Properties

Label 20.8.e.b.3.3
Level $20$
Weight $8$
Character 20.3
Analytic conductor $6.248$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [20,8,Mod(3,20)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(20, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("20.3");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 20.e (of order \(4\), degree \(2\), 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: \(6.24770050968\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 3.3
Character \(\chi\) \(=\) 20.3
Dual form 20.8.e.b.7.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-9.99887 - 5.29363i) q^{2} +(51.5668 - 51.5668i) q^{3} +(71.9550 + 105.861i) q^{4} +(278.010 - 28.9057i) q^{5} +(-788.585 + 242.634i) q^{6} +(645.384 + 645.384i) q^{7} +(-159.082 - 1439.39i) q^{8} -3131.26i q^{9} +O(q^{10})\) \(q+(-9.99887 - 5.29363i) q^{2} +(51.5668 - 51.5668i) q^{3} +(71.9550 + 105.861i) q^{4} +(278.010 - 28.9057i) q^{5} +(-788.585 + 242.634i) q^{6} +(645.384 + 645.384i) q^{7} +(-159.082 - 1439.39i) q^{8} -3131.26i q^{9} +(-2932.80 - 1182.66i) q^{10} -5339.44i q^{11} +(9169.38 + 1748.41i) q^{12} +(-149.045 - 149.045i) q^{13} +(-3036.69 - 9869.54i) q^{14} +(12845.5 - 15826.6i) q^{15} +(-6028.96 + 15234.4i) q^{16} +(-20864.6 + 20864.6i) q^{17} +(-16575.8 + 31309.1i) q^{18} -20748.8 q^{19} +(23064.2 + 27350.4i) q^{20} +66560.7 q^{21} +(-28265.0 + 53388.4i) q^{22} +(44759.3 - 44759.3i) q^{23} +(-82428.1 - 66021.4i) q^{24} +(76453.9 - 16072.2i) q^{25} +(701.294 + 2279.27i) q^{26} +(-48692.7 - 48692.7i) q^{27} +(-21882.2 + 114759. i) q^{28} +88593.8i q^{29} +(-212221. + 90249.4i) q^{30} -42483.8i q^{31} +(140928. - 120412. i) q^{32} +(-275338. - 275338. i) q^{33} +(319072. - 98173.0i) q^{34} +(198078. + 160768. i) q^{35} +(331478. - 225310. i) q^{36} +(-316536. + 316536. i) q^{37} +(207465. + 109837. i) q^{38} -15371.6 q^{39} +(-85832.9 - 395566. i) q^{40} +488041. q^{41} +(-665533. - 352348. i) q^{42} +(-456036. + 456036. i) q^{43} +(565236. - 384199. i) q^{44} +(-90511.5 - 870522. i) q^{45} +(-684482. + 210604. i) q^{46} +(-110971. - 110971. i) q^{47} +(474695. + 1.09648e6i) q^{48} +9498.09i q^{49} +(-849533. - 244015. i) q^{50} +2.15184e6i q^{51} +(5053.48 - 26502.6i) q^{52} +(1.13839e6 + 1.13839e6i) q^{53} +(229111. + 744633. i) q^{54} +(-154340. - 1.48442e6i) q^{55} +(826291. - 1.03163e6i) q^{56} +(-1.06995e6 + 1.06995e6i) q^{57} +(468982. - 885838. i) q^{58} -1.06089e6 q^{59} +(2.59972e6 + 221027. i) q^{60} -1.50464e6 q^{61} +(-224893. + 424790. i) q^{62} +(2.02087e6 - 2.02087e6i) q^{63} +(-2.04654e6 + 457961. i) q^{64} +(-45744.3 - 37127.8i) q^{65} +(1.29553e6 + 4.21060e6i) q^{66} +(430338. + 430338. i) q^{67} +(-3.71005e6 - 707428. i) q^{68} -4.61619e6i q^{69} +(-1.12952e6 - 2.65605e6i) q^{70} -1.74713e6i q^{71} +(-4.50711e6 + 498127. i) q^{72} +(2.65975e6 + 2.65975e6i) q^{73} +(4.84062e6 - 1.48938e6i) q^{74} +(3.11369e6 - 4.77127e6i) q^{75} +(-1.49298e6 - 2.19649e6i) q^{76} +(3.44599e6 - 3.44599e6i) q^{77} +(153698. + 81371.4i) q^{78} -1.27155e6 q^{79} +(-1.23575e6 + 4.40959e6i) q^{80} +1.82623e6 q^{81} +(-4.87986e6 - 2.58351e6i) q^{82} +(-2.49865e6 + 2.49865e6i) q^{83} +(4.78938e6 + 7.04616e6i) q^{84} +(-5.19746e6 + 6.40367e6i) q^{85} +(6.97393e6 - 2.14576e6i) q^{86} +(4.56849e6 + 4.56849e6i) q^{87} +(-7.68554e6 + 849407. i) q^{88} +2.86155e6i q^{89} +(-3.70321e6 + 9.18338e6i) q^{90} -192383. i q^{91} +(7.95891e6 + 1.51760e6i) q^{92} +(-2.19075e6 - 2.19075e6i) q^{93} +(522146. + 1.69702e6i) q^{94} +(-5.76838e6 + 599760. i) q^{95} +(1.05796e6 - 1.34765e7i) q^{96} +(-4.61701e6 + 4.61701e6i) q^{97} +(50279.4 - 94970.2i) q^{98} -1.67192e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 14 q^{2} - 560 q^{5} + 104 q^{6} - 3052 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 14 q^{2} - 560 q^{5} + 104 q^{6} - 3052 q^{8} + 390 q^{10} + 10960 q^{12} - 28564 q^{13} - 12104 q^{16} - 27012 q^{17} + 95298 q^{18} + 97180 q^{20} - 2352 q^{21} - 191320 q^{22} - 112580 q^{25} + 604628 q^{26} - 142800 q^{28} - 252760 q^{30} - 73976 q^{32} - 248080 q^{33} - 328580 q^{36} - 108732 q^{37} - 406560 q^{38} - 680660 q^{40} + 2019472 q^{41} + 1616840 q^{42} - 827660 q^{45} - 2690616 q^{46} + 549280 q^{48} + 1343690 q^{50} - 6025332 q^{52} + 5672196 q^{53} + 4064064 q^{56} - 1796160 q^{57} + 3463736 q^{58} + 3280240 q^{60} - 5624928 q^{61} + 2750760 q^{62} + 75940 q^{65} - 2175120 q^{66} - 5673084 q^{68} - 11417280 q^{70} + 4328964 q^{72} - 22930604 q^{73} - 4045600 q^{76} + 10982160 q^{77} + 27127080 q^{78} + 34488560 q^{80} + 21593004 q^{81} - 13289192 q^{82} - 28299060 q^{85} - 2245656 q^{86} - 38612320 q^{88} - 38642970 q^{90} - 22809360 q^{92} + 31343120 q^{93} + 49033664 q^{96} - 11169292 q^{97} + 45095638 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(17\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −9.99887 5.29363i −0.883784 0.467895i
\(3\) 51.5668 51.5668i 1.10267 1.10267i 0.108583 0.994087i \(-0.465369\pi\)
0.994087 0.108583i \(-0.0346312\pi\)
\(4\) 71.9550 + 105.861i 0.562148 + 0.827036i
\(5\) 278.010 28.9057i 0.994638 0.103416i
\(6\) −788.585 + 242.634i −1.49046 + 0.458588i
\(7\) 645.384 + 645.384i 0.711173 + 0.711173i 0.966781 0.255608i \(-0.0822756\pi\)
−0.255608 + 0.966781i \(0.582276\pi\)
\(8\) −159.082 1439.39i −0.109851 0.993948i
\(9\) 3131.26i 1.43176i
\(10\) −2932.80 1182.66i −0.927433 0.373989i
\(11\) 5339.44i 1.20954i −0.796399 0.604771i \(-0.793265\pi\)
0.796399 0.604771i \(-0.206735\pi\)
\(12\) 9169.38 + 1748.41i 1.53181 + 0.292084i
\(13\) −149.045 149.045i −0.0188155 0.0188155i 0.697636 0.716452i \(-0.254235\pi\)
−0.716452 + 0.697636i \(0.754235\pi\)
\(14\) −3036.69 9869.54i −0.295769 0.961277i
\(15\) 12845.5 15826.6i 0.982724 1.21079i
\(16\) −6028.96 + 15234.4i −0.367979 + 0.929834i
\(17\) −20864.6 + 20864.6i −1.03000 + 1.03000i −0.0304678 + 0.999536i \(0.509700\pi\)
−0.999536 + 0.0304678i \(0.990300\pi\)
\(18\) −16575.8 + 31309.1i −0.669915 + 1.26537i
\(19\) −20748.8 −0.693995 −0.346997 0.937866i \(-0.612799\pi\)
−0.346997 + 0.937866i \(0.612799\pi\)
\(20\) 23064.2 + 27350.4i 0.644663 + 0.764467i
\(21\) 66560.7 1.56838
\(22\) −28265.0 + 53388.4i −0.565939 + 1.06897i
\(23\) 44759.3 44759.3i 0.767072 0.767072i −0.210518 0.977590i \(-0.567515\pi\)
0.977590 + 0.210518i \(0.0675150\pi\)
\(24\) −82428.1 66021.4i −1.21713 0.974867i
\(25\) 76453.9 16072.2i 0.978610 0.205724i
\(26\) 701.294 + 2279.27i 0.00782517 + 0.0254326i
\(27\) −48692.7 48692.7i −0.476092 0.476092i
\(28\) −21882.2 + 114759.i −0.188381 + 0.987950i
\(29\) 88593.8i 0.674544i 0.941407 + 0.337272i \(0.109504\pi\)
−0.941407 + 0.337272i \(0.890496\pi\)
\(30\) −212221. + 90249.4i −1.43504 + 0.610267i
\(31\) 42483.8i 0.256128i −0.991766 0.128064i \(-0.959124\pi\)
0.991766 0.128064i \(-0.0408763\pi\)
\(32\) 140928. 120412.i 0.760279 0.649597i
\(33\) −275338. 275338.i −1.33373 1.33373i
\(34\) 319072. 98173.0i 1.39223 0.428367i
\(35\) 198078. + 160768.i 0.780906 + 0.633813i
\(36\) 331478. 225310.i 1.18412 0.804863i
\(37\) −316536. + 316536.i −1.02735 + 1.02735i −0.0277298 + 0.999615i \(0.508828\pi\)
−0.999615 + 0.0277298i \(0.991172\pi\)
\(38\) 207465. + 109837.i 0.613341 + 0.324717i
\(39\) −15371.6 −0.0414946
\(40\) −85832.9 395566.i −0.212053 0.977258i
\(41\) 488041. 1.10589 0.552946 0.833217i \(-0.313504\pi\)
0.552946 + 0.833217i \(0.313504\pi\)
\(42\) −665533. 352348.i −1.38611 0.733836i
\(43\) −456036. + 456036.i −0.874700 + 0.874700i −0.992980 0.118280i \(-0.962262\pi\)
0.118280 + 0.992980i \(0.462262\pi\)
\(44\) 565236. 384199.i 1.00034 0.679942i
\(45\) −90511.5 870522.i −0.148068 1.42409i
\(46\) −684482. + 210604.i −1.03684 + 0.319017i
\(47\) −110971. 110971.i −0.155907 0.155907i 0.624843 0.780750i \(-0.285163\pi\)
−0.780750 + 0.624843i \(0.785163\pi\)
\(48\) 474695. + 1.09648e6i 0.619541 + 1.43106i
\(49\) 9498.09i 0.0115332i
\(50\) −849533. 244015.i −0.961137 0.276072i
\(51\) 2.15184e6i 2.27151i
\(52\) 5053.48 26502.6i 0.00498401 0.0261382i
\(53\) 1.13839e6 + 1.13839e6i 1.05033 + 1.05033i 0.998664 + 0.0516677i \(0.0164537\pi\)
0.0516677 + 0.998664i \(0.483546\pi\)
\(54\) 229111. + 744633.i 0.198001 + 0.643523i
\(55\) −154340. 1.48442e6i −0.125086 1.20306i
\(56\) 826291. 1.03163e6i 0.628745 0.784992i
\(57\) −1.06995e6 + 1.06995e6i −0.765247 + 0.765247i
\(58\) 468982. 885838.i 0.315616 0.596151i
\(59\) −1.06089e6 −0.672494 −0.336247 0.941774i \(-0.609158\pi\)
−0.336247 + 0.941774i \(0.609158\pi\)
\(60\) 2.59972e6 + 221027.i 1.55381 + 0.132104i
\(61\) −1.50464e6 −0.848747 −0.424373 0.905487i \(-0.639506\pi\)
−0.424373 + 0.905487i \(0.639506\pi\)
\(62\) −224893. + 424790.i −0.119841 + 0.226362i
\(63\) 2.02087e6 2.02087e6i 1.01823 1.01823i
\(64\) −2.04654e6 + 457961.i −0.975865 + 0.218373i
\(65\) −45744.3 37127.8i −0.0206605 0.0167688i
\(66\) 1.29553e6 + 4.21060e6i 0.554682 + 1.80277i
\(67\) 430338. + 430338.i 0.174802 + 0.174802i 0.789086 0.614283i \(-0.210555\pi\)
−0.614283 + 0.789086i \(0.710555\pi\)
\(68\) −3.71005e6 707428.i −1.43087 0.272836i
\(69\) 4.61619e6i 1.69165i
\(70\) −1.12952e6 2.65605e6i −0.393595 0.925536i
\(71\) 1.74713e6i 0.579323i −0.957129 0.289662i \(-0.906457\pi\)
0.957129 0.289662i \(-0.0935428\pi\)
\(72\) −4.50711e6 + 498127.i −1.42310 + 0.157281i
\(73\) 2.65975e6 + 2.65975e6i 0.800222 + 0.800222i 0.983130 0.182908i \(-0.0585510\pi\)
−0.182908 + 0.983130i \(0.558551\pi\)
\(74\) 4.84062e6 1.48938e6i 1.38864 0.427261i
\(75\) 3.11369e6 4.77127e6i 0.852239 1.30593i
\(76\) −1.49298e6 2.19649e6i −0.390128 0.573959i
\(77\) 3.44599e6 3.44599e6i 0.860194 0.860194i
\(78\) 153698. + 81371.4i 0.0366723 + 0.0194151i
\(79\) −1.27155e6 −0.290160 −0.145080 0.989420i \(-0.546344\pi\)
−0.145080 + 0.989420i \(0.546344\pi\)
\(80\) −1.23575e6 + 4.40959e6i −0.269846 + 0.962904i
\(81\) 1.82623e6 0.381819
\(82\) −4.87986e6 2.58351e6i −0.977369 0.517441i
\(83\) −2.49865e6 + 2.49865e6i −0.479659 + 0.479659i −0.905023 0.425364i \(-0.860146\pi\)
0.425364 + 0.905023i \(0.360146\pi\)
\(84\) 4.78938e6 + 7.04616e6i 0.881661 + 1.29711i
\(85\) −5.19746e6 + 6.40367e6i −0.917962 + 1.13100i
\(86\) 6.97393e6 2.14576e6i 1.18231 0.363778i
\(87\) 4.56849e6 + 4.56849e6i 0.743799 + 0.743799i
\(88\) −7.68554e6 + 849407.i −1.20222 + 0.132870i
\(89\) 2.86155e6i 0.430266i 0.976585 + 0.215133i \(0.0690185\pi\)
−0.976585 + 0.215133i \(0.930982\pi\)
\(90\) −3.70321e6 + 9.18338e6i −0.535463 + 1.32786i
\(91\) 192383.i 0.0267622i
\(92\) 7.95891e6 + 1.51760e6i 1.06560 + 0.203188i
\(93\) −2.19075e6 2.19075e6i −0.282425 0.282425i
\(94\) 522146. + 1.69702e6i 0.0648402 + 0.210737i
\(95\) −5.76838e6 + 599760.i −0.690273 + 0.0717704i
\(96\) 1.05796e6 1.34765e7i 0.122045 1.55463i
\(97\) −4.61701e6 + 4.61701e6i −0.513641 + 0.513641i −0.915640 0.401999i \(-0.868316\pi\)
0.401999 + 0.915640i \(0.368316\pi\)
\(98\) 50279.4 94970.2i 0.00539633 0.0101929i
\(99\) −1.67192e7 −1.73178
\(100\) 7.20265e6 + 6.93699e6i 0.720265 + 0.693699i
\(101\) −6.96214e6 −0.672385 −0.336193 0.941793i \(-0.609139\pi\)
−0.336193 + 0.941793i \(0.609139\pi\)
\(102\) 1.13910e7 2.15160e7i 1.06283 2.00752i
\(103\) 4.05629e6 4.05629e6i 0.365762 0.365762i −0.500167 0.865929i \(-0.666728\pi\)
0.865929 + 0.500167i \(0.166728\pi\)
\(104\) −190824. + 238245.i −0.0166347 + 0.0207686i
\(105\) 1.85045e7 1.92399e6i 1.55997 0.162196i
\(106\) −5.35642e6 1.74089e7i −0.436821 1.41971i
\(107\) 1.26110e7 + 1.26110e7i 0.995194 + 0.995194i 0.999989 0.00479457i \(-0.00152616\pi\)
−0.00479457 + 0.999989i \(0.501526\pi\)
\(108\) 1.65096e6 8.65832e6i 0.126111 0.661379i
\(109\) 1.14527e7i 0.847062i −0.905882 0.423531i \(-0.860790\pi\)
0.905882 0.423531i \(-0.139210\pi\)
\(110\) −6.31472e6 + 1.56595e7i −0.452355 + 1.12177i
\(111\) 3.26454e7i 2.26565i
\(112\) −1.37230e7 + 5.94105e6i −0.922969 + 0.399576i
\(113\) −1.20471e7 1.20471e7i −0.785430 0.785430i 0.195311 0.980741i \(-0.437428\pi\)
−0.980741 + 0.195311i \(0.937428\pi\)
\(114\) 1.63622e7 5.03438e6i 1.03437 0.318258i
\(115\) 1.11497e7 1.37373e7i 0.683631 0.842287i
\(116\) −9.37859e6 + 6.37476e6i −0.557872 + 0.379194i
\(117\) −466700. + 466700.i −0.0269394 + 0.0269394i
\(118\) 1.06077e7 + 5.61596e6i 0.594340 + 0.314657i
\(119\) −2.69314e7 −1.46502
\(120\) −2.48242e7 1.59720e7i −1.31142 0.843769i
\(121\) −9.02242e6 −0.462993
\(122\) 1.50447e7 + 7.96501e6i 0.750109 + 0.397125i
\(123\) 2.51667e7 2.51667e7i 1.21943 1.21943i
\(124\) 4.49736e6 3.05692e6i 0.211827 0.143982i
\(125\) 2.07904e7 6.67817e6i 0.952088 0.305825i
\(126\) −3.09041e7 + 9.50868e6i −1.37632 + 0.423471i
\(127\) 6.70344e6 + 6.70344e6i 0.290392 + 0.290392i 0.837235 0.546843i \(-0.184171\pi\)
−0.546843 + 0.837235i \(0.684171\pi\)
\(128\) 2.28874e7 + 6.25451e6i 0.964630 + 0.263608i
\(129\) 4.70326e7i 1.92901i
\(130\) 260851. + 613389.i 0.0104133 + 0.0244869i
\(131\) 2.52854e7i 0.982698i −0.870963 0.491349i \(-0.836504\pi\)
0.870963 0.491349i \(-0.163496\pi\)
\(132\) 9.33551e6 4.89593e7i 0.353288 1.85279i
\(133\) −1.33910e7 1.33910e7i −0.493550 0.493550i
\(134\) −2.02484e6 6.58094e6i −0.0726984 0.236277i
\(135\) −1.49445e7 1.21295e7i −0.522774 0.424303i
\(136\) 3.33515e7 + 2.67131e7i 1.13692 + 0.910623i
\(137\) 6.20450e6 6.20450e6i 0.206151 0.206151i −0.596478 0.802629i \(-0.703434\pi\)
0.802629 + 0.596478i \(0.203434\pi\)
\(138\) −2.44364e7 + 4.61567e7i −0.791517 + 1.49506i
\(139\) −1.52257e7 −0.480868 −0.240434 0.970665i \(-0.577290\pi\)
−0.240434 + 0.970665i \(0.577290\pi\)
\(140\) −2.76626e6 + 3.25368e7i −0.0852010 + 1.00213i
\(141\) −1.14448e7 −0.343829
\(142\) −9.24866e6 + 1.74693e7i −0.271063 + 0.511997i
\(143\) −795818. + 795818.i −0.0227582 + 0.0227582i
\(144\) 4.77030e7 + 1.88783e7i 1.33130 + 0.526858i
\(145\) 2.56087e6 + 2.46299e7i 0.0697588 + 0.670927i
\(146\) −1.25148e7 4.06742e7i −0.332803 1.08164i
\(147\) 489786. + 489786.i 0.0127173 + 0.0127173i
\(148\) −5.62850e7 1.07324e7i −1.42717 0.272132i
\(149\) 3.57121e7i 0.884431i −0.896909 0.442215i \(-0.854193\pi\)
0.896909 0.442215i \(-0.145807\pi\)
\(150\) −5.63908e7 + 3.12246e7i −1.36423 + 0.755401i
\(151\) 9.51884e6i 0.224991i −0.993652 0.112495i \(-0.964116\pi\)
0.993652 0.112495i \(-0.0358844\pi\)
\(152\) 3.30076e6 + 2.98657e7i 0.0762362 + 0.689795i
\(153\) 6.53326e7 + 6.53326e7i 1.47472 + 1.47472i
\(154\) −5.26978e7 + 1.62142e7i −1.16271 + 0.357745i
\(155\) −1.22803e6 1.18109e7i −0.0264878 0.254755i
\(156\) −1.10606e6 1.62724e6i −0.0233261 0.0343176i
\(157\) 4.61516e6 4.61516e6i 0.0951783 0.0951783i −0.657914 0.753093i \(-0.728561\pi\)
0.753093 + 0.657914i \(0.228561\pi\)
\(158\) 1.27140e7 + 6.73109e6i 0.256438 + 0.135764i
\(159\) 1.17406e8 2.31634
\(160\) 3.56988e7 3.75493e7i 0.689023 0.724739i
\(161\) 5.77739e7 1.09104
\(162\) −1.82602e7 9.66737e6i −0.337445 0.178651i
\(163\) −2.06551e7 + 2.06551e7i −0.373568 + 0.373568i −0.868775 0.495207i \(-0.835092\pi\)
0.495207 + 0.868775i \(0.335092\pi\)
\(164\) 3.51170e7 + 5.16643e7i 0.621675 + 0.914613i
\(165\) −8.45054e7 6.85877e7i −1.46450 1.18865i
\(166\) 3.82107e7 1.17568e7i 0.648345 0.199485i
\(167\) −6.72725e7 6.72725e7i −1.11771 1.11771i −0.992076 0.125636i \(-0.959903\pi\)
−0.125636 0.992076i \(-0.540097\pi\)
\(168\) −1.05886e7 9.58069e7i −0.172288 1.55889i
\(169\) 6.27041e7i 0.999292i
\(170\) 8.58674e7 3.65161e7i 1.34047 0.570050i
\(171\) 6.49701e7i 0.993635i
\(172\) −8.10903e7 1.54622e7i −1.21512 0.231698i
\(173\) −3.98453e7 3.98453e7i −0.585080 0.585080i 0.351215 0.936295i \(-0.385769\pi\)
−0.936295 + 0.351215i \(0.885769\pi\)
\(174\) −2.14959e7 6.98637e7i −0.309338 1.00538i
\(175\) 5.97149e7 + 3.89694e7i 0.842266 + 0.549656i
\(176\) 8.13432e7 + 3.21913e7i 1.12467 + 0.445086i
\(177\) −5.47067e7 + 5.47067e7i −0.741539 + 0.741539i
\(178\) 1.51480e7 2.86123e7i 0.201319 0.380262i
\(179\) −1.33454e8 −1.73919 −0.869595 0.493766i \(-0.835620\pi\)
−0.869595 + 0.493766i \(0.835620\pi\)
\(180\) 8.56413e7 7.22200e7i 1.09453 0.923005i
\(181\) −2.86524e7 −0.359158 −0.179579 0.983744i \(-0.557474\pi\)
−0.179579 + 0.983744i \(0.557474\pi\)
\(182\) −1.01840e6 + 1.92361e6i −0.0125219 + 0.0236520i
\(183\) −7.75894e7 + 7.75894e7i −0.935888 + 0.935888i
\(184\) −7.15465e7 5.73058e7i −0.846694 0.678166i
\(185\) −7.88503e7 + 9.71497e7i −0.915593 + 1.12808i
\(186\) 1.03080e7 + 3.35021e7i 0.117457 + 0.381748i
\(187\) 1.11405e8 + 1.11405e8i 1.24583 + 1.24583i
\(188\) 3.76255e6 1.97324e7i 0.0412980 0.216584i
\(189\) 6.28510e7i 0.677167i
\(190\) 6.08522e7 + 2.45387e7i 0.643634 + 0.259546i
\(191\) 1.01749e8i 1.05661i −0.849056 0.528303i \(-0.822829\pi\)
0.849056 0.528303i \(-0.177171\pi\)
\(192\) −8.19178e7 + 1.29149e8i −0.835264 + 1.31685i
\(193\) 9.78667e7 + 9.78667e7i 0.979906 + 0.979906i 0.999802 0.0198962i \(-0.00633357\pi\)
−0.0198962 + 0.999802i \(0.506334\pi\)
\(194\) 7.06057e7 2.17242e7i 0.694278 0.213618i
\(195\) −4.27345e6 + 444326.i −0.0412721 + 0.00429122i
\(196\) −1.00547e6 + 683435.i −0.00953838 + 0.00648337i
\(197\) 3.58672e7 3.58672e7i 0.334246 0.334246i −0.519951 0.854196i \(-0.674050\pi\)
0.854196 + 0.519951i \(0.174050\pi\)
\(198\) 1.67173e8 + 8.85052e7i 1.53052 + 0.810290i
\(199\) 9.81320e7 0.882724 0.441362 0.897329i \(-0.354495\pi\)
0.441362 + 0.897329i \(0.354495\pi\)
\(200\) −3.52965e7 1.07490e8i −0.311980 0.950089i
\(201\) 4.43822e7 0.385499
\(202\) 6.96136e7 + 3.68550e7i 0.594243 + 0.314606i
\(203\) −5.71770e7 + 5.71770e7i −0.479717 + 0.479717i
\(204\) −2.27795e8 + 1.54836e8i −1.87862 + 1.27692i
\(205\) 1.35680e8 1.41072e7i 1.09996 0.114367i
\(206\) −6.20308e7 + 1.90858e7i −0.494393 + 0.152116i
\(207\) −1.40153e8 1.40153e8i −1.09826 1.09826i
\(208\) 3.16920e6 1.37203e6i 0.0244190 0.0105716i
\(209\) 1.10787e8i 0.839416i
\(210\) −1.95209e8 7.87185e7i −1.45457 0.586555i
\(211\) 1.06912e8i 0.783495i 0.920073 + 0.391747i \(0.128129\pi\)
−0.920073 + 0.391747i \(0.871871\pi\)
\(212\) −3.85980e7 + 2.02424e8i −0.278221 + 1.45911i
\(213\) −9.00938e7 9.00938e7i −0.638802 0.638802i
\(214\) −5.93380e7 1.92854e8i −0.413890 1.34518i
\(215\) −1.13600e8 + 1.39964e8i −0.779552 + 0.960469i
\(216\) −6.23417e7 + 7.78339e7i −0.420911 + 0.525510i
\(217\) 2.74184e7 2.74184e7i 0.182151 0.182151i
\(218\) −6.06264e7 + 1.14514e8i −0.396336 + 0.748620i
\(219\) 2.74309e8 1.76476
\(220\) 1.46036e8 1.23150e8i 0.924655 0.779747i
\(221\) 6.21954e6 0.0387601
\(222\) 1.72813e8 3.26418e8i 1.06008 2.00234i
\(223\) 1.17604e8 1.17604e8i 0.710160 0.710160i −0.256408 0.966569i \(-0.582539\pi\)
0.966569 + 0.256408i \(0.0825391\pi\)
\(224\) 1.68665e8 + 1.32409e7i 1.00267 + 0.0787135i
\(225\) −5.03262e7 2.39397e8i −0.294547 1.40114i
\(226\) 5.66845e7 + 1.84230e8i 0.326652 + 1.06165i
\(227\) −1.96851e8 1.96851e8i −1.11699 1.11699i −0.992181 0.124805i \(-0.960169\pi\)
−0.124805 0.992181i \(-0.539831\pi\)
\(228\) −1.90254e8 3.62774e7i −1.06307 0.202705i
\(229\) 2.31575e8i 1.27429i 0.770745 + 0.637143i \(0.219884\pi\)
−0.770745 + 0.637143i \(0.780116\pi\)
\(230\) −1.84205e8 + 7.83353e7i −0.998284 + 0.424532i
\(231\) 3.55397e8i 1.89702i
\(232\) 1.27521e8 1.40936e7i 0.670461 0.0740995i
\(233\) −6.34774e7 6.34774e7i −0.328756 0.328756i 0.523357 0.852113i \(-0.324679\pi\)
−0.852113 + 0.523357i \(0.824679\pi\)
\(234\) 7.13701e6 2.19594e6i 0.0364134 0.0112038i
\(235\) −3.40587e7 2.76433e7i −0.171195 0.138948i
\(236\) −7.63364e7 1.12307e8i −0.378041 0.556177i
\(237\) −6.55695e7 + 6.55695e7i −0.319950 + 0.319950i
\(238\) 2.69283e8 + 1.42565e8i 1.29476 + 0.685476i
\(239\) 2.83768e8 1.34453 0.672265 0.740311i \(-0.265322\pi\)
0.672265 + 0.740311i \(0.265322\pi\)
\(240\) 1.63665e8 + 2.91112e8i 0.764214 + 1.35932i
\(241\) −3.95091e6 −0.0181818 −0.00909092 0.999959i \(-0.502894\pi\)
−0.00909092 + 0.999959i \(0.502894\pi\)
\(242\) 9.02141e7 + 4.77614e7i 0.409186 + 0.216632i
\(243\) 2.00664e8 2.00664e8i 0.897112 0.897112i
\(244\) −1.08266e8 1.59282e8i −0.477122 0.701945i
\(245\) 274549. + 2.64056e6i 0.00119272 + 0.0114714i
\(246\) −3.84862e8 + 1.18415e8i −1.64828 + 0.507149i
\(247\) 3.09251e6 + 3.09251e6i 0.0130579 + 0.0130579i
\(248\) −6.11508e7 + 6.75839e6i −0.254578 + 0.0281360i
\(249\) 2.57695e8i 1.05781i
\(250\) −2.43232e8 4.32822e7i −0.984534 0.175194i
\(251\) 5.01760e7i 0.200280i −0.994973 0.100140i \(-0.968071\pi\)
0.994973 0.100140i \(-0.0319291\pi\)
\(252\) 3.59342e8 + 6.85189e7i 1.41451 + 0.269717i
\(253\) −2.38990e8 2.38990e8i −0.927806 0.927806i
\(254\) −3.15413e7 1.02512e8i −0.120771 0.392517i
\(255\) 6.22005e7 + 5.98233e8i 0.234911 + 2.25933i
\(256\) −1.95739e8 1.83695e8i −0.729184 0.684318i
\(257\) 2.24786e8 2.24786e8i 0.826043 0.826043i −0.160924 0.986967i \(-0.551447\pi\)
0.986967 + 0.160924i \(0.0514475\pi\)
\(258\) 2.48973e8 4.70273e8i 0.902575 1.70483i
\(259\) −4.08574e8 −1.46124
\(260\) 638841. 7.51405e6i 0.00225417 0.0265135i
\(261\) 2.77410e8 0.965786
\(262\) −1.33852e8 + 2.52825e8i −0.459800 + 0.868493i
\(263\) −3.94967e8 + 3.94967e8i −1.33880 + 1.33880i −0.441579 + 0.897223i \(0.645581\pi\)
−0.897223 + 0.441579i \(0.854419\pi\)
\(264\) −3.52517e8 + 4.40119e8i −1.17914 + 1.47217i
\(265\) 3.49390e8 + 2.83578e8i 1.15332 + 0.936079i
\(266\) 6.30078e7 + 2.04781e8i 0.205262 + 0.667121i
\(267\) 1.47561e8 + 1.47561e8i 0.474441 + 0.474441i
\(268\) −1.45909e7 + 7.65208e7i −0.0463031 + 0.242833i
\(269\) 1.08964e8i 0.341311i −0.985331 0.170655i \(-0.945412\pi\)
0.985331 0.170655i \(-0.0545885\pi\)
\(270\) 8.52193e7 + 2.00393e8i 0.263490 + 0.619596i
\(271\) 4.93962e7i 0.150765i −0.997155 0.0753826i \(-0.975982\pi\)
0.997155 0.0753826i \(-0.0240178\pi\)
\(272\) −1.92068e8 4.43651e8i −0.578713 1.33675i
\(273\) −9.92056e6 9.92056e6i −0.0295098 0.0295098i
\(274\) −9.48823e7 + 2.91937e7i −0.278650 + 0.0857358i
\(275\) −8.58163e7 4.08221e8i −0.248831 1.18367i
\(276\) 4.88673e8 3.32158e8i 1.39906 0.950961i
\(277\) 2.95854e7 2.95854e7i 0.0836370 0.0836370i −0.664051 0.747688i \(-0.731164\pi\)
0.747688 + 0.664051i \(0.231164\pi\)
\(278\) 1.52240e8 + 8.05993e7i 0.424984 + 0.224996i
\(279\) −1.33028e8 −0.366715
\(280\) 1.99897e8 3.10687e8i 0.544193 0.845805i
\(281\) −5.75963e8 −1.54854 −0.774269 0.632856i \(-0.781882\pi\)
−0.774269 + 0.632856i \(0.781882\pi\)
\(282\) 1.14435e8 + 6.05847e7i 0.303871 + 0.160876i
\(283\) 1.38751e8 1.38751e8i 0.363902 0.363902i −0.501345 0.865247i \(-0.667161\pi\)
0.865247 + 0.501345i \(0.167161\pi\)
\(284\) 1.84952e8 1.25715e8i 0.479121 0.325666i
\(285\) −2.66529e8 + 3.28384e8i −0.682005 + 0.840283i
\(286\) 1.21700e7 3.74452e6i 0.0307617 0.00946487i
\(287\) 3.14974e8 + 3.14974e8i 0.786480 + 0.786480i
\(288\) −3.77041e8 4.41283e8i −0.930069 1.08854i
\(289\) 4.60324e8i 1.12181i
\(290\) 1.04776e8 2.59828e8i 0.252272 0.625594i
\(291\) 4.76169e8i 1.13275i
\(292\) −9.01806e7 + 4.72945e8i −0.211969 + 1.11166i
\(293\) 4.74529e8 + 4.74529e8i 1.10211 + 1.10211i 0.994155 + 0.107958i \(0.0344313\pi\)
0.107958 + 0.994155i \(0.465569\pi\)
\(294\) −2.30456e6 7.49005e6i −0.00528899 0.0171897i
\(295\) −2.94938e8 + 3.06658e7i −0.668888 + 0.0695469i
\(296\) 5.05973e8 + 4.05263e8i 1.13398 + 0.908273i
\(297\) −2.59992e8 + 2.59992e8i −0.575853 + 0.575853i
\(298\) −1.89047e8 + 3.57081e8i −0.413821 + 0.781646i
\(299\) −1.33423e7 −0.0288657
\(300\) 7.29136e8 1.36992e7i 1.55914 0.0292934i
\(301\) −5.88636e8 −1.24413
\(302\) −5.03892e7 + 9.51777e7i −0.105272 + 0.198843i
\(303\) −3.59015e8 + 3.59015e8i −0.741419 + 0.741419i
\(304\) 1.25094e8 3.16096e8i 0.255375 0.645300i
\(305\) −4.18305e8 + 4.34927e7i −0.844196 + 0.0877743i
\(306\) −3.07406e8 9.99098e8i −0.613320 1.99335i
\(307\) 1.76076e8 + 1.76076e8i 0.347308 + 0.347308i 0.859106 0.511798i \(-0.171020\pi\)
−0.511798 + 0.859106i \(0.671020\pi\)
\(308\) 6.12751e8 + 1.16839e8i 1.19497 + 0.227855i
\(309\) 4.18339e8i 0.806629i
\(310\) −5.02437e7 + 1.24597e8i −0.0957890 + 0.237542i
\(311\) 3.18612e8i 0.600622i −0.953841 0.300311i \(-0.902910\pi\)
0.953841 0.300311i \(-0.0970904\pi\)
\(312\) 2.44533e6 + 2.21257e7i 0.00455824 + 0.0412435i
\(313\) −4.41391e8 4.41391e8i −0.813614 0.813614i 0.171560 0.985174i \(-0.445119\pi\)
−0.985174 + 0.171560i \(0.945119\pi\)
\(314\) −7.05774e7 + 2.17155e7i −0.128651 + 0.0395836i
\(315\) 5.03406e8 6.20236e8i 0.907469 1.11807i
\(316\) −9.14940e7 1.34607e8i −0.163113 0.239973i
\(317\) 7.71009e8 7.71009e8i 1.35941 1.35941i 0.484776 0.874639i \(-0.338901\pi\)
0.874639 0.484776i \(-0.161099\pi\)
\(318\) −1.17393e9 6.21506e8i −2.04714 1.08380i
\(319\) 4.73041e8 0.815889
\(320\) −5.55720e8 + 1.86474e8i −0.948050 + 0.318123i
\(321\) 1.30062e9 2.19474
\(322\) −5.77674e8 3.05834e8i −0.964245 0.510493i
\(323\) 4.32916e8 4.32916e8i 0.714817 0.714817i
\(324\) 1.31406e8 + 1.93326e8i 0.214639 + 0.315778i
\(325\) −1.37906e7 8.99961e6i −0.0222839 0.0145423i
\(326\) 3.15867e8 9.71871e7i 0.504944 0.155363i
\(327\) −5.90579e8 5.90579e8i −0.934030 0.934030i
\(328\) −7.76383e7 7.02481e8i −0.121484 1.09920i
\(329\) 1.43238e8i 0.221754i
\(330\) 4.81881e8 + 1.13314e9i 0.738144 + 1.73574i
\(331\) 8.91401e7i 0.135106i 0.997716 + 0.0675531i \(0.0215192\pi\)
−0.997716 + 0.0675531i \(0.978481\pi\)
\(332\) −4.44300e8 8.47185e7i −0.666335 0.127056i
\(333\) 9.91156e8 + 9.91156e8i 1.47091 + 1.47091i
\(334\) 3.16534e8 + 1.02877e9i 0.464844 + 1.51079i
\(335\) 1.32077e8 + 1.07199e8i 0.191943 + 0.155788i
\(336\) −4.01292e8 + 1.01401e9i −0.577129 + 1.45833i
\(337\) −4.63800e8 + 4.63800e8i −0.660124 + 0.660124i −0.955409 0.295285i \(-0.904585\pi\)
0.295285 + 0.955409i \(0.404585\pi\)
\(338\) −3.31932e8 + 6.26970e8i −0.467564 + 0.883158i
\(339\) −1.24246e9 −1.73214
\(340\) −1.05188e9 8.94303e7i −1.45141 0.123398i
\(341\) −2.26840e8 −0.309798
\(342\) 3.43928e8 6.49628e8i 0.464917 0.878159i
\(343\) 5.25372e8 5.25372e8i 0.702971 0.702971i
\(344\) 7.28960e8 + 5.83867e8i 0.965494 + 0.773320i
\(345\) −1.33434e8 1.28335e9i −0.174945 1.68258i
\(346\) 1.87482e8 + 6.09334e8i 0.243328 + 0.790841i
\(347\) 4.94339e8 + 4.94339e8i 0.635144 + 0.635144i 0.949354 0.314210i \(-0.101740\pi\)
−0.314210 + 0.949354i \(0.601740\pi\)
\(348\) −1.54898e8 + 8.12350e8i −0.197024 + 1.03327i
\(349\) 1.27604e9i 1.60684i 0.595409 + 0.803422i \(0.296990\pi\)
−0.595409 + 0.803422i \(0.703010\pi\)
\(350\) −3.90792e8 7.05759e8i −0.487200 0.879869i
\(351\) 1.45148e7i 0.0179158i
\(352\) −6.42931e8 7.52477e8i −0.785715 0.919589i
\(353\) 1.46080e8 + 1.46080e8i 0.176758 + 0.176758i 0.789941 0.613183i \(-0.210111\pi\)
−0.613183 + 0.789941i \(0.710111\pi\)
\(354\) 8.36603e8 2.57408e8i 1.00232 0.308398i
\(355\) −5.05021e7 4.85719e8i −0.0599115 0.576217i
\(356\) −3.02926e8 + 2.05903e8i −0.355845 + 0.241873i
\(357\) −1.38876e9 + 1.38876e9i −1.61543 + 1.61543i
\(358\) 1.33439e9 + 7.06457e8i 1.53707 + 0.813758i
\(359\) 8.52161e8 0.972055 0.486028 0.873943i \(-0.338445\pi\)
0.486028 + 0.873943i \(0.338445\pi\)
\(360\) −1.23862e9 + 2.68766e8i −1.39920 + 0.303609i
\(361\) −4.63358e8 −0.518372
\(362\) 2.86492e8 + 1.51675e8i 0.317418 + 0.168048i
\(363\) −4.65257e8 + 4.65257e8i −0.510528 + 0.510528i
\(364\) 2.03658e7 1.38429e7i 0.0221333 0.0150443i
\(365\) 8.16318e8 + 6.62554e8i 0.878687 + 0.713175i
\(366\) 1.18654e9 3.65077e8i 1.26502 0.389225i
\(367\) −1.06168e9 1.06168e9i −1.12115 1.12115i −0.991570 0.129576i \(-0.958638\pi\)
−0.129576 0.991570i \(-0.541362\pi\)
\(368\) 4.12029e8 + 9.51734e8i 0.430984 + 0.995516i
\(369\) 1.52818e9i 1.58337i
\(370\) 1.30269e9 5.53983e8i 1.33701 0.568579i
\(371\) 1.46940e9i 1.49393i
\(372\) 7.42790e7 3.89550e8i 0.0748110 0.392340i
\(373\) −2.64187e8 2.64187e8i −0.263591 0.263591i 0.562920 0.826511i \(-0.309678\pi\)
−0.826511 + 0.562920i \(0.809678\pi\)
\(374\) −5.24189e8 1.70366e9i −0.518128 1.68397i
\(375\) 7.27720e8 1.41646e9i 0.712615 1.38706i
\(376\) −1.42077e8 + 1.77384e8i −0.137837 + 0.172091i
\(377\) 1.32045e7 1.32045e7i 0.0126919 0.0126919i
\(378\) −3.32710e8 + 6.28439e8i −0.316843 + 0.598469i
\(379\) −1.49762e9 −1.41308 −0.706538 0.707675i \(-0.749744\pi\)
−0.706538 + 0.707675i \(0.749744\pi\)
\(380\) −4.78555e8 5.67489e8i −0.447393 0.530536i
\(381\) 6.91350e8 0.640413
\(382\) −5.38621e8 + 1.01737e9i −0.494380 + 0.933811i
\(383\) 6.90436e8 6.90436e8i 0.627954 0.627954i −0.319599 0.947553i \(-0.603548\pi\)
0.947553 + 0.319599i \(0.103548\pi\)
\(384\) 1.50275e9 8.57702e8i 1.35434 0.772996i
\(385\) 8.58410e8 1.05763e9i 0.766623 0.944539i
\(386\) −4.60487e8 1.49663e9i −0.407532 1.32452i
\(387\) 1.42797e9 + 1.42797e9i 1.25236 + 1.25236i
\(388\) −8.20977e8 1.56543e8i −0.713543 0.136058i
\(389\) 4.56571e8i 0.393264i 0.980477 + 0.196632i \(0.0630005\pi\)
−0.980477 + 0.196632i \(0.936999\pi\)
\(390\) 4.50817e7 + 1.81793e7i 0.0384835 + 0.0155185i
\(391\) 1.86777e9i 1.58017i
\(392\) 1.36715e7 1.51097e6i 0.0114634 0.00126694i
\(393\) −1.30389e9 1.30389e9i −1.08359 1.08359i
\(394\) −5.48499e8 + 1.68764e8i −0.451793 + 0.139009i
\(395\) −3.53502e8 + 3.67549e7i −0.288604 + 0.0300072i
\(396\) −1.20303e9 1.76990e9i −0.973516 1.43224i
\(397\) 7.96123e8 7.96123e8i 0.638577 0.638577i −0.311627 0.950204i \(-0.600874\pi\)
0.950204 + 0.311627i \(0.100874\pi\)
\(398\) −9.81210e8 5.19475e8i −0.780137 0.413022i
\(399\) −1.38106e9 −1.08845
\(400\) −2.16088e8 + 1.26163e9i −0.168819 + 0.985647i
\(401\) −9.18671e8 −0.711467 −0.355734 0.934587i \(-0.615769\pi\)
−0.355734 + 0.934587i \(0.615769\pi\)
\(402\) −4.43772e8 2.34943e8i −0.340698 0.180373i
\(403\) −6.33201e6 + 6.33201e6i −0.00481919 + 0.00481919i
\(404\) −5.00961e8 7.37017e8i −0.377980 0.556087i
\(405\) 5.07709e8 5.27884e7i 0.379771 0.0394863i
\(406\) 8.74379e8 2.69032e8i 0.648424 0.199509i
\(407\) 1.69012e9 + 1.69012e9i 1.24262 + 1.24262i
\(408\) 3.09734e9 3.42318e8i 2.25776 0.249528i
\(409\) 4.07164e8i 0.294265i 0.989117 + 0.147132i \(0.0470043\pi\)
−0.989117 + 0.147132i \(0.952996\pi\)
\(410\) −1.43133e9 5.77184e8i −1.02564 0.413591i
\(411\) 6.39892e8i 0.454632i
\(412\) 7.21271e8 + 1.37531e8i 0.508111 + 0.0968860i
\(413\) −6.84682e8 6.84682e8i −0.478260 0.478260i
\(414\) 6.59456e8 + 2.14329e9i 0.456756 + 1.48450i
\(415\) −6.22425e8 + 7.66875e8i −0.427483 + 0.526692i
\(416\) −3.89515e7 3.05786e6i −0.0265276 0.00208253i
\(417\) −7.85142e8 + 7.85142e8i −0.530239 + 0.530239i
\(418\) 5.86466e8 1.10775e9i 0.392759 0.741862i
\(419\) −2.83494e8 −0.188276 −0.0941379 0.995559i \(-0.530009\pi\)
−0.0941379 + 0.995559i \(0.530009\pi\)
\(420\) 1.53517e9 + 1.82046e9i 1.01108 + 1.19897i
\(421\) 8.02558e8 0.524191 0.262095 0.965042i \(-0.415587\pi\)
0.262095 + 0.965042i \(0.415587\pi\)
\(422\) 5.65950e8 1.06900e9i 0.366593 0.692440i
\(423\) −3.47479e8 + 3.47479e8i −0.223222 + 0.223222i
\(424\) 1.45749e9 1.81969e9i 0.928595 1.15936i
\(425\) −1.25984e9 + 1.93052e9i −0.796076 + 1.21987i
\(426\) 4.23914e8 + 1.37776e9i 0.265671 + 0.863456i
\(427\) −9.71071e8 9.71071e8i −0.603606 0.603606i
\(428\) −4.27586e8 + 2.24244e9i −0.263615 + 1.38251i
\(429\) 8.20755e7i 0.0501895i
\(430\) 1.87680e9 7.98129e8i 1.13835 0.484098i
\(431\) 1.34312e9i 0.808064i −0.914745 0.404032i \(-0.867608\pi\)
0.914745 0.404032i \(-0.132392\pi\)
\(432\) 1.03537e9 4.48238e8i 0.617878 0.267495i
\(433\) 1.31154e9 + 1.31154e9i 0.776377 + 0.776377i 0.979213 0.202836i \(-0.0650157\pi\)
−0.202836 + 0.979213i \(0.565016\pi\)
\(434\) −4.19295e8 + 1.29010e8i −0.246210 + 0.0757547i
\(435\) 1.40214e9 + 1.13803e9i 0.816732 + 0.662890i
\(436\) 1.21239e9 8.24079e8i 0.700551 0.476174i
\(437\) −9.28704e8 + 9.28704e8i −0.532344 + 0.532344i
\(438\) −2.74278e9 1.45209e9i −1.55967 0.825723i
\(439\) 1.55475e8 0.0877072 0.0438536 0.999038i \(-0.486036\pi\)
0.0438536 + 0.999038i \(0.486036\pi\)
\(440\) −2.11210e9 + 4.58300e8i −1.18204 + 0.256487i
\(441\) 2.97410e7 0.0165128
\(442\) −6.21884e7 3.29239e7i −0.0342556 0.0181357i
\(443\) −1.03988e9 + 1.03988e9i −0.568288 + 0.568288i −0.931649 0.363360i \(-0.881629\pi\)
0.363360 + 0.931649i \(0.381629\pi\)
\(444\) −3.45587e9 + 2.34900e9i −1.87377 + 1.27363i
\(445\) 8.27153e7 + 7.95540e8i 0.0444965 + 0.427959i
\(446\) −1.79847e9 + 5.53357e8i −0.959909 + 0.295348i
\(447\) −1.84156e9 1.84156e9i −0.975235 0.975235i
\(448\) −1.61636e9 1.02524e9i −0.849310 0.538708i
\(449\) 1.24484e9i 0.649011i −0.945884 0.324506i \(-0.894802\pi\)
0.945884 0.324506i \(-0.105198\pi\)
\(450\) −7.64076e8 + 2.66011e9i −0.395269 + 1.37612i
\(451\) 2.60586e9i 1.33762i
\(452\) 4.08465e8 2.14216e9i 0.208051 1.09111i
\(453\) −4.90856e8 4.90856e8i −0.248091 0.248091i
\(454\) 9.26234e8 + 3.01035e9i 0.464542 + 1.50981i
\(455\) −5.56097e6 5.34843e7i −0.00276765 0.0266187i
\(456\) 1.71029e9 + 1.36987e9i 0.844679 + 0.676552i
\(457\) 2.28831e9 2.28831e9i 1.12152 1.12152i 0.130008 0.991513i \(-0.458500\pi\)
0.991513 0.130008i \(-0.0415004\pi\)
\(458\) 1.22587e9 2.31549e9i 0.596233 1.12619i
\(459\) 2.03191e9 0.980752
\(460\) 2.25652e9 + 1.91848e8i 1.08090 + 0.0918979i
\(461\) 1.22029e7 0.00580108 0.00290054 0.999996i \(-0.499077\pi\)
0.00290054 + 0.999996i \(0.499077\pi\)
\(462\) −1.88134e9 + 3.55357e9i −0.887606 + 1.67656i
\(463\) 1.02003e8 1.02003e8i 0.0477616 0.0477616i −0.682823 0.730584i \(-0.739248\pi\)
0.730584 + 0.682823i \(0.239248\pi\)
\(464\) −1.34967e9 5.34128e8i −0.627214 0.248218i
\(465\) −6.72376e8 5.45725e8i −0.310118 0.251703i
\(466\) 2.98677e8 + 9.70729e8i 0.136726 + 0.444373i
\(467\) 3.60259e8 + 3.60259e8i 0.163684 + 0.163684i 0.784196 0.620513i \(-0.213075\pi\)
−0.620513 + 0.784196i \(0.713075\pi\)
\(468\) −8.29866e7 1.58238e7i −0.0374237 0.00713592i
\(469\) 5.55466e8i 0.248629i
\(470\) 1.94215e8 + 4.56696e8i 0.0862861 + 0.202901i
\(471\) 4.75978e8i 0.209901i
\(472\) 1.68768e8 + 1.52704e9i 0.0738744 + 0.668424i
\(473\) 2.43497e9 + 2.43497e9i 1.05799 + 1.05799i
\(474\) 1.00272e9 3.08520e8i 0.432470 0.133064i
\(475\) −1.58633e9 + 3.33478e8i −0.679150 + 0.142771i
\(476\) −1.93784e9 2.85097e9i −0.823559 1.21163i
\(477\) 3.56461e9 3.56461e9i 1.50383 1.50383i
\(478\) −2.83736e9 1.50216e9i −1.18827 0.629099i
\(479\) 2.61133e9 1.08564 0.542821 0.839848i \(-0.317356\pi\)
0.542821 + 0.839848i \(0.317356\pi\)
\(480\) −9.54238e7 3.77717e9i −0.0393833 1.55891i
\(481\) 9.43562e7 0.0386601
\(482\) 3.95047e7 + 2.09147e7i 0.0160688 + 0.00850719i
\(483\) 2.97921e9 2.97921e9i 1.20306 1.20306i
\(484\) −6.49208e8 9.55120e8i −0.260271 0.382912i
\(485\) −1.15012e9 + 1.41703e9i −0.457768 + 0.564006i
\(486\) −3.06865e9 + 9.44171e8i −1.21261 + 0.373099i
\(487\) 2.43348e9 + 2.43348e9i 0.954721 + 0.954721i 0.999018 0.0442971i \(-0.0141048\pi\)
−0.0442971 + 0.999018i \(0.514105\pi\)
\(488\) 2.39361e8 + 2.16576e9i 0.0932360 + 0.843610i
\(489\) 2.13023e9i 0.823845i
\(490\) 1.12330e7 2.78560e7i 0.00431329 0.0106963i
\(491\) 3.45389e9i 1.31681i −0.752663 0.658406i \(-0.771231\pi\)
0.752663 0.658406i \(-0.228769\pi\)
\(492\) 4.47503e9 + 8.53294e8i 1.69402 + 0.323013i
\(493\) −1.84847e9 1.84847e9i −0.694782 0.694782i
\(494\) −1.45510e7 4.72923e7i −0.00543062 0.0176501i
\(495\) −4.64810e9 + 4.83281e8i −1.72249 + 0.179094i
\(496\) 6.47215e8 + 2.56133e8i 0.238157 + 0.0942497i
\(497\) 1.12757e9 1.12757e9i 0.411999 0.411999i
\(498\) 1.36414e9 2.57666e9i 0.494945 0.934877i
\(499\) 4.25986e9 1.53477 0.767384 0.641187i \(-0.221558\pi\)
0.767384 + 0.641187i \(0.221558\pi\)
\(500\) 2.20293e9 + 1.72035e9i 0.788143 + 0.615492i
\(501\) −6.93806e9 −2.46494
\(502\) −2.65613e8 + 5.01704e8i −0.0937102 + 0.177004i
\(503\) −1.06415e9 + 1.06415e9i −0.372833 + 0.372833i −0.868508 0.495675i \(-0.834921\pi\)
0.495675 + 0.868508i \(0.334921\pi\)
\(504\) −3.23030e9 2.58734e9i −1.12392 0.900214i
\(505\) −1.93554e9 + 2.01246e8i −0.668780 + 0.0695356i
\(506\) 1.12450e9 + 3.65475e9i 0.385864 + 1.25410i
\(507\) −3.23345e9 3.23345e9i −1.10189 1.10189i
\(508\) −2.27285e8 + 1.19198e9i −0.0769214 + 0.403408i
\(509\) 1.44533e9i 0.485797i −0.970052 0.242898i \(-0.921902\pi\)
0.970052 0.242898i \(-0.0780981\pi\)
\(510\) 2.54489e9 6.31092e9i 0.849518 2.10667i
\(511\) 3.43312e9i 1.13819i
\(512\) 9.84752e8 + 2.87291e9i 0.324252 + 0.945971i
\(513\) 1.01032e9 + 1.01032e9i 0.330405 + 0.330405i
\(514\) −3.43753e9 + 1.05767e9i −1.11654 + 0.343542i
\(515\) 1.01044e9 1.24494e9i 0.325975 0.401626i
\(516\) −4.97890e9 + 3.38423e9i −1.59536 + 1.08439i
\(517\) −5.92523e8 + 5.92523e8i −0.188577 + 0.188577i
\(518\) 4.08528e9 + 2.16284e9i 1.29142 + 0.683707i
\(519\) −4.10938e9 −1.29030
\(520\) −4.61643e7 + 7.17503e7i −0.0143977 + 0.0223775i
\(521\) 4.98957e8 0.154572 0.0772860 0.997009i \(-0.475375\pi\)
0.0772860 + 0.997009i \(0.475375\pi\)
\(522\) −2.77379e9 1.46851e9i −0.853547 0.451887i
\(523\) −2.34017e9 + 2.34017e9i −0.715307 + 0.715307i −0.967640 0.252334i \(-0.918802\pi\)
0.252334 + 0.967640i \(0.418802\pi\)
\(524\) 2.67673e9 1.81941e9i 0.812727 0.552422i
\(525\) 5.08883e9 1.06977e9i 1.53483 0.322652i
\(526\) 6.04004e9 1.85842e9i 1.80963 0.556793i
\(527\) 8.86407e8 + 8.86407e8i 0.263813 + 0.263813i
\(528\) 5.85460e9 2.53460e9i 1.73093 0.749362i
\(529\) 6.01970e8i 0.176799i
\(530\) −1.99235e9 4.68501e9i −0.581301 1.36693i
\(531\) 3.32193e9i 0.962852i
\(532\) 4.54030e8 2.38112e9i 0.130736 0.685632i
\(533\) −7.27401e7 7.27401e7i −0.0208079 0.0208079i
\(534\) −6.94311e8 2.25658e9i −0.197315 0.641292i
\(535\) 3.87052e9 + 3.14146e9i 1.09278 + 0.886939i
\(536\) 5.50965e8 6.87883e8i 0.154542 0.192947i
\(537\) −6.88181e9 + 6.88181e9i −1.91775 + 1.91775i
\(538\) −5.76815e8 + 1.08952e9i −0.159698 + 0.301645i
\(539\) 5.07144e7 0.0139499
\(540\) 2.08708e8 2.45482e9i 0.0570374 0.670875i
\(541\) 4.80780e9 1.30544 0.652719 0.757600i \(-0.273628\pi\)
0.652719 + 0.757600i \(0.273628\pi\)
\(542\) −2.61485e8 + 4.93906e8i −0.0705423 + 0.133244i
\(543\) −1.47751e9 + 1.47751e9i −0.396033 + 0.396033i
\(544\) −4.28064e8 + 5.45275e9i −0.114002 + 1.45218i
\(545\) −3.31049e8 3.18396e9i −0.0876000 0.842520i
\(546\) 4.66787e7 + 1.51710e8i 0.0122728 + 0.0398878i
\(547\) −4.22037e9 4.22037e9i −1.10254 1.10254i −0.994103 0.108438i \(-0.965415\pi\)
−0.108438 0.994103i \(-0.534585\pi\)
\(548\) 1.10326e9 + 2.10368e8i 0.286381 + 0.0546069i
\(549\) 4.71143e9i 1.21520i
\(550\) −1.30290e9 + 4.53603e9i −0.333920 + 1.16254i
\(551\) 1.83822e9i 0.468130i
\(552\) −6.64450e9 + 7.34351e8i −1.68142 + 0.185831i
\(553\) −8.20635e8 8.20635e8i −0.206354 0.206354i
\(554\) −4.52435e8 + 1.39207e8i −0.113050 + 0.0347837i
\(555\) 9.43640e8 + 9.07575e9i 0.234305 + 2.25350i
\(556\) −1.09557e9 1.61181e9i −0.270319 0.397696i
\(557\) 1.39710e9 1.39710e9i 0.342558 0.342558i −0.514770 0.857328i \(-0.672123\pi\)
0.857328 + 0.514770i \(0.172123\pi\)
\(558\) 1.33013e9 + 7.04201e8i 0.324097 + 0.171584i
\(559\) 1.35940e8 0.0329159
\(560\) −3.64341e9 + 2.04834e9i −0.876698 + 0.492884i
\(561\) 1.14896e10 2.74749
\(562\) 5.75898e9 + 3.04893e9i 1.36857 + 0.724554i
\(563\) −5.24879e9 + 5.24879e9i −1.23960 + 1.23960i −0.279429 + 0.960166i \(0.590145\pi\)
−0.960166 + 0.279429i \(0.909855\pi\)
\(564\) −8.23513e8 1.21156e9i −0.193283 0.284359i
\(565\) −3.69744e9 3.00098e9i −0.862445 0.699993i
\(566\) −2.12186e9 + 6.52859e8i −0.491879 + 0.151343i
\(567\) 1.17862e9 + 1.17862e9i 0.271539 + 0.271539i
\(568\) −2.51480e9 + 2.77936e8i −0.575817 + 0.0636394i
\(569\) 1.89520e9i 0.431284i −0.976473 0.215642i \(-0.930816\pi\)
0.976473 0.215642i \(-0.0691844\pi\)
\(570\) 4.40334e9 1.87257e9i 0.995909 0.423522i
\(571\) 1.21093e9i 0.272203i −0.990695 0.136101i \(-0.956543\pi\)
0.990695 0.136101i \(-0.0434573\pi\)
\(572\) −1.41509e8 2.69827e7i −0.0316153 0.00602837i
\(573\) −5.24686e9 5.24686e9i −1.16509 1.16509i
\(574\) −1.48203e9 4.81674e9i −0.327088 1.06307i
\(575\) 2.70265e9 4.14140e9i 0.592860 0.908469i
\(576\) 1.43400e9 + 6.40825e9i 0.312658 + 1.39721i
\(577\) −4.15769e9 + 4.15769e9i −0.901026 + 0.901026i −0.995525 0.0944994i \(-0.969875\pi\)
0.0944994 + 0.995525i \(0.469875\pi\)
\(578\) −2.43678e9 + 4.60272e9i −0.524892 + 0.991442i
\(579\) 1.00933e10 2.16103
\(580\) −2.42307e9 + 2.04334e9i −0.515666 + 0.434854i
\(581\) −3.22518e9 −0.682241
\(582\) 2.52066e9 4.76115e9i 0.530010 1.00111i
\(583\) 6.07838e9 6.07838e9i 1.27042 1.27042i
\(584\) 3.40530e9 4.25153e9i 0.707474 0.883285i
\(585\) −1.16257e8 + 1.43237e8i −0.0240089 + 0.0295809i
\(586\) −2.23278e9 7.25674e9i −0.458357 1.48970i
\(587\) −3.53809e9 3.53809e9i −0.721998 0.721998i 0.247014 0.969012i \(-0.420551\pi\)
−0.969012 + 0.247014i \(0.920551\pi\)
\(588\) −1.66065e7 + 8.70916e7i −0.00336867 + 0.0176667i
\(589\) 8.81489e8i 0.177752i
\(590\) 3.11138e9 + 1.25467e9i 0.623694 + 0.251505i
\(591\) 3.69911e9i 0.737125i
\(592\) −2.91385e9 6.73061e9i −0.577220 1.33330i
\(593\) 1.29096e9 + 1.29096e9i 0.254227 + 0.254227i 0.822701 0.568474i \(-0.192466\pi\)
−0.568474 + 0.822701i \(0.692466\pi\)
\(594\) 3.97592e9 1.22332e9i 0.778368 0.239491i
\(595\) −7.48718e9 + 7.78471e8i −1.45717 + 0.151507i
\(596\) 3.78051e9 2.56967e9i 0.731456 0.497181i
\(597\) 5.06035e9 5.06035e9i 0.973353 0.973353i
\(598\) 1.33408e8 + 7.06293e7i 0.0255111 + 0.0135061i
\(599\) −5.72882e9 −1.08911 −0.544555 0.838725i \(-0.683301\pi\)
−0.544555 + 0.838725i \(0.683301\pi\)
\(600\) −7.36305e9 3.72280e9i −1.39165 0.703623i
\(601\) 4.48169e8 0.0842133 0.0421067 0.999113i \(-0.486593\pi\)
0.0421067 + 0.999113i \(0.486593\pi\)
\(602\) 5.88570e9 + 3.11602e9i 1.09954 + 0.582121i
\(603\) 1.34750e9 1.34750e9i 0.250276 0.250276i
\(604\) 1.00767e9 6.84928e8i 0.186076 0.126478i
\(605\) −2.50832e9 + 2.60800e8i −0.460510 + 0.0478810i
\(606\) 5.49024e9 1.68925e9i 1.00216 0.308348i
\(607\) −2.83783e9 2.83783e9i −0.515022 0.515022i 0.401039 0.916061i \(-0.368649\pi\)
−0.916061 + 0.401039i \(0.868649\pi\)
\(608\) −2.92409e9 + 2.49840e9i −0.527629 + 0.450817i
\(609\) 5.89687e9i 1.05794i
\(610\) 4.41281e9 + 1.77947e9i 0.787156 + 0.317422i
\(611\) 3.30794e7i 0.00586696i
\(612\) −2.21515e9 + 1.16172e10i −0.390636 + 2.04866i
\(613\) −2.02243e9 2.02243e9i −0.354619 0.354619i 0.507206 0.861825i \(-0.330678\pi\)
−0.861825 + 0.507206i \(0.830678\pi\)
\(614\) −8.28478e8 2.69264e9i −0.144441 0.469449i
\(615\) 6.26912e9 7.72405e9i 1.08679 1.33900i
\(616\) −5.50832e9 4.41193e9i −0.949481 0.760494i
\(617\) −4.44212e9 + 4.44212e9i −0.761363 + 0.761363i −0.976569 0.215206i \(-0.930958\pi\)
0.215206 + 0.976569i \(0.430958\pi\)
\(618\) −2.21453e9 + 4.18292e9i −0.377418 + 0.712886i
\(619\) 6.49157e9 1.10010 0.550051 0.835131i \(-0.314608\pi\)
0.550051 + 0.835131i \(0.314608\pi\)
\(620\) 1.16195e9 9.79853e8i 0.195801 0.165116i
\(621\) −4.35890e9 −0.730393
\(622\) −1.68661e9 + 3.18576e9i −0.281028 + 0.530820i
\(623\) −1.84680e9 + 1.84680e9i −0.305993 + 0.305993i
\(624\) 9.26746e7 2.34177e8i 0.0152691 0.0385831i
\(625\) 5.58689e9 2.45756e9i 0.915356 0.402646i
\(626\) 2.07685e9 + 6.74997e9i 0.338373 + 1.09974i
\(627\) 5.71293e9 + 5.71293e9i 0.925599 + 0.925599i
\(628\) 8.20648e8 + 1.56480e8i 0.132220 + 0.0252116i
\(629\) 1.32088e10i 2.11634i
\(630\) −8.31680e9 + 3.53681e9i −1.32515 + 0.563534i
\(631\) 7.92610e8i 0.125591i 0.998026 + 0.0627953i \(0.0200015\pi\)
−0.998026 + 0.0627953i \(0.979998\pi\)
\(632\) 2.02280e8 + 1.83025e9i 0.0318744 + 0.288404i
\(633\) 5.51309e9 + 5.51309e9i 0.863936 + 0.863936i
\(634\) −1.17907e10 + 3.62778e9i −1.83749 + 0.565365i
\(635\) 2.05739e9 + 1.66985e9i 0.318866 + 0.258804i
\(636\) 8.44798e9 + 1.24287e10i 1.30213 + 1.91570i
\(637\) 1.41564e6 1.41564e6i 0.000217003 0.000217003i
\(638\) −4.72988e9 2.50410e9i −0.721070 0.381751i
\(639\) −5.47073e9 −0.829453
\(640\) 6.54370e9 + 1.07724e9i 0.986719 + 0.162436i
\(641\) 8.14394e9 1.22133 0.610663 0.791891i \(-0.290903\pi\)
0.610663 + 0.791891i \(0.290903\pi\)
\(642\) −1.30048e10 6.88501e9i −1.93968 1.02691i
\(643\) 1.43880e9 1.43880e9i 0.213434 0.213434i −0.592291 0.805724i \(-0.701776\pi\)
0.805724 + 0.592291i \(0.201776\pi\)
\(644\) 4.15712e9 + 6.11598e9i 0.613327 + 0.902331i
\(645\) 1.35951e9 + 1.30755e10i 0.199491 + 1.91867i
\(646\) −6.62037e9 + 2.03698e9i −0.966203 + 0.297284i
\(647\) 3.41709e8 + 3.41709e8i 0.0496011 + 0.0496011i 0.731472 0.681871i \(-0.238834\pi\)
−0.681871 + 0.731472i \(0.738834\pi\)
\(648\) −2.90519e8 2.62865e9i −0.0419433 0.379508i
\(649\) 5.66456e9i 0.813410i
\(650\) 9.02496e7 + 1.62988e8i 0.0128899 + 0.0232787i
\(651\) 2.82775e9i 0.401706i
\(652\) −3.67279e9 7.00324e8i −0.518955 0.0989537i
\(653\) 8.65560e9 + 8.65560e9i 1.21647 + 1.21647i 0.968860 + 0.247609i \(0.0796449\pi\)
0.247609 + 0.968860i \(0.420355\pi\)
\(654\) 2.77882e9 + 9.03143e9i 0.388453 + 1.26251i
\(655\) −7.30893e8 7.02959e9i −0.101627 0.977429i
\(656\) −2.94238e9 + 7.43501e9i −0.406944 + 1.02830i
\(657\) 8.32838e9 8.32838e9i 1.14573 1.14573i
\(658\) −7.58248e8 + 1.43222e9i −0.103758 + 0.195983i
\(659\) −1.25763e10 −1.71180 −0.855898 0.517144i \(-0.826995\pi\)
−0.855898 + 0.517144i \(0.826995\pi\)
\(660\) 1.18016e9 1.38810e10i 0.159785 1.87939i
\(661\) −8.66760e9 −1.16733 −0.583665 0.811994i \(-0.698382\pi\)
−0.583665 + 0.811994i \(0.698382\pi\)
\(662\) 4.71875e8 8.91301e8i 0.0632155 0.119405i
\(663\) 3.20721e8 3.20721e8i 0.0427396 0.0427396i
\(664\) 3.99403e9 + 3.19905e9i 0.529447 + 0.424065i
\(665\) −4.10990e9 3.33574e9i −0.541945 0.439863i
\(666\) −4.66363e9 1.51573e10i −0.611737 1.98820i
\(667\) 3.96540e9 + 3.96540e9i 0.517424 + 0.517424i
\(668\) 2.28092e9 1.19621e10i 0.296069 1.55271i
\(669\) 1.21290e10i 1.56615i
\(670\) −7.53153e8 1.77104e9i −0.0967435 0.227492i
\(671\) 8.03393e9i 1.02660i
\(672\) 9.38028e9 8.01470e9i 1.19240 1.01881i
\(673\) 4.18076e9 + 4.18076e9i 0.528691 + 0.528691i 0.920182 0.391491i \(-0.128040\pi\)
−0.391491 + 0.920182i \(0.628040\pi\)
\(674\) 7.09266e9 2.18229e9i 0.892276 0.274538i
\(675\) −4.50534e9 2.94015e9i −0.563851 0.367965i
\(676\) 6.63790e9 4.51187e9i 0.826451 0.561750i
\(677\) 1.82396e9 1.82396e9i 0.225920 0.225920i −0.585066 0.810986i \(-0.698931\pi\)
0.810986 + 0.585066i \(0.198931\pi\)
\(678\) 1.24232e10 + 6.57712e9i 1.53084 + 0.810460i
\(679\) −5.95949e9 −0.730575
\(680\) 1.00442e10 + 6.46246e9i 1.22499 + 0.788164i
\(681\) −2.03020e10 −2.46333
\(682\) 2.26814e9 + 1.20080e9i 0.273794 + 0.144953i
\(683\) 1.13166e9 1.13166e9i 0.135908 0.135908i −0.635880 0.771788i \(-0.719363\pi\)
0.771788 + 0.635880i \(0.219363\pi\)
\(684\) −6.87778e9 + 4.67492e9i −0.821773 + 0.558570i
\(685\) 1.54557e9 1.90426e9i 0.183726 0.226365i
\(686\) −8.03425e9 + 2.47200e9i −0.950191 + 0.292358i
\(687\) 1.19416e10 + 1.19416e10i 1.40512 + 1.40512i
\(688\) −4.19801e9 9.69686e9i −0.491455 1.13520i
\(689\) 3.39344e8i 0.0395251i
\(690\) −5.45936e9 + 1.35384e10i −0.632660 + 1.56890i
\(691\) 1.48594e10i 1.71328i 0.515912 + 0.856641i \(0.327453\pi\)
−0.515912 + 0.856641i \(0.672547\pi\)
\(692\) 1.35098e9 7.08511e9i 0.154981 0.812784i
\(693\) −1.07903e10 1.07903e10i −1.23159 1.23159i
\(694\) −2.32599e9 7.55969e9i −0.264149 0.858510i
\(695\) −4.23290e9 + 4.40111e8i −0.478290 + 0.0497296i
\(696\) 5.84908e9 7.30261e9i 0.657590 0.821005i
\(697\) −1.01828e10 + 1.01828e10i −1.13907 + 1.13907i
\(698\) 6.75486e9 1.27589e10i 0.751835 1.42010i
\(699\) −6.54665e9 −0.725019
\(700\) 1.71452e8 + 9.12550e9i 0.0188929 + 1.00557i
\(701\) −1.56473e9 −0.171564 −0.0857822 0.996314i \(-0.527339\pi\)
−0.0857822 + 0.996314i \(0.527339\pi\)
\(702\) 7.68361e7 1.45132e8i 0.00838273 0.0158337i
\(703\) 6.56774e9 6.56774e9i 0.712972 0.712972i
\(704\) 2.44526e9 + 1.09274e10i 0.264131 + 1.18035i
\(705\) −3.18178e9 + 3.30821e8i −0.341985 + 0.0355575i
\(706\) −6.87341e8 2.23392e9i −0.0735115 0.238920i
\(707\) −4.49325e9 4.49325e9i −0.478182 0.478182i
\(708\) −9.72771e9 1.85487e9i −1.03014 0.196425i
\(709\) 1.64082e10i 1.72902i 0.502619 + 0.864508i \(0.332370\pi\)
−0.502619 + 0.864508i \(0.667630\pi\)
\(710\) −2.06625e9 + 5.12398e9i −0.216660 + 0.537284i
\(711\) 3.98154e9i 0.415440i
\(712\) 4.11889e9 4.55221e8i 0.427662 0.0472653i
\(713\) −1.90155e9 1.90155e9i −0.196469 0.196469i
\(714\) 2.12377e10 6.53447e9i 2.18355 0.671841i
\(715\) −1.98241e8 + 2.44249e8i −0.0202826 + 0.0249897i
\(716\) −9.60270e9 1.41276e10i −0.977682 1.43837i
\(717\) 1.46330e10 1.46330e10i 1.48257 1.48257i
\(718\) −8.52065e9 4.51102e9i −0.859087 0.454820i
\(719\) 1.09801e10 1.10168 0.550840 0.834611i \(-0.314308\pi\)
0.550840 + 0.834611i \(0.314308\pi\)
\(720\) 1.38076e10 + 3.86946e9i 1.37865 + 0.386355i
\(721\) 5.23573e9 0.520240
\(722\) 4.63306e9 + 2.45284e9i 0.458128 + 0.242544i
\(723\) −2.03736e8 + 2.03736e8i −0.0200486 + 0.0200486i
\(724\) −2.06168e9 3.03316e9i −0.201900 0.297037i
\(725\) 1.42389e9 + 6.77334e9i 0.138770 + 0.660115i
\(726\) 7.11495e9 2.18915e9i 0.690071 0.212323i
\(727\) 9.08491e8 + 9.08491e8i 0.0876900 + 0.0876900i 0.749591 0.661901i \(-0.230250\pi\)
−0.661901 + 0.749591i \(0.730250\pi\)
\(728\) −2.76914e8 + 3.06046e7i −0.0266002 + 0.00293986i
\(729\) 1.67012e10i 1.59662i
\(730\) −4.65495e9 1.09461e10i −0.442879 1.04143i
\(731\) 1.90300e10i 1.80189i
\(732\) −1.37966e10 2.63072e9i −1.30012 0.247906i
\(733\) 4.91203e9 + 4.91203e9i 0.460678 + 0.460678i 0.898878 0.438200i \(-0.144384\pi\)
−0.438200 + 0.898878i \(0.644384\pi\)
\(734\) 4.99546e9 + 1.62357e10i 0.466272 + 1.51543i
\(735\) 1.50323e8 + 1.22008e8i 0.0139643 + 0.0113340i
\(736\) 9.18296e8 1.16974e10i 0.0849005 1.08148i
\(737\) 2.29776e9 2.29776e9i 0.211431 0.211431i
\(738\) −8.08964e9 + 1.52801e10i −0.740853 + 1.39936i
\(739\) 7.10183e9 0.647314 0.323657 0.946175i \(-0.395088\pi\)
0.323657 + 0.946175i \(0.395088\pi\)
\(740\) −1.59580e10 1.35674e9i −1.44766 0.123080i
\(741\) 3.18942e8 0.0287970
\(742\) 7.77846e9 1.46924e10i 0.699005 1.32032i
\(743\) −1.17829e10 + 1.17829e10i −1.05388 + 1.05388i −0.0554194 + 0.998463i \(0.517650\pi\)
−0.998463 + 0.0554194i \(0.982350\pi\)
\(744\) −2.80484e9 + 3.50186e9i −0.249691 + 0.311740i
\(745\) −1.03229e9 9.92832e9i −0.0914645 0.879688i
\(746\) 1.24306e9 + 4.04008e9i 0.109625 + 0.356290i
\(747\) 7.82394e9 + 7.82394e9i 0.686758 + 0.686758i
\(748\) −3.77727e9 + 1.98096e10i −0.330006 + 1.73069i
\(749\) 1.62779e10i 1.41551i
\(750\) −1.47746e10 + 1.03108e10i −1.27880 + 0.892435i
\(751\) 2.06162e10i 1.77610i 0.459744 + 0.888052i \(0.347941\pi\)
−0.459744 + 0.888052i \(0.652059\pi\)
\(752\) 2.35962e9 1.02154e9i 0.202339 0.0875975i
\(753\) −2.58742e9 2.58742e9i −0.220843 0.220843i
\(754\) −2.01929e8 + 6.21303e7i −0.0171554 + 0.00527842i
\(755\) −2.75149e8 2.64633e9i −0.0232677 0.223784i
\(756\) 6.65344e9 4.52244e9i 0.560041 0.380668i
\(757\) −1.60631e9 + 1.60631e9i −0.134584 + 0.134584i −0.771189 0.636606i \(-0.780338\pi\)
0.636606 + 0.771189i \(0.280338\pi\)
\(758\) 1.49745e10 + 7.92786e9i 1.24885 + 0.661171i
\(759\) −2.46478e10 −2.04613
\(760\) 1.78093e9 + 8.20754e9i 0.147163 + 0.678212i
\(761\) 2.01084e10 1.65398 0.826991 0.562215i \(-0.190051\pi\)
0.826991 + 0.562215i \(0.190051\pi\)
\(762\) −6.91272e9 3.65975e9i −0.565987 0.299646i
\(763\) 7.39139e9 7.39139e9i 0.602407 0.602407i
\(764\) 1.07712e10 7.32134e9i 0.873851 0.593969i
\(765\) 2.00516e10 + 1.62746e10i 1.61932 + 1.31430i
\(766\) −1.05585e10 + 3.24867e9i −0.848792 + 0.261159i
\(767\) 1.58121e8 + 1.58121e8i 0.0126533 + 0.0126533i
\(768\) −1.95662e10 + 6.21041e8i −1.55863 + 0.0494716i
\(769\) 2.40460e10i 1.90678i −0.301743 0.953389i \(-0.597569\pi\)
0.301743 0.953389i \(-0.402431\pi\)
\(770\) −1.41818e10 + 6.03098e9i −1.11947 + 0.476069i
\(771\) 2.31829e10i 1.82170i
\(772\) −3.31824e9 + 1.74022e10i −0.259565 + 1.36127i
\(773\) −1.46690e10 1.46690e10i −1.14228 1.14228i −0.988032 0.154247i \(-0.950705\pi\)
−0.154247 0.988032i \(-0.549295\pi\)
\(774\) −6.71894e9 2.18372e10i −0.520844 1.69279i
\(775\) −6.82806e8 3.24805e9i −0.0526916 0.250650i
\(776\) 7.38017e9 + 5.91120e9i 0.566957 + 0.454109i
\(777\) −2.10688e10 + 2.10688e10i −1.61127 + 1.61127i
\(778\) 2.41692e9 4.56520e9i 0.184007 0.347561i
\(779\) −1.01263e10 −0.767483
\(780\) −3.54532e8 4.20418e8i −0.0267501 0.0317213i
\(781\) −9.32869e9 −0.700716
\(782\) 9.88728e9 1.86756e10i 0.739356 1.39653i
\(783\) 4.31387e9 4.31387e9i 0.321145 0.321145i
\(784\) −1.44698e8 5.72636e7i −0.0107240 0.00424397i
\(785\) 1.14966e9 1.41646e9i 0.0848250 0.104511i
\(786\) 6.13510e9 + 1.99397e10i 0.450654 + 1.46467i
\(787\) −9.60960e9 9.60960e9i −0.702739 0.702739i 0.262259 0.964998i \(-0.415533\pi\)
−0.964998 + 0.262259i \(0.915533\pi\)
\(788\) 6.37775e9 + 1.21610e9i 0.464329 + 0.0885377i
\(789\) 4.07344e10i 2.95251i
\(790\) 3.72919e9 + 1.50380e9i 0.269104 + 0.108516i
\(791\) 1.55500e10i 1.11715i
\(792\) 2.65972e9 + 2.40654e10i 0.190238 + 1.72130i
\(793\) 2.24259e8 + 2.24259e8i 0.0159696 + 0.0159696i
\(794\) −1.21747e10 + 3.74596e9i −0.863152 + 0.265577i
\(795\) 3.26402e10 3.39372e9i 2.30392 0.239547i
\(796\) 7.06109e9 + 1.03883e10i 0.496222 + 0.730045i
\(797\) −4.84850e9 + 4.84850e9i −0.339237 + 0.339237i −0.856080 0.516843i \(-0.827107\pi\)
0.516843 + 0.856080i \(0.327107\pi\)
\(798\) 1.38090e10 + 7.31081e9i 0.961951 + 0.509278i
\(799\) 4.63073e9 0.321170
\(800\) 8.83923e9 1.14710e10i 0.610379 0.792110i
\(801\) 8.96028e9 0.616038
\(802\) 9.18568e9 + 4.86311e9i 0.628783 + 0.332892i
\(803\) 1.42016e10 1.42016e10i 0.967903 0.967903i
\(804\) 3.19352e9 + 4.69833e9i 0.216708 + 0.318822i
\(805\) 1.60617e10 1.67000e9i 1.08519 0.112831i
\(806\) 9.68322e7 2.97936e7i 0.00651399 0.00200425i
\(807\) −5.61892e9 5.61892e9i −0.376353 0.376353i
\(808\) 1.10755e9 + 1.00212e10i 0.0738624 + 0.668316i
\(809\) 5.88659e8i 0.0390880i −0.999809 0.0195440i \(-0.993779\pi\)
0.999809 0.0195440i \(-0.00622145\pi\)
\(810\) −5.35596e9 2.15980e9i −0.354111 0.142796i
\(811\) 2.13845e10i 1.40775i 0.710323 + 0.703876i \(0.248549\pi\)
−0.710323 + 0.703876i \(0.751451\pi\)
\(812\) −1.01670e10 1.93863e9i −0.666416 0.127071i
\(813\) −2.54720e9 2.54720e9i −0.166244 0.166244i
\(814\) −7.95244e9 2.58462e10i −0.516791 1.67962i
\(815\) −5.14526e9 + 6.33936e9i −0.332932 + 0.410198i
\(816\) −3.27820e10 1.29734e10i −2.11213 0.835866i
\(817\) 9.46221e9 9.46221e9i 0.607037 0.607037i
\(818\) 2.15538e9 4.07118e9i 0.137685 0.260066i
\(819\) −6.02401e8 −0.0383171
\(820\) 1.12563e10 + 1.33481e10i 0.712927 + 0.845417i
\(821\) −5.25130e9 −0.331181 −0.165591 0.986195i \(-0.552953\pi\)
−0.165591 + 0.986195i \(0.552953\pi\)
\(822\) −3.38735e9 + 6.39820e9i −0.212720 + 0.401797i
\(823\) 7.90663e9 7.90663e9i 0.494415 0.494415i −0.415279 0.909694i \(-0.636316\pi\)
0.909694 + 0.415279i \(0.136316\pi\)
\(824\) −6.48386e9 5.19330e9i −0.403728 0.323369i
\(825\) −2.54759e10 1.66254e10i −1.57958 1.03082i
\(826\) 3.22160e9 + 1.04705e10i 0.198903 + 0.646453i
\(827\) 1.23840e10 + 1.23840e10i 0.761360 + 0.761360i 0.976568 0.215208i \(-0.0690429\pi\)
−0.215208 + 0.976568i \(0.569043\pi\)
\(828\) 4.75199e9 2.49214e10i 0.290917 1.52569i
\(829\) 2.94521e10i 1.79546i −0.440549 0.897729i \(-0.645216\pi\)
0.440549 0.897729i \(-0.354784\pi\)
\(830\) 1.02831e10 4.37301e9i 0.624239 0.265465i
\(831\) 3.05125e9i 0.184448i
\(832\) 3.73284e8 + 2.36770e8i 0.0224702 + 0.0142526i
\(833\) −1.98174e8 1.98174e8i −0.0118792 0.0118792i
\(834\) 1.20068e10 3.69428e9i 0.716713 0.220521i
\(835\) −2.06470e10 1.67579e10i −1.22731 0.996130i
\(836\) −1.17280e10 + 7.97168e9i −0.694228 + 0.471876i
\(837\) −2.06865e9 + 2.06865e9i −0.121940 + 0.121940i
\(838\) 2.83462e9 + 1.50071e9i 0.166395 + 0.0880933i
\(839\) 9.55178e9 0.558364 0.279182 0.960238i \(-0.409937\pi\)
0.279182 + 0.960238i \(0.409937\pi\)
\(840\) −5.71310e9 2.63292e10i −0.332579 1.53271i
\(841\) 9.40102e9 0.544991
\(842\) −8.02468e9 4.24845e9i −0.463271 0.245266i
\(843\) −2.97005e10 + 2.97005e10i −1.70753 + 1.70753i
\(844\) −1.13177e10 + 7.69282e9i −0.647979 + 0.440440i
\(845\) −1.81251e9 1.74324e10i −0.103343 0.993934i
\(846\) 5.31383e9 1.63498e9i 0.301725 0.0928357i
\(847\) −5.82293e9 5.82293e9i −0.329268 0.329268i
\(848\) −2.42061e10 + 1.04794e10i −1.36313 + 0.590135i
\(849\) 1.43099e10i 0.802528i
\(850\) 2.28164e10 1.26339e10i 1.27433 0.705620i
\(851\) 2.83358e10i 1.57610i
\(852\) 3.05469e9 1.60201e10i 0.169211 0.887414i
\(853\) 1.98080e10 + 1.98080e10i 1.09275 + 1.09275i 0.995234 + 0.0975141i \(0.0310891\pi\)
0.0975141 + 0.995234i \(0.468911\pi\)
\(854\) 4.56913e9 + 1.48501e10i 0.251033 + 0.815881i
\(855\) 1.87801e9 + 1.80623e10i 0.102758 + 0.988308i
\(856\) 1.61460e10 2.01584e10i 0.879848 1.09849i
\(857\) −1.24882e10 + 1.24882e10i −0.677744 + 0.677744i −0.959489 0.281746i \(-0.909087\pi\)
0.281746 + 0.959489i \(0.409087\pi\)
\(858\) 4.34477e8 8.20663e8i 0.0234834 0.0443567i
\(859\) 1.04650e10 0.563331 0.281665 0.959513i \(-0.409113\pi\)
0.281665 + 0.959513i \(0.409113\pi\)
\(860\) −2.29908e10 1.95467e9i −1.23257 0.104792i
\(861\) 3.24843e10 1.73446
\(862\) −7.11000e9 + 1.34297e10i −0.378089 + 0.714154i
\(863\) 8.40125e9 8.40125e9i 0.444945 0.444945i −0.448725 0.893670i \(-0.648122\pi\)
0.893670 + 0.448725i \(0.148122\pi\)
\(864\) −1.27253e10 9.98994e8i −0.671230 0.0526944i
\(865\) −1.22291e10 9.92562e9i −0.642450 0.521436i
\(866\) −6.17110e9 2.00567e10i −0.322887 1.04941i
\(867\) −2.37374e10 2.37374e10i −1.23699 1.23699i
\(868\) 4.87541e9 + 9.29638e8i 0.253042 + 0.0482497i
\(869\) 6.78934e9i 0.350960i
\(870\) −7.99553e9 1.88014e10i −0.411652 0.967997i
\(871\) 1.28280e8i 0.00657800i
\(872\) −1.64849e10 + 1.82192e9i −0.841936 + 0.0930509i
\(873\) 1.44571e10 + 1.44571e10i 0.735412 + 0.735412i
\(874\) 1.42022e10 4.36978e9i 0.719558 0.221396i
\(875\) 1.77278e10 + 9.10778e9i 0.894593 + 0.459605i
\(876\) 1.97379e10 + 2.90386e10i 0.992058 + 1.45952i
\(877\) 7.17348e9 7.17348e9i 0.359113 0.359113i −0.504373 0.863486i \(-0.668276\pi\)
0.863486 + 0.504373i \(0.168276\pi\)
\(878\) −1.55458e9 8.23028e8i −0.0775142 0.0410378i
\(879\) 4.89399e10 2.43054
\(880\) 2.35447e10 + 6.59820e9i 1.16467 + 0.326390i
\(881\) −3.73437e10 −1.83993 −0.919965 0.392001i \(-0.871783\pi\)
−0.919965 + 0.392001i \(0.871783\pi\)
\(882\) −2.97377e8 1.57438e8i −0.0145938 0.00772626i
\(883\) −2.36186e10 + 2.36186e10i −1.15449 + 1.15449i −0.168853 + 0.985641i \(0.554006\pi\)
−0.985641 + 0.168853i \(0.945994\pi\)
\(884\) 4.47527e8 + 6.58404e8i 0.0217889 + 0.0320560i
\(885\) −1.36277e10 + 1.67903e10i −0.660876 + 0.814251i
\(886\) 1.59023e10 4.89288e9i 0.768144 0.236345i
\(887\) −1.18956e10 1.18956e10i −0.572339 0.572339i 0.360443 0.932781i \(-0.382626\pi\)
−0.932781 + 0.360443i \(0.882626\pi\)
\(888\) 4.69895e10 5.19329e9i 2.25193 0.248884i
\(889\) 8.65259e9i 0.413038i
\(890\) 3.38423e9 8.39237e9i 0.160915 0.399043i
\(891\) 9.75102e9i 0.461826i
\(892\) 2.09119e10 + 3.98746e9i 0.986544 + 0.188113i
\(893\) 2.30252e9 + 2.30252e9i 0.108199 + 0.108199i
\(894\) 8.66499e9 + 2.81620e10i 0.405589 + 1.31820i
\(895\) −3.71016e10 + 3.85759e9i −1.72986 + 0.179861i
\(896\) 1.07346e10 + 1.88077e10i 0.498548 + 0.873489i
\(897\) −6.88021e8 + 6.88021e8i −0.0318294 + 0.0318294i
\(898\) −6.58973e9 + 1.24470e10i −0.303669 + 0.573586i
\(899\) 3.76380e9 0.172770
\(900\) 2.17216e10 2.25534e10i 0.993212 1.03125i
\(901\) −4.75042e10 −2.16369
\(902\) −1.37945e10 + 2.60557e10i −0.625867 + 1.18217i
\(903\) −3.03541e10 + 3.03541e10i −1.37186 + 1.37186i
\(904\) −1.54240e10 + 1.92569e10i −0.694396 + 0.866957i
\(905\) −7.96564e9 + 8.28218e8i −0.357232 + 0.0371428i
\(906\) 2.30960e9 + 7.50642e9i 0.103178 + 0.335339i
\(907\) 1.00274e10 + 1.00274e10i 0.446234 + 0.446234i 0.894101 0.447866i \(-0.147816\pi\)
−0.447866 + 0.894101i \(0.647816\pi\)
\(908\) 6.67438e9 3.50032e10i 0.295876 1.55170i
\(909\) 2.18003e10i 0.962696i
\(910\) −2.27523e8 + 5.64221e8i −0.0100087 + 0.0248201i
\(911\) 1.51202e10i 0.662586i −0.943528 0.331293i \(-0.892515\pi\)
0.943528 0.331293i \(-0.107485\pi\)
\(912\) −9.84937e9 2.27507e10i −0.429958 0.993147i
\(913\) 1.33414e10 + 1.33414e10i 0.580168 + 0.580168i
\(914\) −3.49939e10 + 1.07670e10i −1.51594 + 0.466428i
\(915\) −1.93278e10 + 2.38134e10i −0.834084 + 1.02766i
\(916\) −2.45147e10 + 1.66630e10i −1.05388 + 0.716338i
\(917\) 1.63188e10 1.63188e10i 0.698868 0.698868i
\(918\) −2.03168e10 1.07562e10i −0.866773 0.458889i
\(919\) 2.77128e10 1.17781 0.588905 0.808202i \(-0.299559\pi\)
0.588905 + 0.808202i \(0.299559\pi\)
\(920\) −2.15471e10 1.38635e10i −0.912287 0.586968i
\(921\) 1.81593e10 0.765932
\(922\) −1.22015e8 6.45975e7i −0.00512691 0.00271430i
\(923\) −2.60401e8 + 2.60401e8i −0.0109003 + 0.0109003i
\(924\) 3.76226e10 2.55726e10i 1.56890 1.06641i
\(925\) −1.91130e10 + 2.92878e10i −0.794021 + 1.21672i
\(926\) −1.55988e9 + 4.79948e8i −0.0645583 + 0.0198635i
\(927\) −1.27013e10 1.27013e10i −0.523684 0.523684i
\(928\) 1.06677e10 + 1.24854e10i 0.438182 + 0.512841i
\(929\) 5.82760e9i 0.238471i −0.992866 0.119235i \(-0.961956\pi\)
0.992866 0.119235i \(-0.0380443\pi\)
\(930\) 3.83413e9 + 9.01595e9i 0.156307 + 0.367554i
\(931\) 1.97074e8i 0.00800398i
\(932\) 2.15225e9 1.12873e10i 0.0870836 0.456703i
\(933\) −1.64298e10 1.64298e10i −0.662287 0.662287i
\(934\) −1.69511e9 5.50926e9i −0.0680742 0.221248i
\(935\) 3.41920e10 + 2.77515e10i 1.36799 + 1.11031i
\(936\) 7.46007e8 + 5.97520e8i 0.0297356 + 0.0238170i
\(937\) 2.82676e10 2.82676e10i 1.12254 1.12254i 0.131178 0.991359i \(-0.458124\pi\)
0.991359 0.131178i \(-0.0418761\pi\)
\(938\) 2.94043e9 5.55404e9i 0.116333 0.219735i
\(939\) −4.55222e10 −1.79429
\(940\) 4.75646e8 5.59455e9i 0.0186783 0.219694i
\(941\) 4.05388e10 1.58601 0.793007 0.609212i \(-0.208514\pi\)
0.793007 + 0.609212i \(0.208514\pi\)
\(942\) −2.51965e9 + 4.75924e9i −0.0982115 + 0.185507i
\(943\) 2.18444e10 2.18444e10i 0.848298 0.848298i
\(944\) 6.39607e9 1.61620e10i 0.247463 0.625308i
\(945\) −1.81675e9 1.74732e10i −0.0700301 0.673536i
\(946\) −1.14572e10 3.72369e10i −0.440005 1.43006i
\(947\) 3.34410e10 + 3.34410e10i 1.27954 + 1.27954i 0.940924 + 0.338617i \(0.109959\pi\)
0.338617 + 0.940924i \(0.390041\pi\)
\(948\) −1.16593e10 2.22318e9i −0.444470 0.0847510i
\(949\) 7.92846e8i 0.0301132i
\(950\) 1.76268e10 + 5.06303e9i 0.667024 + 0.191592i
\(951\) 7.95169e10i 2.99797i
\(952\) 4.28429e9 + 3.87647e10i 0.160934 + 1.45615i
\(953\) −1.84343e10 1.84343e10i −0.689926 0.689926i 0.272290 0.962215i \(-0.412219\pi\)
−0.962215 + 0.272290i \(0.912219\pi\)
\(954\) −5.45118e10 + 1.67724e10i −2.03269 + 0.625424i
\(955\) −2.94113e9 2.82872e10i −0.109270 1.05094i
\(956\) 2.04185e10 + 3.00398e10i 0.755825 + 1.11197i
\(957\) 2.43932e10 2.43932e10i 0.899657 0.899657i
\(958\) −2.61103e10 1.38234e10i −0.959474 0.507967i
\(959\) 8.00857e9 0.293217
\(960\) −1.90408e10 + 3.82726e10i −0.694602 + 1.39617i
\(961\) 2.57077e10 0.934398
\(962\) −9.43456e8 4.99487e8i −0.0341672 0.0180889i
\(963\) 3.94885e10 3.94885e10i 1.42488 1.42488i
\(964\) −2.84288e8 4.18246e8i −0.0102209 0.0150370i
\(965\) 3.00368e10 + 2.43790e10i 1.07599 + 0.873314i
\(966\) −4.55596e10 + 1.40179e10i −1.62615 + 0.500339i
\(967\) −1.82599e10 1.82599e10i −0.649390 0.649390i 0.303456 0.952846i \(-0.401860\pi\)
−0.952846 + 0.303456i \(0.901860\pi\)
\(968\) 1.43530e9 + 1.29868e10i 0.0508604 + 0.460191i
\(969\) 4.46482e10i 1.57641i
\(970\) 1.90011e10 8.08044e9i 0.668464 0.284272i
\(971\) 1.37403e9i 0.0481646i −0.999710 0.0240823i \(-0.992334\pi\)
0.999710 0.0240823i \(-0.00766638\pi\)
\(972\) 3.56811e10 + 6.80363e9i 1.24625 + 0.237634i
\(973\) −9.82644e9 9.82644e9i −0.341980 0.341980i
\(974\) −1.14501e10 3.72140e10i −0.397058 1.29048i
\(975\) −1.17522e9 + 2.47054e8i −0.0406071 + 0.00853642i
\(976\) 9.07142e9 2.29223e10i 0.312321 0.789194i
\(977\) −3.84706e10 + 3.84706e10i −1.31977 + 1.31977i −0.405812 + 0.913956i \(0.633011\pi\)
−0.913956 + 0.405812i \(0.866989\pi\)
\(978\) 1.12766e10 2.12999e10i 0.385473 0.728101i
\(979\) 1.52791e10 0.520425
\(980\) −2.59776e8 + 2.19066e8i −0.00881675 + 0.00743503i
\(981\) −3.58614e10 −1.21279
\(982\) −1.82836e10 + 3.45350e10i −0.616130 + 1.16378i
\(983\) −2.33351e10 + 2.33351e10i −0.783560 + 0.783560i −0.980430 0.196869i \(-0.936923\pi\)
0.196869 + 0.980430i \(0.436923\pi\)
\(984\) −4.02282e10 3.22211e10i −1.34601 1.07810i
\(985\) 8.93467e9 1.10082e10i 0.297887 0.367020i
\(986\) 8.69752e9 + 2.82678e10i 0.288952 + 0.939123i
\(987\) −7.38631e9 7.38631e9i −0.244522 0.244522i
\(988\) −1.04854e8 + 5.49897e8i −0.00345888 + 0.0181398i
\(989\) 4.08237e10i 1.34192i
\(990\) 4.90341e10 + 1.97731e10i 1.60611 + 0.647665i
\(991\) 3.00741e10i 0.981599i 0.871272 + 0.490800i \(0.163295\pi\)
−0.871272 + 0.490800i \(0.836705\pi\)
\(992\) −5.11555e9 5.98716e9i −0.166380 0.194729i
\(993\) 4.59667e9 + 4.59667e9i 0.148978 + 0.148978i
\(994\) −1.72434e10 + 5.30549e9i −0.556890 + 0.171346i
\(995\) 2.72817e10 2.83658e9i 0.877991 0.0912881i
\(996\) −2.72798e10 + 1.85424e10i −0.874848 + 0.594647i
\(997\) −1.35996e10 + 1.35996e10i −0.434604 + 0.434604i −0.890191 0.455587i \(-0.849429\pi\)
0.455587 + 0.890191i \(0.349429\pi\)
\(998\) −4.25938e10 2.25501e10i −1.35640 0.718111i
\(999\) 3.08259e10 0.978221
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 20.8.e.b.3.3 36
4.3 odd 2 inner 20.8.e.b.3.12 yes 36
5.2 odd 4 inner 20.8.e.b.7.12 yes 36
5.3 odd 4 100.8.e.e.7.7 36
5.4 even 2 100.8.e.e.43.16 36
20.3 even 4 100.8.e.e.7.16 36
20.7 even 4 inner 20.8.e.b.7.3 yes 36
20.19 odd 2 100.8.e.e.43.7 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
20.8.e.b.3.3 36 1.1 even 1 trivial
20.8.e.b.3.12 yes 36 4.3 odd 2 inner
20.8.e.b.7.3 yes 36 20.7 even 4 inner
20.8.e.b.7.12 yes 36 5.2 odd 4 inner
100.8.e.e.7.7 36 5.3 odd 4
100.8.e.e.7.16 36 20.3 even 4
100.8.e.e.43.7 36 20.19 odd 2
100.8.e.e.43.16 36 5.4 even 2