Properties

Label 24.8.f.b.11.1
Level 24
Weight 8
Character 24.11
Analytic conductor 7.497
Analytic rank 0
Dimension 4
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 24.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.49724061162\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{6}, \sqrt{-26})\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 11.1
Root \(-1.22474 - 2.54951i\)
Character \(\chi\) = 24.11
Dual form 24.8.f.b.11.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.89898 - 10.1980i) q^{2} +(-9.00000 + 45.8912i) q^{3} +(-80.0000 + 99.9200i) q^{4} +97.9796 q^{5} +(512.091 - 133.038i) q^{6} -1548.76i q^{7} +(1410.91 + 326.337i) q^{8} +(-2025.00 - 826.041i) q^{9} +O(q^{10})\) \(q+(-4.89898 - 10.1980i) q^{2} +(-9.00000 + 45.8912i) q^{3} +(-80.0000 + 99.9200i) q^{4} +97.9796 q^{5} +(512.091 - 133.038i) q^{6} -1548.76i q^{7} +(1410.91 + 326.337i) q^{8} +(-2025.00 - 826.041i) q^{9} +(-480.000 - 999.200i) q^{10} +1784.66i q^{11} +(-3865.44 - 4570.57i) q^{12} -10141.9i q^{13} +(-15794.3 + 7587.34i) q^{14} +(-881.816 + 4496.40i) q^{15} +(-3584.00 - 15987.2i) q^{16} -27555.1i q^{17} +(1496.43 + 24697.8i) q^{18} +11570.0 q^{19} +(-7838.37 + 9790.12i) q^{20} +(71074.4 + 13938.8i) q^{21} +(18200.0 - 8743.00i) q^{22} +55534.8 q^{23} +(-27674.2 + 61811.1i) q^{24} -68525.0 q^{25} +(-103427. + 49684.8i) q^{26} +(56133.0 - 85495.3i) q^{27} +(154752. + 123901. i) q^{28} -54770.6 q^{29} +(50174.4 - 13035.0i) q^{30} +71692.6i q^{31} +(-145480. + 114871. i) q^{32} +(-81900.0 - 16061.9i) q^{33} +(-281008. + 134992. i) q^{34} -151747. i q^{35} +(244538. - 136255. i) q^{36} -282823. i q^{37} +(-56681.2 - 117991. i) q^{38} +(465423. + 91276.9i) q^{39} +(138240. + 31974.4i) q^{40} +403638. i q^{41} +(-206043. - 793106. i) q^{42} +495062. q^{43} +(-178323. - 142773. i) q^{44} +(-198409. - 80935.2i) q^{45} +(-272064. - 566346. i) q^{46} -1.13594e6 q^{47} +(765927. - 20589.2i) q^{48} -1.57511e6 q^{49} +(335703. + 698821. i) q^{50} +(1.26454e6 + 247996. i) q^{51} +(1.01338e6 + 811350. i) q^{52} -572416. q^{53} +(-1.14688e6 - 153607. i) q^{54} +174860. i q^{55} +(505418. - 2.18515e6i) q^{56} +(-104130. + 530961. i) q^{57} +(268320. + 558553. i) q^{58} +1.44050e6i q^{59} +(-378735. - 447823. i) q^{60} -1.78632e6i q^{61} +(731124. - 351220. i) q^{62} +(-1.27934e6 + 3.13624e6i) q^{63} +(1.88416e6 + 920862. i) q^{64} -993697. i q^{65} +(237426. + 913906. i) q^{66} +1.40013e6 q^{67} +(2.75330e6 + 2.20441e6i) q^{68} +(-499813. + 2.54856e6i) q^{69} +(-1.54752e6 + 743405. i) q^{70} +3.56947e6 q^{71} +(-2.58752e6 - 1.82630e6i) q^{72} -2.22360e6 q^{73} +(-2.88424e6 + 1.38555e6i) q^{74} +(616725. - 3.14469e6i) q^{75} +(-925600. + 1.15607e6i) q^{76} +2.76400e6 q^{77} +(-1.34925e6 - 5.19356e6i) q^{78} -5.59057e6i q^{79} +(-351159. - 1.56642e6i) q^{80} +(3.41828e6 + 3.34547e6i) q^{81} +(4.11632e6 - 1.97742e6i) q^{82} -3.01333e6i q^{83} +(-7.07872e6 + 5.98664e6i) q^{84} -2.69984e6i q^{85} +(-2.42530e6 - 5.04866e6i) q^{86} +(492935. - 2.51349e6i) q^{87} +(-582400. + 2.51798e6i) q^{88} -5.84533e6i q^{89} +(146620. + 2.41988e6i) q^{90} -1.57073e7 q^{91} +(-4.44279e6 + 5.54904e6i) q^{92} +(-3.29006e6 - 645233. i) q^{93} +(5.56493e6 + 1.15843e7i) q^{94} +1.13362e6 q^{95} +(-3.96223e6 - 7.71009e6i) q^{96} +6.86793e6 q^{97} +(7.71645e6 + 1.60631e7i) q^{98} +(1.47420e6 - 3.61393e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 36q^{3} - 320q^{4} + 1872q^{6} - 8100q^{9} + O(q^{10}) \) \( 4q - 36q^{3} - 320q^{4} + 1872q^{6} - 8100q^{9} - 1920q^{10} + 2880q^{12} - 14336q^{16} - 33696q^{18} + 46280q^{19} + 72800q^{22} - 59904q^{24} - 274100q^{25} + 224532q^{27} + 619008q^{28} + 17280q^{30} - 327600q^{33} - 1124032q^{34} + 648000q^{36} + 552960q^{40} - 1392768q^{42} + 1980248q^{43} - 1088256q^{46} + 129024q^{48} - 6300452q^{49} + 5058144q^{51} + 4053504q^{52} - 3487536q^{54} - 416520q^{57} + 1073280q^{58} - 1797120q^{60} + 7536640q^{64} - 655200q^{66} + 5600504q^{67} - 6190080q^{70} + 1078272q^{72} - 8894392q^{73} + 2466900q^{75} - 3702400q^{76} - 9120384q^{78} + 13673124q^{81} + 16465280q^{82} - 5571072q^{84} - 2329600q^{88} + 3888000q^{90} - 62829312q^{91} + 22259712q^{94} - 21086208q^{96} + 27471704q^{97} + 5896800q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/24\mathbb{Z}\right)^\times\).

\(n\) \(7\) \(13\) \(17\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.89898 10.1980i −0.433013 0.901388i
\(3\) −9.00000 + 45.8912i −0.192450 + 0.981307i
\(4\) −80.0000 + 99.9200i −0.625000 + 0.780625i
\(5\) 97.9796 0.350542 0.175271 0.984520i \(-0.443920\pi\)
0.175271 + 0.984520i \(0.443920\pi\)
\(6\) 512.091 133.038i 0.967871 0.251446i
\(7\) 1548.76i 1.70664i −0.521391 0.853318i \(-0.674587\pi\)
0.521391 0.853318i \(-0.325413\pi\)
\(8\) 1410.91 + 326.337i 0.974279 + 0.225347i
\(9\) −2025.00 826.041i −0.925926 0.377705i
\(10\) −480.000 999.200i −0.151789 0.315975i
\(11\) 1784.66i 0.404278i 0.979357 + 0.202139i \(0.0647893\pi\)
−0.979357 + 0.202139i \(0.935211\pi\)
\(12\) −3865.44 4570.57i −0.645751 0.763548i
\(13\) 10141.9i 1.28031i −0.768244 0.640157i \(-0.778869\pi\)
0.768244 0.640157i \(-0.221131\pi\)
\(14\) −15794.3 + 7587.34i −1.53834 + 0.738995i
\(15\) −881.816 + 4496.40i −0.0674619 + 0.343990i
\(16\) −3584.00 15987.2i −0.218750 0.975781i
\(17\) 27555.1i 1.36029i −0.733079 0.680144i \(-0.761917\pi\)
0.733079 0.680144i \(-0.238083\pi\)
\(18\) 1496.43 + 24697.8i 0.0604789 + 0.998169i
\(19\) 11570.0 0.386986 0.193493 0.981102i \(-0.438018\pi\)
0.193493 + 0.981102i \(0.438018\pi\)
\(20\) −7838.37 + 9790.12i −0.219089 + 0.273642i
\(21\) 71074.4 + 13938.8i 1.67473 + 0.328442i
\(22\) 18200.0 8743.00i 0.364411 0.175058i
\(23\) 55534.8 0.951739 0.475870 0.879516i \(-0.342133\pi\)
0.475870 + 0.879516i \(0.342133\pi\)
\(24\) −27674.2 + 61811.1i −0.408634 + 0.912698i
\(25\) −68525.0 −0.877120
\(26\) −103427. + 49684.8i −1.15406 + 0.554392i
\(27\) 56133.0 85495.3i 0.548839 0.835928i
\(28\) 154752. + 123901.i 1.33224 + 1.06665i
\(29\) −54770.6 −0.417018 −0.208509 0.978020i \(-0.566861\pi\)
−0.208509 + 0.978020i \(0.566861\pi\)
\(30\) 50174.4 13035.0i 0.339280 0.0881425i
\(31\) 71692.6i 0.432223i 0.976369 + 0.216112i \(0.0693375\pi\)
−0.976369 + 0.216112i \(0.930662\pi\)
\(32\) −145480. + 114871.i −0.784836 + 0.619704i
\(33\) −81900.0 16061.9i −0.396721 0.0778034i
\(34\) −281008. + 134992.i −1.22615 + 0.589022i
\(35\) 151747.i 0.598248i
\(36\) 244538. 136255.i 0.873550 0.486735i
\(37\) 282823.i 0.917930i −0.888454 0.458965i \(-0.848220\pi\)
0.888454 0.458965i \(-0.151780\pi\)
\(38\) −56681.2 117991.i −0.167570 0.348825i
\(39\) 465423. + 91276.9i 1.25638 + 0.246397i
\(40\) 138240. + 31974.4i 0.341526 + 0.0789937i
\(41\) 403638.i 0.914637i 0.889303 + 0.457319i \(0.151190\pi\)
−0.889303 + 0.457319i \(0.848810\pi\)
\(42\) −206043. 793106.i −0.429127 1.65180i
\(43\) 495062. 0.949555 0.474777 0.880106i \(-0.342529\pi\)
0.474777 + 0.880106i \(0.342529\pi\)
\(44\) −178323. 142773.i −0.315590 0.252674i
\(45\) −198409. 80935.2i −0.324576 0.132402i
\(46\) −272064. 566346.i −0.412115 0.857886i
\(47\) −1.13594e6 −1.59592 −0.797961 0.602710i \(-0.794088\pi\)
−0.797961 + 0.602710i \(0.794088\pi\)
\(48\) 765927. 20589.2i 0.999639 0.0268717i
\(49\) −1.57511e6 −1.91261
\(50\) 335703. + 698821.i 0.379804 + 0.790625i
\(51\) 1.26454e6 + 247996.i 1.33486 + 0.261788i
\(52\) 1.01338e6 + 811350.i 0.999445 + 0.800196i
\(53\) −572416. −0.528137 −0.264068 0.964504i \(-0.585064\pi\)
−0.264068 + 0.964504i \(0.585064\pi\)
\(54\) −1.14688e6 153607.i −0.991150 0.132749i
\(55\) 174860.i 0.141717i
\(56\) 505418. 2.18515e6i 0.384585 1.66274i
\(57\) −104130. + 530961.i −0.0744756 + 0.379752i
\(58\) 268320. + 558553.i 0.180574 + 0.375895i
\(59\) 1.44050e6i 0.913129i 0.889690 + 0.456565i \(0.150920\pi\)
−0.889690 + 0.456565i \(0.849080\pi\)
\(60\) −378735. 447823.i −0.226363 0.267656i
\(61\) 1.78632e6i 1.00764i −0.863809 0.503819i \(-0.831928\pi\)
0.863809 0.503819i \(-0.168072\pi\)
\(62\) 731124. 351220.i 0.389601 0.187158i
\(63\) −1.27934e6 + 3.13624e6i −0.644605 + 1.58022i
\(64\) 1.88416e6 + 920862.i 0.898438 + 0.439101i
\(65\) 993697.i 0.448804i
\(66\) 237426. + 913906.i 0.101654 + 0.391289i
\(67\) 1.40013e6 0.568729 0.284364 0.958716i \(-0.408217\pi\)
0.284364 + 0.958716i \(0.408217\pi\)
\(68\) 2.75330e6 + 2.20441e6i 1.06187 + 0.850180i
\(69\) −499813. + 2.54856e6i −0.183162 + 0.933948i
\(70\) −1.54752e6 + 743405.i −0.539254 + 0.259049i
\(71\) 3.56947e6 1.18359 0.591793 0.806090i \(-0.298420\pi\)
0.591793 + 0.806090i \(0.298420\pi\)
\(72\) −2.58752e6 1.82630e6i −0.816995 0.576645i
\(73\) −2.22360e6 −0.669000 −0.334500 0.942396i \(-0.608567\pi\)
−0.334500 + 0.942396i \(0.608567\pi\)
\(74\) −2.88424e6 + 1.38555e6i −0.827411 + 0.397475i
\(75\) 616725. 3.14469e6i 0.168802 0.860724i
\(76\) −925600. + 1.15607e6i −0.241867 + 0.302091i
\(77\) 2.76400e6 0.689956
\(78\) −1.34925e6 5.19356e6i −0.321930 1.23918i
\(79\) 5.59057e6i 1.27574i −0.770145 0.637869i \(-0.779816\pi\)
0.770145 0.637869i \(-0.220184\pi\)
\(80\) −351159. 1.56642e6i −0.0766812 0.342053i
\(81\) 3.41828e6 + 3.34547e6i 0.714678 + 0.699454i
\(82\) 4.11632e6 1.97742e6i 0.824443 0.396050i
\(83\) 3.01333e6i 0.578459i −0.957260 0.289230i \(-0.906601\pi\)
0.957260 0.289230i \(-0.0933991\pi\)
\(84\) −7.07872e6 + 5.98664e6i −1.30310 + 1.10206i
\(85\) 2.69984e6i 0.476839i
\(86\) −2.42530e6 5.04866e6i −0.411169 0.855917i
\(87\) 492935. 2.51349e6i 0.0802551 0.409222i
\(88\) −582400. + 2.51798e6i −0.0911029 + 0.393880i
\(89\) 5.84533e6i 0.878910i −0.898265 0.439455i \(-0.855172\pi\)
0.898265 0.439455i \(-0.144828\pi\)
\(90\) 146620. + 2.41988e6i 0.0212004 + 0.349901i
\(91\) −1.57073e7 −2.18503
\(92\) −4.44279e6 + 5.54904e6i −0.594837 + 0.742951i
\(93\) −3.29006e6 645233.i −0.424144 0.0831814i
\(94\) 5.56493e6 + 1.15843e7i 0.691054 + 1.43854i
\(95\) 1.13362e6 0.135655
\(96\) −3.96223e6 7.71009e6i −0.457078 0.889427i
\(97\) 6.86793e6 0.764055 0.382027 0.924151i \(-0.375226\pi\)
0.382027 + 0.924151i \(0.375226\pi\)
\(98\) 7.71645e6 + 1.60631e7i 0.828183 + 1.72400i
\(99\) 1.47420e6 3.61393e6i 0.152698 0.374332i
\(100\) 5.48200e6 6.84702e6i 0.548200 0.684702i
\(101\) 1.14364e7 1.10449 0.552246 0.833681i \(-0.313771\pi\)
0.552246 + 0.833681i \(0.313771\pi\)
\(102\) −3.66586e6 1.41107e7i −0.342039 1.31658i
\(103\) 1.03302e6i 0.0931493i 0.998915 + 0.0465746i \(0.0148305\pi\)
−0.998915 + 0.0465746i \(0.985169\pi\)
\(104\) 3.30967e6 1.43092e7i 0.288515 1.24738i
\(105\) 6.96384e6 + 1.36572e6i 0.587065 + 0.115133i
\(106\) 2.80426e6 + 5.83752e6i 0.228690 + 0.476056i
\(107\) 1.85726e7i 1.46565i 0.680419 + 0.732824i \(0.261798\pi\)
−0.680419 + 0.732824i \(0.738202\pi\)
\(108\) 4.05204e6 + 1.24484e7i 0.309522 + 0.950892i
\(109\) 1.22187e7i 0.903714i 0.892090 + 0.451857i \(0.149238\pi\)
−0.892090 + 0.451857i \(0.850762\pi\)
\(110\) 1.78323e6 856635.i 0.127742 0.0613651i
\(111\) 1.29791e7 + 2.54541e6i 0.900771 + 0.176656i
\(112\) −2.47603e7 + 5.55075e6i −1.66530 + 0.373327i
\(113\) 1.41210e7i 0.920641i −0.887753 0.460320i \(-0.847735\pi\)
0.887753 0.460320i \(-0.152265\pi\)
\(114\) 5.92489e6 1.53924e6i 0.374553 0.0973062i
\(115\) 5.44128e6 0.333625
\(116\) 4.38165e6 5.47268e6i 0.260636 0.325534i
\(117\) −8.37761e6 + 2.05373e7i −0.483581 + 1.18548i
\(118\) 1.46903e7 7.05700e6i 0.823084 0.395397i
\(119\) −4.26762e7 −2.32152
\(120\) −2.71150e6 + 6.05623e6i −0.143244 + 0.319939i
\(121\) 1.63022e7 0.836559
\(122\) −1.82170e7 + 8.75114e6i −0.908273 + 0.436320i
\(123\) −1.85234e7 3.63275e6i −0.897540 0.176022i
\(124\) −7.16352e6 5.73541e6i −0.337404 0.270140i
\(125\) −1.43687e7 −0.658010
\(126\) 3.82509e7 2.31762e6i 1.70351 0.103215i
\(127\) 1.07474e7i 0.465578i −0.972527 0.232789i \(-0.925215\pi\)
0.972527 0.232789i \(-0.0747851\pi\)
\(128\) 160530. 2.37260e7i 0.00676582 0.999977i
\(129\) −4.45556e6 + 2.27190e7i −0.182742 + 0.931804i
\(130\) −1.01338e7 + 4.86810e6i −0.404547 + 0.194338i
\(131\) 3.13305e7i 1.21764i 0.793310 + 0.608818i \(0.208356\pi\)
−0.793310 + 0.608818i \(0.791644\pi\)
\(132\) 8.15691e6 6.89849e6i 0.308686 0.261063i
\(133\) 1.79191e7i 0.660445i
\(134\) −6.85919e6 1.42785e7i −0.246267 0.512645i
\(135\) 5.49989e6 8.37679e6i 0.192391 0.293028i
\(136\) 8.99226e6 3.88777e7i 0.306537 1.32530i
\(137\) 5.53966e6i 0.184061i 0.995756 + 0.0920303i \(0.0293357\pi\)
−0.995756 + 0.0920303i \(0.970664\pi\)
\(138\) 2.84389e7 7.38822e6i 0.921161 0.239311i
\(139\) −1.34182e7 −0.423783 −0.211891 0.977293i \(-0.567962\pi\)
−0.211891 + 0.977293i \(0.567962\pi\)
\(140\) 1.51625e7 + 1.21397e7i 0.467007 + 0.373905i
\(141\) 1.02234e7 5.21294e7i 0.307135 1.56609i
\(142\) −1.74868e7 3.64016e7i −0.512508 1.06687i
\(143\) 1.80998e7 0.517603
\(144\) −5.94848e6 + 3.53346e7i −0.166011 + 0.986124i
\(145\) −5.36640e6 −0.146182
\(146\) 1.08934e7 + 2.26763e7i 0.289686 + 0.603029i
\(147\) 1.41760e7 7.22838e7i 0.368081 1.87685i
\(148\) 2.82597e7 + 2.26259e7i 0.716559 + 0.573706i
\(149\) −2.09354e7 −0.518477 −0.259238 0.965813i \(-0.583472\pi\)
−0.259238 + 0.965813i \(0.583472\pi\)
\(150\) −3.50910e7 + 9.11640e6i −0.848939 + 0.220548i
\(151\) 3.02970e7i 0.716111i 0.933700 + 0.358055i \(0.116560\pi\)
−0.933700 + 0.358055i \(0.883440\pi\)
\(152\) 1.63242e7 + 3.77572e6i 0.377033 + 0.0872062i
\(153\) −2.27616e7 + 5.57991e7i −0.513788 + 1.25953i
\(154\) −1.35408e7 2.81874e7i −0.298760 0.621918i
\(155\) 7.02441e6i 0.151513i
\(156\) −4.63542e7 + 3.92029e7i −0.977581 + 0.826764i
\(157\) 8.03861e7i 1.65780i 0.559397 + 0.828900i \(0.311033\pi\)
−0.559397 + 0.828900i \(0.688967\pi\)
\(158\) −5.70129e7 + 2.73881e7i −1.14993 + 0.552411i
\(159\) 5.15175e6 2.62689e7i 0.101640 0.518264i
\(160\) −1.42541e7 + 1.12550e7i −0.275118 + 0.217233i
\(161\) 8.60101e7i 1.62427i
\(162\) 1.73711e7 5.12491e7i 0.321015 0.947074i
\(163\) 1.08125e8 1.95554 0.977772 0.209669i \(-0.0672388\pi\)
0.977772 + 0.209669i \(0.0672388\pi\)
\(164\) −4.03315e7 3.22911e7i −0.713989 0.571648i
\(165\) −8.02453e6 1.57374e6i −0.139068 0.0272734i
\(166\) −3.07300e7 + 1.47622e7i −0.521416 + 0.250480i
\(167\) 3.92926e7 0.652834 0.326417 0.945226i \(-0.394159\pi\)
0.326417 + 0.945226i \(0.394159\pi\)
\(168\) 9.57305e7 + 4.28606e7i 1.55764 + 0.697390i
\(169\) −4.01091e7 −0.639205
\(170\) −2.75330e7 + 1.32264e7i −0.429816 + 0.206477i
\(171\) −2.34292e7 9.55730e6i −0.358321 0.146167i
\(172\) −3.96050e7 + 4.94666e7i −0.593472 + 0.741246i
\(173\) 1.29099e8 1.89566 0.947831 0.318772i \(-0.103270\pi\)
0.947831 + 0.318772i \(0.103270\pi\)
\(174\) −2.80475e7 + 7.28655e6i −0.403619 + 0.104857i
\(175\) 1.06129e8i 1.49692i
\(176\) 2.85317e7 6.39621e6i 0.394487 0.0884359i
\(177\) −6.61064e7 1.29645e7i −0.896060 0.175732i
\(178\) −5.96109e7 + 2.86362e7i −0.792238 + 0.380579i
\(179\) 2.75640e6i 0.0359216i −0.999839 0.0179608i \(-0.994283\pi\)
0.999839 0.0179608i \(-0.00571741\pi\)
\(180\) 2.39597e7 1.33502e7i 0.306216 0.170621i
\(181\) 1.11231e8i 1.39428i −0.716933 0.697142i \(-0.754455\pi\)
0.716933 0.697142i \(-0.245545\pi\)
\(182\) 7.69499e7 + 1.60184e8i 0.946146 + 1.96956i
\(183\) 8.19763e7 + 1.60769e7i 0.988802 + 0.193920i
\(184\) 7.83544e7 + 1.81231e7i 0.927259 + 0.214472i
\(185\) 2.77109e7i 0.321773i
\(186\) 9.53781e6 + 3.67131e7i 0.108681 + 0.418337i
\(187\) 4.91764e7 0.549935
\(188\) 9.08749e7 1.13503e8i 0.997451 1.24582i
\(189\) −1.32412e8 8.69365e7i −1.42662 0.936669i
\(190\) −5.55360e6 1.15607e7i −0.0587404 0.122278i
\(191\) −1.09860e8 −1.14084 −0.570418 0.821354i \(-0.693219\pi\)
−0.570418 + 0.821354i \(0.693219\pi\)
\(192\) −5.92169e7 + 7.81786e7i −0.603798 + 0.797138i
\(193\) −5.60296e7 −0.561005 −0.280502 0.959853i \(-0.590501\pi\)
−0.280502 + 0.959853i \(0.590501\pi\)
\(194\) −3.36458e7 7.00394e7i −0.330845 0.688710i
\(195\) 4.56019e7 + 8.94327e6i 0.440415 + 0.0863725i
\(196\) 1.26009e8 1.57385e8i 1.19538 1.49303i
\(197\) 9.45130e7 0.880765 0.440382 0.897810i \(-0.354843\pi\)
0.440382 + 0.897810i \(0.354843\pi\)
\(198\) −4.40771e7 + 2.67062e6i −0.403538 + 0.0244503i
\(199\) 9.00414e7i 0.809947i −0.914328 0.404974i \(-0.867281\pi\)
0.914328 0.404974i \(-0.132719\pi\)
\(200\) −9.66823e7 2.23623e7i −0.854559 0.197656i
\(201\) −1.26011e7 + 6.42534e7i −0.109452 + 0.558098i
\(202\) −5.60265e7 1.16628e8i −0.478259 0.995576i
\(203\) 8.48265e7i 0.711697i
\(204\) −1.25943e8 + 1.06513e8i −1.03865 + 0.878407i
\(205\) 3.95483e7i 0.320619i
\(206\) 1.05348e7 5.06076e6i 0.0839636 0.0403348i
\(207\) −1.12458e8 4.58741e7i −0.881240 0.359477i
\(208\) −1.62140e8 + 3.63485e7i −1.24931 + 0.280069i
\(209\) 2.06485e7i 0.156450i
\(210\) −2.01880e7 7.77082e7i −0.150427 0.579027i
\(211\) −9.47083e7 −0.694064 −0.347032 0.937853i \(-0.612810\pi\)
−0.347032 + 0.937853i \(0.612810\pi\)
\(212\) 4.57933e7 5.71958e7i 0.330086 0.412277i
\(213\) −3.21253e7 + 1.63807e8i −0.227781 + 1.16146i
\(214\) 1.89404e8 9.09868e7i 1.32112 0.634644i
\(215\) 4.85060e7 0.332859
\(216\) 1.07099e8 1.02307e8i 0.723096 0.690747i
\(217\) 1.11035e8 0.737648
\(218\) 1.24606e8 5.98590e7i 0.814597 0.391320i
\(219\) 2.00124e7 1.02044e8i 0.128749 0.656494i
\(220\) −1.74720e7 1.39888e7i −0.110628 0.0885729i
\(221\) −2.79460e8 −1.74160
\(222\) −3.76261e7 1.44831e8i −0.230810 0.888438i
\(223\) 1.44671e7i 0.0873601i −0.999046 0.0436801i \(-0.986092\pi\)
0.999046 0.0436801i \(-0.0139082\pi\)
\(224\) 1.77907e8 + 2.25314e8i 1.05761 + 1.33943i
\(225\) 1.38763e8 + 5.66045e7i 0.812148 + 0.331293i
\(226\) −1.44006e8 + 6.91784e7i −0.829855 + 0.398649i
\(227\) 3.50766e7i 0.199034i 0.995036 + 0.0995169i \(0.0317297\pi\)
−0.995036 + 0.0995169i \(0.968270\pi\)
\(228\) −4.47232e7 5.28815e7i −0.249897 0.295483i
\(229\) 1.01759e7i 0.0559949i −0.999608 0.0279975i \(-0.991087\pi\)
0.999608 0.0279975i \(-0.00891303\pi\)
\(230\) −2.66567e7 5.54904e7i −0.144464 0.300726i
\(231\) −2.48760e7 + 1.26843e8i −0.132782 + 0.677058i
\(232\) −7.72762e7 1.78737e7i −0.406291 0.0939737i
\(233\) 1.39333e8i 0.721621i 0.932639 + 0.360811i \(0.117500\pi\)
−0.932639 + 0.360811i \(0.882500\pi\)
\(234\) 2.50482e8 1.51766e7i 1.27797 0.0774320i
\(235\) −1.11299e8 −0.559438
\(236\) −1.43935e8 1.15240e8i −0.712811 0.570706i
\(237\) 2.56558e8 + 5.03151e7i 1.25189 + 0.245516i
\(238\) 2.09070e8 + 4.35214e8i 1.00525 + 2.09259i
\(239\) 6.12372e7 0.290150 0.145075 0.989421i \(-0.453658\pi\)
0.145075 + 0.989421i \(0.453658\pi\)
\(240\) 7.50452e7 2.01732e6i 0.350416 0.00941968i
\(241\) 1.39554e8 0.642218 0.321109 0.947042i \(-0.395944\pi\)
0.321109 + 0.947042i \(0.395944\pi\)
\(242\) −7.98640e7 1.66250e8i −0.362241 0.754064i
\(243\) −1.84292e8 + 1.26760e8i −0.823919 + 0.566708i
\(244\) 1.78489e8 + 1.42906e8i 0.786587 + 0.629774i
\(245\) −1.54329e8 −0.670449
\(246\) 5.36991e7 + 2.06700e8i 0.229982 + 0.885251i
\(247\) 1.17342e8i 0.495464i
\(248\) −2.33960e7 + 1.01151e8i −0.0974002 + 0.421106i
\(249\) 1.38285e8 + 2.71199e7i 0.567646 + 0.111325i
\(250\) 7.03920e7 + 1.46533e8i 0.284927 + 0.593122i
\(251\) 3.29413e7i 0.131487i −0.997837 0.0657436i \(-0.979058\pi\)
0.997837 0.0657436i \(-0.0209419\pi\)
\(252\) −2.11026e8 3.78731e8i −0.830679 1.49083i
\(253\) 9.91106e7i 0.384767i
\(254\) −1.09603e8 + 5.26515e7i −0.419666 + 0.201601i
\(255\) 1.23899e8 + 2.42985e7i 0.467925 + 0.0917676i
\(256\) −2.42745e8 + 1.14596e8i −0.904297 + 0.426904i
\(257\) 3.21918e8i 1.18299i −0.806310 0.591493i \(-0.798539\pi\)
0.806310 0.591493i \(-0.201461\pi\)
\(258\) 2.53517e8 6.58618e7i 0.919047 0.238762i
\(259\) −4.38026e8 −1.56657
\(260\) 9.92902e7 + 7.94958e7i 0.350348 + 0.280503i
\(261\) 1.10910e8 + 4.52428e7i 0.386127 + 0.157510i
\(262\) 3.19509e8 1.53487e8i 1.09756 0.527252i
\(263\) −3.65537e8 −1.23904 −0.619521 0.784980i \(-0.712673\pi\)
−0.619521 + 0.784980i \(0.712673\pi\)
\(264\) −1.10312e8 4.93889e7i −0.368984 0.165202i
\(265\) −5.60851e7 −0.185134
\(266\) −1.82740e8 + 8.77855e7i −0.595317 + 0.285981i
\(267\) 2.68249e8 + 5.26080e7i 0.862480 + 0.169146i
\(268\) −1.12010e8 + 1.39901e8i −0.355456 + 0.443964i
\(269\) 3.85128e8 1.20635 0.603173 0.797611i \(-0.293903\pi\)
0.603173 + 0.797611i \(0.293903\pi\)
\(270\) −1.12371e8 1.50504e7i −0.347440 0.0465343i
\(271\) 3.67394e8i 1.12135i −0.828037 0.560673i \(-0.810543\pi\)
0.828037 0.560673i \(-0.189457\pi\)
\(272\) −4.40529e8 + 9.87575e7i −1.32734 + 0.297563i
\(273\) 1.41366e8 7.20828e8i 0.420509 2.14418i
\(274\) 5.64936e7 2.71387e7i 0.165910 0.0797006i
\(275\) 1.22294e8i 0.354600i
\(276\) −2.14667e8 2.53826e8i −0.614587 0.726699i
\(277\) 8.69908e6i 0.0245920i −0.999924 0.0122960i \(-0.996086\pi\)
0.999924 0.0122960i \(-0.00391404\pi\)
\(278\) 6.57356e7 + 1.36840e8i 0.183503 + 0.381993i
\(279\) 5.92210e7 1.45177e8i 0.163253 0.400207i
\(280\) 4.95206e7 2.14101e8i 0.134813 0.582860i
\(281\) 4.68539e8i 1.25972i 0.776710 + 0.629859i \(0.216887\pi\)
−0.776710 + 0.629859i \(0.783113\pi\)
\(282\) −5.81702e8 + 1.51122e8i −1.54465 + 0.401288i
\(283\) 1.79280e8 0.470197 0.235099 0.971972i \(-0.424459\pi\)
0.235099 + 0.971972i \(0.424459\pi\)
\(284\) −2.85558e8 + 3.56662e8i −0.739742 + 0.923937i
\(285\) −1.02026e7 + 5.20233e7i −0.0261069 + 0.133119i
\(286\) −8.86704e7 1.84582e8i −0.224129 0.466561i
\(287\) 6.25139e8 1.56095
\(288\) 3.89485e8 1.12441e8i 0.960765 0.277364i
\(289\) −3.48945e8 −0.850383
\(290\) 2.62899e7 + 5.47268e7i 0.0632988 + 0.131767i
\(291\) −6.18113e7 + 3.15177e8i −0.147042 + 0.749772i
\(292\) 1.77888e8 2.22182e8i 0.418125 0.522238i
\(293\) 7.75663e7 0.180151 0.0900755 0.995935i \(-0.471289\pi\)
0.0900755 + 0.995935i \(0.471289\pi\)
\(294\) −8.06601e8 + 2.09549e8i −1.85116 + 0.480917i
\(295\) 1.41140e8i 0.320091i
\(296\) 9.22958e7 3.99037e8i 0.206853 0.894319i
\(297\) 1.52580e8 + 1.00178e8i 0.337947 + 0.221884i
\(298\) 1.02562e8 + 2.13500e8i 0.224507 + 0.467349i
\(299\) 5.63227e8i 1.21853i
\(300\) 2.64880e8 + 3.13199e8i 0.566401 + 0.669723i
\(301\) 7.66732e8i 1.62054i
\(302\) 3.08970e8 1.48424e8i 0.645493 0.310085i
\(303\) −1.02927e8 + 5.24828e8i −0.212560 + 1.08385i
\(304\) −4.14669e7 1.84972e8i −0.0846533 0.377614i
\(305\) 1.75023e8i 0.353220i
\(306\) 6.80550e8 4.12344e7i 1.35780 0.0822687i
\(307\) −1.34816e8 −0.265924 −0.132962 0.991121i \(-0.542449\pi\)
−0.132962 + 0.991121i \(0.542449\pi\)
\(308\) −2.21120e8 + 2.76179e8i −0.431222 + 0.538596i
\(309\) −4.74066e7 9.29720e6i −0.0914080 0.0179266i
\(310\) 7.16352e7 3.44124e7i 0.136572 0.0656069i
\(311\) −5.73695e7 −0.108148 −0.0540742 0.998537i \(-0.517221\pi\)
−0.0540742 + 0.998537i \(0.517221\pi\)
\(312\) 6.26881e8 + 2.80668e8i 1.16854 + 0.523181i
\(313\) 3.22598e8 0.594643 0.297321 0.954777i \(-0.403907\pi\)
0.297321 + 0.954777i \(0.403907\pi\)
\(314\) 8.19780e8 3.93810e8i 1.49432 0.717848i
\(315\) −1.25349e8 + 3.07287e8i −0.225961 + 0.553934i
\(316\) 5.58610e8 + 4.47246e8i 0.995873 + 0.797336i
\(317\) −6.42560e8 −1.13294 −0.566469 0.824083i \(-0.691691\pi\)
−0.566469 + 0.824083i \(0.691691\pi\)
\(318\) −2.93129e8 + 7.61529e7i −0.511169 + 0.132798i
\(319\) 9.77467e7i 0.168591i
\(320\) 1.84609e8 + 9.02257e7i 0.314940 + 0.153924i
\(321\) −8.52318e8 1.67153e8i −1.43825 0.282064i
\(322\) −8.77134e8 + 4.21362e8i −1.46410 + 0.703331i
\(323\) 3.18813e8i 0.526413i
\(324\) −6.07741e8 + 7.39172e7i −0.992685 + 0.120736i
\(325\) 6.94972e8i 1.12299i
\(326\) −5.29700e8 1.10266e9i −0.846776 1.76270i
\(327\) −5.60729e8 1.09968e8i −0.886821 0.173920i
\(328\) −1.31722e8 + 5.69496e8i −0.206111 + 0.891112i
\(329\) 1.75929e9i 2.72366i
\(330\) 2.32629e7 + 8.95442e7i 0.0356341 + 0.137163i
\(331\) 1.11052e9 1.68317 0.841583 0.540127i \(-0.181624\pi\)
0.841583 + 0.540127i \(0.181624\pi\)
\(332\) 3.01092e8 + 2.41066e8i 0.451560 + 0.361537i
\(333\) −2.33624e8 + 5.72718e8i −0.346707 + 0.849935i
\(334\) −1.92494e8 4.00707e8i −0.282686 0.588457i
\(335\) 1.37184e8 0.199364
\(336\) −3.18877e7 1.18624e9i −0.0458602 1.70602i
\(337\) −3.54194e8 −0.504123 −0.252062 0.967711i \(-0.581109\pi\)
−0.252062 + 0.967711i \(0.581109\pi\)
\(338\) 1.96494e8 + 4.09035e8i 0.276784 + 0.576171i
\(339\) 6.48028e8 + 1.27089e8i 0.903431 + 0.177177i
\(340\) 2.69768e8 + 2.15987e8i 0.372232 + 0.298024i
\(341\) −1.27947e8 −0.174738
\(342\) 1.73137e7 + 2.85753e8i 0.0234045 + 0.386278i
\(343\) 1.16400e9i 1.55749i
\(344\) 6.98486e8 + 1.61557e8i 0.925131 + 0.213979i
\(345\) −4.89715e7 + 2.49707e8i −0.0642062 + 0.327389i
\(346\) −6.32453e8 1.31656e9i −0.820846 1.70873i
\(347\) 4.20183e8i 0.539865i −0.962879 0.269932i \(-0.912999\pi\)
0.962879 0.269932i \(-0.0870014\pi\)
\(348\) 2.11713e8 + 2.50333e8i 0.269290 + 0.318413i
\(349\) 2.71958e7i 0.0342462i −0.999853 0.0171231i \(-0.994549\pi\)
0.999853 0.0171231i \(-0.00545072\pi\)
\(350\) 1.08231e9 5.19923e8i 1.34931 0.648187i
\(351\) −8.67082e8 5.69294e8i −1.07025 0.702687i
\(352\) −2.05005e8 2.59632e8i −0.250533 0.317292i
\(353\) 8.90412e8i 1.07741i −0.842496 0.538703i \(-0.818914\pi\)
0.842496 0.538703i \(-0.181086\pi\)
\(354\) 1.91641e8 + 7.37669e8i 0.229603 + 0.883792i
\(355\) 3.49736e8 0.414897
\(356\) 5.84065e8 + 4.67627e8i 0.686099 + 0.549318i
\(357\) 3.84086e8 1.95846e9i 0.446776 2.27812i
\(358\) −2.81098e7 + 1.35035e7i −0.0323793 + 0.0155545i
\(359\) 1.13487e9 1.29454 0.647269 0.762261i \(-0.275911\pi\)
0.647269 + 0.762261i \(0.275911\pi\)
\(360\) −2.53524e8 1.78940e8i −0.286391 0.202138i
\(361\) −7.60007e8 −0.850241
\(362\) −1.13434e9 + 5.44919e8i −1.25679 + 0.603743i
\(363\) −1.46720e8 + 7.48126e8i −0.160996 + 0.820921i
\(364\) 1.25659e9 1.56948e9i 1.36564 1.70569i
\(365\) −2.17867e8 −0.234513
\(366\) −2.37648e8 9.14758e8i −0.253367 0.975264i
\(367\) 1.04021e9i 1.09847i 0.835668 + 0.549235i \(0.185081\pi\)
−0.835668 + 0.549235i \(0.814919\pi\)
\(368\) −1.99037e8 8.87846e8i −0.208193 0.928689i
\(369\) 3.33422e8 8.17368e8i 0.345463 0.846886i
\(370\) −2.82597e8 + 1.35755e8i −0.290043 + 0.139332i
\(371\) 8.86535e8i 0.901337i
\(372\) 3.27676e8 2.77124e8i 0.330023 0.279109i
\(373\) 3.18791e7i 0.0318072i −0.999874 0.0159036i \(-0.994938\pi\)
0.999874 0.0159036i \(-0.00506249\pi\)
\(374\) −2.40914e8 5.01503e8i −0.238129 0.495704i
\(375\) 1.29318e8 6.59397e8i 0.126634 0.645710i
\(376\) −1.60270e9 3.70698e8i −1.55487 0.359636i
\(377\) 5.55477e8i 0.533914i
\(378\) −2.37900e8 + 1.77624e9i −0.226555 + 1.69153i
\(379\) 5.34127e7 0.0503973 0.0251987 0.999682i \(-0.491978\pi\)
0.0251987 + 0.999682i \(0.491978\pi\)
\(380\) −9.06899e7 + 1.13272e8i −0.0847845 + 0.105896i
\(381\) 4.93213e8 + 9.67270e7i 0.456874 + 0.0896005i
\(382\) 5.38202e8 + 1.12036e9i 0.493997 + 1.02834i
\(383\) −1.30505e9 −1.18695 −0.593473 0.804854i \(-0.702244\pi\)
−0.593473 + 0.804854i \(0.702244\pi\)
\(384\) 1.08737e9 + 2.20901e8i 0.979982 + 0.199085i
\(385\) 2.70816e8 0.241859
\(386\) 2.74488e8 + 5.71392e8i 0.242922 + 0.505683i
\(387\) −1.00250e9 4.08942e8i −0.879217 0.358652i
\(388\) −5.49434e8 + 6.86243e8i −0.477534 + 0.596440i
\(389\) −7.16057e8 −0.616771 −0.308385 0.951262i \(-0.599789\pi\)
−0.308385 + 0.951262i \(0.599789\pi\)
\(390\) −1.32199e8 5.08863e8i −0.112850 0.434385i
\(391\) 1.53027e9i 1.29464i
\(392\) −2.22234e9 5.14018e8i −1.86341 0.431000i
\(393\) −1.43779e9 2.81974e8i −1.19487 0.234334i
\(394\) −4.63017e8 9.63847e8i −0.381382 0.793910i
\(395\) 5.47762e8i 0.447200i
\(396\) 2.43168e8 + 4.36416e8i 0.196776 + 0.353157i
\(397\) 4.15822e7i 0.0333535i −0.999861 0.0166767i \(-0.994691\pi\)
0.999861 0.0166767i \(-0.00530862\pi\)
\(398\) −9.18246e8 + 4.41111e8i −0.730076 + 0.350717i
\(399\) 8.22331e8 + 1.61272e8i 0.648099 + 0.127103i
\(400\) 2.45594e8 + 1.09552e9i 0.191870 + 0.855877i
\(401\) 1.22525e9i 0.948895i −0.880284 0.474447i \(-0.842648\pi\)
0.880284 0.474447i \(-0.157352\pi\)
\(402\) 7.16992e8 1.86269e8i 0.550456 0.143005i
\(403\) 7.27097e8 0.553382
\(404\) −9.14908e8 + 1.14272e9i −0.690308 + 0.862194i
\(405\) 3.34922e8 + 3.27787e8i 0.250525 + 0.245188i
\(406\) 8.65064e8 4.15563e8i 0.641515 0.308174i
\(407\) 5.04743e8 0.371099
\(408\) 1.70321e9 + 7.62564e8i 1.24153 + 0.555860i
\(409\) 1.98246e9 1.43276 0.716381 0.697710i \(-0.245797\pi\)
0.716381 + 0.697710i \(0.245797\pi\)
\(410\) 4.03315e8 1.93746e8i 0.289002 0.138832i
\(411\) −2.54221e8 4.98569e7i −0.180620 0.0354225i
\(412\) −1.03220e8 8.26418e7i −0.0727146 0.0582183i
\(413\) 2.23099e9 1.55838
\(414\) 8.31042e7 + 1.37159e9i 0.0575601 + 0.949997i
\(415\) 2.95245e8i 0.202775i
\(416\) 1.16500e9 + 1.47544e9i 0.793416 + 1.00484i
\(417\) 1.20764e8 6.15778e8i 0.0815571 0.415861i
\(418\) 2.10574e8 1.01156e8i 0.141022 0.0677449i
\(419\) 2.00028e9i 1.32844i −0.747538 0.664219i \(-0.768764\pi\)
0.747538 0.664219i \(-0.231236\pi\)
\(420\) −6.93570e8 + 5.86569e8i −0.456791 + 0.386319i
\(421\) 2.32447e9i 1.51823i 0.650959 + 0.759113i \(0.274367\pi\)
−0.650959 + 0.759113i \(0.725633\pi\)
\(422\) 4.63974e8 + 9.65839e8i 0.300538 + 0.625620i
\(423\) 2.30027e9 + 9.38330e8i 1.47770 + 0.602788i
\(424\) −8.07626e8 1.86801e8i −0.514552 0.119014i
\(425\) 1.88821e9i 1.19314i
\(426\) 1.82790e9 4.74874e8i 1.14556 0.297608i
\(427\) −2.76658e9 −1.71967
\(428\) −1.85577e9 1.48581e9i −1.14412 0.916029i
\(429\) −1.62898e8 + 8.30620e8i −0.0996128 + 0.507927i
\(430\) −2.37630e8 4.94666e8i −0.144132 0.300035i
\(431\) −7.11491e8 −0.428055 −0.214027 0.976828i \(-0.568658\pi\)
−0.214027 + 0.976828i \(0.568658\pi\)
\(432\) −1.56801e9 5.90994e8i −0.935741 0.352688i
\(433\) 9.95747e8 0.589442 0.294721 0.955583i \(-0.404773\pi\)
0.294721 + 0.955583i \(0.404773\pi\)
\(434\) −5.43956e8 1.13233e9i −0.319411 0.664907i
\(435\) 4.82976e7 2.46270e8i 0.0281328 0.143450i
\(436\) −1.22089e9 9.77493e8i −0.705461 0.564821i
\(437\) 6.42538e8 0.368310
\(438\) −1.13868e9 + 2.95822e8i −0.647506 + 0.168218i
\(439\) 5.41401e8i 0.305417i 0.988271 + 0.152708i \(0.0487995\pi\)
−0.988271 + 0.152708i \(0.951200\pi\)
\(440\) −5.70633e7 + 2.46711e8i −0.0319354 + 0.138072i
\(441\) 3.18960e9 + 1.30111e9i 1.77093 + 0.722401i
\(442\) 1.36907e9 + 2.84995e9i 0.754133 + 1.56985i
\(443\) 2.02764e9i 1.10810i 0.832484 + 0.554050i \(0.186918\pi\)
−0.832484 + 0.554050i \(0.813082\pi\)
\(444\) −1.29267e9 + 1.09324e9i −0.700883 + 0.592754i
\(445\) 5.72723e8i 0.308095i
\(446\) −1.47536e8 + 7.08738e7i −0.0787454 + 0.0378281i
\(447\) 1.88419e8 9.60750e8i 0.0997809 0.508785i
\(448\) 1.42619e9 2.91811e9i 0.749386 1.53331i
\(449\) 2.36412e9i 1.23256i −0.787528 0.616279i \(-0.788639\pi\)
0.787528 0.616279i \(-0.211361\pi\)
\(450\) −1.02543e8 1.69242e9i −0.0530472 0.875514i
\(451\) −7.20356e8 −0.369768
\(452\) 1.41097e9 + 1.12968e9i 0.718675 + 0.575401i
\(453\) −1.39036e9 2.72673e8i −0.702724 0.137816i
\(454\) 3.57712e8 1.71840e8i 0.179407 0.0861842i
\(455\) −1.53900e9 −0.765946
\(456\) −3.20190e8 + 7.15154e8i −0.158136 + 0.353202i
\(457\) 5.36394e8 0.262892 0.131446 0.991323i \(-0.458038\pi\)
0.131446 + 0.991323i \(0.458038\pi\)
\(458\) −1.03774e8 + 4.98515e7i −0.0504731 + 0.0242465i
\(459\) −2.35583e9 1.54675e9i −1.13710 0.746579i
\(460\) −4.35302e8 + 5.43693e8i −0.208516 + 0.260436i
\(461\) −3.68025e9 −1.74954 −0.874770 0.484539i \(-0.838987\pi\)
−0.874770 + 0.484539i \(0.838987\pi\)
\(462\) 1.41542e9 3.67716e8i 0.667788 0.173487i
\(463\) 1.19699e9i 0.560478i −0.959930 0.280239i \(-0.909586\pi\)
0.959930 0.280239i \(-0.0904138\pi\)
\(464\) 1.96298e8 + 8.75628e8i 0.0912226 + 0.406918i
\(465\) −3.22358e8 6.32197e7i −0.148680 0.0291586i
\(466\) 1.42093e9 6.82591e8i 0.650460 0.312471i
\(467\) 1.60918e9i 0.731130i 0.930786 + 0.365565i \(0.119124\pi\)
−0.930786 + 0.365565i \(0.880876\pi\)
\(468\) −1.38188e9 2.48007e9i −0.623174 1.11842i
\(469\) 2.16846e9i 0.970613i
\(470\) 5.45249e8 + 1.13503e9i 0.242244 + 0.504271i
\(471\) −3.68901e9 7.23475e8i −1.62681 0.319044i
\(472\) −4.70090e8 + 2.03242e9i −0.205771 + 0.889642i
\(473\) 8.83516e8i 0.383884i
\(474\) −7.43756e8 2.86288e9i −0.320779 1.23475i
\(475\) −7.92834e8 −0.339434
\(476\) 3.41410e9 4.26421e9i 1.45095 1.81223i
\(477\) 1.15914e9 + 4.72839e8i 0.489016 + 0.199480i
\(478\) −3.00000e8 6.24500e8i −0.125639 0.261538i
\(479\) 1.54958e9 0.644227 0.322114 0.946701i \(-0.395607\pi\)
0.322114 + 0.946701i \(0.395607\pi\)
\(480\) −3.88218e8 7.55431e8i −0.160225 0.311782i
\(481\) −2.86836e9 −1.17524
\(482\) −6.83672e8 1.42318e9i −0.278088 0.578887i
\(483\) 3.94710e9 + 7.74091e8i 1.59391 + 0.312591i
\(484\) −1.30417e9 + 1.62891e9i −0.522849 + 0.653039i
\(485\) 6.72917e8 0.267834
\(486\) 2.19554e9 + 1.25842e9i 0.867591 + 0.497279i
\(487\) 2.60156e9i 1.02066i −0.859978 0.510331i \(-0.829523\pi\)
0.859978 0.510331i \(-0.170477\pi\)
\(488\) 5.82943e8 2.52033e9i 0.227068 0.981720i
\(489\) −9.73121e8 + 4.96196e9i −0.376345 + 1.91899i
\(490\) 7.56054e8 + 1.57385e9i 0.290313 + 0.604335i
\(491\) 4.79977e9i 1.82993i 0.403531 + 0.914966i \(0.367783\pi\)
−0.403531 + 0.914966i \(0.632217\pi\)
\(492\) 1.84486e9 1.56024e9i 0.698370 0.590628i
\(493\) 1.50921e9i 0.567264i
\(494\) −1.19665e9 + 5.74854e8i −0.446605 + 0.214542i
\(495\) 1.44442e8 3.54091e8i 0.0535271 0.131219i
\(496\) 1.14616e9 2.56946e8i 0.421755 0.0945489i
\(497\) 5.52826e9i 2.01995i
\(498\) −4.00886e8 1.54310e9i −0.145451 0.559874i
\(499\) 2.27878e8 0.0821015 0.0410508 0.999157i \(-0.486929\pi\)
0.0410508 + 0.999157i \(0.486929\pi\)
\(500\) 1.14950e9 1.43572e9i 0.411256 0.513659i
\(501\) −3.53633e8 + 1.80318e9i −0.125638 + 0.640631i
\(502\) −3.35937e8 + 1.61379e8i −0.118521 + 0.0569356i
\(503\) −1.71998e9 −0.602609 −0.301304 0.953528i \(-0.597422\pi\)
−0.301304 + 0.953528i \(0.597422\pi\)
\(504\) −2.82850e9 + 4.00744e9i −0.984122 + 1.39431i
\(505\) 1.12053e9 0.387172
\(506\) 1.01073e9 4.85541e8i 0.346825 0.166609i
\(507\) 3.60982e8 1.84066e9i 0.123015 0.627256i
\(508\) 1.07388e9 + 8.59795e8i 0.363441 + 0.290986i
\(509\) 2.37984e9 0.799900 0.399950 0.916537i \(-0.369027\pi\)
0.399950 + 0.916537i \(0.369027\pi\)
\(510\) −3.59180e8 1.38256e9i −0.119899 0.461518i
\(511\) 3.44382e9i 1.14174i
\(512\) 2.35786e9 + 1.91412e9i 0.776378 + 0.630267i
\(513\) 6.49459e8 9.89180e8i 0.212393 0.323493i
\(514\) −3.28294e9 + 1.57707e9i −1.06633 + 0.512248i
\(515\) 1.01215e8i 0.0326528i
\(516\) −1.91363e9 2.26272e9i −0.613176 0.725031i
\(517\) 2.02726e9i 0.645196i
\(518\) 2.14588e9 + 4.46700e9i 0.678345 + 1.41209i
\(519\) −1.16189e9 + 5.92450e9i −0.364820 + 1.86023i
\(520\) 3.24280e8 1.40201e9i 0.101137 0.437261i
\(521\) 1.09986e9i 0.340725i 0.985381 + 0.170362i \(0.0544938\pi\)
−0.985381 + 0.170362i \(0.945506\pi\)
\(522\) −8.19605e7 1.35271e9i −0.0252208 0.416254i
\(523\) 1.33421e9 0.407821 0.203910 0.978990i \(-0.434635\pi\)
0.203910 + 0.978990i \(0.434635\pi\)
\(524\) −3.13054e9 2.50644e9i −0.950516 0.761022i
\(525\) −4.87037e9 9.55159e8i −1.46894 0.288083i
\(526\) 1.79076e9 + 3.72776e9i 0.536521 + 1.11686i
\(527\) 1.97550e9 0.587948
\(528\) 3.67447e7 + 1.36692e9i 0.0108637 + 0.404132i
\(529\) −3.20708e8 −0.0941922
\(530\) 2.74760e8 + 5.71958e8i 0.0801655 + 0.166878i
\(531\) 1.18992e9 2.91702e9i 0.344894 0.845490i
\(532\) 1.79048e9 + 1.43353e9i 0.515560 + 0.412778i
\(533\) 4.09365e9 1.17102
\(534\) −7.77649e8 2.99334e9i −0.220998 0.850671i
\(535\) 1.81974e9i 0.513772i
\(536\) 1.97545e9 + 4.56913e8i 0.554100 + 0.128161i
\(537\) 1.26494e8 + 2.48076e7i 0.0352502 + 0.00691312i
\(538\) −1.88673e9 3.92755e9i −0.522363 1.08739i
\(539\) 2.81104e9i 0.773225i
\(540\) 3.97018e8 + 1.21969e9i 0.108500 + 0.333328i
\(541\) 2.75610e9i 0.748351i −0.927358 0.374175i \(-0.877926\pi\)
0.927358 0.374175i \(-0.122074\pi\)
\(542\) −3.74670e9 + 1.79986e9i −1.01077 + 0.485557i
\(543\) 5.10453e9 + 1.00108e9i 1.36822 + 0.268330i
\(544\) 3.16527e9 + 4.00872e9i 0.842976 + 1.06760i
\(545\) 1.19718e9i 0.316790i
\(546\) −8.04358e9 + 2.08966e9i −2.11483 + 0.549417i
\(547\) 1.81654e9 0.474559 0.237280 0.971441i \(-0.423744\pi\)
0.237280 + 0.971441i \(0.423744\pi\)
\(548\) −5.53522e8 4.43173e8i −0.143682 0.115038i
\(549\) −1.47557e9 + 3.61730e9i −0.380590 + 0.932998i
\(550\) −1.24715e9 + 5.99114e8i −0.319633 + 0.153547i
\(551\) −6.33696e8 −0.161380
\(552\) −1.53688e9 + 3.43267e9i −0.388914 + 0.868651i
\(553\) −8.65845e9 −2.17722
\(554\) −8.87136e7 + 4.26166e7i −0.0221669 + 0.0106487i
\(555\) 1.27169e9 + 2.49398e8i 0.315758 + 0.0619253i
\(556\) 1.07346e9 1.34075e9i 0.264864 0.330815i
\(557\) 2.69747e9 0.661400 0.330700 0.943736i \(-0.392715\pi\)
0.330700 + 0.943736i \(0.392715\pi\)
\(558\) −1.77065e9 + 1.07283e8i −0.431432 + 0.0261404i
\(559\) 5.02086e9i 1.21573i
\(560\) −2.42601e9 + 5.43861e8i −0.583759 + 0.130867i
\(561\) −4.42588e8 + 2.25676e9i −0.105835 + 0.539655i
\(562\) 4.77817e9 2.29536e9i 1.13549 0.545474i
\(563\) 2.68748e9i 0.634695i −0.948309 0.317348i \(-0.897208\pi\)
0.948309 0.317348i \(-0.102792\pi\)
\(564\) 4.39090e9 + 5.19188e9i 1.03057 + 1.21856i
\(565\) 1.38357e9i 0.322724i
\(566\) −8.78291e8 1.82831e9i −0.203601 0.423830i
\(567\) 5.18132e9 5.29410e9i 1.19371 1.21969i
\(568\) 5.03619e9 + 1.16485e9i 1.15314 + 0.266718i
\(569\) 1.62319e9i 0.369383i −0.982797 0.184692i \(-0.940871\pi\)
0.982797 0.184692i \(-0.0591286\pi\)
\(570\) 5.80518e8 1.50815e8i 0.131297 0.0341100i
\(571\) 2.25862e9 0.507712 0.253856 0.967242i \(-0.418301\pi\)
0.253856 + 0.967242i \(0.418301\pi\)
\(572\) −1.44798e9 + 1.80853e9i −0.323502 + 0.404054i
\(573\) 9.88741e8 5.04161e9i 0.219554 1.11951i
\(574\) −3.06254e9 6.37519e9i −0.675912 1.40702i
\(575\) −3.80552e9 −0.834790
\(576\) −3.05475e9 3.42114e9i −0.666036 0.745920i
\(577\) −2.78955e9 −0.604530 −0.302265 0.953224i \(-0.597743\pi\)
−0.302265 + 0.953224i \(0.597743\pi\)
\(578\) 1.70947e9 + 3.55855e9i 0.368227 + 0.766525i
\(579\) 5.04266e8 2.57126e9i 0.107965 0.550518i
\(580\) 4.29312e8 5.36211e8i 0.0913640 0.114114i
\(581\) −4.66692e9 −0.987220
\(582\) 3.51700e9 9.13692e8i 0.739507 0.192119i
\(583\) 1.02157e9i 0.213514i
\(584\) −3.13729e9 7.25643e8i −0.651793 0.150757i
\(585\) −8.20835e8 + 2.01224e9i −0.169516 + 0.415560i
\(586\) −3.79996e8 7.91024e8i −0.0780076 0.162386i
\(587\) 1.54318e9i 0.314907i −0.987526 0.157453i \(-0.949672\pi\)
0.987526 0.157453i \(-0.0503284\pi\)
\(588\) 6.08851e9 + 7.19917e9i 1.23507 + 1.46037i
\(589\) 8.29483e8i 0.167265i
\(590\) 1.43935e9 6.91442e8i 0.288526 0.138603i
\(591\) −8.50617e8 + 4.33731e9i −0.169503 + 0.864300i
\(592\) −4.52155e9 + 1.01364e9i −0.895698 + 0.200797i
\(593\) 2.51226e9i 0.494735i −0.968922 0.247368i \(-0.920434\pi\)
0.968922 0.247368i \(-0.0795655\pi\)
\(594\) 2.74136e8 2.04678e9i 0.0536677 0.400700i
\(595\) −4.18140e9 −0.813790
\(596\) 1.67483e9 2.09186e9i 0.324048 0.404736i
\(597\) 4.13211e9 + 8.10373e8i 0.794806 + 0.155874i
\(598\) −5.74382e9 + 2.75924e9i −1.09836 + 0.527637i
\(599\) 6.19749e9 1.17821 0.589104 0.808058i \(-0.299481\pi\)
0.589104 + 0.808058i \(0.299481\pi\)
\(600\) 1.89637e9 4.23561e9i 0.358421 0.800546i
\(601\) 7.79137e9 1.46404 0.732020 0.681283i \(-0.238578\pi\)
0.732020 + 0.681283i \(0.238578\pi\)
\(602\) −7.81916e9 + 3.75620e9i −1.46074 + 0.701716i
\(603\) −2.83526e9 1.15656e9i −0.526601 0.214812i
\(604\) −3.02727e9 2.42376e9i −0.559014 0.447569i
\(605\) 1.59728e9 0.293249
\(606\) 5.85645e9 1.52146e9i 1.06901 0.277720i
\(607\) 1.08410e9i 0.196748i 0.995150 + 0.0983740i \(0.0313641\pi\)
−0.995150 + 0.0983740i \(0.968636\pi\)
\(608\) −1.68320e9 + 1.32905e9i −0.303721 + 0.239817i
\(609\) −3.89279e9 7.63438e8i −0.698393 0.136966i
\(610\) −1.78489e9 + 8.57433e8i −0.318388 + 0.152949i
\(611\) 1.15205e10i 2.04328i
\(612\) −3.75451e9 6.73827e9i −0.662100 1.18828i
\(613\) 3.88620e9i 0.681418i −0.940169 0.340709i \(-0.889333\pi\)
0.940169 0.340709i \(-0.110667\pi\)
\(614\) 6.60461e8 + 1.37486e9i 0.115148 + 0.239700i
\(615\) −1.81492e9 3.55935e8i −0.314626 0.0617032i
\(616\) 3.89975e9 + 9.01998e8i 0.672209 + 0.155479i
\(617\) 2.18111e9i 0.373834i −0.982376 0.186917i \(-0.940150\pi\)
0.982376 0.186917i \(-0.0598496\pi\)
\(618\) 1.37431e8 + 5.29001e8i 0.0234220 + 0.0901565i
\(619\) 1.16433e10 1.97315 0.986574 0.163316i \(-0.0522191\pi\)
0.986574 + 0.163316i \(0.0522191\pi\)
\(620\) −7.01879e8 5.61953e8i −0.118275 0.0946954i
\(621\) 3.11734e9 4.74796e9i 0.522352 0.795586i
\(622\) 2.81052e8 + 5.85057e8i 0.0468296 + 0.0974836i
\(623\) −9.05301e9 −1.49998
\(624\) −2.08813e8 7.76794e9i −0.0344043 1.27985i
\(625\) 3.94568e9 0.646459
\(626\) −1.58040e9 3.28987e9i −0.257488 0.536004i
\(627\) −9.47583e8 1.85836e8i −0.153526 0.0301089i
\(628\) −8.03217e9 6.43089e9i −1.29412 1.03612i
\(629\) −7.79323e9 −1.24865
\(630\) 3.74781e9 2.27079e8i 0.597153 0.0361814i
\(631\) 1.06242e10i 1.68342i 0.539927 + 0.841712i \(0.318452\pi\)
−0.539927 + 0.841712i \(0.681548\pi\)
\(632\) 1.82441e9 7.88777e9i 0.287484 1.24292i
\(633\) 8.52374e8 4.34627e9i 0.133573 0.681089i
\(634\) 3.14789e9 + 6.55285e9i 0.490577 + 1.02122i
\(635\) 1.05303e9i 0.163205i
\(636\) 2.21264e9 + 2.61627e9i 0.341045 + 0.403258i
\(637\) 1.59746e10i 2.44874i
\(638\) −9.96825e8 + 4.78859e8i −0.151966 + 0.0730021i
\(639\) −7.22819e9 2.94853e9i −1.09591 0.447047i
\(640\) 1.57286e7 2.32467e9i 0.00237171 0.350534i
\(641\) 6.89527e9i 1.03407i 0.855965 + 0.517033i \(0.172964\pi\)
−0.855965 + 0.517033i \(0.827036\pi\)
\(642\) 2.47085e9 + 9.51086e9i 0.368531 + 1.41856i
\(643\) −9.21146e9 −1.36644 −0.683219 0.730213i \(-0.739421\pi\)
−0.683219 + 0.730213i \(0.739421\pi\)
\(644\) 8.59413e9 + 6.88081e9i 1.26795 + 1.01517i
\(645\) −4.36554e8 + 2.22600e9i −0.0640588 + 0.326637i
\(646\) −3.25126e9 + 1.56186e9i −0.474502 + 0.227943i
\(647\) 1.53229e8 0.0222421 0.0111210 0.999938i \(-0.496460\pi\)
0.0111210 + 0.999938i \(0.496460\pi\)
\(648\) 3.73112e9 + 5.83565e9i 0.538675 + 0.842513i
\(649\) −2.57080e9 −0.369158
\(650\) 7.08735e9 3.40465e9i 1.01225 0.486269i
\(651\) −9.99311e8 + 5.09551e9i −0.141960 + 0.723859i
\(652\) −8.64996e9 + 1.08038e10i −1.22222 + 1.52655i
\(653\) −5.61194e9 −0.788710 −0.394355 0.918958i \(-0.629032\pi\)
−0.394355 + 0.918958i \(0.629032\pi\)
\(654\) 1.62554e9 + 6.25707e9i 0.227235 + 0.874679i
\(655\) 3.06975e9i 0.426833i
\(656\) 6.45305e9 1.44664e9i 0.892486 0.200077i
\(657\) 4.50279e9 + 1.83678e9i 0.619445 + 0.252685i
\(658\) 1.79413e10 8.61874e9i 2.45507 1.17938i
\(659\) 1.89758e9i 0.258287i 0.991626 + 0.129143i \(0.0412228\pi\)
−0.991626 + 0.129143i \(0.958777\pi\)
\(660\) 7.99210e8 6.75911e8i 0.108207 0.0915137i
\(661\) 2.56052e9i 0.344844i 0.985023 + 0.172422i \(0.0551592\pi\)
−0.985023 + 0.172422i \(0.944841\pi\)
\(662\) −5.44040e9 1.13251e10i −0.728832 1.51719i
\(663\) 2.51514e9 1.28248e10i 0.335170 1.70904i
\(664\) 9.83361e8 4.25152e9i 0.130354 0.563581i
\(665\) 1.75571e9i 0.231514i
\(666\) 6.98511e9 4.23227e8i 0.916249 0.0555153i
\(667\) −3.04168e9 −0.396892
\(668\) −3.14341e9 + 3.92612e9i −0.408022 + 0.509619i
\(669\) 6.63911e8 + 1.30204e8i 0.0857271 + 0.0168125i
\(670\) −6.72060e8 1.39901e9i −0.0863270 0.179704i
\(671\) 3.18797e9 0.407366
\(672\) −1.19411e10 + 6.13654e9i −1.51793 + 0.780066i
\(673\) 9.40490e9 1.18933 0.594664 0.803974i \(-0.297285\pi\)
0.594664 + 0.803974i \(0.297285\pi\)
\(674\) 1.73519e9 + 3.61209e9i 0.218292 + 0.454411i
\(675\) −3.84651e9 + 5.85856e9i −0.481398 + 0.733209i
\(676\) 3.20873e9 4.00770e9i 0.399503 0.498979i
\(677\) 1.31467e10 1.62838 0.814188 0.580601i \(-0.197182\pi\)
0.814188 + 0.580601i \(0.197182\pi\)
\(678\) −1.87862e9 7.23122e9i −0.231492 0.891062i
\(679\) 1.06368e10i 1.30396i
\(680\) 8.81058e8 3.80922e9i 0.107454 0.464574i
\(681\) −1.60971e9 3.15689e8i −0.195313 0.0383041i
\(682\) 6.26808e8 + 1.30480e9i 0.0756640 + 0.157507i
\(683\) 1.03400e9i 0.124179i −0.998071 0.0620894i \(-0.980224\pi\)
0.998071 0.0620894i \(-0.0197764\pi\)
\(684\) 2.82930e9 1.57647e9i 0.338052 0.188360i
\(685\) 5.42773e8i 0.0645211i
\(686\) 1.18705e10 5.70242e9i 1.40390 0.674411i
\(687\) 4.66984e8 + 9.15831e7i 0.0549482 + 0.0107762i
\(688\) −1.77430e9 7.91465e9i −0.207715 0.926557i
\(689\) 5.80538e9i 0.676181i
\(690\) 2.78643e9 7.23895e8i 0.322906 0.0838887i
\(691\) −5.74897e9 −0.662853 −0.331426 0.943481i \(-0.607530\pi\)
−0.331426 + 0.943481i \(0.607530\pi\)
\(692\) −1.03279e10 + 1.28996e10i −1.18479 + 1.47980i
\(693\) −5.59711e9 2.28318e9i −0.638848 0.260600i
\(694\) −4.28504e9 + 2.05847e9i −0.486628 + 0.233768i
\(695\) −1.31471e9 −0.148554
\(696\) 1.51573e9 3.38543e9i 0.170408 0.380611i
\(697\) 1.11223e10 1.24417
\(698\) −2.77343e8 + 1.33232e8i −0.0308691 + 0.0148290i
\(699\) −6.39417e9 1.25400e9i −0.708132 0.138876i
\(700\) −1.06044e10 8.49030e9i −1.16854 0.935578i
\(701\) −1.30713e10 −1.43319 −0.716596 0.697488i \(-0.754301\pi\)
−0.716596 + 0.697488i \(0.754301\pi\)
\(702\) −1.55786e9 + 1.16315e10i −0.169961 + 1.26898i
\(703\) 3.27227e9i 0.355226i
\(704\) −1.64342e9 + 3.36258e9i −0.177519 + 0.363219i
\(705\) 1.00169e9 5.10762e9i 0.107664 0.548980i
\(706\) −9.08045e9 + 4.36211e9i −0.971161 + 0.466531i
\(707\) 1.77122e10i 1.88497i
\(708\) 6.58393e9 5.56819e9i 0.697218 0.589654i
\(709\) 2.53582e9i 0.267213i −0.991034 0.133606i \(-0.957344\pi\)
0.991034 0.133606i \(-0.0426558\pi\)
\(710\) −1.71335e9 3.56662e9i −0.179656 0.373983i
\(711\) −4.61804e9 + 1.13209e10i −0.481853 + 1.18124i
\(712\) 1.90755e9 8.24722e9i 0.198060 0.856303i
\(713\) 3.98144e9i 0.411364i
\(714\) −2.18541e10 + 5.67754e9i −2.24693 + 0.583736i
\(715\) 1.77341e9 0.181442
\(716\) 2.75419e8 + 2.20512e8i 0.0280413 + 0.0224510i
\(717\) −5.51135e8 + 2.81025e9i −0.0558394 + 0.284726i
\(718\) −5.55970e9 1.15734e10i −0.560552 1.16688i
\(719\) 9.86480e9 0.989777 0.494889 0.868956i \(-0.335209\pi\)
0.494889 + 0.868956i \(0.335209\pi\)
\(720\) −5.82830e8 + 3.46207e9i −0.0581940 + 0.345678i
\(721\) 1.59990e9 0.158972
\(722\) 3.72326e9 + 7.75058e9i 0.368165 + 0.766397i
\(723\) −1.25598e9 + 6.40429e9i −0.123595 + 0.630213i
\(724\) 1.11142e10 + 8.89849e9i 1.08841 + 0.871428i
\(725\) 3.75315e9 0.365775
\(726\) 8.34819e9 2.16880e9i 0.809682 0.210350i
\(727\) 6.26064e9i 0.604294i 0.953261 + 0.302147i \(0.0977033\pi\)
−0.953261 + 0.302147i \(0.902297\pi\)
\(728\) −2.21616e10 5.12589e9i −2.12883 0.492390i
\(729\) −4.15853e9 9.59821e9i −0.397551 0.917580i
\(730\) 1.06733e9 + 2.22182e9i 0.101547 + 0.211387i
\(731\) 1.36415e10i 1.29167i
\(732\) −8.16450e9 + 6.90492e9i −0.769380 + 0.650683i
\(733\) 1.23202e10i 1.15546i −0.816228 0.577730i \(-0.803939\pi\)
0.816228 0.577730i \(-0.196061\pi\)
\(734\) 1.06081e10 5.09595e9i 0.990147 0.475651i
\(735\) 1.38896e9 7.08234e9i 0.129028 0.657917i
\(736\) −8.07921e9 + 6.37933e9i −0.746959 + 0.589797i
\(737\) 2.49874e9i 0.229925i
\(738\) −9.96898e9 + 6.04018e8i −0.912963 + 0.0553162i
\(739\) −4.48620e9 −0.408906 −0.204453 0.978876i \(-0.565542\pi\)
−0.204453 + 0.978876i \(0.565542\pi\)
\(740\) 2.76887e9 + 2.21687e9i 0.251184 + 0.201108i
\(741\) 5.38494e9 + 1.05607e9i 0.486202 + 0.0953521i
\(742\) 9.04092e9 4.34312e9i 0.812454 0.390290i
\(743\) 5.92519e9 0.529958 0.264979 0.964254i \(-0.414635\pi\)
0.264979 + 0.964254i \(0.414635\pi\)
\(744\) −4.43140e9 1.98403e9i −0.394489 0.176621i
\(745\) −2.05124e9 −0.181748
\(746\) −3.25104e8 + 1.56175e8i −0.0286706 + 0.0137729i
\(747\) −2.48913e9 + 6.10199e9i −0.218487 + 0.535611i
\(748\) −3.93411e9 + 4.91370e9i −0.343709 + 0.429293i
\(749\) 2.87645e10 2.50133
\(750\) −7.35808e9 + 1.91158e9i −0.636869 + 0.165454i
\(751\) 8.98243e9i 0.773845i −0.922112 0.386923i \(-0.873538\pi\)
0.922112 0.386923i \(-0.126462\pi\)
\(752\) 4.07120e9 + 1.81604e10i 0.349108 + 1.55727i
\(753\) 1.51172e9 + 2.96472e8i 0.129029 + 0.0253047i
\(754\) 5.66477e9 2.72127e9i 0.481263 0.231191i
\(755\) 2.96849e9i 0.251027i
\(756\) 1.92796e10 6.27564e9i 1.62283 0.528241i
\(757\) 9.92682e9i 0.831715i 0.909430 + 0.415857i \(0.136518\pi\)
−0.909430 + 0.415857i \(0.863482\pi\)
\(758\) −2.61668e8 5.44705e8i −0.0218227 0.0454275i
\(759\) −4.54830e9 8.91996e8i −0.377575 0.0740485i
\(760\) 1.59944e9 + 3.69944e8i 0.132166 + 0.0305695i
\(761\) 1.63216e9i 0.134250i −0.997745 0.0671252i \(-0.978617\pi\)
0.997745 0.0671252i \(-0.0213827\pi\)
\(762\) −1.42981e9 5.50367e9i −0.117068 0.450619i
\(763\) 1.89238e10 1.54231
\(764\) 8.78881e9 1.09772e10i 0.713023 0.890565i
\(765\) −2.23018e9 + 5.46717e9i −0.180104 + 0.441517i
\(766\) 6.39341e9 + 1.33089e10i 0.513963 + 1.06990i
\(767\) 1.46094e10 1.16909
\(768\) −3.07425e9 1.21712e10i −0.244892 0.969550i
\(769\) −2.07502e10 −1.64543 −0.822717 0.568451i \(-0.807543\pi\)
−0.822717 + 0.568451i \(0.807543\pi\)
\(770\) −1.32672e9 2.76179e9i −0.104728 0.218009i
\(771\) 1.47732e10 + 2.89727e9i 1.16087 + 0.227666i
\(772\) 4.48236e9 5.59847e9i 0.350628 0.437934i
\(773\) −8.12995e9 −0.633082 −0.316541 0.948579i \(-0.602521\pi\)
−0.316541 + 0.948579i \(0.602521\pi\)
\(774\) 7.40827e8 + 1.22269e10i 0.0574280 + 0.947817i
\(775\)