Properties

Label 14.12.c.a.9.4
Level $14$
Weight $12$
Character 14.9
Analytic conductor $10.757$
Analytic rank $0$
Dimension $8$
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] = [14,12,Mod(9,14)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(14, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 12, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("14.9");
 
S:= CuspForms(chi, 12);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 14.c (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(10.7568045278\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 101803 x^{6} + 6576400 x^{5} + 8539617914 x^{4} + 333205096780 x^{3} + 195840371083183 x^{2} + \cdots + 33\!\cdots\!81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{12}\cdot 3\cdot 7^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 9.4
Root \(-115.837 + 200.636i\) of defining polynomial
Character \(\chi\) \(=\) 14.9
Dual form 14.12.c.a.11.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-16.0000 + 27.7128i) q^{2} +(265.175 + 459.296i) q^{3} +(-512.000 - 886.810i) q^{4} +(6622.39 - 11470.3i) q^{5} -16971.2 q^{6} +(4344.64 - 44254.4i) q^{7} +32768.0 q^{8} +(-52061.7 + 90173.6i) q^{9} +O(q^{10})\) \(q+(-16.0000 + 27.7128i) q^{2} +(265.175 + 459.296i) q^{3} +(-512.000 - 886.810i) q^{4} +(6622.39 - 11470.3i) q^{5} -16971.2 q^{6} +(4344.64 - 44254.4i) q^{7} +32768.0 q^{8} +(-52061.7 + 90173.6i) q^{9} +(211917. + 367050. i) q^{10} +(-268422. - 464921. i) q^{11} +(271539. - 470319. i) q^{12} +1.10710e6 q^{13} +(1.15690e6 + 828472. i) q^{14} +7.02436e6 q^{15} +(-524288. + 908093. i) q^{16} +(458258. + 793726. i) q^{17} +(-1.66598e6 - 2.88555e6i) q^{18} +(-1.86283e6 + 3.22652e6i) q^{19} -1.35627e7 q^{20} +(2.14780e7 - 9.73967e6i) q^{21} +1.71790e7 q^{22} +(-1.12882e7 + 1.95517e7i) q^{23} +(8.68924e6 + 1.50502e7i) q^{24} +(-6.32981e7 - 1.09636e8i) q^{25} +(-1.77135e7 + 3.06807e7i) q^{26} +3.87280e7 q^{27} +(-4.14697e7 + 1.88054e7i) q^{28} -1.08153e8 q^{29} +(-1.12390e8 + 1.94665e8i) q^{30} +(1.25691e8 + 2.17703e8i) q^{31} +(-1.67772e7 - 2.90590e7i) q^{32} +(1.42357e8 - 2.46570e8i) q^{33} -2.93285e7 q^{34} +(-4.78840e8 - 3.42904e8i) q^{35} +1.06622e8 q^{36} +(2.01780e8 - 3.49493e8i) q^{37} +(-5.96106e7 - 1.03249e8i) q^{38} +(2.93574e8 + 5.08485e8i) q^{39} +(2.17003e8 - 3.75859e8i) q^{40} +1.26266e9 q^{41} +(-7.37336e7 + 7.51049e8i) q^{42} -1.92415e8 q^{43} +(-2.74864e8 + 4.76079e8i) q^{44} +(6.89546e8 + 1.19433e9i) q^{45} +(-3.61223e8 - 6.25656e8i) q^{46} +(5.04901e8 - 8.74515e8i) q^{47} -5.56112e8 q^{48} +(-1.93958e9 - 3.84538e8i) q^{49} +4.05108e9 q^{50} +(-2.43037e8 + 4.20952e8i) q^{51} +(-5.66833e8 - 9.81783e8i) q^{52} +(-2.26218e8 - 3.91821e8i) q^{53} +(-6.19648e8 + 1.07326e9i) q^{54} -7.11039e9 q^{55} +(1.42365e8 - 1.45013e9i) q^{56} -1.97590e9 q^{57} +(1.73045e9 - 2.99723e9i) q^{58} +(1.81367e9 + 3.14138e9i) q^{59} +(-3.59647e9 - 6.22928e9i) q^{60} +(-4.93848e9 + 8.55370e9i) q^{61} -8.04420e9 q^{62} +(3.76439e9 + 2.69573e9i) q^{63} +1.07374e9 q^{64} +(7.33162e9 - 1.26987e10i) q^{65} +(4.55544e9 + 7.89025e9i) q^{66} +(9.55058e9 + 1.65421e10i) q^{67} +(4.69256e8 - 8.12776e8i) q^{68} -1.19734e10 q^{69} +(1.71643e10 - 7.78354e9i) q^{70} +5.71008e9 q^{71} +(-1.70596e9 + 2.95481e9i) q^{72} +(-4.81805e9 - 8.34511e9i) q^{73} +(6.45695e9 + 1.11838e10i) q^{74} +(3.35701e10 - 5.81451e10i) q^{75} +3.81508e9 q^{76} +(-2.17410e10 + 9.85894e9i) q^{77} -1.87887e10 q^{78} +(-7.83278e9 + 1.35668e10i) q^{79} +(6.94408e9 + 1.20275e10i) q^{80} +(1.94923e10 + 3.37616e10i) q^{81} +(-2.02025e10 + 3.49918e10i) q^{82} +1.10230e10 q^{83} +(-1.96339e10 - 1.40602e10i) q^{84} +1.21391e10 q^{85} +(3.07864e9 - 5.33236e9i) q^{86} +(-2.86795e10 - 4.96743e10i) q^{87} +(-8.79565e9 - 1.52345e10i) q^{88} +(2.43330e10 - 4.21460e10i) q^{89} -4.41310e10 q^{90} +(4.80993e9 - 4.89938e10i) q^{91} +2.31182e10 q^{92} +(-6.66600e10 + 1.15458e11i) q^{93} +(1.61568e10 + 2.79845e10i) q^{94} +(2.46728e10 + 4.27345e10i) q^{95} +(8.89779e9 - 1.54114e10i) q^{96} -1.33855e11 q^{97} +(4.16898e10 - 4.75985e10i) q^{98} +5.58981e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 128 q^{2} + 266 q^{3} - 4096 q^{4} + 7504 q^{5} - 17024 q^{6} - 42224 q^{7} + 262144 q^{8} - 123520 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 128 q^{2} + 266 q^{3} - 4096 q^{4} + 7504 q^{5} - 17024 q^{6} - 42224 q^{7} + 262144 q^{8} - 123520 q^{9} + 240128 q^{10} + 213026 q^{11} + 272384 q^{12} - 2609712 q^{13} + 1257536 q^{14} + 2275500 q^{15} - 4194304 q^{16} + 8854244 q^{17} - 3952640 q^{18} + 7232806 q^{19} - 15368192 q^{20} + 49275128 q^{21} - 13633664 q^{22} - 10649134 q^{23} + 8716288 q^{24} - 119407256 q^{25} + 41755392 q^{26} + 19012196 q^{27} + 2996224 q^{28} - 221414576 q^{29} - 36408000 q^{30} + 486231270 q^{31} - 134217728 q^{32} + 489871116 q^{33} - 566671616 q^{34} - 756166390 q^{35} + 252968960 q^{36} + 463131040 q^{37} + 231449792 q^{38} + 493924396 q^{39} + 245891072 q^{40} - 1617723408 q^{41} - 1609760768 q^{42} + 2926896352 q^{43} + 218138624 q^{44} + 2871035832 q^{45} - 340772288 q^{46} - 894091254 q^{47} - 557842432 q^{48} - 11608958872 q^{49} + 7642064384 q^{50} + 6950287158 q^{51} + 1336172544 q^{52} - 1448863512 q^{53} - 304195136 q^{54} - 25123348964 q^{55} - 1383596032 q^{56} + 18014730520 q^{57} + 3542633216 q^{58} + 14386900738 q^{59} - 1165056000 q^{60} + 10854402216 q^{61} - 31118801280 q^{62} - 11833302628 q^{63} + 8589934592 q^{64} + 5495584080 q^{65} + 15675875712 q^{66} + 19629545546 q^{67} + 9066745856 q^{68} - 92767078992 q^{69} + 13390987456 q^{70} + 1474804928 q^{71} - 4047503360 q^{72} + 21420158732 q^{73} + 14820193280 q^{74} + 63738659600 q^{75} - 14812786688 q^{76} + 28657880944 q^{77} - 31611161344 q^{78} - 60246238086 q^{79} + 7868514304 q^{80} + 100835656724 q^{81} + 25883574528 q^{82} - 139893582304 q^{83} + 1054613504 q^{84} + 109585554592 q^{85} - 46830341632 q^{86} - 77636109684 q^{87} + 6980435968 q^{88} + 126354105612 q^{89} - 183746293248 q^{90} + 44156589120 q^{91} + 21809426432 q^{92} - 213975312128 q^{93} - 28610920128 q^{94} + 368499346550 q^{95} + 8925478912 q^{96} - 538182884176 q^{97} + 210290620288 q^{98} + 393415805736 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/14\mathbb{Z}\right)^\times\).

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −16.0000 + 27.7128i −0.353553 + 0.612372i
\(3\) 265.175 + 459.296i 0.630036 + 1.09125i 0.987544 + 0.157344i \(0.0502931\pi\)
−0.357508 + 0.933910i \(0.616374\pi\)
\(4\) −512.000 886.810i −0.250000 0.433013i
\(5\) 6622.39 11470.3i 0.947720 1.64150i 0.197507 0.980301i \(-0.436715\pi\)
0.750212 0.661197i \(-0.229951\pi\)
\(6\) −16971.2 −0.891005
\(7\) 4344.64 44254.4i 0.0977044 0.995215i
\(8\) 32768.0 0.353553
\(9\) −52061.7 + 90173.6i −0.293890 + 0.509032i
\(10\) 211917. + 367050.i 0.670139 + 1.16071i
\(11\) −268422. 464921.i −0.502526 0.870400i −0.999996 0.00291915i \(-0.999071\pi\)
0.497470 0.867481i \(-0.334263\pi\)
\(12\) 271539. 470319.i 0.315018 0.545627i
\(13\) 1.10710e6 0.826983 0.413492 0.910508i \(-0.364309\pi\)
0.413492 + 0.910508i \(0.364309\pi\)
\(14\) 1.15690e6 + 828472.i 0.574899 + 0.411693i
\(15\) 7.02436e6 2.38839
\(16\) −524288. + 908093.i −0.125000 + 0.216506i
\(17\) 458258. + 793726.i 0.0782782 + 0.135582i 0.902507 0.430675i \(-0.141724\pi\)
−0.824229 + 0.566257i \(0.808391\pi\)
\(18\) −1.66598e6 2.88555e6i −0.207812 0.359940i
\(19\) −1.86283e6 + 3.22652e6i −0.172595 + 0.298944i −0.939326 0.343025i \(-0.888549\pi\)
0.766731 + 0.641968i \(0.221882\pi\)
\(20\) −1.35627e7 −0.947720
\(21\) 2.14780e7 9.73967e6i 1.14759 0.520401i
\(22\) 1.71790e7 0.710679
\(23\) −1.12882e7 + 1.95517e7i −0.365697 + 0.633406i −0.988888 0.148664i \(-0.952503\pi\)
0.623190 + 0.782070i \(0.285836\pi\)
\(24\) 8.68924e6 + 1.50502e7i 0.222751 + 0.385816i
\(25\) −6.32981e7 1.09636e8i −1.29635 2.24534i
\(26\) −1.77135e7 + 3.06807e7i −0.292383 + 0.506422i
\(27\) 3.87280e7 0.519427
\(28\) −4.14697e7 + 1.88054e7i −0.455367 + 0.206497i
\(29\) −1.08153e8 −0.979153 −0.489576 0.871960i \(-0.662849\pi\)
−0.489576 + 0.871960i \(0.662849\pi\)
\(30\) −1.12390e8 + 1.94665e8i −0.844423 + 1.46258i
\(31\) 1.25691e8 + 2.17703e8i 0.788522 + 1.36576i 0.926872 + 0.375377i \(0.122487\pi\)
−0.138350 + 0.990383i \(0.544180\pi\)
\(32\) −1.67772e7 2.90590e7i −0.0883883 0.153093i
\(33\) 1.42357e8 2.46570e8i 0.633219 1.09677i
\(34\) −2.93285e7 −0.110702
\(35\) −4.78840e8 3.42904e8i −1.54105 1.10357i
\(36\) 1.06622e8 0.293890
\(37\) 2.01780e8 3.49493e8i 0.478375 0.828569i −0.521318 0.853363i \(-0.674559\pi\)
0.999693 + 0.0247933i \(0.00789275\pi\)
\(38\) −5.96106e7 1.03249e8i −0.122043 0.211385i
\(39\) 2.93574e8 + 5.08485e8i 0.521029 + 0.902449i
\(40\) 2.17003e8 3.75859e8i 0.335069 0.580357i
\(41\) 1.26266e9 1.70206 0.851030 0.525118i \(-0.175979\pi\)
0.851030 + 0.525118i \(0.175979\pi\)
\(42\) −7.37336e7 + 7.51049e8i −0.0870551 + 0.886742i
\(43\) −1.92415e8 −0.199601 −0.0998004 0.995007i \(-0.531820\pi\)
−0.0998004 + 0.995007i \(0.531820\pi\)
\(44\) −2.74864e8 + 4.76079e8i −0.251263 + 0.435200i
\(45\) 6.89546e8 + 1.19433e9i 0.557051 + 0.964840i
\(46\) −3.61223e8 6.25656e8i −0.258587 0.447886i
\(47\) 5.04901e8 8.74515e8i 0.321121 0.556197i −0.659599 0.751618i \(-0.729274\pi\)
0.980720 + 0.195420i \(0.0626071\pi\)
\(48\) −5.56112e8 −0.315018
\(49\) −1.93958e9 3.84538e8i −0.980908 0.194474i
\(50\) 4.05108e9 1.83331
\(51\) −2.43037e8 + 4.20952e8i −0.0986362 + 0.170843i
\(52\) −5.66833e8 9.81783e8i −0.206746 0.358094i
\(53\) −2.26218e8 3.91821e8i −0.0743036 0.128698i 0.826480 0.562967i \(-0.190340\pi\)
−0.900783 + 0.434269i \(0.857007\pi\)
\(54\) −6.19648e8 + 1.07326e9i −0.183645 + 0.318083i
\(55\) −7.11039e9 −1.90501
\(56\) 1.42365e8 1.45013e9i 0.0345437 0.351862i
\(57\) −1.97590e9 −0.434964
\(58\) 1.73045e9 2.99723e9i 0.346183 0.599606i
\(59\) 1.81367e9 + 3.14138e9i 0.330273 + 0.572050i 0.982565 0.185918i \(-0.0595258\pi\)
−0.652292 + 0.757968i \(0.726192\pi\)
\(60\) −3.59647e9 6.22928e9i −0.597097 1.03420i
\(61\) −4.93848e9 + 8.55370e9i −0.748651 + 1.29670i 0.199818 + 0.979833i \(0.435965\pi\)
−0.948469 + 0.316869i \(0.897369\pi\)
\(62\) −8.04420e9 −1.11514
\(63\) 3.76439e9 + 2.69573e9i 0.477883 + 0.342219i
\(64\) 1.07374e9 0.125000
\(65\) 7.33162e9 1.26987e10i 0.783748 1.35749i
\(66\) 4.55544e9 + 7.89025e9i 0.447753 + 0.775531i
\(67\) 9.55058e9 + 1.65421e10i 0.864208 + 1.49685i 0.867831 + 0.496859i \(0.165513\pi\)
−0.00362356 + 0.999993i \(0.501153\pi\)
\(68\) 4.69256e8 8.12776e8i 0.0391391 0.0677909i
\(69\) −1.19734e10 −0.921609
\(70\) 1.71643e10 7.78354e9i 1.22064 0.553526i
\(71\) 5.71008e9 0.375596 0.187798 0.982208i \(-0.439865\pi\)
0.187798 + 0.982208i \(0.439865\pi\)
\(72\) −1.70596e9 + 2.95481e9i −0.103906 + 0.179970i
\(73\) −4.81805e9 8.34511e9i −0.272017 0.471147i 0.697361 0.716720i \(-0.254357\pi\)
−0.969378 + 0.245573i \(0.921024\pi\)
\(74\) 6.45695e9 + 1.11838e10i 0.338262 + 0.585887i
\(75\) 3.35701e10 5.81451e10i 1.63349 2.82928i
\(76\) 3.81508e9 0.172595
\(77\) −2.17410e10 + 9.85894e9i −0.915335 + 0.415080i
\(78\) −1.87887e10 −0.736846
\(79\) −7.83278e9 + 1.35668e10i −0.286396 + 0.496053i −0.972947 0.231029i \(-0.925791\pi\)
0.686551 + 0.727082i \(0.259124\pi\)
\(80\) 6.94408e9 + 1.20275e10i 0.236930 + 0.410375i
\(81\) 1.94923e10 + 3.37616e10i 0.621147 + 1.07586i
\(82\) −2.02025e10 + 3.49918e10i −0.601769 + 1.04229i
\(83\) 1.10230e10 0.307164 0.153582 0.988136i \(-0.450919\pi\)
0.153582 + 0.988136i \(0.450919\pi\)
\(84\) −1.96339e10 1.40602e10i −0.512238 0.366821i
\(85\) 1.21391e10 0.296743
\(86\) 3.07864e9 5.33236e9i 0.0705695 0.122230i
\(87\) −2.86795e10 4.96743e10i −0.616901 1.06850i
\(88\) −8.79565e9 1.52345e10i −0.177670 0.307733i
\(89\) 2.43330e10 4.21460e10i 0.461903 0.800039i −0.537153 0.843485i \(-0.680500\pi\)
0.999056 + 0.0434461i \(0.0138337\pi\)
\(90\) −4.41310e10 −0.787789
\(91\) 4.80993e9 4.89938e10i 0.0807999 0.823027i
\(92\) 2.31182e10 0.365697
\(93\) −6.66600e10 + 1.15458e11i −0.993594 + 1.72096i
\(94\) 1.61568e10 + 2.79845e10i 0.227067 + 0.393291i
\(95\) 2.46728e10 + 4.27345e10i 0.327144 + 0.566629i
\(96\) 8.89779e9 1.54114e10i 0.111376 0.192908i
\(97\) −1.33855e11 −1.58267 −0.791337 0.611381i \(-0.790614\pi\)
−0.791337 + 0.611381i \(0.790614\pi\)
\(98\) 4.16898e10 4.75985e10i 0.465894 0.531924i
\(99\) 5.58981e10 0.590749
\(100\) −6.48173e10 + 1.12267e11i −0.648173 + 1.12267i
\(101\) 1.26243e10 + 2.18660e10i 0.119520 + 0.207015i 0.919578 0.392908i \(-0.128531\pi\)
−0.800057 + 0.599923i \(0.795198\pi\)
\(102\) −7.77718e9 1.34705e10i −0.0697463 0.120804i
\(103\) −4.30703e10 + 7.46000e10i −0.366078 + 0.634065i −0.988949 0.148259i \(-0.952633\pi\)
0.622871 + 0.782325i \(0.285966\pi\)
\(104\) 3.62773e10 0.292383
\(105\) 3.05183e10 3.10859e11i 0.233356 2.37696i
\(106\) 1.44779e10 0.105081
\(107\) −3.55150e10 + 6.15138e10i −0.244794 + 0.423996i −0.962074 0.272789i \(-0.912054\pi\)
0.717279 + 0.696786i \(0.245387\pi\)
\(108\) −1.98287e10 3.43444e10i −0.129857 0.224918i
\(109\) −2.35307e9 4.07563e9i −0.0146483 0.0253717i 0.858608 0.512632i \(-0.171330\pi\)
−0.873257 + 0.487261i \(0.837996\pi\)
\(110\) 1.13766e11 1.97049e11i 0.673524 1.16658i
\(111\) 2.14028e11 1.20557
\(112\) 3.79093e10 + 2.71474e10i 0.203257 + 0.145556i
\(113\) 6.91660e10 0.353152 0.176576 0.984287i \(-0.443498\pi\)
0.176576 + 0.984287i \(0.443498\pi\)
\(114\) 3.16144e10 5.47578e10i 0.153783 0.266360i
\(115\) 1.49510e11 + 2.58959e11i 0.693157 + 1.20058i
\(116\) 5.53745e10 + 9.59114e10i 0.244788 + 0.423986i
\(117\) −5.76373e10 + 9.98308e10i −0.243042 + 0.420961i
\(118\) −1.16075e11 −0.467077
\(119\) 3.71168e10 1.68315e10i 0.142581 0.0646568i
\(120\) 2.30174e11 0.844423
\(121\) −1.44500e9 + 2.50280e9i −0.00506462 + 0.00877218i
\(122\) −1.58031e11 2.73718e11i −0.529376 0.916907i
\(123\) 3.34825e11 + 5.79934e11i 1.07236 + 1.85738i
\(124\) 1.28707e11 2.22928e11i 0.394261 0.682880i
\(125\) −1.03002e12 −3.01885
\(126\) −1.34936e11 + 6.11900e10i −0.378522 + 0.171650i
\(127\) −2.82652e11 −0.759157 −0.379578 0.925160i \(-0.623931\pi\)
−0.379578 + 0.925160i \(0.623931\pi\)
\(128\) −1.71799e10 + 2.97564e10i −0.0441942 + 0.0765466i
\(129\) −5.10236e10 8.83754e10i −0.125756 0.217815i
\(130\) 2.34612e11 + 4.06360e11i 0.554194 + 0.959892i
\(131\) 3.65290e11 6.32701e11i 0.827267 1.43287i −0.0729079 0.997339i \(-0.523228\pi\)
0.900175 0.435529i \(-0.143439\pi\)
\(132\) −2.91548e11 −0.633219
\(133\) 1.34694e11 + 9.64565e10i 0.280650 + 0.200977i
\(134\) −6.11237e11 −1.22217
\(135\) 2.56472e11 4.44222e11i 0.492271 0.852638i
\(136\) 1.50162e10 + 2.60088e10i 0.0276755 + 0.0479354i
\(137\) −2.04365e11 3.53970e11i −0.361779 0.626619i 0.626475 0.779442i \(-0.284497\pi\)
−0.988254 + 0.152822i \(0.951164\pi\)
\(138\) 1.91574e11 3.31816e11i 0.325838 0.564368i
\(139\) −3.27567e11 −0.535450 −0.267725 0.963495i \(-0.586272\pi\)
−0.267725 + 0.963495i \(0.586272\pi\)
\(140\) −5.89248e10 + 6.00207e11i −0.0925964 + 0.943185i
\(141\) 5.35548e11 0.809270
\(142\) −9.13612e10 + 1.58242e11i −0.132793 + 0.230005i
\(143\) −2.97169e11 5.14712e11i −0.415581 0.719807i
\(144\) −5.45907e10 9.45538e10i −0.0734725 0.127258i
\(145\) −7.16233e11 + 1.24055e12i −0.927962 + 1.60728i
\(146\) 3.08355e11 0.384690
\(147\) −3.37709e11 9.92809e11i −0.405786 1.19294i
\(148\) −4.13245e11 −0.478375
\(149\) 6.34371e9 1.09876e10i 0.00707650 0.0122569i −0.862465 0.506116i \(-0.831081\pi\)
0.869542 + 0.493859i \(0.164414\pi\)
\(150\) 1.07424e12 + 1.86064e12i 1.15505 + 2.00061i
\(151\) 2.64247e11 + 4.57689e11i 0.273928 + 0.474458i 0.969864 0.243646i \(-0.0783435\pi\)
−0.695936 + 0.718104i \(0.745010\pi\)
\(152\) −6.10412e10 + 1.05727e11i −0.0610216 + 0.105693i
\(153\) −9.54308e10 −0.0920208
\(154\) 7.46366e10 7.60247e11i 0.0694365 0.707279i
\(155\) 3.32949e12 2.98919
\(156\) 3.00620e11 5.20688e11i 0.260514 0.451224i
\(157\) 5.36413e11 + 9.29095e11i 0.448798 + 0.777342i 0.998308 0.0581457i \(-0.0185188\pi\)
−0.549510 + 0.835487i \(0.685185\pi\)
\(158\) −2.50649e11 4.34137e11i −0.202513 0.350762i
\(159\) 1.19975e11 2.07802e11i 0.0936278 0.162168i
\(160\) −4.44421e11 −0.335069
\(161\) 8.16207e11 + 5.84498e11i 0.594646 + 0.425834i
\(162\) −1.24750e12 −0.878435
\(163\) 2.60469e11 4.51145e11i 0.177306 0.307103i −0.763651 0.645629i \(-0.776595\pi\)
0.940957 + 0.338526i \(0.109928\pi\)
\(164\) −6.46481e11 1.11974e12i −0.425515 0.737013i
\(165\) −1.88549e12 3.26577e12i −1.20023 2.07885i
\(166\) −1.76368e11 + 3.05479e11i −0.108599 + 0.188099i
\(167\) 1.74459e12 1.03933 0.519663 0.854371i \(-0.326058\pi\)
0.519663 + 0.854371i \(0.326058\pi\)
\(168\) 7.03790e11 3.19149e11i 0.405734 0.183990i
\(169\) −5.66500e11 −0.316099
\(170\) −1.94225e11 + 3.36407e11i −0.104915 + 0.181717i
\(171\) −1.93964e11 3.35956e11i −0.101448 0.175713i
\(172\) 9.85165e10 + 1.70636e11i 0.0499002 + 0.0864297i
\(173\) −7.24388e11 + 1.25468e12i −0.355400 + 0.615571i −0.987186 0.159571i \(-0.948989\pi\)
0.631786 + 0.775143i \(0.282322\pi\)
\(174\) 1.83549e12 0.872430
\(175\) −5.12686e12 + 2.32489e12i −2.36125 + 1.07076i
\(176\) 5.62922e11 0.251263
\(177\) −9.61881e11 + 1.66603e12i −0.416168 + 0.720824i
\(178\) 7.78655e11 + 1.34867e12i 0.326614 + 0.565713i
\(179\) 1.29817e12 + 2.24849e12i 0.528007 + 0.914534i 0.999467 + 0.0326470i \(0.0103937\pi\)
−0.471460 + 0.881887i \(0.656273\pi\)
\(180\) 7.06095e11 1.22299e12i 0.278525 0.482420i
\(181\) 2.25762e12 0.863810 0.431905 0.901919i \(-0.357842\pi\)
0.431905 + 0.901919i \(0.357842\pi\)
\(182\) 1.28080e12 + 9.17198e11i 0.475432 + 0.340463i
\(183\) −5.23824e12 −1.88671
\(184\) −3.69892e11 + 6.40672e11i −0.129294 + 0.223943i
\(185\) −2.67253e12 4.62896e12i −0.906730 1.57050i
\(186\) −2.13312e12 3.69467e12i −0.702577 1.21690i
\(187\) 2.46013e11 4.26107e11i 0.0786737 0.136267i
\(188\) −1.03404e12 −0.321121
\(189\) 1.68259e11 1.71388e12i 0.0507503 0.516941i
\(190\) −1.57906e12 −0.462651
\(191\) −1.48382e12 + 2.57005e12i −0.422375 + 0.731575i −0.996171 0.0874231i \(-0.972137\pi\)
0.573796 + 0.818998i \(0.305470\pi\)
\(192\) 2.84729e11 + 4.93165e11i 0.0787545 + 0.136407i
\(193\) 2.46259e12 + 4.26533e12i 0.661953 + 1.14654i 0.980102 + 0.198495i \(0.0636055\pi\)
−0.318149 + 0.948041i \(0.603061\pi\)
\(194\) 2.14169e12 3.70951e12i 0.559560 0.969186i
\(195\) 7.77664e12 1.97516
\(196\) 6.52050e11 + 1.91692e12i 0.161017 + 0.473364i
\(197\) 3.21645e12 0.772347 0.386173 0.922426i \(-0.373797\pi\)
0.386173 + 0.922426i \(0.373797\pi\)
\(198\) −8.94369e11 + 1.54909e12i −0.208861 + 0.361759i
\(199\) −1.49046e12 2.58156e12i −0.338555 0.586395i 0.645606 0.763671i \(-0.276605\pi\)
−0.984161 + 0.177276i \(0.943271\pi\)
\(200\) −2.07415e12 3.59254e12i −0.458327 0.793846i
\(201\) −5.06514e12 + 8.77309e12i −1.08896 + 1.88614i
\(202\) −8.07958e11 −0.169027
\(203\) −4.69887e11 + 4.78626e12i −0.0956676 + 0.974468i
\(204\) 4.97740e11 0.0986362
\(205\) 8.36182e12 1.44831e13i 1.61307 2.79393i
\(206\) −1.37825e12 2.38720e12i −0.258856 0.448352i
\(207\) −1.17537e12 2.03580e12i −0.214950 0.372304i
\(208\) −5.80437e11 + 1.00535e12i −0.103373 + 0.179047i
\(209\) 2.00010e12 0.346934
\(210\) 8.12648e12 + 5.81949e12i 1.37308 + 0.983284i
\(211\) −1.15582e13 −1.90256 −0.951280 0.308328i \(-0.900231\pi\)
−0.951280 + 0.308328i \(0.900231\pi\)
\(212\) −2.31647e11 + 4.01225e11i −0.0371518 + 0.0643488i
\(213\) 1.51417e12 + 2.62262e12i 0.236639 + 0.409871i
\(214\) −1.13648e12 1.96844e12i −0.173096 0.299811i
\(215\) −1.27425e12 + 2.20706e12i −0.189166 + 0.327644i
\(216\) 1.26904e12 0.183645
\(217\) 1.01804e13 4.61653e12i 1.43627 0.651308i
\(218\) 1.50596e11 0.0207159
\(219\) 2.55525e12 4.42582e12i 0.342760 0.593679i
\(220\) 3.64052e12 + 6.30556e12i 0.476254 + 0.824896i
\(221\) 5.07336e11 + 8.78731e11i 0.0647348 + 0.112124i
\(222\) −3.42444e12 + 5.93131e12i −0.426234 + 0.738259i
\(223\) 3.33305e12 0.404730 0.202365 0.979310i \(-0.435137\pi\)
0.202365 + 0.979310i \(0.435137\pi\)
\(224\) −1.35888e12 + 6.16215e11i −0.160997 + 0.0730076i
\(225\) 1.31816e13 1.52393
\(226\) −1.10666e12 + 1.91678e12i −0.124858 + 0.216260i
\(227\) −3.54301e12 6.13667e12i −0.390149 0.675757i 0.602320 0.798255i \(-0.294243\pi\)
−0.992469 + 0.122497i \(0.960910\pi\)
\(228\) 1.01166e12 + 1.75225e12i 0.108741 + 0.188345i
\(229\) −3.58697e12 + 6.21282e12i −0.376386 + 0.651919i −0.990533 0.137272i \(-0.956167\pi\)
0.614148 + 0.789191i \(0.289500\pi\)
\(230\) −9.56863e12 −0.980272
\(231\) −1.02933e13 7.37120e12i −1.02965 0.737348i
\(232\) −3.54397e12 −0.346183
\(233\) −2.56335e12 + 4.43986e12i −0.244541 + 0.423557i −0.962002 0.273041i \(-0.911970\pi\)
0.717462 + 0.696598i \(0.245304\pi\)
\(234\) −1.84439e12 3.19458e12i −0.171857 0.297665i
\(235\) −6.68731e12 1.15828e13i −0.608665 1.05424i
\(236\) 1.85720e12 3.21677e12i 0.165137 0.286025i
\(237\) −8.30822e12 −0.721759
\(238\) −1.27422e11 + 1.29792e12i −0.0108161 + 0.110172i
\(239\) 1.21613e13 1.00877 0.504386 0.863478i \(-0.331719\pi\)
0.504386 + 0.863478i \(0.331719\pi\)
\(240\) −3.68279e12 + 6.37878e12i −0.298549 + 0.517101i
\(241\) −5.80009e12 1.00460e13i −0.459559 0.795979i 0.539379 0.842063i \(-0.318659\pi\)
−0.998938 + 0.0460843i \(0.985326\pi\)
\(242\) −4.62398e10 8.00898e10i −0.00358123 0.00620287i
\(243\) −6.90744e12 + 1.19640e13i −0.522977 + 0.905822i
\(244\) 1.01140e13 0.748651
\(245\) −1.72554e13 + 1.97010e13i −1.24885 + 1.42585i
\(246\) −2.14288e13 −1.51654
\(247\) −2.06233e12 + 3.57206e12i −0.142733 + 0.247221i
\(248\) 4.11863e12 + 7.13368e12i 0.278785 + 0.482869i
\(249\) 2.92302e12 + 5.06283e12i 0.193525 + 0.335194i
\(250\) 1.64803e13 2.85448e13i 1.06732 1.84866i
\(251\) 4.15198e12 0.263057 0.131528 0.991312i \(-0.458012\pi\)
0.131528 + 0.991312i \(0.458012\pi\)
\(252\) 4.63236e11 4.71851e12i 0.0287144 0.292484i
\(253\) 1.21200e13 0.735090
\(254\) 4.52243e12 7.83308e12i 0.268402 0.464887i
\(255\) 3.21897e12 + 5.57542e12i 0.186959 + 0.323822i
\(256\) −5.49756e11 9.52205e11i −0.0312500 0.0541266i
\(257\) 8.52957e12 1.47737e13i 0.474564 0.821969i −0.525011 0.851095i \(-0.675939\pi\)
0.999576 + 0.0291257i \(0.00927230\pi\)
\(258\) 3.26551e12 0.177845
\(259\) −1.45899e13 1.04481e13i −0.777866 0.557041i
\(260\) −1.50152e13 −0.783748
\(261\) 5.63064e12 9.75256e12i 0.287763 0.498421i
\(262\) 1.16893e13 + 2.02464e13i 0.584966 + 1.01319i
\(263\) 1.04469e13 + 1.80946e13i 0.511955 + 0.886732i 0.999904 + 0.0138598i \(0.00441187\pi\)
−0.487949 + 0.872872i \(0.662255\pi\)
\(264\) 4.66477e12 8.07962e12i 0.223877 0.387766i
\(265\) −5.99241e12 −0.281676
\(266\) −4.82819e12 + 2.18945e12i −0.222298 + 0.100806i
\(267\) 2.58100e13 1.16406
\(268\) 9.77979e12 1.69391e13i 0.432104 0.748426i
\(269\) 8.56331e12 + 1.48321e13i 0.370684 + 0.642044i 0.989671 0.143357i \(-0.0457898\pi\)
−0.618987 + 0.785402i \(0.712456\pi\)
\(270\) 8.20710e12 + 1.42151e13i 0.348088 + 0.602906i
\(271\) 8.75729e12 1.51681e13i 0.363948 0.630376i −0.624659 0.780898i \(-0.714762\pi\)
0.988607 + 0.150522i \(0.0480954\pi\)
\(272\) −9.61037e11 −0.0391391
\(273\) 2.37781e13 1.07827e13i 0.949038 0.430363i
\(274\) 1.30794e13 0.511632
\(275\) −3.39812e13 + 5.88572e13i −1.30289 + 2.25668i
\(276\) 6.13037e12 + 1.06181e13i 0.230402 + 0.399069i
\(277\) 1.15398e11 + 1.99875e11i 0.00425167 + 0.00736410i 0.868143 0.496313i \(-0.165313\pi\)
−0.863892 + 0.503678i \(0.831980\pi\)
\(278\) 5.24108e12 9.07781e12i 0.189310 0.327895i
\(279\) −2.61747e13 −0.926955
\(280\) −1.56906e13 1.12363e13i −0.544843 0.390170i
\(281\) −1.58974e13 −0.541303 −0.270651 0.962677i \(-0.587239\pi\)
−0.270651 + 0.962677i \(0.587239\pi\)
\(282\) −8.56877e12 + 1.48416e13i −0.286120 + 0.495575i
\(283\) 1.40611e13 + 2.43546e13i 0.460463 + 0.797546i 0.998984 0.0450667i \(-0.0143500\pi\)
−0.538521 + 0.842612i \(0.681017\pi\)
\(284\) −2.92356e12 5.06375e12i −0.0938990 0.162638i
\(285\) −1.30852e13 + 2.26642e13i −0.412224 + 0.713993i
\(286\) 1.90188e13 0.587720
\(287\) 5.48579e12 5.58782e13i 0.166299 1.69392i
\(288\) 3.49380e12 0.103906
\(289\) 1.67159e13 2.89529e13i 0.487745 0.844799i
\(290\) −2.29195e13 3.96977e13i −0.656169 1.13652i
\(291\) −3.54951e13 6.14792e13i −0.997141 1.72710i
\(292\) −4.93368e12 + 8.54539e12i −0.136008 + 0.235573i
\(293\) −3.82207e13 −1.03401 −0.517007 0.855981i \(-0.672954\pi\)
−0.517007 + 0.855981i \(0.672954\pi\)
\(294\) 3.29169e13 + 6.52607e12i 0.873994 + 0.173277i
\(295\) 4.80435e13 1.25203
\(296\) 6.61192e12 1.14522e13i 0.169131 0.292943i
\(297\) −1.03954e13 1.80054e13i −0.261025 0.452109i
\(298\) 2.02999e11 + 3.51604e11i 0.00500384 + 0.00866691i
\(299\) −1.24971e13 + 2.16457e13i −0.302426 + 0.523816i
\(300\) −6.87516e13 −1.63349
\(301\) −8.35973e11 + 8.51521e12i −0.0195019 + 0.198646i
\(302\) −1.69118e13 −0.387393
\(303\) −6.69531e12 + 1.15966e13i −0.150604 + 0.260854i
\(304\) −1.95332e12 3.38325e12i −0.0431488 0.0747359i
\(305\) 6.54091e13 + 1.13292e14i 1.41902 + 2.45782i
\(306\) 1.52689e12 2.64466e12i 0.0325343 0.0563510i
\(307\) −5.25423e13 −1.09963 −0.549817 0.835285i \(-0.685303\pi\)
−0.549817 + 0.835285i \(0.685303\pi\)
\(308\) 1.98744e13 + 1.42323e13i 0.408568 + 0.292582i
\(309\) −4.56846e13 −0.922569
\(310\) −5.32719e13 + 9.22696e13i −1.05684 + 1.83050i
\(311\) 3.97239e12 + 6.88039e12i 0.0774230 + 0.134101i 0.902137 0.431449i \(-0.141997\pi\)
−0.824714 + 0.565549i \(0.808664\pi\)
\(312\) 9.61982e12 + 1.66620e13i 0.184212 + 0.319064i
\(313\) 2.33312e13 4.04107e13i 0.438978 0.760332i −0.558633 0.829415i \(-0.688674\pi\)
0.997611 + 0.0690832i \(0.0220074\pi\)
\(314\) −3.43304e13 −0.634697
\(315\) 5.58501e13 2.53265e13i 1.01465 0.460116i
\(316\) 1.60415e13 0.286396
\(317\) 4.12269e13 7.14071e13i 0.723360 1.25290i −0.236285 0.971684i \(-0.575930\pi\)
0.959645 0.281213i \(-0.0907368\pi\)
\(318\) 3.83918e12 + 6.64966e12i 0.0662048 + 0.114670i
\(319\) 2.90307e13 + 5.02827e13i 0.492050 + 0.852255i
\(320\) 7.11074e12 1.23162e13i 0.118465 0.205187i
\(321\) −3.76707e13 −0.616917
\(322\) −2.92574e13 + 1.32674e13i −0.471008 + 0.213589i
\(323\) −3.41463e12 −0.0540418
\(324\) 1.99601e13 3.45719e13i 0.310574 0.537929i
\(325\) −7.00770e13 1.21377e14i −1.07206 1.85685i
\(326\) 8.33499e12 + 1.44366e13i 0.125374 + 0.217155i
\(327\) 1.24795e12 2.16151e12i 0.0184580 0.0319701i
\(328\) 4.13748e13 0.601769
\(329\) −3.65075e13 2.61436e13i −0.522161 0.373927i
\(330\) 1.20672e14 1.69738
\(331\) 2.58615e13 4.47934e13i 0.357766 0.619669i −0.629821 0.776740i \(-0.716872\pi\)
0.987587 + 0.157071i \(0.0502051\pi\)
\(332\) −5.64378e12 9.77532e12i −0.0767911 0.133006i
\(333\) 2.10100e13 + 3.63904e13i 0.281179 + 0.487016i
\(334\) −2.79134e13 + 4.83474e13i −0.367457 + 0.636455i
\(335\) 2.52991e14 3.27611
\(336\) −2.41610e12 + 2.46104e13i −0.0307786 + 0.313511i
\(337\) −1.36515e14 −1.71087 −0.855435 0.517911i \(-0.826710\pi\)
−0.855435 + 0.517911i \(0.826710\pi\)
\(338\) 9.06399e12 1.56993e13i 0.111758 0.193570i
\(339\) 1.83411e13 + 3.17677e13i 0.222498 + 0.385378i
\(340\) −6.21520e12 1.07650e13i −0.0741858 0.128494i
\(341\) 6.74763e13 1.16872e14i 0.792505 1.37266i
\(342\) 1.24137e13 0.143469
\(343\) −2.54443e13 + 8.41640e13i −0.289382 + 0.957214i
\(344\) −6.30505e12 −0.0705695
\(345\) −7.92924e13 + 1.37339e14i −0.873427 + 1.51282i
\(346\) −2.31804e13 4.01497e13i −0.251306 0.435275i
\(347\) −1.98692e13 3.44144e13i −0.212015 0.367221i 0.740330 0.672244i \(-0.234669\pi\)
−0.952345 + 0.305022i \(0.901336\pi\)
\(348\) −2.93678e13 + 5.08665e13i −0.308451 + 0.534252i
\(349\) −6.01737e13 −0.622109 −0.311055 0.950392i \(-0.600682\pi\)
−0.311055 + 0.950392i \(0.600682\pi\)
\(350\) 1.76005e13 1.79278e14i 0.179122 1.82454i
\(351\) 4.28756e13 0.429557
\(352\) −9.00675e12 + 1.56001e13i −0.0888349 + 0.153867i
\(353\) 8.07816e13 + 1.39918e14i 0.784425 + 1.35866i 0.929342 + 0.369221i \(0.120375\pi\)
−0.144916 + 0.989444i \(0.546291\pi\)
\(354\) −3.07802e13 5.33129e13i −0.294275 0.509699i
\(355\) 3.78144e13 6.54964e13i 0.355960 0.616541i
\(356\) −4.98339e13 −0.461903
\(357\) 1.75731e13 + 1.25843e13i 0.160388 + 0.114856i
\(358\) −8.30828e13 −0.746714
\(359\) −5.86838e13 + 1.01643e14i −0.519396 + 0.899620i 0.480350 + 0.877077i \(0.340510\pi\)
−0.999746 + 0.0225434i \(0.992824\pi\)
\(360\) 2.25951e13 + 3.91358e13i 0.196947 + 0.341122i
\(361\) 5.13049e13 + 8.88626e13i 0.440422 + 0.762833i
\(362\) −3.61219e13 + 6.25649e13i −0.305403 + 0.528973i
\(363\) −1.53270e12 −0.0127636
\(364\) −4.59109e13 + 2.08194e13i −0.376581 + 0.170769i
\(365\) −1.27628e14 −1.03118
\(366\) 8.38119e13 1.45166e14i 0.667052 1.15537i
\(367\) 2.62280e13 + 4.54283e13i 0.205637 + 0.356175i 0.950336 0.311227i \(-0.100740\pi\)
−0.744698 + 0.667401i \(0.767407\pi\)
\(368\) −1.18365e13 2.05015e13i −0.0914243 0.158352i
\(369\) −6.57362e13 + 1.13858e14i −0.500218 + 0.866403i
\(370\) 1.71042e14 1.28231
\(371\) −1.83226e13 + 8.30881e12i −0.135342 + 0.0613737i
\(372\) 1.36520e14 0.993594
\(373\) −2.37714e13 + 4.11733e13i −0.170474 + 0.295269i −0.938586 0.345047i \(-0.887863\pi\)
0.768112 + 0.640316i \(0.221196\pi\)
\(374\) 7.87242e12 + 1.36354e13i 0.0556307 + 0.0963552i
\(375\) −2.73136e14 4.73085e14i −1.90198 3.29433i
\(376\) 1.65446e13 2.86561e13i 0.113533 0.196646i
\(377\) −1.19736e14 −0.809743
\(378\) 4.48044e13 + 3.20851e13i 0.298618 + 0.213844i
\(379\) 3.35837e13 0.220603 0.110302 0.993898i \(-0.464818\pi\)
0.110302 + 0.993898i \(0.464818\pi\)
\(380\) 2.52649e13 4.37602e13i 0.163572 0.283315i
\(381\) −7.49521e13 1.29821e14i −0.478296 0.828433i
\(382\) −4.74823e13 8.22418e13i −0.298664 0.517302i
\(383\) 3.73327e12 6.46622e12i 0.0231471 0.0400919i −0.854220 0.519912i \(-0.825965\pi\)
0.877367 + 0.479820i \(0.159298\pi\)
\(384\) −1.82227e13 −0.111376
\(385\) −3.08920e13 + 3.14666e14i −0.186128 + 1.89590i
\(386\) −1.57606e14 −0.936143
\(387\) 1.00175e13 1.73507e13i 0.0586607 0.101603i
\(388\) 6.85340e13 + 1.18704e14i 0.395668 + 0.685318i
\(389\) −1.24223e14 2.15161e14i −0.707099 1.22473i −0.965929 0.258808i \(-0.916670\pi\)
0.258830 0.965923i \(-0.416663\pi\)
\(390\) −1.24426e14 + 2.15513e14i −0.698324 + 1.20953i
\(391\) −2.06916e13 −0.114505
\(392\) −6.35560e13 1.26006e13i −0.346803 0.0687569i
\(393\) 3.87463e14 2.08483
\(394\) −5.14632e13 + 8.91368e13i −0.273066 + 0.472964i
\(395\) 1.03744e14 + 1.79689e14i 0.542846 + 0.940238i
\(396\) −2.86198e13 4.95710e13i −0.147687 0.255802i
\(397\) −2.96699e13 + 5.13898e13i −0.150997 + 0.261535i −0.931594 0.363500i \(-0.881582\pi\)
0.780597 + 0.625035i \(0.214915\pi\)
\(398\) 9.53897e13 0.478789
\(399\) −8.58458e12 + 8.74423e13i −0.0424979 + 0.432883i
\(400\) 1.32746e14 0.648173
\(401\) 1.47123e14 2.54824e14i 0.708576 1.22729i −0.256810 0.966462i \(-0.582671\pi\)
0.965385 0.260827i \(-0.0839954\pi\)
\(402\) −1.62085e14 2.80739e14i −0.770014 1.33370i
\(403\) 1.39152e14 + 2.41018e14i 0.652094 + 1.12946i
\(404\) 1.29273e13 2.23908e13i 0.0597601 0.103507i
\(405\) 5.16342e14 2.35469
\(406\) −1.25122e14 8.96020e13i −0.562914 0.403111i
\(407\) −2.16649e14 −0.961583
\(408\) −7.96383e12 + 1.37938e13i −0.0348732 + 0.0604021i
\(409\) 3.00517e12 + 5.20510e12i 0.0129835 + 0.0224880i 0.872444 0.488714i \(-0.162534\pi\)
−0.859461 + 0.511202i \(0.829200\pi\)
\(410\) 2.67578e14 + 4.63459e14i 1.14062 + 1.97561i
\(411\) 1.08385e14 1.87728e14i 0.455867 0.789585i
\(412\) 8.82080e13 0.366078
\(413\) 1.46899e14 6.66149e13i 0.601582 0.272801i
\(414\) 7.52235e13 0.303985
\(415\) 7.29987e13 1.26438e14i 0.291106 0.504210i
\(416\) −1.85740e13 3.21711e13i −0.0730957 0.126605i
\(417\) −8.68626e13 1.50450e14i −0.337353 0.584312i
\(418\) −3.20016e13 + 5.54284e13i −0.122660 + 0.212453i
\(419\) −1.41210e14 −0.534181 −0.267090 0.963671i \(-0.586062\pi\)
−0.267090 + 0.963671i \(0.586062\pi\)
\(420\) −2.91298e14 + 1.32096e14i −1.08759 + 0.493194i
\(421\) −4.08084e14 −1.50383 −0.751915 0.659261i \(-0.770869\pi\)
−0.751915 + 0.659261i \(0.770869\pi\)
\(422\) 1.84932e14 3.20311e14i 0.672657 1.16508i
\(423\) 5.25721e13 + 9.10575e13i 0.188748 + 0.326922i
\(424\) −7.41271e12 1.28392e13i −0.0262703 0.0455015i
\(425\) 5.80137e13 1.00483e14i 0.202951 0.351522i
\(426\) −9.69068e13 −0.334658
\(427\) 3.57083e14 + 2.55712e14i 1.21735 + 0.871763i
\(428\) 7.27348e13 0.244794
\(429\) 1.57603e14 2.72977e14i 0.523661 0.907008i
\(430\) −4.07759e13 7.06260e13i −0.133760 0.231680i
\(431\) 1.50636e14 + 2.60910e14i 0.487871 + 0.845017i 0.999903 0.0139492i \(-0.00444033\pi\)
−0.512032 + 0.858967i \(0.671107\pi\)
\(432\) −2.03046e13 + 3.51686e13i −0.0649283 + 0.112459i
\(433\) 1.30262e13 0.0411278 0.0205639 0.999789i \(-0.493454\pi\)
0.0205639 + 0.999789i \(0.493454\pi\)
\(434\) −3.49491e13 + 3.55991e14i −0.108954 + 1.10980i
\(435\) −7.59708e14 −2.33860
\(436\) −2.40954e12 + 4.17345e12i −0.00732417 + 0.0126858i
\(437\) −4.20560e13 7.28432e13i −0.126235 0.218646i
\(438\) 8.17680e13 + 1.41626e14i 0.242368 + 0.419794i
\(439\) −2.46848e14 + 4.27554e14i −0.722563 + 1.25152i 0.237406 + 0.971410i \(0.423703\pi\)
−0.959969 + 0.280105i \(0.909631\pi\)
\(440\) −2.32993e14 −0.673524
\(441\) 1.35653e14 1.54879e14i 0.387272 0.442160i
\(442\) −3.24695e13 −0.0915488
\(443\) 3.65238e13 6.32611e13i 0.101708 0.176164i −0.810680 0.585489i \(-0.800903\pi\)
0.912389 + 0.409325i \(0.134236\pi\)
\(444\) −1.09582e14 1.89802e14i −0.301393 0.522028i
\(445\) −3.22285e14 5.58214e14i −0.875508 1.51642i
\(446\) −5.33288e13 + 9.23682e13i −0.143094 + 0.247845i
\(447\) 6.72876e12 0.0178338
\(448\) 4.66502e12 4.75178e13i 0.0122131 0.124402i
\(449\) 5.60310e14 1.44902 0.724508 0.689266i \(-0.242067\pi\)
0.724508 + 0.689266i \(0.242067\pi\)
\(450\) −2.10906e14 + 3.65300e14i −0.538791 + 0.933213i
\(451\) −3.38925e14 5.87036e14i −0.855329 1.48147i
\(452\) −3.54130e13 6.13371e13i −0.0882879 0.152919i
\(453\) −1.40143e14 + 2.42735e14i −0.345169 + 0.597851i
\(454\) 2.26753e14 0.551753
\(455\) −5.30122e14 3.79628e14i −1.27442 0.912631i
\(456\) −6.47464e13 −0.153783
\(457\) −1.80385e14 + 3.12436e14i −0.423312 + 0.733198i −0.996261 0.0863927i \(-0.972466\pi\)
0.572949 + 0.819591i \(0.305799\pi\)
\(458\) −1.14783e14 1.98810e14i −0.266145 0.460976i
\(459\) 1.77474e13 + 3.07394e13i 0.0406598 + 0.0704249i
\(460\) 1.53098e14 2.65174e14i 0.346579 0.600292i
\(461\) −6.90916e14 −1.54550 −0.772752 0.634709i \(-0.781120\pi\)
−0.772752 + 0.634709i \(0.781120\pi\)
\(462\) 3.68970e14 1.67318e14i 0.815568 0.369838i
\(463\) 9.81283e13 0.214338 0.107169 0.994241i \(-0.465821\pi\)
0.107169 + 0.994241i \(0.465821\pi\)
\(464\) 5.67034e13 9.82132e13i 0.122394 0.211993i
\(465\) 8.82897e14 + 1.52922e15i 1.88330 + 3.26197i
\(466\) −8.20273e13 1.42075e14i −0.172916 0.299500i
\(467\) 1.50159e13 2.60083e13i 0.0312830 0.0541837i −0.849960 0.526847i \(-0.823374\pi\)
0.881243 + 0.472663i \(0.156707\pi\)
\(468\) 1.18041e14 0.243042
\(469\) 7.73554e14 3.50786e14i 1.57413 0.713824i
\(470\) 4.27988e14 0.860782
\(471\) −2.84486e14 + 4.92745e14i −0.565518 + 0.979506i
\(472\) 5.94305e13 + 1.02937e14i 0.116769 + 0.202250i
\(473\) 5.16484e13 + 8.94577e13i 0.100305 + 0.173733i
\(474\) 1.32932e14 2.30244e14i 0.255180 0.441985i
\(475\) 4.71655e14 0.894971
\(476\) −3.39301e13 2.42979e13i −0.0636425 0.0455753i
\(477\) 4.71092e13 0.0873483
\(478\) −1.94581e14 + 3.37025e14i −0.356655 + 0.617744i
\(479\) −4.01669e14 6.95711e14i −0.727818 1.26062i −0.957803 0.287424i \(-0.907201\pi\)
0.229985 0.973194i \(-0.426132\pi\)
\(480\) −1.17849e14 2.04121e14i −0.211106 0.365646i
\(481\) 2.23390e14 3.86922e14i 0.395608 0.685213i
\(482\) 3.71206e14 0.649914
\(483\) −5.20200e13 + 5.29875e14i −0.0900453 + 0.917200i
\(484\) 2.95935e12 0.00506462
\(485\) −8.86443e14 + 1.53536e15i −1.49993 + 2.59796i
\(486\) −2.21038e14 3.82849e14i −0.369800 0.640513i
\(487\) −3.89752e13 6.75071e13i −0.0644732 0.111671i 0.831987 0.554795i \(-0.187203\pi\)
−0.896460 + 0.443124i \(0.853870\pi\)
\(488\) −1.61824e14 + 2.80288e14i −0.264688 + 0.458453i
\(489\) 2.76279e14 0.446836
\(490\) −2.69883e14 7.93412e14i −0.431616 1.26888i
\(491\) 3.72454e14 0.589013 0.294506 0.955650i \(-0.404845\pi\)
0.294506 + 0.955650i \(0.404845\pi\)
\(492\) 3.42861e14 5.93852e14i 0.536179 0.928689i
\(493\) −4.95621e13 8.58441e13i −0.0766464 0.132755i
\(494\) −6.59946e13 1.14306e14i −0.100928 0.174812i
\(495\) 3.70179e14 6.41169e14i 0.559865 0.969714i
\(496\) −2.63592e14 −0.394261
\(497\) 2.48082e13 2.52696e14i 0.0366974 0.373799i
\(498\) −1.87074e14 −0.273685
\(499\) 5.59420e14 9.68944e14i 0.809440 1.40199i −0.103812 0.994597i \(-0.533104\pi\)
0.913252 0.407395i \(-0.133563\pi\)
\(500\) 5.27371e14 + 9.13433e14i 0.754712 + 1.30720i
\(501\) 4.62620e14 + 8.01281e14i 0.654812 + 1.13417i
\(502\) −6.64317e13 + 1.15063e14i −0.0930047 + 0.161089i
\(503\) −5.11050e14 −0.707685 −0.353842 0.935305i \(-0.615125\pi\)
−0.353842 + 0.935305i \(0.615125\pi\)
\(504\) 1.23351e14 + 8.83337e13i 0.168957 + 0.120993i
\(505\) 3.34413e14 0.453086
\(506\) −1.93920e14 + 3.35880e14i −0.259893 + 0.450149i
\(507\) −1.50221e14 2.60191e14i −0.199153 0.344944i
\(508\) 1.44718e14 + 2.50659e14i 0.189789 + 0.328725i
\(509\) 6.95856e14 1.20526e15i 0.902759 1.56362i 0.0788612 0.996886i \(-0.474872\pi\)
0.823898 0.566739i \(-0.191795\pi\)
\(510\) −2.06014e14 −0.264400
\(511\) −3.90240e14 + 1.76963e14i −0.495470 + 0.224682i
\(512\) 3.51844e13 0.0441942
\(513\) −7.21437e13 + 1.24957e14i −0.0896505 + 0.155279i
\(514\) 2.72946e14 + 4.72757e14i 0.335568 + 0.581220i
\(515\) 5.70457e14 + 9.88061e14i 0.693878 + 1.20183i
\(516\) −5.22481e13 + 9.04964e13i −0.0628778 + 0.108908i
\(517\) −5.42107e14 −0.645486
\(518\) 5.22984e14 2.37159e14i 0.616133 0.279400i
\(519\) −7.68358e14 −0.895659
\(520\) 2.40243e14 4.16112e14i 0.277097 0.479946i
\(521\) −5.32699e14 9.22662e14i −0.607959 1.05302i −0.991576 0.129524i \(-0.958655\pi\)
0.383617 0.923492i \(-0.374678\pi\)
\(522\) 1.80181e14 + 3.12082e14i 0.203479 + 0.352437i
\(523\) −6.82869e13 + 1.18276e14i −0.0763094 + 0.132172i −0.901655 0.432456i \(-0.857647\pi\)
0.825346 + 0.564628i \(0.190980\pi\)
\(524\) −7.48114e14 −0.827267
\(525\) −2.42733e15 1.73824e15i −2.65615 1.90211i
\(526\) −6.68603e14 −0.724014
\(527\) −1.15198e14 + 1.99528e14i −0.123448 + 0.213819i
\(528\) 1.49273e14 + 2.58548e14i 0.158305 + 0.274192i
\(529\) 2.21558e14 + 3.83749e14i 0.232531 + 0.402755i
\(530\) 9.58786e13 1.66067e14i 0.0995874 0.172490i
\(531\) −3.77692e14 −0.388256
\(532\) 1.65751e13 1.68834e14i 0.0168633 0.171769i
\(533\) 1.39788e15 1.40757
\(534\) −4.12959e14 + 7.15267e14i −0.411557 + 0.712838i
\(535\) 4.70389e14 + 8.14737e14i 0.463993 + 0.803659i
\(536\) 3.12953e14 + 5.42051e14i 0.305544 + 0.529217i
\(537\) −6.88483e14 + 1.19249e15i −0.665326 + 1.15238i
\(538\) −5.48052e14 −0.524227
\(539\) 3.41845e14 + 1.00497e15i 0.323661 + 0.951511i
\(540\) −5.25255e14 −0.492271
\(541\) 4.46615e14 7.73560e14i 0.414332 0.717644i −0.581026 0.813885i \(-0.697349\pi\)
0.995358 + 0.0962408i \(0.0306819\pi\)
\(542\) 2.80233e14 + 4.85379e14i 0.257350 + 0.445743i
\(543\) 5.98663e14 + 1.03691e15i 0.544231 + 0.942636i
\(544\) 1.53766e13 2.66330e13i 0.0138378 0.0239677i
\(545\) −6.23317e13 −0.0555301
\(546\) −8.16302e13 + 8.31483e14i −0.0719931 + 0.733321i
\(547\) −2.94327e14 −0.256980 −0.128490 0.991711i \(-0.541013\pi\)
−0.128490 + 0.991711i \(0.541013\pi\)
\(548\) −2.09270e14 + 3.62466e14i −0.180889 + 0.313310i
\(549\) −5.14212e14 8.90641e14i −0.440042 0.762175i
\(550\) −1.08740e15 1.88343e15i −0.921285 1.59571i
\(551\) 2.01471e14 3.48958e14i 0.168997 0.292711i
\(552\) −3.92344e14 −0.325838
\(553\) 5.66359e14 + 4.05578e14i 0.465697 + 0.333492i
\(554\) −7.38546e12 −0.00601276
\(555\) 1.41737e15 2.45496e15i 1.14254 1.97895i
\(556\) 1.67715e14 + 2.90490e14i 0.133863 + 0.231857i
\(557\) −6.13450e14 1.06253e15i −0.484814 0.839723i 0.515033 0.857170i \(-0.327780\pi\)
−0.999848 + 0.0174469i \(0.994446\pi\)
\(558\) 4.18795e14 7.25374e14i 0.327728 0.567642i
\(559\) −2.13022e14 −0.165067
\(560\) 5.62439e14 2.55051e14i 0.431560 0.195701i
\(561\) 2.60946e14 0.198269
\(562\) 2.54358e14 4.40560e14i 0.191379 0.331479i
\(563\) −1.69542e14 2.93656e14i −0.126323 0.218797i 0.795926 0.605393i \(-0.206984\pi\)
−0.922249 + 0.386596i \(0.873651\pi\)
\(564\) −2.74201e14 4.74930e14i −0.202318 0.350424i
\(565\) 4.58044e14 7.93356e14i 0.334689 0.579698i
\(566\) −8.99912e14 −0.651193
\(567\) 1.57879e15 7.15936e14i 1.13140 0.513059i
\(568\) 1.87108e14 0.132793
\(569\) −5.29388e14 + 9.16927e14i −0.372097 + 0.644492i −0.989888 0.141851i \(-0.954695\pi\)
0.617791 + 0.786343i \(0.288028\pi\)
\(570\) −4.18726e14 7.25255e14i −0.291487 0.504870i
\(571\) 7.73567e13 + 1.33986e14i 0.0533334 + 0.0923761i 0.891460 0.453100i \(-0.149682\pi\)
−0.838126 + 0.545476i \(0.816349\pi\)
\(572\) −3.04301e14 + 5.27065e14i −0.207790 + 0.359903i
\(573\) −1.57389e15 −1.06445
\(574\) 1.46077e15 + 1.04608e15i 0.978512 + 0.700726i
\(575\) 2.85809e15 1.89628
\(576\) −5.59009e13 + 9.68231e13i −0.0367362 + 0.0636290i
\(577\) 9.36749e14 + 1.62250e15i 0.609757 + 1.05613i 0.991280 + 0.131770i \(0.0420661\pi\)
−0.381524 + 0.924359i \(0.624601\pi\)
\(578\) 5.34910e14 + 9.26492e14i 0.344888 + 0.597363i
\(579\) −1.30603e15 + 2.26212e15i −0.834108 + 1.44472i
\(580\) 1.46685e15 0.927962
\(581\) 4.78910e13 4.87817e14i 0.0300113 0.305695i
\(582\) 2.27168e15 1.41017
\(583\) −1.21444e14 + 2.10347e14i −0.0746789 + 0.129348i
\(584\) −1.57878e14 2.73452e14i −0.0961724 0.166576i
\(585\) 7.63394e14 + 1.32224e15i 0.460672 + 0.797906i
\(586\) 6.11531e14 1.05920e15i 0.365579 0.633202i
\(587\) −2.97041e15 −1.75916 −0.879582 0.475747i \(-0.842178\pi\)
−0.879582 + 0.475747i \(0.842178\pi\)
\(588\) −7.07526e14 + 8.07802e14i −0.415114 + 0.473947i
\(589\) −9.36562e14 −0.544380
\(590\) −7.68695e14 + 1.33142e15i −0.442658 + 0.766706i
\(591\) 8.52921e14 + 1.47730e15i 0.486606 + 0.842826i
\(592\) 2.11581e14 + 3.66470e14i 0.119594 + 0.207142i
\(593\) −7.29897e14 + 1.26422e15i −0.408753 + 0.707981i −0.994750 0.102332i \(-0.967370\pi\)
0.585997 + 0.810313i \(0.300703\pi\)
\(594\) 6.65309e14 0.369146
\(595\) 5.27398e13 5.37207e14i 0.0289931 0.295324i
\(596\) −1.29919e13 −0.00707650
\(597\) 7.90466e14 1.36913e15i 0.426604 0.738899i
\(598\) −3.99908e14 6.92661e14i −0.213847 0.370394i
\(599\) −1.64855e15 2.85537e15i −0.873482 1.51292i −0.858371 0.513030i \(-0.828523\pi\)
−0.0151111 0.999886i \(-0.504810\pi\)
\(600\) 1.10003e15 1.90530e15i 0.577525 1.00030i
\(601\) 3.21190e15 1.67091 0.835453 0.549562i \(-0.185205\pi\)
0.835453 + 0.549562i \(0.185205\pi\)
\(602\) −2.22605e14 1.59410e14i −0.114750 0.0821743i
\(603\) −1.98888e15 −1.01593
\(604\) 2.70589e14 4.68674e14i 0.136964 0.237229i
\(605\) 1.91386e13 + 3.31491e13i 0.00959968 + 0.0166271i
\(606\) −2.14250e14 3.71092e14i −0.106493 0.184451i
\(607\) −8.86308e14 + 1.53513e15i −0.436563 + 0.756150i −0.997422 0.0717620i \(-0.977138\pi\)
0.560859 + 0.827912i \(0.310471\pi\)
\(608\) 1.25012e14 0.0610216
\(609\) −2.32291e15 + 1.05338e15i −1.12367 + 0.509552i
\(610\) −4.18618e15 −2.00680
\(611\) 5.58974e14 9.68172e14i 0.265561 0.459966i
\(612\) 4.88606e13 + 8.46290e13i 0.0230052 + 0.0398462i
\(613\) −6.28888e14 1.08927e15i −0.293454 0.508278i 0.681170 0.732126i \(-0.261472\pi\)
−0.974624 + 0.223847i \(0.928138\pi\)
\(614\) 8.40677e14 1.45610e15i 0.388779 0.673386i
\(615\) 8.86937e15 4.06518
\(616\) −7.12408e14 + 3.23058e14i −0.323620 + 0.146753i
\(617\) −2.99542e15 −1.34862 −0.674311 0.738448i \(-0.735559\pi\)
−0.674311 + 0.738448i \(0.735559\pi\)
\(618\) 7.30954e14 1.26605e15i 0.326177 0.564956i
\(619\) −8.41793e14 1.45803e15i −0.372312 0.644863i 0.617609 0.786485i \(-0.288101\pi\)
−0.989921 + 0.141623i \(0.954768\pi\)
\(620\) −1.70470e15 2.95263e15i −0.747298 1.29436i
\(621\) −4.37169e14 + 7.57200e14i −0.189953 + 0.329008i
\(622\) −2.54233e14 −0.109493
\(623\) −1.75943e15 1.25995e15i −0.751081 0.537860i
\(624\) −6.15669e14 −0.260514
\(625\) −3.73048e15 + 6.46138e15i −1.56468 + 2.71010i
\(626\) 7.46597e14 + 1.29314e15i 0.310404 + 0.537636i
\(627\) 5.30376e14 + 9.18638e14i 0.218581 + 0.378593i
\(628\) 5.49287e14 9.51393e14i 0.224399 0.388671i
\(629\) 3.69869e14 0.149785
\(630\) −1.91733e14 + 1.95299e15i −0.0769704 + 0.784019i
\(631\) 2.26833e15 0.902701 0.451351 0.892347i \(-0.350942\pi\)
0.451351 + 0.892347i \(0.350942\pi\)
\(632\) −2.56665e14 + 4.44556e14i −0.101256 + 0.175381i
\(633\) −3.06495e15 5.30866e15i −1.19868 2.07618i
\(634\) 1.31926e15 + 2.28503e15i 0.511493 + 0.885932i
\(635\) −1.87183e15 + 3.24211e15i −0.719468 + 1.24615i
\(636\) −2.45708e14 −0.0936278
\(637\) −2.14730e15 4.25721e14i −0.811194 0.160827i
\(638\) −1.85797e15 −0.695863
\(639\) −2.97277e14 + 5.14898e14i −0.110384 + 0.191191i
\(640\) 2.27544e14 + 3.94117e14i 0.0837674 + 0.145089i
\(641\) 1.44278e15 + 2.49896e15i 0.526599 + 0.912097i 0.999520 + 0.0309916i \(0.00986651\pi\)
−0.472920 + 0.881105i \(0.656800\pi\)
\(642\) 6.02732e14 1.04396e15i 0.218113 0.377783i
\(643\) −1.89915e15 −0.681394 −0.340697 0.940173i \(-0.610663\pi\)
−0.340697 + 0.940173i \(0.610663\pi\)
\(644\) 1.00440e14 1.02308e15i 0.0357302 0.363948i
\(645\) −1.35159e15 −0.476724
\(646\) 5.46341e13 9.46290e13i 0.0191067 0.0330937i
\(647\) −1.70611e14 2.95507e14i −0.0591607 0.102469i 0.834928 0.550359i \(-0.185509\pi\)
−0.894089 + 0.447890i \(0.852176\pi\)
\(648\) 6.38722e14 + 1.10630e15i 0.219609 + 0.380374i
\(649\) 9.73661e14 1.68643e15i 0.331942 0.574940i
\(650\) 4.48493e15 1.51612
\(651\) 4.81993e15 + 3.45162e15i 1.61564 + 1.15699i
\(652\) −5.33440e14 −0.177306
\(653\) 2.32967e15 4.03512e15i 0.767844 1.32994i −0.170886 0.985291i \(-0.554663\pi\)
0.938730 0.344653i \(-0.112004\pi\)
\(654\) 3.99343e13 + 6.91683e13i 0.0130517 + 0.0226063i
\(655\) −4.83819e15 8.37998e15i −1.56803 2.71591i
\(656\) −6.61997e14 + 1.14661e15i −0.212757 + 0.368507i
\(657\) 1.00334e15 0.319772
\(658\) 1.30863e15 5.93429e14i 0.413595 0.187554i
\(659\) 5.54119e15 1.73673 0.868367 0.495922i \(-0.165170\pi\)
0.868367 + 0.495922i \(0.165170\pi\)
\(660\) −1.93075e15 + 3.34415e15i −0.600114 + 1.03943i
\(661\) 1.65371e15 + 2.86430e15i 0.509742 + 0.882899i 0.999936 + 0.0112855i \(0.00359237\pi\)
−0.490195 + 0.871613i \(0.663074\pi\)
\(662\) 8.27567e14 + 1.43339e15i 0.252979 + 0.438172i
\(663\) −2.69065e14 + 4.66034e14i −0.0815705 + 0.141284i
\(664\) 3.61202e14 0.108599
\(665\) 1.99838e15 9.06213e14i 0.595882 0.270216i
\(666\) −1.34464e15 −0.397647
\(667\) 1.22086e15 2.11458e15i 0.358074 0.620202i
\(668\) −8.93228e14 1.54712e15i −0.259831 0.450041i
\(669\) 8.83841e14 + 1.53086e15i 0.254994 + 0.441663i
\(670\) −4.04785e15 + 7.01108e15i −1.15828 + 2.00620i
\(671\) 5.30239e15 1.50487
\(672\) −6.43365e14 4.60723e14i −0.181103 0.129691i
\(673\) 6.48265e15 1.80996 0.904982 0.425451i \(-0.139884\pi\)
0.904982 + 0.425451i \(0.139884\pi\)
\(674\) 2.18424e15 3.78322e15i 0.604884 1.04769i
\(675\) −2.45141e15 4.24596e15i −0.673356 1.16629i
\(676\) 2.90048e14 + 5.02378e14i 0.0790247 + 0.136875i
\(677\) 4.28701e14 7.42532e14i 0.115856 0.200668i −0.802266 0.596967i \(-0.796372\pi\)
0.918121 + 0.396299i \(0.129706\pi\)
\(678\) −1.17383e15 −0.314660
\(679\) −5.81553e14 + 5.92369e15i −0.154634 + 1.57510i
\(680\) 3.97773e14 0.104915
\(681\) 1.87903e15 3.25458e15i 0.491615 0.851502i
\(682\) 2.15924e15 + 3.73992e15i 0.560386 + 0.970617i
\(683\) −1.23204e15 2.13396e15i −0.317184 0.549378i 0.662716 0.748871i \(-0.269404\pi\)
−0.979899 + 0.199493i \(0.936071\pi\)
\(684\) −1.98619e14 + 3.44019e14i −0.0507240 + 0.0878565i
\(685\) −5.41354e15 −1.37146
\(686\) −1.92531e15 2.05176e15i −0.483859 0.515636i
\(687\) −3.80470e15 −0.948545
\(688\) 1.00881e14 1.74731e14i 0.0249501 0.0432148i
\(689\) −2.50445e14 4.33783e14i −0.0614478 0.106431i
\(690\) −2.53736e15 4.39483e15i −0.617606 1.06973i
\(691\) −1.74499e15 + 3.02241e15i −0.421369 + 0.729833i −0.996074 0.0885279i \(-0.971784\pi\)
0.574704 + 0.818361i \(0.305117\pi\)
\(692\) 1.48355e15 0.355400
\(693\) 2.42857e14 2.47373e15i 0.0577188 0.587923i
\(694\) 1.27163e15 0.299835
\(695\) −2.16928e15 + 3.75730e15i −0.507457 + 0.878941i
\(696\) −9.39770e14 1.62773e15i −0.218108 0.377773i
\(697\) 5.78623e14 + 1.00221e15i 0.133234 + 0.230768i
\(698\) 9.62779e14 1.66758e15i 0.219949 0.380962i
\(699\) −2.71895e15 −0.616277
\(700\) 4.68669e15 + 3.35621e15i 1.05397 + 0.754761i
\(701\) −6.39900e14 −0.142779 −0.0713893 0.997449i \(-0.522743\pi\)
−0.0713893 + 0.997449i \(0.522743\pi\)
\(702\) −6.86009e14 + 1.18820e15i −0.151871 + 0.263049i
\(703\) 7.51763e14 + 1.30209e15i 0.165130 + 0.286014i
\(704\) −2.88216e14 4.99205e14i −0.0628157 0.108800i
\(705\) 3.54661e15 6.14291e15i 0.766961 1.32842i
\(706\) −5.17002e15 −1.10935
\(707\) 1.02251e15 4.63683e14i 0.217702 0.0987220i
\(708\) 1.96993e15 0.416168
\(709\) −1.71765e15 + 2.97505e15i −0.360064 + 0.623649i −0.987971 0.154639i \(-0.950579\pi\)
0.627907 + 0.778288i \(0.283912\pi\)
\(710\) 1.21006e15 + 2.09589e15i 0.251702 + 0.435960i
\(711\) −8.15576e14 1.41262e15i −0.168338 0.291570i
\(712\) 7.97343e14 1.38104e15i 0.163307 0.282856i
\(713\) −5.67529e15 −1.15344
\(714\) −6.29917e14 + 2.85650e14i −0.127041 + 0.0576095i
\(715\) −7.87188e15 −1.57542
\(716\) 1.32932e15 2.30246e15i 0.264003 0.457267i
\(717\) 3.22488e15 + 5.58566e15i 0.635562 + 1.10083i
\(718\) −1.87788e15 3.25259e15i −0.367268 0.636128i
\(719\) −3.00521e15 + 5.20518e15i −0.583265 + 1.01024i 0.411824 + 0.911263i \(0.364892\pi\)
−0.995089 + 0.0989813i \(0.968442\pi\)
\(720\) −1.44608e15 −0.278525
\(721\) 3.11425e15 + 2.23016e15i 0.595264 + 0.426277i
\(722\) −3.28351e15 −0.622851
\(723\) 3.07607e15 5.32792e15i 0.579077 1.00299i
\(724\) −1.15590e15 2.00208e15i −0.215952 0.374041i
\(725\) 6.84589e15 + 1.18574e16i 1.26932 + 2.19853i
\(726\) 2.45233e13 4.24756e13i 0.00451260 0.00781606i
\(727\) 2.27216e15 0.414954 0.207477 0.978240i \(-0.433475\pi\)
0.207477 + 0.978240i \(0.433475\pi\)
\(728\) 1.57612e14 1.60543e15i 0.0285671 0.290984i
\(729\) −4.20716e14 −0.0756812
\(730\) 2.04205e15 3.53693e15i 0.364578 0.631468i
\(731\) −8.81757e13 1.52725e14i −0.0156244 0.0270623i
\(732\) 2.68198e15 + 4.64533e15i 0.471677 + 0.816968i
\(733\) 4.45928e15 7.72370e15i 0.778382 1.34820i −0.154492 0.987994i \(-0.549374\pi\)
0.932874 0.360203i \(-0.117293\pi\)
\(734\) −1.67859e15 −0.290815
\(735\) −1.36243e16 2.70114e15i −2.34279 0.464479i
\(736\) 7.57539e14 0.129294
\(737\) 5.12717e15 8.88052e15i 0.868574 1.50441i
\(738\) −2.10356e15 3.64347e15i −0.353708 0.612640i
\(739\) 7.73813e14 + 1.34028e15i 0.129149 + 0.223693i 0.923347 0.383966i \(-0.125442\pi\)
−0.794198 + 0.607659i \(0.792109\pi\)
\(740\) −2.73667e15 + 4.74005e15i −0.453365 + 0.785251i
\(741\) −2.18751e15 −0.359708
\(742\) 6.29014e13 6.40713e14i 0.0102669 0.104578i
\(743\) −1.10643e16 −1.79260 −0.896301 0.443446i \(-0.853756\pi\)
−0.896301 + 0.443446i \(0.853756\pi\)
\(744\) −2.18431e15 + 3.78334e15i −0.351289 + 0.608450i
\(745\) −8.40211e13 1.45529e14i −0.0134131 0.0232321i
\(746\) −7.60686e14 1.31755e15i −0.120543 0.208787i
\(747\) −5.73877e14 + 9.93984e14i −0.0902725 + 0.156357i
\(748\) −5.03835e14 −0.0786737
\(749\) 2.56796e15 + 1.83895e15i 0.398050 + 0.285049i
\(750\) 1.74807e16 2.68981
\(751\) −5.48465e15 + 9.49968e15i −0.837778 + 1.45107i 0.0539706 + 0.998543i \(0.482812\pi\)
−0.891749 + 0.452531i \(0.850521\pi\)
\(752\) 5.29428e14 + 9.16995e14i 0.0802802 + 0.139049i
\(753\) 1.10100e15 + 1.90699e15i 0.165735 + 0.287062i
\(754\) 1.91578e15 3.31822e15i 0.286287 0.495864i
\(755\) 6.99979e15 1.03843
\(756\) −1.60604e15 + 7.28295e14i −0.236530 + 0.107260i
\(757\) −7.15456e15 −1.04606 −0.523029 0.852315i \(-0.675198\pi\)
−0.523029 + 0.852315i \(0.675198\pi\)
\(758\) −5.37338e14 + 9.30698e14i −0.0779951 + 0.135091i
\(759\) 3.21392e15 + 5.56667e15i 0.463133 + 0.802169i
\(760\) 8.08478e14 + 1.40032e15i 0.115663 + 0.200334i
\(761\) 1.07138e15 1.85568e15i 0.152169 0.263565i −0.779855 0.625960i \(-0.784707\pi\)
0.932025 + 0.362395i \(0.118041\pi\)
\(762\) 4.79694e15 0.676413
\(763\) −1.90588e14 + 8.64264e13i −0.0266815 + 0.0120993i
\(764\) 3.03887e15 0.422375
\(765\) −6.31980e14 + 1.09462e15i −0.0872099 + 0.151052i
\(766\) 1.19465e14 + 2.06919e14i 0.0163675 + 0.0283493i
\(767\) 2.00791e15 + 3.47780e15i 0.273130 + 0.473076i
\(768\) 2.91563e14 5.05001e14i 0.0393772 0.0682034i
\(769\) −6.61329e15 −0.886795 −0.443397 0.896325i \(-0.646227\pi\)
−0.443397 + 0.896325i \(0.646227\pi\)
\(770\) −8.22600e15 5.89076e15i −1.09519 0.784282i
\(771\) 9.04731e15 1.19597
\(772\) 2.52169e15 4.36770e15i 0.330976 0.573268i
\(773\) 2.38849e15 + 4.13699e15i 0.311270 + 0.539135i 0.978638 0.205593i \(-0.0659124\pi\)
−0.667368 + 0.744728i \(0.732579\pi\)
\(774\) 3.20559e14 + 5.55224e14i 0.0414794 + 0.0718444i
\(775\) 1.59120e16 2.75603e16i 2.04439 3.54099i
\(776\) −4.38617e15 −0.559560
\(777\) 9.29872e14 9.47166e15i 0.117790 1.19980i
\(778\) 7.95029e15 0.999988
\(779\) −2.35212e15 + 4.07399e15i −0.293767 + 0.508820i
\(780\) −3.98164e15 6.89640e15i −0.493789 0.855268i
\(781\) −1.53271e15 2.65473e15i −0.188747 0.326919i
\(782\) 3.31066e14 5.73424e14i 0.0404835 0.0701194i
\(783\) −4.18856e15 −0.508598
\(784\) 1.36609e15 1.55971e15i 0.164718 0.188064i
\(785\) 1.42094e16 1.70134
\(786\) −6.19940e15 + 1.07377e16i −0.737099 + 1.27669i
\(787\) 4.62968e15 + 8.01884e15i 0.546626 + 0.946784i 0.998503 + 0.0547033i \(0.0174213\pi\)
−0.451877 + 0.892080i \(0.649245\pi\)
\(788\) −1.64682e15 2.85238e15i −0.193087 0.334436i
\(789\) −5.54052e15 + 9.59646e15i −0.645100 + 1.11735i
\(790\) −6.63959e15 −0.767701
\(791\) 3.00501e14 3.06090e15i 0.0345045 0.351462i
\(792\) 1.83167e15 0.208861
\(793\) −5.46737e15 + 9.46977e15i −0.619122 + 1.07235i
\(794\) −9.49438e14 1.64448e15i −0.106771 0.184933i
\(795\) −1.58904e15 2.75229e15i −0.177466 0.307380i
\(796\) −1.52623e15 + 2.64352e15i −0.169278 + 0.293197i
\(797\) 1.62475e15 0.178964 0.0894821 0.995988i \(-0.471479\pi\)
0.0894821 + 0.995988i \(0.471479\pi\)
\(798\) −2.28592e15 1.63698e15i −0.250061 0.179072i
\(799\) 9.25501e14 0.100547
\(800\) −2.12393e15 + 3.67876e15i −0.229164 + 0.396923i
\(801\) 2.53363e15 + 4.38838e15i 0.271497 + 0.470247i
\(802\) 4.70793e15 + 8.15438e15i 0.501039 + 0.867825i
\(803\) −2.58654e15 + 4.48002e15i −0.273391 + 0.473527i
\(804\) 1.03734e16 1.08896
\(805\) 1.21096e16 5.49139e15i 1.26256 0.572538i
\(806\) −8.90570e15 −0.922201
\(807\) −4.54155e15 + 7.86619e15i −0.467089 + 0.809022i
\(808\) 4.13674e14 + 7.16505e14i 0.0422568 + 0.0731909i
\(809\) −5.21943e15 9.04033e15i −0.529549 0.917207i −0.999406 0.0344638i \(-0.989028\pi\)
0.469856 0.882743i \(-0.344306\pi\)
\(810\) −8.26147e15 + 1.43093e16i −0.832510 + 1.44195i
\(811\) 3.09719e15 0.309994 0.154997 0.987915i \(-0.450463\pi\)
0.154997 + 0.987915i \(0.450463\pi\)
\(812\) 4.48508e15 2.03386e15i 0.445874 0.202192i
\(813\) 9.28885e15 0.917200
\(814\) 3.46638e15 6.00394e15i 0.339971 0.588847i
\(815\) −3.44985e15 5.97532e15i −0.336073 0.582095i
\(816\) −2.54843e14 4.41400e14i −0.0246590 0.0427107i
\(817\) 3.58436e14 6.20830e14i 0.0344501 0.0596694i
\(818\) −1.92331e14 −0.0183614
\(819\) 4.16754e15 + 2.98443e15i 0.395201 + 0.283009i
\(820\) −1.71250e16 −1.61307
\(821\) −1.77499e15 + 3.07437e15i −0.166077 + 0.287653i −0.937037 0.349230i \(-0.886443\pi\)
0.770960 + 0.636883i \(0.219777\pi\)
\(822\) 3.46831e15 + 6.00729e15i 0.322347 + 0.558321i
\(823\) −6.30252e15 1.09163e16i −0.581856 1.00780i −0.995259 0.0972556i \(-0.968994\pi\)
0.413404 0.910548i \(-0.364340\pi\)
\(824\) −1.41133e15 + 2.44449e15i −0.129428 + 0.224176i
\(825\) −3.60438e16 −3.28348
\(826\) −5.04305e14 + 5.13684e15i −0.0456355 + 0.464842i
\(827\) −1.86886e16 −1.67995 −0.839977 0.542623i \(-0.817431\pi\)
−0.839977 + 0.542623i \(0.817431\pi\)
\(828\) −1.20358e15 + 2.08465e15i −0.107475 + 0.186152i
\(829\) −1.00376e16 1.73856e16i −0.890389 1.54220i −0.839409 0.543500i \(-0.817099\pi\)
−0.0509802 0.998700i \(-0.516235\pi\)
\(830\) 2.33596e15 + 4.04600e15i 0.205843 + 0.356530i
\(831\) −6.12012e13 + 1.06004e14i −0.00535740 + 0.00927929i
\(832\) 1.18873e15 0.103373
\(833\) −5.83608e14 1.71571e15i −0.0504166 0.148216i
\(834\) 5.55921e15 0.477089
\(835\) 1.15533e16 2.00110e16i 0.984990 1.70605i
\(836\) −1.02405e15 1.77371e15i −0.0867335 0.150227i
\(837\) 4.86775e15 + 8.43119e15i 0.409579 + 0.709412i
\(838\) 2.25936e15 3.91333e15i 0.188861 0.327118i
\(839\) 1.37327e16 1.14042 0.570211 0.821498i \(-0.306861\pi\)
0.570211 + 0.821498i \(0.306861\pi\)
\(840\) 1.00002e15 1.01862e16i 0.0825039 0.840383i
\(841\) −5.03388e14 −0.0412596
\(842\) 6.52935e15 1.13092e16i 0.531684 0.920904i
\(843\) −4.21558e15 7.30159e15i −0.341040 0.590699i
\(844\) 5.91782e15 + 1.02500e16i 0.475640 + 0.823833i
\(845\) −3.75158e15 + 6.49793e15i −0.299573 + 0.518876i
\(846\) −3.36461e15 −0.266930
\(847\) 1.04482e14 + 7.48211e13i 0.00823537 + 0.00589747i
\(848\) 4.74413e14 0.0371518
\(849\) −7.45731e15 + 1.29164e16i −0.580216 + 1.00496i
\(850\) 1.85644e15 + 3.21545e15i 0.143508 + 0.248563i
\(851\) 4.55546e15 + 7.89029e15i 0.349881 + 0.606011i
\(852\) 1.55051e15 2.68556e15i 0.118319 0.204935i
\(853\) 1.09276e15 0.0828525 0.0414263 0.999142i \(-0.486810\pi\)
0.0414263 + 0.999142i \(0.486810\pi\)
\(854\) −1.27998e16 + 5.80438e15i −0.964242 + 0.437258i
\(855\) −5.13803e15 −0.384577
\(856\) −1.16376e15 + 2.01569e15i −0.0865479 + 0.149905i
\(857\) −2.46617e15 4.27153e15i −0.182234 0.315638i 0.760407 0.649447i \(-0.224999\pi\)
−0.942641 + 0.333809i \(0.891666\pi\)
\(858\) 5.04331e15 + 8.73526e15i 0.370284 + 0.641351i
\(859\) 1.29644e16 2.24550e16i 0.945778 1.63814i 0.191592 0.981475i \(-0.438635\pi\)
0.754186 0.656661i \(-0.228032\pi\)
\(860\) 2.60966e15 0.189166
\(861\) 2.71193e16 1.22979e16i 1.95327 0.885753i
\(862\) −9.64073e15 −0.689954
\(863\) −6.96822e15 + 1.20693e16i −0.495521 + 0.858268i −0.999987 0.00516371i \(-0.998356\pi\)
0.504465 + 0.863432i \(0.331690\pi\)
\(864\) −6.49748e14 1.12540e15i −0.0459113 0.0795206i
\(865\) 9.59436e15 + 1.66179e16i 0.673640 + 1.16678i
\(866\) −2.08420e14 + 3.60994e14i −0.0145409 + 0.0251855i
\(867\) 1.77306e16 1.22919
\(868\) −9.30633e15 6.66440e15i −0.641092 0.459095i
\(869\) 8.40997e15 0.575686
\(870\) 1.21553e16 2.10536e16i 0.826819 1.43209i
\(871\) 1.05734e16 + 1.83137e16i 0.714685 + 1.23787i
\(872\) −7.71053e13 1.33550e14i −0.00517897 0.00897024i
\(873\) 6.96874e15 1.20702e16i 0.465132 0.805632i
\(874\) 2.69159e15 0.178523
\(875\) −4.47507e15 + 4.55830e16i −0.294955 + 3.00440i
\(876\) −5.23315e15 −0.342760
\(877\) −1.17094e15 + 2.02813e15i −0.0762145 + 0.132007i −0.901614 0.432542i \(-0.857617\pi\)
0.825399 + 0.564549i \(0.190950\pi\)
\(878\) −7.89915e15 1.36817e16i −0.510929 0.884955i
\(879\) −1.01352e16 1.75546e16i −0.651466 1.12837i
\(880\) 3.72789e15 6.45689e15i 0.238127 0.412448i
\(881\) −3.04179e16 −1.93091 −0.965456 0.260567i \(-0.916091\pi\)
−0.965456 + 0.260567i \(0.916091\pi\)
\(882\) 2.12168e15 + 6.23738e15i 0.133845 + 0.393482i
\(883\) −7.32437e15 −0.459184 −0.229592 0.973287i \(-0.573739\pi\)
−0.229592 + 0.973287i \(0.573739\pi\)
\(884\) 5.19512e14 8.99820e14i 0.0323674 0.0560620i
\(885\) 1.27399e16 + 2.20662e16i 0.788821 + 1.36628i
\(886\) 1.16876e15 + 2.02436e15i 0.0719185 + 0.124567i
\(887\) −1.04579e16 + 1.81136e16i −0.639533 + 1.10770i 0.346002 + 0.938234i \(0.387539\pi\)
−0.985535 + 0.169471i \(0.945794\pi\)
\(888\) 7.01326e15 0.426234
\(889\) −1.22802e15 + 1.25086e16i −0.0741730 + 0.755525i
\(890\) 2.06262e16 1.23816
\(891\) 1.04643e16 1.81247e16i 0.624285 1.08129i
\(892\) −1.70652e15 2.95578e15i −0.101182 0.175253i
\(893\) 1.88109e15 + 3.25815e15i 0.110848 + 0.191994i
\(894\) −1.07660e14 + 1.86473e14i −0.00630520 + 0.0109209i
\(895\) 3.43879e16 2.00161
\(896\) 1.24221e15 + 8.89565e14i 0.0718623 + 0.0514617i
\(897\) −1.32557e16 −0.762156
\(898\) −8.96496e15 + 1.55278e16i −0.512305 + 0.887338i
\(899\) −1.35939e16 2.35452e16i −0.772084 1.33729i
\(900\) −6.74900e15 1.16896e16i −0.380983 0.659882i
\(901\) 2.07332e14 3.59110e14i 0.0116327 0.0201484i
\(902\) 2.16912e16 1.20962
\(903\) −4.13268e15 + 1.87406e15i −0.229060 + 0.103872i
\(904\) 2.26643e15 0.124858
\(905\) 1.49508e16 2.58956e16i 0.818649 1.41794i
\(906\) −4.48459e15 7.76753e15i −0.244072 0.422744i
\(907\) −5.20878e15 9.02187e15i −0.281771 0.488041i 0.690050 0.723761i \(-0.257588\pi\)
−0.971821 + 0.235720i \(0.924255\pi\)
\(908\) −3.62804e15 + 6.28395e15i −0.195074 + 0.337879i
\(909\) −2.62898e15 −0.140503
\(910\) 1.90025e16 8.61712e15i 1.00945 0.457756i
\(911\) 3.31593e16 1.75087 0.875435 0.483335i \(-0.160575\pi\)
0.875435 + 0.483335i \(0.160575\pi\)
\(912\) 1.03594e15 1.79430e15i 0.0543705 0.0941726i
\(913\) −2.95882e15 5.12483e15i −0.154358 0.267356i
\(914\) −5.77231e15 9.99794e15i −0.299327 0.518450i
\(915\) −3.46897e16 + 6.00843e16i −1.78807 + 3.09703i
\(916\) 7.34612e15 0.376386
\(917\) −2.64127e16 1.89145e16i −1.34518 0.963306i
\(918\) −1.13583e15 −0.0575017
\(919\) −2.31162e14 + 4.00385e14i −0.0116327 + 0.0201485i −0.871783 0.489892i \(-0.837036\pi\)
0.860150 + 0.510040i \(0.170370\pi\)
\(920\) 4.89914e15 + 8.48556e15i 0.245068 + 0.424470i
\(921\) −1.39329e16 2.41325e16i −0.692809 1.19998i
\(922\) 1.10546e16 1.91472e16i 0.546418 0.946424i
\(923\) 6.32160e15 0.310612
\(924\) −1.26667e15 + 1.29023e16i −0.0618683 + 0.630189i
\(925\) −5.10891e16 −2.48055
\(926\) −1.57005e15 + 2.71941e15i −0.0757799 + 0.131255i
\(927\) −4.48463e15 7.76761e15i −0.215173 0.372691i
\(928\) 1.81451e15 + 3.14282e15i 0.0865457 + 0.149902i
\(929\) 1.18527e16 2.05295e16i 0.561994 0.973401i −0.435329 0.900271i \(-0.643368\pi\)
0.997322 0.0731299i \(-0.0232988\pi\)
\(930\) −5.65054e16 −2.66338
\(931\) 4.85382e15 5.54174e15i 0.227437 0.259671i
\(932\) 5.24975e15 0.244541
\(933\) −2.10676e15 + 3.64901e15i −0.0975585 + 0.168976i
\(934\) 4.80509e14 + 8.32265e14i 0.0221204 + 0.0383137i
\(935\) −3.25839e15 5.64370e15i −0.149121 0.258286i
\(936\) −1.88866e15 + 3.27125e15i −0.0859284 + 0.148832i
\(937\) −2.10718e16 −0.953088 −0.476544 0.879150i \(-0.658111\pi\)
−0.476544 + 0.879150i \(0.658111\pi\)
\(938\) −2.65560e15 + 2.70499e16i −0.119412 + 1.21633i
\(939\) 2.47473e16 1.10629
\(940\) −6.84781e15 + 1.18607e16i −0.304332 + 0.527119i
\(941\) 1.09949e16 + 1.90438e16i 0.485790 + 0.841414i 0.999867 0.0163307i \(-0.00519847\pi\)
−0.514076 + 0.857745i \(0.671865\pi\)
\(942\) −9.10356e15 1.57678e16i −0.399882 0.692615i
\(943\) −1.42531e16 + 2.46872e16i −0.622438 + 1.07810i
\(944\) −3.80355e15 −0.165137
\(945\) −1.85445e16 1.32800e16i −0.800462 0.573222i
\(946\) −3.30550e15 −0.141852
\(947\) 2.75768e14 4.77644e14i 0.0117657 0.0203788i −0.860083 0.510155i \(-0.829588\pi\)
0.871848 + 0.489776i \(0.162921\pi\)
\(948\) 4.25381e15 + 7.36782e15i 0.180440 + 0.312531i
\(949\) −5.33404e15 9.23883e15i −0.224953 0.389630i
\(950\) −7.54647e15 + 1.30709e16i −0.316420 + 0.548056i
\(951\) 4.37293e16 1.82297
\(952\) 1.21624e15 5.51534e14i 0.0504101 0.0228596i
\(953\) 3.68726e16 1.51947 0.759736 0.650232i \(-0.225328\pi\)
0.759736 + 0.650232i \(0.225328\pi\)
\(954\) −7.53747e14 + 1.30553e15i −0.0308823 + 0.0534897i
\(955\) 1.96529e16 + 3.40398e16i 0.800586 + 1.38666i
\(956\) −6.22661e15 1.07848e16i −0.252193 0.436811i
\(957\) −1.53964e16 + 2.66674e16i −0.620018 + 1.07390i
\(958\) 2.57068e16 1.02929
\(959\) −1.65526e16 + 7.50617e15i −0.658969 + 0.298824i
\(960\) 7.54235e15 0.298549
\(961\) −1.88921e16 + 3.27220e16i −0.743534 + 1.28784i
\(962\) 7.14847e15 + 1.23815e16i 0.279737 + 0.484519i
\(963\) −3.69795e15 6.40503e15i −0.143885 0.249216i
\(964\) −5.93929e15 + 1.02872e16i −0.229779 + 0.397989i
\(965\) 6.52330e16 2.50938
\(966\) −1.38520e16 9.91962e15i −0.529832 0.379420i
\(967\) −4.62899e16 −1.76052 −0.880260 0.474492i \(-0.842632\pi\)
−0.880260 + 0.474492i \(0.842632\pi\)
\(968\) −4.73496e13 + 8.20119e13i −0.00179061 + 0.00310143i
\(969\) −9.05473e14 1.56833e15i −0.0340482 0.0589733i
\(970\) −2.83662e16 4.91317e16i −1.06061 1.83703i
\(971\) 2.55588e16 4.42692e16i 0.950244 1.64587i 0.205350 0.978689i \(-0.434167\pi\)
0.744894 0.667183i \(-0.232500\pi\)
\(972\) 1.41464e16 0.522977
\(973\) −1.42316e15 + 1.44963e16i −0.0523159 + 0.532889i
\(974\) 2.49441e15 0.0911789
\(975\) 3.71653e16 6.43722e16i 1.35087 2.33977i
\(976\) −5.17837e15 8.96921e15i −0.187163 0.324175i
\(977\) −1.08836e16 1.88510e16i −0.391160 0.677509i 0.601443 0.798916i \(-0.294593\pi\)
−0.992603 + 0.121407i \(0.961259\pi\)
\(978\) −4.42046e15 + 7.65646e15i −0.157981 + 0.273630i
\(979\) −2.61260e16 −0.928472
\(980\) 2.63058e16 + 5.21536e15i 0.929625 + 0.184307i
\(981\) 4.90019e14 0.0172200
\(982\) −5.95927e15 + 1.03218e16i −0.208247 + 0.360695i
\(983\) −1.12235e16 1.94396e16i −0.390017 0.675529i 0.602435 0.798168i \(-0.294197\pi\)
−0.992451 + 0.122640i \(0.960864\pi\)
\(984\) 1.09715e16 + 1.90033e16i 0.379136 + 0.656683i
\(985\) 2.13006e16 3.68937e16i 0.731968 1.26781i
\(986\) 3.17197e15 0.108394
\(987\) 2.32676e15 2.37004e16i 0.0790693 0.805398i
\(988\) 4.22366e15 0.142733
\(989\) 2.17202e15 3.76205e15i 0.0729935 0.126428i
\(990\) 1.18457e16 + 2.05174e16i 0.395884 + 0.685691i
\(991\) 2.96899e14 + 5.14244e14i 0.00986741 + 0.0170909i 0.870917 0.491430i \(-0.163526\pi\)
−0.861050 + 0.508521i \(0.830192\pi\)
\(992\) 4.21748e15 7.30489e15i 0.139392 0.241435i
\(993\) 2.74312e16 0.901622
\(994\) 6.60599e15 + 4.73064e15i 0.215930 + 0.154630i
\(995\) −3.94817e16 −1.28342
\(996\) 2.99318e15 5.18433e15i 0.0967623 0.167597i
\(997\) 2.07585e16 + 3.59547e16i 0.667379 + 1.15593i 0.978635 + 0.205607i \(0.0659170\pi\)
−0.311256 + 0.950326i \(0.600750\pi\)
\(998\) 1.79014e16 + 3.10062e16i 0.572361 + 0.991358i
\(999\) 7.81453e15 1.35352e16i 0.248481 0.430381i
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 14.12.c.a.9.4 8
3.2 odd 2 126.12.g.e.37.1 8
4.3 odd 2 112.12.i.a.65.1 8
7.2 even 3 98.12.a.j.1.1 4
7.3 odd 6 98.12.c.l.67.1 8
7.4 even 3 inner 14.12.c.a.11.4 yes 8
7.5 odd 6 98.12.a.l.1.4 4
7.6 odd 2 98.12.c.l.79.1 8
21.11 odd 6 126.12.g.e.109.1 8
28.11 odd 6 112.12.i.a.81.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.12.c.a.9.4 8 1.1 even 1 trivial
14.12.c.a.11.4 yes 8 7.4 even 3 inner
98.12.a.j.1.1 4 7.2 even 3
98.12.a.l.1.4 4 7.5 odd 6
98.12.c.l.67.1 8 7.3 odd 6
98.12.c.l.79.1 8 7.6 odd 2
112.12.i.a.65.1 8 4.3 odd 2
112.12.i.a.81.1 8 28.11 odd 6
126.12.g.e.37.1 8 3.2 odd 2
126.12.g.e.109.1 8 21.11 odd 6