Properties

Label 21.30.c.a.20.10
Level $21$
Weight $30$
Character 21.20
Analytic conductor $111.884$
Analytic rank $0$
Dimension $76$
CM no
Inner twists $4$

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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 20.10
Character \(\chi\) \(=\) 21.20
Dual form 21.30.c.a.20.9

$q$-expansion

\(f(q)\) \(=\) \(q+1978.96i q^{2} +(6.63697e6 - 4.95792e6i) q^{3} +5.32955e8 q^{4} -2.10087e10 q^{5} +(9.81152e9 + 1.31343e10i) q^{6} +(1.76916e12 + 2.99987e11i) q^{7} +2.11714e12i q^{8} +(1.94684e13 - 6.58112e13i) q^{9} +O(q^{10})\) \(q+1978.96i q^{2} +(6.63697e6 - 4.95792e6i) q^{3} +5.32955e8 q^{4} -2.10087e10 q^{5} +(9.81152e9 + 1.31343e10i) q^{6} +(1.76916e12 + 2.99987e11i) q^{7} +2.11714e12i q^{8} +(1.94684e13 - 6.58112e13i) q^{9} -4.15753e13i q^{10} -1.97233e15i q^{11} +(3.53721e15 - 2.64235e15i) q^{12} -2.35122e16i q^{13} +(-5.93662e14 + 3.50109e15i) q^{14} +(-1.39434e17 + 1.04159e17i) q^{15} +2.81938e17 q^{16} -4.82044e17 q^{17} +(1.30238e17 + 3.85272e16i) q^{18} -5.67589e17i q^{19} -1.11967e19 q^{20} +(1.32292e19 - 6.78033e18i) q^{21} +3.90316e18 q^{22} +7.46696e19i q^{23} +(1.04966e19 + 1.40514e19i) q^{24} +2.55100e20 q^{25} +4.65296e19 q^{26} +(-1.97075e20 - 5.33310e20i) q^{27} +(9.42880e20 + 1.59879e20i) q^{28} +1.34770e21i q^{29} +(-2.06127e20 - 2.75934e20i) q^{30} +7.84435e20i q^{31} +1.69458e21i q^{32} +(-9.77865e21 - 1.30903e22i) q^{33} -9.53945e20i q^{34} +(-3.71676e22 - 6.30233e21i) q^{35} +(1.03758e22 - 3.50744e22i) q^{36} -8.59247e22 q^{37} +1.12324e21 q^{38} +(-1.16571e23 - 1.56050e23i) q^{39} -4.44783e22i q^{40} +1.02991e23 q^{41} +(1.34180e22 + 2.61800e22i) q^{42} +2.29840e23 q^{43} -1.05116e24i q^{44} +(-4.09006e23 + 1.38261e24i) q^{45} -1.47768e23 q^{46} +1.10078e21 q^{47} +(1.87122e24 - 1.39783e24i) q^{48} +(3.03992e24 + 1.06145e24i) q^{49} +5.04833e23i q^{50} +(-3.19931e24 + 2.38993e24i) q^{51} -1.25309e25i q^{52} -1.34593e25i q^{53} +(1.05540e24 - 3.90003e23i) q^{54} +4.14360e25i q^{55} +(-6.35114e23 + 3.74555e24i) q^{56} +(-2.81406e24 - 3.76707e24i) q^{57} -2.66705e24 q^{58} -4.98939e25 q^{59} +(-7.43120e25 + 5.55122e25i) q^{60} -1.41438e26i q^{61} -1.55236e24 q^{62} +(5.41852e25 - 1.10590e26i) q^{63} +1.48011e26 q^{64} +4.93960e26i q^{65} +(2.59052e25 - 1.93516e25i) q^{66} +2.07066e26 q^{67} -2.56907e26 q^{68} +(3.70206e26 + 4.95580e26i) q^{69} +(1.24720e25 - 7.35532e25i) q^{70} -4.38368e24i q^{71} +(1.39332e26 + 4.12174e25i) q^{72} +1.18319e27i q^{73} -1.70041e26i q^{74} +(1.69309e27 - 1.26477e27i) q^{75} -3.02499e26i q^{76} +(5.91673e26 - 3.48936e27i) q^{77} +(3.08816e26 - 2.30690e26i) q^{78} -4.92576e27 q^{79} -5.92315e27 q^{80} +(-3.95209e27 - 2.56248e27i) q^{81} +2.03815e26i q^{82} -1.26288e28 q^{83} +(7.05054e27 - 3.61361e27i) q^{84} +1.01271e28 q^{85} +4.54844e26i q^{86} +(6.68179e27 + 8.94465e27i) q^{87} +4.17570e27 q^{88} +3.53689e27 q^{89} +(-2.73612e27 - 8.09407e26i) q^{90} +(7.05334e27 - 4.15967e28i) q^{91} +3.97955e28i q^{92} +(3.88916e27 + 5.20627e27i) q^{93} +2.17840e24i q^{94} +1.19243e28i q^{95} +(8.40157e27 + 1.12469e28i) q^{96} +6.07788e28i q^{97} +(-2.10056e27 + 6.01588e27i) q^{98} +(-1.29801e29 - 3.83982e28i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1978.96i 0.0854087i 0.999088 + 0.0427043i \(0.0135973\pi\)
−0.999088 + 0.0427043i \(0.986403\pi\)
\(3\) 6.63697e6 4.95792e6i 0.801146 0.598469i
\(4\) 5.32955e8 0.992705
\(5\) −2.10087e10 −1.53934 −0.769669 0.638444i \(-0.779579\pi\)
−0.769669 + 0.638444i \(0.779579\pi\)
\(6\) 9.81152e9 + 1.31343e10i 0.0511144 + 0.0684248i
\(7\) 1.76916e12 + 2.99987e11i 0.985927 + 0.167179i
\(8\) 2.11714e12i 0.170194i
\(9\) 1.94684e13 6.58112e13i 0.283671 0.958922i
\(10\) 4.15753e13i 0.131473i
\(11\) 1.97233e15i 1.56598i −0.622036 0.782989i \(-0.713694\pi\)
0.622036 0.782989i \(-0.286306\pi\)
\(12\) 3.53721e15 2.64235e15i 0.795302 0.594103i
\(13\) 2.35122e16i 1.65621i −0.560577 0.828103i \(-0.689420\pi\)
0.560577 0.828103i \(-0.310580\pi\)
\(14\) −5.93662e14 + 3.50109e15i −0.0142785 + 0.0842067i
\(15\) −1.39434e17 + 1.04159e17i −1.23323 + 0.921245i
\(16\) 2.81938e17 0.978169
\(17\) −4.82044e17 −0.694348 −0.347174 0.937801i \(-0.612859\pi\)
−0.347174 + 0.937801i \(0.612859\pi\)
\(18\) 1.30238e17 + 3.85272e16i 0.0819002 + 0.0242279i
\(19\) 5.67589e17i 0.162970i −0.996675 0.0814848i \(-0.974034\pi\)
0.996675 0.0814848i \(-0.0259662\pi\)
\(20\) −1.11967e19 −1.52811
\(21\) 1.32292e19 6.78033e18i 0.889923 0.456112i
\(22\) 3.90316e18 0.133748
\(23\) 7.46696e19i 1.34304i 0.740985 + 0.671522i \(0.234359\pi\)
−0.740985 + 0.671522i \(0.765641\pi\)
\(24\) 1.04966e19 + 1.40514e19i 0.101856 + 0.136351i
\(25\) 2.55100e20 1.36956
\(26\) 4.65296e19 0.141454
\(27\) −1.97075e20 5.33310e20i −0.346623 0.938005i
\(28\) 9.42880e20 + 1.59879e20i 0.978735 + 0.165959i
\(29\) 1.34770e21i 0.841051i 0.907281 + 0.420526i \(0.138154\pi\)
−0.907281 + 0.420526i \(0.861846\pi\)
\(30\) −2.06127e20 2.75934e20i −0.0786823 0.105329i
\(31\) 7.84435e20i 0.186128i 0.995660 + 0.0930641i \(0.0296662\pi\)
−0.995660 + 0.0930641i \(0.970334\pi\)
\(32\) 1.69458e21i 0.253738i
\(33\) −9.77865e21 1.30903e22i −0.937188 1.25458i
\(34\) 9.53945e20i 0.0593033i
\(35\) −3.71676e22 6.30233e21i −1.51767 0.257344i
\(36\) 1.03758e22 3.50744e22i 0.281602 0.951927i
\(37\) −8.59247e22 −1.56745 −0.783723 0.621110i \(-0.786682\pi\)
−0.783723 + 0.621110i \(0.786682\pi\)
\(38\) 1.12324e21 0.0139190
\(39\) −1.16571e23 1.56050e23i −0.991187 1.32686i
\(40\) 4.44783e22i 0.261986i
\(41\) 1.02991e23 0.424066 0.212033 0.977263i \(-0.431992\pi\)
0.212033 + 0.977263i \(0.431992\pi\)
\(42\) 1.34180e22 + 2.61800e22i 0.0389559 + 0.0760071i
\(43\) 2.29840e23 0.474387 0.237194 0.971462i \(-0.423772\pi\)
0.237194 + 0.971462i \(0.423772\pi\)
\(44\) 1.05116e24i 1.55455i
\(45\) −4.09006e23 + 1.38261e24i −0.436665 + 1.47610i
\(46\) −1.47768e23 −0.114708
\(47\) 1.10078e21 0.000625579 0.000312789 1.00000i \(-0.499900\pi\)
0.000312789 1.00000i \(0.499900\pi\)
\(48\) 1.87122e24 1.39783e24i 0.783657 0.585404i
\(49\) 3.03992e24 + 1.06145e24i 0.944103 + 0.329652i
\(50\) 5.04833e23i 0.116972i
\(51\) −3.19931e24 + 2.38993e24i −0.556274 + 0.415545i
\(52\) 1.25309e25i 1.64412i
\(53\) 1.34593e25i 1.33975i −0.742474 0.669875i \(-0.766348\pi\)
0.742474 0.669875i \(-0.233652\pi\)
\(54\) 1.05540e24 3.90003e23i 0.0801137 0.0296046i
\(55\) 4.14360e25i 2.41057i
\(56\) −6.35114e23 + 3.74555e24i −0.0284528 + 0.167799i
\(57\) −2.81406e24 3.76707e24i −0.0975322 0.130563i
\(58\) −2.66705e24 −0.0718331
\(59\) −4.98939e25 −1.04880 −0.524401 0.851471i \(-0.675711\pi\)
−0.524401 + 0.851471i \(0.675711\pi\)
\(60\) −7.43120e25 + 5.55122e25i −1.22424 + 0.914525i
\(61\) 1.41438e26i 1.83351i −0.399447 0.916756i \(-0.630798\pi\)
0.399447 0.916756i \(-0.369202\pi\)
\(62\) −1.55236e24 −0.0158970
\(63\) 5.41852e25 1.10590e26i 0.439990 0.898003i
\(64\) 1.48011e26 0.956498
\(65\) 4.93960e26i 2.54946i
\(66\) 2.59052e25 1.93516e25i 0.107152 0.0800440i
\(67\) 2.07066e26 0.688692 0.344346 0.938843i \(-0.388101\pi\)
0.344346 + 0.938843i \(0.388101\pi\)
\(68\) −2.56907e26 −0.689283
\(69\) 3.70206e26 + 4.95580e26i 0.803770 + 1.07597i
\(70\) 1.24720e25 7.35532e25i 0.0219794 0.129622i
\(71\) 4.38368e24i 0.00628916i −0.999995 0.00314458i \(-0.998999\pi\)
0.999995 0.00314458i \(-0.00100095\pi\)
\(72\) 1.39332e26 + 4.12174e25i 0.163203 + 0.0482792i
\(73\) 1.18319e27i 1.13468i 0.823483 + 0.567342i \(0.192028\pi\)
−0.823483 + 0.567342i \(0.807972\pi\)
\(74\) 1.70041e26i 0.133874i
\(75\) 1.69309e27 1.26477e27i 1.09722 0.819638i
\(76\) 3.02499e26i 0.161781i
\(77\) 5.91673e26 3.48936e27i 0.261798 1.54394i
\(78\) 3.08816e26 2.30690e26i 0.113326 0.0846559i
\(79\) −4.92576e27 −1.50273 −0.751364 0.659888i \(-0.770604\pi\)
−0.751364 + 0.659888i \(0.770604\pi\)
\(80\) −5.92315e27 −1.50573
\(81\) −3.95209e27 2.56248e27i −0.839062 0.544036i
\(82\) 2.03815e26i 0.0362189i
\(83\) −1.26288e28 −1.88248 −0.941241 0.337736i \(-0.890339\pi\)
−0.941241 + 0.337736i \(0.890339\pi\)
\(84\) 7.05054e27 3.61361e27i 0.883431 0.452784i
\(85\) 1.01271e28 1.06884
\(86\) 4.54844e26i 0.0405168i
\(87\) 6.68179e27 + 8.94465e27i 0.503343 + 0.673805i
\(88\) 4.17570e27 0.266520
\(89\) 3.53689e27 0.191631 0.0958157 0.995399i \(-0.469454\pi\)
0.0958157 + 0.995399i \(0.469454\pi\)
\(90\) −2.73612e27 8.09407e26i −0.126072 0.0372950i
\(91\) 7.05334e27 4.15967e28i 0.276882 1.63290i
\(92\) 3.97955e28i 1.33325i
\(93\) 3.88916e27 + 5.20627e27i 0.111392 + 0.149116i
\(94\) 2.17840e24i 5.34299e-5i
\(95\) 1.19243e28i 0.250865i
\(96\) 8.40157e27 + 1.12469e28i 0.151854 + 0.203282i
\(97\) 6.07788e28i 0.945283i 0.881255 + 0.472642i \(0.156700\pi\)
−0.881255 + 0.472642i \(0.843300\pi\)
\(98\) −2.10056e27 + 6.01588e27i −0.0281551 + 0.0806345i
\(99\) −1.29801e29 3.83982e28i −1.50165 0.444222i
\(100\) 1.35957e29 1.35957
\(101\) −7.18680e28 −0.622123 −0.311061 0.950390i \(-0.600684\pi\)
−0.311061 + 0.950390i \(0.600684\pi\)
\(102\) −4.72958e27 6.33131e27i −0.0354912 0.0475106i
\(103\) 1.31814e29i 0.858660i −0.903148 0.429330i \(-0.858750\pi\)
0.903148 0.429330i \(-0.141250\pi\)
\(104\) 4.97786e28 0.281877
\(105\) −2.77927e29 + 1.42446e29i −1.36989 + 0.702109i
\(106\) 2.66355e28 0.114426
\(107\) 2.73974e29i 1.02717i −0.858037 0.513587i \(-0.828316\pi\)
0.858037 0.513587i \(-0.171684\pi\)
\(108\) −1.05032e29 2.84230e29i −0.344094 0.931162i
\(109\) 2.85051e28 0.0817030 0.0408515 0.999165i \(-0.486993\pi\)
0.0408515 + 0.999165i \(0.486993\pi\)
\(110\) −8.20002e28 −0.205883
\(111\) −5.70280e29 + 4.26008e29i −1.25575 + 0.938068i
\(112\) 4.98793e29 + 8.45777e28i 0.964403 + 0.163529i
\(113\) 2.49842e29i 0.424647i −0.977199 0.212324i \(-0.931897\pi\)
0.977199 0.212324i \(-0.0681031\pi\)
\(114\) 7.45488e27 5.56891e27i 0.0111512 0.00833009i
\(115\) 1.56871e30i 2.06740i
\(116\) 7.18263e29i 0.834916i
\(117\) −1.54736e30 4.57745e29i −1.58817 0.469817i
\(118\) 9.87381e28i 0.0895768i
\(119\) −8.52811e29 1.44607e29i −0.684576 0.116080i
\(120\) −2.20520e29 2.95202e29i −0.156791 0.209889i
\(121\) −2.30378e30 −1.45229
\(122\) 2.79900e29 0.156598
\(123\) 6.83548e29 5.10621e29i 0.339739 0.253790i
\(124\) 4.18068e29i 0.184770i
\(125\) −1.44615e30 −0.568875
\(126\) 2.18853e29 + 1.07230e29i 0.0766972 + 0.0375789i
\(127\) 1.61971e29 0.0506155 0.0253078 0.999680i \(-0.491943\pi\)
0.0253078 + 0.999680i \(0.491943\pi\)
\(128\) 1.20268e30i 0.335432i
\(129\) 1.52544e30 1.13953e30i 0.380053 0.283906i
\(130\) −9.77526e29 −0.217746
\(131\) −4.01899e30 −0.801093 −0.400546 0.916276i \(-0.631180\pi\)
−0.400546 + 0.916276i \(0.631180\pi\)
\(132\) −5.21158e30 6.97654e30i −0.930352 1.24543i
\(133\) 1.70269e29 1.00415e30i 0.0272450 0.160676i
\(134\) 4.09776e29i 0.0588203i
\(135\) 4.14028e30 + 1.12041e31i 0.533569 + 1.44391i
\(136\) 1.02055e30i 0.118174i
\(137\) 9.93083e30i 1.03404i 0.855973 + 0.517020i \(0.172959\pi\)
−0.855973 + 0.517020i \(0.827041\pi\)
\(138\) −9.80733e29 + 7.32623e29i −0.0918976 + 0.0686489i
\(139\) 1.76006e31i 1.48530i −0.669681 0.742649i \(-0.733569\pi\)
0.669681 0.742649i \(-0.266431\pi\)
\(140\) −1.98087e31 3.35885e30i −1.50660 0.255467i
\(141\) 7.30586e27 5.45759e27i 0.000501180 0.000374389i
\(142\) 8.67512e27 0.000537149
\(143\) −4.63738e31 −2.59358
\(144\) 5.48889e30 1.85547e31i 0.277478 0.937988i
\(145\) 2.83134e31i 1.29466i
\(146\) −2.34149e30 −0.0969118
\(147\) 2.54384e31 8.02689e30i 0.953650 0.300917i
\(148\) −4.57939e31 −1.55601
\(149\) 2.16357e31i 0.666759i −0.942793 0.333380i \(-0.891811\pi\)
0.942793 0.333380i \(-0.108189\pi\)
\(150\) 2.50292e30 + 3.35056e30i 0.0700042 + 0.0937118i
\(151\) −1.76044e28 −0.000447151 −0.000223576 1.00000i \(-0.500071\pi\)
−0.000223576 1.00000i \(0.500071\pi\)
\(152\) 1.20167e30 0.0277365
\(153\) −9.38464e30 + 3.17239e31i −0.196966 + 0.665825i
\(154\) 6.90530e30 + 1.17090e30i 0.131866 + 0.0223598i
\(155\) 1.64799e31i 0.286514i
\(156\) −6.21273e31 8.31674e31i −0.983956 1.31718i
\(157\) 6.76929e31i 0.977233i 0.872499 + 0.488617i \(0.162498\pi\)
−0.872499 + 0.488617i \(0.837502\pi\)
\(158\) 9.74788e30i 0.128346i
\(159\) −6.67303e31 8.93293e31i −0.801798 1.07334i
\(160\) 3.56008e31i 0.390589i
\(161\) −2.23999e31 + 1.32102e32i −0.224528 + 1.32414i
\(162\) 5.07105e30 7.82102e30i 0.0464654 0.0716631i
\(163\) 1.32662e32 1.11180 0.555900 0.831249i \(-0.312374\pi\)
0.555900 + 0.831249i \(0.312374\pi\)
\(164\) 5.48895e31 0.420972
\(165\) 2.05437e32 + 2.75010e32i 1.44265 + 1.93122i
\(166\) 2.49919e31i 0.160780i
\(167\) 6.46226e31 0.381062 0.190531 0.981681i \(-0.438979\pi\)
0.190531 + 0.981681i \(0.438979\pi\)
\(168\) 1.43549e31 + 2.80080e31i 0.0776276 + 0.151460i
\(169\) −3.51284e32 −1.74302
\(170\) 2.00411e31i 0.0912878i
\(171\) −3.73537e31 1.10501e31i −0.156275 0.0462297i
\(172\) 1.22494e32 0.470927
\(173\) 1.74835e32 0.617959 0.308980 0.951069i \(-0.400012\pi\)
0.308980 + 0.951069i \(0.400012\pi\)
\(174\) −1.77011e31 + 1.32230e31i −0.0575488 + 0.0429898i
\(175\) 4.51312e32 + 7.65267e31i 1.35028 + 0.228961i
\(176\) 5.56075e32i 1.53179i
\(177\) −3.31145e32 + 2.47370e32i −0.840244 + 0.627675i
\(178\) 6.99936e30i 0.0163670i
\(179\) 1.94233e32i 0.418749i 0.977836 + 0.209375i \(0.0671428\pi\)
−0.977836 + 0.209375i \(0.932857\pi\)
\(180\) −2.17982e32 + 7.36866e32i −0.433480 + 1.46534i
\(181\) 2.90896e31i 0.0533824i 0.999644 + 0.0266912i \(0.00849707\pi\)
−0.999644 + 0.0266912i \(0.991503\pi\)
\(182\) 8.23182e31 + 1.39583e31i 0.139464 + 0.0236481i
\(183\) −7.01239e32 9.38721e32i −1.09730 1.46891i
\(184\) −1.58086e32 −0.228578
\(185\) 1.80516e33 2.41283
\(186\) −1.03030e31 + 7.69650e30i −0.0127358 + 0.00951383i
\(187\) 9.50749e32i 1.08733i
\(188\) 5.86666e29 0.000621016
\(189\) −1.88670e32 1.00263e33i −0.184930 0.982752i
\(190\) −2.35977e31 −0.0214261
\(191\) 7.24655e32i 0.609744i −0.952393 0.304872i \(-0.901386\pi\)
0.952393 0.304872i \(-0.0986136\pi\)
\(192\) 9.82344e32 7.33826e32i 0.766295 0.572434i
\(193\) 1.23473e33 0.893285 0.446642 0.894713i \(-0.352620\pi\)
0.446642 + 0.894713i \(0.352620\pi\)
\(194\) −1.20279e32 −0.0807354
\(195\) 2.44901e33 + 3.27840e33i 1.52577 + 2.04249i
\(196\) 1.62014e33 + 5.65703e32i 0.937216 + 0.327247i
\(197\) 3.28498e32i 0.176511i −0.996098 0.0882556i \(-0.971871\pi\)
0.996098 0.0882556i \(-0.0281292\pi\)
\(198\) 7.59884e31 2.56871e32i 0.0379404 0.128254i
\(199\) 2.51190e33i 1.16582i 0.812536 + 0.582911i \(0.198086\pi\)
−0.812536 + 0.582911i \(0.801914\pi\)
\(200\) 5.40083e32i 0.233091i
\(201\) 1.37429e33 1.02662e33i 0.551743 0.412160i
\(202\) 1.42224e32i 0.0531347i
\(203\) −4.04292e32 + 2.38429e33i −0.140606 + 0.829215i
\(204\) −1.70509e33 + 1.27373e33i −0.552216 + 0.412514i
\(205\) −2.16370e33 −0.652780
\(206\) 2.60854e32 0.0733370
\(207\) 4.91409e33 + 1.45370e33i 1.28787 + 0.380982i
\(208\) 6.62898e33i 1.62005i
\(209\) −1.11947e33 −0.255207
\(210\) −2.81894e32 5.50006e32i −0.0599662 0.117001i
\(211\) −7.51239e33 −1.49170 −0.745852 0.666112i \(-0.767957\pi\)
−0.745852 + 0.666112i \(0.767957\pi\)
\(212\) 7.17322e33i 1.32998i
\(213\) −2.17339e31 2.90944e31i −0.00376386 0.00503854i
\(214\) 5.42183e32 0.0877296
\(215\) −4.82863e33 −0.730242
\(216\) 1.12909e33 4.17235e32i 0.159643 0.0589932i
\(217\) −2.35320e32 + 1.38779e33i −0.0311166 + 0.183509i
\(218\) 5.64104e31i 0.00697814i
\(219\) 5.86618e33 + 7.85283e33i 0.679072 + 0.909047i
\(220\) 2.20835e34i 2.39298i
\(221\) 1.13339e34i 1.14998i
\(222\) −8.43052e32 1.12856e33i −0.0801191 0.107252i
\(223\) 1.18591e34i 1.05592i −0.849268 0.527962i \(-0.822956\pi\)
0.849268 0.527962i \(-0.177044\pi\)
\(224\) −5.08350e32 + 2.99797e33i −0.0424196 + 0.250167i
\(225\) 4.96640e33 1.67884e34i 0.388504 1.31330i
\(226\) 4.94427e32 0.0362685
\(227\) 1.14437e34 0.787392 0.393696 0.919241i \(-0.371196\pi\)
0.393696 + 0.919241i \(0.371196\pi\)
\(228\) −1.49977e33 2.00768e33i −0.0968207 0.129610i
\(229\) 1.47875e34i 0.895941i −0.894048 0.447971i \(-0.852147\pi\)
0.894048 0.447971i \(-0.147853\pi\)
\(230\) 3.10441e33 0.176574
\(231\) −1.33730e34 2.60923e34i −0.714261 1.39360i
\(232\) −2.85327e33 −0.143142
\(233\) 2.51857e34i 1.18712i −0.804791 0.593558i \(-0.797723\pi\)
0.804791 0.593558i \(-0.202277\pi\)
\(234\) 9.05859e32 3.06217e33i 0.0401265 0.135644i
\(235\) −2.31260e31 −0.000962977
\(236\) −2.65912e34 −1.04115
\(237\) −3.26921e34 + 2.44215e34i −1.20391 + 0.899336i
\(238\) 2.86171e32 1.68768e33i 0.00991424 0.0584687i
\(239\) 1.71355e34i 0.558635i 0.960199 + 0.279318i \(0.0901082\pi\)
−0.960199 + 0.279318i \(0.909892\pi\)
\(240\) −3.93118e34 + 2.93665e34i −1.20631 + 0.901133i
\(241\) 1.04237e34i 0.301145i −0.988599 0.150573i \(-0.951888\pi\)
0.988599 0.150573i \(-0.0481118\pi\)
\(242\) 4.55908e33i 0.124038i
\(243\) −3.89345e34 + 2.58702e33i −0.997800 + 0.0662993i
\(244\) 7.53801e34i 1.82014i
\(245\) −6.38647e34 2.22996e34i −1.45329 0.507445i
\(246\) 1.01050e33 + 1.35271e33i 0.0216759 + 0.0290166i
\(247\) −1.33452e34 −0.269911
\(248\) −1.66076e33 −0.0316780
\(249\) −8.38172e34 + 6.26127e34i −1.50814 + 1.12661i
\(250\) 2.86186e33i 0.0485869i
\(251\) 6.64584e34 1.06483 0.532416 0.846483i \(-0.321284\pi\)
0.532416 + 0.846483i \(0.321284\pi\)
\(252\) 2.88782e34 5.89394e34i 0.436780 0.891452i
\(253\) 1.47273e35 2.10318
\(254\) 3.20534e32i 0.00432300i
\(255\) 6.72133e34 5.02094e34i 0.856293 0.639664i
\(256\) 7.70827e34 0.927849
\(257\) −9.04327e34 −1.02871 −0.514357 0.857576i \(-0.671970\pi\)
−0.514357 + 0.857576i \(0.671970\pi\)
\(258\) 2.25508e33 + 3.01879e33i 0.0242480 + 0.0324599i
\(259\) −1.52014e35 2.57763e34i −1.54539 0.262043i
\(260\) 2.63258e35i 2.53086i
\(261\) 8.86938e34 + 2.62376e34i 0.806503 + 0.238582i
\(262\) 7.95341e33i 0.0684203i
\(263\) 6.75085e34i 0.549541i −0.961510 0.274770i \(-0.911398\pi\)
0.961510 0.274770i \(-0.0886018\pi\)
\(264\) 2.77140e34 2.07028e34i 0.213522 0.159504i
\(265\) 2.82763e35i 2.06233i
\(266\) 1.98718e33 + 3.36956e32i 0.0137231 + 0.00232696i
\(267\) 2.34742e34 1.75356e34i 0.153525 0.114685i
\(268\) 1.10357e35 0.683668
\(269\) 1.02148e35 0.599546 0.299773 0.954011i \(-0.403089\pi\)
0.299773 + 0.954011i \(0.403089\pi\)
\(270\) −2.21725e34 + 8.19345e33i −0.123322 + 0.0455714i
\(271\) 1.68808e35i 0.889896i −0.895556 0.444948i \(-0.853222\pi\)
0.895556 0.444948i \(-0.146778\pi\)
\(272\) −1.35906e35 −0.679190
\(273\) −1.59420e35 3.11046e35i −0.755414 1.47389i
\(274\) −1.96527e34 −0.0883160
\(275\) 5.03142e35i 2.14470i
\(276\) 1.97303e35 + 2.64122e35i 0.797906 + 1.06813i
\(277\) −2.12651e35 −0.816039 −0.408019 0.912973i \(-0.633780\pi\)
−0.408019 + 0.912973i \(0.633780\pi\)
\(278\) 3.48309e34 0.126857
\(279\) 5.16246e34 + 1.52717e34i 0.178482 + 0.0527992i
\(280\) 1.33429e34 7.86891e34i 0.0437985 0.258299i
\(281\) 1.60703e35i 0.500937i 0.968125 + 0.250469i \(0.0805847\pi\)
−0.968125 + 0.250469i \(0.919415\pi\)
\(282\) 1.08003e31 + 1.44580e31i 3.19761e−5 + 4.28051e-5i
\(283\) 2.55313e35i 0.718075i 0.933323 + 0.359038i \(0.116895\pi\)
−0.933323 + 0.359038i \(0.883105\pi\)
\(284\) 2.33630e33i 0.00624328i
\(285\) 5.91197e34 + 7.91412e34i 0.150135 + 0.200980i
\(286\) 9.17718e34i 0.221514i
\(287\) 1.82207e35 + 3.08959e34i 0.418098 + 0.0708947i
\(288\) 1.11522e35 + 3.29907e34i 0.243315 + 0.0719782i
\(289\) −2.49602e35 −0.517881
\(290\) 5.60311e34 0.110575
\(291\) 3.01336e35 + 4.03387e35i 0.565722 + 0.757310i
\(292\) 6.30589e35i 1.12641i
\(293\) 2.44043e35 0.414845 0.207422 0.978251i \(-0.433493\pi\)
0.207422 + 0.978251i \(0.433493\pi\)
\(294\) 1.58849e34 + 5.03416e34i 0.0257009 + 0.0814500i
\(295\) 1.04821e36 1.61446
\(296\) 1.81915e35i 0.266771i
\(297\) −1.05186e36 + 3.88697e35i −1.46889 + 0.542803i
\(298\) 4.28161e34 0.0569470
\(299\) 1.75564e36 2.22436
\(300\) 9.02342e35 6.74063e35i 1.08921 0.813659i
\(301\) 4.06623e35 + 6.89489e34i 0.467711 + 0.0793073i
\(302\) 3.48383e31i 3.81906e-5i
\(303\) −4.76986e35 + 3.56316e35i −0.498411 + 0.372321i
\(304\) 1.60025e35i 0.159412i
\(305\) 2.97143e36i 2.82239i
\(306\) −6.27802e34 1.85718e34i −0.0568672 0.0168226i
\(307\) 8.70461e35i 0.752043i 0.926611 + 0.376022i \(0.122708\pi\)
−0.926611 + 0.376022i \(0.877292\pi\)
\(308\) 3.15335e35 1.85967e36i 0.259888 1.53268i
\(309\) −6.53522e35 8.74844e35i −0.513881 0.687912i
\(310\) 3.26131e34 0.0244708
\(311\) 1.19319e36 0.854446 0.427223 0.904146i \(-0.359492\pi\)
0.427223 + 0.904146i \(0.359492\pi\)
\(312\) 3.30379e35 2.46798e35i 0.225824 0.168694i
\(313\) 1.55805e35i 0.101669i −0.998707 0.0508345i \(-0.983812\pi\)
0.998707 0.0508345i \(-0.0161881\pi\)
\(314\) −1.33961e35 −0.0834642
\(315\) −1.13836e36 + 2.32335e36i −0.677293 + 1.38233i
\(316\) −2.62521e36 −1.49177
\(317\) 2.35251e36i 1.27694i −0.769645 0.638472i \(-0.779567\pi\)
0.769645 0.638472i \(-0.220433\pi\)
\(318\) 1.76779e35 1.32057e35i 0.0916722 0.0684805i
\(319\) 2.65811e36 1.31707
\(320\) −3.10951e36 −1.47237
\(321\) −1.35834e36 1.81836e36i −0.614731 0.822917i
\(322\) −2.61425e35 4.43285e34i −0.113093 0.0191766i
\(323\) 2.73603e35i 0.113158i
\(324\) −2.10628e36 1.36569e36i −0.832941 0.540068i
\(325\) 5.99796e36i 2.26827i
\(326\) 2.62533e35i 0.0949573i
\(327\) 1.89187e35 1.41326e35i 0.0654560 0.0488967i
\(328\) 2.18046e35i 0.0721736i
\(329\) 1.94745e33 + 3.30220e32i 0.000616775 + 0.000104583i
\(330\) −5.44233e35 + 4.06551e35i −0.164943 + 0.123215i
\(331\) 2.47394e36 0.717600 0.358800 0.933414i \(-0.383186\pi\)
0.358800 + 0.933414i \(0.383186\pi\)
\(332\) −6.73059e36 −1.86875
\(333\) −1.67282e36 + 5.65480e36i −0.444639 + 1.50306i
\(334\) 1.27886e35i 0.0325460i
\(335\) −4.35019e36 −1.06013
\(336\) 3.72980e36 1.91163e36i 0.870495 0.446154i
\(337\) 8.95109e35 0.200098 0.100049 0.994983i \(-0.468100\pi\)
0.100049 + 0.994983i \(0.468100\pi\)
\(338\) 6.95177e35i 0.148869i
\(339\) −1.23870e36 1.65820e36i −0.254138 0.340205i
\(340\) 5.39729e36 1.06104
\(341\) 1.54716e36 0.291473
\(342\) 2.18676e34 7.39214e34i 0.00394842 0.0133472i
\(343\) 5.05968e36 + 2.78980e36i 0.875705 + 0.482846i
\(344\) 4.86604e35i 0.0807380i
\(345\) −7.77754e36 1.04115e37i −1.23727 1.65629i
\(346\) 3.45991e35i 0.0527791i
\(347\) 7.30251e36i 1.06830i 0.845388 + 0.534152i \(0.179369\pi\)
−0.845388 + 0.534152i \(0.820631\pi\)
\(348\) 3.56109e36 + 4.76710e36i 0.499671 + 0.668890i
\(349\) 6.48377e36i 0.872688i −0.899780 0.436344i \(-0.856273\pi\)
0.899780 0.436344i \(-0.143727\pi\)
\(350\) −1.51443e35 + 8.93128e35i −0.0195552 + 0.115326i
\(351\) −1.25393e37 + 4.63366e36i −1.55353 + 0.574078i
\(352\) 3.34226e36 0.397349
\(353\) −7.12394e36 −0.812806 −0.406403 0.913694i \(-0.633217\pi\)
−0.406403 + 0.913694i \(0.633217\pi\)
\(354\) −4.89535e35 6.55322e35i −0.0536089 0.0717641i
\(355\) 9.20953e34i 0.00968114i
\(356\) 1.88500e36 0.190233
\(357\) −6.37703e36 + 3.26842e36i −0.617916 + 0.316700i
\(358\) −3.84379e35 −0.0357648
\(359\) 9.29988e36i 0.831013i 0.909590 + 0.415507i \(0.136396\pi\)
−0.909590 + 0.415507i \(0.863604\pi\)
\(360\) −2.92717e36 8.65924e35i −0.251224 0.0743179i
\(361\) 1.18077e37 0.973441
\(362\) −5.75670e34 −0.00455932
\(363\) −1.52901e37 + 1.14219e37i −1.16349 + 0.869148i
\(364\) 3.75911e36 2.21692e37i 0.274862 1.62099i
\(365\) 2.48574e37i 1.74666i
\(366\) 1.85769e36 1.38772e36i 0.125458 0.0937189i
\(367\) 1.60683e36i 0.104306i 0.998639 + 0.0521532i \(0.0166084\pi\)
−0.998639 + 0.0521532i \(0.983392\pi\)
\(368\) 2.10522e37i 1.31372i
\(369\) 2.00507e36 6.77796e36i 0.120295 0.406646i
\(370\) 3.57235e36i 0.206076i
\(371\) 4.03763e36 2.38117e37i 0.223977 1.32090i
\(372\) 2.07275e36 + 2.77471e36i 0.110579 + 0.148028i
\(373\) −1.00669e37 −0.516554 −0.258277 0.966071i \(-0.583155\pi\)
−0.258277 + 0.966071i \(0.583155\pi\)
\(374\) −1.88149e36 −0.0928677
\(375\) −9.59803e36 + 7.16988e36i −0.455752 + 0.340454i
\(376\) 2.33051e33i 0.000106470i
\(377\) 3.16874e37 1.39295
\(378\) 1.98416e36 3.73371e35i 0.0839355 0.0157946i
\(379\) 3.58578e37 1.45987 0.729937 0.683515i \(-0.239550\pi\)
0.729937 + 0.683515i \(0.239550\pi\)
\(380\) 6.35511e36i 0.249035i
\(381\) 1.07500e36 8.03040e35i 0.0405504 0.0302918i
\(382\) 1.43406e36 0.0520774
\(383\) 1.48831e37 0.520369 0.260184 0.965559i \(-0.416217\pi\)
0.260184 + 0.965559i \(0.416217\pi\)
\(384\) 5.96277e36 + 7.98213e36i 0.200745 + 0.268730i
\(385\) −1.24303e37 + 7.33068e37i −0.402995 + 2.37664i
\(386\) 2.44347e36i 0.0762943i
\(387\) 4.47462e36 1.51260e37i 0.134570 0.454900i
\(388\) 3.23923e37i 0.938388i
\(389\) 6.86856e37i 1.91689i −0.285281 0.958444i \(-0.592087\pi\)
0.285281 0.958444i \(-0.407913\pi\)
\(390\) −6.48781e36 + 4.84650e36i −0.174446 + 0.130314i
\(391\) 3.59940e37i 0.932540i
\(392\) −2.24723e36 + 6.43594e36i −0.0561048 + 0.160681i
\(393\) −2.66739e37 + 1.99258e37i −0.641793 + 0.479429i
\(394\) 6.50084e35 0.0150756
\(395\) 1.03484e38 2.31321
\(396\) −6.91782e37 2.04645e37i −1.49070 0.440982i
\(397\) 2.07347e37i 0.430761i −0.976530 0.215380i \(-0.930901\pi\)
0.976530 0.215380i \(-0.0690992\pi\)
\(398\) −4.97094e36 −0.0995712
\(399\) −3.84844e36 7.50872e36i −0.0743323 0.145030i
\(400\) 7.19225e37 1.33966
\(401\) 2.55625e37i 0.459209i 0.973284 + 0.229605i \(0.0737433\pi\)
−0.973284 + 0.229605i \(0.926257\pi\)
\(402\) 2.03164e36 + 2.71967e36i 0.0352021 + 0.0471236i
\(403\) 1.84438e37 0.308267
\(404\) −3.83024e37 −0.617584
\(405\) 8.30282e37 + 5.38343e37i 1.29160 + 0.837455i
\(406\) −4.71842e36 8.00078e35i −0.0708221 0.0120089i
\(407\) 1.69472e38i 2.45459i
\(408\) −5.05983e36 6.77339e36i −0.0707234 0.0946747i
\(409\) 5.28502e37i 0.712950i 0.934305 + 0.356475i \(0.116021\pi\)
−0.934305 + 0.356475i \(0.883979\pi\)
\(410\) 4.28188e36i 0.0557531i
\(411\) 4.92363e37 + 6.59107e37i 0.618841 + 0.828418i
\(412\) 7.02508e37i 0.852396i
\(413\) −8.82702e37 1.49675e37i −1.03404 0.175337i
\(414\) −2.87681e36 + 9.72479e36i −0.0325392 + 0.109996i
\(415\) 2.65315e38 2.89777
\(416\) 3.98432e37 0.420243
\(417\) −8.72625e37 1.16815e38i −0.888904 1.18994i
\(418\) 2.21539e36i 0.0217969i
\(419\) −5.82158e37 −0.553271 −0.276635 0.960975i \(-0.589219\pi\)
−0.276635 + 0.960975i \(0.589219\pi\)
\(420\) −1.48122e38 + 7.59172e37i −1.35990 + 0.696988i
\(421\) 8.94985e37 0.793826 0.396913 0.917856i \(-0.370081\pi\)
0.396913 + 0.917856i \(0.370081\pi\)
\(422\) 1.48667e37i 0.127404i
\(423\) 2.14305e34 7.24437e34i 0.000177459 0.000599881i
\(424\) 2.84953e37 0.228018
\(425\) −1.22969e38 −0.950950
\(426\) 5.75766e34 4.30106e34i 0.000430335 0.000321467i
\(427\) 4.24296e37 2.50226e38i 0.306524 1.80771i
\(428\) 1.46016e38i 1.01968i
\(429\) −3.07781e38 + 2.29917e38i −2.07784 + 1.55218i
\(430\) 9.55567e36i 0.0623690i
\(431\) 1.43236e38i 0.903922i −0.892038 0.451961i \(-0.850725\pi\)
0.892038 0.451961i \(-0.149275\pi\)
\(432\) −5.55629e37 1.50360e38i −0.339056 0.917527i
\(433\) 1.76466e38i 1.04132i 0.853763 + 0.520662i \(0.174315\pi\)
−0.853763 + 0.520662i \(0.825685\pi\)
\(434\) −2.74637e36 4.65689e35i −0.0156732 0.00265763i
\(435\) −1.40376e38 1.87915e38i −0.774814 1.03721i
\(436\) 1.51919e37 0.0811070
\(437\) 4.23816e37 0.218875
\(438\) −1.55404e37 + 1.16089e37i −0.0776405 + 0.0579986i
\(439\) 4.44385e36i 0.0214795i −0.999942 0.0107397i \(-0.996581\pi\)
0.999942 0.0107397i \(-0.00341863\pi\)
\(440\) −8.77260e37 −0.410265
\(441\) 1.29038e38 1.79396e38i 0.583924 0.811808i
\(442\) −2.24293e37 −0.0982185
\(443\) 5.30865e37i 0.224973i 0.993653 + 0.112486i \(0.0358815\pi\)
−0.993653 + 0.112486i \(0.964119\pi\)
\(444\) −3.03933e38 + 2.27043e38i −1.24659 + 0.931225i
\(445\) −7.43054e37 −0.294985
\(446\) 2.34687e37 0.0901850
\(447\) −1.07268e38 1.43595e38i −0.399034 0.534172i
\(448\) 2.61854e38 + 4.44013e37i 0.943037 + 0.159906i
\(449\) 1.24111e38i 0.432750i −0.976310 0.216375i \(-0.930577\pi\)
0.976310 0.216375i \(-0.0694234\pi\)
\(450\) 3.32236e37 + 9.82831e36i 0.112167 + 0.0331816i
\(451\) 2.03132e38i 0.664078i
\(452\) 1.33155e38i 0.421550i
\(453\) −1.16840e35 + 8.72810e34i −0.000358234 + 0.000267606i
\(454\) 2.26466e37i 0.0672501i
\(455\) −1.48181e38 + 8.73892e38i −0.426215 + 2.51358i
\(456\) 7.97542e36 5.95776e36i 0.0222210 0.0165994i
\(457\) −1.68118e38 −0.453762 −0.226881 0.973922i \(-0.572853\pi\)
−0.226881 + 0.973922i \(0.572853\pi\)
\(458\) 2.92638e37 0.0765212
\(459\) 9.49987e37 + 2.57079e38i 0.240677 + 0.651302i
\(460\) 8.36051e38i 2.05232i
\(461\) 4.79870e38 1.14146 0.570729 0.821138i \(-0.306661\pi\)
0.570729 + 0.821138i \(0.306661\pi\)
\(462\) 5.16355e37 2.64647e37i 0.119025 0.0610040i
\(463\) 9.50054e37 0.212238 0.106119 0.994353i \(-0.466158\pi\)
0.106119 + 0.994353i \(0.466158\pi\)
\(464\) 3.79968e38i 0.822691i
\(465\) −8.17062e37 1.09377e38i −0.171470 0.229540i
\(466\) 4.98415e37 0.101390
\(467\) −5.35352e38 −1.05571 −0.527856 0.849334i \(-0.677004\pi\)
−0.527856 + 0.849334i \(0.677004\pi\)
\(468\) −8.24674e38 2.43957e38i −1.57659 0.466390i
\(469\) 3.66333e38 + 6.21172e37i 0.679000 + 0.115135i
\(470\) 4.57653e34i 8.22466e-5i
\(471\) 3.35616e38 + 4.49276e38i 0.584843 + 0.782907i
\(472\) 1.05633e38i 0.178500i
\(473\) 4.53320e38i 0.742880i
\(474\) −4.83292e37 6.46964e37i −0.0768111 0.102824i
\(475\) 1.44792e38i 0.223196i
\(476\) −4.54509e38 7.70688e37i −0.679582 0.115233i
\(477\) −8.85775e38 2.62032e38i −1.28472 0.380048i
\(478\) −3.39105e37 −0.0477123
\(479\) 4.79011e38 0.653854 0.326927 0.945050i \(-0.393987\pi\)
0.326927 + 0.945050i \(0.393987\pi\)
\(480\) −1.76506e38 2.36282e38i −0.233755 0.312919i
\(481\) 2.02028e39i 2.59601i
\(482\) 2.06281e37 0.0257204
\(483\) 5.06285e38 + 9.87816e38i 0.612578 + 1.19521i
\(484\) −1.22781e39 −1.44169
\(485\) 1.27688e39i 1.45511i
\(486\) −5.11961e36 7.70497e37i −0.00566253 0.0852207i
\(487\) 8.62466e38 0.925917 0.462959 0.886380i \(-0.346788\pi\)
0.462959 + 0.886380i \(0.346788\pi\)
\(488\) 2.99444e38 0.312053
\(489\) 8.80474e38 6.57728e38i 0.890714 0.665377i
\(490\) 4.41300e37 1.26386e38i 0.0433402 0.124124i
\(491\) 3.03296e38i 0.289191i −0.989491 0.144596i \(-0.953812\pi\)
0.989491 0.144596i \(-0.0461881\pi\)
\(492\) 3.64300e38 2.72138e38i 0.337260 0.251939i
\(493\) 6.49651e38i 0.583982i
\(494\) 2.64097e37i 0.0230528i
\(495\) 2.72695e39 + 8.06695e38i 2.31155 + 0.683808i
\(496\) 2.21162e38i 0.182065i
\(497\) 1.31505e36 7.75541e36i 0.00105141 0.00620065i
\(498\) −1.23908e38 1.65871e38i −0.0962219 0.128809i
\(499\) −6.83045e36 −0.00515219 −0.00257609 0.999997i \(-0.500820\pi\)
−0.00257609 + 0.999997i \(0.500820\pi\)
\(500\) −7.70730e38 −0.564725
\(501\) 4.28898e38 3.20394e38i 0.305286 0.228054i
\(502\) 1.31519e38i 0.0909459i
\(503\) 1.47544e39 0.991257 0.495628 0.868535i \(-0.334938\pi\)
0.495628 + 0.868535i \(0.334938\pi\)
\(504\) 2.34135e38 + 1.14718e38i 0.152835 + 0.0748838i
\(505\) 1.50985e39 0.957656
\(506\) 2.91447e38i 0.179630i
\(507\) −2.33146e39 + 1.74164e39i −1.39641 + 1.04314i
\(508\) 8.63233e37 0.0502463
\(509\) −1.76025e38 −0.0995790 −0.0497895 0.998760i \(-0.515855\pi\)
−0.0497895 + 0.998760i \(0.515855\pi\)
\(510\) 9.93623e37 + 1.33012e38i 0.0546329 + 0.0731349i
\(511\) −3.54943e38 + 2.09326e39i −0.189695 + 1.11871i
\(512\) 7.98225e38i 0.414678i
\(513\) −3.02701e38 + 1.11858e38i −0.152866 + 0.0564890i
\(514\) 1.78963e38i 0.0878612i
\(515\) 2.76923e39i 1.32177i
\(516\) 8.12991e38 6.07317e38i 0.377281 0.281835i
\(517\) 2.17110e36i 0.000979643i
\(518\) 5.10102e37 3.00830e38i 0.0223808 0.131989i
\(519\) 1.16038e39 8.66818e38i 0.495076 0.369829i
\(520\) −1.04578e39 −0.433903
\(521\) 4.59666e39 1.85479 0.927397 0.374079i \(-0.122041\pi\)
0.927397 + 0.374079i \(0.122041\pi\)
\(522\) −5.19232e37 + 1.75521e38i −0.0203770 + 0.0688823i
\(523\) 1.84113e39i 0.702766i −0.936232 0.351383i \(-0.885712\pi\)
0.936232 0.351383i \(-0.114288\pi\)
\(524\) −2.14194e39 −0.795249
\(525\) 3.37476e39 1.72966e39i 1.21880 0.624672i
\(526\) 1.33597e38 0.0469355
\(527\) 3.78132e38i 0.129238i
\(528\) −2.75697e39 3.69065e39i −0.916729 1.22719i
\(529\) −2.48449e39 −0.803768
\(530\) −5.59577e38 −0.176141
\(531\) −9.71357e38 + 3.28358e39i −0.297515 + 1.00572i
\(532\) 9.07457e37 5.35168e38i 0.0270463 0.159504i
\(533\) 2.42154e39i 0.702340i
\(534\) 3.47023e37 + 4.64546e37i 0.00979512 + 0.0131123i
\(535\) 5.75583e39i 1.58117i
\(536\) 4.38389e38i 0.117211i
\(537\) 9.62991e38 + 1.28912e39i 0.250608 + 0.335479i
\(538\) 2.02147e38i 0.0512064i
\(539\) 2.09352e39 5.99573e39i 0.516227 1.47844i
\(540\) 2.20658e39 + 5.97130e39i 0.529677 + 1.43337i
\(541\) −3.87248e39 −0.904959 −0.452479 0.891775i \(-0.649460\pi\)
−0.452479 + 0.891775i \(0.649460\pi\)
\(542\) 3.34065e38 0.0760049
\(543\) 1.44224e38 + 1.93067e38i 0.0319477 + 0.0427671i
\(544\) 8.16860e38i 0.176183i
\(545\) −5.98854e38 −0.125768
\(546\) 6.15548e38 3.15486e38i 0.125883 0.0645189i
\(547\) 1.53871e39 0.306436 0.153218 0.988192i \(-0.451036\pi\)
0.153218 + 0.988192i \(0.451036\pi\)
\(548\) 5.29268e39i 1.02650i
\(549\) −9.30821e39 2.75358e39i −1.75819 0.520114i
\(550\) 9.95697e38 0.183176
\(551\) 7.64940e38 0.137066
\(552\) −1.04921e39 + 7.83778e38i −0.183125 + 0.136797i
\(553\) −8.71444e39 1.47766e39i −1.48158 0.251224i
\(554\) 4.20828e38i 0.0696968i
\(555\) 1.19808e40 8.94986e39i 1.93303 1.44400i
\(556\) 9.38033e39i 1.47446i
\(557\) 1.96926e39i 0.301580i 0.988566 + 0.150790i \(0.0481817\pi\)
−0.988566 + 0.150790i \(0.951818\pi\)
\(558\) −3.02221e37 + 1.02163e38i −0.00450951 + 0.0152439i
\(559\) 5.40404e39i 0.785682i
\(560\) −1.04790e40 1.77687e39i −1.48454 0.251726i
\(561\) 4.71374e39 + 6.31010e39i 0.650735 + 0.871113i
\(562\) −3.18025e38 −0.0427844
\(563\) 1.17023e40 1.53426 0.767130 0.641491i \(-0.221684\pi\)
0.767130 + 0.641491i \(0.221684\pi\)
\(564\) 3.89369e36 2.90865e36i 0.000497524 0.000371658i
\(565\) 5.24885e39i 0.653675i
\(566\) −5.05255e38 −0.0613299
\(567\) −6.22315e39 5.71900e39i −0.736302 0.676653i
\(568\) 9.28087e36 0.00107038
\(569\) 7.01848e39i 0.789069i −0.918881 0.394534i \(-0.870906\pi\)
0.918881 0.394534i \(-0.129094\pi\)
\(570\) −1.56617e38 + 1.16995e38i −0.0171654 + 0.0128228i
\(571\) −1.23568e40 −1.32033 −0.660165 0.751121i \(-0.729514\pi\)
−0.660165 + 0.751121i \(0.729514\pi\)
\(572\) −2.47151e40 −2.57466
\(573\) −3.59278e39 4.80951e39i −0.364912 0.488494i
\(574\) −6.11418e37 + 3.60580e38i −0.00605502 + 0.0357092i
\(575\) 1.90482e40i 1.83938i
\(576\) 2.88154e39 9.74077e39i 0.271331 0.917207i
\(577\) 1.25657e40i 1.15381i 0.816810 + 0.576907i \(0.195741\pi\)
−0.816810 + 0.576907i \(0.804259\pi\)
\(578\) 4.93953e38i 0.0442315i
\(579\) 8.19485e39 6.12168e39i 0.715652 0.534603i
\(580\) 1.50898e40i 1.28522i
\(581\) −2.23424e40 3.78848e39i −1.85599 0.314711i
\(582\) −7.98287e38 + 5.96333e38i −0.0646809 + 0.0483176i
\(583\) −2.65463e40 −2.09802
\(584\) −2.50499e39 −0.193117
\(585\) 3.25081e40 + 9.61662e39i 2.44473 + 0.723207i
\(586\) 4.82951e38i 0.0354313i
\(587\) 1.00668e40 0.720507 0.360254 0.932854i \(-0.382690\pi\)
0.360254 + 0.932854i \(0.382690\pi\)
\(588\) 1.35575e40 4.27797e39i 0.946694 0.298722i
\(589\) 4.45236e38 0.0303332
\(590\) 2.07436e39i 0.137889i
\(591\) −1.62867e39 2.18023e39i −0.105636 0.141411i
\(592\) −2.42254e40 −1.53323
\(593\) 1.55472e38 0.00960197 0.00480098 0.999988i \(-0.498472\pi\)
0.00480098 + 0.999988i \(0.498472\pi\)
\(594\) −7.69215e38 2.08159e39i −0.0463601 0.125456i
\(595\) 1.79164e40 + 3.03800e39i 1.05379 + 0.178686i
\(596\) 1.15308e40i 0.661896i
\(597\) 1.24538e40 + 1.66714e40i 0.697707 + 0.933994i
\(598\) 3.47435e39i 0.189979i
\(599\) 2.22330e40i 1.18661i 0.804976 + 0.593307i \(0.202178\pi\)
−0.804976 + 0.593307i \(0.797822\pi\)
\(600\) 2.67769e39 + 3.58452e39i 0.139498 + 0.186740i
\(601\) 2.95704e40i 1.50376i 0.659302 + 0.751879i \(0.270852\pi\)
−0.659302 + 0.751879i \(0.729148\pi\)
\(602\) −1.36447e38 + 8.04690e38i −0.00677353 + 0.0399466i
\(603\) 4.03126e39 1.36273e40i 0.195362 0.660402i
\(604\) −9.38233e36 −0.000443890
\(605\) 4.83993e40 2.23556
\(606\) −7.05135e38 9.43936e38i −0.0317994 0.0425686i
\(607\) 3.19733e40i 1.40783i −0.710282 0.703917i \(-0.751433\pi\)
0.710282 0.703917i \(-0.248567\pi\)
\(608\) 9.61822e38 0.0413517
\(609\) 9.13786e39 + 1.78289e40i 0.383613 + 0.748471i
\(610\) −5.88034e39 −0.241057
\(611\) 2.58818e37i 0.00103609i
\(612\) −5.00159e39 + 1.69074e40i −0.195529 + 0.660968i
\(613\) 3.18991e40 1.21787 0.608936 0.793220i \(-0.291597\pi\)
0.608936 + 0.793220i \(0.291597\pi\)
\(614\) −1.72261e39 −0.0642310
\(615\) −1.43604e40 + 1.07275e40i −0.522972 + 0.390668i
\(616\) 7.38747e39 + 1.25265e39i 0.262770 + 0.0445565i
\(617\) 3.69563e40i 1.28397i −0.766719 0.641983i \(-0.778112\pi\)
0.766719 0.641983i \(-0.221888\pi\)
\(618\) 1.73128e39 1.29329e39i 0.0587536 0.0438899i
\(619\) 2.50412e40i 0.830118i 0.909794 + 0.415059i \(0.136239\pi\)
−0.909794 + 0.415059i \(0.863761\pi\)
\(620\) 8.78306e39i 0.284424i
\(621\) 3.98220e40 1.47155e40i 1.25978 0.465529i
\(622\) 2.36128e39i 0.0729771i
\(623\) 6.25731e39 + 1.06102e39i 0.188934 + 0.0320366i
\(624\) −3.28659e40 4.39963e40i −0.969548 1.29790i
\(625\) −1.71345e40 −0.493868
\(626\) 3.08332e38 0.00868342
\(627\) −7.42991e39 + 5.55025e39i −0.204458 + 0.152733i
\(628\) 3.60772e40i 0.970104i
\(629\) 4.14194e40 1.08835
\(630\) −4.59781e39 2.25277e39i −0.118063 0.0578467i
\(631\) −4.78919e40 −1.20181 −0.600906 0.799320i \(-0.705194\pi\)
−0.600906 + 0.799320i \(0.705194\pi\)
\(632\) 1.04285e40i 0.255756i
\(633\) −4.98595e40 + 3.72458e40i −1.19507 + 0.892737i
\(634\) 4.65552e39 0.109062
\(635\) −3.40280e39 −0.0779143
\(636\) −3.55642e40 4.76085e40i −0.795949 1.06551i
\(637\) 2.49569e40 7.14752e40i 0.545971 1.56363i
\(638\) 5.26029e39i 0.112489i
\(639\) −2.88495e38 8.53434e37i −0.00603081 0.00178405i
\(640\) 2.52666e40i 0.516342i
\(641\) 2.95196e40i 0.589751i −0.955536 0.294876i \(-0.904722\pi\)
0.955536 0.294876i \(-0.0952783\pi\)
\(642\) 3.59845e39 2.68810e39i 0.0702842 0.0525034i
\(643\) 7.38431e40i 1.41010i 0.709156 + 0.705052i \(0.249076\pi\)
−0.709156 + 0.705052i \(0.750924\pi\)
\(644\) −1.19381e40 + 7.04045e40i −0.222890 + 1.31448i
\(645\) −3.20475e40 + 2.39400e40i −0.585030 + 0.437027i
\(646\) −5.41449e38 −0.00966464
\(647\) 8.34491e40 1.45650 0.728248 0.685314i \(-0.240335\pi\)
0.728248 + 0.685314i \(0.240335\pi\)
\(648\) 5.42513e39 8.36713e39i 0.0925919 0.142804i
\(649\) 9.84073e40i 1.64240i
\(650\) 1.18697e40 0.193730
\(651\) 5.31873e39 + 1.03774e40i 0.0848952 + 0.165640i
\(652\) 7.07028e40 1.10369
\(653\) 7.49523e40i 1.14431i −0.820145 0.572155i \(-0.806107\pi\)
0.820145 0.572155i \(-0.193893\pi\)
\(654\) 2.79678e38 + 3.74394e38i 0.00417620 + 0.00559051i
\(655\) 8.44336e40 1.23315
\(656\) 2.90371e40 0.414808
\(657\) 7.78674e40 + 2.30349e40i 1.08807 + 0.321877i
\(658\) −6.53492e35 + 3.85393e36i −8.93233e−6 + 5.26779e-5i
\(659\) 8.48295e40i 1.13425i 0.823632 + 0.567125i \(0.191944\pi\)
−0.823632 + 0.567125i \(0.808056\pi\)
\(660\) 1.09488e41 + 1.46568e41i 1.43213 + 1.91713i
\(661\) 1.12075e41i 1.43413i −0.697007 0.717065i \(-0.745485\pi\)
0.697007 0.717065i \(-0.254515\pi\)
\(662\) 4.89582e39i 0.0612893i
\(663\) 5.61925e40 + 7.52228e40i 0.688228 + 0.921304i
\(664\) 2.67370e40i 0.320388i
\(665\) −3.57713e39 + 2.10959e40i −0.0419393 + 0.247335i
\(666\) −1.11906e40 3.31044e39i −0.128374 0.0379760i
\(667\) −1.00632e41 −1.12957
\(668\) 3.44409e40 0.378282
\(669\) −5.87966e40 7.87087e40i −0.631937 0.845949i
\(670\) 8.60885e39i 0.0905442i
\(671\) −2.78963e41 −2.87124
\(672\) 1.14898e40 + 2.24178e40i 0.115733 + 0.225808i
\(673\) 5.52796e40 0.544937 0.272469 0.962165i \(-0.412160\pi\)
0.272469 + 0.962165i \(0.412160\pi\)
\(674\) 1.77139e39i 0.0170901i
\(675\) −5.02738e40 1.36047e41i −0.474720 1.28465i
\(676\) −1.87219e41 −1.73030
\(677\) −4.74373e40 −0.429125 −0.214563 0.976710i \(-0.568833\pi\)
−0.214563 + 0.976710i \(0.568833\pi\)
\(678\) 3.28150e39 2.45133e39i 0.0290564 0.0217056i
\(679\) −1.82328e40 + 1.07527e41i −0.158031 + 0.931980i
\(680\) 2.14405e40i 0.181910i
\(681\) 7.59514e40 5.67369e40i 0.630816 0.471229i
\(682\) 3.06177e39i 0.0248943i
\(683\) 1.82712e41i 1.45434i −0.686456 0.727171i \(-0.740835\pi\)
0.686456 0.727171i \(-0.259165\pi\)
\(684\) −1.99078e40 5.88919e39i −0.155135 0.0458925i
\(685\) 2.08634e41i 1.59174i
\(686\) −5.52090e39 + 1.00129e40i −0.0412392 + 0.0747928i
\(687\) −7.33151e40 9.81441e40i −0.536193 0.717780i
\(688\) 6.48006e40 0.464031
\(689\) −3.16458e41 −2.21890
\(690\) 2.06039e40 1.53914e40i 0.141461 0.105674i
\(691\) 1.17641e41i 0.790909i −0.918486 0.395455i \(-0.870587\pi\)
0.918486 0.395455i \(-0.129413\pi\)
\(692\) 9.31791e40 0.613452
\(693\) −2.18120e41 1.06871e41i −1.40625 0.689014i
\(694\) −1.44514e40 −0.0912424
\(695\) 3.69766e41i 2.28637i
\(696\) −1.89371e40 + 1.41463e40i −0.114678 + 0.0856661i
\(697\) −4.96462e40 −0.294449
\(698\) 1.28311e40 0.0745351
\(699\) −1.24869e41 1.67157e41i −0.710452 0.951054i
\(700\) 2.40529e41 + 4.07852e40i 1.34043 + 0.227291i
\(701\) 1.32146e41i 0.721343i −0.932693 0.360672i \(-0.882548\pi\)
0.932693 0.360672i \(-0.117452\pi\)
\(702\) −9.16982e39 2.48147e40i −0.0490312 0.132685i
\(703\) 4.87699e40i 0.255446i
\(704\) 2.91926e41i 1.49785i
\(705\) −1.53486e38 + 1.14657e38i −0.000771485 + 0.000576311i
\(706\) 1.40980e40i 0.0694207i
\(707\) −1.27146e41 2.15595e40i −0.613367 0.104006i
\(708\) −1.76485e41 + 1.31837e41i −0.834115 + 0.623097i
\(709\) −1.20297e41 −0.557036 −0.278518 0.960431i \(-0.589843\pi\)
−0.278518 + 0.960431i \(0.589843\pi\)
\(710\) −1.82253e38 −0.000826853
\(711\) −9.58969e40 + 3.24170e41i −0.426280 + 1.44100i
\(712\) 7.48810e39i 0.0326146i
\(713\) −5.85734e40 −0.249978
\(714\) −6.46806e39 1.26199e40i −0.0270489 0.0527754i
\(715\) 9.74251e41 3.99239
\(716\) 1.03517e41i 0.415694i
\(717\) 8.49566e40 + 1.13728e41i 0.334326 + 0.447549i
\(718\) −1.84041e40 −0.0709757
\(719\) 4.09014e41 1.54586 0.772929 0.634492i \(-0.218791\pi\)
0.772929 + 0.634492i \(0.218791\pi\)
\(720\) −1.15314e41 + 3.89809e41i −0.427132 + 1.44388i
\(721\) 3.95424e40 2.33199e41i 0.143549 0.846575i
\(722\) 2.33669e40i 0.0831403i
\(723\) −5.16800e40 6.91820e40i −0.180226 0.241262i
\(724\) 1.55034e40i 0.0529929i
\(725\) 3.43799e41i 1.15187i
\(726\) −2.26035e40 3.02585e40i −0.0742327 0.0993725i
\(727\) 4.68908e41i 1.50952i −0.656001 0.754760i \(-0.727753\pi\)
0.656001 0.754760i \(-0.272247\pi\)
\(728\) 8.80661e40 + 1.49329e40i 0.277910 + 0.0471237i
\(729\) −2.45581e41 + 2.10204e41i −0.759706 + 0.650267i
\(730\) 4.91917e40 0.149180
\(731\) −1.10793e41 −0.329390
\(732\) −3.73728e41 5.00296e41i −1.08930 1.45820i
\(733\) 2.91963e41i 0.834297i 0.908838 + 0.417149i \(0.136971\pi\)
−0.908838 + 0.417149i \(0.863029\pi\)
\(734\) −3.17984e39 −0.00890867
\(735\) −5.34428e41 + 1.68634e41i −1.46799 + 0.463212i
\(736\) −1.26533e41 −0.340782
\(737\) 4.08403e41i 1.07848i
\(738\) 1.34133e40 + 3.96796e39i 0.0347311 + 0.0102742i
\(739\) 3.80301e41 0.965568 0.482784 0.875740i \(-0.339626\pi\)
0.482784 + 0.875740i \(0.339626\pi\)
\(740\) 9.62070e41 2.39523
\(741\) −8.85720e40 + 6.61647e40i −0.216238 + 0.161533i
\(742\) 4.71223e40 + 7.99030e39i 0.112816 + 0.0191296i
\(743\) 3.20943e41i 0.753512i 0.926313 + 0.376756i \(0.122960\pi\)
−0.926313 + 0.376756i \(0.877040\pi\)
\(744\) −1.10224e40 + 8.23391e39i −0.0253787 + 0.0189583i
\(745\) 4.54536e41i 1.02637i
\(746\) 1.99219e40i 0.0441182i
\(747\) −2.45864e41 + 8.31118e41i −0.534005 + 1.80515i
\(748\) 5.06706e41i 1.07940i
\(749\) 8.21885e40 4.84702e41i 0.171721 1.01272i
\(750\) −1.41889e40 1.89941e40i −0.0290777 0.0389252i
\(751\) 1.32199e41 0.265736 0.132868 0.991134i \(-0.457581\pi\)
0.132868 + 0.991134i \(0.457581\pi\)
\(752\) 3.10352e38 0.000611922
\(753\) 4.41083e41 3.29496e41i 0.853086 0.637269i