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Properties

Label 74.8.f.b.7.6
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 7.6
Character \(\chi\) \(=\) 74.7
Dual form 74.8.f.b.53.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(7.51754 - 2.73616i) q^{2} +(6.89307 + 2.50887i) q^{3} +(49.0268 - 41.1384i) q^{4} +(-27.8528 - 157.961i) q^{5} +58.6836 q^{6} +(117.132 + 664.288i) q^{7} +(256.000 - 443.405i) q^{8} +(-1634.12 - 1371.19i) q^{9} +O(q^{10})\) \(q+(7.51754 - 2.73616i) q^{2} +(6.89307 + 2.50887i) q^{3} +(49.0268 - 41.1384i) q^{4} +(-27.8528 - 157.961i) q^{5} +58.6836 q^{6} +(117.132 + 664.288i) q^{7} +(256.000 - 443.405i) q^{8} +(-1634.12 - 1371.19i) q^{9} +(-641.591 - 1111.27i) q^{10} +(2487.35 - 4308.21i) q^{11} +(441.156 - 160.568i) q^{12} +(2630.42 - 2207.18i) q^{13} +(2698.14 + 4673.32i) q^{14} +(204.312 - 1158.71i) q^{15} +(711.263 - 4033.77i) q^{16} +(-9594.12 - 8050.42i) q^{17} +(-16036.4 - 5836.75i) q^{18} +(-23867.0 - 8686.88i) q^{19} +(-7863.79 - 6598.50i) q^{20} +(-859.215 + 4872.85i) q^{21} +(6910.78 - 39193.0i) q^{22} +(-8803.85 - 15248.7i) q^{23} +(2877.07 - 2414.15i) q^{24} +(49237.6 - 17921.0i) q^{25} +(13735.1 - 23789.8i) q^{26} +(-15845.3 - 27444.8i) q^{27} +(33070.4 + 27749.3i) q^{28} +(71324.1 - 123537. i) q^{29} +(-1634.50 - 9269.71i) q^{30} -166520. q^{31} +(-5690.10 - 32270.2i) q^{32} +(27954.2 - 23456.4i) q^{33} +(-94151.5 - 34268.3i) q^{34} +(101669. - 37004.5i) q^{35} -136524. q^{36} +(-110465. - 287627. i) q^{37} -203190. q^{38} +(23669.2 - 8614.87i) q^{39} +(-77170.9 - 28087.9i) q^{40} +(150724. - 126473. i) q^{41} +(6873.72 + 38982.8i) q^{42} -451873. q^{43} +(-55286.2 - 313544. i) q^{44} +(-171079. + 296318. i) q^{45} +(-107906. - 90544.1i) q^{46} +(426652. + 738982. i) q^{47} +(15023.0 - 26020.6i) q^{48} +(346319. - 126050. i) q^{49} +(321111. - 269444. i) q^{50} +(-45935.4 - 79562.5i) q^{51} +(38161.1 - 216422. i) q^{52} +(121843. - 691009. i) q^{53} +(-194211. - 162962. i) q^{54} +(-749809. - 272908. i) q^{55} +(324534. + 118121. i) q^{56} +(-142723. - 119758. i) q^{57} +(198165. - 1.12385e6i) q^{58} +(-222923. + 1.26426e6i) q^{59} +(-37650.8 - 65213.2i) q^{60} +(224284. - 188196. i) q^{61} +(-1.25182e6 + 455626. i) q^{62} +(719457. - 1.24614e6i) q^{63} +(-131072. - 227023. i) q^{64} +(-421913. - 354027. i) q^{65} +(145966. - 252821. i) q^{66} +(477661. + 2.70895e6i) q^{67} -801551. q^{68} +(-22428.5 - 127198. i) q^{69} +(663051. - 556366. i) q^{70} +(3.46692e6 + 1.26186e6i) q^{71} +(-1.02633e6 + 373552. i) q^{72} +1.21728e6 q^{73} +(-1.61742e6 - 1.86000e6i) q^{74} +384360. q^{75} +(-1.52749e6 + 555960. i) q^{76} +(3.15324e6 + 1.14769e6i) q^{77} +(154362. - 129525. i) q^{78} +(76251.1 + 432441. i) q^{79} -656989. q^{80} +(769752. + 4.36548e6i) q^{81} +(787027. - 1.36317e6i) q^{82} +(3.94562e6 + 3.31076e6i) q^{83} +(158337. + 274247. i) q^{84} +(-1.00443e6 + 1.73972e6i) q^{85} +(-3.39698e6 + 1.23640e6i) q^{86} +(801580. - 672605. i) q^{87} +(-1.27352e6 - 2.20581e6i) q^{88} +(-1.34987e6 + 7.65551e6i) q^{89} +(-475322. + 2.69569e6i) q^{90} +(1.77431e6 + 1.48882e6i) q^{91} +(-1.05893e6 - 385420. i) q^{92} +(-1.14783e6 - 417777. i) q^{93} +(5.22934e6 + 4.38794e6i) q^{94} +(-707425. + 4.01200e6i) q^{95} +(41739.5 - 236716. i) q^{96} +(7.21964e6 + 1.25048e7i) q^{97} +(2.25857e6 - 1.89517e6i) q^{98} +(-9.97200e6 + 3.62951e6i) 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
\(3\) 6.89307 + 2.50887i 0.147397 + 0.0536480i 0.414665 − 0.909974i \(-0.363899\pi\)
−0.267268 + 0.963622i \(0.586121\pi\)
\(4\) 49.0268 − 41.1384i 0.383022 − 0.321394i
\(5\) −27.8528 − 157.961i −0.0996491 − 0.565138i −0.993223 − 0.116222i \(-0.962921\pi\)
0.893574 − 0.448916i \(-0.148190\pi\)
\(6\) 58.6836 0.110914
\(7\) 117.132 + 664.288i 0.129072 + 0.732004i 0.978806 + 0.204791i \(0.0656516\pi\)
−0.849734 + 0.527212i \(0.823237\pi\)
\(8\) 256.000 − 443.405i 0.176777 − 0.306186i
\(9\) −1634.12 − 1371.19i −0.747197 − 0.626973i
\(10\) −641.591 − 1111.27i −0.202889 − 0.351414i
\(11\) 2487.35 − 4308.21i 0.563459 − 0.975939i −0.433732 − 0.901042i \(-0.642804\pi\)
0.997191 − 0.0748976i \(-0.0238630\pi\)
\(12\) 441.156 − 160.568i 0.0736984 − 0.0268240i
\(13\) 2630.42 − 2207.18i 0.332065 − 0.278636i −0.461476 − 0.887153i \(-0.652680\pi\)
0.793541 + 0.608517i \(0.208235\pi\)
\(14\) 2698.14 + 4673.32i 0.262795 + 0.455174i
\(15\) 204.312 − 1158.71i 0.0156306 − 0.0886455i
\(16\) 711.263 − 4033.77i 0.0434120 − 0.246202i
\(17\) −9594.12 − 8050.42i −0.473624 − 0.397418i 0.374490 − 0.927231i \(-0.377818\pi\)
−0.848115 + 0.529813i \(0.822262\pi\)
\(18\) −16036.4 − 5836.75i −0.648115 − 0.235894i
\(19\) −23867.0 − 8686.88i −0.798289 − 0.290553i −0.0895118 − 0.995986i \(-0.528531\pi\)
−0.708777 + 0.705432i \(0.750753\pi\)
\(20\) −7863.79 − 6598.50i −0.219800 − 0.184434i
\(21\) −859.215 + 4872.85i −0.0202458 + 0.114819i
\(22\) 6910.78 − 39193.0i 0.138372 − 0.784745i
\(23\) −8803.85 − 15248.7i −0.150878 − 0.261328i 0.780673 − 0.624940i \(-0.214877\pi\)
−0.931550 + 0.363612i \(0.881543\pi\)
\(24\) 2877.07 − 2414.15i 0.0424826 − 0.0356471i
\(25\) 49237.6 − 17921.0i 0.630242 − 0.229389i
\(26\) 13735.1 − 23789.8i 0.153258 − 0.265451i
\(27\) −15845.3 − 27444.8i −0.154927 − 0.268341i
\(28\) 33070.4 + 27749.3i 0.284699 + 0.238891i
\(29\) 71324.1 − 123537.i 0.543054 − 0.940598i −0.455672 − 0.890148i \(-0.650601\pi\)
0.998727 − 0.0504501i \(-0.0160656\pi\)
\(30\) −1634.50 − 9269.71i −0.0110525 − 0.0626818i
\(31\) −166520. −1.00392 −0.501962 − 0.864890i \(-0.667388\pi\)
−0.501962 + 0.864890i \(0.667388\pi\)
\(32\) −5690.10 − 32270.2i −0.0306970 − 0.174091i
\(33\) 27954.2 − 23456.4i 0.135409 − 0.113622i
\(34\) −94151.5 − 34268.3i −0.410819 − 0.149526i
\(35\) 101669. − 37004.5i 0.400821 − 0.145887i
\(36\) −136524. −0.487698
\(37\) −110465. − 287627.i −0.358526 − 0.933520i
\(38\) −203190. −0.600702
\(39\) 23669.2 − 8614.87i 0.0638935 − 0.0232553i
\(40\) −77170.9 − 28087.9i −0.190653 − 0.0693920i
\(41\) 150724. − 126473.i 0.341539 − 0.286585i −0.455843 − 0.890060i \(-0.650662\pi\)
0.797382 + 0.603475i \(0.206218\pi\)
\(42\) 6873.72 + 38982.8i 0.0143159 + 0.0811896i
\(43\) −451873. −0.866717 −0.433358 − 0.901222i \(-0.642672\pi\)
−0.433358 + 0.901222i \(0.642672\pi\)
\(44\) −55286.2 − 313544.i −0.0978436 − 0.554899i
\(45\) −171079. + 296318.i −0.279868 + 0.484746i
\(46\) −107906. − 90544.1i −0.163454 − 0.137154i
\(47\) 426652. + 738982.i 0.599419 + 1.03822i 0.992907 + 0.118895i \(0.0379352\pi\)
−0.393487 + 0.919330i \(0.628732\pi\)
\(48\) 15023.0 − 26020.6i 0.0196070 − 0.0339604i
\(49\) 346319. − 126050.i 0.420523 − 0.153058i
\(50\) 321111. − 269444.i 0.363296 − 0.304841i
\(51\) −45935.4 − 79562.5i −0.0484900 − 0.0839871i
\(52\) 38161.1 − 216422.i 0.0376365 − 0.213447i
\(53\) 121843. − 691009.i 0.112418 − 0.637555i −0.875578 − 0.483077i \(-0.839519\pi\)
0.987996 − 0.154479i \(-0.0493697\pi\)
\(54\) −194211. − 162962.i −0.167840 − 0.140834i
\(55\) −749809. − 272908.i −0.607688 − 0.221181i
\(56\) 324534. + 118121.i 0.246946 + 0.0898811i
\(57\) −142723. − 119758.i −0.102078 − 0.0856533i
\(58\) 198165. − 1.12385e6i 0.133361 − 0.756327i
\(59\) −222923. + 1.26426e6i −0.141310 + 0.801408i 0.828946 + 0.559328i \(0.188941\pi\)
−0.970256 + 0.242080i \(0.922170\pi\)
\(60\) −37650.8 − 65213.2i −0.0225032 − 0.0389768i
\(61\) 224284. − 188196.i 0.126515 − 0.106159i −0.577335 − 0.816508i \(-0.695907\pi\)
0.703850 + 0.710349i \(0.251463\pi\)
\(62\) −1.25182e6 + 455626.i −0.667070 + 0.242794i
\(63\) 719457. − 1.24614e6i 0.362504 − 0.627875i
\(64\) −131072. − 227023.i −0.0625000 − 0.108253i
\(65\) −421913. − 354027.i −0.190557 − 0.159897i
\(66\) 145966. − 252821.i 0.0624956 − 0.108246i
\(67\) 477661. + 2.70895e6i 0.194025 + 1.10037i 0.913800 + 0.406164i \(0.133134\pi\)
−0.719775 + 0.694208i \(0.755755\pi\)
\(68\) −801551. −0.309136
\(69\) −22428.5 − 127198.i −0.00821917 − 0.0466132i
\(70\) 663051. − 556366.i 0.231049 − 0.193873i
\(71\) 3.46692e6 + 1.26186e6i 1.14958 + 0.418413i 0.845365 − 0.534190i \(-0.179383\pi\)
0.304216 + 0.952603i \(0.401605\pi\)
\(72\) −1.02633e6 + 373552.i −0.324057 + 0.117947i
\(73\) 1.21728e6 0.366235 0.183118 − 0.983091i \(-0.441381\pi\)
0.183118 + 0.983091i \(0.441381\pi\)
\(74\) −1.61742e6 − 1.86000e6i −0.463994 − 0.533582i
\(75\) 384360. 0.105202
\(76\) −1.52749e6 + 555960.i −0.399145 + 0.145277i
\(77\) 3.15324e6 + 1.14769e6i 0.787118 + 0.286487i
\(78\) 154362. − 129525.i 0.0368307 − 0.0309046i
\(79\) 76251.1 + 432441.i 0.0174001 + 0.0986807i 0.992271 − 0.124090i \(-0.0396011\pi\)
−0.974871 + 0.222770i \(0.928490\pi\)
\(80\) −656989. −0.143464
\(81\) 769752. + 4.36548e6i 0.160936 + 0.912713i
\(82\) 787027. − 1.36317e6i 0.157631 − 0.273025i
\(83\) 3.94562e6 + 3.31076e6i 0.757428 + 0.635558i 0.937456 − 0.348104i \(-0.113174\pi\)
−0.180028 + 0.983662i \(0.557619\pi\)
\(84\) 158337. + 274247.i 0.0291477 + 0.0504853i
\(85\) −1.00443e6 + 1.73972e6i −0.177400 + 0.307265i
\(86\) −3.39698e6 + 1.23640e6i −0.575901 + 0.209611i
\(87\) 801580. − 672605.i 0.130506 − 0.109507i
\(88\) −1.27352e6 − 2.20581e6i −0.199213 − 0.345047i
\(89\) −1.34987e6 + 7.65551e6i −0.202968 + 1.15109i 0.697637 + 0.716451i \(0.254235\pi\)
−0.900605 + 0.434638i \(0.856876\pi\)
\(90\) −475322. + 2.69569e6i −0.0687289 + 0.389781i
\(91\) 1.77431e6 + 1.48882e6i 0.246822 + 0.207109i
\(92\) −1.05893e6 − 385420.i −0.141779 − 0.0516032i
\(93\) −1.14783e6 − 417777.i −0.147975 − 0.0538586i
\(94\) 5.22934e6 + 4.38794e6i 0.649381 + 0.544896i
\(95\) −707425. + 4.01200e6i −0.0846540 + 0.480097i
\(96\) 41739.5 − 236716.i 0.00481501 − 0.0273073i
\(97\) 7.21964e6 + 1.25048e7i 0.803183 + 1.39115i 0.917511 + 0.397710i \(0.130195\pi\)
−0.114329 + 0.993443i \(0.536472\pi\)
\(98\) 2.25857e6 − 1.89517e6i 0.242406 − 0.203403i
\(99\) −9.97200e6 + 3.62951e6i −1.03290 + 0.375945i
\(100\) 1.67672e6 − 2.90417e6i 0.167672 − 0.290417i
\(101\) −928631. − 1.60844e6i −0.0896847 − 0.155338i 0.817693 − 0.575654i \(-0.195253\pi\)
−0.907378 + 0.420316i \(0.861919\pi\)
\(102\) −563017. − 472428.i −0.0525317 − 0.0440793i
\(103\) 4.38450e6 − 7.59417e6i 0.395357 − 0.684778i −0.597790 − 0.801653i \(-0.703954\pi\)
0.993147 + 0.116875i \(0.0372876\pi\)
\(104\) −305289. − 1.73138e6i −0.0266130 − 0.150930i
\(105\) 793651. 0.0669063
\(106\) −974748. − 5.52807e6i −0.0794917 − 0.450820i
\(107\) 3.17824e6 − 2.66686e6i 0.250809 − 0.210454i −0.508712 − 0.860937i \(-0.669878\pi\)
0.759521 + 0.650483i \(0.225434\pi\)
\(108\) −1.90588e6 − 693683.i −0.145584 − 0.0529881i
\(109\) −3.02594e6 + 1.10135e6i −0.223804 + 0.0814579i −0.451488 − 0.892277i \(-0.649107\pi\)
0.227685 + 0.973735i \(0.426885\pi\)
\(110\) −6.38344e6 −0.457278
\(111\) −39826.6 − 2.25977e6i −0.00276403 − 0.156832i
\(112\) 2.76290e6 0.185824
\(113\) 8.45203e6 − 3.07629e6i 0.551044 − 0.200564i −0.0514661 − 0.998675i \(-0.516389\pi\)
0.602510 + 0.798111i \(0.294167\pi\)
\(114\) −1.40060e6 − 509777.i −0.0885416 − 0.0322265i
\(115\) −2.16349e6 + 1.81538e6i −0.132652 + 0.111308i
\(116\) −1.58532e6 − 8.99079e6i −0.0943004 − 0.534804i
\(117\) −7.32488e6 −0.422815
\(118\) 1.78338e6 + 1.01141e7i 0.0999212 + 0.566681i
\(119\) 4.22402e6 − 7.31622e6i 0.229780 − 0.397990i
\(120\) −461475. − 387224.i −0.0243789 − 0.0204563i
\(121\) −2.63022e6 − 4.55567e6i −0.134972 − 0.233778i
\(122\) 1.17113e6 − 2.02845e6i 0.0583908 − 0.101136i
\(123\) 1.35626e6 − 493637.i 0.0657165 − 0.0239188i
\(124\) −8.16396e6 + 6.85037e6i −0.384525 + 0.322655i
\(125\) −1.04678e7 − 1.81307e7i −0.479368 − 0.830289i
\(126\) 1.99892e6 − 1.13364e7i 0.0890221 − 0.504870i
\(127\) 570370. − 3.23473e6i 0.0247083 − 0.140128i −0.969958 − 0.243272i \(-0.921779\pi\)
0.994666 + 0.103144i \(0.0328903\pi\)
\(128\) −1.60651e6 − 1.34802e6i −0.0677094 − 0.0568149i
\(129\) −3.11479e6 − 1.13369e6i −0.127751 − 0.0464976i
\(130\) −4.14042e6 − 1.50699e6i −0.165289 − 0.0601601i
\(131\) −4.83824e6 − 4.05976e6i −0.188034 − 0.157780i 0.543911 − 0.839143i \(-0.316943\pi\)
−0.731945 + 0.681363i \(0.761387\pi\)
\(132\) 405549. − 2.29998e6i 0.0153474 − 0.0870394i
\(133\) 2.97500e6 − 1.68721e7i 0.109649 − 0.621853i
\(134\) 1.10030e7 + 1.90577e7i 0.395042 + 0.684233i
\(135\) −3.89387e6 + 3.26735e6i −0.136211 + 0.114295i
\(136\) −6.02569e6 + 2.19317e6i −0.205410 + 0.0747630i
\(137\) 2.95536e7 − 5.11883e7i 0.981947 − 1.70078i 0.327157 − 0.944970i \(-0.393909\pi\)
0.654790 − 0.755811i \(-0.272757\pi\)
\(138\) −516642. − 894849.i −0.0167345 − 0.0289850i
\(139\) −4.21047e7 − 3.53300e7i −1.32978 − 1.11581i −0.984130 − 0.177450i \(-0.943215\pi\)
−0.345646 − 0.938365i \(-0.612340\pi\)
\(140\) 3.46221e6 − 5.99672e6i 0.106636 − 0.184699i
\(141\) 1.08693e6 + 6.16427e6i 0.0326538 + 0.185189i
\(142\) 2.95153e7 0.865045
\(143\) −2.96625e6 − 1.68224e7i −0.0848265 − 0.481075i
\(144\) −6.69335e6 + 5.61639e6i −0.186799 + 0.156743i
\(145\) −2.15006e7 − 7.82557e6i −0.585682 − 0.213171i
\(146\) 9.15094e6 − 3.33067e6i 0.243350 − 0.0885720i
\(147\) 2.70344e6 0.0701950
\(148\) −1.72483e7 − 9.55707e6i −0.437351 − 0.242331i
\(149\) −6.90850e7 −1.71093 −0.855464 − 0.517863i \(-0.826728\pi\)
−0.855464 + 0.517863i \(0.826728\pi\)
\(150\) 2.88944e6 − 1.05167e6i 0.0699028 − 0.0254425i
\(151\) 2.97196e7 + 1.08171e7i 0.702464 + 0.255676i 0.668463 − 0.743746i \(-0.266953\pi\)
0.0340017 + 0.999422i \(0.489175\pi\)
\(152\) −9.96176e6 + 8.35891e6i −0.230082 + 0.193062i
\(153\) 4.63929e6 + 2.63107e7i 0.104720 + 0.593899i
\(154\) 2.68449e7 0.592296
\(155\) 4.63805e6 + 2.63037e7i 0.100040 + 0.567355i
\(156\) 806023. − 1.39607e6i 0.0169985 − 0.0294423i
\(157\) −3.10345e7 − 2.60411e7i −0.640024 − 0.537044i 0.264001 − 0.964522i \(-0.414958\pi\)
−0.904026 + 0.427478i \(0.859402\pi\)
\(158\) 1.75645e6 + 3.04226e6i 0.0354271 + 0.0613616i
\(159\) 2.57353e6 − 4.45748e6i 0.0507737 − 0.0879426i
\(160\) −4.93894e6 + 1.79763e6i −0.0953265 + 0.0346960i
\(161\) 9.09833e6 − 7.63440e6i 0.171819 − 0.144173i
\(162\) 1.77313e7 + 3.07115e7i 0.327671 + 0.567543i
\(163\) 6.43265e6 − 3.64814e7i 0.116341 − 0.659803i −0.869736 − 0.493517i \(-0.835711\pi\)
0.986077 − 0.166287i \(-0.0531777\pi\)
\(164\) 2.18665e6 − 1.24011e7i 0.0387103 − 0.219537i
\(165\) −4.48379e6 − 3.76235e6i −0.0777054 − 0.0652026i
\(166\) 3.87201e7 + 1.40930e7i 0.656989 + 0.239125i
\(167\) 1.26474e7 + 4.60326e6i 0.210132 + 0.0764818i 0.444942 − 0.895560i \(-0.353224\pi\)
−0.234810 + 0.972041i \(0.575447\pi\)
\(168\) 1.94069e6 + 1.62843e6i 0.0315771 + 0.0264964i
\(169\) −8.84872e6 + 5.01836e7i −0.141019 + 0.799758i
\(170\) −2.79068e6 + 1.58267e7i −0.0435650 + 0.247070i
\(171\) 2.70902e7 + 4.69216e7i 0.414310 + 0.717606i
\(172\) −2.21539e7 + 1.85893e7i −0.331972 + 0.278557i
\(173\) −4.16609e7 + 1.51633e7i −0.611741 + 0.222656i −0.629265 − 0.777191i \(-0.716644\pi\)
0.0175238 + 0.999846i \(0.494422\pi\)
\(174\) 4.18555e6 − 7.24959e6i 0.0602324 − 0.104326i
\(175\) 1.76720e7 + 3.06088e7i 0.249260 + 0.431731i
\(176\) −1.56092e7 − 1.30977e7i −0.215817 − 0.181092i
\(177\) −4.70848e6 + 8.15533e6i −0.0638226 + 0.110544i
\(178\) 1.07990e7 + 6.12441e7i 0.143520 + 0.813943i
\(179\) 1.06954e8 1.39383 0.696916 − 0.717153i \(-0.254555\pi\)
0.696916 + 0.717153i \(0.254555\pi\)
\(180\) 3.80258e6 + 2.15655e7i 0.0485987 + 0.275617i
\(181\) 2.08441e7 − 1.74903e7i 0.261281 − 0.219241i −0.502731 − 0.864443i \(-0.667671\pi\)
0.764012 + 0.645202i \(0.223227\pi\)
\(182\) 1.74121e7 + 6.33749e6i 0.214093 + 0.0779233i
\(183\) 2.01816e6 − 734551.i 0.0243432 − 0.00886019i
\(184\) −9.01514e6 −0.106687
\(185\) −4.23570e7 + 2.54604e7i −0.491841 + 0.295641i
\(186\) −9.77200e6 −0.111349
\(187\) −5.85469e7 + 2.13093e7i −0.654724 + 0.238300i
\(188\) 5.13179e7 + 1.86782e7i 0.563270 + 0.205014i
\(189\) 1.63753e7 − 1.37405e7i 0.176430 − 0.148042i
\(190\) 5.65940e6 + 3.20960e7i 0.0598594 + 0.339480i
\(191\) −4.77994e7 −0.496370 −0.248185 − 0.968713i \(-0.579834\pi\)
−0.248185 + 0.968713i \(0.579834\pi\)
\(192\) −333916. − 1.89373e6i −0.00340473 − 0.0193092i
\(193\) −5.50261e7 + 9.53080e7i −0.550958 + 0.954287i 0.447248 + 0.894410i \(0.352404\pi\)
−0.998206 + 0.0598769i \(0.980929\pi\)
\(194\) 8.84890e7 + 7.42511e7i 0.870128 + 0.730124i
\(195\) −2.02006e6 − 3.49885e6i −0.0195094 − 0.0337913i
\(196\) 1.17934e7 − 2.04268e7i 0.111878 − 0.193778i
\(197\) 1.19358e8 − 4.34429e7i 1.11230 − 0.404843i 0.280462 − 0.959865i \(-0.409512\pi\)
0.831836 + 0.555022i \(0.187290\pi\)
\(198\) −6.50340e7 + 5.45700e7i −0.595405 + 0.499604i
\(199\) −4.55279e7 − 7.88566e7i −0.409536 − 0.709337i 0.585302 − 0.810815i \(-0.300976\pi\)
−0.994838 + 0.101479i \(0.967643\pi\)
\(200\) 4.65856e6 − 2.64200e7i 0.0411762 − 0.233522i
\(201\) −3.50386e6 + 1.98714e7i −0.0304341 + 0.172600i
\(202\) −1.13820e7 − 9.55060e6i −0.0971599 − 0.0815269i
\(203\) 9.04184e7 + 3.29096e7i 0.758614 + 0.276113i
\(204\) −5.52514e6 − 2.01099e6i −0.0455657 − 0.0165846i
\(205\) −2.41758e7 − 2.02859e7i −0.195994 − 0.164459i
\(206\) 1.21818e7 − 6.90862e7i 0.0970900 − 0.550625i
\(207\) −6.52233e6 + 3.69900e7i −0.0511101 + 0.289860i
\(208\) −7.03235e6 − 1.21804e7i −0.0541850 − 0.0938511i
\(209\) −9.67905e7 + 8.12168e7i −0.733366 + 0.615367i
\(210\) 5.96630e6 − 2.17156e6i 0.0444568 − 0.0161809i
\(211\) 1.86138e7 − 3.22400e7i 0.136410 − 0.236269i −0.789725 − 0.613461i \(-0.789777\pi\)
0.926135 + 0.377192i \(0.123110\pi\)
\(212\) −2.24534e7 − 3.88904e7i −0.161848 − 0.280328i
\(213\) 2.07319e7 + 1.73961e7i 0.146997 + 0.123346i
\(214\) 1.65956e7 − 2.87444e7i 0.115756 − 0.200496i
\(215\) 1.25859e7 + 7.13783e7i 0.0863675 + 0.489814i
\(216\) −1.62256e7 −0.109550
\(217\) −1.95048e7 − 1.10617e8i −0.129578 − 0.734876i
\(218\) −1.97341e7 + 1.65589e7i −0.129009 + 0.108252i
\(219\) 8.39078e6 + 3.05399e6i 0.0539819 + 0.0196478i
\(220\) −4.79877e7 + 1.74661e7i −0.303844 + 0.110590i
\(221\) −4.30053e7 −0.268009
\(222\) −6.48251e6 − 1.68790e7i −0.0397656 − 0.103541i
\(223\) 1.64246e8 0.991811 0.495906 − 0.868376i \(-0.334836\pi\)
0.495906 + 0.868376i \(0.334836\pi\)
\(224\) 2.07702e7 − 7.55973e6i 0.123473 − 0.0449406i
\(225\) −1.05033e8 − 3.82290e7i −0.614735 − 0.223745i
\(226\) 5.51213e7 − 4.62522e7i 0.317643 − 0.266534i
\(227\) −2.75673e7 − 1.56342e8i −0.156424 − 0.887126i −0.957472 − 0.288526i \(-0.906835\pi\)
0.801048 − 0.598600i \(-0.204276\pi\)
\(228\) −1.19239e7 −0.0666264
\(229\) 1.67368e7 + 9.49189e7i 0.0920974 + 0.522310i 0.995598 + 0.0937239i \(0.0298771\pi\)
−0.903501 + 0.428586i \(0.859012\pi\)
\(230\) −1.12969e7 + 1.95669e7i −0.0612228 + 0.106041i
\(231\) 1.88561e7 + 1.58222e7i 0.100649 + 0.0844547i
\(232\) −3.65179e7 − 6.32509e7i −0.191999 − 0.332552i
\(233\) 1.59826e8 − 2.76826e8i 0.827753 − 1.43371i −0.0720442 − 0.997401i \(-0.522952\pi\)
0.899797 − 0.436309i \(-0.143714\pi\)
\(234\) −5.50651e7 + 2.00421e7i −0.280945 + 0.102255i
\(235\) 1.04847e8 − 8.79769e7i 0.527009 − 0.442213i
\(236\) 4.10804e7 + 7.11533e7i 0.203443 + 0.352373i
\(237\) −559336. + 3.17215e6i −0.00272931 + 0.0154787i
\(238\) 1.17359e7 − 6.65576e7i 0.0564283 − 0.320021i
\(239\) 2.04033e8 + 1.71204e8i 0.966738 + 0.811189i 0.982036 − 0.188693i \(-0.0604253\pi\)
−0.0152980 + 0.999883i \(0.504870\pi\)
\(240\) −4.52867e6 − 1.64830e6i −0.0211461 − 0.00769656i
\(241\) −6.00928e7 − 2.18720e7i −0.276543 − 0.100653i 0.200026 − 0.979791i \(-0.435897\pi\)
−0.476569 + 0.879137i \(0.658120\pi\)
\(242\) −3.22378e7 − 2.70507e7i −0.146222 − 0.122695i
\(243\) −1.76815e7 + 1.00277e8i −0.0790493 + 0.448311i
\(244\) 3.25382e6 − 1.84533e7i 0.0143394 − 0.0813225i
\(245\) −2.95569e7 − 5.11940e7i −0.128404 − 0.222401i
\(246\) 8.84505e6 − 7.42188e6i 0.0378815 − 0.0317864i
\(247\) −8.19537e7 + 2.98287e7i −0.346042 + 0.125949i
\(248\) −4.26292e7 + 7.38359e7i −0.177470 + 0.307388i
\(249\) 1.88911e7 + 3.27204e7i 0.0775461 + 0.134314i
\(250\) −1.28300e8 − 1.07657e8i −0.519323 − 0.435764i
\(251\) −1.50684e8 + 2.60993e8i −0.601464 + 1.04177i 0.391135 + 0.920333i \(0.372083\pi\)
−0.992600 + 0.121434i \(0.961251\pi\)
\(252\) −1.59913e7 − 9.06914e7i −0.0629481 − 0.356997i
\(253\) −8.75930e7 −0.340054
\(254\) −4.56296e6 − 2.58778e7i −0.0174714 − 0.0990855i
\(255\) −1.12883e7 + 9.47204e6i −0.0426323 + 0.0357728i
\(256\) −1.57654e7 − 5.73815e6i −0.0587308 − 0.0213763i
\(257\) −1.85422e8 + 6.74882e7i −0.681390 + 0.248006i −0.659444 − 0.751753i \(-0.729208\pi\)
−0.0219458 + 0.999759i \(0.506986\pi\)
\(258\) −2.65175e7 −0.0961312
\(259\) 1.78128e8 − 1.07071e8i 0.637064 − 0.382933i
\(260\) −3.52492e7 −0.124378
\(261\) −2.85945e8 + 1.04075e8i −0.995497 + 0.362331i
\(262\) −4.74798e7 − 1.72812e7i −0.163100 − 0.0593636i
\(263\) −1.49917e8 + 1.25796e8i −0.508168 + 0.426403i −0.860484 − 0.509478i \(-0.829839\pi\)
0.352316 + 0.935881i \(0.385394\pi\)
\(264\) −3.24439e6 − 1.83999e7i −0.0108522 − 0.0615461i
\(265\) −1.12546e8 −0.371509
\(266\) −2.38000e7 − 1.34977e8i −0.0775338 − 0.439716i
\(267\) −2.85115e7 + 4.93833e7i −0.0916706 + 0.158778i
\(268\) 1.34860e8 + 1.13161e8i 0.427969 + 0.359108i
\(269\) −1.17623e8 − 2.03729e8i −0.368434 − 0.638147i 0.620887 − 0.783900i \(-0.286773\pi\)
−0.989321 + 0.145753i \(0.953439\pi\)
\(270\) −2.03323e7 + 3.52167e7i −0.0628658 + 0.108887i
\(271\) 4.64996e8 − 1.69245e8i 1.41924 − 0.516562i 0.485415 − 0.874284i \(-0.338669\pi\)
0.933828 + 0.357722i \(0.116446\pi\)
\(272\) −3.92975e7 + 3.29745e7i −0.118406 + 0.0993545i
\(273\) 8.49517e6 + 1.47141e7i 0.0252699 + 0.0437687i
\(274\) 8.21108e7 − 4.65673e8i 0.241142 − 1.36758i
\(275\) 4.52635e7 − 2.56702e8i 0.131245 − 0.744329i
\(276\) −6.33233e6 − 5.31345e6i −0.0181293 − 0.0152123i
\(277\) −9.92624e6 − 3.61286e6i −0.0280612 − 0.0102134i 0.327951 − 0.944695i \(-0.393642\pi\)
−0.356013 + 0.934481i \(0.615864\pi\)
\(278\) −4.13192e8 − 1.50390e8i −1.15344 − 0.419818i
\(279\) 2.72114e8 + 2.28331e8i 0.750129 + 0.629433i
\(280\) 9.61929e6 − 5.45537e7i 0.0261873 − 0.148515i
\(281\) −4.34478e7 + 2.46405e8i −0.116814 + 0.662486i 0.869022 + 0.494774i \(0.164749\pi\)
−0.985836 + 0.167712i \(0.946362\pi\)
\(282\) 2.50374e7 + 4.33661e7i 0.0664841 + 0.115154i
\(283\) 3.80894e8 − 3.19608e8i 0.998967 − 0.838233i 0.0121264 − 0.999926i \(-0.496140\pi\)
0.986841 + 0.161693i \(0.0516955\pi\)
\(284\) 2.21883e8 − 8.07587e7i 0.574790 − 0.209207i
\(285\) −1.49419e7 + 2.58802e7i −0.0382340 + 0.0662232i
\(286\) −6.83278e7 − 1.18347e8i −0.172709 − 0.299142i
\(287\) 1.01669e8 + 8.53104e7i 0.253864 + 0.213018i
\(288\) −3.49502e7 + 6.05355e7i −0.0862136 + 0.149326i
\(289\) −4.40167e7 − 2.49631e8i −0.107269 − 0.608354i
\(290\) −1.83043e8 −0.440719
\(291\) 1.83926e7 + 1.04309e8i 0.0437539 + 0.248141i
\(292\) 5.96793e7 − 5.00769e7i 0.140276 − 0.117706i
\(293\) 2.19545e8 + 7.99079e7i 0.509902 + 0.185589i 0.584143 − 0.811651i \(-0.301431\pi\)
−0.0742401 + 0.997240i \(0.523653\pi\)
\(294\) 2.03232e7 − 7.39705e6i 0.0466420 − 0.0169763i
\(295\) 2.05912e8 0.466988
\(296\) −1.55814e8 − 2.46516e7i −0.349210 − 0.0552489i
\(297\) −1.57651e8 −0.349179
\(298\) −5.19349e8 + 1.89028e8i −1.13685 + 0.413779i
\(299\) −5.68145e7 − 2.06788e7i −0.122916 − 0.0447379i
\(300\) 1.88439e7 − 1.58119e7i 0.0402947 − 0.0338112i
\(301\) −5.29288e7 − 3.00174e8i −0.111869 − 0.634440i
\(302\) 2.53016e8 0.528596
\(303\) −2.36576e6 − 1.34169e7i −0.00488563 − 0.0277078i
\(304\) −5.20166e7 + 9.00954e7i −0.106190 + 0.183927i
\(305\) −3.59746e7 − 3.01862e7i −0.0726016 − 0.0609200i
\(306\) 1.06866e8 + 1.85098e8i 0.213214 + 0.369298i
\(307\) 2.04741e8 − 3.54622e8i 0.403851 − 0.699491i −0.590336 − 0.807158i \(-0.701005\pi\)
0.994187 + 0.107667i \(0.0343380\pi\)
\(308\) 2.01807e8 − 7.34519e7i 0.393559 − 0.143244i
\(309\) 4.92754e7 − 4.13470e7i 0.0950114 − 0.0797240i
\(310\) 1.06838e8 + 1.85048e8i 0.203685 + 0.352793i
\(311\) −1.31165e8 + 7.43873e8i −0.247261 + 1.40229i 0.567921 + 0.823083i \(0.307748\pi\)
−0.815182 + 0.579205i \(0.803363\pi\)
\(312\) 2.23943e6 − 1.27004e7i 0.00417442 − 0.0236743i
\(313\) −9.25346e7 − 7.76457e7i −0.170569 − 0.143124i 0.553507 − 0.832844i \(-0.313289\pi\)
−0.724076 + 0.689720i \(0.757733\pi\)
\(314\) −3.04556e8 − 1.10849e8i −0.555154 − 0.202059i
\(315\) −2.16879e8 − 7.89377e7i −0.390959 − 0.142298i
\(316\) 2.15283e7 + 1.80644e7i 0.0383800 + 0.0322046i
\(317\) −1.26665e8 + 7.18352e8i −0.223331 + 1.26657i 0.642519 + 0.766269i \(0.277889\pi\)
−0.865850 + 0.500303i \(0.833222\pi\)
\(318\) 7.15021e6 − 4.05509e7i 0.0124688 − 0.0707140i
\(319\) −3.54816e8 − 6.14559e8i −0.611978 − 1.05998i
\(320\) −3.22101e7 + 2.70275e7i −0.0549499 + 0.0461084i
\(321\) 2.85986e7 − 1.04090e7i 0.0482589 − 0.0175648i
\(322\) 4.75081e7 − 8.22864e7i 0.0792998 − 0.137351i
\(323\) 1.59050e8 + 2.75482e8i 0.262618 + 0.454868i
\(324\) 2.17327e8 + 1.82359e8i 0.354983 + 0.297866i
\(325\) 8.99605e7 − 1.55816e8i 0.145365 − 0.251780i
\(326\) −5.14612e7 − 2.91851e8i −0.0822656 − 0.466551i
\(327\) −2.36211e7 −0.0373580
\(328\) −1.74932e7 − 9.92090e7i −0.0273723 − 0.155236i
\(329\) −4.40922e8 + 3.69978e8i −0.682616 + 0.572783i
\(330\) −4.40014e7 − 1.60152e7i −0.0674013 − 0.0245321i
\(331\) 4.65981e8 − 1.69603e8i 0.706270 − 0.257061i 0.0361842 − 0.999345i \(-0.488480\pi\)
0.670085 + 0.742284i \(0.266257\pi\)
\(332\) 3.29641e8 0.494376
\(333\) −2.13877e8 + 6.21486e8i −0.317402 + 0.922309i
\(334\) 1.07672e8 0.158122
\(335\) 4.14604e8 − 1.50904e8i 0.602528 − 0.219302i
\(336\) 1.90448e7 + 6.93175e6i 0.0273899 + 0.00996909i
\(337\) 3.81261e8 − 3.19916e8i 0.542648 − 0.455335i −0.329795 − 0.944053i \(-0.606979\pi\)
0.872442 + 0.488717i \(0.162535\pi\)
\(338\) 7.07898e7 + 4.01469e8i 0.0997154 + 0.565514i
\(339\) 6.59784e7 0.0919820
\(340\) 2.23254e7 + 1.26614e8i 0.0308051 + 0.174705i
\(341\) −4.14194e8 + 7.17404e8i −0.565670 + 0.979769i
\(342\) 3.32036e8 + 2.78612e8i 0.448843 + 0.376624i
\(343\) 4.02053e8 + 6.96376e8i 0.537965 + 0.931782i
\(344\) −1.15680e8 + 2.00363e8i −0.153215 + 0.265377i
\(345\) −1.94676e7 + 7.08564e6i −0.0255239 + 0.00928992i
\(346\) −2.71698e8 + 2.27982e8i −0.352631 + 0.295893i
\(347\) 2.48786e8 + 4.30910e8i 0.319648 + 0.553647i 0.980415 − 0.196945i \(-0.0631019\pi\)
−0.660766 + 0.750592i \(0.729769\pi\)
\(348\) 1.16290e7 − 6.59514e7i 0.0147916 − 0.0838874i
\(349\) 1.02877e7 − 5.83446e7i 0.0129548 − 0.0734702i −0.977645 − 0.210262i \(-0.932568\pi\)
0.990600 + 0.136792i \(0.0436793\pi\)
\(350\) 2.16601e8 + 1.81750e8i 0.270036 + 0.226587i
\(351\) −1.02255e8 − 3.72179e7i −0.126215 − 0.0459385i
\(352\) −1.53180e8 − 5.57530e7i −0.187199 − 0.0681348i
\(353\) −5.39148e7 − 4.52399e7i −0.0652374 − 0.0547407i 0.609586 − 0.792720i \(-0.291336\pi\)
−0.674823 + 0.737979i \(0.735780\pi\)
\(354\) −1.30819e7 + 7.41912e7i −0.0156733 + 0.0888876i
\(355\) 1.02760e8 − 5.82784e8i 0.121906 − 0.691366i
\(356\) 2.48755e8 + 4.30857e8i 0.292212 + 0.506126i
\(357\) 4.74719e7 − 3.98337e7i 0.0552202 − 0.0463352i
\(358\) 8.04029e8 − 2.92643e8i 0.926149 − 0.337091i
\(359\) −3.22401e8 + 5.58415e8i −0.367761 + 0.636981i −0.989215 − 0.146470i \(-0.953209\pi\)
0.621454 + 0.783451i \(0.286542\pi\)
\(360\) 8.75927e7 + 1.51715e8i 0.0989485 + 0.171384i
\(361\) −1.90574e8 − 1.59910e8i −0.213200 − 0.178896i
\(362\) 1.08840e8 − 1.88517e8i 0.120589 − 0.208867i
\(363\) −6.70067e6 − 3.80014e7i −0.00735267 − 0.0416991i
\(364\) 1.48237e8 0.161102
\(365\) −3.39046e7 − 1.92282e8i −0.0364950 − 0.206973i
\(366\) 1.31618e7 − 1.10440e7i 0.0140324 − 0.0117745i
\(367\) 1.09465e9 + 3.98420e8i 1.15596 + 0.420736i 0.847654 − 0.530550i \(-0.178015\pi\)
0.308309 + 0.951286i \(0.400237\pi\)
\(368\) −6.77717e7 + 2.46669e7i −0.0708894 + 0.0258016i
\(369\) −4.19720e8 −0.434878
\(370\) −2.48757e8 + 3.07295e8i −0.255311 + 0.315392i
\(371\) 4.73300e8 0.481203
\(372\) −7.34614e7 + 2.67378e7i −0.0739876 + 0.0269293i
\(373\) −1.49572e9 − 5.44398e8i −1.49235 − 0.543170i −0.538280 − 0.842766i \(-0.680926\pi\)
−0.954066 + 0.299596i \(0.903148\pi\)
\(374\) −3.81823e8 + 3.20387e8i −0.377408 + 0.316683i
\(375\) −2.66674e7 − 1.51238e8i −0.0261139 − 0.148099i
\(376\) 4.36891e8 0.423854
\(377\) −8.50564e7 − 4.82379e8i −0.0817547 − 0.463654i
\(378\) 8.55056e7 − 1.48100e8i 0.0814279 − 0.141037i
\(379\) −8.42290e8 − 7.06765e8i −0.794738 − 0.666865i 0.152175 − 0.988354i \(-0.451372\pi\)
−0.946913 + 0.321489i \(0.895817\pi\)
\(380\) 1.30365e8 + 2.25798e8i 0.121876 + 0.211095i
\(381\) 1.20471e7 − 2.08662e7i 0.0111595 − 0.0193289i
\(382\) −3.59334e8 + 1.30787e8i −0.329819 + 0.120044i
\(383\) −6.88068e8 + 5.77357e8i −0.625800 + 0.525108i −0.899621 − 0.436672i \(-0.856157\pi\)
0.273821 + 0.961781i \(0.411712\pi\)
\(384\) −7.69177e6 − 1.33225e7i −0.00693214 − 0.0120068i
\(385\) 9.34630e7 − 5.30055e8i 0.0834694 − 0.473378i
\(386\) −1.52883e8 + 8.67042e8i −0.135302 + 0.767335i
\(387\) 7.38415e8 + 6.19604e8i 0.647608 + 0.543407i
\(388\) 8.68383e8 + 3.16065e8i 0.754745 + 0.274705i
\(389\) −5.44231e8 − 1.98084e8i −0.468770 − 0.170618i 0.0968251 − 0.995301i \(-0.469131\pi\)
−0.565595 + 0.824683i \(0.691353\pi\)
\(390\) −2.47594e7 − 2.07756e7i −0.0211355 − 0.0177348i
\(391\) −3.82934e7 + 2.17173e8i −0.0323971 + 0.183733i
\(392\) 3.27665e7 − 1.85828e8i 0.0274745 − 0.155815i
\(393\) −2.31649e7 − 4.01227e7i −0.0192511 − 0.0333439i
\(394\) 7.78414e8 − 6.53167e8i 0.641171 − 0.538007i
\(395\) 6.61850e7 − 2.40894e7i 0.0540343 − 0.0196669i
\(396\) −3.39583e8 + 5.88176e8i −0.274798 + 0.475964i
\(397\) 6.50280e7 + 1.12632e8i 0.0521596 + 0.0903430i 0.890926 − 0.454148i \(-0.150056\pi\)
−0.838767 + 0.544491i \(0.816723\pi\)
\(398\) −5.58022e8 − 4.68236e8i −0.443671 − 0.372284i
\(399\) 6.28367e7 − 1.08836e8i 0.0495232 − 0.0857766i
\(400\) −3.72685e7 − 2.11360e8i −0.0291160 − 0.165125i
\(401\) −8.02647e7 −0.0621612 −0.0310806 − 0.999517i \(-0.509895\pi\)
−0.0310806 + 0.999517i \(0.509895\pi\)
\(402\) 2.80309e7 + 1.58971e8i 0.0215202 + 0.122047i
\(403\) −4.38017e8 + 3.67540e8i −0.333368 + 0.279729i
\(404\) −1.11696e8 − 4.06541e7i −0.0842760 − 0.0306740i
\(405\) 6.68135e8 − 2.43181e8i 0.499772 − 0.181902i
\(406\) 7.69770e8 0.570847
\(407\) −1.51392e9 − 2.39520e8i −1.11307 − 0.176101i
\(408\) −4.70379e7 −0.0342876
\(409\) 1.14487e9 − 4.16699e8i 0.827417 − 0.301155i 0.106619 − 0.994300i \(-0.465998\pi\)
0.720798 + 0.693145i \(0.243775\pi\)
\(410\) −2.37249e8 − 8.63514e7i −0.170004 − 0.0618765i
\(411\) 3.32139e8 − 2.78698e8i 0.235979 − 0.198010i
\(412\) −9.74540e7 − 5.52689e8i −0.0686530 − 0.389351i
\(413\) −8.65943e8 −0.604873
\(414\) 5.21786e7 + 2.95920e8i 0.0361403 + 0.204962i
\(415\) 4.13075e8 − 7.15467e8i 0.283701 − 0.491384i
\(416\) −8.61935e7 − 7.23249e7i −0.0587013 − 0.0492563i
\(417\) −2.01592e8 − 3.49167e8i −0.136143 − 0.235807i
\(418\) −5.05404e8 + 8.75385e8i −0.338471 + 0.586249i
\(419\) −1.06594e8 + 3.87969e7i −0.0707917 + 0.0257661i −0.377173 − 0.926143i \(-0.623104\pi\)
0.306382 + 0.951909i \(0.400882\pi\)
\(420\) 3.89102e7 − 3.26495e7i 0.0256266 − 0.0215033i
\(421\) −1.28983e9 − 2.23406e9i −0.842454 − 1.45917i −0.887814 − 0.460202i \(-0.847777\pi\)
0.0453604 − 0.998971i \(-0.485556\pi\)
\(422\) 5.17159e7 − 2.93296e8i 0.0334989 − 0.189982i
\(423\) 3.16085e8 − 1.79260e9i 0.203054 − 1.15158i
\(424\) −2.75205e8 − 2.30924e8i −0.175338 − 0.147126i
\(425\) −6.16664e8 − 2.24447e8i −0.389661 − 0.141825i
\(426\) 2.03451e8 + 7.40502e7i 0.127505 + 0.0464080i
\(427\) 1.51287e8 + 1.26945e8i 0.0940383 + 0.0789075i
\(428\) 4.61087e7 − 2.61495e8i 0.0284269 − 0.161217i
\(429\) 2.17588e7 − 1.23400e8i 0.0133056 − 0.0754597i
\(430\) 2.89918e8 + 5.02152e8i 0.175847 + 0.304576i
\(431\) 1.97719e8 − 1.65906e8i 0.118953 − 0.0998138i −0.581371 − 0.813639i \(-0.697483\pi\)
0.700324 + 0.713825i \(0.253039\pi\)
\(432\) −1.21976e8 + 4.43957e7i −0.0727918 + 0.0264940i
\(433\) 5.42695e8 − 9.39975e8i 0.321254 − 0.556427i −0.659493 − 0.751710i \(-0.729229\pi\)
0.980747 + 0.195283i \(0.0625625\pi\)
\(434\) −4.49295e8 − 7.78202e8i −0.263826 − 0.456960i
\(435\) −1.28572e8 − 1.07884e8i −0.0748915 − 0.0628414i
\(436\) −1.03044e8 + 1.78478e8i −0.0595417 + 0.103129i
\(437\) 7.76578e7 + 4.40419e8i 0.0445143 + 0.252453i
\(438\) 7.14343e7 0.0406207
\(439\) −4.65865e8 − 2.64205e9i −0.262806 − 1.49044i −0.775212 − 0.631701i \(-0.782357\pi\)
0.512406 − 0.858743i \(-0.328754\pi\)
\(440\) −3.12960e8 + 2.62604e8i −0.175148 + 0.146966i
\(441\) −7.38764e8 − 2.68888e8i −0.410176 − 0.149292i
\(442\) −3.23294e8 + 1.17669e8i −0.178082 + 0.0648165i
\(443\) −1.81717e8 −0.0993076 −0.0496538 − 0.998766i \(-0.515812\pi\)
−0.0496538 + 0.998766i \(0.515812\pi\)
\(444\) −9.49161e7 − 1.09151e8i −0.0514635 − 0.0591818i
\(445\) 1.24687e9 0.670750
\(446\) 1.23473e9 − 4.49405e8i 0.659022 − 0.239864i
\(447\) −4.76207e8 − 1.73325e8i −0.252185 − 0.0917879i
\(448\) 1.35456e8 − 1.13661e8i 0.0711747 − 0.0597227i
\(449\) 4.76273e7 + 2.70108e8i 0.0248310 + 0.140824i 0.994703 − 0.102792i \(-0.0327776\pi\)
−0.969872 + 0.243616i \(0.921666\pi\)
\(450\) −8.94193e8 −0.462580
\(451\) −1.69968e8 − 9.63935e8i −0.0872466 − 0.494800i
\(452\) 2.87823e8 − 4.98524e8i 0.146602 − 0.253923i
\(453\) 1.77721e8 + 1.49125e8i 0.0898245 + 0.0753717i
\(454\) −6.35015e8 − 1.09988e9i −0.318485 − 0.551632i
\(455\) 1.85756e8 − 3.21739e8i 0.0924493 − 0.160127i
\(456\) −8.96385e7 + 3.26257e7i −0.0442708 + 0.0161133i
\(457\) −1.97853e8 + 1.66018e8i −0.0969696 + 0.0813671i −0.689984 − 0.723825i \(-0.742382\pi\)
0.593014 + 0.805192i \(0.297938\pi\)
\(458\) 3.85533e8 + 6.67762e8i 0.187513 + 0.324783i
\(459\) −6.89209e7 + 3.90870e8i −0.0332665 + 0.188663i
\(460\) −3.13871e7 + 1.78005e8i −0.0150348 + 0.0852668i
\(461\) 9.37950e8 + 7.87033e8i 0.445889 + 0.374145i 0.837908 − 0.545812i \(-0.183779\pi\)
−0.392019 + 0.919957i \(0.628223\pi\)
\(462\) 1.85044e8 + 6.73503e7i 0.0873026 + 0.0317755i
\(463\) 2.11810e9 + 7.70924e8i 0.991773 + 0.360976i 0.786406 − 0.617709i \(-0.211939\pi\)
0.205366 + 0.978685i \(0.434161\pi\)
\(464\) −4.47590e8 − 3.75572e8i −0.208002 − 0.174534i
\(465\) −3.40221e7 + 1.92949e8i −0.0156919 + 0.0889933i
\(466\) 4.44055e8 − 2.51836e9i 0.203276 − 1.15284i
\(467\) 9.71428e8 + 1.68256e9i 0.441369 + 0.764473i 0.997791 − 0.0664263i \(-0.0211597\pi\)
−0.556423 + 0.830899i \(0.687826\pi\)
\(468\) −3.59116e8 + 3.01334e8i −0.161947 + 0.135890i
\(469\) −1.74357e9 + 6.34609e8i −0.780433 + 0.284054i
\(470\) 5.47471e8 − 9.48248e8i 0.243231 − 0.421288i
\(471\) −1.48589e8 − 2.57364e8i −0.0655262 − 0.113495i
\(472\) 5.03510e8 + 4.22495e8i 0.220400 + 0.184937i
\(473\) −1.12397e9 + 1.94677e9i −0.488359 + 0.845863i
\(474\) 4.47469e6 + 2.53772e7i 0.00192992 + 0.0109451i
\(475\) −1.33083e9 −0.569765
\(476\) −9.38872e7 − 5.32461e8i −0.0399008 − 0.226289i
\(477\) −1.14661e9 + 9.62120e8i −0.483728 + 0.405896i
\(478\) 2.00227e9 + 7.28768e8i 0.838544 + 0.305205i
\(479\) 6.80232e8 − 2.47584e8i 0.282802 − 0.102932i −0.196725 − 0.980459i \(-0.563031\pi\)
0.479527 + 0.877527i \(0.340808\pi\)
\(480\) −3.85545e7 −0.0159122
\(481\) −9.25415e8 − 5.12762e8i −0.379166 − 0.210091i
\(482\) −5.11596e8 −0.208095
\(483\) 8.18691e7 − 2.97979e7i 0.0330602 − 0.0120329i
\(484\) −3.16364e8 − 1.15147e8i −0.126832 − 0.0461630i
\(485\) 1.77418e9 − 1.48871e9i 0.706157 − 0.592536i
\(486\) 1.41452e8 + 8.02216e8i 0.0558963 + 0.317004i
\(487\) −2.23059e9 −0.875123 −0.437561 − 0.899189i \(-0.644158\pi\)
−0.437561 + 0.899189i \(0.644158\pi\)
\(488\) −2.60306e7 − 1.47627e8i −0.0101395 − 0.0575037i
\(489\) 1.35868e8 − 2.35330e8i 0.0525455 − 0.0910114i
\(490\) −3.62270e8 − 3.03980e8i −0.139106 − 0.116724i
\(491\) 2.32647e9 + 4.02957e9i 0.886978 + 1.53629i 0.843430 + 0.537239i \(0.180533\pi\)
0.0435476 + 0.999051i \(0.486134\pi\)
\(492\) 4.61856e7 − 7.99958e7i 0.0174835 − 0.0302823i
\(493\) −1.67882e9 + 6.11039e8i −0.631014 + 0.229670i
\(494\) −5.34474e8 + 4.48477e8i −0.199472 + 0.167377i
\(495\) 8.51068e8 + 1.47409e9i 0.315389 + 0.546269i
\(496\) −1.18440e8 + 6.71704e8i −0.0435824 + 0.247168i
\(497\) −4.32148e8 + 2.45084e9i −0.157901 + 0.895503i
\(498\) 2.31543e8 + 1.94288e8i 0.0840095 + 0.0704924i
\(499\) 8.11044e8 + 2.95196e8i 0.292208 + 0.106355i 0.483965 − 0.875087i \(-0.339196\pi\)
−0.191757 + 0.981442i \(0.561418\pi\)
\(500\) −1.25907e9 − 4.58264e8i −0.450458 − 0.163953i
\(501\) 7.56301e7 + 6.34612e7i 0.0268697 + 0.0225463i
\(502\) −4.18657e8 + 2.37432e9i −0.147705 + 0.837677i
\(503\) 7.55401e7 − 4.28409e8i 0.0264661 − 0.150097i −0.968711 − 0.248192i \(-0.920164\pi\)
0.995177 + 0.0980949i \(0.0312749\pi\)
\(504\) −3.68362e8 − 6.38021e8i −0.128164 − 0.221987i
\(505\) −2.28205e8 + 1.91487e8i −0.0788506 + 0.0661635i
\(506\) −6.58484e8 + 2.39669e8i −0.225953 + 0.0822402i
\(507\) −1.86899e8 + 3.23719e8i −0.0636912 + 0.110316i
\(508\) −1.05108e8 − 1.82053e8i −0.0355724 − 0.0616132i
\(509\) 1.87098e9 + 1.56994e9i 0.628866 + 0.527681i 0.900576 − 0.434698i \(-0.143145\pi\)
−0.271711 + 0.962379i \(0.587589\pi\)
\(510\) −5.89435e7 + 1.02093e8i −0.0196762 + 0.0340801i
\(511\) 1.42582e8 + 8.08623e8i 0.0472707 + 0.268085i
\(512\) −1.34218e8 −0.0441942
\(513\) 1.39769e8 + 7.92671e8i 0.0457089 + 0.259228i
\(514\) −1.20926e9 + 1.01469e9i −0.392780 + 0.329581i
\(515\) −1.32170e9 − 4.81060e8i −0.426391 − 0.155194i
\(516\) −1.99347e8 + 7.25563e7i −0.0638756 + 0.0232488i
\(517\) 4.24492e9 1.35099
\(518\) 1.04612e9 − 1.29230e9i 0.330695 − 0.408516i
\(519\) −3.25214e8 −0.102114
\(520\) −2.64987e8 + 9.64474e7i −0.0826443 + 0.0300801i
\(521\) 4.68638e9 + 1.70570e9i 1.45180 + 0.528410i 0.943092 − 0.332532i \(-0.107903\pi\)
0.508703 + 0.860942i \(0.330125\pi\)
\(522\) −1.86483e9 + 1.56478e9i −0.573843 + 0.481512i
\(523\) 9.34044e8 + 5.29723e9i 0.285504 + 1.61917i 0.703481 + 0.710714i \(0.251628\pi\)
−0.417978 + 0.908457i \(0.637261\pi\)
\(524\) −4.04216e8 −0.122731
\(525\) 4.50208e7 + 2.55326e8i 0.0135786 + 0.0770082i
\(526\) −7.82813e8 + 1.35587e9i −0.234535 + 0.406227i
\(527\) 1.59761e9 + 1.34056e9i 0.475483 + 0.398977i
\(528\) −7.47348e7 − 1.29445e8i −0.0220955 − 0.0382706i
\(529\) 1.54740e9 − 2.68017e9i 0.454472 − 0.787168i
\(530\) −8.46069e8 + 3.07944e8i −0.246854 + 0.0898475i
\(531\) 2.09782e9 − 1.76028e9i 0.608047 − 0.510212i
\(532\) −5.48235e8 − 9.49571e8i −0.157861 − 0.273424i
\(533\) 1.17320e8 − 6.65353e8i 0.0335603 − 0.190330i
\(534\) −7.92154e7 + 4.49253e8i −0.0225121 + 0.127672i
\(535\) −5.09782e8 − 4.27758e8i −0.143928 − 0.120770i
\(536\) 1.32344e9 + 4.81694e8i 0.371218 + 0.135112i
\(537\) 7.37239e8 + 2.68333e8i 0.205446 + 0.0747763i
\(538\) −1.44167e9 − 1.20971e9i −0.399143 − 0.334921i
\(539\) 3.18366e8 − 1.80554e9i 0.0875722 − 0.496647i
\(540\) −5.64908e7 + 3.20375e8i −0.0154383 + 0.0875550i
\(541\) 2.34008e9 + 4.05313e9i 0.635389 + 1.10053i 0.986433 + 0.164167i \(0.0524937\pi\)
−0.351043 + 0.936359i \(0.614173\pi\)
\(542\) 3.03255e9 − 2.54461e9i 0.818107 − 0.686473i
\(543\) 1.87560e8 − 6.82664e7i 0.0502738 − 0.0182982i
\(544\) −2.05197e8 + 3.55412e8i −0.0546481 + 0.0946533i
\(545\) 2.58251e8 + 4.47304e8i 0.0683368 + 0.118363i
\(546\) 1.04123e8 + 8.73695e7i 0.0273761 + 0.0229713i
\(547\) −8.42984e7 + 1.46009e8i −0.0220224 + 0.0381438i −0.876827 − 0.480807i \(-0.840344\pi\)
0.854804 + 0.518951i \(0.173677\pi\)
\(548\) −6.56886e8 − 3.72539e9i −0.170513 − 0.967029i
\(549\) −6.24559e8 −0.161091
\(550\) −3.62108e8 − 2.05362e9i −0.0928044 − 0.526320i
\(551\) −2.77544e9 + 2.32887e9i −0.706808 + 0.593083i
\(552\) −6.21420e7 − 2.26178e7i −0.0157253 − 0.00572353i
\(553\) −2.78334e8 + 1.01305e8i −0.0699888 + 0.0254738i
\(554\) −8.45063e7 −0.0211157
\(555\) −3.55847e8 + 6.92320e7i −0.0883563 + 0.0171902i
\(556\) −3.51768e9 −0.867950
\(557\) 6.86225e8 − 2.49766e8i 0.168257 − 0.0612406i −0.256518 − 0.966539i \(-0.582575\pi\)
0.424775 + 0.905299i \(0.360353\pi\)
\(558\) 2.67038e9 + 9.71937e8i 0.650658 + 0.236820i
\(559\) −1.18862e9 + 9.97367e8i −0.287806 + 0.241498i
\(560\) −7.69543e7 − 4.36430e8i −0.0185172 − 0.105016i
\(561\) −4.57030e8 −0.109288
\(562\) 3.47582e8 + 1.97124e9i 0.0826001 + 0.468448i
\(563\) 8.74265e7 − 1.51427e8i 0.0206473 − 0.0357622i −0.855517 − 0.517775i \(-0.826761\pi\)
0.876164 + 0.482012i \(0.160094\pi\)
\(564\) 3.06877e8 + 2.57500e8i 0.0720256 + 0.0604367i
\(565\) −7.21345e8 − 1.24941e9i −0.168257 − 0.291430i
\(566\) 1.98889e9 − 3.44485e9i 0.461055 − 0.798570i
\(567\) −2.80977e9 + 1.02267e9i −0.647337 + 0.235611i
\(568\) 1.44704e9 − 1.21421e9i 0.331331 − 0.278020i
\(569\) −1.42811e9 − 2.47356e9i −0.324989 − 0.562897i 0.656521 − 0.754307i \(-0.272027\pi\)
−0.981510 + 0.191410i \(0.938694\pi\)
\(570\) −4.15142e7 + 2.35439e8i −0.00938933 + 0.0532496i
\(571\) −4.38372e7 + 2.48613e8i −0.00985409 + 0.0558853i −0.989338 − 0.145636i \(-0.953477\pi\)
0.979484 + 0.201521i \(0.0645884\pi\)
\(572\) −8.37474e8 − 7.02724e8i −0.187105 − 0.157000i
\(573\) −3.29484e8 − 1.19922e8i −0.0731633 − 0.0266293i
\(574\) 9.97724e8 + 3.63142e8i 0.220201 + 0.0801465i
\(575\) −7.06754e8 − 5.93037e8i −0.155035 − 0.130090i
\(576\) −9.71046e7 + 5.50708e8i −0.0211720 + 0.120072i
\(577\) 5.25579e8 − 2.98071e9i 0.113900 − 0.645958i −0.873389 − 0.487023i \(-0.838083\pi\)
0.987289 − 0.158935i \(-0.0508060\pi\)
\(578\) −1.01393e9 − 1.75618e9i −0.218404 − 0.378286i
\(579\) −6.18414e8 + 5.18911e8i −0.132405 + 0.111101i
\(580\) −1.37604e9 + 5.00836e8i −0.292841 + 0.106585i
\(581\) −1.73714e9 + 3.00882e9i −0.367468 + 0.636473i
\(582\) 4.23674e8 + 7.33825e8i 0.0890844 + 0.154299i
\(583\) −2.67395e9 − 2.24371e9i −0.558872 − 0.468950i
\(584\) 3.11623e8 − 5.39747e8i 0.0647418 − 0.112136i
\(585\) 2.04018e8 + 1.15704e9i 0.0421331 + 0.238949i
\(586\) 1.86908e9 0.383695
\(587\) −1.41809e8 − 8.04236e8i −0.0289380 − 0.164116i 0.966914 − 0.255102i \(-0.0821091\pi\)
−0.995852 + 0.0909864i \(0.970998\pi\)
\(588\) 1.32541e8 − 1.11215e8i 0.0268862 − 0.0225602i
\(589\) 3.97434e9 + 1.44654e9i 0.801422 + 0.291694i
\(590\) 1.54795e9 − 5.63409e8i 0.310296 − 0.112938i
\(591\) 9.31737e8 0.185668
\(592\) −1.23879e9 + 2.41014e8i −0.245399 + 0.0477437i
\(593\) −4.39652e9 −0.865801 −0.432900 − 0.901442i \(-0.642510\pi\)
−0.432900 + 0.901442i \(0.642510\pi\)
\(594\) −1.18515e9 + 4.31358e8i −0.232017 + 0.0844472i
\(595\) −1.27333e9 − 4.63453e8i −0.247817 − 0.0901979i
\(596\) −3.38702e9 + 2.84204e9i −0.655323 + 0.549881i
\(597\) −1.15986e8 − 6.57787e8i −0.0223097 − 0.126525i
\(598\) −4.83686e8 −0.0924931
\(599\) −1.54664e9 − 8.77143e9i −0.294033 − 1.66754i −0.671109 − 0.741359i \(-0.734182\pi\)
0.377076 − 0.926182i \(-0.376930\pi\)
\(600\) 9.83961e7 − 1.70427e8i 0.0185972 − 0.0322114i
\(601\) 5.70732e9 + 4.78901e9i 1.07244 + 0.899880i 0.995271 − 0.0971380i \(-0.0309688\pi\)
0.0771647 + 0.997018i \(0.475413\pi\)
\(602\) −1.21922e9 − 2.11175e9i −0.227769 − 0.394507i
\(603\) 2.93393e9 − 5.08172e9i 0.544928 − 0.943843i
\(604\) 1.90206e9 − 6.92292e8i 0.351232 − 0.127838i
\(605\) −6.46359e8 + 5.42359e8i −0.118667 + 0.0995734i
\(606\) −5.44954e7 − 9.43888e7i −0.00994731 − 0.0172292i
\(607\) −1.96403e8 + 1.11386e9i −0.0356441 + 0.202148i −0.997429 − 0.0716573i \(-0.977171\pi\)
0.961785 + 0.273805i \(0.0882823\pi\)
\(608\) −1.44521e8 + 8.19622e8i −0.0260777 + 0.147894i
\(609\) 5.40694e8 + 4.53696e8i 0.0970043 + 0.0813963i
\(610\) −3.53035e8 − 1.28494e8i −0.0629743 − 0.0229208i
\(611\) 2.75334e9 + 1.00213e9i 0.488332 + 0.177738i
\(612\) 1.30983e9 + 1.09908e9i 0.230986 + 0.193820i
\(613\) 1.90442e9 − 1.08005e10i 0.333926 − 1.89379i −0.103657 − 0.994613i \(-0.533054\pi\)
0.437583 − 0.899178i \(-0.355835\pi\)
\(614\) 5.68847e8 − 3.22609e9i 0.0991760 − 0.562455i
\(615\) −1.15751e8 − 2.00486e8i −0.0200660 − 0.0347554i
\(616\) 1.31612e9 − 1.10436e9i 0.226863 − 0.190360i
\(617\) −1.44896e9 + 5.27377e8i −0.248346 + 0.0903905i −0.463194 − 0.886257i \(-0.653297\pi\)
0.214848 + 0.976648i \(0.431074\pi\)
\(618\) 2.57298e8 − 4.45653e8i 0.0438507 − 0.0759517i
\(619\) −3.53597e9 − 6.12448e9i −0.599227 − 1.03789i −0.992935 − 0.118656i \(-0.962141\pi\)
0.393709 − 0.919235i \(-0.371192\pi\)
\(620\) 1.30948e9 + 1.09878e9i 0.220662 + 0.185157i
\(621\) −2.78999e8 + 4.83240e8i −0.0467500 + 0.0809734i
\(622\) 1.04932e9 + 5.95098e9i 0.174840 + 0.991567i
\(623\) −5.24358e9 −0.868799
\(624\) −1.79154e7 − 1.01604e8i −0.00295176 − 0.0167403i
\(625\) 5.63467e8 − 4.72805e8i 0.0923185 − 0.0774644i
\(626\) −9.08084e8 − 3.30515e8i −0.147950 − 0.0538495i
\(627\) −8.70946e8 + 3.16998e8i −0.141109 + 0.0513595i
\(628\) −2.59281e9 −0.417746
\(629\) −1.25570e9 + 3.64882e9i −0.201191 + 0.584622i
\(630\) −1.84639e9 −0.294192
\(631\) −6.61894e9 + 2.40910e9i −1.04878 + 0.381726i −0.808203 − 0.588904i \(-0.799560\pi\)
−0.240580 + 0.970629i \(0.577337\pi\)
\(632\) 2.11267e8 + 7.68949e7i 0.0332906 + 0.0121168i
\(633\) 2.09192e8 − 1.75533e8i 0.0327817 − 0.0275071i
\(634\) 1.01332e9 + 5.74682e9i 0.157919 + 0.895602i
\(635\) −5.26847e8 −0.0816538
\(636\) −5.72017e7 − 3.24407e8i −0.00881676 − 0.0500023i
\(637\) 6.32748e8 − 1.09595e9i 0.0969936 − 0.167998i
\(638\) −4.34887e9 − 3.64914e9i −0.662986 − 0.556311i
\(639\) −3.93512e9 − 6.81582e9i −0.596629 − 1.03339i
\(640\) −1.68189e8 + 2.91312e8i −0.0253611 + 0.0439267i
\(641\) 5.56979e9 − 2.02724e9i 0.835287 − 0.304019i 0.111260 − 0.993791i \(-0.464511\pi\)
0.724027 + 0.689772i \(0.242289\pi\)
\(642\) 1.86510e8 − 1.56501e8i 0.0278183 − 0.0233423i
\(643\) −6.74379e8 − 1.16806e9i −0.100038 − 0.173271i 0.811662 − 0.584127i \(-0.198563\pi\)
−0.911700 + 0.410856i \(0.865230\pi\)
\(644\) 1.31995e8 − 7.48581e8i 0.0194741 − 0.110443i
\(645\) −9.23233e7 + 5.23592e8i −0.0135473 + 0.0768305i
\(646\) 1.94943e9 + 1.63576e9i 0.284507 + 0.238730i
\(647\) 7.00828e9 + 2.55080e9i 1.01729 + 0.370265i 0.796229 − 0.604995i \(-0.206825\pi\)
0.221064 + 0.975259i \(0.429047\pi\)
\(648\) 2.13273e9 + 7.76251e8i 0.307910 + 0.112070i
\(649\) 4.89221e9 + 4.10505e9i 0.702503 + 0.589470i
\(650\) 2.49944e8 − 1.41750e9i 0.0356981 − 0.202454i
\(651\) 1.43077e8 − 8.11427e8i 0.0203252 − 0.115270i
\(652\) −1.18541e9 − 2.05320e9i −0.167495 − 0.290111i
\(653\) −1.84024e9 + 1.54414e9i −0.258629 + 0.217016i −0.762878 − 0.646543i \(-0.776214\pi\)
0.504248 + 0.863559i \(0.331770\pi\)
\(654\) −1.77573e8 + 6.46312e7i −0.0248230 + 0.00903484i
\(655\) −5.06525e8 + 8.77327e8i −0.0704298 + 0.121988i
\(656\) −4.02958e8 − 6.97944e8i −0.0557309 − 0.0965288i
\(657\) −1.98918e9 − 1.66912e9i −0.273650 − 0.229619i
\(658\) −2.30233e9 + 3.98776e9i −0.315049 + 0.545680i
\(659\) −1.62507e9 − 9.21621e9i −0.221193 − 1.25445i −0.869830 − 0.493351i \(-0.835772\pi\)
0.648637 − 0.761098i \(-0.275339\pi\)
\(660\) −3.74603e8 −0.0507186
\(661\) 1.30995e9 + 7.42909e9i 0.176421 + 1.00053i 0.936491 + 0.350691i \(0.114053\pi\)
−0.760071 + 0.649840i \(0.774836\pi\)
\(662\) 3.03897e9 − 2.55000e9i 0.407121 − 0.341615i
\(663\) −2.96438e8 − 1.07895e8i −0.0395036 − 0.0143781i
\(664\) 2.47809e9 − 9.01950e8i 0.328495 − 0.119562i
\(665\) −2.74799e9 −0.362359
\(666\) 9.26544e7 + 5.25725e9i 0.0121536 + 0.689602i
\(667\) −2.51171e9 −0.327739
\(668\) 8.09431e8 − 2.94609e8i 0.105066 − 0.0382409i
\(669\) 1.13216e9 + 4.12073e8i 0.146190 + 0.0532087i
\(670\) 2.70391e9 − 2.26885e9i 0.347320 − 0.291436i
\(671\) −2.52918e8 − 1.43437e9i −0.0323185 − 0.183288i
\(672\) 1.62137e8 0.0206105
\(673\) −7.29194e8 − 4.13547e9i −0.0922127 − 0.522964i −0.995566 − 0.0940667i \(-0.970013\pi\)
0.903353 − 0.428897i \(-0.141098\pi\)
\(674\) 1.99080e9 − 3.44817e9i 0.250449 − 0.433790i
\(675\) −1.27202e9 − 1.06735e9i −0.159196 − 0.133581i
\(676\) 1.63065e9 + 2.82437e9i 0.203024 + 0.351648i
\(677\) 5.13040e9 − 8.88611e9i 0.635464 − 1.10066i −0.350953 − 0.936393i \(-0.614142\pi\)
0.986417 − 0.164263i \(-0.0525244\pi\)
\(678\) 4.95995e8 − 1.80528e8i 0.0611186 − 0.0222454i
\(679\) −7.46112e9 + 6.26063e9i −0.914661 + 0.767491i
\(680\) 5.14268e8 + 8.90738e8i 0.0627203 + 0.108635i
\(681\) 2.02219e8 − 1.14684e9i 0.0245361 − 0.139151i
\(682\) −1.15078e9 + 6.52642e9i −0.138915 + 0.787824i
\(683\) −1.38185e9 − 1.15951e9i −0.165954 − 0.139252i 0.556028 − 0.831163i \(-0.312325\pi\)
−0.721983 + 0.691911i \(0.756769\pi\)
\(684\) 3.25842e9 + 1.18597e9i 0.389324 + 0.141702i
\(685\) −8.90889e9 − 3.24257e9i −1.05903 − 0.385454i
\(686\) 4.92785e9 + 4.13495e9i 0.582804 + 0.489031i
\(687\) −1.22772e8 + 6.96273e8i −0.0144461 + 0.0819277i
\(688\) −3.21401e8 + 1.82275e9i −0.0376259 + 0.213387i
\(689\) −1.20468e9 − 2.08657e9i −0.140315 − 0.243033i
\(690\) −1.26961e8 + 1.06533e8i −0.0147129 + 0.0123456i
\(691\) −1.11671e10 + 4.06450e9i −1.28756 + 0.468634i −0.892926 − 0.450203i \(-0.851352\pi\)
−0.394636 + 0.918837i \(0.629129\pi\)
\(692\) −1.41871e9 + 2.45728e9i −0.162750 + 0.281892i
\(693\) −3.57908e9 − 6.19915e9i −0.408512 − 0.707564i
\(694\) 3.04930e9 + 2.55866e9i 0.346291 + 0.290573i
\(695\) −4.40803e9 + 7.63493e9i −0.498078 + 0.862697i
\(696\) −9.30322e7 − 5.27612e8i −0.0104593 − 0.0593174i
\(697\) −2.46423e9 −0.275655
\(698\) −8.23018e7 − 4.66757e8i −0.00916042 − 0.0519513i
\(699\) 1.79621e9 − 1.50720e9i 0.198924 − 0.166917i
\(700\) 2.12560e9 + 7.73656e8i 0.234228 + 0.0852520i
\(701\) 1.38222e10 − 5.03088e9i 1.51553 − 0.551609i 0.555505 − 0.831513i \(-0.312525\pi\)
0.960028 + 0.279904i \(0.0903027\pi\)
\(702\) −8.70543e8 −0.0949752
\(703\) 1.37898e8 + 7.82439e9i 0.0149698 + 0.849390i
\(704\) −1.30409e9 −0.140865
\(705\) 9.43439e8 − 3.43384e8i 0.101403 − 0.0369078i
\(706\) −5.29090e8 − 1.92573e8i −0.0565866 − 0.0205958i
\(707\) 9.59692e8 − 8.05277e8i 0.102133 − 0.0856993i
\(708\) 1.04655e8 + 5.93530e8i 0.0110827 + 0.0628530i
\(709\) 1.88630e8 0.0198769 0.00993844 − 0.999951i \(-0.496836\pi\)
0.00993844 + 0.999951i \(0.496836\pi\)
\(710\) −8.22084e8 − 4.66227e9i −0.0862009 − 0.488870i
\(711\) 4.68355e8 − 8.11215e8i 0.0488688 − 0.0846433i
\(712\) 3.04892e9 + 2.55835e9i 0.316568 + 0.265632i
\(713\) 1.46602e9 + 2.53922e9i 0.151470 + 0.262353i
\(714\) 2.47881e8 − 4.29342e8i 0.0254858 − 0.0441428i
\(715\) −2.57467e9 + 9.37102e8i −0.263421 + 0.0958773i
\(716\) 5.24360e9 − 4.39991e9i 0.533868 − 0.447969i
\(717\) 9.76886e8 + 1.69202e9i 0.0989753 + 0.171430i
\(718\) −8.95749e8 + 5.08005e9i −0.0903132 + 0.512191i
\(719\) −1.99654e9 + 1.13229e10i −0.200321 + 1.13608i 0.704314 + 0.709889i \(0.251255\pi\)
−0.904635 + 0.426188i \(0.859856\pi\)
\(720\) 1.07360e9 + 9.00856e8i 0.107196 + 0.0899480i
\(721\) 5.55828e9 + 2.02305e9i 0.552290 + 0.201017i
\(722\) −1.87019e9 − 6.80692e8i −0.184929 − 0.0673086i
\(723\) −3.59350e8 − 3.01530e8i −0.0353617 − 0.0296720i
\(724\) 3.02398e8 − 1.71499e9i 0.0296138 − 0.167948i
\(725\) 1.29792e9 − 7.36087e9i 0.126493 − 0.717375i
\(726\) −1.54351e8 − 2.67343e8i −0.0149703 − 0.0259293i
\(727\) 7.06930e7 − 5.93184e7i 0.00682348 − 0.00572558i −0.639369 − 0.768900i \(-0.720805\pi\)
0.646193 + 0.763174i \(0.276360\pi\)
\(728\) 1.11437e9 − 4.05599e8i 0.107046 − 0.0389617i
\(729\) 4.47383e9 − 7.74890e9i 0.427694 − 0.740788i
\(730\) −7.80994e8 − 1.35272e9i −0.0743050 − 0.128700i
\(731\) 4.33533e9 + 3.63777e9i 0.410498 + 0.344449i
\(732\) 6.87259e7 − 1.19037e8i 0.00647637 − 0.0112174i
\(733\) 4.18850e8 + 2.37541e9i 0.0392821 + 0.222780i 0.998129 − 0.0611440i \(-0.0194749\pi\)
−0.958847 + 0.283924i \(0.908364\pi\)
\(734\) 9.31922e9 0.869848
\(735\) −7.52983e7 − 4.27038e8i −0.00699487 − 0.0396699i
\(736\) −4.41984e8 + 3.70869e8i −0.0408634 + 0.0342884i
\(737\) 1.28589e10 + 4.68024e9i 1.18322 + 0.430657i
\(738\) −3.15526e9 + 1.14842e9i −0.288960 + 0.105173i
\(739\) 1.00537e10 0.916368 0.458184 − 0.888857i \(-0.348500\pi\)
0.458184 + 0.888857i \(0.348500\pi\)
\(740\) −1.02923e9 + 2.99074e9i −0.0933688 + 0.271312i
\(741\) −6.39748e8 −0.0577624
\(742\) 3.55806e9 − 1.29503e9i 0.319742 − 0.116376i
\(743\) −1.54410e9 − 5.62007e8i −0.138107 − 0.0502668i 0.272042 − 0.962285i \(-0.412301\pi\)
−0.410149 + 0.912019i \(0.634523\pi\)
\(744\) −4.79090e8 + 4.02004e8i −0.0426493 + 0.0357870i
\(745\) 1.92421e9 + 1.09127e10i 0.170492 + 0.966910i
\(746\) −1.27337e10 −1.12297
\(747\) −1.90792e9 − 1.08204e10i −0.167471 − 0.949773i
\(748\) −1.99374e9 + 3.45325e9i −0.174186 + 0.301698i
\(749\) 2.14383e9 + 1.79889e9i 0.186425 + 0.156429i
\(750\) −6.14286e8 − 1.06397e9i −0.0531687 − 0.0920909i
\(751\) −5.38300e9 + 9.32363e9i −0.463751 + 0.803239i −0.999144 − 0.0413632i \(-0.986830\pi\)
0.535394 + 0.844603i \(0.320163\pi\)
\(752\) 3.28435e9 − 1.19540e9i 0.281635 − 0.102507i
\(753\) −1.69347e9 + 1.42099e9i −0.144543 + 0.121286i
\(754\) −1.95928e9 − 3.39358e9i −0.166455 − 0.288309i
\(755\) 8.80899e8 − 4.99583e9i 0.0744924 − 0.422467i
\(756\) 2.37566e8 − 1.34730e9i 0.0199967 − 0.113407i
\(757\) −7.23733e9 − 6.07284e9i