Properties

Label 29.8.e.a.4.9
Level $29$
Weight $8$
Character 29.4
Analytic conductor $9.059$
Analytic rank $0$
Dimension $96$
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] = [29,8,Mod(4,29)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(29, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("29.4");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 29.e (of order \(14\), degree \(6\), 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: \(9.05916573904\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(16\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label 4.9
Character \(\chi\) \(=\) 29.4
Dual form 29.8.e.a.22.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.04671 - 0.238905i) q^{2} +(-39.6898 - 82.4167i) q^{3} +(-114.285 - 55.0370i) q^{4} +(73.7799 - 323.251i) q^{5} +(21.8540 + 95.7484i) q^{6} +(216.705 - 104.360i) q^{7} +(213.918 + 170.594i) q^{8} +(-3853.65 + 4832.33i) q^{9} +O(q^{10})\) \(q+(-1.04671 - 0.238905i) q^{2} +(-39.6898 - 82.4167i) q^{3} +(-114.285 - 55.0370i) q^{4} +(73.7799 - 323.251i) q^{5} +(21.8540 + 95.7484i) q^{6} +(216.705 - 104.360i) q^{7} +(213.918 + 170.594i) q^{8} +(-3853.65 + 4832.33i) q^{9} +(-154.452 + 320.724i) q^{10} +(5753.83 - 4588.53i) q^{11} +11603.4i q^{12} +(-1732.13 - 2172.02i) q^{13} +(-251.760 + 57.4625i) q^{14} +(-29569.6 + 6749.06i) q^{15} +(9940.11 + 12464.5i) q^{16} -25922.8i q^{17} +(5188.13 - 4137.39i) q^{18} +(-5554.62 + 11534.3i) q^{19} +(-26222.7 + 32882.3i) q^{20} +(-17202.0 - 13718.1i) q^{21} +(-7118.81 + 3428.24i) q^{22} +(7199.25 + 31542.0i) q^{23} +(5569.42 - 24401.2i) q^{24} +(-28659.4 - 13801.7i) q^{25} +(1294.13 + 2687.29i) q^{26} +(356174. + 81294.4i) q^{27} -30509.9 q^{28} +(42124.1 - 124400. i) q^{29} +32563.1 q^{30} +(-123026. - 28079.9i) q^{31} +(-22622.2 - 46975.4i) q^{32} +(-606539. - 292094. i) q^{33} +(-6193.08 + 27133.7i) q^{34} +(-17745.9 - 77749.8i) q^{35} +(706374. - 340172. i) q^{36} +(265079. + 211393. i) q^{37} +(8569.67 - 10746.0i) q^{38} +(-110263. + 228963. i) q^{39} +(70927.4 - 56562.7i) q^{40} -307097. i q^{41} +(14728.2 + 18468.5i) q^{42} +(-366880. + 83738.0i) q^{43} +(-910118. + 207728. i) q^{44} +(1.27773e6 + 1.60223e6i) q^{45} -34735.2i q^{46} +(99403.4 - 79271.6i) q^{47} +(632762. - 1.31394e6i) q^{48} +(-477400. + 598641. i) q^{49} +(26700.8 + 21293.2i) q^{50} +(-2.13647e6 + 1.02887e6i) q^{51} +(78415.7 + 343562. i) q^{52} +(-152523. + 668248. i) q^{53} +(-353389. - 170183. i) q^{54} +(-1.05873e6 - 2.19847e6i) q^{55} +(64160.3 + 14644.2i) q^{56} +1.17108e6 q^{57} +(-73811.5 + 120147. i) q^{58} -1.94944e6 q^{59} +(3.75082e6 + 856100. i) q^{60} +(-425268. - 883078. i) q^{61} +(122064. + 58783.0i) q^{62} +(-330807. + 1.44936e6i) q^{63} +(-441635. - 1.93493e6i) q^{64} +(-829904. + 399661. i) q^{65} +(565088. + 450643. i) q^{66} +(625372. - 784191. i) q^{67} +(-1.42671e6 + 2.96260e6i) q^{68} +(2.31385e6 - 1.84523e6i) q^{69} +85621.1i q^{70} +(1.16903e6 + 1.46592e6i) q^{71} +(-1.64873e6 + 376312. i) q^{72} +(2.39120e6 - 545775. i) q^{73} +(-226958. - 284596. i) q^{74} +2.90980e6i q^{75} +(1.26963e6 - 1.01249e6i) q^{76} +(768028. - 1.59483e6i) q^{77} +(170114. - 213316. i) q^{78} +(-141262. - 112652. i) q^{79} +(4.76254e6 - 2.29352e6i) q^{80} +(-4.42855e6 - 1.94028e7i) q^{81} +(-73367.0 + 321442. i) q^{82} +(8.28917e6 + 3.99186e6i) q^{83} +(1.21093e6 + 2.51453e6i) q^{84} +(-8.37957e6 - 1.91258e6i) q^{85} +404022. q^{86} +(-1.19246e7 + 1.46569e6i) q^{87} +2.01362e6 q^{88} +(1.42379e6 + 324971. i) q^{89} +(-954636. - 1.98232e6i) q^{90} +(-602033. - 289924. i) q^{91} +(913205. - 4.00101e6i) q^{92} +(2.56862e6 + 1.12539e7i) q^{93} +(-122985. + 59226.4i) q^{94} +(3.31865e6 + 2.64653e6i) q^{95} +(-2.97369e6 + 3.72889e6i) q^{96} +(2.29026e6 - 4.75577e6i) q^{97} +(642718. - 512551. i) q^{98} +4.54870e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q - 7 q^{2} - 7 q^{3} + 709 q^{4} + 191 q^{5} + 1801 q^{6} - 667 q^{7} + 9086 q^{8} + 9103 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 96 q - 7 q^{2} - 7 q^{3} + 709 q^{4} + 191 q^{5} + 1801 q^{6} - 667 q^{7} + 9086 q^{8} + 9103 q^{9} - 7 q^{10} + 4207 q^{11} + 377 q^{13} - 7 q^{14} - 74473 q^{15} - 125851 q^{16} - 194880 q^{18} - 7 q^{19} + 162901 q^{20} + 86933 q^{21} + 252614 q^{22} + 238675 q^{23} - 490819 q^{24} - 107349 q^{25} + 367017 q^{26} + 75593 q^{27} + 1397540 q^{28} + 379863 q^{29} - 175646 q^{30} - 143885 q^{31} + 473172 q^{32} - 1419437 q^{33} - 2314463 q^{34} - 1018325 q^{35} + 1720462 q^{36} + 662991 q^{37} - 2763860 q^{38} + 42189 q^{39} + 580601 q^{40} - 3296492 q^{42} - 1587425 q^{43} + 2344398 q^{44} + 6508254 q^{45} + 526673 q^{47} + 6175806 q^{48} - 1391517 q^{49} - 4194526 q^{50} - 68204 q^{51} - 7720808 q^{52} + 1762640 q^{53} - 2032428 q^{54} + 2655709 q^{55} + 17091081 q^{56} + 4906842 q^{57} + 13231229 q^{58} - 8638324 q^{59} - 9957136 q^{60} + 2797697 q^{61} - 884069 q^{62} - 20232301 q^{63} - 17528026 q^{64} - 7454088 q^{65} - 17541475 q^{66} - 4890949 q^{67} + 22029140 q^{68} + 13204429 q^{69} - 1091301 q^{71} + 25137595 q^{72} + 14363636 q^{73} + 3185328 q^{74} - 41019881 q^{76} - 25204627 q^{77} - 15753743 q^{78} + 31186057 q^{79} + 24146022 q^{80} - 29435757 q^{81} - 51438506 q^{82} - 8367235 q^{83} + 78906093 q^{84} + 41540198 q^{85} + 65794492 q^{86} + 11089375 q^{87} + 39260390 q^{88} + 6628699 q^{89} + 32127214 q^{90} + 24315293 q^{91} - 39469980 q^{92} - 31050649 q^{93} - 102445588 q^{94} - 75684679 q^{95} - 95069050 q^{96} + 38131380 q^{97} + 19581828 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{14}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.04671 0.238905i −0.0925170 0.0211164i 0.176012 0.984388i \(-0.443680\pi\)
−0.268529 + 0.963272i \(0.586537\pi\)
\(3\) −39.6898 82.4167i −0.848700 1.76234i −0.612183 0.790716i \(-0.709708\pi\)
−0.236517 0.971627i \(-0.576006\pi\)
\(4\) −114.285 55.0370i −0.892855 0.429976i
\(5\) 73.7799 323.251i 0.263963 1.15650i −0.652947 0.757404i \(-0.726468\pi\)
0.916910 0.399094i \(-0.130675\pi\)
\(6\) 21.8540 + 95.7484i 0.0413048 + 0.180968i
\(7\) 216.705 104.360i 0.238796 0.114998i −0.310659 0.950521i \(-0.600550\pi\)
0.549455 + 0.835523i \(0.314835\pi\)
\(8\) 213.918 + 170.594i 0.147718 + 0.117801i
\(9\) −3853.65 + 4832.33i −1.76207 + 2.20957i
\(10\) −154.452 + 320.724i −0.0488421 + 0.101422i
\(11\) 5753.83 4588.53i 1.30341 1.03944i 0.307278 0.951620i \(-0.400582\pi\)
0.996136 0.0878185i \(-0.0279896\pi\)
\(12\) 11603.4i 1.93844i
\(13\) −1732.13 2172.02i −0.218665 0.274197i 0.660385 0.750927i \(-0.270393\pi\)
−0.879049 + 0.476731i \(0.841822\pi\)
\(14\) −251.760 + 57.4625i −0.0245210 + 0.00559676i
\(15\) −29569.6 + 6749.06i −2.26217 + 0.516326i
\(16\) 9940.11 + 12464.5i 0.606696 + 0.760773i
\(17\) 25922.8i 1.27971i −0.768497 0.639854i \(-0.778995\pi\)
0.768497 0.639854i \(-0.221005\pi\)
\(18\) 5188.13 4137.39i 0.209680 0.167214i
\(19\) −5554.62 + 11534.3i −0.185788 + 0.385792i −0.972971 0.230927i \(-0.925824\pi\)
0.787183 + 0.616719i \(0.211538\pi\)
\(20\) −26222.7 + 32882.3i −0.732947 + 0.919087i
\(21\) −17202.0 13718.1i −0.405332 0.323241i
\(22\) −7118.81 + 3428.24i −0.142537 + 0.0686423i
\(23\) 7199.25 + 31542.0i 0.123379 + 0.540557i 0.998404 + 0.0564793i \(0.0179875\pi\)
−0.875025 + 0.484077i \(0.839155\pi\)
\(24\) 5569.42 24401.2i 0.0822376 0.360307i
\(25\) −28659.4 13801.7i −0.366841 0.176661i
\(26\) 1294.13 + 2687.29i 0.0144401 + 0.0299853i
\(27\) 356174. + 81294.4i 3.48248 + 0.794854i
\(28\) −30509.9 −0.262656
\(29\) 42124.1 124400.i 0.320729 0.947171i
\(30\) 32563.1 0.220192
\(31\) −123026. 28079.9i −0.741705 0.169289i −0.165059 0.986284i \(-0.552781\pi\)
−0.576646 + 0.816994i \(0.695639\pi\)
\(32\) −22622.2 46975.4i −0.122042 0.253423i
\(33\) −606539. 292094.i −2.93806 1.41489i
\(34\) −6193.08 + 27133.7i −0.0270228 + 0.118395i
\(35\) −17745.9 77749.8i −0.0699616 0.306522i
\(36\) 706374. 340172.i 2.52334 1.21518i
\(37\) 265079. + 211393.i 0.860338 + 0.686097i 0.950801 0.309803i \(-0.100263\pi\)
−0.0904626 + 0.995900i \(0.528835\pi\)
\(38\) 8569.67 10746.0i 0.0253350 0.0317691i
\(39\) −110263. + 228963.i −0.297648 + 0.618073i
\(40\) 70927.4 56562.7i 0.175228 0.139740i
\(41\) 307097.i 0.695877i −0.937517 0.347938i \(-0.886882\pi\)
0.937517 0.347938i \(-0.113118\pi\)
\(42\) 14728.2 + 18468.5i 0.0306744 + 0.0384644i
\(43\) −366880. + 83738.0i −0.703695 + 0.160614i −0.559372 0.828917i \(-0.688958\pi\)
−0.144323 + 0.989531i \(0.546100\pi\)
\(44\) −910118. + 207728.i −1.61069 + 0.367631i
\(45\) 1.27773e6 + 1.60223e6i 2.09024 + 2.62108i
\(46\) 34735.2i 0.0526160i
\(47\) 99403.4 79271.6i 0.139656 0.111372i −0.551170 0.834393i \(-0.685819\pi\)
0.690826 + 0.723021i \(0.257247\pi\)
\(48\) 632762. 1.31394e6i 0.825840 1.71488i
\(49\) −477400. + 598641.i −0.579691 + 0.726909i
\(50\) 26700.8 + 21293.2i 0.0302086 + 0.0240905i
\(51\) −2.13647e6 + 1.02887e6i −2.25528 + 1.08609i
\(52\) 78415.7 + 343562.i 0.0773377 + 0.338839i
\(53\) −152523. + 668248.i −0.140725 + 0.616555i 0.854543 + 0.519381i \(0.173837\pi\)
−0.995267 + 0.0971740i \(0.969020\pi\)
\(54\) −353389. 170183.i −0.305404 0.147075i
\(55\) −1.05873e6 2.19847e6i −0.858055 1.78177i
\(56\) 64160.3 + 14644.2i 0.0488212 + 0.0111431i
\(57\) 1.17108e6 0.837576
\(58\) −73811.5 + 120147.i −0.0496737 + 0.0808568i
\(59\) −1.94944e6 −1.23574 −0.617871 0.786279i \(-0.712005\pi\)
−0.617871 + 0.786279i \(0.712005\pi\)
\(60\) 3.75082e6 + 856100.i 2.24180 + 0.511676i
\(61\) −425268. 883078.i −0.239888 0.498132i 0.745915 0.666042i \(-0.232013\pi\)
−0.985802 + 0.167909i \(0.946298\pi\)
\(62\) 122064. + 58783.0i 0.0650455 + 0.0313243i
\(63\) −330807. + 1.44936e6i −0.166680 + 0.730271i
\(64\) −441635. 1.93493e6i −0.210588 0.922645i
\(65\) −829904. + 399661.i −0.374827 + 0.180507i
\(66\) 565088. + 450643.i 0.241943 + 0.192943i
\(67\) 625372. 784191.i 0.254025 0.318537i −0.638425 0.769684i \(-0.720414\pi\)
0.892450 + 0.451147i \(0.148985\pi\)
\(68\) −1.42671e6 + 2.96260e6i −0.550244 + 1.14259i
\(69\) 2.31385e6 1.84523e6i 0.847935 0.676206i
\(70\) 85621.1i 0.0298358i
\(71\) 1.16903e6 + 1.46592e6i 0.387635 + 0.486079i 0.936914 0.349560i \(-0.113669\pi\)
−0.549279 + 0.835639i \(0.685098\pi\)
\(72\) −1.64873e6 + 376312.i −0.520578 + 0.118819i
\(73\) 2.39120e6 545775.i 0.719425 0.164204i 0.152892 0.988243i \(-0.451141\pi\)
0.566533 + 0.824039i \(0.308284\pi\)
\(74\) −226958. 284596.i −0.0651080 0.0816428i
\(75\) 2.90980e6i 0.796432i
\(76\) 1.26963e6 1.01249e6i 0.331763 0.264572i
\(77\) 768028. 1.59483e6i 0.191716 0.398103i
\(78\) 170114. 213316.i 0.0405890 0.0508970i
\(79\) −141262. 112652.i −0.0322351 0.0257067i 0.607240 0.794519i \(-0.292277\pi\)
−0.639475 + 0.768812i \(0.720848\pi\)
\(80\) 4.76254e6 2.29352e6i 1.03998 0.500827i
\(81\) −4.42855e6 1.94028e7i −0.925900 4.05663i
\(82\) −73367.0 + 321442.i −0.0146944 + 0.0643804i
\(83\) 8.28917e6 + 3.99186e6i 1.59125 + 0.766305i 0.999215 0.0396092i \(-0.0126113\pi\)
0.592033 + 0.805914i \(0.298326\pi\)
\(84\) 1.21093e6 + 2.51453e6i 0.222916 + 0.462891i
\(85\) −8.37957e6 1.91258e6i −1.47998 0.337795i
\(86\) 404022. 0.0684953
\(87\) −1.19246e7 + 1.46569e6i −1.94144 + 0.238630i
\(88\) 2.01362e6 0.314984
\(89\) 1.42379e6 + 324971.i 0.214083 + 0.0488630i 0.328217 0.944602i \(-0.393552\pi\)
−0.114134 + 0.993465i \(0.536409\pi\)
\(90\) −954636. 1.98232e6i −0.138035 0.286633i
\(91\) −602033. 289924.i −0.0837482 0.0403310i
\(92\) 913205. 4.00101e6i 0.122267 0.535689i
\(93\) 2.56862e6 + 1.12539e7i 0.331139 + 1.45081i
\(94\) −122985. + 59226.4i −0.0152723 + 0.00735475i
\(95\) 3.31865e6 + 2.64653e6i 0.397126 + 0.316698i
\(96\) −2.97369e6 + 3.72889e6i −0.343041 + 0.430160i
\(97\) 2.29026e6 4.75577e6i 0.254791 0.529078i −0.733862 0.679299i \(-0.762284\pi\)
0.988653 + 0.150220i \(0.0479983\pi\)
\(98\) 642718. 512551.i 0.0689810 0.0550105i
\(99\) 4.54870e7i 4.71155i
\(100\) 2.51576e6 + 3.15466e6i 0.251576 + 0.315466i
\(101\) 7.32061e6 1.67088e6i 0.707005 0.161369i 0.146124 0.989266i \(-0.453320\pi\)
0.560880 + 0.827897i \(0.310463\pi\)
\(102\) 2.48207e6 566516.i 0.231586 0.0528581i
\(103\) −5.96243e6 7.47664e6i −0.537641 0.674181i 0.436609 0.899652i \(-0.356179\pi\)
−0.974250 + 0.225471i \(0.927608\pi\)
\(104\) 760125.i 0.0662625i
\(105\) −5.70355e6 + 4.54843e6i −0.480820 + 0.383441i
\(106\) 319295. 663023.i 0.0260388 0.0540702i
\(107\) −1.03059e7 + 1.29232e7i −0.813286 + 1.01983i 0.186019 + 0.982546i \(0.440441\pi\)
−0.999305 + 0.0372818i \(0.988130\pi\)
\(108\) −3.62313e7 2.88935e7i −2.76758 2.20707i
\(109\) 7.35104e6 3.54007e6i 0.543696 0.261830i −0.141814 0.989893i \(-0.545294\pi\)
0.685510 + 0.728063i \(0.259579\pi\)
\(110\) 582956. + 2.55410e6i 0.0417601 + 0.182963i
\(111\) 6.90141e6 3.02371e7i 0.478969 2.09850i
\(112\) 3.45487e6 + 1.66378e6i 0.232364 + 0.111900i
\(113\) 1.78315e6 + 3.70274e6i 0.116255 + 0.241407i 0.950975 0.309269i \(-0.100084\pi\)
−0.834719 + 0.550676i \(0.814370\pi\)
\(114\) −1.22578e6 279776.i −0.0774900 0.0176866i
\(115\) 1.07271e7 0.657720
\(116\) −1.16608e7 + 1.18988e7i −0.693626 + 0.707781i
\(117\) 1.71709e7 0.991160
\(118\) 2.04050e6 + 465731.i 0.114327 + 0.0260944i
\(119\) −2.70530e6 5.61761e6i −0.147164 0.305589i
\(120\) −7.47681e6 3.60064e6i −0.394986 0.190215i
\(121\) 7.71568e6 3.38046e7i 0.395936 1.73471i
\(122\) 234161. + 1.02592e6i 0.0116749 + 0.0511512i
\(123\) −2.53099e7 + 1.21886e7i −1.22637 + 0.590591i
\(124\) 1.25147e7 + 9.98010e6i 0.589445 + 0.470066i
\(125\) 9.57463e6 1.20062e7i 0.438467 0.549820i
\(126\) 692517. 1.43803e6i 0.0308414 0.0640428i
\(127\) −2.36541e7 + 1.88635e7i −1.02469 + 0.817165i −0.983303 0.181978i \(-0.941750\pi\)
−0.0413903 + 0.999143i \(0.513179\pi\)
\(128\) 8.80458e6i 0.371085i
\(129\) 2.14628e7 + 2.69135e7i 0.880283 + 1.10384i
\(130\) 964150. 220061.i 0.0384895 0.00878499i
\(131\) 5.64282e6 1.28794e6i 0.219304 0.0500547i −0.111457 0.993769i \(-0.535552\pi\)
0.330761 + 0.943715i \(0.392695\pi\)
\(132\) 5.32426e7 + 6.67642e7i 2.01489 + 2.52659i
\(133\) 3.07922e6i 0.113491i
\(134\) −841930. + 671417.i −0.0302280 + 0.0241060i
\(135\) 5.25569e7 1.09136e8i 1.83849 3.81767i
\(136\) 4.42227e6 5.54535e6i 0.150751 0.189035i
\(137\) 9.90741e6 + 7.90090e6i 0.329184 + 0.262515i 0.774109 0.633053i \(-0.218198\pi\)
−0.444925 + 0.895568i \(0.646770\pi\)
\(138\) −2.86276e6 + 1.37863e6i −0.0927274 + 0.0446552i
\(139\) −9.06651e6 3.97230e7i −0.286344 1.25456i −0.889501 0.456933i \(-0.848948\pi\)
0.603157 0.797623i \(-0.293909\pi\)
\(140\) −2.25102e6 + 9.86236e6i −0.0693316 + 0.303761i
\(141\) −1.04786e7 5.04623e6i −0.314801 0.151600i
\(142\) −873424. 1.81368e6i −0.0255986 0.0531560i
\(143\) −1.99327e7 4.54952e6i −0.570021 0.130104i
\(144\) −9.85384e7 −2.75002
\(145\) −3.71046e7 2.27949e7i −1.01074 0.620940i
\(146\) −2.63328e6 −0.0700264
\(147\) 6.82859e7 + 1.55858e7i 1.77305 + 0.404687i
\(148\) −1.86602e7 3.87483e7i −0.473152 0.982510i
\(149\) −4.84064e7 2.33113e7i −1.19881 0.577318i −0.275475 0.961308i \(-0.588835\pi\)
−0.923337 + 0.383991i \(0.874550\pi\)
\(150\) 695165. 3.04572e6i 0.0168178 0.0736835i
\(151\) −6.74846e6 2.95669e7i −0.159509 0.698855i −0.989911 0.141690i \(-0.954746\pi\)
0.830402 0.557165i \(-0.188111\pi\)
\(152\) −3.15591e6 + 1.51981e6i −0.0728907 + 0.0351023i
\(153\) 1.25268e8 + 9.98975e7i 2.82760 + 2.25494i
\(154\) −1.18491e6 + 1.48584e6i −0.0261435 + 0.0327830i
\(155\) −1.81537e7 + 3.76965e7i −0.391565 + 0.813093i
\(156\) 2.52029e7 2.00986e7i 0.531514 0.423868i
\(157\) 3.70291e7i 0.763651i −0.924235 0.381825i \(-0.875296\pi\)
0.924235 0.381825i \(-0.124704\pi\)
\(158\) 120947. + 151663.i 0.00243947 + 0.00305899i
\(159\) 6.11283e7 1.39521e7i 1.20601 0.275265i
\(160\) −1.68539e7 + 3.84679e6i −0.325297 + 0.0742470i
\(161\) 4.85183e6 + 6.08400e6i 0.0916252 + 0.114894i
\(162\) 2.13671e7i 0.394859i
\(163\) −4.50989e7 + 3.59652e7i −0.815660 + 0.650467i −0.939772 0.341801i \(-0.888963\pi\)
0.124112 + 0.992268i \(0.460392\pi\)
\(164\) −1.69017e7 + 3.50967e7i −0.299211 + 0.621317i
\(165\) −1.39170e8 + 1.74514e8i −2.41186 + 3.02437i
\(166\) −7.72269e6 6.15864e6i −0.131036 0.104498i
\(167\) −6.69514e7 + 3.22421e7i −1.11238 + 0.535692i −0.897529 0.440955i \(-0.854640\pi\)
−0.214848 + 0.976648i \(0.568925\pi\)
\(168\) −1.33958e6 5.86910e6i −0.0217965 0.0954968i
\(169\) 1.22455e7 5.36508e7i 0.195151 0.855014i
\(170\) 8.31405e6 + 4.00384e6i 0.129790 + 0.0625036i
\(171\) −3.43319e7 7.12909e7i −0.525063 1.09030i
\(172\) 4.65378e7 + 1.06219e7i 0.697358 + 0.159167i
\(173\) 5.21802e7 0.766204 0.383102 0.923706i \(-0.374856\pi\)
0.383102 + 0.923706i \(0.374856\pi\)
\(174\) 1.28317e7 + 1.31468e6i 0.184655 + 0.0189189i
\(175\) −7.65099e6 −0.107916
\(176\) 1.14387e8 + 2.61082e7i 1.58155 + 0.360979i
\(177\) 7.73729e7 + 1.60666e8i 1.04877 + 2.17780i
\(178\) −1.41266e6 680301.i −0.0187745 0.00904131i
\(179\) −3.33344e6 + 1.46048e7i −0.0434418 + 0.190331i −0.991993 0.126293i \(-0.959692\pi\)
0.948551 + 0.316624i \(0.102549\pi\)
\(180\) −5.78446e7 2.53434e8i −0.739280 3.23900i
\(181\) −7.68387e7 + 3.70036e7i −0.963174 + 0.463840i −0.848286 0.529538i \(-0.822365\pi\)
−0.114888 + 0.993378i \(0.536651\pi\)
\(182\) 560890. + 447295.i 0.00689649 + 0.00549976i
\(183\) −5.59015e7 + 7.00983e7i −0.674287 + 0.845529i
\(184\) −3.84082e6 + 7.97554e6i −0.0454528 + 0.0943838i
\(185\) 8.78906e7 7.00904e7i 1.02057 0.813875i
\(186\) 1.23932e7i 0.141217i
\(187\) −1.18947e8 1.49155e8i −1.33018 1.66799i
\(188\) −1.57232e7 + 3.58873e6i −0.172580 + 0.0393902i
\(189\) 8.56686e7 1.95533e7i 0.923008 0.210671i
\(190\) −2.84139e6 3.56300e6i −0.0300534 0.0376858i
\(191\) 5.82871e7i 0.605279i −0.953105 0.302640i \(-0.902132\pi\)
0.953105 0.302640i \(-0.0978679\pi\)
\(192\) −1.41942e8 + 1.13195e8i −1.44729 + 1.15418i
\(193\) −7.30465e6 + 1.51683e7i −0.0731390 + 0.151875i −0.934333 0.356403i \(-0.884003\pi\)
0.861194 + 0.508277i \(0.169717\pi\)
\(194\) −3.53341e6 + 4.43076e6i −0.0347447 + 0.0435685i
\(195\) 6.58774e7 + 5.25355e7i 0.636232 + 0.507378i
\(196\) 8.75074e7 4.21413e7i 0.830134 0.399772i
\(197\) −1.16048e7 5.08438e7i −0.108144 0.473812i −0.999778 0.0210546i \(-0.993298\pi\)
0.891634 0.452757i \(-0.149560\pi\)
\(198\) 1.08671e7 4.76117e7i 0.0994910 0.435899i
\(199\) 1.04050e8 + 5.01078e7i 0.935958 + 0.450733i 0.838741 0.544530i \(-0.183292\pi\)
0.0972162 + 0.995263i \(0.469006\pi\)
\(200\) −3.77629e6 7.84155e6i −0.0333780 0.0693101i
\(201\) −8.94513e7 2.04167e7i −0.776963 0.177337i
\(202\) −8.06173e6 −0.0688175
\(203\) −3.85387e6 3.13543e7i −0.0323341 0.263063i
\(204\) 3.00793e8 2.48063
\(205\) −9.92694e7 2.26576e7i −0.804780 0.183686i
\(206\) 4.45472e6 + 9.25033e6i 0.0355047 + 0.0737262i
\(207\) −1.80165e8 8.67627e7i −1.41180 0.679887i
\(208\) 9.85561e6 4.31803e7i 0.0759385 0.332708i
\(209\) 2.09650e7 + 9.18539e7i 0.158849 + 0.695962i
\(210\) 7.05661e6 3.39828e6i 0.0525809 0.0253216i
\(211\) 1.34237e8 + 1.07050e8i 0.983746 + 0.784511i 0.976512 0.215462i \(-0.0691259\pi\)
0.00723404 + 0.999974i \(0.497697\pi\)
\(212\) 5.42095e7 6.79766e7i 0.390751 0.489986i
\(213\) 7.44177e7 1.54530e8i 0.527652 1.09568i
\(214\) 1.38747e7 1.10647e7i 0.0967778 0.0771777i
\(215\) 1.24772e8i 0.856218i
\(216\) 6.23236e7 + 7.81514e7i 0.420789 + 0.527653i
\(217\) −2.95908e7 + 6.75391e6i −0.196584 + 0.0448690i
\(218\) −8.54015e6 + 1.94923e6i −0.0558300 + 0.0127428i
\(219\) −1.39887e8 1.75413e8i −0.899960 1.12851i
\(220\) 3.09523e8i 1.95980i
\(221\) −5.63049e7 + 4.49016e7i −0.350892 + 0.279827i
\(222\) −1.44476e7 + 3.00007e7i −0.0886256 + 0.184033i
\(223\) 1.33525e8 1.67435e8i 0.806298 1.01107i −0.193254 0.981149i \(-0.561904\pi\)
0.999552 0.0299170i \(-0.00952429\pi\)
\(224\) −9.80469e6 7.81898e6i −0.0582862 0.0464817i
\(225\) 1.77138e8 8.53051e7i 1.03675 0.499271i
\(226\) −981835. 4.30170e6i −0.00565795 0.0247891i
\(227\) 4.84779e7 2.12396e8i 0.275077 1.20519i −0.628859 0.777520i \(-0.716478\pi\)
0.903935 0.427669i \(-0.140665\pi\)
\(228\) −1.33837e8 6.44527e7i −0.747834 0.360138i
\(229\) 1.33916e8 + 2.78079e8i 0.736898 + 1.53018i 0.844242 + 0.535962i \(0.180051\pi\)
−0.107345 + 0.994222i \(0.534235\pi\)
\(230\) −1.12282e7 2.56276e6i −0.0608502 0.0138887i
\(231\) −1.61923e8 −0.864305
\(232\) 3.02330e7 1.94253e7i 0.158955 0.102132i
\(233\) −1.91353e8 −0.991037 −0.495519 0.868597i \(-0.665022\pi\)
−0.495519 + 0.868597i \(0.665022\pi\)
\(234\) −1.79730e7 4.10222e6i −0.0916991 0.0209297i
\(235\) −1.82906e7 3.79809e7i −0.0919372 0.190910i
\(236\) 2.22793e8 + 1.07291e8i 1.10334 + 0.531340i
\(237\) −3.67779e6 + 1.61135e7i −0.0179460 + 0.0786266i
\(238\) 1.48959e6 + 6.52632e6i 0.00716221 + 0.0313797i
\(239\) −2.59610e8 + 1.25022e8i −1.23007 + 0.592369i −0.932098 0.362207i \(-0.882023\pi\)
−0.297969 + 0.954576i \(0.596309\pi\)
\(240\) −3.78048e8 3.01484e8i −1.76526 1.40775i
\(241\) 1.99344e8 2.49969e8i 0.917368 1.15034i −0.0708803 0.997485i \(-0.522581\pi\)
0.988248 0.152858i \(-0.0488477\pi\)
\(242\) −1.61522e7 + 3.35403e7i −0.0732616 + 0.152129i
\(243\) −7.98670e8 + 6.36918e8i −3.57064 + 2.84749i
\(244\) 1.24328e8i 0.547906i
\(245\) 1.58289e8 + 1.98488e8i 0.687652 + 0.862288i
\(246\) 2.94041e7 6.71129e6i 0.125932 0.0287431i
\(247\) 3.46740e7 7.91412e6i 0.146408 0.0334167i
\(248\) −2.15272e7 2.69943e7i −0.0896204 0.112380i
\(249\) 8.41602e8i 3.45469i
\(250\) −1.28902e7 + 1.02796e7i −0.0521759 + 0.0416089i
\(251\) 5.75084e7 1.19417e8i 0.229548 0.476661i −0.754101 0.656758i \(-0.771927\pi\)
0.983649 + 0.180098i \(0.0576414\pi\)
\(252\) 1.17575e8 1.47434e8i 0.462820 0.580358i
\(253\) 1.86154e8 + 1.48453e8i 0.722689 + 0.576325i
\(254\) 2.92656e7 1.40936e7i 0.112057 0.0539638i
\(255\) 1.74955e8 + 7.66526e8i 0.660746 + 2.89492i
\(256\) −5.44258e7 + 2.38455e8i −0.202752 + 0.888314i
\(257\) 1.48501e7 + 7.15142e6i 0.0545711 + 0.0262801i 0.460970 0.887416i \(-0.347501\pi\)
−0.406399 + 0.913696i \(0.633216\pi\)
\(258\) −1.60356e7 3.32982e7i −0.0581320 0.120712i
\(259\) 7.95050e7 + 1.81465e7i 0.284345 + 0.0648998i
\(260\) 1.16842e8 0.412280
\(261\) 4.38812e8 + 6.82953e8i 1.52769 + 2.37766i
\(262\) −6.21409e6 −0.0213463
\(263\) −3.62609e7 8.27631e6i −0.122912 0.0280538i 0.160623 0.987016i \(-0.448650\pi\)
−0.283534 + 0.958962i \(0.591507\pi\)
\(264\) −7.99202e7 1.65956e8i −0.267327 0.555110i
\(265\) 2.04758e8 + 9.86065e7i 0.675898 + 0.325495i
\(266\) 735641. 3.22305e6i 0.00239651 0.0104998i
\(267\) −2.97269e7 1.30242e8i −0.0955786 0.418757i
\(268\) −1.14630e8 + 5.52031e7i −0.363771 + 0.175183i
\(269\) −4.47855e8 3.57152e8i −1.40283 1.11872i −0.976836 0.213991i \(-0.931354\pi\)
−0.425992 0.904727i \(-0.640075\pi\)
\(270\) −8.10849e7 + 1.01677e8i −0.250707 + 0.314377i
\(271\) −1.09615e8 + 2.27618e8i −0.334563 + 0.694728i −0.998596 0.0529760i \(-0.983129\pi\)
0.664033 + 0.747704i \(0.268844\pi\)
\(272\) 3.23115e8 2.57676e8i 0.973567 0.776394i
\(273\) 6.11246e7i 0.181822i
\(274\) −8.48263e6 1.06369e7i −0.0249117 0.0312383i
\(275\) −2.28231e8 + 5.20922e7i −0.661774 + 0.151046i
\(276\) −3.65995e8 + 8.35360e7i −1.04784 + 0.239162i
\(277\) −2.43395e8 3.05207e8i −0.688069 0.862811i 0.308000 0.951386i \(-0.400340\pi\)
−0.996070 + 0.0885748i \(0.971769\pi\)
\(278\) 4.37445e7i 0.122114i
\(279\) 6.09791e8 4.86292e8i 1.68099 1.34055i
\(280\) 9.46748e6 1.96594e7i 0.0257740 0.0535202i
\(281\) 2.30167e8 2.88620e8i 0.618829 0.775988i −0.369350 0.929290i \(-0.620420\pi\)
0.988179 + 0.153303i \(0.0489910\pi\)
\(282\) 9.76249e6 + 7.78532e6i 0.0259232 + 0.0206731i
\(283\) −7.66251e7 + 3.69007e7i −0.200964 + 0.0967792i −0.531659 0.846959i \(-0.678431\pi\)
0.330695 + 0.943738i \(0.392717\pi\)
\(284\) −5.29237e7 2.31874e8i −0.137099 0.600672i
\(285\) 8.64021e7 3.78552e8i 0.221089 0.968655i
\(286\) 1.97769e7 + 9.52405e6i 0.0499893 + 0.0240736i
\(287\) −3.20486e7 6.65496e7i −0.0800244 0.166172i
\(288\) 3.14179e8 + 7.17092e7i 0.775002 + 0.176889i
\(289\) −2.61653e8 −0.637651
\(290\) 3.33919e7 + 3.27241e7i 0.0803986 + 0.0787907i
\(291\) −4.82855e8 −1.14866
\(292\) −3.03317e8 6.92302e7i −0.712947 0.162725i
\(293\) −1.12140e8 2.32861e8i −0.260450 0.540830i 0.729206 0.684295i \(-0.239890\pi\)
−0.989655 + 0.143465i \(0.954176\pi\)
\(294\) −6.77520e7 3.26277e7i −0.155491 0.0748808i
\(295\) −1.43830e8 + 6.30159e8i −0.326190 + 1.42913i
\(296\) 2.06427e7 + 9.04417e7i 0.0462643 + 0.202697i
\(297\) 2.42238e9 1.16656e9i 5.36532 2.58380i
\(298\) 4.50983e7 + 3.59647e7i 0.0987196 + 0.0787263i
\(299\) 5.60398e7 7.02716e7i 0.121240 0.152031i
\(300\) 1.60147e8 3.32548e8i 0.342447 0.711099i
\(301\) −7.07660e7 + 5.64340e7i −0.149569 + 0.119277i
\(302\) 3.25602e7i 0.0680242i
\(303\) −4.28262e8 5.37023e8i −0.884423 1.10903i
\(304\) −1.98983e8 + 4.54165e7i −0.406217 + 0.0927163i
\(305\) −3.16832e8 + 7.23148e7i −0.639410 + 0.145941i
\(306\) −1.07253e8 1.34491e8i −0.213985 0.268329i
\(307\) 8.01256e8i 1.58047i 0.612802 + 0.790236i \(0.290042\pi\)
−0.612802 + 0.790236i \(0.709958\pi\)
\(308\) −1.75549e8 + 1.39996e8i −0.342350 + 0.273015i
\(309\) −3.79553e8 + 7.88149e8i −0.731842 + 1.51969i
\(310\) 2.80075e7 3.51203e7i 0.0533960 0.0669565i
\(311\) 5.81887e8 + 4.64039e8i 1.09693 + 0.874769i 0.992799 0.119795i \(-0.0382237\pi\)
0.104127 + 0.994564i \(0.466795\pi\)
\(312\) −6.26469e7 + 3.01692e7i −0.116777 + 0.0562370i
\(313\) −3.54626e7 1.55372e8i −0.0653681 0.286396i 0.931670 0.363306i \(-0.118352\pi\)
−0.997038 + 0.0769093i \(0.975495\pi\)
\(314\) −8.84643e6 + 3.87588e7i −0.0161255 + 0.0706506i
\(315\) 4.44099e8 + 2.13867e8i 0.800559 + 0.385529i
\(316\) 9.94411e6 + 2.06492e7i 0.0177281 + 0.0368127i
\(317\) 3.10353e8 + 7.08359e7i 0.547202 + 0.124895i 0.487180 0.873302i \(-0.338026\pi\)
0.0600224 + 0.998197i \(0.480883\pi\)
\(318\) −6.73169e7 −0.117389
\(319\) −3.28439e8 9.09066e8i −0.566484 1.56793i
\(320\) −6.58051e8 −1.12262
\(321\) 1.47413e9 + 3.36460e8i 2.48752 + 0.567761i
\(322\) −3.62496e6 7.52731e6i −0.00605073 0.0125645i
\(323\) 2.99001e8 + 1.43991e8i 0.493701 + 0.237754i
\(324\) −5.61750e8 + 2.46119e9i −0.917562 + 4.02010i
\(325\) 1.96644e7 + 8.61552e7i 0.0317752 + 0.139216i
\(326\) 5.57977e7 2.68708e7i 0.0891979 0.0429555i
\(327\) −5.83522e8 4.65343e8i −0.922869 0.735964i
\(328\) 5.23889e7 6.56936e7i 0.0819749 0.102793i
\(329\) 1.32685e7 2.75523e7i 0.0205417 0.0426552i
\(330\) 1.87363e8 1.49417e8i 0.287002 0.228876i
\(331\) 7.32880e8i 1.11080i −0.831584 0.555398i \(-0.812566\pi\)
0.831584 0.555398i \(-0.187434\pi\)
\(332\) −7.27632e8 9.12422e8i −1.09126 1.36840i
\(333\) −2.04305e9 + 4.66312e8i −3.03196 + 0.692025i
\(334\) 7.77815e7 1.77531e7i 0.114226 0.0260712i
\(335\) −2.07351e8 2.60010e8i −0.301334 0.377861i
\(336\) 3.50774e8i 0.504475i
\(337\) −5.35154e8 + 4.26771e8i −0.761683 + 0.607422i −0.925359 0.379092i \(-0.876236\pi\)
0.163676 + 0.986514i \(0.447665\pi\)
\(338\) −2.56349e7 + 5.32314e7i −0.0361096 + 0.0749824i
\(339\) 2.34395e8 2.93922e8i 0.326775 0.409763i
\(340\) 8.52400e8 + 6.79766e8i 1.17616 + 0.937958i
\(341\) −8.36716e8 + 4.02941e8i −1.14271 + 0.550302i
\(342\) 1.89038e7 + 8.28230e7i 0.0255539 + 0.111959i
\(343\) −8.50586e7 + 3.72666e8i −0.113812 + 0.498644i
\(344\) −9.27674e7 4.46744e7i −0.122869 0.0591704i
\(345\) −4.25757e8 8.84094e8i −0.558207 1.15913i
\(346\) −5.46176e7 1.24661e7i −0.0708869 0.0161795i
\(347\) 9.60277e8 1.23380 0.616898 0.787043i \(-0.288389\pi\)
0.616898 + 0.787043i \(0.288389\pi\)
\(348\) 1.44347e9 + 4.88784e8i 1.83603 + 0.621713i
\(349\) 7.73567e8 0.974112 0.487056 0.873371i \(-0.338071\pi\)
0.487056 + 0.873371i \(0.338071\pi\)
\(350\) 8.00837e6 + 1.82786e6i 0.00998403 + 0.00227879i
\(351\) −4.40366e8 9.14429e8i −0.543549 1.12869i
\(352\) −3.45712e8 1.66486e8i −0.422489 0.203460i
\(353\) 9.49189e7 4.15867e8i 0.114853 0.503202i −0.884477 0.466584i \(-0.845484\pi\)
0.999329 0.0366180i \(-0.0116585\pi\)
\(354\) −4.26030e7 1.86656e8i −0.0510421 0.223630i
\(355\) 5.60112e8 2.69736e8i 0.664470 0.319992i
\(356\) −1.44833e8 1.15501e8i −0.170135 0.135678i
\(357\) −3.55612e8 + 4.45923e8i −0.413654 + 0.518706i
\(358\) 6.97829e6 1.44906e7i 0.00803820 0.0166915i
\(359\) 4.07700e8 3.25130e8i 0.465061 0.370874i −0.362745 0.931888i \(-0.618160\pi\)
0.827806 + 0.561015i \(0.189589\pi\)
\(360\) 5.60718e8i 0.633411i
\(361\) 4.55134e8 + 5.70720e8i 0.509171 + 0.638481i
\(362\) 8.92681e7 2.03749e7i 0.0989046 0.0225743i
\(363\) −3.09229e9 + 7.05796e8i −3.39319 + 0.774473i
\(364\) 5.28471e7 + 6.62682e7i 0.0574337 + 0.0720195i
\(365\) 8.13224e8i 0.875357i
\(366\) 7.52595e7 6.00175e7i 0.0802375 0.0639873i
\(367\) −4.84998e8 + 1.00711e9i −0.512163 + 1.06352i 0.471226 + 0.882012i \(0.343811\pi\)
−0.983390 + 0.181506i \(0.941903\pi\)
\(368\) −3.21594e8 + 4.03266e8i −0.336388 + 0.421817i
\(369\) 1.48399e9 + 1.18345e9i 1.53759 + 1.22619i
\(370\) −1.08741e8 + 5.23669e7i −0.111606 + 0.0537465i
\(371\) 3.66856e7 + 1.60730e8i 0.0372981 + 0.163414i
\(372\) 3.25823e8 1.42752e9i 0.328157 1.43775i
\(373\) 9.51641e8 + 4.58286e8i 0.949494 + 0.457252i 0.843509 0.537115i \(-0.180486\pi\)
0.105986 + 0.994368i \(0.466200\pi\)
\(374\) 8.88695e7 + 1.84540e8i 0.0878420 + 0.182406i
\(375\) −1.36953e9 3.12585e8i −1.34110 0.306097i
\(376\) 3.47874e7 0.0337493
\(377\) −3.43164e8 + 1.23983e8i −0.329843 + 0.119170i
\(378\) −9.43416e7 −0.0898425
\(379\) 4.84341e8 + 1.10548e8i 0.456998 + 0.104307i 0.444822 0.895619i \(-0.353267\pi\)
0.0121760 + 0.999926i \(0.496124\pi\)
\(380\) −2.33616e8 4.85109e8i −0.218404 0.453520i
\(381\) 2.49350e9 + 1.20080e9i 2.30978 + 1.11233i
\(382\) −1.39251e7 + 6.10097e7i −0.0127813 + 0.0559986i
\(383\) 1.56336e8 + 6.84951e8i 0.142188 + 0.622965i 0.994924 + 0.100624i \(0.0320840\pi\)
−0.852737 + 0.522341i \(0.825059\pi\)
\(384\) 7.25644e8 3.49452e8i 0.653980 0.314940i
\(385\) −4.58864e8 3.65932e8i −0.409799 0.326804i
\(386\) 1.12696e7 1.41317e7i 0.00997364 0.0125066i
\(387\) 1.00918e9 2.09558e9i 0.885075 1.83788i
\(388\) −5.23487e8 + 4.17467e8i −0.454983 + 0.362836i
\(389\) 1.25617e9i 1.08199i 0.841026 + 0.540995i \(0.181952\pi\)
−0.841026 + 0.540995i \(0.818048\pi\)
\(390\) −5.64036e7 7.07278e7i −0.0481482 0.0603760i
\(391\) 8.17656e8 1.86625e8i 0.691754 0.157888i
\(392\) −2.04249e8 + 4.66185e7i −0.171261 + 0.0390892i
\(393\) −3.30110e8 4.13945e8i −0.274337 0.344008i
\(394\) 5.59911e7i 0.0461193i
\(395\) −4.68373e7 + 3.73515e7i −0.0382386 + 0.0304942i
\(396\) 2.50347e9 5.19850e9i 2.02586 4.20673i
\(397\) 2.21979e8 2.78352e8i 0.178051 0.223269i −0.684795 0.728736i \(-0.740108\pi\)
0.862846 + 0.505467i \(0.168680\pi\)
\(398\) −9.69392e7 7.73064e7i −0.0770741 0.0614645i
\(399\) 2.53779e8 1.22214e8i 0.200010 0.0963195i
\(400\) −1.12847e8 4.94416e8i −0.0881619 0.386262i
\(401\) −3.98845e7 + 1.74745e8i −0.0308887 + 0.135332i −0.988021 0.154318i \(-0.950682\pi\)
0.957133 + 0.289650i \(0.0935390\pi\)
\(402\) 8.87519e7 + 4.27407e7i 0.0681376 + 0.0328133i
\(403\) 1.52107e8 + 3.15853e8i 0.115766 + 0.240391i
\(404\) −9.28599e8 2.11947e8i −0.700638 0.159916i
\(405\) −6.59869e9 −4.93589
\(406\) −3.45680e6 + 3.37395e7i −0.00256350 + 0.0250206i
\(407\) 2.49520e9 1.83453
\(408\) −6.32548e8 1.44375e8i −0.461087 0.105240i
\(409\) −6.32610e8 1.31363e9i −0.457198 0.949382i −0.994375 0.105912i \(-0.966224\pi\)
0.537177 0.843469i \(-0.319491\pi\)
\(410\) 9.84933e7 + 4.74319e7i 0.0705770 + 0.0339881i
\(411\) 2.57943e8 1.13012e9i 0.183264 0.802931i
\(412\) 2.69927e8 + 1.18263e9i 0.190154 + 0.833119i
\(413\) −4.22454e8 + 2.03443e8i −0.295090 + 0.142108i
\(414\) 1.67852e8 + 1.33858e8i 0.116259 + 0.0927132i
\(415\) 1.90194e9 2.38496e9i 1.30626 1.63800i
\(416\) −6.28471e7 + 1.30503e8i −0.0428014 + 0.0888781i
\(417\) −2.91399e9 + 2.32383e9i −1.96794 + 1.56938i
\(418\) 1.01153e8i 0.0677426i
\(419\) 3.48406e8 + 4.36888e8i 0.231386 + 0.290149i 0.883947 0.467588i \(-0.154877\pi\)
−0.652561 + 0.757736i \(0.726305\pi\)
\(420\) 9.02165e8 2.05913e8i 0.594174 0.135616i
\(421\) 1.40022e9 3.19590e8i 0.914550 0.208740i 0.260749 0.965407i \(-0.416030\pi\)
0.653801 + 0.756666i \(0.273173\pi\)
\(422\) −1.14932e8 1.44120e8i −0.0744472 0.0933538i
\(423\) 7.85836e8i 0.504824i
\(424\) −1.46626e8 + 1.16931e8i −0.0934182 + 0.0744985i
\(425\) −3.57778e8 + 7.42933e8i −0.226075 + 0.469449i
\(426\) −1.14812e8 + 1.43969e8i −0.0719536 + 0.0902270i
\(427\) −1.84316e8 1.46987e8i −0.114568 0.0913652i
\(428\) 1.88907e9 9.09728e8i 1.16465 0.560865i
\(429\) 4.16170e8 + 1.82336e9i 0.254490 + 1.11499i
\(430\) 2.98087e7 1.30601e8i 0.0180802 0.0792147i
\(431\) 1.27272e9 + 6.12911e8i 0.765709 + 0.368746i 0.775616 0.631205i \(-0.217439\pi\)
−0.00990730 + 0.999951i \(0.503154\pi\)
\(432\) 2.52711e9 + 5.24761e9i 1.50811 + 3.13161i
\(433\) −2.69091e8 6.14182e7i −0.159291 0.0363571i 0.142132 0.989848i \(-0.454604\pi\)
−0.301423 + 0.953491i \(0.597461\pi\)
\(434\) 3.25865e7 0.0191348
\(435\) −4.06006e8 + 3.96276e9i −0.236494 + 2.30826i
\(436\) −1.03495e9 −0.598023
\(437\) −4.03803e8 9.21654e7i −0.231465 0.0528303i
\(438\) 1.04514e8 + 2.17026e8i 0.0594314 + 0.123411i
\(439\) −2.65438e9 1.27828e9i −1.49740 0.721110i −0.507340 0.861746i \(-0.669371\pi\)
−0.990061 + 0.140636i \(0.955085\pi\)
\(440\) 1.48565e8 6.50905e8i 0.0831441 0.364278i
\(441\) −1.05310e9 4.61391e9i −0.584699 2.56174i
\(442\) 6.96621e7 3.35475e7i 0.0383724 0.0184792i
\(443\) 2.00195e9 + 1.59650e9i 1.09406 + 0.872481i 0.992487 0.122348i \(-0.0390423\pi\)
0.101569 + 0.994829i \(0.467614\pi\)
\(444\) −2.45289e9 + 3.07583e9i −1.32996 + 1.66771i
\(445\) 2.10094e8 4.36265e8i 0.113020 0.234688i
\(446\) −1.79763e8 + 1.43356e8i −0.0959463 + 0.0765146i
\(447\) 4.91472e9i 2.60269i
\(448\) −2.97633e8 3.73220e8i −0.156390 0.196107i
\(449\) −2.09268e8 + 4.77641e7i −0.109104 + 0.0249023i −0.276724 0.960949i \(-0.589249\pi\)
0.167620 + 0.985852i \(0.446392\pi\)
\(450\) −2.05792e8 + 4.69706e7i −0.106459 + 0.0242987i
\(451\) −1.40912e9 1.76698e9i −0.723321 0.907016i
\(452\) 5.21309e8i 0.265528i
\(453\) −2.16896e9 + 1.72969e9i −1.09625 + 0.874228i
\(454\) −1.01485e8 + 2.10735e8i −0.0508985 + 0.105692i
\(455\) −1.38136e8 + 1.73217e8i −0.0687491 + 0.0862087i
\(456\) 2.50515e8 + 1.99779e8i 0.123725 + 0.0986672i
\(457\) 1.67478e9 8.06530e8i 0.820824 0.395288i 0.0241583 0.999708i \(-0.492309\pi\)
0.796666 + 0.604420i \(0.206595\pi\)
\(458\) −7.37365e7 3.23061e8i −0.0358636 0.157129i
\(459\) 2.10738e9 9.23302e9i 1.01718 4.45656i
\(460\) −1.22595e9 5.90389e8i −0.587249 0.282804i
\(461\) −9.95840e8 2.06788e9i −0.473409 0.983044i −0.991788 0.127893i \(-0.959179\pi\)
0.518379 0.855151i \(-0.326536\pi\)
\(462\) 1.69487e8 + 3.86842e7i 0.0799628 + 0.0182510i
\(463\) −2.41736e9 −1.13190 −0.565951 0.824439i \(-0.691491\pi\)
−0.565951 + 0.824439i \(0.691491\pi\)
\(464\) 1.96931e9 7.11497e8i 0.915167 0.330644i
\(465\) 3.82734e9 1.76527
\(466\) 2.00291e8 + 4.57152e7i 0.0916878 + 0.0209271i
\(467\) 1.65205e9 + 3.43052e9i 0.750611 + 1.55866i 0.827401 + 0.561612i \(0.189819\pi\)
−0.0767897 + 0.997047i \(0.524467\pi\)
\(468\) −1.96239e9 9.45037e8i −0.884963 0.426175i
\(469\) 5.36834e7 2.35202e8i 0.0240289 0.105278i
\(470\) 1.00712e7 + 4.41247e7i 0.00447443 + 0.0196038i
\(471\) −3.05182e9 + 1.46968e9i −1.34581 + 0.648110i
\(472\) −4.17020e8 3.32563e8i −0.182541 0.145572i
\(473\) −1.72673e9 + 2.16525e9i −0.750258 + 0.940794i
\(474\) 7.69917e6 1.59875e7i 0.00332062 0.00689534i
\(475\) 3.18385e8 2.53903e8i 0.136309 0.108703i
\(476\) 7.90903e8i 0.336123i
\(477\) −2.64142e9 3.31224e9i −1.11435 1.39736i
\(478\) 3.01605e8 6.88393e7i 0.126311 0.0288296i
\(479\) −2.20463e9 + 5.03191e8i −0.916559 + 0.209199i −0.654684 0.755903i \(-0.727198\pi\)
−0.261876 + 0.965102i \(0.584341\pi\)
\(480\) 9.85967e8 + 1.23636e9i 0.406929 + 0.510272i
\(481\) 9.41918e8i 0.385927i
\(482\) −2.68374e8 + 2.14021e8i −0.109163 + 0.0870547i
\(483\) 3.08855e8 6.41344e8i 0.124721 0.258986i
\(484\) −2.74229e9 + 3.43873e9i −1.09940 + 1.37860i
\(485\) −1.36833e9 1.09121e9i −0.544622 0.434322i
\(486\) 9.88139e8 4.75863e8i 0.390473 0.188042i
\(487\) −1.77819e8 7.79078e8i −0.0697634 0.305654i 0.927993 0.372597i \(-0.121533\pi\)
−0.997757 + 0.0669432i \(0.978675\pi\)
\(488\) 5.96752e7 2.61454e8i 0.0232447 0.101842i
\(489\) 4.75409e9 + 2.28945e9i 1.83860 + 0.885422i
\(490\) −1.18263e8 2.45575e8i −0.0454111 0.0942970i
\(491\) −7.18608e8 1.64018e8i −0.273972 0.0625324i 0.0833272 0.996522i \(-0.473445\pi\)
−0.357300 + 0.933990i \(0.616302\pi\)
\(492\) 3.56338e9 1.34891
\(493\) −3.22480e9 1.09197e9i −1.21210 0.410439i
\(494\) −3.81844e7 −0.0142509
\(495\) 1.47037e10 + 3.35603e9i 5.44890 + 1.24368i
\(496\) −8.72890e8 1.81258e9i −0.321199 0.666976i
\(497\) 4.06319e8 + 1.95673e8i 0.148464 + 0.0714963i
\(498\) −2.01063e8 + 8.80913e8i −0.0729506 + 0.319617i
\(499\) −2.94987e8 1.29242e9i −0.106280 0.465643i −0.999860 0.0167389i \(-0.994672\pi\)
0.893580 0.448904i \(-0.148186\pi\)
\(500\) −1.75503e9 + 8.45177e8i −0.627898 + 0.302380i
\(501\) 5.31457e9 + 4.23823e9i 1.88815 + 1.50575i
\(502\) −8.87240e7 + 1.11256e8i −0.0313024 + 0.0392520i
\(503\) 1.15943e9 2.40759e9i 0.406217 0.843518i −0.593048 0.805167i \(-0.702075\pi\)
0.999264 0.0383505i \(-0.0122103\pi\)
\(504\) −3.18017e8 + 2.53610e8i −0.110648 + 0.0882388i
\(505\) 2.48967e9i 0.860244i
\(506\) −1.59383e8 1.99860e8i −0.0546911 0.0685804i
\(507\) −4.90774e9 + 1.12016e9i −1.67245 + 0.381726i
\(508\) 3.74151e9 8.53976e8i 1.26626 0.289017i
\(509\) 3.14418e8 + 3.94268e8i 0.105681 + 0.132519i 0.831859 0.554987i \(-0.187277\pi\)
−0.726178 + 0.687506i \(0.758705\pi\)
\(510\) 8.44128e8i 0.281782i
\(511\) 4.61228e8 3.67817e8i 0.152912 0.121944i
\(512\) 6.02917e8 1.25197e9i 0.198524 0.412239i
\(513\) −2.91608e9 + 3.65665e9i −0.953650 + 1.19584i
\(514\) −1.38352e7 1.10332e7i −0.00449381 0.00358370i
\(515\) −2.85674e9 + 1.37573e9i −0.921606 + 0.443822i
\(516\) −9.71648e8 4.25707e9i −0.311340 1.36407i
\(517\) 2.08211e8 9.12230e8i 0.0662653 0.290327i
\(518\) −7.88834e7 3.79882e7i −0.0249363 0.0120087i
\(519\) −2.07102e9 4.30052e9i −0.650278 1.35032i
\(520\) −2.45711e8 5.60819e7i −0.0766325 0.0174909i
\(521\) −2.74161e9 −0.849324 −0.424662 0.905352i \(-0.639607\pi\)
−0.424662 + 0.905352i \(0.639607\pi\)
\(522\) −2.96148e8 8.19688e8i −0.0911301 0.252233i
\(523\) −2.36643e8 −0.0723331 −0.0361666 0.999346i \(-0.511515\pi\)
−0.0361666 + 0.999346i \(0.511515\pi\)
\(524\) −7.15777e8 1.63371e8i −0.217329 0.0496040i
\(525\) 3.03666e8 + 6.30569e8i 0.0915880 + 0.190185i
\(526\) 3.59774e7 + 1.73258e7i 0.0107790 + 0.00519090i
\(527\) −7.27909e8 + 3.18918e9i −0.216641 + 0.949165i
\(528\) −2.38826e9 1.04637e10i −0.706095 3.09360i
\(529\) 2.12458e9 1.02314e9i 0.623990 0.300498i
\(530\) −1.90765e8 1.52130e8i −0.0556588 0.0443864i
\(531\) 7.51247e9 9.42034e9i 2.17747 2.73046i
\(532\) 1.69471e8 3.51910e8i 0.0487983 0.101331i
\(533\) −6.67021e8 + 5.31932e8i −0.190807 + 0.152164i
\(534\) 1.43428e8i 0.0407604i
\(535\) 3.41707e9 + 4.28487e9i 0.964751 + 1.20976i
\(536\) 2.67556e8 6.10680e7i 0.0750479 0.0171292i
\(537\) 1.33598e9 3.04929e8i 0.372297 0.0849744i
\(538\) 3.83449e8 + 4.80830e8i 0.106162 + 0.133123i
\(539\) 5.63504e9i 1.55002i
\(540\) −1.20130e10 + 9.58004e9i −3.28302 + 2.61812i
\(541\) 2.31847e9 4.81435e9i 0.629521 1.30721i −0.305354 0.952239i \(-0.598775\pi\)
0.934876 0.354976i \(-0.115511\pi\)
\(542\) 1.69114e8 2.12063e8i 0.0456229 0.0572093i
\(543\) 6.09942e9 + 4.86412e9i 1.63489 + 1.30378i
\(544\) −1.21773e9 + 5.86430e8i −0.324307 + 0.156178i
\(545\) −6.01973e8 2.63742e9i −0.159290 0.697896i
\(546\) 1.46030e7 6.39797e7i 0.00383943 0.0168216i
\(547\) −3.04989e9 1.46875e9i −0.796762 0.383700i −0.00921697 0.999958i \(-0.502934\pi\)
−0.787545 + 0.616257i \(0.788648\pi\)
\(548\) −6.97432e8 1.44823e9i −0.181038 0.375929i
\(549\) 5.90616e9 + 1.34804e9i 1.52336 + 0.347696i
\(550\) 2.51337e8 0.0644149
\(551\) 1.20089e9 + 1.17687e9i 0.305824 + 0.299707i
\(552\) 8.09758e8 0.204913
\(553\) −4.23685e7 9.67034e6i −0.0106538 0.00243167i
\(554\) 1.81848e8 + 3.77612e8i 0.0454386 + 0.0943542i
\(555\) −9.26497e9 4.46178e9i −2.30048 1.10785i
\(556\) −1.15006e9 + 5.03875e9i −0.283766 + 1.24326i
\(557\) −9.20516e8 4.03305e9i −0.225704 0.988872i −0.953100 0.302655i \(-0.902127\pi\)
0.727397 0.686217i \(-0.240730\pi\)
\(558\) −7.54452e8 + 3.63325e8i −0.183828 + 0.0885269i
\(559\) 8.17364e8 + 6.51826e8i 0.197913 + 0.157830i
\(560\) 7.92717e8 9.94036e8i 0.190748 0.239190i
\(561\) −7.57189e9 + 1.57232e10i −1.81065 + 3.75985i
\(562\) −3.09871e8 + 2.47114e8i −0.0736383 + 0.0587246i
\(563\) 1.43539e8i 0.0338994i 0.999856 + 0.0169497i \(0.00539551\pi\)
−0.999856 + 0.0169497i \(0.994604\pi\)
\(564\) 9.19823e8 + 1.15342e9i 0.215887 + 0.270714i
\(565\) 1.32848e9 3.03216e8i 0.309873 0.0707265i
\(566\) 8.90200e7 2.03182e7i 0.0206362 0.00471008i
\(567\) −2.98456e9 3.74252e9i −0.687605 0.862230i
\(568\) 5.13017e8i 0.117466i
\(569\) 1.75842e9 1.40230e9i 0.400157 0.319115i −0.402649 0.915354i \(-0.631911\pi\)
0.802807 + 0.596240i \(0.203339\pi\)
\(570\) −1.80876e8 + 3.75593e8i −0.0409090 + 0.0849484i
\(571\) −2.58957e9 + 3.24722e9i −0.582106 + 0.729938i −0.982470 0.186418i \(-0.940312\pi\)
0.400365 + 0.916356i \(0.368883\pi\)
\(572\) 2.02763e9 + 1.61698e9i 0.453005 + 0.361259i
\(573\) −4.80383e9 + 2.31340e9i −1.06671 + 0.513700i
\(574\) 1.76466e7 + 7.73147e7i 0.00389465 + 0.0170636i
\(575\) 2.29005e8 1.00334e9i 0.0502351 0.220094i
\(576\) 1.10521e10 + 5.32242e9i 2.40972 + 1.16046i
\(577\) −2.21236e9 4.59400e9i −0.479446 0.995580i −0.990689 0.136144i \(-0.956529\pi\)
0.511243 0.859436i \(-0.329185\pi\)
\(578\) 2.73875e8 + 6.25101e7i 0.0589935 + 0.0134649i
\(579\) 1.54004e9 0.329728
\(580\) 2.98595e9 + 4.64725e9i 0.635456 + 0.989004i
\(581\) 2.21290e9 0.468107
\(582\) 5.05409e8 + 1.15356e8i 0.106270 + 0.0242555i
\(583\) 2.18868e9 + 4.54484e9i 0.457448 + 0.949901i
\(584\) 6.04626e8 + 2.91173e8i 0.125615 + 0.0604931i
\(585\) 1.26687e9 5.55052e9i 0.261630 1.14627i
\(586\) 6.17465e7 + 2.70529e8i 0.0126757 + 0.0555357i
\(587\) −1.07647e9 + 5.18401e8i −0.219669 + 0.105787i −0.540482 0.841356i \(-0.681758\pi\)
0.320813 + 0.947142i \(0.396044\pi\)
\(588\) −6.94629e9 5.53948e9i −1.40907 1.12370i
\(589\) 1.00724e9 1.26304e9i 0.203110 0.254692i
\(590\) 3.01096e8 6.25232e8i 0.0603563 0.125331i
\(591\) −3.72978e9 + 2.97440e9i −0.743237 + 0.592712i
\(592\) 5.40535e9i 1.07077i
\(593\) −4.36479e8 5.47327e8i −0.0859552 0.107784i 0.736994 0.675899i \(-0.236244\pi\)
−0.822949 + 0.568115i \(0.807673\pi\)
\(594\) −2.81423e9 + 6.42330e8i −0.550944 + 0.125749i
\(595\) −2.01549e9 + 4.60023e8i −0.392258 + 0.0895304i
\(596\) 4.24917e9 + 5.32829e9i 0.822133 + 1.03092i
\(597\) 1.05642e10i 2.03202i
\(598\) −7.54456e7 + 6.01659e7i −0.0144271 + 0.0115053i
\(599\) 3.87201e9 8.04030e9i 0.736109 1.52855i −0.109053 0.994036i \(-0.534782\pi\)
0.845162 0.534510i \(-0.179504\pi\)
\(600\) −4.96394e8 + 6.22458e8i −0.0938204 + 0.117647i
\(601\) −6.81093e9 5.43154e9i −1.27981 1.02062i −0.998131 0.0611074i \(-0.980537\pi\)
−0.281680 0.959508i \(-0.590892\pi\)
\(602\) 8.75538e7 4.21637e7i 0.0163564 0.00787682i
\(603\) 1.37950e9 + 6.04401e9i 0.256220 + 1.12257i
\(604\) −8.56024e8 + 3.75049e9i −0.158073 + 0.692561i
\(605\) −1.03581e10 4.98820e9i −1.90167 0.915798i
\(606\) 3.19968e8 + 6.64421e8i 0.0584054 + 0.121280i
\(607\) 7.49618e9 + 1.71095e9i 1.36044 + 0.310512i 0.839629 0.543160i \(-0.182772\pi\)
0.520811 + 0.853672i \(0.325630\pi\)
\(608\) 6.67486e8 0.120442
\(609\) −2.43115e9 + 1.56207e9i −0.436166 + 0.280246i
\(610\) 3.48907e8 0.0622380
\(611\) −3.44359e8 7.85977e7i −0.0610755 0.0139401i
\(612\) −8.81820e9 1.83112e10i −1.55507 3.22914i
\(613\) 8.93796e9 + 4.30429e9i 1.56721 + 0.754728i 0.997734 0.0672813i \(-0.0214325\pi\)
0.569474 + 0.822009i \(0.307147\pi\)
\(614\) 1.91424e8 8.38683e8i 0.0333739 0.146221i
\(615\) 2.07262e9 + 9.08073e9i 0.359299 + 1.57419i
\(616\) 4.36362e8 2.10141e8i 0.0752168 0.0362225i
\(617\) 2.62743e9 + 2.09530e9i 0.450332 + 0.359128i 0.822239 0.569142i \(-0.192725\pi\)
−0.371907 + 0.928270i \(0.621296\pi\)
\(618\) 5.85574e8 7.34287e8i 0.0997981 0.125143i
\(619\) 4.00067e9 8.30748e9i 0.677978 1.40784i −0.223368 0.974734i \(-0.571705\pi\)
0.901345 0.433101i \(-0.142581\pi\)
\(620\) 4.14941e9 3.30904e9i 0.699222 0.557611i
\(621\) 1.18197e10i 1.98055i
\(622\) −4.98206e8 6.24730e8i −0.0830123 0.104094i
\(623\) 3.42457e8 7.81636e7i 0.0567411 0.0129508i
\(624\) −3.94994e9 + 9.01548e8i −0.650795 + 0.148540i
\(625\) −4.72405e9 5.92377e9i −0.773989 0.970551i
\(626\) 1.71102e8i 0.0278769i
\(627\) 6.73819e9 5.37353e9i 1.09171 0.870609i
\(628\) −2.03797e9 + 4.23189e9i −0.328352 + 0.681830i
\(629\) 5.47991e9 6.87159e9i 0.878003 1.10098i
\(630\) −4.13749e8 3.29954e8i −0.0659243 0.0525729i
\(631\) 1.18644e9 5.71358e8i 0.187993 0.0905327i −0.337519 0.941319i \(-0.609588\pi\)
0.525513 + 0.850786i \(0.323874\pi\)
\(632\) −1.10006e7 4.81967e7i −0.00173343 0.00759465i
\(633\) 3.49490e9 1.53122e10i 0.547673 2.39951i
\(634\) −3.07926e8 1.48289e8i −0.0479882 0.0231099i
\(635\) 4.35245e9 + 9.03796e9i 0.674569 + 1.40076i
\(636\) −7.75397e9 1.76979e9i −1.19515 0.272786i
\(637\) 2.12718e9 0.326074
\(638\) 1.26600e8 + 1.02999e9i 0.0193002 + 0.157023i
\(639\) −1.15889e10 −1.75707
\(640\) 2.84609e9 + 6.49601e8i 0.429159 + 0.0979528i
\(641\) 1.53123e9 + 3.17963e9i 0.229635 + 0.476841i 0.983667 0.179996i \(-0.0576083\pi\)
−0.754033 + 0.656837i \(0.771894\pi\)
\(642\) −1.46260e9 7.04351e8i −0.218149 0.105055i
\(643\) −5.78123e8 + 2.53292e9i −0.0857595 + 0.375737i −0.999535 0.0304820i \(-0.990296\pi\)
0.913776 + 0.406219i \(0.133153\pi\)
\(644\) −2.19648e8 9.62343e8i −0.0324062 0.141981i
\(645\) 1.02833e10 4.95219e9i 1.50895 0.726672i
\(646\) −2.78567e8 2.22150e8i −0.0406552 0.0324214i
\(647\) −5.43912e9 + 6.82044e9i −0.789521 + 0.990027i 0.210402 + 0.977615i \(0.432523\pi\)
−0.999923 + 0.0124126i \(0.996049\pi\)
\(648\) 2.36264e9 4.90608e9i 0.341103 0.708308i
\(649\) −1.12168e10 + 8.94506e9i −1.61069 + 1.28448i
\(650\) 9.48774e7i 0.0135508i
\(651\) 1.73109e9 + 2.17071e9i 0.245915 + 0.308368i
\(652\) 7.13356e9 1.62819e9i 1.00795 0.230058i
\(653\) 3.36116e9 7.67163e8i 0.472382 0.107818i 0.0202988 0.999794i \(-0.493538\pi\)
0.452083 + 0.891976i \(0.350681\pi\)
\(654\) 4.99606e8 + 6.26486e8i 0.0698402 + 0.0875768i
\(655\) 1.91907e9i 0.266837i
\(656\) 3.82781e9 3.05258e9i 0.529404 0.422186i
\(657\) −6.57749e9 + 1.36583e10i −0.904860 + 1.87896i
\(658\) −2.04706e7 + 2.56694e7i −0.00280118 + 0.00351257i
\(659\) −1.48168e9 1.18160e9i −0.201677 0.160832i 0.517444 0.855717i \(-0.326884\pi\)
−0.719121 + 0.694885i \(0.755455\pi\)
\(660\) 2.55098e10 1.22849e10i 3.45385 1.66329i
\(661\) 6.37757e8 + 2.79420e9i 0.0858915 + 0.376315i 0.999544 0.0301797i \(-0.00960797\pi\)
−0.913653 + 0.406495i \(0.866751\pi\)
\(662\) −1.75088e8 + 7.67112e8i −0.0234560 + 0.102768i
\(663\) 5.93537e9 + 2.85832e9i 0.790952 + 0.380903i
\(664\) 1.09222e9 + 2.26801e9i 0.144784 + 0.300647i
\(665\) 9.95361e8 + 2.27185e8i 0.131252 + 0.0299573i
\(666\) 2.24988e9 0.295121
\(667\) 4.22709e9 + 4.33088e8i 0.551571 + 0.0565114i
\(668\) 9.42608e9 1.22353
\(669\) −1.90990e10 4.35922e9i −2.46615 0.562883i
\(670\) 1.54919e8 + 3.21692e8i 0.0198995 + 0.0413217i
\(671\) −6.49894e9 3.12973e9i −0.830451 0.399924i
\(672\) −2.55268e8 + 1.11840e9i −0.0324492 + 0.142169i
\(673\) 2.71073e9 + 1.18765e10i 0.342794 + 1.50188i 0.793147 + 0.609030i \(0.208441\pi\)
−0.450353 + 0.892851i \(0.648702\pi\)
\(674\) 6.62109e8 3.18855e8i 0.0832951 0.0401128i
\(675\) −9.08575e9 7.24564e9i −1.13710 0.906804i
\(676\) −4.35226e9 + 5.45756e9i −0.541878 + 0.679493i
\(677\) −5.90474e8 + 1.22613e9i −0.0731376 + 0.151872i −0.934332 0.356404i \(-0.884003\pi\)
0.861194 + 0.508276i \(0.169717\pi\)
\(678\) −3.15563e8 + 2.51653e8i −0.0388850 + 0.0310098i
\(679\) 1.26961e9i 0.155642i
\(680\) −1.46626e9 1.83864e9i −0.178826 0.224241i
\(681\) −1.94290e10 + 4.43455e9i −2.35741 + 0.538064i
\(682\) 9.72063e8 2.21867e8i 0.117341 0.0267823i
\(683\) −3.04155e9 3.81398e9i −0.365277 0.458043i 0.564897 0.825161i \(-0.308916\pi\)
−0.930174 + 0.367118i \(0.880344\pi\)
\(684\) 1.00370e10i 1.19925i
\(685\) 3.28494e9 2.61965e9i 0.390490 0.311406i
\(686\) 1.78063e8 3.69753e8i 0.0210591 0.0437297i
\(687\) 1.76032e10 2.20738e10i 2.07130 2.59733i
\(688\) −4.69058e9 3.74061e9i −0.549120 0.437908i
\(689\) 1.71564e9 8.26207e8i 0.199829 0.0962325i
\(690\) 2.34430e8 + 1.02711e9i 0.0271670 + 0.119026i
\(691\) 2.68498e8 1.17637e9i 0.0309576 0.135634i −0.957088 0.289799i \(-0.906412\pi\)
0.988045 + 0.154165i \(0.0492687\pi\)
\(692\) −5.96344e9 2.87184e9i −0.684110 0.329450i
\(693\) 4.74701e9 + 9.85727e9i 0.541819 + 1.12510i
\(694\) −1.00513e9 2.29415e8i −0.114147 0.0260533i
\(695\) −1.35094e10 −1.52647
\(696\) −2.80091e9 1.72072e9i −0.314896 0.193454i
\(697\) −7.96082e9 −0.890519
\(698\) −8.09700e8 1.84809e8i −0.0901219 0.0205697i
\(699\) 7.59476e9 + 1.57707e10i 0.841093 + 1.74655i
\(700\) 8.74397e8 + 4.21088e8i 0.0963531 + 0.0464012i
\(701\) −3.27319e9 + 1.43408e10i −0.358887 + 1.57239i 0.397085 + 0.917782i \(0.370022\pi\)
−0.755971 + 0.654605i \(0.772835\pi\)
\(702\) 2.42474e8 + 1.06235e9i 0.0264536 + 0.115901i
\(703\) −3.91069e9 + 1.88329e9i −0.424531 + 0.204443i
\(704\) −1.14196e10 9.10679e9i −1.23352 0.983696i
\(705\) −2.40431e9 + 3.01491e9i −0.258421 + 0.324050i
\(706\) −1.98705e8 + 4.12615e8i −0.0212516 + 0.0441295i
\(707\) 1.41204e9 1.12607e9i 0.150273 0.119838i
\(708\) 2.26202e10i 2.39541i
\(709\) −8.41131e9 1.05474e10i −0.886343 1.11144i −0.993114 0.117155i \(-0.962623\pi\)
0.106771 0.994284i \(-0.465949\pi\)
\(710\) −6.50716e8 + 1.48522e8i −0.0682319 + 0.0155735i
\(711\) 1.08875e9 2.48500e8i 0.113601 0.0259288i
\(712\) 2.49136e8 + 3.12407e8i 0.0258677 + 0.0324370i
\(713\) 4.08263e9i 0.421820i
\(714\) 4.78756e8 3.81795e8i 0.0492232 0.0392542i
\(715\) −2.94127e9 + 6.10761e9i −0.300929 + 0.624885i
\(716\) 1.18477e9 1.48565e9i 0.120625 0.151259i
\(717\) 2.06077e10 + 1.64341e10i 2.08791 + 1.66506i
\(718\) −5.04418e8 + 2.42915e8i −0.0508575 + 0.0244917i
\(719\) −2.19397e9 9.61241e9i −0.220130 0.964453i −0.957380 0.288832i \(-0.906733\pi\)
0.737250 0.675620i \(-0.236124\pi\)
\(720\) −7.27015e9 + 3.18526e10i −0.725905 + 3.18040i
\(721\) −2.07235e9 9.97991e8i −0.205916 0.0991638i
\(722\) −3.40046e8 7.06112e8i −0.0336246 0.0698222i
\(723\) −2.85136e10 6.50803e9i −2.80587 0.640421i
\(724\) 1.08181e10 1.05942
\(725\) −2.92418e9 + 2.98386e9i −0.284985 + 0.290801i
\(726\) 3.40535e9 0.330281
\(727\) 1.06749e10 + 2.43649e9i 1.03037 + 0.235176i 0.704101 0.710099i \(-0.251350\pi\)
0.326273 + 0.945276i \(0.394207\pi\)
\(728\) −7.93264e7 1.64723e8i −0.00762006 0.0158232i
\(729\) 4.49770e10 + 2.16598e10i 4.29976 + 2.07065i
\(730\) −1.94283e8 + 8.51210e8i −0.0184844 + 0.0809854i
\(731\) 2.17072e9 + 9.51056e9i 0.205539 + 0.900524i
\(732\) 1.02467e10 4.93457e9i 0.965599 0.465008i
\(733\) 7.73496e9 + 6.16843e9i 0.725428 + 0.578509i 0.915046 0.403348i \(-0.132154\pi\)
−0.189619 + 0.981858i \(0.560725\pi\)
\(734\) 7.48255e8 9.38282e8i 0.0698415 0.0875785i
\(735\) 1.00763e10 2.09236e10i 0.936038 1.94370i
\(736\) 1.31883e9 1.05173e9i 0.121932 0.0972375i
\(737\) 7.38164e9i 0.679229i
\(738\) −1.27058e9 1.59326e9i −0.116360 0.145911i
\(739\) 9.27355e9 2.11663e9i 0.845260 0.192925i 0.222104 0.975023i \(-0.428707\pi\)
0.623156 + 0.782098i \(0.285850\pi\)
\(740\) −1.39022e10 + 3.17308e9i −1.26117 + 0.287853i
\(741\) −2.02846e9 2.54361e9i −0.183148 0.229661i
\(742\) 1.77002e8i 0.0159061i
\(743\) 9.86562e9 7.86757e9i 0.882396 0.703687i −0.0735307 0.997293i \(-0.523427\pi\)
0.955927 + 0.293606i \(0.0948553\pi\)
\(744\) −1.37037e9 + 2.84560e9i −0.121992 + 0.253319i
\(745\) −1.11068e10 + 1.39275e10i −0.984108 + 1.23403i
\(746\) −8.86606e8 7.07045e8i −0.0781888 0.0623535i
\(747\) −5.12336e10 + 2.46728e10i −4.49710 + 2.16569i
\(748\) 5.38490e9 + 2.35928e10i 0.470460 + 2.06122i
\(749\) −8.84683e8 + 3.87605e9i −0.0769310 + 0.337057i
\(750\) 1.35882e9 + 6.54373e8i 0.117611 + 0.0566384i
\(751\) −3.55623e9 7.38459e9i −0.306373 0.636189i 0.689761 0.724037i \(-0.257715\pi\)
−0.996134 + 0.0878474i \(0.972001\pi\)
\(752\) 1.97616e9 + 4.51046e8i 0.169457 + 0.0386775i
\(753\) −1.21245e10 −1.03486
\(754\) 3.88814e8 4.77906e7i 0.0330325 0.00406015i
\(755\) −1.00554e10 −0.850328
\(756\) −1.08668e10 2.48028e9i −0.914696 0.208773i
\(757\) −8.98150e9 1.86503e10i −0.752511 1.56261i −0.824932 0.565232i \(-0.808787\pi\)
0.0724208 0.997374i \(-0.476928\pi\)
\(758\) −4.80554e8 2.31423e8i −0.0400775 0.0193003i
\(759\) 4.84659e9 2.12343e10i 0.402337 1.76275i
\(760\) 2.58436e8 + 1.13228e9i 0.0213553 + 0.0935637i
\(761\) 1.10395e10 5.31634e9i 0.908036 0.437287i 0.0792514 0.996855i \(-0.474747\pi\)
0.828785 + 0.559567i \(0.189033\pi\)
\(762\) −2.32309e9 1.85260e9i −0.190206 0.151684i
\(763\) 1.22357e9 1.53431e9i 0.0997223 0.125048i
\(764\) −3.20795e9 + 6.66137e9i −0.260256 + 0.540427i
\(765\) 4.15342e10 3.31224e10i 3.35421 2.67490i
\(766\) 7.54295e8i 0.0606374i
\(767\) 3.37668e9 + 4.23423e9i 0.270213 + 0.338837i
\(768\) 2.18128e10 4.97863e9i 1.73759 0.396593i
\(769\) −1.94021e10 + 4.42840e9i −1.53853 + 0.351159i −0.905967 0.423349i \(-0.860854\pi\)
−0.632563 + 0.774509i \(0.717997\pi\)
\(770\) 3.92875e8 + 4.92649e8i 0.0310125 + 0.0388884i
\(771\) 1.50773e9i 0.118477i
\(772\) 1.66963e9 1.33149e9i 0.130605 0.104154i
\(773\) 2.06152e9 4.28078e9i 0.160531 0.333346i −0.805153 0.593068i \(-0.797917\pi\)
0.965683 + 0.259722i \(0.0836309\pi\)
\(774\) −1.55696e9 + 1.95237e9i −0.120694 + 0.151345i
\(775\) 3.13831e9 + 2.50272e9i 0.242181 + 0.193133i
\(776\) 1.30123e9 6.26641e8i 0.0999629 0.0481396i
\(777\) −1.65996e9 7.27277e9i −0.126948 0.556194i
\(778\) 3.00104e8 1.31484e9i 0.0228477 0.100103i
\(779\) 3.54215e9 + 1.70581e9i 0.268464 + 0.129285i
\(780\) −4.63744e9 9.62973e9i −0.349902 0.726580i
\(781\) 1.34528e10 + 3.07052e9i 1.01050 + 0.230640i
\(782\) −9.00434e8 −0.0673330
\(783\) 2.51165e10 4.08837e10i 1.86979 3.04357i
\(784\) −1.22072e10 −0.904709
\(785\) −1.19697e10 2.73201e9i −0.883160 0.201575i
\(786\) 2.46636e8 + 5.12145e8i 0.0181166 + 0.0376196i
\(787\) 3.56654e9 + 1.71756e9i 0.260817 + 0.125603i 0.559723 0.828680i \(-0.310907\pi\)
−0.298906 + 0.954283i \(0.596622\pi\)
\(788\) −1.47203e9 + 6.44939e9i −0.107171 + 0.469545i
\(789\) 7.57080e8 + 3.31698e9i 0.0548747 + 0.240422i
\(790\) 5.79485e7 2.79065e7i 0.00418165 0.00201377i
\(791\) 7.72835e8 + 6.16315e8i 0.0555225 + 0.0442777i
\(792\) −7.75980e9 + 9.73048e9i −0.555025 + 0.695979i
\(793\) −1.18144e9 + 2.45329e9i −0.0841312 + 0.174700i
\(794\) −2.98847e8 + 2.38322e8i −0.0211874 + 0.0168964i
\(795\) 2.07892e10i 1.46741i
\(796\) −9.13362e9 1.14532e10i −0.641870 0.804880i
\(797\) −4.11881e9 + 9.40092e8i −0.288183 + 0.0657758i −0.364169 0.931333i \(-0.618647\pi\)
0.0759857 + 0.997109i \(0.475790\pi\)
\(798\) −2.94831e8 + 6.72931e7i −0.0205382 + 0.00468771i
\(799\) −2.05494e9 2.57682e9i −0.142523 0.178719i
\(800\) 1.65851e9i 0.114526i
\(801\) −7.05717e9 + 5.62790e9i −0.485195 + 0.386930i
\(802\) 8.34950e7 1.73379e8i 0.00571545 0.0118683i
\(803\) 1.12542e10 1.41124e10i 0.767029 0.961824i
\(804\) 9.09931e9 + 7.25646e9i 0.617465 + 0.492412i
\(805\) 2.32462e9 1.11948e9i 0.157061 0.0756364i
\(806\) −8.37529e7 3.66946e8i −0.00563414 0.0246848i
\(807\) −1.16600e10 + 5.10860e10i −0.780985 + 3.42172i
\(808\) 1.85105e9 + 8.91419e8i 0.123446 + 0.0594487i
\(809\) −3.89042e9 8.07854e9i −0.258331 0.536430i 0.730954 0.682427i \(-0.239075\pi\)
−0.989285 + 0.145997i \(0.953361\pi\)
\(810\) 6.90692e9 + 1.57646e9i 0.456653 + 0.104228i
\(811\) 1.98105e10 1.30414 0.652068 0.758161i \(-0.273902\pi\)
0.652068 + 0.758161i \(0.273902\pi\)
\(812\) −1.28520e9 + 3.79544e9i −0.0842414 + 0.248781i
\(813\) 2.31101e10 1.50829
\(814\) −2.61175e9 5.96116e8i −0.169725 0.0387387i
\(815\) 8.29838e9 + 1.72318e10i 0.536959 + 1.11501i
\(816\) −3.40611e10 1.64030e10i −2.19454 1.05683i
\(817\) 1.07202e9 4.69683e9i 0.0687743 0.301320i
\(818\) 3.48327e8 + 1.52612e9i 0.0222511 + 0.0974883i
\(819\) 3.72104e9 1.79196e9i 0.236685 0.113981i
\(820\) 1.00980e10 + 8.05292e9i 0.639571 + 0.510041i
\(821\) 1.48497e10 1.86210e10i 0.936520 1.17436i −0.0479572 0.998849i \(-0.515271\pi\)
0.984478 0.175510i \(-0.0561575\pi\)
\(822\) −5.39982e8 + 1.12128e9i −0.0339100 + 0.0704149i
\(823\) −8.99535e9 + 7.17355e9i −0.562495 + 0.448575i −0.862999 0.505206i \(-0.831417\pi\)
0.300504 + 0.953781i \(0.402845\pi\)
\(824\) 2.61654e9i 0.162923i
\(825\) 1.33517e10 + 1.67425e10i 0.827842 + 1.03808i
\(826\) 4.90791e8 1.12020e8i 0.0303016 0.00691615i
\(827\) −5.48092e8 + 1.25099e8i −0.0336965 + 0.00769100i −0.239336 0.970937i \(-0.576930\pi\)
0.205639 + 0.978628i \(0.434073\pi\)
\(828\) 1.58150e10 + 1.98314e10i 0.968198 + 1.21408i
\(829\) 9.18311e9i 0.559821i 0.960026 + 0.279910i \(0.0903047\pi\)
−0.960026 + 0.279910i \(0.909695\pi\)
\(830\) −2.56056e9 + 2.04198e9i −0.155440 + 0.123959i
\(831\) −1.54939e10 + 3.21734e10i −0.936606 + 1.94488i
\(832\) −3.43774e9 + 4.31078e9i −0.206938 + 0.259492i
\(833\) 1.55185e10 + 1.23756e10i 0.930231 + 0.741835i
\(834\) 3.60527e9 1.73621e9i 0.215207 0.103638i
\(835\) 5.48262e9 + 2.40209e10i 0.325901 + 1.42786i
\(836\) 2.65936e9 1.16514e10i 0.157418 0.689694i
\(837\) −4.15359e10 2.00026e10i −2.44841 1.17909i
\(838\) −2.60306e8 5.40531e8i −0.0152802 0.0317297i
\(839\) 1.41300e10 + 3.22509e9i 0.825993 + 0.188527i 0.614565 0.788866i \(-0.289332\pi\)
0.211428 + 0.977394i \(0.432189\pi\)
\(840\) −1.99603e9 −0.116195
\(841\) −1.37010e10 1.04805e10i −0.794266 0.607570i
\(842\) −1.54197e9 −0.0890193
\(843\) −3.29224e10 7.51432e9i −1.89276 0.432009i
\(844\) −9.44959e9 1.96223e10i −0.541022 1.12344i
\(845\) −1.64392e10 7.91671e9i −0.937308 0.451384i
\(846\) 1.87740e8 8.22542e8i 0.0106601 0.0467048i
\(847\) −1.85581e9 8.13084e9i −0.104940 0.459773i
\(848\) −9.84547e9 + 4.74133e9i −0.554436 + 0.267002i
\(849\) 6.08246e9 + 4.85060e9i 0.341116 + 0.272031i
\(850\) 5.51980e8 6.92161e8i 0.0308288 0.0386581i
\(851\) −4.75939e9 + 9.88298e9i −0.264727 + 0.549711i
\(852\) −1.70097e10 + 1.35648e10i −0.942234 + 0.751407i
\(853\) 1.54869e10i 0.854362i −0.904166 0.427181i \(-0.859507\pi\)
0.904166 0.427181i \(-0.140493\pi\)
\(854\) 1.57809e8 + 1.97886e8i 0.00867021 + 0.0108721i
\(855\) −2.55779e10 + 5.83798e9i −1.39953 + 0.319434i
\(856\) −4.40924e9 + 1.00638e9i −0.240273 + 0.0548408i
\(857\) 1.02369e10 + 1.28366e10i 0.555563 + 0.696654i 0.977731 0.209863i \(-0.0673020\pi\)
−0.422167 + 0.906518i \(0.638731\pi\)
\(858\) 2.00795e9i 0.108530i
\(859\) 1.60399e10 1.27914e10i 0.863425 0.688559i −0.0881057 0.996111i \(-0.528081\pi\)
0.951531 + 0.307552i \(0.0995099\pi\)
\(860\) 6.86710e9 1.42597e10i 0.368153 0.764479i
\(861\) −4.21279e9 + 5.28268e9i −0.224936 + 0.282061i
\(862\) −1.18574e9 9.45600e8i −0.0630545 0.0502843i
\(863\) 1.51111e10 7.27712e9i 0.800310 0.385409i 0.0114135 0.999935i \(-0.496367\pi\)
0.788897 + 0.614526i \(0.210653\pi\)
\(864\) −4.23859e9 1.85705e10i −0.223575 0.979546i
\(865\) 3.84985e9 1.68673e10i 0.202250 0.886113i
\(866\) 2.66987e8 + 1.28574e8i 0.0139694 + 0.00672730i
\(867\) 1.03849e10 + 2.15646e10i 0.541174 + 1.12376i
\(868\) 3.75351e9 + 8.56715e8i 0.194813 + 0.0444649i
\(869\) −1.32970e9 −0.0687362
\(870\) 1.37169e9 4.05086e9i 0.0706219 0.208560i
\(871\) −2.78650e9 −0.142888
\(872\) 2.17643e9 + 4.96757e8i 0.111157 + 0.0253709i
\(873\) 1.41556e10 + 2.93944e10i 0.720076 + 1.49525i
\(874\) 4.00646e8 + 1.92941e8i 0.0202988 + 0.00977540i
\(875\) 8.21908e8 3.60102e9i 0.0414758 0.181718i
\(876\) 6.33287e9 + 2.77461e10i 0.318300 + 1.39456i
\(877\) −1.19514e10 + 5.75550e9i −0.598303 + 0.288128i −0.708420 0.705791i \(-0.750592\pi\)
0.110117 + 0.993919i \(0.464877\pi\)
\(878\) 2.47298e9 + 1.97214e9i 0.123308 + 0.0983346i
\(879\) −1.47408e10 + 1.84844e10i −0.732084 + 0.918004i
\(880\) 1.68790e10 3.50496e10i 0.834943 1.73378i
\(881\) 1.51520e10 1.20833e10i 0.746541 0.595346i −0.174571 0.984645i \(-0.555854\pi\)
0.921112 + 0.389298i \(0.127282\pi\)
\(882\) 5.08102e9i 0.249351i
\(883\) −2.05701e9 2.57941e9i −0.100548 0.126083i 0.729012 0.684501i \(-0.239980\pi\)
−0.829560 + 0.558418i \(0.811409\pi\)
\(884\) 8.90608e9 2.03275e9i 0.433614 0.0989696i
\(885\) 5.76441e10 1.31569e10i 2.79546 0.638046i
\(886\) −1.71405e9 2.14935e9i −0.0827951 0.103822i
\(887\) 3.50978e10i 1.68868i 0.535810 + 0.844339i \(0.320006\pi\)
−0.535810 + 0.844339i \(0.679994\pi\)
\(888\) 6.63459e9 5.29091e9i 0.317957 0.253563i
\(889\) −3.15738e9 + 6.55637e9i −0.150720 + 0.312973i
\(890\) −3.24134e8 + 4.06451e8i −0.0154120 + 0.0193260i
\(891\) −1.14511e11 9.13196e10i −5.42345 4.32506i
\(892\) −2.44751e10 + 1.17866e10i −1.15464 + 0.556046i
\(893\) 3.62193e8 + 1.58687e9i 0.0170200 + 0.0745696i
\(894\) 1.17415e9 5.14428e9i 0.0549594 0.240793i
\(895\) 4.47506e9 + 2.15508e9i 0.208650 + 0.100481i
\(896\) 9.18844e8 + 1.90800e9i 0.0426740 + 0.0886136i
\(897\) −8.01576e9 1.82954e9i −0.370827 0.0846388i
\(898\) 2.30454e8 0.0106198
\(899\) −8.67551e9 + 1.41216e10i −0.398232 + 0.648225i
\(900\) −2.49392e10 −1.14034
\(901\) 1.73228e10 + 3.95383e9i 0.789010 + 0.180086i
\(902\) 1.05280e9 + 2.18617e9i 0.0477666 + 0.0991883i
\(903\) 7.45979e9 + 3.59244e9i 0.337147 + 0.162361i
\(904\) −2.50218e8 + 1.09628e9i −0.0112649 + 0.0493550i
\(905\) 6.29228e9 + 2.75683e10i 0.282188 + 1.23634i
\(906\) 2.68351e9 1.29231e9i 0.119882 0.0577321i
\(907\) −1.57898e10 1.25919e10i −0.702668 0.560359i 0.205657 0.978624i \(-0.434067\pi\)
−0.908325 + 0.418265i \(0.862638\pi\)
\(908\) −1.72299e10 + 2.16057e10i −0.763806 + 0.957783i
\(909\) −2.01368e10 + 4.18146e10i −0.889238 + 1.84652i
\(910\) 1.85971e8 1.48307e8i 0.00818088 0.00652403i
\(911\) 4.09750e10i 1.79558i 0.440426 + 0.897789i \(0.354827\pi\)
−0.440426 + 0.897789i \(0.645173\pi\)
\(912\) 1.16407e10 + 1.45969e10i 0.508154 + 0.637205i
\(913\) 6.60112e10 1.50666e10i 2.87058 0.655192i
\(914\) −1.94569e9 + 4.44091e8i −0.0842872 + 0.0192380i
\(915\) 1.85349e10 + 2.32421e10i 0.799866 + 1.00300i
\(916\) 3.91507e10i 1.68308i
\(917\) 1.08842e9 8.67986e8i 0.0466127 0.0371724i
\(918\) −4.41163e9 + 9.16084e9i −0.188213 + 0.390828i
\(919\) −8.18265e9 + 1.02607e10i −0.347768 + 0.436088i −0.924695 0.380708i \(-0.875680\pi\)
0.576927 + 0.816796i \(0.304252\pi\)
\(920\) 2.29472e9 + 1.82998e9i 0.0971568 + 0.0774799i
\(921\) 6.60368e10 3.18017e10i 2.78534 1.34135i
\(922\) 5.48329e8 + 2.40239e9i 0.0230400 + 0.100945i
\(923\) 1.15910e9 5.07833e9i 0.0485192 0.212576i
\(924\) 1.85055e10 + 8.91176e9i 0.771699 + 0.371631i
\(925\) −4.67943e9 9.71695e9i −0.194400 0.403677i
\(926\) 2.53028e9 + 5.77520e8i 0.104720 + 0.0239017i
\(927\) 5.91067e10 2.43701
\(928\) −6.79669e9 + 8.35407e8i −0.279177 + 0.0343147i
\(929\) −3.56869e9 −0.146034 −0.0730170 0.997331i \(-0.523263\pi\)
−0.0730170 + 0.997331i \(0.523263\pi\)
\(930\) −4.00611e9 9.14369e8i −0.163318 0.0372762i
\(931\) −4.25312e9 8.83170e9i −0.172736 0.358691i
\(932\) 2.18689e10 + 1.05315e10i 0.884853 + 0.426123i
\(933\) 1.51496e10 6.63748e10i 0.610683 2.67558i
\(934\) −9.09652e8 3.98545e9i −0.0365310 0.160053i
\(935\) −5.69905e10 + 2.74452e10i −2.28014 + 1.09806i
\(936\) 3.67317e9 + 2.92926e9i 0.146412 + 0.116759i
\(937\) 1.79887e10 2.25571e10i 0.714349 0.895765i −0.283655 0.958926i \(-0.591547\pi\)
0.998003 + 0.0631617i \(0.0201184\pi\)
\(938\) −1.12382e8 + 2.33363e8i −0.00444617 + 0.00923257i
\(939\) −1.13977e10 + 9.08939e9i −0.449251 + 0.358266i
\(940\) 5.34733e9i 0.209985i
\(941\) −9.51410e9 1.19303e10i −0.372224 0.466754i 0.560076 0.828441i \(-0.310772\pi\)
−0.932299 + 0.361688i \(0.882201\pi\)
\(942\) 3.54548e9 8.09233e8i 0.138196 0.0315424i
\(943\) 9.68645e9 2.21087e9i 0.376161 0.0858562i
\(944\) −1.93777e10 2.42988e10i −0.749721 0.940120i
\(945\) 2.91351e10i 1.12307i
\(946\) 2.32468e9 1.85387e9i 0.0892778 0.0711967i
\(947\) 1.76571e10 3.66653e10i 0.675607 1.40291i −0.227620 0.973750i \(-0.573095\pi\)
0.903227 0.429162i \(-0.141191\pi\)
\(948\) 1.30716e9 1.63912e9i 0.0498308 0.0624859i
\(949\) −5.32730e9 4.24838e9i −0.202337 0.161358i
\(950\) −3.93915e8 + 1.89700e8i −0.0149063 + 0.00717850i
\(951\) −6.47976e9 2.83897e10i −0.244302 1.07036i
\(952\) 3.79618e8 1.66321e9i 0.0142599 0.0624768i
\(953\) −3.86592e10 1.86173e10i −1.44686 0.696773i −0.464817 0.885407i \(-0.653880\pi\)
−0.982047 + 0.188634i \(0.939594\pi\)
\(954\) 1.97349e9 + 4.09800e9i 0.0735896 + 0.152810i
\(955\) −1.88414e10 4.30042e9i −0.700004 0.159771i
\(956\) 3.65505e10 1.35298
\(957\) −6.18865e10 + 6.31495e10i −2.28246 + 2.32904i
\(958\) 2.42782e9 0.0892148
\(959\) 2.97153e9 + 6.78231e8i 0.108796 + 0.0248321i
\(960\) 2.61179e10 + 5.42343e10i 0.952771 + 1.97845i
\(961\) −1.04411e10 5.02816e9i −0.379502 0.182759i
\(962\) −2.25029e8 + 9.85915e8i −0.00814939 + 0.0357048i
\(963\) −2.27338e10 9.96031e10i −0.820312 3.59402i
\(964\) −3.65397e10 + 1.75966e10i −1.31370 + 0.632643i
\(965\) 4.36422e9 + 3.48035e9i 0.156337 + 0.124674i
\(966\) −4.76502e8 + 5.97514e8i −0.0170077 + 0.0213269i
\(967\) −8.09273e9 + 1.68047e10i −0.287808 + 0.597638i −0.993876 0.110506i \(-0.964753\pi\)
0.706068 + 0.708144i \(0.250467\pi\)
\(968\) 7.41738e9 5.91516e9i 0.262837 0.209606i
\(969\) 3.03577e10i 1.07185i
\(970\) 1.17155e9 + 1.46908e9i 0.0412155 + 0.0516826i
\(971\) −2.77972e10 + 6.34453e9i −0.974392 + 0.222399i −0.679940 0.733268i \(-0.737994\pi\)
−0.294452 + 0.955666i \(0.595137\pi\)
\(972\) 1.26330e11 2.88341e10i 4.41241 1.00710i
\(973\) −6.11024e9 7.66200e9i −0.212649 0.266653i
\(974\) 8.57950e8i 0.0297513i
\(975\) 6.32015e9 5.04015e9i 0.218379 0.174151i
\(976\) 6.77992e9 1.40786e10i 0.233426 0.484715i
\(977\) 2.16918e10 2.72006e10i 0.744156 0.933142i −0.255275 0.966868i \(-0.582166\pi\)
0.999431 + 0.0337267i \(0.0107376\pi\)
\(978\) −4.42920e9 3.53217e9i −0.151405 0.120741i
\(979\) 9.68339e9 4.66327e9i 0.329828 0.158837i
\(980\) −7.16593e9 3.13960e10i −0.243210 1.06557i
\(981\) −1.12216e10 + 4.91649e10i −0.379500 + 1.66270i
\(982\) 7.12990e8 + 3.43358e8i 0.0240266 + 0.0115706i
\(983\) 1.28019e10 + 2.65834e10i 0.429870 + 0.892635i 0.997588 + 0.0694117i \(0.0221122\pi\)
−0.567718 + 0.823223i \(0.692174\pi\)
\(984\) −7.49355e9 1.71035e9i −0.250729 0.0572273i
\(985\) −1.72915e10 −0.576508
\(986\) 3.11456e9 + 1.91340e9i 0.103473 + 0.0635678i
\(987\) −2.79739e9 −0.0926069
\(988\) −4.39831e9 1.00389e9i −0.145090 0.0331158i
\(989\) −5.28252e9 1.09693e10i −0.173642 0.360571i
\(990\) −1.45887e10 7.02557e9i −0.477854 0.230122i
\(991\) −8.58814e9 + 3.76271e10i −0.280312 + 1.22813i 0.617083 + 0.786898i \(0.288314\pi\)
−0.897395 + 0.441228i \(0.854543\pi\)
\(992\) 1.46405e9 + 6.41442e9i 0.0476174 + 0.208625i
\(993\) −6.04015e10 + 2.90878e10i −1.95761 + 0.942733i
\(994\) −3.78551e8 3.01885e8i −0.0122257 0.00974964i
\(995\) 2.38742e10 2.99373e10i 0.768330 0.963456i
\(996\) −4.63192e10 + 9.61829e10i −1.48543 + 3.08454i
\(997\) −3.51927e9 + 2.80653e9i −0.112466 + 0.0896883i −0.678108 0.734962i \(-0.737200\pi\)
0.565642 + 0.824651i \(0.308628\pi\)
\(998\) 1.42327e9i 0.0453241i
\(999\) 7.72291e10 + 9.68422e10i 2.45077 + 3.07316i
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 29.8.e.a.4.9 96
29.22 even 14 inner 29.8.e.a.22.9 yes 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.8.e.a.4.9 96 1.1 even 1 trivial
29.8.e.a.22.9 yes 96 29.22 even 14 inner