Properties

Label 16.12.e.a.5.1
Level 16
Weight 12
Character 16.5
Analytic conductor 12.293
Analytic rank 0
Dimension 42
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 16.e (of order \(4\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(12.293490889\)
Analytic rank: \(0\)
Dimension: \(42\)
Relative dimension: \(21\) over \(\Q(i)\)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 5.1
Character \(\chi\) = 16.5
Dual form 16.12.e.a.13.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-45.0143 - 4.65973i) q^{2} +(13.6026 - 13.6026i) q^{3} +(2004.57 + 419.509i) q^{4} +(-3501.81 - 3501.81i) q^{5} +(-675.697 + 548.928i) q^{6} +37649.1i q^{7} +(-88279.7 - 28224.7i) q^{8} +176777. i q^{9} +O(q^{10})\) \(q+(-45.0143 - 4.65973i) q^{2} +(13.6026 - 13.6026i) q^{3} +(2004.57 + 419.509i) q^{4} +(-3501.81 - 3501.81i) q^{5} +(-675.697 + 548.928i) q^{6} +37649.1i q^{7} +(-88279.7 - 28224.7i) q^{8} +176777. i q^{9} +(141314. + 173949. i) q^{10} +(-283274. - 283274. i) q^{11} +(32973.9 - 21561.0i) q^{12} +(1.70921e6 - 1.70921e6i) q^{13} +(175435. - 1.69475e6i) q^{14} -95267.6 q^{15} +(3.84233e6 + 1.68187e6i) q^{16} +1.57559e6 q^{17} +(823733. - 7.95749e6i) q^{18} +(1.25182e7 - 1.25182e7i) q^{19} +(-5.55059e6 - 8.48867e6i) q^{20} +(512127. + 512127. i) q^{21} +(1.14314e7 + 1.40714e7i) q^{22} +6.83457e6i q^{23} +(-1.58477e6 + 816906. i) q^{24} -2.43028e7i q^{25} +(-8.49036e7 + 6.89746e7i) q^{26} +(4.81430e6 + 4.81430e6i) q^{27} +(-1.57942e7 + 7.54705e7i) q^{28} +(5.00021e7 - 5.00021e7i) q^{29} +(4.28840e6 + 443921. i) q^{30} +7.19392e7 q^{31} +(-1.65123e8 - 9.36126e7i) q^{32} -7.70654e6 q^{33} +(-7.09241e7 - 7.34183e6i) q^{34} +(1.31840e8 - 1.31840e8i) q^{35} +(-7.41595e7 + 3.54362e8i) q^{36} +(9.81694e7 + 9.81694e7i) q^{37} +(-6.21828e8 + 5.05165e8i) q^{38} -4.64996e7i q^{39} +(2.10301e8 + 4.07976e8i) q^{40} -7.24665e8i q^{41} +(-2.06667e7 - 2.54394e7i) q^{42} +(1.93444e8 + 1.93444e8i) q^{43} +(-4.49008e8 - 6.86679e8i) q^{44} +(6.19039e8 - 6.19039e8i) q^{45} +(3.18473e7 - 3.07653e8i) q^{46} +1.39935e9 q^{47} +(7.51437e7 - 2.93879e7i) q^{48} +5.59869e8 q^{49} +(-1.13245e8 + 1.09397e9i) q^{50} +(2.14322e7 - 2.14322e7i) q^{51} +(4.14328e9 - 2.70922e9i) q^{52} +(-3.32394e9 - 3.32394e9i) q^{53} +(-1.94279e8 - 2.39145e8i) q^{54} +1.98394e9i q^{55} +(1.06263e9 - 3.32365e9i) q^{56} -3.40560e8i q^{57} +(-2.48380e9 + 2.01781e9i) q^{58} +(5.46840e9 + 5.46840e9i) q^{59} +(-1.90971e8 - 3.99656e7i) q^{60} +(-4.88510e9 + 4.88510e9i) q^{61} +(-3.23829e9 - 3.35217e8i) q^{62} -6.65550e9 q^{63} +(6.99667e9 + 4.98333e9i) q^{64} -1.19707e10 q^{65} +(3.46904e8 + 3.59104e7i) q^{66} +(-7.47892e9 + 7.47892e9i) q^{67} +(3.15839e9 + 6.60975e8i) q^{68} +(9.29681e7 + 9.29681e7i) q^{69} +(-6.54903e9 + 5.32035e9i) q^{70} +2.58697e10i q^{71} +(4.98947e9 - 1.56058e10i) q^{72} -1.88841e10i q^{73} +(-3.96158e9 - 4.87647e9i) q^{74} +(-3.30582e8 - 3.30582e8i) q^{75} +(3.03451e10 - 1.98421e10i) q^{76} +(1.06650e10 - 1.06650e10i) q^{77} +(-2.16676e8 + 2.09315e9i) q^{78} +3.09391e10 q^{79} +(-7.56550e9 - 1.93447e10i) q^{80} -3.11845e10 q^{81} +(-3.37675e9 + 3.26203e10i) q^{82} +(2.96846e10 - 2.96846e10i) q^{83} +(8.11755e8 + 1.24144e9i) q^{84} +(-5.51742e9 - 5.51742e9i) q^{85} +(-7.80635e9 - 9.60915e9i) q^{86} -1.36032e9i q^{87} +(1.70120e10 + 3.30026e10i) q^{88} -6.42083e10i q^{89} +(-3.07502e10 + 2.49810e10i) q^{90} +(6.43504e10 + 6.43504e10i) q^{91} +(-2.86716e9 + 1.37004e10i) q^{92} +(9.78562e8 - 9.78562e8i) q^{93} +(-6.29908e10 - 6.52060e9i) q^{94} -8.76724e10 q^{95} +(-3.51948e9 + 9.72725e8i) q^{96} +8.87261e10 q^{97} +(-2.52021e10 - 2.60884e9i) q^{98} +(5.00763e10 - 5.00763e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42q - 2q^{2} - 2q^{3} + 3080q^{4} - 2q^{5} + 30352q^{6} + 74836q^{8} + O(q^{10}) \) \( 42q - 2q^{2} - 2q^{3} + 3080q^{4} - 2q^{5} + 30352q^{6} + 74836q^{8} - 988948q^{10} - 540846q^{11} + 2300260q^{12} - 2q^{13} - 1829956q^{14} - 6075004q^{15} - 3721448q^{16} - 4q^{17} - 32219106q^{18} - 11291290q^{19} + 68655164q^{20} + 354292q^{21} - 85011388q^{22} - 66180944q^{24} + 305685384q^{26} - 66463304q^{27} - 322075880q^{28} + 77673206q^{29} + 290643636q^{30} + 343549808q^{31} + 404698568q^{32} - 4q^{33} - 882461836q^{34} - 434731684q^{35} + 1854387628q^{36} - 522762058q^{37} - 1276252832q^{38} - 483241016q^{40} + 2372079160q^{42} + 3824193658q^{43} - 2657283740q^{44} + 97301954q^{45} - 1032658964q^{46} - 4586900144q^{47} - 1058870552q^{48} - 8474257474q^{49} + 6515930886q^{50} + 7074245796q^{51} - 13915491564q^{52} - 2100608058q^{53} + 4385621536q^{54} + 12910845976q^{56} - 21491153128q^{58} + 955824746q^{59} + 25615752768q^{60} + 2150827022q^{61} - 15814519760q^{62} + 27758037828q^{63} + 9674332160q^{64} - 1884965292q^{65} + 10932459412q^{66} - 3186519018q^{67} + 13817664656q^{68} - 16193060732q^{69} - 27206453120q^{70} - 20773133628q^{72} + 14141420908q^{74} + 28890034486q^{75} - 11786004940q^{76} - 22711870540q^{77} + 37031200508q^{78} + 48011833792q^{79} - 8952586328q^{80} - 90656394430q^{81} - 81555388352q^{82} + 55713221118q^{83} + 61178517160q^{84} - 84575506252q^{85} + 10047297860q^{86} - 162855622152q^{88} + 160133627736q^{90} - 147369662716q^{91} - 169766721928q^{92} - 69689773328q^{93} + 160320530128q^{94} + 375702304500q^{95} + 230764310192q^{96} - 4q^{97} - 108887063494q^{98} - 286271331106q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(15\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −45.0143 4.65973i −0.994685 0.102966i
\(3\) 13.6026 13.6026i 0.0323189 0.0323189i −0.690763 0.723082i \(-0.742725\pi\)
0.723082 + 0.690763i \(0.242725\pi\)
\(4\) 2004.57 + 419.509i 0.978796 + 0.204838i
\(5\) −3501.81 3501.81i −0.501138 0.501138i 0.410653 0.911791i \(-0.365301\pi\)
−0.911791 + 0.410653i \(0.865301\pi\)
\(6\) −675.697 + 548.928i −0.0354748 + 0.0288193i
\(7\) 37649.1i 0.846673i 0.905972 + 0.423337i \(0.139141\pi\)
−0.905972 + 0.423337i \(0.860859\pi\)
\(8\) −88279.7 28224.7i −0.952502 0.304533i
\(9\) 176777.i 0.997911i
\(10\) 141314. + 173949.i 0.446874 + 0.550075i
\(11\) −283274. 283274.i −0.530331 0.530331i 0.390340 0.920671i \(-0.372357\pi\)
−0.920671 + 0.390340i \(0.872357\pi\)
\(12\) 32973.9 21561.0i 0.0382537 0.0250134i
\(13\) 1.70921e6 1.70921e6i 1.27676 1.27676i 0.334284 0.942472i \(-0.391506\pi\)
0.942472 0.334284i \(-0.108494\pi\)
\(14\) 175435. 1.69475e6i 0.0871790 0.842173i
\(15\) −95267.6 −0.0323924
\(16\) 3.84233e6 + 1.68187e6i 0.916082 + 0.400990i
\(17\) 1.57559e6 0.269138 0.134569 0.990904i \(-0.457035\pi\)
0.134569 + 0.990904i \(0.457035\pi\)
\(18\) 823733. 7.95749e6i 0.102751 0.992607i
\(19\) 1.25182e7 1.25182e7i 1.15983 1.15983i 0.175323 0.984511i \(-0.443903\pi\)
0.984511 0.175323i \(-0.0560971\pi\)
\(20\) −5.55059e6 8.48867e6i −0.387859 0.593164i
\(21\) 512127. + 512127.i 0.0273635 + 0.0273635i
\(22\) 1.14314e7 + 1.40714e7i 0.472906 + 0.582118i
\(23\) 6.83457e6i 0.221416i 0.993853 + 0.110708i \(0.0353118\pi\)
−0.993853 + 0.110708i \(0.964688\pi\)
\(24\) −1.58477e6 + 816906.i −0.0406259 + 0.0209416i
\(25\) 2.43028e7i 0.497721i
\(26\) −8.49036e7 + 6.89746e7i −1.40143 + 1.13851i
\(27\) 4.81430e6 + 4.81430e6i 0.0645702 + 0.0645702i
\(28\) −1.57942e7 + 7.54705e7i −0.173431 + 0.828720i
\(29\) 5.00021e7 5.00021e7i 0.452688 0.452688i −0.443558 0.896246i \(-0.646284\pi\)
0.896246 + 0.443558i \(0.146284\pi\)
\(30\) 4.28840e6 + 443921.i 0.0322202 + 0.00333533i
\(31\) 7.19392e7 0.451311 0.225656 0.974207i \(-0.427548\pi\)
0.225656 + 0.974207i \(0.427548\pi\)
\(32\) −1.65123e8 9.36126e7i −0.869925 0.493184i
\(33\) −7.70654e6 −0.0342794
\(34\) −7.09241e7 7.34183e6i −0.267707 0.0277122i
\(35\) 1.31840e8 1.31840e8i 0.424300 0.424300i
\(36\) −7.41595e7 + 3.54362e8i −0.204411 + 0.976751i
\(37\) 9.81694e7 + 9.81694e7i 0.232738 + 0.232738i 0.813834 0.581097i \(-0.197376\pi\)
−0.581097 + 0.813834i \(0.697376\pi\)
\(38\) −6.21828e8 + 5.05165e8i −1.27309 + 1.03425i
\(39\) 4.64996e7i 0.0825266i
\(40\) 2.10301e8 + 4.07976e8i 0.324722 + 0.629948i
\(41\) 7.24665e8i 0.976846i −0.872607 0.488423i \(-0.837572\pi\)
0.872607 0.488423i \(-0.162428\pi\)
\(42\) −2.06667e7 2.54394e7i −0.0244005 0.0300356i
\(43\) 1.93444e8 + 1.93444e8i 0.200668 + 0.200668i 0.800286 0.599618i \(-0.204681\pi\)
−0.599618 + 0.800286i \(0.704681\pi\)
\(44\) −4.49008e8 6.86679e8i −0.410453 0.627718i
\(45\) 6.19039e8 6.19039e8i 0.500091 0.500091i
\(46\) 3.18473e7 3.07653e8i 0.0227984 0.220239i
\(47\) 1.39935e9 0.889997 0.444999 0.895531i \(-0.353204\pi\)
0.444999 + 0.895531i \(0.353204\pi\)
\(48\) 7.51437e7 2.93879e7i 0.0425663 0.0166472i
\(49\) 5.59869e8 0.283144
\(50\) −1.13245e8 + 1.09397e9i −0.0512486 + 0.495076i
\(51\) 2.14322e7 2.14322e7i 0.00869822 0.00869822i
\(52\) 4.14328e9 2.70922e9i 1.51121 0.988155i
\(53\) −3.32394e9 3.32394e9i −1.09178 1.09178i −0.995338 0.0964437i \(-0.969253\pi\)
−0.0964437 0.995338i \(-0.530747\pi\)
\(54\) −1.94279e8 2.39145e8i −0.0575784 0.0708756i
\(55\) 1.98394e9i 0.531538i
\(56\) 1.06263e9 3.32365e9i 0.257840 0.806458i
\(57\) 3.40560e8i 0.0749690i
\(58\) −2.48380e9 + 2.01781e9i −0.496894 + 0.403670i
\(59\) 5.46840e9 + 5.46840e9i 0.995805 + 0.995805i 0.999991 0.00418651i \(-0.00133261\pi\)
−0.00418651 + 0.999991i \(0.501333\pi\)
\(60\) −1.90971e8 3.99656e7i −0.0317056 0.00663521i
\(61\) −4.88510e9 + 4.88510e9i −0.740558 + 0.740558i −0.972685 0.232127i \(-0.925431\pi\)
0.232127 + 0.972685i \(0.425431\pi\)
\(62\) −3.23829e9 3.35217e8i −0.448912 0.0464699i
\(63\) −6.65550e9 −0.844905
\(64\) 6.99667e9 + 4.98333e9i 0.814520 + 0.580136i
\(65\) −1.19707e10 −1.27966
\(66\) 3.46904e8 + 3.59104e7i 0.0340972 + 0.00352963i
\(67\) −7.47892e9 + 7.47892e9i −0.676749 + 0.676749i −0.959263 0.282514i \(-0.908832\pi\)
0.282514 + 0.959263i \(0.408832\pi\)
\(68\) 3.15839e9 + 6.60975e8i 0.263431 + 0.0551297i
\(69\) 9.29681e7 + 9.29681e7i 0.00715590 + 0.00715590i
\(70\) −6.54903e9 + 5.32035e9i −0.465734 + 0.378356i
\(71\) 2.58697e10i 1.70165i 0.525446 + 0.850827i \(0.323898\pi\)
−0.525446 + 0.850827i \(0.676102\pi\)
\(72\) 4.98947e9 1.56058e10i 0.303897 0.950512i
\(73\) 1.88841e10i 1.06615i −0.846067 0.533077i \(-0.821036\pi\)
0.846067 0.533077i \(-0.178964\pi\)
\(74\) −3.96158e9 4.87647e9i −0.207536 0.255465i
\(75\) −3.30582e8 3.30582e8i −0.0160858 0.0160858i
\(76\) 3.03451e10 1.98421e10i 1.37282 0.897662i
\(77\) 1.06650e10 1.06650e10i 0.449017 0.449017i
\(78\) −2.16676e8 + 2.09315e9i −0.00849748 + 0.0820880i
\(79\) 3.09391e10 1.13125 0.565626 0.824662i \(-0.308635\pi\)
0.565626 + 0.824662i \(0.308635\pi\)
\(80\) −7.56550e9 1.93447e10i −0.258132 0.660035i
\(81\) −3.11845e10 −0.993737
\(82\) −3.37675e9 + 3.26203e10i −0.100582 + 0.971654i
\(83\) 2.96846e10 2.96846e10i 0.827183 0.827183i −0.159943 0.987126i \(-0.551131\pi\)
0.987126 + 0.159943i \(0.0511312\pi\)
\(84\) 8.11755e8 + 1.24144e9i 0.0211782 + 0.0323884i
\(85\) −5.51742e9 5.51742e9i −0.134875 0.134875i
\(86\) −7.80635e9 9.60915e9i −0.178940 0.220264i
\(87\) 1.36032e9i 0.0292607i
\(88\) 1.70120e10 + 3.30026e10i 0.343638 + 0.666644i
\(89\) 6.42083e10i 1.21884i −0.792848 0.609419i \(-0.791403\pi\)
0.792848 0.609419i \(-0.208597\pi\)
\(90\) −3.07502e10 + 2.49810e10i −0.548926 + 0.445940i
\(91\) 6.43504e10 + 6.43504e10i 1.08100 + 1.08100i
\(92\) −2.86716e9 + 1.37004e10i −0.0453544 + 0.216721i
\(93\) 9.78562e8 9.78562e8i 0.0145859 0.0145859i
\(94\) −6.29908e10 6.52060e9i −0.885267 0.0916399i
\(95\) −8.76724e10 −1.16247
\(96\) −3.51948e9 + 9.72725e8i −0.0440541 + 0.0121758i
\(97\) 8.87261e10 1.04908 0.524538 0.851387i \(-0.324238\pi\)
0.524538 + 0.851387i \(0.324238\pi\)
\(98\) −2.52021e10 2.60884e9i −0.281640 0.0291544i
\(99\) 5.00763e10 5.00763e10i 0.529223 0.529223i
\(100\) 1.01952e10 4.87168e10i 0.101952 0.487168i
\(101\) 2.42328e10 + 2.42328e10i 0.229422 + 0.229422i 0.812451 0.583029i \(-0.198133\pi\)
−0.583029 + 0.812451i \(0.698133\pi\)
\(102\) −1.06462e9 + 8.64886e8i −0.00954761 + 0.00775636i
\(103\) 2.02400e9i 0.0172031i −0.999963 0.00860155i \(-0.997262\pi\)
0.999963 0.00860155i \(-0.00273799\pi\)
\(104\) −1.99131e11 + 1.02647e11i −1.60493 + 0.827299i
\(105\) 3.58674e9i 0.0274258i
\(106\) 1.34136e11 + 1.65114e11i 0.973562 + 1.19840i
\(107\) −8.81978e10 8.81978e10i −0.607921 0.607921i 0.334482 0.942402i \(-0.391439\pi\)
−0.942402 + 0.334482i \(0.891439\pi\)
\(108\) 7.63097e9 + 1.16703e10i 0.0499746 + 0.0764275i
\(109\) −1.43460e10 + 1.43460e10i −0.0893067 + 0.0893067i −0.750349 0.661042i \(-0.770114\pi\)
0.661042 + 0.750349i \(0.270114\pi\)
\(110\) 9.24464e9 8.93058e10i 0.0547306 0.528713i
\(111\) 2.67072e9 0.0150436
\(112\) −6.33211e10 + 1.44660e11i −0.339507 + 0.775622i
\(113\) −2.02263e11 −1.03273 −0.516363 0.856370i \(-0.672715\pi\)
−0.516363 + 0.856370i \(0.672715\pi\)
\(114\) −1.58692e9 + 1.53301e10i −0.00771930 + 0.0745705i
\(115\) 2.39334e10 2.39334e10i 0.110960 0.110960i
\(116\) 1.21209e11 7.92565e10i 0.535817 0.350361i
\(117\) 3.02150e11 + 3.02150e11i 1.27409 + 1.27409i
\(118\) −2.20675e11 2.71637e11i −0.887977 1.09305i
\(119\) 5.93196e10i 0.227872i
\(120\) 8.41019e9 + 2.68890e9i 0.0308538 + 0.00986455i
\(121\) 1.24823e11i 0.437499i
\(122\) 2.42662e11 1.97136e11i 0.812875 0.660369i
\(123\) −9.85735e9 9.85735e9i −0.0315706 0.0315706i
\(124\) 1.44207e11 + 3.01791e10i 0.441741 + 0.0924459i
\(125\) −2.56090e11 + 2.56090e11i −0.750565 + 0.750565i
\(126\) 2.99593e11 + 3.10128e10i 0.840414 + 0.0869969i
\(127\) −7.32920e11 −1.96850 −0.984251 0.176774i \(-0.943434\pi\)
−0.984251 + 0.176774i \(0.943434\pi\)
\(128\) −2.91729e11 2.56924e11i −0.750456 0.660921i
\(129\) 5.26270e9 0.0129707
\(130\) 5.38852e11 + 5.57802e10i 1.27286 + 0.131762i
\(131\) 5.27271e11 5.27271e11i 1.19410 1.19410i 0.218198 0.975905i \(-0.429982\pi\)
0.975905 0.218198i \(-0.0700178\pi\)
\(132\) −1.54483e10 3.23296e9i −0.0335525 0.00702173i
\(133\) 4.71298e11 + 4.71298e11i 0.982001 + 0.982001i
\(134\) 3.71508e11 3.01809e11i 0.742834 0.603470i
\(135\) 3.37175e10i 0.0647172i
\(136\) −1.39093e11 4.44706e10i −0.256354 0.0819612i
\(137\) 2.26117e11i 0.400286i −0.979767 0.200143i \(-0.935859\pi\)
0.979767 0.200143i \(-0.0641406\pi\)
\(138\) −3.75169e9 4.61810e9i −0.00638104 0.00785468i
\(139\) −1.23904e11 1.23904e11i −0.202537 0.202537i 0.598549 0.801086i \(-0.295744\pi\)
−0.801086 + 0.598549i \(0.795744\pi\)
\(140\) 3.19591e11 2.08975e11i 0.502216 0.328390i
\(141\) 1.90349e10 1.90349e10i 0.0287637 0.0287637i
\(142\) 1.20546e11 1.16451e12i 0.175213 1.69261i
\(143\) −9.68352e11 −1.35421
\(144\) −2.97316e11 + 6.79235e11i −0.400152 + 0.914169i
\(145\) −3.50195e11 −0.453718
\(146\) −8.79947e10 + 8.50054e11i −0.109778 + 1.06049i
\(147\) 7.61569e9 7.61569e9i 0.00915090 0.00915090i
\(148\) 1.55605e11 + 2.37971e11i 0.180129 + 0.275476i
\(149\) 6.94464e11 + 6.94464e11i 0.774686 + 0.774686i 0.978922 0.204236i \(-0.0654710\pi\)
−0.204236 + 0.978922i \(0.565471\pi\)
\(150\) 1.33405e10 + 1.64213e10i 0.0143440 + 0.0176566i
\(151\) 9.65622e11i 1.00100i 0.865737 + 0.500500i \(0.166850\pi\)
−0.865737 + 0.500500i \(0.833150\pi\)
\(152\) −1.45842e12 + 7.51778e11i −1.45795 + 0.751537i
\(153\) 2.78528e11i 0.268575i
\(154\) −5.29774e11 + 4.30382e11i −0.492864 + 0.400397i
\(155\) −2.51917e11 2.51917e11i −0.226169 0.226169i
\(156\) 1.95070e10 9.32119e10i 0.0169046 0.0807767i
\(157\) −4.89896e11 + 4.89896e11i −0.409879 + 0.409879i −0.881696 0.471817i \(-0.843598\pi\)
0.471817 + 0.881696i \(0.343598\pi\)
\(158\) −1.39270e12 1.44168e11i −1.12524 0.116481i
\(159\) −9.04287e10 −0.0705703
\(160\) 2.50414e11 + 9.06041e11i 0.188799 + 0.683106i
\(161\) −2.57316e11 −0.187467
\(162\) 1.40375e12 + 1.45312e11i 0.988455 + 0.102322i
\(163\) 1.72041e12 1.72041e12i 1.17112 1.17112i 0.189174 0.981944i \(-0.439419\pi\)
0.981944 0.189174i \(-0.0605809\pi\)
\(164\) 3.04004e11 1.45264e12i 0.200096 0.956133i
\(165\) 2.69868e10 + 2.69868e10i 0.0171787 + 0.0171787i
\(166\) −1.47455e12 + 1.19791e12i −0.907958 + 0.737614i
\(167\) 9.34742e11i 0.556867i −0.960456 0.278433i \(-0.910185\pi\)
0.960456 0.278433i \(-0.0898151\pi\)
\(168\) −3.07558e10 5.96651e10i −0.0177307 0.0343969i
\(169\) 4.05067e12i 2.26021i
\(170\) 2.22653e11 + 2.74072e11i 0.120271 + 0.148046i
\(171\) 2.21292e12 + 2.21292e12i 1.15741 + 1.15741i
\(172\) 3.06622e11 + 4.68925e11i 0.155309 + 0.237518i
\(173\) 1.11086e12 1.11086e12i 0.545011 0.545011i −0.379982 0.924994i \(-0.624070\pi\)
0.924994 + 0.379982i \(0.124070\pi\)
\(174\) −6.33872e9 + 6.12338e10i −0.00301287 + 0.0291052i
\(175\) 9.14979e11 0.421407
\(176\) −6.12000e11 1.56486e12i −0.273169 0.698484i
\(177\) 1.48769e11 0.0643665
\(178\) −2.99193e11 + 2.89029e12i −0.125499 + 1.21236i
\(179\) −3.71029e11 + 3.71029e11i −0.150909 + 0.150909i −0.778524 0.627615i \(-0.784031\pi\)
0.627615 + 0.778524i \(0.284031\pi\)
\(180\) 1.50060e12 9.81217e11i 0.591925 0.387049i
\(181\) 5.02297e11 + 5.02297e11i 0.192189 + 0.192189i 0.796641 0.604452i \(-0.206608\pi\)
−0.604452 + 0.796641i \(0.706608\pi\)
\(182\) −2.59683e12 3.19655e12i −0.963943 1.18656i
\(183\) 1.32900e11i 0.0478680i
\(184\) 1.92904e11 6.03354e11i 0.0674283 0.210899i
\(185\) 6.87541e11i 0.233267i
\(186\) −4.86091e10 + 3.94894e10i −0.0160102 + 0.0130065i
\(187\) −4.46324e11 4.46324e11i −0.142732 0.142732i
\(188\) 2.80510e12 + 5.87041e11i 0.871126 + 0.182306i
\(189\) −1.81254e11 + 1.81254e11i −0.0546699 + 0.0546699i
\(190\) 3.94651e12 + 4.08530e11i 1.15630 + 0.119696i
\(191\) −4.16083e11 −0.118439 −0.0592197 0.998245i \(-0.518861\pi\)
−0.0592197 + 0.998245i \(0.518861\pi\)
\(192\) 1.62960e11 2.73867e10i 0.0450737 0.00757500i
\(193\) −1.46842e12 −0.394716 −0.197358 0.980331i \(-0.563236\pi\)
−0.197358 + 0.980331i \(0.563236\pi\)
\(194\) −3.99394e12 4.13440e11i −1.04350 0.108020i
\(195\) −1.62833e11 + 1.62833e11i −0.0413572 + 0.0413572i
\(196\) 1.12230e12 + 2.34870e11i 0.277141 + 0.0579989i
\(197\) −2.84431e12 2.84431e12i −0.682987 0.682987i 0.277685 0.960672i \(-0.410433\pi\)
−0.960672 + 0.277685i \(0.910433\pi\)
\(198\) −2.48749e12 + 2.02081e12i −0.580902 + 0.471918i
\(199\) 8.06275e12i 1.83143i 0.401823 + 0.915717i \(0.368377\pi\)
−0.401823 + 0.915717i \(0.631623\pi\)
\(200\) −6.85939e11 + 2.14544e12i −0.151572 + 0.474080i
\(201\) 2.03466e11i 0.0437435i
\(202\) −9.77903e11 1.20374e12i −0.204580 0.251826i
\(203\) 1.88254e12 + 1.88254e12i 0.383279 + 0.383279i
\(204\) 5.19534e10 3.39714e10i 0.0102955 0.00673205i
\(205\) −2.53764e12 + 2.53764e12i −0.489535 + 0.489535i
\(206\) −9.43131e9 + 9.11091e10i −0.00177134 + 0.0171117i
\(207\) −1.20819e12 −0.220953
\(208\) 9.44204e12 3.69268e12i 1.68158 0.657648i
\(209\) −7.09214e12 −1.23019
\(210\) −1.67133e10 + 1.61455e11i −0.00282394 + 0.0272800i
\(211\) −4.42900e11 + 4.42900e11i −0.0729041 + 0.0729041i −0.742619 0.669715i \(-0.766416\pi\)
0.669715 + 0.742619i \(0.266416\pi\)
\(212\) −5.26866e12 8.05751e12i −0.844993 1.29227i
\(213\) 3.51896e11 + 3.51896e11i 0.0549955 + 0.0549955i
\(214\) 3.55918e12 + 4.38114e12i 0.542094 + 0.667285i
\(215\) 1.35481e12i 0.201125i
\(216\) −2.89123e11 5.60886e11i −0.0418395 0.0811670i
\(217\) 2.70845e12i 0.382113i
\(218\) 7.12622e11 5.78925e11i 0.0980276 0.0796364i
\(219\) −2.56873e11 2.56873e11i −0.0344569 0.0344569i
\(220\) −8.32282e11 + 3.97696e12i −0.108879 + 0.520267i
\(221\) 2.69302e12 2.69302e12i 0.343623 0.343623i
\(222\) −1.20221e11 1.24449e10i −0.0149637 0.00154899i
\(223\) −1.29842e12 −0.157666 −0.0788328 0.996888i \(-0.525119\pi\)
−0.0788328 + 0.996888i \(0.525119\pi\)
\(224\) 3.52443e12 6.21672e12i 0.417566 0.736542i
\(225\) 4.29617e12 0.496682
\(226\) 9.10473e12 + 9.42492e11i 1.02724 + 0.106336i
\(227\) −7.45606e12 + 7.45606e12i −0.821045 + 0.821045i −0.986258 0.165213i \(-0.947169\pi\)
0.165213 + 0.986258i \(0.447169\pi\)
\(228\) 1.42868e11 6.82678e11i 0.0153565 0.0733794i
\(229\) −5.34297e12 5.34297e12i −0.560644 0.560644i 0.368846 0.929490i \(-0.379753\pi\)
−0.929490 + 0.368846i \(0.879753\pi\)
\(230\) −1.18887e12 + 9.65820e11i −0.121795 + 0.0989449i
\(231\) 2.90145e11i 0.0290234i
\(232\) −5.82546e12 + 3.00287e12i −0.569045 + 0.293328i
\(233\) 1.06344e13i 1.01450i 0.861798 + 0.507252i \(0.169339\pi\)
−0.861798 + 0.507252i \(0.830661\pi\)
\(234\) −1.21931e13 1.50090e13i −1.13613 1.39851i
\(235\) −4.90026e12 4.90026e12i −0.446012 0.446012i
\(236\) 8.66777e12 + 1.32559e13i 0.770710 + 1.17867i
\(237\) 4.20854e11 4.20854e11i 0.0365608 0.0365608i
\(238\) 2.76414e11 2.67023e12i 0.0234631 0.226660i
\(239\) 2.22235e13 1.84342 0.921711 0.387876i \(-0.126791\pi\)
0.921711 + 0.387876i \(0.126791\pi\)
\(240\) −3.66049e11 1.60228e11i −0.0296741 0.0129890i
\(241\) 1.82051e13 1.44245 0.721223 0.692703i \(-0.243580\pi\)
0.721223 + 0.692703i \(0.243580\pi\)
\(242\) −5.81644e11 + 5.61884e12i −0.0450477 + 0.435173i
\(243\) −1.27703e12 + 1.27703e12i −0.0966866 + 0.0966866i
\(244\) −1.18419e13 + 7.74320e12i −0.876550 + 0.573160i
\(245\) −1.96055e12 1.96055e12i −0.141894 0.141894i
\(246\) 3.97789e11 + 4.89654e11i 0.0281520 + 0.0346535i
\(247\) 4.27925e13i 2.96165i
\(248\) −6.35077e12 2.03046e12i −0.429875 0.137439i
\(249\) 8.07577e11i 0.0534672i
\(250\) 1.27210e13 1.03344e13i 0.823859 0.669293i
\(251\) −7.53196e12 7.53196e12i −0.477202 0.477202i 0.427034 0.904236i \(-0.359559\pi\)
−0.904236 + 0.427034i \(0.859559\pi\)
\(252\) −1.33414e13 2.79204e12i −0.826989 0.173069i
\(253\) 1.93606e12 1.93606e12i 0.117423 0.117423i
\(254\) 3.29919e13 + 3.41521e12i 1.95804 + 0.202690i
\(255\) −1.50103e11 −0.00871802
\(256\) 1.19348e13 + 1.29246e13i 0.678414 + 0.734680i
\(257\) 1.74570e13 0.971265 0.485632 0.874163i \(-0.338589\pi\)
0.485632 + 0.874163i \(0.338589\pi\)
\(258\) −2.36897e11 2.45228e10i −0.0129018 0.00133555i
\(259\) −3.69599e12 + 3.69599e12i −0.197053 + 0.197053i
\(260\) −2.39961e13 5.02181e12i −1.25253 0.262124i
\(261\) 8.83921e12 + 8.83921e12i 0.451742 + 0.451742i
\(262\) −2.61917e13 + 2.12778e13i −1.31071 + 1.06480i
\(263\) 1.00586e13i 0.492927i 0.969152 + 0.246463i \(0.0792685\pi\)
−0.969152 + 0.246463i \(0.920731\pi\)
\(264\) 6.80331e11 + 2.17515e11i 0.0326512 + 0.0104392i
\(265\) 2.32796e13i 1.09427i
\(266\) −1.90190e13 2.34113e13i −0.875668 1.07789i
\(267\) −8.73401e11 8.73401e11i −0.0393914 0.0393914i
\(268\) −1.81295e13 + 1.18546e13i −0.801023 + 0.523775i
\(269\) 1.01600e13 1.01600e13i 0.439801 0.439801i −0.452144 0.891945i \(-0.649341\pi\)
0.891945 + 0.452144i \(0.149341\pi\)
\(270\) −1.57114e11 + 1.51777e12i −0.00666370 + 0.0643732i
\(271\) −8.09279e12 −0.336331 −0.168166 0.985759i \(-0.553784\pi\)
−0.168166 + 0.985759i \(0.553784\pi\)
\(272\) 6.05394e12 + 2.64994e12i 0.246552 + 0.107921i
\(273\) 1.75067e12 0.0698731
\(274\) −1.05364e12 + 1.01785e13i −0.0412160 + 0.398158i
\(275\) −6.88435e12 + 6.88435e12i −0.263957 + 0.263957i
\(276\) 1.47361e11 + 2.25362e11i 0.00553836 + 0.00846997i
\(277\) −2.98040e13 2.98040e13i −1.09809 1.09809i −0.994635 0.103451i \(-0.967012\pi\)
−0.103451 0.994635i \(-0.532988\pi\)
\(278\) 5.00009e12 + 6.15481e12i 0.180606 + 0.222315i
\(279\) 1.27172e13i 0.450368i
\(280\) −1.53599e13 + 7.91766e12i −0.533360 + 0.274933i
\(281\) 4.65745e13i 1.58585i 0.609316 + 0.792927i \(0.291444\pi\)
−0.609316 + 0.792927i \(0.708556\pi\)
\(282\) −9.45538e11 + 7.68144e11i −0.0315725 + 0.0256491i
\(283\) −2.43231e13 2.43231e13i −0.796514 0.796514i 0.186030 0.982544i \(-0.440438\pi\)
−0.982544 + 0.186030i \(0.940438\pi\)
\(284\) −1.08526e13 + 5.18578e13i −0.348564 + 1.66557i
\(285\) −1.19258e12 + 1.19258e12i −0.0375698 + 0.0375698i
\(286\) 4.35897e13 + 4.51226e12i 1.34701 + 0.139438i
\(287\) 2.72830e13 0.827070
\(288\) 1.65485e13 2.91899e13i 0.492154 0.868107i
\(289\) −3.17894e13 −0.927565
\(290\) 1.57638e13 + 1.63182e12i 0.451307 + 0.0467178i
\(291\) 1.20691e12 1.20691e12i 0.0339049 0.0339049i
\(292\) 7.92204e12 3.78545e13i 0.218389 1.04355i
\(293\) 1.69439e13 + 1.69439e13i 0.458395 + 0.458395i 0.898129 0.439733i \(-0.144927\pi\)
−0.439733 + 0.898129i \(0.644927\pi\)
\(294\) −3.78302e11 + 3.07328e11i −0.0100445 + 0.00816003i
\(295\) 3.82986e13i 0.998071i
\(296\) −5.89556e12 1.14372e13i −0.150807 0.292559i
\(297\) 2.72753e12i 0.0684871i
\(298\) −2.80248e13 3.44968e13i −0.690801 0.850335i
\(299\) 1.16817e13 + 1.16817e13i 0.282694 + 0.282694i
\(300\) −5.23994e11 8.01358e11i −0.0124497 0.0190397i
\(301\) −7.28301e12 + 7.28301e12i −0.169901 + 0.169901i
\(302\) 4.49954e12 4.34668e13i 0.103069 0.995679i
\(303\) 6.59259e11 0.0148293
\(304\) 6.91529e13 2.70449e13i 1.52759 0.597422i
\(305\) 3.42133e13 0.742244
\(306\) 1.29787e12 1.25377e13i 0.0276543 0.267148i
\(307\) −4.62265e13 + 4.62265e13i −0.967453 + 0.967453i −0.999487 0.0320342i \(-0.989801\pi\)
0.0320342 + 0.999487i \(0.489801\pi\)
\(308\) 2.58529e13 1.69047e13i 0.531472 0.347520i
\(309\) −2.75318e10 2.75318e10i −0.000555984 0.000555984i
\(310\) 1.01660e13 + 1.25137e13i 0.201679 + 0.248255i
\(311\) 4.23251e13i 0.824927i 0.910974 + 0.412464i \(0.135332\pi\)
−0.910974 + 0.412464i \(0.864668\pi\)
\(312\) −1.31244e12 + 4.10497e12i −0.0251321 + 0.0786067i
\(313\) 9.67939e13i 1.82119i −0.413305 0.910593i \(-0.635626\pi\)
0.413305 0.910593i \(-0.364374\pi\)
\(314\) 2.43351e13 1.97695e13i 0.449904 0.365497i
\(315\) 2.33063e13 + 2.33063e13i 0.423414 + 0.423414i
\(316\) 6.20198e13 + 1.29792e13i 1.10726 + 0.231724i
\(317\) −1.40318e13 + 1.40318e13i −0.246199 + 0.246199i −0.819409 0.573210i \(-0.805698\pi\)
0.573210 + 0.819409i \(0.305698\pi\)
\(318\) 4.07058e12 + 4.21373e11i 0.0701952 + 0.00726638i
\(319\) −2.83286e13 −0.480149
\(320\) −7.05032e12 4.19517e13i −0.117458 0.698915i
\(321\) −2.39944e12 −0.0392946
\(322\) 1.15829e13 + 1.19902e12i 0.186470 + 0.0193028i
\(323\) 1.97235e13 1.97235e13i 0.312155 0.312155i
\(324\) −6.25117e13 1.30822e13i −0.972666 0.203556i
\(325\) −4.15387e13 4.15387e13i −0.635469 0.635469i
\(326\) −8.54598e13 + 6.94264e13i −1.28548 + 1.04431i
\(327\) 3.90286e11i 0.00577258i
\(328\) −2.04534e13 + 6.39732e13i −0.297482 + 0.930448i
\(329\) 5.26844e13i 0.753537i
\(330\) −1.08904e12 1.34054e12i −0.0153186 0.0188562i
\(331\) 1.57682e13 + 1.57682e13i 0.218136 + 0.218136i 0.807712 0.589577i \(-0.200705\pi\)
−0.589577 + 0.807712i \(0.700705\pi\)
\(332\) 7.19579e13 4.70520e13i 0.979082 0.640204i
\(333\) −1.73541e13 + 1.73541e13i −0.232252 + 0.232252i
\(334\) −4.35565e12 + 4.20768e13i −0.0573386 + 0.553907i
\(335\) 5.23795e13 0.678289
\(336\) 1.10643e12 + 2.82909e12i 0.0140947 + 0.0360397i
\(337\) −1.08071e14 −1.35440 −0.677199 0.735800i \(-0.736806\pi\)
−0.677199 + 0.735800i \(0.736806\pi\)
\(338\) −1.88750e13 + 1.82338e14i −0.232726 + 2.24820i
\(339\) −2.75131e12 + 2.75131e12i −0.0333765 + 0.0333765i
\(340\) −8.74546e12 1.33747e13i −0.104388 0.159643i
\(341\) −2.03785e13 2.03785e13i −0.239344 0.239344i
\(342\) −8.93015e13 1.09925e14i −1.03208 1.27043i
\(343\) 9.55232e13i 1.08640i
\(344\) −1.16173e13 2.25371e13i −0.130027 0.252247i
\(345\) 6.51113e11i 0.00717218i
\(346\) −5.51809e13 + 4.48282e13i −0.598232 + 0.485997i
\(347\) 5.48946e13 + 5.48946e13i 0.585757 + 0.585757i 0.936479 0.350722i \(-0.114064\pi\)
−0.350722 + 0.936479i \(0.614064\pi\)
\(348\) 5.70666e11 2.72686e12i 0.00599372 0.0286403i
\(349\) 9.06961e13 9.06961e13i 0.937667 0.937667i −0.0605011 0.998168i \(-0.519270\pi\)
0.998168 + 0.0605011i \(0.0192699\pi\)
\(350\) −4.11872e13 4.26356e12i −0.419167 0.0433908i
\(351\) 1.64573e13 0.164881
\(352\) 2.02569e13 + 7.32929e13i 0.199797 + 0.722899i
\(353\) −1.21957e12 −0.0118426 −0.00592130 0.999982i \(-0.501885\pi\)
−0.00592130 + 0.999982i \(0.501885\pi\)
\(354\) −6.69674e12 6.93225e11i −0.0640244 0.00662760i
\(355\) 9.05909e13 9.05909e13i 0.852763 0.852763i
\(356\) 2.69359e13 1.28710e14i 0.249665 1.19299i
\(357\) 8.06903e11 + 8.06903e11i 0.00736455 + 0.00736455i
\(358\) 1.84305e13 1.49727e13i 0.165646 0.134569i
\(359\) 4.50417e12i 0.0398653i −0.999801 0.0199327i \(-0.993655\pi\)
0.999801 0.0199327i \(-0.00634518\pi\)
\(360\) −7.21207e13 + 3.71764e13i −0.628632 + 0.324044i
\(361\) 1.96919e14i 1.69043i
\(362\) −2.02700e13 2.49511e13i −0.171378 0.210956i
\(363\) −1.69793e12 1.69793e12i −0.0141395 0.0141395i
\(364\) 1.02000e14 + 1.55991e14i 0.836644 + 1.27950i
\(365\) −6.61284e13 + 6.61284e13i −0.534291 + 0.534291i
\(366\) 6.19280e11 5.98241e12i 0.00492880 0.0476135i
\(367\) −1.64509e14 −1.28981 −0.644905 0.764263i \(-0.723103\pi\)
−0.644905 + 0.764263i \(0.723103\pi\)
\(368\) −1.14949e13 + 2.62607e13i −0.0887854 + 0.202835i
\(369\) 1.28104e14 0.974806
\(370\) −3.20376e12 + 3.09492e13i −0.0240187 + 0.232028i
\(371\) 1.25144e14 1.25144e14i 0.924383 0.924383i
\(372\) 2.37211e12 1.55108e12i 0.0172643 0.0112888i
\(373\) 1.52240e14 + 1.52240e14i 1.09177 + 1.09177i 0.995340 + 0.0964284i \(0.0307419\pi\)
0.0964284 + 0.995340i \(0.469258\pi\)
\(374\) 1.80112e13 + 2.21707e13i 0.127277 + 0.156670i
\(375\) 6.96701e12i 0.0485148i
\(376\) −1.23534e14 3.94963e13i −0.847724 0.271033i
\(377\) 1.70929e14i 1.15594i
\(378\) 9.00362e12 7.31443e12i 0.0600084 0.0487501i
\(379\) 4.13623e13 + 4.13623e13i 0.271700 + 0.271700i 0.829784 0.558085i \(-0.188464\pi\)
−0.558085 + 0.829784i \(0.688464\pi\)
\(380\) −1.75746e14 3.67794e13i −1.13782 0.238119i
\(381\) −9.96964e12 + 9.96964e12i −0.0636198 + 0.0636198i
\(382\) 1.87297e13 + 1.93883e12i 0.117810 + 0.0121953i
\(383\) −6.41682e13 −0.397857 −0.198928 0.980014i \(-0.563746\pi\)
−0.198928 + 0.980014i \(0.563746\pi\)
\(384\) −7.46312e12 + 4.73445e11i −0.0456141 + 0.00289366i
\(385\) −7.46937e13 −0.450039
\(386\) 6.60999e13 + 6.84244e12i 0.392618 + 0.0406426i
\(387\) −3.41965e13 + 3.41965e13i −0.200249 + 0.200249i
\(388\) 1.77858e14 + 3.72214e13i 1.02683 + 0.214891i
\(389\) 1.21900e14 + 1.21900e14i 0.693877 + 0.693877i 0.963083 0.269206i \(-0.0867612\pi\)
−0.269206 + 0.963083i \(0.586761\pi\)
\(390\) 8.08856e12 6.57104e12i 0.0453958 0.0368790i
\(391\) 1.07685e13i 0.0595913i
\(392\) −4.94251e13 1.58021e13i −0.269696 0.0862268i
\(393\) 1.43445e13i 0.0771840i
\(394\) 1.14781e14 + 1.41288e14i 0.609032 + 0.749681i
\(395\) −1.08343e14 1.08343e14i −0.566913 0.566913i
\(396\) 1.21389e14 7.93742e13i 0.626406 0.409596i
\(397\) 5.19861e13 5.19861e13i 0.264570 0.264570i −0.562338 0.826908i \(-0.690098\pi\)
0.826908 + 0.562338i \(0.190098\pi\)
\(398\) 3.75703e13 3.62939e14i 0.188576 1.82170i
\(399\) 1.28218e13 0.0634743
\(400\) 4.08742e13 9.33793e13i 0.199581 0.455954i
\(401\) −2.94281e14 −1.41732 −0.708661 0.705549i \(-0.750700\pi\)
−0.708661 + 0.705549i \(0.750700\pi\)
\(402\) 9.48097e11 9.15888e12i 0.00450412 0.0435110i
\(403\) 1.22959e14 1.22959e14i 0.576214 0.576214i
\(404\) 3.84105e13 + 5.87422e13i 0.177563 + 0.271552i
\(405\) 1.09202e14 + 1.09202e14i 0.498000 + 0.498000i
\(406\) −7.59689e13 9.35131e13i −0.341777 0.420707i
\(407\) 5.56177e13i 0.246856i
\(408\) −2.49694e12 + 1.28711e12i −0.0109340 + 0.00563618i
\(409\) 3.29100e14i 1.42184i 0.703274 + 0.710919i \(0.251721\pi\)
−0.703274 + 0.710919i \(0.748279\pi\)
\(410\) 1.26055e14 1.02405e14i 0.537339 0.436527i
\(411\) −3.07578e12 3.07578e12i −0.0129368 0.0129368i
\(412\) 8.49088e11 4.05726e12i 0.00352385 0.0168383i
\(413\) −2.05881e14 + 2.05881e14i −0.843121 + 0.843121i
\(414\) 5.43860e13 + 5.62986e12i 0.219779 + 0.0227508i
\(415\) −2.07899e14 −0.829065
\(416\) −4.42234e14 + 1.22226e14i −1.74036 + 0.481006i
\(417\) −3.37084e12 −0.0130915
\(418\) 3.19248e14 + 3.30475e13i 1.22365 + 0.126669i
\(419\) −7.64006e13 + 7.64006e13i −0.289015 + 0.289015i −0.836691 0.547676i \(-0.815513\pi\)
0.547676 + 0.836691i \(0.315513\pi\)
\(420\) 1.50467e12 7.18989e12i 0.00561786 0.0268442i
\(421\) 1.13866e13 + 1.13866e13i 0.0419608 + 0.0419608i 0.727776 0.685815i \(-0.240554\pi\)
−0.685815 + 0.727776i \(0.740554\pi\)
\(422\) 2.20006e13 1.78730e13i 0.0800233 0.0650099i
\(423\) 2.47373e14i 0.888138i
\(424\) 1.99619e14 + 3.87254e14i 0.707441 + 1.37241i
\(425\) 3.82913e13i 0.133956i
\(426\) −1.42006e13 1.74801e13i −0.0490405 0.0603659i
\(427\) −1.83920e14 1.83920e14i −0.627011 0.627011i
\(428\) −1.39799e14 2.13799e14i −0.470505 0.719556i
\(429\) −1.31721e13 + 1.31721e13i −0.0437664 + 0.0437664i
\(430\) −6.31305e12 + 6.09858e13i −0.0207092 + 0.200056i
\(431\) −4.52834e14 −1.46661 −0.733304 0.679901i \(-0.762023\pi\)
−0.733304 + 0.679901i \(0.762023\pi\)
\(432\) 1.04011e13 + 2.65951e13i 0.0332596 + 0.0850436i
\(433\) 3.07829e14 0.971910 0.485955 0.873984i \(-0.338472\pi\)
0.485955 + 0.873984i \(0.338472\pi\)
\(434\) 1.26206e13 1.21919e14i 0.0393448 0.380082i
\(435\) −4.76358e12 + 4.76358e12i −0.0146637 + 0.0146637i
\(436\) −3.47758e13 + 2.27393e13i −0.105706 + 0.0691196i
\(437\) 8.55563e13 + 8.55563e13i 0.256805 + 0.256805i
\(438\) 1.03660e13 + 1.27599e13i 0.0307258 + 0.0378216i
\(439\) 2.23842e14i 0.655218i −0.944813 0.327609i \(-0.893757\pi\)
0.944813 0.327609i \(-0.106243\pi\)
\(440\) 5.59961e13 1.75142e14i 0.161871 0.506291i
\(441\) 9.89719e13i 0.282553i
\(442\) −1.33773e14 + 1.08676e14i −0.377178 + 0.306415i
\(443\) 1.88897e14 + 1.88897e14i 0.526022 + 0.526022i 0.919384 0.393362i \(-0.128688\pi\)
−0.393362 + 0.919384i \(0.628688\pi\)
\(444\) 5.35366e12 + 1.12039e12i 0.0147246 + 0.00308151i
\(445\) −2.24845e14 + 2.24845e14i −0.610806 + 0.610806i
\(446\) 5.84473e13 + 6.05027e12i 0.156828 + 0.0162343i
\(447\) 1.88931e13 0.0500739
\(448\) −1.87618e14 + 2.63419e14i −0.491186 + 0.689632i
\(449\) 1.84294e14 0.476603 0.238301 0.971191i \(-0.423409\pi\)
0.238301 + 0.971191i \(0.423409\pi\)
\(450\) −1.93389e14 2.00190e13i −0.494042 0.0511416i
\(451\) −2.05279e14 + 2.05279e14i −0.518052 + 0.518052i
\(452\) −4.05451e14 8.48512e13i −1.01083 0.211542i
\(453\) 1.31350e13 + 1.31350e13i 0.0323512 + 0.0323512i
\(454\) 3.70373e14 3.00886e14i 0.901222 0.732141i
\(455\) 4.50686e14i 1.08346i
\(456\) −9.61220e12 + 3.00645e13i −0.0228305 + 0.0714081i
\(457\) 3.30279e13i 0.0775073i −0.999249 0.0387536i \(-0.987661\pi\)
0.999249 0.0387536i \(-0.0123388\pi\)
\(458\) 2.15613e14 + 2.65407e14i 0.499937 + 0.615392i
\(459\) 7.58536e12 + 7.58536e12i 0.0173783 + 0.0173783i
\(460\) 5.80164e13 3.79359e13i 0.131336 0.0858781i
\(461\) 2.66530e14 2.66530e14i 0.596198 0.596198i −0.343101 0.939299i \(-0.611477\pi\)
0.939299 + 0.343101i \(0.111477\pi\)
\(462\) −1.35200e12 + 1.30607e13i −0.00298844 + 0.0288692i
\(463\) 4.98919e14 1.08977 0.544885 0.838511i \(-0.316573\pi\)
0.544885 + 0.838511i \(0.316573\pi\)
\(464\) 2.76222e14 1.08027e14i 0.596223 0.233176i
\(465\) −6.85347e12 −0.0146191
\(466\) 4.95533e13 4.78698e14i 0.104460 1.00911i
\(467\) 4.27807e14 4.27807e14i 0.891262 0.891262i −0.103380 0.994642i \(-0.532966\pi\)
0.994642 + 0.103380i \(0.0329658\pi\)
\(468\) 4.78927e14 + 7.32436e14i 0.986091 + 1.50806i
\(469\) −2.81575e14 2.81575e14i −0.572985 0.572985i
\(470\) 1.97748e14 + 2.43416e14i 0.397717 + 0.489565i
\(471\) 1.33278e13i 0.0264937i
\(472\) −3.28405e14 6.37092e14i −0.645251 1.25176i
\(473\) 1.09595e14i 0.212841i
\(474\) −2.09055e13 + 1.69834e13i −0.0401310 + 0.0326019i
\(475\) −3.04226e14 3.04226e14i −0.577274 0.577274i
\(476\) −2.48851e13 + 1.18911e14i −0.0466769 + 0.223040i
\(477\) 5.87596e14 5.87596e14i 1.08950 1.08950i
\(478\) −1.00038e15 1.03556e14i −1.83362 0.189811i
\(479\) 1.01796e15 1.84453 0.922264 0.386561i \(-0.126337\pi\)
0.922264 + 0.386561i \(0.126337\pi\)
\(480\) 1.57308e13 + 8.91825e12i 0.0281790 + 0.0159754i
\(481\) 3.35585e14 0.594299
\(482\) −8.19490e14 8.48309e13i −1.43478 0.148524i
\(483\) −3.50017e12 + 3.50017e12i −0.00605871 + 0.00605871i
\(484\) 5.23646e13 2.50218e14i 0.0896165 0.428222i
\(485\) −3.10702e14 3.10702e14i −0.525732 0.525732i
\(486\) 6.34352e13 5.15340e13i 0.106128 0.0862173i
\(487\) 3.80487e14i 0.629405i 0.949190 + 0.314702i \(0.101905\pi\)
−0.949190 + 0.314702i \(0.898095\pi\)
\(488\) 5.69135e14 2.93375e14i 0.930907 0.479859i
\(489\) 4.68042e13i 0.0756983i
\(490\) 7.91173e13 + 9.73886e13i 0.126530 + 0.155751i
\(491\) 4.01164e14 + 4.01164e14i 0.634416 + 0.634416i 0.949172 0.314757i \(-0.101923\pi\)
−0.314757 + 0.949172i \(0.601923\pi\)
\(492\) −1.56245e13 2.38950e13i −0.0244343 0.0373680i
\(493\) 7.87828e13 7.87828e13i 0.121835 0.121835i
\(494\) −1.99401e14 + 1.92627e15i −0.304951 + 2.94591i
\(495\) −3.50715e14 −0.530427
\(496\) 2.76414e14 + 1.20993e14i 0.413438 + 0.180971i
\(497\) −9.73973e14 −1.44074
\(498\) −3.76309e12 + 3.63525e13i −0.00550533 + 0.0531830i
\(499\) −7.67694e14 + 7.67694e14i −1.11080 + 1.11080i −0.117755 + 0.993043i \(0.537570\pi\)
−0.993043 + 0.117755i \(0.962430\pi\)
\(500\) −6.20785e14 + 4.05920e14i −0.888395 + 0.580905i
\(501\) −1.27150e13 1.27150e13i −0.0179973 0.0179973i
\(502\) 3.03949e14 + 3.74143e14i 0.425530 + 0.523801i
\(503\) 1.56404e14i 0.216583i 0.994119 + 0.108291i \(0.0345379\pi\)
−0.994119 + 0.108291i \(0.965462\pi\)
\(504\) 5.87545e14 + 1.87849e14i 0.804773 + 0.257301i
\(505\) 1.69717e14i 0.229944i
\(506\) −9.61717e13 + 7.81287e13i −0.128890 + 0.104709i
\(507\) −5.50997e13 5.50997e13i −0.0730475 0.0730475i
\(508\) −1.46919e15 3.07467e14i −1.92676 0.403225i
\(509\) −5.43363e14 + 5.43363e14i −0.704924 + 0.704924i −0.965463 0.260539i \(-0.916100\pi\)
0.260539 + 0.965463i \(0.416100\pi\)
\(510\) 6.75677e12 + 6.99439e11i 0.00867168 + 0.000897664i
\(511\) 7.10969e14 0.902684
\(512\) −4.77011e14 6.37406e14i −0.599161 0.800629i
\(513\) 1.20532e14 0.149781
\(514\) −7.85815e14 8.13450e13i −0.966102 0.100008i
\(515\) −7.08767e12 + 7.08767e12i −0.00862112 + 0.00862112i
\(516\) 1.05495e13 + 2.20775e12i 0.0126957 + 0.00265691i
\(517\) −3.96400e14 3.96400e14i −0.471993 0.471993i
\(518\) 1.83595e14 1.49150e14i 0.216295 0.175716i
\(519\) 3.02212e13i 0.0352283i
\(520\) 1.05677e15 + 3.37869e14i 1.21888 + 0.389699i
\(521\) 9.64380e14i 1.10063i 0.834958 + 0.550314i \(0.185492\pi\)
−0.834958 + 0.550314i \(0.814508\pi\)
\(522\) −3.56703e14 4.39079e14i −0.402827 0.495856i
\(523\) 2.60723e14 + 2.60723e14i 0.291353 + 0.291353i 0.837615 0.546261i \(-0.183949\pi\)
−0.546261 + 0.837615i \(0.683949\pi\)
\(524\) 1.27815e15 8.35758e14i 1.41338 0.924184i
\(525\) 1.24461e13 1.24461e13i 0.0136194 0.0136194i
\(526\) 4.68705e13 4.52782e14i 0.0507549 0.490307i
\(527\) 1.13347e14 0.121465
\(528\) −2.96111e13 1.29614e13i −0.0314027 0.0137457i
\(529\) 9.06098e14 0.950975
\(530\) 1.08477e14 1.04792e15i 0.112673 1.08845i
\(531\) −9.66687e14 + 9.66687e14i −0.993724 + 0.993724i
\(532\) 7.47038e14 + 1.14247e15i 0.760027 + 1.16233i
\(533\) −1.23861e15 1.23861e15i −1.24719 1.24719i
\(534\) 3.52457e13 + 4.33853e13i 0.0351261 + 0.0432381i
\(535\) 6.17703e14i 0.609304i
\(536\) 8.71327e14 4.49147e14i 0.850697 0.438512i
\(537\) 1.00939e13i 0.00975444i
\(538\) −5.04688e14 + 4.10002e14i −0.482748 + 0.392178i
\(539\) −1.58596e14 1.58596e14i −0.150160 0.150160i
\(540\) 1.41448e13 6.75892e13i 0.0132566 0.0633449i
\(541\) 7.80888e14 7.80888e14i 0.724442 0.724442i −0.245064 0.969507i \(-0.578809\pi\)
0.969507 + 0.245064i \(0.0788091\pi\)
\(542\) 3.64291e14 + 3.77102e13i 0.334544 + 0.0346309i
\(543\) 1.36651e13 0.0124226
\(544\) −2.60166e14 1.47495e14i −0.234129 0.132734i
\(545\) 1.00474e14 0.0895099
\(546\) −7.88052e13 8.15765e12i −0.0695017 0.00719458i
\(547\) −4.05263e13 + 4.05263e13i −0.0353839 + 0.0353839i −0.724577 0.689193i \(-0.757965\pi\)
0.689193 + 0.724577i \(0.257965\pi\)
\(548\) 9.48581e13 4.53268e14i 0.0819939 0.391798i
\(549\) −8.63573e14 8.63573e14i −0.739011 0.739011i
\(550\) 3.41973e14 2.77815e14i 0.289733 0.235375i
\(551\) 1.25187e15i 1.05009i
\(552\) −5.58320e12 1.08312e13i −0.00463680 0.00899521i
\(553\) 1.16483e15i 0.957801i
\(554\) 1.20273e15 + 1.48049e15i 0.979183 + 1.20531i
\(555\) −9.35237e12 9.35237e12i −0.00753894 0.00753894i
\(556\) −1.96396e14 3.00354e14i −0.156755 0.239729i
\(557\) −9.73064e14 + 9.73064e14i −0.769021 + 0.769021i −0.977934 0.208913i \(-0.933007\pi\)
0.208913 + 0.977934i \(0.433007\pi\)
\(558\) 5.92587e13 5.72455e14i 0.0463729 0.447975i
\(559\) 6.61275e14 0.512409
\(560\) 7.28311e14 2.84834e14i 0.558834 0.218554i
\(561\) −1.21424e13 −0.00922587
\(562\) 2.17025e14 2.09652e15i 0.163290 1.57743i
\(563\) −4.90526e14 + 4.90526e14i −0.365482 + 0.365482i −0.865826 0.500345i \(-0.833207\pi\)
0.500345 + 0.865826i \(0.333207\pi\)
\(564\) 4.61421e13 3.01715e13i 0.0340457 0.0222619i
\(565\) 7.08287e14 + 7.08287e14i 0.517539 + 0.517539i
\(566\) 9.81548e14 + 1.20823e15i 0.710266 + 0.874295i
\(567\) 1.17407e15i 0.841371i
\(568\) 7.30165e14 2.28377e15i 0.518209 1.62083i
\(569\) 6.24602e14i 0.439022i 0.975610 + 0.219511i \(0.0704461\pi\)
−0.975610 + 0.219511i \(0.929554\pi\)
\(570\) 5.92400e13 4.81259e13i 0.0412386 0.0335017i
\(571\) 7.95287e14 + 7.95287e14i 0.548309 + 0.548309i 0.925952 0.377642i \(-0.123265\pi\)
−0.377642 + 0.925952i \(0.623265\pi\)
\(572\) −1.94113e15 4.06232e14i −1.32549 0.277394i
\(573\) −5.65982e12 + 5.65982e12i −0.00382783 + 0.00382783i
\(574\) −1.22813e15 1.27132e14i −0.822674 0.0851605i
\(575\) 1.66099e14 0.110203
\(576\) −8.80938e14 + 1.23685e15i −0.578924 + 0.812818i
\(577\) −1.00625e15 −0.654999 −0.327499 0.944851i \(-0.606206\pi\)
−0.327499 + 0.944851i \(0.606206\pi\)
\(578\) 1.43098e15 + 1.48130e14i 0.922635 + 0.0955081i
\(579\) −1.99744e13 + 1.99744e13i −0.0127568 + 0.0127568i
\(580\) −7.01993e14 1.46910e14i −0.444098 0.0929390i
\(581\) 1.11760e15 + 1.11760e15i 0.700353 + 0.700353i
\(582\) −5.99520e13 + 4.87043e13i −0.0372158 + 0.0302337i
\(583\) 1.88317e15i 1.15801i
\(584\) −5.32997e14 + 1.66708e15i −0.324679 + 1.01551i
\(585\) 2.11614e15i 1.27699i
\(586\) −6.83762e14 8.41669e14i −0.408760 0.503158i
\(587\) −1.53564e15 1.53564e15i −0.909453 0.909453i 0.0867748 0.996228i \(-0.472344\pi\)
−0.996228 + 0.0867748i \(0.972344\pi\)
\(588\) 1.84611e13 1.20714e13i 0.0108313 0.00708241i
\(589\) 9.00546e14 9.00546e14i 0.523446 0.523446i
\(590\) −1.78461e14 + 1.72398e15i −0.102768 + 0.992766i
\(591\) −7.73801e13 −0.0441467
\(592\) 2.12091e14 + 5.42308e14i 0.119881 + 0.306532i
\(593\) 1.63157e15 0.913704 0.456852 0.889543i \(-0.348977\pi\)
0.456852 + 0.889543i \(0.348977\pi\)
\(594\) −1.27096e13 + 1.22778e14i −0.00705188 + 0.0681231i
\(595\) 2.07726e14 2.07726e14i 0.114195 0.114195i
\(596\) 1.10077e15 + 1.68344e15i 0.599574 + 0.916944i
\(597\) 1.09675e14 + 1.09675e14i 0.0591899 + 0.0591899i
\(598\) −4.71412e14 5.80279e14i −0.252083 0.310299i
\(599\) 1.76391e15i 0.934608i −0.884097 0.467304i \(-0.845225\pi\)
0.884097 0.467304i \(-0.154775\pi\)
\(600\) 1.98531e13 + 3.85142e13i 0.0104231 + 0.0202204i
\(601\) 5.73310e14i 0.298250i 0.988818 + 0.149125i \(0.0476457\pi\)
−0.988818 + 0.149125i \(0.952354\pi\)
\(602\) 3.61776e14 2.93903e14i 0.186492 0.151503i
\(603\) −1.32210e15 1.32210e15i −0.675335 0.675335i
\(604\) −4.05087e14 + 1.93566e15i −0.205043 + 0.979775i
\(605\) −4.37108e14 + 4.37108e14i −0.219247 + 0.219247i
\(606\) −2.96761e13 3.07197e12i −0.0147505 0.00152692i
\(607\) −2.36189e15 −1.16338 −0.581690 0.813411i \(-0.697608\pi\)
−0.581690 + 0.813411i \(0.697608\pi\)
\(608\) −3.23889e15 + 8.95175e14i −1.58098 + 0.436956i
\(609\) 5.12149e13 0.0247743
\(610\) −1.54009e15 1.59425e14i −0.738298 0.0764262i
\(611\) 2.39179e15 2.39179e15i 1.13631 1.13631i
\(612\) −1.16845e14 + 5.58330e14i −0.0550146 + 0.262880i
\(613\) 2.34434e15 + 2.34434e15i 1.09392 + 1.09392i 0.995105 + 0.0988186i \(0.0315064\pi\)
0.0988186 + 0.995105i \(0.468494\pi\)
\(614\) 2.29626e15 1.86545e15i 1.06193 0.862695i
\(615\) 6.90371e13i 0.0316424i
\(616\) −1.24252e15 + 6.40488e14i −0.564430 + 0.290949i
\(617\) 1.75185e15i 0.788728i 0.918954 + 0.394364i \(0.129035\pi\)
−0.918954 + 0.394364i \(0.870965\pi\)
\(618\) 1.11103e12 + 1.36761e12i 0.000495781 + 0.000610277i
\(619\) −8.88285e14 8.88285e14i −0.392874 0.392874i 0.482836 0.875711i \(-0.339607\pi\)
−0.875711 + 0.482836i \(0.839607\pi\)
\(620\) −3.99305e14 6.10668e14i −0.175045 0.267702i
\(621\) −3.29036e13 + 3.29036e13i −0.0142968 + 0.0142968i
\(622\) 1.97223e14 1.90523e15i 0.0849399 0.820543i
\(623\) 2.41739e15 1.03196
\(624\) 7.82065e13 1.78667e14i 0.0330923 0.0756012i
\(625\) 6.06900e14 0.254552
\(626\) −4.51034e14 + 4.35711e15i −0.187521 + 1.81151i
\(627\) −9.64718e13 + 9.64718e13i −0.0397584 + 0.0397584i
\(628\) −1.18755e15 + 7.76517e14i −0.485147 + 0.317229i
\(629\) 1.54675e14 + 1.54675e14i 0.0626385 + 0.0626385i
\(630\) −9.40515e14 1.15772e15i −0.377566 0.464761i
\(631\) 7.19169e14i 0.286200i −0.989708 0.143100i \(-0.954293\pi\)
0.989708 0.143100i \(-0.0457071\pi\)
\(632\) −2.73130e15 8.73247e14i −1.07752 0.344503i
\(633\) 1.20492e13i 0.00471235i
\(634\) 6.97014e14 5.66245e14i 0.270240 0.219540i
\(635\) 2.56655e15 + 2.56655e15i 0.986492 + 0.986492i
\(636\) −1.81271e14 3.79356e13i −0.0690739 0.0144555i
\(637\) 9.56936e14 9.56936e14i 0.361507 0.361507i
\(638\) 1.27519e15 + 1.32004e14i 0.477597 + 0.0494392i
\(639\) −4.57317e15 −1.69810
\(640\) 1.21882e14 + 1.92128e15i 0.0448693 + 0.707294i
\(641\) −2.50058e15 −0.912686 −0.456343 0.889804i \(-0.650841\pi\)
−0.456343 + 0.889804i \(0.650841\pi\)
\(642\) 1.08009e14 + 1.11808e13i 0.0390857 + 0.00404603i
\(643\) 9.02176e14 9.02176e14i 0.323691 0.323691i −0.526490 0.850181i \(-0.676492\pi\)
0.850181 + 0.526490i \(0.176492\pi\)
\(644\) −5.15808e14 1.07946e14i −0.183492 0.0384004i
\(645\) −1.84290e13 1.84290e13i −0.00650014 0.00650014i
\(646\) −9.79746e14 + 7.95934e14i −0.342637 + 0.278354i
\(647\) 9.34714e14i 0.324120i 0.986781 + 0.162060i \(0.0518138\pi\)
−0.986781 + 0.162060i \(0.948186\pi\)
\(648\) 2.75296e15 + 8.80173e14i 0.946537 + 0.302626i
\(649\) 3.09811e15i 1.05621i
\(650\) 1.67628e15 + 2.06339e15i 0.566659 + 0.697523i
\(651\) 3.68420e13 + 3.68420e13i 0.0123495 + 0.0123495i
\(652\) 4.17042e15 2.72696e15i 1.38617 0.906395i
\(653\) −1.81794e15 + 1.81794e15i −0.599179 + 0.599179i −0.940094 0.340915i \(-0.889263\pi\)
0.340915 + 0.940094i \(0.389263\pi\)
\(654\) 1.81863e12 1.75684e13i 0.000594382 0.00574190i
\(655\) −3.69280e15 −1.19682
\(656\) 1.21880e15 2.78440e15i 0.391706 0.894872i
\(657\) 3.33827e15 1.06393
\(658\) 2.45495e14 2.37155e15i 0.0775891 0.749532i
\(659\) 3.21447e15 3.21447e15i 1.00749 1.00749i 0.00751594 0.999972i \(-0.497608\pi\)
0.999972 0.00751594i \(-0.00239242\pi\)
\(660\) 4.27759e13 + 6.54183e13i 0.0132956 + 0.0203333i
\(661\) 1.30629e15 + 1.30629e15i 0.402653 + 0.402653i 0.879167 0.476514i \(-0.158100\pi\)
−0.476514 + 0.879167i \(0.658100\pi\)
\(662\) −6.36317e14 7.83268e14i −0.194516 0.239437i
\(663\) 7.32644e13i 0.0222110i
\(664\) −3.45838e15 + 1.78271e15i −1.03980 + 0.535989i
\(665\) 3.30079e15i 0.984236i
\(666\) 8.62048e14 7.00317e14i 0.254931 0.207103i
\(667\) 3.41743e14 + 3.41743e14i 0.100232 + 0.100232i
\(668\) 3.92133e14 1.87376e15i 0.114068 0.545059i
\(669\) −1.76619e13 + 1.76619e13i −0.00509557 + 0.00509557i
\(670\) −2.35783e15 2.44074e14i −0.674684 0.0698411i
\(671\) 2.76764e15 0.785481
\(672\) −3.66222e13 1.32505e14i −0.0103089 0.0372994i
\(673\) 6.94406e14 0.193879 0.0969395 0.995290i \(-0.469095\pi\)
0.0969395 + 0.995290i \(0.469095\pi\)
\(674\) 4.86476e15 + 5.03583e14i 1.34720 + 0.139458i
\(675\) 1.17001e14 1.17001e14i 0.0321380 0.0321380i
\(676\) 1.69929e15 8.11986e15i 0.462979 2.21229i
\(677\) −3.20116e14 3.20116e14i −0.0865107 0.0865107i 0.662527 0.749038i \(-0.269484\pi\)
−0.749038 + 0.662527i \(0.769484\pi\)
\(678\) 1.36669e14 1.11028e14i 0.0366358 0.0297625i
\(679\) 3.34046e15i 0.888225i
\(680\) 3.31349e14 + 6.42803e14i 0.0873949 + 0.169543i
\(681\) 2.02844e14i 0.0530705i
\(682\) 8.22365e14 + 1.01228e15i 0.213428 + 0.262716i
\(683\) −4.63633e13 4.63633e13i −0.0119360 0.0119360i 0.701114 0.713050i \(-0.252687\pi\)
−0.713050 + 0.701114i \(0.752687\pi\)
\(684\) 3.50763e15 + 5.36431e15i 0.895787 + 1.36995i
\(685\) −7.91818e14 + 7.91818e14i −0.200598 + 0.200598i
\(686\) 4.45113e14 4.29991e15i 0.111863 1.08063i
\(687\) −1.45357e14 −0.0362388
\(688\) 4.17927e14 + 1.06862e15i 0.103363 + 0.264295i
\(689\) −1.13627e16 −2.78788
\(690\) −3.03401e12 + 2.93094e13i −0.000738495 + 0.00713406i
\(691\) −4.46516e15 + 4.46516e15i −1.07822 + 1.07822i −0.0815506 + 0.996669i \(0.525987\pi\)
−0.996669 + 0.0815506i \(0.974013\pi\)
\(692\) 2.69281e15 1.76078e15i 0.645094 0.421815i
\(693\) 1.88533e15 + 1.88533e15i 0.448079 + 0.448079i
\(694\) −2.21525e15 2.72684e15i −0.522330 0.642957i
\(695\) 8.67776e14i 0.202998i
\(696\) −3.83946e13 + 1.20089e14i −0.00891085 + 0.0278709i
\(697\) 1.14178e15i 0.262906i
\(698\) −4.50524e15 + 3.66000e15i −1.02923 + 0.836135i
\(699\) 1.44655e14 + 1.44655e14i 0.0327876 + 0.0327876i
\(700\) 1.83414e15 + 3.83842e14i 0.412472 + 0.0863204i
\(701\) −2.39258e15 + 2.39258e15i −0.533847 + 0.533847i −0.921715 0.387868i \(-0.873212\pi\)
0.387868 + 0.921715i \(0.373212\pi\)
\(702\) −7.40815e14 7.66867e13i −0.164004 0.0169772i
\(703\) 2.45780e15 0.539874
\(704\) −5.70326e14 3.39362e15i −0.124301 0.739629i
\(705\) −1.33313e14 −0.0288292
\(706\) 5.48982e13 + 5.68288e12i 0.0117797 + 0.00121939i
\(707\) −9.12343e14 + 9.12343e14i −0.194246 + 0.194246i
\(708\) 2.98219e14 + 6.24100e13i 0.0630017 + 0.0131847i
\(709\) −9.78586e14 9.78586e14i −0.205137 0.205137i 0.597060 0.802197i \(-0.296336\pi\)
−0.802197 + 0.597060i \(0.796336\pi\)
\(710\) −4.50001e15 + 3.65576e15i −0.936037 + 0.760425i
\(711\) 5.46933e15i 1.12889i
\(712\) −1.81226e15 + 5.66828e15i −0.371176 + 1.16095i
\(713\) 4.91673e14i 0.0999273i
\(714\) −3.25622e13 4.00821e13i −0.00656710 0.00808371i
\(715\) 3.39098e15 + 3.39098e15i 0.678644 + 0.678644i
\(716\) −8.99406e14 + 5.88105e14i −0.178622 + 0.116797i
\(717\) 3.02299e14 3.02299e14i 0.0595773 0.0595773i
\(718\) −2.09882e13 + 2.02752e14i −0.00410479 + 0.0396534i
\(719\) −8.22741e15 −1.59681 −0.798406 0.602119i \(-0.794323\pi\)
−0.798406 + 0.602119i \(0.794323\pi\)
\(720\) 3.41970e15 1.33741e15i 0.658656 0.257593i
\(721\) 7.62020e13 0.0145654
\(722\) −9.17588e14 + 8.86416e15i −0.174058 + 1.68145i
\(723\) 2.47637e14 2.47637e14i 0.0466182 0.0466182i
\(724\) 7.96173e14 + 1.21761e15i 0.148746 + 0.227481i
\(725\) −1.21519e15 1.21519e15i −0.225313 0.225313i
\(726\) 6.85191e13 + 8.43429e13i 0.0126084 + 0.0155202i
\(727\) 4.13322e14i 0.0754831i 0.999288 + 0.0377415i \(0.0120164\pi\)
−0.999288 + 0.0377415i \(0.987984\pi\)
\(728\) −3.86457e15 7.49711e15i −0.700452 1.35885i
\(729\) 5.48950e15i 0.987488i
\(730\) 3.28487e15 2.66858e15i 0.586465 0.476437i
\(731\) 3.04789e14 + 3.04789e14i 0.0540074 + 0.0540074i
\(732\) −5.57529e13 + 2.66409e14i −0.00980520 + 0.0468530i
\(733\) 5.11410e14 5.11410e14i 0.0892683 0.0892683i −0.661063 0.750331i \(-0.729894\pi\)
0.750331 + 0.661063i \(0.229894\pi\)
\(734\) 7.40525e15 + 7.66567e14i 1.28295 + 0.132807i
\(735\) −5.33374e13 −0.00917173
\(736\) 6.39802e14 1.12854e15i 0.109199 0.192615i
\(737\) 4.23717e15 0.717802
\(738\) −5.76652e15 5.96931e14i −0.969624 0.100372i
\(739\) 6.68018e15 6.68018e15i 1.11492 1.11492i 0.122445 0.992475i \(-0.460926\pi\)
0.992475 0.122445i \(-0.0390736\pi\)
\(740\) 2.88430e14 1.37823e15i 0.0477821 0.228321i
\(741\) −5.82090e14 5.82090e14i −0.0957172 0.0957172i
\(742\) −6.21638e15 + 5.05011e15i −1.01465 + 0.824289i
\(743\) 1.04581e15i 0.169440i −0.996405 0.0847200i \(-0.973000\pi\)
0.996405 0.0847200i \(-0.0269996\pi\)
\(744\) −1.14007e14 + 5.87675e13i −0.0183349 + 0.00945118i
\(745\) 4.86376e15i 0.776449i
\(746\) −6.14358e15 7.56238e15i −0.973550 1.19838i
\(747\) 5.24755e15 + 5.24755e15i 0.825455 + 0.825455i
\(748\) −7.07452e14 1.08193e15i −0.110468 0.168942i
\(749\) 3.32057e15 3.32057e15i 0.514710 0.514710i
\(750\) 3.24644e13 3.13615e14i 0.00499540 0.0482569i
\(751\) −1.46013e15 −0.223034 −0.111517 0.993763i \(-0.535571\pi\)
−0.111517 + 0.993763i \(0.535571\pi\)
\(752\) 5.37677e15 + 2.35353e15i 0.815311 + 0.356880i
\(753\) −2.04909e14 −0.0308452
\(754\) −7.96481e14 + 7.69423e15i −0.119024 + 1.14980i
\(755\) 3.38142e15 3.38142e15i 0.501639 0.501639i
\(756\) −4.39375e14 + 2.87299e14i −0.0647091 + 0.0423121i
\(757\) −1.31824e15 1.31824e15i −0.192737 0.192737i 0.604140 0.796878i \(-0.293517\pi\)
−0.796878 + 0.604140i \(0.793517\pi\)
\(758\) −1.66916e15 2.05463e15i −0.242279 0.298231i
\(759\) 5.26709e13i 0.00758999i
\(760\) 7.73970e15 + 2.47453e15i 1.10726 + 0.354012i
\(761\) 1.34562e15i 0.191121i