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Properties

Label 25.9.c.a.18.2
Level $25$
Weight $9$
Character 25.18
Analytic conductor $10.184$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 25.c (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.1844652515\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{141})\)
Defining polynomial: \(x^{4} + 71 x^{2} + 1225\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 18.2
Root \(5.43717i\) of defining polynomial
Character \(\chi\) \(=\) 25.18
Dual form 25.9.c.a.7.2

$q$-expansion

\(f(q)\) \(=\) \(q+(11.8743 - 11.8743i) q^{2} +(11.8743 + 11.8743i) q^{3} -26.0000i q^{4} +282.000 q^{6} +(2742.97 - 2742.97i) q^{7} +(2731.10 + 2731.10i) q^{8} -6279.00i q^{9} +O(q^{10})\) \(q+(11.8743 - 11.8743i) q^{2} +(11.8743 + 11.8743i) q^{3} -26.0000i q^{4} +282.000 q^{6} +(2742.97 - 2742.97i) q^{7} +(2731.10 + 2731.10i) q^{8} -6279.00i q^{9} +12132.0 q^{11} +(308.733 - 308.733i) q^{12} +(-2422.37 - 2422.37i) q^{13} -65142.0i q^{14} +71516.0 q^{16} +(-76993.2 + 76993.2i) q^{17} +(-74559.0 - 74559.0i) q^{18} -168380. i q^{19} +65142.0 q^{21} +(144060. - 144060. i) q^{22} +(221350. + 221350. i) q^{23} +64860.0i q^{24} -57528.0 q^{26} +(152467. - 152467. i) q^{27} +(-71317.3 - 71317.3i) q^{28} +666630. i q^{29} -1.04281e6 q^{31} +(150044. - 150044. i) q^{32} +(144060. + 144060. i) q^{33} +1.82849e6i q^{34} -163254. q^{36} +(-2.07639e6 + 2.07639e6i) q^{37} +(-1.99940e6 - 1.99940e6i) q^{38} -57528.0i q^{39} -1.32113e6 q^{41} +(773518. - 773518. i) q^{42} +(2.78134e6 + 2.78134e6i) q^{43} -315432. i q^{44} +5.25676e6 q^{46} +(3.63024e6 - 3.63024e6i) q^{47} +(849205. + 849205. i) q^{48} -9.28300e6i q^{49} -1.82849e6 q^{51} +(-62981.5 + 62981.5i) q^{52} +(-3.14105e6 - 3.14105e6i) q^{53} -3.62088e6i q^{54} +1.49827e7 q^{56} +(1.99940e6 - 1.99940e6i) q^{57} +(7.91579e6 + 7.91579e6i) q^{58} -6.49854e6i q^{59} -1.43940e7 q^{61} +(-1.23827e7 + 1.23827e7i) q^{62} +(-1.72231e7 - 1.72231e7i) q^{63} +1.47447e7i q^{64} +3.42122e6 q^{66} +(-1.14565e7 + 1.14565e7i) q^{67} +(2.00182e6 + 2.00182e6i) q^{68} +5.25676e6i q^{69} -2.30655e7 q^{71} +(1.71486e7 - 1.71486e7i) q^{72} +(1.74329e7 + 1.74329e7i) q^{73} +4.93116e7i q^{74} -4.37788e6 q^{76} +(3.32777e7 - 3.32777e7i) q^{77} +(-683107. - 683107. i) q^{78} +2.76068e6i q^{79} -3.75756e7 q^{81} +(-1.56875e7 + 1.56875e7i) q^{82} +(-1.15239e7 - 1.15239e7i) q^{83} -1.69369e6i q^{84} +6.60531e7 q^{86} +(-7.91579e6 + 7.91579e6i) q^{87} +(3.31337e7 + 3.31337e7i) q^{88} -2.61305e7i q^{89} -1.32890e7 q^{91} +(5.75509e6 - 5.75509e6i) q^{92} +(-1.23827e7 - 1.23827e7i) q^{93} -8.62133e7i q^{94} +3.56335e6 q^{96} +(-8.09308e7 + 8.09308e7i) q^{97} +(-1.10230e8 - 1.10230e8i) q^{98} -7.61768e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 1128q^{6} + O(q^{10}) \) \( 4q + 1128q^{6} + 48528q^{11} + 286064q^{16} + 260568q^{21} - 230112q^{26} - 4171232q^{31} - 653016q^{36} - 5284512q^{41} + 21027048q^{46} - 7313952q^{51} + 59930640q^{56} - 57575872q^{61} + 13684896q^{66} - 92261952q^{71} - 17511520q^{76} - 150302556q^{81} + 264212568q^{86} - 53155872q^{91} + 14253408q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 11.8743 − 11.8743i 0.742146 − 0.742146i −0.230844 − 0.972991i \(-0.574149\pi\)
0.972991 + 0.230844i \(0.0741488\pi\)
\(3\) 11.8743 + 11.8743i 0.146597 + 0.146597i 0.776596 − 0.629999i \(-0.216945\pi\)
−0.629999 + 0.776596i \(0.716945\pi\)
\(4\) − 26.0000i − 0.101562i
\(5\) 0 0
\(6\) 282.000 0.217593
\(7\) 2742.97 − 2742.97i 1.14243 − 1.14243i 0.154425 − 0.988005i \(-0.450648\pi\)
0.988005 − 0.154425i \(-0.0493525\pi\)
\(8\) 2731.10 + 2731.10i 0.666772 + 0.666772i
\(9\) − 6279.00i − 0.957019i
\(10\) 0 0
\(11\) 12132.0 0.828632 0.414316 − 0.910133i \(-0.364021\pi\)
0.414316 + 0.910133i \(0.364021\pi\)
\(12\) 308.733 − 308.733i 0.0148887 − 0.0148887i
\(13\) −2422.37 − 2422.37i −0.0848138 − 0.0848138i 0.663427 − 0.748241i \(-0.269101\pi\)
−0.748241 + 0.663427i \(0.769101\pi\)
\(14\) − 65142.0i − 1.69570i
\(15\) 0 0
\(16\) 71516.0 1.09125
\(17\) −76993.2 + 76993.2i −0.921843 + 0.921843i −0.997160 − 0.0753168i \(-0.976003\pi\)
0.0753168 + 0.997160i \(0.476003\pi\)
\(18\) −74559.0 − 74559.0i −0.710248 − 0.710248i
\(19\) − 168380.i − 1.29204i −0.763320 − 0.646020i \(-0.776432\pi\)
0.763320 − 0.646020i \(-0.223568\pi\)
\(20\) 0 0
\(21\) 65142.0 0.334953
\(22\) 144060. − 144060.i 0.614966 − 0.614966i
\(23\) 221350. + 221350.i 0.790983 + 0.790983i 0.981654 − 0.190671i \(-0.0610662\pi\)
−0.190671 + 0.981654i \(0.561066\pi\)
\(24\) 64860.0i 0.195493i
\(25\) 0 0
\(26\) −57528.0 −0.125888
\(27\) 152467. − 152467.i 0.286893 − 0.286893i
\(28\) −71317.3 − 71317.3i −0.116028 − 0.116028i
\(29\) 666630.i 0.942525i 0.881993 + 0.471262i \(0.156202\pi\)
−0.881993 + 0.471262i \(0.843798\pi\)
\(30\) 0 0
\(31\) −1.04281e6 −1.12917 −0.564583 − 0.825376i \(-0.690963\pi\)
−0.564583 + 0.825376i \(0.690963\pi\)
\(32\) 150044. − 150044.i 0.143093 − 0.143093i
\(33\) 144060. + 144060.i 0.121475 + 0.121475i
\(34\) 1.82849e6i 1.36828i
\(35\) 0 0
\(36\) −163254. −0.0971972
\(37\) −2.07639e6 + 2.07639e6i −1.10791 + 1.10791i −0.114481 + 0.993425i \(0.536520\pi\)
−0.993425 + 0.114481i \(0.963480\pi\)
\(38\) −1.99940e6 − 1.99940e6i −0.958883 − 0.958883i
\(39\) − 57528.0i − 0.0248669i
\(40\) 0 0
\(41\) −1.32113e6 −0.467530 −0.233765 − 0.972293i \(-0.575105\pi\)
−0.233765 + 0.972293i \(0.575105\pi\)
\(42\) 773518. − 773518.i 0.248584 − 0.248584i
\(43\) 2.78134e6 + 2.78134e6i 0.813542 + 0.813542i 0.985163 − 0.171621i \(-0.0549004\pi\)
−0.171621 + 0.985163i \(0.554900\pi\)
\(44\) − 315432.i − 0.0841579i
\(45\) 0 0
\(46\) 5.25676e6 1.17405
\(47\) 3.63024e6 − 3.63024e6i 0.743949 − 0.743949i −0.229386 − 0.973336i \(-0.573672\pi\)
0.973336 + 0.229386i \(0.0736718\pi\)
\(48\) 849205. + 849205.i 0.159973 + 0.159973i
\(49\) − 9.28300e6i − 1.61029i
\(50\) 0 0
\(51\) −1.82849e6 −0.270278
\(52\) −62981.5 + 62981.5i −0.00861390 + 0.00861390i
\(53\) −3.14105e6 − 3.14105e6i −0.398081 − 0.398081i 0.479475 − 0.877556i \(-0.340827\pi\)
−0.877556 + 0.479475i \(0.840827\pi\)
\(54\) − 3.62088e6i − 0.425833i
\(55\) 0 0
\(56\) 1.49827e7 1.52348
\(57\) 1.99940e6 − 1.99940e6i 0.189409 − 0.189409i
\(58\) 7.91579e6 + 7.91579e6i 0.699491 + 0.699491i
\(59\) − 6.49854e6i − 0.536300i −0.963377 − 0.268150i \(-0.913588\pi\)
0.963377 − 0.268150i \(-0.0864123\pi\)
\(60\) 0 0
\(61\) −1.43940e7 −1.03959 −0.519794 − 0.854292i \(-0.673991\pi\)
−0.519794 + 0.854292i \(0.673991\pi\)
\(62\) −1.23827e7 + 1.23827e7i −0.838006 + 0.838006i
\(63\) −1.72231e7 − 1.72231e7i −1.09333 − 1.09333i
\(64\) 1.47447e7i 0.878855i
\(65\) 0 0
\(66\) 3.42122e6 0.180304
\(67\) −1.14565e7 + 1.14565e7i −0.568528 + 0.568528i −0.931716 − 0.363188i \(-0.881688\pi\)
0.363188 + 0.931716i \(0.381688\pi\)
\(68\) 2.00182e6 + 2.00182e6i 0.0936247 + 0.0936247i
\(69\) 5.25676e6i 0.231911i
\(70\) 0 0
\(71\) −2.30655e7 −0.907673 −0.453836 − 0.891085i \(-0.649945\pi\)
−0.453836 + 0.891085i \(0.649945\pi\)
\(72\) 1.71486e7 − 1.71486e7i 0.638113 − 0.638113i
\(73\) 1.74329e7 + 1.74329e7i 0.613873 + 0.613873i 0.943953 − 0.330080i \(-0.107076\pi\)
−0.330080 + 0.943953i \(0.607076\pi\)
\(74\) 4.93116e7i 1.64446i
\(75\) 0 0
\(76\) −4.37788e6 −0.131223
\(77\) 3.32777e7 − 3.32777e7i 0.946653 − 0.946653i
\(78\) −683107. − 683107.i −0.0184548 − 0.0184548i
\(79\) 2.76068e6i 0.0708774i 0.999372 + 0.0354387i \(0.0112828\pi\)
−0.999372 + 0.0354387i \(0.988717\pi\)
\(80\) 0 0
\(81\) −3.75756e7 −0.872904
\(82\) −1.56875e7 + 1.56875e7i −0.346976 + 0.346976i
\(83\) −1.15239e7 − 1.15239e7i −0.242822 − 0.242822i 0.575195 − 0.818017i \(-0.304926\pi\)
−0.818017 + 0.575195i \(0.804926\pi\)
\(84\) − 1.69369e6i − 0.0340187i
\(85\) 0 0
\(86\) 6.60531e7 1.20753
\(87\) −7.91579e6 + 7.91579e6i −0.138171 + 0.138171i
\(88\) 3.31337e7 + 3.31337e7i 0.552509 + 0.552509i
\(89\) − 2.61305e7i − 0.416474i −0.978078 − 0.208237i \(-0.933227\pi\)
0.978078 − 0.208237i \(-0.0667725\pi\)
\(90\) 0 0
\(91\) −1.32890e7 −0.193787
\(92\) 5.75509e6 − 5.75509e6i 0.0803343 − 0.0803343i
\(93\) −1.23827e7 − 1.23827e7i −0.165532 − 0.165532i
\(94\) − 8.62133e7i − 1.10424i
\(95\) 0 0
\(96\) 3.56335e6 0.0419540
\(97\) −8.09308e7 + 8.09308e7i −0.914170 + 0.914170i −0.996597 − 0.0824271i \(-0.973733\pi\)
0.0824271 + 0.996597i \(0.473733\pi\)
\(98\) −1.10230e8 − 1.10230e8i −1.19507 − 1.19507i
\(99\) − 7.61768e7i − 0.793016i
\(100\) 0 0
\(101\) 1.80720e8 1.73668 0.868341 − 0.495968i \(-0.165187\pi\)
0.868341 + 0.495968i \(0.165187\pi\)
\(102\) −2.17121e7 + 2.17121e7i −0.200586 + 0.200586i
\(103\) 7.33591e7 + 7.33591e7i 0.651786 + 0.651786i 0.953423 − 0.301637i \(-0.0975330\pi\)
−0.301637 + 0.953423i \(0.597533\pi\)
\(104\) − 1.32314e7i − 0.113103i
\(105\) 0 0
\(106\) −7.45958e7 −0.590868
\(107\) 5.06569e7 − 5.06569e7i 0.386459 − 0.386459i −0.486963 − 0.873422i \(-0.661895\pi\)
0.873422 + 0.486963i \(0.161895\pi\)
\(108\) −3.96413e6 − 3.96413e6i −0.0291375 − 0.0291375i
\(109\) − 3.65622e7i − 0.259016i −0.991578 − 0.129508i \(-0.958660\pi\)
0.991578 − 0.129508i \(-0.0413398\pi\)
\(110\) 0 0
\(111\) −4.93116e7 −0.324831
\(112\) 1.96166e8 − 1.96166e8i 1.24667 − 1.24667i
\(113\) 1.29733e8 + 1.29733e8i 0.795677 + 0.795677i 0.982411 − 0.186733i \(-0.0597900\pi\)
−0.186733 + 0.982411i \(0.559790\pi\)
\(114\) − 4.74832e7i − 0.281138i
\(115\) 0 0
\(116\) 1.73324e7 0.0957252
\(117\) −1.52100e7 + 1.52100e7i −0.0811684 + 0.0811684i
\(118\) −7.71659e7 − 7.71659e7i −0.398013 − 0.398013i
\(119\) 4.22381e8i 2.10628i
\(120\) 0 0
\(121\) −6.71735e7 −0.313369
\(122\) −1.70919e8 + 1.70919e8i −0.771526 + 0.771526i
\(123\) −1.56875e7 − 1.56875e7i −0.0685384 − 0.0685384i
\(124\) 2.71130e7i 0.114681i
\(125\) 0 0
\(126\) −4.09027e8 −1.62282
\(127\) 5.09023e7 − 5.09023e7i 0.195669 − 0.195669i −0.602471 − 0.798141i \(-0.705817\pi\)
0.798141 + 0.602471i \(0.205817\pi\)
\(128\) 2.13495e8 + 2.13495e8i 0.795333 + 0.795333i
\(129\) 6.60531e7i 0.238525i
\(130\) 0 0
\(131\) 3.84564e8 1.30582 0.652911 − 0.757435i \(-0.273548\pi\)
0.652911 + 0.757435i \(0.273548\pi\)
\(132\) 3.74555e6 − 3.74555e6i 0.0123373 − 0.0123373i
\(133\) −4.61862e8 − 4.61862e8i −1.47606 − 1.47606i
\(134\) 2.72076e8i 0.843862i
\(135\) 0 0
\(136\) −4.20552e8 −1.22932
\(137\) −1.62634e8 + 1.62634e8i −0.461668 + 0.461668i −0.899202 − 0.437534i \(-0.855852\pi\)
0.437534 + 0.899202i \(0.355852\pi\)
\(138\) 6.24206e7 + 6.24206e7i 0.172112 + 0.172112i
\(139\) 9.16665e7i 0.245557i 0.992434 + 0.122778i \(0.0391804\pi\)
−0.992434 + 0.122778i \(0.960820\pi\)
\(140\) 0 0
\(141\) 8.62133e7 0.218121
\(142\) −2.73887e8 + 2.73887e8i −0.673626 + 0.673626i
\(143\) −2.93881e7 − 2.93881e7i −0.0702794 − 0.0702794i
\(144\) − 4.49049e8i − 1.04434i
\(145\) 0 0
\(146\) 4.14009e8 0.911167
\(147\) 1.10230e8 − 1.10230e8i 0.236063 − 0.236063i
\(148\) 5.39863e7 + 5.39863e7i 0.112522 + 0.112522i
\(149\) − 1.45300e8i − 0.294794i −0.989077 − 0.147397i \(-0.952910\pi\)
0.989077 − 0.147397i \(-0.0470896\pi\)
\(150\) 0 0
\(151\) −2.35910e7 −0.0453774 −0.0226887 − 0.999743i \(-0.507223\pi\)
−0.0226887 + 0.999743i \(0.507223\pi\)
\(152\) 4.59862e8 − 4.59862e8i 0.861497 − 0.861497i
\(153\) 4.83441e8 + 4.83441e8i 0.882221 + 0.882221i
\(154\) − 7.90303e8i − 1.40511i
\(155\) 0 0
\(156\) −1.49573e6 −0.00252554
\(157\) 6.67495e8 − 6.67495e8i 1.09863 − 1.09863i 0.104054 − 0.994572i \(-0.466819\pi\)
0.994572 − 0.104054i \(-0.0331814\pi\)
\(158\) 3.27813e7 + 3.27813e7i 0.0526014 + 0.0526014i
\(159\) − 7.45958e7i − 0.116715i
\(160\) 0 0
\(161\) 1.21431e9 1.80729
\(162\) −4.46186e8 + 4.46186e8i −0.647822 + 0.647822i
\(163\) −2.57869e8 − 2.57869e8i −0.365300 − 0.365300i 0.500460 − 0.865760i \(-0.333164\pi\)
−0.865760 + 0.500460i \(0.833164\pi\)
\(164\) 3.43493e7i 0.0474835i
\(165\) 0 0
\(166\) −2.73678e8 −0.360419
\(167\) −4.92455e8 + 4.92455e8i −0.633142 + 0.633142i −0.948855 − 0.315713i \(-0.897756\pi\)
0.315713 + 0.948855i \(0.397756\pi\)
\(168\) 1.77909e8 + 1.77909e8i 0.223337 + 0.223337i
\(169\) − 8.03995e8i − 0.985613i
\(170\) 0 0
\(171\) −1.05726e9 −1.23651
\(172\) 7.23148e7 − 7.23148e7i 0.0826254 − 0.0826254i
\(173\) −3.51863e8 − 3.51863e8i −0.392816 − 0.392816i 0.482874 − 0.875690i \(-0.339593\pi\)
−0.875690 + 0.482874i \(0.839593\pi\)
\(174\) 1.87990e8i 0.205086i
\(175\) 0 0
\(176\) 8.67632e8 0.904243
\(177\) 7.71659e7 − 7.71659e7i 0.0786199 − 0.0786199i
\(178\) −3.10283e8 − 3.10283e8i −0.309085 − 0.309085i
\(179\) 1.16205e9i 1.13191i 0.824436 + 0.565955i \(0.191492\pi\)
−0.824436 + 0.565955i \(0.808508\pi\)
\(180\) 0 0
\(181\) −4.84017e8 −0.450968 −0.225484 − 0.974247i \(-0.572396\pi\)
−0.225484 + 0.974247i \(0.572396\pi\)
\(182\) −1.57798e8 + 1.57798e8i −0.143819 + 0.143819i
\(183\) −1.70919e8 − 1.70919e8i −0.152400 − 0.152400i
\(184\) 1.20906e9i 1.05481i
\(185\) 0 0
\(186\) −2.94072e8 −0.245698
\(187\) −9.34082e8 + 9.34082e8i −0.763868 + 0.763868i
\(188\) −9.43861e7 − 9.43861e7i −0.0755574 − 0.0755574i
\(189\) − 8.36423e8i − 0.655509i
\(190\) 0 0
\(191\) −1.49354e9 −1.12223 −0.561117 − 0.827736i \(-0.689628\pi\)
−0.561117 + 0.827736i \(0.689628\pi\)
\(192\) −1.75084e8 + 1.75084e8i −0.128837 + 0.128837i
\(193\) 8.77896e8 + 8.77896e8i 0.632723 + 0.632723i 0.948750 − 0.316027i \(-0.102349\pi\)
−0.316027 + 0.948750i \(0.602349\pi\)
\(194\) 1.92200e9i 1.35690i
\(195\) 0 0
\(196\) −2.41358e8 −0.163545
\(197\) 2.10520e8 − 2.10520e8i 0.139775 − 0.139775i −0.633757 − 0.773532i \(-0.718488\pi\)
0.773532 + 0.633757i \(0.218488\pi\)
\(198\) −9.04550e8 − 9.04550e8i −0.588534 − 0.588534i
\(199\) 1.44381e9i 0.920655i 0.887749 + 0.460327i \(0.152268\pi\)
−0.887749 + 0.460327i \(0.847732\pi\)
\(200\) 0 0
\(201\) −2.72076e8 −0.166689
\(202\) 2.14593e9 − 2.14593e9i 1.28887 − 1.28887i
\(203\) 1.82855e9 + 1.82855e9i 1.07677 + 1.07677i
\(204\) 4.75407e7i 0.0274502i
\(205\) 0 0
\(206\) 1.74218e9 0.967441
\(207\) 1.38985e9 − 1.38985e9i 0.756986 − 0.756986i
\(208\) −1.73238e8 − 1.73238e8i −0.0925528 − 0.0925528i
\(209\) − 2.04279e9i − 1.07063i
\(210\) 0 0
\(211\) −1.57176e9 −0.792968 −0.396484 − 0.918042i \(-0.629770\pi\)
−0.396484 + 0.918042i \(0.629770\pi\)
\(212\) −8.16673e7 + 8.16673e7i −0.0404301 + 0.0404301i
\(213\) −2.73887e8 − 2.73887e8i −0.133062 − 0.133062i
\(214\) − 1.20303e9i − 0.573618i
\(215\) 0 0
\(216\) 8.32802e8 0.382584
\(217\) −2.86039e9 + 2.86039e9i −1.28999 + 1.28999i
\(218\) −4.34153e8 − 4.34153e8i −0.192228 − 0.192228i
\(219\) 4.14009e8i 0.179984i
\(220\) 0 0
\(221\) 3.73012e8 0.156370
\(222\) −5.85543e8 + 5.85543e8i −0.241072 + 0.241072i
\(223\) −4.52258e8 − 4.52258e8i −0.182880 − 0.182880i 0.609729 − 0.792610i \(-0.291278\pi\)
−0.792610 + 0.609729i \(0.791278\pi\)
\(224\) − 8.23134e8i − 0.326948i
\(225\) 0 0
\(226\) 3.08099e9 1.18102
\(227\) 1.41755e9 − 1.41755e9i 0.533871 − 0.533871i −0.387851 − 0.921722i \(-0.626783\pi\)
0.921722 + 0.387851i \(0.126783\pi\)
\(228\) −5.19844e7 − 5.19844e7i −0.0192369 − 0.0192369i
\(229\) − 5.09083e9i − 1.85117i −0.378536 − 0.925586i \(-0.623572\pi\)
0.378536 − 0.925586i \(-0.376428\pi\)
\(230\) 0 0
\(231\) 7.90303e8 0.277553
\(232\) −1.82063e9 + 1.82063e9i −0.628449 + 0.628449i
\(233\) −3.23753e9 − 3.23753e9i −1.09848 − 1.09848i −0.994589 − 0.103887i \(-0.966872\pi\)
−0.103887 − 0.994589i \(-0.533128\pi\)
\(234\) 3.61218e8i 0.120478i
\(235\) 0 0
\(236\) −1.68962e8 −0.0544680
\(237\) −3.27813e7 + 3.27813e7i −0.0103904 + 0.0103904i
\(238\) 5.01549e9 + 5.01549e9i 1.56317 + 1.56317i
\(239\) − 6.45678e8i − 0.197890i −0.995093 − 0.0989452i \(-0.968453\pi\)
0.995093 − 0.0989452i \(-0.0315468\pi\)
\(240\) 0 0
\(241\) 1.04063e9 0.308482 0.154241 − 0.988033i \(-0.450707\pi\)
0.154241 + 0.988033i \(0.450707\pi\)
\(242\) −7.97641e8 + 7.97641e8i −0.232566 + 0.232566i
\(243\) −1.44652e9 − 1.44652e9i −0.414858 − 0.414858i
\(244\) 3.74243e8i 0.105583i
\(245\) 0 0
\(246\) −3.72558e8 −0.101731
\(247\) −4.07878e8 + 4.07878e8i −0.109583 + 0.109583i
\(248\) −2.84801e9 − 2.84801e9i −0.752896 − 0.752896i
\(249\) − 2.73678e8i − 0.0711938i
\(250\) 0 0
\(251\) −4.15092e9 −1.04580 −0.522901 − 0.852394i \(-0.675150\pi\)
−0.522901 + 0.852394i \(0.675150\pi\)
\(252\) −4.47801e8 + 4.47801e8i −0.111041 + 0.111041i
\(253\) 2.68541e9 + 2.68541e9i 0.655434 + 0.655434i
\(254\) − 1.20886e9i − 0.290431i
\(255\) 0 0
\(256\) 1.29558e9 0.301651
\(257\) 5.71495e9 − 5.71495e9i 1.31003 − 1.31003i 0.388635 − 0.921392i \(-0.372947\pi\)
0.921392 − 0.388635i \(-0.127053\pi\)
\(258\) 7.84338e8 + 7.84338e8i 0.177021 + 0.177021i
\(259\) 1.13910e10i 2.53141i
\(260\) 0 0
\(261\) 4.18577e9 0.902014
\(262\) 4.56645e9 − 4.56645e9i 0.969111 − 0.969111i
\(263\) 1.59379e9 + 1.59379e9i 0.333127 + 0.333127i 0.853773 − 0.520646i \(-0.174309\pi\)
−0.520646 + 0.853773i \(0.674309\pi\)
\(264\) 7.86882e8i 0.161992i
\(265\) 0 0
\(266\) −1.09686e10 −2.19091
\(267\) 3.10283e8 − 3.10283e8i 0.0610538 − 0.0610538i
\(268\) 2.97868e8 + 2.97868e8i 0.0577411 + 0.0577411i
\(269\) − 2.62849e9i − 0.501992i −0.967988 − 0.250996i \(-0.919242\pi\)
0.967988 − 0.250996i \(-0.0807581\pi\)
\(270\) 0 0
\(271\) −2.04396e9 −0.378961 −0.189481 − 0.981884i \(-0.560680\pi\)
−0.189481 + 0.981884i \(0.560680\pi\)
\(272\) −5.50625e9 + 5.50625e9i −1.00596 + 1.00596i
\(273\) −1.57798e8 − 1.57798e8i −0.0284086 − 0.0284086i
\(274\) 3.86235e9i 0.685250i
\(275\) 0 0
\(276\) 1.36676e8 0.0235535
\(277\) −4.31300e9 + 4.31300e9i −0.732589 + 0.732589i −0.971132 − 0.238543i \(-0.923330\pi\)
0.238543 + 0.971132i \(0.423330\pi\)
\(278\) 1.08848e9 + 1.08848e9i 0.182239 + 0.182239i
\(279\) 6.54779e9i 1.08063i
\(280\) 0 0
\(281\) 5.50789e9 0.883405 0.441703 − 0.897162i \(-0.354375\pi\)
0.441703 + 0.897162i \(0.354375\pi\)
\(282\) 1.02373e9 − 1.02373e9i 0.161878 − 0.161878i
\(283\) −7.63368e9 − 7.63368e9i −1.19011 − 1.19011i −0.977035 − 0.213078i \(-0.931651\pi\)
−0.213078 − 0.977035i \(-0.568349\pi\)
\(284\) 5.99703e8i 0.0921855i
\(285\) 0 0
\(286\) −6.97930e8 −0.104315
\(287\) −3.62382e9 + 3.62382e9i −0.534120 + 0.534120i
\(288\) −9.42127e8 − 9.42127e8i −0.136943 − 0.136943i
\(289\) − 4.88016e9i − 0.699588i
\(290\) 0 0
\(291\) −1.92200e9 −0.268029
\(292\) 4.53256e8 − 4.53256e8i 0.0623465 − 0.0623465i
\(293\) 4.49841e9 + 4.49841e9i 0.610364 + 0.610364i 0.943041 − 0.332677i \(-0.107952\pi\)
−0.332677 + 0.943041i \(0.607952\pi\)
\(294\) − 2.61781e9i − 0.350387i
\(295\) 0 0
\(296\) −1.13417e10 −1.47744
\(297\) 1.84972e9 − 1.84972e9i 0.237728 − 0.237728i
\(298\) −1.72534e9 − 1.72534e9i −0.218781 − 0.218781i
\(299\) − 1.07238e9i − 0.134173i
\(300\) 0 0
\(301\) 1.52583e10 1.85883
\(302\) −2.80128e8 + 2.80128e8i −0.0336767 + 0.0336767i
\(303\) 2.14593e9 + 2.14593e9i 0.254592 + 0.254592i
\(304\) − 1.20419e10i − 1.40994i
\(305\) 0 0
\(306\) 1.14811e10 1.30947
\(307\) −1.53928e9 + 1.53928e9i −0.173287 + 0.173287i −0.788422 − 0.615135i \(-0.789101\pi\)
0.615135 + 0.788422i \(0.289101\pi\)
\(308\) −8.65221e8 − 8.65221e8i −0.0961445 − 0.0961445i
\(309\) 1.74218e9i 0.191100i
\(310\) 0 0
\(311\) −5.22581e8 −0.0558614 −0.0279307 − 0.999610i \(-0.508892\pi\)
−0.0279307 + 0.999610i \(0.508892\pi\)
\(312\) 1.57115e8 − 1.57115e8i 0.0165805 − 0.0165805i
\(313\) −3.27149e9 − 3.27149e9i −0.340854 − 0.340854i 0.515834 − 0.856688i \(-0.327482\pi\)
−0.856688 + 0.515834i \(0.827482\pi\)
\(314\) − 1.58521e10i − 1.63068i
\(315\) 0 0
\(316\) 7.17777e7 0.00719848
\(317\) 3.24669e9 − 3.24669e9i 0.321517 − 0.321517i −0.527832 − 0.849349i \(-0.676995\pi\)
0.849349 + 0.527832i \(0.176995\pi\)
\(318\) −8.85776e8 − 8.85776e8i −0.0866194 − 0.0866194i
\(319\) 8.08756e9i 0.781006i
\(320\) 0 0
\(321\) 1.20303e9 0.113307
\(322\) 1.44192e10 − 1.44192e10i 1.34127 − 1.34127i
\(323\) 1.29641e10 + 1.29641e10i 1.19106 + 1.19106i
\(324\) 9.76967e8i 0.0886543i
\(325\) 0 0
\(326\) −6.12406e9 −0.542212
\(327\) 4.34153e8 − 4.34153e8i 0.0379709 − 0.0379709i
\(328\) −3.60813e9 − 3.60813e9i −0.311736 − 0.311736i
\(329\) − 1.99153e10i − 1.69982i
\(330\) 0 0
\(331\) 8.55909e9 0.713043 0.356522 − 0.934287i \(-0.383963\pi\)
0.356522 + 0.934287i \(0.383963\pi\)
\(332\) −2.99622e8 + 2.99622e8i −0.0246616 + 0.0246616i
\(333\) 1.30377e10 + 1.30377e10i 1.06029 + 1.06029i
\(334\) 1.16952e10i 0.939767i
\(335\) 0 0
\(336\) 4.65870e9 0.365517
\(337\) −7.19609e9 + 7.19609e9i −0.557926 + 0.557926i −0.928717 − 0.370790i \(-0.879087\pi\)
0.370790 + 0.928717i \(0.379087\pi\)
\(338\) −9.54691e9 − 9.54691e9i −0.731469 − 0.731469i
\(339\) 3.08099e9i 0.233288i
\(340\) 0 0
\(341\) −1.26513e10 −0.935663
\(342\) −1.25542e10 + 1.25542e10i −0.917669 + 0.917669i
\(343\) −9.65033e9 − 9.65033e9i −0.697213 − 0.697213i
\(344\) 1.51922e10i 1.08489i
\(345\) 0 0
\(346\) −8.35628e9 −0.583053
\(347\) −2.76044e9 + 2.76044e9i −0.190397 + 0.190397i −0.795868 − 0.605471i \(-0.792985\pi\)
0.605471 + 0.795868i \(0.292985\pi\)
\(348\) 2.05811e8 + 2.05811e8i 0.0140330 + 0.0140330i
\(349\) 7.99627e9i 0.538996i 0.963001 + 0.269498i \(0.0868578\pi\)
−0.963001 + 0.269498i \(0.913142\pi\)
\(350\) 0 0
\(351\) −7.38660e8 −0.0486649
\(352\) 1.82034e9 − 1.82034e9i 0.118572 − 0.118572i
\(353\) −1.99730e10 − 1.99730e10i −1.28630 − 1.28630i −0.937015 − 0.349290i \(-0.886423\pi\)
−0.349290 − 0.937015i \(-0.613577\pi\)
\(354\) − 1.83259e9i − 0.116695i
\(355\) 0 0
\(356\) −6.79393e8 −0.0422981
\(357\) −5.01549e9 + 5.01549e9i −0.308774 + 0.308774i
\(358\) 1.37986e10 + 1.37986e10i 0.840043 + 0.840043i
\(359\) 1.92076e10i 1.15637i 0.815906 + 0.578184i \(0.196238\pi\)
−0.815906 + 0.578184i \(0.803762\pi\)
\(360\) 0 0
\(361\) −1.13683e10 −0.669368
\(362\) −5.74738e9 + 5.74738e9i −0.334685 + 0.334685i
\(363\) −7.97641e8 − 7.97641e8i −0.0459389 − 0.0459389i
\(364\) 3.45513e8i 0.0196815i
\(365\) 0 0
\(366\) −4.05910e9 −0.226207
\(367\) 1.85651e10 − 1.85651e10i 1.02337 − 1.02337i 0.0236511 − 0.999720i \(-0.492471\pi\)
0.999720 − 0.0236511i \(-0.00752907\pi\)
\(368\) 1.58300e10 + 1.58300e10i 0.863159 + 0.863159i
\(369\) 8.29536e9i 0.447435i
\(370\) 0 0
\(371\) −1.72316e10 −0.909558
\(372\) −3.21949e8 + 3.21949e8i −0.0168118 + 0.0168118i
\(373\) −7.55571e9 − 7.55571e9i −0.390337 − 0.390337i 0.484470 − 0.874808i \(-0.339012\pi\)
−0.874808 + 0.484470i \(0.839012\pi\)
\(374\) 2.21832e10i 1.13380i
\(375\) 0 0
\(376\) 1.98291e10 0.992089
\(377\) 1.61482e9 − 1.61482e9i 0.0799391 − 0.0799391i
\(378\) −9.93198e9 − 9.93198e9i −0.486484 − 0.486484i
\(379\) − 1.95966e10i − 0.949783i −0.880044 − 0.474892i \(-0.842487\pi\)
0.880044 − 0.474892i \(-0.157513\pi\)
\(380\) 0 0
\(381\) 1.20886e9 0.0573690
\(382\) −1.77348e10 + 1.77348e10i −0.832862 + 0.832862i
\(383\) 1.07480e10 + 1.07480e10i 0.499497 + 0.499497i 0.911281 − 0.411784i \(-0.135094\pi\)
−0.411784 + 0.911281i \(0.635094\pi\)
\(384\) 5.07024e9i 0.233186i
\(385\) 0 0
\(386\) 2.08489e10 0.939146
\(387\) 1.74640e10 − 1.74640e10i 0.778575 − 0.778575i
\(388\) 2.10420e9 + 2.10420e9i 0.0928454 + 0.0928454i
\(389\) − 3.58035e10i − 1.56361i −0.623526 − 0.781803i \(-0.714300\pi\)
0.623526 − 0.781803i \(-0.285700\pi\)
\(390\) 0 0
\(391\) −3.40848e10 −1.45832
\(392\) 2.53528e10 − 2.53528e10i 1.07370 − 1.07370i
\(393\) 4.56645e9 + 4.56645e9i 0.191429 + 0.191429i
\(394\) − 4.99958e9i − 0.207467i
\(395\) 0 0
\(396\) −1.98060e9 −0.0805407
\(397\) 3.85643e9 − 3.85643e9i 0.155247 − 0.155247i −0.625210 − 0.780457i \(-0.714987\pi\)
0.780457 + 0.625210i \(0.214987\pi\)
\(398\) 1.71443e10 + 1.71443e10i 0.683261 + 0.683261i
\(399\) − 1.09686e10i − 0.432773i
\(400\) 0 0
\(401\) 3.39784e10 1.31409 0.657046 − 0.753851i \(-0.271806\pi\)
0.657046 + 0.753851i \(0.271806\pi\)
\(402\) −3.23073e9 + 3.23073e9i −0.123707 + 0.123707i
\(403\) 2.52606e9 + 2.52606e9i 0.0957688 + 0.0957688i
\(404\) − 4.69871e9i − 0.176382i
\(405\) 0 0
\(406\) 4.34256e10 1.59824
\(407\) −2.51908e10 + 2.51908e10i −0.918047 + 0.918047i
\(408\) −4.99378e9 − 4.99378e9i −0.180214 − 0.180214i
\(409\) 1.10826e10i 0.396048i 0.980197 + 0.198024i \(0.0634523\pi\)
−0.980197 + 0.198024i \(0.936548\pi\)
\(410\) 0 0
\(411\) −3.86235e9 −0.135358
\(412\) 1.90734e9 − 1.90734e9i 0.0661970 − 0.0661970i
\(413\) −1.78253e10 − 1.78253e10i −0.612685 − 0.612685i
\(414\) − 3.30072e10i − 1.12359i
\(415\) 0 0
\(416\) −7.26924e8 −0.0242726
\(417\) −1.08848e9 + 1.08848e9i −0.0359978 + 0.0359978i
\(418\) −2.42567e10 − 2.42567e10i −0.794561 − 0.794561i
\(419\) − 3.54167e10i − 1.14909i −0.818474 − 0.574543i \(-0.805180\pi\)
0.818474 − 0.574543i \(-0.194820\pi\)
\(420\) 0 0
\(421\) −2.98731e10 −0.950938 −0.475469 − 0.879733i \(-0.657722\pi\)
−0.475469 + 0.879733i \(0.657722\pi\)
\(422\) −1.86636e10 + 1.86636e10i −0.588498 + 0.588498i
\(423\) −2.27943e10 − 2.27943e10i −0.711974 − 0.711974i
\(424\) − 1.71570e10i − 0.530858i
\(425\) 0 0
\(426\) −6.50447e9 −0.197503
\(427\) −3.94823e10 + 3.94823e10i −1.18766 + 1.18766i
\(428\) −1.31708e9 − 1.31708e9i −0.0392498 − 0.0392498i
\(429\) − 6.97930e8i − 0.0206055i
\(430\) 0 0
\(431\) 6.06834e10 1.75857 0.879287 − 0.476293i \(-0.158020\pi\)
0.879287 + 0.476293i \(0.158020\pi\)
\(432\) 1.09038e10 − 1.09038e10i 0.313071 − 0.313071i
\(433\) 4.29956e10 + 4.29956e10i 1.22313 + 1.22313i 0.966513 + 0.256617i \(0.0826079\pi\)
0.256617 + 0.966513i \(0.417392\pi\)
\(434\) 6.79306e10i 1.91473i
\(435\) 0 0
\(436\) −9.50618e8 −0.0263063
\(437\) 3.72708e10 − 3.72708e10i 1.02198 − 1.02198i
\(438\) 4.91608e9 + 4.91608e9i 0.133574 + 0.133574i
\(439\) − 8.86294e9i − 0.238627i −0.992857 − 0.119314i \(-0.961931\pi\)
0.992857 − 0.119314i \(-0.0380694\pi\)
\(440\) 0 0
\(441\) −5.82880e10 −1.54108
\(442\) 4.42927e9 − 4.42927e9i 0.116049 − 0.116049i
\(443\) −1.68455e10 − 1.68455e10i −0.437390 − 0.437390i 0.453743 − 0.891133i \(-0.350088\pi\)
−0.891133 + 0.453743i \(0.850088\pi\)
\(444\) 1.28210e9i 0.0329907i
\(445\) 0 0
\(446\) −1.07405e10 −0.271448
\(447\) 1.72534e9 − 1.72534e9i 0.0432159 − 0.0432159i
\(448\) 4.04444e10 + 4.04444e10i 1.00403 + 1.00403i
\(449\) 5.95055e10i 1.46410i 0.681250 + 0.732051i \(0.261437\pi\)
−0.681250 + 0.732051i \(0.738563\pi\)
\(450\) 0 0
\(451\) −1.60279e10 −0.387410
\(452\) 3.37306e9 − 3.37306e9i 0.0808110 − 0.0808110i
\(453\) −2.80128e8 − 2.80128e8i −0.00665218 − 0.00665218i
\(454\) − 3.36650e10i − 0.792421i
\(455\) 0 0
\(456\) 1.09211e10 0.252585
\(457\) −2.91131e9 + 2.91131e9i −0.0667459 + 0.0667459i −0.739692 − 0.672946i \(-0.765029\pi\)
0.672946 + 0.739692i \(0.265029\pi\)
\(458\) −6.04503e10 − 6.04503e10i −1.37384 − 1.37384i
\(459\) 2.34778e10i 0.528940i
\(460\) 0 0
\(461\) 4.79933e9 0.106262 0.0531309 − 0.998588i \(-0.483080\pi\)
0.0531309 + 0.998588i \(0.483080\pi\)
\(462\) 9.38433e9 − 9.38433e9i 0.205985 − 0.205985i
\(463\) 4.23409e10 + 4.23409e10i 0.921375 + 0.921375i 0.997127 − 0.0757516i \(-0.0241356\pi\)
−0.0757516 + 0.997127i \(0.524136\pi\)
\(464\) 4.76747e10i 1.02853i
\(465\) 0 0
\(466\) −7.68872e10 −1.63046
\(467\) 2.55795e10 − 2.55795e10i 0.537805 − 0.537805i −0.385079 − 0.922884i \(-0.625826\pi\)
0.922884 + 0.385079i \(0.125826\pi\)
\(468\) 3.95461e8 + 3.95461e8i 0.00824366 + 0.00824366i
\(469\) 6.28496e10i 1.29901i
\(470\) 0 0
\(471\) 1.58521e10 0.322110
\(472\) 1.77482e10 − 1.77482e10i 0.357590 − 0.357590i
\(473\) 3.37432e10 + 3.37432e10i 0.674127 + 0.674127i
\(474\) 7.78512e8i 0.0154224i
\(475\) 0 0
\(476\) 1.09819e10 0.213919
\(477\) −1.97226e10 + 1.97226e10i −0.380971 + 0.380971i
\(478\) −7.66701e9 − 7.66701e9i −0.146864 − 0.146864i
\(479\) − 4.66044e10i − 0.885288i −0.896697 − 0.442644i \(-0.854041\pi\)
0.896697 − 0.442644i \(-0.145959\pi\)
\(480\) 0 0
\(481\) 1.00596e10 0.187931
\(482\) 1.23568e10 − 1.23568e10i 0.228938 − 0.228938i
\(483\) 1.44192e10 + 1.44192e10i 0.264942 + 0.264942i
\(484\) 1.74651e9i 0.0318266i
\(485\) 0 0
\(486\) −3.43529e10 −0.615770
\(487\) −1.63896e10 + 1.63896e10i −0.291375 + 0.291375i −0.837623 − 0.546248i \(-0.816055\pi\)
0.546248 + 0.837623i \(0.316055\pi\)
\(488\) −3.93113e10 − 3.93113e10i −0.693168 − 0.693168i
\(489\) − 6.12406e9i − 0.107104i
\(490\) 0 0
\(491\) 7.94765e10 1.36745 0.683727 − 0.729738i \(-0.260358\pi\)
0.683727 + 0.729738i \(0.260358\pi\)
\(492\) −4.07876e8 + 4.07876e8i −0.00696093 + 0.00696093i
\(493\) −5.13260e10 − 5.13260e10i −0.868860 − 0.868860i
\(494\) 9.68656e9i 0.162653i
\(495\) 0 0
\(496\) −7.45775e10 −1.23220
\(497\) −6.32680e10 + 6.32680e10i −1.03695 + 1.03695i
\(498\) −3.24974e9 − 3.24974e9i −0.0528362 − 0.0528362i
\(499\) − 1.83615e10i − 0.296146i −0.988976 − 0.148073i \(-0.952693\pi\)
0.988976 − 0.148073i \(-0.0473070\pi\)
\(500\) 0 0
\(501\) −1.16952e10 −0.185633
\(502\) −4.92894e10 + 4.92894e10i −0.776138 + 0.776138i
\(503\) −6.21239e9 − 6.21239e9i −0.0970480 − 0.0970480i 0.656916 − 0.753964i \(-0.271861\pi\)
−0.753964 + 0.656916i \(0.771861\pi\)
\(504\) − 9.40761e10i − 1.45800i
\(505\) 0 0
\(506\) 6.37750e10 0.972856
\(507\) 9.54691e9 − 9.54691e9i 0.144488 − 0.144488i
\(508\) −1.32346e9 − 1.32346e9i −0.0198727 − 0.0198727i
\(509\) 4.31615e10i 0.643021i 0.946906 + 0.321511i \(0.104191\pi\)
−0.946906 + 0.321511i \(0.895809\pi\)
\(510\) 0 0
\(511\) 9.56360e10 1.40261
\(512\) −3.92707e10 + 3.92707e10i −0.571463 + 0.571463i
\(513\) −2.56723e10 − 2.56723e10i −0.370677 − 0.370677i
\(514\) − 1.35723e11i − 1.94446i
\(515\) 0 0
\(516\) 1.71738e9 0.0242252
\(517\) 4.40420e10 − 4.40420e10i 0.616460 − 0.616460i
\(518\) 1.35261e11 + 1.35261e11i 1.87868 + 1.87868i
\(519\) − 8.35628e9i − 0.115171i
\(520\) 0 0
\(521\) 2.90244e10 0.393923 0.196962 − 0.980411i \(-0.436893\pi\)
0.196962 + 0.980411i \(0.436893\pi\)
\(522\) 4.97033e10 − 4.97033e10i 0.669426 − 0.669426i
\(523\) −4.27429e10 − 4.27429e10i −0.571291 − 0.571291i 0.361198 − 0.932489i \(-0.382368\pi\)
−0.932489 + 0.361198i \(0.882368\pi\)
\(524\) − 9.99868e9i − 0.132623i
\(525\) 0 0
\(526\) 3.78505e10 0.494457
\(527\) 8.02892e10 − 8.02892e10i 1.04091 − 1.04091i
\(528\) 1.03026e10 + 1.03026e10i 0.132559 + 0.132559i
\(529\) 1.96803e10i 0.251310i
\(530\) 0 0
\(531\) −4.08043e10 −0.513249
\(532\) −1.20084e10 + 1.20084e10i −0.149913 + 0.149913i
\(533\) 3.20026e9 + 3.20026e9i 0.0396530 + 0.0396530i
\(534\) − 7.36880e9i − 0.0906217i
\(535\) 0 0
\(536\) −6.25775e10 −0.758157
\(537\) −1.37986e10 + 1.37986e10i −0.165934 + 0.165934i
\(538\) −3.12116e10 − 3.12116e10i −0.372552 − 0.372552i
\(539\) − 1.12621e11i − 1.33434i
\(540\) 0 0
\(541\) −6.67715e9 −0.0779475 −0.0389738 − 0.999240i \(-0.512409\pi\)
−0.0389738 + 0.999240i \(0.512409\pi\)
\(542\) −2.42707e10 + 2.42707e10i −0.281245 + 0.281245i
\(543\) −5.74738e9 − 5.74738e9i −0.0661105 − 0.0661105i
\(544\) 2.31048e10i 0.263819i
\(545\) 0 0
\(546\) −3.74749e9 −0.0421667
\(547\) 7.25792e10 − 7.25792e10i 0.810705 − 0.810705i −0.174035 − 0.984740i \(-0.555681\pi\)
0.984740 + 0.174035i \(0.0556805\pi\)
\(548\) 4.22849e9 + 4.22849e9i 0.0468881 + 0.0468881i
\(549\) 9.03797e10i 0.994905i
\(550\) 0 0
\(551\) 1.12247e11 1.21778
\(552\) −1.43567e10 + 1.43567e10i −0.154632 + 0.154632i
\(553\) 7.57247e9 + 7.57247e9i 0.0809724 + 0.0809724i
\(554\) 1.02428e11i 1.08738i
\(555\) 0 0
\(556\) 2.38333e9 0.0249393
\(557\) −2.52569e10 + 2.52569e10i −0.262397 + 0.262397i −0.826027 − 0.563630i \(-0.809404\pi\)
0.563630 + 0.826027i \(0.309404\pi\)
\(558\) 7.77507e10 + 7.77507e10i 0.801987 + 0.801987i
\(559\) − 1.34748e10i − 0.137999i
\(560\) 0 0
\(561\) −2.21832e10 −0.223961
\(562\) 6.54026e10 − 6.54026e10i 0.655616 − 0.655616i
\(563\) 1.77029e10 + 1.77029e10i 0.176202 + 0.176202i 0.789698 − 0.613496i \(-0.210237\pi\)
−0.613496 + 0.789698i \(0.710237\pi\)
\(564\) − 2.24155e9i − 0.0221529i
\(565\) 0 0
\(566\) −1.81290e11 −1.76648
\(567\) −1.03069e11 + 1.03069e11i −0.997231 + 0.997231i
\(568\) −6.29941e10 − 6.29941e10i −0.605211 − 0.605211i
\(569\) 5.69768e10i 0.543562i 0.962359 + 0.271781i \(0.0876126\pi\)
−0.962359 + 0.271781i \(0.912387\pi\)
\(570\) 0 0
\(571\) −1.40041e11 −1.31738 −0.658690 − 0.752415i \(-0.728889\pi\)
−0.658690 + 0.752415i \(0.728889\pi\)
\(572\) −7.64092e8 + 7.64092e8i −0.00713775 + 0.00713775i
\(573\) −1.77348e10 − 1.77348e10i −0.164516 − 0.164516i
\(574\) 8.60609e10i 0.792790i
\(575\) 0 0
\(576\) 9.25822e10 0.841081
\(577\) 4.33597e10 − 4.33597e10i 0.391186 − 0.391186i −0.483924 − 0.875110i \(-0.660789\pi\)
0.875110 + 0.483924i \(0.160789\pi\)
\(578\) −5.79487e10 − 5.79487e10i −0.519197 − 0.519197i
\(579\) 2.08489e10i 0.185510i
\(580\) 0 0
\(581\) −6.32196e10 −0.554814
\(582\) −2.28225e10 + 2.28225e10i −0.198917 + 0.198917i
\(583\) −3.81072e10 − 3.81072e10i −0.329862 − 0.329862i
\(584\) 9.52220e10i 0.818627i
\(585\) 0 0
\(586\) 1.06831e11 0.905959
\(587\) −1.52268e11 + 1.52268e11i −1.28250 + 1.28250i −0.343258 + 0.939241i \(0.611530\pi\)
−0.939241 + 0.343258i \(0.888470\pi\)
\(588\) −2.86597e9 − 2.86597e9i −0.0239752 − 0.0239752i
\(589\) 1.75588e11i 1.45893i
\(590\) 0 0
\(591\) 4.99958e9 0.0409811
\(592\) −1.48495e11 + 1.48495e11i −1.20900 + 1.20900i
\(593\) 5.29744e8 + 5.29744e8i 0.00428397 + 0.00428397i 0.709246 − 0.704962i \(-0.249036\pi\)
−0.704962 + 0.709246i \(0.749036\pi\)
\(594\) − 4.39285e10i − 0.352859i
\(595\) 0 0
\(596\) −3.77779e9 −0.0299401
\(597\) −1.71443e10 + 1.71443e10i −0.134965 + 0.134965i
\(598\) −1.27338e10 − 1.27338e10i −0.0995757 − 0.0995757i
\(599\) − 1.98446e11i − 1.54147i −0.637157 − 0.770734i \(-0.719890\pi\)
0.637157 − 0.770734i \(-0.280110\pi\)
\(600\) 0 0
\(601\) −2.01430e11 −1.54393 −0.771964 − 0.635666i \(-0.780726\pi\)
−0.771964 + 0.635666i \(0.780726\pi\)
\(602\) 1.81182e11 − 1.81182e11i 1.37952 − 1.37952i
\(603\) 7.19352e10 + 7.19352e10i 0.544092 + 0.544092i
\(604\) 6.13367e8i 0.00460864i
\(605\) 0 0
\(606\) 5.09630e10 0.377889
\(607\) 1.38674e11 − 1.38674e11i 1.02150 − 1.02150i 0.0217387 − 0.999764i \(-0.493080\pi\)
0.999764 − 0.0217387i \(-0.00692018\pi\)
\(608\) −2.52644e10 − 2.52644e10i −0.184882 − 0.184882i
\(609\) 4.34256e10i 0.315702i
\(610\) 0 0
\(611\) −1.75875e10 −0.126194
\(612\) 1.25695e10 − 1.25695e10i 0.0896006 − 0.0896006i
\(613\) 1.07154e11 + 1.07154e11i 0.758871 + 0.758871i 0.976117 − 0.217246i \(-0.0697074\pi\)
−0.217246 + 0.976117i \(0.569707\pi\)
\(614\) 3.65559e10i 0.257208i
\(615\) 0 0
\(616\) 1.81770e11 1.26240
\(617\) 8.73671e10 − 8.73671e10i 0.602847 − 0.602847i −0.338220 − 0.941067i \(-0.609825\pi\)
0.941067 + 0.338220i \(0.109825\pi\)
\(618\) 2.06873e10 + 2.06873e10i 0.141824 + 0.141824i
\(619\) − 1.24104e11i − 0.845325i −0.906287 − 0.422663i \(-0.861096\pi\)
0.906287 − 0.422663i \(-0.138904\pi\)
\(620\) 0 0
\(621\) 6.74968e10 0.453855
\(622\) −6.20531e9 + 6.20531e9i −0.0414574 + 0.0414574i
\(623\) −7.16753e10 − 7.16753e10i −0.475792 − 0.475792i
\(624\) − 4.11417e9i − 0.0271359i
\(625\) 0 0
\(626\) −7.76936e10 −0.505927
\(627\) 2.42567e10 − 2.42567e10i 0.156950 − 0.156950i
\(628\) −1.73549e10 − 1.73549e10i −0.111579 − 0.111579i
\(629\) − 3.19737e11i − 2.04263i
\(630\) 0 0
\(631\) 2.11881e11 1.33652 0.668258 − 0.743929i \(-0.267040\pi\)
0.668258 + 0.743929i \(0.267040\pi\)
\(632\) −7.53969e9 + 7.53969e9i −0.0472591 + 0.0472591i
\(633\) −1.86636e10 − 1.86636e10i −0.116247 − 0.116247i
\(634\) − 7.71045e10i − 0.477225i
\(635\) 0 0
\(636\) −1.93949e9 −0.0118538
\(637\) −2.24868e10 + 2.24868e10i −0.136575 + 0.136575i
\(638\) 9.60344e10 + 9.60344e10i 0.579621 + 0.579621i
\(639\) 1.44828e11i 0.868660i
\(640\) 0 0
\(641\) −1.20192e11 −0.711940 −0.355970 − 0.934497i \(-0.615849\pi\)
−0.355970 + 0.934497i \(0.615849\pi\)
\(642\) 1.42852e10 − 1.42852e10i 0.0840906 − 0.0840906i
\(643\) 8.34104e10 + 8.34104e10i 0.487951 + 0.487951i 0.907659 − 0.419708i \(-0.137868\pi\)
−0.419708 + 0.907659i \(0.637868\pi\)
\(644\) − 3.15721e10i − 0.183552i
\(645\) 0 0
\(646\) 3.07881e11 1.76788
\(647\) −1.74293e11 + 1.74293e11i −0.994635 + 0.994635i −0.999986 − 0.00535087i \(-0.998297\pi\)
0.00535087 + 0.999986i \(0.498297\pi\)
\(648\) −1.02623e11 − 1.02623e11i −0.582028 − 0.582028i
\(649\) − 7.88403e10i − 0.444395i
\(650\) 0 0
\(651\) −6.79306e10 −0.378217
\(652\) −6.70461e9 + 6.70461e9i −0.0371008 + 0.0371008i
\(653\) 1.69727e11 + 1.69727e11i 0.933465 + 0.933465i 0.997921 − 0.0644553i \(-0.0205310\pi\)
−0.0644553 + 0.997921i \(0.520531\pi\)
\(654\) − 1.03106e10i − 0.0563600i
\(655\) 0 0
\(656\) −9.44818e10 −0.510191
\(657\) 1.09461e11 − 1.09461e11i 0.587488 − 0.587488i
\(658\) −2.36481e11 − 2.36481e11i −1.26151 − 1.26151i
\(659\) − 2.61429e11i − 1.38616i −0.720862 − 0.693078i \(-0.756254\pi\)
0.720862 − 0.693078i \(-0.243746\pi\)
\(660\) 0 0
\(661\) −9.90557e10 −0.518888 −0.259444 − 0.965758i \(-0.583539\pi\)
−0.259444 + 0.965758i \(0.583539\pi\)
\(662\) 1.01634e11 − 1.01634e11i 0.529182 − 0.529182i
\(663\) 4.42927e9 + 4.42927e9i 0.0229233 + 0.0229233i
\(664\) − 6.29459e10i − 0.323814i
\(665\) 0 0
\(666\) 3.09628e11 1.57378
\(667\) −1.47558e11 + 1.47558e11i −0.745522 + 0.745522i
\(668\) 1.28038e10 + 1.28038e10i 0.0643034 + 0.0643034i
\(669\) − 1.07405e10i − 0.0536193i
\(670\) 0 0
\(671\) −1.74628e11 −0.861436
\(672\) 9.77418e9 − 9.77418e9i 0.0479295 − 0.0479295i
\(673\) −1.05855e11 − 1.05855e11i −0.516003 − 0.516003i 0.400357 − 0.916359i \(-0.368886\pi\)
−0.916359 + 0.400357i \(0.868886\pi\)
\(674\) 1.70898e11i 0.828126i
\(675\) 0 0
\(676\) −2.09039e10 −0.100101
\(677\) −2.34302e11 + 2.34302e11i −1.11538 + 1.11538i −0.122965 + 0.992411i \(0.539240\pi\)
−0.992411 + 0.122965i \(0.960760\pi\)
\(678\) 3.65847e10 + 3.65847e10i 0.173133 + 0.173133i
\(679\) 4.43982e11i 2.08875i
\(680\) 0 0
\(681\) 3.36650e10 0.156528
\(682\) −1.50226e11 + 1.50226e11i −0.694399 + 0.694399i
\(683\) −2.10586e11 − 2.10586e11i −0.967715 − 0.967715i 0.0317802 − 0.999495i \(-0.489882\pi\)
−0.999495 + 0.0317802i \(0.989882\pi\)
\(684\) 2.74887e10i 0.125583i
\(685\) 0 0
\(686\) −2.29183e11 −1.03487
\(687\) 6.04503e10 − 6.04503e10i 0.271376 − 0.271376i
\(688\) 1.98910e11 + 1.98910e11i 0.887776 + 0.887776i
\(689\) 1.52175e10i 0.0675254i
\(690\) 0 0
\(691\) −4.57396e10 −0.200623 −0.100311 − 0.994956i \(-0.531984\pi\)
−0.100311 + 0.994956i \(0.531984\pi\)
\(692\) −9.14843e9 + 9.14843e9i −0.0398953 + 0.0398953i
\(693\) −2.08951e11 − 2.08951e11i −0.905965 − 0.905965i
\(694\) 6.55567e10i 0.282605i
\(695\) 0 0
\(696\) −4.32376e10 −0.184257
\(697\) 1.01718e11 − 1.01718e11i 0.430989 − 0.430989i
\(698\) 9.49504e10 + 9.49504e10i 0.400014 + 0.400014i
\(699\) − 7.68872e10i − 0.322066i
\(700\) 0 0
\(701\) 9.83586e10 0.407324 0.203662 − 0.979041i \(-0.434716\pi\)
0.203662 + 0.979041i \(0.434716\pi\)
\(702\) −8.77110e9 + 8.77110e9i −0.0361165 + 0.0361165i
\(703\) 3.49623e11 + 3.49623e11i 1.43146 + 1.43146i
\(704\) 1.78883e11i 0.728247i
\(705\) 0 0
\(706\) −4.74332e11 −1.90925
\(707\) 4.95710e11 − 4.95710e11i 1.98404 − 1.98404i
\(708\) −2.00631e9 − 2.00631e9i −0.00798483 − 0.00798483i
\(709\) 1.32351e11i 0.523771i 0.965099 + 0.261885i \(0.0843443\pi\)
−0.965099 + 0.261885i \(0.915656\pi\)
\(710\) 0 0
\(711\) 1.73343e10 0.0678310
\(712\) 7.13650e10 − 7.13650e10i 0.277693 − 0.277693i
\(713\) −2.30825e11 − 2.30825e11i −0.893151 − 0.893151i
\(714\) 1.19111e11i 0.458311i
\(715\) 0 0
\(716\) 3.02132e10 0.114960
\(717\) 7.66701e9 − 7.66701e9i 0.0290101 − 0.0290101i
\(718\) 2.28078e11 + 2.28078e11i 0.858194 + 0.858194i
\(719\) 2.14771e11i 0.803636i 0.915720 + 0.401818i \(0.131622\pi\)
−0.915720 + 0.401818i \(0.868378\pi\)
\(720\) 0 0
\(721\) 4.02444e11 1.48924
\(722\) −1.34991e11 + 1.34991e11i −0.496769 + 0.496769i
\(723\) 1.23568e10 + 1.23568e10i 0.0452224 + 0.0452224i
\(724\) 1.25844e10i 0.0458015i
\(725\) 0 0
\(726\) −1.89429e10 −0.0681868
\(727\) 3.41170e10 − 3.41170e10i 0.122133 − 0.122133i −0.643398 − 0.765531i \(-0.722476\pi\)
0.765531 + 0.643398i \(0.222476\pi\)
\(728\) −3.62935e10 − 3.62935e10i −0.129212 − 0.129212i
\(729\) 2.12181e11i 0.751270i
\(730\) 0 0
\(731\) −4.28289e11 −1.49992
\(732\) −4.44389e9 + 4.44389e9i −0.0154782 + 0.0154782i
\(733\) 6.69873e10 + 6.69873e10i 0.232047 + 0.232047i 0.813547 − 0.581499i \(-0.197534\pi\)
−0.581499 + 0.813547i \(0.697534\pi\)
\(734\) − 4.40897e11i − 1.51898i
\(735\) 0 0
\(736\) 6.64244e10 0.226369
\(737\) −1.38990e11 + 1.38990e11i −0.471100 + 0.471100i
\(738\) 9.85020e10 + 9.85020e10i 0.332062 + 0.332062i
\(739\) − 6.08310e10i − 0.203961i −0.994786 − 0.101981i \(-0.967482\pi\)
0.994786 − 0.101981i \(-0.0325180\pi\)
\(740\) 0 0
\(741\) −9.68656e9 −0.0321290
\(742\) −2.04614e11 + 2.04614e11i −0.675025 + 0.675025i
\(743\) −1.90364e11 − 1.90364e11i −0.624639 − 0.624639i 0.322075 − 0.946714i \(-0.395620\pi\)
−0.946714 + 0.322075i \(0.895620\pi\)
\(744\) − 6.76365e10i − 0.220744i
\(745\) 0 0
\(746\) −1.79438e11 −0.579375
\(747\) −7.23587e10 + 7.23587e10i −0.232385 + 0.232385i
\(748\) 2.42861e10 + 2.42861e10i 0.0775804 + 0.0775804i
\(749\) − 2.77901e11i − 0.883004i
\(750\) 0 0
\(751\) 3.43050e11 1.07844 0.539222 − 0.842164i \(-0.318718\pi\)
0.539222 + 0.842164i \(0.318718\pi\)
\(752\) 2.59620e11 − 2.59620e11i 0.811833 − 0.811833i
\(753\) −4.92894e10 − 4.92894e10i −0.153311 − 0.153311i
\(754\) − 3.83499e10i − 0.118653i
\(755\) 0 0
\(756\) −2.17470e10 −0.0665752
\(757\) −7.34063e10 + 7.34063e10i −0.223537 + 0.223537i −0.809986 − 0.586449i \(-0.800525\pi\)
0.586449 + 0.809986i \(0.300525\pi\)
\(758\) −2.32697e11 − 2.32697e11i −0.704878 − 0.704878i
\(759\) 6.37750e10i 0.192169i
\(760\) 0 0
\(761\) 5.88790e11 1.75558 0.877792 − 0.479042i \(-0.159016\pi\)
0.877792 + 0.479042i \(0.159016\pi\)
\(762\) 1.43545e10 − 1.43545e10i 0.0425762 − 0.0425762i
\(763\) −1.00289e11 − 1.00289e11i −0.295908 − 0.295908i
\(764\) 3.88321e10i 0.113977i
\(765\) 0 0
\(766\) 2.55251e11 0.741400
\(767\) −1.57418e10 + 1.57418e10i −0.0454856 + 0.0454856i
\(768\) 1.53842e10 + 1.53842e10i 0.0442211 + 0.0442211i
\(769\) − 3.95721e11i − 1.13158i −0.824550 − 0.565789i \(-0.808572\pi\)
0.824550 − 0.565789i \(-0.191428\pi\)
\(770\) 0 0
\(771\) 1.35723e11 0.384091
\(772\) 2.28253e10 − 2.28253e10i 0.0642609 − 0.0642609i
\(773\) 3.23931e11 + 3.23931e11i 0.907265 + 0.907265i 0.996051 − 0.0887861i \(-0.0282988\pi\)
−0.0887861 + 0.996051i \(0.528299\pi\)
\(774\) − 4.14748e11i − 1.15563i
\(775\)