Properties

Label 69.8.g.a.5.16
Level $69$
Weight $8$
Character 69.5
Analytic conductor $21.555$
Analytic rank $0$
Dimension $540$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [69,8,Mod(5,69)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(69, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 1]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("69.5");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 69.g (of order \(22\), degree \(10\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(21.5545667584\)
Analytic rank: \(0\)
Dimension: \(540\)
Relative dimension: \(54\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 5.16
Character \(\chi\) \(=\) 69.5
Dual form 69.8.g.a.14.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.09645 + 10.5455i) q^{2} +(-20.3936 - 42.0844i) q^{3} +(6.06031 + 3.89472i) q^{4} +(37.8324 - 263.130i) q^{5} +(506.950 - 84.7496i) q^{6} +(-1413.39 + 645.472i) q^{7} +(-1123.04 + 973.116i) q^{8} +(-1355.20 + 1716.51i) q^{9} +O(q^{10})\) \(q+(-3.09645 + 10.5455i) q^{2} +(-20.3936 - 42.0844i) q^{3} +(6.06031 + 3.89472i) q^{4} +(37.8324 - 263.130i) q^{5} +(506.950 - 84.7496i) q^{6} +(-1413.39 + 645.472i) q^{7} +(-1123.04 + 973.116i) q^{8} +(-1355.20 + 1716.51i) q^{9} +(2657.70 + 1213.73i) q^{10} +(4830.81 - 1418.45i) q^{11} +(40.3154 - 334.472i) q^{12} +(-1760.71 + 3855.42i) q^{13} +(-2430.37 - 16903.6i) q^{14} +(-11845.2 + 3774.03i) q^{15} +(-6401.55 - 14017.4i) q^{16} +(20746.5 - 13333.0i) q^{17} +(-13905.2 - 19606.4i) q^{18} +(7530.32 - 11717.4i) q^{19} +(1254.10 - 1447.30i) q^{20} +(55988.4 + 46318.0i) q^{21} +55335.6i q^{22} +(58060.5 - 5814.20i) q^{23} +(63855.8 + 27416.9i) q^{24} +(7154.09 + 2100.63i) q^{25} +(-35205.5 - 30505.7i) q^{26} +(99875.8 + 22026.8i) q^{27} +(-11079.5 - 1592.99i) q^{28} +(4867.69 + 7574.28i) q^{29} +(-3121.03 - 136600. i) q^{30} +(26999.6 + 31159.2i) q^{31} +(-20627.3 + 2965.76i) q^{32} +(-158213. - 174374. i) q^{33} +(76362.9 + 260068. i) q^{34} +(116371. + 396325. i) q^{35} +(-14898.2 + 5124.46i) q^{36} +(409900. - 58934.7i) q^{37} +(100249. + 115693. i) q^{38} +(198160. - 4527.55i) q^{39} +(213569. + 332320. i) q^{40} +(-620266. - 89180.7i) q^{41} +(-661813. + 447006. i) q^{42} +(620271. + 537468. i) q^{43} +(34800.7 + 10218.4i) q^{44} +(400395. + 421534. i) q^{45} +(-118467. + 630282. i) q^{46} -616741. i q^{47} +(-459365. + 555272. i) q^{48} +(1.04172e6 - 1.20221e6i) q^{49} +(-44304.5 + 68939.2i) q^{50} +(-984209. - 601198. i) q^{51} +(-25686.2 + 16507.5i) q^{52} +(518406. + 1.13515e6i) q^{53} +(-541545. + 985038. i) q^{54} +(-190477. - 1.32480e6i) q^{55} +(959164. - 2.10028e6i) q^{56} +(-646691. - 77948.5i) q^{57} +(-94947.3 + 27879.0i) q^{58} +(637787. + 291267. i) q^{59} +(-86484.6 - 23262.1i) q^{60} +(1.05841e6 - 917117. i) q^{61} +(-412193. + 188242. i) q^{62} +(807460. - 3.30083e6i) q^{63} +(313309. - 2.17911e6i) q^{64} +(947866. + 609157. i) q^{65} +(2.32877e6 - 1.12849e6i) q^{66} +(-1.05004e6 + 3.57612e6i) q^{67} +177659. q^{68} +(-1.42875e6 - 2.32487e6i) q^{69} -4.53979e6 q^{70} +(234869. - 799889. i) q^{71} +(-148427. - 3.24647e6i) q^{72} +(1.34547e6 + 864683. i) q^{73} +(-647735. + 4.50509e6i) q^{74} +(-57494.2 - 343915. i) q^{75} +(91272.1 - 41682.6i) q^{76} +(-5.91223e6 + 5.12298e6i) q^{77} +(-565848. + 2.10373e6i) q^{78} +(-2.92394e6 - 1.33532e6i) q^{79} +(-3.93060e6 + 1.15413e6i) q^{80} +(-1.10984e6 - 4.65242e6i) q^{81} +(2.86108e6 - 6.26488e6i) q^{82} +(534825. + 3.71979e6i) q^{83} +(158911. + 498761. i) q^{84} +(-2.72342e6 - 5.96346e6i) q^{85} +(-7.58852e6 + 4.87684e6i) q^{86} +(219489. - 359321. i) q^{87} +(-4.04485e6 + 6.29391e6i) q^{88} +(1.90131e6 - 2.19422e6i) q^{89} +(-5.68510e6 + 2.91712e6i) q^{90} -6.58569e6i q^{91} +(374509. + 190894. i) q^{92} +(760697. - 1.77171e6i) q^{93} +(6.50386e6 + 1.90971e6i) q^{94} +(-2.79831e6 - 2.42475e6i) q^{95} +(545479. + 807607. i) q^{96} +(2.19587e6 + 315719. i) q^{97} +(9.45231e6 + 1.47081e7i) q^{98} +(-4.11192e6 + 1.02144e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 540 q - 35 q^{3} + 3362 q^{4} - 1280 q^{6} - 22 q^{7} - 659 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 540 q - 35 q^{3} + 3362 q^{4} - 1280 q^{6} - 22 q^{7} - 659 q^{9} - 22 q^{10} + 4756 q^{12} + 4970 q^{13} + 3828 q^{15} - 174622 q^{16} + 250050 q^{18} - 22 q^{19} - 221738 q^{21} + 94934 q^{24} - 788392 q^{25} + 1020934 q^{27} - 22 q^{28} - 1480875 q^{30} + 738458 q^{31} + 1215192 q^{33} + 1815924 q^{34} - 394502 q^{36} - 905234 q^{37} - 1635803 q^{39} + 10260228 q^{40} - 11 q^{42} - 1694330 q^{43} - 6978726 q^{46} + 134426 q^{48} + 7785740 q^{49} - 11 q^{51} + 16219654 q^{52} - 10697559 q^{54} - 1371960 q^{55} + 7508908 q^{57} - 21860696 q^{58} - 21971851 q^{60} - 11102850 q^{61} - 9022926 q^{63} + 2572060 q^{64} + 16582830 q^{66} + 6031564 q^{67} + 12019470 q^{69} - 2949828 q^{70} + 12828949 q^{72} - 1809596 q^{73} - 16620656 q^{75} - 42651158 q^{76} - 47106384 q^{78} - 1156914 q^{79} + 48837101 q^{81} + 47208588 q^{82} + 124183367 q^{84} + 5833252 q^{85} - 17916287 q^{87} + 360426 q^{88} - 142298860 q^{90} - 51670516 q^{93} - 18401348 q^{94} + 36462337 q^{96} - 63860500 q^{97} + 135683977 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(e\left(\frac{1}{22}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.09645 + 10.5455i −0.273690 + 0.932102i 0.701859 + 0.712316i \(0.252354\pi\)
−0.975548 + 0.219785i \(0.929464\pi\)
\(3\) −20.3936 42.0844i −0.436084 0.899906i
\(4\) 6.06031 + 3.89472i 0.0473462 + 0.0304275i
\(5\) 37.8324 263.130i 0.135353 0.941404i −0.803062 0.595895i \(-0.796797\pi\)
0.938416 0.345509i \(-0.112294\pi\)
\(6\) 506.950 84.7496i 0.958155 0.160180i
\(7\) −1413.39 + 645.472i −1.55746 + 0.711270i −0.993426 0.114480i \(-0.963480\pi\)
−0.564037 + 0.825749i \(0.690753\pi\)
\(8\) −1123.04 + 973.116i −0.775494 + 0.671970i
\(9\) −1355.20 + 1716.51i −0.619661 + 0.784870i
\(10\) 2657.70 + 1213.73i 0.840439 + 0.383816i
\(11\) 4830.81 1418.45i 1.09432 0.321322i 0.315729 0.948850i \(-0.397751\pi\)
0.778595 + 0.627527i \(0.215933\pi\)
\(12\) 40.3154 334.472i 0.00673499 0.0558760i
\(13\) −1760.71 + 3855.42i −0.222273 + 0.486710i −0.987612 0.156918i \(-0.949844\pi\)
0.765339 + 0.643628i \(0.222571\pi\)
\(14\) −2430.37 16903.6i −0.236714 1.64638i
\(15\) −11845.2 + 3774.03i −0.906200 + 0.288726i
\(16\) −6401.55 14017.4i −0.390719 0.855556i
\(17\) 20746.5 13333.0i 1.02418 0.658198i 0.0831515 0.996537i \(-0.473501\pi\)
0.941024 + 0.338339i \(0.109865\pi\)
\(18\) −13905.2 19606.4i −0.561984 0.792398i
\(19\) 7530.32 11717.4i 0.251870 0.391917i −0.692178 0.721727i \(-0.743349\pi\)
0.944047 + 0.329811i \(0.106985\pi\)
\(20\) 1254.10 1447.30i 0.0350531 0.0404534i
\(21\) 55988.4 + 46318.0i 1.31926 + 1.09140i
\(22\) 55335.6i 1.10796i
\(23\) 58060.5 5814.20i 0.995023 0.0996421i
\(24\) 63855.8 + 27416.9i 0.942890 + 0.404836i
\(25\) 7154.09 + 2100.63i 0.0915724 + 0.0268881i
\(26\) −35205.5 30505.7i −0.392829 0.340388i
\(27\) 99875.8 + 22026.8i 0.976533 + 0.215367i
\(28\) −11079.5 1592.99i −0.0953821 0.0137139i
\(29\) 4867.69 + 7574.28i 0.0370621 + 0.0576698i 0.859290 0.511488i \(-0.170906\pi\)
−0.822228 + 0.569158i \(0.807269\pi\)
\(30\) −3121.03 136600.i −0.0211044 0.923692i
\(31\) 26999.6 + 31159.2i 0.162776 + 0.187854i 0.831278 0.555856i \(-0.187610\pi\)
−0.668502 + 0.743710i \(0.733064\pi\)
\(32\) −20627.3 + 2965.76i −0.111280 + 0.0159997i
\(33\) −158213. 174374.i −0.766377 0.844664i
\(34\) 76362.9 + 260068.i 0.333201 + 1.13478i
\(35\) 116371. + 396325.i 0.458784 + 1.56247i
\(36\) −14898.2 + 5124.46i −0.0532202 + 0.0183058i
\(37\) 409900. 58934.7i 1.33037 0.191278i 0.559795 0.828631i \(-0.310880\pi\)
0.770572 + 0.637353i \(0.219971\pi\)
\(38\) 100249. + 115693.i 0.296372 + 0.342032i
\(39\) 198160. 4527.55i 0.534923 0.0122218i
\(40\) 213569. + 332320.i 0.527629 + 0.821007i
\(41\) −620266. 89180.7i −1.40551 0.202082i −0.602535 0.798093i \(-0.705842\pi\)
−0.802976 + 0.596011i \(0.796752\pi\)
\(42\) −661813. + 447006.i −1.37836 + 0.930981i
\(43\) 620271. + 537468.i 1.18971 + 1.03089i 0.998785 + 0.0492874i \(0.0156950\pi\)
0.190928 + 0.981604i \(0.438850\pi\)
\(44\) 34800.7 + 10218.4i 0.0615890 + 0.0180842i
\(45\) 400395. + 421534.i 0.655006 + 0.689586i
\(46\) −118467. + 630282.i −0.179451 + 0.954734i
\(47\) 616741.i 0.866484i −0.901278 0.433242i \(-0.857370\pi\)
0.901278 0.433242i \(-0.142630\pi\)
\(48\) −459365. + 555272.i −0.599533 + 0.724705i
\(49\) 1.04172e6 1.20221e6i 1.26493 1.45980i
\(50\) −44304.5 + 68939.2i −0.0501248 + 0.0779958i
\(51\) −984209. 601198.i −1.03894 0.634632i
\(52\) −25686.2 + 16507.5i −0.0253331 + 0.0162806i
\(53\) 518406. + 1.13515e6i 0.478305 + 1.04734i 0.982926 + 0.184000i \(0.0589048\pi\)
−0.504622 + 0.863341i \(0.668368\pi\)
\(54\) −541545. + 985038.i −0.468011 + 0.851284i
\(55\) −190477. 1.32480e6i −0.154374 1.07369i
\(56\) 959164. 2.10028e6i 0.729852 1.59815i
\(57\) −646691. 77948.5i −0.462524 0.0557501i
\(58\) −94947.3 + 27879.0i −0.0638976 + 0.0187620i
\(59\) 637787. + 291267.i 0.404290 + 0.184633i 0.607173 0.794570i \(-0.292304\pi\)
−0.202882 + 0.979203i \(0.565031\pi\)
\(60\) −86484.6 23262.1i −0.0516903 0.0139034i
\(61\) 1.05841e6 917117.i 0.597034 0.517333i −0.303093 0.952961i \(-0.598019\pi\)
0.900127 + 0.435628i \(0.143474\pi\)
\(62\) −412193. + 188242.i −0.219649 + 0.100310i
\(63\) 807460. 3.30083e6i 0.406845 1.66315i
\(64\) 313309. 2.17911e6i 0.149397 1.03908i
\(65\) 947866. + 609157.i 0.428105 + 0.275126i
\(66\) 2.32877e6 1.12849e6i 0.997062 0.483165i
\(67\) −1.05004e6 + 3.57612e6i −0.426526 + 1.45262i 0.413717 + 0.910406i \(0.364230\pi\)
−0.840243 + 0.542210i \(0.817588\pi\)
\(68\) 177659. 0.0685181
\(69\) −1.42875e6 2.32487e6i −0.523583 0.851975i
\(70\) −4.53979e6 −1.58195
\(71\) 234869. 799889.i 0.0778791 0.265232i −0.911345 0.411644i \(-0.864955\pi\)
0.989224 + 0.146413i \(0.0467727\pi\)
\(72\) −148427. 3.24647e6i −0.0468652 1.02506i
\(73\) 1.34547e6 + 864683.i 0.404804 + 0.260152i 0.727162 0.686466i \(-0.240839\pi\)
−0.322358 + 0.946618i \(0.604475\pi\)
\(74\) −647735. + 4.50509e6i −0.185817 + 1.29239i
\(75\) −57494.2 343915.i −0.0157365 0.0941320i
\(76\) 91272.1 41682.6i 0.0238501 0.0108920i
\(77\) −5.91223e6 + 5.12298e6i −1.47582 + 1.27881i
\(78\) −565848. + 2.10373e6i −0.135011 + 0.501947i
\(79\) −2.92394e6 1.33532e6i −0.667227 0.304712i 0.0528543 0.998602i \(-0.483168\pi\)
−0.720081 + 0.693890i \(0.755895\pi\)
\(80\) −3.93060e6 + 1.15413e6i −0.858309 + 0.252022i
\(81\) −1.10984e6 4.65242e6i −0.232041 0.972706i
\(82\) 2.86108e6 6.26488e6i 0.573035 1.25477i
\(83\) 534825. + 3.71979e6i 0.102669 + 0.714077i 0.974519 + 0.224305i \(0.0720110\pi\)
−0.871850 + 0.489772i \(0.837080\pi\)
\(84\) 158911. + 498761.i 0.0292534 + 0.0918153i
\(85\) −2.72342e6 5.96346e6i −0.481004 1.05325i
\(86\) −7.58852e6 + 4.87684e6i −1.28651 + 0.826788i
\(87\) 219489. 359321.i 0.0357351 0.0585013i
\(88\) −4.04485e6 + 6.29391e6i −0.632723 + 0.984536i
\(89\) 1.90131e6 2.19422e6i 0.285882 0.329926i −0.594585 0.804033i \(-0.702684\pi\)
0.880467 + 0.474107i \(0.157229\pi\)
\(90\) −5.68510e6 + 2.91712e6i −0.822033 + 0.421800i
\(91\) 6.58569e6i 0.916128i
\(92\) 374509. + 190894.i 0.0501424 + 0.0255584i
\(93\) 760697. 1.77171e6i 0.0980666 0.228404i
\(94\) 6.50386e6 + 1.90971e6i 0.807651 + 0.237148i
\(95\) −2.79831e6 2.42475e6i −0.334860 0.290158i
\(96\) 545479. + 807607.i 0.0629258 + 0.0931646i
\(97\) 2.19587e6 + 315719.i 0.244290 + 0.0351236i 0.263372 0.964694i \(-0.415165\pi\)
−0.0190821 + 0.999818i \(0.506074\pi\)
\(98\) 9.45231e6 + 1.47081e7i 1.01449 + 1.57857i
\(99\) −4.11192e6 + 1.02144e7i −0.425913 + 1.05801i
\(100\) 35174.6 + 40593.7i 0.00351746 + 0.00405937i
\(101\) 1.33639e7 1.92144e6i 1.29065 0.185568i 0.537415 0.843318i \(-0.319401\pi\)
0.753236 + 0.657751i \(0.228492\pi\)
\(102\) 9.38750e6 8.51742e6i 0.875889 0.794708i
\(103\) 5.36928e6 + 1.82861e7i 0.484156 + 1.64889i 0.732915 + 0.680320i \(0.238159\pi\)
−0.248759 + 0.968565i \(0.580023\pi\)
\(104\) −1.77443e6 6.04315e6i −0.154683 0.526801i
\(105\) 1.43059e7 1.29799e7i 1.20601 1.09423i
\(106\) −1.35760e7 + 1.95193e6i −1.10714 + 0.159182i
\(107\) −5.89766e6 6.80627e6i −0.465411 0.537113i 0.473718 0.880676i \(-0.342911\pi\)
−0.939130 + 0.343563i \(0.888366\pi\)
\(108\) 519489. + 522478.i 0.0396820 + 0.0399103i
\(109\) −7.00554e6 1.09008e7i −0.518142 0.806245i 0.479306 0.877648i \(-0.340889\pi\)
−0.997448 + 0.0714035i \(0.977252\pi\)
\(110\) 1.45605e7 + 2.09348e6i 1.04304 + 0.149967i
\(111\) −1.08396e7 1.60485e7i −0.752284 1.11379i
\(112\) 1.80957e7 + 1.56800e7i 1.21706 + 1.05459i
\(113\) −7.91844e6 2.32506e6i −0.516256 0.151586i 0.0132180 0.999913i \(-0.495792\pi\)
−0.529474 + 0.848326i \(0.677611\pi\)
\(114\) 2.82445e6 6.57833e6i 0.178553 0.415862i
\(115\) 666677. 1.54974e7i 0.0408764 0.950206i
\(116\) 64860.8i 0.00385815i
\(117\) −4.23175e6 8.24714e6i −0.244270 0.476050i
\(118\) −5.04644e6 + 5.82390e6i −0.282747 + 0.326307i
\(119\) −2.07168e7 + 3.22360e7i −1.12696 + 1.75358i
\(120\) 9.63005e6 1.57652e7i 0.508738 0.832845i
\(121\) 4.93106e6 3.16900e6i 0.253042 0.162620i
\(122\) 6.39417e6 + 1.40013e7i 0.318805 + 0.698085i
\(123\) 8.89636e6 + 2.79222e7i 0.431067 + 1.35295i
\(124\) 42269.4 + 293990.i 0.00199090 + 0.0138470i
\(125\) 9.45092e6 2.06946e7i 0.432802 0.947704i
\(126\) 3.23088e7 + 1.87359e7i 1.43888 + 0.834408i
\(127\) −3.02425e7 + 8.88000e6i −1.31010 + 0.384680i −0.860911 0.508756i \(-0.830105\pi\)
−0.449190 + 0.893436i \(0.648287\pi\)
\(128\) 1.95834e7 + 8.94342e6i 0.825377 + 0.376937i
\(129\) 9.96944e6 3.70647e7i 0.408890 1.52018i
\(130\) −9.35889e6 + 8.10953e6i −0.373614 + 0.323738i
\(131\) 1.00228e6 457728.i 0.0389530 0.0177892i −0.395843 0.918318i \(-0.629548\pi\)
0.434796 + 0.900529i \(0.356820\pi\)
\(132\) −279677. 1.67296e6i −0.0105840 0.0633105i
\(133\) −3.07999e6 + 2.14218e7i −0.113519 + 0.789543i
\(134\) −3.44607e7 2.21465e7i −1.23725 0.795132i
\(135\) 9.57448e6 2.54470e7i 0.334924 0.890161i
\(136\) −1.03246e7 + 3.51622e7i −0.351954 + 1.19864i
\(137\) 5.11540e7 1.69964 0.849821 0.527072i \(-0.176710\pi\)
0.849821 + 0.527072i \(0.176710\pi\)
\(138\) 2.89410e7 7.86811e6i 0.937426 0.254855i
\(139\) 3.44897e7 1.08928 0.544638 0.838671i \(-0.316667\pi\)
0.544638 + 0.838671i \(0.316667\pi\)
\(140\) −838328. + 2.85508e6i −0.0258206 + 0.0879368i
\(141\) −2.59552e7 + 1.25776e7i −0.779754 + 0.377860i
\(142\) 7.70799e6 + 4.95363e6i 0.225908 + 0.145182i
\(143\) −3.03693e6 + 2.11223e7i −0.0868477 + 0.604039i
\(144\) 3.27364e7 + 8.00808e6i 0.913614 + 0.223491i
\(145\) 2.17718e6 994284.i 0.0593070 0.0270846i
\(146\) −1.32847e7 + 1.15113e7i −0.353279 + 0.306118i
\(147\) −7.18388e7 1.93228e7i −1.86530 0.501717i
\(148\) 2.71365e6 + 1.23928e6i 0.0688079 + 0.0314235i
\(149\) −6.41953e7 + 1.88495e7i −1.58983 + 0.466817i −0.952694 0.303932i \(-0.901701\pi\)
−0.637139 + 0.770749i \(0.719882\pi\)
\(150\) 3.80480e6 + 458609.i 0.0920475 + 0.0110949i
\(151\) 7.93708e6 1.73798e7i 0.187604 0.410795i −0.792337 0.610083i \(-0.791136\pi\)
0.979941 + 0.199289i \(0.0638632\pi\)
\(152\) 2.94558e6 + 2.04869e7i 0.0680327 + 0.473178i
\(153\) −5.22946e6 + 5.36805e7i −0.118042 + 1.21170i
\(154\) −3.57176e7 7.82106e7i −0.788060 1.72561i
\(155\) 9.22039e6 5.92559e6i 0.198879 0.127812i
\(156\) 1.21855e6 + 744342.i 0.0256984 + 0.0156977i
\(157\) 2.31465e7 3.60167e7i 0.477350 0.742772i −0.516163 0.856491i \(-0.672640\pi\)
0.993513 + 0.113719i \(0.0362764\pi\)
\(158\) 2.31354e7 2.66997e7i 0.466636 0.538527i
\(159\) 3.72000e7 4.49667e7i 0.733927 0.887158i
\(160\) 5.53988e6i 0.106925i
\(161\) −7.83090e7 + 4.56941e7i −1.47884 + 0.862919i
\(162\) 5.24988e7 + 2.70208e6i 0.970168 + 0.0499340i
\(163\) 4.18906e7 + 1.23002e7i 0.757635 + 0.222462i 0.637663 0.770316i \(-0.279901\pi\)
0.119972 + 0.992777i \(0.461720\pi\)
\(164\) −3.41167e6 2.95623e6i −0.0603967 0.0523340i
\(165\) −5.18688e7 + 3.50335e7i −0.898902 + 0.607142i
\(166\) −4.08832e7 5.87812e6i −0.693692 0.0997378i
\(167\) 7.15765e6 + 1.11375e7i 0.118922 + 0.185046i 0.895611 0.444838i \(-0.146739\pi\)
−0.776689 + 0.629884i \(0.783102\pi\)
\(168\) −1.07950e8 + 2.46642e6i −1.75646 + 0.0401315i
\(169\) 2.93274e7 + 3.38456e7i 0.467380 + 0.539385i
\(170\) 7.13208e7 1.02544e7i 1.11338 0.160080i
\(171\) 9.90796e6 + 2.88053e7i 0.151530 + 0.440540i
\(172\) 1.66574e6 + 5.67300e6i 0.0249608 + 0.0850087i
\(173\) 1.29241e7 + 4.40155e7i 0.189775 + 0.646315i 0.998323 + 0.0578846i \(0.0184356\pi\)
−0.808548 + 0.588430i \(0.799746\pi\)
\(174\) 3.10959e6 + 3.42725e6i 0.0447488 + 0.0493200i
\(175\) −1.14674e7 + 1.64876e6i −0.161745 + 0.0232555i
\(176\) −5.08077e7 5.86353e7i −0.702483 0.810708i
\(177\) −748974. 3.27809e7i −0.0101522 0.444339i
\(178\) 1.72520e7 + 2.68446e7i 0.229281 + 0.356769i
\(179\) 6.21779e7 + 8.93984e6i 0.810309 + 0.116505i 0.535001 0.844851i \(-0.320311\pi\)
0.275308 + 0.961356i \(0.411220\pi\)
\(180\) 784763. + 4.11405e6i 0.0100296 + 0.0525795i
\(181\) −8.42355e7 7.29905e7i −1.05589 0.914937i −0.0593692 0.998236i \(-0.518909\pi\)
−0.996525 + 0.0832989i \(0.973454\pi\)
\(182\) 6.94495e7 + 2.03922e7i 0.853925 + 0.250735i
\(183\) −6.01812e7 2.58392e7i −0.725908 0.311674i
\(184\) −5.95461e7 + 6.30292e7i −0.704679 + 0.745897i
\(185\) 1.10087e8i 1.27830i
\(186\) 1.63282e7 + 1.35080e7i 0.186056 + 0.153920i
\(187\) 8.13104e7 9.38372e7i 0.909286 1.04937i
\(188\) 2.40204e6 3.73764e6i 0.0263650 0.0410247i
\(189\) −1.55381e8 + 3.33346e7i −1.67410 + 0.359152i
\(190\) 3.42351e7 2.20016e7i 0.362105 0.232711i
\(191\) −1.90137e7 4.16341e7i −0.197446 0.432347i 0.784849 0.619687i \(-0.212741\pi\)
−0.982295 + 0.187340i \(0.940013\pi\)
\(192\) −9.80962e7 + 3.12546e7i −1.00023 + 0.318684i
\(193\) −2.26038e7 1.57213e8i −0.226324 1.57412i −0.713398 0.700759i \(-0.752845\pi\)
0.487074 0.873361i \(-0.338064\pi\)
\(194\) −1.01288e7 + 2.21790e7i −0.0995985 + 0.218090i
\(195\) 6.30556e6 5.23133e7i 0.0608979 0.505232i
\(196\) 1.09954e7 3.22855e6i 0.104308 0.0306275i
\(197\) −1.13986e8 5.20558e7i −1.06224 0.485107i −0.193868 0.981028i \(-0.562103\pi\)
−0.868368 + 0.495921i \(0.834830\pi\)
\(198\) −9.49841e7 7.49907e7i −0.869607 0.686561i
\(199\) 1.34248e8 1.16327e8i 1.20760 1.04639i 0.209962 0.977709i \(-0.432666\pi\)
0.997639 0.0686828i \(-0.0218796\pi\)
\(200\) −1.00785e7 + 4.60268e6i −0.0890818 + 0.0406823i
\(201\) 1.71913e8 2.87397e7i 1.49322 0.249629i
\(202\) −2.11180e7 + 1.46879e8i −0.180270 + 1.25381i
\(203\) −1.17689e7 7.56342e6i −0.0987416 0.0634574i
\(204\) −3.62311e6 7.47667e6i −0.0298797 0.0616598i
\(205\) −4.69323e7 + 1.59837e8i −0.380481 + 1.29580i
\(206\) −2.09462e8 −1.66944
\(207\) −6.87033e7 + 1.07541e8i −0.538371 + 0.842708i
\(208\) 6.53144e7 0.503254
\(209\) 1.97569e7 6.72859e7i 0.149695 0.509815i
\(210\) 9.25829e7 + 1.91054e8i 0.689863 + 1.42361i
\(211\) −4.63024e7 2.97568e7i −0.339324 0.218071i 0.359870 0.933003i \(-0.382821\pi\)
−0.699194 + 0.714932i \(0.746458\pi\)
\(212\) −1.27940e6 + 8.89841e6i −0.00922211 + 0.0641412i
\(213\) −3.84527e7 + 6.42834e6i −0.272645 + 0.0455796i
\(214\) 9.00375e7 4.11187e7i 0.628022 0.286808i
\(215\) 1.64890e8 1.42878e8i 1.13152 0.980465i
\(216\) −1.33599e8 + 7.24538e7i −0.902016 + 0.489185i
\(217\) −5.82733e7 2.66125e7i −0.387133 0.176798i
\(218\) 1.36647e8 4.01233e7i 0.893312 0.262300i
\(219\) 8.95058e6 7.42575e7i 0.0575833 0.477734i
\(220\) 4.00537e6 8.77053e6i 0.0253608 0.0555324i
\(221\) 1.48756e7 + 1.03462e8i 0.0927048 + 0.644776i
\(222\) 2.02804e8 6.46158e7i 1.24406 0.396372i
\(223\) 1.12106e8 + 2.45478e8i 0.676958 + 1.48233i 0.865834 + 0.500331i \(0.166788\pi\)
−0.188876 + 0.982001i \(0.560484\pi\)
\(224\) 2.72401e7 1.75061e7i 0.161935 0.104069i
\(225\) −1.33010e7 + 9.43330e6i −0.0778475 + 0.0552109i
\(226\) 4.90380e7 7.63047e7i 0.282588 0.439715i
\(227\) −6.41753e7 + 7.40623e7i −0.364148 + 0.420249i −0.908025 0.418916i \(-0.862410\pi\)
0.543877 + 0.839165i \(0.316956\pi\)
\(228\) −3.61556e6 2.99107e6i −0.0202024 0.0167130i
\(229\) 9.73871e7i 0.535892i 0.963434 + 0.267946i \(0.0863449\pi\)
−0.963434 + 0.267946i \(0.913655\pi\)
\(230\) 1.61364e8 + 5.50175e7i 0.874501 + 0.298163i
\(231\) 3.36169e8 + 1.44337e8i 1.79439 + 0.770433i
\(232\) −1.28372e7 3.76935e6i −0.0674938 0.0198180i
\(233\) −1.30914e8 1.13438e8i −0.678018 0.587506i 0.246270 0.969201i \(-0.420795\pi\)
−0.924288 + 0.381695i \(0.875340\pi\)
\(234\) 1.00074e8 1.90893e7i 0.510581 0.0973943i
\(235\) −1.62283e8 2.33328e7i −0.815711 0.117282i
\(236\) 2.73078e6 + 4.24917e6i 0.0135237 + 0.0210432i
\(237\) 3.43368e6 + 1.50284e8i 0.0167548 + 0.733321i
\(238\) −2.75797e8 3.18287e8i −1.32608 1.53038i
\(239\) 3.30289e8 4.74884e7i 1.56495 0.225006i 0.695318 0.718702i \(-0.255264\pi\)
0.869635 + 0.493696i \(0.164354\pi\)
\(240\) 1.28730e8 + 1.41880e8i 0.601092 + 0.662494i
\(241\) 7.69918e7 + 2.62210e8i 0.354311 + 1.20667i 0.923220 + 0.384272i \(0.125547\pi\)
−0.568909 + 0.822400i \(0.692634\pi\)
\(242\) 1.81500e7 + 6.18133e7i 0.0823234 + 0.280368i
\(243\) −1.73161e8 + 1.41587e8i −0.774154 + 0.632997i
\(244\) 9.98620e6 1.43580e6i 0.0440084 0.00632746i
\(245\) −2.76927e8 3.19591e8i −1.20305 1.38840i
\(246\) −3.22002e8 + 7.35706e6i −1.37907 + 0.0315088i
\(247\) 3.19168e7 + 4.96635e7i 0.134766 + 0.209700i
\(248\) −6.06430e7 8.71915e6i −0.252464 0.0362989i
\(249\) 1.45638e8 9.83679e7i 0.597830 0.403790i
\(250\) 1.88972e8 + 1.63745e8i 0.764903 + 0.662792i
\(251\) 2.32937e8 + 6.83966e7i 0.929782 + 0.273009i 0.711345 0.702843i \(-0.248086\pi\)
0.218437 + 0.975851i \(0.429904\pi\)
\(252\) 1.77493e7 1.68592e7i 0.0698681 0.0663645i
\(253\) 2.72232e8 1.10443e8i 1.05686 0.428764i
\(254\) 3.46419e8i 1.32643i
\(255\) −1.95428e8 + 2.36230e8i −0.738069 + 0.892165i
\(256\) 2.95845e7 3.41423e7i 0.110211 0.127190i
\(257\) 1.40179e8 2.18122e8i 0.515129 0.801557i −0.482087 0.876123i \(-0.660121\pi\)
0.997216 + 0.0745668i \(0.0237574\pi\)
\(258\) 3.59997e8 + 2.19902e8i 1.30506 + 0.797186i
\(259\) −5.41306e8 + 3.47876e8i −1.93595 + 1.24416i
\(260\) 3.37186e6 + 7.38335e6i 0.0118977 + 0.0260523i
\(261\) −1.95980e7 1.90920e6i −0.0682292 0.00664677i
\(262\) 1.72346e6 + 1.19869e7i 0.00592035 + 0.0411769i
\(263\) −1.78347e8 + 3.90525e8i −0.604533 + 1.32374i 0.321718 + 0.946836i \(0.395740\pi\)
−0.926251 + 0.376907i \(0.876988\pi\)
\(264\) 3.47365e8 + 4.18695e7i 1.16191 + 0.140050i
\(265\) 3.18305e8 9.34629e7i 1.05071 0.308517i
\(266\) −2.16367e8 9.88117e7i −0.704865 0.321901i
\(267\) −1.31117e8 3.52672e7i −0.421571 0.113392i
\(268\) −2.02916e7 + 1.75828e7i −0.0643939 + 0.0557976i
\(269\) 3.07009e7 1.40206e7i 0.0961653 0.0439172i −0.366752 0.930319i \(-0.619530\pi\)
0.462917 + 0.886402i \(0.346803\pi\)
\(270\) 2.38705e8 + 1.79763e8i 0.738056 + 0.555812i
\(271\) −6.91020e7 + 4.80615e8i −0.210910 + 1.46691i 0.559215 + 0.829022i \(0.311102\pi\)
−0.770126 + 0.637892i \(0.779807\pi\)
\(272\) −3.19704e8 2.05461e8i −0.963291 0.619069i
\(273\) −2.77155e8 + 1.34306e8i −0.824429 + 0.399509i
\(274\) −1.58396e8 + 5.39446e8i −0.465175 + 1.58424i
\(275\) 3.75397e7 0.108850
\(276\) 396044. 1.96540e7i 0.00113387 0.0562691i
\(277\) −3.37458e7 −0.0953983 −0.0476991 0.998862i \(-0.515189\pi\)
−0.0476991 + 0.998862i \(0.515189\pi\)
\(278\) −1.06796e8 + 3.63712e8i −0.298124 + 1.01532i
\(279\) −9.00749e7 + 4.11819e6i −0.248307 + 0.0113525i
\(280\) −5.16359e8 3.31844e8i −1.40572 0.903401i
\(281\) 6.27461e7 4.36409e8i 0.168700 1.17333i −0.712876 0.701290i \(-0.752608\pi\)
0.881576 0.472043i \(-0.156483\pi\)
\(282\) −5.22686e7 3.12657e8i −0.138793 0.830226i
\(283\) 5.34210e8 2.43965e8i 1.40107 0.639847i 0.435546 0.900166i \(-0.356555\pi\)
0.965522 + 0.260320i \(0.0838280\pi\)
\(284\) 4.53872e6 3.93283e6i 0.0117576 0.0101880i
\(285\) −4.49765e7 + 1.67215e8i −0.115088 + 0.427876i
\(286\) −2.13342e8 9.74300e7i −0.539256 0.246270i
\(287\) 9.34239e8 2.74317e8i 2.33277 0.684962i
\(288\) 2.28634e7 3.94262e7i 0.0563984 0.0972550i
\(289\) 8.21894e7 1.79970e8i 0.200297 0.438588i
\(290\) 3.74373e6 + 2.60382e7i 0.00901388 + 0.0626929i
\(291\) −3.14950e7 9.88507e7i −0.0749232 0.235155i
\(292\) 4.78628e6 + 1.04805e7i 0.0112501 + 0.0246344i
\(293\) −6.16201e7 + 3.96008e7i −0.143115 + 0.0919746i −0.610239 0.792217i \(-0.708927\pi\)
0.467124 + 0.884192i \(0.345290\pi\)
\(294\) 4.26214e8 6.97746e8i 0.978165 1.60133i
\(295\) 1.00770e8 1.56802e8i 0.228537 0.355610i
\(296\) −4.02982e8 + 4.65066e8i −0.903159 + 1.04230i
\(297\) 5.13725e8 3.52617e7i 1.13785 0.0781008i
\(298\) 7.35340e8i 1.60965i
\(299\) −7.98116e7 + 2.34085e8i −0.172670 + 0.506435i
\(300\) 991023. 2.30816e6i 0.00211914 0.00493561i
\(301\) −1.22360e9 3.59282e8i −2.58617 0.759369i
\(302\) 1.58702e8 + 1.37516e8i 0.331557 + 0.287296i
\(303\) −3.53402e8 5.23227e8i −0.729826 1.08054i
\(304\) −2.12454e8 3.05462e7i −0.433717 0.0623591i
\(305\) −2.01279e8 3.13196e8i −0.406209 0.632073i
\(306\) −5.49896e8 2.21366e8i −1.09712 0.441658i
\(307\) 1.72140e8 + 1.98661e8i 0.339546 + 0.391857i 0.899684 0.436543i \(-0.143797\pi\)
−0.560138 + 0.828400i \(0.689252\pi\)
\(308\) −5.57825e7 + 8.02031e6i −0.108785 + 0.0156410i
\(309\) 6.60060e8 5.98883e8i 1.27271 1.15475i
\(310\) 3.39380e7 + 1.15582e8i 0.0647023 + 0.220356i
\(311\) −1.08111e7 3.68191e7i −0.0203801 0.0694084i 0.948675 0.316252i \(-0.102425\pi\)
−0.969055 + 0.246844i \(0.920606\pi\)
\(312\) −2.18135e8 + 1.97918e8i −0.406617 + 0.368930i
\(313\) 7.77694e8 1.11816e8i 1.43352 0.206109i 0.618611 0.785698i \(-0.287696\pi\)
0.814909 + 0.579588i \(0.196787\pi\)
\(314\) 3.08143e8 + 3.55616e8i 0.561693 + 0.648228i
\(315\) −8.38002e8 3.37346e8i −1.51063 0.608119i
\(316\) −1.25193e7 1.94804e7i −0.0223190 0.0347290i
\(317\) 7.20755e6 + 1.03629e6i 0.0127081 + 0.00182715i 0.148666 0.988887i \(-0.452502\pi\)
−0.135958 + 0.990715i \(0.543411\pi\)
\(318\) 3.59010e8 + 5.31530e8i 0.626053 + 0.926901i
\(319\) 3.42587e7 + 2.96853e7i 0.0590885 + 0.0512005i
\(320\) −5.61538e8 1.64882e8i −0.957974 0.281287i
\(321\) −1.66163e8 + 3.87004e8i −0.280393 + 0.653053i
\(322\) −2.39389e8 9.67299e8i −0.399585 1.61460i
\(323\) 3.43497e8i 0.567171i
\(324\) 1.13939e7 3.25176e7i 0.0186108 0.0531143i
\(325\) −2.06951e7 + 2.38834e7i −0.0334407 + 0.0385927i
\(326\) −2.59424e8 + 4.03671e8i −0.414714 + 0.645307i
\(327\) −3.15887e8 + 5.17132e8i −0.499591 + 0.817870i
\(328\) 7.83364e8 5.03437e8i 1.22576 0.787747i
\(329\) 3.98089e8 + 8.71694e8i 0.616304 + 1.34952i
\(330\) −2.08838e8 6.55463e8i −0.319898 1.00404i
\(331\) 1.43442e8 + 9.97663e8i 0.217410 + 1.51212i 0.747548 + 0.664208i \(0.231231\pi\)
−0.530138 + 0.847911i \(0.677860\pi\)
\(332\) −1.12463e7 + 2.46261e7i −0.0168666 + 0.0369328i
\(333\) −4.54333e8 + 7.83465e8i −0.674248 + 1.16269i
\(334\) −1.39614e8 + 4.09945e7i −0.205030 + 0.0602022i
\(335\) 9.01261e8 + 4.11592e8i 1.30977 + 0.598150i
\(336\) 2.90847e8 1.08132e9i 0.418290 1.55513i
\(337\) 7.01475e8 6.07831e8i 0.998407 0.865124i 0.00754014 0.999972i \(-0.497600\pi\)
0.990866 + 0.134847i \(0.0430544\pi\)
\(338\) −4.47730e8 + 2.04472e8i −0.630679 + 0.288021i
\(339\) 6.36369e7 + 3.80660e8i 0.0887177 + 0.530686i
\(340\) 6.72126e6 4.67474e7i 0.00927416 0.0645032i
\(341\) 1.74628e8 + 1.12226e8i 0.238492 + 0.153269i
\(342\) −3.34446e8 + 1.52908e7i −0.452100 + 0.0206699i
\(343\) −3.35850e8 + 1.14380e9i −0.449383 + 1.53046i
\(344\) −1.21961e9 −1.61534
\(345\) −6.65797e8 + 2.87993e8i −0.872921 + 0.377585i
\(346\) −5.04185e8 −0.654370
\(347\) 1.36679e6 4.65487e6i 0.00175610 0.00598073i −0.958610 0.284722i \(-0.908099\pi\)
0.960366 + 0.278741i \(0.0899170\pi\)
\(348\) 2.72963e6 1.32275e6i 0.00347197 0.00168248i
\(349\) −8.30136e8 5.33496e8i −1.04535 0.671803i −0.0990429 0.995083i \(-0.531578\pi\)
−0.946303 + 0.323280i \(0.895214\pi\)
\(350\) 1.81211e7 1.26035e8i 0.0225916 0.157128i
\(351\) −2.60775e8 + 3.46280e8i −0.321878 + 0.427418i
\(352\) −9.54400e7 + 4.35860e7i −0.116636 + 0.0532657i
\(353\) −1.04881e9 + 9.08801e8i −1.26907 + 1.09966i −0.278823 + 0.960342i \(0.589944\pi\)
−0.990248 + 0.139314i \(0.955510\pi\)
\(354\) 3.48011e8 + 9.36059e7i 0.416948 + 0.112148i
\(355\) −2.01589e8 9.20628e7i −0.239149 0.109216i
\(356\) 2.00684e7 5.89261e6i 0.0235742 0.00692202i
\(357\) 1.77912e9 + 2.14446e8i 2.06951 + 0.249447i
\(358\) −2.86806e8 + 6.28017e8i −0.330368 + 0.723404i
\(359\) 7.42887e7 + 5.16689e8i 0.0847407 + 0.589385i 0.987306 + 0.158831i \(0.0507726\pi\)
−0.902565 + 0.430554i \(0.858318\pi\)
\(360\) −8.59859e8 8.37660e7i −0.971334 0.0946257i
\(361\) 2.90736e8 + 6.36623e8i 0.325255 + 0.712208i
\(362\) 1.03055e9 6.62297e8i 1.14180 0.733791i
\(363\) −2.33928e8 1.42894e8i −0.256690 0.156798i
\(364\) 2.56494e7 3.99113e7i 0.0278755 0.0433751i
\(365\) 2.78427e8 3.21322e8i 0.299699 0.345872i
\(366\) 4.58836e8 5.54632e8i 0.489185 0.591318i
\(367\) 7.14561e8i 0.754584i −0.926094 0.377292i \(-0.876855\pi\)
0.926094 0.377292i \(-0.123145\pi\)
\(368\) −4.53177e8 7.76639e8i −0.474024 0.812366i
\(369\) 9.93663e8 9.43835e8i 1.02955 0.977921i
\(370\) 1.16092e9 + 3.40877e8i 1.19151 + 0.349858i
\(371\) −1.46542e9 1.26979e9i −1.48988 1.29099i
\(372\) 1.15104e7 7.77442e6i 0.0115928 0.00783011i
\(373\) −1.50439e9 2.16299e8i −1.50100 0.215811i −0.657711 0.753271i \(-0.728475\pi\)
−0.843290 + 0.537459i \(0.819384\pi\)
\(374\) 7.37789e8 + 1.14802e9i 0.729259 + 1.13475i
\(375\) −1.06366e9 + 2.43024e7i −1.04158 + 0.0237980i
\(376\) 6.00161e8 + 6.92623e8i 0.582251 + 0.671953i
\(377\) −3.77726e7 + 5.43088e6i −0.0363063 + 0.00522006i
\(378\) 1.29598e8 1.74179e9i 0.123417 1.65873i
\(379\) 2.67484e8 + 9.10968e8i 0.252384 + 0.859539i 0.984052 + 0.177879i \(0.0569236\pi\)
−0.731669 + 0.681660i \(0.761258\pi\)
\(380\) −7.51490e6 2.55934e7i −0.00702556 0.0239268i
\(381\) 9.90464e8 + 1.09164e9i 0.917490 + 1.01121i
\(382\) 4.97929e8 7.15913e7i 0.457031 0.0657111i
\(383\) −9.04188e8 1.04349e9i −0.822362 0.949057i 0.177020 0.984207i \(-0.443354\pi\)
−0.999382 + 0.0351505i \(0.988809\pi\)
\(384\) −2.29974e7 1.00654e9i −0.0207262 0.907137i
\(385\) 1.12434e9 + 1.74950e9i 1.00412 + 1.56243i
\(386\) 1.72788e9 + 2.48432e8i 1.52918 + 0.219863i
\(387\) −1.76316e9 + 3.36326e8i −1.54633 + 0.294966i
\(388\) 1.20780e7 + 1.04657e7i 0.0104975 + 0.00909611i
\(389\) 1.69217e9 + 4.96865e8i 1.45754 + 0.427971i 0.912026 0.410133i \(-0.134518\pi\)
0.545510 + 0.838104i \(0.316336\pi\)
\(390\) 5.32147e8 + 2.28481e8i 0.454261 + 0.195040i
\(391\) 1.12703e9 8.94745e8i 0.953495 0.756973i
\(392\) 2.36384e9i 1.98206i
\(393\) −3.97034e7 3.28458e7i −0.0329955 0.0272964i
\(394\) 9.01908e8 1.04086e9i 0.742891 0.857342i
\(395\) −4.61982e8 + 7.18859e8i −0.377169 + 0.586886i
\(396\) −6.47018e7 + 4.58878e7i −0.0523580 + 0.0371333i
\(397\) 7.30181e8 4.69259e8i 0.585684 0.376396i −0.213985 0.976837i \(-0.568644\pi\)
0.799669 + 0.600440i \(0.205008\pi\)
\(398\) 8.11036e8 + 1.77592e9i 0.644836 + 1.41199i
\(399\) 9.64337e8 3.07249e8i 0.760018 0.242151i
\(400\) −1.63518e7 1.13729e8i −0.0127748 0.0888510i
\(401\) −1.82829e8 + 4.00339e8i −0.141592 + 0.310044i −0.967121 0.254316i \(-0.918150\pi\)
0.825529 + 0.564360i \(0.190877\pi\)
\(402\) −2.29245e8 + 1.90191e9i −0.175999 + 1.46015i
\(403\) −1.67670e8 + 4.92324e7i −0.127611 + 0.0374700i
\(404\) 8.84729e7 + 4.04042e7i 0.0667537 + 0.0304854i
\(405\) −1.26618e9 + 1.16021e8i −0.947117 + 0.0867851i
\(406\) 1.16202e8 1.00690e8i 0.0861733 0.0746696i
\(407\) 1.89655e9 8.66126e8i 1.39439 0.636796i
\(408\) 1.69034e9 2.82583e8i 1.23215 0.205985i
\(409\) 2.92656e8 2.03547e9i 0.211508 1.47107i −0.556618 0.830768i \(-0.687901\pi\)
0.768126 0.640299i \(-0.221190\pi\)
\(410\) −1.54024e9 9.89852e8i −1.10368 0.709295i
\(411\) −1.04322e9 2.15279e9i −0.741187 1.52952i
\(412\) −3.86798e7 + 1.31731e8i −0.0272486 + 0.0928001i
\(413\) −1.08944e9 −0.760991
\(414\) −9.21338e8 1.05751e9i −0.638143 0.732457i
\(415\) 9.99023e8 0.686131
\(416\) 2.48845e7 8.47489e7i 0.0169474 0.0577175i
\(417\) −7.03371e8 1.45148e9i −0.475016 0.980246i
\(418\) 6.48389e8 + 4.16695e8i 0.434229 + 0.279062i
\(419\) 1.17375e8 8.16362e8i 0.0779519 0.542167i −0.913001 0.407957i \(-0.866241\pi\)
0.990953 0.134210i \(-0.0428497\pi\)
\(420\) 1.37251e8 2.29450e7i 0.0903948 0.0151118i
\(421\) −8.32765e7 + 3.80311e7i −0.0543920 + 0.0248400i −0.442425 0.896805i \(-0.645882\pi\)
0.388033 + 0.921645i \(0.373155\pi\)
\(422\) 4.57174e8 3.96143e8i 0.296133 0.256601i
\(423\) 1.05864e9 + 8.35807e8i 0.680077 + 0.536926i
\(424\) −1.68682e9 7.70346e8i −1.07470 0.490801i
\(425\) 1.76430e8 5.18046e7i 0.111484 0.0327346i
\(426\) 5.12764e7 4.25409e8i 0.0321354 0.266608i
\(427\) −9.03968e8 + 1.97941e9i −0.561896 + 1.23038i
\(428\) −9.23313e6 6.42178e7i −0.00569241 0.0395915i
\(429\) 9.50854e8 3.02953e8i 0.581451 0.185257i
\(430\) 9.96154e8 + 2.18127e9i 0.604208 + 1.32303i
\(431\) −6.28644e8 + 4.04005e8i −0.378211 + 0.243062i −0.715910 0.698193i \(-0.753988\pi\)
0.337699 + 0.941254i \(0.390352\pi\)
\(432\) −3.30600e8 1.54101e9i −0.197292 0.919627i
\(433\) 1.18564e8 1.84489e8i 0.0701852 0.109210i −0.804387 0.594106i \(-0.797506\pi\)
0.874572 + 0.484896i \(0.161142\pi\)
\(434\) 4.61083e8 5.32118e8i 0.270748 0.312460i
\(435\) −8.62445e7 7.13482e7i −0.0502365 0.0415596i
\(436\) 9.33470e7i 0.0539384i
\(437\) 3.69087e8 7.24101e8i 0.211565 0.415063i
\(438\) 7.55369e8 + 3.24323e8i 0.429536 + 0.184424i
\(439\) −4.42282e8 1.29866e8i −0.249501 0.0732602i 0.154590 0.987979i \(-0.450594\pi\)
−0.404092 + 0.914718i \(0.632412\pi\)
\(440\) 1.50309e9 + 1.30244e9i 0.841204 + 0.728908i
\(441\) 6.51867e8 + 3.41736e9i 0.361930 + 1.89738i
\(442\) −1.13712e9 1.63494e8i −0.626369 0.0900582i
\(443\) 1.05163e9 + 1.63637e9i 0.574712 + 0.894269i 0.999941 0.0108166i \(-0.00344311\pi\)
−0.425230 + 0.905085i \(0.639807\pi\)
\(444\) −3.18673e6 1.39476e8i −0.00172785 0.0756239i
\(445\) −5.05436e8 5.83304e8i −0.271898 0.313787i
\(446\) −2.93582e9 + 4.22108e8i −1.56696 + 0.225295i
\(447\) 2.10245e9 + 2.31721e9i 1.11339 + 1.22713i
\(448\) 9.63729e8 + 3.28216e9i 0.506386 + 1.72459i
\(449\) −6.92413e8 2.35814e9i −0.360996 1.22944i −0.917211 0.398402i \(-0.869565\pi\)
0.556215 0.831039i \(-0.312253\pi\)
\(450\) −5.82934e7 1.69475e8i −0.0301561 0.0876724i
\(451\) −3.12288e9 + 4.49003e8i −1.60302 + 0.230479i
\(452\) −3.89327e7 4.49307e7i −0.0198303 0.0228854i
\(453\) −8.93284e8 + 2.04096e7i −0.451488 + 0.0103155i
\(454\) −5.82310e8 9.06093e8i −0.292051 0.454441i
\(455\) −1.73289e9 2.49153e8i −0.862447 0.124001i
\(456\) 8.02110e8 5.41766e8i 0.396147 0.267568i
\(457\) −7.83737e8 6.79112e8i −0.384117 0.332839i 0.441303 0.897358i \(-0.354516\pi\)
−0.825420 + 0.564519i \(0.809062\pi\)
\(458\) −1.02700e9 3.01554e8i −0.499506 0.146668i
\(459\) 2.36576e9 8.74662e8i 1.14190 0.422178i
\(460\) 6.43985e7 9.13227e7i 0.0308477 0.0437448i
\(461\) 6.09736e8i 0.289860i 0.989442 + 0.144930i \(0.0462957\pi\)
−0.989442 + 0.144930i \(0.953704\pi\)
\(462\) −2.56304e9 + 3.09815e9i −1.20923 + 1.46169i
\(463\) −1.46825e9 + 1.69445e9i −0.687491 + 0.793407i −0.987006 0.160684i \(-0.948630\pi\)
0.299514 + 0.954092i \(0.403175\pi\)
\(464\) 7.50112e7 1.16720e8i 0.0348588 0.0542414i
\(465\) −4.37412e8 2.67191e8i −0.201746 0.123236i
\(466\) 1.60163e9 1.02931e9i 0.733182 0.471188i
\(467\) −3.31208e8 7.25243e8i −0.150484 0.329515i 0.819345 0.573301i \(-0.194338\pi\)
−0.969829 + 0.243787i \(0.921610\pi\)
\(468\) 6.47458e6 6.64617e7i 0.00291979 0.0299717i
\(469\) −8.24169e8 5.73222e9i −0.368902 2.56577i
\(470\) 7.48559e8 1.63911e9i 0.332570 0.728227i
\(471\) −1.98779e9 2.39597e8i −0.876589 0.105659i
\(472\) −9.99694e8 + 2.93537e8i −0.437593 + 0.128489i
\(473\) 3.75879e9 + 1.71658e9i 1.63318 + 0.745847i
\(474\) −1.59546e9 4.29137e8i −0.688116 0.185085i
\(475\) 7.84865e7 6.80090e7i 0.0336022 0.0291165i
\(476\) −2.51100e8 + 1.14674e8i −0.106714 + 0.0487348i
\(477\) −2.65104e9 6.48505e8i −1.11841 0.273589i
\(478\) −5.21932e8 + 3.63011e9i −0.218583 + 1.52028i
\(479\) −2.57484e9 1.65475e9i −1.07047 0.687950i −0.118135 0.992998i \(-0.537691\pi\)
−0.952337 + 0.305047i \(0.901328\pi\)
\(480\) 2.33143e8 1.12978e8i 0.0962227 0.0466285i
\(481\) −4.94497e8 + 1.68410e9i −0.202608 + 0.690018i
\(482\) −3.00354e9 −1.22171
\(483\) 3.52002e9 + 2.36372e9i 1.42144 + 0.954511i
\(484\) 4.22262e7 0.0169287
\(485\) 1.66150e8 5.65856e8i 0.0661310 0.225222i
\(486\) −9.56927e8 2.26449e9i −0.378139 0.894835i
\(487\) −3.46232e9 2.22510e9i −1.35836 0.872966i −0.360158 0.932891i \(-0.617277\pi\)
−0.998203 + 0.0599254i \(0.980914\pi\)
\(488\) −2.96170e8 + 2.05991e9i −0.115365 + 0.802378i
\(489\) −3.36656e8 2.01379e9i −0.130198 0.778812i
\(490\) 4.22775e9 1.93075e9i 1.62339 0.741377i
\(491\) 1.75281e9 1.51882e9i 0.668267 0.579056i −0.253247 0.967402i \(-0.581499\pi\)
0.921514 + 0.388345i \(0.126953\pi\)
\(492\) −5.48347e7 + 2.03866e8i −0.0207576 + 0.0771734i
\(493\) 2.01976e8 + 9.22391e7i 0.0759162 + 0.0346698i
\(494\) −6.22556e8 + 1.82799e8i −0.232346 + 0.0682228i
\(495\) 2.53216e9 + 1.46841e9i 0.938368 + 0.544162i
\(496\) 2.63933e8 5.77932e8i 0.0971197 0.212663i
\(497\) 1.84346e8 + 1.28215e9i 0.0673575 + 0.468482i
\(498\) 5.86380e8 + 1.84042e9i 0.212753 + 0.667751i
\(499\) −1.26879e9 2.77826e9i −0.457127 1.00097i −0.988133 0.153600i \(-0.950913\pi\)
0.531006 0.847368i \(-0.321814\pi\)
\(500\) 1.37875e8 8.86071e7i 0.0493278 0.0317010i
\(501\) 3.22746e8 5.28360e8i 0.114664 0.187715i
\(502\) −1.44256e9 + 2.24466e9i −0.508944 + 0.791932i
\(503\) −1.56929e9 + 1.81106e9i −0.549813 + 0.634518i −0.960839 0.277106i \(-0.910625\pi\)
0.411027 + 0.911623i \(0.365170\pi\)
\(504\) 2.30529e9 + 4.49271e9i 0.802081 + 1.56315i
\(505\) 3.58914e9i 1.24014i
\(506\) 3.21732e8 + 3.21281e9i 0.110400 + 1.10245i
\(507\) 8.26280e8 1.92446e9i 0.281579 0.655815i
\(508\) −2.17864e8 6.39706e7i −0.0737331 0.0216500i
\(509\) −3.82162e8 3.31146e8i −0.128450 0.111303i 0.588267 0.808667i \(-0.299811\pi\)
−0.716717 + 0.697364i \(0.754356\pi\)
\(510\) −1.88604e9 2.79237e9i −0.629587 0.932132i
\(511\) −2.45980e9 3.53666e8i −0.815505 0.117252i
\(512\) 1.75828e9 + 2.73594e9i 0.578954 + 0.900870i
\(513\) 1.01019e9 1.00442e9i 0.330365 0.328475i
\(514\) 1.86616e9 + 2.15366e9i 0.606147 + 0.699531i
\(515\) 5.01476e9 7.21013e8i 1.61780 0.232604i
\(516\) 2.04775e8 1.85795e8i 0.0656148 0.0595334i
\(517\) −8.74819e8 2.97936e9i −0.278421 0.948214i
\(518\) −1.99241e9 6.78553e9i −0.629832 2.14501i
\(519\) 1.58880e9 1.44154e9i 0.498864 0.452627i
\(520\) −1.65727e9 + 2.38279e8i −0.516870 + 0.0743146i
\(521\) 1.16197e8 + 1.34099e8i 0.0359968 + 0.0415425i 0.773462 0.633842i \(-0.218523\pi\)
−0.737466 + 0.675385i \(0.763978\pi\)
\(522\) 8.08177e7 2.00760e8i 0.0248691 0.0617774i
\(523\) −2.92910e7 4.55777e7i −0.00895321 0.0139315i 0.836748 0.547588i \(-0.184454\pi\)
−0.845701 + 0.533657i \(0.820818\pi\)
\(524\) 7.85687e6 + 1.12965e6i 0.00238556 + 0.000342992i
\(525\) 3.03249e8 + 4.48975e8i 0.0914623 + 0.135414i
\(526\) −3.56605e9 3.09000e9i −1.06841 0.925781i
\(527\) 9.75594e8 + 2.86460e8i 0.290357 + 0.0852564i
\(528\) −1.43148e9 + 3.33400e9i −0.423219 + 0.985705i
\(529\) 3.33722e9 6.75151e8i 0.980143 0.198292i
\(530\) 3.64610e9i 1.06381i
\(531\) −1.36429e9 + 7.00042e8i −0.395436 + 0.202905i
\(532\) −1.02098e8 + 1.17827e8i −0.0293985 + 0.0339277i
\(533\) 1.43594e9 2.23436e9i 0.410762 0.639158i
\(534\) 7.77908e8 1.27350e9i 0.221072 0.361913i
\(535\) −2.01406e9 + 1.29436e9i −0.568635 + 0.365440i
\(536\) −2.30075e9 5.03793e9i −0.645345 1.41311i
\(537\) −8.91807e8 2.79904e9i −0.248520 0.780008i
\(538\) 5.27913e7 + 3.67172e8i 0.0146159 + 0.101656i
\(539\) 3.32708e9 7.28528e9i 0.915171 2.00394i
\(540\) 1.57133e8 1.16927e8i 0.0429428 0.0319548i
\(541\) 5.50937e9 1.61770e9i 1.49593 0.439245i 0.571502 0.820601i \(-0.306361\pi\)
0.924428 + 0.381356i \(0.124543\pi\)
\(542\) −4.85437e9 2.21691e9i −1.30959 0.598069i
\(543\) −1.35389e9 + 5.03355e9i −0.362899 + 1.34919i
\(544\) −3.88404e8 + 3.36554e8i −0.103440 + 0.0896310i
\(545\) −3.13338e9 + 1.43096e9i −0.829134 + 0.378653i
\(546\) −5.58134e8 3.33862e9i −0.146745 0.877793i
\(547\) −4.07312e8 + 2.83292e9i −0.106407 + 0.740080i 0.864847 + 0.502036i \(0.167415\pi\)
−0.971254 + 0.238044i \(0.923494\pi\)
\(548\) 3.10009e8 + 1.99231e8i 0.0804715 + 0.0517159i
\(549\) 1.39886e8 + 3.05965e9i 0.0360803 + 0.789165i
\(550\) −1.16240e8 + 3.95876e8i −0.0297910 + 0.101459i
\(551\) 1.25406e8 0.0319366
\(552\) 3.86691e9 + 1.22057e9i 0.978537 + 0.308870i
\(553\) 4.99457e9 1.25591
\(554\) 1.04492e8 3.55867e8i 0.0261095 0.0889209i
\(555\) −4.63293e9 + 2.24507e9i −1.15035 + 0.557448i
\(556\) 2.09018e8 + 1.34328e8i 0.0515730 + 0.0331440i
\(557\) 8.59741e8 5.97963e9i 0.210802 1.46616i −0.559686 0.828705i \(-0.689078\pi\)
0.770488 0.637455i \(-0.220013\pi\)
\(558\) 2.35484e8 9.62639e8i 0.0573774 0.234554i
\(559\) −3.16428e9 + 1.44508e9i −0.766186 + 0.349905i
\(560\) 4.81050e9 4.16832e9i 1.15753 1.00300i
\(561\) −5.60730e9 1.50822e9i −1.34086 0.360657i
\(562\) 4.40787e9 + 2.01301e9i 1.04749 + 0.478375i
\(563\) −7.86647e8 + 2.30980e8i −0.185781 + 0.0545501i −0.373299 0.927711i \(-0.621774\pi\)
0.187519 + 0.982261i \(0.439955\pi\)
\(564\) −2.06283e8 2.48642e7i −0.0484157 0.00583576i
\(565\) −9.11369e8 + 1.99562e9i −0.212581 + 0.465488i
\(566\) 9.18592e8 + 6.38895e9i 0.212944 + 1.48106i
\(567\) 4.57165e9 + 5.85930e9i 1.05325 + 1.34991i
\(568\) 5.14619e8 + 1.12686e9i 0.117833 + 0.258018i
\(569\) 2.34107e9 1.50451e9i 0.532747 0.342375i −0.246450 0.969156i \(-0.579264\pi\)
0.779196 + 0.626780i \(0.215628\pi\)
\(570\) −1.62410e9 9.92073e8i −0.367326 0.224379i
\(571\) −2.65733e8 + 4.13488e8i −0.0597336 + 0.0929473i −0.869836 0.493342i \(-0.835775\pi\)
0.810102 + 0.586289i \(0.199412\pi\)
\(572\) −1.00670e8 + 1.16180e8i −0.0224913 + 0.0259564i
\(573\) −1.36439e9 + 1.64925e9i −0.302968 + 0.366223i
\(574\) 1.07014e10i 2.36184i
\(575\) 4.27584e8 + 8.03683e7i 0.0937958 + 0.0176298i
\(576\) 3.31587e9 + 3.49093e9i 0.722968 + 0.761136i
\(577\) 6.14523e9 + 1.80440e9i 1.33175 + 0.391037i 0.868719 0.495305i \(-0.164944\pi\)
0.463031 + 0.886342i \(0.346762\pi\)
\(578\) 1.64338e9 + 1.42400e9i 0.353990 + 0.306734i
\(579\) −6.15524e9 + 4.15741e9i −1.31786 + 0.890119i
\(580\) 1.70668e7 + 2.45384e6i 0.00363208 + 0.000522214i
\(581\) −3.15693e9 4.91229e9i −0.667804 1.03912i
\(582\) 1.13995e9 2.60456e7i 0.239694 0.00547650i
\(583\) 4.11448e9 + 4.74836e9i 0.859954 + 0.992440i
\(584\) −2.35245e9 + 3.38231e8i −0.488737 + 0.0702698i
\(585\) −2.33017e9 + 8.01494e8i −0.481218 + 0.165522i
\(586\) −2.26808e8 7.72438e8i −0.0465605 0.158570i
\(587\) 8.98028e8 + 3.05840e9i 0.183255 + 0.624110i 0.998958 + 0.0456388i \(0.0145323\pi\)
−0.815703 + 0.578471i \(0.803649\pi\)
\(588\) −3.60108e8 3.96894e8i −0.0730487 0.0805108i
\(589\) 5.68420e8 8.17265e7i 0.114621 0.0164801i
\(590\) 1.34153e9 + 1.54820e9i 0.268916 + 0.310346i
\(591\) 1.33858e8 + 5.85865e9i 0.0266740 + 1.16746i
\(592\) −3.45010e9 5.36847e9i −0.683449 1.06347i
\(593\) −2.32520e9 3.34314e8i −0.457899 0.0658359i −0.0904940 0.995897i \(-0.528845\pi\)
−0.367405 + 0.930061i \(0.619754\pi\)
\(594\) −1.21887e9 + 5.52669e9i −0.238619 + 1.08196i
\(595\) 7.69850e9 + 6.67079e9i 1.49829 + 1.29828i
\(596\) −4.62457e8 1.35790e8i −0.0894766 0.0262727i
\(597\) −7.63337e9 3.27744e9i −1.46827 0.630412i
\(598\) −2.22141e9 1.56649e9i −0.424791 0.299552i
\(599\) 8.68760e9i 1.65160i 0.563960 + 0.825802i \(0.309277\pi\)
−0.563960 + 0.825802i \(0.690723\pi\)
\(600\) 3.99238e8 + 3.30281e8i 0.0754574 + 0.0624243i
\(601\) 2.81418e9 3.24774e9i 0.528800 0.610268i −0.427012 0.904246i \(-0.640434\pi\)
0.955812 + 0.293978i \(0.0949793\pi\)
\(602\) 7.57764e9 1.17910e10i 1.41562 2.20275i
\(603\) −4.71543e9 6.64877e9i −0.875812 1.23490i
\(604\) 1.15791e8 7.44141e7i 0.0213818 0.0137412i
\(605\) −6.47307e8 1.41740e9i −0.118841 0.260225i
\(606\) 6.61200e9 2.10666e9i 1.20692 0.384539i
\(607\) −4.19471e8 2.91749e9i −0.0761275 0.529478i −0.991825 0.127609i \(-0.959270\pi\)
0.915697 0.401869i \(-0.131639\pi\)
\(608\) −1.20579e8 + 2.64032e8i −0.0217576 + 0.0476425i
\(609\) −7.82912e7 + 6.49534e8i −0.0140460 + 0.116531i
\(610\) 3.92607e9 1.15280e9i 0.700332 0.205636i
\(611\) 2.37780e9 + 1.08590e9i 0.421726 + 0.192596i
\(612\) −2.40763e8 + 3.04953e8i −0.0424580 + 0.0537778i
\(613\) −2.51208e9 + 2.17673e9i −0.440476 + 0.381675i −0.846675 0.532110i \(-0.821399\pi\)
0.406199 + 0.913785i \(0.366854\pi\)
\(614\) −2.62801e9 + 1.20017e9i −0.458181 + 0.209244i
\(615\) 7.68376e9 1.28454e9i 1.33202 0.222681i
\(616\) 1.65440e9 1.15066e10i 0.285172 1.98341i
\(617\) −6.92110e9 4.44792e9i −1.18625 0.762358i −0.209727 0.977760i \(-0.567257\pi\)
−0.976525 + 0.215402i \(0.930894\pi\)
\(618\) 4.27170e9 + 8.81509e9i 0.728016 + 1.50234i
\(619\) 9.27470e8 3.15867e9i 0.157175 0.535288i −0.842821 0.538194i \(-0.819107\pi\)
0.999996 + 0.00290588i \(0.000924972\pi\)
\(620\) 7.89569e7 0.0133051
\(621\) 5.92691e9 + 6.98191e8i 0.993133 + 0.116991i
\(622\) 4.21753e8 0.0702735
\(623\) −1.27097e9 + 4.32853e9i −0.210585 + 0.717186i
\(624\) −1.33200e9 2.74872e9i −0.219461 0.452881i
\(625\) −4.59780e9 2.95483e9i −0.753303 0.484119i
\(626\) −1.22893e9 + 8.54743e9i −0.200225 + 1.39260i
\(627\) −3.23461e9 + 5.40746e8i −0.524065 + 0.0876107i
\(628\) 2.80550e8 1.28123e8i 0.0452014 0.0206428i
\(629\) 7.71822e9 6.68788e9i 1.23663 1.07155i
\(630\) 6.15232e9 7.79259e9i 0.980272 1.24162i
\(631\) −4.86421e9 2.22141e9i −0.770743 0.351986i −0.00907900 0.999959i \(-0.502890\pi\)
−0.761664 + 0.647972i \(0.775617\pi\)
\(632\) 4.58311e9 1.34572e9i 0.722188 0.212054i
\(633\) −3.08021e8 + 2.55546e9i −0.0482689 + 0.400457i
\(634\) −3.32460e7 + 7.27986e7i −0.00518116 + 0.0113452i
\(635\) 1.19245e9 + 8.29367e9i 0.184813 + 1.28540i
\(636\) 4.00576e8 1.27628e8i 0.0617426 0.0196719i
\(637\) 2.80086e9 + 6.13302e9i 0.429341 + 0.940126i
\(638\) −4.19127e8 + 2.69357e8i −0.0638960 + 0.0410634i
\(639\) 1.05472e9 + 1.48716e9i 0.159914 + 0.225479i
\(640\) 3.09417e9 4.81462e9i 0.466567 0.725993i
\(641\) −3.08965e9 + 3.56565e9i −0.463347 + 0.534731i −0.938549 0.345145i \(-0.887830\pi\)
0.475202 + 0.879877i \(0.342375\pi\)
\(642\) −3.56665e9 2.95061e9i −0.531971 0.440088i
\(643\) 5.37723e9i 0.797664i 0.917024 + 0.398832i \(0.130584\pi\)
−0.917024 + 0.398832i \(0.869416\pi\)
\(644\) −6.52543e8 2.80714e7i −0.0962738 0.00414156i
\(645\) −9.37568e9 4.02551e9i −1.37576 0.590693i
\(646\) 3.62236e9 + 1.06362e9i 0.528661 + 0.155229i
\(647\) −3.51825e9 3.04858e9i −0.510694 0.442519i 0.361002 0.932565i \(-0.382435\pi\)
−0.871697 + 0.490046i \(0.836980\pi\)
\(648\) 5.77374e9 + 4.14483e9i 0.833575 + 0.598404i
\(649\) 3.49418e9 + 5.02387e8i 0.501751 + 0.0721409i
\(650\) −1.87782e8 2.92195e8i −0.0268199 0.0417326i
\(651\) 6.84322e7 + 2.99512e9i 0.00972136 + 0.425482i
\(652\) 2.05964e8 + 2.37695e8i 0.0291021 + 0.0335856i
\(653\) −1.94607e9 + 2.79803e8i −0.273504 + 0.0393239i −0.277702 0.960667i \(-0.589573\pi\)
0.00419826 + 0.999991i \(0.498664\pi\)
\(654\) −4.47530e9 4.93246e9i −0.625605 0.689512i
\(655\) −8.25232e7 2.81048e8i −0.0114744 0.0390784i
\(656\) 2.72057e9 + 9.26543e9i 0.376268 + 1.28145i
\(657\) −3.30762e9 + 1.13770e9i −0.455026 + 0.156513i
\(658\) −1.04251e10 + 1.49891e9i −1.42656 + 0.205109i
\(659\) −4.09578e9 4.72678e9i −0.557491 0.643379i 0.405121 0.914263i \(-0.367229\pi\)
−0.962612 + 0.270884i \(0.912684\pi\)
\(660\) −4.50787e8 + 1.02995e7i −0.0610334 + 0.00139448i
\(661\) 2.02658e9 + 3.15341e9i 0.272934 + 0.424694i 0.950480 0.310787i \(-0.100593\pi\)
−0.677545 + 0.735481i \(0.736956\pi\)
\(662\) −1.09650e10 1.57654e9i −1.46895 0.211203i
\(663\) 4.05078e9 2.73600e9i 0.539810 0.364602i
\(664\) −4.22041e9 3.65701e9i −0.559457 0.484772i
\(665\) 5.52021e9 + 1.62088e9i 0.727913 + 0.213735i
\(666\) −6.85523e9 7.21714e9i −0.899212 0.946684i
\(667\) 3.26659e8 + 4.11464e8i 0.0426240 + 0.0536898i
\(668\) 9.53739e7i 0.0123797i
\(669\) 8.04455e9 9.72411e9i 1.03875 1.25562i
\(670\) −7.13116e9 + 8.22980e9i −0.916006 + 1.05713i
\(671\) 3.81209e9 5.93172e9i 0.487118 0.757970i
\(672\) −1.29226e9 7.89370e8i −0.164270 0.100343i
\(673\) −7.05726e9 + 4.53542e9i −0.892449 + 0.573542i −0.904542 0.426385i \(-0.859787\pi\)
0.0120932 + 0.999927i \(0.496151\pi\)
\(674\) 4.23782e9 + 9.27954e9i 0.533130 + 1.16739i
\(675\) 6.68250e8 + 3.67384e8i 0.0836327 + 0.0459788i
\(676\) 4.59137e7 + 3.19337e8i 0.00571648 + 0.0397590i
\(677\) −3.23637e9 + 7.08667e9i −0.400865 + 0.877772i 0.596317 + 0.802749i \(0.296630\pi\)
−0.997182 + 0.0750228i \(0.976097\pi\)
\(678\) −4.21130e9 5.07607e8i −0.518935 0.0625495i
\(679\) −3.30740e9 + 9.71141e8i −0.405455 + 0.119052i
\(680\) 8.86164e9 + 4.04698e9i 1.08077 + 0.493571i
\(681\) 4.42564e9 + 1.19038e9i 0.536984 + 0.144435i
\(682\) −1.72421e9 + 1.49404e9i −0.208135 + 0.180350i
\(683\) 2.36881e9 1.08180e9i 0.284484 0.129920i −0.268063 0.963402i \(-0.586383\pi\)
0.552547 + 0.833482i \(0.313656\pi\)
\(684\) −5.21432e7 + 2.13158e8i −0.00623019 + 0.0254686i
\(685\) 1.93528e9 1.34602e10i 0.230052 1.60005i
\(686\) −1.10220e10 7.08344e9i −1.30355 0.837741i
\(687\) 4.09848e9 1.98608e9i 0.482252 0.233694i
\(688\) 3.56323e9 1.21352e10i 0.417142 1.42066i
\(689\) −5.28925e9 −0.616065
\(690\) −9.75430e8 7.91293e9i −0.113038 0.916992i
\(691\) 3.54246e9 0.408443 0.204222 0.978925i \(-0.434534\pi\)
0.204222 + 0.978925i \(0.434534\pi\)
\(692\) −9.31040e7 + 3.17083e8i −0.0106806 + 0.0363749i
\(693\) −7.81397e8 1.70910e10i −0.0891877 1.95075i
\(694\) 4.48559e7 + 2.88271e7i 0.00509402 + 0.00327373i
\(695\) 1.30483e9 9.07529e9i 0.147437 1.02545i
\(696\) 1.03167e8 + 6.17119e8i 0.0115987 + 0.0693803i
\(697\) −1.40574e10 + 6.41981e9i −1.57250 + 0.718137i
\(698\) 8.19647e9 7.10228e9i 0.912289 0.790503i
\(699\) −2.10415e9 + 7.82287e9i −0.233027 + 0.866355i
\(700\) −7.59174e7 3.46703e7i −0.00836562 0.00382045i
\(701\) −9.20577e9 + 2.70306e9i −1.00936 + 0.296376i −0.744293 0.667854i \(-0.767213\pi\)
−0.265070 + 0.964229i \(0.585395\pi\)
\(702\) −2.84423e9 3.82225e9i −0.310302 0.417003i
\(703\) 2.39611e9 5.24675e9i 0.260114 0.569570i
\(704\) −1.57743e9 1.09713e10i −0.170391 1.18510i
\(705\) 2.32760e9 + 7.30544e9i 0.250177 + 0.785208i
\(706\) −6.33619e9 1.38743e10i −0.677660 1.48387i
\(707\) −1.76481e10 + 1.13418e10i −1.87815 + 1.20702i
\(708\) 1.23133e8 2.01579e8i 0.0130395 0.0213466i
\(709\) −4.40662e9 + 6.85684e9i −0.464348 + 0.722540i −0.991905 0.126980i \(-0.959472\pi\)
0.527557 + 0.849520i \(0.323108\pi\)
\(710\) 1.59506e9 1.84080e9i 0.167253 0.193020i
\(711\) 6.25460e9 3.20935e9i 0.652614 0.334868i
\(712\) 4.31438e9i 0.447960i
\(713\) 1.74878e9 + 1.65214e9i 0.180684 + 0.170700i
\(714\) −7.77040e9 + 1.80978e10i −0.798914 + 1.86072i
\(715\) 5.44302e9 + 1.59822e9i 0.556889 + 0.163517i
\(716\) 3.41999e8 + 2.96344e8i 0.0348201 + 0.0301717i
\(717\) −8.73431e9 1.29316e10i −0.884936 1.31019i
\(718\) −5.67879e9 8.16487e8i −0.572559 0.0823216i
\(719\) 4.55532e9 + 7.08821e9i 0.457054 + 0.711190i 0.990931 0.134372i \(-0.0429018\pi\)
−0.533877 + 0.845562i \(0.679265\pi\)
\(720\) 3.34567e9 8.31098e9i 0.334056 0.829829i
\(721\) −1.93920e10 2.23796e10i −1.92686 2.22371i
\(722\) −7.61377e9 + 1.09470e9i −0.752869 + 0.108246i
\(723\) 9.46481e9 8.58757e9i 0.931382 0.845057i
\(724\) −2.26215e8 7.70419e8i −0.0221532 0.0754470i
\(725\) 1.89132e7 + 6.44123e7i 0.00184324 + 0.00627749i
\(726\) 2.23123e9 2.02443e9i 0.216405 0.196347i
\(727\) 8.40470e9 1.20841e9i 0.811245 0.116639i 0.275806 0.961213i \(-0.411055\pi\)
0.535439 + 0.844574i \(0.320146\pi\)
\(728\) 6.40864e9 + 7.39596e9i 0.615610 + 0.710452i
\(729\) 9.48999e9 + 4.39990e9i 0.907234 + 0.420626i
\(730\) 2.52637e9 + 3.93111e9i 0.240363 + 0.374012i
\(731\) 2.00345e10 + 2.88053e9i 1.89700 + 0.272748i
\(732\) −2.64080e8 3.90982e8i −0.0248855 0.0368441i
\(733\) 5.01123e9 + 4.34225e9i 0.469981 + 0.407241i 0.857390 0.514667i \(-0.172085\pi\)
−0.387409 + 0.921908i \(0.626630\pi\)
\(734\) 7.53542e9 + 2.21260e9i 0.703349 + 0.206522i
\(735\) −7.80225e9 + 1.81719e10i −0.724793 + 1.68809i
\(736\) −1.18039e9 + 2.92125e8i −0.109132 + 0.0270083i
\(737\) 1.87650e10i 1.72668i
\(738\) 6.87641e9 + 1.34012e10i 0.629745 + 1.22729i
\(739\) −3.78269e9 + 4.36546e9i −0.344783 + 0.397900i −0.901484 0.432812i \(-0.857521\pi\)
0.556701 + 0.830713i \(0.312067\pi\)
\(740\) 4.28757e8 6.67159e8i 0.0388956 0.0605227i
\(741\) 1.43916e9 2.35602e9i 0.129941 0.212723i
\(742\) 1.79282e10 1.15217e10i 1.61110 1.03539i
\(743\) 3.29767e9 + 7.22090e9i 0.294949 + 0.645848i 0.997857 0.0654327i \(-0.0208428\pi\)
−0.702908 + 0.711281i \(0.748115\pi\)
\(744\) 8.69792e8 + 2.72994e9i 0.0774302 + 0.243023i
\(745\) 2.53120e9 + 1.76049e10i 0.224274 + 1.55986i
\(746\) 6.93926e9 1.51949e10i 0.611966 1.34002i
\(747\) −7.10985e9 4.12302e9i −0.624077 0.361904i
\(748\) 8.58236e8 2.52001e8i 0.0749809 0.0220164i
\(749\) 1.27289e10 + 5.81311e9i 1.10689 + 0.505501i
\(750\) 3.03729e9 1.12921e10i 0.262888 0.977374i
\(751\) −1.09063e10 + 9.45035e9i −0.939587 + 0.814157i −0.982755 0.184911i \(-0.940800\pi\)
0.0431685 + 0.999068i \(0.486255\pi\)
\(752\) −8.64513e9 + 3.94810e9i −0.741326 + 0.338552i
\(753\) −1.87201e9 1.11979e10i −0.159781 0.955771i
\(754\) 5.96894e7 4.15149e8i 0.00507104 0.0352699i
\(755\) −4.27287e9 2.74601e9i −0.361331 0.232213i
\(756\) −1.07148e9 4.03147e8i −0.0901902 0.0339342i
\(757\) 1.55884e9 5.30891e9i 0.130606 0.444805i −0.868058 0.496462i \(-0.834632\pi\)
0.998665 + 0.0516573i \(0.0164504\pi\)
\(758\) −1.04349e10 −0.870253
\(759\) −1.01998e10 9.20439e9i −0.846727 0.764097i
\(760\) 5.50217e9 0.454660
\(761\) −4.09478e9 + 1.39455e10i −0.336809 + 1.14707i 0.600807 + 0.799394i \(0.294846\pi\)
−0.937616 + 0.347673i \(0.886972\pi\)
\(762\) −1.45789e10 + 7.06476e9i −1.19366 + 0.578435i
\(763\) 1.69377e10 + 1.08852e10i 1.38044 + 0.887158i
\(764\) 4.69247e7 3.26369e8i 0.00380693 0.0264778i
\(765\) 1.39271e10 + 3.40689e9i 1.12473 + 0.275134i
\(766\) 1.38039e10 6.30404e9i 1.10969 0.506778i
\(767\) −2.24592e9 + 1.94610e9i −0.179726 + 0.155733i
\(768\) −2.04020e9 5.48760e8i −0.162520 0.0437138i
\(769\) 3.09454e9 + 1.41323e9i 0.245388 + 0.112065i 0.534313 0.845287i \(-0.320570\pi\)
−0.288925 + 0.957352i \(0.593298\pi\)
\(770\) −2.19309e10 + 6.43948e9i −1.73116 + 0.508316i
\(771\) −1.20383e10 1.45103e9i −0.945965 0.114021i
\(772\) 4.75315e8 1.04079e9i 0.0371810 0.0814150i
\(773\) −2.56940e9 1.78706e10i −0.200080 1.39159i −0.804041 0.594574i \(-0.797321\pi\)
0.603961 0.797014i \(-0.293588\pi\)
\(774\) 1.91279e9 1.96349e10i 0.148277 1.52207i
\(775\) 1.27704e8 + 2.79632e8i 0.00985479 + 0.0215790i
\(776\) −2.77327e9 + 1.78227e9i −0.213048 + 0.136917i
\(777\) 2.56794e10 + 1.56861e10i 1.96386 + 1.19961i
\(778\) −1.04794e10 + 1.63063e10i −0.797825 + 1.24144i
\(779\) −5.71576e9 + 6.59634e9i −0.433205 + 0.499945i
\(780\) 2.41960e8 2.92476e8i 0.0182563 0.0220678i
\(781\) 4.19726e9i 0.315274i
\(782\) 5.94575e9 + 1.46557e10i 0.444614 + 1.09593i
\(783\) 3.19327e8 + 8.63707e8i 0.0237722 + 0.0642984i
\(784\) −2.35205e10 6.90625e9i −1.74317 0.511842i
\(785\) −8.60140e9 7.45316e9i −0.634637 0.549916i
\(786\) 4.69316e8 3.16988e8i 0.0344736 0.0232844i
\(787\) 7.20557e9 + 1.03601e9i 0.526935 + 0.0757618i 0.400648 0.916232i \(-0.368785\pi\)
0.126287 + 0.991994i \(0.459694\pi\)
\(788\) −4.88049e8 7.59419e8i −0.0355322 0.0552891i
\(789\) 2.00722e10 4.58606e8i 1.45487 0.0332407i
\(790\) −6.15024e9 7.09776e9i −0.443810 0.512184i
\(791\) 1.26926e10 1.82492e9i 0.911868 0.131107i
\(792\) −5.32199e9 1.54725e10i −0.380659 1.10668i
\(793\) 1.67232e9 + 5.69539e9i 0.119087 + 0.405571i
\(794\) 2.68761e9 + 9.15318e9i 0.190544 + 0.648933i
\(795\) −1.04247e10 1.14896e10i −0.735835 0.811002i
\(796\) 1.26665e9 1.82116e8i 0.0890144 0.0127983i
\(797\) −3.85946e9 4.45405e9i −0.270036 0.311639i 0.604494 0.796610i \(-0.293375\pi\)
−0.874530 + 0.484971i \(0.838830\pi\)
\(798\) 2.54087e8 + 1.11208e10i 0.0177000 + 0.774688i
\(799\) −8.22301e9 1.27952e10i −0.570318 0.887432i
\(800\) −1.53800e8 2.21131e7i −0.0106204 0.00152698i
\(801\) 1.18976e9 + 6.23722e9i 0.0817986 + 0.428822i
\(802\) −3.65567e9 3.16766e9i −0.250240 0.216834i
\(803\) 7.72623e9 + 2.26863e9i 0.526579 + 0.154618i
\(804\) 1.15378e9 + 4.95384e8i 0.0782938 + 0.0336160i
\(805\) 9.06089e9 + 2.23342e10i 0.612189 + 1.50898i
\(806\) 1.92062e9i 0.129202i
\(807\) −1.21615e9 1.00610e9i −0.0814575 0.0673881i
\(808\) −1.31384e10 + 1.51625e10i −0.876196 + 1.01118i
\(809\) −5.63445e9 + 8.76737e9i −0.374138 + 0.582170i −0.976358 0.216160i \(-0.930647\pi\)
0.602220 + 0.798330i \(0.294283\pi\)
\(810\) 2.69716e9 1.37118e10i 0.178324 0.906561i
\(811\) 2.54615e9 1.63631e9i 0.167614 0.107719i −0.454144 0.890928i \(-0.650055\pi\)
0.621758 + 0.783209i \(0.286419\pi\)
\(812\) −4.18658e7 9.16733e7i −0.00274418 0.00600893i
\(813\) 2.16356e10 6.89337e9i 1.41206 0.449899i
\(814\) 3.26118e9 + 2.26820e10i 0.211929 + 1.47400i
\(815\) 4.82138e9 1.05573e10i 0.311975 0.683129i
\(816\) −2.12679e9 + 1.76447e10i −0.137028 + 1.13684i
\(817\) 1.09686e10 3.22066e9i 0.703676 0.206618i
\(818\) 2.05589e10 + 9.38893e9i 1.31330 + 0.599763i
\(819\) 1.13044e10 + 8.92491e9i 0.719041 + 0.567689i
\(820\) −9.06944e8 + 7.85872e8i −0.0574423 + 0.0497741i
\(821\) −4.64911e9 + 2.12318e9i −0.293203 + 0.133901i −0.556586 0.830790i \(-0.687889\pi\)
0.263383 + 0.964691i \(0.415162\pi\)
\(822\) 2.59325e10 4.33528e9i 1.62852 0.272249i
\(823\) −2.61877e9 + 1.82139e10i −0.163756 + 1.13895i 0.727718 + 0.685877i \(0.240581\pi\)
−0.891474 + 0.453072i \(0.850328\pi\)
\(824\) −2.38244e10 1.53110e10i −1.48346 0.953363i
\(825\) −7.65572e8 1.57984e9i −0.0474676 0.0979543i
\(826\) 3.37340e9 1.14888e10i 0.208276 0.709321i
\(827\) 1.04310e10 0.641294 0.320647 0.947199i \(-0.396100\pi\)
0.320647 + 0.947199i \(0.396100\pi\)
\(828\) −8.35205e8 + 3.84150e8i −0.0511313 + 0.0235177i
\(829\) −1.11462e10 −0.679495 −0.339748 0.940517i \(-0.610342\pi\)
−0.339748 + 0.940517i \(0.610342\pi\)
\(830\) −3.09342e9 + 1.05352e10i −0.187787 + 0.639544i
\(831\) 6.88200e8 + 1.42017e9i 0.0416017 + 0.0858495i
\(832\) 7.84975e9 + 5.04473e9i 0.472524 + 0.303673i
\(833\) 5.58305e9 3.88310e10i 0.334668 2.32767i
\(834\) 1.74846e10 2.92299e9i 1.04370 0.174480i
\(835\) 3.20141e9 1.46204e9i 0.190300 0.0869071i
\(836\) 3.81793e8 3.30826e8i 0.0225999 0.0195829i
\(837\) 2.01027e9 + 3.70677e9i 0.118499 + 0.218502i
\(838\) 8.24552e9 + 3.76560e9i 0.484021 + 0.221045i
\(839\) 1.90636e9 5.59756e8i 0.111439 0.0327214i −0.225538 0.974234i \(-0.572414\pi\)
0.336977 + 0.941513i \(0.390596\pi\)
\(840\) −3.43501e9 + 2.84982e10i −0.199964 + 1.65897i
\(841\) 7.13218e9 1.56173e10i 0.413463 0.905357i
\(842\) −1.43197e8 9.95956e8i −0.00826687 0.0574973i
\(843\) −1.96456e10 + 6.25933e9i −1.12946 + 0.359858i
\(844\) −1.64713e8 3.60670e8i −0.00943036 0.0206496i
\(845\) 1.00153e10 6.43646e9i 0.571040 0.366985i
\(846\) −1.20921e10 + 8.57591e9i −0.686600 + 0.486950i
\(847\) −4.92400e9 + 7.66189e9i −0.278436 + 0.433255i
\(848\) 1.25933e10 1.45334e10i 0.709176 0.818433i
\(849\) −2.11616e10 1.75066e10i −1.18679 0.981803i
\(850\) 2.02096e9i 0.112873i
\(851\) 2.34563e10 5.80501e9i 1.30469 0.322886i
\(852\) −2.58072e8 1.10805e8i −0.0142956 0.00613791i
\(853\) −4.09755e9 1.20315e9i −0.226049 0.0663739i 0.166747 0.986000i \(-0.446674\pi\)
−0.392795 + 0.919626i \(0.628492\pi\)
\(854\) −1.80749e10 1.56620e10i −0.993054 0.860486i
\(855\) 7.95438e9 1.51731e9i 0.435236 0.0830221i
\(856\) 1.32466e10 + 1.90457e9i 0.721847 + 0.103786i
\(857\) 1.33261e10 + 2.07357e10i 0.723217 + 1.12535i 0.986993 + 0.160764i \(0.0513958\pi\)
−0.263776 + 0.964584i \(0.584968\pi\)
\(858\) 2.50535e8 + 1.09653e10i 0.0135414 + 0.592674i
\(859\) −1.16818e10 1.34815e10i −0.628832 0.725711i 0.348527 0.937299i \(-0.386682\pi\)
−0.977359 + 0.211588i \(0.932137\pi\)
\(860\) 1.55576e9 2.23684e8i 0.0834061 0.0119920i
\(861\) −3.05970e10 3.37226e10i −1.63368 1.80057i
\(862\) −2.31388e9 7.88037e9i −0.123046 0.419055i
\(863\) −5.98364e9 2.03784e10i −0.316904 1.07928i −0.951811 0.306687i \(-0.900780\pi\)
0.634907 0.772589i \(-0.281039\pi\)
\(864\) −2.12550e9 1.58147e8i −0.112115 0.00834187i
\(865\) 1.20708e10 1.73551e9i 0.634130 0.0911741i
\(866\) 1.57841e9 + 1.82158e9i 0.0825861 + 0.0953094i
\(867\) −9.25007e9 + 2.11344e8i −0.482034 + 0.0110135i
\(868\) −2.49505e8 3.88238e8i −0.0129497 0.0201502i
\(869\) −1.60191e10 2.30320e9i −0.828072 0.119059i
\(870\) 1.01946e9 6.88568e8i 0.0524869 0.0354511i
\(871\) −1.19386e10 1.03449e10i −0.612197 0.530472i
\(872\) 1.84752e10 + 5.42482e9i 0.943588 + 0.277062i
\(873\) −3.51778e9 + 3.34137e9i −0.178944 + 0.169971i
\(874\) 6.49317e9 + 6.13435e9i 0.328978 + 0.310798i
\(875\) 3.53498e10i 1.78385i
\(876\) 3.43456e8 4.15163e8i 0.0172626 0.0208667i
\(877\) 1.89702e10 2.18927e10i 0.949669 1.09598i −0.0456132 0.998959i \(-0.514524\pi\)
0.995283 0.0970178i \(-0.0309304\pi\)
\(878\) 2.73900e9 4.26197e9i 0.136572 0.212510i
\(879\) 2.92324e9 + 1.78564e9i 0.145179 + 0.0886815i
\(880\) −1.73509e10 + 1.11507e10i −0.858287 + 0.551588i
\(881\) 5.16299e9 + 1.13054e10i 0.254381 + 0.557017i 0.993137 0.116956i \(-0.0373136\pi\)
−0.738756 + 0.673973i \(0.764586\pi\)
\(882\) −3.80563e10 3.70738e9i −1.86761 0.181940i
\(883\) −2.67012e8 1.85711e9i −0.0130517 0.0907767i 0.982254 0.187553i \(-0.0600558\pi\)
−0.995306 + 0.0967768i \(0.969147\pi\)
\(884\) −3.12806e8 + 6.84949e8i −0.0152297 + 0.0333484i
\(885\) −8.65398e9 1.04310e9i −0.419676 0.0505855i
\(886\) −2.05127e10 + 6.02307e9i −0.990842 + 0.290937i
\(887\) 1.02510e9 + 4.68149e8i 0.0493214 + 0.0225243i 0.439923 0.898035i \(-0.355006\pi\)
−0.390602 + 0.920560i \(0.627733\pi\)
\(888\) 2.77903e10 + 7.47487e9i 1.33183 + 0.358227i
\(889\) 3.70125e10 3.20715e10i 1.76682 1.53096i
\(890\) 7.71631e9 3.52392e9i 0.366897 0.167556i
\(891\) −1.19607e10 2.09007e10i −0.566480 0.989895i
\(892\) −2.76672e8 + 1.92429e9i −0.0130523 + 0.0907809i
\(893\) −7.22661e9 4.64426e9i −0.339589 0.218241i
\(894\) −3.09464e10 + 1.49963e10i −1.44853 + 0.701943i
\(895\) 4.70468e9 1.60227e10i 0.219356 0.747059i
\(896\) −3.34516e10 −1.55360
\(897\) 1.14790e10 1.41502e9i 0.531043 0.0654618i
\(898\) 2.70119e10 1.24476
\(899\) −1.04583e8 + 3.56176e8i −0.00480066 + 0.0163495i
\(900\) −1.17348e8 + 5.36511e6i −0.00536571 + 0.000245318i
\(901\) 2.58901e10 + 1.66386e10i 1.17923 + 0.757842i
\(902\) 4.93487e9 3.43228e10i 0.223899 1.55725i
\(903\) 9.83354e9 + 5.88217e10i 0.444429 + 2.65846i
\(904\) 1.11552e10 5.09443e9i 0.502215 0.229354i
\(905\) −2.23929e10 + 1.94035e10i −1.00424 + 0.870183i
\(906\) 2.55077e9 9.48335e9i 0.113952 0.423656i
\(907\) −3.34046e10 1.52554e10i −1.48655 0.678887i −0.503803 0.863819i \(-0.668066\pi\)
−0.982751 + 0.184932i \(0.940794\pi\)
\(908\) −6.77374e8 + 1.98895e8i −0.0300281 + 0.00881705i
\(909\) −1.48126e10 + 2.55432e10i −0.654119 + 1.12798i
\(910\) 7.99326e9 1.75028e10i 0.351624 0.769950i
\(911\) −3.42102e9 2.37937e10i −0.149914 1.04267i −0.916357 0.400362i \(-0.868884\pi\)
0.766443 0.642312i \(-0.222025\pi\)
\(912\) 3.04718e9 + 9.56394e9i 0.133020 + 0.417498i
\(913\) 7.85999e9 + 1.72110e10i 0.341802 + 0.748441i
\(914\) 9.58839e9 6.16208e9i 0.415369 0.266941i
\(915\) −9.07588e9 + 1.48579e10i −0.391665 + 0.641187i
\(916\) −3.79296e8 + 5.90196e8i −0.0163059 + 0.0253724i
\(917\) −1.12116e9 + 1.29389e9i −0.0480149 + 0.0554122i
\(918\) 1.89832e9 + 2.76565e10i 0.0809880 + 1.17991i
\(919\) 3.70286e10i 1.57374i 0.617119 + 0.786870i \(0.288300\pi\)
−0.617119 + 0.786870i \(0.711700\pi\)
\(920\) 1.43321e10 + 1.80529e10i 0.606810 + 0.764347i
\(921\) 4.84995e9 1.12958e10i 0.204564 0.476442i
\(922\) −6.42999e9 1.88801e9i −0.270179 0.0793318i
\(923\) 2.67037e9 + 2.31389e9i 0.111780 + 0.0968583i
\(924\) 1.47514e9 + 2.18401e9i 0.0615150 + 0.0910758i
\(925\) 3.05626e9 + 4.39424e8i 0.126968 + 0.0182552i
\(926\) −1.33225e10 2.07303e10i −0.551377 0.857959i
\(927\) −3.86647e10 1.55649e10i −1.59417 0.641750i
\(928\) −1.22871e8 1.41801e8i −0.00504698 0.00582453i
\(929\) 1.96951e10 2.83172e9i 0.805939 0.115877i 0.272982 0.962019i \(-0.411990\pi\)
0.532957 + 0.846143i \(0.321081\pi\)
\(930\) 4.17209e9 3.78540e9i 0.170084 0.154320i
\(931\) −6.24229e9 2.12593e10i −0.253525 0.863425i
\(932\) −3.51572e8 1.19734e9i −0.0142252 0.0484466i
\(933\) −1.32903e9 + 1.20585e9i −0.0535735 + 0.0486081i
\(934\) 8.67364e9 1.24708e9i 0.348327 0.0500819i
\(935\) −2.16152e10 2.49453e10i −0.864807 0.998041i
\(936\) 1.27778e10 + 5.14384e9i 0.509321 + 0.205032i
\(937\) 3.12916e9 + 4.86907e9i 0.124262 + 0.193356i 0.897811 0.440381i \(-0.145157\pi\)
−0.773549 + 0.633737i \(0.781520\pi\)
\(938\) 6.30013e10 + 9.05821e9i 2.49252 + 0.358371i
\(939\) −2.05657e10 3.04485e10i −0.810614 1.20015i
\(940\) −8.92612e8 7.73453e8i −0.0350522 0.0303729i
\(941\) −3.81236e10 1.11941e10i −1.49152 0.437951i −0.568496 0.822686i \(-0.692475\pi\)
−0.923027 + 0.384735i \(0.874293\pi\)
\(942\) 8.68174e9 2.02203e10i 0.338399 0.788153i
\(943\) −3.65314e10 1.57153e9i −1.41865 0.0610283i
\(944\) 1.08047e10i 0.418033i
\(945\) 2.89290e9 + 4.21465e10i 0.111512 + 1.62462i
\(946\) −2.97411e10 + 3.43231e10i −1.14219 + 1.31816i
\(947\) 2.09643e9 3.26211e9i 0.0802151 0.124817i −0.798828 0.601560i \(-0.794546\pi\)
0.879043 + 0.476742i \(0.158183\pi\)
\(948\) −5.64507e8 + 9.24142e8i −0.0215199 + 0.0352298i
\(949\) −5.70270e9 + 3.66490e9i −0.216595 + 0.139197i
\(950\) 4.74161e8 + 1.03827e9i 0.0179429 + 0.0392895i
\(951\) −1.03377e8 3.24460e8i −0.00389754 0.0122329i
\(952\) −8.10363e9 5.63620e10i −0.304404 2.11718i
\(953\) −1.74560e10 + 3.82234e10i −0.653311 + 1.43055i 0.235314 + 0.971919i \(0.424388\pi\)
−0.888626 + 0.458633i \(0.848339\pi\)
\(954\) 1.50476e10 2.59486e10i 0.561111 0.967596i
\(955\) −1.16745e10 + 3.42795e9i −0.433738 + 0.127357i
\(956\) 2.18661e9 + 9.98589e8i 0.0809409 + 0.0369645i
\(957\) 5.50630e8 2.04715e9i 0.0203080 0.0755018i
\(958\) 2.54230e10 2.20292e10i 0.934217 0.809503i
\(959\) −7.23003e10 + 3.30185e10i −2.64713 + 1.20890i
\(960\) 4.51282e9 + 2.69945e10i 0.164626 + 0.984751i
\(961\) 3.67354e9 2.55500e10i 0.133522 0.928665i
\(962\) −1.62286e10 1.04295e10i −0.587716 0.377702i
\(963\) 1.96755e10 8.99558e8i 0.709961 0.0324592i
\(964\) −5.54641e8 + 1.88893e9i −0.0199408 + 0.0679121i
\(965\) −4.22226e10 −1.51252
\(966\) −3.58262e10 + 2.98013e10i −1.27874 + 1.06369i
\(967\) 2.33038e10 0.828771 0.414385 0.910101i \(-0.363997\pi\)
0.414385 + 0.910101i \(0.363997\pi\)
\(968\) −2.45395e9 + 8.35740e9i −0.0869566 + 0.296147i
\(969\) −1.44559e10 + 7.00516e9i −0.510401 + 0.247335i
\(970\) 5.45277e9 + 3.50429e9i 0.191830 + 0.123282i
\(971\) −5.34705e9 + 3.71896e10i −0.187434 + 1.30363i 0.651189 + 0.758916i \(0.274271\pi\)
−0.838622 + 0.544713i \(0.816639\pi\)
\(972\) −1.60085e9 + 1.83648e8i −0.0559138 + 0.00641436i
\(973\) −4.87473e10 + 2.22621e10i −1.69651 + 0.774769i
\(974\) 3.41857e10 2.96221e10i 1.18546 1.02721i
\(975\) 1.42717e9 + 3.83872e8i 0.0493128 + 0.0132639i
\(976\) −1.96311e10 8.96522e9i −0.675880 0.308664i
\(977\) −3.88580e10 + 1.14098e10i −1.33306 + 0.391422i −0.869189 0.494480i \(-0.835358\pi\)
−0.463872 + 0.885902i \(0.653540\pi\)
\(978\) 2.22789e10 + 2.68537e9i 0.761566 + 0.0917949i
\(979\) 6.07244e9 1.32968e10i 0.206835 0.452906i
\(980\) −4.33545e8 3.01537e9i −0.0147144 0.102341i
\(981\) 2.82053e10 + 2.74771e9i 0.953869 + 0.0929243i
\(982\) 1.05893e10 + 2.31872e10i 0.356842 + 0.781374i
\(983\) 3.21829e10 2.06827e10i 1.08066 0.694496i 0.125948 0.992037i \(-0.459803\pi\)
0.954709 + 0.297541i \(0.0961665\pi\)
\(984\) −3.71625e10 2.27005e10i −1.24343 0.759543i
\(985\) −1.80098e10 + 2.80238e10i −0.600458 + 0.934331i
\(986\) −1.59812e9 + 1.84432e9i −0.0530932 + 0.0612729i
\(987\) 2.85662e10 3.45304e10i 0.945678 1.14312i
\(988\) 4.25283e8i 0.0140291i
\(989\) 3.91382e10 + 2.75993e10i 1.28651 + 0.907216i
\(990\) −2.33258e10 + 2.21561e10i −0.764036 + 0.725723i
\(991\) 4.32771e10 + 1.27073e10i 1.41254 + 0.414758i 0.896970 0.442091i \(-0.145763\pi\)
0.515567 + 0.856849i \(0.327581\pi\)
\(992\) −6.49341e8 5.62657e8i −0.0211194 0.0183001i
\(993\) 3.90608e10 2.63827e10i 1.26596 0.855060i
\(994\) −1.40918e10 2.02610e9i −0.455108 0.0654346i
\(995\) −2.55302e10 3.97258e10i −0.821625 1.27847i
\(996\) 1.26573e9 2.89192e7i 0.0405913 0.000927425i
\(997\) −2.76304e10 3.18872e10i −0.882986 1.01902i −0.999666 0.0258505i \(-0.991771\pi\)
0.116680 0.993170i \(-0.462775\pi\)
\(998\) 3.32269e10 4.77731e9i 1.05812 0.152134i
\(999\) 4.22372e10 + 3.14265e9i 1.34034 + 0.0997279i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 69.8.g.a.5.16 540
3.2 odd 2 inner 69.8.g.a.5.39 yes 540
23.14 odd 22 inner 69.8.g.a.14.39 yes 540
69.14 even 22 inner 69.8.g.a.14.16 yes 540
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.8.g.a.5.16 540 1.1 even 1 trivial
69.8.g.a.5.39 yes 540 3.2 odd 2 inner
69.8.g.a.14.16 yes 540 69.14 even 22 inner
69.8.g.a.14.39 yes 540 23.14 odd 22 inner