Properties

Label 8.21.d.b.3.8
Level 8
Weight 21
Character 8.3
Analytic conductor 20.281
Analytic rank 0
Dimension 18
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 21 \)
Character orbit: \([\chi]\) = 8.d (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(20.2811012082\)
Analytic rank: \(0\)
Dimension: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: multiple of \( 2^{153}\cdot 3^{15}\cdot 5^{4}\cdot 7^{2} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 3.8
Root \(22670.7 + 1.21630e6i\)
Character \(\chi\) = 8.3
Dual form 8.21.d.b.3.7

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+(-340.525 + 965.722i) q^{2}\) \(+84336.7 q^{3}\) \(+(-816662. - 657705. i) q^{4}\) \(-4.86521e6i q^{5}\) \(+(-2.87188e7 + 8.14458e7i) q^{6}\) \(+1.26224e8i q^{7}\) \(+(9.13253e8 - 5.64703e8i) q^{8}\) \(+3.62590e9 q^{9}\) \(+O(q^{10})\) \(q\)\(+(-340.525 + 965.722i) q^{2}\) \(+84336.7 q^{3}\) \(+(-816662. - 657705. i) q^{4}\) \(-4.86521e6i q^{5}\) \(+(-2.87188e7 + 8.14458e7i) q^{6}\) \(+1.26224e8i q^{7}\) \(+(9.13253e8 - 5.64703e8i) q^{8}\) \(+3.62590e9 q^{9}\) \(+(4.69844e9 + 1.65673e9i) q^{10}\) \(+1.51387e10 q^{11}\) \(+(-6.88746e10 - 5.54687e10i) q^{12}\) \(-1.95170e11i q^{13}\) \(+(-1.21897e11 - 4.29823e10i) q^{14}\) \(-4.10316e11i q^{15}\) \(+(2.34361e11 + 1.07424e12i) q^{16}\) \(+3.56201e12 q^{17}\) \(+(-1.23471e12 + 3.50161e12i) q^{18}\) \(+3.48807e12 q^{19}\) \(+(-3.19987e12 + 3.97323e12i) q^{20}\) \(+1.06453e13i q^{21}\) \(+(-5.15512e12 + 1.46198e13i) q^{22}\) \(+1.17677e13i q^{23}\) \(+(7.70208e13 - 4.76252e13i) q^{24}\) \(+7.16971e13 q^{25}\) \(+(1.88480e14 + 6.64604e13i) q^{26}\) \(+1.17326e13 q^{27}\) \(+(8.30179e13 - 1.03082e14i) q^{28}\) \(+7.56048e14i q^{29}\) \(+(3.96251e14 + 1.39723e14i) q^{30}\) \(-1.11233e15i q^{31}\) \(+(-1.11723e15 - 1.39479e14i) q^{32}\) \(+1.27675e15 q^{33}\) \(+(-1.21295e15 + 3.43992e15i) q^{34}\) \(+6.14105e14 q^{35}\) \(+(-2.96113e15 - 2.38477e15i) q^{36}\) \(+7.17444e14i q^{37}\) \(+(-1.18778e15 + 3.36851e15i) q^{38}\) \(-1.64600e16i q^{39}\) \(+(-2.74740e15 - 4.44317e15i) q^{40}\) \(+3.23458e15 q^{41}\) \(+(-1.02804e16 - 3.62499e15i) q^{42}\) \(-1.36789e16 q^{43}\) \(+(-1.23632e16 - 9.95682e15i) q^{44}\) \(-1.76408e16i q^{45}\) \(+(-1.13644e16 - 4.00720e15i) q^{46}\) \(+4.28694e16i q^{47}\) \(+(1.97652e16 + 9.05983e16i) q^{48}\) \(+6.38598e16 q^{49}\) \(+(-2.44147e16 + 6.92395e16i) q^{50}\) \(+3.00409e17 q^{51}\) \(+(-1.28364e17 + 1.59388e17i) q^{52}\) \(-3.34779e17i q^{53}\) \(+(-3.99524e15 + 1.13304e16i) q^{54}\) \(-7.36531e16i q^{55}\) \(+(7.12790e16 + 1.15274e17i) q^{56}\) \(+2.94173e17 q^{57}\) \(+(-7.30133e17 - 2.57453e17i) q^{58}\) \(+2.74237e17 q^{59}\) \(+(-2.69867e17 + 3.35089e17i) q^{60}\) \(-1.49210e17i q^{61}\) \(+(1.07420e18 + 3.78775e17i) q^{62}\) \(+4.57675e17i q^{63}\) \(+(5.15142e17 - 1.03143e18i) q^{64}\) \(-9.49545e17 q^{65}\) \(+(-4.34766e17 + 1.23299e18i) q^{66}\) \(-2.92321e18 q^{67}\) \(+(-2.90896e18 - 2.34275e18i) q^{68}\) \(+9.92452e17i q^{69}\) \(+(-2.09118e17 + 5.93055e17i) q^{70}\) \(-3.51233e18i q^{71}\) \(+(3.31137e18 - 2.04756e18i) q^{72}\) \(+5.45402e17 q^{73}\) \(+(-6.92851e17 - 2.44307e17i) q^{74}\) \(+6.04670e18 q^{75}\) \(+(-2.84858e18 - 2.29412e18i) q^{76}\) \(+1.91087e18i q^{77}\) \(+(1.58958e19 + 5.60505e18i) q^{78}\) \(+1.64097e19i q^{79}\) \(+(5.22643e18 - 1.14022e18i) q^{80}\) \(-1.16532e19 q^{81}\) \(+(-1.10145e18 + 3.12370e18i) q^{82}\) \(-1.30232e19 q^{83}\) \(+(7.00146e18 - 8.69361e18i) q^{84}\) \(-1.73300e19i q^{85}\) \(+(4.65801e18 - 1.32100e19i) q^{86}\) \(+6.37627e19i q^{87}\) \(+(1.38255e19 - 8.54889e18i) q^{88}\) \(-2.43956e19 q^{89}\) \(+(1.70361e19 + 6.00712e18i) q^{90}\) \(+2.46351e19 q^{91}\) \(+(7.73969e18 - 9.61025e18i) q^{92}\) \(-9.38101e19i q^{93}\) \(+(-4.13999e19 - 1.45981e19i) q^{94}\) \(-1.69702e19i q^{95}\) \(+(-9.42233e19 - 1.17632e19i) q^{96}\) \(-7.85794e18 q^{97}\) \(+(-2.17459e19 + 6.16708e19i) q^{98}\) \(+5.48915e19 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(18q \) \(\mathstrut -\mathstrut 398q^{2} \) \(\mathstrut -\mathstrut 114228q^{3} \) \(\mathstrut +\mathstrut 724980q^{4} \) \(\mathstrut -\mathstrut 91643748q^{6} \) \(\mathstrut -\mathstrut 3105291368q^{8} \) \(\mathstrut +\mathstrut 10197650262q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(18q \) \(\mathstrut -\mathstrut 398q^{2} \) \(\mathstrut -\mathstrut 114228q^{3} \) \(\mathstrut +\mathstrut 724980q^{4} \) \(\mathstrut -\mathstrut 91643748q^{6} \) \(\mathstrut -\mathstrut 3105291368q^{8} \) \(\mathstrut +\mathstrut 10197650262q^{9} \) \(\mathstrut +\mathstrut 742754160q^{10} \) \(\mathstrut +\mathstrut 27862395020q^{11} \) \(\mathstrut -\mathstrut 212292734088q^{12} \) \(\mathstrut -\mathstrut 431248136928q^{14} \) \(\mathstrut -\mathstrut 958534870512q^{16} \) \(\mathstrut +\mathstrut 4343925139172q^{17} \) \(\mathstrut -\mathstrut 4517494524426q^{18} \) \(\mathstrut -\mathstrut 360681653556q^{19} \) \(\mathstrut -\mathstrut 32520172742880q^{20} \) \(\mathstrut -\mathstrut 66275482922148q^{22} \) \(\mathstrut +\mathstrut 22289322475152q^{24} \) \(\mathstrut -\mathstrut 395727477008910q^{25} \) \(\mathstrut +\mathstrut 154289718058128q^{26} \) \(\mathstrut -\mathstrut 1208398438889064q^{27} \) \(\mathstrut -\mathstrut 394619539621440q^{28} \) \(\mathstrut +\mathstrut 223250517248160q^{30} \) \(\mathstrut -\mathstrut 2833814588985248q^{32} \) \(\mathstrut +\mathstrut 4461969540487176q^{33} \) \(\mathstrut -\mathstrut 939462769526748q^{34} \) \(\mathstrut +\mathstrut 3615863153468160q^{35} \) \(\mathstrut +\mathstrut 1560521174396700q^{36} \) \(\mathstrut +\mathstrut 12905383833568412q^{38} \) \(\mathstrut +\mathstrut 11813880412973760q^{40} \) \(\mathstrut +\mathstrut 16990829756398820q^{41} \) \(\mathstrut +\mathstrut 38127588900300480q^{42} \) \(\mathstrut -\mathstrut 27498466356753396q^{43} \) \(\mathstrut +\mathstrut 33178844343953144q^{44} \) \(\mathstrut -\mathstrut 21739818881100192q^{46} \) \(\mathstrut +\mathstrut 28364131397385312q^{48} \) \(\mathstrut -\mathstrut 252965388018862638q^{49} \) \(\mathstrut +\mathstrut 41705619584456530q^{50} \) \(\mathstrut -\mathstrut 34182574557901800q^{51} \) \(\mathstrut -\mathstrut 44583718369992480q^{52} \) \(\mathstrut -\mathstrut 579400710808894920q^{54} \) \(\mathstrut -\mathstrut 505574909383001472q^{56} \) \(\mathstrut -\mathstrut 522453489061123704q^{57} \) \(\mathstrut -\mathstrut 677523738697093680q^{58} \) \(\mathstrut +\mathstrut 93112194700366220q^{59} \) \(\mathstrut +\mathstrut 1631640690429240000q^{60} \) \(\mathstrut +\mathstrut 1780090172849178240q^{62} \) \(\mathstrut +\mathstrut 175441813011570240q^{64} \) \(\mathstrut +\mathstrut 1575343920200472960q^{65} \) \(\mathstrut +\mathstrut 8001047667731567880q^{66} \) \(\mathstrut -\mathstrut 1452645642074335668q^{67} \) \(\mathstrut +\mathstrut 1153770320813215592q^{68} \) \(\mathstrut -\mathstrut 6151558949299572480q^{70} \) \(\mathstrut -\mathstrut 5306529204268842936q^{72} \) \(\mathstrut +\mathstrut 9882821313863175972q^{73} \) \(\mathstrut -\mathstrut 5642095430673385488q^{74} \) \(\mathstrut +\mathstrut 13414715768769378060q^{75} \) \(\mathstrut -\mathstrut 8416781249057544840q^{76} \) \(\mathstrut -\mathstrut 14599907290310144160q^{78} \) \(\mathstrut -\mathstrut 22104885212702947200q^{80} \) \(\mathstrut -\mathstrut 32315102667184036518q^{81} \) \(\mathstrut +\mathstrut 10320950271478847652q^{82} \) \(\mathstrut -\mathstrut 46425529968268557748q^{83} \) \(\mathstrut +\mathstrut 17095266896298568320q^{84} \) \(\mathstrut +\mathstrut 33555485282446075868q^{86} \) \(\mathstrut +\mathstrut 32344350945394345872q^{88} \) \(\mathstrut -\mathstrut 28075170672250840156q^{89} \) \(\mathstrut -\mathstrut 33204348719592139440q^{90} \) \(\mathstrut +\mathstrut 161045136122144660736q^{91} \) \(\mathstrut -\mathstrut 932896292396925120q^{92} \) \(\mathstrut -\mathstrut 107259275077774974528q^{94} \) \(\mathstrut +\mathstrut 68580843917215697472q^{96} \) \(\mathstrut +\mathstrut 127276645173366650724q^{97} \) \(\mathstrut +\mathstrut 154837385163137764402q^{98} \) \(\mathstrut +\mathstrut 62802542261652714084q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −340.525 + 965.722i −0.332544 + 0.943088i
\(3\) 84336.7 1.42825 0.714125 0.700018i \(-0.246825\pi\)
0.714125 + 0.700018i \(0.246825\pi\)
\(4\) −816662. 657705.i −0.778829 0.627236i
\(5\) 4.86521e6i 0.498198i −0.968478 0.249099i \(-0.919866\pi\)
0.968478 0.249099i \(-0.0801344\pi\)
\(6\) −2.87188e7 + 8.14458e7i −0.474956 + 1.34697i
\(7\) 1.26224e8i 0.446849i 0.974721 + 0.223424i \(0.0717236\pi\)
−0.974721 + 0.223424i \(0.928276\pi\)
\(8\) 9.13253e8 5.64703e8i 0.850533 0.525921i
\(9\) 3.62590e9 1.03990
\(10\) 4.69844e9 + 1.65673e9i 0.469844 + 0.165673i
\(11\) 1.51387e10 0.583664 0.291832 0.956470i \(-0.405735\pi\)
0.291832 + 0.956470i \(0.405735\pi\)
\(12\) −6.88746e10 5.54687e10i −1.11236 0.895850i
\(13\) 1.95170e11i 1.41573i −0.706348 0.707865i \(-0.749659\pi\)
0.706348 0.707865i \(-0.250341\pi\)
\(14\) −1.21897e11 4.29823e10i −0.421418 0.148597i
\(15\) 4.10316e11i 0.711551i
\(16\) 2.34361e11 + 1.07424e12i 0.213150 + 0.977019i
\(17\) 3.56201e12 1.76688 0.883439 0.468546i \(-0.155222\pi\)
0.883439 + 0.468546i \(0.155222\pi\)
\(18\) −1.23471e12 + 3.50161e12i −0.345812 + 0.980715i
\(19\) 3.48807e12 0.568918 0.284459 0.958688i \(-0.408186\pi\)
0.284459 + 0.958688i \(0.408186\pi\)
\(20\) −3.19987e12 + 3.97323e12i −0.312488 + 0.388011i
\(21\) 1.06453e13i 0.638212i
\(22\) −5.15512e12 + 1.46198e13i −0.194094 + 0.550446i
\(23\) 1.17677e13i 0.284063i 0.989862 + 0.142031i \(0.0453634\pi\)
−0.989862 + 0.142031i \(0.954637\pi\)
\(24\) 7.70208e13 4.76252e13i 1.21477 0.751147i
\(25\) 7.16971e13 0.751799
\(26\) 1.88480e14 + 6.64604e13i 1.33516 + 0.470792i
\(27\) 1.17326e13 0.0569844
\(28\) 8.30179e13 1.03082e14i 0.280280 0.348019i
\(29\) 7.56048e14i 1.79709i 0.438882 + 0.898545i \(0.355375\pi\)
−0.438882 + 0.898545i \(0.644625\pi\)
\(30\) 3.96251e14 + 1.39723e14i 0.671055 + 0.236622i
\(31\) 1.11233e15i 1.35711i −0.734548 0.678557i \(-0.762606\pi\)
0.734548 0.678557i \(-0.237394\pi\)
\(32\) −1.11723e15 1.39479e14i −0.992297 0.123883i
\(33\) 1.27675e15 0.833618
\(34\) −1.21295e15 + 3.43992e15i −0.587564 + 1.66632i
\(35\) 6.14105e14 0.222619
\(36\) −2.96113e15 2.38477e15i −0.809903 0.652261i
\(37\) 7.17444e14i 0.149201i 0.997214 + 0.0746003i \(0.0237681\pi\)
−0.997214 + 0.0746003i \(0.976232\pi\)
\(38\) −1.18778e15 + 3.36851e15i −0.189190 + 0.536540i
\(39\) 1.64600e16i 2.02202i
\(40\) −2.74740e15 4.44317e15i −0.262013 0.423734i
\(41\) 3.23458e15 0.240979 0.120490 0.992715i \(-0.461554\pi\)
0.120490 + 0.992715i \(0.461554\pi\)
\(42\) −1.02804e16 3.62499e15i −0.601890 0.212233i
\(43\) −1.36789e16 −0.632946 −0.316473 0.948602i \(-0.602499\pi\)
−0.316473 + 0.948602i \(0.602499\pi\)
\(44\) −1.23632e16 9.95682e15i −0.454574 0.366095i
\(45\) 1.76408e16i 0.518075i
\(46\) −1.13644e16 4.00720e15i −0.267896 0.0944633i
\(47\) 4.28694e16i 0.815021i 0.913201 + 0.407510i \(0.133603\pi\)
−0.913201 + 0.407510i \(0.866397\pi\)
\(48\) 1.97652e16 + 9.05983e16i 0.304431 + 1.39543i
\(49\) 6.38598e16 0.800326
\(50\) −2.44147e16 + 6.92395e16i −0.250006 + 0.709013i
\(51\) 3.00409e17 2.52354
\(52\) −1.28364e17 + 1.59388e17i −0.887997 + 1.10261i
\(53\) 3.34779e17i 1.91425i −0.289671 0.957126i \(-0.593546\pi\)
0.289671 0.957126i \(-0.406454\pi\)
\(54\) −3.99524e15 + 1.13304e16i −0.0189498 + 0.0537413i
\(55\) 7.36531e16i 0.290780i
\(56\) 7.12790e16 + 1.15274e17i 0.235007 + 0.380060i
\(57\) 2.94173e17 0.812557
\(58\) −7.30133e17 2.57453e17i −1.69481 0.597611i
\(59\) 2.74237e17 0.536545 0.268272 0.963343i \(-0.413547\pi\)
0.268272 + 0.963343i \(0.413547\pi\)
\(60\) −2.69867e17 + 3.35089e17i −0.446310 + 0.554177i
\(61\) 1.49210e17i 0.209170i −0.994516 0.104585i \(-0.966648\pi\)
0.994516 0.104585i \(-0.0333515\pi\)
\(62\) 1.07420e18 + 3.78775e17i 1.27988 + 0.451300i
\(63\) 4.57675e17i 0.464677i
\(64\) 5.15142e17 1.03143e18i 0.446814 0.894627i
\(65\) −9.49545e17 −0.705313
\(66\) −4.34766e17 + 1.23299e18i −0.277214 + 0.786175i
\(67\) −2.92321e18 −1.60366 −0.801828 0.597555i \(-0.796139\pi\)
−0.801828 + 0.597555i \(0.796139\pi\)
\(68\) −2.90896e18 2.34275e18i −1.37610 1.10825i
\(69\) 9.92452e17i 0.405712i
\(70\) −2.09118e17 + 5.93055e17i −0.0740306 + 0.209949i
\(71\) 3.51233e18i 1.07898i −0.841993 0.539489i \(-0.818618\pi\)
0.841993 0.539489i \(-0.181382\pi\)
\(72\) 3.31137e18 2.04756e18i 0.884468 0.546904i
\(73\) 5.45402e17 0.126908 0.0634539 0.997985i \(-0.479788\pi\)
0.0634539 + 0.997985i \(0.479788\pi\)
\(74\) −6.92851e17 2.44307e17i −0.140709 0.0496157i
\(75\) 6.04670e18 1.07376
\(76\) −2.84858e18 2.29412e18i −0.443090 0.356846i
\(77\) 1.91087e18i 0.260809i
\(78\) 1.58958e19 + 5.60505e18i 1.90694 + 0.672409i
\(79\) 1.64097e19i 1.73312i 0.499070 + 0.866562i \(0.333675\pi\)
−0.499070 + 0.866562i \(0.666325\pi\)
\(80\) 5.22643e18 1.14022e18i 0.486749 0.106191i
\(81\) −1.16532e19 −0.958510
\(82\) −1.10145e18 + 3.12370e18i −0.0801361 + 0.227264i
\(83\) −1.30232e19 −0.839335 −0.419668 0.907678i \(-0.637853\pi\)
−0.419668 + 0.907678i \(0.637853\pi\)
\(84\) 7.00146e18 8.69361e18i 0.400309 0.497058i
\(85\) 1.73300e19i 0.880254i
\(86\) 4.65801e18 1.32100e19i 0.210482 0.596924i
\(87\) 6.37627e19i 2.56669i
\(88\) 1.38255e19 8.54889e18i 0.496426 0.306961i
\(89\) −2.43956e19 −0.782368 −0.391184 0.920313i \(-0.627934\pi\)
−0.391184 + 0.920313i \(0.627934\pi\)
\(90\) 1.70361e19 + 6.00712e18i 0.488590 + 0.172283i
\(91\) 2.46351e19 0.632617
\(92\) 7.73969e18 9.61025e18i 0.178174 0.221236i
\(93\) 9.38101e19i 1.93830i
\(94\) −4.13999e19 1.45981e19i −0.768636 0.271030i
\(95\) 1.69702e19i 0.283434i
\(96\) −9.42233e19 1.17632e19i −1.41725 0.176935i
\(97\) −7.85794e18 −0.106559 −0.0532796 0.998580i \(-0.516967\pi\)
−0.0532796 + 0.998580i \(0.516967\pi\)
\(98\) −2.17459e19 + 6.16708e19i −0.266143 + 0.754778i
\(99\) 5.48915e19 0.606951
\(100\) −5.85523e19 4.71555e19i −0.585523 0.471555i
\(101\) 1.53362e20i 1.38837i −0.719799 0.694183i \(-0.755766\pi\)
0.719799 0.694183i \(-0.244234\pi\)
\(102\) −1.02297e20 + 2.90111e20i −0.839189 + 2.37992i
\(103\) 7.06517e19i 0.525715i 0.964835 + 0.262857i \(0.0846649\pi\)
−0.964835 + 0.262857i \(0.915335\pi\)
\(104\) −1.10213e20 1.78240e20i −0.744562 1.20413i
\(105\) 5.17916e19 0.317956
\(106\) 3.23303e20 + 1.14001e20i 1.80531 + 0.636573i
\(107\) 1.69073e20 0.859483 0.429742 0.902952i \(-0.358605\pi\)
0.429742 + 0.902952i \(0.358605\pi\)
\(108\) −9.58155e18 7.71657e18i −0.0443811 0.0357427i
\(109\) 1.46975e20i 0.620838i 0.950600 + 0.310419i \(0.100469\pi\)
−0.950600 + 0.310419i \(0.899531\pi\)
\(110\) 7.11285e19 + 2.50807e19i 0.274231 + 0.0966971i
\(111\) 6.05069e19i 0.213096i
\(112\) −1.35595e20 + 2.95819e19i −0.436580 + 0.0952458i
\(113\) 1.92152e20 0.566059 0.283029 0.959111i \(-0.408661\pi\)
0.283029 + 0.959111i \(0.408661\pi\)
\(114\) −1.00173e20 + 2.84089e20i −0.270211 + 0.766313i
\(115\) 5.72525e19 0.141519
\(116\) 4.97257e20 6.17436e20i 1.12720 1.39963i
\(117\) 7.07668e20i 1.47221i
\(118\) −9.33845e19 + 2.64837e20i −0.178425 + 0.506009i
\(119\) 4.49611e20i 0.789527i
\(120\) −2.31707e20 3.74723e20i −0.374219 0.605198i
\(121\) −4.43569e20 −0.659337
\(122\) 1.44096e20 + 5.08098e19i 0.197266 + 0.0695583i
\(123\) 2.72794e20 0.344178
\(124\) −7.31584e20 + 9.08396e20i −0.851230 + 1.05696i
\(125\) 8.12805e20i 0.872742i
\(126\) −4.41986e20 1.55850e20i −0.438231 0.154526i
\(127\) 1.52243e21i 1.39476i 0.716702 + 0.697379i \(0.245651\pi\)
−0.716702 + 0.697379i \(0.754349\pi\)
\(128\) 8.20660e20 + 8.48713e20i 0.695126 + 0.718888i
\(129\) −1.15363e21 −0.904005
\(130\) 3.23344e20 9.16996e20i 0.234548 0.665172i
\(131\) −8.13929e20 −0.546857 −0.273428 0.961892i \(-0.588158\pi\)
−0.273428 + 0.961892i \(0.588158\pi\)
\(132\) −1.04267e21 8.39725e20i −0.649246 0.522875i
\(133\) 4.40278e20i 0.254220i
\(134\) 9.95424e20 2.82300e21i 0.533286 1.51239i
\(135\) 5.70815e19i 0.0283895i
\(136\) 3.25302e21 2.01148e21i 1.50279 0.929238i
\(137\) −1.95796e21 −0.840615 −0.420308 0.907382i \(-0.638078\pi\)
−0.420308 + 0.907382i \(0.638078\pi\)
\(138\) −9.58432e20 3.37954e20i −0.382623 0.134917i
\(139\) −3.33138e21 −1.23731 −0.618653 0.785665i \(-0.712321\pi\)
−0.618653 + 0.785665i \(0.712321\pi\)
\(140\) −5.01516e20 4.03900e20i −0.173382 0.139635i
\(141\) 3.61546e21i 1.16405i
\(142\) 3.39194e21 + 1.19604e21i 1.01757 + 0.358807i
\(143\) 2.95463e21i 0.826310i
\(144\) 8.49769e20 + 3.89510e21i 0.221654 + 1.01600i
\(145\) 3.67834e21 0.895306
\(146\) −1.85723e20 + 5.26707e20i −0.0422024 + 0.119685i
\(147\) 5.38573e21 1.14307
\(148\) 4.71866e20 5.85909e20i 0.0935840 0.116202i
\(149\) 7.16621e21i 1.32870i 0.747422 + 0.664350i \(0.231291\pi\)
−0.747422 + 0.664350i \(0.768709\pi\)
\(150\) −2.05905e21 + 5.83943e21i −0.357071 + 1.01265i
\(151\) 4.35389e21i 0.706493i −0.935530 0.353246i \(-0.885078\pi\)
0.935530 0.353246i \(-0.114922\pi\)
\(152\) 3.18550e21 1.96973e21i 0.483884 0.299206i
\(153\) 1.29155e22 1.83737
\(154\) −1.84537e21 6.50698e20i −0.245966 0.0867306i
\(155\) −5.41171e21 −0.676111
\(156\) −1.08258e22 + 1.34423e22i −1.26828 + 1.57481i
\(157\) 3.66999e21i 0.403338i 0.979454 + 0.201669i \(0.0646365\pi\)
−0.979454 + 0.201669i \(0.935364\pi\)
\(158\) −1.58472e22 5.58791e21i −1.63449 0.576339i
\(159\) 2.82342e22i 2.73403i
\(160\) −6.78597e20 + 5.43555e21i −0.0617180 + 0.494360i
\(161\) −1.48537e21 −0.126933
\(162\) 3.96822e21 1.12538e22i 0.318747 0.903959i
\(163\) 3.23237e20 0.0244144 0.0122072 0.999925i \(-0.496114\pi\)
0.0122072 + 0.999925i \(0.496114\pi\)
\(164\) −2.64156e21 2.12740e21i −0.187682 0.151151i
\(165\) 6.21167e21i 0.415306i
\(166\) 4.43471e21 1.25768e22i 0.279116 0.791567i
\(167\) 1.38936e22i 0.823474i 0.911303 + 0.411737i \(0.135078\pi\)
−0.911303 + 0.411737i \(0.864922\pi\)
\(168\) 6.01143e21 + 9.72185e21i 0.335649 + 0.542821i
\(169\) −1.90865e22 −1.00429
\(170\) 1.67359e22 + 5.90128e21i 0.830157 + 0.292723i
\(171\) 1.26474e22 0.591617
\(172\) 1.11710e22 + 8.99668e21i 0.492957 + 0.397006i
\(173\) 4.49412e21i 0.187147i −0.995612 0.0935737i \(-0.970171\pi\)
0.995612 0.0935737i \(-0.0298291\pi\)
\(174\) −6.15770e22 2.17128e22i −2.42062 0.853538i
\(175\) 9.04988e21i 0.335941i
\(176\) 3.54793e21 + 1.62627e22i 0.124408 + 0.570251i
\(177\) 2.31283e22 0.766320
\(178\) 8.30730e21 2.35593e22i 0.260172 0.737842i
\(179\) −3.47973e22 −1.03042 −0.515211 0.857063i \(-0.672286\pi\)
−0.515211 + 0.857063i \(0.672286\pi\)
\(180\) −1.16024e22 + 1.44065e22i −0.324955 + 0.403492i
\(181\) 2.34167e22i 0.620497i 0.950655 + 0.310248i \(0.100412\pi\)
−0.950655 + 0.310248i \(0.899588\pi\)
\(182\) −8.38887e21 + 2.37907e22i −0.210373 + 0.596613i
\(183\) 1.25839e22i 0.298748i
\(184\) 6.64527e21 + 1.07469e22i 0.149395 + 0.241605i
\(185\) 3.49052e21 0.0743314
\(186\) 9.05945e22 + 3.19447e22i 1.82798 + 0.644569i
\(187\) 5.39244e22 1.03126
\(188\) 2.81954e22 3.50098e22i 0.511210 0.634762i
\(189\) 1.48093e21i 0.0254634i
\(190\) 1.63885e22 + 5.77878e21i 0.267303 + 0.0942541i
\(191\) 2.58648e22i 0.400291i 0.979766 + 0.200145i \(0.0641415\pi\)
−0.979766 + 0.200145i \(0.935859\pi\)
\(192\) 4.34454e22 8.69878e22i 0.638163 1.27775i
\(193\) 2.68246e22 0.374076 0.187038 0.982353i \(-0.440111\pi\)
0.187038 + 0.982353i \(0.440111\pi\)
\(194\) 2.67582e21 7.58858e21i 0.0354356 0.100495i
\(195\) −8.00815e22 −1.00736
\(196\) −5.21519e22 4.20009e22i −0.623317 0.501993i
\(197\) 4.69360e22i 0.533143i 0.963815 + 0.266572i \(0.0858909\pi\)
−0.963815 + 0.266572i \(0.914109\pi\)
\(198\) −1.86919e22 + 5.30100e22i −0.201838 + 0.572408i
\(199\) 6.01397e22i 0.617491i 0.951145 + 0.308746i \(0.0999092\pi\)
−0.951145 + 0.308746i \(0.900091\pi\)
\(200\) 6.54777e22 4.04876e22i 0.639430 0.395387i
\(201\) −2.46534e23 −2.29042
\(202\) 1.48105e23 + 5.22235e22i 1.30935 + 0.461692i
\(203\) −9.54313e22 −0.803027
\(204\) −2.45332e23 1.97580e23i −1.96541 1.58286i
\(205\) 1.57369e22i 0.120055i
\(206\) −6.82299e22 2.40587e22i −0.495795 0.174823i
\(207\) 4.26686e22i 0.295396i
\(208\) 2.09661e23 4.57403e22i 1.38320 0.301763i
\(209\) 5.28050e22 0.332057
\(210\) −1.76363e22 + 5.00163e22i −0.105734 + 0.299860i
\(211\) 2.54766e23 1.45652 0.728262 0.685299i \(-0.240329\pi\)
0.728262 + 0.685299i \(0.240329\pi\)
\(212\) −2.20186e23 + 2.73401e23i −1.20069 + 1.49088i
\(213\) 2.96219e23i 1.54105i
\(214\) −5.75737e22 + 1.63278e23i −0.285816 + 0.810568i
\(215\) 6.65507e22i 0.315332i
\(216\) 1.07148e22 6.62543e21i 0.0484671 0.0299693i
\(217\) 1.40402e23 0.606424
\(218\) −1.41937e23 5.00486e22i −0.585505 0.206456i
\(219\) 4.59974e22 0.181256
\(220\) −4.84420e22 + 6.01497e22i −0.182388 + 0.226468i
\(221\) 6.95200e23i 2.50142i
\(222\) −5.84328e22 2.06041e22i −0.200968 0.0708637i
\(223\) 3.52305e23i 1.15843i 0.815174 + 0.579216i \(0.196641\pi\)
−0.815174 + 0.579216i \(0.803359\pi\)
\(224\) 1.76056e22 1.41021e23i 0.0553568 0.443407i
\(225\) 2.59967e23 0.781794
\(226\) −6.54327e22 + 1.85566e23i −0.188239 + 0.533843i
\(227\) 4.23328e23 1.16525 0.582624 0.812742i \(-0.302026\pi\)
0.582624 + 0.812742i \(0.302026\pi\)
\(228\) −2.40240e23 1.93479e23i −0.632843 0.509665i
\(229\) 9.70854e22i 0.244793i −0.992481 0.122396i \(-0.960942\pi\)
0.992481 0.122396i \(-0.0390580\pi\)
\(230\) −1.94959e22 + 5.52900e22i −0.0470614 + 0.133465i
\(231\) 1.61156e23i 0.372501i
\(232\) 4.26943e23 + 6.90464e23i 0.945127 + 1.52848i
\(233\) −4.99591e23 −1.05939 −0.529694 0.848189i \(-0.677693\pi\)
−0.529694 + 0.848189i \(0.677693\pi\)
\(234\) 6.83411e23 + 2.40979e23i 1.38843 + 0.489576i
\(235\) 2.08569e23 0.406042
\(236\) −2.23959e23 1.80367e23i −0.417877 0.336540i
\(237\) 1.38394e24i 2.47533i
\(238\) −4.34199e23 1.53104e23i −0.744594 0.262552i
\(239\) 4.59439e23i 0.755525i −0.925902 0.377763i \(-0.876694\pi\)
0.925902 0.377763i \(-0.123306\pi\)
\(240\) 4.40780e23 9.61620e22i 0.695199 0.151667i
\(241\) 6.71339e23 1.01571 0.507857 0.861441i \(-0.330438\pi\)
0.507857 + 0.861441i \(0.330438\pi\)
\(242\) 1.51046e23 4.28364e23i 0.219258 0.621812i
\(243\) −1.02371e24 −1.42598
\(244\) −9.81363e22 + 1.21854e23i −0.131199 + 0.162908i
\(245\) 3.10692e23i 0.398721i
\(246\) −9.28931e22 + 2.63443e23i −0.114454 + 0.324590i
\(247\) 6.80769e23i 0.805434i
\(248\) −6.28136e23 1.01584e24i −0.713734 1.15427i
\(249\) −1.09833e24 −1.19878
\(250\) 7.84943e23 + 2.76780e23i 0.823073 + 0.290225i
\(251\) −5.67208e23 −0.571486 −0.285743 0.958306i \(-0.592240\pi\)
−0.285743 + 0.958306i \(0.592240\pi\)
\(252\) 3.01015e23 3.73765e23i 0.291462 0.361904i
\(253\) 1.78148e23i 0.165797i
\(254\) −1.47024e24 5.18424e23i −1.31538 0.463818i
\(255\) 1.46155e24i 1.25722i
\(256\) −1.09908e24 + 5.03522e23i −0.909134 + 0.416503i
\(257\) 1.43742e24 1.14354 0.571770 0.820414i \(-0.306257\pi\)
0.571770 + 0.820414i \(0.306257\pi\)
\(258\) 3.92841e23 1.11409e24i 0.300621 0.852556i
\(259\) −9.05584e22 −0.0666701
\(260\) 7.75457e23 + 6.24520e23i 0.549319 + 0.442398i
\(261\) 2.74136e24i 1.86879i
\(262\) 2.77163e23 7.86029e23i 0.181854 0.515734i
\(263\) 4.04959e23i 0.255773i −0.991789 0.127886i \(-0.959181\pi\)
0.991789 0.127886i \(-0.0408193\pi\)
\(264\) 1.16600e24 7.20986e23i 0.709020 0.438417i
\(265\) −1.62877e24 −0.953676
\(266\) −4.25186e23 1.49926e23i −0.239752 0.0845394i
\(267\) −2.05744e24 −1.11742
\(268\) 2.38727e24 + 1.92261e24i 1.24897 + 1.00587i
\(269\) 7.34903e23i 0.370431i 0.982698 + 0.185215i \(0.0592983\pi\)
−0.982698 + 0.185215i \(0.940702\pi\)
\(270\) 5.51248e22 + 1.94377e22i 0.0267738 + 0.00944075i
\(271\) 4.11047e24i 1.92397i 0.273100 + 0.961986i \(0.411951\pi\)
−0.273100 + 0.961986i \(0.588049\pi\)
\(272\) 8.34797e23 + 3.82647e24i 0.376610 + 1.72627i
\(273\) 2.07765e24 0.903535
\(274\) 6.66733e23 1.89084e24i 0.279541 0.792774i
\(275\) 1.08540e24 0.438798
\(276\) 6.52740e23 8.10497e23i 0.254477 0.315981i
\(277\) 6.38513e23i 0.240089i −0.992769 0.120044i \(-0.961696\pi\)
0.992769 0.120044i \(-0.0383037\pi\)
\(278\) 1.13442e24 3.21719e24i 0.411458 1.16689i
\(279\) 4.03319e24i 1.41126i
\(280\) 5.60834e23 3.46787e23i 0.189345 0.117080i
\(281\) −4.28449e24 −1.39584 −0.697921 0.716175i \(-0.745891\pi\)
−0.697921 + 0.716175i \(0.745891\pi\)
\(282\) −3.49153e24 1.23116e24i −1.09780 0.387099i
\(283\) 4.08346e24 1.23927 0.619633 0.784892i \(-0.287282\pi\)
0.619633 + 0.784892i \(0.287282\pi\)
\(284\) −2.31008e24 + 2.86839e24i −0.676773 + 0.840339i
\(285\) 1.43121e24i 0.404814i
\(286\) 2.85335e24 + 1.00613e24i 0.779283 + 0.274784i
\(287\) 4.08281e23i 0.107681i
\(288\) −4.05095e24 5.05738e23i −1.03189 0.128825i
\(289\) 8.62372e24 2.12186
\(290\) −1.25256e24 + 3.55225e24i −0.297728 + 0.844352i
\(291\) −6.62713e23 −0.152193
\(292\) −4.45409e23 3.58713e23i −0.0988394 0.0796011i
\(293\) 2.47467e24i 0.530690i −0.964154 0.265345i \(-0.914514\pi\)
0.964154 0.265345i \(-0.0854858\pi\)
\(294\) −1.83397e24 + 5.20112e24i −0.380119 + 1.07801i
\(295\) 1.33422e24i 0.267305i
\(296\) 4.05143e23 + 6.55208e23i 0.0784677 + 0.126900i
\(297\) 1.77616e23 0.0332597
\(298\) −6.92056e24 2.44027e24i −1.25308 0.441851i
\(299\) 2.29671e24 0.402156
\(300\) −4.93811e24 3.97694e24i −0.836273 0.673499i
\(301\) 1.72660e24i 0.282831i
\(302\) 4.20464e24 + 1.48261e24i 0.666285 + 0.234940i
\(303\) 1.29340e25i 1.98293i
\(304\) 8.17468e23 + 3.74704e24i 0.121265 + 0.555844i
\(305\) −7.25940e23 −0.104208
\(306\) −4.39805e24 + 1.24728e25i −0.611007 + 1.73280i
\(307\) −8.40302e24 −1.12993 −0.564965 0.825115i \(-0.691110\pi\)
−0.564965 + 0.825115i \(0.691110\pi\)
\(308\) 1.25679e24 1.56053e24i 0.163589 0.203126i
\(309\) 5.95853e24i 0.750852i
\(310\) 1.84282e24 5.22621e24i 0.224836 0.637632i
\(311\) 1.49760e25i 1.76926i 0.466292 + 0.884631i \(0.345590\pi\)
−0.466292 + 0.884631i \(0.654410\pi\)
\(312\) −9.29503e24 1.50322e25i −1.06342 1.71979i
\(313\) −1.48295e25 −1.64318 −0.821588 0.570081i \(-0.806912\pi\)
−0.821588 + 0.570081i \(0.806912\pi\)
\(314\) −3.54419e24 1.24972e24i −0.380383 0.134127i
\(315\) 2.22668e24 0.231501
\(316\) 1.07927e25 1.34012e25i 1.08708 1.34981i
\(317\) 6.07588e24i 0.592948i −0.955041 0.296474i \(-0.904189\pi\)
0.955041 0.296474i \(-0.0958108\pi\)
\(318\) 2.72663e25 + 9.61443e24i 2.57843 + 0.909185i
\(319\) 1.14456e25i 1.04890i
\(320\) −5.01815e24 2.50627e24i −0.445701 0.222602i
\(321\) 1.42591e25 1.22756
\(322\) 5.05804e23 1.43445e24i 0.0422108 0.119709i
\(323\) 1.24246e25 1.00521
\(324\) 9.51676e24 + 7.66439e24i 0.746516 + 0.601212i
\(325\) 1.39932e25i 1.06434i
\(326\) −1.10070e23 + 3.12157e23i −0.00811885 + 0.0230249i
\(327\) 1.23954e25i 0.886712i
\(328\) 2.95399e24 1.82658e24i 0.204961 0.126736i
\(329\) −5.41114e24 −0.364191
\(330\) 5.99874e24 + 2.11523e24i 0.391670 + 0.138108i
\(331\) −8.24033e24 −0.521993 −0.260996 0.965340i \(-0.584051\pi\)
−0.260996 + 0.965340i \(0.584051\pi\)
\(332\) 1.06355e25 + 8.56539e24i 0.653699 + 0.526461i
\(333\) 2.60138e24i 0.155153i
\(334\) −1.34173e25 4.73111e24i −0.776608 0.273841i
\(335\) 1.42220e25i 0.798938i
\(336\) −1.14357e25 + 2.49484e24i −0.623545 + 0.136035i
\(337\) −3.21488e25 −1.70163 −0.850815 0.525465i \(-0.823891\pi\)
−0.850815 + 0.525465i \(0.823891\pi\)
\(338\) 6.49943e24 1.84323e25i 0.333970 0.947134i
\(339\) 1.62055e25 0.808473
\(340\) −1.13980e25 + 1.41527e25i −0.552127 + 0.685568i
\(341\) 1.68392e25i 0.792098i
\(342\) −4.30676e24 + 1.22139e25i −0.196738 + 0.557947i
\(343\) 1.81323e25i 0.804474i
\(344\) −1.24923e25 + 7.72452e24i −0.538342 + 0.332880i
\(345\) 4.82849e24 0.202125
\(346\) 4.34007e24 + 1.53036e24i 0.176496 + 0.0622347i
\(347\) −1.27479e25 −0.503667 −0.251834 0.967771i \(-0.581034\pi\)
−0.251834 + 0.967771i \(0.581034\pi\)
\(348\) 4.19370e25 5.20725e25i 1.60992 1.99902i
\(349\) 1.13915e25i 0.424940i −0.977168 0.212470i \(-0.931849\pi\)
0.977168 0.212470i \(-0.0681508\pi\)
\(350\) −8.73967e24 3.08171e24i −0.316821 0.111715i
\(351\) 2.28985e24i 0.0806745i
\(352\) −1.69134e25 2.11154e24i −0.579168 0.0723058i
\(353\) 2.47620e25 0.824211 0.412106 0.911136i \(-0.364793\pi\)
0.412106 + 0.911136i \(0.364793\pi\)
\(354\) −7.87575e24 + 2.23355e25i −0.254835 + 0.722707i
\(355\) −1.70882e25 −0.537544
\(356\) 1.99229e25 + 1.60451e25i 0.609331 + 0.490729i
\(357\) 3.79187e25i 1.12764i
\(358\) 1.18493e25 3.36045e25i 0.342660 0.971778i
\(359\) 4.85328e25i 1.36487i −0.730947 0.682434i \(-0.760922\pi\)
0.730947 0.682434i \(-0.239078\pi\)
\(360\) −9.96180e24 1.61105e25i −0.272466 0.440640i
\(361\) −2.54233e25 −0.676332
\(362\) −2.26140e25 7.97396e24i −0.585183 0.206342i
\(363\) −3.74091e25 −0.941698
\(364\) −2.01186e25 1.62026e25i −0.492701 0.396800i
\(365\) 2.65350e24i 0.0632251i
\(366\) 1.21526e25 + 4.28513e24i 0.281745 + 0.0993467i
\(367\) 5.19588e25i 1.17219i −0.810242 0.586096i \(-0.800664\pi\)
0.810242 0.586096i \(-0.199336\pi\)
\(368\) −1.26414e25 + 2.75789e24i −0.277535 + 0.0605480i
\(369\) 1.17283e25 0.250594
\(370\) −1.18861e24 + 3.37087e24i −0.0247184 + 0.0701010i
\(371\) 4.22570e25 0.855382
\(372\) −6.16994e25 + 7.66111e25i −1.21577 + 1.50960i
\(373\) 3.44797e25i 0.661417i 0.943733 + 0.330708i \(0.107288\pi\)
−0.943733 + 0.330708i \(0.892712\pi\)
\(374\) −1.83626e25 + 5.20760e25i −0.342940 + 0.972571i
\(375\) 6.85493e25i 1.24649i
\(376\) 2.42085e25 + 3.91506e25i 0.428637 + 0.693203i
\(377\) 1.47558e26 2.54419
\(378\) −1.43017e24 5.04294e23i −0.0240142 0.00846770i
\(379\) 7.98002e25 1.30500 0.652502 0.757787i \(-0.273719\pi\)
0.652502 + 0.757787i \(0.273719\pi\)
\(380\) −1.11614e25 + 1.38589e25i −0.177780 + 0.220746i
\(381\) 1.28396e26i 1.99206i
\(382\) −2.49782e25 8.80761e24i −0.377509 0.133114i
\(383\) 3.01797e25i 0.444352i −0.975007 0.222176i \(-0.928684\pi\)
0.975007 0.222176i \(-0.0713160\pi\)
\(384\) 6.92118e25 + 7.15777e25i 0.992814 + 1.02675i
\(385\) 9.29678e24 0.129935
\(386\) −9.13445e24 + 2.59051e25i −0.124397 + 0.352787i
\(387\) −4.95983e25 −0.658199
\(388\) 6.41728e24 + 5.16820e24i 0.0829915 + 0.0668378i
\(389\) 9.38588e25i 1.18298i −0.806311 0.591492i \(-0.798539\pi\)
0.806311 0.591492i \(-0.201461\pi\)
\(390\) 2.72697e25 7.73365e25i 0.334992 0.950032i
\(391\) 4.19168e25i 0.501904i
\(392\) 5.83202e25 3.60619e25i 0.680704 0.420908i
\(393\) −6.86441e25 −0.781048
\(394\) −4.53271e25 1.59829e25i −0.502801 0.177293i
\(395\) 7.98366e25 0.863438
\(396\) −4.48278e25 3.61024e25i −0.472711 0.380701i
\(397\) 4.72991e25i 0.486349i −0.969983 0.243174i \(-0.921811\pi\)
0.969983 0.243174i \(-0.0781887\pi\)
\(398\) −5.80783e25 2.04791e25i −0.582348 0.205343i
\(399\) 3.71316e25i 0.363090i
\(400\) 1.68030e25 + 7.70203e25i 0.160246 + 0.734522i
\(401\) −1.29001e26 −1.19991 −0.599957 0.800032i \(-0.704816\pi\)
−0.599957 + 0.800032i \(0.704816\pi\)
\(402\) 8.39508e25 2.38083e26i 0.761666 2.16007i
\(403\) −2.17094e26 −1.92131
\(404\) −1.00867e26 + 1.25245e26i −0.870833 + 1.08130i
\(405\) 5.66955e25i 0.477527i
\(406\) 3.24967e25 9.21601e25i 0.267042 0.757325i
\(407\) 1.08612e25i 0.0870830i
\(408\) 2.74349e26 1.69642e26i 2.14636 1.32718i
\(409\) 9.77077e25 0.745926 0.372963 0.927846i \(-0.378342\pi\)
0.372963 + 0.927846i \(0.378342\pi\)
\(410\) 1.51975e25 + 5.35881e24i 0.113223 + 0.0399236i
\(411\) −1.65128e26 −1.20061
\(412\) 4.64679e25 5.76985e25i 0.329747 0.409442i
\(413\) 3.46152e25i 0.239754i
\(414\) −4.12060e25 1.45297e25i −0.278585 0.0982322i
\(415\) 6.33604e25i 0.418155i
\(416\) −2.72222e25 + 2.18050e26i −0.175384 + 1.40482i
\(417\) −2.80958e26 −1.76718
\(418\) −1.79814e25 + 5.09950e25i −0.110423 + 0.313159i
\(419\) 1.45698e26 0.873603 0.436801 0.899558i \(-0.356111\pi\)
0.436801 + 0.899558i \(0.356111\pi\)
\(420\) −4.22962e25 3.40636e25i −0.247633 0.199433i
\(421\) 1.12181e26i 0.641354i 0.947189 + 0.320677i \(0.103910\pi\)
−0.947189 + 0.320677i \(0.896090\pi\)
\(422\) −8.67543e25 + 2.46033e26i −0.484358 + 1.37363i
\(423\) 1.55440e26i 0.847539i
\(424\) −1.89051e26 3.05738e26i −1.00675 1.62814i
\(425\) 2.55386e26 1.32834
\(426\) 2.86065e26 + 1.00870e26i 1.45334 + 0.512466i
\(427\) 1.88339e25 0.0934676
\(428\) −1.38076e26 1.11200e26i −0.669391 0.539099i
\(429\) 2.49184e26i 1.18018i
\(430\) −6.42695e25 2.26622e25i −0.297386 0.104862i
\(431\) 1.82538e26i 0.825240i −0.910903 0.412620i \(-0.864614\pi\)
0.910903 0.412620i \(-0.135386\pi\)
\(432\) 2.74966e24 + 1.26037e25i 0.0121462 + 0.0556749i
\(433\) −2.27223e26 −0.980785 −0.490392 0.871502i \(-0.663147\pi\)
−0.490392 + 0.871502i \(0.663147\pi\)
\(434\) −4.78105e25 + 1.35590e26i −0.201663 + 0.571912i
\(435\) 3.10219e26 1.27872
\(436\) 9.66661e25 1.20029e26i 0.389412 0.483527i
\(437\) 4.10467e25i 0.161608i
\(438\) −1.56633e25 + 4.44207e25i −0.0602755 + 0.170940i
\(439\) 2.33052e26i 0.876614i −0.898825 0.438307i \(-0.855578\pi\)
0.898825 0.438307i \(-0.144422\pi\)
\(440\) −4.15922e25 6.72640e25i −0.152927 0.247318i
\(441\) 2.31549e26 0.832258
\(442\) 6.71370e26 + 2.36733e26i 2.35906 + 0.831832i
\(443\) −1.40927e26 −0.484124 −0.242062 0.970261i \(-0.577824\pi\)
−0.242062 + 0.970261i \(0.577824\pi\)
\(444\) 3.97956e25 4.94136e25i 0.133661 0.165965i
\(445\) 1.18690e26i 0.389774i
\(446\) −3.40229e26 1.19969e26i −1.09250 0.385230i
\(447\) 6.04374e26i 1.89771i
\(448\) 1.30191e26 + 6.50231e25i 0.399763 + 0.199658i
\(449\) 1.40666e26 0.422400 0.211200 0.977443i \(-0.432263\pi\)
0.211200 + 0.977443i \(0.432263\pi\)
\(450\) −8.85251e25 + 2.51056e26i −0.259981 + 0.737301i
\(451\) 4.89674e25 0.140651
\(452\) −1.56924e26 1.26380e26i −0.440863 0.355052i
\(453\) 3.67193e26i 1.00905i
\(454\) −1.44154e26 + 4.08817e26i −0.387496 + 1.09893i
\(455\) 1.19855e26i 0.315168i
\(456\) 2.68654e26 1.66120e26i 0.691107 0.427341i
\(457\) 1.27721e26 0.321441 0.160720 0.987000i \(-0.448618\pi\)
0.160720 + 0.987000i \(0.448618\pi\)
\(458\) 9.37575e25 + 3.30600e25i 0.230861 + 0.0814044i
\(459\) 4.17916e25 0.100684
\(460\) −4.67559e25 3.76552e25i −0.110219 0.0887660i
\(461\) 3.61599e26i 0.834100i −0.908883 0.417050i \(-0.863064\pi\)
0.908883 0.417050i \(-0.136936\pi\)
\(462\) −1.55632e26 5.48777e25i −0.351301 0.123873i
\(463\) 4.74287e26i 1.04769i 0.851815 + 0.523843i \(0.175502\pi\)
−0.851815 + 0.523843i \(0.824498\pi\)
\(464\) −8.12181e26 + 1.77188e26i −1.75579 + 0.383050i
\(465\) −4.56406e26 −0.965655
\(466\) 1.70123e26 4.82466e26i 0.352293 0.999096i
\(467\) 3.26188e26 0.661150 0.330575 0.943780i \(-0.392757\pi\)
0.330575 + 0.943780i \(0.392757\pi\)
\(468\) −4.65437e26 + 5.77925e26i −0.923426 + 1.14660i
\(469\) 3.68978e26i 0.716592i
\(470\) −7.10228e25 + 2.01419e26i −0.135027 + 0.382933i
\(471\) 3.09515e26i 0.576067i
\(472\) 2.50448e26 1.54863e26i 0.456349 0.282180i
\(473\) −2.07081e26 −0.369428
\(474\) −1.33650e27 4.71266e26i −2.33446 0.823157i
\(475\) 2.50085e26 0.427712
\(476\) 2.95711e26 3.67180e26i 0.495220 0.614907i
\(477\) 1.21387e27i 1.99063i
\(478\) 4.43690e26 + 1.56450e26i 0.712527 + 0.251245i
\(479\) 9.19723e26i 1.44644i −0.690615 0.723222i \(-0.742660\pi\)
0.690615 0.723222i \(-0.257340\pi\)
\(480\) −5.72306e25 + 4.58416e26i −0.0881488 + 0.706070i
\(481\) 1.40024e26 0.211228
\(482\) −2.28608e26 + 6.48327e26i −0.337769 + 0.957907i
\(483\) −1.25271e26 −0.181292
\(484\) 3.62246e26 + 2.91737e26i 0.513511 + 0.413560i
\(485\) 3.82305e25i 0.0530876i
\(486\) 3.48597e26 9.88615e26i 0.474200 1.34482i
\(487\) 3.19780e26i 0.426149i 0.977036 + 0.213074i \(0.0683477\pi\)
−0.977036 + 0.213074i \(0.931652\pi\)
\(488\) −8.42595e25 1.36267e26i −0.110007 0.177906i
\(489\) 2.72608e25 0.0348698
\(490\) 3.00042e26 + 1.05798e26i 0.376029 + 0.132592i
\(491\) 7.81706e25 0.0959905 0.0479953 0.998848i \(-0.484717\pi\)
0.0479953 + 0.998848i \(0.484717\pi\)
\(492\) −2.22780e26 1.79418e26i −0.268056 0.215881i
\(493\) 2.69306e27i 3.17524i
\(494\) 6.57433e26 + 2.31819e26i 0.759595 + 0.267842i
\(495\) 2.67059e26i 0.302381i
\(496\) 1.19491e27 2.60686e26i 1.32593 0.289269i
\(497\) 4.43340e26 0.482140
\(498\) 3.74009e26 1.06068e27i 0.398647 1.13056i
\(499\) −9.10365e26 −0.951064 −0.475532 0.879698i \(-0.657744\pi\)
−0.475532 + 0.879698i \(0.657744\pi\)
\(500\) −5.34585e26 + 6.63786e26i −0.547415 + 0.679717i
\(501\) 1.17174e27i 1.17613i
\(502\) 1.93149e26 5.47766e26i 0.190044 0.538961i
\(503\) 1.52189e26i 0.146792i −0.997303 0.0733959i \(-0.976616\pi\)
0.997303 0.0733959i \(-0.0233837\pi\)
\(504\) 2.58450e26 + 4.17973e26i 0.244383 + 0.395224i
\(505\) −7.46138e26 −0.691680
\(506\) −1.72042e26 6.06640e25i −0.156361 0.0551348i
\(507\) −1.60969e27 −1.43438
\(508\) 1.00131e27 1.24331e27i 0.874843 1.08628i
\(509\) 6.41114e26i 0.549234i 0.961554 + 0.274617i \(0.0885510\pi\)
−0.961554 + 0.274617i \(0.911449\pi\)
\(510\) 1.41145e27 + 4.97695e26i 1.18567 + 0.418082i
\(511\) 6.88427e25i 0.0567086i
\(512\) −1.11999e26 1.23286e27i −0.0904724 0.995899i
\(513\) 4.09241e25 0.0324194
\(514\) −4.89476e26 + 1.38814e27i −0.380277 + 1.07846i
\(515\) 3.43735e26 0.261910
\(516\) 9.42128e26 + 7.58750e26i 0.704066 + 0.567024i
\(517\) 6.48988e26i 0.475698i
\(518\) 3.08374e25 8.74543e25i 0.0221707 0.0628758i
\(519\) 3.79020e26i 0.267293i
\(520\) −8.67175e26 + 5.36211e26i −0.599892 + 0.370939i
\(521\) 1.33712e27 0.907388 0.453694 0.891157i \(-0.350106\pi\)
0.453694 + 0.891157i \(0.350106\pi\)
\(522\) −2.64739e27 9.33500e26i −1.76243 0.621454i
\(523\) −4.93173e26 −0.322094 −0.161047 0.986947i \(-0.551487\pi\)
−0.161047 + 0.986947i \(0.551487\pi\)
\(524\) 6.64705e26 + 5.35325e26i 0.425908 + 0.343008i
\(525\) 7.63237e26i 0.479807i
\(526\) 3.91078e26 + 1.37899e26i 0.241216 + 0.0850556i
\(527\) 3.96213e27i 2.39785i
\(528\) 2.99221e26 + 1.37154e27i 0.177686 + 0.814461i
\(529\) 1.57768e27 0.919308
\(530\) 5.54637e26 1.57294e27i 0.317139 0.899400i
\(531\) 9.94356e26 0.557952
\(532\) 2.89573e26 3.59558e26i 0.159456 0.197994i
\(533\) 6.31294e26i 0.341161i
\(534\) 7.00610e26 1.98692e27i 0.371590 1.05382i
\(535\) 8.22578e26i 0.428192i
\(536\) −2.66963e27 + 1.65074e27i −1.36396 + 0.843396i
\(537\) −2.93469e27 −1.47170
\(538\) −7.09712e26 2.50253e26i −0.349349 0.123184i
\(539\) 9.66757e26 0.467121
\(540\) −3.75428e25 + 4.66163e25i −0.0178069 + 0.0221106i
\(541\) 2.72131e27i 1.26708i −0.773709 0.633541i \(-0.781601\pi\)
0.773709 0.633541i \(-0.218399\pi\)
\(542\) −3.96957e27 1.39972e27i −1.81447 0.639805i
\(543\) 1.97489e27i 0.886225i
\(544\) −3.97958e27 4.96828e26i −1.75327 0.218885i
\(545\) 7.15064e26 0.309300
\(546\) −7.07490e26 + 2.00643e27i −0.300465 + 0.852113i
\(547\) −3.35783e26 −0.140019 −0.0700093 0.997546i \(-0.522303\pi\)
−0.0700093 + 0.997546i \(0.522303\pi\)
\(548\) 1.59899e27 + 1.28776e27i 0.654696 + 0.527264i
\(549\) 5.41022e26i 0.217516i
\(550\) −3.69607e26 + 1.04820e27i −0.145920 + 0.413825i
\(551\) 2.63715e27i 1.02240i
\(552\) 5.60441e26 + 9.06360e26i 0.213373 + 0.345072i
\(553\) −2.07129e27 −0.774444
\(554\) 6.16626e26 + 2.17430e26i 0.226425 + 0.0798401i
\(555\) 2.94379e26 0.106164
\(556\) 2.72061e27 + 2.19107e27i 0.963649 + 0.776082i
\(557\) 1.68401e27i 0.585859i −0.956134 0.292929i \(-0.905370\pi\)
0.956134 0.292929i \(-0.0946301\pi\)
\(558\) 3.89494e27 + 1.37340e27i 1.33094 + 0.469306i
\(559\) 2.66972e27i 0.896080i
\(560\) 1.43922e26 + 6.59699e26i 0.0474512 + 0.217503i
\(561\) 4.54781e27 1.47290
\(562\) 1.45898e27 4.13763e27i 0.464179 1.31640i
\(563\) 1.64929e27 0.515481 0.257741 0.966214i \(-0.417022\pi\)
0.257741 + 0.966214i \(0.417022\pi\)
\(564\) 2.37791e27 2.95261e27i 0.730136 0.906599i
\(565\) 9.34862e26i 0.282009i
\(566\) −1.39052e27 + 3.94349e27i −0.412110 + 1.16874i
\(567\) 1.47092e27i 0.428309i
\(568\) −1.98343e27 3.20765e27i −0.567457 0.917706i
\(569\) 4.44042e26 0.124825 0.0624125 0.998050i \(-0.480121\pi\)
0.0624125 + 0.998050i \(0.480121\pi\)
\(570\) 1.38215e27 + 4.87363e26i 0.381775 + 0.134618i
\(571\) 1.78241e27 0.483777 0.241889 0.970304i \(-0.422233\pi\)
0.241889 + 0.970304i \(0.422233\pi\)
\(572\) −1.94328e27 + 2.41293e27i −0.518291 + 0.643554i
\(573\) 2.18135e27i 0.571715i
\(574\) −3.94286e26 1.39030e26i −0.101553 0.0358087i
\(575\) 8.43712e26i 0.213558i
\(576\) 1.86785e27 3.73988e27i 0.464641 0.930321i
\(577\) −5.12768e26 −0.125361 −0.0626805 0.998034i \(-0.519965\pi\)
−0.0626805 + 0.998034i \(0.519965\pi\)
\(578\) −2.93659e27 + 8.32811e27i −0.705610 + 2.00110i
\(579\) 2.26230e27 0.534275
\(580\) −3.00396e27 2.41926e27i −0.697290 0.561568i
\(581\) 1.64383e27i 0.375056i
\(582\) 2.25670e26 6.39996e26i 0.0506109 0.143532i
\(583\) 5.06813e27i 1.11728i
\(584\) 4.98090e26 3.07990e26i 0.107939 0.0667434i
\(585\) −3.44296e27 −0.733454
\(586\) 2.38984e27 + 8.42686e26i 0.500487 + 0.176478i
\(587\) −4.59426e27 −0.945878 −0.472939 0.881095i \(-0.656807\pi\)
−0.472939 + 0.881095i \(0.656807\pi\)
\(588\) −4.39832e27 3.54222e27i −0.890253 0.716972i
\(589\) 3.87988e27i 0.772086i
\(590\) 1.28849e27 + 4.54336e26i 0.252092 + 0.0888908i
\(591\) 3.95843e27i 0.761462i
\(592\) −7.70710e26 + 1.68141e26i −0.145772 + 0.0318021i
\(593\) 5.91413e27 1.09988 0.549939 0.835205i \(-0.314651\pi\)
0.549939 + 0.835205i \(0.314651\pi\)
\(594\) −6.04828e25 + 1.71528e26i −0.0110603 + 0.0313668i
\(595\) 2.18745e27 0.393341
\(596\) 4.71325e27 5.85237e27i 0.833408 1.03483i
\(597\) 5.07199e27i 0.881932i
\(598\) −7.82087e26 + 2.21798e27i −0.133734 + 0.379268i
\(599\) 8.24036e27i 1.38573i 0.721068 + 0.692864i \(0.243651\pi\)
−0.721068 + 0.692864i \(0.756349\pi\)
\(600\) 5.52217e27 3.41459e27i 0.913266 0.564711i
\(601\) −8.63115e27 −1.40386 −0.701930 0.712246i \(-0.747678\pi\)
−0.701930 + 0.712246i \(0.747678\pi\)
\(602\) 1.66742e27 + 5.87951e26i 0.266735 + 0.0940537i
\(603\) −1.05993e28 −1.66764
\(604\) −2.86357e27 + 3.55565e27i −0.443138 + 0.550237i
\(605\) 2.15806e27i 0.328480i
\(606\) 1.24907e28 + 4.40436e27i 1.87008 + 0.659412i
\(607\) 3.90613e27i 0.575254i 0.957742 + 0.287627i \(0.0928664\pi\)
−0.957742 + 0.287627i \(0.907134\pi\)
\(608\) −3.89697e27 4.86514e26i −0.564536 0.0704790i
\(609\) −8.04836e27 −1.14692
\(610\) 2.47200e26 7.01056e26i 0.0346538 0.0982775i
\(611\) 8.36683e27 1.15385
\(612\) −1.05476e28 8.49459e27i −1.43100 1.15247i
\(613\) 8.78457e27i 1.17251i −0.810127 0.586254i \(-0.800602\pi\)
0.810127 0.586254i \(-0.199398\pi\)
\(614\) 2.86144e27 8.11498e27i 0.375751 1.06562i
\(615\) 1.32720e27i 0.171469i
\(616\) 1.07907e27 + 1.74511e27i 0.137165 + 0.221827i
\(617\) −9.93663e27 −1.24276 −0.621381 0.783509i \(-0.713428\pi\)
−0.621381 + 0.783509i \(0.713428\pi\)
\(618\) −5.75429e27 2.02903e27i −0.708120 0.249691i
\(619\) −1.10877e28 −1.34256 −0.671281 0.741203i \(-0.734256\pi\)
−0.671281 + 0.741203i \(0.734256\pi\)
\(620\) 4.41954e27 + 3.55931e27i 0.526575 + 0.424081i
\(621\) 1.38066e26i 0.0161871i
\(622\) −1.44627e28 5.09970e27i −1.66857 0.588357i
\(623\) 3.07930e27i 0.349600i
\(624\) 1.76821e28 3.85759e27i 1.97555 0.430993i
\(625\) 2.88311e27 0.317001
\(626\) 5.04983e27 1.43212e28i 0.546428 1.54966i
\(627\) 4.45340e27 0.474260
\(628\) 2.41377e27 2.99714e27i 0.252988 0.314131i
\(629\) 2.55554e27i 0.263619i
\(630\) −7.58241e26 + 2.15036e27i −0.0769843 + 0.218326i
\(631\) 1.33853e28i 1.33763i 0.743429 + 0.668815i \(0.233198\pi\)
−0.743429 + 0.668815i \(0.766802\pi\)
\(632\) 9.26661e27 + 1.49862e28i 0.911486 + 1.47408i
\(633\) 2.14862e28 2.08028
\(634\) 5.86761e27 + 2.06899e27i 0.559202 + 0.197181i
\(635\) 7.40692e27 0.694865
\(636\) −1.85697e28 + 2.30578e28i −1.71488 + 2.12934i
\(637\) 1.24635e28i 1.13305i
\(638\) −1.10533e28 3.89752e27i −0.989201 0.348804i
\(639\) 1.27354e28i 1.12203i
\(640\) 4.12917e27 3.99269e27i 0.358148 0.346310i
\(641\) 6.17579e27 0.527366 0.263683 0.964609i \(-0.415063\pi\)
0.263683 + 0.964609i \(0.415063\pi\)
\(642\) −4.85558e27 + 1.37703e28i −0.408216 + 1.15769i
\(643\) 1.45988e28 1.20839 0.604195 0.796837i \(-0.293495\pi\)
0.604195 + 0.796837i \(0.293495\pi\)
\(644\) 1.21304e27 + 9.76932e26i 0.0988592 + 0.0796170i
\(645\) 5.61267e27i 0.450373i
\(646\) −4.23088e27 + 1.19987e28i −0.334276 + 0.948000i
\(647\) 1.88186e27i 0.146401i −0.997317 0.0732004i \(-0.976679\pi\)
0.997317 0.0732004i \(-0.0233213\pi\)
\(648\) −1.06424e28 + 6.58063e27i −0.815245 + 0.504101i
\(649\) 4.15160e27 0.313162
\(650\) 1.35135e28 + 4.76502e27i 1.00377 + 0.353941i
\(651\) 1.18411e28 0.866126
\(652\) −2.63976e26 2.12595e26i −0.0190146 0.0153136i
\(653\) 7.52706e27i 0.533941i 0.963705 + 0.266971i \(0.0860227\pi\)
−0.963705 + 0.266971i \(0.913977\pi\)
\(654\) −1.19705e28 4.22094e27i −0.836247 0.294870i
\(655\) 3.95994e27i 0.272443i
\(656\) 7.58059e26 + 3.47473e27i 0.0513647 + 0.235441i
\(657\) 1.97757e27 0.131971
\(658\) 1.84263e27 5.22565e27i 0.121110 0.343464i
\(659\) −2.74243e28 −1.77534 −0.887669 0.460482i \(-0.847677\pi\)
−0.887669 + 0.460482i \(0.847677\pi\)
\(660\) −4.08544e27 + 5.07283e27i −0.260495 + 0.323453i
\(661\) 1.11450e28i 0.699950i 0.936759 + 0.349975i \(0.113810\pi\)
−0.936759 + 0.349975i \(0.886190\pi\)
\(662\) 2.80604e27 7.95786e27i 0.173585 0.492285i
\(663\) 5.86309e28i 3.57265i
\(664\) −1.18934e28 + 7.35422e27i −0.713883 + 0.441424i
\(665\) 2.14204e27 0.126652
\(666\) −2.51221e27 8.85834e26i −0.146323 0.0515953i
\(667\) −8.89697e27 −0.510486
\(668\) 9.13788e27 1.13464e28i 0.516512 0.641345i
\(669\) 2.97123e28i 1.65453i
\(670\) −1.37345e28 4.84295e27i −0.753469 0.265682i
\(671\) 2.25885e27i 0.122085i
\(672\) 1.48480e27 1.18932e28i 0.0790633 0.633296i
\(673\) −8.66157e27 −0.454408 −0.227204 0.973847i \(-0.572958\pi\)
−0.227204 + 0.973847i \(0.572958\pi\)
\(674\) 1.09475e28 3.10468e28i 0.565867 1.60479i
\(675\) 8.41193e26 0.0428408
\(676\) 1.55872e28 + 1.25533e28i 0.782171 + 0.629927i
\(677\) 6.27182e27i 0.310104i −0.987906 0.155052i \(-0.950446\pi\)
0.987906 0.155052i \(-0.0495545\pi\)
\(678\) −5.51838e27 + 1.56500e28i −0.268853 + 0.762461i
\(679\) 9.91858e26i 0.0476159i
\(680\) −9.78628e27 1.58266e28i −0.462944 0.748686i
\(681\) 3.57021e28 1.66426
\(682\) 1.62620e28 + 5.73418e27i 0.747018 + 0.263407i
\(683\) −2.46439e28 −1.11559 −0.557793 0.829980i \(-0.688352\pi\)
−0.557793 + 0.829980i \(0.688352\pi\)
\(684\) −1.03287e28 8.31826e27i −0.460768 0.371083i
\(685\) 9.52587e27i 0.418792i
\(686\) −1.75108e28 6.17450e27i −0.758689 0.267523i
\(687\) 8.18786e27i 0.349626i
\(688\) −3.20580e27 1.46945e28i −0.134912 0.618401i
\(689\) −6.53389e28 −2.71006
\(690\) −1.64422e27 + 4.66298e27i −0.0672154 + 0.190622i
\(691\) 3.79505e28 1.52910 0.764552 0.644562i \(-0.222960\pi\)
0.764552 + 0.644562i \(0.222960\pi\)
\(692\) −2.95580e27 + 3.67018e27i −0.117386 + 0.145756i
\(693\) 6.92862e27i 0.271215i
\(694\) 4.34097e27 1.23109e28i 0.167491 0.475002i
\(695\) 1.62079e28i 0.616422i
\(696\) 3.60070e28 + 5.82315e28i 1.34988 + 2.18306i
\(697\) 1.15216e28 0.425780
\(698\) 1.10010e28 + 3.87910e27i 0.400756 + 0.141311i
\(699\) −4.21338e28 −1.51307
\(700\) 5.95215e27 7.39069e27i 0.210714 0.261640i
\(701\) 2.03325e27i 0.0709596i 0.999370 + 0.0354798i \(0.0112959\pi\)
−0.999370 + 0.0354798i \(0.988704\pi\)
\(702\) 2.21136e27 + 7.79751e26i 0.0760831 + 0.0268278i
\(703\) 2.50250e27i 0.0848829i
\(704\) 7.79860e27 1.56146e28i 0.260789 0.522161i
\(705\) 1.75900e28 0.579929
\(706\) −8.43208e27 + 2.39132e28i −0.274086 + 0.777304i
\(707\) 1.93579e28 0.620389
\(708\) −1.88880e28 1.52116e28i −0.596833 0.480664i
\(709\) 3.94725e28i 1.22979i −0.788608 0.614896i \(-0.789198\pi\)
0.788608 0.614896i \(-0.210802\pi\)
\(710\) 5.81897e27 1.65025e28i 0.178757 0.506951i
\(711\) 5.94999e28i 1.80227i
\(712\) −2.22793e28 + 1.37763e28i −0.665430 + 0.411464i
\(713\) 1.30896e28 0.385505
\(714\) −3.66189e28 1.29123e28i −1.06347 0.374990i
\(715\) −1.43749e28 −0.411666
\(716\) 2.84176e28 + 2.28863e28i 0.802523 + 0.646318i
\(717\) 3.87476e28i 1.07908i
\(718\) 4.68692e28 + 1.65266e28i 1.28719 + 0.453878i
\(719\) 2.52527e28i 0.683942i 0.939710 + 0.341971i \(0.111095\pi\)
−0.939710 + 0.341971i \(0.888905\pi\)
\(720\) 1.89505e28 4.13431e27i 0.506169 0.110428i
\(721\) −8.91792e27 −0.234915
\(722\) 8.65727e27 2.45519e28i 0.224910 0.637841i
\(723\) 5.66185e28 1.45069
\(724\) 1.54013e28 1.91235e28i 0.389198 0.483261i
\(725\) 5.42065e28i 1.35105i
\(726\) 1.27387e28 3.61268e28i 0.313156 0.888103i
\(727\) 6.02907e28i 1.46186i 0.682452 + 0.730931i \(0.260914\pi\)
−0.682452 + 0.730931i \(0.739086\pi\)
\(728\) 2.24981e28 1.39115e28i 0.538062 0.332707i
\(729\) −4.57036e28 −1.07814
\(730\) 2.56254e27 + 9.03581e26i 0.0596268 + 0.0210251i
\(731\) −4.87244e28 −1.11834
\(732\) −8.27649e27 + 1.02768e28i −0.187385 + 0.232673i
\(733\) 2.73732e28i 0.611345i −0.952137 0.305673i \(-0.901119\pi\)
0.952137 0.305673i \(-0.0988813\pi\)
\(734\) 5.01778e28 + 1.76933e28i 1.10548 + 0.389805i
\(735\) 2.62027e28i 0.569473i
\(736\) 1.64136e27 1.31472e28i 0.0351904 0.281874i
\(737\) −4.42536e28 −0.935996
\(738\) −3.99376e27 + 1.13262e28i −0.0833334 + 0.236332i
\(739\) 8.14966e28 1.67763 0.838813 0.544419i \(-0.183250\pi\)
0.838813 + 0.544419i \(0.183250\pi\)
\(740\) −2.85057e27 2.29573e27i −0.0578915 0.0466233i
\(741\) 5.74138e28i 1.15036i
\(742\) −1.43896e28 + 4.08085e28i −0.284452 + 0.806700i
\(743\) 4.08224e28i 0.796178i −0.917347 0.398089i \(-0.869674\pi\)
0.917347 0.398089i \(-0.130326\pi\)
\(744\) −5.29749e28 8.56724e28i −1.01939 1.64859i
\(745\) 3.48651e28 0.661955
\(746\) −3.32978e28 1.17412e28i −0.623774 0.219950i
\(747\) −4.72207e28 −0.872823
\(748\) −4.40380e28 3.54663e28i −0.803177 0.646845i
\(749\) 2.13411e28i 0.384059i
\(750\) 6.61995e28 + 2.33427e28i 1.17555 + 0.414514i
\(751\) 1.72660e28i 0.302547i 0.988492 + 0.151273i \(0.0483374\pi\)
−0.988492 + 0.151273i \(0.951663\pi\)
\(752\) −4.60522e28 + 1.00469e28i −0.796291 + 0.173722i
\(753\) −4.78365e28 −0.816225
\(754\) −5.02472e28 + 1.42500e29i −0.846055 + 2.39940i
\(755\) −2.11826e28 −0.351973
\(756\) 9.74015e26 1.20942e27i 0.0159716 0.0198316i
\(757\) 6.18361e28i 1.00065i −0.865837 0.500326i \(-0.833213\pi\)
0.865837 0.500326i \(-0.166787\pi\)
\(758\) −2.71739e28 + 7.70648e28i −0.433971 + 1.23073i
\(759\) 1.50245e28i 0.236800i
\(760\) −9.58314e27 1.54981e28i