \(0.536546\pi\)
\(104\) 1.03691e8i 0.886352i
\(105\) −1.55973e6 6.87852e7i −0.0128320 0.565897i
\(106\) 2.61269e7 0.206949
\(107\) 4.73497e7 4.73497e7i 0.361228 0.361228i −0.503037 0.864265i \(-0.667784\pi\)
0.864265 + 0.503037i \(0.167784\pi\)
\(108\) 2.91707e7 + 2.91707e7i 0.214414 + 0.214414i
\(109\) 2.29072e7i 0.162280i −0.996703 0.0811401i \(-0.974144\pi\)
0.996703 0.0811401i \(-0.0258561\pi\)
\(110\) 5.50583e7 + 5.26168e7i 0.376056 + 0.359380i
\(111\) −3.67264e7 −0.241928
\(112\) −2.72996e7 + 2.72996e7i −0.173494 + 0.173494i
\(113\) −1.95361e8 1.95361e8i −1.19819 1.19819i −0.974709 0.223480i \(-0.928258\pi\)
−0.223480 0.974709i \(-0.571742\pi\)
\(114\) 1.13555e8i 0.672337i
\(115\) −8.06538e7 + 8.43964e7i −0.461141 + 0.482539i
\(116\) −2.76075e7 −0.152474
\(117\) 1.19059e8 1.19059e8i 0.635360 0.635360i
\(118\) 1.37951e6 + 1.37951e6i 0.00711537 + 0.00711537i
\(119\) 1.65038e7i 0.0822994i
\(120\) −1.95807e8 + 4.44001e6i −0.944287 + 0.0214121i
\(121\) 1.69794e8 0.792100
\(122\) −7.78004e7 + 7.78004e7i −0.351190 + 0.351190i
\(123\) 1.88808e8 + 1.88808e8i 0.824895 + 0.824895i
\(124\) 2.08811e8i 0.883213i
\(125\) 1.65923e7 + 2.43576e8i 0.0679622 + 0.997688i
\(126\) −3.07120e7 −0.121850
\(127\) 1.84792e8 1.84792e8i 0.710343 0.710343i −0.256264 0.966607i \(-0.582492\pi\)
0.966607 + 0.256264i \(0.0824917\pi\)
\(128\) 1.93495e8 + 1.93495e8i 0.720826 + 0.720826i
\(129\) 1.01862e6i 0.00367837i
\(130\) −3.10371e6 1.36876e8i −0.0108670 0.479240i
\(131\) −3.05076e8 −1.03591 −0.517956 0.855407i \(-0.673307\pi\)
−0.517956 + 0.855407i \(0.673307\pi\)
\(132\) −3.20770e8 + 3.20770e8i −1.05657 + 1.05657i
\(133\) 1.25383e8 + 1.25383e8i 0.400713 + 0.400713i
\(134\) 3.88041e7i 0.120353i
\(135\) −8.57622e7 8.19590e7i −0.258203 0.246753i
\(136\) 4.69806e7 0.137329
\(137\) 3.75735e8 3.75735e8i 1.06659 1.06659i 0.0689766 0.997618i \(-0.478027\pi\)
0.997618 0.0689766i \(-0.0219734\pi\)
\(138\) 8.74373e7 + 8.74373e7i 0.241091 + 0.241091i
\(139\) 1.10575e8i 0.296208i −0.988972 0.148104i \(-0.952683\pi\)
0.988972 0.148104i \(-0.0473171\pi\)
\(140\) 9.70236e7 1.01526e8i 0.252560 0.264280i
\(141\) −2.70161e8 −0.683512
\(142\) 3.90950e7 3.90950e7i 0.0961540 0.0961540i
\(143\) −4.88331e8 4.88331e8i −1.16781 1.16781i
\(144\) 1.78461e8i 0.415044i
\(145\) 7.93665e7 1.79967e6i 0.179542 0.00407118i
\(146\) −1.71513e8 −0.377474
\(147\) −3.53607e8 + 3.53607e8i −0.757272 + 0.757272i
\(148\) −5.30056e7 5.30056e7i −0.110478 0.110478i
\(149\) 7.23744e8i 1.46838i 0.678942 + 0.734192i \(0.262439\pi\)
−0.678942 + 0.734192i \(0.737561\pi\)
\(150\) 2.58340e8 1.17220e7i 0.510302 0.0231545i
\(151\) 7.67246e8 1.47580 0.737899 0.674911i \(-0.235818\pi\)
0.737899 + 0.674911i \(0.235818\pi\)
\(152\) 3.56922e8 3.56922e8i 0.668651 0.668651i
\(153\) −5.39439e7 5.39439e7i −0.0984411 0.0984411i
\(154\) 1.25968e8i 0.223963i
\(155\) 1.36119e7 + 6.00293e8i 0.0235826 + 1.04001i
\(156\) 8.15519e8 1.37701
\(157\) −8.03264e8 + 8.03264e8i −1.32209 + 1.32209i −0.410001 + 0.912085i \(0.634472\pi\)
−0.912085 + 0.410001i \(0.865528\pi\)
\(158\) −4.89162e7 4.89162e7i −0.0784918 0.0784918i
\(159\) 4.47514e8i 0.700193i
\(160\) −4.45312e8 4.25565e8i −0.679492 0.649360i
\(161\) −1.93090e8 −0.287380
\(162\) −2.26680e8 + 2.26680e8i −0.329119 + 0.329119i
\(163\) −4.34915e8 4.34915e8i −0.616103 0.616103i 0.328426 0.944530i \(-0.393482\pi\)
−0.944530 + 0.328426i \(0.893482\pi\)
\(164\) 5.44996e8i 0.753386i
\(165\) 9.01245e8 9.43066e8i 1.21593 1.27235i
\(166\) −1.39542e8 −0.183769
\(167\) 7.16803e8 7.16803e8i 0.921582 0.921582i −0.0755590 0.997141i \(-0.524074\pi\)
0.997141 + 0.0755590i \(0.0240741\pi\)
\(168\) −2.29073e8 2.29073e8i −0.287565 0.287565i
\(169\) 4.25794e8i 0.521979i
\(170\) −6.20162e7 + 1.40624e6i −0.0742522 + 0.00168370i
\(171\) −8.19649e8 −0.958613
\(172\) 1.47014e6 1.47014e6i 0.00167975 0.00167975i
\(173\) 3.40359e8 + 3.40359e8i 0.379973 + 0.379973i 0.871092 0.491119i \(-0.163412\pi\)
−0.491119 + 0.871092i \(0.663412\pi\)
\(174\) 8.40907e7i 0.0917383i
\(175\) −2.72307e8 + 2.98193e8i −0.290340 + 0.317940i
\(176\) −7.31974e8 −0.762860
\(177\) 2.36289e7 2.36289e7i 0.0240741 0.0240741i
\(178\) 2.13224e8 + 2.13224e8i 0.212401 + 0.212401i
\(179\) 1.29181e9i 1.25830i −0.777283 0.629151i \(-0.783403\pi\)
0.777283 0.629151i \(-0.216597\pi\)
\(180\) 1.47157e7 + 6.48973e8i 0.0140182 + 0.618211i
\(181\) 1.92912e8 0.179740 0.0898700 0.995954i \(-0.471355\pi\)
0.0898700 + 0.995954i \(0.471355\pi\)
\(182\) 1.60129e8 1.60129e8i 0.145944 0.145944i
\(183\) 1.33260e9 + 1.33260e9i 1.18822 + 1.18822i
\(184\) 5.49660e8i 0.479538i
\(185\) 1.55837e8 + 1.48926e8i 0.133040 + 0.127141i
\(186\) 6.36024e8 0.531400
\(187\) −2.21255e8 + 2.21255e8i −0.180937 + 0.180937i
\(188\) −3.89912e8 3.89912e8i −0.312130 0.312130i
\(189\) 1.96215e8i 0.153775i
\(190\) −4.60468e8 + 4.81835e8i −0.353334 + 0.369729i
\(191\) 7.64646e8 0.574549 0.287274 0.957848i \(-0.407251\pi\)
0.287274 + 0.957848i \(0.407251\pi\)
\(192\) 2.58535e8 2.58535e8i 0.190246 0.190246i
\(193\) 1.15389e8 + 1.15389e8i 0.0831641 + 0.0831641i 0.747465 0.664301i \(-0.231271\pi\)
−0.664301 + 0.747465i \(0.731271\pi\)
\(194\) 9.44378e8i 0.666713i
\(195\) −2.34447e9 + 5.31619e7i −1.62146 + 0.0367673i
\(196\) −1.02069e9 −0.691626
\(197\) −9.95415e7 + 9.95415e7i −0.0660906 + 0.0660906i −0.739379 0.673289i \(-0.764881\pi\)
0.673289 + 0.739379i \(0.264881\pi\)
\(198\) −4.11735e8 4.11735e8i −0.267890 0.267890i
\(199\) 1.71187e9i 1.09159i −0.837919 0.545795i \(-0.816228\pi\)
0.837919 0.545795i \(-0.183772\pi\)
\(200\) 8.48852e8 + 7.75163e8i 0.530532 + 0.484477i
\(201\) 6.64655e8 0.407204
\(202\) 3.14769e8 3.14769e8i 0.189054 0.189054i
\(203\) 9.28499e7 + 9.28499e7i 0.0546761 + 0.0546761i
\(204\) 3.69499e8i 0.213350i
\(205\) −3.55271e7 1.56676e9i −0.0201161 0.887132i
\(206\) −8.69683e8 −0.482939
\(207\) 6.31129e8 6.31129e8i 0.343745 0.343745i
\(208\) 9.30479e8 + 9.30479e8i 0.497111 + 0.497111i
\(209\) 3.36185e9i 1.76195i
\(210\) 3.09242e8 + 2.95528e8i 0.159009 + 0.151957i
\(211\) −6.81230e8 −0.343688 −0.171844 0.985124i \(-0.554972\pi\)
−0.171844 + 0.985124i \(0.554972\pi\)
\(212\) 6.45878e8 6.45878e8i 0.319747 0.319747i
\(213\) −6.69637e8 6.69637e8i −0.325328 0.325328i
\(214\) 4.16305e8i 0.198498i
\(215\) −4.13055e6 + 4.32222e6i −0.00193310 + 0.00202280i
\(216\) −5.58555e8 −0.256597
\(217\) −7.02275e8 + 7.02275e8i −0.316715 + 0.316715i
\(218\) 1.00702e8 + 1.00702e8i 0.0445872 + 0.0445872i
\(219\) 2.93776e9i 1.27715i
\(220\) 2.66182e9 6.03578e7i 1.13628 0.0257657i
\(221\) 5.62515e8 0.235812
\(222\) 1.61452e8 1.61452e8i 0.0664708 0.0664708i
\(223\) 9.37608e8 + 9.37608e8i 0.379142 + 0.379142i 0.870793 0.491651i \(-0.163606\pi\)
−0.491651 + 0.870793i \(0.663606\pi\)
\(224\) 1.01883e9i 0.404677i
\(225\) −8.46102e7 1.86472e9i −0.0330136 0.727585i
\(226\) 1.71765e9 0.658416
\(227\) −3.47956e9 + 3.47956e9i −1.31045 + 1.31045i −0.389368 + 0.921082i \(0.627307\pi\)
−0.921082 + 0.389368i \(0.872693\pi\)
\(228\) −2.80717e9 2.80717e9i −1.03879 1.03879i
\(229\) 3.67273e9i 1.33551i −0.744382 0.667754i \(-0.767256\pi\)
0.744382 0.667754i \(-0.232744\pi\)
\(230\) −1.64527e7 7.25573e8i −0.00587930 0.259281i
\(231\) 2.15764e9 0.757758
\(232\) 2.64311e8 2.64311e8i 0.0912354 0.0912354i
\(233\) −3.62893e9 3.62893e9i −1.23128 1.23128i −0.963474 0.267801i \(-0.913703\pi\)
−0.267801 0.963474i \(-0.586297\pi\)
\(234\) 1.04679e9i 0.349136i
\(235\) 1.14634e9 + 1.09551e9i 0.375875 + 0.359207i
\(236\) 6.82053e7 0.0219872
\(237\) −8.37860e8 + 8.37860e8i −0.265569 + 0.265569i
\(238\) −7.25520e7 7.25520e7i −0.0226121 0.0226121i
\(239\) 2.64336e9i 0.810148i −0.914284 0.405074i \(-0.867246\pi\)
0.914284 0.405074i \(-0.132754\pi\)
\(240\) −1.71725e9 + 1.79694e9i −0.517595 + 0.541613i
\(241\) −7.20231e7 −0.0213503 −0.0106751 0.999943i \(-0.503398\pi\)
−0.0106751 + 0.999943i \(0.503398\pi\)
\(242\) −7.46425e8 + 7.46425e8i −0.217633 + 0.217633i
\(243\) 3.00212e9 + 3.00212e9i 0.860999 + 0.860999i
\(244\) 3.84658e9i 1.08521i
\(245\) 2.93431e9 6.65367e7i 0.814407 0.0184670i
\(246\) −1.66002e9 −0.453288
\(247\) 4.27356e9 4.27356e9i 1.14816 1.14816i
\(248\) 1.99913e9 + 1.99913e9i 0.528487 + 0.528487i
\(249\) 2.39014e9i 0.621764i
\(250\) −1.14372e9 9.97838e8i −0.292792 0.255447i
\(251\) 5.78911e7 0.0145854 0.00729268 0.999973i \(-0.497679\pi\)
0.00729268 + 0.999973i \(0.497679\pi\)
\(252\) −7.59226e8 + 7.59226e8i −0.188265 + 0.188265i
\(253\) −2.58863e9 2.58863e9i −0.631811 0.631811i
\(254\) 1.62472e9i 0.390340i
\(255\) 2.40868e7 + 1.06224e9i 0.00569664 + 0.251225i
\(256\) −8.22267e8 −0.191449
\(257\) −4.73425e8 + 4.73425e8i −0.108522 + 0.108522i −0.759283 0.650761i \(-0.774450\pi\)
0.650761 + 0.759283i \(0.274450\pi\)
\(258\) 4.47795e6 + 4.47795e6i 0.00101065 + 0.00101065i
\(259\) 3.56539e8i 0.0792333i
\(260\) −3.46040e9 3.30695e9i −0.757240 0.723660i
\(261\) −6.06973e8 −0.130800
\(262\) 1.34114e9 1.34114e9i 0.284622 0.284622i
\(263\) 6.55957e9 + 6.55957e9i 1.37105 + 1.37105i 0.858893 + 0.512155i \(0.171153\pi\)
0.512155 + 0.858893i \(0.328847\pi\)
\(264\) 6.14204e9i 1.26444i
\(265\) −1.81468e9 + 1.89889e9i −0.367973 + 0.385048i
\(266\) −1.10239e9 −0.220195
\(267\) 3.65220e9 3.65220e9i 0.718637 0.718637i
\(268\) 9.59269e8 + 9.59269e8i 0.185952 + 0.185952i
\(269\) 5.38818e9i 1.02904i −0.857478 0.514521i \(-0.827970\pi\)
0.857478 0.514521i \(-0.172030\pi\)
\(270\) 7.37315e8 1.67189e7i 0.138739 0.00314596i
\(271\) −8.79497e9 −1.63064 −0.815318 0.579013i \(-0.803438\pi\)
−0.815318 + 0.579013i \(0.803438\pi\)
\(272\) 4.21585e8 4.21585e8i 0.0770211 0.0770211i
\(273\) −2.74277e9 2.74277e9i −0.493786 0.493786i
\(274\) 3.30352e9i 0.586104i
\(275\) −7.64831e9 + 3.47036e8i −1.33732 + 0.0606797i
\(276\) 4.32304e9 0.744994
\(277\) −4.78151e9 + 4.78151e9i −0.812168 + 0.812168i −0.984959 0.172790i \(-0.944722\pi\)
0.172790 + 0.984959i \(0.444722\pi\)
\(278\) 4.86096e8 + 4.86096e8i 0.0813846 + 0.0813846i
\(279\) 4.59087e9i 0.757667i
\(280\) 4.31035e7 + 1.90089e9i 0.00701263 + 0.309261i
\(281\) 1.22255e10 1.96083 0.980416 0.196936i \(-0.0630990\pi\)
0.980416 + 0.196936i \(0.0630990\pi\)
\(282\) 1.18765e9 1.18765e9i 0.187798 0.187798i
\(283\) −2.86857e8 2.86857e8i −0.0447219 0.0447219i 0.684392 0.729114i \(-0.260068\pi\)
−0.729114 + 0.684392i \(0.760068\pi\)
\(284\) 1.93292e9i 0.297126i
\(285\) 8.25310e9 + 7.88712e9i 1.25094 + 1.19547i
\(286\) 4.29348e9 0.641720
\(287\) 1.83294e9 1.83294e9i 0.270160 0.270160i
\(288\) 3.33011e9 + 3.33011e9i 0.484048 + 0.484048i
\(289\) 6.72089e9i 0.963464i
\(290\) −3.40990e8 + 3.56813e8i −0.0482113 + 0.0504485i
\(291\) −1.61757e10 −2.25576
\(292\) −4.23995e9 + 4.23995e9i −0.583216 + 0.583216i
\(293\) −1.02814e9 1.02814e9i −0.139503 0.139503i 0.633907 0.773410i \(-0.281450\pi\)
−0.773410 + 0.633907i \(0.781450\pi\)
\(294\) 3.10897e9i 0.416128i
\(295\) −1.96078e8 + 4.44615e6i −0.0258905 + 0.000587078i
\(296\) 1.01494e9 0.132213
\(297\) 2.63052e9 2.63052e9i 0.338077 0.338077i
\(298\) −3.18163e9 3.18163e9i −0.403445 0.403445i
\(299\) 6.58128e9i 0.823428i
\(300\) 6.09661e9 6.67616e9i 0.752667 0.824217i
\(301\) −9.88879e6 −0.00120469
\(302\) −3.37287e9 + 3.37287e9i −0.405482 + 0.405482i
\(303\) −5.39151e9 5.39151e9i −0.639647 0.639647i
\(304\) 6.40576e9i 0.750026i
\(305\) −2.50750e8 1.10582e10i −0.0289762 1.27787i
\(306\) 4.74283e8 0.0540943
\(307\) 7.92159e9 7.92159e9i 0.891783 0.891783i −0.102908 0.994691i \(-0.532815\pi\)
0.994691 + 0.102908i \(0.0328148\pi\)
\(308\) 3.11403e9 + 3.11403e9i 0.346034 + 0.346034i
\(309\) 1.48963e10i 1.63398i
\(310\) −2.69877e9 2.57909e9i −0.292226 0.279267i
\(311\) 3.74059e9 0.399851 0.199926 0.979811i \(-0.435930\pi\)
0.199926 + 0.979811i \(0.435930\pi\)
\(312\) −7.80770e9 + 7.80770e9i −0.823958 + 0.823958i
\(313\) −4.79633e9 4.79633e9i −0.499725 0.499725i 0.411627 0.911352i \(-0.364961\pi\)
−0.911352 + 0.411627i \(0.864961\pi\)
\(314\) 7.06242e9i 0.726499i
\(315\) 2.13314e9 2.23213e9i 0.216660 0.226713i
\(316\) −2.41850e9 −0.242548
\(317\) −5.54903e9 + 5.54903e9i −0.549516 + 0.549516i −0.926301 0.376785i \(-0.877030\pi\)
0.376785 + 0.926301i \(0.377030\pi\)
\(318\) 1.96730e9 + 1.96730e9i 0.192381 + 0.192381i
\(319\) 2.48955e9i 0.240413i
\(320\) −2.14538e9 + 4.86474e7i −0.204599 + 0.00463937i
\(321\) 7.13068e9 0.671600
\(322\) 8.48839e8 8.48839e8i 0.0789591 0.0789591i
\(323\) −1.93628e9 1.93628e9i −0.177893 0.177893i
\(324\) 1.12074e10i 1.01701i
\(325\) 1.01636e10 + 9.28131e9i 0.910992 + 0.831909i
\(326\) 3.82384e9 0.338555
\(327\) 1.72487e9 1.72487e9i 0.150857 0.150857i
\(328\) −5.21774e9 5.21774e9i −0.450803 0.450803i
\(329\) 2.62272e9i 0.223855i
\(330\) 1.83846e8 + 8.10773e9i 0.0155024 + 0.683665i
\(331\) 1.49782e10 1.24780 0.623902 0.781503i \(-0.285546\pi\)
0.623902 + 0.781503i \(0.285546\pi\)
\(332\) −3.44958e9 + 3.44958e9i −0.283932 + 0.283932i
\(333\) −1.16537e9 1.16537e9i −0.0947737 0.0947737i
\(334\) 6.30224e9i 0.506418i
\(335\) −2.82026e9 2.69519e9i −0.223929 0.213998i
\(336\) −4.11121e9 −0.322562
\(337\) 6.29203e9 6.29203e9i 0.487833 0.487833i −0.419789 0.907622i \(-0.637896\pi\)
0.907622 + 0.419789i \(0.137896\pi\)
\(338\) −1.87182e9 1.87182e9i −0.143416 0.143416i
\(339\) 2.94207e10i 2.22769i
\(340\) −1.49833e9 + 1.56785e9i −0.112122 + 0.117325i
\(341\) −1.88298e10 −1.39261
\(342\) 3.60324e9 3.60324e9i 0.263383 0.263383i
\(343\) 7.64684e9 + 7.64684e9i 0.552466 + 0.552466i
\(344\) 2.81499e7i 0.00201022i
\(345\) −1.24280e10 + 2.81809e8i −0.877251 + 0.0198920i
\(346\) −2.99249e9 −0.208799
\(347\) −8.28230e9 + 8.28230e9i −0.571259 + 0.571259i −0.932480 0.361221i \(-0.882360\pi\)
0.361221 + 0.932480i \(0.382360\pi\)
\(348\) −2.07879e9 2.07879e9i −0.141740 0.141740i
\(349\) 1.11611e10i 0.752328i −0.926553 0.376164i \(-0.877243\pi\)
0.926553 0.376164i \(-0.122757\pi\)
\(350\) −1.13797e8 2.50796e9i −0.00758329 0.167128i
\(351\) −6.68778e9 −0.440609
\(352\) 1.36587e10 1.36587e10i 0.889692 0.889692i
\(353\) 1.05904e10 + 1.05904e10i 0.682047 + 0.682047i 0.960461 0.278414i \(-0.0898088\pi\)
−0.278414 + 0.960461i \(0.589809\pi\)
\(354\) 2.07749e8i 0.0132290i
\(355\) 1.26003e8 + 5.55679e9i 0.00793352 + 0.349873i
\(356\) 1.05421e10 0.656339
\(357\) −1.24271e9 + 1.24271e9i −0.0765060 + 0.0765060i
\(358\) 5.67888e9 + 5.67888e9i 0.345725 + 0.345725i
\(359\) 9.48530e9i 0.571049i 0.958371 + 0.285524i \(0.0921677\pi\)
−0.958371 + 0.285524i \(0.907832\pi\)
\(360\) −6.35409e9 6.07232e9i −0.378306 0.361530i
\(361\) −1.24372e10 −0.732309
\(362\) −8.48055e8 + 8.48055e8i −0.0493844 + 0.0493844i
\(363\) 1.27851e10 + 1.27851e10i 0.736340 + 0.736340i
\(364\) 7.91704e9i 0.450980i
\(365\) 1.19127e10 1.24655e10i 0.671179 0.702324i
\(366\) −1.17164e10 −0.652937
\(367\) −9.59996e9 + 9.59996e9i −0.529182 + 0.529182i −0.920329 0.391146i \(-0.872079\pi\)
0.391146 + 0.920329i \(0.372079\pi\)
\(368\) 4.93244e9 + 4.93244e9i 0.268949 + 0.268949i
\(369\) 1.19822e10i 0.646295i
\(370\) −1.33976e9 + 3.03797e7i −0.0714860 + 0.00162097i
\(371\) −4.34445e9 −0.229319
\(372\) 1.57230e10 1.57230e10i 0.821040 0.821040i
\(373\) 8.48382e9 + 8.48382e9i 0.438285 + 0.438285i 0.891434 0.453150i \(-0.149700\pi\)
−0.453150 + 0.891434i \(0.649700\pi\)
\(374\) 1.94531e9i 0.0994265i
\(375\) −1.70914e10 + 1.95902e10i −0.864278 + 0.990634i
\(376\) 7.46595e9 0.373537
\(377\) 3.16469e9 3.16469e9i 0.156663 0.156663i
\(378\) 8.62576e8 + 8.62576e8i 0.0422503 + 0.0422503i
\(379\) 2.19075e10i 1.06178i −0.847440 0.530891i \(-0.821857\pi\)
0.847440 0.530891i \(-0.178143\pi\)
\(380\) 5.28212e8 + 2.32945e10i 0.0253323 + 1.11717i
\(381\) 2.78289e10 1.32068
\(382\) −3.36144e9 + 3.36144e9i −0.157860 + 0.157860i
\(383\) −2.31285e10 2.31285e10i −1.07486 1.07486i −0.996961 0.0778987i \(-0.975179\pi\)
−0.0778987 0.996961i \(-0.524821\pi\)
\(384\) 2.91396e10i 1.34017i
\(385\) −9.15526e9 8.74927e9i −0.416704 0.398225i
\(386\) −1.01452e9 −0.0456995
\(387\) 3.23222e7 3.23222e7i 0.00144098 0.00144098i
\(388\) −2.33458e10 2.33458e10i −1.03010 1.03010i
\(389\) 2.23175e10i 0.974647i −0.873221 0.487324i \(-0.837973\pi\)
0.873221 0.487324i \(-0.162027\pi\)
\(390\) 1.00728e10 1.05402e10i 0.435402 0.455606i
\(391\) 2.98188e9 0.127580
\(392\) 9.77202e9 9.77202e9i 0.413847 0.413847i
\(393\) −2.29716e10 2.29716e10i −0.962989 0.962989i
\(394\) 8.75184e8i 0.0363174i
\(395\) 6.95274e9 1.57656e8i 0.285606 0.00647624i
\(396\) −2.03568e10 −0.827807
\(397\) −2.26036e10 + 2.26036e10i −0.909947 + 0.909947i −0.996267 0.0863200i \(-0.972489\pi\)
0.0863200 + 0.996267i \(0.472489\pi\)
\(398\) 7.52553e9 + 7.52553e9i 0.299919 + 0.299919i
\(399\) 1.88822e10i 0.745010i
\(400\) 1.45733e10 6.61250e8i 0.569268 0.0258301i
\(401\) 1.77913e10 0.688064 0.344032 0.938958i \(-0.388207\pi\)
0.344032 + 0.938958i \(0.388207\pi\)
\(402\) −2.92187e9 + 2.92187e9i −0.111881 + 0.111881i
\(403\) 2.39363e10 + 2.39363e10i 0.907480 + 0.907480i
\(404\) 1.55627e10i 0.584197i
\(405\) −7.30586e8 3.22193e10i −0.0271551 1.19756i
\(406\) −8.16350e8 −0.0300450
\(407\) −4.77987e9 + 4.77987e9i −0.174196 + 0.174196i
\(408\) 3.53755e9 + 3.53755e9i 0.127662 + 0.127662i
\(409\) 4.37112e10i 1.56206i 0.624490 + 0.781032i \(0.285307\pi\)
−0.624490 + 0.781032i \(0.714693\pi\)
\(410\) 7.04380e9 + 6.73144e9i 0.249271 + 0.238217i
\(411\) 5.65843e10 1.98303
\(412\) −2.14993e10 + 2.14993e10i −0.746165 + 0.746165i
\(413\) −2.29389e8 2.29389e8i −0.00788447 0.00788447i
\(414\) 5.54898e9i 0.188891i
\(415\) 9.69206e9 1.01418e10i 0.326756 0.341919i
\(416\) −3.47257e10 −1.15952
\(417\) 8.32607e9 8.32607e9i 0.275357 0.275357i
\(418\) −1.47790e10 1.47790e10i −0.484104 0.484104i
\(419\) 2.98593e10i 0.968776i 0.874853 + 0.484388i \(0.160958\pi\)
−0.874853 + 0.484388i \(0.839042\pi\)
\(420\) 1.49504e10 3.39006e8i 0.480458 0.0108946i
\(421\) −5.33816e10 −1.69927 −0.849637 0.527368i \(-0.823179\pi\)
−0.849637 + 0.527368i \(0.823179\pi\)
\(422\) 2.99474e9 2.99474e9i 0.0944298 0.0944298i
\(423\) −8.57253e9 8.57253e9i −0.267761 0.267761i
\(424\) 1.23671e10i 0.382654i
\(425\) 4.20522e9 4.60497e9i 0.128894 0.141147i
\(426\) 5.88755e9 0.178771
\(427\) 1.29369e10 1.29369e10i 0.389151 0.389151i
\(428\) 1.02914e10 + 1.02914e10i 0.306690 + 0.306690i
\(429\) 7.35408e10i 2.17120i
\(430\) −842596. 3.71590e7i −2.46459e−5 0.00108690i
\(431\) 1.68739e10 0.488997 0.244499 0.969650i \(-0.421377\pi\)
0.244499 + 0.969650i \(0.421377\pi\)
\(432\) −5.01225e9 + 5.01225e9i −0.143912 + 0.143912i
\(433\) 7.15187e9 + 7.15187e9i 0.203455 + 0.203455i 0.801478 0.598024i \(-0.204047\pi\)
−0.598024 + 0.801478i \(0.704047\pi\)
\(434\) 6.17451e9i 0.174038i
\(435\) 6.11165e9 + 5.84063e9i 0.170688 + 0.163118i
\(436\) 4.97885e9 0.137779
\(437\) 2.26540e10 2.26540e10i 0.621182 0.621182i
\(438\) −1.29146e10 1.29146e10i −0.350902 0.350902i
\(439\) 2.62124e9i 0.0705747i −0.999377 0.0352873i \(-0.988765\pi\)
0.999377 0.0352873i \(-0.0112346\pi\)
\(440\) −2.49061e10 + 2.60618e10i −0.664500 + 0.695335i
\(441\) −2.24408e10 −0.593313
\(442\) −2.47286e9 + 2.47286e9i −0.0647904 + 0.0647904i
\(443\) −3.30317e10 3.30317e10i −0.857663 0.857663i 0.133400 0.991062i \(-0.457411\pi\)
−0.991062 + 0.133400i \(0.957411\pi\)
\(444\) 7.98244e9i 0.205402i
\(445\) −3.03067e10 + 6.87218e8i −0.772857 + 0.0175249i
\(446\) −8.24359e9 −0.208342
\(447\) −5.44965e10 + 5.44965e10i −1.36502 + 1.36502i
\(448\) −2.50985e9 2.50985e9i −0.0623069 0.0623069i
\(449\) 2.56081e10i 0.630074i 0.949079 + 0.315037i \(0.102017\pi\)
−0.949079 + 0.315037i \(0.897983\pi\)
\(450\) 8.56941e9 + 7.82550e9i 0.208978 + 0.190837i
\(451\) 4.91459e10 1.18790
\(452\) 4.24616e10 4.24616e10i 1.01729 1.01729i
\(453\) 5.77721e10 + 5.77721e10i 1.37191 + 1.37191i
\(454\) 3.05928e10i 0.720105i
\(455\) 5.16094e8 + 2.27601e10i 0.0120416 + 0.531041i
\(456\) 5.37511e10 1.24316
\(457\) 1.31162e10 1.31162e10i 0.300707 0.300707i −0.540583 0.841290i \(-0.681796\pi\)
0.841290 + 0.540583i \(0.181796\pi\)
\(458\) 1.61456e10 + 1.61456e10i 0.366937 + 0.366937i
\(459\) 3.03013e9i 0.0682669i
\(460\) −1.83435e10 1.75300e10i −0.409685 0.391518i
\(461\) −3.99207e10 −0.883883 −0.441942 0.897044i \(-0.645710\pi\)
−0.441942 + 0.897044i \(0.645710\pi\)
\(462\) −9.48513e9 + 9.48513e9i −0.208197 + 0.208197i
\(463\) 1.43482e10 + 1.43482e10i 0.312229 + 0.312229i 0.845772 0.533544i \(-0.179140\pi\)
−0.533544 + 0.845772i \(0.679140\pi\)
\(464\) 4.74365e9i 0.102339i
\(465\) −4.41759e10 + 4.62258e10i −0.944874 + 0.988719i
\(466\) 3.19061e10 0.676597
\(467\) 2.44200e10 2.44200e10i 0.513427 0.513427i −0.402148 0.915575i \(-0.631736\pi\)
0.915575 + 0.402148i \(0.131736\pi\)
\(468\) 2.58774e10 + 2.58774e10i 0.539433 + 0.539433i
\(469\) 6.45246e9i 0.133363i
\(470\) −9.85535e9 + 2.23474e8i −0.201967 + 0.00457969i
\(471\) −1.20968e11 −2.45804
\(472\) −6.52990e8 + 6.52990e8i −0.0131565 + 0.0131565i
\(473\) −1.32572e8 1.32572e8i −0.00264855 0.00264855i
\(474\) 7.36659e9i 0.145933i
\(475\) −3.03703e9 6.69330e10i −0.0596588 1.31482i
\(476\) −3.58709e9 −0.0698738
\(477\) 1.42002e10 1.42002e10i 0.274296 0.274296i
\(478\) 1.16204e10 + 1.16204e10i 0.222592 + 0.222592i
\(479\) 9.03857e9i 0.171695i 0.996308 + 0.0858475i \(0.0273598\pi\)
−0.996308 + 0.0858475i \(0.972640\pi\)
\(480\) −1.48695e9 6.55753e10i −0.0280111 1.23531i
\(481\) 1.21523e10 0.227026
\(482\) 3.16619e8 3.16619e8i 0.00586609 0.00586609i
\(483\) −1.45393e10 1.45393e10i −0.267150 0.267150i
\(484\) 3.69045e10i 0.672508i
\(485\) 6.86368e10 + 6.55930e10i 1.24048 + 1.18547i
\(486\) −2.63951e10 −0.473127
\(487\) 3.53950e10 3.53950e10i 0.629255 0.629255i −0.318626 0.947881i \(-0.603221\pi\)
0.947881 + 0.318626i \(0.103221\pi\)
\(488\) −3.68268e10 3.68268e10i −0.649358 0.649358i
\(489\) 6.54965e10i 1.14547i
\(490\) −1.26069e10 + 1.31919e10i −0.218688 + 0.228836i
\(491\) −5.87159e10 −1.01025 −0.505126 0.863045i \(-0.668554\pi\)
−0.505126 + 0.863045i \(0.668554\pi\)
\(492\) −4.10371e10 + 4.10371e10i −0.700352 + 0.700352i
\(493\) −1.43387e9 1.43387e9i −0.0242730 0.0242730i
\(494\) 3.75738e10i 0.630924i
\(495\) 5.85222e10 1.32702e9i 0.974765 0.0221032i
\(496\) 3.58788e10 0.592805
\(497\) −6.50082e9 + 6.50082e9i −0.106547 + 0.106547i
\(498\) −1.05072e10 1.05072e10i −0.170833 0.170833i
\(499\) 2.57394e10i 0.415141i −0.978220 0.207571i \(-0.933444\pi\)
0.978220 0.207571i \(-0.0665557\pi\)
\(500\) −5.29410e10 + 3.60633e9i −0.847057 + 0.0577012i
\(501\) 1.07948e11 1.71342
\(502\) −2.54494e8 + 2.54494e8i −0.00400740 + 0.00400740i
\(503\) −4.75499e10 4.75499e10i −0.742810 0.742810i 0.230308 0.973118i \(-0.426027\pi\)
−0.973118 + 0.230308i \(0.926027\pi\)
\(504\) 1.45375e10i 0.225303i
\(505\) 1.01450e9 + 4.47399e10i 0.0155986 + 0.687907i
\(506\) 2.27596e10 0.347186
\(507\) −3.20615e10 + 3.20615e10i −0.485235 + 0.485235i
\(508\) 4.01643e10 + 4.01643e10i 0.603095 + 0.603095i
\(509\) 8.69280e10i 1.29506i 0.762042 + 0.647528i \(0.224197\pi\)
−0.762042 + 0.647528i \(0.775803\pi\)
\(510\) −4.77559e9 4.56381e9i −0.0705905 0.0674601i
\(511\) 2.85197e10 0.418275
\(512\) −4.59200e10 + 4.59200e10i −0.668225 + 0.668225i
\(513\) 2.30206e10 + 2.30206e10i 0.332389 + 0.332389i
\(514\) 4.16243e9i 0.0596340i
\(515\) 6.04050e10 6.32080e10i 0.858705 0.898552i
\(516\) 2.21397e8 0.00312301
\(517\) −3.51609e10 + 3.51609e10i −0.492151 + 0.492151i
\(518\) −1.56737e9 1.56737e9i −0.0217697 0.0217697i
\(519\) 5.12568e10i 0.706451i
\(520\) 6.47900e10 1.46914e9i 0.886124 0.0200932i
\(521\) 6.44123e10 0.874214 0.437107 0.899409i \(-0.356003\pi\)
0.437107 + 0.899409i \(0.356003\pi\)
\(522\) 2.66830e9 2.66830e9i 0.0359379 0.0359379i
\(523\) −5.99903e10 5.99903e10i −0.801815 0.801815i 0.181564 0.983379i \(-0.441884\pi\)
−0.983379 + 0.181564i \(0.941884\pi\)
\(524\) 6.63079e10i 0.879509i
\(525\) −4.29576e10 + 1.94917e9i −0.565461 + 0.0256573i
\(526\) −5.76728e10 −0.753404
\(527\) 1.08452e10 1.08452e10i 0.140603 0.140603i
\(528\) −5.51162e10 5.51162e10i −0.709159 0.709159i
\(529\) 4.34238e10i 0.554505i
\(530\) −3.70179e8 1.63251e10i −0.00469146 0.206896i
\(531\) 1.49955e9 0.0188618
\(532\) −2.72519e10 + 2.72519e10i −0.340213 + 0.340213i
\(533\) −6.24738e10 6.24738e10i −0.774086 0.774086i
\(534\) 3.21107e10i 0.394898i
\(535\) −3.02568e10 2.89151e10i −0.369324 0.352947i
\(536\) −1.83679e10 −0.222536
\(537\) 9.72705e10 9.72705e10i 1.16973 1.16973i
\(538\) 2.36869e10 + 2.36869e10i 0.282734 + 0.282734i
\(539\) 9.20427e10i 1.09052i
\(540\) 1.78137e10 1.86403e10i 0.209498 0.219219i
\(541\) −9.38341e10 −1.09540 −0.547698 0.836676i \(-0.684496\pi\)
−0.547698 + 0.836676i \(0.684496\pi\)
\(542\) 3.86633e10 3.86633e10i 0.448025 0.448025i
\(543\) 1.45259e10 + 1.45259e10i 0.167087 + 0.167087i
\(544\) 1.57337e10i 0.179653i
\(545\) −1.43133e10 + 3.24560e8i −0.162238 + 0.00367883i
\(546\) 2.41148e10 0.271340
\(547\) 1.86813e10 1.86813e10i 0.208669 0.208669i −0.595032 0.803702i \(-0.702861\pi\)
0.803702 + 0.595032i \(0.202861\pi\)
\(548\) 8.16657e10 + 8.16657e10i 0.905560 + 0.905560i
\(549\) 8.45702e10i 0.930954i
\(550\) 3.20969e10 3.51481e10i 0.350762 0.384106i
\(551\) −2.17869e10 −0.236368
\(552\) −4.13884e10 + 4.13884e10i −0.445781 + 0.445781i
\(553\) 8.13393e9 + 8.13393e9i 0.0869761 + 0.0869761i
\(554\) 4.20398e10i 0.446294i
\(555\) 5.20357e8 + 2.29481e10i 0.00548441 + 0.241866i
\(556\) 2.40333e10 0.251487
\(557\) −4.32331e9 + 4.32331e9i −0.0449154 + 0.0449154i −0.729208 0.684292i \(-0.760111\pi\)
0.684292 + 0.729208i \(0.260111\pi\)
\(558\) 2.01818e10 + 2.01818e10i 0.208173 + 0.208173i
\(559\) 3.37049e8i 0.00345180i
\(560\) 1.74447e10 + 1.66711e10i 0.177382 + 0.169516i
\(561\) −3.33202e10 −0.336400
\(562\) −5.37441e10 + 5.37441e10i −0.538748 + 0.538748i
\(563\) 5.85471e10 + 5.85471e10i 0.582736 + 0.582736i 0.935654 0.352918i \(-0.114811\pi\)
−0.352918 + 0.935654i \(0.614811\pi\)
\(564\) 5.87192e10i 0.580315i
\(565\) −1.19302e11 + 1.24837e11i −1.17072 + 1.22504i
\(566\) 2.52209e9 0.0245751
\(567\) 3.76929e10 3.76929e10i 0.364693 0.364693i
\(568\) 1.85056e10 + 1.85056e10i 0.177791 + 0.177791i
\(569\) 1.98793e11i 1.89650i −0.317524 0.948250i \(-0.602851\pi\)
0.317524 0.948250i \(-0.397149\pi\)
\(570\) −7.09536e10 + 1.60890e9i −0.672164 + 0.0152416i
\(571\) 6.21842e10 0.584973 0.292487 0.956270i \(-0.405517\pi\)
0.292487 + 0.956270i \(0.405517\pi\)
\(572\) 1.06138e11 1.06138e11i 0.991490 0.991490i
\(573\) 5.75764e10 + 5.75764e10i 0.534104 + 0.534104i
\(574\) 1.61155e10i 0.148455i
\(575\) 5.38769e10 + 4.91999e10i 0.492869 + 0.450083i
\(576\) 1.64073e10 0.149055
\(577\) −1.02056e11 + 1.02056e11i −0.920739 + 0.920739i −0.997082 0.0763427i \(-0.975676\pi\)
0.0763427 + 0.997082i \(0.475676\pi\)
\(578\) −2.95455e10 2.95455e10i −0.264716 0.264716i
\(579\) 1.73772e10i 0.154620i
\(580\) 3.91156e8 + 1.72502e10i 0.00345651 + 0.152434i
\(581\) 2.32034e10 0.203633
\(582\) 7.11098e10 7.11098e10i 0.619780 0.619780i
\(583\) −5.82431e10 5.82431e10i −0.504162 0.504162i
\(584\) 8.11857e10i 0.697956i
\(585\) −7.60798e10 7.27060e10i −0.649600 0.620793i
\(586\) 9.03959e9 0.0766581
\(587\) −1.52761e11 + 1.52761e11i −1.28665 + 1.28665i −0.349837 + 0.936811i \(0.613763\pi\)
−0.936811 + 0.349837i \(0.886237\pi\)
\(588\) −7.68562e10 7.68562e10i −0.642939 0.642939i
\(589\) 1.64787e11i 1.36918i
\(590\) 8.42427e8 8.81518e8i 0.00695223 0.00727484i
\(591\) −1.49906e10 −0.122876
\(592\) 9.10768e9 9.10768e9i 0.0741517 0.0741517i
\(593\) 9.35153e10 + 9.35153e10i 0.756247 + 0.756247i 0.975637 0.219390i \(-0.0704067\pi\)
−0.219390 + 0.975637i \(0.570407\pi\)
\(594\) 2.31279e10i 0.185776i
\(595\) 1.03122e10 2.33834e8i 0.0822782 0.00186569i
\(596\) −1.57305e11 −1.24669
\(597\) 1.28901e11 1.28901e11i 1.01475 1.01475i
\(598\) −2.89318e10 2.89318e10i −0.226241 0.226241i
\(599\) 5.65120e10i 0.438968i 0.975616 + 0.219484i \(0.0704374\pi\)
−0.975616 + 0.219484i \(0.929563\pi\)
\(600\) 5.54859e9 + 1.22285e11i 0.0428132 + 0.943559i
\(601\) −9.99220e10 −0.765884 −0.382942 0.923772i \(-0.625089\pi\)
−0.382942 + 0.923772i \(0.625089\pi\)
\(602\) 4.34719e7 4.34719e7i 0.000330996 0.000330996i
\(603\) 2.10903e10 + 2.10903e10i 0.159520 + 0.159520i
\(604\) 1.66760e11i 1.25298i
\(605\) −2.40572e9 1.06094e11i −0.0179566 0.791896i
\(606\) 4.74030e10 0.351492
\(607\) 1.27776e11 1.27776e11i 0.941229 0.941229i −0.0571370 0.998366i \(-0.518197\pi\)
0.998366 + 0.0571370i \(0.0181972\pi\)
\(608\) 1.19532e11 + 1.19532e11i 0.874724 + 0.874724i
\(609\) 1.39828e10i 0.101654i
\(610\) 4.97151e10 + 4.75105e10i 0.359062 + 0.343139i
\(611\) 8.93925e10 0.641411
\(612\) 1.17247e10 1.17247e10i 0.0835784 0.0835784i
\(613\) 6.34636e10 + 6.34636e10i 0.449452 + 0.449452i 0.895172 0.445720i \(-0.147052\pi\)
−0.445720 + 0.895172i \(0.647052\pi\)
\(614\) 6.96478e10i 0.490043i
\(615\) 1.15299e11 1.20649e11i 0.805983 0.843383i
\(616\) −5.96267e10 −0.414112
\(617\) −6.39126e10 + 6.39126e10i −0.441007 + 0.441007i −0.892350 0.451343i \(-0.850945\pi\)
0.451343 + 0.892350i \(0.350945\pi\)
\(618\) −6.54854e10 6.54854e10i −0.448943 0.448943i
\(619\) 5.76225e10i 0.392491i 0.980555 + 0.196245i \(0.0628749\pi\)
−0.980555 + 0.196245i \(0.937125\pi\)
\(620\) −1.30473e11 + 2.95853e9i −0.882986 + 0.0200221i
\(621\) −3.54517e10 −0.238381
\(622\) −1.64439e10 + 1.64439e10i −0.109861 + 0.109861i
\(623\) −3.54555e10 3.54555e10i −0.235359 0.235359i
\(624\) 1.40126e11i 0.924234i
\(625\) 1.51961e11 1.38186e10i 0.995891 0.0905619i
\(626\) 4.21700e10 0.274604
\(627\) −2.53141e11 + 2.53141e11i −1.63792 + 1.63792i
\(628\) −1.74589e11 1.74589e11i −1.12248 1.12248i
\(629\) 5.50600e9i 0.0351749i
\(630\) 4.35143e8 + 1.91901e10i 0.00276229 + 0.121819i
\(631\) 1.53061e11 0.965486 0.482743 0.875762i \(-0.339641\pi\)
0.482743 + 0.875762i \(0.339641\pi\)
\(632\) 2.31544e10 2.31544e10i 0.145133 0.145133i
\(633\) −5.12953e10 5.12953e10i −0.319494 0.319494i
\(634\) 4.87880e10i 0.301964i
\(635\) −1.18083e11 1.12847e11i −0.726263 0.694057i
\(636\) 9.72667e10 0.594478
\(637\) 1.17004e11 1.17004e11i 0.710628 0.710628i
\(638\) −1.09442e10 1.09442e10i −0.0660546 0.0660546i
\(639\) 4.24968e10i 0.254890i
\(640\) 1.18162e11 1.23645e11i 0.704300 0.736982i
\(641\) 1.10388e11 0.653867 0.326934 0.945047i \(-0.393985\pi\)
0.326934 + 0.945047i \(0.393985\pi\)
\(642\) −3.13470e10 + 3.13470e10i −0.184525 + 0.184525i
\(643\) 4.62452e10 + 4.62452e10i 0.270535 + 0.270535i 0.829315 0.558781i \(-0.188731\pi\)
−0.558781 + 0.829315i \(0.688731\pi\)
\(644\) 4.19680e10i 0.243991i
\(645\) −6.36477e8 + 1.44324e7i −0.00367743 + 8.33872e-5i
\(646\) 1.70241e10 0.0977539
\(647\) −9.64071e10 + 9.64071e10i −0.550164 + 0.550164i −0.926488 0.376324i \(-0.877188\pi\)
0.376324 + 0.926488i \(0.377188\pi\)
\(648\) −1.07299e11 1.07299e11i −0.608547 0.608547i
\(649\) 6.15052e9i 0.0346683i
\(650\) −8.54813e10 + 3.87864e9i −0.478870 + 0.0217283i
\(651\) −1.05760e11 −0.588840
\(652\) 9.45283e10 9.45283e10i 0.523084 0.523084i
\(653\) −2.02786e11 2.02786e11i −1.11528 1.11528i −0.992424 0.122857i \(-0.960794\pi\)
−0.122857 0.992424i \(-0.539206\pi\)
\(654\) 1.51653e10i 0.0828971i
\(655\) 4.32247e9 + 1.90623e11i 0.0234837 + 1.03565i
\(656\) −9.36438e10 −0.505666
\(657\) −9.32188e10 + 9.32188e10i −0.500313 + 0.500313i
\(658\) −1.15297e10 1.15297e10i −0.0615053 0.0615053i
\(659\) 5.78139e10i 0.306542i −0.988184 0.153271i \(-0.951019\pi\)
0.988184 0.153271i \(-0.0489808\pi\)
\(660\) 2.04974e11 + 1.95885e11i 1.08025 + 1.03234i
\(661\) 3.80376e10 0.199254 0.0996271 0.995025i \(-0.468235\pi\)
0.0996271 + 0.995025i \(0.468235\pi\)
\(662\) −6.58451e10 + 6.58451e10i −0.342840 + 0.342840i
\(663\) 4.23563e10 + 4.23563e10i 0.219212 + 0.219212i
\(664\) 6.60520e10i 0.339792i
\(665\) 7.65679e10 8.01209e10i 0.391526 0.409694i
\(666\) 1.02461e10 0.0520790
\(667\) 1.67759e10 1.67759e10i 0.0847585 0.0847585i
\(668\) 1.55797e11 + 1.55797e11i 0.782442 + 0.782442i
\(669\) 1.41200e11i 0.704905i
\(670\) 2.42463e10 5.49796e8i 0.120323 0.00272836i
\(671\) 3.46872e11 1.71111
\(672\) 7.67158e10 7.67158e10i 0.376190 0.376190i
\(673\) 1.23735e11 + 1.23735e11i 0.603158 + 0.603158i 0.941149 0.337991i \(-0.109747\pi\)
−0.337991 + 0.941149i \(0.609747\pi\)
\(674\) 5.53205e10i 0.268069i
\(675\) −4.99961e10 + 5.47488e10i −0.240836 + 0.263730i
\(676\) −9.25460e10 −0.443170
\(677\) −8.44279e10 + 8.44279e10i −0.401912 + 0.401912i −0.878906 0.476994i \(-0.841726\pi\)
0.476994 + 0.878906i \(0.341726\pi\)
\(678\) 1.29336e11 + 1.29336e11i 0.612067 + 0.612067i
\(679\) 1.57034e11i 0.738778i
\(680\) −6.65644e8 2.93553e10i −0.00311320 0.137294i
\(681\) −5.24008e11 −2.43640
\(682\) 8.27774e10 8.27774e10i 0.382626 0.382626i
\(683\) −2.87370e10 2.87370e10i −0.132056 0.132056i 0.637989 0.770045i \(-0.279766\pi\)
−0.770045 + 0.637989i \(0.779766\pi\)
\(684\) 1.78150e11i 0.813881i
\(685\) −2.40098e11 2.29450e11i −1.09050 1.04214i
\(686\) −6.72321e10 −0.303585
\(687\) 2.76549e11 2.76549e11i 1.24150 1.24150i
\(688\) 2.52606e8 + 2.52606e8i 0.00112743 + 0.00112743i
\(689\) 1.48076e11i 0.657065i
\(690\) 5.33954e10 5.58731e10i 0.235563 0.246494i
\(691\) −8.87703e10 −0.389364 −0.194682 0.980866i \(-0.562367\pi\)
−0.194682 + 0.980866i \(0.562367\pi\)
\(692\) −7.39768e10 + 7.39768e10i −0.322605 + 0.322605i
\(693\) 6.84644e10 + 6.84644e10i 0.296847 + 0.296847i
\(694\) 7.28192e10i 0.313912i
\(695\) −6.90915e10 + 1.56668e9i −0.296132 + 0.00671492i
\(696\) 3.98042e10 0.169626
\(697\) −2.83059e10 + 2.83059e10i −0.119935 + 0.119935i
\(698\) 4.90652e10 + 4.90652e10i 0.206706 + 0.206706i
\(699\) 5.46503e11i 2.28920i
\(700\) −6.48120e10 5.91857e10i −0.269938 0.246504i
\(701\) 1.22790e11 0.508499 0.254249 0.967139i \(-0.418172\pi\)
0.254249 + 0.967139i \(0.418172\pi\)
\(702\) 2.94000e10 2.94000e10i 0.121060 0.121060i
\(703\) −4.18303e10 4.18303e10i −0.171266 0.171266i
\(704\) 6.72957e10i 0.273966i
\(705\) 3.82777e9 + 1.68807e11i 0.0154949 + 0.683336i
\(706\) −9.31125e10 −0.374791
\(707\) −5.23407e10 + 5.23407e10i −0.209489 + 0.209489i
\(708\) 5.13572e9 + 5.13572e9i 0.0204394 + 0.0204394i
\(709\) 2.07670e11i 0.821842i 0.911671 + 0.410921i \(0.134793\pi\)
−0.911671 + 0.410921i \(0.865207\pi\)
\(710\) −2.49820e10 2.38742e10i −0.0983091 0.0939495i
\(711\) −5.31726e10 −0.208070
\(712\) −1.00929e11 + 1.00929e11i −0.392733 + 0.392733i
\(713\) 1.26886e11 + 1.26886e11i 0.490969 + 0.490969i
\(714\) 1.09261e10i 0.0420408i
\(715\) −2.98210e11 + 3.12048e11i −1.14103 + 1.19398i
\(716\) 2.80773e11 1.06832
\(717\) 1.99040e11 1.99040e11i 0.753119 0.753119i
\(718\) −4.16981e10 4.16981e10i −0.156898 0.156898i
\(719\) 1.66571e11i 0.623281i −0.950200 0.311640i \(-0.899122\pi\)
0.950200 0.311640i \(-0.100878\pi\)
\(720\) −1.11510e11 + 2.52853e9i −0.414937 + 0.00940888i
\(721\) 1.44613e11 0.535140
\(722\) 5.46750e10 5.46750e10i 0.201205 0.201205i
\(723\) −5.42320e9 5.42320e9i −0.0198474 0.0198474i
\(724\) 4.19292e10i 0.152603i
\(725\) −2.24901e9 4.95658e10i −0.00814027 0.179403i
\(726\) −1.12409e11 −0.404626
\(727\) 1.61369e11 1.61369e11i 0.577673 0.577673i −0.356588 0.934262i \(-0.616060\pi\)
0.934262 + 0.356588i \(0.116060\pi\)
\(728\) 7.57970e10 + 7.57970e10i 0.269853 + 0.269853i
\(729\) 1.13795e11i 0.402915i
\(730\) 2.43009e9 + 1.07168e11i 0.00855717 + 0.377377i
\(731\) 1.52712e8 0.000534814
\(732\) −2.89640e11 + 2.89640e11i −1.00882 + 1.00882i
\(733\) 4.72057e10 + 4.72057e10i 0.163523 + 0.163523i 0.784125 0.620603i \(-0.213112\pi\)
−0.620603 + 0.784125i \(0.713112\pi\)
\(734\) 8.44043e10i 0.290791i
\(735\) 2.25958e11 + 2.15938e11i 0.774245 + 0.739911i
\(736\) −1.84080e11 −0.627328
\(737\) 8.65036e10 8.65036e10i 0.293200 0.293200i
\(738\) −5.26746e10 5.26746e10i −0.177572 0.177572i
\(739\) 2.13693e11i 0.716494i 0.933627 + 0.358247i \(0.116625\pi\)
−0.933627 + 0.358247i \(0.883375\pi\)
\(740\) −3.23690e10 + 3.38710e10i −0.107945 + 0.112954i
\(741\) 6.43582e11 2.13467
\(742\) 1.90985e10 1.90985e10i 0.0630064 0.0630064i
\(743\) −3.10741e11 3.10741e11i −1.01963 1.01963i −0.999803 0.0198284i \(-0.993688\pi\)
−0.0198284 0.999803i \(-0.506312\pi\)
\(744\) 3.01061e11i 0.982570i
\(745\) 4.52224e11 1.02544e10i 1.46801 0.0332877i
\(746\) −7.45910e10 −0.240841
\(747\) −7.58420e10 + 7.58420e10i −0.243572 + 0.243572i
\(748\) −4.80896e10 4.80896e10i −0.153619 0.153619i
\(749\) 6.92245e10i 0.219954i
\(750\) −1.09847e10 1.61255e11i −0.0347169 0.509646i
\(751\) −5.29510e11 −1.66462 −0.832308 0.554313i \(-0.812981\pi\)
−0.832308 + 0.554313i \(0.812981\pi\)
\(752\) 6.69965e10 6.69965e10i 0.209498 0.209498i
\(753\) 4.35909e9 + 4.35909e9i 0.0135586 + 0.0135586i
\(754\) 2.78245e10i 0.0860877i
\(755\) −1.08707e10 4.79405e11i −0.0334557 1.47542i
\(756\) 4.26471e10 0.130558
\(757\) −1.66172e11 + 1.66172e11i −0.506029 + 0.506029i −0.913305 0.407276i \(-0.866479\pi\)
0.407276 + 0.913305i \(0.366479\pi\)
\(758\) 9.63068e10 + 9.63068e10i 0.291729 + 0.291729i
\(759\) 3.89837e11i 1.17467i
\(760\) −2.28076e11 2.17962e11i −0.683637 0.653321i
\(761\) −3.61095e11 −1.07667 −0.538335 0.842731i \(-0.680946\pi\)
−0.538335 + 0.842731i \(0.680946\pi\)
\(762\) −1.22338e11 + 1.22338e11i −0.362862 + 0.362862i
\(763\) −1.67450e10 1.67450e10i −0.0494067 0.0494067i
\(764\) 1.66195e11i 0.487803i
\(765\) −3.29420e10 + 3.44706e10i −0.0961842 + 0.100647i
\(766\) 2.03349e11 0.590646
\(767\) −7.81849e9 + 7.81849e9i −0.0225913 + 0.0225913i
\(768\) −6.19151e10 6.19151e10i −0.177972 0.177972i
\(769\) 2.04700e11i 0.585345i −0.956213 0.292672i \(-0.905455\pi\)
0.956213 0.292672i \(-0.0945446\pi\)
\(770\) 7.87096e10 1.78477e9i 0.223906 0.00507716i
\(771\) −7.12960e10 −0.201766
\(772\) −2.50797e10 + 2.50797e10i −0.0706080 + 0.0706080i
\(773\) −8.07889e10 8.07889e10i −0.226274 0.226274i 0.584860 0.811134i \(-0.301149\pi\)
−0.811134 + 0.584860i \(0.801149\pi\)
\(774\) 2.84182e8i 0.000791831i
\(775\) 3.74894e11 1.70105e10i 1.03921 0.0471531i