Properties

Label 22.9.d.a.7.5
Level $22$
Weight $9$
Character 22.7
Analytic conductor $8.962$
Analytic rank $0$
Dimension $32$
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] = [22,9,Mod(7,22)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(22, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([7]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("22.7");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 22 = 2 \cdot 11 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 22.d (of order \(10\), 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: \(8.96232942134\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 7.5
Character \(\chi\) \(=\) 22.7
Dual form 22.9.d.a.19.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(6.65003 - 9.15298i) q^{2} +(-43.1911 + 132.929i) q^{3} +(-39.5542 - 121.735i) q^{4} +(371.274 - 269.746i) q^{5} +(929.471 + 1279.31i) q^{6} +(-2980.04 + 968.273i) q^{7} +(-1377.28 - 447.504i) q^{8} +(-10496.6 - 7626.22i) q^{9} +O(q^{10})\) \(q+(6.65003 - 9.15298i) q^{2} +(-43.1911 + 132.929i) q^{3} +(-39.5542 - 121.735i) q^{4} +(371.274 - 269.746i) q^{5} +(929.471 + 1279.31i) q^{6} +(-2980.04 + 968.273i) q^{7} +(-1377.28 - 447.504i) q^{8} +(-10496.6 - 7626.22i) q^{9} -5192.08i q^{10} +(-14387.1 - 2714.69i) q^{11} +17890.5 q^{12} +(-15425.0 + 21230.7i) q^{13} +(-10954.8 + 33715.3i) q^{14} +(19821.3 + 61003.6i) q^{15} +(-13254.9 + 9630.27i) q^{16} +(-37909.1 - 52177.4i) q^{17} +(-139605. + 45360.5i) q^{18} +(141104. + 45847.3i) q^{19} +(-47523.1 - 34527.5i) q^{20} -437953. i q^{21} +(-120522. + 113632. i) q^{22} -181813. q^{23} +(118972. - 163751. i) q^{24} +(-55628.5 + 171207. i) q^{25} +(91747.6 + 282370. i) q^{26} +(725212. - 526897. i) q^{27} +(235746. + 324476. i) q^{28} +(-248547. + 80757.9i) q^{29} +(690177. + 224252. i) q^{30} +(1.18362e6 + 859952. i) q^{31} +185364. i q^{32} +(982256. - 1.79521e6i) q^{33} -729676. q^{34} +(-845222. + 1.16335e6i) q^{35} +(-513196. + 1.57945e6i) q^{36} +(-801447. - 2.46660e6i) q^{37} +(1.35798e6 - 986632. i) q^{38} +(-2.15595e6 - 2.96741e6i) q^{39} +(-632060. + 205369. i) q^{40} +(3.13029e6 + 1.01709e6i) q^{41} +(-4.00858e6 - 2.91240e6i) q^{42} +6.20970e6i q^{43} +(238598. + 1.85880e6i) q^{44} -5.95425e6 q^{45} +(-1.20906e6 + 1.66413e6i) q^{46} +(-1.90525e6 + 5.86375e6i) q^{47} +(-707644. - 2.17790e6i) q^{48} +(3.27925e6 - 2.38251e6i) q^{49} +(1.19712e6 + 1.64770e6i) q^{50} +(8.57321e6 - 2.78560e6i) q^{51} +(3.19465e6 + 1.03801e6i) q^{52} +(-8.14563e6 - 5.91815e6i) q^{53} -1.01417e7i q^{54} +(-6.07384e6 + 2.87298e6i) q^{55} +4.53764e6 q^{56} +(-1.21888e7 + 1.67765e7i) q^{57} +(-913671. + 2.81199e6i) q^{58} +(-5.33219e6 - 1.64108e7i) q^{59} +(6.64227e6 - 4.82589e6i) q^{60} +(5.56400e6 + 7.65818e6i) q^{61} +(1.57422e7 - 5.11497e6i) q^{62} +(3.86645e7 + 1.25629e7i) q^{63} +(1.69663e6 + 1.23268e6i) q^{64} +1.20433e7i q^{65} +(-9.89950e6 - 2.09288e7i) q^{66} -9.29903e6 q^{67} +(-4.85237e6 + 6.67871e6i) q^{68} +(7.85273e6 - 2.41682e7i) q^{69} +(5.02735e6 + 1.54726e7i) q^{70} +(1.53599e7 - 1.11596e7i) q^{71} +(1.10439e7 + 1.52007e7i) q^{72} +(-2.04906e7 + 6.65779e6i) q^{73} +(-2.79064e7 - 9.06734e6i) q^{74} +(-2.03556e7 - 1.47892e7i) q^{75} -1.89907e7i q^{76} +(4.55027e7 - 5.84079e6i) q^{77} -4.14977e7 q^{78} +(-1.55508e7 + 2.14039e7i) q^{79} +(-2.32348e6 + 7.15094e6i) q^{80} +(1.24117e7 + 3.81994e7i) q^{81} +(3.01259e7 - 2.18878e7i) q^{82} +(-1.74413e7 - 2.40059e7i) q^{83} +(-5.33143e7 + 1.73229e7i) q^{84} +(-2.81493e7 - 9.14627e6i) q^{85} +(5.68373e7 + 4.12947e7i) q^{86} -3.65271e7i q^{87} +(1.86002e7 + 1.01772e7i) q^{88} -1.07053e7 q^{89} +(-3.95960e7 + 5.44992e7i) q^{90} +(2.54100e7 - 7.82040e7i) q^{91} +(7.19148e6 + 2.21331e7i) q^{92} +(-1.65434e8 + 1.20195e8i) q^{93} +(4.10009e7 + 5.64329e7i) q^{94} +(6.47552e7 - 2.10402e7i) q^{95} +(-2.46402e7 - 8.00607e6i) q^{96} +(-7.62538e7 - 5.54016e7i) q^{97} -4.58587e7i q^{98} +(1.30313e8 + 1.38214e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 182 q^{3} + 1024 q^{4} + 1410 q^{5} + 4480 q^{6} - 10950 q^{7} - 1402 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 182 q^{3} + 1024 q^{4} + 1410 q^{5} + 4480 q^{6} - 10950 q^{7} - 1402 q^{9} - 47598 q^{11} - 21504 q^{12} + 24990 q^{13} + 106752 q^{14} + 273582 q^{15} - 131072 q^{16} - 553530 q^{17} + 152320 q^{18} + 442680 q^{19} - 180480 q^{20} - 359040 q^{22} - 317064 q^{23} + 573440 q^{24} - 918738 q^{25} - 782592 q^{26} + 714484 q^{27} + 51200 q^{28} + 2380710 q^{29} + 4488960 q^{30} + 181654 q^{31} - 628628 q^{33} - 3865088 q^{34} - 12788370 q^{35} + 5097216 q^{36} - 6976698 q^{37} - 15360 q^{38} + 17382010 q^{39} + 3768320 q^{40} + 5153790 q^{41} - 15355648 q^{42} + 2744064 q^{44} + 5954792 q^{45} - 15447040 q^{46} - 13476378 q^{47} - 2981888 q^{48} + 19896222 q^{49} + 13816320 q^{50} + 37405440 q^{51} + 18368000 q^{52} - 847422 q^{53} - 47212238 q^{55} + 1572864 q^{56} - 119710960 q^{57} - 29125376 q^{58} - 49425120 q^{59} + 12710144 q^{60} + 26432690 q^{61} + 64485120 q^{62} + 289643740 q^{63} + 16777216 q^{64} - 78840064 q^{66} - 133260476 q^{67} - 70851840 q^{68} - 33873776 q^{69} - 50942720 q^{70} + 38304066 q^{71} + 61603840 q^{72} + 208728710 q^{73} + 56355840 q^{74} - 62835924 q^{75} + 92206590 q^{77} - 74988544 q^{78} - 247776110 q^{79} - 22609920 q^{80} - 622273104 q^{81} + 17468928 q^{82} + 434637000 q^{83} + 159336960 q^{84} + 286821150 q^{85} - 7040640 q^{86} + 101498880 q^{88} - 336205452 q^{89} - 270179840 q^{90} - 167007498 q^{91} + 29901312 q^{92} + 65388262 q^{93} + 429944320 q^{94} + 1032904950 q^{95} - 75153432 q^{97} - 459062342 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/22\mathbb{Z}\right)^\times\).

\(n\) \(13\)
\(\chi(n)\) \(e\left(\frac{7}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6.65003 9.15298i 0.415627 0.572061i
\(3\) −43.1911 + 132.929i −0.533224 + 1.64109i 0.214232 + 0.976783i \(0.431275\pi\)
−0.747456 + 0.664311i \(0.768725\pi\)
\(4\) −39.5542 121.735i −0.154508 0.475528i
\(5\) 371.274 269.746i 0.594038 0.431594i −0.249720 0.968318i \(-0.580338\pi\)
0.843758 + 0.536724i \(0.180338\pi\)
\(6\) 929.471 + 1279.31i 0.717185 + 0.987120i
\(7\) −2980.04 + 968.273i −1.24116 + 0.403279i −0.854747 0.519045i \(-0.826288\pi\)
−0.386418 + 0.922324i \(0.626288\pi\)
\(8\) −1377.28 447.504i −0.336249 0.109254i
\(9\) −10496.6 7626.22i −1.59985 1.16236i
\(10\) 5192.08i 0.519208i
\(11\) −14387.1 2714.69i −0.982660 0.185417i
\(12\) 17890.5 0.862774
\(13\) −15425.0 + 21230.7i −0.540073 + 0.743347i −0.988624 0.150411i \(-0.951940\pi\)
0.448550 + 0.893757i \(0.351940\pi\)
\(14\) −10954.8 + 33715.3i −0.285161 + 0.877636i
\(15\) 19821.3 + 61003.6i 0.391531 + 1.20501i
\(16\) −13254.9 + 9630.27i −0.202254 + 0.146946i
\(17\) −37909.1 52177.4i −0.453887 0.624722i 0.519340 0.854568i \(-0.326178\pi\)
−0.973227 + 0.229846i \(0.926178\pi\)
\(18\) −139605. + 45360.5i −1.32988 + 0.432104i
\(19\) 141104. + 45847.3i 1.08274 + 0.351803i 0.795436 0.606037i \(-0.207242\pi\)
0.287302 + 0.957840i \(0.407242\pi\)
\(20\) −47523.1 34527.5i −0.297019 0.215797i
\(21\) 437953.i 2.25191i
\(22\) −120522. + 113632.i −0.514490 + 0.485078i
\(23\) −181813. −0.649702 −0.324851 0.945765i \(-0.605314\pi\)
−0.324851 + 0.945765i \(0.605314\pi\)
\(24\) 118972. 163751.i 0.358592 0.493560i
\(25\) −55628.5 + 171207.i −0.142409 + 0.438290i
\(26\) 91747.6 + 282370.i 0.200771 + 0.617910i
\(27\) 725212. 526897.i 1.36461 0.991450i
\(28\) 235746. + 324476.i 0.383541 + 0.527899i
\(29\) −248547. + 80757.9i −0.351412 + 0.114181i −0.479404 0.877595i \(-0.659147\pi\)
0.127991 + 0.991775i \(0.459147\pi\)
\(30\) 690177. + 224252.i 0.852070 + 0.276854i
\(31\) 1.18362e6 + 859952.i 1.28164 + 0.931167i 0.999601 0.0282362i \(-0.00898907\pi\)
0.282040 + 0.959403i \(0.408989\pi\)
\(32\) 185364.i 0.176777i
\(33\) 982256. 1.79521e6i 0.828264 1.51377i
\(34\) −729676. −0.546027
\(35\) −845222. + 1.16335e6i −0.563247 + 0.775243i
\(36\) −513196. + 1.57945e6i −0.305543 + 0.940366i
\(37\) −801447. 2.46660e6i −0.427630 1.31611i −0.900454 0.434952i \(-0.856765\pi\)
0.472824 0.881157i \(-0.343235\pi\)
\(38\) 1.35798e6 986632.i 0.651268 0.473174i
\(39\) −2.15595e6 2.96741e6i −0.931922 1.28268i
\(40\) −632060. + 205369.i −0.246898 + 0.0802221i
\(41\) 3.13029e6 + 1.01709e6i 1.10777 + 0.359936i 0.805087 0.593156i \(-0.202118\pi\)
0.302681 + 0.953092i \(0.402118\pi\)
\(42\) −4.00858e6 2.91240e6i −1.28823 0.935953i
\(43\) 6.20970e6i 1.81634i 0.418602 + 0.908170i \(0.362520\pi\)
−0.418602 + 0.908170i \(0.637480\pi\)
\(44\) 238598. + 1.85880e6i 0.0636584 + 0.495931i
\(45\) −5.95425e6 −1.45204
\(46\) −1.20906e6 + 1.66413e6i −0.270034 + 0.371670i
\(47\) −1.90525e6 + 5.86375e6i −0.390445 + 1.20167i 0.542007 + 0.840374i \(0.317665\pi\)
−0.932452 + 0.361293i \(0.882335\pi\)
\(48\) −707644. 2.17790e6i −0.133306 0.410274i
\(49\) 3.27925e6 2.38251e6i 0.568839 0.413286i
\(50\) 1.19712e6 + 1.64770e6i 0.191540 + 0.263632i
\(51\) 8.57321e6 2.78560e6i 1.26725 0.411755i
\(52\) 3.19465e6 + 1.03801e6i 0.436928 + 0.141967i
\(53\) −8.14563e6 5.91815e6i −1.03234 0.750036i −0.0635616 0.997978i \(-0.520246\pi\)
−0.968775 + 0.247941i \(0.920246\pi\)
\(54\) 1.01417e7i 1.19272i
\(55\) −6.07384e6 + 2.87298e6i −0.663762 + 0.313966i
\(56\) 4.53764e6 0.461401
\(57\) −1.21888e7 + 1.67765e7i −1.15468 + 1.58929i
\(58\) −913671. + 2.81199e6i −0.0807380 + 0.248486i
\(59\) −5.33219e6 1.64108e7i −0.440045 1.35432i −0.887827 0.460178i \(-0.847786\pi\)
0.447781 0.894143i \(-0.352214\pi\)
\(60\) 6.64227e6 4.82589e6i 0.512521 0.372368i
\(61\) 5.56400e6 + 7.65818e6i 0.401853 + 0.553103i 0.961208 0.275825i \(-0.0889510\pi\)
−0.559355 + 0.828928i \(0.688951\pi\)
\(62\) 1.57422e7 5.11497e6i 1.06537 0.346159i
\(63\) 3.86645e7 + 1.25629e7i 2.45443 + 0.797491i
\(64\) 1.69663e6 + 1.23268e6i 0.101127 + 0.0734732i
\(65\) 1.20433e7i 0.674669i
\(66\) −9.89950e6 2.09288e7i −0.521720 1.10298i
\(67\) −9.29903e6 −0.461465 −0.230732 0.973017i \(-0.574112\pi\)
−0.230732 + 0.973017i \(0.574112\pi\)
\(68\) −4.85237e6 + 6.67871e6i −0.226944 + 0.312361i
\(69\) 7.85273e6 2.41682e7i 0.346437 1.06622i
\(70\) 5.02735e6 + 1.54726e7i 0.209386 + 0.644423i
\(71\) 1.53599e7 1.11596e7i 0.604442 0.439153i −0.243011 0.970024i \(-0.578135\pi\)
0.847453 + 0.530871i \(0.178135\pi\)
\(72\) 1.10439e7 + 1.52007e7i 0.410955 + 0.565631i
\(73\) −2.04906e7 + 6.65779e6i −0.721544 + 0.234444i −0.646692 0.762751i \(-0.723848\pi\)
−0.0748513 + 0.997195i \(0.523848\pi\)
\(74\) −2.79064e7 9.06734e6i −0.930630 0.302380i
\(75\) −2.03556e7 1.47892e7i −0.643339 0.467413i
\(76\) 1.89907e7i 0.569229i
\(77\) 4.55027e7 5.84079e6i 1.29442 0.166153i
\(78\) −4.14977e7 −1.12110
\(79\) −1.55508e7 + 2.14039e7i −0.399251 + 0.549521i −0.960556 0.278088i \(-0.910299\pi\)
0.561305 + 0.827609i \(0.310299\pi\)
\(80\) −2.32348e6 + 7.15094e6i −0.0567256 + 0.174583i
\(81\) 1.24117e7 + 3.81994e7i 0.288331 + 0.887393i
\(82\) 3.01259e7 2.18878e7i 0.666324 0.484112i
\(83\) −1.74413e7 2.40059e7i −0.367509 0.505832i 0.584713 0.811240i \(-0.301207\pi\)
−0.952222 + 0.305408i \(0.901207\pi\)
\(84\) −5.33143e7 + 1.73229e7i −1.07085 + 0.347939i
\(85\) −2.81493e7 9.14627e6i −0.539253 0.175214i
\(86\) 5.68373e7 + 4.12947e7i 1.03906 + 0.754919i
\(87\) 3.65271e7i 0.637585i
\(88\) 1.86002e7 + 1.01772e7i 0.310161 + 0.169706i
\(89\) −1.07053e7 −0.170623 −0.0853115 0.996354i \(-0.527189\pi\)
−0.0853115 + 0.996354i \(0.527189\pi\)
\(90\) −3.95960e7 + 5.44992e7i −0.603505 + 0.830654i
\(91\) 2.54100e7 7.82040e7i 0.370544 1.14042i
\(92\) 7.19148e6 + 2.21331e7i 0.100385 + 0.308952i
\(93\) −1.65434e8 + 1.20195e8i −2.21153 + 1.60677i
\(94\) 4.10009e7 + 5.64329e7i 0.525148 + 0.722804i
\(95\) 6.47552e7 2.10402e7i 0.795024 0.258319i
\(96\) −2.46402e7 8.00607e6i −0.290107 0.0942616i
\(97\) −7.62538e7 5.54016e7i −0.861340 0.625800i 0.0669093 0.997759i \(-0.478686\pi\)
−0.928249 + 0.371959i \(0.878686\pi\)
\(98\) 4.58587e7i 0.497184i
\(99\) 1.30313e8 + 1.38214e8i 1.35658 + 1.43884i
\(100\) 2.30423e7 0.230423
\(101\) 4.73947e7 6.52332e7i 0.455454 0.626878i −0.518105 0.855317i \(-0.673362\pi\)
0.973558 + 0.228439i \(0.0733622\pi\)
\(102\) 3.15155e7 9.69948e7i 0.291155 0.896082i
\(103\) −2.35398e7 7.24480e7i −0.209148 0.643691i −0.999517 0.0310608i \(-0.990111\pi\)
0.790370 0.612630i \(-0.209889\pi\)
\(104\) 3.07454e7 2.23378e7i 0.262813 0.190945i
\(105\) −1.18136e8 1.62601e8i −0.971910 1.33772i
\(106\) −1.08337e8 + 3.52010e7i −0.858134 + 0.278825i
\(107\) 2.96683e7 + 9.63982e6i 0.226338 + 0.0735418i 0.419991 0.907528i \(-0.362033\pi\)
−0.193652 + 0.981070i \(0.562033\pi\)
\(108\) −9.28271e7 6.74428e7i −0.682307 0.495725i
\(109\) 7.03263e7i 0.498209i −0.968477 0.249104i \(-0.919864\pi\)
0.968477 0.249104i \(-0.0801363\pi\)
\(110\) −1.40949e7 + 7.46992e7i −0.0962699 + 0.510205i
\(111\) 3.62497e8 2.38788
\(112\) 3.01755e7 4.15330e7i 0.191771 0.263949i
\(113\) −3.18703e7 + 9.80867e7i −0.195466 + 0.601584i 0.804504 + 0.593947i \(0.202431\pi\)
−0.999971 + 0.00763722i \(0.997569\pi\)
\(114\) 7.24989e7 + 2.23129e8i 0.429251 + 1.32110i
\(115\) −6.75026e7 + 4.90435e7i −0.385948 + 0.280408i
\(116\) 1.96622e7 + 2.70626e7i 0.108592 + 0.149465i
\(117\) 3.23820e8 1.05216e8i 1.72807 0.561483i
\(118\) −1.85667e8 6.03268e7i −0.957649 0.311159i
\(119\) 1.63492e8 + 1.18784e8i 0.815286 + 0.592340i
\(120\) 9.28889e7i 0.447960i
\(121\) 1.99620e8 + 7.81131e7i 0.931241 + 0.364403i
\(122\) 1.07096e8 0.483430
\(123\) −2.70401e8 + 3.72176e8i −1.18138 + 1.62603i
\(124\) 5.78692e7 1.78103e8i 0.244772 0.753330i
\(125\) 8.09251e7 + 2.49062e8i 0.331469 + 1.02016i
\(126\) 3.72108e8 2.70352e8i 1.47634 1.07262i
\(127\) −1.19151e8 1.63997e8i −0.458017 0.630406i 0.516079 0.856541i \(-0.327391\pi\)
−0.974096 + 0.226135i \(0.927391\pi\)
\(128\) 2.25653e7 7.33191e6i 0.0840623 0.0273135i
\(129\) −8.25447e8 2.68204e8i −2.98078 0.968515i
\(130\) 1.10232e8 + 8.00881e7i 0.385952 + 0.280411i
\(131\) 5.01055e8i 1.70138i 0.525670 + 0.850688i \(0.323815\pi\)
−0.525670 + 0.850688i \(0.676185\pi\)
\(132\) −2.57393e8 4.85671e7i −0.847814 0.159973i
\(133\) −4.64886e8 −1.48573
\(134\) −6.18389e7 + 8.51139e7i −0.191797 + 0.263986i
\(135\) 1.27124e8 3.91246e8i 0.382729 1.17792i
\(136\) 2.88617e7 + 8.88272e7i 0.0843658 + 0.259651i
\(137\) 2.08345e8 1.51372e8i 0.591428 0.429697i −0.251398 0.967884i \(-0.580890\pi\)
0.842826 + 0.538186i \(0.180890\pi\)
\(138\) −1.68990e8 2.32595e8i −0.465956 0.641334i
\(139\) −4.48685e8 + 1.45787e8i −1.20194 + 0.390534i −0.840474 0.541852i \(-0.817723\pi\)
−0.361465 + 0.932386i \(0.617723\pi\)
\(140\) 1.75053e8 + 5.68780e7i 0.455676 + 0.148058i
\(141\) −6.97171e8 5.06524e8i −1.76385 1.28152i
\(142\) 2.14800e8i 0.528301i
\(143\) 2.79557e8 2.63575e8i 0.668537 0.630319i
\(144\) 2.12574e8 0.494380
\(145\) −7.04950e7 + 9.70280e7i −0.159473 + 0.219495i
\(146\) −7.53243e7 + 2.31824e8i −0.165777 + 0.510208i
\(147\) 1.75070e8 + 5.38809e8i 0.374923 + 1.15389i
\(148\) −2.68572e8 + 1.95129e8i −0.559775 + 0.406700i
\(149\) 1.30190e8 + 1.79191e8i 0.264139 + 0.363556i 0.920400 0.390978i \(-0.127863\pi\)
−0.656261 + 0.754534i \(0.727863\pi\)
\(150\) −2.70731e8 + 8.79660e7i −0.534778 + 0.173760i
\(151\) 6.67667e8 + 2.16938e8i 1.28426 + 0.417281i 0.870078 0.492914i \(-0.164068\pi\)
0.414180 + 0.910195i \(0.364068\pi\)
\(152\) −1.73822e8 1.26289e8i −0.325634 0.236587i
\(153\) 8.36788e8i 1.52704i
\(154\) 2.49134e8 4.55327e8i 0.442945 0.809544i
\(155\) 6.71417e8 1.16323
\(156\) −2.75961e8 + 3.79828e8i −0.465961 + 0.641341i
\(157\) −2.09053e8 + 6.43398e8i −0.344078 + 1.05896i 0.617998 + 0.786180i \(0.287944\pi\)
−0.962076 + 0.272783i \(0.912056\pi\)
\(158\) 9.24959e7 + 2.84673e8i 0.148421 + 0.456792i
\(159\) 1.13851e9 8.27176e8i 1.78135 1.29422i
\(160\) 5.00012e7 + 6.88207e7i 0.0762958 + 0.105012i
\(161\) 5.41811e8 1.76045e8i 0.806388 0.262011i
\(162\) 4.32176e8 + 1.40423e8i 0.627481 + 0.203881i
\(163\) −8.24420e8 5.98976e8i −1.16788 0.848514i −0.177126 0.984188i \(-0.556680\pi\)
−0.990754 + 0.135674i \(0.956680\pi\)
\(164\) 4.21297e8i 0.582388i
\(165\) −1.19565e8 9.31475e8i −0.161313 1.25671i
\(166\) −3.35711e8 −0.442114
\(167\) −8.78263e7 + 1.20883e8i −0.112917 + 0.155417i −0.861735 0.507359i \(-0.830622\pi\)
0.748818 + 0.662776i \(0.230622\pi\)
\(168\) −1.95986e8 + 6.03183e8i −0.246030 + 0.757202i
\(169\) 3.92622e7 + 1.20837e8i 0.0481314 + 0.148133i
\(170\) −2.70910e8 + 1.96827e8i −0.324361 + 0.235662i
\(171\) −1.13146e9 1.55733e9i −1.32329 1.82136i
\(172\) 7.55940e8 2.45620e8i 0.863721 0.280640i
\(173\) 6.30115e8 + 2.04737e8i 0.703454 + 0.228566i 0.638835 0.769344i \(-0.279417\pi\)
0.0646191 + 0.997910i \(0.479417\pi\)
\(174\) −3.34332e8 2.42906e8i −0.364737 0.264997i
\(175\) 5.64067e8i 0.601420i
\(176\) 2.16844e8 1.02569e8i 0.225993 0.106897i
\(177\) 2.41177e9 2.45721
\(178\) −7.11904e7 + 9.79852e7i −0.0709155 + 0.0976069i
\(179\) −1.59530e8 + 4.90982e8i −0.155392 + 0.478249i −0.998200 0.0599657i \(-0.980901\pi\)
0.842808 + 0.538214i \(0.180901\pi\)
\(180\) 2.35516e8 + 7.24842e8i 0.224352 + 0.690484i
\(181\) 6.04863e8 4.39459e8i 0.563564 0.409453i −0.269198 0.963085i \(-0.586759\pi\)
0.832761 + 0.553632i \(0.186759\pi\)
\(182\) −5.46822e8 7.52636e8i −0.498380 0.685961i
\(183\) −1.25831e9 + 4.08849e8i −1.12197 + 0.364551i
\(184\) 2.50407e8 + 8.13623e7i 0.218462 + 0.0709826i
\(185\) −9.62913e8 6.99597e8i −0.822053 0.597257i
\(186\) 2.31352e9i 1.93295i
\(187\) 4.03758e8 + 8.53594e8i 0.330183 + 0.698048i
\(188\) 7.89186e8 0.631754
\(189\) −1.65098e9 + 2.27238e9i −1.29388 + 1.78087i
\(190\) 2.38043e8 7.32622e8i 0.182659 0.562167i
\(191\) −4.96774e8 1.52891e9i −0.373272 1.14881i −0.944637 0.328116i \(-0.893586\pi\)
0.571366 0.820696i \(-0.306414\pi\)
\(192\) −2.37137e8 + 1.72290e8i −0.174500 + 0.126782i
\(193\) 7.28208e8 + 1.00229e9i 0.524839 + 0.722379i 0.986333 0.164764i \(-0.0526863\pi\)
−0.461494 + 0.887143i \(0.652686\pi\)
\(194\) −1.01418e9 + 3.29527e8i −0.715992 + 0.232640i
\(195\) −1.60089e9 5.20162e8i −1.10720 0.359750i
\(196\) −4.19744e8 3.04962e8i −0.284420 0.206643i
\(197\) 3.56512e8i 0.236706i 0.992972 + 0.118353i \(0.0377614\pi\)
−0.992972 + 0.118353i \(0.962239\pi\)
\(198\) 2.13166e9 2.73623e8i 1.38694 0.178029i
\(199\) −9.81270e8 −0.625715 −0.312857 0.949800i \(-0.601286\pi\)
−0.312857 + 0.949800i \(0.601286\pi\)
\(200\) 1.53232e8 2.10905e8i 0.0957698 0.131816i
\(201\) 4.01636e8 1.23611e9i 0.246064 0.757307i
\(202\) −2.81902e8 8.67606e8i −0.169314 0.521095i
\(203\) 6.62484e8 4.81323e8i 0.390114 0.283434i
\(204\) −6.78212e8 9.33479e8i −0.391602 0.538994i
\(205\) 1.43655e9 4.66764e8i 0.813403 0.264291i
\(206\) −8.19656e8 2.66322e8i −0.455158 0.147890i
\(207\) 1.90842e9 + 1.38655e9i 1.03942 + 0.755186i
\(208\) 4.29959e8i 0.229707i
\(209\) −1.90561e9 1.04266e9i −0.998733 0.546461i
\(210\) −2.27389e9 −1.16921
\(211\) −1.94409e9 + 2.67581e9i −0.980814 + 1.34997i −0.0444242 + 0.999013i \(0.514145\pi\)
−0.936390 + 0.350962i \(0.885855\pi\)
\(212\) −3.98253e8 + 1.22570e9i −0.197159 + 0.606792i
\(213\) 8.20021e8 + 2.52376e9i 0.398388 + 1.22611i
\(214\) 2.85528e8 2.07449e8i 0.136143 0.0989134i
\(215\) 1.67504e9 + 2.30550e9i 0.783921 + 1.07897i
\(216\) −1.23461e9 + 4.01148e8i −0.567170 + 0.184285i
\(217\) −4.35991e9 1.41662e9i −1.96625 0.638873i
\(218\) −6.43695e8 4.67672e8i −0.285006 0.207069i
\(219\) 3.01134e9i 1.30913i
\(220\) 5.89989e8 + 6.25762e8i 0.251856 + 0.267127i
\(221\) 1.69251e9 0.709517
\(222\) 2.41062e9 3.31793e9i 0.992468 1.36601i
\(223\) 4.78260e8 1.47193e9i 0.193395 0.595207i −0.806597 0.591102i \(-0.798693\pi\)
0.999992 0.00410562i \(-0.00130686\pi\)
\(224\) −1.79483e8 5.52391e8i −0.0712903 0.219409i
\(225\) 1.88957e9 1.37285e9i 0.737281 0.535666i
\(226\) 6.85847e8 + 9.43988e8i 0.262902 + 0.361853i
\(227\) −4.95325e7 + 1.60941e7i −0.0186546 + 0.00606126i −0.318329 0.947980i \(-0.603122\pi\)
0.299675 + 0.954041i \(0.403122\pi\)
\(228\) 2.52441e9 + 8.20231e8i 0.934159 + 0.303527i
\(229\) 3.00093e9 + 2.18030e9i 1.09122 + 0.792821i 0.979606 0.200930i \(-0.0643964\pi\)
0.111619 + 0.993751i \(0.464396\pi\)
\(230\) 9.43990e8i 0.337331i
\(231\) −1.18891e9 + 6.30089e9i −0.417541 + 2.21286i
\(232\) 3.78458e8 0.130637
\(233\) 9.64932e8 1.32812e9i 0.327396 0.450622i −0.613311 0.789841i \(-0.710163\pi\)
0.940707 + 0.339219i \(0.110163\pi\)
\(234\) 1.19038e9 3.66361e9i 0.397029 1.22193i
\(235\) 8.74357e8 + 2.69099e9i 0.286693 + 0.882350i
\(236\) −1.78686e9 + 1.29823e9i −0.576027 + 0.418508i
\(237\) −2.17353e9 2.99161e9i −0.688926 0.948226i
\(238\) 2.17446e9 7.06525e8i 0.677710 0.220201i
\(239\) −2.61947e9 8.51119e8i −0.802828 0.260855i −0.121271 0.992619i \(-0.538697\pi\)
−0.681557 + 0.731765i \(0.738697\pi\)
\(240\) −8.50211e8 6.17714e8i −0.256260 0.186184i
\(241\) 2.38139e9i 0.705931i −0.935636 0.352966i \(-0.885173\pi\)
0.935636 0.352966i \(-0.114827\pi\)
\(242\) 2.04245e9 1.30766e9i 0.595510 0.381271i
\(243\) 2.67488e8 0.0767148
\(244\) 7.12191e8 9.80247e8i 0.200927 0.276552i
\(245\) 5.74825e8 1.76913e9i 0.159541 0.491015i
\(246\) 1.60834e9 + 4.94996e9i 0.439175 + 1.35164i
\(247\) −3.14990e9 + 2.28854e9i −0.846270 + 0.614851i
\(248\) −1.24534e9 1.71407e9i −0.329217 0.453128i
\(249\) 3.94439e9 1.28161e9i 1.02608 0.333394i
\(250\) 2.81781e9 + 9.15563e8i 0.721360 + 0.234384i
\(251\) −5.84160e9 4.24417e9i −1.47176 1.06930i −0.980099 0.198508i \(-0.936390\pi\)
−0.491660 0.870787i \(-0.663610\pi\)
\(252\) 5.20374e9i 1.29037i
\(253\) 2.61577e9 + 4.93566e8i 0.638437 + 0.120466i
\(254\) −2.29341e9 −0.550995
\(255\) 2.43160e9 3.34681e9i 0.575085 0.791536i
\(256\) 8.29511e7 2.55297e8i 0.0193136 0.0594410i
\(257\) −3.77457e7 1.16169e8i −0.00865236 0.0266292i 0.946637 0.322301i \(-0.104456\pi\)
−0.955289 + 0.295672i \(0.904456\pi\)
\(258\) −7.94412e9 + 5.77174e9i −1.79294 + 1.30265i
\(259\) 4.77668e9 + 6.57454e9i 1.06152 + 1.46105i
\(260\) 1.46609e9 4.76361e8i 0.320824 0.104242i
\(261\) 3.22477e9 + 1.04779e9i 0.694924 + 0.225795i
\(262\) 4.58615e9 + 3.33203e9i 0.973292 + 0.707138i
\(263\) 1.93793e8i 0.0405055i 0.999795 + 0.0202527i \(0.00644709\pi\)
−0.999795 + 0.0202527i \(0.993553\pi\)
\(264\) −2.15620e9 + 2.03294e9i −0.443889 + 0.418513i
\(265\) −4.62066e9 −0.936959
\(266\) −3.09151e9 + 4.25510e9i −0.617510 + 0.849930i
\(267\) 4.62373e8 1.42304e9i 0.0909803 0.280009i
\(268\) 3.67816e8 + 1.13202e9i 0.0713002 + 0.219440i
\(269\) −3.77561e9 + 2.74314e9i −0.721070 + 0.523888i −0.886726 0.462296i \(-0.847026\pi\)
0.165656 + 0.986184i \(0.447026\pi\)
\(270\) −2.73569e9 3.76536e9i −0.514769 0.708519i
\(271\) −2.90452e9 + 9.43735e8i −0.538514 + 0.174974i −0.565631 0.824659i \(-0.691367\pi\)
0.0271172 + 0.999632i \(0.491367\pi\)
\(272\) 1.00497e9 + 3.26533e8i 0.183601 + 0.0596556i
\(273\) 9.29806e9 + 6.75544e9i 1.67395 + 1.21619i
\(274\) 2.91361e9i 0.516927i
\(275\) 1.26511e9 2.31216e9i 0.221206 0.404285i
\(276\) −3.25273e9 −0.560547
\(277\) −1.39800e6 + 1.92418e6i −0.000237459 + 0.000326834i −0.809136 0.587622i \(-0.800064\pi\)
0.808898 + 0.587949i \(0.200064\pi\)
\(278\) −1.64939e9 + 5.07629e9i −0.276149 + 0.849899i
\(279\) −5.86581e9 1.80531e10i −0.968081 2.97945i
\(280\) 1.68471e9 1.22401e9i 0.274090 0.199138i
\(281\) 4.10658e8 + 5.65223e8i 0.0658651 + 0.0906555i 0.840679 0.541534i \(-0.182156\pi\)
−0.774814 + 0.632190i \(0.782156\pi\)
\(282\) −9.27242e9 + 3.01279e9i −1.46621 + 0.476401i
\(283\) −3.39423e9 1.10285e9i −0.529171 0.171938i 0.0322325 0.999480i \(-0.489738\pi\)
−0.561403 + 0.827542i \(0.689738\pi\)
\(284\) −1.96606e9 1.42843e9i −0.302221 0.219576i
\(285\) 9.51657e9i 1.44245i
\(286\) −5.53438e8 4.31156e9i −0.0827189 0.644422i
\(287\) −1.03132e10 −1.52008
\(288\) 1.41362e9 1.94569e9i 0.205477 0.282815i
\(289\) 8.70246e8 2.67834e9i 0.124753 0.383950i
\(290\) 4.19302e8 + 1.29048e9i 0.0592836 + 0.182456i
\(291\) 1.06580e10 7.74345e9i 1.48628 1.07985i
\(292\) 1.62098e9 + 2.23108e9i 0.222969 + 0.306891i
\(293\) 1.48389e9 4.82146e8i 0.201341 0.0654196i −0.206611 0.978423i \(-0.566243\pi\)
0.407951 + 0.913004i \(0.366243\pi\)
\(294\) 6.09593e9 + 1.98069e9i 0.815926 + 0.265110i
\(295\) −6.40645e9 4.65456e9i −0.845921 0.614597i
\(296\) 3.75584e9i 0.489261i
\(297\) −1.18641e10 + 5.61181e9i −1.52478 + 0.721236i
\(298\) 2.50590e9 0.317760
\(299\) 2.80448e9 3.86003e9i 0.350887 0.482954i
\(300\) −9.95221e8 + 3.06298e9i −0.122867 + 0.378145i
\(301\) −6.01269e9 1.85051e10i −0.732491 2.25438i
\(302\) 6.42564e9 4.66850e9i 0.772482 0.561241i
\(303\) 6.62433e9 + 9.11761e9i 0.785907 + 1.08171i
\(304\) −2.31184e9 + 7.51162e8i −0.270685 + 0.0879508i
\(305\) 4.13153e9 + 1.34242e9i 0.477432 + 0.155127i
\(306\) 7.65910e9 + 5.56467e9i 0.873559 + 0.634678i
\(307\) 1.39571e10i 1.57123i 0.618713 + 0.785617i \(0.287654\pi\)
−0.618713 + 0.785617i \(0.712346\pi\)
\(308\) −2.51085e9 5.30826e9i −0.279009 0.589860i
\(309\) 1.06471e10 1.16788
\(310\) 4.46494e9 6.14547e9i 0.483470 0.665439i
\(311\) −4.84920e9 + 1.49243e10i −0.518357 + 1.59534i 0.258734 + 0.965949i \(0.416695\pi\)
−0.777091 + 0.629389i \(0.783305\pi\)
\(312\) 1.64141e9 + 5.05174e9i 0.173220 + 0.533117i
\(313\) −4.53868e9 + 3.29755e9i −0.472882 + 0.343569i −0.798563 0.601911i \(-0.794406\pi\)
0.325682 + 0.945479i \(0.394406\pi\)
\(314\) 4.49880e9 + 6.19207e9i 0.462784 + 0.636967i
\(315\) 1.77439e10 5.76534e9i 1.80222 0.585575i
\(316\) 3.22071e9 + 1.04647e9i 0.323000 + 0.104949i
\(317\) 1.01506e10 + 7.37486e9i 1.00521 + 0.730326i 0.963199 0.268791i \(-0.0866241\pi\)
0.0420093 + 0.999117i \(0.486624\pi\)
\(318\) 1.59215e10i 1.55695i
\(319\) 3.79511e9 4.87146e8i 0.366490 0.0470431i
\(320\) 9.62425e8 0.0917840
\(321\) −2.56282e9 + 3.52742e9i −0.241378 + 0.332228i
\(322\) 1.99172e9 6.12989e9i 0.185270 0.570202i
\(323\) −2.95691e9 9.10045e9i −0.271662 0.836089i
\(324\) 4.15927e9 3.02189e9i 0.377431 0.274219i
\(325\) −2.77678e9 3.82191e9i −0.248890 0.342568i
\(326\) −1.09648e10 + 3.56269e9i −0.970804 + 0.315433i
\(327\) 9.34837e9 + 3.03747e9i 0.817608 + 0.265657i
\(328\) −3.85612e9 2.80164e9i −0.333162 0.242056i
\(329\) 1.93190e10i 1.64893i
\(330\) −9.32089e9 5.09996e9i −0.785962 0.430042i
\(331\) 1.19142e10 0.992553 0.496277 0.868164i \(-0.334700\pi\)
0.496277 + 0.868164i \(0.334700\pi\)
\(332\) −2.23249e9 + 3.07276e9i −0.183754 + 0.252916i
\(333\) −1.03984e10 + 3.20029e10i −0.845646 + 2.60263i
\(334\) 5.22388e8 + 1.60775e9i 0.0419766 + 0.129191i
\(335\) −3.45249e9 + 2.50838e9i −0.274128 + 0.199165i
\(336\) 4.21761e9 + 5.80504e9i 0.330909 + 0.455458i
\(337\) −2.37925e9 + 7.73065e8i −0.184468 + 0.0599372i −0.399794 0.916605i \(-0.630918\pi\)
0.215327 + 0.976542i \(0.430918\pi\)
\(338\) 1.36711e9 + 4.44202e8i 0.104746 + 0.0340340i
\(339\) −1.16620e10 8.47295e9i −0.883029 0.641558i
\(340\) 3.78854e9i 0.283502i
\(341\) −1.46944e10 1.55854e10i −1.08676 1.15266i
\(342\) −2.17785e10 −1.59193
\(343\) 3.15205e9 4.33842e9i 0.227728 0.313441i
\(344\) 2.77887e9 8.55248e9i 0.198442 0.610743i
\(345\) −3.60377e9 1.10913e10i −0.254379 0.782897i
\(346\) 6.06424e9 4.40593e9i 0.423128 0.307421i
\(347\) 1.76152e9 + 2.42453e9i 0.121498 + 0.167228i 0.865434 0.501023i \(-0.167043\pi\)
−0.743935 + 0.668252i \(0.767043\pi\)
\(348\) −4.44663e9 + 1.44480e9i −0.303189 + 0.0985122i
\(349\) −3.88608e9 1.26266e9i −0.261945 0.0851111i 0.175100 0.984551i \(-0.443975\pi\)
−0.437045 + 0.899440i \(0.643975\pi\)
\(350\) −5.16289e9 3.75106e9i −0.344049 0.249967i
\(351\) 2.35242e10i 1.54984i
\(352\) 5.03205e8 2.66685e9i 0.0327774 0.173711i
\(353\) 1.06293e10 0.684551 0.342275 0.939600i \(-0.388802\pi\)
0.342275 + 0.939600i \(0.388802\pi\)
\(354\) 1.60383e10 2.20749e10i 1.02128 1.40568i
\(355\) 2.69246e9 8.28654e9i 0.169526 0.521747i
\(356\) 4.23438e8 + 1.30321e9i 0.0263627 + 0.0811361i
\(357\) −2.28513e10 + 1.66024e10i −1.40682 + 1.02211i
\(358\) 3.43307e9 + 4.72522e9i 0.209002 + 0.287667i
\(359\) 7.12240e9 2.31421e9i 0.428794 0.139324i −0.0866658 0.996237i \(-0.527621\pi\)
0.515460 + 0.856914i \(0.327621\pi\)
\(360\) 8.20066e9 + 2.66455e9i 0.488246 + 0.158641i
\(361\) 4.06824e9 + 2.95575e9i 0.239540 + 0.174036i
\(362\) 8.45872e9i 0.492573i
\(363\) −1.90053e10 + 2.31614e10i −1.09458 + 1.33395i
\(364\) −1.05253e10 −0.599552
\(365\) −5.81170e9 + 7.99912e9i −0.327440 + 0.450682i
\(366\) −4.62560e9 + 1.42361e10i −0.257776 + 0.793354i
\(367\) 3.55073e9 + 1.09280e10i 0.195728 + 0.602390i 0.999967 + 0.00808396i \(0.00257323\pi\)
−0.804239 + 0.594306i \(0.797427\pi\)
\(368\) 2.40992e9 1.75091e9i 0.131405 0.0954714i
\(369\) −2.51008e10 3.45483e10i −1.35388 1.86346i
\(370\) −1.28068e10 + 4.16118e9i −0.683335 + 0.222029i
\(371\) 3.00047e10 + 9.74911e9i 1.58377 + 0.514599i
\(372\) 2.11756e10 + 1.53850e10i 1.10577 + 0.803387i
\(373\) 3.10435e10i 1.60375i 0.597494 + 0.801873i \(0.296163\pi\)
−0.597494 + 0.801873i \(0.703837\pi\)
\(374\) 1.04979e10 + 1.98084e9i 0.536559 + 0.101243i
\(375\) −3.66027e10 −1.85092
\(376\) 5.24811e9 7.22341e9i 0.262574 0.361402i
\(377\) 2.11930e9 6.52253e9i 0.104912 0.322887i
\(378\) 9.81996e9 + 3.02227e10i 0.480997 + 1.48036i
\(379\) −1.39964e10 + 1.01690e10i −0.678358 + 0.492856i −0.872812 0.488056i \(-0.837706\pi\)
0.194455 + 0.980912i \(0.437706\pi\)
\(380\) −5.12268e9 7.05076e9i −0.245676 0.338144i
\(381\) 2.69461e10 8.75532e9i 1.27878 0.415501i
\(382\) −1.72977e10 5.62035e9i −0.812333 0.263943i
\(383\) 1.44700e10 + 1.05131e10i 0.672472 + 0.488580i 0.870852 0.491546i \(-0.163568\pi\)
−0.198380 + 0.980125i \(0.563568\pi\)
\(384\) 3.31625e9i 0.152518i
\(385\) 1.53184e10 1.44427e10i 0.697223 0.657364i
\(386\) 1.40166e10 0.631383
\(387\) 4.73565e10 6.51807e10i 2.11123 2.90586i
\(388\) −3.72817e9 + 1.14741e10i −0.164501 + 0.506283i
\(389\) −8.70665e9 2.67963e10i −0.380235 1.17024i −0.939878 0.341510i \(-0.889062\pi\)
0.559643 0.828734i \(-0.310938\pi\)
\(390\) −1.54070e10 + 1.11939e10i −0.665979 + 0.483862i
\(391\) 6.89238e9 + 9.48655e9i 0.294892 + 0.405883i
\(392\) −5.58262e9 + 1.81390e9i −0.236425 + 0.0768191i
\(393\) −6.66046e10 2.16411e10i −2.79212 0.907215i
\(394\) 3.26314e9 + 2.37081e9i 0.135410 + 0.0983813i
\(395\) 1.21415e10i 0.498751i
\(396\) 1.16711e10 2.13306e10i 0.474605 0.867407i
\(397\) 2.34205e10 0.942831 0.471416 0.881911i \(-0.343743\pi\)
0.471416 + 0.881911i \(0.343743\pi\)
\(398\) −6.52548e9 + 8.98155e9i −0.260064 + 0.357947i
\(399\) 2.00790e10 6.17967e10i 0.792228 2.43823i
\(400\) −9.11417e8 2.80505e9i −0.0356022 0.109572i
\(401\) 4.07013e9 2.95712e9i 0.157409 0.114365i −0.506292 0.862362i \(-0.668984\pi\)
0.663702 + 0.747997i \(0.268984\pi\)
\(402\) −8.64318e9 1.18963e10i −0.330955 0.455521i
\(403\) −3.65148e10 + 1.18644e10i −1.38436 + 0.449806i
\(404\) −9.81584e9 3.18936e9i −0.368470 0.119723i
\(405\) 1.49123e10 + 1.08344e10i 0.554273 + 0.402703i
\(406\) 9.26452e9i 0.340972i
\(407\) 4.83447e9 + 3.76630e10i 0.176186 + 1.37258i
\(408\) −1.30543e10 −0.471098
\(409\) −5.29737e9 + 7.29120e9i −0.189307 + 0.260559i −0.893112 0.449835i \(-0.851483\pi\)
0.703805 + 0.710393i \(0.251483\pi\)
\(410\) 5.28083e9 1.62527e10i 0.186882 0.575163i
\(411\) 1.11230e10 + 3.42330e10i 0.389810 + 1.19971i
\(412\) −7.88838e9 + 5.73124e9i −0.273778 + 0.198911i
\(413\) 3.17802e10 + 4.37418e10i 1.09234 + 1.50347i
\(414\) 2.53821e10 8.24715e9i 0.864025 0.280739i
\(415\) −1.29510e10 4.20804e9i −0.436628 0.141869i
\(416\) −3.93541e9 2.85924e9i −0.131406 0.0954723i
\(417\) 6.59398e10i 2.18074i
\(418\) −2.22159e10 + 1.05083e10i −0.727710 + 0.344213i
\(419\) 5.95217e10 1.93117 0.965583 0.260097i \(-0.0837545\pi\)
0.965583 + 0.260097i \(0.0837545\pi\)
\(420\) −1.51214e10 + 2.08129e10i −0.485955 + 0.668859i
\(421\) −1.19830e9 + 3.68800e9i −0.0381451 + 0.117398i −0.968316 0.249729i \(-0.919659\pi\)
0.930171 + 0.367127i \(0.119659\pi\)
\(422\) 1.15634e10 + 3.55885e10i 0.364616 + 1.12217i
\(423\) 6.47169e10 4.70196e10i 2.02142 1.46865i
\(424\) 8.57039e9 + 1.17961e10i 0.265178 + 0.364986i
\(425\) 1.10420e10 3.58775e9i 0.338447 0.109968i
\(426\) 2.85531e10 + 9.27748e9i 0.866993 + 0.281703i
\(427\) −2.39961e10 1.74342e10i −0.721821 0.524434i
\(428\) 3.99298e9i 0.118993i
\(429\) 2.29623e10 + 4.85452e10i 0.677932 + 1.43323i
\(430\) 3.22413e10 0.943059
\(431\) −2.77890e10 + 3.82483e10i −0.805312 + 1.10842i 0.186717 + 0.982414i \(0.440215\pi\)
−0.992030 + 0.126004i \(0.959785\pi\)
\(432\) −4.53847e9 + 1.39680e10i −0.130309 + 0.401050i
\(433\) −2.59893e9 7.99870e9i −0.0739339 0.227545i 0.907260 0.420570i \(-0.138170\pi\)
−0.981194 + 0.193025i \(0.938170\pi\)
\(434\) −4.19598e10 + 3.04856e10i −1.18270 + 0.859282i
\(435\) −9.85304e9 1.35615e10i −0.275178 0.378750i
\(436\) −8.56118e9 + 2.78170e9i −0.236912 + 0.0769775i
\(437\) −2.56545e10 8.33566e9i −0.703458 0.228567i
\(438\) −2.75628e10 2.00255e10i −0.748904 0.544111i
\(439\) 5.15925e9i 0.138908i −0.997585 0.0694542i \(-0.977874\pi\)
0.997585 0.0694542i \(-0.0221258\pi\)
\(440\) 9.65103e9 1.23882e9i 0.257492 0.0330520i
\(441\) −5.25905e10 −1.39044
\(442\) 1.12553e10 1.54915e10i 0.294895 0.405888i
\(443\) 2.59142e9 7.97557e9i 0.0672857 0.207084i −0.911761 0.410722i \(-0.865277\pi\)
0.979046 + 0.203638i \(0.0652766\pi\)
\(444\) −1.43383e10 4.41287e10i −0.368948 1.13551i
\(445\) −3.97459e9 + 2.88771e9i −0.101357 + 0.0736399i
\(446\) −1.02921e10 1.41659e10i −0.260115 0.358018i
\(447\) −2.94427e10 + 9.56651e9i −0.737475 + 0.239620i
\(448\) −6.24959e9 2.03062e9i −0.155146 0.0504099i
\(449\) 3.39361e10 + 2.46560e10i 0.834981 + 0.606649i 0.920964 0.389647i \(-0.127403\pi\)
−0.0859832 + 0.996297i \(0.527403\pi\)
\(450\) 2.64247e10i 0.644407i
\(451\) −4.22748e10 2.31308e10i −1.02182 0.559093i
\(452\) 1.32012e10 0.316271
\(453\) −5.76746e10 + 7.93823e10i −1.36959 + 1.88508i
\(454\) −1.82084e8 + 5.60396e8i −0.00428596 + 0.0131908i
\(455\) −1.16612e10 3.58894e10i −0.272080 0.837375i
\(456\) 2.42950e10 1.76513e10i 0.561897 0.408242i
\(457\) −1.14101e9 1.57047e9i −0.0261592 0.0360051i 0.795737 0.605642i \(-0.207084\pi\)
−0.821896 + 0.569637i \(0.807084\pi\)
\(458\) 3.99126e10 1.29684e10i 0.907084 0.294730i
\(459\) −5.49842e10 1.78655e10i −1.23876 0.402498i
\(460\) 8.64033e9 + 6.27757e9i 0.192974 + 0.140204i
\(461\) 3.51919e10i 0.779183i −0.920988 0.389591i \(-0.872616\pi\)
0.920988 0.389591i \(-0.127384\pi\)
\(462\) 4.97656e10 + 5.27831e10i 1.09235 + 1.15858i
\(463\) 4.06408e10 0.884378 0.442189 0.896922i \(-0.354202\pi\)
0.442189 + 0.896922i \(0.354202\pi\)
\(464\) 2.51676e9 3.46402e9i 0.0542962 0.0747323i
\(465\) −2.89993e10 + 8.92505e10i −0.620262 + 1.90897i
\(466\) −5.73939e9 1.76640e10i −0.121709 0.374581i
\(467\) −4.40225e10 + 3.19842e10i −0.925566 + 0.672463i −0.944903 0.327350i \(-0.893845\pi\)
0.0193369 + 0.999813i \(0.493845\pi\)
\(468\) −2.56169e10 3.52586e10i −0.534002 0.734991i
\(469\) 2.77115e10 9.00400e9i 0.572754 0.186099i
\(470\) 3.04451e10 + 9.89222e9i 0.623916 + 0.202723i
\(471\) −7.64968e10 5.55781e10i −1.55439 1.12933i
\(472\) 2.49884e10i 0.503466i
\(473\) 1.68574e10 8.93398e10i 0.336780 1.78484i
\(474\) −4.18362e10 −0.828780
\(475\) −1.56988e10 + 2.16075e10i −0.308383 + 0.424453i
\(476\) 7.99342e9 2.46012e10i 0.155706 0.479213i
\(477\) 4.03683e10 + 1.24241e11i 0.779770 + 2.39989i
\(478\) −2.52099e10 + 1.83160e10i −0.482902 + 0.350849i
\(479\) 3.02469e10 + 4.16313e10i 0.574565 + 0.790821i 0.993086 0.117386i \(-0.0374514\pi\)
−0.418521 + 0.908207i \(0.637451\pi\)
\(480\) −1.13079e10 + 3.67415e9i −0.213018 + 0.0692136i
\(481\) 6.47301e10 + 2.10321e10i 1.20928 + 0.392918i
\(482\) −2.17968e10 1.58363e10i −0.403836 0.293404i
\(483\) 7.96257e10i 1.46307i
\(484\) 1.61331e9 2.73905e10i 0.0293993 0.499135i
\(485\) −4.32554e10 −0.781760
\(486\) 1.77880e9 2.44831e9i 0.0318847 0.0438856i
\(487\) 2.93717e10 9.03969e10i 0.522172 1.60708i −0.247668 0.968845i \(-0.579664\pi\)
0.769841 0.638236i \(-0.220336\pi\)
\(488\) −4.23609e9 1.30374e10i −0.0746941 0.229885i
\(489\) 1.15229e11 8.37186e10i 2.01523 1.46415i
\(490\) −1.23702e10 1.70261e10i −0.214582 0.295346i
\(491\) −8.07978e10 + 2.62528e10i −1.39019 + 0.451700i −0.906005 0.423267i \(-0.860883\pi\)
−0.484183 + 0.874966i \(0.660883\pi\)
\(492\) 5.60024e10 + 1.81963e10i 0.955754 + 0.310543i
\(493\) 1.36359e10 + 9.90709e9i 0.230833 + 0.167710i
\(494\) 4.40498e10i 0.739667i
\(495\) 8.56646e10 + 1.61639e10i 1.42686 + 0.269232i
\(496\) −2.39704e10 −0.396049
\(497\) −3.49675e10 + 4.81286e10i −0.573111 + 0.788820i
\(498\) 1.44998e10 4.46257e10i 0.235745 0.725550i
\(499\) −5.48745e8 1.68886e9i −0.00885051 0.0272391i 0.946534 0.322605i \(-0.104558\pi\)
−0.955384 + 0.295366i \(0.904558\pi\)
\(500\) 2.71187e10 1.97029e10i 0.433899 0.315246i
\(501\) −1.22754e10 1.68957e10i −0.194843 0.268179i
\(502\) −7.76936e10 + 2.52442e10i −1.22341 + 0.397508i
\(503\) 5.19060e10 + 1.68653e10i 0.810860 + 0.263464i 0.684962 0.728579i \(-0.259819\pi\)
0.125898 + 0.992043i \(0.459819\pi\)
\(504\) −4.76298e10 3.46051e10i −0.738170 0.536312i
\(505\) 3.70039e10i 0.568961i
\(506\) 2.19126e10 2.06599e10i 0.334265 0.315156i
\(507\) −1.77584e10 −0.268765
\(508\) −1.52513e10 + 2.09916e10i −0.229008 + 0.315203i
\(509\) 1.75211e10 5.39243e10i 0.261029 0.803365i −0.731552 0.681785i \(-0.761204\pi\)
0.992582 0.121580i \(-0.0387962\pi\)
\(510\) −1.44631e10 4.45128e10i −0.213787 0.657968i
\(511\) 5.46161e10 3.96809e10i 0.801008 0.581967i
\(512\) −1.78510e9 2.45699e9i −0.0259767 0.0357538i
\(513\) 1.26487e11 4.10980e10i 1.82631 0.593406i
\(514\) −1.31430e9 4.27044e8i −0.0188297 0.00611814i
\(515\) −2.82823e10 2.05483e10i −0.402055 0.292110i
\(516\) 1.11095e11i 1.56709i
\(517\) 4.33293e10 7.91904e10i 0.606484 1.10844i
\(518\) 9.19418e10 1.27701
\(519\) −5.44308e10 + 7.49175e10i −0.750197 + 1.03256i
\(520\) 5.38941e9 1.65869e10i 0.0737103 0.226857i
\(521\) 3.42308e9 + 1.05351e10i 0.0464586 + 0.142985i 0.971595 0.236650i \(-0.0760496\pi\)
−0.925136 + 0.379635i \(0.876050\pi\)
\(522\) 3.10353e10 2.25485e10i 0.417997 0.303693i
\(523\) −3.56571e10 4.90777e10i −0.476583 0.655960i 0.501261 0.865296i \(-0.332870\pi\)
−0.977844 + 0.209336i \(0.932870\pi\)
\(524\) 6.09961e10 1.98188e10i 0.809053 0.262877i
\(525\) 7.49806e10 + 2.43627e10i 0.986988 + 0.320692i
\(526\) 1.77378e9 + 1.28873e9i 0.0231716 + 0.0168352i
\(527\) 9.43583e10i 1.22331i
\(528\) 4.26863e9 + 3.32548e10i 0.0549228 + 0.427877i
\(529\) −4.52549e10 −0.577887
\(530\) −3.07275e10 + 4.22928e10i −0.389425 + 0.535998i
\(531\) −6.91825e10 + 2.12922e11i −0.870198 + 2.67819i
\(532\) 1.83882e10 + 5.65931e10i 0.229558 + 0.706507i
\(533\) −6.98784e10 + 5.07696e10i −0.865833 + 0.629064i
\(534\) −9.95024e9 1.36953e10i −0.122368 0.168425i
\(535\) 1.36154e10 4.42391e9i 0.166194 0.0539996i
\(536\) 1.28073e10 + 4.16136e9i 0.155167 + 0.0504169i
\(537\) −5.83753e10 4.24122e10i −0.701992 0.510027i
\(538\) 5.28000e10i 0.630238i
\(539\) −5.36467e10 + 2.53754e10i −0.635606 + 0.300647i
\(540\) −5.26567e10 −0.619268
\(541\) −1.80579e10 + 2.48546e10i −0.210804 + 0.290147i −0.901305 0.433184i \(-0.857390\pi\)
0.690501 + 0.723331i \(0.257390\pi\)
\(542\) −1.06771e10 + 3.28609e10i −0.123725 + 0.380787i
\(543\) 3.22919e10 + 9.93844e10i 0.371445 + 1.14319i
\(544\) 9.67180e9 7.02698e9i 0.110436 0.0802367i
\(545\) −1.89702e10 2.61103e10i −0.215024 0.295955i
\(546\) 1.23665e11 4.01811e10i 1.39148 0.452118i
\(547\) 5.14353e10 + 1.67123e10i 0.574529 + 0.186676i 0.581848 0.813297i \(-0.302330\pi\)
−0.00731923 + 0.999973i \(0.502330\pi\)
\(548\) −2.66682e10 1.93756e10i −0.295714 0.214849i
\(549\) 1.22817e11i 1.35198i
\(550\) −1.27502e10 2.69555e10i −0.139337 0.294575i
\(551\) −3.87734e10 −0.420657
\(552\) −2.16308e10 + 2.97722e10i −0.232978 + 0.320667i
\(553\) 2.56173e10 7.88419e10i 0.273925 0.843056i
\(554\) 8.31526e6 + 2.55917e7i 8.82748e−5 + 0.000271682i
\(555\) 1.34586e11 9.77823e10i 1.41849 1.03060i
\(556\) 3.54947e10 + 4.88543e10i 0.371420 + 0.511215i
\(557\) −5.95643e10 + 1.93536e10i −0.618821 + 0.201067i −0.601617 0.798785i \(-0.705477\pi\)
−0.0172042 + 0.999852i \(0.505477\pi\)
\(558\) −2.04248e11 6.63641e10i −2.10679 0.684536i
\(559\) −1.31837e11 9.57848e10i −1.35017 0.980956i
\(560\) 2.35598e10i 0.239563i
\(561\) −1.30906e11 + 1.68033e10i −1.32162 + 0.169645i
\(562\) 7.90436e9 0.0792358
\(563\) 6.42246e10 8.83976e10i 0.639246 0.879846i −0.359329 0.933211i \(-0.616995\pi\)
0.998575 + 0.0533645i \(0.0169945\pi\)
\(564\) −3.40858e10 + 1.04905e11i −0.336866 + 1.03677i
\(565\) 1.46259e10 + 4.50139e10i 0.143525 + 0.441726i
\(566\) −3.26661e10 + 2.37333e10i −0.318297 + 0.231256i
\(567\) −7.39748e10 1.01818e11i −0.715734 0.985123i
\(568\) −2.61488e10 + 8.49626e9i −0.251222 + 0.0816271i
\(569\) −1.63420e11 5.30982e10i −1.55903 0.506560i −0.602483 0.798132i \(-0.705822\pi\)
−0.956549 + 0.291572i \(0.905822\pi\)
\(570\) 8.71050e10 + 6.32855e10i 0.825171 + 0.599522i
\(571\) 9.48939e10i 0.892676i 0.894864 + 0.446338i \(0.147272\pi\)
−0.894864 + 0.446338i \(0.852728\pi\)
\(572\) −4.31440e10 2.36064e10i −0.403029 0.220519i
\(573\) 2.24692e11 2.08435
\(574\) −6.85831e10 + 9.43965e10i −0.631785 + 0.869578i
\(575\) 1.01140e10 3.11277e10i 0.0925235 0.284758i
\(576\) −8.40820e9 2.58778e10i −0.0763858 0.235091i
\(577\) −5.63509e10 + 4.09413e10i −0.508391 + 0.369367i −0.812213 0.583361i \(-0.801737\pi\)
0.303822 + 0.952729i \(0.401737\pi\)
\(578\) −1.87277e10 2.57764e10i −0.167792 0.230946i
\(579\) −1.64685e11 + 5.35096e10i −1.46535 + 0.476121i
\(580\) 1.46001e10 + 4.74386e9i 0.129016 + 0.0419198i
\(581\) 7.52201e10 + 5.46506e10i 0.660130 + 0.479613i
\(582\) 1.49046e11i 1.29906i
\(583\) 1.01126e11 + 1.07258e11i 0.875367 + 0.928443i
\(584\) 3.12006e10 0.268232
\(585\) 9.18445e10 1.26413e11i 0.784205 1.07937i
\(586\) 5.45486e9 1.67883e10i 0.0462586 0.142369i
\(587\) 5.61367e6 + 1.72771e7i 4.72818e−5 + 0.000145519i 0.951080 0.308944i \(-0.0999756\pi\)
−0.951033 + 0.309090i \(0.899976\pi\)
\(588\) 5.86673e10 4.26243e10i 0.490780 0.356573i
\(589\) 1.27587e11 + 1.75608e11i 1.06009 + 1.45909i
\(590\) −8.52062e10 + 2.76852e10i −0.703175 + 0.228475i
\(591\) −4.73906e10 1.53981e10i −0.388456 0.126217i
\(592\) 3.43772e10 + 2.49765e10i 0.279887 + 0.203350i
\(593\) 1.12222e11i 0.907529i 0.891122 + 0.453764i \(0.149919\pi\)
−0.891122 + 0.453764i \(0.850081\pi\)
\(594\) −2.75316e10 + 1.45910e11i −0.221150 + 1.17203i
\(595\) 9.27421e10 0.739961
\(596\) 1.66643e10 2.29365e10i 0.132069 0.181778i
\(597\) 4.23822e10 1.30439e11i 0.333646 1.02686i
\(598\) −1.66809e10 5.13386e10i −0.130441 0.401458i
\(599\) −1.08879e11 + 7.91053e10i −0.845741 + 0.614467i −0.923968 0.382469i \(-0.875074\pi\)
0.0782274 + 0.996936i \(0.475074\pi\)
\(600\) 2.14171e10 + 2.94781e10i 0.165255 + 0.227455i
\(601\) 4.77918e10 1.55285e10i 0.366316 0.119023i −0.120074 0.992765i \(-0.538313\pi\)
0.486390 + 0.873742i \(0.338313\pi\)
\(602\) −2.09362e11 6.80258e10i −1.59408 0.517950i
\(603\) 9.76081e10 + 7.09164e10i 0.738272 + 0.536386i
\(604\) 8.98594e10i 0.675174i
\(605\) 9.51843e10 2.48454e10i 0.710467 0.185449i
\(606\) 1.27505e11 0.945448
\(607\) 6.67009e10 9.18059e10i 0.491334 0.676263i −0.489299 0.872116i \(-0.662747\pi\)
0.980633 + 0.195853i \(0.0627474\pi\)
\(608\) −8.49843e9 + 2.61555e10i −0.0621906 + 0.191403i
\(609\) 3.53682e10 + 1.08852e11i 0.257124 + 0.791348i
\(610\) 3.97619e10 2.88887e10i 0.287176 0.208646i
\(611\) −9.51033e10 1.30898e11i −0.682387 0.939225i
\(612\) 1.01867e11 3.30985e10i 0.726149 0.235940i
\(613\) 4.79185e10 + 1.55697e10i 0.339360 + 0.110265i 0.473739 0.880665i \(-0.342904\pi\)
−0.134379 + 0.990930i \(0.542904\pi\)
\(614\) 1.27749e11 + 9.28150e10i 0.898843 + 0.653047i
\(615\) 2.11119e11i 1.47580i
\(616\) −6.52836e10 1.23183e10i −0.453400 0.0855514i
\(617\) −6.99646e9 −0.0482767 −0.0241384 0.999709i \(-0.507684\pi\)
−0.0241384 + 0.999709i \(0.507684\pi\)
\(618\) 7.08037e10 9.74529e10i 0.485403 0.668099i
\(619\) 5.45105e9 1.67766e10i 0.0371294 0.114272i −0.930774 0.365595i \(-0.880866\pi\)
0.967903 + 0.251323i \(0.0808655\pi\)
\(620\) −2.65573e10 8.17351e10i −0.179729 0.553149i
\(621\) −1.31853e11 + 9.57969e10i −0.886593 + 0.644147i
\(622\) 1.04355e11 + 1.43632e11i 0.697188 + 0.959597i
\(623\) 3.19021e10 1.03656e10i 0.211771 0.0688087i
\(624\) 5.71539e10 + 1.85704e10i 0.376971 + 0.122485i
\(625\) 4.03393e10 + 2.93082e10i 0.264368 + 0.192075i
\(626\) 6.34713e10i 0.413314i
\(627\) 2.20905e11 2.08277e11i 1.42934 1.34763i
\(628\) 8.65931e10 0.556730
\(629\) −9.83187e10 + 1.35324e11i −0.628107 + 0.864515i
\(630\) 6.52274e10 2.00749e11i 0.414064 1.27436i
\(631\) −5.56452e10 1.71258e11i −0.351002 1.08027i −0.958291 0.285793i \(-0.907743\pi\)
0.607289 0.794481i \(-0.292257\pi\)
\(632\) 3.09962e10 2.25200e10i 0.194285 0.141156i
\(633\) −2.71724e11 3.73997e11i −1.69244 2.32945i
\(634\) 1.35004e11 4.38655e10i 0.835583 0.271497i
\(635\) −8.84750e10 2.87473e10i −0.544159 0.176808i
\(636\) −1.45729e11 1.05879e11i −0.890674 0.647112i
\(637\) 1.06371e11i 0.646050i
\(638\) 2.07788e10 3.79761e10i 0.125411 0.229207i
\(639\) −2.46332e11 −1.47747
\(640\) 6.40015e9 8.80906e9i 0.0381479 0.0525061i
\(641\) 2.47028e10 7.60273e10i 0.146323 0.450337i −0.850856 0.525400i \(-0.823916\pi\)
0.997179 + 0.0750630i \(0.0239158\pi\)
\(642\) 1.52436e10 + 4.69148e10i 0.0897318 + 0.276166i
\(643\) −2.15847e11 + 1.56822e11i −1.26271 + 0.917411i −0.998887 0.0471610i \(-0.984983\pi\)
−0.263820 + 0.964572i \(0.584983\pi\)
\(644\) −4.28617e10 5.89941e10i −0.249188 0.342977i
\(645\) −3.78814e11 + 1.23084e11i −2.18871 + 0.711153i
\(646\) −1.02960e11 3.34537e10i −0.591204 0.192094i
\(647\) 1.98055e11 + 1.43895e11i 1.13023 + 0.821162i 0.985729 0.168342i \(-0.0538413\pi\)
0.144504 + 0.989504i \(0.453841\pi\)
\(648\) 5.81654e10i 0.329887i
\(649\) 3.21647e10 + 2.50579e11i 0.181301 + 1.41243i
\(650\) −5.34475e10 −0.299415
\(651\) 3.76619e11 5.18371e11i 2.09690 2.88614i
\(652\) −4.03072e10 + 1.24053e11i −0.223045 + 0.686462i
\(653\) 3.75635e10 + 1.15608e11i 0.206592 + 0.635824i 0.999644 + 0.0266707i \(0.00849057\pi\)
−0.793053 + 0.609153i \(0.791509\pi\)
\(654\) 8.99689e10 6.53662e10i 0.491792 0.357308i
\(655\) 1.35158e11 + 1.86029e11i 0.734304 + 1.01068i
\(656\) −5.12866e10 + 1.66640e10i −0.276942 + 0.0899839i
\(657\) 2.65855e11 + 8.63815e10i 1.42687 + 0.463617i
\(658\) −1.76827e11 1.28472e11i −0.943287 0.685338i
\(659\) 2.46959e11i 1.30943i −0.755876 0.654715i \(-0.772789\pi\)
0.755876 0.654715i \(-0.227211\pi\)
\(660\) −1.08664e11 + 5.13990e10i −0.572677 + 0.270881i
\(661\) −1.81261e11 −0.949509 −0.474755 0.880118i \(-0.657463\pi\)
−0.474755 + 0.880118i \(0.657463\pi\)
\(662\) 7.92300e10 1.09051e11i 0.412532 0.567802i
\(663\) −7.31016e10 + 2.24984e11i −0.378332 + 1.16438i
\(664\) 1.32788e10 + 4.08679e10i 0.0683103 + 0.210237i
\(665\) −1.72600e11 + 1.25401e11i −0.882581 + 0.641233i
\(666\) 2.23772e11 + 3.07996e11i 1.13739 + 1.56548i
\(667\) 4.51892e10 1.46829e10i 0.228313 0.0741835i
\(668\) 1.81896e10 + 5.91015e9i 0.0913516 + 0.0296819i
\(669\) 1.75005e11 + 1.27149e11i 0.873669 + 0.634758i
\(670\) 4.82814e10i 0.239596i
\(671\) −5.92603e10 1.25284e11i −0.292330 0.618023i
\(672\) 8.11806e10 0.398085
\(673\) 8.61904e9 1.18631e10i 0.0420144 0.0578279i −0.787493 0.616324i \(-0.788621\pi\)
0.829507 + 0.558496i \(0.188621\pi\)
\(674\) −8.74623e9 + 2.69181e10i −0.0423820 + 0.130438i
\(675\) 4.98660e10 + 1.53472e11i 0.240209 + 0.739288i
\(676\) 1.31571e10 9.55920e9i 0.0630048 0.0457757i
\(677\) 1.02258e10 + 1.40746e10i 0.0486790 + 0.0670009i 0.832663 0.553781i \(-0.186815\pi\)
−0.783984 + 0.620782i \(0.786815\pi\)
\(678\) −1.55106e11 + 5.03968e10i −0.734021 + 0.238498i
\(679\) 2.80883e11 + 9.12644e10i 1.32144 + 0.429361i
\(680\) 3.46764e10 + 2.51939e10i 0.162180 + 0.117831i
\(681\) 7.27941e9i 0.0338460i
\(682\) −2.40371e11 + 3.08544e10i −1.11108 + 0.142620i
\(683\) 2.59965e11 1.19463 0.597313 0.802008i \(-0.296235\pi\)
0.597313 + 0.802008i \(0.296235\pi\)
\(684\) −1.44827e11 + 1.99338e11i −0.661647 + 0.910679i
\(685\) 3.65212e10 1.12401e11i 0.165876 0.510513i
\(686\) −1.87483e10 5.77013e10i −0.0846575 0.260549i
\(687\) −4.19438e11 + 3.04740e11i −1.88296 + 1.36805i
\(688\) −5.98011e10 8.23092e10i −0.266904 0.367362i
\(689\) 2.51293e11 8.16501e10i 1.11507 0.362310i
\(690\) −1.25483e11 4.07720e10i −0.553592 0.179873i
\(691\) −1.54784e11 1.12457e11i −0.678914 0.493260i 0.194083 0.980985i \(-0.437827\pi\)
−0.872997 + 0.487725i \(0.837827\pi\)
\(692\) 8.48054e10i 0.369828i
\(693\) −5.22167e11 2.85705e11i −2.26400 1.23875i
\(694\) 3.39059e10 0.146163
\(695\) −1.27260e11 + 1.75158e11i −0.545446 + 0.750742i
\(696\) −1.63460e10 + 5.03079e10i −0.0696587 + 0.214387i
\(697\) −6.55972e10 2.01887e11i −0.277942 0.855417i
\(698\) −3.73997e10 + 2.71725e10i −0.157560 + 0.114474i
\(699\) 1.34868e11 + 1.85630e11i 0.564937 + 0.777570i
\(700\) −6.86668e10 + 2.23112e10i −0.285992 + 0.0929246i
\(701\) −4.72699e10 1.53589e10i −0.195755 0.0636046i 0.209499 0.977809i \(-0.432817\pi\)
−0.405254 + 0.914204i \(0.632817\pi\)
\(702\) 2.15316e11 + 1.56436e11i 0.886602 + 0.644154i
\(703\) 3.84790e11i 1.57544i
\(704\) −2.10633e10 2.23405e10i −0.0857504 0.0909498i
\(705\) −3.95474e11 −1.60089
\(706\) 7.06851e10 9.72897e10i 0.284518 0.391605i
\(707\) −7.80744e10 + 2.40288e11i −0.312486 + 0.961734i
\(708\) −9.53955e10 2.93597e11i −0.379660 1.16847i
\(709\) 2.42339e11 1.76069e11i 0.959043 0.696785i 0.00611446 0.999981i \(-0.498054\pi\)
0.952928 + 0.303196i \(0.0980537\pi\)
\(710\) −5.79416e10 7.97498e10i −0.228012 0.313831i
\(711\) 3.26462e11 1.06074e11i 1.27748 0.415078i
\(712\) 1.47441e10 + 4.79066e9i 0.0573719 + 0.0186413i
\(713\) −2.15198e11 1.56351e11i −0.832685 0.604981i
\(714\) 3.19564e11i 1.22960i
\(715\) 3.26937e10 1.73268e11i 0.125095 0.662970i
\(716\) 6.60799e10 0.251430
\(717\) 2.26276e11 3.11442e11i 0.856174 1.17842i
\(718\) 2.61823e10 8.05807e10i 0.0985166 0.303203i
\(719\) −7.02282e10 2.16140e11i −0.262782 0.808761i −0.992196 0.124688i \(-0.960207\pi\)
0.729414 0.684073i \(-0.239793\pi\)
\(720\) 7.89232e10 5.73411e10i 0.293680 0.213371i
\(721\) 1.40299e11 + 1.93105e11i 0.519174 + 0.714582i
\(722\) 5.41079e10 1.75807e10i 0.199119 0.0646975i
\(723\) 3.16555e11 + 1.02855e11i 1.15850 + 0.376419i
\(724\) −7.74225e10 5.62507e10i −0.281782 0.204726i
\(725\) 4.70454e10i 0.170281i
\(726\) 8.56103e10 + 3.27979e11i 0.308162 + 1.18059i
\(727\) −3.41077e11 −1.22100 −0.610498 0.792018i \(-0.709031\pi\)
−0.610498 + 0.792018i \(0.709031\pi\)
\(728\) −6.99933e10 + 9.63375e10i −0.249190 + 0.342981i
\(729\) −9.29864e10 + 2.86183e11i −0.329238 + 1.01329i
\(730\) 3.45678e10 + 1.06389e11i 0.121725 + 0.374632i
\(731\) 3.24006e11 2.35404e11i 1.13471 0.824413i
\(732\) 9.95426e10 + 1.37009e11i 0.346709 + 0.477203i
\(733\) −1.95945e11 + 6.36665e10i −0.678764 + 0.220544i −0.628054 0.778170i \(-0.716148\pi\)
−0.0507098 + 0.998713i \(0.516148\pi\)
\(734\) 1.23637e11 + 4.01720e10i 0.425954 + 0.138401i
\(735\) 2.10341e11 + 1.52821e11i 0.720732 + 0.523642i
\(736\) 3.37016e10i 0.114852i
\(737\) 1.33786e11 + 2.52440e10i 0.453463 + 0.0855633i
\(738\) −4.83141e11 −1.62873
\(739\) −1.84958e11 + 2.54572e11i −0.620147 + 0.853559i −0.997364 0.0725663i \(-0.976881\pi\)
0.377217 + 0.926125i \(0.376881\pi\)
\(740\) −4.70784e10 + 1.44892e11i −0.156998 + 0.483191i
\(741\) −1.68164e11 5.17556e11i −0.557777 1.71666i
\(742\) 2.88765e11 2.09800e11i 0.952642 0.692135i
\(743\) 6.69623e10 + 9.21657e10i 0.219723 + 0.302422i 0.904621 0.426216i \(-0.140154\pi\)
−0.684899 + 0.728638i \(0.740154\pi\)
\(744\) 2.81637e11 9.15093e10i 0.919173 0.298657i
\(745\) 9.66723e10 + 3.14107e10i 0.313817 + 0.101965i
\(746\) 2.84141e11 + 2.06440e11i 0.917441 + 0.666560i
\(747\) 3.84992e11i 1.23643i
\(748\) 8.79422e10 8.29148e10i 0.280925 0.264866i
\(749\) −9.77467e10 −0.310581
\(750\) −2.43409e11 + 3.35024e11i −0.769293 + 1.05884i
\(751\) 5.21656e10 1.60549e11i 0.163993 0.504718i −0.834968 0.550299i \(-0.814514\pi\)
0.998961 + 0.0455810i \(0.0145139\pi\)
\(752\) −3.12156e10 9.60718e10i −0.0976114 0.300417i
\(753\) 8.16477e11 5.93205e11i 2.53959 1.84512i
\(754\) −4.56072e10 6.27729e10i −0.141107 0.194217i
\(755\) 3.06406e11 9.95572e10i 0.942994 0.306397i
\(756\) 3.41931e11 + 1.11100e11i 1.04677 + 0.340116i
\(757\) −2.99433e11 2.17550e11i −0.911833 0.662486i 0.0296444 0.999561i \(-0.490562\pi\)
−0.941478 + 0.337075i \(0.890562\pi\)
\(758\) 1.95733e11i 0.592906i
\(759\) −1.78587e11 + 3.26393e11i −0.538125 + 0.983499i
\(760\) −9.86015e10 −0.295549
\(761\) 2.14889e11 2.95769e11i 0.640731 0.881890i −0.357923 0.933751i \(-0.616515\pi\)
0.998654 + 0.0518606i \(0.0165151\pi\)
\(762\) 9.90552e10 3.04861e11i 0.293804 0.904235i
\(763\) 6.80950e10 + 2.09575e11i 0.200917 + 0.618359i
\(764\) −1.66473e11 + 1.20950e11i −0.488619 + 0.355002i
\(765\) 2.25720e11 + 3.10677e11i 0.659060 + 0.907119i
\(766\) 1.92452e11 6.25316e10i 0.558995 0.181629i
\(767\) 4.30662e11 + 1.39931e11i 1.24439 + 0.404326i
\(768\) 3.03536e10 + 2.20532e10i 0.0872499 + 0.0633908i
\(769\) 1.08067e11i 0.309022i −0.987991 0.154511i \(-0.950620\pi\)
0.987991 0.154511i \(-0.0493802\pi\)
\(770\) −3.03259e10 2.36254e11i −0.0862682 0.672073i
\(771\) 1.70725e10 0.0483147
\(772\) 9.32106e10 1.28293e11i 0.262420 0.361190i
\(773\) −1.24822e11 + 3.84161e11i −0.349600 + 1.07596i 0.609475 + 0.792806i \(0.291380\pi\)
−0.959075 + 0.283153i \(0.908620\pi\)
\(774\) −2.81675e11 8.66907e11i −0.784847 2.41551i
\(775\) −2.13073e11 + 1.54806e11i −0.590638 + 0.429124i
\(776\) 8.02301e10 + 1.10427e11i 0.221254 + 0.304530i
\(777\) −1.08026e12 + 3.50996e11i −2.96375 + 0.962982i
\(778\) −3.03166e11 9.85045e10i −0.827488 0.268867i
\(779\) 3.95064e11 + 2.87031e11i 1.07280 + 0.779432i
\(780\) 2.15460e11i 0.582087i
\(781\) −2.51279e11 + 1.18857e11i −0.675387 + 0.319464i
\(782\) 1.32665e11 0.354755
\(783\) −1.37698e11 + 1.89525e11i −0.366337 + 0.504220i
\(784\) −2.05220e10 + 6.31601e10i −0.0543193 + 0.167178i
\(785\) 9.59384e10 + 2.95268e11i 0.252647 + 0.777567i
\(786\) −6.41004e11 + 4.65717e11i −1.67946 + 1.22020i
\(787\) −4.10970e11 5.65652e11i −1.07130 1.47452i −0.868752 0.495247i \(-0.835077\pi\)
−0.202549 0.979272i \(-0.564923\pi\)
\(788\) 4.34000e10 1.41015e10i 0.112560 0.0365730i
\(789\) −2.57606e10 8.37012e9i −0.0664733 0.0215985i
\(790\) 1.11131e11 + 8.07413e10i 0.285316 + 0.207294i
\(791\) 3.23161e11i 0.825492i
\(792\) −1.17625e11 2.48675e11i −0.298952 0.632021i
\(793\) −2.48414e11 −0.628178
\(794\) 1.55747e11 2.14367e11i 0.391866 0.539357i
\(795\) 1.99572e11 6.14218e11i 0.499609 1.53764i
\(796\) 3.88133e10 + 1.19455e11i 0.0966782 + 0.297545i
\(797\) −3.37538e10 + 2.45236e10i −0.0836545 + 0.0607786i −0.628826 0.777546i \(-0.716464\pi\)
0.545172 + 0.838324i \(0.316464\pi\)
\(798\) −4.32099e11 5.94733e11i −1.06554 1.46660i
\(799\) 3.78182e11 1.22879e11i 0.927926 0.301502i
\(800\) −3.17356e10 1.03115e10i −0.0774794 0.0251746i
\(801\) 1.12369e11 + 8.16407e10i 0.272971 + 0.198325i
\(802\) 5.69188e10i 0.137581i
\(803\) 3.12874e11 4.01610e10i 0.752502 0.0965922i
\(804\) −1.66364e11 −0.398140
\(805\) 1.53673e11 2.11512e11i 0.365943 0.503677i
\(806\) −1.34230e11 + 4.13118e11i −0.318061 + 0.978890i
\(807\) −2.01569e11 6.20365e11i −0.475258 1.46269i
\(808\) −9.44678e10 + 6.86348e10i −0.221635 + 0.161027i
\(809\) 3.75074e11 + 5.16245e11i 0.875634 + 1.20521i 0.977611 + 0.210420i \(0.0674831\pi\)
−0.101977 + 0.994787i \(0.532517\pi\)
\(810\) 1.98334e11 6.44427e10i 0.460742 0.149704i
\(811\) −3.19473e11 1.03803e11i −0.738501 0.239953i −0.0844748 0.996426i \(-0.526921\pi\)
−0.654026 + 0.756472i \(0.726921\pi\)
\(812\) −8.47980e10 6.16093e10i −0.195057 0.141717i
\(813\) 4.26854e11i 0.977052i
\(814\) 3.76878e11 + 2.06210e11i 0.858426 + 0.469691i
\(815\) −4.67657e11 −1.05998
\(816\) −8.68112e10 + 1.19485e11i −0.195801 + 0.269497i
\(817\) −2.84698e11 + 8.76211e11i −0.638994 + 1.96662i
\(818\) 3.15086e10 + 9.69734e10i 0.0703745 + 0.216590i
\(819\) −8.63119e11 + 6.27093e11i −1.91838 + 1.39379i
\(820\) −1.13643e11 1.56416e11i −0.251355 0.345961i
\(821\) −2.66388e11 + 8.65546e10i −0.586329 + 0.190510i −0.587134 0.809490i \(-0.699744\pi\)
0.000804948 1.00000i \(0.499744\pi\)
\(822\) 3.87302e11 + 1.25842e11i 0.848325 + 0.275638i
\(823\) −1.68952e11 1.22751e11i −0.368269 0.267563i 0.388224 0.921565i \(-0.373089\pi\)
−0.756493 + 0.654002i \(0.773089\pi\)
\(824\) 1.10315e11i 0.239291i
\(825\) 2.52711e11 + 2.68034e11i 0.545517 + 0.578594i
\(826\) 6.11707e11 1.31408
\(827\) −4.67627e11 + 6.43634e11i −0.999718 + 1.37599i −0.0742205 + 0.997242i \(0.523647\pi\)
−0.925498 + 0.378753i \(0.876353\pi\)
\(828\) 9.33058e10 2.87166e11i 0.198512 0.610958i
\(829\) 1.77790e11 + 5.47183e11i 0.376435 + 1.15855i 0.942505 + 0.334191i \(0.108463\pi\)
−0.566070 + 0.824357i \(0.691537\pi\)
\(830\) −1.24641e11 + 9.05569e10i −0.262632 + 0.190814i
\(831\) −1.95398e8 2.68942e8i −0.000409746 0.000563967i
\(832\) −5.23412e10 + 1.70067e10i −0.109232 + 0.0354917i
\(833\) −2.48627e11 8.07837e10i −0.516378 0.167781i
\(834\) −6.03546e11 4.38502e11i −1.24752 0.906373i
\(835\) 6.85713e10i 0.141058i
\(836\) −5.15539e10 + 2.73222e11i −0.105545 + 0.559359i
\(837\) 1.31148e12 2.67215
\(838\) 3.95821e11 5.44801e11i 0.802644 1.10474i
\(839\) 4.73799e10 1.45820e11i 0.0956194 0.294286i −0.891795 0.452439i \(-0.850554\pi\)
0.987415 + 0.158153i \(0.0505539\pi\)
\(840\) 8.99418e10 + 2.76812e11i 0.180653 + 0.555992i
\(841\) −3.49454e11 + 2.53893e11i −0.698564 + 0.507536i
\(842\) 2.57874e10 + 3.54934e10i 0.0513050 + 0.0706153i
\(843\) −9.28711e10 + 3.01756e10i −0.183895 + 0.0597511i
\(844\) 4.02637e11 + 1.30825e11i 0.793495 + 0.257822i
\(845\) 4.71723e10 + 3.42727e10i 0.0925253 + 0.0672235i
\(846\) 9.05034e11i 1.76678i
\(847\) −6.70509e11 3.94934e10i −1.30278 0.0767345i
\(848\) 1.64963e11 0.319010
\(849\) 2.93201e11 4.03557e11i 0.564333 0.776738i
\(850\) 4.05908e10 1.24926e11i 0.0777592 0.239318i
\(851\) 1.45714e11 + 4.48461e11i 0.277832 + 0.855079i
\(852\) 2.74796e11 1.99651e11i 0.521497 0.378890i
\(853\) 3.97783e11 + 5.47502e11i 0.751364 + 1.03416i 0.997884 + 0.0650261i \(0.0207131\pi\)
−0.246519 + 0.969138i \(0.579287\pi\)
\(854\) −3.19150e11 + 1.03698e11i −0.600017 + 0.194957i
\(855\) −8.40166e11 2.72987e11i −1.57217 0.510830i
\(856\) −3.65476e10 2.65534e10i −0.0680713 0.0494567i
\(857\) 6.23598e11i 1.15606i −0.816015 0.578031i \(-0.803821\pi\)
0.816015 0.578031i \(-0.196179\pi\)
\(858\) 5.97033e11 + 1.12653e11i 1.10166 + 0.207872i
\(859\) −8.88179e11 −1.63128 −0.815639 0.578561i \(-0.803614\pi\)
−0.815639 + 0.578561i \(0.803614\pi\)
\(860\) 2.14406e11 2.95104e11i 0.391961 0.539487i
\(861\) 4.45439e11 1.37092e12i 0.810542 2.49459i
\(862\) 1.65288e11 + 5.08705e11i 0.299373 + 0.921376i
\(863\) 7.51468e11 5.45973e11i 1.35478 0.984302i 0.356017 0.934479i \(-0.384134\pi\)
0.998758 0.0498227i \(-0.0158656\pi\)
\(864\) 9.76676e10 + 1.34428e11i 0.175265 + 0.241232i
\(865\) 2.89172e11 9.39578e10i 0.516526 0.167830i
\(866\) −9.04949e10 2.94036e10i −0.160899 0.0522792i
\(867\) 3.18441e11 + 2.31361e11i 0.563577 + 0.409463i
\(868\) 5.86787e11i 1.03372i
\(869\) 2.81837e11 2.65725e11i 0.494218 0.465965i
\(870\) −1.89652e11 −0.331039
\(871\) 1.43438e11 1.97425e11i 0.249225 0.343028i
\(872\) −3.14713e10 + 9.68587e10i −0.0544313 + 0.167522i
\(873\) 3.77900e11 + 1.16306e12i 0.650609 + 2.00237i
\(874\) −2.46899e11 + 1.79383e11i −0.423130 + 0.307422i
\(875\) −4.82320e11 6.63856e11i −0.822816 1.13251i
\(876\) −3.66586e11 + 1.19111e11i −0.622529 + 0.202272i
\(877\) −8.85990e10 2.87875e10i −0.149772 0.0486638i 0.233172 0.972436i \(-0.425090\pi\)
−0.382943 + 0.923772i \(0.625090\pi\)
\(878\) −4.72225e10 3.43092e10i −0.0794641 0.0577341i
\(879\) 2.18076e11i 0.365302i
\(880\) 5.28408e10 9.65739e10i 0.0881127 0.161038i
\(881\) −7.51292e10 −0.124711 −0.0623555 0.998054i \(-0.519861\pi\)
−0.0623555 + 0.998054i \(0.519861\pi\)
\(882\) −3.49728e11 + 4.81360e11i −0.577905 + 0.795418i
\(883\) 2.67850e11 8.24359e11i 0.440605 1.35604i −0.446627 0.894720i \(-0.647375\pi\)
0.887232 0.461323i \(-0.152625\pi\)
\(884\) −6.69460e10 2.06039e11i −0.109626 0.337396i
\(885\) 8.95426e11 6.50565e11i 1.45968 1.06052i
\(886\) −5.57672e10 7.67570e10i −0.0904991 0.124561i
\(887\) 5.35997e11 1.74156e11i 0.865900 0.281348i 0.157810 0.987470i \(-0.449557\pi\)
0.708091 + 0.706122i \(0.249557\pi\)
\(888\) −4.99259e11 1.62219e11i −0.802923 0.260886i
\(889\) 5.13867e11 + 3.73346e11i 0.822704 + 0.597729i
\(890\) 5.55827e10i 0.0885889i
\(891\) −7.48697e10 5.83273e11i −0.118794 0.925467i
\(892\) −1.98103e11 −0.312919
\(893\) −5.37675e11 + 7.40046e11i −0.845501 + 1.16373i
\(894\) −1.08233e11 + 3.33106e11i −0.169437 + 0.521473i
\(895\) 7.32114e10 + 2.25321e11i 0.114100 + 0.351164i
\(896\) −6.01462e10 + 4.36987e10i −0.0933202 + 0.0678011i
\(897\) 3.91980e11 + 5.39514e11i 0.605472 + 0.833361i
\(898\) 4.51352e11 1.46653e11i 0.694081 0.225521i
\(899\) −3.63634e11 1.18152e11i −0.556706 0.180885i
\(900\) −2.41865e11 1.75725e11i −0.368641 0.267833i
\(901\) 6.49370e11i 0.985355i
\(902\) −4.92844e11 + 2.33120e11i −0.744532 + 0.352170i
\(903\) 2.71956e12 4.09023
\(904\) 8.77884e10 1.20830e11i 0.131451 0.180927i
\(905\) 1.06028e11 3.26319e11i 0.158061 0.486461i
\(906\) 3.43047e11 + 1.05579e12i 0.509144 + 1.56698i
\(907\) −3.98195e11 + 2.89306e11i −0.588393 + 0.427492i −0.841740 0.539883i \(-0.818468\pi\)
0.253347 + 0.967375i \(0.418468\pi\)
\(908\) 3.91843e9 + 5.39326e9i 0.00576460 + 0.00793429i
\(909\) −9.94965e11 + 3.23284e11i −1.45731 + 0.473509i
\(910\) −4.06042e11 1.31931e11i −0.592114 0.192389i
\(911\) 8.00259e11 + 5.81422e11i 1.16187 + 0.844147i 0.990013 0.140975i \(-0.0450238\pi\)
0.171856 + 0.985122i \(0.445024\pi\)
\(912\) 3.39753e11i 0.491116i
\(913\) 1.85762e11 + 3.92724e11i 0.267346 + 0.565203i
\(914\) −2.19622e10 −0.0314696
\(915\) −3.56891e11 + 4.91219e11i −0.509157 + 0.700794i
\(916\) 1.46720e11 4.51559e11i 0.208405 0.641406i
\(917\) −4.85158e11 1.49316e12i −0.686129 2.11169i
\(918\) −5.29169e11 + 3.84464e11i −0.745116 + 0.541358i
\(919\) −5.39015e11 7.41891e11i −0.755682 1.04011i −0.997561 0.0698008i \(-0.977764\pi\)
0.241879 0.970306i \(-0.422236\pi\)
\(920\) 1.14917e11 3.73388e10i 0.160410 0.0521205i
\(921\) −1.85530e12 6.02822e11i −2.57854 0.837820i
\(922\) −3.22111e11 2.34027e11i −0.445740 0.323849i
\(923\) 4.98239e11i 0.686484i
\(924\) 8.14066e11 1.04495e11i 1.11679 0.143353i
\(925\) 4.66882e11 0.637735
\(926\) 2.70262e11 3.71984e11i 0.367571 0.505918i
\(927\) −3.05417e11 + 9.39976e11i −0.413594 + 1.27291i
\(928\) −1.49696e10 4.60717e10i −0.0201845 0.0621215i
\(929\) 7.78464e11 5.65587e11i 1.04514 0.759341i 0.0738599 0.997269i \(-0.476468\pi\)
0.971283 + 0.237928i \(0.0764682\pi\)
\(930\) 6.24063e11 + 8.58948e11i 0.834250 + 1.14825i
\(931\) 5.71945e11 1.85836e11i 0.761300 0.247361i
\(932\) −1.99846e11 6.49338e10i −0.264869 0.0860611i
\(933\) −1.77443e12 1.28920e12i −2.34170 1.70134i
\(934\) 6.15634e11i 0.808975i
\(935\) 3.80159e11 + 2.08005e11i 0.497414 + 0.272162i
\(936\) −4.93075e11 −0.642406
\(937\) 4.51936e11 6.22037e11i 0.586299 0.806971i −0.408070 0.912951i \(-0.633798\pi\)
0.994368 + 0.105980i \(0.0337979\pi\)
\(938\) 1.01869e11 3.13519e11i 0.131592 0.404998i
\(939\) −2.42307e11 7.45746e11i −0.311677 0.959242i
\(940\) 2.93004e11 2.12880e11i 0.375286 0.272661i
\(941\) −8.14277e11 1.12076e12i −1.03852 1.42940i −0.898357 0.439267i \(-0.855238\pi\)
−0.140160 0.990129i \(-0.544762\pi\)
\(942\) −1.01741e12 + 3.30577e11i −1.29209 + 0.419826i
\(943\) −5.69128e11 1.84921e11i −0.719720 0.233851i
\(944\) 2.28718e11 + 1.66174e11i 0.288013 + 0.209254i
\(945\) 1.28902e12i 1.61634i
\(946\) −7.05623e11 7.48408e11i −0.881066 0.934488i
\(947\) −1.18284e12 −1.47071 −0.735355 0.677682i \(-0.762985\pi\)
−0.735355 + 0.677682i \(0.762985\pi\)
\(948\) −2.78212e11 + 3.82926e11i −0.344463 + 0.474113i
\(949\) 1.74718e11 5.37726e11i 0.215413 0.662974i
\(950\) 9.33757e10 + 2.87381e11i 0.114641 + 0.352828i
\(951\) −1.41875e12 + 1.03078e12i −1.73453 + 1.26021i
\(952\) −1.72018e11 2.36762e11i −0.209424 0.288247i
\(953\) 7.21947e11 2.34575e11i 0.875253 0.284387i 0.163268 0.986582i \(-0.447796\pi\)
0.711985 + 0.702195i \(0.247796\pi\)
\(954\) 1.40562e12 + 4.56715e11i 1.69698 + 0.551381i
\(955\) −5.96857e11 4.33642e11i −0.717558 0.521336i
\(956\) 3.52548e11i 0.422072i
\(957\) −9.91595e10 + 5.25519e11i −0.118219 + 0.626529i
\(958\) 5.82194e11 0.691203
\(959\) −4.74308e11 + 6.52829e11i −0.560771 + 0.771836i
\(960\) −4.15682e10 + 1.27934e11i −0.0489414 + 0.150626i
\(961\) 3.97886e11 + 1.22457e12i 0.466515 + 1.43579i
\(962\) 6.22963e11 4.52609e11i 0.727381 0.528473i
\(963\) −2.37901e11 3.27442e11i −0.276625 0.380741i
\(964\) −2.89899e11 + 9.41939e10i −0.335690 + 0.109072i
\(965\) 5.40729e11 + 1.75694e11i 0.623549 + 0.202603i
\(966\) 7.28813e11 + 5.29514e11i 0.836965 + 0.608091i
\(967\) 1.02464e12i 1.17183i 0.810371 + 0.585917i \(0.199266\pi\)
−0.810371 + 0.585917i \(0.800734\pi\)
\(968\) −2.39976e11 1.96914e11i −0.273317 0.224272i
\(969\) 1.33742e12 1.51696
\(970\) −2.87650e11 + 3.95916e11i −0.324921 + 0.447215i
\(971\) −4.52002e11 + 1.39112e12i −0.508468 + 1.56490i 0.286392 + 0.958112i \(0.407544\pi\)
−0.794861 + 0.606792i \(0.792456\pi\)
\(972\) −1.05803e10 3.25627e10i −0.0118531 0.0364800i
\(973\) 1.19594e12 8.68899e11i 1.33431 0.969433i
\(974\) −6.32078e11 8.69981e11i −0.702320 0.966661i
\(975\) 6.27973e11 2.04041e11i 0.694900 0.225787i
\(976\) −1.47501e11 4.79259e10i −0.162553 0.0528167i
\(977\) −9.43647e11 6.85599e11i −1.03569 0.752475i −0.0662531 0.997803i \(-0.521104\pi\)
−0.969440 + 0.245328i \(0.921104\pi\)
\(978\) 1.61142e12i 1.76138i
\(979\) 1.54018e11 + 2.90615e10i 0.167664 + 0.0316364i
\(980\) −2.38102e11 −0.258142
\(981\) −5.36323e11 + 7.38186e11i −0.579096 + 0.797058i
\(982\) −2.97017e11 + 9.14123e11i −0.319400 + 0.983012i
\(983\) −1.71334e10 5.27313e10i −0.0183498 0.0564747i 0.941462 0.337118i \(-0.109452\pi\)
−0.959812 + 0.280643i \(0.909452\pi\)
\(984\) 5.38968e11 3.91583e11i 0.574887 0.417680i
\(985\) 9.61677e10 + 1.32363e11i 0.102161 + 0.140612i
\(986\) 1.81359e11 5.89271e10i 0.191881 0.0623458i
\(987\) 2.56805e12 + 8.34410e11i 2.70604 + 0.879247i
\(988\) 4.03187e11 + 2.92932e11i 0.423135 + 0.307425i
\(989\) 1.12901e12i 1.18008i
\(990\) 7.17620e11 6.76596e11i 0.747057 0.704350i
\(991\) 2.23267e11 0.231489 0.115745 0.993279i \(-0.463075\pi\)
0.115745 + 0.993279i \(0.463075\pi\)
\(992\) −1.59404e11 + 2.19401e11i −0.164609 + 0.226564i
\(993\) −5.14589e11 + 1.58374e12i −0.529253 + 1.62887i
\(994\) 2.07985e11 + 6.40113e11i 0.213053 + 0.655709i
\(995\) −3.64320e11 + 2.64694e11i −0.371698 + 0.270055i
\(996\) −3.12034e11 4.29478e11i −0.317077 0.436419i
\(997\) 1.03474e12 3.36206e11i 1.04725 0.340271i 0.265660 0.964067i \(-0.414410\pi\)
0.781587 + 0.623796i \(0.214410\pi\)
\(998\) −1.91073e10 6.20834e9i −0.0192609 0.00625826i
\(999\) −1.88086e12 1.36653e12i −1.88841 1.37201i
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 22.9.d.a.7.5 32
11.5 even 5 242.9.b.e.241.6 32
11.6 odd 10 242.9.b.e.241.5 32
11.8 odd 10 inner 22.9.d.a.19.5 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
22.9.d.a.7.5 32 1.1 even 1 trivial
22.9.d.a.19.5 yes 32 11.8 odd 10 inner
242.9.b.e.241.5 32 11.6 odd 10
242.9.b.e.241.6 32 11.5 even 5