Properties

Label 21.30.c.a.20.14
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 20.14
Character \(\chi\) \(=\) 21.20
Dual form 21.30.c.a.20.13

$q$-expansion

\(f(q)\) \(=\) \(q+42628.6i q^{2} +(-4.19005e6 - 7.14660e6i) q^{3} -1.28033e9 q^{4} -1.62384e10 q^{5} +(3.04650e11 - 1.78616e11i) q^{6} +(1.66265e12 - 6.74901e11i) q^{7} -3.16925e13i q^{8} +(-3.35174e13 + 5.98892e13i) q^{9} +O(q^{10})\) \(q+42628.6i q^{2} +(-4.19005e6 - 7.14660e6i) q^{3} -1.28033e9 q^{4} -1.62384e10 q^{5} +(3.04650e11 - 1.78616e11i) q^{6} +(1.66265e12 - 6.74901e11i) q^{7} -3.16925e13i q^{8} +(-3.35174e13 + 5.98892e13i) q^{9} -6.92219e14i q^{10} -1.89246e15i q^{11} +(5.36463e15 + 9.14999e15i) q^{12} +1.67013e16i q^{13} +(2.87701e16 + 7.08766e16i) q^{14} +(6.80395e16 + 1.16049e17i) q^{15} +6.63637e17 q^{16} +1.70898e17 q^{17} +(-2.55299e18 - 1.42880e18i) q^{18} +2.87863e18i q^{19} +2.07904e19 q^{20} +(-1.17898e19 - 9.05445e18i) q^{21} +8.06728e19 q^{22} +8.58865e18i q^{23} +(-2.26494e20 + 1.32793e20i) q^{24} +7.74198e19 q^{25} -7.11953e20 q^{26} +(5.68443e20 - 1.14028e19i) q^{27} +(-2.12874e21 + 8.64094e20i) q^{28} -1.33896e21i q^{29} +(-4.94701e21 + 2.90043e21i) q^{30} +8.21487e21i q^{31} +1.12751e22i q^{32} +(-1.35246e22 + 7.92948e21i) q^{33} +7.28513e21i q^{34} +(-2.69988e22 + 1.09593e22i) q^{35} +(4.29133e22 - 7.66777e22i) q^{36} -6.15011e22 q^{37} -1.22712e23 q^{38} +(1.19358e23 - 6.99792e22i) q^{39} +5.14634e23i q^{40} -2.49794e21 q^{41} +(3.85979e23 - 5.02584e23i) q^{42} +8.52749e23 q^{43} +2.42296e24i q^{44} +(5.44268e23 - 9.72502e23i) q^{45} -3.66122e23 q^{46} -2.18694e24 q^{47} +(-2.78067e24 - 4.74275e24i) q^{48} +(2.30892e24 - 2.24425e24i) q^{49} +3.30030e24i q^{50} +(-7.16069e23 - 1.22134e24i) q^{51} -2.13831e25i q^{52} +1.34081e25i q^{53} +(4.86084e23 + 2.42320e25i) q^{54} +3.07304e25i q^{55} +(-2.13893e25 - 5.26936e25i) q^{56} +(2.05724e25 - 1.20616e25i) q^{57} +5.70780e25 q^{58} -2.12081e25 q^{59} +(-8.71128e25 - 1.48581e26i) q^{60} -5.23975e25i q^{61} -3.50188e26 q^{62} +(-1.53086e25 + 1.22196e26i) q^{63} -1.24356e26 q^{64} -2.71202e26i q^{65} +(-3.38023e26 - 5.76536e26i) q^{66} +1.73869e26 q^{67} -2.18805e26 q^{68} +(6.13796e25 - 3.59868e25i) q^{69} +(-4.67179e26 - 1.15092e27i) q^{70} +1.36215e26i q^{71} +(1.89804e27 + 1.06225e27i) q^{72} +1.03806e27i q^{73} -2.62171e27i q^{74} +(-3.24393e26 - 5.53288e26i) q^{75} -3.68558e27i q^{76} +(-1.27722e27 - 3.14650e27i) q^{77} +(2.98312e27 + 5.08804e27i) q^{78} +1.92827e27 q^{79} -1.07764e28 q^{80} +(-2.46329e27 - 4.01466e27i) q^{81} -1.06484e26i q^{82} +5.55458e27 q^{83} +(1.50949e28 + 1.15927e28i) q^{84} -2.77510e27 q^{85} +3.63515e28i q^{86} +(-9.56902e27 + 5.61031e27i) q^{87} -5.99767e28 q^{88} -3.90521e26 q^{89} +(4.14564e28 + 2.32014e28i) q^{90} +(1.12717e28 + 2.77685e28i) q^{91} -1.09963e28i q^{92} +(5.87084e28 - 3.44207e28i) q^{93} -9.32264e28i q^{94} -4.67442e28i q^{95} +(8.05790e28 - 4.72434e28i) q^{96} +2.98614e28i q^{97} +(9.56693e28 + 9.84262e28i) q^{98} +(1.13338e29 + 6.34302e28i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 42628.6i 1.83978i 0.392175 + 0.919891i \(0.371723\pi\)
−0.392175 + 0.919891i \(0.628277\pi\)
\(3\) −4.19005e6 7.14660e6i −0.505779 0.862663i
\(4\) −1.28033e9 −2.38480
\(5\) −1.62384e10 −1.18981 −0.594904 0.803797i \(-0.702810\pi\)
−0.594904 + 0.803797i \(0.702810\pi\)
\(6\) 3.04650e11 1.78616e11i 1.58711 0.930522i
\(7\) 1.66265e12 6.74901e11i 0.926574 0.376113i
\(8\) 3.16925e13i 2.54772i
\(9\) −3.35174e13 + 5.98892e13i −0.488376 + 0.872633i
\(10\) 6.92219e14i 2.18899i
\(11\) 1.89246e15i 1.50256i −0.659984 0.751280i \(-0.729437\pi\)
0.659984 0.751280i \(-0.270563\pi\)
\(12\) 5.36463e15 + 9.14999e15i 1.20618 + 2.05728i
\(13\) 1.67013e16i 1.17644i 0.808699 + 0.588222i \(0.200172\pi\)
−0.808699 + 0.588222i \(0.799828\pi\)
\(14\) 2.87701e16 + 7.08766e16i 0.691966 + 1.70469i
\(15\) 6.80395e16 + 1.16049e17i 0.601780 + 1.02640i
\(16\) 6.63637e17 2.30245
\(17\) 1.70898e17 0.246165 0.123083 0.992396i \(-0.460722\pi\)
0.123083 + 0.992396i \(0.460722\pi\)
\(18\) −2.55299e18 1.42880e18i −1.60545 0.898505i
\(19\) 2.87863e18i 0.826529i 0.910611 + 0.413265i \(0.135612\pi\)
−0.910611 + 0.413265i \(0.864388\pi\)
\(20\) 2.07904e19 2.83745
\(21\) −1.17898e19 9.05445e18i −0.793100 0.609091i
\(22\) 8.06728e19 2.76438
\(23\) 8.58865e18i 0.154480i 0.997013 + 0.0772398i \(0.0246107\pi\)
−0.997013 + 0.0772398i \(0.975389\pi\)
\(24\) −2.26494e20 + 1.32793e20i −2.19783 + 1.28858i
\(25\) 7.74198e19 0.415644
\(26\) −7.11953e20 −2.16440
\(27\) 5.68443e20 1.14028e19i 0.999799 0.0200556i
\(28\) −2.12874e21 + 8.64094e20i −2.20969 + 0.896953i
\(29\) 1.33896e21i 0.835597i −0.908540 0.417799i \(-0.862802\pi\)
0.908540 0.417799i \(-0.137198\pi\)
\(30\) −4.94701e21 + 2.90043e21i −1.88836 + 1.10714i
\(31\) 8.21487e21i 1.94920i 0.223955 + 0.974599i \(0.428103\pi\)
−0.223955 + 0.974599i \(0.571897\pi\)
\(32\) 1.12751e22i 1.68829i
\(33\) −1.35246e22 + 7.92948e21i −1.29620 + 0.759963i
\(34\) 7.28513e21i 0.452890i
\(35\) −2.69988e22 + 1.09593e22i −1.10245 + 0.447503i
\(36\) 4.29133e22 7.66777e22i 1.16468 2.08105i
\(37\) −6.15011e22 −1.12191 −0.560955 0.827846i \(-0.689566\pi\)
−0.560955 + 0.827846i \(0.689566\pi\)
\(38\) −1.22712e23 −1.52063
\(39\) 1.19358e23 6.99792e22i 1.01488 0.595021i
\(40\) 5.14634e23i 3.03130i
\(41\) −2.49794e21 −0.0102853 −0.00514264 0.999987i \(-0.501637\pi\)
−0.00514264 + 0.999987i \(0.501637\pi\)
\(42\) 3.85979e23 5.02584e23i 1.12059 1.45913i
\(43\) 8.52749e23 1.76006 0.880032 0.474914i \(-0.157521\pi\)
0.880032 + 0.474914i \(0.157521\pi\)
\(44\) 2.42296e24i 3.58330i
\(45\) 5.44268e23 9.72502e23i 0.581074 1.03827i
\(46\) −3.66122e23 −0.284209
\(47\) −2.18694e24 −1.24285 −0.621425 0.783474i \(-0.713446\pi\)
−0.621425 + 0.783474i \(0.713446\pi\)
\(48\) −2.78067e24 4.74275e24i −1.16453 1.98624i
\(49\) 2.30892e24 2.24425e24i 0.717078 0.696993i
\(50\) 3.30030e24i 0.764695i
\(51\) −7.16069e23 1.22134e24i −0.124505 0.212358i
\(52\) 2.13831e25i 2.80558i
\(53\) 1.34081e25i 1.33465i 0.744768 + 0.667323i \(0.232560\pi\)
−0.744768 + 0.667323i \(0.767440\pi\)
\(54\) 4.86084e23 + 2.42320e25i 0.0368979 + 1.83941i
\(55\) 3.07304e25i 1.78776i
\(56\) −2.13893e25 5.26936e25i −0.958231 2.36065i
\(57\) 2.05724e25 1.20616e25i 0.713016 0.418041i
\(58\) 5.70780e25 1.53732
\(59\) −2.12081e25 −0.445807 −0.222904 0.974840i \(-0.571554\pi\)
−0.222904 + 0.974840i \(0.571554\pi\)
\(60\) −8.71128e25 1.48581e26i −1.43512 2.44776i
\(61\) 5.23975e25i 0.679247i −0.940561 0.339623i \(-0.889700\pi\)
0.940561 0.339623i \(-0.110300\pi\)
\(62\) −3.50188e26 −3.58610
\(63\) −1.53086e25 + 1.22196e26i −0.124307 + 0.992244i
\(64\) −1.24356e26 −0.803633
\(65\) 2.71202e26i 1.39974i
\(66\) −3.38023e26 5.76536e26i −1.39817 2.38473i
\(67\) 1.73869e26 0.578279 0.289140 0.957287i \(-0.406631\pi\)
0.289140 + 0.957287i \(0.406631\pi\)
\(68\) −2.18805e26 −0.587053
\(69\) 6.13796e25 3.59868e25i 0.133264 0.0781325i
\(70\) −4.67179e26 1.15092e27i −0.823307 2.02826i
\(71\) 1.36215e26i 0.195424i 0.995215 + 0.0977121i \(0.0311524\pi\)
−0.995215 + 0.0977121i \(0.968848\pi\)
\(72\) 1.89804e27 + 1.06225e27i 2.22323 + 1.24425i
\(73\) 1.03806e27i 0.995504i 0.867320 + 0.497752i \(0.165841\pi\)
−0.867320 + 0.497752i \(0.834159\pi\)
\(74\) 2.62171e27i 2.06407i
\(75\) −3.24393e26 5.53288e26i −0.210224 0.358561i
\(76\) 3.68558e27i 1.97110i
\(77\) −1.27722e27 3.14650e27i −0.565133 1.39223i
\(78\) 2.98312e27 + 5.08804e27i 1.09471 + 1.86715i
\(79\) 1.92827e27 0.588267 0.294133 0.955764i \(-0.404969\pi\)
0.294133 + 0.955764i \(0.404969\pi\)
\(80\) −1.07764e28 −2.73948
\(81\) −2.46329e27 4.01466e27i −0.522978 0.852346i
\(82\) 1.06484e26i 0.0189227i
\(83\) 5.55458e27 0.827978 0.413989 0.910282i \(-0.364135\pi\)
0.413989 + 0.910282i \(0.364135\pi\)
\(84\) 1.50949e28 + 1.15927e28i 1.89138 + 1.45256i
\(85\) −2.77510e27 −0.292889
\(86\) 3.63515e28i 3.23813i
\(87\) −9.56902e27 + 5.61031e27i −0.720839 + 0.422627i
\(88\) −5.99767e28 −3.82810
\(89\) −3.90521e26 −0.0211587 −0.0105794 0.999944i \(-0.503368\pi\)
−0.0105794 + 0.999944i \(0.503368\pi\)
\(90\) 4.14564e28 + 2.32014e28i 1.91018 + 1.06905i
\(91\) 1.12717e28 + 2.77685e28i 0.442476 + 1.09006i
\(92\) 1.09963e28i 0.368402i
\(93\) 5.87084e28 3.44207e28i 1.68150 0.985863i
\(94\) 9.32264e28i 2.28657i
\(95\) 4.67442e28i 0.983411i
\(96\) 8.05790e28 4.72434e28i 1.45643 0.853902i
\(97\) 2.98614e28i 0.464429i 0.972665 + 0.232215i \(0.0745972\pi\)
−0.972665 + 0.232215i \(0.925403\pi\)
\(98\) 9.56693e28 + 9.84262e28i 1.28231 + 1.31927i
\(99\) 1.13338e29 + 6.34302e28i 1.31118 + 0.733814i
\(100\) −9.91227e28 −0.991227
\(101\) 1.65441e29 1.43213 0.716066 0.698032i \(-0.245941\pi\)
0.716066 + 0.698032i \(0.245941\pi\)
\(102\) 5.20639e28 3.05250e28i 0.390692 0.229062i
\(103\) 4.45488e28i 0.290199i −0.989417 0.145099i \(-0.953650\pi\)
0.989417 0.145099i \(-0.0463502\pi\)
\(104\) 5.29306e29 2.99725
\(105\) 1.91448e29 + 1.47029e29i 0.943637 + 0.724702i
\(106\) −5.71567e29 −2.45546
\(107\) 1.85090e29i 0.693933i −0.937878 0.346966i \(-0.887212\pi\)
0.937878 0.346966i \(-0.112788\pi\)
\(108\) −7.27794e29 + 1.45993e28i −2.38432 + 0.0478285i
\(109\) −1.95150e29 −0.559350 −0.279675 0.960095i \(-0.590227\pi\)
−0.279675 + 0.960095i \(0.590227\pi\)
\(110\) −1.30999e30 −3.28909
\(111\) 2.57693e29 + 4.39524e29i 0.567438 + 0.967831i
\(112\) 1.10340e30 4.47889e29i 2.13339 0.865983i
\(113\) 8.95088e29i 1.52135i −0.649135 0.760673i \(-0.724869\pi\)
0.649135 0.760673i \(-0.275131\pi\)
\(114\) 5.14168e29 + 8.76973e29i 0.769104 + 1.31179i
\(115\) 1.39466e29i 0.183801i
\(116\) 1.71431e30i 1.99273i
\(117\) −1.00023e30 5.59784e29i −1.02661 0.574547i
\(118\) 9.04071e29i 0.820188i
\(119\) 2.84143e29 1.15339e29i 0.228090 0.0925859i
\(120\) 3.67789e30 2.15634e30i 2.61499 1.53317i
\(121\) −1.99508e30 −1.25769
\(122\) 2.23363e30 1.24967
\(123\) 1.04665e28 + 1.78518e28i 0.00520208 + 0.00887274i
\(124\) 1.05177e31i 4.64844i
\(125\) 1.76746e30 0.695271
\(126\) −5.20904e30 6.52583e29i −1.82551 0.228698i
\(127\) 7.73525e29 0.241724 0.120862 0.992669i \(-0.461434\pi\)
0.120862 + 0.992669i \(0.461434\pi\)
\(128\) 7.52166e29i 0.209782i
\(129\) −3.57306e30 6.09426e30i −0.890203 1.51834i
\(130\) 1.15610e31 2.57522
\(131\) −7.88995e30 −1.57268 −0.786340 0.617794i \(-0.788027\pi\)
−0.786340 + 0.617794i \(0.788027\pi\)
\(132\) 1.73159e31 1.01523e31i 3.09118 1.81236i
\(133\) 1.94279e30 + 4.78616e30i 0.310868 + 0.765840i
\(134\) 7.41180e30i 1.06391i
\(135\) −9.23059e30 + 1.85162e29i −1.18957 + 0.0238623i
\(136\) 5.41617e30i 0.627160i
\(137\) 7.65395e30i 0.796962i −0.917177 0.398481i \(-0.869537\pi\)
0.917177 0.398481i \(-0.130463\pi\)
\(138\) 1.53407e30 + 2.61653e30i 0.143747 + 0.245176i
\(139\) 1.56074e31i 1.31709i 0.752540 + 0.658547i \(0.228828\pi\)
−0.752540 + 0.658547i \(0.771172\pi\)
\(140\) 3.45672e31 1.40315e31i 2.62911 1.06720i
\(141\) 9.16339e30 + 1.56292e31i 0.628607 + 1.07216i
\(142\) −5.80665e30 −0.359538
\(143\) 3.16065e31 1.76768
\(144\) −2.22434e31 + 3.97447e31i −1.12446 + 2.00920i
\(145\) 2.17425e31i 0.994201i
\(146\) −4.42512e31 −1.83151
\(147\) −2.57133e31 7.09743e30i −0.963953 0.266072i
\(148\) 7.87416e31 2.67553
\(149\) 3.20467e31i 0.987603i 0.869575 + 0.493801i \(0.164393\pi\)
−0.869575 + 0.493801i \(0.835607\pi\)
\(150\) 2.35859e31 1.38284e31i 0.659674 0.386766i
\(151\) −4.16619e31 −1.05821 −0.529107 0.848555i \(-0.677473\pi\)
−0.529107 + 0.848555i \(0.677473\pi\)
\(152\) 9.12309e31 2.10577
\(153\) −5.72804e30 + 1.02349e31i −0.120221 + 0.214812i
\(154\) 1.34131e32 5.44461e31i 2.56140 1.03972i
\(155\) 1.33396e32i 2.31917i
\(156\) −1.52817e32 + 8.95963e31i −2.42027 + 1.41900i
\(157\) 5.28389e31i 0.762797i −0.924411 0.381399i \(-0.875443\pi\)
0.924411 0.381399i \(-0.124557\pi\)
\(158\) 8.21993e31i 1.08228i
\(159\) 9.58221e31 5.61804e31i 1.15135 0.675035i
\(160\) 1.83090e32i 2.00874i
\(161\) 5.79649e30 + 1.42799e31i 0.0581018 + 0.143137i
\(162\) 1.71139e32 1.05007e32i 1.56813 0.962166i
\(163\) −2.67602e31 −0.224269 −0.112134 0.993693i \(-0.535769\pi\)
−0.112134 + 0.993693i \(0.535769\pi\)
\(164\) 3.19818e30 0.0245283
\(165\) 2.19618e32 1.28762e32i 1.54223 0.904210i
\(166\) 2.36784e32i 1.52330i
\(167\) −2.65867e32 −1.56774 −0.783872 0.620923i \(-0.786758\pi\)
−0.783872 + 0.620923i \(0.786758\pi\)
\(168\) −2.86958e32 + 3.73650e32i −1.55179 + 2.02060i
\(169\) −7.73952e31 −0.384023
\(170\) 1.18298e32i 0.538852i
\(171\) −1.72399e32 9.64841e31i −0.721257 0.403657i
\(172\) −1.09180e33 −4.19739
\(173\) 8.39332e31 0.296664 0.148332 0.988938i \(-0.452610\pi\)
0.148332 + 0.988938i \(0.452610\pi\)
\(174\) −2.39160e32 4.07914e32i −0.777542 1.32619i
\(175\) 1.28722e32 5.22507e31i 0.385125 0.156329i
\(176\) 1.25590e33i 3.45958i
\(177\) 8.88629e31 + 1.51566e32i 0.225480 + 0.384582i
\(178\) 1.66474e31i 0.0389274i
\(179\) 2.95712e32i 0.637529i −0.947834 0.318764i \(-0.896732\pi\)
0.947834 0.318764i \(-0.103268\pi\)
\(180\) −6.96841e32 + 1.24512e33i −1.38574 + 2.47605i
\(181\) 4.15225e32i 0.761981i 0.924579 + 0.380991i \(0.124417\pi\)
−0.924579 + 0.380991i \(0.875583\pi\)
\(182\) −1.18373e33 + 4.80498e32i −2.00548 + 0.814060i
\(183\) −3.74464e32 + 2.19548e32i −0.585961 + 0.343549i
\(184\) 2.72196e32 0.393571
\(185\) 9.98678e32 1.33486
\(186\) 1.46731e33 + 2.50266e33i 1.81377 + 3.09360i
\(187\) 3.23416e32i 0.369878i
\(188\) 2.80000e33 2.96394
\(189\) 9.37428e32 4.02602e32i 0.918844 0.394620i
\(190\) 1.99264e33 1.80926
\(191\) 1.57626e33i 1.32631i −0.748483 0.663154i \(-0.769218\pi\)
0.748483 0.663154i \(-0.230782\pi\)
\(192\) 5.21058e32 + 8.88724e32i 0.406460 + 0.693265i
\(193\) −2.12406e33 −1.53669 −0.768343 0.640038i \(-0.778919\pi\)
−0.768343 + 0.640038i \(0.778919\pi\)
\(194\) −1.27295e33 −0.854448
\(195\) −1.93817e33 + 1.13635e33i −1.20751 + 0.707961i
\(196\) −2.95618e33 + 2.87338e33i −1.71008 + 1.66219i
\(197\) 3.51020e31i 0.0188613i 0.999956 + 0.00943065i \(0.00300191\pi\)
−0.999956 + 0.00943065i \(0.996998\pi\)
\(198\) −2.70394e33 + 4.83142e33i −1.35006 + 2.41229i
\(199\) 4.24135e33i 1.96849i −0.176799 0.984247i \(-0.556574\pi\)
0.176799 0.984247i \(-0.443426\pi\)
\(200\) 2.45363e33i 1.05895i
\(201\) −7.28519e32 1.24257e33i −0.292481 0.498860i
\(202\) 7.05252e33i 2.63481i
\(203\) −9.03666e32 2.22623e33i −0.314279 0.774242i
\(204\) 9.16802e32 + 1.56371e33i 0.296919 + 0.506429i
\(205\) 4.05625e31 0.0122375
\(206\) 1.89905e33 0.533903
\(207\) −5.14367e32 2.87869e32i −0.134804 0.0754441i
\(208\) 1.10836e34i 2.70871i
\(209\) 5.44767e33 1.24191
\(210\) −6.26766e33 + 8.16115e33i −1.33329 + 1.73609i
\(211\) −9.91975e32 −0.196972 −0.0984861 0.995138i \(-0.531400\pi\)
−0.0984861 + 0.995138i \(0.531400\pi\)
\(212\) 1.71667e34i 3.18286i
\(213\) 9.73473e32 5.70746e32i 0.168585 0.0988414i
\(214\) 7.89011e33 1.27668
\(215\) −1.38472e34 −2.09414
\(216\) −3.61382e32 1.80154e34i −0.0510961 2.54721i
\(217\) 5.54422e33 + 1.36585e34i 0.733119 + 1.80608i
\(218\) 8.31897e33i 1.02908i
\(219\) 7.41863e33 4.34954e33i 0.858784 0.503505i
\(220\) 3.93449e34i 4.26344i
\(221\) 2.85421e33i 0.289600i
\(222\) −1.87363e34 + 1.09851e34i −1.78060 + 1.04396i
\(223\) 1.85405e34i 1.65083i −0.564528 0.825414i \(-0.690942\pi\)
0.564528 0.825414i \(-0.309058\pi\)
\(224\) 7.60961e33 + 1.87467e34i 0.634989 + 1.56433i
\(225\) −2.59491e33 + 4.63661e33i −0.202991 + 0.362705i
\(226\) 3.81563e34 2.79895
\(227\) −1.20656e33 −0.0830186 −0.0415093 0.999138i \(-0.513217\pi\)
−0.0415093 + 0.999138i \(0.513217\pi\)
\(228\) −2.63394e34 + 1.54428e34i −1.70040 + 0.996942i
\(229\) 1.39988e34i 0.848159i −0.905625 0.424079i \(-0.860598\pi\)
0.905625 0.424079i \(-0.139402\pi\)
\(230\) 5.94522e33 0.338154
\(231\) −1.71351e34 + 2.23117e34i −0.915196 + 1.19168i
\(232\) −4.24350e34 −2.12887
\(233\) 5.02379e33i 0.236794i −0.992966 0.118397i \(-0.962224\pi\)
0.992966 0.118397i \(-0.0377756\pi\)
\(234\) 2.38628e34 4.26383e34i 1.05704 1.88873i
\(235\) 3.55124e34 1.47875
\(236\) 2.71533e34 1.06316
\(237\) −8.07953e33 1.37806e34i −0.297533 0.507476i
\(238\) 4.91674e33 + 1.21126e34i 0.170338 + 0.419636i
\(239\) 2.45052e34i 0.798894i −0.916756 0.399447i \(-0.869202\pi\)
0.916756 0.399447i \(-0.130798\pi\)
\(240\) 4.51535e34 + 7.70145e34i 1.38557 + 2.36325i
\(241\) 4.09826e34i 1.18400i −0.805938 0.592000i \(-0.798338\pi\)
0.805938 0.592000i \(-0.201662\pi\)
\(242\) 8.50475e34i 2.31387i
\(243\) −1.83698e34 + 3.44258e34i −0.470776 + 0.882253i
\(244\) 6.70859e34i 1.61986i
\(245\) −3.74931e34 + 3.64430e34i −0.853185 + 0.829288i
\(246\) −7.60997e32 + 4.46172e32i −0.0163239 + 0.00957069i
\(247\) −4.80768e34 −0.972366
\(248\) 2.60350e35 4.96602
\(249\) −2.32739e34 3.96963e34i −0.418774 0.714266i
\(250\) 7.53443e34i 1.27915i
\(251\) −9.77945e34 −1.56691 −0.783457 0.621446i \(-0.786546\pi\)
−0.783457 + 0.621446i \(0.786546\pi\)
\(252\) 1.96000e34 1.56451e35i 0.296447 2.36630i
\(253\) 1.62536e34 0.232115
\(254\) 3.29743e34i 0.444720i
\(255\) 1.16278e34 + 1.98325e34i 0.148137 + 0.252665i
\(256\) −9.88270e34 −1.18959
\(257\) 3.16712e34 0.360275 0.180137 0.983641i \(-0.442346\pi\)
0.180137 + 0.983641i \(0.442346\pi\)
\(258\) 2.59790e35 1.52314e35i 2.79342 1.63778i
\(259\) −1.02255e35 + 4.15072e34i −1.03953 + 0.421965i
\(260\) 3.47227e35i 3.33810i
\(261\) 8.01893e34 + 4.48785e34i 0.729170 + 0.408085i
\(262\) 3.36338e35i 2.89339i
\(263\) 8.13052e34i 0.661851i 0.943657 + 0.330925i \(0.107361\pi\)
−0.943657 + 0.330925i \(0.892639\pi\)
\(264\) 2.51305e35 + 4.28629e35i 1.93617 + 3.30236i
\(265\) 2.17725e35i 1.58797i
\(266\) −2.04027e35 + 8.28183e34i −1.40898 + 0.571930i
\(267\) 1.63630e33 + 2.79090e33i 0.0107016 + 0.0182528i
\(268\) −2.22609e35 −1.37908
\(269\) −2.19676e35 −1.28936 −0.644679 0.764453i \(-0.723009\pi\)
−0.644679 + 0.764453i \(0.723009\pi\)
\(270\) −7.89321e33 3.93487e35i −0.0439015 2.18855i
\(271\) 7.81113e34i 0.411774i −0.978576 0.205887i \(-0.933992\pi\)
0.978576 0.205887i \(-0.0660080\pi\)
\(272\) 1.13414e35 0.566784
\(273\) 1.51221e35 1.96906e35i 0.716562 0.933039i
\(274\) 3.26277e35 1.46624
\(275\) 1.46514e35i 0.624531i
\(276\) −7.85860e34 + 4.60749e34i −0.317807 + 0.186330i
\(277\) 3.47632e35 1.33402 0.667011 0.745048i \(-0.267573\pi\)
0.667011 + 0.745048i \(0.267573\pi\)
\(278\) −6.65323e35 −2.42316
\(279\) −4.91982e35 2.75341e35i −1.70094 0.951941i
\(280\) 3.47327e35 + 8.55658e35i 1.14011 + 2.80872i
\(281\) 3.03762e35i 0.946872i −0.880828 0.473436i \(-0.843014\pi\)
0.880828 0.473436i \(-0.156986\pi\)
\(282\) −6.66252e35 + 3.90623e35i −1.97254 + 1.15650i
\(283\) 2.26273e35i 0.636400i 0.948024 + 0.318200i \(0.103078\pi\)
−0.948024 + 0.318200i \(0.896922\pi\)
\(284\) 1.74400e35i 0.466047i
\(285\) −3.34062e35 + 1.95860e35i −0.848353 + 0.497389i
\(286\) 1.34734e36i 3.25214i
\(287\) −4.15321e33 + 1.68586e33i −0.00953008 + 0.00386843i
\(288\) −6.75259e35 3.77914e35i −1.47326 0.824521i
\(289\) −4.52763e35 −0.939403
\(290\) −9.26854e35 −1.82911
\(291\) 2.13407e35 1.25120e35i 0.400646 0.234898i
\(292\) 1.32906e36i 2.37407i
\(293\) 1.20746e35 0.205254 0.102627 0.994720i \(-0.467275\pi\)
0.102627 + 0.994720i \(0.467275\pi\)
\(294\) 3.02554e35 1.09612e36i 0.489515 1.77346i
\(295\) 3.44385e35 0.530426
\(296\) 1.94913e36i 2.85832i
\(297\) −2.15792e34 1.07575e36i −0.0301348 1.50226i
\(298\) −1.36611e36 −1.81697
\(299\) −1.43442e35 −0.181737
\(300\) 4.15329e35 + 7.08390e35i 0.501342 + 0.855095i
\(301\) 1.41783e36 5.75521e35i 1.63083 0.661983i
\(302\) 1.77599e36i 1.94688i
\(303\) −6.93205e35 1.18234e36i −0.724342 1.23545i
\(304\) 1.91036e36i 1.90305i
\(305\) 8.50849e35i 0.808174i
\(306\) −4.36300e35 2.44179e35i −0.395207 0.221181i
\(307\) 4.19561e35i 0.362484i 0.983439 + 0.181242i \(0.0580117\pi\)
−0.983439 + 0.181242i \(0.941988\pi\)
\(308\) 1.63526e36 + 4.02855e36i 1.34773 + 3.32019i
\(309\) −3.18372e35 + 1.86661e35i −0.250344 + 0.146776i
\(310\) 5.68649e36 4.26677
\(311\) 1.38364e34 0.00990823 0.00495411 0.999988i \(-0.498423\pi\)
0.00495411 + 0.999988i \(0.498423\pi\)
\(312\) −2.21782e36 3.78274e36i −1.51595 2.58562i
\(313\) 4.32475e35i 0.282207i 0.989995 + 0.141104i \(0.0450651\pi\)
−0.989995 + 0.141104i \(0.954935\pi\)
\(314\) 2.25245e36 1.40338
\(315\) 2.48586e35 1.98426e36i 0.147902 1.18058i
\(316\) −2.46881e36 −1.40290
\(317\) 1.15872e36i 0.628954i −0.949265 0.314477i \(-0.898171\pi\)
0.949265 0.314477i \(-0.101829\pi\)
\(318\) 2.39489e36 + 4.08476e36i 1.24192 + 2.11823i
\(319\) −2.53392e36 −1.25553
\(320\) 2.01934e36 0.956169
\(321\) −1.32276e36 + 7.75534e35i −0.598630 + 0.350976i
\(322\) −6.08734e35 + 2.47096e35i −0.263340 + 0.106895i
\(323\) 4.91950e35i 0.203463i
\(324\) 3.15382e36 + 5.14008e36i 1.24720 + 2.03267i
\(325\) 1.29301e36i 0.488983i
\(326\) 1.14075e36i 0.412606i
\(327\) 8.17687e35 + 1.39466e36i 0.282908 + 0.482531i
\(328\) 7.91661e34i 0.0262041i
\(329\) −3.63613e36 + 1.47597e36i −1.15159 + 0.467452i
\(330\) 5.48893e36 + 9.36200e36i 1.66355 + 2.83737i
\(331\) −3.22513e36 −0.935494 −0.467747 0.883863i \(-0.654934\pi\)
−0.467747 + 0.883863i \(0.654934\pi\)
\(332\) −7.11168e36 −1.97456
\(333\) 2.06136e36 3.68325e36i 0.547914 0.979017i
\(334\) 1.13335e37i 2.88430i
\(335\) −2.82335e36 −0.688042
\(336\) −7.82418e36 6.00887e36i −1.82608 1.40240i
\(337\) −1.45896e36 −0.326144 −0.163072 0.986614i \(-0.552140\pi\)
−0.163072 + 0.986614i \(0.552140\pi\)
\(338\) 3.29925e36i 0.706518i
\(339\) −6.39683e36 + 3.75046e36i −1.31241 + 0.769465i
\(340\) 3.55303e36 0.698481
\(341\) 1.55463e37 2.92879
\(342\) 4.11298e36 7.34911e36i 0.742640 1.32695i
\(343\) 2.32429e36 5.28971e36i 0.402277 0.915518i
\(344\) 2.70258e37i 4.48415i
\(345\) −9.96705e35 + 5.84367e35i −0.158559 + 0.0929627i
\(346\) 3.57796e36i 0.545798i
\(347\) 3.82608e36i 0.559727i 0.960040 + 0.279864i \(0.0902893\pi\)
−0.960040 + 0.279864i \(0.909711\pi\)
\(348\) 1.22515e37 7.18303e36i 1.71905 1.00788i
\(349\) 2.85704e36i 0.384545i −0.981342 0.192272i \(-0.938414\pi\)
0.981342 0.192272i \(-0.0615857\pi\)
\(350\) 2.22737e36 + 5.48725e36i 0.287612 + 0.708546i
\(351\) 1.90441e35 + 9.49374e36i 0.0235943 + 1.17621i
\(352\) 2.13377e37 2.53676
\(353\) 1.00942e36 0.115170 0.0575850 0.998341i \(-0.481660\pi\)
0.0575850 + 0.998341i \(0.481660\pi\)
\(354\) −6.46104e36 + 3.78810e36i −0.707546 + 0.414834i
\(355\) 2.21191e36i 0.232517i
\(356\) 4.99994e35 0.0504592
\(357\) −2.01485e36 1.54738e36i −0.195234 0.149937i
\(358\) 1.26058e37 1.17291
\(359\) 9.97546e36i 0.891381i −0.895187 0.445691i \(-0.852958\pi\)
0.895187 0.445691i \(-0.147042\pi\)
\(360\) −3.08210e37 1.72492e37i −2.64521 1.48041i
\(361\) 3.84333e36 0.316850
\(362\) −1.77005e37 −1.40188
\(363\) 8.35947e36 + 1.42580e37i 0.636111 + 1.08496i
\(364\) −1.44315e37 3.55527e37i −1.05522 2.59958i
\(365\) 1.68565e37i 1.18446i
\(366\) −9.35901e36 1.59629e37i −0.632054 1.07804i
\(367\) 1.83505e37i 1.19122i 0.803275 + 0.595608i \(0.203089\pi\)
−0.803275 + 0.595608i \(0.796911\pi\)
\(368\) 5.69975e36i 0.355682i
\(369\) 8.37246e34 1.49600e35i 0.00502309 0.00897529i
\(370\) 4.25722e37i 2.45585i
\(371\) 9.04912e36 + 2.22930e37i 0.501978 + 1.23665i
\(372\) −7.51660e37 + 4.40697e37i −4.01004 + 2.35108i
\(373\) −1.43895e37 −0.738360 −0.369180 0.929358i \(-0.620361\pi\)
−0.369180 + 0.929358i \(0.620361\pi\)
\(374\) 1.37868e37 0.680494
\(375\) −7.40574e36 1.26313e37i −0.351653 0.599785i
\(376\) 6.93097e37i 3.16643i
\(377\) 2.23624e37 0.983034
\(378\) 1.71624e37 + 3.99613e37i 0.726015 + 1.69047i
\(379\) 3.90053e37 1.58802 0.794008 0.607907i \(-0.207991\pi\)
0.794008 + 0.607907i \(0.207991\pi\)
\(380\) 5.98478e37i 2.34523i
\(381\) −3.24110e36 5.52807e36i −0.122259 0.208527i
\(382\) 6.71938e37 2.44012
\(383\) 5.07083e37 1.77295 0.886476 0.462775i \(-0.153146\pi\)
0.886476 + 0.462775i \(0.153146\pi\)
\(384\) 5.37543e36 3.15161e36i 0.180972 0.106104i
\(385\) 2.07400e37 + 5.10939e37i 0.672399 + 1.65649i
\(386\) 9.05456e37i 2.82717i
\(387\) −2.85819e37 + 5.10704e37i −0.859573 + 1.53589i
\(388\) 3.82323e37i 1.10757i
\(389\) 2.09477e37i 0.584612i 0.956325 + 0.292306i \(0.0944225\pi\)
−0.956325 + 0.292306i \(0.905578\pi\)
\(390\) −4.84409e37 8.26215e37i −1.30249 2.22155i
\(391\) 1.46778e36i 0.0380275i
\(392\) −7.11260e37 7.31756e37i −1.77574 1.82691i
\(393\) 3.30592e37 + 5.63863e37i 0.795428 + 1.35669i
\(394\) −1.49635e36 −0.0347007
\(395\) −3.13119e37 −0.699925
\(396\) −1.45109e38 8.12114e37i −3.12691 1.75000i
\(397\) 3.28408e37i 0.682262i 0.940016 + 0.341131i \(0.110810\pi\)
−0.940016 + 0.341131i \(0.889190\pi\)
\(398\) 1.80803e38 3.62160
\(399\) 2.60644e37 3.39385e37i 0.503431 0.655520i
\(400\) 5.13787e37 0.957002
\(401\) 5.91548e37i 1.06267i −0.847163 0.531333i \(-0.821691\pi\)
0.847163 0.531333i \(-0.178309\pi\)
\(402\) 5.29691e37 3.10558e37i 0.917794 0.538102i
\(403\) −1.37199e38 −2.29313
\(404\) −2.11819e38 −3.41534
\(405\) 3.99999e37 + 6.51915e37i 0.622244 + 1.01413i
\(406\) 9.49010e37 3.85220e37i 1.42444 0.578205i
\(407\) 1.16388e38i 1.68574i
\(408\) −3.87072e37 + 2.26940e37i −0.541028 + 0.317204i
\(409\) 4.47203e37i 0.603277i −0.953422 0.301638i \(-0.902466\pi\)
0.953422 0.301638i \(-0.0975336\pi\)
\(410\) 1.72912e36i 0.0225144i
\(411\) −5.46997e37 + 3.20704e37i −0.687510 + 0.403086i
\(412\) 5.70370e37i 0.692065i
\(413\) −3.52617e37 + 1.43134e37i −0.413074 + 0.167674i
\(414\) 1.22715e37 2.19267e37i 0.138801 0.248010i
\(415\) −9.01972e37 −0.985135
\(416\) −1.88310e38 −1.98618
\(417\) 1.11540e38 6.53958e37i 1.13621 0.666158i
\(418\) 2.32227e38i 2.28484i
\(419\) −1.08659e38 −1.03268 −0.516338 0.856385i \(-0.672705\pi\)
−0.516338 + 0.856385i \(0.672705\pi\)
\(420\) −2.45116e38 1.88246e38i −2.25038 1.72827i
\(421\) −1.13162e38 −1.00372 −0.501858 0.864950i \(-0.667350\pi\)
−0.501858 + 0.864950i \(0.667350\pi\)
\(422\) 4.22865e37i 0.362386i
\(423\) 7.33007e37 1.30974e38i 0.606978 1.08455i
\(424\) 4.24935e38 3.40031
\(425\) 1.32309e37 0.102317
\(426\) 2.43301e37 + 4.14978e37i 0.181847 + 0.310160i
\(427\) −3.53631e37 8.71188e37i −0.255474 0.629372i
\(428\) 2.36975e38i 1.65489i
\(429\) −1.32433e38 2.25879e38i −0.894054 1.52491i
\(430\) 5.90289e38i 3.85276i
\(431\) 1.11081e38i 0.701002i 0.936562 + 0.350501i \(0.113989\pi\)
−0.936562 + 0.350501i \(0.886011\pi\)
\(432\) 3.77240e38 7.56730e36i 2.30199 0.0461771i
\(433\) 5.00180e37i 0.295156i 0.989050 + 0.147578i \(0.0471478\pi\)
−0.989050 + 0.147578i \(0.952852\pi\)
\(434\) −5.82242e38 + 2.36343e38i −3.32279 + 1.34878i
\(435\) 1.55385e38 9.11022e37i 0.857660 0.502846i
\(436\) 2.49856e38 1.33394
\(437\) −2.47235e37 −0.127682
\(438\) 1.85415e38 + 3.16246e38i 0.926338 + 1.57998i
\(439\) 2.71259e38i 1.31114i 0.755135 + 0.655569i \(0.227571\pi\)
−0.755135 + 0.655569i \(0.772429\pi\)
\(440\) 9.73923e38 4.55471
\(441\) 5.70172e37 + 2.13501e38i 0.258016 + 0.966141i
\(442\) −1.21671e38 −0.532800
\(443\) 1.09543e38i 0.464228i 0.972689 + 0.232114i \(0.0745643\pi\)
−0.972689 + 0.232114i \(0.925436\pi\)
\(444\) −3.29931e38 5.62735e38i −1.35322 2.30808i
\(445\) 6.34142e36 0.0251748
\(446\) 7.90357e38 3.03716
\(447\) 2.29025e38 1.34277e38i 0.851969 0.499508i
\(448\) −2.06761e38 + 8.39281e37i −0.744625 + 0.302257i
\(449\) 2.09076e38i 0.729008i −0.931202 0.364504i \(-0.881238\pi\)
0.931202 0.364504i \(-0.118762\pi\)
\(450\) −1.97652e38 1.10617e38i −0.667298 0.373458i
\(451\) 4.72725e36i 0.0154543i
\(452\) 1.14601e39i 3.62810i
\(453\) 1.74565e38 + 2.97741e38i 0.535222 + 0.912882i
\(454\) 5.14342e37i 0.152736i
\(455\) −1.83034e38 4.50914e38i −0.526462 1.29697i
\(456\) −3.82262e38 6.51991e38i −1.06505 1.81657i
\(457\) 5.95107e38 1.60624 0.803119 0.595818i \(-0.203172\pi\)
0.803119 + 0.595818i \(0.203172\pi\)
\(458\) 5.96750e38 1.56043
\(459\) 9.71456e37 1.94871e36i 0.246116 0.00493699i
\(460\) 1.78562e38i 0.438328i
\(461\) −2.80849e38 −0.668051 −0.334025 0.942564i \(-0.608407\pi\)
−0.334025 + 0.942564i \(0.608407\pi\)
\(462\) −9.51119e38 7.30447e38i −2.19243 1.68376i
\(463\) 3.33521e37 0.0745074 0.0372537 0.999306i \(-0.488139\pi\)
0.0372537 + 0.999306i \(0.488139\pi\)
\(464\) 8.88584e38i 1.92392i
\(465\) −9.53328e38 + 5.58935e38i −2.00067 + 1.17299i
\(466\) 2.14157e38 0.435649
\(467\) −4.61986e38 −0.911034 −0.455517 0.890227i \(-0.650545\pi\)
−0.455517 + 0.890227i \(0.650545\pi\)
\(468\) 1.28062e39 + 7.16707e38i 2.44824 + 1.37018i
\(469\) 2.89084e38 1.17344e38i 0.535819 0.217498i
\(470\) 1.51384e39i 2.72058i
\(471\) −3.77619e38 + 2.21398e38i −0.658037 + 0.385807i
\(472\) 6.72138e38i 1.13579i
\(473\) 1.61379e39i 2.64460i
\(474\) 5.87446e38 3.44419e38i 0.933645 0.547395i
\(475\) 2.22863e38i 0.343542i
\(476\) −3.63796e38 + 1.47672e38i −0.543948 + 0.220799i
\(477\) −8.02998e38 4.49404e38i −1.16466 0.651809i
\(478\) 1.04462e39 1.46979
\(479\) −1.28353e39 −1.75203 −0.876014 0.482287i \(-0.839806\pi\)
−0.876014 + 0.482287i \(0.839806\pi\)
\(480\) −1.30847e39 + 7.67155e38i −1.73287 + 1.01598i
\(481\) 1.02715e39i 1.31987i
\(482\) 1.74703e39 2.17830
\(483\) 7.77655e37 1.01259e38i 0.0940922 0.122518i
\(484\) 2.55436e39 2.99933
\(485\) 4.84900e38i 0.552582i
\(486\) −1.46752e39 7.83081e38i −1.62315 0.866126i
\(487\) −7.13633e38 −0.766135 −0.383067 0.923720i \(-0.625132\pi\)
−0.383067 + 0.923720i \(0.625132\pi\)
\(488\) −1.66061e39 −1.73053
\(489\) 1.12126e38 + 1.91244e38i 0.113430 + 0.193469i
\(490\) −1.55351e39 1.59828e39i −1.52571 1.56967i
\(491\) 7.76737e38i 0.740615i 0.928909 + 0.370307i \(0.120748\pi\)
−0.928909 + 0.370307i \(0.879252\pi\)
\(492\) −1.34005e37 2.28561e37i −0.0124059 0.0211597i
\(493\) 2.28825e38i 0.205695i
\(494\) 2.04945e39i 1.78894i
\(495\) −1.84042e39 1.03000e39i −1.56006 0.873098i
\(496\) 5.45169e39i 4.48794i
\(497\) 9.19315e37 + 2.26478e38i 0.0735016 + 0.181075i
\(498\) 1.69220e39 9.92135e38i 1.31409 0.770452i
\(499\) 9.62333e37 0.0725884 0.0362942 0.999341i \(-0.488445\pi\)
0.0362942 + 0.999341i \(0.488445\pi\)
\(500\) −2.26293e39 −1.65808
\(501\) 1.11399e39 + 1.90004e39i 0.792931 + 1.35243i
\(502\) 4.16884e39i 2.88278i
\(503\) 6.01385e38 0.404033 0.202017 0.979382i \(-0.435251\pi\)
0.202017 + 0.979382i \(0.435251\pi\)
\(504\) 3.87269e39 + 4.85167e38i 2.52796 + 0.316700i
\(505\) −2.68649e39 −1.70396
\(506\) 6.92870e38i 0.427041i
\(507\) 3.24290e38 + 5.53113e38i 0.194231 + 0.331282i
\(508\) −9.90365e38 −0.576463
\(509\) 4.89063e38 0.276667 0.138333 0.990386i \(-0.455825\pi\)
0.138333 + 0.990386i \(0.455825\pi\)
\(510\) −8.45432e38 + 4.95676e38i −0.464848 + 0.272540i
\(511\) 7.00591e38 + 1.72594e39i 0.374422 + 0.922407i
\(512\) 3.80904e39i 1.97880i
\(513\) 3.28243e37 + 1.63634e39i 0.0165765 + 0.826363i
\(514\) 1.35010e39i 0.662826i
\(515\) 7.23399e38i 0.345281i
\(516\) 4.57468e39 + 7.80264e39i 2.12295 + 3.62094i
\(517\) 4.13869e39i 1.86746i
\(518\) −1.76939e39 4.35899e39i −0.776324 1.91251i
\(519\) −3.51684e38 5.99837e38i −0.150047 0.255921i
\(520\) −8.59506e39 −3.56616
\(521\) −4.65997e39 −1.88034 −0.940170 0.340707i \(-0.889334\pi\)
−0.940170 + 0.340707i \(0.889334\pi\)
\(522\) −1.91311e39 + 3.41836e39i −0.750788 + 1.34151i
\(523\) 6.05568e38i 0.231147i −0.993299 0.115573i \(-0.963129\pi\)
0.993299 0.115573i \(-0.0368706\pi\)
\(524\) 1.01017e40 3.75052
\(525\) −9.12767e38 7.00994e38i −0.329648 0.253165i
\(526\) −3.46593e39 −1.21766
\(527\) 1.40390e39i 0.479825i
\(528\) −8.97545e39 + 5.26230e39i −2.98445 + 1.74978i
\(529\) 3.01729e39 0.976136
\(530\) 9.28131e39 2.92152
\(531\) 7.10840e38 1.27013e39i 0.217722 0.389027i
\(532\) −2.48740e39 6.12785e39i −0.741358 1.82637i
\(533\) 4.17189e37i 0.0121001i
\(534\) −1.18972e38 + 6.97532e37i −0.0335812 + 0.0196886i
\(535\) 3.00555e39i 0.825647i
\(536\) 5.51035e39i 1.47329i
\(537\) −2.11333e39 + 1.23905e39i −0.549973 + 0.322449i
\(538\) 9.36446e39i 2.37214i
\(539\) −4.24715e39 4.36953e39i −1.04727 1.07745i
\(540\) 1.18182e40 2.37068e38i 2.83688 0.0569068i
\(541\) 3.55979e39 0.831886 0.415943 0.909391i \(-0.363452\pi\)
0.415943 + 0.909391i \(0.363452\pi\)
\(542\) 3.32978e39 0.757575
\(543\) 2.96745e39 1.73981e39i 0.657333 0.385394i
\(544\) 1.92689e39i 0.415598i
\(545\) 3.16891e39 0.665520
\(546\) 8.39381e39 + 6.44634e39i 1.71659 + 1.31832i
\(547\) −8.86194e39 −1.76487 −0.882434 0.470436i \(-0.844097\pi\)
−0.882434 + 0.470436i \(0.844097\pi\)
\(548\) 9.79957e39i 1.90059i
\(549\) 3.13804e39 + 1.75623e39i 0.592733 + 0.331728i
\(550\) 6.24567e39 1.14900
\(551\) 3.85437e39 0.690645
\(552\) −1.14051e39 1.94528e39i −0.199060 0.339519i
\(553\) 3.20604e39 1.30139e39i 0.545073 0.221255i
\(554\) 1.48191e40i 2.45431i
\(555\) −4.18451e39 7.13715e39i −0.675143 1.15153i
\(556\) 1.99826e40i 3.14100i
\(557\) 1.32679e39i 0.203189i 0.994826 + 0.101595i \(0.0323945\pi\)
−0.994826 + 0.101595i \(0.967606\pi\)
\(558\) 1.17374e40 2.09725e40i 1.75136 3.12935i
\(559\) 1.42420e40i 2.07062i
\(560\) −1.79174e40 + 7.27299e39i −2.53833 + 1.03035i
\(561\) −2.31133e39 + 1.35513e39i −0.319080 + 0.187076i
\(562\) 1.29489e40 1.74204
\(563\) 8.43743e39 1.10621 0.553106 0.833111i \(-0.313443\pi\)
0.553106 + 0.833111i \(0.313443\pi\)
\(564\) −1.17321e40 2.00105e40i −1.49910 2.55688i
\(565\) 1.45348e40i 1.81011i
\(566\) −9.64572e39 −1.17084
\(567\) −6.80510e39 5.01250e39i −0.805156 0.593063i
\(568\) 4.31699e39 0.497886
\(569\) 5.26041e39i 0.591414i 0.955279 + 0.295707i \(0.0955553\pi\)
−0.955279 + 0.295707i \(0.904445\pi\)
\(570\) −8.34925e39 1.42406e40i −0.915086 1.56078i
\(571\) −1.34038e40 −1.43220 −0.716099 0.697999i \(-0.754074\pi\)
−0.716099 + 0.697999i \(0.754074\pi\)
\(572\) −4.04666e40 −4.21555
\(573\) −1.12649e40 + 6.60460e39i −1.14416 + 0.670818i
\(574\) −7.18660e37 1.77046e38i −0.00711707 0.0175333i
\(575\) 6.64932e38i 0.0642086i
\(576\) 4.16810e39 7.44759e39i 0.392475 0.701277i
\(577\) 1.01243e40i 0.929643i −0.885404 0.464822i \(-0.846118\pi\)
0.885404 0.464822i \(-0.153882\pi\)
\(578\) 1.93006e40i 1.72830i
\(579\) 8.89990e39 + 1.51798e40i 0.777223 + 1.32564i
\(580\) 2.78376e40i 2.37097i
\(581\) 9.23533e39 3.74879e39i 0.767182 0.311413i
\(582\) 5.33371e39 + 9.09725e39i 0.432162 + 0.737101i
\(583\) 2.53742e40 2.00539
\(584\) 3.28989e40 2.53627
\(585\) 1.62420e40 + 9.08998e39i 1.22146 + 0.683601i
\(586\) 5.14723e39i 0.377623i
\(587\) 6.26225e39 0.448206 0.224103 0.974565i \(-0.428055\pi\)
0.224103 + 0.974565i \(0.428055\pi\)
\(588\) 3.29214e40 + 9.08704e39i 2.29883 + 0.634528i
\(589\) −2.36475e40 −1.61107
\(590\) 1.46806e40i 0.975867i
\(591\) 2.50860e38 1.47079e38i 0.0162710 0.00953965i
\(592\) −4.08145e40 −2.58315
\(593\) −1.54878e40 −0.956527 −0.478264 0.878216i \(-0.658734\pi\)
−0.478264 + 0.878216i \(0.658734\pi\)
\(594\) 4.58579e40 9.19893e38i 2.76383 0.0554414i
\(595\) −4.61402e39 + 1.87292e39i −0.271384 + 0.110160i
\(596\) 4.10303e40i 2.35523i
\(597\) −3.03112e40 + 1.77714e40i −1.69815 + 0.995622i
\(598\) 6.11472e39i 0.334356i
\(599\) 1.20812e39i 0.0644795i −0.999480 0.0322398i \(-0.989736\pi\)
0.999480 0.0322398i \(-0.0102640\pi\)
\(600\) −1.75351e40 + 1.02808e40i −0.913514 + 0.535592i
\(601\) 2.22116e40i 1.12953i −0.825250 0.564767i \(-0.808966\pi\)
0.825250 0.564767i \(-0.191034\pi\)
\(602\) 2.45337e40 + 6.04399e40i 1.21790 + 3.00037i
\(603\) −5.82764e39 + 1.04129e40i −0.282418 + 0.504626i
\(604\) 5.33408e40 2.52362
\(605\) 3.23968e40 1.49641
\(606\) 5.04015e40 2.95504e40i 2.27295 1.33263i
\(607\) 5.52437e39i 0.243247i −0.992576 0.121623i \(-0.961190\pi\)
0.992576 0.121623i \(-0.0388100\pi\)
\(608\) −3.24569e40 −1.39542
\(609\) −1.21236e40 + 1.57861e40i −0.508955 + 0.662712i
\(610\) −3.62705e40 −1.48686
\(611\) 3.65248e40i 1.46214i
\(612\) 7.33377e39 1.31040e40i 0.286703 0.512282i
\(613\) 3.71583e39 0.141866 0.0709332 0.997481i \(-0.477402\pi\)
0.0709332 + 0.997481i \(0.477402\pi\)
\(614\) −1.78853e40 −0.666891
\(615\) −1.69959e38 2.89884e38i −0.00618948 0.0105569i
\(616\) −9.97204e40 + 4.04783e40i −3.54702 + 1.43980i
\(617\) 2.67277e40i 0.928595i 0.885679 + 0.464297i \(0.153693\pi\)
−0.885679 + 0.464297i \(0.846307\pi\)
\(618\) −7.95711e39 1.35718e40i −0.270037 0.460578i
\(619\) 4.32119e40i 1.43248i 0.697853 + 0.716241i \(0.254139\pi\)
−0.697853 + 0.716241i \(0.745861\pi\)
\(620\) 1.70791e41i 5.53075i
\(621\) 9.79344e37 + 4.88216e39i 0.00309818 + 0.154449i
\(622\) 5.89825e38i 0.0182290i
\(623\) −6.49301e38 + 2.63563e38i −0.0196051 + 0.00795807i
\(624\) 7.92101e40 4.64408e40i 2.33671 1.37001i
\(625\) −4.31212e40 −1.24288
\(626\) −1.84358e40 −0.519200
\(627\) −2.28260e40 3.89323e40i −0.628131 1.07135i
\(628\) 6.76512e40i 1.81912i
\(629\) −1.05104e40 −0.276175
\(630\) 8.45862e40 + 1.05969e40i 2.17201 + 0.272107i
\(631\) −3.99053e40 −1.00139 −0.500696 0.865623i \(-0.666923\pi\)
−0.500696 + 0.865623i \(0.666923\pi\)
\(632\) 6.11116e40i 1.49874i
\(633\) 4.15642e39 + 7.08925e39i 0.0996244 + 0.169921i
\(634\) 4.93946e40 1.15714
\(635\) −1.25608e40 −0.287606
\(636\) −1.22684e41 + 7.19293e40i −2.74573 + 1.60982i
\(637\) 3.74819e40 + 3.85620e40i 0.819974 + 0.843603i
\(638\) 1.08018e41i 2.30991i
\(639\) −8.15779e39 4.56557e39i −0.170534 0.0954404i
\(640\) 1.22139e40i 0.249601i
\(641\) 4.28272e40i 0.855614i −0.903870 0.427807i \(-0.859286\pi\)
0.903870 0.427807i \(-0.140714\pi\)
\(642\) −3.30599e40 5.63875e40i −0.645720 1.10135i
\(643\) 9.04997e40i 1.72818i −0.503340 0.864088i \(-0.667896\pi\)
0.503340 0.864088i \(-0.332104\pi\)
\(644\) −7.42140e39 1.82830e40i −0.138561 0.341352i
\(645\) 5.80206e40 + 9.89607e40i 1.05917 + 1.80654i
\(646\) −2.09712e40 −0.374327
\(647\) −3.67746e38 −0.00641853 −0.00320926 0.999995i \(-0.501022\pi\)
−0.00320926 + 0.999995i \(0.501022\pi\)
\(648\) −1.27235e41 + 7.80680e40i −2.17154 + 1.33240i
\(649\) 4.01354e40i 0.669852i
\(650\) −5.51193e40 −0.899621
\(651\) 7.43811e40 9.68520e40i 1.18724 1.54591i
\(652\) 3.42618e40 0.534836
\(653\) 5.73825e39i 0.0876069i 0.999040 + 0.0438035i \(0.0139475\pi\)
−0.999040 + 0.0438035i \(0.986052\pi\)
\(654\) −5.94523e40 + 3.48568e40i −0.887752 + 0.520488i
\(655\) 1.28120e41 1.87119
\(656\) −1.65773e39 −0.0236814
\(657\) −6.21688e40 3.47932e40i −0.868710 0.486180i
\(658\) −6.29186e40 1.55003e41i −0.860010 2.11868i
\(659\) 8.55947e40i 1.14448i −0.820086 0.572241i \(-0.806074\pi\)
0.820086 0.572241i \(-0.193926\pi\)
\(660\) −2.81183e41 + 1.64857e41i −3.67791 + 2.15636i
\(661\) 3.55669e40i 0.455119i 0.973764 + 0.227560i \(0.0730747\pi\)
−0.973764 + 0.227560i \(0.926925\pi\)
\(662\) 1.37483e41i 1.72110i
\(663\) 2.03979e40 1.19593e40i 0.249827 0.146473i
\(664\) 1.76039e41i 2.10946i
\(665\) −3.15477e40 7.77193e40i −0.369874 0.911203i
\(666\) 1.57012e41 + 8.78729e40i 1.80118 + 1.00804i
\(667\) 1.14999e40 0.129083
\(668\) 3.40396e41 3.73875
\(669\) −1.32502e41 + 7.76857e40i −1.42411 + 0.834954i
\(670\) 1.20355e41i 1.26585i
\(671\) −9.91599e40 −1.02061
\(672\) 1.02090e41 1.32932e41i 1.02832 1.33898i
\(673\) 3.87780e40 0.382268 0.191134 0.981564i \(-0.438784\pi\)
0.191134 + 0.981564i \(0.438784\pi\)
\(674\) 6.21933e40i 0.600033i
\(675\) 4.40088e40 8.82800e38i 0.415561 0.00833600i
\(676\) 9.90912e40 0.915816
\(677\) 8.03411e39 0.0726779 0.0363389 0.999340i \(-0.488430\pi\)
0.0363389 + 0.999340i \(0.488430\pi\)
\(678\) −1.59877e41 2.72688e41i −1.41565 2.41455i
\(679\) 2.01535e40 + 4.96491e40i 0.174678 + 0.430328i
\(680\) 8.79498e40i 0.746200i
\(681\) 5.05556e39 + 8.62283e39i 0.0419890 + 0.0716171i
\(682\) 6.62716e41i 5.38833i
\(683\) 6.79765e40i 0.541077i 0.962709 + 0.270538i \(0.0872017\pi\)
−0.962709 + 0.270538i \(0.912798\pi\)
\(684\) 2.20727e41 + 1.23531e41i 1.72005 + 0.962639i
\(685\) 1.24288e41i 0.948232i
\(686\) 2.25493e41 + 9.90812e40i 1.68435 + 0.740102i
\(687\) −1.00044e41 + 5.86557e40i −0.731675 + 0.428981i
\(688\) 5.65916e41 4.05247
\(689\) −2.23932e41 −1.57014
\(690\) −2.49108e40 4.24881e40i −0.171031 0.291713i
\(691\) 2.70551e41i 1.81893i −0.415775 0.909467i \(-0.636490\pi\)
0.415775 0.909467i \(-0.363510\pi\)
\(692\) −1.07462e41 −0.707484
\(693\) 2.31250e41 + 2.89708e40i 1.49091 + 0.186779i
\(694\) −1.63100e41 −1.02978
\(695\) 2.53439e41i 1.56709i
\(696\) 1.77805e41 + 3.03266e41i 1.07674 + 1.83650i
\(697\) −4.26892e38 −0.00253188
\(698\) 1.21791e41 0.707479
\(699\) −3.59030e40 + 2.10499e40i −0.204274 + 0.119765i
\(700\) −1.64807e41 + 6.68980e40i −0.918445 + 0.372813i
\(701\) 2.10589e41i 1.14954i 0.818314 + 0.574771i \(0.194909\pi\)
−0.818314 + 0.574771i \(0.805091\pi\)
\(702\) −4.04705e41 + 8.11824e39i −2.16397 + 0.0434084i
\(703\) 1.77039e41i 0.927292i
\(704\) 2.35339e41i 1.20751i
\(705\) −1.48798e41 2.53793e41i −0.747922 1.27567i
\(706\) 4.30302e40i 0.211888i
\(707\) 2.75071e41 1.11656e41i 1.32698 0.538644i
\(708\) −1.13774e41 1.94054e41i −0.537724 0.917149i
\(709\) 1.75830e41 0.814183 0.407091 0.913387i \(-0.366543\pi\)
0.407091 + 0.913387i \(0.366543\pi\)
\(710\) 9.42905e40 0.427781
\(711\) −6.46305e40 + 1.15482e41i −0.287295 + 0.513341i
\(712\) 1.23766e40i 0.0539065i
\(713\) −7.05546e40 −0.301112
\(714\) 6.59628e40 8.58905e40i 0.275851 0.359187i
\(715\) −5.13237e41 −2.10320
\(716\) 3.78608e41i 1.52038i
\(717\) −1.75129e41 + 1.02678e41i −0.689176 + 0.404063i
\(718\) 4.25240e41 1.63995
\(719\) 6.69236e40 0.252936 0.126468 0.991971i \(-0.459636\pi\)
0.126468 + 0.991971i \(0.459636\pi\)
\(720\) 3.61196e41 6.45388e41i 1.33790 2.39056i
\(721\) −3.00660e40 7.40691e40i −0.109148 0.268891i
\(722\) 1.63836e41i 0.582934i
\(723\) −2.92886e41 + 1.71719e41i −1.02139 + 0.598842i
\(724\) 5.31624e41i 1.81717i
\(725\) 1.03662e41i 0.347311i
\(726\) −6.07800e41 + 3.56353e41i −1.99609 + 1.17031i
\(727\) 9.31430e40i 0.299848i 0.988698 + 0.149924i \(0.0479029\pi\)
−0.988698 + 0.149924i \(0.952097\pi\)
\(728\) 8.80052e41 3.57229e41i 2.77718 1.12731i
\(729\) 3.22998e41 1.29637e40i 0.999196 0.0401031i
\(730\) 7.18568e41 2.17914
\(731\) 1.45733e41 0.433266
\(732\) 4.79436e41 2.81093e41i 1.39740 0.819293i
\(733\) 2.83486e41i 0.810072i −0.914301 0.405036i \(-0.867259\pi\)
0.914301 0.405036i \(-0.132741\pi\)
\(734\) −7.82258e41 −2.19158
\(735\) 4.17541e41 + 1.15251e41i 1.14692 + 0.316575i
\(736\) −9.68383e40 −0.260807
\(737\) 3.29040e41i 0.868899i
\(738\) 6.37723e39 + 3.56906e39i 0.0165126 + 0.00924138i
\(739\) 3.16897e41 0.804590 0.402295 0.915510i \(-0.368213\pi\)
0.402295 + 0.915510i \(0.368213\pi\)
\(740\) −1.27863e42 −3.18337
\(741\) 2.01444e41 + 3.43586e41i 0.491802 + 0.838824i
\(742\) −9.50318e41 + 3.85751e41i −2.27516 + 0.923529i
\(743\) 2.03599e41i 0.478012i −0.971018 0.239006i \(-0.923178\pi\)
0.971018 0.239006i \(-0.0768216\pi\)
\(744\) −1.09088e42 1.86062e42i −2.51170 4.28400i
\(745\) 5.20386e41i 1.17506i
\(746\) 6.13405e41i 1.35842i
\(747\) −1.86175e41 + 3.32659e41i −0.404364 + 0.722521i
\(748\) 4.14078e41i 0.882083i
\(749\) −1.24917e41 3.07740e41i −0.260997 0.642980i
\(750\) 5.38456e41 3.15696e41i 1.10347 0.646965i
\(751\) 1.13321e41 0.227789 0.113894 0.993493i \(-0.463667\pi\)
0.113894 + 0.993493i \(0.463667\pi\)
\(752\) −1.45134e42 −2.86160
\(753\) 4.09763e41 + 6.98898e41i 0.792512 + 1.35172i
\(754\) 9.53277e41i