Properties

Label 6.25.b.a.5.1
Level $6$
Weight $25$
Character 6.5
Analytic conductor $21.898$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 6 = 2 \cdot 3 \)
Weight: \( k \) \(=\) \( 25 \)
Character orbit: \([\chi]\) \(=\) 6.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.8980291355\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \(x^{8} + 9921984 x^{6} + 31297402621425 x^{4} + 35629505313218665424 x^{2} + 11190322069687119538557504\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{53}\cdot 3^{32}\cdot 17^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.1
Root \(-2234.51i\) of defining polynomial
Character \(\chi\) \(=\) 6.5
Dual form 6.25.b.a.5.5

$q$-expansion

\(f(q)\) \(=\) \(q-2896.31i q^{2} +(-490828. - 203759. i) q^{3} -8.38861e6 q^{4} +1.24013e8i q^{5} +(-5.90150e8 + 1.42159e9i) q^{6} +1.50611e10 q^{7} +2.42960e10i q^{8} +(1.99394e11 + 2.00021e11i) q^{9} +O(q^{10})\) \(q-2896.31i q^{2} +(-490828. - 203759. i) q^{3} -8.38861e6 q^{4} +1.24013e8i q^{5} +(-5.90150e8 + 1.42159e9i) q^{6} +1.50611e10 q^{7} +2.42960e10i q^{8} +(1.99394e11 + 2.00021e11i) q^{9} +3.59180e11 q^{10} -2.25660e12i q^{11} +(4.11736e12 + 1.70926e12i) q^{12} +4.78761e12 q^{13} -4.36217e13i q^{14} +(2.52688e13 - 6.08691e13i) q^{15} +7.03687e13 q^{16} +5.31661e14i q^{17} +(5.79323e14 - 5.77507e14i) q^{18} -2.04629e15 q^{19} -1.04030e15i q^{20} +(-7.39242e15 - 3.06885e15i) q^{21} -6.53582e15 q^{22} -3.16079e16i q^{23} +(4.95053e15 - 1.19251e16i) q^{24} +4.42254e16 q^{25} -1.38664e16i q^{26} +(-5.71119e16 - 1.38804e17i) q^{27} -1.26342e17 q^{28} -6.82228e17i q^{29} +(-1.76296e17 - 7.31863e16i) q^{30} -6.83154e17 q^{31} -2.03810e17i q^{32} +(-4.59804e17 + 1.10760e18i) q^{33} +1.53985e18 q^{34} +1.86778e18i q^{35} +(-1.67264e18 - 1.67790e18i) q^{36} +9.74472e18 q^{37} +5.92669e18i q^{38} +(-2.34989e18 - 9.75520e17i) q^{39} -3.01302e18 q^{40} +1.91167e19i q^{41} +(-8.88833e18 + 2.14107e19i) q^{42} +6.07042e19 q^{43} +1.89298e19i q^{44} +(-2.48053e19 + 2.47275e19i) q^{45} -9.15463e19 q^{46} -1.14305e20i q^{47} +(-3.45389e19 - 1.43383e19i) q^{48} +3.52568e19 q^{49} -1.28090e20i q^{50} +(1.08331e20 - 2.60954e20i) q^{51} -4.01614e19 q^{52} -5.21591e20i q^{53} +(-4.02020e20 + 1.65414e20i) q^{54} +2.79848e20 q^{55} +3.65926e20i q^{56} +(1.00438e21 + 4.16951e20i) q^{57} -1.97594e21 q^{58} -5.99992e20i q^{59} +(-2.11970e20 + 5.10607e20i) q^{60} +7.42263e19 q^{61} +1.97862e21i q^{62} +(3.00310e21 + 3.01255e21i) q^{63} -5.90296e20 q^{64} +5.93727e20i q^{65} +(3.20796e21 + 1.33173e21i) q^{66} +8.52972e21 q^{67} -4.45989e21i q^{68} +(-6.44041e21 + 1.55140e22i) q^{69} +5.40967e21 q^{70} -2.05121e22i q^{71} +(-4.85972e21 + 4.84448e21i) q^{72} -3.58499e22 q^{73} -2.82237e22i q^{74} +(-2.17070e22 - 9.01133e21i) q^{75} +1.71655e22 q^{76} -3.39870e22i q^{77} +(-2.82541e21 + 6.80602e21i) q^{78} +2.61248e22 q^{79} +8.72665e21i q^{80} +(-2.50559e20 + 7.97660e22i) q^{81} +5.53680e22 q^{82} -1.17460e23i q^{83} +(6.20122e22 + 2.57433e22i) q^{84} -6.59329e22 q^{85} -1.75818e23i q^{86} +(-1.39010e23 + 3.34856e23i) q^{87} +5.48264e22 q^{88} +1.60364e23i q^{89} +(7.16184e22 + 7.18437e22i) q^{90} +7.21069e22 q^{91} +2.65147e23i q^{92} +(3.35311e23 + 1.39199e23i) q^{93} -3.31063e23 q^{94} -2.53767e23i q^{95} +(-4.15281e22 + 1.00035e23i) q^{96} -8.32244e22 q^{97} -1.02115e23i q^{98} +(4.51369e23 - 4.49953e23i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 131880q^{3} - 67108864q^{4} + 33718272q^{6} - 10160794640q^{7} + 295169053896q^{9} + O(q^{10}) \) \( 8q - 131880q^{3} - 67108864q^{4} + 33718272q^{6} - 10160794640q^{7} + 295169053896q^{9} - 1863369424896q^{10} + 1106289623040q^{12} + 50568363679120q^{13} - 348034956760512q^{15} + 562949953421312q^{16} - 514738292981760q^{18} - 978083631341264q^{19} + 3640012304241936q^{21} - 336450979430400q^{22} - 282849366245376q^{24} + 7630618767014024q^{25} - 86594528606057640q^{27} + 85234923203461120q^{28} - 725410188900237312q^{30} + 3092119786822709104q^{31} - 8158685952668529600q^{33} + 3821138032531341312q^{34} - 2476057486864416768q^{36} + 22590293223992782480q^{37} - 40190176581881465040q^{39} + 15631075664637984768q^{40} - 79119883835565342720q^{42} + 226487466371803896880q^{43} - 347709996757177504128q^{45} + 139842130561120468992q^{46} - 9280229982150328320q^{48} + 104686700473616731800q^{49} + 558091874936566543104q^{51} - 424198180105575464960q^{52} + 334066775626796728320q^{54} - 2212687664250467338368q^{55} + 3588879995640760725840q^{57} - 1867706355469718323200q^{58} + 2919528822560885047296q^{60} - 6507010783838092385648q^{61} + 10112982777612899380080q^{63} - 4722366482869645213696q^{64} - 1924112442339530440704q^{66} - 7042120118150060144720q^{67} - 4323335967368731345536q^{69} + 16481910236435553583104q^{70} + 4317937762413135790080q^{72} + 36259820324758576687120q^{73} - 108081978448612908655272q^{75} + 8204760174538377920512q^{76} - 74188898027329578270720q^{78} + 316807052777330015315824q^{79} - 268518660504396776813304q^{81} + 83114941529654645882880q^{82} - 30534636335462338265088q^{84} - 222512862545524200678912q^{85} + 449461577201807342128320q^{87} + 2822355377657688883200q^{88} + 612683975543382025371648q^{90} - 1196839602335690774367520q^{91} + 873237537450828783745680q^{93} - 1298887117621773403422720q^{94} + 2372712456480891076608q^{96} + 816517576248201265716880q^{97} + 695858883367208922313344q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2896.31i 0.707107i
\(3\) −490828. 203759.i −0.923579 0.383409i
\(4\) −8.38861e6 −0.500000
\(5\) 1.24013e8i 0.507958i 0.967210 + 0.253979i \(0.0817394\pi\)
−0.967210 + 0.253979i \(0.918261\pi\)
\(6\) −5.90150e8 + 1.42159e9i −0.271111 + 0.653069i
\(7\) 1.50611e10 1.08813 0.544066 0.839043i \(-0.316884\pi\)
0.544066 + 0.839043i \(0.316884\pi\)
\(8\) 2.42960e10i 0.353553i
\(9\) 1.99394e11 + 2.00021e11i 0.705995 + 0.708216i
\(10\) 3.59180e11 0.359180
\(11\) 2.25660e12i 0.719023i −0.933141 0.359512i \(-0.882943\pi\)
0.933141 0.359512i \(-0.117057\pi\)
\(12\) 4.11736e12 + 1.70926e12i 0.461789 + 0.191704i
\(13\) 4.78761e12 0.205494 0.102747 0.994708i \(-0.467237\pi\)
0.102747 + 0.994708i \(0.467237\pi\)
\(14\) 4.36217e13i 0.769425i
\(15\) 2.52688e13 6.08691e13i 0.194756 0.469139i
\(16\) 7.03687e13 0.250000
\(17\) 5.31661e14i 0.912531i 0.889844 + 0.456265i \(0.150813\pi\)
−0.889844 + 0.456265i \(0.849187\pi\)
\(18\) 5.79323e14 5.77507e14i 0.500785 0.499214i
\(19\) −2.04629e15 −0.924537 −0.462269 0.886740i \(-0.652964\pi\)
−0.462269 + 0.886740i \(0.652964\pi\)
\(20\) 1.04030e15i 0.253979i
\(21\) −7.39242e15 3.06885e15i −1.00498 0.417199i
\(22\) −6.53582e15 −0.508426
\(23\) 3.16079e16i 1.44232i −0.692768 0.721161i \(-0.743609\pi\)
0.692768 0.721161i \(-0.256391\pi\)
\(24\) 4.95053e15 1.19251e16i 0.135555 0.326534i
\(25\) 4.42254e16 0.741979
\(26\) 1.38664e16i 0.145306i
\(27\) −5.71119e16 1.38804e17i −0.380506 0.924779i
\(28\) −1.26342e17 −0.544066
\(29\) 6.82228e17i 1.92821i −0.265527 0.964103i \(-0.585546\pi\)
0.265527 0.964103i \(-0.414454\pi\)
\(30\) −1.76296e17 7.31863e16i −0.331731 0.137713i
\(31\) −6.83154e17 −0.867318 −0.433659 0.901077i \(-0.642778\pi\)
−0.433659 + 0.901077i \(0.642778\pi\)
\(32\) 2.03810e17i 0.176777i
\(33\) −4.59804e17 + 1.10760e18i −0.275680 + 0.664075i
\(34\) 1.53985e18 0.645257
\(35\) 1.86778e18i 0.552725i
\(36\) −1.67264e18 1.67790e18i −0.352998 0.354108i
\(37\) 9.74472e18 1.48030 0.740148 0.672444i \(-0.234755\pi\)
0.740148 + 0.672444i \(0.234755\pi\)
\(38\) 5.92669e18i 0.653747i
\(39\) −2.34989e18 9.75520e17i −0.189790 0.0787882i
\(40\) −3.01302e18 −0.179590
\(41\) 1.91167e19i 0.847242i 0.905840 + 0.423621i \(0.139241\pi\)
−0.905840 + 0.423621i \(0.860759\pi\)
\(42\) −8.88833e18 + 2.14107e19i −0.295004 + 0.710625i
\(43\) 6.07042e19 1.51914 0.759569 0.650426i \(-0.225410\pi\)
0.759569 + 0.650426i \(0.225410\pi\)
\(44\) 1.89298e19i 0.359512i
\(45\) −2.48053e19 + 2.47275e19i −0.359744 + 0.358616i
\(46\) −9.15463e19 −1.01988
\(47\) 1.14305e20i 0.983766i −0.870661 0.491883i \(-0.836309\pi\)
0.870661 0.491883i \(-0.163691\pi\)
\(48\) −3.45389e19 1.43383e19i −0.230895 0.0958522i
\(49\) 3.52568e19 0.184030
\(50\) 1.28090e20i 0.524658i
\(51\) 1.08331e20 2.60954e20i 0.349872 0.842794i
\(52\) −4.01614e19 −0.102747
\(53\) 5.21591e20i 1.06174i −0.847452 0.530872i \(-0.821864\pi\)
0.847452 0.530872i \(-0.178136\pi\)
\(54\) −4.02020e20 + 1.65414e20i −0.653917 + 0.269058i
\(55\) 2.79848e20 0.365233
\(56\) 3.65926e20i 0.384713i
\(57\) 1.00438e21 + 4.16951e20i 0.853883 + 0.354476i
\(58\) −1.97594e21 −1.36345
\(59\) 5.99992e20i 0.337226i −0.985682 0.168613i \(-0.946071\pi\)
0.985682 0.168613i \(-0.0539289\pi\)
\(60\) −2.11970e20 + 5.10607e20i −0.0973778 + 0.234570i
\(61\) 7.42263e19 0.0279640 0.0139820 0.999902i \(-0.495549\pi\)
0.0139820 + 0.999902i \(0.495549\pi\)
\(62\) 1.97862e21i 0.613286i
\(63\) 3.00310e21 + 3.01255e21i 0.768216 + 0.770633i
\(64\) −5.90296e20 −0.125000
\(65\) 5.93727e20i 0.104382i
\(66\) 3.20796e21 + 1.33173e21i 0.469572 + 0.194935i
\(67\) 8.52972e21 1.04241 0.521203 0.853433i \(-0.325483\pi\)
0.521203 + 0.853433i \(0.325483\pi\)
\(68\) 4.45989e21i 0.456265i
\(69\) −6.44041e21 + 1.55140e22i −0.552999 + 1.33210i
\(70\) 5.40967e21 0.390836
\(71\) 2.05121e22i 1.25000i −0.780625 0.624999i \(-0.785099\pi\)
0.780625 0.624999i \(-0.214901\pi\)
\(72\) −4.85972e21 + 4.84448e21i −0.250392 + 0.249607i
\(73\) −3.58499e22 −1.56536 −0.782679 0.622425i \(-0.786148\pi\)
−0.782679 + 0.622425i \(0.786148\pi\)
\(74\) 2.82237e22i 1.04673i
\(75\) −2.17070e22 9.01133e21i −0.685276 0.284481i
\(76\) 1.71655e22 0.462269
\(77\) 3.39870e22i 0.782392i
\(78\) −2.82541e21 + 6.80602e21i −0.0557116 + 0.134202i
\(79\) 2.61248e22 0.442108 0.221054 0.975262i \(-0.429050\pi\)
0.221054 + 0.975262i \(0.429050\pi\)
\(80\) 8.72665e21i 0.126989i
\(81\) −2.50559e20 + 7.97660e22i −0.00314115 + 0.999995i
\(82\) 5.53680e22 0.599091
\(83\) 1.17460e23i 1.09889i −0.835530 0.549445i \(-0.814839\pi\)
0.835530 0.549445i \(-0.185161\pi\)
\(84\) 6.20122e22 + 2.57433e22i 0.502488 + 0.208600i
\(85\) −6.59329e22 −0.463527
\(86\) 1.75818e23i 1.07419i
\(87\) −1.39010e23 + 3.34856e23i −0.739291 + 1.78085i
\(88\) 5.48264e22 0.254213
\(89\) 1.60364e23i 0.649273i 0.945839 + 0.324637i \(0.105242\pi\)
−0.945839 + 0.324637i \(0.894758\pi\)
\(90\) 7.16184e22 + 7.18437e22i 0.253580 + 0.254377i
\(91\) 7.21069e22 0.223604
\(92\) 2.65147e23i 0.721161i
\(93\) 3.35311e23 + 1.39199e23i 0.801036 + 0.332537i
\(94\) −3.31063e23 −0.695628
\(95\) 2.53767e23i 0.469626i
\(96\) −4.15281e22 + 1.00035e23i −0.0677777 + 0.163267i
\(97\) −8.32244e22 −0.119947 −0.0599736 0.998200i \(-0.519102\pi\)
−0.0599736 + 0.998200i \(0.519102\pi\)
\(98\) 1.02115e23i 0.130129i
\(99\) 4.51369e23 4.49953e23i 0.509224 0.507627i
\(100\) −3.70989e23 −0.370989
\(101\) 2.20951e24i 1.96083i −0.196945 0.980415i \(-0.563102\pi\)
0.196945 0.980415i \(-0.436898\pi\)
\(102\) −7.55803e23 3.13759e23i −0.595945 0.247397i
\(103\) 3.85825e23 0.270610 0.135305 0.990804i \(-0.456799\pi\)
0.135305 + 0.990804i \(0.456799\pi\)
\(104\) 1.16320e23i 0.0726530i
\(105\) 3.80577e23 9.16758e23i 0.211920 0.510485i
\(106\) −1.51069e24 −0.750767
\(107\) 3.07071e24i 1.36343i 0.731617 + 0.681716i \(0.238766\pi\)
−0.731617 + 0.681716i \(0.761234\pi\)
\(108\) 4.79089e23 + 1.16437e24i 0.190253 + 0.462389i
\(109\) 1.69282e24 0.601857 0.300929 0.953647i \(-0.402703\pi\)
0.300929 + 0.953647i \(0.402703\pi\)
\(110\) 8.10528e23i 0.258259i
\(111\) −4.78298e24 1.98558e24i −1.36717 0.567558i
\(112\) 1.05983e24 0.272033
\(113\) 2.70784e24i 0.624715i 0.949965 + 0.312358i \(0.101119\pi\)
−0.949965 + 0.312358i \(0.898881\pi\)
\(114\) 1.20762e24 2.90899e24i 0.250652 0.603786i
\(115\) 3.91980e24 0.732638
\(116\) 5.72294e24i 0.964103i
\(117\) 9.54621e23 + 9.57624e23i 0.145078 + 0.145534i
\(118\) −1.73776e24 −0.238455
\(119\) 8.00742e24i 0.992954i
\(120\) 1.47888e24 + 6.13931e23i 0.165866 + 0.0688565i
\(121\) 4.75748e24 0.483006
\(122\) 2.14982e23i 0.0197736i
\(123\) 3.89521e24 9.38302e24i 0.324840 0.782495i
\(124\) 5.73071e24 0.433659
\(125\) 1.28763e25i 0.884852i
\(126\) 8.72527e24 8.69791e24i 0.544920 0.543211i
\(127\) −2.15801e25 −1.22577 −0.612886 0.790172i \(-0.709991\pi\)
−0.612886 + 0.790172i \(0.709991\pi\)
\(128\) 1.70968e24i 0.0883883i
\(129\) −2.97953e25 1.23690e25i −1.40304 0.582451i
\(130\) 1.71962e24 0.0738094
\(131\) 1.13650e25i 0.444954i −0.974938 0.222477i \(-0.928586\pi\)
0.974938 0.222477i \(-0.0714143\pi\)
\(132\) 3.85711e24 9.29125e24i 0.137840 0.332037i
\(133\) −3.08195e25 −1.00602
\(134\) 2.47047e25i 0.737093i
\(135\) 1.72136e25 7.08262e24i 0.469748 0.193281i
\(136\) −1.29172e25 −0.322628
\(137\) 1.38297e25i 0.316349i −0.987411 0.158175i \(-0.949439\pi\)
0.987411 0.158175i \(-0.0505609\pi\)
\(138\) 4.49335e25 + 1.86534e25i 0.941935 + 0.391029i
\(139\) 6.91088e25 1.32848 0.664241 0.747518i \(-0.268755\pi\)
0.664241 + 0.747518i \(0.268755\pi\)
\(140\) 1.56681e25i 0.276362i
\(141\) −2.32907e25 + 5.61042e25i −0.377185 + 0.908586i
\(142\) −5.94093e25 −0.883882
\(143\) 1.08037e25i 0.147755i
\(144\) 1.40311e25 + 1.40752e25i 0.176499 + 0.177054i
\(145\) 8.46052e25 0.979448
\(146\) 1.03832e26i 1.10688i
\(147\) −1.73050e25 7.18389e24i −0.169967 0.0705589i
\(148\) −8.17446e25 −0.740148
\(149\) 1.45823e25i 0.121785i 0.998144 + 0.0608923i \(0.0193946\pi\)
−0.998144 + 0.0608923i \(0.980605\pi\)
\(150\) −2.60996e25 + 6.28703e25i −0.201159 + 0.484563i
\(151\) 1.28532e26 0.914720 0.457360 0.889282i \(-0.348795\pi\)
0.457360 + 0.889282i \(0.348795\pi\)
\(152\) 4.97167e25i 0.326873i
\(153\) −1.06343e26 + 1.06010e26i −0.646269 + 0.644242i
\(154\) −9.84369e25 −0.553235
\(155\) 8.47200e25i 0.440561i
\(156\) 1.97123e25 + 8.18326e24i 0.0948949 + 0.0393941i
\(157\) 1.95529e26 0.871796 0.435898 0.899996i \(-0.356431\pi\)
0.435898 + 0.899996i \(0.356431\pi\)
\(158\) 7.56656e25i 0.312617i
\(159\) −1.06279e26 + 2.56011e26i −0.407082 + 0.980604i
\(160\) 2.52751e25 0.0897951
\(161\) 4.76052e26i 1.56944i
\(162\) 2.31027e26 + 7.25695e23i 0.707103 + 0.00222113i
\(163\) 1.44368e26 0.410413 0.205206 0.978719i \(-0.434213\pi\)
0.205206 + 0.978719i \(0.434213\pi\)
\(164\) 1.60363e26i 0.423621i
\(165\) −1.37357e26 5.70217e25i −0.337322 0.140034i
\(166\) −3.40202e26 −0.777033
\(167\) 4.74707e26i 1.00885i −0.863455 0.504426i \(-0.831704\pi\)
0.863455 0.504426i \(-0.168296\pi\)
\(168\) 7.45607e25 1.79606e26i 0.147502 0.355312i
\(169\) −5.19880e26 −0.957772
\(170\) 1.90962e26i 0.327763i
\(171\) −4.08018e26 4.09302e26i −0.652719 0.654772i
\(172\) −5.09224e26 −0.759569
\(173\) 7.88219e26i 1.09671i 0.836244 + 0.548357i \(0.184747\pi\)
−0.836244 + 0.548357i \(0.815253\pi\)
\(174\) 9.69848e26 + 4.02617e26i 1.25925 + 0.522758i
\(175\) 6.66085e26 0.807371
\(176\) 1.58794e26i 0.179756i
\(177\) −1.22254e26 + 2.94493e26i −0.129296 + 0.311455i
\(178\) 4.64465e26 0.459106
\(179\) 1.71671e27i 1.58657i 0.608847 + 0.793287i \(0.291632\pi\)
−0.608847 + 0.793287i \(0.708368\pi\)
\(180\) 2.08082e26 2.07429e26i 0.179872 0.179308i
\(181\) −6.59970e26 −0.533804 −0.266902 0.963724i \(-0.586000\pi\)
−0.266902 + 0.963724i \(0.586000\pi\)
\(182\) 2.08844e26i 0.158112i
\(183\) −3.64323e25 1.51243e25i −0.0258270 0.0107217i
\(184\) 7.67946e26 0.509938
\(185\) 1.20847e27i 0.751928i
\(186\) 4.03163e26 9.71164e26i 0.235139 0.566418i
\(187\) 1.19975e27 0.656131
\(188\) 9.58862e26i 0.491883i
\(189\) −8.60170e26 2.09055e27i −0.414040 1.00628i
\(190\) −7.34988e26 −0.332076
\(191\) 8.80733e26i 0.373632i −0.982395 0.186816i \(-0.940183\pi\)
0.982395 0.186816i \(-0.0598168\pi\)
\(192\) 2.89733e26 + 1.20278e26i 0.115447 + 0.0479261i
\(193\) −1.65998e27 −0.621461 −0.310730 0.950498i \(-0.600574\pi\)
−0.310730 + 0.950498i \(0.600574\pi\)
\(194\) 2.41044e26i 0.0848155i
\(195\) 1.20977e26 2.91418e26i 0.0400211 0.0964052i
\(196\) −2.95755e26 −0.0920152
\(197\) 2.80575e27i 0.821209i 0.911814 + 0.410604i \(0.134682\pi\)
−0.911814 + 0.410604i \(0.865318\pi\)
\(198\) −1.30320e27 1.30730e27i −0.358947 0.360076i
\(199\) 6.04163e27 1.56645 0.783226 0.621737i \(-0.213573\pi\)
0.783226 + 0.621737i \(0.213573\pi\)
\(200\) 1.07450e27i 0.262329i
\(201\) −4.18662e27 1.73801e27i −0.962745 0.399668i
\(202\) −6.39943e27 −1.38652
\(203\) 1.02751e28i 2.09814i
\(204\) −9.08744e26 + 2.18904e27i −0.174936 + 0.421397i
\(205\) −2.37073e27 −0.430363
\(206\) 1.11747e27i 0.191350i
\(207\) 6.32226e27 6.30243e27i 1.02148 1.01827i
\(208\) 3.36898e26 0.0513735
\(209\) 4.61767e27i 0.664764i
\(210\) −2.65521e27 1.10227e27i −0.360967 0.149850i
\(211\) 9.62629e27 1.23615 0.618073 0.786121i \(-0.287914\pi\)
0.618073 + 0.786121i \(0.287914\pi\)
\(212\) 4.37543e27i 0.530872i
\(213\) −4.17952e27 + 1.00679e28i −0.479260 + 1.15447i
\(214\) 8.89372e27 0.964092
\(215\) 7.52812e27i 0.771658i
\(216\) 3.37239e27 1.38759e27i 0.326959 0.134529i
\(217\) −1.02891e28 −0.943756
\(218\) 4.90294e27i 0.425577i
\(219\) 1.75961e28 + 7.30475e27i 1.44573 + 0.600172i
\(220\) −2.34754e27 −0.182617
\(221\) 2.54539e27i 0.187519i
\(222\) −5.75084e27 + 1.38530e28i −0.401324 + 0.966735i
\(223\) −1.86863e28 −1.23556 −0.617782 0.786349i \(-0.711969\pi\)
−0.617782 + 0.786349i \(0.711969\pi\)
\(224\) 3.06961e27i 0.192356i
\(225\) 8.81827e27 + 8.84602e27i 0.523834 + 0.525482i
\(226\) 7.84275e27 0.441741
\(227\) 1.80444e28i 0.963901i −0.876198 0.481951i \(-0.839928\pi\)
0.876198 0.481951i \(-0.160072\pi\)
\(228\) −8.42532e27 3.49764e27i −0.426941 0.177238i
\(229\) −1.96660e28 −0.945562 −0.472781 0.881180i \(-0.656750\pi\)
−0.472781 + 0.881180i \(0.656750\pi\)
\(230\) 1.13529e28i 0.518054i
\(231\) −6.92517e27 + 1.66818e28i −0.299976 + 0.722601i
\(232\) 1.65754e28 0.681724
\(233\) 3.90415e28i 1.52495i −0.647018 0.762474i \(-0.723984\pi\)
0.647018 0.762474i \(-0.276016\pi\)
\(234\) 2.77358e27 2.76488e27i 0.102908 0.102585i
\(235\) 1.41754e28 0.499712
\(236\) 5.03310e27i 0.168613i
\(237\) −1.28228e28 5.32317e27i −0.408321 0.169508i
\(238\) 2.31920e28 0.702124
\(239\) 1.14900e28i 0.330785i 0.986228 + 0.165392i \(0.0528891\pi\)
−0.986228 + 0.165392i \(0.947111\pi\)
\(240\) 1.77813e27 4.28328e27i 0.0486889 0.117285i
\(241\) −2.26729e28 −0.590612 −0.295306 0.955403i \(-0.595422\pi\)
−0.295306 + 0.955403i \(0.595422\pi\)
\(242\) 1.37791e28i 0.341537i
\(243\) 1.63760e28 3.91003e28i 0.386308 0.922370i
\(244\) −6.22655e26 −0.0139820
\(245\) 4.37231e27i 0.0934797i
\(246\) −2.71761e28 1.12817e28i −0.553307 0.229697i
\(247\) −9.79685e27 −0.189987
\(248\) 1.65979e28i 0.306643i
\(249\) −2.39336e28 + 5.76528e28i −0.421324 + 1.01491i
\(250\) 3.72937e28 0.625685
\(251\) 2.74981e27i 0.0439762i 0.999758 + 0.0219881i \(0.00699960\pi\)
−0.999758 + 0.0219881i \(0.993000\pi\)
\(252\) −2.51918e28 2.52711e28i −0.384108 0.385316i
\(253\) −7.13265e28 −1.03706
\(254\) 6.25027e28i 0.866751i
\(255\) 3.23617e28 + 1.34344e28i 0.428104 + 0.177720i
\(256\) 4.95176e27 0.0625000
\(257\) 1.14943e29i 1.38447i 0.721671 + 0.692236i \(0.243374\pi\)
−0.721671 + 0.692236i \(0.756626\pi\)
\(258\) −3.58246e28 + 8.62964e28i −0.411855 + 0.992102i
\(259\) 1.46767e29 1.61076
\(260\) 4.98054e27i 0.0521911i
\(261\) 1.36460e29 1.36032e29i 1.36559 1.36130i
\(262\) −3.29167e28 −0.314630
\(263\) 1.67988e28i 0.153394i 0.997054 + 0.0766970i \(0.0244374\pi\)
−0.997054 + 0.0766970i \(0.975563\pi\)
\(264\) −2.69103e28 1.11714e28i −0.234786 0.0974675i
\(265\) 6.46842e28 0.539321
\(266\) 8.92628e28i 0.711362i
\(267\) 3.26757e28 7.87112e28i 0.248937 0.599655i
\(268\) −7.15525e28 −0.521203
\(269\) 7.11629e28i 0.495708i 0.968797 + 0.247854i \(0.0797254\pi\)
−0.968797 + 0.247854i \(0.920275\pi\)
\(270\) −2.05135e28 4.98558e28i −0.136670 0.332162i
\(271\) −8.35305e28 −0.532370 −0.266185 0.963922i \(-0.585763\pi\)
−0.266185 + 0.963922i \(0.585763\pi\)
\(272\) 3.74123e28i 0.228133i
\(273\) −3.53921e28 1.46924e28i −0.206516 0.0857319i
\(274\) −4.00552e28 −0.223693
\(275\) 9.97991e28i 0.533500i
\(276\) 5.40260e28 1.30141e29i 0.276499 0.666049i
\(277\) −1.50267e29 −0.736389 −0.368194 0.929749i \(-0.620024\pi\)
−0.368194 + 0.929749i \(0.620024\pi\)
\(278\) 2.00161e29i 0.939379i
\(279\) −1.36217e29 1.36645e29i −0.612322 0.614249i
\(280\) −4.53796e28 −0.195418
\(281\) 1.37645e29i 0.567918i −0.958836 0.283959i \(-0.908352\pi\)
0.958836 0.283959i \(-0.0916479\pi\)
\(282\) 1.62495e29 + 6.74572e28i 0.642467 + 0.266710i
\(283\) −4.27935e28 −0.162159 −0.0810794 0.996708i \(-0.525837\pi\)
−0.0810794 + 0.996708i \(0.525837\pi\)
\(284\) 1.72068e29i 0.624999i
\(285\) −5.17074e28 + 1.24556e29i −0.180059 + 0.433737i
\(286\) −3.12910e28 −0.104478
\(287\) 2.87920e29i 0.921911i
\(288\) 4.07663e28 4.06384e28i 0.125196 0.124804i
\(289\) 5.67855e28 0.167288
\(290\) 2.45043e29i 0.692574i
\(291\) 4.08489e28 + 1.69577e28i 0.110781 + 0.0459888i
\(292\) 3.00731e29 0.782679
\(293\) 1.71498e29i 0.428397i −0.976790 0.214199i \(-0.931286\pi\)
0.976790 0.214199i \(-0.0687140\pi\)
\(294\) −2.08068e28 + 5.01206e28i −0.0498927 + 0.120185i
\(295\) 7.44069e28 0.171297
\(296\) 2.36758e29i 0.523364i
\(297\) −3.13226e29 + 1.28879e29i −0.664937 + 0.273593i
\(298\) 4.22350e28 0.0861147
\(299\) 1.51327e29i 0.296388i
\(300\) 1.82092e29 + 7.55925e28i 0.342638 + 0.142241i
\(301\) 9.14275e29 1.65302
\(302\) 3.72269e29i 0.646805i
\(303\) −4.50208e29 + 1.08449e30i −0.751799 + 1.81098i
\(304\) −1.43995e29 −0.231134
\(305\) 9.20503e27i 0.0142045i
\(306\) 3.07038e29 + 3.08004e29i 0.455548 + 0.456981i
\(307\) −9.60156e29 −1.36988 −0.684938 0.728601i \(-0.740171\pi\)
−0.684938 + 0.728601i \(0.740171\pi\)
\(308\) 2.85104e29i 0.391196i
\(309\) −1.89374e29 7.86154e28i −0.249930 0.103754i
\(310\) −2.45375e29 −0.311523
\(311\) 1.83314e29i 0.223909i 0.993713 + 0.111955i \(0.0357111\pi\)
−0.993713 + 0.111955i \(0.964289\pi\)
\(312\) 2.37012e28 5.70930e28i 0.0278558 0.0671008i
\(313\) 1.66337e30 1.88130 0.940648 0.339385i \(-0.110219\pi\)
0.940648 + 0.339385i \(0.110219\pi\)
\(314\) 5.66312e29i 0.616453i
\(315\) −3.73596e29 + 3.72424e29i −0.391449 + 0.390221i
\(316\) −2.19151e29 −0.221054
\(317\) 5.50864e29i 0.534975i −0.963561 0.267487i \(-0.913807\pi\)
0.963561 0.267487i \(-0.0861934\pi\)
\(318\) 7.41488e29 + 3.07817e29i 0.693392 + 0.287851i
\(319\) −1.53952e30 −1.38643
\(320\) 7.32044e28i 0.0634947i
\(321\) 6.25685e29 1.50719e30i 0.522752 1.25924i
\(322\) −1.37879e30 −1.10976
\(323\) 1.08793e30i 0.843669i
\(324\) 2.10184e27 6.69126e29i 0.00157058 0.499998i
\(325\) 2.11734e29 0.152472
\(326\) 4.18136e29i 0.290206i
\(327\) −8.30884e29 3.44928e29i −0.555862 0.230757i
\(328\) −4.64460e29 −0.299545
\(329\) 1.72157e30i 1.07047i
\(330\) −1.65152e29 + 3.97829e29i −0.0990188 + 0.238523i
\(331\) 2.52531e30 1.46009 0.730045 0.683399i \(-0.239499\pi\)
0.730045 + 0.683399i \(0.239499\pi\)
\(332\) 9.85329e29i 0.549445i
\(333\) 1.94304e30 + 1.94915e30i 1.04508 + 1.04837i
\(334\) −1.37490e30 −0.713366
\(335\) 1.05780e30i 0.529499i
\(336\) −5.20196e29 2.15951e29i −0.251244 0.104300i
\(337\) 6.18579e29 0.288295 0.144147 0.989556i \(-0.453956\pi\)
0.144147 + 0.989556i \(0.453956\pi\)
\(338\) 1.50573e30i 0.677247i
\(339\) 5.51748e29 1.32908e30i 0.239521 0.576974i
\(340\) 5.53085e29 0.231764
\(341\) 1.54161e30i 0.623621i
\(342\) −1.18546e30 + 1.18175e30i −0.462994 + 0.461542i
\(343\) −2.35442e30 −0.887882
\(344\) 1.47487e30i 0.537097i
\(345\) −1.92395e30 7.98695e29i −0.676649 0.280900i
\(346\) 2.28292e30 0.775494
\(347\) 3.27882e30i 1.07588i 0.842983 + 0.537940i \(0.180797\pi\)
−0.842983 + 0.537940i \(0.819203\pi\)
\(348\) 1.16610e30 2.80898e30i 0.369646 0.890425i
\(349\) −1.23269e30 −0.377527 −0.188764 0.982023i \(-0.560448\pi\)
−0.188764 + 0.982023i \(0.560448\pi\)
\(350\) 1.92919e30i 0.570897i
\(351\) −2.73430e29 6.64541e29i −0.0781916 0.190036i
\(352\) −4.59917e29 −0.127107
\(353\) 5.25121e30i 1.40269i 0.712820 + 0.701347i \(0.247418\pi\)
−0.712820 + 0.701347i \(0.752582\pi\)
\(354\) 8.52942e29 + 3.54085e29i 0.220232 + 0.0914258i
\(355\) 2.54377e30 0.634946
\(356\) 1.34523e30i 0.324637i
\(357\) 1.63158e30 3.93026e30i 0.380707 0.917071i
\(358\) 4.97212e30 1.12188
\(359\) 3.10562e30i 0.677664i 0.940847 + 0.338832i \(0.110032\pi\)
−0.940847 + 0.338832i \(0.889968\pi\)
\(360\) −6.00779e29 6.02669e29i −0.126790 0.127189i
\(361\) −7.11452e29 −0.145231
\(362\) 1.91148e30i 0.377456i
\(363\) −2.33510e30 9.69379e29i −0.446094 0.185189i
\(364\) −6.04877e29 −0.111802
\(365\) 4.44586e30i 0.795136i
\(366\) −4.38046e28 + 1.05519e29i −0.00758135 + 0.0182624i
\(367\) −1.54480e30 −0.258749 −0.129374 0.991596i \(-0.541297\pi\)
−0.129374 + 0.991596i \(0.541297\pi\)
\(368\) 2.22421e30i 0.360580i
\(369\) −3.82375e30 + 3.81176e30i −0.600031 + 0.598149i
\(370\) 3.50011e30 0.531693
\(371\) 7.85576e30i 1.15532i
\(372\) −2.81279e30 1.16768e30i −0.400518 0.166269i
\(373\) −8.17121e30 −1.12663 −0.563314 0.826243i \(-0.690474\pi\)
−0.563314 + 0.826243i \(0.690474\pi\)
\(374\) 3.47484e30i 0.463955i
\(375\) 2.62366e30 6.32004e30i 0.339260 0.817230i
\(376\) 2.77716e30 0.347814
\(377\) 3.26624e30i 0.396235i
\(378\) −6.05488e30 + 2.49132e30i −0.711548 + 0.292771i
\(379\) −1.36135e31 −1.54989 −0.774944 0.632029i \(-0.782222\pi\)
−0.774944 + 0.632029i \(0.782222\pi\)
\(380\) 2.12875e30i 0.234813i
\(381\) 1.05921e31 + 4.39715e30i 1.13210 + 0.469971i
\(382\) −2.55087e30 −0.264197
\(383\) 2.14155e29i 0.0214953i 0.999942 + 0.0107477i \(0.00342115\pi\)
−0.999942 + 0.0107477i \(0.996579\pi\)
\(384\) 3.48363e29 8.39158e29i 0.0338889 0.0816336i
\(385\) 4.21484e30 0.397422
\(386\) 4.80780e30i 0.439439i
\(387\) 1.21041e31 + 1.21421e31i 1.07250 + 1.07588i
\(388\) 6.98137e29 0.0599736
\(389\) 2.46642e30i 0.205433i 0.994711 + 0.102717i \(0.0327535\pi\)
−0.994711 + 0.102717i \(0.967246\pi\)
\(390\) −8.44035e29 3.50388e29i −0.0681688 0.0282992i
\(391\) 1.68047e31 1.31616
\(392\) 8.56599e29i 0.0650646i
\(393\) −2.31573e30 + 5.57828e30i −0.170599 + 0.410950i
\(394\) 8.12631e30 0.580682
\(395\) 3.23982e30i 0.224572i
\(396\) −3.78635e30 + 3.77448e30i −0.254612 + 0.253814i
\(397\) −1.20449e31 −0.785809 −0.392904 0.919579i \(-0.628530\pi\)
−0.392904 + 0.919579i \(0.628530\pi\)
\(398\) 1.74984e31i 1.10765i
\(399\) 1.51271e31 + 6.27976e30i 0.929137 + 0.385716i
\(400\) 3.11208e30 0.185495
\(401\) 4.88143e30i 0.282367i −0.989983 0.141184i \(-0.954909\pi\)
0.989983 0.141184i \(-0.0450908\pi\)
\(402\) −5.03381e30 + 1.21258e31i −0.282608 + 0.680763i
\(403\) −3.27068e30 −0.178228
\(404\) 1.85347e31i 0.980415i
\(405\) −9.89204e30 3.10726e28i −0.507955 0.00159557i
\(406\) −2.97600e31 −1.48361
\(407\) 2.19900e31i 1.06437i
\(408\) 6.34013e30 + 2.63200e30i 0.297973 + 0.123699i
\(409\) 2.14098e31 0.977085 0.488543 0.872540i \(-0.337529\pi\)
0.488543 + 0.872540i \(0.337529\pi\)
\(410\) 6.86636e30i 0.304313i
\(411\) −2.81793e30 + 6.78801e30i −0.121291 + 0.292173i
\(412\) −3.23654e30 −0.135305
\(413\) 9.03657e30i 0.366947i
\(414\) −1.82538e31 1.83112e31i −0.720027 0.722292i
\(415\) 1.45666e31 0.558190
\(416\) 9.75762e29i 0.0363265i
\(417\) −3.39205e31 1.40816e31i −1.22696 0.509352i
\(418\) 1.33742e31 0.470059
\(419\) 9.90044e28i 0.00338132i −0.999999 0.00169066i \(-0.999462\pi\)
0.999999 0.00169066i \(-0.000538154\pi\)
\(420\) −3.19251e30 + 7.69032e30i −0.105960 + 0.255243i
\(421\) −1.38801e31 −0.447720 −0.223860 0.974621i \(-0.571866\pi\)
−0.223860 + 0.974621i \(0.571866\pi\)
\(422\) 2.78807e31i 0.874087i
\(423\) 2.28635e31 2.27918e31i 0.696720 0.694535i
\(424\) 1.26726e31 0.375383
\(425\) 2.35129e31i 0.677079i
\(426\) 2.91597e31 + 1.21052e31i 0.816335 + 0.338888i
\(427\) 1.11793e30 0.0304285
\(428\) 2.57590e31i 0.681716i
\(429\) −2.20136e30 + 5.30277e30i −0.0566505 + 0.136463i
\(430\) 2.18038e31 0.545645
\(431\) 4.58411e31i 1.11565i −0.829959 0.557824i \(-0.811636\pi\)
0.829959 0.557824i \(-0.188364\pi\)
\(432\) −4.01889e30 9.76748e30i −0.0951265 0.231195i
\(433\) −6.04562e31 −1.39183 −0.695915 0.718124i \(-0.745001\pi\)
−0.695915 + 0.718124i \(0.745001\pi\)
\(434\) 2.98003e31i 0.667336i
\(435\) −4.15266e31 1.72391e31i −0.904597 0.375529i
\(436\) −1.42004e31 −0.300929
\(437\) 6.46790e31i 1.33348i
\(438\) 2.11568e31 5.09638e31i 0.424386 1.02229i
\(439\) 4.04585e31 0.789652 0.394826 0.918756i \(-0.370805\pi\)
0.394826 + 0.918756i \(0.370805\pi\)
\(440\) 6.79920e30i 0.129130i
\(441\) 7.02999e30 + 7.05211e30i 0.129925 + 0.130333i
\(442\) 7.37223e30 0.132596
\(443\) 1.03672e32i 1.81474i 0.420329 + 0.907372i \(0.361915\pi\)
−0.420329 + 0.907372i \(0.638085\pi\)
\(444\) 4.01225e31 + 1.66562e31i 0.683585 + 0.283779i
\(445\) −1.98873e31 −0.329803
\(446\) 5.41214e31i 0.873676i
\(447\) 2.97129e30 7.15742e30i 0.0466933 0.112478i
\(448\) −8.89053e30 −0.136016
\(449\) 5.40229e31i 0.804677i 0.915491 + 0.402338i \(0.131803\pi\)
−0.915491 + 0.402338i \(0.868197\pi\)
\(450\) 2.56208e31 2.55404e31i 0.371572 0.370406i
\(451\) 4.31389e31 0.609187
\(452\) 2.27150e31i 0.312358i
\(453\) −6.30871e31 2.61896e31i −0.844816 0.350712i
\(454\) −5.22622e31 −0.681581
\(455\) 8.94221e30i 0.113582i
\(456\) −1.01302e31 + 2.44023e31i −0.125326 + 0.301893i
\(457\) 5.79920e31 0.698834 0.349417 0.936967i \(-0.386380\pi\)
0.349417 + 0.936967i \(0.386380\pi\)
\(458\) 5.69588e31i 0.668613i
\(459\) 7.37968e31 3.03641e31i 0.843889 0.347223i
\(460\) −3.28817e31 −0.366319
\(461\) 5.22421e31i 0.567034i −0.958967 0.283517i \(-0.908499\pi\)
0.958967 0.283517i \(-0.0915013\pi\)
\(462\) 4.83156e31 + 2.00574e31i 0.510956 + 0.212115i
\(463\) −2.10907e31 −0.217330 −0.108665 0.994078i \(-0.534658\pi\)
−0.108665 + 0.994078i \(0.534658\pi\)
\(464\) 4.80075e31i 0.482052i
\(465\) −1.72625e31 + 4.15829e31i −0.168915 + 0.406893i
\(466\) −1.13076e32 −1.07830
\(467\) 1.62891e32i 1.51389i −0.653479 0.756945i \(-0.726691\pi\)
0.653479 0.756945i \(-0.273309\pi\)
\(468\) −8.00794e30 8.03314e30i −0.0725389 0.0727671i
\(469\) 1.28467e32 1.13428
\(470\) 4.10562e31i 0.353350i
\(471\) −9.59709e31 3.98408e31i −0.805172 0.334254i
\(472\) 1.45774e31 0.119228
\(473\) 1.36985e32i 1.09230i
\(474\) −1.54176e31 + 3.71387e31i −0.119860 + 0.288727i
\(475\) −9.04981e31 −0.685987
\(476\) 6.71711e31i 0.496477i
\(477\) 1.04329e32 1.04002e32i 0.751945 0.749587i
\(478\) 3.32786e31 0.233900
\(479\) 1.75158e32i 1.20062i 0.799769 + 0.600308i \(0.204955\pi\)
−0.799769 + 0.600308i \(0.795045\pi\)
\(480\) −1.24057e31 5.15003e30i −0.0829328 0.0344282i
\(481\) 4.66539e31 0.304192
\(482\) 6.56677e31i 0.417626i
\(483\) −9.69999e31 + 2.33659e32i −0.601735 + 1.44950i
\(484\) −3.99086e31 −0.241503
\(485\) 1.03209e31i 0.0609281i
\(486\) −1.13247e32 4.74301e31i −0.652214 0.273161i
\(487\) −7.23439e31 −0.406494 −0.203247 0.979127i \(-0.565149\pi\)
−0.203247 + 0.979127i \(0.565149\pi\)
\(488\) 1.80340e30i 0.00988678i
\(489\) −7.08600e31 2.94164e31i −0.379049 0.157356i
\(490\) 1.26635e31 0.0661001
\(491\) 1.04300e32i 0.531260i −0.964075 0.265630i \(-0.914420\pi\)
0.964075 0.265630i \(-0.0855799\pi\)
\(492\) −3.26754e31 + 7.87105e31i −0.162420 + 0.391247i
\(493\) 3.62714e32 1.75955
\(494\) 2.83747e31i 0.134341i
\(495\) 5.58001e31 + 5.59756e31i 0.257853 + 0.258664i
\(496\) −4.80727e31 −0.216829
\(497\) 3.08935e32i 1.36016i
\(498\) 1.66980e32 + 6.93192e31i 0.717651 + 0.297921i
\(499\) −1.57053e32 −0.658931 −0.329466 0.944168i \(-0.606869\pi\)
−0.329466 + 0.944168i \(0.606869\pi\)
\(500\) 1.08014e32i 0.442426i
\(501\) −9.67258e31 + 2.32999e32i −0.386803 + 0.931755i
\(502\) 7.96430e30 0.0310959
\(503\) 2.71086e32i 1.03345i 0.856151 + 0.516726i \(0.172850\pi\)
−0.856151 + 0.516726i \(0.827150\pi\)
\(504\) −7.31929e31 + 7.29633e31i −0.272460 + 0.271605i
\(505\) 2.74008e32 0.996019
\(506\) 2.06584e32i 0.733314i
\(507\) 2.55171e32 + 1.05930e32i 0.884578 + 0.367218i
\(508\) 1.81027e32 0.612886
\(509\) 2.32358e31i 0.0768324i −0.999262 0.0384162i \(-0.987769\pi\)
0.999262 0.0384162i \(-0.0122313\pi\)
\(510\) 3.89103e31 9.37295e31i 0.125667 0.302715i
\(511\) −5.39941e32 −1.70332
\(512\) 1.43418e31i 0.0441942i
\(513\) 1.16868e32 + 2.84034e32i 0.351792 + 0.854992i
\(514\) 3.32910e32 0.978970
\(515\) 4.78474e31i 0.137458i
\(516\) 2.49941e32 + 1.03759e32i 0.701522 + 0.291226i
\(517\) −2.57942e32 −0.707351
\(518\) 4.25081e32i 1.13898i
\(519\) 1.60607e32 3.86879e32i 0.420490 1.01290i
\(520\) −1.44252e31 −0.0369047
\(521\) 2.99413e32i 0.748546i 0.927319 + 0.374273i \(0.122108\pi\)
−0.927319 + 0.374273i \(0.877892\pi\)
\(522\) −3.93991e32 3.95231e32i −0.962588 0.965616i
\(523\) −5.02363e32 −1.19949 −0.599746 0.800190i \(-0.704732\pi\)
−0.599746 + 0.800190i \(0.704732\pi\)
\(524\) 9.53369e31i 0.222477i
\(525\) −3.26933e32 1.35721e32i −0.745670 0.309553i
\(526\) 4.86544e31 0.108466
\(527\) 3.63206e32i 0.791454i
\(528\) −3.23558e31 + 7.79406e31i −0.0689200 + 0.166019i
\(529\) −5.18810e32 −1.08029
\(530\) 1.87345e32i 0.381358i
\(531\) 1.20011e32 1.19635e32i 0.238829 0.238080i
\(532\) 2.58533e32 0.503009
\(533\) 9.15235e31i 0.174103i
\(534\) −2.27972e32 9.46389e31i −0.424020 0.176025i
\(535\) −3.80808e32 −0.692566
\(536\) 2.07238e32i 0.368546i
\(537\) 3.49795e32 8.42609e32i 0.608307 1.46533i
\(538\) 2.06110e32 0.350519
\(539\) 7.95606e31i 0.132322i
\(540\) −1.44398e32 + 5.94134e31i −0.234874 + 0.0966405i
\(541\) 1.14877e33 1.82754 0.913768 0.406236i \(-0.133159\pi\)
0.913768 + 0.406236i \(0.133159\pi\)
\(542\) 2.41930e32i 0.376443i
\(543\) 3.23932e32 + 1.34475e32i 0.493010 + 0.204665i
\(544\) 1.08358e32 0.161314
\(545\) 2.09932e32i 0.305718i
\(546\) −4.25539e31 + 1.02506e32i −0.0606216 + 0.146029i
\(547\) 2.72421e32 0.379658 0.189829 0.981817i \(-0.439207\pi\)
0.189829 + 0.981817i \(0.439207\pi\)
\(548\) 1.16012e32i 0.158175i
\(549\) 1.48003e31 + 1.48468e31i 0.0197425 + 0.0198046i
\(550\) −2.89049e32 −0.377241
\(551\) 1.39604e33i 1.78270i
\(552\) −3.76929e32 1.56476e32i −0.470967 0.195515i
\(553\) 3.93470e32 0.481072
\(554\) 4.35221e32i 0.520706i
\(555\) 2.46237e32 5.93152e32i 0.288296 0.694465i
\(556\) −5.79727e32 −0.664241
\(557\) 3.73854e32i 0.419218i −0.977785 0.209609i \(-0.932781\pi\)
0.977785 0.209609i \(-0.0672191\pi\)
\(558\) −3.95767e32 + 3.94526e32i −0.434339 + 0.432977i
\(559\) 2.90628e32 0.312174
\(560\) 1.31433e32i 0.138181i
\(561\) −5.88869e32 2.44459e32i −0.605988 0.251566i
\(562\) −3.98663e32 −0.401578
\(563\) 3.96278e32i 0.390751i −0.980729 0.195375i \(-0.937408\pi\)
0.980729 0.195375i \(-0.0625925\pi\)
\(564\) 1.95377e32 4.70636e32i 0.188592 0.454293i
\(565\) −3.35808e32 −0.317329
\(566\) 1.23943e32i 0.114664i
\(567\) −3.77370e30 + 1.20137e33i −0.00341799 + 1.08813i
\(568\) 4.98361e32 0.441941
\(569\) 1.91705e33i 1.66451i 0.554395 + 0.832254i \(0.312950\pi\)
−0.554395 + 0.832254i \(0.687050\pi\)
\(570\) 3.60752e32 + 1.49761e32i 0.306698 + 0.127321i
\(571\) 7.07277e32 0.588784 0.294392 0.955685i \(-0.404883\pi\)
0.294392 + 0.955685i \(0.404883\pi\)
\(572\) 9.06284e31i 0.0738774i
\(573\) −1.79457e32 + 4.32288e32i −0.143254 + 0.345078i
\(574\) 8.33905e32 0.651889
\(575\) 1.39787e33i 1.07017i
\(576\) −1.17701e32 1.18072e32i −0.0882494 0.0885271i
\(577\) −5.60843e32 −0.411843 −0.205921 0.978569i \(-0.566019\pi\)
−0.205921 + 0.978569i \(0.566019\pi\)
\(578\) 1.64468e32i 0.118290i
\(579\) 8.14762e32 + 3.38235e32i 0.573968 + 0.238274i
\(580\) −7.09720e32 −0.489724
\(581\) 1.76909e33i 1.19574i
\(582\) 4.91149e31 1.18311e32i 0.0325190 0.0783338i
\(583\) −1.17702e33 −0.763419
\(584\) 8.71010e32i 0.553438i
\(585\) −1.18758e32 + 1.18386e32i −0.0739252 + 0.0736934i
\(586\) −4.96710e32 −0.302923
\(587\) 1.55484e33i 0.929027i −0.885566 0.464514i \(-0.846229\pi\)
0.885566 0.464514i \(-0.153771\pi\)
\(588\) 1.45165e32 + 6.02629e31i 0.0849833 + 0.0352795i
\(589\) 1.39793e33 0.801867
\(590\) 2.15506e32i 0.121125i
\(591\) 5.71696e32 1.37714e33i 0.314859 0.758451i
\(592\) 6.85723e32 0.370074
\(593\) 8.57869e32i 0.453696i −0.973930 0.226848i \(-0.927158\pi\)
0.973930 0.226848i \(-0.0728420\pi\)
\(594\) 3.73273e32 + 9.07200e32i 0.193459 + 0.470182i
\(595\) −9.93025e32 −0.504379
\(596\) 1.22326e32i 0.0608923i
\(597\) −2.96540e33 1.23104e33i −1.44674 0.600592i
\(598\) −4.38288e32 −0.209578
\(599\) 1.41388e33i 0.662658i 0.943515 + 0.331329i \(0.107497\pi\)
−0.943515 + 0.331329i \(0.892503\pi\)
\(600\) 2.18939e32 5.27394e32i 0.100579 0.242282i
\(601\) −1.65022e33 −0.743103 −0.371552 0.928412i \(-0.621174\pi\)
−0.371552 + 0.928412i \(0.621174\pi\)
\(602\) 2.64802e33i 1.16886i
\(603\) 1.70077e33 + 1.70613e33i 0.735934 + 0.738250i
\(604\) −1.07821e33 −0.457360
\(605\) 5.89990e32i 0.245346i
\(606\) 3.14102e33 + 1.30394e33i 1.28056 + 0.531602i
\(607\) −2.77181e33 −1.10790 −0.553948 0.832552i \(-0.686879\pi\)
−0.553948 + 0.832552i \(0.686879\pi\)
\(608\) 4.17054e32i 0.163437i
\(609\) −2.09365e33 + 5.04332e33i −0.804446 + 1.93780i
\(610\) 2.66606e31 0.0100441
\(611\) 5.47249e32i 0.202158i
\(612\) 8.92073e32 8.89276e32i 0.323135 0.322121i
\(613\) 3.92257e33 1.39330 0.696651 0.717410i \(-0.254673\pi\)
0.696651 + 0.717410i \(0.254673\pi\)
\(614\) 2.78091e33i 0.968649i
\(615\) 1.16362e33 + 4.83057e32i 0.397474 + 0.165005i
\(616\) 8.25749e32 0.276617
\(617\) 2.49852e33i 0.820844i −0.911896 0.410422i \(-0.865381\pi\)
0.911896 0.410422i \(-0.134619\pi\)
\(618\) −2.27695e32 + 5.48485e32i −0.0733654 + 0.176727i
\(619\) 3.36013e33 1.06186 0.530931 0.847415i \(-0.321842\pi\)
0.530931 + 0.847415i \(0.321842\pi\)
\(620\) 7.10683e32i 0.220280i
\(621\) −4.38732e33 + 1.80519e33i −1.33383 + 0.548812i
\(622\) 5.30935e32 0.158328
\(623\) 2.41527e33i 0.706495i
\(624\) −1.65359e32 6.86461e31i −0.0474474 0.0196970i
\(625\) 1.03921e33 0.292511
\(626\) 4.81764e33i 1.33028i
\(627\) 9.40892e32 2.26648e33i 0.254876 0.613962i
\(628\) −1.64021e33 −0.435898
\(629\) 5.18088e33i 1.35082i
\(630\) 1.07865e33 + 1.08205e33i 0.275928 + 0.276796i
\(631\) 4.71285e33 1.18285 0.591427 0.806359i \(-0.298565\pi\)
0.591427 + 0.806359i \(0.298565\pi\)
\(632\) 6.34729e32i 0.156309i
\(633\) −4.72485e33 1.96145e33i −1.14168 0.473949i
\(634\) −1.59547e33 −0.378284
\(635\) 2.67622e33i 0.622640i
\(636\) 8.91533e32 2.14758e33i 0.203541 0.490302i
\(637\) 1.68796e32 0.0378171
\(638\) 4.45892e33i 0.980351i
\(639\) 4.10285e33 4.08998e33i 0.885269 0.882493i
\(640\) −2.12023e32 −0.0448976
\(641\) 4.12036e33i 0.856326i 0.903702 + 0.428163i \(0.140839\pi\)
−0.903702 + 0.428163i \(0.859161\pi\)
\(642\) −4.36529e33 1.81218e33i −0.890415 0.369641i
\(643\) −1.45104e33 −0.290501 −0.145250 0.989395i \(-0.546399\pi\)
−0.145250 + 0.989395i \(0.546399\pi\)
\(644\) 3.99341e33i 0.784718i
\(645\) 1.53392e33 3.69501e33i 0.295861 0.712687i
\(646\) −3.15099e33 −0.596564
\(647\) 9.20942e33i 1.71152i −0.517377 0.855758i \(-0.673091\pi\)
0.517377 0.855758i \(-0.326909\pi\)
\(648\) −1.93800e33 6.08757e30i −0.353552 0.00111057i
\(649\) −1.35394e33 −0.242474
\(650\) 6.13247e32i 0.107814i
\(651\) 5.05016e33 + 2.09649e33i 0.871633 + 0.361844i
\(652\) −1.21105e33 −0.205206
\(653\) 3.83686e33i 0.638289i −0.947706 0.319144i \(-0.896604\pi\)
0.947706 0.319144i \(-0.103396\pi\)
\(654\) −9.99018e32 + 2.40650e33i −0.163170 + 0.393054i
\(655\) 1.40941e33 0.226018
\(656\) 1.34522e33i 0.211810i
\(657\) −7.14826e33 7.17075e33i −1.10514 1.10861i
\(658\) −4.98619e33 −0.756935
\(659\) 1.22388e34i 1.82437i 0.409774 + 0.912187i \(0.365608\pi\)
−0.409774 + 0.912187i \(0.634392\pi\)
\(660\) 1.15224e33 + 4.78333e32i 0.168661 + 0.0700169i
\(661\) 4.50499e33 0.647555 0.323777 0.946133i \(-0.395047\pi\)
0.323777 + 0.946133i \(0.395047\pi\)
\(662\) 7.31409e33i 1.03244i
\(663\) 5.18646e32 1.24935e33i 0.0718966 0.173189i
\(664\) 2.85382e33 0.388516
\(665\) 3.82202e33i 0.511015i
\(666\) 5.64534e33 5.62764e33i 0.741309 0.738984i
\(667\) −2.15638e34 −2.78109
\(668\) 3.98213e33i 0.504426i
\(669\) 9.17176e33 + 3.80751e33i 1.14114 + 0.473726i
\(670\) 3.06371e33 0.374412
\(671\) 1.67499e32i 0.0201068i
\(672\) −6.25460e32 + 1.50665e33i −0.0737511 + 0.177656i
\(673\) 1.47939e34 1.71356 0.856782 0.515678i \(-0.172460\pi\)
0.856782 + 0.515678i \(0.172460\pi\)
\(674\) 1.79160e33i 0.203855i
\(675\) −2.52580e33 6.13867e33i −0.282327 0.686166i
\(676\) 4.36107e33 0.478886
\(677\) 9.47154e33i 1.02178i 0.859647 + 0.510889i \(0.170684\pi\)
−0.859647 + 0.510889i \(0.829316\pi\)
\(678\) −3.84944e33 1.59803e33i −0.407982 0.169367i
\(679\) −1.25346e33 −0.130518
\(680\) 1.60191e33i 0.163882i
\(681\) −3.67672e33 + 8.85670e33i −0.369568 + 0.890239i
\(682\) 4.46497e33 0.440967
\(683\) 1.32859e34i 1.28927i 0.764492 + 0.644633i \(0.222990\pi\)
−0.764492 + 0.644633i \(0.777010\pi\)
\(684\) 3.42270e33 + 3.43347e33i 0.326359 + 0.327386i
\(685\) 1.71507e33 0.160692
\(686\) 6.81914e33i 0.627828i
\(687\) 9.65261e33 + 4.00713e33i 0.873301 + 0.362537i
\(688\) 4.27168e33 0.379785
\(689\) 2.49718e33i 0.218182i
\(690\) −2.31327e33 + 5.57234e33i −0.198626 + 0.478463i
\(691\) −1.22829e34 −1.03649 −0.518246 0.855232i \(-0.673415\pi\)
−0.518246 + 0.855232i \(0.673415\pi\)
\(692\) 6.61206e33i 0.548357i
\(693\) 6.79813e33 6.77681e33i 0.554103 0.552365i
\(694\) 9.49647e33 0.760761
\(695\) 8.57040e33i 0.674813i
\(696\) −8.13567e33 3.37739e33i −0.629626 0.261379i
\(697\) −1.01636e34 −0.773134
\(698\) 3.57025e33i 0.266952i
\(699\) −7.95506e33 + 1.91626e34i −0.584679 + 1.40841i
\(700\) −5.58752e33 −0.403685
\(701\) 2.57975e34i 1.83215i −0.401007 0.916075i \(-0.631340\pi\)
0.401007 0.916075i \(-0.368660\pi\)
\(702\) −1.92472e33 + 7.91937e32i −0.134376 + 0.0552898i
\(703\) −1.99405e34 −1.36859
\(704\) 1.33206e33i 0.0898779i
\(705\) −6.95766e33 2.88836e33i −0.461523 0.191594i
\(706\) 1.52091e34 0.991854
\(707\) 3.32778e34i 2.13364i
\(708\) 1.02554e33 2.47038e33i 0.0646478 0.155728i
\(709\) 1.67711e34 1.03946 0.519728 0.854332i \(-0.326033\pi\)
0.519728 + 0.854332i \(0.326033\pi\)
\(710\) 7.36754e33i 0.448975i
\(711\) 5.20913e33 + 5.22552e33i 0.312126 + 0.313108i
\(712\) −3.89621e33 −0.229553
\(713\) 2.15931e34i 1.25095i
\(714\) −1.13833e34 4.72557e33i −0.648467 0.269201i
\(715\) 1.33981e33 0.0750532
\(716\) 1.44008e34i 0.793287i
\(717\) 2.34120e33 5.63961e33i 0.126826 0.305506i
\(718\) 8.99482e33 0.479181
\(719\) 1.42987e34i 0.749115i −0.927204 0.374558i \(-0.877795\pi\)
0.927204 0.374558i \(-0.122205\pi\)
\(720\) −1.74552e33 + 1.74004e33i −0.0899360 + 0.0896540i
\(721\) 5.81097e33 0.294459
\(722\) 2.06058e33i 0.102694i
\(723\) 1.11285e34 + 4.61981e33i 0.545477 + 0.226446i
\(724\) 5.53623e33 0.266902
\(725\) 3.01718e34i 1.43069i
\(726\) −2.80762e33 + 6.76317e33i −0.130948 + 0.315436i
\(727\) −1.19847e34 −0.549813 −0.274907 0.961471i \(-0.588647\pi\)
−0.274907 + 0.961471i \(0.588647\pi\)
\(728\) 1.75191e33i 0.0790561i
\(729\) −1.60049e34 + 1.58547e34i −0.710431 + 0.703767i
\(730\) −1.28766e34 −0.562246
\(731\) 3.22740e34i 1.38626i
\(732\) 3.05616e32 + 1.26872e32i 0.0129135 + 0.00536083i
\(733\) 3.29541e34 1.36981 0.684906 0.728631i \(-0.259843\pi\)
0.684906 + 0.728631i \(0.259843\pi\)
\(734\) 4.47421e33i 0.182963i
\(735\) 8.90897e32 2.14605e33i 0.0358410 0.0863359i
\(736\) −6.44200e33 −0.254969
\(737\) 1.92482e34i 0.749515i
\(738\) 1.10400e34 + 1.10748e34i 0.422955 + 0.424286i
\(739\) −1.97092e34 −0.742909 −0.371455 0.928451i \(-0.621141\pi\)
−0.371455 + 0.928451i \(0.621141\pi\)
\(740\) 1.01374e34i 0.375964i
\(741\) 4.80857e33 + 1.99620e33i 0.175468 + 0.0728426i
\(742\) −2.27527e34 −0.816933
\(743\) 1.02403e34i 0.361780i −0.983503 0.180890i \(-0.942102\pi\)
0.983503 0.180890i \(-0.0578979\pi\)
\(744\) −3.38198e33 + 8.14671e33i −0.117570 + 0.283209i
\(745\) −1.80840e33 −0.0618614
\(746\) 2.36663e34i 0.796646i
\(747\) 2.34946e34 2.34209e34i 0.778252 0.775811i
\(748\) −1.00642e34 −0.328065
\(749\) 4.62484e34i 1.48359i
\(750\) −1.83048e34 7.59894e33i −0.577869 0.239893i
\(751\) −1.34386e34 −0.417519 −0.208759 0.977967i \(-0.566943\pi\)
−0.208759 + 0.977967i \(0.566943\pi\)
\(752\) 8.04352e33i 0.245942i
\(753\) 5.60299e32 1.34968e33i 0.0168609 0.0406155i
\(754\) −9.46005e33 −0.280180
\(755\) 1.59397e34i 0.464639i
\(756\) 7.21563e33 + 1.75368e34i 0.207020 + 0.503140i
\(757\) 5.51041e34 1.55608 0.778042 0.628212i \(-0.216213\pi\)
0.778042 + 0.628212i \(0.216213\pi\)
\(758\)