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Properties

Label 10.7.c.a.7.1
Level $10$
Weight $7$
Character 10.7
Analytic conductor $2.301$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [10,7,Mod(3,10)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(10, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("10.3");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 10 = 2 \cdot 5 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 10.c (of order \(4\), 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: \(2.30054083620\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 7.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 10.7
Dual form 10.7.c.a.3.1

$q$-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 - 4.00000i) q^{2} +(-23.0000 + 23.0000i) q^{3} +32.0000i q^{4} +(-75.0000 + 100.000i) q^{5} +184.000 q^{6} +(-247.000 - 247.000i) q^{7} +(128.000 - 128.000i) q^{8} -329.000i q^{9} +(700.000 - 100.000i) q^{10} +1402.00 q^{11} +(-736.000 - 736.000i) q^{12} +(-2703.00 + 2703.00i) q^{13} +1976.00i q^{14} +(-575.000 - 4025.00i) q^{15} -1024.00 q^{16} +(2593.00 + 2593.00i) q^{17} +(-1316.00 + 1316.00i) q^{18} +1720.00i q^{19} +(-3200.00 - 2400.00i) q^{20} +11362.0 q^{21} +(-5608.00 - 5608.00i) q^{22} +(2137.00 - 2137.00i) q^{23} +5888.00i q^{24} +(-4375.00 - 15000.0i) q^{25} +21624.0 q^{26} +(-9200.00 - 9200.00i) q^{27} +(7904.00 - 7904.00i) q^{28} +30520.0i q^{29} +(-13800.0 + 18400.0i) q^{30} -37838.0 q^{31} +(4096.00 + 4096.00i) q^{32} +(-32246.0 + 32246.0i) q^{33} -20744.0i q^{34} +(43225.0 - 6175.00i) q^{35} +10528.0 q^{36} +(37113.0 + 37113.0i) q^{37} +(6880.00 - 6880.00i) q^{38} -124338. i q^{39} +(3200.00 + 22400.0i) q^{40} -35438.0 q^{41} +(-45448.0 - 45448.0i) q^{42} +(39177.0 - 39177.0i) q^{43} +44864.0i q^{44} +(32900.0 + 24675.0i) q^{45} -17096.0 q^{46} +(95193.0 + 95193.0i) q^{47} +(23552.0 - 23552.0i) q^{48} +4369.00i q^{49} +(-42500.0 + 77500.0i) q^{50} -119278. q^{51} +(-86496.0 - 86496.0i) q^{52} +(36017.0 - 36017.0i) q^{53} +73600.0i q^{54} +(-105150. + 140200. i) q^{55} -63232.0 q^{56} +(-39560.0 - 39560.0i) q^{57} +(122080. - 122080. i) q^{58} -35960.0i q^{59} +(128800. - 18400.0i) q^{60} +83322.0 q^{61} +(151352. + 151352. i) q^{62} +(-81263.0 + 81263.0i) q^{63} -32768.0i q^{64} +(-67575.0 - 473025. i) q^{65} +257968. q^{66} +(60833.0 + 60833.0i) q^{67} +(-82976.0 + 82976.0i) q^{68} +98302.0i q^{69} +(-197600. - 148200. i) q^{70} -40318.0 q^{71} +(-42112.0 - 42112.0i) q^{72} +(-129023. + 129023. i) q^{73} -296904. i q^{74} +(445625. + 244375. i) q^{75} -55040.0 q^{76} +(-346294. - 346294. i) q^{77} +(-497352. + 497352. i) q^{78} +524640. i q^{79} +(76800.0 - 102400. i) q^{80} +663041. q^{81} +(141752. + 141752. i) q^{82} +(-114423. + 114423. i) q^{83} +363584. i q^{84} +(-453775. + 64825.0i) q^{85} -313416. q^{86} +(-701960. - 701960. i) q^{87} +(179456. - 179456. i) q^{88} +187280. i q^{89} +(-32900.0 - 230300. i) q^{90} +1.33528e6 q^{91} +(68384.0 + 68384.0i) q^{92} +(870274. - 870274. i) q^{93} -761544. i q^{94} +(-172000. - 129000. i) q^{95} -188416. q^{96} +(532833. + 532833. i) q^{97} +(17476.0 - 17476.0i) q^{98} -461258. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 8 q^{2} - 46 q^{3} - 150 q^{5} + 368 q^{6} - 494 q^{7} + 256 q^{8} + 1400 q^{10} + 2804 q^{11} - 1472 q^{12} - 5406 q^{13} - 1150 q^{15} - 2048 q^{16} + 5186 q^{17} - 2632 q^{18} - 6400 q^{20} + 22724 q^{21}+ \cdots + 34952 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/10\mathbb{Z}\right)^\times\).

\(n\) \(7\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\)

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 − 4.00000i −0.500000 − 0.500000i
\(3\) −23.0000 + 23.0000i −0.851852 + 0.851852i −0.990361 − 0.138509i \(-0.955769\pi\)
0.138509 + 0.990361i \(0.455769\pi\)
\(4\) 32.0000i 0.500000i
\(5\) −75.0000 + 100.000i −0.600000 + 0.800000i
\(6\) 184.000 0.851852
\(7\) −247.000 − 247.000i −0.720117 − 0.720117i 0.248512 − 0.968629i \(-0.420058\pi\)
−0.968629 + 0.248512i \(0.920058\pi\)
\(8\) 128.000 − 128.000i 0.250000 − 0.250000i
\(9\) − 329.000i − 0.451303i
\(10\) 700.000 − 100.000i 0.700000 − 0.100000i
\(11\) 1402.00 1.05334 0.526672 − 0.850069i \(-0.323440\pi\)
0.526672 + 0.850069i \(0.323440\pi\)
\(12\) −736.000 − 736.000i −0.425926 − 0.425926i
\(13\) −2703.00 + 2703.00i −1.23031 + 1.23031i −0.266471 + 0.963843i \(0.585858\pi\)
−0.963843 + 0.266471i \(0.914142\pi\)
\(14\) 1976.00i 0.720117i
\(15\) −575.000 − 4025.00i −0.170370 − 1.19259i
\(16\) −1024.00 −0.250000
\(17\) 2593.00 + 2593.00i 0.527783 + 0.527783i 0.919911 − 0.392127i \(-0.128261\pi\)
−0.392127 + 0.919911i \(0.628261\pi\)
\(18\) −1316.00 + 1316.00i −0.225652 + 0.225652i
\(19\) 1720.00i 0.250765i 0.992108 + 0.125383i \(0.0400159\pi\)
−0.992108 + 0.125383i \(0.959984\pi\)
\(20\) −3200.00 − 2400.00i −0.400000 − 0.300000i
\(21\) 11362.0 1.22687
\(22\) −5608.00 − 5608.00i −0.526672 − 0.526672i
\(23\) 2137.00 − 2137.00i 0.175639 − 0.175639i −0.613813 − 0.789452i \(-0.710365\pi\)
0.789452 + 0.613813i \(0.210365\pi\)
\(24\) 5888.00i 0.425926i
\(25\) −4375.00 − 15000.0i −0.280000 − 0.960000i
\(26\) 21624.0 1.23031
\(27\) −9200.00 − 9200.00i −0.467408 − 0.467408i
\(28\) 7904.00 − 7904.00i 0.360058 − 0.360058i
\(29\) 30520.0i 1.25138i 0.780070 + 0.625692i \(0.215183\pi\)
−0.780070 + 0.625692i \(0.784817\pi\)
\(30\) −13800.0 + 18400.0i −0.511111 + 0.681481i
\(31\) −37838.0 −1.27012 −0.635058 − 0.772465i \(-0.719024\pi\)
−0.635058 + 0.772465i \(0.719024\pi\)
\(32\) 4096.00 + 4096.00i 0.125000 + 0.125000i
\(33\) −32246.0 + 32246.0i −0.897292 + 0.897292i
\(34\) − 20744.0i − 0.527783i
\(35\) 43225.0 − 6175.00i 1.00816 − 0.144023i
\(36\) 10528.0 0.225652
\(37\) 37113.0 + 37113.0i 0.732691 + 0.732691i 0.971152 − 0.238461i \(-0.0766429\pi\)
−0.238461 + 0.971152i \(0.576643\pi\)
\(38\) 6880.00 − 6880.00i 0.125383 − 0.125383i
\(39\) − 124338.i − 2.09609i
\(40\) 3200.00 + 22400.0i 0.0500000 + 0.350000i
\(41\) −35438.0 −0.514183 −0.257091 − 0.966387i \(-0.582764\pi\)
−0.257091 + 0.966387i \(0.582764\pi\)
\(42\) −45448.0 − 45448.0i −0.613433 − 0.613433i
\(43\) 39177.0 − 39177.0i 0.492749 − 0.492749i −0.416422 − 0.909171i \(-0.636716\pi\)
0.909171 + 0.416422i \(0.136716\pi\)
\(44\) 44864.0i 0.526672i
\(45\) 32900.0 + 24675.0i 0.361043 + 0.270782i
\(46\) −17096.0 −0.175639
\(47\) 95193.0 + 95193.0i 0.916878 + 0.916878i 0.996801 − 0.0799233i \(-0.0254675\pi\)
−0.0799233 + 0.996801i \(0.525468\pi\)
\(48\) 23552.0 − 23552.0i 0.212963 − 0.212963i
\(49\) 4369.00i 0.0371359i
\(50\) −42500.0 + 77500.0i −0.340000 + 0.620000i
\(51\) −119278. −0.899187
\(52\) −86496.0 − 86496.0i −0.615157 − 0.615157i
\(53\) 36017.0 − 36017.0i 0.241925 − 0.241925i −0.575721 − 0.817646i \(-0.695279\pi\)
0.817646 + 0.575721i \(0.195279\pi\)
\(54\) 73600.0i 0.467408i
\(55\) −105150. + 140200.i −0.632006 + 0.842675i
\(56\) −63232.0 −0.360058
\(57\) −39560.0 − 39560.0i −0.213615 − 0.213615i
\(58\) 122080. − 122080.i 0.625692 − 0.625692i
\(59\) − 35960.0i − 0.175091i −0.996161 − 0.0875455i \(-0.972098\pi\)
0.996161 − 0.0875455i \(-0.0279023\pi\)
\(60\) 128800. − 18400.0i 0.596296 − 0.0851852i
\(61\) 83322.0 0.367088 0.183544 − 0.983011i \(-0.441243\pi\)
0.183544 + 0.983011i \(0.441243\pi\)
\(62\) 151352. + 151352.i 0.635058 + 0.635058i
\(63\) −81263.0 + 81263.0i −0.324991 + 0.324991i
\(64\) − 32768.0i − 0.125000i
\(65\) −67575.0 − 473025.i −0.246063 − 1.72244i
\(66\) 257968. 0.897292
\(67\) 60833.0 + 60833.0i 0.202262 + 0.202262i 0.800969 − 0.598706i \(-0.204318\pi\)
−0.598706 + 0.800969i \(0.704318\pi\)
\(68\) −82976.0 + 82976.0i −0.263892 + 0.263892i
\(69\) 98302.0i 0.299237i
\(70\) −197600. − 148200.i −0.576093 − 0.432070i
\(71\) −40318.0 −0.112648 −0.0563241 − 0.998413i \(-0.517938\pi\)
−0.0563241 + 0.998413i \(0.517938\pi\)
\(72\) −42112.0 − 42112.0i −0.112826 − 0.112826i
\(73\) −129023. + 129023.i −0.331664 + 0.331664i −0.853218 − 0.521554i \(-0.825352\pi\)
0.521554 + 0.853218i \(0.325352\pi\)
\(74\) − 296904.i − 0.732691i
\(75\) 445625. + 244375.i 1.05630 + 0.579259i
\(76\) −55040.0 −0.125383
\(77\) −346294. − 346294.i −0.758530 − 0.758530i
\(78\) −497352. + 497352.i −1.04805 + 1.04805i
\(79\) 524640.i 1.06409i 0.846715 + 0.532047i \(0.178577\pi\)
−0.846715 + 0.532047i \(0.821423\pi\)
\(80\) 76800.0 − 102400.i 0.150000 − 0.200000i
\(81\) 663041. 1.24763
\(82\) 141752. + 141752.i 0.257091 + 0.257091i
\(83\) −114423. + 114423.i −0.200115 + 0.200115i −0.800049 − 0.599934i \(-0.795193\pi\)
0.599934 + 0.800049i \(0.295193\pi\)
\(84\) 363584.i 0.613433i
\(85\) −453775. + 64825.0i −0.738897 + 0.105557i
\(86\) −313416. −0.492749
\(87\) −701960. − 701960.i −1.06599 − 1.06599i
\(88\) 179456. − 179456.i 0.263336 − 0.263336i
\(89\) 187280.i 0.265657i 0.991139 + 0.132829i \(0.0424060\pi\)
−0.991139 + 0.132829i \(0.957594\pi\)
\(90\) −32900.0 − 230300.i −0.0451303 − 0.315912i
\(91\) 1.33528e6 1.77194
\(92\) 68384.0 + 68384.0i 0.0878195 + 0.0878195i
\(93\) 870274. − 870274.i 1.08195 − 1.08195i
\(94\) − 761544.i − 0.916878i
\(95\) −172000. − 129000.i −0.200612 − 0.150459i
\(96\) −188416. −0.212963
\(97\) 532833. + 532833.i 0.583816 + 0.583816i 0.935950 − 0.352134i \(-0.114544\pi\)
−0.352134 + 0.935950i \(0.614544\pi\)
\(98\) 17476.0 − 17476.0i 0.0185679 − 0.0185679i
\(99\) − 461258.i − 0.475377i
\(100\) 480000. − 140000.i 0.480000 − 0.140000i
\(101\) −1.70508e6 −1.65493 −0.827466 − 0.561516i \(-0.810218\pi\)
−0.827466 + 0.561516i \(0.810218\pi\)
\(102\) 477112. + 477112.i 0.449593 + 0.449593i
\(103\) −665063. + 665063.i −0.608627 + 0.608627i −0.942587 − 0.333960i \(-0.891615\pi\)
0.333960 + 0.942587i \(0.391615\pi\)
\(104\) 691968.i 0.615157i
\(105\) −852150. + 1.13620e6i −0.736119 + 0.981492i
\(106\) −288136. −0.241925
\(107\) 309073. + 309073.i 0.252296 + 0.252296i 0.821911 − 0.569616i \(-0.192908\pi\)
−0.569616 + 0.821911i \(0.692908\pi\)
\(108\) 294400. − 294400.i 0.233704 − 0.233704i
\(109\) − 362440.i − 0.279870i −0.990161 − 0.139935i \(-0.955311\pi\)
0.990161 − 0.139935i \(-0.0446894\pi\)
\(110\) 981400. − 140200.i 0.737340 − 0.105334i
\(111\) −1.70720e6 −1.24829
\(112\) 252928. + 252928.i 0.180029 + 0.180029i
\(113\) 722657. − 722657.i 0.500838 − 0.500838i −0.410861 − 0.911698i \(-0.634772\pi\)
0.911698 + 0.410861i \(0.134772\pi\)
\(114\) 316480.i 0.213615i
\(115\) 53425.0 + 373975.i 0.0351278 + 0.245895i
\(116\) −976640. −0.625692
\(117\) 889287. + 889287.i 0.555245 + 0.555245i
\(118\) −143840. + 143840.i −0.0875455 + 0.0875455i
\(119\) − 1.28094e6i − 0.760131i
\(120\) −588800. − 441600.i −0.340741 − 0.255556i
\(121\) 194043. 0.109532
\(122\) −333288. − 333288.i −0.183544 − 0.183544i
\(123\) 815074. − 815074.i 0.438008 − 0.438008i
\(124\) − 1.21082e6i − 0.635058i
\(125\) 1.82812e6 + 687500.i 0.936000 + 0.352000i
\(126\) 650104. 0.324991
\(127\) −1.94641e6 − 1.94641e6i −0.950216 − 0.950216i 0.0486019 − 0.998818i \(-0.484523\pi\)
−0.998818 + 0.0486019i \(0.984523\pi\)
\(128\) −131072. + 131072.i −0.0625000 + 0.0625000i
\(129\) 1.80214e6i 0.839498i
\(130\) −1.62180e6 + 2.16240e6i −0.738188 + 0.984251i
\(131\) 3.75620e6 1.67084 0.835420 − 0.549612i \(-0.185224\pi\)
0.835420 + 0.549612i \(0.185224\pi\)
\(132\) −1.03187e6 − 1.03187e6i −0.448646 − 0.448646i
\(133\) 424840. − 424840.i 0.180580 − 0.180580i
\(134\) − 486664.i − 0.202262i
\(135\) 1.61000e6 − 230000.i 0.654372 − 0.0934817i
\(136\) 663808. 0.263892
\(137\) 1.04283e6 + 1.04283e6i 0.405558 + 0.405558i 0.880186 − 0.474628i \(-0.157417\pi\)
−0.474628 + 0.880186i \(0.657417\pi\)
\(138\) 393208. − 393208.i 0.149618 − 0.149618i
\(139\) − 3.24700e6i − 1.20903i −0.796593 − 0.604516i \(-0.793366\pi\)
0.796593 − 0.604516i \(-0.206634\pi\)
\(140\) 197600. + 1.38320e6i 0.0720117 + 0.504082i
\(141\) −4.37888e6 −1.56209
\(142\) 161272. + 161272.i 0.0563241 + 0.0563241i
\(143\) −3.78961e6 + 3.78961e6i −1.29594 + 1.29594i
\(144\) 336896.i 0.112826i
\(145\) −3.05200e6 − 2.28900e6i −1.00111 − 0.750830i
\(146\) 1.03218e6 0.331664
\(147\) −100487. − 100487.i −0.0316343 − 0.0316343i
\(148\) −1.18762e6 + 1.18762e6i −0.366346 + 0.366346i
\(149\) 5.76420e6i 1.74253i 0.490813 + 0.871265i \(0.336700\pi\)
−0.490813 + 0.871265i \(0.663300\pi\)
\(150\) −805000. − 2.76000e6i −0.238519 − 0.817778i
\(151\) 1.03280e6 0.299976 0.149988 − 0.988688i \(-0.452077\pi\)
0.149988 + 0.988688i \(0.452077\pi\)
\(152\) 220160. + 220160.i 0.0626914 + 0.0626914i
\(153\) 853097. − 853097.i 0.238190 − 0.238190i
\(154\) 2.77035e6i 0.758530i
\(155\) 2.83785e6 − 3.78380e6i 0.762069 − 1.01609i
\(156\) 3.97882e6 1.04805
\(157\) 2.30055e6 + 2.30055e6i 0.594475 + 0.594475i 0.938837 − 0.344362i \(-0.111905\pi\)
−0.344362 + 0.938837i \(0.611905\pi\)
\(158\) 2.09856e6 − 2.09856e6i 0.532047 − 0.532047i
\(159\) 1.65678e6i 0.412168i
\(160\) −716800. + 102400.i −0.175000 + 0.0250000i
\(161\) −1.05568e6 −0.252961
\(162\) −2.65216e6 − 2.65216e6i −0.623814 − 0.623814i
\(163\) −4.02178e6 + 4.02178e6i −0.928658 + 0.928658i −0.997619 − 0.0689613i \(-0.978032\pi\)
0.0689613 + 0.997619i \(0.478032\pi\)
\(164\) − 1.13402e6i − 0.257091i
\(165\) −806150. − 5.64305e6i −0.179458 − 1.25621i
\(166\) 915384. 0.200115
\(167\) −710167. − 710167.i −0.152479 − 0.152479i 0.626745 − 0.779224i \(-0.284387\pi\)
−0.779224 + 0.626745i \(0.784387\pi\)
\(168\) 1.45434e6 − 1.45434e6i 0.306716 − 0.306716i
\(169\) − 9.78561e6i − 2.02735i
\(170\) 2.07440e6 + 1.55580e6i 0.422227 + 0.316670i
\(171\) 565880. 0.113171
\(172\) 1.25366e6 + 1.25366e6i 0.246375 + 0.246375i
\(173\) 3.77650e6 − 3.77650e6i 0.729375 − 0.729375i −0.241120 − 0.970495i \(-0.577515\pi\)
0.970495 + 0.241120i \(0.0775148\pi\)
\(174\) 5.61568e6i 1.06599i
\(175\) −2.62438e6 + 4.78562e6i −0.489679 + 0.892945i
\(176\) −1.43565e6 −0.263336
\(177\) 827080. + 827080.i 0.149152 + 0.149152i
\(178\) 749120. − 749120.i 0.132829 − 0.132829i
\(179\) 5.46380e6i 0.952655i 0.879268 + 0.476328i \(0.158032\pi\)
−0.879268 + 0.476328i \(0.841968\pi\)
\(180\) −789600. + 1.05280e6i −0.135391 + 0.180521i
\(181\) 9.02436e6 1.52188 0.760941 − 0.648821i \(-0.224738\pi\)
0.760941 + 0.648821i \(0.224738\pi\)
\(182\) −5.34113e6 − 5.34113e6i −0.885970 − 0.885970i
\(183\) −1.91641e6 + 1.91641e6i −0.312705 + 0.312705i
\(184\) − 547072.i − 0.0878195i
\(185\) −6.49478e6 + 927825.i −1.02577 + 0.146538i
\(186\) −6.96219e6 −1.08195
\(187\) 3.63539e6 + 3.63539e6i 0.555937 + 0.555937i
\(188\) −3.04618e6 + 3.04618e6i −0.458439 + 0.458439i
\(189\) 4.54480e6i 0.673177i
\(190\) 172000. + 1.20400e6i 0.0250765 + 0.175536i
\(191\) −4.02120e6 −0.577106 −0.288553 − 0.957464i \(-0.593174\pi\)
−0.288553 + 0.957464i \(0.593174\pi\)
\(192\) 753664. + 753664.i 0.106481 + 0.106481i
\(193\) −1.05414e6 + 1.05414e6i −0.146632 + 0.146632i −0.776611 − 0.629980i \(-0.783063\pi\)
0.629980 + 0.776611i \(0.283063\pi\)
\(194\) − 4.26266e6i − 0.583816i
\(195\) 1.24338e7 + 9.32535e6i 1.67687 + 1.25765i
\(196\) −139808. −0.0185679
\(197\) −7.29489e6 − 7.29489e6i −0.954157 − 0.954157i 0.0448372 − 0.998994i \(-0.485723\pi\)
−0.998994 + 0.0448372i \(0.985723\pi\)
\(198\) −1.84503e6 + 1.84503e6i −0.237689 + 0.237689i
\(199\) − 1.41170e7i − 1.79137i −0.444693 − 0.895683i \(-0.646687\pi\)
0.444693 − 0.895683i \(-0.353313\pi\)
\(200\) −2.48000e6 − 1.36000e6i −0.310000 − 0.170000i
\(201\) −2.79832e6 −0.344595
\(202\) 6.82031e6 + 6.82031e6i 0.827466 + 0.827466i
\(203\) 7.53844e6 − 7.53844e6i 0.901142 − 0.901142i
\(204\) − 3.81690e6i − 0.449593i
\(205\) 2.65785e6 − 3.54380e6i 0.308510 − 0.411346i
\(206\) 5.32050e6 0.608627
\(207\) −703073. − 703073.i −0.0792664 − 0.0792664i
\(208\) 2.76787e6 − 2.76787e6i 0.307579 − 0.307579i
\(209\) 2.41144e6i 0.264142i
\(210\) 7.95340e6 − 1.13620e6i 0.858806 − 0.122687i
\(211\) −1.23188e7 −1.31136 −0.655681 − 0.755038i \(-0.727618\pi\)
−0.655681 + 0.755038i \(0.727618\pi\)
\(212\) 1.15254e6 + 1.15254e6i 0.120962 + 0.120962i
\(213\) 927314. − 927314.i 0.0959595 − 0.0959595i
\(214\) − 2.47258e6i − 0.252296i
\(215\) 979425. + 6.85598e6i 0.0985498 + 0.689849i
\(216\) −2.35520e6 −0.233704
\(217\) 9.34599e6 + 9.34599e6i 0.914631 + 0.914631i
\(218\) −1.44976e6 + 1.44976e6i −0.139935 + 0.139935i
\(219\) − 5.93506e6i − 0.565057i
\(220\) −4.48640e6 − 3.36480e6i −0.421337 − 0.316003i
\(221\) −1.40178e7 −1.29868
\(222\) 6.82879e6 + 6.82879e6i 0.624144 + 0.624144i
\(223\) 328857. − 328857.i 0.0296546 − 0.0296546i −0.692124 − 0.721779i \(-0.743325\pi\)
0.721779 + 0.692124i \(0.243325\pi\)
\(224\) − 2.02342e6i − 0.180029i
\(225\) −4.93500e6 + 1.43938e6i −0.433251 + 0.126365i
\(226\) −5.78126e6 −0.500838
\(227\) −7.95085e6 − 7.95085e6i −0.679729 − 0.679729i 0.280210 − 0.959939i \(-0.409596\pi\)
−0.959939 + 0.280210i \(0.909596\pi\)
\(228\) 1.26592e6 − 1.26592e6i 0.106807 − 0.106807i
\(229\) 2.28695e7i 1.90436i 0.305532 + 0.952182i \(0.401166\pi\)
−0.305532 + 0.952182i \(0.598834\pi\)
\(230\) 1.28220e6 − 1.70960e6i 0.105383 − 0.140511i
\(231\) 1.59295e7 1.29231
\(232\) 3.90656e6 + 3.90656e6i 0.312846 + 0.312846i
\(233\) 8.59050e6 − 8.59050e6i 0.679126 − 0.679126i −0.280676 − 0.959803i \(-0.590559\pi\)
0.959803 + 0.280676i \(0.0905587\pi\)
\(234\) − 7.11430e6i − 0.555245i
\(235\) −1.66588e7 + 2.37982e6i −1.28363 + 0.183376i
\(236\) 1.15072e6 0.0875455
\(237\) −1.20667e7 − 1.20667e7i −0.906451 − 0.906451i
\(238\) −5.12377e6 + 5.12377e6i −0.380066 + 0.380066i
\(239\) 9.66576e6i 0.708015i 0.935243 + 0.354007i \(0.115181\pi\)
−0.935243 + 0.354007i \(0.884819\pi\)
\(240\) 588800. + 4.12160e6i 0.0425926 + 0.298148i
\(241\) 1.85926e7 1.32828 0.664141 − 0.747608i \(-0.268798\pi\)
0.664141 + 0.747608i \(0.268798\pi\)
\(242\) −776172. − 776172.i −0.0547661 − 0.0547661i
\(243\) −8.54314e6 + 8.54314e6i −0.595386 + 0.595386i
\(244\) 2.66630e6i 0.183544i
\(245\) −436900. − 327675.i −0.0297087 − 0.0222815i
\(246\) −6.52059e6 −0.438008
\(247\) −4.64916e6 − 4.64916e6i −0.308520 − 0.308520i
\(248\) −4.84326e6 + 4.84326e6i −0.317529 + 0.317529i
\(249\) − 5.26346e6i − 0.340936i
\(250\) −4.56250e6 − 1.00625e7i −0.292000 − 0.644000i
\(251\) 1.19350e7 0.754747 0.377373 − 0.926061i \(-0.376827\pi\)
0.377373 + 0.926061i \(0.376827\pi\)
\(252\) −2.60042e6 − 2.60042e6i −0.162495 − 0.162495i
\(253\) 2.99607e6 − 2.99607e6i 0.185008 − 0.185008i
\(254\) 1.55713e7i 0.950216i
\(255\) 8.94585e6 − 1.19278e7i 0.539512 − 0.719349i
\(256\) 1.04858e6 0.0625000
\(257\) 1.54304e7 + 1.54304e7i 0.909031 + 0.909031i 0.996194 − 0.0871630i \(-0.0277801\pi\)
−0.0871630 + 0.996194i \(0.527780\pi\)
\(258\) 7.20857e6 − 7.20857e6i 0.419749 − 0.419749i
\(259\) − 1.83338e7i − 1.05525i
\(260\) 1.51368e7 − 2.16240e6i 0.861220 − 0.123031i
\(261\) 1.00411e7 0.564753
\(262\) −1.50248e7 − 1.50248e7i −0.835420 − 0.835420i
\(263\) 1.27108e7 − 1.27108e7i 0.698723 − 0.698723i −0.265412 − 0.964135i \(-0.585508\pi\)
0.964135 + 0.265412i \(0.0855081\pi\)
\(264\) 8.25498e6i 0.448646i
\(265\) 900425. + 6.30298e6i 0.0483849 + 0.338694i
\(266\) −3.39872e6 −0.180580
\(267\) −4.30744e6 − 4.30744e6i −0.226300 − 0.226300i
\(268\) −1.94666e6 + 1.94666e6i −0.101131 + 0.101131i
\(269\) 2.54188e6i 0.130586i 0.997866 + 0.0652932i \(0.0207983\pi\)
−0.997866 + 0.0652932i \(0.979202\pi\)
\(270\) −7.36000e6 − 5.52000e6i −0.373927 − 0.280445i
\(271\) 6.13384e6 0.308194 0.154097 − 0.988056i \(-0.450753\pi\)
0.154097 + 0.988056i \(0.450753\pi\)
\(272\) −2.65523e6 − 2.65523e6i −0.131946 − 0.131946i
\(273\) −3.07115e7 + 3.07115e7i −1.50943 + 1.50943i
\(274\) − 8.34266e6i − 0.405558i
\(275\) −6.13375e6 − 2.10300e7i −0.294936 − 1.01121i
\(276\) −3.14566e6 −0.149618
\(277\) −3.00513e6 − 3.00513e6i −0.141392 − 0.141392i 0.632868 − 0.774260i \(-0.281878\pi\)
−0.774260 + 0.632868i \(0.781878\pi\)
\(278\) −1.29880e7 + 1.29880e7i −0.604516 + 0.604516i
\(279\) 1.24487e7i 0.573207i
\(280\) 4.74240e6 − 6.32320e6i 0.216035 − 0.288047i
\(281\) −6.49352e6 −0.292658 −0.146329 − 0.989236i \(-0.546746\pi\)
−0.146329 + 0.989236i \(0.546746\pi\)
\(282\) 1.75155e7 + 1.75155e7i 0.781044 + 0.781044i
\(283\) −2.71607e7 + 2.71607e7i −1.19834 + 1.19834i −0.223680 + 0.974663i \(0.571807\pi\)
−0.974663 + 0.223680i \(0.928193\pi\)
\(284\) − 1.29018e6i − 0.0563241i
\(285\) 6.92300e6 − 989000.i 0.299061 − 0.0427230i
\(286\) 3.03168e7 1.29594
\(287\) 8.75319e6 + 8.75319e6i 0.370272 + 0.370272i
\(288\) 1.34758e6 − 1.34758e6i 0.0564129 − 0.0564129i
\(289\) − 1.06903e7i − 0.442889i
\(290\) 3.05200e6 + 2.13640e7i 0.125138 + 0.875969i
\(291\) −2.45103e7 −0.994649
\(292\) −4.12874e6 − 4.12874e6i −0.165832 − 0.165832i
\(293\) −4.78734e6 + 4.78734e6i −0.190323 + 0.190323i −0.795836 − 0.605513i \(-0.792968\pi\)
0.605513 + 0.795836i \(0.292968\pi\)
\(294\) 803896.i 0.0316343i
\(295\) 3.59600e6 + 2.69700e6i 0.140073 + 0.105055i
\(296\) 9.50093e6 0.366346
\(297\) −1.28984e7 − 1.28984e7i −0.492342 − 0.492342i
\(298\) 2.30568e7 − 2.30568e7i 0.871265 − 0.871265i
\(299\) 1.15526e7i 0.432182i
\(300\) −7.82000e6 + 1.42600e7i −0.289630 + 0.528148i
\(301\) −1.93534e7 −0.709674
\(302\) −4.13121e6 − 4.13121e6i −0.149988 − 0.149988i
\(303\) 3.92168e7 − 3.92168e7i 1.40976 − 1.40976i
\(304\) − 1.76128e6i − 0.0626914i
\(305\) −6.24915e6 + 8.33220e6i −0.220253 + 0.293670i
\(306\) −6.82478e6 −0.238190
\(307\) 9.72339e6 + 9.72339e6i 0.336049 + 0.336049i 0.854878 − 0.518829i \(-0.173632\pi\)
−0.518829 + 0.854878i \(0.673632\pi\)
\(308\) 1.10814e7 − 1.10814e7i 0.379265 − 0.379265i
\(309\) − 3.05929e7i − 1.03692i
\(310\) −2.64866e7 + 3.78380e6i −0.889081 + 0.127012i
\(311\) 7.03344e6 0.233823 0.116911 − 0.993142i \(-0.462701\pi\)
0.116911 + 0.993142i \(0.462701\pi\)
\(312\) −1.59153e7 − 1.59153e7i −0.524023 − 0.524023i
\(313\) 2.98895e7 − 2.98895e7i 0.974734 − 0.974734i −0.0249545 − 0.999689i \(-0.507944\pi\)
0.999689 + 0.0249545i \(0.00794407\pi\)
\(314\) − 1.84044e7i − 0.594475i
\(315\) −2.03158e6 − 1.42210e7i −0.0649982 − 0.454987i
\(316\) −1.67885e7 −0.532047
\(317\) 2.11266e7 + 2.11266e7i 0.663212 + 0.663212i 0.956136 − 0.292924i \(-0.0946282\pi\)
−0.292924 + 0.956136i \(0.594628\pi\)
\(318\) 6.62713e6 − 6.62713e6i 0.206084 − 0.206084i
\(319\) 4.27890e7i 1.31814i
\(320\) 3.27680e6 + 2.45760e6i 0.100000 + 0.0750000i
\(321\) −1.42174e7 −0.429837
\(322\) 4.22271e6 + 4.22271e6i 0.126481 + 0.126481i
\(323\) −4.45996e6 + 4.45996e6i −0.132350 + 0.132350i
\(324\) 2.12173e7i 0.623814i
\(325\) 5.23706e7 + 2.87194e7i 1.52559 + 0.836614i
\(326\) 3.21743e7 0.928658
\(327\) 8.33612e6 + 8.33612e6i 0.238408 + 0.238408i
\(328\) −4.53606e6 + 4.53606e6i −0.128546 + 0.128546i
\(329\) − 4.70253e7i − 1.32052i
\(330\) −1.93476e7 + 2.57968e7i −0.538375 + 0.717834i
\(331\) −4.23279e7 −1.16719 −0.583596 − 0.812044i \(-0.698355\pi\)
−0.583596 + 0.812044i \(0.698355\pi\)
\(332\) −3.66154e6 − 3.66154e6i −0.100057 − 0.100057i
\(333\) 1.22102e7 − 1.22102e7i 0.330666 − 0.330666i
\(334\) 5.68134e6i 0.152479i
\(335\) −1.06458e7 + 1.52082e6i −0.283167 + 0.0404524i
\(336\) −1.16347e7 −0.306716
\(337\) −1.46217e7 − 1.46217e7i −0.382040 − 0.382040i 0.489797 − 0.871837i \(-0.337071\pi\)
−0.871837 + 0.489797i \(0.837071\pi\)
\(338\) −3.91424e7 + 3.91424e7i −1.01367 + 1.01367i
\(339\) 3.32422e7i 0.853279i
\(340\) −2.07440e6 − 1.45208e7i −0.0527783 − 0.369448i
\(341\) −5.30489e7 −1.33787
\(342\) −2.26352e6 − 2.26352e6i −0.0565856 − 0.0565856i
\(343\) −2.79802e7 + 2.79802e7i −0.693374 + 0.693374i
\(344\) − 1.00293e7i − 0.246375i
\(345\) −9.83020e6 − 7.37265e6i −0.239389 − 0.179542i
\(346\) −3.02120e7 −0.729375
\(347\) 4.59792e7 + 4.59792e7i 1.10046 + 1.10046i 0.994355 + 0.106100i \(0.0338364\pi\)
0.106100 + 0.994355i \(0.466164\pi\)
\(348\) 2.24627e7 − 2.24627e7i 0.532997 − 0.532997i
\(349\) − 5.03359e7i − 1.18414i −0.805888 − 0.592068i \(-0.798312\pi\)
0.805888 − 0.592068i \(-0.201688\pi\)
\(350\) 2.96400e7 − 8.64500e6i 0.691312 − 0.201633i
\(351\) 4.97352e7 1.15012
\(352\) 5.74259e6 + 5.74259e6i 0.131668 + 0.131668i
\(353\) −1.59140e7 + 1.59140e7i −0.361789 + 0.361789i −0.864471 − 0.502683i \(-0.832346\pi\)
0.502683 + 0.864471i \(0.332346\pi\)
\(354\) − 6.61664e6i − 0.149152i
\(355\) 3.02385e6 − 4.03180e6i 0.0675889 − 0.0901185i
\(356\) −5.99296e6 −0.132829
\(357\) 2.94617e7 + 2.94617e7i 0.647519 + 0.647519i
\(358\) 2.18552e7 − 2.18552e7i 0.476328 − 0.476328i
\(359\) − 4.47023e7i − 0.966155i −0.875578 − 0.483077i \(-0.839519\pi\)
0.875578 − 0.483077i \(-0.160481\pi\)
\(360\) 7.36960e6 − 1.05280e6i 0.157956 − 0.0225652i
\(361\) 4.40875e7 0.937117
\(362\) −3.60974e7 − 3.60974e7i −0.760941 − 0.760941i
\(363\) −4.46299e6 + 4.46299e6i −0.0933052 + 0.0933052i
\(364\) 4.27290e7i 0.885970i
\(365\) −3.22558e6 − 2.25790e7i −0.0663328 − 0.464330i
\(366\) 1.53312e7 0.312705
\(367\) −2.70624e7 − 2.70624e7i −0.547480 − 0.547480i 0.378231 − 0.925711i \(-0.376532\pi\)
−0.925711 + 0.378231i \(0.876532\pi\)
\(368\) −2.18829e6 + 2.18829e6i −0.0439098 + 0.0439098i
\(369\) 1.16591e7i 0.232052i
\(370\) 2.96904e7 + 2.22678e7i 0.586153 + 0.439615i
\(371\) −1.77924e7 −0.348428
\(372\) 2.78488e7 + 2.78488e7i 0.540975 + 0.540975i
\(373\) −3.82355e7 + 3.82355e7i −0.736784 + 0.736784i −0.971954 − 0.235170i \(-0.924435\pi\)
0.235170 + 0.971954i \(0.424435\pi\)
\(374\) − 2.90831e7i − 0.555937i
\(375\) −5.78594e7 + 2.62344e7i −1.09719 + 0.497481i
\(376\) 2.43694e7 0.458439
\(377\) −8.24956e7 − 8.24956e7i −1.53960 − 1.53960i
\(378\) 1.81792e7 − 1.81792e7i 0.336589 − 0.336589i
\(379\) 2.50612e6i 0.0460346i 0.999735 + 0.0230173i \(0.00732728\pi\)
−0.999735 + 0.0230173i \(0.992673\pi\)
\(380\) 4.12800e6 − 5.50400e6i 0.0752296 − 0.100306i
\(381\) 8.95347e7 1.61889
\(382\) 1.60848e7 + 1.60848e7i 0.288553 + 0.288553i
\(383\) 4.72095e7 − 4.72095e7i 0.840297 − 0.840297i −0.148600 − 0.988897i \(-0.547477\pi\)
0.988897 + 0.148600i \(0.0474767\pi\)
\(384\) − 6.02931e6i − 0.106481i
\(385\) 6.06014e7 − 8.65735e6i 1.06194 − 0.151706i
\(386\) 8.43314e6 0.146632
\(387\) −1.28892e7 − 1.28892e7i −0.222379 − 0.222379i
\(388\) −1.70507e7 + 1.70507e7i −0.291908 + 0.291908i
\(389\) 1.00159e8i 1.70153i 0.525547 + 0.850765i \(0.323861\pi\)
−0.525547 + 0.850765i \(0.676139\pi\)
\(390\) −1.24338e7 − 8.70366e7i −0.209609 − 1.46726i
\(391\) 1.10825e7 0.185399
\(392\) 559232. + 559232.i 0.00928397 + 0.00928397i
\(393\) −8.63926e7 + 8.63926e7i −1.42331 + 1.42331i
\(394\) 5.83591e7i 0.954157i
\(395\) −5.24640e7 − 3.93480e7i −0.851275 − 0.638457i
\(396\) 1.47603e7 0.237689
\(397\) −7.26282e7 − 7.26282e7i −1.16074 − 1.16074i −0.984314 − 0.176423i \(-0.943547\pi\)
−0.176423 − 0.984314i \(-0.556453\pi\)
\(398\) −5.64682e7 + 5.64682e7i −0.895683 + 0.895683i
\(399\) 1.95426e7i 0.307655i
\(400\) 4.48000e6 + 1.53600e7i 0.0700000 + 0.240000i
\(401\) 5.26293e7 0.816196 0.408098 − 0.912938i \(-0.366192\pi\)
0.408098 + 0.912938i \(0.366192\pi\)
\(402\) 1.11933e7 + 1.11933e7i 0.172297 + 0.172297i
\(403\) 1.02276e8 − 1.02276e8i 1.56264 − 1.56264i
\(404\) − 5.45625e7i − 0.827466i
\(405\) −4.97281e7 + 6.63041e7i −0.748577 + 0.998103i
\(406\) −6.03075e7 −0.901142
\(407\) 5.20324e7 + 5.20324e7i 0.771775 + 0.771775i
\(408\) −1.52676e7 + 1.52676e7i −0.224797 + 0.224797i
\(409\) 1.10687e8i 1.61781i 0.587939 + 0.808906i \(0.299940\pi\)
−0.587939 + 0.808906i \(0.700060\pi\)
\(410\) −2.48066e7 + 3.54380e6i −0.359928 + 0.0514183i
\(411\) −4.79703e7 −0.690951
\(412\) −2.12820e7 − 2.12820e7i −0.304313 − 0.304313i
\(413\) −8.88212e6 + 8.88212e6i −0.126086 + 0.126086i
\(414\) 5.62458e6i 0.0792664i
\(415\) −2.86058e6 − 2.00240e7i −0.0400229 − 0.280161i
\(416\) −2.21430e7 −0.307579
\(417\) 7.46810e7 + 7.46810e7i 1.02992 + 1.02992i
\(418\) 9.64576e6 − 9.64576e6i 0.132071 − 0.132071i
\(419\) − 9.92484e6i − 0.134922i −0.997722 − 0.0674608i \(-0.978510\pi\)
0.997722 − 0.0674608i \(-0.0214898\pi\)
\(420\) −3.63584e7 − 2.72688e7i −0.490746 − 0.368060i
\(421\) 3.46957e7 0.464975 0.232488 − 0.972599i \(-0.425314\pi\)
0.232488 + 0.972599i \(0.425314\pi\)
\(422\) 4.92754e7 + 4.92754e7i 0.655681 + 0.655681i
\(423\) 3.13185e7 − 3.13185e7i 0.413790 − 0.413790i
\(424\) − 9.22035e6i − 0.120962i
\(425\) 2.75506e7 − 5.02394e7i 0.358893 − 0.654451i
\(426\) −7.41851e6 −0.0959595
\(427\) −2.05805e7 − 2.05805e7i −0.264346 − 0.264346i
\(428\) −9.89034e6 + 9.89034e6i −0.126148 + 0.126148i
\(429\) − 1.74322e8i − 2.20790i
\(430\) 2.35062e7 − 3.13416e7i 0.295649 − 0.394199i
\(431\) −2.72975e7 −0.340951 −0.170475 − 0.985362i \(-0.554530\pi\)
−0.170475 + 0.985362i \(0.554530\pi\)
\(432\) 9.42080e6 + 9.42080e6i 0.116852 + 0.116852i
\(433\) 4.50017e7 − 4.50017e7i 0.554326 − 0.554326i −0.373360 − 0.927686i \(-0.621795\pi\)
0.927686 + 0.373360i \(0.121795\pi\)
\(434\) − 7.47679e7i − 0.914631i
\(435\) 1.22843e8 − 1.75490e7i 1.49239 − 0.213199i
\(436\) 1.15981e7 0.139935
\(437\) 3.67564e6 + 3.67564e6i 0.0440442 + 0.0440442i
\(438\) −2.37402e7 + 2.37402e7i −0.282529 + 0.282529i
\(439\) 4.79986e7i 0.567330i 0.958924 + 0.283665i \(0.0915503\pi\)
−0.958924 + 0.283665i \(0.908450\pi\)
\(440\) 4.48640e6 + 3.14048e7i 0.0526672 + 0.368670i
\(441\) 1.43740e6 0.0167595
\(442\) 5.60710e7 + 5.60710e7i 0.649339 + 0.649339i
\(443\) −3.36631e7 + 3.36631e7i −0.387206 + 0.387206i −0.873690 − 0.486483i \(-0.838279\pi\)
0.486483 + 0.873690i \(0.338279\pi\)
\(444\) − 5.46303e7i − 0.624144i
\(445\) −1.87280e7 − 1.40460e7i −0.212526 − 0.159394i
\(446\) −2.63086e6 −0.0296546
\(447\) −1.32577e8 − 1.32577e8i −1.48438 − 1.48438i
\(448\) −8.09370e6 + 8.09370e6i −0.0900146 + 0.0900146i
\(449\) 8.64789e7i 0.955369i 0.878532 + 0.477684i \(0.158524\pi\)
−0.878532 + 0.477684i \(0.841476\pi\)
\(450\) 2.54975e7 + 1.39825e7i 0.279808 + 0.153443i
\(451\) −4.96841e7 −0.541611
\(452\) 2.31250e7 + 2.31250e7i 0.250419 + 0.250419i
\(453\) −2.37544e7 + 2.37544e7i −0.255535 + 0.255535i
\(454\) 6.36068e7i 0.679729i
\(455\) −1.00146e8 + 1.33528e8i −1.06316 + 1.41755i
\(456\) −1.01274e7 −0.106807
\(457\) −3.72501e6 − 3.72501e6i −0.0390282 − 0.0390282i 0.687323 − 0.726352i \(-0.258786\pi\)
−0.726352 + 0.687323i \(0.758786\pi\)
\(458\) 9.14779e7 − 9.14779e7i 0.952182 − 0.952182i
\(459\) − 4.77112e7i − 0.493381i
\(460\) −1.19672e7 + 1.70960e6i −0.122947 + 0.0175639i
\(461\) 4.07112e7 0.415538 0.207769 − 0.978178i \(-0.433380\pi\)
0.207769 + 0.978178i \(0.433380\pi\)
\(462\) −6.37181e7 − 6.37181e7i −0.646155 − 0.646155i
\(463\) −2.69113e7 + 2.69113e7i −0.271139 + 0.271139i −0.829559 − 0.558420i \(-0.811408\pi\)
0.558420 + 0.829559i \(0.311408\pi\)
\(464\) − 3.12525e7i − 0.312846i
\(465\) 2.17568e7 + 1.52298e8i 0.216390 + 1.51473i
\(466\) −6.87240e7 −0.679126
\(467\) 1.38966e8 + 1.38966e8i 1.36446 + 1.36446i 0.868146 + 0.496310i \(0.165312\pi\)
0.496310 + 0.868146i \(0.334688\pi\)
\(468\) −2.84572e7 + 2.84572e7i −0.277622 + 0.277622i
\(469\) − 3.00515e7i − 0.291305i
\(470\) 7.61544e7 + 5.71158e7i 0.733502 + 0.550127i
\(471\) −1.05825e8 −1.01281
\(472\) −4.60288e6 − 4.60288e6i −0.0437727 − 0.0437727i
\(473\) 5.49262e7 − 5.49262e7i 0.519034 − 0.519034i
\(474\) 9.65338e7i 0.906451i
\(475\) 2.58000e7 − 7.52500e6i 0.240735 − 0.0702143i
\(476\) 4.09901e7 0.380066
\(477\) −1.18496e7 − 1.18496e7i −0.109181 − 0.109181i
\(478\) 3.86630e7 − 3.86630e7i 0.354007 − 0.354007i
\(479\) − 3.19942e7i − 0.291115i −0.989350 − 0.145558i \(-0.953502\pi\)
0.989350 − 0.145558i \(-0.0464977\pi\)
\(480\) 1.41312e7 − 1.88416e7i 0.127778 − 0.170370i
\(481\) −2.00633e8 −1.80288
\(482\) −7.43706e7 − 7.43706e7i −0.664141 − 0.664141i
\(483\) 2.42806e7 − 2.42806e7i 0.215485 − 0.215485i
\(484\) 6.20938e6i 0.0547661i
\(485\) −9.32458e7 + 1.33208e7i −0.817342 + 0.116763i
\(486\) 6.83451e7 0.595386
\(487\) −7.96441e7 − 7.96441e7i −0.689551 − 0.689551i 0.272581 − 0.962133i \(-0.412123\pi\)
−0.962133 + 0.272581i \(0.912123\pi\)
\(488\) 1.06652e7 − 1.06652e7i 0.0917720 − 0.0917720i
\(489\) − 1.85002e8i − 1.58216i
\(490\) 436900. + 3.05830e6i 0.00371359 + 0.0259951i
\(491\) 1.53965e8 1.30070 0.650350 − 0.759634i \(-0.274622\pi\)
0.650350 + 0.759634i \(0.274622\pi\)
\(492\) 2.60824e7 + 2.60824e7i 0.219004 + 0.219004i
\(493\) −7.91384e7 + 7.91384e7i −0.660460 + 0.660460i
\(494\) 3.71933e7i 0.308520i
\(495\) 4.61258e7 + 3.45944e7i 0.380302 + 0.285226i
\(496\) 3.87461e7 0.317529
\(497\) 9.95855e6 + 9.95855e6i 0.0811198 + 0.0811198i
\(498\) −2.10538e7 + 2.10538e7i −0.170468 + 0.170468i
\(499\) − 1.02698e8i − 0.826537i −0.910609 − 0.413268i \(-0.864387\pi\)
0.910609 − 0.413268i \(-0.135613\pi\)
\(500\) −2.20000e7 + 5.85000e7i −0.176000 + 0.468000i
\(501\) 3.26677e7 0.259780
\(502\) −4.77400e7 − 4.77400e7i −0.377373 − 0.377373i
\(503\) 8.43625e7 − 8.43625e7i 0.662896 − 0.662896i −0.293166 − 0.956062i \(-0.594709\pi\)
0.956062 + 0.293166i \(0.0947088\pi\)
\(504\) 2.08033e7i 0.162495i
\(505\) 1.27881e8 − 1.70508e8i 0.992959 − 1.32395i
\(506\) −2.39686e7 −0.185008
\(507\) 2.25069e8 + 2.25069e8i 1.72700 + 1.72700i
\(508\) 6.22850e7 − 6.22850e7i 0.475108 − 0.475108i
\(509\) 4.03774e7i 0.306186i 0.988212 + 0.153093i \(0.0489234\pi\)
−0.988212 + 0.153093i \(0.951077\pi\)
\(510\) −8.34946e7 + 1.19278e7i −0.629431 + 0.0899187i
\(511\) 6.37374e7 0.477674
\(512\) −4.19430e6 − 4.19430e6i −0.0312500 − 0.0312500i
\(513\) 1.58240e7 − 1.58240e7i 0.117210 − 0.117210i
\(514\) − 1.23443e8i − 0.909031i
\(515\) −1.66266e7 − 1.16386e8i −0.121725 − 0.852078i
\(516\) −5.76685e7 −0.419749
\(517\) 1.33461e8 + 1.33461e8i 0.965787 + 0.965787i
\(518\) −7.33353e7 + 7.33353e7i −0.527623 + 0.527623i
\(519\) 1.73719e8i 1.24264i
\(520\) −6.91968e7 − 5.18976e7i −0.492126 − 0.369094i
\(521\) −3.68161e7 −0.260330 −0.130165 − 0.991492i \(-0.541551\pi\)
−0.130165 + 0.991492i \(0.541551\pi\)
\(522\) −4.01643e7 − 4.01643e7i −0.282377 − 0.282377i
\(523\) −1.60054e8 + 1.60054e8i −1.11882 + 1.11882i −0.126907 + 0.991915i \(0.540505\pi\)
−0.991915 + 0.126907i \(0.959495\pi\)
\(524\) 1.20198e8i 0.835420i
\(525\) −4.97088e7 − 1.70430e8i −0.343522 − 1.17779i
\(526\) −1.01686e8 −0.698723
\(527\) −9.81139e7 − 9.81139e7i −0.670346 − 0.670346i
\(528\) 3.30199e7 − 3.30199e7i 0.224323 − 0.224323i
\(529\) 1.38902e8i 0.938302i
\(530\) 2.16102e7 − 2.88136e7i 0.145155 − 0.193540i
\(531\) −1.18308e7 −0.0790191
\(532\) 1.35949e7 + 1.35949e7i 0.0902902 + 0.0902902i
\(533\) 9.57889e7 − 9.57889e7i 0.632606 − 0.632606i
\(534\) 3.44595e7i 0.226300i
\(535\) −5.40878e7 + 7.72682e6i −0.353214 + 0.0504591i
\(536\) 1.55732e7 0.101131
\(537\) −1.25667e8 − 1.25667e8i −0.811521 − 0.811521i
\(538\) 1.01675e7 − 1.01675e7i 0.0652932 − 0.0652932i
\(539\) 6.12534e6i 0.0391168i
\(540\) 7.36000e6 + 5.15200e7i 0.0467408 + 0.327186i
\(541\) 1.30022e7 0.0821155 0.0410577 − 0.999157i \(-0.486927\pi\)
0.0410577 + 0.999157i \(0.486927\pi\)
\(542\) −2.45354e7 − 2.45354e7i −0.154097 − 0.154097i
\(543\) −2.07560e8 + 2.07560e8i −1.29642 + 1.29642i
\(544\) 2.12419e7i 0.131946i
\(545\) 3.62440e7 + 2.71830e7i 0.223896 + 0.167922i
\(546\) 2.45692e8 1.50943
\(547\) 7.28319e7 + 7.28319e7i 0.444999 + 0.444999i 0.893688 − 0.448689i \(-0.148109\pi\)
−0.448689 + 0.893688i \(0.648109\pi\)
\(548\) −3.33707e7 + 3.33707e7i −0.202779 + 0.202779i
\(549\) − 2.74129e7i − 0.165668i
\(550\) −5.95850e7 + 1.08655e8i −0.358137 + 0.653073i
\(551\) −5.24944e7 −0.313804
\(552\) 1.25827e7 + 1.25827e7i 0.0748092 + 0.0748092i
\(553\) 1.29586e8 − 1.29586e8i 0.766272 − 0.766272i
\(554\) 2.40410e7i 0.141392i
\(555\) 1.28040e8 − 1.70720e8i 0.748973 − 0.998631i
\(556\) 1.03904e8 0.604516
\(557\) −4.55401e7 − 4.55401e7i −0.263529 − 0.263529i 0.562957 − 0.826486i \(-0.309664\pi\)
−0.826486 + 0.562957i \(0.809664\pi\)
\(558\) 4.97948e7 − 4.97948e7i 0.286603 − 0.286603i
\(559\) 2.11791e8i 1.21247i
\(560\) −4.42624e7 + 6.32320e6i −0.252041 + 0.0360058i
\(561\) −1.67228e8 −0.947152
\(562\) 2.59741e7 + 2.59741e7i 0.146329 + 0.146329i
\(563\) −1.85012e8 + 1.85012e8i −1.03675 + 1.03675i −0.0374524 + 0.999298i \(0.511924\pi\)
−0.999298 + 0.0374524i \(0.988076\pi\)
\(564\) − 1.40124e8i − 0.781044i
\(565\) 1.80664e7 + 1.26465e8i 0.100168 + 0.701173i
\(566\) 2.17285e8 1.19834
\(567\) −1.63771e8 − 1.63771e8i −0.898438 − 0.898438i
\(568\) −5.16070e6 + 5.16070e6i −0.0281620 + 0.0281620i
\(569\) − 7.17210e7i − 0.389323i −0.980871 − 0.194661i \(-0.937639\pi\)
0.980871 − 0.194661i \(-0.0623608\pi\)
\(570\) −3.16480e7 − 2.37360e7i −0.170892 − 0.128169i
\(571\) 3.09478e8 1.66234 0.831172 − 0.556015i \(-0.187670\pi\)
0.831172 + 0.556015i \(0.187670\pi\)
\(572\) −1.21267e8 − 1.21267e8i −0.647972 − 0.647972i
\(573\) 9.24876e7 − 9.24876e7i 0.491609 − 0.491609i
\(574\) − 7.00255e7i − 0.370272i
\(575\) −4.14044e7 − 2.27056e7i −0.217792 − 0.119435i
\(576\) −1.07807e7 −0.0564129
\(577\) −2.15868e7 − 2.15868e7i −0.112373 − 0.112373i 0.648684 − 0.761057i \(-0.275319\pi\)
−0.761057 + 0.648684i \(0.775319\pi\)
\(578\) −4.27611e7 + 4.27611e7i −0.221445 + 0.221445i
\(579\) − 4.84906e7i − 0.249817i
\(580\) 7.32480e7 − 9.76640e7i 0.375415 − 0.500554i
\(581\) 5.65250e7 0.288212
\(582\) 9.80413e7 + 9.80413e7i 0.497325 + 0.497325i
\(583\) 5.04958e7 − 5.04958e7i 0.254830 − 0.254830i
\(584\) 3.30299e7i 0.165832i
\(585\) −1.55625e8 + 2.22322e7i −0.777342 + 0.111049i
\(586\) 3.82987e7 0.190323
\(587\) −2.30927e8 − 2.30927e8i −1.14172 − 1.14172i −0.988135 − 0.153588i \(-0.950917\pi\)
−0.153588 − 0.988135i \(-0.549083\pi\)
\(588\) 3.21558e6 − 3.21558e6i 0.0158171 − 0.0158171i
\(589\) − 6.50814e7i − 0.318501i
\(590\) −3.59600e6 − 2.51720e7i −0.0175091 − 0.122564i
\(591\) 3.35565e8 1.62560
\(592\) −3.80037e7 − 3.80037e7i −0.183173 − 0.183173i
\(593\) −2.66433e7 + 2.66433e7i −0.127768 + 0.127768i −0.768099 − 0.640331i \(-0.778797\pi\)
0.640331 + 0.768099i \(0.278797\pi\)
\(594\) 1.03187e8i 0.492342i
\(595\) 1.28094e8 + 9.60706e7i 0.608105 + 0.456079i
\(596\) −1.84454e8 −0.871265
\(597\) 3.24692e8 + 3.24692e8i 1.52598 + 1.52598i
\(598\) 4.62105e7 − 4.62105e7i 0.216091 − 0.216091i
\(599\) − 3.14489e8i − 1.46327i −0.681695 − 0.731637i \(-0.738757\pi\)
0.681695 − 0.731637i \(-0.261243\pi\)
\(600\) 8.83200e7 − 2.57600e7i 0.408889 − 0.119259i
\(601\) −2.50382e8 −1.15340 −0.576700 − 0.816956i \(-0.695660\pi\)
−0.576700 + 0.816956i \(0.695660\pi\)
\(602\) 7.74138e7 + 7.74138e7i 0.354837 + 0.354837i
\(603\) 2.00141e7 − 2.00141e7i 0.0912816 − 0.0912816i
\(604\) 3.30497e7i 0.149988i
\(605\) −1.45532e7 + 1.94043e7i −0.0657193 + 0.0876258i
\(606\) −3.13734e8 −1.40976
\(607\) 9.40326e7 + 9.40326e7i 0.420448 + 0.420448i 0.885358 − 0.464910i \(-0.153913\pi\)
−0.464910 + 0.885358i \(0.653913\pi\)
\(608\) −7.04512e6 + 7.04512e6i −0.0313457 + 0.0313457i
\(609\) 3.46768e8i 1.53528i
\(610\) 5.83254e7 − 8.33220e6i 0.256962 − 0.0367088i
\(611\) −5.14613e8 −2.25610
\(612\) 2.72991e7 + 2.72991e7i 0.119095 + 0.119095i
\(613\) −1.72963e8 + 1.72963e8i −0.750880 + 0.750880i −0.974644 − 0.223763i \(-0.928166\pi\)
0.223763 + 0.974644i \(0.428166\pi\)
\(614\) − 7.77871e7i − 0.336049i
\(615\) 2.03768e7 + 1.42638e8i 0.0876015 + 0.613211i
\(616\) −8.86513e7 −0.379265
\(617\) 1.31974e8 + 1.31974e8i 0.561868 + 0.561868i 0.929838 − 0.367970i \(-0.119947\pi\)
−0.367970 + 0.929838i \(0.619947\pi\)
\(618\) −1.22372e8 + 1.22372e8i −0.518460 + 0.518460i
\(619\) − 4.22584e8i − 1.78173i −0.454271 − 0.890863i \(-0.650100\pi\)
0.454271 − 0.890863i \(-0.349900\pi\)
\(620\) 1.21082e8 + 9.08112e7i 0.508046 + 0.381035i
\(621\) −3.93208e7 −0.164190
\(622\) −2.81338e7 − 2.81338e7i −0.116911 − 0.116911i
\(623\) 4.62582e7 − 4.62582e7i 0.191304 − 0.191304i
\(624\) 1.27322e8i 0.524023i
\(625\) −2.05859e8 + 1.31250e8i −0.843200 + 0.537600i
\(626\) −2.39116e8 −0.974734
\(627\) −5.54631e7 − 5.54631e7i −0.225010 − 0.225010i
\(628\) −7.36177e7 + 7.36177e7i −0.297237 + 0.297237i
\(629\) 1.92468e8i 0.773404i
\(630\) −4.87578e7 + 6.50104e7i −0.194995 + 0.259993i
\(631\) 2.95144e8 1.17475 0.587376 − 0.809314i \(-0.300161\pi\)
0.587376 + 0.809314i \(0.300161\pi\)
\(632\) 6.71539e7 + 6.71539e7i 0.266024 + 0.266024i
\(633\) 2.83333e8 − 2.83333e8i 1.11709 − 1.11709i
\(634\) − 1.69013e8i − 0.663212i
\(635\) 3.40621e8 − 4.86602e7i 1.33030 − 0.190043i
\(636\) −5.30170e7 −0.206084
\(637\) −1.18094e7 − 1.18094e7i −0.0456888 − 0.0456888i
\(638\) 1.71156e8 − 1.71156e8i 0.659068 − 0.659068i
\(639\) 1.32646e7i 0.0508385i
\(640\) −3.27680e6 − 2.29376e7i −0.0125000 − 0.0875000i
\(641\) 3.85293e8 1.46291 0.731453 − 0.681891i \(-0.238842\pi\)
0.731453 + 0.681891i \(0.238842\pi\)
\(642\) 5.68694e7 + 5.68694e7i 0.214919 + 0.214919i
\(643\) 1.75998e8 − 1.75998e8i 0.662024 − 0.662024i −0.293833 − 0.955857i \(-0.594931\pi\)
0.955857 + 0.293833i \(0.0949309\pi\)
\(644\) − 3.37817e7i − 0.126481i
\(645\) −1.80214e8 − 1.35161e8i −0.671599 − 0.503699i
\(646\) 3.56797e7 0.132350
\(647\) −1.00835e8 − 1.00835e8i −0.372304 − 0.372304i 0.496012 − 0.868316i \(-0.334797\pi\)
−0.868316 + 0.496012i \(0.834797\pi\)
\(648\) 8.48692e7 − 8.48692e7i 0.311907 − 0.311907i
\(649\) − 5.04159e7i − 0.184431i
\(650\) −9.46050e7 − 3.24360e8i −0.344488 − 1.18110i
\(651\) −4.29915e8 −1.55826
\(652\) −1.28697e8 − 1.28697e8i −0.464329 − 0.464329i
\(653\) 1.92563e8 − 1.92563e8i 0.691566 − 0.691566i −0.271010 − 0.962576i \(-0.587358\pi\)
0.962576 + 0.271010i \(0.0873577\pi\)
\(654\) − 6.66890e7i − 0.238408i
\(655\) −2.81715e8 + 3.75620e8i −1.00250 + 1.33667i
\(656\) 3.62885e7 0.128546
\(657\) 4.24486e7 + 4.24486e7i 0.149681 + 0.149681i
\(658\) −1.88101e8 + 1.88101e8i −0.660259 + 0.660259i
\(659\) 1.31172e8i 0.458337i 0.973387 + 0.229168i \(0.0736007\pi\)
−0.973387 + 0.229168i \(0.926399\pi\)
\(660\) 1.80578e8 − 2.57968e7i 0.628105 − 0.0897292i
\(661\) −1.97154e8 −0.682656 −0.341328 − 0.939944i \(-0.610877\pi\)
−0.341328 + 0.939944i \(0.610877\pi\)
\(662\) 1.69312e8 + 1.69312e8i 0.583596 + 0.583596i
\(663\) 3.22408e8 − 3.22408e8i 1.10628 − 1.10628i
\(664\) 2.92923e7i 0.100057i
\(665\) 1.06210e7 + 7.43470e7i 0.0361161 + 0.252812i
\(666\) −9.76814e7 −0.330666
\(667\) 6.52212e7 + 6.52212e7i 0.219792 + 0.219792i
\(668\) 2.27253e7 − 2.27253e7i 0.0762397 − 0.0762397i
\(669\) 1.51274e7i 0.0505227i
\(670\) 4.86664e7 + 3.64998e7i 0.161810 + 0.121357i
\(671\) 1.16817e8 0.386670
\(672\) 4.65388e7 + 4.65388e7i 0.153358 + 0.153358i
\(673\) −1.93253e8 + 1.93253e8i −0.633987 + 0.633987i −0.949066 − 0.315079i \(-0.897969\pi\)
0.315079 + 0.949066i \(0.397969\pi\)
\(674\) 1.16974e8i 0.382040i
\(675\) −9.77500e7 + 1.78250e8i −0.317838 + 0.579586i
\(676\) 3.13139e8 1.01367
\(677\) −2.07906e8 − 2.07906e8i −0.670042 − 0.670042i 0.287684 − 0.957725i \(-0.407115\pi\)
−0.957725 + 0.287684i \(0.907115\pi\)
\(678\) 1.32969e8 − 1.32969e8i 0.426639 − 0.426639i
\(679\) − 2.63220e8i − 0.840831i
\(680\) −4.97856e7 + 6.63808e7i −0.158335 + 0.211113i
\(681\) 3.65739e8 1.15806
\(682\) 2.12196e8 + 2.12196e8i 0.668934 + 0.668934i
\(683\) −3.57632e8 + 3.57632e8i −1.12247 + 1.12247i −0.131099 + 0.991369i \(0.541851\pi\)
−0.991369 + 0.131099i \(0.958149\pi\)
\(684\) 1.81082e7i 0.0565856i
\(685\) −1.82496e8 + 2.60708e7i −0.567781 + 0.0811116i
\(686\) 2.23841e8 0.693374
\(687\) −5.25998e8 − 5.25998e8i −1.62224 − 1.62224i
\(688\) −4.01172e7 + 4.01172e7i −0.123187 + 0.123187i
\(689\) 1.94708e8i 0.595286i
\(690\) 9.83020e6 + 6.88114e7i 0.0299237 + 0.209466i
\(691\) −1.76748e8 −0.535698 −0.267849 − 0.963461i \(-0.586313\pi\)
−0.267849 + 0.963461i \(0.586313\pi\)
\(692\) 1.20848e8 + 1.20848e8i 0.364687 + 0.364687i
\(693\) −1.13931e8 + 1.13931e8i −0.342327 + 0.342327i
\(694\) − 3.67833e8i − 1.10046i
\(695\) 3.24700e8 + 2.43525e8i 0.967226 + 0.725419i
\(696\) −1.79702e8 −0.532997
\(697\) −9.18907e7 − 9.18907e7i −0.271377 − 0.271377i
\(698\) −2.01344e8 + 2.01344e8i −0.592068 + 0.592068i
\(699\) 3.95163e8i 1.15703i
\(700\) −1.53140e8 − 8.39800e7i −0.446472 − 0.244840i
\(701\) −3.12897e8 −0.908338 −0.454169 − 0.890916i \(-0.650064\pi\)
−0.454169 + 0.890916i \(0.650064\pi\)
\(702\) −1.98941e8 − 1.98941e8i −0.575059 − 0.575059i
\(703\) −6.38344e7 + 6.38344e7i −0.183734 + 0.183734i
\(704\) − 4.59407e7i − 0.131668i
\(705\) 3.28416e8 − 4.37888e8i 0.937253 − 1.24967i
\(706\) 1.27312e8 0.361789
\(707\) 4.21154e8 + 4.21154e8i 1.19174 + 1.19174i
\(708\) −2.64666e7 + 2.64666e7i −0.0745758 + 0.0745758i
\(709\) 1.07924e8i 0.302817i 0.988471 + 0.151408i \(0.0483809\pi\)
−0.988471 + 0.151408i \(0.951619\pi\)
\(710\) −2.82226e7 + 4.03180e6i −0.0788537 + 0.0112648i
\(711\) 1.72607e8 0.480229
\(712\) 2.39718e7 + 2.39718e7i 0.0664143 + 0.0664143i
\(713\) −8.08598e7 + 8.08598e7i −0.223082 + 0.223082i
\(714\) − 2.35693e8i − 0.647519i
\(715\) −9.47402e7 − 6.63181e8i −0.259189 − 1.81432i
\(716\) −1.74842e8 −0.476328
\(717\) −2.22312e8 − 2.22312e8i −0.603124 − 0.603124i
\(718\) −1.78809e8 + 1.78809e8i −0.483077 + 0.483077i
\(719\) 1.83233e8i 0.492967i 0.969147 + 0.246484i \(0.0792752\pi\)
−0.969147 + 0.246484i \(0.920725\pi\)
\(720\) −3.36896e7 − 2.52672e7i −0.0902606 − 0.0676955i
\(721\) 3.28541e8 0.876565
\(722\) −1.76350e8 − 1.76350e8i −0.468558 − 0.468558i
\(723\) −4.27631e8 + 4.27631e8i −1.13150 + 1.13150i
\(724\) 2.88780e8i 0.760941i
\(725\) 4.57800e8 − 1.33525e8i 1.20133 − 0.350387i
\(726\) 3.57039e7 0.0933052
\(727\) 2.98719e8 + 2.98719e8i 0.777428 + 0.777428i 0.979393 − 0.201965i \(-0.0647327\pi\)
−0.201965 + 0.979393i \(0.564733\pi\)
\(728\) 1.70916e8 − 1.70916e8i 0.442985 − 0.442985i
\(729\) 9.03723e7i 0.233267i
\(730\) −7.74138e7 + 1.03218e8i −0.198999 + 0.265331i
\(731\) 2.03172e8 0.520130
\(732\) −6.13250e7 − 6.13250e7i −0.156352 − 0.156352i
\(733\) 4.34598e8 − 4.34598e8i 1.10351 − 1.10351i 0.109524 − 0.993984i \(-0.465067\pi\)
0.993984 − 0.109524i \(-0.0349325\pi\)
\(734\) 2.16499e8i 0.547480i
\(735\) 1.75852e7 − 2.51218e6i 0.0442880 − 0.00632685i
\(736\) 1.75063e7 0.0439098
\(737\) 8.52879e7 + 8.52879e7i 0.213052 + 0.213052i
\(738\) 4.66364e7 − 4.66364e7i 0.116026 − 0.116026i
\(739\) − 5.77645e8i − 1.43129i −0.698463 − 0.715646i \(-0.746133\pi\)
0.698463 − 0.715646i \(-0.253867\pi\)
\(740\) −2.96904e7 − 2.07833e8i −0.0732691 − 0.512884i
\(741\) 2.13861e8 0.525627
\(742\) 7.11696e7 + 7.11696e7i 0.174214 + 0.174214i
\(743\) 9.71697e7 − 9.71697e7i 0.236900 − 0.236900i −0.578665 − 0.815565i \(-0.696426\pi\)
0.815565 + 0.578665i \(0.196426\pi\)
\(744\) − 2.22790e8i − 0.540975i
\(745\) −5.76420e8 − 4.32315e8i −1.39402 − 1.04552i
\(746\) 3.05884e8 0.736784
\(747\) 3.76452e7 + 3.76452e7i 0.0903124 + 0.0903124i
\(748\) −1.16332e8 + 1.16332e8i −0.277969 + 0.277969i
\(749\) − 1.52682e8i − 0.363365i
\(750\) 3.36375e8 + 1.26500e8i 0.797333 + 0.299852i
\(751\) 6.96310e8 1.64393 0.821963 − 0.569540i \(-0.192879\pi\)
0.821963 + 0.569540i \(0.192879\pi\)
\(752\) −9.74776e7 − 9.74776e7i −0.229219 − 0.229219i
\(753\) −2.74505e8 + 2.74505e8i −0.642933 + 0.642933i
\(754\) 6.59964e8i 1.53960i
\(755\) −7.74602e7 + 1.03280e8i −0.179985 + 0.239981i
\(756\) −1.45434e8 −0.336589
\(757\) −2.26996e8 − 2.26996e8i −0.523276 − 0.523276i 0.395283 − 0.918559i \(-0.370646\pi\)
−0.918559 + 0.395283i \(0.870646\pi\)
\(758\) 1.00245e7 − 1.00245e7i 0.0230173 − 0.0230173i
\(759\) 1.37819e8i 0.315199i
\(760\) −3.85280e7 + 5.50400e6i −0.0877679 + 0.0125383i
\(761\) −3.36900e8 −0.764447 −0.382224 − 0.924070i \(-0.624842\pi\)
−0.382224 + 0.924070i \(0.624842\pi\)
\(762\) −3.58139e8 − 3.58139e8i −0.809444 − 0.809444i