Properties

Label 6.25.b.a.5.2
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 5.2
Root \(1694.95i\) of defining polynomial
Character \(\chi\) \(=\) 6.5
Dual form 6.25.b.a.5.6

$q$-expansion

\(f(q)\) \(=\) \(q-2896.31i q^{2} +(-317945. + 425841. i) q^{3} -8.38861e6 q^{4} -6.76938e7i q^{5} +(1.23337e9 + 9.20867e8i) q^{6} -2.41596e10 q^{7} +2.42960e10i q^{8} +(-8.02515e10 - 2.70788e11i) q^{9} +O(q^{10})\) \(q-2896.31i q^{2} +(-317945. + 425841. i) q^{3} -8.38861e6 q^{4} -6.76938e7i q^{5} +(1.23337e9 + 9.20867e8i) q^{6} -2.41596e10 q^{7} +2.42960e10i q^{8} +(-8.02515e10 - 2.70788e11i) q^{9} -1.96062e11 q^{10} +4.00004e12i q^{11} +(2.66712e12 - 3.57221e12i) q^{12} +2.67023e13 q^{13} +6.99737e13i q^{14} +(2.88268e13 + 2.15229e13i) q^{15} +7.03687e13 q^{16} -6.60084e14i q^{17} +(-7.84286e14 + 2.32433e14i) q^{18} -3.05285e14 q^{19} +5.67857e14i q^{20} +(7.68142e15 - 1.02881e16i) q^{21} +1.15854e16 q^{22} -7.66067e14i q^{23} +(-1.03462e16 - 7.72479e15i) q^{24} +5.50222e16 q^{25} -7.73381e16i q^{26} +(1.40828e17 + 5.19213e16i) q^{27} +2.02665e17 q^{28} -4.00191e17i q^{29} +(6.23370e16 - 8.34913e16i) q^{30} +1.08492e18 q^{31} -2.03810e17i q^{32} +(-1.70338e18 - 1.27179e18i) q^{33} -1.91181e18 q^{34} +1.63546e18i q^{35} +(6.73199e17 + 2.27153e18i) q^{36} +2.67466e18 q^{37} +8.84200e17i q^{38} +(-8.48986e18 + 1.13709e19i) q^{39} +1.64469e18 q^{40} +3.10777e19i q^{41} +(-2.97976e19 - 2.22478e19i) q^{42} -2.43678e19 q^{43} -3.35548e19i q^{44} +(-1.83307e19 + 5.43253e18i) q^{45} -2.21877e18 q^{46} -3.79896e19i q^{47} +(-2.23734e19 + 2.99659e19i) q^{48} +3.92105e20 q^{49} -1.59361e20i q^{50} +(2.81091e20 + 2.09870e20i) q^{51} -2.23995e20 q^{52} -8.82597e19i q^{53} +(1.50380e20 - 4.07882e20i) q^{54} +2.70778e20 q^{55} -5.86982e20i q^{56} +(9.70638e19 - 1.30003e20i) q^{57} -1.15908e21 q^{58} +1.88092e21i q^{59} +(-2.41817e20 - 1.80547e20i) q^{60} -1.92240e21 q^{61} -3.14226e21i q^{62} +(1.93884e21 + 6.54213e21i) q^{63} -5.90296e20 q^{64} -1.80758e21i q^{65} +(-3.68351e21 + 4.93352e21i) q^{66} -7.96234e21 q^{67} +5.53718e21i q^{68} +(3.26223e20 + 2.43567e20i) q^{69} +4.73678e21 q^{70} -2.04327e22i q^{71} +(6.57907e21 - 1.94979e21i) q^{72} +3.28296e22 q^{73} -7.74666e21i q^{74} +(-1.74940e22 + 2.34307e22i) q^{75} +2.56092e21 q^{76} -9.66394e22i q^{77} +(3.29337e22 + 2.45893e22i) q^{78} +5.13170e21 q^{79} -4.76353e21i q^{80} +(-6.68858e22 + 4.34623e22i) q^{81} +9.00105e22 q^{82} +1.14963e21i q^{83} +(-6.44364e22 + 8.63032e22i) q^{84} -4.46836e22 q^{85} +7.05766e22i q^{86} +(1.70418e23 + 1.27239e23i) q^{87} -9.71851e22 q^{88} -3.69857e23i q^{89} +(1.57343e22 + 5.30913e22i) q^{90} -6.45117e23 q^{91} +6.42623e21i q^{92} +(-3.44945e23 + 4.62003e23i) q^{93} -1.10030e23 q^{94} +2.06659e22i q^{95} +(8.67905e22 + 6.48003e22i) q^{96} +1.10819e24 q^{97} -1.13566e24i q^{98} +(1.08316e24 - 3.21010e23i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 131880 q^{3} - 67108864 q^{4} + 33718272 q^{6} - 10160794640 q^{7} + 295169053896 q^{9} + O(q^{10}) \) \( 8 q - 131880 q^{3} - 67108864 q^{4} + 33718272 q^{6} - 10160794640 q^{7} + 295169053896 q^{9} - 1863369424896 q^{10} + 1106289623040 q^{12} + 50568363679120 q^{13} - 348034956760512 q^{15} + 562949953421312 q^{16} - 514738292981760 q^{18} - 978083631341264 q^{19} + 3640012304241936 q^{21} - 336450979430400 q^{22} - 282849366245376 q^{24} + 7630618767014024 q^{25} - 86594528606057640 q^{27} + 85234923203461120 q^{28} - 725410188900237312 q^{30} + 3092119786822709104 q^{31} - 8158685952668529600 q^{33} + 3821138032531341312 q^{34} - 2476057486864416768 q^{36} + 22590293223992782480 q^{37} - 40190176581881465040 q^{39} + 15631075664637984768 q^{40} - 79119883835565342720 q^{42} + 226487466371803896880 q^{43} - 347709996757177504128 q^{45} + 139842130561120468992 q^{46} - 9280229982150328320 q^{48} + 104686700473616731800 q^{49} + 558091874936566543104 q^{51} - 424198180105575464960 q^{52} + 334066775626796728320 q^{54} - 2212687664250467338368 q^{55} + 3588879995640760725840 q^{57} - 1867706355469718323200 q^{58} + 2919528822560885047296 q^{60} - 6507010783838092385648 q^{61} + 10112982777612899380080 q^{63} - 4722366482869645213696 q^{64} - 1924112442339530440704 q^{66} - 7042120118150060144720 q^{67} - 4323335967368731345536 q^{69} + 16481910236435553583104 q^{70} + 4317937762413135790080 q^{72} + 36259820324758576687120 q^{73} - 108081978448612908655272 q^{75} + 8204760174538377920512 q^{76} - 74188898027329578270720 q^{78} + 316807052777330015315824 q^{79} - 268518660504396776813304 q^{81} + 83114941529654645882880 q^{82} - 30534636335462338265088 q^{84} - 222512862545524200678912 q^{85} + 449461577201807342128320 q^{87} + 2822355377657688883200 q^{88} + 612683975543382025371648 q^{90} - 1196839602335690774367520 q^{91} + 873237537450828783745680 q^{93} - 1298887117621773403422720 q^{94} + 2372712456480891076608 q^{96} + 816517576248201265716880 q^{97} + 695858883367208922313344 q^{99} + O(q^{100}) \)

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
\(3\) −317945. + 425841.i −0.598270 + 0.801295i
\(4\) −8.38861e6 −0.500000
\(5\) 6.76938e7i 0.277274i −0.990343 0.138637i \(-0.955728\pi\)
0.990343 0.138637i \(-0.0442721\pi\)
\(6\) 1.23337e9 + 9.20867e8i 0.566601 + 0.423040i
\(7\) −2.41596e10 −1.74547 −0.872736 0.488192i \(-0.837657\pi\)
−0.872736 + 0.488192i \(0.837657\pi\)
\(8\) 2.42960e10i 0.353553i
\(9\) −8.02515e10 2.70788e11i −0.284147 0.958781i
\(10\) −1.96062e11 −0.196062
\(11\) 4.00004e12i 1.27454i 0.770642 + 0.637268i \(0.219936\pi\)
−0.770642 + 0.637268i \(0.780064\pi\)
\(12\) 2.66712e12 3.57221e12i 0.299135 0.400647i
\(13\) 2.67023e13 1.14612 0.573058 0.819515i \(-0.305757\pi\)
0.573058 + 0.819515i \(0.305757\pi\)
\(14\) 6.99737e13i 1.23424i
\(15\) 2.88268e13 + 2.15229e13i 0.222178 + 0.165885i
\(16\) 7.03687e13 0.250000
\(17\) 6.60084e14i 1.13295i −0.824078 0.566477i \(-0.808306\pi\)
0.824078 0.566477i \(-0.191694\pi\)
\(18\) −7.84286e14 + 2.32433e14i −0.677960 + 0.200922i
\(19\) −3.05285e14 −0.137931 −0.0689656 0.997619i \(-0.521970\pi\)
−0.0689656 + 0.997619i \(0.521970\pi\)
\(20\) 5.67857e14i 0.138637i
\(21\) 7.68142e15 1.02881e16i 1.04426 1.39864i
\(22\) 1.15854e16 0.901234
\(23\) 7.66067e14i 0.0349569i −0.999847 0.0174784i \(-0.994436\pi\)
0.999847 0.0174784i \(-0.00556384\pi\)
\(24\) −1.03462e16 7.72479e15i −0.283301 0.211520i
\(25\) 5.50222e16 0.923119
\(26\) 7.73381e16i 0.810426i
\(27\) 1.40828e17 + 5.19213e16i 0.938263 + 0.345924i
\(28\) 2.02665e17 0.872736
\(29\) 4.00191e17i 1.13107i −0.824723 0.565537i \(-0.808669\pi\)
0.824723 0.565537i \(-0.191331\pi\)
\(30\) 6.23370e16 8.34913e16i 0.117298 0.157104i
\(31\) 1.08492e18 1.37739 0.688696 0.725051i \(-0.258184\pi\)
0.688696 + 0.725051i \(0.258184\pi\)
\(32\) 2.03810e17i 0.176777i
\(33\) −1.70338e18 1.27179e18i −1.02128 0.762517i
\(34\) −1.91181e18 −0.801119
\(35\) 1.63546e18i 0.483974i
\(36\) 6.73199e17 + 2.27153e18i 0.142074 + 0.479390i
\(37\) 2.67466e18 0.406302 0.203151 0.979147i \(-0.434882\pi\)
0.203151 + 0.979147i \(0.434882\pi\)
\(38\) 8.84200e17i 0.0975320i
\(39\) −8.48986e18 + 1.13709e19i −0.685686 + 0.918377i
\(40\) 1.64469e18 0.0980311
\(41\) 3.10777e19i 1.37734i 0.725074 + 0.688671i \(0.241806\pi\)
−0.725074 + 0.688671i \(0.758194\pi\)
\(42\) −2.97976e19 2.22478e19i −0.988987 0.738406i
\(43\) −2.43678e19 −0.609810 −0.304905 0.952383i \(-0.598625\pi\)
−0.304905 + 0.952383i \(0.598625\pi\)
\(44\) 3.35548e19i 0.637268i
\(45\) −1.83307e19 + 5.43253e18i −0.265845 + 0.0787866i
\(46\) −2.21877e18 −0.0247182
\(47\) 3.79896e19i 0.326957i −0.986547 0.163478i \(-0.947729\pi\)
0.986547 0.163478i \(-0.0522714\pi\)
\(48\) −2.23734e19 + 2.99659e19i −0.149567 + 0.200324i
\(49\) 3.92105e20 2.04668
\(50\) 1.59361e20i 0.652744i
\(51\) 2.81091e20 + 2.09870e20i 0.907830 + 0.677811i
\(52\) −2.23995e20 −0.573058
\(53\) 8.82597e19i 0.179660i −0.995957 0.0898301i \(-0.971368\pi\)
0.995957 0.0898301i \(-0.0286324\pi\)
\(54\) 1.50380e20 4.07882e20i 0.244605 0.663452i
\(55\) 2.70778e20 0.353396
\(56\) 5.86982e20i 0.617118i
\(57\) 9.70638e19 1.30003e20i 0.0825200 0.110524i
\(58\) −1.15908e21 −0.799791
\(59\) 1.88092e21i 1.05718i 0.848879 + 0.528588i \(0.177278\pi\)
−0.848879 + 0.528588i \(0.822722\pi\)
\(60\) −2.41817e20 1.80547e20i −0.111089 0.0829423i
\(61\) −1.92240e21 −0.724244 −0.362122 0.932131i \(-0.617948\pi\)
−0.362122 + 0.932131i \(0.617948\pi\)
\(62\) 3.14226e21i 0.973963i
\(63\) 1.93884e21 + 6.54213e21i 0.495971 + 1.67353i
\(64\) −5.90296e20 −0.125000
\(65\) 1.80758e21i 0.317788i
\(66\) −3.68351e21 + 4.93352e21i −0.539181 + 0.722154i
\(67\) −7.96234e21 −0.973068 −0.486534 0.873662i \(-0.661739\pi\)
−0.486534 + 0.873662i \(0.661739\pi\)
\(68\) 5.53718e21i 0.566477i
\(69\) 3.26223e20 + 2.43567e20i 0.0280108 + 0.0209136i
\(70\) 4.73678e21 0.342221
\(71\) 2.04327e22i 1.24516i −0.782557 0.622579i \(-0.786085\pi\)
0.782557 0.622579i \(-0.213915\pi\)
\(72\) 6.57907e21 1.94979e21i 0.338980 0.100461i
\(73\) 3.28296e22 1.43348 0.716740 0.697340i \(-0.245633\pi\)
0.716740 + 0.697340i \(0.245633\pi\)
\(74\) 7.74666e21i 0.287299i
\(75\) −1.74940e22 + 2.34307e22i −0.552274 + 0.739691i
\(76\) 2.56092e21 0.0689656
\(77\) 9.66394e22i 2.22467i
\(78\) 3.29337e22 + 2.45893e22i 0.649390 + 0.484853i
\(79\) 5.13170e21 0.0868433 0.0434216 0.999057i \(-0.486174\pi\)
0.0434216 + 0.999057i \(0.486174\pi\)
\(80\) 4.76353e21i 0.0693185i
\(81\) −6.68858e22 + 4.34623e22i −0.838521 + 0.544870i
\(82\) 9.00105e22 0.973928
\(83\) 1.14963e21i 0.0107552i 0.999986 + 0.00537761i \(0.00171175\pi\)
−0.999986 + 0.00537761i \(0.998288\pi\)
\(84\) −6.44364e22 + 8.63032e22i −0.522132 + 0.699319i
\(85\) −4.46836e22 −0.314138
\(86\) 7.05766e22i 0.431201i
\(87\) 1.70418e23 + 1.27239e23i 0.906324 + 0.676688i
\(88\) −9.71851e22 −0.450617
\(89\) 3.69857e23i 1.49745i −0.662879 0.748727i \(-0.730665\pi\)
0.662879 0.748727i \(-0.269335\pi\)
\(90\) 1.57343e22 + 5.30913e22i 0.0557105 + 0.187981i
\(91\) −6.45117e23 −2.00051
\(92\) 6.42623e21i 0.0174784i
\(93\) −3.44945e23 + 4.62003e23i −0.824051 + 1.10370i
\(94\) −1.10030e23 −0.231193
\(95\) 2.06659e22i 0.0382447i
\(96\) 8.67905e22 + 6.48003e22i 0.141650 + 0.105760i
\(97\) 1.10819e24 1.59718 0.798592 0.601873i \(-0.205579\pi\)
0.798592 + 0.601873i \(0.205579\pi\)
\(98\) 1.13566e24i 1.44722i
\(99\) 1.08316e24 3.21010e23i 1.22200 0.362156i
\(100\) −4.61560e23 −0.461560
\(101\) 1.86377e24i 1.65400i 0.562202 + 0.827000i \(0.309954\pi\)
−0.562202 + 0.827000i \(0.690046\pi\)
\(102\) 6.07849e23 8.14126e23i 0.479285 0.641933i
\(103\) 1.22843e24 0.861594 0.430797 0.902449i \(-0.358232\pi\)
0.430797 + 0.902449i \(0.358232\pi\)
\(104\) 6.48759e23i 0.405213i
\(105\) −6.96444e23 5.19985e23i −0.387806 0.289547i
\(106\) −2.55627e23 −0.127039
\(107\) 3.55456e24i 1.57827i −0.614220 0.789134i \(-0.710529\pi\)
0.614220 0.789134i \(-0.289471\pi\)
\(108\) −1.18135e24 4.35547e23i −0.469131 0.172962i
\(109\) 2.18543e23 0.0776995 0.0388497 0.999245i \(-0.487631\pi\)
0.0388497 + 0.999245i \(0.487631\pi\)
\(110\) 7.84257e23i 0.249889i
\(111\) −8.50396e23 + 1.13898e24i −0.243078 + 0.325567i
\(112\) −1.70008e24 −0.436368
\(113\) 5.66320e24i 1.30653i 0.757128 + 0.653267i \(0.226602\pi\)
−0.757128 + 0.653267i \(0.773398\pi\)
\(114\) −3.76529e23 2.81127e23i −0.0781519 0.0583504i
\(115\) −5.18580e22 −0.00969263
\(116\) 3.35705e24i 0.565537i
\(117\) −2.14290e24 7.23066e24i −0.325666 1.09887i
\(118\) 5.44774e24 0.747536
\(119\) 1.59474e25i 1.97754i
\(120\) −5.22921e23 + 7.00376e23i −0.0586490 + 0.0785518i
\(121\) −6.15061e24 −0.624444
\(122\) 5.56786e24i 0.512118i
\(123\) −1.32341e25 9.88098e24i −1.10366 0.824022i
\(124\) −9.10097e24 −0.688696
\(125\) 7.75953e24i 0.533231i
\(126\) 1.89480e25 5.61549e24i 1.18336 0.350705i
\(127\) 1.31873e25 0.749051 0.374526 0.927217i \(-0.377806\pi\)
0.374526 + 0.927217i \(0.377806\pi\)
\(128\) 1.70968e24i 0.0883883i
\(129\) 7.74761e24 1.03768e25i 0.364831 0.488638i
\(130\) −5.23531e24 −0.224710
\(131\) 2.72828e25i 1.06815i −0.845436 0.534077i \(-0.820659\pi\)
0.845436 0.534077i \(-0.179341\pi\)
\(132\) 1.42890e25 + 1.06686e25i 0.510640 + 0.381258i
\(133\) 7.37556e24 0.240755
\(134\) 2.30614e25i 0.688063i
\(135\) 3.51475e24 9.53320e24i 0.0959156 0.260156i
\(136\) 1.60374e25 0.400559
\(137\) 1.88032e25i 0.430115i −0.976601 0.215058i \(-0.931006\pi\)
0.976601 0.215058i \(-0.0689939\pi\)
\(138\) 7.05445e23 9.44841e23i 0.0147882 0.0198066i
\(139\) 4.16312e24 0.0800279 0.0400140 0.999199i \(-0.487260\pi\)
0.0400140 + 0.999199i \(0.487260\pi\)
\(140\) 1.37192e25i 0.241987i
\(141\) 1.61775e25 + 1.20786e25i 0.261989 + 0.195608i
\(142\) −5.91793e25 −0.880460
\(143\) 1.06810e26i 1.46077i
\(144\) −5.64720e24 1.90550e25i −0.0710368 0.239695i
\(145\) −2.70905e25 −0.313618
\(146\) 9.50848e25i 1.01362i
\(147\) −1.24668e26 + 1.66974e26i −1.22446 + 1.63999i
\(148\) −2.24367e25 −0.203151
\(149\) 9.17379e25i 0.766149i −0.923717 0.383075i \(-0.874865\pi\)
0.923717 0.383075i \(-0.125135\pi\)
\(150\) 6.78626e25 + 5.06681e25i 0.523040 + 0.390517i
\(151\) 1.86184e26 1.32501 0.662505 0.749058i \(-0.269493\pi\)
0.662505 + 0.749058i \(0.269493\pi\)
\(152\) 7.41721e24i 0.0487660i
\(153\) −1.78743e26 + 5.29727e25i −1.08625 + 0.321925i
\(154\) −2.79898e26 −1.57308
\(155\) 7.34424e25i 0.381915i
\(156\) 7.12181e25 9.53863e25i 0.342843 0.459188i
\(157\) 1.58923e26 0.708584 0.354292 0.935135i \(-0.384722\pi\)
0.354292 + 0.935135i \(0.384722\pi\)
\(158\) 1.48630e25i 0.0614075i
\(159\) 3.75846e25 + 2.80617e25i 0.143961 + 0.107485i
\(160\) −1.37967e25 −0.0490156
\(161\) 1.85079e25i 0.0610163i
\(162\) 1.25880e26 + 1.93722e26i 0.385281 + 0.592924i
\(163\) 4.86804e26 1.38390 0.691948 0.721948i \(-0.256753\pi\)
0.691948 + 0.721948i \(0.256753\pi\)
\(164\) 2.60698e26i 0.688671i
\(165\) −8.60926e25 + 1.15308e26i −0.211426 + 0.283174i
\(166\) 3.32967e24 0.00760509
\(167\) 6.29000e26i 1.33676i −0.743821 0.668379i \(-0.766989\pi\)
0.743821 0.668379i \(-0.233011\pi\)
\(168\) 2.49961e26 + 1.86628e26i 0.494493 + 0.369203i
\(169\) 1.70212e26 0.313582
\(170\) 1.29418e26i 0.222129i
\(171\) 2.44996e25 + 8.26675e25i 0.0391927 + 0.132246i
\(172\) 2.04412e26 0.304905
\(173\) 1.85146e26i 0.257609i −0.991670 0.128805i \(-0.958886\pi\)
0.991670 0.128805i \(-0.0411140\pi\)
\(174\) 3.68523e26 4.93582e26i 0.478490 0.640868i
\(175\) −1.32931e27 −1.61128
\(176\) 2.81478e26i 0.318634i
\(177\) −8.00974e26 5.98030e26i −0.847109 0.632476i
\(178\) −1.07122e27 −1.05886
\(179\) 1.47704e27i 1.36507i 0.730853 + 0.682535i \(0.239123\pi\)
−0.730853 + 0.682535i \(0.760877\pi\)
\(180\) 1.53769e26 4.55714e25i 0.132922 0.0393933i
\(181\) −6.65463e26 −0.538246 −0.269123 0.963106i \(-0.586734\pi\)
−0.269123 + 0.963106i \(0.586734\pi\)
\(182\) 1.86846e27i 1.41458i
\(183\) 6.11216e26 8.18635e26i 0.433293 0.580333i
\(184\) 1.86124e25 0.0123591
\(185\) 1.81058e26i 0.112657i
\(186\) 1.33810e27 + 9.99067e26i 0.780431 + 0.582692i
\(187\) 2.64036e27 1.44399
\(188\) 3.18680e26i 0.163478i
\(189\) −3.40235e27 1.25440e27i −1.63771 0.603800i
\(190\) 5.98549e25 0.0270431
\(191\) 2.76451e27i 1.17279i 0.810027 + 0.586393i \(0.199452\pi\)
−0.810027 + 0.586393i \(0.800548\pi\)
\(192\) 1.87682e26 2.51372e26i 0.0747837 0.100162i
\(193\) 7.06698e26 0.264573 0.132287 0.991212i \(-0.457768\pi\)
0.132287 + 0.991212i \(0.457768\pi\)
\(194\) 3.20967e27i 1.12938i
\(195\) 7.69742e26 + 5.74711e26i 0.254642 + 0.190123i
\(196\) −3.28921e27 −1.02334
\(197\) 4.71662e27i 1.38050i −0.723571 0.690250i \(-0.757501\pi\)
0.723571 0.690250i \(-0.242499\pi\)
\(198\) −9.29743e26 3.13718e27i −0.256083 0.864085i
\(199\) 2.25704e27 0.585197 0.292598 0.956235i \(-0.405480\pi\)
0.292598 + 0.956235i \(0.405480\pi\)
\(200\) 1.33682e27i 0.326372i
\(201\) 2.53159e27 3.39069e27i 0.582157 0.779714i
\(202\) 5.39805e27 1.16955
\(203\) 9.66845e27i 1.97426i
\(204\) −2.35796e27 1.76052e27i −0.453915 0.338906i
\(205\) 2.10377e27 0.381901
\(206\) 3.55791e27i 0.609239i
\(207\) −2.07442e26 + 6.14780e25i −0.0335160 + 0.00993289i
\(208\) 1.87901e27 0.286529
\(209\) 1.22115e27i 0.175798i
\(210\) −1.50604e27 + 2.01712e27i −0.204741 + 0.274220i
\(211\) 3.37907e27 0.433918 0.216959 0.976181i \(-0.430386\pi\)
0.216959 + 0.976181i \(0.430386\pi\)
\(212\) 7.40376e26i 0.0898301i
\(213\) 8.70106e27 + 6.49646e27i 0.997739 + 0.744940i
\(214\) −1.02951e28 −1.11600
\(215\) 1.64955e27i 0.169084i
\(216\) −1.26148e27 + 3.42156e27i −0.122302 + 0.331726i
\(217\) −2.62112e28 −2.40420
\(218\) 6.32967e26i 0.0549418i
\(219\) −1.04380e28 + 1.39802e28i −0.857608 + 1.14864i
\(220\) −2.27145e27 −0.176698
\(221\) 1.76258e28i 1.29850i
\(222\) 3.29884e27 + 2.46301e27i 0.230211 + 0.171882i
\(223\) 1.36332e28 0.901443 0.450722 0.892665i \(-0.351167\pi\)
0.450722 + 0.892665i \(0.351167\pi\)
\(224\) 4.92396e27i 0.308559i
\(225\) −4.41562e27 1.48993e28i −0.262302 0.885069i
\(226\) 1.64024e28 0.923859
\(227\) 6.82027e27i 0.364327i −0.983268 0.182164i \(-0.941690\pi\)
0.983268 0.182164i \(-0.0583100\pi\)
\(228\) −8.14231e26 + 1.09054e27i −0.0412600 + 0.0552618i
\(229\) −2.90439e28 −1.39646 −0.698231 0.715872i \(-0.746029\pi\)
−0.698231 + 0.715872i \(0.746029\pi\)
\(230\) 1.50197e26i 0.00685372i
\(231\) 4.11530e28 + 3.07260e28i 1.78262 + 1.33095i
\(232\) 9.72304e27 0.399895
\(233\) 8.69231e27i 0.339519i −0.985486 0.169760i \(-0.945701\pi\)
0.985486 0.169760i \(-0.0542991\pi\)
\(234\) −2.09422e28 + 6.20650e27i −0.777021 + 0.230280i
\(235\) −2.57166e27 −0.0906566
\(236\) 1.57783e28i 0.528588i
\(237\) −1.63160e27 + 2.18529e27i −0.0519557 + 0.0695871i
\(238\) 4.61885e28 1.39833
\(239\) 3.86579e28i 1.11292i −0.830875 0.556459i \(-0.812160\pi\)
0.830875 0.556459i \(-0.187840\pi\)
\(240\) 2.02851e27 + 1.51454e27i 0.0555445 + 0.0414711i
\(241\) 1.20605e28 0.314168 0.157084 0.987585i \(-0.449791\pi\)
0.157084 + 0.987585i \(0.449791\pi\)
\(242\) 1.78141e28i 0.441549i
\(243\) 2.75798e27 4.23013e28i 0.0650603 0.997881i
\(244\) 1.61262e28 0.362122
\(245\) 2.65431e28i 0.567490i
\(246\) −2.86184e28 + 3.83302e28i −0.582672 + 0.780404i
\(247\) −8.15181e27 −0.158085
\(248\) 2.63592e28i 0.486981i
\(249\) −4.89557e26 3.65518e26i −0.00861810 0.00643452i
\(250\) −2.24740e28 −0.377051
\(251\) 8.43194e28i 1.34848i 0.738515 + 0.674238i \(0.235528\pi\)
−0.738515 + 0.674238i \(0.764472\pi\)
\(252\) −1.62642e28 5.48793e28i −0.247986 0.836763i
\(253\) 3.06430e27 0.0445538
\(254\) 3.81945e28i 0.529659i
\(255\) 1.42069e28 1.90281e28i 0.187939 0.251717i
\(256\) 4.95176e27 0.0625000
\(257\) 5.82077e28i 0.701105i 0.936543 + 0.350553i \(0.114006\pi\)
−0.936543 + 0.350553i \(0.885994\pi\)
\(258\) −3.00544e28 2.24395e28i −0.345519 0.257974i
\(259\) −6.46188e28 −0.709189
\(260\) 1.51631e28i 0.158894i
\(261\) −1.08367e29 + 3.21159e28i −1.08445 + 0.321392i
\(262\) −7.90195e28 −0.755299
\(263\) 1.33775e29i 1.22153i 0.791810 + 0.610767i \(0.209139\pi\)
−0.791810 + 0.610767i \(0.790861\pi\)
\(264\) 3.08995e28 4.13854e28i 0.269590 0.361077i
\(265\) −5.97464e27 −0.0498151
\(266\) 2.13619e28i 0.170240i
\(267\) 1.57500e29 + 1.17594e29i 1.19990 + 0.895881i
\(268\) 6.67930e28 0.486534
\(269\) 4.31823e28i 0.300800i −0.988625 0.150400i \(-0.951944\pi\)
0.988625 0.150400i \(-0.0480562\pi\)
\(270\) −2.76111e28 1.01798e28i −0.183958 0.0678226i
\(271\) 1.25855e28 0.0802119 0.0401059 0.999195i \(-0.487230\pi\)
0.0401059 + 0.999195i \(0.487230\pi\)
\(272\) 4.64493e28i 0.283238i
\(273\) 2.05112e29 2.74717e29i 1.19685 1.60300i
\(274\) −5.44599e28 −0.304137
\(275\) 2.20091e29i 1.17655i
\(276\) −2.73655e27 2.04319e27i −0.0140054 0.0104568i
\(277\) 9.17464e28 0.449606 0.224803 0.974404i \(-0.427826\pi\)
0.224803 + 0.974404i \(0.427826\pi\)
\(278\) 1.20577e28i 0.0565883i
\(279\) −8.70665e28 2.93783e29i −0.391382 1.32062i
\(280\) −3.97350e28 −0.171111
\(281\) 2.21314e28i 0.0913131i −0.998957 0.0456566i \(-0.985462\pi\)
0.998957 0.0456566i \(-0.0145380\pi\)
\(282\) 3.49834e28 4.68551e28i 0.138316 0.185254i
\(283\) 3.26573e28 0.123749 0.0618747 0.998084i \(-0.480292\pi\)
0.0618747 + 0.998084i \(0.480292\pi\)
\(284\) 1.71402e29i 0.622579i
\(285\) −8.80039e27 6.57062e27i −0.0306453 0.0228806i
\(286\) 3.09356e29 1.03292
\(287\) 7.50824e29i 2.40411i
\(288\) −5.51892e28 + 1.63560e28i −0.169490 + 0.0502306i
\(289\) −9.62619e28 −0.283583
\(290\) 7.84623e28i 0.221761i
\(291\) −3.52344e29 + 4.71914e29i −0.955546 + 1.27981i
\(292\) −2.75395e29 −0.716740
\(293\) 3.37056e29i 0.841958i 0.907070 + 0.420979i \(0.138313\pi\)
−0.907070 + 0.420979i \(0.861687\pi\)
\(294\) 4.83609e29 + 3.61076e29i 1.15965 + 0.865827i
\(295\) 1.27327e29 0.293127
\(296\) 6.49837e28i 0.143649i
\(297\) −2.07687e29 + 5.63319e29i −0.440892 + 1.19585i
\(298\) −2.65701e29 −0.541749
\(299\) 2.04557e28i 0.0400646i
\(300\) 1.46751e29 1.96551e29i 0.276137 0.369845i
\(301\) 5.88716e29 1.06441
\(302\) 5.39247e29i 0.936923i
\(303\) −7.93669e29 5.92576e29i −1.32534 0.989538i
\(304\) −2.14825e28 −0.0344828
\(305\) 1.30134e29i 0.200814i
\(306\) 1.53425e29 + 5.17694e29i 0.227636 + 0.768097i
\(307\) −6.58441e29 −0.939412 −0.469706 0.882823i \(-0.655640\pi\)
−0.469706 + 0.882823i \(0.655640\pi\)
\(308\) 8.10670e29i 1.11233i
\(309\) −3.90572e29 + 5.23115e29i −0.515466 + 0.690391i
\(310\) −2.12712e29 −0.270054
\(311\) 1.25703e30i 1.53540i −0.640810 0.767700i \(-0.721401\pi\)
0.640810 0.767700i \(-0.278599\pi\)
\(312\) −2.76268e29 2.06270e29i −0.324695 0.242427i
\(313\) −4.01699e29 −0.454328 −0.227164 0.973857i \(-0.572945\pi\)
−0.227164 + 0.973857i \(0.572945\pi\)
\(314\) 4.60291e29i 0.501045i
\(315\) 4.42862e29 1.31248e29i 0.464025 0.137520i
\(316\) −4.30478e28 −0.0434216
\(317\) 4.83365e29i 0.469422i −0.972065 0.234711i \(-0.924586\pi\)
0.972065 0.234711i \(-0.0754144\pi\)
\(318\) 8.12755e28 1.08857e29i 0.0760036 0.101796i
\(319\) 1.60078e30 1.44160
\(320\) 3.99594e28i 0.0346592i
\(321\) 1.51368e30 + 1.13016e30i 1.26466 + 0.944230i
\(322\) 5.36045e28 0.0431450
\(323\) 2.01514e29i 0.156270i
\(324\) 5.61079e29 3.64588e29i 0.419260 0.272435i
\(325\) 1.46922e30 1.05800
\(326\) 1.40994e30i 0.978562i
\(327\) −6.94845e28 + 9.30644e28i −0.0464852 + 0.0622602i
\(328\) −7.55063e29 −0.486964
\(329\) 9.17814e29i 0.570694i
\(330\) 3.33969e29 + 2.49351e29i 0.200234 + 0.149501i
\(331\) −1.33834e29 −0.0773802 −0.0386901 0.999251i \(-0.512319\pi\)
−0.0386901 + 0.999251i \(0.512319\pi\)
\(332\) 9.64375e27i 0.00537761i
\(333\) −2.14646e29 7.24267e29i −0.115449 0.389554i
\(334\) −1.82178e30 −0.945230
\(335\) 5.39001e29i 0.269806i
\(336\) 5.40532e29 7.23964e29i 0.261066 0.349660i
\(337\) 2.49698e26 0.000116374 5.81870e−5 1.00000i \(-0.499981\pi\)
5.81870e−5 1.00000i \(0.499981\pi\)
\(338\) 4.92988e29i 0.221736i
\(339\) −2.41162e30 1.80059e30i −1.04692 0.781660i
\(340\) 3.74833e29 0.157069
\(341\) 4.33973e30i 1.75554i
\(342\) 2.39431e29 7.09584e28i 0.0935118 0.0277134i
\(343\) −4.84457e30 −1.82694
\(344\) 5.92040e29i 0.215600i
\(345\) 1.64880e28 2.20833e28i 0.00579880 0.00776665i
\(346\) −5.36241e29 −0.182157
\(347\) 1.01133e30i 0.331847i −0.986139 0.165923i \(-0.946940\pi\)
0.986139 0.165923i \(-0.0530605\pi\)
\(348\) −1.42957e30 1.06736e30i −0.453162 0.338344i
\(349\) 4.79831e30 1.46955 0.734773 0.678314i \(-0.237289\pi\)
0.734773 + 0.678314i \(0.237289\pi\)
\(350\) 3.85010e30i 1.13935i
\(351\) 3.76044e30 + 1.38642e30i 1.07536 + 0.396469i
\(352\) 8.15247e29 0.225308
\(353\) 4.36735e29i 0.116660i −0.998297 0.0583300i \(-0.981422\pi\)
0.998297 0.0583300i \(-0.0185776\pi\)
\(354\) −1.73208e30 + 2.31987e30i −0.447228 + 0.598997i
\(355\) −1.38316e30 −0.345250
\(356\) 3.10258e30i 0.748727i
\(357\) −6.79104e30 5.07038e30i −1.58459 1.18310i
\(358\) 4.27796e30 0.965250
\(359\) 1.36292e30i 0.297397i 0.988883 + 0.148699i \(0.0475084\pi\)
−0.988883 + 0.148699i \(0.952492\pi\)
\(360\) −1.31989e29 4.45362e29i −0.0278553 0.0939904i
\(361\) −4.80556e30 −0.980975
\(362\) 1.92739e30i 0.380597i
\(363\) 1.95556e30 2.61918e30i 0.373586 0.500364i
\(364\) 5.41163e30 1.00026
\(365\) 2.22236e30i 0.397467i
\(366\) −2.37102e30 1.77027e30i −0.410358 0.306385i
\(367\) 1.44710e30 0.242384 0.121192 0.992629i \(-0.461328\pi\)
0.121192 + 0.992629i \(0.461328\pi\)
\(368\) 5.39071e28i 0.00873922i
\(369\) 8.41546e30 2.49403e30i 1.32057 0.391368i
\(370\) −5.24401e29 −0.0796604
\(371\) 2.13232e30i 0.313592i
\(372\) 2.89361e30 3.87556e30i 0.412026 0.551848i
\(373\) 2.12953e30 0.293614 0.146807 0.989165i \(-0.453100\pi\)
0.146807 + 0.989165i \(0.453100\pi\)
\(374\) 7.64731e30i 1.02106i
\(375\) 3.30433e30 + 2.46710e30i 0.427275 + 0.319016i
\(376\) 9.22996e29 0.115597
\(377\) 1.06860e31i 1.29634i
\(378\) −3.63312e30 + 9.85426e30i −0.426951 + 1.15804i
\(379\) −4.51756e30 −0.514320 −0.257160 0.966369i \(-0.582787\pi\)
−0.257160 + 0.966369i \(0.582787\pi\)
\(380\) 1.73358e29i 0.0191224i
\(381\) −4.19284e30 + 5.61570e30i −0.448135 + 0.600211i
\(382\) 8.00689e30 0.829284
\(383\) 5.00583e30i 0.502448i −0.967929 0.251224i \(-0.919167\pi\)
0.967929 0.251224i \(-0.0808330\pi\)
\(384\) −7.28051e29 5.43584e29i −0.0708251 0.0528801i
\(385\) −6.54189e30 −0.616843
\(386\) 2.04681e30i 0.187082i
\(387\) 1.95555e30 + 6.59850e30i 0.173276 + 0.584674i
\(388\) −9.29620e30 −0.798592
\(389\) 7.79334e30i 0.649125i 0.945864 + 0.324563i \(0.105217\pi\)
−0.945864 + 0.324563i \(0.894783\pi\)
\(390\) 1.66454e30 2.22941e30i 0.134437 0.180059i
\(391\) −5.05668e29 −0.0396045
\(392\) 9.52658e30i 0.723609i
\(393\) 1.16181e31 + 8.67443e30i 0.855906 + 0.639044i
\(394\) −1.36608e31 −0.976161
\(395\) 3.47384e29i 0.0240794i
\(396\) −9.08623e30 + 2.69282e30i −0.611001 + 0.181078i
\(397\) −1.68507e31 −1.09934 −0.549669 0.835383i \(-0.685246\pi\)
−0.549669 + 0.835383i \(0.685246\pi\)
\(398\) 6.53708e30i 0.413797i
\(399\) −2.34502e30 + 3.14082e30i −0.144036 + 0.192916i
\(400\) 3.87184e30 0.230780
\(401\) 1.09723e31i 0.634693i 0.948310 + 0.317346i \(0.102792\pi\)
−0.948310 + 0.317346i \(0.897208\pi\)
\(402\) −9.82049e30 7.33226e30i −0.551341 0.411647i
\(403\) 2.89699e31 1.57865
\(404\) 1.56344e31i 0.827000i
\(405\) 2.94213e30 + 4.52776e30i 0.151078 + 0.232500i
\(406\) 2.80028e31 1.39601
\(407\) 1.06988e31i 0.517846i
\(408\) −5.09901e30 + 6.82938e30i −0.239643 + 0.320966i
\(409\) −3.46568e31 −1.58164 −0.790822 0.612046i \(-0.790347\pi\)
−0.790822 + 0.612046i \(0.790347\pi\)
\(410\) 6.09316e30i 0.270045i
\(411\) 8.00717e30 + 5.97838e30i 0.344649 + 0.257325i
\(412\) −1.03048e31 −0.430797
\(413\) 4.54423e31i 1.84527i
\(414\) 1.78059e29 + 6.00815e29i 0.00702362 + 0.0236994i
\(415\) 7.78225e28 0.00298214
\(416\) 5.44219e30i 0.202607i
\(417\) −1.32364e30 + 1.77283e30i −0.0478783 + 0.0641260i
\(418\) −3.53684e30 −0.124308
\(419\) 4.32637e30i 0.147759i 0.997267 + 0.0738797i \(0.0235381\pi\)
−0.997267 + 0.0738797i \(0.976462\pi\)
\(420\) 5.84219e30 + 4.36195e30i 0.193903 + 0.144773i
\(421\) 5.35766e31 1.72818 0.864092 0.503334i \(-0.167893\pi\)
0.864092 + 0.503334i \(0.167893\pi\)
\(422\) 9.78683e30i 0.306826i
\(423\) −1.02871e31 + 3.04872e30i −0.313480 + 0.0929039i
\(424\) 2.14436e30 0.0635195
\(425\) 3.63193e31i 1.04585i
\(426\) 1.88158e31 2.52010e31i 0.526752 0.705508i
\(427\) 4.64443e31 1.26415
\(428\) 2.98178e31i 0.789134i
\(429\) −4.54842e31 3.39598e31i −1.17051 0.873932i
\(430\) 4.77760e30 0.119561
\(431\) 7.38282e31i 1.79678i 0.439197 + 0.898391i \(0.355263\pi\)
−0.439197 + 0.898391i \(0.644737\pi\)
\(432\) 9.90990e30 + 3.65364e30i 0.234566 + 0.0864809i
\(433\) 2.54475e30 0.0585856 0.0292928 0.999571i \(-0.490674\pi\)
0.0292928 + 0.999571i \(0.490674\pi\)
\(434\) 7.59158e31i 1.70003i
\(435\) 8.61327e30 1.15362e31i 0.187628 0.251300i
\(436\) −1.83327e30 −0.0388497
\(437\) 2.33869e29i 0.00482164i
\(438\) 4.04910e31 + 3.02317e31i 0.812212 + 0.606420i
\(439\) −6.51383e31 −1.27134 −0.635671 0.771960i \(-0.719276\pi\)
−0.635671 + 0.771960i \(0.719276\pi\)
\(440\) 6.57883e30i 0.124944i
\(441\) −3.14670e31 1.06177e32i −0.581557 1.96231i
\(442\) −5.10496e31 −0.918175
\(443\) 3.26967e31i 0.572347i −0.958178 0.286173i \(-0.907617\pi\)
0.958178 0.286173i \(-0.0923833\pi\)
\(444\) 7.13364e30 9.55447e30i 0.121539 0.162784i
\(445\) −2.50370e31 −0.415205
\(446\) 3.94859e31i 0.637417i
\(447\) 3.90657e31 + 2.91676e31i 0.613912 + 0.458364i
\(448\) 1.42613e31 0.218184
\(449\) 7.64915e31i 1.13935i 0.821870 + 0.569675i \(0.192931\pi\)
−0.821870 + 0.569675i \(0.807069\pi\)
\(450\) −4.31531e31 + 1.27890e31i −0.625838 + 0.185475i
\(451\) −1.24312e32 −1.75547
\(452\) 4.75064e31i 0.653267i
\(453\) −5.91963e31 + 7.92848e31i −0.792713 + 1.06172i
\(454\) −1.97536e31 −0.257618
\(455\) 4.36704e31i 0.554690i
\(456\) 3.15855e30 + 2.35826e30i 0.0390760 + 0.0291752i
\(457\) 5.89189e31 0.710003 0.355001 0.934866i \(-0.384480\pi\)
0.355001 + 0.934866i \(0.384480\pi\)
\(458\) 8.41201e31i 0.987448i
\(459\) 3.42724e31 9.29584e31i 0.391915 1.06301i
\(460\) 4.35016e29 0.00484631
\(461\) 4.35731e31i 0.472941i 0.971639 + 0.236470i \(0.0759907\pi\)
−0.971639 + 0.236470i \(0.924009\pi\)
\(462\) 8.89920e31 1.19192e32i 0.941125 1.26050i
\(463\) 1.14041e32 1.17514 0.587569 0.809174i \(-0.300085\pi\)
0.587569 + 0.809174i \(0.300085\pi\)
\(464\) 2.81609e31i 0.282769i
\(465\) 3.12748e31 + 2.33506e31i 0.306026 + 0.228488i
\(466\) −2.51756e31 −0.240076
\(467\) 2.25380e31i 0.209466i −0.994500 0.104733i \(-0.966601\pi\)
0.994500 0.104733i \(-0.0333988\pi\)
\(468\) 1.79760e31 + 6.06552e31i 0.162833 + 0.549437i
\(469\) 1.92367e32 1.69846
\(470\) 7.44833e30i 0.0641039i
\(471\) −5.05288e31 + 6.76760e31i −0.423924 + 0.567785i
\(472\) −4.56989e31 −0.373768
\(473\) 9.74722e31i 0.777225i
\(474\) 6.32927e30 + 4.72561e30i 0.0492055 + 0.0367382i
\(475\) −1.67975e31 −0.127327
\(476\) 1.33776e32i 0.988770i
\(477\) −2.38997e31 + 7.08298e30i −0.172255 + 0.0510499i
\(478\) −1.11965e32 −0.786951
\(479\) 8.30835e31i 0.569493i −0.958603 0.284747i \(-0.908090\pi\)
0.958603 0.284747i \(-0.0919095\pi\)
\(480\) 4.38658e30 5.87518e30i 0.0293245 0.0392759i
\(481\) 7.14197e31 0.465669
\(482\) 3.49310e31i 0.222150i
\(483\) −7.88140e30 5.88448e30i −0.0488920 0.0365042i
\(484\) 5.15950e31 0.312222
\(485\) 7.50178e31i 0.442857i
\(486\) −1.22518e32 7.98797e30i −0.705609 0.0460046i
\(487\) 2.38724e32 1.34137 0.670686 0.741741i \(-0.266000\pi\)
0.670686 + 0.741741i \(0.266000\pi\)
\(488\) 4.67066e31i 0.256059i
\(489\) −1.54777e32 + 2.07301e32i −0.827942 + 1.10891i
\(490\) −7.68769e31 −0.401276
\(491\) 1.30787e32i 0.666173i −0.942896 0.333087i \(-0.891910\pi\)
0.942896 0.333087i \(-0.108090\pi\)
\(492\) 1.11016e32 + 8.28877e31i 0.551829 + 0.412011i
\(493\) −2.64160e32 −1.28145
\(494\) 2.36102e31i 0.111783i
\(495\) −2.17304e31 7.33235e31i −0.100416 0.338829i
\(496\) 7.63444e31 0.344348
\(497\) 4.93645e32i 2.17339i
\(498\) −1.05865e30 + 1.41791e30i −0.00454989 + 0.00609392i
\(499\) −2.33308e32 −0.978868 −0.489434 0.872040i \(-0.662797\pi\)
−0.489434 + 0.872040i \(0.662797\pi\)
\(500\) 6.50916e31i 0.266615i
\(501\) 2.67854e32 + 1.99987e32i 1.07114 + 0.799741i
\(502\) 2.44215e32 0.953516
\(503\) 3.12030e32i 1.18954i −0.803895 0.594772i \(-0.797242\pi\)
0.803895 0.594772i \(-0.202758\pi\)
\(504\) −1.58948e32 + 4.71062e31i −0.591681 + 0.175352i
\(505\) 1.26166e32 0.458611
\(506\) 8.87516e30i 0.0315043i
\(507\) −5.41182e31 + 7.24834e31i −0.187606 + 0.251271i
\(508\) −1.10623e32 −0.374526
\(509\) 7.26199e31i 0.240128i 0.992766 + 0.120064i \(0.0383099\pi\)
−0.992766 + 0.120064i \(0.961690\pi\)
\(510\) −5.51113e31 4.11476e31i −0.177991 0.132893i
\(511\) −7.93151e32 −2.50210
\(512\) 1.43418e31i 0.0441942i
\(513\) −4.29927e31 1.58508e31i −0.129416 0.0477136i
\(514\) 1.68588e32 0.495756
\(515\) 8.31569e31i 0.238898i
\(516\) −6.49917e31 + 8.70469e31i −0.182415 + 0.244319i
\(517\) 1.51960e32 0.416719
\(518\) 1.87156e32i 0.501472i
\(519\) 7.88429e31 + 5.88663e31i 0.206421 + 0.154120i
\(520\) 4.39170e31 0.112355
\(521\) 6.64395e32i 1.66102i −0.557007 0.830508i \(-0.688050\pi\)
0.557007 0.830508i \(-0.311950\pi\)
\(522\) 9.30177e31 + 3.13864e32i 0.227258 + 0.766824i
\(523\) −5.25543e31 −0.125484 −0.0627420 0.998030i \(-0.519985\pi\)
−0.0627420 + 0.998030i \(0.519985\pi\)
\(524\) 2.28865e32i 0.534077i
\(525\) 4.22649e32 5.66076e32i 0.963980 1.29111i
\(526\) 3.87453e32 0.863755
\(527\) 7.16138e32i 1.56052i
\(528\) −1.19865e32 8.94945e31i −0.255320 0.190629i
\(529\) 4.79664e32 0.998778
\(530\) 1.73044e31i 0.0352246i
\(531\) 5.09332e32 1.50947e32i 1.01360 0.300393i
\(532\) −6.18707e31 −0.120378
\(533\) 8.29845e32i 1.57859i
\(534\) 3.40589e32 4.56169e32i 0.633484 0.848459i
\(535\) −2.40622e32 −0.437613
\(536\) 1.93453e32i 0.344031i
\(537\) −6.28983e32 4.69616e32i −1.09382 0.816680i
\(538\) −1.25069e32 −0.212698
\(539\) 1.56844e33i 2.60856i
\(540\) −2.94839e31 + 7.99703e31i −0.0479578 + 0.130078i
\(541\) −1.00798e32 −0.160356 −0.0801778 0.996781i \(-0.525549\pi\)
−0.0801778 + 0.996781i \(0.525549\pi\)
\(542\) 3.64515e31i 0.0567184i
\(543\) 2.11581e32 2.83381e32i 0.322016 0.431294i
\(544\) −1.34531e32 −0.200280
\(545\) 1.47940e31i 0.0215440i
\(546\) −7.95666e32 5.94067e32i −1.13349 0.846298i
\(547\) 2.11119e32 0.294225 0.147113 0.989120i \(-0.453002\pi\)
0.147113 + 0.989120i \(0.453002\pi\)
\(548\) 1.57733e32i 0.215058i
\(549\) 1.54275e32 + 5.20562e32i 0.205792 + 0.694391i
\(550\) 6.37452e32 0.831946
\(551\) 1.22172e32i 0.156010i
\(552\) −5.91771e30 + 7.92590e30i −0.00739408 + 0.00990330i
\(553\) −1.23980e32 −0.151583
\(554\) 2.65726e32i 0.317919i
\(555\) 7.71020e31 + 5.75666e31i 0.0902714 + 0.0673992i
\(556\) −3.49228e31 −0.0400140
\(557\) 1.33948e32i 0.150201i −0.997176 0.0751005i \(-0.976072\pi\)
0.997176 0.0751005i \(-0.0239278\pi\)
\(558\) −8.50887e32 + 2.52171e32i −0.933817 + 0.276749i
\(559\) −6.50676e32 −0.698913
\(560\) 1.15085e32i 0.120994i
\(561\) −8.39490e32 + 1.12437e33i −0.863896 + 1.15706i
\(562\) −6.40994e31 −0.0645681
\(563\) 6.33412e32i 0.624576i 0.949987 + 0.312288i \(0.101095\pi\)
−0.949987 + 0.312288i \(0.898905\pi\)
\(564\) −1.35707e32 1.01323e32i −0.130994 0.0978042i
\(565\) 3.83364e32 0.362268
\(566\) 9.45857e31i 0.0875040i
\(567\) 1.61593e33 1.05003e33i 1.46362 0.951055i
\(568\) 4.96432e32 0.440230
\(569\) 3.30678e32i 0.287116i 0.989642 + 0.143558i \(0.0458544\pi\)
−0.989642 + 0.143558i \(0.954146\pi\)
\(570\) −1.90306e31 + 2.54887e31i −0.0161791 + 0.0216695i
\(571\) −1.57897e33 −1.31444 −0.657218 0.753700i \(-0.728267\pi\)
−0.657218 + 0.753700i \(0.728267\pi\)
\(572\) 8.95990e32i 0.730383i
\(573\) −1.17724e33 8.78964e32i −0.939747 0.701642i
\(574\) −2.17462e33 −1.69997
\(575\) 4.21507e31i 0.0322694i
\(576\) 4.73721e31 + 1.59845e32i 0.0355184 + 0.119848i
\(577\) 2.68744e33 1.97346 0.986730 0.162371i \(-0.0519140\pi\)
0.986730 + 0.162371i \(0.0519140\pi\)
\(578\) 2.78804e32i 0.200523i
\(579\) −2.24691e32 + 3.00941e32i −0.158286 + 0.212001i
\(580\) 2.27251e32 0.156809
\(581\) 2.77745e31i 0.0187729i
\(582\) 1.36681e33 + 1.02050e33i 0.904966 + 0.675673i
\(583\) 3.53043e32 0.228984
\(584\) 7.97629e32i 0.506812i
\(585\) −4.89471e32 + 1.45061e32i −0.304689 + 0.0902986i
\(586\) 9.76218e32 0.595354
\(587\) 1.59247e33i 0.951510i −0.879578 0.475755i \(-0.842175\pi\)
0.879578 0.475755i \(-0.157825\pi\)
\(588\) 1.04579e33 1.40068e33i 0.612232 0.819996i
\(589\) −3.31210e32 −0.189985
\(590\) 3.68778e32i 0.207272i
\(591\) 2.00853e33 + 1.49963e33i 1.10619 + 0.825911i
\(592\) 1.88213e32 0.101575
\(593\) 2.89338e33i 1.53020i −0.643910 0.765102i \(-0.722689\pi\)
0.643910 0.765102i \(-0.277311\pi\)
\(594\) 1.63155e33 + 6.01527e32i 0.845594 + 0.311758i
\(595\) 1.07954e33 0.548320
\(596\) 7.69553e32i 0.383075i
\(597\) −7.17614e32 + 9.61139e32i −0.350105 + 0.468915i
\(598\) −5.92462e31 −0.0283300
\(599\) 1.27146e33i 0.595911i −0.954580 0.297955i \(-0.903695\pi\)
0.954580 0.297955i \(-0.0963047\pi\)
\(600\) −5.69272e32 4.25035e32i −0.261520 0.195258i
\(601\) −1.15108e33 −0.518337 −0.259169 0.965832i \(-0.583449\pi\)
−0.259169 + 0.965832i \(0.583449\pi\)
\(602\) 1.70510e33i 0.752649i
\(603\) 6.38990e32 + 2.15611e33i 0.276494 + 0.932959i
\(604\) −1.56183e33 −0.662505
\(605\) 4.16358e32i 0.173142i
\(606\) −1.71628e33 + 2.29871e33i −0.699709 + 0.937158i
\(607\) 4.18715e32 0.167361 0.0836805 0.996493i \(-0.473332\pi\)
0.0836805 + 0.996493i \(0.473332\pi\)
\(608\) 6.22200e31i 0.0243830i
\(609\) −4.11722e33 3.07404e33i −1.58196 1.18114i
\(610\) 3.76910e32 0.141997
\(611\) 1.01441e33i 0.374731i
\(612\) 1.49940e33 4.44367e32i 0.543127 0.160963i
\(613\) −3.03008e33 −1.07629 −0.538144 0.842853i \(-0.680874\pi\)
−0.538144 + 0.842853i \(0.680874\pi\)
\(614\) 1.90705e33i 0.664265i
\(615\) −6.68882e32 + 8.95870e32i −0.228480 + 0.306015i
\(616\) 2.34795e33 0.786540
\(617\) 3.78856e33i 1.24466i −0.782753 0.622332i \(-0.786185\pi\)
0.782753 0.622332i \(-0.213815\pi\)
\(618\) 1.51510e33 + 1.13122e33i 0.488180 + 0.364489i
\(619\) −2.01070e33 −0.635418 −0.317709 0.948188i \(-0.602913\pi\)
−0.317709 + 0.948188i \(0.602913\pi\)
\(620\) 6.16079e32i 0.190957i
\(621\) 3.97752e31 1.07884e32i 0.0120924 0.0327987i
\(622\) −3.64075e33 −1.08569
\(623\) 8.93559e33i 2.61377i
\(624\) −5.97421e32 + 8.00158e32i −0.171422 + 0.229594i
\(625\) 2.75431e33 0.775268
\(626\) 1.16345e33i 0.321258i
\(627\) 5.20017e32 + 3.88260e32i 0.140866 + 0.105175i
\(628\) −1.33314e33 −0.354292
\(629\) 1.76550e33i 0.460321i
\(630\) −3.80134e32 1.28266e33i −0.0972412 0.328115i
\(631\) 2.99733e33 0.752284 0.376142 0.926562i \(-0.377250\pi\)
0.376142 + 0.926562i \(0.377250\pi\)
\(632\) 1.24680e32i 0.0307037i
\(633\) −1.07436e33 + 1.43895e33i −0.259600 + 0.347696i
\(634\) −1.39997e33 −0.331932
\(635\) 8.92699e32i 0.207692i
\(636\) −3.15282e32 2.35399e32i −0.0719804 0.0537426i
\(637\) 1.04701e34 2.34573
\(638\) 4.63636e33i 1.01936i
\(639\) −5.53292e33 + 1.63975e33i −1.19383 + 0.353808i
\(640\) 1.15735e32 0.0245078
\(641\) 6.59215e33i 1.37003i 0.728528 + 0.685016i \(0.240205\pi\)
−0.728528 + 0.685016i \(0.759795\pi\)
\(642\) 3.27328e33 4.38408e33i 0.667672 0.894249i
\(643\) 1.70251e32 0.0340845 0.0170423 0.999855i \(-0.494575\pi\)
0.0170423 + 0.999855i \(0.494575\pi\)
\(644\) 1.55255e32i 0.0305081i
\(645\) −7.02445e32 5.24466e32i −0.135486 0.101158i
\(646\) 5.83646e32 0.110499
\(647\) 2.44965e33i 0.455253i −0.973749 0.227626i \(-0.926904\pi\)
0.973749 0.227626i \(-0.0730965\pi\)
\(648\) −1.05596e33 1.62506e33i −0.192640 0.296462i
\(649\) −7.52378e33 −1.34741
\(650\) 4.25531e33i 0.748120i
\(651\) 8.33373e33 1.11618e34i 1.43836 1.92647i
\(652\) −4.08361e33 −0.691948
\(653\) 1.61675e32i 0.0268958i −0.999910 0.0134479i \(-0.995719\pi\)
0.999910 0.0134479i \(-0.00428073\pi\)
\(654\) 2.69543e32 + 2.01249e32i 0.0440246 + 0.0328700i
\(655\) −1.84688e33 −0.296171
\(656\) 2.18690e33i 0.344336i
\(657\) −2.63463e33 8.88987e33i −0.407319 1.37439i
\(658\) 2.65827e33 0.403542
\(659\) 1.23809e34i 1.84556i 0.385333 + 0.922778i \(0.374087\pi\)
−0.385333 + 0.922778i \(0.625913\pi\)
\(660\) 7.22197e32 9.67277e32i 0.105713 0.141587i
\(661\) 1.28758e34 1.85079 0.925395 0.379003i \(-0.123733\pi\)
0.925395 + 0.379003i \(0.123733\pi\)
\(662\) 3.87624e32i 0.0547160i
\(663\) 7.50577e33 + 5.60402e33i 1.04048 + 0.776850i
\(664\) −2.79313e31 −0.00380254
\(665\) 4.99280e32i 0.0667551i
\(666\) −2.09770e33 + 6.21681e32i −0.275456 + 0.0816351i
\(667\) −3.06573e32 −0.0395388
\(668\) 5.27643e33i 0.668379i
\(669\) −4.33460e33 + 5.80556e33i −0.539306 + 0.722322i
\(670\) 1.56111e33 0.190782
\(671\) 7.68967e33i 0.923076i
\(672\) −2.09682e33 1.56555e33i −0.247247 0.184601i
\(673\) −4.97150e33 −0.575847 −0.287923 0.957653i \(-0.592965\pi\)
−0.287923 + 0.957653i \(0.592965\pi\)
\(674\) 7.23202e29i 8.22888e-5i
\(675\) 7.74868e33 + 2.85682e33i 0.866128 + 0.319329i
\(676\) −1.42784e33 −0.156791
\(677\) 3.16889e33i 0.341856i 0.985283 + 0.170928i \(0.0546766\pi\)
−0.985283 + 0.170928i \(0.945323\pi\)
\(678\) −5.21506e33 + 6.98481e33i −0.552717 + 0.740284i
\(679\) −2.67735e34 −2.78784
\(680\) 1.08563e33i 0.111065i
\(681\) 2.90435e33 + 2.16847e33i 0.291933 + 0.217966i
\(682\) 1.25692e34 1.24135
\(683\) 6.57986e33i 0.638510i −0.947669 0.319255i \(-0.896567\pi\)
0.947669 0.319255i \(-0.103433\pi\)
\(684\) −2.05517e32 6.93465e32i −0.0195964 0.0661229i
\(685\) −1.27286e33 −0.119260
\(686\) 1.40314e34i 1.29184i
\(687\) 9.23436e33 1.23681e34i 0.835461 1.11898i
\(688\) −1.71473e33 −0.152453
\(689\) 2.35674e33i 0.205911i
\(690\) −6.39599e31 4.77543e31i −0.00549185 0.00410037i
\(691\) −2.28870e34 −1.93131 −0.965657 0.259819i \(-0.916337\pi\)
−0.965657 + 0.259819i \(0.916337\pi\)
\(692\) 1.55312e33i 0.128805i
\(693\) −2.61688e34 + 7.75546e33i −2.13297 + 0.632133i
\(694\) −2.92911e33 −0.234651
\(695\) 2.81818e32i 0.0221897i
\(696\) −3.09139e33 + 4.14047e33i −0.239245 + 0.320434i
\(697\) 2.05139e34 1.56046
\(698\) 1.38974e34i 1.03913i
\(699\) 3.70154e33 + 2.76368e33i 0.272055 + 0.203124i
\(700\) 1.11511e34 0.805640
\(701\) 2.42814e34i 1.72448i 0.506504 + 0.862238i \(0.330938\pi\)
−0.506504 + 0.862238i \(0.669062\pi\)
\(702\) 4.01550e33 1.08914e34i 0.280346 0.760393i
\(703\) −8.16535e32 −0.0560417
\(704\) 2.36121e33i 0.159317i
\(705\) 8.17647e32 1.09512e33i 0.0542371 0.0726427i
\(706\) −1.26492e33 −0.0824910
\(707\) 4.50279e34i 2.88701i
\(708\) 6.71906e33 + 5.01664e33i 0.423555 + 0.316238i
\(709\) 3.13216e34 1.94129 0.970643 0.240526i \(-0.0773201\pi\)
0.970643 + 0.240526i \(0.0773201\pi\)
\(710\) 4.00607e33i 0.244129i
\(711\) −4.11827e32 1.38960e33i −0.0246763 0.0832636i
\(712\) 8.98604e33 0.529430
\(713\) 8.31121e32i 0.0481493i
\(714\) −1.46854e34 + 1.96689e34i −0.836579 + 1.12048i
\(715\) 7.23040e33 0.405033
\(716\) 1.23903e34i 0.682535i
\(717\) 1.64621e34 + 1.22911e34i 0.891775 + 0.665825i
\(718\) 3.94744e33 0.210292
\(719\) 6.69265e33i 0.350632i −0.984512 0.175316i \(-0.943905\pi\)
0.984512 0.175316i \(-0.0560947\pi\)
\(720\) −1.28991e33 + 3.82281e32i −0.0664612 + 0.0196966i
\(721\) −2.96783e34 −1.50389
\(722\) 1.39184e34i 0.693654i
\(723\) −3.83458e33 + 5.13586e33i −0.187957 + 0.251741i
\(724\) 5.58231e33 0.269123
\(725\) 2.20194e34i 1.04412i
\(726\) −7.58596e33 5.66389e33i −0.353811 0.264165i
\(727\) −3.17481e32 −0.0145648 −0.00728241 0.999973i \(-0.502318\pi\)
−0.00728241 + 0.999973i \(0.502318\pi\)
\(728\) 1.56738e34i 0.707289i
\(729\) 1.71368e34 + 1.46240e34i 0.760674 + 0.649135i
\(730\) −6.43665e33 −0.281051
\(731\) 1.60848e34i 0.690886i
\(732\) −5.12726e33 + 6.86721e33i −0.216647 + 0.290167i
\(733\) 9.81929e33 0.408162 0.204081 0.978954i \(-0.434579\pi\)
0.204081 + 0.978954i \(0.434579\pi\)
\(734\) 4.19123e33i 0.171392i
\(735\) 1.13031e34 + 8.43923e33i 0.454727 + 0.339512i
\(736\) −1.56132e32 −0.00617956
\(737\) 3.18497e34i 1.24021i
\(738\) −7.22348e33 2.43738e34i −0.276739 0.933784i
\(739\) −9.87359e33 −0.372171 −0.186085 0.982534i \(-0.559580\pi\)
−0.186085 + 0.982534i \(0.559580\pi\)
\(740\) 1.51883e33i 0.0563284i
\(741\) 2.59183e33 3.47138e33i 0.0945775 0.126673i
\(742\) 6.17585e33 0.221743
\(743\) 4.57424e34i 1.61604i 0.589153 + 0.808022i \(0.299462\pi\)
−0.589153 + 0.808022i \(0.700538\pi\)
\(744\) −1.12248e34 8.38078e33i −0.390216 0.291346i
\(745\) −6.21009e33 −0.212433
\(746\) 6.16777e33i 0.207617i
\(747\) 3.11305e32 9.22592e31i 0.0103119 0.00305606i
\(748\) −2.21490e34 −0.721995
\(749\) 8.58768e34i 2.75483i
\(750\) 7.14549e33 9.57035e33i 0.225578 0.302129i
\(751\) −2.95235e34 −0.917253 −0.458626 0.888629i \(-0.651658\pi\)
−0.458626 + 0.888629i \(0.651658\pi\)
\(752\) 2.67328e33i 0.0817392i
\(753\) −3.59067e34 2.68089e34i −1.08053 0.806752i
\(754\) −3.09500e34 −0.916653
\(755\) 1.26035e34i 0.367391i
\(756\) 2.85410e34 + 1.05226e34i 0.818856 + 0.301900i
\(757\) 2.19612e34 0.620163 0.310082 0.950710i \(-0.399644\pi\)
0.310082 + 0.950710i \(0.399644\pi\)