Properties

Label 75.9.f.a.7.2
Level $75$
Weight $9$
Character 75.7
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 7.2
Root \(1.22474 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 75.7
Dual form 75.9.f.a.43.2

$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).

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

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 \(-0.144717\pi\)
−0.439140 + 0.898419i \(0.644717\pi\)
\(3\) 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 0.975301 + 0.220878i \(0.0708922\pi\)
0.220878 + 0.975301i \(0.429108\pi\)
\(8\) 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 \(-0.845442\pi\)
0.466703 + 0.884414i \(0.345442\pi\)
\(14\) 42210.0i 1.09876i
\(15\) 0 0
\(16\) 5744.00 0.0876465
\(17\) 89012.0 + 89012.0i 1.06574 + 1.06574i 0.997681 + 0.0680630i \(0.0216819\pi\)
0.0680630 + 0.997681i \(0.478318\pi\)
\(18\) 16071.1 16071.1i 0.153093 0.153093i
\(19\) 181693.i 1.39420i −0.716976 0.697098i \(-0.754474\pi\)
0.716976 0.697098i \(-0.245526\pi\)
\(20\) 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 \(-0.511630\pi\)
0.999333 + 0.0365300i \(0.0116305\pi\)
\(24\) 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 \(0.0543079\pi\)
−0.985481 + 0.169787i \(0.945692\pi\)
\(30\) 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 \(-0.176291\pi\)
−0.525952 + 0.850514i \(0.676291\pi\)
\(38\) 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 \(-0.553233\pi\)
0.986049 + 0.166458i \(0.0532330\pi\)
\(44\) 34632.0i 0.00923989i
\(45\) 0 0
\(46\) 3.95982e6 0.884391
\(47\) −5.39321e6 5.39321e6i −1.10524 1.10524i −0.993768 0.111471i \(-0.964444\pi\)
−0.111471 0.993768i \(-0.535556\pi\)
\(48\) 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 \(-0.784084\pi\)
0.627486 + 0.778628i \(0.284084\pi\)
\(54\) 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 \(0.176904\pi\)
−0.849500 + 0.527588i \(0.823096\pi\)
\(60\) 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 \(-0.226902\pi\)
−0.653979 + 0.756513i \(0.726902\pi\)
\(68\) 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 0.0168598 0.999858i \(-0.494633\pi\)
0.999858 0.0168598i \(-0.00536689\pi\)
\(74\) 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 \(0.182168\pi\)
−0.840659 + 0.541564i \(0.817832\pi\)
\(80\) 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 −0.621642 + 0.783302i \(0.713534\pi\)
−0.783302 + 0.621642i \(0.786466\pi\)
\(84\) 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 \(-0.726005\pi\)
0.651845 0.758352i \(-0.273995\pi\)
\(90\) 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 \(-0.0584748\pi\)
−0.182672 + 0.983174i \(0.558475\pi\)
\(98\) −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 \(-0.908712\pi\)
0.282875 + 0.959157i \(0.408712\pi\)
\(104\) 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 \(-0.450681\pi\)
−0.988021 + 0.154320i \(0.950681\pi\)
\(108\) −1.07034e7 + 1.07034e7i −0.0786728 + 0.0786728i
\(109\) 5.04631e7i 0.357494i −0.983895 0.178747i \(-0.942796\pi\)
0.983895 0.178747i \(-0.0572043\pi\)
\(110\) 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 \(-0.926238\pi\)
0.229660 + 0.973271i \(0.426238\pi\)
\(114\) 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 \(-0.333654\pi\)
−0.866529 + 0.499126i \(0.833654\pi\)
\(128\) −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 \(-0.217698\pi\)
−0.631836 + 0.775102i \(0.717698\pi\)
\(138\) 1.30944e8 1.30944e8i 0.361051 0.361051i
\(139\) 5.26688e8i 1.41089i −0.708763 0.705446i \(-0.750747\pi\)
0.708763 0.705446i \(-0.249253\pi\)
\(140\) 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 \(0.365639\pi\)
−0.409683 + 0.912228i \(0.634361\pi\)
\(150\) 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 \(-0.0619504\pi\)
−0.193397 + 0.981121i \(0.561950\pi\)
\(158\) −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 \(-0.598814\pi\)
0.952201 + 0.305472i \(0.0988144\pi\)
\(164\) 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 \(-0.169789\pi\)
−0.508470 + 0.861079i \(0.669789\pi\)
\(168\) 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 \(-0.794185\pi\)
0.602467 + 0.798144i \(0.294185\pi\)
\(174\) 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 \(0.297447\pi\)
−0.594255 + 0.804277i \(0.702553\pi\)
\(180\) 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 −0.276197 + 0.961101i \(0.589074\pi\)
−0.961101 + 0.276197i \(0.910926\pi\)
\(194\) 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 \(-0.312816\pi\)
−0.832020 + 0.554745i \(0.812816\pi\)
\(198\) −3.76064e6 + 3.76064e6i −0.00244681 + 0.00244681i
\(199\) 1.06994e9i 0.682258i 0.940017 + 0.341129i \(0.110809\pi\)
−0.940017 + 0.341129i \(0.889191\pi\)
\(200\) 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 \(-0.556693\pi\)
0.984181 + 0.177166i \(0.0566928\pi\)
\(224\) 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 \(-0.135554\pi\)
−0.413099 + 0.910686i \(0.635554\pi\)
\(228\) −8.89220e8 + 8.89220e8i −0.329056 + 0.329056i
\(229\) 2.03118e9i 0.738595i 0.929311 + 0.369297i \(0.120402\pi\)
−0.929311 + 0.369297i \(0.879598\pi\)
\(230\) 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 \(-0.868051\pi\)
0.402760 + 0.915305i \(0.368051\pi\)
\(234\) 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 \(-0.822955\pi\)
0.849266 0.527965i \(-0.177045\pi\)
\(240\) 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 \(-0.304774\pi\)
−0.817741 + 0.575586i \(0.804774\pi\)
\(258\) 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 \(-0.609172\pi\)
0.941758 + 0.336290i \(0.109172\pi\)
\(264\) 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 \(-0.849930\pi\)
0.890906 0.454187i \(-0.150070\pi\)
\(270\) 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 \(-0.338259\pi\)
−0.873659 + 0.486539i \(0.838259\pi\)
\(278\) 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 \(-0.637302\pi\)
0.908403 + 0.418095i \(0.137302\pi\)
\(284\) 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 \(-0.637720\pi\)
0.907854 + 0.419286i \(0.137720\pi\)
\(294\) 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 −0.831420 0.555644i \(-0.812472\pi\)
−0.555644 0.831420i \(-0.687528\pi\)
\(308\) −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 \(-0.679921\pi\)
0.844462 + 0.535616i \(0.179921\pi\)
\(314\) 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 \(-0.294351\pi\)
−0.798459 + 0.602050i \(0.794351\pi\)
\(318\) −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 \(-0.252075\pi\)
−0.711700 + 0.702483i \(0.752075\pi\)
\(338\) −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 −0.990492 0.137569i \(-0.956071\pi\)
−0.137569 0.990492i \(-0.543929\pi\)
\(348\) 1.17543e9 1.17543e9i 0.0801457 0.0801457i
\(349\) 2.63406e10i 1.77552i −0.460310 0.887758i \(-0.652262\pi\)
0.460310 0.887758i \(-0.347738\pi\)
\(350\) 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 \(-0.684541\pi\)
0.836599 + 0.547816i \(0.184541\pi\)
\(354\) 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 \(0.177749\pi\)
−0.848097 + 0.529841i \(0.822251\pi\)
\(360\) 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 \(-0.319842\pi\)
−0.844063 + 0.536245i \(0.819842\pi\)
\(368\) 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 \(-0.772636\pi\)
0.655078 + 0.755561i \(0.272636\pi\)
\(374\) 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 \(-0.898164\pi\)
0.949258 0.314498i \(-0.101836\pi\)
\(380\) 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 \(-0.956696\pi\)
0.135625 + 0.990760i \(0.456696\pi\)
\(384\) 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 \(-0.988205\pi\)
0.999314 0.0370472i \(-0.0117952\pi\)
\(390\) 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 \(-0.0976029\pi\)
−0.301846 + 0.953357i \(0.597603\pi\)
\(398\) −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 \(0.144119\pi\)
−0.899242 + 0.437452i \(0.855881\pi\)
\(410\) 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 \(0.109162\pi\)
−0.941769 + 0.336261i \(0.890838\pi\)
\(420\) 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 \(-0.728828\pi\)
0.752542 + 0.658544i \(0.228828\pi\)
\(434\) 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 \(-0.863076\pi\)
0.908899 0.417016i \(-0.136924\pi\)
\(440\) 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 \(-0.520832\pi\)
0.997859 + 0.0653990i \(0.0208320\pi\)
\(444\) 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 \(-0.868880\pi\)
0.916351 0.400376i \(-0.131120\pi\)
\(450\) 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 \(-0.150810\pi\)
−0.456256 + 0.889849i \(0.650810\pi\)
\(458\) −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 0.355636 0.934625i \(-0.384264\pi\)
0.934625 0.355636i \(-0.115736\pi\)
\(464\) 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 \(-0.419891\pi\)
−0.968498 + 0.249021i \(0.919891\pi\)
\(468\) 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 \(0.125793\pi\)
−0.922923 + 0.384985i \(0.874207\pi\)
\(480\) 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 \(-0.101517\pi\)
−0.313545 + 0.949573i \(0.601517\pi\)
\(488\) 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 \(-0.943844\pi\)
0.984478 0.175506i \(-0.0561560\pi\)
\(500\) 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 \(-0.798031\pi\)
0.592779 + 0.805365i \(0.298031\pi\)
\(504\) 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 \(0.218329\pi\)
−0.773849 + 0.633370i \(0.781671\pi\)
\(510\) 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 \(-0.694989\pi\)
0.818169 + 0.574977i \(0.194989\pi\)
\(524\) 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 \(-0.245469\pi\)
−0.696971 + 0.717100i \(0.745469\pi\)
\(548\) 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 \(-0.299803\pi\)
−0.808653 + 0.588286i \(0.799803\pi\)
\(558\) 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 \(-0.816670\pi\)
0.544629 + 0.838677i \(0.316670\pi\)
\(564\) 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 \(0.100980\pi\)
−0.950101 + 0.311943i \(0.899020\pi\)
\(570\) 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 \(-0.250188\pi\)
−0.707524 + 0.706689i \(0.750188\pi\)
\(578\) −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 \(-0.484020\pi\)
−0.998740 + 0.0501803i \(0.984020\pi\)
\(588\) 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 0.114661 0.993405i \(-0.463422\pi\)
0.993405 0.114661i \(-0.0365782\pi\)
\(594\) 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 \(-0.782515\pi\)
0.775525 0.631317i \(-0.217485\pi\)
\(600\) 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 \(-0.111020\pi\)
−0.341751 + 0.939791i \(0.611020\pi\)
\(608\) −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 \(-0.683589\pi\)
0.838234 + 0.545311i \(0.183589\pi\)
\(614\) 1.81083e11i 1.27410i
\(615\) 0 0
\(616\) −3.99036e9 −0.0277134
\(617\) 1.45292e11 + 1.45292e11i 1.00254 + 1.00254i 0.999997 + 0.00254243i \(0.000809283\pi\)
0.00254243 + 0.999997i \(0.499191\pi\)
\(618\) −3.69924e10 + 3.69924e10i −0.253606 + 0.253606i
\(619\) 1.15947e11i 0.789765i 0.918732 + 0.394882i \(0.129215\pi\)
−0.918732 + 0.394882i \(0.870785\pi\)
\(620\) 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 \(-0.984509\pi\)
0.0486457 + 0.998816i \(0.484509\pi\)
\(644\) 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 \(-0.354135\pi\)
−0.896829 + 0.442378i \(0.854135\pi\)
\(648\) −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 \(-0.754331\pi\)
0.697420 + 0.716662i \(0.254331\pi\)
\(654\) 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 \(0.229602\pi\)
−0.750938 + 0.660373i \(0.770398\pi\)
\(660\) 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 \(-0.957015\pi\)
0.134632 + 0.990896i \(0.457015\pi\)
\(674\) 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 \(-0.0825025\pi\)
−0.256297 + 0.966598i \(0.582502\pi\)
\(678\) −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 0.0730842 0.997326i \(-0.476716\pi\)
0.997326 0.0730842i \(-0.0232842\pi\)
\(684\) 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 \(0.00664007\pi\)
−0.999782 + 0.0208589i \(0.993360\pi\)
\(710\) 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 \(-0.974569\pi\)
0.996810 0.0798104i \(-0.0254315\pi\)
\(720\) 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 \(-0.204959\pi\)
−0.600318 + 0.799762i \(0.704959\pi\)
\(728\) −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 \(-0.804222\pi\)
0.577003 + 0.816742i \(0.304222\pi\)
\(734\) 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 \(0.363364\pi\)
−0.416193 + 0.909276i \(0.636636\pi\)
\(740\) 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 \(-0.828917\pi\)
0.511967 + 0.859005i \(0.328917\pi\)
\(744\) 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 \(-0.0761715\pi\)
−0.237022 + 0.971504i \(0.576171\pi\)
\(758\) 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 \(-0.812383\pi\)
0.831265 0.555876i \(-0.187617\pi\)
\(770\) 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 \(-0.916107\pi\)
0.260518 + 0.965469i \(0.416107\pi\)