Properties

Label 43.8.g.a.24.1
Level 43
Weight 8
Character 43.24
Analytic conductor 13.433
Analytic rank 0
Dimension 300
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 43.g (of order \(21\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.4325560958\)
Analytic rank: \(0\)
Dimension: \(300\)
Relative dimension: \(25\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 24.1
Character \(\chi\) \(=\) 43.24
Dual form 43.8.g.a.9.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-13.3861 + 16.7857i) q^{2} +(9.91222 - 1.49403i) q^{3} +(-74.0876 - 324.599i) q^{4} +(247.262 - 168.580i) q^{5} +(-107.608 + 186.382i) q^{6} +(-560.464 - 970.753i) q^{7} +(3964.38 + 1909.15i) q^{8} +(-1993.82 + 615.011i) q^{9} +O(q^{10})\) \(q+(-13.3861 + 16.7857i) q^{2} +(9.91222 - 1.49403i) q^{3} +(-74.0876 - 324.599i) q^{4} +(247.262 - 168.580i) q^{5} +(-107.608 + 186.382i) q^{6} +(-560.464 - 970.753i) q^{7} +(3964.38 + 1909.15i) q^{8} +(-1993.82 + 615.011i) q^{9} +(-480.145 + 6407.09i) q^{10} +(-736.137 + 3225.23i) q^{11} +(-1219.33 - 3106.81i) q^{12} +(725.353 + 9679.17i) q^{13} +(23797.2 + 3586.85i) q^{14} +(2199.05 - 2040.42i) q^{15} +(-46717.3 + 22497.8i) q^{16} +(2017.35 + 1375.41i) q^{17} +(16366.1 - 41700.2i) q^{18} +(-28988.4 - 8941.74i) q^{19} +(-73040.0 - 67771.2i) q^{20} +(-7005.78 - 8784.97i) q^{21} +(-44283.6 - 55529.8i) q^{22} +(83611.8 + 77580.4i) q^{23} +(42148.2 + 13001.0i) q^{24} +(4176.83 - 10642.4i) q^{25} +(-172181. - 117391. i) q^{26} +(-38596.2 + 18586.9i) q^{27} +(-273582. + 253847. i) q^{28} +(-65789.8 - 9916.21i) q^{29} +(4813.06 + 64225.8i) q^{30} +(96263.4 + 245275. i) q^{31} +(122394. - 536243. i) q^{32} +(-2478.18 + 33069.0i) q^{33} +(-50091.7 + 15451.2i) q^{34} +(-302231. - 145547. i) q^{35} +(347349. + 601626. i) q^{36} +(84355.9 - 146109. i) q^{37} +(538135. - 366894. i) q^{38} +(21650.8 + 94858.3i) q^{39} +(1.30208e6 - 196258. i) q^{40} +(-68961.3 + 86474.8i) q^{41} +241242. q^{42} +(-64625.6 + 517341. i) q^{43} +1.10144e6 q^{44} +(-389316. + 488187. i) q^{45} +(-2.42148e6 + 364979. i) q^{46} +(-102094. - 447305. i) q^{47} +(-429459. + 292800. i) q^{48} +(-216469. + 374936. i) q^{49} +(122728. + 212571. i) q^{50} +(22051.3 + 10619.4i) q^{51} +(3.08811e6 - 952555. i) q^{52} +(-65740.6 + 877247. i) q^{53} +(204659. - 896669. i) q^{54} +(361691. + 921574. i) q^{55} +(-368587. - 4.91845e6i) q^{56} +(-300699. - 45323.0i) q^{57} +(1.04712e6 - 971585. i) q^{58} +(-2.67214e6 + 1.28683e6i) q^{59} +(-825240. - 562639. i) q^{60} +(578991. - 1.47524e6i) q^{61} +(-5.40570e6 - 1.66744e6i) q^{62} +(1.71449e6 + 1.59081e6i) q^{63} +(3.22465e6 + 4.04359e6i) q^{64} +(1.81107e6 + 2.27101e6i) q^{65} +(-521911. - 484263. i) q^{66} +(-3.26436e6 - 1.00692e6i) q^{67} +(296995. - 756731. i) q^{68} +(944685. + 644076. i) q^{69} +(6.48880e6 - 3.12484e6i) q^{70} +(401770. - 372788. i) q^{71} +(-9.07840e6 - 1.36835e6i) q^{72} +(-174899. - 2.33387e6i) q^{73} +(1.32333e6 + 3.37180e6i) q^{74} +(25501.6 - 111730. i) q^{75} +(-754798. + 1.00721e7i) q^{76} +(3.54348e6 - 1.09302e6i) q^{77} +(-1.88208e6 - 906362. i) q^{78} +(3.18626e6 + 5.51876e6i) q^{79} +(-7.75870e6 + 1.34385e7i) q^{80} +(3.41550e6 - 2.32865e6i) q^{81} +(-528412. - 2.31512e6i) q^{82} +(559090. - 84269.3i) q^{83} +(-2.33255e6 + 2.92492e6i) q^{84} +730681. q^{85} +(-7.81883e6 - 8.00998e6i) q^{86} -666938. q^{87} +(-9.07576e6 + 1.13806e7i) q^{88} +(-2.04141e6 + 307693. i) q^{89} +(-2.98311e6 - 1.30699e7i) q^{90} +(8.98955e6 - 6.12897e6i) q^{91} +(1.89879e7 - 3.28880e7i) q^{92} +(1.32063e6 + 2.28740e6i) q^{93} +(8.87495e6 + 4.27395e6i) q^{94} +(-8.67513e6 + 2.67592e6i) q^{95} +(412034. - 5.49821e6i) q^{96} +(-1.48789e6 + 6.51888e6i) q^{97} +(-3.39586e6 - 8.65252e6i) q^{98} +(-515828. - 6.88325e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 300q - 40q^{2} - 12q^{3} - 3028q^{4} + 235q^{5} + 1274q^{6} - 4122q^{7} + 762q^{8} + 8097q^{9} + O(q^{10}) \) \( 300q - 40q^{2} - 12q^{3} - 3028q^{4} + 235q^{5} + 1274q^{6} - 4122q^{7} + 762q^{8} + 8097q^{9} - 1681q^{10} + 4580q^{11} + 9330q^{12} - 20444q^{13} - 45798q^{14} + 50477q^{15} - 74504q^{16} - 25312q^{17} + 2046q^{18} + 4046q^{19} + 140781q^{20} + 100555q^{21} + 95810q^{22} + 1648q^{23} - 292592q^{24} + 419068q^{25} + 393435q^{26} + 274140q^{27} + 233644q^{28} + 605697q^{29} - 1216016q^{30} + 358580q^{31} - 19194q^{32} + 1280291q^{33} + 1137255q^{34} + 652739q^{35} - 8980975q^{36} - 2360047q^{37} - 308490q^{38} + 536339q^{39} + 3057993q^{40} - 1376320q^{41} + 8417790q^{42} + 7173000q^{43} - 3856780q^{44} + 2761486q^{45} - 7073993q^{46} + 1437090q^{47} - 9543469q^{48} - 16053170q^{49} - 3046893q^{50} + 2972901q^{51} + 17415142q^{52} + 3320604q^{53} + 6000486q^{54} + 13427750q^{55} - 5450793q^{56} + 3333100q^{57} - 7876190q^{58} - 7084765q^{59} + 7356443q^{60} + 3354606q^{61} - 719427q^{62} + 14716815q^{63} - 16086234q^{64} - 19914646q^{65} - 8293345q^{66} + 13025470q^{67} - 22191927q^{68} - 33964295q^{69} + 8094727q^{70} + 30843495q^{71} + 93841607q^{72} - 3067637q^{73} + 18179570q^{74} - 41508571q^{75} - 19751872q^{76} - 15169179q^{77} - 69509396q^{78} - 12090149q^{79} - 69662530q^{80} + 3387954q^{81} + 39226888q^{82} + 16408777q^{83} + 98603231q^{84} - 13423424q^{85} + 111906660q^{86} + 49022010q^{87} + 76213954q^{88} - 12540205q^{89} - 92608607q^{90} - 59091937q^{91} - 50489370q^{92} - 52218334q^{93} - 3441600q^{94} - 79947551q^{95} - 23449784q^{96} - 116467587q^{97} + 73909552q^{98} - 20061115q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{20}{21}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −13.3861 + 16.7857i −1.18318 + 1.48366i −0.344706 + 0.938711i \(0.612021\pi\)
−0.838471 + 0.544946i \(0.816550\pi\)
\(3\) 9.91222 1.49403i 0.211956 0.0319473i −0.0422056 0.999109i \(-0.513438\pi\)
0.254162 + 0.967162i \(0.418200\pi\)
\(4\) −74.0876 324.599i −0.578809 2.53593i
\(5\) 247.262 168.580i 0.884631 0.603131i −0.0334869 0.999439i \(-0.510661\pi\)
0.918118 + 0.396308i \(0.129709\pi\)
\(6\) −107.608 + 186.382i −0.203383 + 0.352270i
\(7\) −560.464 970.753i −0.617597 1.06971i −0.989923 0.141607i \(-0.954773\pi\)
0.372326 0.928102i \(-0.378560\pi\)
\(8\) 3964.38 + 1909.15i 2.73754 + 1.31833i
\(9\) −1993.82 + 615.011i −0.911668 + 0.281212i
\(10\) −480.145 + 6407.09i −0.151835 + 2.02610i
\(11\) −736.137 + 3225.23i −0.166757 + 0.730611i 0.820522 + 0.571615i \(0.193683\pi\)
−0.987279 + 0.158996i \(0.949174\pi\)
\(12\) −1219.33 3106.81i −0.203698 0.519015i
\(13\) 725.353 + 9679.17i 0.0915689 + 1.22190i 0.833918 + 0.551888i \(0.186093\pi\)
−0.742349 + 0.670013i \(0.766288\pi\)
\(14\) 23797.2 + 3586.85i 2.31781 + 0.349353i
\(15\) 2199.05 2040.42i 0.168235 0.156099i
\(16\) −46717.3 + 22497.8i −2.85139 + 1.37316i
\(17\) 2017.35 + 1375.41i 0.0995889 + 0.0678985i 0.612091 0.790788i \(-0.290329\pi\)
−0.512502 + 0.858686i \(0.671281\pi\)
\(18\) 16366.1 41700.2i 0.661442 1.68533i
\(19\) −28988.4 8941.74i −0.969587 0.299078i −0.230788 0.973004i \(-0.574130\pi\)
−0.738799 + 0.673926i \(0.764607\pi\)
\(20\) −73040.0 67771.2i −2.04153 1.89426i
\(21\) −7005.78 8784.97i −0.165078 0.207001i
\(22\) −44283.6 55529.8i −0.886672 1.11185i
\(23\) 83611.8 + 77580.4i 1.43291 + 1.32955i 0.860365 + 0.509679i \(0.170236\pi\)
0.572549 + 0.819870i \(0.305955\pi\)
\(24\) 42148.2 + 13001.0i 0.622356 + 0.191972i
\(25\) 4176.83 10642.4i 0.0534634 0.136223i
\(26\) −172181. 117391.i −1.92123 1.30987i
\(27\) −38596.2 + 18586.9i −0.377373 + 0.181733i
\(28\) −273582. + 253847.i −2.35523 + 2.18534i
\(29\) −65789.8 9916.21i −0.500917 0.0755010i −0.106276 0.994337i \(-0.533893\pi\)
−0.394640 + 0.918836i \(0.629131\pi\)
\(30\) 4813.06 + 64225.8i 0.0325459 + 0.434295i
\(31\) 96263.4 + 245275.i 0.580357 + 1.47873i 0.855748 + 0.517393i \(0.173097\pi\)
−0.275391 + 0.961332i \(0.588807\pi\)
\(32\) 122394. 536243.i 0.660290 2.89292i
\(33\) −2478.18 + 33069.0i −0.0120042 + 0.160185i
\(34\) −50091.7 + 15451.2i −0.218569 + 0.0674197i
\(35\) −302231. 145547.i −1.19152 0.573806i
\(36\) 347349. + 601626.i 1.24082 + 2.14916i
\(37\) 84355.9 146109.i 0.273785 0.474209i −0.696043 0.718000i \(-0.745058\pi\)
0.969828 + 0.243791i \(0.0783910\pi\)
\(38\) 538135. 366894.i 1.59092 1.08467i
\(39\) 21650.8 + 94858.3i 0.0584451 + 0.256065i
\(40\) 1.30208e6 196258.i 3.21684 0.484860i
\(41\) −68961.3 + 86474.8i −0.156265 + 0.195950i −0.853801 0.520600i \(-0.825708\pi\)
0.697536 + 0.716550i \(0.254280\pi\)
\(42\) 241242. 0.502435
\(43\) −64625.6 + 517341.i −0.123955 + 0.992288i
\(44\) 1.10144e6 1.94930
\(45\) −389316. + 488187.i −0.636882 + 0.798624i
\(46\) −2.42148e6 + 364979.i −3.66799 + 0.552860i
\(47\) −102094. 447305.i −0.143436 0.628436i −0.994622 0.103571i \(-0.966973\pi\)
0.851186 0.524865i \(-0.175884\pi\)
\(48\) −429459. + 292800.i −0.560503 + 0.382144i
\(49\) −216469. + 374936.i −0.262851 + 0.455272i
\(50\) 122728. + 212571.i 0.138851 + 0.240497i
\(51\) 22051.3 + 10619.4i 0.0232777 + 0.0112099i
\(52\) 3.08811e6 952555.i 3.04565 0.939460i
\(53\) −65740.6 + 877247.i −0.0606552 + 0.809387i 0.881066 + 0.472993i \(0.156826\pi\)
−0.941721 + 0.336394i \(0.890793\pi\)
\(54\) 204659. 896669.i 0.176869 0.774915i
\(55\) 361691. + 921574.i 0.293135 + 0.746897i
\(56\) −368587. 4.91845e6i −0.280467 3.74257i
\(57\) −300699. 45323.0i −0.215065 0.0324158i
\(58\) 1.04712e6 971585.i 0.704691 0.653857i
\(59\) −2.67214e6 + 1.28683e6i −1.69386 + 0.815719i −0.698924 + 0.715196i \(0.746337\pi\)
−0.994935 + 0.100523i \(0.967948\pi\)
\(60\) −825240. 562639.i −0.493232 0.336280i
\(61\) 578991. 1.47524e6i 0.326601 0.832165i −0.669407 0.742896i \(-0.733452\pi\)
0.996008 0.0892692i \(-0.0284531\pi\)
\(62\) −5.40570e6 1.66744e6i −2.88059 0.888543i
\(63\) 1.71449e6 + 1.59081e6i 0.863858 + 0.801543i
\(64\) 3.22465e6 + 4.04359e6i 1.53763 + 1.92813i
\(65\) 1.81107e6 + 2.27101e6i 0.817971 + 1.02570i
\(66\) −521911. 484263.i −0.223457 0.207337i
\(67\) −3.26436e6 1.00692e6i −1.32598 0.409010i −0.450720 0.892665i \(-0.648833\pi\)
−0.875259 + 0.483655i \(0.839309\pi\)
\(68\) 296995. 756731.i 0.114543 0.291851i
\(69\) 944685. + 644076.i 0.346191 + 0.236029i
\(70\) 6.48880e6 3.12484e6i 2.26111 1.08889i
\(71\) 401770. 372788.i 0.133221 0.123611i −0.610748 0.791825i \(-0.709131\pi\)
0.743970 + 0.668214i \(0.232941\pi\)
\(72\) −9.07840e6 1.36835e6i −2.86646 0.432049i
\(73\) −174899. 2.33387e6i −0.0526209 0.702177i −0.959666 0.281143i \(-0.909286\pi\)
0.907045 0.421034i \(-0.138333\pi\)
\(74\) 1.32333e6 + 3.37180e6i 0.379628 + 0.967277i
\(75\) 25501.6 111730.i 0.00697997 0.0305813i
\(76\) −754798. + 1.00721e7i −0.197235 + 2.63191i
\(77\) 3.54348e6 1.09302e6i 0.884529 0.272841i
\(78\) −1.88208e6 906362.i −0.449063 0.216257i
\(79\) 3.18626e6 + 5.51876e6i 0.727086 + 1.25935i 0.958110 + 0.286402i \(0.0924592\pi\)
−0.231024 + 0.972948i \(0.574207\pi\)
\(80\) −7.75870e6 + 1.34385e7i −1.69424 + 2.93450i
\(81\) 3.41550e6 2.32865e6i 0.714096 0.486862i
\(82\) −528412. 2.31512e6i −0.105834 0.463688i
\(83\) 559090. 84269.3i 0.107327 0.0161769i −0.0951592 0.995462i \(-0.530336\pi\)
0.202486 + 0.979285i \(0.435098\pi\)
\(84\) −2.33255e6 + 2.92492e6i −0.429391 + 0.538440i
\(85\) 730681. 0.129051
\(86\) −7.81883e6 8.00998e6i −1.32555 1.35796i
\(87\) −666938. −0.108585
\(88\) −9.07576e6 + 1.13806e7i −1.41969 + 1.78024i
\(89\) −2.04141e6 + 307693.i −0.306949 + 0.0462651i −0.300710 0.953715i \(-0.597224\pi\)
−0.00623815 + 0.999981i \(0.501986\pi\)
\(90\) −2.98311e6 1.30699e7i −0.431341 1.88983i
\(91\) 8.98955e6 6.12897e6i 1.25053 0.852595i
\(92\) 1.89879e7 3.28880e7i 2.54226 4.40332i
\(93\) 1.32063e6 + 2.28740e6i 0.170252 + 0.294884i
\(94\) 8.87495e6 + 4.27395e6i 1.10209 + 0.530740i
\(95\) −8.67513e6 + 2.67592e6i −1.03811 + 0.320214i
\(96\) 412034. 5.49821e6i 0.0475318 0.634267i
\(97\) −1.48789e6 + 6.51888e6i −0.165528 + 0.725224i 0.822221 + 0.569169i \(0.192735\pi\)
−0.987748 + 0.156055i \(0.950122\pi\)
\(98\) −3.39586e6 8.65252e6i −0.364468 0.928648i
\(99\) −515828. 6.88325e6i −0.0534296 0.712968i
\(100\) −3.76396e6 567325.i −0.376396 0.0567325i
\(101\) 3.46087e6 3.21122e6i 0.334242 0.310131i −0.495140 0.868813i \(-0.664883\pi\)
0.829382 + 0.558682i \(0.188693\pi\)
\(102\) −473435. + 227994.i −0.0441733 + 0.0212727i
\(103\) −1.30961e7 8.92880e6i −1.18090 0.805124i −0.196403 0.980523i \(-0.562926\pi\)
−0.984497 + 0.175399i \(0.943878\pi\)
\(104\) −1.56034e7 + 3.97567e7i −1.36020 + 3.46572i
\(105\) −3.21323e6 991151.i −0.270882 0.0835559i
\(106\) −1.38452e7 1.28464e7i −1.12909 1.04764i
\(107\) 2.52180e6 + 3.16224e6i 0.199007 + 0.249547i 0.871314 0.490725i \(-0.163268\pi\)
−0.672308 + 0.740272i \(0.734697\pi\)
\(108\) 8.89279e6 + 1.11512e7i 0.679290 + 0.851802i
\(109\) 1.75864e7 + 1.63178e7i 1.30072 + 1.20689i 0.964187 + 0.265223i \(0.0854455\pi\)
0.336535 + 0.941671i \(0.390745\pi\)
\(110\) −2.03109e7 6.26507e6i −1.45497 0.448799i
\(111\) 617864. 1.57429e6i 0.0428808 0.109258i
\(112\) 4.80232e7 + 3.27417e7i 3.22989 + 2.20210i
\(113\) −9.50369e6 + 4.57673e6i −0.619609 + 0.298388i −0.717231 0.696836i \(-0.754591\pi\)
0.0976220 + 0.995224i \(0.468876\pi\)
\(114\) 4.78596e6 4.44073e6i 0.302554 0.280729i
\(115\) 3.37525e7 + 5.08737e6i 2.06949 + 0.311926i
\(116\) 1.65541e6 + 2.20900e7i 0.0984699 + 1.31399i
\(117\) −7.39902e6 1.88524e7i −0.427094 1.08822i
\(118\) 1.41692e7 6.20794e7i 0.793887 3.47824i
\(119\) 204527. 2.72922e6i 0.0111259 0.148465i
\(120\) 1.26133e7 3.89070e6i 0.666340 0.205539i
\(121\) 7.69714e6 + 3.70675e6i 0.394985 + 0.190215i
\(122\) 1.70125e7 + 2.94665e7i 0.848221 + 1.46916i
\(123\) −554364. + 960187.i −0.0268613 + 0.0465252i
\(124\) 7.24841e7 4.94188e7i 3.41403 2.32764i
\(125\) 4.44118e6 + 1.94581e7i 0.203382 + 0.891076i
\(126\) −4.96532e7 + 7.48401e6i −2.21131 + 0.333302i
\(127\) −1.10251e7 + 1.38251e7i −0.477606 + 0.598899i −0.961015 0.276495i \(-0.910827\pi\)
0.483409 + 0.875395i \(0.339398\pi\)
\(128\) −4.06356e7 −1.71266
\(129\) 132338. + 5.22455e6i 0.00542777 + 0.214282i
\(130\) −6.23635e7 −2.48960
\(131\) −117280. + 147065.i −0.00455801 + 0.00571556i −0.784105 0.620628i \(-0.786878\pi\)
0.779547 + 0.626343i \(0.215449\pi\)
\(132\) 1.09178e7 1.64559e6i 0.413166 0.0622747i
\(133\) 7.56675e6 + 3.31521e7i 0.278887 + 1.22189i
\(134\) 6.05990e7 4.13157e7i 2.17570 1.48337i
\(135\) −6.40997e6 + 1.11024e7i −0.224227 + 0.388372i
\(136\) 5.37171e6 + 9.30407e6i 0.183116 + 0.317166i
\(137\) −3.61854e7 1.74260e7i −1.20230 0.578995i −0.277966 0.960591i \(-0.589660\pi\)
−0.924329 + 0.381596i \(0.875375\pi\)
\(138\) −2.34569e7 + 7.23550e6i −0.759791 + 0.234364i
\(139\) 3.18466e6 4.24963e7i 0.100580 1.34214i −0.687326 0.726349i \(-0.741216\pi\)
0.787906 0.615796i \(-0.211165\pi\)
\(140\) −2.48528e7 + 1.08887e8i −0.765468 + 3.35373i
\(141\) −1.68027e6 4.28125e6i −0.0504791 0.128619i
\(142\) 879355. + 1.17342e7i 0.0257724 + 0.343909i
\(143\) −3.17515e7 4.78577e6i −0.908004 0.136860i
\(144\) 7.93093e7 7.35882e7i 2.21338 2.05371i
\(145\) −1.79390e7 + 8.63896e6i −0.488663 + 0.235328i
\(146\) 4.15168e7 + 2.83057e7i 1.10405 + 0.752729i
\(147\) −1.58553e6 + 4.03986e6i −0.0411683 + 0.104895i
\(148\) −5.36765e7 1.65570e7i −1.36103 0.419822i
\(149\) −2.34973e7 2.18023e7i −0.581925 0.539947i 0.333337 0.942808i \(-0.391825\pi\)
−0.915261 + 0.402861i \(0.868016\pi\)
\(150\) 1.53409e6 + 1.92369e6i 0.0371135 + 0.0465389i
\(151\) 1.88820e7 + 2.36773e7i 0.446302 + 0.559645i 0.953192 0.302366i \(-0.0977763\pi\)
−0.506890 + 0.862011i \(0.669205\pi\)
\(152\) −9.78501e7 9.07916e7i −2.26000 2.09697i
\(153\) −4.86813e6 1.50162e6i −0.109886 0.0338953i
\(154\) −2.90864e7 + 7.41109e7i −0.641752 + 1.63516i
\(155\) 6.51508e7 + 4.44191e7i 1.40527 + 0.958094i
\(156\) 2.91869e7 1.40556e7i 0.615533 0.296425i
\(157\) −3.43989e7 + 3.19175e7i −0.709407 + 0.658233i −0.949949 0.312406i \(-0.898865\pi\)
0.240542 + 0.970639i \(0.422675\pi\)
\(158\) −1.35288e8 2.03913e7i −2.72871 0.411288i
\(159\) 658995. + 8.79368e6i 0.0130015 + 0.173493i
\(160\) −6.01366e7 1.53226e8i −1.16070 2.95741i
\(161\) 2.84500e7 1.24647e8i 0.537268 2.35393i
\(162\) −6.63238e6 + 8.85029e7i −0.122565 + 1.63552i
\(163\) −7.06211e7 + 2.17837e7i −1.27725 + 0.393981i −0.857888 0.513836i \(-0.828224\pi\)
−0.419367 + 0.907817i \(0.637748\pi\)
\(164\) 3.31788e7 + 1.59781e7i 0.587364 + 0.282860i
\(165\) 4.96202e6 + 8.59447e6i 0.0859933 + 0.148945i
\(166\) −6.06953e6 + 1.05127e7i −0.102986 + 0.178376i
\(167\) 1.36423e7 9.30114e6i 0.226662 0.154536i −0.444665 0.895697i \(-0.646677\pi\)
0.671327 + 0.741162i \(0.265725\pi\)
\(168\) −1.10018e7 4.82020e7i −0.179012 0.784301i
\(169\) −3.11125e7 + 4.68945e6i −0.495828 + 0.0747341i
\(170\) −9.78098e6 + 1.22650e7i −0.152690 + 0.191468i
\(171\) 6.32969e7 0.968046
\(172\) 1.72716e8 1.73512e7i 2.58812 0.260003i
\(173\) 4.26447e7 0.626186 0.313093 0.949722i \(-0.398635\pi\)
0.313093 + 0.949722i \(0.398635\pi\)
\(174\) 8.92771e6 1.11950e7i 0.128475 0.161102i
\(175\) −1.26721e7 + 1.91001e6i −0.178737 + 0.0269403i
\(176\) −3.81704e7 1.67235e8i −0.527754 2.31224i
\(177\) −2.45643e7 + 1.67476e7i −0.332964 + 0.227011i
\(178\) 2.21617e7 3.83853e7i 0.294533 0.510146i
\(179\) −3.86123e6 6.68784e6i −0.0503199 0.0871566i 0.839768 0.542945i \(-0.182691\pi\)
−0.890088 + 0.455788i \(0.849357\pi\)
\(180\) 1.87308e8 + 9.02030e7i 2.39389 + 1.15284i
\(181\) −4.99652e7 + 1.54122e7i −0.626315 + 0.193192i −0.591635 0.806206i \(-0.701517\pi\)
−0.0346797 + 0.999398i \(0.511041\pi\)
\(182\) −1.74563e7 + 2.32939e8i −0.214636 + 2.86412i
\(183\) 3.53503e6 1.54880e7i 0.0426397 0.186817i
\(184\) 1.83357e8 + 4.67186e8i 2.16987 + 5.52875i
\(185\) −3.77305e6 5.03479e7i −0.0438118 0.584628i
\(186\) −5.60736e7 8.45174e6i −0.638945 0.0963055i
\(187\) −5.92105e6 + 5.49394e6i −0.0662146 + 0.0614381i
\(188\) −1.37631e8 + 6.62794e7i −1.51065 + 0.727489i
\(189\) 3.96751e7 + 2.70500e7i 0.427466 + 0.291441i
\(190\) 7.12091e7 1.81438e8i 0.753179 1.91907i
\(191\) 1.51390e6 + 466975.i 0.0157210 + 0.00484928i 0.302606 0.953116i \(-0.402143\pi\)
−0.286885 + 0.957965i \(0.592620\pi\)
\(192\) 3.80047e7 + 3.52632e7i 0.387510 + 0.359557i
\(193\) 6.74141e6 + 8.45346e6i 0.0674994 + 0.0846416i 0.814435 0.580255i \(-0.197047\pi\)
−0.746936 + 0.664896i \(0.768476\pi\)
\(194\) −8.95066e7 1.12238e8i −0.880135 1.10365i
\(195\) 2.13447e7 + 1.98049e7i 0.206143 + 0.191273i
\(196\) 1.37741e8 + 4.24876e7i 1.30668 + 0.403057i
\(197\) 6.41160e7 1.63365e8i 0.597495 1.52239i −0.237074 0.971492i \(-0.576189\pi\)
0.834570 0.550902i \(-0.185716\pi\)
\(198\) 1.22445e8 + 8.34815e7i 1.12102 + 0.764297i
\(199\) −1.60981e8 + 7.75244e7i −1.44807 + 0.697353i −0.982259 0.187532i \(-0.939951\pi\)
−0.465810 + 0.884885i \(0.654237\pi\)
\(200\) 3.68764e7 3.42163e7i 0.325945 0.302432i
\(201\) −3.38615e7 5.10379e6i −0.294117 0.0443309i
\(202\) 7.57481e6 + 1.01079e8i 0.0646609 + 0.862840i
\(203\) 2.72466e7 + 6.94233e7i 0.228600 + 0.582464i
\(204\) 1.81330e6 7.94461e6i 0.0149543 0.0655189i
\(205\) −2.47357e6 + 3.30074e7i −0.0200533 + 0.267592i
\(206\) 3.25182e8 1.00306e8i 2.59174 0.799447i
\(207\) −2.14419e8 1.03259e8i −1.68023 0.809155i
\(208\) −2.51647e8 4.35865e8i −1.93896 3.35839i
\(209\) 5.01786e7 8.69119e7i 0.380195 0.658517i
\(210\) 5.96498e7 4.06686e7i 0.444469 0.303034i
\(211\) −2.77958e7 1.21781e8i −0.203700 0.892468i −0.968660 0.248390i \(-0.920099\pi\)
0.764960 0.644078i \(-0.222759\pi\)
\(212\) 2.89624e8 4.36538e7i 2.08766 0.314664i
\(213\) 3.42548e6 4.29542e6i 0.0242881 0.0304563i
\(214\) −8.68375e7 −0.605702
\(215\) 7.12341e7 + 1.38813e8i 0.488825 + 0.952570i
\(216\) −1.88495e8 −1.27266
\(217\) 1.84149e8 2.30916e8i 1.22338 1.53407i
\(218\) −5.09319e8 + 7.67675e7i −3.32960 + 0.501856i
\(219\) −5.22051e6 2.28725e7i −0.0335860 0.147150i
\(220\) 2.72345e8 1.85682e8i 1.72441 1.17568i
\(221\) −1.18495e7 + 2.05240e7i −0.0738461 + 0.127905i
\(222\) 1.81547e7 + 3.14449e7i 0.111366 + 0.192892i
\(223\) −1.97552e8 9.51361e7i −1.19293 0.574484i −0.271277 0.962501i \(-0.587446\pi\)
−0.921652 + 0.388017i \(0.873160\pi\)
\(224\) −5.89157e8 + 1.81731e8i −3.50238 + 1.08034i
\(225\) −1.78265e6 + 2.37878e7i −0.0104334 + 0.139224i
\(226\) 5.03940e7 2.20790e8i 0.290402 1.27233i
\(227\) 2.12681e6 + 5.41901e6i 0.0120681 + 0.0307489i 0.936781 0.349917i \(-0.113790\pi\)
−0.924713 + 0.380666i \(0.875695\pi\)
\(228\) 7.56623e6 + 1.00964e8i 0.0422773 + 0.564152i
\(229\) 3.33245e8 + 5.02286e7i 1.83375 + 0.276393i 0.972689 0.232114i \(-0.0745641\pi\)
0.861058 + 0.508506i \(0.169802\pi\)
\(230\) −5.37210e8 + 4.98458e8i −2.91137 + 2.70135i
\(231\) 3.34907e7 1.61283e7i 0.178765 0.0860887i
\(232\) −2.41884e8 1.64914e8i −1.27174 0.867061i
\(233\) 1.27621e8 3.25174e8i 0.660963 1.68411i −0.0663467 0.997797i \(-0.521134\pi\)
0.727310 0.686309i \(-0.240770\pi\)
\(234\) 4.15494e8 + 1.28163e8i 2.11987 + 0.653893i
\(235\) −1.00651e8 9.33902e7i −0.505917 0.469423i
\(236\) 6.15677e8 + 7.72035e8i 3.04903 + 3.82336i
\(237\) 3.98280e7 + 4.99428e7i 0.194343 + 0.243699i
\(238\) 4.30739e7 + 3.99668e7i 0.207107 + 0.192167i
\(239\) 4.08562e7 + 1.26025e7i 0.193582 + 0.0597122i 0.390030 0.920802i \(-0.372465\pi\)
−0.196448 + 0.980514i \(0.562941\pi\)
\(240\) −5.68285e7 + 1.44797e8i −0.265355 + 0.676113i
\(241\) 1.74158e8 + 1.18739e8i 0.801462 + 0.546428i 0.893360 0.449341i \(-0.148341\pi\)
−0.0918982 + 0.995768i \(0.529293\pi\)
\(242\) −1.65255e8 + 7.95826e7i −0.749550 + 0.360964i
\(243\) 9.90541e7 9.19088e7i 0.442844 0.410899i
\(244\) −5.21759e8 7.86425e7i −2.29935 0.346571i
\(245\) 9.68219e6 + 1.29200e8i 0.0420622 + 0.561281i
\(246\) −8.69659e6 2.21586e7i −0.0372457 0.0949005i
\(247\) 6.55218e7 2.87070e8i 0.276660 1.21213i
\(248\) −8.66411e7 + 1.15615e9i −0.360697 + 4.81317i
\(249\) 5.41592e6 1.67059e6i 0.0222318 0.00685760i
\(250\) −3.86067e8 1.85920e8i −1.56269 0.752551i
\(251\) −6.93886e7 1.20185e8i −0.276968 0.479723i 0.693661 0.720301i \(-0.255996\pi\)
−0.970630 + 0.240578i \(0.922663\pi\)
\(252\) 3.89354e8 6.74380e8i 1.53265 2.65462i
\(253\) −3.11764e8 + 2.12557e8i −1.21033 + 0.825190i
\(254\) −8.44792e7 3.70128e8i −0.323468 1.41721i
\(255\) 7.24267e6 1.09166e6i 0.0273532 0.00412283i
\(256\) 1.31197e8 1.64516e8i 0.488748 0.612871i
\(257\) 9.85701e7 0.362226 0.181113 0.983462i \(-0.442030\pi\)
0.181113 + 0.983462i \(0.442030\pi\)
\(258\) −8.94691e7 6.77151e7i −0.324343 0.245480i
\(259\) −1.89114e8 −0.676355
\(260\) 6.02989e8 7.56124e8i 2.12766 2.66800i
\(261\) 1.37271e8 2.06903e7i 0.477901 0.0720321i
\(262\) −898652. 3.93725e6i −0.00308700 0.0135250i
\(263\) 1.34929e8 9.19928e7i 0.457361 0.311824i −0.312634 0.949874i \(-0.601211\pi\)
0.769995 + 0.638050i \(0.220259\pi\)
\(264\) −7.29580e7 + 1.26367e8i −0.244039 + 0.422688i
\(265\) 1.31631e8 + 2.27992e8i 0.434509 + 0.752592i
\(266\) −6.57769e8 3.16765e8i −2.14283 1.03193i
\(267\) −1.97752e7 + 6.09985e6i −0.0635817 + 0.0196123i
\(268\) −8.49972e7 + 1.13421e9i −0.269732 + 3.59933i
\(269\) −1.13309e8 + 4.96438e8i −0.354920 + 1.55501i 0.410735 + 0.911755i \(0.365272\pi\)
−0.765655 + 0.643252i \(0.777585\pi\)
\(270\) −1.00556e8 2.56213e8i −0.310911 0.792189i
\(271\) 4.10718e7 + 5.48065e8i 0.125358 + 1.67278i 0.605694 + 0.795698i \(0.292896\pi\)
−0.480336 + 0.877085i \(0.659485\pi\)
\(272\) −1.25189e8 1.88692e7i −0.377203 0.0568542i
\(273\) 7.99495e7 7.41823e7i 0.237819 0.220664i
\(274\) 7.76888e8 3.74130e8i 2.28156 1.09874i
\(275\) 3.12494e7 + 2.13055e7i 0.0906103 + 0.0617770i
\(276\) 1.39077e8 3.54362e8i 0.398174 1.01453i
\(277\) −9.88113e7 3.04792e7i −0.279336 0.0861638i 0.151922 0.988393i \(-0.451454\pi\)
−0.431258 + 0.902229i \(0.641930\pi\)
\(278\) 6.70698e8 + 6.22317e8i 1.87228 + 1.73722i
\(279\) −3.42779e8 4.29831e8i −0.944928 1.18490i
\(280\) −9.20290e8 1.15401e9i −2.50537 3.14163i
\(281\) 6.24151e6 + 5.79128e6i 0.0167810 + 0.0155705i 0.688519 0.725219i \(-0.258261\pi\)
−0.671738 + 0.740789i \(0.734452\pi\)
\(282\) 9.43558e7 + 2.91049e7i 0.250551 + 0.0772849i
\(283\) −8.58952e7 + 2.18857e8i −0.225277 + 0.573996i −0.998165 0.0605458i \(-0.980716\pi\)
0.772889 + 0.634542i \(0.218811\pi\)
\(284\) −1.50773e8 1.02795e8i −0.390579 0.266292i
\(285\) −8.19919e7 + 3.94852e7i −0.209804 + 0.101036i
\(286\) 5.05361e8 4.68907e8i 1.27738 1.18524i
\(287\) 1.22596e8 + 1.84784e7i 0.306119 + 0.0461400i
\(288\) 8.57642e7 + 1.14444e9i 0.211559 + 2.82306i
\(289\) −1.47736e8 3.76424e8i −0.360033 0.917350i
\(290\) 9.51227e7 4.16760e8i 0.229029 1.00344i
\(291\) −5.00893e6 + 6.68395e7i −0.0119157 + 0.159004i
\(292\) −7.44614e8 + 2.29683e8i −1.75021 + 0.539870i
\(293\) −5.88026e7 2.83178e7i −0.136571 0.0657693i 0.364350 0.931262i \(-0.381291\pi\)
−0.500921 + 0.865493i \(0.667005\pi\)
\(294\) −4.65876e7 8.06921e7i −0.106919 0.185189i
\(295\) −4.43783e8 + 7.68655e8i −1.00645 + 1.74323i
\(296\) 6.13362e8 4.18183e8i 1.37466 0.937229i
\(297\) −3.15350e7 1.38164e8i −0.0698466 0.306018i
\(298\) 6.80505e8 1.02570e8i 1.48962 0.224523i
\(299\) −6.90266e8 + 8.65566e8i −1.49337 + 1.87263i
\(300\) −3.81568e7 −0.0815920
\(301\) 5.38431e8 2.27216e8i 1.13801 0.480238i
\(302\) −6.50196e8 −1.35838
\(303\) 2.95073e7 3.70009e7i 0.0609368 0.0764124i
\(304\) 1.55543e9 2.34443e8i 3.17536 0.478608i
\(305\) −1.05535e8 4.62378e8i −0.212984 0.933142i
\(306\) 9.03710e7 6.16139e7i 0.180303 0.122929i
\(307\) −2.83590e8 + 4.91192e8i −0.559380 + 0.968874i 0.438169 + 0.898893i \(0.355627\pi\)
−0.997548 + 0.0699813i \(0.977706\pi\)
\(308\) −6.17320e8 1.06923e9i −1.20388 2.08518i
\(309\) −1.43152e8 6.89383e7i −0.276021 0.132925i
\(310\) −1.61772e9 + 4.99000e8i −3.08416 + 0.951338i
\(311\) −2.67780e7 + 3.57327e8i −0.0504796 + 0.673604i 0.913365 + 0.407141i \(0.133474\pi\)
−0.963845 + 0.266463i \(0.914145\pi\)
\(312\) −9.52664e7 + 4.17389e8i −0.177582 + 0.778037i
\(313\) 1.06199e8 + 2.70591e8i 0.195756 + 0.498778i 0.994723 0.102597i \(-0.0327151\pi\)
−0.798967 + 0.601375i \(0.794620\pi\)
\(314\) −7.52887e7 1.00466e9i −0.137239 1.83132i
\(315\) 6.92107e8 + 1.04318e8i 1.24763 + 0.188050i
\(316\) 1.55532e9 1.44313e9i 2.77278 2.57276i
\(317\) 7.83306e8 3.77220e8i 1.38110 0.665101i 0.411863 0.911246i \(-0.364878\pi\)
0.969233 + 0.246144i \(0.0791638\pi\)
\(318\) −1.56429e8 1.06652e8i −0.272786 0.185983i
\(319\) 8.04124e7 2.04887e8i 0.138693 0.353385i
\(320\) 1.47900e9 + 4.56212e8i 2.52315 + 0.778290i
\(321\) 2.97211e7 + 2.75772e7i 0.0501531 + 0.0465353i
\(322\) 1.71145e9 + 2.14610e9i 2.85673 + 3.58223i
\(323\) −4.61813e7 5.79096e7i −0.0762531 0.0956184i
\(324\) −1.00892e9 9.36143e8i −1.64797 1.52910i
\(325\) 1.06039e8 + 3.27087e7i 0.171346 + 0.0528533i
\(326\) 5.79688e8 1.47702e9i 0.926686 2.36116i
\(327\) 1.98700e8 + 1.35471e8i 0.314253 + 0.214254i
\(328\) −4.38482e8 + 2.11162e8i −0.686110 + 0.330413i
\(329\) −3.77002e8 + 3.49807e8i −0.583657 + 0.541555i
\(330\) −2.10686e8 3.17558e7i −0.322728 0.0486434i
\(331\) 4.82206e7 + 6.43459e8i 0.0730860 + 0.975265i 0.906388 + 0.422447i \(0.138829\pi\)
−0.833302 + 0.552818i \(0.813552\pi\)
\(332\) −6.87753e7 1.75237e8i −0.103145 0.262810i
\(333\) −7.83318e7 + 3.43194e8i −0.116247 + 0.509313i
\(334\) −2.64912e7 + 3.53501e8i −0.0389035 + 0.519132i
\(335\) −9.76900e8 + 3.01334e8i −1.41969 + 0.437916i
\(336\) 5.24934e8 + 2.52795e8i 0.754948 + 0.363564i
\(337\) 4.77380e8 + 8.26846e8i 0.679453 + 1.17685i 0.975146 + 0.221564i \(0.0711163\pi\)
−0.295692 + 0.955283i \(0.595550\pi\)
\(338\) 3.37760e8 5.85017e8i 0.475773 0.824063i
\(339\) −8.73649e7 + 5.95644e7i −0.121797 + 0.0830400i
\(340\) −5.41344e7 2.37178e8i −0.0746960 0.327264i
\(341\) −8.61931e8 + 1.29915e8i −1.17715 + 0.177427i
\(342\) −8.47299e8 + 1.06248e9i −1.14537 + 1.43625i
\(343\) −4.37840e8 −0.585849
\(344\) −1.24388e9 + 1.92756e9i −1.64750 + 2.55301i
\(345\) 3.42163e8 0.448607
\(346\) −5.70847e8 + 7.15819e8i −0.740889 + 0.929045i
\(347\) 2.29618e8 3.46094e7i 0.295021 0.0444673i 0.000136123 1.00000i \(-0.499957\pi\)
0.294885 + 0.955533i \(0.404719\pi\)
\(348\) 4.94118e7 + 2.16487e8i 0.0628497 + 0.275363i
\(349\) 7.78889e8 5.31038e8i 0.980814 0.668708i 0.0370451 0.999314i \(-0.488205\pi\)
0.943769 + 0.330606i \(0.107253\pi\)
\(350\) 1.37569e8 2.38277e8i 0.171508 0.297060i
\(351\) −2.07902e8 3.60097e8i −0.256616 0.444472i
\(352\) 1.63941e9 + 7.89496e8i 2.00349 + 0.964830i
\(353\) 4.63138e8 1.42859e8i 0.560401 0.172861i −0.00159813 0.999999i \(-0.500509\pi\)
0.561999 + 0.827138i \(0.310033\pi\)
\(354\) 4.77001e7 6.36513e8i 0.0571489 0.762599i
\(355\) 3.64977e7 1.59907e8i 0.0432978 0.189700i
\(356\) 2.51120e8 + 6.39844e8i 0.294990 + 0.751621i
\(357\) −2.05021e6 2.73582e7i −0.00238485 0.0318236i
\(358\) 1.63947e8 + 2.47110e7i 0.188848 + 0.0284642i
\(359\) 3.62978e8 3.36795e8i 0.414047 0.384180i −0.445461 0.895301i \(-0.646960\pi\)
0.859508 + 0.511121i \(0.170770\pi\)
\(360\) −2.47542e9 + 1.19210e9i −2.79634 + 1.34665i
\(361\) 2.18216e7 + 1.48777e7i 0.0244124 + 0.0166441i
\(362\) 4.10136e8 1.04501e9i 0.454410 1.15782i
\(363\) 8.18337e7 + 2.52424e7i 0.0897964 + 0.0276985i
\(364\) −2.65547e9 2.46392e9i −2.88594 2.67776i
\(365\) −4.36690e8 5.47593e8i −0.470055 0.589430i
\(366\) 2.12656e8 + 2.66662e8i 0.226722 + 0.284300i
\(367\) −1.06334e7 9.86636e6i −0.0112290 0.0104190i 0.674538 0.738240i \(-0.264343\pi\)
−0.685767 + 0.727821i \(0.740533\pi\)
\(368\) −5.65150e9 1.74326e9i −5.91149 1.82345i
\(369\) 8.43134e7 2.14827e8i 0.0873583 0.222585i
\(370\) 8.95628e8 + 6.10629e8i 0.919225 + 0.626717i
\(371\) 8.88435e8 4.27848e8i 0.903269 0.434991i
\(372\) 6.44645e8 5.98143e8i 0.649263 0.602428i
\(373\) 2.78502e8 + 4.19775e7i 0.277874 + 0.0418827i 0.286501 0.958080i \(-0.407508\pi\)
−0.00862680 + 0.999963i \(0.502746\pi\)
\(374\) −1.29594e7 1.72931e8i −0.0128096 0.170932i
\(375\) 7.30928e7 + 1.86237e8i 0.0715756 + 0.182372i
\(376\) 4.49229e8 1.96820e9i 0.435823 1.90947i
\(377\) 4.82599e7 6.43983e8i 0.0463865 0.618984i
\(378\) −9.85148e8 + 3.03878e8i −0.938167 + 0.289386i
\(379\) −1.23837e9 5.96369e8i −1.16846 0.562701i −0.253932 0.967222i \(-0.581724\pi\)
−0.914529 + 0.404521i \(0.867438\pi\)
\(380\) 1.51132e9 + 2.61768e9i 1.41291 + 2.44723i
\(381\) −8.86283e7 + 1.53509e8i −0.0820985 + 0.142199i
\(382\) −2.81037e7 + 1.91608e7i −0.0257954 + 0.0175870i
\(383\) −1.08765e8 4.76532e8i −0.0989225 0.433408i 0.901077 0.433658i \(-0.142777\pi\)
−1.00000 0.000250391i \(0.999920\pi\)
\(384\) −4.02789e8 + 6.07107e7i −0.363010 + 0.0547149i
\(385\) 6.91905e8 8.67622e8i 0.617923 0.774851i
\(386\) −2.32138e8 −0.205443
\(387\) −1.89319e8 1.07123e9i −0.166037 0.939495i
\(388\) 2.22626e9 1.93492
\(389\) 1.06950e9 1.34111e9i 0.921207 1.15516i −0.0663349 0.997797i \(-0.521131\pi\)
0.987541 0.157359i \(-0.0502980\pi\)
\(390\) −6.18161e8 + 9.31728e7i −0.527686 + 0.0795359i
\(391\) 6.19698e7 + 2.71507e8i 0.0524278 + 0.229701i
\(392\) −1.57398e9 + 1.07312e9i −1.31977 + 0.899801i
\(393\) −942788. + 1.63296e6i −0.000783502 + 0.00135707i
\(394\) 1.88392e9 + 3.26305e9i 1.55177 + 2.68774i
\(395\) 1.71819e9 + 8.27438e8i 1.40276 + 0.675531i
\(396\) −2.19608e9 + 6.77400e8i −1.77711 + 0.548166i
\(397\) 1.76425e7 2.35423e8i 0.0141512 0.188835i −0.985648 0.168812i \(-0.946007\pi\)
0.999800 0.0200230i \(-0.00637393\pi\)
\(398\) 8.53613e8 3.73992e9i 0.678688 2.97353i
\(399\) 1.24533e8 + 3.17306e8i 0.0981479 + 0.250077i
\(400\) 4.43008e7 + 5.91153e8i 0.0346100 + 0.461838i
\(401\) −1.10700e9 1.66853e8i −0.857317 0.129220i −0.294349 0.955698i \(-0.595103\pi\)
−0.562968 + 0.826478i \(0.690341\pi\)
\(402\) 5.38944e8 5.00067e8i 0.413764 0.383917i
\(403\) −2.30423e9 + 1.10966e9i −1.75371 + 0.844544i
\(404\) −1.29877e9 8.85483e8i −0.979932 0.668106i
\(405\) 4.51958e8 1.15157e9i 0.338069 0.861386i
\(406\) −1.53004e9 4.71956e8i −1.13465 0.349994i
\(407\) 4.09136e8 + 3.79623e8i 0.300807 + 0.279108i
\(408\) 6.71461e7 + 8.41985e7i 0.0489452 + 0.0613753i
\(409\) 2.83116e8 + 3.55017e8i 0.204613 + 0.256577i 0.873541 0.486751i \(-0.161818\pi\)
−0.668928 + 0.743327i \(0.733247\pi\)
\(410\) −5.20940e8 4.83362e8i −0.373288 0.346361i
\(411\) −3.84712e8 1.18668e8i −0.273332 0.0843116i
\(412\) −1.92802e9 + 4.91251e9i −1.35822 + 3.46069i
\(413\) 2.74684e9 + 1.87276e9i 1.91870 + 1.30815i
\(414\) 4.60351e9 2.21694e9i 3.18851 1.53551i
\(415\) 1.24035e8 1.15088e8i 0.0851878 0.0790428i
\(416\) 5.27916e9 + 7.95706e8i 3.59533 + 0.541908i
\(417\) −3.19236e7 4.25991e8i −0.0215593 0.287689i
\(418\) 7.87177e8 + 2.00569e9i 0.527175 + 1.34322i
\(419\) 1.21510e8 5.32368e8i 0.0806977 0.353560i −0.918418 0.395612i \(-0.870532\pi\)
0.999115 + 0.0420523i \(0.0133896\pi\)
\(420\) −8.36659e7 + 1.11644e9i −0.0551031 + 0.735300i
\(421\) −6.77571e8 + 2.09003e8i −0.442555 + 0.136510i −0.508021 0.861345i \(-0.669623\pi\)
0.0654660 + 0.997855i \(0.479147\pi\)
\(422\) 2.41626e9 + 1.16361e9i 1.56513 + 0.753726i
\(423\) 4.78655e8 + 8.29055e8i 0.307490 + 0.532589i
\(424\) −1.93541e9 + 3.35223e9i −1.23309 + 2.13577i
\(425\) 2.30638e7 1.57246e7i 0.0145737 0.00993616i
\(426\) 2.62475e7 + 1.14998e8i 0.0164496 + 0.0720703i
\(427\) −1.75660e9 + 2.64765e8i −1.09188 + 0.164575i
\(428\) 8.39626e8 1.05286e9i 0.517646 0.649107i
\(429\) −3.21878e8 −0.196830
\(430\) −3.28362e9 6.62461e8i −1.99165 0.401810i
\(431\) −1.49791e9 −0.901189 −0.450595 0.892729i \(-0.648788\pi\)
−0.450595 + 0.892729i \(0.648788\pi\)
\(432\) 1.38494e9 1.73666e9i 0.826491 1.03639i
\(433\) −2.57182e9 + 3.87639e8i −1.52241 + 0.229467i −0.856337 0.516417i \(-0.827265\pi\)
−0.666076 + 0.745884i \(0.732027\pi\)
\(434\) 1.41103e9 + 6.18214e9i 0.828558 + 3.63015i
\(435\) −1.64908e8 + 1.12433e8i −0.0960572 + 0.0654907i
\(436\) 3.99381e9 6.91748e9i 2.30773 3.99710i
\(437\) −1.73007e9 2.99657e9i −0.991695 1.71767i
\(438\) 4.53813e8 + 2.18545e8i 0.258058 + 0.124274i
\(439\) 2.56859e9 7.92306e8i 1.44900 0.446958i 0.532310 0.846550i \(-0.321324\pi\)
0.916693 + 0.399591i \(0.130848\pi\)
\(440\) −3.25537e8 + 4.34399e9i −0.182187 + 2.43111i
\(441\) 2.01011e8 8.80685e8i 0.111605 0.488974i
\(442\) −1.85889e8 4.73638e8i −0.102394 0.260897i
\(443\) −7.91629e7 1.05636e9i −0.0432622 0.577294i −0.976146 0.217116i \(-0.930335\pi\)
0.932884 0.360178i \(-0.117284\pi\)
\(444\) −5.56789e8 8.39225e7i −0.301891 0.0455028i
\(445\) −4.52892e8 + 4.20223e8i −0.243632 + 0.226058i
\(446\) 4.24138e9 2.04254e9i 2.26378 1.09018i
\(447\) −2.65484e8 1.81004e8i −0.140592 0.0958543i
\(448\) 2.11802e9 5.39663e9i 1.11290 2.83563i
\(449\) 1.67547e9 + 5.16814e8i 0.873524 + 0.269446i 0.698927 0.715193i \(-0.253661\pi\)
0.174597 + 0.984640i \(0.444138\pi\)
\(450\) −3.75431e8 3.48349e8i −0.194217 0.180207i
\(451\) −2.28136e8 2.86073e8i −0.117105 0.146845i
\(452\) 2.18971e9 + 2.74581e9i 1.11533 + 1.39857i
\(453\) 2.22537e8 + 2.06484e8i 0.112476 + 0.104362i
\(454\) −1.19431e8 3.68397e7i −0.0598995 0.0184765i
\(455\) 1.18955e9 3.03092e9i 0.592028 1.50846i
\(456\) −1.10556e9 7.53756e8i −0.546014 0.372266i
\(457\) 1.71077e9 8.23865e8i 0.838467 0.403784i 0.0351829 0.999381i \(-0.488799\pi\)
0.803284 + 0.595597i \(0.203084\pi\)
\(458\) −5.30398e9 + 4.92137e9i −2.57972 + 2.39363i
\(459\) −1.03427e8 1.55891e7i −0.0499216 0.00752447i
\(460\) −8.49286e8 1.13329e10i −0.406820 5.42863i
\(461\) −2.01488e8 5.13383e8i −0.0957847 0.244055i 0.874948 0.484216i \(-0.160895\pi\)
−0.970733 + 0.240161i \(0.922800\pi\)
\(462\) −1.77587e8 + 7.78059e8i −0.0837846 + 0.367084i
\(463\) 1.63250e8 2.17843e9i 0.0764400 1.02002i −0.818696 0.574228i \(-0.805302\pi\)
0.895136 0.445794i \(-0.147079\pi\)
\(464\) 3.29661e9 1.01687e9i 1.53199 0.472555i
\(465\) 7.12152e8 + 3.42954e8i 0.328464 + 0.158180i
\(466\) 3.74990e9 + 6.49502e9i 1.71660 + 2.97324i
\(467\) −9.02778e8 + 1.56366e9i −0.410178 + 0.710448i −0.994909 0.100779i \(-0.967867\pi\)
0.584731 + 0.811227i \(0.301200\pi\)
\(468\) −5.57129e9 + 3.79844e9i −2.51244 + 1.71295i
\(469\) 8.52087e8 + 3.73324e9i 0.381398 + 1.67102i
\(470\) 2.91494e9 4.39356e8i 1.29505 0.195198i
\(471\) −2.93283e8 + 3.67766e8i −0.129334 + 0.162180i
\(472\) −1.30501e10 −5.71240
\(473\) −1.62097e9 5.89267e8i −0.704306 0.256034i
\(474\) −1.37147e9 −0.591508
\(475\) −2.16241e8 + 2.71158e8i −0.0925786 + 0.116090i
\(476\) −9.01054e8 + 1.35812e8i −0.382936 + 0.0577184i
\(477\) −4.08442e8 1.78950e9i −0.172312 0.754949i
\(478\) −7.58447e8 + 5.17101e8i −0.317635 + 0.216560i
\(479\) −1.34918e9 + 2.33685e9i −0.560915 + 0.971533i 0.436502 + 0.899703i \(0.356217\pi\)
−0.997417 + 0.0718294i \(0.977116\pi\)
\(480\) −8.25010e8 1.42896e9i −0.340498 0.589760i
\(481\) 1.47540e9 + 7.10515e8i 0.604508 + 0.291116i
\(482\) −4.32440e9 + 1.33390e9i −1.75898 + 0.542574i
\(483\) 9.57757e7 1.27804e9i 0.0386759 0.516094i
\(484\) 6.32943e8 2.77311e9i 0.253750 1.11175i
\(485\) 7.31056e8 + 1.86270e9i 0.290974 + 0.741390i
\(486\) 2.16800e8 + 2.89299e9i 0.0856706 + 1.14319i
\(487\) −2.39017e7 3.60261e6i −0.00937731 0.00141340i 0.144352 0.989526i \(-0.453890\pi\)
−0.153729 + 0.988113i \(0.549128\pi\)
\(488\) 5.11180e9 4.74306e9i 1.99115 1.84752i
\(489\) −6.67466e8 + 3.21435e8i −0.258136 + 0.124312i
\(490\) −2.29831e9 1.56696e9i −0.882516 0.601689i
\(491\) −1.34373e9 + 3.42377e9i −0.512303 + 1.30533i 0.407592 + 0.913164i \(0.366368\pi\)
−0.919896 + 0.392163i \(0.871727\pi\)
\(492\) 3.52747e8 + 1.08808e8i 0.133532 + 0.0411892i
\(493\) −1.19082e8 1.10492e8i −0.0447593 0.0415306i
\(494\) 3.94157e9 + 4.94257e9i 1.47104 + 1.84463i
\(495\) −1.28792e9 1.61501e9i −0.477279 0.598489i
\(496\) −1.00153e10 9.29286e9i −3.68535 3.41951i
\(497\) −5.87063e8 1.81085e8i −0.214505 0.0661661i
\(498\) −4.44562e7 + 1.13273e8i −0.0161298 + 0.0410981i
\(499\) −3.28201e9 2.23764e9i −1.18247 0.806191i −0.197731 0.980256i \(-0.563357\pi\)
−0.984734 + 0.174065i \(0.944310\pi\)
\(500\) 5.98703e9 2.88320e9i 2.14199 1.03153i
\(501\) 1.21329e8 1.12577e8i 0.0431055 0.0399960i
\(502\) 2.94622e9 + 4.44072e8i 1.03945 + 0.156672i
\(503\) 2.79974e8 + 3.73600e9i 0.0980912 + 1.30894i 0.801433 + 0.598084i \(0.204071\pi\)
−0.703342 + 0.710852i \(0.748310\pi\)
\(504\) 3.75979e9 + 9.57980e9i 1.30815 + 3.33311i
\(505\) 3.14393e8 1.37745e9i 0.108631 0.475943i
\(506\) 6.05399e8 8.07848e9i 0.207737 2.77206i
\(507\) −3.01388e8 + 9.29658e7i −0.102706 + 0.0316807i
\(508\) 5.30442e9 + 2.55447e9i 1.79521 + 0.864527i
\(509\) −1.57028e9 2.71980e9i −0.527794 0.914165i −0.999475 0.0323964i \(-0.989686\pi\)
0.471681 0.881769i \(-0.343647\pi\)
\(510\) −7.86271e7 + 1.36186e8i −0.0262468 + 0.0454608i
\(511\) −2.16759e9 + 1.47784e9i −0.718627 + 0.489951i
\(512\) −1.52119e8 6.66478e8i −0.0500887 0.219453i
\(513\) 1.28504e9 1.93689e8i 0.420248 0.0633422i
\(514\) −1.31947e9 + 1.65456e9i −0.428577 + 0.537418i
\(515\) −4.74340e9 −1.53026
\(516\) 1.68608e9 4.30031e8i 0.540262 0.137793i
\(517\) 1.51781e9 0.483061
\(518\) 2.53150e9 3.17440e9i 0.800247 1.00348i
\(519\) 4.22703e8 6.37123e7i 0.132724 0.0200049i
\(520\) 2.84408e9 + 1.24607e10i 0.887014 + 3.88626i
\(521\) 4.74998e8 3.23848e8i 0.147150 0.100325i −0.487507 0.873119i \(-0.662094\pi\)
0.634657 + 0.772794i \(0.281141\pi\)
\(522\) −1.49023e9 + 2.58115e9i −0.458571 + 0.794268i
\(523\) 9.77288e8 + 1.69271e9i 0.298722 + 0.517401i 0.975844 0.218470i \(-0.0701064\pi\)
−0.677122 + 0.735871i \(0.736773\pi\)
\(524\) 5.64260e7 + 2.71734e7i 0.0171325 + 0.00825057i
\(525\) −1.22755e8 + 3.78649e7i −0.0370238 + 0.0114203i
\(526\) −2.62011e8 + 3.49629e9i −0.0785000 + 1.04751i
\(527\) −1.43156e8 + 6.27208e8i −0.0426062 + 0.186670i
\(528\) −6.28207e8 1.60065e9i −0.185731 0.473234i
\(529\) 7.17769e8 + 9.57796e9i 0.210809 + 2.81306i
\(530\) −5.58903e9 8.42411e8i −1.63069 0.245787i
\(531\) 4.53634e9 4.20911e9i 1.31485 1.22000i
\(532\) 1.02005e10 4.91232e9i 2.93719 1.41448i
\(533\) −8.87025e8 6.04764e8i −0.253741 0.172998i
\(534\) 1.62323e8 4.13593e8i 0.0461304 0.117538i
\(535\) 1.15664e9 + 3.56775e8i 0.326557 + 0.100729i
\(536\) −1.10188e10 1.02240e10i −3.09071 2.86776i
\(537\) −4.82651e7 6.05226e7i −0.0134500 0.0168658i
\(538\) −6.81628e9 8.54734e9i −1.88716 2.36643i
\(539\) −1.04990e9 9.74167e8i −0.288794 0.267962i
\(540\) 4.07872e9 + 1.25812e9i 1.11467 + 0.343830i
\(541\) −7.21491e8 + 1.83833e9i −0.195903 + 0.499152i −0.994744 0.102389i \(-0.967351\pi\)
0.798842 + 0.601541i \(0.205447\pi\)
\(542\) −9.74942e9 6.64704e9i −2.63016 1.79321i
\(543\) −4.72240e8 + 2.27419e8i −0.126579 + 0.0609574i
\(544\) 9.84464e8 9.13450e8i 0.262183 0.243270i
\(545\) 7.09931e9 + 1.07005e9i 1.87857 + 0.283149i
\(546\) 1.74985e8 + 2.33502e9i 0.0460074 + 0.613926i
\(547\) 1.67068e9 + 4.25681e9i 0.436452 + 1.11206i 0.964788 + 0.263027i \(0.0847208\pi\)
−0.528336 + 0.849035i \(0.677184\pi\)
\(548\) −2.97556e9 + 1.30368e10i −0.772391 + 3.38406i
\(549\) −2.47110e8 + 3.29745e9i −0.0637364 + 0.850503i
\(550\) −7.75935e8 + 2.39344e8i −0.198864 + 0.0613414i
\(551\) 1.81847e9 + 8.75730e8i 0.463102 + 0.223018i
\(552\) 2.51546e9 + 4.35691e9i 0.636547 + 1.10253i
\(553\) 3.57157e9 6.18613e9i 0.898092 1.55554i
\(554\) 1.83431e9 1.25061e9i 0.458342 0.312492i
\(555\) −1.12620e8 4.93422e8i −0.0279635 0.122516i
\(556\) −1.40302e10 + 2.11471e9i −3.46180 + 0.521782i
\(557\) 2.74618e9 3.44360e9i 0.673341 0.844343i −0.321381 0.946950i \(-0.604147\pi\)
0.994722 + 0.102607i \(0.0327183\pi\)
\(558\) 1.18035e10 2.87601
\(559\) −5.05431e9 2.50267e8i −1.22383 0.0605986i
\(560\) 1.73939e10 4.18542
\(561\) −5.04827e7 + 6.33033e7i −0.0120718 + 0.0151376i
\(562\) −1.80760e8 + 2.72452e7i −0.0429562 + 0.00647460i
\(563\) 5.11677e8 + 2.24180e9i 0.120842 + 0.529442i 0.998721 + 0.0505600i \(0.0161006\pi\)
−0.877879 + 0.478882i \(0.841042\pi\)
\(564\) −1.26520e9 + 8.62600e8i −0.296950 + 0.202457i
\(565\) −1.57835e9 + 2.73379e9i −0.368158 + 0.637668i
\(566\) −2.52386e9 4.37146e9i −0.585071 1.01337i
\(567\) −4.17481e9 2.01048e9i −0.961824 0.463190i
\(568\) 2.30448e9 7.10838e8i 0.527659 0.162761i
\(569\) 1.93879e8 2.58713e9i 0.0441202 0.588743i −0.930705 0.365772i \(-0.880805\pi\)
0.974825 0.222972i \(-0.0715758\pi\)
\(570\) 4.34768e8 1.90484e9i 0.0983320 0.430821i
\(571\) 1.05017e9 + 2.67580e9i 0.236067 + 0.601488i 0.998987 0.0450049i \(-0.0143303\pi\)
−0.762920 + 0.646493i \(0.776235\pi\)
\(572\) 7.98936e8 + 1.06611e10i 0.178495 + 2.38185i
\(573\) 1.57038e7 + 2.36696e6i 0.00348708 + 0.000525593i
\(574\) −1.95126e9 + 1.81050e9i −0.430648 + 0.399583i
\(575\) 1.17487e9 5.65789e8i 0.257723 0.124113i
\(576\) −8.91622e9 6.07898e9i −1.94403 1.32541i
\(577\) 3.26771e8 8.32598e8i 0.0708154 0.180435i −0.891084 0.453839i \(-0.850054\pi\)
0.961899 + 0.273404i \(0.0881495\pi\)
\(578\) 8.29613e9 + 2.55902e9i 1.78702 + 0.551221i
\(579\) 7.94520e7 + 7.37207e7i 0.0170110 + 0.0157839i
\(580\) 4.13325e9 + 5.18293e9i 0.879617 + 1.10301i
\(581\) −3.95155e8 4.95508e8i −0.0835893 0.104818i
\(582\) −1.05490e9 9.78800e8i −0.221809 0.205809i
\(583\) −2.78093e9 8.57802e8i −0.581232 0.179286i
\(584\) 3.76233e9 9.58627e9i 0.781650 1.99161i
\(585\) −5.00764e9 3.41415e9i −1.03416 0.705078i
\(586\) 1.26247e9 6.07974e8i 0.259167 0.124808i
\(587\) 1.18820e9 1.10249e9i 0.242469 0.224978i −0.549572 0.835446i \(-0.685209\pi\)
0.792041 + 0.610468i \(0.209019\pi\)
\(588\) 1.42880e9 + 2.15357e8i 0.289835 + 0.0436856i
\(589\) −5.97336e8 7.97090e9i −0.120452 1.60732i
\(590\) −6.96185e9 1.77385e10i −1.39554 3.55578i
\(591\) 3.91460e8 1.71510e9i 0.0780066 0.341769i
\(592\) −6.53745e8 + 8.72363e9i −0.129504 + 1.72811i
\(593\) −4.14929e9 + 1.27989e9i −0.817113 + 0.252046i −0.675013 0.737806i \(-0.735862\pi\)
−0.142101 + 0.989852i \(0.545386\pi\)
\(594\) 2.74130e9 + 1.32014e9i 0.536667 + 0.258445i
\(595\) −4.09521e8 7.09311e8i −0.0797015 0.138047i
\(596\) −5.33616e9 + 9.24249e9i −1.03244 + 1.78825i
\(597\) −1.47986e9 + 1.00895e9i −0.284649 + 0.194070i
\(598\) −5.28911e9 2.31731e10i −1.01141 4.43129i
\(599\) 7.80680e9 1.17669e9i 1.48415 0.223700i 0.643573 0.765385i \(-0.277451\pi\)
0.840582 + 0.541685i \(0.182213\pi\)
\(600\) 3.14407e8 3.94254e8i 0.0594242 0.0745155i
\(601\) −5.82935e9 −1.09537 −0.547683 0.836686i \(-0.684490\pi\)
−0.547683 + 0.836686i \(0.684490\pi\)
\(602\) −3.39353e9 + 1.20795e10i −0.633963 + 2.25663i
\(603\) 7.12782e9 1.32387
\(604\) 6.28670e9 7.88328e9i 1.16090 1.45572i
\(605\) 2.52809e9 3.81049e8i 0.464140 0.0699579i
\(606\) 2.26097e8 + 9.90598e8i 0.0412707 + 0.180819i
\(607\) −2.48778e9 + 1.69614e9i −0.451493 + 0.307823i −0.767633 0.640890i \(-0.778566\pi\)
0.316140 + 0.948713i \(0.397613\pi\)
\(608\) −8.34295e9 + 1.44504e10i −1.50542 + 2.60746i
\(609\) 3.73795e8 + 6.47432e8i 0.0670614 + 0.116154i
\(610\) 9.17402e9 + 4.41798e9i 1.63646 + 0.788077i
\(611\) 4.25548e9 1.31264e9i 0.754752 0.232810i
\(612\) −1.26756e8 + 1.69144e9i −0.0223531 + 0.298282i
\(613\) 7.17119e8 3.14190e9i 0.125742 0.550911i −0.872334 0.488910i \(-0.837395\pi\)
0.998076 0.0620010i \(-0.0197482\pi\)
\(614\) −4.44882e9 1.13354e10i −0.775632 1.97628i
\(615\) 2.47955e7 + 3.30872e8i 0.00429843 + 0.0573585i
\(616\) 1.61344e10 + 2.43188e9i 2.78113 + 0.419188i
\(617\) −4.28095e9 + 3.97214e9i −0.733740 + 0.680811i −0.955732 0.294237i \(-0.904934\pi\)
0.221992 + 0.975048i \(0.428744\pi\)
\(618\) 3.07342e9 1.48008e9i 0.523796 0.252247i
\(619\) 4.78043e9 + 3.25924e9i 0.810120 + 0.552331i 0.896041 0.443971i \(-0.146431\pi\)
−0.0859207 + 0.996302i \(0.527383\pi\)
\(620\) 9.59151e9 2.44388e10i 1.61628 4.11821i
\(621\) −4.66907e9 1.44022e9i −0.782366 0.241328i
\(622\) −5.63952e9 5.23271e9i −0.939671 0.871887i
\(623\) 1.44283e9 + 1.80926e9i 0.239061 + 0.299772i
\(624\) −3.14557e9 3.94442e9i −0.518267 0.649887i
\(625\) 5.03313e9 + 4.67006e9i 0.824627 + 0.765142i
\(626\) −5.96363e9 1.83954e9i −0.971630 0.299708i
\(627\) 3.67533e8 9.36458e8i 0.0595469 0.151723i
\(628\) 1.29089e10 + 8.80114e9i 2.07984 + 1.41801i
\(629\) 3.71135e8 1.78729e8i 0.0594641 0.0286364i
\(630\) −1.10157e10 + 1.02211e10i −1.75517 + 1.62856i
\(631\) 5.16641e9 + 7.78710e8i 0.818626 + 0.123388i 0.544987 0.838444i \(-0.316534\pi\)
0.273639 + 0.961832i \(0.411773\pi\)
\(632\) 2.09542e9 + 2.79615e10i 0.330189 + 4.40606i
\(633\) −4.57463e8 1.16560e9i −0.0716874 0.182657i
\(634\) −4.15353e9 + 1.81978e10i −0.647300 + 2.83601i
\(635\) −3.95458e8 + 5.27702e9i −0.0612904 + 0.817864i
\(636\) 2.80560e9 8.65412e8i 0.432439 0.133390i
\(637\) −3.78608e9 1.82328e9i −0.580366 0.279490i
\(638\) 2.36276e9 + 4.09242e9i 0.360203 + 0.623890i
\(639\) −5.71788e8 + 9.90366e8i −0.0866926 + 0.150156i
\(640\) −1.00476e10 + 6.85036e9i −1.51507 + 1.03296i
\(641\) 1.94986e9 + 8.54289e9i 0.292415 + 1.28116i 0.881153 + 0.472831i \(0.156768\pi\)
−0.588737 + 0.808324i \(0.700375\pi\)
\(642\) −8.60752e8 + 1.29737e8i −0.128382 + 0.0193505i
\(643\) 5.08551e8 6.37703e8i 0.0754390 0.0945976i −0.742680 0.669647i \(-0.766446\pi\)
0.818119 + 0.575049i \(0.195017\pi\)
\(644\) −4.25682e10 −6.28036
\(645\) 9.13479e8 + 1.26952e9i 0.134042 + 0.186287i
\(646\) 1.59024e9 0.232086
\(647\) 3.71674e9 4.66064e9i 0.539507 0.676520i −0.435116 0.900375i \(-0.643293\pi\)
0.974623 + 0.223854i \(0.0718640\pi\)
\(648\) 1.79861e10 2.71096e9i 2.59671 0.391391i
\(649\) −2.18327e9 9.56555e9i −0.313510 1.37358i
\(650\) −1.96849e9 + 1.34209e9i −0.281149 + 0.191684i
\(651\) 1.48033e9 2.56401e9i 0.210294 0.364239i
\(652\) 1.23031e10 + 2.13096e10i 1.73839 + 3.01099i
\(653\) 2.27619e9 + 1.09616e9i 0.319899 + 0.154055i 0.586941 0.809630i \(-0.300332\pi\)
−0.267042 + 0.963685i \(0.586046\pi\)
\(654\) −4.93379e9 + 1.52187e9i −0.689697 + 0.212743i
\(655\) −4.20671e6 + 5.61346e7i −0.000584922 + 0.00780524i
\(656\) 1.27619e9 5.59135e9i 0.176503 0.773309i
\(657\) 1.78407e9 + 4.54575e9i 0.245434 + 0.625355i
\(658\) −8.25144e8 1.10108e10i −0.112912 1.50670i
\(659\) 8.21083e9 + 1.23758e9i 1.11760 + 0.168452i 0.681764 0.731572i \(-0.261213\pi\)
0.435841 + 0.900024i \(0.356451\pi\)
\(660\) 2.42213e9 2.24741e9i 0.327939 0.304283i
\(661\) −2.51869e9 + 1.21294e9i −0.339210 + 0.163355i −0.595732 0.803183i \(-0.703138\pi\)
0.256521 + 0.966539i \(0.417424\pi\)
\(662\) −1.14464e10 7.80400e9i −1.53343 1.04548i
\(663\) −8.67916e7 + 2.21142e8i −0.0115659 + 0.0294695i
\(664\) 2.37733e9 + 7.33309e8i 0.315138 + 0.0972073i
\(665\) 7.45976e9 + 6.92164e9i 0.983669 + 0.912712i
\(666\) −4.71218e9 5.90889e9i −0.618105 0.775079i
\(667\) −4.73150e9 5.93311e9i −0.617388 0.774180i
\(668\) −4.02986e9 3.73916e9i −0.523085 0.485352i
\(669\) −2.10032e9 6.47862e8i −0.271202 0.0836548i
\(670\) 8.01881e9 2.04316e10i 1.03003 2.62446i
\(671\) 4.33178e9 + 2.95336e9i 0.553526 + 0.377388i
\(672\) −5.56834e9 + 2.68157e9i −0.707837 + 0.340876i
\(673\) 4.24614e9 3.93984e9i 0.536960 0.498226i −0.364432 0.931230i \(-0.618737\pi\)
0.901392 + 0.433004i \(0.142546\pi\)
\(674\) −2.02694e10 3.05512e9i −2.54995 0.384343i
\(675\) 3.65997e7 + 4.88390e8i 0.00458052 + 0.0611228i
\(676\) 3.82724e9 + 9.75165e9i 0.476510 + 1.21413i
\(677\) −2.02996e9 + 8.89385e9i −0.251436 + 1.10161i 0.678704 + 0.734412i \(0.262542\pi\)
−0.930141 + 0.367203i \(0.880315\pi\)
\(678\) 1.69649e8 2.26381e9i 0.0209049 0.278957i
\(679\) 7.16213e9 2.20923e9i 0.878007 0.270829i
\(680\) 2.89670e9 + 1.39498e9i 0.353283 + 0.170132i
\(681\) 2.91775e7 + 5.05369e7i 0.00354025 + 0.00613189i
\(682\) 9.35720e9 1.62071e10i 1.12954 1.95642i
\(683\) 1.89868e9 1.29450e9i 0.228023 0.155464i −0.443920 0.896067i \(-0.646412\pi\)
0.671943 + 0.740603i \(0.265460\pi\)
\(684\) −4.68951e9 2.05461e10i −0.560314 2.45489i
\(685\) −1.18849e10 + 1.79137e9i −1.41280 + 0.212945i
\(686\) 5.86097e9 7.34943e9i 0.693163 0.869199i
\(687\) 3.37824e9 0.397504
\(688\) −8.61993e9 2.56227e10i −1.00912 2.99961i
\(689\) −8.53871e9 −0.994546
\(690\) −4.58023e9 + 5.74343e9i −0.530782 + 0.665579i
\(691\) −7.19603e7 + 1.08463e7i −0.00829697 + 0.00125057i −0.153189 0.988197i \(-0.548954\pi\)
0.144892 + 0.989447i \(0.453716\pi\)
\(692\) −3.15944e9 1.38424e10i −0.362442 1.58796i
\(693\) −6.39283e9 + 4.35856e9i −0.729671 + 0.497481i
\(694\) −2.49276e9 + 4.31758e9i −0.283088 + 0.490323i
\(695\) −6.37659e9 1.10446e10i −0.720513 1.24797i
\(696\) −2.64400e9 1.27328e9i −0.297255 0.143150i
\(697\) −2.58058e8 + 7.96002e7i −0.0288670 + 0.00890430i
\(698\) −1.51248e9 + 2.01827e10i −0.168344 + 2.24639i
\(699\) 7.79191e8 3.41386e9i 0.0862927 0.378073i
\(700\) 1.55883e9 + 3.97184e9i 0.171774 + 0.437672i
\(701\) −1.14714e9 1.53075e10i −0.125777 1.67838i −0.601566 0.798823i \(-0.705456\pi\)
0.475788 0.879560i \(-0.342163\pi\)
\(702\) 8.82746e9 + 1.33053e9i 0.963065 + 0.145159i
\(703\) −3.75181e9 + 3.48117e9i −0.407284 + 0.377904i
\(704\) −1.54153e10 + 7.42360e9i −1.66513 + 0.801882i
\(705\) −1.13720e9 7.75330e8i −0.122229 0.0833344i
\(706\) −3.80163e9 + 9.68640e9i −0.406587 + 1.03597i
\(707\) −5.05700e9 1.55988e9i −0.538176 0.166005i
\(708\) 7.25617e9 + 6.73274e9i 0.768407 + 0.712977i
\(709\) 3.72209e9 + 4.66735e9i 0.392216 + 0.491823i 0.938259 0.345934i \(-0.112438\pi\)
−0.546043 + 0.837757i \(0.683867\pi\)
\(710\) 2.19558e9 + 2.75317e9i 0.230221 + 0.288688i
\(711\) −9.74691e9 9.04381e9i −1.01701 0.943643i
\(712\) −8.68037e9 2.67754e9i −0.901277 0.278007i
\(713\) −1.09798e10 + 2.79760e10i −1.13444 + 2.89050i
\(714\) 4.86670e8 + 3.31806e8i 0.0500369 + 0.0341146i
\(715\) −8.65771e9 + 4.16934e9i −0.885793 + 0.426575i
\(716\) −1.88480e9 + 1.74884e9i −0.191897 + 0.178055i
\(717\) 4.23804e8 + 6.38782e7i 0.0429387 + 0.00647196i
\(718\) 7.94450e8 + 1.06012e10i 0.0800997 + 1.06886i
\(719\) 4.88176e9 + 1.24385e10i 0.489807 + 1.24801i 0.935660 + 0.352902i \(0.114805\pi\)
−0.445853 + 0.895106i \(0.647100\pi\)
\(720\) 7.20463e9 3.15655e10i 0.719362 3.15173i
\(721\) −1.32774e9 + 1.77174e10i −0.131928 + 1.76046i
\(722\) −5.41838e8 + 1.67135e8i −0.0535783 + 0.0165267i
\(723\) 1.90369e9 + 9.16768e8i 0.187332 + 0.0902143i
\(724\) 8.70459e9 + 1.50768e10i 0.852439 + 1.47647i
\(725\) −3.80325e8 + 6.58742e8i −0.0370657 + 0.0641996i
\(726\) −1.51915e9 + 1.03574e9i −0.147340 + 0.100455i
\(727\) 1.18503e9 + 5.19196e9i 0.114382 + 0.501142i 0.999369 + 0.0355252i \(0.0113104\pi\)
−0.884986 + 0.465617i \(0.845832\pi\)
\(728\) 4.73391e10 7.13522e9i 4.54737 0.685406i
\(729\) −4.79219e9 + 6.00921e9i −0.458129 + 0.574475i
\(730\) 1.50373e10 1.43067
\(731\) −8.41929e8 + 9.54774e8i −0.0797195 + 0.0904044i
\(732\) −5.28928e9 −0.498434
\(733\) 6.86708e9 8.61105e9i 0.644033 0.807592i −0.347468 0.937692i \(-0.612958\pi\)
0.991501 + 0.130100i \(0.0415298\pi\)
\(734\) 3.07953e8 4.64165e7i 0.0287441 0.00433248i
\(735\) 2.89000e8 + 1.26619e9i 0.0268468 + 0.117623i
\(736\) 5.18355e10 3.53408e10i 4.79242 3.26742i
\(737\) 5.65058e9 9.78708e9i 0.519944 0.900569i
\(738\) 2.47738e9 + 4.29096e9i 0.226880 + 0.392968i
\(739\) 1.76649e9 + 8.50695e8i 0.161011 + 0.0775386i 0.512653 0.858596i \(-0.328663\pi\)
−0.351643 + 0.936134i \(0.614377\pi\)
\(740\) −1.60633e10 + 4.95488e9i −1.45722 + 0.449492i
\(741\) 2.20576e8 2.94339e9i 0.0199157 0.265756i
\(742\) −4.71099e9 + 2.06402e10i −0.423349 + 1.85481i
\(743\) −2.63130e9 6.70444e9i −0.235347 0.599655i 0.763592 0.645699i \(-0.223434\pi\)
−0.998939 + 0.0460436i \(0.985339\pi\)
\(744\) 8.68506e8 + 1.15894e10i 0.0773157 + 1.03171i
\(745\) −9.48544e9 1.42970e9i −0.840447 0.126677i
\(746\) −4.43268e9 + 4.11293e9i −0.390914 + 0.362715i
\(747\) −1.06290e9 + 5.11864e8i −0.0932973 + 0.0449296i
\(748\) 2.22200e9 + 1.51494e9i 0.194128 + 0.132354i
\(749\) 1.65637e9 4.22037e9i 0.144036 0.366999i
\(750\) −4.10455e9 1.26608e9i −0.355264 0.109584i
\(751\) −5.10736e9 4.73894e9i −0.440004 0.408264i 0.428816 0.903392i \(-0.358931\pi\)
−0.868820 + 0.495128i \(0.835121\pi\)
\(752\) 1.48330e10 + 1.85999e10i 1.27194 + 1.59496i
\(753\) &mi