Properties

Label 6.25.b.a.5.4
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 5.4
Root \(1246.64i\) of defining polynomial
Character \(\chi\) \(=\) 6.5
Dual form 6.25.b.a.5.8

$q$-expansion

\(f(q)\) \(=\) \(q-2896.31i q^{2} +(473275. + 241744. i) q^{3} -8.38861e6 q^{4} +7.85820e7i q^{5} +(7.00165e8 - 1.37075e9i) q^{6} +2.19870e9 q^{7} +2.42960e10i q^{8} +(1.65549e11 + 2.28823e11i) q^{9} +O(q^{10})\) \(q-2896.31i q^{2} +(473275. + 241744. i) q^{3} -8.38861e6 q^{4} +7.85820e7i q^{5} +(7.00165e8 - 1.37075e9i) q^{6} +2.19870e9 q^{7} +2.42960e10i q^{8} +(1.65549e11 + 2.28823e11i) q^{9} +2.27598e11 q^{10} +1.55920e12i q^{11} +(-3.97012e12 - 2.02789e12i) q^{12} -3.72207e13 q^{13} -6.36811e12i q^{14} +(-1.89967e13 + 3.71909e13i) q^{15} +7.03687e13 q^{16} +6.73556e14i q^{17} +(6.62742e14 - 4.79482e14i) q^{18} +9.37274e14 q^{19} -6.59193e14i q^{20} +(1.04059e15 + 5.31522e14i) q^{21} +4.51594e15 q^{22} +3.13424e16i q^{23} +(-5.87341e15 + 1.14987e16i) q^{24} +5.34295e16 q^{25} +1.07803e17i q^{26} +(2.30339e16 + 1.48317e17i) q^{27} -1.84440e16 q^{28} +2.21159e17i q^{29} +(1.07716e17 + 5.50203e16i) q^{30} +6.76426e17 q^{31} -2.03810e17i q^{32} +(-3.76928e17 + 7.37933e17i) q^{33} +1.95083e18 q^{34} +1.72778e17i q^{35} +(-1.38873e18 - 1.91950e18i) q^{36} -4.23578e18 q^{37} -2.71464e18i q^{38} +(-1.76157e19 - 8.99789e18i) q^{39} -1.90923e18 q^{40} -2.43094e19i q^{41} +(1.53945e18 - 3.01387e18i) q^{42} +2.27505e19 q^{43} -1.30796e19i q^{44} +(-1.79813e19 + 1.30092e19i) q^{45} +9.07774e19 q^{46} +6.93806e19i q^{47} +(3.33038e19 + 1.70112e19i) q^{48} -1.86747e20 q^{49} -1.54748e20i q^{50} +(-1.62828e20 + 3.18777e20i) q^{51} +3.12230e20 q^{52} +8.43863e20i q^{53} +(4.29571e20 - 6.67133e19i) q^{54} -1.22525e20 q^{55} +5.34196e19i q^{56} +(4.43589e20 + 2.26580e20i) q^{57} +6.40546e20 q^{58} -2.79071e21i q^{59} +(1.59356e20 - 3.11980e20i) q^{60} -4.56793e21 q^{61} -1.95914e21i q^{62} +(3.63993e20 + 5.03112e20i) q^{63} -5.90296e20 q^{64} -2.92488e21i q^{65} +(2.13728e21 + 1.09170e21i) q^{66} -1.20142e21 q^{67} -5.65019e21i q^{68} +(-7.57684e21 + 1.48336e22i) q^{69} +5.00419e20 q^{70} -1.60117e22i q^{71} +(-5.55948e21 + 4.02219e21i) q^{72} +2.60444e22 q^{73} +1.22681e22i q^{74} +(2.52869e22 + 1.29163e22i) q^{75} -7.86242e21 q^{76} +3.42822e21i q^{77} +(-2.60607e22 + 5.10204e22i) q^{78} +8.00431e22 q^{79} +5.52971e21i q^{80} +(-2.49533e22 + 7.57629e22i) q^{81} -7.04077e22 q^{82} -1.65147e23i q^{83} +(-8.72910e21 - 4.45873e21i) q^{84} -5.29293e22 q^{85} -6.58923e22i q^{86} +(-5.34639e22 + 1.04669e23i) q^{87} -3.78824e22 q^{88} -4.33073e23i q^{89} +(3.76786e22 + 5.20795e22i) q^{90} -8.18372e22 q^{91} -2.62919e23i q^{92} +(3.20136e23 + 1.63522e23i) q^{93} +2.00948e23 q^{94} +7.36528e22i q^{95} +(4.92697e22 - 9.64581e22i) q^{96} -4.08706e23 q^{97} +5.40877e23i q^{98} +(-3.56782e23 + 2.58125e23i) 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
\(3\) 473275. + 241744.i 0.890551 + 0.454884i
\(4\) −8.38861e6 −0.500000
\(5\) 7.85820e7i 0.321872i 0.986965 + 0.160936i \(0.0514512\pi\)
−0.986965 + 0.160936i \(0.948549\pi\)
\(6\) 7.00165e8 1.37075e9i 0.321651 0.629715i
\(7\) 2.19870e9 0.158851 0.0794254 0.996841i \(-0.474691\pi\)
0.0794254 + 0.996841i \(0.474691\pi\)
\(8\) 2.42960e10i 0.353553i
\(9\) 1.65549e11 + 2.28823e11i 0.586162 + 0.810194i
\(10\) 2.27598e11 0.227598
\(11\) 1.55920e12i 0.496811i 0.968656 + 0.248405i \(0.0799065\pi\)
−0.968656 + 0.248405i \(0.920094\pi\)
\(12\) −3.97012e12 2.02789e12i −0.445275 0.227442i
\(13\) −3.72207e13 −1.59759 −0.798794 0.601605i \(-0.794528\pi\)
−0.798794 + 0.601605i \(0.794528\pi\)
\(14\) 6.36811e12i 0.112324i
\(15\) −1.89967e13 + 3.71909e13i −0.146414 + 0.286643i
\(16\) 7.03687e13 0.250000
\(17\) 6.73556e14i 1.15608i 0.816010 + 0.578038i \(0.196181\pi\)
−0.816010 + 0.578038i \(0.803819\pi\)
\(18\) 6.62742e14 4.79482e14i 0.572894 0.414479i
\(19\) 9.37274e14 0.423471 0.211735 0.977327i \(-0.432089\pi\)
0.211735 + 0.977327i \(0.432089\pi\)
\(20\) 6.59193e14i 0.160936i
\(21\) 1.04059e15 + 5.31522e14i 0.141465 + 0.0722586i
\(22\) 4.51594e15 0.351298
\(23\) 3.13424e16i 1.43021i 0.699019 + 0.715103i \(0.253620\pi\)
−0.699019 + 0.715103i \(0.746380\pi\)
\(24\) −5.87341e15 + 1.14987e16i −0.160826 + 0.314857i
\(25\) 5.34295e16 0.896399
\(26\) 1.07803e17i 1.12967i
\(27\) 2.30339e16 + 1.48317e17i 0.153462 + 0.988154i
\(28\) −1.84440e16 −0.0794254
\(29\) 2.21159e17i 0.625071i 0.949906 + 0.312535i \(0.101178\pi\)
−0.949906 + 0.312535i \(0.898822\pi\)
\(30\) 1.07716e17 + 5.50203e16i 0.202687 + 0.103530i
\(31\) 6.76426e17 0.858776 0.429388 0.903120i \(-0.358729\pi\)
0.429388 + 0.903120i \(0.358729\pi\)
\(32\) 2.03810e17i 0.176777i
\(33\) −3.76928e17 + 7.37933e17i −0.225991 + 0.442435i
\(34\) 1.95083e18 0.817469
\(35\) 1.72778e17i 0.0511296i
\(36\) −1.38873e18 1.91950e18i −0.293081 0.405097i
\(37\) −4.23578e18 −0.643448 −0.321724 0.946834i \(-0.604262\pi\)
−0.321724 + 0.946834i \(0.604262\pi\)
\(38\) 2.71464e18i 0.299439i
\(39\) −1.76157e19 8.99789e18i −1.42273 0.726717i
\(40\) −1.90923e18 −0.113799
\(41\) 2.43094e19i 1.07738i −0.842504 0.538690i \(-0.818919\pi\)
0.842504 0.538690i \(-0.181081\pi\)
\(42\) 1.53945e18 3.01387e18i 0.0510946 0.100031i
\(43\) 2.27505e19 0.569336 0.284668 0.958626i \(-0.408117\pi\)
0.284668 + 0.958626i \(0.408117\pi\)
\(44\) 1.30796e19i 0.248405i
\(45\) −1.79813e19 + 1.30092e19i −0.260779 + 0.188669i
\(46\) 9.07774e19 1.01131
\(47\) 6.93806e19i 0.597123i 0.954390 + 0.298561i \(0.0965068\pi\)
−0.954390 + 0.298561i \(0.903493\pi\)
\(48\) 3.33038e19 + 1.70112e19i 0.222638 + 0.113721i
\(49\) −1.86747e20 −0.974766
\(50\) 1.54748e20i 0.633850i
\(51\) −1.62828e20 + 3.18777e20i −0.525880 + 1.02954i
\(52\) 3.12230e20 0.798794
\(53\) 8.43863e20i 1.71776i 0.512180 + 0.858878i \(0.328838\pi\)
−0.512180 + 0.858878i \(0.671162\pi\)
\(54\) 4.29571e20 6.67133e19i 0.698731 0.108514i
\(55\) −1.22525e20 −0.159909
\(56\) 5.34196e19i 0.0561622i
\(57\) 4.43589e20 + 2.26580e20i 0.377122 + 0.192630i
\(58\) 6.40546e20 0.441992
\(59\) 2.79071e21i 1.56852i −0.620432 0.784260i \(-0.713043\pi\)
0.620432 0.784260i \(-0.286957\pi\)
\(60\) 1.59356e20 3.11980e20i 0.0732071 0.143322i
\(61\) −4.56793e21 −1.72092 −0.860461 0.509517i \(-0.829824\pi\)
−0.860461 + 0.509517i \(0.829824\pi\)
\(62\) 1.95914e21i 0.607246i
\(63\) 3.63993e20 + 5.03112e20i 0.0931122 + 0.128700i
\(64\) −5.90296e20 −0.125000
\(65\) 2.92488e21i 0.514218i
\(66\) 2.13728e21 + 1.09170e21i 0.312849 + 0.159800i
\(67\) −1.20142e21 −0.146824 −0.0734118 0.997302i \(-0.523389\pi\)
−0.0734118 + 0.997302i \(0.523389\pi\)
\(68\) 5.65019e21i 0.578038i
\(69\) −7.57684e21 + 1.48336e22i −0.650577 + 1.27367i
\(70\) 5.00419e20 0.0361541
\(71\) 1.60117e22i 0.975748i −0.872914 0.487874i \(-0.837773\pi\)
0.872914 0.487874i \(-0.162227\pi\)
\(72\) −5.55948e21 + 4.02219e21i −0.286447 + 0.207239i
\(73\) 2.60444e22 1.13721 0.568605 0.822611i \(-0.307483\pi\)
0.568605 + 0.822611i \(0.307483\pi\)
\(74\) 1.22681e22i 0.454986i
\(75\) 2.52869e22 + 1.29163e22i 0.798289 + 0.407757i
\(76\) −7.86242e21 −0.211735
\(77\) 3.42822e21i 0.0789187i
\(78\) −2.60607e22 + 5.10204e22i −0.513866 + 1.00602i
\(79\) 8.00431e22 1.35456 0.677281 0.735725i \(-0.263158\pi\)
0.677281 + 0.735725i \(0.263158\pi\)
\(80\) 5.52971e21i 0.0804679i
\(81\) −2.49533e22 + 7.57629e22i −0.312829 + 0.949809i
\(82\) −7.04077e22 −0.761823
\(83\) 1.65147e23i 1.54502i −0.635002 0.772511i \(-0.719001\pi\)
0.635002 0.772511i \(-0.280999\pi\)
\(84\) −8.72910e21 4.45873e21i −0.0707323 0.0361293i
\(85\) −5.29293e22 −0.372108
\(86\) 6.58923e22i 0.402581i
\(87\) −5.34639e22 + 1.04669e23i −0.284335 + 0.556657i
\(88\) −3.78824e22 −0.175649
\(89\) 4.33073e23i 1.75340i −0.481038 0.876700i \(-0.659740\pi\)
0.481038 0.876700i \(-0.340260\pi\)
\(90\) 3.76786e22 + 5.20795e22i 0.133409 + 0.184398i
\(91\) −8.18372e22 −0.253778
\(92\) 2.62919e23i 0.715103i
\(93\) 3.20136e23 + 1.63522e23i 0.764784 + 0.390643i
\(94\) 2.00948e23 0.422230
\(95\) 7.36528e22i 0.136303i
\(96\) 4.92697e22 9.64581e22i 0.0804128 0.157429i
\(97\) −4.08706e23 −0.589048 −0.294524 0.955644i \(-0.595161\pi\)
−0.294524 + 0.955644i \(0.595161\pi\)
\(98\) 5.40877e23i 0.689264i
\(99\) −3.56782e23 + 2.58125e23i −0.402513 + 0.291211i
\(100\) −4.48199e23 −0.448199
\(101\) 8.79558e23i 0.780563i 0.920696 + 0.390281i \(0.127622\pi\)
−0.920696 + 0.390281i \(0.872378\pi\)
\(102\) 9.23277e23 + 4.71600e23i 0.727998 + 0.371853i
\(103\) −4.26954e23 −0.299457 −0.149728 0.988727i \(-0.547840\pi\)
−0.149728 + 0.988727i \(0.547840\pi\)
\(104\) 9.04315e23i 0.564833i
\(105\) −4.17680e22 + 8.17716e22i −0.0232580 + 0.0455335i
\(106\) 2.44409e24 1.21464
\(107\) 3.07226e24i 1.36412i 0.731297 + 0.682059i \(0.238915\pi\)
−0.731297 + 0.682059i \(0.761085\pi\)
\(108\) −1.93222e23 1.24417e24i −0.0767312 0.494077i
\(109\) 2.05754e24 0.731527 0.365763 0.930708i \(-0.380808\pi\)
0.365763 + 0.930708i \(0.380808\pi\)
\(110\) 3.54871e23i 0.113073i
\(111\) −2.00469e24 1.02397e24i −0.573023 0.292694i
\(112\) 1.54720e23 0.0397127
\(113\) 2.56925e24i 0.592742i −0.955073 0.296371i \(-0.904224\pi\)
0.955073 0.296371i \(-0.0957764\pi\)
\(114\) 6.56247e23 1.28477e24i 0.136210 0.266666i
\(115\) −2.46295e24 −0.460343
\(116\) 1.85522e24i 0.312535i
\(117\) −6.16187e24 8.51695e24i −0.936445 1.29436i
\(118\) −8.08275e24 −1.10911
\(119\) 1.48095e24i 0.183644i
\(120\) −9.03590e23 4.61544e23i −0.101344 0.0517652i
\(121\) 7.41861e24 0.753179
\(122\) 1.32301e25i 1.21688i
\(123\) 5.87666e24 1.15051e25i 0.490083 0.959461i
\(124\) −5.67427e24 −0.429388
\(125\) 8.88245e24i 0.610397i
\(126\) 1.45717e24 1.05424e24i 0.0910046 0.0658403i
\(127\) 1.69658e25 0.963673 0.481836 0.876261i \(-0.339970\pi\)
0.481836 + 0.876261i \(0.339970\pi\)
\(128\) 1.70968e24i 0.0883883i
\(129\) 1.07672e25 + 5.49978e24i 0.507023 + 0.258982i
\(130\) −8.47135e24 −0.363607
\(131\) 1.19460e25i 0.467701i 0.972273 + 0.233851i \(0.0751326\pi\)
−0.972273 + 0.233851i \(0.924867\pi\)
\(132\) 3.16190e24 6.19023e24i 0.112996 0.221218i
\(133\) 2.06078e24 0.0672686
\(134\) 3.47967e24i 0.103820i
\(135\) −1.16550e25 + 1.81005e24i −0.318059 + 0.0493952i
\(136\) −1.63647e25 −0.408735
\(137\) 2.33983e25i 0.535226i 0.963527 + 0.267613i \(0.0862348\pi\)
−0.963527 + 0.267613i \(0.913765\pi\)
\(138\) 4.29627e25 + 2.19449e25i 0.900622 + 0.460028i
\(139\) 1.59193e25 0.306018 0.153009 0.988225i \(-0.451104\pi\)
0.153009 + 0.988225i \(0.451104\pi\)
\(140\) 1.44937e24i 0.0255648i
\(141\) −1.67723e25 + 3.28361e25i −0.271621 + 0.531768i
\(142\) −4.63749e25 −0.689958
\(143\) 5.80348e25i 0.793699i
\(144\) 1.16495e25 + 1.61020e25i 0.146540 + 0.202549i
\(145\) −1.73791e25 −0.201193
\(146\) 7.54328e25i 0.804129i
\(147\) −8.83827e25 4.51449e25i −0.868079 0.443405i
\(148\) 3.55323e25 0.321724
\(149\) 1.86675e26i 1.55901i −0.626393 0.779507i \(-0.715469\pi\)
0.626393 0.779507i \(-0.284531\pi\)
\(150\) 3.74095e25 7.32386e25i 0.288328 0.564475i
\(151\) 1.57212e24 0.0111883 0.00559414 0.999984i \(-0.498219\pi\)
0.00559414 + 0.999984i \(0.498219\pi\)
\(152\) 2.27720e25i 0.149720i
\(153\) −1.54125e26 + 1.11507e26i −0.936646 + 0.677647i
\(154\) 9.92919e24 0.0558040
\(155\) 5.31549e25i 0.276416i
\(156\) 1.47771e26 + 7.54797e25i 0.711367 + 0.363358i
\(157\) 2.61155e26 1.16440 0.582199 0.813046i \(-0.302192\pi\)
0.582199 + 0.813046i \(0.302192\pi\)
\(158\) 2.31830e26i 0.957820i
\(159\) −2.03999e26 + 3.99379e26i −0.781379 + 1.52975i
\(160\) 1.60158e25 0.0568994
\(161\) 6.89125e25i 0.227189i
\(162\) 2.19433e26 + 7.22724e25i 0.671617 + 0.221204i
\(163\) −1.85589e26 −0.527596 −0.263798 0.964578i \(-0.584975\pi\)
−0.263798 + 0.964578i \(0.584975\pi\)
\(164\) 2.03922e26i 0.538690i
\(165\) −5.79882e25 2.96198e25i −0.142407 0.0727401i
\(166\) −4.78318e26 −1.09250
\(167\) 4.33404e25i 0.0921076i 0.998939 + 0.0460538i \(0.0146646\pi\)
−0.998939 + 0.0460538i \(0.985335\pi\)
\(168\) −1.29139e25 + 2.52822e25i −0.0255473 + 0.0500153i
\(169\) 8.42583e26 1.55229
\(170\) 1.53300e26i 0.263120i
\(171\) 1.55165e26 + 2.14470e26i 0.248222 + 0.343094i
\(172\) −1.90845e26 −0.284668
\(173\) 5.82910e26i 0.811051i −0.914084 0.405525i \(-0.867089\pi\)
0.914084 0.405525i \(-0.132911\pi\)
\(174\) 3.03154e26 + 1.54848e26i 0.393616 + 0.201055i
\(175\) 1.17475e26 0.142394
\(176\) 1.09719e26i 0.124203i
\(177\) 6.74636e26 1.32077e27i 0.713494 1.39685i
\(178\) −1.25431e27 −1.23984
\(179\) 4.62261e26i 0.427219i 0.976919 + 0.213610i \(0.0685221\pi\)
−0.976919 + 0.213610i \(0.931478\pi\)
\(180\) 1.50838e26 1.09129e26i 0.130389 0.0943344i
\(181\) 4.20265e26 0.339923 0.169961 0.985451i \(-0.445636\pi\)
0.169961 + 0.985451i \(0.445636\pi\)
\(182\) 2.37026e26i 0.179448i
\(183\) −2.16189e27 1.10427e27i −1.53257 0.782819i
\(184\) −7.61496e26 −0.505654
\(185\) 3.32856e26i 0.207108i
\(186\) 4.73610e26 9.27212e26i 0.276226 0.540784i
\(187\) −1.05021e27 −0.574351
\(188\) 5.82006e26i 0.298561i
\(189\) 5.06446e25 + 3.26104e26i 0.0243776 + 0.156969i
\(190\) 2.13321e26 0.0963809
\(191\) 2.10635e27i 0.893571i 0.894641 + 0.446786i \(0.147431\pi\)
−0.894641 + 0.446786i \(0.852569\pi\)
\(192\) −2.79372e26 1.42700e26i −0.111319 0.0568605i
\(193\) 2.28503e27 0.855467 0.427734 0.903905i \(-0.359312\pi\)
0.427734 + 0.903905i \(0.359312\pi\)
\(194\) 1.18374e27i 0.416520i
\(195\) 7.07071e26 1.38427e27i 0.233910 0.457938i
\(196\) 1.56655e27 0.487383
\(197\) 3.36890e27i 0.986037i 0.870019 + 0.493019i \(0.164107\pi\)
−0.870019 + 0.493019i \(0.835893\pi\)
\(198\) 7.47611e26 + 1.03335e27i 0.205917 + 0.284620i
\(199\) 1.75228e27 0.454324 0.227162 0.973857i \(-0.427055\pi\)
0.227162 + 0.973857i \(0.427055\pi\)
\(200\) 1.29812e27i 0.316925i
\(201\) −5.68600e26 2.90435e26i −0.130754 0.0667876i
\(202\) 2.54747e27 0.551941
\(203\) 4.86263e26i 0.0992929i
\(204\) 1.36590e27 2.67410e27i 0.262940 0.514772i
\(205\) 1.91028e27 0.346778
\(206\) 1.23659e27i 0.211748i
\(207\) −7.17186e27 + 5.18872e27i −1.15874 + 0.838332i
\(208\) −2.61918e27 −0.399397
\(209\) 1.46140e27i 0.210385i
\(210\) 2.36836e26 + 1.20973e26i 0.0321970 + 0.0164459i
\(211\) −1.49978e28 −1.92592 −0.962962 0.269638i \(-0.913096\pi\)
−0.962962 + 0.269638i \(0.913096\pi\)
\(212\) 7.07884e27i 0.858878i
\(213\) 3.87073e27 7.57795e27i 0.443852 0.868953i
\(214\) 8.89821e27 0.964578
\(215\) 1.78778e27i 0.183253i
\(216\) −3.60350e27 + 5.59632e26i −0.349365 + 0.0542572i
\(217\) 1.48726e27 0.136417
\(218\) 5.95927e27i 0.517268i
\(219\) 1.23262e28 + 6.29609e27i 1.01274 + 0.517299i
\(220\) 1.02782e27 0.0799547
\(221\) 2.50702e28i 1.84693i
\(222\) −2.96575e27 + 5.80621e27i −0.206966 + 0.405188i
\(223\) −2.04706e28 −1.35354 −0.676771 0.736194i \(-0.736621\pi\)
−0.676771 + 0.736194i \(0.736621\pi\)
\(224\) 4.48116e26i 0.0280811i
\(225\) 8.84522e27 + 1.22259e28i 0.525434 + 0.726257i
\(226\) −7.44135e27 −0.419132
\(227\) 1.50976e28i 0.806485i −0.915093 0.403243i \(-0.867883\pi\)
0.915093 0.403243i \(-0.132117\pi\)
\(228\) −3.72109e27 1.90069e27i −0.188561 0.0963150i
\(229\) 2.46646e28 1.18590 0.592950 0.805239i \(-0.297963\pi\)
0.592950 + 0.805239i \(0.297963\pi\)
\(230\) 7.13346e27i 0.325512i
\(231\) −8.28751e26 + 1.62249e27i −0.0358988 + 0.0702811i
\(232\) −5.37329e27 −0.220996
\(233\) 1.81404e28i 0.708559i −0.935140 0.354279i \(-0.884726\pi\)
0.935140 0.354279i \(-0.115274\pi\)
\(234\) −2.46677e28 + 1.78467e28i −0.915248 + 0.662166i
\(235\) −5.45206e27 −0.192197
\(236\) 2.34101e28i 0.784260i
\(237\) 3.78824e28 + 1.93499e28i 1.20631 + 0.616168i
\(238\) 4.28928e27 0.129856
\(239\) 6.04731e28i 1.74096i 0.492208 + 0.870478i \(0.336190\pi\)
−0.492208 + 0.870478i \(0.663810\pi\)
\(240\) −1.33677e27 + 2.61708e27i −0.0366036 + 0.0716608i
\(241\) 3.08193e28 0.802820 0.401410 0.915899i \(-0.368520\pi\)
0.401410 + 0.915899i \(0.368520\pi\)
\(242\) 2.14866e28i 0.532578i
\(243\) −3.01250e28 + 2.98244e28i −0.710643 + 0.703553i
\(244\) 3.83185e28 0.860461
\(245\) 1.46749e28i 0.313750i
\(246\) −3.33222e28 1.70206e28i −0.678442 0.346541i
\(247\) −3.48860e28 −0.676532
\(248\) 1.64344e28i 0.303623i
\(249\) 3.99234e28 7.81601e28i 0.702805 1.37592i
\(250\) 2.57263e28 0.431616
\(251\) 2.37397e28i 0.379656i −0.981817 0.189828i \(-0.939207\pi\)
0.981817 0.189828i \(-0.0607931\pi\)
\(252\) −3.05339e27 4.22041e27i −0.0465561 0.0643500i
\(253\) −4.88693e28 −0.710542
\(254\) 4.91382e28i 0.681419i
\(255\) −2.50501e28 1.27953e28i −0.331381 0.169266i
\(256\) 4.95176e27 0.0625000
\(257\) 1.17021e28i 0.140951i −0.997514 0.0704754i \(-0.977548\pi\)
0.997514 0.0704754i \(-0.0224516\pi\)
\(258\) 1.59291e28 3.11852e28i 0.183128 0.358519i
\(259\) −9.31321e27 −0.102212
\(260\) 2.45357e28i 0.257109i
\(261\) −5.06063e28 + 3.66128e28i −0.506429 + 0.366392i
\(262\) 3.45994e28 0.330715
\(263\) 5.43156e28i 0.495971i 0.968764 + 0.247985i \(0.0797685\pi\)
−0.968764 + 0.247985i \(0.920232\pi\)
\(264\) −1.79288e28 9.15785e27i −0.156424 0.0798999i
\(265\) −6.63124e28 −0.552897
\(266\) 5.96866e27i 0.0475661i
\(267\) 1.04693e29 2.04963e29i 0.797593 1.56149i
\(268\) 1.00782e28 0.0734118
\(269\) 1.47463e29i 1.02720i 0.858028 + 0.513602i \(0.171689\pi\)
−0.858028 + 0.513602i \(0.828311\pi\)
\(270\) 5.24246e27 + 3.37565e28i 0.0349277 + 0.224902i
\(271\) −2.09550e29 −1.33554 −0.667770 0.744368i \(-0.732751\pi\)
−0.667770 + 0.744368i \(0.732751\pi\)
\(272\) 4.73973e28i 0.289019i
\(273\) −3.87315e28 1.97836e28i −0.226002 0.115439i
\(274\) 6.77686e28 0.378462
\(275\) 8.33076e28i 0.445340i
\(276\) 6.35591e28 1.24433e29i 0.325289 0.636836i
\(277\) 8.59896e28 0.421394 0.210697 0.977551i \(-0.432427\pi\)
0.210697 + 0.977551i \(0.432427\pi\)
\(278\) 4.61073e28i 0.216388i
\(279\) 1.11982e29 + 1.54782e29i 0.503381 + 0.695775i
\(280\) −4.19782e27 −0.0180770
\(281\) 2.34014e29i 0.965530i 0.875750 + 0.482765i \(0.160367\pi\)
−0.875750 + 0.482765i \(0.839633\pi\)
\(282\) 9.51035e28 + 4.85779e28i 0.376017 + 0.192065i
\(283\) 4.67446e29 1.77131 0.885654 0.464346i \(-0.153711\pi\)
0.885654 + 0.464346i \(0.153711\pi\)
\(284\) 1.34316e29i 0.487874i
\(285\) −1.78051e28 + 3.48581e28i −0.0620021 + 0.121385i
\(286\) −1.68087e29 −0.561230
\(287\) 5.34491e28i 0.171143i
\(288\) 4.66363e28 3.37406e28i 0.143223 0.103620i
\(289\) −1.14229e29 −0.336512
\(290\) 5.03353e28i 0.142265i
\(291\) −1.93431e29 9.88022e28i −0.524577 0.267948i
\(292\) −2.18477e29 −0.568605
\(293\) 3.03480e29i 0.758085i −0.925379 0.379043i \(-0.876253\pi\)
0.925379 0.379043i \(-0.123747\pi\)
\(294\) −1.30754e29 + 2.55984e29i −0.313535 + 0.613825i
\(295\) 2.19299e29 0.504862
\(296\) 1.02913e29i 0.227493i
\(297\) −2.31256e29 + 3.59146e28i −0.490926 + 0.0762418i
\(298\) −5.40668e29 −1.10239
\(299\) 1.16659e30i 2.28488i
\(300\) −2.12122e29 1.08349e29i −0.399144 0.203879i
\(301\) 5.00214e28 0.0904394
\(302\) 4.55336e27i 0.00791131i
\(303\) −2.12628e29 + 4.16273e29i −0.355065 + 0.695131i
\(304\) 6.59548e28 0.105868
\(305\) 3.58957e29i 0.553916i
\(306\) 3.22958e29 + 4.46393e29i 0.479169 + 0.662309i
\(307\) 9.11333e29 1.30022 0.650110 0.759840i \(-0.274723\pi\)
0.650110 + 0.759840i \(0.274723\pi\)
\(308\) 2.87580e28i 0.0394594i
\(309\) −2.02067e29 1.03213e29i −0.266681 0.136218i
\(310\) 1.53953e29 0.195455
\(311\) 4.35089e29i 0.531439i 0.964050 + 0.265719i \(0.0856095\pi\)
−0.964050 + 0.265719i \(0.914391\pi\)
\(312\) 2.18613e29 4.27990e29i 0.256933 0.503012i
\(313\) 2.73884e29 0.309767 0.154883 0.987933i \(-0.450500\pi\)
0.154883 + 0.987933i \(0.450500\pi\)
\(314\) 7.56384e29i 0.823354i
\(315\) −3.95355e28 + 2.86033e28i −0.0414249 + 0.0299702i
\(316\) −6.71450e29 −0.677281
\(317\) 5.05172e29i 0.490600i 0.969447 + 0.245300i \(0.0788865\pi\)
−0.969447 + 0.245300i \(0.921113\pi\)
\(318\) 1.15673e30 + 5.90843e29i 1.08170 + 0.552519i
\(319\) −3.44833e29 −0.310542
\(320\) 4.63866e28i 0.0402340i
\(321\) −7.42699e29 + 1.45402e30i −0.620515 + 1.21482i
\(322\) 1.99592e29 0.160647
\(323\) 6.31306e29i 0.489564i
\(324\) 2.09323e29 6.35545e29i 0.156415 0.474905i
\(325\) −1.98869e30 −1.43208
\(326\) 5.37524e29i 0.373067i
\(327\) 9.73783e29 + 4.97398e29i 0.651462 + 0.332760i
\(328\) 5.90622e29 0.380911
\(329\) 1.52547e29i 0.0948534i
\(330\) −8.57880e28 + 1.67952e29i −0.0514350 + 0.100697i
\(331\) 1.25611e30 0.726260 0.363130 0.931738i \(-0.381708\pi\)
0.363130 + 0.931738i \(0.381708\pi\)
\(332\) 1.38536e30i 0.772511i
\(333\) −7.01231e29 9.69244e29i −0.377164 0.521317i
\(334\) 1.25527e29 0.0651299
\(335\) 9.44096e28i 0.0472583i
\(336\) 7.32250e28 + 3.74025e28i 0.0353662 + 0.0180647i
\(337\) 2.14072e29 0.0997704 0.0498852 0.998755i \(-0.484114\pi\)
0.0498852 + 0.998755i \(0.484114\pi\)
\(338\) 2.44038e30i 1.09763i
\(339\) 6.21101e29 1.21596e30i 0.269629 0.527867i
\(340\) 4.44003e29 0.186054
\(341\) 1.05469e30i 0.426649i
\(342\) 6.21170e29 4.49406e29i 0.242604 0.175520i
\(343\) −8.31830e29 −0.313693
\(344\) 5.52745e29i 0.201291i
\(345\) −1.16565e30 5.95403e29i −0.409959 0.209402i
\(346\) −1.68829e30 −0.573499
\(347\) 3.33922e30i 1.09570i −0.836577 0.547849i \(-0.815447\pi\)
0.836577 0.547849i \(-0.184553\pi\)
\(348\) 4.48488e29 8.78029e29i 0.142167 0.278329i
\(349\) −4.90589e29 −0.150249 −0.0751247 0.997174i \(-0.523935\pi\)
−0.0751247 + 0.997174i \(0.523935\pi\)
\(350\) 3.40245e29i 0.100687i
\(351\) −8.57339e29 5.52046e30i −0.245170 1.57866i
\(352\) 3.17781e29 0.0878246
\(353\) 3.94390e30i 1.05349i 0.850024 + 0.526744i \(0.176587\pi\)
−0.850024 + 0.526744i \(0.823413\pi\)
\(354\) −3.82537e30 1.95396e30i −0.987720 0.504517i
\(355\) 1.25823e30 0.314066
\(356\) 3.63288e30i 0.876700i
\(357\) −3.58010e29 + 7.00895e29i −0.0835364 + 0.163544i
\(358\) 1.33885e30 0.302090
\(359\) 2.87184e30i 0.626653i 0.949646 + 0.313326i \(0.101443\pi\)
−0.949646 + 0.313326i \(0.898557\pi\)
\(360\) −3.16071e29 4.36875e29i −0.0667045 0.0921992i
\(361\) −4.02028e30 −0.820673
\(362\) 1.21722e30i 0.240362i
\(363\) 3.51105e30 + 1.79340e30i 0.670744 + 0.342609i
\(364\) 6.86500e29 0.126889
\(365\) 2.04662e30i 0.366036i
\(366\) −3.19830e30 + 6.26149e30i −0.553537 + 1.08369i
\(367\) 1.02914e31 1.72378 0.861889 0.507097i \(-0.169281\pi\)
0.861889 + 0.507097i \(0.169281\pi\)
\(368\) 2.20553e30i 0.357552i
\(369\) 5.56256e30 4.02441e30i 0.872887 0.631519i
\(370\) −9.64055e29 −0.146447
\(371\) 1.85540e30i 0.272867i
\(372\) −2.68549e30 1.37172e30i −0.382392 0.195322i
\(373\) 6.01783e30 0.829724 0.414862 0.909884i \(-0.363830\pi\)
0.414862 + 0.909884i \(0.363830\pi\)
\(374\) 3.04174e30i 0.406127i
\(375\) −2.14728e30 + 4.20384e30i −0.277660 + 0.543590i
\(376\) −1.68567e30 −0.211115
\(377\) 8.23171e30i 0.998605i
\(378\) 9.44497e29 1.46682e29i 0.110994 0.0172376i
\(379\) −1.59790e31 −1.81920 −0.909598 0.415489i \(-0.863610\pi\)
−0.909598 + 0.415489i \(0.863610\pi\)
\(380\) 6.17845e29i 0.0681516i
\(381\) 8.02949e30 + 4.10138e30i 0.858199 + 0.438359i
\(382\) 6.10063e30 0.631850
\(383\) 9.46058e29i 0.0949582i −0.998872 0.0474791i \(-0.984881\pi\)
0.998872 0.0474791i \(-0.0151188\pi\)
\(384\) −4.13304e29 + 8.09149e29i −0.0402064 + 0.0787143i
\(385\) −2.69396e29 −0.0254017
\(386\) 6.61814e30i 0.604907i
\(387\) 3.76632e30 + 5.20582e30i 0.333723 + 0.461273i
\(388\) 3.42848e30 0.294524
\(389\) 1.00139e31i 0.834084i −0.908887 0.417042i \(-0.863067\pi\)
0.908887 0.417042i \(-0.136933\pi\)
\(390\) −4.00928e30 2.04790e30i −0.323811 0.165399i
\(391\) −2.11109e31 −1.65343
\(392\) 4.53720e30i 0.344632i
\(393\) −2.88788e30 + 5.65376e30i −0.212750 + 0.416512i
\(394\) 9.75738e30 0.697234
\(395\) 6.28994e30i 0.435995i
\(396\) 2.99290e30 2.16531e30i 0.201257 0.145606i
\(397\) −9.09072e30 −0.593079 −0.296539 0.955021i \(-0.595833\pi\)
−0.296539 + 0.955021i \(0.595833\pi\)
\(398\) 5.07513e30i 0.321255i
\(399\) 9.75317e29 + 4.98182e29i 0.0599061 + 0.0305994i
\(400\) 3.75977e30 0.224100
\(401\) 1.62871e31i 0.942129i −0.882099 0.471064i \(-0.843870\pi\)
0.882099 0.471064i \(-0.156130\pi\)
\(402\) −8.41189e29 + 1.64684e30i −0.0472260 + 0.0924569i
\(403\) −2.51771e31 −1.37197
\(404\) 7.37827e30i 0.390281i
\(405\) −5.95360e30 1.96088e30i −0.305717 0.100691i
\(406\) 1.40837e30 0.0702107
\(407\) 6.60445e30i 0.319672i
\(408\) −7.74501e30 3.95607e30i −0.363999 0.185927i
\(409\) 4.21235e31 1.92240 0.961202 0.275844i \(-0.0889574\pi\)
0.961202 + 0.275844i \(0.0889574\pi\)
\(410\) 5.53277e30i 0.245209i
\(411\) −5.65639e30 + 1.10738e31i −0.243465 + 0.476646i
\(412\) 3.58155e30 0.149728
\(413\) 6.13592e30i 0.249161i
\(414\) 1.50281e31 + 2.07719e31i 0.592790 + 0.819356i
\(415\) 1.29776e31 0.497299
\(416\) 7.58595e30i 0.282416i
\(417\) 7.53423e30 + 3.84840e30i 0.272525 + 0.139203i
\(418\) 4.23267e30 0.148764
\(419\) 3.32650e31i 1.13611i 0.822992 + 0.568054i \(0.192303\pi\)
−0.822992 + 0.568054i \(0.807697\pi\)
\(420\) 3.50376e29 6.85950e29i 0.0116290 0.0227667i
\(421\) 2.84585e31 0.917966 0.458983 0.888445i \(-0.348214\pi\)
0.458983 + 0.888445i \(0.348214\pi\)
\(422\) 4.34384e31i 1.36183i
\(423\) −1.58759e31 + 1.14859e31i −0.483785 + 0.350010i
\(424\) −2.05025e31 −0.607319
\(425\) 3.59878e31i 1.03630i
\(426\) −2.19481e31 1.12108e31i −0.614443 0.313851i
\(427\) −1.00435e31 −0.273370
\(428\) 2.57720e31i 0.682059i
\(429\) 1.40295e31 2.74664e31i 0.361041 0.706829i
\(430\) 5.17795e30 0.129580
\(431\) 3.37981e31i 0.822554i −0.911510 0.411277i \(-0.865083\pi\)
0.911510 0.411277i \(-0.134917\pi\)
\(432\) 1.62087e30 + 1.04369e31i 0.0383656 + 0.247039i
\(433\) −2.18119e31 −0.502155 −0.251077 0.967967i \(-0.580785\pi\)
−0.251077 + 0.967967i \(0.580785\pi\)
\(434\) 4.30755e30i 0.0964615i
\(435\) −8.22511e30 4.20130e30i −0.179172 0.0915192i
\(436\) −1.72599e31 −0.365763
\(437\) 2.93764e31i 0.605650i
\(438\) 1.82354e31 3.57005e31i 0.365785 0.716118i
\(439\) 2.90476e31 0.566938 0.283469 0.958981i \(-0.408515\pi\)
0.283469 + 0.958981i \(0.408515\pi\)
\(440\) 2.97688e30i 0.0565365i
\(441\) −3.09158e31 4.27320e31i −0.571371 0.789750i
\(442\) −7.26112e31 −1.30598
\(443\) 2.02953e30i 0.0355263i −0.999842 0.0177632i \(-0.994346\pi\)
0.999842 0.0177632i \(-0.00565449\pi\)
\(444\) 1.68166e31 + 8.58972e30i 0.286511 + 0.146347i
\(445\) 3.40317e31 0.564370
\(446\) 5.92891e31i 0.957098i
\(447\) 4.51275e31 8.83485e31i 0.709171 1.38838i
\(448\) −1.29788e30 −0.0198563
\(449\) 2.79159e31i 0.415810i −0.978149 0.207905i \(-0.933335\pi\)
0.978149 0.207905i \(-0.0666645\pi\)
\(450\) 3.54100e31 2.56185e31i 0.513541 0.371538i
\(451\) 3.79034e31 0.535254
\(452\) 2.15525e31i 0.296371i
\(453\) 7.44048e29 + 3.80051e29i 0.00996374 + 0.00508937i
\(454\) −4.37272e31 −0.570271
\(455\) 6.43093e30i 0.0816840i
\(456\) −5.50499e30 + 1.07774e31i −0.0681050 + 0.133333i
\(457\) 7.70981e30 0.0929072 0.0464536 0.998920i \(-0.485208\pi\)
0.0464536 + 0.998920i \(0.485208\pi\)
\(458\) 7.14363e31i 0.838558i
\(459\) −9.98995e31 + 1.55146e31i −1.14238 + 0.177414i
\(460\) 2.06607e31 0.230171
\(461\) 1.16682e31i 0.126646i −0.997993 0.0633230i \(-0.979830\pi\)
0.997993 0.0633230i \(-0.0201698\pi\)
\(462\) 4.69924e30 + 2.40032e30i 0.0496963 + 0.0253843i
\(463\) −1.20430e32 −1.24098 −0.620488 0.784216i \(-0.713066\pi\)
−0.620488 + 0.784216i \(0.713066\pi\)
\(464\) 1.55627e31i 0.156268i
\(465\) −1.28499e31 + 2.51569e31i −0.125737 + 0.246162i
\(466\) −5.25402e31 −0.501027
\(467\) 1.03648e32i 0.963297i 0.876365 + 0.481648i \(0.159962\pi\)
−0.876365 + 0.481648i \(0.840038\pi\)
\(468\) 5.16895e31 + 7.14454e31i 0.468222 + 0.647178i
\(469\) −2.64155e30 −0.0233230
\(470\) 1.57909e31i 0.135904i
\(471\) 1.23598e32 + 6.31325e31i 1.03696 + 0.529666i
\(472\) 6.78030e31 0.554556
\(473\) 3.54726e31i 0.282852i
\(474\) 5.60434e31 1.09719e32i 0.435697 0.852987i
\(475\) 5.00781e31 0.379599
\(476\) 1.24231e31i 0.0918218i
\(477\) −1.93095e32 + 1.39701e32i −1.39172 + 1.00688i
\(478\) 1.75149e32 1.23104
\(479\) 1.27488e32i 0.873863i 0.899495 + 0.436931i \(0.143935\pi\)
−0.899495 + 0.436931i \(0.856065\pi\)
\(480\) 7.57986e30 + 3.87171e30i 0.0506718 + 0.0258826i
\(481\) 1.57659e32 1.02796
\(482\) 8.92622e31i 0.567679i
\(483\) −1.66592e31 + 3.26146e31i −0.103345 + 0.202324i
\(484\) −6.22318e31 −0.376590
\(485\) 3.21169e31i 0.189598i
\(486\) 8.63807e31 + 8.72513e31i 0.497487 + 0.502501i
\(487\) 7.43336e31 0.417674 0.208837 0.977950i \(-0.433032\pi\)
0.208837 + 0.977950i \(0.433032\pi\)
\(488\) 1.10982e32i 0.608438i
\(489\) −8.78348e31 4.48651e31i −0.469851 0.239995i
\(490\) −4.25032e31 −0.221855
\(491\) 3.80259e32i 1.93687i −0.249258 0.968437i \(-0.580187\pi\)
0.249258 0.968437i \(-0.419813\pi\)
\(492\) −4.92970e31 + 9.65114e31i −0.245041 + 0.479731i
\(493\) −1.48963e32 −0.722629
\(494\) 1.01041e32i 0.478380i
\(495\) −2.02840e31 2.80366e31i −0.0937327 0.129558i
\(496\) 4.75992e31 0.214694
\(497\) 3.52049e31i 0.154998i
\(498\) −2.26376e32 1.15630e32i −0.972922 0.496958i
\(499\) −1.36860e32 −0.574207 −0.287104 0.957900i \(-0.592692\pi\)
−0.287104 + 0.957900i \(0.592692\pi\)
\(500\) 7.45114e31i 0.305199i
\(501\) −1.04773e31 + 2.05119e31i −0.0418982 + 0.0820265i
\(502\) −6.87576e31 −0.268458
\(503\) 2.04771e32i 0.780645i −0.920678 0.390323i \(-0.872364\pi\)
0.920678 0.390323i \(-0.127636\pi\)
\(504\) −1.22236e31 + 8.84358e30i −0.0455023 + 0.0329201i
\(505\) −6.91174e31 −0.251241
\(506\) 1.41541e32i 0.502429i
\(507\) 3.98773e32 + 2.03689e32i 1.38239 + 0.706110i
\(508\) −1.42319e32 −0.481836
\(509\) 2.83630e32i 0.937861i −0.883235 0.468931i \(-0.844639\pi\)
0.883235 0.468931i \(-0.155361\pi\)
\(510\) −3.70593e31 + 7.25529e31i −0.119689 + 0.234322i
\(511\) 5.72639e31 0.180647
\(512\) 1.43418e31i 0.0441942i
\(513\) 2.15891e31 + 1.39013e32i 0.0649869 + 0.418454i
\(514\) −3.38930e31 −0.0996673
\(515\) 3.35508e31i 0.0963866i
\(516\) −9.03220e31 4.61355e31i −0.253511 0.129491i
\(517\) −1.08179e32 −0.296657
\(518\) 2.69739e31i 0.0722749i
\(519\) 1.40915e32 2.75877e32i 0.368934 0.722282i
\(520\) 7.10629e31 0.181804
\(521\) 2.17793e32i 0.544493i 0.962228 + 0.272246i \(0.0877666\pi\)
−0.962228 + 0.272246i \(0.912233\pi\)
\(522\) 1.06042e32 + 1.46571e32i 0.259079 + 0.358099i
\(523\) 4.75878e32 1.13625 0.568127 0.822941i \(-0.307668\pi\)
0.568127 + 0.822941i \(0.307668\pi\)
\(524\) 1.00211e32i 0.233851i
\(525\) 5.55982e31 + 2.83990e31i 0.126809 + 0.0647725i
\(526\) 1.57315e32 0.350704
\(527\) 4.55610e32i 0.992810i
\(528\) −2.65240e31 + 5.19274e31i −0.0564978 + 0.110609i
\(529\) −5.02097e32 −1.04549
\(530\) 1.92061e32i 0.390957i
\(531\) 6.38577e32 4.62000e32i 1.27081 0.919406i
\(532\) −1.72871e31 −0.0336343
\(533\) 9.04816e32i 1.72121i
\(534\) −5.93635e32 3.03223e32i −1.10414 0.563984i
\(535\) −2.41424e32 −0.439071
\(536\) 2.91896e31i 0.0519100i
\(537\) −1.11749e32 + 2.18777e32i −0.194335 + 0.380460i
\(538\) 4.27100e32 0.726343
\(539\) 2.91177e32i 0.484274i
\(540\) 9.77694e31 1.51838e31i 0.159029 0.0246976i
\(541\) 3.58979e32 0.571086 0.285543 0.958366i \(-0.407826\pi\)
0.285543 + 0.958366i \(0.407826\pi\)
\(542\) 6.06923e32i 0.944370i
\(543\) 1.98901e32 + 1.01597e32i 0.302719 + 0.154625i
\(544\) 1.37277e32 0.204367
\(545\) 1.61686e32i 0.235458i
\(546\) −5.72995e31 + 1.12178e32i −0.0816280 + 0.159808i
\(547\) −6.21413e32 −0.866028 −0.433014 0.901387i \(-0.642550\pi\)
−0.433014 + 0.901387i \(0.642550\pi\)
\(548\) 1.96279e32i 0.267613i
\(549\) −7.56217e32 1.04525e33i −1.00874 1.39428i
\(550\) 2.41284e32 0.314903
\(551\) 2.07287e32i 0.264699i
\(552\) −3.60397e32 1.84087e32i −0.450311 0.230014i
\(553\) 1.75991e32 0.215173
\(554\) 2.49053e32i 0.297971i
\(555\) 8.04660e31 1.57533e32i 0.0942099 0.184440i
\(556\) −1.33541e32 −0.153009
\(557\) 2.54222e32i 0.285070i 0.989790 + 0.142535i \(0.0455254\pi\)
−0.989790 + 0.142535i \(0.954475\pi\)
\(558\) 4.48296e32 3.24334e32i 0.491987 0.355944i
\(559\) −8.46789e32 −0.909564
\(560\) 1.21582e31i 0.0127824i
\(561\) −4.97039e32 2.53882e32i −0.511489 0.261263i
\(562\) 6.77776e32 0.682733
\(563\) 1.20736e33i 1.19052i −0.803533 0.595261i \(-0.797049\pi\)
0.803533 0.595261i \(-0.202951\pi\)
\(564\) 1.40696e32 2.75449e32i 0.135811 0.265884i
\(565\) 2.01897e32 0.190787
\(566\) 1.35387e33i 1.25250i
\(567\) −5.48647e31 + 1.66580e32i −0.0496932 + 0.150878i
\(568\) 3.89021e32 0.344979
\(569\) 6.61064e32i 0.573980i −0.957934 0.286990i \(-0.907345\pi\)
0.957934 0.286990i \(-0.0926546\pi\)
\(570\) 1.00960e32 + 5.15691e31i 0.0858321 + 0.0438421i
\(571\) −1.14492e33 −0.953105 −0.476553 0.879146i \(-0.658114\pi\)
−0.476553 + 0.879146i \(0.658114\pi\)
\(572\) 4.86831e32i 0.396849i
\(573\) −5.09196e32 + 9.96881e32i −0.406471 + 0.795771i
\(574\) −1.54805e32 −0.121016
\(575\) 1.67461e33i 1.28203i
\(576\) −9.77231e31 1.35073e32i −0.0732702 0.101274i
\(577\) 2.27547e33 1.67094 0.835470 0.549537i \(-0.185196\pi\)
0.835470 + 0.549537i \(0.185196\pi\)
\(578\) 3.30841e32i 0.237950i
\(579\) 1.08145e33 + 5.52391e32i 0.761837 + 0.389138i
\(580\) 1.45787e32 0.100596
\(581\) 3.63109e32i 0.245428i
\(582\) −2.86162e32 + 5.60235e32i −0.189468 + 0.370932i
\(583\) −1.31576e33 −0.853400
\(584\) 6.32776e32i 0.402065i
\(585\) 6.69279e32 4.84212e32i 0.416617 0.301415i
\(586\) −8.78971e32 −0.536047
\(587\) 2.64271e33i 1.57904i 0.613725 + 0.789520i \(0.289670\pi\)
−0.613725 + 0.789520i \(0.710330\pi\)
\(588\) 7.41408e32 + 3.78703e32i 0.434040 + 0.221703i
\(589\) 6.33996e32 0.363666
\(590\) 6.35158e32i 0.356992i
\(591\) −8.14411e32 + 1.59442e33i −0.448532 + 0.878116i
\(592\) −2.98067e32 −0.160862
\(593\) 3.60659e33i 1.90739i −0.300772 0.953696i \(-0.597244\pi\)
0.300772 0.953696i \(-0.402756\pi\)
\(594\) 1.04020e32 + 6.69789e32i 0.0539111 + 0.347137i
\(595\) −1.16376e32 −0.0591097
\(596\) 1.56594e33i 0.779507i
\(597\) 8.29309e32 + 4.23602e32i 0.404598 + 0.206665i
\(598\) −3.37880e33 −1.61565
\(599\) 2.13018e33i 0.998379i −0.866493 0.499189i \(-0.833631\pi\)
0.866493 0.499189i \(-0.166369\pi\)
\(600\) −3.13813e32 + 6.14370e32i −0.144164 + 0.282238i
\(601\) 3.19212e33 1.43743 0.718713 0.695306i \(-0.244731\pi\)
0.718713 + 0.695306i \(0.244731\pi\)
\(602\) 1.44877e32i 0.0639503i
\(603\) −1.98894e32 2.74911e32i −0.0860623 0.118956i
\(604\) −1.31879e31 −0.00559414
\(605\) 5.82969e32i 0.242427i
\(606\) 1.20566e33 + 6.15836e32i 0.491532 + 0.251069i
\(607\) 1.31960e33 0.527446 0.263723 0.964598i \(-0.415049\pi\)
0.263723 + 0.964598i \(0.415049\pi\)
\(608\) 1.91025e32i 0.0748598i
\(609\) −1.17551e32 + 2.30136e32i −0.0451667 + 0.0884254i
\(610\) −1.03965e33 −0.391678
\(611\) 2.58240e33i 0.953956i
\(612\) 1.29289e33 9.35386e32i 0.468323 0.338824i
\(613\) 1.42736e33 0.506999 0.253499 0.967336i \(-0.418418\pi\)
0.253499 + 0.967336i \(0.418418\pi\)
\(614\) 2.63950e33i 0.919394i
\(615\) 9.04090e32 + 4.61799e32i 0.308824 + 0.157744i
\(616\) −8.32921e31 −0.0279020
\(617\) 5.36476e32i 0.176250i 0.996109 + 0.0881248i \(0.0280874\pi\)
−0.996109 + 0.0881248i \(0.971913\pi\)
\(618\) −2.98938e32 + 5.85247e32i −0.0963206 + 0.188572i
\(619\) −3.63419e33 −1.14847 −0.574235 0.818691i \(-0.694700\pi\)
−0.574235 + 0.818691i \(0.694700\pi\)
\(620\) 4.45895e32i 0.138208i
\(621\) −4.64861e33 + 7.21938e32i −1.41326 + 0.219483i
\(622\) 1.26015e33 0.375784
\(623\) 9.52197e32i 0.278529i
\(624\) −1.23959e33 6.33170e32i −0.355683 0.181679i
\(625\) 2.48665e33 0.699929
\(626\) 7.93253e32i 0.219038i
\(627\) −3.53285e32 + 6.91645e32i −0.0957006 + 0.187358i
\(628\) −2.19072e33 −0.582199
\(629\) 2.85304e33i 0.743874i
\(630\) 8.28440e31 + 1.14507e32i 0.0211921 + 0.0292918i
\(631\) −6.10564e33 −1.53242 −0.766212 0.642588i \(-0.777861\pi\)
−0.766212 + 0.642588i \(0.777861\pi\)
\(632\) 1.94473e33i 0.478910i
\(633\) −7.09810e33 3.62563e33i −1.71513 0.876071i
\(634\) 1.46313e33 0.346907
\(635\) 1.33321e33i 0.310179i
\(636\) 1.71127e33 3.35024e33i 0.390690 0.764875i
\(637\) 6.95086e33 1.55728
\(638\) 9.98742e32i 0.219586i
\(639\) 3.66385e33 2.65073e33i 0.790545 0.571946i
\(640\) −1.34350e32 −0.0284497
\(641\) 9.25569e33i 1.92359i 0.273771 + 0.961795i \(0.411729\pi\)
−0.273771 + 0.961795i \(0.588271\pi\)
\(642\) 4.21130e33 + 2.15109e33i 0.859005 + 0.438771i
\(643\) 9.93440e32 0.198889 0.0994443 0.995043i \(-0.468293\pi\)
0.0994443 + 0.995043i \(0.468293\pi\)
\(644\) 5.78080e32i 0.113595i
\(645\) −4.32184e32 + 8.46110e32i −0.0833589 + 0.163196i
\(646\) 1.82846e33 0.346174
\(647\) 6.13374e33i 1.13992i 0.821673 + 0.569960i \(0.193041\pi\)
−0.821673 + 0.569960i \(0.806959\pi\)
\(648\) −1.84074e33 6.06265e32i −0.335808 0.110602i
\(649\) 4.35128e33 0.779258
\(650\) 5.75985e33i 1.01263i
\(651\) 7.03882e32 + 3.59535e32i 0.121486 + 0.0620540i
\(652\) 1.55684e33 0.263798
\(653\) 4.06146e33i 0.675653i −0.941208 0.337826i \(-0.890308\pi\)
0.941208 0.337826i \(-0.109692\pi\)
\(654\) 1.44062e33 2.82038e33i 0.235297 0.460653i
\(655\) −9.38743e32 −0.150540
\(656\) 1.71063e33i 0.269345i
\(657\) 4.31164e33 + 5.95956e33i 0.666589 + 0.921361i
\(658\) 4.41823e32 0.0670715
\(659\) 9.06217e33i 1.35085i 0.737428 + 0.675425i \(0.236040\pi\)
−0.737428 + 0.675425i \(0.763960\pi\)
\(660\) 4.86440e32 + 2.48469e32i 0.0712037 + 0.0363701i
\(661\) −1.08028e34 −1.55281 −0.776403 0.630236i \(-0.782958\pi\)
−0.776403 + 0.630236i \(0.782958\pi\)
\(662\) 3.63809e33i 0.513544i
\(663\) 6.06058e33 1.18651e34i 0.840140 1.64479i
\(664\) 4.01242e33 0.546248
\(665\) 1.61940e32i 0.0216519i
\(666\) −2.80723e33 + 2.03098e33i −0.368627 + 0.266695i
\(667\) −6.93167e33 −0.893980
\(668\) 3.63566e32i 0.0460538i
\(669\) −9.68821e33 4.94863e33i −1.20540 0.615704i
\(670\) −2.73439e32 −0.0334167
\(671\) 7.12233e33i 0.854972i
\(672\) 1.08329e32 2.12082e32i 0.0127736 0.0250077i
\(673\) 1.84641e33 0.213869 0.106934 0.994266i \(-0.465897\pi\)
0.106934 + 0.994266i \(0.465897\pi\)
\(674\) 6.20019e32i 0.0705483i
\(675\) 1.23069e33 + 7.92449e33i 0.137564 + 0.885780i
\(676\) −7.06810e33 −0.776144
\(677\) 1.58418e34i 1.70899i 0.519458 + 0.854496i \(0.326134\pi\)
−0.519458 + 0.854496i \(0.673866\pi\)
\(678\) −3.52181e33 1.79890e33i −0.373258 0.190656i
\(679\) −8.98622e32 −0.0935706
\(680\) 1.28597e33i 0.131560i
\(681\) 3.64974e33 7.14530e33i 0.366857 0.718216i
\(682\) 3.05470e33 0.301686
\(683\) 1.01164e34i 0.981699i −0.871244 0.490849i \(-0.836687\pi\)
0.871244 0.490849i \(-0.163313\pi\)
\(684\) −1.30162e33 1.79910e33i −0.124111 0.171547i
\(685\) −1.83868e33 −0.172274
\(686\) 2.40924e33i 0.221814i
\(687\) 1.16731e34 + 5.96251e33i 1.05610 + 0.539447i
\(688\) 1.60092e33 0.142334
\(689\) 3.14092e34i 2.74427i
\(690\) −1.72447e33 + 3.37609e33i −0.148070 + 0.289885i
\(691\) 1.09063e33 0.0920320 0.0460160 0.998941i \(-0.485347\pi\)
0.0460160 + 0.998941i \(0.485347\pi\)
\(692\) 4.88980e33i 0.405525i
\(693\) −7.84455e32 + 5.67540e32i −0.0639395 + 0.0462591i
\(694\) −9.67141e33 −0.774776
\(695\) 1.25097e33i 0.0984987i
\(696\) −2.54304e33 1.29896e33i −0.196808 0.100527i
\(697\) 1.63738e34 1.24553
\(698\) 1.42090e33i 0.106242i
\(699\) 4.38533e33 8.58540e33i 0.322312 0.631008i
\(700\) −9.85455e32 −0.0711968
\(701\) 1.22710e33i 0.0871493i 0.999050 + 0.0435746i \(0.0138746\pi\)
−0.999050 + 0.0435746i \(0.986125\pi\)
\(702\) −1.59890e34 + 2.48312e33i −1.11628 + 0.173361i
\(703\) −3.97009e33 −0.272481
\(704\) 9.20392e32i 0.0621013i
\(705\) −2.58033e33 1.31800e33i −0.171161 0.0874272i
\(706\) 1.14228e34 0.744928
\(707\) 1.93388e33i 0.123993i
\(708\) −5.65926e33 + 1.10794e34i −0.356747 + 0.698423i
\(709\) −1.02023e34 −0.632327 −0.316163 0.948705i \(-0.602395\pi\)
−0.316163 + 0.948705i \(0.602395\pi\)
\(710\) 3.64423e33i 0.222078i
\(711\) 1.32511e34 + 1.83157e34i 0.793992 + 1.09746i
\(712\) 1.05219e34 0.619921
\(713\) 2.12008e34i 1.22823i
\(714\) 2.03001e33 + 1.03691e33i 0.115643 + 0.0590692i
\(715\) 4.56048e33 0.255469
\(716\) 3.87773e33i 0.213610i
\(717\) −1.46190e34 + 2.86204e34i −0.791932 + 1.55041i
\(718\) 8.31774e33 0.443110
\(719\) 3.09786e34i 1.62299i −0.584362 0.811493i \(-0.698655\pi\)
0.584362 0.811493i \(-0.301345\pi\)
\(720\) −1.26532e33 + 9.15440e32i −0.0651946 + 0.0471672i
\(721\) −9.38742e32 −0.0475689
\(722\) 1.16440e34i 0.580303i
\(723\) 1.45860e34 + 7.45037e33i 0.714952 + 0.365190i
\(724\) −3.52544e33 −0.169961
\(725\) 1.18164e34i 0.560313i
\(726\) 5.19425e33 1.01691e34i 0.242261 0.474288i
\(727\) 1.06499e34 0.488578 0.244289 0.969702i \(-0.421445\pi\)
0.244289 + 0.969702i \(0.421445\pi\)
\(728\) 1.98832e33i 0.0897241i
\(729\) −2.14673e34 + 6.83262e33i −0.952899 + 0.303289i
\(730\) 5.92766e33 0.258826
\(731\) 1.53237e34i 0.658196i
\(732\) 1.81352e34 + 9.26327e33i 0.766284 + 0.391410i
\(733\) −1.29281e34 −0.537389 −0.268694 0.963226i \(-0.586592\pi\)
−0.268694 + 0.963226i \(0.586592\pi\)
\(734\) 2.98071e34i 1.21890i
\(735\) 3.54758e33 6.94529e33i 0.142720 0.279410i
\(736\) 6.38789e33 0.252827
\(737\) 1.87325e33i 0.0729435i
\(738\) −1.16559e34 1.61109e34i −0.446551 0.617224i
\(739\) −4.14836e34 −1.56366 −0.781832 0.623489i \(-0.785715\pi\)
−0.781832 + 0.623489i \(0.785715\pi\)
\(740\) 2.79220e33i 0.103554i
\(741\) −1.65107e34 8.43348e33i −0.602486 0.307743i
\(742\) 5.37381e33 0.192946
\(743\) 3.70596e34i 1.30929i −0.755938 0.654643i \(-0.772819\pi\)
0.755938 0.654643i \(-0.227181\pi\)
\(744\) −3.97293e33 + 7.77802e33i −0.138113 + 0.270392i
\(745\) 1.46693e34 0.501803
\(746\) 1.74295e34i 0.586704i
\(747\) 3.77895e34 2.73400e34i 1.25177 0.905632i
\(748\) 8.80981e33 0.287175
\(749\) 6.75497e33i 0.216691i
\(750\) 1.21756e34 + 6.21918e33i 0.384376 + 0.196335i
\(751\) −4.89324e33 −0.152026 −0.0760129 0.997107i \(-0.524219\pi\)
−0.0760129 + 0.997107i \(0.524219\pi\)
\(752\) 4.88222e33i 0.149281i
\(753\) 5.73893e33 1.12354e34i 0.172700 0.338103i
\(754\) −2.38416e34 −0.706121
\(755\) 1.23541e32i 0.00360119i
\(756\) −4.24838e32 2.73556e33i −0.0121888 0.0784845i
\(757\) −4.02832e34 −1.13756 −0.568779 0.822490i \(-0.692584\pi\)
−0.568779 + 0.822490i \(0.692584\pi\)
\(758\) 4.62802e34i