Properties

Label 21.30.c.a.20.8
Level $21$
Weight $30$
Character 21.20
Analytic conductor $111.884$
Analytic rank $0$
Dimension $76$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 30 \)
Character orbit: \([\chi]\) \(=\) 21.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(111.883889004\)
Analytic rank: \(0\)
Dimension: \(76\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 20.8
Character \(\chi\) \(=\) 21.20
Dual form 21.30.c.a.20.7

$q$-expansion

\(f(q)\) \(=\) \(q+21897.4i q^{2} +(-3.41396e6 - 7.54819e6i) q^{3} +5.73727e7 q^{4} -2.19660e10 q^{5} +(1.65286e11 - 7.47571e10i) q^{6} +(7.76630e11 + 1.61764e12i) q^{7} +1.30124e13i q^{8} +(-4.53201e13 + 5.15385e13i) q^{9} +O(q^{10})\) \(q+21897.4i q^{2} +(-3.41396e6 - 7.54819e6i) q^{3} +5.73727e7 q^{4} -2.19660e10 q^{5} +(1.65286e11 - 7.47571e10i) q^{6} +(7.76630e11 + 1.61764e12i) q^{7} +1.30124e13i q^{8} +(-4.53201e13 + 5.15385e13i) q^{9} -4.81000e14i q^{10} +2.40340e15i q^{11} +(-1.95868e14 - 4.33060e14i) q^{12} -1.13407e16i q^{13} +(-3.54221e16 + 1.70062e16i) q^{14} +(7.49912e16 + 1.65804e17i) q^{15} -2.54137e17 q^{16} -2.64385e17 q^{17} +(-1.12856e18 - 9.92395e17i) q^{18} +3.62583e18i q^{19} -1.26025e18 q^{20} +(9.55886e18 - 1.13847e19i) q^{21} -5.26284e19 q^{22} +1.89636e19i q^{23} +(9.82203e19 - 4.44239e19i) q^{24} +2.96242e20 q^{25} +2.48332e20 q^{26} +(5.43744e20 + 1.66134e20i) q^{27} +(4.45574e19 + 9.28082e19i) q^{28} +1.75722e21i q^{29} +(-3.63068e21 + 1.64212e21i) q^{30} +5.25929e21i q^{31} +1.42104e21i q^{32} +(1.81414e22 - 8.20513e21i) q^{33} -5.78936e21i q^{34} +(-1.70595e22 - 3.55331e22i) q^{35} +(-2.60014e21 + 2.95690e21i) q^{36} +7.21764e22 q^{37} -7.93963e22 q^{38} +(-8.56016e22 + 3.87166e22i) q^{39} -2.85831e23i q^{40} -6.20335e22 q^{41} +(2.49296e23 + 2.09315e23i) q^{42} +4.32096e23 q^{43} +1.37890e23i q^{44} +(9.95503e23 - 1.13210e24i) q^{45} -4.15254e23 q^{46} +2.59257e24 q^{47} +(8.67614e23 + 1.91828e24i) q^{48} +(-2.01360e24 + 2.51261e24i) q^{49} +6.48695e24i q^{50} +(9.02602e23 + 1.99563e24i) q^{51} -6.50645e23i q^{52} -2.18705e24i q^{53} +(-3.63792e24 + 1.19066e25i) q^{54} -5.27933e25i q^{55} +(-2.10494e25 + 1.01058e25i) q^{56} +(2.73684e25 - 1.23784e25i) q^{57} -3.84786e25 q^{58} -3.87703e25 q^{59} +(4.30245e24 + 9.51262e24i) q^{60} +1.06739e26i q^{61} -1.15165e26 q^{62} +(-1.18568e26 - 3.32852e25i) q^{63} -1.67556e26 q^{64} +2.49110e26i q^{65} +(1.79671e26 + 3.97249e26i) q^{66} -3.98782e26 q^{67} -1.51685e25 q^{68} +(1.43141e26 - 6.47410e25i) q^{69} +(7.78084e26 - 3.73559e26i) q^{70} +9.94824e26i q^{71} +(-6.70640e26 - 5.89724e26i) q^{72} +8.49053e25i q^{73} +1.58048e27i q^{74} +(-1.01136e27 - 2.23610e27i) q^{75} +2.08023e26i q^{76} +(-3.88784e27 + 1.86656e27i) q^{77} +(-8.47796e26 - 1.87446e27i) q^{78} +1.57874e27 q^{79} +5.58238e27 q^{80} +(-6.02305e26 - 4.67146e27i) q^{81} -1.35838e27i q^{82} +3.67441e27 q^{83} +(5.48417e26 - 6.53171e26i) q^{84} +5.80750e27 q^{85} +9.46180e27i q^{86} +(1.32638e28 - 5.99908e27i) q^{87} -3.12741e28 q^{88} -2.12846e28 q^{89} +(2.47900e28 + 2.17990e28i) q^{90} +(1.83451e28 - 8.80751e27i) q^{91} +1.08799e27i q^{92} +(3.96981e28 - 1.79550e28i) q^{93} +5.67706e28i q^{94} -7.96450e28i q^{95} +(1.07263e28 - 4.85136e27i) q^{96} -7.01706e28i q^{97} +(-5.50198e28 - 4.40926e28i) q^{98} +(-1.23868e29 - 1.08923e29i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 76q - 20401094660q^{4} + 1962751543872q^{7} - 89581451225964q^{9} + O(q^{10}) \) \( 76q - 20401094660q^{4} + 1962751543872q^{7} - 89581451225964q^{9} - 116668222909200048q^{15} + 4964525139713333892q^{16} + 1542346202347854996q^{18} + 33840646982361357348q^{21} - 9870996616978150672q^{22} + \)\(32\!\cdots\!12\)\(q^{25} - \)\(31\!\cdots\!64\)\(q^{28} + \)\(51\!\cdots\!44\)\(q^{30} - \)\(85\!\cdots\!52\)\(q^{36} - \)\(17\!\cdots\!76\)\(q^{37} + \)\(38\!\cdots\!96\)\(q^{39} + \)\(80\!\cdots\!56\)\(q^{42} + \)\(23\!\cdots\!20\)\(q^{43} - \)\(10\!\cdots\!00\)\(q^{46} - \)\(51\!\cdots\!40\)\(q^{49} - \)\(96\!\cdots\!00\)\(q^{51} + \)\(20\!\cdots\!48\)\(q^{57} - \)\(40\!\cdots\!72\)\(q^{58} - \)\(16\!\cdots\!96\)\(q^{60} - \)\(36\!\cdots\!84\)\(q^{63} - \)\(16\!\cdots\!28\)\(q^{64} + \)\(48\!\cdots\!64\)\(q^{67} - \)\(65\!\cdots\!20\)\(q^{70} + \)\(19\!\cdots\!24\)\(q^{72} - \)\(80\!\cdots\!36\)\(q^{78} - \)\(11\!\cdots\!52\)\(q^{79} + \)\(18\!\cdots\!32\)\(q^{81} - \)\(72\!\cdots\!52\)\(q^{84} + \)\(14\!\cdots\!48\)\(q^{85} - \)\(16\!\cdots\!84\)\(q^{88} + \)\(44\!\cdots\!40\)\(q^{91} + \)\(22\!\cdots\!32\)\(q^{93} - \)\(23\!\cdots\!24\)\(q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 21897.4i 0.945058i 0.881315 + 0.472529i \(0.156659\pi\)
−0.881315 + 0.472529i \(0.843341\pi\)
\(3\) −3.41396e6 7.54819e6i −0.412098 0.911140i
\(4\) 5.73727e7 0.106865
\(5\) −2.19660e10 −1.60948 −0.804742 0.593625i \(-0.797696\pi\)
−0.804742 + 0.593625i \(0.797696\pi\)
\(6\) 1.65286e11 7.47571e10i 0.861080 0.389457i
\(7\) 7.76630e11 + 1.61764e12i 0.432805 + 0.901487i
\(8\) 1.30124e13i 1.04605i
\(9\) −4.53201e13 + 5.15385e13i −0.660351 + 0.750958i
\(10\) 4.81000e14i 1.52106i
\(11\) 2.40340e15i 1.90824i 0.299426 + 0.954120i \(0.403205\pi\)
−0.299426 + 0.954120i \(0.596795\pi\)
\(12\) −1.95868e14 4.33060e14i −0.0440388 0.0973689i
\(13\) 1.13407e16i 0.798841i −0.916768 0.399421i \(-0.869211\pi\)
0.916768 0.399421i \(-0.130789\pi\)
\(14\) −3.54221e16 + 1.70062e16i −0.851958 + 0.409026i
\(15\) 7.49912e16 + 1.65804e17i 0.663265 + 1.46646i
\(16\) −2.54137e17 −0.881715
\(17\) −2.64385e17 −0.380827 −0.190414 0.981704i \(-0.560983\pi\)
−0.190414 + 0.981704i \(0.560983\pi\)
\(18\) −1.12856e18 9.92395e17i −0.709699 0.624070i
\(19\) 3.62583e18i 1.04107i 0.853840 + 0.520535i \(0.174267\pi\)
−0.853840 + 0.520535i \(0.825733\pi\)
\(20\) −1.26025e18 −0.171997
\(21\) 9.55886e18 1.13847e19i 0.643023 0.765847i
\(22\) −5.26284e19 −1.80340
\(23\) 1.89636e19i 0.341089i 0.985350 + 0.170544i \(0.0545526\pi\)
−0.985350 + 0.170544i \(0.945447\pi\)
\(24\) 9.82203e19 4.44239e19i 0.953099 0.431076i
\(25\) 2.96242e20 1.59044
\(26\) 2.48332e20 0.754951
\(27\) 5.43744e20 + 1.66134e20i 0.956356 + 0.292203i
\(28\) 4.45574e19 + 9.28082e19i 0.0462517 + 0.0963374i
\(29\) 1.75722e21i 1.09662i 0.836276 + 0.548309i \(0.184728\pi\)
−0.836276 + 0.548309i \(0.815272\pi\)
\(30\) −3.63068e21 + 1.64212e21i −1.38589 + 0.626824i
\(31\) 5.25929e21i 1.24791i 0.781462 + 0.623953i \(0.214475\pi\)
−0.781462 + 0.623953i \(0.785525\pi\)
\(32\) 1.42104e21i 0.212780i
\(33\) 1.81414e22 8.20513e21i 1.73867 0.786381i
\(34\) 5.78936e21i 0.359904i
\(35\) −1.70595e22 3.55331e22i −0.696593 1.45093i
\(36\) −2.60014e21 + 2.95690e21i −0.0705683 + 0.0802510i
\(37\) 7.21764e22 1.31665 0.658325 0.752734i \(-0.271265\pi\)
0.658325 + 0.752734i \(0.271265\pi\)
\(38\) −7.93963e22 −0.983871
\(39\) −8.56016e22 + 3.87166e22i −0.727856 + 0.329201i
\(40\) 2.85831e23i 1.68360i
\(41\) −6.20335e22 −0.255423 −0.127712 0.991811i \(-0.540763\pi\)
−0.127712 + 0.991811i \(0.540763\pi\)
\(42\) 2.49296e23 + 2.09315e23i 0.723770 + 0.607694i
\(43\) 4.32096e23 0.891841 0.445921 0.895072i \(-0.352876\pi\)
0.445921 + 0.895072i \(0.352876\pi\)
\(44\) 1.37890e23i 0.203924i
\(45\) 9.95503e23 1.13210e24i 1.06282 1.20865i
\(46\) −4.15254e23 −0.322349
\(47\) 2.59257e24 1.47337 0.736684 0.676237i \(-0.236391\pi\)
0.736684 + 0.676237i \(0.236391\pi\)
\(48\) 8.67614e23 + 1.91828e24i 0.363353 + 0.803365i
\(49\) −2.01360e24 + 2.51261e24i −0.625359 + 0.780337i
\(50\) 6.48695e24i 1.50306i
\(51\) 9.02602e23 + 1.99563e24i 0.156938 + 0.346987i
\(52\) 6.50645e23i 0.0853681i
\(53\) 2.18705e24i 0.217700i −0.994058 0.108850i \(-0.965283\pi\)
0.994058 0.108850i \(-0.0347168\pi\)
\(54\) −3.63792e24 + 1.19066e25i −0.276149 + 0.903812i
\(55\) 5.27933e25i 3.07128i
\(56\) −2.10494e25 + 1.01058e25i −0.943003 + 0.452737i
\(57\) 2.73684e25 1.23784e25i 0.948560 0.429023i
\(58\) −3.84786e25 −1.03637
\(59\) −3.87703e25 −0.814975 −0.407488 0.913211i \(-0.633595\pi\)
−0.407488 + 0.913211i \(0.633595\pi\)
\(60\) 4.30245e24 + 9.51262e24i 0.0708798 + 0.156714i
\(61\) 1.06739e26i 1.38369i 0.722044 + 0.691847i \(0.243203\pi\)
−0.722044 + 0.691847i \(0.756797\pi\)
\(62\) −1.15165e26 −1.17934
\(63\) −1.18568e26 3.32852e25i −0.962782 0.270279i
\(64\) −1.67556e26 −1.08280
\(65\) 2.49110e26i 1.28572i
\(66\) 1.79671e26 + 3.97249e26i 0.743176 + 1.64315i
\(67\) −3.98782e26 −1.32633 −0.663164 0.748474i \(-0.730787\pi\)
−0.663164 + 0.748474i \(0.730787\pi\)
\(68\) −1.51685e25 −0.0406971
\(69\) 1.43141e26 6.47410e25i 0.310779 0.140562i
\(70\) 7.78084e26 3.73559e26i 1.37121 0.658321i
\(71\) 9.94824e26i 1.42725i 0.700527 + 0.713625i \(0.252948\pi\)
−0.700527 + 0.713625i \(0.747052\pi\)
\(72\) −6.70640e26 5.89724e26i −0.785540 0.690761i
\(73\) 8.49053e25i 0.0814242i 0.999171 + 0.0407121i \(0.0129626\pi\)
−0.999171 + 0.0407121i \(0.987037\pi\)
\(74\) 1.58048e27i 1.24431i
\(75\) −1.01136e27 2.23610e27i −0.655417 1.44911i
\(76\) 2.08023e26i 0.111254i
\(77\) −3.88784e27 + 1.86656e27i −1.72025 + 0.825896i
\(78\) −8.47796e26 1.87446e27i −0.311114 0.687866i
\(79\) 1.57874e27 0.481635 0.240817 0.970570i \(-0.422585\pi\)
0.240817 + 0.970570i \(0.422585\pi\)
\(80\) 5.58238e27 1.41911
\(81\) −6.02305e26 4.67146e27i −0.127874 0.991790i
\(82\) 1.35838e27i 0.241390i
\(83\) 3.67441e27 0.547715 0.273858 0.961770i \(-0.411700\pi\)
0.273858 + 0.961770i \(0.411700\pi\)
\(84\) 5.48417e26 6.53171e26i 0.0687166 0.0818422i
\(85\) 5.80750e27 0.612935
\(86\) 9.46180e27i 0.842842i
\(87\) 1.32638e28 5.99908e27i 0.999172 0.451914i
\(88\) −3.12741e28 −1.99612
\(89\) −2.12846e28 −1.15321 −0.576607 0.817022i \(-0.695623\pi\)
−0.576607 + 0.817022i \(0.695623\pi\)
\(90\) 2.47900e28 + 2.17990e28i 1.14225 + 1.00443i
\(91\) 1.83451e28 8.80751e27i 0.720145 0.345743i
\(92\) 1.08799e27i 0.0364504i
\(93\) 3.96981e28 1.79550e28i 1.13702 0.514260i
\(94\) 5.67706e28i 1.39242i
\(95\) 7.96450e28i 1.67558i
\(96\) 1.07263e28 4.85136e27i 0.193872 0.0876862i
\(97\) 7.01706e28i 1.09135i −0.837996 0.545676i \(-0.816273\pi\)
0.837996 0.545676i \(-0.183727\pi\)
\(98\) −5.50198e28 4.40926e28i −0.737464 0.591001i
\(99\) −1.23868e29 1.08923e29i −1.43301 1.26011i
\(100\) 1.69962e28 0.169962
\(101\) −5.37882e28 −0.465615 −0.232808 0.972523i \(-0.574791\pi\)
−0.232808 + 0.972523i \(0.574791\pi\)
\(102\) −4.36993e28 + 1.97647e28i −0.327923 + 0.148316i
\(103\) 1.26950e27i 0.00826978i 0.999991 + 0.00413489i \(0.00131618\pi\)
−0.999991 + 0.00413489i \(0.998684\pi\)
\(104\) 1.47570e29 0.835629
\(105\) −2.09970e29 + 2.50077e29i −1.03493 + 1.23262i
\(106\) 4.78908e28 0.205739
\(107\) 3.07470e28i 0.115276i −0.998338 0.0576379i \(-0.981643\pi\)
0.998338 0.0576379i \(-0.0183569\pi\)
\(108\) 3.11960e28 + 9.53158e27i 0.102201 + 0.0312263i
\(109\) −4.56998e29 −1.30988 −0.654938 0.755683i \(-0.727305\pi\)
−0.654938 + 0.755683i \(0.727305\pi\)
\(110\) 1.15604e30 2.90254
\(111\) −2.46407e29 5.44801e29i −0.542589 1.19965i
\(112\) −1.97370e29 4.11102e29i −0.381611 0.794855i
\(113\) 3.63848e29i 0.618418i −0.950994 0.309209i \(-0.899936\pi\)
0.950994 0.309209i \(-0.100064\pi\)
\(114\) 2.71056e29 + 5.99299e29i 0.405451 + 0.896444i
\(115\) 4.16555e29i 0.548977i
\(116\) 1.00816e29i 0.117190i
\(117\) 5.84482e29 + 5.13961e29i 0.599896 + 0.527515i
\(118\) 8.48970e29i 0.770199i
\(119\) −2.05330e29 4.27680e29i −0.164824 0.343311i
\(120\) −2.15751e30 + 9.75817e29i −1.53400 + 0.693810i
\(121\) −4.19004e30 −2.64138
\(122\) −2.33731e30 −1.30767
\(123\) 2.11780e29 + 4.68241e29i 0.105259 + 0.232726i
\(124\) 3.01739e29i 0.133358i
\(125\) −2.41578e30 −0.950302
\(126\) 7.28860e29 2.59633e30i 0.255430 0.909885i
\(127\) 4.56878e30 1.42773 0.713865 0.700283i \(-0.246943\pi\)
0.713865 + 0.700283i \(0.246943\pi\)
\(128\) 2.90613e30i 0.810533i
\(129\) −1.47516e30 3.26154e30i −0.367526 0.812592i
\(130\) −5.45487e30 −1.21508
\(131\) 3.50396e30 0.698433 0.349217 0.937042i \(-0.386448\pi\)
0.349217 + 0.937042i \(0.386448\pi\)
\(132\) 1.04082e30 4.70750e29i 0.185803 0.0840366i
\(133\) −5.86527e30 + 2.81593e30i −0.938511 + 0.450580i
\(134\) 8.73231e30i 1.25346i
\(135\) −1.19439e31 3.64932e30i −1.53924 0.470297i
\(136\) 3.44029e30i 0.398365i
\(137\) 7.58548e30i 0.789832i 0.918717 + 0.394916i \(0.129226\pi\)
−0.918717 + 0.394916i \(0.870774\pi\)
\(138\) 1.41766e30 + 3.13442e30i 0.132839 + 0.293705i
\(139\) 2.33968e30i 0.197443i 0.995115 + 0.0987214i \(0.0314753\pi\)
−0.995115 + 0.0987214i \(0.968525\pi\)
\(140\) −9.78749e29 2.03863e30i −0.0744414 0.155054i
\(141\) −8.85093e30 1.95692e31i −0.607172 1.34244i
\(142\) −2.17841e31 −1.34884
\(143\) 2.72562e31 1.52438
\(144\) 1.15175e31 1.30978e31i 0.582241 0.662130i
\(145\) 3.85992e31i 1.76499i
\(146\) −1.85921e30 −0.0769506
\(147\) 2.58400e31 + 6.62106e30i 0.968705 + 0.248214i
\(148\) 4.14095e30 0.140704
\(149\) 1.50710e31i 0.464452i 0.972662 + 0.232226i \(0.0746009\pi\)
−0.972662 + 0.232226i \(0.925399\pi\)
\(150\) 4.89648e31 2.21462e31i 1.36950 0.619407i
\(151\) −2.61445e31 −0.664070 −0.332035 0.943267i \(-0.607735\pi\)
−0.332035 + 0.943267i \(0.607735\pi\)
\(152\) −4.71808e31 −1.08901
\(153\) 1.19820e31 1.36260e31i 0.251479 0.285985i
\(154\) −4.08728e31 8.51337e31i −0.780520 1.62574i
\(155\) 1.15526e32i 2.00849i
\(156\) −4.91120e30 + 2.22128e30i −0.0777823 + 0.0351800i
\(157\) 1.20234e32i 1.73573i 0.496796 + 0.867867i \(0.334510\pi\)
−0.496796 + 0.867867i \(0.665490\pi\)
\(158\) 3.45704e31i 0.455173i
\(159\) −1.65083e31 + 7.46650e30i −0.198355 + 0.0897137i
\(160\) 3.12145e31i 0.342466i
\(161\) −3.06762e31 + 1.47277e31i −0.307487 + 0.147625i
\(162\) 1.02293e32 1.31889e31i 0.937300 0.120849i
\(163\) 2.51953e31 0.211154 0.105577 0.994411i \(-0.466331\pi\)
0.105577 + 0.994411i \(0.466331\pi\)
\(164\) −3.55903e30 −0.0272958
\(165\) −3.98494e32 + 1.80234e32i −2.79837 + 1.26567i
\(166\) 8.04602e31i 0.517623i
\(167\) −4.27606e31 −0.252148 −0.126074 0.992021i \(-0.540238\pi\)
−0.126074 + 0.992021i \(0.540238\pi\)
\(168\) 1.48143e32 + 1.24384e32i 0.801116 + 0.672635i
\(169\) 7.29271e31 0.361853
\(170\) 1.27169e32i 0.579260i
\(171\) −1.86870e32 1.64323e32i −0.781799 0.687471i
\(172\) 2.47905e31 0.0953066
\(173\) −2.31530e32 −0.818350 −0.409175 0.912456i \(-0.634183\pi\)
−0.409175 + 0.912456i \(0.634183\pi\)
\(174\) 1.31365e32 + 2.90444e32i 0.427085 + 0.944275i
\(175\) 2.30071e32 + 4.79213e32i 0.688351 + 1.43376i
\(176\) 6.10794e32i 1.68252i
\(177\) 1.32360e32 + 2.92645e32i 0.335850 + 0.742556i
\(178\) 4.66078e32i 1.08985i
\(179\) 1.69293e32i 0.364982i 0.983208 + 0.182491i \(0.0584160\pi\)
−0.983208 + 0.182491i \(0.941584\pi\)
\(180\) 5.71147e31 6.49514e31i 0.113579 0.129163i
\(181\) 2.15005e32i 0.394557i 0.980347 + 0.197279i \(0.0632104\pi\)
−0.980347 + 0.197279i \(0.936790\pi\)
\(182\) 1.92862e32 + 4.01711e32i 0.326747 + 0.680579i
\(183\) 8.05685e32 3.64402e32i 1.26074 0.570217i
\(184\) −2.46762e32 −0.356796
\(185\) −1.58543e33 −2.11913
\(186\) 3.93169e32 + 8.69287e32i 0.486006 + 1.07455i
\(187\) 6.35425e32i 0.726709i
\(188\) 1.48743e32 0.157451
\(189\) 1.53542e32 + 1.00861e33i 0.150498 + 0.988610i
\(190\) 1.74402e33 1.58353
\(191\) 2.23371e32i 0.187950i −0.995575 0.0939750i \(-0.970043\pi\)
0.995575 0.0939750i \(-0.0299574\pi\)
\(192\) 5.72029e32 + 1.26474e33i 0.446221 + 0.986586i
\(193\) 1.36259e33 0.985793 0.492897 0.870088i \(-0.335938\pi\)
0.492897 + 0.870088i \(0.335938\pi\)
\(194\) 1.53656e33 1.03139
\(195\) 1.88033e33 8.50451e32i 1.17147 0.529844i
\(196\) −1.15525e32 + 1.44155e32i −0.0668290 + 0.0833907i
\(197\) 3.00287e33i 1.61353i −0.590875 0.806763i \(-0.701217\pi\)
0.590875 0.806763i \(-0.298783\pi\)
\(198\) 2.38512e33 2.71239e33i 1.19087 1.35427i
\(199\) 2.91566e33i 1.35322i 0.736343 + 0.676608i \(0.236551\pi\)
−0.736343 + 0.676608i \(0.763449\pi\)
\(200\) 3.85483e33i 1.66368i
\(201\) 1.36143e33 + 3.01008e33i 0.546577 + 1.20847i
\(202\) 1.17782e33i 0.440033i
\(203\) −2.84255e33 + 1.36471e33i −0.988587 + 0.474622i
\(204\) 5.17847e31 + 1.14495e32i 0.0167712 + 0.0370807i
\(205\) 1.36263e33 0.411100
\(206\) −2.77989e31 −0.00781543
\(207\) −9.77356e32 8.59432e32i −0.256143 0.225238i
\(208\) 2.88209e33i 0.704350i
\(209\) −8.71432e33 −1.98661
\(210\) −5.47605e33 4.59781e33i −1.16490 0.978074i
\(211\) 3.24786e33 0.644913 0.322457 0.946584i \(-0.395491\pi\)
0.322457 + 0.946584i \(0.395491\pi\)
\(212\) 1.25477e32i 0.0232645i
\(213\) 7.50913e33 3.39629e33i 1.30042 0.588167i
\(214\) 6.73281e32 0.108942
\(215\) −9.49144e33 −1.43540
\(216\) −2.16181e33 + 7.07542e33i −0.305660 + 1.00040i
\(217\) −8.50762e33 + 4.08452e33i −1.12497 + 0.540101i
\(218\) 1.00071e34i 1.23791i
\(219\) 6.40882e32 2.89864e32i 0.0741888 0.0335547i
\(220\) 3.02889e33i 0.328212i
\(221\) 2.99831e33i 0.304221i
\(222\) 1.19298e34 5.39569e33i 1.13374 0.512778i
\(223\) 3.14572e33i 0.280091i −0.990145 0.140045i \(-0.955275\pi\)
0.990145 0.140045i \(-0.0447249\pi\)
\(224\) −2.29872e33 + 1.10362e33i −0.191818 + 0.0920923i
\(225\) −1.34257e34 + 1.52679e34i −1.05025 + 1.19435i
\(226\) 7.96734e33 0.584441
\(227\) 1.49046e34 1.02552 0.512761 0.858531i \(-0.328623\pi\)
0.512761 + 0.858531i \(0.328623\pi\)
\(228\) 1.57020e33 7.10184e32i 0.101368 0.0458475i
\(229\) 1.96703e34i 1.19178i −0.803065 0.595891i \(-0.796799\pi\)
0.803065 0.595891i \(-0.203201\pi\)
\(230\) 9.12150e33 0.518815
\(231\) 2.73620e34 + 2.29738e34i 1.46142 + 1.22704i
\(232\) −2.28657e34 −1.14712
\(233\) 1.34458e34i 0.633763i 0.948465 + 0.316882i \(0.102636\pi\)
−0.948465 + 0.316882i \(0.897364\pi\)
\(234\) −1.12544e34 + 1.27987e34i −0.498533 + 0.566936i
\(235\) −5.69484e34 −2.37136
\(236\) −2.22435e33 −0.0870923
\(237\) −5.38976e33 1.19166e34i −0.198481 0.438836i
\(238\) 9.36509e33 4.49619e33i 0.324449 0.155768i
\(239\) 5.26810e31i 0.00171745i 1.00000 0.000858726i \(0.000273341\pi\)
−1.00000 0.000858726i \(0.999727\pi\)
\(240\) −1.90580e34 4.21369e34i −0.584811 1.29300i
\(241\) 2.27777e34i 0.658057i −0.944320 0.329028i \(-0.893279\pi\)
0.944320 0.329028i \(-0.106721\pi\)
\(242\) 9.17512e34i 2.49625i
\(243\) −3.32048e34 + 2.04945e34i −0.850963 + 0.525226i
\(244\) 6.12389e33i 0.147868i
\(245\) 4.42308e34 5.51921e34i 1.00651 1.25594i
\(246\) −1.02533e34 + 4.63744e33i −0.219940 + 0.0994763i
\(247\) 4.11193e34 0.831649
\(248\) −6.84360e34 −1.30538
\(249\) −1.25443e34 2.77351e34i −0.225712 0.499045i
\(250\) 5.28994e34i 0.898091i
\(251\) 3.42737e34 0.549151 0.274575 0.961566i \(-0.411463\pi\)
0.274575 + 0.961566i \(0.411463\pi\)
\(252\) −6.80254e33 1.90966e33i −0.102888 0.0288834i
\(253\) −4.55772e34 −0.650879
\(254\) 1.00045e35i 1.34929i
\(255\) −1.98266e34 4.38361e34i −0.252589 0.558470i
\(256\) −2.63190e34 −0.316803
\(257\) 5.24054e34 0.596137 0.298068 0.954545i \(-0.403658\pi\)
0.298068 + 0.954545i \(0.403658\pi\)
\(258\) 7.14195e34 3.23022e34i 0.767947 0.347333i
\(259\) 5.60544e34 + 1.16755e35i 0.569853 + 1.18694i
\(260\) 1.42921e34i 0.137399i
\(261\) −9.05645e34 7.96374e34i −0.823513 0.724152i
\(262\) 7.67277e34i 0.660060i
\(263\) 3.50044e34i 0.284947i −0.989799 0.142474i \(-0.954494\pi\)
0.989799 0.142474i \(-0.0455056\pi\)
\(264\) 1.06769e35 + 2.36063e35i 0.822596 + 1.81874i
\(265\) 4.80408e34i 0.350385i
\(266\) −6.16616e34 1.28434e35i −0.425825 0.886948i
\(267\) 7.26647e34 + 1.60660e35i 0.475237 + 1.05074i
\(268\) −2.28792e34 −0.141738
\(269\) −3.67604e34 −0.215761 −0.107880 0.994164i \(-0.534406\pi\)
−0.107880 + 0.994164i \(0.534406\pi\)
\(270\) 7.99107e34 2.61541e35i 0.444458 1.45467i
\(271\) 3.33205e35i 1.75653i −0.478171 0.878267i \(-0.658700\pi\)
0.478171 0.878267i \(-0.341300\pi\)
\(272\) 6.71901e34 0.335781
\(273\) −1.29110e35 1.08404e35i −0.611790 0.513673i
\(274\) −1.66103e35 −0.746437
\(275\) 7.11990e35i 3.03494i
\(276\) 8.21238e33 3.71437e33i 0.0332114 0.0150211i
\(277\) 3.53976e35 1.35837 0.679183 0.733969i \(-0.262334\pi\)
0.679183 + 0.733969i \(0.262334\pi\)
\(278\) −5.12330e34 −0.186595
\(279\) −2.71056e35 2.38351e35i −0.937125 0.824056i
\(280\) 4.62371e35 2.21985e35i 1.51775 0.728673i
\(281\) 3.54541e35i 1.10516i 0.833460 + 0.552579i \(0.186356\pi\)
−0.833460 + 0.552579i \(0.813644\pi\)
\(282\) 4.28516e35 1.93813e35i 1.26869 0.573813i
\(283\) 4.63712e34i 0.130420i −0.997872 0.0652101i \(-0.979228\pi\)
0.997872 0.0652101i \(-0.0207717\pi\)
\(284\) 5.70757e34i 0.152523i
\(285\) −6.01176e35 + 2.71905e35i −1.52669 + 0.690505i
\(286\) 5.96842e35i 1.44063i
\(287\) −4.81771e34 1.00348e35i −0.110549 0.230261i
\(288\) −7.32381e34 6.44015e34i −0.159789 0.140509i
\(289\) −4.12069e35 −0.854971
\(290\) 8.45223e35 1.66802
\(291\) −5.29662e35 + 2.39560e35i −0.994375 + 0.449744i
\(292\) 4.87125e33i 0.00870139i
\(293\) 3.34930e35 0.569342 0.284671 0.958625i \(-0.408116\pi\)
0.284671 + 0.958625i \(0.408116\pi\)
\(294\) −1.44984e35 + 5.65831e35i −0.234577 + 0.915483i
\(295\) 8.51629e35 1.31169
\(296\) 9.39189e35i 1.37728i
\(297\) −3.99288e35 + 1.30684e36i −0.557594 + 1.82496i
\(298\) −3.30016e35 −0.438934
\(299\) 2.15060e35 0.272476
\(300\) −5.80244e34 1.28291e35i −0.0700411 0.154859i
\(301\) 3.35579e35 + 6.98975e35i 0.385994 + 0.803984i
\(302\) 5.72497e35i 0.627585i
\(303\) 1.83631e35 + 4.06004e35i 0.191879 + 0.424240i
\(304\) 9.21457e35i 0.917927i
\(305\) 2.34463e36i 2.22703i
\(306\) 2.98375e35 + 2.62375e35i 0.270273 + 0.237663i
\(307\) 8.52543e34i 0.0736563i 0.999322 + 0.0368281i \(0.0117254\pi\)
−0.999322 + 0.0368281i \(0.988275\pi\)
\(308\) −2.23056e35 + 1.07089e35i −0.183835 + 0.0882593i
\(309\) 9.58246e33 4.33404e33i 0.00753493 0.00340796i
\(310\) 2.52972e36 1.89814
\(311\) −8.00785e35 −0.573443 −0.286722 0.958014i \(-0.592565\pi\)
−0.286722 + 0.958014i \(0.592565\pi\)
\(312\) −5.03797e35 1.11388e36i −0.344361 0.761375i
\(313\) 3.66167e35i 0.238938i −0.992838 0.119469i \(-0.961881\pi\)
0.992838 0.119469i \(-0.0381193\pi\)
\(314\) −2.63282e36 −1.64037
\(315\) 2.60446e36 + 7.31143e35i 1.54958 + 0.435010i
\(316\) 9.05765e34 0.0514699
\(317\) 1.30822e36i 0.710102i −0.934847 0.355051i \(-0.884463\pi\)
0.934847 0.355051i \(-0.115537\pi\)
\(318\) −1.63497e35 3.61489e35i −0.0847847 0.187457i
\(319\) −4.22331e36 −2.09261
\(320\) 3.68054e36 1.74276
\(321\) −2.32084e35 + 1.04969e35i −0.105032 + 0.0475049i
\(322\) −3.22499e35 6.71731e35i −0.139514 0.290593i
\(323\) 9.58615e35i 0.396468i
\(324\) −3.45559e34 2.68014e35i −0.0136653 0.105988i
\(325\) 3.35959e36i 1.27051i
\(326\) 5.51712e35i 0.199553i
\(327\) 1.56017e36 + 3.44951e36i 0.539797 + 1.19348i
\(328\) 8.07206e35i 0.267186i
\(329\) 2.01347e36 + 4.19383e36i 0.637681 + 1.32822i
\(330\) −3.94667e36 8.72600e36i −1.19613 2.64462i
\(331\) 4.26098e36 1.23596 0.617978 0.786195i \(-0.287952\pi\)
0.617978 + 0.786195i \(0.287952\pi\)
\(332\) 2.10811e35 0.0585316
\(333\) −3.27104e36 + 3.71986e36i −0.869450 + 0.988748i
\(334\) 9.36348e35i 0.238294i
\(335\) 8.75966e36 2.13470
\(336\) −2.42926e36 + 2.89328e36i −0.566963 + 0.675259i
\(337\) −1.86913e36 −0.417835 −0.208918 0.977933i \(-0.566994\pi\)
−0.208918 + 0.977933i \(0.566994\pi\)
\(338\) 1.59692e36i 0.341972i
\(339\) −2.74639e36 + 1.24216e36i −0.563466 + 0.254849i
\(340\) 3.33192e35 0.0655013
\(341\) −1.26402e37 −2.38130
\(342\) 3.59825e36 4.09197e36i 0.649700 0.738846i
\(343\) −5.62832e36 1.30590e36i −0.974123 0.226019i
\(344\) 5.62261e36i 0.932912i
\(345\) −3.14424e36 + 1.42210e36i −0.500194 + 0.226232i
\(346\) 5.06992e36i 0.773388i
\(347\) 9.08226e36i 1.32867i −0.747436 0.664334i \(-0.768715\pi\)
0.747436 0.664334i \(-0.231285\pi\)
\(348\) 7.60982e35 3.44183e35i 0.106776 0.0482938i
\(349\) 3.64732e36i 0.490914i 0.969407 + 0.245457i \(0.0789381\pi\)
−0.969407 + 0.245457i \(0.921062\pi\)
\(350\) −1.04935e37 + 5.03796e36i −1.35499 + 0.650531i
\(351\) 1.88408e36 6.16642e36i 0.233424 0.763977i
\(352\) −3.41532e36 −0.406035
\(353\) −1.22050e37 −1.39253 −0.696263 0.717787i \(-0.745155\pi\)
−0.696263 + 0.717787i \(0.745155\pi\)
\(354\) −6.40819e36 + 2.89835e36i −0.701759 + 0.317398i
\(355\) 2.18523e37i 2.29714i
\(356\) −1.22115e36 −0.123238
\(357\) −2.52722e36 + 3.00995e36i −0.244881 + 0.291655i
\(358\) −3.70709e36 −0.344929
\(359\) 1.78777e37i 1.59751i −0.601657 0.798754i \(-0.705493\pi\)
0.601657 0.798754i \(-0.294507\pi\)
\(360\) 1.47313e37 + 1.29539e37i 1.26431 + 1.11177i
\(361\) −1.01679e36 −0.0838257
\(362\) −4.70807e36 −0.372880
\(363\) 1.43046e37 + 3.16272e37i 1.08851 + 2.40666i
\(364\) 1.05251e36 5.05311e35i 0.0769583 0.0369478i
\(365\) 1.86503e36i 0.131051i
\(366\) 7.97948e36 + 1.76425e37i 0.538888 + 1.19147i
\(367\) 5.42324e36i 0.352047i 0.984386 + 0.176024i \(0.0563235\pi\)
−0.984386 + 0.176024i \(0.943676\pi\)
\(368\) 4.81935e36i 0.300743i
\(369\) 2.81137e36 3.19712e36i 0.168669 0.191812i
\(370\) 3.47169e37i 2.00270i
\(371\) 3.53785e36 1.69853e36i 0.196254 0.0942217i
\(372\) 2.27759e36 1.03013e36i 0.121507 0.0549564i
\(373\) −3.01156e36 −0.154530 −0.0772651 0.997011i \(-0.524619\pi\)
−0.0772651 + 0.997011i \(0.524619\pi\)
\(374\) 1.39142e37 0.686783
\(375\) 8.24737e36 + 1.82348e37i 0.391618 + 0.865858i
\(376\) 3.37356e37i 1.54122i
\(377\) 1.99281e37 0.876023
\(378\) −2.20859e37 + 3.36219e36i −0.934294 + 0.142230i
\(379\) 4.09990e37 1.66919 0.834594 0.550866i \(-0.185702\pi\)
0.834594 + 0.550866i \(0.185702\pi\)
\(380\) 4.56945e36i 0.179061i
\(381\) −1.55976e37 3.44860e37i −0.588365 1.30086i
\(382\) 4.89125e36 0.177624
\(383\) 3.77532e37 1.31999 0.659996 0.751269i \(-0.270558\pi\)
0.659996 + 0.751269i \(0.270558\pi\)
\(384\) −2.19361e37 + 9.92143e36i −0.738509 + 0.334019i
\(385\) 8.54004e37 4.10008e37i 2.76872 1.32927i
\(386\) 2.98374e37i 0.931632i
\(387\) −1.95826e37 + 2.22696e37i −0.588928 + 0.669735i
\(388\) 4.02588e36i 0.116627i
\(389\) 5.53900e37i 1.54583i −0.634509 0.772915i \(-0.718798\pi\)
0.634509 0.772915i \(-0.281202\pi\)
\(390\) 1.86227e37 + 4.11744e37i 0.500733 + 1.10711i
\(391\) 5.01370e36i 0.129896i
\(392\) −3.26952e37 2.62018e37i −0.816273 0.654158i
\(393\) −1.19624e37 2.64485e37i −0.287823 0.636370i
\(394\) 6.57552e37 1.52488
\(395\) −3.46787e37 −0.775183
\(396\) −7.10663e36 6.24918e36i −0.153138 0.134661i
\(397\) 5.20498e37i 1.08133i 0.841239 + 0.540663i \(0.181827\pi\)
−0.841239 + 0.540663i \(0.818173\pi\)
\(398\) −6.38455e37 −1.27887
\(399\) 4.12790e37 + 3.46588e37i 0.797300 + 0.669431i
\(400\) −7.52862e37 −1.40231
\(401\) 6.29881e37i 1.13153i 0.824567 + 0.565764i \(0.191419\pi\)
−0.824567 + 0.565764i \(0.808581\pi\)
\(402\) −6.59131e37 + 2.98118e37i −1.14207 + 0.516547i
\(403\) 5.96439e37 0.996879
\(404\) −3.08597e36 −0.0497579
\(405\) 1.32303e37 + 1.02613e38i 0.205812 + 1.59627i
\(406\) −2.98837e37 6.22445e37i −0.448545 0.934272i
\(407\) 1.73469e38i 2.51248i
\(408\) −2.59680e37 + 1.17450e37i −0.362966 + 0.164165i
\(409\) 3.88534e37i 0.524133i −0.965050 0.262066i \(-0.915596\pi\)
0.965050 0.262066i \(-0.0844040\pi\)
\(410\) 2.98381e37i 0.388513i
\(411\) 5.72566e37 2.58965e37i 0.719647 0.325488i
\(412\) 7.28348e34i 0.000883750i
\(413\) −3.01101e37 6.27162e37i −0.352726 0.734690i
\(414\) 1.88194e37 2.14016e37i 0.212863 0.242070i
\(415\) −8.07122e37 −0.881539
\(416\) 1.61155e37 0.169977
\(417\) 1.76603e37 7.98757e36i 0.179898 0.0813658i
\(418\) 1.90821e38i 1.87746i
\(419\) 1.74807e38 1.66133 0.830664 0.556774i \(-0.187961\pi\)
0.830664 + 0.556774i \(0.187961\pi\)
\(420\) −1.20466e37 + 1.43476e37i −0.110598 + 0.131724i
\(421\) 1.75218e38 1.55413 0.777067 0.629418i \(-0.216706\pi\)
0.777067 + 0.629418i \(0.216706\pi\)
\(422\) 7.11198e37i 0.609480i
\(423\) −1.17495e38 + 1.33617e38i −0.972939 + 1.10644i
\(424\) 2.84588e37 0.227726
\(425\) −7.83221e37 −0.605683
\(426\) 7.43701e37 + 1.64431e38i 0.555852 + 1.22898i
\(427\) −1.72665e38 + 8.28966e37i −1.24738 + 0.598870i
\(428\) 1.76404e36i 0.0123189i
\(429\) −9.30517e37 2.05735e38i −0.628194 1.38892i
\(430\) 2.07838e38i 1.35654i
\(431\) 2.27636e38i 1.43655i 0.695759 + 0.718275i \(0.255068\pi\)
−0.695759 + 0.718275i \(0.744932\pi\)
\(432\) −1.38185e38 4.22209e37i −0.843234 0.257640i
\(433\) 2.67289e38i 1.57727i −0.614861 0.788636i \(-0.710788\pi\)
0.614861 0.788636i \(-0.289212\pi\)
\(434\) −8.94405e37 1.86295e38i −0.510427 1.06316i
\(435\) −2.91354e38 + 1.31776e38i −1.60815 + 0.727348i
\(436\) −2.62192e37 −0.139980
\(437\) −6.87587e37 −0.355097
\(438\) 6.34727e36 + 1.40337e37i 0.0317112 + 0.0701127i
\(439\) 1.23795e38i 0.598368i 0.954195 + 0.299184i \(0.0967144\pi\)
−0.954195 + 0.299184i \(0.903286\pi\)
\(440\) 6.86968e38 3.21272
\(441\) −3.82398e37 2.17650e38i −0.173044 0.984914i
\(442\) −6.56553e37 −0.287506
\(443\) 2.63871e38i 1.11825i −0.829084 0.559124i \(-0.811138\pi\)
0.829084 0.559124i \(-0.188862\pi\)
\(444\) −1.41371e37 3.12567e37i −0.0579837 0.128201i
\(445\) 4.67537e38 1.85608
\(446\) 6.88832e37 0.264702
\(447\) 1.13759e38 5.14518e37i 0.423180 0.191400i
\(448\) −1.30129e38 2.71045e38i −0.468644 0.976134i
\(449\) 3.98673e38i 1.39010i −0.718963 0.695048i \(-0.755383\pi\)
0.718963 0.695048i \(-0.244617\pi\)
\(450\) −3.34328e38 2.93989e38i −1.12873 0.992545i
\(451\) 1.49092e38i 0.487409i
\(452\) 2.08749e37i 0.0660873i
\(453\) 8.92562e37 + 1.97344e38i 0.273662 + 0.605061i
\(454\) 3.26372e38i 0.969178i
\(455\) −4.02969e38 + 1.93466e38i −1.15906 + 0.556467i
\(456\) 1.61073e38 + 3.56130e38i 0.448780 + 0.992242i
\(457\) −2.56102e38 −0.691239 −0.345620 0.938375i \(-0.612331\pi\)
−0.345620 + 0.938375i \(0.612331\pi\)
\(458\) 4.30730e38 1.12630
\(459\) −1.43758e38 4.39235e37i −0.364207 0.111279i
\(460\) 2.38989e37i 0.0586664i
\(461\) −4.38167e37 −0.104226 −0.0521130 0.998641i \(-0.516596\pi\)
−0.0521130 + 0.998641i \(0.516596\pi\)
\(462\) −5.03067e38 + 5.99159e38i −1.15963 + 1.38113i
\(463\) 1.24196e38 0.277448 0.138724 0.990331i \(-0.455700\pi\)
0.138724 + 0.990331i \(0.455700\pi\)
\(464\) 4.46575e38i 0.966904i
\(465\) −8.72010e38 + 3.94400e38i −1.83001 + 0.827693i
\(466\) −2.94430e38 −0.598943
\(467\) 4.25993e38 0.840054 0.420027 0.907512i \(-0.362021\pi\)
0.420027 + 0.907512i \(0.362021\pi\)
\(468\) 3.35333e37 + 2.94873e37i 0.0641078 + 0.0563729i
\(469\) −3.09706e38 6.45085e38i −0.574042 1.19567i
\(470\) 1.24703e39i 2.24108i
\(471\) 9.07551e38 4.10475e38i 1.58150 0.715293i
\(472\) 5.04495e38i 0.852506i
\(473\) 1.03850e39i 1.70185i
\(474\) 2.60944e38 1.18022e38i 0.414726 0.187576i
\(475\) 1.07412e39i 1.65576i
\(476\) −1.17803e37 2.45371e37i −0.0176139 0.0366879i
\(477\) 1.12717e38 + 9.91173e37i 0.163483 + 0.143758i
\(478\) −1.15358e36 −0.00162309
\(479\) −9.45275e38 −1.29031 −0.645153 0.764053i \(-0.723207\pi\)
−0.645153 + 0.764053i \(0.723207\pi\)
\(480\) −2.35613e38 + 1.06565e38i −0.312034 + 0.141129i
\(481\) 8.18529e38i 1.05179i
\(482\) 4.98774e38 0.621902
\(483\) 2.15895e38 + 1.81270e38i 0.261222 + 0.219328i
\(484\) −2.40394e38 −0.282271
\(485\) 1.54137e39i 1.75652i
\(486\) −4.48777e38 7.27101e38i −0.496369 0.804209i
\(487\) −2.50491e38 −0.268920 −0.134460 0.990919i \(-0.542930\pi\)
−0.134460 + 0.990919i \(0.542930\pi\)
\(488\) −1.38893e39 −1.44741
\(489\) −8.60157e37 1.90179e38i −0.0870161 0.192391i
\(490\) 1.20857e39 + 9.68541e38i 1.18694 + 0.951206i
\(491\) 7.94407e38i 0.757463i 0.925507 + 0.378732i \(0.123640\pi\)
−0.925507 + 0.378732i \(0.876360\pi\)
\(492\) 1.21504e37 + 2.68643e37i 0.0112485 + 0.0248703i
\(493\) 4.64583e38i 0.417622i
\(494\) 9.00408e38i 0.785957i
\(495\) 2.72089e39 + 2.39260e39i 2.30640 + 2.02812i
\(496\) 1.33658e39i 1.10030i
\(497\) −1.60927e39 + 7.72610e38i −1.28665 + 0.617722i
\(498\) 6.07329e38 2.74688e38i 0.471627 0.213311i
\(499\) 1.96619e39 1.48309 0.741546 0.670902i \(-0.234093\pi\)
0.741546 + 0.670902i \(0.234093\pi\)
\(500\) −1.38600e38 −0.101554
\(501\) 1.45983e38 + 3.22765e38i 0.103910 + 0.229742i
\(502\) 7.50506e38i 0.518980i
\(503\) 1.11150e39 0.746748 0.373374 0.927681i \(-0.378201\pi\)
0.373374 + 0.927681i \(0.378201\pi\)
\(504\) 4.33120e38 1.54285e39i 0.282726 1.00712i
\(505\) 1.18151e39 0.749400
\(506\) 9.98024e38i 0.615118i
\(507\) −2.48970e38 5.50468e38i −0.149119 0.329698i
\(508\) 2.62123e38 0.152574
\(509\) −8.58590e38 −0.485711 −0.242856 0.970062i \(-0.578084\pi\)
−0.242856 + 0.970062i \(0.578084\pi\)
\(510\) 9.59899e38 4.34152e38i 0.527786 0.238712i
\(511\) −1.37346e38 + 6.59400e37i −0.0734029 + 0.0352408i
\(512\) 2.13654e39i 1.10993i
\(513\) −6.02375e38 + 1.97152e39i −0.304204 + 0.995633i
\(514\) 1.14754e39i 0.563384i
\(515\) 2.78860e37i 0.0133101i
\(516\) −8.46338e37 1.87124e38i −0.0392756 0.0868376i
\(517\) 6.23099e39i 2.81154i
\(518\) −2.55664e39 + 1.22745e39i −1.12173 + 0.538544i
\(519\) 7.90435e38 + 1.74763e39i 0.337240 + 0.745631i
\(520\) −3.24152e39 −1.34493
\(521\) 1.57313e39 0.634773 0.317386 0.948296i \(-0.397195\pi\)
0.317386 + 0.948296i \(0.397195\pi\)
\(522\) 1.74386e39 1.98313e39i 0.684366 0.778268i
\(523\) 6.19575e38i 0.236494i −0.992984 0.118247i \(-0.962273\pi\)
0.992984 0.118247i \(-0.0377274\pi\)
\(524\) 2.01031e38 0.0746380
\(525\) 2.83174e39 3.37263e39i 1.02269 1.21803i
\(526\) 7.66507e38 0.269292
\(527\) 1.39048e39i 0.475237i
\(528\) −4.61039e39 + 2.08523e39i −1.53301 + 0.693364i
\(529\) 2.73144e39 0.883659
\(530\) −1.05197e39 −0.331134
\(531\) 1.75707e39 1.99816e39i 0.538169 0.612012i
\(532\) −3.36506e38 + 1.61557e38i −0.100294 + 0.0481513i
\(533\) 7.03502e38i 0.204043i
\(534\) −3.51804e39 + 1.59117e39i −0.993009 + 0.449126i
\(535\) 6.75390e38i 0.185535i
\(536\) 5.18912e39i 1.38741i
\(537\) 1.27786e39 5.77961e38i 0.332549 0.150408i
\(538\) 8.04959e38i 0.203906i
\(539\) −6.03882e39 4.83949e39i −1.48907 1.19333i
\(540\) −6.85253e38 2.09371e38i −0.164491 0.0502582i
\(541\) 3.88333e39 0.907495 0.453748 0.891130i \(-0.350087\pi\)
0.453748 + 0.891130i \(0.350087\pi\)
\(542\) 7.29633e39 1.66003
\(543\) 1.62290e39 7.34020e38i 0.359497 0.162596i
\(544\) 3.75701e38i 0.0810324i
\(545\) 1.00384e40 2.10822
\(546\) 2.37377e39 2.82719e39i 0.485451 0.578177i
\(547\) −2.41811e39 −0.481570 −0.240785 0.970578i \(-0.577405\pi\)
−0.240785 + 0.970578i \(0.577405\pi\)
\(548\) 4.35199e38i 0.0844053i
\(549\) −5.50116e39 4.83741e39i −1.03909 0.913723i
\(550\) −1.55908e40 −2.86819
\(551\) −6.37137e39 −1.14166
\(552\) 8.42437e38 + 1.86261e39i 0.147035 + 0.325091i
\(553\) 1.22610e39 + 2.55383e39i 0.208454 + 0.434188i
\(554\) 7.75117e39i 1.28374i
\(555\) 5.41260e39 + 1.19671e40i 0.873288 + 1.93082i
\(556\) 1.34234e38i 0.0210997i
\(557\) 7.29364e39i 1.11698i −0.829513 0.558488i \(-0.811382\pi\)
0.829513 0.558488i \(-0.188618\pi\)
\(558\) 5.21929e39 5.93543e39i 0.778781 0.885638i
\(559\) 4.90026e39i 0.712440i
\(560\) 4.33545e39 + 9.03027e39i 0.614197 + 1.27931i
\(561\) −4.79631e39 + 2.16932e39i −0.662134 + 0.299475i
\(562\) −7.76354e39 −1.04444
\(563\) −4.96577e39 −0.651051 −0.325525 0.945533i \(-0.605541\pi\)
−0.325525 + 0.945533i \(0.605541\pi\)
\(564\) −5.07801e38 1.12274e39i −0.0648854 0.143460i
\(565\) 7.99230e39i 0.995335i
\(566\) 1.01541e39 0.123255
\(567\) 7.08896e39 4.60231e39i 0.838742 0.544529i
\(568\) −1.29451e40 −1.49298
\(569\) 3.34448e39i 0.376011i −0.982168 0.188006i \(-0.939798\pi\)
0.982168 0.188006i \(-0.0602023\pi\)
\(570\) −5.95403e39 1.31642e40i −0.652568 1.44281i
\(571\) 4.89459e39 0.522989 0.261494 0.965205i \(-0.415785\pi\)
0.261494 + 0.965205i \(0.415785\pi\)
\(572\) 1.56376e39 0.162903
\(573\) −1.68605e39 + 7.62579e38i −0.171249 + 0.0774538i
\(574\) 2.19736e39 1.05496e39i 0.217610 0.104475i
\(575\) 5.61782e39i 0.542481i
\(576\) 7.59365e39 8.63558e39i 0.715030 0.813140i
\(577\) 3.45684e39i 0.317417i 0.987326 + 0.158708i \(0.0507329\pi\)
−0.987326 + 0.158708i \(0.949267\pi\)
\(578\) 9.02326e39i 0.807997i
\(579\) −4.65185e39 1.02851e40i −0.406243 0.898195i
\(580\) 2.21454e39i 0.188615i
\(581\) 2.85366e39 + 5.94386e39i 0.237054 + 0.493759i
\(582\) −5.24575e39 1.15982e40i −0.425035 0.939742i
\(583\) 5.25636e39 0.415424
\(584\) −1.10482e39 −0.0851739
\(585\) −1.28387e40 1.12897e40i −0.965523 0.849027i
\(586\) 7.33410e39i 0.538061i
\(587\) −6.89040e39 −0.493165 −0.246583 0.969122i \(-0.579308\pi\)
−0.246583 + 0.969122i \(0.579308\pi\)
\(588\) 1.48251e39 + 3.79868e38i 0.103521 + 0.0265254i
\(589\) −1.90693e40 −1.29916
\(590\) 1.86485e40i 1.23962i
\(591\) −2.26662e40 + 1.02517e40i −1.47015 + 0.664931i
\(592\) −1.83427e40 −1.16091
\(593\) −3.60617e39 −0.222717 −0.111358 0.993780i \(-0.535520\pi\)
−0.111358 + 0.993780i \(0.535520\pi\)
\(594\) −2.86164e40 8.74339e39i −1.72469 0.526959i
\(595\) 4.51028e39 + 9.39443e39i 0.265282 + 0.552554i
\(596\) 8.64663e38i 0.0496336i
\(597\) 2.20080e40 9.95395e39i 1.23297 0.557658i
\(598\) 4.70927e39i 0.257505i
\(599\) 6.74977e39i 0.360247i 0.983644 + 0.180123i \(0.0576497\pi\)
−0.983644 + 0.180123i \(0.942350\pi\)
\(600\) 2.90970e40 1.31602e40i 1.51585 0.685600i
\(601\) 1.72976e40i 0.879642i 0.898086 + 0.439821i \(0.144958\pi\)
−0.898086 + 0.439821i \(0.855042\pi\)
\(602\) −1.53058e40 + 7.34832e39i −0.759811 + 0.364787i
\(603\) 1.80728e40 2.05526e40i 0.875841 0.996016i
\(604\) −1.49998e39 −0.0709658
\(605\) 9.20386e40 4.25125
\(606\) −8.89045e39 + 4.02105e39i −0.400932 + 0.181337i
\(607\) 4.03223e40i 1.77545i 0.460371 + 0.887726i \(0.347716\pi\)
−0.460371 + 0.887726i \(0.652284\pi\)
\(608\) −5.15243e39 −0.221519
\(609\) 2.00054e40 + 1.67970e40i 0.839842 + 0.705150i
\(610\) 5.13414e40 2.10468
\(611\) 2.94015e40i 1.17699i
\(612\) 6.87438e38 7.81762e38i 0.0268743 0.0305618i
\(613\) 3.64404e40 1.39125 0.695627 0.718403i \(-0.255127\pi\)
0.695627 + 0.718403i \(0.255127\pi\)
\(614\) −1.86685e39 −0.0696095
\(615\) −4.65197e39 1.02854e40i −0.169413 0.374569i
\(616\) −2.42884e40 5.05901e40i −0.863930 1.79947i
\(617\) 1.67933e40i 0.583445i 0.956503 + 0.291723i \(0.0942284\pi\)
−0.956503 + 0.291723i \(0.905772\pi\)
\(618\) 9.49043e37 + 2.09831e38i 0.00322072 + 0.00712094i
\(619\) 3.40129e40i 1.12753i 0.825935 + 0.563766i \(0.190648\pi\)
−0.825935 + 0.563766i \(0.809352\pi\)
\(620\) 6.62802e39i 0.214637i
\(621\) −3.15051e39 + 1.03113e40i −0.0996672 + 0.326202i
\(622\) 1.75352e40i 0.541937i
\(623\) −1.65302e40 3.44307e40i −0.499117 1.03961i
\(624\) 2.17545e40 9.83933e39i 0.641761 0.290261i
\(625\) −2.11437e39 −0.0609425
\(626\) 8.01811e39 0.225811
\(627\) 2.97504e40 + 6.57774e40i 0.818678 + 1.81008i
\(628\) 6.89816e39i 0.185489i
\(629\) −1.90824e40 −0.501416
\(630\) −1.60102e40 + 5.70310e40i −0.411110 + 1.46445i
\(631\) 2.25030e39 0.0564695 0.0282348 0.999601i \(-0.491011\pi\)
0.0282348 + 0.999601i \(0.491011\pi\)
\(632\) 2.05432e40i 0.503815i
\(633\) −1.10881e40 2.45155e40i −0.265767 0.587606i
\(634\) 2.86466e40 0.671088
\(635\) −1.00358e41 −2.29791
\(636\) −9.47124e38 + 4.28373e38i −0.0211972 + 0.00958725i
\(637\) 2.84947e40 + 2.28356e40i 0.623365 + 0.499563i
\(638\) 9.24797e40i 1.97764i
\(639\) −5.12717e40 4.50855e40i −1.07180 0.942486i
\(640\) 6.38362e40i 1.30454i
\(641\) 7.96830e40i 1.59193i 0.605342 + 0.795965i \(0.293036\pi\)
−0.605342 + 0.795965i \(0.706964\pi\)
\(642\) −2.29856e39 5.08206e39i −0.0448949 0.0992617i
\(643\) 5.54592e40i 1.05905i −0.848296 0.529523i \(-0.822371\pi\)
0.848296 0.529523i \(-0.177629\pi\)
\(644\) −1.75998e39 + 8.44968e38i −0.0328596 + 0.0157759i
\(645\) 3.24034e40 + 7.16432e40i 0.591527 + 1.30785i
\(646\) 2.09912e40 0.374685
\(647\) −1.94441e40 −0.339372 −0.169686 0.985498i \(-0.554275\pi\)
−0.169686 + 0.985498i \(0.554275\pi\)
\(648\) 6.07870e40 7.83744e39i 1.03746 0.133763i
\(649\) 9.31806e40i 1.55517i
\(650\) 7.35664e40 1.20070
\(651\) 5.98754e40 + 5.02728e40i 0.955706 + 0.802432i
\(652\) 1.44552e39 0.0225649
\(653\) 8.42089e40i 1.28563i 0.766020 + 0.642816i \(0.222234\pi\)
−0.766020 + 0.642816i \(0.777766\pi\)
\(654\) −7.55355e40 + 3.41638e40i −1.12791 + 0.510140i
\(655\) −7.69680e40 −1.12412
\(656\) 1.57650e40 0.225211
\(657\) −4.37589e39 3.84792e39i −0.0611461 0.0537685i
\(658\) −9.18343e40 + 4.40898e40i −1.25525 + 0.602646i
\(659\) 2.47918e40i 0.331489i −0.986169 0.165745i \(-0.946997\pi\)
0.986169 0.165745i \(-0.0530027\pi\)
\(660\) −2.28627e40 + 1.03405e40i −0.299047 + 0.135256i
\(661\) 4.90162e40i 0.627218i −0.949552 0.313609i \(-0.898462\pi\)
0.949552 0.313609i \(-0.101538\pi\)
\(662\) 9.33045e40i 1.16805i
\(663\) 2.26318e40 1.02361e40i 0.277187 0.125369i
\(664\) 4.78129e40i 0.572939i
\(665\) 1.28837e41 6.18547e40i 1.51052 0.725202i
\(666\) −8.14555e40 7.16275e40i −0.934424 0.821681i
\(667\) −3.33232e40 −0.374044
\(668\) −2.45329e39 −0.0269458
\(669\) −2.37445e40 + 1.07394e40i −0.255202 + 0.115425i
\(670\) 1.91814e41i 2.01742i
\(671\) −2.56536e41 −2.64042
\(672\) 1.61781e40 + 1.35835e40i 0.162957 + 0.136822i
\(673\) 3.96130e40 0.390499 0.195249 0.980754i \(-0.437448\pi\)
0.195249 + 0.980754i \(0.437448\pi\)
\(674\) 4.09291e40i 0.394879i
\(675\) 1.61080e41 + 4.92161e40i 1.52103 + 0.464732i
\(676\) 4.18403e39 0.0386694
\(677\) −7.59452e40 −0.687012 −0.343506 0.939150i \(-0.611615\pi\)
−0.343506 + 0.939150i \(0.611615\pi\)
\(678\) −2.72002e40 6.01390e40i −0.240847 0.532508i
\(679\) 1.13511e41 5.44966e40i 0.983841 0.472343i
\(680\) 7.55696e40i 0.641162i
\(681\) −5.08837e40 1.12503e41i −0.422616 0.934394i
\(682\) 2.76788e41i 2.25047i
\(683\) 1.13829e41i 0.906054i −0.891497 0.453027i \(-0.850344\pi\)
0.891497 0.453027i \(-0.149656\pi\)
\(684\) −1.07212e40 9.42764e39i −0.0835469 0.0734665i
\(685\) 1.66623e41i 1.27122i
\(686\) 2.85959e40 1.23246e41i 0.213601 0.920603i
\(687\) −1.48475e41 + 6.71537e40i −1.08588 + 0.491131i
\(688\) −1.09812e41 −0.786350
\(689\) −2.48026e40 −0.173908
\(690\) −3.11404e40 6.88508e40i −0.213803 0.472713i
\(691\) 1.08632e41i 0.730338i −0.930941 0.365169i \(-0.881011\pi\)
0.930941 0.365169i \(-0.118989\pi\)
\(692\) −1.32835e40 −0.0874529
\(693\) 7.99977e40 2.84966e41i 0.515757 1.83722i
\(694\) 1.98878e41 1.25567
\(695\) 5.13935e40i 0.317781i
\(696\) 7.80626e40 + 1.72595e41i 0.472725 + 1.04519i
\(697\) 1.64008e40 0.0972722
\(698\) −7.98671e40 −0.463943
\(699\) 1.01492e41 4.59036e40i 0.577447 0.261173i
\(700\) 1.31998e40 + 2.74937e40i 0.0735605 + 0.153219i
\(701\) 2.18266e41i 1.19145i 0.803189 + 0.595725i \(0.203135\pi\)
−0.803189 + 0.595725i \(0.796865\pi\)
\(702\) 1.35029e41 + 4.12565e40i 0.722002 + 0.220599i
\(703\) 2.61699e41i 1.37072i
\(704\) 4.02704e41i 2.06625i
\(705\) 1.94420e41 + 4.29858e41i 0.977233 + 2.16064i
\(706\) 2.67258e41i 1.31602i
\(707\) −4.17735e40 8.70098e40i −0.201521 0.419746i
\(708\) 7.59386e39 + 1.67899e40i 0.0358906 + 0.0793532i
\(709\) −1.65763e41 −0.767568 −0.383784 0.923423i \(-0.625379\pi\)
−0.383784 + 0.923423i \(0.625379\pi\)
\(710\) 4.78511e41 2.17093
\(711\) −7.15486e40 + 8.13659e40i −0.318048 + 0.361687i
\(712\) 2.76964e41i 1.20632i
\(713\) −9.97350e40 −0.425647
\(714\) −6.59102e40 5.53397e40i −0.275631 0.231426i
\(715\) −5.98711e41 −2.45347
\(716\) 9.71282e39i 0.0390038i
\(717\) 3.97647e38 1.79851e38i 0.00156484 0.000707758i
\(718\) 3.91477e41 1.50974
\(719\) 1.69268e41 0.639745 0.319873 0.947461i \(-0.396360\pi\)
0.319873 + 0.947461i \(0.396360\pi\)
\(720\) −2.52994e41 + 2.87708e41i −0.937107 + 1.06569i
\(721\) −2.05360e39 + 9.85934e38i −0.00745510 + 0.00357921i
\(722\) 2.22651e40i 0.0792201i
\(723\) −1.71931e41 + 7.77623e40i −0.599581 + 0.271184i
\(724\) 1.23354e40i 0.0421643i
\(725\) 5.20563e41i 1.74410i
\(726\) −6.92556e41 + 3.13235e41i −2.27444 + 1.02870i
\(727\) 8.07078e40i 0.259816i −0.991526 0.129908i \(-0.958532\pi\)
0.991526 0.129908i \(-0.0414682\pi\)
\(728\) 1.14607e41 + 2.38714e41i 0.361665 + 0.753309i
\(729\) 2.68057e41 + 1.80669e41i 0.829234 + 0.558901i
\(730\) 4.08395e40 0.123851
\(731\) −1.14240e41 −0.339637
\(732\) 4.62243e40 2.09067e40i 0.134729 0.0609362i
\(733\) 2.55511e41i 0.730134i −0.930981 0.365067i \(-0.881046\pi\)
0.930981 0.365067i \(-0.118954\pi\)
\(734\) −1.18755e41 −0.332705
\(735\) −5.67603e41 1.45438e41i −1.55912 0.399496i
\(736\) −2.69480e40 −0.0725768
\(737\) 9.58434e41i 2.53095i
\(738\) 7.00087e40 + 6.15617e40i 0.181274 + 0.159402i
\(739\) 9.41730e40 0.239101 0.119551 0.992828i \(-0.461855\pi\)
0.119551 + 0.992828i \(0.461855\pi\)
\(740\) −9.09603e40 −0.226460
\(741\) −1.40380e41 3.10377e41i −0.342721 0.757748i
\(742\) 3.71934e40 + 7.74700e40i 0.0890450 + 0.185471i
\(743\) 4.06339e41i 0.954005i 0.878902 + 0.477003i \(0.158277\pi\)
−0.878902 + 0.477003i \(0.841723\pi\)
\(744\) 2.33638e41 + 5.16568e41i 0.537943 + 1.18938i
\(745\) 3.31050e41i 0.747528i
\(746\) 6.59455e40i 0.146040i
\(747\) −1.66525e41 + 1.89373e41i −0.361684 + 0.411311i
\(748\) 3.64560e40i 0.0776598i
\(749\) 4.97375e40 2.38791e40i 0.103920 0.0498920i
\(750\) −3.99295e41 + 1.80596e41i −0.818286 + 0.370102i
\(751\) 8.78253e41 1.76539 0.882695 0.469947i \(-0.155727\pi\)
0.882695 + 0.469947i \(0.155727\pi\)
\(752\) −6.58867e41 −1.29909
\(753\) −1.17009e41 2.58704e41i −0.226304 0.500353i
\(754\)