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Properties

Label 74.8.f.b.7.5
Level $74$
Weight $8$
Character 74.7
Analytic conductor $23.116$
Analytic rank $0$
Dimension $66$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [74,8,Mod(7,74)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(74, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("74.7");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 74.f (of order \(9\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(23.1164918858\)
Analytic rank: \(0\)
Dimension: \(66\)
Relative dimension: \(11\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 7.5
Character \(\chi\) \(=\) 74.7
Dual form 74.8.f.b.53.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(7.51754 - 2.73616i) q^{2} +(-19.5402 - 7.11207i) q^{3} +(49.0268 - 41.1384i) q^{4} +(69.5532 + 394.456i) q^{5} -166.354 q^{6} +(-65.8495 - 373.451i) q^{7} +(256.000 - 443.405i) q^{8} +(-1344.10 - 1127.83i) q^{9} +O(q^{10})\) \(q+(7.51754 - 2.73616i) q^{2} +(-19.5402 - 7.11207i) q^{3} +(49.0268 - 41.1384i) q^{4} +(69.5532 + 394.456i) q^{5} -166.354 q^{6} +(-65.8495 - 373.451i) q^{7} +(256.000 - 443.405i) q^{8} +(-1344.10 - 1127.83i) q^{9} +(1602.16 + 2775.03i) q^{10} +(-2613.11 + 4526.04i) q^{11} +(-1250.58 + 455.172i) q^{12} +(1585.75 - 1330.61i) q^{13} +(-1516.85 - 2627.26i) q^{14} +(1446.31 - 8202.43i) q^{15} +(711.263 - 4033.77i) q^{16} +(-24229.4 - 20330.9i) q^{17} +(-13190.3 - 4800.86i) q^{18} +(-26014.3 - 9468.44i) q^{19} +(19637.3 + 16477.6i) q^{20} +(-1369.29 + 7765.65i) q^{21} +(-7260.19 + 41174.6i) q^{22} +(15526.8 + 26893.3i) q^{23} +(-8155.83 + 6843.55i) q^{24} +(-77344.4 + 28151.1i) q^{25} +(8280.22 - 14341.8i) q^{26} +(40981.4 + 70981.8i) q^{27} +(-18591.6 - 15600.2i) q^{28} +(-127626. + 221054. i) q^{29} +(-11570.5 - 65619.5i) q^{30} -290895. q^{31} +(-5690.10 - 32270.2i) q^{32} +(83250.3 - 69855.3i) q^{33} +(-237774. - 86542.6i) q^{34} +(142730. - 51949.5i) q^{35} -112294. q^{36} +(287351. - 111180. i) q^{37} -221471. q^{38} +(-40449.4 + 14722.4i) q^{39} +(192709. + 70140.5i) q^{40} +(-376589. + 315996. i) q^{41} +(10954.3 + 62125.2i) q^{42} -240092. q^{43} +(58081.5 + 329397. i) q^{44} +(351394. - 608633. i) q^{45} +(190308. + 159687. i) q^{46} +(-196561. - 340454. i) q^{47} +(-42586.7 + 73762.3i) q^{48} +(638748. - 232485. i) q^{49} +(-504414. + 423254. i) q^{50} +(328853. + 569591. i) q^{51} +(23005.5 - 130471. i) q^{52} +(-148522. + 842309. i) q^{53} +(502297. + 421477. i) q^{54} +(-1.96707e6 - 715956. i) q^{55} +(-182448. - 66405.5i) q^{56} +(440986. + 370031. i) q^{57} +(-354592. + 2.01099e6i) q^{58} +(163523. - 927386. i) q^{59} +(-266527. - 461638. i) q^{60} +(1.02383e6 - 859095. i) q^{61} +(-2.18682e6 + 795937. i) q^{62} +(-332682. + 576223. i) q^{63} +(-131072. - 227023. i) q^{64} +(635160. + 532963. i) q^{65} +(434702. - 752926. i) q^{66} +(-668754. - 3.79269e6i) q^{67} -2.02427e6 q^{68} +(-112131. - 635929. i) q^{69} +(930836. - 781064. i) q^{70} +(-2.35061e6 - 855551. i) q^{71} +(-844177. + 307255. i) q^{72} +5.32491e6 q^{73} +(1.85597e6 - 1.62204e6i) q^{74} +1.71154e6 q^{75} +(-1.66492e6 + 605980. i) q^{76} +(1.86233e6 + 677831. i) q^{77} +(-263797. + 221352. i) q^{78} +(-192573. - 1.09214e6i) q^{79} +1.64062e6 q^{80} +(370383. + 2.10054e6i) q^{81} +(-1.96641e6 + 3.40592e6i) q^{82} +(7.07888e6 + 5.93989e6i) q^{83} +(252334. + 437056. i) q^{84} +(6.33440e6 - 1.09715e7i) q^{85} +(-1.80490e6 + 656930. i) q^{86} +(4.06599e6 - 3.41177e6i) q^{87} +(1.33791e6 + 2.31733e6i) q^{88} +(-2.16712e6 + 1.22903e7i) q^{89} +(976304. - 5.53689e6i) q^{90} +(-601337. - 504582. i) q^{91} +(1.86758e6 + 679743. i) q^{92} +(5.68417e6 + 2.06887e6i) q^{93} +(-2.40919e6 - 2.02155e6i) q^{94} +(1.92550e6 - 1.09201e7i) q^{95} +(-118322. + 671035. i) q^{96} +(-749774. - 1.29865e6i) q^{97} +(4.16570e6 - 3.49543e6i) q^{98} +(8.61690e6 - 3.13630e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 66 q - 39 q^{3} + 459 q^{5} - 918 q^{7} + 16896 q^{8} + 3237 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 66 q - 39 q^{3} + 459 q^{5} - 918 q^{7} + 16896 q^{8} + 3237 q^{9} + 4704 q^{10} + 4539 q^{11} - 2496 q^{12} - 10542 q^{13} + 6744 q^{14} - 39894 q^{15} - 78822 q^{17} + 51792 q^{18} + 79461 q^{19} + 29376 q^{20} - 5835 q^{21} + 18168 q^{22} - 199479 q^{23} + 19968 q^{24} + 356301 q^{25} + 186744 q^{26} - 91689 q^{27} - 91584 q^{28} - 38526 q^{29} + 319152 q^{30} + 1917246 q^{31} - 902847 q^{33} - 205776 q^{34} - 1574793 q^{35} + 3079296 q^{36} - 396513 q^{37} - 692880 q^{38} + 2514306 q^{39} + 470016 q^{40} + 2989350 q^{41} + 46680 q^{42} + 6006348 q^{43} - 145344 q^{44} + 1083726 q^{45} - 588744 q^{46} - 894135 q^{47} + 7973742 q^{49} + 2012400 q^{50} - 524880 q^{51} - 2262720 q^{52} + 1457844 q^{53} + 1452312 q^{54} + 2415690 q^{55} - 1202688 q^{56} + 2734338 q^{57} - 3423360 q^{58} + 3099522 q^{59} - 3102912 q^{60} - 10968396 q^{61} - 3067320 q^{62} - 10727970 q^{63} - 8650752 q^{64} - 13497300 q^{65} - 4598712 q^{66} - 1978119 q^{67} + 5026176 q^{68} - 7251108 q^{69} + 435744 q^{70} - 19555002 q^{71} + 3314688 q^{72} - 31332840 q^{73} + 7607472 q^{74} + 44758074 q^{75} + 5085504 q^{76} + 1982007 q^{77} - 22512264 q^{78} + 10522902 q^{79} + 4816896 q^{80} - 7548876 q^{81} - 7150320 q^{82} + 19771926 q^{83} + 3556224 q^{84} - 6684072 q^{85} + 22982496 q^{86} - 67769667 q^{87} - 2323968 q^{88} - 42018963 q^{89} - 25158672 q^{90} + 4847565 q^{91} - 1096704 q^{92} - 14558475 q^{93} + 3175680 q^{94} + 4508415 q^{95} - 2555904 q^{96} - 39286662 q^{97} + 71630904 q^{98} + 66155463 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.51754 − 2.73616i 0.664463 − 0.241845i
\(3\) −19.5402 − 7.11207i −0.417836 − 0.152080i 0.124542 − 0.992214i \(-0.460254\pi\)
−0.542378 + 0.840135i \(0.682476\pi\)
\(4\) 49.0268 − 41.1384i 0.383022 − 0.321394i
\(5\) 69.5532 + 394.456i 0.248841 + 1.41125i 0.811400 + 0.584491i \(0.198706\pi\)
−0.562559 + 0.826757i \(0.690183\pi\)
\(6\) −166.354 −0.314416
\(7\) −65.8495 − 373.451i −0.0725620 − 0.411520i −0.999354 − 0.0359441i \(-0.988556\pi\)
0.926792 − 0.375576i \(-0.122555\pi\)
\(8\) 256.000 − 443.405i 0.176777 − 0.306186i
\(9\) −1344.10 − 1127.83i −0.614586 − 0.515699i
\(10\) 1602.16 + 2775.03i 0.506649 + 0.877542i
\(11\) −2613.11 + 4526.04i −0.591948 + 1.02528i 0.402022 + 0.915630i \(0.368307\pi\)
−0.993970 + 0.109654i \(0.965026\pi\)
\(12\) −1250.58 + 455.172i −0.208918 + 0.0760399i
\(13\) 1585.75 − 1330.61i 0.200186 − 0.167976i −0.537184 − 0.843465i \(-0.680512\pi\)
0.737370 + 0.675489i \(0.236067\pi\)
\(14\) −1516.85 − 2627.26i −0.147739 − 0.255891i
\(15\) 1446.31 − 8202.43i 0.110648 − 0.627514i
\(16\) 711.263 − 4033.77i 0.0434120 − 0.246202i
\(17\) −24229.4 − 20330.9i −1.19611 − 1.00366i −0.999733 − 0.0231267i \(-0.992638\pi\)
−0.196377 − 0.980528i \(-0.562918\pi\)
\(18\) −13190.3 − 4800.86i −0.533089 − 0.194028i
\(19\) −26014.3 − 9468.44i −0.870112 − 0.316695i −0.131899 − 0.991263i \(-0.542108\pi\)
−0.738212 + 0.674568i \(0.764330\pi\)
\(20\) 19637.3 + 16477.6i 0.548878 + 0.460564i
\(21\) −1369.29 + 7765.65i −0.0322648 + 0.182983i
\(22\) −7260.19 + 41174.6i −0.145368 + 0.824422i
\(23\) 15526.8 + 26893.3i 0.266094 + 0.460889i 0.967850 − 0.251529i \(-0.0809334\pi\)
−0.701756 + 0.712418i \(0.747600\pi\)
\(24\) −8155.83 + 6843.55i −0.120428 + 0.101051i
\(25\) −77344.4 + 28151.1i −0.990009 + 0.360334i
\(26\) 8280.22 − 14341.8i 0.0923922 − 0.160028i
\(27\) 40981.4 + 70981.8i 0.400694 + 0.694023i
\(28\) −18591.6 − 15600.2i −0.160053 − 0.134300i
\(29\) −127626. + 221054.i −0.971729 + 1.68308i −0.281397 + 0.959591i \(0.590798\pi\)
−0.690332 + 0.723493i \(0.742536\pi\)
\(30\) −11570.5 − 65619.5i −0.0782397 − 0.443719i
\(31\) −290895. −1.75376 −0.876882 − 0.480706i \(-0.840380\pi\)
−0.876882 + 0.480706i \(0.840380\pi\)
\(32\) −5690.10 − 32270.2i −0.0306970 − 0.174091i
\(33\) 83250.3 − 69855.3i 0.403262 − 0.338377i
\(34\) −237774. − 86542.6i −1.03750 − 0.377619i
\(35\) 142730. − 51949.5i 0.562700 − 0.204806i
\(36\) −112294. −0.401143
\(37\) 287351. − 111180.i 0.932625 − 0.360846i
\(38\) −221471. −0.654748
\(39\) −40449.4 + 14722.4i −0.109191 + 0.0397422i
\(40\) 192709. + 70140.5i 0.476094 + 0.173284i
\(41\) −376589. + 315996.i −0.853345 + 0.716041i −0.960524 − 0.278199i \(-0.910263\pi\)
0.107179 + 0.994240i \(0.465818\pi\)
\(42\) 10954.3 + 62125.2i 0.0228147 + 0.129388i
\(43\) −240092. −0.460509 −0.230254 − 0.973130i \(-0.573956\pi\)
−0.230254 + 0.973130i \(0.573956\pi\)
\(44\) 58081.5 + 329397.i 0.102791 + 0.582955i
\(45\) 351394. − 608633.i 0.574845 − 0.995661i
\(46\) 190308. + 159687.i 0.288273 + 0.241890i
\(47\) −196561. − 340454.i −0.276157 − 0.478317i 0.694270 − 0.719715i \(-0.255728\pi\)
−0.970426 + 0.241398i \(0.922394\pi\)
\(48\) −42586.7 + 73762.3i −0.0555814 + 0.0962699i
\(49\) 638748. − 232485.i 0.775609 − 0.282299i
\(50\) −504414. + 423254.i −0.570679 + 0.478857i
\(51\) 328853. + 569591.i 0.347142 + 0.601267i
\(52\) 23005.5 − 130471.i 0.0226893 − 0.128677i
\(53\) −148522. + 842309.i −0.137033 + 0.777152i 0.836390 + 0.548135i \(0.184662\pi\)
−0.973422 + 0.229017i \(0.926449\pi\)
\(54\) 502297. + 421477.i 0.434092 + 0.364247i
\(55\) −1.96707e6 − 715956.i −1.59423 − 0.580253i
\(56\) −182448. − 66405.5i −0.138829 − 0.0505296i
\(57\) 440986. + 370031.i 0.315401 + 0.264653i
\(58\) −354592. + 2.01099e6i −0.238633 + 1.35335i
\(59\) 163523. − 927386.i 0.103657 − 0.587866i −0.888092 − 0.459666i \(-0.847969\pi\)
0.991748 − 0.128200i \(-0.0409199\pi\)
\(60\) −266527. − 461638.i −0.159299 − 0.275913i
\(61\) 1.02383e6 − 859095.i 0.577528 − 0.484604i −0.306606 − 0.951836i \(-0.599193\pi\)
0.884134 + 0.467233i \(0.154749\pi\)
\(62\) −2.18682e6 + 795937.i −1.16531 + 0.424138i
\(63\) −332682. + 576223.i −0.167625 + 0.290334i
\(64\) −131072. − 227023.i −0.0625000 − 0.108253i
\(65\) 635160. + 532963.i 0.286871 + 0.240713i
\(66\) 434702. − 752926.i 0.186118 − 0.322366i
\(67\) −668754. − 3.79269e6i −0.271647 − 1.54059i −0.749415 − 0.662100i \(-0.769665\pi\)
0.477768 − 0.878486i \(-0.341446\pi\)
\(68\) −2.02427e6 −0.780705
\(69\) −112131. − 635929.i −0.0410918 − 0.233043i
\(70\) 930836. − 781064.i 0.324362 − 0.272172i
\(71\) −2.35061e6 − 855551.i −0.779428 − 0.283689i −0.0784938 − 0.996915i \(-0.525011\pi\)
−0.700934 + 0.713226i \(0.747233\pi\)
\(72\) −844177. + 307255.i −0.266544 + 0.0970142i
\(73\) 5.32491e6 1.60207 0.801037 − 0.598615i \(-0.204282\pi\)
0.801037 + 0.598615i \(0.204282\pi\)
\(74\) 1.85597e6 − 1.62204e6i 0.532426 − 0.465319i
\(75\) 1.71154e6 0.468460
\(76\) −1.66492e6 + 605980.i −0.435056 + 0.158347i
\(77\) 1.86233e6 + 677831.i 0.464877 + 0.169201i
\(78\) −263797. + 221352.i −0.0629418 + 0.0528144i
\(79\) −192573. − 1.09214e6i −0.0439441 − 0.249220i 0.954920 − 0.296862i \(-0.0959402\pi\)
−0.998864 + 0.0476427i \(0.984829\pi\)
\(80\) 1.64062e6 0.358255
\(81\) 370383. + 2.10054e6i 0.0774378 + 0.439172i
\(82\) −1.96641e6 + 3.40592e6i −0.393845 + 0.682160i
\(83\) 7.07888e6 + 5.93989e6i 1.35891 + 1.14026i 0.976317 + 0.216346i \(0.0694140\pi\)
0.382595 + 0.923916i \(0.375030\pi\)
\(84\) 252334. + 437056.i 0.0464514 + 0.0804562i
\(85\) 6.33440e6 − 1.09715e7i 1.11877 − 1.93776i
\(86\) −1.80490e6 + 656930.i −0.305991 + 0.111372i
\(87\) 4.06599e6 − 3.41177e6i 0.661986 − 0.555472i
\(88\) 1.33791e6 + 2.31733e6i 0.209285 + 0.362492i
\(89\) −2.16712e6 + 1.22903e7i −0.325850 + 1.84799i 0.177785 + 0.984069i \(0.443107\pi\)
−0.503634 + 0.863917i \(0.668004\pi\)
\(90\) 976304. − 5.53689e6i 0.141168 − 0.800603i
\(91\) −601337. − 504582.i −0.0836514 − 0.0701919i
\(92\) 1.86758e6 + 679743.i 0.250047 + 0.0910096i
\(93\) 5.68417e6 + 2.06887e6i 0.732785 + 0.266712i
\(94\) −2.40919e6 − 2.02155e6i −0.299174 − 0.251037i
\(95\) 1.92550e6 − 1.09201e7i 0.230415 − 1.30675i
\(96\) −118322. + 671035.i −0.0136494 + 0.0774098i
\(97\) −749774. − 1.29865e6i −0.0834121 − 0.144474i 0.821301 − 0.570495i \(-0.193248\pi\)
−0.904713 + 0.426021i \(0.859915\pi\)
\(98\) 4.16570e6 − 3.49543e6i 0.447091 − 0.375154i
\(99\) 8.61690e6 − 3.13630e6i 0.892540 − 0.324858i
\(100\) −2.63386e6 + 4.56199e6i −0.263386 + 0.456199i
\(101\) −3.48833e6 − 6.04197e6i −0.336894 − 0.583517i 0.646953 − 0.762530i \(-0.276043\pi\)
−0.983847 + 0.179013i \(0.942710\pi\)
\(102\) 4.03066e6 + 3.38213e6i 0.376076 + 0.315565i
\(103\) 6.49974e6 − 1.12579e7i 0.586092 − 1.01514i −0.408646 − 0.912693i \(-0.633999\pi\)
0.994738 − 0.102448i \(-0.0326676\pi\)
\(104\) −184044. − 1.04377e6i −0.0160437 − 0.0909886i
\(105\) −3.15845e6 −0.266263
\(106\) 1.18818e6 + 6.73848e6i 0.0968969 + 0.549530i
\(107\) 4.34706e6 − 3.64761e6i 0.343046 − 0.287850i −0.454945 − 0.890520i \(-0.650341\pi\)
0.797990 + 0.602670i \(0.205896\pi\)
\(108\) 4.92926e6 + 1.79411e6i 0.376529 + 0.137046i
\(109\) −8.34538e6 + 3.03747e6i −0.617239 + 0.224657i −0.631668 − 0.775239i \(-0.717629\pi\)
0.0144287 + 0.999896i \(0.495407\pi\)
\(110\) −1.67465e7 −1.19964
\(111\) −6.40564e6 + 128828.i −0.444562 + 0.00894090i
\(112\) −1.55325e6 −0.104467
\(113\) −1.69315e7 + 6.16255e6i −1.10388 + 0.401778i −0.828743 − 0.559629i \(-0.810944\pi\)
−0.275132 + 0.961407i \(0.588721\pi\)
\(114\) 4.32759e6 + 1.57512e6i 0.273577 + 0.0995739i
\(115\) −9.52827e6 + 7.99517e6i −0.584213 + 0.490213i
\(116\) 2.83673e6 + 1.60879e7i 0.168739 + 0.956966i
\(117\) −3.63211e6 −0.209657
\(118\) −1.30819e6 − 7.41909e6i −0.0732963 − 0.415684i
\(119\) −5.99709e6 + 1.03873e7i −0.326232 + 0.565050i
\(120\) −3.26674e6 − 2.74112e6i −0.172576 − 0.144809i
\(121\) −3.91311e6 − 6.77770e6i −0.200804 − 0.347803i
\(122\) 5.34606e6 − 9.25964e6i 0.266547 − 0.461673i
\(123\) 9.60603e6 − 3.49631e6i 0.465453 − 0.169411i
\(124\) −1.42617e7 + 1.19670e7i −0.671730 + 0.563649i
\(125\) −837780. − 1.45108e6i −0.0383659 − 0.0664516i
\(126\) −924315. + 5.24205e6i −0.0411645 + 0.233456i
\(127\) −4.51064e6 + 2.55811e7i −0.195400 + 1.10817i 0.716447 + 0.697642i \(0.245767\pi\)
−0.911847 + 0.410529i \(0.865344\pi\)
\(128\) −1.60651e6 − 1.34802e6i −0.0677094 − 0.0568149i
\(129\) 4.69145e6 + 1.70755e6i 0.192417 + 0.0700341i
\(130\) 6.23311e6 + 2.26867e6i 0.248830 + 0.0905668i
\(131\) −1.01170e7 − 8.48920e6i −0.393191 − 0.329927i 0.424664 − 0.905351i \(-0.360392\pi\)
−0.817855 + 0.575425i \(0.804837\pi\)
\(132\) 1.20776e6 − 6.84957e6i 0.0457060 − 0.259212i
\(133\) −1.82297e6 + 1.03386e7i −0.0671890 + 0.381048i
\(134\) −1.54048e7 − 2.66819e7i −0.553082 − 0.957966i
\(135\) −2.51488e7 + 2.11024e7i −0.879730 + 0.738181i
\(136\) −1.52175e7 + 5.53873e6i −0.518750 + 0.188809i
\(137\) 287861. − 498590.i 0.00956446 − 0.0165661i −0.861204 − 0.508260i \(-0.830289\pi\)
0.870768 + 0.491694i \(0.163622\pi\)
\(138\) −2.58296e6 − 4.47381e6i −0.0836643 − 0.144911i
\(139\) 3.96881e7 + 3.33023e7i 1.25345 + 1.05177i 0.996348 + 0.0853904i \(0.0272138\pi\)
0.257107 + 0.966383i \(0.417231\pi\)
\(140\) 4.86048e6 − 8.41860e6i 0.149703 − 0.259294i
\(141\) 1.41952e6 + 8.05051e6i 0.0426457 + 0.241856i
\(142\) −2.00117e7 −0.586510
\(143\) 1.87862e6 + 1.06542e7i 0.0537234 + 0.304681i
\(144\) −5.50543e6 + 4.61961e6i −0.153647 + 0.128925i
\(145\) −9.60730e7 − 3.49677e7i −2.61706 − 0.952531i
\(146\) 4.00303e7 − 1.45698e7i 1.06452 − 0.387453i
\(147\) −1.41347e7 −0.367009
\(148\) 9.51415e6 − 1.72720e7i 0.241243 − 0.437952i
\(149\) 1.15839e6 0.0286882 0.0143441 − 0.999897i \(-0.495434\pi\)
0.0143441 + 0.999897i \(0.495434\pi\)
\(150\) 1.28666e7 − 4.68305e6i 0.311275 − 0.113295i
\(151\) −3.26719e7 − 1.18916e7i −0.772244 − 0.281074i −0.0743095 − 0.997235i \(-0.523675\pi\)
−0.697935 + 0.716161i \(0.745897\pi\)
\(152\) −1.08580e7 + 9.11096e6i −0.250783 + 0.210432i
\(153\) 9.63687e6 + 5.46534e7i 0.217528 + 1.23366i
\(154\) 1.58548e7 0.349814
\(155\) −2.02327e7 − 1.14745e8i −0.436409 − 2.47500i
\(156\) −1.37745e6 + 2.38581e6i −0.0290496 + 0.0503154i
\(157\) 3.31795e7 + 2.78409e7i 0.684259 + 0.574162i 0.917247 − 0.398318i \(-0.130406\pi\)
−0.232988 + 0.972480i \(0.574850\pi\)
\(158\) −4.43594e6 − 7.68327e6i −0.0894717 − 0.154969i
\(159\) 8.89271e6 − 1.54026e7i 0.175446 − 0.303882i
\(160\) 1.23334e7 − 4.48899e6i 0.238047 − 0.0866421i
\(161\) 9.02088e6 − 7.56942e6i 0.170356 − 0.142946i
\(162\) 8.53179e6 + 1.47775e7i 0.157666 + 0.273085i
\(163\) 1.36702e6 − 7.75275e6i 0.0247240 − 0.140217i −0.969947 − 0.243316i \(-0.921765\pi\)
0.994671 + 0.103099i \(0.0328759\pi\)
\(164\) −5.46342e6 + 3.09846e7i −0.0967188 + 0.548519i
\(165\) 3.33452e7 + 2.79799e7i 0.577882 + 0.484901i
\(166\) 6.94683e7 + 2.52844e7i 1.17871 + 0.429017i
\(167\) −4.19139e7 − 1.52554e7i −0.696387 − 0.253464i −0.0305197 − 0.999534i \(-0.509716\pi\)
−0.665868 + 0.746070i \(0.731938\pi\)
\(168\) 3.09279e6 + 2.59516e6i 0.0503231 + 0.0422261i
\(169\) −1.01521e7 + 5.75752e7i −0.161790 + 0.917555i
\(170\) 1.75993e7 − 9.98106e7i 0.274742 − 1.55814i
\(171\) 2.42870e7 + 4.20664e7i 0.371439 + 0.643352i
\(172\) −1.17709e7 + 9.87700e6i −0.176385 + 0.148005i
\(173\) −1.38960e7 + 5.05772e6i −0.204046 + 0.0742666i −0.442021 − 0.897005i \(-0.645738\pi\)
0.237975 + 0.971271i \(0.423516\pi\)
\(174\) 2.12311e7 − 3.67733e7i 0.305527 − 0.529189i
\(175\) 1.56061e7 + 2.70306e7i 0.220121 + 0.381262i
\(176\) 1.63984e7 + 1.37599e7i 0.226729 + 0.190248i
\(177\) −9.79091e6 + 1.69584e7i −0.132714 + 0.229867i
\(178\) 1.73369e7 + 9.83227e7i 0.230411 + 1.30672i
\(179\) −3.78975e7 −0.493884 −0.246942 − 0.969030i \(-0.579426\pi\)
−0.246942 + 0.969030i \(0.579426\pi\)
\(180\) −7.81043e6 − 4.42951e7i −0.0998208 − 0.566112i
\(181\) 6.24442e6 − 5.23969e6i 0.0782739 − 0.0656796i −0.602811 − 0.797884i \(-0.705953\pi\)
0.681085 + 0.732204i \(0.261508\pi\)
\(182\) −5.90120e6 − 2.14786e6i −0.0725588 − 0.0264092i
\(183\) −2.61158e7 + 9.50538e6i −0.315010 + 0.114654i
\(184\) 1.58995e7 0.188157
\(185\) 6.38420e7 + 1.05615e8i 0.741319 + 1.22637i
\(186\) 4.83917e7 0.551411
\(187\) 1.55332e8 − 5.65363e7i 1.73707 − 0.632240i
\(188\) −2.36425e7 − 8.60517e6i −0.259502 − 0.0944511i
\(189\) 2.38096e7 − 1.99786e7i 0.256529 − 0.215253i
\(190\) −1.54040e7 − 8.73605e7i −0.162928 − 0.924012i
\(191\) 5.20812e7 0.540834 0.270417 − 0.962743i \(-0.412838\pi\)
0.270417 + 0.962743i \(0.412838\pi\)
\(192\) 946573. + 5.36828e6i 0.00965161 + 0.0547370i
\(193\) 7.50547e7 − 1.29999e8i 0.751497 − 1.30163i −0.195600 − 0.980684i \(-0.562665\pi\)
0.947097 − 0.320947i \(-0.104001\pi\)
\(194\) −9.18976e6 − 7.71112e6i −0.0903645 − 0.0758248i
\(195\) −8.62071e6 − 1.49315e7i −0.0832573 − 0.144206i
\(196\) 2.17517e7 − 3.76751e7i 0.206347 − 0.357403i
\(197\) −1.05885e8 + 3.85388e7i −0.986736 + 0.359142i −0.784455 − 0.620185i \(-0.787057\pi\)
−0.202280 + 0.979328i \(0.564835\pi\)
\(198\) 5.61965e7 − 4.71545e7i 0.514495 − 0.431712i
\(199\) −2.54944e7 − 4.41575e7i −0.229329 − 0.397209i 0.728281 − 0.685279i \(-0.240320\pi\)
−0.957609 + 0.288070i \(0.906986\pi\)
\(200\) −7.31785e6 + 4.15016e7i −0.0646813 + 0.366826i
\(201\) −1.39063e7 + 7.88664e7i −0.120788 + 0.685024i
\(202\) −4.27555e7 − 3.58761e7i −0.364974 − 0.306250i
\(203\) 9.09570e7 + 3.31056e7i 0.763133 + 0.277758i
\(204\) 3.95547e7 + 1.43967e7i 0.326206 + 0.118729i
\(205\) −1.50840e8 − 1.26569e8i −1.22286 − 1.02610i
\(206\) 1.80587e7 − 1.02416e8i 0.143930 − 0.816267i
\(207\) 9.46151e6 − 5.36589e7i 0.0741420 − 0.420480i
\(208\) −4.23947e6 − 7.34298e6i −0.0326656 − 0.0565784i
\(209\) 1.10833e8 − 9.29998e7i 0.839762 − 0.704644i
\(210\) −2.37437e7 + 8.64202e6i −0.176922 + 0.0643943i
\(211\) −1.74343e7 + 3.01970e7i −0.127766 + 0.221297i −0.922811 − 0.385254i \(-0.874114\pi\)
0.795045 + 0.606551i \(0.207447\pi\)
\(212\) 2.73697e7 + 4.74057e7i 0.197285 + 0.341708i
\(213\) 3.98467e7 + 3.34354e7i 0.282529 + 0.237070i
\(214\) 2.26987e7 − 3.93153e7i 0.158326 − 0.274229i
\(215\) −1.66992e7 − 9.47057e7i −0.114594 − 0.649893i
\(216\) 4.19649e7 0.283334
\(217\) 1.91553e7 + 1.08635e8i 0.127257 + 0.721708i
\(218\) −5.44257e7 + 4.56686e7i −0.355800 + 0.298552i
\(219\) −1.04050e8 − 3.78711e7i −0.669404 − 0.243643i
\(220\) −1.25893e8 + 4.58212e7i −0.797116 + 0.290126i
\(221\) −6.54742e7 −0.408035
\(222\) −4.78021e7 + 1.84953e7i −0.293232 + 0.113456i
\(223\) −1.77664e8 −1.07283 −0.536417 − 0.843953i \(-0.680223\pi\)
−0.536417 + 0.843953i \(0.680223\pi\)
\(224\) −1.16766e7 + 4.24995e6i −0.0694144 + 0.0252648i
\(225\) 1.35708e8 + 4.93938e7i 0.794269 + 0.289090i
\(226\) −1.10421e8 + 9.26544e7i −0.636316 + 0.533933i
\(227\) 4.44079e7 + 2.51849e8i 0.251982 + 1.42906i 0.803703 + 0.595031i \(0.202860\pi\)
−0.551721 + 0.834029i \(0.686029\pi\)
\(228\) 3.68426e7 0.205863
\(229\) 1.41977e7 + 8.05192e7i 0.0781257 + 0.443073i 0.998629 + 0.0523389i \(0.0166676\pi\)
−0.920504 + 0.390734i \(0.872221\pi\)
\(230\) −4.97531e7 + 8.61749e7i −0.269633 + 0.467018i
\(231\) −3.15695e7 − 2.64900e7i −0.168510 − 0.141397i
\(232\) 6.53444e7 + 1.13180e8i 0.343558 + 0.595060i
\(233\) 5.81443e7 − 1.00709e8i 0.301135 − 0.521582i −0.675258 − 0.737582i \(-0.735968\pi\)
0.976393 + 0.216000i \(0.0693011\pi\)
\(234\) −2.73046e7 + 9.93805e6i −0.139309 + 0.0507044i
\(235\) 1.20623e8 − 1.01214e8i 0.606306 − 0.508751i
\(236\) −3.01341e7 − 5.21939e7i −0.149234 − 0.258480i
\(237\) −4.00442e6 + 2.27102e7i −0.0195398 + 0.110816i
\(238\) −1.66621e7 + 9.44957e7i −0.0801145 + 0.454352i
\(239\) −9.54420e7 − 8.00853e7i −0.452217 − 0.379455i 0.388041 − 0.921642i \(-0.373152\pi\)
−0.840258 + 0.542187i \(0.817596\pi\)
\(240\) −3.20580e7 − 1.16682e7i −0.149692 − 0.0544833i
\(241\) 1.42513e8 + 5.18706e7i 0.655837 + 0.238705i 0.648438 − 0.761268i \(-0.275423\pi\)
0.00739882 + 0.999973i \(0.497645\pi\)
\(242\) −4.79618e7 − 4.02447e7i −0.217541 − 0.182539i
\(243\) 3.88287e7 − 2.20209e8i 0.173593 − 0.984492i
\(244\) 1.48533e7 − 8.42374e7i 0.0654575 − 0.371228i
\(245\) 1.36132e8 + 2.35788e8i 0.591397 + 1.02433i
\(246\) 6.26473e7 − 5.25673e7i 0.268305 − 0.225135i
\(247\) −5.38511e7 + 1.96002e7i −0.227382 + 0.0827601i
\(248\) −7.44692e7 + 1.28984e8i −0.310024 + 0.536978i
\(249\) −9.60782e7 − 1.66412e8i −0.394391 − 0.683105i
\(250\) −1.02684e7 − 8.61623e6i −0.0415637 − 0.0348761i
\(251\) 1.37244e8 − 2.37713e8i 0.547817 − 0.948846i −0.450607 − 0.892722i \(-0.648793\pi\)
0.998424 − 0.0561238i \(-0.0178741\pi\)
\(252\) 7.39452e6 + 4.19364e7i 0.0291077 + 0.165078i
\(253\) −1.62293e8 −0.630055
\(254\) 3.60851e7 + 2.04649e8i 0.138169 + 0.783595i
\(255\) −2.01806e8 + 1.69335e8i −0.762154 + 0.639523i
\(256\) −1.57654e7 − 5.73815e6i −0.0587308 − 0.0213763i
\(257\) −3.10980e8 + 1.13187e8i −1.14279 + 0.415941i −0.842920 − 0.538039i \(-0.819165\pi\)
−0.299869 + 0.953980i \(0.596943\pi\)
\(258\) 3.99403e7 0.144791
\(259\) −6.04423e7 − 9.99905e7i −0.216168 − 0.357610i
\(260\) 5.30651e7 0.187242
\(261\) 4.20854e8 − 1.53178e8i 1.46518 − 0.533280i
\(262\) −9.92831e7 − 3.61361e7i −0.341052 − 0.124133i
\(263\) −8.46613e6 + 7.10392e6i −0.0286972 + 0.0240798i −0.657023 − 0.753870i \(-0.728185\pi\)
0.628326 + 0.777950i \(0.283740\pi\)
\(264\) −9.66211e6 − 5.47965e7i −0.0323190 − 0.183290i
\(265\) −3.42584e8 −1.13085
\(266\) 1.45837e7 + 8.27085e7i 0.0475098 + 0.269442i
\(267\) 1.29756e8 − 2.24743e8i 0.417193 − 0.722599i
\(268\) −1.88812e8 − 1.58432e8i −0.599182 − 0.502773i
\(269\) 2.70433e8 + 4.68403e8i 0.847084 + 1.46719i 0.883799 + 0.467866i \(0.154977\pi\)
−0.0367159 + 0.999326i \(0.511690\pi\)
\(270\) −1.31318e8 + 2.27449e8i −0.406023 + 0.703252i
\(271\) −5.58498e8 + 2.03277e8i −1.70463 + 0.620433i −0.996339 − 0.0854905i \(-0.972754\pi\)
−0.708288 + 0.705924i \(0.750532\pi\)
\(272\) −9.92435e7 + 8.32752e7i −0.299027 + 0.250914i
\(273\) 8.16166e6 + 1.41364e7i 0.0242778 + 0.0420504i
\(274\) 799784. − 4.53580e6i 0.00234880 − 0.0133207i
\(275\) 7.46967e7 − 4.23626e8i 0.216589 − 1.22834i
\(276\) −3.16585e7 − 2.65647e7i −0.0906377 − 0.0760541i
\(277\) −4.98533e8 − 1.81451e8i −1.40934 − 0.512957i −0.478402 − 0.878141i \(-0.658784\pi\)
−0.930935 + 0.365184i \(0.881006\pi\)
\(278\) 3.89477e8 + 1.41758e8i 1.08724 + 0.395723i
\(279\) 3.90992e8 + 3.28082e8i 1.07784 + 0.904414i
\(280\) 1.35042e7 − 7.65862e7i 0.0367635 − 0.208496i
\(281\) 6.15441e7 − 3.49034e8i 0.165468 − 0.938416i −0.783113 − 0.621880i \(-0.786369\pi\)
0.948581 − 0.316536i \(-0.102520\pi\)
\(282\) 3.26988e7 + 5.66360e7i 0.0868281 + 0.150391i
\(283\) 5.25057e8 − 4.40575e8i 1.37706 − 1.15549i 0.406779 − 0.913527i \(-0.366652\pi\)
0.970285 − 0.241967i \(-0.0777925\pi\)
\(284\) −1.50439e8 + 5.47553e7i −0.389714 + 0.141844i
\(285\) −1.15289e8 + 1.99686e8i −0.295006 + 0.510966i
\(286\) 4.32743e7 + 7.49532e7i 0.109383 + 0.189456i
\(287\) 1.42807e8 + 1.19829e8i 0.356585 + 0.299211i
\(288\) −2.87473e7 + 4.97918e7i −0.0709127 + 0.122824i
\(289\) 1.02464e8 + 5.81103e8i 0.249706 + 1.41616i
\(290\) −8.17910e8 −1.96930
\(291\) 5.41470e6 + 3.07083e7i 0.0128810 + 0.0730517i
\(292\) 2.61064e8 − 2.19058e8i 0.613630 − 0.514897i
\(293\) −1.11269e8 − 4.04987e7i −0.258427 − 0.0940598i 0.209558 − 0.977796i \(-0.432798\pi\)
−0.467985 + 0.883736i \(0.655020\pi\)
\(294\) −1.06258e8 + 3.86749e7i −0.243864 + 0.0887593i
\(295\) 3.77186e8 0.855419
\(296\) 2.42640e7 − 1.55875e8i 0.0543804 − 0.349346i
\(297\) −4.28355e8 −0.948760
\(298\) 8.70826e6 − 3.16955e6i 0.0190623 − 0.00693810i
\(299\) 6.04061e7 + 2.19860e7i 0.130687 + 0.0475661i
\(300\) 8.39115e7 − 7.04101e7i 0.179431 − 0.150560i
\(301\) 1.58099e7 + 8.96626e7i 0.0334154 + 0.189508i
\(302\) −2.78149e8 −0.581104
\(303\) 2.51920e7 + 1.42871e8i 0.0520251 + 0.295049i
\(304\) −5.66966e7 + 9.82013e7i −0.115744 + 0.200475i
\(305\) 4.10086e8 + 3.44103e8i 0.827609 + 0.694447i
\(306\) 2.21986e8 + 3.84491e8i 0.442895 + 0.767117i
\(307\) 2.87352e7 − 4.97709e7i 0.0566801 − 0.0981728i −0.836293 − 0.548283i \(-0.815282\pi\)
0.892973 + 0.450110i \(0.148615\pi\)
\(308\) 1.19189e8 − 4.33812e7i 0.232439 − 0.0846007i
\(309\) −2.07073e8 + 1.73755e8i −0.399273 + 0.335029i
\(310\) −4.66062e8 − 8.07244e8i −0.888542 − 1.53900i
\(311\) 1.15887e8 − 6.57230e8i 0.218462 − 1.23896i −0.656336 − 0.754468i \(-0.727895\pi\)
0.874798 − 0.484488i \(-0.160994\pi\)
\(312\) −3.82707e6 + 2.17044e7i −0.00713387 + 0.0404582i
\(313\) 2.98963e8 + 2.50860e8i 0.551077 + 0.462409i 0.875306 − 0.483570i \(-0.160660\pi\)
−0.324228 + 0.945979i \(0.605105\pi\)
\(314\) 3.25605e8 + 1.18511e8i 0.593523 + 0.216025i
\(315\) −2.50434e8 − 9.11504e7i −0.451446 − 0.164313i
\(316\) −5.43700e7 − 4.56218e7i −0.0969292 − 0.0813332i
\(317\) 3.70090e7 − 2.09889e8i 0.0652530 − 0.370068i −0.934642 − 0.355590i \(-0.884280\pi\)
0.999895 − 0.0144784i \(-0.00460878\pi\)
\(318\) 2.47073e7 − 1.40122e8i 0.0430853 − 0.244349i
\(319\) −6.67000e8 − 1.15528e9i −1.15043 − 1.99260i
\(320\) 8.04343e7 − 6.74924e7i 0.137220 − 0.115141i
\(321\) −1.10885e8 + 4.03587e7i −0.187113 + 0.0681035i
\(322\) 4.71037e7 − 8.15860e7i 0.0786248 − 0.136182i
\(323\) 4.37809e8 + 7.58308e8i 0.722897 + 1.25209i
\(324\) 1.04572e8 + 8.77461e7i 0.170807 + 0.143324i
\(325\) −8.51913e7 + 1.47556e8i −0.137659 + 0.238432i
\(326\) −1.09362e7 − 6.20220e7i −0.0174825 − 0.0991481i
\(327\) 1.84673e8 0.292070
\(328\) 4.37073e7 + 2.47877e8i 0.0683905 + 0.387862i
\(329\) −1.14199e8 + 9.58247e7i −0.176798 + 0.148352i
\(330\) 3.27231e8 + 1.19102e8i 0.501252 + 0.182441i
\(331\) −6.68454e8 + 2.43297e8i −1.01315 + 0.368756i −0.794642 − 0.607079i \(-0.792341\pi\)
−0.218508 + 0.975835i \(0.570119\pi\)
\(332\) 5.91413e8 0.886967
\(333\) −5.11622e8 − 1.74647e8i −0.759266 − 0.259183i
\(334\) −3.56831e8 −0.524023
\(335\) 1.44954e9 − 5.27588e8i 2.10655 − 0.766723i
\(336\) 3.03509e7 + 1.10468e7i 0.0436500 + 0.0158873i
\(337\) −4.74429e8 + 3.98093e8i −0.675253 + 0.566604i −0.914615 − 0.404326i \(-0.867506\pi\)
0.239362 + 0.970930i \(0.423062\pi\)
\(338\) 8.12165e7 + 4.60602e8i 0.114403 + 0.648809i
\(339\) 3.74673e8 0.522341
\(340\) −1.40794e8 − 7.98485e8i −0.194272 − 1.10177i
\(341\) 7.60142e8 − 1.31660e9i 1.03814 − 1.79810i
\(342\) 2.97679e8 + 2.49782e8i 0.402399 + 0.337653i
\(343\) −2.85032e8 − 4.93690e8i −0.381385 − 0.660579i
\(344\) −6.14635e7 + 1.06458e8i −0.0814072 + 0.141001i
\(345\) 2.43047e8 − 8.84618e7i 0.318657 − 0.115982i
\(346\) −9.06249e7 + 7.60433e7i −0.117620 + 0.0986949i
\(347\) −2.49414e8 − 4.31997e8i −0.320455 − 0.555044i 0.660127 − 0.751154i \(-0.270502\pi\)
−0.980582 + 0.196110i \(0.937169\pi\)
\(348\) 5.89878e7 − 3.34537e8i 0.0750300 − 0.425516i
\(349\) −1.61710e8 + 9.17102e8i −0.203633 + 1.15486i 0.695944 + 0.718096i \(0.254986\pi\)
−0.899577 + 0.436762i \(0.856125\pi\)
\(350\) 1.91280e8 + 1.60503e8i 0.238469 + 0.200099i
\(351\) 1.59435e8 + 5.80297e7i 0.196793 + 0.0716267i
\(352\) 1.60925e8 + 5.85719e7i 0.196664 + 0.0715797i
\(353\) 5.72582e8 + 4.80453e8i 0.692829 + 0.581352i 0.919723 − 0.392567i \(-0.128413\pi\)
−0.226895 + 0.973919i \(0.572857\pi\)
\(354\) −2.72028e7 + 1.54275e8i −0.0325913 + 0.184835i
\(355\) 1.73985e8 − 9.86718e8i 0.206401 − 1.17056i
\(356\) 3.99358e8 + 6.91708e8i 0.469124 + 0.812546i
\(357\) 1.91059e8 − 1.60318e8i 0.222244 − 0.186485i
\(358\) −2.84896e8 + 1.03694e8i −0.328168 + 0.119443i
\(359\) −4.13974e8 + 7.17024e8i −0.472218 + 0.817906i −0.999495 − 0.0317879i \(-0.989880\pi\)
0.527276 + 0.849694i \(0.323213\pi\)
\(360\) −1.79914e8 − 3.11620e8i −0.203238 − 0.352019i
\(361\) −9.76518e7 − 8.19396e7i −0.109246 − 0.0916681i
\(362\) 3.26060e7 − 5.64753e7i 0.0361259 − 0.0625718i
\(363\) 2.82596e7 + 1.60268e8i 0.0310093 + 0.175863i
\(364\) −5.02394e7 −0.0545996
\(365\) 3.70365e8 + 2.10044e9i 0.398662 + 2.26093i
\(366\) −1.70318e8 + 1.42914e8i −0.181584 + 0.152367i
\(367\) −4.17284e7 − 1.51879e7i −0.0440657 − 0.0160386i 0.319893 − 0.947454i \(-0.396353\pi\)
−0.363959 + 0.931415i \(0.618575\pi\)
\(368\) 1.19525e8 − 4.35035e7i 0.125023 − 0.0455048i
\(369\) 8.62564e8 0.893715
\(370\) 7.68913e8 + 6.19280e8i 0.789171 + 0.635595i
\(371\) 3.24341e8 0.329757
\(372\) 3.63787e8 − 1.32408e8i 0.366392 − 0.133356i
\(373\) −6.73525e8 − 2.45143e8i −0.672006 − 0.244590i −0.0165944 − 0.999862i \(-0.505282\pi\)
−0.655411 + 0.755272i \(0.727505\pi\)
\(374\) 1.01302e9 − 8.50028e8i 1.00131 − 0.840200i
\(375\) 6.05026e6 + 3.43127e7i 0.00592468 + 0.0336005i
\(376\) −2.01279e8 −0.195272
\(377\) 9.17530e7 + 5.20357e8i 0.0881913 + 0.500158i
\(378\) 1.24325e8 − 2.15337e8i 0.118396 − 0.205068i
\(379\) −1.38243e9 − 1.15999e9i −1.30438 − 1.09451i −0.989370 − 0.145418i \(-0.953547\pi\)
−0.315011 − 0.949088i \(-0.602008\pi\)
\(380\) −3.54833e8 − 6.14589e8i −0.331727 − 0.574569i
\(381\) 2.70074e8 − 4.67781e8i 0.250176 − 0.433317i
\(382\) 3.91522e8 − 1.42502e8i 0.359364 − 0.130798i
\(383\) 4.76404e8 − 3.99750e8i 0.433291 − 0.363574i −0.399901 − 0.916558i \(-0.630955\pi\)
0.833192 + 0.552984i \(0.186511\pi\)
\(384\) 2.18044e7 + 3.77663e7i 0.0196510 + 0.0340365i
\(385\) −1.37844e8 + 7.81751e8i −0.123105 + 0.698162i
\(386\) 2.08530e8 − 1.18263e9i 0.184549 − 1.04663i
\(387\) 3.22707e8 + 2.70784e8i 0.283022 + 0.237484i
\(388\) −9.01833e7 − 3.28240e7i −0.0783817 − 0.0285286i
\(389\) −8.92282e8 − 3.24764e8i −0.768561 − 0.279733i −0.0721666 − 0.997393i \(-0.522991\pi\)
−0.696394 + 0.717659i \(0.745214\pi\)
\(390\) −1.05662e8 − 8.86606e7i −0.0901968 − 0.0756841i
\(391\) 1.70558e8 − 9.67281e8i 0.144295 − 0.818340i
\(392\) 6.04343e7 − 3.42740e8i 0.0506737 − 0.287385i
\(393\) 1.37314e8 + 2.37834e8i 0.114114 + 0.197652i
\(394\) −6.90543e8 + 5.79434e8i −0.568793 + 0.477274i
\(395\) 4.17406e8 − 1.51923e8i 0.340776 − 0.124032i
\(396\) 2.93437e8 − 5.08248e8i 0.237455 − 0.411285i
\(397\) −2.86648e8 − 4.96490e8i −0.229923 − 0.398239i 0.727862 − 0.685724i \(-0.240514\pi\)
−0.957785 + 0.287485i \(0.907181\pi\)
\(398\) −3.12477e8 − 2.62199e8i −0.248443 − 0.208469i
\(399\) 1.09150e8 − 1.89053e8i 0.0860236 − 0.148997i
\(400\) 5.85428e7 + 3.32013e8i 0.0457366 + 0.259385i
\(401\) 4.91756e8 0.380842 0.190421 − 0.981703i \(-0.439015\pi\)
0.190421 + 0.981703i \(0.439015\pi\)
\(402\) 1.11250e8 + 6.30931e8i 0.0854101 + 0.484385i
\(403\) −4.61289e8 + 3.87067e8i −0.351079 + 0.294591i
\(404\) −4.19579e8 − 1.52714e8i −0.316577 − 0.115224i
\(405\) −8.02811e8 + 2.92199e8i −0.600511 + 0.218568i
\(406\) 7.74355e8 0.574248
\(407\) −2.47674e8 + 1.59109e9i −0.182096 + 1.16981i
\(408\) 3.36746e8 0.245466
\(409\) −1.46706e9 + 5.33966e8i −1.06027 + 0.385907i −0.812530 − 0.582920i \(-0.801910\pi\)
−0.247740 + 0.968826i \(0.579688\pi\)
\(410\) −1.48026e9 − 5.38769e8i −1.06070 − 0.386064i
\(411\) −9.17087e6 + 7.69528e6i −0.00651575 + 0.00546736i
\(412\) −1.44470e8 − 8.19328e8i −0.101774 − 0.577188i
\(413\) −3.57101e8 −0.249440
\(414\) −7.56921e7 − 4.29271e8i −0.0524263 − 0.297324i
\(415\) −1.85067e9 + 3.20545e9i −1.27104 + 2.20151i
\(416\) −5.19620e7 − 4.36013e7i −0.0353883 − 0.0296943i
\(417\) −5.38667e8 − 9.32999e8i −0.363785 − 0.630093i
\(418\) 5.78728e8 − 1.00239e9i 0.387577 − 0.671302i
\(419\) −2.63954e9 + 9.60713e8i −1.75299 + 0.638035i −0.999804 − 0.0197762i \(-0.993705\pi\)
−0.753183 + 0.657811i \(0.771482\pi\)
\(420\) −1.54849e8 + 1.29933e8i −0.101985 + 0.0855753i
\(421\) 9.31276e8 + 1.61302e9i 0.608262 + 1.05354i 0.991527 + 0.129903i \(0.0414665\pi\)
−0.383264 + 0.923639i \(0.625200\pi\)
\(422\) −4.84388e7 + 2.74710e8i −0.0313762 + 0.177943i
\(423\) −1.19778e8 + 6.79293e8i −0.0769457 + 0.436381i
\(424\) 3.35463e8 + 2.81487e8i 0.213729 + 0.179340i
\(425\) 2.44634e9 + 8.90396e8i 1.54581 + 0.562629i
\(426\) 3.91034e8 + 1.42325e8i 0.245065 + 0.0891962i
\(427\) −3.88249e8 − 3.25779e8i −0.241331 − 0.202500i
\(428\) 6.30655e7 − 3.57662e8i 0.0388811 − 0.220506i
\(429\) 3.90647e7 − 2.21547e8i 0.0238882 − 0.135477i
\(430\) −3.84667e8 − 6.66262e8i −0.233316 − 0.404116i
\(431\) 8.58673e8 − 7.20512e8i 0.516604 − 0.433482i −0.346842 − 0.937924i \(-0.612746\pi\)
0.863446 + 0.504442i \(0.168302\pi\)
\(432\) 3.15473e8 − 1.14823e8i 0.188265 − 0.0685228i
\(433\) −9.49059e8 + 1.64382e9i −0.561805 + 0.973075i 0.435534 + 0.900172i \(0.356560\pi\)
−0.997339 + 0.0729028i \(0.976774\pi\)
\(434\) 4.41244e8 + 7.64258e8i 0.259099 + 0.448772i
\(435\) 1.62860e9 + 1.36655e9i 0.948639 + 0.796003i
\(436\) −2.84191e8 + 4.92233e8i −0.164213 + 0.284425i
\(437\) −1.49283e8 − 8.46625e8i −0.0855706 − 0.485295i
\(438\) −8.85822e8 −0.503718
\(439\) −4.97741e8 − 2.82283e9i −0.280787 − 1.59242i −0.719956 − 0.694020i \(-0.755838\pi\)
0.439168 − 0.898405i \(-0.355273\pi\)
\(440\) −8.21030e8 + 6.88926e8i −0.459488 + 0.385556i
\(441\) −1.12075e9 − 4.07918e8i −0.622260 − 0.226484i
\(442\) −4.92205e8 + 1.79148e8i −0.271124 + 0.0986811i
\(443\) −2.96320e9 −1.61938 −0.809689 − 0.586859i \(-0.800364\pi\)
−0.809689 + 0.586859i \(0.800364\pi\)
\(444\) −3.08748e8 + 2.69834e8i −0.167403 + 0.146304i
\(445\) −4.99873e9 −2.68905
\(446\) −1.33560e9 + 4.86118e8i −0.712859 + 0.259459i
\(447\) −2.26353e7 − 8.23856e6i −0.0119870 − 0.00436290i
\(448\) −7.61511e7 + 6.38983e7i −0.0400132 + 0.0335750i
\(449\) 1.63004e8 + 9.24439e8i 0.0849835 + 0.481966i 0.997360 + 0.0726137i \(0.0231340\pi\)
−0.912377 + 0.409352i \(0.865755\pi\)
\(450\) 1.15534e9 0.597678
\(451\) −4.46141e8 − 2.53019e9i −0.229010 − 1.29878i
\(452\) −5.76579e8 + 9.98664e8i −0.293680 + 0.508668i
\(453\) 5.53842e8 + 4.64729e8i 0.279926 + 0.234885i
\(454\) 1.02294e9 + 1.77178e9i 0.513043 + 0.888617i
\(455\) 1.57210e8 − 2.72296e8i 0.0782423 − 0.135520i
\(456\) 2.76966e8 − 1.00807e8i 0.136789 − 0.0497869i
\(457\) 1.94484e9 − 1.63191e9i 0.953184 − 0.799816i −0.0266467 − 0.999645i \(-0.508483\pi\)
0.979831 + 0.199828i \(0.0640385\pi\)
\(458\) 3.27045e8 + 5.66459e8i 0.159066 + 0.275511i
\(459\) 4.50168e8 − 2.55303e9i 0.217285 − 1.23229i
\(460\) −1.38233e8 + 7.83956e8i −0.0662152 + 0.375525i
\(461\) 1.65417e9 + 1.38801e9i 0.786370 + 0.659843i 0.944844 − 0.327520i \(-0.106213\pi\)
−0.158474 + 0.987363i \(0.550657\pi\)
\(462\) −3.09806e8 − 1.12760e8i −0.146165 − 0.0531996i
\(463\) −1.51504e9 − 5.51431e8i −0.709401 − 0.258201i −0.0379818 − 0.999278i \(-0.512093\pi\)
−0.671420 + 0.741077i \(0.734315\pi\)
\(464\) 8.00907e8 + 6.72041e8i 0.372194 + 0.312308i
\(465\) −4.20725e8 + 2.38605e9i −0.194050 + 1.10051i
\(466\) 1.61547e8 − 9.16176e8i 0.0739515 − 0.419400i
\(467\) −3.13533e8 − 5.43055e8i −0.142454 − 0.246737i 0.785966 − 0.618269i \(-0.212166\pi\)
−0.928420 + 0.371532i \(0.878833\pi\)
\(468\) −1.78071e8 + 1.49419e8i −0.0803032 + 0.0673824i
\(469\) −1.37235e9 + 4.99494e8i −0.614270 + 0.223576i
\(470\) 6.29847e8 − 1.09093e9i 0.279829 − 0.484678i
\(471\) −4.50329e8 − 7.79992e8i −0.198590 − 0.343967i
\(472\) −3.69346e8 − 3.09918e8i −0.161672 − 0.135659i
\(473\) 6.27387e8 − 1.08667e9i 0.272597 − 0.472152i
\(474\) 3.20354e7 + 1.81682e8i 0.0138167 + 0.0783586i
\(475\) 2.27861e9 0.975534
\(476\) 1.33297e8 + 7.55965e8i 0.0566495 + 0.321275i
\(477\) 1.14961e9 − 9.64640e8i 0.484995 − 0.406959i
\(478\) −9.36615e8 − 3.40900e8i −0.392251 − 0.142768i
\(479\) 9.02998e8 − 3.28664e8i 0.375416 − 0.136640i −0.147419 − 0.989074i \(-0.547097\pi\)
0.522835 + 0.852434i \(0.324874\pi\)
\(480\) −2.72924e8 −0.112641
\(481\) 3.07732e8 − 5.58656e8i 0.126085 − 0.228895i
\(482\) 1.21328e9 0.493509
\(483\) −2.30104e8 + 8.37511e7i −0.0929202 + 0.0338202i
\(484\) −4.70671e8 − 1.71310e8i −0.188694 − 0.0686791i
\(485\) 4.60110e8 − 3.86078e8i 0.183132 − 0.153666i
\(486\) −3.10630e8 − 1.76167e9i −0.122748 − 0.696141i
\(487\) −1.44443e9 −0.566688 −0.283344 − 0.959018i \(-0.591444\pi\)
−0.283344 + 0.959018i \(0.591444\pi\)
\(488\) −1.18827e8 − 6.73899e8i −0.0462854 − 0.262498i
\(489\) −8.18500e7 + 1.41768e8i −0.0316547 + 0.0548275i
\(490\) 1.66853e9 + 1.40007e9i 0.640691 + 0.537603i
\(491\) 1.08116e9 + 1.87263e9i 0.412197 + 0.713947i 0.995130 − 0.0985738i \(-0.0314281\pi\)
−0.582932 + 0.812521i \(0.698095\pi\)
\(492\) 3.27121e8 − 5.66590e8i 0.123831 − 0.214482i
\(493\) 7.58651e9 − 2.76127e9i 2.85153 − 1.03787i
\(494\) −3.51199e8 + 2.94691e8i −0.131072 + 0.109982i
\(495\) 1.83646e9 + 3.18085e9i 0.680557 + 1.17876i
\(496\) −2.06903e8 + 1.17341e9i −0.0761345 + 0.431780i
\(497\) −1.64720e8 + 9.34174e8i −0.0601865 + 0.341335i
\(498\) −1.17760e9 − 9.88126e8i −0.427264 − 0.358517i
\(499\) 1.16815e9 + 4.25171e8i 0.420868 + 0.153183i 0.543768 − 0.839236i \(-0.316997\pi\)
−0.122900 + 0.992419i \(0.539219\pi\)
\(500\) −1.00769e8 − 3.66768e7i −0.0360521 − 0.0131219i
\(501\) 7.10511e8 + 5.96189e8i 0.252429 + 0.211813i
\(502\) 3.81315e8 − 2.16254e9i 0.134530 − 0.762960i
\(503\) 6.03056e8 − 3.42010e9i 0.211285 − 1.19826i −0.675952 − 0.736946i \(-0.736267\pi\)
0.887237 − 0.461313i \(-0.152622\pi\)
\(504\) 1.70333e8 + 2.95026e8i 0.0592643 + 0.102649i
\(505\) 2.14067e9 − 1.79623e9i 0.739655 − 0.620644i
\(506\) −1.22005e9 + 4.44061e8i −0.418648 + 0.152376i
\(507\) 6.07852e8 − 1.05283e9i 0.207143 − 0.358782i
\(508\) 8.31224e8 + 1.43972e9i 0.281317 + 0.487255i
\(509\) −3.57535e9 − 3.00007e9i −1.20173 − 1.00837i −0.999579 − 0.0290146i \(-0.990763\pi\)
−0.202149 − 0.979355i \(-0.564792\pi\)
\(510\) −1.05375e9 + 1.82516e9i −0.351758 + 0.609263i
\(511\) −3.50643e8 − 1.98859e9i −0.116250 − 0.659285i
\(512\) −1.34218e8 −0.0441942
\(513\) −3.94016e8 − 2.23457e9i −0.128855 − 0.730775i
\(514\) −2.02810e9 + 1.70178e9i −0.658748 + 0.552755i
\(515\) 4.89282e9 + 1.78084e9i 1.57846 + 0.574513i
\(516\) 3.00253e8 − 1.09283e8i 0.0962085 − 0.0350170i
\(517\) 2.05455e9 0.653881
\(518\) −7.27968e8 − 5.86303e8i −0.230122 − 0.185339i
\(519\) 3.07502e8 0.0965521
\(520\) 3.98919e8 − 1.45195e8i 0.124415 − 0.0452834i
\(521\) 5.76987e8 + 2.10006e8i 0.178745 + 0.0650579i 0.429842 − 0.902904i \(-0.358569\pi\)
−0.251097 + 0.967962i \(0.580791\pi\)
\(522\) 2.74467e9 − 2.30305e9i 0.844584 − 0.708690i
\(523\) 2.67661e8 + 1.51798e9i 0.0818142 + 0.463991i 0.997999 + 0.0632347i \(0.0201417\pi\)
−0.916184 + 0.400757i \(0.868747\pi\)
\(524\) −8.45239e8 −0.256637
\(525\) −1.12704e8 − 6.39177e8i −0.0339924 − 0.192781i
\(526\) −4.42070e7 + 7.65687e7i −0.0132447 + 0.0229404i
\(527\) 7.04821e9 + 5.91415e9i 2.09769 + 1.76017i
\(528\) −2.22567e8 − 3.85498e8i −0.0658026 − 0.113973i
\(529\) 1.22025e9 − 2.11353e9i 0.358388 − 0.620746i
\(530\) −2.57539e9 + 9.37366e8i −0.751411 + 0.273491i
\(531\) −1.26573e9 + 1.06207e9i −0.366868 + 0.307839i
\(532\) 3.35938e8 + 5.81861e8i 0.0967316 + 0.167544i
\(533\) −1.76712e8 + 1.00218e9i −0.0505500 + 0.286683i
\(534\) 3.60509e8 − 2.04455e9i 0.102452 − 0.581036i
\(535\) 1.74118e9 + 1.46102e9i 0.491592 + 0.412494i
\(536\) −1.85290e9 − 6.74401e8i −0.519727 − 0.189165i
\(537\) 7.40526e8 + 2.69529e8i 0.206362 + 0.0751097i
\(538\) 3.31462e9 + 2.78129e9i 0.917688 + 0.770032i
\(539\) −6.16881e8 + 3.49851e9i −0.169684 + 0.962326i
\(540\) −3.64849e8 + 2.06916e9i −0.0997093 + 0.565479i
\(541\) −1.11198e9 − 1.92600e9i −0.301930 − 0.522958i 0.674643 − 0.738144i \(-0.264298\pi\)
−0.976573 + 0.215186i \(0.930964\pi\)
\(542\) −3.64234e9 + 3.05628e9i −0.982613 + 0.824510i
\(543\) −1.59282e8 + 5.79741e7i −0.0426942 + 0.0155394i
\(544\) −5.18213e8 + 8.97571e8i −0.138010 + 0.239041i
\(545\) −1.77860e9 − 3.08062e9i −0.470641 − 0.815174i
\(546\) 1.00035e8 + 8.39394e7i 0.0263013 + 0.0220695i
\(547\) −1.33006e9 + 2.30372e9i −0.347468 + 0.601832i −0.985799 − 0.167930i \(-0.946292\pi\)
0.638331 + 0.769762i \(0.279625\pi\)
\(548\) −6.39827e6 − 3.62864e7i −0.00166085 − 0.00941916i
\(549\) −2.34504e9 −0.604850
\(550\) −5.97573e8 − 3.38901e9i −0.153152 − 0.868567i
\(551\) 5.41314e9 − 4.54216e9i 1.37854 − 1.15673i
\(552\) −3.10680e8 − 1.13078e8i −0.0786187 − 0.0286149i
\(553\) −3.95179e8 + 1.43833e8i −0.0993700 + 0.0361677i
\(554\) −4.24423e9 −1.06051
\(555\) −4.96350e8 − 2.51778e9i −0.123243 − 0.625162i
\(556\) 3.31579e9 0.818134
\(557\) −3.26911e9 + 1.18986e9i −0.801561 + 0.291744i −0.710133 − 0.704067i \(-0.751365\pi\)
−0.0914277 + 0.995812i \(0.529143\pi\)
\(558\) 3.83699e9 + 1.39655e9i 0.934912 + 0.340280i
\(559\) −3.80727e8 + 3.19468e8i −0.0921875 + 0.0773545i
\(560\) −1.08034e8 − 6.12690e8i −0.0259957 − 0.147429i
\(561\) −3.43732e9 −0.821959
\(562\) −4.92352e8 − 2.79227e9i −0.117004 − 0.663560i
\(563\) −4.09198e8 + 7.08752e8i −0.0966394 + 0.167384i −0.910292 − 0.413968i \(-0.864143\pi\)
0.813652 + 0.581352i \(0.197476\pi\)
\(564\) 4.00780e8 + 3.36294e8i 0.0940652 + 0.0789301i
\(565\) −3.60849e9 − 6.25009e9i −0.841698 − 1.45786i
\(566\) 2.74165e9 − 4.74868e9i 0.635558 − 1.10082i
\(567\) 7.60061e8 − 2.76640e8i 0.175109 − 0.0637343i
\(568\) −9.81111e8 + 8.23250e8i −0.224646 + 0.188501i
\(569\) −1.97382e9 − 3.41875e9i −0.449174 − 0.777991i 0.549159 − 0.835718i \(-0.314948\pi\)
−0.998332 + 0.0577266i \(0.981615\pi\)
\(570\) −3.20316e8 + 1.81660e9i −0.0724463 + 0.410863i
\(571\) −8.91782e8 + 5.05755e9i −0.200462 + 1.13688i 0.703961 + 0.710239i \(0.251413\pi\)
−0.904423 + 0.426638i \(0.859698\pi\)
\(572\) 5.30400e8 + 4.45059e8i 0.118500 + 0.0994331i
\(573\) −1.01768e9 − 3.70405e8i −0.225980 − 0.0822499i
\(574\) 1.40143e9 + 5.10080e8i 0.309300 + 0.112576i
\(575\) −1.95799e9 − 1.64295e9i −0.429509 − 0.360401i
\(576\) −7.98707e7 + 4.52969e8i −0.0174144 + 0.0987621i
\(577\) 1.14587e8 − 6.49856e8i 0.0248325 − 0.140832i −0.969871 − 0.243620i \(-0.921665\pi\)
0.994703 + 0.102788i \(0.0327762\pi\)
\(578\) 2.36027e9 + 4.08811e9i 0.508410 + 0.880593i
\(579\) −2.39114e9 + 2.00641e9i −0.511954 + 0.429580i
\(580\) −6.14867e9 + 2.23793e9i −1.30853 + 0.476265i
\(581\) 1.75212e9 − 3.03475e9i 0.370635 − 0.641959i
\(582\) 1.24728e8 + 2.16035e8i 0.0262261 + 0.0454249i
\(583\) −3.42422e9 − 2.87326e9i −0.715685 − 0.600531i
\(584\) 1.36318e9 − 2.36109e9i 0.283209 − 0.490533i
\(585\) −2.52625e8 − 1.43271e9i −0.0521713 − 0.295878i
\(586\) −9.47282e8 −0.194463
\(587\) −1.14767e9 − 6.50877e9i −0.234199 − 1.32821i −0.844295 − 0.535879i \(-0.819980\pi\)
0.610096 − 0.792327i \(-0.291131\pi\)
\(588\) −6.92981e8 + 5.81480e8i −0.140573 + 0.117954i
\(589\) 7.56745e9 + 2.75433e9i 1.52597 + 0.555408i
\(590\) 2.83551e9 − 1.03204e9i 0.568395 − 0.206879i
\(591\) 2.34310e9 0.466912
\(592\) −2.44094e8 − 1.23819e9i −0.0483538 − 0.245279i
\(593\) −7.85671e8 −0.154721 −0.0773605 − 0.997003i \(-0.524649\pi\)
−0.0773605 + 0.997003i \(0.524649\pi\)
\(594\) −3.22018e9 + 1.17205e9i −0.630416 + 0.229453i
\(595\) −4.51444e9 − 1.64312e9i −0.878606 − 0.319786i
\(596\) 5.67923e7 − 4.76544e7i 0.0109882 − 0.00922022i
\(597\) 1.84115e8 + 1.04417e9i 0.0354143 + 0.200844i
\(598\) 5.14262e8 0.0983401
\(599\) 5.64564e8 + 3.20180e9i 0.107330 + 0.608697i 0.990264 + 0.139201i \(0.0444533\pi\)
−0.882935 + 0.469496i \(0.844436\pi\)
\(600\) 4.38155e8 − 7.58906e8i 0.0828129 − 0.143436i
\(601\) 2.24435e9 + 1.88324e9i 0.421726 + 0.353871i 0.828819 − 0.559516i \(-0.189013\pi\)
−0.407093 + 0.913387i \(0.633457\pi\)
\(602\) 3.64183e8 + 6.30784e8i 0.0680349 + 0.117840i
\(603\) −3.37866e9 + 5.85200e9i −0.627528 + 1.08691i
\(604\) −2.09100e9 + 7.61062e8i −0.386122 + 0.140537i
\(605\) 2.40133e9 − 2.01496e9i 0.440868 − 0.369932i
\(606\) 5.80299e8 + 1.00511e9i 0.105925 + 0.183467i
\(607\) −1.57702e9 + 8.94371e9i −0.286204 + 1.62314i 0.414748 + 0.909936i \(0.363870\pi\)
−0.700952 + 0.713208i \(0.747241\pi\)
\(608\) −1.57524e8 + 8.93363e8i −0.0284239 + 0.161200i
\(609\) −1.54187e9 − 1.29378e9i −0.276623 − 0.232114i
\(610\) 4.02436e9 + 1.46475e9i 0.717864 + 0.261281i
\(611\) −7.64708e8 − 2.78331e8i −0.135629 − 0.0493648i
\(612\) 2.72082e9 + 2.28304e9i 0.479810 + 0.402609i
\(613\) −1.55545e9 + 8.82141e9i −0.272738 + 1.54677i 0.473320 + 0.880891i \(0.343056\pi\)
−0.746057 + 0.665882i \(0.768056\pi\)
\(614\) 7.98372e7 − 4.52779e8i 0.0139192 − 0.0789400i
\(615\) 2.04727e9 + 3.54598e9i 0.354905 + 0.614714i
\(616\) 7.77309e8 − 6.52240e8i 0.133987 − 0.112428i
\(617\) 9.65951e9 − 3.51577e9i 1.65561 − 0.602591i 0.665943 − 0.746003i \(-0.268030\pi\)
0.989663 + 0.143412i \(0.0458073\pi\)
\(618\) −1.08126e9 + 1.87280e9i −0.184277 + 0.319177i
\(619\) 1.78181e8 + 3.08619e8i 0.0301957 + 0.0523004i 0.880728 − 0.473622i \(-0.157054\pi\)
−0.850533 + 0.525922i \(0.823720\pi\)
\(620\) −5.71239e9 − 4.79327e9i −0.962603 − 0.807720i
\(621\) −1.27262e9 + 2.20424e9i −0.213245 + 0.369351i
\(622\) −9.27099e8 − 5.25784e9i −0.154476 − 0.876075i
\(623\) 4.73254e9 0.784127
\(624\) 3.06166e7 + 1.73635e8i 0.00504441 + 0.0286083i
\(625\) −4.41180e9 + 3.70194e9i −0.722830 + 0.606526i
\(626\) 2.93386e9 + 1.06784e9i 0.478002 + 0.173978i
\(627\) −2.82712e9 + 1.02899e9i −0.458045 + 0.166715i
\(628\) 2.77201e9 0.446619
\(629\) −9.22274e9 − 3.14827e9i −1.47769 − 0.504423i
\(630\) −2.13205e9 −0.339707
\(631\) −3.25150e8 + 1.18345e8i −0.0515207 + 0.0187520i −0.367652 − 0.929963i \(-0.619838\pi\)
0.316131 + 0.948715i \(0.397616\pi\)
\(632\) −5.33557e8 − 1.94199e8i −0.0840759 − 0.0306011i
\(633\) 5.55433e8 − 4.66063e8i 0.0870399 − 0.0730351i
\(634\) −2.96072e8 − 1.67911e9i −0.0461408 − 0.261678i
\(635\) −1.04044e10 −1.61253
\(636\) −1.97658e8 − 1.12097e9i −0.0304659 − 0.172781i
\(637\) 7.03551e8 − 1.21859e9i 0.107847 − 0.186796i
\(638\) −8.17523e9 − 6.85983e9i −1.24631 − 1.04578i
\(639\) 2.19453e9 + 3.80104e9i 0.332728 + 0.576301i
\(640\) 4.19998e8 − 7.27458e8i 0.0633311 − 0.109693i
\(641\) −5.60303e9 + 2.03934e9i −0.840271 + 0.305834i −0.726067 − 0.687624i \(-0.758654\pi\)
−0.114204 + 0.993457i \(0.536432\pi\)
\(642\) −7.23152e8 + 6.06796e8i −0.107859 + 0.0905046i
\(643\) 6.18550e8 + 1.07136e9i 0.0917565 + 0.158927i 0.908250 − 0.418427i \(-0.137419\pi\)
−0.816494 + 0.577354i \(0.804085\pi\)
\(644\) 1.30872e8 − 7.42209e8i 0.0193083 − 0.109503i
\(645\) −3.47247e8 + 1.96934e9i −0.0509542 + 0.288976i
\(646\) 5.36610e9 + 4.50269e9i 0.783150 + 0.657141i
\(647\) 3.69161e9 + 1.34364e9i 0.535859 + 0.195037i 0.595753 − 0.803168i \(-0.296854\pi\)
−0.0598935 + 0.998205i \(0.519076\pi\)
\(648\) 1.02621e9 + 3.73510e8i 0.148157 + 0.0539249i
\(649\) 3.77008e9 + 3.16347e9i 0.541370 + 0.454263i
\(650\) −2.36693e8 + 1.34235e9i −0.0338056 + 0.191721i
\(651\) 3.98321e8 − 2.25899e9i 0.0565848 − 0.320908i
\(652\) −2.51915e8 − 4.36330e8i −0.0355949 − 0.0616522i
\(653\) 2.32537e7 − 1.95122e7i 0.00326811 − 0.00274227i −0.641152 − 0.767414i \(-0.721543\pi\)
0.644420 + 0.764672i \(0.277099\pi\)
\(654\) 1.38829e9 − 5.05296e8i 0.194070 − 0.0706356i
\(655\) 2.64494e9 − 4.58118e9i 0.367766 − 0.636990i
\(656\) 1.00680e9 + 1.74383e9i 0.139245 + 0.241180i
\(657\) −7.15722e9 − 6.00562e9i −0.984612 − 0.826188i
\(658\) −5.96307e8 + 1.03283e9i −0.0815980 + 0.141332i
\(659\) −1.86197e9 − 1.05598e10i −0.253440 − 1.43733i −0.800046 − 0.599938i \(-0.795192\pi\)
0.546607 − 0.837389i \(-0.315919\pi\)
\(660\) 2.78586e9 0.377186
\(661\) 2.91880e8 + 1.65533e9i 0.0393097 + 0.222936i 0.998134 − 0.0610642i \(-0.0194494\pi\)
−0.958824 + 0.284000i \(0.908338\pi\)
\(662\) −4.35943e9 + 3.65800e9i −0.584019 + 0.490050i
\(663\) 1.27938e9 + 4.65657e8i 0.170492 + 0.0620538i
\(664\) 4.44597e9 − 1.61820e9i 0.589357 − 0.214508i
\(665\) −4.20490e9 −0.554473
\(666\) −4.32400e9 + 8.69631e7i −0.567187 + 0.0114071i
\(667\) −7.92649e9 −1.03429
\(668\) −2.68249e9 + 9.76347e8i −0.348194 + 0.126732i
\(669\) 3.47160e9 + 1.26356e9i 0.448269 + 0.163156i
\(670\) 9.45339e9 − 7.93233e9i 1.21430 − 1.01892i
\(671\) 1.21292e9 + 6.87880e9i 0.154990 + 0.878990i
\(672\) 2.58390e8 0.0328461
\(673\) 1.05477e9 + 5.98189e9i 0.133384 + 0.756460i 0.975971 + 0.217900i \(0.0699206\pi\)
−0.842587 + 0.538560i \(0.818968\pi\)
\(674\) −2.47729e9 + 4.29079e9i −0.311650 + 0.539794i
\(675\) −5.16789e9 − 4.33638e9i −0.646771 − 0.542705i
\(676\) 1.87083e9 + 3.24037e9i 0.232927 + 0.403442i
\(677\) −7.24164e8 + 1.25429e9i −0.0896968 + 0.155359i −0.907383 − 0.420305i \(-0.861923\pi\)
0.817686 + 0.575664i \(0.195256\pi\)
\(678\) 2.81662e9 − 1.02517e9i 0.347076 − 0.126325i
\(679\) −4.35608e8 + 3.65519e8i −0.0534013 + 0.0448090i
\(680\) −3.24321e9 − 5.61741e9i −0.395543 − 0.685101i
\(681\) 9.23430e8 − 5.23703e9i 0.112044 − 0.635434i
\(682\) 2.11196e9 − 1.19775e10i 0.254941 − 1.44584i
\(683\) 3.59622e9 + 3.01758e9i 0.431890 + 0.362399i 0.832664 − 0.553778i \(-0.186814\pi\)
−0.400774 + 0.916177i \(0.631259\pi\)
\(684\) 2.92126e9 + 1.06325e9i 0.349039 + 0.127040i
\(685\) 2.16693e8 + 7.88699e7i 0.0257590 + 0.00937550i
\(686\) −3.49355e9 − 2.93144e9i −0.413174 − 0.346694i
\(687\) 2.95231e8 − 1.67434e9i 0.0347387 − 0.197013i
\(688\) −1.70768e8 + 9.68476e8i −0.0199916 + 0.113378i
\(689\) 8.85263e8 + 1.53332e9i 0.103111 + 0.178593i
\(690\) 1.58507e9 − 1.33003e9i 0.183686 − 0.154131i
\(691\) 2.52298e9 − 9.18291e8i 0.290898 − 0.105878i −0.192449 − 0.981307i \(-0.561643\pi\)
0.483347 + 0.875429i \(0.339421\pi\)
\(692\) −4.73210e8 + 8.19623e8i −0.0542853 + 0.0940249i
\(693\) −1.73867e9 − 3.01147e9i −0.198450 − 0.343726i
\(694\) −3.05699e9 − 2.56512e9i −0.347165 − 0.291306i
\(695\) −1.03758e10 + 1.79715e10i −1.17240 + 2.03066i
\(696\) −4.71903e8 − 2.67629e9i −0.0530542 − 0.300886i
\(697\) 1.55490e10 1.73935
\(698\) 1.29368e9 + 7.33682e9i 0.143990 + 0.816608i
\(699\) −1.85240e9 + 1.55435e9i −0.205147 + 0.172139i
\(700\) 1.87712e9 + 6.83215e8i 0.206846 + 0.0752860i
\(701\) 1.03200e10 − 3.75618e9i 1.13153 − 0.411844i 0.292684 − 0.956209i \(-0.405451\pi\)
0.838849 + 0.544365i \(0.183229\pi\)
\(702\) 1.35734e9 0.148084
\(703\) −8.52796e9 + 1.71512e8i −0.925766 + 0.0186188i
\(704\) 1.37002e9 0.147987
\(705\) −3.07684e9 + 1.11988e9i −0.330707 + 0.120367i
\(706\) 5.61900e9 + 2.04515e9i 0.600956 + 0.218730i
\(707\) −2.02667e9 + 1.70058e9i −0.215683 + 0.180980i
\(708\) 2.17622e8 + 1.23420e9i 0.0230455 + 0.130698i
\(709\) 1.26334e10 1.33124 0.665621 − 0.746290i \(-0.268167\pi\)
0.665621 + 0.746290i \(0.268167\pi\)
\(710\) −1.39188e9 − 7.89374e9i −0.145948 − 0.827711i
\(711\) −9.72911e8 + 1.68513e9i −0.101515 + 0.175829i
\(712\) 4.89481e9 + 4.10724e9i 0.508225 + 0.426452i
\(713\) −4.51668e9 − 7.82313e9i −0.466666 − 0.808290i
\(714\) 9.97641e8 − 1.72797e9i 0.102572 − 0.177661i
\(715\) −4.07195e9 + 1.48207e9i −0.416612 + 0.151634i
\(716\) −1.85799e9 + 1.55904e9i −0.189169 + 0.158731i
\(717\) 1.29539e9 + 2.24368e9i 0.131245 + 0.227323i
\(718\) −1.15017e9 + 6.52296e9i −0.115965 + 0.657672i
\(719\) −2.31580e9 + 1.31336e10i −0.232354 + 1.31775i 0.615760 + 0.787933i \(0.288849\pi\)
−0.848115 + 0.529813i \(0.822262\pi\)
\(720\) −2.20515e9 − 1.85034e9i −0.220178 − 0.184752i
\(721\) −4.63227e9 − 1.68601e9i −0.460278 − 0.167528i
\(722\) −9.58301e8 − 3.48793e8i −0.0947593 − 0.0344896i
\(723\) −2.41584e9 − 2.02713e9i −0.237730 − 0.199479i
\(724\) 9.05917e7 − 5.13771e8i 0.00887163 − 0.0503135i
\(725\) 3.64823e9 − 2.06901e10i 0.355548 − 2.01642i
\(726\) 6.50962e8 + 1.12750e9i 0.0631360 + 0.109355i
\(727\) 8.04187e8 − 6.74793e8i 0.0776224 − 0.0651329i −0.603151 − 0.797627i \(-0.706088\pi\)
0.680773 + 0.732494i \(0.261644\pi\)
\(728\) −3.77677e8 + 1.37463e8i −0.0362794 + 0.0132046i
\(729\) 7.51949e6 − 1.30241e7i 0.000718856 − 0.00124510i
\(730\) 8.53139e9 + 1.47768e10i 0.811689 + 1.40589i
\(731\) 5.81728e9 + 4.88127e9i 0.550819 + 0.462192i
\(732\) −8.89340e8 + 1.54038e9i −0.0838067 + 0.145158i
\(733\) 3.36430e8 + 1.90799e9i 0.0315523 + 0.178942i 0.996511 − 0.0834591i \(-0.0265968\pi\)
−0.964959 + 0.262401i \(0.915486\pi\)
\(734\) −3.55252e8 −0.0331589
\(735\) −9.83117e8 − 5.57553e9i −0.0913270 − 0.517941i
\(736\) 7.79501e8 − 6.54079e8i 0.0720683 − 0.0604725i
\(737\) 1.89134e10 + 6.88392e9i 1.74034 + 0.633431i
\(738\) 6.48436e9 − 2.36012e9i 0.593841 − 0.216140i
\(739\) 1.20398e9 0.109740 0.0548699 − 0.998494i \(-0.482526\pi\)
0.0548699 + 0.998494i \(0.482526\pi\)
\(740\) 7.47478e9 + 2.55159e9i 0.678090 + 0.231473i
\(741\) 1.19166e9 0.107594
\(742\) 2.43825e9 − 8.87450e8i 0.219111 − 0.0797499i
\(743\) −4.64468e9 − 1.69053e9i −0.415427 − 0.151203i 0.125846 − 0.992050i \(-0.459835\pi\)
−0.541273 + 0.840847i \(0.682058\pi\)
\(744\) 2.37249e9 − 1.99076e9i 0.211203 − 0.177220i
\(745\) 8.05699e7 + 4.56935e8i 0.00713881 + 0.0404862i
\(746\) −5.73400e9 −0.505676
\(747\) −2.81552e9 − 1.59676e10i −0.247136 − 1.40158i
\(748\) 5.28964e9 − 9.16192e9i 0.462137 − 0.800444i
\(749\) −1.64846e9 − 1.38322e9i −0.143348 − 0.120283i
\(750\) 1.39368e8 + 2.41393e8i 0.0120628 + 0.0208935i
\(751\) 2.65937e8 − 4.60616e8i 0.0229107 − 0.0396825i −0.854343 − 0.519710i \(-0.826040\pi\)
0.877253 + 0.480027i \(0.159373\pi\)
\(752\) −1.51312e9 + 5.50731e8i −0.129751 + 0.0472256i
\(753\) −4.37241e9 + 3.66889e9i −0.373198 + 0.313150i
\(754\) 2.11354e9 + 3.66076e9i 0.179560 + 0.311008i
\(755\) 2.41827e9 − 1.37147e10i 0.204499 − 1.15977i
\(756\) 3.45421e8 − 1.95898e9i 0.0290752 − 0.164894i
\(757\) −8.05922e9 − 6.76249e9i −0.675239 − 0.566593i 0.239372 − 0.970928i \(-0.423059\pi\)
−0.914611 +