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Properties

Label 74.8.f.b.9.9
Level $74$
Weight $8$
Character 74.9
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 9.9
Character \(\chi\) \(=\) 74.9
Dual form 74.8.f.b.33.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.38919 - 7.87846i) q^{2} +(9.76159 - 55.3608i) q^{3} +(-60.1403 + 21.8893i) q^{4} +(-282.513 - 237.057i) q^{5} -449.718 q^{6} +(-1337.20 - 1122.04i) q^{7} +(256.000 + 443.405i) q^{8} +(-914.416 - 332.820i) q^{9} +O(q^{10})\) \(q+(-1.38919 - 7.87846i) q^{2} +(9.76159 - 55.3608i) q^{3} +(-60.1403 + 21.8893i) q^{4} +(-282.513 - 237.057i) q^{5} -449.718 q^{6} +(-1337.20 - 1122.04i) q^{7} +(256.000 + 443.405i) q^{8} +(-914.416 - 332.820i) q^{9} +(-1475.18 + 2555.09i) q^{10} +(-677.878 - 1174.12i) q^{11} +(624.742 + 3543.09i) q^{12} +(7734.60 - 2815.16i) q^{13} +(-6982.36 + 12093.8i) q^{14} +(-15881.4 + 13326.1i) q^{15} +(3137.72 - 2632.86i) q^{16} +(-1857.85 - 676.201i) q^{17} +(-1351.82 + 7666.54i) q^{18} +(5389.24 - 30563.9i) q^{19} +(22179.5 + 8072.66i) q^{20} +(-75170.4 + 63075.5i) q^{21} +(-8308.56 + 6971.71i) q^{22} +(4357.48 - 7547.38i) q^{23} +(27046.2 - 9844.01i) q^{24} +(10051.6 + 57005.4i) q^{25} +(-32923.9 - 57025.9i) q^{26} +(34119.5 - 59096.7i) q^{27} +(104980. + 38209.7i) q^{28} +(-35273.0 - 61094.6i) q^{29} +(127051. + 106609. i) q^{30} +181572. q^{31} +(-25101.7 - 21062.9i) q^{32} +(-71617.3 + 26066.6i) q^{33} +(-2746.53 + 15576.3i) q^{34} +(111789. + 633985. i) q^{35} +62278.5 q^{36} +(32292.5 + 306413. i) q^{37} -248283. q^{38} +(-80347.5 - 455673. i) q^{39} +(32788.8 - 185954. i) q^{40} +(633535. - 230588. i) q^{41} +(601363. + 504604. i) q^{42} -842620. q^{43} +(66468.5 + 55773.7i) q^{44} +(179438. + 310795. i) q^{45} +(-65515.1 - 23845.6i) q^{46} +(-215414. + 373107. i) q^{47} +(-115128. - 199407. i) q^{48} +(386114. + 2.18976e6i) q^{49} +(435152. - 158382. i) q^{50} +(-55570.5 + 96251.0i) q^{51} +(-403539. + 338610. i) q^{52} +(688013. - 577312. i) q^{53} +(-512990. - 186713. i) q^{54} +(-86823.5 + 492400. i) q^{55} +(155197. - 880165. i) q^{56} +(-1.63943e6 - 596705. i) q^{57} +(-432331. + 362769. i) q^{58} +(-690320. + 579247. i) q^{59} +(663416. - 1.14907e6i) q^{60} +(2.82851e6 - 1.02949e6i) q^{61} +(-252236. - 1.43050e6i) q^{62} +(849318. + 1.47106e6i) q^{63} +(-131072. + 227023. i) q^{64} +(-2.85248e6 - 1.03822e6i) q^{65} +(304854. + 528023. i) q^{66} +(-2.03726e6 - 1.70946e6i) q^{67} +126533. q^{68} +(-375293. - 314908. i) q^{69} +(4.83953e6 - 1.76145e6i) q^{70} +(-51412.3 + 291573. i) q^{71} +(-86516.4 - 490659. i) q^{72} -2.39926e6 q^{73} +(2.36920e6 - 680080. i) q^{74} +3.25398e6 q^{75} +(344911. + 1.95609e6i) q^{76} +(-410955. + 2.33064e6i) q^{77} +(-3.47839e6 + 1.26603e6i) q^{78} +(-5.24708e6 - 4.40282e6i) q^{79} -1.51058e6 q^{80} +(-4.56885e6 - 3.83372e6i) q^{81} +(-2.69678e6 - 4.67095e6i) q^{82} +(4.59173e6 + 1.67125e6i) q^{83} +(3.14010e6 - 5.43881e6i) q^{84} +(364569. + 631451. i) q^{85} +(1.17056e6 + 6.63855e6i) q^{86} +(-3.72656e6 + 1.35636e6i) q^{87} +(347074. - 601149. i) q^{88} +(-6.31365e6 + 5.29778e6i) q^{89} +(2.19931e6 - 1.84544e6i) q^{90} +(-1.35014e7 - 4.91412e6i) q^{91} +(-96853.6 + 549284. i) q^{92} +(1.77243e6 - 1.00519e7i) q^{93} +(3.23876e6 + 1.17881e6i) q^{94} +(-8.76792e6 + 7.35715e6i) q^{95} +(-1.41109e6 + 1.18404e6i) q^{96} +(-2.82033e6 + 4.88496e6i) q^{97} +(1.67156e7 - 6.08398e6i) q^{98} +(229092. + 1.29925e6i) 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 \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.38919 − 7.87846i −0.122788 − 0.696364i
\(3\) 9.76159 − 55.3608i 0.208736 − 1.18380i −0.682717 − 0.730683i \(-0.739202\pi\)
0.891452 − 0.453115i \(-0.149687\pi\)
\(4\) −60.1403 + 21.8893i −0.469846 + 0.171010i
\(5\) −282.513 − 237.057i −1.01075 − 0.848121i −0.0223136 − 0.999751i \(-0.507103\pi\)
−0.988437 + 0.151630i \(0.951548\pi\)
\(6\) −449.718 −0.849985
\(7\) −1337.20 − 1122.04i −1.47351 − 1.23642i −0.912798 − 0.408412i \(-0.866083\pi\)
−0.560713 − 0.828010i \(-0.689473\pi\)
\(8\) 256.000 + 443.405i 0.176777 + 0.306186i
\(9\) −914.416 − 332.820i −0.418114 − 0.152181i
\(10\) −1475.18 + 2555.09i −0.466493 + 0.807990i
\(11\) −677.878 − 1174.12i −0.153560 − 0.265973i 0.778974 − 0.627056i \(-0.215740\pi\)
−0.932534 + 0.361083i \(0.882407\pi\)
\(12\) 624.742 + 3543.09i 0.104368 + 0.591899i
\(13\) 7734.60 − 2815.16i 0.976418 − 0.355387i 0.195972 − 0.980610i \(-0.437214\pi\)
0.780447 + 0.625222i \(0.214992\pi\)
\(14\) −6982.36 + 12093.8i −0.680071 + 1.17792i
\(15\) −15881.4 + 13326.1i −1.21498 + 1.01949i
\(16\) 3137.72 − 2632.86i 0.191511 − 0.160697i
\(17\) −1857.85 − 676.201i −0.0917146 − 0.0333814i 0.295755 − 0.955264i \(-0.404429\pi\)
−0.387470 + 0.921882i \(0.626651\pi\)
\(18\) −1351.82 + 7666.54i −0.0546342 + 0.309846i
\(19\) 5389.24 − 30563.9i 0.180256 − 1.02228i −0.751644 − 0.659569i \(-0.770739\pi\)
0.931900 − 0.362714i \(-0.118150\pi\)
\(20\) 22179.5 + 8072.66i 0.619935 + 0.225638i
\(21\) −75170.4 + 63075.5i −1.77125 + 1.48625i
\(22\) −8308.56 + 6971.71i −0.166359 + 0.139592i
\(23\) 4357.48 − 7547.38i 0.0746772 − 0.129345i −0.826269 − 0.563276i \(-0.809541\pi\)
0.900946 + 0.433931i \(0.142874\pi\)
\(24\) 27046.2 − 9844.01i 0.399362 − 0.145356i
\(25\) 10051.6 + 57005.4i 0.128660 + 0.729670i
\(26\) −32923.9 − 57025.9i −0.367371 − 0.636306i
\(27\) 34119.5 − 59096.7i 0.333603 − 0.577817i
\(28\) 104980. + 38209.7i 0.903764 + 0.328943i
\(29\) −35273.0 − 61094.6i −0.268565 − 0.465168i 0.699927 − 0.714215i \(-0.253216\pi\)
−0.968491 + 0.249047i \(0.919883\pi\)
\(30\) 127051. + 106609.i 0.859123 + 0.720890i
\(31\) 181572. 1.09467 0.547333 − 0.836915i \(-0.315643\pi\)
0.547333 + 0.836915i \(0.315643\pi\)
\(32\) −25101.7 − 21062.9i −0.135419 − 0.113630i
\(33\) −71617.3 + 26066.6i −0.346912 + 0.126266i
\(34\) −2746.53 + 15576.3i −0.0119842 + 0.0679656i
\(35\) 111789. + 633985.i 0.440717 + 2.49943i
\(36\) 62278.5 0.222474
\(37\) 32292.5 + 306413.i 0.104808 + 0.994492i
\(38\) −248283. −0.734014
\(39\) −80347.5 − 455673.i −0.216893 − 1.23006i
\(40\) 32788.8 − 185954.i 0.0810057 − 0.459406i
\(41\) 633535. − 230588.i 1.43558 − 0.522508i 0.497054 − 0.867720i \(-0.334415\pi\)
0.938525 + 0.345212i \(0.112193\pi\)
\(42\) 601363. + 504604.i 1.25246 + 1.05094i
\(43\) −842620. −1.61619 −0.808095 − 0.589053i \(-0.799501\pi\)
−0.808095 + 0.589053i \(0.799501\pi\)
\(44\) 66468.5 + 55773.7i 0.117634 + 0.0987063i
\(45\) 179438. + 310795.i 0.293541 + 0.508429i
\(46\) −65515.1 − 23845.6i −0.0992405 − 0.0361206i
\(47\) −215414. + 373107.i −0.302643 + 0.524193i −0.976734 − 0.214455i \(-0.931202\pi\)
0.674091 + 0.738649i \(0.264536\pi\)
\(48\) −115128. − 199407.i −0.150257 − 0.260254i
\(49\) 386114. + 2.18976e6i 0.468845 + 2.65895i
\(50\) 435152. − 158382.i 0.492318 − 0.179189i
\(51\) −55570.5 + 96251.0i −0.0586609 + 0.101604i
\(52\) −403539. + 338610.i −0.397992 + 0.333955i
\(53\) 688013. − 577312.i 0.634792 − 0.532654i −0.267622 − 0.963524i \(-0.586238\pi\)
0.902414 + 0.430870i \(0.141793\pi\)
\(54\) −512990. − 186713.i −0.443334 − 0.161360i
\(55\) −86823.5 + 492400.i −0.0703668 + 0.399070i
\(56\) 155197. − 880165.i 0.118093 − 0.669739i
\(57\) −1.63943e6 − 596705.i −1.17255 − 0.426773i
\(58\) −432331. + 362769.i −0.290950 + 0.244136i
\(59\) −690320. + 579247.i −0.437591 + 0.367182i −0.834807 − 0.550543i \(-0.814421\pi\)
0.397216 + 0.917725i \(0.369976\pi\)
\(60\) 663416. − 1.14907e6i 0.396512 − 0.686779i
\(61\) 2.82851e6 − 1.02949e6i 1.59552 − 0.580722i 0.617017 − 0.786950i \(-0.288341\pi\)
0.978504 + 0.206227i \(0.0661186\pi\)
\(62\) −252236. − 1.43050e6i −0.134412 − 0.762287i
\(63\) 849318. + 1.47106e6i 0.427936 + 0.741207i
\(64\) −131072. + 227023.i −0.0625000 + 0.108253i
\(65\) −2.85248e6 − 1.03822e6i −1.28833 − 0.468913i
\(66\) 304854. + 528023.i 0.130523 + 0.226073i
\(67\) −2.03726e6 − 1.70946e6i −0.827530 − 0.694380i 0.127193 − 0.991878i \(-0.459403\pi\)
−0.954722 + 0.297498i \(0.903848\pi\)
\(68\) 126533. 0.0488003
\(69\) −375293. − 314908.i −0.137530 − 0.115402i
\(70\) 4.83953e6 − 1.76145e6i 1.68640 − 0.613799i
\(71\) −51412.3 + 291573.i −0.0170476 + 0.0966816i −0.992144 − 0.125098i \(-0.960075\pi\)
0.975097 + 0.221780i \(0.0711866\pi\)
\(72\) −86516.4 − 490659.i −0.0273171 − 0.154923i
\(73\) −2.39926e6 −0.721851 −0.360926 − 0.932595i \(-0.617539\pi\)
−0.360926 + 0.932595i \(0.617539\pi\)
\(74\) 2.36920e6 − 680080.i 0.679660 − 0.195096i
\(75\) 3.25398e6 0.890638
\(76\) 344911. + 1.95609e6i 0.0901280 + 0.511141i
\(77\) −410955. + 2.33064e6i −0.102583 + 0.581779i
\(78\) −3.47839e6 + 1.26603e6i −0.829941 + 0.302074i
\(79\) −5.24708e6 − 4.40282e6i −1.19736 − 1.00470i −0.999702 − 0.0244283i \(-0.992223\pi\)
−0.197654 − 0.980272i \(-0.563332\pi\)
\(80\) −1.51058e6 −0.329860
\(81\) −4.56885e6 − 3.83372e6i −0.955234 − 0.801536i
\(82\) −2.69678e6 − 4.67095e6i −0.540127 − 0.935528i
\(83\) 4.59173e6 + 1.67125e6i 0.881461 + 0.320826i 0.742799 − 0.669514i \(-0.233498\pi\)
0.138662 + 0.990340i \(0.455720\pi\)
\(84\) 3.14010e6 − 5.43881e6i 0.578050 − 1.00121i
\(85\) 364569. + 631451.i 0.0643892 + 0.111525i
\(86\) 1.17056e6 + 6.63855e6i 0.198448 + 1.12546i
\(87\) −3.72656e6 + 1.35636e6i −0.606724 + 0.220830i
\(88\) 347074. − 601149.i 0.0542916 − 0.0940357i
\(89\) −6.31365e6 + 5.29778e6i −0.949327 + 0.796580i −0.979184 − 0.202974i \(-0.934939\pi\)
0.0298573 + 0.999554i \(0.490495\pi\)
\(90\) 2.19931e6 − 1.84544e6i 0.318008 − 0.266841i
\(91\) −1.35014e7 − 4.91412e6i −1.87817 − 0.683598i
\(92\) −96853.6 + 549284.i −0.0129676 + 0.0735427i
\(93\) 1.77243e6 − 1.00519e7i 0.228496 − 1.29586i
\(94\) 3.23876e6 + 1.17881e6i 0.402190 + 0.146385i
\(95\) −8.76792e6 + 7.35715e6i −1.04921 + 0.880394i
\(96\) −1.41109e6 + 1.18404e6i −0.162782 + 0.136590i
\(97\) −2.82033e6 + 4.88496e6i −0.313761 + 0.543450i −0.979173 − 0.203026i \(-0.934922\pi\)
0.665412 + 0.746476i \(0.268256\pi\)
\(98\) 1.67156e7 − 6.08398e6i 1.79403 − 0.652974i
\(99\) 229092. + 1.29925e6i 0.0237294 + 0.134576i
\(100\) −1.85232e6 − 3.20830e6i −0.185232 − 0.320830i
\(101\) 1.02499e7 − 1.77534e7i 0.989911 − 1.71458i 0.372251 − 0.928132i \(-0.378586\pi\)
0.617661 − 0.786445i \(-0.288081\pi\)
\(102\) 835508. + 304100.i 0.0779560 + 0.0283737i
\(103\) −2.92232e6 − 5.06161e6i −0.263511 − 0.456414i 0.703662 − 0.710535i \(-0.251547\pi\)
−0.967172 + 0.254121i \(0.918214\pi\)
\(104\) 3.22831e6 + 2.70888e6i 0.281423 + 0.236142i
\(105\) 3.61891e7 3.05081
\(106\) −5.50411e6 − 4.61849e6i −0.448866 − 0.376643i
\(107\) −4.71151e6 + 1.71485e6i −0.371806 + 0.135326i −0.521163 − 0.853457i \(-0.674502\pi\)
0.149357 + 0.988783i \(0.452280\pi\)
\(108\) −758373. + 4.30095e6i −0.0579295 + 0.328535i
\(109\) 1.18117e6 + 6.69875e6i 0.0873615 + 0.495451i 0.996822 + 0.0796612i \(0.0253838\pi\)
−0.909461 + 0.415790i \(0.863505\pi\)
\(110\) 3.99997e6 0.286538
\(111\) 1.72785e7 + 1.20334e6i 1.19916 + 0.0835141i
\(112\) −7.14994e6 −0.480883
\(113\) 2.44029e6 + 1.38396e7i 0.159099 + 0.902294i 0.954942 + 0.296792i \(0.0959166\pi\)
−0.795844 + 0.605502i \(0.792972\pi\)
\(114\) −2.42364e6 + 1.37451e7i −0.153215 + 0.868925i
\(115\) −3.02021e6 + 1.09927e6i −0.185180 + 0.0674000i
\(116\) 3.45865e6 + 2.90215e6i 0.205733 + 0.172630i
\(117\) −8.00958e6 −0.462338
\(118\) 5.52256e6 + 4.63398e6i 0.309423 + 0.259637i
\(119\) 1.72559e6 + 2.98880e6i 0.0938690 + 0.162586i
\(120\) −9.97451e6 − 3.63042e6i −0.526935 − 0.191789i
\(121\) 8.82455e6 − 1.52846e7i 0.452839 − 0.784340i
\(122\) −1.20401e7 − 2.08541e7i −0.600305 − 1.03976i
\(123\) −6.58121e6 − 3.73239e7i −0.318888 − 1.80850i
\(124\) −1.09198e7 + 3.97447e6i −0.514325 + 0.187199i
\(125\) −3.73223e6 + 6.46442e6i −0.170916 + 0.296036i
\(126\) 1.04099e7 − 8.73490e6i 0.463604 − 0.389010i
\(127\) −1.24397e7 + 1.04382e7i −0.538888 + 0.452181i −0.871157 − 0.491004i \(-0.836630\pi\)
0.332270 + 0.943184i \(0.392186\pi\)
\(128\) 1.97068e6 + 717268.i 0.0830579 + 0.0302306i
\(129\) −8.22532e6 + 4.66481e7i −0.337356 + 1.91324i
\(130\) −4.21694e6 + 2.39154e7i −0.168343 + 0.954721i
\(131\) 5.92776e6 + 2.15753e6i 0.230378 + 0.0838507i 0.454630 − 0.890681i \(-0.349772\pi\)
−0.224252 + 0.974531i \(0.571994\pi\)
\(132\) 3.73651e6 − 3.13530e6i 0.141403 − 0.118651i
\(133\) −4.15005e7 + 3.48231e7i −1.52958 + 1.28347i
\(134\) −1.06378e7 + 1.84252e7i −0.381931 + 0.661524i
\(135\) −2.36485e7 + 8.60736e6i −0.827248 + 0.301094i
\(136\) −175778. − 996886.i −0.00599209 − 0.0339828i
\(137\) 2.26358e7 + 3.92063e7i 0.752096 + 1.30267i 0.946805 + 0.321808i \(0.104290\pi\)
−0.194709 + 0.980861i \(0.562376\pi\)
\(138\) −1.95964e6 + 3.39420e6i −0.0634745 + 0.109941i
\(139\) 2.15097e7 + 7.82890e6i 0.679334 + 0.247257i 0.658561 − 0.752527i \(-0.271165\pi\)
0.0207722 + 0.999784i \(0.493388\pi\)
\(140\) −2.06005e7 − 3.56811e7i −0.634497 − 1.09898i
\(141\) 1.85527e7 + 1.55676e7i 0.557367 + 0.467686i
\(142\) 2.36857e6 0.0694188
\(143\) −8.54845e6 − 7.17300e6i −0.244462 − 0.205128i
\(144\) −3.74545e6 + 1.36323e6i −0.104529 + 0.0380453i
\(145\) −4.51781e6 + 2.56218e7i −0.123066 + 0.697945i
\(146\) 3.33302e6 + 1.89025e7i 0.0886345 + 0.502671i
\(147\) 1.24996e8 3.24553
\(148\) −8.64925e6 − 1.77209e7i −0.219312 − 0.449335i
\(149\) 1.95606e7 0.484430 0.242215 − 0.970223i \(-0.422126\pi\)
0.242215 + 0.970223i \(0.422126\pi\)
\(150\) −4.52039e6 − 2.56364e7i −0.109359 − 0.620208i
\(151\) −1.24962e6 + 7.08697e6i −0.0295366 + 0.167510i −0.996008 − 0.0892640i \(-0.971549\pi\)
0.966471 + 0.256774i \(0.0826596\pi\)
\(152\) 1.49318e7 − 5.43474e6i 0.344874 − 0.125524i
\(153\) 1.47379e6 + 1.23666e6i 0.0332672 + 0.0279145i
\(154\) 1.89328e7 0.417726
\(155\) −5.12964e7 − 4.30428e7i −1.10643 − 0.928409i
\(156\) 1.48065e7 + 2.56456e7i 0.312260 + 0.540850i
\(157\) −3.38875e7 − 1.23340e7i −0.698861 − 0.254364i −0.0319363 − 0.999490i \(-0.510167\pi\)
−0.666924 + 0.745125i \(0.732390\pi\)
\(158\) −2.73983e7 + 4.74553e7i −0.552617 + 0.957160i
\(159\) −2.52443e7 − 4.37244e7i −0.498051 − 0.862649i
\(160\) 2.09848e6 + 1.19011e7i 0.0405028 + 0.229703i
\(161\) −1.42953e7 + 5.20307e6i −0.269962 + 0.0982583i
\(162\) −2.38569e7 + 4.13213e7i −0.440870 + 0.763610i
\(163\) 3.03178e7 − 2.54397e7i 0.548329 − 0.460103i −0.326046 − 0.945354i \(-0.605716\pi\)
0.874375 + 0.485251i \(0.161272\pi\)
\(164\) −3.30536e7 + 2.77353e7i −0.585147 + 0.490997i
\(165\) 2.64121e7 + 9.61322e6i 0.457730 + 0.166600i
\(166\) 6.78814e6 − 3.84975e7i 0.115179 − 0.653211i
\(167\) 1.17873e7 − 6.68491e7i 0.195842 − 1.11068i −0.715372 − 0.698744i \(-0.753743\pi\)
0.911214 − 0.411933i \(-0.135146\pi\)
\(168\) −4.72116e7 − 1.71836e7i −0.768186 − 0.279597i
\(169\) 3.83067e6 − 3.21432e6i 0.0610481 − 0.0512254i
\(170\) 4.46841e6 − 3.74944e6i 0.0697561 − 0.0585323i
\(171\) −1.51003e7 + 2.61545e7i −0.230940 + 0.400000i
\(172\) 5.06754e7 − 1.84444e7i 0.759361 − 0.276385i
\(173\) −1.63159e7 − 9.25318e7i −0.239579 − 1.35872i −0.832753 − 0.553645i \(-0.813236\pi\)
0.593174 − 0.805074i \(-0.297875\pi\)
\(174\) 1.58629e7 + 2.74754e7i 0.228276 + 0.395386i
\(175\) 5.05216e7 − 8.75060e7i 0.712597 − 1.23425i
\(176\) −5.21828e6 − 1.89930e6i −0.0721495 − 0.0262603i
\(177\) 2.53289e7 + 4.38710e7i 0.343329 + 0.594663i
\(178\) 5.05092e7 + 4.23823e7i 0.671275 + 0.563267i
\(179\) 7.69150e6 0.100236 0.0501182 − 0.998743i \(-0.484040\pi\)
0.0501182 + 0.998743i \(0.484040\pi\)
\(180\) −1.75945e7 − 1.47635e7i −0.224866 − 0.188685i
\(181\) 1.21946e8 − 4.43848e7i 1.52860 − 0.556365i 0.565321 − 0.824871i \(-0.308752\pi\)
0.963278 + 0.268506i \(0.0865300\pi\)
\(182\) −1.99597e7 + 1.13197e8i −0.245417 + 1.39183i
\(183\) −2.93827e7 − 1.66638e8i −0.354416 − 2.00999i
\(184\) 4.46206e6 0.0528048
\(185\) 6.35143e7 − 9.42210e7i 0.737515 − 1.09407i
\(186\) −8.16560e7 −0.930450
\(187\) 465453. + 2.63972e6i 0.00520512 + 0.0295197i
\(188\) 4.78799e6 − 2.71541e7i 0.0525534 − 0.298045i
\(189\) −1.11934e8 + 4.07406e7i −1.20599 + 0.438946i
\(190\) 7.01433e7 + 5.88572e7i 0.741906 + 0.622533i
\(191\) 1.25821e8 1.30658 0.653289 − 0.757109i \(-0.273389\pi\)
0.653289 + 0.757109i \(0.273389\pi\)
\(192\) 1.12887e7 + 9.47235e6i 0.115104 + 0.0965837i
\(193\) −8.05562e6 − 1.39527e7i −0.0806582 − 0.139704i 0.822875 − 0.568223i \(-0.192369\pi\)
−0.903533 + 0.428519i \(0.859036\pi\)
\(194\) 4.24039e7 + 1.54338e7i 0.416965 + 0.151763i
\(195\) −8.53213e7 + 1.47781e8i −0.824017 + 1.42724i
\(196\) −7.11534e7 − 1.23241e8i −0.674993 − 1.16912i
\(197\) −1.84091e7 − 1.04403e8i −0.171554 − 0.972931i −0.942047 − 0.335482i \(-0.891101\pi\)
0.770493 − 0.637449i \(-0.220010\pi\)
\(198\) 9.91781e6 − 3.60979e6i 0.0908003 − 0.0330486i
\(199\) 2.85651e7 − 4.94762e7i 0.256951 − 0.445052i −0.708473 − 0.705738i \(-0.750616\pi\)
0.965424 + 0.260686i \(0.0839489\pi\)
\(200\) −2.27033e7 + 1.90503e7i −0.200671 + 0.168383i
\(201\) −1.14524e8 + 9.60969e7i −0.994740 + 0.834686i
\(202\) −1.54109e8 − 5.60910e7i −1.31552 − 0.478810i
\(203\) −2.13838e7 + 1.21274e8i −0.179411 + 1.01749i
\(204\) 1.23516e6 − 7.00497e6i 0.0101864 − 0.0577697i
\(205\) −2.33645e8 − 8.50397e7i −1.89416 − 0.689419i
\(206\) −3.58181e7 + 3.00549e7i −0.285474 + 0.239541i
\(207\) −6.49647e6 + 5.45119e6i −0.0509075 + 0.0427164i
\(208\) 1.68571e7 − 2.91973e7i 0.129885 − 0.224968i
\(209\) −3.95389e7 + 1.43910e7i −0.299580 + 0.109038i
\(210\) −5.02734e7 − 2.85115e8i −0.374603 − 2.12448i
\(211\) 6.70745e7 + 1.16176e8i 0.491551 + 0.851391i 0.999953 − 0.00972870i \(-0.00309679\pi\)
−0.508402 + 0.861120i \(0.669763\pi\)
\(212\) −2.87404e7 + 4.97798e7i −0.207165 + 0.358821i
\(213\) 1.56399e7 + 5.69244e6i 0.110893 + 0.0403618i
\(214\) 2.00555e7 + 3.47372e7i 0.139890 + 0.242296i
\(215\) 2.38052e8 + 1.99749e8i 1.63356 + 1.37072i
\(216\) 3.49384e7 0.235893
\(217\) −2.42797e8 − 2.03731e8i −1.61300 − 1.35347i
\(218\) 5.11350e7 − 1.86116e7i 0.334288 − 0.121671i
\(219\) −2.34206e7 + 1.32825e8i −0.150676 + 0.854526i
\(220\) −5.55670e6 − 3.15136e7i −0.0351834 − 0.199535i
\(221\) −1.62733e7 −0.101415
\(222\) −1.45225e7 − 1.37800e8i −0.0890854 − 0.845303i
\(223\) −2.11674e8 −1.27821 −0.639103 − 0.769121i \(-0.720694\pi\)
−0.639103 + 0.769121i \(0.720694\pi\)
\(224\) 9.93259e6 + 5.63305e7i 0.0590466 + 0.334870i
\(225\) 9.78123e6 − 5.54721e7i 0.0572472 − 0.324665i
\(226\) 1.05644e8 − 3.84515e7i 0.608790 − 0.221581i
\(227\) −1.20402e8 − 1.01029e8i −0.683192 − 0.573266i 0.233745 − 0.972298i \(-0.424902\pi\)
−0.916937 + 0.399031i \(0.869346\pi\)
\(228\) 1.11657e8 0.623901
\(229\) −4.49682e7 − 3.77328e7i −0.247446 − 0.207632i 0.510625 − 0.859803i \(-0.329414\pi\)
−0.758072 + 0.652171i \(0.773858\pi\)
\(230\) 1.28561e7 + 2.22675e7i 0.0696728 + 0.120677i
\(231\) 1.25015e8 + 4.55016e7i 0.667296 + 0.242876i
\(232\) 1.80598e7 − 3.12804e7i 0.0949521 − 0.164462i
\(233\) 1.51704e8 + 2.62759e8i 0.785692 + 1.36086i 0.928585 + 0.371120i \(0.121026\pi\)
−0.142894 + 0.989738i \(0.545641\pi\)
\(234\) 1.11268e7 + 6.31032e7i 0.0567694 + 0.321956i
\(235\) 1.49305e8 − 5.43426e7i 0.750476 − 0.273151i
\(236\) 2.88367e7 − 4.99467e7i 0.142809 − 0.247352i
\(237\) −2.94964e8 + 2.47504e8i −1.43929 + 1.20771i
\(238\) 2.11500e7 − 1.77470e7i 0.101693 − 0.0853306i
\(239\) 3.39418e8 + 1.23538e8i 1.60821 + 0.585340i 0.981084 − 0.193580i \(-0.0620100\pi\)
0.627123 + 0.778920i \(0.284232\pi\)
\(240\) −1.47457e7 + 8.36271e7i −0.0688536 + 0.390488i
\(241\) −2.95114e7 + 1.67367e8i −0.135809 + 0.770214i 0.838483 + 0.544927i \(0.183443\pi\)
−0.974293 + 0.225286i \(0.927668\pi\)
\(242\) −1.32678e8 − 4.82908e7i −0.601789 − 0.219033i
\(243\) −1.42514e8 + 1.19583e8i −0.637139 + 0.534623i
\(244\) −1.47572e8 + 1.23828e8i −0.650340 + 0.545700i
\(245\) 4.10016e8 − 7.10169e8i 1.78123 − 3.08518i
\(246\) −2.84912e8 + 1.03700e8i −1.22022 + 0.444124i
\(247\) −4.43587e7 − 2.51571e8i −0.187301 − 1.06224i
\(248\) 4.64823e7 + 8.05097e7i 0.193512 + 0.335172i
\(249\) 1.37344e8 − 2.37888e8i 0.563785 − 0.976504i
\(250\) 5.61145e7 + 2.04240e7i 0.227135 + 0.0826705i
\(251\) 1.93491e8 + 3.35136e8i 0.772329 + 1.33771i 0.936283 + 0.351246i \(0.114242\pi\)
−0.163954 + 0.986468i \(0.552425\pi\)
\(252\) −8.32788e7 − 6.98792e7i −0.327818 − 0.275072i
\(253\) −1.18154e7 −0.0458697
\(254\) 9.95179e7 + 8.35055e7i 0.381051 + 0.319740i
\(255\) 3.85164e7 − 1.40188e7i 0.145464 − 0.0529445i
\(256\) 2.91333e6 − 1.65223e7i 0.0108530 − 0.0615505i
\(257\) 7.39188e7 + 4.19215e8i 0.271637 + 1.54053i 0.749445 + 0.662067i \(0.230320\pi\)
−0.477808 + 0.878464i \(0.658568\pi\)
\(258\) 3.78942e8 1.37374
\(259\) 3.00628e8 − 4.45969e8i 1.07518 − 1.59498i
\(260\) 1.94275e8 0.685504
\(261\) 1.19207e7 + 6.76055e7i 0.0415010 + 0.235364i
\(262\) 8.76324e6 − 4.96988e7i 0.0301030 − 0.170723i
\(263\) −4.10526e7 + 1.49419e7i −0.139154 + 0.0506480i −0.410658 − 0.911789i \(-0.634701\pi\)
0.271504 + 0.962437i \(0.412479\pi\)
\(264\) −2.98921e7 − 2.50824e7i −0.0999867 − 0.0838988i
\(265\) −3.31229e8 −1.09337
\(266\) 3.32004e8 + 2.78585e8i 1.08158 + 0.907552i
\(267\) 2.31658e8 + 4.01243e8i 0.744831 + 1.29009i
\(268\) 1.59940e8 + 5.82134e7i 0.507558 + 0.184736i
\(269\) −1.97974e8 + 3.42901e8i −0.620120 + 1.07408i 0.369343 + 0.929293i \(0.379583\pi\)
−0.989463 + 0.144786i \(0.953751\pi\)
\(270\) 1.00665e8 + 1.74357e8i 0.311247 + 0.539095i
\(271\) −6.48345e7 − 3.67694e8i −0.197885 − 1.12226i −0.908250 − 0.418429i \(-0.862581\pi\)
0.710364 − 0.703834i \(-0.248530\pi\)
\(272\) −7.60974e6 + 2.76972e6i −0.0229287 + 0.00834535i
\(273\) −4.03845e8 + 6.99480e8i −1.20128 + 2.08068i
\(274\) 2.77440e8 − 2.32800e8i 0.814784 − 0.683685i
\(275\) 6.01175e7 − 5.04445e7i 0.174316 − 0.146268i
\(276\) 2.94633e7 + 1.07238e7i 0.0843529 + 0.0307020i
\(277\) 1.22211e7 − 6.93091e7i 0.0345485 − 0.195934i −0.962649 − 0.270754i \(-0.912727\pi\)
0.997197 + 0.0748196i \(0.0238381\pi\)
\(278\) 3.17987e7 − 1.80339e8i 0.0887672 − 0.503424i
\(279\) −1.66032e8 − 6.04307e7i −0.457696 − 0.166588i
\(280\) −2.52494e8 + 2.11868e8i −0.687382 + 0.576782i
\(281\) −3.22608e8 + 2.70700e8i −0.867367 + 0.727807i −0.963542 − 0.267557i \(-0.913784\pi\)
0.0961751 + 0.995364i \(0.469339\pi\)
\(282\) 9.68755e7 − 1.67793e8i 0.257242 − 0.445556i
\(283\) 3.17738e8 − 1.15647e8i 0.833329 − 0.303307i 0.110105 − 0.993920i \(-0.464881\pi\)
0.723225 + 0.690613i \(0.242659\pi\)
\(284\) −3.29039e6 − 1.86607e7i −0.00852379 − 0.0483408i
\(285\) 3.21709e8 + 5.57216e8i 0.823201 + 1.42583i
\(286\) −4.46368e7 + 7.73133e7i −0.112827 + 0.195422i
\(287\) −1.10589e9 − 4.02512e8i −2.76138 − 1.00506i
\(288\) 1.59433e7 + 2.76146e7i 0.0393282 + 0.0681185i
\(289\) −3.11343e8 − 2.61248e8i −0.758747 − 0.636664i
\(290\) 2.08136e8 0.501135
\(291\) 2.42904e8 + 2.03821e8i 0.577842 + 0.484867i
\(292\) 1.44292e8 − 5.25181e7i 0.339159 − 0.123444i
\(293\) −1.13518e8 + 6.43792e8i −0.263650 + 1.49523i 0.509202 + 0.860647i \(0.329941\pi\)
−0.772852 + 0.634587i \(0.781170\pi\)
\(294\) −1.73643e8 − 9.84777e8i −0.398512 − 2.26007i
\(295\) 3.32339e8 0.753710
\(296\) −1.27598e8 + 9.27604e7i −0.285972 + 0.207894i
\(297\) −9.25155e7 −0.204912
\(298\) −2.71734e7 − 1.54108e8i −0.0594821 − 0.337340i
\(299\) 1.24563e7 − 7.06430e7i 0.0269487 − 0.152834i
\(300\) −1.95696e8 + 7.12274e7i −0.418463 + 0.152308i
\(301\) 1.12675e9 + 9.45457e8i 2.38147 + 1.99829i
\(302\) 5.75704e7 0.120275
\(303\) −8.82786e8 − 7.40746e8i −1.82308 − 1.52975i
\(304\) −6.35605e7 − 1.10090e8i −0.129757 − 0.224745i
\(305\) −1.04314e9 − 3.79672e8i −2.10520 − 0.766229i
\(306\) 7.69559e6 − 1.33292e7i 0.0153538 − 0.0265936i
\(307\) −3.63793e8 − 6.30108e8i −0.717579 − 1.24288i −0.961956 − 0.273204i \(-0.911917\pi\)
0.244377 − 0.969680i \(-0.421417\pi\)
\(308\) −2.63011e7 − 1.49161e8i −0.0512917 − 0.290890i
\(309\) −3.08741e8 + 1.12373e8i −0.595306 + 0.216674i
\(310\) −2.67851e8 + 4.63931e8i −0.510654 + 0.884479i
\(311\) 2.08359e8 − 1.74834e8i 0.392782 − 0.329583i −0.424914 − 0.905234i \(-0.639696\pi\)
0.817696 + 0.575651i \(0.195251\pi\)
\(312\) 1.81479e8 − 1.52279e8i 0.338287 − 0.283856i
\(313\) −4.92410e8 − 1.79223e8i −0.907657 − 0.330360i −0.154340 − 0.988018i \(-0.549325\pi\)
−0.753317 + 0.657658i \(0.771547\pi\)
\(314\) −5.00972e7 + 2.84116e8i −0.0913188 + 0.517894i
\(315\) 1.08782e8 − 6.16932e8i 0.196096 − 1.11212i
\(316\) 4.11936e8 + 1.49932e8i 0.734387 + 0.267295i
\(317\) 1.91043e8 − 1.60304e8i 0.336840 − 0.282642i −0.458640 − 0.888622i \(-0.651663\pi\)
0.795480 + 0.605980i \(0.207219\pi\)
\(318\) −3.09412e8 + 2.59628e8i −0.539563 + 0.452747i
\(319\) −4.78216e7 + 8.28294e7i −0.0824815 + 0.142862i
\(320\) 9.08471e7 − 3.30656e7i 0.154984 − 0.0564094i
\(321\) 4.89435e7 + 2.77572e8i 0.0825900 + 0.468391i
\(322\) 6.08511e7 + 1.05397e8i 0.101572 + 0.175927i
\(323\) −3.06797e7 + 5.31388e7i −0.0506573 + 0.0877411i
\(324\) 3.58690e8 + 1.30552e8i 0.585884 + 0.213244i
\(325\) 2.38225e8 + 4.12617e8i 0.384942 + 0.666739i
\(326\) −2.42543e8 − 2.03517e8i −0.387727 − 0.325342i
\(327\) 3.82378e8 0.604750
\(328\) 2.64429e8 + 2.21882e8i 0.413762 + 0.347187i
\(329\) 7.06694e8 − 2.57216e8i 1.09407 − 0.398210i
\(330\) 3.90461e7 − 2.21441e8i 0.0598107 − 0.339203i
\(331\) −7.84084e7 − 4.44676e8i −0.118841 − 0.673978i −0.984777 − 0.173824i \(-0.944388\pi\)
0.865936 − 0.500155i \(-0.166723\pi\)
\(332\) −3.12731e8 −0.469016
\(333\) 7.24518e7 − 2.90937e8i 0.107521 − 0.431761i
\(334\) −5.43043e8 −0.797483
\(335\) 1.70313e8 + 9.65891e8i 0.247508 + 1.40369i
\(336\) −6.97948e7 + 3.95826e8i −0.100377 + 0.569268i
\(337\) 1.72135e8 − 6.26520e7i 0.244999 − 0.0891723i −0.216602 − 0.976260i \(-0.569497\pi\)
0.461601 + 0.887088i \(0.347275\pi\)
\(338\) −3.06454e7 − 2.57145e7i −0.0431675 − 0.0362218i
\(339\) 7.89990e8 1.10134
\(340\) −3.57473e7 − 2.99955e7i −0.0493250 − 0.0413886i
\(341\) −1.23083e8 − 2.13187e8i −0.168097 − 0.291152i
\(342\) 2.27034e8 + 8.26337e7i 0.306902 + 0.111703i
\(343\) 1.22191e9 − 2.11642e9i 1.63498 − 2.83186i
\(344\) −2.15711e8 − 3.73622e8i −0.285705 − 0.494855i
\(345\) 3.13741e7 + 1.77931e8i 0.0411344 + 0.233285i
\(346\) −7.06343e8 + 2.57088e8i −0.916746 + 0.333668i
\(347\) −6.26008e7 + 1.08428e8i −0.0804317 + 0.139312i −0.903435 − 0.428724i \(-0.858963\pi\)
0.823004 + 0.568036i \(0.192297\pi\)
\(348\) 1.94427e8 − 1.63144e8i 0.247303 − 0.207512i
\(349\) −2.44216e8 + 2.04921e8i −0.307528 + 0.258046i −0.783469 − 0.621430i \(-0.786552\pi\)
0.475942 + 0.879477i \(0.342107\pi\)
\(350\) −7.59597e8 − 2.76471e8i −0.946989 − 0.344676i
\(351\) 9.75338e7 − 5.53141e8i 0.120387 − 0.682749i
\(352\) −7.71440e6 + 4.37505e7i −0.00942763 + 0.0534668i
\(353\) 3.87305e8 + 1.40968e8i 0.468643 + 0.170572i 0.565537 − 0.824723i \(-0.308669\pi\)
−0.0968948 + 0.995295i \(0.530891\pi\)
\(354\) 3.10449e8 − 2.60498e8i 0.371946 − 0.312099i
\(355\) 8.36442e7 − 7.01858e7i 0.0992285 − 0.0832626i
\(356\) 2.63740e8 − 4.56812e8i 0.309815 − 0.536614i
\(357\) 1.82307e8 − 6.63542e7i 0.212063 − 0.0771845i
\(358\) −1.06849e7 − 6.05972e7i −0.0123078 − 0.0698011i
\(359\) −7.08907e8 − 1.22786e9i −0.808646 − 1.40062i −0.913802 − 0.406161i \(-0.866867\pi\)
0.105155 − 0.994456i \(-0.466466\pi\)
\(360\) −9.18720e7 + 1.59127e8i −0.103783 + 0.179757i
\(361\) −6.51430e7 − 2.37101e7i −0.0728773 − 0.0265252i
\(362\) −5.19090e8 − 8.99091e8i −0.575126 − 0.996147i
\(363\) −7.60023e8 − 6.37735e8i −0.833976 − 0.699789i
\(364\) 9.19548e8 0.999354
\(365\) 6.77824e8 + 5.68762e8i 0.729612 + 0.612217i
\(366\) −1.27203e9 + 4.62981e8i −1.35617 + 0.493605i
\(367\) −2.40892e8 + 1.36617e9i −0.254385 + 1.44269i 0.543262 + 0.839563i \(0.317189\pi\)
−0.797647 + 0.603125i \(0.793922\pi\)
\(368\) −6.19863e6 − 3.51542e7i −0.00648378 − 0.0367714i
\(369\) −6.56059e8 −0.679752
\(370\) −8.30550e8 − 3.69505e8i −0.852432 − 0.379240i
\(371\) −1.56778e9 −1.59396
\(372\) 1.13435e8 + 6.43324e8i 0.114248 + 0.647932i
\(373\) 9.99307e7 − 5.66735e8i 0.0997052 − 0.565456i −0.893498 − 0.449066i \(-0.851757\pi\)
0.993204 − 0.116390i \(-0.0371322\pi\)
\(374\) 2.01503e7 − 7.33411e6i 0.0199173 − 0.00724931i
\(375\) 3.21443e8 + 2.69722e8i 0.314770 + 0.264124i
\(376\) −2.20584e8 −0.214001
\(377\) −4.44814e8 − 3.73243e8i −0.427547 − 0.358754i
\(378\) 4.76470e8 + 8.25270e8i 0.453747 + 0.785913i
\(379\) −9.32695e7 − 3.39473e7i −0.0880040 − 0.0320308i 0.297643 − 0.954677i \(-0.403800\pi\)
−0.385647 + 0.922646i \(0.626022\pi\)
\(380\) 3.66262e8 − 6.34385e8i 0.342413 − 0.593076i
\(381\) 4.56434e8 + 7.90567e8i 0.422805 + 0.732321i
\(382\) −1.74788e8 − 9.91273e8i −0.160432 − 0.909854i
\(383\) 1.04343e7 − 3.79777e6i 0.00949003 − 0.00345409i −0.337271 − 0.941408i \(-0.609504\pi\)
0.346761 + 0.937954i \(0.387282\pi\)
\(384\) 5.89455e7 − 1.02097e8i 0.0531240 − 0.0920135i
\(385\) 6.68595e8 − 5.61018e8i 0.597105 − 0.501031i
\(386\) −9.87354e7 + 8.28488e7i −0.0873811 + 0.0733214i
\(387\) 7.70505e8 + 2.80441e8i 0.675752 + 0.245954i
\(388\) 6.26874e7 − 3.55518e8i 0.0544841 − 0.308995i
\(389\) 2.71487e8 − 1.53968e9i 0.233844 − 1.32619i −0.611192 − 0.791483i \(-0.709310\pi\)
0.845035 − 0.534710i \(-0.179579\pi\)
\(390\) 1.28281e9 + 4.66906e8i 1.09506 + 0.398569i
\(391\) −1.31991e7 + 1.10753e7i −0.0111667 + 0.00936998i
\(392\) −8.72107e8 + 7.31785e8i −0.731254 + 0.613595i
\(393\) 1.77307e8 − 3.07104e8i 0.147350 − 0.255218i
\(394\) −7.96963e8 + 2.90071e8i −0.656450 + 0.238928i
\(395\) 4.38651e8 + 2.48771e9i 0.358121 + 2.03100i
\(396\) −4.22172e7 − 7.31224e7i −0.0341631 − 0.0591721i
\(397\) −5.08171e8 + 8.80178e8i −0.407608 + 0.705998i −0.994621 − 0.103579i \(-0.966970\pi\)
0.587013 + 0.809578i \(0.300304\pi\)
\(398\) −4.29478e8 − 1.56317e8i −0.341468 − 0.124284i
\(399\) 1.52272e9 + 2.63743e9i 1.20009 + 2.07862i
\(400\) 1.81626e8 + 1.52403e8i 0.141896 + 0.119065i
\(401\) −1.56957e9 −1.21556 −0.607779 − 0.794106i \(-0.707939\pi\)
−0.607779 + 0.794106i \(0.707939\pi\)
\(402\) 9.16191e8 + 7.68775e8i 0.703388 + 0.590212i
\(403\) 1.40438e9 − 5.11153e8i 1.06885 − 0.389030i
\(404\) −2.27825e8 + 1.29206e9i −0.171896 + 0.974872i
\(405\) 3.81952e8 + 2.16616e9i 0.285704 + 1.62031i
\(406\) 9.85156e8 0.730573
\(407\) 3.37875e8 − 2.45626e8i 0.248414 − 0.180590i
\(408\) −5.69042e7 −0.0414795
\(409\) −2.45953e8 − 1.39487e9i −0.177755 − 1.00810i −0.934916 − 0.354869i \(-0.884526\pi\)
0.757161 − 0.653228i \(-0.226586\pi\)
\(410\) −3.45406e8 + 1.95890e9i −0.247507 + 1.40368i
\(411\) 2.39145e9 − 8.70417e8i 1.69909 − 0.618417i
\(412\) 2.86545e8 + 2.40440e8i 0.201861 + 0.169381i
\(413\) 1.57304e9 1.09879
\(414\) 5.19718e7 + 4.36095e7i 0.0359970 + 0.0302051i
\(415\) −9.01043e8 − 1.56065e9i −0.618839 − 1.07186i
\(416\) −2.53447e8 − 9.22472e7i −0.172608 − 0.0628242i
\(417\) 6.43383e8 − 1.11437e9i 0.434504 − 0.752582i
\(418\) 1.68306e8 + 2.91514e8i 0.112715 + 0.195228i
\(419\) 4.65790e8 + 2.64162e9i 0.309343 + 1.75437i 0.602321 + 0.798254i \(0.294243\pi\)
−0.292978 + 0.956119i \(0.594646\pi\)
\(420\) −2.17643e9 + 7.92154e8i −1.43341 + 0.521720i
\(421\) −5.36506e8 + 9.29256e8i −0.350419 + 0.606943i −0.986323 − 0.164825i \(-0.947294\pi\)
0.635904 + 0.771768i \(0.280627\pi\)
\(422\) 8.22112e8 − 6.89834e8i 0.532522 − 0.446839i
\(423\) 3.21156e8 − 2.69482e8i 0.206312 − 0.173116i
\(424\) 4.32114e8 + 1.57277e8i 0.275308 + 0.100204i
\(425\) 1.98728e7 − 1.12704e8i 0.0125573 − 0.0712163i
\(426\) 2.31210e7 − 1.31126e8i 0.0144902 − 0.0821779i
\(427\) −4.93741e9 − 1.79707e9i −3.06904 − 1.11704i
\(428\) 2.45815e8 − 2.06263e8i 0.151550 − 0.127165i
\(429\) −4.80549e8 + 4.03229e8i −0.293858 + 0.246576i
\(430\) 1.24302e9 − 2.15297e9i 0.753941 − 1.30586i
\(431\) −1.21177e8 + 4.41049e7i −0.0729039 + 0.0265348i −0.378215 − 0.925718i \(-0.623462\pi\)
0.305311 + 0.952253i \(0.401240\pi\)
\(432\) −4.85359e7 − 2.75261e8i −0.0289648 − 0.164267i
\(433\) −1.35924e9 − 2.35427e9i −0.804613 − 1.39363i −0.916552 − 0.399916i \(-0.869039\pi\)
0.111939 − 0.993715i \(-0.464294\pi\)
\(434\) −1.26780e9 + 2.19589e9i −0.744451 + 1.28943i
\(435\) 1.37434e9 + 5.00218e8i 0.800537 + 0.291372i
\(436\) −2.17667e8 − 3.77010e8i −0.125774 − 0.217846i
\(437\) −2.07194e8 − 1.73856e8i −0.118766 − 0.0996564i
\(438\) 1.07899e9 0.613563
\(439\) 1.00475e8 + 8.43083e7i 0.0566801 + 0.0475603i 0.670688 − 0.741740i \(-0.265999\pi\)
−0.614008 + 0.789300i \(0.710444\pi\)
\(440\) −2.40560e8 + 8.75565e7i −0.134629 + 0.0490009i
\(441\) 3.75729e8 − 2.13086e9i 0.208612 − 1.18310i
\(442\) 2.26066e7 + 1.28209e8i 0.0124525 + 0.0706219i
\(443\) −3.28622e9 −1.79591 −0.897954 − 0.440090i \(-0.854947\pi\)
−0.897954 + 0.440090i \(0.854947\pi\)
\(444\) −1.06547e9 + 3.05844e8i −0.577700 + 0.165829i
\(445\) 3.03957e9 1.63513
\(446\) 2.94055e8 + 1.66767e9i 0.156948 + 0.890098i
\(447\) 1.90943e8 − 1.08289e9i 0.101118 − 0.573468i
\(448\) 4.30000e8 − 1.56507e8i 0.225941 − 0.0822358i
\(449\) 4.13567e8 + 3.47024e8i 0.215617 + 0.180925i 0.744199 − 0.667958i \(-0.232831\pi\)
−0.528581 + 0.848883i \(0.677276\pi\)
\(450\) −4.50623e8 −0.233114
\(451\) −7.00197e8 − 5.87535e8i −0.359420 − 0.301589i
\(452\) −4.49698e8 − 7.78900e8i −0.229053 − 0.396732i
\(453\) 3.80142e8 + 1.38360e8i 0.192133 + 0.0699306i
\(454\) −6.28694e8 + 1.08893e9i −0.315315 + 0.546141i
\(455\) 2.64941e9 + 4.58892e9i 1.31859 + 2.28386i
\(456\) −1.55113e8 − 8.79689e8i −0.0766074 − 0.434462i
\(457\) −2.94719e9 + 1.07269e9i −1.44444 + 0.525735i −0.941034 − 0.338313i \(-0.890144\pi\)
−0.503411 + 0.864047i \(0.667922\pi\)
\(458\) −2.34807e8 + 4.06698e8i −0.114204 + 0.197808i
\(459\) −1.03350e8 + 8.67210e7i −0.0498846 + 0.0418582i
\(460\) 1.57574e8 − 1.32220e8i 0.0754801 − 0.0633353i
\(461\) 5.47822e8 + 1.99391e8i 0.260427 + 0.0947877i 0.468934 − 0.883233i \(-0.344638\pi\)
−0.208507 + 0.978021i \(0.566860\pi\)
\(462\) 1.84814e8 − 1.04813e9i 0.0871943 − 0.494503i
\(463\) 5.62800e8 − 3.19180e9i 0.263524 − 1.49452i −0.509680 − 0.860364i \(-0.670236\pi\)
0.773205 − 0.634157i \(-0.218653\pi\)
\(464\) −2.71530e8 − 9.88289e7i −0.126184 − 0.0459273i
\(465\) −2.88362e9 + 2.41964e9i −1.33000 + 1.11600i
\(466\) 1.85940e9 − 1.56022e9i 0.851179 − 0.714224i
\(467\) 1.75976e9 − 3.04800e9i 0.799549 − 1.38486i −0.120361 − 0.992730i \(-0.538405\pi\)
0.919910 − 0.392130i \(-0.128262\pi\)
\(468\) 4.81699e8 − 1.75324e8i 0.217228 − 0.0790644i
\(469\) 8.06128e8 + 4.57178e9i 0.360827 + 2.04635i
\(470\) −6.35548e8 − 1.10080e9i −0.282362 − 0.489065i
\(471\) −1.01362e9 + 1.75564e9i −0.446993 + 0.774215i
\(472\) −4.33563e8 − 1.57804e8i −0.189782 − 0.0690750i
\(473\) 5.71194e8 + 9.89337e8i 0.248182 + 0.429863i
\(474\) 2.35971e9 + 1.98003e9i 1.01773 + 0.853980i
\(475\) 1.79648e9 0.769121
\(476\) −1.69200e8 − 1.41976e8i −0.0719078 − 0.0603378i
\(477\) −8.21272e8 + 2.98918e8i −0.346475 + 0.126107i
\(478\) 5.01775e8 − 2.84571e9i 0.210141 − 1.19177i
\(479\) 1.31407e8 + 7.45249e8i 0.0546318 + 0.309832i 0.999863 − 0.0165700i \(-0.00527463\pi\)
−0.945231 + 0.326402i \(0.894164\pi\)
\(480\) 6.79338e8 0.280376
\(481\) 1.11237e9 + 2.27907e9i 0.455767 + 0.933793i
\(482\) 1.35959e9 0.553025
\(483\) 1.48501e8 + 8.42190e8i 0.0599672 + 0.340091i
\(484\) −1.96143e8 + 1.11238e9i −0.0786346 + 0.445959i
\(485\) 1.95480e9 − 7.11487e8i 0.778046 − 0.283186i
\(486\) 1.14011e9 + 9.56665e8i 0.450525 + 0.378036i
\(487\) −1.67450e7 −0.00656954 −0.00328477 − 0.999995i \(-0.501046\pi\)
−0.00328477 + 0.999995i \(0.501046\pi\)
\(488\) 1.18058e9 + 9.90624e8i 0.459860 + 0.385869i
\(489\) −1.11241e9 − 1.92675e9i −0.430213 − 0.745151i
\(490\) −6.16463e9 − 2.24374e9i −2.36712 − 0.861562i
\(491\) −5.69608e6 + 9.86591e6i −0.00217166 + 0.00376142i −0.867109 − 0.498118i \(-0.834025\pi\)
0.864938 + 0.501880i \(0.167358\pi\)
\(492\) 1.21279e9 + 2.10061e9i 0.459100 + 0.795185i
\(493\) 2.42196e7 + 1.37356e8i 0.00910337 + 0.0516278i
\(494\) −1.92037e9 + 6.98957e8i −0.716705 + 0.260859i
\(495\) 2.43274e8 − 4.21362e8i 0.0901523 − 0.156148i
\(496\) 5.69720e8 − 4.78052e8i 0.209641 − 0.175909i
\(497\) 3.95907e8 − 3.32205e8i 0.144659 − 0.121383i
\(498\) −2.06498e9 − 7.51593e8i −0.749228 − 0.272697i
\(499\) 3.68474e8 − 2.08972e9i 0.132756 − 0.752898i −0.843640 − 0.536910i \(-0.819592\pi\)
0.976396 − 0.215988i \(-0.0692973\pi\)
\(500\) 8.29563e7 − 4.70468e8i 0.0296793 − 0.168320i
\(501\) −3.58575e9 − 1.30511e9i −1.27394 − 0.463676i
\(502\) 2.37156e9 − 1.98998e9i 0.836703 − 0.702077i
\(503\) 2.52049e9 − 2.11494e9i 0.883073 − 0.740986i −0.0837356 − 0.996488i \(-0.526685\pi\)
0.966809 + 0.255502i \(0.0822407\pi\)
\(504\) −4.34851e8 + 7.53184e8i −0.151298 + 0.262056i
\(505\) −7.10431e9 + 2.58576e9i −2.45472 + 0.893446i
\(506\) 1.64137e7 + 9.30870e7i 0.00563224 + 0.0319420i
\(507\) −1.40554e8 − 2.43446e8i −0.0478976 − 0.0829611i
\(508\) 5.19646e8 − 9.00053e8i 0.175867 − 0.304611i
\(509\) 1.45767e9 + 5.30548e8i 0.489944 + 0.178325i 0.575166 − 0.818037i \(-0.304938\pi\)
−0.0852215 + 0.996362i \(0.527160\pi\)
\(510\) −1.63953e8 − 2.83975e8i −0.0547298 − 0.0947949i
\(511\) 3.20829e9 + 2.69208e9i 1.06366 + 0.892513i
\(512\) −1.34218e8 −0.0441942
\(513\) −1.62235e9 − 1.36131e9i −0.530559 − 0.445191i
\(514\) 3.20008e9 − 1.16473e9i 1.03942 − 0.378317i
\(515\) −3.74295e8 + 2.12273e9i −0.120750 + 0.684809i
\(516\) −5.26420e8 − 2.98548e9i −0.168678 − 0.956621i
\(517\) 5.84097e8 0.185895
\(518\) −3.93118e9 − 1.74895e9i −1.24271 − 0.552870i
\(519\) −5.28190e9 −1.65846
\(520\) −2.69884e8 − 1.53059e9i −0.0841716 − 0.477361i
\(521\) 6.69019e8 − 3.79419e9i 0.207256 − 1.17540i −0.686595 − 0.727040i \(-0.740895\pi\)
0.893851 − 0.448365i \(-0.147993\pi\)
\(522\) 5.16067e8 − 1.87833e8i 0.158803 − 0.0577997i
\(523\) −4.12994e9 − 3.46543e9i −1.26237 − 1.05926i −0.995425 − 0.0955465i \(-0.969540\pi\)
−0.266949 − 0.963711i \(-0.586015\pi\)
\(524\) −4.03724e8 −0.122582
\(525\) −4.35123e9 − 3.65111e9i −1.31236 − 1.10120i
\(526\) 1.74749e8 + 3.02675e8i 0.0523559 + 0.0906830i
\(527\) −3.37332e8 − 1.22779e8i −0.100397 − 0.0365415i
\(528\) −1.56085e8 + 2.70348e8i −0.0461470 + 0.0799289i
\(529\) 1.66444e9 + 2.88289e9i 0.488847 + 0.846707i
\(530\) 4.60138e8 + 2.60957e9i 0.134253 + 0.761384i
\(531\) 8.24025e8 − 2.99920e8i 0.238841 − 0.0869311i
\(532\) 1.73360e9 − 3.00269e9i 0.499182 − 0.864609i
\(533\) 4.25099e9 − 3.56701e9i 1.21603 − 1.02037i
\(534\) 2.83937e9 − 2.38251e9i 0.806913 − 0.677081i
\(535\) 1.73758e9 + 6.32428e8i 0.490577 + 0.178555i
\(536\) 2.36446e8 − 1.34095e9i 0.0663216 − 0.376128i
\(537\) 7.50813e7 − 4.25807e8i 0.0209229 − 0.118660i
\(538\) 2.97656e9 + 1.08338e9i 0.824093 + 0.299945i
\(539\) 2.30931e9 − 1.93774e9i 0.635215 − 0.533009i
\(540\) 1.23382e9 − 1.03530e9i 0.337189 − 0.282935i
\(541\) 1.38248e9 − 2.39452e9i 0.375377 − 0.650172i −0.615007 − 0.788522i \(-0.710847\pi\)
0.990383 + 0.138350i \(0.0441800\pi\)
\(542\) −2.80680e9 + 1.02159e9i −0.757206 + 0.275600i
\(543\) −1.26679e9 − 7.18431e9i −0.339550 − 1.92569i
\(544\) 3.23925e7 + 5.61054e7i 0.00862676 + 0.0149420i
\(545\) 1.25429e9 − 2.17249e9i 0.331902 − 0.574871i
\(546\) 6.07184e9 + 2.20997e9i 1.59642 + 0.581048i
\(547\) 2.67229e9 + 4.62854e9i 0.698116 + 1.20917i 0.969119 + 0.246594i \(0.0793113\pi\)
−0.271003 + 0.962578i \(0.587355\pi\)
\(548\) −2.21952e9 − 1.86240e9i −0.576139 − 0.483438i
\(549\) −2.92907e9 −0.755486
\(550\) −4.80940e8 − 4.03556e8i −0.123260 − 0.103427i
\(551\) −2.05738e9 + 7.48827e8i −0.523944 + 0.190700i
\(552\) 4.35568e7 − 2.47023e8i 0.0110222 − 0.0625102i
\(553\) 2.07624e9 + 1.17749e10i 0.522082 + 2.96087i
\(554\) −5.63026e8 −0.140684
\(555\) −4.59615e9 − 4.43595e9i −1.14122 − 1.10144i
\(556\) −1.46497e9 −0.361466
\(557\) 6.45009e8 + 3.65803e9i 0.158151 + 0.896921i 0.955848 + 0.293862i \(0.0949405\pi\)
−0.797697 + 0.603059i \(0.793948\pi\)
\(558\) −2.45452e8 + 1.39203e9i −0.0598062 + 0.339178i
\(559\) −6.51733e9 + 2.37211e9i −1.57808 + 0.574373i
\(560\) 2.01995e9 + 1.69494e9i 0.486053 + 0.407847i
\(561\) 1.50680e8 0.0360318
\(562\) 2.58086e9 + 2.16560e9i 0.613321 + 0.514637i
\(563\) 2.34345e9 + 4.05897e9i 0.553447 + 0.958598i 0.998023 + 0.0628568i \(0.0200211\pi\)
−0.444576 + 0.895741i \(0.646646\pi\)
\(564\) −1.45653e9 − 5.30134e8i −0.341856 − 0.124425i
\(565\) 2.59135e9 − 4.48835e9i 0.604445 − 1.04693i
\(566\) −1.35252e9 − 2.34263e9i −0.313535 − 0.543058i
\(567\) 1.80787e9 + 1.02529e10i 0.416510 + 2.36214i
\(568\) −1.42447e8 + 5.18463e7i −0.0326162 + 0.0118713i
\(569\) 8.15079e8 − 1.41176e9i 0.185484 − 0.321268i −0.758255 − 0.651958i \(-0.773948\pi\)
0.943740 + 0.330690i \(0.107281\pi\)
\(570\) 3.94309e9 − 3.30865e9i 0.891815 − 0.748322i
\(571\) −1.30942e9 + 1.09873e9i −0.294342 + 0.246983i −0.777985 − 0.628283i \(-0.783758\pi\)
0.483642 + 0.875266i \(0.339314\pi\)
\(572\) 6.71119e8 + 2.44267e8i 0.149939 + 0.0545732i
\(573\) 1.22821e9 − 6.96552e9i 0.272729 − 1.54672i
\(574\) −1.63489e9 + 9.27190e9i −0.360824 + 2.04634i
\(575\) 4.74042e8 + 1.72537e8i 0.103987 + 0.0378482i
\(576\) 1.95412e8 − 1.63970e8i 0.0426063 − 0.0357509i
\(577\) −2.01784e9 + 1.69316e9i −0.437291 + 0.366931i −0.834694 − 0.550713i \(-0.814356\pi\)
0.397404 + 0.917644i \(0.369911\pi\)
\(578\) −1.62572e9 + 2.81583e9i −0.350185 + 0.606539i
\(579\) −8.51070e8 + 3.09764e8i −0.182218 + 0.0663218i
\(580\) −2.89140e8 − 1.63979e9i −0.0615332 − 0.348972i
\(581\) −4.26484e9 − 7.38692e9i −0.902166 − 1.56260i
\(582\) 1.26836e9 − 2.19686e9i 0.266692 − 0.461925i
\(583\) −1.14422e9 − 4.16463e8i −0.239150 − 0.0870435i
\(584\) −6.14211e8 − 1.06384e9i −0.127606 − 0.221021i
\(585\) 2.26282e9 + 1.89873e9i 0.467308 + 0.392118i
\(586\) 5.22979e9 1.07360
\(587\) −3.97134e9 − 3.33235e9i −0.810409 − 0.680014i 0.140296 − 0.990110i \(-0.455194\pi\)
−0.950705 + 0.310096i \(0.899639\pi\)
\(588\) −7.51730e9 + 2.73607e9i −1.52490 + 0.555018i
\(589\) 9.78532e8 − 5.54953e9i 0.197320 − 1.11906i
\(590\) −4.61681e8 − 2.61832e9i −0.0925464 − 0.524857i
\(591\) −5.95954e9 −1.18756
\(592\) 9.08067e8 + 8.76417e8i 0.179884 + 0.173614i
\(593\) −1.20229e9 −0.236765 −0.118382 − 0.992968i \(-0.537771\pi\)
−0.118382 + 0.992968i \(0.537771\pi\)
\(594\) 1.28521e8 + 7.28880e8i 0.0251607 + 0.142693i
\(595\) 2.21015e8 − 1.25344e9i 0.0430143 − 0.243946i
\(596\) −1.17638e9 + 4.28169e8i −0.227608 + 0.0828424i
\(597\) −2.46020e9 − 2.06435e9i −0.473216 − 0.397076i
\(598\) −5.73862e8 −0.109737
\(599\) 6.10929e9 + 5.12630e9i 1.16144 + 0.974564i 0.999924 − 0.0123063i \(-0.00391731\pi\)
0.161516 + 0.986870i \(0.448362\pi\)
\(600\) 8.33020e8 + 1.44283e9i 0.157444 + 0.272701i
\(601\) −9.24876e9 − 3.36627e9i −1.73789 − 0.632541i −0.738751 − 0.673978i \(-0.764584\pi\)
−0.999141 + 0.0414371i \(0.986806\pi\)
\(602\) 5.88348e9 − 1.01905e10i 1.09912 − 1.90374i
\(603\) 1.29396e9 + 2.24120e9i 0.240331 + 0.416265i
\(604\) −7.99759e7 − 4.53566e8i −0.0147683 − 0.0837551i
\(605\) −6.11637e9 + 2.22618e9i −1.12292 + 0.408710i
\(606\) −4.60958e9 + 7.98403e9i −0.841410 + 1.45736i
\(607\) 3.47443e9 − 2.91540e9i 0.630556 − 0.529099i −0.270546 − 0.962707i \(-0.587204\pi\)
0.901102 + 0.433608i \(0.142760\pi\)
\(608\) −7.79042e8 + 6.53694e8i −0.140572 + 0.117954i
\(609\) 6.50506e9 + 2.36765e9i 1.16705 + 0.424773i
\(610\) −1.54211e9 + 8.74577e9i −0.275082 + 1.56007i
\(611\) −6.15780e8 + 3.49226e9i −0.109215 + 0.619387i
\(612\) −1.15704e8 − 4.21128e7i −0.0204041 − 0.00742649i
\(613\) −4.85562e9 + 4.07435e9i −0.851399 + 0.714409i −0.960097 − 0.279666i \(-0.909776\pi\)
0.108698 + 0.994075i \(0.465332\pi\)
\(614\) −4.45891e9 + 3.74147e9i −0.777390 + 0.652308i
\(615\) −6.98860e9 + 1.21046e10i −1.21151 + 2.09840i
\(616\) −1.13862e9 + 4.14425e8i −0.196267 + 0.0714354i
\(617\) 8.39384e8 + 4.76038e9i 0.143867 + 0.815913i 0.968270 + 0.249908i \(0.0804005\pi\)
−0.824402 + 0.566005i \(0.808488\pi\)
\(618\) 1.31422e9 + 2.27630e9i 0.223980 + 0.387945i
\(619\) 1.31907e9 − 2.28470e9i 0.223538 − 0.387179i −0.732342 − 0.680937i \(-0.761573\pi\)
0.955880 + 0.293758i \(0.0949060\pi\)
\(620\) 4.02716e9 + 1.46577e9i 0.678622 + 0.246998i
\(621\) −2.97350e8 − 5.15026e8i −0.0498251 − 0.0862996i
\(622\) −1.66687e9 − 1.39867e9i −0.277739 − 0.233050i
\(623\) 1.43870e10 2.38375
\(624\) −1.45183e9 − 1.21823e9i −0.239205 − 0.200717i
\(625\) 6.83637e9 − 2.48824e9i 1.12007 − 0.407672i
\(626\) −7.27950e8 + 4.12841e9i −0.118602 + 0.672624i
\(627\) 4.10733e8 + 2.32938e9i 0.0665462 + 0.377402i
\(628\) 2.30799e9 0.371856
\(629\) 1.47202e8 − 5.91105e8i 0.0235851 − 0.0947082i
\(630\) −5.01159e9 −0.798516
\(631\) −5.42933e8 − 3.07913e9i −0.0860288 − 0.487893i −0.997130 − 0.0757104i \(-0.975878\pi\)
0.911101 − 0.412183i \(-0.135234\pi\)
\(632\) 6.08981e8 − 3.45371e9i 0.0959609 − 0.544221i
\(633\) 7.08637e9 − 2.57923e9i 1.11048 − 0.404181i
\(634\) −1.52834e9 − 1.28243e9i −0.238182 − 0.199858i
\(635\) 5.98884e9 0.928185
\(636\) 2.47530e9 + 2.07702e9i 0.381529 + 0.320141i
\(637\) 9.15098e9 + 1.58500e10i 1.40275 + 2.42963i
\(638\) 7.19002e8 + 2.61695e8i 0.109612 + 0.0398954i
\(639\) 1.44054e8 − 2.49508e8i 0.0218410 − 0.0378296i
\(640\) −3.86710e8 − 6.69801e8i −0.0583116 − 0.100999i
\(641\) −1.82177e9 − 1.03317e10i −0.273205 − 1.54943i −0.744605 − 0.667506i \(-0.767362\pi\)
0.471399 − 0.881920i \(-0.343749\pi\)
\(642\) 2.11885e9 − 7.71199e8i 0.316030 − 0.115025i
\(643\) −4.67179e9 + 8.09178e9i −0.693019 + 1.20034i 0.277826 + 0.960632i \(0.410386\pi\)
−0.970844 + 0.239712i \(0.922947\pi\)
\(644\) 7.45834e8 − 6.25829e8i 0.110038 − 0.0923326i
\(645\) 1.33820e10 − 1.12288e10i 1.96364 − 1.64769i
\(646\) 4.61272e8 + 1.67889e8i 0.0673199 + 0.0245024i
\(647\) 7.75751e8 − 4.39950e9i 0.112605 − 0.638614i −0.875303 − 0.483574i \(-0.839338\pi\)
0.987908 − 0.155040i \(-0.0495506\pi\)
\(648\) 5.30266e8 − 3.00729e9i 0.0765563 − 0.434172i
\(649\) 1.14806e9 + 4.17859e8i 0.164857 + 0.0600030i
\(650\) 2.91985e9 − 2.45005e9i 0.417027 − 0.349927i
\(651\) −1.36488e10 + 1.14527e10i −1.93893 + 1.62695i
\(652\) −1.26647e9 + 2.19359e9i −0.178948 + 0.309947i
\(653\) 7.60025e9 − 2.76626e9i 1.06815 − 0.388774i 0.252665 − 0.967554i \(-0.418693\pi\)
0.815484 + 0.578780i \(0.196471\pi\)
\(654\) −5.31194e8 − 3.01255e9i −0.0742559 − 0.421126i
\(655\) −1.16321e9 − 2.01475e9i −0.161739 − 0.280141i
\(656\) 1.38075e9 − 2.39153e9i 0.190964 − 0.330759i
\(657\) 2.19392e9 + 7.98523e8i 0.301816 + 0.109852i
\(658\) −3.00819e9 − 5.21034e9i −0.411638 − 0.712977i
\(659\) −2.38513e9 − 2.00136e9i −0.324648 − 0.272412i 0.465867 − 0.884855i \(-0.345743\pi\)
−0.790515 + 0.612443i \(0.790187\pi\)
\(660\) −1.79886e9 −0.243553
\(661\) −2.81243e9 − 2.35991e9i −0.378771 − 0.317827i 0.433449 − 0.901178i \(-0.357297\pi\)
−0.812220 + 0.583351i \(0.801741\pi\)
\(662\) −3.39444e9 + 1.23548e9i −0.454742 + 0.165513i
\(663\) −1.58853e8 + 9.00903e8i −0.0211689 + 0.120055i
\(664\) 4.34441e8 + 2.46384e9i 0.0575894 + 0.326606i
\(665\) 1.99795e10 2.63457
\(666\) −2.39278e9 − 1.66643e8i −0.313866 − 0.0218589i
\(667\) −6.14806e8 −0.0802228
\(668\) 7.54387e8 + 4.27834e9i 0.0979212 + 0.555339i
\(669\) −2.06628e9 + 1.17185e10i −0.266807 + 1.51314i
\(670\) 7.37314e9 − 2.68360e9i 0.947089 − 0.344712i
\(671\) −3.12613e9 − 2.62313e9i −0.399464 − 0.335190i
\(672\) 3.21546e9 0.408743
\(673\) 2.52845e9 + 2.12162e9i 0.319743 + 0.268296i 0.788505 − 0.615028i \(-0.210855\pi\)
−0.468762 + 0.883324i \(0.655300\pi\)
\(674\) −7.32728e8 − 1.26912e9i −0.0921793 − 0.159659i
\(675\) 3.71179e9 + 1.35098e9i 0.464537 + 0.169078i
\(676\) −1.60019e8 + 2.77161e8i −0.0199231 + 0.0345079i
\(677\) 1.52579e9 + 2.64275e9i 0.188988 + 0.327337i 0.944913 − 0.327321i \(-0.106146\pi\)
−0.755925 + 0.654658i \(0.772813\pi\)
\(678\) −1.09744e9 − 6.22391e9i −0.135232 − 0.766936i
\(679\) 9.25249e9 − 3.36763e9i 1.13426 − 0.412839i
\(680\) −1.86659e8 + 3.23303e8i −0.0227650 + 0.0394302i
\(681\) −6.76837e9 + 5.67934e9i −0.821238 + 0.689101i
\(682\) −1.50860e9 + 1.26586e9i −0.182108 + 0.152806i
\(683\) −4.93345e9 − 1.79563e9i −0.592486 − 0.215647i 0.0283366 − 0.999598i \(-0.490979\pi\)
−0.620822 + 0.783951i \(0.713201\pi\)
\(684\) 3.35634e8 − 1.90347e9i 0.0401023 − 0.227431i
\(685\) 2.89922e9 − 1.64423e10i 0.344638 − 1.95454i
\(686\) −1.83716e10 − 6.68671e9i −2.17276 − 0.790821i
\(687\) −2.52788e9 + 2.12114e9i −0.297446 + 0.249586i
\(688\) −2.64390e9 + 2.21850e9i −0.309518 + 0.259717i
\(689\) 3.69628e9 − 6.40214e9i 0.430524 − 0.745689i
\(690\) 1.35824e9 − 4.94360e8i 0.157400 − 0.0572890i
\(691\) 3.78566e8 + 2.14695e9i 0.0436484 + 0.247542i 0.998823 − 0.0485001i \(-0.0154441\pi\)
−0.955175 + 0.296042i \(0.904333\pi\)
\(692\) 3.00670e9 + 5.20775e9i 0.344920 + 0.597419i
\(693\) 1.15147e9 − 1.99440e9i 0.131427 − 0.227639i
\(694\) 9.41209e8 + 3.42572e8i 0.106888 + 0.0389040i
\(695\) −4.22089e9 − 7.31080e9i −0.476933 − 0.826072i
\(696\) −1.55542e9 − 1.30515e9i −0.174870 − 0.146733i
\(697\) −1.33293e9 −0.149106
\(698\) 1.95372e9 + 1.63937e9i 0.217455 + 0.182466i
\(699\) 1.60274e10 − 5.83351e9i 1.77498 − 0.646041i
\(700\) −1.12294e9 + 6.36852e9i −0.123741 + 0.701771i
\(701\) 2.59944e9 + 1.47422e10i 0.285015 + 1.61640i 0.705233 + 0.708976i \(0.250842\pi\)
−0.420218 + 0.907423i \(0.638046\pi\)
\(702\) −4.49340e9 −0.490224
\(703\) 9.53921e9 + 6.64350e8i 1.03554 + 0.0721196i
\(704\) 3.55403e8 0.0383899
\(705\) −1.55099e9 − 8.79611e9i −0.166705 − 0.945428i
\(706\) 5.72569e8 − 3.24720e9i 0.0612366 − 0.347290i
\(707\) −3.36263e10 + 1.22390e10i −3.57859 + 1.30250i
\(708\) −2.48359e9 − 2.08398e9i −0.263005 − 0.220688i
\(709\) −1.60842e10 −1.69487 −0.847435 − 0.530899i \(-0.821854\pi\)
−0.847435 + 0.530899i \(0.821854\pi\)
\(710\) −6.69153e8 − 5.61486e8i −0.0701651 − 0.0588756i
\(711\) 3.33267e9 + 5.77235e9i 0.347735 + 0.602295i
\(712\) −3.96536e9 − 1.44327e9i −0.411721 − 0.149854i
\(713\) 7.91195e8 − 1.37039e9i 0.0817467 − 0.141589i
\(714\) −7.76027e8 − 1.34412e9i −0.0797872 − 0.138195i
\(715\) 7.14643e8 + 4.05294e9i 0.0731169 + 0.414667i
\(716\) −4.62569e8 + 1.68361e8i −0.0470957 + 0.0171414i
\(717\) 1.01524e10 − 1.75845e10i 1.02861 − 1.78161i
\(718\) −8.68887e9 + 7.29083e9i −0.876047 + 0.735091i
\(719\) 2.47505e9 − 2.07681e9i 0.248332 − 0.208375i −0.510122 − 0.860102i \(-0.670400\pi\)
0.758454 + 0.651727i \(0.225955\pi\)
\(720\) 1.38130e9 + 5.02753e8i 0.137919 + 0.0501986i
\(721\) −1.77162e9 + 1.00474e10i −0.176034 + 0.998341i
\(722\) −9.63035e7 + 5.46164e8i −0.00952274 + 0.0540061i
\(723\) 8.97751e9 + 3.26755e9i 0.883429 + 0.321542i
\(724\) −6.36234e9 + 5.33864e9i −0.623063 + 0.522812i
\(725\) 3.12818e9 − 2.62485e9i 0.304865 − 0.255812i
\(726\) −3.96856e9 + 6.87375e9i −0.384906 + 0.666677i
\(727\) −7.05723e9 + 2.56862e9i −0.681183 + 0.247930i −0.659355 − 0.751831i \(-0.729171\pi\)
−0.0218275 + 0.999762i \(0.506948\pi\)
\(728\) −1.27742e9 − 7.24462e9i −0.122708 − 0.695914i
\(729\) −1.29282e9 − 2.23923e9i −0.123592 − 0.214068i
\(730\) 3.53934e9 − 6.13033e9i 0.336739 − 0.583248i
\(731\) 1.56546e9 + 5.69780e8i 0.148228 + 0.0539507i
\(732\) 5.41467e9 + 9.37848e9i 0.510250 + 0.883779i
\(733\) −6.19727e9 − 5.20013e9i −0.581215 − 0.487697i 0.304131 − 0.952630i \(-0.401634\pi\)
−0.885346 + 0.464933i \(0.846078\pi\)
\(734\) 1.10979e10 1.03587
\(735\) −3.53131e10 − 2.96312e10i −3.28042 − 2.75260i
\(736\) −2.68350e8 + 9.76714e7i −0.0248101 + 0.00903015i
\(737\) −6.26100e8 + 3.55079e9i −0.0576112 + 0.326730i
\(738\) 9.11388e8 + 5.16874e9i 0.0834653 + 0.473355i
\(739\) −4.72782e9 −0.430929 −0.215465 − 0.976512i \(-0.569127\pi\)
−0.215465 + 0.976512i \(0.569127\pi\)
\(740\) −1.75734e9 + 7.05677e9i −0.159421 + 0.640169i
\(741\) −1.43602e10 −1.29657
\(742\) 2.17794e9 + 1.23517e10i 0.195718 + 1.10997i
\(743\) 9.33144e8 − 5.29212e9i 0.0834619 − 0.473336i −0.914216 − 0.405227i \(-0.867192\pi\)
0.997678 − 0.0681086i \(-0.0216964\pi\)
\(744\) 4.91082e9 − 1.78739e9i 0.437168 − 0.159116i
\(745\) −5.52615e9 − 4.63699e9i −0.489638 − 0.410855i
\(746\) −4.60382e9 −0.406006
\(747\) −3.64253e9 − 3.05644e9i −0.319728 − 0.268284i
\(748\) −8.57740e7 − 1.48565e8i −0.00749377 − 0.0129796i
\(749\) 8.22437e9 + 2.99342e9i 0.715181 + 0.260305i
\(750\) 1.67845e9 − 2.90717e9i 0.145276 − 0.251626i
\(751\) −9.57960e9 − 1.65924e10i −0.825292 − 1.42945i −0.901696 − 0.432371i \(-0.857677\pi\)
0.0764034 − 0.997077i \(-0.475656\pi\)
\(752\) 3.06432e8 + 1.73786e9i 0.0262767 + 0.149023i
\(753\) 2.04422e10 − 7.44034e9i 1.74480 − 0.635053i
\(754\) −2.32265e9 + 4.02295e9i −0.197326 + 0.341779i
\(755\) 2.03305e9 − 1.70593e9i 0.171923 − 0.144260i
\(756\) 5.83995e9 − 4.90030e9i 0.491567 − 0.412474i
\(757\) −7.82642e8 − 2.84858e8i −0.0655733 − 0.0238667i 0.309025 − 0.951054i \(-0.399997\pi\)
−0.374599 +