Properties

Label 43.10.c.a.6.17
Level $43$
Weight $10$
Character 43.6
Analytic conductor $22.147$
Analytic rank $0$
Dimension $64$
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] = [43,10,Mod(6,43)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(43, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("43.6");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 43.c (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: \(22.1465409550\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(32\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 6.17
Character \(\chi\) \(=\) 43.6
Dual form 43.10.c.a.36.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.79962 q^{2} +(-100.854 + 174.685i) q^{3} -508.761 q^{4} +(-371.655 + 643.725i) q^{5} +(-181.499 + 314.366i) q^{6} +(-4777.62 - 8275.08i) q^{7} -1836.98 q^{8} +(-10501.7 - 18189.4i) q^{9} +O(q^{10})\) \(q+1.79962 q^{2} +(-100.854 + 174.685i) q^{3} -508.761 q^{4} +(-371.655 + 643.725i) q^{5} +(-181.499 + 314.366i) q^{6} +(-4777.62 - 8275.08i) q^{7} -1836.98 q^{8} +(-10501.7 - 18189.4i) q^{9} +(-668.837 + 1158.46i) q^{10} -90787.3 q^{11} +(51310.8 - 88872.8i) q^{12} +(70075.7 + 121375. i) q^{13} +(-8597.88 - 14892.0i) q^{14} +(-74966.0 - 129845. i) q^{15} +257180. q^{16} +(54843.8 + 94992.3i) q^{17} +(-18899.0 - 32734.0i) q^{18} +(-91420.6 + 158345. i) q^{19} +(189084. - 327503. i) q^{20} +1.92737e6 q^{21} -163382. q^{22} +(-432097. + 748415. i) q^{23} +(185267. - 320892. i) q^{24} +(700307. + 1.21297e6i) q^{25} +(126109. + 218428. i) q^{26} +266325. q^{27} +(2.43067e6 + 4.21004e6i) q^{28} +(-2.36213e6 - 4.09134e6i) q^{29} +(-134910. - 233671. i) q^{30} +(305225. - 528665. i) q^{31} +1.40336e6 q^{32} +(9.15628e6 - 1.58591e7i) q^{33} +(98697.8 + 170950. i) q^{34} +7.10250e6 q^{35} +(5.34285e6 + 9.25408e6i) q^{36} +(6.11112e6 - 1.05848e7i) q^{37} +(-164522. + 284961. i) q^{38} -2.82697e7 q^{39} +(682723. - 1.18251e6i) q^{40} +1.72489e7 q^{41} +3.46853e6 q^{42} +(-1.87110e7 + 1.23488e7i) q^{43} +4.61891e7 q^{44} +1.56120e7 q^{45} +(-777610. + 1.34686e6i) q^{46} +4.37638e7 q^{47} +(-2.59377e7 + 4.49254e7i) q^{48} +(-2.54745e7 + 4.41231e7i) q^{49} +(1.26028e6 + 2.18288e6i) q^{50} -2.21249e7 q^{51} +(-3.56518e7 - 6.17508e7i) q^{52} +(6.47355e6 - 1.12125e7i) q^{53} +479282. q^{54} +(3.37415e7 - 5.84421e7i) q^{55} +(8.77638e6 + 1.52011e7i) q^{56} +(-1.84403e7 - 3.19396e7i) q^{57} +(-4.25094e6 - 7.36284e6i) q^{58} -3.13262e7 q^{59} +(3.81398e7 + 6.60601e7i) q^{60} +(-5.12049e7 - 8.86895e7i) q^{61} +(549287. - 951394. i) q^{62} +(-1.00346e8 + 1.73804e8i) q^{63} -1.29151e8 q^{64} -1.04176e8 q^{65} +(1.64778e7 - 2.85404e7i) q^{66} +(-3.17175e7 + 5.49364e7i) q^{67} +(-2.79024e7 - 4.83284e7i) q^{68} +(-8.71578e7 - 1.50962e8i) q^{69} +1.27818e7 q^{70} +(-1.73624e8 - 3.00725e8i) q^{71} +(1.92914e7 + 3.34136e7i) q^{72} +(5.04976e7 + 8.74645e7i) q^{73} +(1.09977e7 - 1.90485e7i) q^{74} -2.82516e8 q^{75} +(4.65113e7 - 8.05599e7i) q^{76} +(4.33747e8 + 7.51272e8i) q^{77} -5.08747e7 q^{78} +(2.05457e8 + 3.55863e8i) q^{79} +(-9.55822e7 + 1.65553e8i) q^{80} +(1.79844e8 - 3.11500e8i) q^{81} +3.10414e7 q^{82} +(-1.54309e8 + 2.67272e8i) q^{83} -9.80573e8 q^{84} -8.15319e7 q^{85} +(-3.36726e7 + 2.22231e7i) q^{86} +9.52925e8 q^{87} +1.66774e8 q^{88} +(2.81540e8 - 4.87641e8i) q^{89} +2.80956e7 q^{90} +(6.69590e8 - 1.15976e9i) q^{91} +(2.19835e8 - 3.80765e8i) q^{92} +(6.15664e7 + 1.06636e8i) q^{93} +7.87581e7 q^{94} +(-6.79539e7 - 1.17700e8i) q^{95} +(-1.41535e8 + 2.45145e8i) q^{96} +5.14501e8 q^{97} +(-4.58443e7 + 7.94046e7i) q^{98} +(9.53418e8 + 1.65137e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 70 q^{2} + 307 q^{3} + 16038 q^{4} + 681 q^{5} - 1281 q^{6} + 957 q^{7} - 10920 q^{8} - 255339 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 70 q^{2} + 307 q^{3} + 16038 q^{4} + 681 q^{5} - 1281 q^{6} + 957 q^{7} - 10920 q^{8} - 255339 q^{9} - 6237 q^{10} - 180682 q^{11} + 274344 q^{12} + 115245 q^{13} - 171208 q^{14} + 138833 q^{15} + 4289206 q^{16} + 65180 q^{17} + 603985 q^{18} + 39150 q^{19} - 2709775 q^{20} - 3105162 q^{21} + 598456 q^{22} + 1285907 q^{23} - 292550 q^{24} - 14709917 q^{25} + 5332695 q^{26} - 20118002 q^{27} - 5475298 q^{28} + 1274091 q^{29} + 28424751 q^{30} + 2899781 q^{31} - 16322030 q^{32} + 30668912 q^{33} + 6822099 q^{34} - 14750922 q^{35} - 113819232 q^{36} - 13772217 q^{37} + 2700532 q^{38} + 49876982 q^{39} - 55802359 q^{40} + 5375394 q^{41} - 62768266 q^{42} - 4250879 q^{43} - 125171958 q^{44} + 74719384 q^{45} - 91405220 q^{46} + 46104596 q^{47} + 294588191 q^{48} - 233221733 q^{49} + 380339342 q^{50} + 229598406 q^{51} + 166281612 q^{52} + 125396641 q^{53} - 137752484 q^{54} + 139471854 q^{55} + 41104589 q^{56} - 289586721 q^{57} - 183782516 q^{58} - 637949078 q^{59} - 70735747 q^{60} - 95573327 q^{61} + 181277053 q^{62} + 226632970 q^{63} + 712599660 q^{64} - 498753718 q^{65} - 349240445 q^{66} - 276270786 q^{67} + 1034771928 q^{68} - 199705103 q^{69} + 1780847990 q^{70} + 651945247 q^{71} - 270063054 q^{72} - 182725322 q^{73} - 193737672 q^{74} - 3155252572 q^{75} + 492133584 q^{76} + 216024528 q^{77} + 2562586420 q^{78} - 376932221 q^{79} - 783129021 q^{80} - 2146956496 q^{81} + 2373824428 q^{82} + 1008544071 q^{83} - 9413139208 q^{84} - 1131353054 q^{85} - 1641459050 q^{86} + 5060470018 q^{87} + 369936980 q^{88} + 2244184366 q^{89} + 3302428348 q^{90} + 3951711 q^{91} + 4361095637 q^{92} + 3133616089 q^{93} + 3002217406 q^{94} + 1515822931 q^{95} + 69408612 q^{96} - 6951085934 q^{97} + 1120193981 q^{98} + 1264470179 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.79962 0.0795326 0.0397663 0.999209i \(-0.487339\pi\)
0.0397663 + 0.999209i \(0.487339\pi\)
\(3\) −100.854 + 174.685i −0.718867 + 1.24511i 0.242582 + 0.970131i \(0.422006\pi\)
−0.961449 + 0.274984i \(0.911328\pi\)
\(4\) −508.761 −0.993675
\(5\) −371.655 + 643.725i −0.265935 + 0.460612i −0.967808 0.251689i \(-0.919014\pi\)
0.701873 + 0.712302i \(0.252347\pi\)
\(6\) −181.499 + 314.366i −0.0571734 + 0.0990272i
\(7\) −4777.62 8275.08i −0.752091 1.30266i −0.946808 0.321800i \(-0.895712\pi\)
0.194717 0.980859i \(-0.437621\pi\)
\(8\) −1836.98 −0.158562
\(9\) −10501.7 18189.4i −0.533540 0.924119i
\(10\) −668.837 + 1158.46i −0.0211505 + 0.0366337i
\(11\) −90787.3 −1.86964 −0.934820 0.355123i \(-0.884439\pi\)
−0.934820 + 0.355123i \(0.884439\pi\)
\(12\) 51310.8 88872.8i 0.714320 1.23724i
\(13\) 70075.7 + 121375.i 0.680491 + 1.17865i 0.974831 + 0.222944i \(0.0715668\pi\)
−0.294340 + 0.955701i \(0.595100\pi\)
\(14\) −8597.88 14892.0i −0.0598157 0.103604i
\(15\) −74966.0 129845.i −0.382344 0.662238i
\(16\) 257180. 0.981064
\(17\) 54843.8 + 94992.3i 0.159260 + 0.275847i 0.934602 0.355695i \(-0.115756\pi\)
−0.775342 + 0.631542i \(0.782422\pi\)
\(18\) −18899.0 32734.0i −0.0424338 0.0734975i
\(19\) −91420.6 + 158345.i −0.160936 + 0.278749i −0.935205 0.354108i \(-0.884785\pi\)
0.774269 + 0.632857i \(0.218118\pi\)
\(20\) 189084. 327503.i 0.264253 0.457699i
\(21\) 1.92737e6 2.16261
\(22\) −163382. −0.148697
\(23\) −432097. + 748415.i −0.321963 + 0.557657i −0.980893 0.194548i \(-0.937676\pi\)
0.658930 + 0.752205i \(0.271009\pi\)
\(24\) 185267. 320892.i 0.113985 0.197428i
\(25\) 700307. + 1.21297e6i 0.358557 + 0.621040i
\(26\) 126109. + 218428.i 0.0541212 + 0.0937407i
\(27\) 266325. 0.0964439
\(28\) 2.43067e6 + 4.21004e6i 0.747333 + 1.29442i
\(29\) −2.36213e6 4.09134e6i −0.620174 1.07417i −0.989453 0.144854i \(-0.953729\pi\)
0.369279 0.929319i \(-0.379605\pi\)
\(30\) −134910. 233671.i −0.0304088 0.0526695i
\(31\) 305225. 528665.i 0.0593598 0.102814i −0.834818 0.550525i \(-0.814427\pi\)
0.894178 + 0.447711i \(0.147761\pi\)
\(32\) 1.40336e6 0.236589
\(33\) 9.15628e6 1.58591e7i 1.34402 2.32792i
\(34\) 98697.8 + 170950.i 0.0126664 + 0.0219388i
\(35\) 7.10250e6 0.800028
\(36\) 5.34285e6 + 9.25408e6i 0.530165 + 0.918273i
\(37\) 6.11112e6 1.05848e7i 0.536060 0.928483i −0.463052 0.886331i \(-0.653246\pi\)
0.999111 0.0421513i \(-0.0134211\pi\)
\(38\) −164522. + 284961.i −0.0127996 + 0.0221696i
\(39\) −2.82697e7 −1.95673
\(40\) 682723. 1.18251e6i 0.0421672 0.0730357i
\(41\) 1.72489e7 0.953308 0.476654 0.879091i \(-0.341849\pi\)
0.476654 + 0.879091i \(0.341849\pi\)
\(42\) 3.46853e6 0.171998
\(43\) −1.87110e7 + 1.23488e7i −0.834619 + 0.550828i
\(44\) 4.61891e7 1.85781
\(45\) 1.56120e7 0.567548
\(46\) −777610. + 1.34686e6i −0.0256066 + 0.0443519i
\(47\) 4.37638e7 1.30820 0.654101 0.756407i \(-0.273047\pi\)
0.654101 + 0.756407i \(0.273047\pi\)
\(48\) −2.59377e7 + 4.49254e7i −0.705255 + 1.22154i
\(49\) −2.54745e7 + 4.41231e7i −0.631281 + 1.09341i
\(50\) 1.26028e6 + 2.18288e6i 0.0285170 + 0.0493929i
\(51\) −2.21249e7 −0.457948
\(52\) −3.56518e7 6.17508e7i −0.676187 1.17119i
\(53\) 6.47355e6 1.12125e7i 0.112694 0.195192i −0.804162 0.594411i \(-0.797385\pi\)
0.916856 + 0.399219i \(0.130719\pi\)
\(54\) 479282. 0.00767043
\(55\) 3.37415e7 5.84421e7i 0.497202 0.861179i
\(56\) 8.77638e6 + 1.52011e7i 0.119253 + 0.206552i
\(57\) −1.84403e7 3.19396e7i −0.231383 0.400767i
\(58\) −4.25094e6 7.36284e6i −0.0493240 0.0854317i
\(59\) −3.13262e7 −0.336568 −0.168284 0.985739i \(-0.553823\pi\)
−0.168284 + 0.985739i \(0.553823\pi\)
\(60\) 3.81398e7 + 6.60601e7i 0.379925 + 0.658049i
\(61\) −5.12049e7 8.86895e7i −0.473508 0.820140i 0.526032 0.850465i \(-0.323679\pi\)
−0.999540 + 0.0303245i \(0.990346\pi\)
\(62\) 549287. 951394.i 0.00472103 0.00817707i
\(63\) −1.00346e8 + 1.73804e8i −0.802541 + 1.39004i
\(64\) −1.29151e8 −0.962247
\(65\) −1.04176e8 −0.723865
\(66\) 1.64778e7 2.85404e7i 0.106894 0.185145i
\(67\) −3.17175e7 + 5.49364e7i −0.192293 + 0.333061i −0.946010 0.324138i \(-0.894926\pi\)
0.753717 + 0.657199i \(0.228259\pi\)
\(68\) −2.79024e7 4.83284e7i −0.158253 0.274102i
\(69\) −8.71578e7 1.50962e8i −0.462898 0.801763i
\(70\) 1.27818e7 0.0636283
\(71\) −1.73624e8 3.00725e8i −0.810860 1.40445i −0.912263 0.409606i \(-0.865666\pi\)
0.101403 0.994845i \(-0.467667\pi\)
\(72\) 1.92914e7 + 3.34136e7i 0.0845992 + 0.146530i
\(73\) 5.04976e7 + 8.74645e7i 0.208122 + 0.360478i 0.951123 0.308812i \(-0.0999315\pi\)
−0.743001 + 0.669290i \(0.766598\pi\)
\(74\) 1.09977e7 1.90485e7i 0.0426342 0.0738446i
\(75\) −2.82516e8 −1.03102
\(76\) 4.65113e7 8.05599e7i 0.159918 0.276986i
\(77\) 4.33747e8 + 7.51272e8i 1.40614 + 2.43550i
\(78\) −5.08747e7 −0.155624
\(79\) 2.05457e8 + 3.55863e8i 0.593471 + 1.02792i 0.993761 + 0.111534i \(0.0355763\pi\)
−0.400289 + 0.916389i \(0.631090\pi\)
\(80\) −9.55822e7 + 1.65553e8i −0.260899 + 0.451890i
\(81\) 1.79844e8 3.11500e8i 0.464210 0.804035i
\(82\) 3.10414e7 0.0758190
\(83\) −1.54309e8 + 2.67272e8i −0.356896 + 0.618161i −0.987440 0.157991i \(-0.949498\pi\)
0.630545 + 0.776153i \(0.282831\pi\)
\(84\) −9.80573e8 −2.14893
\(85\) −8.15319e7 −0.169411
\(86\) −3.36726e7 + 2.22231e7i −0.0663794 + 0.0438088i
\(87\) 9.52925e8 1.78329
\(88\) 1.66774e8 0.296454
\(89\) 2.81540e8 4.87641e8i 0.475647 0.823844i −0.523964 0.851740i \(-0.675547\pi\)
0.999611 + 0.0278960i \(0.00888073\pi\)
\(90\) 2.80956e7 0.0451385
\(91\) 6.69590e8 1.15976e9i 1.02358 1.77290i
\(92\) 2.19835e8 3.80765e8i 0.319927 0.554130i
\(93\) 6.15664e7 + 1.06636e8i 0.0853436 + 0.147819i
\(94\) 7.87581e7 0.104045
\(95\) −6.79539e7 1.17700e8i −0.0855969 0.148258i
\(96\) −1.41535e8 + 2.45145e8i −0.170076 + 0.294580i
\(97\) 5.14501e8 0.590084 0.295042 0.955484i \(-0.404666\pi\)
0.295042 + 0.955484i \(0.404666\pi\)
\(98\) −4.58443e7 + 7.94046e7i −0.0502074 + 0.0869617i
\(99\) 9.53418e8 + 1.65137e9i 0.997528 + 1.72777i
\(100\) −3.56289e8 6.17111e8i −0.356289 0.617111i
\(101\) −9.18818e8 1.59144e9i −0.878584 1.52175i −0.852895 0.522082i \(-0.825156\pi\)
−0.0256885 0.999670i \(-0.508178\pi\)
\(102\) −3.98164e7 −0.0364218
\(103\) −3.54468e8 6.13956e8i −0.310320 0.537490i 0.668112 0.744061i \(-0.267103\pi\)
−0.978432 + 0.206571i \(0.933769\pi\)
\(104\) −1.28728e8 2.22963e8i −0.107900 0.186888i
\(105\) −7.16318e8 + 1.24070e9i −0.575114 + 0.996127i
\(106\) 1.16499e7 2.01782e7i 0.00896286 0.0155241i
\(107\) 1.43343e9 1.05718 0.528591 0.848877i \(-0.322721\pi\)
0.528591 + 0.848877i \(0.322721\pi\)
\(108\) −1.35496e8 −0.0958338
\(109\) −7.20533e8 + 1.24800e9i −0.488917 + 0.846828i −0.999919 0.0127511i \(-0.995941\pi\)
0.511002 + 0.859579i \(0.329274\pi\)
\(110\) 6.07218e7 1.05173e8i 0.0395438 0.0684918i
\(111\) 1.23267e9 + 2.13504e9i 0.770711 + 1.33491i
\(112\) −1.22871e9 2.12818e9i −0.737849 1.27799i
\(113\) 1.58269e9 0.913152 0.456576 0.889684i \(-0.349076\pi\)
0.456576 + 0.889684i \(0.349076\pi\)
\(114\) −3.31855e7 5.74790e7i −0.0184025 0.0318741i
\(115\) −3.21182e8 5.56304e8i −0.171242 0.296601i
\(116\) 1.20176e9 + 2.08151e9i 0.616251 + 1.06738i
\(117\) 1.47182e9 2.54927e9i 0.726139 1.25771i
\(118\) −5.63751e7 −0.0267681
\(119\) 5.24046e8 9.07673e8i 0.239556 0.414924i
\(120\) 1.37711e8 + 2.38522e8i 0.0606252 + 0.105006i
\(121\) 5.88438e9 2.49555
\(122\) −9.21492e7 1.59607e8i −0.0376593 0.0652279i
\(123\) −1.73962e9 + 3.01311e9i −0.685302 + 1.18698i
\(124\) −1.55287e8 + 2.68964e8i −0.0589843 + 0.102164i
\(125\) −2.49287e9 −0.913281
\(126\) −1.80584e8 + 3.12781e8i −0.0638282 + 0.110554i
\(127\) −4.91530e9 −1.67662 −0.838308 0.545198i \(-0.816455\pi\)
−0.838308 + 0.545198i \(0.816455\pi\)
\(128\) −9.50941e8 −0.313119
\(129\) −2.70065e8 4.51395e9i −0.0858646 1.43517i
\(130\) −1.87477e8 −0.0575708
\(131\) 3.28003e9 0.973098 0.486549 0.873653i \(-0.338256\pi\)
0.486549 + 0.873653i \(0.338256\pi\)
\(132\) −4.65836e9 + 8.06852e9i −1.33552 + 2.31319i
\(133\) 1.74709e9 0.484154
\(134\) −5.70794e7 + 9.88644e7i −0.0152935 + 0.0264892i
\(135\) −9.89809e7 + 1.71440e8i −0.0256478 + 0.0444232i
\(136\) −1.00747e8 1.74499e8i −0.0252526 0.0437389i
\(137\) −4.30090e8 −0.104308 −0.0521539 0.998639i \(-0.516609\pi\)
−0.0521539 + 0.998639i \(0.516609\pi\)
\(138\) −1.56851e8 2.71673e8i −0.0368155 0.0637662i
\(139\) 2.28414e9 3.95625e9i 0.518986 0.898911i −0.480770 0.876847i \(-0.659643\pi\)
0.999757 0.0220641i \(-0.00702380\pi\)
\(140\) −3.61348e9 −0.794968
\(141\) −4.41377e9 + 7.64487e9i −0.940424 + 1.62886i
\(142\) −3.12456e8 5.41189e8i −0.0644898 0.111700i
\(143\) −6.36198e9 1.10193e10i −1.27227 2.20364i
\(144\) −2.70082e9 4.67796e9i −0.523437 0.906619i
\(145\) 3.51160e9 0.659703
\(146\) 9.08764e7 + 1.57403e8i 0.0165525 + 0.0286698i
\(147\) −5.13842e9 8.90000e9i −0.907614 1.57203i
\(148\) −3.10910e9 + 5.38512e9i −0.532669 + 0.922610i
\(149\) −1.92619e9 + 3.33626e9i −0.320156 + 0.554527i −0.980520 0.196419i \(-0.937069\pi\)
0.660364 + 0.750946i \(0.270402\pi\)
\(150\) −5.08421e8 −0.0819997
\(151\) −1.21388e10 −1.90012 −0.950059 0.312071i \(-0.898977\pi\)
−0.950059 + 0.312071i \(0.898977\pi\)
\(152\) 1.67938e8 2.90877e8i 0.0255183 0.0441991i
\(153\) 1.15190e9 1.99516e9i 0.169944 0.294351i
\(154\) 7.80578e8 + 1.35200e9i 0.111834 + 0.193702i
\(155\) 2.26877e8 + 3.92962e8i 0.0315716 + 0.0546837i
\(156\) 1.43826e10 1.94435
\(157\) 4.24066e9 + 7.34505e9i 0.557039 + 0.964820i 0.997742 + 0.0671666i \(0.0213959\pi\)
−0.440703 + 0.897653i \(0.645271\pi\)
\(158\) 3.69744e8 + 6.40416e8i 0.0472003 + 0.0817533i
\(159\) 1.30577e9 + 2.26166e9i 0.162024 + 0.280634i
\(160\) −5.21565e8 + 9.03378e8i −0.0629171 + 0.108976i
\(161\) 8.25759e9 0.968583
\(162\) 3.23651e8 5.60580e8i 0.0369198 0.0639470i
\(163\) 7.03474e9 + 1.21845e10i 0.780556 + 1.35196i 0.931618 + 0.363438i \(0.118397\pi\)
−0.151062 + 0.988524i \(0.548269\pi\)
\(164\) −8.77556e9 −0.947278
\(165\) 6.80596e9 + 1.17883e10i 0.714844 + 1.23815i
\(166\) −2.77698e8 + 4.80987e8i −0.0283848 + 0.0491640i
\(167\) 8.34850e9 1.44600e10i 0.830586 1.43862i −0.0669887 0.997754i \(-0.521339\pi\)
0.897574 0.440863i \(-0.145328\pi\)
\(168\) −3.54054e9 −0.342908
\(169\) −4.51896e9 + 7.82707e9i −0.426136 + 0.738090i
\(170\) −1.46726e8 −0.0134737
\(171\) 3.84028e9 0.343463
\(172\) 9.51941e9 6.28259e9i 0.829339 0.547344i
\(173\) 2.15678e9 0.183062 0.0915311 0.995802i \(-0.470824\pi\)
0.0915311 + 0.995802i \(0.470824\pi\)
\(174\) 1.71490e9 0.141830
\(175\) 6.69160e9 1.15902e10i 0.539335 0.934156i
\(176\) −2.33487e10 −1.83424
\(177\) 3.15938e9 5.47220e9i 0.241948 0.419066i
\(178\) 5.06663e8 8.77567e8i 0.0378294 0.0655225i
\(179\) −2.92312e9 5.06300e9i −0.212818 0.368612i 0.739777 0.672852i \(-0.234931\pi\)
−0.952595 + 0.304240i \(0.901597\pi\)
\(180\) −7.94278e9 −0.563958
\(181\) 8.84208e9 + 1.53149e10i 0.612352 + 1.06062i 0.990843 + 0.135019i \(0.0431096\pi\)
−0.378491 + 0.925605i \(0.623557\pi\)
\(182\) 1.20501e9 2.08713e9i 0.0814081 0.141003i
\(183\) 2.06569e10 1.36156
\(184\) 7.93754e8 1.37482e9i 0.0510512 0.0884232i
\(185\) 4.54246e9 + 7.86777e9i 0.285114 + 0.493832i
\(186\) 1.10796e8 + 1.91904e8i 0.00678759 + 0.0117565i
\(187\) −4.97912e9 8.62409e9i −0.297759 0.515734i
\(188\) −2.22653e10 −1.29993
\(189\) −1.27240e9 2.20386e9i −0.0725345 0.125633i
\(190\) −1.22291e8 2.11814e8i −0.00680774 0.0117914i
\(191\) 4.14251e9 7.17504e9i 0.225224 0.390099i −0.731163 0.682203i \(-0.761022\pi\)
0.956386 + 0.292104i \(0.0943554\pi\)
\(192\) 1.30254e10 2.25606e10i 0.691728 1.19811i
\(193\) −1.56419e10 −0.811490 −0.405745 0.913986i \(-0.632988\pi\)
−0.405745 + 0.913986i \(0.632988\pi\)
\(194\) 9.25905e8 0.0469309
\(195\) 1.05066e10 1.81980e10i 0.520363 0.901295i
\(196\) 1.29604e10 2.24481e10i 0.627288 1.08649i
\(197\) 1.43688e10 + 2.48875e10i 0.679708 + 1.17729i 0.975069 + 0.221903i \(0.0712268\pi\)
−0.295361 + 0.955386i \(0.595440\pi\)
\(198\) 1.71579e9 + 2.97183e9i 0.0793359 + 0.137414i
\(199\) −2.17991e10 −0.985369 −0.492684 0.870208i \(-0.663984\pi\)
−0.492684 + 0.870208i \(0.663984\pi\)
\(200\) −1.28645e9 2.22820e9i −0.0568536 0.0984733i
\(201\) −6.39770e9 1.10811e10i −0.276466 0.478853i
\(202\) −1.65352e9 2.86398e9i −0.0698760 0.121029i
\(203\) −2.25707e10 + 3.90937e10i −0.932854 + 1.61575i
\(204\) 1.12563e10 0.455051
\(205\) −6.41063e9 + 1.11035e10i −0.253518 + 0.439106i
\(206\) −6.37906e8 1.10489e9i −0.0246805 0.0427479i
\(207\) 1.81510e10 0.687122
\(208\) 1.80221e10 + 3.12151e10i 0.667605 + 1.15633i
\(209\) 8.29983e9 1.43757e10i 0.300892 0.521160i
\(210\) −1.28910e9 + 2.23278e9i −0.0457403 + 0.0792245i
\(211\) 3.04854e10 1.05882 0.529408 0.848367i \(-0.322414\pi\)
0.529408 + 0.848367i \(0.322414\pi\)
\(212\) −3.29349e9 + 5.70450e9i −0.111981 + 0.193957i
\(213\) 7.00427e10 2.33160
\(214\) 2.57962e9 0.0840803
\(215\) −9.95207e8 1.66342e10i −0.0317644 0.530920i
\(216\) −4.89233e8 −0.0152923
\(217\) −5.83299e9 −0.178576
\(218\) −1.29668e9 + 2.24592e9i −0.0388848 + 0.0673504i
\(219\) −2.03716e10 −0.598449
\(220\) −1.71664e10 + 2.97331e10i −0.494057 + 0.855732i
\(221\) −7.68644e9 + 1.33133e10i −0.216750 + 0.375423i
\(222\) 2.21833e9 + 3.84225e9i 0.0612967 + 0.106169i
\(223\) −4.04183e10 −1.09448 −0.547238 0.836977i \(-0.684321\pi\)
−0.547238 + 0.836977i \(0.684321\pi\)
\(224\) −6.70471e9 1.16129e10i −0.177936 0.308194i
\(225\) 1.47088e10 2.54764e10i 0.382610 0.662699i
\(226\) 2.84824e9 0.0726253
\(227\) 2.68919e10 4.65782e10i 0.672211 1.16430i −0.305065 0.952332i \(-0.598678\pi\)
0.977276 0.211972i \(-0.0679886\pi\)
\(228\) 9.38173e9 + 1.62496e10i 0.229920 + 0.398232i
\(229\) 1.53757e10 + 2.66315e10i 0.369466 + 0.639934i 0.989482 0.144655i \(-0.0462072\pi\)
−0.620016 + 0.784589i \(0.712874\pi\)
\(230\) −5.78005e8 1.00113e9i −0.0136194 0.0235894i
\(231\) −1.74981e11 −4.04331
\(232\) 4.33919e9 + 7.51570e9i 0.0983361 + 0.170323i
\(233\) −5.62090e9 9.73569e9i −0.124941 0.216404i 0.796769 0.604284i \(-0.206541\pi\)
−0.921710 + 0.387880i \(0.873207\pi\)
\(234\) 2.64872e9 4.58772e9i 0.0577517 0.100029i
\(235\) −1.62650e10 + 2.81719e10i −0.347896 + 0.602574i
\(236\) 1.59375e10 0.334439
\(237\) −8.28850e10 −1.70651
\(238\) 9.43081e8 1.63346e9i 0.0190525 0.0330000i
\(239\) −3.21332e10 + 5.56563e10i −0.637035 + 1.10338i 0.349045 + 0.937106i \(0.386506\pi\)
−0.986080 + 0.166271i \(0.946827\pi\)
\(240\) −1.92798e10 3.33935e10i −0.375103 0.649698i
\(241\) −1.38185e10 2.39343e10i −0.263866 0.457029i 0.703400 0.710794i \(-0.251664\pi\)
−0.967266 + 0.253765i \(0.918331\pi\)
\(242\) 1.05896e10 0.198478
\(243\) 3.88972e10 + 6.73719e10i 0.715632 + 1.23951i
\(244\) 2.60511e10 + 4.51218e10i 0.470513 + 0.814953i
\(245\) −1.89354e10 3.27971e10i −0.335759 0.581552i
\(246\) −3.13065e9 + 5.42245e9i −0.0545038 + 0.0944034i
\(247\) −2.56255e10 −0.438062
\(248\) −5.60691e8 + 9.71146e8i −0.00941220 + 0.0163024i
\(249\) −3.11255e10 5.39110e10i −0.513121 0.888752i
\(250\) −4.48621e9 −0.0726356
\(251\) −1.87460e10 3.24690e10i −0.298110 0.516342i 0.677593 0.735437i \(-0.263023\pi\)
−0.975704 + 0.219095i \(0.929690\pi\)
\(252\) 5.10521e10 8.84249e10i 0.797465 1.38125i
\(253\) 3.92289e10 6.79465e10i 0.601955 1.04262i
\(254\) −8.84566e9 −0.133345
\(255\) 8.22284e9 1.42424e10i 0.121784 0.210937i
\(256\) 6.44138e10 0.937344
\(257\) −9.88757e9 −0.141381 −0.0706904 0.997498i \(-0.522520\pi\)
−0.0706904 + 0.997498i \(0.522520\pi\)
\(258\) −4.86013e8 8.12337e9i −0.00682903 0.114143i
\(259\) −1.16786e11 −1.61266
\(260\) 5.30007e10 0.719286
\(261\) −4.96127e10 + 8.59317e10i −0.661776 + 1.14623i
\(262\) 5.90279e9 0.0773930
\(263\) 4.09698e10 7.09617e10i 0.528035 0.914583i −0.471431 0.881903i \(-0.656262\pi\)
0.999466 0.0326804i \(-0.0104044\pi\)
\(264\) −1.68199e10 + 2.91329e10i −0.213111 + 0.369119i
\(265\) 4.81186e9 + 8.33438e9i 0.0599386 + 0.103817i
\(266\) 3.14409e9 0.0385060
\(267\) 5.67890e10 + 9.83614e10i 0.683854 + 1.18447i
\(268\) 1.61367e10 2.79495e10i 0.191076 0.330954i
\(269\) −9.02915e10 −1.05138 −0.525692 0.850675i \(-0.676194\pi\)
−0.525692 + 0.850675i \(0.676194\pi\)
\(270\) −1.78128e8 + 3.08526e8i −0.00203983 + 0.00353309i
\(271\) 1.85305e10 + 3.20957e10i 0.208701 + 0.361481i 0.951306 0.308249i \(-0.0997432\pi\)
−0.742605 + 0.669730i \(0.766410\pi\)
\(272\) 1.41047e10 + 2.44301e10i 0.156244 + 0.270623i
\(273\) 1.35062e11 + 2.33934e11i 1.47164 + 2.54895i
\(274\) −7.73997e8 −0.00829587
\(275\) −6.35790e10 1.10122e11i −0.670373 1.16112i
\(276\) 4.43425e10 + 7.68035e10i 0.459970 + 0.796691i
\(277\) 8.99531e10 1.55803e11i 0.918031 1.59008i 0.115629 0.993293i \(-0.463112\pi\)
0.802402 0.596784i \(-0.203555\pi\)
\(278\) 4.11057e9 7.11972e9i 0.0412763 0.0714927i
\(279\) −1.28215e10 −0.126683
\(280\) −1.30472e10 −0.126854
\(281\) 6.02588e10 1.04371e11i 0.576556 0.998625i −0.419314 0.907841i \(-0.637729\pi\)
0.995871 0.0907839i \(-0.0289373\pi\)
\(282\) −7.94309e9 + 1.37578e10i −0.0747943 + 0.129548i
\(283\) 8.52548e10 + 1.47666e11i 0.790096 + 1.36849i 0.925907 + 0.377752i \(0.123303\pi\)
−0.135810 + 0.990735i \(0.543364\pi\)
\(284\) 8.83329e10 + 1.52997e11i 0.805731 + 1.39557i
\(285\) 2.74138e10 0.246131
\(286\) −1.14491e10 1.98305e10i −0.101187 0.175261i
\(287\) −8.24085e10 1.42736e11i −0.716974 1.24184i
\(288\) −1.47376e10 2.55263e10i −0.126230 0.218636i
\(289\) 5.32783e10 9.22806e10i 0.449272 0.778162i
\(290\) 6.31953e9 0.0524679
\(291\) −5.18897e10 + 8.98755e10i −0.424192 + 0.734722i
\(292\) −2.56913e10 4.44986e10i −0.206806 0.358198i
\(293\) −1.43952e11 −1.14107 −0.570536 0.821272i \(-0.693265\pi\)
−0.570536 + 0.821272i \(0.693265\pi\)
\(294\) −9.24718e9 1.60166e10i −0.0721849 0.125028i
\(295\) 1.16425e10 2.01654e10i 0.0895052 0.155028i
\(296\) −1.12260e10 + 1.94440e10i −0.0849987 + 0.147222i
\(297\) −2.41789e10 −0.180315
\(298\) −3.46641e9 + 6.00400e9i −0.0254628 + 0.0441029i
\(299\) −1.21118e11 −0.876373
\(300\) 1.43733e11 1.02450
\(301\) 1.91581e11 + 9.58368e10i 1.34525 + 0.672951i
\(302\) −2.18452e10 −0.151121
\(303\) 3.70667e11 2.52634
\(304\) −2.35116e10 + 4.07232e10i −0.157888 + 0.273471i
\(305\) 7.61223e10 0.503689
\(306\) 2.07298e9 3.59051e9i 0.0135160 0.0234105i
\(307\) 6.07117e10 1.05156e11i 0.390077 0.675633i −0.602383 0.798207i \(-0.705782\pi\)
0.992459 + 0.122575i \(0.0391152\pi\)
\(308\) −2.20674e11 3.82218e11i −1.39724 2.42010i
\(309\) 1.42998e11 0.892315
\(310\) 4.08291e8 + 7.07181e8i 0.00251097 + 0.00434913i
\(311\) −3.74984e8 + 6.49492e8i −0.00227296 + 0.00393688i −0.867160 0.498030i \(-0.834057\pi\)
0.864887 + 0.501967i \(0.167390\pi\)
\(312\) 5.19309e10 0.310263
\(313\) −1.85064e10 + 3.20541e10i −0.108987 + 0.188770i −0.915360 0.402636i \(-0.868094\pi\)
0.806373 + 0.591407i \(0.201427\pi\)
\(314\) 7.63157e9 + 1.32183e10i 0.0443027 + 0.0767346i
\(315\) −7.45882e10 1.29190e11i −0.426847 0.739321i
\(316\) −1.04529e11 1.81049e11i −0.589717 1.02142i
\(317\) −1.75299e11 −0.975019 −0.487510 0.873118i \(-0.662095\pi\)
−0.487510 + 0.873118i \(0.662095\pi\)
\(318\) 2.34989e9 + 4.07013e9i 0.0128862 + 0.0223196i
\(319\) 2.14452e11 + 3.71441e11i 1.15950 + 2.00832i
\(320\) 4.79995e10 8.31376e10i 0.255895 0.443223i
\(321\) −1.44568e11 + 2.50398e11i −0.759973 + 1.31631i
\(322\) 1.48605e10 0.0770339
\(323\) −2.00554e10 −0.102523
\(324\) −9.14979e10 + 1.58479e11i −0.461274 + 0.798949i
\(325\) −9.81491e10 + 1.69999e11i −0.487990 + 0.845224i
\(326\) 1.26598e10 + 2.19275e10i 0.0620796 + 0.107525i
\(327\) −1.45338e11 2.51732e11i −0.702932 1.21751i
\(328\) −3.16858e10 −0.151159
\(329\) −2.09087e11 3.62149e11i −0.983887 1.70414i
\(330\) 1.22481e10 + 2.12144e10i 0.0568534 + 0.0984730i
\(331\) 1.24883e11 + 2.16304e11i 0.571843 + 0.990462i 0.996377 + 0.0850495i \(0.0271049\pi\)
−0.424533 + 0.905412i \(0.639562\pi\)
\(332\) 7.85067e10 1.35978e11i 0.354638 0.614251i
\(333\) −2.56708e11 −1.14404
\(334\) 1.50241e10 2.60225e10i 0.0660586 0.114417i
\(335\) −2.35760e10 4.08348e10i −0.102275 0.177145i
\(336\) 4.95682e11 2.12166
\(337\) −3.03878e10 5.26333e10i −0.128341 0.222293i 0.794693 0.607012i \(-0.207632\pi\)
−0.923034 + 0.384719i \(0.874299\pi\)
\(338\) −8.13240e9 + 1.40857e10i −0.0338917 + 0.0587022i
\(339\) −1.59621e11 + 2.76472e11i −0.656435 + 1.13698i
\(340\) 4.14803e10 0.168340
\(341\) −2.77105e10 + 4.79960e10i −0.110981 + 0.192225i
\(342\) 6.91103e9 0.0273165
\(343\) 1.01241e11 0.394940
\(344\) 3.43716e10 2.26845e10i 0.132339 0.0873405i
\(345\) 1.29571e11 0.492402
\(346\) 3.88138e9 0.0145594
\(347\) 6.95761e10 1.20509e11i 0.257619 0.446209i −0.707985 0.706228i \(-0.750395\pi\)
0.965604 + 0.260019i \(0.0837288\pi\)
\(348\) −4.84812e11 −1.77201
\(349\) −9.58825e10 + 1.66073e11i −0.345959 + 0.599219i −0.985528 0.169515i \(-0.945780\pi\)
0.639568 + 0.768734i \(0.279113\pi\)
\(350\) 1.20423e10 2.08579e10i 0.0428947 0.0742959i
\(351\) 1.86629e10 + 3.23251e10i 0.0656292 + 0.113673i
\(352\) −1.27407e11 −0.442335
\(353\) −9.78742e10 1.69523e11i −0.335492 0.581089i 0.648087 0.761566i \(-0.275569\pi\)
−0.983579 + 0.180477i \(0.942236\pi\)
\(354\) 5.68567e9 9.84786e9i 0.0192427 0.0333294i
\(355\) 2.58112e11 0.862544
\(356\) −1.43237e11 + 2.48093e11i −0.472638 + 0.818633i
\(357\) 1.05704e11 + 1.83086e11i 0.344418 + 0.596550i
\(358\) −5.26050e9 9.11145e9i −0.0169260 0.0293166i
\(359\) −1.64360e11 2.84680e11i −0.522242 0.904550i −0.999665 0.0258764i \(-0.991762\pi\)
0.477423 0.878674i \(-0.341571\pi\)
\(360\) −2.86789e10 −0.0899915
\(361\) 1.44628e11 + 2.50504e11i 0.448199 + 0.776304i
\(362\) 1.59124e10 + 2.75610e10i 0.0487019 + 0.0843542i
\(363\) −5.93465e11 + 1.02791e12i −1.79397 + 3.10725i
\(364\) −3.40662e11 + 5.90043e11i −1.01711 + 1.76168i
\(365\) −7.50708e10 −0.221388
\(366\) 3.71746e10 0.108288
\(367\) 2.98391e11 5.16828e11i 0.858594 1.48713i −0.0146765 0.999892i \(-0.504672\pi\)
0.873270 0.487236i \(-0.161995\pi\)
\(368\) −1.11127e11 + 1.92477e11i −0.315867 + 0.547097i
\(369\) −1.81142e11 3.13747e11i −0.508628 0.880970i
\(370\) 8.17468e9 + 1.41590e10i 0.0226758 + 0.0392757i
\(371\) −1.23713e11 −0.339025
\(372\) −3.13226e10 5.42524e10i −0.0848037 0.146884i
\(373\) −1.76908e11 3.06414e11i −0.473214 0.819631i 0.526316 0.850289i \(-0.323573\pi\)
−0.999530 + 0.0306581i \(0.990240\pi\)
\(374\) −8.96051e9 1.55201e10i −0.0236816 0.0410177i
\(375\) 2.51417e11 4.35466e11i 0.656528 1.13714i
\(376\) −8.03932e10 −0.207431
\(377\) 3.31056e11 5.73407e11i 0.844046 1.46193i
\(378\) −2.28983e9 3.96610e9i −0.00576886 0.00999195i
\(379\) −6.98248e10 −0.173833 −0.0869167 0.996216i \(-0.527701\pi\)
−0.0869167 + 0.996216i \(0.527701\pi\)
\(380\) 3.45723e10 + 5.98810e10i 0.0850555 + 0.147320i
\(381\) 4.95729e11 8.58628e11i 1.20526 2.08758i
\(382\) 7.45493e9 1.29123e10i 0.0179126 0.0310255i
\(383\) 3.07526e11 0.730276 0.365138 0.930953i \(-0.381022\pi\)
0.365138 + 0.930953i \(0.381022\pi\)
\(384\) 9.59065e10 1.66115e11i 0.225091 0.389868i
\(385\) −6.44817e11 −1.49576
\(386\) −2.81495e10 −0.0645399
\(387\) 4.21114e11 + 2.10659e11i 0.954333 + 0.477398i
\(388\) −2.61758e11 −0.586351
\(389\) 4.61522e11 1.02192 0.510962 0.859603i \(-0.329289\pi\)
0.510962 + 0.859603i \(0.329289\pi\)
\(390\) 1.89078e10 3.27493e10i 0.0413858 0.0716823i
\(391\) −9.47915e10 −0.205104
\(392\) 4.67960e10 8.10531e10i 0.100097 0.173373i
\(393\) −3.30805e11 + 5.72970e11i −0.699528 + 1.21162i
\(394\) 2.58583e10 + 4.47879e10i 0.0540589 + 0.0936328i
\(395\) −3.05437e11 −0.631299
\(396\) −4.85062e11 8.40152e11i −0.991218 1.71684i
\(397\) 2.94343e11 5.09817e11i 0.594698 1.03005i −0.398892 0.916998i \(-0.630605\pi\)
0.993589 0.113048i \(-0.0360615\pi\)
\(398\) −3.92299e10 −0.0783689
\(399\) −1.76202e11 + 3.05190e11i −0.348042 + 0.602827i
\(400\) 1.80105e11 + 3.11951e11i 0.351768 + 0.609280i
\(401\) −2.09391e11 3.62676e11i −0.404398 0.700437i 0.589854 0.807510i \(-0.299185\pi\)
−0.994251 + 0.107073i \(0.965852\pi\)
\(402\) −1.15134e10 1.99418e10i −0.0219880 0.0380844i
\(403\) 8.55554e10 0.161575
\(404\) 4.67459e11 + 8.09663e11i 0.873026 + 1.51213i
\(405\) 1.33680e11 + 2.31541e11i 0.246899 + 0.427642i
\(406\) −4.06187e10 + 7.03536e10i −0.0741923 + 0.128505i
\(407\) −5.54812e11 + 9.60962e11i −1.00224 + 1.73593i
\(408\) 4.06430e10 0.0726132
\(409\) 4.49397e11 0.794101 0.397050 0.917797i \(-0.370034\pi\)
0.397050 + 0.917797i \(0.370034\pi\)
\(410\) −1.15367e10 + 1.99821e10i −0.0201629 + 0.0349232i
\(411\) 4.33764e10 7.51302e10i 0.0749835 0.129875i
\(412\) 1.80340e11 + 3.12357e11i 0.308357 + 0.534090i
\(413\) 1.49664e11 + 2.59226e11i 0.253130 + 0.438434i
\(414\) 3.26648e10 0.0546485
\(415\) −1.14700e11 1.98666e11i −0.189822 0.328781i
\(416\) 9.83414e10 + 1.70332e11i 0.160996 + 0.278854i
\(417\) 4.60730e11 + 7.98009e11i 0.746165 + 1.29240i
\(418\) 1.49365e10 2.58708e10i 0.0239307 0.0414492i
\(419\) 8.87378e11 1.40652 0.703260 0.710933i \(-0.251727\pi\)
0.703260 + 0.710933i \(0.251727\pi\)
\(420\) 3.64435e11 6.31220e11i 0.571476 0.989826i
\(421\) −2.35456e11 4.07822e11i −0.365292 0.632705i 0.623531 0.781799i \(-0.285698\pi\)
−0.988823 + 0.149094i \(0.952364\pi\)
\(422\) 5.48620e10 0.0842103
\(423\) −4.59593e11 7.96039e11i −0.697978 1.20893i
\(424\) −1.18918e10 + 2.05972e10i −0.0178690 + 0.0309500i
\(425\) −7.68151e10 + 1.33048e11i −0.114208 + 0.197814i
\(426\) 1.26050e11 0.185438
\(427\) −4.89275e11 + 8.47450e11i −0.712242 + 1.23364i
\(428\) −7.29274e11 −1.05049
\(429\) 2.56653e12 3.65838
\(430\) −1.79099e9 2.99352e10i −0.00252630 0.0422254i
\(431\) 9.59616e10 0.133952 0.0669761 0.997755i \(-0.478665\pi\)
0.0669761 + 0.997755i \(0.478665\pi\)
\(432\) 6.84934e10 0.0946176
\(433\) 6.33440e11 1.09715e12i 0.865985 1.49993i −8.17470e−5 1.00000i \(-0.500026\pi\)
0.866066 0.499929i \(-0.166641\pi\)
\(434\) −1.04971e10 −0.0142026
\(435\) −3.54160e11 + 6.13422e11i −0.474239 + 0.821406i
\(436\) 3.66579e11 6.34934e11i 0.485824 0.841472i
\(437\) −7.90053e10 1.36841e11i −0.103631 0.179494i
\(438\) −3.66611e10 −0.0475962
\(439\) 2.89207e11 + 5.00920e11i 0.371636 + 0.643692i 0.989817 0.142343i \(-0.0454636\pi\)
−0.618181 + 0.786035i \(0.712130\pi\)
\(440\) −6.19825e10 + 1.07357e11i −0.0788374 + 0.136550i
\(441\) 1.07010e12 1.34725
\(442\) −1.38326e10 + 2.39588e10i −0.0172387 + 0.0298583i
\(443\) −2.48939e11 4.31175e11i −0.307097 0.531908i 0.670629 0.741793i \(-0.266024\pi\)
−0.977726 + 0.209885i \(0.932691\pi\)
\(444\) −6.27133e11 1.08623e12i −0.765836 1.32647i
\(445\) 2.09271e11 + 3.62469e11i 0.252982 + 0.438178i
\(446\) −7.27374e10 −0.0870465
\(447\) −3.88530e11 6.72953e11i −0.460299 0.797262i
\(448\) 6.17032e11 + 1.06873e12i 0.723697 + 1.25348i
\(449\) −3.14558e11 + 5.44830e11i −0.365251 + 0.632633i −0.988816 0.149138i \(-0.952350\pi\)
0.623565 + 0.781771i \(0.285684\pi\)
\(450\) 2.64702e10 4.58477e10i 0.0304299 0.0527062i
\(451\) −1.56598e12 −1.78234
\(452\) −8.05212e11 −0.907376
\(453\) 1.22425e12 2.12047e12i 1.36593 2.36586i
\(454\) 4.83952e10 8.38229e10i 0.0534627 0.0926001i
\(455\) 4.97713e11 + 8.62064e11i 0.544412 + 0.942949i
\(456\) 3.38745e10 + 5.86723e10i 0.0366886 + 0.0635465i
\(457\) −9.63187e11 −1.03297 −0.516485 0.856296i \(-0.672760\pi\)
−0.516485 + 0.856296i \(0.672760\pi\)
\(458\) 2.76703e10 + 4.79264e10i 0.0293846 + 0.0508956i
\(459\) 1.46063e10 + 2.52988e10i 0.0153597 + 0.0266037i
\(460\) 1.63405e11 + 2.83026e11i 0.170159 + 0.294725i
\(461\) −7.65850e11 + 1.32649e12i −0.789750 + 1.36789i 0.136371 + 0.990658i \(0.456456\pi\)
−0.926120 + 0.377229i \(0.876877\pi\)
\(462\) −3.14899e11 −0.321575
\(463\) 2.83628e11 4.91259e11i 0.286837 0.496816i −0.686216 0.727398i \(-0.740730\pi\)
0.973053 + 0.230582i \(0.0740629\pi\)
\(464\) −6.07494e11 1.05221e12i −0.608430 1.05383i
\(465\) −9.15259e10 −0.0907833
\(466\) −1.01155e10 1.75205e10i −0.00993686 0.0172112i
\(467\) 1.82638e11 3.16338e11i 0.177691 0.307769i −0.763399 0.645928i \(-0.776471\pi\)
0.941089 + 0.338159i \(0.109804\pi\)
\(468\) −7.48807e11 + 1.29697e12i −0.721546 + 1.24975i
\(469\) 6.06137e11 0.578486
\(470\) −2.92708e10 + 5.06986e10i −0.0276691 + 0.0479243i
\(471\) −1.71076e12 −1.60175
\(472\) 5.75455e10 0.0533669
\(473\) 1.69872e12 1.12111e12i 1.56044 1.02985i
\(474\) −1.49161e11 −0.135723
\(475\) −2.56090e11 −0.230819
\(476\) −2.66614e11 + 4.61789e11i −0.238041 + 0.412299i
\(477\) −2.71933e11 −0.240507
\(478\) −5.78274e10 + 1.00160e11i −0.0506650 + 0.0877544i
\(479\) 8.30831e11 1.43904e12i 0.721113 1.24900i −0.239442 0.970911i \(-0.576964\pi\)
0.960554 0.278093i \(-0.0897023\pi\)
\(480\) −1.05204e11 1.82219e11i −0.0904581 0.156678i
\(481\) 1.71296e12 1.45914
\(482\) −2.48679e10 4.30725e10i −0.0209859 0.0363487i
\(483\) −8.32813e11 + 1.44247e12i −0.696282 + 1.20600i
\(484\) −2.99374e12 −2.47977
\(485\) −1.91217e11 + 3.31198e11i −0.156924 + 0.271800i
\(486\) 7.00000e10 + 1.21244e11i 0.0569161 + 0.0985816i
\(487\) −5.57638e10 9.65858e10i −0.0449234 0.0778095i 0.842689 0.538400i \(-0.180971\pi\)
−0.887613 + 0.460590i \(0.847638\pi\)
\(488\) 9.40624e10 + 1.62921e11i 0.0750804 + 0.130043i
\(489\) −2.83794e12 −2.24446
\(490\) −3.40765e10 5.90222e10i −0.0267038 0.0462523i
\(491\) 2.77378e10 + 4.80432e10i 0.0215380 + 0.0373048i 0.876593 0.481232i \(-0.159810\pi\)
−0.855056 + 0.518536i \(0.826477\pi\)
\(492\) 8.85053e11 1.53296e12i 0.680967 1.17947i
\(493\) 2.59097e11 4.48769e11i 0.197538 0.342146i
\(494\) −4.61160e10 −0.0348402
\(495\) −1.41737e12 −1.06111
\(496\) 7.84977e10 1.35962e11i 0.0582357 0.100867i
\(497\) −1.65901e12 + 2.87350e12i −1.21968 + 2.11255i
\(498\) −5.60140e10 9.70192e10i −0.0408098 0.0706847i
\(499\) 8.89624e11 + 1.54087e12i 0.642324 + 1.11254i 0.984913 + 0.173052i \(0.0553630\pi\)
−0.342588 + 0.939486i \(0.611304\pi\)
\(500\) 1.26828e12 0.907504
\(501\) 1.68396e12 + 2.91671e12i 1.19416 + 2.06835i
\(502\) −3.37356e10 5.84318e10i −0.0237095 0.0410660i
\(503\) −3.63142e11 6.28981e11i −0.252942 0.438108i 0.711393 0.702795i \(-0.248065\pi\)
−0.964335 + 0.264687i \(0.914732\pi\)
\(504\) 1.84333e11 3.19275e11i 0.127253 0.220408i
\(505\) 1.36593e12 0.934584
\(506\) 7.05971e10 1.22278e11i 0.0478751 0.0829220i
\(507\) −9.11513e11 1.57879e12i −0.612671 1.06118i
\(508\) 2.50072e12 1.66601
\(509\) −7.36645e11 1.27591e12i −0.486439 0.842537i 0.513440 0.858126i \(-0.328371\pi\)
−0.999878 + 0.0155888i \(0.995038\pi\)
\(510\) 1.47980e10 2.56308e10i 0.00968582 0.0167763i
\(511\) 4.82517e11 8.35744e11i 0.313053 0.542224i
\(512\) 6.02802e11 0.387668
\(513\) −2.43476e10 + 4.21712e10i −0.0155213 + 0.0268836i
\(514\) −1.77938e10 −0.0112444
\(515\) 5.26959e11 0.330099
\(516\) 1.37399e11 + 2.29652e12i 0.0853215 + 1.42609i
\(517\) −3.97320e12 −2.44587
\(518\) −2.10171e11 −0.128259
\(519\) −2.17521e11 + 3.76757e11i −0.131597 + 0.227933i
\(520\) 1.91369e11 0.114778
\(521\) −4.76302e11 + 8.24980e11i −0.283213 + 0.490539i −0.972174 0.234259i \(-0.924734\pi\)
0.688961 + 0.724798i \(0.258067\pi\)
\(522\) −8.92839e10 + 1.54644e11i −0.0526327 + 0.0911625i
\(523\) −1.00891e12 1.74748e12i −0.589651 1.02131i −0.994278 0.106823i \(-0.965932\pi\)
0.404627 0.914482i \(-0.367401\pi\)
\(524\) −1.66875e12 −0.966942
\(525\) 1.34975e12 + 2.33784e12i 0.775421 + 1.34307i
\(526\) 7.37299e10 1.27704e11i 0.0419960 0.0727392i
\(527\) 6.69587e10 0.0378146
\(528\) 2.35481e12 4.07866e12i 1.31857 2.28383i
\(529\) 5.27160e11 + 9.13068e11i 0.292679 + 0.506935i
\(530\) 8.65950e9 + 1.49987e10i 0.00476707 + 0.00825681i
\(531\) 3.28977e11 + 5.69805e11i 0.179573 + 0.311029i
\(532\) −8.88853e11 −0.481091
\(533\) 1.20873e12 + 2.09358e12i 0.648718 + 1.12361i
\(534\) 1.02198e11 + 1.77013e11i 0.0543886 + 0.0942039i
\(535\) −5.32742e11 + 9.22735e11i −0.281141 + 0.486951i
\(536\) 5.82645e10 1.00917e11i 0.0304903 0.0528108i
\(537\) 1.17924e12 0.611952
\(538\) −1.62490e11 −0.0836193
\(539\) 2.31276e12 4.00581e12i 1.18027 2.04428i
\(540\) 5.03577e10 8.72221e10i 0.0254855 0.0441422i
\(541\) −1.47438e12 2.55369e12i −0.739981 1.28168i −0.952503 0.304529i \(-0.901501\pi\)
0.212522 0.977156i \(-0.431832\pi\)
\(542\) 3.33477e10 + 5.77599e10i 0.0165985 + 0.0287495i
\(543\) −3.56705e12 −1.76080
\(544\) 7.69655e10 + 1.33308e11i 0.0376792 + 0.0652622i
\(545\) −5.35580e11 9.27651e11i −0.260040 0.450402i
\(546\) 2.43060e11 + 4.20992e11i 0.117043 + 0.202725i
\(547\) −4.31766e11 + 7.47841e11i −0.206208 + 0.357163i −0.950517 0.310673i \(-0.899446\pi\)
0.744309 + 0.667835i \(0.232779\pi\)
\(548\) 2.18813e11 0.103648
\(549\) −1.07547e12 + 1.86278e12i −0.505271 + 0.875156i
\(550\) −1.14418e11 1.98177e11i −0.0533165 0.0923469i
\(551\) 8.63791e11 0.399233
\(552\) 1.60107e11 + 2.77313e11i 0.0733980 + 0.127129i
\(553\) 1.96319e12 3.40035e12i 0.892689 1.54618i
\(554\) 1.61881e11 2.80386e11i 0.0730134 0.126463i
\(555\) −1.83251e12 −0.819836
\(556\) −1.16208e12 + 2.01278e12i −0.515704 + 0.893225i
\(557\) 1.06334e12 0.468084 0.234042 0.972226i \(-0.424805\pi\)
0.234042 + 0.972226i \(0.424805\pi\)
\(558\) −2.30737e10 −0.0100754
\(559\) −2.81001e12 1.40569e12i −1.21718 0.608885i
\(560\) 1.82662e12 0.784879
\(561\) 2.00866e12 0.856198
\(562\) 1.08443e11 1.87828e11i 0.0458550 0.0794232i
\(563\) 5.27778e11 0.221393 0.110696 0.993854i \(-0.464692\pi\)
0.110696 + 0.993854i \(0.464692\pi\)
\(564\) 2.24556e12 3.88942e12i 0.934475 1.61856i
\(565\) −5.88215e11 + 1.01882e12i −0.242839 + 0.420609i
\(566\) 1.53426e11 + 2.65742e11i 0.0628384 + 0.108839i
\(567\) −3.43691e12 −1.39651
\(568\) 3.18943e11 + 5.52425e11i 0.128572 + 0.222693i
\(569\) 1.59383e12 2.76060e12i 0.637438 1.10408i −0.348555 0.937288i \(-0.613328\pi\)
0.985993 0.166787i \(-0.0533392\pi\)
\(570\) 4.93343e10 0.0195755
\(571\) 1.27732e12 2.21238e12i 0.502847 0.870957i −0.497147 0.867666i \(-0.665619\pi\)
0.999995 0.00329067i \(-0.00104745\pi\)
\(572\) 3.23673e12 + 5.60618e12i 1.26423 + 2.18970i
\(573\) 8.35580e11 + 1.44727e12i 0.323812 + 0.560858i
\(574\) −1.48304e11 2.56870e11i −0.0570228 0.0987664i
\(575\) −1.21040e12 −0.461769
\(576\) 1.35630e12 + 2.34918e12i 0.513398 + 0.889231i
\(577\) 8.05202e11 + 1.39465e12i 0.302422 + 0.523811i 0.976684 0.214682i \(-0.0688714\pi\)
−0.674262 + 0.738492i \(0.735538\pi\)
\(578\) 9.58804e10 1.66070e11i 0.0357318 0.0618893i
\(579\) 1.57756e12 2.73241e12i 0.583353 1.01040i
\(580\) −1.78656e12 −0.655530
\(581\) 2.94893e12 1.07367
\(582\) −9.33815e10 + 1.61741e11i −0.0337371 + 0.0584343i
\(583\) −5.87716e11 + 1.01795e12i −0.210697 + 0.364939i
\(584\) −9.27631e10 1.60670e11i −0.0330003 0.0571582i
\(585\) 1.09402e12 + 1.89490e12i 0.386211 + 0.668937i
\(586\) −2.59058e11 −0.0907524
\(587\) −3.71368e11 6.43229e11i −0.129102 0.223611i 0.794227 0.607621i \(-0.207876\pi\)
−0.923329 + 0.384010i \(0.874543\pi\)
\(588\) 2.61423e12 + 4.52798e12i 0.901873 + 1.56209i
\(589\) 5.58077e10 + 9.66617e10i 0.0191062 + 0.0330930i
\(590\) 2.09521e10 3.62901e10i 0.00711858 0.0123297i
\(591\) −5.79662e12 −1.95448
\(592\) 1.57166e12 2.72219e12i 0.525909 0.910901i
\(593\) 1.13036e12 + 1.95784e12i 0.375380 + 0.650177i 0.990384 0.138347i \(-0.0441789\pi\)
−0.615004 + 0.788524i \(0.710846\pi\)
\(594\) −4.35127e10 −0.0143409
\(595\) 3.89528e11 + 6.74683e11i 0.127413 + 0.220685i
\(596\) 9.79973e11 1.69736e12i 0.318131 0.551019i
\(597\) 2.19853e12 3.80796e12i 0.708349 1.22690i
\(598\) −2.17966e11 −0.0697002
\(599\) −7.30510e11 + 1.26528e12i −0.231849 + 0.401574i −0.958352 0.285589i \(-0.907811\pi\)
0.726503 + 0.687163i \(0.241144\pi\)
\(600\) 5.18976e11 0.163481
\(601\) 3.81242e12 1.19197 0.595986 0.802995i \(-0.296761\pi\)
0.595986 + 0.802995i \(0.296761\pi\)
\(602\) 3.44772e11 + 1.72470e11i 0.106991 + 0.0535215i
\(603\) 1.33235e12 0.410384
\(604\) 6.17577e12 1.88810
\(605\) −2.18696e12 + 3.78792e12i −0.663654 + 1.14948i
\(606\) 6.67058e11 0.200926
\(607\) −1.09419e12 + 1.89519e12i −0.327147 + 0.566636i −0.981945 0.189169i \(-0.939421\pi\)
0.654797 + 0.755805i \(0.272754\pi\)
\(608\) −1.28296e11 + 2.22215e11i −0.0380756 + 0.0659489i
\(609\) −4.55271e12 7.88553e12i −1.34120 2.32302i
\(610\) 1.36991e11 0.0400597
\(611\) 3.06678e12 + 5.31182e12i 0.890220 + 1.54191i
\(612\) −5.86044e11 + 1.01506e12i −0.168869 + 0.292489i
\(613\) 4.90449e12 1.40289 0.701443 0.712726i \(-0.252540\pi\)
0.701443 + 0.712726i \(0.252540\pi\)
\(614\) 1.09258e11 1.89240e11i 0.0310238 0.0537348i
\(615\) −1.29308e12 2.23968e12i −0.364491 0.631317i
\(616\) −7.96784e11 1.38007e12i −0.222960 0.386178i
\(617\) −2.09961e12 3.63663e12i −0.583251 1.01022i −0.995091 0.0989641i \(-0.968447\pi\)
0.411840 0.911256i \(-0.364886\pi\)
\(618\) 2.57342e11 0.0709681
\(619\) 1.07326e12 + 1.85895e12i 0.293832 + 0.508932i 0.974712 0.223463i \(-0.0717361\pi\)
−0.680881 + 0.732394i \(0.738403\pi\)
\(620\) −1.15426e11 1.99924e11i −0.0313719 0.0543378i
\(621\) −1.15078e11 + 1.99321e11i −0.0310514 + 0.0537826i
\(622\) −6.74828e8 + 1.16884e9i −0.000180774 + 0.000313110i
\(623\) −5.38036e12 −1.43092
\(624\) −7.27041e12 −1.91968
\(625\) −4.41301e11 + 7.64355e11i −0.115684 + 0.200371i
\(626\) −3.33045e10 + 5.76850e10i −0.00866798 + 0.0150134i
\(627\) 1.67415e12 + 2.89971e12i 0.432603 + 0.749290i
\(628\) −2.15749e12 3.73688e12i −0.553515 0.958717i
\(629\) 1.34063e12 0.341492
\(630\) −1.34230e11 2.32493e11i −0.0339483 0.0588001i
\(631\) −2.50715e12 4.34252e12i −0.629577 1.09046i −0.987637 0.156761i \(-0.949895\pi\)
0.358059 0.933699i \(-0.383439\pi\)
\(632\) −3.77421e11 6.53712e11i −0.0941020 0.162990i
\(633\) −3.07458e12 + 5.32533e12i −0.761148 + 1.31835i
\(634\) −3.15471e11 −0.0775458
\(635\) 1.82680e12 3.16410e12i 0.445870 0.772270i
\(636\) −6.64326e11 1.15065e12i −0.160999 0.278859i
\(637\) −7.14056e12 −1.71832
\(638\) 3.85931e11 + 6.68452e11i 0.0922181 + 0.159727i
\(639\) −3.64667e12 + 6.31623e12i −0.865253 + 1.49866i
\(640\) 3.53422e11 6.12145e11i 0.0832691 0.144226i
\(641\) −2.36643e11 −0.0553647 −0.0276823 0.999617i \(-0.508813\pi\)
−0.0276823 + 0.999617i \(0.508813\pi\)
\(642\) −2.60166e11 + 4.50621e11i −0.0604426 + 0.104690i
\(643\) −4.34700e12 −1.00286 −0.501431 0.865198i \(-0.667193\pi\)
−0.501431 + 0.865198i \(0.667193\pi\)
\(644\) −4.20114e12 −0.962456
\(645\) 3.00611e12 + 1.50378e12i 0.683891 + 0.342111i
\(646\) −3.60921e10 −0.00815390
\(647\) −2.40644e12 −0.539892 −0.269946 0.962876i \(-0.587006\pi\)
−0.269946 + 0.962876i \(0.587006\pi\)
\(648\) −3.30370e11 + 5.72218e11i −0.0736061 + 0.127489i
\(649\) 2.84402e12 0.629261
\(650\) −1.76631e11 + 3.05933e11i −0.0388111 + 0.0672228i
\(651\) 5.88282e11 1.01893e12i 0.128372 0.222347i
\(652\) −3.57901e12 6.19902e12i −0.775619 1.34341i
\(653\) −6.60645e12 −1.42187 −0.710934 0.703259i \(-0.751727\pi\)
−0.710934 + 0.703259i \(0.751727\pi\)
\(654\) −2.61552e11 4.53022e11i −0.0559060 0.0968320i
\(655\) −1.21904e12 + 2.11144e12i −0.258780 + 0.448221i
\(656\) 4.43606e12 0.935256
\(657\) 1.06062e12 1.83705e12i 0.222083 0.384659i
\(658\) −3.76276e11 6.51729e11i −0.0782510 0.135535i
\(659\) 1.87004e12 + 3.23901e12i 0.386249 + 0.669003i 0.991942 0.126696i \(-0.0404373\pi\)
−0.605693 + 0.795699i \(0.707104\pi\)
\(660\) −3.46261e12 5.99741e12i −0.710323 1.23032i
\(661\) 2.66804e12 0.543608 0.271804 0.962353i \(-0.412380\pi\)
0.271804 + 0.962353i \(0.412380\pi\)
\(662\) 2.24741e11 + 3.89264e11i 0.0454802 + 0.0787740i
\(663\) −1.55042e12 2.68541e12i −0.311630 0.539758i
\(664\) 2.83463e11 4.90973e11i 0.0565901 0.0980169i
\(665\) −6.49315e11 + 1.12465e12i −0.128753 + 0.223007i
\(666\) −4.61976e11 −0.0909882
\(667\) 4.08269e12 0.798693
\(668\) −4.24740e12 + 7.35671e12i −0.825332 + 1.42952i
\(669\) 4.07636e12 7.06046e12i 0.786783 1.36275i
\(670\) −4.24277e10 7.34869e10i −0.00813416 0.0140888i
\(671\) 4.64876e12 + 8.05188e12i 0.885290 + 1.53337i
\(672\) 2.70480e12 0.511650
\(673\) −4.43774e11 7.68639e11i −0.0833862 0.144429i 0.821316 0.570473i \(-0.193240\pi\)
−0.904702 + 0.426044i \(0.859907\pi\)
\(674\) −5.46865e10 9.47197e10i −0.0102073 0.0176795i
\(675\) 1.86509e11 + 3.23043e11i 0.0345807 + 0.0598955i
\(676\) 2.29907e12 3.98211e12i 0.423441 0.733421i
\(677\) 4.52082e12 0.827120 0.413560 0.910477i \(-0.364285\pi\)
0.413560 + 0.910477i \(0.364285\pi\)
\(678\) −2.87257e11 + 4.97543e11i −0.0522080 + 0.0904268i
\(679\) −2.45809e12 4.25754e12i −0.443796 0.768678i
\(680\) 1.49772e11 0.0268622
\(681\) 5.42433e12 + 9.39522e12i 0.966461 + 1.67396i
\(682\) −4.98683e10 + 8.63744e10i −0.00882663 + 0.0152882i
\(683\) 1.45894e11 2.52696e11i 0.0256534 0.0444330i −0.852914 0.522052i \(-0.825167\pi\)
0.878567 + 0.477619i \(0.158500\pi\)
\(684\) −1.95379e12 −0.341291
\(685\) 1.59845e11 2.76860e11i 0.0277391 0.0480455i
\(686\) 1.82194e11 0.0314106
\(687\) −6.20281e12 −1.06239
\(688\) −4.81208e12 + 3.17586e12i −0.818814 + 0.540398i
\(689\) 1.81456e12 0.306749
\(690\) 2.33177e11 0.0391620
\(691\) −5.03109e12 + 8.71411e12i −0.839482 + 1.45403i 0.0508468 + 0.998706i \(0.483808\pi\)
−0.890329 + 0.455319i \(0.849525\pi\)
\(692\) −1.09729e12 −0.181904
\(693\) 9.11013e12 1.57792e13i 1.50046 2.59888i
\(694\) 1.25210e11 2.16871e11i 0.0204891 0.0354881i
\(695\) 1.69782e12 + 2.94072e12i 0.276033 + 0.478103i
\(696\) −1.75050e12 −0.282762
\(697\) 9.45994e11 + 1.63851e12i 0.151824 + 0.262967i
\(698\) −1.72552e11 + 2.98868e11i −0.0275150 + 0.0476574i
\(699\) 2.26757e12 0.359263
\(700\) −3.40443e12 + 5.89664e12i −0.535924 + 0.928247i
\(701\) 4.92305e12 + 8.52698e12i 0.770023 + 1.33372i 0.937550 + 0.347851i \(0.113089\pi\)
−0.167527 + 0.985867i \(0.553578\pi\)
\(702\) 3.35861e10 + 5.81728e10i 0.00521966 + 0.00904071i
\(703\) 1.11737e12 + 1.93533e12i 0.172543 + 0.298852i
\(704\) 1.17252e13 1.79906
\(705\) −3.28080e12 5.68251e12i −0.500183 0.866342i
\(706\) −1.76136e11 3.05077e11i −0.0266825 0.0462155i
\(707\) −8.77952e12 + 1.52066e13i −1.32155 + 2.28899i
\(708\) −1.60737e12 + 2.78404e12i −0.240417 + 0.416415i
\(709\) −1.10662e12 −0.164471 −0.0822357 0.996613i \(-0.526206\pi\)
−0.0822357 + 0.996613i \(0.526206\pi\)
\(710\) 4.64503e11 0.0686003
\(711\) 4.31529e12 7.47430e12i 0.633282 1.09688i
\(712\) −5.17182e11 + 8.95786e11i −0.0754195 + 0.130630i
\(713\) 2.63774e11 + 4.56869e11i 0.0382233 + 0.0662048i
\(714\) 1.90228e11 + 3.29484e11i 0.0273925 + 0.0474452i
\(715\) 9.45785e12 1.35337
\(716\) 1.48717e12 + 2.57586e12i 0.211472 + 0.366280i
\(717\) −6.48154e12 1.12264e13i −0.915887 1.58636i
\(718\) −2.95786e11 5.12316e11i −0.0415353 0.0719412i
\(719\) 5.74275e12 9.94674e12i 0.801383 1.38804i −0.117323 0.993094i \(-0.537431\pi\)
0.918706 0.394943i \(-0.129236\pi\)
\(720\) 4.01509e12 0.556800
\(721\) −3.38702e12 + 5.86650e12i −0.466777 + 0.808482i
\(722\) 2.60276e11 + 4.50811e11i 0.0356464 + 0.0617414i
\(723\) 5.57461e12 0.758738
\(724\) −4.49851e12 7.79165e12i −0.608478 1.05392i
\(725\) 3.30844e12 5.73039e12i 0.444736 0.770305i
\(726\) −1.06801e12 + 1.84985e12i −0.142679 + 0.247127i
\(727\) −3.07771e12 −0.408624 −0.204312 0.978906i \(-0.565496\pi\)
−0.204312 + 0.978906i \(0.565496\pi\)
\(728\) −1.23002e12 + 2.13046e12i −0.162301 + 0.281114i
\(729\) −8.61204e12 −1.12936
\(730\) −1.35099e11 −0.0176075
\(731\) −2.19922e12 1.10014e12i −0.284866 0.142502i
\(732\) −1.05095e13 −1.35295
\(733\) −5.64679e12 −0.722493 −0.361247 0.932470i \(-0.617649\pi\)
−0.361247 + 0.932470i \(0.617649\pi\)
\(734\) 5.36989e11 9.30091e11i 0.0682862 0.118275i
\(735\) 7.63887e12 0.965465
\(736\) −6.06388e11 + 1.05029e12i −0.0761729 + 0.131935i
\(737\) 2.87955e12 4.98752e12i 0.359518 0.622703i
\(738\) −3.25986e11 5.64625e11i −0.0404525 0.0700658i
\(739\) −4.50869e12 −0.556096 −0.278048 0.960567i \(-0.589688\pi\)
−0.278048 + 0.960567i \(0.589688\pi\)
\(740\) −2.31103e12 4.00282e12i −0.283310 0.490708i
\(741\) 2.58444e12 4.47638e12i 0.314908 0.545437i
\(742\) −2.22635e11 −0.0269635
\(743\) 1.96229e12 3.39878e12i 0.236218 0.409142i −0.723408 0.690421i \(-0.757425\pi\)
0.959626 + 0.281279i \(0.0907587\pi\)
\(744\) −1.13096e11 1.95888e11i −0.0135323 0.0234385i
\(745\) −1.43176e12 2.47988e12i −0.170281 0.294936i
\(746\) −3.18367e11 5.51427e11i −0.0376359 0.0651874i
\(747\) 6.48203e12 0.761673
\(748\) 2.53318e12 + 4.38760e12i 0.295876 + 0.512472i
\(749\) −6.84838e12 1.18617e13i −0.795096 1.37715i
\(750\) 4.52453e11 7.83672e11i 0.0522153 0.0904396i
\(751\) 3.56008e12 6.16624e12i 0.408395 0.707360i −0.586315 0.810083i \(-0.699422\pi\)
0.994710 + 0.102722i \(0.0327554\pi\)
\(752\) 1.12552e13 1.28343
\(753\) 7.56246e12 0.857207
\(754\) 5.95775e11 1.03191e12i 0.0671291 0.116271i
\(755\) 4.51146e12 7.81407e12i 0.505307 0.875218i
\(756\) 6.47347e11 + 1.12124e12i 0.0720757 + 0.124839i
\(757\) −1.97227e12 3.41607e12i −0.218290 0.378090i 0.735995 0.676987i \(-0.236715\pi\)
−0.954285 + 0.298897i \(0.903381\pi\)
\(758\) −1.25658e11 −0.0138254
\(759\) 7.91281e12 + 1.37054e13i 0.865452 + 1.49901i
\(760\) 1.24830e11 + 2.16212e11i 0.0135724 + 0.0235081i
\(761\) 5.62495e12 + 9.74270e12i 0.607978 + 1.05305i 0.991573 + 0.129547i \(0.0413523\pi\)
−0.383596 + 0.923501i \(0.625314\pi\)
\(762\) 8.92122e11 1.54520e12i 0.0958577 0.166030i
\(763\) 1.37697e13 1.47084
\(764\) −2.10755e12 + 3.65038e12i −0.223799 + 0.387631i
\(765\) 8.56222e11 + 1.48302e12i 0.0903878 + 0.156556i
\(766\) 5.53429e11 0.0580807
\(767\) −2.19520e12 3.80220e12i −0.229032 0.396694i
\(768\) −6.49641e12 + 1.12521e13i −0.673826 + 1.16710i
\(769\) −8.55036e12 + 1.48097e13i −0.881690 + 1.52713i −0.0322289 + 0.999481i \(0.510261\pi\)
−0.849461 + 0.527651i \(0.823073\pi\)
\(770\) −1.16042e12 −0.118962
\(771\) 9.97204e11 1.72721e12i 0.101634 0.176035i
\(772\) 7.95802e12 0.806357
\(773\) −4.81342e12 −0.484894 −0.242447 0.970165i \(-0.577950\pi\)
−0.242447 + 0.970165i \(0.577950\pi\)
\(774\) 7.57843e11 + 3.79105e11i 0.0759006 + 0.0379686i
\(775\) 8.55005e11 0.0851355
\(776\) −9.45128e11 −0.0935649
\(777\) 1.17784e13 2.04008e13i 1.15929 2.00795i
\(778\) 8.30562e11 0.0812763
\(779\) −1.57690e12 + 2.73128e12i −0.153422 + 0.265734i
\(780\) −5.34535e12 + 9.25842e12i −0.517071 + 0.895594i
\(781\) 1.57628e13 + 2.73020e13i 1.51602 + 2.62582i
\(782\) −1.70588e11 −0.0163124
\(783\) −6.29095e11 1.08962e12i −0.0598120 0.103597i
\(784\) −6.55152e12 + 1.13476e13i −0.619327 + 1.07271i
\(785\) −6.30426e12 −0.592544
\(786\) −5.95322e11 + 1.03113e12i −0.0556353 + 0.0963631i
\(787\) −2.78345e12 4.82108e12i −0.258641 0.447979i 0.707237 0.706976i \(-0.249941\pi\)
−0.965878 + 0.258997i \(0.916608\pi\)
\(788\) −7.31029e12 1.26618e13i −0.675408 1.16984i
\(789\) 8.26395e12 + 1.43136e13i 0.759174 + 1.31493i
\(790\) −5.49670e11 −0.0502088
\(791\) −7.56149e12 1.30969e13i −0.686773 1.18953i
\(792\) −1.75141e12 3.03353e12i −0.158170 0.273959i
\(793\) 7.17645e12 1.24300e13i 0.644436 1.11620i
\(794\) 5.29704e11 9.17475e11i 0.0472978 0.0819222i
\(795\) −1.94119e12 −0.172352
\(796\) 1.10905e13 0.979136
\(797\) −8.01902e12 + 1.38893e13i −0.703977 + 1.21932i 0.263082 + 0.964774i \(0.415261\pi\)
−0.967059 + 0.254551i \(0.918072\pi\)
\(798\) −3.17095e11 + 5.49225e11i −0.0276807 + 0.0479444i
\(799\) 2.40017e12 + 4.15722e12i 0.208345 + 0.360864i
\(800\) 9.82783e11 + 1.70223e12i 0.0848306 + 0.146931i
\(801\) −1.18265e13 −1.01511
\(802\) −3.76824e11 6.52678e11i −0.0321628 0.0557076i
\(803\) −4.58454e12 7.94066e12i −0.389113 0.673964i
\(804\) 3.25490e12 + 5.63766e12i 0.274717 + 0.475824i
\(805\) −3.06897e12 + 5.31562e12i −0.257580 + 0.446141i
\(806\) 1.53967e11 0.0128505
\(807\) 9.10628e12 1.57725e13i 0.755806 1.30909i
\(808\) 1.68785e12 + 2.92344e12i 0.139310 + 0.241292i
\(809\) −9.32459e12 −0.765352 −0.382676 0.923883i \(-0.624997\pi\)
−0.382676 + 0.923883i \(0.624997\pi\)
\(810\) 2.40573e11 + 4.16685e11i 0.0196365 + 0.0340114i
\(811\) 3.92148e12 6.79220e12i 0.318314 0.551337i −0.661822 0.749661i \(-0.730217\pi\)
0.980136 + 0.198324i \(0.0635499\pi\)
\(812\) 1.14831e13 1.98894e13i 0.926953 1.60553i
\(813\) −7.47550e12 −0.600113
\(814\) −9.98449e11 + 1.72936e12i −0.0797106 + 0.138063i
\(815\) −1.04580e13 −0.830308
\(816\) −5.69009e12 −0.449276
\(817\) −2.44804e11 4.09172e12i −0.0192229 0.321297i
\(818\) 8.08743e11 0.0631569
\(819\) −2.81273e13 −2.18449
\(820\) 3.26148e12 5.64905e12i 0.251914 0.436328i
\(821\) −1.51320e13 −1.16239 −0.581197 0.813763i \(-0.697415\pi\)
−0.581197 + 0.813763i \(0.697415\pi\)
\(822\) 7.80609e10 1.35206e11i 0.00596363 0.0103293i
\(823\) 2.53778e11 4.39557e11i 0.0192821 0.0333977i −0.856223 0.516606i \(-0.827195\pi\)
0.875505 + 0.483208i \(0.160529\pi\)
\(824\) 6.51150e11 + 1.12783e12i 0.0492049 + 0.0852255i
\(825\) 2.56489e13 1.92764
\(826\) 2.69339e11 + 4.66508e11i 0.0201321 + 0.0348698i
\(827\) −1.03825e13 + 1.79831e13i −0.771843 + 1.33687i 0.164709 + 0.986342i \(0.447332\pi\)
−0.936552 + 0.350529i \(0.886002\pi\)
\(828\) −9.23452e12 −0.682775
\(829\) 6.77481e11 1.17343e12i 0.0498198 0.0862904i −0.840040 0.542524i \(-0.817469\pi\)
0.889860 + 0.456234i \(0.150802\pi\)
\(830\) −2.06416e11 3.57522e11i −0.0150970 0.0261488i
\(831\) 1.81443e13 + 3.14269e13i 1.31988 + 2.28611i
\(832\) −9.05032e12 1.56756e13i −0.654801 1.13415i
\(833\) −5.58847e12 −0.402152
\(834\) 8.29138e11 + 1.43611e12i 0.0593444 + 0.102787i
\(835\) 6.20553e12 + 1.07483e13i 0.441763 + 0.765156i
\(836\) −4.22263e12 + 7.31381e12i −0.298989 + 0.517864i
\(837\) 8.12889e10 1.40796e11i 0.00572488 0.00991579i
\(838\) 1.59694e12 0.111864
\(839\) −6.29644e12 −0.438699 −0.219349 0.975646i \(-0.570393\pi\)
−0.219349 + 0.975646i \(0.570393\pi\)
\(840\) 1.31586e12 2.27914e12i 0.0911913 0.157948i
\(841\) −3.90578e12 + 6.76501e12i −0.269232 + 0.466323i
\(842\) −4.23731e11 7.33923e11i −0.0290526 0.0503206i
\(843\) 1.21547e13 + 2.10526e13i 0.828935 + 1.43576i
\(844\) −1.55098e13 −1.05212
\(845\) −3.35899e12 5.81794e12i −0.226649 0.392567i
\(846\) −8.27092e11 1.43256e12i −0.0555120 0.0961496i
\(847\) −2.81133e13 4.86937e13i −1.87688 3.25085i
\(848\) 1.66487e12 2.88364e12i 0.110560 0.191496i
\(849\) −3.43933e13 −2.27190
\(850\) −1.38238e11 + 2.39435e11i −0.00908325 + 0.0157326i
\(851\) 5.28120e12 + 9.14731e12i 0.345183 + 0.597875i
\(852\) −3.56350e13 −2.31685
\(853\) 8.57771e12 + 1.48570e13i 0.554754 + 0.960862i 0.997923 + 0.0644240i \(0.0205210\pi\)
−0.443168 + 0.896438i \(0.646146\pi\)
\(854\) −8.80508e11 + 1.52508e12i −0.0566465 + 0.0981145i
\(855\) −1.42726e12 + 2.47208e12i −0.0913388 + 0.158203i
\(856\) −2.63318e12 −0.167629
\(857\) 1.06538e13 1.84528e13i 0.674666 1.16856i −0.301900 0.953340i \(-0.597621\pi\)
0.976566 0.215217i \(-0.0690457\pi\)
\(858\) 4.61877e12 0.290960
\(859\) 9.30555e12 0.583140 0.291570 0.956550i \(-0.405822\pi\)
0.291570 + 0.956550i \(0.405822\pi\)
\(860\) 5.06323e11 + 8.46284e12i 0.0315635 + 0.527562i
\(861\) 3.32450e13 2.06164
\(862\) 1.72694e11 0.0106536
\(863\) 1.54356e13 2.67353e13i 0.947274 1.64073i 0.196142 0.980576i \(-0.437159\pi\)
0.751133 0.660151i \(-0.229508\pi\)
\(864\) 3.73749e11 0.0228175
\(865\) −8.01579e11 + 1.38838e12i −0.0486826 + 0.0843208i
\(866\) 1.13995e12 1.97445e12i 0.0688740 0.119293i
\(867\) 1.07467e13 + 1.86138e13i 0.645934 + 1.11879i
\(868\) 2.96760e12 0.177446
\(869\) −1.86529e13 3.23078e13i −1.10958 1.92184i
\(870\) −6.37351e11 + 1.10392e12i −0.0377174 + 0.0653285i
\(871\) −8.89052e12 −0.523414
\(872\) 1.32360e12 2.29255e12i 0.0775236 0.134275i
\(873\) −5.40312e12 9.35848e12i −0.314833 0.545307i
\(874\) −1.42179e11 2.46262e11i −0.00824204 0.0142756i
\(875\) 1.19100e13 + 2.06287e13i 0.686870 + 1.18969i
\(876\) 1.03643e13 0.594663
\(877\) −5.63149e12 9.75403e12i −0.321459 0.556783i 0.659331 0.751853i \(-0.270840\pi\)
−0.980789 + 0.195070i \(0.937506\pi\)
\(878\) 5.20461e11 + 9.01465e11i 0.0295572 + 0.0511945i
\(879\) 1.45182e13 2.51462e13i 0.820280 1.42077i
\(880\) 8.67765e12 1.50301e13i 0.487787 0.844872i
\(881\) −4.80298e12 −0.268608 −0.134304 0.990940i \(-0.542880\pi\)
−0.134304 + 0.990940i \(0.542880\pi\)
\(882\) 1.92577e12 0.107151
\(883\) −7.23490e12 + 1.25312e13i −0.400507 + 0.693698i −0.993787 0.111298i \(-0.964499\pi\)
0.593281 + 0.804996i \(0.297832\pi\)
\(884\) 3.91056e12 6.77329e12i 0.215379 0.373048i
\(885\) 2.34840e12 + 4.06754e12i 0.128685 + 0.222888i
\(886\) −4.47995e11 7.75950e11i −0.0244243 0.0423040i
\(887\) 4.67749e12 0.253721 0.126861 0.991921i \(-0.459510\pi\)
0.126861 + 0.991921i \(0.459510\pi\)
\(888\) −2.26438e12 3.92202e12i −0.122206 0.211666i
\(889\) 2.34834e13 + 4.06745e13i 1.26097 + 2.18406i
\(890\) 3.76608e11 + 6.52304e11i 0.0201203 + 0.0348494i
\(891\) −1.63276e13 + 2.82802e13i −0.867905 + 1.50326i
\(892\) 2.05633e13 1.08755
\(893\) −4.00092e12 + 6.92979e12i −0.210537 + 0.364660i
\(894\) −6.99205e11 1.21106e12i −0.0366088 0.0634083i
\(895\) 4.34557e12 0.226383
\(896\) 4.54323e12 + 7.86911e12i 0.235494 + 0.407887i
\(897\) 1.22153e13 2.11575e13i 0.629996 1.09118i
\(898\) −5.66083e11 + 9.80484e11i −0.0290494 + 0.0503150i
\(899\) −2.88393e12 −0.147253
\(900\) −7.48327e12 + 1.29614e13i −0.380189 + 0.658507i
\(901\) 1.42014e12 0.0717908
\(902\) −2.81816e12 −0.141754
\(903\) −3.60630e13 + 2.38007e13i −1.80496 + 1.19123i
\(904\) −2.90737e12 −0.144791
\(905\) −1.31448e13 −0.651382
\(906\) 2.20319e12 3.81603e12i 0.108636 0.188163i
\(907\) −2.06871e13 −1.01500 −0.507501 0.861651i \(-0.669431\pi\)
−0.507501 + 0.861651i \(0.669431\pi\)
\(908\) −1.36816e13 + 2.36972e13i −0.667959 + 1.15694i
\(909\) −1.92982e13 + 3.34255e13i −0.937520 + 1.62383i
\(910\) 8.95693e11 + 1.55139e12i 0.0432985 + 0.0749952i
\(911\) 7.22173e12 0.347383 0.173691 0.984800i \(-0.444430\pi\)
0.173691 + 0.984800i \(0.444430\pi\)
\(912\) −4.74248e12 8.21422e12i −0.227002 0.393178i
\(913\) 1.40093e13 2.42649e13i 0.667266 1.15574i
\(914\) −1.73337e12 −0.0821547
\(915\) −7.67726e12 + 1.32974e13i −0.362086 + 0.627151i
\(916\) −7.82255e12 1.35491e13i −0.367129 0.635887i
\(917\) −1.56707e13 2.71425e13i −0.731858 1.26761i
\(918\) 2.62857e10 + 4.55281e10i 0.00122159 + 0.00211586i
\(919\) 4.27506e13 1.97707 0.988535 0.150992i \(-0.0482468\pi\)
0.988535 + 0.150992i \(0.0482468\pi\)
\(920\) 5.90005e11 + 1.02192e12i 0.0271526 + 0.0470296i
\(921\) 1.22461e13 + 2.12108e13i 0.560827 + 0.971380i
\(922\) −1.37824e12 + 2.38717e12i −0.0628108 + 0.108792i
\(923\) 2.43336e13 4.21470e13i 1.10357 1.91143i
\(924\) 8.90235e13 4.01773
\(925\) 1.71187e13 0.768833
\(926\) 5.10422e11 8.84077e11i 0.0228129 0.0395131i
\(927\) −7.44501e12 + 1.28951e13i −0.331136 + 0.573545i
\(928\) −3.31492e12 5.74161e12i −0.146726 0.254137i
\(929\) 1.23126e11 + 2.13261e11i 0.00542351 + 0.00939379i 0.868724 0.495296i \(-0.164940\pi\)
−0.863301 + 0.504690i \(0.831607\pi\)
\(930\) −1.64712e11 −0.00722023
\(931\) −4.65778e12 8.06752e12i −0.203192 0.351938i
\(932\) 2.85970e12 + 4.95314e12i 0.124151 + 0.215035i
\(933\) −7.56375e10 1.31008e11i −0.00326791 0.00566018i
\(934\) 3.28678e11 5.69287e11i 0.0141322 0.0244777i
\(935\) 7.40206e12 0.316738
\(936\) −2.70371e12 + 4.68296e12i −0.115138 + 0.199425i
\(937\) −1.23868e12 2.14546e12i −0.0524967 0.0909270i 0.838583 0.544774i \(-0.183385\pi\)
−0.891080 + 0.453847i \(0.850051\pi\)
\(938\) 1.09081e12 0.0460085
\(939\) −3.73290e12 6.46558e12i −0.156694 0.271401i
\(940\) 8.27503e12 1.43328e13i 0.345696 0.598763i
\(941\) 5.01419e12 8.68483e12i 0.208472 0.361084i −0.742761 0.669556i \(-0.766484\pi\)
0.951233 + 0.308472i \(0.0998177\pi\)
\(942\) −3.07871e12 −0.127391
\(943\) −7.45319e12 + 1.29093e13i −0.306930 + 0.531619i
\(944\) −8.05646e12 −0.330195
\(945\) 1.89157e12 0.0771578
\(946\) 3.05704e12 2.01757e12i 0.124105 0.0819067i
\(947\) 7.73377e12 0.312476 0.156238 0.987719i \(-0.450063\pi\)
0.156238 + 0.987719i \(0.450063\pi\)
\(948\) 4.21687e13 1.69571
\(949\) −7.07732e12 + 1.22583e13i −0.283251 + 0.490604i
\(950\) −4.60864e11 −0.0183576
\(951\) 1.76797e13 3.06221e13i 0.700909 1.21401i
\(952\) −9.62661e11 + 1.66738e12i −0.0379845 + 0.0657912i
\(953\) 5.43353e12 + 9.41116e12i 0.213385 + 0.369594i 0.952772 0.303687i \(-0.0982177\pi\)
−0.739387 + 0.673281i \(0.764884\pi\)
\(954\) −4.89374e11 −0.0191282
\(955\) 3.07917e12 + 5.33328e12i 0.119790 + 0.207482i
\(956\) 1.63481e13 2.83158e13i 0.633005 1.09640i
\(957\) −8.65135e13 −3.33411
\(958\) 1.49518e12 2.58972e12i 0.0573519 0.0993365i
\(959\) 2.05481e12 + 3.55903e12i 0.0784489 + 0.135878i
\(960\) 9.68191e12 + 1.67696e13i 0.367909 + 0.637237i
\(961\) 1.30335e13 + 2.25747e13i 0.492953 + 0.853819i
\(962\) 3.08268e12 0.116049
\(963\) −1.50534e13 2.60733e13i −0.564049 0.976961i
\(964\) 7.03030e12 + 1.21768e13i 0.262197 + 0.454138i
\(965\) 5.81341e12 1.00691e13i 0.215803 0.373782i
\(966\) −1.49874e12 + 2.59590e12i −0.0553771 + 0.0959160i
\(967\) 4.88036e13 1.79487 0.897434 0.441149i \(-0.145429\pi\)
0.897434 + 0.441149i \(0.145429\pi\)
\(968\) −1.08095e13 −0.395700
\(969\) 2.02268e12 3.50338e12i 0.0737003 0.127653i
\(970\) −3.44117e11 + 5.96029e11i −0.0124805 + 0.0216169i
\(971\) −1.51692e13 2.62738e13i −0.547614 0.948496i −0.998437 0.0558827i \(-0.982203\pi\)
0.450823 0.892613i \(-0.351131\pi\)
\(972\) −1.97894e13 3.42762e13i −0.711106 1.23167i
\(973\) −4.36510e13 −1.56130
\(974\) −1.00354e11 1.73817e11i −0.00357287 0.00618839i
\(975\) −1.97975e13 3.42903e13i −0.701600 1.21521i
\(976\) −1.31689e13 2.28092e13i −0.464542 0.804610i
\(977\) 1.27406e13 2.20673e13i 0.447367 0.774862i −0.550847 0.834606i \(-0.685695\pi\)
0.998214 + 0.0597445i \(0.0190286\pi\)
\(978\) −5.10720e12 −0.178508
\(979\) −2.55602e13 + 4.42716e13i −0.889288 + 1.54029i
\(980\) 9.63361e12 + 1.66859e13i 0.333635 + 0.577873i
\(981\) 3.02672e13 1.04343
\(982\) 4.99173e10 + 8.64593e10i 0.00171297 + 0.00296695i
\(983\) −1.13122e13 + 1.95933e13i −0.386416 + 0.669293i −0.991965 0.126516i \(-0.959621\pi\)
0.605548 + 0.795809i \(0.292954\pi\)
\(984\) 3.19565e12 5.53503e12i 0.108663 0.188210i
\(985\) −2.13609e13 −0.723032
\(986\) 4.66275e11 8.07612e11i 0.0157107 0.0272118i
\(987\) 8.43492e13 2.82914
\(988\) 1.30372e13 0.435291
\(989\) −1.15706e12 1.93394e13i −0.0384567 0.642777i
\(990\) −2.55072e12 −0.0843927
\(991\) −1.38090e13 −0.454812 −0.227406 0.973800i \(-0.573024\pi\)
−0.227406 + 0.973800i \(0.573024\pi\)
\(992\) 4.28340e11 7.41906e11i 0.0140438 0.0243246i
\(993\) −5.03799e13 −1.64432
\(994\) −2.98559e12 + 5.17119e12i −0.0970043 + 0.168016i
\(995\) 8.10173e12 1.40326e13i 0.262044 0.453873i
\(996\) 1.58355e13 + 2.74278e13i 0.509875 + 0.883130i
\(997\) 1.57051e13 0.503399 0.251700 0.967805i \(-0.419010\pi\)
0.251700 + 0.967805i \(0.419010\pi\)
\(998\) 1.60098e12 + 2.77298e12i 0.0510857 + 0.0884830i
\(999\) 1.62754e12 2.81899e12i 0.0516997 0.0895464i
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 43.10.c.a.6.17 64
43.36 even 3 inner 43.10.c.a.36.17 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.10.c.a.6.17 64 1.1 even 1 trivial
43.10.c.a.36.17 yes 64 43.36 even 3 inner