Properties

Label 49.12.c.b.18.1
Level $49$
Weight $12$
Character 49.18
Analytic conductor $37.649$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 49.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(37.6488158474\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 18.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 49.18
Dual form 49.12.c.b.30.1

$q$-expansion

\(f(q)\) \(=\) \(q+(12.0000 + 20.7846i) q^{2} +(-126.000 + 218.238i) q^{3} +(736.000 - 1274.79i) q^{4} +(-2415.00 - 4182.90i) q^{5} -6048.00 q^{6} +84480.0 q^{8} +(56821.5 + 98417.7i) q^{9} +O(q^{10})\) \(q+(12.0000 + 20.7846i) q^{2} +(-126.000 + 218.238i) q^{3} +(736.000 - 1274.79i) q^{4} +(-2415.00 - 4182.90i) q^{5} -6048.00 q^{6} +84480.0 q^{8} +(56821.5 + 98417.7i) q^{9} +(57960.0 - 100390. i) q^{10} +(-267306. + 462988. i) q^{11} +(185472. + 321247. i) q^{12} -577738. q^{13} +1.21716e6 q^{15} +(-493568. - 854885. i) q^{16} +(3.45297e6 - 5.98071e6i) q^{17} +(-1.36372e6 + 2.36203e6i) q^{18} +(-5.33071e6 - 9.23306e6i) q^{19} -7.10976e6 q^{20} -1.28307e7 q^{22} +(-9.32164e6 - 1.61455e7i) q^{23} +(-1.06445e7 + 1.84368e7i) q^{24} +(1.27496e7 - 2.20830e7i) q^{25} +(-6.93286e6 - 1.20081e7i) q^{26} -7.32791e7 q^{27} +1.28407e8 q^{29} +(1.46059e7 + 2.52982e7i) q^{30} +(2.64216e7 - 4.57635e7i) q^{31} +(9.83532e7 - 1.70353e8i) q^{32} +(-6.73611e7 - 1.16673e8i) q^{33} +1.65742e8 q^{34} +1.67282e8 q^{36} +(9.11067e7 + 1.57801e8i) q^{37} +(1.27937e8 - 2.21593e8i) q^{38} +(7.27950e7 - 1.26085e8i) q^{39} +(-2.04019e8 - 3.53372e8i) q^{40} +3.08120e8 q^{41} -1.71257e7 q^{43} +(3.93474e8 + 6.81518e8i) q^{44} +(2.74448e8 - 4.75358e8i) q^{45} +(2.23719e8 - 3.87493e8i) q^{46} +(-1.34367e9 - 2.32731e9i) q^{47} +2.48758e8 q^{48} +6.11981e8 q^{50} +(8.70148e8 + 1.50714e9i) q^{51} +(-4.25215e8 + 7.36494e8i) q^{52} +(7.98028e8 - 1.38222e9i) q^{53} +(-8.79349e8 - 1.52308e9i) q^{54} +2.58218e9 q^{55} +2.68668e9 q^{57} +(1.54088e9 + 2.66888e9i) q^{58} +(2.59460e9 - 4.49398e9i) q^{59} +(8.95830e8 - 1.55162e9i) q^{60} +(-3.47824e9 - 6.02449e9i) q^{61} +1.26824e9 q^{62} +2.69930e9 q^{64} +(1.39524e9 + 2.41662e9i) q^{65} +(1.61667e9 - 2.80015e9i) q^{66} +(7.74091e9 - 1.34077e10i) q^{67} +(-5.08277e9 - 8.80361e9i) q^{68} +4.69810e9 q^{69} +9.79149e9 q^{71} +(4.80028e9 + 8.31433e9i) q^{72} +(-7.31896e8 + 1.26768e9i) q^{73} +(-2.18656e9 + 3.78723e9i) q^{74} +(3.21290e9 + 5.56491e9i) q^{75} -1.56936e10 q^{76} +3.49416e9 q^{78} +(-1.90584e10 - 3.30102e10i) q^{79} +(-2.38393e9 + 4.12909e9i) q^{80} +(-8.32594e8 + 1.44210e9i) q^{81} +(3.69745e9 + 6.40416e9i) q^{82} -2.93351e10 q^{83} -3.33557e10 q^{85} +(-2.05508e8 - 3.55951e8i) q^{86} +(-1.61792e10 + 2.80233e10i) q^{87} +(-2.25820e10 + 3.91132e10i) q^{88} +(1.24965e10 + 2.16445e10i) q^{89} +1.31735e10 q^{90} -2.74429e10 q^{92} +(6.65824e9 + 1.15324e10i) q^{93} +(3.22482e10 - 5.58555e10i) q^{94} +(-2.57473e10 + 4.45957e10i) q^{95} +(2.47850e10 + 4.29289e10i) q^{96} +7.50136e10 q^{97} -6.07549e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 24q^{2} - 252q^{3} + 1472q^{4} - 4830q^{5} - 12096q^{6} + 168960q^{8} + 113643q^{9} + O(q^{10}) \) \( 2q + 24q^{2} - 252q^{3} + 1472q^{4} - 4830q^{5} - 12096q^{6} + 168960q^{8} + 113643q^{9} + 115920q^{10} - 534612q^{11} + 370944q^{12} - 1155476q^{13} + 2434320q^{15} - 987136q^{16} + 6905934q^{17} - 2727432q^{18} - 10661420q^{19} - 14219520q^{20} - 25661376q^{22} - 18643272q^{23} - 21288960q^{24} + 25499225q^{25} - 13865712q^{26} - 146558160q^{27} + 256813260q^{29} + 29211840q^{30} + 52843168q^{31} + 196706304q^{32} - 134722224q^{33} + 331484832q^{34} + 334564992q^{36} + 182213314q^{37} + 255874080q^{38} + 145589976q^{39} - 408038400q^{40} + 616240884q^{41} - 34251416q^{43} + 786948864q^{44} + 548895690q^{45} + 447438528q^{46} - 2687348496q^{47} + 497516544q^{48} + 1223962800q^{50} + 1740295368q^{51} - 850430336q^{52} + 1596055698q^{53} - 1758697920q^{54} + 5164351920q^{55} + 5373355680q^{57} + 3081759120q^{58} + 5189203740q^{59} + 1791659520q^{60} - 6956478662q^{61} + 2536472064q^{62} + 5398593536q^{64} + 2790474540q^{65} + 3233333376q^{66} + 15481826884q^{67} - 10165534848q^{68} + 9396209088q^{69} + 19582970544q^{71} + 9600560640q^{72} - 1463791322q^{73} - 4373119536q^{74} + 6425804700q^{75} - 31387220480q^{76} + 6988318848q^{78} - 38116845680q^{79} - 4767866880q^{80} - 1665188361q^{81} + 7394890608q^{82} - 58670199336q^{83} - 66711322440q^{85} - 411016992q^{86} - 32358470760q^{87} - 45164021760q^{88} + 24992917110q^{89} + 26346993120q^{90} - 54885792768q^{92} + 13316478336q^{93} + 64496363904q^{94} - 51494658600q^{95} + 49569988608q^{96} + 150027137092q^{97} - 121509823032q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 12.0000 + 20.7846i 0.265165 + 0.459279i 0.967607 0.252462i \(-0.0812402\pi\)
−0.702442 + 0.711741i \(0.747907\pi\)
\(3\) −126.000 + 218.238i −0.299367 + 0.518519i −0.975991 0.217810i \(-0.930109\pi\)
0.676624 + 0.736328i \(0.263442\pi\)
\(4\) 736.000 1274.79i 0.359375 0.622456i
\(5\) −2415.00 4182.90i −0.345607 0.598608i 0.639857 0.768494i \(-0.278994\pi\)
−0.985464 + 0.169886i \(0.945660\pi\)
\(6\) −6048.00 −0.317526
\(7\) 0 0
\(8\) 84480.0 0.911505
\(9\) 56821.5 + 98417.7i 0.320759 + 0.555571i
\(10\) 57960.0 100390.i 0.183286 0.317460i
\(11\) −267306. + 462988.i −0.500436 + 0.866781i 0.499563 + 0.866277i \(0.333494\pi\)
−1.00000 0.000504048i \(0.999840\pi\)
\(12\) 185472. + 321247.i 0.215170 + 0.372685i
\(13\) −577738. −0.431561 −0.215781 0.976442i \(-0.569230\pi\)
−0.215781 + 0.976442i \(0.569230\pi\)
\(14\) 0 0
\(15\) 1.21716e6 0.413853
\(16\) −493568. 854885.i −0.117676 0.203820i
\(17\) 3.45297e6 5.98071e6i 0.589825 1.02161i −0.404430 0.914569i \(-0.632530\pi\)
0.994255 0.107038i \(-0.0341367\pi\)
\(18\) −1.36372e6 + 2.36203e6i −0.170108 + 0.294636i
\(19\) −5.33071e6 9.23306e6i −0.493901 0.855462i 0.506074 0.862490i \(-0.331096\pi\)
−0.999975 + 0.00702781i \(0.997763\pi\)
\(20\) −7.10976e6 −0.496810
\(21\) 0 0
\(22\) −1.28307e7 −0.530793
\(23\) −9.32164e6 1.61455e7i −0.301988 0.523058i 0.674599 0.738185i \(-0.264317\pi\)
−0.976586 + 0.215127i \(0.930983\pi\)
\(24\) −1.06445e7 + 1.84368e7i −0.272874 + 0.472632i
\(25\) 1.27496e7 2.20830e7i 0.261112 0.452259i
\(26\) −6.93286e6 1.20081e7i −0.114435 0.198207i
\(27\) −7.32791e7 −0.982832
\(28\) 0 0
\(29\) 1.28407e8 1.16251 0.581257 0.813720i \(-0.302561\pi\)
0.581257 + 0.813720i \(0.302561\pi\)
\(30\) 1.46059e7 + 2.52982e7i 0.109739 + 0.190074i
\(31\) 2.64216e7 4.57635e7i 0.165756 0.287098i −0.771167 0.636632i \(-0.780327\pi\)
0.936924 + 0.349534i \(0.113660\pi\)
\(32\) 9.83532e7 1.70353e8i 0.518159 0.897478i
\(33\) −6.73611e7 1.16673e8i −0.299628 0.518971i
\(34\) 1.65742e8 0.625604
\(35\) 0 0
\(36\) 1.67282e8 0.461091
\(37\) 9.11067e7 + 1.57801e8i 0.215993 + 0.374112i 0.953579 0.301142i \(-0.0973677\pi\)
−0.737586 + 0.675253i \(0.764034\pi\)
\(38\) 1.27937e8 2.21593e8i 0.261931 0.453677i
\(39\) 7.27950e7 1.26085e8i 0.129195 0.223773i
\(40\) −2.04019e8 3.53372e8i −0.315022 0.545634i
\(41\) 3.08120e8 0.415345 0.207673 0.978198i \(-0.433411\pi\)
0.207673 + 0.978198i \(0.433411\pi\)
\(42\) 0 0
\(43\) −1.71257e7 −0.0177653 −0.00888264 0.999961i \(-0.502827\pi\)
−0.00888264 + 0.999961i \(0.502827\pi\)
\(44\) 3.93474e8 + 6.81518e8i 0.359689 + 0.622999i
\(45\) 2.74448e8 4.75358e8i 0.221713 0.384018i
\(46\) 2.23719e8 3.87493e8i 0.160153 0.277393i
\(47\) −1.34367e9 2.32731e9i −0.854586 1.48019i −0.877029 0.480438i \(-0.840478\pi\)
0.0224426 0.999748i \(-0.492856\pi\)
\(48\) 2.48758e8 0.140913
\(49\) 0 0
\(50\) 6.11981e8 0.276951
\(51\) 8.70148e8 + 1.50714e9i 0.353148 + 0.611671i
\(52\) −4.25215e8 + 7.36494e8i −0.155092 + 0.268628i
\(53\) 7.98028e8 1.38222e9i 0.262120 0.454006i −0.704685 0.709520i \(-0.748912\pi\)
0.966805 + 0.255515i \(0.0822449\pi\)
\(54\) −8.79349e8 1.52308e9i −0.260613 0.451394i
\(55\) 2.58218e9 0.691817
\(56\) 0 0
\(57\) 2.68668e9 0.591431
\(58\) 1.54088e9 + 2.66888e9i 0.308258 + 0.533919i
\(59\) 2.59460e9 4.49398e9i 0.472481 0.818362i −0.527023 0.849851i \(-0.676692\pi\)
0.999504 + 0.0314895i \(0.0100251\pi\)
\(60\) 8.95830e8 1.55162e9i 0.148728 0.257605i
\(61\) −3.47824e9 6.02449e9i −0.527285 0.913284i −0.999494 0.0317979i \(-0.989877\pi\)
0.472209 0.881486i \(-0.343457\pi\)
\(62\) 1.26824e9 0.175811
\(63\) 0 0
\(64\) 2.69930e9 0.314240
\(65\) 1.39524e9 + 2.41662e9i 0.149150 + 0.258336i
\(66\) 1.61667e9 2.80015e9i 0.158902 0.275226i
\(67\) 7.74091e9 1.34077e10i 0.700456 1.21323i −0.267851 0.963460i \(-0.586313\pi\)
0.968307 0.249765i \(-0.0803533\pi\)
\(68\) −5.08277e9 8.80361e9i −0.423937 0.734280i
\(69\) 4.69810e9 0.361620
\(70\) 0 0
\(71\) 9.79149e9 0.644062 0.322031 0.946729i \(-0.395634\pi\)
0.322031 + 0.946729i \(0.395634\pi\)
\(72\) 4.80028e9 + 8.31433e9i 0.292373 + 0.506406i
\(73\) −7.31896e8 + 1.26768e9i −0.0413212 + 0.0715705i −0.885946 0.463788i \(-0.846490\pi\)
0.844625 + 0.535358i \(0.179823\pi\)
\(74\) −2.18656e9 + 3.78723e9i −0.114548 + 0.198403i
\(75\) 3.21290e9 + 5.56491e9i 0.156337 + 0.270783i
\(76\) −1.56936e10 −0.709983
\(77\) 0 0
\(78\) 3.49416e9 0.137032
\(79\) −1.90584e10 3.30102e10i −0.696848 1.20698i −0.969554 0.244878i \(-0.921252\pi\)
0.272706 0.962097i \(-0.412081\pi\)
\(80\) −2.38393e9 + 4.12909e9i −0.0813391 + 0.140883i
\(81\) −8.32594e8 + 1.44210e9i −0.0265317 + 0.0459543i
\(82\) 3.69745e9 + 6.40416e9i 0.110135 + 0.190760i
\(83\) −2.93351e10 −0.817444 −0.408722 0.912659i \(-0.634025\pi\)
−0.408722 + 0.912659i \(0.634025\pi\)
\(84\) 0 0
\(85\) −3.33557e10 −0.815390
\(86\) −2.05508e8 3.55951e8i −0.00471073 0.00815923i
\(87\) −1.61792e10 + 2.80233e10i −0.348018 + 0.602785i
\(88\) −2.25820e10 + 3.91132e10i −0.456150 + 0.790075i
\(89\) 1.24965e10 + 2.16445e10i 0.237215 + 0.410868i 0.959914 0.280294i \(-0.0904321\pi\)
−0.722699 + 0.691163i \(0.757099\pi\)
\(90\) 1.31735e10 0.235162
\(91\) 0 0
\(92\) −2.74429e10 −0.434107
\(93\) 6.65824e9 + 1.15324e10i 0.0992438 + 0.171895i
\(94\) 3.22482e10 5.58555e10i 0.453213 0.784987i
\(95\) −2.57473e10 + 4.45957e10i −0.341391 + 0.591307i
\(96\) 2.47850e10 + 4.29289e10i 0.310239 + 0.537351i
\(97\) 7.50136e10 0.886942 0.443471 0.896289i \(-0.353747\pi\)
0.443471 + 0.896289i \(0.353747\pi\)
\(98\) 0 0
\(99\) −6.07549e10 −0.642078
\(100\) −1.87674e10 3.25061e10i −0.187674 0.325061i
\(101\) −4.08715e10 + 7.07915e10i −0.386948 + 0.670214i −0.992037 0.125944i \(-0.959804\pi\)
0.605089 + 0.796158i \(0.293137\pi\)
\(102\) −2.08835e10 + 3.61714e10i −0.187285 + 0.324387i
\(103\) 1.12878e11 + 1.95510e11i 0.959407 + 1.66174i 0.723944 + 0.689858i \(0.242327\pi\)
0.235463 + 0.971883i \(0.424339\pi\)
\(104\) −4.88073e10 −0.393370
\(105\) 0 0
\(106\) 3.83053e10 0.278021
\(107\) −4.51206e10 7.81512e10i −0.311003 0.538673i 0.667577 0.744541i \(-0.267332\pi\)
−0.978580 + 0.205868i \(0.933998\pi\)
\(108\) −5.39334e10 + 9.34154e10i −0.353205 + 0.611769i
\(109\) −3.67413e10 + 6.36379e10i −0.228723 + 0.396159i −0.957430 0.288666i \(-0.906788\pi\)
0.728707 + 0.684825i \(0.240122\pi\)
\(110\) 3.09861e10 + 5.36695e10i 0.183446 + 0.317737i
\(111\) −4.59178e10 −0.258645
\(112\) 0 0
\(113\) −8.51469e10 −0.434748 −0.217374 0.976088i \(-0.569749\pi\)
−0.217374 + 0.976088i \(0.569749\pi\)
\(114\) 3.22401e10 + 5.58416e10i 0.156827 + 0.271632i
\(115\) −4.50235e10 + 7.79830e10i −0.208738 + 0.361545i
\(116\) 9.45073e10 1.63691e11i 0.417779 0.723614i
\(117\) −3.28279e10 5.68597e10i −0.138427 0.239763i
\(118\) 1.24541e11 0.501142
\(119\) 0 0
\(120\) 1.02826e11 0.377229
\(121\) −2.49160e8 4.31558e8i −0.000873290 0.00151258i
\(122\) 8.34777e10 1.44588e11i 0.279635 0.484342i
\(123\) −3.88232e10 + 6.72437e10i −0.124341 + 0.215364i
\(124\) −3.88926e10 6.73639e10i −0.119137 0.206352i
\(125\) −3.59001e11 −1.05218
\(126\) 0 0
\(127\) −2.62717e11 −0.705615 −0.352808 0.935696i \(-0.614773\pi\)
−0.352808 + 0.935696i \(0.614773\pi\)
\(128\) −1.69036e11 2.92778e11i −0.434834 0.753155i
\(129\) 2.15784e9 3.73749e9i 0.00531833 0.00921163i
\(130\) −3.34857e10 + 5.79989e10i −0.0790990 + 0.137003i
\(131\) −3.15764e11 5.46920e11i −0.715107 1.23860i −0.962918 0.269793i \(-0.913045\pi\)
0.247811 0.968808i \(-0.420289\pi\)
\(132\) −1.98311e11 −0.430715
\(133\) 0 0
\(134\) 3.71564e11 0.742946
\(135\) 1.76969e11 + 3.06519e11i 0.339673 + 0.588331i
\(136\) 2.91707e11 5.05251e11i 0.537629 0.931200i
\(137\) 1.48599e11 2.57382e11i 0.263059 0.455632i −0.703994 0.710206i \(-0.748602\pi\)
0.967053 + 0.254574i \(0.0819351\pi\)
\(138\) 5.63773e10 + 9.76483e10i 0.0958890 + 0.166085i
\(139\) 5.96794e11 0.975535 0.487767 0.872974i \(-0.337811\pi\)
0.487767 + 0.872974i \(0.337811\pi\)
\(140\) 0 0
\(141\) 6.77212e11 1.02334
\(142\) 1.17498e11 + 2.03512e11i 0.170783 + 0.295804i
\(143\) 1.54433e11 2.67486e11i 0.215969 0.374069i
\(144\) 5.60905e10 9.71517e10i 0.0754911 0.130754i
\(145\) −3.10102e11 5.37112e11i −0.401773 0.695891i
\(146\) −3.51310e10 −0.0438278
\(147\) 0 0
\(148\) 2.68218e11 0.310491
\(149\) 5.57717e11 + 9.65994e11i 0.622142 + 1.07758i 0.989086 + 0.147338i \(0.0470705\pi\)
−0.366945 + 0.930243i \(0.619596\pi\)
\(150\) −7.71097e10 + 1.33558e11i −0.0829100 + 0.143604i
\(151\) 4.12224e11 7.13992e11i 0.427326 0.740151i −0.569308 0.822124i \(-0.692789\pi\)
0.996635 + 0.0819732i \(0.0261222\pi\)
\(152\) −4.50338e11 7.80009e11i −0.450194 0.779758i
\(153\) 7.84811e11 0.756767
\(154\) 0 0
\(155\) −2.55233e11 −0.229146
\(156\) −1.07154e11 1.85597e11i −0.0928590 0.160837i
\(157\) −6.57558e11 + 1.13892e12i −0.550156 + 0.952899i 0.448106 + 0.893980i \(0.352099\pi\)
−0.998263 + 0.0589187i \(0.981235\pi\)
\(158\) 4.57402e11 7.92244e11i 0.369559 0.640096i
\(159\) 2.01103e11 + 3.48321e11i 0.156940 + 0.271829i
\(160\) −9.50091e11 −0.716317
\(161\) 0 0
\(162\) −3.99645e10 −0.0281412
\(163\) 1.78916e11 + 3.09892e11i 0.121792 + 0.210950i 0.920474 0.390803i \(-0.127803\pi\)
−0.798682 + 0.601753i \(0.794469\pi\)
\(164\) 2.26777e11 3.92789e11i 0.149265 0.258534i
\(165\) −3.25354e11 + 5.63530e11i −0.207107 + 0.358720i
\(166\) −3.52021e11 6.09719e11i −0.216758 0.375435i
\(167\) 2.75483e12 1.64117 0.820587 0.571521i \(-0.193646\pi\)
0.820587 + 0.571521i \(0.193646\pi\)
\(168\) 0 0
\(169\) −1.45838e12 −0.813755
\(170\) −4.00268e11 6.93284e11i −0.216213 0.374492i
\(171\) 6.05798e11 1.04927e12i 0.316847 0.548795i
\(172\) −1.26045e10 + 2.18317e10i −0.00638440 + 0.0110581i
\(173\) 4.75194e11 + 8.23060e11i 0.233140 + 0.403811i 0.958731 0.284316i \(-0.0917666\pi\)
−0.725590 + 0.688127i \(0.758433\pi\)
\(174\) −7.76603e11 −0.369129
\(175\) 0 0
\(176\) 5.27735e11 0.235557
\(177\) 6.53840e11 + 1.13248e12i 0.282890 + 0.489981i
\(178\) −2.99915e11 + 5.19468e11i −0.125802 + 0.217896i
\(179\) −8.40692e11 + 1.45612e12i −0.341936 + 0.592251i −0.984792 0.173736i \(-0.944416\pi\)
0.642856 + 0.765987i \(0.277749\pi\)
\(180\) −4.03987e11 6.99726e11i −0.159356 0.276013i
\(181\) −9.96774e11 −0.381386 −0.190693 0.981650i \(-0.561073\pi\)
−0.190693 + 0.981650i \(0.561073\pi\)
\(182\) 0 0
\(183\) 1.75303e12 0.631406
\(184\) −7.87492e11 1.36398e12i −0.275263 0.476770i
\(185\) 4.40045e11 7.62181e11i 0.149298 0.258591i
\(186\) −1.59798e11 + 2.76778e11i −0.0526319 + 0.0911612i
\(187\) 1.84600e12 + 3.19736e12i 0.590340 + 1.02250i
\(188\) −3.95578e12 −1.22847
\(189\) 0 0
\(190\) −1.23587e12 −0.362100
\(191\) −1.38120e12 2.39231e12i −0.393164 0.680980i 0.599701 0.800224i \(-0.295286\pi\)
−0.992865 + 0.119244i \(0.961953\pi\)
\(192\) −3.40111e11 + 5.89090e11i −0.0940729 + 0.162939i
\(193\) −2.72119e12 + 4.71325e12i −0.731466 + 1.26694i 0.224790 + 0.974407i \(0.427830\pi\)
−0.956256 + 0.292530i \(0.905503\pi\)
\(194\) 9.00163e11 + 1.55913e12i 0.235186 + 0.407354i
\(195\) −7.03200e11 −0.178603
\(196\) 0 0
\(197\) −2.87609e12 −0.690619 −0.345309 0.938489i \(-0.612226\pi\)
−0.345309 + 0.938489i \(0.612226\pi\)
\(198\) −7.29059e11 1.26277e12i −0.170257 0.294893i
\(199\) −3.64196e11 + 6.30805e11i −0.0827262 + 0.143286i −0.904420 0.426643i \(-0.859696\pi\)
0.821694 + 0.569929i \(0.193029\pi\)
\(200\) 1.07709e12 1.86557e12i 0.238005 0.412237i
\(201\) 1.95071e12 + 3.37873e12i 0.419386 + 0.726399i
\(202\) −1.96183e12 −0.410421
\(203\) 0 0
\(204\) 2.56171e12 0.507651
\(205\) −7.44111e11 1.28884e12i −0.143546 0.248629i
\(206\) −2.70906e12 + 4.69223e12i −0.508802 + 0.881272i
\(207\) 1.05934e12 1.83483e12i 0.193730 0.335551i
\(208\) 2.85153e11 + 4.93899e11i 0.0507843 + 0.0879610i
\(209\) 5.69972e12 0.988665
\(210\) 0 0
\(211\) −6.79317e12 −1.11820 −0.559099 0.829101i \(-0.688853\pi\)
−0.559099 + 0.829101i \(0.688853\pi\)
\(212\) −1.17470e12 2.03463e12i −0.188399 0.326317i
\(213\) −1.23373e12 + 2.13688e12i −0.192811 + 0.333958i
\(214\) 1.08290e12 1.87563e12i 0.164934 0.285674i
\(215\) 4.13586e10 + 7.16352e10i 0.00613980 + 0.0106344i
\(216\) −6.19062e12 −0.895856
\(217\) 0 0
\(218\) −1.76358e12 −0.242597
\(219\) −1.84438e11 3.19455e11i −0.0247404 0.0428517i
\(220\) 1.90048e12 3.29173e12i 0.248622 0.430625i
\(221\) −1.99491e12 + 3.45529e12i −0.254546 + 0.440886i
\(222\) −5.51013e11 9.54383e11i −0.0685836 0.118790i
\(223\) 7.33486e12 0.890667 0.445333 0.895365i \(-0.353085\pi\)
0.445333 + 0.895365i \(0.353085\pi\)
\(224\) 0 0
\(225\) 2.89781e12 0.335016
\(226\) −1.02176e12 1.76974e12i −0.115280 0.199671i
\(227\) 6.79920e11 1.17766e12i 0.0748713 0.129681i −0.826159 0.563437i \(-0.809479\pi\)
0.901030 + 0.433756i \(0.142812\pi\)
\(228\) 1.97739e12 3.42495e12i 0.212545 0.368139i
\(229\) 5.91221e12 + 1.02402e13i 0.620375 + 1.07452i 0.989416 + 0.145108i \(0.0463530\pi\)
−0.369041 + 0.929413i \(0.620314\pi\)
\(230\) −2.16113e12 −0.221400
\(231\) 0 0
\(232\) 1.08478e13 1.05964
\(233\) 8.78168e12 + 1.52103e13i 0.837761 + 1.45104i 0.891763 + 0.452503i \(0.149469\pi\)
−0.0540024 + 0.998541i \(0.517198\pi\)
\(234\) 7.87871e11 1.36463e12i 0.0734121 0.127153i
\(235\) −6.48995e12 + 1.12409e13i −0.590701 + 1.02312i
\(236\) −3.81925e12 6.61514e12i −0.339596 0.588197i
\(237\) 9.60545e12 0.834452
\(238\) 0 0
\(239\) −7.13958e12 −0.592221 −0.296111 0.955154i \(-0.595690\pi\)
−0.296111 + 0.955154i \(0.595690\pi\)
\(240\) −6.00751e11 1.04053e12i −0.0487004 0.0843516i
\(241\) 1.15653e11 2.00318e11i 0.00916357 0.0158718i −0.861407 0.507915i \(-0.830416\pi\)
0.870571 + 0.492043i \(0.163750\pi\)
\(242\) 5.97984e9 1.03574e10i 0.000463132 0.000802169i
\(243\) −6.70040e12 1.16054e13i −0.507301 0.878672i
\(244\) −1.02399e13 −0.757972
\(245\) 0 0
\(246\) −1.86351e12 −0.131883
\(247\) 3.07975e12 + 5.33429e12i 0.213149 + 0.369184i
\(248\) 2.23210e12 3.86610e12i 0.151087 0.261691i
\(249\) 3.69622e12 6.40205e12i 0.244716 0.423860i
\(250\) −4.30801e12 7.46170e12i −0.279002 0.483245i
\(251\) 1.29831e13 0.822567 0.411284 0.911507i \(-0.365081\pi\)
0.411284 + 0.911507i \(0.365081\pi\)
\(252\) 0 0
\(253\) 9.96692e12 0.604502
\(254\) −3.15261e12 5.46047e12i −0.187105 0.324075i
\(255\) 4.20281e12 7.27949e12i 0.244101 0.422795i
\(256\) 6.82094e12 1.18142e13i 0.387725 0.671560i
\(257\) −1.19806e13 2.07510e13i −0.666571 1.15453i −0.978857 0.204546i \(-0.934428\pi\)
0.312286 0.949988i \(-0.398905\pi\)
\(258\) 1.03576e11 0.00564095
\(259\) 0 0
\(260\) 4.10758e12 0.214404
\(261\) 7.29626e12 + 1.26375e13i 0.372887 + 0.645859i
\(262\) 7.57835e12 1.31261e13i 0.379243 0.656868i
\(263\) 1.21369e13 2.10217e13i 0.594771 1.03017i −0.398808 0.917034i \(-0.630576\pi\)
0.993579 0.113139i \(-0.0360907\pi\)
\(264\) −5.69067e12 9.85652e12i −0.273112 0.473045i
\(265\) −7.70895e12 −0.362362
\(266\) 0 0
\(267\) −6.29822e12 −0.284057
\(268\) −1.13946e13 1.97361e13i −0.503453 0.872006i
\(269\) −1.29189e13 + 2.23761e13i −0.559225 + 0.968606i 0.438337 + 0.898811i \(0.355568\pi\)
−0.997561 + 0.0697949i \(0.977766\pi\)
\(270\) −4.24726e12 + 7.35646e12i −0.180139 + 0.312010i
\(271\) 1.88397e12 + 3.26313e12i 0.0782964 + 0.135613i 0.902515 0.430658i \(-0.141719\pi\)
−0.824219 + 0.566272i \(0.808385\pi\)
\(272\) −6.81710e12 −0.277633
\(273\) 0 0
\(274\) 7.13277e12 0.279017
\(275\) 6.81610e12 + 1.18058e13i 0.261340 + 0.452654i
\(276\) 3.45780e12 5.98909e12i 0.129957 0.225093i
\(277\) 8.20947e12 1.42192e13i 0.302466 0.523886i −0.674228 0.738523i \(-0.735524\pi\)
0.976694 + 0.214637i \(0.0688569\pi\)
\(278\) 7.16152e12 + 1.24041e13i 0.258678 + 0.448043i
\(279\) 6.00526e12 0.212671
\(280\) 0 0
\(281\) 2.10357e13 0.716263 0.358132 0.933671i \(-0.383414\pi\)
0.358132 + 0.933671i \(0.383414\pi\)
\(282\) 8.12654e12 + 1.40756e13i 0.271354 + 0.469998i
\(283\) −8.35659e12 + 1.44740e13i −0.273655 + 0.473985i −0.969795 0.243922i \(-0.921566\pi\)
0.696140 + 0.717906i \(0.254899\pi\)
\(284\) 7.20653e12 1.24821e13i 0.231460 0.400900i
\(285\) −6.48833e12 1.12381e13i −0.204402 0.354035i
\(286\) 7.41278e12 0.229070
\(287\) 0 0
\(288\) 2.23543e13 0.664817
\(289\) −6.71001e12 1.16221e13i −0.195788 0.339114i
\(290\) 7.44245e12 1.28907e13i 0.213072 0.369052i
\(291\) −9.45171e12 + 1.63708e13i −0.265521 + 0.459896i
\(292\) 1.07735e12 + 1.86603e12i 0.0296996 + 0.0514413i
\(293\) −2.39269e13 −0.647312 −0.323656 0.946175i \(-0.604912\pi\)
−0.323656 + 0.946175i \(0.604912\pi\)
\(294\) 0 0
\(295\) −2.50639e13 −0.653171
\(296\) 7.69669e12 + 1.33311e13i 0.196879 + 0.341005i
\(297\) 1.95879e13 3.39273e13i 0.491845 0.851900i
\(298\) −1.33852e13 + 2.31839e13i −0.329940 + 0.571474i
\(299\) 5.38546e12 + 9.32790e12i 0.130326 + 0.225731i
\(300\) 9.45878e12 0.224734
\(301\) 0 0
\(302\) 1.97867e13 0.453248
\(303\) −1.02996e13 1.78395e13i −0.231679 0.401280i
\(304\) −5.26214e12 + 9.11429e12i −0.116240 + 0.201334i
\(305\) −1.67999e13 + 2.90983e13i −0.364466 + 0.631274i
\(306\) 9.41773e12 + 1.63120e13i 0.200668 + 0.347567i
\(307\) 1.53111e13 0.320439 0.160219 0.987081i \(-0.448780\pi\)
0.160219 + 0.987081i \(0.448780\pi\)
\(308\) 0 0
\(309\) −5.68903e13 −1.14886
\(310\) −3.06279e12 5.30491e12i −0.0607614 0.105242i
\(311\) −2.49376e13 + 4.31932e13i −0.486040 + 0.841846i −0.999871 0.0160451i \(-0.994892\pi\)
0.513831 + 0.857891i \(0.328226\pi\)
\(312\) 6.14972e12 1.06516e13i 0.117762 0.203970i
\(313\) 4.97404e13 + 8.61529e13i 0.935870 + 1.62097i 0.773075 + 0.634315i \(0.218718\pi\)
0.162795 + 0.986660i \(0.447949\pi\)
\(314\) −3.15628e13 −0.583529
\(315\) 0 0
\(316\) −5.61080e13 −1.00172
\(317\) −4.16846e13 7.21999e13i −0.731392 1.26681i −0.956289 0.292425i \(-0.905538\pi\)
0.224897 0.974383i \(-0.427795\pi\)
\(318\) −4.82647e12 + 8.35970e12i −0.0832301 + 0.144159i
\(319\) −3.43239e13 + 5.94507e13i −0.581765 + 1.00765i
\(320\) −6.51880e12 1.12909e13i −0.108603 0.188106i
\(321\) 2.27408e13 0.372416
\(322\) 0 0
\(323\) −7.36271e13 −1.16526
\(324\) 1.22558e12 + 2.12276e12i 0.0190697 + 0.0330297i
\(325\) −7.36594e12 + 1.27582e13i −0.112686 + 0.195178i
\(326\) −4.29399e12 + 7.43741e12i −0.0645899 + 0.111873i
\(327\) −9.25882e12 1.60367e13i −0.136944 0.237194i
\(328\) 2.60300e13 0.378589
\(329\) 0 0
\(330\) −1.56170e13 −0.219670
\(331\) 3.17920e13 + 5.50654e13i 0.439809 + 0.761771i 0.997674 0.0681600i \(-0.0217128\pi\)
−0.557865 + 0.829931i \(0.688379\pi\)
\(332\) −2.15906e13 + 3.73961e13i −0.293769 + 0.508823i
\(333\) −1.03536e13 + 1.79330e13i −0.138564 + 0.239999i
\(334\) 3.30580e13 + 5.72581e13i 0.435182 + 0.753758i
\(335\) −7.47772e13 −0.968329
\(336\) 0 0
\(337\) 1.21001e14 1.51644 0.758221 0.651997i \(-0.226069\pi\)
0.758221 + 0.651997i \(0.226069\pi\)
\(338\) −1.75006e13 3.03118e13i −0.215779 0.373741i
\(339\) 1.07285e13 1.85823e13i 0.130149 0.225425i
\(340\) −2.45498e13 + 4.25214e13i −0.293031 + 0.507544i
\(341\) 1.41253e13 + 2.44657e13i 0.165901 + 0.287349i
\(342\) 2.90783e13 0.336067
\(343\) 0 0
\(344\) −1.44678e12 −0.0161931
\(345\) −1.13459e13 1.96517e13i −0.124978 0.216469i
\(346\) −1.14046e13 + 1.97534e13i −0.123641 + 0.214153i
\(347\) 7.78308e13 1.34807e14i 0.830499 1.43847i −0.0671435 0.997743i \(-0.521389\pi\)
0.897643 0.440724i \(-0.145278\pi\)
\(348\) 2.38158e13 + 4.12502e13i 0.250138 + 0.433252i
\(349\) −2.56430e13 −0.265112 −0.132556 0.991176i \(-0.542318\pi\)
−0.132556 + 0.991176i \(0.542318\pi\)
\(350\) 0 0
\(351\) 4.23361e13 0.424152
\(352\) 5.25808e13 + 9.10726e13i 0.518612 + 0.898262i
\(353\) −1.24549e13 + 2.15725e13i −0.120943 + 0.209479i −0.920140 0.391590i \(-0.871925\pi\)
0.799197 + 0.601069i \(0.205258\pi\)
\(354\) −1.56922e13 + 2.71796e13i −0.150025 + 0.259851i
\(355\) −2.36464e13 4.09568e13i −0.222592 0.385541i
\(356\) 3.67896e13 0.340996
\(357\) 0 0
\(358\) −4.03532e13 −0.362678
\(359\) −7.87921e13 1.36472e14i −0.697370 1.20788i −0.969375 0.245584i \(-0.921020\pi\)
0.272006 0.962296i \(-0.412313\pi\)
\(360\) 2.31854e13 4.01582e13i 0.202092 0.350034i
\(361\) 1.41219e12 2.44599e12i 0.0121228 0.0209974i
\(362\) −1.19613e13 2.07176e13i −0.101130 0.175163i
\(363\) 1.25577e11 0.00104574
\(364\) 0 0
\(365\) 7.07011e12 0.0571236
\(366\) 2.10364e13 + 3.64361e13i 0.167427 + 0.289992i
\(367\) 8.89506e13 1.54067e14i 0.697406 1.20794i −0.271957 0.962309i \(-0.587671\pi\)
0.969363 0.245633i \(-0.0789958\pi\)
\(368\) −9.20172e12 + 1.59379e13i −0.0710732 + 0.123102i
\(369\) 1.75079e13 + 3.03245e13i 0.133226 + 0.230754i
\(370\) 2.11222e13 0.158354
\(371\) 0 0
\(372\) 1.96019e13 0.142663
\(373\) 2.75809e13 + 4.77715e13i 0.197792 + 0.342586i 0.947812 0.318829i \(-0.103290\pi\)
−0.750020 + 0.661415i \(0.769956\pi\)
\(374\) −4.43039e13 + 7.67367e13i −0.313075 + 0.542262i
\(375\) 4.52341e13 7.83478e13i 0.314988 0.545576i
\(376\) −1.13514e14 1.96611e14i −0.778959 1.34920i
\(377\) −7.41854e13 −0.501696
\(378\) 0 0
\(379\) 1.46463e14 0.962083 0.481042 0.876698i \(-0.340259\pi\)
0.481042 + 0.876698i \(0.340259\pi\)
\(380\) 3.79001e13 + 6.56448e13i 0.245375 + 0.425002i
\(381\) 3.31024e13 5.73350e13i 0.211238 0.365875i
\(382\) 3.31488e13 5.74155e13i 0.208507 0.361144i
\(383\) −1.15725e14 2.00441e14i −0.717519 1.24278i −0.961980 0.273120i \(-0.911945\pi\)
0.244462 0.969659i \(-0.421389\pi\)
\(384\) 8.51940e13 0.520700
\(385\) 0 0
\(386\) −1.30617e14 −0.775837
\(387\) −9.73108e11 1.68547e12i −0.00569837 0.00986987i
\(388\) 5.52100e13 9.56265e13i 0.318745 0.552082i
\(389\) 7.49358e13 1.29793e14i 0.426547 0.738800i −0.570017 0.821633i \(-0.693063\pi\)
0.996563 + 0.0828326i \(0.0263967\pi\)
\(390\) −8.43840e12 1.46157e13i −0.0473592 0.0820286i
\(391\) −1.28749e14 −0.712480
\(392\) 0 0
\(393\) 1.59145e14 0.856317
\(394\) −3.45131e13 5.97784e13i −0.183128 0.317187i
\(395\) −9.20522e13 + 1.59439e14i −0.481671 + 0.834278i
\(396\) −4.47156e13 + 7.74497e13i −0.230747 + 0.399665i
\(397\) −1.04055e14 1.80229e14i −0.529562 0.917228i −0.999405 0.0344782i \(-0.989023\pi\)
0.469844 0.882750i \(-0.344310\pi\)
\(398\) −1.74814e13 −0.0877443
\(399\) 0 0
\(400\) −2.51712e13 −0.122906
\(401\) 6.67040e13 + 1.15535e14i 0.321261 + 0.556440i 0.980748 0.195275i \(-0.0625601\pi\)
−0.659488 + 0.751715i \(0.729227\pi\)
\(402\) −4.68170e13 + 8.10895e13i −0.222413 + 0.385231i
\(403\) −1.52648e13 + 2.64393e13i −0.0715339 + 0.123900i
\(404\) 6.01628e13 + 1.04205e14i 0.278119 + 0.481716i
\(405\) 8.04286e12 0.0366782
\(406\) 0 0
\(407\) −9.74134e13 −0.432364
\(408\) 7.35101e13 + 1.27323e14i 0.321896 + 0.557541i
\(409\) 1.03084e14 1.78546e14i 0.445361 0.771388i −0.552716 0.833369i \(-0.686409\pi\)
0.998077 + 0.0619816i \(0.0197420\pi\)
\(410\) 1.78587e13 3.09321e13i 0.0761268 0.131856i
\(411\) 3.74470e13 + 6.48602e13i 0.157503 + 0.272802i
\(412\) 3.32312e14 1.37915
\(413\) 0 0
\(414\) 5.08483e13 0.205482
\(415\) 7.08443e13 + 1.22706e14i 0.282514 + 0.489329i
\(416\) −5.68224e13 + 9.84192e13i −0.223618 + 0.387317i
\(417\) −7.51960e13 + 1.30243e14i −0.292043 + 0.505833i
\(418\) 6.83967e13 + 1.18467e14i 0.262159 + 0.454073i
\(419\) 7.34035e13 0.277677 0.138838 0.990315i \(-0.455663\pi\)
0.138838 + 0.990315i \(0.455663\pi\)
\(420\) 0 0
\(421\) 1.71112e14 0.630563 0.315282 0.948998i \(-0.397901\pi\)
0.315282 + 0.948998i \(0.397901\pi\)
\(422\) −8.15180e13 1.41193e14i −0.296507 0.513565i
\(423\) 1.52699e14 2.64483e14i 0.548232 0.949566i
\(424\) 6.74174e13 1.16770e14i 0.238924 0.413828i
\(425\) −8.80480e13 1.52504e14i −0.308021 0.533508i
\(426\) −5.92189e13 −0.204507
\(427\) 0 0
\(428\) −1.32835e14 −0.447067
\(429\) 3.89171e13 + 6.74063e13i 0.129308 + 0.223968i
\(430\) −9.92606e11 + 1.71924e12i −0.00325612 + 0.00563977i
\(431\) 3.58879e13 6.21597e13i 0.116231 0.201319i −0.802040 0.597270i \(-0.796252\pi\)
0.918271 + 0.395952i \(0.129585\pi\)
\(432\) 3.61682e13 + 6.26452e13i 0.115656 + 0.200321i
\(433\) 9.98812e13 0.315356 0.157678 0.987491i \(-0.449599\pi\)
0.157678 + 0.987491i \(0.449599\pi\)
\(434\) 0 0
\(435\) 1.56291e14 0.481110
\(436\) 5.40832e13 + 9.36749e13i 0.164394 + 0.284739i
\(437\) −9.93819e13 + 1.72134e14i −0.298304 + 0.516678i
\(438\) 4.42650e12 7.66693e12i 0.0131206 0.0227255i
\(439\) 1.45156e13 + 2.51418e13i 0.0424894 + 0.0735938i 0.886488 0.462752i \(-0.153138\pi\)
−0.843999 + 0.536345i \(0.819804\pi\)
\(440\) 2.18142e14 0.630594
\(441\) 0 0
\(442\) −9.57557e13 −0.269987
\(443\) −1.64185e14 2.84377e14i −0.457207 0.791906i 0.541605 0.840633i \(-0.317817\pi\)
−0.998812 + 0.0487274i \(0.984483\pi\)
\(444\) −3.37955e13 + 5.85355e13i −0.0929506 + 0.160995i
\(445\) 6.03579e13 1.04543e14i 0.163966 0.283998i
\(446\) 8.80184e13 + 1.52452e14i 0.236174 + 0.409065i
\(447\) −2.81089e14 −0.744994
\(448\) 0 0
\(449\) −6.12368e14 −1.58364 −0.791822 0.610752i \(-0.790867\pi\)
−0.791822 + 0.610752i \(0.790867\pi\)
\(450\) 3.47737e13 + 6.02298e13i 0.0888346 + 0.153866i
\(451\) −8.23624e13 + 1.42656e14i −0.207854 + 0.360014i
\(452\) −6.26681e13 + 1.08544e14i −0.156237 + 0.270611i
\(453\) 1.03880e14 + 1.79926e14i 0.255855 + 0.443153i
\(454\) 3.26361e13 0.0794130
\(455\) 0 0
\(456\) 2.26971e14 0.539092
\(457\) −1.51742e14 2.62824e14i −0.356095 0.616774i 0.631210 0.775612i \(-0.282559\pi\)
−0.987305 + 0.158838i \(0.949225\pi\)
\(458\) −1.41893e14 + 2.45766e14i −0.329004 + 0.569851i
\(459\) −2.53030e14 + 4.38261e14i −0.579699 + 1.00407i
\(460\) 6.62746e13 + 1.14791e14i 0.150030 + 0.259860i
\(461\) −7.29308e14 −1.63138 −0.815691 0.578487i \(-0.803643\pi\)
−0.815691 + 0.578487i \(0.803643\pi\)
\(462\) 0 0
\(463\) 1.22188e14 0.266891 0.133445 0.991056i \(-0.457396\pi\)
0.133445 + 0.991056i \(0.457396\pi\)
\(464\) −6.33774e13 1.09773e14i −0.136800 0.236944i
\(465\) 3.21593e13 5.57015e13i 0.0685986 0.118816i
\(466\) −2.10760e14 + 3.65047e14i −0.444290 + 0.769532i
\(467\) 3.08690e14 + 5.34667e14i 0.643103 + 1.11389i 0.984736 + 0.174053i \(0.0556864\pi\)
−0.341634 + 0.939833i \(0.610980\pi\)
\(468\) −9.66455e13 −0.198989
\(469\) 0 0
\(470\) −3.11517e14 −0.626533
\(471\) −1.65705e14 2.87009e14i −0.329397 0.570533i
\(472\) 2.19192e14 3.79652e14i 0.430669 0.745941i
\(473\) 4.57780e12 7.92899e12i 0.00889039 0.0153986i
\(474\) 1.15265e14 + 1.99645e14i 0.221268 + 0.383247i
\(475\) −2.71858e14 −0.515854
\(476\) 0 0
\(477\) 1.81381e14 0.336310
\(478\) −8.56749e13 1.48393e14i −0.157036 0.271995i
\(479\) −5.25419e14 + 9.10052e14i −0.952052 + 1.64900i −0.211076 + 0.977470i \(0.567697\pi\)
−0.740976 + 0.671532i \(0.765637\pi\)
\(480\) 1.19712e14 2.07346e14i 0.214442 0.371424i
\(481\) −5.26358e13 9.11678e13i −0.0932144 0.161452i
\(482\) 5.55137e12 0.00971944
\(483\) 0 0
\(484\) −7.33527e11 −0.00125536
\(485\) −1.81158e14 3.13774e14i −0.306533 0.530931i
\(486\) 1.60810e14 2.78530e14i 0.269037 0.465986i
\(487\) 1.09955e14 1.90448e14i 0.181889 0.315040i −0.760635 0.649180i \(-0.775112\pi\)
0.942524 + 0.334139i \(0.108446\pi\)
\(488\) −2.93842e14 5.08949e14i −0.480623 0.832463i
\(489\) −9.01739e13 −0.145842
\(490\) 0 0
\(491\) −4.83863e14 −0.765199 −0.382599 0.923914i \(-0.624971\pi\)
−0.382599 + 0.923914i \(0.624971\pi\)
\(492\) 5.71477e13 + 9.89827e13i 0.0893698 + 0.154793i
\(493\) 4.43384e14 7.67963e14i 0.685681 1.18763i
\(494\) −7.39141e13 + 1.28023e14i −0.113039 + 0.195790i
\(495\) 1.46723e14 + 2.54132e14i 0.221906 + 0.384353i
\(496\) −5.21634e13 −0.0780219
\(497\) 0 0
\(498\) 1.77419e14 0.259560
\(499\) 5.44389e13 + 9.42909e13i 0.0787691 + 0.136432i 0.902719 0.430230i \(-0.141568\pi\)
−0.823950 + 0.566663i \(0.808234\pi\)
\(500\) −2.64225e14 + 4.57651e14i −0.378128 + 0.654937i
\(501\) −3.47109e14 + 6.01211e14i −0.491313 + 0.850979i
\(502\) 1.55797e14 + 2.69848e14i 0.218116 + 0.377788i
\(503\) 5.06588e14 0.701506 0.350753 0.936468i \(-0.385926\pi\)
0.350753 + 0.936468i \(0.385926\pi\)
\(504\) 0 0
\(505\) 3.94818e14 0.534927
\(506\) 1.19603e14 + 2.07158e14i 0.160293 + 0.277635i
\(507\) 1.83756e14 3.18274e14i 0.243611 0.421947i
\(508\) −1.93360e14 + 3.34909e14i −0.253581 + 0.439214i
\(509\) −4.28767e13 7.42646e13i −0.0556254 0.0963461i 0.836872 0.547399i \(-0.184382\pi\)
−0.892497 + 0.451053i \(0.851049\pi\)
\(510\) 2.01735e14 0.258908
\(511\) 0 0
\(512\) −3.64965e14 −0.458423
\(513\) 3.90630e14 + 6.76590e14i 0.485422 + 0.840776i
\(514\) 2.87534e14 4.98024e14i 0.353503 0.612284i
\(515\) 5.45199e14 9.44312e14i 0.663155 1.14862i
\(516\) −3.17634e12 5.50158e12i −0.00382255 0.00662086i
\(517\) 1.43669e15 1.71066
\(518\) 0 0
\(519\) −2.39498e14 −0.279178
\(520\) 1.17870e14 + 2.04156e14i 0.135951 + 0.235475i
\(521\) −4.63787e14 + 8.03303e14i −0.529312 + 0.916795i 0.470104 + 0.882611i \(0.344216\pi\)
−0.999416 + 0.0341835i \(0.989117\pi\)
\(522\) −1.75110e14 + 3.03300e14i −0.197753 + 0.342519i
\(523\) 1.09093e13 + 1.88955e13i 0.0121910 + 0.0211154i 0.872057 0.489405i \(-0.162786\pi\)
−0.859866 + 0.510521i \(0.829453\pi\)
\(524\) −9.29610e14 −1.02797
\(525\) 0 0
\(526\) 5.82569e14 0.630850
\(527\) −1.82466e14 3.16040e14i −0.195534 0.338675i
\(528\) −6.64946e13 + 1.15172e14i −0.0705179 + 0.122141i
\(529\) 3.02619e14 5.24152e14i 0.317607 0.550112i
\(530\) −9.25074e13 1.60227e14i −0.0960858 0.166425i
\(531\) 5.89717e14 0.606211
\(532\) 0 0
\(533\) −1.78013e14 −0.179247
\(534\) −7.55786e13 1.30906e14i −0.0753220 0.130462i
\(535\) −2.17933e14 + 3.77470e14i −0.214969 + 0.372338i
\(536\) 6.53952e14 1.13268e15i 0.638469 1.10586i
\(537\) −2.11854e14 3.66943e14i −0.204729 0.354601i
\(538\) −6.20105e14 −0.593147
\(539\) 0 0
\(540\) 5.20997e14 0.488280
\(541\) 8.47633e14 + 1.46814e15i 0.786363 + 1.36202i 0.928181 + 0.372128i \(0.121372\pi\)
−0.141819 + 0.989893i \(0.545295\pi\)
\(542\) −4.52152e13 + 7.83150e13i −0.0415230 + 0.0719199i
\(543\) 1.25594e14 2.17534e14i 0.114174 0.197756i
\(544\) −6.79220e14 1.17644e15i −0.611247 1.05871i
\(545\) 3.54921e14 0.316192
\(546\) 0 0
\(547\) 7.52145e14 0.656706 0.328353 0.944555i \(-0.393506\pi\)
0.328353 + 0.944555i \(0.393506\pi\)
\(548\) −2.18738e14 3.78866e14i −0.189074 0.327486i
\(549\) 3.95278e14 6.84641e14i 0.338263 0.585888i
\(550\) −1.63586e14 + 2.83340e14i −0.138596 + 0.240056i
\(551\) −6.84499e14 1.18559e15i −0.574168 0.994488i
\(552\) 3.96896e14 0.329619
\(553\) 0 0
\(554\) 3.94054e14 0.320813
\(555\) 1.10891e14 + 1.92070e14i 0.0893895 + 0.154827i
\(556\) 4.39240e14 7.60786e14i 0.350583 0.607227i
\(557\) −9.37445e13 + 1.62370e14i −0.0740870 + 0.128323i −0.900689 0.434465i \(-0.856938\pi\)
0.826602 + 0.562787i \(0.190271\pi\)
\(558\) 7.20631e13 + 1.24817e14i 0.0563929 + 0.0976754i
\(559\) 9.89417e12 0.00766681
\(560\) 0 0
\(561\) −9.30383e14 −0.706913
\(562\) 2.52429e14 + 4.37219e14i 0.189928 + 0.328965i
\(563\) −1.22486e14 + 2.12151e14i −0.0912618 + 0.158070i −0.908042 0.418878i \(-0.862423\pi\)
0.816781 + 0.576949i \(0.195757\pi\)
\(564\) 4.98428e14 8.63302e14i 0.367762 0.636983i
\(565\) 2.05630e14 + 3.56161e14i 0.150252 + 0.260244i
\(566\) −4.01116e14 −0.290255
\(567\) 0 0
\(568\) 8.27185e14 0.587066
\(569\) −6.76213e14 1.17124e15i −0.475298 0.823240i 0.524302 0.851533i \(-0.324326\pi\)
−0.999600 + 0.0282923i \(0.990993\pi\)
\(570\) 1.55720e14 2.69715e14i 0.108401 0.187756i
\(571\) −7.16114e14 + 1.24035e15i −0.493723 + 0.855154i −0.999974 0.00723249i \(-0.997698\pi\)
0.506250 + 0.862387i \(0.331031\pi\)
\(572\) −2.27325e14 3.93739e14i −0.155228 0.268862i
\(573\) 6.96126e14 0.470801
\(574\) 0 0
\(575\) −4.75389e14 −0.315410
\(576\) 1.53378e14 + 2.65659e14i 0.100795 + 0.174582i
\(577\) 4.38830e14 7.60075e14i 0.285647 0.494754i −0.687119 0.726545i \(-0.741125\pi\)
0.972766 + 0.231790i \(0.0744583\pi\)
\(578\) 1.61040e14 2.78930e14i 0.103832 0.179842i
\(579\) −6.85741e14 1.18774e15i −0.437953 0.758558i
\(580\) −9.12940e14 −0.577548
\(581\) 0 0
\(582\) −4.53682e14 −0.281628
\(583\) 4.26635e14 + 7.38954e14i 0.262349 + 0.454402i
\(584\) −6.18305e13 + 1.07094e14i −0.0376645 + 0.0652369i
\(585\) −1.58559e14 + 2.74632e14i −0.0956827 + 0.165727i
\(586\) −2.87122e14 4.97310e14i −0.171645 0.297297i
\(587\) −2.43425e15 −1.44164 −0.720818 0.693124i \(-0.756234\pi\)
−0.720818 + 0.693124i \(0.756234\pi\)
\(588\) 0 0
\(589\) −5.63383e14 −0.327469
\(590\) −3.00766e14 5.20942e14i −0.173198 0.299988i
\(591\) 3.62388e14 6.27674e14i 0.206748 0.358099i
\(592\) 8.99347e13 1.55771e14i 0.0508344 0.0880478i
\(593\) 1.51659e14 + 2.62681e14i 0.0849313 + 0.147105i 0.905362 0.424641i \(-0.139600\pi\)
−0.820431 + 0.571746i \(0.806266\pi\)
\(594\) 9.40221e14 0.521680
\(595\) 0 0
\(596\) 1.64192e15 0.894329
\(597\) −9.17773e13 1.58963e14i −0.0495309 0.0857901i
\(598\) −1.29251e14 + 2.23870e14i −0.0691159 + 0.119712i
\(599\) 8.50992e14 1.47396e15i 0.450898 0.780978i −0.547544 0.836777i \(-0.684437\pi\)
0.998442 + 0.0557990i \(0.0177706\pi\)
\(600\) 2.71426e14 + 4.70124e14i 0.142502 + 0.246820i
\(601\) 2.33922e15 1.21692 0.608458 0.793586i \(-0.291788\pi\)
0.608458 + 0.793586i \(0.291788\pi\)
\(602\) 0 0
\(603\) 1.75940e15 0.898710
\(604\) −6.06793e14 1.05100e15i −0.307141 0.531984i
\(605\) −1.20344e12 + 2.08442e12i −0.000603630 + 0.00104552i
\(606\) 2.47191e14 4.28147e14i 0.122866 0.212811i
\(607\) 1.24804e15 + 2.16166e15i 0.614737 + 1.06476i 0.990431 + 0.138012i \(0.0440712\pi\)
−0.375694 + 0.926744i \(0.622595\pi\)
\(608\) −2.09717e15 −1.02368
\(609\) 0 0
\(610\) −8.06395e14 −0.386575
\(611\) 7.76292e14 + 1.34458e15i 0.368806 + 0.638791i
\(612\) 5.77621e14 1.00047e15i 0.271963 0.471054i
\(613\) −1.23650e15 + 2.14169e15i −0.576983 + 0.999364i 0.418840 + 0.908060i \(0.362437\pi\)
−0.995823 + 0.0913040i \(0.970897\pi\)
\(614\) 1.83733e14 + 3.18235e14i 0.0849692 + 0.147171i
\(615\) 3.75032e14 0.171892
\(616\) 0 0
\(617\) 2.43368e13 0.0109571 0.00547854 0.999985i \(-0.498256\pi\)
0.00547854 + 0.999985i \(0.498256\pi\)
\(618\) −6.82684e14 1.18244e15i −0.304637 0.527647i
\(619\) −2.11273e15 + 3.65935e15i −0.934425 + 1.61847i −0.158769 + 0.987316i \(0.550753\pi\)
−0.775656 + 0.631156i \(0.782581\pi\)
\(620\) −1.87851e14 + 3.25368e14i −0.0823492 + 0.142633i
\(621\) 6.83081e14 + 1.18313e15i 0.296803 + 0.514078i
\(622\) −1.19700e15 −0.515523
\(623\) 0 0
\(624\) −1.43717e14 −0.0608126
\(625\) 2.44448e14 + 4.23396e14i 0.102529 + 0.177585i
\(626\) −1.19377e15 + 2.06767e15i −0.496320 + 0.859652i
\(627\) −7.18165e14 + 1.24390e15i −0.295973 + 0.512641i
\(628\) 9.67926e14 + 1.67650e15i 0.395425 + 0.684896i
\(629\) 1.25835e15 0.509594
\(630\) 0 0
\(631\) −4.26326e15 −1.69660 −0.848302 0.529513i \(-0.822375\pi\)
−0.848302 + 0.529513i \(0.822375\pi\)
\(632\) −1.61006e15 2.78870e15i −0.635180 1.10016i
\(633\) 8.55939e14 1.48253e15i 0.334751 0.579807i
\(634\) 1.00043e15 1.73280e15i 0.387879 0.671826i
\(635\) 6.34462e14 + 1.09892e15i 0.243865 + 0.422387i
\(636\) 5.92047e14 0.225602
\(637\) 0 0
\(638\) −1.64755e15 −0.617055
\(639\) 5.56367e14 + 9.63656e14i 0.206589 + 0.357822i
\(640\) −8.16442e14 + 1.41412e15i −0.300563 + 0.520591i
\(641\) −5.04148e14 + 8.73210e14i −0.184009 + 0.318713i −0.943242 0.332106i \(-0.892241\pi\)
0.759233 + 0.650819i \(0.225574\pi\)
\(642\) 2.72890e14 + 4.72659e14i 0.0987516 + 0.171043i
\(643\) 3.03982e14 0.109066 0.0545328 0.998512i \(-0.482633\pi\)
0.0545328 + 0.998512i \(0.482633\pi\)
\(644\) 0 0
\(645\) −2.08447e13 −0.00735221
\(646\) −8.83525e14 1.53031e15i −0.308987 0.535181i
\(647\) −1.71791e15 + 2.97551e15i −0.595700 + 1.03178i 0.397747 + 0.917495i \(0.369792\pi\)
−0.993448 + 0.114288i \(0.963541\pi\)
\(648\) −7.03376e13 + 1.21828e14i −0.0241838 + 0.0418876i
\(649\) 1.38711e15 + 2.40254e15i 0.472894 + 0.819076i
\(650\) −3.53565e14 −0.119521
\(651\) 0 0
\(652\) 5.26730e14 0.175076
\(653\) 5.92694e14 + 1.02658e15i 0.195347 + 0.338352i 0.947014 0.321191i \(-0.104083\pi\)
−0.751667 + 0.659543i \(0.770750\pi\)
\(654\) 2.22212e14 3.84882e14i 0.0726255 0.125791i
\(655\) −1.52514e15 + 2.64162e15i −0.494291 + 0.856138i
\(656\) −1.52078e14 2.63407e14i −0.0488761 0.0846559i
\(657\) −1.66350e14 −0.0530167
\(658\) 0 0
\(659\) −2.26510e15 −0.709934 −0.354967 0.934879i \(-0.615508\pi\)
−0.354967 + 0.934879i \(0.615508\pi\)
\(660\) 4.78921e14 + 8.29516e14i 0.148858 + 0.257830i
\(661\) 2.66506e15 4.61602e15i 0.821484 1.42285i −0.0830931 0.996542i \(-0.526480\pi\)
0.904577 0.426310i \(-0.140187\pi\)
\(662\) −7.63008e14 + 1.32157e15i −0.233244 + 0.403990i
\(663\) −5.02717e14 8.70732e14i −0.152405 0.263973i
\(664\) −2.47823e15 −0.745104
\(665\) 0 0
\(666\) −4.96974e14 −0.146969
\(667\) −1.19696e15 2.07320e15i −0.351065 0.608062i
\(668\) 2.02756e15 3.51183e15i 0.589797 1.02156i
\(669\) −9.24193e14 + 1.60075e15i −0.266636 + 0.461827i
\(670\) −8.97327e14 1.55422e15i −0.256767 0.444733i
\(671\) 3.71902e15 1.05549
\(672\) 0 0
\(673\) 4.74120e15 1.32375 0.661874 0.749615i \(-0.269761\pi\)
0.661874 + 0.749615i \(0.269761\pi\)
\(674\) 1.45202e15 + 2.51497e15i 0.402108 + 0.696471i
\(675\) −9.34280e14 + 1.61822e15i −0.256629 + 0.444495i
\(676\) −1.07337e15 + 1.85913e15i −0.292443 + 0.506526i
\(677\) 7.06536e14 + 1.22376e15i 0.190940 + 0.330717i 0.945562 0.325442i \(-0.105513\pi\)
−0.754622 + 0.656160i \(0.772180\pi\)
\(678\) 5.14968e14 0.138044
\(679\) 0 0
\(680\) −2.81789e15 −0.743232
\(681\) 1.71340e14 + 2.96769e14i 0.0448280 + 0.0776443i
\(682\) −3.39007e14 + 5.87178e14i −0.0879822 + 0.152390i
\(683\) 1.51558e15 2.62506e15i 0.390180 0.675811i −0.602293 0.798275i \(-0.705746\pi\)
0.992473 + 0.122464i \(0.0390796\pi\)
\(684\) −8.91734e14 1.54453e15i −0.227734 0.394446i
\(685\) −1.43547e15 −0.363660
\(686\) 0 0
\(687\) −2.97975e15 −0.742879
\(688\) 8.45270e12 + 1.46405e13i 0.00209054 + 0.00362093i
\(689\) −4.61051e14 + 7.98564e14i −0.113121 + 0.195931i
\(690\) 2.72302e14 4.71641e14i 0.0662798 0.114800i
\(691\) 1.37366e15 + 2.37924e15i 0.331703 + 0.574526i 0.982846 0.184429i \(-0.0590436\pi\)
−0.651143 + 0.758955i \(0.725710\pi\)
\(692\) 1.39897e15 0.335139
\(693\) 0 0
\(694\) 3.73588e15 0.880878
\(695\) −1.44126e15 2.49633e15i −0.337151 0.583963i
\(696\) −1.36682e15 + 2.36740e15i −0.317220 + 0.549442i
\(697\) 1.06393e15 1.84278e15i 0.244981 0.424320i
\(698\) −3.07716e14 5.32980e14i −0.0702984 0.121760i
\(699\) −4.42597e15 −1.00319
\(700\) 0 0
\(701\) 5.72747e15 1.27795 0.638974 0.769228i \(-0.279359\pi\)
0.638974 + 0.769228i \(0.279359\pi\)
\(702\) 5.08033e14 + 8.79940e14i 0.112470 + 0.194804i
\(703\) 9.71326e14 1.68239e15i 0.213359 0.369549i
\(704\) −7.21538e14 + 1.24974e15i −0.157257 + 0.272377i
\(705\) −1.63547e15 2.83271e15i −0.353673 0.612579i
\(706\) −5.97836e14 −0.128279
\(707\) 0 0
\(708\) 1.92490e15 0.406655
\(709\) −3.49163e14 6.04768e14i −0.0731938 0.126775i 0.827106 0.562047i \(-0.189986\pi\)
−0.900299 + 0.435271i \(0.856652\pi\)
\(710\) 5.67514e14 9.82964e14i 0.118047 0.204464i
\(711\) 2.16586e15 3.75137e15i 0.447040 0.774297i
\(712\) 1.05570e15 + 1.82853e15i 0.216223 + 0.374508i
\(713\) −9.85170e14 −0.200225
\(714\) 0 0
\(715\) −1.49182e15 −0.298561
\(716\) 1.23750e15 + 2.14341e15i 0.245767 + 0.425681i
\(717\) 8.99587e14 1.55813e15i 0.177291 0.307078i
\(718\) 1.89101e15 3.27533e15i 0.369836 0.640575i
\(719\) −4.85489e15 8.40892e15i −0.942260 1.63204i −0.761146 0.648580i \(-0.775363\pi\)
−0.181114 0.983462i \(-0.557970\pi\)
\(720\) −5.41835e14 −0.104361
\(721\) 0 0
\(722\) 6.77852e13 0.0128582
\(723\) 2.91447e13 + 5.04801e13i 0.00548654 + 0.00950297i
\(724\) −7.33626e14 + 1.27068e15i −0.137061 + 0.237396i
\(725\) 1.63713e15 2.83560e15i 0.303547 0.525758i
\(726\) 1.50692e12 + 2.61006e12i 0.000277293 + 0.000480285i
\(727\) 2.46469e15 0.450114 0.225057 0.974346i \(-0.427743\pi\)
0.225057 + 0.974346i \(0.427743\pi\)
\(728\) 0 0
\(729\) 3.08202e15 0.554413
\(730\) 8.48413e13 + 1.46950e14i 0.0151472 + 0.0262357i
\(731\) −5.91345e13 + 1.02424e14i −0.0104784 + 0.0181491i
\(732\) 1.29023e15 2.23475e15i 0.226912 0.393023i
\(733\) −3.95643e15 6.85273e15i −0.690607 1.19617i −0.971639 0.236469i \(-0.924010\pi\)
0.281032 0.959698i \(-0.409323\pi\)
\(734\) 4.26963e15 0.739711
\(735\) 0 0
\(736\) −3.66725e15 −0.625911
\(737\) 4.13839e15 + 7.16789e15i 0.701067 + 1.21428i
\(738\) −4.20189e14 + 7.27788e14i −0.0706536 + 0.122376i
\(739\) 4.20347e15 7.28062e15i 0.701558 1.21513i −0.266362 0.963873i \(-0.585822\pi\)
0.967920 0.251260i \(-0.0808450\pi\)
\(740\) −6.47746e14 1.12193e15i −0.107308 0.185862i
\(741\) −1.55220e15 −0.255239
\(742\) 0 0
\(743\) 1.36287e15 0.220809 0.110404 0.993887i \(-0.464785\pi\)
0.110404 + 0.993887i \(0.464785\pi\)
\(744\) 5.62488e14 + 9.74258e14i 0.0904612 + 0.156683i
\(745\) 2.69377e15 4.66575e15i 0.430033 0.744838i
\(746\) −6.61941e14 + 1.14652e15i −0.104895 + 0.181684i
\(747\) −1.66686e15 2.88709e15i −0.262203 0.454148i
\(748\) 5.43462e15 0.848614
\(749\) 0 0
\(750\) 2.17124e15 0.334095
\(751\) −3.40861e15 5.90389e15i −0.520664 0.901817i −0.999711 0.0240276i \(-0.992351\pi\)
0.479047 0.877789i \(-0.340982\pi\)
\(752\) −1.32639e15 + 2.29737e15i −0.201128 + 0.348364i
\(753\) −1.63586e15 + 2.83340e15i −0.246249 + 0.426516i
\(754\) −8.90225e14 1.54191e15i −0.133032 0.230419i
\(755\) −3.98208e15 −0.590747
\(756\) 0 0
\(757\) −6.67049e14 −0.0975282 −0.0487641 0.998810i \(-0.515528\pi\)
−0.0487641 + 0.998810i \(0.515528\pi\)
\(758\) 1.75756e15 + 3.04418e15i 0.255111 + 0.441865i
\(759\) −1.25583e15 + 2.17516e15i −0.180968 + 0.313446i
\(760\) −2.17513e15 + 3.76744e15i −0.311180 + 0.538979i
\(761\) 3.87204e15 + 6.70657e15i 0.549951 + 0.952544i 0.998277 + 0.0586734i \(0.0186871\pi\)
−0.448326 + 0.893870i \(0.647980\pi\)
\(762\) 1.58891e15 0.224052
\(763\) 0 0
\(764\) −4.06626e15 −0.565173
\(765\) −1.89532e15 3.28279e15i −0.261544 0.453007i
\(766\) 2.77739e15 4.81059e15i 0.380522 0.659083i