Properties

Label 91.8.e.b.53.8
Level $91$
Weight $8$
Character 91.53
Analytic conductor $28.427$
Analytic rank $0$
Dimension $58$
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] = [91,8,Mod(53,91)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(91, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("91.53");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 91.e (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(28.4270373191\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 53.8
Character \(\chi\) \(=\) 91.53
Dual form 91.8.e.b.79.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-6.60583 - 11.4416i) q^{2} +(33.9784 - 58.8524i) q^{3} +(-23.2740 + 40.3117i) q^{4} +(-146.782 - 254.233i) q^{5} -897.823 q^{6} +(420.880 - 803.992i) q^{7} -1076.12 q^{8} +(-1215.57 - 2105.43i) q^{9} +O(q^{10})\) \(q+(-6.60583 - 11.4416i) q^{2} +(33.9784 - 58.8524i) q^{3} +(-23.2740 + 40.3117i) q^{4} +(-146.782 - 254.233i) q^{5} -897.823 q^{6} +(420.880 - 803.992i) q^{7} -1076.12 q^{8} +(-1215.57 - 2105.43i) q^{9} +(-1939.23 + 3358.84i) q^{10} +(2237.87 - 3876.11i) q^{11} +(1581.63 + 2739.46i) q^{12} -2197.00 q^{13} +(-11979.2 + 495.475i) q^{14} -19949.6 q^{15} +(10087.7 + 17472.4i) q^{16} +(2573.70 - 4457.77i) q^{17} +(-16059.7 + 27816.2i) q^{18} +(16189.5 + 28041.0i) q^{19} +13664.8 q^{20} +(-33016.0 - 52088.2i) q^{21} -59132.0 q^{22} +(-53248.4 - 92229.0i) q^{23} +(-36564.8 + 63332.0i) q^{24} +(-4027.15 + 6975.23i) q^{25} +(14513.0 + 25137.3i) q^{26} -16590.8 q^{27} +(22614.7 + 35678.5i) q^{28} -39835.4 q^{29} +(131784. + 228256. i) q^{30} +(103718. - 179645. i) q^{31} +(64404.0 - 111551. i) q^{32} +(-152079. - 263408. i) q^{33} -68005.6 q^{34} +(-266179. + 11009.5i) q^{35} +113165. q^{36} +(224794. + 389354. i) q^{37} +(213890. - 370468. i) q^{38} +(-74650.6 + 129299. i) q^{39} +(157954. + 273584. i) q^{40} +447578. q^{41} +(-377876. + 721843. i) q^{42} +544147. q^{43} +(104168. + 180425. i) q^{44} +(-356846. + 618076. i) q^{45} +(-703500. + 1.21850e6i) q^{46} +(516300. + 894257. i) q^{47} +1.37106e6 q^{48} +(-469263. - 676769. i) q^{49} +106411. q^{50} +(-174900. - 302936. i) q^{51} +(51133.0 - 88564.9i) q^{52} +(-430049. + 744868. i) q^{53} +(109596. + 189826. i) q^{54} -1.31391e6 q^{55} +(-452916. + 865189. i) q^{56} +2.20037e6 q^{57} +(263146. + 455782. i) q^{58} +(313033. - 542188. i) q^{59} +(464308. - 804204. i) q^{60} +(611179. + 1.05859e6i) q^{61} -2.74058e6 q^{62} +(-2.20436e6 + 91174.7i) q^{63} +880687. q^{64} +(322479. + 558550. i) q^{65} +(-2.00921e6 + 3.48006e6i) q^{66} +(1.17620e6 - 2.03723e6i) q^{67} +(119800. + 207500. i) q^{68} -7.23720e6 q^{69} +(1.88430e6 + 2.97279e6i) q^{70} +4.87020e6 q^{71} +(1.30809e6 + 2.26568e6i) q^{72} +(-43486.3 + 75320.5i) q^{73} +(2.96990e6 - 5.14402e6i) q^{74} +(273673. + 474015. i) q^{75} -1.50717e6 q^{76} +(-2.17448e6 - 3.43061e6i) q^{77} +1.97252e6 q^{78} +(107141. + 185574. i) q^{79} +(2.96138e6 - 5.12926e6i) q^{80} +(2.09472e6 - 3.62816e6i) q^{81} +(-2.95663e6 - 5.12103e6i) q^{82} -2.50406e6 q^{83} +(2.86818e6 - 118631. i) q^{84} -1.51108e6 q^{85} +(-3.59454e6 - 6.22593e6i) q^{86} +(-1.35355e6 + 2.34441e6i) q^{87} +(-2.40821e6 + 4.17114e6i) q^{88} +(2.25116e6 + 3.89912e6i) q^{89} +9.42906e6 q^{90} +(-924674. + 1.76637e6i) q^{91} +4.95722e6 q^{92} +(-7.04836e6 - 1.22081e7i) q^{93} +(6.82117e6 - 1.18146e7i) q^{94} +(4.75263e6 - 8.23180e6i) q^{95} +(-4.37669e6 - 7.58066e6i) q^{96} -1.40497e7 q^{97} +(-4.64347e6 + 9.83975e6i) q^{98} -1.08811e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58 q - 31 q^{2} - 1893 q^{4} + 48 q^{5} - 4602 q^{6} + 85 q^{7} + 11436 q^{8} - 25535 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 58 q - 31 q^{2} - 1893 q^{4} + 48 q^{5} - 4602 q^{6} + 85 q^{7} + 11436 q^{8} - 25535 q^{9} + 3029 q^{10} - 15843 q^{11} + 10995 q^{12} - 127426 q^{13} - 65720 q^{14} + 115668 q^{15} - 154909 q^{16} + 43475 q^{17} - 67288 q^{18} + 64641 q^{19} + 40146 q^{20} - 321354 q^{21} + 170964 q^{22} - 96894 q^{23} + 501382 q^{24} - 637413 q^{25} + 68107 q^{26} + 156816 q^{27} - 877133 q^{28} + 155846 q^{29} - 335448 q^{30} + 393806 q^{31} - 1827215 q^{32} + 299052 q^{33} - 38692 q^{34} - 133704 q^{35} + 5417220 q^{36} - 597180 q^{37} - 502034 q^{38} + 1223016 q^{40} - 1436280 q^{41} - 2542432 q^{42} + 3496372 q^{43} - 2679210 q^{44} - 2509582 q^{45} + 2358719 q^{46} + 2368643 q^{47} - 843698 q^{48} + 995403 q^{49} + 3451796 q^{50} - 2396956 q^{51} + 4158921 q^{52} - 1919163 q^{53} - 4029674 q^{54} + 6075808 q^{55} + 3653181 q^{56} + 11452960 q^{57} - 4051049 q^{58} + 48733 q^{59} - 2792030 q^{60} + 1417921 q^{61} - 10244784 q^{62} + 7636291 q^{63} + 30707792 q^{64} - 105456 q^{65} - 22397813 q^{66} - 7025007 q^{67} + 5107354 q^{68} - 19729612 q^{69} - 13744304 q^{70} + 29267486 q^{71} - 7267524 q^{72} - 2417490 q^{73} + 2601511 q^{74} + 17567528 q^{75} - 19814476 q^{76} - 824982 q^{77} + 10110594 q^{78} - 7837082 q^{79} - 7428483 q^{80} - 24976533 q^{81} - 11520562 q^{82} - 38573688 q^{83} - 14286428 q^{84} + 41189436 q^{85} + 17943598 q^{86} - 37502020 q^{87} - 2949879 q^{88} + 15969588 q^{89} - 114635026 q^{90} - 186745 q^{91} + 83440638 q^{92} - 14525204 q^{93} - 30315990 q^{94} - 8678760 q^{95} + 23478593 q^{96} - 14169276 q^{97} + 14221151 q^{98} + 83443706 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −6.60583 11.4416i −0.583878 1.01131i −0.995014 0.0997330i \(-0.968201\pi\)
0.411136 0.911574i \(-0.365132\pi\)
\(3\) 33.9784 58.8524i 0.726573 1.25846i −0.231751 0.972775i \(-0.574445\pi\)
0.958323 0.285686i \(-0.0922213\pi\)
\(4\) −23.2740 + 40.3117i −0.181828 + 0.314935i
\(5\) −146.782 254.233i −0.525142 0.909572i −0.999571 0.0292786i \(-0.990679\pi\)
0.474430 0.880293i \(-0.342654\pi\)
\(6\) −897.823 −1.69692
\(7\) 420.880 803.992i 0.463784 0.885948i
\(8\) −1076.12 −0.743095
\(9\) −1215.57 2105.43i −0.555816 0.962701i
\(10\) −1939.23 + 3358.84i −0.613238 + 1.06216i
\(11\) 2237.87 3876.11i 0.506945 0.878054i −0.493023 0.870016i \(-0.664108\pi\)
0.999968 0.00803796i \(-0.00255859\pi\)
\(12\) 1581.63 + 2739.46i 0.264223 + 0.457647i
\(13\) −2197.00 −0.277350
\(14\) −11979.2 + 495.475i −1.16676 + 0.0482585i
\(15\) −19949.6 −1.52621
\(16\) 10087.7 + 17472.4i 0.615705 + 1.06643i
\(17\) 2573.70 4457.77i 0.127053 0.220063i −0.795480 0.605979i \(-0.792781\pi\)
0.922534 + 0.385917i \(0.126115\pi\)
\(18\) −16059.7 + 27816.2i −0.649058 + 1.12420i
\(19\) 16189.5 + 28041.0i 0.541496 + 0.937898i 0.998818 + 0.0485971i \(0.0154750\pi\)
−0.457323 + 0.889301i \(0.651192\pi\)
\(20\) 13664.8 0.381942
\(21\) −33016.0 52088.2i −0.777959 1.22736i
\(22\) −59132.0 −1.18398
\(23\) −53248.4 92229.0i −0.912556 1.58059i −0.810441 0.585821i \(-0.800772\pi\)
−0.102115 0.994773i \(-0.532561\pi\)
\(24\) −36564.8 + 63332.0i −0.539912 + 0.935156i
\(25\) −4027.15 + 6975.23i −0.0515476 + 0.0892830i
\(26\) 14513.0 + 25137.3i 0.161939 + 0.280486i
\(27\) −16590.8 −0.162217
\(28\) 22614.7 + 35678.5i 0.194688 + 0.307152i
\(29\) −39835.4 −0.303303 −0.151651 0.988434i \(-0.548459\pi\)
−0.151651 + 0.988434i \(0.548459\pi\)
\(30\) 131784. + 228256.i 0.891124 + 1.54347i
\(31\) 103718. 179645.i 0.625301 1.08305i −0.363182 0.931718i \(-0.618310\pi\)
0.988483 0.151334i \(-0.0483570\pi\)
\(32\) 64404.0 111551.i 0.347446 0.601795i
\(33\) −152079. 263408.i −0.736665 1.27594i
\(34\) −68005.6 −0.296735
\(35\) −266179. + 11009.5i −1.04939 + 0.0434038i
\(36\) 113165. 0.404252
\(37\) 224794. + 389354.i 0.729589 + 1.26369i 0.957057 + 0.289900i \(0.0936219\pi\)
−0.227468 + 0.973786i \(0.573045\pi\)
\(38\) 213890. 370468.i 0.632335 1.09524i
\(39\) −74650.6 + 129299.i −0.201515 + 0.349034i
\(40\) 157954. + 273584.i 0.390230 + 0.675898i
\(41\) 447578. 1.01420 0.507102 0.861886i \(-0.330717\pi\)
0.507102 + 0.861886i \(0.330717\pi\)
\(42\) −377876. + 721843.i −0.787004 + 1.50338i
\(43\) 544147. 1.04370 0.521851 0.853037i \(-0.325242\pi\)
0.521851 + 0.853037i \(0.325242\pi\)
\(44\) 104168. + 180425.i 0.184354 + 0.319310i
\(45\) −356846. + 618076.i −0.583764 + 1.01111i
\(46\) −703500. + 1.21850e6i −1.06564 + 1.84575i
\(47\) 516300. + 894257.i 0.725369 + 1.25638i 0.958822 + 0.284008i \(0.0916644\pi\)
−0.233452 + 0.972368i \(0.575002\pi\)
\(48\) 1.37106e6 1.78942
\(49\) −469263. 676769.i −0.569809 0.821777i
\(50\) 106411. 0.120390
\(51\) −174900. 302936.i −0.184627 0.319783i
\(52\) 51133.0 88564.9i 0.0504300 0.0873474i
\(53\) −430049. + 744868.i −0.396783 + 0.687248i −0.993327 0.115332i \(-0.963207\pi\)
0.596544 + 0.802580i \(0.296540\pi\)
\(54\) 109596. + 189826.i 0.0947148 + 0.164051i
\(55\) −1.31391e6 −1.06487
\(56\) −452916. + 865189.i −0.344635 + 0.658344i
\(57\) 2.20037e6 1.57374
\(58\) 263146. + 455782.i 0.177092 + 0.306732i
\(59\) 313033. 542188.i 0.198430 0.343691i −0.749590 0.661903i \(-0.769749\pi\)
0.948020 + 0.318212i \(0.103082\pi\)
\(60\) 464308. 804204.i 0.277509 0.480659i
\(61\) 611179. + 1.05859e6i 0.344758 + 0.597138i 0.985310 0.170777i \(-0.0546277\pi\)
−0.640552 + 0.767915i \(0.721294\pi\)
\(62\) −2.74058e6 −1.46040
\(63\) −2.20436e6 + 91174.7i −1.11068 + 0.0459391i
\(64\) 880687. 0.419944
\(65\) 322479. + 558550.i 0.145648 + 0.252270i
\(66\) −2.00921e6 + 3.48006e6i −0.860245 + 1.48999i
\(67\) 1.17620e6 2.03723e6i 0.477769 0.827520i −0.521906 0.853003i \(-0.674779\pi\)
0.999675 + 0.0254828i \(0.00811232\pi\)
\(68\) 119800. + 207500.i 0.0462037 + 0.0800272i
\(69\) −7.23720e6 −2.65215
\(70\) 1.88430e6 + 2.97279e6i 0.656609 + 1.03591i
\(71\) 4.87020e6 1.61489 0.807445 0.589943i \(-0.200850\pi\)
0.807445 + 0.589943i \(0.200850\pi\)
\(72\) 1.30809e6 + 2.26568e6i 0.413024 + 0.715378i
\(73\) −43486.3 + 75320.5i −0.0130835 + 0.0226612i −0.872493 0.488627i \(-0.837498\pi\)
0.859410 + 0.511288i \(0.170831\pi\)
\(74\) 2.96990e6 5.14402e6i 0.851982 1.47568i
\(75\) 273673. + 474015.i 0.0749061 + 0.129741i
\(76\) −1.50717e6 −0.393836
\(77\) −2.17448e6 3.43061e6i −0.542798 0.856354i
\(78\) 1.97252e6 0.470641
\(79\) 107141. + 185574.i 0.0244490 + 0.0423469i 0.877991 0.478677i \(-0.158884\pi\)
−0.853542 + 0.521024i \(0.825550\pi\)
\(80\) 2.96138e6 5.12926e6i 0.646665 1.12006i
\(81\) 2.09472e6 3.62816e6i 0.437954 0.758558i
\(82\) −2.95663e6 5.12103e6i −0.592172 1.02567i
\(83\) −2.50406e6 −0.480697 −0.240348 0.970687i \(-0.577262\pi\)
−0.240348 + 0.970687i \(0.577262\pi\)
\(84\) 2.86818e6 118631.i 0.527994 0.0218384i
\(85\) −1.51108e6 −0.266884
\(86\) −3.59454e6 6.22593e6i −0.609395 1.05550i
\(87\) −1.35355e6 + 2.34441e6i −0.220372 + 0.381695i
\(88\) −2.40821e6 + 4.17114e6i −0.376708 + 0.652478i
\(89\) 2.25116e6 + 3.89912e6i 0.338486 + 0.586275i 0.984148 0.177348i \(-0.0567519\pi\)
−0.645662 + 0.763623i \(0.723419\pi\)
\(90\) 9.42906e6 1.36339
\(91\) −924674. + 1.76637e6i −0.128630 + 0.245718i
\(92\) 4.95722e6 0.663713
\(93\) −7.04836e6 1.22081e7i −0.908653 1.57383i
\(94\) 6.82117e6 1.18146e7i 0.847055 1.46714i
\(95\) 4.75263e6 8.23180e6i 0.568724 0.985059i
\(96\) −4.37669e6 7.58066e6i −0.504890 0.874496i
\(97\) −1.40497e7 −1.56303 −0.781515 0.623886i \(-0.785553\pi\)
−0.781515 + 0.623886i \(0.785553\pi\)
\(98\) −4.64347e6 + 9.83975e6i −0.498369 + 1.05607i
\(99\) −1.08811e7 −1.12707
\(100\) −187456. 324683.i −0.0187456 0.0324683i
\(101\) 1.36578e6 2.36560e6i 0.131903 0.228463i −0.792507 0.609863i \(-0.791224\pi\)
0.924410 + 0.381400i \(0.124558\pi\)
\(102\) −2.31072e6 + 4.00229e6i −0.215599 + 0.373429i
\(103\) −1.91054e6 3.30915e6i −0.172276 0.298391i 0.766939 0.641720i \(-0.221779\pi\)
−0.939215 + 0.343329i \(0.888446\pi\)
\(104\) 2.36423e6 0.206097
\(105\) −8.39641e6 + 1.60393e7i −0.707833 + 1.35215i
\(106\) 1.13633e7 0.926692
\(107\) −7.56596e6 1.31046e7i −0.597064 1.03415i −0.993252 0.115976i \(-0.963000\pi\)
0.396188 0.918169i \(-0.370333\pi\)
\(108\) 386135. 668806.i 0.0294955 0.0510878i
\(109\) −1.24017e7 + 2.14803e7i −0.917250 + 1.58872i −0.113678 + 0.993518i \(0.536263\pi\)
−0.803573 + 0.595207i \(0.797070\pi\)
\(110\) 8.67949e6 + 1.50333e7i 0.621756 + 1.07691i
\(111\) 3.05526e7 2.12040
\(112\) 1.82934e7 756637.i 1.23036 0.0508891i
\(113\) −2.31386e7 −1.50856 −0.754280 0.656553i \(-0.772014\pi\)
−0.754280 + 0.656553i \(0.772014\pi\)
\(114\) −1.45353e7 2.51758e7i −0.918875 1.59154i
\(115\) −1.56318e7 + 2.70750e7i −0.958442 + 1.66007i
\(116\) 927130. 1.60584e6i 0.0551490 0.0955208i
\(117\) 2.67060e6 + 4.62562e6i 0.154156 + 0.267005i
\(118\) −8.27136e6 −0.463436
\(119\) −2.50079e6 3.94542e6i −0.136039 0.214624i
\(120\) 2.14681e7 1.13412
\(121\) −272554. 472077.i −0.0139863 0.0242250i
\(122\) 8.07469e6 1.39858e7i 0.402593 0.697312i
\(123\) 1.52080e7 2.63411e7i 0.736893 1.27634i
\(124\) 4.82787e6 + 8.36212e6i 0.227394 + 0.393859i
\(125\) −2.05702e7 −0.942004
\(126\) 1.56048e7 + 2.46191e7i 0.694962 + 1.09642i
\(127\) 2.44710e7 1.06008 0.530040 0.847973i \(-0.322177\pi\)
0.530040 + 0.847973i \(0.322177\pi\)
\(128\) −1.40614e7 2.43550e7i −0.592643 1.02649i
\(129\) 1.84893e7 3.20243e7i 0.758325 1.31346i
\(130\) 4.26048e6 7.37938e6i 0.170082 0.294590i
\(131\) −1.07122e7 1.85540e7i −0.416321 0.721088i 0.579246 0.815153i \(-0.303347\pi\)
−0.995566 + 0.0940648i \(0.970014\pi\)
\(132\) 1.41579e7 0.535785
\(133\) 2.93585e7 1.21430e6i 1.08207 0.0447555i
\(134\) −3.10790e7 −1.11584
\(135\) 2.43523e6 + 4.21794e6i 0.0851867 + 0.147548i
\(136\) −2.76960e6 + 4.79708e6i −0.0944127 + 0.163528i
\(137\) −1.11364e7 + 1.92888e7i −0.370017 + 0.640889i −0.989568 0.144068i \(-0.953982\pi\)
0.619550 + 0.784957i \(0.287315\pi\)
\(138\) 4.78077e7 + 8.28053e7i 1.54853 + 2.68214i
\(139\) 3.48172e7 1.09962 0.549809 0.835290i \(-0.314701\pi\)
0.549809 + 0.835290i \(0.314701\pi\)
\(140\) 5.75123e6 1.09864e7i 0.177138 0.338381i
\(141\) 7.01722e7 2.10813
\(142\) −3.21717e7 5.57231e7i −0.942899 1.63315i
\(143\) −4.91660e6 + 8.51581e6i −0.140601 + 0.243528i
\(144\) 2.45246e7 4.24779e7i 0.684437 1.18548i
\(145\) 5.84711e6 + 1.01275e7i 0.159277 + 0.275876i
\(146\) 1.14905e6 0.0305566
\(147\) −5.57743e7 + 4.62168e6i −1.44818 + 0.120002i
\(148\) −2.09274e7 −0.530639
\(149\) 1.02450e7 + 1.77449e7i 0.253724 + 0.439463i 0.964548 0.263907i \(-0.0850112\pi\)
−0.710824 + 0.703370i \(0.751678\pi\)
\(150\) 3.61567e6 6.26253e6i 0.0874721 0.151506i
\(151\) −3.57506e7 + 6.19218e7i −0.845013 + 1.46361i 0.0405968 + 0.999176i \(0.487074\pi\)
−0.885610 + 0.464430i \(0.846259\pi\)
\(152\) −1.74218e7 3.01754e7i −0.402383 0.696947i
\(153\) −1.25140e7 −0.282473
\(154\) −2.48875e7 + 4.75416e7i −0.549109 + 1.04894i
\(155\) −6.08957e7 −1.31349
\(156\) −3.47484e6 6.01859e6i −0.0732822 0.126928i
\(157\) −1.40633e7 + 2.43583e7i −0.290026 + 0.502340i −0.973816 0.227339i \(-0.926997\pi\)
0.683789 + 0.729680i \(0.260331\pi\)
\(158\) 1.41551e6 2.45174e6i 0.0285505 0.0494509i
\(159\) 2.92248e7 + 5.06189e7i 0.576583 + 0.998671i
\(160\) −3.78133e7 −0.729834
\(161\) −9.65626e7 + 3.99394e6i −1.82355 + 0.0754243i
\(162\) −5.53494e7 −1.02285
\(163\) −2.63404e7 4.56230e7i −0.476394 0.825138i 0.523240 0.852185i \(-0.324723\pi\)
−0.999634 + 0.0270468i \(0.991390\pi\)
\(164\) −1.04169e7 + 1.80427e7i −0.184411 + 0.319409i
\(165\) −4.46447e7 + 7.73269e7i −0.773707 + 1.34010i
\(166\) 1.65414e7 + 2.86505e7i 0.280668 + 0.486132i
\(167\) 6.34970e6 0.105498 0.0527491 0.998608i \(-0.483202\pi\)
0.0527491 + 0.998608i \(0.483202\pi\)
\(168\) 3.55290e7 + 5.60530e7i 0.578097 + 0.912045i
\(169\) 4.82681e6 0.0769231
\(170\) 9.98197e6 + 1.72893e7i 0.155828 + 0.269902i
\(171\) 3.93588e7 6.81715e7i 0.601943 1.04260i
\(172\) −1.26645e7 + 2.19355e7i −0.189774 + 0.328699i
\(173\) −1.56746e7 2.71493e7i −0.230163 0.398655i 0.727693 0.685903i \(-0.240593\pi\)
−0.957856 + 0.287249i \(0.907259\pi\)
\(174\) 3.57652e7 0.514681
\(175\) 3.91308e6 + 6.17354e6i 0.0551932 + 0.0870765i
\(176\) 9.03000e7 1.24851
\(177\) −2.12727e7 3.68454e7i −0.288348 0.499433i
\(178\) 2.97415e7 5.15138e7i 0.395269 0.684627i
\(179\) 3.84196e7 6.65447e7i 0.500688 0.867217i −0.499311 0.866423i \(-0.666414\pi\)
1.00000 0.000794869i \(-0.000253015\pi\)
\(180\) −1.66105e7 2.87702e7i −0.212289 0.367696i
\(181\) −9.00686e7 −1.12901 −0.564506 0.825429i \(-0.690933\pi\)
−0.564506 + 0.825429i \(0.690933\pi\)
\(182\) 2.63184e7 1.08856e6i 0.323601 0.0133845i
\(183\) 8.30677e7 1.00197
\(184\) 5.73015e7 + 9.92491e7i 0.678116 + 1.17453i
\(185\) 6.59912e7 1.14300e8i 0.766275 1.32723i
\(186\) −9.31206e7 + 1.61290e8i −1.06109 + 1.83785i
\(187\) −1.15192e7 1.99518e7i −0.128818 0.223119i
\(188\) −4.80654e7 −0.527570
\(189\) −6.98276e6 + 1.33389e7i −0.0752334 + 0.143716i
\(190\) −1.25580e8 −1.32826
\(191\) −3.30056e6 5.71674e6i −0.0342745 0.0593651i 0.848379 0.529389i \(-0.177579\pi\)
−0.882654 + 0.470024i \(0.844245\pi\)
\(192\) 2.99244e7 5.18305e7i 0.305120 0.528483i
\(193\) −3.42358e7 + 5.92982e7i −0.342791 + 0.593732i −0.984950 0.172840i \(-0.944706\pi\)
0.642159 + 0.766572i \(0.278039\pi\)
\(194\) 9.28102e7 + 1.60752e8i 0.912620 + 1.58070i
\(195\) 4.38293e7 0.423296
\(196\) 3.82033e7 3.16568e6i 0.362414 0.0300311i
\(197\) 8.47324e7 0.789620 0.394810 0.918763i \(-0.370810\pi\)
0.394810 + 0.918763i \(0.370810\pi\)
\(198\) 7.18790e7 + 1.24498e8i 0.658073 + 1.13982i
\(199\) −6.21238e7 + 1.07602e8i −0.558820 + 0.967905i 0.438775 + 0.898597i \(0.355413\pi\)
−0.997595 + 0.0693084i \(0.977921\pi\)
\(200\) 4.33369e6 7.50616e6i 0.0383047 0.0663457i
\(201\) −7.99306e7 1.38444e8i −0.694268 1.20251i
\(202\) −3.60885e7 −0.308062
\(203\) −1.67659e7 + 3.20274e7i −0.140667 + 0.268711i
\(204\) 1.62825e7 0.134281
\(205\) −6.56963e7 1.13789e8i −0.532601 0.922492i
\(206\) −2.52414e7 + 4.37194e7i −0.201177 + 0.348449i
\(207\) −1.29454e8 + 2.24221e8i −1.01443 + 1.75704i
\(208\) −2.21627e7 3.83869e7i −0.170766 0.295775i
\(209\) 1.44920e8 1.09803
\(210\) 2.38982e8 9.88455e6i 1.78072 0.0736528i
\(211\) 7.77462e7 0.569759 0.284879 0.958563i \(-0.408046\pi\)
0.284879 + 0.958563i \(0.408046\pi\)
\(212\) −2.00179e7 3.46721e7i −0.144293 0.249922i
\(213\) 1.65482e8 2.86623e8i 1.17333 2.03227i
\(214\) −9.99589e7 + 1.73134e8i −0.697226 + 1.20763i
\(215\) −7.98707e7 1.38340e8i −0.548091 0.949322i
\(216\) 1.78537e7 0.120542
\(217\) −1.00780e8 1.58998e8i −0.669525 1.05629i
\(218\) 3.27694e8 2.14225
\(219\) 2.95519e6 + 5.11855e6i 0.0190122 + 0.0329300i
\(220\) 3.05800e7 5.29661e7i 0.193624 0.335366i
\(221\) −5.65441e6 + 9.79372e6i −0.0352382 + 0.0610344i
\(222\) −2.01825e8 3.49571e8i −1.23805 2.14437i
\(223\) 2.96625e8 1.79118 0.895592 0.444875i \(-0.146752\pi\)
0.895592 + 0.444875i \(0.146752\pi\)
\(224\) −6.25797e7 9.87299e7i −0.372019 0.586922i
\(225\) 1.95811e7 0.114604
\(226\) 1.52850e8 + 2.64743e8i 0.880815 + 1.52562i
\(227\) 2.05867e7 3.56572e7i 0.116814 0.202328i −0.801689 0.597741i \(-0.796065\pi\)
0.918504 + 0.395413i \(0.129398\pi\)
\(228\) −5.12114e7 + 8.87008e7i −0.286151 + 0.495628i
\(229\) −1.44781e8 2.50768e8i −0.796688 1.37990i −0.921762 0.387756i \(-0.873250\pi\)
0.125074 0.992147i \(-0.460083\pi\)
\(230\) 4.13044e8 2.23846
\(231\) −2.75785e8 + 1.14068e7i −1.47207 + 0.0608866i
\(232\) 4.28676e7 0.225383
\(233\) −1.38287e6 2.39520e6i −0.00716201 0.0124050i 0.862422 0.506190i \(-0.168946\pi\)
−0.869584 + 0.493785i \(0.835613\pi\)
\(234\) 3.52831e7 6.11122e7i 0.180016 0.311797i
\(235\) 1.51567e8 2.62521e8i 0.761843 1.31955i
\(236\) 1.45710e7 + 2.52378e7i 0.0721603 + 0.124985i
\(237\) 1.45619e7 0.0710559
\(238\) −2.86222e7 + 5.46759e7i −0.137621 + 0.262892i
\(239\) 1.33579e8 0.632917 0.316459 0.948606i \(-0.397506\pi\)
0.316459 + 0.948606i \(0.397506\pi\)
\(240\) −2.01246e8 3.48569e8i −0.939698 1.62760i
\(241\) −1.00733e8 + 1.74475e8i −0.463568 + 0.802923i −0.999136 0.0415694i \(-0.986764\pi\)
0.535568 + 0.844492i \(0.320098\pi\)
\(242\) −3.60089e6 + 6.23692e6i −0.0163326 + 0.0282889i
\(243\) −1.60493e8 2.77981e8i −0.717518 1.24278i
\(244\) −5.68983e7 −0.250747
\(245\) −1.03178e8 + 2.18639e8i −0.448235 + 0.949832i
\(246\) −4.01846e8 −1.72102
\(247\) −3.55683e7 6.16060e7i −0.150184 0.260126i
\(248\) −1.11613e8 + 1.93319e8i −0.464658 + 0.804811i
\(249\) −8.50840e7 + 1.47370e8i −0.349261 + 0.604938i
\(250\) 1.35883e8 + 2.35356e8i 0.550016 + 0.952656i
\(251\) 1.35582e8 0.541181 0.270590 0.962695i \(-0.412781\pi\)
0.270590 + 0.962695i \(0.412781\pi\)
\(252\) 4.76287e7 9.09834e7i 0.187485 0.358146i
\(253\) −4.76653e8 −1.85046
\(254\) −1.61651e8 2.79988e8i −0.618958 1.07207i
\(255\) −5.13443e7 + 8.89309e7i −0.193911 + 0.335863i
\(256\) −1.29410e8 + 2.24145e8i −0.482091 + 0.835006i
\(257\) −2.31430e8 4.00849e8i −0.850460 1.47304i −0.880794 0.473500i \(-0.842990\pi\)
0.0303334 0.999540i \(-0.490343\pi\)
\(258\) −4.88547e8 −1.77108
\(259\) 4.07649e8 1.68608e7i 1.45793 0.0603017i
\(260\) −3.00215e7 −0.105932
\(261\) 4.84227e7 + 8.38706e7i 0.168581 + 0.291990i
\(262\) −1.41526e8 + 2.45129e8i −0.486161 + 0.842056i
\(263\) 1.39272e8 2.41225e8i 0.472082 0.817670i −0.527408 0.849612i \(-0.676836\pi\)
0.999490 + 0.0319423i \(0.0101693\pi\)
\(264\) 1.63654e8 + 2.83458e8i 0.547412 + 0.948145i
\(265\) 2.52493e8 0.833469
\(266\) −2.07831e8 3.27888e8i −0.677057 1.06817i
\(267\) 3.05963e8 0.983739
\(268\) 5.47495e7 + 9.48290e7i 0.173744 + 0.300933i
\(269\) −1.73001e8 + 2.99647e8i −0.541896 + 0.938592i 0.456899 + 0.889519i \(0.348960\pi\)
−0.998795 + 0.0490733i \(0.984373\pi\)
\(270\) 3.21734e7 5.57260e7i 0.0994773 0.172300i
\(271\) 1.11580e8 + 1.93262e8i 0.340561 + 0.589868i 0.984537 0.175177i \(-0.0560498\pi\)
−0.643976 + 0.765045i \(0.722717\pi\)
\(272\) 1.03851e8 0.312909
\(273\) 7.25361e7 + 1.14438e8i 0.215767 + 0.340408i
\(274\) 2.94260e8 0.864181
\(275\) 1.80245e7 + 3.12194e7i 0.0522636 + 0.0905231i
\(276\) 1.68438e8 2.91744e8i 0.482236 0.835257i
\(277\) −2.22423e8 + 3.85248e8i −0.628783 + 1.08908i 0.359013 + 0.933333i \(0.383113\pi\)
−0.987796 + 0.155752i \(0.950220\pi\)
\(278\) −2.29996e8 3.98365e8i −0.642043 1.11205i
\(279\) −5.04306e8 −1.39021
\(280\) 2.86439e8 1.18475e7i 0.779794 0.0322532i
\(281\) 4.00328e8 1.07633 0.538163 0.842841i \(-0.319118\pi\)
0.538163 + 0.842841i \(0.319118\pi\)
\(282\) −4.63546e8 8.02885e8i −1.23089 2.13197i
\(283\) 6.63755e7 1.14966e8i 0.174083 0.301520i −0.765761 0.643125i \(-0.777637\pi\)
0.939843 + 0.341606i \(0.110971\pi\)
\(284\) −1.13349e8 + 1.96326e8i −0.293632 + 0.508586i
\(285\) −3.22974e8 5.59407e8i −0.826438 1.43143i
\(286\) 1.29913e8 0.328376
\(287\) 1.88377e8 3.59849e8i 0.470372 0.898533i
\(288\) −3.13150e8 −0.772465
\(289\) 1.91922e8 + 3.32418e8i 0.467715 + 0.810106i
\(290\) 7.72500e7 1.33801e8i 0.185997 0.322156i
\(291\) −4.77388e8 + 8.26861e8i −1.13565 + 1.96701i
\(292\) −2.02420e6 3.50602e6i −0.00475788 0.00824089i
\(293\) −2.14142e8 −0.497353 −0.248677 0.968587i \(-0.579996\pi\)
−0.248677 + 0.968587i \(0.579996\pi\)
\(294\) 4.21315e8 + 6.07619e8i 0.966921 + 1.39449i
\(295\) −1.83790e8 −0.416816
\(296\) −2.41904e8 4.18990e8i −0.542154 0.939038i
\(297\) −3.71282e7 + 6.43079e7i −0.0822349 + 0.142435i
\(298\) 1.35354e8 2.34440e8i 0.296288 0.513186i
\(299\) 1.16987e8 + 2.02627e8i 0.253097 + 0.438378i
\(300\) −2.54778e7 −0.0544801
\(301\) 2.29021e8 4.37489e8i 0.484052 0.924666i
\(302\) 9.44648e8 1.97354
\(303\) −9.28142e7 1.60759e8i −0.191675 0.331991i
\(304\) −3.26629e8 + 5.65739e8i −0.666803 + 1.15494i
\(305\) 1.79420e8 3.10764e8i 0.362093 0.627164i
\(306\) 8.26655e7 + 1.43181e8i 0.164930 + 0.285667i
\(307\) 6.63004e7 0.130777 0.0653886 0.997860i \(-0.479171\pi\)
0.0653886 + 0.997860i \(0.479171\pi\)
\(308\) 1.88903e8 7.81323e6i 0.368392 0.0152371i
\(309\) −2.59669e8 −0.500685
\(310\) 4.02266e8 + 6.96746e8i 0.766916 + 1.32834i
\(311\) 5.82161e7 1.00833e8i 0.109744 0.190083i −0.805922 0.592021i \(-0.798330\pi\)
0.915667 + 0.401939i \(0.131664\pi\)
\(312\) 8.03328e7 1.39140e8i 0.149745 0.259366i
\(313\) 1.47892e8 + 2.56156e8i 0.272608 + 0.472171i 0.969529 0.244977i \(-0.0787805\pi\)
−0.696921 + 0.717148i \(0.745447\pi\)
\(314\) 3.71598e8 0.677361
\(315\) 3.46738e8 + 5.47037e8i 0.625050 + 0.986121i
\(316\) −9.97440e6 −0.0177821
\(317\) 3.63688e8 + 6.29926e8i 0.641241 + 1.11066i 0.985156 + 0.171661i \(0.0549135\pi\)
−0.343915 + 0.939001i \(0.611753\pi\)
\(318\) 3.86108e8 6.68759e8i 0.673309 1.16621i
\(319\) −8.91466e7 + 1.54406e8i −0.153758 + 0.266316i
\(320\) −1.29269e8 2.23900e8i −0.220530 0.381970i
\(321\) −1.02832e9 −1.73524
\(322\) 6.83573e8 + 1.07845e9i 1.14101 + 1.80013i
\(323\) 1.66667e8 0.275195
\(324\) 9.75049e7 + 1.68883e8i 0.159264 + 0.275854i
\(325\) 8.84766e6 1.53246e7i 0.0142967 0.0247626i
\(326\) −3.48001e8 + 6.02755e8i −0.556312 + 0.963561i
\(327\) 8.42780e8 + 1.45974e9i 1.33290 + 2.30865i
\(328\) −4.81646e8 −0.753650
\(329\) 9.36276e8 3.87254e7i 1.44950 0.0599530i
\(330\) 1.17966e9 1.80700
\(331\) 3.54866e8 + 6.14647e8i 0.537857 + 0.931596i 0.999019 + 0.0442798i \(0.0140993\pi\)
−0.461162 + 0.887316i \(0.652567\pi\)
\(332\) 5.82794e7 1.00943e8i 0.0874041 0.151388i
\(333\) 5.46505e8 9.46574e8i 0.811034 1.40475i
\(334\) −4.19450e7 7.26509e7i −0.0615982 0.106691i
\(335\) −6.90575e8 −1.00359
\(336\) 5.77052e8 1.10232e9i 0.829903 1.58533i
\(337\) −8.52515e8 −1.21338 −0.606690 0.794938i \(-0.707503\pi\)
−0.606690 + 0.794938i \(0.707503\pi\)
\(338\) −3.18851e7 5.52266e7i −0.0449137 0.0777929i
\(339\) −7.86214e8 + 1.36176e9i −1.09608 + 1.89846i
\(340\) 3.51690e7 6.09144e7i 0.0485270 0.0840512i
\(341\) −4.64216e8 8.04046e8i −0.633986 1.09810i
\(342\) −1.03999e9 −1.40585
\(343\) −7.41620e8 + 9.24447e7i −0.992320 + 0.123695i
\(344\) −5.85565e8 −0.775569
\(345\) 1.06229e9 + 1.83993e9i 1.39276 + 2.41232i
\(346\) −2.07088e8 + 3.58687e8i −0.268775 + 0.465532i
\(347\) −5.50930e8 + 9.54239e8i −0.707854 + 1.22604i 0.257798 + 0.966199i \(0.417003\pi\)
−0.965652 + 0.259840i \(0.916330\pi\)
\(348\) −6.30048e7 1.09128e8i −0.0801395 0.138806i
\(349\) −2.60359e8 −0.327857 −0.163928 0.986472i \(-0.552417\pi\)
−0.163928 + 0.986472i \(0.552417\pi\)
\(350\) 4.47862e7 8.55534e7i 0.0558349 0.106659i
\(351\) 3.64501e7 0.0449908
\(352\) −2.88256e8 4.99274e8i −0.352272 0.610154i
\(353\) 6.03663e8 1.04558e9i 0.730438 1.26516i −0.226259 0.974067i \(-0.572649\pi\)
0.956696 0.291088i \(-0.0940172\pi\)
\(354\) −2.81048e8 + 4.86789e8i −0.336720 + 0.583216i
\(355\) −7.14856e8 1.23817e9i −0.848046 1.46886i
\(356\) −2.09574e8 −0.246185
\(357\) −3.17170e8 + 1.31185e7i −0.368938 + 0.0152597i
\(358\) −1.01517e9 −1.16936
\(359\) 5.80695e8 + 1.00579e9i 0.662396 + 1.14730i 0.979984 + 0.199075i \(0.0637937\pi\)
−0.317588 + 0.948229i \(0.602873\pi\)
\(360\) 3.84008e8 6.65121e8i 0.433792 0.751350i
\(361\) −7.72618e7 + 1.33821e8i −0.0864350 + 0.149710i
\(362\) 5.94978e8 + 1.03053e9i 0.659206 + 1.14178i
\(363\) −3.70438e7 −0.0406483
\(364\) −4.96846e7 7.83857e7i −0.0539967 0.0851887i
\(365\) 2.55320e7 0.0274827
\(366\) −5.48731e8 9.50430e8i −0.585027 1.01330i
\(367\) 4.01198e8 6.94895e8i 0.423670 0.733818i −0.572625 0.819817i \(-0.694075\pi\)
0.996295 + 0.0859996i \(0.0274084\pi\)
\(368\) 1.07431e9 1.86076e9i 1.12373 1.94636i
\(369\) −5.44062e8 9.42344e8i −0.563711 0.976376i
\(370\) −1.74371e9 −1.78965
\(371\) 4.17868e8 + 6.59256e8i 0.424845 + 0.670264i
\(372\) 6.56174e8 0.660874
\(373\) 7.45389e7 + 1.29105e8i 0.0743707 + 0.128814i 0.900812 0.434208i \(-0.142972\pi\)
−0.826442 + 0.563022i \(0.809639\pi\)
\(374\) −1.52188e8 + 2.63597e8i −0.150428 + 0.260549i
\(375\) −6.98942e8 + 1.21060e9i −0.684435 + 1.18548i
\(376\) −5.55598e8 9.62325e8i −0.539018 0.933607i
\(377\) 8.75185e7 0.0841211
\(378\) 1.98746e8 8.22035e6i 0.189268 0.00782833i
\(379\) 1.03156e9 0.973321 0.486661 0.873591i \(-0.338215\pi\)
0.486661 + 0.873591i \(0.338215\pi\)
\(380\) 2.21225e8 + 3.83174e8i 0.206820 + 0.358223i
\(381\) 8.31486e8 1.44018e9i 0.770225 1.33407i
\(382\) −4.36059e7 + 7.55276e7i −0.0400242 + 0.0693240i
\(383\) −4.35337e8 7.54025e8i −0.395940 0.685788i 0.597281 0.802032i \(-0.296248\pi\)
−0.993221 + 0.116244i \(0.962915\pi\)
\(384\) −1.91114e9 −1.72239
\(385\) −5.53000e8 + 1.05638e9i −0.493870 + 0.943421i
\(386\) 9.04624e8 0.800594
\(387\) −6.61448e8 1.14566e9i −0.580106 1.00477i
\(388\) 3.26994e8 5.66370e8i 0.284203 0.492254i
\(389\) −4.45958e8 + 7.72423e8i −0.384123 + 0.665321i −0.991647 0.128980i \(-0.958830\pi\)
0.607524 + 0.794301i \(0.292163\pi\)
\(390\) −2.89529e8 5.01479e8i −0.247153 0.428082i
\(391\) −5.48181e8 −0.463773
\(392\) 5.04981e8 + 7.28282e8i 0.423423 + 0.610658i
\(393\) −1.45593e9 −1.20995
\(394\) −5.59728e8 9.69478e8i −0.461042 0.798548i
\(395\) 3.14527e7 5.44776e7i 0.0256784 0.0444763i
\(396\) 2.53248e8 4.38638e8i 0.204933 0.354955i
\(397\) 6.46248e8 + 1.11933e9i 0.518361 + 0.897827i 0.999772 + 0.0213326i \(0.00679089\pi\)
−0.481412 + 0.876495i \(0.659876\pi\)
\(398\) 1.64152e9 1.30513
\(399\) 9.26093e8 1.76908e9i 0.729877 1.39426i
\(400\) −1.62499e8 −0.126952
\(401\) −6.05022e8 1.04793e9i −0.468560 0.811571i 0.530794 0.847501i \(-0.321894\pi\)
−0.999354 + 0.0359305i \(0.988561\pi\)
\(402\) −1.05602e9 + 1.82907e9i −0.810736 + 1.40424i
\(403\) −2.27869e8 + 3.94680e8i −0.173427 + 0.300385i
\(404\) 6.35743e7 + 1.10114e8i 0.0479675 + 0.0830821i
\(405\) −1.22986e9 −0.919951
\(406\) 4.77198e8 1.97375e7i 0.353882 0.0146370i
\(407\) 2.01224e9 1.47945
\(408\) 1.88213e8 + 3.25995e8i 0.137195 + 0.237629i
\(409\) 1.16180e9 2.01230e9i 0.839652 1.45432i −0.0505333 0.998722i \(-0.516092\pi\)
0.890186 0.455598i \(-0.150575\pi\)
\(410\) −8.67957e8 + 1.50334e9i −0.621949 + 1.07725i
\(411\) 7.56794e8 + 1.31081e9i 0.537689 + 0.931305i
\(412\) 1.77864e8 0.125299
\(413\) −3.04166e8 4.79872e8i −0.212464 0.335197i
\(414\) 3.42061e9 2.36921
\(415\) 3.67550e8 + 6.36615e8i 0.252434 + 0.437228i
\(416\) −1.41496e8 + 2.45078e8i −0.0963643 + 0.166908i
\(417\) 1.18303e9 2.04907e9i 0.798952 1.38383i
\(418\) −9.57316e8 1.65812e9i −0.641118 1.11045i
\(419\) −8.49808e8 −0.564380 −0.282190 0.959359i \(-0.591061\pi\)
−0.282190 + 0.959359i \(0.591061\pi\)
\(420\) −4.51156e8 7.11773e8i −0.297135 0.468780i
\(421\) 3.38548e8 0.221122 0.110561 0.993869i \(-0.464735\pi\)
0.110561 + 0.993869i \(0.464735\pi\)
\(422\) −5.13579e8 8.89544e8i −0.332670 0.576201i
\(423\) 1.25520e9 2.17406e9i 0.806343 1.39663i
\(424\) 4.62783e8 8.01564e8i 0.294847 0.510691i
\(425\) 2.07293e7 + 3.59043e7i 0.0130986 + 0.0226874i
\(426\) −4.37258e9 −2.74034
\(427\) 1.10833e9 4.58420e7i 0.688927 0.0284948i
\(428\) 7.04360e8 0.434252
\(429\) 3.34117e8 + 5.78708e8i 0.204314 + 0.353882i
\(430\) −1.05522e9 + 1.82770e9i −0.640037 + 1.10858i
\(431\) −5.74014e7 + 9.94221e7i −0.0345344 + 0.0598153i −0.882776 0.469794i \(-0.844328\pi\)
0.848242 + 0.529609i \(0.177661\pi\)
\(432\) −1.67364e8 2.89882e8i −0.0998776 0.172993i
\(433\) 1.46767e9 0.868802 0.434401 0.900719i \(-0.356960\pi\)
0.434401 + 0.900719i \(0.356960\pi\)
\(434\) −1.15346e9 + 2.20340e9i −0.677309 + 1.29384i
\(435\) 7.94702e8 0.462905
\(436\) −5.77273e8 9.99867e8i −0.333564 0.577749i
\(437\) 1.72413e9 2.98628e9i 0.988290 1.71177i
\(438\) 3.90430e7 6.76245e7i 0.0222016 0.0384543i
\(439\) −8.82214e8 1.52804e9i −0.497677 0.862003i 0.502319 0.864682i \(-0.332480\pi\)
−0.999996 + 0.00267982i \(0.999147\pi\)
\(440\) 1.41392e9 0.791301
\(441\) −8.54466e8 + 1.81066e9i −0.474416 + 1.00531i
\(442\) 1.49408e8 0.0822994
\(443\) −4.63885e8 8.03473e8i −0.253511 0.439095i 0.710979 0.703214i \(-0.248252\pi\)
−0.964490 + 0.264119i \(0.914919\pi\)
\(444\) −7.11080e8 + 1.23163e9i −0.385548 + 0.667788i
\(445\) 6.60857e8 1.14464e9i 0.355506 0.615755i
\(446\) −1.95945e9 3.39387e9i −1.04583 1.81144i
\(447\) 1.39244e9 0.737395
\(448\) 3.70664e8 7.08065e8i 0.194763 0.372049i
\(449\) 2.52528e9 1.31658 0.658290 0.752765i \(-0.271280\pi\)
0.658290 + 0.752765i \(0.271280\pi\)
\(450\) −1.29350e8 2.24040e8i −0.0669147 0.115900i
\(451\) 1.00162e9 1.73486e9i 0.514146 0.890527i
\(452\) 5.38528e8 9.32757e8i 0.274298 0.475099i
\(453\) 2.42950e9 + 4.20801e9i 1.22793 + 2.12683i
\(454\) −5.43969e8 −0.272822
\(455\) 5.84795e8 2.41878e7i 0.291047 0.0120381i
\(456\) −2.36786e9 −1.16944
\(457\) 4.73249e8 + 8.19691e8i 0.231944 + 0.401739i 0.958380 0.285495i \(-0.0921581\pi\)
−0.726436 + 0.687234i \(0.758825\pi\)
\(458\) −1.91280e9 + 3.31307e9i −0.930338 + 1.61139i
\(459\) −4.26998e7 + 7.39582e7i −0.0206102 + 0.0356978i
\(460\) −7.27628e8 1.26029e9i −0.348543 0.603695i
\(461\) 1.88125e9 0.894319 0.447160 0.894454i \(-0.352436\pi\)
0.447160 + 0.894454i \(0.352436\pi\)
\(462\) 1.95230e9 + 3.08008e9i 0.921085 + 1.45317i
\(463\) −3.61479e9 −1.69258 −0.846291 0.532721i \(-0.821170\pi\)
−0.846291 + 0.532721i \(0.821170\pi\)
\(464\) −4.01848e8 6.96022e8i −0.186745 0.323452i
\(465\) −2.06914e9 + 3.58386e9i −0.954343 + 1.65297i
\(466\) −1.82700e7 + 3.16445e7i −0.00836348 + 0.0144860i
\(467\) 2.04845e8 + 3.54802e8i 0.0930714 + 0.161204i 0.908802 0.417228i \(-0.136998\pi\)
−0.815731 + 0.578432i \(0.803665\pi\)
\(468\) −2.48623e8 −0.112119
\(469\) −1.14288e9 1.80308e9i −0.511559 0.807069i
\(470\) −4.00489e9 −1.77930
\(471\) 9.55696e8 + 1.65531e9i 0.421450 + 0.729974i
\(472\) −3.36859e8 + 5.83458e8i −0.147452 + 0.255395i
\(473\) 1.21773e9 2.10917e9i 0.529099 0.916427i
\(474\) −9.61937e7 1.66612e8i −0.0414880 0.0718593i
\(475\) −2.60790e8 −0.111651
\(476\) 2.17250e8 8.98572e6i 0.0923285 0.00381881i
\(477\) 2.09102e9 0.882153
\(478\) −8.82403e8 1.52837e9i −0.369547 0.640074i
\(479\) 1.01615e9 1.76003e9i 0.422459 0.731720i −0.573720 0.819051i \(-0.694500\pi\)
0.996179 + 0.0873309i \(0.0278337\pi\)
\(480\) −1.28484e9 + 2.22540e9i −0.530278 + 0.918468i
\(481\) −4.93872e8 8.55411e8i −0.202352 0.350483i
\(482\) 2.66171e9 1.08267
\(483\) −3.04599e9 + 5.81865e9i −1.23003 + 2.34967i
\(484\) 2.53737e7 0.0101724
\(485\) 2.06224e9 + 3.57191e9i 0.820812 + 1.42169i
\(486\) −2.12037e9 + 3.67260e9i −0.837887 + 1.45126i
\(487\) 1.12049e9 1.94075e9i 0.439599 0.761409i −0.558059 0.829801i \(-0.688454\pi\)
0.997658 + 0.0683927i \(0.0217871\pi\)
\(488\) −6.57700e8 1.13917e9i −0.256188 0.443730i
\(489\) −3.58003e9 −1.38454
\(490\) 3.18317e9 2.63770e8i 1.22229 0.101284i
\(491\) −1.52738e9 −0.582320 −0.291160 0.956674i \(-0.594041\pi\)
−0.291160 + 0.956674i \(0.594041\pi\)
\(492\) 7.07902e8 + 1.22612e9i 0.267976 + 0.464148i
\(493\) −1.02524e8 + 1.77577e8i −0.0385356 + 0.0667457i
\(494\) −4.69916e8 + 8.13918e8i −0.175378 + 0.303764i
\(495\) 1.59715e9 + 2.76635e9i 0.591872 + 1.02515i
\(496\) 4.18512e9 1.54000
\(497\) 2.04977e9 3.91560e9i 0.748959 1.43071i
\(498\) 2.24820e9 0.815704
\(499\) −1.76647e9 3.05961e9i −0.636434 1.10234i −0.986209 0.165503i \(-0.947075\pi\)
0.349775 0.936834i \(-0.386258\pi\)
\(500\) 4.78750e8 8.29219e8i 0.171283 0.296671i
\(501\) 2.15753e8 3.73695e8i 0.0766522 0.132765i
\(502\) −8.95628e8 1.55127e9i −0.315984 0.547300i
\(503\) −2.26909e9 −0.794993 −0.397497 0.917604i \(-0.630121\pi\)
−0.397497 + 0.917604i \(0.630121\pi\)
\(504\) 2.37214e9 9.81146e7i 0.825342 0.0341371i
\(505\) −8.01886e8 −0.277072
\(506\) 3.14869e9 + 5.45369e9i 1.08045 + 1.87139i
\(507\) 1.64007e8 2.84069e8i 0.0558902 0.0968047i
\(508\) −5.69538e8 + 9.86468e8i −0.192752 + 0.333857i
\(509\) 2.56497e9 + 4.44265e9i 0.862123 + 1.49324i 0.869875 + 0.493271i \(0.164199\pi\)
−0.00775208 + 0.999970i \(0.502468\pi\)
\(510\) 1.35669e9 0.452881
\(511\) 4.22545e7 + 6.66635e7i 0.0140088 + 0.0221012i
\(512\) −1.80266e8 −0.0593564
\(513\) −2.68597e8 4.65223e8i −0.0878396 0.152143i
\(514\) −3.05758e9 + 5.29588e9i −0.993131 + 1.72015i
\(515\) −5.60864e8 + 9.71445e8i −0.180939 + 0.313396i
\(516\) 8.60637e8 + 1.49067e9i 0.275770 + 0.477647i
\(517\) 4.62165e9 1.47089
\(518\) −2.88577e9 4.55279e9i −0.912238 1.43921i
\(519\) −2.13040e9 −0.668922
\(520\) −3.47025e8 6.01065e8i −0.108230 0.187460i
\(521\) 8.64358e7 1.49711e8i 0.0267770 0.0463791i −0.852326 0.523010i \(-0.824809\pi\)
0.879103 + 0.476631i \(0.158142\pi\)
\(522\) 6.39745e8 1.10807e9i 0.196861 0.340973i
\(523\) −2.95225e9 5.11344e9i −0.902395 1.56299i −0.824377 0.566041i \(-0.808474\pi\)
−0.0780179 0.996952i \(-0.524859\pi\)
\(524\) 9.97260e8 0.302795
\(525\) 4.96288e8 2.05270e7i 0.149684 0.00619111i
\(526\) −3.68002e9 −1.10255
\(527\) −5.33878e8 9.24704e8i −0.158893 0.275211i
\(528\) 3.06825e9 5.31437e9i 0.907136 1.57121i
\(529\) −3.96838e9 + 6.87344e9i −1.16552 + 2.01873i
\(530\) −1.66793e9 2.88894e9i −0.486644 0.842893i
\(531\) −1.52205e9 −0.441162
\(532\) −6.34340e8 + 1.21176e9i −0.182655 + 0.348919i
\(533\) −9.83330e8 −0.281290
\(534\) −2.02114e9 3.50072e9i −0.574384 0.994862i
\(535\) −2.22109e9 + 3.84704e9i −0.627086 + 1.08615i
\(536\) −1.26572e9 + 2.19230e9i −0.355028 + 0.614926i
\(537\) −2.61088e9 4.52217e9i −0.727573 1.26019i
\(538\) 4.57127e9 1.26561
\(539\) −3.67338e9 + 3.04391e8i −1.01043 + 0.0837281i
\(540\) −2.26710e8 −0.0619573
\(541\) −1.06599e9 1.84635e9i −0.289444 0.501331i 0.684233 0.729263i \(-0.260137\pi\)
−0.973677 + 0.227932i \(0.926804\pi\)
\(542\) 1.47416e9 2.55332e9i 0.397692 0.688823i
\(543\) −3.06039e9 + 5.30075e9i −0.820309 + 1.42082i
\(544\) −3.31513e8 5.74197e8i −0.0882884 0.152920i
\(545\) 7.28135e9 1.92675
\(546\) 8.30194e8 1.58589e9i 0.218276 0.416964i
\(547\) 1.81445e9 0.474013 0.237006 0.971508i \(-0.423834\pi\)
0.237006 + 0.971508i \(0.423834\pi\)
\(548\) −5.18376e8 8.97854e8i −0.134559 0.233063i
\(549\) 1.48586e9 2.57359e9i 0.383244 0.663798i
\(550\) 2.38134e8 4.12460e8i 0.0610311 0.105709i
\(551\) −6.44914e8 1.11702e9i −0.164237 0.284467i
\(552\) 7.78807e9 1.97080
\(553\) 1.94293e8 8.03620e6i 0.0488562 0.00202075i
\(554\) 5.87716e9 1.46853
\(555\) −4.48455e9 7.76747e9i −1.11351 1.92865i
\(556\) −8.10335e8 + 1.40354e9i −0.199941 + 0.346309i
\(557\) −1.13993e9 + 1.97442e9i −0.279503 + 0.484113i −0.971261 0.238016i \(-0.923503\pi\)
0.691758 + 0.722129i \(0.256836\pi\)
\(558\) 3.33136e9 + 5.77009e9i 0.811712 + 1.40593i
\(559\) −1.19549e9 −0.289471
\(560\) −2.87750e9 4.53973e9i −0.692400 1.09238i
\(561\) −1.56562e9 −0.374383
\(562\) −2.64450e9 4.58041e9i −0.628444 1.08850i
\(563\) 7.89537e8 1.36752e9i 0.186463 0.322964i −0.757605 0.652713i \(-0.773631\pi\)
0.944069 + 0.329749i \(0.106964\pi\)
\(564\) −1.63319e9 + 2.82876e9i −0.383318 + 0.663926i
\(565\) 3.39632e9 + 5.88260e9i 0.792208 + 1.37214i
\(566\) −1.75386e9 −0.406572
\(567\) −2.03538e9 3.21116e9i −0.468927 0.739811i
\(568\) −5.24090e9 −1.20002
\(569\) 2.94169e9 + 5.09516e9i 0.669429 + 1.15948i 0.978064 + 0.208304i \(0.0667943\pi\)
−0.308636 + 0.951180i \(0.599872\pi\)
\(570\) −4.26702e9 + 7.39070e9i −0.965079 + 1.67157i
\(571\) −4.03802e9 + 6.99406e9i −0.907700 + 1.57218i −0.0904476 + 0.995901i \(0.528830\pi\)
−0.817252 + 0.576281i \(0.804504\pi\)
\(572\) −2.28858e8 3.96394e8i −0.0511305 0.0885606i
\(573\) −4.48591e8 −0.0996116
\(574\) −5.36165e9 + 2.21764e8i −1.18333 + 0.0489440i
\(575\) 8.57759e8 0.188160
\(576\) −1.07054e9 1.85422e9i −0.233412 0.404281i
\(577\) 3.27424e9 5.67115e9i 0.709570 1.22901i −0.255447 0.966823i \(-0.582223\pi\)
0.965017 0.262188i \(-0.0844440\pi\)
\(578\) 2.53560e9 4.39179e9i 0.546177 0.946007i
\(579\) 2.32656e9 + 4.02972e9i 0.498126 + 0.862779i
\(580\) −5.44342e8 −0.115844
\(581\) −1.05391e9 + 2.01324e9i −0.222939 + 0.425872i
\(582\) 1.26142e10 2.65234
\(583\) 1.92479e9 + 3.33384e9i 0.402294 + 0.696794i
\(584\) 4.67963e7 8.10536e7i 0.00972225 0.0168394i
\(585\) 7.83991e8 1.35791e9i 0.161907 0.280431i
\(586\) 1.41459e9 + 2.45013e9i 0.290394 + 0.502977i
\(587\) −4.22714e9 −0.862608 −0.431304 0.902207i \(-0.641946\pi\)
−0.431304 + 0.902207i \(0.641946\pi\)
\(588\) 1.11178e9 2.35592e9i 0.225527 0.477904i
\(589\) 6.71657e9 1.35439
\(590\) 1.21408e9 + 2.10285e9i 0.243370 + 0.421529i
\(591\) 2.87908e9 4.98671e9i 0.573716 0.993705i
\(592\) −4.53531e9 + 7.85539e9i −0.898423 + 1.55611i
\(593\) 4.01690e9 + 6.95748e9i 0.791042 + 1.37013i 0.925322 + 0.379182i \(0.123795\pi\)
−0.134280 + 0.990943i \(0.542872\pi\)
\(594\) 9.81050e8 0.192061
\(595\) −6.35985e8 + 1.21490e9i −0.123776 + 0.236445i
\(596\) −9.53771e8 −0.184536
\(597\) 4.22174e9 + 7.31227e9i 0.812047 + 1.40651i
\(598\) 1.54559e9 2.67704e9i 0.295556 0.511919i
\(599\) −1.49634e9 + 2.59173e9i −0.284469 + 0.492715i −0.972480 0.232985i \(-0.925151\pi\)
0.688011 + 0.725700i \(0.258484\pi\)
\(600\) −2.94504e8 5.10095e8i −0.0556623 0.0964100i
\(601\) 2.98025e9 0.560005 0.280002 0.959999i \(-0.409665\pi\)
0.280002 + 0.959999i \(0.409665\pi\)
\(602\) −6.51846e9 + 2.69611e8i −1.21775 + 0.0503675i
\(603\) −5.71899e9 −1.06221
\(604\) −1.66412e9 2.88233e9i −0.307294 0.532249i
\(605\) −8.00118e7 + 1.38584e8i −0.0146896 + 0.0254431i
\(606\) −1.22623e9 + 2.12389e9i −0.223830 + 0.387684i
\(607\) −3.33539e9 5.77706e9i −0.605321 1.04845i −0.992001 0.126233i \(-0.959711\pi\)
0.386680 0.922214i \(-0.373622\pi\)
\(608\) 4.17067e9 0.752563
\(609\) 1.31521e9 + 2.07496e9i 0.235957 + 0.372262i
\(610\) −4.74086e9 −0.845674
\(611\) −1.13431e9 1.96468e9i −0.201181 0.348456i
\(612\) 2.91251e8 5.04462e8i 0.0513615 0.0889607i
\(613\) 4.31494e9 7.47370e9i 0.756595 1.31046i −0.187983 0.982172i \(-0.560195\pi\)
0.944578 0.328288i \(-0.106472\pi\)
\(614\) −4.37969e8 7.58585e8i −0.0763580 0.132256i
\(615\) −8.92902e9 −1.54789
\(616\) 2.34000e9 + 3.69173e9i 0.403351 + 0.636353i
\(617\) −9.50443e9 −1.62903 −0.814513 0.580146i \(-0.802996\pi\)
−0.814513 + 0.580146i \(0.802996\pi\)
\(618\) 1.71533e9 + 2.97103e9i 0.292339 + 0.506347i
\(619\) −1.07843e9 + 1.86789e9i −0.182756 + 0.316543i −0.942818 0.333307i \(-0.891835\pi\)
0.760062 + 0.649851i \(0.225169\pi\)
\(620\) 1.41729e9 2.45481e9i 0.238829 0.413663i
\(621\) 8.83436e8 + 1.53016e9i 0.148032 + 0.256398i
\(622\) −1.53826e9 −0.256309
\(623\) 4.08233e9 1.68850e8i 0.676394 0.0279764i
\(624\) −3.01222e9 −0.496295
\(625\) 3.33394e9 + 5.77456e9i 0.546233 + 0.946104i
\(626\) 1.95389e9 3.38424e9i 0.318340 0.551381i
\(627\) 4.92415e9 8.52888e9i 0.797801 1.38183i
\(628\) −6.54617e8 1.13383e9i −0.105470 0.182679i
\(629\) 2.31420e9 0.370787
\(630\) 3.96851e9 7.58089e9i 0.632317 1.20789i
\(631\) 1.79820e9 0.284928 0.142464 0.989800i \(-0.454498\pi\)
0.142464 + 0.989800i \(0.454498\pi\)
\(632\) −1.15296e8 1.99699e8i −0.0181679 0.0314678i
\(633\) 2.64170e9 4.57555e9i 0.413971 0.717019i
\(634\) 4.80492e9 8.32237e9i 0.748814 1.29698i
\(635\) −3.59189e9 6.22134e9i −0.556692 0.964219i
\(636\) −2.72071e9 −0.419356
\(637\) 1.03097e9 + 1.48686e9i 0.158037 + 0.227920i
\(638\) 2.35555e9 0.359104
\(639\) −5.92007e9 1.02539e10i −0.897581 1.55466i
\(640\) −4.12790e9 + 7.14974e9i −0.622443 + 1.07810i
\(641\) −7.88963e8 + 1.36652e9i −0.118319 + 0.204934i −0.919102 0.394021i \(-0.871084\pi\)
0.800783 + 0.598955i \(0.204417\pi\)
\(642\) 6.79290e9 + 1.17656e10i 1.01317 + 1.75486i
\(643\) 6.35442e9 0.942622 0.471311 0.881967i \(-0.343781\pi\)
0.471311 + 0.881967i \(0.343781\pi\)
\(644\) 2.08639e9 3.98556e9i 0.307819 0.588016i
\(645\) −1.08555e10 −1.59291
\(646\) −1.10097e9 1.90694e9i −0.160681 0.278307i
\(647\) 4.45097e9 7.70930e9i 0.646084 1.11905i −0.337965 0.941159i \(-0.609739\pi\)
0.984050 0.177893i \(-0.0569280\pi\)
\(648\) −2.25416e9 + 3.90432e9i −0.325441 + 0.563680i
\(649\) −1.40105e9 2.42670e9i −0.201186 0.348465i
\(650\) −2.33784e8 −0.0333902
\(651\) −1.27817e10 + 5.28668e8i −1.81575 + 0.0751017i
\(652\) 2.45219e9 0.346487
\(653\) −6.88746e9 1.19294e10i −0.967973 1.67658i −0.701406 0.712762i \(-0.747444\pi\)
−0.266567 0.963816i \(-0.585889\pi\)
\(654\) 1.11345e10 1.92856e10i 1.55650 2.69594i
\(655\) −3.14470e9 + 5.44678e9i −0.437255 + 0.757347i
\(656\) 4.51504e9 + 7.82028e9i 0.624451 + 1.08158i
\(657\) 2.11442e8 0.0290880
\(658\) −6.62796e9 1.04567e10i −0.906962 1.43088i
\(659\) 1.12808e10 1.53547 0.767735 0.640767i \(-0.221384\pi\)
0.767735 + 0.640767i \(0.221384\pi\)
\(660\) −2.07812e9 3.59941e9i −0.281363 0.487335i
\(661\) −3.31722e9 + 5.74559e9i −0.446754 + 0.773801i −0.998173 0.0604279i \(-0.980753\pi\)
0.551418 + 0.834229i \(0.314087\pi\)
\(662\) 4.68837e9 8.12050e9i 0.628086 1.08788i
\(663\) 3.84256e8 + 6.65551e8i 0.0512063 + 0.0886919i
\(664\) 2.69466e9 0.357203
\(665\) −4.61801e9 7.28568e9i −0.608946 0.960714i
\(666\) −1.44405e10 −1.89418
\(667\) 2.12117e9 + 3.67398e9i 0.276781 + 0.479399i
\(668\) −1.47783e8 + 2.55967e8i −0.0191825 + 0.0332251i
\(669\) 1.00788e10 1.74571e10i 1.30143 2.25414i
\(670\) 4.56182e9 + 7.90131e9i 0.585972 + 1.01493i
\(671\) 5.47096e9 0.699093
\(672\) −7.93685e9 + 3.28277e8i −1.00892 + 0.0417300i
\(673\) 7.84908e9 0.992581 0.496291 0.868156i \(-0.334695\pi\)
0.496291 + 0.868156i \(0.334695\pi\)
\(674\) 5.63157e9 + 9.75416e9i 0.708467 + 1.22710i
\(675\) 6.68139e7 1.15725e8i 0.00836187 0.0144832i
\(676\) −1.12339e8 + 1.94577e8i −0.0139868 + 0.0242258i
\(677\) 6.09084e9 + 1.05496e10i 0.754426 + 1.30670i 0.945659 + 0.325160i \(0.105418\pi\)
−0.191233 + 0.981545i \(0.561249\pi\)
\(678\) 2.07744e10 2.55991
\(679\) −5.91326e9 + 1.12959e10i −0.724908 + 1.38476i
\(680\) 1.62610e9 0.198320
\(681\) −1.39901e9 2.42315e9i −0.169748 0.294013i
\(682\) −6.13306e9 + 1.06228e10i −0.740342 + 1.28231i
\(683\) −6.86981e9 + 1.18989e10i −0.825035 + 1.42900i 0.0768582 + 0.997042i \(0.475511\pi\)
−0.901893 + 0.431960i \(0.857822\pi\)
\(684\) 1.83207e9 + 3.17324e9i 0.218900 + 0.379147i
\(685\) 6.53846e9 0.777246
\(686\) 5.95673e9 + 7.87467e9i 0.704488 + 0.931318i
\(687\) −1.96778e10 −2.31541
\(688\) 5.48919e9 + 9.50756e9i 0.642612 + 1.11304i
\(689\) 9.44819e8 1.63647e9i 0.110048 0.190608i
\(690\) 1.40346e10 2.43086e10i 1.62640 2.81701i
\(691\) −2.73866e9 4.74350e9i −0.315766 0.546923i 0.663834 0.747880i \(-0.268928\pi\)
−0.979600 + 0.200957i \(0.935595\pi\)
\(692\) 1.45925e9 0.167401
\(693\) −4.57966e9 + 8.74835e9i −0.522717 + 0.998528i
\(694\) 1.45574e10 1.65320
\(695\) −5.11052e9 8.85168e9i −0.577455 1.00018i
\(696\) 1.45657e9 2.52286e9i 0.163757 0.283636i
\(697\) 1.15193e9 1.99520e9i 0.128858 0.223189i
\(698\) 1.71989e9 + 2.97894e9i 0.191428 + 0.331564i
\(699\) −1.87951e8 −0.0208149
\(700\) −3.39939e8 + 1.40603e7i −0.0374591 + 0.00154935i
\(701\) −2.47648e9 −0.271532 −0.135766 0.990741i \(-0.543350\pi\)
−0.135766 + 0.990741i \(0.543350\pi\)
\(702\) −2.40783e8 4.17048e8i −0.0262691 0.0454995i
\(703\) −7.27858e9 + 1.26069e10i −0.790138 + 1.36856i
\(704\) 1.97086e9 3.41364e9i 0.212889 0.368734i
\(705\) −1.03000e10 1.78401e10i −1.10707 1.91750i
\(706\) −1.59508e10 −1.70595
\(707\) −1.32709e9 2.09371e9i −0.141232 0.222817i
\(708\) 1.98040e9 0.209719
\(709\) −6.05097e9 1.04806e10i −0.637622 1.10439i −0.985953 0.167022i \(-0.946585\pi\)
0.348331 0.937372i \(-0.386749\pi\)
\(710\) −9.44443e9 + 1.63582e10i −0.990311 + 1.71527i
\(711\) 2.60475e8 4.51155e8i 0.0271783 0.0470742i
\(712\) −2.42251e9 4.19591e9i −0.251527 0.435658i
\(713\) −2.20913e10 −2.28249
\(714\) 2.24527e9 + 3.54229e9i 0.230847 + 0.364200i
\(715\) 2.88667e9 0.295342
\(716\) 1.78836e9 + 3.09752e9i 0.182078 + 0.315369i
\(717\) 4.53882e9 7.86147e9i 0.459860 0.796502i
\(718\) 7.67195e9 1.32882e10i 0.773518 1.33977i
\(719\) −5.33876e9 9.24701e9i −0.535660 0.927791i −0.999131 0.0416788i \(-0.986729\pi\)
0.463471 0.886112i \(-0.346604\pi\)
\(720\) −1.43990e10 −1.43771
\(721\) −3.46464e9 + 1.43302e8i −0.344258 + 0.0142389i
\(722\) 2.04151e9 0.201870
\(723\) 6.84552e9 + 1.18568e10i 0.673631 + 1.16676i
\(724\) 2.09626e9 3.63082e9i 0.205286 0.355566i
\(725\) 1.60423e8 2.77862e8i 0.0156345 0.0270798i
\(726\) 2.44705e8 + 4.23842e8i 0.0237337 + 0.0411079i
\(727\) 3.62551e9 0.349945 0.174972 0.984573i \(-0.444016\pi\)
0.174972 + 0.984573i \(0.444016\pi\)
\(728\) 9.95057e8 1.90082e9i 0.0955846 0.182592i
\(729\) −1.26509e10 −1.20941
\(730\) −1.68660e8 2.92127e8i −0.0160465 0.0277934i
\(731\) 1.40047e9 2.42568e9i 0.132606 0.229680i
\(732\) −1.93332e9 + 3.34860e9i −0.182186 + 0.315555i
\(733\) 1.14582e9 + 1.98462e9i 0.107462 + 0.186129i 0.914741 0.404040i \(-0.132394\pi\)
−0.807280 + 0.590169i \(0.799061\pi\)
\(734\) −1.06010e10 −0.989487
\(735\) 9.36162e9 + 1.35013e10i 0.869651 + 1.25421i
\(736\) −1.37177e10 −1.26826
\(737\) −5.26435e9 9.11812e9i −0.484405 0.839014i
\(738\) −7.18797e9 + 1.24499e10i −0.658277 + 1.14017i
\(739\) 7.72430e9 1.33789e10i 0.704050 1.21945i −0.262983 0.964801i \(-0.584706\pi\)
0.967033 0.254650i \(-0.0819604\pi\)
\(740\) 3.07176e9 + 5.32044e9i 0.278661 + 0.482654i
\(741\) −4.83422e9 −0.436478
\(742\) 4.78260e9 9.13603e9i 0.429785 0.821001i
\(743\) −1.88618e10 −1.68703 −0.843516 0.537104i \(-0.819518\pi\)
−0.843516 + 0.537104i \(0.819518\pi\)
\(744\) 7.58486e9 + 1.31374e10i 0.675215 + 1.16951i
\(745\) 3.00756e9 5.20925e9i 0.266482 0.461560i
\(746\) 9.84782e8 1.70569e9i 0.0868469 0.150423i
\(747\) 3.04386e9 + 5.27211e9i 0.267179 + 0.462767i
\(748\) 1.07239e9 0.0936909
\(749\) −1.37204e10 + 5.67491e8i −1.19311 + 0.0493483i
\(750\) 1.84684e10 1.59851
\(751\) 1.02205e10 + 1.77024e10i 0.880507 + 1.52508i 0.850779 + 0.525524i \(0.176131\pi\)
0.0297282 + 0.999558i \(0.490536\pi\)
\(752\) −1.04166e10 + 1.80420e10i −0.893227 + 1.54712i
\(753\) 4.60685e9 7.97929e9i 0.393207 0.681055i
\(754\) −5.78132e8 1.00135e9i −0.0491165 0.0850723i
\(755\) 2.09901e10 1.77501
\(756\) −3.75198e8 5.91937e8i −0.0315816 0.0498252i
\(757\) 1.08833e10 0.911851 0.455925 0.890018i \(-0.349308\pi\)
0.455925 + 0.890018i \(0.349308\pi\)
\(758\) −6.81429e9 1.18027e10i −0.568301 0.984327i
\(759\) −1.61959e10 + 2.80521e10i −1.34450 + 2.32873i
\(760\) −5.11438e9 + 8.85837e9i −0.422616 + 0.731992i
\(761\) −2.77353e9 4.80390e9i −0.228133 0.395137i 0.729122 0.684384i \(-0.239929\pi\)
−0.957255 + 0.289246i \(0.906595\pi\)
\(762\) −2.19706e10 −1.79887
\(763\) 1.20504e10 + 1.90115e10i 0.982122 + 1.54946i
\(764\) 3.07269e8 0.0249282
\(765\) 1.83683e9 + 3.18148e9i 0.148338 + 0.256929i
\(766\) −5.75152e9 + 9.96192e9i −0.462362 + 0.800834i
\(767\) −6.87732e8 + 1.19119e9i −0.0550346 + 0.0953227i
\(768\) 8.79432e9 + 1.52322e10i 0.700548 + 1.21338i
\(769\) −2.63244e9 −0.208745 −0.104372 0.994538i \(-0.533283\pi\)
−0.104372 + 0.994538i \(0.533283\pi\)
\(770\) 1.57397e10 6.51012e8i 1.24245 0.0513891i
\(771\) −3.14545e10 −2.47168
\(772\) −1.59361e9 2.76021e9i −0.124658 0.215914i
\(773\) −4.49486e9 + 7.78533e9i −0.350016 + 0.606246i −0.986252 0.165249i \(-0.947157\pi\)
0.636236 + 0.771495i \(0.280491\pi\)
\(774\) −8.73882e9 + 1.51361e10i −0.677422 + 1.17333i
\(775\) 8.35378e8 + 1.44692e9i 0.0644655 + 0.111657i
\(776\) 1.51192e10 1.16148
\(777\) 1.28590e10 2.45640e10i 0.983406 1.87856i
\(778\) 1.17837e10 0.897125
\(779\) 7.24606e9 + 1.25505e10i 0.549187 + 0.951220i
\(780\) −1.02008e9 + 1.76684e9i −0.0769670 + 0.133311i
\(781\) 1.08989e10 1.88774e10i 0.818660 1.41796i
\(782\) 3.62119e9 + 6.27209e9i 0.270787 + 0.469017i
\(783\) 6.60903e8 0.0492008
\(784\) 7.09101e9 1.50262e10i 0.525535 1.11364i
\(785\) 8.25691e9 0.609220
\(786\) 9.61763e9 + 1.66582e10i 0.706463 + 1.22363i
\(787\) 5.02834e8 8.70935e8i 0.0367717 0.0636904i −0.847054 0.531507i \(-0.821626\pi\)
0.883826 + 0.467817i \(0.154959\pi\)
\(788\) −1.97206e9 + 3.41571e9i −0.143575 + 0.248679i
\(789\) −9.46446e9 1.63929e10i −0.686004 1.18819i
\(790\) −8.31084e8 −0.0599722
\(791\) −9.73858e9 + 1.86032e10i −0.699645 + 1.33651i
\(792\) 1.17094e10 0.837521
\(793\) −1.34276e9 2.32573e9i −0.0956186 0.165616i
\(794\) 8.53800e9 1.47883e10i 0.605319 1.04844i
\(795\) 8.57933e9 1.48598e10i 0.605576 1.04889i
\(796\) −2.89174e9 5.00864e9i −0.203218 0.351985i
\(797\) 2.41558e10 1.69012 0.845058 0.534675i \(-0.179566\pi\)
0.845058 + 0.534675i \(0.179566\pi\)
\(798\) −2.63588e10 + 1.09023e9i −1.83618 + 0.0759465i
\(799\) 5.31519e9 0.368642
\(800\) 5.18730e8 + 8.98466e8i 0.0358200 + 0.0620421i
\(801\) 5.47287e9 9.47929e9i 0.376272 0.651722i
\(802\) −7.99334e9 + 1.38449e10i −0.547165 + 0.947717i
\(803\) 1.94634e8 + 3.37115e8i 0.0132652 + 0.0229760i
\(804\) 7.44122e9 0.504949
\(805\) 1.51890e10 + 2.39632e10i 1.02623 + 1.61904i
\(806\) 6.02105e9 0.405042
\(807\) 1.17566e10 + 2.03631e10i 0.787454 + 1.36391i
\(808\) −1.46974e9 + 2.54566e9i −0.0980168 + 0.169770i
\(809\) 2.06898e9 3.58359e9i 0.137384 0.237957i −0.789121 0.614237i \(-0.789464\pi\)
0.926506 + 0.376281i \(0.122797\pi\)
\(810\) 8.12427e9 + 1.40717e10i 0.537139 + 0.930353i
\(811\) 7.55881e9 0.497600 0.248800 0.968555i \(-0.419964\pi\)
0.248800 + 0.968555i \(0.419964\pi\)
\(812\) −9.00868e8 1.42127e9i −0.0590493 0.0931602i
\(813\) 1.51653e10 0.989768
\(814\) −1.32925e10 2.30233e10i −0.863816 1.49617i
\(815\) −7.73258e9 + 1.33932e10i −0.500349 + 0.866629i
\(816\) 3.52869e9 6.11187e9i 0.227351 0.393784i
\(817\) 8.80944e9 + 1.52584e10i 0.565160 + 0.978885i
\(818\) −3.06986e10 −1.96102
\(819\) 4.84297e9 2.00311e8i 0.308048 0.0127412i
\(820\) 6.11606e9 0.387367
\(821\) 3.47583e9 + 6.02032e9i 0.219209 + 0.379681i 0.954566 0.297999i \(-0.0963191\pi\)
−0.735358 + 0.677679i \(0.762986\pi\)
\(822\) 9.99850e9 1.73179e10i 0.627890 1.08754i
\(823\) 3.43719e9 5.95339e9i 0.214934 0.372276i −0.738318 0.674452i \(-0.764380\pi\)
0.953252 + 0.302176i \(0.0977132\pi\)
\(824\) 2.05596e9 + 3.56103e9i 0.128018 + 0.221733i
\(825\) 2.44978e9 0.151893
\(826\) −3.48125e9 + 6.65010e9i −0.214934 + 0.410580i
\(827\) 1.93783e10 1.19137 0.595686 0.803218i \(-0.296880\pi\)
0.595686 + 0.803218i \(0.296880\pi\)
\(828\) −6.02584e9 1.04371e10i −0.368902 0.638957i
\(829\) 7.49680e9 1.29848e10i 0.457020 0.791581i −0.541782 0.840519i \(-0.682250\pi\)
0.998802 + 0.0489377i \(0.0155836\pi\)
\(830\) 4.85594e9 8.41074e9i 0.294781 0.510576i
\(831\) 1.51152e10 + 2.61803e10i 0.913713 + 1.58260i
\(832\) −1.93487e9 −0.116472
\(833\) −4.22462e9 + 3.50069e8i −0.253239 + 0.0209844i
\(834\) −3.12597e10 −1.86596
\(835\) −9.32019e8 1.61430e9i −0.0554015 0.0959583i
\(836\) −3.37286e9 + 5.84197e9i −0.199653 + 0.345810i
\(837\) −1.72077e9 + 2.98046e9i −0.101434 + 0.175689i
\(838\) 5.61368e9 + 9.72319e9i 0.329529 + 0.570761i
\(839\) −9.53521e9 −0.557395 −0.278698 0.960379i \(-0.589903\pi\)
−0.278698 + 0.960379i \(0.589903\pi\)
\(840\) 9.03551e9 1.72602e10i 0.525987 1.00477i
\(841\) −1.56630e10 −0.908007
\(842\) −2.23639e9 3.87354e9i −0.129109 0.223623i
\(843\) 1.36025e10 2.35603e10i 0.782029 1.35451i
\(844\) −1.80947e9 + 3.13409e9i −0.103598 + 0.179437i
\(845\) −7.08487e8 1.22713e9i −0.0403955 0.0699671i
\(846\) −3.31664e10 −1.88323
\(847\) −4.94259e8 + 2.04431e7i −0.0279487 + 0.00115599i
\(848\) −1.73529e10 −0.977205
\(849\) −4.51067e9 7.81271e9i −0.252967 0.438152i
\(850\) 2.73869e8 4.74355e8i 0.0152960 0.0264934i
\(851\) 2.39398e10 4.14650e10i 1.33158 2.30637i
\(852\) 7.70285e9 + 1.33417e10i 0.426690 + 0.739049i
\(853\) 3.16190e10 1.74432 0.872160 0.489220i \(-0.162719\pi\)
0.872160 + 0.489220i \(0.162719\pi\)
\(854\) −7.84597e9 1.23783e10i −0.431067 0.680079i
\(855\) −2.31086e10 −1.26442
\(856\) 8.14186e9 + 1.41021e10i 0.443675 + 0.768468i
\(857\) 3.29133e9 5.70075e9i 0.178623 0.309385i −0.762786 0.646651i \(-0.776169\pi\)
0.941409 + 0.337266i \(0.109502\pi\)
\(858\) 4.41424e9 7.64569e9i 0.238589 0.413248i
\(859\) −1.78685e9 3.09491e9i −0.0961859 0.166599i 0.813917 0.580981i \(-0.197331\pi\)
−0.910103 + 0.414382i \(0.863998\pi\)
\(860\) 7.43564e9 0.398633
\(861\) −1.47772e10 2.33136e10i −0.789010 1.24479i
\(862\) 1.51673e9 0.0806556
\(863\) −9.28238e9 1.60776e10i −0.491611 0.851495i 0.508342 0.861155i \(-0.330258\pi\)
−0.999953 + 0.00965997i \(0.996925\pi\)
\(864\) −1.06852e9 + 1.85072e9i −0.0563616 + 0.0976211i
\(865\) −4.60150e9 + 7.97003e9i −0.241737 + 0.418701i
\(866\) −9.69518e9 1.67926e10i −0.507275 0.878626i
\(867\) 2.60848e10 1.35932
\(868\) 8.75503e9 3.62118e8i 0.454400 0.0187945i
\(869\) 9.59072e8 0.0495772
\(870\) −5.24967e9 9.09269e9i −0.270280 0.468139i
\(871\) −2.58410e9 + 4.47580e9i −0.132509 + 0.229513i
\(872\) 1.33457e10 2.31154e10i 0.681604 1.18057i
\(873\) 1.70784e10 + 2.95807e10i 0.868757 + 1.50473i
\(874\) −4.55572e10 −2.30816
\(875\) −8.65758e9 + 1.65382e10i −0.436886 + 0.834567i
\(876\) −2.75117e8 −0.0138278
\(877\) 1.23166e10 + 2.13330e10i 0.616586 + 1.06796i 0.990104 + 0.140335i \(0.0448179\pi\)
−0.373518 + 0.927623i \(0.621849\pi\)
\(878\) −1.16555e10 + 2.01879e10i −0.581166 + 1.00661i
\(879\) −7.27621e9 + 1.26028e10i −0.361363 + 0.625900i
\(880\) −1.32544e10 2.29573e10i −0.655647 1.13561i
\(881\) −1.75167e10 −0.863054 −0.431527 0.902100i \(-0.642025\pi\)
−0.431527 + 0.902100i \(0.642025\pi\)
\(882\) 2.63613e10 2.18441e9i 1.29368 0.107200i
\(883\) 4.33197e9 0.211750 0.105875 0.994379i \(-0.466236\pi\)
0.105875 + 0.994379i \(0.466236\pi\)
\(884\) −2.63201e8 4.55878e8i −0.0128146 0.0221955i
\(885\) −6.24488e9 + 1.08165e10i −0.302847 + 0.524546i
\(886\) −6.12869e9 + 1.06152e10i −0.296040 + 0.512756i
\(887\) 2.05251e9 + 3.55506e9i 0.0987537 + 0.171046i 0.911169 0.412033i \(-0.135181\pi\)
−0.812415 + 0.583079i \(0.801848\pi\)
\(888\) −3.28781e10 −1.57566
\(889\) 1.02994e10 1.96745e10i 0.491648 0.939176i
\(890\) −1.74620e10 −0.830290
\(891\) −9.37542e9 1.62387e10i −0.444037 0.769094i
\(892\) −6.90364e9 + 1.19575e10i −0.325688 + 0.564108i
\(893\) −1.67172e10 + 2.89551e10i −0.785569 + 1.36064i
\(894\) −9.19823e9 1.59318e10i −0.430549 0.745733i
\(895\) −2.25572e10 −1.05173
\(896\) −2.54994e10 + 1.05468e9i −1.18427 + 0.0489829i
\(897\) 1.59001e10 0.735575
\(898\) −1.66816e10 2.88933e10i −0.768722 1.33147i
\(899\) −4.13166e9 + 7.15624e9i −0.189656 + 0.328493i
\(900\) −4.55731e8 + 7.89349e8i −0.0208382 + 0.0360928i
\(901\) 2.21363e9 + 3.83412e9i 0.100825 + 0.174634i
\(902\) −2.64662e10 −1.20079
\(903\) −1.79655e10 2.83436e10i −0.811957 1.28100i
\(904\) 2.48998e10 1.12100
\(905\) 1.32204e10 + 2.28984e10i 0.592891 + 1.02692i
\(906\) 3.20977e10 5.55948e10i 1.43392 2.48362i
\(907\) −1.44195e10 + 2.49754e10i −0.641691 + 1.11144i 0.343364 + 0.939203i \(0.388434\pi\)
−0.985055 + 0.172240i \(0.944900\pi\)
\(908\) 9.58270e8 + 1.65977e9i 0.0424803 + 0.0735780i
\(909\) −6.64080e9 −0.293256
\(910\) −4.13980e9 6.53123e9i −0.182110 0.287309i
\(911\) −3.54050e10 −1.55149 −0.775747 0.631045i \(-0.782627\pi\)
−0.775747 + 0.631045i \(0.782627\pi\)
\(912\) 2.21967e10 + 3.84458e10i 0.968962 + 1.67829i
\(913\) −5.60376e9 + 9.70600e9i −0.243687 + 0.422078i
\(914\) 6.25241e9 1.08295e10i 0.270854 0.469133i
\(915\) −1.21928e10 2.11186e10i −0.526174 0.911361i
\(916\) 1.34786e10 0.579441
\(917\) −1.94258e10 + 8.03475e8i −0.831930 + 0.0344096i
\(918\) 1.12827e9 0.0481353
\(919\) 7.52133e9 + 1.30273e10i 0.319662 + 0.553670i 0.980417 0.196931i \(-0.0630974\pi\)
−0.660756 + 0.750601i \(0.729764\pi\)
\(920\) 1.68216e10 2.91359e10i 0.712214 1.23359i
\(921\) 2.25279e9 3.90194e9i 0.0950191 0.164578i
\(922\) −1.24272e10 2.15245e10i −0.522174 0.904431i
\(923\) −1.06998e10 −0.447890
\(924\) 5.95879e9 1.13829e10i 0.248488 0.474678i
\(925\) −3.62112e9 −0.150434
\(926\) 2.38787e10 + 4.13591e10i 0.988262 + 1.71172i
\(927\) −4.64479e9 + 8.04500e9i −0.191508 + 0.331701i
\(928\) −2.56556e9 + 4.44368e9i −0.105382 + 0.182526i
\(929\) −2.42758e10 4.20469e10i −0.993386 1.72060i −0.596130 0.802888i \(-0.703296\pi\)
−0.397257 0.917708i \(-0.630038\pi\)
\(930\) 5.46735e10 2.22888
\(931\) 1.13801e10 2.41151e10i 0.462193 0.979412i
\(932\) 1.28739e8 0.00520901
\(933\) −3.95618e9 6.85231e9i −0.159474 0.276218i
\(934\) 2.70634e9 4.68752e9i 0.108685 0.188247i
\(935\) −3.38161e9 + 5.85712e9i −0.135295 + 0.234339i
\(936\) −2.87388e9 4.97771e9i −0.114552 0.198410i
\(937\) −1.47623e10 −0.586228 −0.293114 0.956078i \(-0.594692\pi\)
−0.293114 + 0.956078i \(0.594692\pi\)
\(938\) −1.30805e10 + 2.49873e10i −0.517506 + 0.988573i
\(939\) 2.01005e10 0.792278
\(940\) 7.05512e9 + 1.22198e10i 0.277049 + 0.479863i
\(941\) 1.23063e10 2.13151e10i 0.481464 0.833919i −0.518310 0.855193i \(-0.673439\pi\)
0.999774 + 0.0212733i \(0.00677201\pi\)
\(942\) 1.26263e10 2.18694e10i 0.492152 0.852432i
\(943\) −2.38329e10 4.12797e10i −0.925518 1.60304i
\(944\) 1.26311e10 0.488698
\(945\) 4.41613e9 1.82656e8i 0.170228 0.00704082i
\(946\) −3.21765e10 −1.23572
\(947\) 1.30173e10 + 2.25466e10i 0.498076 + 0.862694i 0.999998 0.00221985i \(-0.000706600\pi\)
−0.501921 + 0.864913i \(0.667373\pi\)
\(948\) −3.38915e8 + 5.87017e8i −0.0129200 + 0.0223780i
\(949\) 9.55394e7 1.65479e8i 0.00362870 0.00628509i
\(950\) 1.72273e9 + 2.98386e9i 0.0651907 + 0.112914i
\(951\) 4.94302e10 1.86363
\(952\) 2.69115e9 + 4.24573e9i 0.101090 + 0.159486i
\(953\) −1.26955e10 −0.475145 −0.237572 0.971370i \(-0.576352\pi\)
−0.237572 + 0.971370i \(0.576352\pi\)
\(954\) −1.38129e10 2.39247e10i −0.515070 0.892127i
\(955\) −9.68922e8 + 1.67822e9i −0.0359979 + 0.0623502i
\(956\) −3.10893e9 + 5.38482e9i −0.115082 + 0.199328i
\(957\) 6.05812e9 + 1.04930e10i 0.223433 + 0.386997i
\(958\) −2.68501e10 −0.986659
\(959\) 1.08209e10 + 1.70718e10i 0.396186 + 0.625050i
\(960\) −1.75694e10 −0.640925
\(961\) −7.75862e9 1.34383e10i −0.282002 0.488442i
\(962\) −6.52487e9 + 1.13014e10i −0.236297 + 0.409279i
\(963\) −1.83939e10 + 3.18592e10i −0.663715 + 1.14959i
\(964\) −4.68893e9 8.12146e9i −0.168579 0.291988i
\(965\) 2.01007e10 0.720056
\(966\) 8.66961e10 3.58585e9i 3.09442 0.127989i
\(967\) 4.10863e10 1.46118 0.730591 0.682815i \(-0.239245\pi\)
0.730591 + 0.682815i \(0.239245\pi\)
\(968\) 2.93300e8 + 5.08010e8i 0.0103932 + 0.0180015i
\(969\) 5.66309e9 9.80875e9i 0.199949 0.346322i
\(970\) 2.72457e10 4.71909e10i 0.958509 1.66019i
\(971\) 1.06987e10 + 1.85307e10i 0.375028 + 0.649568i 0.990331 0.138723i \(-0.0442996\pi\)
−0.615303 + 0.788291i \(0.710966\pi\)
\(972\) 1.49412e10 0.521860
\(973\) 1.46539e10 2.79927e10i 0.509985 0.974205i
\(974\) −2.96071e10 −1.02669
\(975\) −6.01259e8 1.04141e9i −0.0207752 0.0359837i
\(976\) −1.23308e10 + 2.13576e10i −0.424538 + 0.735322i
\(977\) −1.16361e10 + 2.01543e10i −0.399187 + 0.691411i −0.993626 0.112729i \(-0.964041\pi\)
0.594439 + 0.804141i \(0.297374\pi\)
\(978\) 2.36490e10 + 4.09614e10i 0.808402 + 1.40019i
\(979\) 2.01512e10 0.686375
\(980\) −6.41237e9 9.24789e9i −0.217634 0.313871i
\(981\) 6.03004e10 2.03929
\(982\) 1.00896e10 + 1.74757e10i 0.340004 + 0.588904i
\(983\) −9.24769e9 + 1.60175e10i −0.310525 + 0.537844i −0.978476 0.206361i \(-0.933838\pi\)
0.667951 + 0.744205i \(0.267171\pi\)
\(984\) −1.63656e10 + 2.83460e10i −0.547582 + 0.948439i
\(985\) −1.24372e10 2.15418e10i −0.414662 0.718216i
\(986\) 2.70903e9 0.0900005
\(987\) 2.95341e10 5.64179e10i 0.977718 1.86770i
\(988\) 3.31126e9 0.109231
\(989\) −2.89750e10 5.01861e10i −0.952436 1.64967i
\(990\) 2.11010e10 3.65481e10i 0.691163 1.19713i
\(991\) −6.38736e9 + 1.10632e10i −0.208480 + 0.361098i −0.951236 0.308465i \(-0.900185\pi\)
0.742756 + 0.669562i \(0.233518\pi\)
\(992\) −1.33597e10 2.31397e10i −0.434517 0.752606i
\(993\) 4.82312e10 1.56317
\(994\) −5.83413e10 + 2.41307e9i −1.88419 + 0.0779322i
\(995\) 3.64745e10 1.17384
\(996\) −3.96049e9 6.85977e9i −0.127011 0.219989i
\(997\) 7.37625e9 1.27760e10i 0.235723 0.408285i −0.723759 0.690052i \(-0.757587\pi\)
0.959483 + 0.281768i \(0.0909208\pi\)
\(998\) −2.33380e10 + 4.04225e10i −0.743200 + 1.28726i
\(999\) −3.72952e9 6.45971e9i −0.118351 0.204991i
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 91.8.e.b.53.8 58
7.2 even 3 inner 91.8.e.b.79.8 yes 58
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.8.e.b.53.8 58 1.1 even 1 trivial
91.8.e.b.79.8 yes 58 7.2 even 3 inner