Properties

Label 75.9.f.a.43.1
Level $75$
Weight $9$
Character 75.43
Analytic conductor $30.553$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 75.f (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(30.5533957546\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{6})\)
Defining polynomial: \( x^{4} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.1
Root \(-1.22474 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 75.43
Dual form 75.9.f.a.7.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-7.34847 + 7.34847i) q^{2} +(-33.0681 - 33.0681i) q^{3} +148.000i q^{4} +486.000 q^{6} +(-2872.03 + 2872.03i) q^{7} +(-2968.78 - 2968.78i) q^{8} +2187.00i q^{9} +O(q^{10})\) \(q+(-7.34847 + 7.34847i) q^{2} +(-33.0681 - 33.0681i) q^{3} +148.000i q^{4} +486.000 q^{6} +(-2872.03 + 2872.03i) q^{7} +(-2968.78 - 2968.78i) q^{8} +2187.00i q^{9} -234.000 q^{11} +(4894.08 - 4894.08i) q^{12} +(11930.2 + 11930.2i) q^{13} -42210.0i q^{14} +5744.00 q^{16} +(-89012.0 + 89012.0i) q^{17} +(-16071.1 - 16071.1i) q^{18} +181693. i q^{19} +189945. q^{21} +(1719.54 - 1719.54i) q^{22} +(-269432. - 269432. i) q^{23} +196344. i q^{24} -175338. q^{26} +(72320.0 - 72320.0i) q^{27} +(-425060. - 425060. i) q^{28} -240174. i q^{29} +836725. q^{31} +(717798. - 717798. i) q^{32} +(7737.94 + 7737.94i) q^{33} -1.30820e6i q^{34} -323676. q^{36} +(-608282. + 608282. i) q^{37} +(-1.33517e6 - 1.33517e6i) q^{38} -789021. i q^{39} +2.82222e6 q^{41} +(-1.39580e6 + 1.39580e6i) q^{42} +(-2.80202e6 - 2.80202e6i) q^{43} -34632.0i q^{44} +3.95982e6 q^{46} +(5.39321e6 - 5.39321e6i) q^{47} +(-189943. - 189943. i) q^{48} -1.07323e7i q^{49} +5.88692e6 q^{51} +(-1.76568e6 + 1.76568e6i) q^{52} +(1.19258e6 + 1.19258e6i) q^{53} +1.06288e6i q^{54} +1.70528e7 q^{56} +(6.00824e6 - 6.00824e6i) q^{57} +(1.76491e6 + 1.76491e6i) q^{58} -1.27860e7i q^{59} +517403. q^{61} +(-6.14865e6 + 6.14865e6i) q^{62} +(-6.28112e6 - 6.28112e6i) q^{63} +1.20199e7i q^{64} -113724. q^{66} +(-2.06617e6 + 2.06617e6i) q^{67} +(-1.31738e7 - 1.31738e7i) q^{68} +1.78192e7i q^{69} -2.08286e7 q^{71} +(6.49273e6 - 6.49273e6i) q^{72} +(-2.88730e7 - 2.88730e7i) q^{73} -8.93988e6i q^{74} -2.68906e7 q^{76} +(672054. - 672054. i) q^{77} +(5.79810e6 + 5.79810e6i) q^{78} -4.21879e7i q^{79} -4.78297e6 q^{81} +(-2.07390e7 + 2.07390e7i) q^{82} +(6.66763e7 + 6.66763e7i) q^{83} +2.81119e7i q^{84} +4.11811e7 q^{86} +(-7.94210e6 + 7.94210e6i) q^{87} +(694695. + 694695. i) q^{88} +9.51614e7i q^{89} -6.85279e7 q^{91} +(3.98759e7 - 3.98759e7i) q^{92} +(-2.76689e7 - 2.76689e7i) q^{93} +7.92637e7i q^{94} -4.74725e7 q^{96} +(-7.08678e7 + 7.08678e7i) q^{97} +(7.88658e7 + 7.88658e7i) q^{98} -511758. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 1944 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 1944 q^{6} - 936 q^{11} + 22976 q^{16} + 759780 q^{21} - 701352 q^{26} + 3346900 q^{31} - 1294704 q^{36} + 11288880 q^{41} + 15839280 q^{46} + 23547672 q^{51} + 68211360 q^{56} + 2069612 q^{61} - 454896 q^{66} - 83314512 q^{71} - 107562256 q^{76} - 19131876 q^{81} + 164724264 q^{86} - 274111740 q^{91} - 189889920 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).

\(n\) \(26\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −7.34847 + 7.34847i −0.459279 + 0.459279i −0.898419 0.439140i \(-0.855283\pi\)
0.439140 + 0.898419i \(0.355283\pi\)
\(3\) −33.0681 33.0681i −0.408248 0.408248i
\(4\) 148.000i 0.578125i
\(5\) 0 0
\(6\) 486.000 0.375000
\(7\) −2872.03 + 2872.03i −1.19618 + 1.19618i −0.220878 + 0.975301i \(0.570892\pi\)
−0.975301 + 0.220878i \(0.929108\pi\)
\(8\) −2968.78 2968.78i −0.724800 0.724800i
\(9\) 2187.00i 0.333333i
\(10\) 0 0
\(11\) −234.000 −0.0159825 −0.00799126 0.999968i \(-0.502544\pi\)
−0.00799126 + 0.999968i \(0.502544\pi\)
\(12\) 4894.08 4894.08i 0.236019 0.236019i
\(13\) 11930.2 + 11930.2i 0.417711 + 0.417711i 0.884414 0.466703i \(-0.154558\pi\)
−0.466703 + 0.884414i \(0.654558\pi\)
\(14\) 42210.0i 1.09876i
\(15\) 0 0
\(16\) 5744.00 0.0876465
\(17\) −89012.0 + 89012.0i −1.06574 + 1.06574i −0.0680630 + 0.997681i \(0.521682\pi\)
−0.997681 + 0.0680630i \(0.978318\pi\)
\(18\) −16071.1 16071.1i −0.153093 0.153093i
\(19\) 181693.i 1.39420i 0.716976 + 0.697098i \(0.245526\pi\)
−0.716976 + 0.697098i \(0.754474\pi\)
\(20\) 0 0
\(21\) 189945. 0.976676
\(22\) 1719.54 1719.54i 0.00734044 0.00734044i
\(23\) −269432. 269432.i −0.962803 0.962803i 0.0365300 0.999333i \(-0.488370\pi\)
−0.999333 + 0.0365300i \(0.988370\pi\)
\(24\) 196344.i 0.591797i
\(25\) 0 0
\(26\) −175338. −0.383692
\(27\) 72320.0 72320.0i 0.136083 0.136083i
\(28\) −425060. 425060.i −0.691541 0.691541i
\(29\) 240174.i 0.339574i −0.985481 0.169787i \(-0.945692\pi\)
0.985481 0.169787i \(-0.0543079\pi\)
\(30\) 0 0
\(31\) 836725. 0.906016 0.453008 0.891506i \(-0.350351\pi\)
0.453008 + 0.891506i \(0.350351\pi\)
\(32\) 717798. 717798.i 0.684546 0.684546i
\(33\) 7737.94 + 7737.94i 0.00652483 + 0.00652483i
\(34\) 1.30820e6i 0.978948i
\(35\) 0 0
\(36\) −323676. −0.192708
\(37\) −608282. + 608282.i −0.324562 + 0.324562i −0.850514 0.525952i \(-0.823709\pi\)
0.525952 + 0.850514i \(0.323709\pi\)
\(38\) −1.33517e6 1.33517e6i −0.640325 0.640325i
\(39\) 789021.i 0.341059i
\(40\) 0 0
\(41\) 2.82222e6 0.998747 0.499373 0.866387i \(-0.333564\pi\)
0.499373 + 0.866387i \(0.333564\pi\)
\(42\) −1.39580e6 + 1.39580e6i −0.448567 + 0.448567i
\(43\) −2.80202e6 2.80202e6i −0.819590 0.819590i 0.166458 0.986049i \(-0.446767\pi\)
−0.986049 + 0.166458i \(0.946767\pi\)
\(44\) 34632.0i 0.00923989i
\(45\) 0 0
\(46\) 3.95982e6 0.884391
\(47\) 5.39321e6 5.39321e6i 1.10524 1.10524i 0.111471 0.993768i \(-0.464444\pi\)
0.993768 0.111471i \(-0.0355561\pi\)
\(48\) −189943. 189943.i −0.0357815 0.0357815i
\(49\) 1.07323e7i 1.86169i
\(50\) 0 0
\(51\) 5.88692e6 0.870176
\(52\) −1.76568e6 + 1.76568e6i −0.241489 + 0.241489i
\(53\) 1.19258e6 + 1.19258e6i 0.151142 + 0.151142i 0.778628 0.627486i \(-0.215916\pi\)
−0.627486 + 0.778628i \(0.715916\pi\)
\(54\) 1.06288e6i 0.125000i
\(55\) 0 0
\(56\) 1.70528e7 1.73398
\(57\) 6.00824e6 6.00824e6i 0.569178 0.569178i
\(58\) 1.76491e6 + 1.76491e6i 0.155959 + 0.155959i
\(59\) 1.27860e7i 1.05518i −0.849500 0.527588i \(-0.823096\pi\)
0.849500 0.527588i \(-0.176904\pi\)
\(60\) 0 0
\(61\) 517403. 0.0373688 0.0186844 0.999825i \(-0.494052\pi\)
0.0186844 + 0.999825i \(0.494052\pi\)
\(62\) −6.14865e6 + 6.14865e6i −0.416115 + 0.416115i
\(63\) −6.28112e6 6.28112e6i −0.398726 0.398726i
\(64\) 1.20199e7i 0.716442i
\(65\) 0 0
\(66\) −113724. −0.00599344
\(67\) −2.06617e6 + 2.06617e6i −0.102534 + 0.102534i −0.756513 0.653979i \(-0.773098\pi\)
0.653979 + 0.756513i \(0.273098\pi\)
\(68\) −1.31738e7 1.31738e7i −0.616133 0.616133i
\(69\) 1.78192e7i 0.786125i
\(70\) 0 0
\(71\) −2.08286e7 −0.819648 −0.409824 0.912165i \(-0.634410\pi\)
−0.409824 + 0.912165i \(0.634410\pi\)
\(72\) 6.49273e6 6.49273e6i 0.241600 0.241600i
\(73\) −2.88730e7 2.88730e7i −1.01672 1.01672i −0.999858 0.0168598i \(-0.994633\pi\)
−0.0168598 0.999858i \(-0.505367\pi\)
\(74\) 8.93988e6i 0.298129i
\(75\) 0 0
\(76\) −2.68906e7 −0.806019
\(77\) 672054. 672054.i 0.0191180 0.0191180i
\(78\) 5.79810e6 + 5.79810e6i 0.156642 + 0.156642i
\(79\) 4.21879e7i 1.08313i −0.840659 0.541564i \(-0.817832\pi\)
0.840659 0.541564i \(-0.182168\pi\)
\(80\) 0 0
\(81\) −4.78297e6 −0.111111
\(82\) −2.07390e7 + 2.07390e7i −0.458704 + 0.458704i
\(83\) 6.66763e7 + 6.66763e7i 1.40494 + 1.40494i 0.783302 + 0.621642i \(0.213534\pi\)
0.621642 + 0.783302i \(0.286466\pi\)
\(84\) 2.81119e7i 0.564641i
\(85\) 0 0
\(86\) 4.11811e7 0.752842
\(87\) −7.94210e6 + 7.94210e6i −0.138630 + 0.138630i
\(88\) 694695. + 694695.i 0.0115841 + 0.0115841i
\(89\) 9.51614e7i 1.51670i 0.651845 + 0.758352i \(0.273995\pi\)
−0.651845 + 0.758352i \(0.726005\pi\)
\(90\) 0 0
\(91\) −6.85279e7 −0.999314
\(92\) 3.98759e7 3.98759e7i 0.556620 0.556620i
\(93\) −2.76689e7 2.76689e7i −0.369880 0.369880i
\(94\) 7.92637e7i 1.01523i
\(95\) 0 0
\(96\) −4.74725e7 −0.558929
\(97\) −7.08678e7 + 7.08678e7i −0.800501 + 0.800501i −0.983174 0.182672i \(-0.941525\pi\)
0.182672 + 0.983174i \(0.441525\pi\)
\(98\) 7.88658e7 + 7.88658e7i 0.855036 + 0.855036i
\(99\) 511758.i 0.00532750i
\(100\) 0 0
\(101\) −8.63379e7 −0.829690 −0.414845 0.909892i \(-0.636164\pi\)
−0.414845 + 0.909892i \(0.636164\pi\)
\(102\) −4.32598e7 + 4.32598e7i −0.399654 + 0.399654i
\(103\) 7.61161e7 + 7.61161e7i 0.676282 + 0.676282i 0.959157 0.282875i \(-0.0912881\pi\)
−0.282875 + 0.959157i \(0.591288\pi\)
\(104\) 7.08366e7i 0.605514i
\(105\) 0 0
\(106\) −1.75273e7 −0.138833
\(107\) 1.09281e8 1.09281e8i 0.833701 0.833701i −0.154320 0.988021i \(-0.549319\pi\)
0.988021 + 0.154320i \(0.0493186\pi\)
\(108\) 1.07034e7 + 1.07034e7i 0.0786728 + 0.0786728i
\(109\) 5.04631e7i 0.357494i 0.983895 + 0.178747i \(0.0572043\pi\)
−0.983895 + 0.178747i \(0.942796\pi\)
\(110\) 0 0
\(111\) 4.02295e7 0.265004
\(112\) −1.64969e7 + 1.64969e7i −0.104841 + 0.104841i
\(113\) 1.21244e8 + 1.21244e8i 0.743611 + 0.743611i 0.973271 0.229660i \(-0.0737615\pi\)
−0.229660 + 0.973271i \(0.573762\pi\)
\(114\) 8.83028e7i 0.522823i
\(115\) 0 0
\(116\) 3.55458e7 0.196316
\(117\) −2.60914e7 + 2.60914e7i −0.139237 + 0.139237i
\(118\) 9.39572e7 + 9.39572e7i 0.484621 + 0.484621i
\(119\) 5.11290e8i 2.54964i
\(120\) 0 0
\(121\) −2.14304e8 −0.999745
\(122\) −3.80212e6 + 3.80212e6i −0.0171627 + 0.0171627i
\(123\) −9.33255e7 9.33255e7i −0.407737 0.407737i
\(124\) 1.23835e8i 0.523791i
\(125\) 0 0
\(126\) 9.23133e7 0.366254
\(127\) 9.55780e7 9.55780e7i 0.367403 0.367403i −0.499126 0.866529i \(-0.666346\pi\)
0.866529 + 0.499126i \(0.166346\pi\)
\(128\) 9.54285e7 + 9.54285e7i 0.355499 + 0.355499i
\(129\) 1.85315e8i 0.669193i
\(130\) 0 0
\(131\) −3.13838e8 −1.06566 −0.532832 0.846221i \(-0.678872\pi\)
−0.532832 + 0.846221i \(0.678872\pi\)
\(132\) −1.14521e6 + 1.14521e6i −0.00377217 + 0.00377217i
\(133\) −5.21827e8 5.21827e8i −1.66771 1.66771i
\(134\) 3.03664e7i 0.0941834i
\(135\) 0 0
\(136\) 5.28514e8 1.54490
\(137\) −5.04691e7 + 5.04691e7i −0.143266 + 0.143266i −0.775102 0.631836i \(-0.782302\pi\)
0.631836 + 0.775102i \(0.282302\pi\)
\(138\) −1.30944e8 1.30944e8i −0.361051 0.361051i
\(139\) 5.26688e8i 1.41089i 0.708763 + 0.705446i \(0.249253\pi\)
−0.708763 + 0.705446i \(0.750747\pi\)
\(140\) 0 0
\(141\) −3.56687e8 −0.902423
\(142\) 1.53059e8 1.53059e8i 0.376447 0.376447i
\(143\) −2.79168e6 2.79168e6i −0.00667607 0.00667607i
\(144\) 1.25621e7i 0.0292155i
\(145\) 0 0
\(146\) 4.24345e8 0.933915
\(147\) −3.54896e8 + 3.54896e8i −0.760032 + 0.760032i
\(148\) −9.00257e7 9.00257e7i −0.187638 0.187638i
\(149\) 8.99246e8i 1.82446i −0.409683 0.912228i \(-0.634361\pi\)
0.409683 0.912228i \(-0.365639\pi\)
\(150\) 0 0
\(151\) 8.05999e8 1.55034 0.775170 0.631753i \(-0.217664\pi\)
0.775170 + 0.631753i \(0.217664\pi\)
\(152\) 5.39407e8 5.39407e8i 1.01051 1.01051i
\(153\) −1.94669e8 1.94669e8i −0.355248 0.355248i
\(154\) 9.87714e6i 0.0175610i
\(155\) 0 0
\(156\) 1.16775e8 0.197175
\(157\) −4.78600e8 + 4.78600e8i −0.787724 + 0.787724i −0.981121 0.193397i \(-0.938050\pi\)
0.193397 + 0.981121i \(0.438050\pi\)
\(158\) 3.10017e8 + 3.10017e8i 0.497458 + 0.497458i
\(159\) 7.88729e7i 0.123407i
\(160\) 0 0
\(161\) 1.54763e9 2.30337
\(162\) 3.51475e7 3.51475e7i 0.0510310 0.0510310i
\(163\) −4.56533e8 4.56533e8i −0.646729 0.646729i 0.305472 0.952201i \(-0.401186\pi\)
−0.952201 + 0.305472i \(0.901186\pi\)
\(164\) 4.17689e8i 0.577401i
\(165\) 0 0
\(166\) −9.79937e8 −1.29052
\(167\) −2.74258e8 + 2.74258e8i −0.352609 + 0.352609i −0.861079 0.508470i \(-0.830211\pi\)
0.508470 + 0.861079i \(0.330211\pi\)
\(168\) −5.63905e8 5.63905e8i −0.707895 0.707895i
\(169\) 5.31069e8i 0.651035i
\(170\) 0 0
\(171\) −3.97363e8 −0.464732
\(172\) 4.14698e8 4.14698e8i 0.473826 0.473826i
\(173\) 1.75277e8 + 1.75277e8i 0.195677 + 0.195677i 0.798144 0.602467i \(-0.205815\pi\)
−0.602467 + 0.798144i \(0.705815\pi\)
\(174\) 1.16725e8i 0.127340i
\(175\) 0 0
\(176\) −1.34410e6 −0.00140081
\(177\) −4.22807e8 + 4.22807e8i −0.430774 + 0.430774i
\(178\) −6.99291e8 6.99291e8i −0.696591 0.696591i
\(179\) 1.65138e9i 1.60855i −0.594255 0.804277i \(-0.702553\pi\)
0.594255 0.804277i \(-0.297447\pi\)
\(180\) 0 0
\(181\) −3.19153e8 −0.297362 −0.148681 0.988885i \(-0.547503\pi\)
−0.148681 + 0.988885i \(0.547503\pi\)
\(182\) 5.03575e8 5.03575e8i 0.458964 0.458964i
\(183\) −1.71095e7 1.71095e7i −0.0152558 0.0152558i
\(184\) 1.59977e9i 1.39568i
\(185\) 0 0
\(186\) 4.06648e8 0.339756
\(187\) 2.08288e7 2.08288e7i 0.0170333 0.0170333i
\(188\) 7.98195e8 + 7.98195e8i 0.638966 + 0.638966i
\(189\) 4.15410e8i 0.325559i
\(190\) 0 0
\(191\) −1.13627e9 −0.853785 −0.426893 0.904302i \(-0.640392\pi\)
−0.426893 + 0.904302i \(0.640392\pi\)
\(192\) 3.97476e8 3.97476e8i 0.292486 0.292486i
\(193\) 1.71674e9 + 1.71674e9i 1.23730 + 1.23730i 0.961101 + 0.276197i \(0.0890742\pi\)
0.276197 + 0.961101i \(0.410926\pi\)
\(194\) 1.04154e9i 0.735307i
\(195\) 0 0
\(196\) 1.58838e9 1.07629
\(197\) 4.17614e8 4.17614e8i 0.277275 0.277275i −0.554745 0.832020i \(-0.687184\pi\)
0.832020 + 0.554745i \(0.187184\pi\)
\(198\) 3.76064e6 + 3.76064e6i 0.00244681 + 0.00244681i
\(199\) 1.06994e9i 0.682258i −0.940017 0.341129i \(-0.889191\pi\)
0.940017 0.341129i \(-0.110809\pi\)
\(200\) 0 0
\(201\) 1.36649e8 0.0837186
\(202\) 6.34451e8 6.34451e8i 0.381059 0.381059i
\(203\) 6.89786e8 + 6.89786e8i 0.406191 + 0.406191i
\(204\) 8.71264e8i 0.503071i
\(205\) 0 0
\(206\) −1.11867e9 −0.621205
\(207\) 5.89247e8 5.89247e8i 0.320934 0.320934i
\(208\) 6.85273e7 + 6.85273e7i 0.0366109 + 0.0366109i
\(209\) 4.25162e7i 0.0222828i
\(210\) 0 0
\(211\) −2.26915e9 −1.14481 −0.572406 0.819971i \(-0.693990\pi\)
−0.572406 + 0.819971i \(0.693990\pi\)
\(212\) −1.76502e8 + 1.76502e8i −0.0873790 + 0.0873790i
\(213\) 6.88763e8 + 6.88763e8i 0.334620 + 0.334620i
\(214\) 1.60610e9i 0.765803i
\(215\) 0 0
\(216\) −4.29404e8 −0.197266
\(217\) −2.40310e9 + 2.40310e9i −1.08376 + 1.08376i
\(218\) −3.70827e8 3.70827e8i −0.164189 0.164189i
\(219\) 1.90955e9i 0.830146i
\(220\) 0 0
\(221\) −2.12387e9 −0.890346
\(222\) −2.95625e8 + 2.95625e8i −0.121711 + 0.121711i
\(223\) −1.99573e9 1.99573e9i −0.807015 0.807015i 0.177166 0.984181i \(-0.443307\pi\)
−0.984181 + 0.177166i \(0.943307\pi\)
\(224\) 4.12307e9i 1.63768i
\(225\) 0 0
\(226\) −1.78191e9 −0.683050
\(227\) −1.32121e9 + 1.32121e9i −0.497588 + 0.497588i −0.910686 0.413099i \(-0.864446\pi\)
0.413099 + 0.910686i \(0.364446\pi\)
\(228\) 8.89220e8 + 8.89220e8i 0.329056 + 0.329056i
\(229\) 2.03118e9i 0.738595i −0.929311 0.369297i \(-0.879598\pi\)
0.929311 0.369297i \(-0.120402\pi\)
\(230\) 0 0
\(231\) −4.44471e7 −0.0156097
\(232\) −7.13024e8 + 7.13024e8i −0.246123 + 0.246123i
\(233\) 1.51062e9 + 1.51062e9i 0.512545 + 0.512545i 0.915305 0.402760i \(-0.131949\pi\)
−0.402760 + 0.915305i \(0.631949\pi\)
\(234\) 3.83464e8i 0.127897i
\(235\) 0 0
\(236\) 1.89232e9 0.610024
\(237\) −1.39508e9 + 1.39508e9i −0.442185 + 0.442185i
\(238\) 3.75720e9 + 3.75720e9i 1.17100 + 1.17100i
\(239\) 3.44530e9i 1.05593i 0.849266 + 0.527965i \(0.177045\pi\)
−0.849266 + 0.527965i \(0.822955\pi\)
\(240\) 0 0
\(241\) 2.45959e7 0.00729112 0.00364556 0.999993i \(-0.498840\pi\)
0.00364556 + 0.999993i \(0.498840\pi\)
\(242\) 1.57481e9 1.57481e9i 0.459162 0.459162i
\(243\) 1.58164e8 + 1.58164e8i 0.0453609 + 0.0453609i
\(244\) 7.65756e7i 0.0216039i
\(245\) 0 0
\(246\) 1.37160e9 0.374530
\(247\) −2.16764e9 + 2.16764e9i −0.582371 + 0.582371i
\(248\) −2.48405e9 2.48405e9i −0.656681 0.656681i
\(249\) 4.40972e9i 1.14713i
\(250\) 0 0
\(251\) −3.62820e9 −0.914106 −0.457053 0.889440i \(-0.651095\pi\)
−0.457053 + 0.889440i \(0.651095\pi\)
\(252\) 9.29606e8 9.29606e8i 0.230514 0.230514i
\(253\) 6.30470e7 + 6.30470e7i 0.0153880 + 0.0153880i
\(254\) 1.40470e9i 0.337482i
\(255\) 0 0
\(256\) −4.47960e9 −1.04299
\(257\) 1.05639e9 1.05639e9i 0.242154 0.242154i −0.575586 0.817741i \(-0.695226\pi\)
0.817741 + 0.575586i \(0.195226\pi\)
\(258\) −1.36178e9 1.36178e9i −0.307346 0.307346i
\(259\) 3.49400e9i 0.776469i
\(260\) 0 0
\(261\) 5.25261e8 0.113191
\(262\) 2.30623e9 2.30623e9i 0.489438 0.489438i
\(263\) −2.89677e9 2.89677e9i −0.605468 0.605468i 0.336290 0.941758i \(-0.390828\pi\)
−0.941758 + 0.336290i \(0.890828\pi\)
\(264\) 4.59445e7i 0.00945840i
\(265\) 0 0
\(266\) 7.66926e9 1.53189
\(267\) 3.14681e9 3.14681e9i 0.619192 0.619192i
\(268\) −3.05794e8 3.05794e8i −0.0592774 0.0592774i
\(269\) 4.75635e9i 0.908374i 0.890906 + 0.454187i \(0.150070\pi\)
−0.890906 + 0.454187i \(0.849930\pi\)
\(270\) 0 0
\(271\) 4.98291e9 0.923860 0.461930 0.886916i \(-0.347157\pi\)
0.461930 + 0.886916i \(0.347157\pi\)
\(272\) −5.11285e8 + 5.11285e8i −0.0934087 + 0.0934087i
\(273\) 2.26609e9 + 2.26609e9i 0.407968 + 0.407968i
\(274\) 7.41741e8i 0.131598i
\(275\) 0 0
\(276\) −2.63724e9 −0.454479
\(277\) 2.27910e9 2.27910e9i 0.387119 0.387119i −0.486539 0.873659i \(-0.661741\pi\)
0.873659 + 0.486539i \(0.161741\pi\)
\(278\) −3.87035e9 3.87035e9i −0.647994 0.647994i
\(279\) 1.82992e9i 0.302005i
\(280\) 0 0
\(281\) −1.00667e9 −0.161459 −0.0807294 0.996736i \(-0.525725\pi\)
−0.0807294 + 0.996736i \(0.525725\pi\)
\(282\) 2.62110e9 2.62110e9i 0.414464 0.414464i
\(283\) −3.14496e9 3.14496e9i −0.490308 0.490308i 0.418095 0.908403i \(-0.362698\pi\)
−0.908403 + 0.418095i \(0.862698\pi\)
\(284\) 3.08264e9i 0.473859i
\(285\) 0 0
\(286\) 4.10291e7 0.00613236
\(287\) −8.10549e9 + 8.10549e9i −1.19468 + 1.19468i
\(288\) 1.56983e9 + 1.56983e9i 0.228182 + 0.228182i
\(289\) 8.87052e9i 1.27162i
\(290\) 0 0
\(291\) 4.68693e9 0.653607
\(292\) 4.27320e9 4.27320e9i 0.587790 0.587790i
\(293\) −3.60077e9 3.60077e9i −0.488568 0.488568i 0.419286 0.907854i \(-0.362280\pi\)
−0.907854 + 0.419286i \(0.862280\pi\)
\(294\) 5.21589e9i 0.698134i
\(295\) 0 0
\(296\) 3.61171e9 0.470485
\(297\) −1.69229e7 + 1.69229e7i −0.00217494 + 0.00217494i
\(298\) 6.60808e9 + 6.60808e9i 0.837935 + 0.837935i
\(299\) 6.42877e9i 0.804346i
\(300\) 0 0
\(301\) 1.60949e10 1.96075
\(302\) −5.92286e9 + 5.92286e9i −0.712039 + 0.712039i
\(303\) 2.85503e9 + 2.85503e9i 0.338719 + 0.338719i
\(304\) 1.04364e9i 0.122196i
\(305\) 0 0
\(306\) 2.86104e9 0.326316
\(307\) 1.23211e10 1.23211e10i 1.38706 1.38706i 0.555644 0.831420i \(-0.312472\pi\)
0.831420 0.555644i \(-0.187528\pi\)
\(308\) 9.94640e7 + 9.94640e7i 0.0110526 + 0.0110526i
\(309\) 5.03403e9i 0.552182i
\(310\) 0 0
\(311\) −8.62846e9 −0.922341 −0.461170 0.887312i \(-0.652570\pi\)
−0.461170 + 0.887312i \(0.652570\pi\)
\(312\) −2.34243e9 + 2.34243e9i −0.247200 + 0.247200i
\(313\) −2.96428e9 2.96428e9i −0.308846 0.308846i 0.535616 0.844462i \(-0.320079\pi\)
−0.844462 + 0.535616i \(0.820079\pi\)
\(314\) 7.03396e9i 0.723571i
\(315\) 0 0
\(316\) 6.24381e9 0.626183
\(317\) 1.98335e9 1.98335e9i 0.196409 0.196409i −0.602050 0.798459i \(-0.705649\pi\)
0.798459 + 0.602050i \(0.205649\pi\)
\(318\) 5.79595e8 + 5.79595e8i 0.0566782 + 0.0566782i
\(319\) 5.62007e7i 0.00542724i
\(320\) 0 0
\(321\) −7.22745e9 −0.680714
\(322\) −1.13727e10 + 1.13727e10i −1.05789 + 1.05789i
\(323\) −1.61729e10 1.61729e10i −1.48586 1.48586i
\(324\) 7.07879e8i 0.0642361i
\(325\) 0 0
\(326\) 6.70964e9 0.594058
\(327\) 1.66872e9 1.66872e9i 0.145946 0.145946i
\(328\) −8.37855e9 8.37855e9i −0.723892 0.723892i
\(329\) 3.09789e10i 2.64413i
\(330\) 0 0
\(331\) −4.30793e9 −0.358886 −0.179443 0.983768i \(-0.557430\pi\)
−0.179443 + 0.983768i \(0.557430\pi\)
\(332\) −9.86809e9 + 9.86809e9i −0.812233 + 0.812233i
\(333\) −1.33031e9 1.33031e9i −0.108187 0.108187i
\(334\) 4.03075e9i 0.323892i
\(335\) 0 0
\(336\) 1.09104e9 0.0856023
\(337\) 1.18877e8 1.18877e8i 0.00921677 0.00921677i −0.702483 0.711700i \(-0.747925\pi\)
0.711700 + 0.702483i \(0.247925\pi\)
\(338\) 3.90255e9 + 3.90255e9i 0.299007 + 0.299007i
\(339\) 8.01860e9i 0.607156i
\(340\) 0 0
\(341\) −1.95794e8 −0.0144804
\(342\) 2.92001e9 2.92001e9i 0.213442 0.213442i
\(343\) 1.42667e10 + 1.42667e10i 1.03074 + 1.03074i
\(344\) 1.66372e10i 1.18808i
\(345\) 0 0
\(346\) −2.57603e9 −0.179741
\(347\) 1.63550e10 1.63550e10i 1.12806 1.12806i 0.137569 0.990492i \(-0.456071\pi\)
0.990492 0.137569i \(-0.0439289\pi\)
\(348\) −1.17543e9 1.17543e9i −0.0801457 0.0801457i
\(349\) 2.63406e10i 1.77552i 0.460310 + 0.887758i \(0.347738\pi\)
−0.460310 + 0.887758i \(0.652262\pi\)
\(350\) 0 0
\(351\) 1.72559e9 0.113686
\(352\) −1.67965e8 + 1.67965e8i −0.0109408 + 0.0109408i
\(353\) −4.48404e9 4.48404e9i −0.288783 0.288783i 0.547816 0.836599i \(-0.315459\pi\)
−0.836599 + 0.547816i \(0.815459\pi\)
\(354\) 6.21398e9i 0.395691i
\(355\) 0 0
\(356\) −1.40839e10 −0.876845
\(357\) −1.69074e10 + 1.69074e10i −1.04089 + 1.04089i
\(358\) 1.21351e10 + 1.21351e10i 0.738775 + 0.738775i
\(359\) 1.76017e10i 1.05968i −0.848097 0.529841i \(-0.822251\pi\)
0.848097 0.529841i \(-0.177749\pi\)
\(360\) 0 0
\(361\) −1.60288e10 −0.943782
\(362\) 2.34529e9 2.34529e9i 0.136572 0.136572i
\(363\) 7.08663e9 + 7.08663e9i 0.408144 + 0.408144i
\(364\) 1.01421e10i 0.577729i
\(365\) 0 0
\(366\) 2.51458e8 0.0140133
\(367\) 5.58417e9 5.58417e9i 0.307818 0.307818i −0.536245 0.844063i \(-0.680158\pi\)
0.844063 + 0.536245i \(0.180158\pi\)
\(368\) −1.54762e9 1.54762e9i −0.0843863 0.0843863i
\(369\) 6.17220e9i 0.332916i
\(370\) 0 0
\(371\) −6.85026e9 −0.361586
\(372\) 4.09500e9 4.09500e9i 0.213837 0.213837i
\(373\) 1.94503e9 + 1.94503e9i 0.100483 + 0.100483i 0.755561 0.655078i \(-0.227364\pi\)
−0.655078 + 0.755561i \(0.727364\pi\)
\(374\) 3.06120e8i 0.0156461i
\(375\) 0 0
\(376\) −3.20225e10 −1.60215
\(377\) 2.86533e9 2.86533e9i 0.141844 0.141844i
\(378\) −3.05263e9 3.05263e9i −0.149522 0.149522i
\(379\) 1.29779e10i 0.628996i 0.949258 + 0.314498i \(0.101836\pi\)
−0.949258 + 0.314498i \(0.898164\pi\)
\(380\) 0 0
\(381\) −6.32117e9 −0.299984
\(382\) 8.34986e9 8.34986e9i 0.392126 0.392126i
\(383\) 1.84005e10 + 1.84005e10i 0.855135 + 0.855135i 0.990760 0.135625i \(-0.0433044\pi\)
−0.135625 + 0.990760i \(0.543304\pi\)
\(384\) 6.31128e9i 0.290264i
\(385\) 0 0
\(386\) −2.52308e10 −1.13653
\(387\) 6.12801e9 6.12801e9i 0.273197 0.273197i
\(388\) −1.04884e10 1.04884e10i −0.462790 0.462790i
\(389\) 1.69662e9i 0.0740944i 0.999314 + 0.0370472i \(0.0117952\pi\)
−0.999314 + 0.0370472i \(0.988205\pi\)
\(390\) 0 0
\(391\) 4.79653e10 2.05220
\(392\) −3.18618e10 + 3.18618e10i −1.34935 + 1.34935i
\(393\) 1.03780e10 + 1.03780e10i 0.435056 + 0.435056i
\(394\) 6.13765e9i 0.254693i
\(395\) 0 0
\(396\) 7.57402e7 0.00307996
\(397\) −1.61839e10 + 1.61839e10i −0.651510 + 0.651510i −0.953357 0.301846i \(-0.902397\pi\)
0.301846 + 0.953357i \(0.402397\pi\)
\(398\) 7.86245e9 + 7.86245e9i 0.313347 + 0.313347i
\(399\) 3.45117e10i 1.36168i
\(400\) 0 0
\(401\) −3.67977e9 −0.142313 −0.0711563 0.997465i \(-0.522669\pi\)
−0.0711563 + 0.997465i \(0.522669\pi\)
\(402\) −1.00416e9 + 1.00416e9i −0.0384502 + 0.0384502i
\(403\) 9.98233e9 + 9.98233e9i 0.378453 + 0.378453i
\(404\) 1.27780e10i 0.479664i
\(405\) 0 0
\(406\) −1.01377e10 −0.373110
\(407\) 1.42338e8 1.42338e8i 0.00518732 0.00518732i
\(408\) −1.74770e10 1.74770e10i −0.630704 0.630704i
\(409\) 2.44824e10i 0.874905i −0.899242 0.437452i \(-0.855881\pi\)
0.899242 0.437452i \(-0.144119\pi\)
\(410\) 0 0
\(411\) 3.33783e9 0.116976
\(412\) −1.12652e10 + 1.12652e10i −0.390976 + 0.390976i
\(413\) 3.67216e10 + 3.67216e10i 1.26218 + 1.26218i
\(414\) 8.66013e9i 0.294797i
\(415\) 0 0
\(416\) 1.71270e10 0.571885
\(417\) 1.74166e10 1.74166e10i 0.575995 0.575995i
\(418\) 3.12429e8 + 3.12429e8i 0.0102340 + 0.0102340i
\(419\) 2.07283e10i 0.672522i −0.941769 0.336261i \(-0.890838\pi\)
0.941769 0.336261i \(-0.109162\pi\)
\(420\) 0 0
\(421\) −1.53035e10 −0.487150 −0.243575 0.969882i \(-0.578320\pi\)
−0.243575 + 0.969882i \(0.578320\pi\)
\(422\) 1.66748e10 1.66748e10i 0.525788 0.525788i
\(423\) 1.17950e10 + 1.17950e10i 0.368413 + 0.368413i
\(424\) 7.08104e9i 0.219095i
\(425\) 0 0
\(426\) −1.01227e10 −0.307368
\(427\) −1.48600e9 + 1.48600e9i −0.0446998 + 0.0446998i
\(428\) 1.61736e10 + 1.61736e10i 0.481983 + 0.481983i
\(429\) 1.84631e8i 0.00545099i
\(430\) 0 0
\(431\) 3.04251e10 0.881705 0.440852 0.897580i \(-0.354676\pi\)
0.440852 + 0.897580i \(0.354676\pi\)
\(432\) 4.15406e8 4.15406e8i 0.0119272 0.0119272i
\(433\) −3.30421e9 3.30421e9i −0.0939974 0.0939974i 0.658544 0.752542i \(-0.271172\pi\)
−0.752542 + 0.658544i \(0.771172\pi\)
\(434\) 3.53182e10i 0.995495i
\(435\) 0 0
\(436\) −7.46855e9 −0.206676
\(437\) 4.89538e10 4.89538e10i 1.34234 1.34234i
\(438\) −1.40323e10 1.40323e10i −0.381269 0.381269i
\(439\) 3.09771e10i 0.834032i 0.908899 + 0.417016i \(0.136924\pi\)
−0.908899 + 0.417016i \(0.863076\pi\)
\(440\) 0 0
\(441\) 2.34715e10 0.620563
\(442\) 1.56072e10 1.56072e10i 0.408917 0.408917i
\(443\) −3.59125e10 3.59125e10i −0.932460 0.932460i 0.0653990 0.997859i \(-0.479168\pi\)
−0.997859 + 0.0653990i \(0.979168\pi\)
\(444\) 5.95396e9i 0.153205i
\(445\) 0 0
\(446\) 2.93311e10 0.741291
\(447\) −2.97364e10 + 2.97364e10i −0.744831 + 0.744831i
\(448\) −3.45215e10 3.45215e10i −0.856993 0.856993i
\(449\) 3.25449e10i 0.800751i 0.916351 + 0.400376i \(0.131120\pi\)
−0.916351 + 0.400376i \(0.868880\pi\)
\(450\) 0 0
\(451\) −6.60399e8 −0.0159625
\(452\) −1.79441e10 + 1.79441e10i −0.429900 + 0.429900i
\(453\) −2.66529e10 2.66529e10i −0.632924 0.632924i
\(454\) 1.94178e10i 0.457064i
\(455\) 0 0
\(456\) −3.56743e10 −0.825081
\(457\) −1.89124e10 + 1.89124e10i −0.433593 + 0.433593i −0.889849 0.456256i \(-0.849190\pi\)
0.456256 + 0.889849i \(0.349190\pi\)
\(458\) 1.49261e10 + 1.49261e10i 0.339221 + 0.339221i
\(459\) 1.28747e10i 0.290059i
\(460\) 0 0
\(461\) 3.64502e10 0.807042 0.403521 0.914970i \(-0.367786\pi\)
0.403521 + 0.914970i \(0.367786\pi\)
\(462\) 3.26618e8 3.26618e8i 0.00716923 0.00716923i
\(463\) −5.92927e10 5.92927e10i −1.29026 1.29026i −0.934625 0.355636i \(-0.884264\pi\)
−0.355636 0.934625i \(-0.615736\pi\)
\(464\) 1.37956e9i 0.0297624i
\(465\) 0 0
\(466\) −2.22015e10 −0.470803
\(467\) 3.42203e10 3.42203e10i 0.719476 0.719476i −0.249021 0.968498i \(-0.580109\pi\)
0.968498 + 0.249021i \(0.0801090\pi\)
\(468\) −3.86153e9 3.86153e9i −0.0804964 0.0804964i
\(469\) 1.18682e10i 0.245298i
\(470\) 0 0
\(471\) 3.16528e10 0.643174
\(472\) −3.79587e10 + 3.79587e10i −0.764792 + 0.764792i
\(473\) 6.55672e8 + 6.55672e8i 0.0130991 + 0.0130991i
\(474\) 2.05033e10i 0.406173i
\(475\) 0 0
\(476\) 7.56709e10 1.47401
\(477\) −2.60818e9 + 2.60818e9i −0.0503807 + 0.0503807i
\(478\) −2.53177e10 2.53177e10i −0.484967 0.484967i
\(479\) 4.05336e10i 0.769970i −0.922923 0.384985i \(-0.874207\pi\)
0.922923 0.384985i \(-0.125793\pi\)
\(480\) 0 0
\(481\) −1.45139e10 −0.271146
\(482\) −1.80742e8 + 1.80742e8i −0.00334866 + 0.00334866i
\(483\) −5.11772e10 5.11772e10i −0.940346 0.940346i
\(484\) 3.17170e10i 0.577977i
\(485\) 0 0
\(486\) −2.32452e9 −0.0416667
\(487\) −3.57760e10 + 3.57760e10i −0.636028 + 0.636028i −0.949573 0.313545i \(-0.898483\pi\)
0.313545 + 0.949573i \(0.398483\pi\)
\(488\) −1.53606e9 1.53606e9i −0.0270849 0.0270849i
\(489\) 3.01934e10i 0.528052i
\(490\) 0 0
\(491\) −5.52678e10 −0.950925 −0.475462 0.879736i \(-0.657719\pi\)
−0.475462 + 0.879736i \(0.657719\pi\)
\(492\) 1.38122e10 1.38122e10i 0.235723 0.235723i
\(493\) 2.13784e10 + 2.13784e10i 0.361899 + 0.361899i
\(494\) 3.18577e10i 0.534942i
\(495\) 0 0
\(496\) 4.80615e9 0.0794091
\(497\) 5.98204e10 5.98204e10i 0.980446 0.980446i
\(498\) 3.24047e10 + 3.24047e10i 0.526854 + 0.526854i
\(499\) 2.17632e10i 0.351011i 0.984478 + 0.175506i \(0.0561560\pi\)
−0.984478 + 0.175506i \(0.943844\pi\)
\(500\) 0 0
\(501\) 1.81384e10 0.287904
\(502\) 2.66617e10 2.66617e10i 0.419830 0.419830i
\(503\) 1.36083e10 + 1.36083e10i 0.212585 + 0.212585i 0.805365 0.592779i \(-0.201969\pi\)
−0.592779 + 0.805365i \(0.701969\pi\)
\(504\) 3.72946e10i 0.577994i
\(505\) 0 0
\(506\) −9.26598e8 −0.0141348
\(507\) −1.75615e10 + 1.75615e10i −0.265784 + 0.265784i
\(508\) 1.41455e10 + 1.41455e10i 0.212405 + 0.212405i
\(509\) 8.50274e10i 1.26674i −0.773849 0.633370i \(-0.781671\pi\)
0.773849 0.633370i \(-0.218329\pi\)
\(510\) 0 0
\(511\) 1.65848e11 2.43235
\(512\) 8.48852e9 8.48852e9i 0.123524 0.123524i
\(513\) 1.31400e10 + 1.31400e10i 0.189726 + 0.189726i
\(514\) 1.55257e10i 0.222433i
\(515\) 0 0
\(516\) −2.74266e10 −0.386877
\(517\) −1.26201e9 + 1.26201e9i −0.0176645 + 0.0176645i
\(518\) 2.56756e10 + 2.56756e10i 0.356616 + 0.356616i
\(519\) 1.15921e10i 0.159770i
\(520\) 0 0
\(521\) −1.04749e11 −1.42167 −0.710836 0.703358i \(-0.751683\pi\)
−0.710836 + 0.703358i \(0.751683\pi\)
\(522\) −3.85986e9 + 3.85986e9i −0.0519864 + 0.0519864i
\(523\) −1.81952e10 1.81952e10i −0.243192 0.243192i 0.574977 0.818169i \(-0.305011\pi\)
−0.818169 + 0.574977i \(0.805011\pi\)
\(524\) 4.64480e10i 0.616087i
\(525\) 0 0
\(526\) 4.25737e10 0.556158
\(527\) −7.44786e10 + 7.44786e10i −0.965581 + 0.965581i
\(528\) 4.44467e7 + 4.44467e7i 0.000571879 + 0.000571879i
\(529\) 6.68758e10i 0.853977i
\(530\) 0 0
\(531\) 2.79629e10 0.351726
\(532\) 7.72304e10 7.72304e10i 0.964144 0.964144i
\(533\) 3.36698e10 + 3.36698e10i 0.417187 + 0.417187i
\(534\) 4.62485e10i 0.568764i
\(535\) 0 0
\(536\) 1.22680e10 0.148633
\(537\) −5.46081e10 + 5.46081e10i −0.656689 + 0.656689i
\(538\) −3.49519e10 3.49519e10i −0.417198 0.417198i
\(539\) 2.51135e9i 0.0297545i
\(540\) 0 0
\(541\) −6.68793e10 −0.780733 −0.390367 0.920660i \(-0.627652\pi\)
−0.390367 + 0.920660i \(0.627652\pi\)
\(542\) −3.66168e10 + 3.66168e10i −0.424310 + 0.424310i
\(543\) 1.05538e10 + 1.05538e10i 0.121397 + 0.121397i
\(544\) 1.27785e11i 1.45910i
\(545\) 0 0
\(546\) −3.33046e10 −0.374743
\(547\) −1.80208e9 + 1.80208e9i −0.0201291 + 0.0201291i −0.717100 0.696971i \(-0.754531\pi\)
0.696971 + 0.717100i \(0.254531\pi\)
\(548\) −7.46942e9 7.46942e9i −0.0828256 0.0828256i
\(549\) 1.13156e9i 0.0124563i
\(550\) 0 0
\(551\) 4.36379e10 0.473432
\(552\) 5.29013e10 5.29013e10i 0.569784 0.569784i
\(553\) 1.21165e11 + 1.21165e11i 1.29562 + 1.29562i
\(554\) 3.34958e10i 0.355592i
\(555\) 0 0
\(556\) −7.79498e10 −0.815672
\(557\) 2.12113e10 2.12113e10i 0.220367 0.220367i −0.588286 0.808653i \(-0.700197\pi\)
0.808653 + 0.588286i \(0.200197\pi\)
\(558\) −1.34471e10 1.34471e10i −0.138705 0.138705i
\(559\) 6.68575e10i 0.684704i
\(560\) 0 0
\(561\) −1.37754e9 −0.0139076
\(562\) 7.39748e9 7.39748e9i 0.0741547 0.0741547i
\(563\) 2.95427e10 + 2.95427e10i 0.294047 + 0.294047i 0.838677 0.544629i \(-0.183330\pi\)
−0.544629 + 0.838677i \(0.683330\pi\)
\(564\) 5.27896e10i 0.521713i
\(565\) 0 0
\(566\) 4.62212e10 0.450377
\(567\) 1.37368e10 1.37368e10i 0.132909 0.132909i
\(568\) 6.18356e10 + 6.18356e10i 0.594081 + 0.594081i
\(569\) 6.53964e10i 0.623886i −0.950101 0.311943i \(-0.899020\pi\)
0.950101 0.311943i \(-0.100980\pi\)
\(570\) 0 0
\(571\) −1.87778e11 −1.76644 −0.883221 0.468957i \(-0.844630\pi\)
−0.883221 + 0.468957i \(0.844630\pi\)
\(572\) 4.13168e8 4.13168e8i 0.00385960 0.00385960i
\(573\) 3.75744e10 + 3.75744e10i 0.348556 + 0.348556i
\(574\) 1.19126e11i 1.09738i
\(575\) 0 0
\(576\) −2.62875e10 −0.238814
\(577\) 9.25087e7 9.25087e7i 0.000834602 0.000834602i −0.706689 0.707524i \(-0.749812\pi\)
0.707524 + 0.706689i \(0.249812\pi\)
\(578\) 6.51847e10 + 6.51847e10i 0.584029 + 0.584029i
\(579\) 1.13538e11i 1.01025i
\(580\) 0 0
\(581\) −3.82992e11 −3.36113
\(582\) −3.44418e10 + 3.44418e10i −0.300188 + 0.300188i
\(583\) −2.79064e8 2.79064e8i −0.00241563 0.00241563i
\(584\) 1.71435e11i 1.47383i
\(585\) 0 0
\(586\) 5.29204e10 0.448779
\(587\) 1.12620e11 1.12620e11i 0.948560 0.948560i −0.0501803 0.998740i \(-0.515980\pi\)
0.998740 + 0.0501803i \(0.0159796\pi\)
\(588\) −5.25246e10 5.25246e10i −0.439393 0.439393i
\(589\) 1.52027e11i 1.26316i
\(590\) 0 0
\(591\) −2.76194e10 −0.226394
\(592\) −3.49397e9 + 3.49397e9i −0.0284467 + 0.0284467i
\(593\) −1.37020e11 1.37020e11i −1.10807 1.10807i −0.993405 0.114661i \(-0.963422\pi\)
−0.114661 0.993405i \(-0.536578\pi\)
\(594\) 2.48714e8i 0.00199781i
\(595\) 0 0
\(596\) 1.33088e11 1.05476
\(597\) −3.53810e10 + 3.53810e10i −0.278531 + 0.278531i
\(598\) 4.72416e10 + 4.72416e10i 0.369420 + 0.369420i
\(599\) 1.62549e11i 1.26263i 0.775525 + 0.631317i \(0.217485\pi\)
−0.775525 + 0.631317i \(0.782515\pi\)
\(600\) 0 0
\(601\) 1.32519e10 0.101574 0.0507869 0.998710i \(-0.483827\pi\)
0.0507869 + 0.998710i \(0.483827\pi\)
\(602\) −1.18273e11 + 1.18273e11i −0.900534 + 0.900534i
\(603\) −4.51872e9 4.51872e9i −0.0341780 0.0341780i
\(604\) 1.19288e11i 0.896290i
\(605\) 0 0
\(606\) −4.19602e10 −0.311134
\(607\) −8.11866e10 + 8.11866e10i −0.598039 + 0.598039i −0.939791 0.341751i \(-0.888980\pi\)
0.341751 + 0.939791i \(0.388980\pi\)
\(608\) 1.30419e11 + 1.30419e11i 0.954391 + 0.954391i
\(609\) 4.56199e10i 0.331654i
\(610\) 0 0
\(611\) 1.28685e11 0.923340
\(612\) 2.88111e10 2.88111e10i 0.205378 0.205378i
\(613\) −4.13613e10 4.13613e10i −0.292922 0.292922i 0.545311 0.838234i \(-0.316411\pi\)
−0.838234 + 0.545311i \(0.816411\pi\)
\(614\) 1.81083e11i 1.27410i
\(615\) 0 0
\(616\) −3.99036e9 −0.0277134
\(617\) −1.45292e11 + 1.45292e11i −1.00254 + 1.00254i −0.00254243 + 0.999997i \(0.500809\pi\)
−0.999997 + 0.00254243i \(0.999191\pi\)
\(618\) 3.69924e10 + 3.69924e10i 0.253606 + 0.253606i
\(619\) 1.15947e11i 0.789765i −0.918732 0.394882i \(-0.870785\pi\)
0.918732 0.394882i \(-0.129215\pi\)
\(620\) 0 0
\(621\) −3.89706e10 −0.262042
\(622\) 6.34059e10 6.34059e10i 0.423612 0.423612i
\(623\) −2.73306e11 2.73306e11i −1.81425 1.81425i
\(624\) 4.53214e9i 0.0298927i
\(625\) 0 0
\(626\) 4.35658e10 0.283693
\(627\) −1.40593e9 + 1.40593e9i −0.00909690 + 0.00909690i
\(628\) −7.08328e10 7.08328e10i −0.455403 0.455403i
\(629\) 1.08289e11i 0.691800i
\(630\) 0 0
\(631\) −3.77923e10 −0.238389 −0.119194 0.992871i \(-0.538031\pi\)
−0.119194 + 0.992871i \(0.538031\pi\)
\(632\) −1.25247e11 + 1.25247e11i −0.785052 + 0.785052i
\(633\) 7.50366e10 + 7.50366e10i 0.467367 + 0.467367i
\(634\) 2.91491e10i 0.180413i
\(635\) 0 0
\(636\) 1.16732e10 0.0713446
\(637\) 1.28039e11 1.28039e11i 0.777648 0.777648i
\(638\) −4.12989e8 4.12989e8i −0.00249262 0.00249262i
\(639\) 4.55522e10i 0.273216i
\(640\) 0 0
\(641\) −1.49659e10 −0.0886484 −0.0443242 0.999017i \(-0.514113\pi\)
−0.0443242 + 0.999017i \(0.514113\pi\)
\(642\) 5.31107e10 5.31107e10i 0.312638 0.312638i
\(643\) 1.62422e11 + 1.62422e11i 0.950170 + 0.950170i 0.998816 0.0486457i \(-0.0154905\pi\)
−0.0486457 + 0.998816i \(0.515491\pi\)
\(644\) 2.29049e11i 1.33164i
\(645\) 0 0
\(646\) 2.37692e11 1.36485
\(647\) 7.96349e10 7.96349e10i 0.454450 0.454450i −0.442378 0.896829i \(-0.645865\pi\)
0.896829 + 0.442378i \(0.145865\pi\)
\(648\) 1.41996e10 + 1.41996e10i 0.0805334 + 0.0805334i
\(649\) 2.99191e9i 0.0168644i
\(650\) 0 0
\(651\) 1.58932e11 0.884885
\(652\) 6.75669e10 6.75669e10i 0.373890 0.373890i
\(653\) 3.49865e9 + 3.49865e9i 0.0192419 + 0.0192419i 0.716662 0.697420i \(-0.245669\pi\)
−0.697420 + 0.716662i \(0.745669\pi\)
\(654\) 2.45251e10i 0.134060i
\(655\) 0 0
\(656\) 1.62108e10 0.0875367
\(657\) 6.31452e10 6.31452e10i 0.338906 0.338906i
\(658\) −2.27647e11 2.27647e11i −1.21439 1.21439i
\(659\) 2.49093e11i 1.32075i −0.750938 0.660373i \(-0.770398\pi\)
0.750938 0.660373i \(-0.229602\pi\)
\(660\) 0 0
\(661\) 8.01902e9 0.0420064 0.0210032 0.999779i \(-0.493314\pi\)
0.0210032 + 0.999779i \(0.493314\pi\)
\(662\) 3.16567e10 3.16567e10i 0.164829 0.164829i
\(663\) 7.02323e10 + 7.02323e10i 0.363482 + 0.363482i
\(664\) 3.95894e11i 2.03661i
\(665\) 0 0
\(666\) 1.95515e10 0.0993765
\(667\) −6.47105e10 + 6.47105e10i −0.326942 + 0.326942i
\(668\) −4.05902e10 4.05902e10i −0.203852 0.203852i
\(669\) 1.31990e11i 0.658925i
\(670\) 0 0
\(671\) −1.21072e8 −0.000597248
\(672\) 1.36342e11 1.36342e11i 0.668580 0.668580i
\(673\) 1.75658e11 + 1.75658e11i 0.856264 + 0.856264i 0.990896 0.134632i \(-0.0429852\pi\)
−0.134632 + 0.990896i \(0.542985\pi\)
\(674\) 1.74713e9i 0.00846614i
\(675\) 0 0
\(676\) 7.85983e10 0.376380
\(677\) −1.49210e11 + 1.49210e11i −0.710301 + 0.710301i −0.966598 0.256297i \(-0.917498\pi\)
0.256297 + 0.966598i \(0.417498\pi\)
\(678\) 5.89245e10 + 5.89245e10i 0.278854 + 0.278854i
\(679\) 4.07068e11i 1.91509i
\(680\) 0 0
\(681\) 8.73801e10 0.406279
\(682\) 1.43878e9 1.43878e9i 0.00665056 0.00665056i
\(683\) −2.32934e11 2.32934e11i −1.07041 1.07041i −0.997326 0.0730842i \(-0.976716\pi\)
−0.0730842 0.997326i \(-0.523284\pi\)
\(684\) 5.88097e10i 0.268673i
\(685\) 0 0
\(686\) −2.09677e11 −0.946792
\(687\) −6.71672e10 + 6.71672e10i −0.301530 + 0.301530i
\(688\) −1.60948e10 1.60948e10i −0.0718342 0.0718342i
\(689\) 2.84556e10i 0.126267i
\(690\) 0 0
\(691\) 2.85720e11 1.25322 0.626611 0.779332i \(-0.284441\pi\)
0.626611 + 0.779332i \(0.284441\pi\)
\(692\) −2.59410e10 + 2.59410e10i −0.113126 + 0.113126i
\(693\) 1.46978e9 + 1.46978e9i 0.00637265 + 0.00637265i
\(694\) 2.40368e11i 1.03619i
\(695\) 0 0
\(696\) 4.71567e10 0.200959
\(697\) −2.51211e11 + 2.51211e11i −1.06441 + 1.06441i
\(698\) −1.93563e11 1.93563e11i −0.815458 0.815458i
\(699\) 9.99068e10i 0.418491i
\(700\) 0 0
\(701\) −6.05393e10 −0.250706 −0.125353 0.992112i \(-0.540006\pi\)
−0.125353 + 0.992112i \(0.540006\pi\)
\(702\) −1.26804e10 + 1.26804e10i −0.0522139 + 0.0522139i
\(703\) −1.10521e11 1.10521e11i −0.452503 0.452503i
\(704\) 2.81266e9i 0.0114505i
\(705\) 0 0
\(706\) 6.59017e10 0.265264
\(707\) 2.47965e11 2.47965e11i 0.992458 0.992458i
\(708\) −6.25755e10 6.25755e10i −0.249041 0.249041i
\(709\) 1.05416e10i 0.0417178i −0.999782 0.0208589i \(-0.993360\pi\)
0.999782 0.0208589i \(-0.00664007\pi\)
\(710\) 0 0
\(711\) 9.22650e10 0.361043
\(712\) 2.82513e11 2.82513e11i 1.09931 1.09931i
\(713\) −2.25440e11 2.25440e11i −0.872315 0.872315i
\(714\) 2.48487e11i 0.956116i
\(715\) 0 0
\(716\) 2.44405e11 0.929945
\(717\) 1.13929e11 1.13929e11i 0.431082 0.431082i
\(718\) 1.29345e11 + 1.29345e11i 0.486690 + 0.486690i
\(719\) 4.26585e10i 0.159621i 0.996810 + 0.0798104i \(0.0254315\pi\)
−0.996810 + 0.0798104i \(0.974569\pi\)
\(720\) 0 0
\(721\) −4.37215e11 −1.61791
\(722\) 1.17787e11 1.17787e11i 0.433460 0.433460i
\(723\) −8.13339e8 8.13339e8i −0.00297659 0.00297659i
\(724\) 4.72347e10i 0.171912i
\(725\) 0 0
\(726\) −1.04152e11 −0.374904
\(727\) −5.57133e10 + 5.57133e10i −0.199444 + 0.199444i −0.799762 0.600318i \(-0.795041\pi\)
0.600318 + 0.799762i \(0.295041\pi\)
\(728\) 2.03444e11 + 2.03444e11i 0.724303 + 0.724303i
\(729\) 1.04604e10i 0.0370370i
\(730\) 0 0
\(731\) 4.98826e11 1.74695
\(732\) 2.53221e9 2.53221e9i 0.00881974 0.00881974i
\(733\) 6.92078e10 + 6.92078e10i 0.239739 + 0.239739i 0.816742 0.577003i \(-0.195778\pi\)
−0.577003 + 0.816742i \(0.695778\pi\)
\(734\) 8.20702e10i 0.282749i
\(735\) 0 0
\(736\) −3.86795e11 −1.31817
\(737\) 4.83484e8 4.83484e8i 0.00163875 0.00163875i
\(738\) −4.53562e10 4.53562e10i −0.152901 0.152901i
\(739\) 5.42380e11i 1.81855i −0.416193 0.909276i \(-0.636636\pi\)
0.416193 0.909276i \(-0.363364\pi\)
\(740\) 0 0
\(741\) 1.43360e11 0.475504
\(742\) 5.03389e10 5.03389e10i 0.166069 0.166069i
\(743\) 1.05763e11 + 1.05763e11i 0.347038 + 0.347038i 0.859005 0.511967i \(-0.171083\pi\)
−0.511967 + 0.859005i \(0.671083\pi\)
\(744\) 1.64286e11i 0.536178i
\(745\) 0 0
\(746\) −2.85860e10 −0.0922992
\(747\) −1.45821e11 + 1.45821e11i −0.468314 + 0.468314i
\(748\) 3.08266e9 + 3.08266e9i 0.00984736 + 0.00984736i
\(749\) 6.27717e11i 1.99451i
\(750\) 0 0
\(751\) 4.27682e11 1.34450 0.672251 0.740323i \(-0.265328\pi\)
0.672251 + 0.740323i \(0.265328\pi\)
\(752\) 3.09786e10 3.09786e10i 0.0968703 0.0968703i
\(753\) 1.19978e11 + 1.19978e11i 0.373182 + 0.373182i
\(754\) 4.21116e10i 0.130292i
\(755\) 0 0
\(756\) −6.14806e10 −0.188214
\(757\) −2.41193e11 + 2.41193e11i −0.734482 + 0.734482i −0.971504 0.237022i \(-0.923829\pi\)
0.237022 + 0.971504i \(0.423829\pi\)
\(758\) −9.53677e10 9.53677e10i −0.288885 0.288885i
\(759\) 4.16969e9i 0.0125643i
\(760\) 0 0
\(761\) −4.31324e11 −1.28607 −0.643035 0.765837i \(-0.722325\pi\)
−0.643035 + 0.765837i \(0.722325\pi\)
\(762\) 4.64509e10 4.64509e10i 0.137776 0.137776i
\(763\) −1.44931e11 1.44931e11i −0.427627 0.427627i
\(764\) 1.68168e11i 0.493595i
\(765\) 0 0
\(766\) −2.70431e11 −0.785491
\(767\) 1.52540e11 1.52540e11i 0.440759 0.440759i
\(768\) 1.48132e11 + 1.48132e11i 0.425798 + 0.425798i
\(769\) 3.88788e11i 1.11175i 0.831265 + 0.555876i \(0.187617\pi\)
−0.831265 + 0.555876i \(0.812383\pi\)
\(770\) 0 0
\(771\) −6.98658e10 −0.197718
\(772\) −2.54077e11 + 2.54077e11i −0.715313 + 0.715313i
\(773\) 2.51696e11 + 2.51696e11i 0.704951 + 0.704951i 0.965469 0.260518i \(-0.0838933\pi\)
−0.260518 + 0.965469i \(0.583893\pi\)