Properties

Label 32.8.g.a.21.23
Level $32$
Weight $8$
Character 32.21
Analytic conductor $9.996$
Analytic rank $0$
Dimension $108$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [32,8,Mod(5,32)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(32, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("32.5");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 32.g (of order \(8\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.99632081549\)
Analytic rank: \(0\)
Dimension: \(108\)
Relative dimension: \(27\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 21.23
Character \(\chi\) \(=\) 32.21
Dual form 32.8.g.a.29.23

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(9.26745 - 6.48956i) q^{2} +(-13.5755 + 5.62318i) q^{3} +(43.7711 - 120.283i) q^{4} +(-202.831 + 489.678i) q^{5} +(-89.3187 + 140.212i) q^{6} +(-1160.57 - 1160.57i) q^{7} +(-374.940 - 1398.78i) q^{8} +(-1393.77 + 1393.77i) q^{9} +O(q^{10})\) \(q+(9.26745 - 6.48956i) q^{2} +(-13.5755 + 5.62318i) q^{3} +(43.7711 - 120.283i) q^{4} +(-202.831 + 489.678i) q^{5} +(-89.3187 + 140.212i) q^{6} +(-1160.57 - 1160.57i) q^{7} +(-374.940 - 1398.78i) q^{8} +(-1393.77 + 1393.77i) q^{9} +(1298.07 + 5854.35i) q^{10} +(-1984.96 - 822.196i) q^{11} +(82.1576 + 1879.05i) q^{12} +(3512.84 + 8480.76i) q^{13} +(-18287.1 - 3223.93i) q^{14} -7788.21i q^{15} +(-12552.2 - 10529.9i) q^{16} -6874.72i q^{17} +(-3871.72 + 21961.6i) q^{18} +(5404.16 + 13046.8i) q^{19} +(50022.0 + 45831.0i) q^{20} +(22281.5 + 9229.29i) q^{21} +(-23731.2 + 5261.85i) q^{22} +(-7914.10 + 7914.10i) q^{23} +(12955.6 + 16880.8i) q^{24} +(-143401. - 143401. i) q^{25} +(87591.5 + 55798.1i) q^{26} +(23381.6 - 56448.3i) q^{27} +(-190397. + 88797.9i) q^{28} +(51050.7 - 21145.9i) q^{29} +(-50542.1 - 72176.8i) q^{30} +1216.54 q^{31} +(-184661. - 16126.9i) q^{32} +31570.2 q^{33} +(-44613.9 - 63711.1i) q^{34} +(803706. - 332906. i) q^{35} +(106640. + 228654. i) q^{36} +(-49570.5 + 119674. i) q^{37} +(134751. + 85839.9i) q^{38} +(-95377.6 - 95377.6i) q^{39} +(760999. + 100116. i) q^{40} +(252687. - 252687. i) q^{41} +(266386. - 59065.1i) q^{42} +(-752975. - 311892. i) q^{43} +(-185780. + 202769. i) q^{44} +(-399798. - 965197. i) q^{45} +(-21984.4 + 124703. i) q^{46} +95612.2i q^{47} +(229614. + 72365.8i) q^{48} +1.87030e6i q^{49} +(-2.25958e6 - 398352. i) q^{50} +(38657.7 + 93328.1i) q^{51} +(1.17385e6 - 51324.5i) q^{52} +(414402. + 171651. i) q^{53} +(-149637. - 674868. i) q^{54} +(805223. - 805223. i) q^{55} +(-1.18823e6 + 2.05852e6i) q^{56} +(-146729. - 146729. i) q^{57} +(335882. - 527265. i) q^{58} +(-726399. + 1.75368e6i) q^{59} +(-936792. - 340899. i) q^{60} +(-2.37025e6 + 981790. i) q^{61} +(11274.3 - 7894.85i) q^{62} +3.23513e6 q^{63} +(-1.81599e6 + 1.04891e6i) q^{64} -4.86536e6 q^{65} +(292576. - 204877. i) q^{66} +(1.34736e6 - 558096. i) q^{67} +(-826914. - 300914. i) q^{68} +(62935.9 - 151941. i) q^{69} +(5.28789e6 - 8.30089e6i) q^{70} +(124974. + 124974. i) q^{71} +(2.47215e6 + 1.42699e6i) q^{72} +(-2.10570e6 + 2.10570e6i) q^{73} +(317238. + 1.43076e6i) q^{74} +(2.75313e6 + 1.14038e6i) q^{75} +(1.80586e6 - 78957.7i) q^{76} +(1.34947e6 + 3.25790e6i) q^{77} +(-1.50287e6 - 264948. i) q^{78} +6.34026e6i q^{79} +(7.70223e6 - 4.01074e6i) q^{80} -3.41297e6i q^{81} +(701936. - 3.98160e6i) q^{82} +(-1.62242e6 - 3.91687e6i) q^{83} +(2.08542e6 - 2.27611e6i) q^{84} +(3.36640e6 + 1.39441e6i) q^{85} +(-9.00220e6 + 1.99603e6i) q^{86} +(-574134. + 574134. i) q^{87} +(-405828. + 3.08478e6i) q^{88} +(706032. + 706032. i) q^{89} +(-9.96881e6 - 6.35040e6i) q^{90} +(5.76561e6 - 1.39194e7i) q^{91} +(605526. + 1.29834e6i) q^{92} +(-16515.3 + 6840.85i) q^{93} +(620481. + 886081. i) q^{94} -7.48487e6 q^{95} +(2.59756e6 - 819449. i) q^{96} -2.89743e6 q^{97} +(1.21375e7 + 1.73329e7i) q^{98} +(3.91252e6 - 1.62062e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 108 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 108 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 13004 q^{10} - 4 q^{11} + 30668 q^{12} - 4 q^{13} - 26196 q^{14} - 52784 q^{16} + 102056 q^{18} - 4 q^{19} + 81996 q^{20} - 4 q^{21} - 374240 q^{22} - 143420 q^{23} + 380880 q^{24} - 4 q^{25} - 363984 q^{26} + 476084 q^{27} - 195464 q^{28} - 4 q^{29} + 870468 q^{30} - 714992 q^{31} + 535656 q^{32} - 8 q^{33} - 201072 q^{34} + 816500 q^{35} - 1669712 q^{36} - 4 q^{37} - 2533100 q^{38} - 283948 q^{39} + 2746344 q^{40} - 4 q^{41} + 4924936 q^{42} + 366180 q^{43} - 1585404 q^{44} + 8744 q^{45} - 2715812 q^{46} - 5044368 q^{48} - 1653804 q^{50} + 3002072 q^{51} + 8882212 q^{52} - 1815636 q^{53} + 6815776 q^{54} - 4191012 q^{55} - 3655000 q^{56} - 4 q^{57} - 12448736 q^{58} - 1835940 q^{59} - 6364808 q^{60} - 4559780 q^{61} + 12948600 q^{62} + 10001872 q^{63} + 16915544 q^{64} - 8 q^{65} - 11246068 q^{66} - 1940684 q^{67} - 8895536 q^{68} + 9580892 q^{69} - 8149480 q^{70} - 12348708 q^{71} + 12884564 q^{72} - 4 q^{73} + 10931436 q^{74} + 11573008 q^{75} + 14443516 q^{76} - 11914452 q^{77} - 38252364 q^{78} - 11333192 q^{80} + 15827196 q^{82} - 9565884 q^{83} + 8101984 q^{84} + 312496 q^{85} - 14812992 q^{86} + 40789108 q^{87} + 5716448 q^{88} - 4 q^{89} + 5335400 q^{90} - 3406996 q^{91} + 27562664 q^{92} - 8752 q^{93} - 14227032 q^{94} - 54872008 q^{95} - 25080448 q^{96} - 8 q^{97} + 57598104 q^{98} - 9738480 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 9.26745 6.48956i 0.819134 0.573602i
\(3\) −13.5755 + 5.62318i −0.290291 + 0.120242i −0.523077 0.852286i \(-0.675216\pi\)
0.232786 + 0.972528i \(0.425216\pi\)
\(4\) 43.7711 120.283i 0.341962 0.939714i
\(5\) −202.831 + 489.678i −0.725672 + 1.75193i −0.0691655 + 0.997605i \(0.522034\pi\)
−0.656506 + 0.754321i \(0.727966\pi\)
\(6\) −89.3187 + 140.212i −0.168816 + 0.265006i
\(7\) −1160.57 1160.57i −1.27888 1.27888i −0.941297 0.337578i \(-0.890392\pi\)
−0.337578 0.941297i \(-0.609608\pi\)
\(8\) −374.940 1398.78i −0.258909 0.965902i
\(9\) −1393.77 + 1393.77i −0.637296 + 0.637296i
\(10\) 1298.07 + 5854.35i 0.410486 + 1.85131i
\(11\) −1984.96 822.196i −0.449652 0.186252i 0.146353 0.989232i \(-0.453246\pi\)
−0.596006 + 0.802980i \(0.703246\pi\)
\(12\) 82.1576 + 1879.05i 0.0137250 + 0.313908i
\(13\) 3512.84 + 8480.76i 0.443463 + 1.07061i 0.974725 + 0.223407i \(0.0717178\pi\)
−0.531263 + 0.847207i \(0.678282\pi\)
\(14\) −18287.1 3223.93i −1.78114 0.314006i
\(15\) 7788.21i 0.595824i
\(16\) −12552.2 10529.9i −0.766124 0.642693i
\(17\) 6874.72i 0.339378i −0.985498 0.169689i \(-0.945724\pi\)
0.985498 0.169689i \(-0.0542763\pi\)
\(18\) −3871.72 + 21961.6i −0.156477 + 0.887586i
\(19\) 5404.16 + 13046.8i 0.180755 + 0.436382i 0.988123 0.153667i \(-0.0491084\pi\)
−0.807367 + 0.590049i \(0.799108\pi\)
\(20\) 50022.0 + 45831.0i 1.39816 + 1.28102i
\(21\) 22281.5 + 9229.29i 0.525021 + 0.217471i
\(22\) −23731.2 + 5261.85i −0.475160 + 0.105356i
\(23\) −7914.10 + 7914.10i −0.135630 + 0.135630i −0.771662 0.636033i \(-0.780574\pi\)
0.636033 + 0.771662i \(0.280574\pi\)
\(24\) 12955.6 + 16880.8i 0.191301 + 0.249260i
\(25\) −143401. 143401.i −1.83554 1.83554i
\(26\) 87591.5 + 55798.1i 0.977362 + 0.622605i
\(27\) 23381.6 56448.3i 0.228613 0.551922i
\(28\) −190397. + 88797.9i −1.63910 + 0.764450i
\(29\) 51050.7 21145.9i 0.388695 0.161003i −0.179773 0.983708i \(-0.557536\pi\)
0.568468 + 0.822705i \(0.307536\pi\)
\(30\) −50542.1 72176.8i −0.341766 0.488060i
\(31\) 1216.54 0.00733436 0.00366718 0.999993i \(-0.498833\pi\)
0.00366718 + 0.999993i \(0.498833\pi\)
\(32\) −184661. 16126.9i −0.996208 0.0870014i
\(33\) 31570.2 0.152925
\(34\) −44613.9 63711.1i −0.194668 0.277996i
\(35\) 803706. 332906.i 3.16854 1.31245i
\(36\) 106640. + 228654.i 0.380945 + 0.816807i
\(37\) −49570.5 + 119674.i −0.160886 + 0.388412i −0.983680 0.179927i \(-0.942414\pi\)
0.822794 + 0.568339i \(0.192414\pi\)
\(38\) 134751. + 85839.9i 0.398372 + 0.253774i
\(39\) −95377.6 95377.6i −0.257466 0.257466i
\(40\) 760999. + 100116.i 1.88007 + 0.247338i
\(41\) 252687. 252687.i 0.572585 0.572585i −0.360265 0.932850i \(-0.617314\pi\)
0.932850 + 0.360265i \(0.117314\pi\)
\(42\) 266386. 59065.1i 0.554804 0.123015i
\(43\) −752975. 311892.i −1.44424 0.598226i −0.483421 0.875388i \(-0.660606\pi\)
−0.960823 + 0.277162i \(0.910606\pi\)
\(44\) −185780. + 202769.i −0.328788 + 0.358853i
\(45\) −399798. 965197.i −0.654028 1.57896i
\(46\) −21984.4 + 124703.i −0.0333015 + 0.188896i
\(47\) 95612.2i 0.134329i 0.997742 + 0.0671646i \(0.0213953\pi\)
−0.997742 + 0.0671646i \(0.978605\pi\)
\(48\) 229614. + 72365.8i 0.299678 + 0.0944471i
\(49\) 1.87030e6i 2.27105i
\(50\) −2.25958e6 398352.i −2.55642 0.450684i
\(51\) 38657.7 + 93328.1i 0.0408076 + 0.0985182i
\(52\) 1.17385e6 51324.5i 1.15772 0.0506189i
\(53\) 414402. + 171651.i 0.382346 + 0.158373i 0.565574 0.824698i \(-0.308655\pi\)
−0.183228 + 0.983070i \(0.558655\pi\)
\(54\) −149637. 674868.i −0.129318 0.583231i
\(55\) 805223. 805223.i 0.652600 0.652600i
\(56\) −1.18823e6 + 2.05852e6i −0.904156 + 1.56638i
\(57\) −146729. 146729.i −0.104943 0.104943i
\(58\) 335882. 527265.i 0.226042 0.354839i
\(59\) −726399. + 1.75368e6i −0.460461 + 1.11165i 0.507747 + 0.861506i \(0.330478\pi\)
−0.968208 + 0.250145i \(0.919522\pi\)
\(60\) −936792. 340899.i −0.559904 0.203749i
\(61\) −2.37025e6 + 981790.i −1.33703 + 0.553814i −0.932651 0.360779i \(-0.882511\pi\)
−0.404375 + 0.914593i \(0.632511\pi\)
\(62\) 11274.3 7894.85i 0.00600783 0.00420700i
\(63\) 3.23513e6 1.63005
\(64\) −1.81599e6 + 1.04891e6i −0.865932 + 0.500161i
\(65\) −4.86536e6 −2.19744
\(66\) 292576. 204877.i 0.125266 0.0877182i
\(67\) 1.34736e6 558096.i 0.547296 0.226698i −0.0918634 0.995772i \(-0.529282\pi\)
0.639160 + 0.769074i \(0.279282\pi\)
\(68\) −826914. 300914.i −0.318918 0.116054i
\(69\) 62935.9 151941.i 0.0230636 0.0556804i
\(70\) 5.28789e6 8.30089e6i 1.84263 2.89255i
\(71\) 124974. + 124974.i 0.0414395 + 0.0414395i 0.727523 0.686083i \(-0.240672\pi\)
−0.686083 + 0.727523i \(0.740672\pi\)
\(72\) 2.47215e6 + 1.42699e6i 0.780567 + 0.450564i
\(73\) −2.10570e6 + 2.10570e6i −0.633529 + 0.633529i −0.948951 0.315422i \(-0.897854\pi\)
0.315422 + 0.948951i \(0.397854\pi\)
\(74\) 317238. + 1.43076e6i 0.0910070 + 0.410446i
\(75\) 2.75313e6 + 1.14038e6i 0.753549 + 0.312130i
\(76\) 1.80586e6 78957.7i 0.471885 0.0206323i
\(77\) 1.34947e6 + 3.25790e6i 0.336856 + 0.813243i
\(78\) −1.50287e6 264948.i −0.358582 0.0632163i
\(79\) 6.34026e6i 1.44681i 0.690423 + 0.723406i \(0.257425\pi\)
−0.690423 + 0.723406i \(0.742575\pi\)
\(80\) 7.70223e6 4.01074e6i 1.68190 0.875809i
\(81\) 3.41297e6i 0.713566i
\(82\) 701936. 3.98160e6i 0.140588 0.797460i
\(83\) −1.62242e6 3.91687e6i −0.311451 0.751909i −0.999652 0.0263889i \(-0.991599\pi\)
0.688201 0.725520i \(-0.258401\pi\)
\(84\) 2.08542e6 2.27611e6i 0.383897 0.419002i
\(85\) 3.36640e6 + 1.39441e6i 0.594565 + 0.246277i
\(86\) −9.00220e6 + 1.99603e6i −1.52617 + 0.338394i
\(87\) −574134. + 574134.i −0.0934752 + 0.0934752i
\(88\) −405828. + 3.08478e6i −0.0634823 + 0.482542i
\(89\) 706032. + 706032.i 0.106160 + 0.106160i 0.758192 0.652032i \(-0.226083\pi\)
−0.652032 + 0.758192i \(0.726083\pi\)
\(90\) −9.96881e6 6.35040e6i −1.44143 0.918232i
\(91\) 5.76561e6 1.39194e7i 0.802048 1.93632i
\(92\) 605526. + 1.29834e6i 0.0810728 + 0.173833i
\(93\) −16515.3 + 6840.85i −0.00212910 + 0.000881900i
\(94\) 620481. + 886081.i 0.0770515 + 0.110034i
\(95\) −7.48487e6 −0.895678
\(96\) 2.59756e6 819449.i 0.299651 0.0945307i
\(97\) −2.89743e6 −0.322338 −0.161169 0.986927i \(-0.551526\pi\)
−0.161169 + 0.986927i \(0.551526\pi\)
\(98\) 1.21375e7 + 1.73329e7i 1.30268 + 1.86029i
\(99\) 3.91252e6 1.62062e6i 0.405260 0.167864i
\(100\) −2.35257e7 + 1.09720e7i −2.35257 + 1.09720i
\(101\) 3.26396e6 7.87991e6i 0.315225 0.761020i −0.684270 0.729229i \(-0.739879\pi\)
0.999495 0.0317911i \(-0.0101211\pi\)
\(102\) 963917. + 614041.i 0.0899371 + 0.0572924i
\(103\) 9.27797e6 + 9.27797e6i 0.836610 + 0.836610i 0.988411 0.151801i \(-0.0485074\pi\)
−0.151801 + 0.988411i \(0.548507\pi\)
\(104\) 1.05456e7 8.09345e6i 0.919291 0.705533i
\(105\) −9.03876e6 + 9.03876e6i −0.761985 + 0.761985i
\(106\) 4.95439e6 1.09852e6i 0.404036 0.0895857i
\(107\) −1.00310e7 4.15496e6i −0.791588 0.327887i −0.0500062 0.998749i \(-0.515924\pi\)
−0.741582 + 0.670862i \(0.765924\pi\)
\(108\) −5.76635e6 5.28323e6i −0.440471 0.403567i
\(109\) 6.24714e6 + 1.50819e7i 0.462049 + 1.11549i 0.967555 + 0.252662i \(0.0813061\pi\)
−0.505505 + 0.862823i \(0.668694\pi\)
\(110\) 2.23682e6 1.26879e7i 0.160234 0.908899i
\(111\) 1.90338e6i 0.132098i
\(112\) 2.34702e6 + 2.67884e7i 0.157853 + 1.80170i
\(113\) 1.87551e7i 1.22277i −0.791333 0.611385i \(-0.790613\pi\)
0.791333 0.611385i \(-0.209387\pi\)
\(114\) −2.31201e6 407596.i −0.146158 0.0257669i
\(115\) −2.27014e6 5.48059e6i −0.139190 0.336035i
\(116\) −308953. 7.06613e6i −0.0183776 0.420319i
\(117\) −1.67163e7 6.92411e6i −0.964915 0.399681i
\(118\) 4.64877e6 + 2.09662e7i 0.260466 + 1.17471i
\(119\) −7.97859e6 + 7.97859e6i −0.434022 + 0.434022i
\(120\) −1.08940e7 + 2.92011e6i −0.575508 + 0.154264i
\(121\) −1.05155e7 1.05155e7i −0.539609 0.539609i
\(122\) −1.55948e7 + 2.44806e7i −0.777535 + 1.22057i
\(123\) −2.00946e6 + 4.85127e6i −0.0973671 + 0.235065i
\(124\) 53249.5 146330.i 0.00250807 0.00689220i
\(125\) 6.10508e7 2.52881e7i 2.79580 1.15806i
\(126\) 2.99814e7 2.09946e7i 1.33523 0.934997i
\(127\) 3.77742e6 0.163637 0.0818186 0.996647i \(-0.473927\pi\)
0.0818186 + 0.996647i \(0.473927\pi\)
\(128\) −1.00226e7 + 2.15057e7i −0.422422 + 0.906399i
\(129\) 1.19759e7 0.491183
\(130\) −4.50894e7 + 3.15740e7i −1.80000 + 1.26046i
\(131\) −2.00691e7 + 8.31288e6i −0.779969 + 0.323074i −0.736903 0.675998i \(-0.763713\pi\)
−0.0430661 + 0.999072i \(0.513713\pi\)
\(132\) 1.38187e6 3.79738e6i 0.0522946 0.143706i
\(133\) 8.86983e6 2.14137e7i 0.326915 0.789242i
\(134\) 8.86481e6 1.39159e7i 0.318275 0.499626i
\(135\) 2.28990e7 + 2.28990e7i 0.801028 + 0.801028i
\(136\) −9.61618e6 + 2.57761e6i −0.327806 + 0.0878679i
\(137\) −1.94735e7 + 1.94735e7i −0.647028 + 0.647028i −0.952274 0.305246i \(-0.901261\pi\)
0.305246 + 0.952274i \(0.401261\pi\)
\(138\) −402774. 1.81653e6i −0.0130462 0.0588390i
\(139\) −3.79751e7 1.57298e7i −1.19935 0.496788i −0.308563 0.951204i \(-0.599848\pi\)
−0.890790 + 0.454416i \(0.849848\pi\)
\(140\) −4.86393e6 1.11244e8i −0.149809 3.42633i
\(141\) −537644. 1.29799e6i −0.0161521 0.0389945i
\(142\) 1.96921e6 + 347162.i 0.0577142 + 0.0101747i
\(143\) 1.97222e7i 0.564000i
\(144\) 3.21710e7 2.81862e6i 0.897834 0.0786624i
\(145\) 2.92875e7i 0.797800i
\(146\) −5.84939e6 + 3.31796e7i −0.155552 + 0.882339i
\(147\) −1.05171e7 2.53904e7i −0.273076 0.659264i
\(148\) 1.22250e7 + 1.12008e7i 0.309979 + 0.284009i
\(149\) 3.34350e7 + 1.38492e7i 0.828037 + 0.342984i 0.756125 0.654427i \(-0.227090\pi\)
0.0719116 + 0.997411i \(0.477090\pi\)
\(150\) 3.29150e7 7.29816e6i 0.796296 0.176561i
\(151\) −2.61925e7 + 2.61925e7i −0.619094 + 0.619094i −0.945299 0.326205i \(-0.894230\pi\)
0.326205 + 0.945299i \(0.394230\pi\)
\(152\) 1.62233e7 1.24510e7i 0.374703 0.287575i
\(153\) 9.58175e6 + 9.58175e6i 0.216284 + 0.216284i
\(154\) 3.36485e7 + 2.14350e7i 0.742408 + 0.472934i
\(155\) −246753. + 595715.i −0.00532234 + 0.0128493i
\(156\) −1.56471e7 + 7.29755e6i −0.329988 + 0.153901i
\(157\) 1.90669e7 7.89777e6i 0.393216 0.162876i −0.177310 0.984155i \(-0.556739\pi\)
0.570526 + 0.821280i \(0.306739\pi\)
\(158\) 4.11455e7 + 5.87580e7i 0.829894 + 1.18513i
\(159\) −6.59096e6 −0.130035
\(160\) 4.53520e7 8.71534e7i 0.875340 1.68215i
\(161\) 1.83697e7 0.346907
\(162\) −2.21487e7 3.16295e7i −0.409303 0.584507i
\(163\) 7.31044e7 3.02808e7i 1.32217 0.547660i 0.393758 0.919214i \(-0.371175\pi\)
0.928411 + 0.371554i \(0.121175\pi\)
\(164\) −1.93337e7 4.14545e7i −0.342264 0.733868i
\(165\) −6.40344e6 + 1.54593e7i −0.110973 + 0.267914i
\(166\) −4.04544e7 2.57706e7i −0.686417 0.437266i
\(167\) −6.79952e7 6.79952e7i −1.12972 1.12972i −0.990222 0.139498i \(-0.955451\pi\)
−0.139498 0.990222i \(-0.544549\pi\)
\(168\) 4.55548e6 3.46272e7i 0.0741228 0.563423i
\(169\) −1.52132e7 + 1.52132e7i −0.242448 + 0.242448i
\(170\) 4.02470e7 8.92386e6i 0.628293 0.139310i
\(171\) −2.57164e7 1.06521e7i −0.393299 0.162910i
\(172\) −7.04740e7 + 7.69185e7i −1.05604 + 1.15261i
\(173\) 2.94812e6 + 7.11740e6i 0.0432897 + 0.104511i 0.944045 0.329816i \(-0.106987\pi\)
−0.900756 + 0.434326i \(0.856987\pi\)
\(174\) −1.59488e6 + 9.04664e6i −0.0229512 + 0.130186i
\(175\) 3.32855e8i 4.69485i
\(176\) 1.62579e7 + 3.12217e7i 0.224787 + 0.431680i
\(177\) 2.78919e7i 0.378069i
\(178\) 1.11250e7 + 1.96127e6i 0.147852 + 0.0260656i
\(179\) 1.57079e7 + 3.79222e7i 0.204707 + 0.494206i 0.992574 0.121638i \(-0.0388148\pi\)
−0.787867 + 0.615845i \(0.788815\pi\)
\(180\) −1.33597e8 + 5.84125e6i −1.70743 + 0.0746539i
\(181\) 3.72229e7 + 1.54182e7i 0.466589 + 0.193268i 0.603576 0.797305i \(-0.293742\pi\)
−0.136987 + 0.990573i \(0.543742\pi\)
\(182\) −3.68985e7 1.66414e8i −0.453689 2.04616i
\(183\) 2.66567e7 2.66567e7i 0.321534 0.321534i
\(184\) 1.40374e7 + 8.10274e6i 0.166120 + 0.0958891i
\(185\) −4.85472e7 4.85472e7i −0.563719 0.563719i
\(186\) −108660. + 170574.i −0.00123816 + 0.00194365i
\(187\) −5.65237e6 + 1.36460e7i −0.0632098 + 0.152602i
\(188\) 1.15006e7 + 4.18505e6i 0.126231 + 0.0459355i
\(189\) −9.26483e7 + 3.83762e7i −0.998208 + 0.413471i
\(190\) −6.93656e7 + 4.85736e7i −0.733680 + 0.513762i
\(191\) −4.83656e7 −0.502250 −0.251125 0.967955i \(-0.580801\pi\)
−0.251125 + 0.967955i \(0.580801\pi\)
\(192\) 1.87549e7 2.44512e7i 0.191232 0.249314i
\(193\) −1.54941e8 −1.55137 −0.775684 0.631122i \(-0.782595\pi\)
−0.775684 + 0.631122i \(0.782595\pi\)
\(194\) −2.68517e7 + 1.88030e7i −0.264038 + 0.184894i
\(195\) 6.60499e7 2.73588e7i 0.637898 0.264226i
\(196\) 2.24967e8 + 8.18653e7i 2.13413 + 0.776612i
\(197\) 4.33562e7 1.04671e8i 0.404035 0.975428i −0.582641 0.812730i \(-0.697980\pi\)
0.986676 0.162698i \(-0.0520195\pi\)
\(198\) 2.57420e7 4.04095e7i 0.235675 0.369961i
\(199\) −8.78823e7 8.78823e7i −0.790525 0.790525i 0.191055 0.981579i \(-0.438809\pi\)
−0.981579 + 0.191055i \(0.938809\pi\)
\(200\) −1.46819e8 + 2.54353e8i −1.29771 + 2.24819i
\(201\) −1.51529e7 + 1.51529e7i −0.131616 + 0.131616i
\(202\) −2.08885e7 9.42083e7i −0.178311 0.804191i
\(203\) −8.37893e7 3.47067e7i −0.702995 0.291190i
\(204\) 1.29179e7 564810.i 0.106534 0.00465797i
\(205\) 7.24826e7 + 1.74988e8i 0.587618 + 1.41863i
\(206\) 1.46193e8 + 2.57731e7i 1.16518 + 0.205415i
\(207\) 2.20608e7i 0.172872i
\(208\) 4.52075e7 1.43442e8i 0.348328 1.10523i
\(209\) 3.03406e7i 0.229886i
\(210\) −2.51086e7 + 1.42424e8i −0.187092 + 1.06124i
\(211\) −1.13439e7 2.73867e7i −0.0831333 0.200702i 0.876847 0.480770i \(-0.159643\pi\)
−0.959980 + 0.280069i \(0.909643\pi\)
\(212\) 3.87856e7 4.23323e7i 0.279573 0.305138i
\(213\) −2.39933e6 993837.i −0.0170123 0.00704671i
\(214\) −1.19925e8 + 2.65907e7i −0.836493 + 0.185473i
\(215\) 3.05454e8 3.05454e8i 2.09609 2.09609i
\(216\) −8.77252e7 1.15409e7i −0.592292 0.0779208i
\(217\) −1.41189e6 1.41189e6i −0.00937974 0.00937974i
\(218\) 1.55770e8 + 9.92297e7i 1.01832 + 0.648700i
\(219\) 1.67453e7 4.04268e7i 0.107731 0.260085i
\(220\) −6.16094e7 1.32100e8i −0.390093 0.836421i
\(221\) 5.83028e7 2.41498e7i 0.363343 0.150501i
\(222\) −1.23521e7 1.76395e7i −0.0757715 0.108206i
\(223\) 2.75019e8 1.66072 0.830359 0.557229i \(-0.188136\pi\)
0.830359 + 0.557229i \(0.188136\pi\)
\(224\) 1.95596e8 + 2.33028e8i 1.16276 + 1.38529i
\(225\) 3.99736e8 2.33956
\(226\) −1.21712e8 1.73812e8i −0.701384 1.00161i
\(227\) 1.00082e8 4.14555e7i 0.567893 0.235229i −0.0802145 0.996778i \(-0.525561\pi\)
0.648108 + 0.761548i \(0.275561\pi\)
\(228\) −2.40716e7 + 1.12266e7i −0.134503 + 0.0627300i
\(229\) −1.85683e7 + 4.48278e7i −0.102176 + 0.246674i −0.966698 0.255921i \(-0.917621\pi\)
0.864522 + 0.502595i \(0.167621\pi\)
\(230\) −5.66050e7 3.60589e7i −0.306766 0.195418i
\(231\) −3.66395e7 3.66395e7i −0.195572 0.195572i
\(232\) −4.87193e7 6.34800e7i −0.256149 0.333756i
\(233\) −1.93922e8 + 1.93922e8i −1.00434 + 1.00434i −0.00435279 + 0.999991i \(0.501386\pi\)
−0.999991 + 0.00435279i \(0.998614\pi\)
\(234\) −1.99852e8 + 4.43126e7i −1.01965 + 0.226085i
\(235\) −4.68192e7 1.93931e7i −0.235335 0.0974789i
\(236\) 1.79143e8 + 1.64134e8i 0.887174 + 0.812844i
\(237\) −3.56524e7 8.60725e7i −0.173968 0.419996i
\(238\) −2.21636e7 + 1.25719e8i −0.106567 + 0.604478i
\(239\) 2.82931e8i 1.34057i −0.742105 0.670283i \(-0.766173\pi\)
0.742105 0.670283i \(-0.233827\pi\)
\(240\) −8.20089e7 + 9.77590e7i −0.382932 + 0.456475i
\(241\) 2.79022e8i 1.28404i −0.766687 0.642021i \(-0.778096\pi\)
0.766687 0.642021i \(-0.221904\pi\)
\(242\) −1.65692e8 2.92107e7i −0.751534 0.132492i
\(243\) 7.03274e7 + 1.69785e8i 0.314414 + 0.759063i
\(244\) 1.43445e7 + 3.28076e8i 0.0632150 + 1.44581i
\(245\) −9.15847e8 3.79356e8i −3.97871 1.64803i
\(246\) 1.28601e7 + 5.79995e7i 0.0550770 + 0.248400i
\(247\) −9.16628e7 + 9.16628e7i −0.387038 + 0.387038i
\(248\) −456131. 1.70167e6i −0.00189893 0.00708427i
\(249\) 4.40505e7 + 4.40505e7i 0.180823 + 0.180823i
\(250\) 4.01676e8 6.30549e8i 1.62587 2.55228i
\(251\) −1.39512e8 + 3.36811e8i −0.556869 + 1.34440i 0.355363 + 0.934728i \(0.384357\pi\)
−0.912233 + 0.409673i \(0.865643\pi\)
\(252\) 1.41605e8 3.89132e8i 0.557414 1.53178i
\(253\) 2.22161e7 9.20221e6i 0.0862474 0.0357248i
\(254\) 3.50070e7 2.45138e7i 0.134041 0.0938626i
\(255\) −5.35417e7 −0.202210
\(256\) 4.66788e7 + 2.64346e8i 0.173892 + 0.984765i
\(257\) 1.80366e8 0.662811 0.331406 0.943488i \(-0.392477\pi\)
0.331406 + 0.943488i \(0.392477\pi\)
\(258\) 1.10986e8 7.77182e7i 0.402345 0.281743i
\(259\) 1.96420e8 8.13598e7i 0.702484 0.290978i
\(260\) −2.12962e8 + 5.85221e8i −0.751442 + 2.06497i
\(261\) −4.16804e7 + 1.00625e8i −0.145107 + 0.350320i
\(262\) −1.32042e8 + 2.07279e8i −0.453584 + 0.712033i
\(263\) 2.55751e8 + 2.55751e8i 0.866905 + 0.866905i 0.992129 0.125224i \(-0.0399648\pi\)
−0.125224 + 0.992129i \(0.539965\pi\)
\(264\) −1.18369e7 4.41597e7i −0.0395937 0.147711i
\(265\) −1.68107e8 + 1.68107e8i −0.554915 + 0.554915i
\(266\) −5.67646e7 2.56011e8i −0.184924 0.834014i
\(267\) −1.35549e7 5.61463e6i −0.0435820 0.0180523i
\(268\) −8.15407e6 1.86494e8i −0.0258763 0.591824i
\(269\) 4.02726e7 + 9.72267e7i 0.126147 + 0.304546i 0.974318 0.225177i \(-0.0722960\pi\)
−0.848171 + 0.529723i \(0.822296\pi\)
\(270\) 3.60819e8 + 6.36106e7i 1.11562 + 0.196678i
\(271\) 4.10014e7i 0.125143i 0.998040 + 0.0625714i \(0.0199301\pi\)
−0.998040 + 0.0625714i \(0.980070\pi\)
\(272\) −7.23899e7 + 8.62927e7i −0.218116 + 0.260006i
\(273\) 2.21385e8i 0.658535i
\(274\) −5.40952e7 + 3.06845e8i −0.158866 + 0.901139i
\(275\) 1.66742e8 + 4.02550e8i 0.483481 + 1.16723i
\(276\) −1.55212e7 1.42208e7i −0.0444368 0.0407137i
\(277\) 4.14160e7 + 1.71551e7i 0.117082 + 0.0484969i 0.440455 0.897775i \(-0.354817\pi\)
−0.323374 + 0.946271i \(0.604817\pi\)
\(278\) −4.54012e8 + 1.00667e8i −1.26739 + 0.281015i
\(279\) −1.69558e6 + 1.69558e6i −0.00467416 + 0.00467416i
\(280\) −7.67002e8 9.99384e8i −2.08806 2.72069i
\(281\) 6.83675e7 + 6.83675e7i 0.183814 + 0.183814i 0.793015 0.609202i \(-0.208510\pi\)
−0.609202 + 0.793015i \(0.708510\pi\)
\(282\) −1.34060e7 8.53996e6i −0.0355980 0.0226769i
\(283\) 2.04493e8 4.93691e8i 0.536324 1.29480i −0.390949 0.920412i \(-0.627853\pi\)
0.927272 0.374387i \(-0.122147\pi\)
\(284\) 2.05025e7 9.56201e6i 0.0531119 0.0247705i
\(285\) 1.01611e8 4.20888e7i 0.260007 0.107698i
\(286\) −1.27988e8 1.82774e8i −0.323511 0.461992i
\(287\) −5.86523e8 −1.46453
\(288\) 2.79851e8 2.34897e8i 0.690326 0.579434i
\(289\) 3.63077e8 0.884823
\(290\) 1.90063e8 + 2.71420e8i 0.457619 + 0.653505i
\(291\) 3.93342e7 1.62927e7i 0.0935717 0.0387586i
\(292\) 1.61112e8 + 3.45450e8i 0.378693 + 0.811979i
\(293\) −2.17185e8 + 5.24332e8i −0.504422 + 1.21778i 0.442631 + 0.896704i \(0.354045\pi\)
−0.947053 + 0.321078i \(0.895955\pi\)
\(294\) −2.62239e8 1.67053e8i −0.601841 0.383389i
\(295\) −7.11403e8 7.11403e8i −1.61339 1.61339i
\(296\) 1.85983e8 + 2.44675e7i 0.416823 + 0.0548363i
\(297\) −9.28231e7 + 9.28231e7i −0.205593 + 0.205593i
\(298\) 3.99733e8 8.86316e7i 0.875010 0.194013i
\(299\) −9.49186e7 3.93166e7i −0.205353 0.0850602i
\(300\) 2.57676e8 2.81239e8i 0.550998 0.601384i
\(301\) 5.11907e8 + 1.23585e9i 1.08195 + 2.61207i
\(302\) −7.27596e7 + 4.12715e8i −0.152008 + 0.862235i
\(303\) 1.25328e8i 0.258820i
\(304\) 6.95472e7 2.20671e8i 0.141978 0.450493i
\(305\) 1.35980e9i 2.74426i
\(306\) 1.50980e8 + 2.66170e7i 0.301227 + 0.0531048i
\(307\) 9.23161e7 + 2.22871e8i 0.182093 + 0.439611i 0.988398 0.151889i \(-0.0485357\pi\)
−0.806305 + 0.591501i \(0.798536\pi\)
\(308\) 4.50939e8 1.97164e7i 0.879407 0.0384504i
\(309\) −1.78125e8 7.37819e7i −0.343456 0.142264i
\(310\) 1.57916e6 + 7.12208e6i 0.00301065 + 0.0135782i
\(311\) 2.93017e7 2.93017e7i 0.0552372 0.0552372i −0.678949 0.734186i \(-0.737564\pi\)
0.734186 + 0.678949i \(0.237564\pi\)
\(312\) −9.76509e7 + 1.69173e8i −0.182027 + 0.315347i
\(313\) 3.05448e8 + 3.05448e8i 0.563031 + 0.563031i 0.930167 0.367136i \(-0.119662\pi\)
−0.367136 + 0.930167i \(0.619662\pi\)
\(314\) 1.25448e8 1.96928e8i 0.228671 0.358967i
\(315\) −6.56186e8 + 1.58417e9i −1.18288 + 2.85572i
\(316\) 7.62628e8 + 2.77520e8i 1.35959 + 0.494755i
\(317\) −1.34028e7 + 5.55160e6i −0.0236312 + 0.00978838i −0.394468 0.918910i \(-0.629071\pi\)
0.370837 + 0.928698i \(0.379071\pi\)
\(318\) −6.10814e7 + 4.27725e7i −0.106516 + 0.0745881i
\(319\) −1.18720e8 −0.204765
\(320\) −1.45290e8 1.10200e9i −0.247863 1.88000i
\(321\) 1.59540e8 0.269216
\(322\) 1.70241e8 1.19212e8i 0.284163 0.198986i
\(323\) 8.96931e7 3.71521e7i 0.148098 0.0613444i
\(324\) −4.10523e8 1.49389e8i −0.670548 0.244013i
\(325\) 7.12406e8 1.71990e9i 1.15116 2.77915i
\(326\) 4.80982e8 7.55042e8i 0.768895 1.20701i
\(327\) −1.69617e8 1.69617e8i −0.268257 0.268257i
\(328\) −4.48195e8 2.58710e8i −0.701308 0.404813i
\(329\) 1.10965e8 1.10965e8i 0.171790 0.171790i
\(330\) 4.09804e7 + 1.84823e8i 0.0627736 + 0.283112i
\(331\) −6.05626e8 2.50858e8i −0.917923 0.380216i −0.126839 0.991923i \(-0.540483\pi\)
−0.791084 + 0.611707i \(0.790483\pi\)
\(332\) −5.42149e8 + 2.37044e7i −0.813084 + 0.0355505i
\(333\) −9.77076e7 2.35887e8i −0.145002 0.350065i
\(334\) −1.07140e9 1.88883e8i −1.57340 0.277383i
\(335\) 7.72973e8i 1.12333i
\(336\) −1.82498e8 3.50469e8i −0.262464 0.504036i
\(337\) 5.92841e8i 0.843789i 0.906645 + 0.421894i \(0.138635\pi\)
−0.906645 + 0.421894i \(0.861365\pi\)
\(338\) −4.22606e7 + 2.39715e8i −0.0595288 + 0.337666i
\(339\) 1.05463e8 + 2.54611e8i 0.147029 + 0.354959i
\(340\) 3.15075e8 3.43887e8i 0.434748 0.474504i
\(341\) −2.41479e6 1.00024e6i −0.00329791 0.00136604i
\(342\) −3.07452e8 + 6.81705e7i −0.415610 + 0.0921521i
\(343\) 1.21484e9 1.21484e9i 1.62551 1.62551i
\(344\) −1.53947e8 + 1.17018e9i −0.203900 + 1.54988i
\(345\) 6.16367e7 + 6.16367e7i 0.0808113 + 0.0808113i
\(346\) 7.35104e7 + 4.68281e7i 0.0954075 + 0.0607771i
\(347\) 2.11077e8 5.09585e8i 0.271199 0.654732i −0.728336 0.685220i \(-0.759706\pi\)
0.999535 + 0.0304878i \(0.00970608\pi\)
\(348\) 4.39283e7 + 9.41893e7i 0.0558750 + 0.119805i
\(349\) −8.67771e8 + 3.59442e8i −1.09274 + 0.452627i −0.854961 0.518693i \(-0.826419\pi\)
−0.237777 + 0.971320i \(0.576419\pi\)
\(350\) 2.16008e9 + 3.08472e9i 2.69298 + 3.84571i
\(351\) 5.60860e8 0.692277
\(352\) 3.53285e8 + 1.83839e8i 0.431743 + 0.224666i
\(353\) 1.26020e9 1.52485 0.762427 0.647074i \(-0.224008\pi\)
0.762427 + 0.647074i \(0.224008\pi\)
\(354\) −1.81006e8 2.58486e8i −0.216861 0.309689i
\(355\) −8.65454e7 + 3.58483e7i −0.102670 + 0.0425274i
\(356\) 1.15828e8 5.40201e7i 0.136062 0.0634571i
\(357\) 6.34488e7 1.53179e8i 0.0738048 0.178180i
\(358\) 3.91671e8 + 2.49505e8i 0.451160 + 0.287401i
\(359\) −6.34279e8 6.34279e8i −0.723519 0.723519i 0.245801 0.969320i \(-0.420949\pi\)
−0.969320 + 0.245801i \(0.920949\pi\)
\(360\) −1.20019e9 + 9.21118e8i −1.35579 + 1.04053i
\(361\) 4.91049e8 4.91049e8i 0.549350 0.549350i
\(362\) 4.45019e8 9.86727e7i 0.493058 0.109324i
\(363\) 2.01883e8 + 8.36229e7i 0.221527 + 0.0917597i
\(364\) −1.42191e9 1.30278e9i −1.54531 1.41584i
\(365\) −6.04014e8 1.45822e9i −0.650162 1.56963i
\(366\) 7.40491e7 4.20030e8i 0.0789471 0.447812i
\(367\) 7.66961e8i 0.809920i 0.914334 + 0.404960i \(0.132715\pi\)
−0.914334 + 0.404960i \(0.867285\pi\)
\(368\) 1.82674e8 1.60047e7i 0.191077 0.0167409i
\(369\) 7.04374e8i 0.729813i
\(370\) −7.64958e8 1.34858e8i −0.785112 0.138411i
\(371\) −2.81730e8 6.80156e8i −0.286434 0.691512i
\(372\) 99948.4 + 2.28594e6i 0.000100664 + 0.00230232i
\(373\) −2.20332e8 9.12643e7i −0.219834 0.0910584i 0.270048 0.962847i \(-0.412960\pi\)
−0.489883 + 0.871788i \(0.662960\pi\)
\(374\) 3.61737e7 + 1.63145e8i 0.0357555 + 0.161259i
\(375\) −6.86599e8 + 6.86599e8i −0.672347 + 0.672347i
\(376\) 1.33740e8 3.58488e7i 0.129749 0.0347790i
\(377\) 3.58666e8 + 3.58666e8i 0.344743 + 0.344743i
\(378\) −6.09568e8 + 9.56896e8i −0.580498 + 0.911262i
\(379\) −1.93009e8 + 4.65966e8i −0.182113 + 0.439660i −0.988402 0.151863i \(-0.951473\pi\)
0.806289 + 0.591522i \(0.201473\pi\)
\(380\) −3.27621e8 + 9.00306e8i −0.306288 + 0.841681i
\(381\) −5.12805e7 + 2.12411e7i −0.0475023 + 0.0196761i
\(382\) −4.48226e8 + 3.13872e8i −0.411410 + 0.288092i
\(383\) −6.52658e8 −0.593594 −0.296797 0.954941i \(-0.595919\pi\)
−0.296797 + 0.954941i \(0.595919\pi\)
\(384\) 1.51319e7 3.48311e8i 0.0136375 0.313912i
\(385\) −1.86904e9 −1.66919
\(386\) −1.43590e9 + 1.00550e9i −1.27078 + 0.889867i
\(387\) 1.48418e9 6.14766e8i 1.30166 0.539165i
\(388\) −1.26824e8 + 3.48512e8i −0.110227 + 0.302905i
\(389\) −2.51784e8 + 6.07861e8i −0.216873 + 0.523577i −0.994450 0.105210i \(-0.966448\pi\)
0.777577 + 0.628787i \(0.216448\pi\)
\(390\) 4.34567e8 6.82181e8i 0.370963 0.582336i
\(391\) 5.44072e7 + 5.44072e7i 0.0460297 + 0.0460297i
\(392\) 2.61614e9 7.01252e8i 2.19361 0.587994i
\(393\) 2.25704e8 2.25704e8i 0.187571 0.187571i
\(394\) −2.77469e8 1.25140e9i −0.228548 1.03076i
\(395\) −3.10469e9 1.28600e9i −2.53471 1.04991i
\(396\) −2.36781e7 5.41547e8i −0.0191608 0.438231i
\(397\) 2.66916e8 + 6.44393e8i 0.214096 + 0.516873i 0.994045 0.108970i \(-0.0347552\pi\)
−0.779949 + 0.625843i \(0.784755\pi\)
\(398\) −1.38476e9 2.44127e8i −1.10099 0.194099i
\(399\) 3.40579e8i 0.268418i
\(400\) 2.90001e8 + 3.31000e9i 0.226563 + 2.58594i
\(401\) 7.17723e8i 0.555842i −0.960604 0.277921i \(-0.910355\pi\)
0.960604 0.277921i \(-0.0896453\pi\)
\(402\) −4.20930e7 + 2.38765e8i −0.0323161 + 0.183307i
\(403\) 4.27353e6 + 1.03172e7i 0.00325252 + 0.00785227i
\(404\) −8.04954e8 7.37513e8i −0.607346 0.556461i
\(405\) 1.67126e9 + 6.92256e8i 1.25012 + 0.517815i
\(406\) −1.00174e9 + 2.22114e8i −0.742874 + 0.164715i
\(407\) 1.96791e8 1.96791e8i 0.144685 0.144685i
\(408\) 1.16051e8 8.90659e7i 0.0845935 0.0649234i
\(409\) −1.06454e9 1.06454e9i −0.769359 0.769359i 0.208635 0.977994i \(-0.433098\pi\)
−0.977994 + 0.208635i \(0.933098\pi\)
\(410\) 1.80733e9 + 1.15132e9i 1.29507 + 0.824994i
\(411\) 1.54861e8 3.73867e8i 0.110026 0.265626i
\(412\) 1.52209e9 7.09879e8i 1.07226 0.500085i
\(413\) 2.87831e9 1.19223e9i 2.01054 0.832792i
\(414\) −1.43165e8 2.04448e8i −0.0991599 0.141606i
\(415\) 2.24708e9 1.54330
\(416\) −5.11917e8 1.62272e9i −0.348636 1.10514i
\(417\) 6.03984e8 0.407896
\(418\) −1.96898e8 2.81180e8i −0.131863 0.188308i
\(419\) −2.44094e8 + 1.01107e8i −0.162109 + 0.0671478i −0.462262 0.886743i \(-0.652962\pi\)
0.300153 + 0.953891i \(0.402962\pi\)
\(420\) 6.91576e8 + 1.48285e9i 0.455478 + 0.976618i
\(421\) −9.27134e8 + 2.23830e9i −0.605557 + 1.46194i 0.262229 + 0.965006i \(0.415542\pi\)
−0.867786 + 0.496938i \(0.834458\pi\)
\(422\) −2.82857e8 1.80187e8i −0.183220 0.116716i
\(423\) −1.33261e8 1.33261e8i −0.0856076 0.0856076i
\(424\) 8.47252e7 6.44014e8i 0.0539799 0.410313i
\(425\) −9.85844e8 + 9.85844e8i −0.622941 + 0.622941i
\(426\) −2.86853e7 + 6.36030e6i −0.0179773 + 0.00398606i
\(427\) 3.89028e9 + 1.61141e9i 2.41815 + 1.00163i
\(428\) −9.38839e8 + 1.02469e9i −0.578812 + 0.631742i
\(429\) 1.10901e8 + 2.67740e8i 0.0678166 + 0.163724i
\(430\) 8.48515e8 4.81304e9i 0.514659 2.91931i
\(431\) 1.47608e9i 0.888053i −0.896014 0.444026i \(-0.853550\pi\)
0.896014 0.444026i \(-0.146450\pi\)
\(432\) −8.87884e8 + 4.62343e8i −0.529862 + 0.275912i
\(433\) 9.38422e8i 0.555508i 0.960652 + 0.277754i \(0.0895901\pi\)
−0.960652 + 0.277754i \(0.910410\pi\)
\(434\) −2.22471e7 3.92205e6i −0.0130635 0.00230303i
\(435\) −1.64689e8 3.97594e8i −0.0959293 0.231594i
\(436\) 2.08755e9 9.12739e7i 1.20624 0.0527405i
\(437\) −1.46023e8 6.04847e7i −0.0837020 0.0346705i
\(438\) −1.07166e8 4.83323e8i −0.0609392 0.274839i
\(439\) −1.76455e9 + 1.76455e9i −0.995427 + 0.995427i −0.999990 0.00456274i \(-0.998548\pi\)
0.00456274 + 0.999990i \(0.498548\pi\)
\(440\) −1.42824e9 8.24416e8i −0.799311 0.461383i
\(441\) −2.60677e9 2.60677e9i −1.44733 1.44733i
\(442\) 3.83596e8 6.02167e8i 0.211299 0.331695i
\(443\) 8.50744e8 2.05388e9i 0.464928 1.12244i −0.501422 0.865203i \(-0.667189\pi\)
0.966350 0.257232i \(-0.0828106\pi\)
\(444\) −2.28945e8 8.33131e7i −0.124134 0.0451724i
\(445\) −4.88934e8 + 2.02523e8i −0.263021 + 0.108947i
\(446\) 2.54872e9 1.78475e9i 1.36035 0.952590i
\(447\) −5.31775e8 −0.281613
\(448\) 3.32492e9 + 8.90249e8i 1.74706 + 0.467776i
\(449\) −2.06603e9 −1.07715 −0.538574 0.842578i \(-0.681037\pi\)
−0.538574 + 0.842578i \(0.681037\pi\)
\(450\) 3.70454e9 2.59412e9i 1.91642 1.34198i
\(451\) −7.09332e8 + 2.93815e8i −0.364109 + 0.150819i
\(452\) −2.25593e9 8.20932e8i −1.14905 0.418141i
\(453\) 2.08292e8 5.02862e8i 0.105276 0.254159i
\(454\) 6.58480e8 1.03368e9i 0.330253 0.518429i
\(455\) 5.64659e9 + 5.64659e9i 2.81026 + 2.81026i
\(456\) −1.50226e8 + 2.60255e8i −0.0741941 + 0.128535i
\(457\) −2.26006e9 + 2.26006e9i −1.10768 + 1.10768i −0.114221 + 0.993455i \(0.536437\pi\)
−0.993455 + 0.114221i \(0.963563\pi\)
\(458\) 1.18832e8 + 5.35940e8i 0.0577971 + 0.260667i
\(459\) −3.88066e8 1.60742e8i −0.187310 0.0775864i
\(460\) −7.58590e8 + 3.31679e7i −0.363375 + 0.0158879i
\(461\) 6.97818e8 + 1.68468e9i 0.331733 + 0.800874i 0.998455 + 0.0555677i \(0.0176969\pi\)
−0.666722 + 0.745307i \(0.732303\pi\)
\(462\) −5.77329e8 1.01780e8i −0.272381 0.0480194i
\(463\) 1.05439e9i 0.493706i −0.969053 0.246853i \(-0.920604\pi\)
0.969053 0.246853i \(-0.0793964\pi\)
\(464\) −8.63461e8 2.72131e8i −0.401264 0.126463i
\(465\) 9.47470e6i 0.00436999i
\(466\) −5.38694e8 + 3.05564e9i −0.246599 + 1.39879i
\(467\) −1.96755e8 4.75009e8i −0.0893957 0.215820i 0.872858 0.487974i \(-0.162264\pi\)
−0.962254 + 0.272154i \(0.912264\pi\)
\(468\) −1.56455e9 + 1.70761e9i −0.705550 + 0.770069i
\(469\) −2.21142e9 9.15999e8i −0.989842 0.410006i
\(470\) −5.59747e8 + 1.24111e8i −0.248685 + 0.0551402i
\(471\) −2.14433e8 + 2.14433e8i −0.0945625 + 0.0945625i
\(472\) 2.72536e9 + 3.58543e8i 1.19296 + 0.156944i
\(473\) 1.23819e9 + 1.23819e9i 0.537987 + 0.537987i
\(474\) −8.88980e8 5.66304e8i −0.383414 0.244245i
\(475\) 1.09597e9 2.64590e9i 0.469212 1.13278i
\(476\) 6.10460e8 + 1.30892e9i 0.259438 + 0.556276i
\(477\) −8.16822e8 + 3.38339e8i −0.344598 + 0.142737i
\(478\) −1.83610e9 2.62205e9i −0.768951 1.09810i
\(479\) −3.79078e9 −1.57599 −0.787996 0.615680i \(-0.788882\pi\)
−0.787996 + 0.615680i \(0.788882\pi\)
\(480\) −1.25600e8 + 1.43818e9i −0.0518375 + 0.593565i
\(481\) −1.18906e9 −0.487186
\(482\) −1.81073e9 2.58582e9i −0.736528 1.05180i
\(483\) −2.49379e8 + 1.03296e8i −0.100704 + 0.0417129i
\(484\) −1.72511e9 + 8.04562e8i −0.691604 + 0.322553i
\(485\) 5.87689e8 1.41881e9i 0.233911 0.564712i
\(486\) 1.75359e9 + 1.11708e9i 0.692948 + 0.441426i
\(487\) −1.93681e9 1.93681e9i −0.759863 0.759863i 0.216435 0.976297i \(-0.430557\pi\)
−0.976297 + 0.216435i \(0.930557\pi\)
\(488\) 2.26201e9 + 2.94734e9i 0.881098 + 1.14805i
\(489\) −8.22158e8 + 8.22158e8i −0.317961 + 0.317961i
\(490\) −1.09494e10 + 2.42779e9i −4.20441 + 0.932232i
\(491\) 3.74533e9 + 1.55137e9i 1.42792 + 0.591465i 0.956838 0.290623i \(-0.0938626\pi\)
0.471085 + 0.882088i \(0.343863\pi\)
\(492\) 4.95571e8 + 4.54051e8i 0.187598 + 0.171880i
\(493\) −1.45372e8 3.50959e8i −0.0546408 0.131914i
\(494\) −2.54629e8 + 1.44433e9i −0.0950304 + 0.539042i
\(495\) 2.24459e9i 0.831799i
\(496\) −1.52703e7 1.28101e7i −0.00561903 0.00471374i
\(497\) 2.90081e8i 0.105992i
\(498\) 6.94103e8 + 1.22367e8i 0.251838 + 0.0443978i
\(499\) −8.44183e8 2.03804e9i −0.304148 0.734278i −0.999872 0.0159694i \(-0.994917\pi\)
0.695725 0.718309i \(-0.255083\pi\)
\(500\) −3.69472e8 8.45028e9i −0.132186 3.02326i
\(501\) 1.30542e9 + 5.40724e8i 0.463787 + 0.192107i
\(502\) 8.92841e8 + 4.02675e9i 0.315000 + 1.42067i
\(503\) −1.32321e9 + 1.32321e9i −0.463597 + 0.463597i −0.899832 0.436236i \(-0.856311\pi\)
0.436236 + 0.899832i \(0.356311\pi\)
\(504\) −1.21298e9 4.52522e9i −0.422033 1.57446i
\(505\) 3.19658e9 + 3.19658e9i 1.10450 + 1.10450i
\(506\) 1.46168e8 2.29454e8i 0.0501564 0.0787351i
\(507\) 1.20981e8 2.92075e8i 0.0412278 0.0995328i
\(508\) 1.65342e8 4.54360e8i 0.0559577 0.153772i
\(509\) 2.26900e9 9.39851e8i 0.762645 0.315898i 0.0327556 0.999463i \(-0.489572\pi\)
0.729889 + 0.683566i \(0.239572\pi\)
\(510\) −4.96195e8 + 3.47462e8i −0.165637 + 0.115988i
\(511\) 4.88763e9 1.62041
\(512\) 2.14808e9 + 2.14688e9i 0.707304 + 0.706910i
\(513\) 8.62828e8 0.282172
\(514\) 1.67154e9 1.17050e9i 0.542931 0.380190i
\(515\) −6.42509e9 + 2.66136e9i −2.07278 + 0.858574i
\(516\) 5.24197e8 1.44050e9i 0.167966 0.461571i
\(517\) 7.86120e7 1.89786e8i 0.0250191 0.0604015i
\(518\) 1.29232e9 2.02868e9i 0.408523 0.641296i
\(519\) −8.00448e7 8.00448e7i −0.0251332 0.0251332i
\(520\) 1.82422e9 + 6.80554e9i 0.568938 + 2.12252i
\(521\) 4.67520e8 4.67520e8i 0.144833 0.144833i −0.630972 0.775805i \(-0.717344\pi\)
0.775805 + 0.630972i \(0.217344\pi\)
\(522\) 2.66744e8 + 1.20303e9i 0.0820819 + 0.370193i
\(523\) −1.01684e9 4.21191e8i −0.310813 0.128743i 0.221824 0.975087i \(-0.428799\pi\)
−0.532637 + 0.846344i \(0.678799\pi\)
\(524\) 1.21455e8 + 2.77784e9i 0.0368772 + 0.843427i
\(525\) −1.87170e9 4.51869e9i −0.564520 1.36287i
\(526\) 4.02986e9 + 7.10445e8i 1.20737 + 0.212853i
\(527\) 8.36340e6i 0.00248912i
\(528\) −3.96275e8 3.32431e8i −0.117160 0.0982839i
\(529\) 3.27956e9i 0.963209i
\(530\) −4.66983e8 + 2.64887e9i −0.136250 + 0.772850i
\(531\) −1.43179e9 3.45665e9i −0.415001 1.00190i
\(532\) −2.18746e9 2.00419e9i −0.629869 0.577097i
\(533\) 3.03063e9 + 1.25533e9i 0.866937 + 0.359097i
\(534\) −1.62056e8 + 3.59322e7i −0.0460544 + 0.0102115i
\(535\) 4.06919e9 4.06919e9i 1.14887 1.14887i
\(536\) −1.28583e9 1.67540e9i −0.360667 0.469940i
\(537\) −4.26487e8 4.26487e8i −0.118849 0.118849i
\(538\) 1.00418e9 + 6.39692e8i 0.278019 + 0.177106i
\(539\) 1.53776e9 3.71248e9i 0.422987 1.02118i
\(540\) 3.75668e9 1.75205e9i 1.02666 0.478816i
\(541\) −5.16386e9 + 2.13894e9i −1.40212 + 0.580775i −0.950300 0.311336i \(-0.899223\pi\)
−0.451815 + 0.892112i \(0.649223\pi\)
\(542\) 2.66081e8 + 3.79978e8i 0.0717822 + 0.102509i
\(543\) −5.92020e8 −0.158686
\(544\) −1.10868e8 + 1.26949e9i −0.0295264 + 0.338091i
\(545\) −8.65240e9 −2.28954
\(546\) 1.43669e9 + 2.05167e9i 0.377737 + 0.539428i
\(547\) 6.75577e7 2.79833e7i 0.0176490 0.00731044i −0.373841 0.927493i \(-0.621960\pi\)
0.391490 + 0.920182i \(0.371960\pi\)
\(548\) 1.48996e9 + 3.19472e9i 0.386762 + 0.829279i
\(549\) 1.93519e9 4.67196e9i 0.499138 1.20503i
\(550\) 4.15764e9 + 2.64853e9i 1.06556 + 0.678790i
\(551\) 5.51773e8 + 5.51773e8i 0.140517 + 0.140517i
\(552\) −2.36128e8 3.10645e7i −0.0597532 0.00786100i
\(553\) 7.35832e9 7.35832e9i 1.85029 1.85029i
\(554\) 4.95150e8 1.09788e8i 0.123724 0.0274329i
\(555\) 9.32044e8 + 3.86065e8i 0.231425 + 0.0958595i
\(556\) −3.55425e9 + 3.87926e9i −0.876972 + 0.957166i
\(557\) −2.00229e9 4.83397e9i −0.490947 1.18525i −0.954239 0.299045i \(-0.903332\pi\)
0.463292 0.886206i \(-0.346668\pi\)
\(558\) −4.71012e6 + 2.67173e7i −0.00114766 + 0.00650987i
\(559\) 7.48142e9i 1.81152i
\(560\) −1.35937e10 4.28423e9i −3.27100 1.03090i
\(561\) 2.17036e8i 0.0518994i
\(562\) 1.07727e9 + 1.89917e8i 0.256004 + 0.0451322i
\(563\) 2.10016e9 + 5.07023e9i 0.495990 + 1.19742i 0.951626 + 0.307259i \(0.0994118\pi\)
−0.455636 + 0.890166i \(0.650588\pi\)
\(564\) −1.79660e8 + 7.85526e6i −0.0421671 + 0.00184367i
\(565\) 9.18397e9 + 3.80412e9i 2.14220 + 0.887330i
\(566\) −1.30871e9 5.90233e9i −0.303378 1.36825i
\(567\) −3.96099e9 + 3.96099e9i −0.912563 + 0.912563i
\(568\) 1.27952e8 2.21668e8i 0.0292974 0.0507555i
\(569\) −1.45583e9 1.45583e9i −0.331298 0.331298i 0.521781 0.853079i \(-0.325268\pi\)
−0.853079 + 0.521781i \(0.825268\pi\)
\(570\) 6.68539e8 1.04947e9i 0.151205 0.237360i
\(571\) −3.17363e9 + 7.66182e9i −0.713395 + 1.72229i −0.0220567 + 0.999757i \(0.507021\pi\)
−0.691338 + 0.722531i \(0.742979\pi\)
\(572\) −2.37225e9 8.63262e8i −0.529998 0.192866i
\(573\) 6.56590e8 2.71968e8i 0.145798 0.0603917i
\(574\) −5.43557e9 + 3.80628e9i −1.19965 + 0.840057i
\(575\) 2.26979e9 0.497907
\(576\) 1.06913e9 3.99301e9i 0.233105 0.870606i
\(577\) 4.17121e9 0.903956 0.451978 0.892029i \(-0.350719\pi\)
0.451978 + 0.892029i \(0.350719\pi\)
\(578\) 3.36480e9 2.35621e9i 0.724789 0.507536i
\(579\) 2.10340e9 8.71259e8i 0.450348 0.186540i
\(580\) 3.52280e9 + 1.28195e9i 0.749704 + 0.272817i
\(581\) −2.66287e9 + 6.42873e9i −0.563291 + 1.35991i
\(582\) 2.58794e8 4.06254e8i 0.0544157 0.0854214i
\(583\) −6.81440e8 6.81440e8i −0.142425 0.142425i
\(584\) 3.73491e9 + 2.15589e9i 0.775954 + 0.447901i
\(585\) 6.78117e9 6.78117e9i 1.40042 1.40042i
\(586\) 1.38993e9 + 6.26865e9i 0.285333 + 1.28686i
\(587\) 1.42361e9 + 5.89680e8i 0.290509 + 0.120333i 0.523178 0.852223i \(-0.324746\pi\)
−0.232670 + 0.972556i \(0.574746\pi\)
\(588\) −3.51439e9 + 1.53660e8i −0.712901 + 0.0311702i
\(589\) 6.57441e6 + 1.58720e7i 0.00132572 + 0.00320058i
\(590\) −1.12096e10 1.97619e9i −2.24702 0.396139i
\(591\) 1.66477e9i 0.331740i
\(592\) 1.88237e9 9.80195e8i 0.372888 0.194172i
\(593\) 4.36028e9i 0.858663i −0.903147 0.429332i \(-0.858749\pi\)
0.903147 0.429332i \(-0.141251\pi\)
\(594\) −2.57852e8 + 1.46262e9i −0.0504798 + 0.286337i
\(595\) −2.28863e9 5.52525e9i −0.445417 1.07533i
\(596\) 3.12932e9 3.41548e9i 0.605464 0.660830i
\(597\) 1.68723e9 + 6.98872e8i 0.324536 + 0.134427i
\(598\) −1.13480e9 + 2.51616e8i −0.217003 + 0.0481154i
\(599\) −5.16166e9 + 5.16166e9i −0.981285 + 0.981285i −0.999828 0.0185430i \(-0.994097\pi\)
0.0185430 + 0.999828i \(0.494097\pi\)
\(600\) 5.62881e8 4.27858e9i 0.106387 0.808668i
\(601\) −2.77678e9 2.77678e9i −0.521772 0.521772i 0.396334 0.918106i \(-0.370282\pi\)
−0.918106 + 0.396334i \(0.870282\pi\)
\(602\) 1.27642e10 + 8.13115e9i 2.38455 + 1.51902i
\(603\) −1.10005e9 + 2.65576e9i −0.204316 + 0.493263i
\(604\) 2.00404e9 + 4.29699e9i 0.370065 + 0.793478i
\(605\) 7.28206e9 3.01633e9i 1.33694 0.553777i
\(606\) 8.13323e8 + 1.16147e9i 0.148460 + 0.212009i
\(607\) −9.32470e9 −1.69229 −0.846145 0.532953i \(-0.821082\pi\)
−0.846145 + 0.532953i \(0.821082\pi\)
\(608\) −7.87533e8 2.49639e9i −0.142104 0.450453i
\(609\) 1.33265e9 0.239086
\(610\) −8.82449e9 1.26019e10i −1.57411 2.24792i
\(611\) −8.10864e8 + 3.35871e8i −0.143815 + 0.0595700i
\(612\) 1.57193e9 7.33122e8i 0.277206 0.129284i
\(613\) −2.11651e9 + 5.10971e9i −0.371115 + 0.895952i 0.622447 + 0.782662i \(0.286139\pi\)
−0.993562 + 0.113290i \(0.963861\pi\)
\(614\) 2.30187e9 + 1.46635e9i 0.401320 + 0.255652i
\(615\) −1.96798e9 1.96798e9i −0.341160 0.341160i
\(616\) 4.05110e9 3.10912e9i 0.698298 0.535926i
\(617\) −1.60027e8 + 1.60027e8i −0.0274281 + 0.0274281i −0.720688 0.693260i \(-0.756174\pi\)
0.693260 + 0.720688i \(0.256174\pi\)
\(618\) −2.12958e9 + 4.72186e8i −0.362939 + 0.0804735i
\(619\) −4.41588e9 1.82912e9i −0.748341 0.309973i −0.0242766 0.999705i \(-0.507728\pi\)
−0.724065 + 0.689732i \(0.757728\pi\)
\(620\) 6.08540e7 + 5.57555e7i 0.0102546 + 0.00939543i
\(621\) 2.61693e8 + 6.31782e8i 0.0438502 + 0.105864i
\(622\) 8.13967e7 4.61707e8i 0.0135625 0.0769308i
\(623\) 1.63880e9i 0.271530i
\(624\) 1.92882e8 + 2.20151e9i 0.0317794 + 0.362723i
\(625\) 1.91807e10i 3.14256i
\(626\) 4.81295e9 + 8.48499e8i 0.784153 + 0.138242i
\(627\) 1.70611e8 + 4.11891e8i 0.0276420 + 0.0667338i
\(628\) −1.15391e8 2.63913e9i −0.0185914 0.425208i
\(629\) 8.22723e8 + 3.40783e8i 0.131819 + 0.0546010i
\(630\) 4.19942e9 + 1.89396e10i 0.669110 + 3.01772i
\(631\) −3.66542e9 + 3.66542e9i −0.580792 + 0.580792i −0.935121 0.354329i \(-0.884709\pi\)
0.354329 + 0.935121i \(0.384709\pi\)
\(632\) 8.86860e9 2.37722e9i 1.39748 0.374593i
\(633\) 3.08000e8 + 3.08000e8i 0.0482656 + 0.0482656i
\(634\) −8.81818e7 + 1.38427e8i −0.0137425 + 0.0215729i
\(635\) −7.66179e8 + 1.84972e9i −0.118747 + 0.286680i
\(636\) −2.88494e8 + 7.92783e8i −0.0444669 + 0.122195i
\(637\) −1.58616e10 + 6.57009e9i −2.43141 + 1.00712i
\(638\) −1.10023e9 + 7.70438e8i −0.167730 + 0.117453i
\(639\) −3.48368e8 −0.0528184
\(640\) −8.49799e9 9.26990e9i −1.28141 1.39780i
\(641\) 8.88599e8 0.133261 0.0666304 0.997778i \(-0.478775\pi\)
0.0666304 + 0.997778i \(0.478775\pi\)
\(642\) 1.47853e9 1.03534e9i 0.220524 0.154423i
\(643\) 5.37964e9 2.22832e9i 0.798023 0.330552i 0.0538584 0.998549i \(-0.482848\pi\)
0.744164 + 0.667997i \(0.232848\pi\)
\(644\) 8.04065e8 2.20958e9i 0.118629 0.325993i
\(645\) −2.42908e9 + 5.86432e9i −0.356437 + 0.860516i
\(646\) 5.90125e8 9.26374e8i 0.0861252 0.135199i
\(647\) 5.03417e9 + 5.03417e9i 0.730739 + 0.730739i 0.970766 0.240027i \(-0.0771562\pi\)
−0.240027 + 0.970766i \(0.577156\pi\)
\(648\) −4.77397e9 + 1.27966e9i −0.689235 + 0.184749i
\(649\) 2.88374e9 2.88374e9i 0.414095 0.414095i
\(650\) −4.55922e9 2.05623e10i −0.651169 2.93680i
\(651\) 2.71064e7 + 1.12278e7i 0.00385069 + 0.00159501i
\(652\) −4.42419e8 1.01187e10i −0.0625125 1.42974i
\(653\) 3.23573e8 + 7.81174e8i 0.0454753 + 0.109787i 0.944985 0.327114i \(-0.106076\pi\)
−0.899510 + 0.436901i \(0.856076\pi\)
\(654\) −2.67265e9 4.71175e8i −0.373611 0.0658658i
\(655\) 1.15135e10i 1.60089i
\(656\) −5.83254e9 + 5.11010e8i −0.806667 + 0.0706750i
\(657\) 5.86971e9i 0.807492i
\(658\) 3.08247e8 1.74847e9i 0.0421801 0.239259i
\(659\) 4.10124e9 + 9.90127e9i 0.558234 + 1.34770i 0.911163 + 0.412046i \(0.135186\pi\)
−0.352930 + 0.935650i \(0.614814\pi\)
\(660\) 1.57921e9 + 1.44690e9i 0.213813 + 0.195900i
\(661\) −7.76859e9 3.21785e9i −1.04625 0.433372i −0.207700 0.978192i \(-0.566598\pi\)
−0.838553 + 0.544820i \(0.816598\pi\)
\(662\) −7.24056e9 + 1.60543e9i −0.969995 + 0.215074i
\(663\) −6.55694e8 + 6.55694e8i −0.0873783 + 0.0873783i
\(664\) −4.87050e9 + 3.73799e9i −0.645633 + 0.495507i
\(665\) 8.68672e9 + 8.68672e9i 1.14546 + 1.14546i
\(666\) −2.43630e9 1.55199e9i −0.319574 0.203577i
\(667\) −2.36670e8 + 5.71371e8i −0.0308818 + 0.0745552i
\(668\) −1.11549e10 + 5.20247e9i −1.44793 + 0.675292i
\(669\) −3.73353e9 + 1.54648e9i −0.482091 + 0.199688i
\(670\) 5.01626e9 + 7.16349e9i 0.644344 + 0.920159i
\(671\) 5.51207e9 0.704346
\(672\) −3.96568e9 2.06362e9i −0.504110 0.262324i
\(673\) 3.82014e9 0.483088 0.241544 0.970390i \(-0.422346\pi\)
0.241544 + 0.970390i \(0.422346\pi\)
\(674\) 3.84728e9 + 5.49412e9i 0.483999 + 0.691176i
\(675\) −1.14477e10 + 4.74180e9i −1.43270 + 0.593445i
\(676\) 1.16400e9 + 2.49580e9i 0.144924 + 0.310739i
\(677\) 5.04782e9 1.21865e10i 0.625235 1.50945i −0.220245 0.975445i \(-0.570686\pi\)
0.845480 0.534007i \(-0.179314\pi\)
\(678\) 2.62969e9 + 1.67518e9i 0.324041 + 0.206423i
\(679\) 3.36267e9 + 3.36267e9i 0.412230 + 0.412230i
\(680\) 6.88266e8 5.23165e9i 0.0839412 0.638055i
\(681\) −1.12556e9 + 1.12556e9i −0.136570 + 0.136570i
\(682\) −2.88700e7 + 6.40127e6i −0.00348500 + 0.000772718i
\(683\) 1.00138e10 + 4.14784e9i 1.20261 + 0.498137i 0.891841 0.452348i \(-0.149414\pi\)
0.310769 + 0.950486i \(0.399414\pi\)
\(684\) −2.40690e9 + 2.62700e9i −0.287582 + 0.313880i
\(685\) −5.58592e9 1.34856e10i −0.664015 1.60307i
\(686\) 3.37469e9 1.91423e10i 0.399116 2.26391i
\(687\) 7.12975e8i 0.0838930i
\(688\) 6.16728e9 + 1.18437e10i 0.721995 + 1.38652i
\(689\) 4.11743e9i 0.479577i
\(690\) 9.71210e8 + 1.71219e8i 0.112549 + 0.0198418i
\(691\) 2.03692e9 + 4.91756e9i 0.234856 + 0.566992i 0.996736 0.0807256i \(-0.0257237\pi\)
−0.761881 + 0.647717i \(0.775724\pi\)
\(692\) 9.85148e8 4.30736e7i 0.113013 0.00494129i
\(693\) −6.42160e9 2.65991e9i −0.732954 0.303599i
\(694\) −1.35084e9 6.09235e9i −0.153407 0.691874i
\(695\) 1.54051e10 1.54051e10i 1.74067 1.74067i
\(696\) 1.01835e9 + 5.87819e8i 0.114489 + 0.0660863i
\(697\) −1.73715e9 1.73715e9i −0.194323 0.194323i
\(698\) −5.70939e9 + 8.96257e9i −0.635471 + 0.997559i
\(699\) 1.54214e9 3.72306e9i 0.170787 0.412316i
\(700\) 4.00369e10 + 1.45694e10i 4.41182 + 1.60546i
\(701\) 2.36690e9 9.80402e8i 0.259518 0.107496i −0.249131 0.968470i \(-0.580145\pi\)
0.508649 + 0.860974i \(0.330145\pi\)
\(702\) 5.19774e9 3.63974e9i 0.567068 0.397091i
\(703\) −1.82925e9 −0.198577
\(704\) 4.46708e9 5.88947e8i 0.482525 0.0636168i
\(705\) 7.44647e8 0.0800366
\(706\) 1.16788e10 8.17815e9i 1.24906 0.874659i
\(707\) −1.29332e10 + 5.35713e9i −1.37638 + 0.570117i
\(708\) −3.35493e9 1.22086e9i −0.355277 0.129285i
\(709\) −3.16467e9 + 7.64020e9i −0.333478 + 0.805087i 0.664833 + 0.746992i \(0.268503\pi\)
−0.998311 + 0.0580952i \(0.981497\pi\)
\(710\) −5.69415e8 + 8.93864e8i −0.0597069 + 0.0937275i
\(711\) −8.83685e9 8.83685e9i −0.922048 0.922048i
\(712\) 7.22861e8 1.25230e9i 0.0750541 0.130025i
\(713\) −9.62786e6 + 9.62786e6i −0.000994756 + 0.000994756i
\(714\) −4.06056e8 1.83133e9i −0.0417486 0.188288i
\(715\) 9.65752e9 + 4.00028e9i 0.988086 + 0.409279i
\(716\) 5.24897e9 2.29501e8i 0.534415 0.0233662i
\(717\) 1.59097e9 + 3.84095e9i 0.161193 + 0.389154i
\(718\) −9.99434e9 1.76195e9i −1.00767 0.177647i
\(719\) 5.97817e9i 0.599815i −0.953968 0.299907i \(-0.903044\pi\)
0.953968 0.299907i \(-0.0969558\pi\)
\(720\) −5.14507e9 + 1.63251e10i −0.513722 + 1.63002i
\(721\) 2.15355e10i 2.13984i
\(722\) 1.36408e9 7.73746e9i 0.134883 0.765100i
\(723\) 1.56899e9 + 3.78788e9i 0.154396 + 0.372745i
\(724\) 3.48384e9 3.80242e9i 0.341172 0.372370i
\(725\) −1.03531e10 4.28839e9i −1.00899 0.417938i
\(726\) 2.41362e9 5.35165e8i 0.234094 0.0519051i
\(727\) 5.45824e9 5.45824e9i 0.526844 0.526844i −0.392786 0.919630i \(-0.628489\pi\)
0.919630 + 0.392786i \(0.128489\pi\)
\(728\) −2.16319e10 2.84585e9i −2.07795 0.273371i
\(729\) 3.36849e9 + 3.36849e9i 0.322025 + 0.322025i
\(730\) −1.50609e10 9.59417e9i −1.43291 0.912804i
\(731\) −2.14417e9 + 5.17649e9i −0.203025 + 0.490145i
\(732\) −2.03956e9 4.37315e9i −0.192198 0.412103i
\(733\) 5.72433e9 2.37110e9i 0.536860 0.222375i −0.0977450 0.995211i \(-0.531163\pi\)
0.634605 + 0.772837i \(0.281163\pi\)
\(734\) 4.97724e9 + 7.10777e9i 0.464572 + 0.663433i
\(735\) 1.45663e10 1.35314
\(736\) 1.58906e9 1.33380e9i 0.146915 0.123315i
\(737\) −3.13332e9 −0.288316
\(738\) 4.57108e9 + 6.52775e9i 0.418622 + 0.597814i
\(739\) 6.14527e9 2.54545e9i 0.560125 0.232012i −0.0846142 0.996414i \(-0.526966\pi\)
0.644740 + 0.764402i \(0.276966\pi\)
\(740\) −7.96438e9 + 3.71445e9i −0.722505 + 0.336964i
\(741\) 7.28937e8 1.75981e9i 0.0658152 0.158892i
\(742\) −7.02483e9 4.47501e9i −0.631280 0.402142i
\(743\) 2.28783e9 + 2.28783e9i 0.204627 + 0.204627i 0.801979 0.597352i \(-0.203780\pi\)
−0.597352 + 0.801979i \(0.703780\pi\)
\(744\) 1.57610e7 + 2.05362e7i 0.00140307 + 0.00182817i
\(745\) −1.35633e10 + 1.35633e10i −1.20177 + 1.20177i
\(746\) −2.63418e9 + 5.84069e8i −0.232305 + 0.0515084i
\(747\) 7.72047e9 + 3.19792e9i 0.677675 + 0.280702i
\(748\) 1.39398e9 + 1.27719e9i 0.121787 + 0.111583i
\(749\) 6.81951e9 + 1.64638e10i 0.593017 + 1.43167i
\(750\) −1.90729e9 + 1.08187e10i −0.165083 + 0.936402i
\(751\) 7.76165e9i 0.668674i −0.942454 0.334337i \(-0.891488\pi\)
0.942454 0.334337i \(-0.108512\pi\)
\(752\) 1.00678e9 1.20014e9i 0.0863325 0.102913i
\(753\) 5.35690e9i 0.457226i
\(754\) 5.65151e9 + 9.96333e8i 0.480137 + 0.0846457i
\(755\) −7.51322e9 1.81385e10i −0.635348 1.53387i
\(756\) 5.60696e8 + 1.28238e10i 0.0471956 + 1.07942i
\(757\) 9.47657e9 + 3.92532e9i 0.793991 + 0.328882i 0.742547 0.669794i \(-0.233618\pi\)
0.0514440 + 0.998676i \(0.483618\pi\)
\(758\) 1.23521e9 + 5.57086e9i 0.103015 + 0.464601i
\(759\) −2.49850e8 + 2.49850e8i −0.0207412 + 0.0207412i
\(760\) 2.80638e9 + 1.04697e10i 0.231899 + 0.865137i
\(761\) 6.64143e9 + 6.64143e9i 0.546280 + 0.546280i 0.925363 0.379083i \(-0.123760\pi\)
−0.379083 + 0.925363i \(0.623760\pi\)
\(762\) −3.37394e8 + 5.29639e8i −0.0276245 + 0.0433648i
\(763\) 1.02534e10 2.47539e10i 0.835664 2.01747i
\(764\) −2.11702e9 + 5.81758e9i −0.171750 + 0.471971i
\(765\) −6.63546e9 + 2.74850e9i −0.535865 + 0.221963i
\(766\) −6.04847e9 + 4.23546e9i −0.486233 + 0.340487i
\(767\) −1.74243e10 −1.39435
\(768\) −2.12015e9 3.32616e9i −0.168890 0.264959i
\(769\) −1.39663e9 −0.110749 −0.0553745 0.998466i \(-0.517635\pi\)
−0.0553745 + 0.998466i \(0.517635\pi\)
\(770\) −1.73212e10 + 1.21292e10i −1.36729 + 0.957449i
\(771\) −2.44857e9 + 1.01423e9i −0.192408 + 0.0796980i
\(772\) −6.78193e9 + 1.86368e10i −0.530509 + 1.45784i
\(773\) 1.24846e9 3.01406e9i 0.0972182 0.234706i −0.867787 0.496936i \(-0.834458\pi\)
0.965005 + 0.262231i \(0.0844582\pi\)
\(774\) 9.76496e9 1.53290e10i 0.756968 1.18828i
\(775\) −1.74454e8 1.74454e8i −0.0134625 0.0134625i
\(776\) 1.08636e9 + 4.05285e9i 0.0834561 + 0.311347i
\(777\) −2.20901e9 + 2.20901e9i −0.168937 + 0.168937i
\(778\) 1.61135e9 + 7.26729e9i 0.122677 + 0.553278i
\(779\) 4.66233e9 + 1.93120e9i 0.353363 + 0.146368i
\(780\) −3.99726e8 9.14223e9i −0.0301600 0.689796i
\(781\) −1.45314e8 3.50820e8i −0.0109152 0.0263515i
\(782\) 8.57295e8 + 1.51137e8i 0.0641072 + 0.0113018i
\(783\) 3.37615e9i 0.251337i
\(784\) 1.96941e10 2.34764e10i 1.45959 1.73990i
\(785\) 1.09386e10i 0.807080i
\(786\) 6.26978e8 3.55642e9i 0.0460547 0.261236i
\(787\) −4.95582e9 1.19644e10i −0.362413 0.874942i −0.994946 0.100409i \(-0.967985\pi\)
0.632533 0.774533i \(-0.282015\pi\)
\(788\) −1.06924e10 9.79660e9i −0.778458 0.713237i
\(789\) −4.91009e9 2.03382e9i −0.355893 0.147416i
\(790\) −3.71181e10 + 8.23010e9i −2.67850 + 0.593896i
\(791\) −2.17666e10 + 2.17666e10i −1.56377 + 1.56377i
\(792\) −3.73384e9 4.86510e9i −0.267065 0.347979i
\(793\) −1.66526e10 1.66526e10i −1.18584 1.18584i
\(794\) 6.65546e9 + 4.23971e9i 0.471853 + 0.300583i
\(795\) 1.33685e9 3.22745e9i 0.0943624 0.227811i
\(796\) −1.44175e10 + 6.72407e9i −1.01320 + 0.472538i
\(797\) −8.97119e9 + 3.71599e9i −0.627691 + 0.259998i −0.673772 0.738940i \(-0.735327\pi\)
0.0460808 + 0.998938i \(0.485327\pi\)
\(798\) 2.21021e9 + 3.15630e9i 0.153965 + 0.219871i
\(799\) 6.57307e8 0.0455884
\(800\) 2.41680e10 + 2.87933e10i 1.66888 + 1.98827i
\(801\) −1.96809e9 −0.135310
\(802\) −4.65771e9 6.65146e9i −0.318832 0.455309i
\(803\) 5.91103e9 2.44843e9i 0.402864 0.166872i
\(804\) 1.15938e9 + 2.48590e9i 0.0786739 + 0.168689i
\(805\) −3.72596e9 + 8.99527e9i −0.251740 + 0.607755i
\(806\) 1.06559e8 + 6.78809e7i 0.00716832 + 0.00456641i
\(807\) −1.09345e9 1.09345e9i −0.0732386 0.0732386i
\(808\) −1.22460e10 1.61106e9i −0.816685 0.107441i
\(809\) 9.05213e9 9.05213e9i 0.601078 0.601078i −0.339521 0.940599i \(-0.610265\pi\)
0.940599 + 0.339521i \(0.110265\pi\)
\(810\) 1.99807e10 4.43027e9i 1.32103 0.292909i
\(811\) −1.02479e10 4.24481e9i −0.674622 0.279438i 0.0189545 0.999820i \(-0.493966\pi\)
−0.693577 + 0.720383i \(0.743966\pi\)
\(812\) −7.84218e9 + 8.55931e9i −0.514033 + 0.561038i
\(813\) −2.30558e8 5.56616e8i −0.0150475 0.0363278i
\(814\) 5.46661e8 3.10083e9i 0.0355249 0.201508i
\(815\) 4.19395e10i 2.71376i
\(816\) 4.97494e8 1.57853e9i 0.0320533 0.101704i
\(817\) 1.15094e10i 0.738375i
\(818\) −1.67739e10 2.95716e9i −1.07151 0.188903i
\(819\) 1.13645e10 + 2.74363e10i 0.722865 + 1.74515i
\(820\) 2.42208e10 1.05901e9i 1.53405 0.0670735i
\(821\) −8.53921e9 3.53706e9i −0.538539 0.223070i 0.0967998 0.995304i \(-0.469139\pi\)
−0.635338 + 0.772234i \(0.719139\pi\)
\(822\) −9.91070e8 4.46977e9i −0.0622376 0.280695i
\(823\) 6.17113e9 6.17113e9i 0.385891 0.385891i −0.487328 0.873219i \(-0.662028\pi\)
0.873219 + 0.487328i \(0.162028\pi\)
\(824\) 9.49912e9 1.64565e10i 0.591477 1.02469i
\(825\) −4.52722e9 4.52722e9i −0.280700 0.280700i
\(826\) 1.89375e10 2.97279e10i 1.16921 1.83542i
\(827\) −5.55165e9 + 1.34029e10i −0.341313 + 0.824002i 0.656271 + 0.754526i \(0.272133\pi\)
−0.997584 + 0.0694767i \(0.977867\pi\)
\(828\) −2.65355e9 9.65627e8i −0.162451 0.0591158i
\(829\) 2.70945e10 1.12229e10i 1.65174 0.684171i 0.654333 0.756207i \(-0.272949\pi\)
0.997402 + 0.0720355i \(0.0229495\pi\)
\(830\) 2.08247e10 1.45826e10i 1.26417 0.885240i
\(831\) −6.58711e8 −0.0398191
\(832\) −1.52749e10 1.17163e10i −0.919488 0.705276i
\(833\) 1.28578e10 0.770743
\(834\) 5.59739e9 3.91959e9i 0.334122 0.233970i
\(835\) 4.70874e10 1.95042e10i 2.79899 1.15938i
\(836\) −3.64947e9 1.32804e9i −0.216027 0.0786123i
\(837\) 2.84448e7 6.86719e7i 0.00167673 0.00404799i
\(838\) −1.60599e9 + 2.52106e9i −0.0942730 + 0.147989i
\(839\) −8.40195e9 8.40195e9i −0.491149 0.491149i 0.417519 0.908668i \(-0.362900\pi\)
−0.908668 + 0.417519i \(0.862900\pi\)
\(840\) 1.60322e10 + 9.25420e9i 0.933287 + 0.538718i
\(841\) −1.00385e10 + 1.00385e10i −0.581945 + 0.581945i
\(842\) 5.93342e9 + 2.67600e10i 0.342541 + 1.54488i
\(843\) −1.31257e9 5.43684e8i −0.0754616 0.0312572i
\(844\) −3.79070e9 + 1.65741e8i −0.217030 + 0.00948923i
\(845\) −4.36387e9 1.05353e10i −0.248813 0.600688i
\(846\) −2.09980e9 3.70184e8i −0.119229 0.0210194i
\(847\) 2.44079e10i 1.38019i
\(848\) −3.39419e9 6.51820e9i −0.191139 0.367064i
\(849\) 7.85203e9i 0.440357i
\(850\) −2.73856e9 + 1.55340e10i −0.152952 + 0.867593i
\(851\) −5.54804e8 1.33942e9i −0.0308593 0.0745010i
\(852\) −2.24564e8 + 2.45099e8i −0.0124394 + 0.0135770i
\(853\) 5.03640e9 + 2.08615e9i 0.277842 + 0.115086i 0.517254 0.855832i \(-0.326954\pi\)
−0.239411 + 0.970918i \(0.576954\pi\)
\(854\) 4.65103e10 1.03126e10i 2.55533 0.566585i
\(855\) 1.04322e10 1.04322e10i 0.570812 0.570812i
\(856\) −2.05085e9 + 1.55889e10i −0.111757 + 0.849489i
\(857\) −1.84424e9 1.84424e9i −0.100089 0.100089i 0.655289 0.755378i \(-0.272547\pi\)
−0.755378 + 0.655289i \(0.772547\pi\)
\(858\) 2.76528e9 + 1.76156e9i 0.149463 + 0.0952121i
\(859\) −1.15918e10 + 2.79852e10i −0.623988 + 1.50644i 0.222995 + 0.974820i \(0.428417\pi\)
−0.846983 + 0.531620i \(0.821583\pi\)
\(860\) −2.33710e10 5.01111e10i −1.25294 2.68651i
\(861\) 7.96237e9 3.29812e9i 0.425139 0.176098i
\(862\) −9.57910e9 1.36795e10i −0.509389 0.727434i
\(863\) 3.12215e10 1.65354 0.826771 0.562538i \(-0.190175\pi\)
0.826771 + 0.562538i \(0.190175\pi\)
\(864\) −5.22801e9 + 1.00467e10i −0.275765 + 0.529939i
\(865\) −4.08321e9 −0.214509
\(866\) 6.08995e9 + 8.69678e9i 0.318641 + 0.455036i
\(867\) −4.92897e9 + 2.04165e9i −0.256856 + 0.106393i
\(868\) −2.31626e8 + 1.08027e8i −0.0120218 + 0.00560675i
\(869\) 5.21294e9 1.25851e10i 0.269472 0.650563i
\(870\) −4.10645e9 2.61592e9i −0.211422 0.134681i
\(871\) 9.46615e9 + 9.46615e9i 0.485411 + 0.485411i
\(872\) 1.87539e10 1.43932e10i 0.957821 0.735103i
\(873\) 4.03834e9 4.03834e9i 0.205425 0.205425i
\(874\) −1.74578e9 + 3.87087e8i −0.0884503 + 0.0196118i
\(875\) −1.00202e11 4.15052e10i −5.05649 2.09447i
\(876\) −4.12971e9 3.78371e9i −0.207565 0.190175i
\(877\) 8.22833e9 + 1.98650e10i 0.411920 + 0.994464i 0.984622 + 0.174700i \(0.0558954\pi\)
−0.572701 + 0.819764i \(0.694105\pi\)
\(878\) −4.90173e9 + 2.78041e10i −0.244410 + 1.38637i
\(879\) 8.33936e9i 0.414163i
\(880\) −1.85862e10 + 1.62840e9i −0.919393 + 0.0805513i
\(881\) 3.22048e10i 1.58674i 0.608743 + 0.793368i \(0.291674\pi\)
−0.608743 + 0.793368i \(0.708326\pi\)
\(882\) −4.10749e10 7.24130e9i −2.01575 0.355366i
\(883\) −2.35055e9 5.67473e9i −0.114897 0.277385i 0.855962 0.517039i \(-0.172966\pi\)
−0.970858 + 0.239654i \(0.922966\pi\)
\(884\) −3.52841e8 8.06992e9i −0.0171789 0.392904i
\(885\) 1.36580e10 + 5.65734e9i 0.662349 + 0.274354i
\(886\) −5.44454e9 2.45551e10i −0.262993 1.18611i
\(887\) 2.63129e10 2.63129e10i 1.26601 1.26601i 0.317872 0.948134i \(-0.397032\pi\)
0.948134 0.317872i \(-0.102968\pi\)
\(888\) −2.66240e9 + 7.13653e8i −0.127593 + 0.0342012i
\(889\) −4.38396e9 4.38396e9i −0.209272 0.209272i
\(890\) −3.21688e9 + 5.04984e9i −0.152957 + 0.240111i
\(891\) −2.80613e9 + 6.77459e9i −0.132903 + 0.320857i
\(892\) 1.20379e10 3.30802e10i 0.567902 1.56060i
\(893\) −1.24743e9 + 5.16704e8i −0.0586189 + 0.0242807i
\(894\) −4.92820e9 + 3.45099e9i −0.230678 + 0.161533i
\(895\) −2.17557e10 −1.01436
\(896\) 3.65909e10 1.33270e10i 1.69940 0.618947i
\(897\) 1.50966e9 0.0698400
\(898\) −1.91469e10 + 1.34077e10i −0.882329 + 0.617854i
\(899\) 6.21055e7 2.57249e7i 0.00285083 0.00118085i
\(900\) 1.74969e10 4.80817e10i 0.800042 2.19852i
\(901\) 1.18005e9 2.84890e9i 0.0537483 0.129760i
\(902\) −4.66697e9 + 7.32617e9i −0.211744 + 0.332395i
\(903\) −1.38988e10 1.38988e10i −0.628162 0.628162i
\(904\) −2.62342e10 + 7.03204e9i −1.18108 + 0.316586i
\(905\) −1.50999e10 + 1.50999e10i −0.677181 + 0.677181i
\(906\) −1.33302e9 6.01197e9i −0.0595507 0.268577i
\(907\) 4.60009e9 + 1.90542e9i 0.204711 + 0.0847940i 0.482683 0.875795i \(-0.339662\pi\)
−0.277972 + 0.960589i \(0.589662\pi\)
\(908\) −6.05686e8 1.38528e10i −0.0268502 0.614097i
\(909\) 6.43355e9 + 1.55320e10i 0.284104 + 0.685887i
\(910\) 8.89734e10 + 1.56856e10i 3.91395 + 0.690010i
\(911\) 3.68292e10i 1.61390i 0.590617 + 0.806952i \(0.298884\pi\)
−0.590617 + 0.806952i \(0.701116\pi\)
\(912\) 2.96730e8 + 3.38681e9i 0.0129533 + 0.147846i
\(913\) 9.10876e9i 0.396106i
\(914\) −6.27817e9 + 3.56117e10i −0.271970 + 1.54270i
\(915\) 7.64638e9 + 1.84600e10i 0.329976 + 0.796632i
\(916\) 4.57929e9 + 4.19562e9i 0.196863 + 0.180369i
\(917\) 3.29392e10 + 1.36439e10i 1.41066 + 0.584312i
\(918\) −4.63953e9 + 1.02871e9i −0.197936 + 0.0438877i
\(919\) −2.57385e10 + 2.57385e10i −1.09390 + 1.09390i −0.0987948 + 0.995108i \(0.531499\pi\)
−0.995108 + 0.0987948i \(0.968501\pi\)
\(920\) −6.81495e9 + 5.23030e9i −0.288540 + 0.221447i
\(921\) −2.50648e9 2.50648e9i −0.105720 0.105720i
\(922\) 1.73998e10 + 1.10842e10i 0.731117 + 0.465741i
\(923\) −6.20858e8 + 1.49888e9i −0.0259888 + 0.0627425i
\(924\) −6.01087e9 + 2.80337e9i −0.250660 + 0.116904i
\(925\) 2.42699e10 1.00529e10i 1.00826 0.417634i
\(926\) −6.84253e9 9.77151e9i −0.283190 0.404411i
\(927\) −2.58627e10 −1.06634
\(928\) −9.76809e9 + 3.08153e9i −0.401229 + 0.126575i
\(929\) 3.58176e10 1.46569 0.732843 0.680398i \(-0.238193\pi\)
0.732843 + 0.680398i \(0.238193\pi\)
\(930\) −6.14867e7 8.78063e7i −0.00250663 0.00357961i
\(931\) −2.44015e10 + 1.01074e10i −0.991044 + 0.410504i
\(932\) 1.48374e10 + 3.18138e10i 0.600348 + 1.28724i
\(933\) −2.33018e8 + 5.62556e8i −0.00939299 + 0.0226767i
\(934\) −4.90602e9 3.12526e9i −0.197022 0.125508i
\(935\) −5.53568e9 5.53568e9i −0.221478 0.221478i
\(936\) −3.41767e9 + 2.59785e10i −0.136228 + 1.03549i
\(937\) −1.33026e10 + 1.33026e10i −0.528260 + 0.528260i −0.920053 0.391793i \(-0.871855\pi\)
0.391793 + 0.920053i \(0.371855\pi\)
\(938\) −2.64386e10 + 5.86216e9i −1.04599 + 0.231925i
\(939\) −5.86421e9 2.42904e9i −0.231143 0.0957424i
\(940\) −4.38200e9 + 4.78271e9i −0.172078 + 0.187813i
\(941\) −9.51915e9 2.29813e10i −0.372421 0.899104i −0.993339 0.115229i \(-0.963240\pi\)
0.620918 0.783876i \(-0.286760\pi\)
\(942\) −5.95670e8 + 3.37883e9i −0.0232182 + 0.131701i
\(943\) 3.99959e9i 0.155319i
\(944\) 2.75839e10 1.43636e10i 1.06722 0.555728i
\(945\) 5.31517e10i 2.04883i
\(946\) 1.95101e10 + 3.43954e9i 0.749274 + 0.132093i
\(947\) −1.46508e10 3.53701e10i −0.560578 1.35335i −0.909305 0.416130i \(-0.863386\pi\)
0.348727 0.937224i \(-0.386614\pi\)
\(948\) −1.19136e10 + 5.20900e8i −0.454167 + 0.0198575i
\(949\) −2.52549e10 1.04609e10i −0.959212 0.397319i
\(950\) −7.01391e9 3.16330e10i −0.265416 1.19704i
\(951\) 1.50732e8 1.50732e8i 0.00568295 0.00568295i
\(952\) 1.41518e10 + 8.16876e9i 0.531595 + 0.306851i
\(953\) −1.11316e10 1.11316e10i −0.416614 0.416614i 0.467421 0.884035i \(-0.345183\pi\)
−0.884035 + 0.467421i \(0.845183\pi\)
\(954\) −5.37418e9 + 8.43635e9i −0.200398 + 0.314583i
\(955\) 9.81006e9 2.36836e10i 0.364469 0.879905i
\(956\) −3.40319e10 1.23842e10i −1.25975 0.458423i
\(957\) 1.61168e9 6.67581e8i 0.0594413 0.0246214i
\(958\) −3.51308e10 + 2.46005e10i −1.29095 + 0.903992i
\(959\) 4.52008e10 1.65494
\(960\) 8.16916e9 + 1.41433e10i 0.298008 + 0.515943i
\(961\) −2.75111e10 −0.999946
\(962\) −1.10195e10 + 7.71646e9i −0.399071 + 0.279451i
\(963\) 1.97719e10 8.18978e9i 0.713437 0.295515i
\(964\) −3.35617e10 1.22131e10i −1.20663 0.439093i
\(965\) 3.14268e10 7.58711e10i 1.12578 2.71788i
\(966\) −1.64076e9 + 2.57566e9i −0.0585633 + 0.0919323i
\(967\) 6.58421e8 + 6.58421e8i 0.0234159 + 0.0234159i 0.718718 0.695302i \(-0.244729\pi\)
−0.695302 + 0.718718i \(0.744729\pi\)
\(968\) −1.07661e10 + 1.86514e10i −0.381500 + 0.660919i
\(969\) −1.00872e9 + 1.00872e9i −0.0356154 + 0.0356154i
\(970\) −3.76106e9 1.69626e10i −0.132315 0.596747i
\(971\) 4.19677e10 + 1.73836e10i 1.47112 + 0.609358i 0.967114 0.254342i \(-0.0818589\pi\)
0.504006 + 0.863700i \(0.331859\pi\)
\(972\) 2.35007e10 1.02752e9i 0.820820 0.0358887i
\(973\) 2.58172e10 + 6.23283e10i 0.898493 + 2.16915i
\(974\) −3.05183e10 5.38022e9i −1.05829 0.186571i
\(975\) 2.73546e10i 0.945178i
\(976\) 4.00899e10 + 1.26348e10i 1.38026 + 0.435006i
\(977\) 4.04824e10i 1.38879i −0.719596 0.694393i \(-0.755673\pi\)
0.719596 0.694393i \(-0.244327\pi\)
\(978\) −2.28386e9 + 1.29548e10i −0.0780698 + 0.442836i
\(979\) −8.20947e8 1.98194e9i −0.0279625 0.0675074i
\(980\) −8.57179e10 + 9.35564e10i −2.90925 + 3.17528i
\(981\) −2.97277e10 1.23136e10i −1.00536 0.416433i
\(982\) 4.47773e10 9.92835e9i 1.50893 0.334570i
\(983\) −2.61535e10 + 2.61535e10i −0.878199 + 0.878199i −0.993348 0.115149i \(-0.963265\pi\)
0.115149 + 0.993348i \(0.463265\pi\)
\(984\) 7.53927e9 + 9.91851e8i 0.252259 + 0.0331867i
\(985\) 4.24612e10 + 4.24612e10i 1.41568 + 1.41568i
\(986\) −3.62480e9 2.30909e9i −0.120425 0.0767136i
\(987\) −8.82432e8 + 2.13038e9i −0.0292127 + 0.0705257i
\(988\) 7.01333e9 + 1.50377e10i 0.231353 + 0.496057i
\(989\) 8.42747e9 3.49077e9i 0.277019 0.114745i
\(990\) 1.45664e10 + 2.08016e10i 0.477121 + 0.681355i
\(991\) −4.87777e10 −1.59207 −0.796037 0.605247i \(-0.793074\pi\)
−0.796037 + 0.605247i \(0.793074\pi\)
\(992\) −2.24648e8 1.96191e7i −0.00730655 0.000638100i
\(993\) 9.63232e9 0.312183
\(994\) −1.88250e9 2.68831e9i −0.0607971 0.0868215i
\(995\) 6.08593e10 2.52087e10i 1.95860 0.811279i
\(996\) 7.22668e9 3.37040e9i 0.231756 0.108087i
\(997\) −2.79337e9 + 6.74380e9i −0.0892681 + 0.215512i −0.962208 0.272315i \(-0.912211\pi\)
0.872940 + 0.487828i \(0.162211\pi\)
\(998\) −2.10494e10 1.34090e10i −0.670321 0.427012i
\(999\) 5.59634e9 + 5.59634e9i 0.177592 + 0.177592i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 32.8.g.a.21.23 108
32.29 even 8 inner 32.8.g.a.29.23 yes 108
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
32.8.g.a.21.23 108 1.1 even 1 trivial
32.8.g.a.29.23 yes 108 32.29 even 8 inner