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Properties

Label 74.8.f.b.9.7
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 9.7
Character \(\chi\) \(=\) 74.9
Dual form 74.8.f.b.33.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.38919 - 7.87846i) q^{2} +(2.48533 - 14.0950i) q^{3} +(-60.1403 + 21.8893i) q^{4} +(-356.271 - 298.947i) q^{5} -114.500 q^{6} +(1364.62 + 1145.05i) q^{7} +(256.000 + 443.405i) q^{8} +(1862.62 + 677.936i) q^{9} +O(q^{10})\) \(q+(-1.38919 - 7.87846i) q^{2} +(2.48533 - 14.0950i) q^{3} +(-60.1403 + 21.8893i) q^{4} +(-356.271 - 298.947i) q^{5} -114.500 q^{6} +(1364.62 + 1145.05i) q^{7} +(256.000 + 443.405i) q^{8} +(1862.62 + 677.936i) q^{9} +(-1860.32 + 3222.16i) q^{10} +(1473.11 + 2551.51i) q^{11} +(159.061 + 902.081i) q^{12} +(949.590 - 345.623i) q^{13} +(7125.53 - 12341.8i) q^{14} +(-5099.12 + 4278.67i) q^{15} +(3137.72 - 2632.86i) q^{16} +(-7321.52 - 2664.81i) q^{17} +(2753.58 - 15616.3i) q^{18} +(8290.16 - 47015.9i) q^{19} +(27970.0 + 10180.3i) q^{20} +(19531.0 - 16388.5i) q^{21} +(18055.5 - 15150.4i) q^{22} +(-22825.7 + 39535.3i) q^{23} +(6886.04 - 2506.32i) q^{24} +(23993.6 + 136075. i) q^{25} +(-4042.13 - 7001.18i) q^{26} +(29835.4 - 51676.4i) q^{27} +(-107133. - 38993.2i) q^{28} +(-13270.0 - 22984.4i) q^{29} +(40792.9 + 34229.3i) q^{30} +309825. q^{31} +(-25101.7 - 21062.9i) q^{32} +(39624.7 - 14422.2i) q^{33} +(-10823.7 + 61384.2i) q^{34} +(-143865. - 815898. i) q^{35} -126858. q^{36} +(-217183. - 218549. i) q^{37} -381929. q^{38} +(-2511.51 - 14243.5i) q^{39} +(41349.2 - 234503. i) q^{40} +(189184. - 68857.4i) q^{41} +(-156248. - 131108. i) q^{42} +522466. q^{43} +(-144444. - 121203. i) q^{44} +(-460929. - 798353. i) q^{45} +(343187. + 124910. i) q^{46} +(359906. - 623375. i) q^{47} +(-29311.9 - 50769.7i) q^{48} +(408036. + 2.31409e6i) q^{49} +(1.03873e6 - 378066. i) q^{50} +(-55757.0 + 96574.0i) q^{51} +(-49543.2 + 41571.7i) q^{52} +(4908.61 - 4118.81i) q^{53} +(-448578. - 163269. i) q^{54} +(237938. - 1.34941e6i) q^{55} +(-158379. + 898212. i) q^{56} +(-642085. - 233700. i) q^{57} +(-162647. + 136477. i) q^{58} +(640356. - 537323. i) q^{59} +(213006. - 368937. i) q^{60} +(-1.62215e6 + 590414. i) q^{61} +(-430404. - 2.44094e6i) q^{62} +(1.76549e6 + 3.05791e6i) q^{63} +(-131072. + 227023. i) q^{64} +(-441635. - 160742. i) q^{65} +(-168671. - 292147. i) q^{66} +(1.02677e6 + 861566. i) q^{67} +498649. q^{68} +(500521. + 419987. i) q^{69} +(-6.22817e6 + 2.26687e6i) q^{70} +(919621. - 5.21543e6i) q^{71} +(176229. + 999445. i) q^{72} +2.56179e6 q^{73} +(-1.42012e6 + 2.01467e6i) q^{74} +1.97761e6 q^{75} +(530570. + 3.00901e6i) q^{76} +(-911368. + 5.16862e6i) q^{77} +(-108728. + 39573.7i) q^{78} +(6.15969e6 + 5.16859e6i) q^{79} -1.90497e6 q^{80} +(2.66655e6 + 2.23750e6i) q^{81} +(-805303. - 1.39483e6i) q^{82} +(-4.68073e6 - 1.70365e6i) q^{83} +(-815871. + 1.41313e6i) q^{84} +(1.81181e6 + 3.13815e6i) q^{85} +(-725802. - 4.11623e6i) q^{86} +(-356945. + 129917. i) q^{87} +(-754234. + 1.30637e6i) q^{88} +(1.37984e6 - 1.15782e6i) q^{89} +(-5.64948e6 + 4.74048e6i) q^{90} +(1.69158e6 + 615686. i) q^{91} +(507346. - 2.87730e6i) q^{92} +(770017. - 4.36698e6i) q^{93} +(-5.41121e6 - 1.96952e6i) q^{94} +(-1.70088e7 + 1.42721e7i) q^{95} +(-359268. + 301461. i) q^{96} +(4.41019e6 - 7.63868e6i) q^{97} +(1.76646e7 - 6.42939e6i) q^{98} +(1.01408e6 + 5.75115e6i) 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
\(3\) 2.48533 − 14.0950i 0.0531447 − 0.301399i −0.946637 − 0.322302i \(-0.895543\pi\)
0.999781 + 0.0209038i \(0.00665436\pi\)
\(4\) −60.1403 + 21.8893i −0.469846 + 0.171010i
\(5\) −356.271 − 298.947i −1.27464 − 1.06955i −0.993960 − 0.109744i \(-0.964997\pi\)
−0.280676 − 0.959803i \(-0.590559\pi\)
\(6\) −114.500 −0.216409
\(7\) 1364.62 + 1145.05i 1.50372 + 1.26177i 0.874977 + 0.484165i \(0.160877\pi\)
0.628748 + 0.777609i \(0.283568\pi\)
\(8\) 256.000 + 443.405i 0.176777 + 0.306186i
\(9\) 1862.62 + 677.936i 0.851676 + 0.309985i
\(10\) −1860.32 + 3222.16i −0.588284 + 1.01894i
\(11\) 1473.11 + 2551.51i 0.333704 + 0.577993i 0.983235 − 0.182343i \(-0.0583680\pi\)
−0.649531 + 0.760335i \(0.725035\pi\)
\(12\) 159.061 + 902.081i 0.0265723 + 0.150699i
\(13\) 949.590 − 345.623i 0.119877 − 0.0436315i −0.281385 − 0.959595i \(-0.590794\pi\)
0.401262 + 0.915963i \(0.368572\pi\)
\(14\) 7125.53 − 12341.8i 0.694016 − 1.20207i
\(15\) −5099.12 + 4278.67i −0.390100 + 0.327333i
\(16\) 3137.72 − 2632.86i 0.191511 − 0.160697i
\(17\) −7321.52 − 2664.81i −0.361435 − 0.131552i 0.154918 − 0.987927i \(-0.450489\pi\)
−0.516353 + 0.856376i \(0.672711\pi\)
\(18\) 2753.58 − 15616.3i 0.111287 − 0.631139i
\(19\) 8290.16 − 47015.9i 0.277284 − 1.57256i −0.454326 − 0.890835i \(-0.650120\pi\)
0.731611 − 0.681723i \(-0.238769\pi\)
\(20\) 27970.0 + 10180.3i 0.781786 + 0.284547i
\(21\) 19531.0 − 16388.5i 0.460212 − 0.386164i
\(22\) 18055.5 − 15150.4i 0.361519 − 0.303350i
\(23\) −22825.7 + 39535.3i −0.391180 + 0.677544i −0.992606 − 0.121385i \(-0.961266\pi\)
0.601425 + 0.798929i \(0.294600\pi\)
\(24\) 6886.04 − 2506.32i 0.101679 − 0.0370081i
\(25\) 23993.6 + 136075.i 0.307118 + 1.74176i
\(26\) −4042.13 − 7001.18i −0.0451028 − 0.0781204i
\(27\) 29835.4 − 51676.4i 0.291715 − 0.505265i
\(28\) −107133. − 38993.2i −0.922296 − 0.335688i
\(29\) −13270.0 − 22984.4i −0.101037 − 0.175001i 0.811075 − 0.584942i \(-0.198883\pi\)
−0.912112 + 0.409941i \(0.865549\pi\)
\(30\) 40792.9 + 34229.3i 0.275842 + 0.231459i
\(31\) 309825. 1.86788 0.933942 − 0.357424i \(-0.116345\pi\)
0.933942 + 0.357424i \(0.116345\pi\)
\(32\) −25101.7 − 21062.9i −0.135419 − 0.113630i
\(33\) 39624.7 − 14422.2i 0.191941 − 0.0698607i
\(34\) −10823.7 + 61384.2i −0.0472280 + 0.267843i
\(35\) −143865. − 815898.i −0.567174 − 3.21661i
\(36\) −126858. −0.453167
\(37\) −217183. − 218549.i −0.704886 − 0.709320i
\(38\) −381929. −1.12912
\(39\) −2511.51 − 14243.5i −0.00677967 − 0.0384494i
\(40\) 41349.2 − 234503.i 0.102154 − 0.579347i
\(41\) 189184. − 68857.4i 0.428688 − 0.156030i −0.118660 − 0.992935i \(-0.537860\pi\)
0.547348 + 0.836905i \(0.315638\pi\)
\(42\) −156248. − 131108.i −0.325419 − 0.273059i
\(43\) 522466. 1.00212 0.501059 − 0.865413i \(-0.332944\pi\)
0.501059 + 0.865413i \(0.332944\pi\)
\(44\) −144444. − 121203.i −0.255632 − 0.214501i
\(45\) −460929. − 798353.i −0.754033 − 1.30602i
\(46\) 343187. + 124910.i 0.519850 + 0.189210i
\(47\) 359906. − 623375.i 0.505646 − 0.875804i −0.494333 − 0.869273i \(-0.664588\pi\)
0.999979 − 0.00653147i \(-0.00207905\pi\)
\(48\) −29311.9 − 50769.7i −0.0382560 − 0.0662614i
\(49\) 408036. + 2.31409e6i 0.495464 + 2.80991i
\(50\) 1.03873e6 − 378066.i 1.17519 − 0.427733i
\(51\) −55757.0 + 96574.0i −0.0588578 + 0.101945i
\(52\) −49543.2 + 41571.7i −0.0488622 + 0.0410002i
\(53\) 4908.61 − 4118.81i 0.00452890 − 0.00380020i −0.640520 − 0.767941i \(-0.721281\pi\)
0.645049 + 0.764141i \(0.276837\pi\)
\(54\) −448578. − 163269.i −0.387668 − 0.141100i
\(55\) 237938. − 1.34941e6i 0.192839 − 1.09364i
\(56\) −158379. + 898212.i −0.120515 + 0.683472i
\(57\) −642085. − 233700.i −0.459231 − 0.167146i
\(58\) −162647. + 136477.i −0.109458 + 0.0918462i
\(59\) 640356. − 537323.i 0.405919 − 0.340607i −0.416857 − 0.908972i \(-0.636868\pi\)
0.822776 + 0.568365i \(0.192424\pi\)
\(60\) 213006. − 368937.i 0.127310 − 0.220507i
\(61\) −1.62215e6 + 590414.i −0.915032 + 0.333045i −0.756260 − 0.654271i \(-0.772976\pi\)
−0.158772 + 0.987315i \(0.550753\pi\)
\(62\) −430404. − 2.44094e6i −0.229353 − 1.30073i
\(63\) 1.76549e6 + 3.05791e6i 0.889555 + 1.54075i
\(64\) −131072. + 227023.i −0.0625000 + 0.108253i
\(65\) −441635. − 160742.i −0.199465 − 0.0725993i
\(66\) −168671. − 292147.i −0.0722165 − 0.125083i
\(67\) 1.02677e6 + 861566.i 0.417074 + 0.349967i 0.827049 − 0.562130i \(-0.190018\pi\)
−0.409975 + 0.912097i \(0.634462\pi\)
\(68\) 498649. 0.192315
\(69\) 500521. + 419987.i 0.183422 + 0.153909i
\(70\) −6.22817e6 + 2.26687e6i −2.17029 + 0.789920i
\(71\) 919621. − 5.21543e6i 0.304933 − 1.72936i −0.318886 − 0.947793i \(-0.603309\pi\)
0.623819 − 0.781569i \(-0.285580\pi\)
\(72\) 176229. + 999445.i 0.0556434 + 0.315569i
\(73\) 2.56179e6 0.770751 0.385376 − 0.922760i \(-0.374072\pi\)
0.385376 + 0.922760i \(0.374072\pi\)
\(74\) −1.42012e6 + 2.01467e6i −0.407394 + 0.577953i
\(75\) 1.97761e6 0.541284
\(76\) 530570. + 3.00901e6i 0.138642 + 0.786279i
\(77\) −911368. + 5.16862e6i −0.227497 + 1.29020i
\(78\) −108728. + 39573.7i −0.0259423 + 0.00944224i
\(79\) 6.15969e6 + 5.16859e6i 1.40561 + 1.17944i 0.958545 + 0.284942i \(0.0919744\pi\)
0.447063 + 0.894503i \(0.352470\pi\)
\(80\) −1.90497e6 −0.415980
\(81\) 2.66655e6 + 2.23750e6i 0.557509 + 0.467806i
\(82\) −805303. − 1.39483e6i −0.161291 − 0.279365i
\(83\) −4.68073e6 − 1.70365e6i −0.898547 − 0.327044i −0.148876 − 0.988856i \(-0.547566\pi\)
−0.749670 + 0.661812i \(0.769788\pi\)
\(84\) −815871. + 1.41313e6i −0.150191 + 0.260138i
\(85\) 1.81181e6 + 3.13815e6i 0.319997 + 0.554251i
\(86\) −725802. − 4.11623e6i −0.123048 − 0.697839i
\(87\) −356945. + 129917.i −0.0581145 + 0.0211519i
\(88\) −754234. + 1.30637e6i −0.117982 + 0.204351i
\(89\) 1.37984e6 − 1.15782e6i 0.207474 − 0.174091i −0.533129 − 0.846034i \(-0.678984\pi\)
0.740604 + 0.671942i \(0.234540\pi\)
\(90\) −5.64948e6 + 4.74048e6i −0.816882 + 0.685446i
\(91\) 1.69158e6 + 615686.i 0.235315 + 0.0856475i
\(92\) 507346. − 2.87730e6i 0.0679277 − 0.385237i
\(93\) 770017. − 4.36698e6i 0.0992682 − 0.562978i
\(94\) −5.41121e6 − 1.96952e6i −0.671966 − 0.244576i
\(95\) −1.70088e7 + 1.42721e7i −2.03536 + 1.70787i
\(96\) −359268. + 301461.i −0.0414447 + 0.0347762i
\(97\) 4.41019e6 − 7.63868e6i 0.490633 − 0.849800i −0.509309 − 0.860584i \(-0.670099\pi\)
0.999942 + 0.0107830i \(0.00343242\pi\)
\(98\) 1.76646e7 − 6.42939e6i 1.89589 − 0.690046i
\(99\) 1.01408e6 + 5.75115e6i 0.105039 + 0.595706i
\(100\) −4.42156e6 − 7.65837e6i −0.442156 − 0.765837i
\(101\) 1.43147e6 − 2.47938e6i 0.138248 − 0.239452i −0.788586 − 0.614925i \(-0.789186\pi\)
0.926833 + 0.375473i \(0.122520\pi\)
\(102\) 838311. + 305120.i 0.0782176 + 0.0284689i
\(103\) 1.83972e6 + 3.18649e6i 0.165891 + 0.287331i 0.936971 − 0.349407i \(-0.113617\pi\)
−0.771081 + 0.636738i \(0.780283\pi\)
\(104\) 396346. + 332574.i 0.0345508 + 0.0289915i
\(105\) −1.18576e7 −0.999622
\(106\) −39268.9 − 32950.5i −0.00320242 − 0.00268715i
\(107\) −9.74152e6 + 3.54562e6i −0.768747 + 0.279801i −0.696472 − 0.717584i \(-0.745248\pi\)
−0.0722747 + 0.997385i \(0.523026\pi\)
\(108\) −663151. + 3.76091e6i −0.0506558 + 0.287283i
\(109\) −1.52243e6 − 8.63412e6i −0.112602 − 0.638595i −0.987910 − 0.155030i \(-0.950453\pi\)
0.875308 − 0.483565i \(-0.160658\pi\)
\(110\) −1.09618e7 −0.785251
\(111\) −3.62022e6 + 2.51803e6i −0.251249 + 0.174755i
\(112\) 7.29655e6 0.490743
\(113\) 1.70800e6 + 9.68655e6i 0.111356 + 0.631531i 0.988490 + 0.151286i \(0.0483413\pi\)
−0.877134 + 0.480245i \(0.840548\pi\)
\(114\) −949221. + 5.38330e6i −0.0600068 + 0.340315i
\(115\) 1.99511e7 − 7.26161e6i 1.22328 − 0.445236i
\(116\) 1.30118e6 + 1.09182e6i 0.0773985 + 0.0649451i
\(117\) 2.00303e6 0.115621
\(118\) −5.12285e6 − 4.29858e6i −0.287028 − 0.240845i
\(119\) −6.93973e6 − 1.20200e7i −0.377510 − 0.653866i
\(120\) −3.20256e6 − 1.16564e6i −0.169185 − 0.0615784i
\(121\) 5.40346e6 − 9.35907e6i 0.277283 − 0.480268i
\(122\) 6.90502e6 + 1.19598e7i 0.344275 + 0.596302i
\(123\) −500361. − 2.83769e6i −0.0242446 − 0.137498i
\(124\) −1.86330e7 + 6.78184e6i −0.877619 + 0.319427i
\(125\) 1.39637e7 − 2.41859e7i 0.639465 − 1.10759i
\(126\) 2.16391e7 − 1.81573e7i 0.963700 − 0.808640i
\(127\) −6.63706e6 + 5.56916e6i −0.287517 + 0.241255i −0.775126 − 0.631807i \(-0.782314\pi\)
0.487609 + 0.873062i \(0.337869\pi\)
\(128\) 1.97068e6 + 717268.i 0.0830579 + 0.0302306i
\(129\) 1.29850e6 − 7.36417e6i 0.0532572 − 0.302037i
\(130\) −652887. + 3.70270e6i −0.0260637 + 0.147815i
\(131\) 3.86621e7 + 1.40718e7i 1.50257 + 0.546892i 0.956725 − 0.290993i \(-0.0939857\pi\)
0.545847 + 0.837885i \(0.316208\pi\)
\(132\) −2.06735e6 + 1.73471e6i −0.0782358 + 0.0656476i
\(133\) 6.51485e7 − 5.46661e7i 2.40117 − 2.01482i
\(134\) 5.36144e6 − 9.28628e6i 0.192493 − 0.333407i
\(135\) −2.60780e7 + 9.49163e6i −0.912235 + 0.332026i
\(136\) −692717. − 3.92859e6i −0.0236140 − 0.133922i
\(137\) 7.69960e6 + 1.33361e7i 0.255827 + 0.443105i 0.965120 − 0.261809i \(-0.0843189\pi\)
−0.709293 + 0.704914i \(0.750986\pi\)
\(138\) 2.61354e6 − 4.52678e6i 0.0846548 − 0.146626i
\(139\) −2.98694e7 − 1.08716e7i −0.943356 − 0.343353i −0.175866 − 0.984414i \(-0.556272\pi\)
−0.767490 + 0.641061i \(0.778495\pi\)
\(140\) 2.65115e7 + 4.59193e7i 0.816557 + 1.41432i
\(141\) −7.89200e6 − 6.62217e6i −0.237094 − 0.198945i
\(142\) −4.23671e7 −1.24171
\(143\) 2.28071e6 + 1.91374e6i 0.0652220 + 0.0547278i
\(144\) 7.62927e6 − 2.77683e6i 0.212919 − 0.0774962i
\(145\) −2.14338e6 + 1.21557e7i −0.0583863 + 0.331125i
\(146\) −3.55881e6 − 2.01830e7i −0.0946388 − 0.536723i
\(147\) 3.36312e7 0.873235
\(148\) 1.78453e7 + 8.38962e6i 0.452489 + 0.212729i
\(149\) −5.50377e7 −1.36304 −0.681520 − 0.731799i \(-0.738681\pi\)
−0.681520 + 0.731799i \(0.738681\pi\)
\(150\) −2.74726e6 − 1.55805e7i −0.0664631 − 0.376931i
\(151\) −5.18003e6 + 2.93774e7i −0.122437 + 0.694375i 0.860360 + 0.509687i \(0.170239\pi\)
−0.982797 + 0.184689i \(0.940872\pi\)
\(152\) 2.29693e7 − 8.36016e6i 0.530513 − 0.193091i
\(153\) −1.18306e7 − 9.92705e6i −0.267046 − 0.224079i
\(154\) 4.19869e7 0.926384
\(155\) −1.10382e8 − 9.26212e7i −2.38087 − 1.99779i
\(156\) 462822. + 801632.i 0.00976064 + 0.0169059i
\(157\) 5.68361e7 + 2.06866e7i 1.17213 + 0.426620i 0.853415 − 0.521231i \(-0.174527\pi\)
0.318713 + 0.947851i \(0.396749\pi\)
\(158\) 3.21636e7 − 5.57090e7i 0.648732 − 1.12364i
\(159\) −45855.2 − 79423.5i −0.000904687 − 0.00156696i
\(160\) 2.64635e6 + 1.50082e7i 0.0510772 + 0.289673i
\(161\) −7.64183e7 + 2.78140e7i −1.44314 + 0.525258i
\(162\) 1.39237e7 − 2.41166e7i 0.257308 − 0.445671i
\(163\) 2.07784e7 − 1.74352e7i 0.375799 − 0.315333i −0.435251 − 0.900309i \(-0.643340\pi\)
0.811051 + 0.584976i \(0.198896\pi\)
\(164\) −9.87036e6 + 8.28222e6i −0.174735 + 0.146620i
\(165\) −1.84286e7 − 6.70747e6i −0.319374 − 0.116243i
\(166\) −6.91972e6 + 3.92437e7i −0.117411 + 0.665873i
\(167\) 9.26072e6 − 5.25201e7i 0.153864 − 0.872606i −0.805953 − 0.591979i \(-0.798347\pi\)
0.959817 − 0.280627i \(-0.0905422\pi\)
\(168\) 1.22667e7 + 4.46471e6i 0.199593 + 0.0726458i
\(169\) −4.72859e7 + 3.96776e7i −0.753578 + 0.632327i
\(170\) 2.22068e7 − 1.86337e7i 0.346669 − 0.290890i
\(171\) 4.73151e7 − 8.19522e7i 0.723625 − 1.25336i
\(172\) −3.14213e7 + 1.14364e7i −0.470841 + 0.171372i
\(173\) 1.04200e7 + 5.90948e7i 0.153005 + 0.867736i 0.960587 + 0.277980i \(0.0896650\pi\)
−0.807581 + 0.589756i \(0.799224\pi\)
\(174\) 1.51941e6 + 2.63170e6i 0.0218652 + 0.0378716i
\(175\) −1.23070e8 + 2.13164e8i −1.73588 + 3.00663i
\(176\) 1.13400e7 + 4.12741e6i 0.156790 + 0.0570668i
\(177\) −5.98207e6 − 1.03613e7i −0.0810859 − 0.140445i
\(178\) −1.10387e7 − 9.26259e6i −0.146706 − 0.123101i
\(179\) −3.31845e7 −0.432464 −0.216232 − 0.976342i \(-0.569377\pi\)
−0.216232 + 0.976342i \(0.569377\pi\)
\(180\) 4.51958e7 + 3.79238e7i 0.577623 + 0.484683i
\(181\) −6.08701e7 + 2.21549e7i −0.763008 + 0.277712i −0.694069 − 0.719909i \(-0.744184\pi\)
−0.0689393 + 0.997621i \(0.521961\pi\)
\(182\) 2.50074e6 − 1.41824e7i 0.0307481 − 0.174381i
\(183\) 4.29032e6 + 2.43316e7i 0.0517500 + 0.293489i
\(184\) −2.33735e7 −0.276606
\(185\) 1.20414e7 + 1.42789e8i 0.139822 + 1.65803i
\(186\) −3.54748e7 −0.404226
\(187\) −3.98613e6 − 2.26065e7i −0.0445765 − 0.252806i
\(188\) −7.99961e6 + 4.53681e7i −0.0878045 + 0.497964i
\(189\) 9.98861e7 − 3.63556e7i 1.07619 − 0.391701i
\(190\) 1.36070e8 + 1.14177e8i 1.43922 + 1.20765i
\(191\) 1.72804e8 1.79447 0.897236 − 0.441552i \(-0.145572\pi\)
0.897236 + 0.441552i \(0.145572\pi\)
\(192\) 2.87414e6 + 2.41169e6i 0.0293058 + 0.0245905i
\(193\) −6.80761e7 − 1.17911e8i −0.681623 − 1.18060i −0.974486 − 0.224450i \(-0.927941\pi\)
0.292863 − 0.956154i \(-0.405392\pi\)
\(194\) −6.63076e7 − 2.41340e7i −0.652014 − 0.237314i
\(195\) −3.36327e6 + 5.82535e6i −0.0324818 + 0.0562602i
\(196\) −7.51931e7 − 1.30238e8i −0.713316 − 1.23550i
\(197\) −1.37462e7 − 7.79586e7i −0.128100 − 0.726494i −0.979418 − 0.201843i \(-0.935307\pi\)
0.851317 − 0.524651i \(-0.175804\pi\)
\(198\) 4.39015e7 − 1.59788e7i 0.401931 − 0.146291i
\(199\) −7.90145e7 + 1.36857e8i −0.710756 + 1.23107i 0.253817 + 0.967252i \(0.418314\pi\)
−0.964574 + 0.263814i \(0.915019\pi\)
\(200\) −5.41938e7 + 4.54740e7i −0.479010 + 0.401937i
\(201\) 1.46957e7 − 1.23311e7i 0.127645 − 0.107107i
\(202\) −2.15223e7 − 7.83348e6i −0.183721 − 0.0668690i
\(203\) 8.20974e6 − 4.65598e7i 0.0688800 − 0.390638i
\(204\) 1.23931e6 − 7.02847e6i 0.0102205 − 0.0579636i
\(205\) −8.79857e7 − 3.20242e7i −0.713302 − 0.259621i
\(206\) 2.25489e7 − 1.89208e7i 0.179718 − 0.150801i
\(207\) −6.93179e7 + 5.81647e7i −0.543187 + 0.455788i
\(208\) 2.06957e6 − 3.58460e6i 0.0159463 − 0.0276197i
\(209\) 1.32174e8 − 4.81073e7i 1.00146 − 0.364501i
\(210\) 1.64725e7 + 9.34200e7i 0.122741 + 0.696101i
\(211\) −3.62253e7 − 6.27441e7i −0.265475 − 0.459816i 0.702213 − 0.711967i \(-0.252195\pi\)
−0.967688 + 0.252151i \(0.918862\pi\)
\(212\) −205047. + 355153.i −0.00147801 + 0.00256000i
\(213\) −7.12260e7 − 2.59241e7i −0.505022 − 0.183813i
\(214\) 4.14668e7 + 7.18226e7i 0.289236 + 0.500972i
\(215\) −1.86140e8 − 1.56190e8i −1.27733 − 1.07181i
\(216\) 3.05515e7 0.206274
\(217\) 4.22793e8 + 3.54765e8i 2.80878 + 2.35685i
\(218\) −6.59087e7 + 2.39888e7i −0.430869 + 0.156823i
\(219\) 6.36691e6 − 3.61085e7i 0.0409613 − 0.232303i
\(220\) 1.52280e7 + 8.63624e7i 0.0964193 + 0.546821i
\(221\) −7.87346e6 −0.0490674
\(222\) 2.48673e7 + 2.50238e7i 0.152543 + 0.153503i
\(223\) 2.51882e7 0.152100 0.0760500 − 0.997104i \(-0.475769\pi\)
0.0760500 + 0.997104i \(0.475769\pi\)
\(224\) −1.01363e7 − 5.74856e7i −0.0602573 − 0.341736i
\(225\) −4.75591e7 + 2.69721e8i −0.278352 + 1.57861i
\(226\) 7.39424e7 − 2.69128e7i 0.426102 − 0.155089i
\(227\) 1.34729e8 + 1.13051e8i 0.764489 + 0.641482i 0.939291 − 0.343121i \(-0.111484\pi\)
−0.174802 + 0.984604i \(0.555929\pi\)
\(228\) 4.37307e7 0.244351
\(229\) 3.89518e7 + 3.26844e7i 0.214340 + 0.179853i 0.743636 − 0.668584i \(-0.233099\pi\)
−0.529296 + 0.848437i \(0.677544\pi\)
\(230\) −8.49262e7 − 1.47096e8i −0.460250 − 0.797177i
\(231\) 7.05868e7 + 2.56915e7i 0.376774 + 0.137135i
\(232\) 6.79425e6 − 1.17680e7i 0.0357218 − 0.0618720i
\(233\) 6.62973e7 + 1.14830e8i 0.343360 + 0.594718i 0.985054 − 0.172243i \(-0.0551014\pi\)
−0.641694 + 0.766961i \(0.721768\pi\)
\(234\) −2.78258e6 − 1.57808e7i −0.0141969 − 0.0805144i
\(235\) −3.14580e8 + 1.14498e8i −1.58123 + 0.575520i
\(236\) −2.67496e7 + 4.63317e7i −0.132472 + 0.229449i
\(237\) 8.81603e7 − 7.39753e7i 0.430184 − 0.360967i
\(238\) −8.50583e7 + 7.13724e7i −0.408976 + 0.343171i
\(239\) −2.37075e8 − 8.62882e7i −1.12329 − 0.408845i −0.287440 − 0.957799i \(-0.592804\pi\)
−0.835853 + 0.548954i \(0.815026\pi\)
\(240\) −4.73447e6 + 2.68505e7i −0.0221071 + 0.125376i
\(241\) −1.15474e7 + 6.54887e7i −0.0531405 + 0.301375i −0.999781 − 0.0209159i \(-0.993342\pi\)
0.946641 + 0.322291i \(0.104453\pi\)
\(242\) −8.12415e7 − 2.95695e7i −0.368489 − 0.134119i
\(243\) 1.38134e8 − 1.15908e8i 0.617558 − 0.518193i
\(244\) 8.46329e7 − 7.10154e7i 0.372971 − 0.312960i
\(245\) 5.46418e8 − 9.46424e8i 2.37380 − 4.11154i
\(246\) −2.16615e7 + 7.88415e6i −0.0927718 + 0.0337662i
\(247\) −8.37748e6 − 4.75111e7i −0.0353732 − 0.200611i
\(248\) 7.93151e7 + 1.37378e8i 0.330198 + 0.571921i
\(249\) −3.56461e7 + 6.17409e7i −0.146324 + 0.253440i
\(250\) −2.09946e8 − 7.64140e7i −0.849801 − 0.309302i
\(251\) 1.09988e8 + 1.90505e8i 0.439023 + 0.760410i 0.997614 − 0.0690329i \(-0.0219913\pi\)
−0.558591 + 0.829443i \(0.688658\pi\)
\(252\) −1.73113e8 − 1.45259e8i −0.681439 − 0.571795i
\(253\) −1.34499e8 −0.522154
\(254\) 5.30965e7 + 4.45532e7i 0.203305 + 0.170593i
\(255\) 4.87352e7 − 1.77381e7i 0.184057 − 0.0669912i
\(256\) 2.91333e6 − 1.65223e7i 0.0108530 − 0.0615505i
\(257\) −6.77480e7 − 3.84218e8i −0.248961 − 1.41193i −0.811112 − 0.584891i \(-0.801137\pi\)
0.562151 − 0.827034i \(-0.309974\pi\)
\(258\) −5.98222e7 −0.216867
\(259\) −4.61219e7 − 5.46921e8i −0.164952 − 1.95603i
\(260\) 3.00786e7 0.106133
\(261\) −9.13502e6 − 5.18073e7i −0.0318030 − 0.180364i
\(262\) 5.71557e7 − 3.24146e8i 0.196338 − 1.11349i
\(263\) −4.18284e8 + 1.52243e8i −1.41784 + 0.516050i −0.933419 − 0.358787i \(-0.883190\pi\)
−0.484417 + 0.874837i \(0.660968\pi\)
\(264\) 1.65388e7 + 1.38777e7i 0.0553210 + 0.0464199i
\(265\) −2.98010e6 −0.00983719
\(266\) −5.21188e8 − 4.37328e8i −1.69789 − 1.42470i
\(267\) −1.28902e7 − 2.23265e7i −0.0414448 − 0.0717844i
\(268\) −8.06097e7 − 2.93395e7i −0.255809 − 0.0931067i
\(269\) 1.73572e8 − 3.00636e8i 0.543686 − 0.941691i −0.455003 − 0.890490i \(-0.650362\pi\)
0.998688 − 0.0512010i \(-0.0163049\pi\)
\(270\) 1.11007e8 + 1.92269e8i 0.343223 + 0.594479i
\(271\) 2.15770e7 + 1.22369e8i 0.0658564 + 0.373490i 0.999868 + 0.0162474i \(0.00517195\pi\)
−0.934012 + 0.357243i \(0.883717\pi\)
\(272\) −2.99889e7 + 1.09151e7i −0.0903587 + 0.0328879i
\(273\) 1.28823e7 − 2.23127e7i 0.0383197 − 0.0663717i
\(274\) 9.43718e7 − 7.91874e7i 0.277150 − 0.232557i
\(275\) −3.11850e8 + 2.61673e8i −0.904235 + 0.758743i
\(276\) −3.92947e7 − 1.43021e7i −0.112500 − 0.0409466i
\(277\) −8.32630e7 + 4.72208e8i −0.235382 + 1.33492i 0.606426 + 0.795140i \(0.292603\pi\)
−0.841808 + 0.539777i \(0.818509\pi\)
\(278\) −4.41572e7 + 2.50428e8i −0.123266 + 0.699079i
\(279\) 5.77084e8 + 2.10041e8i 1.59083 + 0.579016i
\(280\) 3.24944e8 − 2.72660e8i 0.884617 − 0.742282i
\(281\) 2.76808e8 − 2.32269e8i 0.744228 − 0.624481i −0.189742 − 0.981834i \(-0.560765\pi\)
0.933970 + 0.357353i \(0.116321\pi\)
\(282\) −4.12091e7 + 7.13762e7i −0.109426 + 0.189532i
\(283\) 1.84744e8 − 6.72414e7i 0.484528 − 0.176354i −0.0881944 − 0.996103i \(-0.528110\pi\)
0.572722 + 0.819750i \(0.305887\pi\)
\(284\) 5.88558e7 + 3.33788e8i 0.152467 + 0.864681i
\(285\) 1.58893e8 + 2.75210e8i 0.406581 + 0.704219i
\(286\) 1.19090e7 − 2.06271e7i 0.0301020 − 0.0521382i
\(287\) 3.37010e8 + 1.22662e8i 0.841503 + 0.306282i
\(288\) −3.24756e7 − 5.62494e7i −0.0801094 − 0.138754i
\(289\) −2.67834e8 − 2.24740e8i −0.652715 − 0.547693i
\(290\) 9.87459e7 0.237753
\(291\) −9.67064e7 − 8.11463e7i −0.230054 − 0.193038i
\(292\) −1.54067e8 + 5.60758e7i −0.362135 + 0.131806i
\(293\) −3.24917e7 + 1.84269e8i −0.0754632 + 0.427973i 0.923547 + 0.383486i \(0.125277\pi\)
−0.999010 + 0.0444873i \(0.985835\pi\)
\(294\) −4.67199e7 − 2.64962e8i −0.107223 − 0.608090i
\(295\) −3.88772e8 −0.881693
\(296\) 4.13069e7 − 1.52248e8i 0.0925767 − 0.341218i
\(297\) 1.75804e8 0.389386
\(298\) 7.64576e7 + 4.33613e8i 0.167365 + 0.949172i
\(299\) −8.01078e6 + 4.54314e7i −0.0173311 + 0.0982895i
\(300\) −1.18934e8 + 4.32884e7i −0.254320 + 0.0925651i
\(301\) 7.12967e8 + 5.98250e8i 1.50691 + 1.26445i
\(302\) 2.38645e8 0.498572
\(303\) −3.13893e7 − 2.63387e7i −0.0648234 − 0.0543933i
\(304\) −9.77739e7 − 1.69349e8i −0.199602 − 0.345721i
\(305\) 7.54428e8 + 2.74589e8i 1.52254 + 0.554159i
\(306\) −6.17750e7 + 1.06997e8i −0.123250 + 0.213476i
\(307\) 6.23020e7 + 1.07910e8i 0.122890 + 0.212852i 0.920906 − 0.389784i \(-0.127450\pi\)
−0.798016 + 0.602636i \(0.794117\pi\)
\(308\) −5.83275e7 − 3.30792e8i −0.113749 − 0.645101i
\(309\) 4.94860e7 − 1.80114e7i 0.0954173 − 0.0347291i
\(310\) −5.76372e8 + 9.98306e8i −1.09885 + 1.90326i
\(311\) −2.58939e8 + 2.17276e8i −0.488131 + 0.409590i −0.853356 − 0.521329i \(-0.825436\pi\)
0.365225 + 0.930919i \(0.380992\pi\)
\(312\) 5.67268e6 − 4.75995e6i 0.0105742 − 0.00887280i
\(313\) −8.20180e8 − 2.98521e8i −1.51183 − 0.550262i −0.552740 − 0.833354i \(-0.686418\pi\)
−0.959093 + 0.283091i \(0.908640\pi\)
\(314\) 8.40231e7 − 4.76518e8i 0.153160 − 0.868612i
\(315\) 2.85162e8 − 1.61724e9i 0.514050 − 2.91532i
\(316\) −4.83583e8 − 1.76010e8i −0.862116 − 0.313785i
\(317\) −6.26772e8 + 5.25924e8i −1.10510 + 0.927290i −0.997758 − 0.0669317i \(-0.978679\pi\)
−0.107344 + 0.994222i \(0.534235\pi\)
\(318\) −562034. + 471602.i −0.000980093 + 0.000822396i
\(319\) 3.90965e7 − 6.77171e7i 0.0674327 − 0.116797i
\(320\) 1.14565e8 − 4.16983e7i 0.195446 − 0.0711367i
\(321\) 2.57647e7 + 1.46119e8i 0.0434768 + 0.246569i
\(322\) 3.25291e8 + 5.63420e8i 0.542971 + 0.940453i
\(323\) −1.85985e8 + 3.22136e8i −0.307093 + 0.531900i
\(324\) −2.09345e8 − 7.61952e7i −0.341943 − 0.124457i
\(325\) 6.98146e7 + 1.20922e8i 0.112812 + 0.195396i
\(326\) −1.66227e8 − 1.39481e8i −0.265730 − 0.222974i
\(327\) −1.25482e8 −0.198456
\(328\) 7.89629e7 + 6.62577e7i 0.123556 + 0.103676i
\(329\) 1.20493e9 − 4.38559e8i 1.86542 − 0.678957i
\(330\) −2.72438e7 + 1.54507e8i −0.0417319 + 0.236674i
\(331\) 1.65892e6 + 9.40818e6i 0.00251435 + 0.0142596i 0.986039 − 0.166514i \(-0.0532510\pi\)
−0.983525 + 0.180773i \(0.942140\pi\)
\(332\) 3.18793e8 0.478107
\(333\) −2.56365e8 − 5.54308e8i −0.380456 − 0.822615i
\(334\) −4.26643e8 −0.626544
\(335\) −1.08248e8 − 6.13903e8i −0.157312 − 0.892160i
\(336\) 1.81343e7 − 1.02845e8i 0.0260804 − 0.147909i
\(337\) 1.06614e9 − 3.88042e8i 1.51743 − 0.552299i 0.556924 − 0.830563i \(-0.311981\pi\)
0.960505 + 0.278264i \(0.0897592\pi\)
\(338\) 3.78287e8 + 3.17421e8i 0.532860 + 0.447123i
\(339\) 1.40777e8 0.196260
\(340\) −1.77655e8 − 1.49070e8i −0.245132 − 0.205690i
\(341\) 4.56407e8 + 7.90520e8i 0.623321 + 1.07962i
\(342\) −7.11387e8 − 2.58924e8i −0.961645 − 0.350010i
\(343\) −1.35941e9 + 2.35457e9i −1.81895 + 3.15052i
\(344\) 1.33751e8 + 2.31664e8i 0.177151 + 0.306834i
\(345\) −5.27674e7 − 2.99259e8i −0.0691829 − 0.392356i
\(346\) 4.51101e8 − 1.64187e8i 0.585473 − 0.213095i
\(347\) −7.70665e8 + 1.33483e9i −0.990176 + 1.71504i −0.373995 + 0.927431i \(0.622012\pi\)
−0.616181 + 0.787604i \(0.711321\pi\)
\(348\) 1.86230e7 − 1.56266e7i 0.0236877 − 0.0198763i
\(349\) 3.64542e7 − 3.05887e7i 0.0459049 − 0.0385188i −0.619547 − 0.784960i \(-0.712684\pi\)
0.665451 + 0.746441i \(0.268239\pi\)
\(350\) 1.85037e9 + 6.73480e8i 2.30686 + 0.839628i
\(351\) 1.04709e7 − 5.93832e7i 0.0129243 − 0.0732975i
\(352\) 1.67643e7 − 9.50753e7i 0.0204874 − 0.116190i
\(353\) −5.36903e8 − 1.95417e8i −0.649658 − 0.236456i −0.00389287 − 0.999992i \(-0.501239\pi\)
−0.645765 + 0.763536i \(0.723461\pi\)
\(354\) −7.33205e7 + 6.15232e7i −0.0878444 + 0.0737102i
\(355\) −1.88677e9 + 1.58319e9i −2.23831 + 1.87817i
\(356\) −5.76401e7 + 9.98357e7i −0.0677096 + 0.117276i
\(357\) −1.86669e8 + 6.79420e7i −0.217137 + 0.0790314i
\(358\) 4.60994e7 + 2.61443e8i 0.0531013 + 0.301152i
\(359\) 2.65652e8 + 4.60123e8i 0.303028 + 0.524860i 0.976820 − 0.214061i \(-0.0686690\pi\)
−0.673792 + 0.738921i \(0.735336\pi\)
\(360\) 2.35996e8 − 4.08757e8i 0.266591 − 0.461749i
\(361\) −1.30180e9 − 4.73816e8i −1.45636 − 0.530072i
\(362\) 2.59107e8 + 4.48786e8i 0.287077 + 0.497232i
\(363\) −1.18487e8 − 9.94222e7i −0.130016 − 0.109096i
\(364\) −1.15209e8 −0.125208
\(365\) −9.12694e8 − 7.65841e8i −0.982427 − 0.824354i
\(366\) 1.85736e8 − 6.76022e7i 0.198021 − 0.0720737i
\(367\) 3.02222e7 − 1.71399e8i 0.0319150 − 0.180999i −0.964683 − 0.263413i \(-0.915152\pi\)
0.996598 + 0.0824139i \(0.0262629\pi\)
\(368\) 3.24702e7 + 1.84147e8i 0.0339639 + 0.192619i
\(369\) 3.99058e8 0.413470
\(370\) 1.10823e9 − 2.93228e8i 1.13743 − 0.300953i
\(371\) 1.14146e7 0.0116052
\(372\) 4.92811e7 + 2.79487e8i 0.0496341 + 0.281489i
\(373\) −6.67251e7 + 3.78417e8i −0.0665745 + 0.377563i 0.933257 + 0.359209i \(0.116954\pi\)
−0.999832 + 0.0183536i \(0.994158\pi\)
\(374\) −1.72567e8 + 6.28092e7i −0.170572 + 0.0620830i
\(375\) −3.06196e8 − 2.56929e8i −0.299840 − 0.251596i
\(376\) 3.68544e8 0.357546
\(377\) −2.05450e7 − 1.72393e7i −0.0197475 − 0.0165701i
\(378\) −4.25186e8 − 7.36444e8i −0.404910 − 0.701324i
\(379\) 2.79050e8 + 1.01566e8i 0.263297 + 0.0958321i 0.470295 − 0.882509i \(-0.344147\pi\)
−0.206999 + 0.978341i \(0.566370\pi\)
\(380\) 7.10510e8 − 1.23064e9i 0.664243 − 1.15050i
\(381\) 6.20020e7 + 1.07391e8i 0.0574339 + 0.0994785i
\(382\) −2.40057e8 − 1.36143e9i −0.220339 − 1.24961i
\(383\) −1.67510e9 + 6.09688e8i −1.52351 + 0.554513i −0.962023 − 0.272970i \(-0.911994\pi\)
−0.561490 + 0.827483i \(0.689772\pi\)
\(384\) 1.50077e7 − 2.59941e7i 0.0135255 − 0.0234269i
\(385\) 1.86984e9 − 1.56898e9i 1.66991 − 1.40122i
\(386\) −8.34389e8 + 7.00135e8i −0.738436 + 0.619621i
\(387\) 9.73153e8 + 3.54199e8i 0.853479 + 0.310641i
\(388\) −9.80252e7 + 5.55928e8i −0.0851974 + 0.483179i
\(389\) −7.62454e7 + 4.32409e8i −0.0656734 + 0.372453i 0.934203 + 0.356742i \(0.116112\pi\)
−0.999877 + 0.0157111i \(0.994999\pi\)
\(390\) 5.05670e7 + 1.84049e7i 0.0431659 + 0.0157111i
\(391\) 2.72473e8 − 2.28632e8i 0.230518 − 0.193428i
\(392\) −9.21620e8 + 7.73331e8i −0.772771 + 0.648432i
\(393\) 2.94431e8 − 5.09969e8i 0.244686 − 0.423809i
\(394\) −5.95098e8 + 2.16598e8i −0.490175 + 0.178409i
\(395\) −6.49385e8 − 3.68285e9i −0.530167 − 3.00672i
\(396\) −1.86876e8 − 3.23679e8i −0.151224 − 0.261927i
\(397\) −5.73479e8 + 9.93295e8i −0.459993 + 0.796731i −0.998960 − 0.0455960i \(-0.985481\pi\)
0.538967 + 0.842327i \(0.318815\pi\)
\(398\) 1.18799e9 + 4.32393e8i 0.944543 + 0.343785i
\(399\) −6.08603e8 − 1.05413e9i −0.479655 − 0.830787i
\(400\) 4.33550e8 + 3.63792e8i 0.338711 + 0.284213i
\(401\) 5.98885e8 0.463808 0.231904 − 0.972739i \(-0.425504\pi\)
0.231904 + 0.972739i \(0.425504\pi\)
\(402\) −1.17565e8 − 9.86490e7i −0.0902585 − 0.0757359i
\(403\) 2.94206e8 − 1.07082e8i 0.223916 − 0.0814987i
\(404\) −3.18173e7 + 1.80445e8i −0.0240065 + 0.136148i
\(405\) −2.81121e8 − 1.59432e9i −0.210281 − 1.19256i
\(406\) −3.78224e8 −0.280484
\(407\) 2.37694e8 − 8.76090e8i 0.174758 − 0.644122i
\(408\) −5.70952e7 −0.0416187
\(409\) −4.48521e7 − 2.54369e8i −0.0324154 − 0.183837i 0.964301 − 0.264809i \(-0.0853088\pi\)
−0.996716 + 0.0809717i \(0.974198\pi\)
\(410\) −1.30073e8 + 7.37679e8i −0.0932058 + 0.528596i
\(411\) 2.07109e8 − 7.53814e7i 0.147147 − 0.0535572i
\(412\) −1.80391e8 − 1.51366e8i −0.127080 − 0.106632i
\(413\) 1.48910e9 1.04016
\(414\) 5.54544e8 + 4.65317e8i 0.384091 + 0.322291i
\(415\) 1.15831e9 + 2.00625e9i 0.795531 + 1.37790i
\(416\) −3.11162e7 − 1.13254e7i −0.0211914 − 0.00771304i
\(417\) −2.27471e8 + 3.93991e8i −0.153621 + 0.266079i
\(418\) −5.62625e8 − 9.74495e8i −0.376792 − 0.652623i
\(419\) 3.42104e8 + 1.94017e9i 0.227200 + 1.28852i 0.858434 + 0.512924i \(0.171438\pi\)
−0.631234 + 0.775592i \(0.717451\pi\)
\(420\) 7.13123e8 − 2.59555e8i 0.469669 − 0.170946i
\(421\) 6.07736e8 − 1.05263e9i 0.396942 − 0.687525i −0.596405 − 0.802684i \(-0.703405\pi\)
0.993347 + 0.115159i \(0.0367379\pi\)
\(422\) −4.44003e8 + 3.72563e8i −0.287603 + 0.241327i
\(423\) 1.09297e9 − 9.17115e8i 0.702132 − 0.589159i
\(424\) 3.08291e6 + 1.12209e6i 0.00196417 + 0.000714900i
\(425\) 1.86944e8 − 1.06021e9i 0.118127 − 0.669933i
\(426\) −1.05296e8 + 5.97165e8i −0.0659902 + 0.374249i
\(427\) −2.88967e9 − 1.05175e9i −1.79618 − 0.653757i
\(428\) 5.08247e8 − 4.26470e8i 0.313344 − 0.262927i
\(429\) 3.26426e7 − 2.73904e7i 0.0199611 − 0.0167493i
\(430\) −9.71953e8 + 1.68347e9i −0.589529 + 1.02110i
\(431\) 1.57884e9 − 5.74651e8i 0.949878 − 0.345727i 0.179819 − 0.983700i \(-0.442449\pi\)
0.770059 + 0.637972i \(0.220227\pi\)
\(432\) −4.24416e7 − 2.40698e8i −0.0253279 − 0.143642i
\(433\) 9.70012e7 + 1.68011e8i 0.0574208 + 0.0994558i 0.893307 − 0.449447i \(-0.148379\pi\)
−0.835886 + 0.548903i \(0.815046\pi\)
\(434\) 2.20767e9 − 3.82379e9i 1.29634 − 2.24533i
\(435\) 1.66008e8 + 6.04219e7i 0.0966978 + 0.0351951i
\(436\) 2.80554e8 + 4.85934e8i 0.162112 + 0.280785i
\(437\) 1.66956e9 + 1.40092e9i 0.957009 + 0.803026i
\(438\) −2.93324e8 −0.166797
\(439\) −2.16847e9 − 1.81956e9i −1.22328 − 1.02646i −0.998646 − 0.0520145i \(-0.983436\pi\)
−0.224637 − 0.974442i \(-0.572120\pi\)
\(440\) 6.59248e8 − 2.39947e8i 0.368948 − 0.134286i
\(441\) −8.08789e8 + 4.58687e9i −0.449056 + 2.54672i
\(442\) 1.09377e7 + 6.20308e7i 0.00602488 + 0.0341688i
\(443\) 1.01789e9 0.556271 0.278136 − 0.960542i \(-0.410284\pi\)
0.278136 + 0.960542i \(0.410284\pi\)
\(444\) 1.62603e8 − 2.30679e8i 0.0881636 − 0.125074i
\(445\) −8.37726e8 −0.450653
\(446\) −3.49910e7 − 1.98444e8i −0.0186760 − 0.105917i
\(447\) −1.36787e8 + 7.75758e8i −0.0724383 + 0.410818i
\(448\) −4.38817e8 + 1.59716e8i −0.230574 + 0.0839220i
\(449\) −1.49692e9 − 1.25606e9i −0.780434 − 0.654862i 0.162924 − 0.986639i \(-0.447908\pi\)
−0.943358 + 0.331777i \(0.892352\pi\)
\(450\) 2.19105e9 1.13347
\(451\) 4.54380e8 + 3.81270e8i 0.233239 + 0.195711i
\(452\) −3.14751e8 − 5.45165e8i −0.160318 − 0.277680i
\(453\) 4.01201e8 + 1.46025e8i 0.202777 + 0.0738047i
\(454\) 7.03506e8 − 1.21851e9i 0.352835 − 0.611129i
\(455\) −4.18605e8 − 7.25046e8i −0.208336 − 0.360849i
\(456\) −6.07501e7 − 3.44531e8i −0.0300034 − 0.170158i
\(457\) −5.55386e8 + 2.02144e8i −0.272200 + 0.0990727i −0.474514 − 0.880248i \(-0.657376\pi\)
0.202314 + 0.979321i \(0.435154\pi\)
\(458\) 2.03392e8 − 3.52285e8i 0.0989246 − 0.171343i
\(459\) −3.56149e8 + 2.98844e8i −0.171904 + 0.144245i
\(460\) −1.04092e9 + 8.73432e8i −0.498612 + 0.418385i
\(461\) −3.16394e9 − 1.15158e9i −1.50410 − 0.547446i −0.546978 − 0.837147i \(-0.684222\pi\)
−0.957117 + 0.289701i \(0.906444\pi\)
\(462\) 1.04351e8 − 5.91806e8i 0.0492324 − 0.279211i
\(463\) 3.57644e8 − 2.02830e9i 0.167462 − 0.949727i −0.779027 − 0.626991i \(-0.784286\pi\)
0.946489 − 0.322736i \(-0.104603\pi\)
\(464\) −1.02152e8 − 3.71803e7i −0.0474717 − 0.0172783i
\(465\) −1.57983e9 + 1.32564e9i −0.728661 + 0.611420i
\(466\) 8.12587e8 − 6.81842e8i 0.371980 − 0.312128i
\(467\) 8.18730e8 − 1.41808e9i 0.371990 − 0.644306i −0.617881 − 0.786271i \(-0.712009\pi\)
0.989872 + 0.141965i \(0.0453421\pi\)
\(468\) −1.20463e8 + 4.38449e7i −0.0543242 + 0.0197724i
\(469\) 4.14619e8 + 2.35142e9i 0.185585 + 1.05251i
\(470\) 1.33908e9 + 2.31935e9i 0.594927 + 1.03044i
\(471\) 4.32835e8 − 7.49692e8i 0.190875 − 0.330605i
\(472\) 4.02183e8 + 1.46383e8i 0.176046 + 0.0640755i
\(473\) 7.69652e8 + 1.33308e9i 0.334411 + 0.579216i
\(474\) −7.05282e8 − 5.91802e8i −0.304186 − 0.255242i
\(475\) 6.59658e9 2.82417
\(476\) 6.80466e8 + 5.70979e8i 0.289189 + 0.242659i
\(477\) 1.19351e7 − 4.34404e6i 0.00503516 − 0.00183265i
\(478\) −3.50477e8 + 1.98766e9i −0.146778 + 0.832422i
\(479\) −2.35253e8 − 1.33419e9i −0.0978049 − 0.554679i −0.993852 − 0.110720i \(-0.964684\pi\)
0.896047 − 0.443960i \(-0.146427\pi\)
\(480\) 2.18118e8 0.0900216
\(481\) −2.81770e8 − 1.32469e8i −0.115448 − 0.0542757i
\(482\) 5.31992e8 0.216392
\(483\) 2.02114e8 + 1.14624e9i 0.0816171 + 0.462874i
\(484\) −1.20103e8 + 6.81135e8i −0.0481497 + 0.273070i
\(485\) −3.85479e9 + 1.40303e9i −1.53428 + 0.558432i
\(486\) −1.10507e9 − 9.27264e8i −0.436679 − 0.366418i
\(487\) −4.23502e9 −1.66151 −0.830757 − 0.556635i \(-0.812092\pi\)
−0.830757 + 0.556635i \(0.812092\pi\)
\(488\) −6.77063e8 − 5.68123e8i −0.263730 − 0.221296i
\(489\) −1.94108e8 − 3.36204e8i −0.0750692 − 0.130024i
\(490\) −8.21544e9 − 2.99018e9i −3.15460 − 1.14818i
\(491\) −1.81514e8 + 3.14392e8i −0.0692030 + 0.119863i −0.898551 − 0.438870i \(-0.855379\pi\)
0.829348 + 0.558733i \(0.188712\pi\)
\(492\) 9.22069e7 + 1.59707e8i 0.0349048 + 0.0604569i
\(493\) 3.59077e7 + 2.03643e8i 0.0134966 + 0.0765428i
\(494\) −3.62676e8 + 1.32003e8i −0.135355 + 0.0492652i
\(495\) 1.35800e9 − 2.35213e9i 0.503248 − 0.871652i
\(496\) 9.72142e8 − 8.15724e8i 0.357721 − 0.300163i
\(497\) 7.22687e9 − 6.06406e9i 2.64060 − 2.21573i
\(498\) 5.35942e8 + 1.95067e8i 0.194453 + 0.0707752i
\(499\) −9.23268e8 + 5.23612e9i −0.332641 + 1.88650i 0.116741 + 0.993162i \(0.462755\pi\)
−0.449382 + 0.893340i \(0.648356\pi\)
\(500\) −3.10371e8 + 1.76020e9i −0.111042 + 0.629750i
\(501\) −7.17256e8 − 2.61060e8i −0.254825 − 0.0927488i
\(502\) 1.34809e9 − 1.13118e9i 0.475616 − 0.399089i
\(503\) −3.15858e8 + 2.65036e8i −0.110663 + 0.0928576i −0.696440 − 0.717615i \(-0.745234\pi\)
0.585777 + 0.810472i \(0.300789\pi\)
\(504\) −9.03930e8 + 1.56565e9i −0.314505 + 0.544739i
\(505\) −1.25120e9 + 4.55399e8i −0.432321 + 0.157352i
\(506\) 1.86845e8 + 1.05965e9i 0.0641142 + 0.363609i
\(507\) 4.41735e8 + 7.65107e8i 0.150534 + 0.260732i
\(508\) 2.77250e8 − 4.80211e8i 0.0938315 − 0.162521i
\(509\) 2.14104e9 + 7.79275e8i 0.719635 + 0.261926i 0.675771 − 0.737112i \(-0.263811\pi\)
0.0438643 + 0.999037i \(0.486033\pi\)
\(510\) −2.07451e8 − 3.59316e8i −0.0692502 − 0.119945i
\(511\) 3.49587e9 + 2.93338e9i 1.15900 + 0.972514i
\(512\) −1.34218e8 −0.0441942
\(513\) −2.18227e9 − 1.83114e9i −0.713671 − 0.598841i
\(514\) −2.93293e9 + 1.06750e9i −0.952645 + 0.346734i
\(515\) 2.97152e8 − 1.68524e9i 0.0958637 − 0.543670i
\(516\) 8.31041e7 + 4.71307e8i 0.0266286 + 0.151018i
\(517\) 2.12073e9 0.674945
\(518\) −4.24482e9 + 1.12314e9i −1.34186 + 0.355043i
\(519\) 8.58839e8 0.269666
\(520\) −4.17847e7 − 2.36973e8i −0.0130318 − 0.0739073i
\(521\) −1.50664e8 + 8.54459e8i −0.0466743 + 0.264703i −0.999211 − 0.0397213i \(-0.987353\pi\)
0.952536 + 0.304424i \(0.0984641\pi\)
\(522\) −3.95471e8 + 1.43940e8i −0.121694 + 0.0442929i
\(523\) −3.35228e9 − 2.81290e9i −1.02467 − 0.859801i −0.0344635 − 0.999406i \(-0.510972\pi\)
−0.990207 + 0.139605i \(0.955417\pi\)
\(524\) −2.63317e9 −0.799502
\(525\) 2.69868e9 + 2.26446e9i 0.813942 + 0.682979i
\(526\) 1.78051e9 + 3.08394e9i 0.533452 + 0.923966i
\(527\) −2.26839e9 − 8.25625e8i −0.675119 − 0.245723i
\(528\) 8.63595e7 − 1.49579e8i 0.0255324 − 0.0442234i
\(529\) 6.60386e8 + 1.14382e9i 0.193956 + 0.335942i
\(530\) 4.13992e6 + 2.34786e7i 0.00120789 + 0.00685026i
\(531\) 1.55701e9 − 5.66704e8i 0.451294 − 0.164258i
\(532\) −2.72145e9 + 4.71369e9i −0.783627 + 1.35728i
\(533\) 1.55849e8 − 1.30773e8i 0.0445819 − 0.0374086i
\(534\) −1.57991e8 + 1.32570e8i −0.0448992 + 0.0376749i
\(535\) 4.53058e9 + 1.64900e9i 1.27913 + 0.465566i
\(536\) −1.19169e8 + 6.75838e8i −0.0334260 + 0.189568i
\(537\) −8.24745e7 + 4.67736e8i −0.0229832 + 0.130344i
\(538\) −2.60968e9 − 9.49844e8i −0.722518 − 0.262975i
\(539\) −5.30332e9 + 4.45002e9i −1.45877 + 1.22405i
\(540\) 1.36058e9 − 1.14166e9i 0.371830 − 0.312003i
\(541\) 7.48909e8 − 1.29715e9i 0.203347 − 0.352208i −0.746258 − 0.665657i \(-0.768151\pi\)
0.949605 + 0.313449i \(0.101485\pi\)
\(542\) 9.34105e8 − 3.39987e8i 0.251999 − 0.0917200i
\(543\) 1.60991e8 + 9.13028e8i 0.0431522 + 0.244728i
\(544\) 1.27654e8 + 2.21104e8i 0.0339969 + 0.0588843i
\(545\) −2.03875e9 + 3.53122e9i −0.539481 + 0.934408i
\(546\) −1.93686e8 − 7.04959e7i −0.0509241 − 0.0185349i
\(547\) −7.76160e8 − 1.34435e9i −0.202766 − 0.351202i 0.746652 − 0.665214i \(-0.231660\pi\)
−0.949419 + 0.314013i \(0.898327\pi\)
\(548\) −7.54975e8 − 6.33499e8i −0.195975 − 0.164442i
\(549\) −3.42170e9 −0.882550
\(550\) 2.49480e9 + 2.09339e9i 0.639391 + 0.536513i
\(551\) −1.19064e9 + 4.33358e8i −0.303214 + 0.110361i
\(552\) −5.80910e7 + 3.29450e8i −0.0147002 + 0.0833687i
\(553\) 2.48733e9 + 1.41063e10i 0.625453 + 3.54712i
\(554\) 3.83594e9 0.958491
\(555\) 2.04254e9 + 1.85154e8i 0.507160 + 0.0459735i
\(556\) 2.03433e9 0.501949
\(557\) −2.34910e8 − 1.33224e9i −0.0575981 − 0.326655i 0.942371 − 0.334571i \(-0.108591\pi\)
−0.999969 + 0.00791588i \(0.997480\pi\)
\(558\) 8.53127e8 − 4.83832e9i 0.207871 − 1.17889i
\(559\) 4.96129e8 − 1.80576e8i 0.120130 − 0.0437239i
\(560\) −2.59955e9 − 2.18128e9i −0.625519 − 0.524873i
\(561\) −3.28546e8 −0.0785644
\(562\) −2.21446e9 − 1.85815e9i −0.526249 − 0.441575i
\(563\) 2.12736e9 + 3.68470e9i 0.502415 + 0.870208i 0.999996 + 0.00279086i \(0.000888359\pi\)
−0.497581 + 0.867417i \(0.665778\pi\)
\(564\) 6.19582e8 + 2.25509e8i 0.145419 + 0.0529283i
\(565\) 2.28726e9 − 3.96164e9i 0.533513 − 0.924072i
\(566\) −7.86403e8 − 1.36209e9i −0.182300 − 0.315754i
\(567\) 1.07677e9 + 6.10667e9i 0.248075 + 1.40690i
\(568\) 2.54797e9 − 9.27386e8i 0.583412 − 0.212345i
\(569\) 3.17703e9 − 5.50278e9i 0.722984 − 1.25225i −0.236814 − 0.971555i \(-0.576103\pi\)
0.959798 − 0.280691i \(-0.0905635\pi\)
\(570\) 1.94750e9 − 1.63415e9i 0.440470 − 0.369598i
\(571\) 3.58307e9 − 3.00655e9i 0.805431 − 0.675837i −0.144081 − 0.989566i \(-0.546023\pi\)
0.949513 + 0.313729i \(0.101578\pi\)
\(572\) −1.79053e8 − 6.51701e7i −0.0400033 − 0.0145600i
\(573\) 4.29475e8 − 2.43567e9i 0.0953666 − 0.540851i
\(574\) 4.98215e8 − 2.82552e9i 0.109958 − 0.623600i
\(575\) −5.92742e9 − 2.15741e9i −1.30025 − 0.473254i
\(576\) −3.98044e8 + 3.33999e8i −0.0867866 + 0.0728226i
\(577\) −1.16988e8 + 9.81646e7i −0.0253528 + 0.0212735i −0.655376 − 0.755303i \(-0.727490\pi\)
0.630023 + 0.776576i \(0.283045\pi\)
\(578\) −1.39853e9 + 2.42233e9i −0.301248 + 0.521777i
\(579\) −1.83115e9 + 6.66485e8i −0.392057 + 0.142697i
\(580\) −1.37176e8 − 7.77965e8i −0.0291932 − 0.165563i
\(581\) −4.43665e9 − 7.68451e9i −0.938511 − 1.62555i
\(582\) −5.04965e8 + 8.74625e8i −0.106177 + 0.183904i
\(583\) 1.77401e7 + 6.45687e6i 0.00370780 + 0.00134953i
\(584\) 6.55819e8 + 1.13591e9i 0.136251 + 0.235993i
\(585\) −7.13623e8 − 5.98801e8i −0.147375 − 0.123662i
\(586\) 1.49690e9 0.307291
\(587\) −9.37655e8 − 7.86786e8i −0.191342 − 0.160555i 0.542084 − 0.840324i \(-0.317635\pi\)
−0.733426 + 0.679769i \(0.762080\pi\)
\(588\) −2.02259e9 + 7.36162e8i −0.410286 + 0.149332i
\(589\) 2.56850e9 − 1.45667e10i 0.517935 − 2.93736i
\(590\) 5.40076e8 + 3.06292e9i 0.108261 + 0.613980i
\(591\) −1.13299e9 −0.225772
\(592\) −1.25687e9 − 1.13934e8i −0.248979 − 0.0225697i
\(593\) −6.41867e9 −1.26402 −0.632010 − 0.774960i \(-0.717770\pi\)
−0.632010 + 0.774960i \(0.717770\pi\)
\(594\) −2.44224e8 − 1.38506e9i −0.0478119 − 0.271155i
\(595\) −1.12091e9 + 6.35699e9i −0.218153 + 1.23721i
\(596\) 3.30999e9 − 1.20474e9i 0.640419 − 0.233094i
\(597\) 1.73263e9 + 1.45385e9i 0.333269 + 0.279646i
\(598\) 3.69058e8 0.0705733
\(599\) 4.85169e9 + 4.07106e9i 0.922358 + 0.773950i 0.974430 − 0.224693i \(-0.0721379\pi\)
−0.0520714 + 0.998643i \(0.516582\pi\)
\(600\) 5.06267e8 + 8.76880e8i 0.0956864 + 0.165734i
\(601\) 6.28186e9 + 2.28641e9i 1.18040 + 0.429629i 0.856342 − 0.516409i \(-0.172732\pi\)
0.324054 + 0.946038i \(0.394954\pi\)
\(602\) 3.72285e9 − 6.44816e9i 0.695485 − 1.20462i
\(603\) 1.32840e9 + 2.30085e9i 0.246728 + 0.427345i
\(604\) −3.31522e8 − 1.88016e9i −0.0612186 − 0.347188i
\(605\) −4.72297e9 + 1.71902e9i −0.867104 + 0.315600i
\(606\) −1.63903e8 + 2.83889e8i −0.0299180 + 0.0518196i
\(607\) −1.35551e8 + 1.13741e8i −0.0246004 + 0.0206422i −0.655005 − 0.755625i \(-0.727333\pi\)
0.630405 + 0.776267i \(0.282889\pi\)
\(608\) −1.19839e9 + 1.00557e9i −0.216239 + 0.181446i
\(609\) −6.35857e8 − 2.31433e8i −0.114077 − 0.0415207i
\(610\) 1.11530e9 − 6.32519e9i 0.198947 − 1.12829i
\(611\) 1.26311e8 − 7.16343e8i 0.0224024 − 0.127051i
\(612\) 9.28792e8 + 3.38053e8i 0.163790 + 0.0596148i
\(613\) 3.80419e9 − 3.19210e9i 0.667039 − 0.559712i −0.245148 − 0.969486i \(-0.578837\pi\)
0.912187 + 0.409774i \(0.134392\pi\)
\(614\) 7.63618e8 − 6.40752e8i 0.133133 − 0.111712i
\(615\) −6.70055e8 + 1.16057e9i −0.116158 + 0.201191i
\(616\) −2.52510e9 + 9.19063e8i −0.435258 + 0.158421i
\(617\) 4.08408e8 + 2.31620e9i 0.0699998 + 0.396988i 0.999596 + 0.0284098i \(0.00904435\pi\)
−0.929597 + 0.368579i \(0.879845\pi\)
\(618\) −2.10647e8 − 3.64852e8i −0.0359002 − 0.0621809i
\(619\) 1.93024e9 − 3.34327e9i 0.327110 − 0.566571i −0.654827 − 0.755779i \(-0.727259\pi\)
0.981937 + 0.189207i \(0.0605918\pi\)
\(620\) 8.66580e9 + 3.15409e9i 1.46029 + 0.531501i
\(621\) 1.36203e9 + 2.35910e9i 0.228226 + 0.395300i
\(622\) 2.07151e9 + 1.73821e9i 0.345161 + 0.289624i
\(623\) 3.20872e9 0.531648
\(624\) −4.53815e7 − 3.80796e7i −0.00747709 − 0.00627402i
\(625\) −2.06136e9 + 7.50275e8i −0.337734 + 0.122925i
\(626\) −1.21250e9 + 6.87646e9i −0.197548 + 1.12035i
\(627\) −3.49577e8 − 1.98255e9i −0.0566379 − 0.321209i
\(628\) −3.87096e9 −0.623677
\(629\) 1.00771e9 + 2.17886e9i 0.161458 + 0.349102i
\(630\) −1.31375e10 −2.09324
\(631\) −3.94173e8 − 2.23547e9i −0.0624575 − 0.354214i −0.999980 − 0.00628992i \(-0.997998\pi\)
0.937523 − 0.347924i \(-0.113113\pi\)
\(632\) −7.14900e8 + 4.05440e9i −0.112651 + 0.638876i
\(633\) −9.74411e8 + 3.54657e8i −0.152697 + 0.0555770i
\(634\) 5.01418e9 + 4.20739e9i 0.781425 + 0.655693i
\(635\) 4.02948e9 0.624512
\(636\) 4.49627e6 + 3.77282e6i 0.000693031 + 0.000581522i
\(637\) 1.18727e9 + 2.05641e9i 0.181995 + 0.315225i
\(638\) −5.87819e8 − 2.13949e8i −0.0896131 − 0.0326165i
\(639\) 5.24863e9 − 9.09090e9i 0.795780 − 1.37833i
\(640\) −4.87671e8 − 8.44671e8i −0.0735355 − 0.127367i
\(641\) −2.01823e8 − 1.14459e9i −0.0302668 − 0.171652i 0.965927 − 0.258813i \(-0.0833315\pi\)
−0.996194 + 0.0871616i \(0.972220\pi\)
\(642\) 1.11540e9 − 4.05972e8i 0.166363 − 0.0605514i
\(643\) 2.33293e8 − 4.04075e8i 0.0346069 − 0.0599409i −0.848203 − 0.529671i \(-0.822315\pi\)
0.882810 + 0.469730i \(0.155649\pi\)
\(644\) 3.98700e9 − 3.34549e9i 0.588227 − 0.493581i
\(645\) −2.66412e9 + 2.23546e9i −0.390926 + 0.328026i
\(646\) 2.79630e9 + 1.01777e9i 0.408103 + 0.148537i
\(647\) 2.20999e9 − 1.25335e10i 0.320794 − 1.81931i −0.216926 − 0.976188i \(-0.569603\pi\)
0.537720 − 0.843123i \(-0.319286\pi\)
\(648\) −3.09482e8 + 1.75516e9i −0.0446811 + 0.253399i
\(649\) 2.31430e9 + 8.42336e8i 0.332325 + 0.120956i
\(650\) 8.55697e8 − 7.18015e8i 0.122215 − 0.102550i
\(651\) 6.05120e9 − 5.07756e9i 0.859623 − 0.721309i
\(652\) −8.67978e8 + 1.50338e9i −0.122643 + 0.212424i
\(653\) −7.63756e9 + 2.77984e9i −1.07339 + 0.390683i −0.817444 − 0.576008i \(-0.804610\pi\)
−0.255948 + 0.966691i \(0.582388\pi\)
\(654\) 1.74317e8 + 9.88604e8i 0.0243679 + 0.138197i
\(655\) −9.56745e9 − 1.65713e10i −1.33031 − 2.30416i
\(656\) 4.12315e8 − 7.14151e8i 0.0570251 − 0.0987703i
\(657\) 4.77164e9 + 1.73673e9i 0.656430 + 0.238921i
\(658\) −5.12904e9 − 8.88376e9i −0.701852 − 1.21564i
\(659\) −4.28910e9 − 3.59898e9i −0.583804 − 0.489870i 0.302390 − 0.953184i \(-0.402216\pi\)
−0.886194 + 0.463314i \(0.846660\pi\)
\(660\) 1.25513e9 0.169935
\(661\) −8.65471e9 − 7.26216e9i −1.16559 − 0.978049i −0.165627 − 0.986188i \(-0.552965\pi\)
−0.999967 + 0.00813908i \(0.997409\pi\)
\(662\) 7.18174e7 − 2.61394e7i 0.00962115 − 0.00350181i
\(663\) −1.95682e7 + 1.10977e8i −0.00260767 + 0.0147888i
\(664\) −4.42862e8 − 2.51159e9i −0.0587057 − 0.332936i
\(665\) −3.95528e10 −5.21557
\(666\) −4.01096e9 + 2.78980e9i −0.526124 + 0.365943i
\(667\) 1.21159e9 0.158094
\(668\) 5.92686e8 + 3.36129e9i 0.0769320 + 0.436303i
\(669\) 6.26009e7 − 3.55028e8i 0.00808331 − 0.0458427i
\(670\) −4.68624e9 + 1.70565e9i −0.601953 + 0.219093i
\(671\) −3.89606e9 − 3.26918e9i −0.497848 − 0.417744i
\(672\) −8.35452e8 −0.106201
\(673\) −9.86925e9 − 8.28129e9i −1.24805 − 1.04724i −0.996851 − 0.0793017i \(-0.974731\pi\)
−0.251198 − 0.967936i \(-0.580825\pi\)
\(674\) −4.53824e9 − 7.86046e9i −0.570923 − 0.988868i
\(675\) 7.74771e9 + 2.81994e9i 0.969640 + 0.352920i
\(676\) 1.97527e9 − 3.42128e9i 0.245931 − 0.425966i
\(677\) 6.73782e9 + 1.16703e10i 0.834563 + 1.44551i 0.894386 + 0.447297i \(0.147613\pi\)
−0.0598222 + 0.998209i \(0.519053\pi\)
\(678\) −1.95565e8 − 1.10911e9i −0.0240984 − 0.136669i
\(679\) 1.47649e10 − 5.37399e9i 1.81003 − 0.658798i
\(680\) −9.27646e8 + 1.60673e9i −0.113136 + 0.195957i
\(681\) 1.92831e9 − 1.61804e9i 0.233970 − 0.196324i
\(682\) 5.59405e9 − 4.69396e9i 0.675275 − 0.566623i
\(683\) −1.11846e9 − 4.07087e8i −0.134323 − 0.0488894i 0.273984 − 0.961734i \(-0.411658\pi\)
−0.408307 + 0.912845i \(0.633881\pi\)
\(684\) −1.05167e9 + 5.96433e9i −0.125656 + 0.712632i
\(685\) 1.24364e9 − 7.05305e9i 0.147835 − 0.838417i
\(686\) 2.04388e10 + 7.43913e9i 2.41725 + 0.879808i
\(687\) 5.57496e8 − 4.67795e8i 0.0655984 − 0.0550436i
\(688\) 1.63935e9 − 1.37558e9i 0.191917 − 0.161037i
\(689\) 3.23761e6 − 5.60771e6i 0.000377101 − 0.000653158i
\(690\) −2.28440e9 + 8.31452e8i −0.264728 + 0.0963530i
\(691\) 1.75605e9 + 9.95907e9i 0.202472 + 1.14827i 0.901369 + 0.433052i \(0.142563\pi\)
−0.698897 + 0.715222i \(0.746326\pi\)
\(692\) −1.92021e9 − 3.32589e9i −0.220281 − 0.381537i
\(693\) −5.20153e9 + 9.00931e9i −0.593697 + 1.02831i
\(694\) 1.15870e10 + 4.21733e9i 1.31587 + 0.478938i
\(695\) 7.39160e9 + 1.28026e10i 0.835202 + 1.44661i
\(696\) −1.48984e8 − 1.25012e8i −0.0167497 − 0.0140547i
\(697\) −1.56861e9 −0.175469
\(698\) −2.91634e8 − 2.44710e8i −0.0324597 − 0.0272369i
\(699\) 1.78331e9 − 6.49070e8i 0.197495 − 0.0718822i
\(700\) 2.73548e9 − 1.55137e10i 0.301433 − 1.70951i
\(701\) 2.00478e9 + 1.13697e10i 0.219813 + 1.24662i 0.872357 + 0.488870i \(0.162591\pi\)
−0.652544 + 0.757751i \(0.726298\pi\)
\(702\) −4.82395e8 −0.0526287
\(703\) −1.20757e10 + 8.39922e9i −1.31090 + 0.911791i
\(704\) −7.72336e8 −0.0834261
\(705\) 8.32013e8 + 4.71858e9i 0.0894269 + 0.507165i
\(706\) −7.93726e8 + 4.50144e9i −0.0848895 + 0.481432i
\(707\) 4.79244e9 − 1.74430e9i 0.510022 − 0.185633i
\(708\) 5.86564e8 + 4.92186e8i 0.0621154 + 0.0521210i
\(709\) 2.07355e8 0.0218501 0.0109250 − 0.999940i \(-0.496522\pi\)
0.0109250 + 0.999940i \(0.496522\pi\)
\(710\) 1.50942e10 + 1.26655e10i 1.58273 + 1.32806i
\(711\) 7.96916e9 + 1.38030e10i 0.831512 + 1.44022i
\(712\) 8.66624e8 + 3.15425e8i 0.0899810 + 0.0327504i
\(713\) −7.07197e9 + 1.22490e10i −0.730680 + 1.26557i
\(714\) 7.94597e8 + 1.37628e9i 0.0816964 + 0.141502i
\(715\) −2.40444e8 − 1.36363e9i −0.0246004 − 0.139516i
\(716\) 1.99573e9 − 7.26385e8i 0.203192 − 0.0739557i
\(717\) −1.80544e9 + 3.12712e9i −0.182922 + 0.316831i
\(718\) 3.25602e9 − 2.73213e9i 0.328286 − 0.275465i
\(719\) 8.41483e9 − 7.06088e9i 0.844295 − 0.708448i −0.114230 − 0.993454i \(-0.536440\pi\)
0.958526 + 0.285007i \(0.0919958\pi\)
\(720\) −3.54822e9 − 1.29145e9i −0.354280 − 0.128947i
\(721\) −1.13818e9 + 6.45492e9i −0.113093 + 0.641383i
\(722\) −1.92450e9 + 1.09144e10i −0.190300 + 1.07924i
\(723\) 8.94366e8 + 3.25522e8i 0.0880098 + 0.0320329i
\(724\) 3.17579e9 − 2.66481e9i 0.311005 − 0.260964i
\(725\) 2.80919e9 − 2.35719e9i 0.273778 − 0.229727i
\(726\) −6.18694e8 + 1.07161e9i −0.0600064 + 0.103934i
\(727\) −8.72406e9 + 3.17530e9i −0.842070 + 0.306488i −0.726803 − 0.686846i \(-0.758995\pi\)
−0.115267 + 0.993335i \(0.536772\pi\)
\(728\) 1.60047e8 + 9.07673e8i 0.0153740 + 0.0871906i
\(729\) 2.51599e9 + 4.35781e9i 0.240526 + 0.416603i
\(730\) −4.76575e9 + 8.25452e9i −0.453421 + 0.785347i
\(731\) −3.82525e9 − 1.39228e9i −0.362200 − 0.131830i
\(732\) −7.90622e8 − 1.36940e9i −0.0745041 − 0.129045i
\(733\) −1.15832e10 − 9.71943e9i −1.08633 − 0.911543i −0.0899031 − 0.995951i \(-0.528656\pi\)
−0.996431 + 0.0844078i \(0.973100\pi\)
\(734\) −1.39234e9 −0.129960
\(735\) −1.19818e10 − 1.00539e10i −1.11306 − 0.933966i
\(736\) 1.40569e9 − 5.11630e8i 0.129962 − 0.0473025i
\(737\) −6.85737e8 + 3.88901e9i −0.0630988 + 0.357851i
\(738\) −5.54366e8 − 3.14397e9i −0.0507691 − 0.287926i
\(739\) 1.17834e10 1.07402 0.537011 − 0.843575i \(-0.319553\pi\)
0.537011 + 0.843575i \(0.319553\pi\)
\(740\) −3.84972e9 − 8.32379e9i −0.349235 − 0.755110i
\(741\) −6.90490e8 −0.0623438
\(742\) −1.58570e7 − 8.99297e7i −0.00142498 − 0.00808146i
\(743\) −3.39970e8 + 1.92806e9i −0.0304074 + 0.172449i −0.996230 − 0.0867568i \(-0.972350\pi\)
0.965822 + 0.259206i \(0.0834608\pi\)
\(744\) 2.13347e9 − 7.76518e8i 0.189924 − 0.0691268i
\(745\) 1.96084e10 + 1.64534e10i 1.73738 + 1.45783i
\(746\) 3.07403e9 0.271096
\(747\) −7.56344e9 − 6.34648e9i −0.663892 − 0.557071i
\(748\) 7.34567e8 + 1.27231e9i 0.0641765 + 0.111157i
\(749\) −1.73534e10 − 6.31611e9i −1.50903 − 0.549242i
\(750\) −1.59884e9 + 2.76928e9i −0.138386 + 0.239691i
\(751\) 3.76466e9 + 6.52058e9i 0.324329 + 0.561754i 0.981376 − 0.192095i \(-0.0615282\pi\)
−0.657047 + 0.753849i \(0.728195\pi\)
\(752\) −5.11975e8 − 2.90356e9i −0.0439022 − 0.248982i
\(753\) 2.95852e9 − 1.07681e9i 0.252518 − 0.0919091i
\(754\) −1.07278e8 + 1.85812e8i −0.00911407 + 0.0157860i
\(755\) 1.06278e10 − 8.91778e9i 0.898729 − 0.754123i
\(756\) −5.21139e9 + 4.37287e9i −0.438659 + 0.368079i
\(757\) −3.68559e9 − 1.34144e9i −0.308796 − 0.112392i 0.182974 − 0.983118i \(-0.441428\pi\)