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Properties

Label 74.8.f.b.7.7
Level $74$
Weight $8$
Character 74.7
Analytic conductor $23.116$
Analytic rank $0$
Dimension $66$
Inner twists $2$

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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 7.7
Character \(\chi\) \(=\) 74.7
Dual form 74.8.f.b.53.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(7.51754 - 2.73616i) q^{2} +(25.6856 + 9.34879i) q^{3} +(49.0268 - 41.1384i) q^{4} +(46.1726 + 261.858i) q^{5} +218.672 q^{6} +(-206.971 - 1173.79i) q^{7} +(256.000 - 443.405i) q^{8} +(-1102.99 - 925.518i) q^{9} +O(q^{10})\) \(q+(7.51754 - 2.73616i) q^{2} +(25.6856 + 9.34879i) q^{3} +(49.0268 - 41.1384i) q^{4} +(46.1726 + 261.858i) q^{5} +218.672 q^{6} +(-206.971 - 1173.79i) q^{7} +(256.000 - 443.405i) q^{8} +(-1102.99 - 925.518i) q^{9} +(1063.59 + 1842.19i) q^{10} +(2460.07 - 4260.96i) q^{11} +(1643.88 - 598.323i) q^{12} +(5749.47 - 4824.38i) q^{13} +(-4767.60 - 8257.72i) q^{14} +(-1262.08 + 7157.63i) q^{15} +(711.263 - 4033.77i) q^{16} +(15827.8 + 13281.1i) q^{17} +(-10824.1 - 3939.66i) q^{18} +(45611.6 + 16601.3i) q^{19} +(13036.1 + 10938.6i) q^{20} +(5657.36 - 32084.5i) q^{21} +(6834.98 - 38763.1i) q^{22} +(-12636.0 - 21886.2i) q^{23} +(10720.8 - 8995.83i) q^{24} +(6975.87 - 2539.01i) q^{25} +(30021.6 - 51998.9i) q^{26} +(-49568.2 - 85854.7i) q^{27} +(-58435.1 - 49032.8i) q^{28} +(-56852.0 + 98470.5i) q^{29} +(10096.7 + 57261.1i) q^{30} +111177. q^{31} +(-5690.10 - 32270.2i) q^{32} +(103023. - 86446.6i) q^{33} +(155326. + 56533.9i) q^{34} +(297810. - 108394. i) q^{35} -92150.4 q^{36} +(-306309. - 33270.7i) q^{37} +388311. q^{38} +(192781. - 70166.4i) q^{39} +(127929. + 46562.4i) q^{40} +(-297583. + 249702. i) q^{41} +(-45258.9 - 256676. i) q^{42} +189203. q^{43} +(-54679.8 - 310105. i) q^{44} +(191426. - 331560. i) q^{45} +(-154876. - 129956. i) q^{46} +(-453281. - 785105. i) q^{47} +(55980.1 - 96960.4i) q^{48} +(-561072. + 204214. i) q^{49} +(45494.3 - 38174.2i) q^{50} +(282385. + 489105. i) q^{51} +(83411.1 - 473048. i) q^{52} +(59688.1 - 338508. i) q^{53} +(-607544. - 509790. i) q^{54} +(1.22935e6 + 447448. i) q^{55} +(-573450. - 208719. i) q^{56} +(1.01636e6 + 852827. i) q^{57} +(-157956. + 895812. i) q^{58} +(476326. - 2.70138e6i) q^{59} +(232578. + 402836. i) q^{60} +(-1.31399e6 + 1.10257e6i) q^{61} +(835774. - 304197. i) q^{62} +(-858078. + 1.48623e6i) q^{63} +(-131072. - 227023. i) q^{64} +(1.52877e6 + 1.28279e6i) q^{65} +(537948. - 931754. i) q^{66} +(759062. + 4.30486e6i) q^{67} +1.32235e6 q^{68} +(-119954. - 680290. i) q^{69} +(1.94222e6 - 1.62971e6i) q^{70} +(-1.49686e6 - 544812. i) q^{71} +(-692744. + 252138. i) q^{72} -2.66391e6 q^{73} +(-2.39372e6 + 587996. i) q^{74} +202916. q^{75} +(2.91914e6 - 1.06248e6i) q^{76} +(-5.51064e6 - 2.00571e6i) q^{77} +(1.25725e6 - 1.05496e6i) q^{78} +(1.17635e6 + 6.67143e6i) q^{79} +1.08912e6 q^{80} +(76257.8 + 432480. i) q^{81} +(-1.55387e6 + 2.69138e6i) q^{82} +(-3.12393e6 - 2.62129e6i) q^{83} +(-1.04254e6 - 1.80573e6i) q^{84} +(-2.74695e6 + 4.75786e6i) q^{85} +(1.42234e6 - 517690. i) q^{86} +(-2.38086e6 + 1.99778e6i) q^{87} +(-1.25955e6 - 2.18161e6i) q^{88} +(-606227. + 3.43809e6i) q^{89} +(531853. - 3.01629e6i) q^{90} +(-6.85279e6 - 5.75017e6i) q^{91} +(-1.51986e6 - 553185. i) q^{92} +(2.85564e6 + 1.03937e6i) q^{93} +(-5.55573e6 - 4.66181e6i) q^{94} +(-2.24117e6 + 1.27103e7i) q^{95} +(155534. - 882075. i) q^{96} +(7.04736e6 + 1.22064e7i) q^{97} +(-3.65912e6 + 3.07037e6i) q^{98} +(-6.65702e6 + 2.42296e6i) 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
\(3\) 25.6856 + 9.34879i 0.549244 + 0.199908i 0.601711 − 0.798714i \(-0.294486\pi\)
−0.0524666 + 0.998623i \(0.516708\pi\)
\(4\) 49.0268 − 41.1384i 0.383022 − 0.321394i
\(5\) 46.1726 + 261.858i 0.165192 + 0.936851i 0.948866 + 0.315679i \(0.102232\pi\)
−0.783674 + 0.621172i \(0.786657\pi\)
\(6\) 218.672 0.413299
\(7\) −206.971 − 1173.79i −0.228069 − 1.29344i −0.856730 − 0.515765i \(-0.827508\pi\)
0.628661 − 0.777680i \(-0.283603\pi\)
\(8\) 256.000 − 443.405i 0.176777 − 0.306186i
\(9\) −1102.99 − 925.518i −0.504339 − 0.423191i
\(10\) 1063.59 + 1842.19i 0.336337 + 0.582552i
\(11\) 2460.07 − 4260.96i 0.557279 − 0.965235i −0.440444 − 0.897780i \(-0.645179\pi\)
0.997722 − 0.0674547i \(-0.0214878\pi\)
\(12\) 1643.88 − 598.323i 0.274622 − 0.0999542i
\(13\) 5749.47 − 4824.38i 0.725815 − 0.609031i −0.203172 − 0.979143i \(-0.565125\pi\)
0.928987 + 0.370112i \(0.120681\pi\)
\(14\) −4767.60 − 8257.72i −0.464356 − 0.804289i
\(15\) −1262.08 + 7157.63i −0.0965537 + 0.547583i
\(16\) 711.263 − 4033.77i 0.0434120 − 0.246202i
\(17\) 15827.8 + 13281.1i 0.781358 + 0.655637i 0.943590 − 0.331116i \(-0.107425\pi\)
−0.162232 + 0.986753i \(0.551869\pi\)
\(18\) −10824.1 − 3939.66i −0.437461 − 0.159223i
\(19\) 45611.6 + 16601.3i 1.52559 + 0.555270i 0.962537 − 0.271151i \(-0.0874042\pi\)
0.563054 + 0.826420i \(0.309626\pi\)
\(20\) 13036.1 + 10938.6i 0.364370 + 0.305743i
\(21\) 5657.36 − 32084.5i 0.133305 − 0.756010i
\(22\) 6834.98 − 38763.1i 0.136854 − 0.776138i
\(23\) −12636.0 − 21886.2i −0.216552 − 0.375078i 0.737200 − 0.675675i \(-0.236148\pi\)
−0.953751 + 0.300596i \(0.902814\pi\)
\(24\) 10720.8 − 8995.83i 0.158303 − 0.132832i
\(25\) 6975.87 − 2539.01i 0.0892911 − 0.0324993i
\(26\) 30021.6 − 51998.9i 0.334986 − 0.580213i
\(27\) −49568.2 − 85854.7i −0.484652 − 0.839442i
\(28\) −58435.1 − 49032.8i −0.503061 − 0.422118i
\(29\) −56852.0 + 98470.5i −0.432865 + 0.749744i −0.997119 − 0.0758571i \(-0.975831\pi\)
0.564254 + 0.825602i \(0.309164\pi\)
\(30\) 10096.7 + 57261.1i 0.0682738 + 0.387200i
\(31\) 111177. 0.670266 0.335133 − 0.942171i \(-0.391219\pi\)
0.335133 + 0.942171i \(0.391219\pi\)
\(32\) −5690.10 − 32270.2i −0.0306970 − 0.174091i
\(33\) 103023. − 86446.6i 0.499041 − 0.418745i
\(34\) 155326. + 56533.9i 0.677746 + 0.246679i
\(35\) 297810. − 108394.i 1.17409 − 0.427334i
\(36\) −92150.4 −0.329184
\(37\) −306309. − 33270.7i −0.994153 − 0.107983i
\(38\) 388311. 1.14799
\(39\) 192781. − 70166.4i 0.520400 − 0.189410i
\(40\) 127929. + 46562.4i 0.316053 + 0.115034i
\(41\) −297583. + 249702.i −0.674318 + 0.565820i −0.914340 − 0.404947i \(-0.867290\pi\)
0.240022 + 0.970767i \(0.422845\pi\)
\(42\) −45258.9 − 256676.i −0.0942608 − 0.534580i
\(43\) 189203. 0.362901 0.181451 − 0.983400i \(-0.441921\pi\)
0.181451 + 0.983400i \(0.441921\pi\)
\(44\) −54679.8 − 310105.i −0.0967704 − 0.548812i
\(45\) 191426. − 331560.i 0.313154 − 0.542398i
\(46\) −154876. − 129956.i −0.234601 − 0.196854i
\(47\) −453281. − 785105.i −0.636832 − 1.10303i −0.986124 − 0.166011i \(-0.946911\pi\)
0.349292 − 0.937014i \(-0.386422\pi\)
\(48\) 55980.1 − 96960.4i 0.0730617 − 0.126546i
\(49\) −561072. + 204214.i −0.681291 + 0.247970i
\(50\) 45494.3 − 38174.2i 0.0514709 − 0.0431892i
\(51\) 282385. + 489105.i 0.298089 + 0.516305i
\(52\) 83411.1 − 473048.i 0.0822645 − 0.466545i
\(53\) 59688.1 − 338508.i 0.0550709 − 0.312323i −0.944812 − 0.327612i \(-0.893756\pi\)
0.999883 + 0.0152898i \(0.00486710\pi\)
\(54\) −607544. − 509790.i −0.525048 − 0.440568i
\(55\) 1.22935e6 + 447448.i 0.996339 + 0.362638i
\(56\) −573450. − 208719.i −0.436352 − 0.158819i
\(57\) 1.01636e6 + 852827.i 0.726918 + 0.609957i
\(58\) −157956. + 895812.i −0.106301 + 0.602864i
\(59\) 476326. − 2.70138e6i 0.301941 − 1.71239i −0.335623 − 0.941996i \(-0.608947\pi\)
0.637564 − 0.770397i \(-0.279942\pi\)
\(60\) 232578. + 402836.i 0.139008 + 0.240768i
\(61\) −1.31399e6 + 1.10257e6i −0.741204 + 0.621944i −0.933161 − 0.359460i \(-0.882961\pi\)
0.191957 + 0.981403i \(0.438517\pi\)
\(62\) 835774. − 304197.i 0.445367 − 0.162100i
\(63\) −858078. + 1.48623e6i −0.432349 + 0.748851i
\(64\) −131072. − 227023.i −0.0625000 − 0.108253i
\(65\) 1.52877e6 + 1.28279e6i 0.690471 + 0.579374i
\(66\) 537948. − 931754.i 0.230323 − 0.398931i
\(67\) 759062. + 4.30486e6i 0.308330 + 1.74863i 0.607401 + 0.794395i \(0.292212\pi\)
−0.299071 + 0.954231i \(0.596677\pi\)
\(68\) 1.32235e6 0.509995
\(69\) −119954. − 680290.i −0.0439583 − 0.249300i
\(70\) 1.94222e6 − 1.62971e6i 0.676791 − 0.567895i
\(71\) −1.49686e6 − 544812.i −0.496337 − 0.180652i 0.0817089 − 0.996656i \(-0.473962\pi\)
−0.578046 + 0.816004i \(0.696184\pi\)
\(72\) −692744. + 252138.i −0.218730 + 0.0796114i
\(73\) −2.66391e6 −0.801475 −0.400737 − 0.916193i \(-0.631246\pi\)
−0.400737 + 0.916193i \(0.631246\pi\)
\(74\) −2.39372e6 + 587996.i −0.686693 + 0.168680i
\(75\) 202916. 0.0555395
\(76\) 2.91914e6 − 1.06248e6i 0.762795 − 0.277635i
\(77\) −5.51064e6 − 2.00571e6i −1.37558 − 0.500669i
\(78\) 1.25725e6 − 1.05496e6i 0.299979 − 0.251712i
\(79\) 1.17635e6 + 6.67143e6i 0.268437 + 1.52238i 0.759065 + 0.651014i \(0.225656\pi\)
−0.490628 + 0.871369i \(0.663233\pi\)
\(80\) 1.08912e6 0.237826
\(81\) 76257.8 + 432480.i 0.0159436 + 0.0904208i
\(82\) −1.55387e6 + 2.69138e6i −0.311219 + 0.539047i
\(83\) −3.12393e6 − 2.62129e6i −0.599692 − 0.503202i 0.291654 − 0.956524i \(-0.405794\pi\)
−0.891347 + 0.453322i \(0.850239\pi\)
\(84\) −1.04254e6 − 1.80573e6i −0.191918 − 0.332412i
\(85\) −2.74695e6 + 4.75786e6i −0.485160 + 0.840322i
\(86\) 1.42234e6 − 517690.i 0.241134 − 0.0877657i
\(87\) −2.38086e6 + 1.99778e6i −0.387629 + 0.325259i
\(88\) −1.25955e6 − 2.18161e6i −0.197028 − 0.341262i
\(89\) −606227. + 3.43809e6i −0.0911529 + 0.516954i 0.904706 + 0.426037i \(0.140091\pi\)
−0.995859 + 0.0909165i \(0.971020\pi\)
\(90\) 531853. − 3.01629e6i 0.0769029 − 0.436138i
\(91\) −6.85279e6 − 5.75017e6i −0.953284 − 0.799901i
\(92\) −1.51986e6 − 553185.i −0.203492 − 0.0740650i
\(93\) 2.85564e6 + 1.03937e6i 0.368140 + 0.133992i
\(94\) −5.55573e6 − 4.66181e6i −0.689912 − 0.578905i
\(95\) −2.24117e6 + 1.27103e7i −0.268189 + 1.52098i
\(96\) 155534. − 882075.i 0.0179422 − 0.101755i
\(97\) 7.04736e6 + 1.22064e7i 0.784017 + 1.35796i 0.929585 + 0.368608i \(0.120166\pi\)
−0.145568 + 0.989348i \(0.546501\pi\)
\(98\) −3.65912e6 + 3.07037e6i −0.392722 + 0.329533i
\(99\) −6.65702e6 + 2.42296e6i −0.689536 + 0.250970i
\(100\) 237554. − 411456.i 0.0237554 − 0.0411456i
\(101\) 2.29115e6 + 3.96840e6i 0.221274 + 0.383257i 0.955195 − 0.295977i \(-0.0956453\pi\)
−0.733921 + 0.679234i \(0.762312\pi\)
\(102\) 3.46111e6 + 2.90421e6i 0.322934 + 0.270974i
\(103\) 3.31455e6 − 5.74097e6i 0.298879 − 0.517673i −0.677001 − 0.735982i \(-0.736721\pi\)
0.975880 + 0.218309i \(0.0700541\pi\)
\(104\) −667289. − 3.78438e6i −0.0581698 − 0.329897i
\(105\) 8.66278e6 0.730289
\(106\) −477505. − 2.70806e6i −0.0389410 − 0.220845i
\(107\) −2.82498e6 + 2.37044e6i −0.222932 + 0.187062i −0.747412 − 0.664360i \(-0.768704\pi\)
0.524480 + 0.851423i \(0.324260\pi\)
\(108\) −5.96210e6 − 2.17003e6i −0.455424 − 0.165761i
\(109\) 4.27701e6 − 1.55670e6i 0.316335 − 0.115136i −0.178973 − 0.983854i \(-0.557277\pi\)
0.495308 + 0.868718i \(0.335055\pi\)
\(110\) 1.04660e7 0.749733
\(111\) −7.55668e6 − 3.71819e6i −0.524446 − 0.258049i
\(112\) −4.88202e6 −0.328350
\(113\) 3.11590e6 − 1.13410e6i 0.203146 − 0.0739393i −0.238443 − 0.971156i \(-0.576637\pi\)
0.441589 + 0.897217i \(0.354415\pi\)
\(114\) 9.97400e6 + 3.63024e6i 0.630525 + 0.229492i
\(115\) 5.14763e6 − 4.31937e6i 0.315620 − 0.264837i
\(116\) 1.26365e6 + 7.16650e6i 0.0751662 + 0.426289i
\(117\) −1.08067e7 −0.623793
\(118\) −3.81061e6 − 2.16110e7i −0.213505 − 1.21085i
\(119\) 1.23134e7 − 2.13274e7i 0.669827 − 1.16017i
\(120\) 2.85064e6 + 2.39197e6i 0.150594 + 0.126363i
\(121\) −2.36026e6 − 4.08810e6i −0.121119 − 0.209784i
\(122\) −6.86117e6 + 1.18839e7i −0.342089 + 0.592515i
\(123\) −9.97801e6 + 3.63170e6i −0.483477 + 0.175971i
\(124\) 5.45063e6 − 4.57363e6i 0.256727 − 0.215419i
\(125\) 1.13736e7 + 1.96996e7i 0.520849 + 0.902137i
\(126\) −2.38406e6 + 1.35207e7i −0.106174 + 0.602145i
\(127\) 342205. − 1.94074e6i 0.0148243 − 0.0840727i −0.976498 − 0.215526i \(-0.930853\pi\)
0.991322 + 0.131454i \(0.0419644\pi\)
\(128\) −1.60651e6 − 1.34802e6i −0.0677094 − 0.0568149i
\(129\) 4.85979e6 + 1.76882e6i 0.199321 + 0.0725470i
\(130\) 1.50025e7 + 5.46046e6i 0.598911 + 0.217986i
\(131\) −1.47723e7 − 1.23954e7i −0.574113 − 0.481738i 0.308895 − 0.951096i \(-0.400041\pi\)
−0.883008 + 0.469358i \(0.844485\pi\)
\(132\) 1.49462e6 − 8.47641e6i 0.0565617 − 0.320777i
\(133\) 1.00461e7 − 5.69745e7i 0.370270 − 2.09991i
\(134\) 1.74851e7 + 3.02850e7i 0.627770 + 1.08733i
\(135\) 2.01930e7 − 1.69440e7i 0.706372 − 0.592716i
\(136\) 9.94084e6 − 3.61817e6i 0.338873 − 0.123340i
\(137\) 2.02009e7 − 3.49889e7i 0.671194 − 1.16254i −0.306372 − 0.951912i \(-0.599115\pi\)
0.977566 − 0.210630i \(-0.0675514\pi\)
\(138\) −2.76314e6 − 4.78590e6i −0.0895006 − 0.155020i
\(139\) 2.64506e7 + 2.21947e7i 0.835378 + 0.700966i 0.956519 − 0.291670i \(-0.0942108\pi\)
−0.121141 + 0.992635i \(0.538655\pi\)
\(140\) 1.01415e7 − 1.75657e7i 0.312360 − 0.541023i
\(141\) −4.30300e6 − 2.44035e7i −0.129272 − 0.733138i
\(142\) −1.27434e7 −0.373487
\(143\) −6.41240e6 − 3.63665e7i −0.183377 − 1.03998i
\(144\) −4.51784e6 + 3.79092e6i −0.126085 + 0.105798i
\(145\) −2.84103e7 − 1.03405e7i −0.773905 − 0.281678i
\(146\) −2.00261e7 + 7.28889e6i −0.532550 + 0.193833i
\(147\) −1.63206e7 −0.423766
\(148\) −1.63860e7 + 1.09699e7i −0.415488 + 0.278155i
\(149\) 7.31411e7 1.81138 0.905690 − 0.423940i \(-0.139353\pi\)
0.905690 + 0.423940i \(0.139353\pi\)
\(150\) 1.52543e6 − 555211.i 0.0369039 − 0.0134319i
\(151\) 3.61669e7 + 1.31637e7i 0.854854 + 0.311141i 0.732018 − 0.681285i \(-0.238579\pi\)
0.122836 + 0.992427i \(0.460801\pi\)
\(152\) 1.90377e7 − 1.59745e7i 0.439705 − 0.368956i
\(153\) −5.16600e6 − 2.92979e7i −0.116610 − 0.661326i
\(154\) −4.69144e7 −1.03510
\(155\) 5.13331e6 + 2.91124e7i 0.110723 + 0.627939i
\(156\) 6.56489e6 − 1.13707e7i 0.138450 − 0.239802i
\(157\) −1.01108e7 − 8.48395e6i −0.208514 − 0.174964i 0.532550 − 0.846399i \(-0.321234\pi\)
−0.741064 + 0.671435i \(0.765678\pi\)
\(158\) 2.70974e7 + 4.69341e7i 0.546547 + 0.946647i
\(159\) 4.69777e6 − 8.13677e6i 0.0926833 − 0.160532i
\(160\) 8.18747e6 − 2.98000e6i 0.158027 − 0.0575169i
\(161\) −2.30745e7 + 1.93618e7i −0.435754 + 0.365641i
\(162\) 1.75661e6 + 3.04253e6i 0.0324617 + 0.0562254i
\(163\) −1.57943e7 + 8.95737e7i −0.285655 + 1.62003i 0.417280 + 0.908778i \(0.362984\pi\)
−0.702935 + 0.711254i \(0.748128\pi\)
\(164\) −4.31722e6 + 2.44842e7i −0.0764277 + 0.433443i
\(165\) 2.73936e7 + 2.29859e7i 0.474739 + 0.398353i
\(166\) −3.06566e7 − 1.11581e7i −0.520170 − 0.189326i
\(167\) 6.40462e7 + 2.33109e7i 1.06411 + 0.387304i 0.813970 − 0.580906i \(-0.197302\pi\)
0.250138 + 0.968210i \(0.419524\pi\)
\(168\) −1.27781e7 − 1.07221e7i −0.207915 − 0.174461i
\(169\) −1.11438e6 + 6.31999e6i −0.0177595 + 0.100719i
\(170\) −7.63206e6 + 4.32835e7i −0.119143 + 0.675696i
\(171\) −3.49444e7 − 6.05254e7i −0.534430 − 0.925660i
\(172\) 9.27602e6 − 7.78351e6i 0.138999 − 0.116634i
\(173\) −1.18446e8 + 4.31109e7i −1.73924 + 0.633032i −0.999218 − 0.0395473i \(-0.987408\pi\)
−0.740025 + 0.672580i \(0.765186\pi\)
\(174\) −1.24320e7 + 2.15328e7i −0.178903 + 0.309869i
\(175\) −4.42407e6 − 7.66272e6i −0.0624006 − 0.108081i
\(176\) −1.54380e7 − 1.29540e7i −0.213450 − 0.179106i
\(177\) 3.74894e7 − 6.49335e7i 0.508161 − 0.880161i
\(178\) 4.84982e6 + 2.75047e7i 0.0644548 + 0.365542i
\(179\) −1.37195e8 −1.78794 −0.893971 − 0.448124i \(-0.852092\pi\)
−0.893971 + 0.448124i \(0.852092\pi\)
\(180\) −4.25482e6 − 2.41303e7i −0.0543786 − 0.308396i
\(181\) −6.99672e7 + 5.87095e7i −0.877041 + 0.735925i −0.965568 − 0.260149i \(-0.916228\pi\)
0.0885277 + 0.996074i \(0.471784\pi\)
\(182\) −6.72495e7 − 2.44768e7i −0.826874 − 0.300958i
\(183\) −4.40583e7 + 1.60359e7i −0.531433 + 0.193426i
\(184\) −1.29392e7 −0.153125
\(185\) −5.43087e6 − 8.17455e7i −0.0630620 − 0.949211i
\(186\) 2.43112e7 0.277020
\(187\) 9.55278e7 − 3.47693e7i 1.06828 − 0.388821i
\(188\) −5.45209e7 − 1.98440e7i −0.598426 − 0.217809i
\(189\) −9.05163e7 + 7.59522e7i −0.975238 + 0.818322i
\(190\) 1.79293e7 + 1.01682e8i 0.189639 + 1.07549i
\(191\) 1.46914e8 1.52562 0.762811 − 0.646622i \(-0.223819\pi\)
0.762811 + 0.646622i \(0.223819\pi\)
\(192\) −1.24427e6 − 7.05660e6i −0.0126870 − 0.0719517i
\(193\) 4.17881e7 − 7.23792e7i 0.418410 − 0.724708i −0.577369 − 0.816483i \(-0.695921\pi\)
0.995780 + 0.0917751i \(0.0292541\pi\)
\(194\) 8.63774e7 + 7.24793e7i 0.849365 + 0.712702i
\(195\) 2.72748e7 + 4.72414e7i 0.263415 + 0.456248i
\(196\) −1.91066e7 + 3.30936e7i −0.181254 + 0.313941i
\(197\) −1.47486e8 + 5.36807e7i −1.37442 + 0.500249i −0.920483 − 0.390784i \(-0.872204\pi\)
−0.453940 + 0.891032i \(0.649982\pi\)
\(198\) −4.34148e7 + 3.64294e7i −0.397475 + 0.333521i
\(199\) 2.03554e7 + 3.52566e7i 0.183102 + 0.317142i 0.942935 − 0.332976i \(-0.108053\pi\)
−0.759833 + 0.650118i \(0.774719\pi\)
\(200\) 660013. − 3.74312e6i 0.00583375 − 0.0330848i
\(201\) −2.07482e7 + 1.17669e8i −0.180217 + 1.02206i
\(202\) 2.80820e7 + 2.35636e7i 0.239717 + 0.201146i
\(203\) 1.27351e8 + 4.63518e7i 1.06848 + 0.388893i
\(204\) 3.39654e7 + 1.23624e7i 0.280112 + 0.101952i
\(205\) −7.91266e7 − 6.63951e7i −0.641481 − 0.538267i
\(206\) 9.20906e6 − 5.22272e7i 0.0733973 − 0.416257i
\(207\) −6.31868e6 + 3.58350e7i −0.0495142 + 0.280809i
\(208\) −1.53711e7 − 2.66235e7i −0.118436 − 0.205136i
\(209\) 1.82945e8 − 1.53509e8i 1.38614 − 1.16311i
\(210\) 6.51228e7 − 2.37028e7i 0.485250 − 0.176617i
\(211\) −2.99678e7 + 5.19058e7i −0.219617 + 0.380389i −0.954691 − 0.297599i \(-0.903814\pi\)
0.735074 + 0.677987i \(0.237148\pi\)
\(212\) −1.09994e7 − 1.90515e7i −0.0792852 − 0.137326i
\(213\) −3.33544e7 − 2.79876e7i −0.236496 − 0.198444i
\(214\) −1.47510e7 + 2.55495e7i −0.102890 + 0.178211i
\(215\) 8.73599e6 + 4.95443e7i 0.0599484 + 0.339984i
\(216\) −5.07579e7 −0.342701
\(217\) −2.30103e7 − 1.30498e8i −0.152867 − 0.866952i
\(218\) 2.78932e7 − 2.34052e7i 0.182348 − 0.153008i
\(219\) −6.84242e7 − 2.49044e7i −0.440205 − 0.160222i
\(220\) 7.86786e7 − 2.86367e7i 0.498170 − 0.181319i
\(221\) 1.55075e8 0.966425
\(222\) −6.69812e7 − 7.27539e6i −0.410882 − 0.0446294i
\(223\) −1.13204e8 −0.683588 −0.341794 − 0.939775i \(-0.611034\pi\)
−0.341794 + 0.939775i \(0.611034\pi\)
\(224\) −3.67008e7 + 1.33580e7i −0.218176 + 0.0794096i
\(225\) −1.00442e7 − 3.65579e6i −0.0587864 − 0.0213965i
\(226\) 2.03209e7 − 1.70512e7i 0.117101 − 0.0982598i
\(227\) 4.75422e7 + 2.69625e8i 0.269767 + 1.52993i 0.755108 + 0.655600i \(0.227584\pi\)
−0.485341 + 0.874325i \(0.661305\pi\)
\(228\) 8.49129e7 0.474462
\(229\) −4.66499e7 − 2.64565e8i −0.256700 − 1.45582i −0.791670 − 0.610949i \(-0.790788\pi\)
0.534970 − 0.844871i \(-0.320323\pi\)
\(230\) 2.68790e7 − 4.65558e7i 0.145668 − 0.252305i
\(231\) −1.22793e8 − 1.03036e8i −0.655439 − 0.549979i
\(232\) 2.91082e7 + 5.04169e7i 0.153041 + 0.265075i
\(233\) 762226. − 1.32021e6i 0.00394765 − 0.00683752i −0.864045 − 0.503415i \(-0.832077\pi\)
0.867992 + 0.496577i \(0.165410\pi\)
\(234\) −8.12394e7 + 2.95687e7i −0.414487 + 0.150861i
\(235\) 1.84657e8 − 1.54945e8i 0.928171 − 0.778828i
\(236\) −8.77777e7 − 1.52035e8i −0.434703 − 0.752927i
\(237\) −3.21545e7 + 1.82357e8i −0.156900 + 0.889823i
\(238\) 3.42111e7 − 1.94021e8i 0.164493 − 0.932887i
\(239\) −7.84368e7 − 6.58163e7i −0.371644 − 0.311846i 0.437767 − 0.899088i \(-0.355769\pi\)
−0.809412 + 0.587242i \(0.800214\pi\)
\(240\) 2.79746e7 + 1.01819e7i 0.130624 + 0.0475434i
\(241\) 1.22654e8 + 4.46423e7i 0.564445 + 0.205441i 0.608453 − 0.793590i \(-0.291790\pi\)
−0.0440080 + 0.999031i \(0.514013\pi\)
\(242\) −2.89291e7 − 2.42744e7i −0.131214 − 0.110102i
\(243\) −3.97334e7 + 2.25339e8i −0.177637 + 1.00743i
\(244\) −1.90629e7 + 1.08111e8i −0.0840086 + 0.476437i
\(245\) −7.93811e7 − 1.37492e8i −0.344854 − 0.597305i
\(246\) −6.50732e7 + 5.46029e7i −0.278695 + 0.233853i
\(247\) 3.42334e8 − 1.24599e8i 1.44547 − 0.526109i
\(248\) 2.84612e7 − 4.92962e7i 0.118487 − 0.205226i
\(249\) −5.57342e7 − 9.65344e7i −0.228783 − 0.396264i
\(250\) 1.39403e8 + 1.16973e8i 0.564262 + 0.473472i
\(251\) −1.00716e8 + 1.74445e8i −0.402012 + 0.696306i −0.993969 − 0.109664i \(-0.965022\pi\)
0.591956 + 0.805970i \(0.298356\pi\)
\(252\) 1.90725e7 + 1.08165e8i 0.0750767 + 0.425781i
\(253\) −1.24341e8 −0.482718
\(254\) −2.73764e6 − 1.55259e7i −0.0104823 − 0.0594484i
\(255\) −1.15037e8 + 9.65279e7i −0.434459 + 0.364554i
\(256\) −1.57654e7 − 5.73815e6i −0.0587308 − 0.0213763i
\(257\) 9.55792e7 − 3.47880e7i 0.351235 − 0.127839i −0.160377 − 0.987056i \(-0.551271\pi\)
0.511612 + 0.859217i \(0.329049\pi\)
\(258\) 4.13735e7 0.149987
\(259\) 2.43441e7 + 3.66428e8i 0.0870653 + 1.31051i
\(260\) 1.27723e8 0.450673
\(261\) 1.53843e8 − 5.59944e7i 0.535595 − 0.194941i
\(262\) −1.44967e8 − 5.27636e7i −0.497983 − 0.181251i
\(263\) −3.50328e8 + 2.93960e8i −1.18749 + 0.996421i −0.187589 + 0.982248i \(0.560067\pi\)
−0.999900 + 0.0141734i \(0.995488\pi\)
\(264\) −1.19570e7 − 6.78113e7i −0.0399951 − 0.226824i
\(265\) 9.13969e7 0.301697
\(266\) −8.03692e7 − 4.55796e8i −0.261821 − 1.48486i
\(267\) −4.77133e7 + 8.26418e7i −0.153409 + 0.265712i
\(268\) 2.14309e8 + 1.79827e8i 0.680095 + 0.570667i
\(269\) −2.22902e7 − 3.86078e7i −0.0698203 − 0.120932i 0.829002 − 0.559246i \(-0.188909\pi\)
−0.898822 + 0.438314i \(0.855576\pi\)
\(270\) 1.05441e8 − 1.82628e8i 0.326013 − 0.564670i
\(271\) 1.48618e8 − 5.40926e7i 0.453607 − 0.165099i −0.105105 − 0.994461i \(-0.533518\pi\)
0.558712 + 0.829362i \(0.311296\pi\)
\(272\) 6.48308e7 − 5.43995e7i 0.195339 − 0.163909i
\(273\) −1.22261e8 − 2.11762e8i −0.363679 − 0.629910i
\(274\) 5.61255e7 − 3.18303e8i 0.164829 − 0.934790i
\(275\) 6.34249e6 − 3.59700e7i 0.0183906 − 0.104298i
\(276\) −3.38670e7 − 2.84178e7i −0.0969605 − 0.0813595i
\(277\) 1.86575e8 + 6.79078e7i 0.527442 + 0.191973i 0.591996 − 0.805941i \(-0.298340\pi\)
−0.0645539 + 0.997914i \(0.520562\pi\)
\(278\) 2.59571e8 + 9.44763e7i 0.724603 + 0.263734i
\(279\) −1.22627e8 − 1.02896e8i −0.338041 − 0.283650i
\(280\) 2.81769e7 − 1.59799e8i 0.0767080 − 0.435033i
\(281\) 5.47287e7 − 3.10382e8i 0.147144 − 0.834496i −0.818476 − 0.574540i \(-0.805181\pi\)
0.965621 − 0.259956i \(-0.0837080\pi\)
\(282\) −9.91200e7 − 1.71681e8i −0.263202 − 0.455879i
\(283\) 3.90114e8 − 3.27344e8i 1.02315 − 0.858524i 0.0331289 − 0.999451i \(-0.489453\pi\)
0.990020 + 0.140927i \(0.0450084\pi\)
\(284\) −9.57989e7 + 3.48680e7i −0.248168 + 0.0903259i
\(285\) −1.76392e8 + 3.05519e8i −0.451358 + 0.781774i
\(286\) −1.47710e8 − 2.55842e8i −0.373361 − 0.646681i
\(287\) 3.54689e8 + 2.97619e8i 0.885648 + 0.743147i
\(288\) −2.35905e7 + 4.08600e7i −0.0581920 + 0.100792i
\(289\) 2.87725e6 + 1.63177e7i 0.00701189 + 0.0397664i
\(290\) −2.41869e8 −0.582354
\(291\) 6.69007e7 + 3.79413e8i 0.159149 + 0.902581i
\(292\) −1.30603e8 + 1.09589e8i −0.306983 + 0.257589i
\(293\) −5.22052e8 − 1.90011e8i −1.21249 − 0.441309i −0.344922 − 0.938631i \(-0.612095\pi\)
−0.867566 + 0.497322i \(0.834317\pi\)
\(294\) −1.22691e8 + 4.46559e7i −0.281577 + 0.102486i
\(295\) 7.29371e8 1.65414
\(296\) −9.31674e7 + 1.27301e8i −0.208806 + 0.285307i
\(297\) −4.87765e8 −1.08035
\(298\) 5.49841e8 − 2.00126e8i 1.20360 − 0.438073i
\(299\) −1.78237e8 − 6.48731e7i −0.385611 − 0.140351i
\(300\) 9.94833e6 − 8.34764e6i 0.0212729 − 0.0178501i
\(301\) −3.91595e7 − 2.22085e8i −0.0827666 − 0.469393i
\(302\) 3.07904e8 0.643267
\(303\) 2.17500e7 + 1.23350e8i 0.0449168 + 0.254736i
\(304\) 9.94076e7 − 1.72179e8i 0.202937 − 0.351498i
\(305\) −3.49386e8 − 2.93170e8i −0.705110 − 0.591657i
\(306\) −1.18999e8 − 2.06113e8i −0.237421 − 0.411226i
\(307\) 2.02739e6 − 3.51154e6i 0.00399901 − 0.00692649i −0.864019 − 0.503459i \(-0.832060\pi\)
0.868018 + 0.496533i \(0.165394\pi\)
\(308\) −3.52681e8 + 1.28365e8i −0.687788 + 0.250334i
\(309\) 1.38807e8 − 1.16473e8i 0.267644 − 0.224580i
\(310\) 1.18246e8 + 2.04808e8i 0.225435 + 0.390465i
\(311\) 7.18239e7 − 4.07334e8i 0.135397 − 0.767872i −0.839186 − 0.543844i \(-0.816968\pi\)
0.974583 − 0.224028i \(-0.0719206\pi\)
\(312\) 1.82397e7 − 1.03443e8i 0.0339998 − 0.192823i
\(313\) 5.24531e8 + 4.40134e8i 0.966865 + 0.811296i 0.982056 − 0.188588i \(-0.0603912\pi\)
−0.0151909 + 0.999885i \(0.504836\pi\)
\(314\) −9.92216e7 − 3.61137e7i −0.180864 − 0.0658292i
\(315\) −4.28802e8 − 1.56071e8i −0.772983 − 0.281343i
\(316\) 3.32125e8 + 2.78686e8i 0.592102 + 0.496833i
\(317\) 6.42645e7 − 3.64462e8i 0.113309 − 0.642607i −0.874265 − 0.485449i \(-0.838656\pi\)
0.987574 − 0.157157i \(-0.0502329\pi\)
\(318\) 1.30521e7 − 7.40223e7i 0.0227608 − 0.129083i
\(319\) 2.79719e8 + 4.84488e8i 0.482453 + 0.835633i
\(320\) 5.33959e7 − 4.48045e7i 0.0910926 − 0.0764358i
\(321\) −9.47221e7 + 3.44760e7i −0.159839 + 0.0581768i
\(322\) −1.20486e8 + 2.08689e8i −0.201114 + 0.348340i
\(323\) 5.01449e8 + 8.68536e8i 0.827977 + 1.43410i
\(324\) 2.15302e7 + 1.80660e7i 0.0351674 + 0.0295090i
\(325\) 2.78584e7 − 4.82522e7i 0.0450158 − 0.0779696i
\(326\) 1.26354e8 + 7.16589e8i 0.201989 + 1.14554i
\(327\) 1.24411e8 0.196762
\(328\) 3.45378e7 + 1.95874e8i 0.0540426 + 0.306491i
\(329\) −8.27734e8 + 6.94551e8i −1.28146 + 1.07527i
\(330\) 2.68826e8 + 9.78445e7i 0.411786 + 0.149878i
\(331\) −6.02357e8 + 2.19240e8i −0.912970 + 0.332294i −0.755438 − 0.655220i \(-0.772576\pi\)
−0.157532 + 0.987514i \(0.550354\pi\)
\(332\) −2.60992e8 −0.391421
\(333\) 3.07062e8 + 3.20191e8i 0.455692 + 0.475176i
\(334\) 5.45253e8 0.800728
\(335\) −1.09221e9 + 3.97533e8i −1.58727 + 0.577718i
\(336\) −1.25398e8 − 4.56410e7i −0.180344 − 0.0656398i
\(337\) −4.67090e8 + 3.91935e8i −0.664807 + 0.557840i −0.911523 − 0.411248i \(-0.865093\pi\)
0.246716 + 0.969088i \(0.420649\pi\)
\(338\) 8.91508e6 + 5.05599e7i 0.0125579 + 0.0712194i
\(339\) 9.06362e7 0.126358
\(340\) 6.10564e7 + 3.46268e8i 0.0842472 + 0.477789i
\(341\) 2.73502e8 − 4.73719e8i 0.373525 − 0.646964i
\(342\) −4.28303e8 − 3.59389e8i −0.578975 − 0.485818i
\(343\) −1.34960e8 − 2.33758e8i −0.180583 − 0.312778i
\(344\) 4.84360e7 − 8.38935e7i 0.0641525 − 0.111115i
\(345\) 1.72601e8 − 6.28215e7i 0.226295 − 0.0823648i
\(346\) −7.72466e8 + 6.48176e8i −1.00257 + 0.841253i
\(347\) −6.09691e7 − 1.05602e8i −0.0783351 − 0.135680i 0.824197 − 0.566304i \(-0.191627\pi\)
−0.902532 + 0.430623i \(0.858294\pi\)
\(348\) −3.45406e7 + 1.95889e8i −0.0439342 + 0.249163i
\(349\) 1.23335e8 − 6.99470e8i 0.155310 − 0.880806i −0.803192 − 0.595720i \(-0.796867\pi\)
0.958502 − 0.285086i \(-0.0920221\pi\)
\(350\) −5.42246e7 − 4.54998e7i −0.0676017 − 0.0567246i
\(351\) −6.99187e8 − 2.54483e8i −0.863015 − 0.314112i
\(352\) −1.51500e8 − 5.51415e7i −0.185146 − 0.0673875i
\(353\) −7.03468e8 − 5.90280e8i −0.851202 − 0.714244i 0.108852 − 0.994058i \(-0.465283\pi\)
−0.960054 + 0.279814i \(0.909727\pi\)
\(354\) 1.04159e8 − 5.90717e8i 0.124792 − 0.707731i
\(355\) 7.35494e7 − 4.17119e8i 0.0872529 − 0.494836i
\(356\) 1.11716e8 + 1.93498e8i 0.131232 + 0.227301i
\(357\) 5.15661e8 − 4.32691e8i 0.599827 − 0.503314i
\(358\) −1.03137e9 + 3.75388e8i −1.18802 + 0.432405i
\(359\) −2.61796e8 + 4.53444e8i −0.298629 + 0.517241i −0.975823 − 0.218564i \(-0.929863\pi\)
0.677193 + 0.735805i \(0.263196\pi\)
\(360\) −9.80102e7 − 1.69759e8i −0.110717 − 0.191767i
\(361\) 1.12007e9 + 9.39853e8i 1.25306 + 1.05144i
\(362\) −3.65343e8 + 6.32793e8i −0.404782 + 0.701102i
\(363\) −2.24060e7 − 1.27071e8i −0.0245862 − 0.139435i
\(364\) −5.72524e8 −0.622212
\(365\) −1.23000e8 − 6.97566e8i −0.132397 − 0.750863i
\(366\) −2.87333e8 + 2.41101e8i −0.306339 + 0.257049i
\(367\) 9.24502e8 + 3.36491e8i 0.976285 + 0.355339i 0.780395 − 0.625287i \(-0.215018\pi\)
0.195890 + 0.980626i \(0.437240\pi\)
\(368\) −9.72713e7 + 3.54038e7i −0.101746 + 0.0370325i
\(369\) 5.59334e8 0.579534
\(370\) −2.64496e8 − 5.99665e8i −0.271464 − 0.615464i
\(371\) −4.09692e8 −0.416532
\(372\) 1.82761e8 − 6.65194e7i 0.184070 − 0.0669959i
\(373\) 1.09113e9 + 3.97138e8i 1.08867 + 0.396242i 0.823127 − 0.567857i \(-0.192227\pi\)
0.265540 + 0.964100i \(0.414450\pi\)
\(374\) 6.23000e8 − 5.22759e8i 0.615797 − 0.516715i
\(375\) 1.07969e8 + 6.12325e8i 0.105728 + 0.599615i
\(376\) −4.64160e8 −0.450308
\(377\) 1.48190e8 + 8.40429e8i 0.142438 + 0.807804i
\(378\) −4.72643e8 + 8.18641e8i −0.450103 + 0.779601i
\(379\) 4.01555e7 + 3.36944e7i 0.0378885 + 0.0317922i 0.661535 − 0.749914i \(-0.269905\pi\)
−0.623647 + 0.781706i \(0.714350\pi\)
\(380\) 4.13004e8 + 7.15343e8i 0.386110 + 0.668763i
\(381\) 2.69333e7 − 4.66499e7i 0.0249490 − 0.0432129i
\(382\) 1.10443e9 − 4.01981e8i 1.01372 − 0.368964i
\(383\) −4.40043e8 + 3.69240e8i −0.400220 + 0.335825i −0.820579 − 0.571533i \(-0.806349\pi\)
0.420359 + 0.907358i \(0.361904\pi\)
\(384\) −2.86618e7 − 4.96437e7i −0.0258312 − 0.0447409i
\(385\) 2.70770e8 − 1.53561e9i 0.241818 − 1.37142i
\(386\) 1.16103e8 − 6.58452e8i 0.102751 − 0.582732i
\(387\) −2.08689e8 − 1.75111e8i −0.183025 − 0.153576i
\(388\) 8.47661e8 + 3.08523e8i 0.736735 + 0.268150i
\(389\) −6.96065e8 − 2.53347e8i −0.599551 − 0.218219i 0.0243742 − 0.999703i \(-0.492241\pi\)
−0.623925 + 0.781484i \(0.714463\pi\)
\(390\) 3.34300e8 + 2.80511e8i 0.285371 + 0.239455i
\(391\) 9.06726e7 − 5.14230e8i 0.0767110 − 0.435050i
\(392\) −5.30852e7 + 3.01061e8i −0.0445115 + 0.252437i
\(393\) −2.63552e8 − 4.56486e8i −0.219025 − 0.379362i
\(394\) −9.61856e8 + 8.07093e8i −0.792270 + 0.664794i
\(395\) −1.69265e9 + 6.16075e8i −1.38190 + 0.502972i
\(396\) −2.26696e8 + 3.92649e8i −0.183447 + 0.317740i
\(397\) −9.69116e8 − 1.67856e9i −0.777337 − 1.34639i −0.933472 − 0.358651i \(-0.883237\pi\)
0.156135 − 0.987736i \(-0.450096\pi\)
\(398\) 2.49490e8 + 2.09347e8i 0.198364 + 0.166447i
\(399\) 7.90684e8 − 1.36951e9i 0.623158 − 1.07934i
\(400\) −5.28011e6 − 2.99450e7i −0.00412508 − 0.0233945i
\(401\) 1.14860e8 0.0889538 0.0444769 − 0.999010i \(-0.485838\pi\)
0.0444769 + 0.999010i \(0.485838\pi\)
\(402\) 1.65986e8 + 9.41353e8i 0.127432 + 0.722706i
\(403\) 6.39206e8 − 5.36358e8i 0.486489 − 0.408213i
\(404\) 2.75582e8 + 1.00303e8i 0.207929 + 0.0756800i
\(405\) −1.09727e8 + 3.99374e7i −0.0820770 + 0.0298736i
\(406\) 1.08419e9 0.804015
\(407\) −8.95304e8 + 1.22332e9i −0.658249 + 0.899414i
\(408\) 2.89162e8 0.210781
\(409\) 1.66778e9 − 6.07021e8i 1.20533 − 0.438705i 0.340249 − 0.940335i \(-0.389489\pi\)
0.865082 + 0.501631i \(0.167266\pi\)
\(410\) −7.76505e8 − 2.82625e8i −0.556417 − 0.202519i
\(411\) 8.45975e8 − 7.09858e8i 0.601051 − 0.504342i
\(412\) −7.36725e7 − 4.17817e8i −0.0518997 − 0.294338i
\(413\) −3.26944e9 −2.28375
\(414\) 5.05494e7 + 2.86680e8i 0.0350119 + 0.198562i
\(415\) 5.42166e8 − 9.39058e8i 0.372360 − 0.644947i
\(416\) −1.88399e8 − 1.58085e8i −0.128307 − 0.107663i
\(417\) 4.71905e8 + 8.17364e8i 0.318698 + 0.552000i
\(418\) 9.55271e8 − 1.65458e9i 0.639749 − 1.10808i
\(419\) 1.59810e9 − 5.81660e8i 1.06134 − 0.386296i 0.248408 − 0.968656i \(-0.420093\pi\)
0.812931 + 0.582360i \(0.197870\pi\)
\(420\) 4.24709e8 − 3.56373e8i 0.279717 − 0.234710i
\(421\) 2.72473e7 + 4.71937e7i 0.0177965 + 0.0308245i 0.874787 − 0.484509i \(-0.161002\pi\)
−0.856990 + 0.515333i \(0.827668\pi\)
\(422\) −8.32618e7 + 4.72201e8i −0.0539327 + 0.305868i
\(423\) −2.26665e8 + 1.28548e9i −0.145611 + 0.825800i
\(424\) −1.34816e8 − 1.13124e8i −0.0858936 − 0.0720733i
\(425\) 1.44134e8 + 5.24604e7i 0.0910761 + 0.0331490i
\(426\) −3.27321e8 − 1.19135e8i −0.205136 − 0.0746632i
\(427\) 1.56614e9 + 1.31415e9i 0.973496 + 0.816860i
\(428\) −4.09838e7 + 2.32431e8i −0.0252673 + 0.143298i
\(429\) 1.75277e8 − 9.94045e8i 0.107183 − 0.607863i
\(430\) 2.01234e8 + 3.48548e8i 0.122057 + 0.211409i
\(431\) 1.78582e9 − 1.49848e9i 1.07441 − 0.901533i 0.0789612 − 0.996878i \(-0.474840\pi\)
0.995444 + 0.0953444i \(0.0303952\pi\)
\(432\) −3.81574e8 + 1.38882e8i −0.227712 + 0.0828804i
\(433\) 1.25643e9 − 2.17620e9i 0.743756 − 1.28822i −0.207018 − 0.978337i \(-0.566376\pi\)
0.950774 − 0.309886i \(-0.100291\pi\)
\(434\) −5.30045e8 − 9.18065e8i −0.311242 − 0.539087i
\(435\) −6.33064e8 − 5.31204e8i −0.368753 − 0.309420i
\(436\) 1.45648e8 − 2.52269e8i 0.0841591 − 0.145768i
\(437\) −2.13009e8 − 1.20804e9i −0.122099 − 0.692461i
\(438\) −5.82524e8 −0.331249
\(439\) 1.56068e8 + 8.85108e8i 0.0880419 + 0.499310i 0.996659 + 0.0816794i \(0.0260284\pi\)
−0.908617 + 0.417631i \(0.862861\pi\)
\(440\) 5.13115e8 − 4.30555e8i 0.287164 − 0.240959i
\(441\) 8.07860e8 + 2.94037e8i 0.448540 + 0.163255i
\(442\) 1.16578e9 − 4.24309e8i 0.642154 − 0.233725i
\(443\) 9.64798e8 0.527258 0.263629 − 0.964624i \(-0.415081\pi\)
0.263629 + 0.964624i \(0.415081\pi\)
\(444\) −5.23441e8 + 1.28578e8i −0.283810 + 0.0697152i
\(445\) −9.28281e8 −0.499366
\(446\) −8.51015e8 + 3.09744e8i −0.454219 + 0.165322i
\(447\) 1.87867e9 + 6.83781e8i 0.994890 + 0.362110i
\(448\) −2.39350e8 + 2.00838e8i −0.125765 + 0.105530i
\(449\) 6.20112e7 + 3.51683e8i 0.0323302 + 0.183354i 0.996696 − 0.0812173i \(-0.0258808\pi\)
−0.964366 + 0.264571i \(0.914770\pi\)
\(450\) −8.55106e7 −0.0442360
\(451\) 3.31895e8 + 1.88227e9i 0.170366 + 0.966195i
\(452\) 1.06108e8 − 1.83784e8i 0.0540460 − 0.0936104i
\(453\) 8.05904e8 + 6.76234e8i 0.407324 + 0.341785i
\(454\) 1.09514e9 + 1.89684e9i 0.549255 + 0.951337i
\(455\) 1.18932e9 − 2.05996e9i 0.591913 − 1.02522i
\(456\) 6.38336e8 − 2.32335e8i 0.315263 − 0.114746i
\(457\) −2.62355e9 + 2.20142e9i −1.28583 + 1.07894i −0.293417 + 0.955985i \(0.594792\pi\)
−0.992412 + 0.122954i \(0.960763\pi\)
\(458\) −1.07458e9 − 1.86123e9i −0.522650 − 0.905257i
\(459\) 3.55689e8 − 2.01721e9i 0.171683 − 0.973661i
\(460\) 7.46798e7 − 4.23530e8i 0.0357726 − 0.202877i
\(461\) −1.85681e8 − 1.55805e8i −0.0882701 − 0.0740674i 0.597585 − 0.801806i \(-0.296127\pi\)
−0.685855 + 0.727738i \(0.740572\pi\)
\(462\) −1.20502e9 − 4.38593e8i −0.568524 − 0.206926i
\(463\) −3.07876e9 − 1.12058e9i −1.44159 − 0.524696i −0.501362 − 0.865238i \(-0.667167\pi\)
−0.940230 + 0.340541i \(0.889390\pi\)
\(464\) 3.56771e8 + 2.99366e8i 0.165797 + 0.139120i
\(465\) −1.40314e8 + 7.95761e8i −0.0647166 + 0.367026i
\(466\) 2.11775e6 − 1.20103e7i 0.000969445 − 0.00549800i
\(467\) 1.37306e9 + 2.37821e9i 0.623850 + 1.08054i 0.988762 + 0.149498i \(0.0477658\pi\)
−0.364912 + 0.931042i \(0.618901\pi\)
\(468\) −5.29816e8 + 4.44568e8i −0.238927 + 0.200483i
\(469\) 4.89590e9 − 1.78196e9i 2.19143 − 0.797615i
\(470\) 9.64210e8 − 1.67006e9i 0.428380 − 0.741976i
\(471\) −1.80387e8 − 3.12439e8i −0.0795484 − 0.137782i
\(472\) −1.07587e9 − 9.02759e8i −0.470935 − 0.395162i
\(473\) 4.65452e8 − 8.06186e8i 0.202237 − 0.350285i
\(474\) 2.57236e8 + 1.45886e9i 0.110945 + 0.629200i
\(475\) 3.60332e8 0.154268
\(476\) −2.73689e8 − 1.55217e9i −0.116314 − 0.659650i
\(477\) −3.79130e8 + 3.18128e8i −0.159946 + 0.134211i
\(478\) −7.69736e8 − 2.80161e8i −0.322362 − 0.117330i
\(479\) −1.08373e9 + 3.94445e8i −0.450553 + 0.163988i −0.557323 − 0.830296i \(-0.688171\pi\)
0.106770 + 0.994284i \(0.465949\pi\)
\(480\) 2.38160e8 0.0982932
\(481\) −1.92162e9 + 1.28646e9i −0.787336 + 0.527094i
\(482\) 1.04420e9 0.424738
\(483\) −7.73692e8 + 2.81601e8i −0.312430 + 0.113715i
\(484\) −2.83894e8 − 1.03329e8i −0.113815 − 0.0414251i
\(485\) −2.87094e9 + 2.40901e9i −1.14269 + 0.958831i
\(486\) 3.17867e8 + 1.80271e9i 0.125608 + 0.712360i
\(487\) −6.13665e8 −0.240757 −0.120379 − 0.992728i \(-0.538411\pi\)
−0.120379 + 0.992728i \(0.538411\pi\)
\(488\) 1.52503e8 + 8.64887e8i 0.0594031 + 0.336892i
\(489\) −1.24309e9 + 2.15310e9i −0.480753 + 0.832688i
\(490\) −9.72951e8 − 8.16403e8i −0.373598 − 0.313486i
\(491\) −2.07352e9 − 3.59144e9i −0.790539 − 1.36925i −0.925634 − 0.378421i \(-0.876467\pi\)
0.135095 − 0.990833i \(-0.456866\pi\)
\(492\) −3.39788e8 + 5.88530e8i −0.128626 + 0.222788i
\(493\) −2.20764e9 + 8.03516e8i −0.829783 + 0.302016i
\(494\) 2.23258e9 − 1.87336e9i 0.833227 − 0.699160i
\(495\) −9.41842e8 − 1.63132e9i −0.349028 − 0.604534i
\(496\) 7.90757e7 − 4.48461e8i 0.0290976 − 0.165021i
\(497\) −3.29689e8 + 1.86976e9i −0.120464 + 0.683185i
\(498\) −6.83118e8 − 5.73204e8i −0.247852 − 0.207973i
\(499\) 2.73218e9 + 9.94431e8i 0.984366 + 0.358280i 0.783536 − 0.621346i \(-0.213414\pi\)
0.200830 + 0.979626i \(0.435636\pi\)
\(500\) 1.36802e9 + 4.97919e8i 0.489438 + 0.178141i
\(501\) 1.42714e9 + 1.19751e9i 0.507030 + 0.425449i
\(502\) −2.79826e8 + 1.58697e9i −0.0987244 + 0.559894i
\(503\) −4.85481e8 + 2.75330e9i −0.170092 + 0.964642i 0.773565 + 0.633717i \(0.218472\pi\)
−0.943657 + 0.330924i \(0.892639\pi\)
\(504\) 4.39336e8 + 7.60952e8i 0.152859 + 0.264759i
\(505\) −9.33367e8 + 7.83188e8i −0.322502 + 0.270611i
\(506\) −9.34741e8 + 3.40218e8i −0.320748 + 0.116743i
\(507\) −8.77079e7 + 1.51915e8i −0.0298890 + 0.0517692i
\(508\) −6.30618e7 − 1.09226e8i −0.0213424 − 0.0369661i
\(509\) −5.21587e8 − 4.37663e8i −0.175313 − 0.147105i 0.550909 − 0.834565i \(-0.314281\pi\)
−0.726222 + 0.687460i \(0.758726\pi\)
\(510\) −6.00683e8 + 1.04041e9i −0.200516 + 0.347304i
\(511\) 5.51353e8 + 3.12688e9i 0.182792 + 1.03666i
\(512\) −1.34218e8 −0.0441942
\(513\) −8.35591e8 − 4.73887e9i −0.273264 − 1.54976i
\(514\) 6.23335e8 − 5.23040e8i 0.202465 − 0.169889i
\(515\) 1.65636e9 + 6.02866e8i 0.534355 + 0.194489i
\(516\) 3.11027e8 − 1.13204e8i 0.0996606 − 0.0362735i
\(517\) −4.46040e9 −1.41957
\(518\) 1.18562e9 + 2.68803e9i 0.374791 + 0.849729i
\(519\) −3.44540e9 −1.08182
\(520\) 9.60160e8 − 3.49470e8i 0.299455 − 0.108993i
\(521\) −9.94848e8 − 3.62095e8i −0.308194 − 0.112174i 0.183293 − 0.983058i \(-0.441324\pi\)
−0.491487 + 0.870885i \(0.663547\pi\)
\(522\) 1.00331e9 − 8.41880e8i 0.308738 − 0.259062i
\(523\) 3.64522e7 + 2.06731e8i 0.0111421 + 0.0631901i 0.989872 − 0.141964i \(-0.0453416\pi\)
−0.978730 + 0.205154i \(0.934231\pi\)
\(524\) −1.23416e9 −0.374726
\(525\) −4.19978e7 − 2.38181e8i −0.0126669 − 0.0718373i
\(526\) −1.82928e9 + 3.16841e9i −0.548063 + 0.949273i
\(527\) 1.75968e9 + 1.47655e9i 0.523718 + 0.439451i
\(528\) −2.75430e8 − 4.77058e8i −0.0814314 − 0.141043i
\(529\) 1.38308e9 − 2.39556e9i 0.406211 − 0.703578i
\(530\) 6.87080e8 − 2.50077e8i 0.200467 − 0.0729638i
\(531\) −3.02556e9 + 2.53874e9i −0.876950 + 0.735848i
\(532\) −1.85131e9 − 3.20656e9i −0.533075 − 0.923314i
\(533\) −5.06289e8 + 2.87131e9i −0.144828 + 0.821362i
\(534\) −1.32565e8 + 7.51814e8i −0.0376734 + 0.213657i
\(535\) −7.51155e8 − 6.30294e8i −0.212076 − 0.177953i
\(536\) 2.10312e9 + 7.65471e8i 0.589911 + 0.214710i
\(537\) −3.52394e9 − 1.28261e9i −0.982017 − 0.357425i
\(538\) −2.73205e8 − 2.29246e8i −0.0756398 − 0.0634693i
\(539\) −5.10129e8 + 2.89309e9i −0.140320 + 0.795794i
\(540\) 2.92953e8 − 1.66142e9i 0.0800607 − 0.454047i
\(541\) 1.24887e9 + 2.16310e9i 0.339098 + 0.587335i 0.984263 − 0.176708i \(-0.0565448\pi\)
−0.645165 + 0.764043i \(0.723212\pi\)
\(542\) 9.69237e8 − 8.13287e8i 0.261476 − 0.219405i
\(543\) −2.34601e9 + 8.53879e8i −0.628827 + 0.228874i
\(544\) 3.38522e8 − 5.86338e8i 0.0901552 − 0.156153i
\(545\) 6.05115e8 + 1.04809e9i 0.160122 + 0.277339i
\(546\) −1.49852e9 − 1.25740e9i −0.393992 − 0.330598i
\(547\) −2.51187e9 + 4.35069e9i −0.656208 + 1.13659i 0.325382 + 0.945583i \(0.394507\pi\)
−0.981590 + 0.191003i \(0.938826\pi\)
\(548\) −4.49004e8 − 2.54643e9i −0.116552 − 0.660997i
\(549\) 2.46976e9 0.637019
\(550\) −5.07399e7 − 2.87760e8i −0.0130041 − 0.0737499i
\(551\) −4.22785e9 + 3.54759e9i −1.07669 + 0.903446i
\(552\) −3.32352e8 − 1.20966e8i −0.0841030 − 0.0306110i
\(553\) 7.58740e9 − 2.76159e9i 1.90790 − 0.694418i
\(554\) 1.58839e9 0.396893
\(555\) 6.24727e8 − 2.15045e9i 0.155119 − 0.533955i
\(556\) 2.20984e9 0.545254
\(557\) −2.24446e9 + 8.16918e8i −0.550325 + 0.200302i −0.602191 − 0.798352i \(-0.705705\pi\)
0.0518656 + 0.998654i \(0.483483\pi\)
\(558\) −1.20339e9 − 4.37998e8i −0.293215 − 0.106722i
\(559\) 1.08782e9 − 9.12787e8i 0.263399 − 0.221018i
\(560\) −2.25416e8 − 1.27839e9i −0.0542408 − 0.307615i
\(561\) 2.77874e9 0.664474
\(562\) −4.37829e8 − 2.48305e9i −0.104047 − 0.590078i
\(563\) 1.48429e9 − 2.57086e9i 0.350540 − 0.607154i −0.635804 − 0.771851i \(-0.719331\pi\)
0.986344 + 0.164697i \(0.0526646\pi\)
\(564\) −1.21489e9 − 1.01941e9i −0.285140 − 0.239261i
\(565\) 4.40841e8 + 7.63559e8i 0.102828 + 0.178104i
\(566\) 2.03703e9 − 3.52824e9i 0.472215 − 0.817901i
\(567\) 4.91858e8 − 1.79022e8i 0.113318 − 0.0412444i
\(568\) −6.24768e8 + 5.24242e8i −0.143054 + 0.120036i
\(569\) 3.09335e9 + 5.35783e9i 0.703940 + 1.21926i 0.967073 + 0.254500i \(0.0819109\pi\)
−0.263133 + 0.964760i \(0.584756\pi\)
\(570\) −4.90081e8 + 2.77939e9i −0.110842 + 0.628619i
\(571\) −6.67305e8 + 3.78448e9i −0.150002 + 0.850706i 0.813211 + 0.581969i \(0.197717\pi\)
−0.963214 + 0.268737i \(0.913394\pi\)
\(572\) −1.81044e9 − 1.51914e9i −0.404481 − 0.339400i
\(573\) 3.77358e9 + 1.37347e9i 0.837939 + 0.304985i
\(574\) 3.48072e9 + 1.26688e9i 0.768207 + 0.279604i
\(575\) −1.43716e8 − 1.20592e8i −0.0315259 − 0.0264534i
\(576\) −6.55432e7 + 3.71714e8i −0.0142905 + 0.0810457i
\(577\) 1.60297e8 − 9.09091e8i 0.0347385 − 0.197012i −0.962500 − 0.271283i \(-0.912552\pi\)
0.997238 + 0.0742715i \(0.0236631\pi\)
\(578\) 6.62777e7 + 1.14796e8i 0.0142764 + 0.0247275i
\(579\) 1.75001e9 − 1.46843e9i 0.374685 − 0.314398i
\(580\) −1.81826e9 + 6.61792e8i −0.386952 + 0.140839i
\(581\) −2.43029e9 + 4.20938e9i −0.514092 + 0.890434i
\(582\) 1.54106e9 + 2.66920e9i 0.324033 + 0.561242i
\(583\) −1.29553e9 − 1.08708e9i −0.270775 − 0.227207i
\(584\) −6.81962e8 + 1.18119e9i −0.141682 + 0.245401i
\(585\) −4.98971e8 − 2.82981e9i −0.103046 − 0.584401i
\(586\) −4.44445e9 −0.912382
\(587\) −1.27764e9 − 7.24585e9i −0.260720 − 1.47862i −0.780951 − 0.624592i \(-0.785265\pi\)
0.520231 − 0.854026i \(-0.325846\pi\)
\(588\) −8.00149e8 + 6.71405e8i −0.162312 + 0.136196i
\(589\) 5.07094e9 + 1.84567e9i 1.02255 + 0.372178i
\(590\) 5.48307e9 − 1.99568e9i 1.09911 − 0.400044i
\(591\) −4.29013e9 −0.854897
\(592\) −3.52072e8 + 1.21191e9i −0.0697439 + 0.240075i
\(593\) 4.72680e9 0.930841 0.465421 − 0.885090i \(-0.345903\pi\)
0.465421 + 0.885090i \(0.345903\pi\)
\(594\) −3.66679e9 + 1.33460e9i −0.717850 + 0.261276i
\(595\) 6.15328e9 + 2.23961e9i 1.19756 + 0.435876i
\(596\) 3.58588e9 − 3.00891e9i 0.693799 − 0.582166i
\(597\) 1.93234e8 + 1.09588e9i 0.0371684 + 0.210792i
\(598\) −1.51741e9 −0.290167
\(599\) −7.46139e8 − 4.23156e9i −0.141849 − 0.804465i −0.969843 − 0.243729i \(-0.921629\pi\)
0.827995 − 0.560736i \(-0.189482\pi\)
\(600\) 5.19465e7 − 8.99740e7i 0.00981809 − 0.0170054i
\(601\) 1.39659e9 + 1.17188e9i 0.262427 + 0.220202i 0.764501 − 0.644622i \(-0.222985\pi\)
−0.502075 + 0.864824i \(0.667430\pi\)
\(602\) −9.02043e8 − 1.56238e9i −0.168515 − 0.291877i
\(603\) 3.14698e9 − 5.45074e9i 0.584499 − 1.01238i
\(604\) 2.31468e9 − 8.42475e8i 0.427427 − 0.155571i
\(605\) 9.61521e8 − 8.06812e8i 0.176529 − 0.148125i
\(606\) 5.01012e8 + 8.67778e8i 0.0914522 + 0.158400i
\(607\) 1.38727e9 − 7.86759e9i 0.251768 − 1.42785i −0.552467 − 0.833534i \(-0.686314\pi\)
0.804235 − 0.594311i \(-0.202575\pi\)
\(608\) 2.76191e8 − 1.56636e9i 0.0498365 − 0.282637i
\(609\) 2.83774e9 + 2.38115e9i 0.509111 + 0.427195i
\(610\) −3.42869e9 − 1.24794e9i −0.611608 − 0.222607i
\(611\) −6.39377e9 − 2.32714e9i −1.13400 − 0.412742i
\(612\) −1.45854e9 − 1.22386e9i −0.257210 − 0.215825i
\(613\) 4.97932e8 − 2.82391e9i 0.0873089 − 0.495153i −0.909526 − 0.415648i \(-0.863555\pi\)
0.996834 − 0.0795053i \(-0.0253341\pi\)
\(614\) 5.63283e6 − 3.19454e7i 0.000982059 − 0.00556953i
\(615\) −1.41170e9 − 2.44514e9i −0.244726 − 0.423877i
\(616\) −2.30007e9 + 1.92998e9i −0.396468 + 0.332676i
\(617\) 4.21490e9 − 1.53410e9i 0.722418 − 0.262939i 0.0454663 − 0.998966i \(-0.485523\pi\)
0.676952 + 0.736027i \(0.263300\pi\)
\(618\) 7.24801e8 − 1.25539e9i 0.123526 − 0.213954i
\(619\) −5.52823e9 − 9.57517e9i −0.936847 − 1.62267i −0.771307 − 0.636463i \(-0.780397\pi\)
−0.165539 − 0.986203i \(-0.552936\pi\)
\(620\) 1.44931e9 + 1.21612e9i 0.244225 + 0.204929i
\(621\) −1.25269e9 + 2.16972e9i −0.209904 + 0.363565i
\(622\) −5.74591e8 − 3.25867e9i −0.0957398 − 0.542967i
\(623\) 4.16107e9 0.689440
\(624\) −1.45918e8 − 8.27540e8i −0.0240415 − 0.136346i
\(625\) −4.18907e9 + 3.51505e9i −0.686337 + 0.575905i
\(626\) 5.14746e9 + 1.87352e9i 0.838654 + 0.305245i
\(627\) 6.13418e9 − 2.23266e9i 0.993848 − 0.361731i
\(628\) −8.44716e8 −0.136098
\(629\) −4.40633e9 − 4.59472e9i −0.705991 − 0.736177i
\(630\) −3.65057e9 −0.581660
\(631\) −8.94410e9 + 3.25539e9i −1.41721 + 0.515822i −0.933237 − 0.359262i \(-0.883029\pi\)
−0.483972 + 0.875083i \(0.660806\pi\)
\(632\) 3.25929e9 + 1.18629e9i 0.513586 + 0.186930i
\(633\) −1.25500e9 + 1.05307e9i −0.196666 + 0.165023i
\(634\) −5.14116e8 − 2.91570e9i −0.0801215 − 0.454391i
\(635\) 5.23999e8 0.0812124
\(636\) −1.04417e8 − 5.92179e8i −0.0160943 − 0.0912752i
\(637\) −2.24066e9 + 3.88095e9i −0.343470 + 0.594908i
\(638\) 3.42844e9 + 2.87680e9i 0.522666 + 0.438569i
\(639\) 1.14679e9 + 1.98629e9i 0.173872 + 0.301155i
\(640\) 2.78814e8 − 4.82919e8i 0.0420421 − 0.0728190i
\(641\) −3.59008e9 + 1.30668e9i −0.538395 + 0.195960i −0.596883 − 0.802328i \(-0.703594\pi\)
0.0584878 + 0.998288i \(0.481372\pi\)
\(642\) −6.17745e8 + 5.18350e8i −0.0921376 + 0.0773126i
\(643\) 1.35856e9 + 2.35310e9i 0.201531 + 0.349062i 0.949022 − 0.315210i \(-0.102075\pi\)
−0.747491 + 0.664272i \(0.768742\pi\)
\(644\) −3.34756e8 + 1.89850e9i −0.0493888 + 0.280098i
\(645\) −2.38790e8 + 1.35425e9i −0.0350394 + 0.198719i
\(646\) 6.14612e9 + 5.15721e9i 0.896989 + 0.752663i
\(647\) 1.24160e8 + 4.51905e7i 0.0180225 + 0.00655967i 0.351016 − 0.936370i \(-0.385836\pi\)
−0.332993 + 0.942929i \(0.608059\pi\)
\(648\) 2.11286e8 + 7.69017e7i 0.0305041 + 0.0111026i
\(649\) −1.03387e10 − 8.67518e9i −1.48460 − 1.24572i
\(650\) 7.74010e7 − 4.38963e8i 0.0110548 − 0.0626947i
\(651\) 6.28965e8 − 3.56704e9i 0.0893497 − 0.506728i
\(652\) 2.91058e9 + 5.04126e9i 0.411256 + 0.712316i
\(653\) 3.08967e9 − 2.59254e9i 0.434226 − 0.364359i −0.399318 − 0.916813i \(-0.630753\pi\)
0.833543 + 0.552454i \(0.186309\pi\)
\(654\) 9.35263e8 − 3.40408e8i 0.130741 − 0.0475858i
\(655\) 2.56376e9 − 4.44056e9i 0.356478 − 0.617438i
\(656\) 7.95581e8 + 1.37799e9i 0.110032 + 0.190582i
\(657\) 2.93827e9 + 2.46550e9i 0.404215 + 0.339177i
\(658\) −4.32212e9 + 7.48613e9i −0.591434 + 1.02439i
\(659\) −1.38614e9 − 7.86116e9i −0.188672 − 1.07001i −0.921147 − 0.389216i \(-0.872746\pi\)
0.732475 − 0.680794i \(-0.238365\pi\)
\(660\) 2.28863e9 0.309864
\(661\) 1.06255e9 + 6.02600e9i 0.143101 + 0.811566i 0.968872 + 0.247561i \(0.0796291\pi\)
−0.825771 + 0.564005i \(0.809260\pi\)
\(662\) −3.92837e9 + 3.29629e9i −0.526271 + 0.441594i
\(663\) 3.98319e9 + 1.44976e9i 0.530803 + 0.193196i
\(664\) −1.96202e9 + 7.14117e8i −0.260085 + 0.0946632i
\(665\) 1.53831e10 2.02847
\(666\) 3.18445e9 + 1.56688e9i 0.417710 + 0.205530i
\(667\) 2.87352e9 0.374951
\(668\) 4.09896e9 − 1.49190e9i 0.532054 − 0.193652i
\(669\) −2.90771e9 − 1.05832e9i −0.375456 − 0.136655i
\(670\) −7.12304e9 + 5.97694e9i −0.914963 + 0.767745i
\(671\) 1.46550e9 + 8.31125e9i 0.187265 + 1.06203i
\(672\) −1.06756e9 −0.135707
\(673\) −2.52845e9 − 1.43396e10i −0.319744 − 1.81336i −0.544293 − 0.838895i \(-0.683202\pi\)
0.224549 − 0.974463i \(-0.427909\pi\)
\(674\) −2.43897e9 + 4.22442e9i −0.306829 + 0.531444i
\(675\) −5.63767e8 − 4.73057e8i −0.0705565 − 0.0592039i
\(676\) 2.05360e8 + 3.55693e8i 0.0255683 + 0.0442856i
\(677\) −4.66128e9 + 8.07357e9i −0.577357 + 1.00001i 0.418424 + 0.908252i \(0.362583\pi\)
−0.995781 + 0.0917603i \(0.970751\pi\)
\(678\) 6.81362e8 − 2.47995e8i 0.0839602 − 0.0305590i
\(679\) 1.28692e10 − 1.07985e10i 1.57763 − 1.32379i
\(680\) 1.40644e9 + 2.43603e9i 0.171530 + 0.297099i
\(681\) −1.29952e9 + 7.36995e9i −0.157677 + 0.894231i
\(682\) 7.59889e8 − 4.30954e9i 0.0917286 − 0.520219i
\(683\) 3.57434e9 + 2.99923e9i 0.429263 + 0.360194i 0.831673 − 0.555265i \(-0.187383\pi\)
−0.402411 + 0.915459i \(0.631828\pi\)
\(684\) −4.20313e9 − 1.52981e9i −0.502200 − 0.182786i
\(685\) 1.00948e10 + 3.67422e9i 1.20000 + 0.436766i
\(686\) −1.65417e9 − 1.38801e9i −0.195634 − 0.164157i
\(687\) 1.27513e9 − 7.23162e9i 0.150040 − 0.850917i
\(688\) 1.34573e8 − 7.63202e8i 0.0157543 − 0.0893470i
\(689\) −1.28992e9 − 2.23420e9i −0.150243 − 0.260228i
\(690\) 1.12564e9 − 9.44527e8i 0.130445 − 0.109457i
\(691\) −4.04470e9 + 1.47215e9i −0.466351 + 0.169738i −0.564499 − 0.825434i \(-0.690931\pi\)
0.0981474 + 0.995172i \(0.468708\pi\)
\(692\) −4.03353e9 + 6.98628e9i −0.462716 + 0.801447i
\(693\) 4.22186e9 + 7.31247e9i 0.481878 + 0.834637i
\(694\) −7.47280e8 − 6.27043e8i −0.0848644 − 0.0712097i
\(695\) −4.59055e9 + 7.95107e9i −0.518703 + 0.898419i
\(696\) 2.76325e8 + 1.56712e9i 0.0310661 + 0.176185i
\(697\) −8.02641e9 −0.897856
\(698\) −9.86684e8 − 5.59576e9i −0.109821 − 0.622824i
\(699\) 3.19207e7 − 2.67846e7i 0.00353510 − 0.00296630i
\(700\) −5.32130e8 − 1.93680e8i −0.0586374 − 0.0213423i
\(701\) −1.95546e9 + 7.11729e8i −0.214405 + 0.0780372i −0.446990 − 0.894539i \(-0.647504\pi\)
0.232584 + 0.972576i \(0.425282\pi\)
\(702\) −5.95247e9 −0.649408
\(703\) −1.34189e10 − 6.60264e9i −1.45671 − 0.716761i
\(704\) −1.28978e9 −0.139320
\(705\) 6.19158e9 − 2.25355e9i 0.665486 − 0.242217i
\(706\) −6.90345e9 − 2.51265e9i −0.738328 − 0.268730i
\(707\) 4.18387e9 − 3.51068e9i 0.445256 − 0.373614i
\(708\) −8.33275e8 − 4.72574e9i −0.0882413 − 0.500441i
\(709\) −1.84733e10 −1.94663 −0.973314 − 0.229478i \(-0.926298\pi\)
−0.973314 + 0.229478i \(0.926298\pi\)
\(710\) −5.88395e8 − 3.33695e9i −0.0616971 − 0.349902i
\(711\) 4.87702e9 − 8.44725e9i 0.508875 − 0.881397i
\(712\) 1.36927e9 + 1.14895e9i 0.142170 + 0.119295i
\(713\) −1.40482e9 − 2.43323e9i −0.145147 − 0.251402i
\(714\) 2.69259e9 − 4.66371e9i 0.276839 − 0.479499i
\(715\) 9.22679e9 − 3.35828e9i 0.944016 − 0.343594i
\(716\) −6.72625e9 + 5.64400e9i −0.684822 + 0.574634i
\(717\) −1.39939e9 − 2.42382e9i −0.141783 − 0.245575i
\(718\) −7.27366e8 + 4.12510e9i −0.0733360 + 0.415909i
\(719\) 8.46377e8 − 4.80004e9i 0.0849205 − 0.481608i −0.912453 − 0.409181i \(-0.865814\pi\)
0.997374 − 0.0724271i \(-0.0230745\pi\)
\(720\) −1.20128e9 − 1.00800e9i −0.119945 − 0.100646i
\(721\) −7.42472e9 − 2.70238e9i −0.737746 − 0.268518i
\(722\) 1.09918e10 + 4.00068e9i 1.08690 + 0.395598i
\(723\) 2.73308e9 + 2.29333e9i 0.268948 + 0.225675i
\(724\) −1.01506e9 + 5.75668e9i −0.0994045 + 0.563751i
\(725\) −1.46574e8 + 8.31265e8i −0.0142848 + 0.0810134i
\(726\) −5.16125e8 − 8.93954e8i −0.0500583 − 0.0867036i
\(727\) −1.33450e10 + 1.11978e10i −1.28810 + 1.08084i −0.296027 + 0.955180i \(0.595662\pi\)
−0.992073 + 0.125664i \(0.959894\pi\)
\(728\) −4.30397e9 + 1.56652e9i −0.413437 + 0.150479i
\(729\) −2.64701e9 + 4.58476e9i −0.253052 + 0.438299i
\(730\) −2.83331e9 − 4.90744e9i −0.269565 − 0.466901i
\(731\) 2.99467e9 + 2.51283e9i 0.283556 + 0.237931i
\(732\) −1.50035e9 + 2.59868e9i −0.141385 + 0.244886i
\(733\) −3.28458e9 − 1.86278e10i −0.308046 − 1.74702i −0.608808 − 0.793318i \(-0.708352\pi\)
0.300761 − 0.953699i \(-0.402759\pi\)
\(734\) 7.87068e9 0.734642
\(735\) −7.53566e8 − 4.27368e9i −0.0700028 − 0.397006i
\(736\) −6.34370e8 + 5.32300e8i −0.0586503 + 0.0492135i
\(737\) 2.02102e10 + 7.35590e9i 1.85966 + 0.676861i
\(738\) 4.20482e9 − 1.53043e9i 0.385079 − 0.140157i
\(739\) 3.06663e9 0.279515 0.139758 − 0.990186i \(-0.455368\pi\)
0.139758 + 0.990186i \(0.455368\pi\)
\(740\) −3.62914e9 − 3.78431e9i −0.329225 − 0.343301i
\(741\) 9.95789e9 0.899091
\(742\) −3.07987e9 + 1.12098e9i −0.276770 + 0.100736i
\(743\) −8.82270e9 − 3.21120e9i −0.789116 − 0.287215i −0.0841475 − 0.996453i \(-0.526817\pi\)
−0.704969 + 0.709239i \(0.749039\pi\)
\(744\) 1.19190e9 − 1.00013e9i 0.106105 − 0.0890326i
\(745\) 3.37712e9 + 1.91526e10i 0.299226 + 1.69699i
\(746\) 9.28924e9 0.819208
\(747\) 1.01961e9 + 5.78251e9i 0.0894980 + 0.507568i
\(748\) 3.25307e9 − 5.63449e9i 0.284209 − 0.492265i
\(749\) 3.36709e9 + 2.82533e9i 0.292799 + 0.245687i
\(750\) 2.48709e9 + 4.30776e9i 0.215266 + 0.372852i
\(751\) −3.63487e9 + 6.29578e9i −0.313148 + 0.542388i −0.979042 − 0.203658i \(-0.934717\pi\)
0.665894 + 0.746046i \(0.268050\pi\)
\(752\) −3.48934e9 + 1.27002e9i −0.299213 + 0.108905i
\(753\) −4.21779e9 + 3.53915e9i −0.360000 + 0.302076i
\(754\) 3.41357e9 + 5.91249e9i 0.290008 + 0.502308i
\(755\) −1.77709e9 + 1.00784e10i −0.150278 + 0.852269i
\(756\) −1.31318e9 + 7.44740e9i −0.110534 + 0.626871i
\(757\) 6.92963e9 + 5.81465e9i 0.580596 + 0.487178i 0.885143 − 0.465319i \(-0.154060\pi\)