Properties

Label 32.6.g.a.5.5
Level $32$
Weight $6$
Character 32.5
Analytic conductor $5.132$
Analytic rank $0$
Dimension $76$
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] = [32,6,Mod(5,32)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(32, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("32.5");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 32.g (of order \(8\), degree \(4\), 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: \(5.13228223402\)
Analytic rank: \(0\)
Dimension: \(76\)
Relative dimension: \(19\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 5.5
Character \(\chi\) \(=\) 32.5
Dual form 32.6.g.a.13.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.77244 + 4.21529i) q^{2} +(1.59693 + 3.85534i) q^{3} +(-3.53735 - 31.8039i) q^{4} +(-32.3386 - 13.3951i) q^{5} +(-22.2757 - 7.81250i) q^{6} +(-71.7275 - 71.7275i) q^{7} +(147.407 + 105.067i) q^{8} +(159.514 - 159.514i) q^{9} +O(q^{10})\) \(q+(-3.77244 + 4.21529i) q^{2} +(1.59693 + 3.85534i) q^{3} +(-3.53735 - 31.8039i) q^{4} +(-32.3386 - 13.3951i) q^{5} +(-22.2757 - 7.81250i) q^{6} +(-71.7275 - 71.7275i) q^{7} +(147.407 + 105.067i) q^{8} +(159.514 - 159.514i) q^{9} +(178.459 - 85.7843i) q^{10} +(182.095 - 439.617i) q^{11} +(116.966 - 64.4264i) q^{12} +(-45.9833 + 19.0469i) q^{13} +(572.940 - 31.7644i) q^{14} -146.067i q^{15} +(-998.974 + 225.003i) q^{16} -1447.51i q^{17} +(70.6402 + 1274.15i) q^{18} +(-1447.36 + 599.515i) q^{19} +(-311.622 + 1075.87i) q^{20} +(161.990 - 391.078i) q^{21} +(1166.17 + 2426.02i) q^{22} +(-1563.42 + 1563.42i) q^{23} +(-169.671 + 736.090i) q^{24} +(-1343.35 - 1343.35i) q^{25} +(93.1810 - 265.686i) q^{26} +(1806.56 + 748.301i) q^{27} +(-2027.49 + 2534.94i) q^{28} +(-1419.70 - 3427.45i) q^{29} +(615.715 + 551.030i) q^{30} -1489.88 q^{31} +(2820.12 - 5059.78i) q^{32} +1985.67 q^{33} +(6101.70 + 5460.67i) q^{34} +(1358.77 + 3280.36i) q^{35} +(-5637.40 - 4508.89i) q^{36} +(5166.14 + 2139.88i) q^{37} +(2932.94 - 8362.67i) q^{38} +(-146.864 - 146.864i) q^{39} +(-3359.55 - 5372.25i) q^{40} +(11538.9 - 11538.9i) q^{41} +(1037.41 + 2158.15i) q^{42} +(-4888.76 + 11802.5i) q^{43} +(-14625.7 - 4236.26i) q^{44} +(-7295.13 + 3021.74i) q^{45} +(-692.358 - 12488.2i) q^{46} +12645.2i q^{47} +(-2462.76 - 3492.07i) q^{48} -6517.33i q^{49} +(10730.4 - 594.902i) q^{50} +(5580.66 - 2311.58i) q^{51} +(768.424 + 1395.07i) q^{52} +(1970.47 - 4757.15i) q^{53} +(-9969.44 + 4792.25i) q^{54} +(-11777.4 + 11777.4i) q^{55} +(-3036.92 - 18109.4i) q^{56} +(-4622.67 - 4622.67i) q^{57} +(19803.4 + 6945.43i) q^{58} +(31638.1 + 13104.9i) q^{59} +(-4645.50 + 516.691i) q^{60} +(17051.2 + 41165.3i) q^{61} +(5620.49 - 6280.28i) q^{62} -22883.0 q^{63} +(10689.7 + 30975.3i) q^{64} +1742.17 q^{65} +(-7490.82 + 8370.16i) q^{66} +(5027.10 + 12136.5i) q^{67} +(-46036.6 + 5120.37i) q^{68} +(-8524.19 - 3530.84i) q^{69} +(-18953.5 - 6647.36i) q^{70} +(-55422.5 - 55422.5i) q^{71} +(40273.1 - 6753.76i) q^{72} +(7698.14 - 7698.14i) q^{73} +(-28509.2 + 13704.2i) q^{74} +(3033.84 - 7324.33i) q^{75} +(24186.7 + 43910.9i) q^{76} +(-44593.9 + 18471.4i) q^{77} +(1173.11 - 65.0386i) q^{78} -42879.8i q^{79} +(35319.3 + 6105.05i) q^{80} -46657.6i q^{81} +(5109.98 + 92169.7i) q^{82} +(89333.4 - 37003.1i) q^{83} +(-13010.8 - 3768.52i) q^{84} +(-19389.6 + 46810.5i) q^{85} +(-31308.4 - 65131.8i) q^{86} +(10946.8 - 10946.8i) q^{87} +(73031.6 - 45670.4i) q^{88} +(-65284.9 - 65284.9i) q^{89} +(14782.9 - 42150.4i) q^{90} +(4664.45 + 1932.08i) q^{91} +(55253.2 + 44192.5i) q^{92} +(-2379.24 - 5743.99i) q^{93} +(-53303.1 - 47703.2i) q^{94} +54836.0 q^{95} +(24010.7 + 2792.39i) q^{96} +103957. q^{97} +(27472.4 + 24586.3i) q^{98} +(-41078.2 - 99171.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 76 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 76 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 204 q^{10} - 4 q^{11} - 1588 q^{12} - 4 q^{13} + 2476 q^{14} + 4176 q^{16} - 1624 q^{18} - 4 q^{19} - 7604 q^{20} - 4 q^{21} - 12384 q^{22} + 1668 q^{23} + 21456 q^{24} - 4 q^{25} + 12976 q^{26} - 7468 q^{27} - 2184 q^{28} - 4 q^{29} - 32316 q^{30} + 23056 q^{31} - 18584 q^{32} - 8 q^{33} - 6256 q^{34} - 4780 q^{35} + 65584 q^{36} - 4 q^{37} + 404 q^{38} - 44908 q^{39} - 28952 q^{40} - 4 q^{41} - 53624 q^{42} + 32068 q^{43} + 3716 q^{44} + 968 q^{45} + 63324 q^{46} + 112368 q^{48} - 4524 q^{50} - 19912 q^{51} + 18468 q^{52} - 49460 q^{53} + 1312 q^{54} + 110044 q^{55} - 80984 q^{56} - 4 q^{57} - 84576 q^{58} - 28964 q^{59} - 46088 q^{60} + 96156 q^{61} + 63480 q^{62} - 158768 q^{63} - 49192 q^{64} - 8 q^{65} - 145012 q^{66} - 61164 q^{67} - 151216 q^{68} - 44644 q^{69} - 56296 q^{70} + 143836 q^{71} + 27092 q^{72} - 4 q^{73} + 213100 q^{74} + 205744 q^{75} + 255996 q^{76} - 14900 q^{77} + 83508 q^{78} - 97096 q^{80} + 435196 q^{82} - 329244 q^{83} + 597472 q^{84} + 12496 q^{85} + 269888 q^{86} - 282188 q^{87} - 199840 q^{88} - 4 q^{89} - 706840 q^{90} + 200108 q^{91} - 650328 q^{92} - 976 q^{93} - 261592 q^{94} + 577592 q^{95} - 501376 q^{96} - 8 q^{97} - 395624 q^{98} + 338544 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/32\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(31\)
\(\chi(n)\) \(e\left(\frac{1}{8}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.77244 + 4.21529i −0.666880 + 0.745165i
\(3\) 1.59693 + 3.85534i 0.102443 + 0.247320i 0.966788 0.255580i \(-0.0822664\pi\)
−0.864345 + 0.502900i \(0.832266\pi\)
\(4\) −3.53735 31.8039i −0.110542 0.993871i
\(5\) −32.3386 13.3951i −0.578490 0.239618i 0.0742003 0.997243i \(-0.476360\pi\)
−0.652690 + 0.757625i \(0.726360\pi\)
\(6\) −22.2757 7.81250i −0.252612 0.0885956i
\(7\) −71.7275 71.7275i −0.553274 0.553274i 0.374110 0.927384i \(-0.377948\pi\)
−0.927384 + 0.374110i \(0.877948\pi\)
\(8\) 147.407 + 105.067i 0.814317 + 0.580421i
\(9\) 159.514 159.514i 0.656434 0.656434i
\(10\) 178.459 85.7843i 0.564338 0.271274i
\(11\) 182.095 439.617i 0.453751 1.09545i −0.517134 0.855904i \(-0.673001\pi\)
0.970885 0.239547i \(-0.0769988\pi\)
\(12\) 116.966 64.4264i 0.234480 0.129155i
\(13\) −45.9833 + 19.0469i −0.0754643 + 0.0312583i −0.420096 0.907480i \(-0.638004\pi\)
0.344632 + 0.938738i \(0.388004\pi\)
\(14\) 572.940 31.7644i 0.781248 0.0433132i
\(15\) 146.067i 0.167619i
\(16\) −998.974 + 225.003i −0.975561 + 0.219730i
\(17\) 1447.51i 1.21479i −0.794401 0.607394i \(-0.792215\pi\)
0.794401 0.607394i \(-0.207785\pi\)
\(18\) 70.6402 + 1274.15i 0.0513891 + 0.926915i
\(19\) −1447.36 + 599.515i −0.919797 + 0.380992i −0.791799 0.610782i \(-0.790855\pi\)
−0.127998 + 0.991774i \(0.540855\pi\)
\(20\) −311.622 + 1075.87i −0.174202 + 0.601432i
\(21\) 161.990 391.078i 0.0801566 0.193515i
\(22\) 1166.17 + 2426.02i 0.513695 + 1.06865i
\(23\) −1563.42 + 1563.42i −0.616249 + 0.616249i −0.944567 0.328318i \(-0.893518\pi\)
0.328318 + 0.944567i \(0.393518\pi\)
\(24\) −169.671 + 736.090i −0.0601284 + 0.260857i
\(25\) −1343.35 1343.35i −0.429873 0.429873i
\(26\) 93.1810 265.686i 0.0270330 0.0770789i
\(27\) 1806.56 + 748.301i 0.476917 + 0.197545i
\(28\) −2027.49 + 2534.94i −0.488723 + 0.611044i
\(29\) −1419.70 3427.45i −0.313473 0.756792i −0.999571 0.0292825i \(-0.990678\pi\)
0.686098 0.727509i \(-0.259322\pi\)
\(30\) 615.715 + 551.030i 0.124904 + 0.111782i
\(31\) −1489.88 −0.278450 −0.139225 0.990261i \(-0.544461\pi\)
−0.139225 + 0.990261i \(0.544461\pi\)
\(32\) 2820.12 5059.78i 0.486847 0.873487i
\(33\) 1985.67 0.317411
\(34\) 6101.70 + 5460.67i 0.905218 + 0.810118i
\(35\) 1358.77 + 3280.36i 0.187489 + 0.452638i
\(36\) −5637.40 4508.89i −0.724975 0.579847i
\(37\) 5166.14 + 2139.88i 0.620385 + 0.256972i 0.670662 0.741763i \(-0.266010\pi\)
−0.0502764 + 0.998735i \(0.516010\pi\)
\(38\) 2932.94 8362.67i 0.329492 0.939477i
\(39\) −146.864 146.864i −0.0154616 0.0154616i
\(40\) −3359.55 5372.25i −0.331994 0.530893i
\(41\) 11538.9 11538.9i 1.07203 1.07203i 0.0748290 0.997196i \(-0.476159\pi\)
0.997196 0.0748290i \(-0.0238411\pi\)
\(42\) 1037.41 + 2158.15i 0.0907459 + 0.188781i
\(43\) −4888.76 + 11802.5i −0.403206 + 0.973426i 0.583676 + 0.811987i \(0.301614\pi\)
−0.986883 + 0.161440i \(0.948386\pi\)
\(44\) −14625.7 4236.26i −1.13890 0.329876i
\(45\) −7295.13 + 3021.74i −0.537034 + 0.222447i
\(46\) −692.358 12488.2i −0.0482432 0.870172i
\(47\) 12645.2i 0.834988i 0.908680 + 0.417494i \(0.137092\pi\)
−0.908680 + 0.417494i \(0.862908\pi\)
\(48\) −2462.76 3492.07i −0.154283 0.218766i
\(49\) 6517.33i 0.387775i
\(50\) 10730.4 594.902i 0.607001 0.0336527i
\(51\) 5580.66 2311.58i 0.300442 0.124447i
\(52\) 768.424 + 1395.07i 0.0394087 + 0.0715464i
\(53\) 1970.47 4757.15i 0.0963565 0.232625i −0.868350 0.495951i \(-0.834819\pi\)
0.964707 + 0.263326i \(0.0848195\pi\)
\(54\) −9969.44 + 4792.25i −0.465250 + 0.223643i
\(55\) −11777.4 + 11777.4i −0.524980 + 0.524980i
\(56\) −3036.92 18109.4i −0.129409 0.771673i
\(57\) −4622.67 4622.67i −0.188454 0.188454i
\(58\) 19803.4 + 6945.43i 0.772984 + 0.271100i
\(59\) 31638.1 + 13104.9i 1.18326 + 0.490122i 0.885555 0.464535i \(-0.153779\pi\)
0.297705 + 0.954658i \(0.403779\pi\)
\(60\) −4645.50 + 516.691i −0.166592 + 0.0185290i
\(61\) 17051.2 + 41165.3i 0.586720 + 1.41647i 0.886621 + 0.462498i \(0.153047\pi\)
−0.299900 + 0.953971i \(0.596953\pi\)
\(62\) 5620.49 6280.28i 0.185693 0.207491i
\(63\) −22883.0 −0.726377
\(64\) 10689.7 + 30975.3i 0.326224 + 0.945293i
\(65\) 1742.17 0.0511454
\(66\) −7490.82 + 8370.16i −0.211675 + 0.236523i
\(67\) 5027.10 + 12136.5i 0.136814 + 0.330298i 0.977406 0.211371i \(-0.0677927\pi\)
−0.840592 + 0.541669i \(0.817793\pi\)
\(68\) −46036.6 + 5120.37i −1.20734 + 0.134285i
\(69\) −8524.19 3530.84i −0.215541 0.0892802i
\(70\) −18953.5 6647.36i −0.462323 0.162145i
\(71\) −55422.5 55422.5i −1.30479 1.30479i −0.925124 0.379666i \(-0.876039\pi\)
−0.379666 0.925124i \(-0.623961\pi\)
\(72\) 40273.1 6753.76i 0.915553 0.153537i
\(73\) 7698.14 7698.14i 0.169075 0.169075i −0.617498 0.786573i \(-0.711854\pi\)
0.786573 + 0.617498i \(0.211854\pi\)
\(74\) −28509.2 + 13704.2i −0.605209 + 0.290920i
\(75\) 3033.84 7324.33i 0.0622786 0.150354i
\(76\) 24186.7 + 43910.9i 0.480334 + 0.872044i
\(77\) −44593.9 + 18471.4i −0.857134 + 0.355036i
\(78\) 1173.11 65.0386i 0.0218325 0.00121042i
\(79\) 42879.8i 0.773009i −0.922287 0.386505i \(-0.873682\pi\)
0.922287 0.386505i \(-0.126318\pi\)
\(80\) 35319.3 + 6105.05i 0.617003 + 0.106651i
\(81\) 46657.6i 0.790150i
\(82\) 5109.98 + 92169.7i 0.0839237 + 1.51375i
\(83\) 89333.4 37003.1i 1.42337 0.589580i 0.467667 0.883905i \(-0.345095\pi\)
0.955706 + 0.294324i \(0.0950946\pi\)
\(84\) −13010.8 3768.52i −0.201190 0.0582737i
\(85\) −19389.6 + 46810.5i −0.291086 + 0.702743i
\(86\) −31308.4 65131.8i −0.456473 0.949614i
\(87\) 10946.8 10946.8i 0.155057 0.155057i
\(88\) 73031.6 45670.4i 1.00532 0.628678i
\(89\) −65284.9 65284.9i −0.873650 0.873650i 0.119218 0.992868i \(-0.461961\pi\)
−0.992868 + 0.119218i \(0.961961\pi\)
\(90\) 14782.9 42150.4i 0.192378 0.548524i
\(91\) 4664.45 + 1932.08i 0.0590469 + 0.0244580i
\(92\) 55253.2 + 44192.5i 0.680594 + 0.544351i
\(93\) −2379.24 5743.99i −0.0285253 0.0688663i
\(94\) −53303.1 47703.2i −0.622204 0.556837i
\(95\) 54836.0 0.623386
\(96\) 24010.7 + 2792.39i 0.265905 + 0.0309241i
\(97\) 103957. 1.12183 0.560914 0.827874i \(-0.310450\pi\)
0.560914 + 0.827874i \(0.310450\pi\)
\(98\) 27472.4 + 24586.3i 0.288956 + 0.258599i
\(99\) −41078.2 99171.6i −0.421234 1.01695i
\(100\) −37972.0 + 47475.8i −0.379720 + 0.474758i
\(101\) 74446.0 + 30836.5i 0.726169 + 0.300789i 0.714977 0.699148i \(-0.246437\pi\)
0.0111925 + 0.999937i \(0.496437\pi\)
\(102\) −11308.7 + 32244.4i −0.107625 + 0.306870i
\(103\) −70235.3 70235.3i −0.652323 0.652323i 0.301229 0.953552i \(-0.402603\pi\)
−0.953552 + 0.301229i \(0.902603\pi\)
\(104\) −8779.46 2023.69i −0.0795948 0.0183468i
\(105\) −10477.0 + 10477.0i −0.0927395 + 0.0927395i
\(106\) 12619.3 + 26252.2i 0.109086 + 0.226935i
\(107\) −19899.0 + 48040.4i −0.168024 + 0.405646i −0.985353 0.170525i \(-0.945454\pi\)
0.817329 + 0.576171i \(0.195454\pi\)
\(108\) 17408.4 60102.6i 0.143615 0.495831i
\(109\) −182515. + 75600.2i −1.47141 + 0.609476i −0.967179 0.254095i \(-0.918222\pi\)
−0.504226 + 0.863572i \(0.668222\pi\)
\(110\) −5215.60 94074.8i −0.0410982 0.741296i
\(111\) 23334.5i 0.179759i
\(112\) 87792.8 + 55515.0i 0.661324 + 0.418182i
\(113\) 234416.i 1.72699i 0.504353 + 0.863497i \(0.331731\pi\)
−0.504353 + 0.863497i \(0.668269\pi\)
\(114\) 36924.6 2047.14i 0.266106 0.0147532i
\(115\) 71500.9 29616.6i 0.504158 0.208829i
\(116\) −103984. + 57276.0i −0.717502 + 0.395210i
\(117\) −4296.71 + 10373.2i −0.0290183 + 0.0700564i
\(118\) −174594. + 83926.2i −1.15431 + 0.554871i
\(119\) −103827. + 103827.i −0.672111 + 0.672111i
\(120\) 15346.9 21531.3i 0.0972898 0.136495i
\(121\) −46224.3 46224.3i −0.287017 0.287017i
\(122\) −237849. 83417.9i −1.44677 0.507411i
\(123\) 62913.3 + 26059.5i 0.374955 + 0.155312i
\(124\) 5270.23 + 47384.0i 0.0307805 + 0.276743i
\(125\) 67307.4 + 162494.i 0.385290 + 0.930173i
\(126\) 86324.8 96458.5i 0.484406 0.541270i
\(127\) 186554. 1.02635 0.513174 0.858285i \(-0.328470\pi\)
0.513174 + 0.858285i \(0.328470\pi\)
\(128\) −170896. 71792.6i −0.921951 0.387306i
\(129\) −53309.7 −0.282054
\(130\) −6572.22 + 7343.74i −0.0341078 + 0.0381117i
\(131\) 16567.1 + 39996.5i 0.0843467 + 0.203631i 0.960425 0.278537i \(-0.0898495\pi\)
−0.876079 + 0.482168i \(0.839850\pi\)
\(132\) −7024.00 63151.9i −0.0350873 0.315465i
\(133\) 146817. + 60813.6i 0.719694 + 0.298107i
\(134\) −70123.3 24593.5i −0.337365 0.118320i
\(135\) −48397.9 48397.9i −0.228556 0.228556i
\(136\) 152087. 213374.i 0.705088 0.989223i
\(137\) 212262. 212262.i 0.966211 0.966211i −0.0332368 0.999448i \(-0.510582\pi\)
0.999448 + 0.0332368i \(0.0105815\pi\)
\(138\) 47040.5 22612.1i 0.210269 0.101075i
\(139\) −116937. + 282311.i −0.513352 + 1.23934i 0.428570 + 0.903509i \(0.359018\pi\)
−0.941922 + 0.335832i \(0.890982\pi\)
\(140\) 99521.7 54817.9i 0.429139 0.236375i
\(141\) −48751.5 + 20193.5i −0.206509 + 0.0855390i
\(142\) 442700. 24543.8i 1.84242 0.102146i
\(143\) 23683.4i 0.0968509i
\(144\) −123459. + 195241.i −0.496153 + 0.784630i
\(145\) 129856.i 0.512910i
\(146\) 3409.11 + 61490.7i 0.0132361 + 0.238741i
\(147\) 25126.5 10407.7i 0.0959045 0.0397249i
\(148\) 49782.2 171873.i 0.186818 0.644990i
\(149\) 165049. 398464.i 0.609042 1.47036i −0.255002 0.966941i \(-0.582076\pi\)
0.864044 0.503417i \(-0.167924\pi\)
\(150\) 19429.2 + 40419.1i 0.0705061 + 0.146676i
\(151\) −75897.7 + 75897.7i −0.270886 + 0.270886i −0.829457 0.558571i \(-0.811350\pi\)
0.558571 + 0.829457i \(0.311350\pi\)
\(152\) −276340. 63697.3i −0.970142 0.223621i
\(153\) −230898. 230898.i −0.797429 0.797429i
\(154\) 90365.6 257658.i 0.307045 0.875473i
\(155\) 48180.6 + 19957.1i 0.161080 + 0.0667217i
\(156\) −4151.35 + 5190.37i −0.0136577 + 0.0170760i
\(157\) −149486. 360891.i −0.484006 1.16849i −0.957691 0.287799i \(-0.907076\pi\)
0.473685 0.880694i \(-0.342924\pi\)
\(158\) 180751. + 161762.i 0.576020 + 0.515505i
\(159\) 21487.1 0.0674040
\(160\) −158975. + 125850.i −0.490940 + 0.388646i
\(161\) 224281. 0.681910
\(162\) 196675. + 176013.i 0.588792 + 0.526935i
\(163\) −216319. 522239.i −0.637712 1.53957i −0.829720 0.558180i \(-0.811500\pi\)
0.192007 0.981394i \(-0.438500\pi\)
\(164\) −407799. 326165.i −1.18396 0.946951i
\(165\) −64213.6 26598.1i −0.183619 0.0760574i
\(166\) −181026. + 516158.i −0.509884 + 1.45383i
\(167\) 182340. + 182340.i 0.505931 + 0.505931i 0.913275 0.407344i \(-0.133545\pi\)
−0.407344 + 0.913275i \(0.633545\pi\)
\(168\) 64967.9 40627.8i 0.177593 0.111058i
\(169\) −260792. + 260792.i −0.702389 + 0.702389i
\(170\) −124174. 258323.i −0.329540 0.685552i
\(171\) −135242. + 326504.i −0.353690 + 0.853883i
\(172\) 392659. + 113732.i 1.01203 + 0.293131i
\(173\) 148174. 61375.7i 0.376406 0.155913i −0.186456 0.982463i \(-0.559700\pi\)
0.562862 + 0.826551i \(0.309700\pi\)
\(174\) 4847.78 + 87440.3i 0.0121386 + 0.218947i
\(175\) 192711.i 0.475676i
\(176\) −82993.4 + 480138.i −0.201958 + 1.16838i
\(177\) 142903.i 0.342854i
\(178\) 521478. 28911.3i 1.23363 0.0683939i
\(179\) −112402. + 46558.4i −0.262205 + 0.108609i −0.509914 0.860226i \(-0.670323\pi\)
0.247708 + 0.968835i \(0.420323\pi\)
\(180\) 121909. + 221325.i 0.280448 + 0.509153i
\(181\) 266514. 643421.i 0.604676 1.45982i −0.264042 0.964511i \(-0.585056\pi\)
0.868718 0.495306i \(-0.164944\pi\)
\(182\) −25740.6 + 12373.4i −0.0576024 + 0.0276891i
\(183\) −131477. + 131477.i −0.290215 + 0.290215i
\(184\) −394724. + 66194.8i −0.859506 + 0.144138i
\(185\) −138401. 138401.i −0.297311 0.297311i
\(186\) 33188.1 + 11639.7i 0.0703397 + 0.0246694i
\(187\) −636352. 263586.i −1.33074 0.551211i
\(188\) 402166. 44730.5i 0.829871 0.0923015i
\(189\) −75906.1 183254.i −0.154569 0.373163i
\(190\) −206866. + 231150.i −0.415724 + 0.464525i
\(191\) 967329. 1.91863 0.959314 0.282340i \(-0.0911106\pi\)
0.959314 + 0.282340i \(0.0911106\pi\)
\(192\) −102350. + 90678.0i −0.200370 + 0.177521i
\(193\) 217442. 0.420195 0.210097 0.977680i \(-0.432622\pi\)
0.210097 + 0.977680i \(0.432622\pi\)
\(194\) −392174. + 438211.i −0.748125 + 0.835947i
\(195\) 2782.12 + 6716.64i 0.00523950 + 0.0126493i
\(196\) −207276. + 23054.1i −0.385398 + 0.0428655i
\(197\) 186959. + 77441.0i 0.343227 + 0.142169i 0.547637 0.836716i \(-0.315528\pi\)
−0.204410 + 0.978885i \(0.565528\pi\)
\(198\) 573002. + 200962.i 1.03871 + 0.364294i
\(199\) −540732. 540732.i −0.967942 0.967942i 0.0315603 0.999502i \(-0.489952\pi\)
−0.999502 + 0.0315603i \(0.989952\pi\)
\(200\) −56877.2 339163.i −0.100546 0.599561i
\(201\) −38762.4 + 38762.4i −0.0676737 + 0.0676737i
\(202\) −410828. + 197482.i −0.708405 + 0.340526i
\(203\) −144011. + 347674.i −0.245277 + 0.592150i
\(204\) −93258.1 169310.i −0.156896 0.284844i
\(205\) −527716. + 218587.i −0.877032 + 0.363279i
\(206\) 561021. 31103.6i 0.921109 0.0510672i
\(207\) 498773.i 0.809054i
\(208\) 41650.5 29373.7i 0.0667516 0.0470761i
\(209\) 745453.i 1.18047i
\(210\) −4639.73 83687.7i −0.00726013 0.130952i
\(211\) −82362.7 + 34115.8i −0.127358 + 0.0527532i −0.445452 0.895306i \(-0.646957\pi\)
0.318095 + 0.948059i \(0.396957\pi\)
\(212\) −158266. 45841.1i −0.241851 0.0700511i
\(213\) 125166. 302179.i 0.189034 0.456368i
\(214\) −127436. 265110.i −0.190221 0.395723i
\(215\) 316191. 316191.i 0.466501 0.466501i
\(216\) 187677. + 300115.i 0.273702 + 0.437677i
\(217\) 106865. + 106865.i 0.154059 + 0.154059i
\(218\) 369851. 1.05455e6i 0.527090 1.50289i
\(219\) 41972.4 + 17385.5i 0.0591362 + 0.0244950i
\(220\) 416228. + 332906.i 0.579795 + 0.463730i
\(221\) 27570.7 + 66561.4i 0.0379723 + 0.0916731i
\(222\) −98361.5 88027.9i −0.133950 0.119878i
\(223\) 526236. 0.708628 0.354314 0.935127i \(-0.384714\pi\)
0.354314 + 0.935127i \(0.384714\pi\)
\(224\) −565205. + 160645.i −0.752638 + 0.213918i
\(225\) −428566. −0.564367
\(226\) −988131. 884321.i −1.28690 1.15170i
\(227\) −134730. 325268.i −0.173541 0.418964i 0.813047 0.582198i \(-0.197807\pi\)
−0.986587 + 0.163234i \(0.947807\pi\)
\(228\) −130667. + 163371.i −0.166467 + 0.208131i
\(229\) 516642. + 214000.i 0.651030 + 0.269666i 0.683659 0.729802i \(-0.260388\pi\)
−0.0326283 + 0.999468i \(0.510388\pi\)
\(230\) −144890. + 413124.i −0.180601 + 0.514945i
\(231\) −142427. 142427.i −0.175615 0.175615i
\(232\) 150840. 654395.i 0.183991 0.798215i
\(233\) −219827. + 219827.i −0.265272 + 0.265272i −0.827192 0.561920i \(-0.810063\pi\)
0.561920 + 0.827192i \(0.310063\pi\)
\(234\) −27516.9 57244.2i −0.0328518 0.0683426i
\(235\) 169383. 408927.i 0.200078 0.483032i
\(236\) 304872. 1.05257e6i 0.356318 1.23019i
\(237\) 165316. 68476.1i 0.191181 0.0791897i
\(238\) −45979.4 829339.i −0.0526164 0.949052i
\(239\) 449887.i 0.509458i 0.967012 + 0.254729i \(0.0819863\pi\)
−0.967012 + 0.254729i \(0.918014\pi\)
\(240\) 32865.5 + 145917.i 0.0368309 + 0.163523i
\(241\) 200902.i 0.222813i 0.993775 + 0.111407i \(0.0355356\pi\)
−0.993775 + 0.111407i \(0.964464\pi\)
\(242\) 369227. 20470.3i 0.405280 0.0224691i
\(243\) 618874. 256346.i 0.672337 0.278491i
\(244\) 1.24890e6 687912.i 1.34293 0.739704i
\(245\) −87300.1 + 210761.i −0.0929179 + 0.224324i
\(246\) −347185. + 166890.i −0.365783 + 0.175829i
\(247\) 55135.3 55135.3i 0.0575026 0.0575026i
\(248\) −219619. 156538.i −0.226747 0.161618i
\(249\) 285319. + 285319.i 0.291630 + 0.291630i
\(250\) −938875. 329281.i −0.950074 0.333209i
\(251\) 548084. + 227024.i 0.549115 + 0.227451i 0.639952 0.768415i \(-0.278954\pi\)
−0.0908372 + 0.995866i \(0.528954\pi\)
\(252\) 80945.3 + 727769.i 0.0802953 + 0.721925i
\(253\) 402615. + 971998.i 0.395447 + 0.954694i
\(254\) −703763. + 786378.i −0.684451 + 0.764798i
\(255\) −211434. −0.203622
\(256\) 947323. 449545.i 0.903438 0.428719i
\(257\) 306264. 0.289244 0.144622 0.989487i \(-0.453803\pi\)
0.144622 + 0.989487i \(0.453803\pi\)
\(258\) 201108. 224716.i 0.188096 0.210177i
\(259\) −217066. 524043.i −0.201067 0.485419i
\(260\) −6162.66 55407.7i −0.00565372 0.0508319i
\(261\) −773186. 320264.i −0.702559 0.291009i
\(262\) −231095. 81049.4i −0.207988 0.0729451i
\(263\) 1.20183e6 + 1.20183e6i 1.07140 + 1.07140i 0.997247 + 0.0741551i \(0.0236260\pi\)
0.0741551 + 0.997247i \(0.476374\pi\)
\(264\) 292701. + 208629.i 0.258473 + 0.184232i
\(265\) −127445. + 127445.i −0.111483 + 0.111483i
\(266\) −810206. + 389461.i −0.702088 + 0.337489i
\(267\) 147440. 355951.i 0.126572 0.305571i
\(268\) 368205. 202812.i 0.313150 0.172487i
\(269\) −937950. + 388512.i −0.790313 + 0.327358i −0.741069 0.671428i \(-0.765681\pi\)
−0.0492435 + 0.998787i \(0.515681\pi\)
\(270\) 386590. 21432.9i 0.322731 0.0178925i
\(271\) 2.35122e6i 1.94478i −0.233368 0.972388i \(-0.574975\pi\)
0.233368 0.972388i \(-0.425025\pi\)
\(272\) 325695. + 1.44603e6i 0.266925 + 1.18510i
\(273\) 21068.4i 0.0171090i
\(274\) 94000.0 + 1.69550e6i 0.0756400 + 1.36433i
\(275\) −835180. + 345943.i −0.665961 + 0.275850i
\(276\) −82141.3 + 283592.i −0.0649066 + 0.224090i
\(277\) −692891. + 1.67279e6i −0.542582 + 1.30991i 0.380313 + 0.924858i \(0.375816\pi\)
−0.922895 + 0.385051i \(0.874184\pi\)
\(278\) −748884. 1.55793e6i −0.581170 1.20902i
\(279\) −237656. + 237656.i −0.182784 + 0.182784i
\(280\) −144366. + 626310.i −0.110045 + 0.477413i
\(281\) −124792. 124792.i −0.0942806 0.0942806i 0.658393 0.752674i \(-0.271236\pi\)
−0.752674 + 0.658393i \(0.771236\pi\)
\(282\) 98790.5 281680.i 0.0739763 0.210928i
\(283\) −42645.5 17664.3i −0.0316524 0.0131109i 0.366801 0.930299i \(-0.380453\pi\)
−0.398453 + 0.917189i \(0.630453\pi\)
\(284\) −1.56660e6 + 1.95870e6i −1.15256 + 1.44103i
\(285\) 87569.5 + 211411.i 0.0638617 + 0.154176i
\(286\) −99832.3 89344.2i −0.0721699 0.0645879i
\(287\) −1.65531e6 −1.18625
\(288\) −357256. 1.25695e6i −0.253804 0.892970i
\(289\) −675442. −0.475711
\(290\) −547380. 489874.i −0.382203 0.342050i
\(291\) 166013. + 400791.i 0.114924 + 0.277451i
\(292\) −272062. 217600.i −0.186728 0.149349i
\(293\) 7886.57 + 3266.72i 0.00536684 + 0.00222302i 0.385365 0.922764i \(-0.374075\pi\)
−0.379998 + 0.924987i \(0.624075\pi\)
\(294\) −50916.7 + 145178.i −0.0343551 + 0.0979564i
\(295\) −847589. 847589.i −0.567061 0.567061i
\(296\) 536693. + 858226.i 0.356038 + 0.569341i
\(297\) 657932. 657932.i 0.432803 0.432803i
\(298\) 1.05700e6 + 2.19891e6i 0.689501 + 1.43439i
\(299\) 42112.9 101669.i 0.0272419 0.0657677i
\(300\) −243674. 70579.1i −0.156317 0.0452765i
\(301\) 1.19722e6 495906.i 0.761656 0.315488i
\(302\) −33611.1 606250.i −0.0212063 0.382503i
\(303\) 336258.i 0.210410i
\(304\) 1.31098e6 924561.i 0.813603 0.573788i
\(305\) 1.55963e6i 0.960001i
\(306\) 1.84435e6 102253.i 1.12601 0.0624269i
\(307\) 1.11769e6 462964.i 0.676826 0.280351i −0.0176733 0.999844i \(-0.505626\pi\)
0.694499 + 0.719493i \(0.255626\pi\)
\(308\) 745206. + 1.35292e6i 0.447610 + 0.812634i
\(309\) 158620. 382942.i 0.0945064 0.228159i
\(310\) −265883. + 127808.i −0.157140 + 0.0755362i
\(311\) 910647. 910647.i 0.533887 0.533887i −0.387840 0.921727i \(-0.626779\pi\)
0.921727 + 0.387840i \(0.126779\pi\)
\(312\) −6218.20 37079.5i −0.00361641 0.0215649i
\(313\) −228.236 228.236i −0.000131681 0.000131681i 0.707041 0.707173i \(-0.250030\pi\)
−0.707173 + 0.707041i \(0.750030\pi\)
\(314\) 2.08519e6 + 731313.i 1.19349 + 0.418581i
\(315\) 740004. + 306519.i 0.420201 + 0.174053i
\(316\) −1.36374e6 + 151681.i −0.768272 + 0.0854502i
\(317\) −1.16342e6 2.80875e6i −0.650264 1.56988i −0.812395 0.583107i \(-0.801837\pi\)
0.162131 0.986769i \(-0.448163\pi\)
\(318\) −81059.0 + 90574.5i −0.0449504 + 0.0502271i
\(319\) −1.76529e6 −0.971267
\(320\) 69227.6 1.14489e6i 0.0377924 0.625011i
\(321\) −216989. −0.117537
\(322\) −846085. + 945408.i −0.454752 + 0.508135i
\(323\) 867807. + 2.09507e6i 0.462825 + 1.11736i
\(324\) −1.48389e6 + 165044.i −0.785307 + 0.0873449i
\(325\) 87358.5 + 36185.1i 0.0458772 + 0.0190030i
\(326\) 3.01744e6 + 1.05827e6i 1.57251 + 0.551510i
\(327\) −582929. 582929.i −0.301471 0.301471i
\(328\) 2.91328e6 488554.i 1.49519 0.250743i
\(329\) 907007. 907007.i 0.461978 0.461978i
\(330\) 354361. 170339.i 0.179127 0.0861052i
\(331\) 677086. 1.63463e6i 0.339683 0.820067i −0.658063 0.752963i \(-0.728624\pi\)
0.997746 0.0671042i \(-0.0213760\pi\)
\(332\) −1.49285e6 2.71026e6i −0.743310 1.34948i
\(333\) 1.16541e6 482728.i 0.575927 0.238557i
\(334\) −1.45649e6 + 80749.1i −0.714398 + 0.0396069i
\(335\) 459815.i 0.223857i
\(336\) −73829.9 + 427125.i −0.0356766 + 0.206399i
\(337\) 1.87560e6i 0.899634i −0.893121 0.449817i \(-0.851489\pi\)
0.893121 0.449817i \(-0.148511\pi\)
\(338\) −115491. 2.08314e6i −0.0549867 0.991805i
\(339\) −903753. + 374347.i −0.427120 + 0.176919i
\(340\) 1.55734e6 + 451078.i 0.730613 + 0.211619i
\(341\) −271300. + 654977.i −0.126347 + 0.305028i
\(342\) −866115. 1.80180e6i −0.400415 0.832995i
\(343\) −1.67300e6 + 1.67300e6i −0.767820 + 0.767820i
\(344\) −1.96070e6 + 1.22612e6i −0.893335 + 0.558648i
\(345\) 228364. + 228364.i 0.103295 + 0.103295i
\(346\) −300262. + 856133.i −0.134837 + 0.384460i
\(347\) 136441. + 56515.9i 0.0608307 + 0.0251969i 0.412891 0.910780i \(-0.364519\pi\)
−0.352061 + 0.935977i \(0.614519\pi\)
\(348\) −386874. 309429.i −0.171247 0.136966i
\(349\) 1.29053e6 + 3.11561e6i 0.567157 + 1.36924i 0.903941 + 0.427656i \(0.140661\pi\)
−0.336784 + 0.941582i \(0.609339\pi\)
\(350\) −812332. 726991.i −0.354457 0.317219i
\(351\) −97324.2 −0.0421651
\(352\) −1.71083e6 2.16114e6i −0.735955 0.929663i
\(353\) 395898. 0.169101 0.0845506 0.996419i \(-0.473055\pi\)
0.0845506 + 0.996419i \(0.473055\pi\)
\(354\) −602379. 539094.i −0.255483 0.228642i
\(355\) 1.04990e6 + 2.53467e6i 0.442156 + 1.06746i
\(356\) −1.84538e6 + 2.30725e6i −0.771721 + 0.964871i
\(357\) −566091. 234483.i −0.235080 0.0973733i
\(358\) 227773. 649446.i 0.0939279 0.267815i
\(359\) 605044. + 605044.i 0.247771 + 0.247771i 0.820055 0.572284i \(-0.193943\pi\)
−0.572284 + 0.820055i \(0.693943\pi\)
\(360\) −1.39284e6 321054.i −0.566429 0.130564i
\(361\) −15439.1 + 15439.1i −0.00623527 + 0.00623527i
\(362\) 1.70680e6 + 3.55070e6i 0.684559 + 1.42411i
\(363\) 104393. 252027.i 0.0415820 0.100388i
\(364\) 44947.8 155182.i 0.0177810 0.0613886i
\(365\) −352064. + 145830.i −0.138321 + 0.0572946i
\(366\) −58224.1 1.05020e6i −0.0227196 0.409797i
\(367\) 2.30685e6i 0.894035i 0.894525 + 0.447017i \(0.147514\pi\)
−0.894525 + 0.447017i \(0.852486\pi\)
\(368\) 1.21004e6 1.91359e6i 0.465780 0.736597i
\(369\) 3.68122e6i 1.40743i
\(370\) 1.10551e6 61290.8i 0.419817 0.0232751i
\(371\) −482556. + 199881.i −0.182017 + 0.0753940i
\(372\) −174265. + 95987.6i −0.0652910 + 0.0359632i
\(373\) −1.70481e6 + 4.11577e6i −0.634459 + 1.53172i 0.199502 + 0.979897i \(0.436068\pi\)
−0.833961 + 0.551823i \(0.813932\pi\)
\(374\) 3.51169e6 1.68805e6i 1.29819 0.624030i
\(375\) −518986. + 518986.i −0.190580 + 0.190580i
\(376\) −1.32860e6 + 1.86399e6i −0.484645 + 0.679945i
\(377\) 130565. + 130565.i 0.0473121 + 0.0473121i
\(378\) 1.05882e6 + 371347.i 0.381147 + 0.133675i
\(379\) 141619. + 58660.7i 0.0506436 + 0.0209773i 0.407861 0.913044i \(-0.366275\pi\)
−0.357218 + 0.934021i \(0.616275\pi\)
\(380\) −193974. 1.74400e6i −0.0689105 0.619565i
\(381\) 297914. + 719227.i 0.105142 + 0.253836i
\(382\) −3.64919e6 + 4.07757e6i −1.27950 + 1.42970i
\(383\) −3.47509e6 −1.21051 −0.605255 0.796031i \(-0.706929\pi\)
−0.605255 + 0.796031i \(0.706929\pi\)
\(384\) 3874.46 773511.i 0.00134086 0.267694i
\(385\) 1.68953e6 0.580916
\(386\) −820288. + 916582.i −0.280219 + 0.313114i
\(387\) 1.10284e6 + 2.66248e6i 0.374312 + 0.903669i
\(388\) −367734. 3.30625e6i −0.124009 1.11495i
\(389\) −2.61566e6 1.08344e6i −0.876411 0.363021i −0.101307 0.994855i \(-0.532302\pi\)
−0.775104 + 0.631834i \(0.782302\pi\)
\(390\) −38808.0 13610.7i −0.0129199 0.00453125i
\(391\) 2.26307e6 + 2.26307e6i 0.748612 + 0.748612i
\(392\) 684759. 960701.i 0.225073 0.315772i
\(393\) −127743. + 127743.i −0.0417212 + 0.0417212i
\(394\) −1.03173e6 + 495945.i −0.334830 + 0.160951i
\(395\) −574378. + 1.38667e6i −0.185227 + 0.447178i
\(396\) −3.00873e6 + 1.65725e6i −0.964152 + 0.531068i
\(397\) 4.16657e6 1.72585e6i 1.32679 0.549575i 0.397052 0.917796i \(-0.370033\pi\)
0.929738 + 0.368222i \(0.120033\pi\)
\(398\) 4.31922e6 239462.i 1.36678 0.0757755i
\(399\) 663145.i 0.208534i
\(400\) 1.64424e6 + 1.03972e6i 0.513824 + 0.324912i
\(401\) 2.33922e6i 0.726458i −0.931700 0.363229i \(-0.881674\pi\)
0.931700 0.363229i \(-0.118326\pi\)
\(402\) −17165.8 309623.i −0.00529785 0.0955583i
\(403\) 68509.6 28377.6i 0.0210130 0.00870388i
\(404\) 717380. 2.47675e6i 0.218673 0.754969i
\(405\) −624981. + 1.50884e6i −0.189334 + 0.457094i
\(406\) −922273. 1.91863e6i −0.277680 0.577665i
\(407\) 1.88146e6 1.88146e6i 0.563001 0.563001i
\(408\) 1.06550e6 + 245601.i 0.316886 + 0.0730432i
\(409\) 3.69884e6 + 3.69884e6i 1.09335 + 1.09335i 0.995169 + 0.0981762i \(0.0313009\pi\)
0.0981762 + 0.995169i \(0.468699\pi\)
\(410\) 1.06937e6 3.04908e6i 0.314173 0.895797i
\(411\) 1.15731e6 + 479375.i 0.337945 + 0.139981i
\(412\) −1.98531e6 + 2.48220e6i −0.576216 + 0.720434i
\(413\) −1.32934e6 3.20930e6i −0.383495 0.925840i
\(414\) −2.10248e6 1.88159e6i −0.602879 0.539542i
\(415\) −3.38457e6 −0.964681
\(416\) −33305.3 + 286380.i −0.00943582 + 0.0811351i
\(417\) −1.27514e6 −0.359103
\(418\) −3.14230e6 2.81218e6i −0.879644 0.787231i
\(419\) 175695. + 424166.i 0.0488906 + 0.118032i 0.946438 0.322886i \(-0.104653\pi\)
−0.897547 + 0.440918i \(0.854653\pi\)
\(420\) 370271. + 296149.i 0.102423 + 0.0819195i
\(421\) −111926. 46361.5i −0.0307771 0.0127483i 0.367242 0.930126i \(-0.380302\pi\)
−0.398019 + 0.917377i \(0.630302\pi\)
\(422\) 166901. 475883.i 0.0456223 0.130082i
\(423\) 2.01708e6 + 2.01708e6i 0.548115 + 0.548115i
\(424\) 790283. 494205.i 0.213485 0.133503i
\(425\) −1.94453e6 + 1.94453e6i −0.522205 + 0.522205i
\(426\) 801587. + 1.66756e6i 0.214006 + 0.445204i
\(427\) 1.72964e6 4.17573e6i 0.459078 1.10831i
\(428\) 1.59826e6 + 462929.i 0.421734 + 0.122153i
\(429\) −91307.4 + 37820.8i −0.0239532 + 0.00992173i
\(430\) 140024. + 2.52565e6i 0.0365202 + 0.658721i
\(431\) 4.86314e6i 1.26103i −0.776179 0.630513i \(-0.782845\pi\)
0.776179 0.630513i \(-0.217155\pi\)
\(432\) −1.97307e6 341052.i −0.508668 0.0879248i
\(433\) 2.57930e6i 0.661123i 0.943785 + 0.330561i \(0.107238\pi\)
−0.943785 + 0.330561i \(0.892762\pi\)
\(434\) −853612. + 47325.1i −0.217539 + 0.0120606i
\(435\) −500638. + 207371.i −0.126853 + 0.0525442i
\(436\) 3.05000e6 + 5.53726e6i 0.768393 + 1.39502i
\(437\) 1.32554e6 3.20012e6i 0.332038 0.801610i
\(438\) −231623. + 111340.i −0.0576895 + 0.0277310i
\(439\) 3.13352e6 3.13352e6i 0.776016 0.776016i −0.203135 0.979151i \(-0.565113\pi\)
0.979151 + 0.203135i \(0.0651130\pi\)
\(440\) −2.97349e6 + 498652.i −0.732210 + 0.122791i
\(441\) −1.03960e6 1.03960e6i −0.254549 0.254549i
\(442\) −384585. 134881.i −0.0936346 0.0328394i
\(443\) −5.53493e6 2.29264e6i −1.33999 0.555044i −0.406505 0.913649i \(-0.633252\pi\)
−0.933489 + 0.358605i \(0.883252\pi\)
\(444\) 742126. 82542.2i 0.178657 0.0198709i
\(445\) 1.23672e6 + 2.98571e6i 0.296055 + 0.714740i
\(446\) −1.98519e6 + 2.21824e6i −0.472570 + 0.528045i
\(447\) 1.79978e6 0.426041
\(448\) 1.45504e6 2.98853e6i 0.342515 0.703497i
\(449\) −6.39099e6 −1.49607 −0.748036 0.663658i \(-0.769003\pi\)
−0.748036 + 0.663658i \(0.769003\pi\)
\(450\) 1.61674e6 1.80653e6i 0.376365 0.420547i
\(451\) −2.97152e6 7.17388e6i −0.687919 1.66078i
\(452\) 7.45534e6 829212.i 1.71641 0.190906i
\(453\) −413815. 171408.i −0.0947459 0.0392450i
\(454\) 1.87936e6 + 659127.i 0.427928 + 0.150082i
\(455\) −124961. 124961.i −0.0282974 0.0282974i
\(456\) −195722. 1.16711e6i −0.0440787 0.262844i
\(457\) −884261. + 884261.i −0.198057 + 0.198057i −0.799167 0.601110i \(-0.794725\pi\)
0.601110 + 0.799167i \(0.294725\pi\)
\(458\) −2.85108e6 + 1.37049e6i −0.635104 + 0.305291i
\(459\) 1.08318e6 2.61502e6i 0.239976 0.579353i
\(460\) −1.19485e6 2.16924e6i −0.263280 0.477984i
\(461\) 2.63521e6 1.09154e6i 0.577514 0.239214i −0.0747549 0.997202i \(-0.523817\pi\)
0.652269 + 0.757988i \(0.273817\pi\)
\(462\) 1.13767e6 63073.5i 0.247977 0.0137481i
\(463\) 2.13502e6i 0.462860i −0.972852 0.231430i \(-0.925660\pi\)
0.972852 0.231430i \(-0.0743404\pi\)
\(464\) 2.18943e6 + 3.10450e6i 0.472102 + 0.669417i
\(465\) 217623.i 0.0466736i
\(466\) −97349.9 1.75592e6i −0.0207669 0.374576i
\(467\) −5.22052e6 + 2.16241e6i −1.10770 + 0.458824i −0.860145 0.510050i \(-0.829627\pi\)
−0.247554 + 0.968874i \(0.579627\pi\)
\(468\) 345107. + 99958.6i 0.0728348 + 0.0210963i
\(469\) 509939. 1.23110e6i 0.107050 0.258441i
\(470\) 1.08476e6 + 2.25665e6i 0.226510 + 0.471216i
\(471\) 1.15264e6 1.15264e6i 0.239409 0.239409i
\(472\) 3.28678e6 + 5.25589e6i 0.679071 + 1.08590i
\(473\) 4.29836e6 + 4.29836e6i 0.883386 + 0.883386i
\(474\) −334998. + 955177.i −0.0684852 + 0.195271i
\(475\) 2.74968e6 + 1.13895e6i 0.559175 + 0.231618i
\(476\) 3.66936e6 + 2.93482e6i 0.742289 + 0.593696i
\(477\) −444512. 1.07315e6i −0.0894515 0.215955i
\(478\) −1.89640e6 1.69717e6i −0.379631 0.339748i
\(479\) 6.23378e6 1.24140 0.620701 0.784047i \(-0.286848\pi\)
0.620701 + 0.784047i \(0.286848\pi\)
\(480\) −739067. 411927.i −0.146413 0.0816050i
\(481\) −278314. −0.0548494
\(482\) −846859. 757890.i −0.166033 0.148590i
\(483\) 358161. + 864677.i 0.0698571 + 0.168650i
\(484\) −1.30660e6 + 1.63362e6i −0.253530 + 0.316985i
\(485\) −3.36183e6 1.39252e6i −0.648966 0.268811i
\(486\) −1.25409e6 + 3.57579e6i −0.240846 + 0.686722i
\(487\) −1.22059e6 1.22059e6i −0.233210 0.233210i 0.580821 0.814031i \(-0.302732\pi\)
−0.814031 + 0.580821i \(0.802732\pi\)
\(488\) −1.81166e6 + 7.85959e6i −0.344371 + 1.49400i
\(489\) 1.66796e6 1.66796e6i 0.315438 0.315438i
\(490\) −559085. 1.16308e6i −0.105193 0.218836i
\(491\) 1.80472e6 4.35699e6i 0.337837 0.815610i −0.660086 0.751190i \(-0.729480\pi\)
0.997923 0.0644201i \(-0.0205198\pi\)
\(492\) 606248. 2.09307e6i 0.112911 0.389826i
\(493\) −4.96129e6 + 2.05503e6i −0.919342 + 0.380804i
\(494\) 24416.6 + 440406.i 0.00450161 + 0.0811963i
\(495\) 3.75731e6i 0.689230i
\(496\) 1.48835e6 335228.i 0.271645 0.0611837i
\(497\) 7.95064e6i 1.44381i
\(498\) −2.27905e6 + 126353.i −0.411795 + 0.0228303i
\(499\) −1.78715e6 + 740262.i −0.321299 + 0.133086i −0.537503 0.843262i \(-0.680632\pi\)
0.216204 + 0.976348i \(0.430632\pi\)
\(500\) 4.92986e6 2.71544e6i 0.881881 0.485752i
\(501\) −411798. + 994169.i −0.0732977 + 0.176956i
\(502\) −3.02459e6 + 1.45390e6i −0.535682 + 0.257499i
\(503\) −1.12302e6 + 1.12302e6i −0.197909 + 0.197909i −0.799103 0.601194i \(-0.794692\pi\)
0.601194 + 0.799103i \(0.294692\pi\)
\(504\) −3.37312e6 2.40426e6i −0.591501 0.421604i
\(505\) −1.99442e6 1.99442e6i −0.348007 0.348007i
\(506\) −5.61610e6 1.96967e6i −0.975121 0.341993i
\(507\) −1.42191e6 588974.i −0.245670 0.101760i
\(508\) −659906. 5.93313e6i −0.113455 1.02006i
\(509\) −2.41720e6 5.83563e6i −0.413540 0.998375i −0.984180 0.177174i \(-0.943305\pi\)
0.570639 0.821201i \(-0.306695\pi\)
\(510\) 797624. 891257.i 0.135792 0.151732i
\(511\) −1.10434e6 −0.187089
\(512\) −1.67876e6 + 5.68912e6i −0.283018 + 0.959115i
\(513\) −3.06335e6 −0.513930
\(514\) −1.15536e6 + 1.29099e6i −0.192891 + 0.215534i
\(515\) 1.33050e6 + 3.21212e6i 0.221054 + 0.533670i
\(516\) 188575. + 1.69545e6i 0.0311788 + 0.280325i
\(517\) 5.55904e6 + 2.30263e6i 0.914689 + 0.378877i
\(518\) 3.02786e6 + 1.06193e6i 0.495805 + 0.173888i
\(519\) 473248. + 473248.i 0.0771206 + 0.0771206i
\(520\) 256808. + 183045.i 0.0416485 + 0.0296858i
\(521\) −4.50403e6 + 4.50403e6i −0.726954 + 0.726954i −0.970012 0.243058i \(-0.921849\pi\)
0.243058 + 0.970012i \(0.421849\pi\)
\(522\) 4.26681e6 2.05103e6i 0.685372 0.329454i
\(523\) −2.56781e6 + 6.19925e6i −0.410496 + 0.991026i 0.574508 + 0.818499i \(0.305193\pi\)
−0.985005 + 0.172527i \(0.944807\pi\)
\(524\) 1.21344e6 668379.i 0.193059 0.106340i
\(525\) −742966. + 307746.i −0.117644 + 0.0487298i
\(526\) −9.59987e6 + 532226.i −1.51287 + 0.0838749i
\(527\) 2.15662e6i 0.338258i
\(528\) −1.98363e6 + 446781.i −0.309653 + 0.0697445i
\(529\) 1.54777e6i 0.240474i
\(530\) −56438.6 1.01799e6i −0.00872743 0.157418i
\(531\) 7.13711e6 2.95629e6i 1.09847 0.454999i
\(532\) 1.41477e6 4.88447e6i 0.216723 0.748236i
\(533\) −310816. + 750377.i −0.0473899 + 0.114409i
\(534\) 944229. + 1.96431e6i 0.143293 + 0.298096i
\(535\) 1.28701e6 1.28701e6i 0.194400 0.194400i
\(536\) −534119. + 2.31719e6i −0.0803020 + 0.348377i
\(537\) −358997. 358997.i −0.0537224 0.0537224i
\(538\) 1.90067e6 5.41937e6i 0.283108 0.807222i
\(539\) −2.86513e6 1.18678e6i −0.424788 0.175953i
\(540\) −1.36804e6 + 1.71044e6i −0.201890 + 0.252420i
\(541\) −665473. 1.60659e6i −0.0977546 0.236000i 0.867436 0.497549i \(-0.165767\pi\)
−0.965190 + 0.261549i \(0.915767\pi\)
\(542\) 9.91107e6 + 8.86984e6i 1.44918 + 1.29693i
\(543\) 2.90621e6 0.422987
\(544\) −7.32410e6 4.08217e6i −1.06110 0.591416i
\(545\) 6.91494e6 0.997235
\(546\) −88809.6 79479.4i −0.0127491 0.0114097i
\(547\) −2.31233e6 5.58246e6i −0.330431 0.797732i −0.998558 0.0536844i \(-0.982904\pi\)
0.668126 0.744048i \(-0.267096\pi\)
\(548\) −7.50162e6 5.99993e6i −1.06710 0.853482i
\(549\) 9.28632e6 + 3.84652e6i 1.31496 + 0.544675i
\(550\) 1.69242e6 4.82558e6i 0.238562 0.680209i
\(551\) 4.10962e6 + 4.10962e6i 0.576664 + 0.576664i
\(552\) −885551. 1.41608e6i −0.123699 0.197807i
\(553\) −3.07566e6 + 3.07566e6i −0.427686 + 0.427686i
\(554\) −4.43739e6 9.23123e6i −0.614261 1.27787i
\(555\) 312567. 754602.i 0.0430735 0.103989i
\(556\) 9.39223e6 + 2.72042e6i 1.28849 + 0.373206i
\(557\) 5.32043e6 2.20380e6i 0.726623 0.300977i 0.0114595 0.999934i \(-0.496352\pi\)
0.715163 + 0.698957i \(0.246352\pi\)
\(558\) −105246. 1.89833e6i −0.0143093 0.258099i
\(559\) 635833.i 0.0860625i
\(560\) −2.09547e6 2.97127e6i −0.282365 0.400379i
\(561\) 2.87428e6i 0.385587i
\(562\) 996808. 55264.0i 0.133128 0.00738077i
\(563\) −7.68270e6 + 3.18228e6i −1.02151 + 0.423124i −0.829641 0.558297i \(-0.811455\pi\)
−0.191870 + 0.981420i \(0.561455\pi\)
\(564\) 814683. + 1.47905e6i 0.107843 + 0.195788i
\(565\) 3.14002e6 7.58067e6i 0.413820 0.999049i
\(566\) 235338. 113125.i 0.0308781 0.0148429i
\(567\) −3.34663e6 + 3.34663e6i −0.437170 + 0.437170i
\(568\) −2.34657e6 1.39928e7i −0.305185 1.81984i
\(569\) 2.15736e6 + 2.15736e6i 0.279346 + 0.279346i 0.832848 0.553502i \(-0.186709\pi\)
−0.553502 + 0.832848i \(0.686709\pi\)
\(570\) −1.22151e6 428407.i −0.157475 0.0552292i
\(571\) 48674.1 + 20161.5i 0.00624752 + 0.00258781i 0.385805 0.922580i \(-0.373924\pi\)
−0.379557 + 0.925168i \(0.623924\pi\)
\(572\) 753224. 83776.5i 0.0962573 0.0107061i
\(573\) 1.54476e6 + 3.72938e6i 0.196551 + 0.474515i
\(574\) 6.24458e6 6.97763e6i 0.791085 0.883951i
\(575\) 4.20046e6 0.529818
\(576\) 6.64614e6 + 3.23584e6i 0.834667 + 0.406378i
\(577\) 5.52255e6 0.690558 0.345279 0.938500i \(-0.387784\pi\)
0.345279 + 0.938500i \(0.387784\pi\)
\(578\) 2.54807e6 2.84718e6i 0.317242 0.354484i
\(579\) 347241. + 838313.i 0.0430461 + 0.103923i
\(580\) 4.12992e6 459346.i 0.509767 0.0566983i
\(581\) −9.06180e6 3.75352e6i −1.11372 0.461316i
\(582\) −2.31573e6 812168.i −0.283387 0.0993890i
\(583\) −1.73251e6 1.73251e6i −0.211108 0.211108i
\(584\) 1.94358e6 325937.i 0.235815 0.0395459i
\(585\) 277899. 277899.i 0.0335736 0.0335736i
\(586\) −43521.8 + 20920.6i −0.00523556 + 0.00251670i
\(587\) −3.97952e6 + 9.60741e6i −0.476689 + 1.15083i 0.484463 + 0.874812i \(0.339015\pi\)
−0.961152 + 0.276018i \(0.910985\pi\)
\(588\) −419888. 762305.i −0.0500830 0.0909254i
\(589\) 2.15639e6 893206.i 0.256118 0.106087i
\(590\) 6.77031e6 375353.i 0.800716 0.0443925i
\(591\) 844458.i 0.0994511i
\(592\) −5.64232e6 975292.i −0.661688 0.114375i
\(593\) 3.61973e6i 0.422707i 0.977410 + 0.211353i \(0.0677871\pi\)
−0.977410 + 0.211353i \(0.932213\pi\)
\(594\) 291364. + 5.25538e6i 0.0338820 + 0.611137i
\(595\) 4.74837e6 1.96684e6i 0.549860 0.227759i
\(596\) −1.32565e7 3.83969e6i −1.52867 0.442773i
\(597\) 1.22119e6 2.94822e6i 0.140232 0.338550i
\(598\) 269698. + 561060.i 0.0308407 + 0.0641589i
\(599\) 72804.9 72804.9i 0.00829075 0.00829075i −0.702949 0.711240i \(-0.748134\pi\)
0.711240 + 0.702949i \(0.248134\pi\)
\(600\) 1.21676e6 760901.i 0.137983 0.0862879i
\(601\) −1.01470e7 1.01470e7i −1.14591 1.14591i −0.987349 0.158562i \(-0.949314\pi\)
−0.158562 0.987349i \(-0.550686\pi\)
\(602\) −2.42607e6 + 6.91742e6i −0.272842 + 0.777952i
\(603\) 2.73783e6 + 1.13404e6i 0.306629 + 0.127010i
\(604\) 2.68232e6 + 2.14536e6i 0.299170 + 0.239281i
\(605\) 875649. + 2.11400e6i 0.0972617 + 0.234810i
\(606\) −1.41743e6 1.26852e6i −0.156790 0.140318i
\(607\) 8.64415e6 0.952249 0.476125 0.879378i \(-0.342041\pi\)
0.476125 + 0.879378i \(0.342041\pi\)
\(608\) −1.04831e6 + 9.01402e6i −0.115009 + 0.988916i
\(609\) −1.57038e6 −0.171578
\(610\) 6.57429e6 + 5.88361e6i 0.715359 + 0.640205i
\(611\) −240851. 581467.i −0.0261003 0.0630118i
\(612\) −6.52669e6 + 8.16023e6i −0.704392 + 0.880691i
\(613\) −5.44665e6 2.25607e6i −0.585434 0.242495i 0.0702509 0.997529i \(-0.477620\pi\)
−0.655685 + 0.755035i \(0.727620\pi\)
\(614\) −2.26491e6 + 6.45791e6i −0.242454 + 0.691308i
\(615\) −1.68545e6 1.68545e6i −0.179692 0.179692i
\(616\) −8.51420e6 1.96255e6i −0.904049 0.208386i
\(617\) 6.13515e6 6.13515e6i 0.648802 0.648802i −0.303901 0.952704i \(-0.598289\pi\)
0.952704 + 0.303901i \(0.0982893\pi\)
\(618\) 1.01583e6 + 2.11326e6i 0.106991 + 0.222577i
\(619\) −3.67045e6 + 8.86124e6i −0.385028 + 0.929540i 0.605949 + 0.795504i \(0.292794\pi\)
−0.990976 + 0.134036i \(0.957206\pi\)
\(620\) 464280. 1.60292e6i 0.0485066 0.167469i
\(621\) −3.99432e6 + 1.65450e6i −0.415637 + 0.172162i
\(622\) 403278. + 7.27401e6i 0.0417955 + 0.753872i
\(623\) 9.36544e6i 0.966737i
\(624\) 179759. + 113669.i 0.0184811 + 0.0116864i
\(625\) 219580.i 0.0224849i
\(626\) 1823.09 101.074i 0.000185940 1.03087e-5i
\(627\) −2.87397e6 + 1.19044e6i −0.291953 + 0.120931i
\(628\) −1.09489e7 + 6.03082e6i −1.10783 + 0.610208i
\(629\) 3.09751e6 7.47806e6i 0.312167 0.753637i
\(630\) −4.08369e6 + 1.96300e6i −0.409922 + 0.197047i
\(631\) −8.87683e6 + 8.87683e6i −0.887533 + 0.887533i −0.994286 0.106753i \(-0.965955\pi\)
0.106753 + 0.994286i \(0.465955\pi\)
\(632\) 4.50527e6 6.32078e6i 0.448671 0.629475i
\(633\) −263056. 263056.i −0.0260939 0.0260939i
\(634\) 1.62287e7 + 5.69169e6i 1.60347 + 0.562365i
\(635\) −6.03288e6 2.49890e6i −0.593731 0.245932i
\(636\) −76007.5 683374.i −0.00745099 0.0669909i
\(637\) 124135. + 299688.i 0.0121212 + 0.0292631i
\(638\) 6.65945e6 7.44120e6i 0.647719 0.723755i
\(639\) −1.76813e7 −1.71302
\(640\) 4.56488e6 + 4.61084e6i 0.440534 + 0.444969i
\(641\) 6.34454e6 0.609895 0.304947 0.952369i \(-0.401361\pi\)
0.304947 + 0.952369i \(0.401361\pi\)
\(642\) 818580. 914673.i 0.0783833 0.0875847i
\(643\) −1.57294e6 3.79741e6i −0.150032 0.362210i 0.830939 0.556364i \(-0.187804\pi\)
−0.980971 + 0.194154i \(0.937804\pi\)
\(644\) −793359. 7.13299e6i −0.0753798 0.677731i
\(645\) 1.72396e6 + 714087.i 0.163165 + 0.0675852i
\(646\) −1.21051e7 4.24548e6i −1.14127 0.400263i
\(647\) −8.64716e6 8.64716e6i −0.812106 0.812106i 0.172844 0.984949i \(-0.444704\pi\)
−0.984949 + 0.172844i \(0.944704\pi\)
\(648\) 4.90219e6 6.87766e6i 0.458619 0.643432i
\(649\) 1.15223e7 1.15223e7i 1.07381 1.07381i
\(650\) −482086. + 231735.i −0.0447549 + 0.0215134i
\(651\) −241345. + 582659.i −0.0223196 + 0.0538843i
\(652\) −1.58440e7 + 8.72712e6i −1.45964 + 0.803992i
\(653\) −1.53905e7 + 6.37497e6i −1.41244 + 0.585053i −0.952950 0.303129i \(-0.901969\pi\)
−0.459493 + 0.888182i \(0.651969\pi\)
\(654\) 4.65628e6 258149.i 0.425691 0.0236007i
\(655\) 1.51535e6i 0.138009i
\(656\) −8.93078e6 + 1.41234e7i −0.810270 + 1.28138i
\(657\) 2.45592e6i 0.221973i
\(658\) 401666. + 7.24493e6i 0.0361660 + 0.652333i
\(659\) 1.64381e7 6.80889e6i 1.47448 0.610749i 0.506603 0.862180i \(-0.330901\pi\)
0.967875 + 0.251431i \(0.0809011\pi\)
\(660\) −618778. + 2.13633e6i −0.0552936 + 0.190901i
\(661\) 1.45786e6 3.51959e6i 0.129781 0.313320i −0.845610 0.533802i \(-0.820763\pi\)
0.975391 + 0.220482i \(0.0707629\pi\)
\(662\) 4.33617e6 + 9.02066e6i 0.384558 + 0.800006i
\(663\) −212588. + 212588.i −0.0187826 + 0.0187826i
\(664\) 1.70562e7 + 3.93151e6i 1.50128 + 0.346050i
\(665\) −3.93325e6 3.93325e6i −0.344903 0.344903i
\(666\) −2.36160e6 + 6.73360e6i −0.206310 + 0.588250i
\(667\) 7.57814e6 + 3.13897e6i 0.659550 + 0.273195i
\(668\) 5.15413e6 6.44413e6i 0.446904 0.558757i
\(669\) 840363. + 2.02882e6i 0.0725942 + 0.175258i
\(670\) 1.93825e6 + 1.73463e6i 0.166811 + 0.149286i
\(671\) 2.12019e7 1.81790
\(672\) −1.52194e6 1.92252e6i −0.130009 0.164228i
\(673\) −982227. −0.0835938 −0.0417969 0.999126i \(-0.513308\pi\)
−0.0417969 + 0.999126i \(0.513308\pi\)
\(674\) 7.90621e6 + 7.07560e6i 0.670376 + 0.599948i
\(675\) −1.42161e6 3.43208e6i −0.120094 0.289933i
\(676\) 9.21672e6 + 7.37169e6i 0.775728 + 0.620441i
\(677\) 1.19116e7 + 4.93396e6i 0.998848 + 0.413736i 0.821375 0.570389i \(-0.193208\pi\)
0.177473 + 0.984126i \(0.443208\pi\)
\(678\) 1.83138e6 5.22178e6i 0.153004 0.436259i
\(679\) −7.45661e6 7.45661e6i −0.620679 0.620679i
\(680\) −7.77642e6 + 4.86299e6i −0.644922 + 0.403303i
\(681\) 1.03886e6 1.03886e6i 0.0858401 0.0858401i
\(682\) −1.73745e6 3.61447e6i −0.143038 0.297567i
\(683\) −4.01198e6 + 9.68577e6i −0.329084 + 0.794479i 0.669577 + 0.742743i \(0.266475\pi\)
−0.998661 + 0.0517361i \(0.983525\pi\)
\(684\) 1.08625e7 + 3.14627e6i 0.887747 + 0.257132i
\(685\) −9.70753e6 + 4.02099e6i −0.790465 + 0.327421i
\(686\) −740883. 1.33634e7i −0.0601090 1.08420i
\(687\) 2.33357e6i 0.188638i
\(688\) 2.22814e6 1.28904e7i 0.179462 1.03823i
\(689\) 256281.i 0.0205668i
\(690\) −1.82411e6 + 101131.i −0.145858 + 0.00808649i
\(691\) 1.28695e7 5.33072e6i 1.02534 0.424709i 0.194310 0.980940i \(-0.437753\pi\)
0.831027 + 0.556232i \(0.187753\pi\)
\(692\) −2.47613e6 4.49540e6i −0.196566 0.356864i
\(693\) −4.16689e6 + 1.00598e7i −0.329594 + 0.795710i
\(694\) −752948. + 361937.i −0.0593426 + 0.0285256i
\(695\) 7.56315e6 7.56315e6i 0.593937 0.593937i
\(696\) 2.76379e6 463485.i 0.216263 0.0362671i
\(697\) −1.67027e7 1.67027e7i −1.30228 1.30228i
\(698\) −1.80016e7 6.31350e6i −1.39853 0.490492i
\(699\) −1.19856e6 496458.i −0.0927823 0.0384317i
\(700\) 6.12896e6 681686.i 0.472761 0.0525823i
\(701\) −1.14522e6 2.76480e6i −0.0880225 0.212505i 0.873738 0.486397i \(-0.161689\pi\)
−0.961761 + 0.273892i \(0.911689\pi\)
\(702\) 367150. 410250.i 0.0281191 0.0314200i
\(703\) −8.76014e6 −0.668533
\(704\) 1.55638e7 + 941095.i 1.18355 + 0.0715652i
\(705\) 1.84705e6 0.139960
\(706\) −1.49350e6 + 1.66883e6i −0.112770 + 0.126008i
\(707\) −3.12800e6 7.55165e6i −0.235352 0.568190i
\(708\) 4.54488e6 505499.i 0.340752 0.0378998i
\(709\) 1.06749e7 + 4.42169e6i 0.797532 + 0.330348i 0.743967 0.668216i \(-0.232942\pi\)
0.0535643 + 0.998564i \(0.482942\pi\)
\(710\) −1.46451e7 5.13629e6i −1.09030 0.382388i
\(711\) −6.83990e6 6.83990e6i −0.507430 0.507430i
\(712\) −2.76414e6 1.64828e7i −0.204343 1.21851i
\(713\) 2.32931e6 2.32931e6i 0.171595 0.171595i
\(714\) 3.12396e6 1.50167e6i 0.229329 0.110237i
\(715\) 317241. 765886.i 0.0232072 0.0560272i
\(716\) 1.87835e6 + 3.41013e6i 0.136928 + 0.248593i
\(717\) −1.73447e6 + 718439.i −0.125999 + 0.0521906i
\(718\) −4.83293e6 + 267942.i −0.349864 + 0.0193968i
\(719\) 1.89332e7i 1.36584i −0.730492 0.682921i \(-0.760709\pi\)
0.730492 0.682921i \(-0.239291\pi\)
\(720\) 6.60775e6 4.66007e6i 0.475031 0.335013i
\(721\) 1.00756e7i 0.721827i
\(722\) −6837.20 123324.i −0.000488129 0.00880448i
\(723\) −774544. + 320826.i −0.0551062 + 0.0228257i
\(724\) −2.14060e7 6.20016e6i −1.51771 0.439599i
\(725\) −2.69713e6 + 6.51144e6i −0.190571 + 0.460079i
\(726\) 668552. + 1.39081e6i 0.0470753 + 0.0979321i
\(727\) −1.76362e7 + 1.76362e7i −1.23757 + 1.23757i −0.276577 + 0.960992i \(0.589200\pi\)
−0.960992 + 0.276577i \(0.910800\pi\)
\(728\) 484575. + 774883.i 0.0338869 + 0.0541886i
\(729\) −6.04042e6 6.04042e6i −0.420968 0.420968i
\(730\) 713427. 2.03419e6i 0.0495498 0.141281i
\(731\) 1.70843e7 + 7.07655e6i 1.18251 + 0.489811i
\(732\) 4.64654e6 + 3.71638e6i 0.320518 + 0.256356i
\(733\) 4.13232e6 + 9.97629e6i 0.284075 + 0.685819i 0.999923 0.0124382i \(-0.00395931\pi\)
−0.715847 + 0.698257i \(0.753959\pi\)
\(734\) −9.72405e6 8.70246e6i −0.666204 0.596214i
\(735\) −951968. −0.0649986
\(736\) 3.50153e6 + 1.23196e7i 0.238267 + 0.838305i
\(737\) 6.25083e6 0.423905
\(738\) 1.55174e7 + 1.38872e7i 1.04877 + 0.938586i
\(739\) 4.46642e6 + 1.07829e7i 0.300849 + 0.726313i 0.999936 + 0.0112771i \(0.00358970\pi\)
−0.699088 + 0.715036i \(0.746410\pi\)
\(740\) −3.91213e6 + 4.89128e6i −0.262624 + 0.328355i
\(741\) 300613. + 124518.i 0.0201123 + 0.00833079i
\(742\) 977856. 2.78815e6i 0.0652027 0.185912i
\(743\) −3.92656e6 3.92656e6i −0.260939 0.260939i 0.564496 0.825436i \(-0.309070\pi\)
−0.825436 + 0.564496i \(0.809070\pi\)
\(744\) 252789. 1.09669e6i 0.0167427 0.0726357i
\(745\) −1.06749e7 + 1.06749e7i −0.704649 + 0.704649i
\(746\) −1.09179e7 2.27128e7i −0.718276 1.49425i
\(747\) 8.34739e6 2.01524e7i 0.547330 1.32137i
\(748\) −6.13205e6 + 2.11709e7i −0.400730 + 1.38352i
\(749\) 4.87312e6 2.01851e6i 0.317397 0.131470i
\(750\) −229832. 4.14552e6i −0.0149196 0.269107i
\(751\) 1.08196e6i 0.0700020i −0.999387 0.0350010i \(-0.988857\pi\)
0.999387 0.0350010i \(-0.0111434\pi\)
\(752\) −2.84521e6 1.26322e7i −0.183472 0.814582i
\(753\) 2.47559e6i 0.159108i
\(754\) −1.04292e6 + 57820.3i −0.0668068 + 0.00370384i
\(755\) 3.47108e6 1.43777e6i 0.221614 0.0917954i
\(756\) −5.55967e6 + 3.06234e6i −0.353789 + 0.194872i
\(757\) −1.74843e6 + 4.22109e6i −0.110894 + 0.267722i −0.969578 0.244784i \(-0.921283\pi\)
0.858683 + 0.512506i \(0.171283\pi\)
\(758\) −781523. + 375673.i −0.0494048 + 0.0237485i
\(759\) −3.10443e6 + 3.10443e6i −0.195604 + 0.195604i
\(760\) 8.08322e6 + 5.76148e6i 0.507634 + 0.361826i
\(761\) 2.02553e7 + 2.02553e7i 1.26788 + 1.26788i 0.947182 + 0.320695i \(0.103917\pi\)
0.320695 + 0.947182i \(0.396083\pi\)
\(762\) −4.15561e6 1.45745e6i −0.259267 0.0909299i
\(763\) 1.85140e7 + 7.66873e6i 1.15130 + 0.476883i
\(764\) −3.42178e6 3.07648e7i −0.212090 1.90687i
\(765\) 4.37402e6 + 1.05598e7i 0.270226 + 0.652383i
\(766\) 1.31096e7 1.46485e7i 0.807265 0.902030i
\(767\) −1.70443e6 −0.104614
\(768\) 3.24596e6 + 2.93436e6i 0.198582 + 0.179519i
\(769\) 1.60922e7 0.981292 0.490646 0.871359i \(-0.336761\pi\)
0.490646 + 0.871359i \(0.336761\pi\)
\(770\) −6.37365e6 + 7.12185e6i −0.387401 + 0.432879i
\(771\) 489084. + 1.18075e6i 0.0296311 + 0.0715357i
\(772\) −769170. 6.91551e6i −0.0464493 0.417620i
\(773\) 7.09213e6 + 2.93766e6i 0.426902 + 0.176828i 0.585781 0.810470i \(-0.300788\pi\)
−0.158879 + 0.987298i \(0.550788\pi\)
\(774\) −1.53835e7 5.39529e6i −0.923004 0.323714i
\(775\) 2.00144e6 + 2.00144e6i 0.119698 + 0.119698i
\(776\) 1.53241e7 + 1.09225e7i 0.913524 + 0.651132i
\(777\) 1.67372e6 1.67372e6i 0.0994559 0.0994559i
\(778\) 1.44345e7 6.93855e6i 0.854972 0.410979i
\(779\) −9.78318e6 + 2.36187e7i −0.577612 + 1.39448i
\(780\) 203774. 112241.i 0.0119926 0.00660567i
\(781\) −3.44569e7 + 1.42725e7i −2.02138 + 0.837284i
\(782\) −1.80768e7 + 1.00220e6i −1.05707 + 0.0586053i
\(783\) 7.25425e6i 0.422852i
\(784\) 1.46642e6 + 6.51065e6i 0.0852056 + 0.378298i
\(785\) 1.36731e7i 0.791938i
\(786\) −56570.9 1.02038e6i −0.00326616 0.0589123i
\(787\) −9.21890e6 + 3.81859e6i −0.530569 + 0.219769i −0.631853 0.775089i \(-0.717705\pi\)
0.101283 + 0.994858i \(0.467705\pi\)
\(788\) 1.80158e6 6.21996e6i 0.103357 0.356839i
\(789\) −2.71421e6 + 6.55268e6i −0.155221 + 0.374737i
\(790\) −3.67841e6 7.65230e6i −0.209697 0.436239i
\(791\) 1.68141e7 1.68141e7i 0.955502 0.955502i
\(792\) 4.36448e6 1.89346e7i 0.247240 1.07261i
\(793\) −1.56814e6 1.56814e6i −0.0885528 0.0885528i
\(794\) −8.44319e6 + 2.40740e7i −0.475286 + 1.35518i
\(795\) −694863. 287822.i −0.0389925 0.0161512i
\(796\) −1.52846e7 + 1.91101e7i −0.855011 + 1.06901i
\(797\) −2.15914e6 5.21263e6i −0.120403 0.290677i 0.852175 0.523257i \(-0.175283\pi\)
−0.972577 + 0.232580i \(0.925283\pi\)
\(798\) −2.79535e6 2.50168e6i −0.155392 0.139067i
\(799\) 1.83041e7 1.01433
\(800\) −1.05855e7 + 3.00865e6i −0.584772 + 0.166206i
\(801\) −2.08276e7 −1.14699
\(802\) 9.86050e6 + 8.82458e6i 0.541331 + 0.484460i
\(803\) −1.98244e6 4.78603e6i −0.108495 0.261931i
\(804\) 1.36991e6 + 1.09568e6i 0.0747398 + 0.0597782i
\(805\) −7.25291e6 3.00425e6i −0.394478 0.163398i
\(806\) −138829. + 395841.i −0.00752734 + 0.0214626i
\(807\) −2.99569e6 2.99569e6i −0.161925 0.161925i
\(808\) 7.73395e6 + 1.23674e7i 0.416748 + 0.666421i
\(809\) −3.02974e6 + 3.02974e6i −0.162755 + 0.162755i −0.783786 0.621031i \(-0.786714\pi\)
0.621031 + 0.783786i \(0.286714\pi\)
\(810\) −4.00249e6 8.32648e6i −0.214347 0.445912i
\(811\) 7.73917e6 1.86840e7i 0.413183 0.997511i −0.571095 0.820884i \(-0.693481\pi\)
0.984278 0.176627i \(-0.0565188\pi\)
\(812\) 1.15668e7 + 3.35027e6i 0.615635 + 0.178316i
\(813\) 9.06474e6 3.75474e6i 0.480982 0.199229i
\(814\) 833201. + 1.50286e7i 0.0440746 + 0.794982i
\(815\) 1.97861e7i 1.04344i
\(816\) −5.05482e6 + 3.56488e6i −0.265754 + 0.187421i
\(817\) 2.00133e7i 1.04897i
\(818\) −2.95454e7 + 1.63802e6i −1.54385 + 0.0855928i
\(819\) 1.05224e6 435850.i 0.0548155 0.0227053i
\(820\) 8.81864e6 + 1.60102e7i 0.458002 + 0.831500i
\(821\) −1.50918e6 + 3.64349e6i −0.0781419 + 0.188651i −0.958123 0.286358i \(-0.907555\pi\)
0.879981 + 0.475009i \(0.157555\pi\)
\(822\) −6.38660e6 + 3.07000e6i −0.329678 + 0.158474i
\(823\) −7.92811e6 + 7.92811e6i −0.408009 + 0.408009i −0.881044 0.473034i \(-0.843159\pi\)
0.473034 + 0.881044i \(0.343159\pi\)
\(824\) −2.97374e6 1.77326e7i −0.152576 0.909819i
\(825\) −2.66745e6 2.66745e6i −0.136446 0.136446i
\(826\) 1.85430e7 + 6.50337e6i 0.945649 + 0.331657i
\(827\) −3.58369e7 1.48441e7i −1.82208 0.754729i −0.974621 0.223862i \(-0.928134\pi\)
−0.847455 0.530867i \(-0.821866\pi\)
\(828\) 1.58629e7 1.76434e6i 0.804096 0.0894346i
\(829\) 3.95892e6 + 9.55768e6i 0.200074 + 0.483021i 0.991791 0.127866i \(-0.0408128\pi\)
−0.791717 + 0.610887i \(0.790813\pi\)
\(830\) 1.27681e7 1.42670e7i 0.643326 0.718846i
\(831\) −7.55566e6 −0.379551
\(832\) −1.08153e6 1.22074e6i −0.0541665 0.0611386i
\(833\) −9.43393e6 −0.471064
\(834\) 4.81041e6 5.37511e6i 0.239479 0.267591i
\(835\) −3.45416e6 8.33908e6i −0.171446 0.413906i
\(836\) 2.37083e7 2.63693e6i 1.17323 0.130492i
\(837\) −2.69156e6 1.11488e6i −0.132797 0.0550065i
\(838\) −2.45078e6 859535.i −0.120558 0.0422818i
\(839\) 6.20481e6 + 6.20481e6i 0.304315 + 0.304315i 0.842700 0.538384i \(-0.180965\pi\)
−0.538384 + 0.842700i \(0.680965\pi\)
\(840\) −2.64518e6 + 443594.i −0.129347 + 0.0216914i
\(841\) 4.77168e6 4.77168e6i 0.232638 0.232638i
\(842\) 617663. 296907.i 0.0300242 0.0144324i
\(843\) 281832. 680402.i 0.0136591 0.0329759i
\(844\) 1.37636e6 + 2.49878e6i 0.0665083 + 0.120746i
\(845\) 1.19270e7 4.94031e6i 0.574630 0.238020i
\(846\) −1.61119e7 + 893259.i −0.773963 + 0.0429093i
\(847\) 6.63111e6i 0.317598i
\(848\) −898081. + 5.19563e6i −0.0428870 + 0.248113i
\(849\) 192621.i 0.00917140i
\(850\) −861129. 1.55323e7i −0.0408810 0.737377i
\(851\) −1.14224e7 + 4.73131e6i −0.540671 + 0.223953i
\(852\) −1.00532e7 2.91187e6i −0.474467 0.137427i
\(853\) 1.38535e7 3.34454e7i 0.651911 1.57385i −0.158090 0.987425i \(-0.550534\pi\)
0.810001 0.586428i \(-0.199466\pi\)
\(854\) 1.10769e7 + 2.30436e7i 0.519726 + 1.08120i
\(855\) 8.74709e6 8.74709e6i 0.409212 0.409212i
\(856\) −7.98073e6 + 4.99076e6i −0.372270 + 0.232800i
\(857\) 1.10274e7 + 1.10274e7i 0.512888 + 0.512888i 0.915410 0.402522i \(-0.131866\pi\)
−0.402522 + 0.915410i \(0.631866\pi\)
\(858\) 185026. 527564.i 0.00858056 0.0244657i
\(859\) 1.58083e7 + 6.54800e6i 0.730973 + 0.302779i 0.716952 0.697123i \(-0.245537\pi\)
0.0140215 + 0.999902i \(0.495537\pi\)
\(860\) −1.11746e7 8.93762e6i −0.515211 0.412074i
\(861\) −2.64343e6 6.38179e6i −0.121523 0.293383i
\(862\) 2.04996e7 + 1.83459e7i 0.939672 + 0.840953i
\(863\) −4.03178e6 −0.184276 −0.0921382 0.995746i \(-0.529370\pi\)
−0.0921382 + 0.995746i \(0.529370\pi\)
\(864\) 8.88095e6 7.03048e6i 0.404739 0.320406i
\(865\) −5.61387e6 −0.255107
\(866\) −1.08725e7 9.73026e6i −0.492646 0.440889i
\(867\) −1.07864e6 2.60406e6i −0.0487334 0.117653i
\(868\) 3.02071e6 3.77676e6i 0.136085 0.170145i
\(869\) −1.88507e7 7.80821e6i −0.846794 0.350754i
\(870\) 1.01450e6 2.89263e6i 0.0454416 0.129567i
\(871\) −462325. 462325.i −0.0206491 0.0206491i
\(872\) −3.48471e7 8.03237e6i −1.55194 0.357728i
\(873\) 1.65826e7 1.65826e7i 0.736407 0.736407i
\(874\) 8.48895e6 + 1.76598e7i 0.375903 + 0.782001i
\(875\) 6.82753e6 1.64831e7i 0.301470 0.727812i
\(876\) 404456. 1.39638e6i 0.0178078 0.0614815i
\(877\) 1.94778e7 8.06799e6i 0.855149 0.354214i 0.0883408 0.996090i \(-0.471844\pi\)
0.766809 + 0.641876i \(0.221844\pi\)
\(878\) 1.38767e6 + 2.50297e7i 0.0607506 + 1.09577i
\(879\) 35622.1i 0.00155506i
\(880\) 9.11537e6 1.44153e7i 0.396796 0.627504i
\(881\) 1.24196e7i 0.539097i 0.962987 + 0.269549i \(0.0868745\pi\)
−0.962987 + 0.269549i \(0.913126\pi\)
\(882\) 8.30407e6 460386.i 0.359434 0.0199274i
\(883\) 9.96392e6 4.12719e6i 0.430059 0.178136i −0.157144 0.987576i \(-0.550229\pi\)
0.587204 + 0.809439i \(0.300229\pi\)
\(884\) 2.01939e6 1.11231e6i 0.0869138 0.0478733i
\(885\) 1.91420e6 4.62128e6i 0.0821540 0.198337i
\(886\) 3.05444e7 1.46825e7i 1.30721 0.628369i
\(887\) 2.04689e7 2.04689e7i 0.873544 0.873544i −0.119313 0.992857i \(-0.538069\pi\)
0.992857 + 0.119313i \(0.0380692\pi\)
\(888\) −2.45169e6 + 3.43966e6i −0.104336 + 0.146381i
\(889\) −1.33810e7 1.33810e7i −0.567852 0.567852i
\(890\) −1.72511e7 6.05029e6i −0.730033 0.256036i
\(891\) −2.05115e7 8.49613e6i −0.865571 0.358531i
\(892\) −1.86148e6 1.67363e7i −0.0783333 0.704285i
\(893\) −7.58098e6 1.83021e7i −0.318124 0.768020i
\(894\) −6.78958e6 + 7.58661e6i −0.284118 + 0.317471i
\(895\) 4.25857e6 0.177708
\(896\) 7.10847e6 + 1.74075e7i 0.295805 + 0.724379i
\(897\) 459222. 0.0190564
\(898\) 2.41097e7 2.69399e7i 0.997700 1.11482i
\(899\) 2.11518e6 + 5.10650e6i 0.0872867 + 0.210729i
\(900\) 1.51599e6 + 1.36301e7i 0.0623864 + 0.560908i
\(901\) −6.88604e6 2.85229e6i −0.282591 0.117053i
\(902\) 4.14499e7 + 1.45372e7i 1.69632 + 0.594930i
\(903\) 3.82377e6 + 3.82377e6i 0.156053 + 0.156053i
\(904\) −2.46295e7 + 3.45546e7i −1.00238 + 1.40632i
\(905\) −1.72373e7 + 1.72373e7i −0.699598 + 0.699598i
\(906\) 2.28363e6 1.09772e6i 0.0924282 0.0444296i
\(907\) −1.67142e7 + 4.03516e7i −0.674632 + 1.62871i 0.0990121 + 0.995086i \(0.468432\pi\)
−0.773644 + 0.633620i \(0.781568\pi\)
\(908\) −9.86819e6 + 5.43554e6i −0.397213 + 0.218790i
\(909\) 1.67940e7 6.95630e6i 0.674131 0.279234i
\(910\) 998157. 55338.8i 0.0399572 0.00221527i
\(911\) 1.90730e7i 0.761418i −0.924695 0.380709i \(-0.875680\pi\)
0.924695 0.380709i \(-0.124320\pi\)
\(912\) 5.65804e6 + 3.57781e6i 0.225257 + 0.142440i
\(913\) 4.60106e7i 1.82676i
\(914\) −391593. 7.06324e6i −0.0155049 0.279665i
\(915\) 6.01290e6 2.49062e6i 0.237428 0.0983457i
\(916\) 4.97849e6 1.71882e7i 0.196047 0.676850i
\(917\) 1.68053e6 4.05716e6i 0.0659969 0.159331i
\(918\) 6.93685e6 + 1.44309e7i 0.271679 + 0.565180i
\(919\) −2.60724e7 + 2.60724e7i −1.01834 + 1.01834i −0.0185098 + 0.999829i \(0.505892\pi\)
−0.999829 + 0.0185098i \(0.994108\pi\)
\(920\) 1.36515e7 + 3.14671e6i 0.531753 + 0.122571i
\(921\) 3.56977e6 + 3.56977e6i 0.138673 + 0.138673i
\(922\) −5.34001e6 + 1.52259e7i −0.206878 + 0.589870i
\(923\) 3.60414e6 + 1.49288e6i 0.139251 + 0.0576795i
\(924\) −4.02592e6 + 5.03354e6i −0.155126 + 0.193952i
\(925\) −4.06533e6 9.81457e6i −0.156222 0.377153i
\(926\) 8.99973e6 + 8.05424e6i 0.344907 + 0.308672i
\(927\) −2.24070e7 −0.856414
\(928\) −2.13459e7 2.48247e6i −0.813662 0.0946269i
\(929\) 2.17177e7 0.825609 0.412804 0.910820i \(-0.364549\pi\)
0.412804 + 0.910820i \(0.364549\pi\)
\(930\) −917342. 820968.i −0.0347796 0.0311257i
\(931\) 3.90724e6 + 9.43291e6i 0.147739 + 0.356674i
\(932\) 7.76895e6 + 6.21374e6i 0.292970 + 0.234322i
\(933\) 4.96510e6 + 2.05661e6i 0.186734 + 0.0773478i
\(934\) 1.05789e7 3.01636e7i 0.396803 1.13140i
\(935\) 1.70480e7 + 1.70480e7i 0.637740 + 0.637740i
\(936\) −1.72325e6 + 1.07764e6i −0.0642922 + 0.0402052i
\(937\) −1.56850e7 + 1.56850e7i −0.583626 + 0.583626i −0.935898 0.352272i \(-0.885409\pi\)
0.352272 + 0.935898i \(0.385409\pi\)
\(938\) 3.26574e6 + 6.79380e6i 0.121192 + 0.252119i
\(939\) 515.450 1244.41i 1.90775e−5 4.60573e-5i
\(940\) −1.36046e7 3.94052e6i −0.502189 0.145457i
\(941\) 9.86173e6 4.08486e6i 0.363060 0.150385i −0.193693 0.981062i \(-0.562047\pi\)
0.556754 + 0.830678i \(0.312047\pi\)
\(942\) 510443. + 9.20695e6i 0.0187422 + 0.338056i
\(943\) 3.60803e7i 1.32127i
\(944\) −3.45543e7 5.97282e6i −1.26204 0.218147i
\(945\) 6.94293e6i 0.252908i
\(946\) −3.43342e7 + 1.90352e6i −1.24738 + 0.0691560i
\(947\) −3.47835e7 + 1.44078e7i −1.26037 + 0.522063i −0.910024 0.414556i \(-0.863937\pi\)
−0.350349 + 0.936619i \(0.613937\pi\)
\(948\) −2.76259e6 5.01547e6i −0.0998379 0.181255i
\(949\) −207360. + 500611.i −0.00747411 + 0.0180441i
\(950\) −1.51740e7 + 7.29405e6i −0.545496 + 0.262216i
\(951\) 8.97078e6 8.97078e6i 0.321647 0.321647i
\(952\) −2.62136e7 + 4.39599e6i −0.937419 + 0.157204i
\(953\) 2.97233e7 + 2.97233e7i 1.06015 + 1.06015i 0.998072 + 0.0620737i \(0.0197714\pi\)
0.0620737 + 0.998072i \(0.480229\pi\)
\(954\) 6.20052e6 + 2.17464e6i 0.220575 + 0.0773599i
\(955\) −3.12820e7 1.29574e7i −1.10991 0.459739i
\(956\) 1.43082e7 1.59141e6i 0.506336 0.0563167i
\(957\) −2.81905e6 6.80578e6i −0.0994998 0.240214i
\(958\) −2.35166e7 + 2.62772e7i −0.827866 + 0.925050i
\(959\) −3.04501e7 −1.06916
\(960\) 4.52448e6 1.56141e6i 0.158449 0.0546814i
\(961\) −2.64094e7 −0.922466
\(962\) 1.04992e6 1.17317e6i 0.0365780 0.0408719i
\(963\) 4.48893e6 + 1.08372e7i 0.155983 + 0.376577i
\(964\) 6.38945e6 710660.i 0.221448 0.0246303i
\(965\) −7.03177e6 2.91265e6i −0.243078 0.100686i
\(966\) −4.99601e6 1.75219e6i −0.172258 0.0604142i
\(967\) 3.99910e7 + 3.99910e7i 1.37530 + 1.37530i 0.852391 + 0.522904i \(0.175152\pi\)
0.522904 + 0.852391i \(0.324848\pi\)
\(968\) −1.95712e6 1.16705e7i −0.0671320 0.400313i
\(969\) −6.69138e6 + 6.69138e6i −0.228932 + 0.228932i
\(970\) 1.85522e7 8.91792e6i 0.633091 0.304323i
\(971\) 5.99048e6 1.44623e7i 0.203898 0.492254i −0.788542 0.614981i \(-0.789164\pi\)
0.992441 + 0.122727i \(0.0391638\pi\)
\(972\) −1.03420e7 1.87758e7i −0.351106 0.637431i
\(973\) 2.86371e7 1.18619e7i 0.969720 0.401671i
\(974\) 9.74974e6 540535.i 0.329303 0.0182569i
\(975\) 394582.i 0.0132931i
\(976\) −2.62961e7 3.72865e7i −0.883621 1.25293i
\(977\) 1.18957e7i 0.398707i 0.979928 + 0.199353i \(0.0638842\pi\)
−0.979928 + 0.199353i \(0.936116\pi\)
\(978\) 738654. + 1.33232e7i 0.0246941 + 0.445413i
\(979\) −4.05884e7 + 1.68123e7i −1.35346 + 0.560622i
\(980\) 7.01183e6 + 2.03095e6i 0.233220 + 0.0675512i
\(981\) −1.70544e7 + 4.11729e7i −0.565800 + 1.36596i
\(982\) 1.15578e7 + 2.40439e7i 0.382468 + 0.795658i
\(983\) 9.59252e6 9.59252e6i 0.316628 0.316628i −0.530843 0.847470i \(-0.678125\pi\)
0.847470 + 0.530843i \(0.178125\pi\)
\(984\) 6.53585e6 + 1.04515e7i 0.215186 + 0.344105i
\(985\) −5.00866e6 5.00866e6i −0.164487 0.164487i
\(986\) 1.00536e7 2.86658e7i 0.329329 0.939012i
\(987\) 4.94525e6 + 2.04839e6i 0.161583 + 0.0669298i
\(988\) −1.94855e6 1.55849e6i −0.0635067 0.0507938i
\(989\) −1.08091e7 2.60955e7i −0.351398 0.848349i
\(990\) −1.58382e7 1.41742e7i −0.513590 0.459634i
\(991\) 4.79721e7 1.55169 0.775844 0.630925i \(-0.217324\pi\)
0.775844 + 0.630925i \(0.217324\pi\)
\(992\) −4.20164e6 + 7.53847e6i −0.135563 + 0.243223i
\(993\) 7.38331e6 0.237617
\(994\) −3.35143e7 2.99933e7i −1.07588 0.962850i
\(995\) 1.02433e7 + 2.47296e7i 0.328008 + 0.791881i
\(996\) 8.06498e6 1.00835e7i 0.257605 0.322080i
\(997\) 8.05972e6 + 3.33845e6i 0.256792 + 0.106367i 0.507366 0.861731i \(-0.330619\pi\)
−0.250574 + 0.968098i \(0.580619\pi\)
\(998\) 3.62150e6 1.03259e7i 0.115097 0.328174i
\(999\) 7.73165e6 + 7.73165e6i 0.245108 + 0.245108i
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 32.6.g.a.5.5 76
4.3 odd 2 128.6.g.a.113.8 76
32.13 even 8 inner 32.6.g.a.13.5 yes 76
32.19 odd 8 128.6.g.a.17.8 76
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
32.6.g.a.5.5 76 1.1 even 1 trivial
32.6.g.a.13.5 yes 76 32.13 even 8 inner
128.6.g.a.17.8 76 32.19 odd 8
128.6.g.a.113.8 76 4.3 odd 2