Properties

Label 3.9.b.a.2.1
Level 3
Weight 9
Character 3.2
Analytic conductor 1.222
Analytic rank 0
Dimension 2
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 9 \)
Character orbit: \([\chi]\) = 3.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(1.22213583018\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-14}) \)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2\cdot 3 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2.1
Root \(-3.74166i\)
Character \(\chi\) = 3.2
Dual form 3.9.b.a.2.2

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-22.4499i q^{2}\) \(+(45.0000 + 67.3498i) q^{3}\) \(-248.000 q^{4}\) \(+224.499i q^{5}\) \(+(1512.00 - 1010.25i) q^{6}\) \(-1750.00 q^{7}\) \(-179.600i q^{8}\) \(+(-2511.00 + 6061.48i) q^{9}\) \(+O(q^{10})\) \(q\)\(-22.4499i q^{2}\) \(+(45.0000 + 67.3498i) q^{3}\) \(-248.000 q^{4}\) \(+224.499i q^{5}\) \(+(1512.00 - 1010.25i) q^{6}\) \(-1750.00 q^{7}\) \(-179.600i q^{8}\) \(+(-2511.00 + 6061.48i) q^{9}\) \(+5040.00 q^{10}\) \(-6959.48i q^{11}\) \(+(-11160.0 - 16702.8i) q^{12}\) \(+25730.0 q^{13}\) \(+39287.4i q^{14}\) \(+(-15120.0 + 10102.5i) q^{15}\) \(-67520.0 q^{16}\) \(-74893.0i q^{17}\) \(+(136080. + 56371.8i) q^{18}\) \(+18938.0 q^{19}\) \(-55675.9i q^{20}\) \(+(-78750.0 - 117862. i) q^{21}\) \(-156240. q^{22}\) \(+470461. i q^{23}\) \(+(12096.0 - 8081.98i) q^{24}\) \(+340225. q^{25}\) \(-577637. i q^{26}\) \(+(-521235. + 103651. i) q^{27}\) \(+434000. q^{28}\) \(-460897. i q^{29}\) \(+(226800. + 339443. i) q^{30}\) \(-351478. q^{31}\) \(+1.46984e6i q^{32}\) \(+(468720. - 313177. i) q^{33}\) \(-1.68134e6 q^{34}\) \(-392874. i q^{35}\) \(+(622728. - 1.50325e6i) q^{36}\) \(+1.33517e6 q^{37}\) \(-425157. i q^{38}\) \(+(1.15785e6 + 1.73291e6i) q^{39}\) \(+40320.0 q^{40}\) \(-1.87547e6i q^{41}\) \(+(-2.64600e6 + 1.76793e6i) q^{42}\) \(-3.52615e6 q^{43}\) \(+1.72595e6i q^{44}\) \(+(-1.36080e6 - 563718. i) q^{45}\) \(+1.05618e7 q^{46}\) \(+4.08104e6i q^{47}\) \(+(-3.03840e6 - 4.54746e6i) q^{48}\) \(-2.70230e6 q^{49}\) \(-7.63803e6i q^{50}\) \(+(5.04403e6 - 3.37019e6i) q^{51}\) \(-6.38104e6 q^{52}\) \(+6.60177e6i q^{53}\) \(+(2.32697e6 + 1.17017e7i) q^{54}\) \(+1.56240e6 q^{55}\) \(+314299. i q^{56}\) \(+(852210. + 1.27547e6i) q^{57}\) \(-1.03471e7 q^{58}\) \(-1.37149e7i q^{59}\) \(+(3.74976e6 - 2.50541e6i) q^{60}\) \(+753602. q^{61}\) \(+7.89066e6i q^{62}\) \(+(4.39425e6 - 1.06076e7i) q^{63}\) \(+1.57128e7 q^{64}\) \(+5.77637e6i q^{65}\) \(+(-7.03080e6 - 1.05227e7i) q^{66}\) \(+2.26889e6 q^{67}\) \(+1.85735e7i q^{68}\) \(+(-3.16855e7 + 2.11707e7i) q^{69}\) \(-8.82000e6 q^{70}\) \(-1.70220e7i q^{71}\) \(+(1.08864e6 + 450974. i) q^{72}\) \(+2.76728e7 q^{73}\) \(-2.99745e7i q^{74}\) \(+(1.53101e7 + 2.29141e7i) q^{75}\) \(-4.69662e6 q^{76}\) \(+1.21791e7i q^{77}\) \(+(3.89038e7 - 2.59937e7i) q^{78}\) \(-2.29810e7 q^{79}\) \(-1.51582e7i q^{80}\) \(+(-3.04365e7 - 3.04408e7i) q^{81}\) \(-4.21042e7 q^{82}\) \(+4.63952e7i q^{83}\) \(+(1.95300e7 + 2.92298e7i) q^{84}\) \(+1.68134e7 q^{85}\) \(+7.91619e7i q^{86}\) \(+(3.10414e7 - 2.07404e7i) q^{87}\) \(-1.24992e6 q^{88}\) \(-7.26152e7i q^{89}\) \(+(-1.26554e7 + 3.05499e7i) q^{90}\) \(-4.50275e7 q^{91}\) \(-1.16674e8i q^{92}\) \(+(-1.58165e7 - 2.36720e7i) q^{93}\) \(+9.16191e7 q^{94}\) \(+4.25157e6i q^{95}\) \(+(-9.89937e7 + 6.61429e7i) q^{96}\) \(+1.47271e8 q^{97}\) \(+6.06665e7i q^{98}\) \(+(4.21848e7 + 1.74753e7i) q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut +\mathstrut 90q^{3} \) \(\mathstrut -\mathstrut 496q^{4} \) \(\mathstrut +\mathstrut 3024q^{6} \) \(\mathstrut -\mathstrut 3500q^{7} \) \(\mathstrut -\mathstrut 5022q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut 90q^{3} \) \(\mathstrut -\mathstrut 496q^{4} \) \(\mathstrut +\mathstrut 3024q^{6} \) \(\mathstrut -\mathstrut 3500q^{7} \) \(\mathstrut -\mathstrut 5022q^{9} \) \(\mathstrut +\mathstrut 10080q^{10} \) \(\mathstrut -\mathstrut 22320q^{12} \) \(\mathstrut +\mathstrut 51460q^{13} \) \(\mathstrut -\mathstrut 30240q^{15} \) \(\mathstrut -\mathstrut 135040q^{16} \) \(\mathstrut +\mathstrut 272160q^{18} \) \(\mathstrut +\mathstrut 37876q^{19} \) \(\mathstrut -\mathstrut 157500q^{21} \) \(\mathstrut -\mathstrut 312480q^{22} \) \(\mathstrut +\mathstrut 24192q^{24} \) \(\mathstrut +\mathstrut 680450q^{25} \) \(\mathstrut -\mathstrut 1042470q^{27} \) \(\mathstrut +\mathstrut 868000q^{28} \) \(\mathstrut +\mathstrut 453600q^{30} \) \(\mathstrut -\mathstrut 702956q^{31} \) \(\mathstrut +\mathstrut 937440q^{33} \) \(\mathstrut -\mathstrut 3362688q^{34} \) \(\mathstrut +\mathstrut 1245456q^{36} \) \(\mathstrut +\mathstrut 2670340q^{37} \) \(\mathstrut +\mathstrut 2315700q^{39} \) \(\mathstrut +\mathstrut 80640q^{40} \) \(\mathstrut -\mathstrut 5292000q^{42} \) \(\mathstrut -\mathstrut 7052300q^{43} \) \(\mathstrut -\mathstrut 2721600q^{45} \) \(\mathstrut +\mathstrut 21123648q^{46} \) \(\mathstrut -\mathstrut 6076800q^{48} \) \(\mathstrut -\mathstrut 5404602q^{49} \) \(\mathstrut +\mathstrut 10088064q^{51} \) \(\mathstrut -\mathstrut 12762080q^{52} \) \(\mathstrut +\mathstrut 4653936q^{54} \) \(\mathstrut +\mathstrut 3124800q^{55} \) \(\mathstrut +\mathstrut 1704420q^{57} \) \(\mathstrut -\mathstrut 20694240q^{58} \) \(\mathstrut +\mathstrut 7499520q^{60} \) \(\mathstrut +\mathstrut 1507204q^{61} \) \(\mathstrut +\mathstrut 8788500q^{63} \) \(\mathstrut +\mathstrut 31425536q^{64} \) \(\mathstrut -\mathstrut 14061600q^{66} \) \(\mathstrut +\mathstrut 4537780q^{67} \) \(\mathstrut -\mathstrut 63370944q^{69} \) \(\mathstrut -\mathstrut 17640000q^{70} \) \(\mathstrut +\mathstrut 2177280q^{72} \) \(\mathstrut +\mathstrut 55345540q^{73} \) \(\mathstrut +\mathstrut 30620250q^{75} \) \(\mathstrut -\mathstrut 9393248q^{76} \) \(\mathstrut +\mathstrut 77807520q^{78} \) \(\mathstrut -\mathstrut 45961964q^{79} \) \(\mathstrut -\mathstrut 60872958q^{81} \) \(\mathstrut -\mathstrut 84208320q^{82} \) \(\mathstrut +\mathstrut 39060000q^{84} \) \(\mathstrut +\mathstrut 33626880q^{85} \) \(\mathstrut +\mathstrut 62082720q^{87} \) \(\mathstrut -\mathstrut 2499840q^{88} \) \(\mathstrut -\mathstrut 25310880q^{90} \) \(\mathstrut -\mathstrut 90055000q^{91} \) \(\mathstrut -\mathstrut 31633020q^{93} \) \(\mathstrut +\mathstrut 183238272q^{94} \) \(\mathstrut -\mathstrut 197987328q^{96} \) \(\mathstrut +\mathstrut 294542020q^{97} \) \(\mathstrut +\mathstrut 84369600q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 22.4499i 1.40312i −0.712610 0.701561i \(-0.752487\pi\)
0.712610 0.701561i \(-0.247513\pi\)
\(3\) 45.0000 + 67.3498i 0.555556 + 0.831479i
\(4\) −248.000 −0.968750
\(5\) 224.499i 0.359199i 0.983740 + 0.179600i \(0.0574802\pi\)
−0.983740 + 0.179600i \(0.942520\pi\)
\(6\) 1512.00 1010.25i 1.16667 0.779512i
\(7\) −1750.00 −0.728863 −0.364431 0.931230i \(-0.618737\pi\)
−0.364431 + 0.931230i \(0.618737\pi\)
\(8\) 179.600i 0.0438475i
\(9\) −2511.00 + 6061.48i −0.382716 + 0.923866i
\(10\) 5040.00 0.504000
\(11\) 6959.48i 0.475342i −0.971346 0.237671i \(-0.923616\pi\)
0.971346 0.237671i \(-0.0763840\pi\)
\(12\) −11160.0 16702.8i −0.538194 0.805496i
\(13\) 25730.0 0.900879 0.450439 0.892807i \(-0.351267\pi\)
0.450439 + 0.892807i \(0.351267\pi\)
\(14\) 39287.4i 1.02268i
\(15\) −15120.0 + 10102.5i −0.298667 + 0.199555i
\(16\) −67520.0 −1.03027
\(17\) 74893.0i 0.896697i −0.893859 0.448348i \(-0.852012\pi\)
0.893859 0.448348i \(-0.147988\pi\)
\(18\) 136080. + 56371.8i 1.29630 + 0.536997i
\(19\) 18938.0 0.145318 0.0726590 0.997357i \(-0.476852\pi\)
0.0726590 + 0.997357i \(0.476852\pi\)
\(20\) 55675.9i 0.347974i
\(21\) −78750.0 117862.i −0.404924 0.606035i
\(22\) −156240. −0.666963
\(23\) 470461.i 1.68117i 0.541678 + 0.840586i \(0.317789\pi\)
−0.541678 + 0.840586i \(0.682211\pi\)
\(24\) 12096.0 8081.98i 0.0364583 0.0243597i
\(25\) 340225. 0.870976
\(26\) 577637.i 1.26404i
\(27\) −521235. + 103651.i −0.980796 + 0.195038i
\(28\) 434000. 0.706086
\(29\) 460897.i 0.651647i −0.945431 0.325823i \(-0.894359\pi\)
0.945431 0.325823i \(-0.105641\pi\)
\(30\) 226800. + 339443.i 0.280000 + 0.419066i
\(31\) −351478. −0.380585 −0.190292 0.981727i \(-0.560944\pi\)
−0.190292 + 0.981727i \(0.560944\pi\)
\(32\) 1.46984e6i 1.40175i
\(33\) 468720. 313177.i 0.395237 0.264079i
\(34\) −1.68134e6 −1.25817
\(35\) 392874.i 0.261807i
\(36\) 622728. 1.50325e6i 0.370756 0.894995i
\(37\) 1.33517e6 0.712409 0.356205 0.934408i \(-0.384071\pi\)
0.356205 + 0.934408i \(0.384071\pi\)
\(38\) 425157.i 0.203899i
\(39\) 1.15785e6 + 1.73291e6i 0.500488 + 0.749062i
\(40\) 40320.0 0.0157500
\(41\) 1.87547e6i 0.663704i −0.943331 0.331852i \(-0.892327\pi\)
0.943331 0.331852i \(-0.107673\pi\)
\(42\) −2.64600e6 + 1.76793e6i −0.850340 + 0.568157i
\(43\) −3.52615e6 −1.03140 −0.515700 0.856769i \(-0.672468\pi\)
−0.515700 + 0.856769i \(0.672468\pi\)
\(44\) 1.72595e6i 0.460488i
\(45\) −1.36080e6 563718.i −0.331852 0.137471i
\(46\) 1.05618e7 2.35889
\(47\) 4.08104e6i 0.836333i 0.908370 + 0.418167i \(0.137327\pi\)
−0.908370 + 0.418167i \(0.862673\pi\)
\(48\) −3.03840e6 4.54746e6i −0.572374 0.856651i
\(49\) −2.70230e6 −0.468759
\(50\) 7.63803e6i 1.22209i
\(51\) 5.04403e6 3.37019e6i 0.745585 0.498165i
\(52\) −6.38104e6 −0.872726
\(53\) 6.60177e6i 0.836675i 0.908292 + 0.418337i \(0.137387\pi\)
−0.908292 + 0.418337i \(0.862613\pi\)
\(54\) 2.32697e6 + 1.17017e7i 0.273663 + 1.37618i
\(55\) 1.56240e6 0.170742
\(56\) 314299.i 0.0319589i
\(57\) 852210. + 1.27547e6i 0.0807323 + 0.120829i
\(58\) −1.03471e7 −0.914340
\(59\) 1.37149e7i 1.13184i −0.824461 0.565919i \(-0.808521\pi\)
0.824461 0.565919i \(-0.191479\pi\)
\(60\) 3.74976e6 2.50541e6i 0.289333 0.193319i
\(61\) 753602. 0.0544280 0.0272140 0.999630i \(-0.491336\pi\)
0.0272140 + 0.999630i \(0.491336\pi\)
\(62\) 7.89066e6i 0.534007i
\(63\) 4.39425e6 1.06076e7i 0.278948 0.673372i
\(64\) 1.57128e7 0.936554
\(65\) 5.77637e6i 0.323595i
\(66\) −7.03080e6 1.05227e7i −0.370535 0.554566i
\(67\) 2.26889e6 0.112594 0.0562969 0.998414i \(-0.482071\pi\)
0.0562969 + 0.998414i \(0.482071\pi\)
\(68\) 1.85735e7i 0.868675i
\(69\) −3.16855e7 + 2.11707e7i −1.39786 + 0.933985i
\(70\) −8.82000e6 −0.367347
\(71\) 1.70220e7i 0.669849i −0.942245 0.334925i \(-0.891289\pi\)
0.942245 0.334925i \(-0.108711\pi\)
\(72\) 1.08864e6 + 450974.i 0.0405093 + 0.0167812i
\(73\) 2.76728e7 0.974454 0.487227 0.873275i \(-0.338008\pi\)
0.487227 + 0.873275i \(0.338008\pi\)
\(74\) 2.99745e7i 0.999597i
\(75\) 1.53101e7 + 2.29141e7i 0.483876 + 0.724199i
\(76\) −4.69662e6 −0.140777
\(77\) 1.21791e7i 0.346459i
\(78\) 3.89038e7 2.59937e7i 1.05103 0.702246i
\(79\) −2.29810e7 −0.590011 −0.295006 0.955496i \(-0.595322\pi\)
−0.295006 + 0.955496i \(0.595322\pi\)
\(80\) 1.51582e7i 0.370073i
\(81\) −3.04365e7 3.04408e7i −0.707057 0.707157i
\(82\) −4.21042e7 −0.931257
\(83\) 4.63952e7i 0.977599i 0.872396 + 0.488799i \(0.162565\pi\)
−0.872396 + 0.488799i \(0.837435\pi\)
\(84\) 1.95300e7 + 2.92298e7i 0.392270 + 0.587096i
\(85\) 1.68134e7 0.322093
\(86\) 7.91619e7i 1.44718i
\(87\) 3.10414e7 2.07404e7i 0.541831 0.362026i
\(88\) −1.24992e6 −0.0208426
\(89\) 7.26152e7i 1.15736i −0.815555 0.578679i \(-0.803568\pi\)
0.815555 0.578679i \(-0.196432\pi\)
\(90\) −1.26554e7 + 3.05499e7i −0.192889 + 0.465628i
\(91\) −4.50275e7 −0.656617
\(92\) 1.16674e8i 1.62864i
\(93\) −1.58165e7 2.36720e7i −0.211436 0.316448i
\(94\) 9.16191e7 1.17348
\(95\) 4.25157e6i 0.0521981i
\(96\) −9.89937e7 + 6.61429e7i −1.16553 + 0.778751i
\(97\) 1.47271e8 1.66353 0.831764 0.555129i \(-0.187331\pi\)
0.831764 + 0.555129i \(0.187331\pi\)
\(98\) 6.06665e7i 0.657726i
\(99\) 4.21848e7 + 1.74753e7i 0.439152 + 0.181921i
\(100\) −8.43758e7 −0.843758
\(101\) 1.03545e8i 0.995045i 0.867451 + 0.497522i \(0.165757\pi\)
−0.867451 + 0.497522i \(0.834243\pi\)
\(102\) −7.56605e7 1.13238e8i −0.698986 1.04615i
\(103\) −1.66064e8 −1.47545 −0.737726 0.675100i \(-0.764101\pi\)
−0.737726 + 0.675100i \(0.764101\pi\)
\(104\) 4.62110e6i 0.0395013i
\(105\) 2.64600e7 1.76793e7i 0.217687 0.145448i
\(106\) 1.48209e8 1.17396
\(107\) 2.25540e7i 0.172063i 0.996292 + 0.0860316i \(0.0274186\pi\)
−0.996292 + 0.0860316i \(0.972581\pi\)
\(108\) 1.29266e8 2.57055e7i 0.950146 0.188943i
\(109\) −1.09975e8 −0.779091 −0.389546 0.921007i \(-0.627368\pi\)
−0.389546 + 0.921007i \(0.627368\pi\)
\(110\) 3.50758e7i 0.239572i
\(111\) 6.00826e7 + 8.99235e7i 0.395783 + 0.592354i
\(112\) 1.18160e8 0.750928
\(113\) 2.87748e8i 1.76481i −0.470490 0.882405i \(-0.655923\pi\)
0.470490 0.882405i \(-0.344077\pi\)
\(114\) 2.86343e7 1.91321e7i 0.169538 0.113277i
\(115\) −1.05618e8 −0.603876
\(116\) 1.14303e8i 0.631283i
\(117\) −6.46080e7 + 1.55962e8i −0.344781 + 0.832291i
\(118\) −3.07899e8 −1.58811
\(119\) 1.31063e8i 0.653569i
\(120\) 1.81440e6 + 2.71555e6i 0.00875000 + 0.0130958i
\(121\) 1.65924e8 0.774050
\(122\) 1.69183e7i 0.0763692i
\(123\) 1.26312e8 8.43961e7i 0.551856 0.368724i
\(124\) 8.71665e7 0.368691
\(125\) 1.64075e8i 0.672053i
\(126\) −2.38140e8 9.86507e7i −0.944822 0.391397i
\(127\) 2.75994e8 1.06092 0.530462 0.847708i \(-0.322018\pi\)
0.530462 + 0.847708i \(0.322018\pi\)
\(128\) 2.35290e7i 0.0876523i
\(129\) −1.58677e8 2.37486e8i −0.573000 0.857588i
\(130\) 1.29679e8 0.454043
\(131\) 2.89118e8i 0.981725i −0.871237 0.490862i \(-0.836682\pi\)
0.871237 0.490862i \(-0.163318\pi\)
\(132\) −1.16243e8 + 7.76678e7i −0.382886 + 0.255826i
\(133\) −3.31415e7 −0.105917
\(134\) 5.09365e7i 0.157983i
\(135\) −2.32697e7 1.17017e8i −0.0700576 0.352301i
\(136\) −1.34508e7 −0.0393180
\(137\) 2.07562e8i 0.589205i 0.955620 + 0.294602i \(0.0951872\pi\)
−0.955620 + 0.294602i \(0.904813\pi\)
\(138\) 4.75282e8 + 7.11337e8i 1.31049 + 1.96137i
\(139\) −1.42668e8 −0.382180 −0.191090 0.981573i \(-0.561202\pi\)
−0.191090 + 0.981573i \(0.561202\pi\)
\(140\) 9.74328e7i 0.253625i
\(141\) −2.74857e8 + 1.83647e8i −0.695394 + 0.464630i
\(142\) −3.82143e8 −0.939880
\(143\) 1.79067e8i 0.428226i
\(144\) 1.69543e8 4.09271e8i 0.394302 0.951835i
\(145\) 1.03471e8 0.234071
\(146\) 6.21252e8i 1.36728i
\(147\) −1.21604e8 1.82000e8i −0.260422 0.389763i
\(148\) −3.31122e8 −0.690147
\(149\) 8.19236e8i 1.66213i 0.556179 + 0.831063i \(0.312267\pi\)
−0.556179 + 0.831063i \(0.687733\pi\)
\(150\) 5.14420e8 3.43711e8i 1.01614 0.678936i
\(151\) 4.23861e8 0.815296 0.407648 0.913139i \(-0.366349\pi\)
0.407648 + 0.913139i \(0.366349\pi\)
\(152\) 3.40126e6i 0.00637184i
\(153\) 4.53963e8 + 1.88056e8i 0.828428 + 0.343180i
\(154\) 2.73420e8 0.486124
\(155\) 7.89066e7i 0.136706i
\(156\) −2.87147e8 4.29762e8i −0.484848 0.725654i
\(157\) −7.59851e8 −1.25063 −0.625316 0.780371i \(-0.715030\pi\)
−0.625316 + 0.780371i \(0.715030\pi\)
\(158\) 5.15922e8i 0.827857i
\(159\) −4.44628e8 + 2.97079e8i −0.695678 + 0.464819i
\(160\) −3.29979e8 −0.503508
\(161\) 8.23307e8i 1.22534i
\(162\) −6.83394e8 + 6.83297e8i −0.992227 + 0.992087i
\(163\) 6.68160e8 0.946520 0.473260 0.880923i \(-0.343077\pi\)
0.473260 + 0.880923i \(0.343077\pi\)
\(164\) 4.65116e8i 0.642963i
\(165\) 7.03080e7 + 1.05227e8i 0.0948569 + 0.141969i
\(166\) 1.04157e9 1.37169
\(167\) 1.96306e8i 0.252387i −0.992006 0.126194i \(-0.959724\pi\)
0.992006 0.126194i \(-0.0402761\pi\)
\(168\) −2.11680e7 + 1.41435e7i −0.0265731 + 0.0177549i
\(169\) −1.53698e8 −0.188417
\(170\) 3.77461e8i 0.451935i
\(171\) −4.75533e7 + 1.14792e8i −0.0556156 + 0.134254i
\(172\) 8.74485e8 0.999168
\(173\) 1.02319e9i 1.14228i −0.820852 0.571141i \(-0.806501\pi\)
0.820852 0.571141i \(-0.193499\pi\)
\(174\) −4.65620e8 6.96877e8i −0.507966 0.760255i
\(175\) −5.95394e8 −0.634822
\(176\) 4.69904e8i 0.489732i
\(177\) 9.23696e8 6.17170e8i 0.941100 0.628799i
\(178\) −1.63021e9 −1.62391
\(179\) 1.28895e9i 1.25552i 0.778408 + 0.627759i \(0.216028\pi\)
−0.778408 + 0.627759i \(0.783972\pi\)
\(180\) 3.37478e8 + 1.39802e8i 0.321481 + 0.133175i
\(181\) 4.71707e8 0.439499 0.219749 0.975556i \(-0.429476\pi\)
0.219749 + 0.975556i \(0.429476\pi\)
\(182\) 1.01086e9i 0.921314i
\(183\) 3.39121e7 + 5.07550e7i 0.0302378 + 0.0452558i
\(184\) 8.44946e7 0.0737153
\(185\) 2.99745e8i 0.255897i
\(186\) −5.31435e8 + 3.55080e8i −0.444016 + 0.296670i
\(187\) −5.21217e8 −0.426238
\(188\) 1.01210e9i 0.810198i
\(189\) 9.12161e8 1.81390e8i 0.714866 0.142156i
\(190\) 9.54475e7 0.0732403
\(191\) 1.61787e8i 0.121565i 0.998151 + 0.0607827i \(0.0193597\pi\)
−0.998151 + 0.0607827i \(0.980640\pi\)
\(192\) 7.07075e8 + 1.05825e9i 0.520308 + 0.778725i
\(193\) −1.58840e9 −1.14480 −0.572401 0.819974i \(-0.693988\pi\)
−0.572401 + 0.819974i \(0.693988\pi\)
\(194\) 3.30623e9i 2.33413i
\(195\) −3.89038e8 + 2.59937e8i −0.269062 + 0.179775i
\(196\) 6.70171e8 0.454110
\(197\) 5.37769e8i 0.357052i 0.983935 + 0.178526i \(0.0571328\pi\)
−0.983935 + 0.178526i \(0.942867\pi\)
\(198\) 3.92319e8 9.47046e8i 0.255257 0.616184i
\(199\) 6.47586e8 0.412938 0.206469 0.978453i \(-0.433803\pi\)
0.206469 + 0.978453i \(0.433803\pi\)
\(200\) 6.11043e7i 0.0381902i
\(201\) 1.02100e8 + 1.52809e8i 0.0625521 + 0.0936194i
\(202\) 2.32457e9 1.39617
\(203\) 8.06570e8i 0.474961i
\(204\) −1.25092e9 + 8.35806e8i −0.722285 + 0.482597i
\(205\) 4.21042e8 0.238402
\(206\) 3.72812e9i 2.07024i
\(207\) −2.85169e9 1.18133e9i −1.55318 0.643412i
\(208\) −1.73729e9 −0.928152
\(209\) 1.31799e8i 0.0690758i
\(210\) −3.96900e8 5.94026e8i −0.204082 0.305441i
\(211\) 5.81104e7 0.0293173 0.0146586 0.999893i \(-0.495334\pi\)
0.0146586 + 0.999893i \(0.495334\pi\)
\(212\) 1.63724e9i 0.810529i
\(213\) 1.14643e9 7.65990e8i 0.556966 0.372139i
\(214\) 5.06336e8 0.241426
\(215\) 7.91619e8i 0.370478i
\(216\) 1.86157e7 + 9.36136e7i 0.00855195 + 0.0430055i
\(217\) 6.15087e8 0.277394
\(218\) 2.46893e9i 1.09316i
\(219\) 1.24527e9 + 1.86376e9i 0.541363 + 0.810238i
\(220\) −3.87475e8 −0.165407
\(221\) 1.92700e9i 0.807815i
\(222\) 2.01878e9 1.34885e9i 0.831144 0.555332i
\(223\) 4.40200e9 1.78004 0.890021 0.455920i \(-0.150690\pi\)
0.890021 + 0.455920i \(0.150690\pi\)
\(224\) 2.57222e9i 1.02168i
\(225\) −8.54305e8 + 2.06227e9i −0.333336 + 0.804665i
\(226\) −6.45992e9 −2.47624
\(227\) 3.53592e9i 1.33168i −0.746095 0.665839i \(-0.768074\pi\)
0.746095 0.665839i \(-0.231926\pi\)
\(228\) −2.11348e8 3.16317e8i −0.0782094 0.117053i
\(229\) −1.86569e9 −0.678420 −0.339210 0.940711i \(-0.610160\pi\)
−0.339210 + 0.940711i \(0.610160\pi\)
\(230\) 2.37112e9i 0.847311i
\(231\) −8.20260e8 + 5.48059e8i −0.288074 + 0.192477i
\(232\) −8.27770e7 −0.0285731
\(233\) 2.72132e9i 0.923328i 0.887055 + 0.461664i \(0.152747\pi\)
−0.887055 + 0.461664i \(0.847253\pi\)
\(234\) 3.50134e9 + 1.45045e9i 1.16781 + 0.483769i
\(235\) −9.16191e8 −0.300410
\(236\) 3.40129e9i 1.09647i
\(237\) −1.03414e9 1.54777e9i −0.327784 0.490582i
\(238\) 2.94235e9 0.917037
\(239\) 2.27461e9i 0.697132i 0.937284 + 0.348566i \(0.113331\pi\)
−0.937284 + 0.348566i \(0.886669\pi\)
\(240\) 1.02090e9 6.82119e8i 0.307708 0.205596i
\(241\) −1.74667e9 −0.517778 −0.258889 0.965907i \(-0.583356\pi\)
−0.258889 + 0.965907i \(0.583356\pi\)
\(242\) 3.72500e9i 1.08609i
\(243\) 6.80540e8 3.41973e9i 0.195177 0.980768i
\(244\) −1.86893e8 −0.0527272
\(245\) 6.06665e8i 0.168378i
\(246\) −1.89469e9 2.83571e9i −0.517365 0.774321i
\(247\) 4.87275e8 0.130914
\(248\) 6.31253e7i 0.0166877i
\(249\) −3.12471e9 + 2.08778e9i −0.812853 + 0.543110i
\(250\) 3.68348e9 0.942972
\(251\) 1.37549e9i 0.346547i −0.984874 0.173274i \(-0.944566\pi\)
0.984874 0.173274i \(-0.0554345\pi\)
\(252\) −1.08977e9 + 2.63068e9i −0.270230 + 0.652329i
\(253\) 3.27417e9 0.799132
\(254\) 6.19605e9i 1.48861i
\(255\) 7.56605e8 + 1.13238e9i 0.178940 + 0.267813i
\(256\) 4.55069e9 1.05954
\(257\) 7.93672e9i 1.81932i 0.415356 + 0.909659i \(0.363657\pi\)
−0.415356 + 0.909659i \(0.636343\pi\)
\(258\) −5.33154e9 + 3.56228e9i −1.20330 + 0.803988i
\(259\) −2.33655e9 −0.519249
\(260\) 1.43254e9i 0.313483i
\(261\) 2.79372e9 + 1.15731e9i 0.602034 + 0.249396i
\(262\) −6.49068e9 −1.37748
\(263\) 3.22555e8i 0.0674187i −0.999432 0.0337093i \(-0.989268\pi\)
0.999432 0.0337093i \(-0.0107320\pi\)
\(264\) −5.62464e7 8.41819e7i −0.0115792 0.0173302i
\(265\) −1.48209e9 −0.300533
\(266\) 7.44025e8i 0.148614i
\(267\) 4.89062e9 3.26769e9i 0.962319 0.642977i
\(268\) −5.62685e8 −0.109075
\(269\) 3.47314e9i 0.663304i −0.943402 0.331652i \(-0.892394\pi\)
0.943402 0.331652i \(-0.107606\pi\)
\(270\) −2.62702e9 + 5.22403e8i −0.494321 + 0.0982993i
\(271\) −1.44216e9 −0.267385 −0.133693 0.991023i \(-0.542683\pi\)
−0.133693 + 0.991023i \(0.542683\pi\)
\(272\) 5.05678e9i 0.923843i
\(273\) −2.02624e9 3.03259e9i −0.364787 0.545964i
\(274\) 4.65976e9 0.826726
\(275\) 2.36779e9i 0.414012i
\(276\) 7.85800e9 5.25035e9i 1.35418 0.904798i
\(277\) 3.38046e9 0.574192 0.287096 0.957902i \(-0.407310\pi\)
0.287096 + 0.957902i \(0.407310\pi\)
\(278\) 3.20289e9i 0.536245i
\(279\) 8.82561e8 2.13048e9i 0.145656 0.351609i
\(280\) −7.05600e7 −0.0114796
\(281\) 4.02262e9i 0.645184i −0.946538 0.322592i \(-0.895446\pi\)
0.946538 0.322592i \(-0.104554\pi\)
\(282\) 4.12286e9 + 6.17053e9i 0.651932 + 0.975722i
\(283\) −1.04253e10 −1.62533 −0.812666 0.582730i \(-0.801984\pi\)
−0.812666 + 0.582730i \(0.801984\pi\)
\(284\) 4.22146e9i 0.648917i
\(285\) −2.86343e8 + 1.91321e8i −0.0434017 + 0.0289990i
\(286\) −4.02006e9 −0.600853
\(287\) 3.28207e9i 0.483749i
\(288\) −8.90943e9 3.69078e9i −1.29503 0.536473i
\(289\) 1.36679e9 0.195935
\(290\) 2.32292e9i 0.328430i
\(291\) 6.62720e9 + 9.91868e9i 0.924183 + 1.38319i
\(292\) −6.86285e9 −0.944002
\(293\) 1.03927e10i 1.41012i −0.709146 0.705061i \(-0.750919\pi\)
0.709146 0.705061i \(-0.249081\pi\)
\(294\) −4.08588e9 + 2.72999e9i −0.546885 + 0.365403i
\(295\) 3.07899e9 0.406555
\(296\) 2.39796e8i 0.0312374i
\(297\) 7.21360e8 + 3.62753e9i 0.0927099 + 0.466213i
\(298\) 1.83918e10 2.33216
\(299\) 1.21050e10i 1.51453i
\(300\) −3.79691e9 5.68270e9i −0.468754 0.701567i
\(301\) 6.17076e9 0.751749
\(302\) 9.51565e9i 1.14396i
\(303\) −6.97372e9 + 4.65951e9i −0.827359 + 0.552803i
\(304\) −1.27869e9 −0.149717
\(305\) 1.69183e8i 0.0195505i
\(306\) 4.22185e9 1.01914e10i 0.481524 1.16238i
\(307\) −2.99309e9 −0.336951 −0.168476 0.985706i \(-0.553884\pi\)
−0.168476 + 0.985706i \(0.553884\pi\)
\(308\) 3.02042e9i 0.335632i
\(309\) −7.47286e9 1.11843e10i −0.819696 1.22681i
\(310\) −1.77145e9 −0.191815
\(311\) 6.44832e9i 0.689295i −0.938732 0.344647i \(-0.887998\pi\)
0.938732 0.344647i \(-0.112002\pi\)
\(312\) 3.11230e8 2.07949e8i 0.0328445 0.0219452i
\(313\) 3.27737e7 0.00341467 0.00170733 0.999999i \(-0.499457\pi\)
0.00170733 + 0.999999i \(0.499457\pi\)
\(314\) 1.70586e10i 1.75479i
\(315\) 2.38140e9 + 9.86507e8i 0.241875 + 0.100198i
\(316\) 5.69928e9 0.571573
\(317\) 1.17797e10i 1.16653i 0.812282 + 0.583264i \(0.198225\pi\)
−0.812282 + 0.583264i \(0.801775\pi\)
\(318\) 6.66942e9 + 9.98187e9i 0.652198 + 0.976120i
\(319\) −3.20761e9 −0.309755
\(320\) 3.52751e9i 0.336409i
\(321\) −1.51901e9 + 1.01493e9i −0.143067 + 0.0955907i
\(322\) −1.84832e10 −1.71931
\(323\) 1.41832e9i 0.130306i
\(324\) 7.54825e9 + 7.54931e9i 0.684961 + 0.685058i
\(325\) 8.75399e9 0.784644
\(326\) 1.50002e10i 1.32808i
\(327\) −4.94888e9 7.40680e9i −0.432829 0.647798i
\(328\) −3.36833e8 −0.0291018
\(329\) 7.14182e9i 0.609573i
\(330\) 2.36235e9 1.57841e9i 0.199200 0.133096i
\(331\) −1.20100e10 −1.00053 −0.500265 0.865872i \(-0.666764\pi\)
−0.500265 + 0.865872i \(0.666764\pi\)
\(332\) 1.15060e10i 0.947049i
\(333\) −3.35261e9 + 8.09311e9i −0.272651 + 0.658171i
\(334\) −4.40705e9 −0.354130
\(335\) 5.09365e8i 0.0404436i
\(336\) 5.31720e9 + 7.95806e9i 0.417182 + 0.624381i
\(337\) 1.59214e10 1.23441 0.617207 0.786801i \(-0.288264\pi\)
0.617207 + 0.786801i \(0.288264\pi\)
\(338\) 3.45051e9i 0.264372i
\(339\) 1.93798e10 1.29486e10i 1.46740 0.980451i
\(340\) −4.16973e9 −0.312027
\(341\) 2.44611e9i 0.180908i
\(342\) 2.57708e9 + 1.06757e9i 0.188375 + 0.0780354i
\(343\) 1.48174e10 1.07052
\(344\) 6.33295e8i 0.0452243i
\(345\) −4.75282e9 7.11337e9i −0.335487 0.502110i
\(346\) −2.29706e10 −1.60276
\(347\) 4.94792e9i 0.341275i 0.985334 + 0.170638i \(0.0545828\pi\)
−0.985334 + 0.170638i \(0.945417\pi\)
\(348\) −7.69826e9 + 5.14361e9i −0.524899 + 0.350713i
\(349\) −7.29567e9 −0.491772 −0.245886 0.969299i \(-0.579079\pi\)
−0.245886 + 0.969299i \(0.579079\pi\)
\(350\) 1.33666e10i 0.890733i
\(351\) −1.34114e10 + 2.66695e9i −0.883578 + 0.175706i
\(352\) 1.02293e10 0.666311
\(353\) 6.93875e9i 0.446871i 0.974719 + 0.223436i \(0.0717272\pi\)
−0.974719 + 0.223436i \(0.928273\pi\)
\(354\) −1.38554e10 2.07369e10i −0.882282 1.32048i
\(355\) 3.82143e9 0.240609
\(356\) 1.80086e10i 1.12119i
\(357\) −8.82706e9 + 5.89782e9i −0.543429 + 0.363094i
\(358\) 2.89368e10 1.76164
\(359\) 1.60096e10i 0.963838i −0.876216 0.481919i \(-0.839940\pi\)
0.876216 0.481919i \(-0.160060\pi\)
\(360\) −1.01244e8 + 2.44399e8i −0.00602778 + 0.0145509i
\(361\) −1.66249e10 −0.978883
\(362\) 1.05898e10i 0.616670i
\(363\) 7.46660e9 + 1.11750e10i 0.430028 + 0.643607i
\(364\) 1.11668e10 0.636098
\(365\) 6.21252e9i 0.350023i
\(366\) 1.13945e9 7.61325e8i 0.0634994 0.0424273i
\(367\) 1.36364e10 0.751686 0.375843 0.926683i \(-0.377353\pi\)
0.375843 + 0.926683i \(0.377353\pi\)
\(368\) 3.17655e10i 1.73207i
\(369\) 1.13681e10 + 4.70930e9i 0.613173 + 0.254010i
\(370\) 6.72926e9 0.359054
\(371\) 1.15531e10i 0.609821i
\(372\) 3.92249e9 + 5.87065e9i 0.204829 + 0.306559i
\(373\) −2.44062e10 −1.26085 −0.630427 0.776248i \(-0.717120\pi\)
−0.630427 + 0.776248i \(0.717120\pi\)
\(374\) 1.17013e10i 0.598063i
\(375\) −1.10505e10 + 7.38339e9i −0.558798 + 0.373363i
\(376\) 7.32953e8 0.0366712
\(377\) 1.18589e10i 0.587055i
\(378\) −4.07219e9 2.04780e10i −0.199463 1.00304i
\(379\) −1.98392e10 −0.961542 −0.480771 0.876846i \(-0.659643\pi\)
−0.480771 + 0.876846i \(0.659643\pi\)
\(380\) 1.05439e9i 0.0505669i
\(381\) 1.24197e10 + 1.85881e10i 0.589403 + 0.882137i
\(382\) 3.63211e9 0.170571
\(383\) 1.51133e10i 0.702366i 0.936307 + 0.351183i \(0.114220\pi\)
−0.936307 + 0.351183i \(0.885780\pi\)
\(384\) −1.58467e9 + 1.05880e9i −0.0728811 + 0.0486957i
\(385\) −2.73420e9 −0.124448
\(386\) 3.56594e10i 1.60630i
\(387\) 8.85416e9 2.13737e10i 0.394733 0.952875i
\(388\) −3.65232e10 −1.61154
\(389\) 1.79991e10i 0.786056i 0.919527 + 0.393028i \(0.128572\pi\)
−0.919527 + 0.393028i \(0.871428\pi\)
\(390\) 5.83556e9 + 8.73387e9i 0.252246 + 0.377527i
\(391\) 3.52342e10 1.50750
\(392\) 4.85332e8i 0.0205539i
\(393\) 1.94720e10 1.30103e10i 0.816284 0.545403i
\(394\) 1.20729e10 0.500987
\(395\) 5.15922e9i 0.211931i
\(396\) −1.04618e10 4.33386e9i −0.425429 0.176236i
\(397\) −2.35673e10 −0.948739 −0.474370 0.880326i \(-0.657324\pi\)
−0.474370 + 0.880326i \(0.657324\pi\)
\(398\) 1.45383e10i 0.579403i
\(399\) −1.49137e9 2.23207e9i −0.0588428 0.0880678i
\(400\) −2.29720e10 −0.897343
\(401\) 1.37692e10i 0.532515i −0.963902 0.266257i \(-0.914213\pi\)
0.963902 0.266257i \(-0.0857871\pi\)
\(402\) 3.43056e9 2.29214e9i 0.131359 0.0877682i
\(403\) −9.04353e9 −0.342861
\(404\) 2.56791e10i 0.963950i
\(405\) 6.83394e9 6.83297e9i 0.254010 0.253974i
\(406\) 1.81075e10 0.666428
\(407\) 9.29209e9i 0.338638i
\(408\) −6.05284e8 9.05906e8i −0.0218433 0.0326921i
\(409\) 3.58480e10 1.28107 0.640533 0.767931i \(-0.278714\pi\)
0.640533 + 0.767931i \(0.278714\pi\)
\(410\) 9.45236e9i 0.334507i
\(411\) −1.39793e10 + 9.34031e9i −0.489912 + 0.327336i
\(412\) 4.11838e10 1.42934
\(413\) 2.40011e10i 0.824955i
\(414\) −2.65207e10 + 6.40203e10i −0.902785 + 2.17930i
\(415\) −1.04157e10 −0.351153
\(416\) 3.78191e10i 1.26281i
\(417\) −6.42007e9 9.60868e9i −0.212322 0.317775i
\(418\) −2.95887e9 −0.0969217
\(419\) 2.23996e10i 0.726750i −0.931643 0.363375i \(-0.881624\pi\)
0.931643 0.363375i \(-0.118376\pi\)
\(420\) −6.56208e9 + 4.38447e9i −0.210884 + 0.140903i
\(421\) −1.49535e10 −0.476008 −0.238004 0.971264i \(-0.576493\pi\)
−0.238004 + 0.971264i \(0.576493\pi\)
\(422\) 1.30457e9i 0.0411357i
\(423\) −2.47372e10 1.02475e10i −0.772660 0.320078i
\(424\) 1.18567e9 0.0366861
\(425\) 2.54805e10i 0.781001i
\(426\) −1.71964e10 2.57373e10i −0.522156 0.781491i
\(427\) −1.31880e9 −0.0396706
\(428\) 5.59339e9i 0.166686i
\(429\) 1.20602e10 8.05804e9i 0.356061 0.237903i
\(430\) −1.77718e10 −0.519825
\(431\) 6.40436e10i 1.85595i 0.372640 + 0.927976i \(0.378453\pi\)
−0.372640 + 0.927976i \(0.621547\pi\)
\(432\) 3.51938e10 6.99854e9i 1.01049 0.200943i
\(433\) −5.22954e9 −0.148769 −0.0743843 0.997230i \(-0.523699\pi\)
−0.0743843 + 0.997230i \(0.523699\pi\)
\(434\) 1.38087e10i 0.389218i
\(435\) 4.65620e9 + 6.96877e9i 0.130039 + 0.194625i
\(436\) 2.72738e10 0.754745
\(437\) 8.90959e9i 0.244305i
\(438\) 4.18412e10 2.79563e10i 1.13686 0.759598i
\(439\) 4.34801e10 1.17066 0.585332 0.810793i \(-0.300964\pi\)
0.585332 + 0.810793i \(0.300964\pi\)
\(440\) 2.80606e8i 0.00748664i
\(441\) 6.78548e9 1.63800e10i 0.179402 0.433070i
\(442\) −4.32610e10 −1.13346
\(443\) 3.78737e10i 0.983383i 0.870770 + 0.491691i \(0.163621\pi\)
−0.870770 + 0.491691i \(0.836379\pi\)
\(444\) −1.49005e10 2.23010e10i −0.383415 0.573843i
\(445\) 1.63021e10 0.415722
\(446\) 9.88246e10i 2.49761i
\(447\) −5.51754e10 + 3.68656e10i −1.38202 + 0.923403i
\(448\) −2.74973e10 −0.682620
\(449\) 2.95505e10i 0.727076i −0.931579 0.363538i \(-0.881569\pi\)
0.931579 0.363538i \(-0.118431\pi\)
\(450\) 4.62978e10 + 1.91791e10i 1.12904 + 0.467712i
\(451\) −1.30523e10 −0.315486
\(452\) 7.13614e10i 1.70966i
\(453\) 1.90737e10 + 2.85469e10i 0.452942 + 0.677902i
\(454\) −7.93813e10 −1.86851
\(455\) 1.01086e10i 0.235856i
\(456\) 2.29074e8 1.53057e8i 0.00529806 0.00353991i
\(457\) −2.02181e10 −0.463529 −0.231764 0.972772i \(-0.574450\pi\)
−0.231764 + 0.972772i \(0.574450\pi\)
\(458\) 4.18847e10i 0.951905i
\(459\) 7.76277e9 + 3.90369e10i 0.174890 + 0.879476i
\(460\) 2.61933e10 0.585005
\(461\) 7.01826e10i 1.55391i −0.629556 0.776955i \(-0.716763\pi\)
0.629556 0.776955i \(-0.283237\pi\)
\(462\) 1.23039e10 + 1.84148e10i 0.270069 + 0.404202i
\(463\) 4.16009e9 0.0905271 0.0452635 0.998975i \(-0.485587\pi\)
0.0452635 + 0.998975i \(0.485587\pi\)
\(464\) 3.11198e10i 0.671374i
\(465\) 5.31435e9 3.55080e9i 0.113668 0.0759476i
\(466\) 6.10935e10 1.29554
\(467\) 2.88138e10i 0.605806i −0.953021 0.302903i \(-0.902044\pi\)
0.953021 0.302903i \(-0.0979558\pi\)
\(468\) 1.60228e10 3.86786e10i 0.334006 0.806282i
\(469\) −3.97056e9 −0.0820654
\(470\) 2.05684e10i 0.421512i
\(471\) −3.41933e10 5.11758e10i −0.694796 1.03988i
\(472\) −2.46319e9 −0.0496283
\(473\) 2.45402e10i 0.490268i
\(474\) −3.47472e10 + 2.32165e10i −0.688346 + 0.459921i
\(475\) 6.44318e9 0.126569
\(476\) 3.25036e10i 0.633145i
\(477\) −4.00165e10 1.65770e10i −0.772975 0.320209i
\(478\) 5.10649e10 0.978161
\(479\) 4.47149e10i 0.849395i −0.905335 0.424698i \(-0.860380\pi\)
0.905335 0.424698i \(-0.139620\pi\)
\(480\) −1.48490e10 2.22240e10i −0.279727 0.418656i
\(481\) 3.43539e10 0.641795
\(482\) 3.92127e10i 0.726505i
\(483\) 5.54496e10 3.70488e10i 1.01885 0.680747i
\(484\) −4.11493e10 −0.749861
\(485\) 3.30623e10i 0.597538i
\(486\) −7.67727e10 1.52781e10i −1.37614 0.273857i
\(487\) 5.72836e10 1.01839 0.509195 0.860651i \(-0.329943\pi\)
0.509195 + 0.860651i \(0.329943\pi\)
\(488\) 1.35347e8i 0.00238654i
\(489\) 3.00672e10 + 4.50005e10i 0.525845 + 0.787012i
\(490\) −1.36196e10 −0.236254
\(491\) 7.25262e10i 1.24787i 0.781477 + 0.623934i \(0.214467\pi\)
−0.781477 + 0.623934i \(0.785533\pi\)
\(492\) −3.13255e10 + 2.09302e10i −0.534611 + 0.357202i
\(493\) −3.45180e10 −0.584330
\(494\) 1.09393e10i 0.183688i
\(495\) −3.92319e9 + 9.47046e9i −0.0653459 + 0.157743i
\(496\) 2.37318e10 0.392106
\(497\) 2.97885e10i 0.488228i
\(498\) 4.68706e10 + 7.01495e10i 0.762050 + 1.14053i
\(499\) −2.64368e10 −0.426389 −0.213195 0.977010i \(-0.568387\pi\)
−0.213195 + 0.977010i \(0.568387\pi\)
\(500\) 4.06907e10i 0.651051i
\(501\) 1.32212e10 8.83376e9i 0.209855 0.140215i
\(502\) −3.08797e10 −0.486248
\(503\) 7.52828e10i 1.17604i −0.808845 0.588022i \(-0.799907\pi\)
0.808845 0.588022i \(-0.200093\pi\)
\(504\) −1.90512e9 7.89205e8i −0.0295257 0.0122312i
\(505\) −2.32457e10 −0.357419
\(506\) 7.35048e10i 1.12128i
\(507\) −6.91640e9 1.03515e10i −0.104676 0.156665i
\(508\) −6.84465e10 −1.02777
\(509\) 6.45184e10i 0.961197i 0.876941 + 0.480599i \(0.159581\pi\)
−0.876941 + 0.480599i \(0.840419\pi\)
\(510\) 2.54219e10 1.69857e10i 0.375775 0.251075i
\(511\) −4.84273e10 −0.710243
\(512\) 9.61394e10i 1.39901i
\(513\) −9.87115e9 + 1.96295e9i −0.142527 + 0.0283426i
\(514\) 1.78179e11 2.55272
\(515\) 3.72812e10i 0.529981i
\(516\) 3.93518e10 + 5.88964e10i 0.555094 + 0.830788i
\(517\) 2.84019e10 0.397544
\(518\) 5.24554e10i 0.728569i
\(519\) 6.89119e10 4.60437e10i 0.949783 0.634601i
\(520\) 1.03743e9 0.0141888
\(521\) 7.65146e10i 1.03847i 0.854632 + 0.519235i \(0.173783\pi\)
−0.854632 + 0.519235i \(0.826217\pi\)
\(522\) 2.59816e10 6.27189e10i 0.349932 0.844727i
\(523\) −8.46771e10 −1.13177 −0.565886 0.824483i \(-0.691466\pi\)
−0.565886 + 0.824483i \(0.691466\pi\)
\(524\) 7.17012e10i 0.951046i
\(525\) −2.67927e10 4.00997e10i −0.352679 0.527842i
\(526\) −7.24133e9 −0.0945966
\(527\) 2.63232e10i 0.341269i
\(528\) −3.16480e10 + 2.11457e10i −0.407202 + 0.272073i
\(529\) −1.43023e11 −1.82634
\(530\) 3.32729e10i 0.421684i
\(531\) 8.31326e10 + 3.44381e10i 1.04567 + 0.433173i
\(532\) 8.21909e9 0.102607
\(533\) 4.82558e10i 0.597917i
\(534\) −7.33594e10 1.09794e11i −0.902175 1.35025i
\(535\) −5.06336e9 −0.0618050
\(536\) 4.07492e8i 0.00493696i
\(537\) −8.68104e10 + 5.80026e10i −1.04394 + 0.697510i
\(538\) −7.79717e10 −0.930696
\(539\) 1.88066e10i 0.222821i
\(540\) 5.77088e9 + 2.90202e10i 0.0678683 + 0.341292i
\(541\) 1.43470e11 1.67483 0.837415 0.546568i \(-0.184066\pi\)
0.837415 + 0.546568i \(0.184066\pi\)
\(542\) 3.23765e10i 0.375174i
\(543\) 2.12268e10 + 3.17694e10i 0.244166 + 0.365434i
\(544\) 1.10081e11 1.25695
\(545\) 2.46893e10i 0.279849i
\(546\) −6.80816e10 + 4.54889e10i −0.766053 + 0.511841i
\(547\) 1.64171e11 1.83378 0.916892 0.399134i \(-0.130689\pi\)
0.916892 + 0.399134i \(0.130689\pi\)
\(548\) 5.14755e10i 0.570792i
\(549\) −1.89229e9 + 4.56795e9i −0.0208305 + 0.0502842i
\(550\) −5.31568e10 −0.580908
\(551\) 8.72847e9i 0.0946961i
\(552\) 3.80226e9 + 5.69070e9i 0.0409529 + 0.0612928i
\(553\) 4.02167e10 0.430037
\(554\) 7.58912e10i 0.805661i
\(555\) −2.01878e10 + 1.34885e10i −0.212773 + 0.142165i
\(556\) 3.53817e10 0.370237
\(557\) 1.54420e11i 1.60429i −0.597130 0.802145i \(-0.703692\pi\)
0.597130 0.802145i \(-0.296308\pi\)
\(558\) −4.78291e10 1.98135e10i −0.493351 0.204373i
\(559\) −9.07278e10 −0.929166
\(560\) 2.65269e10i 0.269733i
\(561\) −2.34547e10 3.51039e10i −0.236799 0.354408i
\(562\) −9.03075e10 −0.905271
\(563\) 1.54622e11i 1.53900i −0.638646 0.769500i \(-0.720505\pi\)
0.638646 0.769500i \(-0.279495\pi\)
\(564\) 6.81646e10 4.55444e10i 0.673663 0.450110i
\(565\) 6.45992e10 0.633919
\(566\) 2.34047e11i 2.28054i
\(567\) 5.32638e10 + 5.32714e10i 0.515348 + 0.515420i
\(568\) −3.05714e9 −0.0293712
\(569\) 1.15380e11i 1.10073i 0.834925 + 0.550364i \(0.185511\pi\)
−0.834925 + 0.550364i \(0.814489\pi\)
\(570\) 4.29514e9 + 6.42837e9i 0.0406891 + 0.0608978i
\(571\) −1.63410e11 −1.53722 −0.768608 0.639720i \(-0.779050\pi\)
−0.768608 + 0.639720i \(0.779050\pi\)
\(572\) 4.44087e10i 0.414844i
\(573\) −1.08963e10 + 7.28041e9i −0.101079 + 0.0675363i
\(574\) 7.36823e10 0.678759
\(575\) 1.60063e11i 1.46426i
\(576\) −3.94548e10 + 9.52427e10i −0.358434 + 0.865250i
\(577\) 7.42282e10 0.669678 0.334839 0.942275i \(-0.391318\pi\)
0.334839 + 0.942275i \(0.391318\pi\)
\(578\) 3.06844e10i 0.274920i
\(579\) −7.14779e10 1.06978e11i −0.636001 0.951879i
\(580\) −2.56609e10 −0.226756
\(581\) 8.11916e10i 0.712535i
\(582\) 2.22674e11 1.48780e11i 1.94078 1.29674i
\(583\) 4.59449e10 0.397707
\(584\) 4.97002e9i 0.0427274i
\(585\) −3.50134e10 1.45045e10i −0.298958 0.123845i
\(586\) −2.33315e11 −1.97857
\(587\) 6.72877e10i 0.566739i 0.959011 + 0.283369i \(0.0914523\pi\)
−0.959011 + 0.283369i \(0.908548\pi\)
\(588\) 3.01577e10 + 4.51359e10i 0.252283 + 0.377583i
\(589\) −6.65629e9 −0.0553059
\(590\) 6.91231e10i 0.570447i
\(591\) −3.62187e10 + 2.41996e10i −0.296881 + 0.198362i
\(592\) −9.01507e10 −0.733977
\(593\) 2.36444e10i 0.191210i 0.995419 + 0.0956048i \(0.0304785\pi\)
−0.995419 + 0.0956048i \(0.969521\pi\)
\(594\) 8.14378e10 1.61945e10i 0.654154 0.130083i
\(595\) −2.94235e10 −0.234761
\(596\) 2.03170e11i 1.61018i
\(597\) 2.91414e10 + 4.36148e10i 0.229410 + 0.343350i
\(598\) 2.71756e11 2.12507
\(599\) 3.03370e10i 0.235649i −0.993034 0.117825i \(-0.962408\pi\)
0.993034 0.117825i \(-0.0375921\pi\)
\(600\) 4.11536e9 2.74969e9i 0.0317543 0.0212168i
\(601\) 3.37911e10 0.259003 0.129501 0.991579i \(-0.458662\pi\)
0.129501 + 0.991579i \(0.458662\pi\)
\(602\) 1.38533e11i 1.05480i
\(603\) −5.69718e9 + 1.37528e10i −0.0430914 + 0.104022i
\(604\) −1.05117e11 −0.789818
\(605\) 3.72500e10i 0.278038i
\(606\) 1.04606e11 + 1.56560e11i 0.775649 + 1.16089i
\(607\) −3.82366e10 −0.281660 −0.140830 0.990034i \(-0.544977\pi\)
−0.140830 + 0.990034i \(0.544977\pi\)
\(608\) 2.78359e10i 0.203700i
\(609\) −5.43224e10 + 3.62957e10i −0.394920 + 0.263867i
\(610\) 3.79815e9 0.0274317
\(611\) 1.05005e11i 0.753435i
\(612\) −1.12583e11 4.66380e10i −0.802539 0.332456i
\(613\) 1.08066e11 0.765330 0.382665 0.923887i \(-0.375006\pi\)
0.382665 + 0.923887i \(0.375006\pi\)
\(614\) 6.71948e10i 0.472783i
\(615\) 1.89469e10 + 2.83571e10i 0.132445 + 0.198226i
\(616\) 2.18736e9 0.0151914
\(617\) 4.72538e9i 0.0326059i 0.999867 + 0.0163029i \(0.00518962\pi\)
−0.999867 + 0.0163029i \(0.994810\pi\)
\(618\) −2.51088e11 + 1.67765e11i −1.72136 + 1.15013i
\(619\) 2.29845e10 0.156557 0.0782786 0.996932i \(-0.475058\pi\)
0.0782786 + 0.996932i \(0.475058\pi\)
\(620\) 1.95688e10i 0.132434i
\(621\) −4.87639e10 2.45221e11i −0.327893 1.64889i
\(622\) −1.44764e11 −0.967165
\(623\) 1.27077e11i 0.843555i
\(624\) −7.81780e10 1.17006e11i −0.515640 0.771739i
\(625\) 9.60656e10 0.629575
\(626\) 7.35768e8i 0.00479119i
\(627\) 8.87662e9 5.93094e9i 0.0574351 0.0383754i
\(628\) 1.88443e11 1.21155
\(629\) 9.99949e10i 0.638815i
\(630\) 2.21470e10 5.34623e10i 0.140590 0.339379i
\(631\) −1.01892e11 −0.642722 −0.321361 0.946957i \(-0.604140\pi\)
−0.321361 + 0.946957i \(0.604140\pi\)
\(632\) 4.12737e9i 0.0258705i
\(633\) 2.61497e9 + 3.91372e9i 0.0162874 + 0.0243767i
\(634\) 2.64453e11 1.63678
\(635\) 6.19605e10i 0.381083i
\(636\) 1.10268e11 7.36757e10i 0.673938 0.450294i
\(637\) −6.95302e10 −0.422295
\(638\) 7.20106e10i 0.434624i
\(639\) 1.03179e11 + 4.27422e10i 0.618851 + 0.256362i
\(640\) −5.28224e9 −0.0314846
\(641\) 1.17803e11i 0.697791i −0.937162 0.348896i \(-0.886557\pi\)
0.937162 0.348896i \(-0.113443\pi\)
\(642\) 2.27851e10 + 3.41016e10i 0.134125 + 0.200740i
\(643\) −2.62680e10 −0.153668 −0.0768339 0.997044i \(-0.524481\pi\)
−0.0768339 + 0.997044i \(0.524481\pi\)
\(644\) 2.04180e11i 1.18705i
\(645\) 5.33154e10 3.56228e10i 0.308045 0.205821i
\(646\) −3.18413e10 −0.182836
\(647\) 3.10527e11i 1.77208i −0.463612 0.886038i \(-0.653447\pi\)
0.463612 0.886038i \(-0.346553\pi\)
\(648\) −5.46715e9 + 5.46638e9i −0.0310071 + 0.0310027i
\(649\) −9.54486e10 −0.538010
\(650\) 1.96527e11i 1.10095i
\(651\) 2.76789e10 + 4.14260e10i 0.154108 + 0.230648i
\(652\) −1.65704e11 −0.916942
\(653\) 3.48345e10i 0.191583i −0.995401 0.0957914i \(-0.969462\pi\)
0.995401 0.0957914i \(-0.0305382\pi\)
\(654\) −1.66282e11 + 1.11102e11i −0.908940 + 0.607311i
\(655\) 6.49068e10 0.352635
\(656\) 1.26632e11i 0.683796i
\(657\) −6.94863e10 + 1.67738e11i −0.372939 + 0.900265i
\(658\) −1.60333e11 −0.855304
\(659\) 3.77120e10i 0.199957i −0.994990 0.0999787i \(-0.968123\pi\)
0.994990 0.0999787i \(-0.0318775\pi\)
\(660\) −1.74364e10 2.60964e10i −0.0918926 0.137532i
\(661\) −1.39619e11 −0.731372 −0.365686 0.930738i \(-0.619166\pi\)
−0.365686 + 0.930738i \(0.619166\pi\)
\(662\) 2.69623e11i 1.40386i
\(663\) 1.29783e11 8.67149e10i 0.671682 0.448786i
\(664\) 8.33256e9 0.0428653
\(665\) 7.44025e9i 0.0380453i
\(666\) 1.81690e11 + 7.52659e10i 0.923494 + 0.382562i
\(667\) 2.16834e11 1.09553
\(668\) 4.86838e10i 0.244500i
\(669\) 1.98090e11 + 2.96474e11i 0.988912 + 1.48007i
\(670\) 1.14352e10 0.0567472
\(671\) 5.24468e9i 0.0258719i
\(672\) 1.73239e11 1.15750e11i 0.849510 0.567603i
\(673\) −1.29783e11 −0.632642 −0.316321 0.948652i \(-0.602448\pi\)
−0.316321 + 0.948652i \(0.602448\pi\)
\(674\) 3.57434e11i 1.73203i
\(675\) −1.77337e11 + 3.52648e10i −0.854249 + 0.169874i
\(676\) 3.81171e10 0.182529
\(677\) 3.40648e11i 1.62163i 0.585306 + 0.810813i \(0.300975\pi\)
−0.585306 + 0.810813i \(0.699025\pi\)
\(678\) −2.90696e11 4.35075e11i −1.37569 2.05895i
\(679\) −2.57724e11 −1.21248
\(680\) 3.01969e9i 0.0141230i
\(681\) 2.38144e11 1.59117e11i 1.10726 0.739821i
\(682\) 5.49149e10 0.253836
\(683\) 1.02876e11i 0.472750i −0.971662 0.236375i \(-0.924041\pi\)
0.971662 0.236375i \(-0.0759593\pi\)
\(684\) 1.17932e10 2.84685e10i 0.0538776 0.130059i
\(685\) −4.65976e10 −0.211642
\(686\) 3.32650e11i 1.50208i
\(687\) −8.39562e10 1.25654e11i −0.376900 0.564092i
\(688\) 2.38086e11 1.06262
\(689\) 1.69863e11i 0.753742i
\(690\) −1.59695e11 + 1.06701e11i −0.704522 + 0.470728i
\(691\) 3.58259e11 1.57140 0.785698 0.618611i \(-0.212304\pi\)
0.785698 + 0.618611i \(0.212304\pi\)
\(692\) 2.53752e11i 1.10659i
\(693\) −7.38234e10 3.05817e10i −0.320082 0.132595i
\(694\) 1.11081e11 0.478851
\(695\) 3.20289e10i 0.137279i
\(696\) −3.72496e9 5.57501e9i −0.0158740 0.0237580i
\(697\) −1.40459e11 −0.595141
\(698\) 1.63787e11i 0.690016i
\(699\) −1.83280e11 + 1.22459e11i −0.767728 + 0.512960i
\(700\) 1.47658e11 0.614984
\(701\) 2.49323e11i 1.03250i 0.856438 + 0.516250i \(0.172673\pi\)
−0.856438 + 0.516250i \(0.827327\pi\)
\(702\) 5.98729e10 + 3.01085e11i 0.246537 + 1.23977i
\(703\) 2.52854e10 0.103526
\(704\) 1.09353e11i 0.445183i
\(705\) −4.12286e10 6.17053e10i −0.166895 0.249785i
\(706\) 1.55775e11 0.627015
\(707\) 1.81203e11i 0.725251i
\(708\) −2.29077e11 + 1.53058e11i −0.911691 + 0.609149i
\(709\) −3.88874e11 −1.53895 −0.769474 0.638678i \(-0.779482\pi\)
−0.769474 + 0.638678i \(0.779482\pi\)
\(710\) 8.57909e10i 0.337604i
\(711\) 5.77052e10 1.39299e11i 0.225807 0.545091i
\(712\) −1.30417e10 −0.0507473
\(713\) 1.65357e11i 0.639829i
\(714\) 1.32406e11 + 1.98167e11i 0.509465 + 0.762497i
\(715\) 4.02006e10 0.153818
\(716\) 3.19659e11i 1.21628i
\(717\) −1.53195e11 + 1.02357e11i −0.579651 + 0.387296i
\(718\) −3.59416e11 −1.35238
\(719\) 3.35735e10i 0.125626i −0.998025 0.0628132i \(-0.979993\pi\)
0.998025 0.0628132i \(-0.0200072\pi\)
\(720\) 9.18812e10 + 3.80622e10i 0.341898 + 0.141633i
\(721\) 2.90611e11 1.07540
\(722\) 3.73228e11i 1.37349i
\(723\) −7.86002e10 1.17638e11i −0.287654 0.430521i
\(724\) −1.16983e11 −0.425764
\(725\) 1.56809e11i 0.567569i
\(726\) 2.50878e11 1.67625e11i 0.903058 0.603381i
\(727\) 2.53113e11 0.906102 0.453051 0.891485i \(-0.350336\pi\)
0.453051 + 0.891485i \(0.350336\pi\)
\(728\) 8.08692e9i 0.0287911i
\(729\) 2.60942e11 1.08053e11i 0.923920 0.382586i
\(730\) 1.39471e11 0.491125
\(731\) 2.64084e11i 0.924853i
\(732\) −8.41020e9 1.25872e10i −0.0292929 0.0438416i
\(733\) 2.07602e11 0.719144 0.359572 0.933117i \(-0.382923\pi\)
0.359572 + 0.933117i \(0.382923\pi\)
\(734\) 3.06137e11i 1.05471i
\(735\) 4.08588e10 2.72999e10i 0.140003 0.0935432i
\(736\) −6.91504e11 −2.35659
\(737\) 1.57903e10i 0.0535205i
\(738\) 1.05724e11 2.55214e11i 0.356407 0.860357i
\(739\) 4.15014e11 1.39151 0.695753 0.718281i \(-0.255071\pi\)
0.695753 + 0.718281i \(0.255071\pi\)
\(740\) 7.43367e10i 0.247900i
\(741\) 2.19274e10 + 3.28179e10i 0.0727300 + 0.108852i
\(742\) −2.59366e11 −0.855653
\(743\) 3.30690e11i 1.08509i 0.840027 + 0.542545i \(0.182539\pi\)
−0.840027 + 0.542545i \(0.817461\pi\)
\(744\) −4.25148e9 + 2.84064e9i −0.0138755 + 0.00927095i
\(745\) −1.83918e11 −0.597034
\(746\) 5.47918e11i 1.76913i
\(747\) −2.81224e11 1.16498e11i −0.903170 0.374143i
\(748\) 1.29262e11 0.412918
\(749\) 3.94695e10i 0.125411i
\(750\) 1.65757e11 + 2.48082e11i 0.523873 + 0.784062i
\(751\) −4.77978e11 −1.50262 −0.751308 0.659952i \(-0.770577\pi\)
−0.751308 + 0.659952i \(0.770577\pi\)
\(752\) 2.75552e11i 0.861652i
\(753\) 9.26390e10 6.18970e10i 0.288147 0.192526i
\(754\) −2.66231e11 −0.823709
\(755\) 9.51565e10i 0.292854i
\(756\) −2.26216e11 + 4.49847e10i −0.692526 + 0.137714i
\(757\) −8.95066e10 −0.272566 −0.136283 0.990670i \(-0.543516\pi\)
−0.136283 + 0.990670i \(0.543516\pi\)
\(758\) 4.45390e11i 1.34916i
\(759\) 1.47337e11 + 2.20514e11i 0.443962 + 0.664462i
\(760\) 7.63580e8 0.00228876
\(761\) 5.71473e11i 1.70395i −0.523581 0.851976i \(-0.675404\pi\)
0.523581 0.851976i \(-0.324596\pi\)
\(762\) 4.17303e11 2.78822e11i 1.23775 0.827004i
\(763\) 1.92456e11 0.567851
\(764\) 4.01231e10i 0.117766i
\(765\) −4.22185e10 + 1.01914e11i −0.123270 + 0.297570i
\(766\) 3.39292e11 0.985504
\(767\) 3.52884e11i 1.01965i
\(768\) 2.04781e11 + 3.06488e11i 0.588634 + 0.880986i
\(769\) 2.56194e11 0.732596 0.366298 0.930498i \(-0.380625\pi\)
0.366298 + 0.930498i \(0.380625\pi\)
\(770\) 6.13826e10i 0.174615i
\(771\) −5.34537e11 + 3.57152e11i −1.51273 + 1.01073i
\(772\) 3.93923e11 1.10903
\(773\) 1.00523e11i 0.281543i 0.990042 + 0.140772i \(0.0449584\pi\)
−0.990042 + 0.140772i \(0.955042\pi\)
\(774\) −4.79838e11 1.98775e11i −1.33700 0.553859i
\(775\) −1.19582e11 −0.331480
\(776\) 2.64498e10i 0.0729417i
\(777\) −1.05145e11 1.57366e11i −0.288472 0.431745i
\(778\) 4.04080e11 1.10293
\(779\) 3.55176e10i 0.0964482i
\(780\) 9.64813e10 6.44643e10i 0.260654 0.174157i
\(781\) −1.18464e11 −0.318408
\(782\) 7.91007e11i