Properties

Label 16.12.e.a.5.2
Level 16
Weight 12
Character 16.5
Analytic conductor 12.293
Analytic rank 0
Dimension 42
CM No

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Newspace parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 16.e (of order \(4\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(12.293490889\)
Analytic rank: \(0\)
Dimension: \(42\)
Relative dimension: \(21\) over \(\Q(i)\)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 5.2
Character \(\chi\) = 16.5
Dual form 16.12.e.a.13.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-45.0084 + 4.71633i) q^{2} +(396.720 - 396.720i) q^{3} +(2003.51 - 424.549i) q^{4} +(7616.23 + 7616.23i) q^{5} +(-15984.7 + 19726.8i) q^{6} -16490.4i q^{7} +(-88172.6 + 28557.5i) q^{8} -137626. i q^{9} +O(q^{10})\) \(q+(-45.0084 + 4.71633i) q^{2} +(396.720 - 396.720i) q^{3} +(2003.51 - 424.549i) q^{4} +(7616.23 + 7616.23i) q^{5} +(-15984.7 + 19726.8i) q^{6} -16490.4i q^{7} +(-88172.6 + 28557.5i) q^{8} -137626. i q^{9} +(-378715. - 306874. i) q^{10} +(568615. + 568615. i) q^{11} +(626406. - 963260. i) q^{12} +(-1.11150e6 + 1.11150e6i) q^{13} +(77774.0 + 742205. i) q^{14} +6.04302e6 q^{15} +(3.83382e6 - 1.70118e6i) q^{16} +6.34711e6 q^{17} +(649092. + 6.19434e6i) q^{18} +(3.59606e6 - 3.59606e6i) q^{19} +(1.84927e7 + 1.20257e7i) q^{20} +(-6.54205e6 - 6.54205e6i) q^{21} +(-2.82742e7 - 2.29107e7i) q^{22} -4.79362e7i q^{23} +(-2.36505e7 + 4.63091e7i) q^{24} +6.71858e7i q^{25} +(4.47846e7 - 5.52690e7i) q^{26} +(1.56787e7 + 1.56787e7i) q^{27} +(-7.00097e6 - 3.30386e7i) q^{28} +(-2.69107e7 + 2.69107e7i) q^{29} +(-2.71987e8 + 2.85009e7i) q^{30} +1.46392e8 q^{31} +(-1.64531e8 + 9.46490e7i) q^{32} +4.51162e8 q^{33} +(-2.85673e8 + 2.99351e7i) q^{34} +(1.25594e8 - 1.25594e8i) q^{35} +(-5.84291e7 - 2.75736e8i) q^{36} +(-4.69927e8 - 4.69927e8i) q^{37} +(-1.44893e8 + 1.78813e8i) q^{38} +8.81907e8i q^{39} +(-8.89043e8 - 4.54042e8i) q^{40} -3.61263e8i q^{41} +(3.25302e8 + 2.63593e8i) q^{42} +(5.36452e8 + 5.36452e8i) q^{43} +(1.38063e9 + 8.97823e8i) q^{44} +(1.04819e9 - 1.04819e9i) q^{45} +(2.26083e8 + 2.15753e9i) q^{46} -1.46204e9 q^{47} +(8.46060e8 - 2.19584e9i) q^{48} +1.70539e9 q^{49} +(-3.16871e8 - 3.02393e9i) q^{50} +(2.51802e9 - 2.51802e9i) q^{51} +(-1.75501e9 + 2.69879e9i) q^{52} +(-2.55876e8 - 2.55876e8i) q^{53} +(-7.79617e8 - 6.31726e8i) q^{54} +8.66141e9i q^{55} +(4.70924e8 + 1.45400e9i) q^{56} -2.85325e9i q^{57} +(1.08429e9 - 1.33813e9i) q^{58} +(-2.13617e9 - 2.13617e9i) q^{59} +(1.21073e10 - 2.56556e9i) q^{60} +(-4.43007e9 + 4.43007e9i) q^{61} +(-6.58889e9 + 6.90436e8i) q^{62} -2.26951e9 q^{63} +(6.95887e9 - 5.03598e9i) q^{64} -1.69309e10 q^{65} +(-2.03061e10 + 2.12783e9i) q^{66} +(-7.43238e9 + 7.43238e9i) q^{67} +(1.27165e10 - 2.69466e9i) q^{68} +(-1.90172e10 - 1.90172e10i) q^{69} +(-5.06046e9 + 6.24515e9i) q^{70} -8.28036e9i q^{71} +(3.93027e9 + 1.21349e10i) q^{72} -1.36040e10i q^{73} +(2.33670e10 + 1.89343e10i) q^{74} +(2.66539e10 + 2.66539e10i) q^{75} +(5.67804e9 - 8.73145e9i) q^{76} +(9.37667e9 - 9.37667e9i) q^{77} +(-4.15937e9 - 3.96932e10i) q^{78} -6.96390e8 q^{79} +(4.21558e10 + 1.62427e10i) q^{80} +3.68202e10 q^{81} +(1.70384e9 + 1.62599e10i) q^{82} +(-3.69451e10 + 3.69451e10i) q^{83} +(-1.58845e10 - 1.03297e10i) q^{84} +(4.83410e10 + 4.83410e10i) q^{85} +(-2.66749e10 - 2.16148e10i) q^{86} +2.13520e10i q^{87} +(-6.63745e10 - 3.38980e10i) q^{88} -9.40272e10i q^{89} +(-4.22339e10 + 5.21211e10i) q^{90} +(1.83290e10 + 1.83290e10i) q^{91} +(-2.03513e10 - 9.60408e10i) q^{92} +(5.80768e10 - 5.80768e10i) q^{93} +(6.58040e10 - 6.89546e9i) q^{94} +5.47768e10 q^{95} +(-2.77235e10 + 1.02822e11i) q^{96} -1.46969e11 q^{97} +(-7.67571e10 + 8.04321e9i) q^{98} +(7.82564e10 - 7.82564e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42q - 2q^{2} - 2q^{3} + 3080q^{4} - 2q^{5} + 30352q^{6} + 74836q^{8} + O(q^{10}) \) \( 42q - 2q^{2} - 2q^{3} + 3080q^{4} - 2q^{5} + 30352q^{6} + 74836q^{8} - 988948q^{10} - 540846q^{11} + 2300260q^{12} - 2q^{13} - 1829956q^{14} - 6075004q^{15} - 3721448q^{16} - 4q^{17} - 32219106q^{18} - 11291290q^{19} + 68655164q^{20} + 354292q^{21} - 85011388q^{22} - 66180944q^{24} + 305685384q^{26} - 66463304q^{27} - 322075880q^{28} + 77673206q^{29} + 290643636q^{30} + 343549808q^{31} + 404698568q^{32} - 4q^{33} - 882461836q^{34} - 434731684q^{35} + 1854387628q^{36} - 522762058q^{37} - 1276252832q^{38} - 483241016q^{40} + 2372079160q^{42} + 3824193658q^{43} - 2657283740q^{44} + 97301954q^{45} - 1032658964q^{46} - 4586900144q^{47} - 1058870552q^{48} - 8474257474q^{49} + 6515930886q^{50} + 7074245796q^{51} - 13915491564q^{52} - 2100608058q^{53} + 4385621536q^{54} + 12910845976q^{56} - 21491153128q^{58} + 955824746q^{59} + 25615752768q^{60} + 2150827022q^{61} - 15814519760q^{62} + 27758037828q^{63} + 9674332160q^{64} - 1884965292q^{65} + 10932459412q^{66} - 3186519018q^{67} + 13817664656q^{68} - 16193060732q^{69} - 27206453120q^{70} - 20773133628q^{72} + 14141420908q^{74} + 28890034486q^{75} - 11786004940q^{76} - 22711870540q^{77} + 37031200508q^{78} + 48011833792q^{79} - 8952586328q^{80} - 90656394430q^{81} - 81555388352q^{82} + 55713221118q^{83} + 61178517160q^{84} - 84575506252q^{85} + 10047297860q^{86} - 162855622152q^{88} + 160133627736q^{90} - 147369662716q^{91} - 169766721928q^{92} - 69689773328q^{93} + 160320530128q^{94} + 375702304500q^{95} + 230764310192q^{96} - 4q^{97} - 108887063494q^{98} - 286271331106q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(15\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −45.0084 + 4.71633i −0.994555 + 0.104217i
\(3\) 396.720 396.720i 0.942577 0.942577i −0.0558611 0.998439i \(-0.517790\pi\)
0.998439 + 0.0558611i \(0.0177904\pi\)
\(4\) 2003.51 424.549i 0.978278 0.207300i
\(5\) 7616.23 + 7616.23i 1.08995 + 1.08995i 0.995533 + 0.0944131i \(0.0300974\pi\)
0.0944131 + 0.995533i \(0.469903\pi\)
\(6\) −15984.7 + 19726.8i −0.839212 + 1.03568i
\(7\) 16490.4i 0.370844i −0.982659 0.185422i \(-0.940635\pi\)
0.982659 0.185422i \(-0.0593651\pi\)
\(8\) −88172.6 + 28557.5i −0.951346 + 0.308124i
\(9\) 137626.i 0.776904i
\(10\) −378715. 306874.i −1.19760 0.970420i
\(11\) 568615. + 568615.i 1.06453 + 1.06453i 0.997769 + 0.0667634i \(0.0212673\pi\)
0.0667634 + 0.997769i \(0.478733\pi\)
\(12\) 626406. 963260.i 0.726706 1.11750i
\(13\) −1.11150e6 + 1.11150e6i −0.830272 + 0.830272i −0.987554 0.157282i \(-0.949727\pi\)
0.157282 + 0.987554i \(0.449727\pi\)
\(14\) 77774.0 + 742205.i 0.0386483 + 0.368824i
\(15\) 6.04302e6 2.05472
\(16\) 3.83382e6 1.70118e6i 0.914054 0.405593i
\(17\) 6.34711e6 1.08419 0.542097 0.840316i \(-0.317631\pi\)
0.542097 + 0.840316i \(0.317631\pi\)
\(18\) 649092. + 6.19434e6i 0.0809668 + 0.772674i
\(19\) 3.59606e6 3.59606e6i 0.333182 0.333182i −0.520611 0.853794i \(-0.674296\pi\)
0.853794 + 0.520611i \(0.174296\pi\)
\(20\) 1.84927e7 + 1.20257e7i 1.29222 + 0.840325i
\(21\) −6.54205e6 6.54205e6i −0.349549 0.349549i
\(22\) −2.82742e7 2.29107e7i −1.16968 0.947793i
\(23\) 4.79362e7i 1.55296i −0.630141 0.776480i \(-0.717003\pi\)
0.630141 0.776480i \(-0.282997\pi\)
\(24\) −2.36505e7 + 4.63091e7i −0.606287 + 1.18715i
\(25\) 6.71858e7i 1.37597i
\(26\) 4.47846e7 5.52690e7i 0.739222 0.912279i
\(27\) 1.56787e7 + 1.56787e7i 0.210285 + 0.210285i
\(28\) −7.00097e6 3.30386e7i −0.0768757 0.362788i
\(29\) −2.69107e7 + 2.69107e7i −0.243633 + 0.243633i −0.818351 0.574719i \(-0.805112\pi\)
0.574719 + 0.818351i \(0.305112\pi\)
\(30\) −2.71987e8 + 2.85009e7i −2.04353 + 0.214137i
\(31\) 1.46392e8 0.918395 0.459197 0.888334i \(-0.348137\pi\)
0.459197 + 0.888334i \(0.348137\pi\)
\(32\) −1.64531e8 + 9.46490e7i −0.866807 + 0.498644i
\(33\) 4.51162e8 2.00681
\(34\) −2.85673e8 + 2.99351e7i −1.07829 + 0.112992i
\(35\) 1.25594e8 1.25594e8i 0.404200 0.404200i
\(36\) −5.84291e7 2.75736e8i −0.161052 0.760028i
\(37\) −4.69927e8 4.69927e8i −1.11409 1.11409i −0.992591 0.121501i \(-0.961229\pi\)
−0.121501 0.992591i \(-0.538771\pi\)
\(38\) −1.44893e8 + 1.78813e8i −0.296645 + 0.366091i
\(39\) 8.81907e8i 1.56519i
\(40\) −8.89043e8 4.54042e8i −1.37275 0.701077i
\(41\) 3.61263e8i 0.486981i −0.969903 0.243491i \(-0.921707\pi\)
0.969903 0.243491i \(-0.0782925\pi\)
\(42\) 3.25302e8 + 2.63593e8i 0.384074 + 0.311216i
\(43\) 5.36452e8 + 5.36452e8i 0.556486 + 0.556486i 0.928305 0.371819i \(-0.121266\pi\)
−0.371819 + 0.928305i \(0.621266\pi\)
\(44\) 1.38063e9 + 8.97823e8i 1.26208 + 0.820731i
\(45\) 1.04819e9 1.04819e9i 0.846784 0.846784i
\(46\) 2.26083e8 + 2.15753e9i 0.161845 + 1.54450i
\(47\) −1.46204e9 −0.929866 −0.464933 0.885346i \(-0.653922\pi\)
−0.464933 + 0.885346i \(0.653922\pi\)
\(48\) 8.46060e8 2.19584e9i 0.479264 1.24387i
\(49\) 1.70539e9 0.862475
\(50\) −3.16871e8 3.02393e9i −0.143399 1.36847i
\(51\) 2.51802e9 2.51802e9i 1.02194 1.02194i
\(52\) −1.75501e9 + 2.69879e9i −0.640121 + 0.984351i
\(53\) −2.55876e8 2.55876e8i −0.0840450 0.0840450i 0.663835 0.747879i \(-0.268928\pi\)
−0.747879 + 0.663835i \(0.768928\pi\)
\(54\) −7.79617e8 6.31726e8i −0.231055 0.187225i
\(55\) 8.66141e9i 2.32057i
\(56\) 4.70924e8 + 1.45400e9i 0.114266 + 0.352801i
\(57\) 2.85325e9i 0.628100i
\(58\) 1.08429e9 1.33813e9i 0.216915 0.267697i
\(59\) −2.13617e9 2.13617e9i −0.389000 0.389000i 0.485331 0.874331i \(-0.338699\pi\)
−0.874331 + 0.485331i \(0.838699\pi\)
\(60\) 1.21073e10 2.56556e9i 2.01008 0.425942i
\(61\) −4.43007e9 + 4.43007e9i −0.671578 + 0.671578i −0.958080 0.286502i \(-0.907508\pi\)
0.286502 + 0.958080i \(0.407508\pi\)
\(62\) −6.58889e9 + 6.90436e8i −0.913394 + 0.0957126i
\(63\) −2.26951e9 −0.288110
\(64\) 6.95887e9 5.03598e9i 0.810119 0.586265i
\(65\) −1.69309e10 −1.80990
\(66\) −2.03061e10 + 2.12783e9i −1.99588 + 0.209144i
\(67\) −7.43238e9 + 7.43238e9i −0.672537 + 0.672537i −0.958300 0.285763i \(-0.907753\pi\)
0.285763 + 0.958300i \(0.407753\pi\)
\(68\) 1.27165e10 2.69466e9i 1.06064 0.224753i
\(69\) −1.90172e10 1.90172e10i −1.46379 1.46379i
\(70\) −5.06046e9 + 6.24515e9i −0.359874 + 0.444123i
\(71\) 8.28036e9i 0.544664i −0.962203 0.272332i \(-0.912205\pi\)
0.962203 0.272332i \(-0.0877948\pi\)
\(72\) 3.93027e9 + 1.21349e10i 0.239383 + 0.739105i
\(73\) 1.36040e10i 0.768050i −0.923323 0.384025i \(-0.874538\pi\)
0.923323 0.384025i \(-0.125462\pi\)
\(74\) 2.33670e10 + 1.89343e10i 1.22413 + 0.991918i
\(75\) 2.66539e10 + 2.66539e10i 1.29695 + 1.29695i
\(76\) 5.67804e9 8.73145e9i 0.256876 0.395013i
\(77\) 9.37667e9 9.37667e9i 0.394775 0.394775i
\(78\) −4.15937e9 3.96932e10i −0.163120 1.55667i
\(79\) −6.96390e8 −0.0254626 −0.0127313 0.999919i \(-0.504053\pi\)
−0.0127313 + 0.999919i \(0.504053\pi\)
\(80\) 4.21558e10 + 1.62427e10i 1.43834 + 0.554195i
\(81\) 3.68202e10 1.17332
\(82\) 1.70384e9 + 1.62599e10i 0.0507519 + 0.484330i
\(83\) −3.69451e10 + 3.69451e10i −1.02950 + 1.02950i −0.0299513 + 0.999551i \(0.509535\pi\)
−0.999551 + 0.0299513i \(0.990465\pi\)
\(84\) −1.58845e10 1.03297e10i −0.414417 0.269494i
\(85\) 4.83410e10 + 4.83410e10i 1.18171 + 1.18171i
\(86\) −2.66749e10 2.16148e10i −0.611452 0.495461i
\(87\) 2.13520e10i 0.459285i
\(88\) −6.63745e10 3.38980e10i −1.34075 0.684731i
\(89\) 9.40272e10i 1.78488i −0.451168 0.892439i \(-0.648993\pi\)
0.451168 0.892439i \(-0.351007\pi\)
\(90\) −4.22339e10 + 5.21211e10i −0.753923 + 0.930422i
\(91\) 1.83290e10 + 1.83290e10i 0.307901 + 0.307901i
\(92\) −2.03513e10 9.60408e10i −0.321928 1.51923i
\(93\) 5.80768e10 5.80768e10i 0.865658 0.865658i
\(94\) 6.58040e10 6.89546e9i 0.924803 0.0969081i
\(95\) 5.47768e10 0.726301
\(96\) −2.77235e10 + 1.02822e11i −0.347021 + 1.28704i
\(97\) −1.46969e11 −1.73772 −0.868860 0.495057i \(-0.835147\pi\)
−0.868860 + 0.495057i \(0.835147\pi\)
\(98\) −7.67571e10 + 8.04321e9i −0.857778 + 0.0898848i
\(99\) 7.82564e10 7.82564e10i 0.827040 0.827040i
\(100\) 2.85237e10 + 1.34608e11i 0.285237 + 1.34608i
\(101\) 7.59323e10 + 7.59323e10i 0.718884 + 0.718884i 0.968377 0.249492i \(-0.0802638\pi\)
−0.249492 + 0.968377i \(0.580264\pi\)
\(102\) −1.01456e11 + 1.25208e11i −0.909868 + 1.12287i
\(103\) 3.25333e10i 0.276518i 0.990396 + 0.138259i \(0.0441506\pi\)
−0.990396 + 0.138259i \(0.955849\pi\)
\(104\) 6.62620e10 1.29745e11i 0.534049 1.04570i
\(105\) 9.96515e10i 0.761979i
\(106\) 1.27234e10 + 1.03098e10i 0.0923462 + 0.0748284i
\(107\) 3.22092e10 + 3.22092e10i 0.222008 + 0.222008i 0.809344 0.587336i \(-0.199823\pi\)
−0.587336 + 0.809344i \(0.699823\pi\)
\(108\) 3.80688e10 + 2.47560e10i 0.249309 + 0.162125i
\(109\) −2.01916e11 + 2.01916e11i −1.25697 + 1.25697i −0.304442 + 0.952531i \(0.598470\pi\)
−0.952531 + 0.304442i \(0.901530\pi\)
\(110\) −4.08501e10 3.89836e11i −0.241843 2.30793i
\(111\) −3.72859e11 −2.10024
\(112\) −2.80531e10 6.32211e10i −0.150412 0.338971i
\(113\) 3.70572e10 0.189209 0.0946044 0.995515i \(-0.469841\pi\)
0.0946044 + 0.995515i \(0.469841\pi\)
\(114\) 1.34569e10 + 1.28420e11i 0.0654589 + 0.624680i
\(115\) 3.65093e11 3.65093e11i 1.69264 1.69264i
\(116\) −4.24909e10 + 6.53407e10i −0.187835 + 0.288845i
\(117\) 1.52971e11 + 1.52971e11i 0.645042 + 0.645042i
\(118\) 1.06220e11 + 8.60707e10i 0.427422 + 0.346341i
\(119\) 1.04666e11i 0.402066i
\(120\) −5.32829e11 + 1.72574e11i −1.95475 + 0.633108i
\(121\) 3.61335e11i 1.26646i
\(122\) 1.78497e11 2.20284e11i 0.597931 0.737911i
\(123\) −1.43320e11 1.43320e11i −0.459018 0.459018i
\(124\) 2.93299e11 6.21508e10i 0.898445 0.190383i
\(125\) −1.39816e11 + 1.39816e11i −0.409782 + 0.409782i
\(126\) 1.02147e11 1.07038e10i 0.286541 0.0300260i
\(127\) −2.32003e11 −0.623123 −0.311562 0.950226i \(-0.600852\pi\)
−0.311562 + 0.950226i \(0.600852\pi\)
\(128\) −2.89456e11 + 2.59482e11i −0.744609 + 0.667501i
\(129\) 4.25642e11 1.04906
\(130\) 7.62031e11 7.98516e10i 1.80005 0.188623i
\(131\) −9.04781e9 + 9.04781e9i −0.0204904 + 0.0204904i −0.717278 0.696787i \(-0.754612\pi\)
0.696787 + 0.717278i \(0.254612\pi\)
\(132\) 9.03909e11 1.91541e11i 1.96322 0.416010i
\(133\) −5.93003e10 5.93003e10i −0.123558 0.123558i
\(134\) 2.99466e11 3.69573e11i 0.598785 0.738965i
\(135\) 2.38825e11i 0.458399i
\(136\) −5.59641e11 + 1.81258e11i −1.03144 + 0.334066i
\(137\) 5.75403e11i 1.01861i −0.860585 0.509306i \(-0.829902\pi\)
0.860585 0.509306i \(-0.170098\pi\)
\(138\) 9.45627e11 + 7.66244e11i 1.60837 + 1.30326i
\(139\) −1.59606e11 1.59606e11i −0.260895 0.260895i 0.564522 0.825418i \(-0.309060\pi\)
−0.825418 + 0.564522i \(0.809060\pi\)
\(140\) 1.98309e11 3.04951e11i 0.311629 0.479210i
\(141\) −5.80020e11 + 5.80020e11i −0.876471 + 0.876471i
\(142\) 3.90530e10 + 3.72686e11i 0.0567633 + 0.541698i
\(143\) −1.26403e12 −1.76770
\(144\) −2.34127e11 5.27634e11i −0.315107 0.710132i
\(145\) −4.09916e11 −0.531093
\(146\) 6.41608e10 + 6.12292e11i 0.0800441 + 0.763868i
\(147\) 6.76564e11 6.76564e11i 0.812949 0.812949i
\(148\) −1.14101e12 7.41998e11i −1.32084 0.858941i
\(149\) 2.37904e11 + 2.37904e11i 0.265386 + 0.265386i 0.827238 0.561852i \(-0.189911\pi\)
−0.561852 + 0.827238i \(0.689911\pi\)
\(150\) −1.32536e12 1.07394e12i −1.42506 1.15473i
\(151\) 3.54158e10i 0.0367133i −0.999832 0.0183567i \(-0.994157\pi\)
0.999832 0.0183567i \(-0.00584343\pi\)
\(152\) −2.14379e11 + 4.19768e11i −0.214310 + 0.419633i
\(153\) 8.73529e11i 0.842315i
\(154\) −3.77805e11 + 4.66252e11i −0.351483 + 0.433768i
\(155\) 1.11496e12 + 1.11496e12i 1.00100 + 1.00100i
\(156\) 3.74413e11 + 1.76691e12i 0.324463 + 1.53119i
\(157\) 2.32853e11 2.32853e11i 0.194820 0.194820i −0.602955 0.797775i \(-0.706010\pi\)
0.797775 + 0.602955i \(0.206010\pi\)
\(158\) 3.13434e10 3.28441e9i 0.0253240 0.00265365i
\(159\) −2.03022e11 −0.158438
\(160\) −1.97397e12 5.32236e11i −1.48827 0.401277i
\(161\) −7.90485e11 −0.575906
\(162\) −1.65722e12 + 1.73656e11i −1.16693 + 0.122281i
\(163\) 2.77021e11 2.77021e11i 0.188574 0.188574i −0.606506 0.795079i \(-0.707429\pi\)
0.795079 + 0.606506i \(0.207429\pi\)
\(164\) −1.53374e11 7.23795e11i −0.100951 0.476403i
\(165\) 3.43615e12 + 3.43615e12i 2.18731 + 2.18731i
\(166\) 1.48859e12 1.83709e12i 0.916605 1.13119i
\(167\) 8.77341e11i 0.522670i −0.965248 0.261335i \(-0.915837\pi\)
0.965248 0.261335i \(-0.0841628\pi\)
\(168\) 7.63654e11 + 3.90005e11i 0.440246 + 0.224838i
\(169\) 6.78697e11i 0.378703i
\(170\) −2.40375e12 1.94776e12i −1.29843 1.05212i
\(171\) −4.94912e11 4.94912e11i −0.258851 0.258851i
\(172\) 1.30254e12 + 8.47038e11i 0.659757 + 0.429039i
\(173\) 3.22621e11 3.22621e11i 0.158285 0.158285i −0.623522 0.781806i \(-0.714299\pi\)
0.781806 + 0.623522i \(0.214299\pi\)
\(174\) −1.00703e11 9.61019e11i −0.0478654 0.456784i
\(175\) 1.10792e12 0.510268
\(176\) 3.14729e12 + 1.21265e12i 1.40481 + 0.541273i
\(177\) −1.69492e12 −0.733325
\(178\) 4.43464e11 + 4.23201e12i 0.186015 + 1.77516i
\(179\) 2.68966e12 2.68966e12i 1.09397 1.09397i 0.0988710 0.995100i \(-0.468477\pi\)
0.995100 0.0988710i \(-0.0315231\pi\)
\(180\) 1.65506e12 2.54508e12i 0.652852 1.00393i
\(181\) −8.92753e10 8.92753e10i −0.0341585 0.0341585i 0.689821 0.723980i \(-0.257689\pi\)
−0.723980 + 0.689821i \(0.757689\pi\)
\(182\) −9.11405e11 7.38513e11i −0.338313 0.274136i
\(183\) 3.51499e12i 1.26603i
\(184\) 1.36894e12 + 4.22666e12i 0.478505 + 1.47740i
\(185\) 7.15815e12i 2.42860i
\(186\) −2.34003e12 + 2.88785e12i −0.770728 + 0.951161i
\(187\) 3.60906e12 + 3.60906e12i 1.15416 + 1.15416i
\(188\) −2.92921e12 + 6.20707e11i −0.909667 + 0.192761i
\(189\) 2.58547e11 2.58547e11i 0.0779828 0.0779828i
\(190\) −2.46542e12 + 2.58346e11i −0.722346 + 0.0756931i
\(191\) 4.67234e11 0.133000 0.0664998 0.997786i \(-0.478817\pi\)
0.0664998 + 0.997786i \(0.478817\pi\)
\(192\) 7.62848e11 4.75860e12i 0.211000 1.31620i
\(193\) −1.08304e12 −0.291126 −0.145563 0.989349i \(-0.546499\pi\)
−0.145563 + 0.989349i \(0.546499\pi\)
\(194\) 6.61482e12 6.93153e11i 1.72826 0.181101i
\(195\) −6.71681e12 + 6.71681e12i −1.70597 + 1.70597i
\(196\) 3.41678e12 7.24024e11i 0.843740 0.178791i
\(197\) −5.21414e12 5.21414e12i −1.25204 1.25204i −0.954803 0.297238i \(-0.903935\pi\)
−0.297238 0.954803i \(-0.596065\pi\)
\(198\) −3.15311e12 + 3.89128e12i −0.736344 + 0.908728i
\(199\) 2.25210e12i 0.511559i −0.966735 0.255779i \(-0.917668\pi\)
0.966735 0.255779i \(-0.0823321\pi\)
\(200\) −1.91866e12 5.92395e12i −0.423968 1.30902i
\(201\) 5.89714e12i 1.26784i
\(202\) −3.77571e12 3.05947e12i −0.789890 0.640050i
\(203\) 4.43766e11 + 4.43766e11i 0.0903496 + 0.0903496i
\(204\) 3.97587e12 6.11392e12i 0.787890 1.21158i
\(205\) 2.75146e12 2.75146e12i 0.530784 0.530784i
\(206\) −1.53438e11 1.46427e12i −0.0288179 0.275012i
\(207\) −6.59728e12 −1.20650
\(208\) −2.37043e12 + 6.15214e12i −0.422161 + 1.09567i
\(209\) 4.08955e12 0.709366
\(210\) 4.69990e11 + 4.48516e12i 0.0794113 + 0.757829i
\(211\) −4.10170e12 + 4.10170e12i −0.675165 + 0.675165i −0.958902 0.283737i \(-0.908426\pi\)
0.283737 + 0.958902i \(0.408426\pi\)
\(212\) −6.21282e11 4.04018e11i −0.0996418 0.0647968i
\(213\) −3.28498e12 3.28498e12i −0.513388 0.513388i
\(214\) −1.60159e12 1.29777e12i −0.243936 0.197662i
\(215\) 8.17149e12i 1.21308i
\(216\) −1.83017e12 9.34684e11i −0.264848 0.135260i
\(217\) 2.41406e12i 0.340581i
\(218\) 8.13563e12 1.00402e13i 1.11913 1.38113i
\(219\) −5.39696e12 5.39696e12i −0.723947 0.723947i
\(220\) 3.67720e12 + 1.73532e13i 0.481052 + 2.27016i
\(221\) −7.05480e12 + 7.05480e12i −0.900175 + 0.900175i
\(222\) 1.67818e13 1.75853e12i 2.08880 0.218881i
\(223\) 7.90979e12 0.960479 0.480240 0.877137i \(-0.340550\pi\)
0.480240 + 0.877137i \(0.340550\pi\)
\(224\) 1.56080e12 + 2.71317e12i 0.184919 + 0.321450i
\(225\) 9.24653e12 1.06899
\(226\) −1.66789e12 + 1.74774e11i −0.188178 + 0.0197188i
\(227\) 7.63795e12 7.63795e12i 0.841075 0.841075i −0.147924 0.988999i \(-0.547259\pi\)
0.988999 + 0.147924i \(0.0472590\pi\)
\(228\) −1.21135e12 5.71653e12i −0.130205 0.614456i
\(229\) −8.80754e12 8.80754e12i −0.924186 0.924186i 0.0731355 0.997322i \(-0.476699\pi\)
−0.997322 + 0.0731355i \(0.976699\pi\)
\(230\) −1.47104e13 + 1.81542e13i −1.50702 + 1.85983i
\(231\) 7.43982e12i 0.744212i
\(232\) 1.60428e12 3.14128e12i 0.156710 0.306848i
\(233\) 1.24295e13i 1.18576i 0.805291 + 0.592880i \(0.202009\pi\)
−0.805291 + 0.592880i \(0.797991\pi\)
\(234\) −7.60646e12 6.16353e12i −0.708754 0.574305i
\(235\) −1.11352e13 1.11352e13i −1.01350 1.01350i
\(236\) −5.18675e12 3.37293e12i −0.461190 0.299911i
\(237\) −2.76272e11 + 2.76272e11i −0.0240005 + 0.0240005i
\(238\) 4.93640e11 + 4.71085e12i 0.0419022 + 0.399877i
\(239\) −3.64183e12 −0.302087 −0.151043 0.988527i \(-0.548263\pi\)
−0.151043 + 0.988527i \(0.548263\pi\)
\(240\) 2.31678e13 1.02803e13i 1.87812 0.833379i
\(241\) −1.27249e13 −1.00824 −0.504118 0.863635i \(-0.668182\pi\)
−0.504118 + 0.863635i \(0.668182\pi\)
\(242\) −1.70418e12 1.62631e13i −0.131987 1.25956i
\(243\) 1.18299e13 1.18299e13i 0.895664 0.895664i
\(244\) −6.99492e12 + 1.07565e13i −0.517772 + 0.796207i
\(245\) 1.29887e13 + 1.29887e13i 0.940051 + 0.940051i
\(246\) 7.12656e12 + 5.77467e12i 0.504356 + 0.408681i
\(247\) 7.99402e12i 0.553264i
\(248\) −1.29078e13 + 4.18061e12i −0.873712 + 0.282980i
\(249\) 2.93137e13i 1.94077i
\(250\) 5.63349e12 6.95233e12i 0.364844 0.450257i
\(251\) 2.09351e13 + 2.09351e13i 1.32638 + 1.32638i 0.908502 + 0.417880i \(0.137227\pi\)
0.417880 + 0.908502i \(0.362773\pi\)
\(252\) −4.54698e12 + 9.63517e11i −0.281852 + 0.0597251i
\(253\) 2.72573e13 2.72573e13i 1.65318 1.65318i
\(254\) 1.04421e13 1.09421e12i 0.619730 0.0649402i
\(255\) 3.83557e13 2.22771
\(256\) 1.18042e13 1.30440e13i 0.670989 0.741467i
\(257\) 1.06673e13 0.593500 0.296750 0.954955i \(-0.404097\pi\)
0.296750 + 0.954955i \(0.404097\pi\)
\(258\) −1.91575e13 + 2.00747e12i −1.04335 + 0.109330i
\(259\) −7.74927e12 + 7.74927e12i −0.413154 + 0.413154i
\(260\) −3.39212e13 + 7.18798e12i −1.77059 + 0.375192i
\(261\) 3.70361e12 + 3.70361e12i 0.189279 + 0.189279i
\(262\) 3.64555e11 4.49900e11i 0.0182434 0.0225143i
\(263\) 3.68084e13i 1.80381i −0.431935 0.901905i \(-0.642169\pi\)
0.431935 0.901905i \(-0.357831\pi\)
\(264\) −3.97801e13 + 1.28841e13i −1.90917 + 0.618346i
\(265\) 3.89762e12i 0.183209i
\(266\) 2.94869e12 + 2.38933e12i 0.135763 + 0.110009i
\(267\) −3.73025e13 3.73025e13i −1.68239 1.68239i
\(268\) −1.17354e13 + 1.80463e13i −0.518511 + 0.797345i
\(269\) −3.00347e13 + 3.00347e13i −1.30013 + 1.30013i −0.371825 + 0.928303i \(0.621268\pi\)
−0.928303 + 0.371825i \(0.878732\pi\)
\(270\) −1.12638e12 1.07491e13i −0.0477730 0.455902i
\(271\) −9.23248e11 −0.0383696 −0.0191848 0.999816i \(-0.506107\pi\)
−0.0191848 + 0.999816i \(0.506107\pi\)
\(272\) 2.43337e13 1.07976e13i 0.991011 0.439741i
\(273\) 1.45430e13 0.580441
\(274\) 2.71379e12 + 2.58980e13i 0.106157 + 1.01307i
\(275\) −3.82029e13 + 3.82029e13i −1.46476 + 1.46476i
\(276\) −4.61750e13 3.00275e13i −1.73543 1.12855i
\(277\) −7.75117e12 7.75117e12i −0.285580 0.285580i 0.549749 0.835330i \(-0.314723\pi\)
−0.835330 + 0.549749i \(0.814723\pi\)
\(278\) 7.93634e12 + 6.43084e12i 0.286665 + 0.232285i
\(279\) 2.01475e13i 0.713505i
\(280\) −7.48731e12 + 1.46606e13i −0.259990 + 0.509077i
\(281\) 7.71875e12i 0.262822i 0.991328 + 0.131411i \(0.0419508\pi\)
−0.991328 + 0.131411i \(0.958049\pi\)
\(282\) 2.33702e13 2.88413e13i 0.780355 0.963042i
\(283\) −1.29432e13 1.29432e13i −0.423854 0.423854i 0.462674 0.886528i \(-0.346890\pi\)
−0.886528 + 0.462674i \(0.846890\pi\)
\(284\) −3.51542e12 1.65898e13i −0.112908 0.532832i
\(285\) 2.17310e13 2.17310e13i 0.684595 0.684595i
\(286\) 5.68920e13 5.96159e12i 1.75808 0.184225i
\(287\) −5.95736e12 −0.180594
\(288\) 1.30262e13 + 2.26438e13i 0.387399 + 0.673426i
\(289\) 6.01388e12 0.175475
\(290\) 1.84496e13 1.93330e12i 0.528201 0.0553490i
\(291\) −5.83054e13 + 5.83054e13i −1.63794 + 1.63794i
\(292\) −5.77555e12 2.72557e13i −0.159216 0.751366i
\(293\) −2.08690e13 2.08690e13i −0.564586 0.564586i 0.366021 0.930607i \(-0.380720\pi\)
−0.930607 + 0.366021i \(0.880720\pi\)
\(294\) −2.72602e13 + 3.36420e13i −0.723799 + 0.893246i
\(295\) 3.25391e13i 0.847978i
\(296\) 5.48547e13 + 2.80147e13i 1.40317 + 0.716609i
\(297\) 1.78303e13i 0.447710i
\(298\) −1.18297e13 9.58565e12i −0.291598 0.236283i
\(299\) 5.32810e13 + 5.32810e13i 1.28938 + 1.28938i
\(300\) 6.47174e13 + 4.20856e13i 1.53764 + 0.999923i
\(301\) 8.84629e12 8.84629e12i 0.206369 0.206369i
\(302\) 1.67033e11 + 1.59401e12i 0.00382616 + 0.0365134i
\(303\) 6.02477e13 1.35521
\(304\) 7.66909e12 1.99042e13i 0.169410 0.439683i
\(305\) −6.74809e13 −1.46397
\(306\) 4.11985e12 + 3.93161e13i 0.0877837 + 0.837728i
\(307\) 6.36815e13 6.36815e13i 1.33276 1.33276i 0.429870 0.902891i \(-0.358560\pi\)
0.902891 0.429870i \(-0.141440\pi\)
\(308\) 1.48054e13 2.27671e13i 0.304363 0.468036i
\(309\) 1.29066e13 + 1.29066e13i 0.260639 + 0.260639i
\(310\) −5.54410e13 4.49240e13i −1.09987 0.891229i
\(311\) 3.17271e13i 0.618370i 0.951002 + 0.309185i \(0.100056\pi\)
−0.951002 + 0.309185i \(0.899944\pi\)
\(312\) −2.51851e13 7.77600e13i −0.482273 1.48904i
\(313\) 3.48621e12i 0.0655933i 0.999462 + 0.0327966i \(0.0104414\pi\)
−0.999462 + 0.0327966i \(0.989559\pi\)
\(314\) −9.38214e12 + 1.15786e13i −0.173456 + 0.214063i
\(315\) −1.72851e13 1.72851e13i −0.314024 0.314024i
\(316\) −1.39523e12 + 2.95652e11i −0.0249095 + 0.00527839i
\(317\) −5.05740e11 + 5.05740e11i −0.00887362 + 0.00887362i −0.711530 0.702656i \(-0.751997\pi\)
0.702656 + 0.711530i \(0.251997\pi\)
\(318\) 9.13769e12 9.57519e11i 0.157575 0.0165120i
\(319\) −3.06036e13 −0.518709
\(320\) 9.13555e13 + 1.46452e13i 1.52198 + 0.243989i
\(321\) 2.55560e13 0.418519
\(322\) 3.55785e13 3.72819e12i 0.572770 0.0600193i
\(323\) 2.28246e13 2.28246e13i 0.361234 0.361234i
\(324\) 7.37696e13 1.56320e13i 1.14784 0.243229i
\(325\) −7.46769e13 7.46769e13i −1.14243 1.14243i
\(326\) −1.11617e13 + 1.37748e13i −0.167894 + 0.207199i
\(327\) 1.60209e14i 2.36959i
\(328\) 1.03168e13 + 3.18535e13i 0.150051 + 0.463288i
\(329\) 2.41095e13i 0.344835i
\(330\) −1.70862e14 1.38450e14i −2.40336 1.94745i
\(331\) −3.88311e13 3.88311e13i −0.537187 0.537187i 0.385515 0.922702i \(-0.374024\pi\)
−0.922702 + 0.385515i \(0.874024\pi\)
\(332\) −5.83350e13 + 8.97050e13i −0.793724 + 1.22055i
\(333\) −6.46743e13 + 6.46743e13i −0.865543 + 0.865543i
\(334\) 4.13784e12 + 3.94877e13i 0.0544713 + 0.519824i
\(335\) −1.13213e14 −1.46606
\(336\) −3.62103e13 1.39518e13i −0.461281 0.177732i
\(337\) −1.68879e13 −0.211647 −0.105823 0.994385i \(-0.533748\pi\)
−0.105823 + 0.994385i \(0.533748\pi\)
\(338\) 3.20096e12 + 3.05471e13i 0.0394674 + 0.376641i
\(339\) 1.47013e13 1.47013e13i 0.178344 0.178344i
\(340\) 1.17375e14 + 7.63287e13i 1.40101 + 0.911074i
\(341\) 8.32410e13 + 8.32410e13i 0.977661 + 0.977661i
\(342\) 2.46094e13 + 1.99410e13i 0.284418 + 0.230464i
\(343\) 6.07294e13i 0.690687i
\(344\) −6.26201e13 3.19806e13i −0.700878 0.357944i
\(345\) 2.89679e14i 3.19090i
\(346\) −1.29990e13 + 1.60422e13i −0.140927 + 0.173919i
\(347\) 3.90511e13 + 3.90511e13i 0.416698 + 0.416698i 0.884064 0.467366i \(-0.154797\pi\)
−0.467366 + 0.884064i \(0.654797\pi\)
\(348\) 9.06497e12 + 4.27790e13i 0.0952096 + 0.449308i
\(349\) 4.76750e13 4.76750e13i 0.492891 0.492891i −0.416325 0.909216i \(-0.636682\pi\)
0.909216 + 0.416325i \(0.136682\pi\)
\(350\) −4.98656e13 + 5.22531e12i −0.507489 + 0.0531787i
\(351\) −3.48536e13 −0.349187
\(352\) −1.47374e14 3.97359e13i −1.45357 0.391920i
\(353\) 1.10675e14 1.07470 0.537352 0.843358i \(-0.319425\pi\)
0.537352 + 0.843358i \(0.319425\pi\)
\(354\) 7.62857e13 7.99382e12i 0.729332 0.0764252i
\(355\) 6.30651e13 6.30651e13i 0.593654 0.593654i
\(356\) −3.99192e13 1.88385e14i −0.370004 1.74611i
\(357\) −4.15231e13 4.15231e13i −0.378979 0.378979i
\(358\) −1.08372e14 + 1.33743e14i −0.974003 + 1.20202i
\(359\) 1.55145e14i 1.37315i 0.727059 + 0.686574i \(0.240886\pi\)
−0.727059 + 0.686574i \(0.759114\pi\)
\(360\) −6.24881e13 + 1.22356e14i −0.544670 + 1.06650i
\(361\) 9.06270e13i 0.777979i
\(362\) 4.43919e12 + 3.59709e12i 0.0375324 + 0.0304126i
\(363\) 1.43349e14 + 1.43349e14i 1.19373 + 1.19373i
\(364\) 4.45040e13 + 2.89408e13i 0.365040 + 0.237385i
\(365\) 1.03611e14 1.03611e14i 0.837133 0.837133i
\(366\) −1.65779e13 1.58204e14i −0.131942 1.25913i
\(367\) 2.60665e13 0.204371 0.102186 0.994765i \(-0.467416\pi\)
0.102186 + 0.994765i \(0.467416\pi\)
\(368\) −8.15481e13 1.83779e14i −0.629870 1.41949i
\(369\) −4.97193e13 −0.378338
\(370\) 3.37602e13 + 3.22177e14i 0.253102 + 2.41538i
\(371\) −4.21948e12 + 4.21948e12i −0.0311675 + 0.0311675i
\(372\) 9.17011e13 1.41014e14i 0.667404 1.02630i
\(373\) 4.15009e13 + 4.15009e13i 0.297618 + 0.297618i 0.840080 0.542462i \(-0.182508\pi\)
−0.542462 + 0.840080i \(0.682508\pi\)
\(374\) −1.79460e14 1.45417e14i −1.26816 1.02759i
\(375\) 1.10936e14i 0.772502i
\(376\) 1.28912e14 4.17522e13i 0.884625 0.286514i
\(377\) 5.98223e13i 0.404563i
\(378\) −1.04174e13 + 1.28562e13i −0.0694310 + 0.0856853i
\(379\) 2.23013e13 + 2.23013e13i 0.146492 + 0.146492i 0.776549 0.630057i \(-0.216968\pi\)
−0.630057 + 0.776549i \(0.716968\pi\)
\(380\) 1.09746e14 2.32555e13i 0.710524 0.150562i
\(381\) −9.20404e13 + 9.20404e13i −0.587342 + 0.587342i
\(382\) −2.10294e13 + 2.20363e12i −0.132275 + 0.0138609i
\(383\) 3.42745e13 0.212509 0.106254 0.994339i \(-0.466114\pi\)
0.106254 + 0.994339i \(0.466114\pi\)
\(384\) −1.18915e13 + 2.17775e14i −0.0726797 + 1.33102i
\(385\) 1.42830e14 0.860567
\(386\) 4.87460e13 5.10799e12i 0.289540 0.0303403i
\(387\) 7.38299e13 7.38299e13i 0.432337 0.432337i
\(388\) −2.94453e14 + 6.23954e13i −1.69997 + 0.360229i
\(389\) 3.40257e13 + 3.40257e13i 0.193680 + 0.193680i 0.797284 0.603604i \(-0.206269\pi\)
−0.603604 + 0.797284i \(0.706269\pi\)
\(390\) 2.70634e14 3.33991e14i 1.51889 1.87448i
\(391\) 3.04256e14i 1.68371i
\(392\) −1.50369e14 + 4.87019e13i −0.820512 + 0.265749i
\(393\) 7.17889e12i 0.0386277i
\(394\) 2.59272e14 + 2.10089e14i 1.37571 + 1.11474i
\(395\) −5.30387e12 5.30387e12i −0.0277529 0.0277529i
\(396\) 1.23564e14 1.90011e14i 0.637629 0.980519i
\(397\) −1.49091e14 + 1.49091e14i −0.758759 + 0.758759i −0.976097 0.217337i \(-0.930263\pi\)
0.217337 + 0.976097i \(0.430263\pi\)
\(398\) 1.06217e13 + 1.01363e14i 0.0533133 + 0.508773i
\(399\) −4.70512e13 −0.232927
\(400\) 1.14295e14 + 2.57578e14i 0.558082 + 1.25771i
\(401\) −3.22674e14 −1.55407 −0.777034 0.629459i \(-0.783276\pi\)
−0.777034 + 0.629459i \(0.783276\pi\)
\(402\) −2.78129e13 2.65421e14i −0.132130 1.26093i
\(403\) −1.62715e14 + 1.62715e14i −0.762518 + 0.762518i
\(404\) 1.84368e14 + 1.19894e14i 0.852293 + 0.554244i
\(405\) 2.80431e14 + 2.80431e14i 1.27886 + 1.27886i
\(406\) −2.20662e13 1.78803e13i −0.0992736 0.0804416i
\(407\) 5.34416e14i 2.37197i
\(408\) −1.50112e14 + 2.93929e14i −0.657332 + 1.28710i
\(409\) 2.49725e14i 1.07891i −0.842015 0.539454i \(-0.818631\pi\)
0.842015 0.539454i \(-0.181369\pi\)
\(410\) −1.10862e14 + 1.36816e14i −0.472576 + 0.583210i
\(411\) −2.28274e14 2.28274e14i −0.960121 0.960121i
\(412\) 1.38120e13 + 6.51808e13i 0.0573220 + 0.270511i
\(413\) −3.52262e13 + 3.52262e13i −0.144258 + 0.144258i
\(414\) 2.96933e14 3.11150e13i 1.19993 0.125738i
\(415\) −5.62765e14 −2.24421
\(416\) 7.76735e13 2.88078e14i 0.305675 1.13370i
\(417\) −1.26637e14 −0.491828
\(418\) −1.84064e14 + 1.92877e13i −0.705504 + 0.0739282i
\(419\) 3.13887e14 3.13887e14i 1.18740 1.18740i 0.209613 0.977784i \(-0.432779\pi\)
0.977784 0.209613i \(-0.0672205\pi\)
\(420\) −4.23070e13 1.99653e14i −0.157958 0.745427i
\(421\) 2.84805e14 + 2.84805e14i 1.04953 + 1.04953i 0.998708 + 0.0508239i \(0.0161847\pi\)
0.0508239 + 0.998708i \(0.483815\pi\)
\(422\) 1.65266e14 2.03956e14i 0.601125 0.741853i
\(423\) 2.01215e14i 0.722417i
\(424\) 2.98684e13 + 1.52540e13i 0.105852 + 0.0540596i
\(425\) 4.26436e14i 1.49181i
\(426\) 1.63345e14 + 1.32359e14i 0.564096 + 0.457088i
\(427\) 7.30534e13 + 7.30534e13i 0.249050 + 0.249050i
\(428\) 7.82058e13 + 5.08571e13i 0.263208 + 0.171163i
\(429\) −5.01466e14 + 5.01466e14i −1.66620 + 1.66620i
\(430\) −3.85395e13 3.67786e14i −0.126424 1.20647i
\(431\) 1.79355e14 0.580884 0.290442 0.956893i \(-0.406198\pi\)
0.290442 + 0.956893i \(0.406198\pi\)
\(432\) 8.67814e13 + 3.34369e13i 0.277502 + 0.106922i
\(433\) −4.08904e14 −1.29103 −0.645517 0.763746i \(-0.723358\pi\)
−0.645517 + 0.763746i \(0.723358\pi\)
\(434\) 1.13855e13 + 1.08653e14i 0.0354944 + 0.338726i
\(435\) −1.62622e14 + 1.62622e14i −0.500596 + 0.500596i
\(436\) −3.18819e14 + 4.90266e14i −0.969098 + 1.49024i
\(437\) −1.72381e14 1.72381e14i −0.517419 0.517419i
\(438\) 2.68362e14 + 2.17455e14i 0.795452 + 0.644557i
\(439\) 2.94454e14i 0.861912i 0.902373 + 0.430956i \(0.141824\pi\)
−0.902373 + 0.430956i \(0.858176\pi\)
\(440\) −2.47348e14 7.63699e14i −0.715022 2.20766i
\(441\) 2.34707e14i 0.670061i
\(442\) 2.84252e14 3.50798e14i 0.801460 0.989087i
\(443\) −1.47611e14 1.47611e14i −0.411052 0.411052i 0.471053 0.882105i \(-0.343874\pi\)
−0.882105 + 0.471053i \(0.843874\pi\)
\(444\) −7.47027e14 + 1.58297e14i −2.05461 + 0.435378i
\(445\) 7.16133e14 7.16133e14i 1.94542 1.94542i
\(446\) −3.56007e14 + 3.73052e13i −0.955249 + 0.100099i
\(447\) 1.88763e14 0.500293
\(448\) −8.30451e13 1.14754e14i −0.217413 0.300428i
\(449\) 2.53852e13 0.0656486 0.0328243 0.999461i \(-0.489550\pi\)
0.0328243 + 0.999461i \(0.489550\pi\)
\(450\) −4.16172e14 + 4.36097e13i −1.06317 + 0.111408i
\(451\) 2.05420e14 2.05420e14i 0.518407 0.518407i
\(452\) 7.42446e13 1.57326e13i 0.185099 0.0392229i
\(453\) −1.40501e13 1.40501e13i −0.0346051 0.0346051i
\(454\) −3.07749e14 + 3.79795e14i −0.748841 + 0.924150i
\(455\) 2.79196e14i 0.671191i
\(456\) 8.14819e13 + 2.51579e14i 0.193533 + 0.597541i
\(457\) 1.90513e14i 0.447080i −0.974695 0.223540i \(-0.928239\pi\)
0.974695 0.223540i \(-0.0717613\pi\)
\(458\) 4.37953e14 + 3.54874e14i 1.01547 + 0.822838i
\(459\) 9.95141e13 + 9.95141e13i 0.227990 + 0.227990i
\(460\) 5.76469e14 8.86469e14i 1.30499 2.00676i
\(461\) 7.44533e13 7.44533e13i 0.166544 0.166544i −0.618914 0.785458i \(-0.712427\pi\)
0.785458 + 0.618914i \(0.212427\pi\)
\(462\) 3.50887e13 + 3.34854e14i 0.0775597 + 0.740159i
\(463\) −2.05938e14 −0.449821 −0.224911 0.974379i \(-0.572209\pi\)
−0.224911 + 0.974379i \(0.572209\pi\)
\(464\) −5.73907e13 + 1.48950e14i −0.123878 + 0.321509i
\(465\) 8.84653e14 1.88704
\(466\) −5.86218e13 5.59433e14i −0.123577 1.17930i
\(467\) 1.31003e14 1.31003e14i 0.272922 0.272922i −0.557353 0.830276i \(-0.688183\pi\)
0.830276 + 0.557353i \(0.188183\pi\)
\(468\) 3.71424e14 + 2.41536e14i 0.764747 + 0.497313i
\(469\) 1.22563e14 + 1.22563e14i 0.249406 + 0.249406i
\(470\) 5.53696e14 + 4.48661e14i 1.11361 + 0.902361i
\(471\) 1.84755e14i 0.367266i
\(472\) 2.49355e14 + 1.27348e14i 0.489934 + 0.250213i
\(473\) 6.10070e14i 1.18480i
\(474\) 1.11316e13 1.37375e13i 0.0213686 0.0263711i
\(475\) 2.41604e14 + 2.41604e14i 0.458447 + 0.458447i
\(476\) −4.44359e13 2.09700e14i −0.0833481 0.393332i
\(477\) −3.52152e13 + 3.52152e13i −0.0652949 + 0.0652949i
\(478\) 1.63913e14 1.71761e13i 0.300442 0.0314827i
\(479\) 2.24204e14 0.406255 0.203127 0.979152i \(-0.434889\pi\)
0.203127 + 0.979152i \(0.434889\pi\)
\(480\) −9.94263e14 + 5.71966e14i −1.78104 + 1.02457i
\(481\) 1.04465e15 1.85000
\(482\) 5.72729e14 6.00151e13i 1.00275 0.105076i
\(483\) −3.13601e14 + 3.13601e14i −0.542836 + 0.542836i
\(484\) 1.53405e14 + 7.23940e14i 0.262536 + 1.23895i
\(485\) −1.11935e15 1.11935e15i −1.89402 1.89402i
\(486\) −4.76649e14 + 5.88237e14i −0.797443 + 0.984130i
\(487\) 1.28230e14i 0.212119i 0.994360 + 0.106059i \(0.0338234\pi\)
−0.994360 + 0.106059i \(0.966177\pi\)
\(488\) 2.64099e14 5.17122e14i 0.431974 0.845833i
\(489\) 2.19799e14i 0.355490i
\(490\) −6.45859e14 5.23341e14i −1.03290 0.836963i
\(491\) −2.56345e14 2.56345e14i −0.405394 0.405394i 0.474735 0.880129i \(-0.342544\pi\)
−0.880129 + 0.474735i \(0.842544\pi\)
\(492\) −3.47990e14 2.26297e14i −0.544201 0.353893i
\(493\) −1.70805e14 + 1.70805e14i −0.264145 + 0.264145i
\(494\) −3.77025e13 3.59798e14i −0.0576596 0.550251i
\(495\) 1.19204e15 1.80286
\(496\) 5.61242e14 2.49040e14i 0.839462 0.372494i
\(497\) −1.36546e14 −0.201985
\(498\) −1.38253e14 1.31936e15i −0.202262 1.93020i
\(499\) −3.65085e14 + 3.65085e14i −0.528251 + 0.528251i −0.920051 0.391799i \(-0.871853\pi\)
0.391799 + 0.920051i \(0.371853\pi\)
\(500\) −2.20765e14 + 3.39483e14i −0.315933 + 0.485828i
\(501\) −3.48059e14 3.48059e14i −0.492657 0.492657i
\(502\) −1.04099e15 8.43517e14i −1.45739 1.18093i
\(503\) 5.75270e12i 0.00796614i −0.999992 0.00398307i \(-0.998732\pi\)
0.999992 0.00398307i \(-0.00126785\pi\)
\(504\) 2.00108e14 6.48115e13i 0.274092 0.0887736i
\(505\) 1.15664e15i 1.56709i
\(506\) −1.09825e15 + 1.35536e15i −1.47188 + 1.81646i
\(507\) −2.69253e14 2.69253e14i −0.356957 0.356957i
\(508\) −4.64822e14 + 9.84969e13i −0.609587 + 0.129173i
\(509\) 2.46291e14 2.46291e14i 0.319522 0.319522i −0.529061 0.848584i \(-0.677456\pi\)
0.848584 + 0.529061i \(0.177456\pi\)
\(510\) −1.72633e15 + 1.80898e14i −2.21558 + 0.232166i
\(511\) −2.24334e14 −0.284826
\(512\) −4.69766e14 + 6.42763e14i −0.590061 + 0.807358i
\(513\) 1.12763e14 0.140126
\(514\) −4.80117e14 + 5.03104e13i −0.590268 + 0.0618530i
\(515\) −2.47781e14 + 2.47781e14i −0.301389 + 0.301389i
\(516\) 8.52780e14 1.80706e14i 1.02627 0.217470i
\(517\) −8.31337e14 8.31337e14i −0.989873 0.989873i
\(518\) 3.12234e14 3.85330e14i 0.367846 0.453962i
\(519\) 2.55980e14i 0.298391i
\(520\) 1.49284e15 4.83503e14i 1.72184 0.557675i
\(521\) 6.95866e14i 0.794179i 0.917780 + 0.397089i \(0.129980\pi\)
−0.917780 + 0.397089i \(0.870020\pi\)
\(522\) −1.84161e14 1.49226e14i −0.207975 0.168522i
\(523\) 5.50584e14 + 5.50584e14i 0.615268 + 0.615268i 0.944314 0.329046i \(-0.106727\pi\)
−0.329046 + 0.944314i \(0.606727\pi\)
\(524\) −1.42862e13 + 2.19686e13i −0.0157977 + 0.0242930i
\(525\) 4.39533e14 4.39533e14i 0.480967 0.480967i
\(526\) 1.73601e14 + 1.65669e15i 0.187988 + 1.79399i
\(527\) 9.29169e14 0.995718
\(528\) 1.72967e15 7.67508e14i 1.83433 0.813947i
\(529\) −1.34507e15 −1.41169
\(530\) 1.83825e13 + 1.75425e14i 0.0190935 + 0.182211i
\(531\) −2.93993e14 + 2.93993e14i −0.302216 + 0.302216i
\(532\) −1.43985e14 9.36329e13i −0.146488 0.0952609i
\(533\) 4.01543e14 + 4.01543e14i 0.404327 + 0.404327i
\(534\) 1.85485e15 + 1.50299e15i 1.84856 + 1.49789i
\(535\) 4.90625e14i 0.483954i
\(536\) 4.43081e14 8.67582e14i 0.432591 0.847041i
\(537\) 2.13408e15i 2.06231i
\(538\) 1.21016e15 1.49347e15i 1.15755 1.42854i
\(539\) 9.69714e14 + 9.69714e14i 0.918132 + 0.918132i
\(540\) 1.01393e14 + 4.78488e14i 0.0950258 + 0.448441i
\(541\) −1.77650e14 + 1.77650e14i −0.164808 + 0.164808i −0.784693 0.619885i \(-0.787179\pi\)
0.619885 + 0.784693i \(0.287179\pi\)
\(542\) 4.15539e13 4.35435e12i 0.0381607 0.00399878i
\(543\) −7.08346e13 −0.0643941
\(544\) −1.04429e15 + 6.00747e14i −0.939786 + 0.540627i
\(545\) −3.07568e15 −2.74007
\(546\) −6.54555e14 + 6.85895e13i −0.577280 + 0.0604920i
\(547\) −1.13722e15 + 1.13722e15i −0.992921 + 0.992921i −0.999975 0.00705383i \(-0.997755\pi\)
0.00705383 + 0.999975i \(0.497755\pi\)
\(548\) −2.44287e14 1.15283e15i −0.211158 0.996486i
\(549\) 6.09694e14 + 6.09694e14i 0.521752 + 0.521752i
\(550\) 1.53927e15 1.89963e15i 1.30413 1.60944i
\(551\) 1.93545e14i 0.162348i
\(552\) 2.21988e15 + 1.13371e15i 1.84359 + 0.941539i
\(553\) 1.14837e13i 0.00944266i
\(554\) 3.85425e14 + 3.12311e14i 0.313788 + 0.254263i
\(555\) −2.83978e15 2.83978e15i −2.28914 2.28914i
\(556\) −3.87532e14 2.52011e14i −0.309312 0.201145i
\(557\) 7.54908e14 7.54908e14i 0.596610 0.596610i −0.342799 0.939409i \(-0.611375\pi\)
0.939409 + 0.342799i \(0.111375\pi\)
\(558\) 9.50221e13 + 9.06805e14i 0.0743595 + 0.709620i
\(559\) −1.19253e15 −0.924070
\(560\) 2.67847e14 6.95165e14i 0.205520 0.533401i
\(561\) 2.86357e15 2.17577
\(562\) −3.64042e13 3.47409e14i −0.0273906 0.261391i
\(563\) −2.41426e14 + 2.41426e14i −0.179882 + 0.179882i −0.791304 0.611422i \(-0.790598\pi\)
0.611422 + 0.791304i \(0.290598\pi\)
\(564\) −9.15829e14 + 1.40832e15i −0.675740 + 1.03912i
\(565\) 2.82236e14 + 2.82236e14i 0.206227 + 0.206227i
\(566\) 6.43598e14 + 5.21509e14i 0.465719 + 0.377373i
\(567\) 6.07177e14i 0.435120i
\(568\) 2.36467e14 + 7.30101e14i 0.167824 + 0.518164i
\(569\) 2.70660e14i 0.190242i −0.995466 0.0951212i \(-0.969676\pi\)
0.995466 0.0951212i \(-0.0303239\pi\)
\(570\) −8.75589e14 + 1.08057e15i −0.609521 + 0.752214i
\(571\) −3.17050e13 3.17050e13i −0.0218590 0.0218590i 0.696093 0.717952i \(-0.254920\pi\)
−0.717952 + 0.696093i \(0.754920\pi\)
\(572\) −2.53250e15 + 5.36643e14i −1.72930 + 0.366444i
\(573\) 1.85361e14 1.85361e14i 0.125362 0.125362i
\(574\) 2.68131e14 2.80969e13i 0.179611 0.0188210i
\(575\) 3.22063e15 2.13682
\(576\) −6.93083e14 9.57723e14i −0.455472 0.629385i
\(577\) 1.36724e15 0.889974 0.444987 0.895537i \(-0.353208\pi\)
0.444987 + 0.895537i \(0.353208\pi\)
\(578\) −2.70675e14 + 2.83635e13i −0.174520 + 0.0182876i
\(579\) −4.29665e14 + 4.29665e14i −0.274408 + 0.274408i
\(580\) −8.21271e14 + 1.74029e14i −0.519556 + 0.110095i
\(581\) 6.09238e14 + 6.09238e14i 0.381785 + 0.381785i
\(582\) 2.34924e15 2.89922e15i 1.45832 1.79972i
\(583\) 2.90990e14i 0.178937i
\(584\) 3.88495e14 + 1.19950e15i 0.236655 + 0.730681i
\(585\) 2.33013e15i 1.40612i
\(586\) 1.03771e15 + 8.40856e14i 0.620351 + 0.502672i
\(587\) 1.72013e15 + 1.72013e15i 1.01871 + 1.01871i 0.999822 + 0.0188901i \(0.00601326\pi\)
0.0188901 + 0.999822i \(0.493987\pi\)
\(588\) 1.06827e15 1.64274e15i 0.626766 0.963814i
\(589\) 5.26436e14 5.26436e14i 0.305993 0.305993i
\(590\) 1.53465e14 + 1.46453e15i 0.0883740 + 0.843361i
\(591\) −4.13711e15 −2.36029
\(592\) −2.60105e15 1.00219e15i −1.47021 0.566472i
\(593\) −1.53052e15 −0.857112 −0.428556 0.903515i \(-0.640978\pi\)
−0.428556 + 0.903515i \(0.640978\pi\)
\(594\) −8.40934e13 8.02511e14i −0.0466591 0.445272i
\(595\) 7.97161e14 7.97161e14i 0.438231 0.438231i
\(596\) 5.77646e14 + 3.75642e14i 0.314635 + 0.204607i
\(597\) −8.93453e14 8.93453e14i −0.482184 0.482184i
\(598\) −2.64938e15 2.14680e15i −1.41673 1.14798i
\(599\) 1.99443e15i 1.05675i −0.849012 0.528374i \(-0.822802\pi\)
0.849012 0.528374i \(-0.177198\pi\)
\(600\) −3.11132e15 1.58898e15i −1.63347 0.834229i
\(601\) 2.41177e15i 1.25466i 0.778753 + 0.627331i \(0.215853\pi\)
−0.778753 + 0.627331i \(0.784147\pi\)
\(602\) −3.56435e14 + 4.39879e14i −0.183738 + 0.226753i
\(603\) 1.02289e15 + 1.02289e15i 0.522497 + 0.522497i
\(604\) −1.50357e13 7.09559e13i −0.00761065 0.0359158i
\(605\) −2.75201e15 + 2.75201e15i −1.38037 + 1.38037i
\(606\) −2.71165e15 + 2.84148e14i −1.34783 + 0.141236i
\(607\) 3.38451e15 1.66708 0.833542 0.552456i \(-0.186309\pi\)
0.833542 + 0.552456i \(0.186309\pi\)
\(608\) −2.51299e14 + 9.32025e14i −0.122665 + 0.454944i
\(609\) 3.52102e14 0.170323
\(610\) 3.03721e15 3.18262e14i 1.45600 0.152571i
\(611\) 1.62505e15 1.62505e15i 0.772042 0.772042i
\(612\) −3.70856e14 1.75013e15i −0.174611 0.824017i
\(613\) 1.49201e15 + 1.49201e15i 0.696206 + 0.696206i 0.963590 0.267384i \(-0.0861593\pi\)
−0.267384 + 0.963590i \(0.586159\pi\)
\(614\) −2.56586e15 + 3.16655e15i −1.18661 + 1.46440i
\(615\) 2.18312e15i 1.00061i
\(616\) −5.58991e14 + 1.09454e15i −0.253928 + 0.497207i
\(617\) 3.12865e15i 1.40860i −0.709901 0.704301i \(-0.751260\pi\)
0.709901 0.704301i \(-0.248740\pi\)
\(618\) −6.41777e14 5.20033e14i −0.286383 0.232057i
\(619\) −1.29237e15 1.29237e15i −0.571595 0.571595i 0.360979 0.932574i \(-0.382443\pi\)
−0.932574 + 0.360979i \(0.882443\pi\)
\(620\) 2.70719e15 + 1.76048e15i 1.18676 + 0.771750i
\(621\) 7.51575e14 7.51575e14i 0.326564 0.326564i
\(622\) −1.49636e14 1.42799e15i −0.0644448 0.615002i
\(623\) −1.55054e15 −0.661910
\(624\) 1.50028e15 + 3.38107e15i 0.634830 + 1.43067i
\(625\) 1.15081e15 0.482685
\(626\) −1.64421e13 1.56909e14i −0.00683595 0.0652361i
\(627\) 1.62240e15 1.62240e15i 0.668633 0.668633i
\(628\) 3.67667e14 5.65382e14i 0.150202 0.230974i
\(629\) −2.98268e15 2.98268e15i −1.20789 1.20789i
\(630\) 8.59496e14 + 6.96452e14i 0.345041 + 0.279588i
\(631\) 1.68624e15i 0.671053i 0.942031 + 0.335526i \(0.108914\pi\)
−0.942031 + 0.335526i \(0.891086\pi\)
\(632\) 6.14025e13 1.98872e13i 0.0242238 0.00784565i
\(633\) 3.25445e15i 1.27279i
\(634\) 2.03773e13 2.51478e13i 0.00790052 0.00975009i
\(635\) −1.76699e15 1.76699e15i −0.679171 0.679171i
\(636\) −4.06757e14 + 8.61928e13i −0.154996 + 0.0328441i
\(637\) −1.89554e15 + 1.89554e15i −0.716089 + 0.716089i
\(638\) 1.37742e15 1.44337e14i 0.515885 0.0540585i
\(639\) −1.13960e15 −0.423151
\(640\) −4.18084e15 2.28292e14i −1.53912 0.0840429i
\(641\) 4.46079e15 1.62814 0.814072 0.580764i \(-0.197246\pi\)
0.814072 + 0.580764i \(0.197246\pi\)
\(642\) −1.15024e15 + 1.20531e14i −0.416240 + 0.0436170i
\(643\) 1.45584e15 1.45584e15i 0.522341 0.522341i −0.395937 0.918278i \(-0.629580\pi\)
0.918278 + 0.395937i \(0.129580\pi\)
\(644\) −1.58375e15 + 3.35600e14i −0.563395 + 0.119385i
\(645\) 3.24179e15 + 3.24179e15i 1.14342 + 1.14342i
\(646\) −9.19649e14 + 1.13495e15i −0.321620 + 0.396914i
\(647\) 8.08350e14i 0.280302i 0.990130 + 0.140151i \(0.0447588\pi\)
−0.990130 + 0.140151i \(0.955241\pi\)
\(648\) −3.24653e15 + 1.05149e15i −1.11624 + 0.361529i
\(649\) 2.42932e15i 0.828206i
\(650\) 3.71329e15 + 3.00889e15i 1.25526 + 1.01714i
\(651\) −9.57707e14 9.57707e14i −0.321024 0.321024i
\(652\) 4.37406e14 6.72624e14i 0.145386 0.223568i
\(653\) −2.55968e15 + 2.55968e15i −0.843651 + 0.843651i −0.989332 0.145681i \(-0.953463\pi\)
0.145681 + 0.989332i \(0.453463\pi\)
\(654\) −7.55597e14 7.21073e15i −0.246952 2.35669i
\(655\) −1.37820e14 −0.0446670
\(656\) −6.14574e14 1.38502e15i −0.197516 0.445127i
\(657\) −1.87226e15 −0.596701
\(658\) −1.13709e14 1.08513e15i −0.0359378 0.342957i
\(659\) 3.34914e15 3.34914e15i 1.04969 1.04969i 0.0509959 0.998699i \(-0.483760\pi\)
0.998699 0.0509959i \(-0.0162395\pi\)
\(660\) 8.34319e15 + 5.42556e15i 2.59323 + 1.68637i
\(661\) 2.53860e15 + 2.53860e15i 0.782505 + 0.782505i 0.980253 0.197748i \(-0.0633629\pi\)
−0.197748 + 0.980253i \(0.563363\pi\)
\(662\) 1.93086e15 + 1.56458e15i 0.590246 + 0.478277i
\(663\) 5.59756e15i 1.69697i
\(664\) 2.20248e15 4.31261e15i 0.662199 1.29663i
\(665\) 9.03289e14i 0.269344i
\(666\) 2.60586e15 3.21591e15i 0.770625 0.951034i
\(667\) 1.28999e15 + 1.28999e15i 0.378352 + 0.378352i
\(668\) −3.72475e14 1.75776e15i −0.108349 0.511317i
\(669\) 3.13797e15 3.13797e15i 0.905326 0.905326i
\(670\) 5.09555e15 5.33952e14i 1.45808 0.152789i
\(671\) −5.03801e15 −1.42983
\(672\) 1.69557e15 + 4.57170e14i 0.477292 + 0.128691i
\(673\) −4.21609e15 −1.17714 −0.588568 0.808448i \(-0.700308\pi\)
−0.588568 + 0.808448i \(0.700308\pi\)
\(674\) 7.60099e14 7.96491e13i 0.210494 0.0220573i
\(675\) −1.05338e15 + 1.05338e15i −0.289345 + 0.289345i
\(676\) −2.88140e14 1.35978e15i −0.0785050 0.370477i
\(677\) 1.11815e15 + 1.11815e15i 0.302177 + 0.302177i 0.841865 0.539688i \(-0.181458\pi\)
−0.539688 + 0.841865i \(0.681458\pi\)
\(678\) −5.92347e14 + 7.31020e14i −0.158786 + 0.195959i
\(679\) 2.42356e15i 0.644423i
\(680\) −5.64285e15 2.88185e15i −1.48833 0.760104i
\(681\) 6.06026e15i 1.58556i
\(682\) −4.13914e15 3.35395e15i −1.07423 0.870448i
\(683\) 4.70621e15 + 4.70621e15i 1.21159 + 1.21159i 0.970502 + 0.241093i \(0.0775057\pi\)
0.241093 + 0.970502i \(0.422494\pi\)
\(684\) −1.20168e15 7.81448e14i −0.306887 0.199568i
\(685\) 4.38240e15 4.38240e15i 1.11023 1.11023i
\(686\) 2.86420e14 + 2.73333e15i 0.0719815 + 0.686926i
\(687\) −6.98825e15 −1.74223
\(688\) 2.96926e15 + 1.14406e15i 0.734365 + 0.282952i
\(689\) 5.68811e14 0.139560
\(690\) 1.36622e15 + 1.30380e16i 0.332546 + 3.17352i
\(691\) −2.60319e15 + 2.60319e15i −0.628602 + 0.628602i −0.947716 0.319114i \(-0.896615\pi\)
0.319114 + 0.947716i \(0.396615\pi\)
\(692\) 5.09406e14 7.83343e14i 0.122034 0.187659i
\(693\) −1.29048e15 1.29048e15i −0.306702 0.306702i
\(694\) −1.94181e15 1.57345e15i −0.457856 0.371002i
\(695\) 2.43119e15i 0.568724i
\(696\) −6.09760e14 1.88266e15i −0.141517 0.436939i
\(697\) 2.29298e15i 0.527982i
\(698\) −1.92092e15 + 2.37062e15i −0.438839 + 0.541574i
\(699\) 4.93104e15 + 4.93104e15i 1.11767 + 1.11767i
\(700\) 2.21973e15 4.70366e14i 0.499184 0.105778i
\(701\) −5.24078e15 + 5.24078e15i −1.16936 + 1.16936i −0.186996 + 0.982361i \(0.559875\pi\)
−0.982361 + 0.186996i \(0.940125\pi\)
\(702\) 1.56871e15 1.64381e14i 0.347286 0.0363914i
\(703\) −3.37977e15 −0.742391
\(704\) 6.82046e15 + 1.09338e15i 1.48650 + 0.238300i
\(705\) −8.83512e15 −1.91061
\(706\) −4.98131e15 + 5.21981e14i −1.06885 + 0.112003i
\(707\) 1.25215e15 1.25215e15i 0.266594 0.266594i
\(708\) −3.39580e15 + 7.19578e14i −0.717396 + 0.152018i
\(709\) −1.92644e15 1.92644e15i −0.403832 0.403832i 0.475749 0.879581i \(-0.342177\pi\)
−0.879581 + 0.475749i \(0.842177\pi\)
\(710\) −2.54102e15 + 3.13590e15i −0.528552 + 0.652290i
\(711\) 9.58416e13i 0.0197820i
\(712\) 2.68518e15 + 8.29062e15i 0.549964 + 1.69804i
\(713\) 7.01750e15i 1.42623i
\(714\) 2.06473e15 + 1.67305e15i 0.416411 + 0.337419i
\(715\) −9.62714e15 9.62714e15i −1.92670 1.92670i
\(716\) 4.24688e15 6.53066e15i 0.843428 1.29699i
\(717\) −1.44479e15 + 1.44479e15i −0.284740 + 0.284740i
\(718\) −7.31715e14 6.98282e15i −0.143106 1.36567i
\(719\) 5.69406e15 1.10513 0.552564 0.833470i \(-0.313649\pi\)
0.552564 + 0.833470i \(0.313649\pi\)
\(720\) 2.23542e15 5.80175e15i 0.430557 1.11746i
\(721\) 5.36485e14 0.102545
\(722\) −4.27427e14 4.07898e15i −0.0810789 0.773743i
\(723\) −5.04824e15 + 5.04824e15i −0.950340 + 0.950340i
\(724\) −2.16766e14 1.40962e14i −0.0404976 0.0263355i
\(725\) −1.80801e15 1.80801e15i −0.335230 0.335230i
\(726\) −7.12798e15 5.77582e15i −1.31164 1.06283i
\(727\) 5.41605e15i 0.989107i 0.869147 + 0.494554i \(0.164668\pi\)
−0.869147 + 0.494554i \(0.835332\pi\)
\(728\) −2.13955e15 1.09268e15i −0.387792 0.198049i
\(729\) 2.86370e15i 0.515141i
\(730\) −4.17470e15 + 5.15202e15i −0.745331 + 0.919818i
\(731\) 3.40492e15 + 3.40492e15i 0.603339 + 0.603339i
\(732\) 1.49229e15 + 7.04233e15i 0.262447 + 1.23853i
\(733\) 5.58948e14 5.58948e14i 0.0975663 0.0975663i −0.656639 0.754205i \(-0.728022\pi\)
0.754205 + 0.656639i \(0.228022\pi\)
\(734\) −1.17321e15 + 1.22939e14i −0.203259 + 0.0212990i
\(735\) 1.03057e16 1.77214
\(736\) 4.53711e15 + 7.88698e15i 0.774375 + 1.34612i
\(737\) −8.45233e15 −1.43188
\(738\) 2.23779e15 2.34493e14i 0.376278 0.0394294i
\(739\) −7.72823e14 + 7.72823e14i −0.128984 + 0.128984i −0.768652 0.639668i \(-0.779072\pi\)
0.639668 + 0.768652i \(0.279072\pi\)
\(740\) −3.03899e15 1.43414e16i −0.503448 2.37585i
\(741\) 3.17139e15 + 3.17139e15i 0.521494 + 0.521494i
\(742\) 1.70012e14 2.09813e14i 0.0277496 0.0342460i
\(743\) 2.58158e15i 0.418261i −0.977888 0.209131i \(-0.932937\pi\)
0.977888 0.209131i \(-0.0670634\pi\)
\(744\) −3.46225e15 + 6.77931e15i −0.556811 + 1.09027i
\(745\) 3.62386e15i 0.578512i
\(746\) −2.06362e15 1.67216e15i −0.327014 0.264980i
\(747\) 5.08462e15 + 5.08462e15i 0.799825 + 0.799825i
\(748\) 8.76303e15 + 5.69858e15i 1.36834 + 0.889831i
\(749\) 5.31141e14 5.31141e14i 0.0823303 0.0823303i
\(750\) −5.23211e14 4.99304e15i −0.0805081 0.768296i
\(751\) 1.74701e15 0.266856 0.133428 0.991059i \(-0.457402\pi\)
0.133428 + 0.991059i \(0.457402\pi\)
\(752\) −5.60519e15 + 2.48719e15i −0.849948 + 0.377147i
\(753\) 1.66107e16 2.50044
\(754\) 2.82142e14 + 2.69251e15i 0.0421624 + 0.402360i
\(755\) 2.69735e14 2.69735e14i 0.0400155 0.0400155i
\(756\) 4.08236e14 6.27767e14i 0.0601231 0.0924547i
\(757\) 7.44756e15 + 7.44756e15i 1.08890 + 1.08890i 0.995642 + 0.0932537i \(0.0297268\pi\)
0.0932537 + 0.995642i \(0.470273\pi\)
\(758\) −1.10893e15 8.98565e14i −0.160961 0.130427i
\(759\) 2.16270e16i 3.11649i
\(760\) −4.82981e15 + 1.56429e15i −0.690964 + 0.223791i
\(761\) 9.46000e15i 1.34362i 0.740725 + 0.671809i \(0.234482\pi\)