Properties

Label 14.12.c.b.9.3
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: \( x^{8} - x^{7} + 149344 x^{6} + 5578711 x^{5} + 20557200983 x^{4} + 408905884576 x^{3} + 267736482219682 x^{2} + \cdots + 30\!\cdots\!24 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{12}\cdot 3\cdot 7^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 9.3
Root \(51.3434 + 88.9294i\) of defining polynomial
Character \(\chi\) \(=\) 14.9
Dual form 14.12.c.b.11.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(16.0000 - 27.7128i) q^{2} +(69.1868 + 119.835i) q^{3} +(-512.000 - 886.810i) q^{4} +(274.515 - 475.474i) q^{5} +4427.96 q^{6} +(-25454.3 - 36461.0i) q^{7} -32768.0 q^{8} +(78999.9 - 136832. i) q^{9} +O(q^{10})\) \(q+(16.0000 - 27.7128i) q^{2} +(69.1868 + 119.835i) q^{3} +(-512.000 - 886.810i) q^{4} +(274.515 - 475.474i) q^{5} +4427.96 q^{6} +(-25454.3 - 36461.0i) q^{7} -32768.0 q^{8} +(78999.9 - 136832. i) q^{9} +(-8784.49 - 15215.2i) q^{10} +(-123934. - 214661. i) q^{11} +(70847.3 - 122711. i) q^{12} -1.83800e6 q^{13} +(-1.41771e6 + 122034. i) q^{14} +75971.3 q^{15} +(-524288. + 908093. i) q^{16} +(-3.08342e6 - 5.34065e6i) q^{17} +(-2.52800e6 - 4.37862e6i) q^{18} +(841196. - 1.45699e6i) q^{19} -562207. q^{20} +(2.60820e6 - 5.57294e6i) q^{21} -7.93180e6 q^{22} +(8.79546e6 - 1.52342e7i) q^{23} +(-2.26711e6 - 3.92676e6i) q^{24} +(2.42633e7 + 4.20253e7i) q^{25} +(-2.94079e7 + 5.09360e7i) q^{26} +4.63755e7 q^{27} +(-1.93014e7 + 4.12412e7i) q^{28} +1.50671e8 q^{29} +(1.21554e6 - 2.10538e6i) q^{30} +(5.90206e7 + 1.02227e8i) q^{31} +(1.67772e7 + 2.90590e7i) q^{32} +(1.71493e7 - 2.97034e7i) q^{33} -1.97339e8 q^{34} +(-2.43239e7 + 2.09377e6i) q^{35} -1.61792e8 q^{36} +(2.77318e8 - 4.80329e8i) q^{37} +(-2.69183e7 - 4.66238e7i) q^{38} +(-1.27165e8 - 2.20256e8i) q^{39} +(-8.99531e6 + 1.55803e7i) q^{40} -4.42101e8 q^{41} +(-1.12711e8 - 1.61448e8i) q^{42} -5.11519e8 q^{43} +(-1.26909e8 + 2.19813e8i) q^{44} +(-4.33733e7 - 7.51248e7i) q^{45} +(-2.81455e8 - 4.87494e8i) q^{46} +(3.64835e7 - 6.31913e7i) q^{47} -1.45095e8 q^{48} +(-6.81483e8 + 1.85618e9i) q^{49} +1.55285e9 q^{50} +(4.26665e8 - 7.39005e8i) q^{51} +(9.41054e8 + 1.62995e9i) q^{52} +(-5.60906e8 - 9.71518e8i) q^{53} +(7.42007e8 - 1.28519e9i) q^{54} -1.36088e8 q^{55} +(8.34087e8 + 1.19475e9i) q^{56} +2.32799e8 q^{57} +(2.41074e9 - 4.17553e9i) q^{58} +(4.44766e9 + 7.70358e9i) q^{59} +(-3.88973e7 - 6.73721e7i) q^{60} +(-4.28033e8 + 7.41375e8i) q^{61} +3.77732e9 q^{62} +(-6.99991e9 + 6.02544e8i) q^{63} +1.07374e9 q^{64} +(-5.04558e8 + 8.73920e8i) q^{65} +(-5.48776e8 - 9.50508e8i) q^{66} +(-1.95943e9 - 3.39384e9i) q^{67} +(-3.15743e9 + 5.46882e9i) q^{68} +2.43412e9 q^{69} +(-3.31158e8 + 7.07583e8i) q^{70} -2.40314e9 q^{71} +(-2.58867e9 + 4.48370e9i) q^{72} +(-1.22579e10 - 2.12312e10i) q^{73} +(-8.87419e9 - 1.53705e10i) q^{74} +(-3.35741e9 + 5.81520e9i) q^{75} -1.72277e9 q^{76} +(-4.67208e9 + 9.98281e9i) q^{77} -8.13857e9 q^{78} +(1.75728e10 - 3.04369e10i) q^{79} +(2.87850e8 + 4.98571e8i) q^{80} +(-1.07860e10 - 1.86819e10i) q^{81} +(-7.07361e9 + 1.22519e10i) q^{82} +6.12728e10 q^{83} +(-6.27754e9 + 5.40363e8i) q^{84} -3.38579e9 q^{85} +(-8.18430e9 + 1.41756e10i) q^{86} +(1.04245e10 + 1.80557e10i) q^{87} +(4.06108e9 + 7.03400e9i) q^{88} +(-1.76449e10 + 3.05618e10i) q^{89} -2.77589e9 q^{90} +(4.67849e10 + 6.70152e10i) q^{91} -1.80131e10 q^{92} +(-8.16689e9 + 1.41455e10i) q^{93} +(-1.16747e9 - 2.02212e9i) q^{94} +(-4.61842e8 - 7.99934e8i) q^{95} +(-2.32152e9 + 4.02100e9i) q^{96} +1.31739e11 q^{97} +(4.05362e10 + 4.85847e10i) q^{98} -3.91632e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 128 q^{2} - 266 q^{3} - 4096 q^{4} + 3808 q^{5} - 17024 q^{6} + 110328 q^{7} - 262144 q^{8} - 503848 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 128 q^{2} - 266 q^{3} - 4096 q^{4} + 3808 q^{5} - 17024 q^{6} + 110328 q^{7} - 262144 q^{8} - 503848 q^{9} - 121856 q^{10} + 920150 q^{11} - 272384 q^{12} + 997472 q^{13} + 1396800 q^{14} - 500444 q^{15} - 4194304 q^{16} + 1333724 q^{17} + 16123136 q^{18} - 21551726 q^{19} - 7798784 q^{20} - 90442480 q^{21} + 58889600 q^{22} + 72510158 q^{23} + 8716288 q^{24} - 77154744 q^{25} + 15959552 q^{26} + 156683212 q^{27} - 68278272 q^{28} + 213575104 q^{29} - 8007104 q^{30} - 194359774 q^{31} + 134217728 q^{32} - 164547124 q^{33} + 85358336 q^{34} - 981719074 q^{35} + 1031880704 q^{36} + 171517048 q^{37} + 689655232 q^{38} - 653125236 q^{39} - 124780544 q^{40} - 3312095136 q^{41} - 1152719104 q^{42} + 850279648 q^{43} + 942233600 q^{44} + 6784014272 q^{45} - 2320325056 q^{46} + 2223880974 q^{47} + 557842432 q^{48} - 4232044312 q^{49} - 4937903616 q^{50} + 6968362082 q^{51} - 510705664 q^{52} - 7185483360 q^{53} + 2506931392 q^{54} + 624915620 q^{55} - 3615227904 q^{56} + 4959469112 q^{57} + 3417201664 q^{58} + 6997401502 q^{59} + 256227328 q^{60} - 6476463280 q^{61} - 12439025536 q^{62} - 17252507684 q^{63} + 8589934592 q^{64} + 30625528248 q^{65} + 5265507968 q^{66} - 18660972186 q^{67} + 1365733376 q^{68} + 31319762096 q^{69} - 27279047488 q^{70} + 23224449248 q^{71} + 16510091264 q^{72} + 3731641452 q^{73} - 5488545536 q^{74} - 91204646176 q^{75} + 44137934848 q^{76} - 29345595440 q^{77} - 41800015104 q^{78} + 12221157926 q^{79} + 3992977408 q^{80} - 97333443028 q^{81} - 52993522176 q^{82} + 316739523968 q^{83} + 55726088192 q^{84} - 147794862544 q^{85} + 13604474368 q^{86} - 218122807364 q^{87} - 30151475200 q^{88} - 71204406084 q^{89} + 434176913408 q^{90} + 189816116528 q^{91} - 148500803584 q^{92} + 9838293624 q^{93} - 71164191168 q^{94} - 215091896614 q^{95} + 8925478912 q^{96} + 688251797184 q^{97} + 137152279424 q^{98} - 545487662552 q^{99}+O(q^{100}) \) 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
\(3\) 69.1868 + 119.835i 0.164383 + 0.284719i 0.936436 0.350839i \(-0.114103\pi\)
−0.772053 + 0.635558i \(0.780770\pi\)
\(4\) −512.000 886.810i −0.250000 0.433013i
\(5\) 274.515 475.474i 0.0392854 0.0680443i −0.845714 0.533636i \(-0.820825\pi\)
0.885000 + 0.465592i \(0.154159\pi\)
\(6\) 4427.96 0.232472
\(7\) −25454.3 36461.0i −0.572430 0.819954i
\(8\) −32768.0 −0.353553
\(9\) 78999.9 136832.i 0.445957 0.772419i
\(10\) −8784.49 15215.2i −0.0277790 0.0481146i
\(11\) −123934. 214661.i −0.232024 0.401877i 0.726380 0.687293i \(-0.241201\pi\)
−0.958404 + 0.285417i \(0.907868\pi\)
\(12\) 70847.3 122711.i 0.0821914 0.142360i
\(13\) −1.83800e6 −1.37295 −0.686477 0.727151i \(-0.740844\pi\)
−0.686477 + 0.727151i \(0.740844\pi\)
\(14\) −1.41771e6 + 122034.i −0.704502 + 0.0606427i
\(15\) 75971.3 0.0258314
\(16\) −524288. + 908093.i −0.125000 + 0.216506i
\(17\) −3.08342e6 5.34065e6i −0.526701 0.912273i −0.999516 0.0311114i \(-0.990095\pi\)
0.472815 0.881162i \(-0.343238\pi\)
\(18\) −2.52800e6 4.37862e6i −0.315339 0.546183i
\(19\) 841196. 1.45699e6i 0.0779386 0.134994i −0.824422 0.565976i \(-0.808500\pi\)
0.902360 + 0.430982i \(0.141833\pi\)
\(20\) −562207. −0.0392854
\(21\) 2.60820e6 5.57294e6i 0.139359 0.297768i
\(22\) −7.93180e6 −0.328131
\(23\) 8.79546e6 1.52342e7i 0.284941 0.493533i −0.687654 0.726039i \(-0.741359\pi\)
0.972595 + 0.232506i \(0.0746926\pi\)
\(24\) −2.26711e6 3.92676e6i −0.0581181 0.100663i
\(25\) 2.42633e7 + 4.20253e7i 0.496913 + 0.860679i
\(26\) −2.94079e7 + 5.09360e7i −0.485413 + 0.840760i
\(27\) 4.63755e7 0.621996
\(28\) −1.93014e7 + 4.12412e7i −0.211943 + 0.452858i
\(29\) 1.50671e8 1.36409 0.682043 0.731312i \(-0.261092\pi\)
0.682043 + 0.731312i \(0.261092\pi\)
\(30\) 1.21554e6 2.10538e6i 0.00913278 0.0158184i
\(31\) 5.90206e7 + 1.02227e8i 0.370266 + 0.641320i 0.989606 0.143803i \(-0.0459331\pi\)
−0.619340 + 0.785123i \(0.712600\pi\)
\(32\) 1.67772e7 + 2.90590e7i 0.0883883 + 0.153093i
\(33\) 1.71493e7 2.97034e7i 0.0762814 0.132123i
\(34\) −1.97339e8 −0.744868
\(35\) −2.43239e7 + 2.09377e6i −0.0782814 + 0.00673837i
\(36\) −1.61792e8 −0.445957
\(37\) 2.77318e8 4.80329e8i 0.657460 1.13875i −0.323811 0.946122i \(-0.604964\pi\)
0.981271 0.192632i \(-0.0617023\pi\)
\(38\) −2.69183e7 4.66238e7i −0.0551109 0.0954549i
\(39\) −1.27165e8 2.20256e8i −0.225690 0.390907i
\(40\) −8.99531e6 + 1.55803e7i −0.0138895 + 0.0240573i
\(41\) −4.42101e8 −0.595950 −0.297975 0.954574i \(-0.596311\pi\)
−0.297975 + 0.954574i \(0.596311\pi\)
\(42\) −1.12711e8 1.61448e8i −0.133074 0.190617i
\(43\) −5.11519e8 −0.530622 −0.265311 0.964163i \(-0.585475\pi\)
−0.265311 + 0.964163i \(0.585475\pi\)
\(44\) −1.26909e8 + 2.19813e8i −0.116012 + 0.200938i
\(45\) −4.33733e7 7.51248e7i −0.0350392 0.0606896i
\(46\) −2.81455e8 4.87494e8i −0.201484 0.348980i
\(47\) 3.64835e7 6.31913e7i 0.0232038 0.0401901i −0.854190 0.519960i \(-0.825947\pi\)
0.877394 + 0.479770i \(0.159280\pi\)
\(48\) −1.45095e8 −0.0821914
\(49\) −6.81483e8 + 1.85618e9i −0.344649 + 0.938732i
\(50\) 1.55285e9 0.702742
\(51\) 4.26665e8 7.39005e8i 0.173161 0.299924i
\(52\) 9.41054e8 + 1.62995e9i 0.343239 + 0.594507i
\(53\) −5.60906e8 9.71518e8i −0.184235 0.319105i 0.759083 0.650994i \(-0.225648\pi\)
−0.943319 + 0.331889i \(0.892314\pi\)
\(54\) 7.42007e8 1.28519e9i 0.219909 0.380893i
\(55\) −1.36088e8 −0.0364606
\(56\) 8.34087e8 + 1.19475e9i 0.202384 + 0.289897i
\(57\) 2.32799e8 0.0512470
\(58\) 2.41074e9 4.17553e9i 0.482277 0.835329i
\(59\) 4.44766e9 + 7.70358e9i 0.809927 + 1.40283i 0.912914 + 0.408152i \(0.133827\pi\)
−0.102987 + 0.994683i \(0.532840\pi\)
\(60\) −3.88973e7 6.73721e7i −0.00645785 0.0111853i
\(61\) −4.28033e8 + 7.41375e8i −0.0648878 + 0.112389i −0.896644 0.442752i \(-0.854002\pi\)
0.831756 + 0.555141i \(0.187336\pi\)
\(62\) 3.77732e9 0.523636
\(63\) −6.99991e9 + 6.02544e8i −0.888627 + 0.0764920i
\(64\) 1.07374e9 0.125000
\(65\) −5.04558e8 + 8.73920e8i −0.0539371 + 0.0934218i
\(66\) −5.48776e8 9.50508e8i −0.0539391 0.0934252i
\(67\) −1.95943e9 3.39384e9i −0.177304 0.307100i 0.763652 0.645628i \(-0.223404\pi\)
−0.940956 + 0.338528i \(0.890071\pi\)
\(68\) −3.15743e9 + 5.46882e9i −0.263351 + 0.456137i
\(69\) 2.43412e9 0.187358
\(70\) −3.31158e8 + 7.07583e8i −0.0235503 + 0.0503197i
\(71\) −2.40314e9 −0.158073 −0.0790366 0.996872i \(-0.525184\pi\)
−0.0790366 + 0.996872i \(0.525184\pi\)
\(72\) −2.58867e9 + 4.48370e9i −0.157669 + 0.273092i
\(73\) −1.22579e10 2.12312e10i −0.692052 1.19867i −0.971164 0.238411i \(-0.923373\pi\)
0.279112 0.960259i \(-0.409960\pi\)
\(74\) −8.87419e9 1.53705e10i −0.464894 0.805220i
\(75\) −3.35741e9 + 5.81520e9i −0.163368 + 0.282962i
\(76\) −1.72277e9 −0.0779386
\(77\) −4.67208e9 + 9.98281e9i −0.196703 + 0.420295i
\(78\) −8.13857e9 −0.319174
\(79\) 1.75728e10 3.04369e10i 0.642527 1.11289i −0.342340 0.939576i \(-0.611219\pi\)
0.984867 0.173313i \(-0.0554473\pi\)
\(80\) 2.87850e8 + 4.98571e8i 0.00982136 + 0.0170111i
\(81\) −1.07860e10 1.86819e10i −0.343711 0.595325i
\(82\) −7.07361e9 + 1.22519e10i −0.210700 + 0.364944i
\(83\) 6.12728e10 1.70741 0.853706 0.520756i \(-0.174350\pi\)
0.853706 + 0.520756i \(0.174350\pi\)
\(84\) −6.27754e9 + 5.40363e8i −0.163777 + 0.0140977i
\(85\) −3.38579e9 −0.0827667
\(86\) −8.18430e9 + 1.41756e10i −0.187603 + 0.324938i
\(87\) 1.04245e10 + 1.80557e10i 0.224232 + 0.388382i
\(88\) 4.06108e9 + 7.03400e9i 0.0820327 + 0.142085i
\(89\) −1.76449e10 + 3.05618e10i −0.334945 + 0.580142i −0.983474 0.181048i \(-0.942051\pi\)
0.648529 + 0.761190i \(0.275384\pi\)
\(90\) −2.77589e9 −0.0495529
\(91\) 4.67849e10 + 6.70152e10i 0.785920 + 1.12576i
\(92\) −1.80131e10 −0.284941
\(93\) −8.16689e9 + 1.41455e10i −0.121731 + 0.210844i
\(94\) −1.16747e9 2.02212e9i −0.0164075 0.0284187i
\(95\) −4.61842e8 7.99934e8i −0.00612370 0.0106066i
\(96\) −2.32152e9 + 4.02100e9i −0.0290590 + 0.0503317i
\(97\) 1.31739e11 1.55765 0.778823 0.627244i \(-0.215817\pi\)
0.778823 + 0.627244i \(0.215817\pi\)
\(98\) 4.05362e10 + 4.85847e10i 0.453002 + 0.542945i
\(99\) −3.91632e10 −0.413890
\(100\) 2.48457e10 4.30340e10i 0.248457 0.430340i
\(101\) −8.33062e10 1.44291e11i −0.788696 1.36606i −0.926766 0.375639i \(-0.877423\pi\)
0.138070 0.990422i \(-0.455910\pi\)
\(102\) −1.36533e10 2.36482e10i −0.122443 0.212078i
\(103\) −4.04254e10 + 7.00188e10i −0.343597 + 0.595128i −0.985098 0.171995i \(-0.944979\pi\)
0.641501 + 0.767122i \(0.278312\pi\)
\(104\) 6.02275e10 0.485413
\(105\) −1.93380e9 2.76999e9i −0.0147867 0.0211805i
\(106\) −3.58980e10 −0.260548
\(107\) 3.79280e8 6.56932e8i 0.00261426 0.00452804i −0.864715 0.502262i \(-0.832501\pi\)
0.867330 + 0.497734i \(0.165835\pi\)
\(108\) −2.37442e10 4.11262e10i −0.155499 0.269332i
\(109\) −1.07849e11 1.86799e11i −0.671381 1.16287i −0.977513 0.210877i \(-0.932368\pi\)
0.306131 0.951989i \(-0.400965\pi\)
\(110\) −2.17740e9 + 3.77137e9i −0.0128908 + 0.0223275i
\(111\) 7.67471e10 0.432300
\(112\) 4.64554e10 3.99882e9i 0.249079 0.0214404i
\(113\) −3.70803e11 −1.89327 −0.946634 0.322311i \(-0.895540\pi\)
−0.946634 + 0.322311i \(0.895540\pi\)
\(114\) 3.72478e9 6.45151e9i 0.0181186 0.0313823i
\(115\) −4.82897e9 8.36403e9i −0.0223881 0.0387773i
\(116\) −7.71437e10 1.33617e11i −0.341021 0.590666i
\(117\) −1.45201e11 + 2.51496e11i −0.612278 + 1.06050i
\(118\) 2.84651e11 1.14541
\(119\) −1.16239e11 + 2.48367e11i −0.446523 + 0.954083i
\(120\) −2.48943e9 −0.00913278
\(121\) 1.11936e11 1.93879e11i 0.392330 0.679536i
\(122\) 1.36971e10 + 2.37240e10i 0.0458826 + 0.0794710i
\(123\) −3.05875e10 5.29792e10i −0.0979640 0.169679i
\(124\) 6.04371e10 1.04680e11i 0.185133 0.320660i
\(125\) 5.34508e10 0.156657
\(126\) −9.53004e10 + 2.03628e11i −0.267336 + 0.571215i
\(127\) 6.98521e11 1.87611 0.938056 0.346483i \(-0.112624\pi\)
0.938056 + 0.346483i \(0.112624\pi\)
\(128\) 1.71799e10 2.97564e10i 0.0441942 0.0765466i
\(129\) −3.53904e10 6.12979e10i −0.0872251 0.151078i
\(130\) 1.61459e10 + 2.79654e10i 0.0381393 + 0.0660592i
\(131\) −2.14194e11 + 3.70996e11i −0.485083 + 0.840189i −0.999853 0.0171397i \(-0.994544\pi\)
0.514770 + 0.857328i \(0.327877\pi\)
\(132\) −3.51217e10 −0.0762814
\(133\) −7.45355e10 + 6.41593e9i −0.155303 + 0.0133683i
\(134\) −1.25404e11 −0.250746
\(135\) 1.27308e10 2.20503e10i 0.0244354 0.0423233i
\(136\) 1.01038e11 + 1.75002e11i 0.186217 + 0.322537i
\(137\) −2.06541e11 3.57739e11i −0.365631 0.633291i 0.623247 0.782025i \(-0.285813\pi\)
−0.988877 + 0.148735i \(0.952480\pi\)
\(138\) 3.89459e10 6.74563e10i 0.0662410 0.114733i
\(139\) 1.20077e12 1.96280 0.981402 0.191965i \(-0.0614861\pi\)
0.981402 + 0.191965i \(0.0614861\pi\)
\(140\) 1.43106e10 + 2.04986e10i 0.0224881 + 0.0322122i
\(141\) 1.00967e10 0.0152572
\(142\) −3.84502e10 + 6.65978e10i −0.0558873 + 0.0967996i
\(143\) 2.27791e11 + 3.94546e11i 0.318558 + 0.551758i
\(144\) 8.28374e10 + 1.43479e11i 0.111489 + 0.193105i
\(145\) 4.13616e10 7.16404e10i 0.0535887 0.0928183i
\(146\) −7.84503e11 −0.978710
\(147\) −2.69585e11 + 4.67576e10i −0.323929 + 0.0561832i
\(148\) −5.67948e11 −0.657460
\(149\) 3.73691e11 6.47251e11i 0.416858 0.722019i −0.578764 0.815495i \(-0.696465\pi\)
0.995621 + 0.0934765i \(0.0297980\pi\)
\(150\) 1.07437e11 + 1.86086e11i 0.115519 + 0.200084i
\(151\) −1.85358e10 3.21049e10i −0.0192149 0.0332812i 0.856258 0.516548i \(-0.172783\pi\)
−0.875473 + 0.483267i \(0.839450\pi\)
\(152\) −2.75643e10 + 4.77428e10i −0.0275554 + 0.0477274i
\(153\) −9.74361e11 −0.939544
\(154\) 2.01899e11 + 2.89201e11i 0.187832 + 0.269052i
\(155\) 6.48082e10 0.0581843
\(156\) −1.30217e11 + 2.25543e11i −0.112845 + 0.195453i
\(157\) −1.90703e11 3.30307e11i −0.159554 0.276356i 0.775154 0.631773i \(-0.217672\pi\)
−0.934708 + 0.355416i \(0.884339\pi\)
\(158\) −5.62329e11 9.73982e11i −0.454335 0.786932i
\(159\) 7.76146e10 1.34432e11i 0.0605702 0.104911i
\(160\) 1.84224e10 0.0138895
\(161\) −7.79336e11 + 6.70843e10i −0.567783 + 0.0488741i
\(162\) −6.90305e11 −0.486081
\(163\) 3.95346e11 6.84758e11i 0.269119 0.466128i −0.699515 0.714618i \(-0.746601\pi\)
0.968635 + 0.248489i \(0.0799340\pi\)
\(164\) 2.26356e11 + 3.92059e11i 0.148988 + 0.258054i
\(165\) −9.41546e9 1.63081e10i −0.00599349 0.0103810i
\(166\) 9.80365e11 1.69804e12i 0.603661 1.04557i
\(167\) −1.69644e12 −1.01064 −0.505320 0.862932i \(-0.668626\pi\)
−0.505320 + 0.862932i \(0.668626\pi\)
\(168\) −8.54656e10 + 1.82614e11i −0.0492709 + 0.105277i
\(169\) 1.58607e12 0.885005
\(170\) −5.41726e10 + 9.38297e10i −0.0292625 + 0.0506841i
\(171\) −1.32909e11 2.30205e11i −0.0695144 0.120403i
\(172\) 2.61898e11 + 4.53620e11i 0.132656 + 0.229766i
\(173\) −3.01944e11 + 5.22983e11i −0.148140 + 0.256587i −0.930540 0.366190i \(-0.880662\pi\)
0.782400 + 0.622776i \(0.213995\pi\)
\(174\) 6.67166e11 0.317112
\(175\) 9.14680e11 1.95439e12i 0.421269 0.900124i
\(176\) 2.59909e11 0.116012
\(177\) −6.15439e11 + 1.06597e12i −0.266276 + 0.461204i
\(178\) 5.64636e11 + 9.77979e11i 0.236842 + 0.410222i
\(179\) 2.43231e12 + 4.21288e12i 0.989296 + 1.71351i 0.621019 + 0.783796i \(0.286719\pi\)
0.368278 + 0.929716i \(0.379948\pi\)
\(180\) −4.44143e10 + 7.69278e10i −0.0175196 + 0.0303448i
\(181\) −1.27259e12 −0.486919 −0.243459 0.969911i \(-0.578282\pi\)
−0.243459 + 0.969911i \(0.578282\pi\)
\(182\) 2.60574e12 2.24299e11i 0.967249 0.0832596i
\(183\) −1.18457e11 −0.0426658
\(184\) −2.88210e11 + 4.99194e11i −0.100742 + 0.174490i
\(185\) −1.52256e11 2.63715e11i −0.0516572 0.0894728i
\(186\) 2.61341e11 + 4.52655e11i 0.0860767 + 0.149089i
\(187\) −7.64285e11 + 1.32378e12i −0.244414 + 0.423338i
\(188\) −7.47182e10 −0.0232038
\(189\) −1.18046e12 1.69090e12i −0.356049 0.510008i
\(190\) −2.95579e10 −0.00866022
\(191\) −2.02464e12 + 3.50677e12i −0.576320 + 0.998216i 0.419577 + 0.907720i \(0.362178\pi\)
−0.995897 + 0.0904958i \(0.971155\pi\)
\(192\) 7.42888e10 + 1.28672e11i 0.0205478 + 0.0355899i
\(193\) 2.25493e12 + 3.90565e12i 0.606133 + 1.04985i 0.991871 + 0.127244i \(0.0406132\pi\)
−0.385739 + 0.922608i \(0.626053\pi\)
\(194\) 2.10782e12 3.65085e12i 0.550711 0.953859i
\(195\) −1.39635e11 −0.0354653
\(196\) 1.99500e12 3.46018e11i 0.492645 0.0854457i
\(197\) 4.24499e12 1.01932 0.509662 0.860374i \(-0.329770\pi\)
0.509662 + 0.860374i \(0.329770\pi\)
\(198\) −6.26611e11 + 1.08532e12i −0.146332 + 0.253455i
\(199\) −3.45495e12 5.98414e12i −0.784783 1.35928i −0.929129 0.369756i \(-0.879441\pi\)
0.144346 0.989527i \(-0.453892\pi\)
\(200\) −7.95061e11 1.37709e12i −0.175685 0.304296i
\(201\) 2.71134e11 4.69617e11i 0.0582915 0.100964i
\(202\) −5.33160e12 −1.11538
\(203\) −3.83524e12 5.49363e12i −0.780843 1.11849i
\(204\) −8.73809e11 −0.173161
\(205\) −1.21363e11 + 2.10208e11i −0.0234122 + 0.0405511i
\(206\) 1.29361e12 + 2.24060e12i 0.242960 + 0.420819i
\(207\) −1.38968e12 2.40700e12i −0.254143 0.440188i
\(208\) 9.63639e11 1.66907e12i 0.171619 0.297253i
\(209\) −4.17013e11 −0.0723344
\(210\) −1.07705e11 + 9.27112e9i −0.0181983 + 0.00156648i
\(211\) −1.62122e12 −0.266863 −0.133431 0.991058i \(-0.542600\pi\)
−0.133431 + 0.991058i \(0.542600\pi\)
\(212\) −5.74368e11 + 9.94834e11i −0.0921177 + 0.159552i
\(213\) −1.66266e11 2.87980e11i −0.0259845 0.0450065i
\(214\) −1.21370e10 2.10218e10i −0.00184856 0.00320180i
\(215\) −1.40420e11 + 2.43214e11i −0.0208457 + 0.0361058i
\(216\) −1.51963e12 −0.219909
\(217\) 2.22496e12 4.75406e12i 0.313901 0.670712i
\(218\) −6.90232e12 −0.949477
\(219\) 1.69616e12 2.93784e12i 0.227523 0.394081i
\(220\) 6.96768e10 + 1.20684e11i 0.00911514 + 0.0157879i
\(221\) 5.66732e12 + 9.81609e12i 0.723137 + 1.25251i
\(222\) 1.22795e12 2.12688e12i 0.152841 0.264729i
\(223\) −3.36059e12 −0.408074 −0.204037 0.978963i \(-0.565406\pi\)
−0.204037 + 0.978963i \(0.565406\pi\)
\(224\) 6.32468e11 1.35139e12i 0.0749332 0.160109i
\(225\) 7.66720e12 0.886407
\(226\) −5.93285e12 + 1.02760e13i −0.669371 + 1.15939i
\(227\) 1.03730e12 + 1.79666e12i 0.114225 + 0.197844i 0.917470 0.397806i \(-0.130228\pi\)
−0.803245 + 0.595649i \(0.796895\pi\)
\(228\) −1.19193e11 2.06448e11i −0.0128118 0.0221906i
\(229\) −1.71857e12 + 2.97666e12i −0.180332 + 0.312344i −0.941994 0.335631i \(-0.891051\pi\)
0.761662 + 0.647975i \(0.224384\pi\)
\(230\) −3.09054e11 −0.0316615
\(231\) −1.51954e12 + 1.30800e11i −0.152001 + 0.0130840i
\(232\) −4.93720e12 −0.482277
\(233\) 4.57239e11 7.91961e11i 0.0436200 0.0755520i −0.843391 0.537300i \(-0.819444\pi\)
0.887011 + 0.461748i \(0.152778\pi\)
\(234\) 4.64645e12 + 8.04788e12i 0.432946 + 0.749885i
\(235\) −2.00306e10 3.46939e10i −0.00182314 0.00315777i
\(236\) 4.55441e12 7.88847e12i 0.404964 0.701417i
\(237\) 4.86322e12 0.422482
\(238\) 5.02313e12 + 7.19519e12i 0.426385 + 0.610757i
\(239\) 1.55301e13 1.28820 0.644102 0.764939i \(-0.277231\pi\)
0.644102 + 0.764939i \(0.277231\pi\)
\(240\) −3.98309e10 + 6.89891e10i −0.00322892 + 0.00559266i
\(241\) 1.21702e12 + 2.10793e12i 0.0964279 + 0.167018i 0.910204 0.414161i \(-0.135925\pi\)
−0.813776 + 0.581179i \(0.802592\pi\)
\(242\) −3.58196e12 6.20414e12i −0.277419 0.480504i
\(243\) 5.60014e12 9.69972e12i 0.423998 0.734387i
\(244\) 8.76612e11 0.0648878
\(245\) 6.95488e11 + 8.33577e11i 0.0503357 + 0.0603299i
\(246\) −1.95760e12 −0.138542
\(247\) −1.54612e12 + 2.67795e12i −0.107006 + 0.185340i
\(248\) −1.93399e12 3.34976e12i −0.130909 0.226741i
\(249\) 4.23927e12 + 7.34263e12i 0.280669 + 0.486133i
\(250\) 8.55212e11 1.48127e12i 0.0553865 0.0959322i
\(251\) −9.98228e12 −0.632447 −0.316224 0.948685i \(-0.602415\pi\)
−0.316224 + 0.948685i \(0.602415\pi\)
\(252\) 4.11830e12 + 5.89909e12i 0.255279 + 0.365664i
\(253\) −4.36024e12 −0.264452
\(254\) 1.11763e13 1.93580e13i 0.663306 1.14888i
\(255\) −2.34252e11 4.05736e11i −0.0136054 0.0235653i
\(256\) −5.49756e11 9.52205e11i −0.0312500 0.0541266i
\(257\) −1.49652e13 + 2.59206e13i −0.832629 + 1.44216i 0.0633165 + 0.997993i \(0.479832\pi\)
−0.895946 + 0.444163i \(0.853501\pi\)
\(258\) −2.26498e12 −0.123355
\(259\) −2.45722e13 + 2.11515e12i −1.31007 + 0.112770i
\(260\) 1.03333e12 0.0539371
\(261\) 1.19030e13 2.06166e13i 0.608323 1.05365i
\(262\) 6.85422e12 + 1.18719e13i 0.343006 + 0.594103i
\(263\) −1.41247e13 2.44647e13i −0.692184 1.19890i −0.971121 0.238589i \(-0.923315\pi\)
0.278936 0.960310i \(-0.410018\pi\)
\(264\) −5.61947e11 + 9.73320e11i −0.0269695 + 0.0467126i
\(265\) −6.15909e11 −0.0289511
\(266\) −1.01477e12 + 2.16824e12i −0.0467215 + 0.0998296i
\(267\) −4.88317e12 −0.220237
\(268\) −2.00646e12 + 3.47529e12i −0.0886521 + 0.153550i
\(269\) −2.49399e12 4.31972e12i −0.107959 0.186990i 0.806984 0.590573i \(-0.201098\pi\)
−0.914943 + 0.403583i \(0.867765\pi\)
\(270\) −4.07385e11 7.05611e11i −0.0172784 0.0299271i
\(271\) −1.77202e13 + 3.06924e13i −0.736442 + 1.27555i 0.217646 + 0.976028i \(0.430162\pi\)
−0.954088 + 0.299527i \(0.903171\pi\)
\(272\) 6.46641e12 0.263351
\(273\) −4.79387e12 + 1.02430e13i −0.191334 + 0.408822i
\(274\) −1.32186e13 −0.517080
\(275\) 6.01413e12 1.04168e13i 0.230591 0.399396i
\(276\) −1.24627e12 2.15860e12i −0.0468394 0.0811283i
\(277\) −1.34967e13 2.33770e13i −0.497266 0.861290i 0.502729 0.864444i \(-0.332329\pi\)
−0.999995 + 0.00315412i \(0.998996\pi\)
\(278\) 1.92122e13 3.32766e13i 0.693956 1.20197i
\(279\) 1.86505e13 0.660491
\(280\) 7.97044e11 6.86086e10i 0.0276766 0.00238237i
\(281\) −2.36038e12 −0.0803707 −0.0401853 0.999192i \(-0.512795\pi\)
−0.0401853 + 0.999192i \(0.512795\pi\)
\(282\) 1.61547e11 2.79808e11i 0.00539423 0.00934309i
\(283\) −1.33227e13 2.30755e13i −0.436280 0.755660i 0.561119 0.827735i \(-0.310371\pi\)
−0.997399 + 0.0720756i \(0.977038\pi\)
\(284\) 1.23041e12 + 2.13113e12i 0.0395183 + 0.0684477i
\(285\) 6.39068e10 1.10690e11i 0.00201326 0.00348707i
\(286\) 1.45786e13 0.450509
\(287\) 1.12534e13 + 1.61194e13i 0.341140 + 0.488652i
\(288\) 5.30159e12 0.157669
\(289\) −1.87907e12 + 3.25465e12i −0.0548283 + 0.0949654i
\(290\) −1.32357e12 2.29249e12i −0.0378929 0.0656325i
\(291\) 9.11457e12 + 1.57869e13i 0.256050 + 0.443492i
\(292\) −1.25521e13 + 2.17408e13i −0.346026 + 0.599335i
\(293\) 2.94411e13 0.796494 0.398247 0.917278i \(-0.369619\pi\)
0.398247 + 0.917278i \(0.369619\pi\)
\(294\) −3.01758e12 + 8.21908e12i −0.0801213 + 0.218229i
\(295\) 4.88381e12 0.127273
\(296\) −9.08717e12 + 1.57394e13i −0.232447 + 0.402610i
\(297\) −5.74752e12 9.95499e12i −0.144318 0.249966i
\(298\) −1.19581e13 2.07120e13i −0.294763 0.510544i
\(299\) −1.61660e13 + 2.80004e13i −0.391211 + 0.677598i
\(300\) 6.87597e12 0.163368
\(301\) 1.30204e13 + 1.86505e13i 0.303744 + 0.435086i
\(302\) −1.18629e12 −0.0271740
\(303\) 1.15274e13 1.99660e13i 0.259296 0.449114i
\(304\) 8.82058e11 + 1.52777e12i 0.0194846 + 0.0337484i
\(305\) 2.35003e11 + 4.07037e11i 0.00509829 + 0.00883050i
\(306\) −1.55898e13 + 2.70023e13i −0.332179 + 0.575351i
\(307\) 9.24654e13 1.93517 0.967583 0.252553i \(-0.0812702\pi\)
0.967583 + 0.252553i \(0.0812702\pi\)
\(308\) 1.12450e13 9.67953e11i 0.231169 0.0198987i
\(309\) −1.11876e13 −0.225926
\(310\) 1.03693e12 1.79602e12i 0.0205712 0.0356304i
\(311\) 3.78378e13 + 6.55370e13i 0.737469 + 1.27733i 0.953632 + 0.300976i \(0.0973124\pi\)
−0.216163 + 0.976357i \(0.569354\pi\)
\(312\) 4.16695e12 + 7.21736e12i 0.0797935 + 0.138206i
\(313\) 1.53315e13 2.65550e13i 0.288464 0.499634i −0.684979 0.728563i \(-0.740189\pi\)
0.973443 + 0.228928i \(0.0735221\pi\)
\(314\) −1.22050e13 −0.225644
\(315\) −1.63509e12 + 3.49369e12i −0.0297052 + 0.0634711i
\(316\) −3.59891e13 −0.642527
\(317\) −1.37012e13 + 2.37312e13i −0.240399 + 0.416383i −0.960828 0.277146i \(-0.910612\pi\)
0.720429 + 0.693529i \(0.243945\pi\)
\(318\) −2.48367e12 4.30184e12i −0.0428296 0.0741831i
\(319\) −1.86734e13 3.23432e13i −0.316500 0.548194i
\(320\) 2.94758e11 5.10537e11i 0.00491068 0.00850554i
\(321\) 1.04965e11 0.00171896
\(322\) −1.06103e13 + 2.26709e13i −0.170812 + 0.364974i
\(323\) −1.03751e13 −0.164201
\(324\) −1.10449e13 + 1.91303e13i −0.171856 + 0.297663i
\(325\) −4.45959e13 7.72424e13i −0.682239 1.18167i
\(326\) −1.26511e13 2.19123e13i −0.190296 0.329603i
\(327\) 1.49234e13 2.58481e13i 0.220727 0.382311i
\(328\) 1.44868e13 0.210700
\(329\) −3.23268e12 + 2.78265e11i −0.0462365 + 0.00397999i
\(330\) −6.02590e11 −0.00847608
\(331\) −1.31791e13 + 2.28269e13i −0.182319 + 0.315786i −0.942670 0.333727i \(-0.891694\pi\)
0.760351 + 0.649513i \(0.225027\pi\)
\(332\) −3.13717e13 5.43373e13i −0.426853 0.739331i
\(333\) −4.38162e13 7.58919e13i −0.586397 1.01567i
\(334\) −2.71430e13 + 4.70130e13i −0.357315 + 0.618889i
\(335\) −2.15158e12 −0.0278619
\(336\) 3.69330e12 + 5.29032e12i 0.0470488 + 0.0673932i
\(337\) −4.52730e13 −0.567380 −0.283690 0.958916i \(-0.591559\pi\)
−0.283690 + 0.958916i \(0.591559\pi\)
\(338\) 2.53771e13 4.39545e13i 0.312896 0.541952i
\(339\) −2.56547e13 4.44352e13i −0.311221 0.539050i
\(340\) 1.73352e12 + 3.00255e12i 0.0206917 + 0.0358390i
\(341\) 1.46294e13 2.53388e13i 0.171821 0.297603i
\(342\) −8.50616e12 −0.0983083
\(343\) 8.50248e13 2.24002e13i 0.967004 0.254762i
\(344\) 1.67615e13 0.187603
\(345\) 6.68203e11 1.15736e12i 0.00736043 0.0127486i
\(346\) 9.66222e12 + 1.67355e13i 0.104751 + 0.181434i
\(347\) 4.82957e13 + 8.36506e13i 0.515343 + 0.892600i 0.999841 + 0.0178080i \(0.00566875\pi\)
−0.484499 + 0.874792i \(0.660998\pi\)
\(348\) 1.06747e13 1.84890e13i 0.112116 0.194191i
\(349\) −7.94783e13 −0.821691 −0.410846 0.911705i \(-0.634766\pi\)
−0.410846 + 0.911705i \(0.634766\pi\)
\(350\) −3.95268e13 5.66186e13i −0.402270 0.576216i
\(351\) −8.52379e13 −0.853972
\(352\) 4.15855e12 7.20282e12i 0.0410164 0.0710424i
\(353\) 2.03908e13 + 3.53179e13i 0.198004 + 0.342952i 0.947881 0.318625i \(-0.103221\pi\)
−0.749877 + 0.661577i \(0.769888\pi\)
\(354\) 1.96941e13 + 3.41111e13i 0.188286 + 0.326120i
\(355\) −6.59698e11 + 1.14263e12i −0.00620997 + 0.0107560i
\(356\) 3.61367e13 0.334945
\(357\) −3.78053e13 + 3.25424e12i −0.345047 + 0.0297012i
\(358\) 1.55668e14 1.39908
\(359\) −6.14334e13 + 1.06406e14i −0.543732 + 0.941772i 0.454953 + 0.890515i \(0.349656\pi\)
−0.998686 + 0.0512563i \(0.983677\pi\)
\(360\) 1.42126e12 + 2.46169e12i 0.0123882 + 0.0214570i
\(361\) 5.68299e13 + 9.84323e13i 0.487851 + 0.844983i
\(362\) −2.03614e13 + 3.52671e13i −0.172152 + 0.298176i
\(363\) 3.09781e13 0.257969
\(364\) 3.54759e13 7.58011e13i 0.290988 0.621753i
\(365\) −1.34599e13 −0.108750
\(366\) −1.89531e12 + 3.28278e12i −0.0150846 + 0.0261273i
\(367\) 6.83335e13 + 1.18357e14i 0.535760 + 0.927963i 0.999126 + 0.0417963i \(0.0133081\pi\)
−0.463366 + 0.886167i \(0.653359\pi\)
\(368\) 9.22271e12 + 1.59742e13i 0.0712353 + 0.123383i
\(369\) −3.49259e13 + 6.04934e13i −0.265768 + 0.460324i
\(370\) −9.74440e12 −0.0730543
\(371\) −2.11450e13 + 4.51805e13i −0.156190 + 0.333730i
\(372\) 1.67258e13 0.121731
\(373\) 1.14678e14 1.98629e14i 0.822400 1.42444i −0.0814906 0.996674i \(-0.525968\pi\)
0.903890 0.427764i \(-0.140699\pi\)
\(374\) 2.44571e13 + 4.23610e13i 0.172827 + 0.299345i
\(375\) 3.69809e12 + 6.40527e12i 0.0257517 + 0.0446032i
\(376\) −1.19549e12 + 2.07065e12i −0.00820377 + 0.0142093i
\(377\) −2.76933e14 −1.87283
\(378\) −6.57468e13 + 5.65940e12i −0.438197 + 0.0377195i
\(379\) 1.88377e14 1.23741 0.618704 0.785625i \(-0.287658\pi\)
0.618704 + 0.785625i \(0.287658\pi\)
\(380\) −4.72926e11 + 8.19133e11i −0.00306185 + 0.00530328i
\(381\) 4.83284e13 + 8.37073e13i 0.308401 + 0.534166i
\(382\) 6.47884e13 + 1.12217e14i 0.407520 + 0.705845i
\(383\) 1.32028e14 2.28679e14i 0.818603 1.41786i −0.0881087 0.996111i \(-0.528082\pi\)
0.906712 0.421751i \(-0.138584\pi\)
\(384\) 4.75448e12 0.0290590
\(385\) 3.46401e12 + 4.96189e12i 0.0208711 + 0.0298960i
\(386\) 1.44315e14 0.857201
\(387\) −4.04099e13 + 6.99921e13i −0.236634 + 0.409863i
\(388\) −6.74502e13 1.16827e14i −0.389411 0.674480i
\(389\) −2.60084e12 4.50479e12i −0.0148044 0.0256420i 0.858528 0.512766i \(-0.171379\pi\)
−0.873333 + 0.487124i \(0.838046\pi\)
\(390\) −2.23416e12 + 3.86968e12i −0.0125389 + 0.0217180i
\(391\) −1.08481e14 −0.600316
\(392\) 2.23308e13 6.08233e13i 0.121852 0.331892i
\(393\) −5.92777e13 −0.318957
\(394\) 6.79199e13 1.17641e14i 0.360386 0.624206i
\(395\) −9.64799e12 1.67108e13i −0.0504839 0.0874407i
\(396\) 2.00516e13 + 3.47303e13i 0.103472 + 0.179220i
\(397\) 1.39381e14 2.41414e14i 0.709340 1.22861i −0.255762 0.966740i \(-0.582326\pi\)
0.965102 0.261873i \(-0.0843402\pi\)
\(398\) −2.21117e14 −1.10985
\(399\) −5.92573e12 8.48807e12i −0.0293353 0.0420202i
\(400\) −5.08839e13 −0.248457
\(401\) −1.44350e14 + 2.50021e14i −0.695219 + 1.20416i 0.274887 + 0.961476i \(0.411359\pi\)
−0.970107 + 0.242679i \(0.921974\pi\)
\(402\) −8.67628e12 1.50278e13i −0.0412183 0.0713922i
\(403\) −1.08480e14 1.87892e14i −0.508359 0.880503i
\(404\) −8.53055e13 + 1.47754e14i −0.394348 + 0.683031i
\(405\) −1.18437e13 −0.0540114
\(406\) −2.13608e14 + 1.83871e13i −0.961001 + 0.0827218i
\(407\) −1.37477e14 −0.610185
\(408\) −1.39809e13 + 2.42157e13i −0.0612217 + 0.106039i
\(409\) 1.65770e14 + 2.87123e14i 0.716191 + 1.24048i 0.962498 + 0.271287i \(0.0874494\pi\)
−0.246307 + 0.969192i \(0.579217\pi\)
\(410\) 3.88363e12 + 6.72664e12i 0.0165549 + 0.0286739i
\(411\) 2.85798e13 4.95016e13i 0.120207 0.208204i
\(412\) 8.27912e13 0.343597
\(413\) 1.67668e14 3.58256e14i 0.686634 1.46713i
\(414\) −8.89395e13 −0.359412
\(415\) 1.68203e13 2.91336e13i 0.0670764 0.116180i
\(416\) −3.08365e13 5.34103e13i −0.121353 0.210190i
\(417\) 8.30771e13 + 1.43894e14i 0.322651 + 0.558848i
\(418\) −6.67220e12 + 1.15566e13i −0.0255741 + 0.0442956i
\(419\) −3.88951e14 −1.47136 −0.735679 0.677330i \(-0.763137\pi\)
−0.735679 + 0.677330i \(0.763137\pi\)
\(420\) −1.46635e12 + 3.13315e12i −0.00547478 + 0.0116979i
\(421\) 7.79736e13 0.287340 0.143670 0.989626i \(-0.454110\pi\)
0.143670 + 0.989626i \(0.454110\pi\)
\(422\) −2.59395e13 + 4.49285e13i −0.0943503 + 0.163419i
\(423\) −5.76439e12 9.98421e12i −0.0206957 0.0358461i
\(424\) 1.83798e13 + 3.18347e13i 0.0651370 + 0.112821i
\(425\) 1.49628e14 2.59164e14i 0.523450 0.906641i
\(426\) −1.06410e13 −0.0367476
\(427\) 3.79266e13 3.26467e12i 0.129298 0.0111298i
\(428\) −7.76766e11 −0.00261426
\(429\) −3.15203e13 + 5.45947e13i −0.104731 + 0.181399i
\(430\) 4.49343e12 + 7.78285e12i 0.0147401 + 0.0255307i
\(431\) 1.01136e14 + 1.75173e14i 0.327553 + 0.567338i 0.982026 0.188748i \(-0.0604428\pi\)
−0.654473 + 0.756085i \(0.727109\pi\)
\(432\) −2.43141e13 + 4.21133e13i −0.0777495 + 0.134666i
\(433\) 1.87950e14 0.593417 0.296708 0.954968i \(-0.404111\pi\)
0.296708 + 0.954968i \(0.404111\pi\)
\(434\) −9.61490e13 1.37725e14i −0.299745 0.429357i
\(435\) 1.14467e13 0.0352362
\(436\) −1.10437e14 + 1.91283e14i −0.335691 + 0.581433i
\(437\) −1.47974e13 2.56299e13i −0.0444158 0.0769305i
\(438\) −5.42773e13 9.40110e13i −0.160883 0.278658i
\(439\) 2.19247e13 3.79748e13i 0.0641770 0.111158i −0.832152 0.554548i \(-0.812891\pi\)
0.896329 + 0.443390i \(0.146224\pi\)
\(440\) 4.45932e12 0.0128908
\(441\) 2.00147e14 + 2.39886e14i 0.571396 + 0.684847i
\(442\) 3.62709e14 1.02267
\(443\) 1.14367e14 1.98090e14i 0.318480 0.551623i −0.661691 0.749776i \(-0.730161\pi\)
0.980171 + 0.198154i \(0.0634945\pi\)
\(444\) −3.92945e13 6.80601e13i −0.108075 0.187191i
\(445\) 9.68758e12 + 1.67794e13i 0.0263169 + 0.0455823i
\(446\) −5.37695e13 + 9.31314e13i −0.144276 + 0.249893i
\(447\) 1.03418e14 0.274097
\(448\) −2.73314e13 3.91497e13i −0.0715537 0.102494i
\(449\) 2.07597e14 0.536865 0.268433 0.963298i \(-0.413494\pi\)
0.268433 + 0.963298i \(0.413494\pi\)
\(450\) 1.22675e14 2.12480e14i 0.313392 0.542811i
\(451\) 5.47915e13 + 9.49017e13i 0.138275 + 0.239499i
\(452\) 1.89851e14 + 3.28832e14i 0.473317 + 0.819809i
\(453\) 2.56486e12 4.44247e12i 0.00631719 0.0109417i
\(454\) 6.63872e13 0.161539
\(455\) 4.47072e13 3.84834e12i 0.107477 0.00925147i
\(456\) −7.62835e12 −0.0181186
\(457\) −2.80816e14 + 4.86387e14i −0.658995 + 1.14141i 0.321881 + 0.946780i \(0.395685\pi\)
−0.980876 + 0.194632i \(0.937649\pi\)
\(458\) 5.49944e13 + 9.52530e13i 0.127514 + 0.220861i
\(459\) −1.42995e14 2.47675e14i −0.327606 0.567430i
\(460\) −4.94487e12 + 8.56477e12i −0.0111940 + 0.0193886i
\(461\) 2.58496e14 0.578228 0.289114 0.957295i \(-0.406639\pi\)
0.289114 + 0.957295i \(0.406639\pi\)
\(462\) −2.06878e13 + 4.42035e13i −0.0457280 + 0.0977069i
\(463\) −6.03088e14 −1.31730 −0.658650 0.752449i \(-0.728872\pi\)
−0.658650 + 0.752449i \(0.728872\pi\)
\(464\) −7.89952e13 + 1.36824e14i −0.170511 + 0.295333i
\(465\) 4.48387e12 + 7.76629e12i 0.00956449 + 0.0165662i
\(466\) −1.46316e13 2.53427e13i −0.0308440 0.0534234i
\(467\) −1.59594e14 + 2.76425e14i −0.332487 + 0.575884i −0.982999 0.183612i \(-0.941221\pi\)
0.650512 + 0.759496i \(0.274554\pi\)
\(468\) 2.97373e14 0.612278
\(469\) −7.38667e13 + 1.57831e14i −0.150313 + 0.321174i
\(470\) −1.28196e12 −0.00257831
\(471\) 2.63882e13 4.57057e13i 0.0524560 0.0908565i
\(472\) −1.45741e14 2.52431e14i −0.286352 0.495977i
\(473\) 6.33948e13 + 1.09803e14i 0.123117 + 0.213245i
\(474\) 7.78115e13 1.34773e14i 0.149370 0.258716i
\(475\) 8.16409e13 0.154915
\(476\) 2.79769e14 2.40822e13i 0.524761 0.0451708i
\(477\) −1.77246e14 −0.328644
\(478\) 2.48481e14 4.30382e14i 0.455449 0.788861i
\(479\) −3.21839e14 5.57442e14i −0.583168 1.01008i −0.995101 0.0988630i \(-0.968479\pi\)
0.411933 0.911214i \(-0.364854\pi\)
\(480\) 1.27459e12 + 2.20765e12i 0.00228319 + 0.00395461i
\(481\) −5.09710e14 + 8.82844e14i −0.902662 + 1.56346i
\(482\) 7.78890e13 0.136370
\(483\) −6.19588e13 8.87504e13i −0.107249 0.153625i
\(484\) −2.29246e14 −0.392330
\(485\) 3.61643e13 6.26383e13i 0.0611928 0.105989i
\(486\) −1.79204e14 3.10391e14i −0.299812 0.519290i
\(487\) −3.21937e14 5.57612e14i −0.532552 0.922408i −0.999278 0.0380052i \(-0.987900\pi\)
0.466725 0.884402i \(-0.345434\pi\)
\(488\) 1.40258e13 2.42934e13i 0.0229413 0.0397355i
\(489\) 1.09411e14 0.176954
\(490\) 3.42286e13 5.93670e12i 0.0547407 0.00949438i
\(491\) −1.89651e14 −0.299921 −0.149960 0.988692i \(-0.547915\pi\)
−0.149960 + 0.988692i \(0.547915\pi\)
\(492\) −3.13216e13 + 5.42507e13i −0.0489820 + 0.0848393i
\(493\) −4.64584e14 8.04683e14i −0.718466 1.24442i
\(494\) 4.94757e13 + 8.56944e13i 0.0756648 + 0.131055i
\(495\) −1.07509e13 + 1.86211e13i −0.0162598 + 0.0281629i
\(496\) −1.23775e14 −0.185133
\(497\) 6.11703e13 + 8.76209e13i 0.0904857 + 0.129613i
\(498\) 2.71313e14 0.396926
\(499\) 1.80479e14 3.12599e14i 0.261140 0.452308i −0.705405 0.708805i \(-0.749235\pi\)
0.966545 + 0.256496i \(0.0825681\pi\)
\(500\) −2.73668e13 4.74007e13i −0.0391642 0.0678343i
\(501\) −1.17371e14 2.03292e14i −0.166132 0.287749i
\(502\) −1.59717e14 + 2.76637e14i −0.223604 + 0.387293i
\(503\) 4.66680e14 0.646242 0.323121 0.946358i \(-0.395268\pi\)
0.323121 + 0.946358i \(0.395268\pi\)
\(504\) 2.29373e14 1.97442e13i 0.314177 0.0270440i
\(505\) −9.14753e13 −0.123937
\(506\) −6.97638e13 + 1.20835e14i −0.0934980 + 0.161943i
\(507\) 1.09735e14 + 1.90067e14i 0.145480 + 0.251978i
\(508\) −3.57643e14 6.19455e14i −0.469028 0.812381i
\(509\) 6.50568e14 1.12682e15i 0.844005 1.46186i −0.0424779 0.999097i \(-0.513525\pi\)
0.886483 0.462762i \(-0.153141\pi\)
\(510\) −1.49921e13 −0.0192410
\(511\) −4.62097e14 + 9.87361e14i −0.586703 + 1.25361i
\(512\) −3.51844e13 −0.0441942
\(513\) 3.90109e13 6.75688e13i 0.0484775 0.0839655i
\(514\) 4.78888e14 + 8.29458e14i 0.588758 + 1.01976i
\(515\) 2.21948e13 + 3.84425e13i 0.0269967 + 0.0467597i
\(516\) −3.62397e13 + 6.27691e13i −0.0436126 + 0.0755392i
\(517\) −1.80863e13 −0.0215353
\(518\) −3.34539e14 + 7.14808e14i −0.394124 + 0.842124i
\(519\) −8.35623e13 −0.0974069
\(520\) 1.65334e13 2.86366e13i 0.0190696 0.0330296i
\(521\) 6.08081e14 + 1.05323e15i 0.693991 + 1.20203i 0.970520 + 0.241022i \(0.0774826\pi\)
−0.276529 + 0.961006i \(0.589184\pi\)
\(522\) −3.80897e14 6.59732e14i −0.430149 0.745041i
\(523\) −6.55535e14 + 1.13542e15i −0.732548 + 1.26881i 0.223242 + 0.974763i \(0.428336\pi\)
−0.955791 + 0.294048i \(0.904997\pi\)
\(524\) 4.38670e14 0.485083
\(525\) 2.97488e14 2.56075e13i 0.325532 0.0280214i
\(526\) −9.03979e14 −0.978897
\(527\) 3.63971e14 6.30416e14i 0.390039 0.675568i
\(528\) 1.79823e13 + 3.11462e13i 0.0190703 + 0.0330308i
\(529\) 3.21685e14 + 5.57174e14i 0.337617 + 0.584770i
\(530\) −9.85455e12 + 1.70686e13i −0.0102357 + 0.0177288i
\(531\) 1.40546e15 1.44477
\(532\) 4.38519e13 + 6.28139e13i 0.0446143 + 0.0639060i
\(533\) 8.12580e14 0.818213
\(534\) −7.81308e13 + 1.35326e14i −0.0778655 + 0.134867i
\(535\) −2.08236e11 3.60676e11i −0.000205405 0.000355772i
\(536\) 6.42067e13 + 1.11209e14i 0.0626865 + 0.108576i
\(537\) −3.36567e14 + 5.82951e14i −0.325247 + 0.563344i
\(538\) −1.59616e14 −0.152677
\(539\) 4.82908e14 8.37569e13i 0.457221 0.0793017i
\(540\) −2.60726e13 −0.0244354
\(541\) 5.84730e14 1.01278e15i 0.542463 0.939574i −0.456299 0.889827i \(-0.650825\pi\)
0.998762 0.0497471i \(-0.0158415\pi\)
\(542\) 5.67048e14 + 9.82156e14i 0.520743 + 0.901954i
\(543\) −8.80465e13 1.52501e14i −0.0800411 0.138635i
\(544\) 1.03463e14 1.79202e14i 0.0931085 0.161269i
\(545\) −1.18424e14 −0.105502
\(546\) 2.07162e14 + 2.96740e14i 0.182705 + 0.261708i
\(547\) 7.27016e14 0.634766 0.317383 0.948297i \(-0.397196\pi\)
0.317383 + 0.948297i \(0.397196\pi\)
\(548\) −2.11498e14 + 3.66325e14i −0.182815 + 0.316645i
\(549\) 6.76291e13 + 1.17137e14i 0.0578743 + 0.100241i
\(550\) −1.92452e14 3.33337e14i −0.163053 0.282415i
\(551\) 1.26744e14 2.19527e14i 0.106315 0.184143i
\(552\) −7.97612e13 −0.0662410
\(553\) −1.55706e15 + 1.34030e14i −1.28032 + 0.110208i
\(554\) −8.63789e14 −0.703240
\(555\) 2.10682e13 3.64913e13i 0.0169831 0.0294156i
\(556\) −6.14792e14 1.06485e15i −0.490701 0.849919i
\(557\) −8.66449e14 1.50073e15i −0.684762 1.18604i −0.973512 0.228637i \(-0.926573\pi\)
0.288750 0.957404i \(-0.406760\pi\)
\(558\) 2.98408e14 5.16857e14i 0.233519 0.404466i
\(559\) 9.40170e14 0.728520
\(560\) 1.08514e13 2.31861e13i 0.00832627 0.0177907i
\(561\) −2.11514e14 −0.160710
\(562\) −3.77661e13 + 6.54128e13i −0.0284153 + 0.0492168i
\(563\) −4.37043e14 7.56980e14i −0.325632 0.564012i 0.656008 0.754754i \(-0.272244\pi\)
−0.981640 + 0.190742i \(0.938911\pi\)
\(564\) −5.16952e12 8.95386e12i −0.00381430 0.00660656i
\(565\) −1.01791e14 + 1.76307e14i −0.0743778 + 0.128826i
\(566\) −8.52650e14 −0.616994
\(567\) −4.06611e14 + 8.68805e14i −0.291389 + 0.622609i
\(568\) 7.87461e13 0.0558873
\(569\) −2.94897e14 + 5.10776e14i −0.207278 + 0.359015i −0.950856 0.309633i \(-0.899794\pi\)
0.743578 + 0.668649i \(0.233127\pi\)
\(570\) −2.04502e12 3.54207e12i −0.00142359 0.00246573i
\(571\) 4.92599e12 + 8.53207e12i 0.00339622 + 0.00588242i 0.867719 0.497056i \(-0.165586\pi\)
−0.864322 + 0.502938i \(0.832252\pi\)
\(572\) 2.33258e14 4.04015e14i 0.159279 0.275879i
\(573\) −5.60313e14 −0.378948
\(574\) 6.26769e14 5.39515e13i 0.419848 0.0361400i
\(575\) 8.53629e14 0.566364
\(576\) 8.48255e13 1.46922e14i 0.0557446 0.0965524i
\(577\) −5.63060e14 9.75248e14i −0.366511 0.634816i 0.622506 0.782615i \(-0.286115\pi\)
−0.989017 + 0.147799i \(0.952781\pi\)
\(578\) 6.01303e13 + 1.04149e14i 0.0387695 + 0.0671507i
\(579\) −3.12023e14 + 5.40439e14i −0.199276 + 0.345155i
\(580\) −8.47085e13 −0.0535887
\(581\) −1.55966e15 2.23407e15i −0.977373 1.40000i
\(582\) 5.83333e14 0.362110
\(583\) −1.39031e14 + 2.40809e14i −0.0854939 + 0.148080i
\(584\) 4.01666e14 + 6.95705e14i 0.244678 + 0.423794i
\(585\) 7.97200e13 + 1.38079e14i 0.0481072 + 0.0833241i
\(586\) 4.71058e14 8.15896e14i 0.281603 0.487751i
\(587\) −1.44774e15 −0.857395 −0.428698 0.903448i \(-0.641027\pi\)
−0.428698 + 0.903448i \(0.641027\pi\)
\(588\) 1.79493e14 + 2.15131e14i 0.105310 + 0.126220i
\(589\) 1.98592e14 0.115432
\(590\) 7.81409e13 1.35344e14i 0.0449979 0.0779387i
\(591\) 2.93697e14 + 5.08699e14i 0.167559 + 0.290221i
\(592\) 2.90789e14 + 5.03662e14i 0.164365 + 0.284688i
\(593\) −4.72878e14 + 8.19048e14i −0.264818 + 0.458679i −0.967516 0.252810i \(-0.918645\pi\)
0.702698 + 0.711489i \(0.251979\pi\)
\(594\) −3.67841e14 −0.204096
\(595\) 8.61829e13 + 1.23449e14i 0.0473781 + 0.0678649i
\(596\) −7.65319e14 −0.416858
\(597\) 4.78074e14 8.28048e14i 0.258010 0.446886i
\(598\) 5.17313e14 + 8.96012e14i 0.276628 + 0.479134i
\(599\) 9.94121e14 + 1.72187e15i 0.526734 + 0.912331i 0.999515 + 0.0311505i \(0.00991711\pi\)
−0.472780 + 0.881180i \(0.656750\pi\)
\(600\) 1.10015e14 1.90552e14i 0.0577593 0.100042i
\(601\) −6.84869e14 −0.356285 −0.178143 0.984005i \(-0.557009\pi\)
−0.178143 + 0.984005i \(0.557009\pi\)
\(602\) 7.25184e14 6.24229e13i 0.373824 0.0321783i
\(603\) −6.19180e14 −0.316280
\(604\) −1.89806e13 + 3.28754e13i −0.00960744 + 0.0166406i
\(605\) −6.14565e13 1.06446e14i −0.0308257 0.0533917i
\(606\) −3.68876e14 6.38912e14i −0.183350 0.317572i
\(607\) −8.80297e14 + 1.52472e15i −0.433602 + 0.751021i −0.997180 0.0750418i \(-0.976091\pi\)
0.563578 + 0.826063i \(0.309424\pi\)
\(608\) 5.64517e13 0.0275554
\(609\) 3.92982e14 8.39682e14i 0.190098 0.406181i
\(610\) 1.50402e13 0.00721007
\(611\) −6.70566e13 + 1.16145e14i −0.0318577 + 0.0551792i
\(612\) 4.98873e14 + 8.64073e14i 0.234886 + 0.406834i
\(613\) 1.41227e15 + 2.44613e15i 0.659000 + 1.14142i 0.980875 + 0.194639i \(0.0623537\pi\)
−0.321875 + 0.946782i \(0.604313\pi\)
\(614\) 1.47945e15 2.56248e15i 0.684185 1.18504i
\(615\) −3.35870e13 −0.0153942
\(616\) 1.53095e14 3.27117e14i 0.0695451 0.148597i
\(617\) 4.84445e14 0.218110 0.109055 0.994036i \(-0.465217\pi\)
0.109055 + 0.994036i \(0.465217\pi\)
\(618\) −1.79002e14 + 3.10040e14i −0.0798768 + 0.138351i
\(619\) −3.64048e14 6.30550e14i −0.161013 0.278882i 0.774219 0.632917i \(-0.218143\pi\)
−0.935232 + 0.354035i \(0.884809\pi\)
\(620\) −3.31818e13 5.74726e13i −0.0145461 0.0251945i
\(621\) 4.07893e14 7.06492e14i 0.177232 0.306975i
\(622\) 2.42162e15 1.04294
\(623\) 1.56345e15 1.34580e14i 0.667422 0.0574509i
\(624\) 2.66685e14 0.112845
\(625\) −1.17006e15 + 2.02660e15i −0.490759 + 0.850020i
\(626\) −4.90609e14 8.49760e14i −0.203975 0.353295i
\(627\) −2.88518e13 4.99727e13i −0.0118905 0.0205950i
\(628\) −1.95280e14 + 3.38234e14i −0.0797772 + 0.138178i
\(629\) −3.42036e15 −1.38514
\(630\) 7.06585e13 + 1.01212e14i 0.0283655 + 0.0406311i
\(631\) 3.73026e15 1.48449 0.742245 0.670128i \(-0.233761\pi\)
0.742245 + 0.670128i \(0.233761\pi\)
\(632\) −5.75825e14 + 9.97358e14i −0.227168 + 0.393466i
\(633\) −1.12167e14 1.94279e14i −0.0438677 0.0759810i
\(634\) 4.38438e14 + 7.59397e14i 0.169988 + 0.294427i
\(635\) 1.91755e14 3.32129e14i 0.0737039 0.127659i
\(636\) −1.58955e14 −0.0605702
\(637\) 1.25256e15 3.41165e15i 0.473187 1.28884i
\(638\) −1.19510e15 −0.447599
\(639\) −1.89848e14 + 3.28826e14i −0.0704938 + 0.122099i
\(640\) −9.43227e12 1.63372e13i −0.00347237 0.00601433i
\(641\) 1.48337e15 + 2.56928e15i 0.541417 + 0.937761i 0.998823 + 0.0485033i \(0.0154451\pi\)
−0.457406 + 0.889258i \(0.651222\pi\)
\(642\) 1.67944e12 2.90887e12i 0.000607744 0.00105264i
\(643\) 3.05558e15 1.09631 0.548154 0.836377i \(-0.315331\pi\)
0.548154 + 0.836377i \(0.315331\pi\)
\(644\) 4.58511e14 + 6.56776e14i 0.163109 + 0.233639i
\(645\) −3.88608e13 −0.0137067
\(646\) −1.66001e14 + 2.87522e14i −0.0580539 + 0.100552i
\(647\) −6.62437e14 1.14738e15i −0.229705 0.397861i 0.728015 0.685561i \(-0.240443\pi\)
−0.957721 + 0.287699i \(0.907110\pi\)
\(648\) 3.53436e14 + 6.12170e14i 0.121520 + 0.210479i
\(649\) 1.10244e15 1.90948e15i 0.375844 0.650982i
\(650\) −2.85414e15 −0.964832
\(651\) 7.23641e14 6.22901e13i 0.242565 0.0208797i
\(652\) −8.09668e14 −0.269119
\(653\) −1.70073e15 + 2.94575e15i −0.560548 + 0.970897i 0.436901 + 0.899510i \(0.356076\pi\)
−0.997449 + 0.0713873i \(0.977257\pi\)
\(654\) −4.77549e14 8.27140e14i −0.156078 0.270334i
\(655\) 1.17599e14 + 2.03688e14i 0.0381134 + 0.0660143i
\(656\) 2.31788e14 4.01469e14i 0.0744938 0.129027i
\(657\) −3.87348e15 −1.23450
\(658\) −4.40114e13 + 9.40389e13i −0.0139099 + 0.0297211i
\(659\) −3.73056e15 −1.16924 −0.584621 0.811306i \(-0.698757\pi\)
−0.584621 + 0.811306i \(0.698757\pi\)
\(660\) −9.64143e12 + 1.66995e13i −0.00299675 + 0.00519052i
\(661\) −9.07423e14 1.57170e15i −0.279706 0.484465i 0.691606 0.722275i \(-0.256904\pi\)
−0.971312 + 0.237810i \(0.923570\pi\)
\(662\) 4.21732e14 + 7.30461e14i 0.128919 + 0.223295i
\(663\) −7.84208e14 + 1.35829e15i −0.237743 + 0.411782i
\(664\) −2.00779e15 −0.603661
\(665\) −1.74105e13 + 3.72010e13i −0.00519150 + 0.0110927i
\(666\) −2.80424e15 −0.829290
\(667\) 1.32522e15 2.29535e15i 0.388684 0.673221i
\(668\) 8.68575e14 + 1.50442e15i 0.252660 + 0.437620i
\(669\) −2.32509e14 4.02717e14i −0.0670803 0.116187i
\(670\) −3.44252e13 + 5.96262e13i −0.00985066 + 0.0170618i
\(671\) 2.12192e14 0.0602220
\(672\) 2.05702e14 1.77066e13i 0.0579040 0.00498430i
\(673\) 3.44656e15 0.962284 0.481142 0.876643i \(-0.340222\pi\)
0.481142 + 0.876643i \(0.340222\pi\)
\(674\) −7.24367e14 + 1.25464e15i −0.200599 + 0.347448i
\(675\) 1.12522e15 + 1.94894e15i 0.309078 + 0.535339i
\(676\) −8.12068e14 1.40654e15i −0.221251 0.383218i
\(677\) 2.84223e15 4.92288e15i 0.768106 1.33040i −0.170483 0.985361i \(-0.554533\pi\)
0.938589 0.345038i \(-0.112134\pi\)
\(678\) −1.64190e15 −0.440132
\(679\) −3.35332e15 4.80332e15i −0.891642 1.27720i
\(680\) 1.10946e14 0.0292625
\(681\) −1.43535e14 + 2.48610e14i −0.0375533 + 0.0650443i
\(682\) −4.68140e14 8.10842e14i −0.121496 0.210437i
\(683\) −8.07317e14 1.39831e15i −0.207841 0.359991i 0.743193 0.669077i \(-0.233310\pi\)
−0.951034 + 0.309086i \(0.899977\pi\)
\(684\) −1.36099e14 + 2.35730e14i −0.0347572 + 0.0602013i
\(685\) −2.26794e14 −0.0574558
\(686\) 7.39625e14 2.71468e15i 0.185878 0.682238i
\(687\) −4.75611e14 −0.118574
\(688\) 2.68183e14 4.64507e14i 0.0663278 0.114883i
\(689\) 1.03094e15 + 1.78565e15i 0.252947 + 0.438117i
\(690\) −2.13825e13 3.70355e13i −0.00520461 0.00901465i
\(691\) 7.68868e14 1.33172e15i 0.185662 0.321576i −0.758138 0.652095i \(-0.773890\pi\)
0.943799 + 0.330519i \(0.107224\pi\)
\(692\) 6.18382e14 0.148140
\(693\) 9.96873e14 + 1.42793e15i 0.236923 + 0.339371i
\(694\) 3.09092e15 0.728805
\(695\) 3.29628e14 5.70933e14i 0.0771096 0.133558i
\(696\) −3.41589e14 5.91649e14i −0.0792781 0.137314i
\(697\) 1.36318e15 + 2.36110e15i 0.313888 + 0.543670i
\(698\) −1.27165e15 + 2.20257e15i −0.290512 + 0.503181i
\(699\) 1.26540e14 0.0286815
\(700\) −2.20149e15 + 1.89502e14i −0.495083 + 0.0426161i
\(701\) 3.16112e15 0.705329 0.352664 0.935750i \(-0.385276\pi\)
0.352664 + 0.935750i \(0.385276\pi\)
\(702\) −1.36381e15 + 2.36218e15i −0.301925 + 0.522949i
\(703\) −4.66558e14 8.08103e14i −0.102483 0.177506i
\(704\) −1.33074e14 2.30490e14i −0.0290030 0.0502346i
\(705\) 2.77170e12 4.80073e12i 0.000599385 0.00103817i
\(706\) 1.30501e15 0.280019
\(707\) −3.14048e15 + 6.71024e15i −0.668635 + 1.42867i
\(708\) 1.26042e15 0.266276
\(709\) 5.12422e14 8.87541e14i 0.107417 0.186052i −0.807306 0.590133i \(-0.799075\pi\)
0.914723 + 0.404081i \(0.132409\pi\)
\(710\) 2.11103e13 + 3.65642e13i 0.00439111 + 0.00760563i
\(711\) −2.77649e15 4.80903e15i −0.573078 0.992601i
\(712\) 5.78188e14 1.00145e15i 0.118421 0.205111i
\(713\) 2.07645e15 0.422017
\(714\) −5.14701e14 + 1.09976e15i −0.103804 + 0.221798i
\(715\) 2.50128e14 0.0500587
\(716\) 2.49068e15 4.31399e15i 0.494648 0.856756i
\(717\) 1.07448e15 + 1.86105e15i 0.211759 + 0.366777i
\(718\) 1.96587e15 + 3.40498e15i 0.384477 + 0.665933i
\(719\) −3.46971e15 + 6.00972e15i −0.673418 + 1.16639i 0.303511 + 0.952828i \(0.401841\pi\)
−0.976929 + 0.213566i \(0.931492\pi\)
\(720\) 9.09605e13 0.0175196
\(721\) 3.58196e15 3.08331e14i 0.684662 0.0589349i
\(722\) 3.63711e15 0.689926
\(723\) −1.68403e14 + 2.91682e14i −0.0317022 + 0.0549098i
\(724\) 6.51566e14 + 1.12855e15i 0.121730 + 0.210842i
\(725\) 3.65579e15 + 6.33202e15i 0.677832 + 1.17404i
\(726\) 4.95649e14 8.58490e14i 0.0912059 0.157973i
\(727\) 1.82914e15 0.334046 0.167023 0.985953i \(-0.446585\pi\)
0.167023 + 0.985953i \(0.446585\pi\)
\(728\) −1.53305e15 2.19595e15i −0.277865 0.398016i
\(729\) −2.27160e15 −0.408630
\(730\) −2.15358e14 + 3.73011e14i −0.0384490 + 0.0665957i
\(731\) 1.57723e15 + 2.73184e15i 0.279479 + 0.484072i
\(732\) 6.06500e13 + 1.05049e14i 0.0106664 + 0.0184748i
\(733\) −3.83957e15 + 6.65032e15i −0.670209 + 1.16084i 0.307636 + 0.951504i \(0.400462\pi\)
−0.977845 + 0.209332i \(0.932871\pi\)
\(734\) 4.37334e15 0.757679
\(735\) −5.17732e13 + 1.41016e14i −0.00890275 + 0.0242487i
\(736\) 5.90253e14 0.100742
\(737\) −4.85682e14 + 8.41226e14i −0.0822775 + 0.142509i
\(738\) 1.11763e15 + 1.93579e15i 0.187926 + 0.325498i
\(739\) −2.51463e15 4.35546e15i −0.419690 0.726925i 0.576218 0.817296i \(-0.304528\pi\)
−0.995908 + 0.0903712i \(0.971195\pi\)
\(740\) −1.55910e14 + 2.70045e14i −0.0258286 + 0.0447364i
\(741\) −4.27883e14 −0.0703599
\(742\) 9.13759e14 + 1.30888e15i 0.149145 + 0.213637i
\(743\) −8.16694e15 −1.32319 −0.661593 0.749863i \(-0.730119\pi\)
−0.661593 + 0.749863i \(0.730119\pi\)
\(744\) 2.67613e14 4.63519e14i 0.0430383 0.0745446i
\(745\) −2.05168e14 3.55361e14i −0.0327529 0.0567296i
\(746\) −3.66971e15 6.35612e15i −0.581524 1.00723i
\(747\) 4.84054e15 8.38407e15i 0.761431 1.31884i
\(748\) 1.56526e15 0.244414
\(749\) −3.36067e13 + 2.89283e12i −0.00520926 + 0.000448407i
\(750\) 2.36678e14 0.0364183
\(751\) 2.65889e15 4.60533e15i 0.406144 0.703462i −0.588310 0.808636i \(-0.700206\pi\)
0.994454 + 0.105173i \(0.0335397\pi\)
\(752\) 3.82557e13 + 6.62609e13i 0.00580094 + 0.0100475i
\(753\) −6.90642e14 1.19623e15i −0.103963 0.180070i
\(754\) −4.43093e15 + 7.67460e15i −0.662145 + 1.14687i
\(755\) −2.03534e13 −0.00301946
\(756\) −8.95110e14 + 1.91258e15i −0.131828 + 0.281676i
\(757\) −2.81481e15 −0.411550 −0.205775 0.978599i \(-0.565971\pi\)
−0.205775 + 0.978599i \(0.565971\pi\)
\(758\) 3.01403e15 5.22046e15i 0.437489 0.757754i
\(759\) −3.01671e14 5.22510e14i −0.0434714 0.0752947i
\(760\) 1.51336e13 + 2.62122e13i 0.00216505 + 0.00374998i
\(761\) 4.75454e15 8.23511e15i 0.675295 1.16964i −0.301088 0.953596i \(-0.597350\pi\)
0.976383 0.216048i \(-0.0693168\pi\)
\(762\) 3.09302e15 0.436144
\(763\) −4.06568e15 + 8.68713e15i −0.569178 + 1.21616i
\(764\) 4.14646e15 0.576320
\(765\) −2.67477e14 + 4.63283e14i −0.0369104 + 0.0639306i
\(766\) −4.22490e15 7.31774e15i −0.578840 1.00258i
\(767\) −8.17479e15 1.41592e16i −1.11199 1.92603i
\(768\) 7.60717e13 1.31760e14i 0.0102739 0.0177950i
\(769\) −8.40673e15 −1.12728 −0.563641 0.826020i \(-0.690600\pi\)
−0.563641 + 0.826020i \(0.690600\pi\)
\(770\) 1.92932e14 1.66074e13i 0.0256865 0.00221107i
\(771\) −4.14159e15 −0.547480
\(772\) 2.30905e15 3.99939e15i 0.303066 0.524926i
\(773\) 4.41147e15 + 7.64090e15i 0.574906 + 0.995766i 0.996052 + 0.0887730i \(0.0282946\pi\)
−0.421146 + 0.906993i \(0.638372\pi\)
\(774\) 1.29312e15 + 2.23975e15i 0.167326 + 0.289817i
\(775\) −2.86407e15 + 4.96072e15i −0.367981 + 0.637361i
\(776\) −4.31681e15 −0.550711
\(777\) −1.95354e15 2.79828e15i −0.247461 0.354466i
\(778\) −1.66454e14 −0.0209366
\(779\) −3.71893e14 + 6.44138e14i −0.0464475 + 0.0804495i
\(780\) 7.14931e13 + 1.23830e14i 0.00886633 + 0.0153569i
\(781\) 2.97832e14 + 5.15860e14i 0.0366767 + 0.0635259i
\(782\) −1.73569e15 + 3.00630e15i −0.212244 + 0.367617i
\(783\) 6.98745e15 0.848456
\(784\) −1.32829e15 1.59202e15i −0.160160 0.191960i
\(785\) −2.09403e14 −0.0250727
\(786\) −9.48444e14 + 1.64275e15i −0.112768 + 0.195321i
\(787\) −6.14523e15 1.06438e16i −0.725566 1.25672i −0.958741 0.284283i \(-0.908245\pi\)
0.233174 0.972435i \(-0.425089\pi\)
\(788\) −2.17344e15 3.76450e15i −0.254831 0.441381i
\(789\) 1.95448e15 3.38526e15i 0.227566 0.394157i
\(790\) −6.17471e14 −0.0713950
\(791\) 9.43854e15 + 1.35199e16i 1.08376 + 1.55239i
\(792\) 1.28330e15 0.146332
\(793\) 7.86723e14 1.36264e15i 0.0890880 0.154305i
\(794\) −4.46018e15 7.72526e15i −0.501579 0.868760i
\(795\) −4.26128e13 7.38075e13i −0.00475905 0.00824292i
\(796\) −3.53787e15 + 6.12776e15i −0.392391 + 0.679642i
\(797\) 5.98566e15 0.659313 0.329656 0.944101i \(-0.393067\pi\)
0.329656 + 0.944101i \(0.393067\pi\)
\(798\) −3.30040e14 + 2.84095e13i −0.0361036 + 0.00310776i
\(799\) −4.49977e14 −0.0488858
\(800\) −8.14143e14 + 1.41014e15i −0.0878427 + 0.152148i
\(801\) 2.78789e15 + 4.82876e15i 0.298742 + 0.517436i
\(802\) 4.61919e15 + 8.00067e15i 0.491594 + 0.851466i
\(803\) −3.03834e15 + 5.26256e15i −0.321145 + 0.556239i
\(804\) −5.55282e14 −0.0582915
\(805\) −1.82043e14 + 3.88970e14i −0.0189800 + 0.0405545i
\(806\) −6.94270e15 −0.718928
\(807\) 3.45103e14 5.97736e14i 0.0354931 0.0614759i
\(808\) 2.72978e15 + 4.72811e15i 0.278846 + 0.482976i
\(809\) −1.44371e15 2.50057e15i −0.146475 0.253701i 0.783448 0.621458i \(-0.213459\pi\)
−0.929922 + 0.367757i \(0.880126\pi\)
\(810\) −1.89499e14 + 3.28222e14i −0.0190959 + 0.0330751i
\(811\) 1.78899e16 1.79058 0.895290 0.445485i \(-0.146969\pi\)
0.895290 + 0.445485i \(0.146969\pi\)
\(812\) −2.90816e15 + 6.21386e15i −0.289108 + 0.617737i
\(813\) −4.90403e15 −0.484234
\(814\) −2.19963e15 + 3.80988e15i −0.215733 + 0.373660i
\(815\) −2.17057e14 3.75953e14i −0.0211449 0.0366241i
\(816\) 4.47390e14 + 7.74903e14i 0.0432903 + 0.0749810i
\(817\) −4.30288e14 + 7.45280e14i −0.0413559 + 0.0716306i
\(818\) 1.06093e16 1.01285
\(819\) 1.28658e16 1.10747e15i 1.22004 0.105020i
\(820\) 2.48552e14 0.0234122
\(821\) −2.41355e14 + 4.18039e14i −0.0225823 + 0.0391137i −0.877096 0.480316i \(-0.840522\pi\)
0.854513 + 0.519429i \(0.173855\pi\)
\(822\) −9.14553e14 1.58405e15i −0.0849990 0.147223i
\(823\) −2.43333e14 4.21465e14i −0.0224648 0.0389101i 0.854574 0.519329i \(-0.173818\pi\)
−0.877039 + 0.480419i \(0.840485\pi\)
\(824\) 1.32466e15 2.29438e15i 0.121480 0.210409i
\(825\) 1.66439e15 0.151621
\(826\) −7.24558e15 1.03786e16i −0.655667 0.939183i
\(827\) −8.76609e15 −0.787999 −0.393999 0.919111i \(-0.628909\pi\)
−0.393999 + 0.919111i \(0.628909\pi\)
\(828\) −1.42303e15 + 2.46476e15i −0.127071 + 0.220094i
\(829\) 1.21459e15 + 2.10373e15i 0.107741 + 0.186612i 0.914855 0.403783i \(-0.132305\pi\)
−0.807114 + 0.590396i \(0.798972\pi\)
\(830\) −5.38250e14 9.32277e14i −0.0474302 0.0821515i
\(831\) 1.86759e15 3.23475e15i 0.163484 0.283162i
\(832\) −1.97353e15 −0.171619
\(833\) 1.20145e16 2.08383e15i 1.03791 0.180017i
\(834\) 5.31694e15 0.456298
\(835\) −4.65697e14 + 8.06612e14i −0.0397034 + 0.0687684i
\(836\) 2.13510e14 + 3.69811e14i 0.0180836 + 0.0313217i
\(837\) 2.73711e15 + 4.74081e15i 0.230304 + 0.398898i
\(838\) −6.22322e15 + 1.07789e16i −0.520204 + 0.901019i
\(839\) 1.72884e16 1.43570 0.717852 0.696196i \(-0.245126\pi\)
0.717852 + 0.696196i \(0.245126\pi\)
\(840\) 6.33667e13 + 9.07671e13i 0.00522787 + 0.00748845i
\(841\) 1.05013e16 0.860730
\(842\) 1.24758e15 2.16087e15i 0.101590 0.175959i
\(843\) −1.63307e14 2.82857e14i −0.0132116 0.0228831i
\(844\) 8.30064e14 + 1.43771e15i 0.0667157 + 0.115555i
\(845\) 4.35400e14 7.54136e14i 0.0347678 0.0602196i
\(846\) −3.68921e14 −0.0292682
\(847\) −9.91830e15 + 8.53756e14i −0.781769 + 0.0672938i
\(848\) 1.17631e15 0.0921177
\(849\) 1.84350e15 3.19304e15i 0.143434 0.248435i
\(850\) −4.78811e15 8.29325e15i −0.370135 0.641092i
\(851\) −4.87828e15 8.44944e15i −0.374675 0.648956i
\(852\) −1.70256e14 + 2.94892e14i −0.0129923 + 0.0225032i
\(853\) −2.28186e16 −1.73009 −0.865045 0.501693i \(-0.832711\pi\)
−0.865045 + 0.501693i \(0.832711\pi\)
\(854\) 5.16352e14 1.10329e15i 0.0388980 0.0831132i
\(855\) −1.45942e14 −0.0109236
\(856\) −1.24282e13 + 2.15264e13i −0.000924281 + 0.00160090i
\(857\) −7.62521e15 1.32072e16i −0.563452 0.975928i −0.997192 0.0748895i \(-0.976140\pi\)
0.433740 0.901038i \(-0.357194\pi\)
\(858\) 1.00865e15 + 1.74703e15i 0.0740559 + 0.128269i
\(859\) −5.60743e15 + 9.71235e15i −0.409074 + 0.708536i −0.994786 0.101983i \(-0.967481\pi\)
0.585713 + 0.810519i \(0.300815\pi\)
\(860\) 2.87580e14 0.0208457
\(861\) −1.15309e15 + 2.46380e15i −0.0830511 + 0.177455i
\(862\) 6.47271e15 0.463229
\(863\) −4.21043e15 + 7.29268e15i −0.299410 + 0.518594i −0.976001 0.217765i \(-0.930123\pi\)
0.676591 + 0.736359i \(0.263457\pi\)
\(864\) 7.78051e14 + 1.34762e15i 0.0549772 + 0.0952233i
\(865\) 1.65777e14 + 2.87134e14i 0.0116395 + 0.0201602i
\(866\) 3.00721e15 5.20864e15i 0.209805 0.363392i
\(867\) −5.20028e14 −0.0360513
\(868\) −5.35513e15 + 4.60963e14i −0.368902 + 0.0317547i
\(869\) −8.71149e15 −0.596326
\(870\) 1.83147e14 3.17220e14i 0.0124579 0.0215777i
\(871\) 3.60143e15 + 6.23786e15i 0.243430 + 0.421634i
\(872\) 3.53399e15 + 6.12105e15i 0.237369 + 0.411135i
\(873\) 1.04073e16 1.80260e16i 0.694642 1.20316i
\(874\) −9.47034e14 −0.0628135
\(875\) −1.36055e15 1.94887e15i −0.0896749 0.128451i
\(876\) −3.47375e15 −0.227523
\(877\) −1.02086e16 + 1.76817e16i −0.664456 + 1.15087i 0.314976 + 0.949100i \(0.398004\pi\)
−0.979432 + 0.201773i \(0.935330\pi\)
\(878\) −7.01592e14 1.21519e15i −0.0453800 0.0786005i
\(879\) 2.03694e15 + 3.52808e15i 0.130930 + 0.226777i
\(880\) 7.13491e13 1.23580e14i 0.00455757 0.00789395i
\(881\) −1.92701e16 −1.22326 −0.611628 0.791146i \(-0.709485\pi\)
−0.611628 + 0.791146i \(0.709485\pi\)
\(882\) 9.85029e15 1.70846e15i 0.621401 0.107777i
\(883\) 7.56546e15 0.474298 0.237149 0.971473i \(-0.423787\pi\)
0.237149 + 0.971473i \(0.423787\pi\)
\(884\) 5.80334e15 1.00517e16i 0.361568 0.626255i
\(885\) 3.37895e14 + 5.85251e14i 0.0209215 + 0.0362372i
\(886\) −3.65975e15 6.33888e15i −0.225199 0.390056i
\(887\) 6.90836e14 1.19656e15i 0.0422469 0.0731738i −0.844129 0.536140i \(-0.819882\pi\)
0.886376 + 0.462967i \(0.153215\pi\)
\(888\) −2.51485e15 −0.152841
\(889\) −1.77804e16 2.54688e16i −1.07394 1.53833i
\(890\) 6.20005e14 0.0372178
\(891\) −2.67352e15 + 4.63067e15i −0.159498 + 0.276259i
\(892\) 1.72062e15 + 2.98021e15i 0.102019 + 0.176701i
\(893\) −6.13796e13 1.06313e14i −0.00361694 0.00626472i
\(894\) 1.65469e15 2.86600e15i 0.0969079 0.167849i
\(895\) 2.67082e15 0.155460
\(896\) −1.52225e15 + 1.31033e14i −0.0880627 + 0.00758033i
\(897\) −4.47390e15 −0.257234
\(898\) 3.32155e15 5.75309e15i 0.189811 0.328761i
\(899\) 8.89271e15 + 1.54026e16i 0.505075 + 0.874816i
\(900\) −3.92561e15 6.79935e15i −0.221602 0.383826i
\(901\) −3.45902e15 + 5.99121e15i −0.194074 + 0.336146i
\(902\) 3.50666e15 0.195550
\(903\) −1.33415e15 + 2.85066e15i −0.0739470 + 0.158002i
\(904\) 1.21505e16 0.669371
\(905\) −3.49345e14 + 6.05084e14i −0.0191288 + 0.0331321i
\(906\) −8.20757e13 1.42159e14i −0.00446693 0.00773695i
\(907\) 1.61522e15 + 2.79764e15i 0.0873757 + 0.151339i 0.906401 0.422418i \(-0.138819\pi\)
−0.819025 + 0.573757i \(0.805485\pi\)
\(908\) 1.06219e15 1.83978e15i 0.0571126 0.0989219i
\(909\) −2.63247e16 −1.40690
\(910\) 6.08667e14 1.30054e15i 0.0323334 0.0690867i
\(911\) −1.19187e16 −0.629330 −0.314665 0.949203i \(-0.601892\pi\)
−0.314665 + 0.949203i \(0.601892\pi\)
\(912\) −1.22054e14 + 2.11403e14i −0.00640588 + 0.0110953i
\(913\) −7.59381e15 1.31529e16i −0.396160 0.686169i
\(914\) 8.98610e15 + 1.55644e16i 0.465980 + 0.807100i
\(915\) −3.25182e13 + 5.63232e13i −0.00167614 + 0.00290316i
\(916\) 3.51964e15 0.180332
\(917\) 1.89791e16 1.63369e15i 0.966592 0.0832031i
\(918\) −9.15170e15 −0.463305
\(919\) 9.02982e15 1.56401e16i 0.454406 0.787054i −0.544248 0.838924i \(-0.683185\pi\)
0.998654 + 0.0518705i \(0.0165183\pi\)
\(920\) 1.58236e14 + 2.74073e14i 0.00791538 + 0.0137098i
\(921\) 6.39739e15 + 1.10806e16i 0.318108 + 0.550979i
\(922\) 4.13594e15 7.16365e15i 0.204434 0.354091i
\(923\) 4.41696e15 0.217027
\(924\) 8.93998e14 + 1.28057e15i 0.0436657 + 0.0625472i
\(925\) 2.69147e16 1.30680
\(926\) −9.64940e15 + 1.67133e16i −0.465736 + 0.806679i
\(927\) 6.38720e15 + 1.10630e16i 0.306459 + 0.530802i
\(928\) 2.52785e15 + 4.37836e15i 0.120569 + 0.208832i
\(929\) 1.75307e16 3.03641e16i 0.831215 1.43971i −0.0658599 0.997829i \(-0.520979\pi\)
0.897075 0.441878i \(-0.145688\pi\)
\(930\) 2.86968e14 0.0135262
\(931\) 2.13118e15 + 2.55433e15i 0.0998613 + 0.119689i
\(932\) −9.36425e14 −0.0436200
\(933\) −5.23575e15 + 9.06859e15i −0.242454 + 0.419943i
\(934\) 5.10701e15 + 8.84561e15i 0.235104 + 0.407211i
\(935\) 4.19616e14 + 7.26796e14i 0.0192038 + 0.0332620i
\(936\) 4.75796e15 8.24103e15i 0.216473 0.374942i
\(937\) −2.84640e16 −1.28745 −0.643723 0.765259i \(-0.722611\pi\)
−0.643723 + 0.765259i \(0.722611\pi\)
\(938\) 3.19206e15 + 4.57234e15i 0.143534 + 0.205600i
\(939\) 4.24296e15 0.189674
\(940\) −2.05113e13 + 3.55266e13i −0.000911570 + 0.00157888i
\(941\) 1.44712e16 + 2.50649e16i 0.639385 + 1.10745i 0.985568 + 0.169281i \(0.0541444\pi\)
−0.346183 + 0.938167i \(0.612522\pi\)
\(942\) −8.44423e14 1.46258e15i −0.0370920 0.0642452i
\(943\) −3.88848e15 + 6.73504e15i −0.169811 + 0.294121i
\(944\) −9.32743e15 −0.404964
\(945\) −1.12803e15 + 9.70995e13i −0.0486907 + 0.00419124i
\(946\) 4.05727e15 0.174114
\(947\) 6.05924e15 1.04949e16i 0.258519 0.447769i −0.707326 0.706887i \(-0.750099\pi\)
0.965845 + 0.259119i \(0.0834321\pi\)
\(948\) −2.48997e15 4.31275e15i −0.105620 0.182940i
\(949\) 2.25299e16 + 3.90229e16i 0.950157 + 1.64572i
\(950\) 1.30625e15 2.26250e15i 0.0547707 0.0948656i
\(951\) −3.79177e15 −0.158070
\(952\) 3.80892e15 8.13850e15i 0.157870 0.337319i
\(953\) 1.88726e16 0.777715 0.388858 0.921298i \(-0.372870\pi\)
0.388858 + 0.921298i \(0.372870\pi\)
\(954\) −2.83594e15 + 4.91199e15i −0.116193 + 0.201252i
\(955\) 1.11159e15 + 1.92533e15i 0.0452820 + 0.0784306i
\(956\) −7.95139e15 1.37722e16i −0.322051 0.557809i
\(957\) 2.58390e15 4.47545e15i 0.104054 0.180227i
\(958\) −2.05977e16 −0.824725
\(959\) −7.78617e15 + 1.66367e16i −0.309971 + 0.662315i
\(960\) 8.15736e13 0.00322892
\(961\) 5.73738e15 9.93743e15i 0.225806 0.391107i
\(962\) 1.63107e16 + 2.82510e16i 0.638279 + 1.10553i
\(963\) −5.99262e13 1.03795e14i −0.00233170 0.00403861i
\(964\) 1.24622e15 2.15852e15i 0.0482139 0.0835090i
\(965\) 2.47605e15 0.0952487
\(966\) −3.45086e15 + 2.97046e14i −0.131994 + 0.0113619i
\(967\) 2.86250e16 1.08868 0.544339 0.838865i \(-0.316780\pi\)
0.544339 + 0.838865i \(0.316780\pi\)
\(968\) −3.66793e15 + 6.35304e15i −0.138710 + 0.240252i
\(969\) −7.17817e14 1.24330e15i −0.0269919 0.0467513i
\(970\) −1.15726e15 2.00443e15i −0.0432698 0.0749455i
\(971\) −1.20361e16 + 2.08472e16i −0.447488 + 0.775072i −0.998222 0.0596088i \(-0.981015\pi\)
0.550734 + 0.834681i \(0.314348\pi\)
\(972\) −1.14691e16 −0.423998
\(973\) −3.05647e16 4.37811e16i −1.12357 1.60941i
\(974\) −2.06040e16 −0.753143
\(975\) 6.17090e15 1.06883e16i 0.224297 0.388494i
\(976\) −4.48825e14 7.77388e14i −0.0162220 0.0280973i
\(977\) −5.48333e15 9.49740e15i −0.197072 0.341338i 0.750506 0.660864i \(-0.229810\pi\)
−0.947578 + 0.319526i \(0.896476\pi\)
\(978\) 1.75057e15 3.03208e15i 0.0625628 0.108362i
\(979\) 8.74724e15 0.310861
\(980\) 3.83135e14 1.04356e15i 0.0135397 0.0368785i
\(981\) −3.40801e16 −1.19763
\(982\) −3.03441e15 + 5.25576e15i −0.106038 + 0.183663i
\(983\) −2.04851e16 3.54812e16i −0.711858 1.23297i −0.964159 0.265325i \(-0.914521\pi\)
0.252301 0.967649i \(-0.418813\pi\)
\(984\) 1.00229e15 + 1.73602e15i 0.0346355 + 0.0599904i
\(985\) 1.16531e15 2.01838e15i 0.0400446 0.0693593i
\(986\) −2.97334e16 −1.01606
\(987\) −2.57005e14 3.68136e14i −0.00873367 0.0125102i
\(988\) 3.16644e15 0.107006
\(989\) −4.49904e15 + 7.79257e15i −0.151196 + 0.261879i
\(990\) 3.44029e14 + 5.95875e14i 0.0114974 + 0.0199142i
\(991\) 1.05299e16 + 1.82383e16i 0.349959 + 0.606147i 0.986242 0.165309i \(-0.0528621\pi\)
−0.636283 + 0.771456i \(0.719529\pi\)
\(992\) −1.98040e15 + 3.43016e15i −0.0654545 + 0.113370i
\(993\) −3.64729e15 −0.119881
\(994\) 3.40695e15 2.93266e14i 0.111363 0.00958597i
\(995\) −3.79374e15 −0.123322
\(996\) 4.34101e15 7.51885e15i 0.140335 0.243067i
\(997\) −4.12971e15 7.15286e15i −0.132769 0.229962i 0.791974 0.610555i \(-0.209053\pi\)
−0.924743 + 0.380592i \(0.875720\pi\)
\(998\) −5.77533e15 1.00032e16i −0.184654 0.319830i
\(999\) 1.28608e16 2.22755e16i 0.408937 0.708300i
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.b.9.3 8
3.2 odd 2 126.12.g.c.37.3 8
4.3 odd 2 112.12.i.b.65.2 8
7.2 even 3 98.12.a.i.1.2 4
7.3 odd 6 98.12.c.n.67.2 8
7.4 even 3 inner 14.12.c.b.11.3 yes 8
7.5 odd 6 98.12.a.h.1.3 4
7.6 odd 2 98.12.c.n.79.2 8
21.11 odd 6 126.12.g.c.109.3 8
28.11 odd 6 112.12.i.b.81.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.12.c.b.9.3 8 1.1 even 1 trivial
14.12.c.b.11.3 yes 8 7.4 even 3 inner
98.12.a.h.1.3 4 7.5 odd 6
98.12.a.i.1.2 4 7.2 even 3
98.12.c.n.67.2 8 7.3 odd 6
98.12.c.n.79.2 8 7.6 odd 2
112.12.i.b.65.2 8 4.3 odd 2
112.12.i.b.81.2 8 28.11 odd 6
126.12.g.c.37.3 8 3.2 odd 2
126.12.g.c.109.3 8 21.11 odd 6