Properties

Label 5.10.b.a.4.2
Level 5
Weight 10
Character 5.4
Analytic conductor 2.575
Analytic rank 0
Dimension 4
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 5.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(2.57517918082\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} + \cdots)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{5}\cdot 3^{2}\cdot 5^{2} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 4.2
Root \(-6.05982i\)
Character \(\chi\) = 5.4
Dual form 5.10.b.a.4.3

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.843944i q^{2}\) \(-179.263i q^{3}\) \(+511.288 q^{4}\) \(+(-568.288 - 1276.78i) q^{5}\) \(-151.288 q^{6}\) \(+8712.99i q^{7}\) \(-863.597i q^{8}\) \(-12452.2 q^{9}\) \(+O(q^{10})\) \(q\)\(-0.843944i q^{2}\) \(-179.263i q^{3}\) \(+511.288 q^{4}\) \(+(-568.288 - 1276.78i) q^{5}\) \(-151.288 q^{6}\) \(+8712.99i q^{7}\) \(-863.597i q^{8}\) \(-12452.2 q^{9}\) \(+(-1077.53 + 479.603i) q^{10}\) \(+44557.8 q^{11}\) \(-91654.9i q^{12}\) \(+21430.4i q^{13}\) \(+7353.27 q^{14}\) \(+(-228880. + 101873. i) q^{15}\) \(+261051. q^{16}\) \(+300220. i q^{17}\) \(+10508.9i q^{18}\) \(-565385. q^{19}\) \(+(-290559. - 652803. i) q^{20}\) \(+1.56192e6 q^{21}\) \(-37604.2i q^{22}\) \(-950727. i q^{23}\) \(-154811. q^{24}\) \(+(-1.30722e6 + 1.45116e6i) q^{25}\) \(+18086.1 q^{26}\) \(-1.29622e6i q^{27}\) \(+4.45485e6i q^{28}\) \(+803167. q^{29}\) \(+(85975.0 + 193162. i) q^{30}\) \(-1.99843e6 q^{31}\) \(-662474. i q^{32}\) \(-7.98755e6i q^{33}\) \(+253369. q^{34}\) \(+(1.11246e7 - 4.95149e6i) q^{35}\) \(-6.36665e6 q^{36}\) \(+9.53656e6i q^{37}\) \(+477153. i q^{38}\) \(+3.84168e6 q^{39}\) \(+(-1.10263e6 + 490772. i) q^{40}\) \(-2.54355e7 q^{41}\) \(-1.31817e6i q^{42}\) \(+2.32830e7i q^{43}\) \(+2.27818e7 q^{44}\) \(+(7.07642e6 + 1.58987e7i) q^{45}\) \(-802360. q^{46}\) \(-3.77353e7i q^{47}\) \(-4.67967e7i q^{48}\) \(-3.55626e7 q^{49}\) \(+(1.22470e6 + 1.10322e6i) q^{50}\) \(+5.38183e7 q^{51}\) \(+1.09571e7i q^{52}\) \(+4.79297e7i q^{53}\) \(-1.09393e6 q^{54}\) \(+(-2.53216e7 - 5.68906e7i) q^{55}\) \(+7.52451e6 q^{56}\) \(+1.01353e8i q^{57}\) \(-677827. i q^{58}\) \(-7.00069e7 q^{59}\) \(+(-1.17023e8 + 5.20864e7i) q^{60}\) \(+1.26942e8 q^{61}\) \(+1.68656e6i q^{62}\) \(-1.08496e8i q^{63}\) \(+1.33099e8 q^{64}\) \(+(2.73620e7 - 1.21787e7i) q^{65}\) \(-6.74104e6 q^{66}\) \(-2.66595e8i q^{67}\) \(+1.53499e8i q^{68}\) \(-1.70430e8 q^{69}\) \(+(-4.17877e6 - 9.38853e6i) q^{70}\) \(+6.59169e7 q^{71}\) \(+1.07537e7i q^{72}\) \(-1.47516e7i q^{73}\) \(+8.04832e6 q^{74}\) \(+(2.60139e8 + 2.34337e8i) q^{75}\) \(-2.89074e8 q^{76}\) \(+3.88231e8i q^{77}\) \(-3.24216e6i q^{78}\) \(+4.66498e7 q^{79}\) \(+(-1.48352e8 - 3.33305e8i) q^{80}\) \(-4.77460e8 q^{81}\) \(+2.14661e7i q^{82}\) \(-2.01840e8i q^{83}\) \(+7.98588e8 q^{84}\) \(+(3.83316e8 - 1.70611e8i) q^{85}\) \(+1.96495e7 q^{86}\) \(-1.43978e8i q^{87}\) \(-3.84800e7i q^{88}\) \(-5.54039e8 q^{89}\) \(+(1.34176e7 - 5.97210e6i) q^{90}\) \(-1.86723e8 q^{91}\) \(-4.86095e8i q^{92}\) \(+3.58244e8i q^{93}\) \(-3.18465e7 q^{94}\) \(+(3.21301e8 + 7.21874e8i) q^{95}\) \(-1.18757e8 q^{96}\) \(+3.39489e8i q^{97}\) \(+3.00128e7i q^{98}\) \(-5.54841e8 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(4q \) \(\mathstrut -\mathstrut 1368q^{4} \) \(\mathstrut +\mathstrut 1140q^{5} \) \(\mathstrut +\mathstrut 2808q^{6} \) \(\mathstrut +\mathstrut 11628q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 1368q^{4} \) \(\mathstrut +\mathstrut 1140q^{5} \) \(\mathstrut +\mathstrut 2808q^{6} \) \(\mathstrut +\mathstrut 11628q^{9} \) \(\mathstrut -\mathstrut 69160q^{10} \) \(\mathstrut +\mathstrut 109968q^{11} \) \(\mathstrut -\mathstrut 424536q^{14} \) \(\mathstrut -\mathstrut 396720q^{15} \) \(\mathstrut +\mathstrut 1631264q^{16} \) \(\mathstrut -\mathstrut 636880q^{19} \) \(\mathstrut -\mathstrut 3302280q^{20} \) \(\mathstrut +\mathstrut 3523968q^{21} \) \(\mathstrut -\mathstrut 2435040q^{24} \) \(\mathstrut -\mathstrut 1337900q^{25} \) \(\mathstrut +\mathstrut 6618768q^{26} \) \(\mathstrut -\mathstrut 3531720q^{29} \) \(\mathstrut +\mathstrut 3712680q^{30} \) \(\mathstrut -\mathstrut 10587712q^{31} \) \(\mathstrut +\mathstrut 26434624q^{34} \) \(\mathstrut +\mathstrut 13629840q^{35} \) \(\mathstrut -\mathstrut 56399976q^{36} \) \(\mathstrut +\mathstrut 1686816q^{39} \) \(\mathstrut +\mathstrut 43578400q^{40} \) \(\mathstrut -\mathstrut 16788552q^{41} \) \(\mathstrut +\mathstrut 20638944q^{44} \) \(\mathstrut +\mathstrut 55737180q^{45} \) \(\mathstrut -\mathstrut 61250072q^{46} \) \(\mathstrut -\mathstrut 46921028q^{49} \) \(\mathstrut -\mathstrut 150092400q^{50} \) \(\mathstrut +\mathstrut 84017088q^{51} \) \(\mathstrut +\mathstrut 115855920q^{54} \) \(\mathstrut -\mathstrut 26907120q^{55} \) \(\mathstrut +\mathstrut 315178080q^{56} \) \(\mathstrut -\mathstrut 460829040q^{59} \) \(\mathstrut -\mathstrut 307006560q^{60} \) \(\mathstrut +\mathstrut 360490568q^{61} \) \(\mathstrut +\mathstrut 134995072q^{64} \) \(\mathstrut +\mathstrut 183895680q^{65} \) \(\mathstrut +\mathstrut 18949536q^{66} \) \(\mathstrut -\mathstrut 286524864q^{69} \) \(\mathstrut -\mathstrut 508341960q^{70} \) \(\mathstrut -\mathstrut 47611872q^{71} \) \(\mathstrut +\mathstrut 1176861744q^{74} \) \(\mathstrut +\mathstrut 659239200q^{75} \) \(\mathstrut -\mathstrut 1168489440q^{76} \) \(\mathstrut -\mathstrut 728043520q^{79} \) \(\mathstrut +\mathstrut 965843040q^{80} \) \(\mathstrut -\mathstrut 343387836q^{81} \) \(\mathstrut +\mathstrut 1118898144q^{84} \) \(\mathstrut +\mathstrut 1275419840q^{85} \) \(\mathstrut -\mathstrut 2375904552q^{86} \) \(\mathstrut -\mathstrut 1582700760q^{89} \) \(\mathstrut -\mathstrut 1197088920q^{90} \) \(\mathstrut +\mathstrut 473322528q^{91} \) \(\mathstrut +\mathstrut 3327101704q^{94} \) \(\mathstrut +\mathstrut 1204791600q^{95} \) \(\mathstrut +\mathstrut 399339648q^{96} \) \(\mathstrut -\mathstrut 728787024q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.843944i 0.0372974i −0.999826 0.0186487i \(-0.994064\pi\)
0.999826 0.0186487i \(-0.00593641\pi\)
\(3\) 179.263i 1.27775i −0.769312 0.638873i \(-0.779401\pi\)
0.769312 0.638873i \(-0.220599\pi\)
\(4\) 511.288 0.998609
\(5\) −568.288 1276.78i −0.406634 0.913591i
\(6\) −151.288 −0.0476566
\(7\) 8712.99i 1.37160i 0.727792 + 0.685798i \(0.240547\pi\)
−0.727792 + 0.685798i \(0.759453\pi\)
\(8\) 863.597i 0.0745429i
\(9\) −12452.2 −0.632636
\(10\) −1077.53 + 479.603i −0.0340746 + 0.0151664i
\(11\) 44557.8 0.917606 0.458803 0.888538i \(-0.348278\pi\)
0.458803 + 0.888538i \(0.348278\pi\)
\(12\) 91654.9i 1.27597i
\(13\) 21430.4i 0.208107i 0.994572 + 0.104053i \(0.0331813\pi\)
−0.994572 + 0.104053i \(0.966819\pi\)
\(14\) 7353.27 0.0511569
\(15\) −228880. + 101873.i −1.16734 + 0.519575i
\(16\) 261051. 0.995829
\(17\) 300220.i 0.871805i 0.899994 + 0.435903i \(0.143571\pi\)
−0.899994 + 0.435903i \(0.856429\pi\)
\(18\) 10508.9i 0.0235957i
\(19\) −565385. −0.995298 −0.497649 0.867379i \(-0.665803\pi\)
−0.497649 + 0.867379i \(0.665803\pi\)
\(20\) −290559. 652803.i −0.406068 0.912320i
\(21\) 1.56192e6 1.75255
\(22\) 37604.2i 0.0342243i
\(23\) 950727.i 0.708403i −0.935169 0.354202i \(-0.884753\pi\)
0.935169 0.354202i \(-0.115247\pi\)
\(24\) −154811. −0.0952469
\(25\) −1.30722e6 + 1.45116e6i −0.669298 + 0.742994i
\(26\) 18086.1 0.00776183
\(27\) 1.29622e6i 0.469398i
\(28\) 4.45485e6i 1.36969i
\(29\) 803167. 0.210870 0.105435 0.994426i \(-0.466377\pi\)
0.105435 + 0.994426i \(0.466377\pi\)
\(30\) 85975.0 + 193162.i 0.0193788 + 0.0435387i
\(31\) −1.99843e6 −0.388652 −0.194326 0.980937i \(-0.562252\pi\)
−0.194326 + 0.980937i \(0.562252\pi\)
\(32\) 662474.i 0.111685i
\(33\) 7.98755e6i 1.17247i
\(34\) 253369. 0.0325161
\(35\) 1.11246e7 4.95149e6i 1.25308 0.557737i
\(36\) −6.36665e6 −0.631756
\(37\) 9.53656e6i 0.836535i 0.908324 + 0.418267i \(0.137363\pi\)
−0.908324 + 0.418267i \(0.862637\pi\)
\(38\) 477153.i 0.0371220i
\(39\) 3.84168e6 0.265908
\(40\) −1.10263e6 + 490772.i −0.0681017 + 0.0303116i
\(41\) −2.54355e7 −1.40576 −0.702882 0.711306i \(-0.748104\pi\)
−0.702882 + 0.711306i \(0.748104\pi\)
\(42\) 1.31817e6i 0.0653656i
\(43\) 2.32830e7i 1.03856i 0.854605 + 0.519279i \(0.173800\pi\)
−0.854605 + 0.519279i \(0.826200\pi\)
\(44\) 2.27818e7 0.916329
\(45\) 7.07642e6 + 1.58987e7i 0.257251 + 0.577971i
\(46\) −802360. −0.0264216
\(47\) 3.77353e7i 1.12800i −0.825776 0.563998i \(-0.809262\pi\)
0.825776 0.563998i \(-0.190738\pi\)
\(48\) 4.67967e7i 1.27242i
\(49\) −3.55626e7 −0.881274
\(50\) 1.22470e6 + 1.10322e6i 0.0277117 + 0.0249631i
\(51\) 5.38183e7 1.11395
\(52\) 1.09571e7i 0.207817i
\(53\) 4.79297e7i 0.834379i 0.908819 + 0.417190i \(0.136985\pi\)
−0.908819 + 0.417190i \(0.863015\pi\)
\(54\) −1.09393e6 −0.0175073
\(55\) −2.53216e7 5.68906e7i −0.373129 0.838317i
\(56\) 7.52451e6 0.102243
\(57\) 1.01353e8i 1.27174i
\(58\) 677827.i 0.00786490i
\(59\) −7.00069e7 −0.752154 −0.376077 0.926588i \(-0.622727\pi\)
−0.376077 + 0.926588i \(0.622727\pi\)
\(60\) −1.17023e8 + 5.20864e7i −1.16571 + 0.518852i
\(61\) 1.26942e8 1.17387 0.586936 0.809633i \(-0.300334\pi\)
0.586936 + 0.809633i \(0.300334\pi\)
\(62\) 1.68656e6i 0.0144957i
\(63\) 1.08496e8i 0.867721i
\(64\) 1.33099e8 0.991663
\(65\) 2.73620e7 1.21787e7i 0.190124 0.0846231i
\(66\) −6.74104e6 −0.0437300
\(67\) 2.66595e8i 1.61628i −0.588993 0.808138i \(-0.700475\pi\)
0.588993 0.808138i \(-0.299525\pi\)
\(68\) 1.53499e8i 0.870593i
\(69\) −1.70430e8 −0.905160
\(70\) −4.17877e6 9.38853e6i −0.0208021 0.0467365i
\(71\) 6.59169e7 0.307846 0.153923 0.988083i \(-0.450809\pi\)
0.153923 + 0.988083i \(0.450809\pi\)
\(72\) 1.07537e7i 0.0471585i
\(73\) 1.47516e7i 0.0607977i −0.999538 0.0303989i \(-0.990322\pi\)
0.999538 0.0303989i \(-0.00967775\pi\)
\(74\) 8.04832e6 0.0312006
\(75\) 2.60139e8 + 2.34337e8i 0.949358 + 0.855193i
\(76\) −2.89074e8 −0.993913
\(77\) 3.88231e8i 1.25858i
\(78\) 3.24216e6i 0.00991766i
\(79\) 4.66498e7 0.134750 0.0673748 0.997728i \(-0.478538\pi\)
0.0673748 + 0.997728i \(0.478538\pi\)
\(80\) −1.48352e8 3.33305e8i −0.404937 0.909780i
\(81\) −4.77460e8 −1.23241
\(82\) 2.14661e7i 0.0524313i
\(83\) 2.01840e8i 0.466826i −0.972378 0.233413i \(-0.925011\pi\)
0.972378 0.233413i \(-0.0749895\pi\)
\(84\) 7.98588e8 1.75011
\(85\) 3.83316e8 1.70611e8i 0.796474 0.354505i
\(86\) 1.96495e7 0.0387355
\(87\) 1.43978e8i 0.269438i
\(88\) 3.84800e7i 0.0684010i
\(89\) −5.54039e8 −0.936020 −0.468010 0.883723i \(-0.655029\pi\)
−0.468010 + 0.883723i \(0.655029\pi\)
\(90\) 1.34176e7 5.97210e6i 0.0215568 0.00959480i
\(91\) −1.86723e8 −0.285438
\(92\) 4.86095e8i 0.707418i
\(93\) 3.58244e8i 0.496599i
\(94\) −3.18465e7 −0.0420713
\(95\) 3.21301e8 + 7.21874e8i 0.404722 + 0.909295i
\(96\) −1.18757e8 −0.142705
\(97\) 3.39489e8i 0.389361i 0.980867 + 0.194681i \(0.0623670\pi\)
−0.980867 + 0.194681i \(0.937633\pi\)
\(98\) 3.00128e7i 0.0328692i
\(99\) −5.54841e8 −0.580511
\(100\) −6.68367e8 + 7.41960e8i −0.668367 + 0.741960i
\(101\) 1.33921e9 1.28056 0.640282 0.768140i \(-0.278817\pi\)
0.640282 + 0.768140i \(0.278817\pi\)
\(102\) 4.54196e7i 0.0415473i
\(103\) 3.84306e8i 0.336442i 0.985749 + 0.168221i \(0.0538022\pi\)
−0.985749 + 0.168221i \(0.946198\pi\)
\(104\) 1.85073e7 0.0155129
\(105\) −8.87618e8 1.99423e9i −0.712646 1.60112i
\(106\) 4.04500e7 0.0311202
\(107\) 7.97379e8i 0.588082i −0.955793 0.294041i \(-0.905000\pi\)
0.955793 0.294041i \(-0.0950002\pi\)
\(108\) 6.62740e8i 0.468745i
\(109\) 6.63230e8 0.450034 0.225017 0.974355i \(-0.427756\pi\)
0.225017 + 0.974355i \(0.427756\pi\)
\(110\) −4.80124e7 + 2.13700e7i −0.0312670 + 0.0139168i
\(111\) 1.70955e9 1.06888
\(112\) 2.27453e9i 1.36587i
\(113\) 1.48164e9i 0.854847i −0.904051 0.427424i \(-0.859421\pi\)
0.904051 0.427424i \(-0.140579\pi\)
\(114\) 8.55358e7 0.0474325
\(115\) −1.21387e9 + 5.40286e8i −0.647191 + 0.288060i
\(116\) 4.10649e8 0.210577
\(117\) 2.66856e8i 0.131656i
\(118\) 5.90819e7i 0.0280534i
\(119\) −2.61581e9 −1.19576
\(120\) 8.79771e7 + 1.97660e8i 0.0387306 + 0.0870168i
\(121\) −3.72554e8 −0.157999
\(122\) 1.07132e8i 0.0437824i
\(123\) 4.55964e9i 1.79621i
\(124\) −1.02177e9 −0.388112
\(125\) 2.59569e9 + 8.44363e8i 0.950952 + 0.309339i
\(126\) −9.15643e7 −0.0323637
\(127\) 2.28772e9i 0.780344i −0.920742 0.390172i \(-0.872416\pi\)
0.920742 0.390172i \(-0.127584\pi\)
\(128\) 4.51514e8i 0.148671i
\(129\) 4.17378e9 1.32701
\(130\) −1.02781e7 2.30920e7i −0.00315622 0.00709114i
\(131\) −3.83999e9 −1.13922 −0.569612 0.821914i \(-0.692906\pi\)
−0.569612 + 0.821914i \(0.692906\pi\)
\(132\) 4.08394e9i 1.17084i
\(133\) 4.92619e9i 1.36515i
\(134\) −2.24991e8 −0.0602829
\(135\) −1.65499e9 + 7.36625e8i −0.428838 + 0.190873i
\(136\) 2.59269e8 0.0649869
\(137\) 5.82666e9i 1.41311i 0.707657 + 0.706556i \(0.249752\pi\)
−0.707657 + 0.706556i \(0.750248\pi\)
\(138\) 1.43833e8i 0.0337601i
\(139\) 5.89895e9 1.34032 0.670159 0.742217i \(-0.266226\pi\)
0.670159 + 0.742217i \(0.266226\pi\)
\(140\) 5.68787e9 2.53163e9i 1.25133 0.556961i
\(141\) −6.76455e9 −1.44129
\(142\) 5.56301e7i 0.0114819i
\(143\) 9.54892e8i 0.190960i
\(144\) −3.25065e9 −0.629997
\(145\) −4.56430e8 1.02547e9i −0.0857468 0.192649i
\(146\) −1.24495e7 −0.00226760
\(147\) 6.37505e9i 1.12604i
\(148\) 4.87593e9i 0.835371i
\(149\) −5.39333e9 −0.896436 −0.448218 0.893924i \(-0.647941\pi\)
−0.448218 + 0.893924i \(0.647941\pi\)
\(150\) 1.97767e8 2.19543e8i 0.0318965 0.0354086i
\(151\) 7.92204e8 0.124005 0.0620027 0.998076i \(-0.480251\pi\)
0.0620027 + 0.998076i \(0.480251\pi\)
\(152\) 4.88265e8i 0.0741924i
\(153\) 3.73839e9i 0.551536i
\(154\) 3.27645e8 0.0469419
\(155\) 1.13568e9 + 2.55156e9i 0.158039 + 0.355069i
\(156\) 1.96420e9 0.265538
\(157\) 1.18606e10i 1.55797i −0.627042 0.778985i \(-0.715735\pi\)
0.627042 0.778985i \(-0.284265\pi\)
\(158\) 3.93698e7i 0.00502581i
\(159\) 8.59202e9 1.06613
\(160\) −8.45835e8 + 3.76476e8i −0.102034 + 0.0454148i
\(161\) 8.28367e9 0.971642
\(162\) 4.02949e8i 0.0459656i
\(163\) 3.99906e9i 0.443724i −0.975078 0.221862i \(-0.928787\pi\)
0.975078 0.221862i \(-0.0712135\pi\)
\(164\) −1.30048e10 −1.40381
\(165\) −1.01984e10 + 4.53923e9i −1.07116 + 0.476765i
\(166\) −1.70341e8 −0.0174114
\(167\) 1.09118e10i 1.08560i −0.839861 0.542802i \(-0.817363\pi\)
0.839861 0.542802i \(-0.182637\pi\)
\(168\) 1.34887e9i 0.130640i
\(169\) 1.01452e10 0.956692
\(170\) −1.43986e8 3.23497e8i −0.0132221 0.0297064i
\(171\) 7.04028e9 0.629662
\(172\) 1.19043e10i 1.03711i
\(173\) 1.89328e10i 1.60696i 0.595329 + 0.803482i \(0.297022\pi\)
−0.595329 + 0.803482i \(0.702978\pi\)
\(174\) −1.21509e8 −0.0100493
\(175\) −1.26439e10 1.13898e10i −1.01909 0.918006i
\(176\) 1.16318e10 0.913778
\(177\) 1.25496e10i 0.961062i
\(178\) 4.67577e8i 0.0349111i
\(179\) −2.09763e10 −1.52718 −0.763592 0.645699i \(-0.776566\pi\)
−0.763592 + 0.645699i \(0.776566\pi\)
\(180\) 3.61809e9 + 8.12882e9i 0.256893 + 0.577167i
\(181\) −7.16950e9 −0.496518 −0.248259 0.968694i \(-0.579858\pi\)
−0.248259 + 0.968694i \(0.579858\pi\)
\(182\) 1.57584e8i 0.0106461i
\(183\) 2.27560e10i 1.49991i
\(184\) −8.21045e8 −0.0528064
\(185\) 1.21761e10 5.41951e9i 0.764251 0.340163i
\(186\) 3.02338e8 0.0185218
\(187\) 1.33771e10i 0.799974i
\(188\) 1.92936e10i 1.12643i
\(189\) 1.12939e10 0.643824
\(190\) 6.09221e8 2.71160e8i 0.0339143 0.0150951i
\(191\) 1.75301e10 0.953091 0.476545 0.879150i \(-0.341889\pi\)
0.476545 + 0.879150i \(0.341889\pi\)
\(192\) 2.38597e10i 1.26709i
\(193\) 3.13528e10i 1.62655i 0.581877 + 0.813277i \(0.302319\pi\)
−0.581877 + 0.813277i \(0.697681\pi\)
\(194\) 2.86509e8 0.0145222
\(195\) −2.18318e9 4.90499e9i −0.108127 0.242931i
\(196\) −1.81827e10 −0.880048
\(197\) 1.85971e10i 0.879725i −0.898065 0.439862i \(-0.855027\pi\)
0.898065 0.439862i \(-0.144973\pi\)
\(198\) 4.68255e8i 0.0216515i
\(199\) 1.26662e10 0.572544 0.286272 0.958148i \(-0.407584\pi\)
0.286272 + 0.958148i \(0.407584\pi\)
\(200\) 1.25322e9 + 1.12891e9i 0.0553849 + 0.0498914i
\(201\) −4.77906e10 −2.06519
\(202\) 1.13021e9i 0.0477617i
\(203\) 6.99798e9i 0.289228i
\(204\) 2.75166e10 1.11240
\(205\) 1.44547e10 + 3.24756e10i 0.571631 + 1.28429i
\(206\) 3.24333e8 0.0125484
\(207\) 1.18386e10i 0.448161i
\(208\) 5.59443e9i 0.207239i
\(209\) −2.51923e10 −0.913291
\(210\) −1.68301e9 + 7.49099e8i −0.0597174 + 0.0265798i
\(211\) −6.20579e9 −0.215539 −0.107770 0.994176i \(-0.534371\pi\)
−0.107770 + 0.994176i \(0.534371\pi\)
\(212\) 2.45059e10i 0.833218i
\(213\) 1.18164e10i 0.393350i
\(214\) −6.72943e8 −0.0219339
\(215\) 2.97273e10 1.32314e10i 0.948818 0.422313i
\(216\) −1.11941e9 −0.0349903
\(217\) 1.74123e10i 0.533074i
\(218\) 5.59729e8i 0.0167851i
\(219\) −2.64442e9 −0.0776841
\(220\) −1.29466e10 2.90875e10i −0.372610 0.837151i
\(221\) −6.43385e9 −0.181428
\(222\) 1.44277e9i 0.0398664i
\(223\) 4.30855e10i 1.16670i −0.812221 0.583350i \(-0.801742\pi\)
0.812221 0.583350i \(-0.198258\pi\)
\(224\) 5.77213e9 0.153186
\(225\) 1.62778e10 1.80701e10i 0.423422 0.470045i
\(226\) −1.25042e9 −0.0318836
\(227\) 2.28857e10i 0.572068i 0.958219 + 0.286034i \(0.0923371\pi\)
−0.958219 + 0.286034i \(0.907663\pi\)
\(228\) 5.18203e10i 1.26997i
\(229\) 5.26747e9 0.126573 0.0632867 0.997995i \(-0.479842\pi\)
0.0632867 + 0.997995i \(0.479842\pi\)
\(230\) 4.55971e8 + 1.02444e9i 0.0107439 + 0.0241385i
\(231\) 6.95955e10 1.60815
\(232\) 6.93612e8i 0.0157189i
\(233\) 3.55179e10i 0.789488i −0.918791 0.394744i \(-0.870833\pi\)
0.918791 0.394744i \(-0.129167\pi\)
\(234\) −2.25211e8 −0.00491042
\(235\) −4.81798e10 + 2.14445e10i −1.03053 + 0.458681i
\(236\) −3.57937e10 −0.751108
\(237\) 8.36257e9i 0.172176i
\(238\) 2.20760e9i 0.0445989i
\(239\) −5.72471e10 −1.13491 −0.567457 0.823403i \(-0.692073\pi\)
−0.567457 + 0.823403i \(0.692073\pi\)
\(240\) −5.97492e10 + 2.65940e10i −1.16247 + 0.517407i
\(241\) 3.89830e10 0.744386 0.372193 0.928155i \(-0.378606\pi\)
0.372193 + 0.928155i \(0.378606\pi\)
\(242\) 3.14415e8i 0.00589296i
\(243\) 6.00774e10i 1.10531i
\(244\) 6.49039e10 1.17224
\(245\) 2.02098e10 + 4.54057e10i 0.358356 + 0.805124i
\(246\) 3.84808e9 0.0669939
\(247\) 1.21164e10i 0.207128i
\(248\) 1.72584e9i 0.0289713i
\(249\) −3.61824e10 −0.596486
\(250\) 7.12595e8 2.19062e9i 0.0115375 0.0354680i
\(251\) 4.56895e10 0.726581 0.363291 0.931676i \(-0.381653\pi\)
0.363291 + 0.931676i \(0.381653\pi\)
\(252\) 5.54725e10i 0.866514i
\(253\) 4.23622e10i 0.650035i
\(254\) −1.93071e9 −0.0291048
\(255\) −3.05843e10 6.87143e10i −0.452968 1.01769i
\(256\) 6.77655e10 0.986118
\(257\) 1.29955e10i 0.185821i −0.995674 0.0929104i \(-0.970383\pi\)
0.995674 0.0929104i \(-0.0296170\pi\)
\(258\) 3.52243e9i 0.0494942i
\(259\) −8.30920e10 −1.14739
\(260\) 1.39899e10 6.22680e9i 0.189860 0.0845054i
\(261\) −1.00012e10 −0.133404
\(262\) 3.24073e9i 0.0424901i
\(263\) 4.80103e10i 0.618776i 0.950936 + 0.309388i \(0.100124\pi\)
−0.950936 + 0.309388i \(0.899876\pi\)
\(264\) −6.89803e9 −0.0873991
\(265\) 6.11958e10 2.72379e10i 0.762282 0.339287i
\(266\) −4.15743e9 −0.0509164
\(267\) 9.93185e10i 1.19600i
\(268\) 1.36307e11i 1.61403i
\(269\) 9.98823e10 1.16306 0.581531 0.813524i \(-0.302454\pi\)
0.581531 + 0.813524i \(0.302454\pi\)
\(270\) 6.21670e8 + 1.39672e9i 0.00711906 + 0.0159945i
\(271\) −4.80217e10 −0.540849 −0.270424 0.962741i \(-0.587164\pi\)
−0.270424 + 0.962741i \(0.587164\pi\)
\(272\) 7.83726e10i 0.868169i
\(273\) 3.34725e10i 0.364718i
\(274\) 4.91737e9 0.0527054
\(275\) −5.82469e10 + 6.46604e10i −0.614152 + 0.681776i
\(276\) −8.71388e10 −0.903900
\(277\) 1.77838e10i 0.181495i 0.995874 + 0.0907477i \(0.0289257\pi\)
−0.995874 + 0.0907477i \(0.971074\pi\)
\(278\) 4.97838e9i 0.0499904i
\(279\) 2.48848e10 0.245875
\(280\) −4.27609e9 9.60717e9i −0.0415753 0.0934080i
\(281\) −1.52044e11 −1.45476 −0.727379 0.686236i \(-0.759262\pi\)
−0.727379 + 0.686236i \(0.759262\pi\)
\(282\) 5.70890e9i 0.0537565i
\(283\) 1.86733e11i 1.73055i 0.501301 + 0.865273i \(0.332855\pi\)
−0.501301 + 0.865273i \(0.667145\pi\)
\(284\) 3.37025e10 0.307418
\(285\) 1.29405e11 5.75974e10i 1.16185 0.517132i
\(286\) 8.05875e8 0.00712230
\(287\) 2.21619e11i 1.92814i
\(288\) 8.24924e9i 0.0706558i
\(289\) 2.84558e10 0.239955
\(290\) −8.65438e8 + 3.85201e8i −0.00718530 + 0.00319813i
\(291\) 6.08577e10 0.497505
\(292\) 7.54233e9i 0.0607132i
\(293\) 1.28928e11i 1.02198i −0.859586 0.510991i \(-0.829278\pi\)
0.859586 0.510991i \(-0.170722\pi\)
\(294\) 5.38018e9 0.0419985
\(295\) 3.97841e10 + 8.93836e10i 0.305851 + 0.687161i
\(296\) 8.23575e9 0.0623577
\(297\) 5.77565e10i 0.430722i
\(298\) 4.55167e9i 0.0334347i
\(299\) 2.03745e10 0.147423
\(300\) 1.33006e11 + 1.19813e11i 0.948037 + 0.854004i
\(301\) −2.02865e11 −1.42448
\(302\) 6.68575e8i 0.00462508i
\(303\) 2.40070e11i 1.63624i
\(304\) −1.47594e11 −0.991146
\(305\) −7.21396e10 1.62077e11i −0.477336 1.07244i
\(306\) −3.15499e9 −0.0205708
\(307\) 8.78331e10i 0.564333i 0.959365 + 0.282167i \(0.0910531\pi\)
−0.959365 + 0.282167i \(0.908947\pi\)
\(308\) 1.98498e11i 1.25683i
\(309\) 6.88919e10 0.429887
\(310\) 2.15337e9 9.58452e8i 0.0132432 0.00589444i
\(311\) 2.76204e11 1.67420 0.837101 0.547049i \(-0.184249\pi\)
0.837101 + 0.547049i \(0.184249\pi\)
\(312\) 3.31767e9i 0.0198215i
\(313\) 1.84107e11i 1.08423i 0.840304 + 0.542115i \(0.182376\pi\)
−0.840304 + 0.542115i \(0.817624\pi\)
\(314\) −1.00097e10 −0.0581082
\(315\) −1.38525e11 + 6.16568e10i −0.792742 + 0.352845i
\(316\) 2.38515e10 0.134562
\(317\) 3.48865e11i 1.94040i 0.242313 + 0.970198i \(0.422094\pi\)
−0.242313 + 0.970198i \(0.577906\pi\)
\(318\) 7.25118e9i 0.0397637i
\(319\) 3.57873e10 0.193496
\(320\) −7.56384e10 1.69938e11i −0.403244 0.905975i
\(321\) −1.42940e11 −0.751419
\(322\) 6.99095e9i 0.0362397i
\(323\) 1.69740e11i 0.867706i
\(324\) −2.44119e11 −1.23069
\(325\) −3.10990e10 2.80144e10i −0.154622 0.139285i
\(326\) −3.37498e9 −0.0165498
\(327\) 1.18893e11i 0.575029i
\(328\) 2.19660e10i 0.104790i
\(329\) 3.28788e11 1.54716
\(330\) 3.83085e9 + 8.60685e9i 0.0177821 + 0.0399513i
\(331\) 2.88744e11 1.32217 0.661084 0.750312i \(-0.270097\pi\)
0.661084 + 0.750312i \(0.270097\pi\)
\(332\) 1.03198e11i 0.466177i
\(333\) 1.18751e11i 0.529222i
\(334\) −9.20892e9 −0.0404902
\(335\) −3.40384e11 + 1.51503e11i −1.47662 + 0.657232i
\(336\) 4.07739e11 1.74524
\(337\) 1.25882e11i 0.531654i −0.964021 0.265827i \(-0.914355\pi\)
0.964021 0.265827i \(-0.0856450\pi\)
\(338\) 8.56201e9i 0.0356821i
\(339\) −2.65602e11 −1.09228
\(340\) 1.95985e11 8.72315e10i 0.795366 0.354012i
\(341\) −8.90455e10 −0.356630
\(342\) 5.94160e9i 0.0234847i
\(343\) 4.17441e10i 0.162844i
\(344\) 2.01071e10 0.0774172
\(345\) 9.68533e10 + 2.17602e11i 0.368068 + 0.826946i
\(346\) 1.59782e10 0.0599356
\(347\) 2.95822e11i 1.09534i −0.836695 0.547669i \(-0.815515\pi\)
0.836695 0.547669i \(-0.184485\pi\)
\(348\) 7.36142e10i 0.269064i
\(349\) −3.73474e11 −1.34755 −0.673777 0.738934i \(-0.735329\pi\)
−0.673777 + 0.738934i \(0.735329\pi\)
\(350\) −9.61237e9 + 1.06708e10i −0.0342392 + 0.0380093i
\(351\) 2.77785e10 0.0976848
\(352\) 2.95183e10i 0.102483i
\(353\) 4.89872e11i 1.67918i 0.543223 + 0.839589i \(0.317204\pi\)
−0.543223 + 0.839589i \(0.682796\pi\)
\(354\) 1.05912e10 0.0358451
\(355\) −3.74598e10 8.41615e10i −0.125181 0.281246i
\(356\) −2.83273e11 −0.934718
\(357\) 4.68918e11i 1.52788i
\(358\) 1.77029e10i 0.0569600i
\(359\) 4.27559e11 1.35854 0.679268 0.733891i \(-0.262298\pi\)
0.679268 + 0.733891i \(0.262298\pi\)
\(360\) 1.37301e10 6.11118e9i 0.0430836 0.0191762i
\(361\) −3.02753e9 −0.00938223
\(362\) 6.05065e9i 0.0185188i
\(363\) 6.67851e10i 0.201883i
\(364\) −9.54693e10 −0.285041
\(365\) −1.88346e10 + 8.38317e9i −0.0555443 + 0.0247224i
\(366\) −1.92048e10 −0.0559428
\(367\) 2.54403e10i 0.0732023i 0.999330 + 0.0366012i \(0.0116531\pi\)
−0.999330 + 0.0366012i \(0.988347\pi\)
\(368\) 2.48188e11i 0.705448i
\(369\) 3.16727e11 0.889337
\(370\) −4.57376e9 1.02760e10i −0.0126872 0.0285046i
\(371\) −4.17611e11 −1.14443
\(372\) 1.83166e11i 0.495908i
\(373\) 7.26003e11i 1.94200i −0.239087 0.970998i \(-0.576848\pi\)
0.239087 0.970998i \(-0.423152\pi\)
\(374\) 1.12895e10 0.0298369
\(375\) 1.51363e11 4.65312e11i 0.395256 1.21508i
\(376\) −3.25881e10 −0.0840842
\(377\) 1.72122e10i 0.0438834i
\(378\) 9.53144e9i 0.0240129i
\(379\) 2.76699e11 0.688859 0.344430 0.938812i \(-0.388072\pi\)
0.344430 + 0.938812i \(0.388072\pi\)
\(380\) 1.64277e11 + 3.69085e11i 0.404159 + 0.908031i
\(381\) −4.10103e11 −0.997082
\(382\) 1.47944e10i 0.0355478i
\(383\) 1.71143e11i 0.406410i 0.979136 + 0.203205i \(0.0651358\pi\)
−0.979136 + 0.203205i \(0.934864\pi\)
\(384\) −8.09398e10 −0.189964
\(385\) 4.95687e11 2.20627e11i 1.14983 0.511783i
\(386\) 2.64600e10 0.0606662
\(387\) 2.89924e11i 0.657030i
\(388\) 1.73576e11i 0.388819i
\(389\) −3.92384e10 −0.0868837 −0.0434419 0.999056i \(-0.513832\pi\)
−0.0434419 + 0.999056i \(0.513832\pi\)
\(390\) −4.13954e9 + 1.84248e9i −0.00906068 + 0.00403285i
\(391\) 2.85427e11 0.617590
\(392\) 3.07117e10i 0.0656927i
\(393\) 6.88367e11i 1.45564i
\(394\) −1.56949e10 −0.0328114
\(395\) −2.65105e10 5.95616e10i −0.0547937 0.123106i
\(396\) −2.83684e11 −0.579703
\(397\) 3.91381e11i 0.790756i −0.918519 0.395378i \(-0.870614\pi\)
0.918519 0.395378i \(-0.129386\pi\)
\(398\) 1.06896e10i 0.0213544i
\(399\) −8.83084e11 −1.74431
\(400\) −3.41251e11 + 3.78826e11i −0.666506 + 0.739895i
\(401\) −5.04969e11 −0.975248 −0.487624 0.873054i \(-0.662136\pi\)
−0.487624 + 0.873054i \(0.662136\pi\)
\(402\) 4.03326e10i 0.0770263i
\(403\) 4.28272e10i 0.0808811i
\(404\) 6.84720e11 1.27878
\(405\) 2.71335e11 + 6.09613e11i 0.501138 + 1.12592i
\(406\) 5.90590e9 0.0107875
\(407\) 4.24928e11i 0.767609i
\(408\) 4.64773e10i 0.0830368i
\(409\) −9.44998e9 −0.0166985 −0.00834923 0.999965i \(-0.502658\pi\)
−0.00834923 + 0.999965i \(0.502658\pi\)
\(410\) 2.74075e10 1.21989e10i 0.0479008 0.0213203i
\(411\) 1.04450e12 1.80560
\(412\) 1.96491e11i 0.335974i
\(413\) 6.09969e11i 1.03165i
\(414\) 9.99113e9 0.0167153
\(415\) −2.57706e11 + 1.14703e11i −0.426488 + 0.189827i
\(416\) 1.41971e10 0.0232423
\(417\) 1.05746e12i 1.71259i
\(418\) 2.12609e10i 0.0340634i
\(419\) 5.77328e10 0.0915081 0.0457541 0.998953i \(-0.485431\pi\)
0.0457541 + 0.998953i \(0.485431\pi\)
\(420\) −4.53828e11 1.01962e12i −0.711655 1.59889i
\(421\) 4.38976e9 0.00681038 0.00340519 0.999994i \(-0.498916\pi\)
0.00340519 + 0.999994i \(0.498916\pi\)
\(422\) 5.23734e9i 0.00803905i
\(423\) 4.69887e11i 0.713612i
\(424\) 4.13920e10 0.0621970
\(425\) −4.35667e11 3.92455e11i −0.647746 0.583498i
\(426\) −9.97242e9 −0.0146709
\(427\) 1.10604e12i 1.61008i
\(428\) 4.07690e11i 0.587264i
\(429\) 1.71177e11 0.243998
\(430\) −1.11666e10 2.50882e10i −0.0157512 0.0353884i
\(431\) 9.94476e11 1.38818 0.694091 0.719887i \(-0.255807\pi\)
0.694091 + 0.719887i \(0.255807\pi\)
\(432\) 3.38378e11i 0.467440i
\(433\) 1.91618e11i 0.261963i −0.991385 0.130982i \(-0.958187\pi\)
0.991385 0.130982i \(-0.0418129\pi\)
\(434\) −1.46950e10 −0.0198823
\(435\) −1.83829e11 + 8.18209e10i −0.246157 + 0.109563i
\(436\) 3.39101e11 0.449407
\(437\) 5.37527e11i 0.705072i
\(438\) 2.23174e9i 0.00289741i
\(439\) −1.38202e12 −1.77592 −0.887962 0.459917i \(-0.847879\pi\)
−0.887962 + 0.459917i \(0.847879\pi\)
\(440\) −4.91305e10 + 2.18677e10i −0.0624906 + 0.0278141i
\(441\) 4.42832e11 0.557526
\(442\) 5.42980e9i 0.00676681i
\(443\) 3.05660e11i 0.377070i −0.982066 0.188535i \(-0.939626\pi\)
0.982066 0.188535i \(-0.0603740\pi\)
\(444\) 8.74073e11 1.06739
\(445\) 3.14853e11 + 7.07387e11i 0.380617 + 0.855139i
\(446\) −3.63617e10 −0.0435148
\(447\) 9.66825e11i 1.14542i
\(448\) 1.15969e12i 1.36016i
\(449\) −1.49518e12 −1.73614 −0.868069 0.496444i \(-0.834639\pi\)
−0.868069 + 0.496444i \(0.834639\pi\)
\(450\) −1.52501e10 1.37375e10i −0.0175314 0.0157925i
\(451\) −1.13335e12 −1.28994
\(452\) 7.57542e11i 0.853658i
\(453\) 1.42013e11i 0.158447i
\(454\) 1.93142e10 0.0213367
\(455\) 1.06112e11 + 2.38405e11i 0.116069 + 0.260774i
\(456\) 8.75278e10 0.0947991
\(457\) 1.17977e12i 1.26525i −0.774459 0.632624i \(-0.781978\pi\)
0.774459 0.632624i \(-0.218022\pi\)
\(458\) 4.44545e9i 0.00472086i
\(459\) 3.89151e11 0.409223
\(460\) −6.20638e11 + 2.76242e11i −0.646291 + 0.287660i
\(461\) 1.54415e12 1.59234 0.796170 0.605074i \(-0.206856\pi\)
0.796170 + 0.605074i \(0.206856\pi\)
\(462\) 5.87346e10i 0.0599799i
\(463\) 4.55769e11i 0.460926i −0.973081 0.230463i \(-0.925976\pi\)
0.973081 0.230463i \(-0.0740240\pi\)
\(464\) 2.09667e11 0.209990
\(465\) 4.57400e11 2.03586e11i 0.453689 0.201934i
\(466\) −2.99751e10 −0.0294458
\(467\) 6.97342e11i 0.678454i −0.940705 0.339227i \(-0.889835\pi\)
0.940705 0.339227i \(-0.110165\pi\)
\(468\) 1.36440e11i 0.131473i
\(469\) 2.32284e12 2.21688
\(470\) 1.80980e10 + 4.06611e10i 0.0171076 + 0.0384360i
\(471\) −2.12617e12 −1.99069
\(472\) 6.04578e10i 0.0560677i
\(473\) 1.03744e12i 0.952987i
\(474\) −7.05754e9 −0.00642171
\(475\) 7.39084e11 8.20464e11i 0.666151 0.739500i
\(476\) −1.33743e12 −1.19410
\(477\) 5.96829e11i 0.527858i
\(478\) 4.83134e10i 0.0423294i
\(479\) −2.43471e11 −0.211318 −0.105659 0.994402i \(-0.533695\pi\)
−0.105659 + 0.994402i \(0.533695\pi\)
\(480\) 6.74881e10 + 1.51627e11i 0.0580285 + 0.130374i
\(481\) −2.04373e11 −0.174088
\(482\) 3.28994e10i 0.0277637i
\(483\) 1.48495e12i 1.24151i
\(484\) −1.90482e11 −0.157780
\(485\) 4.33453e11 1.92927e11i 0.355717 0.158327i
\(486\) 5.07019e10 0.0412251
\(487\) 1.56961e12i 1.26448i 0.774773 + 0.632239i \(0.217864\pi\)
−0.774773 + 0.632239i \(0.782136\pi\)
\(488\) 1.09627e11i 0.0875039i
\(489\) −7.16882e11 −0.566967
\(490\) 3.83198e10 1.70559e10i 0.0300290 0.0133657i
\(491\) 6.52870e11 0.506944 0.253472 0.967343i \(-0.418427\pi\)
0.253472 + 0.967343i \(0.418427\pi\)
\(492\) 2.33129e12i 1.79371i
\(493\) 2.41127e11i 0.183838i
\(494\) −1.02256e10 −0.00772534
\(495\) 3.15309e11 + 7.08412e11i 0.236055 + 0.530350i
\(496\) −5.21691e11 −0.387031
\(497\) 5.74333e11i 0.422241i
\(498\) 3.05359e10i 0.0222474i
\(499\) 7.51465e11 0.542571 0.271285 0.962499i \(-0.412551\pi\)
0.271285 + 0.962499i \(0.412551\pi\)
\(500\) 1.32715e12 + 4.31713e11i 0.949629 + 0.308908i
\(501\) −1.95608e12 −1.38713
\(502\) 3.85593e10i 0.0270996i
\(503\) 1.31120e12i 0.913299i 0.889647 + 0.456649i \(0.150951\pi\)
−0.889647 + 0.456649i \(0.849049\pi\)
\(504\) −9.36966e10 −0.0646824
\(505\) −7.61055e11 1.70988e12i −0.520721 1.16991i
\(506\) −3.57513e10 −0.0242446
\(507\) 1.81866e12i 1.22241i
\(508\) 1.16968e12i 0.779259i
\(509\) −1.78629e12 −1.17957 −0.589783 0.807561i \(-0.700787\pi\)
−0.589783 + 0.807561i \(0.700787\pi\)
\(510\) −5.79910e10 + 2.58114e10i −0.0379572 + 0.0168945i
\(511\) 1.28531e11 0.0833899
\(512\) 2.88366e11i 0.185451i
\(513\) 7.32862e11i 0.467191i
\(514\) −1.09675e10 −0.00693063
\(515\) 4.90676e11 2.18397e11i 0.307370 0.136809i
\(516\) 2.13400e12 1.32517
\(517\) 1.68140e12i 1.03506i
\(518\) 7.01249e10i 0.0427946i
\(519\) 3.39394e12 2.05329
\(520\) −1.05175e10 2.36298e10i −0.00630805 0.0141724i
\(521\) 5.88627e11 0.350002 0.175001 0.984568i \(-0.444007\pi\)
0.175001 + 0.984568i \(0.444007\pi\)
\(522\) 8.44043e9i 0.00497562i
\(523\) 6.01202e11i 0.351369i 0.984447 + 0.175684i \(0.0562138\pi\)
−0.984447 + 0.175684i \(0.943786\pi\)
\(524\) −1.96334e12 −1.13764
\(525\) −2.04177e12 + 2.26659e12i −1.17298 + 1.30213i
\(526\) 4.05180e10 0.0230787
\(527\) 5.99968e11i 0.338829i
\(528\) 2.08515e12i 1.16758i
\(529\) 8.97272e11 0.498165
\(530\) −2.29872e10 5.16458e10i −0.0126545 0.0284311i
\(531\) 8.71739e11 0.475840
\(532\) 2.51870e12i 1.36325i
\(533\) 5.45093e11i 0.292549i
\(534\) 8.38193e10 0.0446075
\(535\) −1.01808e12 + 4.53141e11i −0.537266 + 0.239134i
\(536\) −2.30231e11 −0.120482
\(537\) 3.76028e12i 1.95135i
\(538\) 8.42950e10i 0.0433792i
\(539\) −1.58459e12 −0.808662
\(540\) −8.46175e11 + 3.76627e11i −0.428241 + 0.190607i
\(541\) 1.40863e12 0.706982 0.353491 0.935438i \(-0.384995\pi\)
0.353491 + 0.935438i \(0.384995\pi\)
\(542\) 4.05276e10i 0.0201723i
\(543\) 1.28522e12i 0.634424i
\(544\) 1.98888e11 0.0973673
\(545\) −3.76905e11 8.46800e11i −0.182999 0.411147i
\(546\) 2.82489e10 0.0136030
\(547\) 8.05933e10i 0.0384907i 0.999815 + 0.0192454i \(0.00612636\pi\)
−0.999815 + 0.0192454i \(0.993874\pi\)
\(548\) 2.97910e12i 1.41115i
\(549\) −1.58070e12 −0.742635
\(550\) 5.45698e10 + 4.91571e10i 0.0254285 + 0.0229063i
\(551\) −4.54098e11 −0.209878
\(552\) 1.47183e11i 0.0674732i
\(553\) 4.06459e11i 0.184822i
\(554\) 1.50085e10 0.00676930
\(555\) −9.71517e11 2.18273e12i −0.434642 0.976519i
\(556\) 3.01606e12 1.33845
\(557\) 3.92066e12i 1.72588i 0.505305 + 0.862941i \(0.331380\pi\)
−0.505305 + 0.862941i \(0.668620\pi\)
\(558\) 2.10014e10i 0.00917051i
\(559\) −4.98965e11 −0.216131
\(560\) 2.90408e12 1.29259e12i 1.24785 0.555410i
\(561\) 2.39802e12 1.02216
\(562\) 1.28317e11i 0.0542587i
\(563\) 3.86627e12i 1.62182i −0.585168 0.810912i \(-0.698971\pi\)
0.585168 0.810912i \(-0.301029\pi\)
\(564\) −3.45863e12 −1.43929
\(565\) −1.89173e12 + 8.41996e11i −0.780981 + 0.347610i
\(566\) 1.57592e11 0.0645448
\(567\) 4.16010e12i 1.69036i
\(568\) 5.69256e10i 0.0229478i
\(569\) 1.87990e12 0.751849 0.375924 0.926650i \(-0.377325\pi\)
0.375924 + 0.926650i \(0.377325\pi\)
\(570\) −4.86090e10 1.09211e11i −0.0192877 0.0433339i
\(571\) −3.44726e12 −1.35710 −0.678550 0.734554i \(-0.737391\pi\)
−0.678550 + 0.734554i \(0.737391\pi\)
\(572\) 4.88225e11i 0.190694i
\(573\) 3.14250e12i 1.21781i
\(574\) −1.87034e11 −0.0719146
\(575\) 1.37966e12 + 1.24281e12i 0.526339 + 0.474133i
\(576\) −1.65737e12 −0.627362
\(577\) 1.68433e12i 0.632608i 0.948658 + 0.316304i \(0.102442\pi\)
−0.948658 + 0.316304i \(0.897558\pi\)
\(578\) 2.40151e10i 0.00894971i
\(579\) 5.62039e12 2.07832
\(580\) −2.33367e11 5.24310e11i −0.0856275 0.192381i
\(581\) 1.75863e12 0.640297
\(582\) 5.13605e10i 0.0185556i
\(583\) 2.13564e12i 0.765631i
\(584\) −1.27395e10 −0.00453204
\(585\) −3.40717e11 + 1.51651e11i −0.120280 + 0.0535357i
\(586\) −1.08808e11 −0.0381173
\(587\) 5.04715e12i 1.75458i −0.479956 0.877292i \(-0.659348\pi\)
0.479956 0.877292i \(-0.340652\pi\)
\(588\) 3.25949e12i 1.12448i
\(589\) 1.12988e12 0.386825
\(590\) 7.54347e10 3.35755e10i 0.0256293 0.0114074i
\(591\) −3.33377e12 −1.12407
\(592\) 2.48952e12i 0.833045i
\(593\) 6.66924e11i 0.221478i −0.993850 0.110739i \(-0.964678\pi\)
0.993850 0.110739i \(-0.0353217\pi\)
\(594\) −4.87433e10 −0.0160648
\(595\) 1.48654e12 + 3.33983e12i 0.486238 + 1.09244i
\(596\) −2.75755e12 −0.895189
\(597\) 2.27059e12i 0.731566i
\(598\) 1.71949e10i 0.00549851i
\(599\) −3.36479e12 −1.06792 −0.533958 0.845511i \(-0.679296\pi\)
−0.533958 + 0.845511i \(0.679296\pi\)
\(600\) 2.02372e11 2.24655e11i 0.0637486 0.0707679i
\(601\) −2.79891e12 −0.875092 −0.437546 0.899196i \(-0.644152\pi\)
−0.437546 + 0.899196i \(0.644152\pi\)
\(602\) 1.71206e11i 0.0531295i
\(603\) 3.31969e12i 1.02251i
\(604\) 4.05044e11 0.123833
\(605\) 2.11718e11 + 4.75671e11i 0.0642478 + 0.144347i
\(606\) −2.02606e11 −0.0610274
\(607\) 3.38683e12i 1.01261i 0.862353 + 0.506307i \(0.168990\pi\)
−0.862353 + 0.506307i \(0.831010\pi\)
\(608\) 3.74553e11i 0.111160i
\(609\) 1.25448e12 0.369560
\(610\) −1.36784e11 + 6.08817e10i −0.0399992 + 0.0178034i
\(611\) 8.08685e11 0.234744
\(612\) 1.91139e12i 0.550768i
\(613\) 7.53866e11i 0.215636i −0.994171 0.107818i \(-0.965614\pi\)
0.994171 0.107818i \(-0.0343864\pi\)
\(614\) 7.41262e10 0.0210482
\(615\) 5.82166e12 2.59119e12i 1.64100 0.730399i
\(616\) 3.35275e11 0.0938185
\(617\) 1.42132e11i 0.0394827i −0.999805 0.0197414i \(-0.993716\pi\)
0.999805 0.0197414i \(-0.00628428\pi\)
\(618\) 5.81408e10i 0.0160337i
\(619\) 1.03073e12 0.282186 0.141093 0.989996i \(-0.454938\pi\)
0.141093 + 0.989996i \(0.454938\pi\)
\(620\) 5.80661e11 + 1.30458e12i 0.157819 + 0.354575i
\(621\) −1.23235e12 −0.332523
\(622\) 2.33100e11i 0.0624433i
\(623\) 4.82733e12i 1.28384i
\(624\) 1.00287e12 0.264798
\(625\) −3.97033e11 3.79398e12i −0.104080 0.994569i
\(626\) 1.55376e11 0.0404390
\(627\) 4.51604e12i 1.16695i
\(628\) 6.06419e12i 1.55580i
\(629\) −2.86307e12 −0.729296
\(630\) 5.20349e10 + 1.16908e11i 0.0131602 + 0.0295672i
\(631\) −4.61780e12 −1.15959 −0.579793 0.814764i \(-0.696867\pi\)
−0.579793 + 0.814764i \(0.696867\pi\)
\(632\) 4.02866e10i 0.0100446i
\(633\) 1.11247e12i 0.275404i
\(634\) 2.94422e11 0.0723717
\(635\) −2.92092e12 + 1.30008e12i −0.712916 + 0.317314i
\(636\) 4.39299e12 1.06464
\(637\) 7.62122e11i 0.183399i
\(638\) 3.02025e10i 0.00721688i
\(639\) −8.20809e11 −0.194755
\(640\) −5.76486e11 + 2.56590e11i −0.135825 + 0.0604547i
\(641\) 7.51099e12 1.75726 0.878630 0.477503i \(-0.158458\pi\)
0.878630 + 0.477503i \(0.158458\pi\)
\(642\) 1.20634e11i 0.0280260i
\(643\) 4.42841e12i 1.02164i 0.859687 + 0.510821i \(0.170659\pi\)
−0.859687 + 0.510821i \(0.829341\pi\)
\(644\) 4.23534e12 0.970291
\(645\) −2.37191e12 5.32901e12i −0.539609 1.21235i
\(646\) −1.43251e11 −0.0323632
\(647\) 1.09396e12i 0.245432i 0.992442 + 0.122716i \(0.0391604\pi\)
−0.992442 + 0.122716i \(0.960840\pi\)
\(648\) 4.12333e11i 0.0918672i
\(649\) −3.11935e12 −0.690181
\(650\) −2.36425e10 + 2.62458e10i −0.00519498 + 0.00576699i
\(651\) −3.12138e12 −0.681133
\(652\) 2.04467e12i 0.443107i
\(653\) 8.24881e12i 1.77534i 0.460477 + 0.887671i \(0.347678\pi\)
−0.460477 + 0.887671i \(0.652322\pi\)
\(654\) −1.00339e11 −0.0214471
\(655\) 2.18222e12 + 4.90283e12i 0.463247 + 1.04078i
\(656\) −6.63994e12 −1.39990
\(657\) 1.83690e11i 0.0384628i
\(658\) 2.77478e11i 0.0577049i
\(659\) 2.64086e12 0.545458 0.272729 0.962091i \(-0.412074\pi\)
0.272729 + 0.962091i \(0.412074\pi\)
\(660\) −5.21430e12 + 2.32085e12i −1.06967 + 0.476102i
\(661\) 8.94654e12 1.82284 0.911420 0.411478i \(-0.134987\pi\)
0.911420 + 0.411478i \(0.134987\pi\)
\(662\) 2.43683e11i 0.0493134i
\(663\) 1.15335e12i 0.231820i
\(664\) −1.74308e11 −0.0347986
\(665\) −6.28968e12 + 2.79950e12i −1.24719 + 0.555114i
\(666\) −1.00219e11 −0.0197386
\(667\) 7.63592e11i 0.149381i
\(668\) 5.57906e12i 1.08409i
\(669\) −7.72362e12 −1.49075
\(670\) 1.27860e11 + 2.87265e11i 0.0245130 + 0.0550739i
\(671\) 5.65625e12 1.07715
\(672\) 1.03473e12i 0.195733i
\(673\) 6.40541e12i 1.20359i −0.798650 0.601796i \(-0.794452\pi\)
0.798650 0.601796i \(-0.205548\pi\)
\(674\) −1.06237e11 −0.0198293
\(675\) 1.88102e12 + 1.69445e12i 0.348760 + 0.314167i
\(676\) 5.18713e12 0.955361
\(677\) 6.41491e12i 1.17366i −0.809711 0.586829i \(-0.800376\pi\)
0.809711 0.586829i \(-0.199624\pi\)
\(678\) 2.24153e11i 0.0407391i
\(679\) −2.95796e12 −0.534046
\(680\) −1.47339e11 3.31030e11i −0.0264259 0.0593715i
\(681\) 4.10256e12 0.730958
\(682\) 7.51494e10i 0.0133014i
\(683\) 2.15592e12i 0.379088i 0.981872 + 0.189544i \(0.0607009\pi\)
−0.981872 + 0.189544i \(0.939299\pi\)
\(684\) 3.59961e12 0.628786
\(685\) 7.43937e12 3.31122e12i 1.29101 0.574619i
\(686\) 3.52297e10 0.00607366
\(687\) 9.44262e11i 0.161729i
\(688\) 6.07804e12i 1.03423i
\(689\) −1.02715e12 −0.173640
\(690\) 1.83644e11 8.17387e10i 0.0308429 0.0137280i
\(691\) −4.58074e12 −0.764336 −0.382168 0.924093i \(-0.624822\pi\)
−0.382168 + 0.924093i \(0.624822\pi\)
\(692\) 9.68009e12i 1.60473i
\(693\) 4.83433e12i 0.796226i
\(694\) −2.49657e11 −0.0408533
\(695\) −3.35230e12 7.53168e12i −0.545019 1.22450i
\(696\) −1.24339e11 −0.0200847
\(697\) 7.63624e12i 1.22555i
\(698\) 3.15191e11i 0.0502603i
\(699\) −6.36704e12 −1.00877
\(700\) −6.46469e12 5.82348e12i −1.01767 0.916729i
\(701\) −1.22474e12 −0.191564 −0.0957819 0.995402i \(-0.530535\pi\)
−0.0957819 + 0.995402i \(0.530535\pi\)
\(702\) 2.34435e10i 0.00364339i
\(703\) 5.39183e12i 0.832601i
\(704\) 5.93058e12 0.909956
\(705\) 3.84421e12 + 8.63686e12i 0.586079 + 1.31675i
\(706\) 4.13424e11 0.0626289
\(707\) 1.16685e13i 1.75642i
\(708\) 6.41648e12i 0.959725i
\(709\) 5.65887e12 0.841049 0.420525 0.907281i \(-0.361846\pi\)
0.420525 + 0.907281i \(0.361846\pi\)
\(710\) −7.10276e10 + 3.16139e10i −0.0104897 + 0.00466891i
\(711\) −5.80891e11 −0.0852475
\(712\) 4.78466e11i 0.0697736i
\(713\) 1.89996e12i 0.275322i
\(714\) 3.95741e11 0.0569861
\(715\) 1.21919e12 5.42653e11i 0.174459 0.0776507i
\(716\) −1.07250e13 −1.52506
\(717\) 1.02623e13i 1.45013i
\(718\) 3.60836e11i 0.0506698i
\(719\) 6.02904e12 0.841333 0.420667 0.907215i \(-0.361796\pi\)
0.420667 + 0.907215i \(0.361796\pi\)
\(720\) 1.84730e12 + 4.15037e12i 0.256178 + 0.575560i
\(721\) −3.34846e12 −0.461462
\(722\) 2.55506e9i 0.000349933i
\(723\) 6.98820e12i 0.951137i
\(724\) −3.66568e12 −0.495827
\(725\) −1.04992e12 + 1.16552e12i −0.141135 + 0.156675i
\(726\) 5.63629e10 0.00752971
\(727\) 2.63469e12i 0.349805i −0.984586 0.174902i \(-0.944039\pi\)
0.984586 0.174902i \(-0.0559609\pi\)
\(728\) 1.61254e11i 0.0212774i
\(729\) 1.37180e12 0.179894
\(730\) 7.07493e9 + 1.58954e10i 0.000922081 + 0.00207166i
\(731\) −6.99002e12 −0.905421
\(732\) 1.16349e13i 1.49783i
\(733\) 5.28609e12i 0.676343i 0.941085 + 0.338171i \(0.109808\pi\)
−0.941085 + 0.338171i \(0.890192\pi\)
\(734\) 2.14702e10 0.00273026
\(735\) 8.13955e12 3.62286e12i 1.02874 0.457888i
\(736\) −6.29831e11 −0.0791178
\(737\) 1.18789e13i 1.48310i
\(738\) 2.67300e11i 0.0331700i
\(739\) −2.51810e12 −0.310580 −0.155290 0.987869i \(-0.549631\pi\)
−0.155290 + 0.987869i \(0.549631\pi\)
\(740\) 6.22550e12 2.77093e12i 0.763188 0.339690i
\(741\) −2.17203e12 −0.264657
\(742\) 3.52440e11i 0.0426843i
\(743\) 7.02537e11i 0.0845706i 0.999106 + 0.0422853i \(0.0134638\pi\)
−0.999106 + 0.0422853i \(0.986536\pi\)
\(744\) 3.09379e11 0.0370179
\(745\) 3.06497e12 + 6.88612e12i 0.364521 + 0.818976i
\(746\) −6.12705e11 −0.0724314
\(747\) 2.51335e12i 0.295331i
\(748\) 6.83956e12i 0.798861i
\(749\) 6.94755e12 0.806610
\(750\) −3.92697e11 1.27742e11i −0.0453191 0.0147420i
\(751\) 4.60108e12 0.527813 0.263907 0.964548i \(-0.414989\pi\)
0.263907 + 0.964548i \(0.414989\pi\)
\(752\) 9.85083e12i 1.12329i
\(753\) 8.19042e12i 0.928387i
\(754\) 1.45261e10 0.00163674
\(755\) −4.50200e11 1.01147e12i −0.0504248 0.113290i
\(756\) 5.77445e12 0.642928
\(757\) 3.05764e12i 0.338419i 0.985580 + 0.169210i \(0.0541215\pi\)
−0.985580 + 0.169210i \(0.945878\pi\)
\(758\) 2.33518e11i 0.0256927i
\(759\) −7.59398e12 −0.830580
\(760\) 6.23408e11 2.77475e11i 0.0677815 0.0301691i
\(761\) −9.86753e12 −1.06654 −0.533270 0.845945i \(-0.679037\pi\)
−0.533270 + 0.845945i \(0.679037\pi\)
\(762\) 3.46104e11i 0.0371886i
\(763\) 5.77872e12i 0.617264i
\(764\) 8.96293e12 0.951765
\(765\) −4.77312e12 + 2.12448e12i −0.503878 + 0.224273i
\(766\) 1.44435e11 0.0151580
\(767\) 1.50028e12i 0.156528i
\(768\) 1.21478e13i 1.26001i
\(769\) −1.65694e13 −1.70859 −0.854294 0.519790i \(-0.826010\pi\)
−0.854294 + 0.519790i \(0.826010\pi\)
\(770\) −1.86197e11 4.18332e11i −0.0190882 0.0428857i
\(771\) −2.32961e12 −0.237432
\(772\) 1.60303e13i 1.62429i
\(773\) 1.10674e13i 1.11490i 0.830210 + 0.557451i \(0.188221\pi\)
−0.830210 + 0.557451i \(0.811779\pi\)
\(774\) −2.44680e11 −0.0245055
\(775\) 2.61239e12 2.90004e12i 0.260124 0.288766i
\(776\) 2.93181e11 0.0290241
\(777\) 1.48953e13i 1.46607i
\(778\) 3.31150e10i 0.00324054i
\(779\) 1.43808e13 1.39915
\(780\) −1.11623e12 2.50786e12i −0.107977 0.242593i
\(781\) 2.93711e12 0.282482