Properties

Label 38.7.f.a.3.6
Level $38$
Weight $7$
Character 38.3
Analytic conductor $8.742$
Analytic rank $0$
Dimension $60$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [38,7,Mod(3,38)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(38, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([13]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("38.3");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 38.f (of order \(18\), 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: \(8.74205517755\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(10\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 3.6
Character \(\chi\) \(=\) 38.3
Dual form 38.7.f.a.13.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.63616 - 4.33340i) q^{2} +(-14.7348 - 40.4836i) q^{3} +(-5.55674 - 31.5138i) q^{4} +(40.1148 - 227.502i) q^{5} +(-229.010 - 83.3528i) q^{6} +(276.187 + 478.370i) q^{7} +(-156.767 - 90.5097i) q^{8} +(-863.360 + 724.445i) q^{9} +O(q^{10})\) \(q+(3.63616 - 4.33340i) q^{2} +(-14.7348 - 40.4836i) q^{3} +(-5.55674 - 31.5138i) q^{4} +(40.1148 - 227.502i) q^{5} +(-229.010 - 83.3528i) q^{6} +(276.187 + 478.370i) q^{7} +(-156.767 - 90.5097i) q^{8} +(-863.360 + 724.445i) q^{9} +(-839.995 - 1001.07i) q^{10} +(155.096 - 268.634i) q^{11} +(-1193.92 + 689.308i) q^{12} +(246.987 - 678.591i) q^{13} +(3077.23 + 542.599i) q^{14} +(-9801.19 + 1728.21i) q^{15} +(-962.245 + 350.229i) q^{16} +(3905.10 + 3276.77i) q^{17} +6375.48i q^{18} +(534.951 - 6838.11i) q^{19} -7392.37 q^{20} +(15296.6 - 18229.8i) q^{21} +(-600.145 - 1648.89i) q^{22} +(1878.32 + 10652.5i) q^{23} +(-1354.22 + 7680.15i) q^{24} +(-35465.3 - 12908.3i) q^{25} +(-2042.53 - 3537.76i) q^{26} +(14850.7 + 8574.07i) q^{27} +(13540.6 - 11361.9i) q^{28} +(7573.09 + 9025.25i) q^{29} +(-28149.6 + 48756.5i) q^{30} +(12291.6 - 7096.59i) q^{31} +(-1981.19 + 5443.28i) q^{32} +(-13160.6 - 2320.56i) q^{33} +(28399.1 - 5007.53i) q^{34} +(119909. - 43643.5i) q^{35} +(27627.5 + 23182.3i) q^{36} -48685.2i q^{37} +(-27687.1 - 27182.6i) q^{38} -31111.1 q^{39} +(-26879.8 + 32034.1i) q^{40} +(-7628.56 - 20959.3i) q^{41} +(-23376.1 - 132573. i) q^{42} +(-4660.89 + 26433.2i) q^{43} +(-9327.51 - 3394.93i) q^{44} +(130179. + 225477. i) q^{45} +(52991.3 + 30594.5i) q^{46} +(124966. - 104859. i) q^{47} +(28357.0 + 33794.6i) q^{48} +(-93734.4 + 162353. i) q^{49} +(-184894. + 106749. i) q^{50} +(75114.4 - 206375. i) q^{51} +(-22757.5 - 4012.76i) q^{52} +(-257781. + 45453.7i) q^{53} +(91154.4 - 33177.5i) q^{54} +(-54893.1 - 46060.8i) q^{55} -99990.5i q^{56} +(-284714. + 79101.6i) q^{57} +66647.0 q^{58} +(-58853.6 + 70138.9i) q^{59} +(108925. + 299270. i) q^{60} +(-35660.8 - 202243. i) q^{61} +(13942.0 - 79068.9i) q^{62} +(-585003. - 212924. i) q^{63} +(16384.0 + 28377.9i) q^{64} +(-144473. - 83411.6i) q^{65} +(-57909.8 + 48592.1i) q^{66} +(76179.6 + 90787.3i) q^{67} +(81563.9 - 141273. i) q^{68} +(403574. - 233003. i) q^{69} +(246885. - 678310. i) q^{70} +(555066. + 97873.1i) q^{71} +(200916. - 35426.9i) q^{72} +(-241308. + 87828.8i) q^{73} +(-210973. - 177027. i) q^{74} +1.62597e6i q^{75} +(-218468. + 21139.2i) q^{76} +171342. q^{77} +(-113125. + 134817. i) q^{78} +(-92287.5 - 253558. i) q^{79} +(41077.5 + 232962. i) q^{80} +(-14384.8 + 81580.0i) q^{81} +(-118564. - 43153.7i) q^{82} +(425729. + 737384. i) q^{83} +(-659489. - 380756. i) q^{84} +(902124. - 756972. i) q^{85} +(97598.0 + 116313. i) q^{86} +(253787. - 439571. i) q^{87} +(-48627.9 + 28075.3i) q^{88} +(-169167. + 464783. i) q^{89} +(1.45044e6 + 255751. i) q^{90} +(392833. - 69267.0i) q^{91} +(325263. - 118386. i) q^{92} +(-468411. - 393043. i) q^{93} -922809. i q^{94} +(-1.53422e6 - 396012. i) q^{95} +249556. q^{96} +(152828. - 182133. i) q^{97} +(362707. + 996528. i) q^{98} +(60706.9 + 344286. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60 q + 30 q^{3} - 240 q^{6} + 432 q^{7} + 690 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 60 q + 30 q^{3} - 240 q^{6} + 432 q^{7} + 690 q^{9} - 3360 q^{11} + 9660 q^{13} + 2496 q^{14} - 37464 q^{15} + 7704 q^{17} + 46704 q^{19} + 21504 q^{20} + 78732 q^{21} - 20304 q^{22} - 54120 q^{23} + 7680 q^{24} - 41328 q^{25} - 25536 q^{26} - 124830 q^{27} + 65280 q^{28} - 21840 q^{29} + 30780 q^{31} - 54582 q^{33} - 70560 q^{34} - 56796 q^{35} - 22080 q^{36} + 52080 q^{38} + 496344 q^{39} + 83394 q^{41} + 38880 q^{42} - 294384 q^{43} - 8448 q^{44} - 391824 q^{45} + 738720 q^{46} + 639264 q^{47} + 61440 q^{48} - 85530 q^{49} - 689472 q^{50} - 215478 q^{51} - 456960 q^{52} - 1189428 q^{53} - 907200 q^{54} - 316512 q^{55} + 517776 q^{57} + 440640 q^{58} + 957390 q^{59} + 586752 q^{60} + 1390404 q^{61} + 978384 q^{62} + 2002152 q^{63} + 983040 q^{64} - 878940 q^{65} - 976992 q^{66} - 2920854 q^{67} - 78144 q^{68} - 2667600 q^{69} - 643392 q^{70} + 1585980 q^{71} + 706560 q^{72} + 1734648 q^{73} - 1167552 q^{74} - 411264 q^{76} - 1481400 q^{77} - 2170608 q^{78} + 4991952 q^{79} + 40002 q^{81} + 2299392 q^{82} - 30672 q^{83} + 1313280 q^{84} + 815976 q^{85} - 1424976 q^{86} - 125892 q^{87} - 6804636 q^{89} - 2283456 q^{90} - 3838704 q^{91} - 244992 q^{92} - 3271128 q^{93} - 4631640 q^{95} + 2112390 q^{97} + 7177728 q^{98} + 21467982 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).

\(n\) \(21\)
\(\chi(n)\) \(e\left(\frac{13}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.63616 4.33340i 0.454519 0.541675i
\(3\) −14.7348 40.4836i −0.545734 1.49939i −0.839416 0.543489i \(-0.817103\pi\)
0.293682 0.955903i \(-0.405119\pi\)
\(4\) −5.55674 31.5138i −0.0868241 0.492404i
\(5\) 40.1148 227.502i 0.320918 1.82002i −0.216013 0.976391i \(-0.569305\pi\)
0.536931 0.843626i \(-0.319584\pi\)
\(6\) −229.010 83.3528i −1.06023 0.385892i
\(7\) 276.187 + 478.370i 0.805211 + 1.39467i 0.916149 + 0.400839i \(0.131281\pi\)
−0.110938 + 0.993827i \(0.535385\pi\)
\(8\) −156.767 90.5097i −0.306186 0.176777i
\(9\) −863.360 + 724.445i −1.18431 + 0.993752i
\(10\) −839.995 1001.07i −0.839995 1.00107i
\(11\) 155.096 268.634i 0.116526 0.201828i −0.801863 0.597508i \(-0.796158\pi\)
0.918389 + 0.395680i \(0.129491\pi\)
\(12\) −1193.92 + 689.308i −0.690924 + 0.398905i
\(13\) 246.987 678.591i 0.112420 0.308872i −0.870705 0.491805i \(-0.836337\pi\)
0.983125 + 0.182934i \(0.0585593\pi\)
\(14\) 3077.23 + 542.599i 1.12144 + 0.197740i
\(15\) −9801.19 + 1728.21i −2.90406 + 0.512063i
\(16\) −962.245 + 350.229i −0.234923 + 0.0855050i
\(17\) 3905.10 + 3276.77i 0.794850 + 0.666959i 0.946941 0.321408i \(-0.104156\pi\)
−0.152090 + 0.988367i \(0.548600\pi\)
\(18\) 6375.48i 1.09319i
\(19\) 534.951 6838.11i 0.0779926 0.996954i
\(20\) −7392.37 −0.924047
\(21\) 15296.6 18229.8i 1.65172 1.96844i
\(22\) −600.145 1648.89i −0.0563623 0.154854i
\(23\) 1878.32 + 10652.5i 0.154378 + 0.875521i 0.959352 + 0.282212i \(0.0910680\pi\)
−0.804974 + 0.593310i \(0.797821\pi\)
\(24\) −1354.22 + 7680.15i −0.0979614 + 0.555566i
\(25\) −35465.3 12908.3i −2.26978 0.826133i
\(26\) −2042.53 3537.76i −0.116211 0.201283i
\(27\) 14850.7 + 8574.07i 0.754495 + 0.435608i
\(28\) 13540.6 11361.9i 0.616827 0.517580i
\(29\) 7573.09 + 9025.25i 0.310512 + 0.370054i 0.898620 0.438729i \(-0.144571\pi\)
−0.588107 + 0.808783i \(0.700127\pi\)
\(30\) −28149.6 + 48756.5i −1.04258 + 1.80580i
\(31\) 12291.6 7096.59i 0.412596 0.238212i −0.279309 0.960201i \(-0.590105\pi\)
0.691905 + 0.721989i \(0.256772\pi\)
\(32\) −1981.19 + 5443.28i −0.0604612 + 0.166116i
\(33\) −13160.6 2320.56i −0.366212 0.0645731i
\(34\) 28399.1 5007.53i 0.722550 0.127405i
\(35\) 119909. 43643.5i 2.79672 1.01792i
\(36\) 27627.5 + 23182.3i 0.592154 + 0.496876i
\(37\) 48685.2i 0.961152i −0.876953 0.480576i \(-0.840428\pi\)
0.876953 0.480576i \(-0.159572\pi\)
\(38\) −27687.1 27182.6i −0.504576 0.495382i
\(39\) −31111.1 −0.524472
\(40\) −26879.8 + 32034.1i −0.419997 + 0.500533i
\(41\) −7628.56 20959.3i −0.110686 0.304106i 0.871966 0.489566i \(-0.162845\pi\)
−0.982652 + 0.185460i \(0.940623\pi\)
\(42\) −23376.1 132573.i −0.315518 1.78939i
\(43\) −4660.89 + 26433.2i −0.0586223 + 0.332464i −0.999988 0.00492458i \(-0.998432\pi\)
0.941366 + 0.337388i \(0.109544\pi\)
\(44\) −9327.51 3394.93i −0.109498 0.0398541i
\(45\) 130179. + 225477.i 1.42858 + 2.47437i
\(46\) 52991.3 + 30594.5i 0.544416 + 0.314319i
\(47\) 124966. 104859.i 1.20364 1.00998i 0.204124 0.978945i \(-0.434565\pi\)
0.999518 0.0310308i \(-0.00987899\pi\)
\(48\) 28357.0 + 33794.6i 0.256411 + 0.305579i
\(49\) −93734.4 + 162353.i −0.796729 + 1.37998i
\(50\) −184894. + 106749.i −1.47915 + 0.853991i
\(51\) 75114.4 206375.i 0.566256 1.55578i
\(52\) −22757.5 4012.76i −0.161850 0.0285386i
\(53\) −257781. + 45453.7i −1.73150 + 0.305310i −0.948516 0.316730i \(-0.897415\pi\)
−0.782985 + 0.622040i \(0.786304\pi\)
\(54\) 91154.4 33177.5i 0.578890 0.210699i
\(55\) −54893.1 46060.8i −0.329936 0.276849i
\(56\) 99990.5i 0.569370i
\(57\) −284714. + 79101.6i −1.53739 + 0.427130i
\(58\) 66647.0 0.341583
\(59\) −58853.6 + 70138.9i −0.286561 + 0.341510i −0.890051 0.455860i \(-0.849332\pi\)
0.603491 + 0.797370i \(0.293776\pi\)
\(60\) 108925. + 299270.i 0.504284 + 1.38551i
\(61\) −35660.8 202243.i −0.157109 0.891012i −0.956832 0.290642i \(-0.906131\pi\)
0.799723 0.600370i \(-0.204980\pi\)
\(62\) 13942.0 79068.9i 0.0584992 0.331765i
\(63\) −585003. 212924.i −2.33957 0.851534i
\(64\) 16384.0 + 28377.9i 0.0625000 + 0.108253i
\(65\) −144473. 83411.6i −0.526074 0.303729i
\(66\) −57909.8 + 48592.1i −0.201428 + 0.169018i
\(67\) 76179.6 + 90787.3i 0.253288 + 0.301857i 0.877673 0.479260i \(-0.159095\pi\)
−0.624385 + 0.781117i \(0.714650\pi\)
\(68\) 81563.9 141273.i 0.259401 0.449296i
\(69\) 403574. 233003.i 1.22850 0.709275i
\(70\) 246885. 678310.i 0.719781 1.97758i
\(71\) 555066. + 97873.1i 1.55085 + 0.273456i 0.882471 0.470366i \(-0.155878\pi\)
0.668377 + 0.743822i \(0.266989\pi\)
\(72\) 200916. 35426.9i 0.538291 0.0949152i
\(73\) −241308. + 87828.8i −0.620301 + 0.225771i −0.633005 0.774148i \(-0.718179\pi\)
0.0127032 + 0.999919i \(0.495956\pi\)
\(74\) −210973. 177027.i −0.520632 0.436862i
\(75\) 1.62597e6i 3.85414i
\(76\) −218468. + 21139.2i −0.497676 + 0.0481558i
\(77\) 171342. 0.375311
\(78\) −113125. + 134817.i −0.238383 + 0.284093i
\(79\) −92287.5 253558.i −0.187181 0.514275i 0.810236 0.586104i \(-0.199339\pi\)
−0.997417 + 0.0718283i \(0.977117\pi\)
\(80\) 41077.5 + 232962.i 0.0802295 + 0.455004i
\(81\) −14384.8 + 81580.0i −0.0270674 + 0.153507i
\(82\) −118564. 43153.7i −0.215036 0.0782665i
\(83\) 425729. + 737384.i 0.744559 + 1.28961i 0.950401 + 0.311028i \(0.100673\pi\)
−0.205842 + 0.978585i \(0.565993\pi\)
\(84\) −659489. 380756.i −1.11268 0.642405i
\(85\) 902124. 756972.i 1.46896 1.23260i
\(86\) 97598.0 + 116313.i 0.153442 + 0.182866i
\(87\) 253787. 439571.i 0.385399 0.667531i
\(88\) −48627.9 + 28075.3i −0.0713571 + 0.0411980i
\(89\) −169167. + 464783.i −0.239964 + 0.659296i 0.759992 + 0.649932i \(0.225203\pi\)
−0.999956 + 0.00936340i \(0.997019\pi\)
\(90\) 1.45044e6 + 255751.i 1.98962 + 0.350824i
\(91\) 392833. 69267.0i 0.521295 0.0919184i
\(92\) 325263. 118386.i 0.417706 0.152033i
\(93\) −468411. 393043.i −0.582342 0.488643i
\(94\) 922809.i 1.11104i
\(95\) −1.53422e6 396012.i −1.78944 0.461888i
\(96\) 249556. 0.282068
\(97\) 152828. 182133.i 0.167451 0.199560i −0.675793 0.737092i \(-0.736199\pi\)
0.843244 + 0.537531i \(0.180643\pi\)
\(98\) 362707. + 996528.i 0.385369 + 1.05879i
\(99\) 60706.9 + 344286.i 0.0625652 + 0.354825i
\(100\) −209719. + 1.18938e6i −0.209719 + 1.18938i
\(101\) 1.78893e6 + 651116.i 1.73631 + 0.631967i 0.999048 0.0436345i \(-0.0138937\pi\)
0.737267 + 0.675601i \(0.236116\pi\)
\(102\) −621179. 1.07591e6i −0.585351 1.01386i
\(103\) 928887. + 536293.i 0.850063 + 0.490784i 0.860672 0.509160i \(-0.170044\pi\)
−0.0106091 + 0.999944i \(0.503377\pi\)
\(104\) −100139. + 84026.2i −0.0890228 + 0.0746990i
\(105\) −3.53369e6 4.21129e6i −3.05253 3.63787i
\(106\) −740362. + 1.28234e6i −0.621622 + 1.07668i
\(107\) 1.69568e6 979004.i 1.38418 0.799159i 0.391532 0.920165i \(-0.371945\pi\)
0.992652 + 0.121006i \(0.0386120\pi\)
\(108\) 187680. 515647.i 0.148987 0.409337i
\(109\) −1.08811e6 191863.i −0.840221 0.148154i −0.263055 0.964781i \(-0.584730\pi\)
−0.577165 + 0.816627i \(0.695841\pi\)
\(110\) −399200. + 70389.7i −0.299925 + 0.0528848i
\(111\) −1.97095e6 + 717368.i −1.44114 + 0.524533i
\(112\) −433299. 363581.i −0.308414 0.258790i
\(113\) 1.42947e6i 0.990692i −0.868696 0.495346i \(-0.835041\pi\)
0.868696 0.495346i \(-0.164959\pi\)
\(114\) −692484. + 1.52140e6i −0.467407 + 1.02690i
\(115\) 2.49881e6 1.64301
\(116\) 242339. 288808.i 0.155256 0.185027i
\(117\) 278364. + 764798.i 0.173802 + 0.477517i
\(118\) 89939.5 + 510072.i 0.0547400 + 0.310446i
\(119\) −488970. + 2.77309e6i −0.290162 + 1.64559i
\(120\) 1.69293e6 + 616175.i 0.979703 + 0.356583i
\(121\) 837671. + 1.45089e6i 0.472844 + 0.818989i
\(122\) −1.00607e6 580853.i −0.554048 0.319880i
\(123\) −736102. + 617663.i −0.395570 + 0.331922i
\(124\) −291942. 347923.i −0.153120 0.182481i
\(125\) −2.55457e6 + 4.42465e6i −1.30794 + 2.26542i
\(126\) −3.04984e6 + 1.76083e6i −1.52464 + 0.880248i
\(127\) 585947. 1.60988e6i 0.286053 0.785925i −0.710556 0.703641i \(-0.751556\pi\)
0.996609 0.0822840i \(-0.0262215\pi\)
\(128\) 182548. + 32188.1i 0.0870455 + 0.0153485i
\(129\) 1.13879e6 200799.i 0.530486 0.0935390i
\(130\) −886783. + 322763.i −0.403634 + 0.146911i
\(131\) −1.91811e6 1.60948e6i −0.853217 0.715934i 0.107279 0.994229i \(-0.465786\pi\)
−0.960496 + 0.278295i \(0.910231\pi\)
\(132\) 427635.i 0.185931i
\(133\) 3.41890e6 1.63269e6i 1.45322 0.693984i
\(134\) 670419. 0.278633
\(135\) 2.54635e6 3.03462e6i 1.03494 1.23340i
\(136\) −315613. 867140.i −0.125469 0.344725i
\(137\) 300681. + 1.70524e6i 0.116935 + 0.663170i 0.985774 + 0.168076i \(0.0537553\pi\)
−0.868839 + 0.495094i \(0.835134\pi\)
\(138\) 457760. 2.59608e6i 0.174181 0.987828i
\(139\) −128917. 46921.9i −0.0480027 0.0174716i 0.317907 0.948122i \(-0.397020\pi\)
−0.365910 + 0.930650i \(0.619242\pi\)
\(140\) −2.04168e6 3.53629e6i −0.744052 1.28874i
\(141\) −6.08641e6 3.51399e6i −2.17122 1.25355i
\(142\) 2.44243e6 2.04944e6i 0.853015 0.715765i
\(143\) −143986. 171596.i −0.0492393 0.0586811i
\(144\) 577043. 999468.i 0.193251 0.334720i
\(145\) 2.35706e6 1.36085e6i 0.773154 0.446381i
\(146\) −496835. + 1.36504e6i −0.159644 + 0.438619i
\(147\) 7.95378e6 + 1.40247e6i 2.50393 + 0.441510i
\(148\) −1.53426e6 + 270531.i −0.473275 + 0.0834511i
\(149\) −2.67602e6 + 973991.i −0.808966 + 0.294440i −0.713197 0.700964i \(-0.752753\pi\)
−0.0957695 + 0.995404i \(0.530531\pi\)
\(150\) 7.04596e6 + 5.91226e6i 2.08769 + 1.75178i
\(151\) 1.52429e6i 0.442728i −0.975191 0.221364i \(-0.928949\pi\)
0.975191 0.221364i \(-0.0710508\pi\)
\(152\) −702778. + 1.02357e6i −0.200118 + 0.291466i
\(153\) −5.74535e6 −1.60414
\(154\) 623026. 742493.i 0.170586 0.203297i
\(155\) −1.12141e6 3.08105e6i −0.301141 0.827378i
\(156\) 172877. + 980432.i 0.0455368 + 0.258252i
\(157\) 133995. 759923.i 0.0346250 0.196368i −0.962589 0.270967i \(-0.912657\pi\)
0.997214 + 0.0745990i \(0.0237677\pi\)
\(158\) −1.43434e6 522057.i −0.363648 0.132357i
\(159\) 5.63848e6 + 9.76614e6i 1.40272 + 2.42958i
\(160\) 1.15888e6 + 669081.i 0.282930 + 0.163350i
\(161\) −4.57706e6 + 3.84061e6i −1.09675 + 0.920285i
\(162\) 301214. + 358972.i 0.0708483 + 0.0844337i
\(163\) 390844. 676962.i 0.0902487 0.156315i −0.817367 0.576117i \(-0.804567\pi\)
0.907616 + 0.419802i \(0.137900\pi\)
\(164\) −618118. + 356871.i −0.140133 + 0.0809058i
\(165\) −1.05587e6 + 2.90097e6i −0.235048 + 0.645790i
\(166\) 4.74340e6 + 836389.i 1.03697 + 0.182845i
\(167\) 406585. 71691.9i 0.0872975 0.0153929i −0.129829 0.991536i \(-0.541443\pi\)
0.217126 + 0.976144i \(0.430332\pi\)
\(168\) −4.04798e6 + 1.47334e6i −0.853709 + 0.310725i
\(169\) 3.29807e6 + 2.76741e6i 0.683281 + 0.573341i
\(170\) 6.66173e6i 1.35594i
\(171\) 4.49198e6 + 6.29129e6i 0.898358 + 1.25821i
\(172\) 858911. 0.168796
\(173\) 3.14520e6 3.74830e6i 0.607448 0.723929i −0.371410 0.928469i \(-0.621125\pi\)
0.978858 + 0.204540i \(0.0655699\pi\)
\(174\) −982032. 2.69811e6i −0.186414 0.512167i
\(175\) −3.62011e6 2.05307e7i −0.675473 3.83080i
\(176\) −55156.9 + 312810.i −0.0101172 + 0.0573777i
\(177\) 3.70667e6 + 1.34912e6i 0.668443 + 0.243293i
\(178\) 1.39897e6 + 2.42309e6i 0.248056 + 0.429645i
\(179\) 1.55899e6 + 900082.i 0.271821 + 0.156936i 0.629715 0.776826i \(-0.283172\pi\)
−0.357894 + 0.933762i \(0.616505\pi\)
\(180\) 6.38228e6 5.35537e6i 1.09436 0.918274i
\(181\) 1.23889e6 + 1.47645e6i 0.208928 + 0.248991i 0.860325 0.509747i \(-0.170261\pi\)
−0.651396 + 0.758738i \(0.725816\pi\)
\(182\) 1.12824e6 1.95417e6i 0.187149 0.324151i
\(183\) −7.66206e6 + 4.42369e6i −1.25024 + 0.721824i
\(184\) 669693. 1.83997e6i 0.107503 0.295363i
\(185\) −1.10760e7 1.95300e6i −1.74931 0.308451i
\(186\) −3.40643e6 + 600645.i −0.529371 + 0.0933425i
\(187\) 1.48591e6 540829.i 0.227232 0.0827056i
\(188\) −3.99890e6 3.35548e6i −0.601821 0.504988i
\(189\) 9.47219e6i 1.40302i
\(190\) −7.29476e6 + 5.20845e6i −1.06353 + 0.759360i
\(191\) 3.44283e6 0.494101 0.247051 0.969003i \(-0.420539\pi\)
0.247051 + 0.969003i \(0.420539\pi\)
\(192\) 907425. 1.08143e6i 0.128206 0.152790i
\(193\) −1.11377e6 3.06007e6i −0.154926 0.425657i 0.837811 0.545961i \(-0.183835\pi\)
−0.992737 + 0.120304i \(0.961613\pi\)
\(194\) −233550. 1.32453e6i −0.0319871 0.181408i
\(195\) −1.24802e6 + 7.07785e6i −0.168312 + 0.954547i
\(196\) 5.63722e6 + 2.05178e6i 0.748680 + 0.272497i
\(197\) −426793. 739228.i −0.0558237 0.0966896i 0.836763 0.547565i \(-0.184445\pi\)
−0.892587 + 0.450876i \(0.851112\pi\)
\(198\) 1.71267e6 + 988810.i 0.220637 + 0.127385i
\(199\) −9.53313e6 + 7.99924e6i −1.20970 + 1.01506i −0.210397 + 0.977616i \(0.567476\pi\)
−0.999299 + 0.0374393i \(0.988080\pi\)
\(200\) 4.39148e6 + 5.23356e6i 0.548935 + 0.654195i
\(201\) 2.55291e6 4.42176e6i 0.314374 0.544512i
\(202\) 9.32636e6 5.38458e6i 1.13151 0.653277i
\(203\) −2.22582e6 + 6.11540e6i −0.266074 + 0.731033i
\(204\) −6.92107e6 1.22037e6i −0.815234 0.143748i
\(205\) −5.07430e6 + 894737.i −0.588999 + 0.103856i
\(206\) 5.70155e6 2.07519e6i 0.652216 0.237387i
\(207\) −9.33880e6 7.83618e6i −1.05288 0.883473i
\(208\) 739473.i 0.0821736i
\(209\) −1.75398e6 1.20427e6i −0.192125 0.131912i
\(210\) −3.10983e7 −3.35798
\(211\) −8.43850e6 + 1.00566e7i −0.898293 + 1.07054i 0.0988571 + 0.995102i \(0.468481\pi\)
−0.997150 + 0.0754424i \(0.975963\pi\)
\(212\) 2.86484e6 + 7.87109e6i 0.300672 + 0.826090i
\(213\) −4.21654e6 2.39132e7i −0.436333 2.47457i
\(214\) 1.92336e6 1.09079e7i 0.196254 1.11301i
\(215\) 5.82664e6 + 2.12072e6i 0.586277 + 0.213387i
\(216\) −1.55207e6 2.68827e6i −0.154011 0.266754i
\(217\) 6.78959e6 + 3.91997e6i 0.664454 + 0.383622i
\(218\) −4.78796e6 + 4.01757e6i −0.462148 + 0.387788i
\(219\) 7.11126e6 + 8.47486e6i 0.677039 + 0.806864i
\(220\) −1.14653e6 + 1.98584e6i −0.107675 + 0.186499i
\(221\) 3.18810e6 1.84065e6i 0.295362 0.170527i
\(222\) −4.05805e6 + 1.11494e7i −0.370901 + 1.01904i
\(223\) 8.86605e6 + 1.56332e6i 0.799495 + 0.140973i 0.558446 0.829541i \(-0.311398\pi\)
0.241048 + 0.970513i \(0.422509\pi\)
\(224\) −3.15109e6 + 555621.i −0.280360 + 0.0494350i
\(225\) 3.99707e7 1.45482e7i 3.50909 1.27720i
\(226\) −6.19445e6 5.19776e6i −0.536633 0.450289i
\(227\) 7.75257e6i 0.662778i 0.943494 + 0.331389i \(0.107517\pi\)
−0.943494 + 0.331389i \(0.892483\pi\)
\(228\) 4.07487e6 + 8.53287e6i 0.343803 + 0.719931i
\(229\) −1.08004e7 −0.899359 −0.449680 0.893190i \(-0.648462\pi\)
−0.449680 + 0.893190i \(0.648462\pi\)
\(230\) 9.08605e6 1.08283e7i 0.746778 0.889976i
\(231\) −2.52469e6 6.93653e6i −0.204820 0.562738i
\(232\) −370340. 2.10030e6i −0.0296576 0.168197i
\(233\) −786395. + 4.45987e6i −0.0621689 + 0.352577i 0.937816 + 0.347132i \(0.112844\pi\)
−0.999985 + 0.00544525i \(0.998267\pi\)
\(234\) 4.32635e6 + 1.57466e6i 0.337656 + 0.122897i
\(235\) −1.88426e7 3.26364e7i −1.45190 2.51477i
\(236\) 2.53738e6 + 1.46496e6i 0.193041 + 0.111452i
\(237\) −8.90509e6 + 7.47226e6i −0.668950 + 0.561315i
\(238\) 1.02389e7 + 1.22023e7i 0.759493 + 0.905128i
\(239\) −4.95624e6 + 8.58446e6i −0.363043 + 0.628810i −0.988460 0.151481i \(-0.951596\pi\)
0.625417 + 0.780291i \(0.284929\pi\)
\(240\) 8.82588e6 5.09562e6i 0.638446 0.368607i
\(241\) 1.51733e6 4.16882e6i 0.108400 0.297826i −0.873619 0.486611i \(-0.838233\pi\)
0.982018 + 0.188785i \(0.0604551\pi\)
\(242\) 9.33319e6 + 1.64569e6i 0.658543 + 0.116119i
\(243\) 1.58257e7 2.79049e6i 1.10292 0.194474i
\(244\) −6.17529e6 + 2.24762e6i −0.425097 + 0.154723i
\(245\) 3.31754e7 + 2.78375e7i 2.25589 + 1.89292i
\(246\) 5.43575e6i 0.365135i
\(247\) −4.50815e6 2.05194e6i −0.299163 0.136167i
\(248\) −2.56924e6 −0.168442
\(249\) 2.35789e7 2.81003e7i 1.52731 1.82017i
\(250\) 9.88497e6 + 2.71587e7i 0.632638 + 1.73816i
\(251\) −1.07382e6 6.08996e6i −0.0679066 0.385118i −0.999752 0.0222624i \(-0.992913\pi\)
0.931846 0.362855i \(-0.118198\pi\)
\(252\) −3.45933e6 + 1.96188e7i −0.216168 + 1.22595i
\(253\) 3.15293e6 + 1.14757e6i 0.194694 + 0.0708629i
\(254\) −4.84564e6 8.39290e6i −0.295699 0.512166i
\(255\) −4.39376e7 2.53674e7i −2.64982 1.52987i
\(256\) 803256. 674012.i 0.0478778 0.0401742i
\(257\) 2.40025e6 + 2.86051e6i 0.141403 + 0.168517i 0.832098 0.554629i \(-0.187140\pi\)
−0.690695 + 0.723146i \(0.742695\pi\)
\(258\) 3.27067e6 5.66497e6i 0.190448 0.329866i
\(259\) 2.32896e7 1.34462e7i 1.34049 0.773930i
\(260\) −1.82582e6 + 5.01640e6i −0.103881 + 0.285412i
\(261\) −1.30766e7 2.30576e6i −0.735485 0.129686i
\(262\) −1.39491e7 + 2.45960e6i −0.775607 + 0.136760i
\(263\) 4.86630e6 1.77119e6i 0.267505 0.0973638i −0.204785 0.978807i \(-0.565650\pi\)
0.472290 + 0.881443i \(0.343427\pi\)
\(264\) 1.85311e6 + 1.55495e6i 0.100714 + 0.0845091i
\(265\) 6.04690e7i 3.24934i
\(266\) 5.35652e6 2.07522e7i 0.284602 1.10260i
\(267\) 2.13087e7 1.11950
\(268\) 2.43775e6 2.90519e6i 0.126644 0.150928i
\(269\) −6.02461e6 1.65525e7i −0.309508 0.850366i −0.992753 0.120177i \(-0.961654\pi\)
0.683245 0.730190i \(-0.260568\pi\)
\(270\) −3.89131e6 2.20687e7i −0.197699 1.12121i
\(271\) −3.54594e6 + 2.01100e7i −0.178166 + 1.01043i 0.756261 + 0.654271i \(0.227024\pi\)
−0.934426 + 0.356157i \(0.884087\pi\)
\(272\) −4.90528e6 1.78538e6i −0.243757 0.0887203i
\(273\) −8.59250e6 1.48826e7i −0.422310 0.731463i
\(274\) 8.48283e6 + 4.89756e6i 0.412372 + 0.238083i
\(275\) −8.96813e6 + 7.52515e6i −0.431225 + 0.361841i
\(276\) −9.58539e6 1.14234e7i −0.455913 0.543336i
\(277\) −538557. + 932808.i −0.0253392 + 0.0438887i −0.878417 0.477895i \(-0.841400\pi\)
0.853078 + 0.521784i \(0.174733\pi\)
\(278\) −672094. + 388034.i −0.0312821 + 0.0180607i
\(279\) −5.47103e6 + 1.50315e7i −0.251917 + 0.692135i
\(280\) −2.27480e7 4.01109e6i −1.03626 0.182721i
\(281\) 1.74167e7 3.07104e6i 0.784960 0.138410i 0.233218 0.972425i \(-0.425074\pi\)
0.551742 + 0.834015i \(0.313963\pi\)
\(282\) −3.73587e7 + 1.35974e7i −1.66588 + 0.606331i
\(283\) −2.01884e7 1.69401e7i −0.890723 0.747406i 0.0776317 0.996982i \(-0.475264\pi\)
−0.968355 + 0.249576i \(0.919709\pi\)
\(284\) 1.80361e7i 0.787386i
\(285\) 6.57455e6 + 6.79461e7i 0.284009 + 2.93515i
\(286\) −1.26715e6 −0.0541663
\(287\) 7.91940e6 9.43797e6i 0.335001 0.399239i
\(288\) −2.23288e6 6.13478e6i −0.0934733 0.256816i
\(289\) 321153. + 1.82135e6i 0.0133051 + 0.0754571i
\(290\) 2.67353e6 1.51623e7i 0.109620 0.621687i
\(291\) −9.62531e6 3.50332e6i −0.390603 0.142168i
\(292\) 4.10871e6 + 7.11649e6i 0.165028 + 0.285836i
\(293\) −2.24958e7 1.29879e7i −0.894330 0.516342i −0.0189738 0.999820i \(-0.506040\pi\)
−0.875356 + 0.483478i \(0.839373\pi\)
\(294\) 3.49986e7 2.93673e7i 1.37724 1.15564i
\(295\) 1.35959e7 + 1.62029e7i 0.529591 + 0.631142i
\(296\) −4.40648e6 + 7.63225e6i −0.169909 + 0.294291i
\(297\) 4.60656e6 2.65960e6i 0.175836 0.101519i
\(298\) −5.50973e6 + 1.51379e7i −0.208200 + 0.572026i
\(299\) 7.69259e6 + 1.35641e6i 0.287779 + 0.0507432i
\(300\) 5.12404e7 9.03507e6i 1.89779 0.334632i
\(301\) −1.39321e7 + 5.07088e6i −0.510879 + 0.185945i
\(302\) −6.60536e6 5.54255e6i −0.239815 0.201228i
\(303\) 8.20163e7i 2.94830i
\(304\) 1.88015e6 + 6.76729e6i 0.0669223 + 0.240876i
\(305\) −4.74412e7 −1.67208
\(306\) −2.08910e7 + 2.48969e7i −0.729113 + 0.868923i
\(307\) −7.87355e6 2.16324e7i −0.272117 0.747635i −0.998197 0.0600246i \(-0.980882\pi\)
0.726080 0.687610i \(-0.241340\pi\)
\(308\) −952102. 5.39964e6i −0.0325860 0.184805i
\(309\) 8.02409e6 4.55069e7i 0.271970 1.54242i
\(310\) −1.74291e7 6.34366e6i −0.585045 0.212939i
\(311\) 4.17457e6 + 7.23057e6i 0.138781 + 0.240376i 0.927036 0.374973i \(-0.122348\pi\)
−0.788254 + 0.615350i \(0.789015\pi\)
\(312\) 4.87721e6 + 2.81586e6i 0.160586 + 0.0927144i
\(313\) 1.27855e7 1.07283e7i 0.416951 0.349863i −0.410051 0.912063i \(-0.634489\pi\)
0.827002 + 0.562199i \(0.190045\pi\)
\(314\) −2.80583e6 3.34385e6i −0.0906299 0.108009i
\(315\) −7.19078e7 + 1.24548e8i −2.30062 + 3.98478i
\(316\) −7.47777e6 + 4.31729e6i −0.236979 + 0.136820i
\(317\) −1.30935e7 + 3.59741e7i −0.411034 + 1.12931i 0.545608 + 0.838040i \(0.316299\pi\)
−0.956642 + 0.291266i \(0.905924\pi\)
\(318\) 6.28230e7 + 1.10774e7i 1.95361 + 0.344474i
\(319\) 3.59904e6 634608.i 0.110870 0.0195494i
\(320\) 7.11328e6 2.58902e6i 0.217080 0.0790107i
\(321\) −6.46192e7 5.42220e7i −1.95365 1.63931i
\(322\) 3.37993e7i 1.01237i
\(323\) 2.44959e7 2.49506e7i 0.726920 0.740411i
\(324\) 2.65083e6 0.0779376
\(325\) −1.75190e7 + 2.08783e7i −0.510338 + 0.608197i
\(326\) −1.51238e6 4.15523e6i −0.0436524 0.119934i
\(327\) 8.26580e6 + 4.68777e7i 0.236397 + 1.34067i
\(328\) −701110. + 3.97619e6i −0.0198685 + 0.112680i
\(329\) 8.46753e7 + 3.08193e7i 2.37776 + 0.865436i
\(330\) 8.73176e6 + 1.51239e7i 0.242974 + 0.420844i
\(331\) −6.64525e6 3.83664e6i −0.183243 0.105795i 0.405572 0.914063i \(-0.367072\pi\)
−0.588815 + 0.808268i \(0.700406\pi\)
\(332\) 2.08721e7 1.75138e7i 0.570365 0.478593i
\(333\) 3.52698e7 + 4.20329e7i 0.955147 + 1.13830i
\(334\) 1.16774e6 2.02258e6i 0.0313405 0.0542833i
\(335\) 2.37102e7 1.36891e7i 0.630669 0.364117i
\(336\) −8.33448e6 + 2.28988e7i −0.219716 + 0.603664i
\(337\) 3.76433e7 + 6.63753e6i 0.983554 + 0.173427i 0.642224 0.766517i \(-0.278012\pi\)
0.341329 + 0.939944i \(0.389123\pi\)
\(338\) 2.39846e7 4.22913e6i 0.621129 0.109522i
\(339\) −5.78699e7 + 2.10629e7i −1.48544 + 0.540654i
\(340\) −2.88680e7 2.42231e7i −0.734479 0.616301i
\(341\) 4.40260e6i 0.111031i
\(342\) 4.35962e7 + 3.41057e6i 1.08986 + 0.0852607i
\(343\) −3.85667e7 −0.955718
\(344\) 3.12314e6 3.72201e6i 0.0767212 0.0914328i
\(345\) −3.68195e7 1.01161e8i −0.896645 2.46351i
\(346\) −4.80646e6 2.72588e7i −0.116037 0.658079i
\(347\) −6.37474e6 + 3.61530e7i −0.152572 + 0.865277i 0.808401 + 0.588633i \(0.200334\pi\)
−0.960972 + 0.276645i \(0.910778\pi\)
\(348\) −1.52628e7 5.55521e6i −0.362157 0.131814i
\(349\) 2.61550e7 + 4.53018e7i 0.615288 + 1.06571i 0.990334 + 0.138704i \(0.0442935\pi\)
−0.375046 + 0.927006i \(0.622373\pi\)
\(350\) −1.02131e8 5.89653e7i −2.38206 1.37528i
\(351\) 9.48622e6 7.95989e6i 0.219367 0.184071i
\(352\) 1.15497e6 + 1.37644e6i 0.0264816 + 0.0315595i
\(353\) 7.09510e6 1.22891e7i 0.161300 0.279380i −0.774035 0.633143i \(-0.781765\pi\)
0.935335 + 0.353763i \(0.115098\pi\)
\(354\) 1.93243e7 1.11569e7i 0.435607 0.251498i
\(355\) 4.45327e7 1.22352e8i 0.995391 2.73481i
\(356\) 1.55871e7 + 2.74843e6i 0.345474 + 0.0609165i
\(357\) 1.19469e8 2.10657e7i 2.62574 0.462989i
\(358\) 9.56914e6 3.48288e6i 0.208557 0.0759084i
\(359\) 3.94822e7 + 3.31295e7i 0.853331 + 0.716030i 0.960521 0.278209i \(-0.0897407\pi\)
−0.107189 + 0.994239i \(0.534185\pi\)
\(360\) 4.71300e7i 1.01016i
\(361\) −4.64735e7 7.31611e6i −0.987834 0.155510i
\(362\) 1.09029e7 0.229834
\(363\) 4.63943e7 5.52905e7i 0.969939 1.15593i
\(364\) −4.36574e6 1.19948e7i −0.0905219 0.248707i
\(365\) 1.03012e7 + 5.84213e7i 0.211842 + 1.20141i
\(366\) −8.69080e6 + 4.92880e7i −0.177262 + 1.00531i
\(367\) −3.85381e7 1.40267e7i −0.779635 0.283764i −0.0786148 0.996905i \(-0.525050\pi\)
−0.701021 + 0.713141i \(0.747272\pi\)
\(368\) −5.53820e6 9.59245e6i −0.111128 0.192480i
\(369\) 2.17701e7 + 1.25690e7i 0.433292 + 0.250161i
\(370\) −4.87371e7 + 4.08953e7i −0.962177 + 0.807362i
\(371\) −9.29395e7 1.10761e8i −1.82003 2.16903i
\(372\) −9.78347e6 + 1.69455e7i −0.190048 + 0.329173i
\(373\) −7.29024e7 + 4.20902e7i −1.40480 + 0.811064i −0.994881 0.101057i \(-0.967778\pi\)
−0.409923 + 0.912120i \(0.634444\pi\)
\(374\) 3.05939e6 8.40560e6i 0.0584817 0.160677i
\(375\) 2.16767e8 + 3.82219e7i 4.11055 + 0.724800i
\(376\) −2.90813e7 + 5.12781e6i −0.547079 + 0.0964648i
\(377\) 7.99491e6 2.90991e6i 0.149207 0.0543070i
\(378\) 4.10468e7 + 3.44424e7i 0.759983 + 0.637702i
\(379\) 7.18380e7i 1.31958i 0.751449 + 0.659791i \(0.229355\pi\)
−0.751449 + 0.659791i \(0.770645\pi\)
\(380\) −3.95456e6 + 5.05498e7i −0.0720688 + 0.921232i
\(381\) −7.38074e7 −1.33452
\(382\) 1.25187e7 1.49192e7i 0.224579 0.267642i
\(383\) 3.36588e7 + 9.24767e7i 0.599103 + 1.64602i 0.753065 + 0.657946i \(0.228575\pi\)
−0.153961 + 0.988077i \(0.549203\pi\)
\(384\) −1.38672e6 7.86447e6i −0.0244903 0.138892i
\(385\) 6.87334e6 3.89806e7i 0.120444 0.683072i
\(386\) −1.73104e7 6.30046e6i −0.300985 0.109549i
\(387\) −1.51254e7 2.61979e7i −0.260960 0.451996i
\(388\) −6.58895e6 3.80413e6i −0.112803 0.0651269i
\(389\) 6.50468e7 5.45808e7i 1.10504 0.927237i 0.107284 0.994228i \(-0.465784\pi\)
0.997754 + 0.0669915i \(0.0213400\pi\)
\(390\) 2.61332e7 + 3.11443e7i 0.440553 + 0.525031i
\(391\) −2.75707e7 + 4.77538e7i −0.461229 + 0.798872i
\(392\) 2.93890e7 1.69677e7i 0.487895 0.281686i
\(393\) −3.68947e7 + 1.01367e8i −0.607836 + 1.67002i
\(394\) −4.75526e6 838480.i −0.0777473 0.0137089i
\(395\) −6.13870e7 + 1.08242e7i −0.996060 + 0.175632i
\(396\) 1.05124e7 3.82622e6i 0.169285 0.0616147i
\(397\) 4.09084e6 + 3.43262e6i 0.0653793 + 0.0548598i 0.674892 0.737917i \(-0.264190\pi\)
−0.609512 + 0.792777i \(0.708635\pi\)
\(398\) 7.03974e7i 1.11662i
\(399\) −1.16474e8 1.14352e8i −1.83363 1.80021i
\(400\) 3.86472e7 0.603862
\(401\) −2.70993e7 + 3.22957e7i −0.420267 + 0.500855i −0.934088 0.357043i \(-0.883785\pi\)
0.513821 + 0.857897i \(0.328230\pi\)
\(402\) −9.87851e6 2.71410e7i −0.152059 0.417780i
\(403\) −1.77980e6 1.00938e7i −0.0271930 0.154219i
\(404\) 1.05786e7 5.99940e7i 0.160429 0.909838i
\(405\) 1.79826e7 + 6.54512e6i 0.270699 + 0.0985264i
\(406\) 1.84070e7 + 3.18819e7i 0.275046 + 0.476394i
\(407\) −1.30785e7 7.55087e6i −0.193988 0.111999i
\(408\) −3.04544e7 + 2.55543e7i −0.448405 + 0.376256i
\(409\) −2.53099e7 3.01632e7i −0.369931 0.440866i 0.548679 0.836033i \(-0.315131\pi\)
−0.918609 + 0.395167i \(0.870687\pi\)
\(410\) −1.45737e7 + 2.52424e7i −0.211455 + 0.366251i
\(411\) 6.46039e7 3.72991e7i 0.930537 0.537246i
\(412\) 1.17391e7 3.22528e7i 0.167858 0.461186i
\(413\) −4.98070e7 8.78232e6i −0.707034 0.124669i
\(414\) −6.79147e7 + 1.19752e7i −0.957111 + 0.168765i
\(415\) 1.84834e8 6.72742e7i 2.58606 0.941249i
\(416\) 3.20443e6 + 2.68884e6i 0.0445114 + 0.0373495i
\(417\) 5.91041e6i 0.0815097i
\(418\) −1.15963e7 + 3.22178e6i −0.158778 + 0.0441131i
\(419\) −9.44070e7 −1.28340 −0.641700 0.766956i \(-0.721771\pi\)
−0.641700 + 0.766956i \(0.721771\pi\)
\(420\) −1.13078e8 + 1.34761e8i −1.52627 + 1.81893i
\(421\) −1.44103e7 3.95919e7i −0.193120 0.530592i 0.804906 0.593403i \(-0.202216\pi\)
−0.998025 + 0.0628107i \(0.979994\pi\)
\(422\) 1.28956e7 + 7.31349e7i 0.171595 + 0.973166i
\(423\) −3.19261e7 + 1.81062e8i −0.421817 + 2.39224i
\(424\) 4.45256e7 + 1.62060e7i 0.584134 + 0.212607i
\(425\) −9.61981e7 1.66620e8i −1.25314 2.17050i
\(426\) −1.18958e8 6.86802e7i −1.53873 0.888388i
\(427\) 8.68979e7 7.29160e7i 1.11616 0.936567i
\(428\) −4.02747e7 4.79975e7i −0.513689 0.612191i
\(429\) −4.82520e6 + 8.35750e6i −0.0611144 + 0.105853i
\(430\) 3.03765e7 1.75379e7i 0.382061 0.220583i
\(431\) −1.68147e7 + 4.61979e7i −0.210018 + 0.577020i −0.999316 0.0369911i \(-0.988223\pi\)
0.789298 + 0.614011i \(0.210445\pi\)
\(432\) −1.72929e7 3.04921e6i −0.214495 0.0378212i
\(433\) 278682. 49139.1i 0.00343277 0.000605291i −0.171932 0.985109i \(-0.555001\pi\)
0.175364 + 0.984504i \(0.443890\pi\)
\(434\) 4.16748e7 1.51684e7i 0.509806 0.185554i
\(435\) −8.98228e7 7.53703e7i −1.09124 0.915656i
\(436\) 3.53567e7i 0.426591i
\(437\) 7.38475e7 7.14559e6i 0.884895 0.0856236i
\(438\) 6.25826e7 0.744786
\(439\) −7.87904e7 + 9.38988e7i −0.931279 + 1.10986i 0.0624507 + 0.998048i \(0.480108\pi\)
−0.993730 + 0.111807i \(0.964336\pi\)
\(440\) 4.43650e6 + 1.21892e7i 0.0520814 + 0.143092i
\(441\) −3.66891e7 2.08074e8i −0.427781 2.42607i
\(442\) 3.61615e6 2.05082e7i 0.0418773 0.237498i
\(443\) −1.39435e7 5.07501e6i −0.160384 0.0583749i 0.260581 0.965452i \(-0.416086\pi\)
−0.420964 + 0.907077i \(0.638308\pi\)
\(444\) 3.35591e7 + 5.81261e7i 0.383408 + 0.664083i
\(445\) 9.89530e7 + 5.71305e7i 1.12292 + 0.648318i
\(446\) 3.90129e7 3.27357e7i 0.439747 0.368992i
\(447\) 7.88614e7 + 9.39833e7i 0.882961 + 1.05227i
\(448\) −9.05011e6 + 1.56752e7i −0.100651 + 0.174333i
\(449\) 1.26115e8 7.28124e7i 1.39324 0.804389i 0.399570 0.916703i \(-0.369160\pi\)
0.993673 + 0.112314i \(0.0358262\pi\)
\(450\) 8.22968e7 2.26109e8i 0.903120 2.48130i
\(451\) −6.81353e6 1.20141e6i −0.0742750 0.0130967i
\(452\) −4.50480e7 + 7.94317e6i −0.487820 + 0.0860159i
\(453\) −6.17087e7 + 2.24601e7i −0.663822 + 0.241612i
\(454\) 3.35950e7 + 2.81896e7i 0.359011 + 0.301246i
\(455\) 9.21489e7i 0.978264i
\(456\) 5.17933e7 + 1.33688e7i 0.546234 + 0.140993i
\(457\) −9.51564e7 −0.996986 −0.498493 0.866894i \(-0.666113\pi\)
−0.498493 + 0.866894i \(0.666113\pi\)
\(458\) −3.92719e7 + 4.68024e7i −0.408776 + 0.487161i
\(459\) 2.98983e7 + 8.21449e7i 0.309178 + 0.849460i
\(460\) −1.38852e7 7.87470e7i −0.142653 0.809023i
\(461\) −1.67204e7 + 9.48258e7i −0.170664 + 0.967885i 0.772366 + 0.635178i \(0.219073\pi\)
−0.943030 + 0.332707i \(0.892038\pi\)
\(462\) −3.92390e7 1.42818e7i −0.397916 0.144830i
\(463\) 4.61495e7 + 7.99333e7i 0.464969 + 0.805350i 0.999200 0.0399883i \(-0.0127321\pi\)
−0.534231 + 0.845339i \(0.679399\pi\)
\(464\) −1.04481e7 6.03220e6i −0.104588 0.0603839i
\(465\) −1.08208e8 + 9.07976e7i −1.07622 + 0.903058i
\(466\) 1.64669e7 + 1.96245e7i 0.162725 + 0.193929i
\(467\) −4.35870e6 + 7.54950e6i −0.0427964 + 0.0741255i −0.886630 0.462479i \(-0.846960\pi\)
0.843834 + 0.536605i \(0.180293\pi\)
\(468\) 2.25549e7 1.30221e7i 0.220041 0.127041i
\(469\) −2.23901e7 + 6.15164e7i −0.217039 + 0.596310i
\(470\) −2.09941e8 3.70183e7i −2.02211 0.356552i
\(471\) −3.27388e7 + 5.77274e6i −0.313329 + 0.0552483i
\(472\) 1.55746e7 5.66868e6i 0.148112 0.0539083i
\(473\) 6.37796e6 + 5.35175e6i 0.0602696 + 0.0505722i
\(474\) 6.57597e7i 0.617482i
\(475\) −1.07241e8 + 2.35610e8i −1.00064 + 2.19843i
\(476\) 9.01077e7 0.835490
\(477\) 1.89629e8 2.25991e8i 1.74723 2.08226i
\(478\) 1.91783e7 + 5.26918e7i 0.175600 + 0.482458i
\(479\) 1.54298e7 + 8.75065e7i 0.140395 + 0.796222i 0.970950 + 0.239284i \(0.0769127\pi\)
−0.830554 + 0.556938i \(0.811976\pi\)
\(480\) 1.00109e7 5.67746e7i 0.0905209 0.513369i
\(481\) −3.30374e7 1.20246e7i −0.296873 0.108053i
\(482\) −1.25479e7 2.17337e7i −0.112055 0.194085i
\(483\) 2.22924e8 + 1.28705e8i 1.97840 + 1.14223i
\(484\) 4.10684e7 3.44605e7i 0.362219 0.303938i
\(485\) −3.53051e7 4.20749e7i −0.309465 0.368806i
\(486\) 4.54523e7 7.87257e7i 0.395956 0.685816i
\(487\) 1.51039e8 8.72025e7i 1.30768 0.754992i 0.325975 0.945378i \(-0.394308\pi\)
0.981709 + 0.190387i \(0.0609742\pi\)
\(488\) −1.27145e7 + 3.49327e7i −0.109405 + 0.300589i
\(489\) −3.31649e7 5.84787e6i −0.283630 0.0500116i
\(490\) 2.41262e8 4.25410e7i 2.05069 0.361593i
\(491\) −4.52296e7 + 1.64622e7i −0.382101 + 0.139073i −0.525927 0.850530i \(-0.676282\pi\)
0.143826 + 0.989603i \(0.454059\pi\)
\(492\) 2.35553e7 + 1.97652e7i 0.197785 + 0.165961i
\(493\) 6.00598e7i 0.501237i
\(494\) −2.52842e7 + 1.20745e7i −0.209734 + 0.100158i
\(495\) 8.07610e7 0.665865
\(496\) −9.34215e6 + 1.11335e7i −0.0765600 + 0.0912407i
\(497\) 1.06483e8 + 2.92558e8i 0.867380 + 2.38311i
\(498\) −3.60331e7 2.04354e8i −0.291752 1.65461i
\(499\) −1.75686e7 + 9.96364e7i −0.141395 + 0.801893i 0.828796 + 0.559551i \(0.189027\pi\)
−0.970191 + 0.242341i \(0.922085\pi\)
\(500\) 1.53633e8 + 5.59178e7i 1.22906 + 0.447343i
\(501\) −8.89331e6 1.54037e7i −0.0707213 0.122493i
\(502\) −3.02948e7 1.74907e7i −0.239474 0.138260i
\(503\) −2.88498e7 + 2.42079e7i −0.226694 + 0.190219i −0.749059 0.662503i \(-0.769494\pi\)
0.522365 + 0.852722i \(0.325050\pi\)
\(504\) 7.24377e7 + 8.63278e7i 0.565813 + 0.674309i
\(505\) 2.19893e8 3.80865e8i 1.70741 2.95731i
\(506\) 1.64374e7 9.49016e6i 0.126877 0.0732524i
\(507\) 6.34381e7 1.74295e8i 0.486773 1.33740i
\(508\) −5.39893e7 9.51977e6i −0.411829 0.0726165i
\(509\) −2.00674e8 + 3.53843e7i −1.52173 + 0.268323i −0.871114 0.491081i \(-0.836602\pi\)
−0.650620 + 0.759404i \(0.725491\pi\)
\(510\) −2.69691e8 + 9.81595e7i −2.03309 + 0.739983i
\(511\) −1.08661e8 9.11773e7i −0.814349 0.683320i
\(512\) 5.93164e6i 0.0441942i
\(513\) 6.65748e7 9.69641e7i 0.493126 0.718222i
\(514\) 2.11234e7 0.155552
\(515\) 1.59270e8 1.89810e8i 1.16604 1.38963i
\(516\) −1.26559e7 3.47718e7i −0.0921179 0.253092i
\(517\) −8.78693e6 4.98331e7i −0.0635866 0.360617i
\(518\) 2.64165e7 1.49816e8i 0.190058 1.07787i
\(519\) −1.98089e8 7.20983e7i −1.41696 0.515731i
\(520\) 1.50991e7 + 2.61524e7i 0.107384 + 0.185995i
\(521\) 1.28157e8 + 7.39917e7i 0.906213 + 0.523202i 0.879211 0.476433i \(-0.158071\pi\)
0.0270023 + 0.999635i \(0.491404\pi\)
\(522\) −5.75404e7 + 4.82821e7i −0.404540 + 0.339449i
\(523\) 7.89857e7 + 9.41314e7i 0.552132 + 0.658006i 0.967862 0.251483i \(-0.0809181\pi\)
−0.415729 + 0.909488i \(0.636474\pi\)
\(524\) −4.00626e7 + 6.93905e7i −0.278449 + 0.482287i
\(525\) −7.77814e8 + 4.49071e8i −5.37524 + 3.10340i
\(526\) 1.00194e7 2.75279e7i 0.0688466 0.189154i
\(527\) 7.12540e7 + 1.25640e7i 0.486830 + 0.0858413i
\(528\) 1.34764e7 2.37626e6i 0.0915530 0.0161433i
\(529\) 2.91612e7 1.06138e7i 0.196987 0.0716976i
\(530\) 2.62037e8 + 2.19875e8i 1.76009 + 1.47689i
\(531\) 1.03191e8i 0.689223i
\(532\) −7.04504e7 9.86701e7i −0.467895 0.655316i
\(533\) −1.61070e7 −0.106373
\(534\) 7.74819e7 9.23393e7i 0.508834 0.606405i
\(535\) −1.54703e8 4.25044e8i −1.01027 2.77570i
\(536\) −3.72535e6 2.11275e7i −0.0241920 0.137200i
\(537\) 1.34671e7 7.63760e7i 0.0869667 0.493212i
\(538\) −9.36349e7 3.40803e7i −0.601300 0.218855i
\(539\) 2.90756e7 + 5.03604e7i 0.185679 + 0.321605i
\(540\) −1.09782e8 6.33827e7i −0.697188 0.402522i
\(541\) −1.82908e8 + 1.53478e8i −1.15516 + 0.969290i −0.999828 0.0185726i \(-0.994088\pi\)
−0.155328 + 0.987863i \(0.549643\pi\)
\(542\) 7.42513e7 + 8.84893e7i 0.466344 + 0.555767i
\(543\) 4.15173e7 7.19101e7i 0.259316 0.449149i
\(544\) −2.55731e7 + 1.47647e7i −0.158850 + 0.0917121i
\(545\) −8.72986e7 + 2.39851e8i −0.539284 + 1.48167i
\(546\) −9.57362e7 1.68809e7i −0.588164 0.103709i
\(547\) −6.79572e7 + 1.19827e7i −0.415215 + 0.0732136i −0.377353 0.926069i \(-0.623166\pi\)
−0.0378618 + 0.999283i \(0.512055\pi\)
\(548\) 5.20680e7 1.89512e7i 0.316395 0.115158i
\(549\) 1.77302e8 + 1.48774e8i 1.07151 + 0.899104i
\(550\) 6.62251e7i 0.398047i
\(551\) 6.57669e7 4.69575e7i 0.393145 0.280705i
\(552\) −8.43562e7 −0.501533
\(553\) 9.58059e7 1.14177e8i 0.566522 0.675155i
\(554\) 2.08395e6 + 5.72562e6i 0.0122563 + 0.0336739i
\(555\) 8.41385e7 + 4.77173e8i 0.492171 + 2.79124i
\(556\) −762333. + 4.32340e6i −0.00443527 + 0.0251537i
\(557\) −5.49382e7 1.99959e7i −0.317914 0.115711i 0.178134 0.984006i \(-0.442994\pi\)
−0.496048 + 0.868295i \(0.665216\pi\)
\(558\) 4.52442e7 + 7.83652e7i 0.260411 + 0.451046i
\(559\) 1.67862e7 + 9.69150e6i 0.0960984 + 0.0554824i
\(560\) −1.00097e8 + 8.39915e7i −0.569977 + 0.478268i
\(561\) −4.37894e7 5.21861e7i −0.248016 0.295574i
\(562\) 5.00219e7 8.66404e7i 0.281806 0.488103i
\(563\) 2.48677e7 1.43574e7i 0.139351 0.0804544i −0.428704 0.903445i \(-0.641030\pi\)
0.568055 + 0.822991i \(0.307696\pi\)
\(564\) −7.69187e7 + 2.11332e8i −0.428741 + 1.17796i
\(565\) −3.25207e8 5.73427e7i −1.80308 0.317931i
\(566\) −1.46816e8 + 2.58877e7i −0.809702 + 0.142772i
\(567\) −4.29983e7 + 1.56501e7i −0.235886 + 0.0858556i
\(568\) −7.81577e7 6.55821e7i −0.426508 0.357882i
\(569\) 7.00490e7i 0.380246i −0.981760 0.190123i \(-0.939111\pi\)
0.981760 0.190123i \(-0.0608887\pi\)
\(570\) 3.18344e8 + 2.18572e8i 1.71898 + 1.18024i
\(571\) 3.28041e8 1.76206 0.881028 0.473063i \(-0.156852\pi\)
0.881028 + 0.473063i \(0.156852\pi\)
\(572\) −4.60755e6 + 5.49106e6i −0.0246196 + 0.0293405i
\(573\) −5.07295e7 1.39378e8i −0.269648 0.740852i
\(574\) −1.21024e7 6.86359e7i −0.0639933 0.362924i
\(575\) 7.08904e7 4.02039e8i 0.372892 2.11478i
\(576\) −3.47036e7 1.26311e7i −0.181596 0.0660956i
\(577\) −1.86655e8 3.23295e8i −0.971653 1.68295i −0.690565 0.723270i \(-0.742638\pi\)
−0.281088 0.959682i \(-0.590695\pi\)
\(578\) 9.06040e6 + 5.23103e6i 0.0469207 + 0.0270897i
\(579\) −1.07471e8 + 9.01792e7i −0.553678 + 0.464591i
\(580\) −5.59831e7 6.67181e7i −0.286928 0.341947i
\(581\) −2.35162e8 + 4.07312e8i −1.19905 + 2.07682i
\(582\) −5.01804e7 + 2.89717e7i −0.254545 + 0.146962i
\(583\) −2.77703e7 + 7.62982e7i −0.140144 + 0.385043i
\(584\) 4.57785e7 + 8.07199e6i 0.229839 + 0.0405268i
\(585\) 1.85160e8 3.26486e7i 0.924865 0.163079i
\(586\) −1.38080e8 + 5.02570e7i −0.686180 + 0.249749i
\(587\) −1.14701e8 9.62452e7i −0.567089 0.475844i 0.313589 0.949559i \(-0.398468\pi\)
−0.880679 + 0.473714i \(0.842913\pi\)
\(588\) 2.58447e8i 1.27128i
\(589\) −4.19518e7 8.78479e7i −0.205307 0.429918i
\(590\) 1.19650e8 0.582584
\(591\) −2.36379e7 + 2.81705e7i −0.114511 + 0.136469i
\(592\) 1.70510e7 + 4.68471e7i 0.0821833 + 0.225797i
\(593\) −2.48387e7 1.40867e8i −0.119115 0.675532i −0.984630 0.174651i \(-0.944120\pi\)
0.865516 0.500882i \(-0.166991\pi\)
\(594\) 5.22507e6 2.96328e7i 0.0249306 0.141388i
\(595\) 6.11268e8 + 2.22483e8i 2.90189 + 1.05620i
\(596\) 4.55642e7 + 7.89194e7i 0.215221 + 0.372774i
\(597\) 4.64307e8 + 2.68068e8i 2.18214 + 1.25986i
\(598\) 3.38493e7 2.84030e7i 0.158288 0.132819i
\(599\) −1.65498e8 1.97233e8i −0.770040 0.917698i 0.228398 0.973568i \(-0.426651\pi\)
−0.998438 + 0.0558695i \(0.982207\pi\)
\(600\) 1.47166e8 2.54898e8i 0.681322 1.18008i
\(601\) 1.19322e8 6.88905e7i 0.549663 0.317348i −0.199323 0.979934i \(-0.563874\pi\)
0.748986 + 0.662586i \(0.230541\pi\)
\(602\) −2.86853e7 + 7.88121e7i −0.131483 + 0.361246i
\(603\) −1.31541e8 2.31942e7i −0.599942 0.105786i
\(604\) −4.80362e7 + 8.47008e6i −0.218001 + 0.0384394i
\(605\) 3.63683e8 1.32370e8i 1.64232 0.597755i
\(606\) −3.55409e8 2.98224e8i −1.59702 1.34006i
\(607\) 2.40321e8i 1.07455i −0.843408 0.537274i \(-0.819454\pi\)
0.843408 0.537274i \(-0.180546\pi\)
\(608\) 3.61619e7 + 1.64595e7i 0.160894 + 0.0732328i
\(609\) 2.80371e8 1.24131
\(610\) −1.72503e8 + 2.05582e8i −0.759991 + 0.905722i
\(611\) −4.02913e7 1.10699e8i −0.176639 0.485313i
\(612\) 3.19254e7 + 1.81058e8i 0.139278 + 0.789884i
\(613\) −9.85628e6 + 5.58977e7i −0.0427889 + 0.242668i −0.998699 0.0509911i \(-0.983762\pi\)
0.955910 + 0.293659i \(0.0948731\pi\)
\(614\) −1.22371e8 4.45395e7i −0.528658 0.192416i
\(615\) 1.10991e8 + 1.92242e8i 0.477159 + 0.826463i
\(616\) −2.68608e7 1.55081e7i −0.114915 0.0663462i
\(617\) 7.40057e7 6.20981e7i 0.315072 0.264377i −0.471513 0.881859i \(-0.656292\pi\)
0.786585 + 0.617483i \(0.211847\pi\)
\(618\) −1.68023e8 2.00242e8i −0.711873 0.848377i
\(619\) 1.18376e8 2.05034e8i 0.499106 0.864477i −0.500894 0.865509i \(-0.666995\pi\)
0.999999 + 0.00103223i \(0.000328569\pi\)
\(620\) −9.08645e7 + 5.24606e7i −0.381258 + 0.220119i
\(621\) −6.34406e7 + 1.74302e8i −0.264906 + 0.727825i
\(622\) 4.65124e7 + 8.20139e6i 0.193285 + 0.0340813i
\(623\) −2.69060e8 + 4.74426e7i −1.11272 + 0.196202i
\(624\) 2.99365e7 1.08960e7i 0.123211 0.0448450i
\(625\) 4.52398e8 + 3.79607e8i 1.85302 + 1.55487i
\(626\) 9.44146e7i 0.384872i
\(627\) −2.29085e7 + 8.87520e7i −0.0929382 + 0.360060i
\(628\) −2.46927e7 −0.0996986
\(629\) 1.59530e8 1.90121e8i 0.641049 0.763972i
\(630\) 2.78248e8 + 7.64481e8i 1.11278 + 3.05735i
\(631\) 5.39972e7 + 3.06233e8i 0.214923 + 1.21889i 0.881040 + 0.473042i \(0.156844\pi\)
−0.666116 + 0.745848i \(0.732045\pi\)
\(632\) −8.48177e6 + 4.81025e7i −0.0335997 + 0.190553i
\(633\) 5.31468e8 + 1.93439e8i 2.09540 + 0.762661i
\(634\) 1.08280e8 + 1.87547e8i 0.424894 + 0.735939i
\(635\) −3.42745e8 1.97884e8i −1.33860 0.772839i
\(636\) 2.76437e8 2.31958e8i 1.07455 0.901651i
\(637\) 8.70200e7 + 1.03706e8i 0.336667 + 0.401224i
\(638\) 1.03367e7 1.79036e7i 0.0398032 0.0689412i
\(639\) −5.50126e8 + 3.17615e8i −2.10843 + 1.21730i
\(640\) 1.46457e7 4.02388e7i 0.0558690 0.153499i
\(641\) −4.02839e8 7.10313e7i −1.52953 0.269697i −0.655357 0.755319i \(-0.727482\pi\)
−0.874169 + 0.485622i \(0.838593\pi\)
\(642\) −4.69931e8 + 8.28615e7i −1.77594 + 0.313147i
\(643\) −1.33451e8 + 4.85723e7i −0.501984 + 0.182707i −0.580586 0.814199i \(-0.697177\pi\)
0.0786019 + 0.996906i \(0.474954\pi\)
\(644\) 1.46466e8 + 1.22899e8i 0.548377 + 0.460143i
\(645\) 2.67132e8i 0.995512i
\(646\) −1.90499e7 1.96875e8i −0.0706634 0.730286i
\(647\) −1.60316e8 −0.591920 −0.295960 0.955200i \(-0.595639\pi\)
−0.295960 + 0.955200i \(0.595639\pi\)
\(648\) 9.63884e6 1.14871e7i 0.0354242 0.0422169i
\(649\) 9.71374e6 + 2.66883e7i 0.0355347 + 0.0976308i
\(650\) 2.67723e7 + 1.51833e8i 0.0974868 + 0.552875i
\(651\) 5.86512e7 3.32627e8i 0.212586 1.20563i
\(652\) −2.35055e7 8.55531e6i −0.0848061 0.0308669i
\(653\) 3.43934e7 + 5.95712e7i 0.123520 + 0.213942i 0.921153 0.389200i \(-0.127248\pi\)
−0.797634 + 0.603142i \(0.793915\pi\)
\(654\) 2.33196e8 + 1.34636e8i 0.833656 + 0.481312i
\(655\) −4.43105e8 + 3.71810e8i −1.57682 + 1.32311i
\(656\) 1.46811e7 + 1.74962e7i 0.0520052 + 0.0619774i
\(657\) 1.44708e8 2.50642e8i 0.510267 0.883808i
\(658\) 4.41445e8 2.54868e8i 1.54953 0.894619i
\(659\) 1.12784e8 3.09872e8i 0.394087 1.08275i −0.571030 0.820929i \(-0.693456\pi\)
0.965118 0.261817i \(-0.0843216\pi\)
\(660\) 9.72878e7 + 1.71545e7i 0.338397 + 0.0596685i
\(661\) 5.12498e7 9.03672e6i 0.177455 0.0312901i −0.0842145 0.996448i \(-0.526838\pi\)
0.261669 + 0.965158i \(0.415727\pi\)
\(662\) −4.07888e7 + 1.48459e7i −0.140594 + 0.0511721i
\(663\) −1.21492e8 1.01944e8i −0.416877 0.349801i
\(664\) 1.54130e8i 0.526482i
\(665\) −2.34293e8 8.43301e8i −0.796699 2.86759i
\(666\) 3.10392e8 1.05072
\(667\) −8.19166e7 + 9.76244e7i −0.276054 + 0.328989i
\(668\) −4.51858e6 1.24147e7i −0.0151591 0.0416492i
\(669\) −6.73507e7 3.81965e8i −0.224939 1.27569i
\(670\) 2.68937e7 1.52522e8i 0.0894182 0.507116i
\(671\) −5.98600e7 2.17873e7i −0.198139 0.0721166i
\(672\) 6.89242e7 + 1.19380e8i 0.227125 + 0.393391i
\(673\) −3.53320e8 2.03989e8i −1.15911 0.669210i −0.208017 0.978125i \(-0.566701\pi\)
−0.951090 + 0.308915i \(0.900034\pi\)
\(674\) 1.65640e8 1.38989e8i 0.540986 0.453941i
\(675\) −4.16009e8 4.95780e8i −1.35267 1.61205i
\(676\) 6.88851e7 1.19313e8i 0.222990 0.386230i
\(677\) 3.80676e8 2.19783e8i 1.22684 0.708319i 0.260476 0.965480i \(-0.416121\pi\)
0.966368 + 0.257162i \(0.0827873\pi\)
\(678\) −1.19150e8 + 3.27362e8i −0.382300 + 1.05036i
\(679\) 1.29336e8 + 2.28055e7i 0.413153 + 0.0728501i
\(680\) −2.09937e8 + 3.70175e7i −0.667670 + 0.117728i
\(681\) 3.13852e8 1.14233e8i 0.993765 0.361701i
\(682\) −1.90782e7 1.60085e7i −0.0601430 0.0504660i
\(683\) 5.90466e8i 1.85324i 0.375994 + 0.926622i \(0.377301\pi\)
−0.375994 + 0.926622i \(0.622699\pi\)
\(684\) 1.73302e8 1.76519e8i 0.541546 0.551598i
\(685\) 4.00008e8 1.24451
\(686\) −1.40234e8 + 1.67125e8i −0.434392 + 0.517689i
\(687\) 1.59142e8 + 4.37239e8i 0.490811 + 1.34849i
\(688\) −4.77275e6 2.70676e7i −0.0146556 0.0831160i
\(689\) −3.28240e7 + 1.86154e8i −0.100354 + 0.569135i
\(690\) −5.72251e8 2.08283e8i −1.74197 0.634024i
\(691\) 2.76487e8 + 4.78890e8i 0.837994 + 1.45145i 0.891570 + 0.452884i \(0.149605\pi\)
−0.0535758 + 0.998564i \(0.517062\pi\)
\(692\) −1.35600e8 7.82889e7i −0.409207 0.236255i
\(693\) −1.47930e8 + 1.24128e8i −0.444484 + 0.372966i
\(694\) 1.33486e8 + 1.59082e8i 0.399352 + 0.475930i
\(695\) −1.58463e7 + 2.74466e7i −0.0472035 + 0.0817588i
\(696\) −7.95709e7 + 4.59403e7i −0.236008 + 0.136259i
\(697\) 3.88885e7 1.06845e8i 0.114848 0.315542i
\(698\) 2.91414e8 + 5.13842e7i 0.856929 + 0.151100i
\(699\) 1.92139e8 3.38793e7i 0.562579 0.0991979i
\(700\) −6.26885e8 + 2.28167e8i −1.82765 + 0.665211i
\(701\) 4.06490e8 + 3.41086e8i 1.18004 + 0.990169i 0.999979 + 0.00651360i \(0.00207336\pi\)
0.180059 + 0.983656i \(0.442371\pi\)
\(702\) 7.00510e7i 0.202490i
\(703\) −3.32915e8 2.60442e7i −0.958224 0.0749627i
\(704\) 1.01644e7 0.0291314
\(705\) −1.04359e9 + 1.24371e9i −2.97827 + 3.54937i
\(706\) −2.74546e7 7.54309e7i −0.0780192 0.214356i
\(707\) 1.82604e8 + 1.03560e9i 0.516717 + 2.93045i
\(708\) 2.19189e7 1.24308e8i 0.0617617 0.350268i
\(709\) −6.34469e8 2.30928e8i −1.78021 0.647944i −0.999741 0.0227507i \(-0.992758\pi\)
−0.780470 0.625193i \(-0.785020\pi\)
\(710\) −3.68275e8 6.37871e8i −1.02896 1.78220i
\(711\) 2.63366e8 + 1.52055e8i 0.732742 + 0.423049i
\(712\) 6.85872e7 5.75515e7i 0.190022 0.159447i
\(713\) 9.86838e7 + 1.17607e8i 0.272256 + 0.324462i
\(714\) 3.43123e8 5.94307e8i 0.942661 1.63274i
\(715\) −4.48143e7 + 2.58736e7i −0.122602 + 0.0707845i
\(716\) 1.97022e7 5.41312e7i 0.0536753 0.147472i
\(717\) 4.20559e8 + 7.41559e7i 1.14096 + 0.201182i
\(718\) 2.87127e8 5.06282e7i 0.775711 0.136779i
\(719\) −2.02561e8 + 7.37261e7i −0.544965 + 0.198351i −0.599808 0.800144i \(-0.704756\pi\)
0.0548429 + 0.998495i \(0.482534\pi\)
\(720\) −2.04233e8 1.71372e8i −0.547178 0.459137i
\(721\) 5.92469e8i 1.58074i
\(722\) −2.00689e8 + 1.74786e8i −0.533226 + 0.464403i
\(723\) −1.91127e8 −0.505715
\(724\) 3.96445e7 4.72465e7i 0.104464 0.124496i
\(725\) −1.52081e8 4.17839e8i −0.399081 1.09647i
\(726\) −7.08993e7 4.02090e8i −0.185282 1.05078i
\(727\) 6.11847e6 3.46996e7i 0.0159235 0.0903069i −0.975810 0.218619i \(-0.929845\pi\)
0.991734 + 0.128312i \(0.0409559\pi\)
\(728\) −6.78527e7 2.46964e7i −0.175862 0.0640087i
\(729\) −3.15963e8 5.47264e8i −0.815556 1.41259i
\(730\) 2.90620e8 + 1.67789e8i 0.747062 + 0.431316i
\(731\) −1.04817e8 + 8.79517e7i −0.268336 + 0.225160i
\(732\) 1.81984e8 + 2.16880e8i 0.463980 + 0.552949i
\(733\) −1.76849e8 + 3.06311e8i −0.449046 + 0.777770i −0.998324 0.0578693i \(-0.981569\pi\)
0.549278 + 0.835639i \(0.314903\pi\)
\(734\) −2.00914e8 + 1.15998e8i −0.508068 + 0.293333i
\(735\) 6.38128e8 1.75324e9i 1.60711 4.41550i
\(736\) −6.17057e7 1.08804e7i −0.154772 0.0272904i
\(737\) 3.62037e7 6.38368e6i 0.0904378 0.0159466i
\(738\) 1.33626e8 4.86358e7i 0.332446 0.121000i
\(739\) −4.19602e8 3.52088e8i −1.03969 0.872405i −0.0477197 0.998861i \(-0.515195\pi\)
−0.991972 + 0.126456i \(0.959640\pi\)
\(740\) 3.59899e8i 0.888149i
\(741\) −1.66429e7 + 2.12741e8i −0.0409049 + 0.522874i
\(742\) −8.17914e8 −2.00215
\(743\) 3.18712e8 3.79826e8i 0.777019 0.926015i −0.221776 0.975098i \(-0.571185\pi\)
0.998795 + 0.0490826i \(0.0156298\pi\)
\(744\) 3.78573e7 + 1.04012e8i 0.0919244 + 0.252560i
\(745\) 1.14237e8 + 6.47871e8i 0.276273 + 1.56682i
\(746\) −8.26907e7 + 4.68962e8i −0.199177 + 1.12959i
\(747\) −9.01752e8 3.28211e8i −2.16334 0.787392i
\(748\) −2.53004e7 4.38216e7i −0.0604537 0.104709i
\(749\) 9.36653e8 + 5.40777e8i 2.22912 + 1.28698i
\(750\) 9.53830e8 8.00358e8i 2.26093 1.89715i
\(751\) 3.64573e7 + 4.34481e7i 0.0860725 + 0.102577i 0.807362 0.590057i \(-0.200895\pi\)
−0.721289 + 0.692634i \(0.756450\pi\)
\(752\) −8.35232e7 + 1.44666e8i −0.196405 + 0.340184i
\(753\) −2.30721e8 + 1.33207e8i −0.540384 + 0.311991i
\(754\) 1.64609e7 4.52261e7i 0.0384008 0.105505i
\(755\) −3.46779e8 6.11465e7i −0.805772 0.142079i
\(756\) 2.98505e8 5.26345e7i 0.690855 0.121816i
\(757\) −4.10797e8 + 1.49518e8i −0.946976 + 0.344671i −0.768917 0.639349i \(-0.779204\pi\)
−0.178059 + 0.984020i \(0.556982\pi\)
\(758\) 3.11303e8 + 2.61214e8i 0.714785 + 0.599776i
\(759\) 1.44551e8i 0.330595i
\(760\) 2.04673e8 + 2.00944e8i 0.466252 + 0.457756i
\(761\) 6.85052e8 1.55442 0.777212 0.629238i \(-0.216633\pi\)
0.777212 + 0.629238i \(0.216633\pi\)
\(762\) −2.68375e8 + 3.19837e8i −0.606565 + 0.722876i
\(763\) −2.08741e8 5.73510e8i −0.469930 1.29112i
\(764\) −1.91309e7 1.08497e8i −0.0428999 0.243297i
\(765\) −2.30473e8 + 1.30708e9i −0.514797 + 2.91956i
\(766\) 5.23127e8 + 1.90403e8i 1.16391 + 0.423630i
\(767\) 3.30596e7 + 5.72609e7i 0.0732676 + 0.126903i
\(768\) −3.91223e7 2.25872e7i −0.0863655 0.0498631i
\(769\) 4.38506e8 3.67950e8i 0.964264 0.809114i −0.0173771 0.999849i \(-0.505532\pi\)
0.981642 + 0.190735i \(0.0610871\pi\)
\(770\) −1.43926e8 1.71525e8i −0.315259 0.375711i
\(771\) 8.04364e7 1.39320e8i 0.175505 0.303984i
\(772\) −9.02456e7 + 5.21033e7i −0.196144 + 0.113244i
\(773\) 2.65077e8 7.28292e8i 0.573896 1.57677i −0.224398 0.974498i \(-0.572041\pi\)
0.798294 0.602268i \(-0.205736\pi\)
\(774\) −1.68524e8 2.97154e7i −0.363446 0.0640854i
\(775\) −5.27532e8 + 9.30182e7i −1.13330 + 0.199831i
\(776\) −4.04433e7 + 1.47201e7i −0.0865488 + 0.0315012i
\(777\) −8.87520e8 7.44718e8i −1.89197 1.58755i
\(778\) 4.80338e8i 1.02002i
\(779\) −1.47403e8 + 4.09527e7i −0.311813 + 0.0866304i
\(780\) 2.29985e8 0.484636
\(781\) 1.12380e8 1.33930e8i 0.235905 0.281141i
\(782\) 1.06685e8 + 2.93115e8i 0.223092 + 0.612939i
\(783\) 3.50827e7 + 1.98964e8i 0.0730815 + 0.414466i
\(784\) 3.33349e7 1.89052e8i 0.0691753 0.392312i
\(785\) −1.67509e8 6.09683e7i −0.346281 0.126036i
\(786\) 3.05111e8 + 5.28467e8i 0.628333 + 1.08830i
\(787\) −3.37677e7 1.94958e7i −0.0692752 0.0399960i 0.464962 0.885330i \(-0.346068\pi\)
−0.534238 + 0.845334i \(0.679401\pi\)
\(788\) −2.09243e7 + 1.75576e7i −0.0427635 + 0.0358828i
\(789\) −1.43408e8 1.70907e8i −0.291973 0.347960i
\(790\) −1.76307e8 + 3.05373e8i −0.357593 + 0.619369i
\(791\) 6.83814e8 3.94800e8i 1.38168 0.797716i
\(792\) 2.16443e7 5.94674e7i 0.0435681 0.119702i
\(793\) −1.46048e8 2.57522e7i −0.292871 0.0516410i
\(794\) 2.97498e7 5.24570e6i 0.0594324 0.0104795i
\(795\) 2.44800e9 8.91000e8i 4.87204 1.77328i
\(796\) 3.05060e8 + 2.55976e8i 0.604848 + 0.507528i
\(797\) 2.56376e8i 0.506411i −0.967413 0.253205i \(-0.918515\pi\)
0.967413 0.253205i \(-0.0814849\pi\)
\(798\) −9.19050e8 + 8.89285e7i −1.80855 + 0.174998i
\(799\) 8.31602e8 1.63033
\(800\) 1.40527e8 1.67474e8i 0.274467 0.327097i
\(801\) −1.90658e8 5.23828e8i −0.370985 1.01927i
\(802\) 4.14129e7 + 2.34864e8i 0.0802810 + 0.455296i
\(803\) −1.38320e7 + 7.84452e7i −0.0267140 + 0.151503i
\(804\) −1.53533e8 5.58813e7i −0.295415 0.107522i
\(805\) 6.90139e8 + 1.19536e9i 1.32297 + 2.29145i
\(806\) −5.02120e7 2.89899e7i −0.0958964 0.0553658i
\(807\) −5.81332e8 + 4.87795e8i −1.10612 + 0.928148i
\(808\) −2.21513e8 2.63989e8i −0.419919 0.500440i
\(809\) −8.91683e7 + 1.54444e8i −0.168409 + 0.291693i −0.937861 0.347012i \(-0.887196\pi\)
0.769452 + 0.638705i \(0.220530\pi\)
\(810\) 9.37501e7 5.41266e7i 0.176407 0.101849i
\(811\) −1.20069e8 + 3.29886e8i −0.225096 + 0.618445i −0.999905 0.0137491i \(-0.995623\pi\)
0.774810 + 0.632194i \(0.217846\pi\)
\(812\) 2.05088e8 + 3.61626e7i 0.383065 + 0.0675447i
\(813\) 8.66376e8 1.52765e8i 1.61226 0.284285i
\(814\) −8.02764e7 + 2.92182e7i −0.148838 + 0.0541727i
\(815\) −1.38332e8 1.16074e8i −0.255534 0.214419i
\(816\) 2.24891e8i 0.413905i
\(817\) 1.78260e8 + 4.60121e7i 0.326879 + 0.0843735i
\(818\) −2.22740e8 −0.406947
\(819\) −2.88976e8 + 3.44388e8i −0.526030 + 0.626898i
\(820\) 5.63932e7 + 1.54939e8i 0.102279 + 0.281008i
\(821\) −8.52782e7 4.83637e8i −0.154102 0.873957i −0.959602 0.281361i \(-0.909214\pi\)
0.805500 0.592596i \(-0.201897\pi\)
\(822\) 7.32780e7 4.15580e8i 0.131934 0.748237i
\(823\) −2.76280e8 1.00558e8i −0.495621 0.180391i 0.0821024 0.996624i \(-0.473837\pi\)
−0.577723 + 0.816233i \(0.696059\pi\)
\(824\) −9.70794e7 1.68146e8i −0.173518 0.300543i
\(825\) 4.36789e8 + 2.52180e8i 0.777875 + 0.449106i
\(826\) −2.19163e8 + 1.83900e8i −0.388891 + 0.326318i
\(827\) 6.98725e7 + 8.32708e7i 0.123535 + 0.147223i 0.824267 0.566201i \(-0.191588\pi\)
−0.700732 + 0.713425i \(0.747143\pi\)
\(828\) −1.95055e8 + 3.37845e8i −0.343610 + 0.595150i
\(829\) −8.84527e8 + 5.10682e8i −1.55256 + 0.896369i −0.554623 + 0.832102i \(0.687138\pi\)
−0.997933 + 0.0642672i \(0.979529\pi\)
\(830\) 3.80561e8 1.04558e9i 0.665564 1.82862i
\(831\) 4.56990e7 + 8.05796e6i 0.0796349 + 0.0140418i
\(832\) 2.33036e7 4.10906e6i 0.0404626 0.00713465i
\(833\) −8.98034e8 + 3.26858e8i −1.55367 + 0.565488i
\(834\) 2.56122e7 + 2.14912e7i 0.0441518 + 0.0370478i
\(835\) 9.53749e7i 0.163823i
\(836\) −2.82047e7 + 6.19664e7i −0.0482728 + 0.106056i
\(837\) 2.43386e8 0.415069
\(838\) −3.43279e8 + 4.09103e8i −0.583330 + 0.695186i
\(839\) 2.57087e8 + 7.06340e8i 0.435305 + 1.19599i 0.942514 + 0.334168i \(0.108455\pi\)
−0.507209 + 0.861823i \(0.669323\pi\)
\(840\) 1.72805e8 + 9.80026e8i 0.291554 + 1.65348i
\(841\) 7.91864e7 4.49089e8i 0.133126 0.754995i
\(842\) −2.23966e8 8.15169e7i −0.375185 0.136556i
\(843\) −3.80959e8 6.59840e8i −0.635910 1.10143i
\(844\) 3.63813e8 + 2.10048e8i 0.605134 + 0.349374i
\(845\) 7.61892e8 6.39303e8i 1.26277 1.05959i
\(846\) 6.68525e8 + 7.96717e8i 1.10410 + 1.31581i
\(847\) −4.62708e8 + 8.01434e8i −0.761477 + 1.31892i
\(848\) 2.32129e8 1.34020e8i 0.380664 0.219777i
\(849\) −3.88323e8 + 1.06691e9i −0.634556 + 1.74343i
\(850\) −1.07182e9 1.88991e8i −1.74528 0.307741i
\(851\) 5.18618e8 9.14463e7i 0.841509 0.148381i
\(852\) −7.30167e8 + 2.65759e8i −1.18060 + 0.429704i
\(853\) 4.37613e8 + 3.67201e8i 0.705088 + 0.591639i 0.923216 0.384281i \(-0.125551\pi\)
−0.218128 + 0.975920i \(0.569995\pi\)
\(854\) 6.41697e8i 1.03028i
\(855\) 1.61148e9 7.69561e8i 2.57826 1.23125i
\(856\) −3.54437e8 −0.565091
\(857\) 1.35870e8 1.61923e8i 0.215864 0.257256i −0.647236 0.762290i \(-0.724075\pi\)
0.863100 + 0.505033i \(0.168520\pi\)
\(858\) 1.86712e7 + 5.12987e7i 0.0295604 + 0.0812165i
\(859\) 6.51843e6 + 3.69679e7i 0.0102840 + 0.0583237i 0.989518 0.144410i \(-0.0461285\pi\)
−0.979234 + 0.202734i \(0.935017\pi\)
\(860\) 3.44550e7 1.95404e8i 0.0541698 0.307212i
\(861\) −4.98774e8 1.81539e8i −0.781438 0.284420i
\(862\) 1.39053e8 + 2.40848e8i 0.217100 + 0.376028i
\(863\) −1.14880e8 6.63260e7i −0.178736 0.103193i 0.407963 0.912999i \(-0.366239\pi\)
−0.586699 + 0.809805i \(0.699573\pi\)
\(864\) −7.60932e7 + 6.38498e7i −0.117979 + 0.0989961i
\(865\) −7.26577e8 8.65901e8i −1.12262 1.33789i
\(866\) 800391. 1.38632e6i 0.00123239 0.00213456i
\(867\) 6.90027e7 3.98387e7i 0.105879 0.0611291i
\(868\) 8.58055e7 2.35749e8i 0.131207 0.360487i
\(869\) −8.24275e7 1.45342e7i −0.125607 0.0221479i
\(870\) −6.53220e8 + 1.15180e8i −0.991977 + 0.174912i
\(871\) 8.04229e7 2.92715e7i 0.121710 0.0442987i
\(872\) 1.53215e8 + 1.28562e8i 0.231074 + 0.193894i
\(873\) 2.67962e8i 0.402746i
\(874\) 2.37556e8 3.45993e8i 0.355822 0.518243i
\(875\) −2.82216e9 −4.21268
\(876\) 2.27560e8 2.71196e8i 0.338520 0.403432i
\(877\) −4.46619e8 1.22708e9i −0.662122 1.81917i −0.567029 0.823698i \(-0.691907\pi\)
−0.0950931 0.995468i \(-0.530315\pi\)
\(878\) 1.20407e8 + 6.82861e8i 0.177897 + 1.00890i
\(879\) −1.94327e8 + 1.10208e9i −0.286132 + 1.62274i
\(880\) 6.89524e7 + 2.50966e7i 0.101182 + 0.0368271i
\(881\) 4.55972e7 + 7.89766e7i 0.0666822 + 0.115497i 0.897439 0.441139i \(-0.145425\pi\)
−0.830757 + 0.556636i \(0.812092\pi\)
\(882\) −1.03508e9 5.97602e8i −1.50858 0.870976i
\(883\) 7.12424e8 5.97795e8i 1.03480 0.868301i 0.0433863 0.999058i \(-0.486185\pi\)
0.991414 + 0.130757i \(0.0417409\pi\)
\(884\) −7.57213e7 9.02412e7i −0.109613 0.130631i
\(885\) 4.55620e8 7.89157e8i 0.657314 1.13850i
\(886\) −7.26928e7 + 4.19692e7i −0.104518 + 0.0603434i
\(887\) −3.31592e8 + 9.11042e8i −0.475153 + 1.30547i 0.438411 + 0.898775i \(0.355542\pi\)
−0.913563 + 0.406697i \(0.866681\pi\)
\(888\) 3.73910e8 + 6.59304e7i 0.533984 + 0.0941557i
\(889\) 9.31948e8 1.64328e8i 1.32644 0.233886i
\(890\) 6.07378e8 2.21068e8i 0.861567 0.313585i
\(891\) 1.96841e7 + 1.65169e7i 0.0278280 + 0.0233505i
\(892\) 2.88090e8i 0.405914i
\(893\) −6.50185e8 9.10624e8i −0.913024 1.27875i
\(894\) 6.94020e8 0.971313
\(895\) 2.67309e8 3.18566e8i 0.372859 0.444356i
\(896\) 3.50195e7 + 9.62154e7i 0.0486840 + 0.133758i
\(897\) −5.84366e7 3.31410e8i −0.0809669 0.459186i
\(898\) 1.43048e8 8.11263e8i 0.197538 1.12030i
\(899\) 1.57134e8 + 5.71922e7i 0.216268 + 0.0787150i
\(900\) −6.80575e8 1.17879e9i −0.933574 1.61700i
\(901\) −1.15560e9 6.67186e8i −1.57991 0.912164i
\(902\) −2.99812e7 + 2.51573e7i −0.0408536 + 0.0342802i
\(903\) 4.10575e8 + 4.89305e8i 0.557609 + 0.664532i
\(904\) −1.29381e8 + 2.24094e8i −0.175131 + 0.303336i
\(905\) 3.85594e8 2.22623e8i 0.520217 0.300347i
\(906\) −1.27054e8 + 3.49077e8i −0.170845 + 0.469393i
\(907\) −1.28631e8 2.26811e7i −0.172395 0.0303978i 0.0867844 0.996227i \(-0.472341\pi\)
−0.259179 + 0.965829i \(0.583452\pi\)
\(908\) 2.44313e8 4.30791e7i 0.326355 0.0575451i
\(909\) −2.01619e9 + 7.33832e8i −2.68435 + 0.977023i
\(910\) −3.99318e8 3.35068e8i −0.529901 0.444640i
\(911\) 1.12621e9i 1.48959i 0.667296 + 0.744793i \(0.267452\pi\)
−0.667296 + 0.744793i \(0.732548\pi\)
\(912\) 2.46261e8 1.75830e8i 0.324646 0.231797i
\(913\) 2.64115e8 0.347041
\(914\) −3.46003e8 + 4.12351e8i −0.453150 + 0.540043i
\(915\) 6.99037e8 + 1.92059e9i 0.912509 + 2.50710i
\(916\) 6.00150e7 + 3.40362e8i 0.0780860 + 0.442848i
\(917\) 2.40172e8 1.36209e9i 0.311469 1.76643i
\(918\) 4.64682e8 + 1.69130e8i 0.600659 + 0.218622i
\(919\) −7.48024e8 1.29562e9i −0.963760 1.66928i −0.712909 0.701257i \(-0.752623\pi\)
−0.250851 0.968026i \(-0.580711\pi\)
\(920\) −3.91731e8 2.26166e8i −0.503066 0.290445i
\(921\) −7.59742e8 + 6.37499e8i −0.972495 + 0.816020i
\(922\) 3.50121e8 + 4.17257e8i 0.446709 + 0.532367i
\(923\) 2.03510e8 3.52489e8i 0.258810 0.448271i
\(924\) −2.04568e8 + 1.18107e8i −0.259311 + 0.149713i
\(925\) −6.28444e8 + 1.72664e9i −0.794039 + 2.18160i
\(926\) 5.14190e8 + 9.06656e7i 0.647576 + 0.114185i
\(927\) −1.19048e9 + 2.09914e8i −1.49445 + 0.263513i
\(928\) −6.41307e7 + 2.33417e7i −0.0802458 + 0.0292071i
\(929\) 4.02994e8 + 3.38152e8i 0.502633 + 0.421759i 0.858528 0.512767i \(-0.171379\pi\)
−0.355895 + 0.934526i \(0.615824\pi\)
\(930\) 7.99064e8i 0.993420i
\(931\) 1.06004e9 + 7.27816e8i 1.31363 + 0.901930i
\(932\) 1.44917e8 0.179008
\(933\) 2.31208e8 2.75543e8i 0.284681 0.339269i
\(934\) 1.68661e7 + 4.63392e7i 0.0207001 + 0.0568732i
\(935\) −6.34325e7 3.59744e8i −0.0776028 0.440107i
\(936\) 2.55833e7 1.45090e8i 0.0311981 0.176933i
\(937\) 9.39399e8 + 3.41913e8i 1.14191 + 0.415621i 0.842602 0.538536i \(-0.181022\pi\)
0.299307 + 0.954157i \(0.403245\pi\)
\(938\) 1.85161e8 + 3.20709e8i 0.224358 + 0.388599i
\(939\) −6.22713e8 3.59524e8i −0.752127 0.434241i
\(940\) −9.23794e8 + 7.75155e8i −1.11222 + 0.933265i
\(941\) 1.10442e8 + 1.31619e8i 0.132545 + 0.157961i 0.828235 0.560381i \(-0.189345\pi\)
−0.695689 + 0.718343i \(0.744901\pi\)
\(942\) −9.40278e7 + 1.62861e8i −0.112487 + 0.194834i
\(943\) 2.08939e8 1.20631e8i 0.249164 0.143855i
\(944\) 3.20669e7 8.81031e7i 0.0381190 0.104731i
\(945\) 2.15494e9 + 3.79975e8i 2.55353 + 0.450256i
\(946\) 4.63825e7 8.17849e6i 0.0547874 0.00966050i
\(947\) 1.09872e9 3.99902e8i 1.29371 0.470873i 0.398769 0.917051i \(-0.369438\pi\)
0.894944 + 0.446178i \(0.147215\pi\)
\(948\) 2.84963e8 + 2.39112e8i 0.334475 + 0.280658i
\(949\) 1.85442e8i 0.216975i
\(950\) 6.31050e8 + 1.32143e9i 0.736026 + 1.54125i
\(951\) 1.64929e9 1.91759
\(952\) 3.27646e8 3.90473e8i 0.379746 0.452564i
\(953\) −2.42694e8 6.66797e8i −0.280402 0.770398i −0.997315 0.0732349i \(-0.976668\pi\)
0.716913 0.697163i \(-0.245554\pi\)
\(954\) −2.89789e8 1.64348e9i −0.333762 1.89286i
\(955\) 1.38108e8 7.83252e8i 0.158566 0.899272i
\(956\) 2.98070e8 + 1.08489e8i 0.341149 + 0.124168i
\(957\) −7.87224e7 1.36351e8i −0.0898179 0.155569i
\(958\) 4.35306e8 + 2.51324e8i 0.495106 + 0.285850i
\(959\) −7.32694e8 + 6.14804e8i −0.830744 + 0.697077i
\(960\) −2.09626e8 2.49822e8i −0.236936 0.282369i
\(961\) −3.43029e8 + 5.94143e8i −0.386510 + 0.669454i
\(962\) −1.72237e8 + 9.94408e7i −0.193464 + 0.111696i
\(963\) −7.54752e8 + 2.07366e9i −0.845134 + 2.32199i
\(964\) −1.39807e8 2.46518e7i −0.156062 0.0275180i
\(965\) −7.40851e8 + 1.30632e8i −0.824421 + 0.145368i
\(966\) 1.36832e9 4.98027e8i 1.51794 0.552486i
\(967\) −3.95115e8 3.31541e8i −0.436962 0.366655i 0.397609 0.917555i \(-0.369840\pi\)
−0.834571 + 0.550900i \(0.814284\pi\)
\(968\) 3.03269e8i 0.334351i
\(969\) −1.37103e9 6.24041e8i −1.50687 0.685870i
\(970\) −3.10702e8 −0.340431
\(971\) −1.90546e8 + 2.27084e8i −0.208134 + 0.248044i −0.860005 0.510286i \(-0.829540\pi\)
0.651872 + 0.758329i \(0.273984\pi\)
\(972\) −1.75878e8 4.83222e8i −0.191520 0.526196i
\(973\) −1.31592e7 7.46293e7i −0.0142853 0.0810160i
\(974\) 1.71319e8 9.71596e8i 0.185408 1.05150i
\(975\) 1.10337e9 + 4.01592e8i 1.19044 + 0.433283i
\(976\) 1.05146e8 + 1.82118e8i 0.113095 + 0.195886i
\(977\) 3.56256e8 + 2.05684e8i 0.382013 + 0.220555i 0.678694 0.734421i \(-0.262546\pi\)
−0.296681 + 0.954977i \(0.595880\pi\)
\(978\) −1.45934e8 + 1.22453e8i −0.156005 + 0.130904i
\(979\) 9.86192e7 + 1.17530e8i 0.105103 + 0.125256i
\(980\) 6.92920e8 1.20017e9i 0.736215 1.27516i
\(981\) 1.07843e9 6.22629e8i 1.14231 0.659512i
\(982\) −9.31243e7 + 2.55857e8i −0.0983397 + 0.270186i
\(983\) −4.48110e8 7.90139e7i −0.471763 0.0831846i −0.0672880 0.997734i \(-0.521435\pi\)
−0.404475 + 0.914549i \(0.632546\pi\)
\(984\) 1.71301e8 3.02050e7i 0.179794 0.0317026i
\(985\) −1.85297e8 + 6.74424e7i −0.193891 + 0.0705707i
\(986\) 2.60263e8 + 2.18387e8i 0.271508 + 0.227822i
\(987\) 3.88208e9i 4.03750i
\(988\) −3.96138e7 + 1.53471e8i −0.0410748 + 0.159132i
\(989\) −2.90333e8 −0.300129
\(990\) 2.93660e8 3.49970e8i 0.302649 0.360683i
\(991\) −3.14635e8 8.64452e8i −0.323285 0.888219i −0.989766 0.142697i \(-0.954423\pi\)
0.666481 0.745522i \(-0.267800\pi\)
\(992\) 1.42766e7 + 8.09666e7i 0.0146248 + 0.0829413i
\(993\) −5.74043e7 + 3.25556e8i −0.0586268 + 0.332489i
\(994\) 1.65496e9 + 6.02356e8i 1.68511 + 0.613330i
\(995\) 1.43743e9 + 2.48969e9i 1.45920 + 2.52742i
\(996\) −1.01657e9 5.86917e8i −1.02887 0.594016i
\(997\) 8.67457e8 7.27883e8i 0.875311 0.734473i −0.0898982 0.995951i \(-0.528654\pi\)
0.965210 + 0.261477i \(0.0842097\pi\)
\(998\) 3.67882e8 + 4.38425e8i 0.370099 + 0.441066i
\(999\) 4.17430e8 7.23011e8i 0.418685 0.725184i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 38.7.f.a.3.6 60
19.13 odd 18 inner 38.7.f.a.13.6 yes 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.7.f.a.3.6 60 1.1 even 1 trivial
38.7.f.a.13.6 yes 60 19.13 odd 18 inner