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Properties

Label 74.8.f.b.9.2
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 9.2
Character \(\chi\) \(=\) 74.9
Dual form 74.8.f.b.33.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.38919 - 7.87846i) q^{2} +(-11.0757 + 62.8133i) q^{3} +(-60.1403 + 21.8893i) q^{4} +(48.5860 + 40.7685i) q^{5} +510.258 q^{6} +(745.438 + 625.497i) q^{7} +(256.000 + 443.405i) q^{8} +(-1767.73 - 643.401i) q^{9} +O(q^{10})\) \(q+(-1.38919 - 7.87846i) q^{2} +(-11.0757 + 62.8133i) q^{3} +(-60.1403 + 21.8893i) q^{4} +(48.5860 + 40.7685i) q^{5} +510.258 q^{6} +(745.438 + 625.497i) q^{7} +(256.000 + 443.405i) q^{8} +(-1767.73 - 643.401i) q^{9} +(253.698 - 439.418i) q^{10} +(1308.86 + 2267.01i) q^{11} +(-708.843 - 4020.05i) q^{12} +(10811.3 - 3934.99i) q^{13} +(3892.40 - 6741.84i) q^{14} +(-3098.93 + 2600.31i) q^{15} +(3137.72 - 2632.86i) q^{16} +(-10941.9 - 3982.52i) q^{17} +(-2613.31 + 14820.8i) q^{18} +(-3295.54 + 18689.9i) q^{19} +(-3814.37 - 1388.32i) q^{20} +(-47545.7 + 39895.6i) q^{21} +(16042.3 - 13461.1i) q^{22} +(-51555.8 + 89297.2i) q^{23} +(-30687.1 + 11169.2i) q^{24} +(-12867.7 - 72976.6i) q^{25} +(-46020.5 - 79709.9i) q^{26} +(-9752.97 + 16892.6i) q^{27} +(-58522.6 - 21300.5i) q^{28} +(40630.1 + 70373.4i) q^{29} +(24791.4 + 20802.5i) q^{30} -93493.8 q^{31} +(-25101.7 - 21062.9i) q^{32} +(-156895. + 57105.0i) q^{33} +(-16175.8 + 91737.6i) q^{34} +(10717.3 + 60780.8i) q^{35} +120395. q^{36} +(234374. + 200002. i) q^{37} +151826. q^{38} +(127427. + 722675. i) q^{39} +(-5638.94 + 31980.0i) q^{40} +(75210.3 - 27374.3i) q^{41} +(380366. + 319165. i) q^{42} -514325. q^{43} +(-128338. - 107689. i) q^{44} +(-59656.4 - 103328. i) q^{45} +(775145. + 282130. i) q^{46} +(-443029. + 767349. i) q^{47} +(130626. + 226251. i) q^{48} +(21424.9 + 121507. i) q^{49} +(-557067. + 202756. i) q^{50} +(371343. - 643186. i) q^{51} +(-564060. + 473303. i) q^{52} +(1.01891e6 - 854970. i) q^{53} +(146637. + 53371.4i) q^{54} +(-28830.4 + 163505. i) q^{55} +(-86516.3 + 490658. i) q^{56} +(-1.13747e6 - 414007. i) q^{57} +(497991. - 417864. i) q^{58} +(-664363. + 557466. i) q^{59} +(129452. - 224217. i) q^{60} +(-373804. + 136054. i) q^{61} +(129880. + 736588. i) q^{62} +(-915288. - 1.58533e6i) q^{63} +(-131072. + 227023. i) q^{64} +(685701. + 249575. i) q^{65} +(667856. + 1.15676e6i) q^{66} +(-3.33792e6 - 2.80084e6i) q^{67} +745222. q^{68} +(-5.03804e6 - 4.22741e6i) q^{69} +(463971. - 168871. i) q^{70} +(129993. - 737225. i) q^{71} +(-167252. - 948531. i) q^{72} -3.10268e6 q^{73} +(1.25012e6 - 2.12434e6i) q^{74} +4.72642e6 q^{75} +(-210914. - 1.19615e6i) q^{76} +(-442334. + 2.50860e6i) q^{77} +(5.51655e6 - 2.00786e6i) q^{78} +(3.49137e6 + 2.92960e6i) q^{79} +259787. q^{80} +(-4.10467e6 - 3.44423e6i) q^{81} +(-320148. - 554513. i) q^{82} +(5.92024e6 + 2.15479e6i) q^{83} +(1.98613e6 - 3.44008e6i) q^{84} +(-369260. - 639578. i) q^{85} +(714493. + 4.05209e6i) q^{86} +(-4.87039e6 + 1.77268e6i) q^{87} +(-670136. + 1.16071e6i) q^{88} +(3.09775e6 - 2.59932e6i) q^{89} +(-731192. + 613543. i) q^{90} +(1.05205e7 + 3.82914e6i) q^{91} +(1.14593e6 - 6.49888e6i) q^{92} +(1.03551e6 - 5.87265e6i) q^{93} +(6.66098e6 + 2.42440e6i) q^{94} +(-922076. + 773714. i) q^{95} +(1.60105e6 - 1.34344e6i) q^{96} +(1.06495e6 - 1.84455e6i) q^{97} +(927522. - 337590. i) q^{98} +(-855112. - 4.84958e6i) 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
\(3\) −11.0757 + 62.8133i −0.236835 + 1.34316i 0.601880 + 0.798587i \(0.294419\pi\)
−0.838715 + 0.544571i \(0.816692\pi\)
\(4\) −60.1403 + 21.8893i −0.469846 + 0.171010i
\(5\) 48.5860 + 40.7685i 0.173827 + 0.145858i 0.725550 − 0.688169i \(-0.241585\pi\)
−0.551724 + 0.834027i \(0.686030\pi\)
\(6\) 510.258 0.964408
\(7\) 745.438 + 625.497i 0.821426 + 0.689258i 0.953306 − 0.302008i \(-0.0976568\pi\)
−0.131880 + 0.991266i \(0.542101\pi\)
\(8\) 256.000 + 443.405i 0.176777 + 0.306186i
\(9\) −1767.73 − 643.401i −0.808290 − 0.294194i
\(10\) 253.698 − 439.418i 0.0802264 − 0.138956i
\(11\) 1308.86 + 2267.01i 0.296496 + 0.513546i 0.975332 − 0.220744i \(-0.0708486\pi\)
−0.678836 + 0.734290i \(0.737515\pi\)
\(12\) −708.843 − 4020.05i −0.118417 − 0.671579i
\(13\) 10811.3 − 3934.99i 1.36482 − 0.496754i 0.447280 − 0.894394i \(-0.352393\pi\)
0.917542 + 0.397640i \(0.130171\pi\)
\(14\) 3892.40 − 6741.84i 0.379114 − 0.656644i
\(15\) −3098.93 + 2600.31i −0.237078 + 0.198932i
\(16\) 3137.72 − 2632.86i 0.191511 − 0.160697i
\(17\) −10941.9 − 3982.52i −0.540157 − 0.196601i 0.0575106 − 0.998345i \(-0.481684\pi\)
−0.597668 + 0.801744i \(0.703906\pi\)
\(18\) −2613.31 + 14820.8i −0.105618 + 0.598988i
\(19\) −3295.54 + 18689.9i −0.110227 + 0.625129i 0.878776 + 0.477234i \(0.158361\pi\)
−0.989003 + 0.147895i \(0.952750\pi\)
\(20\) −3814.37 − 1388.32i −0.106615 − 0.0388047i
\(21\) −47545.7 + 39895.6i −1.12033 + 0.940064i
\(22\) 16042.3 − 13461.1i 0.321209 − 0.269526i
\(23\) −51555.8 + 89297.2i −0.883547 + 1.53035i −0.0361776 + 0.999345i \(0.511518\pi\)
−0.847370 + 0.531003i \(0.821815\pi\)
\(24\) −30687.1 + 11169.2i −0.453123 + 0.164923i
\(25\) −12867.7 − 72976.6i −0.164707 − 0.934100i
\(26\) −46020.5 − 79709.9i −0.513505 − 0.889417i
\(27\) −9752.97 + 16892.6i −0.0953595 + 0.165167i
\(28\) −58522.6 − 21300.5i −0.503814 − 0.183373i
\(29\) 40630.1 + 70373.4i 0.309353 + 0.535816i 0.978221 − 0.207566i \(-0.0665541\pi\)
−0.668868 + 0.743381i \(0.733221\pi\)
\(30\) 24791.4 + 20802.5i 0.167640 + 0.140666i
\(31\) −93493.8 −0.563660 −0.281830 − 0.959464i \(-0.590941\pi\)
−0.281830 + 0.959464i \(0.590941\pi\)
\(32\) −25101.7 − 21062.9i −0.135419 − 0.113630i
\(33\) −156895. + 57105.0i −0.759993 + 0.276615i
\(34\) −16175.8 + 91737.6i −0.0705813 + 0.400287i
\(35\) 10717.3 + 60780.8i 0.0422520 + 0.239623i
\(36\) 120395. 0.430082
\(37\) 234374. + 200002.i 0.760682 + 0.649125i
\(38\) 151826. 0.448852
\(39\) 127427. + 722675.i 0.343982 + 1.95082i
\(40\) −5638.94 + 31980.0i −0.0139312 + 0.0790075i
\(41\) 75210.3 − 27374.3i 0.170425 − 0.0620297i −0.255398 − 0.966836i \(-0.582207\pi\)
0.425824 + 0.904806i \(0.359984\pi\)
\(42\) 380366. + 319165.i 0.792189 + 0.664726i
\(43\) −514325. −0.986503 −0.493252 − 0.869887i \(-0.664192\pi\)
−0.493252 + 0.869887i \(0.664192\pi\)
\(44\) −128338. − 107689.i −0.227129 − 0.190584i
\(45\) −59656.4 − 103328.i −0.0975918 − 0.169034i
\(46\) 775145. + 282130.i 1.17417 + 0.427363i
\(47\) −443029. + 767349.i −0.622429 + 1.07808i 0.366604 + 0.930377i \(0.380521\pi\)
−0.989032 + 0.147701i \(0.952813\pi\)
\(48\) 130626. + 226251.i 0.170485 + 0.295288i
\(49\) 21424.9 + 121507.i 0.0260155 + 0.147541i
\(50\) −557067. + 202756.i −0.630250 + 0.229392i
\(51\) 371343. − 643186.i 0.391995 − 0.678955i
\(52\) −564060. + 473303.i −0.556306 + 0.466796i
\(53\) 1.01891e6 − 854970.i 0.940095 − 0.788834i −0.0375067 − 0.999296i \(-0.511942\pi\)
0.977602 + 0.210463i \(0.0674971\pi\)
\(54\) 146637. + 53371.4i 0.126726 + 0.0461244i
\(55\) −28830.4 + 163505.i −0.0233658 + 0.132514i
\(56\) −86516.3 + 490658.i −0.0658324 + 0.373354i
\(57\) −1.13747e6 − 414007.i −0.813541 − 0.296105i
\(58\) 497991. − 417864.i 0.335138 − 0.281214i
\(59\) −664363. + 557466.i −0.421137 + 0.353376i −0.828595 − 0.559848i \(-0.810860\pi\)
0.407459 + 0.913224i \(0.366415\pi\)
\(60\) 129452. − 224217.i 0.0773709 − 0.134010i
\(61\) −373804. + 136054.i −0.210858 + 0.0767460i −0.445290 − 0.895387i \(-0.646899\pi\)
0.234432 + 0.972133i \(0.424677\pi\)
\(62\) 129880. + 736588.i 0.0692105 + 0.392513i
\(63\) −915288. − 1.58533e6i −0.461175 − 0.798779i
\(64\) −131072. + 227023.i −0.0625000 + 0.108253i
\(65\) 685701. + 249575.i 0.309698 + 0.112721i
\(66\) 667856. + 1.15676e6i 0.285943 + 0.495267i
\(67\) −3.33792e6 − 2.80084e6i −1.35586 − 1.13770i −0.977238 − 0.212146i \(-0.931955\pi\)
−0.378619 − 0.925553i \(-0.623601\pi\)
\(68\) 745222. 0.287412
\(69\) −5.03804e6 − 4.22741e6i −1.84625 − 1.54918i
\(70\) 463971. − 168871.i 0.161677 − 0.0588455i
\(71\) 129993. − 737225.i 0.0431037 − 0.244453i −0.955642 − 0.294532i \(-0.904836\pi\)
0.998745 + 0.0500790i \(0.0159473\pi\)
\(72\) −167252. − 948531.i −0.0528088 − 0.299494i
\(73\) −3.10268e6 −0.933483 −0.466742 − 0.884394i \(-0.654572\pi\)
−0.466742 + 0.884394i \(0.654572\pi\)
\(74\) 1.25012e6 − 2.12434e6i 0.358625 − 0.609416i
\(75\) 4.72642e6 1.29365
\(76\) −210914. − 1.19615e6i −0.0551135 − 0.312564i
\(77\) −442334. + 2.50860e6i −0.110416 + 0.626202i
\(78\) 5.51655e6 − 2.00786e6i 1.31624 − 0.479074i
\(79\) 3.49137e6 + 2.92960e6i 0.796710 + 0.668519i 0.947397 − 0.320062i \(-0.103704\pi\)
−0.150686 + 0.988582i \(0.548148\pi\)
\(80\) 259787. 0.0567286
\(81\) −4.10467e6 − 3.44423e6i −0.858186 − 0.720103i
\(82\) −320148. − 554513.i −0.0641214 − 0.111062i
\(83\) 5.92024e6 + 2.15479e6i 1.13649 + 0.413649i 0.840645 − 0.541587i \(-0.182176\pi\)
0.295846 + 0.955236i \(0.404399\pi\)
\(84\) 1.98613e6 − 3.44008e6i 0.365620 − 0.633273i
\(85\) −369260. − 639578.i −0.0652179 − 0.112961i
\(86\) 714493. + 4.05209e6i 0.121131 + 0.686965i
\(87\) −4.87039e6 + 1.77268e6i −0.792951 + 0.288611i
\(88\) −670136. + 1.16071e6i −0.104827 + 0.181566i
\(89\) 3.09775e6 − 2.59932e6i 0.465781 − 0.390836i −0.379472 − 0.925203i \(-0.623894\pi\)
0.845253 + 0.534367i \(0.179450\pi\)
\(90\) −731192. + 613543.i −0.105726 + 0.0887148i
\(91\) 1.05205e7 + 3.82914e6i 1.46349 + 0.532667i
\(92\) 1.14593e6 − 6.49888e6i 0.153426 − 0.870124i
\(93\) 1.03551e6 − 5.87265e6i 0.133494 − 0.757084i
\(94\) 6.66098e6 + 2.42440e6i 0.827162 + 0.301062i
\(95\) −922076. + 773714.i −0.110340 + 0.0925865i
\(96\) 1.60105e6 − 1.34344e6i 0.184695 − 0.154977i
\(97\) 1.06495e6 − 1.84455e6i 0.118476 − 0.205206i −0.800688 − 0.599081i \(-0.795533\pi\)
0.919164 + 0.393875i \(0.128866\pi\)
\(98\) 927522. − 337590.i 0.0995481 − 0.0362326i
\(99\) −855112. − 4.84958e6i −0.0885727 − 0.502321i
\(100\) 2.37127e6 + 4.10717e6i 0.237127 + 0.410717i
\(101\) −146763. + 254201.i −0.0141740 + 0.0245501i −0.873025 − 0.487675i \(-0.837845\pi\)
0.858851 + 0.512225i \(0.171179\pi\)
\(102\) −5.58318e6 − 2.03211e6i −0.520932 − 0.189604i
\(103\) −572907. − 992304.i −0.0516599 − 0.0894776i 0.839039 − 0.544071i \(-0.183118\pi\)
−0.890699 + 0.454594i \(0.849785\pi\)
\(104\) 4.51248e6 + 3.78642e6i 0.393368 + 0.330075i
\(105\) −3.93654e6 −0.331858
\(106\) −8.15131e6 − 6.83976e6i −0.664748 − 0.557790i
\(107\) 531357. − 193398.i 0.0419318 − 0.0152619i −0.320969 − 0.947090i \(-0.604009\pi\)
0.362901 + 0.931828i \(0.381786\pi\)
\(108\) 216779. − 1.22941e6i 0.0165590 − 0.0939107i
\(109\) 679234. + 3.85213e6i 0.0502374 + 0.284910i 0.999569 − 0.0293667i \(-0.00934906\pi\)
−0.949331 + 0.314277i \(0.898238\pi\)
\(110\) 1.32822e6 0.0951471
\(111\) −1.51586e7 + 1.25066e7i −1.05203 + 0.867980i
\(112\) 3.98582e6 0.268074
\(113\) 618743. + 3.50906e6i 0.0403400 + 0.228779i 0.998312 − 0.0580832i \(-0.0184989\pi\)
−0.957972 + 0.286862i \(0.907388\pi\)
\(114\) −1.68157e6 + 9.53668e6i −0.106304 + 0.602879i
\(115\) −6.14540e6 + 2.23674e6i −0.376797 + 0.137143i
\(116\) −3.98393e6 − 3.34291e6i −0.236978 − 0.198849i
\(117\) −2.16432e7 −1.24931
\(118\) 5.31490e6 + 4.45973e6i 0.297789 + 0.249874i
\(119\) −5.66544e6 − 9.81282e6i −0.308190 − 0.533801i
\(120\) −1.94631e6 − 708400.i −0.102820 − 0.0374235i
\(121\) 6.31736e6 − 1.09420e7i 0.324181 − 0.561497i
\(122\) 1.59118e6 + 2.75600e6i 0.0793339 + 0.137410i
\(123\) 886465. + 5.02739e6i 0.0429530 + 0.243599i
\(124\) 5.62275e6 − 2.04651e6i 0.264833 − 0.0963915i
\(125\) 4.82747e6 − 8.36143e6i 0.221072 − 0.382909i
\(126\) −1.12184e7 + 9.41337e6i −0.499614 + 0.419226i
\(127\) −3.34290e7 + 2.80503e7i −1.44814 + 1.21513i −0.514219 + 0.857659i \(0.671918\pi\)
−0.933923 + 0.357475i \(0.883638\pi\)
\(128\) 1.97068e6 + 717268.i 0.0830579 + 0.0302306i
\(129\) 5.69650e6 − 3.23065e7i 0.233638 − 1.32503i
\(130\) 1.01370e6 − 5.74897e6i 0.0404676 − 0.229503i
\(131\) 2.39473e7 + 8.71612e6i 0.930696 + 0.338746i 0.762485 − 0.647005i \(-0.223979\pi\)
0.168211 + 0.985751i \(0.446201\pi\)
\(132\) 8.18572e6 − 6.86863e6i 0.309776 − 0.259933i
\(133\) −1.41471e7 + 1.18708e7i −0.521419 + 0.437522i
\(134\) −1.74294e7 + 3.01885e7i −0.625770 + 1.08387i
\(135\) −1.16255e6 + 423132.i −0.0406670 + 0.0148016i
\(136\) −1.03525e6 − 5.87120e6i −0.0352907 − 0.200143i
\(137\) 1.91813e7 + 3.32229e7i 0.637316 + 1.10386i 0.986019 + 0.166631i \(0.0532889\pi\)
−0.348703 + 0.937233i \(0.613378\pi\)
\(138\) −2.63068e7 + 4.55646e7i −0.852100 + 1.47588i
\(139\) 4.00566e7 + 1.45794e7i 1.26509 + 0.460456i 0.885475 − 0.464688i \(-0.153833\pi\)
0.379617 + 0.925144i \(0.376056\pi\)
\(140\) −1.97499e6 − 3.42078e6i −0.0608298 − 0.105360i
\(141\) −4.32928e7 − 3.63270e7i −1.30062 − 1.09135i
\(142\) −5.98878e6 −0.175521
\(143\) 2.30711e7 + 1.93590e7i 0.659770 + 0.553612i
\(144\) −7.24062e6 + 2.63537e6i −0.202073 + 0.0735484i
\(145\) −894963. + 5.07559e6i −0.0243791 + 0.138261i
\(146\) 4.31019e6 + 2.44443e7i 0.114620 + 0.650044i
\(147\) −7.86953e6 −0.204333
\(148\) −1.84732e7 − 6.89792e6i −0.468410 − 0.174905i
\(149\) 6.70794e7 1.66126 0.830630 − 0.556825i \(-0.187981\pi\)
0.830630 + 0.556825i \(0.187981\pi\)
\(150\) −6.56587e6 − 3.72369e7i −0.158845 − 0.900853i
\(151\) 4.48405e6 − 2.54303e7i 0.105987 − 0.601080i −0.884835 − 0.465905i \(-0.845729\pi\)
0.990822 − 0.135176i \(-0.0431599\pi\)
\(152\) −9.13086e6 + 3.32336e6i −0.210891 + 0.0767582i
\(153\) 1.67799e7 + 1.40800e7i 0.378765 + 0.317822i
\(154\) 2.03784e7 0.449622
\(155\) −4.54249e6 − 3.81160e6i −0.0979790 − 0.0822142i
\(156\) −2.34824e7 − 4.06726e7i −0.495229 − 0.857761i
\(157\) 1.12738e7 + 4.10331e6i 0.232498 + 0.0846225i 0.455642 − 0.890163i \(-0.349410\pi\)
−0.223144 + 0.974786i \(0.571632\pi\)
\(158\) 1.82306e7 − 3.15764e7i 0.367707 − 0.636887i
\(159\) 4.24183e7 + 7.34707e7i 0.836881 + 1.44952i
\(160\) −360892. − 2.04672e6i −0.00696558 − 0.0395038i
\(161\) −9.42867e7 + 3.43176e7i −1.78057 + 0.648076i
\(162\) −2.14331e7 + 3.71232e7i −0.396079 + 0.686030i
\(163\) 4.80432e7 − 4.03131e7i 0.868911 − 0.729103i −0.0949572 − 0.995481i \(-0.530271\pi\)
0.963869 + 0.266378i \(0.0858270\pi\)
\(164\) −3.92397e6 + 3.29260e6i −0.0694659 + 0.0582888i
\(165\) −9.95098e6 − 3.62186e6i −0.172453 − 0.0627679i
\(166\) 8.75212e6 − 4.96358e7i 0.148503 − 0.842202i
\(167\) −6.47607e6 + 3.67276e7i −0.107598 + 0.610218i 0.882553 + 0.470213i \(0.155823\pi\)
−0.990151 + 0.140005i \(0.955288\pi\)
\(168\) −2.98616e7 − 1.08687e7i −0.485882 − 0.176847i
\(169\) 5.33317e7 − 4.47506e7i 0.849928 − 0.713174i
\(170\) −4.52592e6 + 3.79770e6i −0.0706538 + 0.0592856i
\(171\) 1.78507e7 − 3.09184e7i 0.273004 − 0.472857i
\(172\) 3.09317e7 − 1.12582e7i 0.463505 − 0.168702i
\(173\) 1.87967e7 + 1.06601e8i 0.276007 + 1.56531i 0.735746 + 0.677257i \(0.236832\pi\)
−0.459740 + 0.888054i \(0.652057\pi\)
\(174\) 2.07318e7 + 3.59086e7i 0.298343 + 0.516745i
\(175\) 3.60545e7 − 6.24482e7i 0.508541 − 0.880819i
\(176\) 1.00755e7 + 3.66720e6i 0.139307 + 0.0507037i
\(177\) −2.76580e7 − 4.79051e7i −0.374899 − 0.649345i
\(178\) −2.47820e7 − 2.07946e7i −0.329357 − 0.276363i
\(179\) −7.66830e7 −0.999340 −0.499670 − 0.866216i \(-0.666545\pi\)
−0.499670 + 0.866216i \(0.666545\pi\)
\(180\) 5.84953e6 + 4.90834e6i 0.0747597 + 0.0627308i
\(181\) −6.66209e7 + 2.42480e7i −0.835094 + 0.303949i −0.723948 − 0.689855i \(-0.757674\pi\)
−0.111146 + 0.993804i \(0.535452\pi\)
\(182\) 1.55528e7 − 8.82045e7i 0.191232 − 1.08453i
\(183\) −4.40584e6 − 2.49868e7i −0.0531435 − 0.301392i
\(184\) −5.27931e7 −0.624762
\(185\) 3.23350e6 + 1.92724e7i 0.0375467 + 0.223787i
\(186\) −4.77060e7 −0.543598
\(187\) −5.29296e6 − 3.00179e7i −0.0591906 − 0.335687i
\(188\) 9.84719e6 − 5.58462e7i 0.108084 − 0.612973i
\(189\) −1.78365e7 + 6.49197e6i −0.192174 + 0.0699455i
\(190\) 7.37661e6 + 6.18971e6i 0.0780224 + 0.0654685i
\(191\) 1.27465e8 1.32366 0.661828 − 0.749655i \(-0.269781\pi\)
0.661828 + 0.749655i \(0.269781\pi\)
\(192\) −1.28084e7 − 1.07475e7i −0.130599 − 0.109586i
\(193\) 9.59784e6 + 1.66239e7i 0.0960999 + 0.166450i 0.910067 − 0.414461i \(-0.136030\pi\)
−0.813967 + 0.580911i \(0.802697\pi\)
\(194\) −1.60117e7 − 5.82777e6i −0.157445 − 0.0573055i
\(195\) −2.32712e7 + 4.03069e7i −0.224749 + 0.389277i
\(196\) −3.94819e6 − 6.83847e6i −0.0374544 − 0.0648728i
\(197\) 1.18538e7 + 6.72260e7i 0.110465 + 0.626477i 0.988896 + 0.148608i \(0.0474794\pi\)
−0.878431 + 0.477869i \(0.841409\pi\)
\(198\) −3.70193e7 + 1.34739e7i −0.338923 + 0.123358i
\(199\) 4.50992e7 − 7.81141e7i 0.405679 − 0.702657i −0.588721 − 0.808336i \(-0.700368\pi\)
0.994400 + 0.105679i \(0.0337016\pi\)
\(200\) 2.90640e7 − 2.43876e7i 0.256892 − 0.215558i
\(201\) 2.12900e8 − 1.78644e8i 1.84922 − 1.55168i
\(202\) 2.20660e6 + 803135.i 0.0188362 + 0.00685581i
\(203\) −1.37311e7 + 7.78730e7i −0.115205 + 0.653357i
\(204\) −8.25384e6 + 4.68098e7i −0.0680692 + 0.386039i
\(205\) 4.77018e6 + 1.73620e6i 0.0386719 + 0.0140754i
\(206\) −7.02195e6 + 5.89212e6i −0.0559658 + 0.0469609i
\(207\) 1.48591e8 − 1.24682e8i 1.16438 − 0.977032i
\(208\) 2.35625e7 − 4.08115e7i 0.181552 − 0.314457i
\(209\) −4.66836e7 + 1.69914e7i −0.353714 + 0.128741i
\(210\) 5.46858e6 + 3.10139e7i 0.0407481 + 0.231094i
\(211\) −8.57809e7 − 1.48577e8i −0.628640 − 1.08884i −0.987825 − 0.155570i \(-0.950279\pi\)
0.359185 − 0.933266i \(-0.383055\pi\)
\(212\) −4.25631e7 + 7.37215e7i −0.306802 + 0.531396i
\(213\) 4.48678e7 + 1.63305e7i 0.318131 + 0.115790i
\(214\) −2.26183e6 − 3.91761e6i −0.0157766 − 0.0273258i
\(215\) −2.49890e7 − 2.09683e7i −0.171480 − 0.143889i
\(216\) −9.98704e6 −0.0674293
\(217\) −6.96939e7 − 5.84801e7i −0.463005 − 0.388507i
\(218\) 2.94053e7 − 1.07026e7i 0.192233 − 0.0699670i
\(219\) 3.43642e7 − 1.94889e8i 0.221081 − 1.25382i
\(220\) −1.84514e6 − 1.04643e7i −0.0116829 − 0.0662570i
\(221\) −1.33967e8 −0.834881
\(222\) 1.19591e8 + 1.02053e8i 0.733607 + 0.626021i
\(223\) 2.63950e8 1.59388 0.796938 − 0.604061i \(-0.206452\pi\)
0.796938 + 0.604061i \(0.206452\pi\)
\(224\) −5.53704e6 − 3.14021e7i −0.0329162 − 0.186677i
\(225\) −2.42065e7 + 1.37282e8i −0.141675 + 0.803479i
\(226\) 2.67865e7 − 9.74948e6i 0.154360 − 0.0561826i
\(227\) −6.26298e7 − 5.25527e7i −0.355378 − 0.298198i 0.447567 − 0.894250i \(-0.352291\pi\)
−0.802945 + 0.596053i \(0.796735\pi\)
\(228\) 7.74704e7 0.432876
\(229\) −8.93193e7 − 7.49478e7i −0.491497 − 0.412415i 0.363065 − 0.931764i \(-0.381730\pi\)
−0.854562 + 0.519349i \(0.826175\pi\)
\(230\) 2.61592e7 + 4.53090e7i 0.141768 + 0.245549i
\(231\) −1.52674e8 − 5.55689e7i −0.814937 − 0.296613i
\(232\) −2.08026e7 + 3.60312e7i −0.109373 + 0.189439i
\(233\) 5.57771e7 + 9.66087e7i 0.288875 + 0.500346i 0.973541 − 0.228510i \(-0.0733855\pi\)
−0.684667 + 0.728856i \(0.740052\pi\)
\(234\) 3.00664e7 + 1.70515e8i 0.153400 + 0.869977i
\(235\) −5.28086e7 + 1.92208e7i −0.265441 + 0.0966125i
\(236\) 2.77524e7 − 4.80686e7i 0.137439 − 0.238051i
\(237\) −2.22687e8 + 1.86857e8i −1.08662 + 0.911779i
\(238\) −6.94396e7 + 5.82668e7i −0.333878 + 0.280157i
\(239\) −3.28608e8 − 1.19604e8i −1.55699 − 0.566698i −0.586945 − 0.809627i \(-0.699670\pi\)
−0.970044 + 0.242929i \(0.921892\pi\)
\(240\) −2.87731e6 + 1.63181e7i −0.0134353 + 0.0761955i
\(241\) −2.27209e7 + 1.28857e8i −0.104560 + 0.592990i 0.886835 + 0.462086i \(0.152899\pi\)
−0.991395 + 0.130904i \(0.958212\pi\)
\(242\) −9.49821e7 − 3.45706e7i −0.430812 − 0.156803i
\(243\) 2.29126e8 − 1.92260e8i 1.02436 − 0.859541i
\(244\) 1.95026e7 − 1.63646e7i 0.0859465 − 0.0721177i
\(245\) −3.91269e6 + 6.77698e6i −0.0169979 + 0.0294412i
\(246\) 3.83767e7 − 1.39680e7i 0.164359 − 0.0598219i
\(247\) 3.79156e7 + 2.15030e8i 0.160095 + 0.907945i
\(248\) −2.39344e7 − 4.14556e7i −0.0996419 − 0.172585i
\(249\) −2.00920e8 + 3.48004e8i −0.824756 + 1.42852i
\(250\) −7.25814e7 − 2.64175e7i −0.293789 − 0.106930i
\(251\) −2.97356e7 − 5.15036e7i −0.118691 − 0.205580i 0.800558 − 0.599255i \(-0.204537\pi\)
−0.919249 + 0.393676i \(0.871203\pi\)
\(252\) 8.97474e7 + 7.53070e7i 0.353281 + 0.296438i
\(253\) −2.69917e8 −1.04787
\(254\) 2.67432e8 + 2.24402e8i 1.02399 + 0.859230i
\(255\) 4.42638e7 − 1.61107e7i 0.167170 − 0.0608449i
\(256\) 2.91333e6 − 1.65223e7i 0.0108530 − 0.0615505i
\(257\) −1.20767e7 − 6.84904e7i −0.0443795 − 0.251689i 0.954544 − 0.298069i \(-0.0963425\pi\)
−0.998924 + 0.0463802i \(0.985231\pi\)
\(258\) −2.62439e8 −0.951391
\(259\) 4.96105e7 + 2.95689e8i 0.177429 + 1.05751i
\(260\) −4.67013e7 −0.164787
\(261\) −2.65447e7 − 1.50543e8i −0.0924137 − 0.524104i
\(262\) 3.54023e7 − 2.00777e8i 0.121612 − 0.689697i
\(263\) −1.53695e8 + 5.59404e7i −0.520972 + 0.189618i −0.589103 − 0.808058i \(-0.700519\pi\)
0.0681306 + 0.997676i \(0.478297\pi\)
\(264\) −6.54857e7 − 5.49491e7i −0.219045 − 0.183800i
\(265\) 8.43608e7 0.278471
\(266\) 1.13177e8 + 9.49666e7i 0.368699 + 0.309375i
\(267\) 1.28962e8 + 2.23369e8i 0.414642 + 0.718181i
\(268\) 2.62052e8 + 9.53791e7i 0.831602 + 0.302678i
\(269\) −2.33774e8 + 4.04908e8i −0.732256 + 1.26831i 0.223660 + 0.974667i \(0.428199\pi\)
−0.955917 + 0.293638i \(0.905134\pi\)
\(270\) 4.94862e6 + 8.57126e6i 0.0153007 + 0.0265016i
\(271\) 993388. + 5.63379e6i 0.00303198 + 0.0171952i 0.986286 − 0.165044i \(-0.0527766\pi\)
−0.983254 + 0.182239i \(0.941665\pi\)
\(272\) −4.48179e7 + 1.63124e7i −0.135039 + 0.0491503i
\(273\) −3.57042e8 + 6.18415e8i −1.06206 + 1.83955i
\(274\) 2.35099e8 − 1.97272e8i 0.690437 − 0.579345i
\(275\) 1.48597e8 − 1.24687e8i 0.430868 − 0.361541i
\(276\) 3.95524e8 + 1.43959e8i 1.13238 + 0.412152i
\(277\) 4.43677e7 − 2.51622e8i 0.125426 − 0.711326i −0.855628 − 0.517591i \(-0.826829\pi\)
0.981054 − 0.193735i \(-0.0620601\pi\)
\(278\) 5.92173e7 − 3.35838e8i 0.165307 − 0.937503i
\(279\) 1.65272e8 + 6.01540e7i 0.455601 + 0.165825i
\(280\) −2.42069e7 + 2.03120e7i −0.0659000 + 0.0552967i
\(281\) 2.94329e8 − 2.46971e8i 0.791335 − 0.664009i −0.154740 − 0.987955i \(-0.549454\pi\)
0.946076 + 0.323946i \(0.105010\pi\)
\(282\) −2.26059e8 + 3.91546e8i −0.600275 + 1.03971i
\(283\) 2.95431e8 − 1.07528e8i 0.774824 − 0.282013i 0.0758115 − 0.997122i \(-0.475845\pi\)
0.699013 + 0.715109i \(0.253623\pi\)
\(284\) 8.31953e6 + 4.71824e7i 0.0215518 + 0.122227i
\(285\) −3.83869e7 − 6.64880e7i −0.0982259 − 0.170132i
\(286\) 1.20469e8 − 2.08658e8i 0.304504 − 0.527417i
\(287\) 7.31871e7 + 2.66379e7i 0.182746 + 0.0665141i
\(288\) 3.08212e7 + 5.33840e7i 0.0760285 + 0.131685i
\(289\) −2.10474e8 − 1.76608e8i −0.512926 − 0.430396i
\(290\) 4.12311e7 0.0992732
\(291\) 1.04067e8 + 8.73229e7i 0.247565 + 0.207732i
\(292\) 1.86596e8 − 6.79154e7i 0.438594 − 0.159635i
\(293\) 8.80505e7 − 4.99359e8i 0.204501 − 1.15978i −0.693722 − 0.720243i \(-0.744030\pi\)
0.898223 − 0.439540i \(-0.144858\pi\)
\(294\) 1.09322e7 + 6.19998e7i 0.0250896 + 0.142290i
\(295\) −5.50058e7 −0.124747
\(296\) −2.86822e7 + 1.55123e8i −0.0642824 + 0.347660i
\(297\) −5.10610e7 −0.113095
\(298\) −9.31858e7 − 5.28483e8i −0.203982 − 1.15684i
\(299\) −2.06001e8 + 1.16829e9i −0.445677 + 2.52756i
\(300\) −2.84248e8 + 1.03458e8i −0.607818 + 0.221228i
\(301\) −3.83398e8 − 3.21709e8i −0.810339 − 0.679955i
\(302\) −2.06581e8 −0.431585
\(303\) −1.43417e7 − 1.20341e7i −0.0296177 − 0.0248522i
\(304\) 3.88674e7 + 6.73203e7i 0.0793466 + 0.137432i
\(305\) −2.37084e7 − 8.62914e6i −0.0478467 − 0.0174148i
\(306\) 8.76185e7 − 1.51760e8i 0.174812 − 0.302783i
\(307\) 2.08932e7 + 3.61880e7i 0.0412116 + 0.0713806i 0.885895 − 0.463885i \(-0.153545\pi\)
−0.844684 + 0.535266i \(0.820212\pi\)
\(308\) −2.83094e7 − 1.60551e8i −0.0552081 − 0.313101i
\(309\) 6.86752e7 − 2.49957e7i 0.132417 − 0.0481960i
\(310\) −2.37192e7 + 4.10829e7i −0.0452204 + 0.0783240i
\(311\) 4.79681e8 − 4.02500e8i 0.904255 − 0.758760i −0.0667622 − 0.997769i \(-0.521267\pi\)
0.971017 + 0.239009i \(0.0768224\pi\)
\(312\) −2.87817e8 + 2.41507e8i −0.536506 + 0.450182i
\(313\) 4.32490e8 + 1.57414e8i 0.797207 + 0.290160i 0.708329 − 0.705883i \(-0.249450\pi\)
0.0888783 + 0.996042i \(0.471672\pi\)
\(314\) 1.66664e7 − 9.45201e7i 0.0303801 − 0.172294i
\(315\) 2.01611e7 − 1.14340e8i 0.0363436 − 0.206115i
\(316\) −2.74099e8 − 9.97638e7i −0.488655 − 0.177856i
\(317\) −5.40525e8 + 4.53554e8i −0.953033 + 0.799690i −0.979806 − 0.199952i \(-0.935922\pi\)
0.0267724 + 0.999642i \(0.491477\pi\)
\(318\) 5.19909e8 − 4.36256e8i 0.906635 − 0.760757i
\(319\) −1.06358e8 + 1.84218e8i −0.183444 + 0.317734i
\(320\) −1.56237e7 + 5.68655e6i −0.0266537 + 0.00970116i
\(321\) 6.26283e6 + 3.55183e7i 0.0105683 + 0.0599355i
\(322\) 4.01351e8 + 6.95161e8i 0.669930 + 1.16035i
\(323\) 1.10492e8 − 1.91378e8i 0.182441 − 0.315997i
\(324\) 3.22248e8 + 1.17289e8i 0.526360 + 0.191579i
\(325\) −4.26279e8 − 7.38336e8i −0.688814 − 1.19306i
\(326\) −3.84346e8 − 3.22504e8i −0.614413 − 0.515554i
\(327\) −2.49488e8 −0.394577
\(328\) 3.13917e7 + 2.63408e7i 0.0491198 + 0.0412164i
\(329\) −8.10225e8 + 2.94898e8i −1.25435 + 0.456547i
\(330\) −1.47109e7 + 8.34298e7i −0.0225342 + 0.127798i
\(331\) −2.06719e8 − 1.17236e9i −0.313315 − 1.77690i −0.581515 − 0.813535i \(-0.697540\pi\)
0.268200 − 0.963363i \(-0.413571\pi\)
\(332\) −4.03212e8 −0.604714
\(333\) −2.85628e8 − 5.04346e8i −0.423883 − 0.748469i
\(334\) 2.98354e8 0.438146
\(335\) −4.79898e7 − 2.72164e8i −0.0697416 − 0.395524i
\(336\) −4.41456e7 + 2.50362e8i −0.0634893 + 0.360066i
\(337\) 6.18479e8 − 2.25108e8i 0.880280 − 0.320396i 0.137957 − 0.990438i \(-0.455946\pi\)
0.742323 + 0.670043i \(0.233724\pi\)
\(338\) −4.26654e8 − 3.58005e8i −0.600990 − 0.504290i
\(339\) −2.27269e8 −0.316841
\(340\) 3.62074e7 + 3.03816e7i 0.0499598 + 0.0419212i
\(341\) −1.22370e8 − 2.11951e8i −0.167123 − 0.289465i
\(342\) −2.68387e8 − 9.76849e7i −0.362803 − 0.132049i
\(343\) 3.40664e8 − 5.90047e8i 0.455823 − 0.789509i
\(344\) −1.31667e8 − 2.28054e8i −0.174391 − 0.302054i
\(345\) −7.24327e7 − 4.10786e8i −0.0949659 − 0.538578i
\(346\) 8.13741e8 − 2.96178e8i 1.05614 − 0.384402i
\(347\) 3.60262e8 − 6.23992e8i 0.462876 − 0.801725i −0.536227 − 0.844074i \(-0.680151\pi\)
0.999103 + 0.0423488i \(0.0134841\pi\)
\(348\) 2.54104e8 − 2.13219e8i 0.323210 − 0.271205i
\(349\) 8.24099e8 − 6.91501e8i 1.03774 − 0.870771i 0.0459920 − 0.998942i \(-0.485355\pi\)
0.991752 + 0.128171i \(0.0409107\pi\)
\(350\) −5.42082e8 − 1.97302e8i −0.675814 − 0.245976i
\(351\) −3.89699e7 + 2.21009e8i −0.0481010 + 0.272794i
\(352\) 1.48951e7 − 8.44742e7i 0.0182030 − 0.103234i
\(353\) −7.86135e8 − 2.86130e8i −0.951230 − 0.346219i −0.180639 − 0.983549i \(-0.557817\pi\)
−0.770591 + 0.637330i \(0.780039\pi\)
\(354\) −3.38996e8 + 2.84452e8i −0.406147 + 0.340798i
\(355\) 3.63714e7 − 3.05192e7i 0.0431480 − 0.0362054i
\(356\) −1.29402e8 + 2.24132e8i −0.152008 + 0.263286i
\(357\) 6.79124e8 − 2.47181e8i 0.789970 − 0.287525i
\(358\) 1.06527e8 + 6.04144e8i 0.122707 + 0.695905i
\(359\) 7.32187e8 + 1.26819e9i 0.835202 + 1.44661i 0.893866 + 0.448335i \(0.147983\pi\)
−0.0586633 + 0.998278i \(0.518684\pi\)
\(360\) 3.05441e7 − 5.29039e7i 0.0345039 − 0.0597626i
\(361\) 5.01513e8 + 1.82536e8i 0.561056 + 0.204208i
\(362\) 2.83586e8 + 4.91185e8i 0.314199 + 0.544208i
\(363\) 6.17334e8 + 5.18004e8i 0.677402 + 0.568408i
\(364\) −7.16522e8 −0.778708
\(365\) −1.50747e8 − 1.26491e8i −0.162264 − 0.136156i
\(366\) −1.90737e8 + 6.94225e7i −0.203353 + 0.0740144i
\(367\) −1.59730e8 + 9.05871e8i −0.168676 + 0.956611i 0.776516 + 0.630097i \(0.216985\pi\)
−0.945193 + 0.326513i \(0.894126\pi\)
\(368\) 7.33394e7 + 4.15928e8i 0.0767132 + 0.435062i
\(369\) −1.50564e8 −0.156002
\(370\) 1.47345e8 − 5.22479e7i 0.151227 − 0.0536244i
\(371\) 1.29432e9 1.31593
\(372\) 6.62725e7 + 3.75850e8i 0.0667472 + 0.378542i
\(373\) −1.38501e8 + 7.85476e8i −0.138188 + 0.783704i 0.834398 + 0.551162i \(0.185815\pi\)
−0.972586 + 0.232542i \(0.925296\pi\)
\(374\) −2.29142e8 + 8.34008e7i −0.226492 + 0.0824365i
\(375\) 4.71741e8 + 3.95838e8i 0.461949 + 0.387621i
\(376\) −4.53662e8 −0.440123
\(377\) 7.16182e8 + 6.00948e8i 0.688381 + 0.577620i
\(378\) 7.59250e7 + 1.31506e8i 0.0723042 + 0.125234i
\(379\) 1.69956e9 + 6.18589e8i 1.60361 + 0.583667i 0.980162 − 0.198198i \(-0.0635088\pi\)
0.623449 + 0.781864i \(0.285731\pi\)
\(380\) 3.85179e7 − 6.67150e7i 0.0360098 − 0.0623707i
\(381\) −1.39168e9 − 2.41046e9i −1.28915 − 2.23287i
\(382\) −1.77073e8 − 1.00423e9i −0.162529 − 0.921747i
\(383\) 1.91114e9 − 6.95599e8i 1.73819 − 0.632649i 0.739031 − 0.673671i \(-0.235283\pi\)
0.999158 + 0.0410216i \(0.0130613\pi\)
\(384\) −6.68806e7 + 1.15841e8i −0.0602755 + 0.104400i
\(385\) −1.23763e8 + 1.03850e8i −0.110530 + 0.0927454i
\(386\) 1.17638e8 − 9.87099e7i 0.104110 − 0.0873585i
\(387\) 9.09189e8 + 3.30918e8i 0.797381 + 0.290223i
\(388\) −2.36707e7 + 1.34243e8i −0.0205731 + 0.116676i
\(389\) −1.99892e8 + 1.13365e9i −0.172176 + 0.976458i 0.769177 + 0.639035i \(0.220666\pi\)
−0.941353 + 0.337423i \(0.890445\pi\)
\(390\) 3.49884e8 + 1.27348e8i 0.298675 + 0.108709i
\(391\) 9.19744e8 − 7.71757e8i 0.778123 − 0.652923i
\(392\) −4.83919e7 + 4.06056e7i −0.0405762 + 0.0340475i
\(393\) −8.12721e8 + 1.40767e9i −0.675410 + 1.16984i
\(394\) 5.13170e8 − 1.86779e8i 0.422693 − 0.153848i
\(395\) 5.01960e7 + 2.84675e8i 0.0409807 + 0.232413i
\(396\) 1.57581e8 + 2.72938e8i 0.127517 + 0.220867i
\(397\) 3.82393e8 − 6.62324e8i 0.306721 − 0.531256i −0.670922 − 0.741528i \(-0.734102\pi\)
0.977643 + 0.210272i \(0.0674350\pi\)
\(398\) −6.78070e8 − 2.46797e8i −0.539118 − 0.196223i
\(399\) −5.88957e8 − 1.02010e9i −0.464171 − 0.803968i
\(400\) −2.32512e8 − 1.95101e8i −0.181650 − 0.152423i
\(401\) −3.59701e8 −0.278571 −0.139285 − 0.990252i \(-0.544481\pi\)
−0.139285 + 0.990252i \(0.544481\pi\)
\(402\) −1.70320e9 − 1.42915e9i −1.30760 − 1.09721i
\(403\) −1.01079e9 + 3.67897e8i −0.769295 + 0.280000i
\(404\) 3.26210e6 − 1.85003e7i 0.00246129 − 0.0139587i
\(405\) −5.90136e7 − 3.34683e8i −0.0441428 − 0.250346i
\(406\) 6.32594e8 0.469120
\(407\) −1.46645e8 + 7.93102e8i −0.107817 + 0.583107i
\(408\) 3.80256e8 0.277182
\(409\) 1.47566e8 + 8.36891e8i 0.106649 + 0.604835i 0.990549 + 0.137160i \(0.0437973\pi\)
−0.883900 + 0.467676i \(0.845092\pi\)
\(410\) 7.05194e6 − 3.99936e7i 0.00505319 − 0.0286580i
\(411\) −2.29929e9 + 8.36872e8i −1.63360 + 0.594583i
\(412\) 5.61756e7 + 4.71369e7i 0.0395738 + 0.0332063i
\(413\) −8.43935e8 −0.589500
\(414\) −1.18872e9 − 9.97459e8i −0.823342 − 0.690866i
\(415\) 1.99793e8 + 3.46052e8i 0.137218 + 0.237669i
\(416\) −3.54264e8 − 1.28942e8i −0.241269 − 0.0878146i
\(417\) −1.35943e9 + 2.35461e9i −0.918083 + 1.59017i
\(418\) 1.98719e8 + 3.44191e8i 0.133083 + 0.230506i
\(419\) 1.79905e8 + 1.02029e9i 0.119480 + 0.677605i 0.984434 + 0.175754i \(0.0562363\pi\)
−0.864954 + 0.501851i \(0.832653\pi\)
\(420\) 2.36745e8 − 8.61681e7i 0.155922 − 0.0567510i
\(421\) 7.54722e8 − 1.30722e9i 0.492946 − 0.853808i −0.507021 − 0.861934i \(-0.669253\pi\)
0.999967 + 0.00812580i \(0.00258655\pi\)
\(422\) −1.05139e9 + 8.82222e8i −0.681037 + 0.571458i
\(423\) 1.27687e9 − 1.07142e9i 0.820266 − 0.688285i
\(424\) 6.39940e8 + 2.32919e8i 0.407717 + 0.148397i
\(425\) −1.49833e8 + 8.49746e8i −0.0946775 + 0.536943i
\(426\) 6.63298e7 − 3.76175e8i 0.0415695 − 0.235753i
\(427\) −3.63749e8 − 1.32394e8i −0.226102 − 0.0822944i
\(428\) −2.77226e7 + 2.32620e7i −0.0170915 + 0.0143415i
\(429\) −1.47153e9 + 1.23476e9i −0.899846 + 0.755060i
\(430\) −1.30483e8 + 2.26004e8i −0.0791436 + 0.137081i
\(431\) −3.31231e7 + 1.20558e7i −0.0199279 + 0.00725315i −0.351965 − 0.936013i \(-0.614486\pi\)
0.332037 + 0.943266i \(0.392264\pi\)
\(432\) 1.38739e7 + 7.86825e7i 0.00827950 + 0.0469554i
\(433\) 1.67849e9 + 2.90723e9i 0.993599 + 1.72096i 0.594629 + 0.804000i \(0.297299\pi\)
0.398970 + 0.916964i \(0.369368\pi\)
\(434\) −3.63916e8 + 6.30320e8i −0.213691 + 0.370124i
\(435\) −3.08902e8 − 1.12431e8i −0.179932 − 0.0654899i
\(436\) −1.25170e8 − 2.16800e8i −0.0723264 − 0.125273i
\(437\) −1.49905e9 − 1.25785e9i −0.859274 − 0.721017i
\(438\) −1.58317e9 −0.900258
\(439\) −2.22706e9 − 1.86872e9i −1.25634 − 1.05419i −0.996062 − 0.0886565i \(-0.971743\pi\)
−0.260274 − 0.965535i \(-0.583813\pi\)
\(440\) −7.98796e7 + 2.90738e7i −0.0447045 + 0.0162711i
\(441\) 4.03041e7 − 2.28576e8i 0.0223776 − 0.126910i
\(442\) 1.86105e8 + 1.05545e9i 0.102513 + 0.581381i
\(443\) −2.49436e9 −1.36316 −0.681580 − 0.731744i \(-0.738707\pi\)
−0.681580 + 0.731744i \(0.738707\pi\)
\(444\) 6.37884e8 − 1.08396e9i 0.345861 − 0.587726i
\(445\) 2.56478e8 0.137972
\(446\) −3.66675e8 − 2.07952e9i −0.195708 − 1.10992i
\(447\) −7.42950e8 + 4.21348e9i −0.393444 + 2.23133i
\(448\) −2.39708e8 + 8.72467e7i −0.125954 + 0.0458433i
\(449\) 9.28625e8 + 7.79209e8i 0.484148 + 0.406248i 0.851924 − 0.523666i \(-0.175436\pi\)
−0.367775 + 0.929915i \(0.619881\pi\)
\(450\) 1.11520e9 0.576910
\(451\) 1.60497e8 + 1.34673e8i 0.0823854 + 0.0691296i
\(452\) −1.14022e8 − 1.97492e8i −0.0580771 − 0.100593i
\(453\) 1.54770e9 + 5.63316e8i 0.782244 + 0.284714i
\(454\) −3.27030e8 + 5.66432e8i −0.164018 + 0.284088i
\(455\) 3.55039e8 + 6.14946e8i 0.176700 + 0.306053i
\(456\) −1.07621e8 − 6.10348e8i −0.0531519 − 0.301440i
\(457\) 1.89742e9 − 6.90604e8i 0.929943 − 0.338472i 0.167756 − 0.985829i \(-0.446348\pi\)
0.762187 + 0.647357i \(0.224126\pi\)
\(458\) −4.66392e8 + 8.07815e8i −0.226841 + 0.392901i
\(459\) 1.73991e8 − 1.45996e8i 0.0839812 − 0.0704686i
\(460\) 3.20626e8 − 2.69037e8i 0.153584 − 0.128872i
\(461\) −2.07445e9 − 7.55037e8i −0.986164 − 0.358934i −0.201930 − 0.979400i \(-0.564721\pi\)
−0.784234 + 0.620466i \(0.786944\pi\)
\(462\) −2.25705e8 + 1.28003e9i −0.106486 + 0.603914i
\(463\) 2.05191e8 − 1.16370e9i 0.0960781 − 0.544886i −0.898334 − 0.439314i \(-0.855222\pi\)
0.994412 − 0.105572i \(-0.0336674\pi\)
\(464\) 3.12769e8 + 1.13839e8i 0.145349 + 0.0529025i
\(465\) 2.89730e8 − 2.43113e8i 0.133631 − 0.112130i
\(466\) 6.83643e8 − 5.73645e8i 0.312953 − 0.262599i
\(467\) 1.38082e9 − 2.39165e9i 0.627376 − 1.08665i −0.360700 − 0.932682i \(-0.617462\pi\)
0.988076 − 0.153965i \(-0.0492044\pi\)
\(468\) 1.30163e9 − 4.73755e8i 0.586985 − 0.213645i
\(469\) −7.36291e8 − 4.17571e9i −0.329568 − 1.86907i
\(470\) 2.24791e8 + 3.89350e8i 0.0998704 + 0.172981i
\(471\) −3.82607e8 + 6.62695e8i −0.168725 + 0.292240i
\(472\) −4.17260e8 − 1.51870e8i −0.182646 − 0.0664777i
\(473\) −6.73179e8 − 1.16598e9i −0.292494 − 0.506614i
\(474\) 1.78150e9 + 1.49485e9i 0.768354 + 0.644725i
\(475\) 1.40633e9 0.602088
\(476\) 5.55517e8 + 4.66134e8i 0.236087 + 0.198101i
\(477\) −2.35125e9 + 8.55786e8i −0.991939 + 0.361036i
\(478\) −4.85795e8 + 2.75508e9i −0.203449 + 1.15382i
\(479\) −1.59378e8 − 9.03880e8i −0.0662606 − 0.375782i −0.999848 − 0.0174327i \(-0.994451\pi\)
0.933587 − 0.358350i \(-0.116660\pi\)
\(480\) 1.32558e8 0.0547095
\(481\) 3.32089e9 + 1.24002e9i 1.36065 + 0.508068i
\(482\) 1.04676e9 0.425776
\(483\) −1.11131e9 − 6.30255e9i −0.448766 − 2.54508i
\(484\) −1.40416e8 + 7.96338e8i −0.0562934 + 0.319256i
\(485\) 1.26941e8 − 4.62029e7i 0.0505251 − 0.0183896i
\(486\) −1.83301e9 − 1.53808e9i −0.724333 − 0.607788i
\(487\) 4.27306e9 1.67644 0.838218 − 0.545335i \(-0.183597\pi\)
0.838218 + 0.545335i \(0.183597\pi\)
\(488\) −1.56021e8 − 1.30917e8i −0.0607733 − 0.0509949i
\(489\) 2.00008e9 + 3.46425e9i 0.773512 + 1.33976i
\(490\) 5.88276e7 + 2.14115e7i 0.0225889 + 0.00822169i
\(491\) −1.02227e9 + 1.77062e9i −0.389743 + 0.675055i −0.992415 − 0.122934i \(-0.960769\pi\)
0.602672 + 0.797989i \(0.294103\pi\)
\(492\) −1.63358e8 − 2.82945e8i −0.0618392 − 0.107109i
\(493\) −1.64306e8 − 9.31826e8i −0.0617575 − 0.350244i
\(494\) 1.64143e9 − 5.97433e8i 0.612603 − 0.222969i
\(495\) 1.56164e8 − 2.70483e8i 0.0578711 − 0.100236i
\(496\) −2.93357e8 + 2.46156e8i −0.107947 + 0.0905784i
\(497\) 5.58033e8 − 4.68245e8i 0.203898 − 0.171091i
\(498\) 3.02085e9 + 1.09950e9i 1.09604 + 0.398926i
\(499\) −4.19605e8 + 2.37970e9i −0.151178 + 0.857373i 0.811019 + 0.585020i \(0.198913\pi\)
−0.962197 + 0.272354i \(0.912198\pi\)
\(500\) −1.07300e8 + 6.08529e8i −0.0383888 + 0.217714i
\(501\) −2.23525e9 − 8.13566e8i −0.794136 − 0.289042i
\(502\) −3.64461e8 + 3.05819e8i −0.128584 + 0.107895i
\(503\) 1.89991e9 − 1.59421e9i 0.665649 − 0.558546i −0.246125 − 0.969238i \(-0.579157\pi\)
0.911774 + 0.410692i \(0.134713\pi\)
\(504\) 4.68627e8 − 8.11687e8i 0.163050 − 0.282411i
\(505\) −1.74940e7 + 6.36731e6i −0.00604463 + 0.00220007i
\(506\) 3.74965e8 + 2.12653e9i 0.128666 + 0.729700i
\(507\) 2.22025e9 + 3.84558e9i 0.756613 + 1.31049i
\(508\) 1.39643e9 − 2.41869e9i 0.472603 − 0.818573i
\(509\) 3.89072e9 + 1.41610e9i 1.30773 + 0.475974i 0.899506 − 0.436909i \(-0.143927\pi\)
0.408222 + 0.912883i \(0.366149\pi\)
\(510\) −1.88418e8 − 3.26350e8i −0.0628966 − 0.108940i
\(511\) −2.31285e9 − 1.94071e9i −0.766787 − 0.643411i
\(512\) −1.34218e8 −0.0441942
\(513\) −2.83581e8 − 2.37952e8i −0.0927397 − 0.0778179i
\(514\) −5.22822e8 + 1.90292e8i −0.169818 + 0.0618086i
\(515\) 1.26195e7 − 7.15686e7i 0.00407114 − 0.0230886i
\(516\) 3.64576e8 + 2.06761e9i 0.116819 + 0.662515i
\(517\) −2.31945e9 −0.738190
\(518\) 2.26066e9 − 8.01621e8i 0.714629 − 0.253405i
\(519\) −6.90416e9 −2.16783
\(520\) 6.48767e7 + 3.67934e8i 0.0202338 + 0.114752i
\(521\) 1.55559e8 − 8.82221e8i 0.0481908 − 0.273304i −0.951185 − 0.308620i \(-0.900133\pi\)
0.999376 + 0.0353166i \(0.0112440\pi\)
\(522\) −1.14917e9 + 4.18263e8i −0.353620 + 0.128707i
\(523\) −3.92401e9 − 3.29264e9i −1.19943 − 1.00644i −0.999646 − 0.0265992i \(-0.991532\pi\)
−0.199782 − 0.979840i \(-0.564023\pi\)
\(524\) −1.63099e9 −0.495213
\(525\) 3.52325e9 + 2.95636e9i 1.06264 + 0.891660i
\(526\) 6.54235e8 + 1.13317e9i 0.196013 + 0.339504i
\(527\) 1.02300e9 + 3.72341e8i 0.304465 + 0.110816i
\(528\) −3.41942e8 + 5.92261e8i −0.101096 + 0.175103i
\(529\) −3.61358e9 − 6.25891e9i −1.06131 − 1.83825i
\(530\) −1.17193e8 − 6.64633e8i −0.0341928 − 0.193917i
\(531\) 1.53309e9 − 5.57999e8i 0.444361 − 0.161734i
\(532\) 5.90967e8 − 1.02359e9i 0.170166 − 0.294736i
\(533\) 7.05403e8 − 5.91903e8i 0.201786 − 0.169319i
\(534\) 1.58065e9 − 1.32633e9i 0.449202 − 0.376926i
\(535\) 3.37010e7 + 1.22662e7i 0.00951492 + 0.00346315i
\(536\) 3.87402e8 − 2.19707e9i 0.108664 − 0.616263i
\(537\) 8.49316e8 − 4.81671e9i 0.236679 − 1.34227i
\(538\) 3.51481e9 + 1.27929e9i 0.973115 + 0.354185i
\(539\) −2.47415e8 + 2.07605e8i −0.0680557 + 0.0571055i
\(540\) 6.06538e7 − 5.08946e7i 0.0165760 − 0.0139089i
\(541\) −7.40585e8 + 1.28273e9i −0.201087 + 0.348293i −0.948879 − 0.315640i \(-0.897781\pi\)
0.747792 + 0.663933i \(0.231114\pi\)
\(542\) 4.30056e7 − 1.56527e7i 0.0116018 − 0.00422273i
\(543\) −7.85226e8 − 4.45324e9i −0.210473 − 1.19365i
\(544\) 1.90777e8 + 3.30435e8i 0.0508077 + 0.0880015i
\(545\) −1.24044e8 + 2.14851e8i −0.0328238 + 0.0568525i
\(546\) 5.36816e9 + 1.95385e9i 1.41140 + 0.513709i
\(547\) −2.48278e9 − 4.30030e9i −0.648609 − 1.12342i −0.983455 − 0.181150i \(-0.942018\pi\)
0.334847 − 0.942273i \(-0.391315\pi\)
\(548\) −1.88079e9 − 1.57817e9i −0.488213 − 0.409659i
\(549\) 7.48322e8 0.193013
\(550\) −1.18877e9 − 9.97498e8i −0.304670 − 0.255648i
\(551\) −1.44917e9 + 5.27455e8i −0.369053 + 0.134324i
\(552\) 5.84719e8 − 3.31611e9i 0.147966 − 0.839154i
\(553\) 7.70139e8 + 4.36768e9i 0.193656 + 1.09828i
\(554\) −2.04403e9 −0.510743
\(555\) −1.24637e9 − 1.03478e7i −0.309473 − 0.00256934i
\(556\) −2.72815e9 −0.673141
\(557\) −6.82856e8 − 3.87267e9i −0.167431 − 0.949548i −0.946522 − 0.322638i \(-0.895430\pi\)
0.779092 − 0.626910i \(-0.215681\pi\)
\(558\) 2.44328e8 − 1.38565e9i 0.0595324 − 0.337625i
\(559\) −5.56052e9 + 2.02386e9i −1.34640 + 0.490050i
\(560\) 1.93655e8 + 1.62496e8i 0.0465983 + 0.0391007i
\(561\) 1.94414e9 0.464899
\(562\) −2.35463e9 − 1.97577e9i −0.559558 − 0.469525i
\(563\) −2.82743e9 − 4.89725e9i −0.667747 − 1.15657i −0.978533 − 0.206092i \(-0.933925\pi\)
0.310785 − 0.950480i \(-0.399408\pi\)
\(564\) 3.39882e9 + 1.23707e9i 0.797721 + 0.290347i
\(565\) −1.12997e8 + 1.95717e8i −0.0263571 + 0.0456518i
\(566\) −1.25756e9 − 2.17816e9i −0.291523 − 0.504932i
\(567\) −9.05425e8 − 5.13492e9i −0.208599 − 1.18302i
\(568\) 3.60167e8 − 1.31090e8i 0.0824679 − 0.0300159i
\(569\) −4.15075e9 + 7.18932e9i −0.944570 + 1.63604i −0.187960 + 0.982177i \(0.560188\pi\)
−0.756610 + 0.653866i \(0.773146\pi\)
\(570\) −4.70497e8 + 3.94794e8i −0.106413 + 0.0892911i
\(571\) −2.93990e9 + 2.46686e9i −0.660854 + 0.554522i −0.910343 − 0.413855i \(-0.864182\pi\)
0.249489 + 0.968378i \(0.419737\pi\)
\(572\) −1.81126e9 − 6.59244e8i −0.404664 − 0.147286i
\(573\) −1.41176e9 + 8.00652e9i −0.313488 + 1.77788i
\(574\) 1.08196e8 − 6.13607e8i 0.0238791 − 0.135425i
\(575\) 7.18001e9 + 2.61331e9i 1.57502 + 0.573262i
\(576\) 3.77767e8 − 3.16984e8i 0.0823655 − 0.0691129i
\(577\) 6.00434e9 − 5.03824e9i 1.30122 − 1.09185i 0.311284 − 0.950317i \(-0.399241\pi\)
0.989933 − 0.141534i \(-0.0452034\pi\)
\(578\) −1.09901e9 + 1.90355e9i −0.236732 + 0.410031i
\(579\) −1.15051e9 + 4.18750e8i −0.246328 + 0.0896562i
\(580\) −5.72776e7 − 3.24838e8i −0.0121895 − 0.0691303i
\(581\) 3.06535e9 + 5.30935e9i 0.648432 + 1.12312i
\(582\) 5.43401e8 − 9.41198e8i 0.114259 − 0.197902i
\(583\) 3.27184e9 + 1.19085e9i 0.683836 + 0.248896i
\(584\) −7.94285e8 − 1.37574e9i −0.165018 − 0.285820i
\(585\) −1.05156e9 − 8.82361e8i −0.217164 − 0.182222i
\(586\) −4.05650e9 −0.832741
\(587\) 9.09147e8 + 7.62865e8i 0.185524 + 0.155673i 0.730820 − 0.682571i \(-0.239138\pi\)
−0.545295 + 0.838244i \(0.683582\pi\)
\(588\) 4.73276e8 − 1.72258e8i 0.0960050 − 0.0349430i
\(589\) 3.08112e8 − 1.74739e9i 0.0621306 − 0.352360i
\(590\) 7.64132e7 + 4.33361e8i 0.0153175 + 0.0868696i
\(591\) −4.35397e9 −0.867620
\(592\) 1.26198e9 + 1.04773e7i 0.249991 + 0.00207550i
\(593\) 7.34024e9 1.44550 0.722751 − 0.691108i \(-0.242877\pi\)
0.722751 + 0.691108i \(0.242877\pi\)
\(594\) 7.09333e7 + 4.02283e8i 0.0138866 + 0.0787551i
\(595\) 1.24793e8 − 7.07737e8i 0.0242874 − 0.137741i
\(596\) −4.03418e9 + 1.46832e9i −0.780537 + 0.284092i
\(597\) 4.40710e9 + 3.69800e9i 0.847701 + 0.711305i
\(598\) 9.49050e9 1.81483
\(599\) 6.18802e8 + 5.19237e8i 0.117641 + 0.0987124i 0.699710 − 0.714427i \(-0.253312\pi\)
−0.582070 + 0.813139i \(0.697757\pi\)
\(600\) 1.20996e9 + 2.09572e9i 0.228688 + 0.396098i
\(601\) −6.16638e9 − 2.24438e9i −1.15870 − 0.421731i −0.310065 − 0.950715i \(-0.600351\pi\)
−0.848632 + 0.528984i \(0.822573\pi\)
\(602\) −2.00196e9 + 3.46750e9i −0.373997 + 0.647781i
\(603\) 4.09847e9 + 7.09876e9i 0.761222 + 1.31847i
\(604\) 2.86979e8 + 1.62754e9i 0.0529933 + 0.300540i
\(605\) 7.53024e8 − 2.74078e8i 0.138250 − 0.0503189i
\(606\) −7.48871e7 + 1.29708e8i −0.0136695 + 0.0236763i
\(607\) −2.62987e9 + 2.20672e9i −0.477280 + 0.400485i −0.849442 − 0.527683i \(-0.823061\pi\)
0.372162 + 0.928168i \(0.378617\pi\)
\(608\) 4.76387e8 − 3.99736e8i 0.0859601 − 0.0721291i
\(609\) −4.73938e9 − 1.72499e9i −0.850278 − 0.309476i
\(610\) −3.50490e7 + 1.98773e8i −0.00625203 + 0.0354571i
\(611\) −1.77021e9 + 1.00393e10i −0.313964 + 1.78058i
\(612\) −1.31735e9 − 4.79477e8i −0.232312 − 0.0845547i
\(613\) −2.23391e8 + 1.87447e8i −0.0391700 + 0.0328675i −0.662162 − 0.749360i \(-0.730361\pi\)
0.622993 + 0.782228i \(0.285917\pi\)
\(614\) 2.56081e8 − 2.14878e8i 0.0446466 − 0.0374630i
\(615\) −1.61889e8 + 2.80401e8i −0.0280644 + 0.0486090i
\(616\) −1.22556e9 + 4.46069e8i −0.211253 + 0.0768899i
\(617\) 8.75048e8 + 4.96264e9i 0.149980 + 0.850579i 0.963233 + 0.268669i \(0.0865836\pi\)
−0.813253 + 0.581911i \(0.802305\pi\)
\(618\) −2.92330e8 − 5.06331e8i −0.0498212 − 0.0862929i
\(619\) −1.25742e9 + 2.17791e9i −0.213089 + 0.369082i −0.952680 − 0.303976i \(-0.901686\pi\)
0.739590 + 0.673057i \(0.235019\pi\)
\(620\) 3.56620e8 + 1.29799e8i 0.0600945 + 0.0218726i
\(621\) −1.00564e9 − 1.74183e9i −0.168509 − 0.291866i
\(622\) −3.83745e9 − 3.22000e9i −0.639405 − 0.536524i
\(623\) 3.93505e9 0.651992
\(624\) 2.30253e9 + 1.93205e9i 0.379367 + 0.318327i
\(625\) −4.86468e9 + 1.77060e9i −0.797029 + 0.290095i
\(626\) 6.39368e8 − 3.62603e9i 0.104169 − 0.590774i
\(627\) −5.50236e8 − 3.12054e9i −0.0891482 − 0.505584i
\(628\) −7.67826e8 −0.123710
\(629\) −1.76798e9 − 3.12179e9i −0.283269 − 0.500181i
\(630\) −9.28827e8 −0.147994
\(631\) 3.87828e8 + 2.19948e9i 0.0614521 + 0.348512i 0.999994 + 0.00334789i \(0.00106567\pi\)
−0.938542 + 0.345164i \(0.887823\pi\)
\(632\) −4.05211e8 + 2.29807e9i −0.0638516 + 0.362120i
\(633\) 1.02827e10 − 3.74259e9i 1.61136 − 0.586488i
\(634\) 4.32420e9 + 3.62843e9i 0.673896 + 0.565466i
\(635\) −2.76775e9 −0.428962
\(636\) −4.15927e9 − 3.49004e9i −0.641088 − 0.537936i
\(637\) 7.09758e8 + 1.22934e9i 0.108798 + 0.188444i
\(638\) 1.59910e9 + 5.82026e8i 0.243783 + 0.0887299i
\(639\) −7.04123e8 + 1.21958e9i −0.106757 + 0.184908i
\(640\) 6.65054e7 + 1.15191e8i 0.0100283 + 0.0173695i
\(641\) −1.00618e8 − 5.70635e8i −0.0150895 − 0.0855766i 0.976333 − 0.216273i \(-0.0693900\pi\)
−0.991423 + 0.130696i \(0.958279\pi\)
\(642\) 2.71129e8 − 9.86830e7i 0.0404393 − 0.0147187i
\(643\) −3.87234e9 + 6.70709e9i −0.574427 + 0.994937i 0.421677 + 0.906746i \(0.361442\pi\)
−0.996104 + 0.0881904i \(0.971892\pi\)
\(644\) 4.91925e9 − 4.12774e9i 0.725769 − 0.608992i
\(645\) 1.59386e9 − 1.33740e9i 0.233878 − 0.196247i
\(646\) −1.66126e9 − 6.04649e8i −0.242451 − 0.0882448i
\(647\) 1.70836e7 − 9.68860e7i 0.00247979 − 0.0140636i −0.983543 − 0.180676i \(-0.942172\pi\)
0.986023 + 0.166612i \(0.0532827\pi\)
\(648\) 4.76393e8 − 2.70176e9i 0.0687785 − 0.390062i
\(649\) −2.13334e9 − 7.76472e8i −0.306340 − 0.111499i
\(650\) −5.22477e9 + 4.38411e9i −0.746227 + 0.626159i
\(651\) 4.44523e9 − 3.72999e9i 0.631482 − 0.529876i
\(652\) −2.00691e9 + 3.47607e9i −0.283571 + 0.491159i
\(653\) 1.15884e10 − 4.21785e9i 1.62866 − 0.592782i 0.643652 − 0.765318i \(-0.277418\pi\)
0.985003 + 0.172536i \(0.0551961\pi\)
\(654\) 3.46585e8 + 1.96558e9i 0.0484493 + 0.274770i
\(655\) 8.08162e8 + 1.39978e9i 0.112371 + 0.194632i
\(656\) 1.63916e8 − 2.83911e8i 0.0226703 − 0.0392662i
\(657\) 5.48469e9 + 1.99627e9i 0.754525 + 0.274625i
\(658\) 3.44889e9 + 5.97366e9i 0.471942 + 0.817428i
\(659\) −1.11225e9 − 9.33285e8i −0.151392 − 0.127033i 0.563946 − 0.825812i \(-0.309283\pi\)
−0.715338 + 0.698779i \(0.753727\pi\)
\(660\) 6.77735e8 0.0917606
\(661\) −9.59611e9 − 8.05209e9i −1.29238 − 1.08444i −0.991409 − 0.130802i \(-0.958245\pi\)
−0.300971 − 0.953633i \(-0.597311\pi\)
\(662\) −8.94922e9 + 3.25725e9i −1.19890 + 0.436363i
\(663\) 1.48377e9 − 8.41490e9i 0.197729 − 1.12138i
\(664\) 5.60136e8 + 3.17669e9i 0.0742515 + 0.421101i
\(665\) −1.17131e9 −0.154452
\(666\) −3.57668e9 + 2.95094e9i −0.469159 + 0.387080i
\(667\) −8.37886e9 −1.09331
\(668\) −4.14468e8 − 2.35057e9i −0.0537989 − 0.305109i
\(669\) −2.92342e9 + 1.65796e10i −0.377486 + 2.14083i
\(670\) −2.07756e9 + 7.56172e8i −0.266866 + 0.0971312i
\(671\) −7.97692e8 − 6.69343e8i −0.101931 − 0.0855303i
\(672\) 2.03380e9 0.258532
\(673\) 6.55557e8 + 5.50077e8i 0.0829006 + 0.0695618i 0.683296 − 0.730141i \(-0.260546\pi\)
−0.600396 + 0.799703i \(0.704990\pi\)
\(674\) −2.63269e9 − 4.55995e9i −0.331200 − 0.573655i
\(675\) 1.35827e9 + 4.94368e8i 0.169989 + 0.0618710i
\(676\) −2.22783e9 + 3.85871e9i −0.277376 + 0.480429i
\(677\) 4.96108e8 + 8.59285e8i 0.0614492 + 0.106433i 0.895113 − 0.445839i \(-0.147094\pi\)
−0.833664 + 0.552272i \(0.813761\pi\)
\(678\) 3.15718e8 + 1.79053e9i 0.0389042 + 0.220636i
\(679\) 1.94762e9 − 7.08875e8i 0.238759 − 0.0869011i
\(680\) 1.89061e8 − 3.27464e8i 0.0230580 − 0.0399376i
\(681\) 3.99467e9 − 3.35193e9i 0.484693 − 0.406705i
\(682\) −1.49986e9 + 1.25853e9i −0.181052 + 0.151921i
\(683\) 2.93335e9 + 1.06765e9i 0.352283 + 0.128220i 0.512099 − 0.858926i \(-0.328868\pi\)
−0.159816 + 0.987147i \(0.551090\pi\)
\(684\) −3.96768e8 + 2.25018e9i −0.0474067 + 0.268857i
\(685\) −4.22508e8 + 2.39616e9i −0.0502247 + 0.284838i
\(686\) −5.12191e9 − 1.86422e9i −0.605756 − 0.220477i
\(687\) 5.69699e9 − 4.78034e9i 0.670342 − 0.562484i
\(688\) −1.61381e9 + 1.35415e9i −0.188926 + 0.158528i
\(689\) 7.65147e9 − 1.32527e10i 0.891205 − 1.54361i
\(690\) −3.13574e9 + 1.14132e9i −0.363386 + 0.132262i
\(691\) 2.57653e9 + 1.46122e10i 0.297072 + 1.68478i 0.658660 + 0.752441i \(0.271124\pi\)
−0.361588 + 0.932338i \(0.617765\pi\)
\(692\) −3.46386e9 − 5.99958e9i −0.397365 − 0.688256i
\(693\) 2.39597e9 − 4.14993e9i 0.273473 − 0.473669i
\(694\) −5.41656e9 − 1.97147e9i −0.615128 − 0.223888i
\(695\) 1.35181e9 + 2.34140e9i 0.152745 + 0.264563i
\(696\) −2.03283e9 − 1.70575e9i −0.228544 − 0.191771i
\(697\) −9.31960e8 −0.104252
\(698\) −6.59279e9 − 5.53201e9i −0.733796 − 0.615728i
\(699\) −6.68608e9 + 2.43353e9i −0.740460 + 0.269505i
\(700\) −8.01382e8 + 4.54486e9i −0.0883073 + 0.500815i
\(701\) 1.85017e9 + 1.04928e10i 0.202861 + 1.15048i 0.900771 + 0.434295i \(0.143002\pi\)
−0.697910 + 0.716185i \(0.745886\pi\)
\(702\) 1.79535e9 0.195870
\(703\) −4.51041e9 + 3.72131e9i −0.489635 + 0.403973i
\(704\) −6.86219e8 −0.0741239
\(705\) −6.22428e8 − 3.52997e9i −0.0669002 − 0.379410i
\(706\) −1.16217e9 + 6.59102e9i −0.124295 + 0.704914i
\(707\) −2.68405e8 + 9.76914e7i −0.0285642 + 0.0103965i
\(708\) 2.71197e9 + 2.27561e9i 0.287190 + 0.240981i
\(709\) −8.59293e8 −0.0905482 −0.0452741 − 0.998975i \(-0.514416\pi\)
−0.0452741 + 0.998975i \(0.514416\pi\)
\(710\) −2.90971e8 − 2.44154e8i −0.0305102 − 0.0256011i
\(711\) −4.28688e9 − 7.42510e9i −0.447299 − 0.774745i
\(712\) 1.94558e9 + 7.08132e8i 0.202008 + 0.0735249i
\(713\) 4.82015e9 − 8.34874e9i 0.498020 − 0.862596i
\(714\) −2.89084e9 − 5.00707e9i −0.297221 − 0.514802i
\(715\) 3.31697e8 + 1.88115e9i 0.0339368 + 0.192465i
\(716\) 4.61174e9 − 1.67854e9i 0.469536 − 0.170897i
\(717\) 1.11522e10 − 1.93163e10i 1.12991 − 1.95707i
\(718\) 8.97421e9 − 7.53026e9i 0.904817 − 0.759231i
\(719\) 7.68515e9 − 6.44860e9i 0.771083 − 0.647015i −0.169903 − 0.985461i \(-0.554346\pi\)
0.940986 + 0.338446i \(0.109901\pi\)
\(720\) −4.59233e8 − 1.67147e8i −0.0458532 − 0.0166892i
\(721\) 1.93616e8 − 1.09805e9i 0.0192384 − 0.109106i
\(722\) 7.41406e8 − 4.20472e9i 0.0733122 − 0.415774i
\(723\) −7.84227e9 − 2.85435e9i −0.771716 − 0.280882i
\(724\) 3.47583e9 − 2.91657e9i 0.340387 − 0.285619i
\(725\) 4.61279e9 − 3.87059e9i 0.449553 − 0.377220i
\(726\) 3.22349e9 − 5.58324e9i 0.312642 − 0.541512i
\(727\) 4.80412e9 − 1.74856e9i 0.463707 − 0.168775i −0.0995928 − 0.995028i \(-0.531754\pi\)
0.563299 + 0.826253i \(0.309532\pi\)
\(728\) 9.95381e8 + 5.64509e9i 0.0956158 + 0.542264i
\(729\) 3.67948e9 + 6.37304e9i 0.351754 + 0.609257i
\(730\) −7.87143e8 + 1.36337e9i −0.0748900 + 0.129713i
\(731\) 5.62768e9 + 2.04831e9i 0.532867 + 0.193948i
\(732\) 8.11911e8 + 1.40627e9i 0.0765103 + 0.132520i
\(733\) −8.67421e9 − 7.27853e9i −0.813516 − 0.682621i 0.137928 − 0.990442i \(-0.455956\pi\)
−0.951444 + 0.307821i \(0.900400\pi\)
\(734\) 7.35876e9 0.686861
\(735\) −3.82349e8 − 3.20829e8i −0.0355184 − 0.0298035i
\(736\) 3.17499e9 − 1.15560e9i 0.293542 − 0.106841i
\(737\) 1.98068e9 − 1.12330e10i 0.182255 − 1.03362i
\(738\) 2.09162e8 + 1.18621e9i 0.0191551 + 0.108634i
\(739\) −7.75931e9 −0.707241 −0.353620 − 0.935389i \(-0.615050\pi\)
−0.353620 + 0.935389i \(0.615050\pi\)
\(740\) −6.16322e8 − 1.08827e9i −0.0559109 − 0.0987244i
\(741\) −1.39267e10 −1.25743
\(742\) −1.79805e9 − 1.01972e10i −0.161580 − 0.916366i
\(743\) −3.40809e9 + 1.93283e10i −0.304825 + 1.72875i 0.319502 + 0.947586i \(0.396484\pi\)
−0.624327 + 0.781163i \(0.714627\pi\)
\(744\) 2.86905e9 − 1.04425e9i 0.255407 − 0.0929607i
\(745\) 3.25912e9 + 2.73473e9i 0.288771 + 0.242308i
\(746\) 6.38075e9 0.562711
\(747\) −9.07899e9 − 7.61817e9i −0.796921 − 0.668696i
\(748\) 9.75390e8 + 1.68943e9i 0.0852163 + 0.147599i
\(749\) 5.17063e8 + 1.88196e8i 0.0449632 + 0.0163653i
\(750\) 2.46326e9 − 4.26649e9i 0.213204 − 0.369280i
\(751\) 1.00562e10 + 1.74179e10i 0.866353 + 1.50057i 0.865698 + 0.500567i \(0.166875\pi\)
0.000655367 1.00000i \(0.499791\pi\)
\(752\) 6.30220e8 + 3.57416e9i 0.0540418 + 0.306486i
\(753\) 3.56445e9 − 1.29736e9i 0.304236 − 0.110733i
\(754\) 3.73964e9 − 6.47724e9i 0.317709 − 0.550289i
\(755\) 1.25462e9 − 1.05275e9i 0.106096 − 0.0890247i
\(756\) 9.30590e8 − 7.80858e8i 0.0783307 − 0.0657273i
\(757\) 1.31972e10 + 4.80340e9i 1.10573 + 0.402451i 0.829424 − 0.558620i \(-0.188669\pi\)
0.276301 + 0.961071i \(0.41