Properties

Label 69.8.e.a.58.9
Level $69$
Weight $8$
Character 69.58
Analytic conductor $21.555$
Analytic rank $0$
Dimension $140$
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] = [69,8,Mod(4,69)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(69, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("69.4");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 69.e (of order \(11\), degree \(10\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(21.5545667584\)
Analytic rank: \(0\)
Dimension: \(140\)
Relative dimension: \(14\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 58.9
Character \(\chi\) \(=\) 69.58
Dual form 69.8.e.a.25.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(5.04389 - 3.24151i) q^{2} +(-3.84250 + 26.7252i) q^{3} +(-38.2397 + 83.7333i) q^{4} +(-133.665 + 39.2476i) q^{5} +(67.2488 + 147.254i) q^{6} +(-394.589 - 455.380i) q^{7} +(187.765 + 1305.93i) q^{8} +(-699.470 - 205.383i) q^{9} +O(q^{10})\) \(q+(5.04389 - 3.24151i) q^{2} +(-3.84250 + 26.7252i) q^{3} +(-38.2397 + 83.7333i) q^{4} +(-133.665 + 39.2476i) q^{5} +(67.2488 + 147.254i) q^{6} +(-394.589 - 455.380i) q^{7} +(187.765 + 1305.93i) q^{8} +(-699.470 - 205.383i) q^{9} +(-546.970 + 631.236i) q^{10} +(-594.734 - 382.212i) q^{11} +(-2090.85 - 1343.71i) q^{12} +(1356.70 - 1565.71i) q^{13} +(-3466.38 - 1017.82i) q^{14} +(-535.291 - 3723.03i) q^{15} +(-2535.73 - 2926.39i) q^{16} +(-1140.51 - 2497.37i) q^{17} +(-4193.80 + 1231.41i) q^{18} +(20020.6 - 43839.0i) q^{19} +(1824.98 - 12693.0i) q^{20} +(13686.3 - 8795.66i) q^{21} -4238.72 q^{22} +(34894.8 - 46767.2i) q^{23} -35622.7 q^{24} +(-49397.0 + 31745.5i) q^{25} +(1767.76 - 12295.0i) q^{26} +(8176.61 - 17904.3i) q^{27} +(53219.4 - 15626.6i) q^{28} +(-71020.4 - 155513. i) q^{29} +(-14768.2 - 17043.4i) q^{30} +(13700.4 + 95288.0i) q^{31} +(-184313. - 54119.3i) q^{32} +(12500.0 - 14425.7i) q^{33} +(-13847.9 - 8899.49i) q^{34} +(70615.2 + 45381.6i) q^{35} +(43944.9 - 50715.2i) q^{36} +(-199135. - 58471.2i) q^{37} +(-41122.9 - 286016. i) q^{38} +(36630.8 + 42274.2i) q^{39} +(-76352.2 - 167188. i) q^{40} +(-231060. + 67845.4i) q^{41} +(40521.0 - 88728.6i) q^{42} +(-17807.8 + 123856. i) q^{43} +(54746.3 - 35183.3i) q^{44} +101555. q^{45} +(24409.2 - 349001. i) q^{46} -772468. q^{47} +(87951.8 - 56523.2i) q^{48} +(65532.0 - 455785. i) q^{49} +(-146250. + 320242. i) q^{50} +(71125.2 - 20884.2i) q^{51} +(79222.5 + 173473. i) q^{52} +(135834. + 156761. i) q^{53} +(-16795.0 - 116812. i) q^{54} +(94495.9 + 27746.5i) q^{55} +(520605. - 600810. i) q^{56} +(1.09468e6 + 703506. i) q^{57} +(-862316. - 554177. i) q^{58} +(563525. - 650343. i) q^{59} +(332211. + 97545.8i) q^{60} +(-54877.9 - 381684. i) q^{61} +(377980. + 436212. i) q^{62} +(182476. + 399566. i) q^{63} +(-629523. + 184845. i) q^{64} +(-119892. + 262528. i) q^{65} +(16287.3 - 113280. i) q^{66} +(-1.12460e6 + 722734. i) q^{67} +252726. q^{68} +(1.11578e6 + 1.11227e6i) q^{69} +503280. q^{70} +(980570. - 630174. i) q^{71} +(136880. - 952024. i) q^{72} +(-762417. + 1.66946e6i) q^{73} +(-1.19395e6 + 350575. i) q^{74} +(-658597. - 1.44213e6i) q^{75} +(2.90520e6 + 3.35278e6i) q^{76} +(60623.6 + 421646. i) q^{77} +(321794. + 94487.3i) q^{78} +(-5.01173e6 + 5.78384e6i) q^{79} +(453791. + 291634. i) q^{80} +(447077. + 287319. i) q^{81} +(-945521. + 1.09119e6i) q^{82} +(8.06714e6 + 2.36873e6i) q^{83} +(213129. + 1.48234e6i) q^{84} +(250462. + 289049. i) q^{85} +(311659. + 682439. i) q^{86} +(4.42901e6 - 1.30047e6i) q^{87} +(387473. - 848447. i) q^{88} +(-91009.2 + 632983. i) q^{89} +(512234. - 329193. i) q^{90} -1.24833e6 q^{91} +(2.58161e6 + 4.71022e6i) q^{92} -2.59923e6 q^{93} +(-3.89624e6 + 2.50396e6i) q^{94} +(-955478. + 6.64550e6i) q^{95} +(2.15457e6 - 4.71785e6i) q^{96} +(-1.29945e7 + 3.81554e6i) q^{97} +(-1.14690e6 - 2.51135e6i) q^{98} +(337499. + 389494. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 140 q - 16 q^{2} - 378 q^{3} - 740 q^{4} - 6 q^{5} + 1647 q^{6} + 978 q^{7} - 824 q^{8} - 10206 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 140 q - 16 q^{2} - 378 q^{3} - 740 q^{4} - 6 q^{5} + 1647 q^{6} + 978 q^{7} - 824 q^{8} - 10206 q^{9} + 1322 q^{10} + 7892 q^{11} - 19980 q^{12} + 39810 q^{13} - 26296 q^{14} + 135 q^{15} - 142164 q^{16} - 97081 q^{17} - 11664 q^{18} + 120905 q^{19} + 124755 q^{20} + 26406 q^{21} - 837266 q^{22} - 224688 q^{23} - 60264 q^{24} - 180624 q^{25} + 385108 q^{26} - 275562 q^{27} + 1121760 q^{28} - 375654 q^{29} + 35694 q^{30} + 505029 q^{31} - 661528 q^{32} - 360423 q^{33} - 1872759 q^{34} - 964610 q^{35} - 1269189 q^{36} - 28802 q^{37} - 1459868 q^{38} + 1074870 q^{39} + 5371901 q^{40} - 1557480 q^{41} + 883116 q^{42} + 1160786 q^{43} - 4521825 q^{44} - 2009124 q^{45} - 4123580 q^{46} + 811422 q^{47} - 1563111 q^{48} - 10960262 q^{49} + 16636695 q^{50} + 4413852 q^{51} - 4843791 q^{52} + 4291672 q^{53} - 98415 q^{54} + 2093539 q^{55} - 12548382 q^{56} - 4007907 q^{57} - 7414367 q^{58} + 2955424 q^{59} + 7289973 q^{60} + 4919292 q^{61} + 16083211 q^{62} + 712962 q^{63} - 1673596 q^{64} - 13246221 q^{65} + 7219449 q^{66} + 148565 q^{67} - 23039568 q^{68} - 657018 q^{69} + 12781104 q^{70} - 7247645 q^{71} - 600696 q^{72} + 32596055 q^{73} + 32550658 q^{74} - 10061874 q^{75} + 12150569 q^{76} - 43349150 q^{77} - 17201700 q^{78} + 4815410 q^{79} + 36529590 q^{80} - 7440174 q^{81} + 20862470 q^{82} + 35160800 q^{83} - 5346540 q^{84} + 48578363 q^{85} + 76972708 q^{86} + 1505088 q^{87} - 35912212 q^{88} + 1401264 q^{89} + 963738 q^{90} - 91970208 q^{91} - 74293537 q^{92} + 555606 q^{93} - 32520253 q^{94} + 79436789 q^{95} + 41519736 q^{96} + 18296816 q^{97} - 38956823 q^{98} - 9731421 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(28\) \(47\)
\(\chi(n)\) \(e\left(\frac{10}{11}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.04389 3.24151i 0.445821 0.286512i −0.298405 0.954439i \(-0.596455\pi\)
0.744226 + 0.667927i \(0.232818\pi\)
\(3\) −3.84250 + 26.7252i −0.0821655 + 0.571474i
\(4\) −38.2397 + 83.7333i −0.298748 + 0.654166i
\(5\) −133.665 + 39.2476i −0.478214 + 0.140416i −0.511951 0.859014i \(-0.671077\pi\)
0.0337373 + 0.999431i \(0.489259\pi\)
\(6\) 67.2488 + 147.254i 0.127103 + 0.278316i
\(7\) −394.589 455.380i −0.434812 0.501800i 0.495480 0.868619i \(-0.334992\pi\)
−0.930292 + 0.366819i \(0.880447\pi\)
\(8\) 187.765 + 1305.93i 0.129658 + 0.901790i
\(9\) −699.470 205.383i −0.319831 0.0939109i
\(10\) −546.970 + 631.236i −0.172967 + 0.199614i
\(11\) −594.734 382.212i −0.134725 0.0865825i 0.471542 0.881843i \(-0.343697\pi\)
−0.606267 + 0.795261i \(0.707334\pi\)
\(12\) −2090.85 1343.71i −0.349292 0.224476i
\(13\) 1356.70 1565.71i 0.171270 0.197656i −0.663625 0.748065i \(-0.730983\pi\)
0.834895 + 0.550409i \(0.185528\pi\)
\(14\) −3466.38 1017.82i −0.337620 0.0991341i
\(15\) −535.291 3723.03i −0.0409515 0.284824i
\(16\) −2535.73 2926.39i −0.154769 0.178612i
\(17\) −1140.51 2497.37i −0.0563026 0.123286i 0.879390 0.476103i \(-0.157951\pi\)
−0.935692 + 0.352817i \(0.885224\pi\)
\(18\) −4193.80 + 1231.41i −0.169494 + 0.0497679i
\(19\) 20020.6 43839.0i 0.669637 1.46630i −0.203624 0.979049i \(-0.565272\pi\)
0.873261 0.487252i \(-0.162001\pi\)
\(20\) 1824.98 12693.0i 0.0510097 0.354781i
\(21\) 13686.3 8795.66i 0.322492 0.207253i
\(22\) −4238.72 −0.0848701
\(23\) 34894.8 46767.2i 0.598017 0.801483i
\(24\) −35622.7 −0.526003
\(25\) −49397.0 + 31745.5i −0.632282 + 0.406343i
\(26\) 1767.76 12295.0i 0.0197250 0.137190i
\(27\) 8176.61 17904.3i 0.0799467 0.175059i
\(28\) 53219.4 15626.6i 0.458160 0.134528i
\(29\) −71020.4 155513.i −0.540742 1.18406i −0.960973 0.276642i \(-0.910778\pi\)
0.420231 0.907417i \(-0.361949\pi\)
\(30\) −14768.2 17043.4i −0.0998625 0.115247i
\(31\) 13700.4 + 95288.0i 0.0825973 + 0.574477i 0.988526 + 0.151048i \(0.0482647\pi\)
−0.905929 + 0.423429i \(0.860826\pi\)
\(32\) −184313. 54119.3i −0.994332 0.291962i
\(33\) 12500.0 14425.7i 0.0605494 0.0698777i
\(34\) −13847.9 8899.49i −0.0604237 0.0388319i
\(35\) 70615.2 + 45381.6i 0.278394 + 0.178913i
\(36\) 43944.9 50715.2i 0.156982 0.181167i
\(37\) −199135. 58471.2i −0.646310 0.189774i −0.0578821 0.998323i \(-0.518435\pi\)
−0.588428 + 0.808550i \(0.700253\pi\)
\(38\) −41122.9 286016.i −0.121574 0.845567i
\(39\) 36630.8 + 42274.2i 0.0988827 + 0.114117i
\(40\) −76352.2 167188.i −0.188630 0.413043i
\(41\) −231060. + 67845.4i −0.523579 + 0.153737i −0.532833 0.846221i \(-0.678872\pi\)
0.00925409 + 0.999957i \(0.497054\pi\)
\(42\) 40521.0 88728.6i 0.0843933 0.184795i
\(43\) −17807.8 + 123856.i −0.0341562 + 0.237562i −0.999747 0.0225055i \(-0.992836\pi\)
0.965590 + 0.260067i \(0.0837448\pi\)
\(44\) 54746.3 35183.3i 0.0968881 0.0622662i
\(45\) 101555. 0.166134
\(46\) 24409.2 349001.i 0.0369744 0.528657i
\(47\) −772468. −1.08527 −0.542635 0.839968i \(-0.682573\pi\)
−0.542635 + 0.839968i \(0.682573\pi\)
\(48\) 87951.8 56523.2i 0.114789 0.0737704i
\(49\) 65532.0 455785.i 0.0795733 0.553444i
\(50\) −146250. + 320242.i −0.165462 + 0.362312i
\(51\) 71125.2 20884.2i 0.0750806 0.0220457i
\(52\) 79222.5 + 173473.i 0.0781334 + 0.171088i
\(53\) 135834. + 156761.i 0.125327 + 0.144635i 0.814945 0.579538i \(-0.196767\pi\)
−0.689618 + 0.724173i \(0.742222\pi\)
\(54\) −16795.0 116812.i −0.0145145 0.100951i
\(55\) 94495.9 + 27746.5i 0.0765850 + 0.0224874i
\(56\) 520605. 600810.i 0.396141 0.457171i
\(57\) 1.09468e6 + 703506.i 0.782931 + 0.503160i
\(58\) −862316. 554177.i −0.580321 0.372950i
\(59\) 563525. 650343.i 0.357216 0.412250i −0.548489 0.836158i \(-0.684797\pi\)
0.905705 + 0.423908i \(0.139342\pi\)
\(60\) 332211. + 97545.8i 0.198556 + 0.0583014i
\(61\) −54877.9 381684.i −0.0309559 0.215303i 0.968472 0.249122i \(-0.0801421\pi\)
−0.999428 + 0.0338192i \(0.989233\pi\)
\(62\) 377980. + 436212.i 0.201418 + 0.232449i
\(63\) 182476. + 399566.i 0.0919419 + 0.201325i
\(64\) −629523. + 184845.i −0.300180 + 0.0881408i
\(65\) −119892. + 262528.i −0.0541496 + 0.118571i
\(66\) 16287.3 113280.i 0.00697340 0.0485011i
\(67\) −1.12460e6 + 722734.i −0.456809 + 0.293573i −0.748737 0.662867i \(-0.769340\pi\)
0.291928 + 0.956440i \(0.405703\pi\)
\(68\) 252726. 0.0974695
\(69\) 1.11578e6 + 1.11227e6i 0.408890 + 0.407606i
\(70\) 503280. 0.175375
\(71\) 980570. 630174.i 0.325143 0.208957i −0.367878 0.929874i \(-0.619916\pi\)
0.693021 + 0.720917i \(0.256279\pi\)
\(72\) 136880. 952024.i 0.0432193 0.300597i
\(73\) −762417. + 1.66946e6i −0.229384 + 0.502280i −0.988968 0.148129i \(-0.952675\pi\)
0.759585 + 0.650409i \(0.225402\pi\)
\(74\) −1.19395e6 + 350575.i −0.342511 + 0.100570i
\(75\) −658597. 1.44213e6i −0.180262 0.394720i
\(76\) 2.90520e6 + 3.35278e6i 0.759152 + 0.876108i
\(77\) 60623.6 + 421646.i 0.0151330 + 0.105252i
\(78\) 321794. + 94487.3i 0.0767798 + 0.0225446i
\(79\) −5.01173e6 + 5.78384e6i −1.14365 + 1.31984i −0.203501 + 0.979075i \(0.565232\pi\)
−0.940148 + 0.340766i \(0.889314\pi\)
\(80\) 453791. + 291634.i 0.0990926 + 0.0636830i
\(81\) 447077. + 287319.i 0.0934726 + 0.0600712i
\(82\) −945521. + 1.09119e6i −0.189375 + 0.218550i
\(83\) 8.06714e6 + 2.36873e6i 1.54862 + 0.454717i 0.940689 0.339269i \(-0.110180\pi\)
0.607935 + 0.793987i \(0.291998\pi\)
\(84\) 213129. + 1.48234e6i 0.0392342 + 0.272880i
\(85\) 250462. + 289049.i 0.0442360 + 0.0510511i
\(86\) 311659. + 682439.i 0.0528367 + 0.115696i
\(87\) 4.42901e6 1.30047e6i 0.721089 0.211731i
\(88\) 387473. 848447.i 0.0606111 0.132720i
\(89\) −91009.2 + 632983.i −0.0136842 + 0.0951759i −0.995519 0.0945623i \(-0.969855\pi\)
0.981835 + 0.189738i \(0.0607639\pi\)
\(90\) 512234. 329193.i 0.0740662 0.0475994i
\(91\) −1.24833e6 −0.173654
\(92\) 2.58161e6 + 4.71022e6i 0.345647 + 0.630644i
\(93\) −2.59923e6 −0.335085
\(94\) −3.89624e6 + 2.50396e6i −0.483836 + 0.310943i
\(95\) −955478. + 6.64550e6i −0.114337 + 0.795234i
\(96\) 2.15457e6 4.71785e6i 0.248549 0.544246i
\(97\) −1.29945e7 + 3.81554e6i −1.44564 + 0.424477i −0.908097 0.418761i \(-0.862465\pi\)
−0.537540 + 0.843238i \(0.680646\pi\)
\(98\) −1.14690e6 2.51135e6i −0.123093 0.269536i
\(99\) 337499. + 389494.i 0.0349582 + 0.0403439i
\(100\) −769230. 5.35011e6i −0.0769230 0.535011i
\(101\) −1.50996e6 443365.i −0.145828 0.0428190i 0.208004 0.978128i \(-0.433303\pi\)
−0.353832 + 0.935309i \(0.615122\pi\)
\(102\) 291051. 335891.i 0.0271562 0.0313399i
\(103\) 1.53711e6 + 987840.i 0.138604 + 0.0890751i 0.608105 0.793857i \(-0.291930\pi\)
−0.469501 + 0.882932i \(0.655566\pi\)
\(104\) 2.29945e6 + 1.47777e6i 0.200451 + 0.128822i
\(105\) −1.48417e6 + 1.71283e6i −0.125119 + 0.144394i
\(106\) 1.19328e6 + 350378.i 0.0973129 + 0.0285737i
\(107\) −3.11384e6 2.16572e7i −0.245727 1.70907i −0.622380 0.782715i \(-0.713834\pi\)
0.376653 0.926355i \(-0.377075\pi\)
\(108\) 1.18651e6 + 1.36931e6i 0.0906336 + 0.104597i
\(109\) −2.64356e6 5.78860e6i −0.195523 0.428135i 0.786323 0.617815i \(-0.211982\pi\)
−0.981846 + 0.189680i \(0.939255\pi\)
\(110\) 566568. 166359.i 0.0405861 0.0119172i
\(111\) 2.32783e6 5.09723e6i 0.161555 0.353756i
\(112\) −332047. + 2.30944e6i −0.0223325 + 0.155326i
\(113\) 7.36797e6 4.73511e6i 0.480367 0.308713i −0.277954 0.960594i \(-0.589656\pi\)
0.758321 + 0.651881i \(0.226020\pi\)
\(114\) 7.80185e6 0.493208
\(115\) −2.82872e6 + 7.62068e6i −0.173439 + 0.467252i
\(116\) 1.57374e7 0.936117
\(117\) −1.27054e6 + 816526.i −0.0733395 + 0.0471324i
\(118\) 734266. 5.10693e6i 0.0411402 0.286136i
\(119\) −687220. + 1.50480e6i −0.0373836 + 0.0818587i
\(120\) 4.76151e6 1.39811e6i 0.251542 0.0738594i
\(121\) −7.88764e6 1.72715e7i −0.404761 0.886302i
\(122\) −1.51403e6 1.74729e6i −0.0754876 0.0871173i
\(123\) −925332. 6.43582e6i −0.0448363 0.311843i
\(124\) −8.50268e6 2.49661e6i −0.400479 0.117591i
\(125\) 1.24838e7 1.44071e7i 0.571693 0.659769i
\(126\) 2.21559e6 + 1.42387e6i 0.0986715 + 0.0634123i
\(127\) −3.42558e7 2.20149e7i −1.48396 0.953681i −0.996764 0.0803868i \(-0.974384\pi\)
−0.487193 0.873294i \(-0.661979\pi\)
\(128\) 1.35257e7 1.56095e7i 0.570066 0.657891i
\(129\) −3.24164e6 951832.i −0.132954 0.0390388i
\(130\) 246262. + 1.71279e6i 0.00983097 + 0.0683759i
\(131\) −8.89120e6 1.02610e7i −0.345550 0.398786i 0.556197 0.831051i \(-0.312260\pi\)
−0.901747 + 0.432265i \(0.857715\pi\)
\(132\) 729918. + 1.59830e6i 0.0276226 + 0.0604852i
\(133\) −2.78633e7 + 8.18141e6i −1.02696 + 0.301542i
\(134\) −3.32959e6 + 7.29078e6i −0.119543 + 0.261762i
\(135\) −390227. + 2.71409e6i −0.0136505 + 0.0949414i
\(136\) 3.04725e6 1.95835e6i 0.103878 0.0667581i
\(137\) −1.18532e7 −0.393836 −0.196918 0.980420i \(-0.563093\pi\)
−0.196918 + 0.980420i \(0.563093\pi\)
\(138\) 9.23332e6 + 1.99338e6i 0.299076 + 0.0645673i
\(139\) −5.40035e7 −1.70557 −0.852785 0.522262i \(-0.825088\pi\)
−0.852785 + 0.522262i \(0.825088\pi\)
\(140\) −6.50026e6 + 4.17746e6i −0.200208 + 0.128666i
\(141\) 2.96821e6 2.06443e7i 0.0891718 0.620204i
\(142\) 2.90317e6 6.35706e6i 0.0850870 0.186315i
\(143\) −1.40531e6 + 412636.i −0.0401879 + 0.0118002i
\(144\) 1.17264e6 + 2.56772e6i 0.0327261 + 0.0716603i
\(145\) 1.55964e7 + 1.79992e7i 0.424852 + 0.490305i
\(146\) 1.56603e6 + 1.08919e7i 0.0416451 + 0.289648i
\(147\) 1.19291e7 + 3.50271e6i 0.309741 + 0.0909480i
\(148\) 1.25108e7 1.44383e7i 0.317227 0.366100i
\(149\) 2.67237e7 + 1.71743e7i 0.661828 + 0.425331i 0.827971 0.560771i \(-0.189495\pi\)
−0.166143 + 0.986102i \(0.553131\pi\)
\(150\) −7.99655e6 5.13907e6i −0.193457 0.124327i
\(151\) −1.93071e6 + 2.22816e6i −0.0456351 + 0.0526657i −0.778108 0.628130i \(-0.783821\pi\)
0.732473 + 0.680796i \(0.238366\pi\)
\(152\) 6.10099e7 + 1.79141e7i 1.40912 + 0.413755i
\(153\) 284836. + 1.98108e6i 0.00642948 + 0.0447180i
\(154\) 1.67255e6 + 1.93023e6i 0.0369026 + 0.0425878i
\(155\) −5.57108e6 1.21990e7i −0.120165 0.263125i
\(156\) −4.94051e6 + 1.45066e6i −0.104192 + 0.0305936i
\(157\) −1.40835e7 + 3.08386e7i −0.290444 + 0.635984i −0.997461 0.0712127i \(-0.977313\pi\)
0.707017 + 0.707196i \(0.250040\pi\)
\(158\) −6.53021e6 + 4.54186e7i −0.131713 + 0.916082i
\(159\) −4.71142e6 + 3.02784e6i −0.0929526 + 0.0597370i
\(160\) 2.67603e7 0.516500
\(161\) −3.50660e7 + 2.56342e6i −0.662209 + 0.0484094i
\(162\) 3.18635e6 0.0588832
\(163\) −2.96550e6 + 1.90581e6i −0.0536341 + 0.0344686i −0.567183 0.823592i \(-0.691967\pi\)
0.513549 + 0.858060i \(0.328330\pi\)
\(164\) 3.15476e6 2.19418e7i 0.0558486 0.388436i
\(165\) −1.10463e6 + 2.41880e6i −0.0191436 + 0.0419186i
\(166\) 4.83680e7 1.42021e7i 0.820691 0.240977i
\(167\) 1.00942e7 + 2.21032e7i 0.167712 + 0.367238i 0.974762 0.223245i \(-0.0716649\pi\)
−0.807051 + 0.590482i \(0.798938\pi\)
\(168\) 1.40563e7 + 1.62219e7i 0.228712 + 0.263948i
\(169\) 8.31922e6 + 5.78614e7i 0.132580 + 0.922116i
\(170\) 2.20026e6 + 646054.i 0.0343481 + 0.0100855i
\(171\) −2.30076e7 + 2.65522e7i −0.351872 + 0.406082i
\(172\) −9.68988e6 6.22731e6i −0.145201 0.0933149i
\(173\) −3.96114e7 2.54567e7i −0.581646 0.373801i 0.216484 0.976286i \(-0.430541\pi\)
−0.798130 + 0.602485i \(0.794177\pi\)
\(174\) 1.81239e7 2.09161e7i 0.260813 0.300995i
\(175\) 3.39478e7 + 9.96796e6i 0.478826 + 0.140596i
\(176\) 389583. + 2.70961e6i 0.00538648 + 0.0374638i
\(177\) 1.52152e7 + 1.75593e7i 0.206239 + 0.238012i
\(178\) 1.59278e6 + 3.48770e6i 0.0211683 + 0.0463521i
\(179\) −5.73106e7 + 1.68279e7i −0.746878 + 0.219303i −0.632957 0.774187i \(-0.718159\pi\)
−0.113920 + 0.993490i \(0.536341\pi\)
\(180\) −3.88345e6 + 8.50357e6i −0.0496322 + 0.108679i
\(181\) 1.78638e6 1.24246e7i 0.0223924 0.155742i −0.975557 0.219745i \(-0.929478\pi\)
0.997950 + 0.0640026i \(0.0203866\pi\)
\(182\) −6.29644e6 + 4.04648e6i −0.0774186 + 0.0497539i
\(183\) 1.04115e7 0.125583
\(184\) 6.76268e7 + 3.67890e7i 0.800307 + 0.435368i
\(185\) 2.89122e7 0.335722
\(186\) −1.31102e7 + 8.42544e6i −0.149388 + 0.0960058i
\(187\) −276226. + 1.92119e6i −0.00308900 + 0.0214845i
\(188\) 2.95389e7 6.46813e7i 0.324222 0.709947i
\(189\) −1.13796e7 + 3.34137e6i −0.122606 + 0.0360004i
\(190\) 1.67221e7 + 3.66163e7i 0.176870 + 0.387291i
\(191\) −3.64438e7 4.20583e7i −0.378448 0.436752i 0.534288 0.845303i \(-0.320580\pi\)
−0.912736 + 0.408550i \(0.866034\pi\)
\(192\) −2.52106e6 1.75344e7i −0.0257057 0.178787i
\(193\) 1.41319e8 + 4.14951e7i 1.41498 + 0.415477i 0.897802 0.440399i \(-0.145163\pi\)
0.517181 + 0.855876i \(0.326981\pi\)
\(194\) −5.31748e7 + 6.13670e7i −0.522877 + 0.603433i
\(195\) −6.55541e6 4.21291e6i −0.0633110 0.0406875i
\(196\) 3.56584e7 + 2.29163e7i 0.338272 + 0.217394i
\(197\) −4.08959e7 + 4.71964e7i −0.381108 + 0.439822i −0.913601 0.406613i \(-0.866710\pi\)
0.532493 + 0.846434i \(0.321255\pi\)
\(198\) 2.96486e6 + 870560.i 0.0271441 + 0.00797023i
\(199\) 2.26326e6 + 1.57413e7i 0.0203586 + 0.141597i 0.997466 0.0711516i \(-0.0226674\pi\)
−0.977107 + 0.212749i \(0.931758\pi\)
\(200\) −5.07325e7 5.85484e7i −0.448416 0.517500i
\(201\) −1.49939e7 3.28321e7i −0.130236 0.285176i
\(202\) −9.05325e6 + 2.65827e6i −0.0772813 + 0.0226918i
\(203\) −4.27936e7 + 9.37049e7i −0.359040 + 0.786188i
\(204\) −971100. + 6.75415e6i −0.00800864 + 0.0557013i
\(205\) 2.82219e7 1.81371e7i 0.228796 0.147038i
\(206\) 1.09551e7 0.0873134
\(207\) −3.40131e7 + 2.55455e7i −0.266532 + 0.200179i
\(208\) −8.02209e6 −0.0618110
\(209\) −2.86627e7 + 1.84204e7i −0.217173 + 0.139569i
\(210\) −1.93385e6 + 1.34503e7i −0.0144097 + 0.100222i
\(211\) −3.91238e6 + 8.56692e6i −0.0286716 + 0.0627821i −0.923426 0.383777i \(-0.874623\pi\)
0.894754 + 0.446559i \(0.147351\pi\)
\(212\) −1.83204e7 + 5.37935e6i −0.132056 + 0.0387752i
\(213\) 1.30737e7 + 2.86274e7i 0.0926977 + 0.202980i
\(214\) −8.59080e7 9.91431e7i −0.599219 0.691536i
\(215\) −2.48076e6 1.72541e7i −0.0170236 0.118402i
\(216\) 2.49170e7 + 7.31631e6i 0.168232 + 0.0493974i
\(217\) 3.79862e7 4.38384e7i 0.252358 0.291237i
\(218\) −3.20976e7 2.06279e7i −0.209834 0.134852i
\(219\) −4.16870e7 2.67906e7i −0.268192 0.172357i
\(220\) −5.93680e6 + 6.85144e6i −0.0375901 + 0.0433813i
\(221\) −5.45750e6 1.60247e6i −0.0340111 0.00998656i
\(222\) −4.78143e6 3.32556e7i −0.0293307 0.203999i
\(223\) −1.14615e8 1.32273e8i −0.692111 0.798738i 0.295553 0.955326i \(-0.404496\pi\)
−0.987664 + 0.156588i \(0.949951\pi\)
\(224\) 4.80831e7 + 1.05287e8i 0.285841 + 0.625905i
\(225\) 4.10717e7 1.20597e7i 0.240383 0.0705829i
\(226\) 2.18143e7 4.77667e7i 0.125708 0.275262i
\(227\) 2.38479e7 1.65866e8i 0.135319 0.941168i −0.803143 0.595786i \(-0.796840\pi\)
0.938462 0.345381i \(-0.112250\pi\)
\(228\) −1.00767e8 + 6.47590e7i −0.563049 + 0.361850i
\(229\) 1.96893e8 1.08344 0.541721 0.840558i \(-0.317773\pi\)
0.541721 + 0.840558i \(0.317773\pi\)
\(230\) 1.04348e7 + 4.76072e7i 0.0565504 + 0.258003i
\(231\) −1.15015e7 −0.0613922
\(232\) 1.89754e8 1.21948e8i 0.997662 0.641158i
\(233\) 2.71760e7 1.89013e8i 0.140747 0.978918i −0.789961 0.613156i \(-0.789900\pi\)
0.930709 0.365761i \(-0.119191\pi\)
\(234\) −3.76168e6 + 8.23694e6i −0.0191923 + 0.0420252i
\(235\) 1.03252e8 3.03175e7i 0.518992 0.152390i
\(236\) 3.29063e7 + 7.20547e7i 0.162962 + 0.356837i
\(237\) −1.35317e8 1.56164e8i −0.660286 0.762011i
\(238\) 1.41157e6 + 9.81768e6i 0.00678708 + 0.0472052i
\(239\) 1.62757e8 + 4.77897e7i 0.771163 + 0.226434i 0.643564 0.765392i \(-0.277455\pi\)
0.127598 + 0.991826i \(0.459273\pi\)
\(240\) −9.53767e6 + 1.10071e7i −0.0445351 + 0.0513963i
\(241\) −9.97259e7 6.40899e7i −0.458932 0.294938i 0.290674 0.956822i \(-0.406121\pi\)
−0.749606 + 0.661885i \(0.769757\pi\)
\(242\) −9.57702e7 6.15478e7i −0.434387 0.279163i
\(243\) −9.39654e6 + 1.08442e7i −0.0420093 + 0.0484814i
\(244\) 3.40582e7 + 1.00004e7i 0.150092 + 0.0440709i
\(245\) 9.12912e6 + 6.34944e7i 0.0396595 + 0.275838i
\(246\) −2.55291e7 2.94621e7i −0.109336 0.126180i
\(247\) −4.14774e7 9.08228e7i −0.175135 0.383491i
\(248\) −1.21867e8 + 3.57834e7i −0.507348 + 0.148971i
\(249\) −9.43026e7 + 2.06494e8i −0.387102 + 0.847636i
\(250\) 1.62663e7 1.13134e8i 0.0658412 0.457936i
\(251\) −4.75611e7 + 3.05657e7i −0.189843 + 0.122005i −0.632110 0.774879i \(-0.717811\pi\)
0.442267 + 0.896884i \(0.354174\pi\)
\(252\) −4.04348e7 −0.159167
\(253\) −3.86282e7 + 1.44768e7i −0.149962 + 0.0562020i
\(254\) −2.44144e8 −0.934820
\(255\) −8.68729e6 + 5.58298e6i −0.0328090 + 0.0210851i
\(256\) 2.95755e7 2.05702e8i 0.110177 0.766301i
\(257\) 1.50055e8 3.28575e8i 0.551423 1.20745i −0.404692 0.914453i \(-0.632621\pi\)
0.956114 0.292994i \(-0.0946516\pi\)
\(258\) −1.94358e7 + 5.70688e6i −0.0704587 + 0.0206885i
\(259\) 5.19497e7 + 1.13754e8i 0.185795 + 0.406834i
\(260\) −1.73977e7 2.00780e7i −0.0613881 0.0708456i
\(261\) 1.77369e7 + 1.23363e8i 0.0617500 + 0.429480i
\(262\) −7.81074e7 2.29344e7i −0.268310 0.0787830i
\(263\) −1.02013e8 + 1.17729e8i −0.345788 + 0.399060i −0.901828 0.432095i \(-0.857775\pi\)
0.556040 + 0.831155i \(0.312320\pi\)
\(264\) 2.11860e7 + 1.36154e7i 0.0708657 + 0.0455426i
\(265\) −2.43088e7 1.56223e7i −0.0802422 0.0515685i
\(266\) −1.14019e8 + 1.31585e8i −0.371443 + 0.428669i
\(267\) −1.65669e7 4.86447e6i −0.0532661 0.0156404i
\(268\) −1.75127e7 1.21803e8i −0.0555751 0.386533i
\(269\) 4.49418e7 + 5.18656e7i 0.140772 + 0.162460i 0.821758 0.569837i \(-0.192994\pi\)
−0.680985 + 0.732297i \(0.738448\pi\)
\(270\) 6.82948e6 + 1.49545e7i 0.0211161 + 0.0462379i
\(271\) −4.13661e8 + 1.21462e8i −1.26256 + 0.370721i −0.843447 0.537212i \(-0.819477\pi\)
−0.419114 + 0.907934i \(0.637659\pi\)
\(272\) −4.41625e6 + 9.67024e6i −0.0133065 + 0.0291371i
\(273\) 4.79671e6 3.33619e7i 0.0142684 0.0992387i
\(274\) −5.97865e7 + 3.84224e7i −0.175580 + 0.112839i
\(275\) 4.15116e7 0.120366
\(276\) −1.35801e8 + 5.08948e7i −0.388797 + 0.145711i
\(277\) 3.53349e8 0.998905 0.499453 0.866341i \(-0.333534\pi\)
0.499453 + 0.866341i \(0.333534\pi\)
\(278\) −2.72387e8 + 1.75053e8i −0.760379 + 0.488666i
\(279\) 9.98756e6 6.94650e7i 0.0275324 0.191492i
\(280\) −4.60063e7 + 1.00740e8i −0.125246 + 0.274251i
\(281\) 3.57064e8 1.04844e8i 0.960007 0.281884i 0.236060 0.971739i \(-0.424144\pi\)
0.723948 + 0.689855i \(0.242326\pi\)
\(282\) −5.19475e7 1.13749e8i −0.137941 0.302049i
\(283\) 3.92479e8 + 4.52944e8i 1.02935 + 1.18793i 0.981966 + 0.189058i \(0.0605433\pi\)
0.0473850 + 0.998877i \(0.484911\pi\)
\(284\) 1.52698e7 + 1.06204e8i 0.0395567 + 0.275123i
\(285\) −1.73931e8 5.10707e7i −0.445061 0.130682i
\(286\) −5.75065e6 + 6.63661e6i −0.0145357 + 0.0167751i
\(287\) 1.22069e8 + 7.84491e7i 0.304803 + 0.195885i
\(288\) 1.17806e8 + 7.57096e7i 0.290600 + 0.186757i
\(289\) 2.63779e8 3.04417e8i 0.642831 0.741867i
\(290\) 1.37011e8 + 4.02302e7i 0.329886 + 0.0968632i
\(291\) −5.20394e7 3.61942e8i −0.123796 0.861021i
\(292\) −1.10635e8 1.27679e8i −0.260047 0.300110i
\(293\) −1.67913e8 3.67678e8i −0.389984 0.853946i −0.998188 0.0601657i \(-0.980837\pi\)
0.608204 0.793781i \(-0.291890\pi\)
\(294\) 7.15233e7 2.10011e7i 0.164147 0.0481978i
\(295\) −4.97992e7 + 1.09045e8i −0.112939 + 0.247303i
\(296\) 3.89690e7 2.71035e8i 0.0873369 0.607441i
\(297\) −1.17061e7 + 7.52308e6i −0.0259278 + 0.0166628i
\(298\) 1.90462e8 0.416919
\(299\) −2.58823e7 1.18084e8i −0.0559955 0.255472i
\(300\) 1.45938e8 0.312065
\(301\) 6.34282e7 4.07628e7i 0.134060 0.0861552i
\(302\) −2.51569e6 + 1.74970e7i −0.00525574 + 0.0365545i
\(303\) 1.76510e7 3.86504e7i 0.0364519 0.0798186i
\(304\) −1.79057e8 + 5.25758e7i −0.365539 + 0.107332i
\(305\) 2.23154e7 + 4.88640e7i 0.0450356 + 0.0986142i
\(306\) 7.85838e6 + 9.06905e6i 0.0156786 + 0.0180941i
\(307\) 1.23768e8 + 8.60826e8i 0.244132 + 1.69797i 0.630954 + 0.775820i \(0.282664\pi\)
−0.386822 + 0.922154i \(0.626427\pi\)
\(308\) −3.76241e7 1.10474e7i −0.0733733 0.0215443i
\(309\) −3.23065e7 + 3.72837e7i −0.0622925 + 0.0718894i
\(310\) −6.76430e7 4.34715e7i −0.128960 0.0828779i
\(311\) 7.58539e8 + 4.87483e8i 1.42993 + 0.918963i 0.999869 + 0.0161658i \(0.00514595\pi\)
0.430066 + 0.902798i \(0.358490\pi\)
\(312\) −4.83293e7 + 5.57749e7i −0.0900884 + 0.103968i
\(313\) 3.60755e8 + 1.05927e8i 0.664979 + 0.195255i 0.596766 0.802415i \(-0.296452\pi\)
0.0682129 + 0.997671i \(0.478270\pi\)
\(314\) 2.89280e7 + 2.01198e8i 0.0527308 + 0.366751i
\(315\) −4.00726e7 4.62463e7i −0.0722372 0.0833662i
\(316\) −2.92653e8 6.40821e8i −0.521733 1.14244i
\(317\) −1.67085e8 + 4.90607e7i −0.294599 + 0.0865021i −0.425692 0.904868i \(-0.639969\pi\)
0.131093 + 0.991370i \(0.458151\pi\)
\(318\) −1.39491e7 + 3.05442e7i −0.0243249 + 0.0532640i
\(319\) −1.72007e7 + 1.19634e8i −0.0296674 + 0.206341i
\(320\) 7.68905e7 4.94145e7i 0.131174 0.0843004i
\(321\) 5.90758e8 0.996879
\(322\) −1.68559e8 + 1.26596e8i −0.281357 + 0.211313i
\(323\) −1.32316e8 −0.218476
\(324\) −4.11542e7 + 2.64482e7i −0.0672213 + 0.0432005i
\(325\) −1.73124e7 + 1.20411e8i −0.0279747 + 0.194569i
\(326\) −8.77994e6 + 1.92254e7i −0.0140356 + 0.0307336i
\(327\) 1.64859e8 4.84070e7i 0.260733 0.0765581i
\(328\) −1.31986e8 2.89010e8i −0.206524 0.452225i
\(329\) 3.04807e8 + 3.51766e8i 0.471889 + 0.544589i
\(330\) 2.26894e6 + 1.57809e7i 0.00347556 + 0.0241731i
\(331\) −2.32608e7 6.82999e6i −0.0352555 0.0103519i 0.264057 0.964507i \(-0.414939\pi\)
−0.299313 + 0.954155i \(0.596757\pi\)
\(332\) −5.06826e8 + 5.84908e8i −0.760109 + 0.877212i
\(333\) 1.27280e8 + 8.17978e7i 0.188888 + 0.121391i
\(334\) 1.22562e8 + 7.87656e7i 0.179987 + 0.115671i
\(335\) 1.21953e8 1.40742e8i 0.177230 0.204534i
\(336\) −6.04443e7 1.77480e7i −0.0869296 0.0255248i
\(337\) 1.35589e8 + 9.43044e8i 0.192984 + 1.34223i 0.824057 + 0.566507i \(0.191706\pi\)
−0.631073 + 0.775723i \(0.717385\pi\)
\(338\) 2.29520e8 + 2.64880e8i 0.323304 + 0.373113i
\(339\) 9.82352e7 + 2.15105e8i 0.136952 + 0.299883i
\(340\) −3.37806e7 + 9.91888e6i −0.0466113 + 0.0136863i
\(341\) 2.82722e7 6.19075e7i 0.0386117 0.0845479i
\(342\) −2.99786e7 + 2.08506e8i −0.0405247 + 0.281856i
\(343\) −6.50868e8 + 4.18287e8i −0.870890 + 0.559687i
\(344\) −1.65091e8 −0.218659
\(345\) −1.92795e8 1.04880e8i −0.252771 0.137508i
\(346\) −2.82314e8 −0.366408
\(347\) −3.97247e8 + 2.55295e8i −0.510396 + 0.328012i −0.770363 0.637606i \(-0.779925\pi\)
0.259967 + 0.965618i \(0.416288\pi\)
\(348\) −6.04710e7 + 4.20585e8i −0.0769165 + 0.534966i
\(349\) −2.25215e8 + 4.93153e8i −0.283602 + 0.621001i −0.996798 0.0799634i \(-0.974520\pi\)
0.713196 + 0.700965i \(0.247247\pi\)
\(350\) 2.03540e8 5.97647e7i 0.253753 0.0745087i
\(351\) −1.69398e7 3.70929e7i −0.0209090 0.0457842i
\(352\) 8.89323e7 + 1.02633e8i 0.108683 + 0.125426i
\(353\) −1.53844e8 1.07001e9i −0.186153 1.29472i −0.841855 0.539703i \(-0.818536\pi\)
0.655702 0.755020i \(-0.272373\pi\)
\(354\) 1.33662e8 + 3.92468e7i 0.160139 + 0.0470211i
\(355\) −1.06335e8 + 1.22717e8i −0.126147 + 0.145581i
\(356\) −4.95216e7 3.18256e7i −0.0581727 0.0373853i
\(357\) −3.75755e7 2.41483e7i −0.0437085 0.0280897i
\(358\) −2.34520e8 + 2.70651e8i −0.270141 + 0.311759i
\(359\) 1.17365e9 + 3.44614e8i 1.33877 + 0.393099i 0.871232 0.490872i \(-0.163322\pi\)
0.467542 + 0.883971i \(0.345140\pi\)
\(360\) 1.90685e7 + 1.32624e8i 0.0215406 + 0.149818i
\(361\) −9.35673e8 1.07982e9i −1.04676 1.20803i
\(362\) −3.12641e7 6.84588e7i −0.0346390 0.0758489i
\(363\) 4.91893e8 1.44433e8i 0.539756 0.158487i
\(364\) 4.77358e7 1.04527e8i 0.0518787 0.113599i
\(365\) 3.63861e7 2.53071e8i 0.0391661 0.272407i
\(366\) 5.25142e7 3.37488e7i 0.0559877 0.0359811i
\(367\) −2.70435e8 −0.285583 −0.142791 0.989753i \(-0.545608\pi\)
−0.142791 + 0.989753i \(0.545608\pi\)
\(368\) −2.25343e8 + 1.64732e7i −0.235709 + 0.0172310i
\(369\) 1.75554e8 0.181894
\(370\) 1.45830e8 9.37191e7i 0.149672 0.0961883i
\(371\) 1.77872e7 1.23712e8i 0.0180841 0.125778i
\(372\) 9.93939e7 2.17642e8i 0.100106 0.219201i
\(373\) −6.43271e8 + 1.88881e8i −0.641820 + 0.188455i −0.586418 0.810009i \(-0.699462\pi\)
−0.0554021 + 0.998464i \(0.517644\pi\)
\(374\) 4.83431e6 + 1.05857e7i 0.00477841 + 0.0104633i
\(375\) 3.37064e8 + 3.88992e8i 0.330067 + 0.380918i
\(376\) −1.45042e8 1.00879e9i −0.140714 0.978686i
\(377\) −3.39842e8 9.97865e7i −0.326649 0.0959129i
\(378\) −4.65666e7 + 5.37407e7i −0.0443459 + 0.0511779i
\(379\) −3.38392e8 2.17471e8i −0.319288 0.205194i 0.371173 0.928564i \(-0.378956\pi\)
−0.690461 + 0.723370i \(0.742592\pi\)
\(380\) −5.19912e8 3.34127e8i −0.486057 0.312370i
\(381\) 7.19979e8 8.30901e8i 0.666934 0.769683i
\(382\) −3.20151e8 9.40047e7i −0.293855 0.0862835i
\(383\) −1.31256e8 9.12906e8i −0.119378 0.830291i −0.958244 0.285953i \(-0.907690\pi\)
0.838866 0.544338i \(-0.183219\pi\)
\(384\) 3.65194e8 + 4.21456e8i 0.329128 + 0.379834i
\(385\) −2.46518e7 5.39800e7i −0.0220159 0.0482081i
\(386\) 8.47306e8 2.48792e8i 0.749868 0.220181i
\(387\) 3.78939e7 8.29760e7i 0.0332339 0.0727720i
\(388\) 1.77419e8 1.23398e9i 0.154202 1.07250i
\(389\) −5.62174e8 + 3.61287e8i −0.484225 + 0.311193i −0.759879 0.650064i \(-0.774742\pi\)
0.275654 + 0.961257i \(0.411106\pi\)
\(390\) −4.67210e7 −0.0398828
\(391\) −1.56593e8 3.38069e7i −0.132481 0.0286013i
\(392\) 6.07529e8 0.509408
\(393\) 3.08391e8 1.98191e8i 0.256288 0.164706i
\(394\) −5.32868e7 + 3.70618e8i −0.0438917 + 0.305274i
\(395\) 4.42890e8 9.69795e8i 0.361582 0.791754i
\(396\) −4.55195e7 + 1.33657e7i −0.0368353 + 0.0108158i
\(397\) −5.60482e8 1.22729e9i −0.449568 0.984416i −0.989742 0.142863i \(-0.954369\pi\)
0.540175 0.841553i \(-0.318358\pi\)
\(398\) 6.24413e7 + 7.20611e7i 0.0496456 + 0.0572941i
\(399\) −1.11585e8 7.76089e8i −0.0879427 0.611655i
\(400\) 2.18157e8 + 6.40567e7i 0.170435 + 0.0500443i
\(401\) 3.51078e8 4.05166e8i 0.271893 0.313782i −0.603339 0.797485i \(-0.706163\pi\)
0.875232 + 0.483703i \(0.160709\pi\)
\(402\) −1.82053e8 1.16999e8i −0.139768 0.0898234i
\(403\) 1.67781e8 + 1.07826e8i 0.127695 + 0.0820647i
\(404\) 9.48648e7 1.09480e8i 0.0715765 0.0826037i
\(405\) −7.10350e7 2.08578e7i −0.0531349 0.0156018i
\(406\) 8.78993e7 + 6.11353e8i 0.0651845 + 0.453368i
\(407\) 9.60837e7 + 1.10887e8i 0.0706430 + 0.0815264i
\(408\) 4.06282e7 + 8.89633e7i 0.0296153 + 0.0648485i
\(409\) −8.20307e7 + 2.40864e7i −0.0592850 + 0.0174076i −0.311241 0.950331i \(-0.600744\pi\)
0.251956 + 0.967739i \(0.418926\pi\)
\(410\) 8.35564e7 1.82963e8i 0.0598737 0.131105i
\(411\) 4.55461e7 3.16780e8i 0.0323597 0.225067i
\(412\) −1.41494e8 + 9.09324e7i −0.0996774 + 0.0640588i
\(413\) −5.18514e8 −0.362189
\(414\) −8.87524e7 + 2.39102e8i −0.0614722 + 0.165609i
\(415\) −1.17126e9 −0.804424
\(416\) −3.34792e8 + 2.15158e8i −0.228007 + 0.146531i
\(417\) 2.07508e8 1.44325e9i 0.140139 0.974689i
\(418\) −8.48617e7 + 1.85821e8i −0.0568322 + 0.124445i
\(419\) −2.18268e9 + 6.40892e8i −1.44957 + 0.425634i −0.909401 0.415920i \(-0.863460\pi\)
−0.540174 + 0.841554i \(0.681641\pi\)
\(420\) −8.66662e7 1.89772e8i −0.0570791 0.124986i
\(421\) 8.28886e8 + 9.56586e8i 0.541387 + 0.624794i 0.958854 0.283898i \(-0.0916278\pi\)
−0.417468 + 0.908692i \(0.637082\pi\)
\(422\) 8.03614e6 + 5.58926e7i 0.00520540 + 0.0362043i
\(423\) 5.40319e8 + 1.58652e8i 0.347103 + 0.101919i
\(424\) −1.79215e8 + 2.06825e8i −0.114181 + 0.131772i
\(425\) 1.35618e8 + 8.71566e7i 0.0856953 + 0.0550730i
\(426\) 1.58738e8 + 1.02015e8i 0.0994826 + 0.0639336i
\(427\) −1.52157e8 + 1.75599e8i −0.0945790 + 0.109150i
\(428\) 1.93250e9 + 5.67434e8i 1.19143 + 0.349834i
\(429\) −5.62786e6 3.91427e7i −0.00344146 0.0239359i
\(430\) −6.84420e7 7.89862e7i −0.0415129 0.0479084i
\(431\) −1.00416e9 2.19880e9i −0.604131 1.32286i −0.926517 0.376253i \(-0.877212\pi\)
0.322386 0.946608i \(-0.395515\pi\)
\(432\) −7.31285e7 + 2.14725e7i −0.0436409 + 0.0128141i
\(433\) −1.89625e8 + 4.15220e8i −0.112250 + 0.245794i −0.957417 0.288709i \(-0.906774\pi\)
0.845167 + 0.534503i \(0.179501\pi\)
\(434\) 4.94955e7 3.44249e8i 0.0290638 0.202143i
\(435\) −5.40962e8 + 3.47655e8i −0.315105 + 0.202505i
\(436\) 5.85787e8 0.338483
\(437\) −1.35161e9 2.46606e9i −0.774761 1.41358i
\(438\) −2.97107e8 −0.168948
\(439\) 2.67546e8 1.71942e8i 0.150929 0.0969963i −0.462997 0.886360i \(-0.653226\pi\)
0.613926 + 0.789364i \(0.289589\pi\)
\(440\) −1.84920e7 + 1.28615e8i −0.0103491 + 0.0719793i
\(441\) −1.39448e8 + 3.05349e8i −0.0774244 + 0.169536i
\(442\) −3.27214e7 + 9.60788e6i −0.0180241 + 0.00529236i
\(443\) 9.30177e8 + 2.03680e9i 0.508338 + 1.11310i 0.973669 + 0.227968i \(0.0732082\pi\)
−0.465331 + 0.885137i \(0.654065\pi\)
\(444\) 3.37793e8 + 3.89833e8i 0.183151 + 0.211368i
\(445\) −1.26783e7 8.81795e7i −0.00682026 0.0474359i
\(446\) −1.00687e9 2.95644e8i −0.537405 0.157796i
\(447\) −5.61672e8 + 6.48204e8i −0.297445 + 0.343270i
\(448\) 3.32577e8 + 2.13734e8i 0.174751 + 0.112306i
\(449\) 1.51885e9 + 9.76107e8i 0.791869 + 0.508903i 0.872953 0.487804i \(-0.162202\pi\)
−0.0810844 + 0.996707i \(0.525838\pi\)
\(450\) 1.68069e8 1.93962e8i 0.0869451 0.100340i
\(451\) 1.63351e8 + 4.79641e7i 0.0838500 + 0.0246206i
\(452\) 1.14737e8 + 7.98014e8i 0.0584412 + 0.406467i
\(453\) −5.21293e7 6.01604e7i −0.0263474 0.0304066i
\(454\) −4.17370e8 9.13913e8i −0.209327 0.458363i
\(455\) 1.66858e8 4.89939e7i 0.0830438 0.0243839i
\(456\) −7.13189e8 + 1.56167e9i −0.352231 + 0.771278i
\(457\) −3.40762e8 + 2.37005e9i −0.167011 + 1.16159i 0.718009 + 0.696034i \(0.245054\pi\)
−0.885020 + 0.465553i \(0.845856\pi\)
\(458\) 9.93106e8 6.38230e8i 0.483021 0.310419i
\(459\) −5.40392e7 −0.0260834
\(460\) −5.29935e8 5.28270e8i −0.253846 0.253048i
\(461\) 1.36593e7 0.00649345 0.00324672 0.999995i \(-0.498967\pi\)
0.00324672 + 0.999995i \(0.498967\pi\)
\(462\) −5.80124e7 + 3.72823e7i −0.0273699 + 0.0175896i
\(463\) 2.48886e8 1.73104e9i 0.116538 0.810540i −0.844783 0.535109i \(-0.820270\pi\)
0.961321 0.275431i \(-0.0888204\pi\)
\(464\) −2.75003e8 + 6.02172e8i −0.127798 + 0.279838i
\(465\) 3.47426e8 1.02014e8i 0.160242 0.0470514i
\(466\) −4.75615e8 1.04145e9i −0.217723 0.476748i
\(467\) 2.19209e9 + 2.52980e9i 0.995976 + 1.14942i 0.988770 + 0.149444i \(0.0477483\pi\)
0.00720593 + 0.999974i \(0.497706\pi\)
\(468\) −1.97854e7 1.37610e8i −0.00892244 0.0620569i
\(469\) 7.72871e8 + 2.26936e8i 0.345941 + 0.101578i
\(470\) 4.22516e8 4.87610e8i 0.187716 0.216636i
\(471\) −7.70051e8 4.94882e8i −0.339583 0.218237i
\(472\) 9.55113e8 + 6.13814e8i 0.418078 + 0.268683i
\(473\) 5.79301e7 6.68549e7i 0.0251704 0.0290482i
\(474\) −1.18873e9 3.49042e8i −0.512694 0.150541i
\(475\) 4.02735e8 + 2.80108e9i 0.172421 + 1.19922i
\(476\) −9.97229e7 1.15086e8i −0.0423809 0.0489102i
\(477\) −6.28160e7 1.37548e8i −0.0265006 0.0580283i
\(478\) 9.75837e8 2.86532e8i 0.408676 0.119998i
\(479\) −1.63059e9 + 3.57050e9i −0.677908 + 1.48441i 0.186936 + 0.982372i \(0.440144\pi\)
−0.864844 + 0.502040i \(0.832583\pi\)
\(480\) −1.02826e8 + 7.15173e8i −0.0424385 + 0.295166i
\(481\) −3.61714e8 + 2.32460e8i −0.148203 + 0.0952445i
\(482\) −7.10754e8 −0.289105
\(483\) 6.62331e7 9.46994e8i 0.0267461 0.382413i
\(484\) 1.74782e9 0.700710
\(485\) 1.58716e9 1.02001e9i 0.631720 0.405982i
\(486\) −1.22436e7 + 8.51558e7i −0.00483816 + 0.0336502i
\(487\) −1.03850e9 + 2.27400e9i −0.407432 + 0.892151i 0.589031 + 0.808111i \(0.299510\pi\)
−0.996462 + 0.0840401i \(0.973218\pi\)
\(488\) 4.88149e8 1.43334e8i 0.190144 0.0558314i
\(489\) −3.95382e7 8.65766e7i −0.0152910 0.0334826i
\(490\) 2.51864e8 + 2.90667e8i 0.0967119 + 0.111612i
\(491\) 4.82027e8 + 3.35257e9i 0.183775 + 1.27818i 0.847737 + 0.530416i \(0.177964\pi\)
−0.663963 + 0.747766i \(0.731127\pi\)
\(492\) 5.74277e8 + 1.68623e8i 0.217392 + 0.0638320i
\(493\) −3.07374e8 + 3.54729e8i −0.115532 + 0.133331i
\(494\) −5.03610e8 3.23651e8i −0.187953 0.120790i
\(495\) −6.03984e7 3.88157e7i −0.0223824 0.0143843i
\(496\) 2.44109e8 2.81717e8i 0.0898252 0.103664i
\(497\) −6.73890e8 1.97872e8i −0.246231 0.0722998i
\(498\) 1.93700e8 + 1.34721e9i 0.0702793 + 0.488803i
\(499\) 7.41724e8 + 8.55995e8i 0.267233 + 0.308404i 0.873467 0.486883i \(-0.161866\pi\)
−0.606234 + 0.795286i \(0.707321\pi\)
\(500\) 7.28977e8 + 1.59624e9i 0.260807 + 0.571087i
\(501\) −6.29498e8 + 1.84837e8i −0.223647 + 0.0656686i
\(502\) −1.40814e8 + 3.08340e8i −0.0496802 + 0.108784i
\(503\) −1.66489e7 + 1.15796e8i −0.00583309 + 0.0405700i −0.992530 0.122000i \(-0.961069\pi\)
0.986697 + 0.162570i \(0.0519783\pi\)
\(504\) −4.87544e8 + 3.13325e8i −0.169632 + 0.109016i
\(505\) 2.19230e8 0.0757495
\(506\) −1.47909e8 + 1.98233e8i −0.0507538 + 0.0680220i
\(507\) −1.57832e9 −0.537859
\(508\) 3.15331e9 2.02651e9i 1.06719 0.685844i
\(509\) 3.65872e8 2.54469e9i 0.122975 0.855309i −0.831182 0.556001i \(-0.812335\pi\)
0.954156 0.299308i \(-0.0967559\pi\)
\(510\) −2.57204e7 + 5.63199e7i −0.00858583 + 0.0188003i
\(511\) 1.06108e9 3.11561e8i 0.351783 0.103293i
\(512\) 5.80644e8 + 1.27143e9i 0.191190 + 0.418648i
\(513\) −6.21206e8 7.16909e8i −0.203154 0.234452i
\(514\) −3.08217e8 2.14370e9i −0.100112 0.696294i
\(515\) −2.44228e8 7.17118e7i −0.0787898 0.0231348i
\(516\) 2.03659e8 2.35035e8i 0.0652575 0.0753112i
\(517\) 4.59413e8 + 2.95247e8i 0.146213 + 0.0939655i
\(518\) 6.30763e8 + 4.05367e8i 0.199394 + 0.128143i
\(519\) 8.32542e8 9.60804e8i 0.261409 0.301682i
\(520\) −3.65355e8 1.07278e8i −0.113947 0.0334579i
\(521\) −1.95818e7 1.36194e8i −0.00606624 0.0421916i 0.986563 0.163378i \(-0.0522391\pi\)
−0.992630 + 0.121187i \(0.961330\pi\)
\(522\) 4.89346e8 + 5.64735e8i 0.150581 + 0.173779i
\(523\) −2.09735e8 4.59256e8i −0.0641085 0.140378i 0.874866 0.484365i \(-0.160949\pi\)
−0.938974 + 0.343987i \(0.888222\pi\)
\(524\) 1.19918e9 3.52112e8i 0.364105 0.106911i
\(525\) −3.96840e8 + 8.68958e8i −0.119690 + 0.262085i
\(526\) −1.32921e8 + 9.24488e8i −0.0398240 + 0.276982i
\(527\) 2.22344e8 1.42892e8i 0.0661743 0.0425276i
\(528\) −7.39117e7 −0.0218522
\(529\) −9.69525e8 3.26387e9i −0.284750 0.958602i
\(530\) −1.73251e8 −0.0505486
\(531\) −5.27739e8 + 3.39157e8i −0.152964 + 0.0983037i
\(532\) 3.80429e8 2.64594e9i 0.109542 0.761885i
\(533\) −2.07252e8 + 4.53820e8i −0.0592863 + 0.129819i
\(534\) −9.93297e7 + 2.91658e7i −0.0282283 + 0.00828858i
\(535\) 1.26620e9 + 2.77260e9i 0.357492 + 0.782797i
\(536\) −1.15500e9 1.33294e9i −0.323970 0.373882i
\(537\) −2.29513e8 1.59630e9i −0.0639583 0.444840i
\(538\) 3.94804e8 + 1.15925e8i 0.109306 + 0.0320951i
\(539\) −2.13181e8 + 2.46024e8i −0.0586391 + 0.0676731i
\(540\) −2.12337e8 1.36461e8i −0.0580294 0.0372932i
\(541\) −3.68520e9 2.36833e9i −1.00062 0.643062i −0.0656736 0.997841i \(-0.520920\pi\)
−0.934950 + 0.354779i \(0.884556\pi\)
\(542\) −1.69274e9 + 1.95353e9i −0.456660 + 0.527014i
\(543\) 3.25185e8 + 9.54829e7i 0.0871627 + 0.0255933i
\(544\) 7.50555e7 + 5.22023e8i 0.0199888 + 0.139025i
\(545\) 5.80540e8 + 6.69979e8i 0.153619 + 0.177286i
\(546\) −8.39487e7 1.83822e8i −0.0220719 0.0483307i
\(547\) 2.18404e9 6.41293e8i 0.570566 0.167533i 0.0162916 0.999867i \(-0.494814\pi\)
0.554274 + 0.832334i \(0.312996\pi\)
\(548\) 4.53265e8 9.92511e8i 0.117658 0.257634i
\(549\) −4.00060e7 + 2.78248e8i −0.0103186 + 0.0717676i
\(550\) 2.09380e8 1.34560e8i 0.0536618 0.0344864i
\(551\) −8.23941e9 −2.09829
\(552\) −1.24305e9 + 1.66598e9i −0.314559 + 0.421582i
\(553\) 4.61142e9 1.15957
\(554\) 1.78225e9 1.14538e9i 0.445333 0.286198i
\(555\) −1.11095e8 + 7.72683e8i −0.0275848 + 0.191856i
\(556\) 2.06508e9 4.52189e9i 0.509535 1.11573i
\(557\) −3.57540e8 + 1.04983e8i −0.0876660 + 0.0257411i −0.325271 0.945621i \(-0.605456\pi\)
0.237605 + 0.971362i \(0.423637\pi\)
\(558\) −1.74795e8 3.82748e8i −0.0425902 0.0932596i
\(559\) 1.69763e8 + 1.95917e8i 0.0411056 + 0.0474384i
\(560\) −4.62568e7 3.21723e8i −0.0111306 0.0774148i
\(561\) −5.02828e7 1.47644e7i −0.0120240 0.00353057i
\(562\) 1.46114e9 1.68625e9i 0.347228 0.400723i
\(563\) −5.76571e9 3.70540e9i −1.36168 0.875096i −0.363278 0.931681i \(-0.618342\pi\)
−0.998398 + 0.0565852i \(0.981979\pi\)
\(564\) 1.61512e9 + 1.03797e9i 0.379076 + 0.243618i
\(565\) −7.98998e8 + 9.22093e8i −0.186370 + 0.215083i
\(566\) 3.44784e9 + 1.01238e9i 0.799263 + 0.234685i
\(567\) −4.55723e7 3.16962e8i −0.0104993 0.0730242i
\(568\) 1.00708e9 + 1.16223e9i 0.230592 + 0.266118i
\(569\) −2.93112e9 6.41825e9i −0.667022 1.46057i −0.875831 0.482618i \(-0.839686\pi\)
0.208809 0.977956i \(-0.433041\pi\)
\(570\) −1.04283e9 + 3.06203e8i −0.235859 + 0.0692545i
\(571\) −2.58507e9 + 5.66051e9i −0.581093 + 1.27242i 0.359585 + 0.933112i \(0.382918\pi\)
−0.940677 + 0.339303i \(0.889809\pi\)
\(572\) 1.91872e7 1.33450e8i 0.00428673 0.0298149i
\(573\) 1.26405e9 8.12357e8i 0.280688 0.180387i
\(574\) 8.69997e8 0.192011
\(575\) −2.39050e8 + 3.41792e9i −0.0524387 + 0.749763i
\(576\) 4.78297e8 0.104284
\(577\) 5.82291e9 3.74216e9i 1.26190 0.810973i 0.273356 0.961913i \(-0.411866\pi\)
0.988543 + 0.150940i \(0.0482299\pi\)
\(578\) 3.43700e8 2.39048e9i 0.0740341 0.514919i
\(579\) −1.65198e9 + 3.61734e9i −0.353697 + 0.774488i
\(580\) −2.10354e9 + 6.17655e8i −0.447664 + 0.131446i
\(581\) −2.10453e9 4.60828e9i −0.445184 0.974816i
\(582\) −1.43572e9 1.65691e9i −0.301883 0.348392i
\(583\) −2.08692e7 1.45149e8i −0.00436181 0.0303371i
\(584\) −2.32335e9 6.82198e8i −0.482692 0.141731i
\(585\) 1.37780e8 1.59007e8i 0.0284538 0.0328374i
\(586\) −2.03876e9 1.31023e9i −0.418529 0.268972i
\(587\) −1.85446e9 1.19179e9i −0.378428 0.243201i 0.337574 0.941299i \(-0.390394\pi\)
−0.716002 + 0.698098i \(0.754030\pi\)
\(588\) −7.49460e8 + 8.64923e8i −0.152029 + 0.175451i
\(589\) 4.45162e9 + 1.30711e9i 0.897666 + 0.263579i
\(590\) 1.02289e8 + 7.11435e8i 0.0205044 + 0.142611i
\(591\) −1.10419e9 1.27430e9i −0.220033 0.253931i
\(592\) 3.33842e8 + 7.31012e8i 0.0661325 + 0.144810i
\(593\) 1.57171e9 4.61496e8i 0.309515 0.0908818i −0.123286 0.992371i \(-0.539343\pi\)
0.432801 + 0.901489i \(0.357525\pi\)
\(594\) −3.46583e7 + 7.58912e7i −0.00678508 + 0.0148573i
\(595\) 3.27974e7 2.28111e8i 0.00638308 0.0443953i
\(596\) −2.45997e9 + 1.58092e9i −0.475956 + 0.305879i
\(597\) −4.29386e8 −0.0825920
\(598\) −5.13319e8 5.11706e8i −0.0981596 0.0978513i
\(599\) −2.26790e9 −0.431152 −0.215576 0.976487i \(-0.569163\pi\)
−0.215576 + 0.976487i \(0.569163\pi\)
\(600\) 1.75966e9 1.13086e9i 0.332582 0.213737i
\(601\) 8.01899e8 5.57733e9i 0.150681 1.04801i −0.764400 0.644742i \(-0.776965\pi\)
0.915082 0.403269i \(-0.132126\pi\)
\(602\) 1.87791e8 4.11206e8i 0.0350823 0.0768195i
\(603\) 9.35059e8 2.74558e8i 0.173671 0.0509945i
\(604\) −1.12741e8 2.46869e8i −0.0208187 0.0455867i
\(605\) 1.73217e9 + 1.99903e9i 0.318014 + 0.367007i
\(606\) −3.62557e7 2.52164e8i −0.00661793 0.0460287i
\(607\) −3.82630e9 1.12350e9i −0.694414 0.203898i −0.0845674 0.996418i \(-0.526951\pi\)
−0.609847 + 0.792519i \(0.708769\pi\)
\(608\) −6.06260e9 + 6.99661e9i −1.09395 + 1.26248i
\(609\) −2.33985e9 1.50373e9i −0.419785 0.269779i
\(610\) 2.70950e8 + 1.74129e8i 0.0483319 + 0.0310610i
\(611\) −1.04801e9 + 1.20946e9i −0.185874 + 0.214510i
\(612\) −1.76774e8 5.19057e7i −0.0311738 0.00915345i
\(613\) 6.04503e8 + 4.20441e9i 0.105995 + 0.737214i 0.971625 + 0.236528i \(0.0760096\pi\)
−0.865629 + 0.500685i \(0.833081\pi\)
\(614\) 3.41465e9 + 3.94072e9i 0.595329 + 0.687046i
\(615\) 3.76275e8 + 8.23927e8i 0.0652292 + 0.142832i
\(616\) −5.39258e8 + 1.58341e8i −0.0929532 + 0.0272935i
\(617\) 3.17585e9 6.95414e9i 0.544329 1.19191i −0.415051 0.909798i \(-0.636236\pi\)
0.959380 0.282116i \(-0.0910365\pi\)
\(618\) −4.20950e7 + 2.92777e8i −0.00717415 + 0.0498973i
\(619\) 3.33507e9 2.14332e9i 0.565182 0.363220i −0.226634 0.973980i \(-0.572772\pi\)
0.791816 + 0.610760i \(0.209136\pi\)
\(620\) 1.23450e9 0.208026
\(621\) −5.52012e8 1.00717e9i −0.0924971 0.168764i
\(622\) 5.40617e9 0.900789
\(623\) 3.24159e8 2.08324e8i 0.0537093 0.0345169i
\(624\) 3.08249e7 2.14392e8i 0.00507874 0.0353234i
\(625\) 8.02455e8 1.75713e9i 0.131474 0.287888i
\(626\) 2.16298e9 6.35107e8i 0.352404 0.103475i
\(627\) −3.82153e8 8.36797e8i −0.0619156 0.135576i
\(628\) −2.04367e9 2.35852e9i −0.329270 0.379997i
\(629\) 8.10911e7 + 5.64001e8i 0.0129926 + 0.0903655i
\(630\) −3.52030e8 1.03365e8i −0.0560902 0.0164696i
\(631\) −7.52665e9 + 8.68621e9i −1.19261 + 1.37635i −0.283935 + 0.958843i \(0.591640\pi\)
−0.908676 + 0.417503i \(0.862905\pi\)
\(632\) −8.49433e9 5.45897e9i −1.33850 0.860203i
\(633\) −2.13919e8 1.37477e8i −0.0335225 0.0215436i
\(634\) −6.83730e8 + 7.89066e8i −0.106555 + 0.122971i
\(635\) 5.44283e9 + 1.59816e9i 0.843561 + 0.247692i
\(636\) −7.33680e7 5.10286e8i −0.0113086 0.0786527i
\(637\) −6.24721e8 7.20966e8i −0.0957631 0.110516i
\(638\) 3.01035e8 + 6.59175e8i 0.0458928 + 0.100491i
\(639\) −8.15307e8 + 2.39396e8i −0.123614 + 0.0362964i
\(640\) −1.19528e9 + 2.61729e9i −0.180235 + 0.394659i
\(641\) −6.67638e8 + 4.64352e9i −0.100124 + 0.696377i 0.876497 + 0.481407i \(0.159874\pi\)
−0.976621 + 0.214969i \(0.931035\pi\)
\(642\) 2.97972e9 1.91495e9i 0.444429 0.285617i
\(643\) 6.06327e9 0.899432 0.449716 0.893172i \(-0.351525\pi\)
0.449716 + 0.893172i \(0.351525\pi\)
\(644\) 1.12627e9 3.03421e9i 0.166166 0.447657i
\(645\) 4.70651e8 0.0690621
\(646\) −6.67388e8 + 4.28904e8i −0.0974013 + 0.0625960i
\(647\) 1.07965e9 7.50912e9i 0.156718 1.08999i −0.747913 0.663797i \(-0.768944\pi\)
0.904630 0.426197i \(-0.140147\pi\)
\(648\) −2.91273e8 + 6.37800e8i −0.0420522 + 0.0920814i
\(649\) −5.83716e8 + 1.71395e8i −0.0838196 + 0.0246116i
\(650\) 3.02990e8 + 6.63456e8i 0.0432744 + 0.0947578i
\(651\) 1.02563e9 + 1.18364e9i 0.145699 + 0.168146i
\(652\) −4.61800e7 3.21189e8i −0.00652510 0.0453830i
\(653\) 5.77984e9 + 1.69712e9i 0.812307 + 0.238515i 0.661400 0.750033i \(-0.269963\pi\)
0.150907 + 0.988548i \(0.451781\pi\)
\(654\) 6.74620e8 7.78553e8i 0.0943055 0.108834i
\(655\) 1.59116e9 + 1.02258e9i 0.221243 + 0.142184i
\(656\) 7.84448e8 + 5.04134e8i 0.108493 + 0.0697241i
\(657\) 8.76166e8 1.01115e9i 0.120534 0.139103i
\(658\) 2.67767e9 + 7.86234e8i 0.366409 + 0.107587i
\(659\) −7.52410e7 5.23313e8i −0.0102413 0.0712299i 0.984060 0.177838i \(-0.0569102\pi\)
−0.994301 + 0.106608i \(0.966001\pi\)
\(660\) −1.60294e8 1.84989e8i −0.0217026 0.0250462i
\(661\) −1.88391e9 4.12518e9i −0.253720 0.555569i 0.739319 0.673355i \(-0.235147\pi\)
−0.993039 + 0.117786i \(0.962420\pi\)
\(662\) −1.39464e8 + 4.09504e7i −0.0186836 + 0.00548600i
\(663\) 6.37966e7 1.39695e8i 0.00850159 0.0186159i
\(664\) −1.57867e9 + 1.09799e10i −0.209268 + 1.45549i
\(665\) 3.40325e9 2.18713e9i 0.448764 0.288403i
\(666\) 9.07133e8 0.118990
\(667\) −9.75116e9 2.10517e9i −1.27238 0.274693i
\(668\) −2.23677e9 −0.290338
\(669\) 3.97543e9 2.55485e9i 0.513325 0.329894i
\(670\) 1.58904e8 1.10520e9i 0.0204114 0.141964i
\(671\) −1.13247e8 + 2.47976e8i −0.0144709 + 0.0316869i
\(672\) −2.99858e9 + 8.80463e8i −0.381174 + 0.111923i
\(673\) −2.10783e9 4.61550e9i −0.266552 0.583668i 0.728271 0.685289i \(-0.240324\pi\)
−0.994823 + 0.101621i \(0.967597\pi\)
\(674\) 3.74078e9 + 4.31709e9i 0.470601 + 0.543103i
\(675\) 1.64481e8 + 1.14399e9i 0.0205850 + 0.143172i
\(676\) −5.16305e9 1.51601e9i −0.642825 0.188751i
\(677\) −3.05633e9 + 3.52719e9i −0.378564 + 0.436887i −0.912774 0.408466i \(-0.866064\pi\)
0.534209 + 0.845352i \(0.320609\pi\)
\(678\) 1.19275e9 + 7.66536e8i 0.146976 + 0.0944557i
\(679\) 6.86501e9 + 4.41187e9i 0.841583 + 0.540853i
\(680\) −3.30450e8 + 3.81360e8i −0.0403018 + 0.0465108i
\(681\) 4.34116e9 + 1.27468e9i 0.526734 + 0.154663i
\(682\) −5.80719e7 4.03899e8i −0.00701004 0.0487559i
\(683\) 7.88962e9 + 9.10511e9i 0.947510 + 1.09349i 0.995512 + 0.0946378i \(0.0301693\pi\)
−0.0480016 + 0.998847i \(0.515285\pi\)
\(684\) −1.34350e9 2.94185e9i −0.160524 0.351499i
\(685\) 1.58436e9 4.65211e8i 0.188338 0.0553010i
\(686\) −1.92702e9 + 4.21959e9i −0.227904 + 0.499040i
\(687\) −7.56561e8 + 5.26200e9i −0.0890216 + 0.619159i
\(688\) 4.07606e8 2.61952e8i 0.0477178 0.0306664i
\(689\) 4.29729e8 0.0500527
\(690\) −1.31241e9 + 9.59406e7i −0.152088 + 0.0111181i
\(691\) −1.53421e10 −1.76893 −0.884465 0.466607i \(-0.845476\pi\)
−0.884465 + 0.466607i \(0.845476\pi\)
\(692\) 3.64630e9 2.34333e9i 0.418293 0.268821i
\(693\) 4.41946e7 3.07380e8i 0.00504432 0.0350840i
\(694\) −1.17613e9 + 2.57536e9i −0.133566 + 0.292469i
\(695\) 7.21837e9 2.11950e9i 0.815628 0.239490i
\(696\) 2.52994e9 + 5.53980e9i 0.284432 + 0.622818i
\(697\) 4.32963e8 + 4.99665e8i 0.0484324 + 0.0558939i
\(698\) 4.62599e8 + 3.21744e9i 0.0514885 + 0.358111i
\(699\) 4.94699e9 + 1.45257e9i 0.547861 + 0.160867i
\(700\) −2.13280e9 + 2.46139e9i −0.235021 + 0.271229i
\(701\) 1.38407e9 + 8.89490e8i 0.151756 + 0.0975277i 0.614315 0.789061i \(-0.289432\pi\)
−0.462559 + 0.886588i \(0.653069\pi\)
\(702\) −2.05679e8 1.32182e8i −0.0224394 0.0144209i
\(703\) −6.55012e9 + 7.55924e9i −0.711059 + 0.820606i
\(704\) 4.45049e8 + 1.30678e8i 0.0480732 + 0.0141156i
\(705\) 4.13495e8 + 2.87592e9i 0.0444435 + 0.309111i
\(706\) −4.24443e9 4.89833e9i −0.453944 0.523880i
\(707\) 3.93914e8 + 8.62552e8i 0.0419212 + 0.0917947i
\(708\) −2.05212e9 + 6.02556e8i −0.217313 + 0.0638089i
\(709\) 1.27111e9 2.78335e9i 0.133944 0.293295i −0.830761 0.556629i \(-0.812095\pi\)
0.964705 + 0.263333i \(0.0848219\pi\)
\(710\) −1.38553e8 + 9.63658e8i −0.0145282 + 0.101046i
\(711\) 4.69346e9 3.01630e9i 0.489722 0.314725i
\(712\) −8.43721e8 −0.0876029
\(713\) 4.93443e9 + 2.68433e9i 0.509828 + 0.277347i
\(714\) −2.67803e8 −0.0275342
\(715\) 1.71645e8 1.10310e8i 0.0175615 0.0112861i
\(716\) 7.82485e8 5.44230e9i 0.0796673 0.554098i
\(717\) −1.90258e9 + 4.16607e9i −0.192764 + 0.422094i
\(718\) 7.03682e9 2.06620e9i 0.709481 0.208322i
\(719\) −5.00079e9 1.09502e10i −0.501750 1.09868i −0.975897 0.218233i \(-0.929971\pi\)
0.474147 0.880446i \(-0.342757\pi\)
\(720\) −2.57517e8 2.97190e8i −0.0257124 0.0296737i
\(721\) −1.56684e8 1.08976e9i −0.0155686 0.108282i
\(722\) −8.21969e9 2.41352e9i −0.812785 0.238655i
\(723\) 2.09601e9 2.41893e9i 0.206257 0.238034i
\(724\) 9.72040e8 + 6.24692e8i 0.0951917 + 0.0611760i
\(725\) 8.44503e9 + 5.42729e9i 0.823035 + 0.528932i
\(726\) 2.01287e9 2.32298e9i 0.195226 0.225303i
\(727\) 5.32974e9 + 1.56495e9i 0.514441 + 0.151054i 0.528641 0.848846i \(-0.322702\pi\)
−0.0141997 + 0.999899i \(0.504520\pi\)
\(728\) −2.34392e8 1.63023e9i −0.0225156 0.156599i
\(729\) −2.53706e8 2.92793e8i −0.0242541 0.0279907i
\(730\) −6.36805e8 1.39441e9i −0.0605866 0.132666i
\(731\) 3.29624e8 9.67864e7i 0.0312110 0.00916439i
\(732\) −3.98131e8 + 8.71785e8i −0.0375178 + 0.0821524i
\(733\) −2.90240e9 + 2.01867e10i −0.272204 + 1.89322i 0.153169 + 0.988200i \(0.451052\pi\)
−0.425373 + 0.905018i \(0.639857\pi\)
\(734\) −1.36405e9 + 8.76619e8i −0.127319 + 0.0818228i
\(735\) −1.73198e9 −0.160893
\(736\) −8.96259e9 + 6.73134e9i −0.828631 + 0.622342i
\(737\) 9.45073e8 0.0869619
\(738\) 8.85475e8 5.69061e8i 0.0810922 0.0521148i
\(739\) 1.18705e9 8.25609e9i 0.108196 0.752521i −0.861421 0.507892i \(-0.830425\pi\)
0.969617 0.244629i \(-0.0786661\pi\)
\(740\) −1.10559e9 + 2.42091e9i −0.100296 + 0.219618i
\(741\) 2.58663e9 7.59504e8i 0.233545 0.0685750i
\(742\) −3.11299e8 6.81649e8i −0.0279746 0.0612558i
\(743\) 8.94176e9 + 1.03193e10i 0.799764 + 0.922977i 0.998368 0.0571024i \(-0.0181862\pi\)
−0.198604 + 0.980080i \(0.563641\pi\)
\(744\) −4.88044e8 3.39442e9i −0.0434464 0.302176i
\(745\) −4.24607e9 1.24676e9i −0.376219 0.110468i
\(746\) −2.63233e9 + 3.03787e9i −0.232142 + 0.267906i
\(747\) −5.15623e9 3.31371e9i −0.452595 0.290865i
\(748\) −1.50305e8 9.65950e7i −0.0131316 0.00843916i
\(749\) −8.63358e9 + 9.96368e9i −0.750766 + 0.866430i
\(750\) 2.96103e9 + 8.69438e8i 0.256288 + 0.0752531i
\(751\) −1.28521e9 8.93880e9i −0.110722 0.770087i −0.967221 0.253938i \(-0.918274\pi\)
0.856499 0.516149i \(-0.172635\pi\)
\(752\) 1.95877e9 + 2.26054e9i 0.167966 + 0.193843i
\(753\) −6.34120e8 1.38853e9i −0.0541239 0.118515i
\(754\) −2.03758e9 + 5.98288e8i −0.173107 + 0.0508289i
\(755\) 1.70619e8 3.73603e8i 0.0144282 0.0315934i
\(756\) 1.55371e8 1.08063e9i 0.0130781 0.0909599i
\(757\) 1.34426e10 8.63901e9i 1.12628 0.723816i 0.161500 0.986873i \(-0.448367\pi\)
0.964780 + 0.263057i \(0.0847306\pi\)
\(758\) −2.41175e9 −0.201136
\(759\) −2.38467e8 1.08797e9i −0.0197962 0.0903174i
\(760\) −8.85797e9 −0.731959
\(761\) 1.39147e10 8.94244e9i 1.14453 0.735545i 0.175988 0.984392i \(-0.443688\pi\)
0.968543 + 0.248847i \(0.0800516\pi\)
\(762\) 9.38123e8 6.52479e9i 0.0768100 0.534225i
\(763\) −1.59289e9 + 3.48794e9i −0.129822 + 0.284271i
\(764\) 4.91528e9 1.44326e9i 0.398769 0.117089i
\(765\) −1.15825e8 2.53622e8i −0.00935380 0.0204820i
\(766\) −3.62123e9 4.17913e9i −0.291109 0.335958i
\(767\) −2.53716e8 1.76464e9i −0.0203032 0.141212i
\(768\) 5.38378e9 + 1.58082e9i 0.428868 + 0.125927i
\(769\) 1.61936e8 1.86884e8i 0.0128411 0.0148194i −0.749293 0.662239i \(-0.769606\pi\)
0.762134 + 0.647420i \(0.224152\pi\)
\(770\) −2.99318e8 1.92360e8i −0.0236274 0.0151844i
\(771\) 8.20463e9 + 5.27279e9i 0.644716 + 0.414334i
\(772\) −8.87853e9 + 1.02464e10i −0.694514 + 0.801511i
\(773\) 2.42752e10 + 7.12785e9i 1.89032 + 0.555048i 0.993675 + 0.112294i \(0.0358198\pi\)
0.896643 + 0.442754i \(0.145998\pi\)
\(774\) −7.78351e7 5.41355e8i −0.00603368 0.0419652i
\(775\) −3.70172e9 4.27202e9i −0.285659 0.329668i
\(776\) −7.42274e9 1.62535e10i −0.570227 1.24862i
\(777\) −3.23971e9 + 9.51265e8i −0.247761 + 0.0727492i
\(778\) −1.66443e9 + 3.64459e9i −0.126717 + 0.277472i
\(779\) −1.65169e9 + 1.14878e10i −0.125184 + 0.870672i
\(780\) 6.03438e8 3.87806e8i 0.0455304 0.0292606i
\(781\) −8.24038e8 −0.0618969
\(782\) −8.99424e8 + 3.37081e8i −0.0672576 + 0.0252064i
\(783\) −3.36505e9 −0.250510
\(784\) −1.49997e9 + 9.63975e8i −0.111167 + 0.0714430i
\(785\) 6.72132e8 4.67478e9i 0.0495919 0.344919i
\(786\) 9.13053e8 1.99931e9i 0.0670683 0.146859i
\(787\) −1.49417e10 + 4.38727e9i −1.09267 + 0.320836i −0.777935 0.628345i \(-0.783733\pi\)
−0.314731 + 0.949181i \(0.601914\pi\)
\(788\) −2.38806e9 5.22912e9i −0.173861 0.380703i
\(789\) −2.75435e9 3.17869e9i −0.199641 0.230398i
\(790\) −9.09710e8 6.32717e9i −0.0656460 0.456578i
\(791\) −5.06359e9 1.48680e9i −0.363782 0.106816i
\(792\) −4.45283e8 + 5.13884e8i −0.0318491 + 0.0367559i
\(793\) −6.72060e8 4.31907e8i −0.0478577 0.0307563i
\(794\) −6.80527e9 4.37348e9i −0.482474 0.310067i
\(795\) 5.10915e8 5.89628e8i 0.0360632 0.0416191i
\(796\) −1.40462e9 4.12433e8i −0.0987103 0.0289840i
\(797\) −2.07185e9 1.44100e10i −0.144962 1.00823i −0.924310 0.381642i \(-0.875359\pi\)
0.779348 0.626591i \(-0.215550\pi\)
\(798\) −3.07852e9 3.55280e9i −0.214453 0.247492i
\(799\) 8.81009e8 + 1.92914e9i 0.0611036 + 0.133798i
\(800\) 1.08226e10 3.17779e9i 0.747335 0.219437i
\(801\) 1.93662e8 4.24061e8i 0.0133147 0.0291551i
\(802\) 4.57450e8 3.18164e9i 0.0313136 0.217791i
\(803\) 1.09152e9 7.01479e8i 0.0743924 0.0478091i
\(804\) 3.32251e9 0.225460
\(805\) 4.58648e9 1.71889e9i 0.309880 0.116135i
\(806\) 1.19579e9 0.0804417
\(807\) −1.55881e9 + 1.00178e9i −0.104408 + 0.0670991i
\(808\) 2.95487e8 2.05515e9i 0.0197060 0.137058i
\(809\) −4.19278e9 + 9.18090e9i −0.278408 + 0.609629i −0.996245 0.0865829i \(-0.972405\pi\)
0.717836 + 0.696212i \(0.245133\pi\)
\(810\) −4.25903e8 + 1.25056e8i −0.0281588 + 0.00826816i
\(811\) −3.20987e9 7.02864e9i −0.211308 0.462699i 0.774067 0.633104i \(-0.218220\pi\)
−0.985374 + 0.170405i \(0.945492\pi\)
\(812\) −6.20980e9 7.16649e9i −0.407035 0.469743i
\(813\) −1.65660e9 1.15219e10i −0.108119 0.751981i
\(814\) 8.44075e8 + 2.47843e8i 0.0548524 + 0.0161061i
\(815\) 3.21585e8 3.71129e8i 0.0208087 0.0240145i
\(816\) −2.41470e8 1.55183e8i −0.0155577 0.00999836i
\(817\) 5.07319e9 + 3.26034e9i 0.325465 + 0.209164i
\(818\) −3.35677e8 + 3.87392e8i −0.0214430 + 0.0247465i
\(819\) 8.73170e8 + 2.56386e8i 0.0555399 + 0.0163080i
\(820\) 4.39483e8 + 3.05667e9i 0.0278351 + 0.193598i
\(821\) −1.99128e10 2.29806e10i −1.25583 1.44931i −0.842470 0.538743i \(-0.818899\pi\)
−0.413363 0.910566i \(-0.635646\pi\)
\(822\) −7.97117e8 1.74544e9i −0.0500577 0.109611i
\(823\) 1.86021e10 5.46206e9i 1.16322 0.341552i 0.357537 0.933899i \(-0.383617\pi\)
0.805683 + 0.592347i \(0.201799\pi\)
\(824\) −1.00144e9 + 2.19284e9i −0.0623560 + 0.136541i
\(825\) −1.59508e8 + 1.10940e9i −0.00988996 + 0.0687862i
\(826\) −2.61532e9 + 1.68077e9i −0.161471 + 0.103771i
\(827\) 1.54451e10 0.949558 0.474779 0.880105i \(-0.342528\pi\)
0.474779 + 0.880105i \(0.342528\pi\)
\(828\) −8.38356e8 3.82488e9i −0.0513242 0.234159i
\(829\) −8.30854e9 −0.506505 −0.253253 0.967400i \(-0.581500\pi\)
−0.253253 + 0.967400i \(0.581500\pi\)
\(830\) −5.90770e9 + 3.79665e9i −0.358629 + 0.230477i
\(831\) −1.35774e9 + 9.44331e9i −0.0820756 + 0.570848i
\(832\) −5.64659e8 + 1.23643e9i −0.0339903 + 0.0744283i
\(833\) −1.21301e9 + 3.56171e8i −0.0727119 + 0.0213501i
\(834\) −3.63167e9 7.95224e9i −0.216783 0.474688i
\(835\) −2.21673e9 2.55825e9i −0.131768 0.152069i
\(836\) −4.46348e8 3.10442e9i −0.0264211 0.183763i
\(837\) 1.81809e9 + 5.33838e8i 0.107171 + 0.0314681i
\(838\) −8.93173e9 + 1.03078e10i −0.524302 + 0.605077i
\(839\) −2.71878e10 1.74725e10i −1.58930 1.02138i −0.972096 0.234583i \(-0.924628\pi\)
−0.617207 0.786801i \(-0.711736\pi\)
\(840\) −2.51551e9 1.61662e9i −0.146436 0.0941087i
\(841\) −7.84411e9 + 9.05259e9i −0.454734 + 0.524791i
\(842\) 7.28159e9 + 2.13807e9i 0.420372 + 0.123432i
\(843\) 1.42994e9 + 9.94547e9i 0.0822095 + 0.571780i
\(844\) −5.67728e8 6.55193e8i −0.0325044 0.0375120i
\(845\) −3.38291e9 7.40753e9i −0.192882 0.422353i
\(846\) 3.23958e9 9.51226e8i 0.183947 0.0540116i
\(847\) −4.75273e9 + 1.04070e10i −0.268752 + 0.588484i
\(848\) 1.14305e8 7.95008e8i 0.00643694 0.0447699i
\(849\) −1.36131e10 + 8.74862e9i −0.763450 + 0.490640i
\(850\) 9.66563e8 0.0539838
\(851\) −9.68331e9 + 7.27264e9i −0.538605 + 0.404518i
\(852\) −2.89700e9 −0.160476
\(853\) 1.09614e10 7.04444e9i 0.604704 0.388620i −0.202164 0.979352i \(-0.564797\pi\)
0.806868 + 0.590732i \(0.201161\pi\)
\(854\) −1.98259e8 + 1.37892e9i −0.0108925 + 0.0757593i
\(855\) 2.03320e9 4.45209e9i 0.111250 0.243603i
\(856\) 2.76982e10 8.13292e9i 1.50936 0.443189i
\(857\) −5.79164e9 1.26819e10i −0.314318 0.688260i 0.684865 0.728670i \(-0.259861\pi\)
−0.999183 + 0.0404096i \(0.987134\pi\)
\(858\) −1.55268e8 1.79188e8i −0.00839219 0.00968511i
\(859\) −3.24217e9 2.25498e10i −0.174526 1.21386i −0.869174 0.494506i \(-0.835349\pi\)
0.694648 0.719350i \(-0.255560\pi\)
\(860\) 1.53960e9 + 4.52069e8i 0.0825400 + 0.0242359i
\(861\) −2.56562e9 + 2.96088e9i −0.136988 + 0.158092i
\(862\) −1.21923e10 7.83550e9i −0.648350 0.416669i
\(863\) 2.75327e10 + 1.76942e10i 1.45818 + 0.937116i 0.998805 + 0.0488748i \(0.0155635\pi\)
0.459377 + 0.888242i \(0.348073\pi\)
\(864\) −2.47602e9 + 2.85748e9i −0.130604 + 0.150725i
\(865\) 6.29377e9 + 1.84802e9i 0.330639 + 0.0970844i
\(866\) 3.89495e8 + 2.70899e9i 0.0203793 + 0.141741i
\(867\) 7.12202e9 + 8.21925e9i 0.371139 + 0.428317i
\(868\) 2.21815e9 + 4.85708e9i 0.115126 + 0.252090i
\(869\) 5.19130e9 1.52430e9i 0.268353 0.0787956i
\(870\) −1.60163e9 + 3.50707e9i −0.0824600 + 0.180562i
\(871\) −3.94143e8 + 2.74132e9i −0.0202111 + 0.140571i
\(872\) 7.06314e9 4.53921e9i 0.360737 0.231831i
\(873\) 9.87293e9 0.502222
\(874\) −1.48112e10 8.05728e9i −0.750411 0.408224i
\(875\) −1.14867e10 −0.579651
\(876\) 3.83736e9 2.46612e9i 0.192872 0.123951i
\(877\) 5.53690e9 3.85100e10i 0.277184 1.92786i −0.0863300 0.996267i \(-0.527514\pi\)
0.363514 0.931589i \(-0.381577\pi\)
\(878\) 7.92124e8 1.73451e9i 0.0394968 0.0864860i
\(879\) 1.04715e10 3.07470e9i 0.520051 0.152701i
\(880\) −1.58419e8 3.46889e8i −0.00783643 0.0171594i
\(881\) −1.91617e9 2.21138e9i −0.0944100 0.108955i 0.706579 0.707635i \(-0.250238\pi\)
−0.800989 + 0.598680i \(0.795692\pi\)
\(882\) 2.86431e8 + 1.99217e9i 0.0140566 + 0.0977656i
\(883\) 2.95755e10 + 8.68414e9i 1.44567 + 0.424487i 0.908107 0.418737i \(-0.137527\pi\)
0.537562 + 0.843224i \(0.319345\pi\)
\(884\) 3.42873e8 3.95696e8i 0.0166936 0.0192654i
\(885\) −2.72289e9 1.74990e9i −0.132047 0.0848616i
\(886\) 1.12940e10 + 7.25823e9i 0.545545 + 0.350601i
\(887\) −1.71756e10 + 1.98218e10i −0.826381 + 0.953695i −0.999513 0.0312038i \(-0.990066\pi\)
0.173132 + 0.984899i \(0.444611\pi\)
\(888\) 7.09372e9 + 2.08290e9i 0.339961 + 0.0998215i
\(889\) 3.49183e9 + 2.42862e10i 0.166685 + 1.15932i
\(890\) −3.49783e8 4.03671e8i −0.0166316 0.0191939i
\(891\) −1.56075e8 3.41756e8i −0.00739198 0.0161862i
\(892\) 1.54585e10 4.53903e9i 0.729274 0.214134i
\(893\) −1.54653e10 + 3.38642e10i −0.726738 + 1.59133i
\(894\) −7.31851e8 + 5.09013e9i −0.0342564 + 0.238258i
\(895\) 6.99996e9 4.49860e9i 0.326374 0.209748i
\(896\) −1.24453e10 −0.578001
\(897\) 3.25528e9 2.37970e8i 0.150596 0.0110090i
\(898\) 1.08250e10 0.498838
\(899\) 1.38455e10 8.89797e9i 0.635551 0.408444i
\(900\) −5.60769e8 + 3.90023e9i −0.0256410 + 0.178337i
\(901\) 2.36571e8 5.18017e8i 0.0107752 0.0235943i
\(902\) 9.79399e8 2.87577e8i 0.0444362 0.0130476i
\(903\) 8.45670e8 + 1.85176e9i 0.0382203 + 0.0836908i
\(904\) 7.56717e9 + 8.73298e9i 0.340678 + 0.393163i
\(905\) 2.48857e8 + 1.73084e9i 0.0111604 + 0.0776224i
\(906\) −4.57945e8 1.34465e8i −0.0204581 0.00600703i
\(907\) 1.75106e10 2.02083e10i 0.779246 0.899297i −0.217809 0.975991i \(-0.569891\pi\)
0.997055 + 0.0766941i \(0.0244365\pi\)
\(908\) 1.29766e10 + 8.33953e9i 0.575254 + 0.369693i
\(909\) 9.65114e8 + 6.20241e8i 0.0426192 + 0.0273897i
\(910\) 6.82799e8 7.87992e8i 0.0300364 0.0346639i
\(911\) 1.35755e10 + 3.98613e9i 0.594897 + 0.174678i 0.565301 0.824884i \(-0.308760\pi\)
0.0295957 + 0.999562i \(0.490578\pi\)
\(912\) −7.17072e8 4.98735e9i −0.0313026 0.217715i
\(913\) −3.89244e9 4.49212e9i −0.169268 0.195346i
\(914\) 5.96379e9 + 1.30589e10i 0.258351 + 0.565710i
\(915\) −1.39165e9 + 4.08624e8i −0.0600558 + 0.0176340i
\(916\) −7.52912e9 + 1.64865e10i −0.323676 + 0.708751i
\(917\) −1.16428e9 + 8.09775e9i −0.0498614 + 0.346794i
\(918\) −2.72568e8 + 1.75169e8i −0.0116285 + 0.00747321i
\(919\) −8.71107e9 −0.370226 −0.185113 0.982717i \(-0.559265\pi\)
−0.185113 + 0.982717i \(0.559265\pi\)
\(920\) −1.04832e10 2.26322e9i −0.443851 0.0958228i
\(921\) −2.34813e10 −0.990407
\(922\) 6.88960e7 4.42768e7i 0.00289492 0.00186045i
\(923\) 3.43665e8 2.39025e9i 0.0143857 0.100054i
\(924\) 4.39815e8 9.63060e8i 0.0183408 0.0401607i
\(925\) 1.16929e10 3.43333e9i 0.485763 0.142633i
\(926\) −4.35584e9 9.53795e9i −0.180274 0.394745i
\(927\) −8.72277e8 1.00666e9i −0.0359646 0.0415054i
\(928\) 4.67375e9 + 3.25067e10i 0.191976 + 1.33523i
\(929\) −4.30232e10 1.26327e10i −1.76055 0.516943i −0.768177 0.640238i \(-0.778836\pi\)
−0.992370 + 0.123295i \(0.960654\pi\)
\(930\) 1.42170e9 1.64073e9i 0.0579586 0.0668878i
\(931\) −1.86692e10 1.19980e10i −0.758231 0.487285i
\(932\) 1.47875e10 + 9.50334e9i 0.598327 + 0.384521i
\(933\) −1.59428e10 + 1.83989e10i −0.642655 + 0.741663i
\(934\) 1.92570e10 + 5.65438e9i 0.773349 + 0.227076i
\(935\) −3.84804e7 2.67637e8i −0.00153957 0.0107079i
\(936\) −1.30489e9 1.50592e9i −0.0520126 0.0600257i
\(937\) −3.08391e9 6.75283e9i −0.122465 0.268162i 0.838463 0.544958i \(-0.183455\pi\)
−0.960929 + 0.276796i \(0.910727\pi\)
\(938\) 4.63389e9 1.36063e9i 0.183331 0.0538308i
\(939\) −4.21713e9 + 9.23423e9i −0.166222 + 0.363975i
\(940\) −1.40974e9 + 9.80495e9i −0.0553594 + 0.385033i
\(941\) −2.43826e10 + 1.56697e10i −0.953929 + 0.613053i −0.922311 0.386447i \(-0.873702\pi\)
−0.0316171 + 0.999500i \(0.510066\pi\)
\(942\) −5.48822e9 −0.213921
\(943\) −4.88987e9 + 1.31735e10i −0.189892 + 0.511576i
\(944\) −3.33210e9 −0.128919
\(945\) 1.38992e9 8.93247e8i 0.0535770 0.0344318i
\(946\) 7.54821e7 5.24989e8i 0.00289884 0.0201619i
\(947\) −1.63052e10 + 3.57034e10i −0.623880 + 1.36611i 0.288784 + 0.957394i \(0.406749\pi\)
−0.912664 + 0.408712i \(0.865978\pi\)
\(948\) 1.82506e10 5.35885e9i 0.695740 0.204288i
\(949\) 1.57952e9 + 3.45867e9i 0.0599922 + 0.131364i
\(950\) 1.11111e10 + 1.28229e10i 0.420459 + 0.485236i
\(951\) −6.69131e8 4.65391e9i −0.0252278 0.175463i
\(952\) −2.09420e9 6.14914e8i −0.0786665 0.0230986i
\(953\) 7.17072e9 8.27546e9i 0.268372 0.309718i −0.605527 0.795825i \(-0.707038\pi\)
0.873900 + 0.486106i \(0.161583\pi\)
\(954\) −7.62700e8 4.90158e8i −0.0284403 0.0182775i
\(955\) 6.52194e9 + 4.19140e9i 0.242306 + 0.155721i
\(956\) −1.02253e10 + 1.18007e10i −0.378508 + 0.436822i
\(957\) −3.13114e9 9.19385e8i −0.115481 0.0339083i
\(958\) 3.34928e9 + 2.32948e10i 0.123076 + 0.856011i
\(959\) 4.67716e9 + 5.39773e9i 0.171245 + 0.197627i
\(960\) 1.02516e9 + 2.24479e9i 0.0373975 + 0.0818890i
\(961\) 1.75061e10 5.14024e9i 0.636292 0.186832i
\(962\) −1.07093e9 + 2.34500e9i −0.0387835 + 0.0849240i
\(963\) −2.26999e9 + 1.57881e10i −0.0819091 + 0.569690i
\(964\) 9.17995e9 5.89959e9i 0.330043 0.212106i
\(965\) −2.05180e10 −0.735005
\(966\) −2.73562e9 4.99123e9i −0.0976418 0.178151i
\(967\) −4.81443e10 −1.71219 −0.856095 0.516818i \(-0.827116\pi\)
−0.856095 + 0.516818i \(0.827116\pi\)
\(968\) 2.10744e10 1.35437e10i 0.746778 0.479925i
\(969\) 5.08425e8 3.53617e9i 0.0179512 0.124853i
\(970\) 4.69910e9 1.02896e10i 0.165316 0.361991i
\(971\) 2.36828e10 6.95389e9i 0.830167 0.243759i 0.161078 0.986942i \(-0.448503\pi\)
0.669089 + 0.743183i \(0.266685\pi\)
\(972\) −5.48698e8 1.20148e9i −0.0191647 0.0419648i
\(973\) 2.13092e10 + 2.45921e10i 0.741603 + 0.855855i
\(974\) 2.13311e9 + 1.48361e10i 0.0739701 + 0.514473i
\(975\) −3.15147e9 9.25355e8i −0.108892 0.0319736i
\(976\) −9.77800e8 + 1.12844e9i −0.0336648 + 0.0388512i
\(977\) 6.67651e9 + 4.29074e9i 0.229044 + 0.147198i 0.650130 0.759823i \(-0.274715\pi\)
−0.421086 + 0.907021i \(0.638351\pi\)
\(978\) −4.80065e8 3.08519e8i −0.0164102 0.0105462i
\(979\) 2.96060e8 3.41672e8i 0.0100842 0.0116378i
\(980\) −5.66569e9 1.66360e9i −0.192292 0.0564621i
\(981\) 6.60215e8 + 4.59190e9i 0.0223277 + 0.155293i
\(982\) 1.32987e10 + 1.53475e10i 0.448145 + 0.517187i
\(983\) −5.13164e9 1.12367e10i −0.172313 0.377314i 0.803697 0.595039i \(-0.202863\pi\)
−0.976010 + 0.217726i \(0.930136\pi\)
\(984\) 8.23100e9 2.41684e9i 0.275404 0.0808658i
\(985\) 3.61400e9 7.91356e9i 0.120493 0.263843i
\(986\) −4.00504e8 + 2.78557e9i −0.0133057 + 0.0925433i
\(987\) −1.05722e10 + 6.79437e9i −0.349991 + 0.224926i
\(988\) 9.19097e9 0.303188
\(989\) 5.17099e9 + 5.15475e9i 0.169976 + 0.169442i
\(990\) −4.30465e8 −0.0140998
\(991\) 2.67322e10 1.71798e10i 0.872524 0.560737i −0.0259999 0.999662i \(-0.508277\pi\)
0.898524 + 0.438925i \(0.144641\pi\)
\(992\) 2.63176e9 1.83043e10i 0.0855964 0.595336i
\(993\) 2.71912e8 5.95405e8i 0.00881265 0.0192970i
\(994\) −4.04043e9 + 1.18638e9i −0.130489 + 0.0383152i
\(995\) −9.20327e8 2.01523e9i −0.0296184 0.0648552i
\(996\) −1.36843e10 1.57925e10i −0.438849 0.506459i
\(997\) 2.35252e9 + 1.63621e10i 0.0751796 + 0.522886i 0.992259 + 0.124182i \(0.0396307\pi\)
−0.917080 + 0.398704i \(0.869460\pi\)
\(998\) 6.51589e9 + 1.91324e9i 0.207499 + 0.0609273i
\(999\) −2.67513e9 + 3.08727e9i −0.0848919 + 0.0979704i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 69.8.e.a.58.9 yes 140
23.2 even 11 inner 69.8.e.a.25.9 140
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.8.e.a.25.9 140 23.2 even 11 inner
69.8.e.a.58.9 yes 140 1.1 even 1 trivial