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Properties

Label 26.8.c.b.9.4
Level $26$
Weight $8$
Character 26.9
Analytic conductor $8.122$
Analytic rank $0$
Dimension $8$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [26,8,Mod(3,26)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(26, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("26.3");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 26 = 2 \cdot 13 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 26.c (of order \(3\), degree \(2\), 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: \(8.12201066259\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 4654x^{6} + 7012369x^{4} + 3763719168x^{2} + 637953638400 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{6}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 9.4
Root \(-41.0833i\) of defining polynomial
Character \(\chi\) \(=\) 26.9
Dual form 26.8.c.b.3.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.00000 - 6.92820i) q^{2} +(35.5792 - 61.6250i) q^{3} +(-32.0000 - 55.4256i) q^{4} +523.489 q^{5} +(-284.634 - 493.000i) q^{6} +(208.401 + 360.960i) q^{7} -512.000 q^{8} +(-1438.26 - 2491.14i) q^{9} +O(q^{10})\) \(q+(4.00000 - 6.92820i) q^{2} +(35.5792 - 61.6250i) q^{3} +(-32.0000 - 55.4256i) q^{4} +523.489 q^{5} +(-284.634 - 493.000i) q^{6} +(208.401 + 360.960i) q^{7} -512.000 q^{8} +(-1438.26 - 2491.14i) q^{9} +(2093.96 - 3626.84i) q^{10} +(-1711.39 + 2964.21i) q^{11} -4554.14 q^{12} +(-6741.24 + 4159.83i) q^{13} +3334.41 q^{14} +(18625.3 - 32260.0i) q^{15} +(-2048.00 + 3547.24i) q^{16} +(3269.02 + 5662.11i) q^{17} -23012.2 q^{18} +(-13990.2 - 24231.8i) q^{19} +(-16751.7 - 29014.7i) q^{20} +29658.9 q^{21} +(13691.1 + 23713.7i) q^{22} +(-53089.0 + 91952.9i) q^{23} +(-18216.6 + 31552.0i) q^{24} +195916. q^{25} +(1855.20 + 63344.0i) q^{26} -49065.2 q^{27} +(13337.6 - 23101.5i) q^{28} +(-34273.0 + 59362.6i) q^{29} +(-149003. - 258080. i) q^{30} +51572.8 q^{31} +(16384.0 + 28377.9i) q^{32} +(121780. + 210929. i) q^{33} +52304.3 q^{34} +(109095. + 188959. i) q^{35} +(-92048.7 + 159433. i) q^{36} +(-24067.7 + 41686.5i) q^{37} -223844. q^{38} +(16501.7 + 563432. i) q^{39} -268026. q^{40} +(301049. - 521432. i) q^{41} +(118636. - 205483. i) q^{42} +(-458126. - 793497. i) q^{43} +219058. q^{44} +(-752914. - 1.30409e6i) q^{45} +(424712. + 735623. i) q^{46} -326201. q^{47} +(145732. + 252416. i) q^{48} +(324910. - 562760. i) q^{49} +(783664. - 1.35735e6i) q^{50} +465237. q^{51} +(446281. + 240523. i) q^{52} +934068. q^{53} +(-196261. + 339934. i) q^{54} +(-895894. + 1.55173e6i) q^{55} +(-106701. - 184812. i) q^{56} -1.99105e6 q^{57} +(274184. + 474900. i) q^{58} +(-587217. - 1.01709e6i) q^{59} -2.38404e6 q^{60} +(1.44545e6 + 2.50359e6i) q^{61} +(206291. - 357307. i) q^{62} +(599469. - 1.03831e6i) q^{63} +262144. q^{64} +(-3.52897e6 + 2.17763e6i) q^{65} +1.94848e6 q^{66} +(-159079. + 275533. i) q^{67} +(209217. - 362375. i) q^{68} +(3.77773e6 + 6.54322e6i) q^{69} +1.74553e6 q^{70} +(-641869. - 1.11175e6i) q^{71} +(736389. + 1.27546e6i) q^{72} -1.67209e6 q^{73} +(192542. + 333492. i) q^{74} +(6.97054e6 - 1.20733e7i) q^{75} +(-895376. + 1.55084e6i) q^{76} -1.42662e6 q^{77} +(3.96958e6 + 2.13940e6i) q^{78} -8.09160e6 q^{79} +(-1.07211e6 + 1.85694e6i) q^{80} +(1.39977e6 - 2.42448e6i) q^{81} +(-2.40839e6 - 4.17146e6i) q^{82} +5.57141e6 q^{83} +(-949085. - 1.64386e6i) q^{84} +(1.71130e6 + 2.96405e6i) q^{85} -7.33001e6 q^{86} +(2.43881e6 + 4.22415e6i) q^{87} +(876231. - 1.51768e6i) q^{88} +(-3.93786e6 + 6.82057e6i) q^{89} -1.20466e7 q^{90} +(-2.90641e6 - 1.56641e6i) q^{91} +6.79540e6 q^{92} +(1.83492e6 - 3.17817e6i) q^{93} +(-1.30480e6 + 2.25999e6i) q^{94} +(-7.32374e6 - 1.26851e7i) q^{95} +2.33172e6 q^{96} +(3.40424e6 + 5.89631e6i) q^{97} +(-2.59928e6 - 4.50208e6i) q^{98} +9.84569e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 32 q^{2} - 256 q^{4} + 556 q^{5} - 548 q^{7} - 4096 q^{8} - 5214 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 32 q^{2} - 256 q^{4} + 556 q^{5} - 548 q^{7} - 4096 q^{8} - 5214 q^{9} + 2224 q^{10} - 7392 q^{11} - 25818 q^{13} - 8768 q^{14} + 15528 q^{15} - 16384 q^{16} + 28316 q^{17} - 83424 q^{18} - 99888 q^{19} - 17792 q^{20} + 182148 q^{21} + 59136 q^{22} - 33388 q^{23} + 173756 q^{25} - 156000 q^{26} + 212544 q^{27} - 35072 q^{28} + 93140 q^{29} - 124224 q^{30} + 622320 q^{31} + 131072 q^{32} + 238638 q^{33} + 453056 q^{34} + 141544 q^{35} - 333696 q^{36} - 9636 q^{37} - 1598208 q^{38} - 22932 q^{39} - 284672 q^{40} + 82892 q^{41} + 728592 q^{42} - 569264 q^{43} + 946176 q^{44} - 2303394 q^{45} + 267104 q^{46} - 1148400 q^{47} - 717798 q^{49} + 695024 q^{50} - 5459856 q^{51} + 404352 q^{52} + 2470700 q^{53} + 850176 q^{54} - 1092512 q^{55} + 280576 q^{56} + 7056924 q^{57} - 745120 q^{58} + 231504 q^{59} - 1987584 q^{60} + 685684 q^{61} + 2489280 q^{62} - 5951712 q^{63} + 2097152 q^{64} - 6216678 q^{65} + 3818208 q^{66} + 3271056 q^{67} + 1812224 q^{68} + 5600034 q^{69} + 2264704 q^{70} - 175012 q^{71} + 2669568 q^{72} + 14275780 q^{73} + 77088 q^{74} + 22200960 q^{75} - 6392832 q^{76} - 27830412 q^{77} + 5028192 q^{78} - 14107904 q^{79} - 1138688 q^{80} + 3758004 q^{81} - 663136 q^{82} + 1314576 q^{83} - 5828736 q^{84} + 11814998 q^{85} - 9108224 q^{86} - 7182900 q^{87} + 3784704 q^{88} - 11452234 q^{89} - 36854304 q^{90} + 16457168 q^{91} + 4273664 q^{92} + 2984688 q^{93} - 4593600 q^{94} - 23334088 q^{95} - 428002 q^{97} + 5742384 q^{98} - 20715312 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/26\mathbb{Z}\right)^\times\).

\(n\) \(15\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.00000 − 6.92820i 0.353553 − 0.612372i
\(3\) 35.5792 − 61.6250i 0.760802 − 1.31775i −0.181635 − 0.983366i \(-0.558139\pi\)
0.942437 − 0.334383i \(-0.108528\pi\)
\(4\) −32.0000 − 55.4256i −0.250000 − 0.433013i
\(5\) 523.489 1.87289 0.936446 − 0.350812i \(-0.114094\pi\)
0.936446 + 0.350812i \(0.114094\pi\)
\(6\) −284.634 − 493.000i −0.537969 − 0.931789i
\(7\) 208.401 + 360.960i 0.229644 + 0.397756i 0.957703 − 0.287759i \(-0.0929104\pi\)
−0.728058 + 0.685515i \(0.759577\pi\)
\(8\) −512.000 −0.353553
\(9\) −1438.26 − 2491.14i −0.657641 − 1.13907i
\(10\) 2093.96 − 3626.84i 0.662167 − 1.14691i
\(11\) −1711.39 + 2964.21i −0.387681 + 0.671483i −0.992137 − 0.125155i \(-0.960057\pi\)
0.604456 + 0.796638i \(0.293390\pi\)
\(12\) −4554.14 −0.760802
\(13\) −6741.24 + 4159.83i −0.851017 + 0.525139i
\(14\) 3334.41 0.324766
\(15\) 18625.3 − 32260.0i 1.42490 − 2.46800i
\(16\) −2048.00 + 3547.24i −0.125000 + 0.216506i
\(17\) 3269.02 + 5662.11i 0.161379 + 0.279516i 0.935363 − 0.353688i \(-0.115073\pi\)
−0.773985 + 0.633204i \(0.781739\pi\)
\(18\) −23012.2 −0.930045
\(19\) −13990.2 − 24231.8i −0.467937 − 0.810491i 0.531391 − 0.847127i \(-0.321669\pi\)
−0.999329 + 0.0366351i \(0.988336\pi\)
\(20\) −16751.7 − 29014.7i −0.468223 − 0.810986i
\(21\) 29658.9 0.698856
\(22\) 13691.1 + 23713.7i 0.274132 + 0.474810i
\(23\) −53089.0 + 91952.9i −0.909824 + 1.57586i −0.0955160 + 0.995428i \(0.530450\pi\)
−0.814308 + 0.580433i \(0.802883\pi\)
\(24\) −18216.6 + 31552.0i −0.268984 + 0.465894i
\(25\) 195916. 2.50772
\(26\) 1855.20 + 63344.0i 0.0207007 + 0.706804i
\(27\) −49065.2 −0.479734
\(28\) 13337.6 − 23101.5i 0.114822 − 0.198878i
\(29\) −34273.0 + 59362.6i −0.260951 + 0.451980i −0.966495 − 0.256686i \(-0.917369\pi\)
0.705544 + 0.708666i \(0.250703\pi\)
\(30\) −149003. − 258080.i −1.00756 − 1.74514i
\(31\) 51572.8 0.310924 0.155462 − 0.987842i \(-0.450313\pi\)
0.155462 + 0.987842i \(0.450313\pi\)
\(32\) 16384.0 + 28377.9i 0.0883883 + 0.153093i
\(33\) 121780. + 210929.i 0.589897 + 1.02173i
\(34\) 52304.3 0.228224
\(35\) 109095. + 188959.i 0.430099 + 0.744954i
\(36\) −92048.7 + 159433.i −0.328820 + 0.569534i
\(37\) −24067.7 + 41686.5i −0.0781140 + 0.135297i −0.902436 − 0.430824i \(-0.858223\pi\)
0.824322 + 0.566121i \(0.191556\pi\)
\(38\) −223844. −0.661763
\(39\) 16501.7 + 563432.i 0.0445452 + 1.52095i
\(40\) −268026. −0.662167
\(41\) 301049. − 521432.i 0.682172 − 1.18156i −0.292145 − 0.956374i \(-0.594369\pi\)
0.974317 − 0.225182i \(-0.0722976\pi\)
\(42\) 118636. − 205483.i 0.247083 − 0.427960i
\(43\) −458126. − 793497.i −0.878709 − 1.52197i −0.852758 − 0.522306i \(-0.825072\pi\)
−0.0259511 − 0.999663i \(-0.508261\pi\)
\(44\) 219058. 0.387681
\(45\) −752914. − 1.30409e6i −1.23169 − 2.13335i
\(46\) 424712. + 735623.i 0.643343 + 1.11430i
\(47\) −326201. −0.458293 −0.229146 − 0.973392i \(-0.573593\pi\)
−0.229146 + 0.973392i \(0.573593\pi\)
\(48\) 145732. + 252416.i 0.190201 + 0.329437i
\(49\) 324910. − 562760.i 0.394527 − 0.683341i
\(50\) 783664. − 1.35735e6i 0.886615 − 1.53566i
\(51\) 465237. 0.491110
\(52\) 446281. + 240523.i 0.440146 + 0.237216i
\(53\) 934068. 0.861813 0.430907 − 0.902397i \(-0.358194\pi\)
0.430907 + 0.902397i \(0.358194\pi\)
\(54\) −196261. + 339934.i −0.169612 + 0.293776i
\(55\) −895894. + 1.55173e6i −0.726085 + 1.25762i
\(56\) −106701. − 184812.i −0.0811915 − 0.140628i
\(57\) −1.99105e6 −1.42403
\(58\) 274184. + 474900.i 0.184520 + 0.319598i
\(59\) −587217. − 1.01709e6i −0.372235 − 0.644729i 0.617674 − 0.786434i \(-0.288075\pi\)
−0.989909 + 0.141705i \(0.954742\pi\)
\(60\) −2.38404e6 −1.42490
\(61\) 1.44545e6 + 2.50359e6i 0.815358 + 1.41224i 0.909071 + 0.416642i \(0.136793\pi\)
−0.0937130 + 0.995599i \(0.529874\pi\)
\(62\) 206291. − 357307.i 0.109928 − 0.190401i
\(63\) 599469. − 1.03831e6i 0.302047 − 0.523161i
\(64\) 262144. 0.125000
\(65\) −3.52897e6 + 2.17763e6i −1.59386 + 0.983528i
\(66\) 1.94848e6 0.834241
\(67\) −159079. + 275533.i −0.0646176 + 0.111921i −0.896524 − 0.442995i \(-0.853916\pi\)
0.831907 + 0.554916i \(0.187249\pi\)
\(68\) 209217. − 362375.i 0.0806894 − 0.139758i
\(69\) 3.77773e6 + 6.54322e6i 1.38439 + 2.39784i
\(70\) 1.74553e6 0.608252
\(71\) −641869. − 1.11175e6i −0.212834 − 0.368640i 0.739766 − 0.672864i \(-0.234936\pi\)
−0.952600 + 0.304224i \(0.901603\pi\)
\(72\) 736389. + 1.27546e6i 0.232511 + 0.402721i
\(73\) −1.67209e6 −0.503070 −0.251535 − 0.967848i \(-0.580935\pi\)
−0.251535 + 0.967848i \(0.580935\pi\)
\(74\) 192542. + 333492.i 0.0552349 + 0.0956697i
\(75\) 6.97054e6 − 1.20733e7i 1.90788 − 3.30455i
\(76\) −895376. + 1.55084e6i −0.233969 + 0.405246i
\(77\) −1.42662e6 −0.356115
\(78\) 3.96958e6 + 2.13940e6i 0.947139 + 0.510460i
\(79\) −8.09160e6 −1.84646 −0.923229 − 0.384250i \(-0.874460\pi\)
−0.923229 + 0.384250i \(0.874460\pi\)
\(80\) −1.07211e6 + 1.85694e6i −0.234112 + 0.405493i
\(81\) 1.39977e6 − 2.42448e6i 0.292658 − 0.506899i
\(82\) −2.40839e6 − 4.17146e6i −0.482368 − 0.835486i
\(83\) 5.57141e6 1.06953 0.534764 − 0.845002i \(-0.320401\pi\)
0.534764 + 0.845002i \(0.320401\pi\)
\(84\) −949085. − 1.64386e6i −0.174714 − 0.302614i
\(85\) 1.71130e6 + 2.96405e6i 0.302245 + 0.523504i
\(86\) −7.33001e6 −1.24268
\(87\) 2.43881e6 + 4.22415e6i 0.397064 + 0.687736i
\(88\) 876231. − 1.51768e6i 0.137066 − 0.237405i
\(89\) −3.93786e6 + 6.82057e6i −0.592100 + 1.02555i 0.401849 + 0.915706i \(0.368368\pi\)
−0.993949 + 0.109842i \(0.964966\pi\)
\(90\) −1.20466e7 −1.74187
\(91\) −2.90641e6 − 1.56641e6i −0.404308 − 0.217902i
\(92\) 6.79540e6 0.909824
\(93\) 1.83492e6 − 3.17817e6i 0.236552 − 0.409720i
\(94\) −1.30480e6 + 2.25999e6i −0.162031 + 0.280646i
\(95\) −7.32374e6 − 1.26851e7i −0.876396 − 1.51796i
\(96\) 2.33172e6 0.268984
\(97\) 3.40424e6 + 5.89631e6i 0.378720 + 0.655963i 0.990876 − 0.134774i \(-0.0430309\pi\)
−0.612156 + 0.790737i \(0.709698\pi\)
\(98\) −2.59928e6 − 4.50208e6i −0.278973 − 0.483195i
\(99\) 9.84569e6 1.01982
\(100\) −6.26931e6 − 1.08588e7i −0.626931 − 1.08588i
\(101\) −805060. + 1.39441e6i −0.0777506 + 0.134668i −0.902279 − 0.431152i \(-0.858107\pi\)
0.824529 + 0.565820i \(0.191440\pi\)
\(102\) 1.86095e6 − 3.22326e6i 0.173633 − 0.300742i
\(103\) 4.93664e6 0.445145 0.222572 − 0.974916i \(-0.428555\pi\)
0.222572 + 0.974916i \(0.428555\pi\)
\(104\) 3.45151e6 − 2.12983e6i 0.300880 − 0.185665i
\(105\) 1.55261e7 1.30888
\(106\) 3.73627e6 − 6.47142e6i 0.304697 − 0.527751i
\(107\) 6.13515e6 − 1.06264e7i 0.484152 − 0.838576i −0.515682 − 0.856780i \(-0.672461\pi\)
0.999834 + 0.0182040i \(0.00579483\pi\)
\(108\) 1.57009e6 + 2.71947e6i 0.119933 + 0.207731i
\(109\) −1.65278e7 −1.22243 −0.611213 − 0.791467i \(-0.709318\pi\)
−0.611213 + 0.791467i \(0.709318\pi\)
\(110\) 7.16715e6 + 1.24139e7i 0.513419 + 0.889268i
\(111\) 1.71262e6 + 2.96634e6i 0.118859 + 0.205869i
\(112\) −1.70722e6 −0.114822
\(113\) −6.64380e6 − 1.15074e7i −0.433154 − 0.750244i 0.563989 − 0.825782i \(-0.309266\pi\)
−0.997143 + 0.0755379i \(0.975933\pi\)
\(114\) −7.96419e6 + 1.37944e7i −0.503471 + 0.872038i
\(115\) −2.77915e7 + 4.81363e7i −1.70400 + 2.95142i
\(116\) 4.38694e6 0.260951
\(117\) 2.00584e7 + 1.08105e7i 1.15783 + 0.624013i
\(118\) −9.39547e6 −0.526419
\(119\) −1.36253e6 + 2.35997e6i −0.0741195 + 0.128379i
\(120\) −9.53617e6 + 1.65171e7i −0.503779 + 0.872570i
\(121\) 3.88588e6 + 6.73054e6i 0.199407 + 0.345383i
\(122\) 2.31272e7 1.15309
\(123\) −2.14222e7 − 3.71043e7i −1.03800 − 1.79786i
\(124\) −1.65033e6 − 2.85845e6i −0.0777311 − 0.134634i
\(125\) 6.16623e7 2.82381
\(126\) −4.79575e6 − 8.30648e6i −0.213579 − 0.369931i
\(127\) −1.36436e6 + 2.36314e6i −0.0591040 + 0.102371i −0.894063 − 0.447940i \(-0.852158\pi\)
0.834959 + 0.550311i \(0.185491\pi\)
\(128\) 1.04858e6 − 1.81619e6i 0.0441942 − 0.0765466i
\(129\) −6.51990e7 −2.67410
\(130\) 971178. + 3.31599e7i 0.0387701 + 1.32377i
\(131\) 1.96041e7 0.761898 0.380949 − 0.924596i \(-0.375597\pi\)
0.380949 + 0.924596i \(0.375597\pi\)
\(132\) 7.79391e6 − 1.34994e7i 0.294949 − 0.510866i
\(133\) 5.83115e6 − 1.00999e7i 0.214918 − 0.372250i
\(134\) 1.27263e6 + 2.20426e6i 0.0456916 + 0.0791401i
\(135\) −2.56851e7 −0.898490
\(136\) −1.67374e6 − 2.89900e6i −0.0570560 − 0.0988240i
\(137\) −326199. − 564993.i −0.0108383 − 0.0187724i 0.860555 − 0.509357i \(-0.170117\pi\)
−0.871394 + 0.490584i \(0.836783\pi\)
\(138\) 6.04437e7 1.95783
\(139\) −4.60831e6 − 7.98182e6i −0.145542 − 0.252087i 0.784033 − 0.620719i \(-0.213159\pi\)
−0.929575 + 0.368633i \(0.879826\pi\)
\(140\) 6.98211e6 − 1.20934e7i 0.215050 − 0.372477i
\(141\) −1.16060e7 + 2.01021e7i −0.348670 + 0.603915i
\(142\) −1.02699e7 −0.300993
\(143\) −793743. − 2.71016e7i −0.0226988 − 0.775030i
\(144\) 1.17822e7 0.328820
\(145\) −1.79415e7 + 3.10757e7i −0.488733 + 0.846510i
\(146\) −6.68835e6 + 1.15846e7i −0.177862 + 0.308066i
\(147\) −2.31201e7 − 4.00451e7i −0.600314 − 1.03977i
\(148\) 3.08067e6 0.0781140
\(149\) 1.22231e6 + 2.11710e6i 0.0302712 + 0.0524312i 0.880764 − 0.473555i \(-0.157030\pi\)
−0.850493 + 0.525986i \(0.823696\pi\)
\(150\) −5.57643e7 − 9.65866e7i −1.34908 − 2.33667i
\(151\) −2.73196e7 −0.645736 −0.322868 − 0.946444i \(-0.604647\pi\)
−0.322868 + 0.946444i \(0.604647\pi\)
\(152\) 7.16301e6 + 1.24067e7i 0.165441 + 0.286552i
\(153\) 9.40341e6 − 1.62872e7i 0.212259 − 0.367643i
\(154\) −5.70647e6 + 9.88390e6i −0.125906 + 0.218075i
\(155\) 2.69978e7 0.582328
\(156\) 3.07005e7 − 1.89445e7i 0.647456 − 0.399527i
\(157\) 5.54490e7 1.14352 0.571761 − 0.820420i \(-0.306260\pi\)
0.571761 + 0.820420i \(0.306260\pi\)
\(158\) −3.23664e7 + 5.60602e7i −0.652821 + 1.13072i
\(159\) 3.32334e7 − 5.75620e7i 0.655670 − 1.13565i
\(160\) 8.57685e6 + 1.48555e7i 0.165542 + 0.286727i
\(161\) −4.42551e7 −0.835744
\(162\) −1.11982e7 − 1.93958e7i −0.206940 − 0.358431i
\(163\) −1.60007e7 − 2.77139e7i −0.289388 − 0.501235i 0.684275 − 0.729224i \(-0.260119\pi\)
−0.973664 + 0.227988i \(0.926785\pi\)
\(164\) −3.85343e7 −0.682172
\(165\) 6.37504e7 + 1.10419e8i 1.10481 + 1.91359i
\(166\) 2.22856e7 − 3.85999e7i 0.378135 − 0.654949i
\(167\) 9.67304e6 − 1.67542e7i 0.160715 − 0.278366i −0.774411 − 0.632683i \(-0.781953\pi\)
0.935125 + 0.354318i \(0.115287\pi\)
\(168\) −1.51854e7 −0.247083
\(169\) 2.81401e7 − 5.60848e7i 0.448459 − 0.893804i
\(170\) 2.73808e7 0.427439
\(171\) −4.02432e7 + 6.97033e7i −0.615469 + 1.06602i
\(172\) −2.93201e7 + 5.07838e7i −0.439355 + 0.760985i
\(173\) −2.06874e7 − 3.58317e7i −0.303770 − 0.526145i 0.673217 − 0.739445i \(-0.264912\pi\)
−0.976987 + 0.213300i \(0.931579\pi\)
\(174\) 3.90210e7 0.561534
\(175\) 4.08290e7 + 7.07179e7i 0.575885 + 0.997462i
\(176\) −7.00985e6 − 1.21414e7i −0.0969202 − 0.167871i
\(177\) −8.35709e7 −1.13279
\(178\) 3.15029e7 + 5.45646e7i 0.418678 + 0.725172i
\(179\) 1.61438e7 − 2.79619e7i 0.210388 − 0.364403i −0.741448 − 0.671010i \(-0.765861\pi\)
0.951836 + 0.306608i \(0.0991940\pi\)
\(180\) −4.81865e7 + 8.34614e7i −0.615845 + 1.06667i
\(181\) −8.08975e7 −1.01405 −0.507026 − 0.861931i \(-0.669255\pi\)
−0.507026 + 0.861931i \(0.669255\pi\)
\(182\) −2.24781e7 + 1.38706e7i −0.276381 + 0.170547i
\(183\) 2.05712e8 2.48130
\(184\) 2.71816e7 − 4.70799e7i 0.321671 − 0.557151i
\(185\) −1.25992e7 + 2.18224e7i −0.146299 + 0.253397i
\(186\) −1.46793e7 − 2.54254e7i −0.167267 − 0.289716i
\(187\) −2.23783e7 −0.250254
\(188\) 1.04384e7 + 1.80799e7i 0.114573 + 0.198447i
\(189\) −1.02252e7 − 1.77106e7i −0.110168 − 0.190817i
\(190\) −1.17180e8 −1.23941
\(191\) 6.81711e6 + 1.18076e7i 0.0707919 + 0.122615i 0.899249 − 0.437438i \(-0.144114\pi\)
−0.828457 + 0.560053i \(0.810781\pi\)
\(192\) 9.32688e6 − 1.61546e7i 0.0951003 − 0.164719i
\(193\) −8.66220e6 + 1.50034e7i −0.0867316 + 0.150224i −0.906128 − 0.423004i \(-0.860976\pi\)
0.819396 + 0.573228i \(0.194309\pi\)
\(194\) 5.44678e7 0.535591
\(195\) 8.63844e6 + 2.94951e8i 0.0834284 + 2.84858i
\(196\) −4.15885e7 −0.394527
\(197\) −3.11874e7 + 5.40181e7i −0.290634 + 0.503393i −0.973960 − 0.226720i \(-0.927200\pi\)
0.683326 + 0.730114i \(0.260533\pi\)
\(198\) 3.93828e7 − 6.82130e7i 0.360561 − 0.624509i
\(199\) 1.20854e6 + 2.09325e6i 0.0108711 + 0.0188293i 0.871410 − 0.490556i \(-0.163206\pi\)
−0.860539 + 0.509385i \(0.829873\pi\)
\(200\) −1.00309e8 −0.886615
\(201\) 1.13198e7 + 1.96065e7i 0.0983225 + 0.170300i
\(202\) 6.44048e6 + 1.11552e7i 0.0549780 + 0.0952246i
\(203\) −2.85700e7 −0.239704
\(204\) −1.48876e7 − 2.57860e7i −0.122777 − 0.212657i
\(205\) 1.57596e8 − 2.72964e8i 1.27763 − 2.21293i
\(206\) 1.97466e7 − 3.42021e7i 0.157382 − 0.272594i
\(207\) 3.05423e8 2.39335
\(208\) −949863. − 3.24321e7i −0.00731879 − 0.249893i
\(209\) 9.57711e7 0.725642
\(210\) 6.21045e7 − 1.07568e8i 0.462760 − 0.801523i
\(211\) −4.86339e7 + 8.42364e7i −0.356411 + 0.617321i −0.987358 − 0.158504i \(-0.949333\pi\)
0.630948 + 0.775825i \(0.282666\pi\)
\(212\) −2.98902e7 − 5.17713e7i −0.215453 − 0.373176i
\(213\) −9.13487e7 −0.647700
\(214\) −4.90812e7 − 8.50111e7i −0.342347 − 0.592963i
\(215\) −2.39824e8 − 4.15387e8i −1.64573 − 2.85048i
\(216\) 2.51214e7 0.169612
\(217\) 1.07478e7 + 1.86157e7i 0.0714020 + 0.123672i
\(218\) −6.61112e7 + 1.14508e8i −0.432193 + 0.748579i
\(219\) −5.94915e7 + 1.03042e8i −0.382737 + 0.662920i
\(220\) 1.14674e8 0.726085
\(221\) −4.55907e7 − 2.45711e7i −0.284121 − 0.153127i
\(222\) 2.74019e7 0.168091
\(223\) −8.35602e7 + 1.44730e8i −0.504583 + 0.873963i 0.495403 + 0.868663i \(0.335020\pi\)
−0.999986 + 0.00529982i \(0.998313\pi\)
\(224\) −6.82887e6 + 1.18280e7i −0.0405958 + 0.0703139i
\(225\) −2.81778e8 − 4.88054e8i −1.64918 − 2.85647i
\(226\) −1.06301e8 −0.612572
\(227\) −2.85340e7 − 4.94223e7i −0.161909 − 0.280435i 0.773644 − 0.633620i \(-0.218432\pi\)
−0.935553 + 0.353185i \(0.885098\pi\)
\(228\) 6.37135e7 + 1.10355e8i 0.356008 + 0.616624i
\(229\) 2.68753e8 1.47886 0.739432 − 0.673231i \(-0.235094\pi\)
0.739432 + 0.673231i \(0.235094\pi\)
\(230\) 2.22332e8 + 3.85091e8i 1.20491 + 2.08697i
\(231\) −5.07580e7 + 8.79154e7i −0.270933 + 0.469270i
\(232\) 1.75478e7 − 3.03936e7i 0.0922601 − 0.159799i
\(233\) −6.53750e7 −0.338584 −0.169292 − 0.985566i \(-0.554148\pi\)
−0.169292 + 0.985566i \(0.554148\pi\)
\(234\) 1.55131e8 − 9.57267e7i 0.791483 − 0.488402i
\(235\) −1.70763e8 −0.858333
\(236\) −3.75819e7 + 6.50938e7i −0.186117 + 0.322365i
\(237\) −2.87893e8 + 4.98645e8i −1.40479 + 2.43317i
\(238\) 1.09003e7 + 1.88798e7i 0.0524104 + 0.0907775i
\(239\) −2.06797e8 −0.979832 −0.489916 − 0.871770i \(-0.662973\pi\)
−0.489916 + 0.871770i \(0.662973\pi\)
\(240\) 7.62894e7 + 1.32137e8i 0.356225 + 0.617000i
\(241\) 1.40238e8 + 2.42899e8i 0.645365 + 1.11780i 0.984217 + 0.176965i \(0.0566280\pi\)
−0.338852 + 0.940840i \(0.610039\pi\)
\(242\) 6.21740e7 0.282004
\(243\) −1.53259e8 − 2.65452e8i −0.685177 − 1.18676i
\(244\) 9.25087e7 − 1.60230e8i 0.407679 − 0.706121i
\(245\) 1.70087e8 − 2.94599e8i 0.738906 − 1.27982i
\(246\) −3.42755e8 −1.46795
\(247\) 1.95112e8 + 1.05155e8i 0.823843 + 0.444010i
\(248\) −2.64053e7 −0.109928
\(249\) 1.98226e8 − 3.43338e8i 0.813699 − 1.40937i
\(250\) 2.46649e8 − 4.27209e8i 0.998366 − 1.72922i
\(251\) 1.55974e8 + 2.70156e8i 0.622580 + 1.07834i 0.989004 + 0.147892i \(0.0472488\pi\)
−0.366423 + 0.930448i \(0.619418\pi\)
\(252\) −7.67320e7 −0.302047
\(253\) −1.81712e8 − 3.14734e8i −0.705443 − 1.22186i
\(254\) 1.09149e7 + 1.89052e7i 0.0417928 + 0.0723873i
\(255\) 2.43546e8 0.919795
\(256\) −8.38861e6 − 1.45295e7i −0.0312500 − 0.0541266i
\(257\) −1.07145e8 + 1.85580e8i −0.393736 + 0.681970i −0.992939 − 0.118627i \(-0.962151\pi\)
0.599203 + 0.800597i \(0.295484\pi\)
\(258\) −2.60796e8 + 4.51712e8i −0.945436 + 1.63754i
\(259\) −2.00629e7 −0.0717537
\(260\) 2.33623e8 + 1.25911e8i 0.824346 + 0.444281i
\(261\) 1.97174e8 0.686448
\(262\) 7.84163e7 − 1.35821e8i 0.269372 − 0.466565i
\(263\) −8.74186e7 + 1.51413e8i −0.296318 + 0.513239i −0.975291 − 0.220925i \(-0.929092\pi\)
0.678972 + 0.734164i \(0.262426\pi\)
\(264\) −6.23512e7 − 1.07996e8i −0.208560 − 0.361237i
\(265\) 4.88975e8 1.61408
\(266\) −4.66492e7 − 8.07988e7i −0.151970 − 0.263220i
\(267\) 2.80212e8 + 4.85341e8i 0.900943 + 1.56048i
\(268\) 2.03621e7 0.0646176
\(269\) −1.41548e8 − 2.45168e8i −0.443374 − 0.767947i 0.554563 − 0.832142i \(-0.312885\pi\)
−0.997937 + 0.0641947i \(0.979552\pi\)
\(270\) −1.02740e8 + 1.77952e8i −0.317664 + 0.550210i
\(271\) −1.08878e8 + 1.88582e8i −0.332312 + 0.575581i −0.982965 − 0.183794i \(-0.941162\pi\)
0.650653 + 0.759375i \(0.274495\pi\)
\(272\) −2.67798e7 −0.0806894
\(273\) −1.99938e8 + 1.23376e8i −0.594738 + 0.366996i
\(274\) −5.21918e6 −0.0153276
\(275\) −3.35289e8 + 5.80737e8i −0.972197 + 1.68389i
\(276\) 2.41775e8 − 4.18766e8i 0.692196 − 1.19892i
\(277\) 2.75129e8 + 4.76538e8i 0.777782 + 1.34716i 0.933218 + 0.359312i \(0.116988\pi\)
−0.155436 + 0.987846i \(0.549678\pi\)
\(278\) −7.37329e7 −0.205828
\(279\) −7.41751e7 − 1.28475e8i −0.204476 − 0.354164i
\(280\) −5.58569e7 − 9.67470e7i −0.152063 − 0.263381i
\(281\) −1.42673e8 −0.383591 −0.191796 − 0.981435i \(-0.561431\pi\)
−0.191796 + 0.981435i \(0.561431\pi\)
\(282\) 9.28479e7 + 1.60817e8i 0.246547 + 0.427032i
\(283\) 1.29624e7 − 2.24515e7i 0.0339963 − 0.0588833i −0.848527 − 0.529153i \(-0.822510\pi\)
0.882523 + 0.470269i \(0.155843\pi\)
\(284\) −4.10796e7 + 7.11519e7i −0.106417 + 0.184320i
\(285\) −1.04229e9 −2.66706
\(286\) −1.90940e8 − 1.02907e8i −0.482632 − 0.260114i
\(287\) 2.50955e8 0.626627
\(288\) 4.71289e7 − 8.16297e7i 0.116256 − 0.201361i
\(289\) 1.83796e8 − 3.18345e8i 0.447914 − 0.775809i
\(290\) 1.43532e8 + 2.48605e8i 0.345586 + 0.598573i
\(291\) 4.84480e8 1.15253
\(292\) 5.35068e7 + 9.26764e7i 0.125768 + 0.217836i
\(293\) −3.71932e8 − 6.44205e8i −0.863827 − 1.49619i −0.868207 − 0.496202i \(-0.834727\pi\)
0.00437957 − 0.999990i \(-0.498606\pi\)
\(294\) −3.69921e8 −0.848972
\(295\) −3.07402e8 − 5.32436e8i −0.697155 − 1.20751i
\(296\) 1.23227e7 − 2.13435e7i 0.0276175 − 0.0478348i
\(297\) 8.39697e7 − 1.45440e8i 0.185984 − 0.322133i
\(298\) 1.95570e7 0.0428099
\(299\) −2.46227e7 − 8.40718e8i −0.0532705 − 1.81887i
\(300\) −8.92229e8 −1.90788
\(301\) 1.90947e8 − 3.30731e8i 0.403581 − 0.699023i
\(302\) −1.09278e8 + 1.89276e8i −0.228302 + 0.395431i
\(303\) 5.72868e7 + 9.92237e7i 0.118306 + 0.204911i
\(304\) 1.14608e8 0.233969
\(305\) 7.56677e8 + 1.31060e9i 1.52708 + 2.64497i
\(306\) −7.52273e7 − 1.30297e8i −0.150090 − 0.259963i
\(307\) 2.86830e8 0.565771 0.282886 − 0.959154i \(-0.408708\pi\)
0.282886 + 0.959154i \(0.408708\pi\)
\(308\) 4.56518e7 + 7.90712e7i 0.0890288 + 0.154202i
\(309\) 1.75642e8 − 3.04221e8i 0.338667 − 0.586589i
\(310\) 1.07991e8 − 1.87046e8i 0.205884 − 0.356601i
\(311\) 7.18890e8 1.35519 0.677596 − 0.735434i \(-0.263022\pi\)
0.677596 + 0.735434i \(0.263022\pi\)
\(312\) −8.44885e6 − 2.88477e8i −0.0157491 − 0.537738i
\(313\) 6.20382e8 1.14355 0.571774 − 0.820411i \(-0.306255\pi\)
0.571774 + 0.820411i \(0.306255\pi\)
\(314\) 2.21796e8 − 3.84162e8i 0.404296 − 0.700262i
\(315\) 3.13815e8 − 5.43544e8i 0.565701 − 0.979824i
\(316\) 2.58931e8 + 4.48482e8i 0.461614 + 0.799540i
\(317\) 1.67254e8 0.294897 0.147448 − 0.989070i \(-0.452894\pi\)
0.147448 + 0.989070i \(0.452894\pi\)
\(318\) −2.65867e8 − 4.60496e8i −0.463628 − 0.803028i
\(319\) −1.17309e8 − 2.03185e8i −0.202331 − 0.350448i
\(320\) 1.37230e8 0.234112
\(321\) −4.36567e8 − 7.56157e8i −0.736688 − 1.27598i
\(322\) −1.77021e8 + 3.06609e8i −0.295480 + 0.511786i
\(323\) 9.14688e7 − 1.58429e8i 0.151030 − 0.261592i
\(324\) −1.79171e8 −0.292658
\(325\) −1.32072e9 + 8.14978e8i −2.13412 + 1.31690i
\(326\) −2.56010e8 −0.409257
\(327\) −5.88046e8 + 1.01853e9i −0.930024 + 1.61085i
\(328\) −1.54137e8 + 2.66973e8i −0.241184 + 0.417743i
\(329\) −6.79805e7 − 1.17746e8i −0.105244 − 0.182289i
\(330\) 1.02001e9 1.56244
\(331\) −3.94643e8 − 6.83541e8i −0.598144 − 1.03602i −0.993095 − 0.117314i \(-0.962572\pi\)
0.394950 − 0.918702i \(-0.370762\pi\)
\(332\) −1.78285e8 − 3.08799e8i −0.267382 − 0.463119i
\(333\) 1.38463e8 0.205484
\(334\) −7.73843e7 − 1.34034e8i −0.113642 − 0.196834i
\(335\) −8.32761e7 + 1.44238e8i −0.121022 + 0.209616i
\(336\) −6.07415e7 + 1.05207e8i −0.0873570 + 0.151307i
\(337\) −6.94195e8 −0.988046 −0.494023 − 0.869449i \(-0.664474\pi\)
−0.494023 + 0.869449i \(0.664474\pi\)
\(338\) −2.76007e8 − 4.19300e8i −0.388787 − 0.590631i
\(339\) −9.45525e8 −1.31818
\(340\) 1.09523e8 − 1.89699e8i 0.151123 − 0.261752i
\(341\) −8.82611e7 + 1.52873e8i −0.120539 + 0.208780i
\(342\) 3.21946e8 + 5.57627e8i 0.435203 + 0.753793i
\(343\) 6.14099e8 0.821692
\(344\) 2.34560e8 + 4.06271e8i 0.310671 + 0.538097i
\(345\) 1.97760e9 + 3.42531e9i 2.59282 + 4.49089i
\(346\) −3.30999e8 −0.429596
\(347\) 1.32264e7 + 2.29088e7i 0.0169937 + 0.0294340i 0.874397 − 0.485211i \(-0.161257\pi\)
−0.857403 + 0.514645i \(0.827924\pi\)
\(348\) 1.56084e8 − 2.70345e8i 0.198532 − 0.343868i
\(349\) −3.89696e8 + 6.74973e8i −0.490723 + 0.849957i −0.999943 − 0.0106791i \(-0.996601\pi\)
0.509220 + 0.860636i \(0.329934\pi\)
\(350\) 6.53264e8 0.814424
\(351\) 3.30760e8 − 2.04103e8i 0.408262 − 0.251927i
\(352\) −1.12158e8 −0.137066
\(353\) 3.64706e8 − 6.31689e8i 0.441297 − 0.764349i −0.556489 − 0.830855i \(-0.687852\pi\)
0.997786 + 0.0665058i \(0.0211851\pi\)
\(354\) −3.34284e8 + 5.78996e8i −0.400501 + 0.693688i
\(355\) −3.36011e8 − 5.81989e8i −0.398616 − 0.690423i
\(356\) 5.04046e8 0.592100
\(357\) 9.69556e7 + 1.67932e8i 0.112781 + 0.195342i
\(358\) −1.29151e8 − 2.23695e8i −0.148767 − 0.257672i
\(359\) −5.70058e8 −0.650262 −0.325131 − 0.945669i \(-0.605408\pi\)
−0.325131 + 0.945669i \(0.605408\pi\)
\(360\) 3.85492e8 + 6.67692e8i 0.435468 + 0.754253i
\(361\) 5.54818e7 − 9.60973e7i 0.0620691 − 0.107507i
\(362\) −3.23590e8 + 5.60474e8i −0.358521 + 0.620977i
\(363\) 5.53026e8 0.606837
\(364\) 6.18600e6 + 2.11215e8i 0.00672288 + 0.229546i
\(365\) −8.75319e8 −0.942196
\(366\) 8.22847e8 − 1.42521e9i 0.877274 − 1.51948i
\(367\) 2.41067e8 − 4.17540e8i 0.254569 − 0.440927i −0.710209 − 0.703991i \(-0.751400\pi\)
0.964778 + 0.263064i \(0.0847330\pi\)
\(368\) −2.17453e8 − 3.76639e8i −0.227456 − 0.393965i
\(369\) −1.73195e9 −1.79450
\(370\) 1.00793e8 + 1.74579e8i 0.103449 + 0.179179i
\(371\) 1.94660e8 + 3.37162e8i 0.197911 + 0.342791i
\(372\) −2.34870e8 −0.236552
\(373\) 1.49680e8 + 2.59253e8i 0.149342 + 0.258668i 0.930984 − 0.365059i \(-0.118951\pi\)
−0.781642 + 0.623727i \(0.785618\pi\)
\(374\) −8.95131e7 + 1.55041e8i −0.0884782 + 0.153249i
\(375\) 2.19390e9 − 3.79994e9i 2.14836 − 3.72107i
\(376\) 1.67015e8 0.162031
\(377\) −1.58958e7 − 5.42747e8i −0.0152788 − 0.521678i
\(378\) −1.63604e8 −0.155801
\(379\) −5.05321e8 + 8.75242e8i −0.476793 + 0.825830i −0.999646 − 0.0265924i \(-0.991534\pi\)
0.522853 + 0.852423i \(0.324868\pi\)
\(380\) −4.68720e8 + 8.11846e8i −0.438198 + 0.758981i
\(381\) 9.70858e7 + 1.68158e8i 0.0899329 + 0.155768i
\(382\) 1.09074e8 0.100115
\(383\) −4.42877e8 − 7.67085e8i −0.402798 − 0.697667i 0.591264 − 0.806478i \(-0.298629\pi\)
−0.994062 + 0.108811i \(0.965296\pi\)
\(384\) −7.46150e7 − 1.29237e8i −0.0672461 − 0.116474i
\(385\) −7.46819e8 −0.666965
\(386\) 6.92976e7 + 1.20027e8i 0.0613285 + 0.106224i
\(387\) −1.31781e9 + 2.28251e9i −1.15575 + 2.00182i
\(388\) 2.17871e8 − 3.77364e8i 0.189360 − 0.327981i
\(389\) 2.15563e9 1.85674 0.928370 − 0.371656i \(-0.121210\pi\)
0.928370 + 0.371656i \(0.121210\pi\)
\(390\) 2.07803e9 + 1.11995e9i 1.77389 + 0.956036i
\(391\) −6.94197e8 −0.587305
\(392\) −1.66354e8 + 2.88133e8i −0.139486 + 0.241597i
\(393\) 6.97498e8 − 1.20810e9i 0.579654 − 1.00399i
\(394\) 2.49499e8 + 4.32145e8i 0.205509 + 0.355953i
\(395\) −4.23586e9 −3.45822
\(396\) −3.15062e8 − 5.45704e8i −0.254955 − 0.441595i
\(397\) 4.73536e8 + 8.20188e8i 0.379827 + 0.657880i 0.991037 − 0.133589i \(-0.0426501\pi\)
−0.611210 + 0.791469i \(0.709317\pi\)
\(398\) 1.93366e7 0.0153741
\(399\) −4.14936e8 − 7.18689e8i −0.327021 − 0.566417i
\(400\) −4.01236e8 + 6.94961e8i −0.313466 + 0.542938i
\(401\) 7.68784e8 − 1.33157e9i 0.595386 − 1.03124i −0.398106 − 0.917339i \(-0.630332\pi\)
0.993492 − 0.113900i \(-0.0363343\pi\)
\(402\) 1.81117e8 0.139049
\(403\) −3.47664e8 + 2.14534e8i −0.264602 + 0.163278i
\(404\) 1.03048e8 0.0777506
\(405\) 7.32767e8 − 1.26919e9i 0.548117 − 0.949366i
\(406\) −1.14280e8 + 1.97939e8i −0.0847481 + 0.146788i
\(407\) −8.23784e7 − 1.42684e8i −0.0605666 − 0.104904i
\(408\) −2.38201e8 −0.173633
\(409\) −4.78055e8 − 8.28015e8i −0.345498 − 0.598421i 0.639946 − 0.768420i \(-0.278957\pi\)
−0.985444 + 0.169999i \(0.945623\pi\)
\(410\) −1.26077e9 − 2.18371e9i −0.903423 − 1.56478i
\(411\) −4.64236e7 −0.0329831
\(412\) −1.57973e8 − 2.73617e8i −0.111286 − 0.192753i
\(413\) 2.44753e8 − 4.23924e8i 0.170963 − 0.296117i
\(414\) 1.22169e9 − 2.11604e9i 0.846177 − 1.46562i
\(415\) 2.91657e9 2.00311
\(416\) −2.28496e8 − 1.23148e8i −0.155615 − 0.0838686i
\(417\) −6.55839e8 −0.442916
\(418\) 3.83084e8 − 6.63521e8i 0.256553 − 0.444363i
\(419\) −1.00065e9 + 1.73318e9i −0.664559 + 1.15105i 0.314846 + 0.949143i \(0.398047\pi\)
−0.979405 + 0.201907i \(0.935286\pi\)
\(420\) −4.96836e8 − 8.60545e8i −0.327220 − 0.566763i
\(421\) 2.08228e9 1.36004 0.680020 − 0.733194i \(-0.261971\pi\)
0.680020 + 0.733194i \(0.261971\pi\)
\(422\) 3.89071e8 + 6.73891e8i 0.252020 + 0.436512i
\(423\) 4.69162e8 + 8.12613e8i 0.301392 + 0.522026i
\(424\) −4.78243e8 −0.304697
\(425\) 6.40454e8 + 1.10930e9i 0.404694 + 0.700950i
\(426\) −3.65395e8 + 6.32882e8i −0.228996 + 0.396634i
\(427\) −6.02465e8 + 1.04350e9i −0.374485 + 0.648626i
\(428\) −7.85299e8 −0.484152
\(429\) −1.69837e9 − 9.15338e8i −1.03856 − 0.559733i
\(430\) −3.83718e9 −2.32741
\(431\) 3.68644e8 − 6.38511e8i 0.221788 − 0.384147i −0.733563 − 0.679621i \(-0.762144\pi\)
0.955351 + 0.295474i \(0.0954775\pi\)
\(432\) 1.00486e8 − 1.74046e8i 0.0599667 − 0.103865i
\(433\) 2.20052e8 + 3.81141e8i 0.130262 + 0.225620i 0.923778 − 0.382930i \(-0.125085\pi\)
−0.793516 + 0.608550i \(0.791751\pi\)
\(434\) 1.71965e8 0.100978
\(435\) 1.27669e9 + 2.21129e9i 0.743659 + 1.28805i
\(436\) 5.28890e8 + 9.16064e8i 0.305606 + 0.529326i
\(437\) 2.97091e9 1.70296
\(438\) 4.75932e8 + 8.24339e8i 0.270636 + 0.468755i
\(439\) 1.08879e9 − 1.88584e9i 0.614212 − 1.06385i −0.376310 − 0.926494i \(-0.622807\pi\)
0.990522 − 0.137353i \(-0.0438595\pi\)
\(440\) 4.58698e8 − 7.94488e8i 0.256710 − 0.444634i
\(441\) −1.86922e9 −1.03783
\(442\) −3.52596e8 + 2.17577e8i −0.194223 + 0.119849i
\(443\) 1.78526e9 0.975639 0.487819 − 0.872945i \(-0.337793\pi\)
0.487819 + 0.872945i \(0.337793\pi\)
\(444\) 1.09608e8 − 1.89846e8i 0.0594293 − 0.102935i
\(445\) −2.06143e9 + 3.57050e9i −1.10894 + 1.92074i
\(446\) 6.68482e8 + 1.15784e9i 0.356794 + 0.617985i
\(447\) 1.73955e8 0.0921216
\(448\) 5.46310e7 + 9.46236e7i 0.0287055 + 0.0497195i
\(449\) 4.68771e8 + 8.11935e8i 0.244398 + 0.423310i 0.961962 − 0.273182i \(-0.0880762\pi\)
−0.717564 + 0.696493i \(0.754743\pi\)
\(450\) −4.50845e9 −2.33230
\(451\) 1.03042e9 + 1.78475e9i 0.528930 + 0.916133i
\(452\) −4.25203e8 + 7.36474e8i −0.216577 + 0.375122i
\(453\) −9.72010e8 + 1.68357e9i −0.491278 + 0.850918i
\(454\) −4.56543e8 −0.228974
\(455\) −1.52148e9 − 8.19998e8i −0.757225 − 0.408106i
\(456\) 1.01942e9 0.503471
\(457\) −1.53717e9 + 2.66245e9i −0.753381 + 1.30489i 0.192794 + 0.981239i \(0.438245\pi\)
−0.946175 + 0.323655i \(0.895088\pi\)
\(458\) 1.07501e9 − 1.86197e9i 0.522858 − 0.905616i
\(459\) −1.60395e8 − 2.77813e8i −0.0774189 − 0.134093i
\(460\) 3.55732e9 1.70400
\(461\) −1.64378e9 − 2.84710e9i −0.781428 − 1.35347i −0.931110 − 0.364739i \(-0.881158\pi\)
0.149681 − 0.988734i \(-0.452175\pi\)
\(462\) 4.06064e8 + 7.03323e8i 0.191579 + 0.331824i
\(463\) 8.40096e7 0.0393365 0.0196682 − 0.999807i \(-0.493739\pi\)
0.0196682 + 0.999807i \(0.493739\pi\)
\(464\) −1.40382e8 − 2.43149e8i −0.0652377 − 0.112995i
\(465\) 9.60560e8 − 1.66374e9i 0.443036 − 0.767361i
\(466\) −2.61500e8 + 4.52932e8i −0.119707 + 0.207339i
\(467\) 3.33082e9 1.51336 0.756681 − 0.653785i \(-0.226820\pi\)
0.756681 + 0.653785i \(0.226820\pi\)
\(468\) −4.26922e7 − 1.45768e9i −0.0192525 − 0.657359i
\(469\) −1.32609e8 −0.0593563
\(470\) −6.83051e8 + 1.18308e9i −0.303467 + 0.525619i
\(471\) 1.97283e9 − 3.41704e9i 0.869995 − 1.50688i
\(472\) 3.00655e8 + 5.20750e8i 0.131605 + 0.227946i
\(473\) 3.13613e9 1.36264
\(474\) 2.30314e9 + 3.98916e9i 0.993336 + 1.72051i
\(475\) −2.74091e9 − 4.74740e9i −1.17346 − 2.03249i
\(476\) 1.74404e8 0.0741195
\(477\) −1.34343e9 − 2.32690e9i −0.566764 − 0.981663i
\(478\) −8.27188e8 + 1.43273e9i −0.346423 + 0.600022i
\(479\) 4.49485e8 − 7.78532e8i 0.186871 − 0.323670i −0.757335 − 0.653027i \(-0.773499\pi\)
0.944205 + 0.329357i \(0.106832\pi\)
\(480\) 1.22063e9 0.503779
\(481\) −1.11626e7 − 3.81136e8i −0.00457360 − 0.156161i
\(482\) 2.24380e9 0.912684
\(483\) −1.57456e9 + 2.72722e9i −0.635836 + 1.10130i
\(484\) 2.48696e8 − 4.30754e8i 0.0997035 − 0.172691i
\(485\) 1.78208e9 + 3.08666e9i 0.709302 + 1.22855i
\(486\) −2.45214e9 −0.968986
\(487\) 1.33482e9 + 2.31197e9i 0.523685 + 0.907048i 0.999620 + 0.0275680i \(0.00877627\pi\)
−0.475935 + 0.879480i \(0.657890\pi\)
\(488\) −7.40070e8 − 1.28184e9i −0.288272 − 0.499303i
\(489\) −2.27716e9 −0.880670
\(490\) −1.36069e9 − 2.35679e9i −0.522486 − 0.904972i
\(491\) −1.70549e9 + 2.95399e9i −0.650225 + 1.12622i 0.332843 + 0.942982i \(0.391992\pi\)
−0.983068 + 0.183241i \(0.941341\pi\)
\(492\) −1.37102e9 + 2.37467e9i −0.518998 + 0.898931i
\(493\) −4.48157e8 −0.168448
\(494\) 1.50899e9 − 9.31153e8i 0.563172 − 0.347518i
\(495\) 5.15412e9 1.91001
\(496\) −1.05621e8 + 1.82941e8i −0.0388655 + 0.0673171i
\(497\) 2.67532e8 − 4.63378e8i 0.0977525 − 0.169312i
\(498\) −1.58581e9 − 2.74670e9i −0.575372 − 0.996573i
\(499\) −5.43259e9 −1.95729 −0.978645 − 0.205559i \(-0.934099\pi\)
−0.978645 + 0.205559i \(0.934099\pi\)
\(500\) −1.97319e9 − 3.41767e9i −0.705951 − 1.22274i
\(501\) −6.88318e8 − 1.19220e9i −0.244544 − 0.423563i
\(502\) 2.49559e9 0.880461
\(503\) −5.84567e8 − 1.01250e9i −0.204808 − 0.354737i 0.745264 − 0.666770i \(-0.232324\pi\)
−0.950071 + 0.312032i \(0.898990\pi\)
\(504\) −3.06928e8 + 5.31615e8i −0.106790 + 0.184965i
\(505\) −4.21440e8 + 7.29956e8i −0.145618 + 0.252219i
\(506\) −2.90739e9 −0.997647
\(507\) −2.45503e9 − 3.72959e9i −0.836620 − 1.27096i
\(508\) 1.74638e8 0.0591040
\(509\) −1.08501e9 + 1.87929e9i −0.364688 + 0.631658i −0.988726 − 0.149736i \(-0.952158\pi\)
0.624038 + 0.781394i \(0.285491\pi\)
\(510\) 9.74186e8 − 1.68734e9i 0.325197 − 0.563257i
\(511\) −3.48464e8 − 6.03557e8i −0.115527 − 0.200099i
\(512\) −1.34218e8 −0.0441942
\(513\) 6.86434e8 + 1.18894e9i 0.224485 + 0.388820i
\(514\) 8.57158e8 + 1.48464e9i 0.278413 + 0.482226i
\(515\) 2.58428e9 0.833708
\(516\) 2.08637e9 + 3.61370e9i 0.668524 + 1.15792i
\(517\) 5.58257e8 − 9.66930e8i 0.177671 − 0.307736i
\(518\) −8.02516e7 + 1.39000e8i −0.0253688 + 0.0439400i
\(519\) −2.94417e9 −0.924436
\(520\) 1.80683e9 − 1.11495e9i 0.563515 − 0.347730i
\(521\) −5.57218e9 −1.72621 −0.863103 − 0.505027i \(-0.831482\pi\)
−0.863103 + 0.505027i \(0.831482\pi\)
\(522\) 7.88696e8 − 1.36606e9i 0.242696 − 0.420362i
\(523\) 3.33759e8 − 5.78087e8i 0.102018 − 0.176700i −0.810498 − 0.585741i \(-0.800803\pi\)
0.912516 + 0.409041i \(0.134137\pi\)
\(524\) −6.27331e8 − 1.08657e9i −0.190475 − 0.329912i
\(525\) 5.81066e9 1.75254
\(526\) 6.99349e8 + 1.21131e9i 0.209529 + 0.362914i
\(527\) 1.68593e8 + 2.92011e8i 0.0501766 + 0.0869084i
\(528\) −9.97620e8 −0.294949
\(529\) −3.93448e9 − 6.81471e9i −1.15556 − 2.00149i
\(530\) 1.95590e9 − 3.38772e9i 0.570665 − 0.988420i
\(531\) −1.68914e9 + 2.92568e9i −0.489593 + 0.848000i
\(532\) −7.46387e8 −0.214918
\(533\) 1.39627e8 + 4.76741e9i 0.0399414 + 1.36376i
\(534\) 4.48339e9 1.27413
\(535\) 3.21168e9 − 5.56280e9i 0.906764 − 1.57056i
\(536\) 8.14484e7 − 1.41073e8i 0.0228458 − 0.0395701i
\(537\) −1.14877e9 − 1.98973e9i −0.320127 − 0.554477i
\(538\) −2.26477e9 −0.627026
\(539\) 1.11209e9 + 1.92620e9i 0.305901 + 0.529836i
\(540\) 8.21923e8 + 1.42361e9i 0.224622 + 0.389058i
\(541\) 4.87524e9 1.32375 0.661875 − 0.749614i \(-0.269761\pi\)
0.661875 + 0.749614i \(0.269761\pi\)
\(542\) 8.71021e8 + 1.50865e9i 0.234980 + 0.406997i
\(543\) −2.87827e9 + 4.98531e9i −0.771493 + 1.33626i
\(544\) −1.07119e8 + 1.85536e8i −0.0285280 + 0.0494120i
\(545\) −8.65212e9 −2.28947
\(546\) 5.50233e7 + 1.87871e9i 0.0144668 + 0.493954i
\(547\) 6.55899e8 0.171349 0.0856744 − 0.996323i \(-0.472696\pi\)
0.0856744 + 0.996323i \(0.472696\pi\)
\(548\) −2.08767e7 + 3.61595e7i −0.00541914 + 0.00938622i
\(549\) 4.15786e9 − 7.20163e9i 1.07242 − 1.85749i
\(550\) 2.68231e9 + 4.64589e9i 0.687447 + 1.19069i
\(551\) 1.91795e9 0.488435
\(552\) −1.93420e9 − 3.35013e9i −0.489457 − 0.847764i
\(553\) −1.68629e9 − 2.92075e9i −0.424029 − 0.734439i
\(554\) 4.40207e9 1.09995
\(555\) 8.96538e8 + 1.55285e9i 0.222609 + 0.385571i
\(556\) −2.94932e8 + 5.10836e8i −0.0727712 + 0.126043i
\(557\) 7.33190e8 − 1.26992e9i 0.179773 − 0.311375i −0.762030 − 0.647542i \(-0.775797\pi\)
0.941803 + 0.336167i \(0.109130\pi\)
\(558\) −1.18680e9 −0.289173
\(559\) 6.38915e9 + 3.44343e9i 1.54704 + 0.833777i
\(560\) −8.93710e8 −0.215050
\(561\) −7.96201e8 + 1.37906e9i −0.190394 + 0.329772i
\(562\) −5.70690e8 + 9.88465e8i −0.135620 + 0.234901i
\(563\) 1.50686e9 + 2.60996e9i 0.355872 + 0.616388i 0.987267 − 0.159074i \(-0.0508507\pi\)
−0.631395 + 0.775461i \(0.717517\pi\)
\(564\) 1.48557e9 0.348670
\(565\) −3.47796e9 − 6.02400e9i −0.811250 − 1.40513i
\(566\) −1.03699e8 − 1.79612e8i −0.0240390 − 0.0416368i
\(567\) 1.16686e9 0.268829
\(568\) 3.28637e8 + 5.69216e8i 0.0752483 + 0.130334i
\(569\) 3.75097e9 − 6.49687e9i 0.853592 − 1.47847i −0.0243527 − 0.999703i \(-0.507752\pi\)
0.877945 − 0.478762i \(-0.158914\pi\)
\(570\) −4.16917e9 + 7.22121e9i −0.942947 + 1.63323i
\(571\) −1.19452e9 −0.268514 −0.134257 − 0.990947i \(-0.542865\pi\)
−0.134257 + 0.990947i \(0.542865\pi\)
\(572\) −1.47672e9 + 9.11244e8i −0.329923 + 0.203586i
\(573\) 9.70190e8 0.215435
\(574\) 1.00382e9 − 1.73867e9i 0.221546 − 0.383729i
\(575\) −1.04010e10 + 1.80150e10i −2.28159 + 3.95183i
\(576\) −3.77031e8 − 6.53037e8i −0.0822051 − 0.142383i
\(577\) −4.85637e9 −1.05244 −0.526219 − 0.850349i \(-0.676391\pi\)
−0.526219 + 0.850349i \(0.676391\pi\)
\(578\) −1.47037e9 − 2.54676e9i −0.316723 − 0.548580i
\(579\) 6.16388e8 + 1.06762e9i 0.131971 + 0.228581i
\(580\) 2.29652e9 0.488733
\(581\) 1.16109e9 + 2.01106e9i 0.245611 + 0.425411i
\(582\) 1.93792e9 − 3.35658e9i 0.407479 − 0.705775i
\(583\) −1.59856e9 + 2.76878e9i −0.334109 + 0.578693i
\(584\) 8.56108e8 0.177862
\(585\) 1.05003e10 + 5.65915e9i 2.16849 + 1.16871i
\(586\) −5.95091e9 −1.22164
\(587\) 1.01242e9 − 1.75356e9i 0.206598 − 0.357839i −0.744043 − 0.668132i \(-0.767094\pi\)
0.950641 + 0.310294i \(0.100427\pi\)
\(588\) −1.47968e9 + 2.56289e9i −0.300157 + 0.519887i
\(589\) −7.21516e8 − 1.24970e9i −0.145493 − 0.252001i
\(590\) −4.91843e9 −0.985926
\(591\) 2.21924e9 + 3.84384e9i 0.442231 + 0.765966i
\(592\) −9.85813e7 − 1.70748e8i −0.0195285 − 0.0338243i
\(593\) 9.30040e8 0.183151 0.0915757 − 0.995798i \(-0.470810\pi\)
0.0915757 + 0.995798i \(0.470810\pi\)
\(594\) −6.71757e8 − 1.16352e9i −0.131510 − 0.227783i
\(595\) −7.13271e8 + 1.23542e9i −0.138818 + 0.240439i
\(596\) 7.82278e7 − 1.35495e8i 0.0151356 − 0.0262156i
\(597\) 1.71995e8 0.0330831
\(598\) −5.92316e9 − 3.19228e9i −1.13266 − 0.610445i
\(599\) 2.25978e9 0.429608 0.214804 − 0.976657i \(-0.431089\pi\)
0.214804 + 0.976657i \(0.431089\pi\)
\(600\) −3.56891e9 + 6.18154e9i −0.674539 + 1.16834i
\(601\) −7.28350e8 + 1.26154e9i −0.136861 + 0.237050i −0.926307 − 0.376770i \(-0.877035\pi\)
0.789446 + 0.613820i \(0.210368\pi\)
\(602\) −1.52758e9 − 2.64584e9i −0.285375 − 0.494284i
\(603\) 9.15188e8 0.169981
\(604\) 8.74228e8 + 1.51421e9i 0.161434 + 0.279612i
\(605\) 2.03422e9 + 3.52336e9i 0.373468 + 0.646865i
\(606\) 9.16589e8 0.167309
\(607\) 2.64143e9 + 4.57510e9i 0.479379 + 0.830309i 0.999720 − 0.0236495i \(-0.00752856\pi\)
−0.520341 + 0.853958i \(0.674195\pi\)
\(608\) 4.58432e8 − 7.94028e8i 0.0827204 − 0.143276i
\(609\) −1.01650e9 + 1.76063e9i −0.182367 + 0.315869i
\(610\) 1.21068e10 2.15961
\(611\) 2.19900e9 − 1.35694e9i 0.390015 − 0.240667i
\(612\) −1.20364e9 −0.212259
\(613\) 1.20643e9 − 2.08960e9i 0.211540 − 0.366397i −0.740657 − 0.671883i \(-0.765486\pi\)
0.952197 + 0.305486i \(0.0988190\pi\)
\(614\) 1.14732e9 − 1.98722e9i 0.200030 − 0.346463i
\(615\) −1.12143e10 − 1.94237e10i −1.94405 − 3.36720i
\(616\) 7.30429e8 0.125906
\(617\) −4.68931e9 − 8.12213e9i −0.803732 − 1.39210i −0.917144 − 0.398556i \(-0.869511\pi\)
0.113412 − 0.993548i \(-0.463822\pi\)
\(618\) −1.40513e9 − 2.43376e9i −0.239474 − 0.414781i
\(619\) 2.73222e9 0.463019 0.231510 − 0.972833i \(-0.425634\pi\)
0.231510 + 0.972833i \(0.425634\pi\)
\(620\) −8.63929e8 − 1.49637e9i −0.145582 − 0.252155i
\(621\) 2.60482e9 − 4.51169e9i 0.436473 − 0.755994i
\(622\) 2.87556e9 − 4.98061e9i 0.479133 − 0.829882i
\(623\) −3.28261e9 −0.543890
\(624\) −2.03243e9 − 1.09537e9i −0.334864 − 0.180475i
\(625\) 1.69736e10 2.78096
\(626\) 2.48153e9 − 4.29814e9i 0.404305 − 0.700277i
\(627\) 3.40746e9 − 5.90189e9i 0.552070 − 0.956213i
\(628\) −1.77437e9 − 3.07329e9i −0.285881 − 0.495160i
\(629\) −3.14711e8 −0.0504238
\(630\) −2.51052e9 − 4.34835e9i −0.400011 − 0.692840i
\(631\) −4.52633e9 − 7.83984e9i −0.717205 − 1.24224i −0.962103 − 0.272687i \(-0.912088\pi\)
0.244897 − 0.969549i \(-0.421246\pi\)
\(632\) 4.14290e9 0.652821
\(633\) 3.46071e9 + 5.99413e9i 0.542316 + 0.939319i
\(634\) 6.69017e8 − 1.15877e9i 0.104262 − 0.180587i
\(635\) −7.14229e8 + 1.23708e9i −0.110695 + 0.191730i
\(636\) −4.25388e9 −0.655670
\(637\) 1.50693e8 + 5.14527e9i 0.0230997 + 0.788716i
\(638\) −1.87694e9 −0.286140
\(639\) −1.84635e9 + 3.19797e9i −0.279937 + 0.484866i
\(640\) 5.48918e8 − 9.50754e8i 0.0827709 − 0.143363i
\(641\) 5.18052e9 + 8.97293e9i 0.776910 + 1.34565i 0.933715 + 0.358018i \(0.116547\pi\)
−0.156805 + 0.987630i \(0.550119\pi\)
\(642\) −6.98508e9 −1.04183
\(643\) 1.96400e9 + 3.40175e9i 0.291342 + 0.504619i 0.974127 − 0.226000i \(-0.0725648\pi\)
−0.682785 + 0.730619i \(0.739232\pi\)
\(644\) 1.41616e9 + 2.45287e9i 0.208936 + 0.361888i
\(645\) −3.41310e10 −5.00829
\(646\) −7.31751e8 − 1.26743e9i −0.106795 − 0.184974i
\(647\) 5.63673e9 − 9.76311e9i 0.818206 − 1.41717i −0.0887973 − 0.996050i \(-0.528302\pi\)
0.907003 − 0.421124i \(-0.138364\pi\)
\(648\) −7.16684e8 + 1.24133e9i −0.103470 + 0.179216i
\(649\) 4.01983e9 0.577233
\(650\) 3.63464e8 + 1.24101e10i 0.0519116 + 1.77247i
\(651\) 1.52959e9 0.217291
\(652\) −1.02404e9 + 1.77369e9i −0.144694 + 0.250618i
\(653\) 6.93321e9 − 1.20087e10i 0.974401 − 1.68771i 0.292505 − 0.956264i \(-0.405511\pi\)
0.681896 − 0.731449i \(-0.261156\pi\)
\(654\) 4.70437e9 + 8.14820e9i 0.657626 + 1.13904i
\(655\) 1.02625e10 1.42695
\(656\) 1.23310e9 + 2.13579e9i 0.170543 + 0.295389i
\(657\) 2.40490e9 + 4.16540e9i 0.330840 + 0.573031i
\(658\) −1.08769e9 −0.148838
\(659\) 7.94245e7 + 1.37567e8i 0.0108107 + 0.0187248i 0.871380 − 0.490608i \(-0.163225\pi\)
−0.860569 + 0.509333i \(0.829892\pi\)
\(660\) 4.08003e9 − 7.06681e9i 0.552407 − 0.956797i
\(661\) −5.58771e9 + 9.67820e9i −0.752539 + 1.30344i 0.194050 + 0.980992i \(0.437838\pi\)
−0.946589 + 0.322443i \(0.895496\pi\)
\(662\) −6.31428e9 −0.845904
\(663\) −3.13627e9 + 1.93531e9i −0.417942 + 0.257901i
\(664\) −2.85256e9 −0.378135
\(665\) 3.05255e9 − 5.28716e9i 0.402519 − 0.697183i
\(666\) 5.53850e8 − 9.59296e8i 0.0726495 − 0.125833i
\(667\) −3.63904e9 − 6.30300e9i −0.474839 − 0.822445i
\(668\) −1.23815e9 −0.160715
\(669\) 5.94601e9 + 1.02988e10i 0.767776 + 1.32983i
\(670\) 6.66209e8 + 1.15391e9i 0.0855754 + 0.148221i
\(671\) −9.89490e9 −1.26439
\(672\) 4.85932e8 + 8.41658e8i 0.0617707 + 0.106990i
\(673\) 2.69956e9 − 4.67577e9i 0.341381 − 0.591289i −0.643308 − 0.765607i \(-0.722439\pi\)
0.984689 + 0.174318i \(0.0557720\pi\)
\(674\) −2.77678e9 + 4.80953e9i −0.349327 + 0.605052i
\(675\) −9.61266e9 −1.20304
\(676\) −4.00902e9 + 2.35032e8i −0.499143 + 0.0292626i
\(677\) −7.69486e9 −0.953104 −0.476552 − 0.879146i \(-0.658114\pi\)
−0.476552 + 0.879146i \(0.658114\pi\)
\(678\) −3.78210e9 + 6.55079e9i −0.466046 + 0.807216i
\(679\) −1.41889e9 + 2.45759e9i −0.173942 + 0.301276i
\(680\) −8.76184e8 − 1.51760e9i −0.106860 − 0.185087i
\(681\) −4.06086e9 −0.492724
\(682\) 7.06089e8 + 1.22298e9i 0.0852342 + 0.147630i
\(683\) 2.54926e9 + 4.41544e9i 0.306155 + 0.530275i 0.977518 − 0.210853i \(-0.0676242\pi\)
−0.671363 + 0.741129i \(0.734291\pi\)
\(684\) 5.15113e9 0.615469
\(685\) −1.70761e8 − 2.95768e8i −0.0202989 − 0.0351588i
\(686\) 2.45640e9 − 4.25461e9i 0.290512 − 0.503182i
\(687\) 9.56200e9 − 1.65619e10i 1.12512 − 1.94877i
\(688\) 3.75297e9 0.439355
\(689\) −6.29678e9 + 3.88557e9i −0.733417 + 0.452572i
\(690\) 3.16416e10 3.66680
\(691\) 1.53611e8 − 2.66062e8i 0.0177112 − 0.0306768i −0.857034 − 0.515260i \(-0.827695\pi\)
0.874745 + 0.484583i \(0.161029\pi\)
\(692\) −1.32400e9 + 2.29323e9i −0.151885 + 0.263073i
\(693\) 2.05185e9 + 3.55391e9i 0.234196 + 0.405639i
\(694\) 2.11623e8 0.0240328
\(695\) −2.41240e9 − 4.17840e9i −0.272585 − 0.472131i
\(696\) −1.24867e9 − 2.16276e9i −0.140383 − 0.243151i
\(697\) 3.93654e9 0.440352
\(698\) 3.11757e9 + 5.39978e9i 0.346994 + 0.601011i
\(699\) −2.32599e9 + 4.02874e9i −0.257595 + 0.446168i
\(700\) 2.61306e9 − 4.52595e9i 0.287942 − 0.498731i
\(701\) 1.35330e9 0.148382 0.0741910 − 0.997244i \(-0.476363\pi\)
0.0741910 + 0.997244i \(0.476363\pi\)
\(702\) −9.10259e7 − 3.10799e9i −0.00993081 − 0.339078i
\(703\) 1.34685e9 0.146210
\(704\) −4.48630e8 + 7.77051e8i −0.0484601 + 0.0839354i
\(705\) −6.07561e9 + 1.05233e10i −0.653022 + 1.13107i
\(706\) −2.91765e9 − 5.05351e9i −0.312044 − 0.540477i
\(707\) −6.71100e8 −0.0714199
\(708\) 2.67427e9 + 4.63197e9i 0.283197 + 0.490512i
\(709\) −5.45562e9 − 9.44942e9i −0.574887 − 0.995734i −0.996054 − 0.0887504i \(-0.971713\pi\)
0.421167 − 0.906983i \(-0.361621\pi\)
\(710\) −5.37618e9 −0.563728
\(711\) 1.16378e10 + 2.01573e10i 1.21431 + 2.10324i
\(712\) 2.01618e9 − 3.49213e9i 0.209339 − 0.362586i
\(713\) −2.73795e9 + 4.74227e9i −0.282886 + 0.489973i
\(714\) 1.55129e9 0.159496
\(715\) −4.15516e8 − 1.41874e10i −0.0425125 − 1.45155i
\(716\) −2.06641e9 −0.210388
\(717\) −7.35768e9 + 1.27439e10i −0.745459 + 1.29117i
\(718\) −2.28023e9 + 3.94948e9i −0.229902 + 0.398203i
\(719\) 5.14659e9 + 8.91415e9i 0.516379 + 0.894394i 0.999819 + 0.0190170i \(0.00605368\pi\)
−0.483440 + 0.875377i \(0.660613\pi\)
\(720\) 6.16787e9 0.615845
\(721\) 1.02880e9 + 1.78193e9i 0.102225 + 0.177059i
\(722\) −4.43854e8 − 7.68779e8i −0.0438895 − 0.0760188i
\(723\) 1.99582e10 1.96398
\(724\) 2.58872e9 + 4.48379e9i 0.253513 + 0.439097i
\(725\) −6.71463e9 + 1.16301e10i −0.654393 + 1.13344i
\(726\) 2.21210e9 − 3.83148e9i 0.214549 − 0.371610i
\(727\) 7.61641e9 0.735156 0.367578 − 0.929993i \(-0.380187\pi\)
0.367578 + 0.929993i \(0.380187\pi\)
\(728\) 1.48808e9 + 8.02002e8i 0.142945 + 0.0770398i
\(729\) −1.56887e10 −1.49982
\(730\) −3.50128e9 + 6.06439e9i −0.333117 + 0.576975i
\(731\) 2.99525e9 − 5.18792e9i 0.283610 − 0.491227i
\(732\) −6.58277e9 − 1.14017e10i −0.620326 − 1.07444i
\(733\) 5.63920e9 0.528875 0.264438 − 0.964403i \(-0.414814\pi\)
0.264438 + 0.964403i \(0.414814\pi\)
\(734\) −1.92853e9 − 3.34032e9i −0.180008 − 0.311782i
\(735\) −1.21031e10 − 2.09632e10i −1.12432 − 1.94739i
\(736\) −3.47924e9 −0.321671
\(737\) −5.44492e8 − 9.43088e8i −0.0501020 − 0.0867793i
\(738\) −6.92779e9 + 1.19993e10i −0.634450 + 1.09890i
\(739\) −1.09173e10 + 1.89093e10i −0.995083 + 1.72353i −0.411766 + 0.911289i \(0.635088\pi\)
−0.583317 + 0.812245i \(0.698245\pi\)
\(740\) 1.61270e9 0.146299
\(741\) 1.34221e10 − 8.28242e9i 1.21187 − 0.747814i
\(742\) 3.11457e9 0.279888
\(743\) 5.74324e9 − 9.94759e9i 0.513684 − 0.889728i −0.486190 − 0.873853i \(-0.661614\pi\)
0.999874 − 0.0158742i \(-0.00505313\pi\)
\(744\) −9.39478e8 + 1.62722e9i −0.0836337 + 0.144858i
\(745\) 6.39866e8 + 1.10828e9i 0.0566947 + 0.0981980i
\(746\) 2.39487e9 0.211201
\(747\) −8.01314e9 − 1.38792e10i −0.703365 − 1.21826i
\(748\) 7.16105e8 + 1.24033e9i 0.0625635 + 0.108363i
\(749\) 5.11427e9 0.444731
\(750\) −1.75512e10 − 3.03995e10i −1.51912 − 2.63119i
\(751\) −3.48748e9 + 6.04050e9i −0.300450 + 0.520395i −0.976238 − 0.216701i \(-0.930470\pi\)
0.675788 + 0.737096i \(0.263804\pi\)
\(752\) 6.68060e8 − 1.15711e9i 0.0572866 − 0.0992233i
\(753\) 2.21978e10 1.89464
\(754\) −3.82385e9 − 2.06086e9i −0.324863 − 0.175085i
\(755\) −1.43015e10 −1.20939
\(756\) −6.54414e8 + 1.13348e9i −0.0550841 + 0.0954085i
\(757\) 1.58758e9 − 2.74977e9i 0.133015 − 0.230389i −0.791822 − 0.610751i \(-0.790867\pi\)
0.924837 + 0.380363i \(0.124201\pi\)
\(758\) 4.04257e9 + 7.00194e9i 0.337144 + 0.583950i
\(759\) −2.58607e10