Properties

Label 69.8.e.a.25.8
Level $69$
Weight $8$
Character 69.25
Analytic conductor $21.555$
Analytic rank $0$
Dimension $140$
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 25.8
Character \(\chi\) \(=\) 69.25
Dual form 69.8.e.a.58.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.14494 + 1.37847i) q^{2} +(-3.84250 - 26.7252i) q^{3} +(-50.4725 - 110.519i) q^{4} +(-464.485 - 136.385i) q^{5} +(28.5978 - 62.6205i) q^{6} +(1029.85 - 1188.50i) q^{7} +(90.5329 - 629.670i) q^{8} +(-699.470 + 205.383i) q^{9} +O(q^{10})\) \(q+(2.14494 + 1.37847i) q^{2} +(-3.84250 - 26.7252i) q^{3} +(-50.4725 - 110.519i) q^{4} +(-464.485 - 136.385i) q^{5} +(28.5978 - 62.6205i) q^{6} +(1029.85 - 1188.50i) q^{7} +(90.5329 - 629.670i) q^{8} +(-699.470 + 205.383i) q^{9} +(-808.288 - 932.814i) q^{10} +(3011.62 - 1935.45i) q^{11} +(-2759.71 + 1773.56i) q^{12} +(-3522.89 - 4065.63i) q^{13} +(3847.27 - 1129.66i) q^{14} +(-1860.13 + 12937.5i) q^{15} +(-9122.15 + 10527.5i) q^{16} +(-14498.6 + 31747.5i) q^{17} +(-1783.43 - 523.663i) q^{18} +(-20754.7 - 45446.5i) q^{19} +(8370.53 + 58218.3i) q^{20} +(-35720.2 - 22956.0i) q^{21} +9127.70 q^{22} +(50820.8 + 28671.8i) q^{23} -17175.9 q^{24} +(131423. + 84460.1i) q^{25} +(-1952.03 - 13576.7i) q^{26} +(8176.61 + 17904.3i) q^{27} +(-183332. - 53831.1i) q^{28} +(68687.9 - 150406. i) q^{29} +(-21823.8 + 25186.0i) q^{30} +(-18300.9 + 127285. i) q^{31} +(-112207. + 32946.8i) q^{32} +(-63297.5 - 73049.2i) q^{33} +(-74861.4 + 48110.5i) q^{34} +(-640442. + 411587. i) q^{35} +(58002.9 + 66938.9i) q^{36} +(146956. - 43150.1i) q^{37} +(18128.9 - 126089. i) q^{38} +(-95118.0 + 109772. i) q^{39} +(-127929. + 280125. i) q^{40} +(-111352. - 32695.9i) q^{41} +(-44973.5 - 98478.1i) q^{42} +(47299.1 + 328973. i) q^{43} +(-365910. - 235156. i) q^{44} +352905. q^{45} +(69484.3 + 131554. i) q^{46} +677797. q^{47} +(316402. + 203339. i) q^{48} +(-234760. - 1.63279e6i) q^{49} +(165467. + 362323. i) q^{50} +(904168. + 265488. i) q^{51} +(-271522. + 594550. i) q^{52} +(-489376. + 564770. i) q^{53} +(-7142.15 + 49674.7i) q^{54} +(-1.66282e6 + 488248. i) q^{55} +(-655131. - 756062. i) q^{56} +(-1.13482e6 + 729302. i) q^{57} +(354660. - 227926. i) q^{58} +(-644099. - 743330. i) q^{59} +(1.52373e6 - 447408. i) q^{60} +(227626. - 1.58317e6i) q^{61} +(-214713. + 247792. i) q^{62} +(-476248. + 1.04284e6i) q^{63} +(1.42471e6 + 418333. i) q^{64} +(1.08184e6 + 2.36889e6i) q^{65} +(-35073.2 - 243939. i) q^{66} +(122681. + 78842.4i) q^{67} +4.24050e6 q^{68} +(570979. - 1.46837e6i) q^{69} -1.94107e6 q^{70} +(2.25335e6 + 1.44814e6i) q^{71} +(65998.5 + 459030. i) q^{72} +(-2.18645e6 - 4.78767e6i) q^{73} +(374692. + 110019. i) q^{74} +(1.75222e6 - 3.83683e6i) q^{75} +(-3.97518e6 + 4.58760e6i) q^{76} +(801211. - 5.57255e6i) q^{77} +(-355339. + 104337. i) q^{78} +(1.36356e6 + 1.57363e6i) q^{79} +(5.67290e6 - 3.64575e6i) q^{80} +(447077. - 287319. i) q^{81} +(-193773. - 223626. i) q^{82} +(-2.15391e6 + 632444. i) q^{83} +(-734193. + 5.10642e6i) q^{84} +(1.10643e7 - 1.27688e7i) q^{85} +(-352024. + 770826. i) q^{86} +(-4.28355e6 - 1.25776e6i) q^{87} +(-946046. - 2.07155e6i) q^{88} +(106792. + 742753. i) q^{89} +(756958. + 486467. i) q^{90} -8.46005e6 q^{91} +(603734. - 7.06383e6i) q^{92} +3.47205e6 q^{93} +(1.45383e6 + 934321. i) q^{94} +(3.44203e6 + 2.39399e7i) q^{95} +(1.31166e6 + 2.87214e6i) q^{96} +(-4.62353e6 - 1.35759e6i) q^{97} +(1.74720e6 - 3.82584e6i) q^{98} +(-1.70903e6 + 1.97233e6i) 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 \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.14494 + 1.37847i 0.189587 + 0.121840i 0.631991 0.774976i \(-0.282238\pi\)
−0.442404 + 0.896816i \(0.645874\pi\)
\(3\) −3.84250 26.7252i −0.0821655 0.571474i
\(4\) −50.4725 110.519i −0.394317 0.863433i
\(5\) −464.485 136.385i −1.66179 0.487946i −0.690005 0.723805i \(-0.742392\pi\)
−0.971787 + 0.235859i \(0.924210\pi\)
\(6\) 28.5978 62.6205i 0.0540510 0.118355i
\(7\) 1029.85 1188.50i 1.13482 1.30966i 0.190111 0.981763i \(-0.439115\pi\)
0.944714 0.327895i \(-0.106339\pi\)
\(8\) 90.5329 629.670i 0.0625161 0.434809i
\(9\) −699.470 + 205.383i −0.319831 + 0.0939109i
\(10\) −808.288 932.814i −0.255603 0.294982i
\(11\) 3011.62 1935.45i 0.682223 0.438438i −0.153090 0.988212i \(-0.548923\pi\)
0.835313 + 0.549774i \(0.185286\pi\)
\(12\) −2759.71 + 1773.56i −0.461030 + 0.296286i
\(13\) −3522.89 4065.63i −0.444731 0.513247i 0.488481 0.872575i \(-0.337551\pi\)
−0.933211 + 0.359328i \(0.883006\pi\)
\(14\) 3847.27 1129.66i 0.374718 0.110027i
\(15\) −1860.13 + 12937.5i −0.142306 + 0.989763i
\(16\) −9122.15 + 10527.5i −0.556772 + 0.642549i
\(17\) −14498.6 + 31747.5i −0.715739 + 1.56725i 0.104042 + 0.994573i \(0.466822\pi\)
−0.819781 + 0.572677i \(0.805905\pi\)
\(18\) −1783.43 523.663i −0.0720780 0.0211640i
\(19\) −20754.7 45446.5i −0.694191 1.52007i −0.846875 0.531792i \(-0.821519\pi\)
0.152683 0.988275i \(-0.451209\pi\)
\(20\) 8370.53 + 58218.3i 0.233963 + 1.62725i
\(21\) −35720.2 22956.0i −0.841678 0.540914i
\(22\) 9127.70 0.182760
\(23\) 50820.8 + 28671.8i 0.870952 + 0.491368i
\(24\) −17175.9 −0.253618
\(25\) 131423. + 84460.1i 1.68221 + 1.08109i
\(26\) −1952.03 13576.7i −0.0217811 0.151491i
\(27\) 8176.61 + 17904.3i 0.0799467 + 0.175059i
\(28\) −183332. 53831.1i −1.57828 0.463426i
\(29\) 68687.9 150406.i 0.522983 1.14517i −0.445315 0.895374i \(-0.646908\pi\)
0.968298 0.249799i \(-0.0803644\pi\)
\(30\) −21823.8 + 25186.0i −0.147573 + 0.170308i
\(31\) −18300.9 + 127285.i −0.110333 + 0.767384i 0.857262 + 0.514880i \(0.172163\pi\)
−0.967596 + 0.252505i \(0.918746\pi\)
\(32\) −112207. + 32946.8i −0.605331 + 0.177741i
\(33\) −63297.5 73049.2i −0.306611 0.353848i
\(34\) −74861.4 + 48110.5i −0.326649 + 0.209925i
\(35\) −640442. + 411587.i −2.52489 + 1.62265i
\(36\) 58002.9 + 66938.9i 0.207200 + 0.239122i
\(37\) 146956. 43150.1i 0.476958 0.140048i −0.0344125 0.999408i \(-0.510956\pi\)
0.511371 + 0.859360i \(0.329138\pi\)
\(38\) 18128.9 126089.i 0.0535957 0.372766i
\(39\) −95118.0 + 109772.i −0.256765 + 0.296323i
\(40\) −127929. + 280125.i −0.316052 + 0.692057i
\(41\) −111352. 32695.9i −0.252322 0.0740884i 0.153126 0.988207i \(-0.451066\pi\)
−0.405448 + 0.914118i \(0.632884\pi\)
\(42\) −44973.5 98478.1i −0.0936664 0.205101i
\(43\) 47299.1 + 328973.i 0.0907222 + 0.630987i 0.983556 + 0.180601i \(0.0578044\pi\)
−0.892834 + 0.450386i \(0.851287\pi\)
\(44\) −365910. 235156.i −0.647574 0.416171i
\(45\) 352905. 0.577316
\(46\) 69484.3 + 131554.i 0.105253 + 0.199274i
\(47\) 677797. 0.952264 0.476132 0.879374i \(-0.342038\pi\)
0.476132 + 0.879374i \(0.342038\pi\)
\(48\) 316402. + 203339.i 0.412947 + 0.265385i
\(49\) −234760. 1.63279e6i −0.285061 1.98264i
\(50\) 165467. + 362323.i 0.187205 + 0.409922i
\(51\) 904168. + 265488.i 0.954451 + 0.280252i
\(52\) −271522. + 594550.i −0.267789 + 0.586377i
\(53\) −489376. + 564770.i −0.451520 + 0.521082i −0.935180 0.354174i \(-0.884762\pi\)
0.483659 + 0.875257i \(0.339307\pi\)
\(54\) −7142.15 + 49674.7i −0.00617235 + 0.0429297i
\(55\) −1.66282e6 + 488248.i −1.34765 + 0.395705i
\(56\) −655131. 756062.i −0.498506 0.575306i
\(57\) −1.13482e6 + 729302.i −0.811640 + 0.521609i
\(58\) 354660. 227926.i 0.238679 0.153390i
\(59\) −644099. 743330.i −0.408292 0.471194i 0.513943 0.857824i \(-0.328184\pi\)
−0.922235 + 0.386630i \(0.873639\pi\)
\(60\) 1.52373e6 447408.i 0.910708 0.267408i
\(61\) 227626. 1.58317e6i 0.128400 0.893045i −0.819182 0.573534i \(-0.805572\pi\)
0.947582 0.319511i \(-0.103519\pi\)
\(62\) −214713. + 247792.i −0.114416 + 0.132043i
\(63\) −476248. + 1.04284e6i −0.239961 + 0.525441i
\(64\) 1.42471e6 + 418333.i 0.679355 + 0.199477i
\(65\) 1.08184e6 + 2.36889e6i 0.488613 + 1.06991i
\(66\) −35073.2 243939.i −0.0150166 0.104443i
\(67\) 122681. + 78842.4i 0.0498329 + 0.0320256i 0.565320 0.824872i \(-0.308753\pi\)
−0.515487 + 0.856897i \(0.672389\pi\)
\(68\) 4.24050e6 1.63544
\(69\) 570979. 1.46837e6i 0.209242 0.538100i
\(70\) −1.94107e6 −0.676390
\(71\) 2.25335e6 + 1.44814e6i 0.747179 + 0.480183i 0.857995 0.513658i \(-0.171710\pi\)
−0.110816 + 0.993841i \(0.535346\pi\)
\(72\) 65998.5 + 459030.i 0.0208387 + 0.144936i
\(73\) −2.18645e6 4.78767e6i −0.657825 1.44044i −0.884535 0.466473i \(-0.845524\pi\)
0.226710 0.973962i \(-0.427203\pi\)
\(74\) 374692. + 110019.i 0.107489 + 0.0315615i
\(75\) 1.75222e6 3.83683e6i 0.479595 1.05017i
\(76\) −3.97518e6 + 4.58760e6i −1.03875 + 1.19878i
\(77\) 801211. 5.57255e6i 0.200000 1.39103i
\(78\) −355339. + 104337.i −0.0847836 + 0.0248947i
\(79\) 1.36356e6 + 1.57363e6i 0.311157 + 0.359095i 0.889690 0.456564i \(-0.150920\pi\)
−0.578533 + 0.815659i \(0.696375\pi\)
\(80\) 5.67290e6 3.64575e6i 1.23877 0.796108i
\(81\) 447077. 287319.i 0.0934726 0.0600712i
\(82\) −193773. 223626.i −0.0388101 0.0447892i
\(83\) −2.15391e6 + 632444.i −0.413479 + 0.121408i −0.481854 0.876251i \(-0.660037\pi\)
0.0683755 + 0.997660i \(0.478218\pi\)
\(84\) −734193. + 5.10642e6i −0.135155 + 0.940024i
\(85\) 1.10643e7 1.27688e7i 1.95414 2.25520i
\(86\) −352024. + 770826.i −0.0596799 + 0.130681i
\(87\) −4.28355e6 1.25776e6i −0.697407 0.204777i
\(88\) −946046. 2.07155e6i −0.147987 0.324046i
\(89\) 106792. + 742753.i 0.0160573 + 0.111681i 0.996274 0.0862477i \(-0.0274877\pi\)
−0.980216 + 0.197929i \(0.936579\pi\)
\(90\) 756958. + 486467.i 0.109452 + 0.0703404i
\(91\) −8.46005e6 −1.17687
\(92\) 603734. 7.06383e6i 0.0808329 0.945764i
\(93\) 3.47205e6 0.447606
\(94\) 1.45383e6 + 934321.i 0.180537 + 0.116024i
\(95\) 3.44203e6 + 2.39399e7i 0.411891 + 2.86476i
\(96\) 1.31166e6 + 2.87214e6i 0.151312 + 0.331327i
\(97\) −4.62353e6 1.35759e6i −0.514367 0.151032i 0.0142399 0.999899i \(-0.495467\pi\)
−0.528607 + 0.848867i \(0.677285\pi\)
\(98\) 1.74720e6 3.82584e6i 0.187522 0.410616i
\(99\) −1.70903e6 + 1.97233e6i −0.177022 + 0.204294i
\(100\) 2.70126e6 1.87877e7i 0.270126 1.87877i
\(101\) −7.96776e6 + 2.33954e6i −0.769505 + 0.225947i −0.642842 0.765999i \(-0.722245\pi\)
−0.126663 + 0.991946i \(0.540427\pi\)
\(102\) 1.57342e6 + 1.81582e6i 0.146806 + 0.169423i
\(103\) −7.49755e6 + 4.81838e6i −0.676066 + 0.434481i −0.833108 0.553111i \(-0.813441\pi\)
0.157042 + 0.987592i \(0.449804\pi\)
\(104\) −2.87894e6 + 1.85018e6i −0.250967 + 0.161287i
\(105\) 1.34606e7 + 1.55344e7i 1.13476 + 1.30958i
\(106\) −1.82820e6 + 536807.i −0.149091 + 0.0437772i
\(107\) 2.06505e6 1.43627e7i 0.162962 1.13343i −0.730049 0.683395i \(-0.760503\pi\)
0.893012 0.450034i \(-0.148588\pi\)
\(108\) 1.56608e6 1.80735e6i 0.119627 0.138057i
\(109\) 1.73025e6 3.78872e6i 0.127972 0.280221i −0.834790 0.550568i \(-0.814411\pi\)
0.962763 + 0.270347i \(0.0871385\pi\)
\(110\) −4.23968e6 1.24488e6i −0.303710 0.0891772i
\(111\) −1.71787e6 3.76161e6i −0.119223 0.261062i
\(112\) 3.11761e6 + 2.16834e7i 0.209681 + 1.45836i
\(113\) 2.28927e6 + 1.47122e6i 0.149253 + 0.0959190i 0.613136 0.789978i \(-0.289908\pi\)
−0.463883 + 0.885896i \(0.653544\pi\)
\(114\) −3.43942e6 −0.217430
\(115\) −1.96951e7 2.02488e7i −1.20758 1.24153i
\(116\) −2.00896e7 −1.19500
\(117\) 3.29917e6 + 2.12025e6i 0.190438 + 0.122387i
\(118\) −356896. 2.48227e6i −0.0199965 0.139079i
\(119\) 2.28007e7 + 4.99267e7i 1.24032 + 2.71593i
\(120\) 7.97796e6 + 2.34254e6i 0.421461 + 0.123752i
\(121\) −2.77136e6 + 6.06844e6i −0.142215 + 0.311407i
\(122\) 2.67059e6 3.08203e6i 0.133152 0.153666i
\(123\) −445934. + 3.10154e6i −0.0216074 + 0.150283i
\(124\) 1.49912e7 4.40182e6i 0.706091 0.207327i
\(125\) −2.47579e7 2.85722e7i −1.13378 1.30845i
\(126\) −2.45904e6 + 1.58033e6i −0.109514 + 0.0703801i
\(127\) −3.52812e7 + 2.26739e7i −1.52838 + 0.982228i −0.538137 + 0.842857i \(0.680872\pi\)
−0.990240 + 0.139371i \(0.955492\pi\)
\(128\) 1.22817e7 + 1.41739e7i 0.517636 + 0.597383i
\(129\) 8.61011e6 2.52816e6i 0.353138 0.103691i
\(130\) −944968. + 6.57240e6i −0.0377238 + 0.262375i
\(131\) 5.71044e6 6.59020e6i 0.221932 0.256123i −0.633855 0.773452i \(-0.718528\pi\)
0.855787 + 0.517329i \(0.173074\pi\)
\(132\) −4.87857e6 + 1.06826e7i −0.184622 + 0.404266i
\(133\) −7.53875e7 2.21358e7i −2.77855 0.815857i
\(134\) 154462. + 338224.i 0.00554566 + 0.0121433i
\(135\) −1.35604e6 9.43144e6i −0.0474355 0.329921i
\(136\) 1.86779e7 + 1.20035e7i 0.636709 + 0.409188i
\(137\) −1.03770e7 −0.344787 −0.172393 0.985028i \(-0.555150\pi\)
−0.172393 + 0.985028i \(0.555150\pi\)
\(138\) 3.24881e6 2.36248e6i 0.105232 0.0765227i
\(139\) 2.76690e7 0.873858 0.436929 0.899496i \(-0.356066\pi\)
0.436929 + 0.899496i \(0.356066\pi\)
\(140\) 7.78131e7 + 5.00075e7i 2.39665 + 1.54023i
\(141\) −2.60444e6 1.81143e7i −0.0782433 0.544194i
\(142\) 2.83708e6 + 6.21234e6i 0.0831500 + 0.182073i
\(143\) −1.84785e7 5.42576e6i −0.528432 0.155162i
\(144\) 4.21850e6 9.23723e6i 0.117731 0.257794i
\(145\) −5.24176e7 + 6.04931e7i −1.42787 + 1.64785i
\(146\) 1.90983e6 1.32832e7i 0.0507880 0.353238i
\(147\) −4.27346e7 + 1.25480e7i −1.10961 + 0.325810i
\(148\) −1.21862e7 1.40636e7i −0.308994 0.356599i
\(149\) −1.71519e6 + 1.10228e6i −0.0424776 + 0.0272987i −0.561707 0.827336i \(-0.689855\pi\)
0.519230 + 0.854635i \(0.326219\pi\)
\(150\) 9.04734e6 5.81437e6i 0.218878 0.140664i
\(151\) −4.59566e7 5.30367e7i −1.08625 1.25359i −0.965358 0.260929i \(-0.915971\pi\)
−0.120888 0.992666i \(-0.538574\pi\)
\(152\) −3.04953e7 + 8.95423e6i −0.704337 + 0.206812i
\(153\) 3.62094e6 2.51842e7i 0.0817338 0.568471i
\(154\) 9.40012e6 1.08483e7i 0.207401 0.239353i
\(155\) 2.58603e7 5.66262e7i 0.557793 1.22140i
\(156\) 1.69328e7 + 4.97191e6i 0.357102 + 0.104855i
\(157\) −1.48846e7 3.25928e7i −0.306965 0.672160i 0.691787 0.722102i \(-0.256824\pi\)
−0.998752 + 0.0499415i \(0.984097\pi\)
\(158\) 755550. + 5.25497e6i 0.0152392 + 0.105991i
\(159\) 1.69740e7 + 1.09085e7i 0.334884 + 0.215217i
\(160\) 5.66117e7 1.09266
\(161\) 8.64141e7 3.08733e7i 1.63190 0.583032i
\(162\) 1.35501e6 0.0250403
\(163\) 8.31260e6 + 5.34218e6i 0.150342 + 0.0966189i 0.613649 0.789579i \(-0.289701\pi\)
−0.463307 + 0.886198i \(0.653337\pi\)
\(164\) 2.00669e6 + 1.39568e7i 0.0355244 + 0.247077i
\(165\) 1.94379e7 + 4.25631e7i 0.336865 + 0.737632i
\(166\) −5.49179e6 1.61254e6i −0.0931828 0.0273609i
\(167\) −892759. + 1.95487e6i −0.0148329 + 0.0324795i −0.916903 0.399109i \(-0.869319\pi\)
0.902071 + 0.431589i \(0.142047\pi\)
\(168\) −1.76885e7 + 2.04137e7i −0.287812 + 0.332153i
\(169\) 4.81144e6 3.34643e7i 0.0766782 0.533309i
\(170\) 4.13336e7 1.21366e7i 0.645255 0.189464i
\(171\) 2.38513e7 + 2.75258e7i 0.364775 + 0.420973i
\(172\) 3.39706e7 2.18316e7i 0.509042 0.327141i
\(173\) −4.42667e7 + 2.84485e7i −0.650004 + 0.417732i −0.823668 0.567073i \(-0.808076\pi\)
0.173664 + 0.984805i \(0.444439\pi\)
\(174\) −7.45415e6 8.60255e6i −0.107269 0.123796i
\(175\) 2.35726e8 6.92154e7i 3.32487 0.976269i
\(176\) −7.09696e6 + 4.93604e7i −0.0981246 + 0.682472i
\(177\) −1.73907e7 + 2.00699e7i −0.235728 + 0.272044i
\(178\) −794798. + 1.74037e6i −0.0105630 + 0.0231297i
\(179\) −8.58431e7 2.52058e7i −1.11872 0.328485i −0.330452 0.943823i \(-0.607201\pi\)
−0.788263 + 0.615338i \(0.789019\pi\)
\(180\) −1.78120e7 3.90028e7i −0.227645 0.498474i
\(181\) −2.34481e6 1.63085e7i −0.0293922 0.204427i 0.969834 0.243768i \(-0.0783834\pi\)
−0.999226 + 0.0393403i \(0.987474\pi\)
\(182\) −1.81463e7 1.16619e7i −0.223119 0.143390i
\(183\) −4.31852e7 −0.520902
\(184\) 2.26547e7 2.94046e7i 0.268100 0.347979i
\(185\) −7.41438e7 −0.860941
\(186\) 7.44732e6 + 4.78610e6i 0.0848603 + 0.0545364i
\(187\) 1.77815e7 + 1.23673e8i 0.198848 + 1.38302i
\(188\) −3.42102e7 7.49098e7i −0.375494 0.822216i
\(189\) 2.97000e7 + 8.72070e6i 0.319992 + 0.0939583i
\(190\) −2.56173e7 + 5.60942e7i −0.270955 + 0.593308i
\(191\) −7.71052e7 + 8.89842e7i −0.800695 + 0.924051i −0.998419 0.0562066i \(-0.982099\pi\)
0.197724 + 0.980258i \(0.436645\pi\)
\(192\) 5.70557e6 3.96831e7i 0.0581761 0.404624i
\(193\) 1.06384e8 3.12370e7i 1.06518 0.312766i 0.298246 0.954489i \(-0.403598\pi\)
0.766936 + 0.641723i \(0.221780\pi\)
\(194\) −8.04579e6 9.28533e6i −0.0791156 0.0913043i
\(195\) 5.91521e7 3.80148e7i 0.571280 0.367140i
\(196\) −1.68606e8 + 1.08357e8i −1.59948 + 1.02792i
\(197\) 8.44546e7 + 9.74658e7i 0.787030 + 0.908282i 0.997596 0.0692981i \(-0.0220760\pi\)
−0.210565 + 0.977580i \(0.567531\pi\)
\(198\) −6.38455e6 + 1.87467e6i −0.0584524 + 0.0171632i
\(199\) 2.65484e7 1.84648e8i 0.238810 1.66096i −0.419158 0.907914i \(-0.637675\pi\)
0.657968 0.753046i \(-0.271416\pi\)
\(200\) 6.50801e7 7.51064e7i 0.575232 0.663853i
\(201\) 1.63567e6 3.58163e6i 0.0142073 0.0311096i
\(202\) −2.03153e7 5.96511e6i −0.173418 0.0509201i
\(203\) −1.08020e8 2.36530e8i −0.906290 1.98450i
\(204\) −1.62941e7 1.13328e8i −0.134377 0.934613i
\(205\) 4.72622e7 + 3.03735e7i 0.383155 + 0.246239i
\(206\) −2.27237e7 −0.181111
\(207\) −4.14363e7 9.61733e6i −0.324702 0.0753630i
\(208\) 7.49373e7 0.577400
\(209\) −1.50465e8 9.66980e7i −1.14005 0.732665i
\(210\) 7.45855e6 + 5.18753e7i 0.0555759 + 0.386539i
\(211\) 5.39019e7 + 1.18029e8i 0.395017 + 0.864966i 0.997751 + 0.0670241i \(0.0213504\pi\)
−0.602735 + 0.797942i \(0.705922\pi\)
\(212\) 8.71182e7 + 2.55802e7i 0.627962 + 0.184386i
\(213\) 3.00433e7 6.57857e7i 0.213019 0.466448i
\(214\) 2.42280e7 2.79605e7i 0.168993 0.195028i
\(215\) 2.28972e7 1.59254e8i 0.157126 1.09284i
\(216\) 1.20140e7 3.52764e6i 0.0811150 0.0238175i
\(217\) 1.32432e8 + 1.52835e8i 0.879802 + 1.01535i
\(218\) 8.93391e6 5.74147e6i 0.0584041 0.0375341i
\(219\) −1.19550e8 + 7.68300e7i −0.769121 + 0.494284i
\(220\) 1.37888e8 + 1.59131e8i 0.873065 + 1.00757i
\(221\) 1.80150e8 5.28970e7i 1.12270 0.329654i
\(222\) 1.50053e6 1.04364e7i 0.00920472 0.0640202i
\(223\) −1.57358e8 + 1.81600e8i −0.950213 + 1.09660i 0.0450115 + 0.998986i \(0.485668\pi\)
−0.995224 + 0.0976173i \(0.968878\pi\)
\(224\) −7.63979e7 + 1.67288e8i −0.454165 + 0.994482i
\(225\) −1.09273e8 3.20854e7i −0.639548 0.187788i
\(226\) 2.88230e6 + 6.31137e6i 0.0166096 + 0.0363700i
\(227\) −7.18349e6 4.99623e7i −0.0407610 0.283499i −1.00000 0.000901548i \(-0.999713\pi\)
0.959239 0.282597i \(-0.0911961\pi\)
\(228\) 1.37879e8 + 8.86095e7i 0.770418 + 0.495118i
\(229\) 9.80945e7 0.539784 0.269892 0.962891i \(-0.413012\pi\)
0.269892 + 0.962891i \(0.413012\pi\)
\(230\) −1.43324e7 7.05814e7i −0.0776733 0.382510i
\(231\) −1.52006e8 −0.811370
\(232\) −8.84874e7 5.68674e7i −0.465236 0.298989i
\(233\) 3.43678e7 + 2.39033e8i 0.177994 + 1.23798i 0.861396 + 0.507934i \(0.169591\pi\)
−0.683402 + 0.730043i \(0.739500\pi\)
\(234\) 4.15381e6 + 9.09558e6i 0.0211929 + 0.0464061i
\(235\) −3.14827e8 9.24415e7i −1.58247 0.464654i
\(236\) −4.96431e7 + 1.08703e8i −0.245848 + 0.538333i
\(237\) 3.68162e7 4.24881e7i 0.179647 0.207323i
\(238\) −1.99161e7 + 1.38520e8i −0.0957602 + 0.666027i
\(239\) 1.71072e8 5.02312e7i 0.810562 0.238002i 0.149914 0.988699i \(-0.452100\pi\)
0.660647 + 0.750697i \(0.270282\pi\)
\(240\) −1.19231e8 1.37600e8i −0.556739 0.642511i
\(241\) −8.76113e7 + 5.63044e7i −0.403181 + 0.259109i −0.726479 0.687188i \(-0.758845\pi\)
0.323298 + 0.946297i \(0.395208\pi\)
\(242\) −1.43095e7 + 9.19618e6i −0.0649040 + 0.0417113i
\(243\) −9.39654e6 1.08442e7i −0.0420093 0.0484814i
\(244\) −1.86460e8 + 5.47496e7i −0.821715 + 0.241277i
\(245\) −1.13646e8 + 7.90425e8i −0.493711 + 3.43383i
\(246\) −5.23187e6 + 6.03790e6i −0.0224070 + 0.0258591i
\(247\) −1.11652e8 + 2.44484e8i −0.471441 + 1.03231i
\(248\) 7.84911e7 + 2.30471e7i 0.326768 + 0.0959477i
\(249\) 2.51786e7 + 5.51333e7i 0.103355 + 0.226317i
\(250\) −1.37184e7 9.54135e7i −0.0555281 0.386207i
\(251\) −7.60937e7 4.89025e7i −0.303732 0.195197i 0.379892 0.925031i \(-0.375961\pi\)
−0.683625 + 0.729834i \(0.739597\pi\)
\(252\) 1.39291e8 0.548304
\(253\) 2.08546e8 1.20127e7i 0.809618 0.0466357i
\(254\) −1.06931e8 −0.409436
\(255\) −3.83764e8 2.46630e8i −1.44935 0.931442i
\(256\) −2.02433e7 1.40795e8i −0.0754123 0.524504i
\(257\) −1.12841e8 2.47088e8i −0.414669 0.907999i −0.995570 0.0940247i \(-0.970027\pi\)
0.580901 0.813975i \(-0.302701\pi\)
\(258\) 2.19531e7 + 6.44601e6i 0.0795842 + 0.0233680i
\(259\) 1.00058e8 2.19096e8i 0.357850 0.783582i
\(260\) 2.07206e8 2.39128e8i 0.731131 0.843770i
\(261\) −1.71544e7 + 1.19312e8i −0.0597220 + 0.415375i
\(262\) 2.13329e7 6.26390e6i 0.0732817 0.0215174i
\(263\) −1.00199e8 1.15636e8i −0.339639 0.391965i 0.560076 0.828441i \(-0.310772\pi\)
−0.899716 + 0.436476i \(0.856226\pi\)
\(264\) −5.17274e7 + 3.32432e7i −0.173024 + 0.111196i
\(265\) 3.04334e8 1.95584e8i 1.00459 0.645613i
\(266\) −1.31188e8 1.51399e8i −0.427374 0.493216i
\(267\) 1.94398e7 5.70805e6i 0.0625034 0.0183526i
\(268\) 2.52159e6 1.75380e7i 0.00800207 0.0556556i
\(269\) −2.55448e8 + 2.94803e8i −0.800148 + 0.923420i −0.998389 0.0567335i \(-0.981931\pi\)
0.198242 + 0.980153i \(0.436477\pi\)
\(270\) 1.00923e7 2.20991e7i 0.0312045 0.0683284i
\(271\) 4.75292e8 + 1.39558e8i 1.45067 + 0.425955i 0.909763 0.415129i \(-0.136263\pi\)
0.540906 + 0.841083i \(0.318082\pi\)
\(272\) −2.01964e8 4.42240e8i −0.608532 1.33250i
\(273\) 3.25077e7 + 2.26096e8i 0.0966980 + 0.672549i
\(274\) −2.22580e7 1.43044e7i −0.0653672 0.0420089i
\(275\) 5.59264e8 1.62163
\(276\) −1.91102e8 + 1.10079e7i −0.547121 + 0.0315153i
\(277\) −4.19243e8 −1.18519 −0.592593 0.805502i \(-0.701896\pi\)
−0.592593 + 0.805502i \(0.701896\pi\)
\(278\) 5.93481e7 + 3.81407e7i 0.165672 + 0.106471i
\(279\) −1.33413e7 9.27911e7i −0.0367777 0.255795i
\(280\) 2.01183e8 + 4.40529e8i 0.547694 + 1.19928i
\(281\) −4.50783e7 1.32362e7i −0.121198 0.0355869i 0.220571 0.975371i \(-0.429208\pi\)
−0.341769 + 0.939784i \(0.611026\pi\)
\(282\) 1.93835e7 4.24440e7i 0.0514709 0.112705i
\(283\) 1.49604e8 1.72653e8i 0.392366 0.452815i −0.524856 0.851191i \(-0.675881\pi\)
0.917222 + 0.398376i \(0.130426\pi\)
\(284\) 4.63154e7 3.22130e8i 0.119981 0.834483i
\(285\) 6.26571e8 1.83978e8i 1.60329 0.470770i
\(286\) −3.21559e7 3.71098e7i −0.0812791 0.0938011i
\(287\) −1.53535e8 + 9.86708e7i −0.383372 + 0.246378i
\(288\) 7.17184e7 4.60906e7i 0.176912 0.113694i
\(289\) −5.28980e8 6.10475e8i −1.28913 1.48773i
\(290\) −1.95820e8 + 5.74980e7i −0.471481 + 0.138439i
\(291\) −1.85160e7 + 1.28781e8i −0.0440474 + 0.306357i
\(292\) −4.18774e8 + 4.83291e8i −0.984329 + 1.13598i
\(293\) 1.99746e7 4.37382e7i 0.0463917 0.101584i −0.885017 0.465559i \(-0.845853\pi\)
0.931409 + 0.363975i \(0.118581\pi\)
\(294\) −1.08960e8 3.19935e7i −0.250064 0.0734254i
\(295\) 1.97795e8 + 4.33111e8i 0.448579 + 0.982251i
\(296\) −1.38660e7 9.64402e7i −0.0310764 0.216141i
\(297\) 5.92778e7 + 3.80955e7i 0.131294 + 0.0843775i
\(298\) −5.19843e6 −0.0113793
\(299\) −6.24672e7 3.07626e8i −0.135146 0.665540i
\(300\) −5.12483e8 −1.09586
\(301\) 4.39697e8 + 2.82576e8i 0.929331 + 0.597245i
\(302\) −2.54646e7 1.77110e8i −0.0532000 0.370014i
\(303\) 9.31409e7 + 2.03950e8i 0.192349 + 0.421187i
\(304\) 6.67767e8 + 1.96074e8i 1.36322 + 0.400279i
\(305\) −3.21650e8 + 7.04314e8i −0.649133 + 1.42140i
\(306\) 4.24823e7 4.90271e7i 0.0847584 0.0978164i
\(307\) −9.54897e7 + 6.64146e8i −0.188353 + 1.31002i 0.647919 + 0.761709i \(0.275639\pi\)
−0.836272 + 0.548314i \(0.815270\pi\)
\(308\) −6.56314e8 + 1.92711e8i −1.27992 + 0.375820i
\(309\) 1.57581e8 + 1.81859e8i 0.303844 + 0.350654i
\(310\) 1.33526e8 8.58120e7i 0.254566 0.163600i
\(311\) −2.07687e8 + 1.33472e8i −0.391515 + 0.251611i −0.721557 0.692355i \(-0.756573\pi\)
0.330042 + 0.943966i \(0.392937\pi\)
\(312\) 6.05088e7 + 6.98309e7i 0.112792 + 0.130169i
\(313\) 9.82569e8 2.88508e8i 1.81116 0.531806i 0.812476 0.582995i \(-0.198119\pi\)
0.998689 + 0.0511894i \(0.0163012\pi\)
\(314\) 1.30015e7 9.04274e7i 0.0236995 0.164834i
\(315\) 3.63437e8 4.19429e8i 0.655153 0.756086i
\(316\) 1.05095e8 2.30125e8i 0.187360 0.410261i
\(317\) 8.54794e8 + 2.50990e8i 1.50714 + 0.442537i 0.927966 0.372666i \(-0.121556\pi\)
0.579176 + 0.815202i \(0.303374\pi\)
\(318\) 2.13711e7 + 4.67962e7i 0.0372677 + 0.0816049i
\(319\) −8.42408e7 5.85907e8i −0.145296 1.01056i
\(320\) −6.04703e8 3.88619e8i −1.03161 0.662978i
\(321\) −3.91782e8 −0.661114
\(322\) 2.27910e8 + 5.28978e7i 0.380425 + 0.0882961i
\(323\) 1.74373e9 2.87919
\(324\) −5.43194e7 3.49090e7i −0.0887253 0.0570203i
\(325\) −1.19603e8 8.31859e8i −0.193264 1.34418i
\(326\) 1.04660e7 + 2.29173e7i 0.0167308 + 0.0366354i
\(327\) −1.07903e8 3.16831e7i −0.170654 0.0501084i
\(328\) −3.06687e7 + 6.71551e7i −0.0479885 + 0.105080i
\(329\) 6.98026e8 8.05566e8i 1.08065 1.24714i
\(330\) −1.69787e7 + 1.18090e8i −0.0260080 + 0.180889i
\(331\) 4.20358e8 1.23428e8i 0.637121 0.187075i 0.0528086 0.998605i \(-0.483183\pi\)
0.584312 + 0.811529i \(0.301364\pi\)
\(332\) 1.78610e8 + 2.06127e8i 0.267870 + 0.309138i
\(333\) −9.39289e7 + 6.03644e7i −0.139394 + 0.0895831i
\(334\) −4.60963e6 + 2.96243e6i −0.00676945 + 0.00435046i
\(335\) −4.62306e7 5.33530e7i −0.0671851 0.0775357i
\(336\) 5.67514e8 1.66637e8i 0.816186 0.239654i
\(337\) 1.27938e8 8.89830e8i 0.182094 1.26649i −0.669707 0.742626i \(-0.733580\pi\)
0.851801 0.523866i \(-0.175511\pi\)
\(338\) 5.64497e7 6.51464e7i 0.0795157 0.0917660i
\(339\) 3.05222e7 6.68343e7i 0.0425517 0.0931753i
\(340\) −1.96965e9 5.78341e8i −2.71777 0.798009i
\(341\) 1.91240e8 + 4.18757e8i 0.261179 + 0.571902i
\(342\) 1.32160e7 + 9.19192e7i 0.0178652 + 0.124255i
\(343\) −1.09282e9 7.02316e8i −1.46225 0.939730i
\(344\) 2.11427e8 0.280030
\(345\) −4.65475e8 + 6.04161e8i −0.610280 + 0.792111i
\(346\) −1.34165e8 −0.174129
\(347\) −4.27474e8 2.74721e8i −0.549233 0.352971i 0.236407 0.971654i \(-0.424030\pi\)
−0.785641 + 0.618683i \(0.787666\pi\)
\(348\) 7.71943e7 + 5.36898e8i 0.0981879 + 0.682912i
\(349\) −3.96189e8 8.67534e8i −0.498900 1.09244i −0.976825 0.214039i \(-0.931338\pi\)
0.477925 0.878401i \(-0.341389\pi\)
\(350\) 6.01028e8 + 1.76478e8i 0.749302 + 0.220015i
\(351\) 4.39869e7 9.63179e7i 0.0542936 0.118886i
\(352\) −2.74157e8 + 3.16394e8i −0.335042 + 0.386660i
\(353\) 1.01950e8 7.09077e8i 0.123360 0.857989i −0.830346 0.557249i \(-0.811857\pi\)
0.953706 0.300741i \(-0.0972339\pi\)
\(354\) −6.49676e7 + 1.90762e7i −0.0778369 + 0.0228550i
\(355\) −8.49143e8 9.79963e8i −1.00735 1.16255i
\(356\) 7.66986e7 4.92912e7i 0.0900974 0.0579021i
\(357\) 1.24669e9 8.01197e8i 1.45017 0.931967i
\(358\) −1.49383e8 1.72397e8i −0.172072 0.198581i
\(359\) −4.89125e8 + 1.43620e8i −0.557942 + 0.163827i −0.548533 0.836129i \(-0.684813\pi\)
−0.00940957 + 0.999956i \(0.502995\pi\)
\(360\) 3.19495e7 2.22214e8i 0.0360915 0.251022i
\(361\) −1.04926e9 + 1.21092e9i −1.17384 + 1.35469i
\(362\) 1.74513e7 3.82129e7i 0.0193351 0.0423380i
\(363\) 1.72829e8 + 5.07472e7i 0.189646 + 0.0556851i
\(364\) 4.27000e8 + 9.35000e8i 0.464059 + 1.01615i
\(365\) 3.62609e8 + 2.52200e9i 0.390313 + 2.71469i
\(366\) −9.26294e7 5.95293e7i −0.0987564 0.0634669i
\(367\) 5.99906e8 0.633508 0.316754 0.948508i \(-0.397407\pi\)
0.316754 + 0.948508i \(0.397407\pi\)
\(368\) −7.65438e8 + 2.73469e8i −0.800650 + 0.286049i
\(369\) 8.46027e7 0.0876581
\(370\) −1.59034e8 1.02205e8i −0.163224 0.104897i
\(371\) 1.67250e8 + 1.16325e9i 0.170043 + 1.18267i
\(372\) −1.75243e8 3.83729e8i −0.176498 0.386478i
\(373\) 3.67278e8 + 1.07843e8i 0.366450 + 0.107599i 0.459773 0.888037i \(-0.347931\pi\)
−0.0933233 + 0.995636i \(0.529749\pi\)
\(374\) −1.32339e8 + 2.89782e8i −0.130809 + 0.286431i
\(375\) −6.68464e8 + 7.71449e8i −0.654589 + 0.755436i
\(376\) 6.13630e7 4.26789e8i 0.0595318 0.414053i
\(377\) −8.53473e8 + 2.50602e8i −0.820342 + 0.240874i
\(378\) 5.16833e7 + 5.96458e7i 0.0492186 + 0.0568013i
\(379\) 1.19299e9 7.66685e8i 1.12564 0.723402i 0.160991 0.986956i \(-0.448531\pi\)
0.964645 + 0.263554i \(0.0848946\pi\)
\(380\) 2.47209e9 1.58872e9i 2.31112 1.48526i
\(381\) 7.41531e8 + 8.55773e8i 0.686898 + 0.792722i
\(382\) −2.88047e8 + 8.45784e7i −0.264388 + 0.0776314i
\(383\) −8.04923e7 + 5.59836e8i −0.0732080 + 0.509173i 0.919917 + 0.392113i \(0.128256\pi\)
−0.993125 + 0.117059i \(0.962653\pi\)
\(384\) 3.31606e8 3.82694e8i 0.298857 0.344900i
\(385\) −1.13216e9 + 2.47909e9i −1.01111 + 2.21401i
\(386\) 2.71245e8 + 7.96448e7i 0.240053 + 0.0704858i
\(387\) −1.00650e8 2.20392e8i −0.0882723 0.193289i
\(388\) 8.33212e7 + 5.79511e8i 0.0724176 + 0.503676i
\(389\) −8.98678e8 5.77545e8i −0.774071 0.497465i 0.0929903 0.995667i \(-0.470357\pi\)
−0.867061 + 0.498202i \(0.833994\pi\)
\(390\) 1.79280e8 0.153040
\(391\) −1.64709e9 + 1.19773e9i −1.39347 + 1.01331i
\(392\) −1.04937e9 −0.879891
\(393\) −1.98067e8 1.27290e8i −0.164603 0.105784i
\(394\) 4.67963e7 + 3.25476e8i 0.0385456 + 0.268091i
\(395\) −4.18734e8 9.16899e8i −0.341860 0.748569i
\(396\) 3.04240e8 + 8.93329e7i 0.246197 + 0.0722900i
\(397\) 2.19347e8 4.80302e8i 0.175940 0.385255i −0.801032 0.598621i \(-0.795716\pi\)
0.976972 + 0.213366i \(0.0684428\pi\)
\(398\) 3.11476e8 3.59462e8i 0.247647 0.285800i
\(399\) −3.01906e8 + 2.09980e9i −0.237939 + 1.65491i
\(400\) −2.08801e9 + 6.13096e8i −1.63126 + 0.478981i
\(401\) −8.99665e8 1.03827e9i −0.696748 0.804090i 0.291562 0.956552i \(-0.405825\pi\)
−0.988309 + 0.152463i \(0.951280\pi\)
\(402\) 8.44557e6 5.42764e6i 0.00648392 0.00416696i
\(403\) 5.81968e8 3.74008e8i 0.442926 0.284651i
\(404\) 6.60718e8 + 7.62509e8i 0.498519 + 0.575321i
\(405\) −2.46846e8 + 7.24806e7i −0.184644 + 0.0542162i
\(406\) 9.43537e7 6.56244e8i 0.0699709 0.486659i
\(407\) 3.59060e8 4.14378e8i 0.263990 0.304660i
\(408\) 2.49027e8 5.45293e8i 0.181525 0.397483i
\(409\) −3.91736e8 1.15024e8i −0.283114 0.0831298i 0.137092 0.990558i \(-0.456224\pi\)
−0.420207 + 0.907428i \(0.638042\pi\)
\(410\) 5.95054e7 + 1.30299e8i 0.0426396 + 0.0933676i
\(411\) 3.98737e7 + 2.77328e8i 0.0283296 + 0.197036i
\(412\) 9.10945e8 + 5.85429e8i 0.641729 + 0.412414i
\(413\) −1.54677e9 −1.08044
\(414\) −7.56211e7 7.77472e7i −0.0523772 0.0538497i
\(415\) 1.08671e9 0.746357
\(416\) 5.29240e8 + 3.40122e8i 0.360434 + 0.231637i
\(417\) −1.06318e8 7.39458e8i −0.0718010 0.499387i
\(418\) −1.89443e8 4.14822e8i −0.126871 0.277808i
\(419\) 1.98543e9 + 5.82975e8i 1.31858 + 0.387169i 0.863979 0.503528i \(-0.167965\pi\)
0.454598 + 0.890697i \(0.349783\pi\)
\(420\) 1.03746e9 2.27172e9i 0.683281 1.49618i
\(421\) 5.27263e8 6.08494e8i 0.344382 0.397437i −0.556965 0.830536i \(-0.688034\pi\)
0.901347 + 0.433098i \(0.142580\pi\)
\(422\) −4.70825e7 + 3.27466e8i −0.0304976 + 0.212115i
\(423\) −4.74099e8 + 1.39208e8i −0.304564 + 0.0894279i
\(424\) 3.11314e8 + 3.59276e8i 0.198344 + 0.228901i
\(425\) −4.58684e9 + 2.94778e9i −2.89836 + 1.86266i
\(426\) 1.55124e8 9.96924e7i 0.0972179 0.0624782i
\(427\) −1.64719e9 1.90095e9i −1.02387 1.18161i
\(428\) −1.69159e9 + 4.96696e8i −1.04290 + 0.306223i
\(429\) −7.40010e7 + 5.14688e8i −0.0452519 + 0.314734i
\(430\) 2.68639e8 3.10026e8i 0.162941 0.188044i
\(431\) 8.81055e8 1.92924e9i 0.530069 1.16069i −0.435416 0.900229i \(-0.643399\pi\)
0.965485 0.260460i \(-0.0838741\pi\)
\(432\) −2.63076e8 7.72461e7i −0.156996 0.0460982i
\(433\) −8.02187e8 1.75654e9i −0.474862 1.03980i −0.983844 0.179026i \(-0.942705\pi\)
0.508982 0.860777i \(-0.330022\pi\)
\(434\) 7.33808e7 + 5.10375e8i 0.0430892 + 0.299692i
\(435\) 1.81810e9 + 1.16842e9i 1.05903 + 0.680594i
\(436\) −5.06058e8 −0.292413
\(437\) 2.48260e8 2.90470e9i 0.142306 1.66501i
\(438\) −3.62334e8 −0.206039
\(439\) 2.48708e9 + 1.59835e9i 1.40302 + 0.901666i 0.999909 0.0134855i \(-0.00429271\pi\)
0.403110 + 0.915151i \(0.367929\pi\)
\(440\) 1.56895e8 + 1.09123e9i 0.0878064 + 0.610707i
\(441\) 4.99555e8 + 1.09387e9i 0.277363 + 0.607340i
\(442\) 4.59328e8 + 1.34871e8i 0.253014 + 0.0742917i
\(443\) −3.40868e8 + 7.46396e8i −0.186283 + 0.407903i −0.979614 0.200887i \(-0.935617\pi\)
0.793331 + 0.608790i \(0.208345\pi\)
\(444\) −3.29026e8 + 3.79716e8i −0.178398 + 0.205882i
\(445\) 5.16972e7 3.59562e8i 0.0278104 0.193426i
\(446\) −5.87852e8 + 1.72609e8i −0.313759 + 0.0921279i
\(447\) 3.60494e7 + 4.16032e7i 0.0190907 + 0.0220318i
\(448\) 1.96442e9 1.26246e9i 1.03220 0.663352i
\(449\) −2.65390e8 + 1.70556e8i −0.138364 + 0.0889209i −0.607991 0.793944i \(-0.708025\pi\)
0.469628 + 0.882865i \(0.344388\pi\)
\(450\) −1.90155e8 2.19450e8i −0.0983700 0.113525i
\(451\) −3.98632e8 + 1.17049e8i −0.204623 + 0.0600828i
\(452\) 4.70537e7 3.27265e8i 0.0239667 0.166692i
\(453\) −1.24083e9 + 1.43199e9i −0.627145 + 0.723763i
\(454\) 5.34632e7 1.17068e8i 0.0268139 0.0587142i
\(455\) 3.92957e9 + 1.15382e9i 1.95571 + 0.574249i
\(456\) 3.56481e8 + 7.80586e8i 0.176060 + 0.385517i
\(457\) 1.80291e8 + 1.25395e9i 0.0883626 + 0.614575i 0.985096 + 0.172004i \(0.0550244\pi\)
−0.896734 + 0.442571i \(0.854067\pi\)
\(458\) 2.10406e8 + 1.35220e8i 0.102336 + 0.0657675i
\(459\) −6.86966e8 −0.331582
\(460\) −1.24383e9 + 3.19870e9i −0.595809 + 1.53222i
\(461\) −1.93029e9 −0.917632 −0.458816 0.888531i \(-0.651726\pi\)
−0.458816 + 0.888531i \(0.651726\pi\)
\(462\) −3.26043e8 2.09535e8i −0.153825 0.0988576i
\(463\) −3.94062e8 2.74076e9i −0.184515 1.28333i −0.845924 0.533304i \(-0.820950\pi\)
0.661409 0.750026i \(-0.269959\pi\)
\(464\) 9.56817e8 + 2.09514e9i 0.444647 + 0.973642i
\(465\) −1.61271e9 4.73536e8i −0.743827 0.218407i
\(466\) −2.55783e8 + 5.60086e8i −0.117090 + 0.256392i
\(467\) 1.35231e9 1.56065e9i 0.614424 0.709083i −0.360214 0.932870i \(-0.617296\pi\)
0.974638 + 0.223786i \(0.0718418\pi\)
\(468\) 6.78111e7 4.71636e8i 0.0305802 0.212690i
\(469\) 2.20047e8 6.46117e7i 0.0984942 0.0289205i
\(470\) −5.47856e8 6.32259e8i −0.243402 0.280901i
\(471\) −8.13854e8 + 5.23032e8i −0.358900 + 0.230651i
\(472\) −5.26365e8 + 3.38274e8i −0.230404 + 0.148072i
\(473\) 7.79159e8 + 8.99197e8i 0.338542 + 0.390698i
\(474\) 1.37537e8 4.03844e7i 0.0593191 0.0174177i
\(475\) 1.11078e9 7.72564e9i 0.475554 3.30755i
\(476\) 4.36706e9 5.03985e9i 1.85594 2.14187i
\(477\) 2.26310e8 4.95550e8i 0.0954749 0.209061i
\(478\) 4.36180e8 + 1.28074e8i 0.182670 + 0.0536369i
\(479\) −1.05606e9 2.31245e9i −0.439050 0.961385i −0.991772 0.128019i \(-0.959138\pi\)
0.552722 0.833366i \(-0.313589\pi\)
\(480\) −2.17530e8 1.51296e9i −0.0897792 0.624428i
\(481\) −6.93141e8 4.45455e8i −0.283997 0.182514i
\(482\) −2.65534e8 −0.108008
\(483\) −1.15714e9 2.19080e9i −0.467273 0.884684i
\(484\) 8.10558e8 0.324957
\(485\) 1.96241e9 + 1.26116e9i 0.781075 + 0.501967i
\(486\) −5.20663e6 3.62129e7i −0.00205745 0.0143099i
\(487\) 2.42314e8 + 5.30594e8i 0.0950665 + 0.208167i 0.951191 0.308603i \(-0.0998616\pi\)
−0.856124 + 0.516770i \(0.827134\pi\)
\(488\) −9.76268e8 2.86658e8i −0.380277 0.111659i
\(489\) 1.10830e8 2.42683e8i 0.0428623 0.0938552i
\(490\) −1.33334e9 + 1.53875e9i −0.511981 + 0.590858i
\(491\) −2.68526e8 + 1.86764e9i −0.102377 + 0.712046i 0.872388 + 0.488813i \(0.162570\pi\)
−0.974765 + 0.223233i \(0.928339\pi\)
\(492\) 3.65288e8 1.07258e8i 0.138279 0.0406025i
\(493\) 3.77912e9 + 4.36134e9i 1.42045 + 1.63929i
\(494\) −5.76499e8 + 3.70494e8i −0.215157 + 0.138273i
\(495\) 1.06282e9 6.83031e8i 0.393858 0.253117i
\(496\) −1.17306e9 1.35378e9i −0.431652 0.498153i
\(497\) 4.04172e9 1.18676e9i 1.47679 0.433625i
\(498\) −2.19931e7 + 1.52965e8i −0.00797964 + 0.0554996i
\(499\) 1.54275e8 1.78043e8i 0.0555833 0.0641465i −0.727277 0.686344i \(-0.759214\pi\)
0.782860 + 0.622197i \(0.213760\pi\)
\(500\) −1.90819e9 + 4.17834e9i −0.682693 + 1.49489i
\(501\) 5.56746e7 + 1.63476e7i 0.0197800 + 0.00580792i
\(502\) −9.58057e7 2.09785e8i −0.0338009 0.0740137i
\(503\) −6.50797e8 4.52639e9i −0.228012 1.58586i −0.706467 0.707746i \(-0.749712\pi\)
0.478455 0.878112i \(-0.341197\pi\)
\(504\) 6.13527e8 + 3.94290e8i 0.213465 + 0.137186i
\(505\) 4.01998e9 1.38901
\(506\) 4.63877e8 + 2.61707e8i 0.159175 + 0.0898026i
\(507\) −9.12828e8 −0.311072
\(508\) 4.28664e9 + 2.75485e9i 1.45075 + 0.932343i
\(509\) 1.40856e8 + 9.79672e8i 0.0473436 + 0.329282i 0.999704 + 0.0243088i \(0.00773850\pi\)
−0.952361 + 0.304973i \(0.901352\pi\)
\(510\) −4.83178e8 1.05801e9i −0.161291 0.353179i
\(511\) −7.94187e9 2.33194e9i −2.63299 0.773117i
\(512\) 1.14791e9 2.51357e9i 0.377974 0.827648i
\(513\) 6.43984e8 7.43197e8i 0.210603 0.243049i
\(514\) 9.85651e7 6.85535e8i 0.0320149 0.222669i
\(515\) 4.13965e9 1.21551e9i 1.33548 0.392133i
\(516\) −7.13985e8 8.23982e8i −0.228778 0.264024i
\(517\) 2.04127e9 1.31185e9i 0.649657 0.417509i
\(518\) 5.16633e8 3.32020e8i 0.163316 0.104957i
\(519\) 9.30386e8 + 1.07372e9i 0.292131 + 0.337137i
\(520\) 1.58956e9 4.66738e8i 0.495754 0.145566i
\(521\) −4.93612e8 + 3.43315e9i −0.152916 + 1.06356i 0.758382 + 0.651810i \(0.225990\pi\)
−0.911298 + 0.411747i \(0.864919\pi\)
\(522\) −2.01262e8 + 2.32269e8i −0.0619320 + 0.0714734i
\(523\) −1.23754e9 + 2.70984e9i −0.378272 + 0.828299i 0.620747 + 0.784011i \(0.286829\pi\)
−0.999019 + 0.0442884i \(0.985898\pi\)
\(524\) −1.01657e9 2.98491e8i −0.308657 0.0906298i
\(525\) −2.75557e9 6.03386e9i −0.831102 1.81986i
\(526\) −5.55203e7 3.86152e8i −0.0166342 0.115693i
\(527\) −3.77566e9 2.42647e9i −1.12371 0.722167i
\(528\) 1.34644e9 0.398077
\(529\) 1.76068e9 + 2.91425e9i 0.517114 + 0.855916i
\(530\) 9.22383e8 0.269120
\(531\) 6.03196e8 + 3.87651e8i 0.174835 + 0.112359i
\(532\) 1.35857e9 + 9.44904e9i 0.391192 + 2.72080i
\(533\) 2.59352e8 + 5.67901e8i 0.0741897 + 0.162453i
\(534\) 4.95656e7 + 1.45538e7i 0.0140859 + 0.00413601i
\(535\) −2.91805e9 + 6.38963e9i −0.823862 + 1.80401i
\(536\) 6.07514e7 7.01108e7i 0.0170404 0.0196656i
\(537\) −3.43778e8 + 2.39103e9i −0.0958004 + 0.666307i
\(538\) −9.54296e8 + 2.80207e8i −0.264208 + 0.0775784i
\(539\) −3.86720e9 4.46299e9i −1.06374 1.22762i
\(540\) −9.73915e8 + 6.25897e8i −0.266160 + 0.171051i
\(541\) −3.49209e9 + 2.24423e9i −0.948190 + 0.609365i −0.920706 0.390258i \(-0.872386\pi\)
−0.0274842 + 0.999622i \(0.508750\pi\)
\(542\) 8.27095e8 + 9.54518e8i 0.223130 + 0.257506i
\(543\) −4.26838e8 + 1.25331e8i −0.114410 + 0.0335938i
\(544\) 5.80858e8 4.03996e9i 0.154694 1.07592i
\(545\) −1.32040e9 + 1.52382e9i −0.349396 + 0.403225i
\(546\) −2.41939e8 + 5.29773e8i −0.0636110 + 0.139289i
\(547\) 1.98706e9 + 5.83454e8i 0.519106 + 0.152423i 0.530782 0.847509i \(-0.321898\pi\)
−0.0116758 + 0.999932i \(0.503717\pi\)
\(548\) 5.23754e8 + 1.14686e9i 0.135955 + 0.297700i
\(549\) 1.65939e8 + 1.15413e9i 0.0428002 + 0.297682i
\(550\) 1.19958e9 + 7.70926e8i 0.307441 + 0.197580i
\(551\) −8.26101e9 −2.10379
\(552\) −8.72894e8 4.92464e8i −0.220889 0.124620i
\(553\) 3.27453e9 0.823400
\(554\) −8.99248e8 5.77912e8i −0.224696 0.144403i
\(555\) 2.84897e8 + 1.98151e9i 0.0707397 + 0.492005i
\(556\) −1.39652e9 3.05796e9i −0.344577 0.754518i
\(557\) −6.69535e9 1.96593e9i −1.64165 0.482031i −0.674931 0.737880i \(-0.735827\pi\)
−0.966717 + 0.255849i \(0.917645\pi\)
\(558\) 9.92931e7 2.17422e8i 0.0241935 0.0529765i
\(559\) 1.17085e9 1.35123e9i 0.283505 0.327182i
\(560\) 1.50922e9 1.04968e10i 0.363156 2.52581i
\(561\) 3.23686e9 9.50426e8i 0.774022 0.227273i
\(562\) −7.84444e7 9.05297e7i −0.0186417 0.0215136i
\(563\) −1.95893e9 + 1.25893e9i −0.462636 + 0.297318i −0.751119 0.660167i \(-0.770486\pi\)
0.288483 + 0.957485i \(0.406849\pi\)
\(564\) −1.87053e9 + 1.20211e9i −0.439022 + 0.282143i
\(565\) −8.62679e8 9.95584e8i −0.201224 0.232225i
\(566\) 5.58887e8 1.64104e8i 0.129559 0.0380419i
\(567\) 1.18940e8 8.27246e8i 0.0274023 0.190587i
\(568\) 1.11585e9 1.28776e9i 0.255498 0.294861i
\(569\) −8.54392e8 + 1.87086e9i −0.194430 + 0.425743i −0.981588 0.191008i \(-0.938824\pi\)
0.787158 + 0.616751i \(0.211552\pi\)
\(570\) 1.59756e9 + 4.69086e8i 0.361323 + 0.106094i
\(571\) 7.86196e8 + 1.72153e9i 0.176728 + 0.386980i 0.977179 0.212418i \(-0.0681340\pi\)
−0.800451 + 0.599398i \(0.795407\pi\)
\(572\) 3.33002e8 + 2.31608e9i 0.0743979 + 0.517449i
\(573\) 2.67439e9 + 1.71873e9i 0.593860 + 0.381651i
\(574\) −4.65337e8 −0.102701
\(575\) 4.25738e9 + 8.06045e9i 0.933909 + 1.76816i
\(576\) −1.08246e9 −0.236012
\(577\) −8.19890e8 5.26911e8i −0.177681 0.114188i 0.448777 0.893644i \(-0.351860\pi\)
−0.626458 + 0.779455i \(0.715496\pi\)
\(578\) −2.93108e8 2.03861e9i −0.0631364 0.439124i
\(579\) −1.24359e9 2.72309e9i −0.266259 0.583025i
\(580\) 9.33132e9 + 2.73992e9i 1.98584 + 0.583096i
\(581\) −1.46653e9 + 3.21125e9i −0.310223 + 0.679293i
\(582\) −2.17236e8 + 2.50704e8i −0.0456774 + 0.0527146i
\(583\) −3.80731e8 + 2.64804e9i −0.0795753 + 0.553458i
\(584\) −3.21260e9 + 9.43304e8i −0.667439 + 0.195978i
\(585\) −1.24324e9 1.43478e9i −0.256750 0.296305i
\(586\) 1.03136e8 6.62813e7i 0.0211723 0.0136066i
\(587\) −5.59821e9 + 3.59775e9i −1.14239 + 0.734172i −0.968110 0.250524i \(-0.919397\pi\)
−0.174283 + 0.984696i \(0.555761\pi\)
\(588\) 3.54372e9 + 4.08967e9i 0.718851 + 0.829598i
\(589\) 6.16451e9 1.81006e9i 1.24307 0.364998i
\(590\) −1.72771e8 + 1.20165e9i −0.0346329 + 0.240877i
\(591\) 2.28027e9 2.63158e9i 0.454392 0.524397i
\(592\) −8.86289e8 + 1.94070e9i −0.175570 + 0.384444i
\(593\) 5.82799e9 + 1.71125e9i 1.14770 + 0.336995i 0.799641 0.600479i \(-0.205023\pi\)
0.348057 + 0.937473i \(0.386841\pi\)
\(594\) 7.46337e7 + 1.63425e8i 0.0146111 + 0.0319938i
\(595\) −3.78135e9 2.62999e10i −0.735932 5.11852i
\(596\) 2.08394e8 + 1.33927e8i 0.0403202 + 0.0259122i
\(597\) −5.03677e9 −0.968817
\(598\) 2.90064e8 7.45947e8i 0.0554676 0.142644i
\(599\) −5.72266e9 −1.08794 −0.543969 0.839105i \(-0.683079\pi\)
−0.543969 + 0.839105i \(0.683079\pi\)
\(600\) −2.25730e9 1.45068e9i −0.426639 0.274184i
\(601\) 8.42773e8 + 5.86162e9i 0.158362 + 1.10143i 0.901653 + 0.432461i \(0.142355\pi\)
−0.743291 + 0.668968i \(0.766736\pi\)
\(602\) 5.53600e8 + 1.21221e9i 0.103421 + 0.226460i
\(603\) −1.02005e8 2.99513e7i −0.0189457 0.00556295i
\(604\) −3.54204e9 + 7.75599e9i −0.654070 + 1.43221i
\(605\) 2.11490e9 2.44073e9i 0.388281 0.448100i
\(606\) −8.13571e7 + 5.65851e8i −0.0148505 + 0.103288i
\(607\) 1.14132e9 3.35123e8i 0.207133 0.0608196i −0.176520 0.984297i \(-0.556484\pi\)
0.383653 + 0.923477i \(0.374666\pi\)
\(608\) 3.82613e9 + 4.41559e9i 0.690395 + 0.796758i
\(609\) −5.90625e9 + 3.79572e9i −1.05962 + 0.680978i
\(610\) −1.66079e9 + 1.06733e9i −0.296252 + 0.190389i
\(611\) −2.38780e9 2.75567e9i −0.423501 0.488746i
\(612\) −2.96610e9 + 8.70926e8i −0.523066 + 0.153586i
\(613\) −8.53260e8 + 5.93455e9i −0.149613 + 1.04058i 0.767241 + 0.641359i \(0.221629\pi\)
−0.916854 + 0.399223i \(0.869280\pi\)
\(614\) −1.12032e9 + 1.29292e9i −0.195323 + 0.225415i
\(615\) 6.30134e8 1.37980e9i 0.109237 0.239196i
\(616\) −3.43633e9 1.00900e9i −0.592328 0.173923i
\(617\) −3.17546e9 6.95329e9i −0.544263 1.19177i −0.959410 0.282015i \(-0.908997\pi\)
0.415147 0.909754i \(-0.363730\pi\)
\(618\) 8.73159e7 + 6.07296e8i 0.0148811 + 0.103500i
\(619\) −2.85949e7 1.83769e7i −0.00484587 0.00311425i 0.538216 0.842807i \(-0.319099\pi\)
−0.543062 + 0.839693i \(0.682735\pi\)
\(620\) −7.56354e9 −1.27454
\(621\) −9.78056e7 + 1.14435e9i −0.0163886 + 0.191751i
\(622\) −6.29463e8 −0.104883
\(623\) 9.92744e8 + 6.37998e8i 0.164486 + 0.105709i
\(624\) −2.87947e8 2.00271e9i −0.0474423 0.329969i
\(625\) 2.53279e9 + 5.54603e9i 0.414972 + 0.908662i
\(626\) 2.50525e9 + 7.35607e8i 0.408169 + 0.119849i
\(627\) −2.00611e9 + 4.39277e9i −0.325026 + 0.711708i
\(628\) −2.85087e9 + 3.29008e9i −0.459324 + 0.530088i
\(629\) −7.60744e8 + 5.29109e9i −0.121888 + 0.847751i
\(630\) 1.35772e9 3.98662e8i 0.216330 0.0635204i
\(631\) 1.97630e8 + 2.28077e8i 0.0313148 + 0.0361392i 0.771191 0.636604i \(-0.219661\pi\)
−0.739876 + 0.672743i \(0.765116\pi\)
\(632\) 1.11432e9 7.16129e8i 0.175590 0.112845i
\(633\) 2.94722e9 1.89406e9i 0.461848 0.296812i
\(634\) 1.48750e9 + 1.71666e9i 0.231816 + 0.267530i
\(635\) 1.94800e10 5.71984e9i 3.01912 0.886494i
\(636\) 3.48884e8 2.42654e9i 0.0537751 0.374014i
\(637\) −5.81129e9 + 6.70659e9i −0.890809 + 1.02805i
\(638\) 6.26963e8 1.37286e9i 0.0955805 0.209292i
\(639\) −1.87358e9 5.50131e8i −0.284065 0.0834091i
\(640\) −3.77157e9 8.25859e9i −0.568712 1.24531i
\(641\) −2.48136e8 1.72582e9i −0.0372123 0.258817i 0.962719 0.270502i \(-0.0871896\pi\)
−0.999932 + 0.0116847i \(0.996281\pi\)
\(642\) −8.40347e8 5.40058e8i −0.125339 0.0805504i
\(643\) 3.76972e9 0.559205 0.279603 0.960116i \(-0.409797\pi\)
0.279603 + 0.960116i \(0.409797\pi\)
\(644\) −7.77364e9 7.99219e9i −1.14690 1.17914i
\(645\) −4.34407e9 −0.637438
\(646\) 3.74018e9 + 2.40367e9i 0.545857 + 0.350801i
\(647\) 1.22235e9 + 8.50160e9i 0.177431 + 1.23406i 0.862680 + 0.505750i \(0.168784\pi\)
−0.685250 + 0.728308i \(0.740307\pi\)
\(648\) −1.40441e8 3.07523e8i −0.0202759 0.0443981i
\(649\) −3.37847e9 9.92007e8i −0.485136 0.142449i
\(650\) 8.90148e8 1.94915e9i 0.127135 0.278387i
\(651\) 3.57567e9 4.12655e9i 0.507954 0.586210i
\(652\) 1.70857e8 1.18834e9i 0.0241416 0.167909i
\(653\) −5.61050e9 + 1.64739e9i −0.788507 + 0.231527i −0.651104 0.758989i \(-0.725694\pi\)
−0.137403 + 0.990515i \(0.543876\pi\)
\(654\) −1.87770e8 2.16699e8i −0.0262485 0.0302924i
\(655\) −3.55122e9 + 2.28223e9i −0.493779 + 0.317333i
\(656\) 1.35998e9 8.74005e8i 0.188091 0.120879i
\(657\) 2.51267e9 + 2.89977e9i 0.345665 + 0.398919i
\(658\) 2.60767e9 7.65680e8i 0.356830 0.104775i
\(659\) −3.97480e7 + 2.76453e8i −0.00541023 + 0.0376290i −0.992348 0.123475i \(-0.960596\pi\)
0.986937 + 0.161104i \(0.0515053\pi\)
\(660\) 3.72297e9 4.29654e9i 0.504064 0.581721i
\(661\) 2.11929e9 4.64059e9i 0.285420 0.624983i −0.711561 0.702624i \(-0.752012\pi\)
0.996981 + 0.0776414i \(0.0247389\pi\)
\(662\) 1.07178e9 + 3.14704e8i 0.143583 + 0.0421599i
\(663\) −2.10591e9 4.61130e9i −0.280635 0.614505i
\(664\) 2.03232e8 + 1.41351e9i 0.0269403 + 0.187374i
\(665\) 3.19974e10 + 2.05635e10i 4.21928 + 2.71157i
\(666\) −2.84682e8 −0.0373422
\(667\) 7.80317e9 5.67433e9i 1.01819 0.740413i
\(668\) 2.61111e8 0.0338928
\(669\) 5.45795e9 + 3.50761e9i 0.704755 + 0.452918i
\(670\) −2.56164e7 1.78166e8i −0.00329046 0.0228856i
\(671\) −2.37863e9 5.20847e9i −0.303947 0.665552i
\(672\) 4.76436e9 + 1.39894e9i 0.605637 + 0.177831i
\(673\) 3.63040e9 7.94947e9i 0.459094 1.00528i −0.528599 0.848872i \(-0.677282\pi\)
0.987693 0.156404i \(-0.0499903\pi\)
\(674\) 1.50102e9 1.73227e9i 0.188833 0.217924i
\(675\) −4.37607e8 + 3.04362e9i −0.0547673 + 0.380915i
\(676\) −3.94130e9 + 1.15727e9i −0.490712 + 0.144086i
\(677\) −3.98512e9 4.59907e9i −0.493607 0.569653i 0.453219 0.891399i \(-0.350276\pi\)
−0.946826 + 0.321747i \(0.895730\pi\)
\(678\) 1.57597e8 1.01282e8i 0.0194198 0.0124803i
\(679\) −6.37503e9 + 4.09698e9i −0.781516 + 0.502250i
\(680\) −7.03848e9 8.12284e9i −0.858416 0.990665i
\(681\) −1.30765e9 + 3.83960e8i −0.158663 + 0.0465877i
\(682\) −1.67045e8 + 1.16182e9i −0.0201645 + 0.140247i
\(683\) 8.47426e9 9.77982e9i 1.01772 1.17451i 0.0331654 0.999450i \(-0.489441\pi\)
0.984557 0.175064i \(-0.0560133\pi\)
\(684\) 1.83830e9 4.02533e9i 0.219645 0.480955i
\(685\) 4.81997e9 + 1.41527e9i 0.572964 + 0.168237i
\(686\) −1.37592e9 3.01284e9i −0.162727 0.356322i
\(687\) −3.76928e8 2.62159e9i −0.0443517 0.308473i
\(688\) −3.89474e9 2.50300e9i −0.455952 0.293022i
\(689\) 4.02017e9 0.468249
\(690\) −1.83123e9 + 6.54246e8i −0.212212 + 0.0758174i
\(691\) −1.67372e9 −0.192979 −0.0964896 0.995334i \(-0.530761\pi\)
−0.0964896 + 0.995334i \(0.530761\pi\)
\(692\) 5.37837e9 + 3.45647e9i 0.616991 + 0.396516i
\(693\) 5.84083e8 + 4.06239e9i 0.0666666 + 0.463676i
\(694\) −5.38211e8 1.17852e9i −0.0611216 0.133838i
\(695\) −1.28518e10 3.77363e9i −1.45217 0.426396i
\(696\) −1.17978e9 + 2.58335e9i −0.132638 + 0.290437i
\(697\) 2.65246e9 3.06111e9i 0.296712 0.342424i
\(698\) 3.46065e8 2.40694e9i 0.0385180 0.267899i
\(699\) 6.25615e9 1.83697e9i 0.692846 0.203438i
\(700\) −1.95473e10 2.25588e10i −2.15399 2.48584i
\(701\) −1.01067e10 + 6.49519e9i −1.10815 + 0.712162i −0.960888 0.276936i \(-0.910681\pi\)
−0.147258 + 0.989098i \(0.547045\pi\)
\(702\) 2.27120e8 1.45961e8i 0.0247785 0.0159242i
\(703\) −5.01105e9 5.78306e9i −0.543982 0.627789i
\(704\) 5.10036e9 1.49760e9i 0.550930 0.161768i
\(705\) −1.26079e9 + 8.76901e9i −0.135513 + 0.942516i
\(706\) 1.19611e9 1.38039e9i 0.127925 0.147634i
\(707\) −5.42500e9 + 1.18791e10i −0.577340 + 1.26420i
\(708\) 3.09587e9 + 9.09029e8i 0.327843 + 0.0962634i
\(709\) −2.61302e9 5.72171e9i −0.275347 0.602927i 0.720551 0.693402i \(-0.243889\pi\)
−0.995899 + 0.0904750i \(0.971161\pi\)
\(710\) −4.70511e8 3.27247e9i −0.0493361 0.343140i
\(711\) −1.27697e9 8.20658e8i −0.133241 0.0856286i
\(712\) 4.77357e8 0.0495637
\(713\) −4.57957e9 + 5.94403e9i −0.473163 + 0.614141i
\(714\) 3.77849e9 0.388485
\(715\) 7.84297e9 + 5.04037e9i 0.802434 + 0.515693i
\(716\) 1.54699e9 + 1.07595e10i 0.157504 + 1.09546i
\(717\) −1.99978e9 4.37891e9i −0.202612 0.443659i
\(718\) −1.24712e9 3.66187e8i −0.125739 0.0369204i
\(719\) 5.15158e9 1.12804e10i 0.516879 1.13181i −0.453728 0.891140i \(-0.649906\pi\)
0.970608 0.240668i \(-0.0773664\pi\)
\(720\) −3.21925e9 + 3.71521e9i −0.321433 + 0.370954i
\(721\) −1.99464e9 + 1.38731e10i −0.198195 + 1.37847i
\(722\) −3.91981e9 + 1.15096e9i −0.387601 + 0.113810i
\(723\) 1.84139e9 + 2.12508e9i 0.181202 + 0.209118i
\(724\) −1.68406e9 + 1.08228e9i −0.164920 + 0.105987i
\(725\) 2.17304e10 1.39653e10i 2.11780 1.36103i
\(726\) 3.00754e8 + 3.47088e8i 0.0291698 + 0.0336637i
\(727\) 7.35488e8 2.15959e8i 0.0709913 0.0208449i −0.246044 0.969259i \(-0.579131\pi\)
0.317035 + 0.948414i \(0.397313\pi\)
\(728\) −7.65913e8 + 5.32704e9i −0.0735732 + 0.511713i
\(729\) −2.53706e8 + 2.92793e8i −0.0242541 + 0.0279907i
\(730\) −2.69872e9 + 5.90937e9i −0.256760 + 0.562226i
\(731\) −1.11298e10 3.26801e9i −1.05385 0.309438i
\(732\) 2.17967e9 + 4.77280e9i 0.205400 + 0.449764i
\(733\) 3.41553e8 + 2.37555e9i 0.0320327 + 0.222792i 0.999549 0.0300145i \(-0.00955534\pi\)
−0.967517 + 0.252807i \(0.918646\pi\)
\(734\) 1.28676e9 + 8.26950e8i 0.120105 + 0.0771868i
\(735\) 2.15609e10 2.00291
\(736\) −6.64707e9 1.54278e9i −0.614551 0.142637i
\(737\) 5.22065e8 0.0480384
\(738\) 1.81467e8 + 1.16622e8i 0.0166189 + 0.0106803i
\(739\) −790423. 5.49752e6i −7.20451e−5 0.000501084i 0.989785 0.142565i \(-0.0455351\pi\)
−0.989857 + 0.142064i \(0.954626\pi\)
\(740\) 3.74222e9 + 8.19433e9i 0.339484 + 0.743365i
\(741\) 6.96290e9 + 2.04449e9i 0.628675 + 0.184596i
\(742\) −1.24476e9 + 2.72565e9i −0.111860 + 0.244938i
\(743\) 7.93958e9 9.16277e9i 0.710128 0.819532i −0.279955 0.960013i \(-0.590320\pi\)
0.990083 + 0.140481i \(0.0448650\pi\)
\(744\) 3.14335e8 2.18625e9i 0.0279825 0.194623i
\(745\) 9.47015e8 2.78069e8i 0.0839092 0.0246380i
\(746\) 6.39131e8 + 7.37596e8i 0.0563643 + 0.0650478i
\(747\) 1.37670e9 8.84751e8i 0.120842 0.0776603i
\(748\) 1.27708e10 8.20729e9i 1.11574 0.717041i
\(749\) −1.49435e10 1.72457e10i −1.29947 1.49967i
\(750\) −2.49723e9 + 7.33253e8i −0.216144 + 0.0634657i
\(751\) 3.20026e9 2.22583e10i 0.275706 1.91757i −0.108062 0.994144i \(-0.534464\pi\)
0.383767 0.923430i \(-0.374627\pi\)
\(752\) −6.18297e9 + 7.13553e9i −0.530194 + 0.611876i
\(753\) −1.01454e9 + 2.22153e9i −0.0865935 + 0.189613i
\(754\) −2.17609e9 6.38958e8i −0.184875 0.0542841i
\(755\) 1.41127e10 + 3.09025e10i 1.19343 + 2.61324i
\(756\) −5.35226e8 3.72258e9i −0.0450517 0.313341i
\(757\) −1.04872e10 6.73973e9i −0.878668 0.564686i 0.0217247 0.999764i \(-0.493084\pi\)
−0.900393 + 0.435078i \(0.856721\pi\)
\(758\) 3.61573e9 0.301546
\(759\) −1.12238e9 5.52727e9i −0.0931737 0.458844i
\(760\) 1.53858e10 1.27137
\(761\) −1.73939e10 1.11784e10i −1.43071 0.919462i −0.999855 0.0170409i \(-0.994575\pi\)
−0.430856 0.902421i \(-0.641788\pi\)
\(762\) 4.10883e8 + 2.85775e9i 0.0336415 + 0.233982i
\(763\) −2.72102e9 5.95821e9i −0.221767 0.485601i
\(764\) 1.37262e10 + 4.03037e9i 1.11358 + 0.326978i
\(765\) −5.11662e9 + 1.12038e10i −0.413208 + 0.904799i
\(766\) −9.44366e8 + 1.08986e9i −0.0759171 + 0.0876130i
\(767\) −7.53016e8 + 5.23734e9i −0.0602588 + 0.419109i
\(768\) −3.68500e9 + 1.08201e9i −0.293544 + 0.0861922i
\(769\) −3.66940e9 4.23471e9i −0.290973 0.335801i 0.591376 0.806396i \(-0.298585\pi\)
−0.882349 + 0.470595i \(0.844039\pi\)
\(770\) −5.84576e9 + 3.75684e9i −0.461449 + 0.296555i
\(771\) −6.16987e9 + 3.96514e9i −0.484826 + 0.311579i
\(772\) −8.82175e9 1.01808e10i −0.690072 0.796385i
\(773\) 2.04481e10 6.00411e9i 1.59230 0.467542i 0.638911 0.769281i \(-0.279385\pi\)
0.953391 + 0.301739i \(0.0975672\pi\)
\(774\) 8.79161e7 6.11470e8i 0.00681514 0.0474003i
\(775\) −1.31557e10 + 1.51825e10i −1.01521 + 1.17162i
\(776\) −1.27342e9 + 2.78839e9i −0.0978261 + 0.214209i
\(777\) −6.23984e9 1.83218e9i −0.477199 0.140118i
\(778\) −1.13148e9 2.47760e9i −0.0861427 0.188626i
\(779\) 8.25167e8 + 5.73916e9i 0.0625404 + 0.434978i
\(780\) −7.18693e9 4.61876e9i −0.542266 0.348493i
\(781\) 9.58906e9 0.720273
\(782\) −5.18393e9 + 2.98605e8i −0.387646 + 0.0223292i
\(783\) 3.25454e9 0.242283
\(784\) 1.93308e10 + 1.24231e10i 1.43266 + 0.920714i
\(785\) 2.46852e9 + 1.71689e10i 0.182135 + 1.26677i
\(786\) −2.49376e8 5.46056e8i −0.0183179 0.0401105i
\(787\) 2.14738e10 + 6.30528e9i 1.57035 + 0.461098i 0.947105 0.320925i \(-0.103994\pi\)
0.623250 + 0.782023i \(0.285812\pi\)
\(788\) 6.50923e9 1.42532e10i 0.473901 1.03770i
\(789\) −2.70537e9 + 3.12217e9i −0.196091 + 0.226301i
\(790\) 3.65758e8 2.54390e9i 0.0263936 0.183571i
\(791\) 4.10615e9 1.20568e9i 0.294997 0.0866189i
\(792\) 1.08719e9 + 1.25469e9i 0.0777622 + 0.0897424i
\(793\) −7.23848e9 + 4.65189e9i −0.515456 + 0.331263i
\(794\) 1.13257e9 7.27856e8i 0.0802956 0.0516028i
\(795\) −6.39642e9 7.38186e9i −0.451494 0.521052i
\(796\) −2.17472e10 + 6.38555e9i −1.52829 + 0.448748i
\(797\) 6.23712e8 4.33801e9i 0.0436395 0.303520i −0.956299 0.292392i \(-0.905549\pi\)
0.999938 0.0111277i \(-0.00354212\pi\)
\(798\) −3.54208e9 + 4.08777e9i −0.246745 + 0.284758i
\(799\) −9.82711e9 + 2.15184e10i −0.681573 + 1.49244i
\(800\) −1.75292e10 5.14702e9i −1.21045 0.355419i
\(801\) −2.27246e8 4.97600e8i −0.0156237 0.0342111i
\(802\) −4.98505e8 3.46718e9i −0.0341239 0.237337i
\(803\) −1.58511e10 1.01869e10i −1.08033 0.694283i
\(804\) −4.78396e8 −0.0324632
\(805\) −4.43487e10 + 2.55458e9i −2.99637 + 0.172597i
\(806\) 1.76384e9 0.118655
\(807\) 8.86023e9 + 5.69412e9i 0.593455 + 0.381390i
\(808\) 7.51797e8 + 5.22887e9i 0.0501373 + 0.348713i
\(809\) −2.06917e9 4.53085e9i −0.137397 0.300857i 0.828409 0.560124i \(-0.189246\pi\)
−0.965806 + 0.259267i \(0.916519\pi\)
\(810\) −6.29382e8 1.84803e8i −0.0416118 0.0122183i
\(811\) −7.38669e9 + 1.61746e10i −0.486269 + 1.06478i 0.494422 + 0.869222i \(0.335380\pi\)
−0.980692 + 0.195560i \(0.937348\pi\)
\(812\) −2.06892e10 + 2.38766e10i −1.35612 + 1.56504i
\(813\) 1.90341e9 1.32385e10i 0.124227 0.864018i
\(814\) 1.34137e9 3.93861e8i 0.0871691 0.0255951i
\(815\) −3.13248e9 3.61508e9i −0.202692 0.233919i
\(816\) −1.10429e10 + 7.09683e9i −0.711487 + 0.457245i
\(817\) 1.39690e10 8.97732e9i 0.896164 0.575930i
\(818\) −6.81691e8 7.86714e8i −0.0435463 0.0502551i
\(819\) 5.91755e9 1.73755e9i 0.376399 0.110521i
\(820\) 9.71426e8 6.75642e9i 0.0615264 0.427925i
\(821\) 8.83619e9 1.01975e10i 0.557268 0.643122i −0.405293 0.914187i \(-0.632830\pi\)
0.962561 + 0.271065i \(0.0873759\pi\)
\(822\) −2.96760e8 + 6.49814e8i −0.0186361 + 0.0408073i
\(823\) 2.02063e10 + 5.93310e9i 1.26353 + 0.371007i 0.843809 0.536644i \(-0.180308\pi\)
0.419726 + 0.907651i \(0.362126\pi\)
\(824\) 2.35522e9 + 5.15720e9i 0.146651 + 0.321121i
\(825\) −2.14897e9 1.49464e10i −0.133242 0.926720i
\(826\) −3.31773e9 2.13218e9i −0.204838 0.131642i
\(827\) −2.18599e10 −1.34393 −0.671967 0.740581i \(-0.734550\pi\)
−0.671967 + 0.740581i \(0.734550\pi\)
\(828\) 1.02850e9 + 5.06493e9i 0.0629646 + 0.310076i
\(829\) −2.82338e10 −1.72119 −0.860596 0.509289i \(-0.829909\pi\)
−0.860596 + 0.509289i \(0.829909\pi\)
\(830\) 2.33093e9 + 1.49800e9i 0.141500 + 0.0909364i
\(831\) 1.61094e9 + 1.12043e10i 0.0973813 + 0.677302i
\(832\) −3.31831e9 7.26609e9i −0.199749 0.437390i
\(833\) 5.52407e10 + 1.62201e10i 3.31133 + 0.972293i
\(834\) 7.91273e8 1.73265e9i 0.0472329 0.103426i
\(835\) 6.81288e8 7.86248e8i 0.0404975 0.0467366i
\(836\) −3.09266e9 + 2.15099e10i −0.183067 + 1.27326i
\(837\) −2.42860e9 + 7.13100e8i −0.143158 + 0.0420350i
\(838\) 3.45501e9 + 3.98729e9i 0.202813 + 0.234058i
\(839\) 6.80127e9 4.37091e9i 0.397579 0.255508i −0.326540 0.945183i \(-0.605883\pi\)
0.724119 + 0.689675i \(0.242247\pi\)
\(840\) 1.10002e10 7.06939e9i 0.640357 0.411533i
\(841\) −6.60754e9 7.62551e9i −0.383049 0.442062i
\(842\) 1.96973e9 5.78366e8i 0.113714 0.0333895i
\(843\) −1.80526e8 + 1.25559e9i −0.0103787 + 0.0721855i
\(844\) 1.03239e10 1.19144e10i 0.591078 0.682141i
\(845\) −6.79888e9 + 1.48875e10i −0.387649 + 0.848833i
\(846\) −1.20881e9 3.54937e8i −0.0686373 0.0201537i
\(847\) 4.35829e9 + 9.54333e9i 0.246447 + 0.539645i
\(848\) −1.48147e9 1.03038e10i −0.0834271 0.580248i
\(849\) −5.18903e9 3.33478e9i −0.291011 0.187021i
\(850\) −1.39019e10 −0.776440
\(851\) 8.70560e9 + 2.02056e9i 0.484223 + 0.112388i
\(852\) −8.78696e9 −0.486743
\(853\) 1.69454e10 + 1.08902e10i 0.934825 + 0.600776i 0.916923 0.399064i \(-0.130665\pi\)
0.0179022 + 0.999840i \(0.494301\pi\)
\(854\) −9.12707e8 6.34802e9i −0.0501451 0.348767i
\(855\) −7.32444e9 1.60383e10i −0.400768 0.877559i
\(856\) −8.85683e9 2.60060e9i −0.482637 0.141715i
\(857\) −8.76015e9 + 1.91821e10i −0.475422 + 1.04103i 0.508275 + 0.861195i \(0.330283\pi\)
−0.983697 + 0.179834i \(0.942444\pi\)
\(858\) −8.68208e8 + 1.00197e9i −0.0469265 + 0.0541561i
\(859\) 2.76332e9 1.92193e10i 0.148749 1.03457i −0.769521 0.638621i \(-0.779505\pi\)
0.918271 0.395954i \(-0.129586\pi\)
\(860\) −1.87563e10 + 5.50735e9i −1.00555 + 0.295256i
\(861\) 3.22695e9 + 3.72410e9i 0.172298 + 0.198843i
\(862\) 4.54920e9 2.92359e9i 0.241913 0.155468i
\(863\) 1.57930e10 1.01496e10i 0.836426 0.537538i −0.0508881 0.998704i \(-0.516205\pi\)
0.887314 + 0.461166i \(0.152569\pi\)
\(864\) −1.50736e9 1.73958e9i −0.0795094 0.0917587i
\(865\) 2.44412e10 7.17658e9i 1.28400 0.377017i
\(866\) 7.00698e8 4.87346e9i 0.0366622 0.254991i
\(867\) −1.42825e10 + 1.64828e10i −0.744279 + 0.858944i
\(868\) 1.02071e10 2.23503e10i 0.529763 1.16002i
\(869\) 7.15223e9 + 2.10008e9i 0.369719 + 0.108559i
\(870\) 2.28908e9 + 5.01239e9i 0.117854 + 0.258064i
\(871\) −1.11648e8 7.76529e8i −0.00572516 0.0398193i
\(872\) −2.22900e9 1.43249e9i −0.113842 0.0731618i
\(873\) 3.51285e9 0.178694
\(874\) 4.53654e9 5.88818e9i 0.229845 0.298326i
\(875\) −5.94550e10 −3.00027
\(876\) 1.45252e10 + 9.33477e9i 0.730058 + 0.469180i
\(877\) 4.12463e8 + 2.86874e9i 0.0206484 + 0.143613i 0.997538 0.0701335i \(-0.0223425\pi\)
−0.976889 + 0.213746i \(0.931433\pi\)
\(878\) 3.13135e9 + 6.85671e9i 0.156135 + 0.341889i
\(879\) −1.24566e9 3.65760e8i −0.0618642 0.0181650i
\(880\) 1.00285e10 2.19593e10i 0.496072 1.08625i
\(881\) 8.68532e9 1.00234e10i 0.427927 0.493854i −0.500308 0.865847i \(-0.666780\pi\)
0.928236 + 0.371993i \(0.121325\pi\)
\(882\) −4.36354e8 + 3.03491e9i −0.0214141 + 0.148938i
\(883\) −6.76166e9 + 1.98540e9i −0.330515 + 0.0970479i −0.442780 0.896630i \(-0.646008\pi\)
0.112265 + 0.993678i \(0.464189\pi\)
\(884\) −1.49388e10 1.72403e10i −0.727332 0.839386i
\(885\) 1.08150e10 6.95035e9i 0.524473 0.337058i
\(886\) −1.76002e9 + 1.13110e9i −0.0850159 + 0.0546364i
\(887\) −4.19069e9 4.83632e9i −0.201629 0.232692i 0.645926 0.763400i \(-0.276472\pi\)
−0.847555 + 0.530708i \(0.821926\pi\)
\(888\) −2.52410e9 + 7.41143e8i −0.120965 + 0.0355187i
\(889\) −9.38620e9 + 6.52825e10i −0.448057 + 3.11631i
\(890\) 6.06532e8 6.99975e8i 0.0288396 0.0332826i
\(891\) 7.90335e8 1.73059e9i 0.0374317 0.0819639i
\(892\) 2.80126e10 + 8.22525e9i 1.32153 + 0.388036i
\(893\) −1.40675e10 3.08035e10i −0.661054 1.44751i
\(894\) 1.99750e7 + 1.38929e8i 0.000934986 + 0.00650297i
\(895\) 3.64351e10 + 2.34154e10i 1.69879 + 1.09175i
\(896\) 2.94940e10 1.36979
\(897\) −7.98133e9 + 2.85150e9i −0.369234 + 0.131917i
\(898\) −8.04350e8 −0.0370662
\(899\) 1.78874e10 + 1.14955e10i 0.821085 + 0.527679i
\(900\) 1.96922e9 + 1.36962e10i 0.0900419 + 0.626255i
\(901\) −1.08348e10 2.37249e10i −0.493496 1.08060i
\(902\) −1.01639e9 2.98439e8i −0.0461144 0.0135404i
\(903\) 5.86235e9 1.28368e10i 0.264951 0.580161i
\(904\) 1.13364e9 1.30829e9i 0.0510371 0.0589000i
\(905\) −1.13511e9 + 7.89485e9i −0.0509058 + 0.354058i
\(906\) −4.63545e9 + 1.36109e9i −0.207082 + 0.0608048i
\(907\) −8.16174e9 9.41915e9i −0.363210 0.419166i 0.544503 0.838759i \(-0.316718\pi\)
−0.907712 + 0.419593i \(0.862173\pi\)
\(908\) −5.15923e9 + 3.31564e9i −0.228710 + 0.146983i
\(909\) 5.09271e9 3.27288e9i 0.224893 0.144530i
\(910\) 6.83816e9 + 7.89165e9i 0.300811 + 0.347155i
\(911\) 1.14071e9 3.34942e8i 0.0499873 0.0146776i −0.256643 0.966506i \(-0.582617\pi\)
0.306631 + 0.951829i \(0.400798\pi\)
\(912\) 2.67422e9 1.85996e10i 0.116739 0.811936i
\(913\) −5.26269e9 + 6.07347e9i −0.228855 + 0.264112i
\(914\) −1.34182e9 + 2.93818e9i −0.0581276 + 0.127282i
\(915\) 2.00589e10 + 5.88981e9i 0.865630 + 0.254172i
\(916\) −4.95108e9 1.08413e10i −0.212846 0.466068i
\(917\) −1.95161e9 1.35738e10i −0.0835798 0.581310i
\(918\) −1.47350e9 9.46959e8i −0.0628637 0.0404000i
\(919\) 2.91017e10 1.23684 0.618421 0.785847i \(-0.287773\pi\)
0.618421 + 0.785847i \(0.287773\pi\)
\(920\) −1.45331e10 + 1.05682e10i −0.615321 + 0.447451i
\(921\) 1.81163e10 0.764120
\(922\) −4.14034e9 2.66083e9i −0.173971 0.111805i
\(923\) −2.05070e9 1.42629e10i −0.0858412 0.597039i
\(924\) 7.67213e9 + 1.67996e10i 0.319937 + 0.700564i
\(925\) 2.29578e10 + 6.74100e9i 0.953747 + 0.280045i
\(926\) 2.93281e9 6.42196e9i 0.121380 0.265784i
\(927\) 4.25470e9 4.91018e9i 0.175424 0.202450i
\(928\) −2.75185e9 + 1.91395e10i −0.113033 + 0.786165i
\(929\) −4.53443e8 + 1.33143e8i −0.0185553 + 0.00544833i −0.290997 0.956724i \(-0.593987\pi\)
0.272442 + 0.962172i \(0.412169\pi\)
\(930\) −2.80642e9 3.23878e9i −0.114409 0.132035i
\(931\) −6.93323e10 + 4.45571e10i −2.81586 + 1.80965i
\(932\) 2.46832e10 1.58629e10i 0.998724 0.641841i
\(933\) 4.36511e9 + 5.03761e9i 0.175958 + 0.203067i
\(934\) 5.05193e9 1.48338e9i 0.202882 0.0595715i
\(935\) 8.60791e9 5.98693e10i 0.344395 2.39532i
\(936\) 1.63374e9 1.88544e9i 0.0651204 0.0751530i
\(937\) 1.04739e10 2.29346e10i 0.415930 0.910759i −0.579474 0.814991i \(-0.696742\pi\)
0.995404 0.0957681i \(-0.0305307\pi\)
\(938\) 5.61052e8 + 1.64740e8i 0.0221969 + 0.00651761i
\(939\) −1.14860e10 2.51507e10i −0.452728 0.991337i
\(940\) 5.67353e9 + 3.94602e10i 0.222795 + 1.54957i
\(941\) −3.09402e10 1.98840e10i −1.21048 0.777931i −0.229744 0.973251i \(-0.573789\pi\)
−0.980740 + 0.195320i \(0.937425\pi\)
\(942\) −2.46665e9 −0.0961455
\(943\) −4.72156e9 4.85430e9i −0.183356 0.188510i
\(944\) 1.37010e10 0.530091
\(945\) −1.26058e10 8.10127e9i −0.485914 0.312278i
\(946\) 4.31732e8 + 3.00276e9i 0.0165804 + 0.115319i
\(947\) 5.85300e9 + 1.28163e10i 0.223951 + 0.490385i 0.987939 0.154847i \(-0.0494883\pi\)
−0.763987 + 0.645231i \(0.776761\pi\)
\(948\) −6.55397e9 1.92442e9i −0.249848 0.0733619i
\(949\) −1.17622e10 + 2.57557e10i −0.446744 + 0.978232i
\(950\) 1.30321e10 1.50398e10i 0.493152 0.569128i
\(951\) 3.42321e9 2.38090e10i 0.129063 0.897653i
\(952\) 3.35016e10 9.83694e9i 1.25845 0.369514i
\(953\) −4.14569e7 4.78438e7i −0.00155157 0.00179061i 0.754973 0.655756i \(-0.227650\pi\)
−0.756525 + 0.653965i \(0.773104\pi\)
\(954\) 1.16852e9 7.50962e8i 0.0435729 0.0280026i
\(955\) 4.79503e10 3.08158e10i 1.78148 1.14488i
\(956\) −1.41860e10 1.63715e10i −0.525117 0.606017i
\(957\) −1.53348e10 + 4.50270e9i −0.565569 + 0.166066i
\(958\) 9.22451e8 6.41579e9i 0.0338972 0.235760i
\(959\) −1.06867e10 + 1.23331e10i −0.391272 + 0.451552i
\(960\) −8.06234e9 + 1.76541e10i −0.294111 + 0.644014i
\(961\) 1.05315e10 + 3.09232e9i 0.382788 + 0.112397i
\(962\) −8.72698e8 1.91094e9i −0.0316047 0.0692046i
\(963\) 1.50542e9 + 1.04704e10i 0.0543208 + 0.377809i
\(964\) 1.06447e10 + 6.84093e9i 0.382704 + 0.245949i
\(965\) −5.36738e10 −1.92272
\(966\) 5.37956e8 6.29421e9i 0.0192011 0.224658i
\(967\) −2.23997e10 −0.796618 −0.398309 0.917251i \(-0.630403\pi\)
−0.398309 + 0.917251i \(0.630403\pi\)
\(968\) 3.57021e9 + 2.29444e9i 0.126512 + 0.0813041i
\(969\) −6.70027e9 4.66014e10i −0.236570 1.64538i
\(970\) 2.47077e9 + 5.41022e9i 0.0869222 + 0.190333i
\(971\) −2.43697e10 7.15559e9i −0.854246 0.250829i −0.174845 0.984596i \(-0.555942\pi\)
−0.679402 + 0.733767i \(0.737761\pi\)
\(972\) −7.24226e8 + 1.58583e9i −0.0252954 + 0.0553893i
\(973\) 2.84947e10 3.28847e10i 0.991676 1.14446i
\(974\) −2.11658e8 + 1.47211e9i −0.00733969 + 0.0510487i
\(975\) −2.17720e10 + 6.39283e9i −0.752284 + 0.220891i
\(976\) 1.45904e10 + 1.68383e10i 0.502335 + 0.579726i
\(977\) 9.35129e9 6.00971e9i 0.320804 0.206168i −0.370320 0.928904i \(-0.620752\pi\)
0.691124 + 0.722736i \(0.257116\pi\)
\(978\) 5.72253e8 3.67765e8i 0.0195615 0.0125714i
\(979\) 1.75918e9 + 2.03020e9i 0.0599199 + 0.0691512i
\(980\) 9.30933e10 2.73347e10i 3.15957 0.927732i
\(981\) −4.32120e8 + 3.00546e9i −0.0146138 + 0.101641i
\(982\) −3.15045e9 + 3.63581e9i −0.106165 + 0.122521i
\(983\) −5.50758e8 + 1.20599e9i −0.0184937 + 0.0404955i −0.918653 0.395064i \(-0.870722\pi\)
0.900160 + 0.435560i \(0.143450\pi\)
\(984\) 1.91258e9 + 5.61583e8i 0.0639935 + 0.0187902i
\(985\) −2.59350e10 5.67898e10i −0.864689 1.89340i
\(986\) 2.09401e9 + 1.45642e10i 0.0695681 + 0.483857i
\(987\) −2.42110e10 1.55595e10i −0.801500 0.515093i
\(988\) 3.26556e10 1.07723
\(989\) −7.02845e9 + 1.80748e10i −0.231032 + 0.594137i
\(990\) 3.22121e9 0.105510
\(991\) −4.85898e10 3.12268e10i −1.58594 1.01922i −0.973494 0.228713i \(-0.926548\pi\)
−0.612448 0.790511i \(-0.709815\pi\)
\(992\) −2.14017e9 1.48852e10i −0.0696078 0.484133i
\(993\) −4.91387e9 1.07599e10i −0.159258 0.348726i
\(994\) 1.03051e10 + 3.02586e9i 0.332814 + 0.0977230i
\(995\) −3.75146e10 + 8.21455e10i −1.20731 + 2.64364i
\(996\) 4.82248e9 5.56544e9i 0.154655 0.178481i
\(997\) 1.04308e9 7.25475e9i 0.0333336 0.231841i −0.966343 0.257256i \(-0.917182\pi\)
0.999677 + 0.0254152i \(0.00809079\pi\)
\(998\) 5.76337e8 1.69228e8i 0.0183535 0.00538908i
\(999\) 1.97417e9 + 2.27832e9i 0.0626478 + 0.0722994i
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.25.8 140
23.12 even 11 inner 69.8.e.a.58.8 yes 140
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.8.e.a.25.8 140 1.1 even 1 trivial
69.8.e.a.58.8 yes 140 23.12 even 11 inner