Properties

Label 16.9.f.a.3.12
Level $16$
Weight $9$
Character 16.3
Analytic conductor $6.518$
Analytic rank $0$
Dimension $30$
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] = [16,9,Mod(3,16)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(16, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("16.3");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 16.f (of order \(4\), 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: \(6.51805776098\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(15\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 3.12
Character \(\chi\) \(=\) 16.3
Dual form 16.9.f.a.11.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(11.2357 + 11.3912i) q^{2} +(23.8972 - 23.8972i) q^{3} +(-3.51862 + 255.976i) q^{4} +(-695.590 + 695.590i) q^{5} +(540.720 + 3.71617i) q^{6} +3167.79 q^{7} +(-2955.40 + 2835.98i) q^{8} +5418.84i q^{9} +O(q^{10})\) \(q+(11.2357 + 11.3912i) q^{2} +(23.8972 - 23.8972i) q^{3} +(-3.51862 + 255.976i) q^{4} +(-695.590 + 695.590i) q^{5} +(540.720 + 3.71617i) q^{6} +3167.79 q^{7} +(-2955.40 + 2835.98i) q^{8} +5418.84i q^{9} +(-15739.0 - 108.169i) q^{10} +(-295.121 - 295.121i) q^{11} +(6033.03 + 6201.20i) q^{12} +(-20441.3 - 20441.3i) q^{13} +(35592.3 + 36084.9i) q^{14} +33245.4i q^{15} +(-65511.2 - 1801.36i) q^{16} +143214. q^{17} +(-61727.1 + 60884.4i) q^{18} +(128582. - 128582. i) q^{19} +(-175607. - 180502. i) q^{20} +(75701.5 - 75701.5i) q^{21} +(45.8931 - 6677.66i) q^{22} -61807.0 q^{23} +(-2853.84 + 138398. i) q^{24} -577067. i q^{25} +(3178.75 - 462522. i) q^{26} +(286285. + 286285. i) q^{27} +(-11146.3 + 810878. i) q^{28} +(233312. + 233312. i) q^{29} +(-378705. + 373535. i) q^{30} +374476. i q^{31} +(-715544. - 766491. i) q^{32} -14105.1 q^{33} +(1.60911e6 + 1.63138e6i) q^{34} +(-2.20348e6 + 2.20348e6i) q^{35} +(-1.38709e6 - 19066.9i) q^{36} +(516796. - 516796. i) q^{37} +(2.90942e6 + 19995.4i) q^{38} -976980. q^{39} +(83068.3 - 4.02843e6i) q^{40} -1.82949e6i q^{41} +(1.71289e6 + 11772.1i) q^{42} +(-834182. - 834182. i) q^{43} +(76582.2 - 74505.3i) q^{44} +(-3.76929e6 - 3.76929e6i) q^{45} +(-694444. - 704055. i) q^{46} +8.50247e6i q^{47} +(-1.60859e6 + 1.52249e6i) q^{48} +4.27010e6 q^{49} +(6.57348e6 - 6.48374e6i) q^{50} +(3.42242e6 - 3.42242e6i) q^{51} +(5.30440e6 - 5.16055e6i) q^{52} +(-3.16752e6 + 3.16752e6i) q^{53} +(-44519.2 + 6.47774e6i) q^{54} +410566. q^{55} +(-9.36210e6 + 8.98380e6i) q^{56} -6.14553e6i q^{57} +(-36281.5 + 5.27912e6i) q^{58} +(-9.18487e6 - 9.18487e6i) q^{59} +(-8.51001e6 - 116978. i) q^{60} +(-132625. - 132625. i) q^{61} +(-4.26573e6 + 4.20750e6i) q^{62} +1.71658e7i q^{63} +(691615. - 1.67630e7i) q^{64} +2.84375e7 q^{65} +(-158481. - 160674. i) q^{66} +(164015. - 164015. i) q^{67} +(-503916. + 3.66593e7i) q^{68} +(-1.47702e6 + 1.47702e6i) q^{69} +(-4.98580e7 - 342656. i) q^{70} +3.54013e7 q^{71} +(-1.53677e7 - 1.60149e7i) q^{72} +9.75074e6i q^{73} +(1.16935e7 + 80365.0i) q^{74} +(-1.37903e7 - 1.37903e7i) q^{75} +(3.24615e7 + 3.33664e7i) q^{76} +(-934880. - 934880. i) q^{77} +(-1.09770e7 - 1.11290e7i) q^{78} -4.97804e7i q^{79} +(4.68220e7 - 4.43160e7i) q^{80} -2.18702e7 q^{81} +(2.08401e7 - 2.05556e7i) q^{82} +(5.00207e7 - 5.00207e7i) q^{83} +(1.91114e7 + 1.96441e7i) q^{84} +(-9.96182e7 + 9.96182e7i) q^{85} +(129721. - 1.88749e7i) q^{86} +1.11510e7 q^{87} +(1.70916e6 + 35243.7i) q^{88} -3.66516e7i q^{89} +(586149. - 8.52874e7i) q^{90} +(-6.47537e7 - 6.47537e7i) q^{91} +(217475. - 1.58211e7i) q^{92} +(8.94895e6 + 8.94895e6i) q^{93} +(-9.68533e7 + 9.55311e7i) q^{94} +1.78881e8i q^{95} +(-3.54166e7 - 1.21749e6i) q^{96} +1.20777e8 q^{97} +(4.79775e7 + 4.86415e7i) q^{98} +(1.59921e6 - 1.59921e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q - 2 q^{2} - 2 q^{3} + 184 q^{4} - 2 q^{5} + 3232 q^{6} - 4 q^{7} - 8732 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 30 q - 2 q^{2} - 2 q^{3} + 184 q^{4} - 2 q^{5} + 3232 q^{6} - 4 q^{7} - 8732 q^{8} - 1860 q^{10} - 19778 q^{11} + 14068 q^{12} - 2 q^{13} - 58900 q^{14} + 245336 q^{16} - 4 q^{17} - 223730 q^{18} + 167550 q^{19} - 135380 q^{20} - 13124 q^{21} + 985700 q^{22} - 845572 q^{23} - 800592 q^{24} - 184760 q^{26} + 38656 q^{27} + 94136 q^{28} + 1066174 q^{29} + 1881700 q^{30} - 3395192 q^{32} - 4 q^{33} + 1634900 q^{34} + 426620 q^{35} + 1877324 q^{36} + 2360254 q^{37} - 3010352 q^{38} - 7650052 q^{39} + 3256936 q^{40} - 3731304 q^{42} + 6314814 q^{43} - 10360940 q^{44} + 794370 q^{45} + 1510780 q^{46} + 4591848 q^{48} + 14823770 q^{49} + 14752710 q^{50} - 28969860 q^{51} + 4335652 q^{52} + 2679358 q^{53} + 18667040 q^{54} + 46326780 q^{55} - 36346408 q^{56} - 1034696 q^{58} - 46004162 q^{59} - 20687200 q^{60} - 24476034 q^{61} - 64043472 q^{62} + 50827456 q^{64} - 14970820 q^{65} + 65035780 q^{66} + 59474558 q^{67} + 74339312 q^{68} + 8623420 q^{69} + 39082496 q^{70} - 79832068 q^{71} + 929812 q^{72} - 168043460 q^{74} + 88519490 q^{75} - 166219388 q^{76} + 35952572 q^{77} + 5059788 q^{78} - 12904856 q^{80} - 66961570 q^{81} + 261305296 q^{82} - 34471682 q^{83} + 456781480 q^{84} - 107741252 q^{85} + 9841444 q^{86} + 149712636 q^{87} - 173775752 q^{88} - 650366536 q^{90} - 76429060 q^{91} - 449169832 q^{92} + 138269056 q^{93} - 239278032 q^{94} + 378359728 q^{96} - 4 q^{97} + 630040554 q^{98} + 184838270 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(15\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 11.2357 + 11.3912i 0.702231 + 0.711950i
\(3\) 23.8972 23.8972i 0.295028 0.295028i −0.544035 0.839063i \(-0.683104\pi\)
0.839063 + 0.544035i \(0.183104\pi\)
\(4\) −3.51862 + 255.976i −0.0137446 + 0.999906i
\(5\) −695.590 + 695.590i −1.11294 + 1.11294i −0.120194 + 0.992750i \(0.538352\pi\)
−0.992750 + 0.120194i \(0.961648\pi\)
\(6\) 540.720 + 3.71617i 0.417222 + 0.00286742i
\(7\) 3167.79 1.31936 0.659681 0.751545i \(-0.270691\pi\)
0.659681 + 0.751545i \(0.270691\pi\)
\(8\) −2955.40 + 2835.98i −0.721534 + 0.692379i
\(9\) 5418.84i 0.825917i
\(10\) −15739.0 108.169i −1.57390 0.0108169i
\(11\) −295.121 295.121i −0.0201571 0.0201571i 0.696956 0.717114i \(-0.254537\pi\)
−0.717114 + 0.696956i \(0.754537\pi\)
\(12\) 6033.03 + 6201.20i 0.290945 + 0.299055i
\(13\) −20441.3 20441.3i −0.715706 0.715706i 0.252017 0.967723i \(-0.418906\pi\)
−0.967723 + 0.252017i \(0.918906\pi\)
\(14\) 35592.3 + 36084.9i 0.926497 + 0.939320i
\(15\) 33245.4i 0.656699i
\(16\) −65511.2 1801.36i −0.999622 0.0274866i
\(17\) 143214. 1.71470 0.857352 0.514730i \(-0.172108\pi\)
0.857352 + 0.514730i \(0.172108\pi\)
\(18\) −61727.1 + 60884.4i −0.588012 + 0.579984i
\(19\) 128582. 128582.i 0.986659 0.986659i −0.0132534 0.999912i \(-0.504219\pi\)
0.999912 + 0.0132534i \(0.00421882\pi\)
\(20\) −175607. 180502.i −1.09754 1.12814i
\(21\) 75701.5 75701.5i 0.389249 0.389249i
\(22\) 45.8931 6677.66i 0.000195910 0.0285058i
\(23\) −61807.0 −0.220865 −0.110432 0.993884i \(-0.535224\pi\)
−0.110432 + 0.993884i \(0.535224\pi\)
\(24\) −2853.84 + 138398.i −0.00860171 + 0.417144i
\(25\) 577067.i 1.47729i
\(26\) 3178.75 462522.i 0.00695605 1.01214i
\(27\) 286285. + 286285.i 0.538696 + 0.538696i
\(28\) −11146.3 + 810878.i −0.0181341 + 1.31924i
\(29\) 233312. + 233312.i 0.329872 + 0.329872i 0.852538 0.522666i \(-0.175062\pi\)
−0.522666 + 0.852538i \(0.675062\pi\)
\(30\) −378705. + 373535.i −0.467537 + 0.461154i
\(31\) 374476.i 0.405487i 0.979232 + 0.202744i \(0.0649858\pi\)
−0.979232 + 0.202744i \(0.935014\pi\)
\(32\) −715544. 766491.i −0.682396 0.730983i
\(33\) −14105.1 −0.0118938
\(34\) 1.60911e6 + 1.63138e6i 1.20412 + 1.22078i
\(35\) −2.20348e6 + 2.20348e6i −1.46838 + 1.46838i
\(36\) −1.38709e6 19066.9i −0.825839 0.0113519i
\(37\) 516796. 516796.i 0.275748 0.275748i −0.555661 0.831409i \(-0.687535\pi\)
0.831409 + 0.555661i \(0.187535\pi\)
\(38\) 2.90942e6 + 19995.4i 1.39531 + 0.00958948i
\(39\) −976980. −0.422306
\(40\) 83068.3 4.02843e6i 0.0324486 1.57361i
\(41\) 1.82949e6i 0.647434i −0.946154 0.323717i \(-0.895067\pi\)
0.946154 0.323717i \(-0.104933\pi\)
\(42\) 1.71289e6 + 11772.1i 0.550468 + 0.00378316i
\(43\) −834182. 834182.i −0.243998 0.243998i 0.574504 0.818502i \(-0.305195\pi\)
−0.818502 + 0.574504i \(0.805195\pi\)
\(44\) 76582.2 74505.3i 0.0204323 0.0198782i
\(45\) −3.76929e6 3.76929e6i −0.919200 0.919200i
\(46\) −694444. 704055.i −0.155098 0.157244i
\(47\) 8.50247e6i 1.74242i 0.490907 + 0.871212i \(0.336665\pi\)
−0.490907 + 0.871212i \(0.663335\pi\)
\(48\) −1.60859e6 + 1.52249e6i −0.303026 + 0.286807i
\(49\) 4.27010e6 0.740719
\(50\) 6.57348e6 6.48374e6i 1.05176 1.03740i
\(51\) 3.42242e6 3.42242e6i 0.505885 0.505885i
\(52\) 5.30440e6 5.16055e6i 0.725475 0.705801i
\(53\) −3.16752e6 + 3.16752e6i −0.401436 + 0.401436i −0.878739 0.477303i \(-0.841614\pi\)
0.477303 + 0.878739i \(0.341614\pi\)
\(54\) −44519.2 + 6.47774e6i −0.00523567 + 0.761814i
\(55\) 410566. 0.0448675
\(56\) −9.36210e6 + 8.98380e6i −0.951966 + 0.913499i
\(57\) 6.14553e6i 0.582183i
\(58\) −36281.5 + 5.27912e6i −0.00320607 + 0.466498i
\(59\) −9.18487e6 9.18487e6i −0.757992 0.757992i 0.217964 0.975957i \(-0.430058\pi\)
−0.975957 + 0.217964i \(0.930058\pi\)
\(60\) −8.51001e6 116978.i −0.656637 0.00902608i
\(61\) −132625. 132625.i −0.00957866 0.00957866i 0.702301 0.711880i \(-0.252156\pi\)
−0.711880 + 0.702301i \(0.752156\pi\)
\(62\) −4.26573e6 + 4.20750e6i −0.288687 + 0.284746i
\(63\) 1.71658e7i 1.08968i
\(64\) 691615. 1.67630e7i 0.0412235 0.999150i
\(65\) 2.84375e7 1.59308
\(66\) −158481. 160674.i −0.00835221 0.00846781i
\(67\) 164015. 164015.i 0.00813926 0.00813926i −0.703025 0.711165i \(-0.748168\pi\)
0.711165 + 0.703025i \(0.248168\pi\)
\(68\) −503916. + 3.66593e7i −0.0235680 + 1.71454i
\(69\) −1.47702e6 + 1.47702e6i −0.0651612 + 0.0651612i
\(70\) −4.98580e7 342656.i −2.07655 0.0142714i
\(71\) 3.54013e7 1.39311 0.696555 0.717504i \(-0.254715\pi\)
0.696555 + 0.717504i \(0.254715\pi\)
\(72\) −1.53677e7 1.60149e7i −0.571848 0.595928i
\(73\) 9.75074e6i 0.343357i 0.985153 + 0.171679i \(0.0549191\pi\)
−0.985153 + 0.171679i \(0.945081\pi\)
\(74\) 1.16935e7 + 80365.0i 0.389957 + 0.00268003i
\(75\) −1.37903e7 1.37903e7i −0.435842 0.435842i
\(76\) 3.24615e7 + 3.33664e7i 0.973004 + 1.00013i
\(77\) −934880. 934880.i −0.0265946 0.0265946i
\(78\) −1.09770e7 1.11290e7i −0.296556 0.300661i
\(79\) 4.97804e7i 1.27806i −0.769183 0.639028i \(-0.779337\pi\)
0.769183 0.639028i \(-0.220663\pi\)
\(80\) 4.68220e7 4.43160e7i 1.14312 1.08193i
\(81\) −2.18702e7 −0.508057
\(82\) 2.08401e7 2.05556e7i 0.460941 0.454648i
\(83\) 5.00207e7 5.00207e7i 1.05399 1.05399i 0.0555358 0.998457i \(-0.482313\pi\)
0.998457 0.0555358i \(-0.0176867\pi\)
\(84\) 1.91114e7 + 1.96441e7i 0.383862 + 0.394562i
\(85\) −9.96182e7 + 9.96182e7i −1.90837 + 1.90837i
\(86\) 129721. 1.88749e7i 0.00237146 0.345058i
\(87\) 1.11510e7 0.194643
\(88\) 1.70916e6 + 35243.7i 0.0285004 + 0.000587693i
\(89\) 3.66516e7i 0.584161i −0.956394 0.292080i \(-0.905653\pi\)
0.956394 0.292080i \(-0.0943475\pi\)
\(90\) 586149. 8.52874e7i 0.00893384 1.29991i
\(91\) −6.47537e7 6.47537e7i −0.944276 0.944276i
\(92\) 217475. 1.58211e7i 0.00303570 0.220844i
\(93\) 8.94895e6 + 8.94895e6i 0.119630 + 0.119630i
\(94\) −9.68533e7 + 9.55311e7i −1.24052 + 1.22358i
\(95\) 1.78881e8i 2.19619i
\(96\) −3.54166e7 1.21749e6i −0.416986 0.0143344i
\(97\) 1.20777e8 1.36426 0.682128 0.731233i \(-0.261055\pi\)
0.682128 + 0.731233i \(0.261055\pi\)
\(98\) 4.79775e7 + 4.86415e7i 0.520155 + 0.527354i
\(99\) 1.59921e6 1.59921e6i 0.0166481 0.0166481i
\(100\) 1.47715e8 + 2.03048e6i 1.47715 + 0.0203048i
\(101\) −6.69104e7 + 6.69104e7i −0.642996 + 0.642996i −0.951291 0.308295i \(-0.900242\pi\)
0.308295 + 0.951291i \(0.400242\pi\)
\(102\) 7.74386e7 + 532207.i 0.715413 + 0.00491677i
\(103\) −1.42395e8 −1.26516 −0.632582 0.774493i \(-0.718005\pi\)
−0.632582 + 0.774493i \(0.718005\pi\)
\(104\) 1.18383e8 + 2.44112e6i 1.01195 + 0.0208668i
\(105\) 1.05314e8i 0.866424i
\(106\) −7.16711e7 492569.i −0.567702 0.00390161i
\(107\) −2.13988e7 2.13988e7i −0.163251 0.163251i 0.620754 0.784005i \(-0.286826\pi\)
−0.784005 + 0.620754i \(0.786826\pi\)
\(108\) −7.42894e7 + 7.22748e7i −0.546050 + 0.531241i
\(109\) −1.34195e8 1.34195e8i −0.950669 0.950669i 0.0481704 0.998839i \(-0.484661\pi\)
−0.998839 + 0.0481704i \(0.984661\pi\)
\(110\) 4.61299e6 + 4.67684e6i 0.0315074 + 0.0319434i
\(111\) 2.47000e7i 0.162706i
\(112\) −2.07526e8 5.70635e6i −1.31886 0.0362649i
\(113\) 4.73205e7 0.290226 0.145113 0.989415i \(-0.453645\pi\)
0.145113 + 0.989415i \(0.453645\pi\)
\(114\) 7.00049e7 6.90492e7i 0.414485 0.408827i
\(115\) 4.29923e7 4.29923e7i 0.245810 0.245810i
\(116\) −6.05432e7 + 5.89013e7i −0.334374 + 0.325307i
\(117\) 1.10768e8 1.10768e8i 0.591114 0.591114i
\(118\) 1.42830e6 2.07825e8i 0.00736704 1.07194i
\(119\) 4.53671e8 2.26232
\(120\) −9.42834e7 9.82536e7i −0.454684 0.473831i
\(121\) 2.14185e8i 0.999187i
\(122\) 20624.0 3.00088e6i 9.30964e−5 0.0135460i
\(123\) −4.37199e7 4.37199e7i −0.191011 0.191011i
\(124\) −9.58568e7 1.31764e6i −0.405449 0.00557327i
\(125\) 1.29687e8 + 1.29687e8i 0.531198 + 0.531198i
\(126\) −1.95539e8 + 1.92869e8i −0.775801 + 0.765210i
\(127\) 3.31500e7i 0.127429i −0.997968 0.0637145i \(-0.979705\pi\)
0.997968 0.0637145i \(-0.0202947\pi\)
\(128\) 1.98721e8 1.80465e8i 0.740293 0.672285i
\(129\) −3.98693e7 −0.143973
\(130\) 3.19515e8 + 3.23937e8i 1.11871 + 1.13419i
\(131\) −3.21149e8 + 3.21149e8i −1.09049 + 1.09049i −0.0950128 + 0.995476i \(0.530289\pi\)
−0.995476 + 0.0950128i \(0.969711\pi\)
\(132\) 49630.7 3.61057e6i 0.000163476 0.0118927i
\(133\) 4.07322e8 4.07322e8i 1.30176 1.30176i
\(134\) 3.71115e6 + 25505.4i 0.0115104 + 7.91066e-5i
\(135\) −3.98275e8 −1.19908
\(136\) −4.23255e8 + 4.06152e8i −1.23722 + 1.18722i
\(137\) 3.35313e8i 0.951849i −0.879486 0.475924i \(-0.842114\pi\)
0.879486 0.475924i \(-0.157886\pi\)
\(138\) −3.34203e7 229685.i −0.0921497 0.000633311i
\(139\) 4.80067e8 + 4.80067e8i 1.28600 + 1.28600i 0.937193 + 0.348812i \(0.113415\pi\)
0.348812 + 0.937193i \(0.386585\pi\)
\(140\) −5.56285e8 5.71792e8i −1.44806 1.48842i
\(141\) 2.03186e8 + 2.03186e8i 0.514063 + 0.514063i
\(142\) 3.97758e8 + 4.03263e8i 0.978284 + 0.991824i
\(143\) 1.20653e7i 0.0288532i
\(144\) 9.76131e6 3.54995e8i 0.0227017 0.825605i
\(145\) −3.24579e8 −0.734258
\(146\) −1.11073e8 + 1.09556e8i −0.244453 + 0.241116i
\(147\) 1.02044e8 1.02044e8i 0.218533 0.218533i
\(148\) 1.30469e8 + 1.34106e8i 0.271932 + 0.279512i
\(149\) −1.55412e8 + 1.55412e8i −0.315312 + 0.315312i −0.846963 0.531651i \(-0.821572\pi\)
0.531651 + 0.846963i \(0.321572\pi\)
\(150\) 2.14448e6 3.12032e8i 0.00423601 0.616359i
\(151\) −3.58922e8 −0.690387 −0.345193 0.938532i \(-0.612187\pi\)
−0.345193 + 0.938532i \(0.612187\pi\)
\(152\) −1.53555e7 + 7.44670e8i −0.0287666 + 1.39505i
\(153\) 7.76053e8i 1.41620i
\(154\) 145380. 2.11534e7i 0.000258477 0.0376095i
\(155\) −2.60482e8 2.60482e8i −0.451285 0.451285i
\(156\) 3.43763e6 2.50083e8i 0.00580444 0.422266i
\(157\) −5.90001e8 5.90001e8i −0.971077 0.971077i 0.0285160 0.999593i \(-0.490922\pi\)
−0.999593 + 0.0285160i \(0.990922\pi\)
\(158\) 5.67058e8 5.59317e8i 0.909912 0.897491i
\(159\) 1.51390e8i 0.236869i
\(160\) 1.03089e9 + 3.54380e7i 1.57301 + 0.0540741i
\(161\) −1.95792e8 −0.291401
\(162\) −2.45726e8 2.49127e8i −0.356773 0.361711i
\(163\) −1.82545e8 + 1.82545e8i −0.258595 + 0.258595i −0.824483 0.565887i \(-0.808534\pi\)
0.565887 + 0.824483i \(0.308534\pi\)
\(164\) 4.68306e8 + 6.43730e6i 0.647373 + 0.00889874i
\(165\) 9.81140e6 9.81140e6i 0.0132372 0.0132372i
\(166\) 1.13181e9 + 7.77854e6i 1.49054 + 0.0102439i
\(167\) −2.64912e8 −0.340593 −0.170296 0.985393i \(-0.554473\pi\)
−0.170296 + 0.985393i \(0.554473\pi\)
\(168\) −9.04037e6 + 4.38417e8i −0.0113488 + 0.550364i
\(169\) 1.99605e7i 0.0244695i
\(170\) −2.25405e9 1.54913e7i −2.69878 0.0185477i
\(171\) 6.96768e8 + 6.96768e8i 0.814899 + 0.814899i
\(172\) 2.16466e8 2.10595e8i 0.247329 0.240622i
\(173\) 4.96669e8 + 4.96669e8i 0.554476 + 0.554476i 0.927729 0.373253i \(-0.121758\pi\)
−0.373253 + 0.927729i \(0.621758\pi\)
\(174\) 1.25289e8 + 1.27024e8i 0.136684 + 0.138576i
\(175\) 1.82803e9i 1.94908i
\(176\) 1.88021e7 + 1.98653e7i 0.0195955 + 0.0207036i
\(177\) −4.38986e8 −0.447258
\(178\) 4.17505e8 4.11805e8i 0.415893 0.410215i
\(179\) −3.33878e6 + 3.33878e6i −0.00325219 + 0.00325219i −0.708731 0.705479i \(-0.750732\pi\)
0.705479 + 0.708731i \(0.250732\pi\)
\(180\) 9.78111e8 9.51586e8i 0.931747 0.906479i
\(181\) 6.56966e8 6.56966e8i 0.612108 0.612108i −0.331387 0.943495i \(-0.607516\pi\)
0.943495 + 0.331387i \(0.107516\pi\)
\(182\) 1.00696e7 1.46517e9i 0.00917755 1.33538i
\(183\) −6.33873e6 −0.00565194
\(184\) 1.82665e8 1.75284e8i 0.159361 0.152922i
\(185\) 7.18956e8i 0.613784i
\(186\) −1.39162e6 + 2.02487e8i −0.00116270 + 0.169178i
\(187\) −4.22654e7 4.22654e7i −0.0345635 0.0345635i
\(188\) −2.17643e9 2.99170e7i −1.74226 0.0239490i
\(189\) 9.06892e8 + 9.06892e8i 0.710736 + 0.710736i
\(190\) −2.03767e9 + 2.00985e9i −1.56358 + 1.54223i
\(191\) 1.21820e9i 0.915343i −0.889121 0.457671i \(-0.848684\pi\)
0.889121 0.457671i \(-0.151316\pi\)
\(192\) −3.84061e8 4.17116e8i −0.282615 0.306939i
\(193\) −1.88102e9 −1.35570 −0.677852 0.735199i \(-0.737089\pi\)
−0.677852 + 0.735199i \(0.737089\pi\)
\(194\) 1.35701e9 + 1.37579e9i 0.958022 + 0.971282i
\(195\) 6.79578e8 6.79578e8i 0.470003 0.470003i
\(196\) −1.50249e7 + 1.09304e9i −0.0101809 + 0.740649i
\(197\) −7.15815e8 + 7.15815e8i −0.475265 + 0.475265i −0.903614 0.428349i \(-0.859096\pi\)
0.428349 + 0.903614i \(0.359096\pi\)
\(198\) 3.61852e7 + 248688.i 0.0235434 + 0.000161806i
\(199\) 7.60687e8 0.485058 0.242529 0.970144i \(-0.422023\pi\)
0.242529 + 0.970144i \(0.422023\pi\)
\(200\) 1.63655e9 + 1.70547e9i 1.02284 + 1.06592i
\(201\) 7.83903e6i 0.00480262i
\(202\) −1.51397e9 1.04050e7i −0.909313 0.00624937i
\(203\) 7.39083e8 + 7.39083e8i 0.435220 + 0.435220i
\(204\) 8.64014e8 + 8.88098e8i 0.498884 + 0.512791i
\(205\) 1.27258e9 + 1.27258e9i 0.720559 + 0.720559i
\(206\) −1.59991e9 1.62205e9i −0.888437 0.900733i
\(207\) 3.34922e8i 0.182416i
\(208\) 1.30231e9 + 1.37596e9i 0.695763 + 0.735108i
\(209\) −7.58946e7 −0.0397764
\(210\) −1.19966e9 + 1.18328e9i −0.616850 + 0.608430i
\(211\) 2.66751e8 2.66751e8i 0.134579 0.134579i −0.636609 0.771187i \(-0.719663\pi\)
0.771187 + 0.636609i \(0.219663\pi\)
\(212\) −7.99663e8 8.21954e8i −0.395880 0.406915i
\(213\) 8.45993e8 8.45993e8i 0.411006 0.411006i
\(214\) 3.32765e6 4.84188e8i 0.00158666 0.230866i
\(215\) 1.16050e9 0.543113
\(216\) −1.65799e9 3.41886e7i −0.761670 0.0157060i
\(217\) 1.18626e9i 0.534985i
\(218\) 2.08681e7 3.03641e9i 0.00923969 1.34442i
\(219\) 2.33016e8 + 2.33016e8i 0.101300 + 0.101300i
\(220\) −1.44463e6 + 1.05095e8i −0.000616687 + 0.0448633i
\(221\) −2.92747e9 2.92747e9i −1.22722 1.22722i
\(222\) 2.81362e8 2.77521e8i 0.115839 0.114257i
\(223\) 8.47191e8i 0.342580i 0.985221 + 0.171290i \(0.0547935\pi\)
−0.985221 + 0.171290i \(0.945206\pi\)
\(224\) −2.26669e9 2.42808e9i −0.900328 0.964431i
\(225\) 3.12703e9 1.22012
\(226\) 5.31679e8 + 5.39037e8i 0.203805 + 0.206626i
\(227\) −2.77203e8 + 2.77203e8i −0.104399 + 0.104399i −0.757377 0.652978i \(-0.773519\pi\)
0.652978 + 0.757377i \(0.273519\pi\)
\(228\) 1.57311e9 + 2.16238e7i 0.582128 + 0.00800189i
\(229\) 6.77332e8 6.77332e8i 0.246297 0.246297i −0.573152 0.819449i \(-0.694279\pi\)
0.819449 + 0.573152i \(0.194279\pi\)
\(230\) 9.72782e8 + 6.68558e6i 0.347620 + 0.00238906i
\(231\) −4.46821e7 −0.0156923
\(232\) −1.35120e9 2.78624e7i −0.466410 0.00961760i
\(233\) 1.65304e9i 0.560867i −0.959873 0.280433i \(-0.909522\pi\)
0.959873 0.280433i \(-0.0904782\pi\)
\(234\) 2.50634e9 + 1.72251e7i 0.835941 + 0.00574512i
\(235\) −5.91424e9 5.91424e9i −1.93922 1.93922i
\(236\) 2.38342e9 2.31879e9i 0.768339 0.747503i
\(237\) −1.18962e9 1.18962e9i −0.377062 0.377062i
\(238\) 5.09731e9 + 5.16786e9i 1.58867 + 1.61066i
\(239\) 5.89940e9i 1.80807i 0.427455 + 0.904037i \(0.359410\pi\)
−0.427455 + 0.904037i \(0.640590\pi\)
\(240\) 5.98871e7 2.17795e9i 0.0180505 0.656451i
\(241\) 3.20243e9 0.949318 0.474659 0.880170i \(-0.342571\pi\)
0.474659 + 0.880170i \(0.342571\pi\)
\(242\) 2.43982e9 2.40651e9i 0.711371 0.701660i
\(243\) −2.40095e9 + 2.40095e9i −0.688587 + 0.688587i
\(244\) 3.44153e7 3.34820e7i 0.00970941 0.00944610i
\(245\) −2.97024e9 + 2.97024e9i −0.824379 + 0.824379i
\(246\) 6.79872e6 9.89245e8i 0.00185646 0.270124i
\(247\) −5.25677e9 −1.41231
\(248\) −1.06201e9 1.10673e9i −0.280751 0.292573i
\(249\) 2.39071e9i 0.621914i
\(250\) −2.01672e7 + 2.93441e9i −0.00516279 + 0.751210i
\(251\) 4.48339e9 + 4.48339e9i 1.12957 + 1.12957i 0.990248 + 0.139318i \(0.0444911\pi\)
0.139318 + 0.990248i \(0.455509\pi\)
\(252\) −4.39402e9 6.03998e7i −1.08958 0.0149773i
\(253\) 1.82405e7 + 1.82405e7i 0.00445200 + 0.00445200i
\(254\) 3.77618e8 3.72463e8i 0.0907230 0.0894845i
\(255\) 4.76120e9i 1.12604i
\(256\) 4.28848e9 + 2.36019e8i 0.998489 + 0.0549525i
\(257\) −3.66793e8 −0.0840792 −0.0420396 0.999116i \(-0.513386\pi\)
−0.0420396 + 0.999116i \(0.513386\pi\)
\(258\) −4.47959e8 4.54159e8i −0.101102 0.102501i
\(259\) 1.63710e9 1.63710e9i 0.363811 0.363811i
\(260\) −1.00061e8 + 7.27931e9i −0.0218963 + 1.59293i
\(261\) −1.26428e9 + 1.26428e9i −0.272447 + 0.272447i
\(262\) −7.26660e9 4.99407e7i −1.54215 0.0105986i
\(263\) 4.42614e9 0.925129 0.462564 0.886586i \(-0.346929\pi\)
0.462564 + 0.886586i \(0.346929\pi\)
\(264\) 4.16864e7 4.00019e7i 0.00858180 0.00823503i
\(265\) 4.40659e9i 0.893551i
\(266\) 9.21643e9 + 6.33411e7i 1.84092 + 0.0126520i
\(267\) −8.75871e8 8.75871e8i −0.172344 0.172344i
\(268\) 4.14068e7 + 4.25610e7i 0.00802662 + 0.00825036i
\(269\) −7.49923e8 7.49923e8i −0.143221 0.143221i 0.631861 0.775082i \(-0.282291\pi\)
−0.775082 + 0.631861i \(0.782291\pi\)
\(270\) −4.47489e9 4.53682e9i −0.842029 0.853683i
\(271\) 6.15923e8i 0.114196i 0.998369 + 0.0570978i \(0.0181847\pi\)
−0.998369 + 0.0570978i \(0.981815\pi\)
\(272\) −9.38212e9 2.57980e8i −1.71406 0.0471315i
\(273\) −3.09487e9 −0.557175
\(274\) 3.81961e9 3.76747e9i 0.677668 0.668417i
\(275\) −1.70304e8 + 1.70304e8i −0.0297779 + 0.0297779i
\(276\) −3.72883e8 3.83278e8i −0.0642594 0.0660506i
\(277\) −3.61003e9 + 3.61003e9i −0.613186 + 0.613186i −0.943775 0.330589i \(-0.892753\pi\)
0.330589 + 0.943775i \(0.392753\pi\)
\(278\) −7.46534e7 + 1.08624e10i −0.0124989 + 1.81864i
\(279\) −2.02923e9 −0.334899
\(280\) 2.63143e8 1.27612e10i 0.0428114 2.07616i
\(281\) 1.95702e9i 0.313885i −0.987608 0.156942i \(-0.949836\pi\)
0.987608 0.156942i \(-0.0501637\pi\)
\(282\) −3.15967e7 + 4.59746e9i −0.00499626 + 0.726978i
\(283\) −3.38369e9 3.38369e9i −0.527527 0.527527i 0.392307 0.919834i \(-0.371677\pi\)
−0.919834 + 0.392307i \(0.871677\pi\)
\(284\) −1.24564e8 + 9.06187e9i −0.0191478 + 1.39298i
\(285\) 4.27477e9 + 4.27477e9i 0.647938 + 0.647938i
\(286\) −1.37438e8 + 1.35562e8i −0.0205420 + 0.0202616i
\(287\) 5.79546e9i 0.854201i
\(288\) 4.15349e9 3.87742e9i 0.603731 0.563603i
\(289\) 1.35344e10 1.94021
\(290\) −3.64687e9 3.69734e9i −0.515618 0.522754i
\(291\) 2.88623e9 2.88623e9i 0.402493 0.402493i
\(292\) −2.49595e9 3.43092e7i −0.343325 0.00471931i
\(293\) 7.39270e9 7.39270e9i 1.00307 1.00307i 0.00307783 0.999995i \(-0.499020\pi\)
0.999995 0.00307783i \(-0.000979704\pi\)
\(294\) 2.30893e9 + 1.58684e7i 0.309044 + 0.00212395i
\(295\) 1.27778e10 1.68721
\(296\) −6.17164e7 + 2.99296e9i −0.00803959 + 0.389883i
\(297\) 1.68977e8i 0.0217171i
\(298\) −3.51650e9 2.41676e7i −0.445908 0.00306456i
\(299\) 1.26341e9 + 1.26341e9i 0.158074 + 0.158074i
\(300\) 3.57851e9 3.48146e9i 0.441791 0.429810i
\(301\) −2.64251e9 2.64251e9i −0.321922 0.321922i
\(302\) −4.03274e9 4.08855e9i −0.484811 0.491521i
\(303\) 3.19795e9i 0.379403i
\(304\) −8.65521e9 + 8.19197e9i −1.01341 + 0.959166i
\(305\) 1.84505e8 0.0213210
\(306\) −8.84017e9 + 8.71949e9i −1.00827 + 0.994502i
\(307\) −5.14116e9 + 5.14116e9i −0.578773 + 0.578773i −0.934565 0.355792i \(-0.884211\pi\)
0.355792 + 0.934565i \(0.384211\pi\)
\(308\) 2.42596e8 2.36017e8i 0.0269576 0.0262265i
\(309\) −3.40286e9 + 3.40286e9i −0.373258 + 0.373258i
\(310\) 4.05066e7 5.89389e9i 0.00438610 0.638198i
\(311\) −2.71733e9 −0.290469 −0.145235 0.989397i \(-0.546394\pi\)
−0.145235 + 0.989397i \(0.546394\pi\)
\(312\) 2.88737e9 2.77070e9i 0.304708 0.292396i
\(313\) 2.51178e9i 0.261700i 0.991402 + 0.130850i \(0.0417706\pi\)
−0.991402 + 0.130850i \(0.958229\pi\)
\(314\) 9.17488e7 1.33499e10i 0.00943804 1.37328i
\(315\) −1.19403e10 1.19403e10i −1.21276 1.21276i
\(316\) 1.27426e10 + 1.75159e8i 1.27794 + 0.0175664i
\(317\) −6.58549e9 6.58549e9i −0.652156 0.652156i 0.301356 0.953512i \(-0.402561\pi\)
−0.953512 + 0.301356i \(0.902561\pi\)
\(318\) −1.72451e9 + 1.70097e9i −0.168639 + 0.166337i
\(319\) 1.37710e8i 0.0132985i
\(320\) 1.11791e10 + 1.21412e10i 1.06612 + 1.15788i
\(321\) −1.02275e9 −0.0963269
\(322\) −2.19985e9 2.23030e9i −0.204630 0.207463i
\(323\) 1.84148e10 1.84148e10i 1.69183 1.69183i
\(324\) 7.69529e7 5.59823e9i 0.00698305 0.508009i
\(325\) −1.17960e10 + 1.17960e10i −1.05731 + 1.05731i
\(326\) −4.13043e9 2.83870e7i −0.365700 0.00251332i
\(327\) −6.41377e9 −0.560947
\(328\) 5.18842e9 + 5.40690e9i 0.448270 + 0.467146i
\(329\) 2.69341e10i 2.29889i
\(330\) 2.22001e8 + 1.52573e6i 0.0187197 + 0.000128654i
\(331\) 9.88763e9 + 9.88763e9i 0.823721 + 0.823721i 0.986640 0.162918i \(-0.0520907\pi\)
−0.162918 + 0.986640i \(0.552091\pi\)
\(332\) 1.26281e10 + 1.29801e10i 1.03941 + 1.06838i
\(333\) 2.80043e9 + 2.80043e9i 0.227745 + 0.227745i
\(334\) −2.97647e9 3.01766e9i −0.239175 0.242485i
\(335\) 2.28175e8i 0.0181171i
\(336\) −5.09566e9 + 4.82293e9i −0.399801 + 0.378402i
\(337\) −1.42761e10 −1.10685 −0.553426 0.832898i \(-0.686680\pi\)
−0.553426 + 0.832898i \(0.686680\pi\)
\(338\) −2.27374e8 + 2.24270e8i −0.0174211 + 0.0171832i
\(339\) 1.13083e9 1.13083e9i 0.0856246 0.0856246i
\(340\) −2.51493e10 2.58504e10i −1.88196 1.93442i
\(341\) 1.10516e8 1.10516e8i 0.00817346 0.00817346i
\(342\) −1.08352e8 + 1.57657e10i −0.00792012 + 1.15241i
\(343\) −4.73491e9 −0.342086
\(344\) 4.83107e9 + 9.96191e7i 0.344993 + 0.00711392i
\(345\) 2.05480e9i 0.145042i
\(346\) −7.72352e7 + 1.12381e10i −0.00538903 + 0.784129i
\(347\) 6.45408e9 + 6.45408e9i 0.445161 + 0.445161i 0.893742 0.448581i \(-0.148071\pi\)
−0.448581 + 0.893742i \(0.648071\pi\)
\(348\) −3.92363e7 + 2.85439e9i −0.00267529 + 0.194624i
\(349\) 1.58170e10 + 1.58170e10i 1.06616 + 1.06616i 0.997650 + 0.0685130i \(0.0218255\pi\)
0.0685130 + 0.997650i \(0.478175\pi\)
\(350\) 2.08234e10 2.05391e10i 1.38765 1.36871i
\(351\) 1.17041e10i 0.771096i
\(352\) −1.50354e7 + 4.37379e8i −0.000979365 + 0.0284897i
\(353\) −2.81679e10 −1.81408 −0.907039 0.421046i \(-0.861663\pi\)
−0.907039 + 0.421046i \(0.861663\pi\)
\(354\) −4.93231e9 5.00058e9i −0.314078 0.318425i
\(355\) −2.46248e10 + 2.46248e10i −1.55045 + 1.55045i
\(356\) 9.38191e9 + 1.28963e8i 0.584106 + 0.00802907i
\(357\) 1.08415e10 1.08415e10i 0.667446 0.667446i
\(358\) −7.55462e7 519202.i −0.00459918 3.16085e-5i
\(359\) −2.15720e9 −0.129871 −0.0649357 0.997889i \(-0.520684\pi\)
−0.0649357 + 0.997889i \(0.520684\pi\)
\(360\) 2.18294e10 + 4.50134e8i 1.29967 + 0.0267998i
\(361\) 1.60833e10i 0.946991i
\(362\) 1.48651e10 + 1.02162e8i 0.865632 + 0.00594917i
\(363\) −5.11842e9 5.11842e9i −0.294788 0.294788i
\(364\) 1.68032e10 1.63475e10i 0.957165 0.931208i
\(365\) −6.78252e9 6.78252e9i −0.382138 0.382138i
\(366\) −7.12199e7 7.22057e7i −0.00396897 0.00402390i
\(367\) 2.90608e10i 1.60193i −0.598710 0.800966i \(-0.704320\pi\)
0.598710 0.800966i \(-0.295680\pi\)
\(368\) 4.04905e9 + 1.11337e8i 0.220781 + 0.00607083i
\(369\) 9.91375e9 0.534727
\(370\) −8.18977e9 + 8.07797e9i −0.436983 + 0.431018i
\(371\) −1.00340e10 + 1.00340e10i −0.529639 + 0.529639i
\(372\) −2.32220e9 + 2.25923e9i −0.121263 + 0.117974i
\(373\) 2.00021e10 2.00021e10i 1.03333 1.03333i 0.0339059 0.999425i \(-0.489205\pi\)
0.999425 0.0339059i \(-0.0107947\pi\)
\(374\) 6.57253e6 9.56333e8i 0.000335928 0.0488791i
\(375\) 6.19833e9 0.313436
\(376\) −2.41129e10 2.51282e10i −1.20642 1.25722i
\(377\) 9.53839e9i 0.472182i
\(378\) −1.41027e8 + 2.05201e10i −0.00690774 + 1.00511i
\(379\) 1.32718e10 + 1.32718e10i 0.643241 + 0.643241i 0.951351 0.308110i \(-0.0996964\pi\)
−0.308110 + 0.951351i \(0.599696\pi\)
\(380\) −4.57893e10 6.29416e8i −2.19599 0.0301858i
\(381\) −7.92193e8 7.92193e8i −0.0375951 0.0375951i
\(382\) 1.38767e10 1.36873e10i 0.651678 0.642782i
\(383\) 5.09072e9i 0.236583i 0.992979 + 0.118292i \(0.0377418\pi\)
−0.992979 + 0.118292i \(0.962258\pi\)
\(384\) 4.36264e8 9.06150e9i 0.0200643 0.416750i
\(385\) 1.30059e9 0.0591966
\(386\) −2.11346e10 2.14271e10i −0.952016 0.965193i
\(387\) 4.52030e9 4.52030e9i 0.201522 0.201522i
\(388\) −4.24967e8 + 3.09159e10i −0.0187512 + 1.36413i
\(389\) 7.86395e9 7.86395e9i 0.343433 0.343433i −0.514223 0.857656i \(-0.671920\pi\)
0.857656 + 0.514223i \(0.171920\pi\)
\(390\) 1.53767e10 + 1.05679e8i 0.664669 + 0.00456803i
\(391\) −8.85161e9 −0.378718
\(392\) −1.26199e10 + 1.21099e10i −0.534454 + 0.512858i
\(393\) 1.53491e10i 0.643449i
\(394\) −1.61967e10 1.11314e8i −0.672110 0.00461917i
\(395\) 3.46268e10 + 3.46268e10i 1.42241 + 1.42241i
\(396\) 4.03733e8 + 4.14987e8i 0.0164177 + 0.0168754i
\(397\) 1.90783e10 + 1.90783e10i 0.768029 + 0.768029i 0.977759 0.209730i \(-0.0672585\pi\)
−0.209730 + 0.977759i \(0.567258\pi\)
\(398\) 8.54684e9 + 8.66513e9i 0.340622 + 0.345337i
\(399\) 1.94677e10i 0.768111i
\(400\) −1.03951e9 + 3.78044e10i −0.0406058 + 1.47673i
\(401\) −1.34169e10 −0.518891 −0.259446 0.965758i \(-0.583540\pi\)
−0.259446 + 0.965758i \(0.583540\pi\)
\(402\) 8.92959e7 8.80768e7i 0.00341922 0.00337254i
\(403\) 7.65477e9 7.65477e9i 0.290210 0.290210i
\(404\) −1.68920e10 1.73629e10i −0.634098 0.651773i
\(405\) 1.52127e10 1.52127e10i 0.565439 0.565439i
\(406\) −1.14932e8 + 1.67232e10i −0.00422997 + 0.615480i
\(407\) −3.05034e8 −0.0111166
\(408\) −4.08709e8 + 1.98205e10i −0.0147494 + 0.715278i
\(409\) 1.71881e10i 0.614236i 0.951671 + 0.307118i \(0.0993646\pi\)
−0.951671 + 0.307118i \(0.900635\pi\)
\(410\) −1.97894e8 + 2.87945e10i −0.00700321 + 1.01900i
\(411\) −8.01306e9 8.01306e9i −0.280822 0.280822i
\(412\) 5.01035e8 3.64498e10i 0.0173892 1.26504i
\(413\) −2.90957e10 2.90957e10i −1.00007 1.00007i
\(414\) 3.81516e9 3.76308e9i 0.129871 0.128098i
\(415\) 6.95879e10i 2.34607i
\(416\) −1.04141e9 + 3.02947e10i −0.0347737 + 1.01156i
\(417\) 2.29446e10 0.758814
\(418\) −8.52728e8 8.64530e8i −0.0279322 0.0283188i
\(419\) −1.16702e9 + 1.16702e9i −0.0378638 + 0.0378638i −0.725785 0.687921i \(-0.758523\pi\)
0.687921 + 0.725785i \(0.258523\pi\)
\(420\) −2.69579e10 3.70562e8i −0.866342 0.0119087i
\(421\) −3.29147e9 + 3.29147e9i −0.104776 + 0.104776i −0.757551 0.652776i \(-0.773604\pi\)
0.652776 + 0.757551i \(0.273604\pi\)
\(422\) 6.03574e9 + 4.14814e7i 0.190318 + 0.00130799i
\(423\) −4.60736e10 −1.43910
\(424\) 3.78270e8 1.83443e10i 0.0117041 0.567595i
\(425\) 8.26439e10i 2.53312i
\(426\) 1.91422e10 + 1.31557e8i 0.581237 + 0.00399463i
\(427\) −4.20127e8 4.20127e8i −0.0126377 0.0126377i
\(428\) 5.55287e9 5.40228e9i 0.165479 0.160991i
\(429\) 2.88327e8 + 2.88327e8i 0.00851248 + 0.00851248i
\(430\) 1.30390e10 + 1.32195e10i 0.381391 + 0.386669i
\(431\) 1.20233e10i 0.348429i −0.984708 0.174214i \(-0.944261\pi\)
0.984708 0.174214i \(-0.0557386\pi\)
\(432\) −1.82392e10 1.92706e10i −0.523686 0.553300i
\(433\) 4.36305e10 1.24119 0.620595 0.784131i \(-0.286891\pi\)
0.620595 + 0.784131i \(0.286891\pi\)
\(434\) −1.35129e10 + 1.33285e10i −0.380882 + 0.375683i
\(435\) −7.75655e9 + 7.75655e9i −0.216626 + 0.216626i
\(436\) 3.48228e10 3.38784e10i 0.963645 0.937512i
\(437\) −7.94729e9 + 7.94729e9i −0.217918 + 0.217918i
\(438\) −3.62354e7 + 5.27242e9i −0.000984548 + 0.143256i
\(439\) −6.61882e8 −0.0178206 −0.00891030 0.999960i \(-0.502836\pi\)
−0.00891030 + 0.999960i \(0.502836\pi\)
\(440\) −1.21339e9 + 1.16436e9i −0.0323735 + 0.0310653i
\(441\) 2.31390e10i 0.611772i
\(442\) 4.55241e8 6.62396e10i 0.0119276 1.73552i
\(443\) −4.04686e10 4.04686e10i −1.05076 1.05076i −0.998641 0.0521171i \(-0.983403\pi\)
−0.0521171 0.998641i \(-0.516597\pi\)
\(444\) 6.32260e9 + 8.69099e7i 0.162691 + 0.00223634i
\(445\) 2.54945e10 + 2.54945e10i 0.650138 + 0.650138i
\(446\) −9.65052e9 + 9.51878e9i −0.243900 + 0.240570i
\(447\) 7.42786e9i 0.186052i
\(448\) 2.19089e9 5.31015e10i 0.0543887 1.31824i
\(449\) −7.08087e10 −1.74221 −0.871107 0.491093i \(-0.836597\pi\)
−0.871107 + 0.491093i \(0.836597\pi\)
\(450\) 3.51344e10 + 3.56207e10i 0.856806 + 0.868664i
\(451\) −5.39922e8 + 5.39922e8i −0.0130504 + 0.0130504i
\(452\) −1.66503e8 + 1.21129e10i −0.00398904 + 0.290198i
\(453\) −8.57725e9 + 8.57725e9i −0.203683 + 0.203683i
\(454\) −6.27224e9 4.31068e7i −0.147638 0.00101467i
\(455\) 9.00840e10 2.10185
\(456\) 1.74286e10 + 1.81625e10i 0.403091 + 0.420065i
\(457\) 7.55905e10i 1.73301i 0.499164 + 0.866507i \(0.333640\pi\)
−0.499164 + 0.866507i \(0.666360\pi\)
\(458\) 1.53259e10 + 1.05329e8i 0.348309 + 0.00239380i
\(459\) 4.10000e10 + 4.10000e10i 0.923705 + 0.923705i
\(460\) 1.08537e10 + 1.11563e10i 0.242408 + 0.249165i
\(461\) −3.00010e10 3.00010e10i −0.664250 0.664250i 0.292129 0.956379i \(-0.405636\pi\)
−0.956379 + 0.292129i \(0.905636\pi\)
\(462\) −5.02034e8 5.08983e8i −0.0110196 0.0111721i
\(463\) 8.11242e10i 1.76533i −0.470000 0.882666i \(-0.655746\pi\)
0.470000 0.882666i \(-0.344254\pi\)
\(464\) −1.48643e10 1.57048e10i −0.320680 0.338814i
\(465\) −1.24496e10 −0.266283
\(466\) 1.88301e10 1.85730e10i 0.399309 0.393858i
\(467\) 2.37442e9 2.37442e9i 0.0499217 0.0499217i −0.681705 0.731627i \(-0.738761\pi\)
0.731627 + 0.681705i \(0.238761\pi\)
\(468\) 2.79642e10 + 2.87437e10i 0.582933 + 0.599183i
\(469\) 5.19566e8 5.19566e8i 0.0107386 0.0107386i
\(470\) 9.19701e8 1.33821e11i 0.0188476 2.74241i
\(471\) −2.81988e10 −0.572989
\(472\) 5.31931e10 + 1.09687e9i 1.07174 + 0.0220997i
\(473\) 4.92369e8i 0.00983662i
\(474\) 1.84993e8 2.69173e10i 0.00366472 0.533234i
\(475\) −7.42006e10 7.42006e10i −1.45758 1.45758i
\(476\) −1.59630e9 + 1.16129e11i −0.0310947 + 2.26210i
\(477\) −1.71643e10 1.71643e10i −0.331553 0.331553i
\(478\) −6.72012e10 + 6.62838e10i −1.28726 + 1.26968i
\(479\) 6.65324e10i 1.26384i 0.775035 + 0.631918i \(0.217732\pi\)
−0.775035 + 0.631918i \(0.782268\pi\)
\(480\) 2.54823e10 2.37885e10i 0.480036 0.448129i
\(481\) −2.11279e10 −0.394708
\(482\) 3.59815e10 + 3.64795e10i 0.666640 + 0.675867i
\(483\) −4.67888e9 + 4.67888e9i −0.0859713 + 0.0859713i
\(484\) 5.48261e10 + 7.53635e8i 0.999093 + 0.0137335i
\(485\) −8.40111e10 + 8.40111e10i −1.51834 + 1.51834i
\(486\) −5.43261e10 3.73364e8i −0.973786 0.00669248i
\(487\) 5.24988e10 0.933327 0.466663 0.884435i \(-0.345456\pi\)
0.466663 + 0.884435i \(0.345456\pi\)
\(488\) 7.68080e8 + 1.58382e7i 0.0135434 + 0.000279272i
\(489\) 8.72467e9i 0.152586i
\(490\) −6.72072e10 4.61891e8i −1.16582 0.00801226i
\(491\) −1.00556e10 1.00556e10i −0.173015 0.173015i 0.615288 0.788303i \(-0.289040\pi\)
−0.788303 + 0.615288i \(0.789040\pi\)
\(492\) 1.13451e10 1.10374e10i 0.193618 0.188368i
\(493\) 3.34135e10 + 3.34135e10i 0.565632 + 0.565632i
\(494\) −5.90635e10 5.98809e10i −0.991770 1.00550i
\(495\) 2.22479e9i 0.0370569i
\(496\) 6.74568e8 2.45324e10i 0.0111455 0.405334i
\(497\) 1.12144e11 1.83802
\(498\) 2.72331e10 2.68613e10i 0.442771 0.436727i
\(499\) −1.39400e9 + 1.39400e9i −0.0224834 + 0.0224834i −0.718259 0.695776i \(-0.755061\pi\)
0.695776 + 0.718259i \(0.255061\pi\)
\(500\) −3.36531e10 + 3.27404e10i −0.538449 + 0.523847i
\(501\) −6.33066e9 + 6.33066e9i −0.100484 + 0.100484i
\(502\) −6.97195e8 + 1.01445e11i −0.0109784 + 1.59741i
\(503\) −5.63295e10 −0.879962 −0.439981 0.898007i \(-0.645015\pi\)
−0.439981 + 0.898007i \(0.645015\pi\)
\(504\) −4.86818e10 5.07318e10i −0.754474 0.786245i
\(505\) 9.30845e10i 1.43124i
\(506\) −2.83651e6 + 4.12726e8i −4.32696e−5 + 0.00629593i
\(507\) 4.77002e8 + 4.77002e8i 0.00721918 + 0.00721918i
\(508\) 8.48559e9 + 1.16642e8i 0.127417 + 0.00175146i
\(509\) 3.78176e10 + 3.78176e10i 0.563408 + 0.563408i 0.930274 0.366866i \(-0.119569\pi\)
−0.366866 + 0.930274i \(0.619569\pi\)
\(510\) −5.42358e10 + 5.34954e10i −0.801687 + 0.790743i
\(511\) 3.08883e10i 0.453013i
\(512\) 4.54955e10 + 5.15027e10i 0.662046 + 0.749463i
\(513\) 7.36225e10 1.06302
\(514\) −4.12117e9 4.17821e9i −0.0590430 0.0598601i
\(515\) 9.90488e10 9.90488e10i 1.40806 1.40806i
\(516\) 1.40285e8 1.02056e10i 0.00197885 0.143959i
\(517\) 2.50925e9 2.50925e9i 0.0351223 0.0351223i
\(518\) 3.70425e10 + 2.54579e8i 0.514495 + 0.00353593i
\(519\) 2.37380e10 0.327172
\(520\) −8.40443e10 + 8.06483e10i −1.14946 + 1.10302i
\(521\) 5.45288e10i 0.740074i 0.929017 + 0.370037i \(0.120655\pi\)
−0.929017 + 0.370037i \(0.879345\pi\)
\(522\) −2.86067e10 1.96604e8i −0.385289 0.00264795i
\(523\) −3.17681e10 3.17681e10i −0.424604 0.424604i 0.462181 0.886786i \(-0.347067\pi\)
−0.886786 + 0.462181i \(0.847067\pi\)
\(524\) −8.10763e10 8.33363e10i −1.07540 1.10537i
\(525\) −4.36848e10 4.36848e10i −0.575034 0.575034i
\(526\) 4.97307e10 + 5.04190e10i 0.649654 + 0.658645i
\(527\) 5.36301e10i 0.695291i
\(528\) 9.24045e8 + 2.54085e7i 0.0118893 + 0.000326921i
\(529\) −7.44909e10 −0.951219
\(530\) 5.01964e10 4.95111e10i 0.636164 0.627479i
\(531\) 4.97714e10 4.97714e10i 0.626039 0.626039i
\(532\) 1.02831e11 + 1.05698e11i 1.28375 + 1.31953i
\(533\) −3.73972e10 + 3.73972e10i −0.463373 + 0.463373i
\(534\) 1.36203e8 1.98182e10i 0.00167503 0.243725i
\(535\) 2.97696e10 0.363378
\(536\) −1.95869e7 + 9.49876e8i −0.000237305 + 0.0115082i
\(537\) 1.59575e8i 0.00191897i
\(538\) 1.16618e8 1.69684e10i 0.00139199 0.202541i
\(539\) −1.26019e9 1.26019e9i −0.0149308 0.0149308i
\(540\) 1.40138e9 1.01949e11i 0.0164809 1.19896i
\(541\) −2.81164e10 2.81164e10i −0.328224 0.328224i 0.523687 0.851911i \(-0.324556\pi\)
−0.851911 + 0.523687i \(0.824556\pi\)
\(542\) −7.01610e9 + 6.92032e9i −0.0813015 + 0.0801916i
\(543\) 3.13993e10i 0.361178i
\(544\) −1.02476e11 1.09772e11i −1.17011 1.25342i
\(545\) 1.86689e11 2.11608
\(546\) −3.47730e10 3.52543e10i −0.391265 0.396681i
\(547\) 4.72086e10 4.72086e10i 0.527317 0.527317i −0.392454 0.919771i \(-0.628374\pi\)
0.919771 + 0.392454i \(0.128374\pi\)
\(548\) 8.58320e10 + 1.17984e9i 0.951759 + 0.0130828i
\(549\) 7.18672e8 7.18672e8i 0.00791118 0.00791118i
\(550\) −3.85346e9 2.64834e7i −0.0421114 0.000289416i
\(551\) 5.99996e10 0.650941
\(552\) 1.76387e8 8.55397e9i 0.00189981 0.0921322i
\(553\) 1.57694e11i 1.68622i
\(554\) −8.16838e10 5.61383e8i −0.867155 0.00595964i
\(555\) 1.71811e10 + 1.71811e10i 0.181083 + 0.181083i
\(556\) −1.24575e11 + 1.21196e11i −1.30356 + 1.26821i
\(557\) −4.42829e10 4.42829e10i −0.460061 0.460061i 0.438614 0.898675i \(-0.355469\pi\)
−0.898675 + 0.438614i \(0.855469\pi\)
\(558\) −2.27998e10 2.31153e10i −0.235176 0.238431i
\(559\) 3.41035e10i 0.349262i
\(560\) 1.48322e11 1.40384e11i 1.50818 1.42746i
\(561\) −2.02005e9 −0.0203944
\(562\) 2.22928e10 2.19885e10i 0.223470 0.220419i
\(563\) −1.27892e11 + 1.27892e11i −1.27294 + 1.27294i −0.328406 + 0.944537i \(0.606511\pi\)
−0.944537 + 0.328406i \(0.893489\pi\)
\(564\) −5.27256e10 + 5.12957e10i −0.521080 + 0.506949i
\(565\) −3.29157e10 + 3.29157e10i −0.323005 + 0.323005i
\(566\) 5.26185e8 7.65623e10i 0.00512711 0.746018i
\(567\) −6.92801e10 −0.670311
\(568\) −1.04625e11 + 1.00397e11i −1.00518 + 0.964559i
\(569\) 6.51664e10i 0.621691i 0.950460 + 0.310846i \(0.100612\pi\)
−0.950460 + 0.310846i \(0.899388\pi\)
\(570\) −6.64754e8 + 9.67247e10i −0.00629740 + 0.916301i
\(571\) −1.63001e10 1.63001e10i −0.153337 0.153337i 0.626270 0.779607i \(-0.284581\pi\)
−0.779607 + 0.626270i \(0.784581\pi\)
\(572\) −3.08842e9 4.24532e7i −0.0288504 0.000396576i
\(573\) −2.91115e10 2.91115e10i −0.270051 0.270051i
\(574\) 6.60172e10 6.51159e10i 0.608148 0.599846i
\(575\) 3.56667e10i 0.326281i
\(576\) 9.08358e10 + 3.74775e9i 0.825215 + 0.0340472i
\(577\) −1.52954e11 −1.37993 −0.689965 0.723843i \(-0.742374\pi\)
−0.689965 + 0.723843i \(0.742374\pi\)
\(578\) 1.52069e11 + 1.54174e11i 1.36248 + 1.38133i
\(579\) −4.49513e10 + 4.49513e10i −0.399970 + 0.399970i
\(580\) 1.14207e9 8.30844e10i 0.0100921 0.734188i
\(581\) 1.58455e11 1.58455e11i 1.39060 1.39060i
\(582\) 6.53064e10 + 4.48827e8i 0.569198 + 0.00391189i
\(583\) 1.86960e9 0.0161836
\(584\) −2.76529e10 2.88174e10i −0.237733 0.247744i
\(585\) 1.54098e11i 1.31575i
\(586\) 1.67274e11 + 1.14961e9i 1.41853 + 0.00974901i
\(587\) 7.45208e10 + 7.45208e10i 0.627661 + 0.627661i 0.947479 0.319818i \(-0.103622\pi\)
−0.319818 + 0.947479i \(0.603622\pi\)
\(588\) 2.57616e10 + 2.64797e10i 0.215508 + 0.221516i
\(589\) 4.81510e10 + 4.81510e10i 0.400078 + 0.400078i
\(590\) 1.43568e11 + 1.45555e11i 1.18481 + 1.20121i
\(591\) 3.42120e10i 0.280433i
\(592\) −3.47869e10 + 3.29250e10i −0.283223 + 0.268064i
\(593\) −1.69443e11 −1.37027 −0.685133 0.728418i \(-0.740256\pi\)
−0.685133 + 0.728418i \(0.740256\pi\)
\(594\) 1.92485e9 1.89858e9i 0.0154615 0.0152504i
\(595\) −3.15569e11 + 3.15569e11i −2.51783 + 2.51783i
\(596\) −3.92350e10 4.03287e10i −0.310948 0.319616i
\(597\) 1.81783e10 1.81783e10i 0.143106 0.143106i
\(598\) −1.96469e8 + 2.85871e10i −0.00153634 + 0.223545i
\(599\) −2.07574e11 −1.61237 −0.806185 0.591663i \(-0.798472\pi\)
−0.806185 + 0.591663i \(0.798472\pi\)
\(600\) 7.98650e10 + 1.64686e9i 0.616242 + 0.0127072i
\(601\) 1.88953e11i 1.44829i −0.689647 0.724146i \(-0.742234\pi\)
0.689647 0.724146i \(-0.257766\pi\)
\(602\) 4.10928e8 5.97918e10i 0.00312881 0.455256i
\(603\) 8.88773e8 + 8.88773e8i 0.00672236 + 0.00672236i
\(604\) 1.26291e9 9.18754e10i 0.00948910 0.690322i
\(605\) 1.48985e11 + 1.48985e11i 1.11204 + 1.11204i
\(606\) −3.64285e10 + 3.59312e10i −0.270116 + 0.266429i
\(607\) 7.61960e10i 0.561277i −0.959813 0.280639i \(-0.909454\pi\)
0.959813 0.280639i \(-0.0905463\pi\)
\(608\) −1.90564e11 6.55084e9i −1.39452 0.0479383i
\(609\) 3.53241e10 0.256804
\(610\) 2.07304e9 + 2.10173e9i 0.0149723 + 0.0151795i
\(611\) 1.73801e11 1.73801e11i 1.24706 1.24706i
\(612\) −1.98651e11 2.73064e9i −1.41607 0.0194652i
\(613\) 2.80322e10 2.80322e10i 0.198525 0.198525i −0.600842 0.799368i \(-0.705168\pi\)
0.799368 + 0.600842i \(0.205168\pi\)
\(614\) −1.16329e11 7.99483e8i −0.818489 0.00562517i
\(615\) 6.08223e10 0.425170
\(616\) 5.41425e9 + 1.11645e8i 0.0376024 + 0.000775381i
\(617\) 1.36999e10i 0.0945315i −0.998882 0.0472658i \(-0.984949\pi\)
0.998882 0.0472658i \(-0.0150508\pi\)
\(618\) −7.69960e10 5.29166e8i −0.527855 0.00362775i
\(619\) 6.45196e10 + 6.45196e10i 0.439470 + 0.439470i 0.891833 0.452364i \(-0.149419\pi\)
−0.452364 + 0.891833i \(0.649419\pi\)
\(620\) 6.75936e10 6.57605e10i 0.457445 0.445039i
\(621\) −1.76944e10 1.76944e10i −0.118979 0.118979i
\(622\) −3.05310e10 3.09536e10i −0.203976 0.206799i
\(623\) 1.16104e11i 0.770720i
\(624\) 6.40032e10 + 1.75990e9i 0.422147 + 0.0116078i
\(625\) 4.49985e10 0.294902
\(626\) −2.86121e10 + 2.82215e10i −0.186317 + 0.183774i
\(627\) −1.81367e9 + 1.81367e9i −0.0117351 + 0.0117351i
\(628\) 1.53102e11 1.48950e11i 0.984333 0.957639i
\(629\) 7.40123e10 7.40123e10i 0.472826 0.472826i
\(630\) 1.85680e9 2.70173e11i 0.0117870 1.71506i
\(631\) −1.59056e10 −0.100331 −0.0501653 0.998741i \(-0.515975\pi\)
−0.0501653 + 0.998741i \(0.515975\pi\)
\(632\) 1.41176e11 + 1.47121e11i 0.884899 + 0.922162i
\(633\) 1.27492e10i 0.0794088i
\(634\) 1.02409e9 1.49009e11i 0.00633839 0.922265i
\(635\) 2.30588e10 + 2.30588e10i 0.141821 + 0.141821i
\(636\) −3.87522e10 5.32684e8i −0.236847 0.00325568i
\(637\) −8.72862e10 8.72862e10i −0.530137 0.530137i
\(638\) 1.56869e9 1.54727e9i 0.00946789 0.00933864i
\(639\) 1.91834e11i 1.15059i
\(640\) −1.26986e10 + 2.63758e11i −0.0756895 + 1.57212i
\(641\) −1.62329e11 −0.961531 −0.480765 0.876849i \(-0.659641\pi\)
−0.480765 + 0.876849i \(0.659641\pi\)
\(642\) −1.14912e10 1.16503e10i −0.0676437 0.0685799i
\(643\) 1.41233e11 1.41233e11i 0.826215 0.826215i −0.160776 0.986991i \(-0.551400\pi\)
0.986991 + 0.160776i \(0.0513996\pi\)
\(644\) 6.88917e8 5.01179e10i 0.00400519 0.291373i
\(645\) 2.77327e10 2.77327e10i 0.160234 0.160234i
\(646\) 4.16669e11 + 2.86361e9i 2.39255 + 0.0164431i
\(647\) 1.50305e11 0.857739 0.428870 0.903366i \(-0.358912\pi\)
0.428870 + 0.903366i \(0.358912\pi\)
\(648\) 6.46352e10 6.20234e10i 0.366580 0.351768i
\(649\) 5.42129e9i 0.0305579i
\(650\) −2.66906e11 1.83435e9i −1.49522 0.0102761i
\(651\) 2.83484e10 + 2.83484e10i 0.157835 + 0.157835i
\(652\) −4.60849e10 4.73695e10i −0.255017 0.262125i
\(653\) −8.21695e10 8.21695e10i −0.451916 0.451916i 0.444074 0.895990i \(-0.353533\pi\)
−0.895990 + 0.444074i \(0.853533\pi\)
\(654\) −7.20631e10 7.30604e10i −0.393914 0.399366i
\(655\) 4.46776e11i 2.42731i
\(656\) −3.29559e9 + 1.19852e11i −0.0177958 + 0.647190i
\(657\) −5.28377e10 −0.283585
\(658\) −3.06811e11 + 3.02623e11i −1.63669 + 1.61435i
\(659\) 3.54829e10 3.54829e10i 0.188139 0.188139i −0.606752 0.794891i \(-0.707528\pi\)
0.794891 + 0.606752i \(0.207528\pi\)
\(660\) 2.47696e9 + 2.54600e9i 0.0130540 + 0.0134179i
\(661\) −2.89050e10 + 2.89050e10i −0.151414 + 0.151414i −0.778749 0.627335i \(-0.784146\pi\)
0.627335 + 0.778749i \(0.284146\pi\)
\(662\) −1.53759e9 + 2.23726e11i −0.00800586 + 1.16489i
\(663\) −1.39917e11 −0.724130
\(664\) −5.97354e9 + 2.89689e11i −0.0307298 + 1.49025i
\(665\) 5.66658e11i 2.89758i
\(666\) −4.35485e8 + 6.33651e10i −0.00221348 + 0.322072i
\(667\) −1.44203e10 1.44203e10i −0.0728570 0.0728570i
\(668\) 9.32125e8 6.78110e10i 0.00468132 0.340561i
\(669\) 2.02455e10 + 2.02455e10i 0.101071 + 0.101071i
\(670\) −2.59918e9 + 2.56370e9i −0.0128985 + 0.0127224i
\(671\) 7.82805e7i 0.000386157i
\(672\) −1.12192e11 3.85674e9i −0.550156 0.0189122i
\(673\) 1.55445e11 0.757736 0.378868 0.925451i \(-0.376313\pi\)
0.378868 + 0.925451i \(0.376313\pi\)
\(674\) −1.60402e11 1.62622e11i −0.777266 0.788023i
\(675\) 1.65206e11 1.65206e11i 0.795811 0.795811i
\(676\) −5.10941e9 7.02336e7i −0.0244672 0.000336324i
\(677\) 8.73806e10 8.73806e10i 0.415969 0.415969i −0.467843 0.883812i \(-0.654969\pi\)
0.883812 + 0.467843i \(0.154969\pi\)
\(678\) 2.55872e10 + 1.75851e8i 0.121089 + 0.000832198i
\(679\) 3.82595e11 1.79995
\(680\) 1.18965e10 5.76927e11i 0.0556397 2.69827i
\(681\) 1.32488e10i 0.0616010i
\(682\) 2.50062e9 + 1.71859e7i 0.0115587 + 7.94390e-5i
\(683\) 1.49587e11 + 1.49587e11i 0.687400 + 0.687400i 0.961657 0.274256i \(-0.0884316\pi\)
−0.274256 + 0.961657i \(0.588432\pi\)
\(684\) −1.80807e11 + 1.75904e11i −0.826022 + 0.803621i
\(685\) 2.33240e11 + 2.33240e11i 1.05935 + 1.05935i
\(686\) −5.32000e10 5.39363e10i −0.240223 0.243548i
\(687\) 3.23727e10i 0.145329i
\(688\) 5.31456e10 + 5.61510e10i 0.237200 + 0.250613i
\(689\) 1.29496e11 0.574620
\(690\) 2.34066e10 2.30871e10i 0.103262 0.101853i
\(691\) −1.35304e11 + 1.35304e11i −0.593469 + 0.593469i −0.938567 0.345098i \(-0.887846\pi\)
0.345098 + 0.938567i \(0.387846\pi\)
\(692\) −1.28883e11 + 1.25388e11i −0.562045 + 0.546802i
\(693\) 5.06597e9 5.06597e9i 0.0219649 0.0219649i
\(694\) −1.00365e9 + 1.46036e11i −0.00432658 + 0.629537i
\(695\) −6.67860e11 −2.86250
\(696\) −3.29558e10 + 3.16241e10i −0.140441 + 0.134766i
\(697\) 2.62009e11i 1.11016i
\(698\) −2.45965e9 + 3.57890e11i −0.0103622 + 1.50775i
\(699\) −3.95031e10 3.95031e10i −0.165471 0.165471i
\(700\) 4.67931e11 + 6.43214e9i 1.94890 + 0.0267894i
\(701\) −6.13294e10 6.13294e10i −0.253978 0.253978i 0.568621 0.822600i \(-0.307477\pi\)
−0.822600 + 0.568621i \(0.807477\pi\)
\(702\) 1.33323e11 1.31503e11i 0.548982 0.541487i
\(703\) 1.32902e11i 0.544138i
\(704\) −5.15120e9 + 4.74298e9i −0.0209709 + 0.0193091i
\(705\) −2.82668e11 −1.14425
\(706\) −3.16486e11 3.20866e11i −1.27390 1.29153i
\(707\) −2.11958e11 + 2.11958e11i −0.848345 + 0.848345i
\(708\) 1.54463e9 1.12370e11i 0.00614739 0.447215i
\(709\) −2.97366e11 + 2.97366e11i −1.17681 + 1.17681i −0.196255 + 0.980553i \(0.562878\pi\)
−0.980553 + 0.196255i \(0.937122\pi\)
\(710\) −5.57182e11 3.82931e9i −2.19262 0.0150691i
\(711\) 2.69752e11 1.05557
\(712\) 1.03943e11 + 1.08320e11i 0.404460 + 0.421492i
\(713\) 2.31452e10i 0.0895578i
\(714\) 2.45309e11 + 1.68592e9i 0.943890 + 0.00648701i
\(715\) −8.39249e9 8.39249e9i −0.0321120 0.0321120i
\(716\) −8.42900e8 8.66395e8i −0.00320718 0.00329658i
\(717\) 1.40979e11 + 1.40979e11i 0.533432 + 0.533432i
\(718\) −2.42377e10 2.45731e10i −0.0911996 0.0924619i
\(719\) 2.39540e11i 0.896317i −0.893954 0.448158i \(-0.852080\pi\)
0.893954 0.448158i \(-0.147920\pi\)
\(720\) 2.40141e11 + 2.53721e11i 0.893587 + 0.944119i
\(721\) −4.51079e11 −1.66921
\(722\) 1.83208e11 1.80707e11i 0.674210 0.665006i
\(723\) 7.65293e10 7.65293e10i 0.280075 0.280075i
\(724\) 1.65856e11 + 1.70479e11i 0.603637 + 0.620464i
\(725\) 1.34637e11 1.34637e11i 0.487316 0.487316i
\(726\) 7.95947e8 1.15814e11i 0.00286509 0.416883i
\(727\) 3.85457e11 1.37987 0.689935 0.723871i \(-0.257639\pi\)
0.689935 + 0.723871i \(0.257639\pi\)
\(728\) 3.75014e11 + 7.73297e9i 1.33512 + 0.0275309i
\(729\) 2.87378e10i 0.101752i
\(730\) 1.05472e9 1.53467e11i 0.00371405 0.540411i
\(731\) −1.19466e11 1.19466e11i −0.418385 0.418385i
\(732\) 2.23036e7 1.62256e9i 7.76838e−5 0.00565141i
\(733\) 1.71097e11 + 1.71097e11i 0.592688 + 0.592688i 0.938357 0.345669i \(-0.112348\pi\)
−0.345669 + 0.938357i \(0.612348\pi\)
\(734\) 3.31038e11 3.26519e11i 1.14049 1.12493i
\(735\) 1.41961e11i 0.486429i
\(736\) 4.42256e10 + 4.73745e10i 0.150717 + 0.161448i
\(737\) −9.68085e7 −0.000328128
\(738\) 1.11388e11 + 1.12929e11i 0.375502 + 0.380699i
\(739\) −1.02838e9 + 1.02838e9i −0.00344807 + 0.00344807i −0.708829 0.705381i \(-0.750776\pi\)
0.705381 + 0.708829i \(0.250776\pi\)
\(740\) −1.84035e11 2.52974e9i −0.613726 0.00843623i
\(741\) −1.25622e11 + 1.25622e11i −0.416672 + 0.416672i
\(742\) −2.27039e11 1.56036e9i −0.749006 0.00514764i
\(743\) −5.54577e11 −1.81973 −0.909864 0.414907i \(-0.863814\pi\)
−0.909864 + 0.414907i \(0.863814\pi\)
\(744\) −5.18268e10 1.06869e9i −0.169146 0.00348788i
\(745\) 2.16207e11i 0.701850i
\(746\) 4.52584e11 + 3.11045e9i 1.46132 + 0.0100431i
\(747\) 2.71054e11 + 2.71054e11i 0.870511 + 0.870511i
\(748\) 1.09676e10 1.06702e10i 0.0350353 0.0340852i
\(749\) −6.77870e10 6.77870e10i −0.215387 0.215387i
\(750\) 6.96425e10 + 7.06064e10i 0.220105 + 0.223151i
\(751\) 1.50943e11i 0.474519i 0.971446 + 0.237259i \(0.0762491\pi\)
−0.971446 + 0.237259i \(0.923751\pi\)
\(752\) 1.53161e10 5.57008e11i 0.0478934 1.74177i
\(753\) 2.14281e11 0.666506
\(754\) 1.08654e11 1.07170e11i 0.336170 0.331581i
\(755\) 2.49663e11 2.49663e11i 0.768362 0.768362i
\(756\) −2.35333e11 + 2.28951e11i −0.720438 + 0.700900i
\(757\) −1.83096e11 + 1.83096e11i −0.557564 + 0.557564i −0.928613 0.371049i \(-0.878998\pi\)
0.371049 + 0.928613i \(0.378998\pi\)
\(758\) −2.06385e9 + 3.00300e11i −0.00625175 + 0.909659i
\(759\) 8.71796e8 0.00262693
\(760\) −5.07304e11 5.28667e11i −1.52060 1.58463i
\(761\) 2.59965e11i 0.775133i 0.921842 + 0.387566i \(0.126684\pi\)
−0.921842 + 0.387566i \(0.873316\pi\)
\(762\) 1.23191e8 1.79249e10i 0.000365392 0.0531662i
\(763\) −4.25101e11 4.25101e11i −1.25428 1.25428i
\(764\) 3.11829e11 + 4.28637e9i 0.915256 + 0.0125810i
\(765\) −5.39815e11 5.39815e11i −1.57616 1.57616i
\(766\) −5.79894e10 + 5.71977e10i −0.168435 + 0.166136i
\(767\) 3.75501e11i 1.08500i
\(768\) 1.08123e11 9.68426e10i 0.310794 0.278369i
\(769\) 2.77968e11 0.794857 0.397429 0.917633i \(-0.369903\pi\)
0.397429 + 0.917633i \(0.369903\pi\)
\(770\) 1.46130e10 + 1.48152e10i 0.0415696 + 0.0421450i
\(771\) −8.76534e9 + 8.76534e9i −0.0248057 + 0.0248057i
\(772\) 6.61861e9 4.81496e11i 0.0186336 1.35558i
\(773\) 1.64912e11 1.64912e11i 0.461884 0.461884i −0.437388 0.899273i \(-0.644096\pi\)
0.899273 + 0.437388i \(0.144096\pi\)
\(774\) 1.02280e11 + 7.02935e8i 0.284989 + 0.00195863i
\(775\) 2.16098e11 0.599023
\(776\) −3.56944e11 + 3.42521e11i −0.984358 + 0.944582i
\(777\) 7.82444e10i 0.214669i
\(778\) 1.77937e11 + 1.22289e9i 0.485677 + 0.00333788i
\(779\) −2.35241e11 2.35241e11i −0.638797 0.638797i
\(780\) 1.71564e11 + 1.76347e11i 0.463499 + 0.476419i
\(781\) −1.04476e10 1.04476e10i −0.0280811 0.0280811i
\(782\) −9.94540e10 1.00830e11i −0.265947 0.269628i
\(783\) 1.33588e11i 0.355401i
\(784\) −2.79739e11 7.69200e9i −0.740439 0.0203599i
\(785\) 8.20797e11 2.16151
\(786\) −1.74845e11 + 1.72458e11i −0.458103 + 0.451849i
\(787\) −4.59612e11 + 4.59612e11i −1.19810 + 1.19810i −0.223363 + 0.974735i \(0.571704\pi\)
−0.974735 + 0.223363i \(0.928296\pi\)
\(788\) −1.80713e11 1.85750e11i −0.468688 0.481752i
\(789\) 1.05773e11 1.05773e11i 0.272939 0.272939i
\(790\) −5.38468e9 + 7.83496e11i −0.0138246 + 2.01154i
\(791\) 1.49902e11 0.382913
\(792\) −1.90980e8 + 9.26166e9i −0.000485386 + 0.0235390i
\(793\) 5.42203e9i 0.0137110i
\(794\) −2.96680e9 + 4.31683e11i −0.00746459 + 1.08613i
\(795\) −1.05305e11 1.05305e11i −0.263622 0.263622i
\(796\) −2.67657e9 + 1.94717e11i −0.00666694 + 0.485012i
\(797\) −3.31197e11 3.31197e11i −0.820829 0.820829i 0.165398 0.986227i \(-0.447109\pi\)
−0.986227 + 0.165398i \(0.947109\pi\)
\(798\) 2.21761e11 2.18734e11i 0.546857 0.539391i
\(799\) 1.21767e12i 2.98774i
\(800\) −4.42316e11 + 4.12917e11i −1.07987 + 1.00810i
\(801\) 1.98609e11 0.482468
\(802\) −1.50749e11 1.52835e11i −0.364381 0.369424i
\(803\) 2.87764e9 2.87764e9i 0.00692110 0.00692110i
\(804\) 2.00660e9 + 2.75826e7i 0.00480216 + 6.60101e-5i
\(805\) 1.36191e11 1.36191e11i 0.324313 0.324313i
\(806\) 1.73203e11 + 1.19036e9i 0.410409 + 0.00282059i
\(807\) −3.58422e10 −0.0845085
\(808\) 7.99053e9 3.87504e11i 0.0187469 0.909141i
\(809\) 4.11196e11i 0.959964i −0.877278 0.479982i \(-0.840643\pi\)
0.877278 0.479982i \(-0.159357\pi\)
\(810\) 3.44216e11 + 2.36567e9i 0.799632 + 0.00549558i
\(811\) 4.48542e11 + 4.48542e11i 1.03686 + 1.03686i 0.999294 + 0.0375659i \(0.0119604\pi\)
0.0375659 + 0.999294i \(0.488040\pi\)
\(812\) −1.91788e11 + 1.86587e11i −0.441161 + 0.429197i
\(813\) 1.47189e10 + 1.47189e10i 0.0336908 + 0.0336908i
\(814\) −3.42727e9 3.47470e9i −0.00780639 0.00791444i
\(815\) 2.53954e11i 0.575604i
\(816\) −2.30372e11 + 2.18042e11i −0.519599 + 0.491789i
\(817\) −2.14522e11 −0.481486
\(818\) −1.95793e11 + 1.93120e11i −0.437305 + 0.431335i
\(819\) 3.50890e11 3.50890e11i 0.779894 0.779894i
\(820\) −3.30227e11 + 3.21272e11i −0.730394 + 0.710587i
\(821\) −3.88002e11 + 3.88002e11i −0.854006 + 0.854006i −0.990624 0.136618i \(-0.956377\pi\)
0.136618 + 0.990624i \(0.456377\pi\)
\(822\) 1.24608e9 1.81310e11i 0.00272935 0.397133i
\(823\) 6.43194e11 1.40198 0.700991 0.713170i \(-0.252741\pi\)
0.700991 + 0.713170i \(0.252741\pi\)
\(824\) 4.20836e11 4.03831e11i 0.912859 0.875973i
\(825\) 8.13961e9i 0.0175706i
\(826\) 4.52457e9 6.58346e11i 0.00971980 1.41428i
\(827\) −5.21402e11 5.21402e11i −1.11468 1.11468i −0.992509 0.122173i \(-0.961014\pi\)
−0.122173 0.992509i \(-0.538986\pi\)
\(828\) 8.57320e10 + 1.17847e9i 0.182399 + 0.00250724i
\(829\) 4.52099e11 + 4.52099e11i 0.957227 + 0.957227i 0.999122 0.0418949i \(-0.0133395\pi\)
−0.0418949 + 0.999122i \(0.513339\pi\)
\(830\) −7.92689e11 + 7.81867e11i −1.67028 + 1.64748i
\(831\) 1.72540e11i 0.361814i
\(832\) −3.56794e11 + 3.28519e11i −0.744601 + 0.685594i
\(833\) 6.11537e11 1.27011
\(834\) 2.57798e11 + 2.61366e11i 0.532862 + 0.540238i
\(835\) 1.84270e11 1.84270e11i 0.379061 0.379061i
\(836\) 2.67044e8 1.94272e10i 0.000546712 0.0397727i
\(837\) −1.07207e11 + 1.07207e11i −0.218434 + 0.218434i
\(838\) −2.64061e10 1.81480e8i −0.0535462 0.000368003i
\(839\) 2.15602e11 0.435117 0.217558 0.976047i \(-0.430191\pi\)
0.217558 + 0.976047i \(0.430191\pi\)
\(840\) −2.98670e11 3.11247e11i −0.599894 0.625155i
\(841\) 3.91377e11i 0.782369i
\(842\) −7.44757e10 5.11844e8i −0.148172 0.00101833i
\(843\) −4.67674e10 4.67674e10i −0.0926047 0.0926047i
\(844\) 6.73432e10 + 6.92204e10i 0.132716 + 0.136416i
\(845\) −1.38843e10 1.38843e10i −0.0272332 0.0272332i
\(846\) −5.17668e11 5.24833e11i −1.01058 1.02457i
\(847\) 6.78492e11i 1.31829i
\(848\) 2.13214e11 2.01802e11i 0.412318 0.390250i
\(849\) −1.61722e11 −0.311270
\(850\) 9.41413e11 9.28562e11i 1.80345 1.77883i
\(851\) −3.19416e10 + 3.19416e10i −0.0609029 + 0.0609029i
\(852\) 2.13577e11 + 2.19530e11i 0.405318 + 0.416616i
\(853\) 1.70081e11 1.70081e11i 0.321262 0.321262i −0.527989 0.849251i \(-0.677054\pi\)
0.849251 + 0.527989i \(0.177054\pi\)
\(854\) 6.53324e7 9.50616e9i 0.000122828 0.0178720i
\(855\) −9.69330e11 −1.81387
\(856\) 1.23929e11 + 2.55547e9i 0.230822 + 0.00475967i
\(857\) 7.04199e11i 1.30548i −0.757580 0.652742i \(-0.773618\pi\)
0.757580 0.652742i \(-0.226382\pi\)
\(858\) −4.48367e7 + 6.52394e9i −8.27340e−5 + 0.0120382i
\(859\) 5.07217e10 + 5.07217e10i 0.0931583 + 0.0931583i 0.752150 0.658992i \(-0.229017\pi\)
−0.658992 + 0.752150i \(0.729017\pi\)
\(860\) −4.08335e9 + 2.97059e11i −0.00746489 + 0.543062i
\(861\) −1.38495e11 1.38495e11i −0.252013 0.252013i
\(862\) 1.36960e11 1.35090e11i 0.248064 0.244677i
\(863\) 1.98911e11i 0.358605i 0.983794 + 0.179303i \(0.0573841\pi\)
−0.983794 + 0.179303i \(0.942616\pi\)
\(864\) 1.45853e10 4.24285e11i 0.0261734 0.761382i
\(865\) −6.90956e11 −1.23420
\(866\) 4.90219e11 + 4.97003e11i 0.871602 + 0.883665i
\(867\) 3.23436e11 3.23436e11i 0.572416 0.572416i
\(868\) −3.03654e11 4.17401e9i −0.534934 0.00735316i
\(869\) −1.46912e10 + 1.46912e10i −0.0257620 + 0.0257620i
\(870\) −1.75506e11 1.20619e9i −0.306349 0.00210542i
\(871\) −6.70536e9 −0.0116506
\(872\) 7.77173e11 + 1.60257e10i 1.34416 + 0.0277173i
\(873\) 6.54470e11i 1.12676i
\(874\) −1.79822e11 1.23585e9i −0.308175 0.00211798i
\(875\) 4.10821e11 + 4.10821e11i 0.700843 + 0.700843i
\(876\) −6.04663e10 + 5.88265e10i −0.102683 + 0.0998980i
\(877\) −2.40245e11 2.40245e11i −0.406122 0.406122i 0.474262 0.880384i \(-0.342715\pi\)
−0.880384 + 0.474262i \(0.842715\pi\)
\(878\) −7.43670e9 7.53962e9i −0.0125142 0.0126874i
\(879\) 3.53330e11i 0.591869i
\(880\) −2.68967e10 7.39579e8i −0.0448506 0.00123326i
\(881\) 9.94503e10 0.165083 0.0825415 0.996588i \(-0.473696\pi\)
0.0825415 + 0.996588i \(0.473696\pi\)
\(882\) −2.63581e11 + 2.59982e11i −0.435551 + 0.429605i
\(883\) −7.99563e11 + 7.99563e11i −1.31525 + 1.31525i −0.397769 + 0.917486i \(0.630215\pi\)
−0.917486 + 0.397769i \(0.869785\pi\)
\(884\) 7.59663e11 7.39062e11i 1.24398 1.21024i
\(885\) 3.05355e11 3.05355e11i 0.497773 0.497773i
\(886\) 6.29311e9 9.15677e11i 0.0102125 1.48596i
\(887\) 2.85580e10 0.0461352 0.0230676 0.999734i \(-0.492657\pi\)
0.0230676 + 0.999734i \(0.492657\pi\)
\(888\) 7.00487e10 + 7.29984e10i 0.112654 + 0.117398i
\(889\) 1.05012e11i 0.168125i
\(890\) −3.96455e9 + 5.76860e11i −0.00631879 + 0.919413i
\(891\) 6.45434e9 + 6.45434e9i 0.0102410 + 0.0102410i
\(892\) −2.16861e11 2.98095e9i −0.342548 0.00470863i
\(893\) 1.09327e12 + 1.09327e12i 1.71918 + 1.71918i
\(894\) −8.46122e10 + 8.34571e10i −0.132459 + 0.130651i
\(895\) 4.64485e9i 0.00723901i
\(896\) 6.29506e11 5.71675e11i 0.976715 0.886987i
\(897\) 6.03842e10 0.0932725
\(898\) −7.95585e11 8.06596e11i −1.22344 1.24037i
\(899\) −8.73697e10 + 8.73697e10i −0.133759 + 0.133759i
\(900\) −1.10029e10 + 8.00445e11i −0.0167701 + 1.22000i
\(901\) −4.53633e11 + 4.53633e11i −0.688344 + 0.688344i
\(902\) −1.22167e10 8.39612e7i −0.0184556 0.000126839i
\(903\) −1.26298e11 −0.189952
\(904\) −1.39851e11 + 1.34200e11i −0.209408 + 0.200946i
\(905\) 9.13958e11i 1.36249i
\(906\) −1.94076e11 1.33382e9i −0.288045 0.00197963i
\(907\) −6.40471e10 6.40471e10i −0.0946390 0.0946390i 0.658202 0.752841i \(-0.271317\pi\)
−0.752841 + 0.658202i \(0.771317\pi\)
\(908\) −6.99820e10 7.19327e10i −0.102954 0.105824i
\(909\) −3.62577e11 3.62577e11i −0.531062 0.531062i
\(910\) 1.01216e12 + 1.02616e12i 1.47599 + 1.49641i
\(911\) 7.81198e9i 0.0113419i 0.999984 + 0.00567097i \(0.00180514\pi\)
−0.999984 + 0.00567097i \(0.998195\pi\)
\(912\) −1.10703e10 + 4.02601e11i −0.0160023 + 0.581963i
\(913\) −2.95243e10 −0.0424909
\(914\) −8.61066e11 + 8.49311e11i −1.23382 + 1.21698i
\(915\) 4.40916e9 4.40916e9i 0.00629030 0.00629030i
\(916\) 1.70997e11 + 1.75764e11i 0.242889 + 0.249659i
\(917\) −1.01733e12 + 1.01733e12i −1.43875 + 1.43875i
\(918\) −6.37576e9 + 9.27703e11i −0.00897762 + 1.30629i
\(919\) 4.51092e11 0.632417 0.316209 0.948690i \(-0.397590\pi\)
0.316209 + 0.948690i \(0.397590\pi\)
\(920\) −5.13420e9 + 2.48985e11i −0.00716674 + 0.347554i
\(921\) 2.45719e11i 0.341508i
\(922\) 4.66534e9 6.78828e11i 0.00645594 0.939369i
\(923\) −7.23647e11 7.23647e11i −0.997057 0.997057i
\(924\) 1.57220e8 1.14375e10i 0.000215684 0.0156908i
\(925\) −2.98226e11 2.98226e11i −0.407360 0.407360i
\(926\) 9.24102e11 9.11486e11i 1.25683 1.23967i
\(927\) 7.71618e11i 1.04492i
\(928\) 1.18865e10 3.45776e11i 0.0160273 0.466234i
\(929\) −7.44358e11 −0.999353 −0.499676 0.866212i \(-0.666548\pi\)
−0.499676 + 0.866212i \(0.666548\pi\)
\(930\) −1.39880e11 1.41816e11i −0.186992 0.189580i
\(931\) 5.49059e11 5.49059e11i 0.730837 0.730837i
\(932\) 4.23138e11 + 5.81643e9i 0.560814 + 0.00770890i
\(933\) −6.49366e10 + 6.49366e10i −0.0856965 + 0.0856965i
\(934\) 5.37257e10 + 3.69237e8i 0.0705983 + 0.000485197i
\(935\) 5.87987e10 0.0769346
\(936\) −1.32281e10 + 6.41501e11i −0.0172343 + 0.835783i
\(937\) 1.06265e12i 1.37859i 0.724483 + 0.689293i \(0.242079\pi\)
−0.724483 + 0.689293i \(0.757921\pi\)
\(938\) 1.17562e10 + 8.07958e7i 0.0151864 + 0.000104370i
\(939\) 6.00245e10 + 6.00245e10i 0.0772087 + 0.0772087i
\(940\) 1.53471e12 1.49309e12i 1.96569 1.91238i
\(941\) −7.14601e11 7.14601e11i −0.911392 0.911392i 0.0849900 0.996382i \(-0.472914\pi\)
−0.996382 + 0.0849900i \(0.972914\pi\)
\(942\) −3.16833e11 3.21218e11i −0.402371 0.407940i
\(943\) 1.13076e11i 0.142995i
\(944\) 5.85167e11 + 6.18257e11i 0.736871 + 0.778541i
\(945\) −1.26165e12 −1.58202
\(946\) −5.60867e9 + 5.53210e9i −0.00700318 + 0.00690757i
\(947\) 5.62085e11 5.62085e11i 0.698879 0.698879i −0.265290 0.964169i \(-0.585468\pi\)
0.964169 + 0.265290i \(0.0854676\pi\)
\(948\) 3.08698e11 3.00327e11i 0.382209 0.371844i
\(949\) 1.99318e11 1.99318e11i 0.245743 0.245743i
\(950\) 1.15387e10 1.67893e12i 0.0141664 2.06128i
\(951\) −3.14750e11 −0.384808
\(952\) −1.34078e12 + 1.28660e12i −1.63234 + 1.56638i
\(953\) 5.74014e11i 0.695906i 0.937512 + 0.347953i \(0.113123\pi\)
−0.937512 + 0.347953i \(0.886877\pi\)
\(954\) 2.66916e9 3.88375e11i 0.00322241 0.468875i
\(955\) 8.47365e11 + 8.47365e11i 1.01873 + 1.01873i
\(956\) −1.51010e12 2.07578e10i −1.80790 0.0248513i
\(957\) −3.29090e9 3.29090e9i −0.00392344 0.00392344i
\(958\) −7.57883e11 + 7.47537e11i −0.899788 + 0.887505i
\(959\) 1.06220e12i 1.25583i
\(960\) 5.57291e11 + 2.29930e10i 0.656141 + 0.0270714i
\(961\) 7.12659e11 0.835580
\(962\) −2.37387e11 2.40672e11i −0.277176 0.281013i
\(963\) 1.15957e11 1.15957e11i 0.134831 0.134831i
\(964\) −1.12682e10 + 8.19745e11i −0.0130480 + 0.949228i
\(965\) 1.30842e12 1.30842e12i 1.50882 1.50882i
\(966\) −1.05868e11 7.27595e8i −0.121579 0.000835567i
\(967\) 7.84920e10 0.0897676 0.0448838 0.998992i \(-0.485708\pi\)
0.0448838 + 0.998992i \(0.485708\pi\)
\(968\) 6.07424e11 + 6.33002e11i 0.691816 + 0.720948i
\(969\) 8.80125e11i 0.998273i
\(970\) −1.90091e12 1.30642e10i −2.14721 0.0147570i
\(971\) 6.36692e11 + 6.36692e11i 0.716230 + 0.716230i 0.967831 0.251601i \(-0.0809571\pi\)
−0.251601 + 0.967831i \(0.580957\pi\)
\(972\) −6.06138e11 6.23034e11i −0.679058 0.697986i
\(973\) 1.52075e12 + 1.52075e12i 1.69671 + 1.69671i
\(974\) 5.89860e11 + 5.98024e11i 0.655411 + 0.664482i
\(975\) 5.63783e11i 0.623869i
\(976\) 8.44950e9 + 8.92731e9i 0.00931176 + 0.00983833i
\(977\) 6.26449e11 0.687555 0.343778 0.939051i \(-0.388293\pi\)
0.343778 + 0.939051i \(0.388293\pi\)
\(978\) −9.93844e10 + 9.80276e10i −0.108633 + 0.107150i
\(979\) −1.08166e10 + 1.08166e10i −0.0117750 + 0.0117750i
\(980\) −7.49858e11 7.70760e11i −0.812970 0.835632i
\(981\) 7.27180e11 7.27180e11i 0.785174 0.785174i
\(982\) 1.56371e9 2.27528e11i 0.00168156 0.244674i
\(983\) −5.92199e11 −0.634240 −0.317120 0.948385i \(-0.602716\pi\)
−0.317120 + 0.948385i \(0.602716\pi\)
\(984\) 2.53199e11 + 5.22109e9i 0.270073 + 0.00556904i
\(985\) 9.95828e11i 1.05789i
\(986\) −5.19601e9 + 7.56043e11i −0.00549746 + 0.799906i
\(987\) 6.43650e11 + 6.43650e11i 0.678236 + 0.678236i
\(988\) 1.84966e10 1.34561e12i 0.0194117 1.41218i
\(989\) 5.15583e10 + 5.15583e10i 0.0538906 + 0.0538906i
\(990\) −2.53431e10 + 2.49971e10i −0.0263826 + 0.0260225i
\(991\) 9.90287e11i 1.02675i −0.858163 0.513377i \(-0.828394\pi\)
0.858163 0.513377i \(-0.171606\pi\)
\(992\) 2.87032e11 2.67954e11i 0.296404 0.276703i
\(993\) 4.72574e11 0.486041
\(994\) 1.26001e12 + 1.27745e12i 1.29071 + 1.30858i
\(995\) −5.29126e11 + 5.29126e11i −0.539842 + 0.539842i
\(996\) 6.11965e11 + 8.41202e9i 0.621855 + 0.00854797i
\(997\) 3.70968e11 3.70968e11i 0.375454 0.375454i −0.494005 0.869459i \(-0.664468\pi\)
0.869459 + 0.494005i \(0.164468\pi\)
\(998\) −3.15420e10 2.16776e8i −0.0317956 0.000218519i
\(999\) 2.95902e11 0.297089
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 16.9.f.a.3.12 30
4.3 odd 2 64.9.f.a.47.6 30
8.3 odd 2 128.9.f.a.95.10 30
8.5 even 2 128.9.f.b.95.6 30
16.3 odd 4 128.9.f.b.31.6 30
16.5 even 4 64.9.f.a.15.6 30
16.11 odd 4 inner 16.9.f.a.11.12 yes 30
16.13 even 4 128.9.f.a.31.10 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
16.9.f.a.3.12 30 1.1 even 1 trivial
16.9.f.a.11.12 yes 30 16.11 odd 4 inner
64.9.f.a.15.6 30 16.5 even 4
64.9.f.a.47.6 30 4.3 odd 2
128.9.f.a.31.10 30 16.13 even 4
128.9.f.a.95.10 30 8.3 odd 2
128.9.f.b.31.6 30 16.3 odd 4
128.9.f.b.95.6 30 8.5 even 2