Properties

Label 69.8.g.a.5.12
Level $69$
Weight $8$
Character 69.5
Analytic conductor $21.555$
Analytic rank $0$
Dimension $540$
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] = [69,8,Mod(5,69)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(69, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 1]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("69.5");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 69.g (of order \(22\), degree \(10\), 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: \(21.5545667584\)
Analytic rank: \(0\)
Dimension: \(540\)
Relative dimension: \(54\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 5.12
Character \(\chi\) \(=\) 69.5
Dual form 69.8.g.a.14.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.89080 + 13.2509i) q^{2} +(-38.0703 - 27.1597i) q^{3} +(-52.7665 - 33.9110i) q^{4} +(-31.2611 + 217.426i) q^{5} +(508.014 - 398.791i) q^{6} +(454.818 - 207.708i) q^{7} +(-681.296 + 590.346i) q^{8} +(711.698 + 2067.96i) q^{9} +O(q^{10})\) \(q+(-3.89080 + 13.2509i) q^{2} +(-38.0703 - 27.1597i) q^{3} +(-52.7665 - 33.9110i) q^{4} +(-31.2611 + 217.426i) q^{5} +(508.014 - 398.791i) q^{6} +(454.818 - 207.708i) q^{7} +(-681.296 + 590.346i) q^{8} +(711.698 + 2067.96i) q^{9} +(-2759.45 - 1260.20i) q^{10} +(-3943.72 + 1157.98i) q^{11} +(1087.82 + 2724.13i) q^{12} +(-4741.43 + 10382.3i) q^{13} +(982.707 + 6834.88i) q^{14} +(7095.36 - 7428.43i) q^{15} +(-8507.02 - 18627.8i) q^{16} +(-3126.12 + 2009.03i) q^{17} +(-30171.3 + 1384.58i) q^{18} +(22333.2 - 34751.1i) q^{19} +(9022.67 - 10412.7i) q^{20} +(-22956.3 - 4445.21i) q^{21} -56763.1i q^{22} +(-34063.9 + 47375.9i) q^{23} +(41970.8 - 3970.85i) q^{24} +(28663.6 + 8416.38i) q^{25} +(-119126. - 103224. i) q^{26} +(29070.7 - 98057.4i) q^{27} +(-31042.7 - 4463.27i) q^{28} +(-27563.6 - 42889.9i) q^{29} +(70826.5 + 122922. i) q^{30} +(-202321. - 233490. i) q^{31} +(165718. - 23826.6i) q^{32} +(181589. + 63025.6i) q^{33} +(-14458.3 - 49240.5i) q^{34} +(30943.1 + 105382. i) q^{35} +(32572.7 - 133253. i) q^{36} +(562280. - 80843.6i) q^{37} +(373588. + 431143. i) q^{38} +(462488. - 266481. i) q^{39} +(-107059. - 166586. i) q^{40} +(433029. + 62260.2i) q^{41} +(148221. - 286896. i) q^{42} +(-424530. - 367857. i) q^{43} +(247364. + 72632.7i) q^{44} +(-471877. + 90094.9i) q^{45} +(-495235. - 635707. i) q^{46} -717704. i q^{47} +(-182061. + 940214. i) q^{48} +(-375590. + 433454. i) q^{49} +(-223049. + 347070. i) q^{50} +(173577. + 8419.97i) q^{51} +(602263. - 387051. i) q^{52} +(-416478. - 911959. i) q^{53} +(1.18624e6 + 766733. i) q^{54} +(-128490. - 893666. i) q^{55} +(-187246. + 410011. i) q^{56} +(-1.79406e6 + 716422. i) q^{57} +(675573. - 198366. i) q^{58} +(-2.15015e6 - 981942. i) q^{59} +(-626303. + 151362. i) q^{60} +(-2.19102e6 + 1.89853e6i) q^{61} +(3.88114e6 - 1.77246e6i) q^{62} +(753225. + 792719. i) q^{63} +(43987.8 - 305942. i) q^{64} +(-2.10916e6 - 1.35547e6i) q^{65} +(-1.54167e6 + 2.16099e6i) q^{66} +(3615.46 - 12313.1i) q^{67} +233083. q^{68} +(2.58354e6 - 878447. i) q^{69} -1.51680e6 q^{70} +(332391. - 1.13202e6i) q^{71} +(-1.70569e6 - 988744. i) q^{72} +(976836. + 627774. i) q^{73} +(-1.11647e6 + 7.76524e6i) q^{74} +(-862644. - 1.09891e6i) q^{75} +(-2.35689e6 + 1.07635e6i) q^{76} +(-1.55315e6 + 1.34581e6i) q^{77} +(1.73165e6 + 7.16519e6i) q^{78} +(-1.68315e6 - 768667. i) q^{79} +(4.31610e6 - 1.26732e6i) q^{80} +(-3.76994e6 + 2.94352e6i) q^{81} +(-2.50983e6 + 5.49577e6i) q^{82} +(-145167. - 1.00966e6i) q^{83} +(1.06059e6 + 1.01303e6i) q^{84} +(-339090. - 742504. i) q^{85} +(6.52619e6 - 4.19413e6i) q^{86} +(-115521. + 2.38145e6i) q^{87} +(2.00323e6 - 3.11709e6i) q^{88} +(4.55138e6 - 5.25257e6i) q^{89} +(642145. - 6.60331e6i) q^{90} +5.70688e6i q^{91} +(3.40400e6 - 1.34472e6i) q^{92} +(1.36087e6 + 1.43840e7i) q^{93} +(9.51019e6 + 2.79244e6i) q^{94} +(6.85763e6 + 5.94217e6i) q^{95} +(-6.95606e6 - 3.59377e6i) q^{96} +(-4.81097e6 - 691713. i) q^{97} +(-4.28229e6 - 6.66337e6i) q^{98} +(-5.20139e6 - 7.33131e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 540 q - 35 q^{3} + 3362 q^{4} - 1280 q^{6} - 22 q^{7} - 659 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 540 q - 35 q^{3} + 3362 q^{4} - 1280 q^{6} - 22 q^{7} - 659 q^{9} - 22 q^{10} + 4756 q^{12} + 4970 q^{13} + 3828 q^{15} - 174622 q^{16} + 250050 q^{18} - 22 q^{19} - 221738 q^{21} + 94934 q^{24} - 788392 q^{25} + 1020934 q^{27} - 22 q^{28} - 1480875 q^{30} + 738458 q^{31} + 1215192 q^{33} + 1815924 q^{34} - 394502 q^{36} - 905234 q^{37} - 1635803 q^{39} + 10260228 q^{40} - 11 q^{42} - 1694330 q^{43} - 6978726 q^{46} + 134426 q^{48} + 7785740 q^{49} - 11 q^{51} + 16219654 q^{52} - 10697559 q^{54} - 1371960 q^{55} + 7508908 q^{57} - 21860696 q^{58} - 21971851 q^{60} - 11102850 q^{61} - 9022926 q^{63} + 2572060 q^{64} + 16582830 q^{66} + 6031564 q^{67} + 12019470 q^{69} - 2949828 q^{70} + 12828949 q^{72} - 1809596 q^{73} - 16620656 q^{75} - 42651158 q^{76} - 47106384 q^{78} - 1156914 q^{79} + 48837101 q^{81} + 47208588 q^{82} + 124183367 q^{84} + 5833252 q^{85} - 17916287 q^{87} + 360426 q^{88} - 142298860 q^{90} - 51670516 q^{93} - 18401348 q^{94} + 36462337 q^{96} - 63860500 q^{97} + 135683977 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(e\left(\frac{1}{22}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.89080 + 13.2509i −0.343902 + 1.17122i 0.588106 + 0.808784i \(0.299874\pi\)
−0.932008 + 0.362438i \(0.881944\pi\)
\(3\) −38.0703 27.1597i −0.814071 0.580766i
\(4\) −52.7665 33.9110i −0.412238 0.264930i
\(5\) −31.2611 + 217.426i −0.111843 + 0.777887i 0.854281 + 0.519811i \(0.173998\pi\)
−0.966125 + 0.258076i \(0.916911\pi\)
\(6\) 508.014 398.791i 0.960166 0.753731i
\(7\) 454.818 207.708i 0.501180 0.228881i −0.148750 0.988875i \(-0.547525\pi\)
0.649931 + 0.759993i \(0.274798\pi\)
\(8\) −681.296 + 590.346i −0.470458 + 0.407654i
\(9\) 711.698 + 2067.96i 0.325422 + 0.945569i
\(10\) −2759.45 1260.20i −0.872615 0.398510i
\(11\) −3943.72 + 1157.98i −0.893370 + 0.262317i −0.696025 0.718017i \(-0.745050\pi\)
−0.197344 + 0.980334i \(0.563232\pi\)
\(12\) 1087.82 + 2724.13i 0.181729 + 0.455085i
\(13\) −4741.43 + 10382.3i −0.598560 + 1.31066i 0.331569 + 0.943431i \(0.392422\pi\)
−0.930129 + 0.367233i \(0.880305\pi\)
\(14\) 982.707 + 6834.88i 0.0957141 + 0.665706i
\(15\) 7095.36 7428.43i 0.542819 0.568300i
\(16\) −8507.02 18627.8i −0.519227 1.13695i
\(17\) −3126.12 + 2009.03i −0.154324 + 0.0991781i −0.615524 0.788118i \(-0.711056\pi\)
0.461200 + 0.887296i \(0.347419\pi\)
\(18\) −30171.3 + 1384.58i −1.21938 + 0.0559585i
\(19\) 22333.2 34751.1i 0.746986 1.16233i −0.234744 0.972057i \(-0.575425\pi\)
0.981731 0.190276i \(-0.0609383\pi\)
\(20\) 9022.67 10412.7i 0.252191 0.291044i
\(21\) −22956.3 4445.21i −0.540923 0.104743i
\(22\) 56763.1i 1.13655i
\(23\) −34063.9 + 47375.9i −0.583778 + 0.811914i
\(24\) 41970.8 3970.85i 0.619738 0.0586333i
\(25\) 28663.6 + 8416.38i 0.366894 + 0.107730i
\(26\) −119126. 103224.i −1.32923 1.15179i
\(27\) 29070.7 98057.4i 0.284238 0.958754i
\(28\) −31042.7 4463.27i −0.267243 0.0384238i
\(29\) −27563.6 42889.9i −0.209867 0.326559i 0.720323 0.693639i \(-0.243994\pi\)
−0.930189 + 0.367080i \(0.880357\pi\)
\(30\) 70826.5 + 122922.i 0.478929 + 0.831200i
\(31\) −202321. 233490.i −1.21976 1.40768i −0.885141 0.465323i \(-0.845938\pi\)
−0.334618 0.942354i \(-0.608607\pi\)
\(32\) 165718. 23826.6i 0.894014 0.128540i
\(33\) 181589. + 63025.6i 0.879611 + 0.305294i
\(34\) −14458.3 49240.5i −0.0630872 0.214855i
\(35\) 30943.1 + 105382.i 0.121990 + 0.415461i
\(36\) 32572.7 133253.i 0.116358 0.476014i
\(37\) 562280. 80843.6i 1.82493 0.262385i 0.857311 0.514798i \(-0.172133\pi\)
0.967620 + 0.252413i \(0.0812240\pi\)
\(38\) 373588. + 431143.i 1.10446 + 1.27461i
\(39\) 462488. 266481.i 1.24846 0.719350i
\(40\) −107059. 166586.i −0.264491 0.411557i
\(41\) 433029. + 62260.2i 0.981237 + 0.141081i 0.614221 0.789134i \(-0.289470\pi\)
0.367016 + 0.930215i \(0.380379\pi\)
\(42\) 148221. 286896.i 0.308701 0.597519i
\(43\) −424530. 367857.i −0.814271 0.705570i 0.144576 0.989494i \(-0.453818\pi\)
−0.958847 + 0.283924i \(0.908364\pi\)
\(44\) 247364. + 72632.7i 0.437777 + 0.128543i
\(45\) −471877. + 90094.9i −0.771942 + 0.147386i
\(46\) −495235. 635707.i −0.750169 0.962952i
\(47\) 717704.i 1.00833i −0.863607 0.504165i \(-0.831800\pi\)
0.863607 0.504165i \(-0.168200\pi\)
\(48\) −182061. + 940214.i −0.237614 + 1.22711i
\(49\) −375590. + 433454.i −0.456066 + 0.526328i
\(50\) −223049. + 347070.i −0.252351 + 0.392665i
\(51\) 173577. + 8419.97i 0.183230 + 0.00888822i
\(52\) 602263. 387051.i 0.593983 0.381730i
\(53\) −416478. 911959.i −0.384261 0.841414i −0.998627 0.0523928i \(-0.983315\pi\)
0.614366 0.789022i \(-0.289412\pi\)
\(54\) 1.18624e6 + 766733.i 1.02516 + 0.662623i
\(55\) −128490. 893666.i −0.104136 0.724279i
\(56\) −187246. + 410011.i −0.142480 + 0.311987i
\(57\) −1.79406e6 + 716422.i −1.28314 + 0.512397i
\(58\) 675573. 198366.i 0.454647 0.133496i
\(59\) −2.15015e6 981942.i −1.36297 0.622449i −0.406334 0.913725i \(-0.633193\pi\)
−0.956639 + 0.291276i \(0.905920\pi\)
\(60\) −626303. + 151362.i −0.374330 + 0.0904665i
\(61\) −2.19102e6 + 1.89853e6i −1.23593 + 1.07094i −0.240978 + 0.970530i \(0.577468\pi\)
−0.994947 + 0.100405i \(0.967986\pi\)
\(62\) 3.88114e6 1.77246e6i 2.06818 0.944506i
\(63\) 753225. + 792719.i 0.379518 + 0.399418i
\(64\) 43987.8 305942.i 0.0209750 0.145884i
\(65\) −2.10916e6 1.35547e6i −0.952604 0.612201i
\(66\) −1.54167e6 + 2.16099e6i −0.660067 + 0.925228i
\(67\) 3615.46 12313.1i 0.00146860 0.00500158i −0.958755 0.284232i \(-0.908261\pi\)
0.960224 + 0.279231i \(0.0900795\pi\)
\(68\) 233083. 0.0898936
\(69\) 2.58354e6 878447.i 0.946768 0.321917i
\(70\) −1.51680e6 −0.528549
\(71\) 332391. 1.13202e6i 0.110216 0.375362i −0.885850 0.463971i \(-0.846424\pi\)
0.996066 + 0.0886095i \(0.0282423\pi\)
\(72\) −1.70569e6 988744.i −0.538563 0.312191i
\(73\) 976836. + 627774.i 0.293895 + 0.188875i 0.679276 0.733883i \(-0.262294\pi\)
−0.385382 + 0.922757i \(0.625930\pi\)
\(74\) −1.11647e6 + 7.76524e6i −0.320285 + 2.22763i
\(75\) −862644. 1.09891e6i −0.236112 0.300779i
\(76\) −2.35689e6 + 1.07635e6i −0.615873 + 0.281260i
\(77\) −1.55315e6 + 1.34581e6i −0.387700 + 0.335944i
\(78\) 1.73165e6 + 7.16519e6i 0.413171 + 1.70961i
\(79\) −1.68315e6 768667.i −0.384085 0.175406i 0.214009 0.976832i \(-0.431348\pi\)
−0.598094 + 0.801426i \(0.704075\pi\)
\(80\) 4.31610e6 1.26732e6i 0.942490 0.276740i
\(81\) −3.76994e6 + 2.94352e6i −0.788201 + 0.615418i
\(82\) −2.50983e6 + 5.49577e6i −0.502686 + 1.10073i
\(83\) −145167. 1.00966e6i −0.0278672 0.193821i 0.971132 0.238541i \(-0.0766693\pi\)
−0.999000 + 0.0447208i \(0.985760\pi\)
\(84\) 1.06059e6 + 1.01303e6i 0.195240 + 0.186485i
\(85\) −339090. 742504.i −0.0598893 0.131139i
\(86\) 6.52619e6 4.19413e6i 1.10641 0.711045i
\(87\) −115521. + 2.38145e6i −0.0188080 + 0.387726i
\(88\) 2.00323e6 3.11709e6i 0.313358 0.487595i
\(89\) 4.55138e6 5.25257e6i 0.684349 0.789781i −0.302200 0.953244i \(-0.597721\pi\)
0.986549 + 0.163463i \(0.0522666\pi\)
\(90\) 642145. 6.60331e6i 0.0928505 0.954802i
\(91\) 5.70688e6i 0.793879i
\(92\) 3.40400e6 1.34472e6i 0.455756 0.180042i
\(93\) 1.36087e6 + 1.43840e7i 0.175439 + 1.85434i
\(94\) 9.51019e6 + 2.79244e6i 1.18098 + 0.346766i
\(95\) 6.85763e6 + 5.94217e6i 0.820619 + 0.711070i
\(96\) −6.95606e6 3.59377e6i −0.802442 0.414572i
\(97\) −4.81097e6 691713.i −0.535219 0.0769528i −0.130594 0.991436i \(-0.541689\pi\)
−0.404624 + 0.914483i \(0.632598\pi\)
\(98\) −4.28229e6 6.66337e6i −0.459605 0.715159i
\(99\) −5.20139e6 7.33131e6i −0.538761 0.759379i
\(100\) −1.22707e6 1.41611e6i −0.122707 0.141611i
\(101\) 6.30331e6 906279.i 0.608757 0.0875260i 0.168959 0.985623i \(-0.445959\pi\)
0.439797 + 0.898097i \(0.355050\pi\)
\(102\) −786926. + 2.26729e6i −0.0734232 + 0.211546i
\(103\) 2.33374e6 + 7.94798e6i 0.210437 + 0.716682i 0.995285 + 0.0969936i \(0.0309226\pi\)
−0.784848 + 0.619688i \(0.787259\pi\)
\(104\) −2.89883e6 9.87250e6i −0.252700 0.860618i
\(105\) 1.68415e6 4.85235e6i 0.141977 0.409062i
\(106\) 1.37047e7 1.97044e6i 1.11763 0.160691i
\(107\) 3.63571e6 + 4.19583e6i 0.286910 + 0.331112i 0.880848 0.473399i \(-0.156973\pi\)
−0.593938 + 0.804511i \(0.702428\pi\)
\(108\) −4.85918e6 + 4.18833e6i −0.371176 + 0.319932i
\(109\) 9.01895e6 + 1.40338e7i 0.667058 + 1.03796i 0.995621 + 0.0934800i \(0.0297991\pi\)
−0.328564 + 0.944482i \(0.606565\pi\)
\(110\) 1.23418e7 + 1.77448e6i 0.884104 + 0.127115i
\(111\) −2.36019e7 1.21936e7i −1.63801 0.846257i
\(112\) −7.73829e6 6.70526e6i −0.520453 0.450975i
\(113\) −1.10455e7 3.24325e6i −0.720130 0.211449i −0.0989222 0.995095i \(-0.531540\pi\)
−0.621208 + 0.783646i \(0.713358\pi\)
\(114\) −2.51287e6 2.65603e7i −0.158856 1.67906i
\(115\) −9.23587e6 8.88741e6i −0.566285 0.544920i
\(116\) 3.19786e6i 0.190220i
\(117\) −2.48446e7 2.41604e6i −1.43411 0.139461i
\(118\) 2.13774e7 2.46708e7i 1.19775 1.38228i
\(119\) −1.00452e6 + 1.56306e6i −0.0546442 + 0.0850281i
\(120\) −448688. + 9.24968e6i −0.0237034 + 0.488644i
\(121\) −2.18167e6 + 1.40208e6i −0.111954 + 0.0719486i
\(122\) −1.66323e7 3.64197e7i −0.829266 1.81584i
\(123\) −1.47946e7 1.41312e7i −0.716861 0.684718i
\(124\) 2.75786e6 + 1.91814e7i 0.129896 + 0.903449i
\(125\) −9.85497e6 + 2.15794e7i −0.451305 + 0.988220i
\(126\) −1.34349e7 + 6.89656e6i −0.598324 + 0.307140i
\(127\) 3.61605e6 1.06177e6i 0.156647 0.0459957i −0.202469 0.979289i \(-0.564897\pi\)
0.359116 + 0.933293i \(0.383078\pi\)
\(128\) 2.33763e7 + 1.06756e7i 0.985236 + 0.449942i
\(129\) 6.17109e6 + 2.55346e7i 0.253103 + 1.04728i
\(130\) 2.61675e7 2.26743e7i 1.04463 0.905173i
\(131\) −4.78896e6 + 2.18705e6i −0.186120 + 0.0849980i −0.506295 0.862360i \(-0.668985\pi\)
0.320176 + 0.947358i \(0.396258\pi\)
\(132\) −7.44455e6 9.48350e6i −0.281728 0.358889i
\(133\) 2.93943e6 2.04442e7i 0.108338 0.753510i
\(134\) 149093. + 95816.0i 0.00535290 + 0.00344010i
\(135\) 2.04114e7 + 9.38611e6i 0.714012 + 0.328335i
\(136\) 943786. 3.21424e6i 0.0321727 0.109570i
\(137\) 3.22478e7 1.07147 0.535733 0.844387i \(-0.320035\pi\)
0.535733 + 0.844387i \(0.320035\pi\)
\(138\) 1.58812e6 + 3.76520e7i 0.0514407 + 1.21958i
\(139\) −1.92552e7 −0.608131 −0.304066 0.952651i \(-0.598344\pi\)
−0.304066 + 0.952651i \(0.598344\pi\)
\(140\) 1.94086e6 6.60997e6i 0.0597787 0.203588i
\(141\) −1.94926e7 + 2.73232e7i −0.585604 + 0.820852i
\(142\) 1.37070e7 + 8.80894e6i 0.401728 + 0.258175i
\(143\) 6.67639e6 4.64353e7i 0.190926 1.32792i
\(144\) 3.24671e7 3.08495e7i 0.906096 0.860954i
\(145\) 1.01870e7 4.65227e6i 0.277498 0.126729i
\(146\) −1.21192e7 + 1.05014e7i −0.322285 + 0.279261i
\(147\) 2.60713e7 6.30080e6i 0.676943 0.163601i
\(148\) −3.24110e7 1.48016e7i −0.821820 0.375313i
\(149\) 1.18088e7 3.46737e6i 0.292451 0.0858713i −0.132216 0.991221i \(-0.542209\pi\)
0.424667 + 0.905350i \(0.360391\pi\)
\(150\) 1.79179e7 7.15514e6i 0.433478 0.173101i
\(151\) −1.64701e7 + 3.60645e7i −0.389293 + 0.852434i 0.608951 + 0.793208i \(0.291590\pi\)
−0.998245 + 0.0592259i \(0.981137\pi\)
\(152\) 5.29968e6 + 3.68601e7i 0.122404 + 0.851341i
\(153\) −6.37945e6 5.03486e6i −0.144000 0.113649i
\(154\) −1.17902e7 2.58169e7i −0.260134 0.569614i
\(155\) 5.70917e7 3.66906e7i 1.23144 0.791396i
\(156\) −3.34405e7 1.62215e6i −0.705240 0.0342102i
\(157\) −2.06899e7 + 3.21940e7i −0.426686 + 0.663937i −0.986327 0.164798i \(-0.947303\pi\)
0.559641 + 0.828735i \(0.310939\pi\)
\(158\) 1.67343e7 1.93124e7i 0.337526 0.389526i
\(159\) −8.91313e6 + 4.60300e7i −0.175849 + 0.908136i
\(160\) 3.67762e7i 0.709818i
\(161\) −5.65252e6 + 2.86227e7i −0.106746 + 0.540531i
\(162\) −2.43361e7 6.14076e7i −0.449727 1.13480i
\(163\) −1.13497e7 3.33257e6i −0.205271 0.0602730i 0.177481 0.984124i \(-0.443205\pi\)
−0.382752 + 0.923851i \(0.625023\pi\)
\(164\) −2.07381e7 1.79697e7i −0.367127 0.318117i
\(165\) −1.93801e7 + 3.75119e7i −0.335863 + 0.650093i
\(166\) 1.39436e7 + 2.00479e6i 0.236590 + 0.0340166i
\(167\) 1.06678e7 + 1.65994e7i 0.177242 + 0.275794i 0.918496 0.395431i \(-0.129405\pi\)
−0.741254 + 0.671225i \(0.765768\pi\)
\(168\) 1.82643e7 1.05237e7i 0.297180 0.171232i
\(169\) −4.42192e7 5.10317e7i −0.704706 0.813274i
\(170\) 1.11582e7 1.60430e6i 0.174189 0.0250446i
\(171\) 8.77583e7 + 2.14518e7i 1.34215 + 0.328078i
\(172\) 9.92657e6 + 3.38068e7i 0.148747 + 0.506587i
\(173\) −2.55408e7 8.69839e7i −0.375036 1.27725i −0.903606 0.428365i \(-0.859090\pi\)
0.528570 0.848890i \(-0.322728\pi\)
\(174\) −3.11068e7 1.07965e7i −0.447645 0.155368i
\(175\) 1.47848e7 2.12574e6i 0.208537 0.0299831i
\(176\) 5.51199e7 + 6.36117e7i 0.762103 + 0.879514i
\(177\) 5.51877e7 + 9.57804e7i 0.748059 + 1.29829i
\(178\) 5.18925e7 + 8.07464e7i 0.689660 + 1.07313i
\(179\) −7.87905e7 1.13284e7i −1.02681 0.147632i −0.391728 0.920081i \(-0.628123\pi\)
−0.635077 + 0.772449i \(0.719032\pi\)
\(180\) 2.79545e7 + 1.12478e7i 0.357271 + 0.143752i
\(181\) −7.43682e7 6.44404e7i −0.932207 0.807762i 0.0493797 0.998780i \(-0.484276\pi\)
−0.981586 + 0.191018i \(0.938821\pi\)
\(182\) −7.56211e7 2.22044e7i −0.929808 0.273016i
\(183\) 1.34976e8 1.27701e7i 1.62809 0.154034i
\(184\) −4.76054e6 5.23865e7i −0.0563370 0.619951i
\(185\) 1.24782e8i 1.44894i
\(186\) −1.95896e8 3.79327e7i −2.23218 0.432234i
\(187\) 1.00021e7 1.15430e7i 0.111852 0.129085i
\(188\) −2.43380e7 + 3.78707e7i −0.267136 + 0.415672i
\(189\) −7.14548e6 5.06364e7i −0.0769866 0.545565i
\(190\) −1.05421e8 + 6.77497e7i −1.11503 + 0.716588i
\(191\) 5.83742e7 + 1.27822e8i 0.606184 + 1.32736i 0.925154 + 0.379592i \(0.123936\pi\)
−0.318970 + 0.947765i \(0.603337\pi\)
\(192\) −9.98392e6 + 1.04526e7i −0.101800 + 0.106579i
\(193\) 1.10288e7 + 7.67069e7i 0.110428 + 0.768040i 0.967505 + 0.252853i \(0.0813687\pi\)
−0.857077 + 0.515188i \(0.827722\pi\)
\(194\) 2.78843e7 6.10581e7i 0.274191 0.600396i
\(195\) 4.34820e7 + 1.08887e8i 0.419941 + 1.05161i
\(196\) 3.45174e7 1.01352e7i 0.327448 0.0961473i
\(197\) −1.74339e8 7.96181e7i −1.62466 0.741959i −0.625400 0.780305i \(-0.715064\pi\)
−0.999265 + 0.0383454i \(0.987791\pi\)
\(198\) 1.17384e8 4.03982e7i 1.07468 0.369857i
\(199\) 1.17043e7 1.01419e7i 0.105284 0.0912287i −0.600628 0.799528i \(-0.705083\pi\)
0.705912 + 0.708300i \(0.250537\pi\)
\(200\) −2.44970e7 + 1.11874e7i −0.216525 + 0.0988834i
\(201\) −472063. + 370570.i −0.00410029 + 0.00321873i
\(202\) −1.25160e7 + 8.70504e7i −0.106840 + 0.743089i
\(203\) −2.14450e7 1.37819e7i −0.179924 0.115630i
\(204\) −8.87353e6 6.33046e6i −0.0731797 0.0522071i
\(205\) −2.70740e7 + 9.22055e7i −0.219489 + 0.747513i
\(206\) −1.14398e8 −0.911763
\(207\) −1.22215e8 3.67256e7i −0.957694 0.287788i
\(208\) 2.33735e8 1.80095
\(209\) −4.78346e7 + 1.62910e8i −0.362435 + 1.23434i
\(210\) 5.77451e7 + 4.11959e7i 0.430276 + 0.306963i
\(211\) −1.45334e8 9.34003e7i −1.06507 0.684478i −0.114007 0.993480i \(-0.536369\pi\)
−0.951061 + 0.309002i \(0.900005\pi\)
\(212\) −8.94935e6 + 6.22441e7i −0.0645084 + 0.448665i
\(213\) −4.33996e7 + 3.40687e7i −0.307721 + 0.241561i
\(214\) −6.97442e7 + 3.18511e7i −0.486474 + 0.222165i
\(215\) 9.32531e7 8.08043e7i 0.639924 0.554498i
\(216\) 3.80821e7 + 8.39679e7i 0.257118 + 0.566924i
\(217\) −1.40517e8 6.41719e7i −0.933510 0.426320i
\(218\) −2.21050e8 + 6.49063e7i −1.44509 + 0.424315i
\(219\) −2.01383e7 5.04302e7i −0.129559 0.324441i
\(220\) −2.35251e7 + 5.15129e7i −0.148954 + 0.326164i
\(221\) −6.03609e6 4.19820e7i −0.0376169 0.261631i
\(222\) 2.53406e8 2.65302e8i 1.55447 1.62744i
\(223\) −1.22934e8 2.69187e8i −0.742342 1.62550i −0.779663 0.626199i \(-0.784610\pi\)
0.0373213 0.999303i \(-0.488118\pi\)
\(224\) 7.04224e7 4.52577e7i 0.418642 0.269045i
\(225\) 2.99506e6 + 6.52650e7i 0.0175294 + 0.381981i
\(226\) 8.59518e7 1.33744e8i 0.495308 0.770714i
\(227\) 9.70095e7 1.11955e8i 0.550457 0.635261i −0.410532 0.911846i \(-0.634657\pi\)
0.960990 + 0.276585i \(0.0892026\pi\)
\(228\) 1.18961e8 + 2.30353e7i 0.664710 + 0.128713i
\(229\) 2.87127e8i 1.57997i −0.613123 0.789987i \(-0.710087\pi\)
0.613123 0.789987i \(-0.289913\pi\)
\(230\) 1.53701e8 8.78040e7i 0.832969 0.475847i
\(231\) 9.56808e7 9.05235e6i 0.510720 0.0483192i
\(232\) 4.40989e7 + 1.29486e7i 0.231857 + 0.0680793i
\(233\) 1.03367e7 + 8.95682e6i 0.0535349 + 0.0463882i 0.681217 0.732081i \(-0.261451\pi\)
−0.627682 + 0.778470i \(0.715996\pi\)
\(234\) 1.28680e8 3.19812e8i 0.656532 1.63170i
\(235\) 1.56047e8 + 2.24362e7i 0.784367 + 0.112775i
\(236\) 8.01575e7 + 1.24727e8i 0.396965 + 0.617689i
\(237\) 4.32011e7 + 7.49772e7i 0.210802 + 0.365856i
\(238\) −1.68036e7 1.93923e7i −0.0807945 0.0932418i
\(239\) −3.12163e8 + 4.48823e7i −1.47907 + 0.212658i −0.834128 0.551571i \(-0.814028\pi\)
−0.644944 + 0.764230i \(0.723119\pi\)
\(240\) −1.98736e8 6.89769e7i −0.927975 0.322080i
\(241\) 3.01166e7 + 1.02568e8i 0.138595 + 0.472011i 0.999313 0.0370718i \(-0.0118030\pi\)
−0.860718 + 0.509082i \(0.829985\pi\)
\(242\) −1.00902e7 3.43642e7i −0.0457665 0.155867i
\(243\) 2.23468e8 9.67027e6i 0.999065 0.0432331i
\(244\) 1.79994e8 2.58792e7i 0.793218 0.114048i
\(245\) −8.25027e7 9.52132e7i −0.358416 0.413634i
\(246\) 2.44814e8 1.41059e8i 1.04849 0.604128i
\(247\) 2.54905e8 + 3.96639e8i 1.07631 + 1.67477i
\(248\) 2.75680e8 + 3.96368e7i 1.14769 + 0.165013i
\(249\) −2.18954e7 + 4.23806e7i −0.0898785 + 0.173968i
\(250\) −2.47602e8 2.14548e8i −1.00222 0.868429i
\(251\) 4.19950e7 + 1.23309e7i 0.167625 + 0.0492193i 0.364468 0.931216i \(-0.381251\pi\)
−0.196843 + 0.980435i \(0.563069\pi\)
\(252\) −1.28632e7 6.73716e7i −0.0506345 0.265201i
\(253\) 7.94782e7 2.26282e8i 0.308551 0.878474i
\(254\) 5.20469e7i 0.199286i
\(255\) −7.25694e6 + 3.74770e7i −0.0274071 + 0.141538i
\(256\) −2.06505e8 + 2.38319e8i −0.769290 + 0.887808i
\(257\) −4.52210e6 + 7.03652e6i −0.0166178 + 0.0258578i −0.849463 0.527648i \(-0.823074\pi\)
0.832845 + 0.553506i \(0.186710\pi\)
\(258\) −3.62366e8 1.75778e7i −1.31364 0.0637230i
\(259\) 2.38943e8 1.53559e8i 0.854565 0.549195i
\(260\) 6.53275e7 + 1.43047e8i 0.230510 + 0.504746i
\(261\) 6.90775e7 8.75251e7i 0.240489 0.304713i
\(262\) −1.03473e7 7.19673e7i −0.0355446 0.247218i
\(263\) −7.31657e7 + 1.60210e8i −0.248006 + 0.543057i −0.992163 0.124947i \(-0.960124\pi\)
0.744157 + 0.668004i \(0.232851\pi\)
\(264\) −1.60923e8 + 6.42612e7i −0.538274 + 0.214949i
\(265\) 2.11303e8 6.20442e7i 0.697502 0.204805i
\(266\) 2.59466e8 + 1.18494e8i 0.845270 + 0.386022i
\(267\) −3.15931e8 + 7.63528e7i −1.01579 + 0.245491i
\(268\) −608326. + 527118.i −0.00193048 + 0.00167277i
\(269\) −4.31310e8 + 1.96973e8i −1.35100 + 0.616982i −0.953715 0.300712i \(-0.902776\pi\)
−0.397288 + 0.917694i \(0.630048\pi\)
\(270\) −2.03791e8 + 2.33950e8i −0.630103 + 0.723352i
\(271\) 8.74383e6 6.08147e7i 0.0266876 0.185616i −0.972117 0.234496i \(-0.924656\pi\)
0.998805 + 0.0488798i \(0.0155651\pi\)
\(272\) 6.40178e7 + 4.11417e7i 0.192890 + 0.123963i
\(273\) 1.54997e8 2.17263e8i 0.461058 0.646273i
\(274\) −1.25470e8 + 4.27312e8i −0.368479 + 1.25492i
\(275\) −1.22787e8 −0.356031
\(276\) −1.66113e8 4.12579e7i −0.475579 0.118120i
\(277\) 5.16159e8 1.45916 0.729582 0.683893i \(-0.239715\pi\)
0.729582 + 0.683893i \(0.239715\pi\)
\(278\) 7.49184e7 2.55149e8i 0.209137 0.712256i
\(279\) 3.38857e8 5.84565e8i 0.934119 1.61146i
\(280\) −8.32935e7 5.35295e7i −0.226756 0.145727i
\(281\) 1.83442e7 1.27587e8i 0.0493204 0.343031i −0.950188 0.311678i \(-0.899109\pi\)
0.999508 0.0313535i \(-0.00998177\pi\)
\(282\) −2.86214e8 3.64603e8i −0.760009 0.968164i
\(283\) −4.05421e8 + 1.85150e8i −1.06330 + 0.485591i −0.868724 0.495297i \(-0.835059\pi\)
−0.194572 + 0.980888i \(0.562332\pi\)
\(284\) −5.59270e7 + 4.84611e7i −0.144880 + 0.125539i
\(285\) −9.96844e7 4.12472e8i −0.255076 1.05545i
\(286\) 5.89331e8 + 2.69139e8i 1.48963 + 0.680291i
\(287\) 2.09881e8 6.16267e7i 0.524067 0.153880i
\(288\) 1.67214e8 + 3.25740e8i 0.412475 + 0.803522i
\(289\) −1.64724e8 + 3.60696e8i −0.401435 + 0.879021i
\(290\) 2.20108e7 + 1.53088e8i 0.0529959 + 0.368594i
\(291\) 1.64368e8 + 1.56998e8i 0.391014 + 0.373482i
\(292\) −3.02558e7 6.62509e7i −0.0711162 0.155723i
\(293\) −4.44211e8 + 2.85477e8i −1.03170 + 0.663032i −0.942920 0.333020i \(-0.891932\pi\)
−0.0887775 + 0.996051i \(0.528296\pi\)
\(294\) −1.79473e7 + 3.69982e8i −0.0411892 + 0.849113i
\(295\) 2.80716e8 4.36803e8i 0.636634 0.990622i
\(296\) −3.35353e8 + 3.87018e8i −0.751591 + 0.867382i
\(297\) −1.09800e6 + 4.20374e8i −0.00243196 + 0.931082i
\(298\) 1.69967e8i 0.372056i
\(299\) −3.30358e8 5.78291e8i −0.714720 1.25112i
\(300\) 8.25365e6 + 8.72387e7i 0.0176491 + 0.186546i
\(301\) −2.69491e8 7.91296e7i −0.569588 0.167246i
\(302\) −4.13804e8 3.58563e8i −0.864510 0.749102i
\(303\) −2.64583e8 1.36694e8i −0.546403 0.282293i
\(304\) −8.37324e8 1.20389e8i −1.70937 0.245770i
\(305\) −3.44296e8 5.35735e8i −0.694837 1.08119i
\(306\) 9.15374e7 6.49436e7i 0.182631 0.129572i
\(307\) 1.09857e8 + 1.26781e8i 0.216692 + 0.250076i 0.853680 0.520798i \(-0.174365\pi\)
−0.636988 + 0.770874i \(0.719820\pi\)
\(308\) 1.27592e8 1.83450e7i 0.248826 0.0357758i
\(309\) 1.27019e8 3.65966e8i 0.244914 0.705644i
\(310\) 2.64049e8 + 8.99269e8i 0.503407 + 1.71445i
\(311\) 2.48288e8 + 8.45591e8i 0.468052 + 1.59404i 0.768242 + 0.640159i \(0.221132\pi\)
−0.300190 + 0.953879i \(0.597050\pi\)
\(312\) −1.57775e8 + 4.54581e8i −0.294102 + 0.847364i
\(313\) 1.26536e8 1.81932e7i 0.233243 0.0335353i −0.0247019 0.999695i \(-0.507864\pi\)
0.257945 + 0.966160i \(0.416955\pi\)
\(314\) −3.46099e8 3.99419e8i −0.630879 0.728073i
\(315\) −1.95904e8 + 1.38989e8i −0.353148 + 0.250550i
\(316\) 6.27475e7 + 9.76370e7i 0.111864 + 0.174064i
\(317\) 7.44230e8 + 1.07004e8i 1.31220 + 0.188666i 0.762659 0.646801i \(-0.223894\pi\)
0.549541 + 0.835467i \(0.314803\pi\)
\(318\) −5.75258e8 2.97200e8i −1.00315 0.518268i
\(319\) 1.58369e8 + 1.37227e8i 0.273151 + 0.236686i
\(320\) 6.51446e7 + 1.91282e7i 0.111136 + 0.0326324i
\(321\) −2.44549e7 2.58481e8i −0.0412666 0.436176i
\(322\) −3.57283e8 1.86266e8i −0.596372 0.310913i
\(323\) 1.53504e8i 0.253461i
\(324\) 2.98745e8 2.74771e7i 0.487969 0.0448811i
\(325\) −2.23288e8 + 2.57688e8i −0.360805 + 0.416392i
\(326\) 8.83189e7 1.37427e8i 0.141186 0.219690i
\(327\) 3.77989e7 7.79222e8i 0.0597809 1.23238i
\(328\) −3.31776e8 + 2.13220e8i −0.519143 + 0.333633i
\(329\) −1.49073e8 3.26424e8i −0.230788 0.505355i
\(330\) −4.21661e8 4.02754e8i −0.645899 0.616938i
\(331\) 9.44162e6 + 6.56679e7i 0.0143103 + 0.0995302i 0.995725 0.0923697i \(-0.0294442\pi\)
−0.981414 + 0.191900i \(0.938535\pi\)
\(332\) −2.65785e7 + 5.81987e7i −0.0398609 + 0.0872831i
\(333\) 5.67355e8 + 1.10524e9i 0.841976 + 1.64021i
\(334\) −2.61462e8 + 7.67723e7i −0.383969 + 0.112744i
\(335\) 2.56417e6 + 1.17102e6i 0.00372641 + 0.00170179i
\(336\) 1.12486e8 + 4.65441e8i 0.161775 + 0.669387i
\(337\) 6.49598e8 5.62880e8i 0.924571 0.801145i −0.0557727 0.998443i \(-0.517762\pi\)
0.980344 + 0.197298i \(0.0632168\pi\)
\(338\) 8.48263e8 3.87389e8i 1.19487 0.545680i
\(339\) 3.32420e8 + 4.23464e8i 0.463434 + 0.590362i
\(340\) −7.28643e6 + 5.06782e7i −0.0100540 + 0.0699271i
\(341\) 1.06827e9 + 6.86537e8i 1.45895 + 0.937612i
\(342\) −6.25705e8 + 1.07941e9i −0.845821 + 1.45913i
\(343\) −1.96803e8 + 6.70249e8i −0.263331 + 0.896823i
\(344\) 5.06394e8 0.670709
\(345\) 1.10233e8 + 5.89190e8i 0.144525 + 0.772483i
\(346\) 1.25199e9 1.62492
\(347\) 1.05843e8 3.60469e8i 0.135991 0.463142i −0.863134 0.504975i \(-0.831502\pi\)
0.999125 + 0.0418331i \(0.0133198\pi\)
\(348\) 8.68530e7 1.21744e8i 0.110473 0.154853i
\(349\) −9.16826e8 5.89208e8i −1.15451 0.741959i −0.183978 0.982930i \(-0.558898\pi\)
−0.970532 + 0.240972i \(0.922534\pi\)
\(350\) −2.93570e7 + 2.04183e8i −0.0365994 + 0.254555i
\(351\) 8.80224e8 + 7.66753e8i 1.08647 + 0.946412i
\(352\) −6.25954e8 + 2.85863e8i −0.764967 + 0.349349i
\(353\) 6.31840e8 5.47493e8i 0.764532 0.662471i −0.182646 0.983179i \(-0.558466\pi\)
0.947178 + 0.320708i \(0.103921\pi\)
\(354\) −1.48390e9 + 3.58622e8i −1.77784 + 0.429660i
\(355\) 2.35740e8 + 1.07659e8i 0.279662 + 0.127717i
\(356\) −4.18280e8 + 1.22818e8i −0.491351 + 0.144274i
\(357\) 8.06948e7 3.22238e7i 0.0938657 0.0374834i
\(358\) 4.56669e8 9.99965e8i 0.526030 1.15185i
\(359\) −4.06768e7 2.82913e8i −0.0463998 0.322717i −0.999781 0.0209476i \(-0.993332\pi\)
0.953381 0.301770i \(-0.0975774\pi\)
\(360\) 2.68301e8 3.39952e8i 0.303084 0.384024i
\(361\) −3.37540e8 7.39108e8i −0.377615 0.826862i
\(362\) 1.14324e9 7.34718e8i 1.26666 0.814030i
\(363\) 1.21137e8 + 5.87617e6i 0.132924 + 0.00644795i
\(364\) 1.93526e8 3.01132e8i 0.210322 0.327267i
\(365\) −1.67031e8 + 1.92765e8i −0.179793 + 0.207492i
\(366\) −3.55952e8 + 1.83824e9i −0.379496 + 1.95983i
\(367\) 1.39329e9i 1.47133i −0.677348 0.735663i \(-0.736871\pi\)
0.677348 0.735663i \(-0.263129\pi\)
\(368\) 1.17229e9 + 2.31508e8i 1.22622 + 0.242158i
\(369\) 1.79434e8 + 9.39798e8i 0.185915 + 0.973738i
\(370\) −1.65346e9 4.85501e8i −1.69703 0.498292i
\(371\) −3.78843e8 3.28269e8i −0.385168 0.333750i
\(372\) 4.15968e8 8.05143e8i 0.418947 0.810910i
\(373\) −1.63143e9 2.34564e8i −1.62774 0.234034i −0.732876 0.680363i \(-0.761822\pi\)
−0.894869 + 0.446328i \(0.852731\pi\)
\(374\) 1.14039e8 + 1.77448e8i 0.112720 + 0.175396i
\(375\) 9.61272e8 5.53875e8i 0.941319 0.542378i
\(376\) 4.23694e8 + 4.88969e8i 0.411050 + 0.474377i
\(377\) 5.75986e8 8.28143e7i 0.553627 0.0795996i
\(378\) 6.98778e8 + 1.02333e8i 0.665454 + 0.0974526i
\(379\) 5.73883e8 + 1.95446e9i 0.541484 + 1.84413i 0.536122 + 0.844140i \(0.319889\pi\)
0.00536202 + 0.999986i \(0.498293\pi\)
\(380\) −1.60348e8 5.46097e8i −0.149907 0.510537i
\(381\) −1.66502e8 5.77891e7i −0.154234 0.0535314i
\(382\) −1.92087e9 + 2.76179e8i −1.76310 + 0.253495i
\(383\) 9.62319e8 + 1.11058e9i 0.875232 + 1.01007i 0.999840 + 0.0178660i \(0.00568724\pi\)
−0.124608 + 0.992206i \(0.539767\pi\)
\(384\) −5.99996e8 1.04132e9i −0.540741 0.938476i
\(385\) −2.44061e8 3.79767e8i −0.217965 0.339160i
\(386\) −1.05934e9 1.52311e8i −0.937522 0.134795i
\(387\) 4.58577e8 1.13971e9i 0.402183 0.999557i
\(388\) 2.30401e8 + 1.99644e8i 0.200251 + 0.173518i
\(389\) −1.57130e9 4.61377e8i −1.35343 0.397404i −0.476989 0.878909i \(-0.658272\pi\)
−0.876443 + 0.481505i \(0.840090\pi\)
\(390\) −1.61203e9 + 1.52514e8i −1.37609 + 0.130192i
\(391\) 1.13082e7 2.16538e8i 0.00956696 0.183196i
\(392\) 5.17038e8i 0.433532i
\(393\) 2.41717e8 + 4.68054e7i 0.200878 + 0.0388976i
\(394\) 1.73333e9 2.00037e9i 1.42772 1.64768i
\(395\) 2.19745e8 3.41930e8i 0.179403 0.279157i
\(396\) 2.58471e7 + 5.63232e8i 0.0209160 + 0.455779i
\(397\) 4.06725e8 2.61386e8i 0.326238 0.209660i −0.367261 0.930118i \(-0.619705\pi\)
0.693499 + 0.720458i \(0.256068\pi\)
\(398\) 8.88491e7 + 1.94552e8i 0.0706418 + 0.154684i
\(399\) −6.67164e8 + 6.98482e8i −0.525808 + 0.550491i
\(400\) −8.70631e7 6.05537e8i −0.0680180 0.473076i
\(401\) 6.38599e8 1.39834e9i 0.494565 1.08295i −0.483633 0.875271i \(-0.660683\pi\)
0.978198 0.207675i \(-0.0665895\pi\)
\(402\) −3.07367e6 7.69706e6i −0.00235975 0.00590927i
\(403\) 3.38345e9 9.93472e8i 2.57509 0.756115i
\(404\) −3.63336e8 1.65930e8i −0.274141 0.125196i
\(405\) −5.22146e8 9.11701e8i −0.390570 0.681962i
\(406\) 2.66060e8 2.30542e8i 0.197305 0.170966i
\(407\) −2.12386e9 + 9.69933e8i −1.56151 + 0.713118i
\(408\) −1.23228e8 + 9.67341e7i −0.0898254 + 0.0705130i
\(409\) 7.64008e7 5.31379e8i 0.0552162 0.384037i −0.943410 0.331630i \(-0.892402\pi\)
0.998626 0.0524072i \(-0.0166894\pi\)
\(410\) −1.11646e9 7.17507e8i −0.800020 0.514142i
\(411\) −1.22769e9 8.75843e8i −0.872249 0.622271i
\(412\) 1.46381e8 4.98526e8i 0.103120 0.351195i
\(413\) −1.18188e9 −0.825562
\(414\) 9.62158e8 1.47656e9i 0.666416 1.02270i
\(415\) 2.24063e8 0.153887
\(416\) −5.38365e8 + 1.83350e9i −0.366649 + 1.24869i
\(417\) 7.33053e8 + 5.22967e8i 0.495062 + 0.353182i
\(418\) −1.97258e9 1.26770e9i −1.32104 0.848984i
\(419\) 5.13457e7 3.57117e8i 0.0341001 0.237171i −0.965642 0.259875i \(-0.916319\pi\)
0.999742 + 0.0227042i \(0.00722760\pi\)
\(420\) −2.53414e8 + 1.98930e8i −0.166901 + 0.131017i
\(421\) −4.55219e8 + 2.07891e8i −0.297326 + 0.135784i −0.558493 0.829510i \(-0.688620\pi\)
0.261167 + 0.965294i \(0.415893\pi\)
\(422\) 1.80310e9 1.56239e9i 1.16795 1.01204i
\(423\) 1.48418e9 5.10788e8i 0.953445 0.328133i
\(424\) 8.22117e8 + 3.75448e8i 0.523785 + 0.239204i
\(425\) −1.06514e8 + 3.12755e7i −0.0673050 + 0.0197625i
\(426\) −2.82580e8 7.07637e8i −0.177096 0.443483i
\(427\) −6.02175e8 + 1.31858e9i −0.374304 + 0.819612i
\(428\) −4.95589e7 3.44690e8i −0.0305540 0.212508i
\(429\) −1.51534e9 + 1.58648e9i −0.926638 + 0.970138i
\(430\) 7.07897e8 + 1.55008e9i 0.429369 + 0.940186i
\(431\) −1.62404e9 + 1.04371e9i −0.977070 + 0.627925i −0.928671 0.370904i \(-0.879048\pi\)
−0.0483983 + 0.998828i \(0.515412\pi\)
\(432\) −2.07390e9 + 2.92654e8i −1.23764 + 0.174647i
\(433\) −1.17493e9 + 1.82822e9i −0.695509 + 1.08223i 0.296373 + 0.955072i \(0.404223\pi\)
−0.991882 + 0.127161i \(0.959413\pi\)
\(434\) 1.39706e9 1.61229e9i 0.820351 0.946736i
\(435\) −5.14178e8 9.95641e7i −0.299503 0.0579950i
\(436\) 1.04635e9i 0.604611i
\(437\) 8.85607e8 + 2.24181e9i 0.507640 + 1.28503i
\(438\) 7.46597e8 7.06355e7i 0.424548 0.0401665i
\(439\) 1.45104e8 + 4.26065e7i 0.0818569 + 0.0240353i 0.322405 0.946602i \(-0.395509\pi\)
−0.240548 + 0.970637i \(0.577327\pi\)
\(440\) 6.15112e8 + 5.32998e8i 0.344247 + 0.298292i
\(441\) −1.16367e9 4.68216e8i −0.646093 0.259963i
\(442\) 5.79782e8 + 8.33601e7i 0.319365 + 0.0459177i
\(443\) 8.88810e8 + 1.38302e9i 0.485731 + 0.755812i 0.994460 0.105114i \(-0.0335209\pi\)
−0.508729 + 0.860927i \(0.669884\pi\)
\(444\) 8.31890e8 + 1.44378e9i 0.451051 + 0.782816i
\(445\) 9.99764e8 + 1.15379e9i 0.537821 + 0.620678i
\(446\) 4.04528e9 5.81623e8i 2.15912 0.310434i
\(447\) −5.43736e8 1.88719e8i −0.287947 0.0999401i
\(448\) −4.35402e7 1.48284e8i −0.0228780 0.0779152i
\(449\) −3.37974e8 1.15103e9i −0.176206 0.600104i −0.999473 0.0324494i \(-0.989669\pi\)
0.823267 0.567654i \(-0.192149\pi\)
\(450\) −8.76471e8 2.14246e8i −0.453413 0.110833i
\(451\) −1.77984e9 + 2.55902e8i −0.913615 + 0.131358i
\(452\) 4.72851e8 + 5.45699e8i 0.240846 + 0.277951i
\(453\) 1.60652e9 9.25663e8i 0.811977 0.467853i
\(454\) 1.10605e9 + 1.72105e9i 0.554729 + 0.863175i
\(455\) −1.24083e9 1.78404e8i −0.617548 0.0887900i
\(456\) 7.99349e8 1.54721e9i 0.394784 0.764140i
\(457\) 2.16275e8 + 1.87404e8i 0.105999 + 0.0918484i 0.706248 0.707965i \(-0.250386\pi\)
−0.600249 + 0.799813i \(0.704932\pi\)
\(458\) 3.80468e9 + 1.11716e9i 1.85050 + 0.543356i
\(459\) 1.06122e8 + 3.64943e8i 0.0512227 + 0.176149i
\(460\) 1.85964e8 + 7.82155e8i 0.0890791 + 0.374663i
\(461\) 4.38820e8i 0.208609i 0.994545 + 0.104304i \(0.0332616\pi\)
−0.994545 + 0.104304i \(0.966738\pi\)
\(462\) −2.52324e8 + 1.30307e9i −0.119045 + 0.614783i
\(463\) −4.09995e8 + 4.73160e8i −0.191975 + 0.221551i −0.843575 0.537012i \(-0.819553\pi\)
0.651599 + 0.758563i \(0.274098\pi\)
\(464\) −5.64459e8 + 8.78315e8i −0.262313 + 0.408166i
\(465\) −3.17000e9 1.53772e8i −1.46209 0.0709239i
\(466\) −1.58904e8 + 1.02121e8i −0.0727417 + 0.0467482i
\(467\) −5.91486e8 1.29517e9i −0.268742 0.588463i 0.726360 0.687314i \(-0.241210\pi\)
−0.995102 + 0.0988515i \(0.968483\pi\)
\(468\) 1.22903e9 + 9.69992e8i 0.554247 + 0.437429i
\(469\) −913164. 6.35119e6i −0.000408737 0.00284283i
\(470\) −9.04450e8 + 1.98047e9i −0.401830 + 0.879884i
\(471\) 1.66205e9 6.63706e8i 0.732944 0.292687i
\(472\) 2.04458e9 6.00342e8i 0.894965 0.262786i
\(473\) 2.10020e9 + 9.59128e8i 0.912528 + 0.416738i
\(474\) −1.16160e9 + 2.80730e8i −0.500994 + 0.121078i
\(475\) 9.32626e8 8.08125e8i 0.399282 0.345980i
\(476\) 1.06010e8 4.84132e7i 0.0450529 0.0205750i
\(477\) 1.58949e9 1.51030e9i 0.670568 0.637160i
\(478\) 6.19837e8 4.31106e9i 0.259585 1.80545i
\(479\) −3.39681e9 2.18300e9i −1.41220 0.907567i −0.412207 0.911090i \(-0.635242\pi\)
−0.999994 + 0.00352345i \(0.998878\pi\)
\(480\) 9.98833e8 1.40008e9i 0.412238 0.577842i
\(481\) −1.82667e9 + 6.22107e9i −0.748432 + 2.54893i
\(482\) −1.47629e9 −0.600492
\(483\) 9.92579e8 9.36156e8i 0.400821 0.378036i
\(484\) 1.62665e8 0.0652132
\(485\) 3.00793e8 1.02441e9i 0.119721 0.407733i
\(486\) −7.41331e8 + 2.99877e9i −0.292945 + 1.18499i
\(487\) −2.65251e8 1.70467e8i −0.104065 0.0668788i 0.487573 0.873082i \(-0.337882\pi\)
−0.591638 + 0.806203i \(0.701519\pi\)
\(488\) 3.71943e8 2.58692e9i 0.144880 1.00766i
\(489\) 3.41575e8 + 4.35127e8i 0.132101 + 0.168281i
\(490\) 1.58266e9 7.22776e8i 0.607717 0.277535i
\(491\) −3.50208e8 + 3.03457e8i −0.133518 + 0.115694i −0.719060 0.694948i \(-0.755427\pi\)
0.585542 + 0.810642i \(0.300882\pi\)
\(492\) 3.01455e8 + 1.24735e9i 0.114116 + 0.472185i
\(493\) 1.72334e8 + 7.87025e7i 0.0647750 + 0.0295818i
\(494\) −6.24760e9 + 1.83446e9i −2.33168 + 0.684643i
\(495\) 1.75662e9 9.01732e8i 0.650968 0.334164i
\(496\) −2.62826e9 + 5.75509e9i −0.967125 + 2.11771i
\(497\) −8.39526e7 5.83903e8i −0.0306752 0.213350i
\(498\) −4.76388e8 4.55028e8i −0.172846 0.165096i
\(499\) −3.72608e8 8.15898e8i −0.134246 0.293957i 0.830556 0.556935i \(-0.188023\pi\)
−0.964802 + 0.262978i \(0.915295\pi\)
\(500\) 1.25179e9 8.04477e8i 0.447854 0.287818i
\(501\) 4.47092e7 9.21678e8i 0.0158842 0.327452i
\(502\) −3.26789e8 + 5.08493e8i −0.115293 + 0.179400i
\(503\) −3.34266e8 + 3.85764e8i −0.117113 + 0.135156i −0.811279 0.584660i \(-0.801228\pi\)
0.694166 + 0.719815i \(0.255773\pi\)
\(504\) −9.81148e8 9.54126e7i −0.341372 0.0331970i
\(505\) 1.39883e9i 0.483333i
\(506\) 2.68920e9 + 1.93358e9i 0.922777 + 0.663490i
\(507\) 2.97432e8 + 3.14378e9i 0.101359 + 1.07133i
\(508\) −2.26812e8 6.65980e7i −0.0767615 0.0225392i
\(509\) −3.23808e9 2.80582e9i −1.08837 0.943077i −0.0897678 0.995963i \(-0.528612\pi\)
−0.998601 + 0.0528862i \(0.983158\pi\)
\(510\) −4.68367e8 2.41976e8i −0.156347 0.0807750i
\(511\) 5.74676e8 + 8.26259e7i 0.190524 + 0.0273932i
\(512\) −5.76070e8 8.96383e8i −0.189684 0.295154i
\(513\) −2.75836e9 3.20017e9i −0.902070 1.04655i
\(514\) −7.56454e7 8.72994e7i −0.0245703 0.0283557i
\(515\) −1.80105e9 + 2.58952e8i −0.581033 + 0.0835400i
\(516\) 5.40276e8 1.55664e9i 0.173118 0.498785i
\(517\) 8.31086e8 + 2.83042e9i 0.264502 + 0.900811i
\(518\) 1.10511e9 + 3.76367e9i 0.349343 + 1.18975i
\(519\) −1.39011e9 + 4.00519e9i −0.436480 + 1.25758i
\(520\) 2.23716e9 3.21655e8i 0.697727 0.100318i
\(521\) −2.34479e9 2.70603e9i −0.726393 0.838302i 0.265667 0.964065i \(-0.414408\pi\)
−0.992060 + 0.125762i \(0.959862\pi\)
\(522\) 8.91016e8 + 1.25588e9i 0.274182 + 0.386457i
\(523\) 2.16403e9 + 3.36730e9i 0.661467 + 1.02926i 0.996212 + 0.0869540i \(0.0277133\pi\)
−0.334745 + 0.942309i \(0.608650\pi\)
\(524\) 3.26862e8 + 4.69957e7i 0.0992441 + 0.0142692i
\(525\) −6.20598e8 3.20625e8i −0.187177 0.0967029i
\(526\) −1.83825e9 1.59286e9i −0.550751 0.477228i
\(527\) 1.10157e9 + 3.23449e8i 0.327849 + 0.0962652i
\(528\) −3.70753e8 3.91876e9i −0.109614 1.15859i
\(529\) −1.08412e9 3.22762e9i −0.318407 0.947954i
\(530\) 3.04135e9i 0.887363i
\(531\) 5.00357e8 5.14527e9i 0.145027 1.49134i
\(532\) −8.48386e8 + 9.79089e8i −0.244288 + 0.281924i
\(533\) −2.69958e9 + 4.20063e9i −0.772239 + 1.20163i
\(534\) 2.17485e8 4.48343e9i 0.0618065 1.27414i
\(535\) −1.02594e9 + 6.59331e8i −0.289657 + 0.186151i
\(536\) 4.80582e6 + 1.05233e7i 0.00134800 + 0.00295171i
\(537\) 2.69190e9 + 2.57120e9i 0.750152 + 0.716517i
\(538\) −9.31914e8 6.48161e9i −0.258011 1.79451i
\(539\) 9.79289e8 2.14434e9i 0.269370 0.589839i
\(540\) −7.58749e8 1.18744e9i −0.207358 0.324515i
\(541\) −2.08415e9 + 6.11960e8i −0.565897 + 0.166162i −0.552153 0.833743i \(-0.686193\pi\)
−0.0137447 + 0.999906i \(0.504375\pi\)
\(542\) 7.71827e8 + 3.52481e8i 0.208220 + 0.0950908i
\(543\) 1.08104e9 + 4.47309e9i 0.289762 + 1.19897i
\(544\) −4.70185e8 + 4.07418e8i −0.125220 + 0.108503i
\(545\) −3.33325e9 + 1.52224e9i −0.882023 + 0.402806i
\(546\) 2.27586e9 + 2.89918e9i 0.598371 + 0.762255i
\(547\) 5.39582e8 3.75288e9i 0.140962 0.980412i −0.789428 0.613843i \(-0.789623\pi\)
0.930391 0.366570i \(-0.119468\pi\)
\(548\) −1.70161e9 1.09356e9i −0.441700 0.283863i
\(549\) −5.48543e9 3.17976e9i −1.41484 0.820147i
\(550\) 4.77740e8 1.62703e9i 0.122440 0.416991i
\(551\) −2.10605e9 −0.536338
\(552\) −1.24157e9 + 2.12367e9i −0.314184 + 0.537402i
\(553\) −9.25183e8 −0.232643
\(554\) −2.00827e9 + 6.83955e9i −0.501809 + 1.70901i
\(555\) 3.38903e9 4.75047e9i 0.841493 1.17954i
\(556\) 1.01603e9 + 6.52964e8i 0.250695 + 0.161112i
\(557\) 5.36627e7 3.73232e8i 0.0131577 0.0915137i −0.982184 0.187920i \(-0.939826\pi\)
0.995342 + 0.0964059i \(0.0307347\pi\)
\(558\) 6.42756e9 + 6.76458e9i 1.56613 + 1.64824i
\(559\) 5.83208e9 2.66342e9i 1.41216 0.644910i
\(560\) 1.69981e9 1.47289e9i 0.409017 0.354415i
\(561\) −6.94289e8 + 1.67793e8i −0.166024 + 0.0401239i
\(562\) 1.61926e9 + 7.39491e8i 0.384804 + 0.175734i
\(563\) 2.19516e9 6.44557e8i 0.518426 0.152224i −0.0120437 0.999927i \(-0.503834\pi\)
0.530470 + 0.847704i \(0.322016\pi\)
\(564\) 1.95512e9 7.80736e8i 0.458876 0.183243i
\(565\) 1.05046e9 2.30019e9i 0.245025 0.536531i
\(566\) −8.75978e8 6.09256e9i −0.203065 1.41235i
\(567\) −1.10324e9 + 2.12181e9i −0.254173 + 0.488840i
\(568\) 4.41827e8 + 9.67467e8i 0.101166 + 0.221522i
\(569\) 1.57812e9 1.01420e9i 0.359127 0.230797i −0.348618 0.937265i \(-0.613349\pi\)
0.707745 + 0.706468i \(0.249713\pi\)
\(570\) 5.85346e9 + 2.83943e8i 1.32389 + 0.0642197i
\(571\) −7.10421e8 + 1.10544e9i −0.159694 + 0.248489i −0.911875 0.410467i \(-0.865366\pi\)
0.752181 + 0.658957i \(0.229002\pi\)
\(572\) −1.92696e9 + 2.22383e9i −0.430512 + 0.496838i
\(573\) 1.24928e9 6.45164e9i 0.277407 1.43261i
\(574\) 3.02089e9i 0.666719i
\(575\) −1.37513e9 + 1.07127e9i −0.301652 + 0.234996i
\(576\) 6.63981e8 1.26773e8i 0.144769 0.0276407i
\(577\) −3.31392e9 9.73056e8i −0.718170 0.210874i −0.0978258 0.995204i \(-0.531189\pi\)
−0.620344 + 0.784330i \(0.713007\pi\)
\(578\) −4.13863e9 3.58614e9i −0.891474 0.772467i
\(579\) 1.66347e9 3.21980e9i 0.356156 0.689372i
\(580\) −6.95298e8 9.99688e7i −0.147970 0.0212748i
\(581\) −2.75738e8 4.29057e8i −0.0583284 0.0907608i
\(582\) −2.71989e9 + 1.56717e9i −0.571900 + 0.329523i
\(583\) 2.69850e9 + 3.11424e9i 0.564004 + 0.650896i
\(584\) −1.03612e9 + 1.48971e8i −0.215261 + 0.0309498i
\(585\) 1.30198e9 5.32634e9i 0.268880 1.09998i
\(586\) −2.05448e9 6.99691e9i −0.421755 1.43636i
\(587\) 5.71693e8 + 1.94701e9i 0.116662 + 0.397314i 0.997033 0.0769708i \(-0.0245248\pi\)
−0.880371 + 0.474285i \(0.842707\pi\)
\(588\) −1.58936e9 5.51632e8i −0.322405 0.111900i
\(589\) −1.26325e10 + 1.81628e9i −2.54733 + 0.366251i
\(590\) 4.69580e9 + 5.41924e9i 0.941299 + 1.08632i
\(591\) 4.47475e9 + 7.76610e9i 0.891687 + 1.54756i
\(592\) −6.28926e9 9.78629e9i −1.24587 1.93862i
\(593\) 8.95134e9 + 1.28701e9i 1.76277 + 0.253449i 0.946152 0.323723i \(-0.104935\pi\)
0.816623 + 0.577172i \(0.195844\pi\)
\(594\) −5.56604e9 1.65014e9i −1.08967 0.323049i
\(595\) −3.08448e8 2.67272e8i −0.0600307 0.0520169i
\(596\) −7.40690e8 2.17486e8i −0.143309 0.0420794i
\(597\) −7.21037e8 + 6.82173e7i −0.138691 + 0.0131215i
\(598\) 8.94822e9 2.12751e9i 1.71113 0.406835i
\(599\) 7.75195e9i 1.47373i 0.676042 + 0.736863i \(0.263694\pi\)
−0.676042 + 0.736863i \(0.736306\pi\)
\(600\) 1.23645e9 + 2.39423e8i 0.233694 + 0.0452520i
\(601\) 2.78999e9 3.21982e9i 0.524254 0.605022i −0.430436 0.902621i \(-0.641640\pi\)
0.954691 + 0.297599i \(0.0961858\pi\)
\(602\) 2.09707e9 3.26311e9i 0.391765 0.609598i
\(603\) 2.80362e7 1.28660e6i 0.00520725 0.000238965i
\(604\) 2.09205e9 1.34448e9i 0.386317 0.248271i
\(605\) −2.36646e8 5.18183e8i −0.0434466 0.0951347i
\(606\) 2.84075e9 2.97411e9i 0.518536 0.542878i
\(607\) 1.06625e9 + 7.41592e9i 0.193507 + 1.34587i 0.822634 + 0.568571i \(0.192504\pi\)
−0.629127 + 0.777303i \(0.716587\pi\)
\(608\) 2.87300e9 6.29100e9i 0.518410 1.13516i
\(609\) 4.42106e8 + 1.10712e9i 0.0793170 + 0.198625i
\(610\) 8.43854e9 2.47778e9i 1.50527 0.441986i
\(611\) 7.45141e9 + 3.40294e9i 1.32158 + 0.603546i
\(612\) 1.65884e8 + 4.82005e8i 0.0292533 + 0.0850006i
\(613\) 9.16929e8 7.94523e8i 0.160777 0.139314i −0.570757 0.821119i \(-0.693350\pi\)
0.731534 + 0.681805i \(0.238805\pi\)
\(614\) −2.10739e9 + 9.62415e8i −0.367415 + 0.167793i
\(615\) 3.53499e9 2.77497e9i 0.612810 0.481056i
\(616\) 2.63660e8 1.83379e9i 0.0454476 0.316095i
\(617\) −8.89190e8 5.71447e8i −0.152404 0.0979441i 0.462216 0.886767i \(-0.347054\pi\)
−0.614620 + 0.788823i \(0.710691\pi\)
\(618\) 4.35515e9 + 3.10701e9i 0.742239 + 0.529521i
\(619\) 6.48690e8 2.20923e9i 0.109931 0.374390i −0.886090 0.463514i \(-0.846588\pi\)
0.996021 + 0.0891237i \(0.0284066\pi\)
\(620\) −4.25674e9 −0.717309
\(621\) 3.65529e9 + 4.71747e9i 0.612493 + 0.790476i
\(622\) −1.21708e10 −2.02794
\(623\) 9.79044e8 3.33432e9i 0.162216 0.552458i
\(624\) −8.89835e9 6.34817e9i −1.46610 1.04593i
\(625\) −2.42046e9 1.55553e9i −0.396567 0.254858i
\(626\) −2.51252e8 + 1.74750e9i −0.0409355 + 0.284713i
\(627\) 6.24566e9 4.90285e9i 1.01191 0.794350i
\(628\) 2.18346e9 9.97154e8i 0.351793 0.160658i
\(629\) −1.59534e9 + 1.38237e9i −0.255608 + 0.221486i
\(630\) −1.07950e9 3.13668e9i −0.172001 0.499780i
\(631\) −3.15801e9 1.44222e9i −0.500393 0.228522i 0.149196 0.988808i \(-0.452332\pi\)
−0.649589 + 0.760286i \(0.725059\pi\)
\(632\) 1.60050e9 4.69949e8i 0.252201 0.0740528i
\(633\) 2.99617e9 + 7.50300e9i 0.469520 + 1.17577i
\(634\) −4.31355e9 + 9.44536e9i −0.672237 + 1.47199i
\(635\) 1.17814e8 + 8.19416e8i 0.0182595 + 0.126998i
\(636\) 2.03124e9 2.12659e9i 0.313084 0.327781i
\(637\) −2.71941e9 5.95467e9i −0.416856 0.912788i
\(638\) −2.43456e9 + 1.56460e9i −0.371149 + 0.238523i
\(639\) 2.57753e9 1.18285e8i 0.390797 0.0179340i
\(640\) −3.05192e9 + 4.74888e9i −0.460196 + 0.716079i
\(641\) −1.10897e9 + 1.27982e9i −0.166309 + 0.191931i −0.832787 0.553594i \(-0.813256\pi\)
0.666477 + 0.745525i \(0.267801\pi\)
\(642\) 3.52025e9 + 6.81652e8i 0.525050 + 0.101669i
\(643\) 8.42727e9i 1.25011i −0.780580 0.625056i \(-0.785076\pi\)
0.780580 0.625056i \(-0.214924\pi\)
\(644\) 1.26889e9 1.31864e9i 0.187207 0.194547i
\(645\) −5.74480e9 + 5.43515e8i −0.842977 + 0.0797540i
\(646\) −2.03406e9 5.97254e8i −0.296859 0.0871656i
\(647\) 2.30082e8 + 1.99367e8i 0.0333978 + 0.0289393i 0.671400 0.741095i \(-0.265693\pi\)
−0.638002 + 0.770035i \(0.720239\pi\)
\(648\) 8.30748e8 4.23098e9i 0.119938 0.610842i
\(649\) 9.61666e9 + 1.38267e9i 1.38092 + 0.198546i
\(650\) −2.54582e9 3.96137e9i −0.363605 0.565781i
\(651\) 3.60663e9 + 6.25944e9i 0.512351 + 0.889206i
\(652\) 4.85873e8 + 5.60728e8i 0.0686525 + 0.0792292i
\(653\) −9.15377e9 + 1.31611e9i −1.28648 + 0.184968i −0.751409 0.659837i \(-0.770625\pi\)
−0.535074 + 0.844805i \(0.679716\pi\)
\(654\) 1.01783e10 + 3.53267e9i 1.42283 + 0.493834i
\(655\) −3.25812e8 1.10962e9i −0.0453026 0.154286i
\(656\) −2.52402e9 8.59603e9i −0.349084 1.18887i
\(657\) −6.03000e8 + 2.46684e9i −0.0829542 + 0.339361i
\(658\) 4.90542e9 7.05292e8i 0.671251 0.0965114i
\(659\) −4.39625e9 5.07354e9i −0.598388 0.690577i 0.373066 0.927805i \(-0.378307\pi\)
−0.971454 + 0.237228i \(0.923761\pi\)
\(660\) 2.29469e9 1.32217e9i 0.310684 0.179013i
\(661\) 3.43048e8 + 5.33793e8i 0.0462008 + 0.0718899i 0.863586 0.504202i \(-0.168213\pi\)
−0.817385 + 0.576092i \(0.804577\pi\)
\(662\) −9.06891e8 1.30391e8i −0.121493 0.0174681i
\(663\) −9.10423e8 + 1.76221e9i −0.121324 + 0.234833i
\(664\) 6.94948e8 + 6.02176e8i 0.0921221 + 0.0798243i
\(665\) 4.35321e9 + 1.27822e9i 0.574029 + 0.168550i
\(666\) −1.68528e10 + 3.21768e9i −2.21061 + 0.422069i
\(667\) 2.97087e9 + 1.55147e8i 0.387653 + 0.0202443i
\(668\) 1.23765e9i 0.160649i
\(669\) −2.63093e9 + 1.35869e10i −0.339717 + 1.75440i
\(670\) −2.54937e7 + 2.94213e7i −0.00327470 + 0.00377920i
\(671\) 6.44231e9 1.00244e10i 0.823214 1.28095i
\(672\) −3.91019e9 1.89678e8i −0.497056 0.0241115i
\(673\) −9.97288e9 + 6.40918e9i −1.26115 + 0.810494i −0.988442 0.151601i \(-0.951557\pi\)
−0.272712 + 0.962096i \(0.587921\pi\)
\(674\) 4.93119e9 + 1.07978e10i 0.620357 + 1.35839i
\(675\) 1.65856e9 2.56600e9i 0.207571 0.321140i
\(676\) 6.02760e8 + 4.19228e9i 0.0750465 + 0.521960i
\(677\) −3.15403e9 + 6.90636e9i −0.390666 + 0.855439i 0.607466 + 0.794345i \(0.292186\pi\)
−0.998132 + 0.0610933i \(0.980541\pi\)
\(678\) −6.90465e9 + 2.75723e9i −0.850820 + 0.339758i
\(679\) −2.33179e9 + 6.84674e8i −0.285854 + 0.0839344i
\(680\) 6.69355e8 + 3.05684e8i 0.0816348 + 0.0372814i
\(681\) −6.73385e9 + 1.62741e9i −0.817049 + 0.197461i
\(682\) −1.32536e10 + 1.14843e10i −1.59989 + 1.38631i
\(683\) −6.90092e9 + 3.15155e9i −0.828771 + 0.378487i −0.784192 0.620519i \(-0.786922\pi\)
−0.0445797 + 0.999006i \(0.514195\pi\)
\(684\) −3.90325e9 4.10791e9i −0.466369 0.490822i
\(685\) −1.00810e9 + 7.01152e9i −0.119836 + 0.833480i
\(686\) −8.11565e9 5.21561e9i −0.959818 0.616838i
\(687\) −7.79830e9 + 1.09310e10i −0.917595 + 1.28621i
\(688\) −3.24088e9 + 1.10374e10i −0.379405 + 1.29214i
\(689\) 1.14429e10 1.33282
\(690\) −8.23617e9 8.31746e8i −0.954451 0.0963871i
\(691\) 5.73889e9 0.661690 0.330845 0.943685i \(-0.392666\pi\)
0.330845 + 0.943685i \(0.392666\pi\)
\(692\) −1.60201e9 + 5.45595e9i −0.183778 + 0.625892i
\(693\) −3.88846e9 2.25404e9i −0.443824 0.257273i
\(694\) 4.36471e9 + 2.80503e9i 0.495675 + 0.318551i
\(695\) 6.01941e8 4.18659e9i 0.0680154 0.473057i
\(696\) −1.32718e9 1.69067e9i −0.149210 0.190076i
\(697\) −1.47878e9 + 6.75338e8i −0.165421 + 0.0755451i
\(698\) 1.13747e10 9.85624e9i 1.26604 1.09703i
\(699\) −1.50257e8 6.21731e8i −0.0166405 0.0688545i
\(700\) −8.52231e8 3.89201e8i −0.0939105 0.0428875i
\(701\) −1.51773e10 + 4.45645e9i −1.66410 + 0.488625i −0.972354 0.233512i \(-0.924978\pi\)
−0.691750 + 0.722137i \(0.743160\pi\)
\(702\) −1.35849e10 + 8.68044e9i −1.48210 + 0.947026i
\(703\) 9.74808e9 2.13453e10i 1.05822 2.31718i
\(704\) 1.80799e8 + 1.25748e9i 0.0195295 + 0.135831i
\(705\) −5.33141e9 5.09236e9i −0.573034 0.547340i
\(706\) 4.79638e9 + 1.05026e10i 0.512976 + 1.12326i
\(707\) 2.67861e9 1.72144e9i 0.285064 0.183199i
\(708\) 3.35944e8 6.92547e9i 0.0355755 0.733386i
\(709\) −3.75697e8 + 5.84596e8i −0.0395891 + 0.0616019i −0.860484 0.509477i \(-0.829839\pi\)
0.820895 + 0.571079i \(0.193475\pi\)
\(710\) −2.34379e9 + 2.70488e9i −0.245762 + 0.283624i
\(711\) 3.91681e8 4.02774e9i 0.0408685 0.420259i
\(712\) 6.26544e9i 0.650537i
\(713\) 1.79536e10 1.63151e9i 1.85498 0.168568i
\(714\) 1.13026e8 + 1.19465e9i 0.0116208 + 0.122828i
\(715\) 9.88753e9 + 2.90324e9i 1.01162 + 0.297038i
\(716\) 3.77334e9 + 3.26962e9i 0.384177 + 0.332891i
\(717\) 1.31031e10 + 6.76959e9i 1.32757 + 0.685876i
\(718\) 3.90711e9 + 5.61757e8i 0.393931 + 0.0566387i
\(719\) −4.23100e9 6.58356e9i −0.424514 0.660556i 0.561451 0.827510i \(-0.310243\pi\)
−0.985965 + 0.166954i \(0.946607\pi\)
\(720\) 5.69253e9 + 8.02358e9i 0.568384 + 0.801132i
\(721\) 2.71228e9 + 3.13014e9i 0.269502 + 0.311022i
\(722\) 1.11071e10 1.59696e9i 1.09830 0.157912i
\(723\) 1.63917e9 4.72275e9i 0.161302 0.464741i
\(724\) 1.73891e9 + 5.92220e9i 0.170291 + 0.579960i
\(725\) −4.29095e8 1.46136e9i −0.0418187 0.142421i
\(726\) −5.49184e8 + 1.58231e9i −0.0532648 + 0.153466i
\(727\) 1.74502e10 2.50897e9i 1.68435 0.242172i 0.767395 0.641174i \(-0.221552\pi\)
0.916950 + 0.399002i \(0.130643\pi\)
\(728\) −3.36904e9 3.88808e9i −0.323628 0.373487i
\(729\) −8.77015e9 5.70119e9i −0.838418 0.545028i
\(730\) −1.90441e9 2.96332e9i −0.181188 0.281935i
\(731\) 2.06617e9 + 2.97070e8i 0.195639 + 0.0281286i
\(732\) −7.55528e9 3.90335e9i −0.711971 0.367831i
\(733\) −5.63756e8 4.88497e8i −0.0528722 0.0458140i 0.628024 0.778194i \(-0.283864\pi\)
−0.680896 + 0.732380i \(0.738409\pi\)
\(734\) 1.84622e10 + 5.42100e9i 1.72325 + 0.505991i
\(735\) 5.54939e8 + 5.86555e9i 0.0515513 + 0.544883i
\(736\) −4.51620e9 + 8.66266e9i −0.417542 + 0.800901i
\(737\) 5.27462e7i 0.00485349i
\(738\) −1.31513e10 1.27891e9i −1.20440 0.117123i
\(739\) −1.20450e9 + 1.39007e9i −0.109787 + 0.126701i −0.807983 0.589205i \(-0.799441\pi\)
0.698196 + 0.715907i \(0.253986\pi\)
\(740\) 4.23147e9 6.58429e9i 0.383866 0.597307i
\(741\) 1.06832e9 2.20233e10i 0.0964578 1.98847i
\(742\) 5.82385e9 3.74276e9i 0.523355 0.336340i
\(743\) 4.92118e9 + 1.07759e10i 0.440158 + 0.963812i 0.991569 + 0.129578i \(0.0413623\pi\)
−0.551411 + 0.834234i \(0.685910\pi\)
\(744\) −9.41871e9 8.99639e9i −0.838467 0.800872i
\(745\) 3.84740e8 + 2.67593e9i 0.0340895 + 0.237098i
\(746\) 9.45573e9 2.07052e10i 0.833890 1.82597i
\(747\) 1.98461e9 1.01877e9i 0.174202 0.0894238i
\(748\) −9.19212e8 + 2.69905e8i −0.0803082 + 0.0235806i
\(749\) 2.52509e9 + 1.15317e9i 0.219579 + 0.100278i
\(750\) 3.59920e9 + 1.48927e10i 0.311524 + 1.28902i
\(751\) 6.17603e8 5.35156e8i 0.0532071 0.0461042i −0.627851 0.778333i \(-0.716065\pi\)
0.681058 + 0.732229i \(0.261520\pi\)
\(752\) −1.33692e10 + 6.10552e9i −1.14642 + 0.523553i
\(753\) −1.26386e9 1.61001e9i −0.107874 0.137419i
\(754\) −1.14369e9 + 7.95453e9i −0.0971646 + 0.675795i
\(755\) −7.32649e9 4.70845e9i −0.619557 0.398165i
\(756\) −1.34009e9 + 2.91422e9i −0.112800 + 0.245299i
\(757\) 1.66970e9 5.68648e9i 0.139895 0.476440i −0.859503 0.511131i \(-0.829227\pi\)
0.999398 + 0.0346914i \(0.0110448\pi\)
\(758\) −2.81312e10 −2.34610
\(759\) −9.17153e9 + 6.45603e9i −0.761370 + 0.535944i
\(760\) −8.18001e9 −0.675937
\(761\) −4.10416e9 + 1.39775e10i −0.337581 + 1.14969i 0.599440 + 0.800420i \(0.295390\pi\)
−0.937020 + 0.349274i \(0.886428\pi\)
\(762\) 1.41358e9 1.98144e9i 0.115739 0.162233i
\(763\) 7.01691e9 + 4.50949e9i 0.571886 + 0.367529i
\(764\) 1.25436e9 8.72423e9i 0.101764 0.707784i
\(765\) 1.29414e9 1.22966e9i 0.104512 0.0993050i
\(766\) −1.84603e10 + 8.43053e9i −1.48401 + 0.677726i
\(767\) 2.03896e10 1.76677e10i 1.63164 1.41383i
\(768\) 1.43344e10 3.46427e9i 1.14187 0.275961i
\(769\) −1.07613e10 4.91451e9i −0.853339 0.389707i −0.0597886 0.998211i \(-0.519043\pi\)
−0.793551 + 0.608504i \(0.791770\pi\)
\(770\) 5.98183e9 1.75642e9i 0.472190 0.138647i
\(771\) 3.63268e8 1.45064e8i 0.0285454 0.0113990i
\(772\) 2.01926e9 4.42156e9i 0.157954 0.345871i
\(773\) −4.10638e8 2.85605e9i −0.0319765 0.222402i 0.967567 0.252615i \(-0.0812905\pi\)
−0.999543 + 0.0302130i \(0.990381\pi\)
\(774\) 1.33180e10 + 1.05109e10i 1.03239 + 0.814795i
\(775\) −3.83408e9 8.39547e9i −0.295873 0.647872i
\(776\) 3.68604e9 2.36888e9i 0.283168 0.181981i
\(777\) −1.32673e10 6.43575e8i −1.01463 0.0492182i
\(778\) 1.22273e10 1.90260e10i 0.930896 1.44850i
\(779\) 1.18345e10 1.36578e10i 0.896953 1.03514i
\(780\) 1.39809e9 7.22013e9i 0.105488 0.544771i
\(781\) 4.84927e9i 0.364248i
\(782\) 2.82532e9 + 9.92351e8i 0.211273 + 0.0742064i
\(783\) −5.00696e9 + 1.45598e9i −0.372742 + 0.108390i
\(784\) 1.12694e10 + 3.30900e9i 0.835210 + 0.245240i
\(785\) −6.35303e9 5.50494e9i −0.468746 0.406171i
\(786\) −1.56069e9 + 3.02085e9i −0.114640 + 0.221896i
\(787\) −6.62611e8 9.52691e7i −0.0484560 0.00696691i 0.118044 0.993008i \(-0.462338\pi\)
−0.166500 + 0.986041i \(0.553247\pi\)
\(788\) 6.49935e9 + 1.01132e10i 0.473182 + 0.736286i
\(789\) 7.13671e9 4.11210e9i 0.517284 0.298054i
\(790\) 3.67589e9 + 4.24220e9i 0.265257 + 0.306123i
\(791\) −5.69734e9 + 8.19154e8i −0.409312 + 0.0588502i
\(792\) 7.87170e9 + 1.92417e9i 0.563028 + 0.137628i
\(793\) −9.32252e9 3.17496e10i −0.663861 2.26090i
\(794\) 1.88111e9 + 6.40646e9i 0.133365 + 0.454199i
\(795\) −9.72949e9 3.37690e9i −0.686760 0.238360i
\(796\) −9.61516e8 + 1.38245e8i −0.0675711 + 0.00971526i
\(797\) 6.91372e9 + 7.97886e9i 0.483735 + 0.558261i 0.944181 0.329428i \(-0.106856\pi\)
−0.460445 + 0.887688i \(0.652310\pi\)
\(798\) −6.65969e9 1.15581e10i −0.463921 0.805153i
\(799\) 1.44189e9 + 2.24363e9i 0.100004 + 0.155610i
\(800\) 4.95060e9 + 7.11789e8i 0.341856 + 0.0491514i
\(801\) 1.41013e10 + 5.67382e9i 0.969495 + 0.390087i
\(802\) 1.60445e10 + 1.39026e10i 1.09829 + 0.951671i
\(803\) −4.57931e9 1.34461e9i −0.312102 0.0916413i
\(804\) 3.74755e7 3.54556e6i 0.00254303 0.000240596i
\(805\) −6.04662e9 2.12379e9i −0.408533 0.143491i
\(806\) 4.86991e10i 3.27603i
\(807\) 2.17698e10 + 4.21545e9i 1.45813 + 0.282349i
\(808\) −3.75940e9 + 4.33858e9i −0.250714 + 0.289339i
\(809\) 1.10795e10 1.72401e10i 0.735702 1.14478i −0.248655 0.968592i \(-0.579989\pi\)
0.984357 0.176183i \(-0.0563751\pi\)
\(810\) 1.41124e10 3.37163e9i 0.933046 0.222917i
\(811\) −1.90223e9 + 1.22249e9i −0.125225 + 0.0804771i −0.601754 0.798682i \(-0.705531\pi\)
0.476529 + 0.879159i \(0.341895\pi\)
\(812\) 6.64222e8 + 1.45444e9i 0.0435379 + 0.0953346i
\(813\) −1.98459e9 + 2.07775e9i −0.129525 + 0.135606i
\(814\) −4.58894e9 3.19168e10i −0.298213 2.07412i
\(815\) 1.07939e9 2.36354e9i 0.0698438 0.152937i
\(816\) −1.31978e9 3.30498e9i −0.0850326 0.212938i
\(817\) −2.22645e10 + 6.53746e9i −1.42836 + 0.419403i
\(818\) 6.74397e9 + 3.07987e9i 0.430804 + 0.196741i
\(819\) −1.18016e10 + 4.06158e9i −0.750667 + 0.258346i
\(820\) 4.55538e9 3.94726e9i 0.288520 0.250004i
\(821\) −1.36554e10 + 6.23620e9i −0.861196 + 0.393295i −0.796521 0.604611i \(-0.793329\pi\)
−0.0646756 + 0.997906i \(0.520601\pi\)
\(822\) 1.63824e10 1.28602e10i 1.02879 0.807597i
\(823\) 2.20062e9 1.53057e10i 0.137609 0.957090i −0.797649 0.603122i \(-0.793923\pi\)
0.935258 0.353968i \(-0.115168\pi\)
\(824\) −6.28202e9 4.03721e9i −0.391160 0.251383i
\(825\) 4.67454e9 + 3.33486e9i 0.289834 + 0.206771i
\(826\) 4.59848e9 1.56610e10i 0.283912 0.966917i
\(827\) −2.60586e10 −1.60207 −0.801036 0.598616i \(-0.795718\pi\)
−0.801036 + 0.598616i \(0.795718\pi\)
\(828\) 5.20344e9 + 6.08230e9i 0.318555 + 0.372359i
\(829\) 5.74832e9 0.350429 0.175214 0.984530i \(-0.443938\pi\)
0.175214 + 0.984530i \(0.443938\pi\)
\(830\) −8.71787e8 + 2.96903e9i −0.0529221 + 0.180236i
\(831\) −1.96503e10 1.40187e10i −1.18786 0.847433i
\(832\) 2.96781e9 + 1.90730e9i 0.178651 + 0.114812i
\(833\) 3.03315e8 2.10960e9i 0.0181818 0.126457i
\(834\) −9.78193e9 + 7.67882e9i −0.583907 + 0.458367i
\(835\) −3.94263e9 + 1.80054e9i −0.234360 + 0.107028i
\(836\) 8.04850e9 6.97406e9i 0.476423 0.412823i
\(837\) −2.87770e10 + 1.30513e10i −1.69632 + 0.769334i
\(838\) 4.53234e9 + 2.06985e9i 0.266053 + 0.121502i
\(839\) 6.30253e9 1.85059e9i 0.368424 0.108179i −0.0922794 0.995733i \(-0.529415\pi\)
0.460704 + 0.887554i \(0.347597\pi\)
\(840\) 1.71716e9 + 4.30011e9i 0.0999618 + 0.250324i
\(841\) 6.08607e9 1.33266e10i 0.352818 0.772564i
\(842\) −9.83574e8 6.84091e9i −0.0567825 0.394931i
\(843\) −4.16359e9 + 4.35904e9i −0.239371 + 0.250608i
\(844\) 4.50146e9 + 9.85682e9i 0.257724 + 0.564336i
\(845\) 1.24780e10 8.01910e9i 0.711452 0.457222i
\(846\) 9.93721e8 + 2.16541e10i 0.0564246 + 1.22954i
\(847\) −7.01040e8 + 1.09084e9i −0.0396416 + 0.0616835i
\(848\) −1.34448e10 + 1.55161e10i −0.757127 + 0.873771i
\(849\) 2.04631e10 + 3.96243e9i 1.14761 + 0.222221i
\(850\) 1.53310e9i 0.0856254i
\(851\) −1.53234e10 + 2.93923e10i −0.852320 + 1.63486i
\(852\) 3.44535e9 3.25964e8i 0.190851 0.0180564i
\(853\) 3.44025e9 + 1.01015e9i 0.189788 + 0.0557267i 0.375245 0.926926i \(-0.377558\pi\)
−0.185457 + 0.982652i \(0.559377\pi\)
\(854\) −1.51294e10 1.31097e10i −0.831224 0.720259i
\(855\) −7.40760e9 + 1.84103e10i −0.405318 + 1.00735i
\(856\) −4.95399e9 7.12276e8i −0.269958 0.0388141i
\(857\) 1.74787e10 + 2.71974e10i 0.948587 + 1.47603i 0.878077 + 0.478519i \(0.158826\pi\)
0.0705092 + 0.997511i \(0.477538\pi\)
\(858\) −1.51263e10 2.62523e10i −0.817574 1.41893i
\(859\) −5.01727e8 5.79024e8i −0.0270079 0.0311688i 0.742085 0.670306i \(-0.233837\pi\)
−0.769093 + 0.639137i \(0.779292\pi\)
\(860\) −7.66079e9 + 1.10146e9i −0.410704 + 0.0590503i
\(861\) −9.66401e9 3.35417e9i −0.515996 0.179091i
\(862\) −7.51119e9 2.55807e10i −0.399423 1.36031i
\(863\) −8.01868e9 2.73091e10i −0.424683 1.44634i −0.842939 0.538008i \(-0.819177\pi\)
0.418257 0.908329i \(-0.362641\pi\)
\(864\) 2.48115e9 1.69425e10i 0.130875 0.893675i
\(865\) 1.97110e10 2.83401e9i 1.03551 0.148883i
\(866\) −1.96541e10 2.26820e10i −1.02835 1.18678i
\(867\) 1.60675e10 9.25795e9i 0.837302 0.482445i
\(868\) 5.23845e9 + 8.15119e9i 0.271884 + 0.423060i
\(869\) 7.52795e9 + 1.08236e9i 0.389142 + 0.0559501i
\(870\) 3.31988e9 6.42592e9i 0.170925 0.330840i
\(871\) 1.10696e8 + 9.59187e7i 0.00567635 + 0.00491858i
\(872\) −1.44294e10 4.23684e9i −0.736952 0.216389i
\(873\) −1.99352e9 1.04412e10i −0.101408 0.531128i
\(874\) −3.31517e10 + 3.01260e9i −1.67964 + 0.152634i
\(875\) 1.18616e10i 0.598572i
\(876\) −6.47510e8 + 3.34393e9i −0.0325449 + 0.168071i
\(877\) −1.22006e10 + 1.40803e10i −0.610779 + 0.704876i −0.973929 0.226855i \(-0.927156\pi\)
0.363150 + 0.931731i \(0.381701\pi\)
\(878\) −1.12915e9 + 1.75699e9i −0.0563014 + 0.0876067i
\(879\) 2.46647e10 + 1.19645e9i 1.22494 + 0.0594201i
\(880\) −1.55540e10 + 9.99592e9i −0.769399 + 0.494463i
\(881\) −1.66116e10 3.63744e10i −0.818458 1.79217i −0.565627 0.824661i \(-0.691366\pi\)
−0.252831 0.967510i \(-0.581362\pi\)
\(882\) 1.07319e10 1.35979e10i 0.526667 0.667316i
\(883\) 2.23522e9 + 1.55463e10i 0.109259 + 0.759913i 0.968621 + 0.248544i \(0.0799522\pi\)
−0.859362 + 0.511368i \(0.829139\pi\)
\(884\) −1.10515e9 + 2.41993e9i −0.0538067 + 0.117820i
\(885\) −2.25504e10 + 9.00504e9i −1.09358 + 0.436701i
\(886\) −2.17843e10 + 6.39646e9i −1.05227 + 0.308974i
\(887\) 3.32207e10 + 1.51714e10i 1.59837 + 0.729949i 0.997584 0.0694647i \(-0.0221291\pi\)
0.600781 + 0.799414i \(0.294856\pi\)
\(888\) 2.32783e10 5.62580e9i 1.11559 0.269612i
\(889\) 1.42411e9 1.23399e9i 0.0679808 0.0589057i
\(890\) −1.91786e10 + 8.75857e9i −0.911909 + 0.416455i
\(891\) 1.14590e10 1.59739e10i 0.542720 0.756554i
\(892\) −2.64162e9 + 1.83729e10i −0.124622 + 0.866763i
\(893\) −2.49410e10 1.60286e10i −1.17202 0.753208i
\(894\) 4.61626e9 6.47071e9i 0.216077 0.302880i
\(895\) 4.92616e9 1.67770e10i 0.229683 0.782227i
\(896\) 1.28493e10 0.596765
\(897\) −3.12940e9 + 3.09882e10i −0.144773 + 1.43358i
\(898\) 1.65672e10 0.763452
\(899\) −4.43768e9 + 1.51133e10i −0.203703 + 0.693748i
\(900\) 2.05516e9 3.54537e9i 0.0939717 0.162111i
\(901\) 3.13412e9 + 2.01417e9i 0.142751 + 0.0917403i
\(902\) 3.53408e9 2.45801e10i 0.160344 1.11522i
\(903\) 8.11046e9 + 1.03318e10i 0.366554 + 0.466948i
\(904\) 9.43990e9 4.31106e9i 0.424989 0.194086i
\(905\) 1.63359e10 1.41551e10i 0.732608 0.634809i
\(906\) 6.01516e9 + 2.48894e10i 0.268719 + 1.11190i
\(907\) −3.34829e10 1.52911e10i −1.49004 0.680479i −0.506679 0.862135i \(-0.669127\pi\)
−0.983362 + 0.181656i \(0.941854\pi\)
\(908\) −8.91535e9 + 2.61778e9i −0.395219 + 0.116047i
\(909\) 6.36020e9 + 1.23900e10i 0.280865 + 0.547138i
\(910\) 7.19181e9 1.57479e10i 0.316369 0.692751i
\(911\) 2.03868e9 + 1.41793e10i 0.0893376 + 0.621357i 0.984470 + 0.175556i \(0.0561722\pi\)
−0.895132 + 0.445801i \(0.852919\pi\)
\(912\) 2.86075e10 + 2.73248e10i 1.24881 + 1.19282i
\(913\) 1.74166e9 + 3.81369e9i 0.0757381 + 0.165843i
\(914\) −3.32475e9 + 2.13668e9i −0.144028 + 0.0925612i
\(915\) −1.44296e9 + 2.97466e10i −0.0622704 + 1.28370i
\(916\) −9.73676e9 + 1.51507e10i −0.418582 + 0.651326i
\(917\) −1.72384e9 + 1.98941e9i −0.0738250 + 0.0851986i
\(918\) −5.24871e9 1.37095e7i −0.223925 0.000584886i
\(919\) 5.68224e9i 0.241499i 0.992683 + 0.120750i \(0.0385298\pi\)
−0.992683 + 0.120750i \(0.961470\pi\)
\(920\) 1.15390e10 + 6.02597e8i 0.488553 + 0.0255135i
\(921\) −7.38931e8 7.81029e9i −0.0311670 0.329426i
\(922\) −5.81474e9 1.70736e9i −0.244327 0.0717410i
\(923\) 1.01770e10 + 8.81838e9i 0.426002 + 0.369133i
\(924\) −5.35572e9 2.76697e9i −0.223340 0.115386i
\(925\) 1.67974e10 + 2.41510e9i 0.697822 + 0.100332i
\(926\) −4.67456e9 7.27376e9i −0.193465 0.301038i
\(927\) −1.47752e10 + 1.04826e10i −0.609191 + 0.432206i
\(928\) −5.58971e9 6.45087e9i −0.229600 0.264972i
\(929\) 4.64120e10 6.67304e9i 1.89922 0.273067i 0.909459 0.415794i \(-0.136496\pi\)
0.989762 + 0.142728i \(0.0455873\pi\)
\(930\) 1.43715e10 4.14070e10i 0.585883 1.68804i
\(931\) 6.67487e9 + 2.27325e10i 0.271094 + 0.923260i
\(932\) −2.41698e8 8.23148e8i −0.00977952 0.0333060i
\(933\) 1.35136e10 3.89353e10i 0.544736 1.56949i
\(934\) 1.94635e10 2.79843e9i 0.781641 0.112383i
\(935\) 2.19708e9 + 2.53557e9i 0.0879033 + 0.101446i
\(936\) 1.83528e10 1.30209e10i 0.731540 0.519010i
\(937\) 6.38889e9 + 9.94130e9i 0.253709 + 0.394780i 0.944623 0.328158i \(-0.106428\pi\)
−0.690913 + 0.722938i \(0.742791\pi\)
\(938\) 8.77117e7 + 1.26110e7i 0.00347015 + 0.000498932i
\(939\) −5.31139e9 2.74407e9i −0.209353 0.108160i
\(940\) −7.47325e9 6.47560e9i −0.293469 0.254292i
\(941\) 3.35592e10 + 9.85388e9i 1.31295 + 0.385517i 0.861944 0.507003i \(-0.169247\pi\)
0.451007 + 0.892521i \(0.351065\pi\)
\(942\) 2.32797e9 + 2.46060e10i 0.0907400 + 0.959096i
\(943\) −1.77003e10 + 1.83943e10i −0.687369 + 0.714320i
\(944\) 4.84060e10i 1.87282i
\(945\) 1.12331e10 + 2.93404e7i 0.432999 + 0.00113098i
\(946\) −2.08807e10 + 2.40976e10i −0.801912 + 0.925456i
\(947\) −1.00949e10 + 1.57079e10i −0.386256 + 0.601026i −0.978876 0.204457i \(-0.934457\pi\)
0.592620 + 0.805482i \(0.298094\pi\)
\(948\) 2.62978e8 5.42128e9i 0.0100251 0.206668i
\(949\) −1.11493e10 + 7.16524e9i −0.423465 + 0.272144i
\(950\) 7.07969e9 + 1.55024e10i 0.267906 + 0.586631i
\(951\) −2.54269e10 2.42868e10i −0.958652 0.915668i
\(952\) −2.38374e8 1.65792e9i −0.00895424 0.0622781i
\(953\) −1.02254e10 + 2.23905e10i −0.382697 + 0.837990i 0.616038 + 0.787716i \(0.288737\pi\)
−0.998735 + 0.0502739i \(0.983991\pi\)
\(954\) 1.38284e10 + 2.69384e10i 0.515646 + 1.00450i
\(955\) −2.96166e10 + 8.69622e9i −1.10033 + 0.323086i
\(956\) 1.79938e10 + 8.21748e9i 0.666070 + 0.304184i
\(957\) −2.30209e9 9.52554e9i −0.0849045 0.351316i
\(958\) 4.21429e10 3.65170e10i 1.54862 1.34189i
\(959\) 1.46669e10 6.69814e9i 0.536998 0.245239i
\(960\) −1.96056e9 2.49752e9i −0.0715205 0.0911088i
\(961\) −9.66869e9 + 6.72472e10i −0.351427 + 2.44423i
\(962\) −7.53273e10 4.84099e10i −2.72797 1.75316i
\(963\) −6.08928e9 + 1.05047e10i −0.219722 + 0.379044i
\(964\) 1.88903e9 6.43343e9i 0.0679154 0.231299i
\(965\) −1.70229e10 −0.609799
\(966\) 8.54294e9 + 1.67949e10i 0.304921 + 0.599457i
\(967\) −5.92863e9 −0.210844 −0.105422 0.994428i \(-0.533619\pi\)
−0.105422 + 0.994428i \(0.533619\pi\)
\(968\) 6.58654e8 2.24317e9i 0.0233396 0.0794874i
\(969\) 4.16913e9 5.84395e9i 0.147201 0.206335i
\(970\) 1.24039e10 + 7.97152e9i 0.436373 + 0.280440i
\(971\) −3.18306e9 + 2.21386e10i −0.111578 + 0.776039i 0.854808 + 0.518944i \(0.173675\pi\)
−0.966386 + 0.257096i \(0.917235\pi\)
\(972\) −1.21196e10 7.06776e9i −0.423307 0.246860i
\(973\) −8.75762e9 + 3.99947e9i −0.304783 + 0.139190i
\(974\) 3.29087e9 2.85156e9i 0.114118 0.0988839i
\(975\) 1.54994e10 3.74582e9i 0.535547 0.129429i
\(976\) 5.40045e10 + 2.46630e10i 1.85933 + 0.849126i
\(977\) −1.80828e10 + 5.30959e9i −0.620348 + 0.182151i −0.576779 0.816900i \(-0.695691\pi\)
−0.0435683 + 0.999050i \(0.513873\pi\)
\(978\) −7.09481e9 + 2.83317e9i −0.242524 + 0.0968470i
\(979\) −1.18670e10 + 2.59850e10i −0.404204 + 0.885083i
\(980\) 1.12461e9 + 7.82182e9i 0.0381689 + 0.265471i
\(981\) −2.26025e10 + 2.86386e10i −0.764389 + 0.968524i
\(982\) −2.65848e9 5.82125e9i −0.0895865 0.196167i
\(983\) −4.42217e10 + 2.84196e10i −1.48490 + 0.954289i −0.488236 + 0.872712i \(0.662359\pi\)
−0.996667 + 0.0815772i \(0.974004\pi\)
\(984\) 1.84218e10 + 8.93615e8i 0.616382 + 0.0298998i
\(985\) 2.27611e10 3.54170e10i 0.758868 1.18082i
\(986\) −1.71339e9 + 1.97736e9i −0.0569231 + 0.0656927i
\(987\) −3.19034e9 + 1.64759e10i −0.105615 + 0.545429i
\(988\) 2.95733e10i 0.975554i
\(989\) 3.18887e10 7.58181e9i 1.04821 0.249222i
\(990\) 5.11406e9 + 2.67852e10i 0.167511 + 0.877347i
\(991\) −2.56165e10 7.52168e9i −0.836107 0.245503i −0.164468 0.986382i \(-0.552591\pi\)
−0.671638 + 0.740879i \(0.734409\pi\)
\(992\) −3.90914e10 3.38729e10i −1.27142 1.10170i
\(993\) 1.42408e9 2.75643e9i 0.0461542 0.0893356i
\(994\) 8.06386e9 + 1.15941e9i 0.260430 + 0.0374442i
\(995\) 1.83921e9 + 2.86187e9i 0.0591904 + 0.0921020i
\(996\) 2.59251e9 1.49378e9i 0.0831406 0.0479048i
\(997\) −1.66103e10 1.91693e10i −0.530816 0.612595i 0.425489 0.904963i \(-0.360102\pi\)
−0.956306 + 0.292369i \(0.905557\pi\)
\(998\) 1.22611e10 1.76288e9i 0.390456 0.0561391i
\(999\) 8.41853e9 5.74859e10i 0.267151 1.82424i
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 69.8.g.a.5.12 540
3.2 odd 2 inner 69.8.g.a.5.43 yes 540
23.14 odd 22 inner 69.8.g.a.14.43 yes 540
69.14 even 22 inner 69.8.g.a.14.12 yes 540
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.8.g.a.5.12 540 1.1 even 1 trivial
69.8.g.a.5.43 yes 540 3.2 odd 2 inner
69.8.g.a.14.12 yes 540 69.14 even 22 inner
69.8.g.a.14.43 yes 540 23.14 odd 22 inner