↑

Properties

Label 74.8.f.b.7.11
Level $74$
Weight $8$
Character 74.7
Analytic conductor $23.116$
Analytic rank $0$
Dimension $66$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [74,8,Mod(7,74)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(74, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("74.7");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 74.f (of order \(9\), degree \(6\), 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: \(23.1164918858\)
Analytic rank: \(0\)
Dimension: \(66\)
Relative dimension: \(11\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 7.11
Character \(\chi\) \(=\) 74.7
Dual form 74.8.f.b.53.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(7.51754 - 2.73616i) q^{2} +(79.5512 + 28.9543i) q^{3} +(49.0268 - 41.1384i) q^{4} +(-57.6869 - 327.158i) q^{5} +677.253 q^{6} +(-6.84167 - 38.8010i) q^{7} +(256.000 - 443.405i) q^{8} +(3814.71 + 3200.92i) q^{9} +O(q^{10})\) \(q+(7.51754 - 2.73616i) q^{2} +(79.5512 + 28.9543i) q^{3} +(49.0268 - 41.1384i) q^{4} +(-57.6869 - 327.158i) q^{5} +677.253 q^{6} +(-6.84167 - 38.8010i) q^{7} +(256.000 - 443.405i) q^{8} +(3814.71 + 3200.92i) q^{9} +(-1328.82 - 2301.59i) q^{10} +(1500.65 - 2599.20i) q^{11} +(5091.28 - 1853.07i) q^{12} +(2437.31 - 2045.15i) q^{13} +(-157.598 - 272.968i) q^{14} +(4883.58 - 27696.1i) q^{15} +(711.263 - 4033.77i) q^{16} +(-15579.1 - 13072.4i) q^{17} +(37435.5 + 13625.4i) q^{18} +(21333.2 + 7764.66i) q^{19} +(-16287.0 - 13666.4i) q^{20} +(579.192 - 3284.76i) q^{21} +(4169.36 - 23645.6i) q^{22} +(23078.7 + 39973.4i) q^{23} +(33203.6 - 27861.1i) q^{24} +(-30291.4 + 11025.2i) q^{25} +(12726.7 - 22043.4i) q^{26} +(118212. + 204750. i) q^{27} +(-1931.64 - 1620.84i) q^{28} +(-98100.0 + 169914. i) q^{29} +(-39068.6 - 221569. i) q^{30} +25432.7 q^{31} +(-5690.10 - 32270.2i) q^{32} +(194636. - 163319. i) q^{33} +(-152885. - 55645.4i) q^{34} +(-12299.4 + 4476.62i) q^{35} +318704. q^{36} +(-304529. + 46836.7i) q^{37} +181619. q^{38} +(253107. - 92123.4i) q^{39} +(-159832. - 58173.9i) q^{40} +(213927. - 179506. i) q^{41} +(-4633.54 - 26278.1i) q^{42} -41867.7 q^{43} +(-33354.9 - 189165. i) q^{44} +(827150. - 1.43266e6i) q^{45} +(282869. + 237355. i) q^{46} +(-227689. - 394369. i) q^{47} +(173377. - 300297. i) q^{48} +(772419. - 281137. i) q^{49} +(-197550. + 165764. i) q^{50} +(-860833. - 1.49101e6i) q^{51} +(35359.6 - 200534. i) q^{52} +(-321178. + 1.82149e6i) q^{53} +(1.44889e6 + 1.21577e6i) q^{54} +(-936918. - 341010. i) q^{55} +(-18956.0 - 6899.43i) q^{56} +(1.47226e6 + 1.23538e6i) q^{57} +(-272558. + 1.54575e6i) q^{58} +(-497018. + 2.81873e6i) q^{59} +(-899949. - 1.55876e6i) q^{60} +(-1.22191e6 + 1.02531e6i) q^{61} +(191191. - 69588.0i) q^{62} +(98100.0 - 169914. i) q^{63} +(-131072. - 227023. i) q^{64} +(-809689. - 679410. i) q^{65} +(1.01632e6 - 1.76032e6i) q^{66} +(-623216. - 3.53444e6i) q^{67} -1.30157e6 q^{68} +(678535. + 3.84816e6i) q^{69} +(-80212.5 + 67306.3i) q^{70} +(-1.80784e6 - 657999. i) q^{71} +(2.39587e6 - 872025. i) q^{72} +3.98373e6 q^{73} +(-2.16116e6 + 1.18534e6i) q^{74} -2.72894e6 q^{75} +(1.36533e6 - 496938. i) q^{76} +(-111119. - 40443.8i) q^{77} +(1.65068e6 - 1.38508e6i) q^{78} +(-29332.0 - 166350. i) q^{79} -1.36071e6 q^{80} +(1.58440e6 + 8.98559e6i) q^{81} +(1.11705e6 - 1.93478e6i) q^{82} +(-4.95154e6 - 4.15483e6i) q^{83} +(-106734. - 184869. i) q^{84} +(-3.37804e6 + 5.85093e6i) q^{85} +(-314742. + 114557. i) q^{86} +(-1.27237e7 + 1.06765e7i) q^{87} +(-768332. - 1.33079e6i) q^{88} +(-1.93468e6 + 1.09721e7i) q^{89} +(2.29813e6 - 1.30333e7i) q^{90} +(-96029.1 - 80578.0i) q^{91} +(2.77592e6 + 1.01035e6i) q^{92} +(2.02320e6 + 736386. i) q^{93} +(-2.79072e6 - 2.34169e6i) q^{94} +(1.30963e6 - 7.42726e6i) q^{95} +(481705. - 2.73189e6i) q^{96} +(-7.77014e6 - 1.34583e7i) q^{97} +(5.03745e6 - 4.22692e6i) q^{98} +(1.40444e7 - 5.11173e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 66 q - 39 q^{3} + 459 q^{5} - 918 q^{7} + 16896 q^{8} + 3237 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 66 q - 39 q^{3} + 459 q^{5} - 918 q^{7} + 16896 q^{8} + 3237 q^{9} + 4704 q^{10} + 4539 q^{11} - 2496 q^{12} - 10542 q^{13} + 6744 q^{14} - 39894 q^{15} - 78822 q^{17} + 51792 q^{18} + 79461 q^{19} + 29376 q^{20} - 5835 q^{21} + 18168 q^{22} - 199479 q^{23} + 19968 q^{24} + 356301 q^{25} + 186744 q^{26} - 91689 q^{27} - 91584 q^{28} - 38526 q^{29} + 319152 q^{30} + 1917246 q^{31} - 902847 q^{33} - 205776 q^{34} - 1574793 q^{35} + 3079296 q^{36} - 396513 q^{37} - 692880 q^{38} + 2514306 q^{39} + 470016 q^{40} + 2989350 q^{41} + 46680 q^{42} + 6006348 q^{43} - 145344 q^{44} + 1083726 q^{45} - 588744 q^{46} - 894135 q^{47} + 7973742 q^{49} + 2012400 q^{50} - 524880 q^{51} - 2262720 q^{52} + 1457844 q^{53} + 1452312 q^{54} + 2415690 q^{55} - 1202688 q^{56} + 2734338 q^{57} - 3423360 q^{58} + 3099522 q^{59} - 3102912 q^{60} - 10968396 q^{61} - 3067320 q^{62} - 10727970 q^{63} - 8650752 q^{64} - 13497300 q^{65} - 4598712 q^{66} - 1978119 q^{67} + 5026176 q^{68} - 7251108 q^{69} + 435744 q^{70} - 19555002 q^{71} + 3314688 q^{72} - 31332840 q^{73} + 7607472 q^{74} + 44758074 q^{75} + 5085504 q^{76} + 1982007 q^{77} - 22512264 q^{78} + 10522902 q^{79} + 4816896 q^{80} - 7548876 q^{81} - 7150320 q^{82} + 19771926 q^{83} + 3556224 q^{84} - 6684072 q^{85} + 22982496 q^{86} - 67769667 q^{87} - 2323968 q^{88} - 42018963 q^{89} - 25158672 q^{90} + 4847565 q^{91} - 1096704 q^{92} - 14558475 q^{93} + 3175680 q^{94} + 4508415 q^{95} - 2555904 q^{96} - 39286662 q^{97} + 71630904 q^{98} + 66155463 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.51754 − 2.73616i 0.664463 − 0.241845i
\(3\) 79.5512 + 28.9543i 1.70107 + 0.619139i 0.995947 − 0.0899444i \(-0.0286689\pi\)
0.705124 + 0.709084i \(0.250891\pi\)
\(4\) 49.0268 − 41.1384i 0.383022 − 0.321394i
\(5\) −57.6869 − 327.158i −0.206387 − 1.17048i −0.895243 − 0.445579i \(-0.852998\pi\)
0.688856 − 0.724898i \(-0.258113\pi\)
\(6\) 677.253 1.28003
\(7\) −6.84167 − 38.8010i −0.00753909 − 0.0427563i 0.980806 − 0.194985i \(-0.0624659\pi\)
−0.988345 + 0.152229i \(0.951355\pi\)
\(8\) 256.000 − 443.405i 0.176777 − 0.306186i
\(9\) 3814.71 + 3200.92i 1.74427 + 1.46361i
\(10\) −1328.82 − 2301.59i −0.420210 − 0.727826i
\(11\) 1500.65 − 2599.20i 0.339942 − 0.588796i −0.644480 − 0.764621i \(-0.722926\pi\)
0.984421 + 0.175825i \(0.0562593\pi\)
\(12\) 5091.28 − 1853.07i 0.850536 − 0.309570i
\(13\) 2437.31 − 2045.15i 0.307687 − 0.258180i −0.475848 − 0.879528i \(-0.657859\pi\)
0.783535 + 0.621347i \(0.213414\pi\)
\(14\) −157.598 − 272.968i −0.0153498 − 0.0265867i
\(15\) 4883.58 − 27696.1i 0.373610 − 2.11885i
\(16\) 711.263 − 4033.77i 0.0434120 − 0.246202i
\(17\) −15579.1 − 13072.4i −0.769078 − 0.645333i 0.171394 − 0.985202i \(-0.445173\pi\)
−0.940473 + 0.339869i \(0.889617\pi\)
\(18\) 37435.5 + 13625.4i 1.51297 + 0.550675i
\(19\) 21333.2 + 7764.66i 0.713541 + 0.259708i 0.673181 − 0.739478i \(-0.264927\pi\)
0.0403597 + 0.999185i \(0.487150\pi\)
\(20\) −16287.0 − 13666.4i −0.455235 − 0.381988i
\(21\) 579.192 − 3284.76i 0.0136476 − 0.0773992i
\(22\) 4169.36 − 23645.6i 0.0834814 − 0.473447i
\(23\) 23078.7 + 39973.4i 0.395515 + 0.685053i 0.993167 − 0.116703i \(-0.0372327\pi\)
−0.597651 + 0.801756i \(0.703899\pi\)
\(24\) 33203.6 − 27861.1i 0.490282 − 0.411395i
\(25\) −30291.4 + 11025.2i −0.387730 + 0.141122i
\(26\) 12726.7 − 22043.4i 0.142007 − 0.245964i
\(27\) 118212. + 204750.i 1.15582 + 2.00194i
\(28\) −1931.64 − 1620.84i −0.0166292 − 0.0139536i
\(29\) −98100.0 + 169914.i −0.746923 + 1.29371i 0.202368 + 0.979310i \(0.435136\pi\)
−0.949291 + 0.314399i \(0.898197\pi\)
\(30\) −39068.6 − 221569.i −0.264182 − 1.49825i
\(31\) 25432.7 0.153330 0.0766649 − 0.997057i \(-0.475573\pi\)
0.0766649 + 0.997057i \(0.475573\pi\)
\(32\) −5690.10 − 32270.2i −0.0306970 − 0.174091i
\(33\) 194636. − 163319.i 0.942812 − 0.791113i
\(34\) −152885. − 55645.4i −0.667095 − 0.242803i
\(35\) −12299.4 + 4476.62i −0.0484893 + 0.0176487i
\(36\) 318704. 1.13849
\(37\) −304529. + 46836.7i −0.988379 + 0.152013i
\(38\) 181619. 0.536930
\(39\) 253107. − 92123.4i 0.683248 − 0.248682i
\(40\) −159832. − 58173.9i −0.394868 − 0.143720i
\(41\) 213927. − 179506.i 0.484755 − 0.406757i −0.367387 − 0.930068i \(-0.619748\pi\)
0.852142 + 0.523311i \(0.175303\pi\)
\(42\) −4633.54 − 26278.1i −0.00965029 − 0.0547295i
\(43\) −41867.7 −0.0803044 −0.0401522 − 0.999194i \(-0.512784\pi\)
−0.0401522 + 0.999194i \(0.512784\pi\)
\(44\) −33354.9 − 189165.i −0.0590303 − 0.334777i
\(45\) 827150. − 1.43266e6i 1.35313 − 2.34369i
\(46\) 282869. + 237355.i 0.428482 + 0.359539i
\(47\) −227689. − 394369.i −0.319889 − 0.554065i 0.660575 − 0.750760i \(-0.270312\pi\)
−0.980465 + 0.196695i \(0.936979\pi\)
\(48\) 173377. − 300297.i 0.226280 − 0.391929i
\(49\) 772419. − 281137.i 0.937921 − 0.341375i
\(50\) −197550. + 165764.i −0.223502 + 0.187541i
\(51\) −860833. − 1.49101e6i −0.908706 − 1.57392i
\(52\) 35359.6 − 200534.i 0.0348735 − 0.197778i
\(53\) −321178. + 1.82149e6i −0.296333 + 1.68059i 0.365400 + 0.930851i \(0.380932\pi\)
−0.661734 + 0.749739i \(0.730179\pi\)
\(54\) 1.44889e6 + 1.21577e6i 1.25216 + 1.05068i
\(55\) −936918. − 341010.i −0.759333 − 0.276374i
\(56\) −18956.0 − 6899.43i −0.0144241 − 0.00524995i
\(57\) 1.47226e6 + 1.23538e6i 1.05299 + 0.883562i
\(58\) −272558. + 1.54575e6i −0.183426 + 1.04026i
\(59\) −497018. + 2.81873e6i −0.315058 + 1.78678i 0.256837 + 0.966455i \(0.417320\pi\)
−0.571895 + 0.820327i \(0.693791\pi\)
\(60\) −899949. − 1.55876e6i −0.537884 − 0.931642i
\(61\) −1.22191e6 + 1.02531e6i −0.689263 + 0.578361i −0.918697 − 0.394964i \(-0.870757\pi\)
0.229433 + 0.973324i \(0.426313\pi\)
\(62\) 191191. − 69588.0i 0.101882 − 0.0370820i
\(63\) 98100.0 − 169914.i 0.0494285 − 0.0856126i
\(64\) −131072. − 227023.i −0.0625000 − 0.108253i
\(65\) −809689. − 679410.i −0.365697 − 0.306856i
\(66\) 1.01632e6 − 1.76032e6i 0.435137 − 0.753680i
\(67\) −623216. − 3.53444e6i −0.253149 − 1.43568i −0.800778 − 0.598961i \(-0.795581\pi\)
0.547629 − 0.836721i \(-0.315531\pi\)
\(68\) −1.30157e6 −0.501980
\(69\) 678535. + 3.84816e6i 0.248657 + 1.41020i
\(70\) −80212.5 + 67306.3i −0.0279511 + 0.0234538i
\(71\) −1.80784e6 − 657999.i −0.599453 − 0.218183i 0.0244293 − 0.999702i \(-0.492223\pi\)
−0.623882 + 0.781519i \(0.714445\pi\)
\(72\) 2.39587e6 − 872025.i 0.756483 − 0.275337i
\(73\) 3.98373e6 1.19856 0.599280 − 0.800540i \(-0.295454\pi\)
0.599280 + 0.800540i \(0.295454\pi\)
\(74\) −2.16116e6 + 1.18534e6i −0.619978 + 0.340041i
\(75\) −2.72894e6 −0.746930
\(76\) 1.36533e6 − 496938.i 0.356770 − 0.129854i
\(77\) −111119. − 40443.8i −0.0277376 − 0.0100957i
\(78\) 1.65068e6 − 1.38508e6i 0.393850 − 0.330480i
\(79\) −29332.0 − 166350.i −0.00669340 − 0.0379601i 0.981278 − 0.192596i \(-0.0616907\pi\)
−0.987972 + 0.154636i \(0.950580\pi\)
\(80\) −1.36071e6 −0.297134
\(81\) 1.58440e6 + 8.98559e6i 0.331259 + 1.87866i
\(82\) 1.11705e6 − 1.93478e6i 0.223729 − 0.387511i
\(83\) −4.95154e6 − 4.15483e6i −0.950532 − 0.797591i 0.0288548 − 0.999584i \(-0.490814\pi\)
−0.979387 + 0.201992i \(0.935258\pi\)
\(84\) −106734. − 184869.i −0.0196483 − 0.0340319i
\(85\) −3.37804e6 + 5.85093e6i −0.596621 + 1.03338i
\(86\) −314742. + 114557.i −0.0533593 + 0.0194212i
\(87\) −1.27237e7 + 1.06765e7i −2.07156 + 1.73824i
\(88\) −768332. − 1.33079e6i −0.120188 − 0.208171i
\(89\) −1.93468e6 + 1.09721e7i −0.290900 + 1.64978i 0.392515 + 0.919746i \(0.371605\pi\)
−0.683415 + 0.730030i \(0.739506\pi\)
\(90\) 2.29813e6 − 1.30333e7i 0.332296 − 1.88455i
\(91\) −96029.1 − 80578.0i −0.0133585 − 0.0112091i
\(92\) 2.77592e6 + 1.01035e6i 0.371663 + 0.135274i
\(93\) 2.02320e6 + 736386.i 0.260825 + 0.0949325i
\(94\) −2.79072e6 − 2.34169e6i −0.346552 − 0.290792i
\(95\) 1.30963e6 − 7.42726e6i 0.156717 − 0.888784i
\(96\) 481705. − 2.73189e6i 0.0555689 − 0.315147i
\(97\) −7.77014e6 − 1.34583e7i −0.864426 − 1.49723i −0.867616 − 0.497235i \(-0.834349\pi\)
0.00319014 − 0.999995i \(-0.498985\pi\)
\(98\) 5.03745e6 − 4.22692e6i 0.540654 − 0.453663i
\(99\) 1.40444e7 − 5.11173e6i 1.45472 − 0.529474i
\(100\) −1.03153e6 + 1.78667e6i −0.103153 + 0.178667i
\(101\) 3.97971e6 + 6.89306e6i 0.384350 + 0.665713i 0.991679 − 0.128737i \(-0.0410924\pi\)
−0.607329 + 0.794450i \(0.707759\pi\)
\(102\) −1.05510e7 − 8.85332e6i −0.984447 − 0.826049i
\(103\) −8.44162e6 + 1.46213e7i −0.761194 + 1.31843i 0.181041 + 0.983476i \(0.442053\pi\)
−0.942235 + 0.334952i \(0.891280\pi\)
\(104\) −282877. − 1.60428e6i −0.0246593 − 0.139850i
\(105\) −1.10805e6 −0.0934107
\(106\) 2.56943e6 + 1.45719e7i 0.209539 + 1.18836i
\(107\) −3.09032e6 + 2.59308e6i −0.243871 + 0.204632i −0.756528 − 0.653962i \(-0.773106\pi\)
0.512657 + 0.858594i \(0.328661\pi\)
\(108\) 1.42187e7 + 5.17517e6i 1.08611 + 0.395313i
\(109\) −1.23178e7 + 4.48330e6i −0.911043 + 0.331593i −0.754669 − 0.656105i \(-0.772203\pi\)
−0.156374 + 0.987698i \(0.549980\pi\)
\(110\) −7.97638e6 −0.571388
\(111\) −2.55818e7 − 5.09152e6i −1.77542 − 0.353360i
\(112\) −161381. −0.0108540
\(113\) −190395. + 69298.2i −0.0124131 + 0.00451801i −0.348219 − 0.937413i \(-0.613214\pi\)
0.335806 + 0.941931i \(0.390991\pi\)
\(114\) 1.44480e7 + 5.25864e6i 0.913357 + 0.332435i
\(115\) 1.17463e7 − 9.85632e6i 0.720210 − 0.604328i
\(116\) 2.18046e6 + 1.23660e7i 0.129702 + 0.735576i
\(117\) 1.58440e7 0.914564
\(118\) 3.97615e6 + 2.25498e7i 0.222780 + 1.26345i
\(119\) −400635. + 693921.i −0.0217939 + 0.0377482i
\(120\) −1.10304e7 − 9.25561e6i −0.582716 − 0.488957i
\(121\) 5.23969e6 + 9.07542e6i 0.268879 + 0.465712i
\(122\) −6.38037e6 + 1.10511e7i −0.318117 + 0.550994i
\(123\) 2.22156e7 − 8.08582e6i 1.07644 − 0.391793i
\(124\) 1.24689e6 − 1.04626e6i 0.0587287 − 0.0492793i
\(125\) −7.62238e6 − 1.32024e7i −0.349065 − 0.604597i
\(126\) 272558. − 1.54575e6i 0.0121384 − 0.0688404i
\(127\) 5.95631e6 − 3.37799e7i 0.258026 − 1.46334i −0.530157 − 0.847900i \(-0.677867\pi\)
0.788183 − 0.615441i \(-0.211022\pi\)
\(128\) −1.60651e6 − 1.34802e6i −0.0677094 − 0.0568149i
\(129\) −3.33063e6 − 1.21225e6i −0.136603 − 0.0497196i
\(130\) −7.94584e6 − 2.89205e6i −0.317204 − 0.115453i
\(131\) 3.18442e7 + 2.67204e7i 1.23760 + 1.03847i 0.997708 + 0.0676697i \(0.0215564\pi\)
0.239892 + 0.970800i \(0.422888\pi\)
\(132\) 2.82371e6 − 1.60141e7i 0.106859 − 0.606028i
\(133\) 155322. − 880874.i 0.00572469 − 0.0324663i
\(134\) −1.43558e7 − 2.48650e7i −0.515421 − 0.892735i
\(135\) 6.01663e7 − 5.04855e7i 2.10468 − 1.76603i
\(136\) −9.78461e6 + 3.56131e6i −0.333547 + 0.121401i
\(137\) 4.91356e6 − 8.51053e6i 0.163258 − 0.282771i −0.772777 − 0.634677i \(-0.781133\pi\)
0.936035 + 0.351906i \(0.114466\pi\)
\(138\) 1.56301e7 + 2.70721e7i 0.506273 + 0.876891i
\(139\) 7.09948e6 + 5.95717e6i 0.224220 + 0.188143i 0.747977 − 0.663725i \(-0.231025\pi\)
−0.523757 + 0.851868i \(0.675470\pi\)
\(140\) −418840. + 725452.i −0.0129003 + 0.0223440i
\(141\) −6.69428e6 − 3.79651e7i −0.201111 − 1.14056i
\(142\) −1.53909e7 −0.451080
\(143\) −1.65820e6 − 9.40411e6i −0.0474199 − 0.268932i
\(144\) 1.56250e7 − 1.31110e7i 0.436066 − 0.365903i
\(145\) 6.12479e7 + 2.22924e7i 1.66841 + 0.607252i
\(146\) 2.99478e7 − 1.09001e7i 0.796399 − 0.289865i
\(147\) 6.95870e7 1.80683
\(148\) −1.30033e7 + 1.48241e7i −0.329715 + 0.375883i
\(149\) 2.69968e7 0.668591 0.334295 − 0.942468i \(-0.391502\pi\)
0.334295 + 0.942468i \(0.391502\pi\)
\(150\) −2.05149e7 + 7.46683e6i −0.496307 + 0.180641i
\(151\) −6.84195e7 − 2.49026e7i −1.61719 − 0.588608i −0.634344 − 0.773051i \(-0.718730\pi\)
−0.982843 + 0.184443i \(0.940952\pi\)
\(152\) 8.90419e6 − 7.47150e6i 0.205656 − 0.172566i
\(153\) −1.75859e7 − 9.97348e7i −0.396959 − 2.25126i
\(154\) −945999. −0.0208722
\(155\) −1.46713e6 − 8.32052e6i −0.0316452 − 0.179469i
\(156\) 8.61923e6 − 1.49289e7i 0.181774 − 0.314842i
\(157\) 2.57599e6 + 2.16152e6i 0.0531247 + 0.0445769i 0.668963 − 0.743295i \(-0.266738\pi\)
−0.615839 + 0.787872i \(0.711183\pi\)
\(158\) −675665. − 1.17029e6i −0.0136280 − 0.0236044i
\(159\) −7.82901e7 + 1.35602e8i −1.54460 + 2.67533i
\(160\) −1.02292e7 + 3.72313e6i −0.197434 + 0.0718602i
\(161\) 1.39311e6 − 1.16896e6i 0.0263085 − 0.0220754i
\(162\) 3.64968e7 + 6.32144e7i 0.674455 + 1.16819i
\(163\) 1.49410e7 − 8.47348e7i 0.270224 − 1.53252i −0.483511 − 0.875338i \(-0.660639\pi\)
0.753735 − 0.657178i \(-0.228250\pi\)
\(164\) 3.10357e6 − 1.76012e7i 0.0549425 − 0.311594i
\(165\) −6.46593e7 − 5.42556e7i −1.12056 − 0.940265i
\(166\) −4.85917e7 − 1.76859e7i −0.824487 − 0.300089i
\(167\) −3.75825e7 − 1.36789e7i −0.624422 − 0.227271i 0.0103798 − 0.999946i \(-0.496696\pi\)
−0.634802 + 0.772675i \(0.718918\pi\)
\(168\) −1.30821e6 − 1.09772e6i −0.0212860 − 0.0178611i
\(169\) −9.13830e6 + 5.18259e7i −0.145634 + 0.825930i
\(170\) −9.38544e6 + 5.32275e7i −0.146515 + 0.830931i
\(171\) 5.65260e7 + 9.79058e7i 0.864493 + 1.49735i
\(172\) −2.05264e6 + 1.72237e6i −0.0307584 + 0.0258093i
\(173\) 2.91446e7 − 1.06078e7i 0.427953 − 0.155762i −0.119058 − 0.992887i \(-0.537988\pi\)
0.547012 + 0.837125i \(0.315765\pi\)
\(174\) −6.64385e7 + 1.15075e8i −0.956087 + 1.65599i
\(175\) 635031. + 1.09991e6i 0.00895698 + 0.0155140i
\(176\) −9.41722e6 − 7.90199e6i −0.130205 − 0.109255i
\(177\) −1.21153e8 + 2.09843e8i −1.64220 + 2.84438i
\(178\) 1.54774e7 + 8.77768e7i 0.205697 + 1.16657i
\(179\) −1.36707e7 −0.178158 −0.0890790 − 0.996025i \(-0.528392\pi\)
−0.0890790 + 0.996025i \(0.528392\pi\)
\(180\) −1.83850e7 − 1.04267e8i −0.234969 − 1.33258i
\(181\) −5.08173e6 + 4.26407e6i −0.0636995 + 0.0534502i −0.674082 − 0.738657i \(-0.735460\pi\)
0.610382 + 0.792107i \(0.291016\pi\)
\(182\) −942377. − 342997.i −0.0115871 − 0.00421736i
\(183\) −1.26892e8 + 4.61847e7i −1.53057 + 0.557083i
\(184\) 2.36326e7 0.279672
\(185\) 3.28904e7 + 9.69275e7i 0.381916 + 1.12550i
\(186\) 1.72244e7 0.196267
\(187\) −5.73565e7 + 2.08761e7i −0.641412 + 0.233455i
\(188\) −2.73866e7 − 9.96791e6i −0.300598 − 0.109409i
\(189\) 7.13573e6 − 5.98759e6i 0.0768815 − 0.0645113i
\(190\) −1.04770e7 − 5.94181e7i −0.110815 − 0.628465i
\(191\) −5.38642e7 −0.559350 −0.279675 − 0.960095i \(-0.590227\pi\)
−0.279675 + 0.960095i \(0.590227\pi\)
\(192\) −3.85364e6 − 2.18551e7i −0.0392932 − 0.222843i
\(193\) 5.79723e7 − 1.00411e8i 0.580457 − 1.00538i −0.414968 − 0.909836i \(-0.636207\pi\)
0.995425 − 0.0955448i \(-0.0304593\pi\)
\(194\) −9.52364e7 − 7.99128e7i −0.936476 − 0.785797i
\(195\) −4.47399e7 − 7.74918e7i −0.432090 − 0.748402i
\(196\) 2.63037e7 − 4.55593e7i 0.249529 − 0.432197i
\(197\) 1.53909e8 − 5.60182e7i 1.43427 − 0.522032i 0.496118 − 0.868255i \(-0.334758\pi\)
0.938152 + 0.346223i \(0.112536\pi\)
\(198\) 9.15926e7 − 7.68553e7i 0.838556 − 0.703632i
\(199\) 5.72902e7 + 9.92296e7i 0.515341 + 0.892597i 0.999841 + 0.0178061i \(0.00566815\pi\)
−0.484500 + 0.874791i \(0.660999\pi\)
\(200\) −2.86598e6 + 1.62538e7i −0.0253319 + 0.143665i
\(201\) 5.27594e7 − 2.99213e8i 0.458262 − 2.59893i
\(202\) 4.87782e7 + 4.09297e7i 0.416385 + 0.349389i
\(203\) 7.26401e6 + 2.64388e6i 0.0609453 + 0.0221823i
\(204\) −1.03542e8 − 3.76860e7i −0.853904 − 0.310796i
\(205\) −7.10677e7 − 5.96329e7i −0.576147 − 0.483445i
\(206\) −2.34540e7 + 1.33014e8i −0.186931 + 1.06014i
\(207\) −3.99134e7 + 2.26360e8i −0.312768 + 1.77379i
\(208\) −6.51609e6 − 1.12862e7i −0.0502072 − 0.0869614i
\(209\) 5.21956e7 − 4.37973e7i 0.395477 − 0.331845i
\(210\) −8.32981e6 + 3.03180e6i −0.0620680 + 0.0225909i
\(211\) 7.01465e7 − 1.21497e8i 0.514064 − 0.890385i −0.485803 − 0.874068i \(-0.661473\pi\)
0.999867 − 0.0163165i \(-0.00519394\pi\)
\(212\) 5.91869e7 + 1.02515e8i 0.426629 + 0.738943i
\(213\) −1.24764e8 − 1.04689e8i −0.884626 − 0.742289i
\(214\) −1.61365e7 + 2.79492e7i −0.112554 + 0.194949i
\(215\) 2.41521e6 + 1.36974e7i 0.0165738 + 0.0939945i
\(216\) 1.21049e8 0.817287
\(217\) −174002. − 986815.i −0.00115597 − 0.00655581i
\(218\) −8.03322e7 + 6.74067e7i −0.525161 + 0.440662i
\(219\) 3.16910e8 + 1.15346e8i 2.03884 + 0.742075i
\(220\) −5.99627e7 + 2.18247e7i −0.379666 + 0.138187i
\(221\) −6.47061e7 −0.403248
\(222\) −2.06244e8 + 3.17203e7i −1.26516 + 0.194581i
\(223\) 2.58695e8 1.56214 0.781072 − 0.624441i \(-0.214673\pi\)
0.781072 + 0.624441i \(0.214673\pi\)
\(224\) −1.21319e6 + 441564.i −0.00721206 + 0.00262497i
\(225\) −1.50843e8 − 5.49025e7i −0.882852 − 0.321332i
\(226\) −1.24169e6 + 1.04190e6i −0.00715541 + 0.00600410i
\(227\) 4.37795e7 + 2.48286e8i 0.248416 + 1.40884i 0.812423 + 0.583069i \(0.198148\pi\)
−0.564006 + 0.825771i \(0.690741\pi\)
\(228\) 1.23002e8 0.687289
\(229\) −5.02830e7 − 2.85169e8i −0.276692 − 1.56920i −0.733535 − 0.679652i \(-0.762131\pi\)
0.456843 − 0.889548i \(-0.348980\pi\)
\(230\) 6.13349e7 − 1.06235e8i 0.332399 − 0.575732i
\(231\) −7.66859e6 − 6.43471e6i −0.0409330 − 0.0343469i
\(232\) 5.02272e7 + 8.69960e7i 0.264077 + 0.457395i
\(233\) −2.67980e7 + 4.64155e7i −0.138790 + 0.240391i −0.927039 − 0.374966i \(-0.877654\pi\)
0.788249 + 0.615356i \(0.210988\pi\)
\(234\) 1.19108e8 − 4.33517e7i 0.607694 − 0.221183i
\(235\) −1.15887e8 + 9.72404e7i −0.582499 + 0.488775i
\(236\) 9.15908e7 + 1.58640e8i 0.453586 + 0.785635i
\(237\) 2.48315e6 − 1.40826e7i 0.0121167 − 0.0687171i
\(238\) −1.11311e6 + 6.31278e6i −0.00535205 + 0.0303530i
\(239\) 5.41449e7 + 4.54330e7i 0.256546 + 0.215268i 0.761985 − 0.647595i \(-0.224225\pi\)
−0.505439 + 0.862862i \(0.668669\pi\)
\(240\) −1.08246e8 − 3.93985e7i −0.505445 − 0.183967i
\(241\) 1.15976e8 + 4.22117e7i 0.533713 + 0.194255i 0.594795 − 0.803877i \(-0.297233\pi\)
−0.0610827 + 0.998133i \(0.519455\pi\)
\(242\) 6.42214e7 + 5.38882e7i 0.291290 + 0.244422i
\(243\) −4.43435e7 + 2.51485e8i −0.198248 + 1.12432i
\(244\) −1.77270e7 + 1.00535e8i −0.0781217 + 0.443050i
\(245\) −1.36535e8 − 2.36485e8i −0.593147 − 1.02736i
\(246\) 1.44883e8 − 1.21571e8i 0.620503 − 0.520663i
\(247\) 6.78756e7 − 2.47047e7i 0.286599 − 0.104313i
\(248\) 6.51077e6 − 1.12770e7i 0.0271051 − 0.0469475i
\(249\) −2.73601e8 − 4.73890e8i −1.12310 − 1.94527i
\(250\) −9.34253e7 − 7.83932e7i −0.378159 − 0.317313i
\(251\) 1.55307e8 − 2.69000e8i 0.619917 − 1.07373i −0.369583 − 0.929198i \(-0.620500\pi\)
0.989500 − 0.144530i \(-0.0461670\pi\)
\(252\) −2.18047e6 − 1.23660e7i −0.00858316 − 0.0486775i
\(253\) 1.38532e8 0.537809
\(254\) −4.76505e7 − 2.70239e8i −0.182452 − 1.03474i
\(255\) −4.38137e8 + 3.67640e8i −1.65470 + 1.38846i
\(256\) −1.57654e7 − 5.73815e6i −0.0587308 − 0.0213763i
\(257\) 2.18249e8 − 7.94360e7i 0.802021 − 0.291912i 0.0916971 − 0.995787i \(-0.470771\pi\)
0.710324 + 0.703875i \(0.248549\pi\)
\(258\) −2.83550e7 −0.102792
\(259\) 3.90080e6 + 1.14956e7i 0.0139510 + 0.0411134i
\(260\) −6.76463e7 −0.238692
\(261\) −9.18104e8 + 3.34163e8i −3.19632 + 1.16337i
\(262\) 3.12501e8 + 1.13741e8i 1.07349 + 0.390718i
\(263\) −1.18325e8 + 9.92868e7i −0.401082 + 0.336548i −0.820912 − 0.571055i \(-0.806534\pi\)
0.419830 + 0.907603i \(0.362090\pi\)
\(264\) −2.25897e7 − 1.28112e8i −0.0755608 − 0.428527i
\(265\) 6.14444e8 2.02825
\(266\) −1.24257e6 − 7.04699e6i −0.00404796 − 0.0229571i
\(267\) −4.71595e8 + 8.16827e8i −1.51628 + 2.62628i
\(268\) −1.75955e8 − 1.47644e8i −0.558381 − 0.468537i
\(269\) 3.79628e7 + 6.57535e7i 0.118912 + 0.205962i 0.919337 − 0.393472i \(-0.128726\pi\)
−0.800425 + 0.599433i \(0.795393\pi\)
\(270\) 3.14166e8 − 5.44152e8i 0.971373 − 1.68247i
\(271\) 3.98209e8 − 1.44936e8i 1.21540 − 0.442369i 0.346825 − 0.937930i \(-0.387260\pi\)
0.868573 + 0.495561i \(0.165037\pi\)
\(272\) −6.38119e7 + 5.35445e7i −0.192270 + 0.161333i
\(273\) −5.30616e6 − 9.19053e6i −0.0157838 − 0.0273383i
\(274\) 1.36517e7 − 7.74226e7i 0.0400922 − 0.227374i
\(275\) −1.68001e7 + 9.52783e7i −0.0487134 + 0.276267i
\(276\) 1.91574e8 + 1.60749e8i 0.548471 + 0.460222i
\(277\) 4.77724e8 + 1.73877e8i 1.35051 + 0.491546i 0.913107 − 0.407719i \(-0.133676\pi\)
0.437404 + 0.899265i \(0.355898\pi\)
\(278\) 6.96704e7 + 2.53580e7i 0.194488 + 0.0707877i
\(279\) 9.70183e7 + 8.14081e7i 0.267448 + 0.224415i
\(280\) −1.16369e6 + 6.59963e6i −0.00316800 + 0.0179666i
\(281\) 3.12623e7 − 1.77298e8i 0.0840523 − 0.476684i −0.913505 − 0.406828i \(-0.866635\pi\)
0.997557 − 0.0698562i \(-0.0222540\pi\)
\(282\) −1.54203e8 − 2.67088e8i −0.409470 − 0.709222i
\(283\) −2.69477e8 + 2.26118e8i −0.706754 + 0.593037i −0.923686 − 0.383149i \(-0.874839\pi\)
0.216932 + 0.976187i \(0.430395\pi\)
\(284\) −1.15702e8 + 4.21119e7i −0.299726 + 0.109091i
\(285\) 3.19233e8 − 5.52929e8i 0.816867 − 1.41486i
\(286\) −3.81967e7 − 6.61587e7i −0.0965484 − 0.167227i
\(287\) −8.42863e6 − 7.07246e6i −0.0210460 − 0.0176597i
\(288\) 8.15882e7 − 1.41315e8i 0.201258 − 0.348589i
\(289\) 565511. + 3.20717e6i 0.00137816 + 0.00781591i
\(290\) 5.21429e8 1.25546
\(291\) −2.28449e8 − 1.29560e9i −0.543456 − 3.08209i
\(292\) 1.95310e8 − 1.63884e8i 0.459075 − 0.385210i
\(293\) −6.28232e8 − 2.28658e8i −1.45909 − 0.531067i −0.513978 − 0.857803i \(-0.671829\pi\)
−0.945115 + 0.326737i \(0.894051\pi\)
\(294\) 5.23123e8 − 1.90401e8i 1.20057 − 0.436972i
\(295\) 9.50843e8 2.15641
\(296\) −5.71919e7 + 1.47020e8i −0.128178 + 0.329500i
\(297\) 7.09581e8 1.57164
\(298\) 2.02950e8 − 7.38676e7i 0.444254 − 0.161695i
\(299\) 1.38002e8 + 5.02285e7i 0.298562 + 0.108668i
\(300\) −1.33791e8 + 1.12264e8i −0.286091 + 0.240059i
\(301\) 286445. + 1.62451e6i 0.000605422 + 0.00343352i
\(302\) −5.82484e8 −1.21691
\(303\) 1.17007e8 + 6.63581e8i 0.241637 + 1.37039i
\(304\) 4.64944e7 − 8.05306e7i 0.0949168 − 0.164401i
\(305\) 4.05925e8 + 3.40612e8i 0.819213 + 0.687401i
\(306\) −4.05093e8 − 7.01642e8i −0.808221 − 1.39988i
\(307\) −5.72120e7 + 9.90941e7i −0.112850 + 0.195462i −0.916918 − 0.399075i \(-0.869331\pi\)
0.804068 + 0.594537i \(0.202665\pi\)
\(308\) −7.11158e6 + 2.58841e6i −0.0138688 + 0.00504783i
\(309\) −1.09489e9 + 9.18723e8i −2.11114 + 1.77145i
\(310\) −3.37955e7 − 5.85356e7i −0.0644308 − 0.111597i
\(311\) 1.45623e7 − 8.25870e7i 0.0274517 − 0.155686i −0.968001 − 0.250948i \(-0.919258\pi\)
0.995452 + 0.0952617i \(0.0303688\pi\)
\(312\) 2.39474e7 − 1.35813e8i 0.0446393 − 0.253162i
\(313\) 3.21177e8 + 2.69499e8i 0.592023 + 0.496767i 0.888871 − 0.458158i \(-0.151491\pi\)
−0.296847 + 0.954925i \(0.595935\pi\)
\(314\) 2.52794e7 + 9.20095e6i 0.0460801 + 0.0167718i
\(315\) −6.12479e7 − 2.22924e7i −0.110409 − 0.0401856i
\(316\) −8.28143e6 − 6.94894e6i −0.0147639 − 0.0123884i
\(317\) −4.59025e7 + 2.60326e8i −0.0809336 + 0.458997i 0.917227 + 0.398366i \(0.130423\pi\)
−0.998160 + 0.0606314i \(0.980689\pi\)
\(318\) −2.17519e8 + 1.23361e9i −0.379317 + 2.15121i
\(319\) 2.94427e8 + 5.09963e8i 0.507821 + 0.879571i
\(320\) −6.67115e7 + 5.59776e7i −0.113809 + 0.0954969i
\(321\) −3.20919e8 + 1.16805e8i −0.541537 + 0.197103i
\(322\) 7.27432e6 − 1.25995e7i 0.0121422 − 0.0210309i
\(323\) −2.30849e8 − 3.99843e8i −0.381171 − 0.660207i
\(324\) 4.47331e8 + 3.75355e8i 0.730671 + 0.613105i
\(325\) −5.12815e7 + 8.88222e7i −0.0828646 + 0.143526i
\(326\) −1.19528e8 − 6.77878e8i −0.191077 − 1.08365i
\(327\) −1.10970e9 −1.75505
\(328\) −2.48286e7 − 1.40810e8i −0.0388502 − 0.220330i
\(329\) −1.37442e7 + 1.15327e7i −0.0212781 + 0.0178544i
\(330\) −6.34531e8 − 2.30950e8i −0.971972 − 0.353769i
\(331\) 9.76891e8 − 3.55559e8i 1.48063 − 0.538907i 0.529669 − 0.848204i \(-0.322316\pi\)
0.950965 + 0.309297i \(0.100094\pi\)
\(332\) −4.13682e8 −0.620416
\(333\) −1.31161e9 − 7.96106e8i −1.94648 − 1.18145i
\(334\) −3.19956e8 −0.469869
\(335\) −1.12037e9 + 4.07781e8i −1.62819 + 0.592612i
\(336\) −1.28380e7 − 4.67266e6i −0.0184634 − 0.00672012i
\(337\) −5.99098e8 + 5.02703e8i −0.852693 + 0.715495i −0.960381 − 0.278690i \(-0.910100\pi\)
0.107688 + 0.994185i \(0.465655\pi\)
\(338\) 7.31064e7 + 4.14607e8i 0.102979 + 0.584021i
\(339\) −1.71526e7 −0.0239129
\(340\) 7.50835e7 + 4.25820e8i 0.103602 + 0.587557i
\(341\) 3.81655e7 − 6.61047e7i 0.0521232 − 0.0902801i
\(342\) 6.92822e8 + 5.81347e8i 0.936549 + 0.785858i
\(343\) −3.24167e7 − 5.61473e7i −0.0433749 − 0.0751276i
\(344\) −1.07181e7 + 1.85643e7i −0.0141959 + 0.0245881i
\(345\) 1.21982e9 − 4.43977e8i 1.59929 − 0.582094i
\(346\) 1.90071e8 − 1.59488e8i 0.246689 − 0.206996i
\(347\) −3.87126e8 − 6.70523e8i −0.497393 − 0.861510i 0.502603 − 0.864518i \(-0.332376\pi\)
−0.999995 + 0.00300775i \(0.999043\pi\)
\(348\) −1.84591e8 + 1.04687e9i −0.234792 + 1.33157i
\(349\) −6.97994e7 + 3.95852e8i −0.0878947 + 0.498476i 0.908800 + 0.417233i \(0.137000\pi\)
−0.996694 + 0.0812429i \(0.974111\pi\)
\(350\) 7.78339e6 + 6.53104e6i 0.00970355 + 0.00814225i
\(351\) 7.06864e8 + 2.57278e8i 0.872491 + 0.317561i
\(352\) −9.24155e7 − 3.36365e7i −0.112939 − 0.0411066i
\(353\) −1.11897e9 − 9.38925e8i −1.35396 − 1.13611i −0.977797 − 0.209554i \(-0.932799\pi\)
−0.376163 − 0.926553i \(-0.622757\pi\)
\(354\) −3.36607e8 + 1.90899e9i −0.403285 + 2.28714i
\(355\) −1.10981e8 + 6.29407e8i −0.131659 + 0.746676i
\(356\) 3.56524e8 + 6.17517e8i 0.418807 + 0.725394i
\(357\) −5.19630e7 + 4.36022e7i −0.0604443 + 0.0507188i
\(358\) −1.02770e8 + 3.74053e7i −0.118379 + 0.0430866i
\(359\) 3.97698e8 − 6.88833e8i 0.453652 − 0.785748i −0.544958 − 0.838464i \(-0.683454\pi\)
0.998610 + 0.0527152i \(0.0167876\pi\)
\(360\) −4.23501e8 − 7.33524e8i −0.478404 − 0.828621i
\(361\) −2.89929e8 − 2.43279e8i −0.324352 − 0.272164i
\(362\) −2.65349e7 + 4.59598e7i −0.0293993 + 0.0509211i
\(363\) 1.54052e8 + 8.73672e8i 0.169042 + 0.958683i
\(364\) −8.02286e6 −0.00871915
\(365\) −2.29809e8 − 1.30331e9i −0.247367 − 1.40289i
\(366\) −8.27543e8 + 6.94391e8i −0.882281 + 0.740322i
\(367\) 5.67058e7 + 2.06392e7i 0.0598820 + 0.0217953i 0.371787 − 0.928318i \(-0.378745\pi\)
−0.311905 + 0.950113i \(0.600967\pi\)
\(368\) 1.77659e8 − 6.46625e7i 0.185831 − 0.0676371i
\(369\) 1.39065e9 1.44088
\(370\) 5.12464e8 + 6.38663e8i 0.525966 + 0.655490i
\(371\) 7.28731e7 0.0740898
\(372\) 1.29485e8 − 4.71287e7i 0.130412 − 0.0474663i
\(373\) 1.18011e9 + 4.29527e8i 1.17745 + 0.428558i 0.855301 − 0.518131i \(-0.173372\pi\)
0.322151 + 0.946688i \(0.395594\pi\)
\(374\) −3.74060e8 + 3.13873e8i −0.369735 + 0.310244i
\(375\) −2.24105e8 − 1.27096e9i −0.219454 − 1.24458i
\(376\) −2.33154e8 −0.226196
\(377\) 1.08399e8 + 6.14763e8i 0.104191 + 0.590899i
\(378\) 3.72601e7 − 6.45364e7i 0.0354832 − 0.0614587i
\(379\) 3.99494e8 + 3.35215e8i 0.376941 + 0.316291i 0.811500 − 0.584352i \(-0.198651\pi\)
−0.434559 + 0.900643i \(0.643096\pi\)
\(380\) −2.41339e8 − 4.18011e8i −0.225624 − 0.390792i
\(381\) 1.45190e9 − 2.51477e9i 1.34493 − 2.32949i
\(382\) −4.04927e8 + 1.47381e8i −0.371667 + 0.135276i
\(383\) −5.01068e8 + 4.20446e8i −0.455723 + 0.382397i −0.841554 − 0.540172i \(-0.818359\pi\)
0.385832 + 0.922569i \(0.373915\pi\)
\(384\) −8.87689e7 − 1.53752e8i −0.0800022 − 0.138568i
\(385\) −6.82146e6 + 3.86864e7i −0.00609207 + 0.0345499i
\(386\) 1.61069e8 − 9.13465e8i 0.142546 − 0.808419i
\(387\) −1.59713e8 − 1.34015e8i −0.140072 − 0.117534i
\(388\) −9.34598e8 − 3.40166e8i −0.812295 − 0.295651i
\(389\) −1.73052e9 − 6.29856e8i −1.49057 − 0.542523i −0.536969 − 0.843602i \(-0.680431\pi\)
−0.953599 + 0.301079i \(0.902653\pi\)
\(390\) −5.48364e8 − 4.60132e8i −0.468105 − 0.392786i
\(391\) 1.63004e8 − 9.24443e8i 0.137905 − 0.782098i
\(392\) 7.30814e7 − 4.14465e8i 0.0612782 − 0.347526i
\(393\) 1.75957e9 + 3.04767e9i 1.46229 + 2.53276i
\(394\) 1.00374e9 − 8.42238e8i 0.826769 − 0.693742i
\(395\) −5.27307e7 + 1.91924e7i −0.0430501 + 0.0156689i
\(396\) 4.78262e8 − 8.28375e8i 0.387020 − 0.670338i
\(397\) −6.99478e8 − 1.21153e9i −0.561057 − 0.971780i −0.997405 − 0.0720014i \(-0.977061\pi\)
0.436347 − 0.899778i \(-0.356272\pi\)
\(398\) 7.02190e8 + 5.89207e8i 0.558295 + 0.468465i
\(399\) 3.78611e7 − 6.55774e7i 0.0298393 − 0.0516831i
\(400\) 2.29279e7 + 1.30030e8i 0.0179124 + 0.101586i
\(401\) −1.80717e9 −1.39956 −0.699782 − 0.714356i \(-0.746720\pi\)
−0.699782 + 0.714356i \(0.746720\pi\)
\(402\) −4.22075e8 − 2.39371e9i −0.324040 − 1.83772i
\(403\) 6.19875e7 − 5.20137e7i 0.0471776 − 0.0395867i
\(404\) 4.78682e8 + 1.74226e8i 0.361171 + 0.131455i
\(405\) 2.84831e9 − 1.03670e9i 2.13057 − 0.775463i
\(406\) 6.18416e7 0.0458606
\(407\) −3.35254e8 + 8.61818e8i −0.246487 + 0.633629i
\(408\) −8.81493e8 −0.642552
\(409\) 2.07784e8 − 7.56271e7i 0.150169 − 0.0546570i −0.265842 − 0.964017i \(-0.585650\pi\)
0.416011 + 0.909360i \(0.363428\pi\)
\(410\) −6.97419e8 − 2.53840e8i −0.499747 − 0.181893i
\(411\) 6.37296e8 − 5.34755e8i 0.452788 − 0.379934i
\(412\) 1.87632e8 + 1.06411e9i 0.132180 + 0.749630i
\(413\) 1.12770e8 0.0787714
\(414\) 3.19307e8 + 1.81088e9i 0.221160 + 1.25426i
\(415\) −1.07365e9 + 1.85962e9i −0.737386 + 1.27719i
\(416\) −7.98659e7 − 6.70154e7i −0.0543920 − 0.0456403i
\(417\) 3.92287e8 + 6.79461e8i 0.264928 + 0.458869i
\(418\) 2.72546e8 − 4.72063e8i 0.182525 − 0.316143i
\(419\) −2.10840e9 + 7.67393e8i −1.40024 + 0.509646i −0.928250 − 0.371957i \(-0.878687\pi\)
−0.471992 + 0.881603i \(0.656465\pi\)
\(420\) −5.43242e7 + 4.55834e7i −0.0357784 + 0.0300216i
\(421\) 5.41850e7 + 9.38512e7i 0.0353909 + 0.0612988i 0.883178 − 0.469037i \(-0.155399\pi\)
−0.847787 + 0.530336i \(0.822066\pi\)
\(422\) 1.94893e8 − 1.10529e9i 0.126242 − 0.715952i
\(423\) 3.93777e8 − 2.23322e9i 0.252964 − 1.43463i
\(424\) 7.25437e8 + 6.08714e8i 0.462189 + 0.387822i
\(425\) 6.16037e8 + 2.24219e8i 0.389265 + 0.141681i
\(426\) −1.22436e9 − 4.45632e8i −0.767320 − 0.279282i
\(427\) 4.81428e7 + 4.03966e7i 0.0299250 + 0.0251100i
\(428\) −4.48332e7 + 2.54261e8i −0.0276405 + 0.156757i
\(429\) 1.40378e8 − 7.96121e8i 0.0858415 − 0.486831i
\(430\) 5.56347e7 + 9.63621e7i 0.0337447 + 0.0584476i
\(431\) −1.63848e9 + 1.37484e9i −0.985757 + 0.827148i −0.984948 − 0.172852i \(-0.944702\pi\)
−0.000808712 1.00000i \(0.500257\pi\)
\(432\) 9.09994e8 − 3.31211e8i 0.543057 − 0.197657i
\(433\) −1.71934e7 + 2.97798e7i −0.0101778 + 0.0176284i −0.871069 − 0.491160i \(-0.836573\pi\)
0.860892 + 0.508788i \(0.169906\pi\)
\(434\) −4.00815e6 − 6.94232e6i −0.00235359 − 0.00407653i
\(435\) 4.22689e9 + 3.54678e9i 2.46211 + 2.06596i
\(436\) −4.19465e8 + 7.26535e8i −0.242378 + 0.419811i
\(437\) 1.81962e8 + 1.03196e9i 0.104303 + 0.591531i
\(438\) 2.69799e9 1.53420
\(439\) −4.25053e8 − 2.41059e9i −0.239782 − 1.35987i −0.832304 − 0.554319i \(-0.812979\pi\)
0.592522 − 0.805554i \(-0.298132\pi\)
\(440\) −3.91057e8 + 3.28135e8i −0.218854 + 0.183641i
\(441\) 3.84645e9 + 1.39999e9i 2.13562 + 0.777304i
\(442\) −4.86431e8 + 1.77046e8i −0.267943 + 0.0975234i
\(443\) −6.32997e8 −0.345930 −0.172965 − 0.984928i \(-0.555335\pi\)
−0.172965 + 0.984928i \(0.555335\pi\)
\(444\) −1.46365e9 + 8.02774e8i −0.793593 + 0.435264i
\(445\) 3.70122e9 1.99106
\(446\) 1.94475e9 − 7.07831e8i 1.03799 − 0.377796i
\(447\) 2.14763e9 + 7.81673e8i 1.13732 + 0.413951i
\(448\) −7.91199e6 + 6.63894e6i −0.00415731 + 0.00348840i
\(449\) 2.33369e8 + 1.32350e9i 0.121669 + 0.690020i 0.983231 + 0.182367i \(0.0583759\pi\)
−0.861561 + 0.507653i \(0.830513\pi\)
\(450\) −1.28419e9 −0.664335
\(451\) −1.45543e8 − 8.25414e8i −0.0747090 − 0.423696i
\(452\) −6.48366e6 + 1.12300e7i −0.00330244 + 0.00572000i
\(453\) −4.72181e9 − 3.96207e9i −2.38652 − 2.00253i
\(454\) 1.00846e9 + 1.74671e9i 0.505784 + 0.876044i
\(455\) −2.08222e7 + 3.60650e7i −0.0103630 + 0.0179493i
\(456\) 9.24671e8 − 3.36553e8i 0.456678 − 0.166217i
\(457\) 7.51264e8 − 6.30385e8i 0.368202 − 0.308958i −0.439848 − 0.898072i \(-0.644968\pi\)
0.808050 + 0.589114i \(0.200523\pi\)
\(458\) −1.15827e9 − 2.00619e9i −0.563354 − 0.975758i
\(459\) 8.34931e8 − 4.73513e9i 0.403001 − 2.28553i
\(460\) 1.70411e8 − 9.66449e8i 0.0816292 − 0.462942i
\(461\) −2.51146e9 − 2.10736e9i −1.19391 − 1.00181i −0.999783 − 0.0208368i \(-0.993367\pi\)
−0.194131 − 0.980976i \(-0.562189\pi\)
\(462\) −7.52554e7 − 2.73907e7i −0.0355051 − 0.0129228i
\(463\) −1.46882e9 − 5.34607e8i −0.687757 − 0.250323i −0.0255826 − 0.999673i \(-0.508144\pi\)
−0.662175 + 0.749350i \(0.730366\pi\)
\(464\) 6.15620e8 + 5.16567e8i 0.286088 + 0.240056i
\(465\) 1.24203e8 − 7.04388e8i 0.0572856 − 0.324883i
\(466\) −7.44548e7 + 4.22254e8i −0.0340833 + 0.193296i
\(467\) 1.90363e8 + 3.29718e8i 0.0864915 + 0.149808i 0.906026 − 0.423222i \(-0.139101\pi\)
−0.819534 + 0.573030i \(0.805768\pi\)
\(468\) 7.76781e8 − 6.51797e8i 0.350298 − 0.293935i
\(469\) −1.32876e8 + 4.83629e7i −0.0594759 + 0.0216475i
\(470\) −6.05117e8 + 1.04809e9i −0.268842 + 0.465647i
\(471\) 1.42338e8 + 2.46537e8i 0.0627695 + 0.108720i
\(472\) 1.12260e9 + 9.41975e8i 0.491393 + 0.412328i
\(473\) −6.28287e7 + 1.08822e8i −0.0272988 + 0.0472829i
\(474\) −1.98652e7 − 1.12661e8i −0.00856778 − 0.0485903i
\(475\) −7.31820e8 −0.313312
\(476\) 8.90491e6 + 5.05023e7i 0.00378447 + 0.0214628i
\(477\) −7.05565e9 + 5.92039e9i −2.97662 + 2.49768i
\(478\) 5.31349e8 + 1.93395e8i 0.222527 + 0.0809931i
\(479\) 2.75265e9 − 1.00188e9i 1.14440 − 0.416526i 0.300897 − 0.953657i \(-0.402714\pi\)
0.843499 + 0.537130i \(0.180492\pi\)
\(480\) −9.21547e8 −0.380341
\(481\) −6.46446e8 + 7.36964e8i −0.264865 + 0.301952i
\(482\) 9.87350e8 0.401612
\(483\) 1.44670e8 − 5.26557e7i 0.0584204 − 0.0212633i
\(484\) 6.30234e8 + 2.29386e8i 0.252664 + 0.0919621i
\(485\) −3.95475e9 + 3.31843e9i −1.57407 + 1.32080i
\(486\) 3.54748e8 + 2.01188e9i 0.140182 + 0.795014i
\(487\) −1.30290e9 −0.511164 −0.255582 − 0.966787i \(-0.582267\pi\)
−0.255582 + 0.966787i \(0.582267\pi\)
\(488\) 1.41816e8 + 8.04280e8i 0.0552404 + 0.313284i
\(489\) 3.64201e9 − 6.30815e9i 1.40851 − 2.43961i
\(490\) −1.67347e9 − 1.40421e9i −0.642586 − 0.539194i
\(491\) 2.41485e9 + 4.18264e9i 0.920672 + 1.59465i 0.798377 + 0.602158i \(0.205692\pi\)
0.122295 + 0.992494i \(0.460975\pi\)
\(492\) 7.56524e8 − 1.31034e9i 0.286381 − 0.496027i
\(493\) 3.74949e9 − 1.36470e9i 1.40932 − 0.512949i
\(494\) 4.42662e8 − 3.71437e8i 0.165207 − 0.138625i
\(495\) −2.48252e9 − 4.29985e9i −0.919972 − 1.59344i
\(496\) 1.80893e7 − 1.02590e8i 0.00665636 − 0.0377501i
\(497\) −1.31624e7 + 7.46477e7i −0.00480937 + 0.0272753i
\(498\) −3.35345e9 − 2.81387e9i −1.21671 − 1.02094i
\(499\) −7.55913e8 − 2.75130e8i −0.272345 − 0.0991256i 0.202237 − 0.979337i \(-0.435179\pi\)
−0.474583 + 0.880211i \(0.657401\pi\)
\(500\) −9.16825e8 − 3.33697e8i −0.328013 − 0.119387i
\(501\) −2.59367e9 − 2.17635e9i −0.921473 − 0.773208i
\(502\) 4.31501e8 − 2.44716e9i 0.152236 − 0.863376i
\(503\) −6.03346e8 + 3.42175e9i −0.211387 + 1.19884i 0.675680 + 0.737195i \(0.263850\pi\)
−0.887067 + 0.461641i \(0.847261\pi\)
\(504\) −5.02272e7 − 8.69961e7i −0.0174756 − 0.0302686i
\(505\) 2.02555e9 − 1.69963e9i 0.699878 − 0.587267i
\(506\) 1.04142e9 − 3.79046e8i 0.357354 − 0.130066i
\(507\) −2.22754e9 + 3.85822e9i −0.759099 + 1.31480i
\(508\) −1.09763e9 − 1.90115e9i −0.371479 − 0.643420i
\(509\) −1.99509e9 − 1.67408e9i −0.670581 − 0.562684i 0.242657 − 0.970112i \(-0.421981\pi\)
−0.913237 + 0.407428i \(0.866426\pi\)
\(510\) −2.28779e9 + 3.96256e9i −0.763695 + 1.32276i
\(511\) −2.72553e7 − 1.54573e8i −0.00903605 − 0.0512460i
\(512\) −1.34218e8 −0.0441942
\(513\) 9.32038e8 + 5.28585e9i 0.304806 + 1.72864i
\(514\) 1.42334e9 − 1.19433e9i 0.462316 − 0.387929i
\(515\) 5.27046e9 + 1.91829e9i 1.70029 + 0.618855i
\(516\) −2.13160e8 + 7.75839e7i −0.0683017 + 0.0248598i
\(517\) −1.36673e9 −0.434975
\(518\) 6.07783e7 + 7.57455e7i 0.0192130 + 0.0239443i
\(519\) 2.62563e9 0.824417
\(520\) −5.08534e8 + 1.85091e8i −0.158602 + 0.0577263i
\(521\) −2.80675e9 − 1.02157e9i −0.869504 − 0.316473i −0.131538 − 0.991311i \(-0.541991\pi\)
−0.737966 + 0.674838i \(0.764214\pi\)
\(522\) −5.98756e9 + 5.02416e9i −1.84248 + 1.54603i
\(523\) −2.11004e8 − 1.19667e9i −0.0644964 − 0.365777i −0.999925 − 0.0122612i \(-0.996097\pi\)
0.935428 − 0.353516i \(-0.115014\pi\)
\(524\) 2.66045e9 0.807786
\(525\) 1.86705e7 + 1.05886e8i 0.00563117 + 0.0319360i
\(526\) −6.17851e8 + 1.07015e9i −0.185112 + 0.320623i
\(527\) −3.96218e8 − 3.32466e8i −0.117923 − 0.0989488i
\(528\) −5.20355e8 − 9.01282e8i −0.153844 − 0.266466i
\(529\) 6.37163e8 − 1.10360e9i 0.187135 − 0.324128i
\(530\) 4.61911e9 − 1.68122e9i 1.34770 − 0.490522i
\(531\) −1.09185e10 + 9.16172e9i −3.16470 + 2.65550i
\(532\) −2.86228e7 − 4.95762e7i −0.00824179 − 0.0142752i
\(533\) 1.54290e8 − 8.75025e8i 0.0441361 − 0.250308i
\(534\) −1.31027e9 + 7.43089e9i −0.372362 + 2.11177i
\(535\) 1.02662e9 + 8.61436e8i 0.289849 + 0.243212i
\(536\) −1.72673e9 − 6.28478e8i −0.484337 − 0.176284i
\(537\) −1.08752e9 − 3.95826e8i −0.303060 − 0.110305i
\(538\) 4.65299e8 + 3.90433e8i 0.128823 + 0.108096i
\(539\) 4.28397e8 − 2.42956e9i 0.117838 − 0.668293i
\(540\) 8.72870e8 − 4.95029e9i 0.238546 − 1.35286i
\(541\) 2.50031e9 + 4.33066e9i 0.678896 + 1.17588i 0.975314 + 0.220823i \(0.0708744\pi\)
−0.296418 + 0.955058i \(0.595792\pi\)
\(542\) 2.59698e9 − 2.17913e9i 0.700603 − 0.587875i
\(543\) −5.27721e8 + 1.92075e8i −0.141451 + 0.0514838i
\(544\) −3.33202e8 + 5.77123e8i −0.0887384 + 0.153699i
\(545\) 2.17732e9 + 3.77123e9i 0.576149 + 0.997919i
\(546\) −6.50360e7 − 5.45717e7i −0.0170994 − 0.0143481i
\(547\) −1.28006e9 + 2.21713e9i −0.334407 + 0.579209i −0.983371 − 0.181610i \(-0.941869\pi\)
0.648964 + 0.760819i \(0.275203\pi\)
\(548\) −1.09214e8 − 6.19381e8i −0.0283494 − 0.160778i
\(549\) −7.94315e9 −2.04875
\(550\) 1.34401e8 + 7.62226e8i 0.0344456 + 0.195350i
\(551\) −3.41211e9 + 2.86310e9i −0.868946 + 0.729132i
\(552\) 1.88000e9 + 6.84264e8i 0.475741 + 0.173156i
\(553\) −6.25387e6 + 2.27622e6i −0.00157257 + 0.000572370i
\(554\) 4.06707e9 1.01624
\(555\) −1.89998e8 + 8.66302e9i −0.0471764 + 2.15102i
\(556\) 5.93134e8 0.146349
\(557\) 2.96846e9 − 1.08043e9i 0.727844 − 0.264914i 0.0485920 − 0.998819i \(-0.484527\pi\)
0.679252 + 0.733905i \(0.262304\pi\)
\(558\) 9.52085e8 + 3.46531e8i 0.231983 + 0.0844349i
\(559\) −1.02045e8 + 8.56256e7i −0.0247086 + 0.0207330i
\(560\) 9.30955e6 + 5.27971e7i 0.00224012 + 0.0127043i
\(561\) −5.16723e9 −1.23563
\(562\) −2.50099e8 − 1.41838e9i −0.0594339 − 0.337067i
\(563\) 2.27855e9 − 3.94656e9i 0.538120 − 0.932051i −0.460886 − 0.887460i \(-0.652468\pi\)
0.999005 − 0.0445912i \(-0.0141985\pi\)
\(564\) −1.89002e9 − 1.58592e9i −0.443599 − 0.372224i
\(565\) 3.36548e7 + 5.82918e7i 0.00785014 + 0.0135968i
\(566\) −1.40711e9 + 2.43718e9i −0.326189 + 0.564976i
\(567\) 3.37810e8 − 1.22953e8i 0.0778273 − 0.0283268i
\(568\) −7.54566e8 + 6.33156e8i −0.172774 + 0.144974i
\(569\) −3.17486e9 − 5.49902e9i −0.722489 − 1.25139i −0.959999 − 0.280003i \(-0.909664\pi\)
0.237510 − 0.971385i \(-0.423669\pi\)
\(570\) 8.86949e8 − 5.03014e9i 0.200603 − 1.13767i
\(571\) 1.08657e8 − 6.16222e8i 0.0244247 − 0.138519i −0.970157 − 0.242478i \(-0.922040\pi\)
0.994582 + 0.103958i \(0.0331509\pi\)
\(572\) −4.68167e8 − 3.92838e8i −0.104596 − 0.0877663i
\(573\) −4.28497e9 − 1.55960e9i −0.951494 − 0.346316i
\(574\) −8.27140e7 − 3.01054e7i −0.0182552 − 0.00664436i
\(575\) −1.13980e9 − 9.56405e8i −0.250029 − 0.209799i
\(576\) 2.26682e8 − 1.28558e9i 0.0494241 − 0.280298i
\(577\) −8.28913e8 + 4.70100e9i −0.179636 + 1.01877i 0.753019 + 0.657999i \(0.228597\pi\)
−0.932655 + 0.360769i \(0.882514\pi\)
\(578\) 1.30266e7 + 2.25627e7i 0.00280597 + 0.00486008i
\(579\) 7.51909e9 − 6.30927e9i 1.60987 − 1.35084i
\(580\) 3.91987e9 − 1.42671e9i 0.834206 − 0.303626i
\(581\) −1.27335e8 + 2.20551e8i −0.0269359 + 0.0466543i
\(582\) −5.26235e9 − 9.11466e9i −1.10649 − 1.91651i
\(583\) 4.25245e9 + 3.56823e9i 0.888789 + 0.745783i
\(584\) 1.01983e9 − 1.76641e9i 0.211877 − 0.366982i
\(585\) −9.13991e8 − 5.18350e9i −0.188754 − 1.07048i
\(586\) −5.34840e9 −1.09795
\(587\) 8.64782e8 + 4.90442e9i 0.176471 + 1.00082i 0.936432 + 0.350848i \(0.114107\pi\)
−0.759961 + 0.649968i \(0.774782\pi\)
\(588\) 3.41163e9 − 2.86270e9i 0.692056 − 0.580704i
\(589\) 5.42562e8 + 1.97476e8i 0.109407 + 0.0398209i
\(590\) 7.14800e9 − 2.60166e9i 1.43286 − 0.521517i
\(591\) 1.38656e10 2.76301
\(592\) −2.76721e7 + 1.26172e9i −0.00548171 + 0.249940i
\(593\) 3.37891e9 0.665404 0.332702 − 0.943032i \(-0.392040\pi\)
0.332702 + 0.943032i \(0.392040\pi\)
\(594\) 5.33430e9 − 1.94153e9i 1.04430 − 0.380094i
\(595\) 2.50134e8 + 9.10412e7i 0.0486813 + 0.0177186i
\(596\) 1.32357e9 − 1.11061e9i 0.256085 − 0.214881i
\(597\) 1.68439e9 + 9.55263e9i 0.323990 + 1.83744i
\(598\) 1.17487e9 0.224664
\(599\) −6.80013e8 − 3.85654e9i −0.129278 − 0.733169i −0.978675 − 0.205415i \(-0.934145\pi\)
0.849397 − 0.527754i \(-0.176966\pi\)
\(600\) −6.98609e8 + 1.21003e9i −0.132040 + 0.228700i
\(601\) −1.69762e9 − 1.42447e9i −0.318992 − 0.267666i 0.469205 − 0.883089i \(-0.344541\pi\)
−0.788197 + 0.615423i \(0.788985\pi\)
\(602\) 6.59828e6 + 1.14285e7i 0.00123266 + 0.00213503i
\(603\) 8.93606e9 − 1.54777e10i 1.65972 − 2.87472i
\(604\) −4.37884e9 + 1.59377e9i −0.808594 + 0.294304i
\(605\) 2.66684e9 − 2.23774e9i 0.489613 − 0.410834i
\(606\) 2.69527e9 + 4.66835e9i 0.491981 + 0.852136i
\(607\) 3.46262e7 − 1.96375e8i 0.00628412 − 0.0356390i −0.981504 − 0.191439i \(-0.938685\pi\)
0.987789 + 0.155800i \(0.0497956\pi\)
\(608\) 1.29179e8 − 7.32609e8i 0.0233092 − 0.132193i
\(609\) 5.01309e8 + 4.20648e8i 0.0899384 + 0.0754673i
\(610\) 3.98353e9 + 1.44989e9i 0.710581 + 0.258630i
\(611\) −1.36149e9 − 4.95543e8i −0.241475 − 0.0878896i
\(612\) −4.96511e9 − 4.16622e9i −0.875587 − 0.734704i
\(613\) 2.61903e8 − 1.48533e9i 0.0459229 − 0.260442i −0.953199 − 0.302344i \(-0.902231\pi\)
0.999122 + 0.0419026i \(0.0133419\pi\)
\(614\) −1.58956e8 + 9.01485e8i −0.0277133 + 0.157170i
\(615\) −3.92689e9 − 6.80158e9i −0.680748 − 1.17909i
\(616\) −4.63793e7 + 3.89169e7i −0.00799451 + 0.00670819i
\(617\) 4.10020e9 − 1.49235e9i 0.702760 − 0.255784i 0.0341714 − 0.999416i \(-0.489121\pi\)
0.668589 + 0.743632i \(0.266899\pi\)
\(618\) −5.71712e9 + 9.90233e9i −0.974355 + 1.68763i
\(619\) −8.96347e8 − 1.55252e9i −0.151900 − 0.263099i 0.780026 − 0.625747i \(-0.215206\pi\)
−0.931926 + 0.362648i \(0.881873\pi\)
\(620\) −4.14222e8 − 3.47574e8i −0.0698011 − 0.0585701i
\(621\) −5.45637e9 + 9.45070e9i −0.914288 + 1.58359i
\(622\) −1.16499e8 − 6.60696e8i −0.0194113 − 0.110087i
\(623\) 4.38965e8 0.0727314
\(624\) −1.91579e8 − 1.08650e9i −0.0315648 − 0.179013i
\(625\) −5.80875e9 + 4.87412e9i −0.951706 + 0.798576i
\(626\) 3.15185e9 + 1.14718e9i 0.513518 + 0.186905i
\(627\) 5.42034e9 − 1.97284e9i 0.878193 − 0.319636i
\(628\) 2.15214e8 0.0346747
\(629\) 5.35656e9 + 3.25126e9i 0.858239 + 0.520924i
\(630\) −5.21430e8 −0.0830814
\(631\) −4.60265e9 + 1.67523e9i −0.729299 + 0.265443i −0.679868 − 0.733335i \(-0.737963\pi\)
−0.0494308 + 0.998778i \(0.515741\pi\)
\(632\) −8.12694e7 − 2.95796e7i −0.0128061 − 0.00466104i
\(633\) 9.09810e9 − 7.63421e9i 1.42573 − 1.19633i
\(634\) 3.67220e8 + 2.08261e9i 0.0572287 + 0.324560i
\(635\) −1.13950e10 −1.76606
\(636\) 1.74015e9 + 9.86889e9i 0.268218 + 1.52114i
\(637\) 1.30766e9 − 2.26493e9i 0.200450 − 0.347190i
\(638\) 3.60871e9 + 3.02807e9i 0.550148 + 0.461629i
\(639\) −4.79017e9 − 8.29681e9i −0.726269 − 1.25794i
\(640\) −3.48343e8 + 6.03347e8i −0.0525263 + 0.0909782i
\(641\) −4.79848e9 + 1.74650e9i −0.719615 + 0.261919i −0.675762 − 0.737119i \(-0.736185\pi\)
−0.0438528 + 0.999038i \(0.513963\pi\)
\(642\) −2.09293e9 + 1.75617e9i −0.312163 + 0.261936i
\(643\) −3.88871e9 − 6.73544e9i −0.576856 − 0.999143i −0.995837 − 0.0911486i \(-0.970946\pi\)
0.418982 − 0.907995i \(-0.362387\pi\)
\(644\) 2.02108e7 − 1.14621e8i 0.00298182 − 0.0169108i
\(645\) −2.04464e8 + 1.15957e9i −0.0300025 + 0.170153i
\(646\) −2.82945e9 − 2.37419e9i −0.412942 − 0.346499i
\(647\) −3.30044e9 − 1.20126e9i −0.479078 − 0.174370i 0.0911821 − 0.995834i \(-0.470935\pi\)
−0.570260 + 0.821464i \(0.693158\pi\)
\(648\) 4.38986e9 + 1.59778e9i 0.633780 + 0.230677i
\(649\) 6.58059e9 + 5.52177e9i 0.944949 + 0.792907i
\(650\) −1.42479e8 + 8.08039e8i −0.0203495 + 0.115408i
\(651\) 1.47304e7 − 8.35404e7i 0.00209258 − 0.0118676i
\(652\) −2.75334e9 − 4.76893e9i −0.389039 − 0.673836i
\(653\) 2.63081e9 − 2.20752e9i 0.369738 − 0.310247i −0.438920 − 0.898526i \(-0.644639\pi\)
0.808658 + 0.588279i \(0.200194\pi\)
\(654\) −8.34224e9 + 3.03633e9i −1.16617 + 0.424450i
\(655\) 6.90482e9 − 1.19595e10i 0.960081 − 1.66291i
\(656\) −5.71928e8 − 9.90608e8i −0.0791003 − 0.137006i
\(657\) 1.51968e10 + 1.27516e10i 2.09061 + 1.75423i
\(658\) −7.17669e7 + 1.24304e8i −0.00982049 + 0.0170096i
\(659\) −3.94506e7 − 2.23735e8i −0.00536975 − 0.0304534i 0.982005 − 0.188854i \(-0.0604773\pi\)
−0.987375 + 0.158401i \(0.949366\pi\)
\(660\) −5.40203e9 −0.731397
\(661\) 8.15995e7 + 4.62774e8i 0.0109896 + 0.0623252i 0.989809 − 0.142399i \(-0.0454815\pi\)
−0.978820 + 0.204724i \(0.934370\pi\)
\(662\) 6.37095e9 − 5.34586e9i 0.853495 − 0.716168i
\(663\) −5.14745e9 − 1.87352e9i −0.685954 − 0.249667i
\(664\) −3.10987e9 + 1.13190e9i −0.412243 + 0.150044i
\(665\) −2.97145e8 −0.0391826
\(666\) −1.20384e10 − 2.39598e9i −1.57909 − 0.314285i
\(667\) −9.05607e9 −1.18168
\(668\) −2.40528e9 + 8.75450e8i −0.312211 + 0.113635i
\(669\) 2.05795e10 + 7.49032e9i 2.65732 + 0.967184i
\(670\) −7.30667e9 + 6.13102e9i −0.938550 + 0.787537i
\(671\) 8.31314e8 + 4.71461e9i 0.106227 + 0.602445i
\(672\) −1.09296e8 −0.0138935
\(673\) −1.14544e9 − 6.49612e9i −0.144851 − 0.821488i −0.967487 − 0.252921i \(-0.918609\pi\)
0.822636 − 0.568568i \(-0.192502\pi\)
\(674\) −3.12827e9 + 5.41831e9i −0.393545 + 0.681639i
\(675\) −5.83822e9 − 4.89884e9i −0.730663 − 0.613099i
\(676\) 1.68401e9 + 2.91679e9i 0.209668 + 0.363155i
\(677\) 5.38935e9 − 9.33463e9i 0.667538 − 1.15621i −0.311052 − 0.950393i \(-0.600681\pi\)
0.978590 − 0.205817i \(-0.0659852\pi\)
\(678\) −1.28946e8 + 4.69324e7i −0.0158892 + 0.00578321i
\(679\) −4.69034e8 + 3.93566e8i −0.0574990 + 0.0482474i
\(680\) 1.72956e9 + 2.99568e9i 0.210937 + 0.365354i
\(681\) −3.70623e9 + 2.10190e10i −0.449694 + 2.55034i
\(682\) 1.06038e8 − 6.01372e8i 0.0128002 − 0.0725935i
\(683\) −2.98392e9 − 2.50380e9i −0.358356 − 0.300696i 0.445779 − 0.895143i \(-0.352927\pi\)
−0.804135 + 0.594447i \(0.797371\pi\)
\(684\) 6.79898e9 + 2.47463e9i 0.812358 + 0.295674i
\(685\) −3.06774e9 − 1.11657e9i −0.364671 − 0.132730i
\(686\) −3.97322e8 − 3.33393e8i −0.0469903 − 0.0394295i
\(687\) 4.25679e9 − 2.41415e10i 0.500880 − 2.84063i
\(688\) −2.97789e7 + 1.68885e8i −0.00348618 + 0.0197711i
\(689\) 2.94241e9 + 5.09640e9i 0.342717 + 0.593604i
\(690\) 7.95523e9 − 6.67523e9i 0.921893 − 0.773560i
\(691\) −2.26693e9 + 8.25097e8i −0.261376 + 0.0951331i −0.469384 − 0.882994i \(-0.655524\pi\)
0.208008 + 0.978127i \(0.433302\pi\)
\(692\) 9.92480e8 − 1.71903e9i 0.113855 − 0.197202i
\(693\) −2.94427e8 − 5.09963e8i −0.0336056 − 0.0582066i
\(694\) −4.74490e9 − 3.98144e9i −0.538851 − 0.452150i
\(695\) 1.53939e9 − 2.66631e9i 0.173941 − 0.301275i
\(696\) 1.47673e9 + 8.37493e9i 0.166023 + 0.941562i
\(697\) −5.67936e9 −0.635308
\(698\) 5.58395e8 + 3.16682e9i 0.0621510 + 0.352476i
\(699\) −3.47574e9 + 2.91649e9i −0.384926 + 0.322991i
\(700\) 7.63820e7 + 2.78008e7i 0.00841681 + 0.00306347i
\(701\) 4.36466e9 − 1.58860e9i 0.478561 − 0.174182i −0.0914657 − 0.995808i \(-0.529155\pi\)
0.570026 + 0.821626i \(0.306933\pi\)
\(702\) 6.01783e9 0.656539
\(703\) −6.86027e9 − 1.36539e9i −0.744727 − 0.148222i
\(704\) −7.86772e8 −0.0849855
\(705\) −1.20344e10 + 4.38018e9i −1.29349 + 0.470793i
\(706\) −1.09809e10 − 3.99673e9i −1.17442 − 0.427453i
\(707\) 2.40230e8 − 2.01577e8i 0.0255658 − 0.0214522i
\(708\) 2.69286e9 + 1.52720e10i 0.285165 + 1.61725i
\(709\) 9.77474e9 1.03001 0.515007 − 0.857186i \(-0.327789\pi\)
0.515007 + 0.857186i \(0.327789\pi\)
\(710\) 8.87851e8 + 5.03525e9i 0.0930971 + 0.527980i
\(711\) 4.20580e8 − 7.28466e8i 0.0438839 − 0.0760091i
\(712\) 4.36981e9 + 3.66671e9i 0.453714 + 0.380712i
\(713\) 5.86953e8 + 1.01663e9i 0.0606443 + 0.105039i
\(714\) −2.71332e8 + 4.69960e8i −0.0278969 + 0.0483189i
\(715\) −2.98098e9 + 1.08499e9i −0.304992 + 0.111008i
\(716\) −6.70232e8 + 5.62391e8i −0.0682385 + 0.0572589i
\(717\) 2.99182e9 + 5.18198e9i 0.303122 + 0.525023i
\(718\) 1.10495e9 − 6.26650e9i 0.111406 − 0.631814i
\(719\) −7.01152e8 + 3.97643e9i −0.0703495 + 0.398972i 0.929217 + 0.369534i \(0.120483\pi\)
−0.999567 + 0.0294375i \(0.990628\pi\)
\(720\) −5.19072e9 − 4.35553e9i −0.518280 − 0.434888i
\(721\) 6.25077e8 + 2.27509e8i 0.0621098 + 0.0226061i
\(722\) −2.84521e9 − 1.03557e9i −0.281341 − 0.102400i
\(723\) 8.00380e9 + 6.71599e9i 0.787612 + 0.660885i
\(724\) −7.37237e7 + 4.18108e8i −0.00721975 + 0.0409453i
\(725\) 1.09825e9 − 6.22850e9i 0.107033 − 0.607017i
\(726\) 3.54860e9 + 6.14635e9i 0.344175 + 0.596128i
\(727\) 5.04735e9 − 4.23523e9i 0.487184 − 0.408796i −0.365832 − 0.930681i \(-0.619215\pi\)
0.853016 + 0.521885i \(0.174771\pi\)
\(728\) −6.03122e7 + 2.19518e7i −0.00579355 + 0.00210868i
\(729\) −8.31818e8 + 1.44075e9i −0.0795210 + 0.137734i
\(730\) −5.29366e9 − 9.16890e9i −0.503647 − 0.872342i
\(731\) 6.52260e8 + 5.47311e8i 0.0617604 + 0.0518231i
\(732\) −4.32112e9 + 7.48441e9i −0.407200 + 0.705291i
\(733\) 5.82537e8 + 3.30373e9i 0.0546336 + 0.309843i 0.999863 − 0.0165648i \(-0.00527299\pi\)
−0.945229 + 0.326407i \(0.894162\pi\)
\(734\) 4.82760e8 0.0450604
\(735\) −4.01425e9 − 2.27660e10i −0.372906 − 2.11485i
\(736\) 1.15863e9 − 9.72206e8i 0.107120 − 0.0898847i
\(737\) −1.01219e10 − 3.68408e9i −0.931381 − 0.338995i
\(738\) 1.04543e10 − 3.80505e9i 0.957409 − 0.348468i
\(739\) −1.75068e10 −1.59570 −0.797851 − 0.602855i \(-0.794030\pi\)
−0.797851 + 0.602855i \(0.794030\pi\)
\(740\) 5.59995e9 + 3.39899e9i 0.508011 + 0.308347i
\(741\) 6.11490e9 0.552110
\(742\) 5.47827e8 − 1.99393e8i 0.0492300 − 0.0179182i
\(743\) 1.40884e10 + 5.12776e9i 1.26009 + 0.458635i 0.883799 − 0.467867i \(-0.154977\pi\)
0.376290 + 0.926502i \(0.377200\pi\)
\(744\) 8.44457e8 − 7.08584e8i 0.0751748 − 0.0630791i
\(745\) −1.55736e9 − 8.83223e9i −0.137988 − 0.782571i
\(746\) 1.00468e10 0.886018
\(747\) −5.58938e9 − 3.16990e10i −0.490616 − 2.78242i
\(748\) −1.95320e9 + 3.38304e9i −0.170644 + 0.295564i
\(749\) 1.21757e8 + 1.02166e8i 0.0105879 + 0.00888427i
\(750\) −5.16228e9 − 8.94134e9i −0.446815 − 0.773906i
\(751\) −8.32639e9 + 1.44217e10i −0.717327 + 1.24245i 0.244728 + 0.969592i \(0.421301\pi\)
−0.962055 + 0.272855i \(0.912032\pi\)
\(752\) −1.75274e9 + 6.37946e8i −0.150299 + 0.0547043i
\(753\) 2.01436e10 − 1.69025e10i 1.71931 − 1.44267i
\(754\) 2.49699e9 + 4.32491e9i 0.212137 + 0.367432i
\(755\) −4.20021e9 + 2.38206e10i −0.355186 + 2.01436i
\(756\) 1.03522e8 − 5.87105e8i 0.00871381 − 0.0494185i
\(757\) 6.29563e9 + 5.28266e9i 0.527477 + 0.442606i 0.867229