Properties

Label 8.18.b.a.5.11
Level $8$
Weight $18$
Character 8.5
Analytic conductor $14.658$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 18 \)
Character orbit: \([\chi]\) \(=\) 8.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.6577669876\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 7 x^{15} + 4022 x^{14} - 1102776 x^{13} - 373411968 x^{12} + 2100004864 x^{11} - 3763915816960 x^{10} + 7317489121656832 x^{9} - 1108241988138827776 x^{8} + 163121042717484777472 x^{7} + 5699397839986467274752 x^{6} + 1127435088957285706235904 x^{5} - 217909345031306501735579648 x^{4} - 78950720850572326734309359616 x^{3} + 13720647095471028734661620662272 x^{2} - 5242030267748791654842336509165568 x + 1286374137827816254118965326485913600\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{120}\cdot 3^{14}\cdot 7 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.11
Root \(99.0623 + 145.965i\) of defining polynomial
Character \(\chi\) \(=\) 8.5
Dual form 8.18.b.a.5.12

$q$-expansion

\(f(q)\) \(=\) \(q+(214.125 - 291.929i) q^{2} +1638.94i q^{3} +(-39373.4 - 125018. i) q^{4} +1.21254e6i q^{5} +(478455. + 350938. i) q^{6} +1.76580e7 q^{7} +(-4.49273e7 - 1.52753e7i) q^{8} +1.26454e8 q^{9} +O(q^{10})\) \(q+(214.125 - 291.929i) q^{2} +1638.94i q^{3} +(-39373.4 - 125018. i) q^{4} +1.21254e6i q^{5} +(478455. + 350938. i) q^{6} +1.76580e7 q^{7} +(-4.49273e7 - 1.52753e7i) q^{8} +1.26454e8 q^{9} +(3.53976e8 + 2.59635e8i) q^{10} +7.26817e8i q^{11} +(2.04898e8 - 6.45307e7i) q^{12} -3.16645e9i q^{13} +(3.78101e9 - 5.15488e9i) q^{14} -1.98729e9 q^{15} +(-1.40793e10 + 9.84479e9i) q^{16} +4.56030e10 q^{17} +(2.70769e10 - 3.69156e10i) q^{18} -1.55789e10i q^{19} +(1.51590e11 - 4.77419e10i) q^{20} +2.89404e10i q^{21} +(2.12179e11 + 1.55629e11i) q^{22} +4.09250e11 q^{23} +(2.50353e10 - 7.36333e10i) q^{24} -7.07318e11 q^{25} +(-9.24380e11 - 6.78015e11i) q^{26} +4.18904e11i q^{27} +(-6.95255e11 - 2.20757e12i) q^{28} +3.11338e12i q^{29} +(-4.25527e11 + 5.80147e11i) q^{30} -6.57077e12 q^{31} +(-1.40750e11 + 6.21818e12i) q^{32} -1.19121e12 q^{33} +(9.76472e12 - 1.33128e13i) q^{34} +2.14111e13i q^{35} +(-4.97892e12 - 1.58091e13i) q^{36} +1.36898e13i q^{37} +(-4.54793e12 - 3.33582e12i) q^{38} +5.18964e12 q^{39} +(1.85219e13 - 5.44763e13i) q^{40} -2.81830e12 q^{41} +(8.44856e12 + 6.19686e12i) q^{42} -1.36024e13i q^{43} +(9.08656e13 - 2.86173e13i) q^{44} +1.53331e14i q^{45} +(8.76304e13 - 1.19472e14i) q^{46} +6.84132e11 q^{47} +(-1.61351e13 - 2.30752e13i) q^{48} +7.91743e13 q^{49} +(-1.51454e14 + 2.06487e14i) q^{50} +7.47407e13i q^{51} +(-3.95865e14 + 1.24674e14i) q^{52} -2.47869e14i q^{53} +(1.22290e14 + 8.96977e13i) q^{54} -8.81297e14 q^{55} +(-7.93327e14 - 2.69731e14i) q^{56} +2.55329e13 q^{57} +(9.08887e14 + 6.66651e14i) q^{58} -2.03296e15i q^{59} +(7.82462e13 + 2.48447e14i) q^{60} +8.92495e14i q^{61} +(-1.40696e15 + 1.91820e15i) q^{62} +2.23292e15 q^{63} +(1.78513e15 + 1.37255e15i) q^{64} +3.83946e15 q^{65} +(-2.55068e14 + 3.47750e14i) q^{66} -5.06693e15i q^{67} +(-1.79554e15 - 5.70121e15i) q^{68} +6.70737e14i q^{69} +(6.25051e15 + 4.58463e15i) q^{70} -6.85113e15 q^{71} +(-5.68124e15 - 1.93162e15i) q^{72} +1.37250e15 q^{73} +(3.99644e15 + 2.93131e15i) q^{74} -1.15925e15i q^{75} +(-1.94765e15 + 6.13392e14i) q^{76} +1.28341e16i q^{77} +(1.11123e15 - 1.51501e15i) q^{78} -1.78556e16 q^{79} +(-1.19372e16 - 1.70718e16i) q^{80} +1.56437e16 q^{81} +(-6.03468e14 + 8.22745e14i) q^{82} +1.48017e15i q^{83} +(3.61809e15 - 1.13948e15i) q^{84} +5.52955e16i q^{85} +(-3.97094e15 - 2.91261e15i) q^{86} -5.10265e15 q^{87} +(1.11023e16 - 3.26540e16i) q^{88} -3.78700e16 q^{89} +(4.47617e16 + 3.28319e16i) q^{90} -5.59132e16i q^{91} +(-1.61135e16 - 5.11638e16i) q^{92} -1.07691e16i q^{93} +(1.46489e14 - 1.99718e14i) q^{94} +1.88900e16 q^{95} +(-1.01912e16 - 2.30681e14i) q^{96} +1.28098e17 q^{97} +(1.69532e16 - 2.31133e16i) q^{98} +9.19090e16i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 270q^{2} - 27436q^{4} + 5839948q^{6} + 11529600q^{7} + 24334920q^{8} - 602654096q^{9} + O(q^{10}) \) \( 16q + 270q^{2} - 27436q^{4} + 5839948q^{6} + 11529600q^{7} + 24334920q^{8} - 602654096q^{9} + 131002712q^{10} - 2795125400q^{12} + 16363788528q^{14} - 9993282176q^{15} + 26500434192q^{16} - 7489125600q^{17} - 113450563870q^{18} - 209445719856q^{20} + 223126527100q^{22} + 746845345920q^{23} - 1099415493232q^{24} - 1809682431664q^{25} + 2467726531080q^{26} + 3220542267040q^{28} - 1188624268048q^{30} - 318979758592q^{31} + 1455647316000q^{32} + 5633526177600q^{33} - 4461251980292q^{34} - 33088278002484q^{36} + 24076283913900q^{38} - 18457706051456q^{39} + 60626292962592q^{40} + 7482251536032q^{41} - 51630378688160q^{42} + 193654716236040q^{44} - 195097141003568q^{46} - 376698804821760q^{47} - 329350060416480q^{48} + 127691292101520q^{49} + 474997408872102q^{50} - 272251877663120q^{52} + 735354219382520q^{54} + 2209036687713152q^{55} - 162767516076480q^{56} - 190521298294720q^{57} - 623262610679960q^{58} - 1973616194963808q^{60} + 695695648144320q^{62} - 8131096607338880q^{63} + 1111931745501248q^{64} + 2385987975356160q^{65} + 3598826202828312q^{66} + 5981109959771880q^{68} - 10044559836180288q^{70} + 9025926285576576q^{71} - 19918679666289160q^{72} + 11332002046118560q^{73} + 11098735408189464q^{74} + 5959440926938280q^{76} + 4184252259031760q^{78} - 45299671392008448q^{79} + 1337342539452480q^{80} + 20101901999290832q^{81} + 15639739637081420q^{82} + 19796542864700224q^{84} - 14252032276026564q^{86} + 25965768920837760q^{87} - 66964872768837680q^{88} - 69879174608766048q^{89} + 136151511125051240q^{90} + 57336249810701280q^{92} - 192318922166254176q^{94} + 93790444358203776q^{95} - 342799224184788928q^{96} + 95593398602180640q^{97} + 339641261743253790q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 214.125 291.929i 0.591441 0.806348i
\(3\) 1638.94i 0.144223i 0.997397 + 0.0721113i \(0.0229737\pi\)
−0.997397 + 0.0721113i \(0.977026\pi\)
\(4\) −39373.4 125018.i −0.300395 0.953815i
\(5\) 1.21254e6i 1.38820i 0.719879 + 0.694100i \(0.244197\pi\)
−0.719879 + 0.694100i \(0.755803\pi\)
\(6\) 478455. + 350938.i 0.116294 + 0.0852991i
\(7\) 1.76580e7 1.15773 0.578866 0.815423i \(-0.303495\pi\)
0.578866 + 0.815423i \(0.303495\pi\)
\(8\) −4.49273e7 1.52753e7i −0.946773 0.321902i
\(9\) 1.26454e8 0.979200
\(10\) 3.53976e8 + 2.59635e8i 1.11937 + 0.821038i
\(11\) 7.26817e8i 1.02232i 0.859485 + 0.511161i \(0.170784\pi\)
−0.859485 + 0.511161i \(0.829216\pi\)
\(12\) 2.04898e8 6.45307e7i 0.137562 0.0433237i
\(13\) 3.16645e9i 1.07660i −0.842753 0.538300i \(-0.819067\pi\)
0.842753 0.538300i \(-0.180933\pi\)
\(14\) 3.78101e9 5.15488e9i 0.684730 0.933535i
\(15\) −1.98729e9 −0.200210
\(16\) −1.40793e10 + 9.84479e9i −0.819526 + 0.573042i
\(17\) 4.56030e10 1.58554 0.792771 0.609520i \(-0.208638\pi\)
0.792771 + 0.609520i \(0.208638\pi\)
\(18\) 2.70769e10 3.69156e10i 0.579139 0.789576i
\(19\) 1.55789e10i 0.210441i −0.994449 0.105220i \(-0.966445\pi\)
0.994449 0.105220i \(-0.0335548\pi\)
\(20\) 1.51590e11 4.77419e10i 1.32408 0.417008i
\(21\) 2.89404e10i 0.166971i
\(22\) 2.12179e11 + 1.55629e11i 0.824347 + 0.604643i
\(23\) 4.09250e11 1.08969 0.544843 0.838538i \(-0.316589\pi\)
0.544843 + 0.838538i \(0.316589\pi\)
\(24\) 2.50353e10 7.36333e10i 0.0464256 0.136546i
\(25\) −7.07318e11 −0.927096
\(26\) −9.24380e11 6.78015e11i −0.868115 0.636746i
\(27\) 4.18904e11i 0.285445i
\(28\) −6.95255e11 2.20757e12i −0.347777 1.10426i
\(29\) 3.11338e12i 1.15571i 0.816139 + 0.577855i \(0.196110\pi\)
−0.816139 + 0.577855i \(0.803890\pi\)
\(30\) −4.25527e11 + 5.80147e11i −0.118412 + 0.161439i
\(31\) −6.57077e12 −1.38370 −0.691850 0.722041i \(-0.743204\pi\)
−0.691850 + 0.722041i \(0.743204\pi\)
\(32\) −1.40750e11 + 6.21818e12i −0.0226295 + 0.999744i
\(33\) −1.19121e12 −0.147442
\(34\) 9.76472e12 1.33128e13i 0.937754 1.27850i
\(35\) 2.14111e13i 1.60716i
\(36\) −4.97892e12 1.58091e13i −0.294147 0.933975i
\(37\) 1.36898e13i 0.640739i 0.947293 + 0.320369i \(0.103807\pi\)
−0.947293 + 0.320369i \(0.896193\pi\)
\(38\) −4.54793e12 3.33582e12i −0.169689 0.124463i
\(39\) 5.18964e12 0.155270
\(40\) 1.85219e13 5.44763e13i 0.446865 1.31431i
\(41\) −2.81830e12 −0.0551220 −0.0275610 0.999620i \(-0.508774\pi\)
−0.0275610 + 0.999620i \(0.508774\pi\)
\(42\) 8.44856e12 + 6.19686e12i 0.134637 + 0.0987535i
\(43\) 1.36024e13i 0.177474i −0.996055 0.0887369i \(-0.971717\pi\)
0.996055 0.0887369i \(-0.0282830\pi\)
\(44\) 9.08656e13 2.86173e13i 0.975106 0.307100i
\(45\) 1.53331e14i 1.35932i
\(46\) 8.76304e13 1.19472e14i 0.644486 0.878667i
\(47\) 6.84132e11 0.00419091 0.00209545 0.999998i \(-0.499333\pi\)
0.00209545 + 0.999998i \(0.499333\pi\)
\(48\) −1.61351e13 2.30752e13i −0.0826456 0.118194i
\(49\) 7.91743e13 0.340343
\(50\) −1.51454e14 + 2.06487e14i −0.548323 + 0.747563i
\(51\) 7.47407e13i 0.228671i
\(52\) −3.95865e14 + 1.24674e14i −1.02688 + 0.323405i
\(53\) 2.47869e14i 0.546862i −0.961892 0.273431i \(-0.911841\pi\)
0.961892 0.273431i \(-0.0881585\pi\)
\(54\) 1.22290e14 + 8.96977e13i 0.230168 + 0.168824i
\(55\) −8.81297e14 −1.41919
\(56\) −7.93327e14 2.69731e14i −1.09611 0.372677i
\(57\) 2.55329e13 0.0303503
\(58\) 9.08887e14 + 6.66651e14i 0.931905 + 0.683535i
\(59\) 2.03296e15i 1.80255i −0.433245 0.901276i \(-0.642632\pi\)
0.433245 0.901276i \(-0.357368\pi\)
\(60\) 7.82462e13 + 2.48447e14i 0.0601419 + 0.190963i
\(61\) 8.92495e14i 0.596077i 0.954554 + 0.298038i \(0.0963324\pi\)
−0.954554 + 0.298038i \(0.903668\pi\)
\(62\) −1.40696e15 + 1.91820e15i −0.818377 + 1.11574i
\(63\) 2.23292e15 1.13365
\(64\) 1.78513e15 + 1.37255e15i 0.792758 + 0.609537i
\(65\) 3.83946e15 1.49454
\(66\) −2.55068e14 + 3.47750e14i −0.0872031 + 0.118889i
\(67\) 5.06693e15i 1.52444i −0.647321 0.762218i \(-0.724111\pi\)
0.647321 0.762218i \(-0.275889\pi\)
\(68\) −1.79554e15 5.70121e15i −0.476289 1.51231i
\(69\) 6.70737e14i 0.157157i
\(70\) 6.25051e15 + 4.58463e15i 1.29593 + 0.950542i
\(71\) −6.85113e15 −1.25912 −0.629559 0.776953i \(-0.716764\pi\)
−0.629559 + 0.776953i \(0.716764\pi\)
\(72\) −5.68124e15 1.93162e15i −0.927080 0.315207i
\(73\) 1.37250e15 0.199191 0.0995954 0.995028i \(-0.468245\pi\)
0.0995954 + 0.995028i \(0.468245\pi\)
\(74\) 3.99644e15 + 2.93131e15i 0.516659 + 0.378959i
\(75\) 1.15925e15i 0.133708i
\(76\) −1.94765e15 + 6.13392e14i −0.200722 + 0.0632154i
\(77\) 1.28341e16i 1.18357i
\(78\) 1.11123e15 1.51501e15i 0.0918331 0.125202i
\(79\) −1.78556e16 −1.32417 −0.662085 0.749429i \(-0.730328\pi\)
−0.662085 + 0.749429i \(0.730328\pi\)
\(80\) −1.19372e16 1.70718e16i −0.795497 1.13766i
\(81\) 1.56437e16 0.938032
\(82\) −6.03468e14 + 8.22745e14i −0.0326014 + 0.0444475i
\(83\) 1.48017e15i 0.0721354i 0.999349 + 0.0360677i \(0.0114832\pi\)
−0.999349 + 0.0360677i \(0.988517\pi\)
\(84\) 3.61809e15 1.13948e15i 0.159259 0.0501573i
\(85\) 5.52955e16i 2.20105i
\(86\) −3.97094e15 2.91261e15i −0.143106 0.104965i
\(87\) −5.10265e15 −0.166680
\(88\) 1.11023e16 3.26540e16i 0.329088 0.967906i
\(89\) −3.78700e16 −1.01972 −0.509859 0.860258i \(-0.670303\pi\)
−0.509859 + 0.860258i \(0.670303\pi\)
\(90\) 4.47617e16 + 3.28319e16i 1.09609 + 0.803960i
\(91\) 5.59132e16i 1.24642i
\(92\) −1.61135e16 5.11638e16i −0.327336 1.03936i
\(93\) 1.07691e16i 0.199561i
\(94\) 1.46489e14 1.99718e14i 0.00247868 0.00337933i
\(95\) 1.88900e16 0.292134
\(96\) −1.01912e16 2.30681e14i −0.144186 0.00326368i
\(97\) 1.28098e17 1.65952 0.829760 0.558121i \(-0.188477\pi\)
0.829760 + 0.558121i \(0.188477\pi\)
\(98\) 1.69532e16 2.31133e16i 0.201293 0.274435i
\(99\) 9.19090e16i 1.00106i
\(100\) 2.78495e16 + 8.84278e16i 0.278495 + 0.884278i
\(101\) 6.82139e16i 0.626818i −0.949618 0.313409i \(-0.898529\pi\)
0.949618 0.313409i \(-0.101471\pi\)
\(102\) 2.18190e16 + 1.60038e16i 0.184388 + 0.135245i
\(103\) −3.08715e16 −0.240127 −0.120063 0.992766i \(-0.538310\pi\)
−0.120063 + 0.992766i \(0.538310\pi\)
\(104\) −4.83684e16 + 1.42260e17i −0.346560 + 1.01930i
\(105\) −3.50915e16 −0.231789
\(106\) −7.23603e16 5.30749e16i −0.440961 0.323437i
\(107\) 2.71861e17i 1.52962i −0.644253 0.764812i \(-0.722832\pi\)
0.644253 0.764812i \(-0.277168\pi\)
\(108\) 5.23707e16 1.64937e16i 0.272262 0.0857463i
\(109\) 1.32808e17i 0.638407i −0.947686 0.319203i \(-0.896585\pi\)
0.947686 0.319203i \(-0.103415\pi\)
\(110\) −1.88707e17 + 2.57276e17i −0.839365 + 1.14436i
\(111\) −2.24367e16 −0.0924090
\(112\) −2.48613e17 + 1.73839e17i −0.948791 + 0.663429i
\(113\) −3.78953e17 −1.34097 −0.670484 0.741924i \(-0.733913\pi\)
−0.670484 + 0.741924i \(0.733913\pi\)
\(114\) 5.46721e15 7.45379e15i 0.0179504 0.0244729i
\(115\) 4.96232e17i 1.51270i
\(116\) 3.89230e17 1.22584e17i 1.10233 0.347170i
\(117\) 4.00411e17i 1.05421i
\(118\) −5.93482e17 4.35308e17i −1.45348 1.06610i
\(119\) 8.05257e17 1.83563
\(120\) 8.92835e16 + 3.03563e16i 0.189553 + 0.0644479i
\(121\) −2.28165e16 −0.0451413
\(122\) 2.60545e17 + 1.91105e17i 0.480646 + 0.352544i
\(123\) 4.61904e15i 0.00794983i
\(124\) 2.58714e17 + 8.21468e17i 0.415657 + 1.31979i
\(125\) 6.74428e16i 0.101205i
\(126\) 4.78124e17 6.51856e17i 0.670488 0.914117i
\(127\) −2.56390e17 −0.336179 −0.168089 0.985772i \(-0.553760\pi\)
−0.168089 + 0.985772i \(0.553760\pi\)
\(128\) 7.82929e17 2.27234e17i 0.960368 0.278734i
\(129\) 2.22936e16 0.0255957
\(130\) 8.22122e17 1.12085e18i 0.883930 1.20512i
\(131\) 1.61862e18i 1.63057i 0.579060 + 0.815285i \(0.303420\pi\)
−0.579060 + 0.815285i \(0.696580\pi\)
\(132\) 4.69020e16 + 1.48923e17i 0.0442908 + 0.140632i
\(133\) 2.75092e17i 0.243634i
\(134\) −1.47918e18 1.08495e18i −1.22923 0.901614i
\(135\) −5.07939e17 −0.396255
\(136\) −2.04882e18 6.96598e17i −1.50115 0.510389i
\(137\) −3.32494e17 −0.228907 −0.114453 0.993429i \(-0.536512\pi\)
−0.114453 + 0.993429i \(0.536512\pi\)
\(138\) 1.95808e17 + 1.43621e17i 0.126724 + 0.0929493i
\(139\) 6.37994e17i 0.388321i 0.980970 + 0.194161i \(0.0621983\pi\)
−0.980970 + 0.194161i \(0.937802\pi\)
\(140\) 2.67678e18 8.43025e17i 1.53294 0.482783i
\(141\) 1.12125e15i 0.000604423i
\(142\) −1.46700e18 + 2.00005e18i −0.744694 + 1.01529i
\(143\) 2.30143e18 1.10063
\(144\) −1.78039e18 + 1.24491e18i −0.802479 + 0.561123i
\(145\) −3.77510e18 −1.60436
\(146\) 2.93887e17 4.00674e17i 0.117810 0.160617i
\(147\) 1.29762e17i 0.0490852i
\(148\) 1.71147e18 5.39012e17i 0.611146 0.192475i
\(149\) 2.77142e18i 0.934585i 0.884103 + 0.467293i \(0.154771\pi\)
−0.884103 + 0.467293i \(0.845229\pi\)
\(150\) −3.38420e17 2.48225e17i −0.107815 0.0790805i
\(151\) −4.43299e18 −1.33473 −0.667364 0.744732i \(-0.732577\pi\)
−0.667364 + 0.744732i \(0.732577\pi\)
\(152\) −2.37971e17 + 6.99917e17i −0.0677414 + 0.199240i
\(153\) 5.76668e18 1.55256
\(154\) 3.74666e18 + 2.74810e18i 0.954373 + 0.700014i
\(155\) 7.96734e18i 1.92085i
\(156\) −2.04333e17 6.48800e17i −0.0466423 0.148099i
\(157\) 3.50626e18i 0.758048i −0.925387 0.379024i \(-0.876260\pi\)
0.925387 0.379024i \(-0.123740\pi\)
\(158\) −3.82332e18 + 5.21257e18i −0.783169 + 1.06774i
\(159\) 4.06244e17 0.0788698
\(160\) −7.53981e18 1.70665e17i −1.38784 0.0314142i
\(161\) 7.22653e18 1.26157
\(162\) 3.34971e18 4.56686e18i 0.554791 0.756381i
\(163\) 2.12490e18i 0.333998i −0.985957 0.166999i \(-0.946592\pi\)
0.985957 0.166999i \(-0.0534076\pi\)
\(164\) 1.10966e17 + 3.52340e17i 0.0165584 + 0.0525762i
\(165\) 1.44439e18i 0.204679i
\(166\) 4.32105e17 + 3.16941e17i 0.0581662 + 0.0426638i
\(167\) 3.81083e18 0.487450 0.243725 0.969844i \(-0.421631\pi\)
0.243725 + 0.969844i \(0.421631\pi\)
\(168\) 4.42073e17 1.30022e18i 0.0537484 0.158084i
\(169\) −1.37601e18 −0.159069
\(170\) 1.61424e19 + 1.18401e19i 1.77481 + 1.30179i
\(171\) 1.97001e18i 0.206064i
\(172\) −1.70055e18 + 5.35573e17i −0.169277 + 0.0533122i
\(173\) 8.51874e18i 0.807204i 0.914935 + 0.403602i \(0.132242\pi\)
−0.914935 + 0.403602i \(0.867758\pi\)
\(174\) −1.09260e18 + 1.48961e18i −0.0985811 + 0.134402i
\(175\) −1.24898e19 −1.07333
\(176\) −7.15537e18 1.02331e19i −0.585834 0.837819i
\(177\) 3.33191e18 0.259969
\(178\) −8.10890e18 + 1.10554e19i −0.603103 + 0.822248i
\(179\) 1.98628e19i 1.40860i −0.709900 0.704302i \(-0.751260\pi\)
0.709900 0.704302i \(-0.248740\pi\)
\(180\) 1.91692e19 6.03715e18i 1.29654 0.408334i
\(181\) 2.34430e19i 1.51267i 0.654182 + 0.756337i \(0.273013\pi\)
−0.654182 + 0.756337i \(0.726987\pi\)
\(182\) −1.63227e19 1.19724e19i −1.00504 0.737181i
\(183\) −1.46275e18 −0.0859677
\(184\) −1.83865e19 6.25140e18i −1.03169 0.350773i
\(185\) −1.65994e19 −0.889473
\(186\) −3.14382e18 2.30593e18i −0.160915 0.118028i
\(187\) 3.31451e19i 1.62093i
\(188\) −2.69366e16 8.55291e16i −0.00125893 0.00399735i
\(189\) 7.39701e18i 0.330469i
\(190\) 4.04482e18 5.51455e18i 0.172780 0.235562i
\(191\) −1.50710e19 −0.615686 −0.307843 0.951437i \(-0.599607\pi\)
−0.307843 + 0.951437i \(0.599607\pi\)
\(192\) −2.24954e18 + 2.92573e18i −0.0879089 + 0.114334i
\(193\) 9.30819e18 0.348039 0.174020 0.984742i \(-0.444324\pi\)
0.174020 + 0.984742i \(0.444324\pi\)
\(194\) 2.74289e19 3.73955e19i 0.981508 1.33815i
\(195\) 6.29265e18i 0.215546i
\(196\) −3.11736e18 9.89824e18i −0.102237 0.324625i
\(197\) 4.15016e19i 1.30347i −0.758445 0.651737i \(-0.774041\pi\)
0.758445 0.651737i \(-0.225959\pi\)
\(198\) 2.68309e19 + 1.96800e19i 0.807201 + 0.592066i
\(199\) 1.63945e19 0.472550 0.236275 0.971686i \(-0.424073\pi\)
0.236275 + 0.971686i \(0.424073\pi\)
\(200\) 3.17779e19 + 1.08045e19i 0.877750 + 0.298435i
\(201\) 8.30440e18 0.219858
\(202\) −1.99136e19 1.46063e19i −0.505433 0.370726i
\(203\) 5.49760e19i 1.33800i
\(204\) 9.34396e18 2.94279e18i 0.218110 0.0686915i
\(205\) 3.41731e18i 0.0765203i
\(206\) −6.61034e18 + 9.01228e18i −0.142021 + 0.193626i
\(207\) 5.17513e19 1.06702
\(208\) 3.11731e19 + 4.45816e19i 0.616938 + 0.882302i
\(209\) 1.13230e19 0.215138
\(210\) −7.51395e18 + 1.02442e19i −0.137090 + 0.186903i
\(211\) 7.37209e19i 1.29178i −0.763429 0.645892i \(-0.776486\pi\)
0.763429 0.645892i \(-0.223514\pi\)
\(212\) −3.09882e19 + 9.75945e18i −0.521605 + 0.164275i
\(213\) 1.12286e19i 0.181593i
\(214\) −7.93642e19 5.82121e19i −1.23341 0.904683i
\(215\) 1.64935e19 0.246369
\(216\) 6.39888e18 1.88203e19i 0.0918855 0.270252i
\(217\) −1.16027e20 −1.60195
\(218\) −3.87704e19 2.84374e19i −0.514778 0.377580i
\(219\) 2.24946e18i 0.0287278i
\(220\) 3.46996e19 + 1.10178e20i 0.426316 + 1.35364i
\(221\) 1.44400e20i 1.70699i
\(222\) −4.80425e18 + 6.54994e18i −0.0546545 + 0.0745138i
\(223\) 3.21618e19 0.352167 0.176083 0.984375i \(-0.443657\pi\)
0.176083 + 0.984375i \(0.443657\pi\)
\(224\) −2.48537e18 + 1.09801e20i −0.0261988 + 1.15744i
\(225\) −8.94433e19 −0.907813
\(226\) −8.11430e19 + 1.10627e20i −0.793103 + 1.08129i
\(227\) 9.66411e19i 0.909792i 0.890545 + 0.454896i \(0.150323\pi\)
−0.890545 + 0.454896i \(0.849677\pi\)
\(228\) −1.00531e18 3.19208e18i −0.00911708 0.0289486i
\(229\) 3.07436e16i 0.000268629i 1.00000 0.000134314i \(4.27536e-5\pi\)
−1.00000 0.000134314i \(0.999957\pi\)
\(230\) 1.44865e20 + 1.06256e20i 1.21976 + 0.894674i
\(231\) −2.10344e19 −0.170698
\(232\) 4.75577e19 1.39876e20i 0.372026 1.09420i
\(233\) 2.21535e20 1.67077 0.835385 0.549666i \(-0.185245\pi\)
0.835385 + 0.549666i \(0.185245\pi\)
\(234\) −1.16892e20 8.57378e19i −0.850058 0.623501i
\(235\) 8.29539e17i 0.00581781i
\(236\) −2.54158e20 + 8.00447e19i −1.71930 + 0.541478i
\(237\) 2.92643e19i 0.190975i
\(238\) 1.72425e20 2.35078e20i 1.08567 1.48016i
\(239\) −4.51465e18 −0.0274310 −0.0137155 0.999906i \(-0.504366\pi\)
−0.0137155 + 0.999906i \(0.504366\pi\)
\(240\) 2.79797e19 1.95644e19i 0.164077 0.114729i
\(241\) −1.81683e19 −0.102842 −0.0514209 0.998677i \(-0.516375\pi\)
−0.0514209 + 0.998677i \(0.516375\pi\)
\(242\) −4.88558e18 + 6.66082e18i −0.0266984 + 0.0363996i
\(243\) 7.97365e19i 0.420731i
\(244\) 1.11578e20 3.51405e19i 0.568547 0.179059i
\(245\) 9.60021e19i 0.472464i
\(246\) −1.34843e18 9.89049e17i −0.00641033 0.00470186i
\(247\) −4.93298e19 −0.226561
\(248\) 2.95207e20 + 1.00370e20i 1.31005 + 0.445416i
\(249\) −2.42592e18 −0.0104035
\(250\) 1.96885e19 + 1.44412e19i 0.0816062 + 0.0598566i
\(251\) 3.26192e20i 1.30691i −0.756964 0.653456i \(-0.773318\pi\)
0.756964 0.653456i \(-0.226682\pi\)
\(252\) −8.79178e19 2.79157e20i −0.340543 1.08129i
\(253\) 2.97450e20i 1.11401i
\(254\) −5.48995e19 + 7.48479e19i −0.198830 + 0.271077i
\(255\) −9.06262e19 −0.317441
\(256\) 1.01308e20 2.77216e20i 0.343245 0.939246i
\(257\) −1.22717e20 −0.402228 −0.201114 0.979568i \(-0.564456\pi\)
−0.201114 + 0.979568i \(0.564456\pi\)
\(258\) 4.77360e18 6.50815e18i 0.0151384 0.0206391i
\(259\) 2.41734e20i 0.741804i
\(260\) −1.51172e20 4.80003e20i −0.448951 1.42551i
\(261\) 3.93699e20i 1.13167i
\(262\) 4.72523e20 + 3.46587e20i 1.31481 + 0.964386i
\(263\) 3.35733e18 0.00904420 0.00452210 0.999990i \(-0.498561\pi\)
0.00452210 + 0.999990i \(0.498561\pi\)
\(264\) 5.35180e19 + 1.81961e19i 0.139594 + 0.0474619i
\(265\) 3.00552e20 0.759153
\(266\) −8.03073e19 5.89038e19i −0.196454 0.144095i
\(267\) 6.20668e19i 0.147066i
\(268\) −6.33459e20 + 1.99502e20i −1.45403 + 0.457933i
\(269\) 2.42496e20i 0.539275i 0.962962 + 0.269637i \(0.0869038\pi\)
−0.962962 + 0.269637i \(0.913096\pi\)
\(270\) −1.08762e20 + 1.48282e20i −0.234361 + 0.319519i
\(271\) −2.38962e20 −0.498988 −0.249494 0.968376i \(-0.580264\pi\)
−0.249494 + 0.968376i \(0.580264\pi\)
\(272\) −6.42060e20 + 4.48952e20i −1.29939 + 0.908582i
\(273\) 9.16386e19 0.179761
\(274\) −7.11951e19 + 9.70647e19i −0.135385 + 0.184579i
\(275\) 5.14091e20i 0.947791i
\(276\) 8.38545e19 2.64092e19i 0.149899 0.0472093i
\(277\) 5.05700e20i 0.876628i −0.898822 0.438314i \(-0.855576\pi\)
0.898822 0.438314i \(-0.144424\pi\)
\(278\) 1.86249e20 + 1.36610e20i 0.313122 + 0.229669i
\(279\) −8.30901e20 −1.35492
\(280\) 3.27060e20 9.61942e20i 0.517349 1.52162i
\(281\) −2.23986e20 −0.343730 −0.171865 0.985120i \(-0.554979\pi\)
−0.171865 + 0.985120i \(0.554979\pi\)
\(282\) 3.27327e17 + 2.40088e17i 0.000487376 + 0.000357481i
\(283\) 5.21843e20i 0.753971i −0.926219 0.376986i \(-0.876961\pi\)
0.926219 0.376986i \(-0.123039\pi\)
\(284\) 2.69752e20 + 8.56518e20i 0.378233 + 1.20097i
\(285\) 3.09597e19i 0.0421323i
\(286\) 4.92793e20 6.71856e20i 0.650959 0.887493i
\(287\) −4.97656e19 −0.0638165
\(288\) −1.77984e19 + 7.86314e20i −0.0221588 + 0.978949i
\(289\) 1.25239e21 1.51394
\(290\) −8.08342e20 + 1.10206e21i −0.948882 + 1.29367i
\(291\) 2.09945e20i 0.239340i
\(292\) −5.40401e19 1.71588e20i −0.0598359 0.189991i
\(293\) 4.94662e20i 0.532027i −0.963969 0.266014i \(-0.914293\pi\)
0.963969 0.266014i \(-0.0857066\pi\)
\(294\) 3.78813e19 + 2.77852e19i 0.0395797 + 0.0290310i
\(295\) 2.46506e21 2.50230
\(296\) 2.09115e20 6.15044e20i 0.206255 0.606634i
\(297\) −3.04467e20 −0.291817
\(298\) 8.09058e20 + 5.93429e20i 0.753601 + 0.552752i
\(299\) 1.29587e21i 1.17316i
\(300\) −1.44928e20 + 4.56437e19i −0.127533 + 0.0401653i
\(301\) 2.40191e20i 0.205467i
\(302\) −9.49212e20 + 1.29412e21i −0.789413 + 1.07626i
\(303\) 1.11799e20 0.0904012
\(304\) 1.53371e20 + 2.19340e20i 0.120592 + 0.172462i
\(305\) −1.08219e21 −0.827473
\(306\) 1.23479e21 1.68346e21i 0.918249 1.25191i
\(307\) 1.86234e21i 1.34705i 0.739166 + 0.673523i \(0.235220\pi\)
−0.739166 + 0.673523i \(0.764780\pi\)
\(308\) 1.60450e21 5.05323e20i 1.12891 0.355540i
\(309\) 5.05965e19i 0.0346317i
\(310\) −2.32590e21 1.70600e21i −1.54888 1.13607i
\(311\) −6.47522e20 −0.419557 −0.209779 0.977749i \(-0.567274\pi\)
−0.209779 + 0.977749i \(0.567274\pi\)
\(312\) −2.33157e20 7.92731e19i −0.147005 0.0499818i
\(313\) −1.62295e21 −0.995817 −0.497909 0.867230i \(-0.665898\pi\)
−0.497909 + 0.867230i \(0.665898\pi\)
\(314\) −1.02358e21 7.50775e20i −0.611251 0.448341i
\(315\) 2.70751e21i 1.57373i
\(316\) 7.03035e20 + 2.23228e21i 0.397774 + 1.26301i
\(317\) 2.11436e21i 1.16460i −0.812976 0.582298i \(-0.802154\pi\)
0.812976 0.582298i \(-0.197846\pi\)
\(318\) 8.69867e19 1.18594e20i 0.0466469 0.0635966i
\(319\) −2.26286e21 −1.18151
\(320\) −1.66428e21 + 2.16455e21i −0.846158 + 1.10051i
\(321\) 4.45565e20 0.220606
\(322\) 1.54738e21 2.10964e21i 0.746142 1.01726i
\(323\) 7.10443e20i 0.333663i
\(324\) −6.15947e20 1.95576e21i −0.281780 0.894709i
\(325\) 2.23969e21i 0.998113i
\(326\) −6.20320e20 4.54993e20i −0.269318 0.197540i
\(327\) 2.17664e20 0.0920726
\(328\) 1.26619e20 + 4.30504e19i 0.0521880 + 0.0177439i
\(329\) 1.20804e19 0.00485195
\(330\) −4.21661e20 3.09280e20i −0.165042 0.121055i
\(331\) 4.36509e21i 1.66516i 0.553908 + 0.832578i \(0.313136\pi\)
−0.553908 + 0.832578i \(0.686864\pi\)
\(332\) 1.85049e20 5.82793e19i 0.0688038 0.0216691i
\(333\) 1.73112e21i 0.627411i
\(334\) 8.15993e20 1.11249e21i 0.288298 0.393054i
\(335\) 6.14386e21 2.11622
\(336\) −2.84913e20 4.07462e20i −0.0956815 0.136837i
\(337\) −2.59518e21 −0.849792 −0.424896 0.905242i \(-0.639689\pi\)
−0.424896 + 0.905242i \(0.639689\pi\)
\(338\) −2.94638e20 + 4.01698e20i −0.0940799 + 0.128265i
\(339\) 6.21082e20i 0.193398i
\(340\) 6.91296e21 2.17717e21i 2.09939 0.661183i
\(341\) 4.77575e21i 1.41459i
\(342\) −5.75104e20 4.21828e20i −0.166159 0.121875i
\(343\) −2.70973e21 −0.763706
\(344\) −2.07781e20 + 6.11120e20i −0.0571292 + 0.168027i
\(345\) −8.13296e20 −0.218166
\(346\) 2.48687e21 + 1.82407e21i 0.650888 + 0.477414i
\(347\) 7.40818e20i 0.189195i −0.995516 0.0945977i \(-0.969844\pi\)
0.995516 0.0945977i \(-0.0301565\pi\)
\(348\) 2.00909e20 + 6.37925e20i 0.0500697 + 0.158981i
\(349\) 1.81507e20i 0.0441446i 0.999756 + 0.0220723i \(0.00702640\pi\)
−0.999756 + 0.0220723i \(0.992974\pi\)
\(350\) −2.67438e21 + 3.64615e21i −0.634811 + 0.865477i
\(351\) 1.32644e21 0.307310
\(352\) −4.51948e21 1.02300e20i −1.02206 0.0231346i
\(353\) 3.26526e21 0.720830 0.360415 0.932792i \(-0.382635\pi\)
0.360415 + 0.932792i \(0.382635\pi\)
\(354\) 7.13444e20 9.72683e20i 0.153756 0.209625i
\(355\) 8.30728e21i 1.74791i
\(356\) 1.49107e21 + 4.73445e21i 0.306318 + 0.972623i
\(357\) 1.31977e21i 0.264739i
\(358\) −5.79852e21 4.25311e21i −1.13583 0.833107i
\(359\) 2.19419e21 0.419732 0.209866 0.977730i \(-0.432697\pi\)
0.209866 + 0.977730i \(0.432697\pi\)
\(360\) 2.34217e21 6.88875e21i 0.437570 1.28697i
\(361\) 5.23769e21 0.955715
\(362\) 6.84370e21 + 5.01972e21i 1.21974 + 0.894658i
\(363\) 3.73950e19i 0.00651040i
\(364\) −6.99018e21 + 2.20149e21i −1.18885 + 0.374417i
\(365\) 1.66422e21i 0.276516i
\(366\) −3.13210e20 + 4.27019e20i −0.0508448 + 0.0693199i
\(367\) −1.08265e22 −1.71723 −0.858615 0.512621i \(-0.828675\pi\)
−0.858615 + 0.512621i \(0.828675\pi\)
\(368\) −5.76197e21 + 4.02898e21i −0.893026 + 0.624437i
\(369\) −3.56386e20 −0.0539755
\(370\) −3.55434e21 + 4.84585e21i −0.526071 + 0.717225i
\(371\) 4.37687e21i 0.633120i
\(372\) −1.34634e21 + 4.24017e20i −0.190344 + 0.0599471i
\(373\) 5.20618e20i 0.0719439i −0.999353 0.0359719i \(-0.988547\pi\)
0.999353 0.0359719i \(-0.0114527\pi\)
\(374\) 9.67601e21 + 7.09717e21i 1.30704 + 0.958686i
\(375\) −1.10535e20 −0.0145960
\(376\) −3.07362e19 1.04503e19i −0.00396784 0.00134906i
\(377\) 9.85837e21 1.24424
\(378\) 2.15940e21 + 1.58388e21i 0.266473 + 0.195453i
\(379\) 2.99720e21i 0.361645i 0.983516 + 0.180823i \(0.0578760\pi\)
−0.983516 + 0.180823i \(0.942124\pi\)
\(380\) −7.43764e20 2.36160e21i −0.0877556 0.278642i
\(381\) 4.20209e20i 0.0484845i
\(382\) −3.22708e21 + 4.39968e21i −0.364142 + 0.496458i
\(383\) −1.22679e22 −1.35388 −0.676939 0.736039i \(-0.736694\pi\)
−0.676939 + 0.736039i \(0.736694\pi\)
\(384\) 3.72424e20 + 1.28318e21i 0.0401997 + 0.138507i
\(385\) −1.55619e22 −1.64304
\(386\) 1.99311e21 2.71733e21i 0.205845 0.280641i
\(387\) 1.72008e21i 0.173782i
\(388\) −5.04365e21 1.60146e22i −0.498511 1.58287i
\(389\) 1.60002e21i 0.154722i 0.997003 + 0.0773612i \(0.0246495\pi\)
−0.997003 + 0.0773612i \(0.975351\pi\)
\(390\) 1.83701e21 + 1.34741e21i 0.173805 + 0.127483i
\(391\) 1.86630e22 1.72774
\(392\) −3.55709e21 1.20941e21i −0.322228 0.109557i
\(393\) −2.65283e21 −0.235165
\(394\) −1.21155e22 8.88652e21i −1.05105 0.770928i
\(395\) 2.16506e22i 1.83821i
\(396\) 1.14903e22 3.61877e21i 0.954823 0.300713i
\(397\) 2.44521e22i 1.98883i 0.105546 + 0.994414i \(0.466341\pi\)
−0.105546 + 0.994414i \(0.533659\pi\)
\(398\) 3.51047e21 4.78604e21i 0.279485 0.381040i
\(399\) 4.50859e20 0.0351375
\(400\) 9.95858e21 6.96340e21i 0.759779 0.531266i
\(401\) 2.46119e22 1.83830 0.919152 0.393903i \(-0.128875\pi\)
0.919152 + 0.393903i \(0.128875\pi\)
\(402\) 1.77818e21 2.42430e21i 0.130033 0.177282i
\(403\) 2.08061e22i 1.48969i
\(404\) −8.52799e21 + 2.68581e21i −0.597868 + 0.188293i
\(405\) 1.89687e22i 1.30218i
\(406\) 1.60491e22 + 1.17717e22i 1.07890 + 0.791350i
\(407\) −9.94995e21 −0.655041
\(408\) 1.14168e21 3.35790e21i 0.0736097 0.216499i
\(409\) −5.67464e21 −0.358336 −0.179168 0.983819i \(-0.557341\pi\)
−0.179168 + 0.983819i \(0.557341\pi\)
\(410\) −9.97613e20 7.31730e20i −0.0617020 0.0452573i
\(411\) 5.44938e20i 0.0330135i
\(412\) 1.21551e21 + 3.85950e21i 0.0721329 + 0.229037i
\(413\) 3.58981e22i 2.08687i
\(414\) 1.10812e22 1.51077e22i 0.631080 0.860391i
\(415\) −1.79477e21 −0.100138
\(416\) 1.96896e22 + 4.45679e20i 1.07632 + 0.0243629i
\(417\) −1.04564e21 −0.0560047
\(418\) 2.42453e21 3.30551e21i 0.127242 0.173476i
\(419\) 2.70146e22i 1.38925i 0.719374 + 0.694623i \(0.244429\pi\)
−0.719374 + 0.694623i \(0.755571\pi\)
\(420\) 1.38167e21 + 4.38708e21i 0.0696283 + 0.221084i
\(421\) 1.26169e22i 0.623094i −0.950231 0.311547i \(-0.899153\pi\)
0.950231 0.311547i \(-0.100847\pi\)
\(422\) −2.15213e22 1.57855e22i −1.04163 0.764014i
\(423\) 8.65113e19 0.00410374
\(424\) −3.78627e21 + 1.11361e22i −0.176036 + 0.517754i
\(425\) −3.22558e22 −1.46995
\(426\) −3.27796e21 2.40432e21i −0.146427 0.107402i
\(427\) 1.57597e22i 0.690097i
\(428\) −3.39876e22 + 1.07041e22i −1.45898 + 0.459492i
\(429\) 3.77192e21i 0.158736i
\(430\) 3.53166e21 4.81493e21i 0.145713 0.198659i
\(431\) 4.26128e21 0.172378 0.0861892 0.996279i \(-0.472531\pi\)
0.0861892 + 0.996279i \(0.472531\pi\)
\(432\) −4.12403e21 5.89790e21i −0.163572 0.233930i
\(433\) −1.62172e21 −0.0630707 −0.0315353 0.999503i \(-0.510040\pi\)
−0.0315353 + 0.999503i \(0.510040\pi\)
\(434\) −2.48442e22 + 3.38716e22i −0.947462 + 1.29173i
\(435\) 6.18718e21i 0.231384i
\(436\) −1.66034e22 + 5.22908e21i −0.608922 + 0.191774i
\(437\) 6.37565e21i 0.229315i
\(438\) 6.56682e20 + 4.81664e20i 0.0231646 + 0.0169908i
\(439\) 1.56475e22 0.541375 0.270687 0.962667i \(-0.412749\pi\)
0.270687 + 0.962667i \(0.412749\pi\)
\(440\) 3.95943e22 + 1.34620e22i 1.34365 + 0.456839i
\(441\) 1.00119e22 0.333264
\(442\) −4.21545e22 3.09195e22i −1.37643 1.00959i
\(443\) 3.08815e22i 0.989161i −0.869132 0.494581i \(-0.835322\pi\)
0.869132 0.494581i \(-0.164678\pi\)
\(444\) 8.83409e20 + 2.80500e21i 0.0277592 + 0.0881410i
\(445\) 4.59190e22i 1.41557i
\(446\) 6.88662e21 9.38896e21i 0.208286 0.283969i
\(447\) −4.54220e21 −0.134788
\(448\) 3.15218e22 + 2.42366e22i 0.917801 + 0.705680i
\(449\) −1.44678e22 −0.413340 −0.206670 0.978411i \(-0.566263\pi\)
−0.206670 + 0.978411i \(0.566263\pi\)
\(450\) −1.91520e22 + 2.61111e22i −0.536918 + 0.732013i
\(451\) 2.04839e21i 0.0563524i
\(452\) 1.49206e22 + 4.73761e22i 0.402820 + 1.27903i
\(453\) 7.26542e21i 0.192498i
\(454\) 2.82124e22 + 2.06932e22i 0.733609 + 0.538088i
\(455\) 6.77971e22 1.73027
\(456\) −1.14712e21 3.90022e20i −0.0287349 0.00976984i
\(457\) −1.09366e22 −0.268903 −0.134452 0.990920i \(-0.542927\pi\)
−0.134452 + 0.990920i \(0.542927\pi\)
\(458\) 8.97495e18 + 6.58295e18i 0.000216608 + 0.000158878i
\(459\) 1.91033e22i 0.452585i
\(460\) 6.20382e22 1.95383e22i 1.44284 0.454408i
\(461\) 3.78938e22i 0.865187i 0.901589 + 0.432594i \(0.142402\pi\)
−0.901589 + 0.432594i \(0.857598\pi\)
\(462\) −4.50398e21 + 6.14056e21i −0.100958 + 0.137642i
\(463\) 5.34510e21 0.117630 0.0588149 0.998269i \(-0.481268\pi\)
0.0588149 + 0.998269i \(0.481268\pi\)
\(464\) −3.06506e22 4.38343e22i −0.662271 0.947135i
\(465\) 1.30580e22 0.277030
\(466\) 4.74360e22 6.46725e22i 0.988162 1.34722i
\(467\) 2.81699e21i 0.0576224i 0.999585 + 0.0288112i \(0.00917216\pi\)
−0.999585 + 0.0288112i \(0.990828\pi\)
\(468\) −5.00587e22 + 1.57655e22i −1.00552 + 0.316679i
\(469\) 8.94718e22i 1.76489i
\(470\) 2.42167e20 + 1.77625e20i 0.00469118 + 0.00344089i
\(471\) 5.74655e21 0.109328
\(472\) −3.10541e22 + 9.13357e22i −0.580246 + 1.70661i
\(473\) 9.88647e21 0.181435
\(474\) −8.54310e21 6.26620e21i −0.153992 0.112951i
\(475\) 1.10192e22i 0.195099i
\(476\) −3.17057e22 1.00672e23i −0.551415 1.75085i
\(477\) 3.13441e22i 0.535487i
\(478\) −9.66697e20 + 1.31796e21i −0.0162238 + 0.0221190i
\(479\) −9.05318e22 −1.49262 −0.746310 0.665598i \(-0.768177\pi\)
−0.746310 + 0.665598i \(0.768177\pi\)
\(480\) 2.79711e20 1.23573e22i 0.00453063 0.200158i
\(481\) 4.33480e22 0.689820
\(482\) −3.89028e21 + 5.30386e21i −0.0608249 + 0.0829263i
\(483\) 1.18439e22i 0.181946i
\(484\) 8.98364e20 + 2.85249e21i 0.0135602 + 0.0430565i
\(485\) 1.55324e23i 2.30374i
\(486\) 2.32774e22 + 1.70735e22i 0.339255 + 0.248837i
\(487\) −3.07462e22 −0.440347 −0.220173 0.975461i \(-0.570662\pi\)
−0.220173 + 0.975461i \(0.570662\pi\)
\(488\) 1.36331e22 4.00974e22i 0.191879 0.564350i
\(489\) 3.48259e21 0.0481700
\(490\) 2.80258e22 + 2.05564e22i 0.380971 + 0.279435i
\(491\) 1.94168e22i 0.259409i 0.991553 + 0.129704i \(0.0414028\pi\)
−0.991553 + 0.129704i \(0.958597\pi\)
\(492\) −5.77465e20 + 1.81867e20i −0.00758267 + 0.00238809i
\(493\) 1.41979e23i 1.83243i
\(494\) −1.05627e22 + 1.44008e22i −0.133997 + 0.182687i
\(495\) −1.11444e23 −1.38967
\(496\) 9.25122e22 6.46879e22i 1.13398 0.792919i
\(497\) −1.20977e23 −1.45772
\(498\) −5.19448e20 + 7.08196e20i −0.00615308 + 0.00838888i
\(499\) 7.79434e22i 0.907664i −0.891087 0.453832i \(-0.850057\pi\)
0.891087 0.453832i \(-0.149943\pi\)
\(500\) 8.43159e21 2.65545e21i 0.0965305 0.0304014i
\(501\) 6.24573e21i 0.0703012i
\(502\) −9.52249e22 6.98457e22i −1.05383 0.772962i
\(503\) 1.18157e23 1.28568 0.642838 0.766002i \(-0.277757\pi\)
0.642838 + 0.766002i \(0.277757\pi\)
\(504\) −1.00319e23 3.41085e22i −1.07331 0.364925i
\(505\) 8.27122e22 0.870148
\(506\) 8.68343e22 + 6.36913e22i 0.898280 + 0.658871i
\(507\) 2.25521e21i 0.0229413i
\(508\) 1.00950e22 + 3.20535e22i 0.100986 + 0.320652i
\(509\) 2.87932e21i 0.0283262i −0.999900 0.0141631i \(-0.995492\pi\)
0.999900 0.0141631i \(-0.00450841\pi\)
\(510\) −1.94053e22 + 2.64564e22i −0.187747 + 0.255968i
\(511\) 2.42357e22 0.230610
\(512\) −5.92351e22 8.89336e22i −0.554350 0.832284i
\(513\) 6.52605e21 0.0600694
\(514\) −2.62767e22 + 3.58246e22i −0.237894 + 0.324336i
\(515\) 3.74329e22i 0.333344i
\(516\) −8.77773e20 2.78711e21i −0.00768882 0.0244136i
\(517\) 4.97239e20i 0.00428446i
\(518\) 7.05691e22 + 5.17611e22i 0.598152 + 0.438733i
\(519\) −1.39617e22 −0.116417
\(520\) −1.72497e23 5.86488e22i −1.41499 0.481095i
\(521\) 1.28391e23 1.03613 0.518066 0.855340i \(-0.326652\pi\)
0.518066 + 0.855340i \(0.326652\pi\)
\(522\) 1.14932e23 + 8.43007e22i 0.912521 + 0.669317i
\(523\) 1.89027e22i 0.147659i 0.997271 + 0.0738293i \(0.0235220\pi\)
−0.997271 + 0.0738293i \(0.976478\pi\)
\(524\) 2.02358e23 6.37306e22i 1.55526 0.489815i
\(525\) 2.04701e22i 0.154798i
\(526\) 7.18887e20 9.80103e20i 0.00534911 0.00729277i
\(527\) −2.99647e23 −2.19391
\(528\) 1.67715e22 1.17272e22i 0.120832 0.0844904i
\(529\) 2.64353e22 0.187418
\(530\) 6.43555e22 8.77399e22i 0.448995 0.612142i
\(531\) 2.57077e23i 1.76506i
\(532\) −3.43915e22 + 1.08313e22i −0.232382 + 0.0731865i
\(533\) 8.92403e21i 0.0593444i
\(534\) −1.81191e22 1.32900e22i −0.118587 0.0869811i
\(535\) 3.29643e23 2.12342
\(536\) −7.73987e22 + 2.27644e23i −0.490719 + 1.44329i
\(537\) 3.25539e22 0.203152
\(538\) 7.07916e22 + 5.19243e22i 0.434843 + 0.318949i
\(539\) 5.75452e22i 0.347940i
\(540\) 1.99993e22 + 6.35017e22i 0.119033 + 0.377954i
\(541\) 3.25660e23i 1.90804i −0.299744 0.954020i \(-0.596901\pi\)
0.299744 0.954020i \(-0.403099\pi\)
\(542\) −5.11676e22 + 6.97600e22i −0.295122 + 0.402358i
\(543\) −3.84218e22 −0.218162
\(544\) −6.41863e21 + 2.83568e23i −0.0358799 + 1.58514i
\(545\) 1.61035e23 0.886236
\(546\) 1.96221e22 2.67520e22i 0.106318 0.144950i
\(547\) 4.90295e22i 0.261556i 0.991412 + 0.130778i \(0.0417476\pi\)
−0.991412 + 0.130778i \(0.958252\pi\)
\(548\) 1.30914e22 + 4.15679e22i 0.0687625 + 0.218335i
\(549\) 1.12860e23i 0.583679i
\(550\) −1.50078e23 1.10080e23i −0.764249 0.560562i
\(551\) 4.85029e22 0.243209
\(552\) 1.02457e22 3.01344e22i 0.0505893 0.148792i
\(553\) −3.15294e23 −1.53303
\(554\) −1.47629e23 1.08283e23i −0.706867 0.518473i
\(555\) 2.72055e22i 0.128282i
\(556\) 7.97611e22 2.51200e22i 0.370387 0.116650i
\(557\) 2.60011e23i 1.18911i 0.804054 + 0.594556i \(0.202672\pi\)
−0.804054 + 0.594556i \(0.797328\pi\)
\(558\) −1.77916e23 + 2.42564e23i −0.801355 + 1.09254i
\(559\) −4.30714e22 −0.191068
\(560\) −2.10787e23 3.01454e23i −0.920972 1.31711i
\(561\) −5.43228e22 −0.233775
\(562\) −4.79610e22 + 6.53882e22i −0.203296 + 0.277166i
\(563\) 1.80701e23i 0.754467i 0.926118 + 0.377233i \(0.123125\pi\)
−0.926118 + 0.377233i \(0.876875\pi\)
\(564\) 1.40177e20 4.41475e19i 0.000576508 0.000181566i
\(565\) 4.59496e23i 1.86153i
\(566\) −1.52341e23 1.11739e23i −0.607963 0.445930i
\(567\) 2.76237e23 1.08599
\(568\) 3.07803e23 + 1.04653e23i 1.19210 + 0.405313i
\(569\) −3.54026e23 −1.35077 −0.675384 0.737467i \(-0.736022\pi\)
−0.675384 + 0.737467i \(0.736022\pi\)
\(570\) 9.03803e21 + 6.62923e21i 0.0339733 + 0.0249188i
\(571\) 1.77850e23i 0.658637i 0.944219 + 0.329318i \(0.106819\pi\)
−0.944219 + 0.329318i \(0.893181\pi\)
\(572\) −9.06152e22 2.87722e23i −0.330624 1.04980i
\(573\) 2.47006e22i 0.0887958i
\(574\) −1.06560e22 + 1.45280e22i −0.0377437 + 0.0514583i
\(575\) −2.89470e23 −1.01024
\(576\) 2.25737e23 + 1.73565e23i 0.776268 + 0.596858i
\(577\) −3.55869e23 −1.20586 −0.602928 0.797796i \(-0.705999\pi\)
−0.602928 + 0.797796i \(0.705999\pi\)
\(578\) 2.68168e23 3.65610e23i 0.895407 1.22076i
\(579\) 1.52556e22i 0.0501951i
\(580\) 1.48639e23 + 4.71958e23i 0.481941 + 1.53026i
\(581\) 2.61369e22i 0.0835134i
\(582\) 6.12891e22 + 4.49544e22i 0.192991 + 0.141556i
\(583\) 1.80156e23 0.559069
\(584\) −6.16629e22 2.09654e22i −0.188588 0.0641200i
\(585\) 4.85515e23 1.46345
\(586\) −1.44406e23 1.05919e23i −0.428999 0.314663i
\(587\) 2.22604e23i 0.651791i 0.945406 + 0.325896i \(0.105666\pi\)
−0.945406 + 0.325896i \(0.894334\pi\)
\(588\) 1.62226e22 5.10917e21i 0.0468182 0.0147449i
\(589\) 1.02365e23i 0.291187i
\(590\) 5.27829e23 7.19622e23i 1.47996 2.01773i
\(591\) 6.80188e22 0.187990
\(592\) −1.34773e23 1.92743e23i −0.367170 0.525102i
\(593\) 6.01922e23 1.61650 0.808250 0.588840i \(-0.200415\pi\)
0.808250 + 0.588840i \(0.200415\pi\)
\(594\) −6.51938e22 + 8.88828e22i −0.172592 + 0.235306i
\(595\) 9.76408e23i 2.54822i
\(596\) 3.46478e23 1.09120e23i 0.891421 0.280745i
\(597\) 2.68697e22i 0.0681523i
\(598\) −3.78302e23 2.77478e23i −0.945974 0.693854i
\(599\) 2.83674e23 0.699346 0.349673 0.936872i \(-0.386293\pi\)
0.349673 + 0.936872i \(0.386293\pi\)
\(600\) −1.77079e22 + 5.20822e22i −0.0430410 + 0.126591i
\(601\) −4.18303e23 −1.00244 −0.501220 0.865320i \(-0.667115\pi\)
−0.501220 + 0.865320i \(0.667115\pi\)
\(602\) −7.01189e22 5.14309e22i −0.165678 0.121522i
\(603\) 6.40734e23i 1.49273i
\(604\) 1.74542e23 + 5.54205e23i 0.400946 + 1.27308i
\(605\) 2.76660e22i 0.0626651i
\(606\) 2.39388e22 3.26373e22i 0.0534670 0.0728949i
\(607\) −2.31638e23 −0.510159 −0.255080 0.966920i \(-0.582102\pi\)
−0.255080 + 0.966920i \(0.582102\pi\)
\(608\) 9.68723e22 + 2.19273e21i 0.210387 + 0.00476216i
\(609\) −9.01026e22 −0.192970
\(610\) −2.31723e23 + 3.15922e23i −0.489402 + 0.667232i
\(611\) 2.16627e21i 0.00451193i
\(612\) −2.27054e23 7.20942e23i −0.466382 1.48086i
\(613\) 2.79613e23i 0.566425i −0.959057 0.283213i \(-0.908600\pi\)
0.959057 0.283213i \(-0.0914002\pi\)
\(614\) 5.43671e23 + 3.98772e23i 1.08619 + 0.796699i
\(615\) 5.60078e21 0.0110360
\(616\) 1.96045e23 5.76604e23i 0.380995 1.12058i
\(617\) −1.73444e23 −0.332457 −0.166229 0.986087i \(-0.553159\pi\)
−0.166229 + 0.986087i \(0.553159\pi\)
\(618\) −1.47706e22 1.08340e22i −0.0279252 0.0204826i
\(619\) 6.77105e23i 1.26266i −0.775515 0.631329i \(-0.782510\pi\)
0.775515 0.631329i \(-0.217490\pi\)
\(620\) −9.96064e23 + 3.13701e23i −1.83214 + 0.577014i
\(621\) 1.71436e23i 0.311046i
\(622\) −1.38650e23 + 1.89031e23i −0.248143 + 0.338309i
\(623\) −6.68708e23 −1.18056
\(624\) −7.30667e22 + 5.10909e22i −0.127248 + 0.0889763i
\(625\) −6.21418e23 −1.06759
\(626\) −3.47514e23 + 4.73788e23i −0.588967 + 0.802975i
\(627\) 1.85577e22i 0.0310278i
\(628\) −4.38347e23 + 1.38053e23i −0.723037 + 0.227714i
\(629\) 6.24294e23i 1.01592i
\(630\) 7.90403e23 + 5.79745e23i 1.26898 + 0.930770i
\(631\) 1.02867e24 1.62940 0.814698 0.579885i \(-0.196903\pi\)
0.814698 + 0.579885i \(0.196903\pi\)
\(632\) 8.02204e23 + 2.72749e23i 1.25369 + 0.426253i
\(633\) 1.20824e23 0.186304
\(634\) −6.17243e23 4.52736e23i −0.939070 0.688790i
\(635\) 3.10884e23i 0.466683i
\(636\) −1.59952e22 5.07879e22i −0.0236921 0.0752272i
\(637\) 2.50702e23i 0.366414i
\(638\) −4.84534e23 + 6.60595e23i −0.698792 + 0.952707i
\(639\) −8.66353e23 −1.23293
\(640\) 2.75531e23 + 9.49335e23i 0.386938 + 1.33318i
\(641\) 7.31083e23 1.01315 0.506575 0.862196i \(-0.330911\pi\)
0.506575 + 0.862196i \(0.330911\pi\)
\(642\) 9.54063e22 1.30073e23i 0.130476 0.177886i
\(643\) 5.31860e23i 0.717801i −0.933376 0.358901i \(-0.883152\pi\)
0.933376 0.358901i \(-0.116848\pi\)
\(644\) −2.84533e23 9.03449e23i −0.378968 1.20330i
\(645\) 2.70319e22i 0.0355319i
\(646\) −2.07399e23 1.52123e23i −0.269048 0.197342i
\(647\) 7.87216e23 1.00788 0.503939 0.863740i \(-0.331884\pi\)
0.503939 + 0.863740i \(0.331884\pi\)
\(648\) −7.02831e23 2.38962e23i −0.888103 0.301955i
\(649\) 1.47759e24 1.84279
\(650\) 6.53831e23 + 4.79573e23i 0.804826 + 0.590325i
\(651\) 1.90161e23i 0.231038i
\(652\) −2.65651e23 + 8.36644e22i −0.318572 + 0.100331i
\(653\) 2.77252e22i 0.0328180i −0.999865 0.0164090i \(-0.994777\pi\)
0.999865 0.0164090i \(-0.00522338\pi\)
\(654\) 4.66072e22 6.35425e22i 0.0544555 0.0742426i
\(655\) −1.96265e24 −2.26356
\(656\) 3.96799e22 2.77456e22i 0.0451739 0.0315872i
\(657\) 1.73559e23 0.195048
\(658\) 2.58671e21 3.52662e21i 0.00286964 0.00391236i
\(659\) 1.48992e24i 1.63169i −0.578273 0.815843i \(-0.696273\pi\)
0.578273 0.815843i \(-0.303727\pi\)
\(660\) −1.80576e23 + 5.68707e22i −0.195225 + 0.0614844i
\(661\) 2.01553e22i 0.0215118i 0.999942 + 0.0107559i \(0.00342377\pi\)
−0.999942 + 0.0107559i \(0.996576\pi\)
\(662\) 1.27430e24 + 9.34672e23i 1.34270 + 0.984842i
\(663\) 2.36663e23 0.246187
\(664\) 2.26100e22 6.65002e22i 0.0232205 0.0682958i
\(665\) 3.33560e23 0.338213
\(666\) 5.05366e23 + 3.70676e23i 0.505912 + 0.371077i
\(667\) 1.27415e24i 1.25936i
\(668\) −1.50045e23 4.76424e23i −0.146427 0.464937i
\(669\) 5.27113e22i 0.0507904i
\(670\) 1.31555e24 1.79357e24i 1.25162 1.70641i
\(671\) −6.48681e23 −0.609382
\(672\) −1.79957e23 4.07337e21i −0.166928 0.00377846i
\(673\) −7.70622e23 −0.705851 −0.352926 0.935651i \(-0.614813\pi\)
−0.352926 + 0.935651i \(0.614813\pi\)
\(674\) −5.55691e23 + 7.57608e23i −0.502602 + 0.685228i
\(675\) 2.96299e23i 0.264635i
\(676\) 5.41782e22 + 1.72027e23i 0.0477835 + 0.151722i
\(677\) 8.03721e23i 0.700006i 0.936749 + 0.350003i \(0.113819\pi\)
−0.936749 + 0.350003i \(0.886181\pi\)
\(678\) −1.81312e23 1.32989e23i −0.155946 0.114383i
\(679\) 2.26195e24 1.92128
\(680\) 8.44655e23 2.48428e24i 0.708522 2.08389i
\(681\) −1.58389e23 −0.131212
\(682\) −1.39418e24 1.02261e24i −1.14065 0.836645i
\(683\) 3.12264e23i 0.252317i 0.992010 + 0.126158i \(0.0402647\pi\)
−0.992010 + 0.126158i \(0.959735\pi\)
\(684\) −2.46288e23 + 7.75659e22i −0.196547 + 0.0619005i
\(685\) 4.03163e23i 0.317768i
\(686\) −5.80220e23 + 7.91049e23i −0.451687 + 0.615813i
\(687\) −5.03869e19 −3.87423e−5
\(688\) 1.33913e23 + 1.91513e23i 0.101700 + 0.145444i
\(689\) −7.84867e23 −0.588752
\(690\) −1.74147e23 + 2.37425e23i −0.129032 + 0.175918i
\(691\) 1.46577e24i 1.07276i 0.843977 + 0.536379i \(0.180208\pi\)
−0.843977 + 0.536379i \(0.819792\pi\)
\(692\) 1.06500e24 3.35411e23i 0.769923 0.242480i
\(693\) 1.62293e24i 1.15896i
\(694\) −2.16266e23 1.58627e23i −0.152557 0.111898i
\(695\) −7.73595e23 −0.539067
\(696\) 2.29249e23 + 7.79444e22i 0.157808 + 0.0536545i
\(697\) −1.28523e23 −0.0873982
\(698\) 5.29872e22 + 3.88651e22i 0.0355959 + 0.0261089i
\(699\) 3.63083e23i 0.240963i
\(700\) 4.91767e23 + 1.56146e24i 0.322423 + 1.02376i
\(701\) 2.04249e24i 1.32299i 0.749950 + 0.661495i \(0.230078\pi\)
−0.749950 + 0.661495i \(0.769922\pi\)
\(702\) 2.84024e23 3.87227e23i 0.181756 0.247799i
\(703\) 2.13271e23 0.134838
\(704\) −9.97597e23 + 1.29746e24i −0.623143 + 0.810453i
\(705\) −1.35957e21 −0.000839060
\(706\) 6.99172e23 9.53225e23i 0.426328 0.581240i
\(707\) 1.20452e24i 0.725687i
\(708\) −1.31189e23 4.16551e23i −0.0780933 0.247962i
\(709\) 2.96920e24i 1.74641i −0.487352 0.873206i \(-0.662037\pi\)
0.487352 0.873206i \(-0.337963\pi\)
\(710\) −2.42514e24 1.77879e24i −1.40942 1.03378i
\(711\) −2.25791e24 −1.29663
\(712\) 1.70140e24 + 5.78475e23i 0.965442 + 0.328250i
\(713\) −2.68909e24 −1.50780
\(714\) 3.85280e23 + 2.82595e23i 0.213472 + 0.156578i
\(715\) 2.79058e24i 1.52790i
\(716\) −2.48321e24 + 7.82064e23i −1.34355 + 0.423138i
\(717\) 7.39925e21i 0.00395617i
\(718\) 4.69831e23 6.40549e23i 0.248247 0.338450i
\(719\) 4.13376e23 0.215849 0.107924 0.994159i \(-0.465580\pi\)
0.107924 + 0.994159i \(0.465580\pi\)
\(720\) −1.50951e24 2.15880e24i −0.778950 1.11400i
\(721\) −5.45128e23 −0.278003
\(722\) 1.12152e24 1.52903e24i 0.565249 0.770639i
\(723\) 2.97768e22i 0.0148321i
\(724\) 2.93081e24 9.23030e23i 1.44281 0.454400i
\(725\) 2.20215e24i 1.07146i
\(726\) −1.09167e22 8.00719e21i −0.00524965 0.00385052i
\(727\) 2.92465e24 1.39005 0.695027 0.718983i \(-0.255392\pi\)
0.695027 + 0.718983i \(0.255392\pi\)
\(728\) −8.54090e23 + 2.51203e24i −0.401224 + 1.18007i
\(729\) 1.88955e24 0.877353
\(730\) 4.85834e23 + 3.56350e23i 0.222969 + 0.163543i
\(731\) 6.20311e23i 0.281392i
\(732\) 5.75933e22 + 1.82871e23i 0.0258243 + 0.0819973i
\(733\) 3.06846e24i 1.35999i −0.733216 0.679996i \(-0.761982\pi\)
0.733216 0.679996i \(-0.238018\pi\)
\(734\) −2.31823e24 + 3.16059e24i −1.01564 + 1.38469i
\(735\) −1.57342e23 −0.0681400
\(736\) −5.76020e22 + 2.54479e24i −0.0246590 + 1.08941i
\(737\) 3.68273e24 1.55846
\(738\) −7.63109e22 + 1.04039e23i −0.0319233 + 0.0435230i
\(739\) 3.06955e24i 1.26939i 0.772761 + 0.634697i \(0.218875\pi\)
−0.772761 + 0.634697i \(0.781125\pi\)
\(740\) 6.53574e23 + 2.07523e24i 0.267193 + 0.848393i
\(741\) 8.08486e22i 0.0326752i
\(742\) −1.27774e24 9.37196e23i −0.510515 0.374453i
\(743\) 4.34334e24 1.71561 0.857805 0.513975i \(-0.171828\pi\)
0.857805 + 0.513975i \(0.171828\pi\)
\(744\) −1.64501e23 + 4.83828e23i −0.0642391 + 0.188939i
\(745\) −3.36046e24 −1.29739
\(746\) −1.51984e23 1.11477e23i −0.0580118 0.0425506i
\(747\) 1.87174e23i 0.0706350i
\(748\) 4.14374e24 1.30503e24i 1.54607 0.486920i
\(749\) 4.80052e24i 1.77090i
\(750\) −2.36682e22 + 3.22684e22i −0.00863266 + 0.0117694i
\(751\) 7.59956e23 0.274062 0.137031 0.990567i \(-0.456244\pi\)
0.137031 + 0.990567i \(0.456244\pi\)
\(752\) −9.63213e21 + 6.73514e21i −0.00343456 + 0.00240157i
\(753\) 5.34610e23 0.188486
\(754\) 2.11092e24 2.87795e24i 0.735894 1.00329i
\(755\) 5.37519e24i 1.85287i
\(756\) 9.24762e23 2.91245e23i 0.315206 0.0992712i
\(757\) 2.36037e24i 0.795544i 0.917484 + 0.397772i \(0.130217\pi\)