Properties

Label 16.10.e.a.5.16
Level $16$
Weight $10$
Character 16.5
Analytic conductor $8.241$
Analytic rank $0$
Dimension $34$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [16,10,Mod(5,16)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(16, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("16.5");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 16.e (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.24057337862\)
Analytic rank: \(0\)
Dimension: \(34\)
Relative dimension: \(17\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 5.16
Character \(\chi\) \(=\) 16.5
Dual form 16.10.e.a.13.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(21.2709 - 7.71668i) q^{2} +(-159.536 + 159.536i) q^{3} +(392.906 - 328.282i) q^{4} +(-1021.24 - 1021.24i) q^{5} +(-2162.40 + 4624.58i) q^{6} -10191.8i q^{7} +(5824.23 - 10014.8i) q^{8} -31220.8i q^{9} +O(q^{10})\) \(q+(21.2709 - 7.71668i) q^{2} +(-159.536 + 159.536i) q^{3} +(392.906 - 328.282i) q^{4} +(-1021.24 - 1021.24i) q^{5} +(-2162.40 + 4624.58i) q^{6} -10191.8i q^{7} +(5824.23 - 10014.8i) q^{8} -31220.8i q^{9} +(-29603.4 - 13842.2i) q^{10} +(3063.82 + 3063.82i) q^{11} +(-10309.9 + 115056. i) q^{12} +(-105330. + 105330. i) q^{13} +(-78647.1 - 216790. i) q^{14} +325851. q^{15} +(46606.0 - 257968. i) q^{16} -451785. q^{17} +(-240921. - 664095. i) q^{18} +(282691. - 282691. i) q^{19} +(-736507. - 65996.7i) q^{20} +(1.62597e6 + 1.62597e6i) q^{21} +(88812.9 + 41527.9i) q^{22} -92307.1i q^{23} +(668547. + 2.52690e6i) q^{24} +132745. i q^{25} +(-1.42767e6 + 3.05326e6i) q^{26} +(1.84070e6 + 1.84070e6i) q^{27} +(-3.34580e6 - 4.00443e6i) q^{28} +(811415. - 811415. i) q^{29} +(6.93115e6 - 2.51448e6i) q^{30} +3.95827e6 q^{31} +(-999300. - 5.84686e6i) q^{32} -977583. q^{33} +(-9.60988e6 + 3.48627e6i) q^{34} +(-1.04083e7 + 1.04083e7i) q^{35} +(-1.02492e7 - 1.22668e7i) q^{36} +(1.09102e7 + 1.09102e7i) q^{37} +(3.83168e6 - 8.19455e6i) q^{38} -3.36079e7i q^{39} +(-1.61755e7 + 4.27957e6i) q^{40} -6.52858e6i q^{41} +(4.71330e7 + 2.20388e7i) q^{42} +(-2.01795e7 - 2.01795e7i) q^{43} +(2.20959e6 + 197996. i) q^{44} +(-3.18840e7 + 3.18840e7i) q^{45} +(-712304. - 1.96346e6i) q^{46} +2.46007e7 q^{47} +(3.37199e7 + 4.85906e7i) q^{48} -6.35200e7 q^{49} +(1.02435e6 + 2.82361e6i) q^{50} +(7.20761e7 - 7.20761e7i) q^{51} +(-6.80683e6 + 7.59625e7i) q^{52} +(-5.89399e6 - 5.89399e6i) q^{53} +(5.33574e7 + 2.49493e7i) q^{54} -6.25781e6i q^{55} +(-1.02069e8 - 5.93597e7i) q^{56} +9.01992e7i q^{57} +(1.09981e7 - 2.35210e7i) q^{58} +(4.86841e7 + 4.86841e7i) q^{59} +(1.28029e8 - 1.06971e8i) q^{60} +(-5.79083e7 + 5.79083e7i) q^{61} +(8.41962e7 - 3.05447e7i) q^{62} -3.18197e8 q^{63} +(-6.63744e7 - 1.16657e8i) q^{64} +2.15134e8 q^{65} +(-2.07941e7 + 7.54369e6i) q^{66} +(2.13332e8 - 2.13332e8i) q^{67} +(-1.77509e8 + 1.48313e8i) q^{68} +(1.47264e7 + 1.47264e7i) q^{69} +(-1.41077e8 + 3.01713e8i) q^{70} +1.65135e8i q^{71} +(-3.12670e8 - 1.81837e8i) q^{72} -2.14951e8i q^{73} +(3.16260e8 + 1.47879e8i) q^{74} +(-2.11777e7 - 2.11777e7i) q^{75} +(1.82686e7 - 2.03874e8i) q^{76} +(3.12260e7 - 3.12260e7i) q^{77} +(-2.59341e8 - 7.14871e8i) q^{78} +1.33443e8 q^{79} +(-3.11043e8 + 2.15851e8i) q^{80} +2.72022e7 q^{81} +(-5.03790e7 - 1.38869e8i) q^{82} +(-2.29998e8 + 2.29998e8i) q^{83} +(1.17263e9 + 1.05077e8i) q^{84} +(4.61381e8 + 4.61381e8i) q^{85} +(-5.84957e8 - 2.73519e8i) q^{86} +2.58901e8i q^{87} +(4.85280e7 - 1.28391e7i) q^{88} -6.55021e8i q^{89} +(-4.32164e8 + 9.24240e8i) q^{90} +(1.07350e9 + 1.07350e9i) q^{91} +(-3.03028e7 - 3.62680e7i) q^{92} +(-6.31489e8 + 6.31489e8i) q^{93} +(5.23280e8 - 1.89836e8i) q^{94} -5.77393e8 q^{95} +(1.09221e9 + 7.73363e8i) q^{96} -4.74582e8 q^{97} +(-1.35113e9 + 4.90164e8i) q^{98} +(9.56549e7 - 9.56549e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34 q - 2 q^{2} - 2 q^{3} + 168 q^{4} - 2 q^{5} - 2192 q^{6} - 716 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 34 q - 2 q^{2} - 2 q^{3} + 168 q^{4} - 2 q^{5} - 2192 q^{6} - 716 q^{8} + 4684 q^{10} + 65858 q^{11} + 217156 q^{12} - 2 q^{13} - 133540 q^{14} + 404996 q^{15} - 817256 q^{16} - 4 q^{17} + 2179902 q^{18} - 480890 q^{19} - 3277988 q^{20} + 39364 q^{21} - 34300 q^{22} + 1863856 q^{24} - 6347768 q^{26} + 6364408 q^{27} + 3629528 q^{28} - 633402 q^{29} - 4677804 q^{30} - 11082256 q^{31} - 1655992 q^{32} - 4 q^{33} - 4528204 q^{34} + 23026556 q^{35} + 23564140 q^{36} - 1214778 q^{37} - 14996352 q^{38} - 11751288 q^{40} + 105399160 q^{42} - 34881078 q^{43} - 94223356 q^{44} + 3866882 q^{45} + 15432396 q^{46} + 97593616 q^{47} + 7831528 q^{48} - 126825626 q^{49} - 6289530 q^{50} - 27382140 q^{51} - 28284428 q^{52} - 74907850 q^{53} + 105311008 q^{54} + 26511256 q^{56} - 178271784 q^{58} + 94503354 q^{59} + 229034112 q^{60} - 90121106 q^{61} - 136788944 q^{62} - 153644796 q^{63} - 349292928 q^{64} + 62806084 q^{65} + 192273844 q^{66} + 406167670 q^{67} - 285757488 q^{68} + 382399540 q^{69} + 606051200 q^{70} + 882075684 q^{72} + 123910860 q^{74} - 1038797114 q^{75} - 453269100 q^{76} + 286751428 q^{77} - 1735024804 q^{78} + 1913565952 q^{79} - 700272856 q^{80} - 774840982 q^{81} - 674287584 q^{82} - 1637053442 q^{83} + 1281919912 q^{84} + 425303748 q^{85} + 243980676 q^{86} + 1781147128 q^{88} + 3084087192 q^{90} + 2019528196 q^{91} - 3131634504 q^{92} + 1071927184 q^{93} - 2068460272 q^{94} - 5087413260 q^{95} - 3896483152 q^{96} - 4 q^{97} - 3100632102 q^{98} + 3713751422 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 21.2709 7.71668i 0.940052 0.341032i
\(3\) −159.536 + 159.536i −1.13714 + 1.13714i −0.148181 + 0.988960i \(0.547342\pi\)
−0.988960 + 0.148181i \(0.952658\pi\)
\(4\) 392.906 328.282i 0.767394 0.641176i
\(5\) −1021.24 1021.24i −0.730741 0.730741i 0.240025 0.970767i \(-0.422844\pi\)
−0.970767 + 0.240025i \(0.922844\pi\)
\(6\) −2162.40 + 4624.58i −0.681170 + 1.45677i
\(7\) 10191.8i 1.60440i −0.597058 0.802198i \(-0.703664\pi\)
0.597058 0.802198i \(-0.296336\pi\)
\(8\) 5824.23 10014.8i 0.502729 0.864444i
\(9\) 31220.8i 1.58618i
\(10\) −29603.4 13842.2i −0.936141 0.437728i
\(11\) 3063.82 + 3063.82i 0.0630952 + 0.0630952i 0.737950 0.674855i \(-0.235794\pi\)
−0.674855 + 0.737950i \(0.735794\pi\)
\(12\) −10309.9 + 115056.i −0.143528 + 1.60174i
\(13\) −105330. + 105330.i −1.02284 + 1.02284i −0.0231031 + 0.999733i \(0.507355\pi\)
−0.999733 + 0.0231031i \(0.992645\pi\)
\(14\) −78647.1 216790.i −0.547150 1.50821i
\(15\) 325851. 1.66191
\(16\) 46606.0 257968.i 0.177788 0.984069i
\(17\) −451785. −1.31193 −0.655966 0.754791i \(-0.727738\pi\)
−0.655966 + 0.754791i \(0.727738\pi\)
\(18\) −240921. 664095.i −0.540938 1.49109i
\(19\) 282691. 282691.i 0.497647 0.497647i −0.413058 0.910705i \(-0.635539\pi\)
0.910705 + 0.413058i \(0.135539\pi\)
\(20\) −736507. 65996.7i −1.02930 0.0922332i
\(21\) 1.62597e6 + 1.62597e6i 1.82442 + 1.82442i
\(22\) 88812.9 + 41527.9i 0.0808303 + 0.0377953i
\(23\) 92307.1i 0.0687797i −0.999408 0.0343898i \(-0.989051\pi\)
0.999408 0.0343898i \(-0.0109488\pi\)
\(24\) 668547. + 2.52690e6i 0.411322 + 1.55467i
\(25\) 132745.i 0.0679654i
\(26\) −1.42767e6 + 3.05326e6i −0.612699 + 1.31034i
\(27\) 1.84070e6 + 1.84070e6i 0.666569 + 0.666569i
\(28\) −3.34580e6 4.00443e6i −1.02870 1.23120i
\(29\) 811415. 811415.i 0.213036 0.213036i −0.592520 0.805556i \(-0.701867\pi\)
0.805556 + 0.592520i \(0.201867\pi\)
\(30\) 6.93115e6 2.51448e6i 1.56228 0.566765i
\(31\) 3.95827e6 0.769800 0.384900 0.922958i \(-0.374236\pi\)
0.384900 + 0.922958i \(0.374236\pi\)
\(32\) −999300. 5.84686e6i −0.168469 0.985707i
\(33\) −977583. −0.143496
\(34\) −9.60988e6 + 3.48627e6i −1.23328 + 0.447411i
\(35\) −1.04083e7 + 1.04083e7i −1.17240 + 1.17240i
\(36\) −1.02492e7 1.22668e7i −1.01702 1.21723i
\(37\) 1.09102e7 + 1.09102e7i 0.957025 + 0.957025i 0.999114 0.0420886i \(-0.0134012\pi\)
−0.0420886 + 0.999114i \(0.513401\pi\)
\(38\) 3.83168e6 8.19455e6i 0.298100 0.637528i
\(39\) 3.36079e7i 2.32622i
\(40\) −1.61755e7 + 4.27957e6i −0.999050 + 0.264320i
\(41\) 6.52858e6i 0.360821i −0.983591 0.180410i \(-0.942257\pi\)
0.983591 0.180410i \(-0.0577426\pi\)
\(42\) 4.71330e7 + 2.20388e7i 2.33724 + 1.09287i
\(43\) −2.01795e7 2.01795e7i −0.900126 0.900126i 0.0953208 0.995447i \(-0.469612\pi\)
−0.995447 + 0.0953208i \(0.969612\pi\)
\(44\) 2.20959e6 + 197996.i 0.0888741 + 0.00796380i
\(45\) −3.18840e7 + 3.18840e7i −1.15909 + 1.15909i
\(46\) −712304. 1.96346e6i −0.0234561 0.0646564i
\(47\) 2.46007e7 0.735372 0.367686 0.929950i \(-0.380150\pi\)
0.367686 + 0.929950i \(0.380150\pi\)
\(48\) 3.37199e7 + 4.85906e7i 0.916855 + 1.32119i
\(49\) −6.35200e7 −1.57409
\(50\) 1.02435e6 + 2.82361e6i 0.0231784 + 0.0638910i
\(51\) 7.20761e7 7.20761e7i 1.49185 1.49185i
\(52\) −6.80683e6 + 7.59625e7i −0.129101 + 1.44074i
\(53\) −5.89399e6 5.89399e6i −0.102605 0.102605i 0.653941 0.756546i \(-0.273115\pi\)
−0.756546 + 0.653941i \(0.773115\pi\)
\(54\) 5.33574e7 + 2.49493e7i 0.853931 + 0.399288i
\(55\) 6.25781e6i 0.0922126i
\(56\) −1.02069e8 5.93597e7i −1.38691 0.806576i
\(57\) 9.01992e7i 1.13179i
\(58\) 1.09981e7 2.35210e7i 0.127612 0.272916i
\(59\) 4.86841e7 + 4.86841e7i 0.523062 + 0.523062i 0.918495 0.395433i \(-0.129406\pi\)
−0.395433 + 0.918495i \(0.629406\pi\)
\(60\) 1.28029e8 1.06971e8i 1.27534 1.06558i
\(61\) −5.79083e7 + 5.79083e7i −0.535496 + 0.535496i −0.922203 0.386707i \(-0.873613\pi\)
0.386707 + 0.922203i \(0.373613\pi\)
\(62\) 8.41962e7 3.05447e7i 0.723652 0.262527i
\(63\) −3.18197e8 −2.54486
\(64\) −6.63744e7 1.16657e8i −0.494528 0.869162i
\(65\) 2.15134e8 1.49486
\(66\) −2.07941e7 + 7.54369e6i −0.134894 + 0.0489369i
\(67\) 2.13332e8 2.13332e8i 1.29336 1.29336i 0.360660 0.932697i \(-0.382551\pi\)
0.932697 0.360660i \(-0.117449\pi\)
\(68\) −1.77509e8 + 1.48313e8i −1.00677 + 0.841179i
\(69\) 1.47264e7 + 1.47264e7i 0.0782122 + 0.0782122i
\(70\) −1.41077e8 + 3.01713e8i −0.702289 + 1.50194i
\(71\) 1.65135e8i 0.771219i 0.922662 + 0.385610i \(0.126009\pi\)
−0.922662 + 0.385610i \(0.873991\pi\)
\(72\) −3.12670e8 1.81837e8i −1.37116 0.797418i
\(73\) 2.14951e8i 0.885903i −0.896546 0.442951i \(-0.853931\pi\)
0.896546 0.442951i \(-0.146069\pi\)
\(74\) 3.16260e8 + 1.47879e8i 1.22603 + 0.573277i
\(75\) −2.11777e7 2.11777e7i −0.0772863 0.0772863i
\(76\) 1.82686e7 2.03874e8i 0.0628123 0.700971i
\(77\) 3.12260e7 3.12260e7i 0.101230 0.101230i
\(78\) −2.59341e8 7.14871e8i −0.793315 2.18677i
\(79\) 1.33443e8 0.385455 0.192728 0.981252i \(-0.438267\pi\)
0.192728 + 0.981252i \(0.438267\pi\)
\(80\) −3.11043e8 + 2.15851e8i −0.849017 + 0.589183i
\(81\) 2.72022e7 0.0702136
\(82\) −5.03790e7 1.38869e8i −0.123052 0.339190i
\(83\) −2.29998e8 + 2.29998e8i −0.531952 + 0.531952i −0.921153 0.389201i \(-0.872751\pi\)
0.389201 + 0.921153i \(0.372751\pi\)
\(84\) 1.17263e9 + 1.05077e8i 2.56983 + 0.230276i
\(85\) 4.61381e8 + 4.61381e8i 0.958683 + 0.958683i
\(86\) −5.84957e8 2.73519e8i −1.15314 0.539193i
\(87\) 2.58901e8i 0.484503i
\(88\) 4.85280e7 1.28391e7i 0.0862621 0.0228225i
\(89\) 6.55021e8i 1.10662i −0.832974 0.553312i \(-0.813364\pi\)
0.832974 0.553312i \(-0.186636\pi\)
\(90\) −4.32164e8 + 9.24240e8i −0.694316 + 1.48489i
\(91\) 1.07350e9 + 1.07350e9i 1.64103 + 1.64103i
\(92\) −3.03028e7 3.62680e7i −0.0440998 0.0527811i
\(93\) −6.31489e8 + 6.31489e8i −0.875371 + 0.875371i
\(94\) 5.23280e8 1.89836e8i 0.691288 0.250786i
\(95\) −5.77393e8 −0.727303
\(96\) 1.09221e9 + 7.73363e8i 1.31246 + 0.929314i
\(97\) −4.74582e8 −0.544300 −0.272150 0.962255i \(-0.587735\pi\)
−0.272150 + 0.962255i \(0.587735\pi\)
\(98\) −1.35113e9 + 4.90164e8i −1.47972 + 0.536814i
\(99\) 9.56549e7 9.56549e7i 0.100080 0.100080i
\(100\) 4.35778e7 + 5.21563e7i 0.0435778 + 0.0521563i
\(101\) −2.97714e8 2.97714e8i −0.284677 0.284677i 0.550294 0.834971i \(-0.314516\pi\)
−0.834971 + 0.550294i \(0.814516\pi\)
\(102\) 9.76939e8 2.08931e9i 0.893648 1.91119i
\(103\) 1.56873e9i 1.37335i −0.726966 0.686673i \(-0.759070\pi\)
0.726966 0.686673i \(-0.240930\pi\)
\(104\) 4.41391e8 + 1.66832e9i 0.369976 + 1.39839i
\(105\) 3.32102e9i 2.66636i
\(106\) −1.70853e8 7.98886e7i −0.131445 0.0614623i
\(107\) −6.25328e8 6.25328e8i −0.461191 0.461191i 0.437855 0.899046i \(-0.355738\pi\)
−0.899046 + 0.437855i \(0.855738\pi\)
\(108\) 1.32749e9 + 1.18953e8i 0.938909 + 0.0841334i
\(109\) 1.14850e9 1.14850e9i 0.779315 0.779315i −0.200400 0.979714i \(-0.564224\pi\)
0.979714 + 0.200400i \(0.0642240\pi\)
\(110\) −4.82895e7 1.33109e8i −0.0314475 0.0866846i
\(111\) −3.48114e9 −2.17655
\(112\) −2.62917e9 4.75001e8i −1.57884 0.285242i
\(113\) −2.27290e9 −1.31138 −0.655689 0.755031i \(-0.727622\pi\)
−0.655689 + 0.755031i \(0.727622\pi\)
\(114\) 6.96038e8 + 1.91862e9i 0.385977 + 1.06394i
\(115\) −9.42679e7 + 9.42679e7i −0.0502601 + 0.0502601i
\(116\) 5.24368e7 5.85183e8i 0.0268891 0.300075i
\(117\) 3.28848e9 + 3.28848e9i 1.62240 + 1.62240i
\(118\) 1.41124e9 + 6.59877e8i 0.670086 + 0.313324i
\(119\) 4.60452e9i 2.10486i
\(120\) 1.89783e9 3.26333e9i 0.835491 1.43663i
\(121\) 2.33917e9i 0.992038i
\(122\) −7.84904e8 + 1.67862e9i −0.320773 + 0.686015i
\(123\) 1.04155e9 + 1.04155e9i 0.410304 + 0.410304i
\(124\) 1.55523e9 1.29943e9i 0.590740 0.493577i
\(125\) −1.85905e9 + 1.85905e9i −0.681076 + 0.681076i
\(126\) −6.76835e9 + 2.45542e9i −2.39230 + 0.867879i
\(127\) 1.48275e9 0.505769 0.252884 0.967497i \(-0.418621\pi\)
0.252884 + 0.967497i \(0.418621\pi\)
\(128\) −2.31205e9 1.96921e9i −0.761294 0.648407i
\(129\) 6.43875e9 2.04714
\(130\) 4.57611e9 1.66012e9i 1.40524 0.509794i
\(131\) 1.14917e9 1.14917e9i 0.340928 0.340928i −0.515788 0.856716i \(-0.672501\pi\)
0.856716 + 0.515788i \(0.172501\pi\)
\(132\) −3.84098e8 + 3.20923e8i −0.110118 + 0.0920064i
\(133\) −2.88115e9 2.88115e9i −0.798423 0.798423i
\(134\) 2.89155e9 6.18398e9i 0.774746 1.65690i
\(135\) 3.75959e9i 0.974179i
\(136\) −2.63130e9 + 4.52453e9i −0.659546 + 1.13409i
\(137\) 6.62752e9i 1.60734i 0.595074 + 0.803671i \(0.297123\pi\)
−0.595074 + 0.803671i \(0.702877\pi\)
\(138\) 4.26882e8 + 1.99605e8i 0.100196 + 0.0468506i
\(139\) 2.65726e9 + 2.65726e9i 0.603765 + 0.603765i 0.941309 0.337545i \(-0.109596\pi\)
−0.337545 + 0.941309i \(0.609596\pi\)
\(140\) −6.72628e8 + 7.50636e9i −0.147979 + 1.65140i
\(141\) −3.92471e9 + 3.92471e9i −0.836222 + 0.836222i
\(142\) 1.27430e9 + 3.51259e9i 0.263010 + 0.724986i
\(143\) −6.45424e8 −0.129072
\(144\) −8.05395e9 1.45508e9i −1.56091 0.282003i
\(145\) −1.65730e9 −0.311348
\(146\) −1.65871e9 4.57221e9i −0.302121 0.832795i
\(147\) 1.01338e10 1.01338e10i 1.78996 1.78996i
\(148\) 7.86827e9 + 7.05058e8i 1.34804 + 0.120794i
\(149\) −2.13779e9 2.13779e9i −0.355326 0.355326i 0.506761 0.862087i \(-0.330843\pi\)
−0.862087 + 0.506761i \(0.830843\pi\)
\(150\) −6.13890e8 2.87048e8i −0.0990102 0.0462960i
\(151\) 3.46899e9i 0.543009i −0.962437 0.271504i \(-0.912479\pi\)
0.962437 0.271504i \(-0.0875211\pi\)
\(152\) −1.18464e9 4.47756e9i −0.180007 0.680370i
\(153\) 1.41051e10i 2.08096i
\(154\) 4.23246e8 9.05167e8i 0.0606386 0.129684i
\(155\) −4.04235e9 4.04235e9i −0.562525 0.562525i
\(156\) −1.10329e10 1.32047e10i −1.49151 1.78513i
\(157\) 3.15259e9 3.15259e9i 0.414113 0.414113i −0.469056 0.883169i \(-0.655406\pi\)
0.883169 + 0.469056i \(0.155406\pi\)
\(158\) 2.83846e9 1.02974e9i 0.362348 0.131453i
\(159\) 1.88061e9 0.233352
\(160\) −4.95053e9 + 6.99159e9i −0.597189 + 0.843404i
\(161\) −9.40780e8 −0.110350
\(162\) 5.78616e8 2.09911e8i 0.0660044 0.0239451i
\(163\) −6.08281e9 + 6.08281e9i −0.674932 + 0.674932i −0.958849 0.283917i \(-0.908366\pi\)
0.283917 + 0.958849i \(0.408366\pi\)
\(164\) −2.14322e9 2.56512e9i −0.231350 0.276892i
\(165\) 9.98349e8 + 9.98349e8i 0.104859 + 0.104859i
\(166\) −3.11745e9 + 6.66709e9i −0.318650 + 0.681475i
\(167\) 6.22360e9i 0.619181i 0.950870 + 0.309590i \(0.100192\pi\)
−0.950870 + 0.309590i \(0.899808\pi\)
\(168\) 2.57538e10 6.81373e9i 2.49430 0.659923i
\(169\) 1.15842e10i 1.09239i
\(170\) 1.33743e10 + 6.25368e9i 1.22815 + 0.574270i
\(171\) −8.82585e9 8.82585e9i −0.789358 0.789358i
\(172\) −1.45532e10 1.30408e9i −1.26789 0.113613i
\(173\) −1.38445e9 + 1.38445e9i −0.117509 + 0.117509i −0.763416 0.645907i \(-0.776479\pi\)
0.645907 + 0.763416i \(0.276479\pi\)
\(174\) 1.99785e9 + 5.50706e9i 0.165231 + 0.455458i
\(175\) 1.35292e9 0.109043
\(176\) 9.33160e8 6.47575e8i 0.0733076 0.0508725i
\(177\) −1.55338e10 −1.18959
\(178\) −5.05459e9 1.39329e10i −0.377395 1.04028i
\(179\) −1.17795e10 + 1.17795e10i −0.857606 + 0.857606i −0.991056 0.133450i \(-0.957395\pi\)
0.133450 + 0.991056i \(0.457395\pi\)
\(180\) −2.06047e9 + 2.29943e10i −0.146298 + 1.63265i
\(181\) 8.12486e9 + 8.12486e9i 0.562681 + 0.562681i 0.930068 0.367387i \(-0.119748\pi\)
−0.367387 + 0.930068i \(0.619748\pi\)
\(182\) 3.11183e10 + 1.45506e10i 2.10230 + 0.983011i
\(183\) 1.84770e10i 1.21787i
\(184\) −9.24437e8 5.37618e8i −0.0594562 0.0345775i
\(185\) 2.22838e10i 1.39868i
\(186\) −8.55936e9 + 1.83054e10i −0.524365 + 1.12142i
\(187\) −1.38419e9 1.38419e9i −0.0827767 0.0827767i
\(188\) 9.66576e9 8.07597e9i 0.564321 0.471503i
\(189\) 1.87601e10 1.87601e10i 1.06944 1.06944i
\(190\) −1.22817e10 + 4.45555e9i −0.683702 + 0.248033i
\(191\) 3.57916e10 1.94595 0.972973 0.230921i \(-0.0741738\pi\)
0.972973 + 0.230921i \(0.0741738\pi\)
\(192\) 2.92002e10 + 8.02190e9i 1.55071 + 0.426012i
\(193\) 1.03490e10 0.536897 0.268448 0.963294i \(-0.413489\pi\)
0.268448 + 0.963294i \(0.413489\pi\)
\(194\) −1.00948e10 + 3.66220e9i −0.511670 + 0.185624i
\(195\) −3.43218e10 + 3.43218e10i −1.69986 + 1.69986i
\(196\) −2.49574e10 + 2.08525e10i −1.20794 + 1.00927i
\(197\) −1.22315e10 1.22315e10i −0.578605 0.578605i 0.355914 0.934519i \(-0.384170\pi\)
−0.934519 + 0.355914i \(0.884170\pi\)
\(198\) 1.29653e9 2.77281e9i 0.0599501 0.128211i
\(199\) 5.73493e8i 0.0259232i −0.999916 0.0129616i \(-0.995874\pi\)
0.999916 0.0129616i \(-0.00412593\pi\)
\(200\) 1.32941e9 + 7.73138e8i 0.0587523 + 0.0341682i
\(201\) 6.80683e10i 2.94146i
\(202\) −8.63002e9 4.03529e9i −0.364696 0.170527i
\(203\) −8.26981e9 8.26981e9i −0.341793 0.341793i
\(204\) 4.65784e9 5.19804e10i 0.188299 2.10138i
\(205\) −6.66726e9 + 6.66726e9i −0.263667 + 0.263667i
\(206\) −1.21054e10 3.33683e10i −0.468355 1.29102i
\(207\) −2.88190e9 −0.109097
\(208\) 2.22627e10 + 3.20807e10i 0.824693 + 1.18839i
\(209\) 1.73223e9 0.0627983
\(210\) −2.56272e10 7.06412e10i −0.909316 2.50652i
\(211\) 2.18016e10 2.18016e10i 0.757213 0.757213i −0.218601 0.975814i \(-0.570149\pi\)
0.975814 + 0.218601i \(0.0701494\pi\)
\(212\) −4.25067e9 3.80893e8i −0.144526 0.0129506i
\(213\) −2.63451e10 2.63451e10i −0.876985 0.876985i
\(214\) −1.81268e10 8.47586e9i −0.590825 0.276263i
\(215\) 4.12164e10i 1.31552i
\(216\) 2.91548e10 7.71355e9i 0.911315 0.241108i
\(217\) 4.03421e10i 1.23506i
\(218\) 1.55671e10 3.32924e10i 0.466825 0.998367i
\(219\) 3.42925e10 + 3.42925e10i 1.00740 + 1.00740i
\(220\) −2.05433e9 2.45873e9i −0.0591245 0.0707634i
\(221\) 4.75864e10 4.75864e10i 1.34189 1.34189i
\(222\) −7.40471e10 + 2.68628e10i −2.04607 + 0.742272i
\(223\) 2.96078e10 0.801743 0.400871 0.916134i \(-0.368707\pi\)
0.400871 + 0.916134i \(0.368707\pi\)
\(224\) −5.95903e10 + 1.01847e10i −1.58146 + 0.270292i
\(225\) 4.14440e9 0.107805
\(226\) −4.83468e10 + 1.75392e10i −1.23276 + 0.447222i
\(227\) −1.21872e9 + 1.21872e9i −0.0304640 + 0.0304640i −0.722175 0.691711i \(-0.756857\pi\)
0.691711 + 0.722175i \(0.256857\pi\)
\(228\) 2.96108e10 + 3.54398e10i 0.725676 + 0.868529i
\(229\) −3.80541e10 3.80541e10i −0.914412 0.914412i 0.0822039 0.996616i \(-0.473804\pi\)
−0.996616 + 0.0822039i \(0.973804\pi\)
\(230\) −1.27773e9 + 2.73260e9i −0.0301068 + 0.0643874i
\(231\) 9.96337e9i 0.230225i
\(232\) −3.40028e9 1.28520e10i −0.0770583 0.291256i
\(233\) 7.40924e10i 1.64692i 0.567376 + 0.823459i \(0.307959\pi\)
−0.567376 + 0.823459i \(0.692041\pi\)
\(234\) 9.53251e10 + 4.45729e10i 2.07843 + 0.971851i
\(235\) −2.51233e10 2.51233e10i −0.537367 0.537367i
\(236\) 3.51104e10 + 3.14616e9i 0.736769 + 0.0660201i
\(237\) −2.12890e10 + 2.12890e10i −0.438317 + 0.438317i
\(238\) 3.55316e10 + 9.79424e10i 0.717824 + 1.97867i
\(239\) −1.39633e10 −0.276819 −0.138410 0.990375i \(-0.544199\pi\)
−0.138410 + 0.990375i \(0.544199\pi\)
\(240\) 1.51866e10 8.40590e10i 0.295468 1.63544i
\(241\) 8.12591e10 1.55166 0.775828 0.630945i \(-0.217333\pi\)
0.775828 + 0.630945i \(0.217333\pi\)
\(242\) −1.80506e10 4.97564e10i −0.338317 0.932567i
\(243\) −4.05702e10 + 4.05702e10i −0.746412 + 0.746412i
\(244\) −3.74226e9 + 4.17627e10i −0.0675896 + 0.754284i
\(245\) 6.48693e10 + 6.48693e10i 1.15025 + 1.15025i
\(246\) 3.01920e10 + 1.41174e10i 0.525634 + 0.245780i
\(247\) 5.95517e10i 1.01802i
\(248\) 2.30539e10 3.96413e10i 0.387001 0.665449i
\(249\) 7.33861e10i 1.20981i
\(250\) −2.51980e10 + 5.38894e10i −0.407978 + 0.872515i
\(251\) −6.02078e10 6.02078e10i −0.957461 0.957461i 0.0416704 0.999131i \(-0.486732\pi\)
−0.999131 + 0.0416704i \(0.986732\pi\)
\(252\) −1.25022e11 + 1.04458e11i −1.95291 + 1.63170i
\(253\) 2.82813e8 2.82813e8i 0.00433967 0.00433967i
\(254\) 3.15395e10 1.14419e10i 0.475449 0.172483i
\(255\) −1.47214e11 −2.18031
\(256\) −6.43752e10 2.40457e10i −0.936783 0.349911i
\(257\) 3.71313e10 0.530934 0.265467 0.964120i \(-0.414474\pi\)
0.265467 + 0.964120i \(0.414474\pi\)
\(258\) 1.36958e11 4.96857e10i 1.92442 0.698141i
\(259\) 1.11195e11 1.11195e11i 1.53545 1.53545i
\(260\) 8.45275e10 7.06247e10i 1.14714 0.958466i
\(261\) −2.53330e10 2.53330e10i −0.337913 0.337913i
\(262\) 1.55761e10 3.33116e10i 0.204223 0.436757i
\(263\) 8.71366e10i 1.12305i −0.827459 0.561526i \(-0.810215\pi\)
0.827459 0.561526i \(-0.189785\pi\)
\(264\) −5.69367e9 + 9.79029e9i −0.0721398 + 0.124045i
\(265\) 1.20384e10i 0.149955i
\(266\) −8.35176e10 3.90518e10i −1.02285 0.478271i
\(267\) 1.04500e11 + 1.04500e11i 1.25839 + 1.25839i
\(268\) 1.37863e10 1.53852e11i 0.163246 1.82178i
\(269\) −1.12331e11 + 1.12331e11i −1.30802 + 1.30802i −0.385182 + 0.922841i \(0.625861\pi\)
−0.922841 + 0.385182i \(0.874139\pi\)
\(270\) −2.90115e10 7.99701e10i −0.332226 0.915779i
\(271\) 1.08524e11 1.22226 0.611128 0.791532i \(-0.290716\pi\)
0.611128 + 0.791532i \(0.290716\pi\)
\(272\) −2.10559e10 + 1.16546e11i −0.233245 + 1.29103i
\(273\) −3.42526e11 −3.73217
\(274\) 5.11424e10 + 1.40973e11i 0.548155 + 1.51098i
\(275\) −4.06707e8 + 4.06707e8i −0.00428830 + 0.00428830i
\(276\) 1.06205e10 + 9.51675e8i 0.110167 + 0.00987184i
\(277\) 1.21041e10 + 1.21041e10i 0.123531 + 0.123531i 0.766169 0.642639i \(-0.222160\pi\)
−0.642639 + 0.766169i \(0.722160\pi\)
\(278\) 7.70277e10 + 3.60172e10i 0.773473 + 0.361667i
\(279\) 1.23580e11i 1.22104i
\(280\) 4.36168e10 + 1.64858e11i 0.424075 + 1.60287i
\(281\) 4.04347e10i 0.386879i −0.981112 0.193440i \(-0.938036\pi\)
0.981112 0.193440i \(-0.0619644\pi\)
\(282\) −5.31966e10 + 1.13768e11i −0.500913 + 1.07127i
\(283\) −7.79605e10 7.79605e10i −0.722497 0.722497i 0.246616 0.969113i \(-0.420681\pi\)
−0.969113 + 0.246616i \(0.920681\pi\)
\(284\) 5.42110e10 + 6.48827e10i 0.494487 + 0.591829i
\(285\) 9.21152e10 9.21152e10i 0.827046 0.827046i
\(286\) −1.37288e10 + 4.98053e9i −0.121335 + 0.0440178i
\(287\) −6.65383e10 −0.578900
\(288\) −1.82544e11 + 3.11989e10i −1.56351 + 0.267223i
\(289\) 8.55214e10 0.721165
\(290\) −3.52524e10 + 1.27889e10i −0.292683 + 0.106180i
\(291\) 7.57132e10 7.57132e10i 0.618946 0.618946i
\(292\) −7.05644e10 8.44554e10i −0.568019 0.679837i
\(293\) 8.27378e10 + 8.27378e10i 0.655843 + 0.655843i 0.954394 0.298551i \(-0.0965032\pi\)
−0.298551 + 0.954394i \(0.596503\pi\)
\(294\) 1.37356e11 2.93754e11i 1.07222 2.29309i
\(295\) 9.94364e10i 0.764445i
\(296\) 1.72806e11 4.57197e10i 1.30842 0.346171i
\(297\) 1.12791e10i 0.0841147i
\(298\) −6.19694e10 2.89761e10i −0.455202 0.212847i
\(299\) 9.72269e9 + 9.72269e9i 0.0703503 + 0.0703503i
\(300\) −1.52731e10 1.36858e9i −0.108863 0.00975497i
\(301\) −2.05667e11 + 2.05667e11i −1.44416 + 1.44416i
\(302\) −2.67691e10 7.37887e10i −0.185183 0.510456i
\(303\) 9.49925e10 0.647437
\(304\) −5.97502e10 8.61004e10i −0.401243 0.578195i
\(305\) 1.18277e11 0.782618
\(306\) 1.08844e11 + 3.00028e11i 0.709674 + 1.95621i
\(307\) −1.08291e11 + 1.08291e11i −0.695775 + 0.695775i −0.963496 0.267721i \(-0.913729\pi\)
0.267721 + 0.963496i \(0.413729\pi\)
\(308\) 2.01795e9 2.25198e10i 0.0127771 0.142589i
\(309\) 2.50269e11 + 2.50269e11i 1.56169 + 1.56169i
\(310\) −1.17178e11 5.47911e10i −0.720641 0.336963i
\(311\) 4.39813e10i 0.266592i −0.991076 0.133296i \(-0.957444\pi\)
0.991076 0.133296i \(-0.0425561\pi\)
\(312\) −3.36576e11 1.95740e11i −2.01089 1.16946i
\(313\) 1.54465e11i 0.909661i −0.890578 0.454830i \(-0.849700\pi\)
0.890578 0.454830i \(-0.150300\pi\)
\(314\) 4.27310e10 9.13860e10i 0.248062 0.530513i
\(315\) 3.24956e11 + 3.24956e11i 1.85963 + 1.85963i
\(316\) 5.24305e10 4.38069e10i 0.295796 0.247144i
\(317\) −1.27450e11 + 1.27450e11i −0.708883 + 0.708883i −0.966300 0.257417i \(-0.917129\pi\)
0.257417 + 0.966300i \(0.417129\pi\)
\(318\) 4.00024e10 1.45121e10i 0.219363 0.0795806i
\(319\) 4.97207e9 0.0268831
\(320\) −5.13507e10 + 1.86919e11i −0.273761 + 0.996504i
\(321\) 1.99525e11 1.04888
\(322\) −2.00113e10 + 7.25969e9i −0.103735 + 0.0376328i
\(323\) −1.27716e11 + 1.27716e11i −0.652879 + 0.652879i
\(324\) 1.06879e10 8.92999e9i 0.0538815 0.0450193i
\(325\) −1.39820e10 1.39820e10i −0.0695175 0.0695175i
\(326\) −8.24481e10 + 1.76326e11i −0.404298 + 0.864645i
\(327\) 3.66456e11i 1.77238i
\(328\) −6.53824e10 3.80240e10i −0.311910 0.181395i
\(329\) 2.50727e11i 1.17983i
\(330\) 2.89398e10 + 1.35319e10i 0.134333 + 0.0628124i
\(331\) −9.06780e10 9.06780e10i −0.415218 0.415218i 0.468334 0.883552i \(-0.344854\pi\)
−0.883552 + 0.468334i \(0.844854\pi\)
\(332\) −1.48634e10 + 1.65872e11i −0.0671422 + 0.749291i
\(333\) 3.40624e11 3.40624e11i 1.51801 1.51801i
\(334\) 4.80255e10 + 1.32382e11i 0.211161 + 0.582062i
\(335\) −4.35726e11 −1.89022
\(336\) 4.95228e11 3.43668e11i 2.11972 1.47100i
\(337\) −3.20838e11 −1.35504 −0.677519 0.735505i \(-0.736945\pi\)
−0.677519 + 0.735505i \(0.736945\pi\)
\(338\) −8.93917e10 2.46407e11i −0.372539 1.02690i
\(339\) 3.62611e11 3.62611e11i 1.49122 1.49122i
\(340\) 3.32743e11 + 2.98163e10i 1.35037 + 0.121004i
\(341\) 1.21274e10 + 1.21274e10i 0.0485707 + 0.0485707i
\(342\) −2.55840e11 1.19628e11i −1.01123 0.472841i
\(343\) 2.36109e11i 0.921061i
\(344\) −3.19624e11 + 8.45636e10i −1.23063 + 0.325589i
\(345\) 3.00783e10i 0.114306i
\(346\) −1.87652e10 + 4.01319e10i −0.0703899 + 0.150538i
\(347\) −3.04577e11 3.04577e11i −1.12775 1.12775i −0.990542 0.137211i \(-0.956186\pi\)
−0.137211 0.990542i \(-0.543814\pi\)
\(348\) 8.49924e10 + 1.01724e11i 0.310651 + 0.371805i
\(349\) 1.57267e11 1.57267e11i 0.567443 0.567443i −0.363968 0.931411i \(-0.618578\pi\)
0.931411 + 0.363968i \(0.118578\pi\)
\(350\) 2.87778e10 1.04400e10i 0.102506 0.0371873i
\(351\) −3.87760e11 −1.36358
\(352\) 1.48521e10 2.09754e10i 0.0515638 0.0728230i
\(353\) 3.52753e11 1.20916 0.604581 0.796544i \(-0.293341\pi\)
0.604581 + 0.796544i \(0.293341\pi\)
\(354\) −3.30418e11 + 1.19869e11i −1.11828 + 0.405688i
\(355\) 1.68643e11 1.68643e11i 0.563562 0.563562i
\(356\) −2.15032e11 2.57362e11i −0.709541 0.849217i
\(357\) −7.34588e11 7.34588e11i −2.39352 2.39352i
\(358\) −1.59662e11 + 3.41459e11i −0.513723 + 1.09866i
\(359\) 2.67473e11i 0.849875i 0.905223 + 0.424937i \(0.139704\pi\)
−0.905223 + 0.424937i \(0.860296\pi\)
\(360\) 1.33612e11 + 5.05011e11i 0.419260 + 1.58467i
\(361\) 1.62859e11i 0.504695i
\(362\) 2.35520e11 + 1.10126e11i 0.720841 + 0.337057i
\(363\) 3.73184e11 + 3.73184e11i 1.12809 + 1.12809i
\(364\) 7.74198e11 + 6.93741e10i 2.31151 + 0.207129i
\(365\) −2.19517e11 + 2.19517e11i −0.647366 + 0.647366i
\(366\) −1.42581e11 3.93022e11i −0.415333 1.14486i
\(367\) 1.71823e11 0.494406 0.247203 0.968964i \(-0.420489\pi\)
0.247203 + 0.968964i \(0.420489\pi\)
\(368\) −2.38123e10 4.30207e9i −0.0676839 0.0122282i
\(369\) −2.03827e11 −0.572327
\(370\) −1.71957e11 4.73998e11i −0.476993 1.31483i
\(371\) −6.00706e10 + 6.00706e10i −0.164619 + 0.164619i
\(372\) −4.08093e10 + 4.55422e11i −0.110488 + 1.23302i
\(373\) 8.91351e10 + 8.91351e10i 0.238429 + 0.238429i 0.816199 0.577770i \(-0.196077\pi\)
−0.577770 + 0.816199i \(0.696077\pi\)
\(374\) −4.01243e10 1.87617e10i −0.106044 0.0495848i
\(375\) 5.93172e11i 1.54896i
\(376\) 1.43280e11 2.46371e11i 0.369693 0.635688i
\(377\) 1.70932e11i 0.435801i
\(378\) 2.54279e11 5.43810e11i 0.640616 1.37004i
\(379\) 1.44679e8 + 1.44679e8i 0.000360189 + 0.000360189i 0.707287 0.706927i \(-0.249919\pi\)
−0.706927 + 0.707287i \(0.749919\pi\)
\(380\) −2.26861e11 + 1.89548e11i −0.558128 + 0.466329i
\(381\) −2.36553e11 + 2.36553e11i −0.575130 + 0.575130i
\(382\) 7.61320e11 2.76192e11i 1.82929 0.663630i
\(383\) 3.00989e11 0.714754 0.357377 0.933960i \(-0.383671\pi\)
0.357377 + 0.933960i \(0.383671\pi\)
\(384\) 6.83018e11 5.46948e10i 1.60303 0.128368i
\(385\) −6.37786e10 −0.147946
\(386\) 2.20133e11 7.98599e10i 0.504711 0.183099i
\(387\) −6.30021e11 + 6.30021e11i −1.42776 + 1.42776i
\(388\) −1.86466e11 + 1.55797e11i −0.417693 + 0.348992i
\(389\) 5.70737e10 + 5.70737e10i 0.126376 + 0.126376i 0.767466 0.641090i \(-0.221518\pi\)
−0.641090 + 0.767466i \(0.721518\pi\)
\(390\) −4.65206e11 + 9.94907e11i −1.01825 + 2.17767i
\(391\) 4.17029e10i 0.0902342i
\(392\) −3.69955e11 + 6.36140e11i −0.791338 + 1.36071i
\(393\) 3.66668e11i 0.775367i
\(394\) −3.54562e11 1.65789e11i −0.741241 0.346596i
\(395\) −1.36278e11 1.36278e11i −0.281668 0.281668i
\(396\) 6.18160e9 6.89852e10i 0.0126320 0.140970i
\(397\) 3.84655e11 3.84655e11i 0.777167 0.777167i −0.202181 0.979348i \(-0.564803\pi\)
0.979348 + 0.202181i \(0.0648030\pi\)
\(398\) −4.42546e9 1.21987e10i −0.00884065 0.0243692i
\(399\) 9.19296e11 1.81584
\(400\) 3.42439e10 + 6.18671e9i 0.0668827 + 0.0120834i
\(401\) 7.63159e11 1.47389 0.736945 0.675952i \(-0.236267\pi\)
0.736945 + 0.675952i \(0.236267\pi\)
\(402\) 5.25261e11 + 1.44788e12i 1.00313 + 2.76512i
\(403\) −4.16924e11 + 4.16924e11i −0.787379 + 0.787379i
\(404\) −2.14708e11 1.92395e10i −0.400988 0.0359316i
\(405\) −2.77800e10 2.77800e10i −0.0513080 0.0513080i
\(406\) −2.39722e11 1.12091e11i −0.437866 0.204741i
\(407\) 6.68536e10i 0.120767i
\(408\) −3.02039e11 1.14162e12i −0.539626 2.03962i
\(409\) 3.83888e11i 0.678344i −0.940724 0.339172i \(-0.889853\pi\)
0.940724 0.339172i \(-0.110147\pi\)
\(410\) −9.03699e10 + 1.93268e11i −0.157942 + 0.337779i
\(411\) −1.05733e12 1.05733e12i −1.82777 1.82777i
\(412\) −5.14985e11 6.16362e11i −0.880556 1.05390i
\(413\) 4.96180e11 4.96180e11i 0.839198 0.839198i
\(414\) −6.13007e10 + 2.22387e10i −0.102557 + 0.0372055i
\(415\) 4.69767e11 0.777438
\(416\) 7.21105e11 + 5.10592e11i 1.18053 + 0.835900i
\(417\) −8.47860e11 −1.37313
\(418\) 3.68462e10 1.33671e10i 0.0590337 0.0214162i
\(419\) −7.35547e10 + 7.35547e10i −0.116586 + 0.116586i −0.762993 0.646407i \(-0.776271\pi\)
0.646407 + 0.762993i \(0.276271\pi\)
\(420\) −1.09023e12 1.30485e12i −1.70961 2.04615i
\(421\) 6.24756e11 + 6.24756e11i 0.969261 + 0.969261i 0.999541 0.0302802i \(-0.00963995\pi\)
−0.0302802 + 0.999541i \(0.509640\pi\)
\(422\) 2.95505e11 6.31978e11i 0.453585 0.970053i
\(423\) 7.68053e11i 1.16643i
\(424\) −9.33550e10 + 2.46991e10i −0.140279 + 0.0371137i
\(425\) 5.99721e10i 0.0891660i
\(426\) −7.63683e11 3.57089e11i −1.12349 0.525331i
\(427\) 5.90192e11 + 5.90192e11i 0.859148 + 0.859148i
\(428\) −4.50979e11 4.04112e10i −0.649620 0.0582109i
\(429\) 1.02969e11 1.02969e11i 0.146773 0.146773i
\(430\) 3.18053e11 + 8.76711e11i 0.448634 + 1.23665i
\(431\) −1.73785e11 −0.242586 −0.121293 0.992617i \(-0.538704\pi\)
−0.121293 + 0.992617i \(0.538704\pi\)
\(432\) 5.60628e11 3.89053e11i 0.774458 0.537442i
\(433\) −8.23069e11 −1.12523 −0.562614 0.826719i \(-0.690204\pi\)
−0.562614 + 0.826719i \(0.690204\pi\)
\(434\) −3.11307e11 8.58114e11i −0.421196 1.16102i
\(435\) 2.64400e11 2.64400e11i 0.354046 0.354046i
\(436\) 7.42208e10 8.28286e11i 0.0983640 1.09772i
\(437\) −2.60944e10 2.60944e10i −0.0342280 0.0342280i
\(438\) 9.94058e11 + 4.64809e11i 1.29056 + 0.603450i
\(439\) 8.91499e11i 1.14559i 0.819697 + 0.572797i \(0.194142\pi\)
−0.819697 + 0.572797i \(0.805858\pi\)
\(440\) −6.26707e10 3.64469e10i −0.0797126 0.0463579i
\(441\) 1.98314e12i 2.49678i
\(442\) 6.44998e11 1.37942e12i 0.803819 1.71907i
\(443\) 4.53578e11 + 4.53578e11i 0.559545 + 0.559545i 0.929178 0.369633i \(-0.120517\pi\)
−0.369633 + 0.929178i \(0.620517\pi\)
\(444\) −1.36776e12 + 1.14279e12i −1.67027 + 1.39555i
\(445\) −6.68935e11 + 6.68935e11i −0.808656 + 0.808656i
\(446\) 6.29787e11 2.28474e11i 0.753679 0.273420i
\(447\) 6.82110e11 0.808111
\(448\) −1.18895e12 + 6.76477e11i −1.39448 + 0.793418i
\(449\) 4.70874e11 0.546759 0.273379 0.961906i \(-0.411859\pi\)
0.273379 + 0.961906i \(0.411859\pi\)
\(450\) 8.81553e10 3.19810e10i 0.101343 0.0367651i
\(451\) 2.00024e10 2.00024e10i 0.0227661 0.0227661i
\(452\) −8.93037e11 + 7.46153e11i −1.00634 + 0.840823i
\(453\) 5.53430e11 + 5.53430e11i 0.617477 + 0.617477i
\(454\) −1.65188e10 + 3.53278e10i −0.0182485 + 0.0390270i
\(455\) 2.19262e12i 2.39834i
\(456\) 9.03326e11 + 5.25341e11i 0.978369 + 0.568983i
\(457\) 8.33482e11i 0.893868i 0.894567 + 0.446934i \(0.147484\pi\)
−0.894567 + 0.446934i \(0.852516\pi\)
\(458\) −1.10310e12 5.15795e11i −1.17144 0.547750i
\(459\) −8.31598e11 8.31598e11i −0.874493 0.874493i
\(460\) −6.09197e9 + 6.79849e10i −0.00634377 + 0.0707949i
\(461\) −3.12982e10 + 3.12982e10i −0.0322749 + 0.0322749i −0.723060 0.690785i \(-0.757265\pi\)
0.690785 + 0.723060i \(0.257265\pi\)
\(462\) 7.68841e10 + 2.11930e11i 0.0785141 + 0.216423i
\(463\) 1.38650e11 0.140218 0.0701092 0.997539i \(-0.477665\pi\)
0.0701092 + 0.997539i \(0.477665\pi\)
\(464\) −1.71502e11 2.47136e11i −0.171767 0.247517i
\(465\) 1.28981e12 1.27934
\(466\) 5.71747e11 + 1.57601e12i 0.561652 + 1.54819i
\(467\) 8.58766e11 8.58766e11i 0.835504 0.835504i −0.152759 0.988263i \(-0.548816\pi\)
0.988263 + 0.152759i \(0.0488159\pi\)
\(468\) 2.37161e12 + 2.12514e11i 2.28527 + 0.204777i
\(469\) −2.17424e12 2.17424e12i −2.07506 2.07506i
\(470\) −7.28264e11 3.40528e11i −0.688412 0.321893i
\(471\) 1.00591e12i 0.941810i
\(472\) 7.71108e11 2.04013e11i 0.715116 0.189199i
\(473\) 1.23653e11i 0.113587i
\(474\) −2.88557e11 + 6.17118e11i −0.262560 + 0.561520i
\(475\) 3.75259e10 + 3.75259e10i 0.0338228 + 0.0338228i
\(476\) 1.51158e12 + 1.80914e12i 1.34958 + 1.61526i
\(477\) −1.84015e11 + 1.84015e11i −0.162750 + 0.162750i
\(478\) −2.97012e11 + 1.07750e11i −0.260224 + 0.0944043i
\(479\) −1.60624e11 −0.139412 −0.0697059 0.997568i \(-0.522206\pi\)
−0.0697059 + 0.997568i \(0.522206\pi\)
\(480\) −3.25623e11 1.90520e12i −0.279981 1.63816i
\(481\) −2.29833e12 −1.95776
\(482\) 1.72846e12 6.27050e11i 1.45864 0.529164i
\(483\) 1.50089e11 1.50089e11i 0.125483 0.125483i
\(484\) −7.67908e11 9.19075e11i −0.636071 0.761284i
\(485\) 4.84663e11 + 4.84663e11i 0.397743 + 0.397743i
\(486\) −5.49899e11 + 1.17603e12i −0.447115 + 0.956216i
\(487\) 7.83392e11i 0.631101i 0.948909 + 0.315550i \(0.102189\pi\)
−0.948909 + 0.315550i \(0.897811\pi\)
\(488\) 2.42668e11 + 9.17211e11i 0.193697 + 0.732116i
\(489\) 1.94086e12i 1.53499i
\(490\) 1.88041e12 + 8.79256e11i 1.47357 + 0.689022i
\(491\) −1.32511e12 1.32511e12i −1.02893 1.02893i −0.999569 0.0293584i \(-0.990654\pi\)
−0.0293584 0.999569i \(-0.509346\pi\)
\(492\) 7.51151e11 + 6.73089e10i 0.577942 + 0.0517880i
\(493\) −3.66585e11 + 3.66585e11i −0.279488 + 0.279488i
\(494\) 4.59541e11 + 1.26672e12i 0.347178 + 0.956994i
\(495\) −1.95374e11 −0.146266
\(496\) 1.84479e11 1.02111e12i 0.136861 0.757536i
\(497\) 1.68303e12 1.23734
\(498\) −5.66297e11 1.56099e12i −0.412584 1.13728i
\(499\) −4.13054e11 + 4.13054e11i −0.298232 + 0.298232i −0.840321 0.542089i \(-0.817633\pi\)
0.542089 + 0.840321i \(0.317633\pi\)
\(500\) −1.20139e11 + 1.34072e12i −0.0859645 + 0.959343i
\(501\) −9.92891e11 9.92891e11i −0.704096 0.704096i
\(502\) −1.74528e12 8.16073e11i −1.22659 0.573538i
\(503\) 1.34103e12i 0.934078i 0.884237 + 0.467039i \(0.154679\pi\)
−0.884237 + 0.467039i \(0.845321\pi\)
\(504\) −1.85325e12 + 3.18668e12i −1.27937 + 2.19989i
\(505\) 6.08076e11i 0.416051i
\(506\) 3.83332e9 8.19807e9i 0.00259955 0.00555948i
\(507\) 1.84811e12 + 1.84811e12i 1.24220 + 1.24220i
\(508\) 5.82582e11 4.86761e11i 0.388124 0.324286i
\(509\) 1.70149e12 1.70149e12i 1.12357 1.12357i 0.132364 0.991201i \(-0.457743\pi\)
0.991201 0.132364i \(-0.0422569\pi\)
\(510\) −3.13139e12 + 1.13600e12i −2.04961 + 0.743557i
\(511\) −2.19074e12 −1.42134
\(512\) −1.55487e12 1.47116e10i −0.999955 0.00946116i
\(513\) 1.04070e12 0.663432
\(514\) 7.89817e11 2.86530e11i 0.499105 0.181066i
\(515\) −1.60205e12 + 1.60205e12i −1.00356 + 1.00356i
\(516\) 2.52982e12 2.11372e12i 1.57096 1.31258i
\(517\) 7.53722e10 + 7.53722e10i 0.0463985 + 0.0463985i
\(518\) 1.50716e12 3.22327e12i 0.919763 1.96704i
\(519\) 4.41740e11i 0.267248i
\(520\) 1.25299e12 2.15453e12i 0.751508 1.29222i
\(521\) 2.74374e11i 0.163145i −0.996667 0.0815725i \(-0.974006\pi\)
0.996667 0.0815725i \(-0.0259942\pi\)
\(522\) −7.34344e11 3.43370e11i −0.432894 0.202416i
\(523\) 1.39884e11 + 1.39884e11i 0.0817544 + 0.0817544i 0.746801 0.665047i \(-0.231589\pi\)
−0.665047 + 0.746801i \(0.731589\pi\)
\(524\) 7.42638e10 8.28766e11i 0.0430315 0.480221i
\(525\) −2.15839e11 + 2.15839e11i −0.123998 + 0.123998i
\(526\) −6.72405e11 1.85348e12i −0.382997 1.05573i
\(527\) −1.78829e12 −1.00993
\(528\) −4.55612e10 + 2.52185e11i −0.0255119 + 0.141210i
\(529\) 1.79263e12 0.995269
\(530\) 9.28962e10 + 2.56067e11i 0.0511395 + 0.140966i
\(531\) 1.51995e12 1.51995e12i 0.829670 0.829670i
\(532\) −2.07785e12 1.86191e11i −1.12463 0.100776i
\(533\) 6.87654e11 + 6.87654e11i 0.369061 + 0.369061i
\(534\) 3.02920e12 + 1.41642e12i 1.61210 + 0.753799i
\(535\) 1.27722e12i 0.674023i
\(536\) −8.93979e11 3.37896e12i −0.467827 1.76824i
\(537\) 3.75852e12i 1.95044i
\(538\) −1.52257e12 + 3.25621e12i −0.783531 + 1.67569i
\(539\) −1.94614e11 1.94614e11i −0.0993173 0.0993173i
\(540\) −1.23421e12 1.47717e12i −0.624620 0.747579i
\(541\) −1.17059e12 + 1.17059e12i −0.587510 + 0.587510i −0.936956 0.349446i \(-0.886370\pi\)
0.349446 + 0.936956i \(0.386370\pi\)
\(542\) 2.30840e12 8.37441e11i 1.14898 0.416828i
\(543\) −2.59242e12 −1.27970
\(544\) 4.51468e11 + 2.64152e12i 0.221020 + 1.29318i
\(545\) −2.34580e12 −1.13895
\(546\) −7.28586e12 + 2.64316e12i −3.50844 + 1.27279i
\(547\) 1.17226e12 1.17226e12i 0.559862 0.559862i −0.369406 0.929268i \(-0.620439\pi\)
0.929268 + 0.369406i \(0.120439\pi\)
\(548\) 2.17569e12 + 2.60399e12i 1.03059 + 1.23346i
\(549\) 1.80794e12 + 1.80794e12i 0.849393 + 0.849393i
\(550\) −5.51262e9 + 1.17895e10i −0.00256877 + 0.00549367i
\(551\) 4.58760e11i 0.212033i
\(552\) 2.33251e11 6.17117e10i 0.106930 0.0282906i
\(553\) 1.36003e12i 0.618422i
\(554\) 3.50870e11 + 1.64063e11i 0.158253 + 0.0739972i
\(555\) 3.55508e12 + 3.55508e12i 1.59049 + 1.59049i
\(556\) 1.91638e12 + 1.71723e11i 0.850445 + 0.0762064i
\(557\) 2.96004e12 2.96004e12i 1.30301 1.30301i 0.376664 0.926350i \(-0.377071\pi\)
0.926350 0.376664i \(-0.122929\pi\)
\(558\) −9.53629e11 2.62867e12i −0.416414 1.14784i
\(559\) 4.25101e12 1.84136
\(560\) 2.19992e12 + 3.17011e12i 0.945282 + 1.36216i
\(561\) 4.41657e11 0.188257
\(562\) −3.12021e11 8.60083e11i −0.131938 0.363686i
\(563\) −1.02234e12 + 1.02234e12i −0.428851 + 0.428851i −0.888237 0.459386i \(-0.848069\pi\)
0.459386 + 0.888237i \(0.348069\pi\)
\(564\) −2.53630e11 + 2.83045e12i −0.105547 + 1.17788i
\(565\) 2.32118e12 + 2.32118e12i 0.958278 + 0.958278i
\(566\) −2.25989e12 1.05670e12i −0.925579 0.432790i
\(567\) 2.77241e11i 0.112650i
\(568\) 1.65380e12 + 9.61787e11i 0.666676 + 0.387714i
\(569\) 2.08440e12i 0.833636i 0.908990 + 0.416818i \(0.136855\pi\)
−0.908990 + 0.416818i \(0.863145\pi\)
\(570\) 1.24855e12 2.67020e12i 0.495416 1.05951i
\(571\) 4.20030e11 + 4.20030e11i 0.165355 + 0.165355i 0.784934 0.619579i \(-0.212697\pi\)
−0.619579 + 0.784934i \(0.712697\pi\)
\(572\) −2.53591e11 + 2.11881e11i −0.0990493 + 0.0827579i
\(573\) −5.71006e12 + 5.71006e12i −2.21281 + 2.21281i
\(574\) −1.41533e12 + 5.13455e11i −0.544195 + 0.197423i
\(575\) 1.22533e10 0.00467464
\(576\) −3.64212e12 + 2.07226e12i −1.37865 + 0.784410i
\(577\) −4.24991e12 −1.59620 −0.798102 0.602522i \(-0.794162\pi\)
−0.798102 + 0.602522i \(0.794162\pi\)
\(578\) 1.81912e12 6.59941e11i 0.677932 0.245940i
\(579\) −1.65104e12 + 1.65104e12i −0.610528 + 0.610528i
\(580\) −6.51164e11 + 5.44062e11i −0.238926 + 0.199629i
\(581\) 2.34410e12 + 2.34410e12i 0.853461 + 0.853461i
\(582\) 1.02624e12 2.19474e12i 0.370761 0.792922i
\(583\) 3.61163e10i 0.0129477i
\(584\) −2.15269e12 1.25192e12i −0.765814 0.445369i
\(585\) 6.71666e12i 2.37111i
\(586\) 2.39837e12 + 1.12145e12i 0.840190 + 0.392863i
\(587\) 2.34203e12 + 2.34203e12i 0.814182 + 0.814182i 0.985258 0.171076i \(-0.0547244\pi\)
−0.171076 + 0.985258i \(0.554724\pi\)
\(588\) 6.54884e11 7.30835e12i 0.225926 2.52128i
\(589\) 1.11897e12 1.11897e12i 0.383089 0.383089i
\(590\) −7.67319e11 2.11511e12i −0.260700 0.718618i
\(591\) 3.90274e12 1.31591
\(592\) 3.32295e12 2.30599e12i 1.11193 0.771631i
\(593\) −2.48605e12 −0.825589 −0.412794 0.910824i \(-0.635447\pi\)
−0.412794 + 0.910824i \(0.635447\pi\)
\(594\) 8.70374e10 + 2.39918e11i 0.0286858 + 0.0790721i
\(595\) 4.70233e12 4.70233e12i 1.53811 1.53811i
\(596\) −1.54175e12 1.38152e11i −0.500501 0.0448487i
\(597\) 9.14930e10 + 9.14930e10i 0.0294784 + 0.0294784i
\(598\) 2.81838e11 + 1.31784e11i 0.0901247 + 0.0421412i
\(599\) 1.49272e12i 0.473759i −0.971539 0.236880i \(-0.923875\pi\)
0.971539 0.236880i \(-0.0761247\pi\)
\(600\) −3.35434e11 + 8.87463e10i −0.105664 + 0.0279556i
\(601\) 1.93258e11i 0.0604230i −0.999544 0.0302115i \(-0.990382\pi\)
0.999544 0.0302115i \(-0.00961809\pi\)
\(602\) −2.78766e12 + 5.96179e12i −0.865079 + 1.85009i
\(603\) −6.66038e12 6.66038e12i −2.05150 2.05150i
\(604\) −1.13881e12 1.36299e12i −0.348164 0.416702i
\(605\) −2.38886e12 + 2.38886e12i −0.724923 + 0.724923i
\(606\) 2.02058e12 7.33026e11i 0.608624 0.220797i
\(607\) −5.71603e12 −1.70901 −0.854507 0.519440i \(-0.826140\pi\)
−0.854507 + 0.519440i \(0.826140\pi\)
\(608\) −1.93535e12 1.37036e12i −0.574372 0.406696i
\(609\) 2.63867e12 0.777335
\(610\) 2.51586e12 9.12703e11i 0.735702 0.266898i
\(611\) −2.59119e12 + 2.59119e12i −0.752166 + 0.752166i
\(612\) 4.63044e12 + 5.54196e12i 1.33426 + 1.59692i
\(613\) −6.81524e11 6.81524e11i −0.194944 0.194944i 0.602885 0.797828i \(-0.294018\pi\)
−0.797828 + 0.602885i \(0.794018\pi\)
\(614\) −1.46780e12 + 3.13909e12i −0.416783 + 0.891347i
\(615\) 2.12734e12i 0.599652i
\(616\) −1.30854e11 4.94589e11i −0.0366164 0.138399i
\(617\) 3.96833e12i 1.10236i 0.834385 + 0.551182i \(0.185823\pi\)
−0.834385 + 0.551182i \(0.814177\pi\)
\(618\) 7.25471e12 + 3.39222e12i 2.00065 + 0.935482i
\(619\) −1.52073e12 1.52073e12i −0.416337 0.416337i 0.467602 0.883939i \(-0.345118\pi\)
−0.883939 + 0.467602i \(0.845118\pi\)
\(620\) −2.91530e12 2.61233e11i −0.792355 0.0710011i
\(621\) 1.69909e11 1.69909e11i 0.0458464 0.0458464i
\(622\) −3.39390e11 9.35524e11i −0.0909163 0.250610i
\(623\) −6.67587e12 −1.77546
\(624\) −8.66975e12 1.56633e12i −2.28916 0.413573i
\(625\) 4.05634e12 1.06335
\(626\) −1.19195e12 3.28561e12i −0.310224 0.855128i
\(627\) −2.76354e11 + 2.76354e11i −0.0714106 + 0.0714106i
\(628\) 2.03733e11 2.27361e12i 0.0522688 0.583307i
\(629\) −4.92904e12 4.92904e12i −1.25555 1.25555i
\(630\) 9.41971e12 + 4.40454e12i 2.38235 + 1.11396i
\(631\) 3.36982e12i 0.846202i −0.906082 0.423101i \(-0.860941\pi\)
0.906082 0.423101i \(-0.139059\pi\)
\(632\) 7.77203e11 1.33640e12i 0.193779 0.333204i
\(633\) 6.95631e12i 1.72212i
\(634\) −1.72750e12 + 3.69449e12i −0.424635 + 0.908139i
\(635\) −1.51425e12 1.51425e12i −0.369586 0.369586i
\(636\) 7.38903e11 6.17371e11i 0.179073 0.149620i
\(637\) 6.69055e12 6.69055e12i 1.61003 1.61003i
\(638\) 1.05761e11 3.83678e10i 0.0252715 0.00916799i
\(639\) 5.15566e12 1.22329
\(640\) 3.50118e11 + 4.37220e12i 0.0824907 + 1.03013i
\(641\) 6.19785e12 1.45004 0.725020 0.688728i \(-0.241831\pi\)
0.725020 + 0.688728i \(0.241831\pi\)
\(642\) 4.24409e12 1.53967e12i 0.986000 0.357701i
\(643\) 1.97672e12 1.97672e12i 0.456033 0.456033i −0.441318 0.897351i \(-0.645489\pi\)
0.897351 + 0.441318i \(0.145489\pi\)
\(644\) −3.69638e11 + 3.08841e11i −0.0846818 + 0.0707536i
\(645\) −6.57552e12 6.57552e12i −1.49593 1.49593i
\(646\) −1.73109e12 + 3.70217e12i −0.391087 + 0.836393i
\(647\) 5.01715e12i 1.12561i −0.826590 0.562804i \(-0.809722\pi\)
0.826590 0.562804i \(-0.190278\pi\)
\(648\) 1.58432e11 2.72424e11i 0.0352984 0.0606958i
\(649\) 2.98319e11i 0.0660054i
\(650\) −4.05305e11 1.89516e11i −0.0890577 0.0416423i
\(651\) 6.43603e12 + 6.43603e12i 1.40444 + 1.40444i
\(652\) −3.93095e11 + 4.38685e12i −0.0851891 + 0.950689i
\(653\) −5.22500e12 + 5.22500e12i −1.12454 + 1.12454i −0.133495 + 0.991049i \(0.542620\pi\)
−0.991049 + 0.133495i \(0.957380\pi\)
\(654\) 2.82782e12 + 7.79487e12i 0.604439 + 1.66613i
\(655\) −2.34716e12 −0.498260
\(656\) −1.68416e12 3.04271e11i −0.355073 0.0641495i
\(657\) −6.71093e12 −1.40520
\(658\) −1.93478e12 5.33319e12i −0.402359 1.10910i
\(659\) 4.77568e12 4.77568e12i 0.986396 0.986396i −0.0135127 0.999909i \(-0.504301\pi\)
0.999909 + 0.0135127i \(0.00430137\pi\)
\(660\) 7.19997e11 + 6.45172e10i 0.147701 + 0.0132351i
\(661\) 4.56864e12 + 4.56864e12i 0.930852 + 0.930852i 0.997759 0.0669070i \(-0.0213131\pi\)
−0.0669070 + 0.997759i \(0.521313\pi\)
\(662\) −2.62854e12 1.22907e12i −0.531929 0.248724i
\(663\) 1.51835e13i 3.05184i
\(664\) 9.63820e11 + 3.64294e12i 0.192415 + 0.727270i
\(665\) 5.88470e12i 1.16688i
\(666\) 4.61690e12 9.87387e12i 0.909320 1.94470i
\(667\) −7.48994e10 7.48994e10i −0.0146525 0.0146525i
\(668\) 2.04310e12 + 2.44529e12i 0.397004 + 0.475156i
\(669\) −4.72353e12 + 4.72353e12i −0.911694 + 0.911694i
\(670\) −9.26831e12 + 3.36236e12i −1.77690 + 0.644625i
\(671\) −3.54841e11 −0.0675745
\(672\) 7.88199e12 1.11317e13i 1.49099 2.10571i
\(673\) −2.44846e12 −0.460071 −0.230036 0.973182i \(-0.573884\pi\)
−0.230036 + 0.973182i \(0.573884\pi\)
\(674\) −6.82453e12 + 2.47580e12i −1.27381 + 0.462112i
\(675\) −2.44343e11 + 2.44343e11i −0.0453037 + 0.0453037i
\(676\) −3.80289e12 4.55151e12i −0.700412 0.838292i
\(677\) 2.22018e12 + 2.22018e12i 0.406199 + 0.406199i 0.880411 0.474212i \(-0.157267\pi\)
−0.474212 + 0.880411i \(0.657267\pi\)
\(678\) 4.91492e12 1.05112e13i 0.893271 1.91038i
\(679\) 4.83687e12i 0.873273i
\(680\) 7.30783e12 1.93345e12i 1.31068 0.346770i
\(681\) 3.88860e11i 0.0692838i
\(682\) 3.51546e11 + 1.64379e11i 0.0622232 + 0.0290948i
\(683\) −6.06265e11 6.06265e11i −0.106603 0.106603i 0.651793 0.758397i \(-0.274017\pi\)
−0.758397 + 0.651793i \(0.774017\pi\)
\(684\) −6.36509e12 5.70361e11i −1.11187 0.0996317i
\(685\) 6.76830e12 6.76830e12i 1.17455 1.17455i
\(686\) 1.82197e12 + 5.02225e12i 0.314111 + 0.865845i
\(687\) 1.21420e13 2.07963
\(688\) −6.14616e12 + 4.26518e12i −1.04582 + 0.725754i
\(689\) 1.24162e12 0.209896
\(690\) −2.32105e11 6.39795e11i −0.0389819 0.107453i
\(691\) −4.99607e11 + 4.99607e11i −0.0833638 + 0.0833638i −0.747559 0.664195i \(-0.768774\pi\)
0.664195 + 0.747559i \(0.268774\pi\)
\(692\) −8.94685e10 + 9.98448e11i −0.0148318 + 0.165519i
\(693\) −9.74900e11 9.74900e11i −0.160569 0.160569i
\(694\) −8.82895e12 4.12831e12i −1.44475 0.675546i
\(695\) 5.42741e12i 0.882391i
\(696\) 2.59284e12 + 1.50790e12i 0.418826 + 0.243574i
\(697\) 2.94951e12i 0.473372i
\(698\) 2.13163e12 4.55879e12i 0.339910 0.726942i
\(699\) −1.18204e13 1.18204e13i −1.87278 1.87278i
\(700\) 5.31569e11 4.44138e11i 0.0836793 0.0699160i
\(701\) 1.99288e12 1.99288e12i 0.311710 0.311710i −0.533862 0.845572i \(-0.679260\pi\)
0.845572 + 0.533862i \(0.179260\pi\)
\(702\) −8.24802e12 + 2.99222e12i −1.28184 + 0.465025i
\(703\) 6.16842e12 0.952522
\(704\) 1.54057e11 5.60776e11i 0.0236376 0.0860423i
\(705\) 8.01616e12 1.22212
\(706\) 7.50338e12 2.72208e12i 1.13667 0.412363i
\(707\) −3.03425e12 + 3.03425e12i −0.456735 + 0.456735i
\(708\) −6.10331e12 + 5.09946e12i −0.912884 + 0.762736i
\(709\) 2.21267e12 + 2.21267e12i 0.328859 + 0.328859i 0.852152 0.523294i \(-0.175297\pi\)
−0.523294 + 0.852152i \(0.675297\pi\)
\(710\) 2.28584e12 4.88857e12i 0.337584 0.721970i
\(711\) 4.16619e12i 0.611401i
\(712\) −6.55990e12 3.81500e12i −0.956615 0.556332i
\(713\) 3.65377e11i 0.0529466i
\(714\) −2.12940e13 9.95681e12i −3.06630 1.43377i
\(715\) 6.59134e11 + 6.59134e11i 0.0943184 + 0.0943184i
\(716\) −7.61237e11 + 8.49522e12i −0.108246 + 1.20800i
\(717\) 2.22765e12 2.22765e12i 0.314783 0.314783i
\(718\) 2.06400e12 + 5.68940e12i 0.289834 + 0.798926i
\(719\) 1.19348e13 1.66546 0.832732 0.553676i \(-0.186775\pi\)
0.832732 + 0.553676i \(0.186775\pi\)
\(720\) 6.73905e12 + 9.71102e12i 0.934550 + 1.34669i
\(721\) −1.59882e13 −2.20339
\(722\) 1.25673e12 + 3.46416e12i 0.172117 + 0.474439i
\(723\) −1.29638e13 + 1.29638e13i −1.76445 + 1.76445i
\(724\) 5.85955e12 + 5.25060e11i 0.792575 + 0.0710208i
\(725\) 1.07711e11 + 1.07711e11i 0.0144791 + 0.0144791i
\(726\) 1.08177e13 + 5.05823e12i 1.44517 + 0.675746i
\(727\) 4.42788e12i 0.587883i −0.955823 0.293942i \(-0.905033\pi\)
0.955823 0.293942i \(-0.0949672\pi\)
\(728\) 1.70033e13 4.49858e12i 2.24358 0.593587i
\(729\) 1.24094e13i 1.62734i
\(730\) −2.97539e12 + 6.36327e12i −0.387785 + 0.829330i
\(731\) 9.11680e12 + 9.11680e12i 1.18090 + 1.18090i
\(732\) −6.06565e12 7.25971e12i −0.780868 0.934586i
\(733\) 7.13591e12 7.13591e12i 0.913023 0.913023i −0.0834863 0.996509i \(-0.526605\pi\)
0.996509 + 0.0834863i \(0.0266055\pi\)
\(734\) 3.65483e12 1.32590e12i 0.464767 0.168608i
\(735\) −2.06980e13 −2.61599
\(736\) −5.39707e11 + 9.22425e10i −0.0677966 + 0.0115873i
\(737\) 1.30722e12 0.163209
\(738\) −4.33560e12 + 1.57287e12i −0.538017 + 0.195182i
\(739\) −7.85837e12 + 7.85837e12i −0.969243 + 0.969243i −0.999541 0.0302981i \(-0.990354\pi\)
0.0302981 + 0.999541i \(0.490354\pi\)
\(740\) −7.31538e12 8.75545e12i −0.896797 1.07334i
\(741\) −9.50066e12 9.50066e12i −1.15764 1.15764i
\(742\) −8.14212e11 + 1.74130e12i −0.0986098 + 0.210890i
\(743\) 3.33667e12i 0.401665i 0.979626 + 0.200832i \(0.0643646\pi\)
−0.979626 + 0.200832i \(0.935635\pi\)
\(744\) 2.64629e12 + 1.00022e13i 0.316635 + 1.19678i
\(745\) 4.36640e12i 0.519302i
\(746\) 2.58382e12 + 1.20816e12i 0.305448 + 0.142824i
\(747\) 7.18071e12 + 7.18071e12i 0.843771 + 0.843771i
\(748\) −9.98259e11 8.94517e10i −0.116597 0.0104480i
\(749\) −6.37325e12 + 6.37325e12i −0.739933 + 0.739933i
\(750\) −4.57732e12 1.26173e13i −0.528245 1.45610i
\(751\) 1.62411e13 1.86310 0.931549 0.363617i \(-0.118458\pi\)
0.931549 + 0.363617i \(0.118458\pi\)
\(752\) 1.14654e12 6.34619e12i 0.130740 0.723657i
\(753\) 1.92107e13 2.17754
\(754\) 1.31903e12 + 3.63589e12i 0.148622 + 0.409675i
\(755\) −3.54268e12 + 3.54268e12i −0.396799 + 0.396799i
\(756\) 1.21235e12 1.35295e13i 0.134983 1.50638i
\(757\) −6.43793e11 6.43793e11i −0.0712549 0.0712549i 0.670581 0.741836i \(-0.266045\pi\)
−0.741836 + 0.670581i \(0.766045\pi\)
\(758\) 4.19391e9 + 1.96102e9i 0.000461432 + 0.000215760i
\(759\) 9.02379e10i 0.00986963i
\(760\) −3.36287e12 + 5.78247e12i −0.365636 + 0.628712i
\(761\) 1.44391e13i 1.56066i −0.625366 0.780332i \(-0.715050\pi\)
0.625366 0.780332i \(-0.284950\pi\)
\(762\) −3.20630e12 + 6.85711e12i −0.344514 + 0.736790i
\(763\) −1.17054e13 1.17054e13i −1.25033 1.25033i
\(764\) 1.40627e13 1.17497e13i 1.49331 1.24769i
\(765\) 1.44047e13 1.44047e13i 1.52064 1.52064i
\(766\) 6.40233e12 2.32264e12i 0.671906 0.243754i
\(767\) −1.02558e13 −1.07001
\(768\) 1.41064e13 6.43403e12i 1.46315 0.667357i
\(769\) −1.54602e12 −0.159422 −0.0797109 0.996818i \(-0.525400\pi\)
−0.0797109 + 0.996818i \(0.525400\pi\)
\(770\) −1.35663e12 + 4.92159e11i −0.139076 + 0.0504542i
\(771\) −5.92379e12 + 5.92379e12i −0.603747 + 0.603747i
\(772\) 4.06619e12 3.39739e12i 0.412012 0.344245i
\(773\) −5.71417e12 5.71417e12i −0.575632 0.575632i 0.358064 0.933697i \(-0.383437\pi\)
−0.933697 + 0.358064i \(0.883437\pi\)
\(774\) −8.53947e12 + 1.82628e13i −0.855257 + 1.82908i
\(775\) 5.25441e11i 0.0523198i
\(776\) −2.76408e12 + 4.75284e12i −0.273635 + 0.470517i
\(777\) 3.54792e13i 3.49204i
\(778\) 1.65443e12 + 7.73592e11i 0.161898 + 0.0757014i
\(779\) −1.84558e12 1.84558e12i −0.179561 0.179561i
\(780\) −2.21801e12 + 2.47524e13i −0.214554 + 2.39438i
\(781\) −5.05946e11 + 5.05946e11i −0.0486603 + 0.0486603i
\(782\) 3.21808e11 + 8.87061e11i 0.0307728 + 0.0848248i
\(783\) 2.98714e12 0.284006
\(784\) −2.96041e12 + 1.63861e13i −0.279853 + 1.54901i
\(785\) −6.43911e12 −0.605219
\(786\) 2.82946e12 + 7.79938e12i 0.264425 + 0.728885i
\(787\) 1.02328e13 1.02328e13i 0.950843 0.950843i −0.0480042 0.998847i \(-0.515286\pi\)
0.998847 + 0.0480042i \(0.0152861\pi\)
\(788\) −8.82121e12 7.90448e11i −0.815005 0.0730307i
\(789\) 1.39015e13 + 1.39015e13i 1.27707 + 1.27707i
\(790\) −3.95036e12 1.84714e12i −0.360840 0.168725i
\(791\) 2.31651e13i 2.10397i
\(792\) −4.00848e11 1.51508e12i −0.0362006 0.136827i
\(793\) 1.21989e13i 1.09545i
\(794\) 5.21372e12 1.11502e13i 0.465538 0.995616i
\(795\) −1.92056e12 1.92056e12i −0.170520 0.170520i
\(796\) −1.88267e11 2.25329e11i −0.0166213 0.0198933i
\(797\) −1.99581e12 + 1.99581e12i −0.175209 + 0.175209i −0.789264 0.614054i \(-0.789538\pi\)
0.614054 + 0.789264i \(0.289538\pi\)
\(798\) 1.95543e13 7.09391e12i 1.70698 0.619259i
\(799\) −1.11142e13 −0.964758
\(800\) 7.76141e11 1.32652e11i 0.0669940 0.0114501i
\(801\) −2.04503e13 −1.75531
\(802\) 1.62331e13 5.88905e12i 1.38553 0.502644i
\(803\) 6.58571e11 6.58571e11i 0.0558963 0.0558963i
\(804\) 2.23456e13 + 2.67445e13i 1.88599 + 2.25726i
\(805\) 9.60764e11 + 9.60764e11i 0.0806372 + 0.0806372i
\(806\) −5.65110e12 + 1.20856e13i −0.471656 + 1.00870i
\(807\) 3.58419e13i 2.97481i
\(808\) −4.71550e12 + 1.24759e12i −0.389203 + 0.102972i
\(809\) 2.00302e13i 1.64405i −0.569449 0.822027i \(-0.692843\pi\)
0.569449 0.822027i \(-0.307157\pi\)
\(810\) −8.05277e11 3.76538e11i −0.0657298 0.0307345i
\(811\) −7.04572e12 7.04572e12i −0.571915 0.571915i 0.360748 0.932663i \(-0.382521\pi\)
−0.932663 + 0.360748i \(0.882521\pi\)
\(812\) −5.96409e12 5.34428e11i −0.481440 0.0431407i
\(813\) −1.73135e13 + 1.73135e13i −1.38988 + 1.38988i
\(814\) 5.15888e11 + 1.42204e12i 0.0411856 + 0.113528i
\(815\) 1.24240e13 0.986402
\(816\) −1.52341e13 2.19525e13i −1.20285 1.73332i
\(817\) −1.14092e13 −0.895890
\(818\) −2.96234e12 8.16567e12i −0.231337 0.637679i
\(819\) 3.35156e13 3.35156e13i 2.60297 2.60297i
\(820\) −4.30865e11 + 4.80835e12i −0.0332797 + 0.371393i
\(821\) −1.64243e13 1.64243e13i −1.26166 1.26166i −0.950287 0.311377i \(-0.899210\pi\)
−0.311377 0.950287i \(-0.600790\pi\)
\(822\) −3.06495e13 1.43313e13i −2.34153 1.09487i
\(823\) 1.81082e13i 1.37586i 0.725775 + 0.687932i \(0.241481\pi\)
−0.725775 + 0.687932i \(0.758519\pi\)
\(824\) −1.57105e13 9.13663e12i −1.18718 0.690421i
\(825\) 1.29769e11i 0.00975279i
\(826\) 6.72536e12 1.43831e13i 0.502696 1.07508i
\(827\) 1.34504e13 + 1.34504e13i 0.999908 + 0.999908i 1.00000 9.20562e-5i \(-2.93024e-5\pi\)
−9.20562e−5 1.00000i \(0.500029\pi\)
\(828\) −1.13232e12 + 9.46076e11i −0.0837203 + 0.0699503i
\(829\) −1.19280e13 + 1.19280e13i −0.877145 + 0.877145i −0.993238 0.116094i \(-0.962963\pi\)
0.116094 + 0.993238i \(0.462963\pi\)
\(830\) 9.99238e12 3.62504e12i 0.730832 0.265131i
\(831\) −3.86210e12 −0.280943
\(832\) 1.92786e13 + 5.29625e12i 1.39483 + 0.383190i
\(833\) 2.86974e13 2.06509
\(834\) −1.80348e13 + 6.54266e12i −1.29081 + 0.468282i
\(835\) 6.35580e12 6.35580e12i 0.452461 0.452461i
\(836\) 6.80605e11 5.68661e11i 0.0481911 0.0402648i
\(837\) 7.28597e12 + 7.28597e12i 0.513125 + 0.513125i
\(838\) −9.96980e11 + 2.13218e12i −0.0698375 + 0.149357i
\(839\) 2.38569e13i 1.66221i −0.556119 0.831103i \(-0.687710\pi\)
0.556119 0.831103i \(-0.312290\pi\)
\(840\) −3.32593e13 1.93424e13i −2.30492 1.34046i
\(841\) 1.31904e13i 0.909232i
\(842\) 1.81102e13 + 8.46811e12i 1.24170 + 0.580606i
\(843\) 6.45080e12 + 6.45080e12i 0.439936 + 0.439936i
\(844\) 1.40891e12 1.57231e13i 0.0955744 1.06659i
\(845\) −1.18303e13 + 1.18303e13i −0.798253 + 0.798253i
\(846\) −5.92682e12 1.63372e13i −0.397791 1.09651i
\(847\) −2.38405e13 −1.59162
\(848\) −1.79515e12 + 1.24576e12i −0.119212 + 0.0827283i
\(849\) 2.48751e13 1.64316
\(850\) −4.62785e11 1.27566e12i −0.0304085 0.0838206i
\(851\) 1.00709e12 1.00709e12i 0.0658239 0.0658239i
\(852\) −1.89998e13 1.70253e12i −1.23529 0.110692i
\(853\) 1.46823e13 + 1.46823e13i 0.949563 + 0.949563i 0.998788 0.0492247i \(-0.0156750\pi\)
−0.0492247 + 0.998788i \(0.515675\pi\)
\(854\) 1.71083e13 + 7.99962e12i 1.10064 + 0.514646i
\(855\) 1.80266e13i 1.15363i
\(856\) −9.90459e12 + 2.62048e12i −0.630528 + 0.166820i
\(857\) 8.52813e12i 0.540057i 0.962852 + 0.270029i \(0.0870332\pi\)
−0.962852 + 0.270029i \(0.912967\pi\)
\(858\) 1.39566e12 2.98481e12i 0.0879201 0.188029i
\(859\) −5.05344e12 5.05344e12i −0.316678 0.316678i 0.530812 0.847490i \(-0.321887\pi\)
−0.847490 + 0.530812i \(0.821887\pi\)
\(860\) 1.35306e13 + 1.61942e13i 0.843478 + 1.00952i
\(861\) 1.06153e13 1.06153e13i 0.658290 0.658290i
\(862\) −3.69658e12 + 1.34105e12i −0.228043 + 0.0827296i
\(863\) −2.15911e12 −0.132503 −0.0662515 0.997803i \(-0.521104\pi\)
−0.0662515 + 0.997803i \(0.521104\pi\)
\(864\) 8.92288e12 1.26017e13i 0.544745 0.769338i
\(865\) 2.82771e12 0.171737
\(866\) −1.75075e13 + 6.35136e12i −1.05777 + 0.383739i
\(867\) −1.36438e13 + 1.36438e13i −0.820066 + 0.820066i
\(868\) −1.32436e13 1.58506e13i −0.791893 0.947781i
\(869\) 4.08846e11 + 4.08846e11i 0.0243204 + 0.0243204i
\(870\) 3.58375e12 7.66433e12i 0.212081 0.453563i
\(871\) 4.49403e13i 2.64579i
\(872\) −4.81287e12 1.81912e13i −0.281890 1.06546i
\(873\) 1.48168e13i 0.863358i
\(874\) −7.56416e11 3.53691e11i −0.0438489 0.0205032i
\(875\) 1.89471e13 + 1.89471e13i 1.09272 + 1.09272i
\(876\) 2.47313e13 + 2.21612e12i 1.41899 + 0.127152i
\(877\) 5.55102e12 5.55102e12i 0.316865 0.316865i −0.530697 0.847562i \(-0.678070\pi\)
0.847562 + 0.530697i \(0.178070\pi\)
\(878\) 6.87941e12 + 1.89630e13i 0.390684 + 1.07692i
\(879\) −2.63994e13 −1.49157
\(880\) −1.61431e12 2.91651e11i −0.0907435 0.0163943i
\(881\) −2.72105e13 −1.52175 −0.760877 0.648896i \(-0.775231\pi\)
−0.760877 + 0.648896i \(0.775231\pi\)
\(882\) 1.53033e13 + 4.21834e13i 0.851483 + 2.34711i
\(883\) 1.90339e13 1.90339e13i 1.05367 1.05367i 0.0551937 0.998476i \(-0.482422\pi\)
0.998476 0.0551937i \(-0.0175776\pi\)
\(884\) 3.07522e12 3.43187e13i 0.169372 1.89015i
\(885\) 1.58637e13 + 1.58637e13i 0.869282 + 0.869282i
\(886\) 1.31481e13 + 6.14791e12i 0.716824 + 0.335178i
\(887\) 2.54203e13i 1.37887i −0.724345 0.689437i \(-0.757858\pi\)
0.724345 0.689437i \(-0.242142\pi\)
\(888\) −2.02750e13 + 3.48629e13i −1.09421 + 1.88150i
\(889\) 1.51120e13i 0.811453i
\(890\) −9.06692e12 + 1.93908e13i −0.484401 + 1.03596i
\(891\) 8.33427e10 + 8.33427e10i 0.00443015 + 0.00443015i
\(892\) 1.16331e13 9.71972e12i 0.615253 0.514058i
\(893\) 6.95441e12 6.95441e12i 0.365956 0.365956i
\(894\) 1.45091e13 5.26362e12i 0.759666 0.275592i
\(895\) 2.40594e13 1.25338
\(896\) −2.00699e13 + 2.35640e13i −1.04030 + 1.22142i
\(897\) −3.10225e12 −0.159997
\(898\) 1.00159e13 3.63358e12i 0.513982 0.186462i
\(899\) 3.21180e12 3.21180e12i 0.163995 0.163995i
\(900\) 1.62836e12 1.36053e12i 0.0827292 0.0691222i
\(901\) 2.66281e12 + 2.66281e12i 0.134610 + 0.134610i
\(902\) 2.71118e11 5.79823e11i 0.0136373 0.0291653i
\(903\) 6.56227e13i 3.28442i
\(904\) −1.32379e13 + 2.27626e13i −0.659267 + 1.13361i
\(905\) 1.65949e13i 0.822348i
\(906\) 1.60426e13 + 7.50134e12i 0.791040 + 0.369881i
\(907\) −4.03506e12 4.03506e12i −0.197978 0.197978i 0.601154 0.799133i \(-0.294708\pi\)
−0.799133 + 0.601154i \(0.794708\pi\)
\(908\) −7.87584e10 + 8.78925e11i −0.00384513 + 0.0429107i
\(909\) −9.29486e12 + 9.29486e12i −0.451550 + 0.451550i
\(910\) −1.69197e13 4.66390e13i −0.817912 2.25457i
\(911\) 2.06981e13 0.995631 0.497815 0.867283i \(-0.334136\pi\)
0.497815 + 0.867283i \(0.334136\pi\)
\(912\) 2.32685e13 + 4.20382e12i 1.11376 + 0.201218i
\(913\) −1.40935e12 −0.0671273
\(914\) 6.43171e12 + 1.77290e13i 0.304838 + 0.840282i
\(915\) −1.88694e13 + 1.88694e13i −0.889947 + 0.889947i
\(916\) −2.74441e13 2.45921e12i −1.28801 0.115416i
\(917\) −1.17121e13 1.17121e13i −0.546983 0.546983i
\(918\) −2.41060e13 1.12717e13i −1.12030 0.523838i
\(919\) 3.44417e13i 1.59281i 0.604762 + 0.796406i \(0.293268\pi\)
−0.604762 + 0.796406i \(0.706732\pi\)
\(920\) 3.95035e11 + 1.49311e12i 0.0181799 + 0.0687143i
\(921\) 3.45527e13i 1.58239i
\(922\) −4.24224e11 + 9.07260e11i −0.0193333 + 0.0413469i
\(923\) −1.73937e13 1.73937e13i −0.788831 0.788831i
\(924\) 3.27080e12 + 3.91467e12i 0.147615 + 0.176673i
\(925\) −1.44827e12 + 1.44827e12i −0.0650446 + 0.0650446i
\(926\) 2.94921e12 1.06992e12i 0.131812 0.0478190i
\(927\) −4.89769e13 −2.17837
\(928\) −5.55508e12 3.93338e12i −0.245881 0.174101i
\(929\) 1.57326e13 0.692997 0.346498 0.938051i \(-0.387371\pi\)
0.346498 + 0.938051i \(0.387371\pi\)
\(930\) 2.74354e13 9.95301e12i 1.20265 0.436296i
\(931\) −1.79566e13 + 1.79566e13i −0.783339 + 0.783339i
\(932\) 2.43232e13 + 2.91113e13i 1.05596 + 1.26384i
\(933\) 7.01663e12 + 7.01663e12i 0.303152 + 0.303152i
\(934\) 1.16399e13 2.48936e13i 0.500483 1.07035i
\(935\) 2.82718e12i 0.120977i
\(936\) 5.20863e13 1.37806e13i 2.21810 0.586848i
\(937\) 1.72462e13i 0.730910i −0.930829 0.365455i \(-0.880913\pi\)
0.930829 0.365455i \(-0.119087\pi\)
\(938\) −6.30261e13 2.94703e13i −2.65832 1.24300i
\(939\) 2.46427e13 + 2.46427e13i 1.03441 + 1.03441i
\(940\) −1.81186e13 1.62357e12i −0.756919 0.0678257i
\(941\) −2.62873e13 + 2.62873e13i −1.09293 + 1.09293i −0.0977177 + 0.995214i \(0.531154\pi\)
−0.995214 + 0.0977177i \(0.968846\pi\)
\(942\) 7.76225e12 + 2.13966e13i 0.321187 + 0.885350i
\(943\) −6.02635e11 −0.0248171
\(944\) 1.48279e13 1.02900e13i 0.607723 0.421735i
\(945\) −3.83172e13 −1.56297
\(946\) −9.54191e11 2.63022e12i −0.0387369 0.106778i
\(947\) 4.20478e12 4.20478e12i 0.169890 0.169890i −0.617041 0.786931i \(-0.711669\pi\)
0.786931 + 0.617041i \(0.211669\pi\)
\(948\) −1.37578e12 + 1.53534e13i −0.0553237 + 0.617400i
\(949\) 2.26407e13 + 2.26407e13i 0.906134 + 0.906134i
\(950\) 1.08779e12 + 5.08636e11i 0.0433298 + 0.0202605i
\(951\) 4.06660e13i 1.61220i
\(952\) 4.61133e13 + 2.68178e13i 1.81953 + 1.05817i
\(953\) 1.71043e12i 0.0671719i 0.999436 + 0.0335859i \(0.0106927\pi\)
−0.999436 + 0.0335859i \(0.989307\pi\)
\(954\) −2.49419e12 + 5.33415e12i −0.0974902 + 0.208496i
\(955\) −3.65518e13 3.65518e13i −1.42198 1.42198i
\(956\) −5.48625e12 + 4.58389e12i −0.212430 + 0.177490i
\(957\) −7.93226e11 + 7.93226e11i −0.0305698 + 0.0305698i
\(958\) −3.41662e12 + 1.23948e12i −0.131054 + 0.0475439i
\(959\) 6.75466e13 2.57881
\(960\) −2.16281e13 3.80127e13i −0.821861 1.44447i
\(961\) −1.07717e13 −0.407408
\(962\) −4.88876e13 + 1.77355e13i −1.84040 + 0.667659i
\(963\) −1.95232e13 + 1.95232e13i −0.731532 + 0.731532i
\(964\) 3.19272e13 2.66759e13i 1.19073 0.994883i
\(965\) −1.05688e13 1.05688e13i −0.392333 0.392333i
\(966\) 2.03434e12 4.35071e12i 0.0751669 0.160755i
\(967\) 1.47472e13i 0.542364i 0.962528 + 0.271182i \(0.0874146\pi\)
−0.962528 + 0.271182i \(0.912585\pi\)
\(968\) −2.34263e13 1.36239e13i −0.857561 0.498726i
\(969\) 4.07506e13i 1.48483i
\(970\) 1.40492e13 + 6.56925e12i 0.509542 + 0.238256i
\(971\) 2.12961e13 + 2.12961e13i 0.768800 + 0.768800i 0.977895 0.209095i \(-0.0670518\pi\)
−0.209095 + 0.977895i \(0.567052\pi\)
\(972\) −2.62180e12 + 2.92587e13i −0.0942111 + 1.05137i
\(973\) 2.70824e13 2.70824e13i 0.968678 0.968678i
\(974\) 6.04518e12 + 1.66635e13i 0.215226 + 0.593267i
\(975\) 4.46128e12 0.158102
\(976\) 1.22396e13 + 1.76373e13i 0.431760 + 0.622170i
\(977\) −3.00255e13 −1.05430 −0.527151 0.849772i \(-0.676740\pi\)
−0.527151 + 0.849772i \(0.676740\pi\)
\(978\) −1.49770e13 4.12839e13i −0.523480 1.44297i
\(979\) 2.00687e12 2.00687e12i 0.0698228 0.0698228i
\(980\) 4.67830e13 + 4.19211e12i 1.62021 + 0.145183i
\(981\) −3.58572e13 3.58572e13i −1.23613 1.23613i
\(982\) −3.84117e13 1.79609e13i −1.31814 0.616348i
\(983\) 3.98401e13i 1.36091i 0.732789 + 0.680456i \(0.238218\pi\)
−0.732789 + 0.680456i \(0.761782\pi\)
\(984\) 1.64971e13 4.36467e12i 0.560957 0.148413i
\(985\) 2.49827e13i 0.845621i
\(986\) −4.96879e12 + 1.06264e13i −0.167419 + 0.358048i
\(987\) 4.00000e13 + 4.00000e13i 1.34163 + 1.34163i
\(988\) 1.95497e13 + 2.33982e13i 0.652731 + 0.781225i
\(989\) −1.86272e12 + 1.86272e12i −0.0619104 + 0.0619104i
\(990\) −4.15578e12 + 1.50764e12i −0.137497 + 0.0498813i
\(991\) −5.90759e13 −1.94571 −0.972857 0.231408i \(-0.925667\pi\)
−0.972857 + 0.231408i \(0.925667\pi\)
\(992\) −3.95550e12 2.31435e13i −0.129688 0.758797i
\(993\) 2.89329e13 0.944322
\(994\) 3.57997e13 1.29874e13i 1.16316 0.421973i
\(995\) −5.85675e11 + 5.85675e11i −0.0189432 + 0.0189432i
\(996\) −2.40913e13 2.88338e13i −0.775700 0.928400i
\(997\) −8.29112e12 8.29112e12i −0.265757 0.265757i 0.561631 0.827388i \(-0.310174\pi\)
−0.827388 + 0.561631i \(0.810174\pi\)
\(998\) −5.59864e12 + 1.19734e13i −0.178647 + 0.382060i
\(999\) 4.01646e13i 1.27585i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 16.10.e.a.5.16 34
4.3 odd 2 64.10.e.a.49.16 34
8.3 odd 2 128.10.e.a.97.2 34
8.5 even 2 128.10.e.b.97.16 34
16.3 odd 4 64.10.e.a.17.16 34
16.5 even 4 128.10.e.b.33.16 34
16.11 odd 4 128.10.e.a.33.2 34
16.13 even 4 inner 16.10.e.a.13.16 yes 34
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
16.10.e.a.5.16 34 1.1 even 1 trivial
16.10.e.a.13.16 yes 34 16.13 even 4 inner
64.10.e.a.17.16 34 16.3 odd 4
64.10.e.a.49.16 34 4.3 odd 2
128.10.e.a.33.2 34 16.11 odd 4
128.10.e.a.97.2 34 8.3 odd 2
128.10.e.b.33.16 34 16.5 even 4
128.10.e.b.97.16 34 8.5 even 2