Properties

Label 21.9.f.b.19.3
Level $21$
Weight $9$
Character 21.19
Analytic conductor $8.555$
Analytic rank $0$
Dimension $12$
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] = [21,9,Mod(10,21)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(21, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("21.10");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 21.f (of order \(6\), 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: \(8.55495081128\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 3 x^{11} + 1331 x^{10} + 1482 x^{9} + 1359381 x^{8} + 1222227 x^{7} + 474169529 x^{6} + 1911324162 x^{5} + 121870629463 x^{4} + \cdots + 556282980265104 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{5}\cdot 7^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.3
Root \(3.88954 + 6.73687i\) of defining polynomial
Character \(\chi\) \(=\) 21.19
Dual form 21.9.f.b.10.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.38954 + 5.87085i) q^{2} +(40.5000 - 23.3827i) q^{3} +(105.022 + 181.904i) q^{4} +(-231.653 - 133.745i) q^{5} +317.026i q^{6} +(2354.84 + 468.558i) q^{7} -3159.35 q^{8} +(1093.50 - 1894.00i) q^{9} +O(q^{10})\) \(q+(-3.38954 + 5.87085i) q^{2} +(40.5000 - 23.3827i) q^{3} +(105.022 + 181.904i) q^{4} +(-231.653 - 133.745i) q^{5} +317.026i q^{6} +(2354.84 + 468.558i) q^{7} -3159.35 q^{8} +(1093.50 - 1894.00i) q^{9} +(1570.39 - 906.668i) q^{10} +(9586.51 + 16604.3i) q^{11} +(8506.79 + 4911.40i) q^{12} +40724.3i q^{13} +(-10732.6 + 12236.7i) q^{14} -12509.3 q^{15} +(-16176.9 + 28019.3i) q^{16} +(-7569.41 + 4370.20i) q^{17} +(7412.92 + 12839.5i) q^{18} +(107434. + 62026.8i) q^{19} -56184.8i q^{20} +(106327. - 36085.8i) q^{21} -129975. q^{22} +(188368. - 326263. i) q^{23} +(-127954. + 73874.0i) q^{24} +(-159537. - 276326. i) q^{25} +(-239086. - 138036. i) q^{26} -102276. i q^{27} +(162078. + 477562. i) q^{28} -927223. q^{29} +(42400.6 - 73440.1i) q^{30} +(837032. - 483261. i) q^{31} +(-514061. - 890380. i) q^{32} +(776507. + 448316. i) q^{33} -59251.8i q^{34} +(-482838. - 423491. i) q^{35} +459367. q^{36} +(-461288. + 798974. i) q^{37} +(-728300. + 420484. i) q^{38} +(952243. + 1.64933e6i) q^{39} +(731873. + 422547. i) q^{40} -2.47157e6i q^{41} +(-148545. + 746544. i) q^{42} +1.37320e6 q^{43} +(-2.01359e6 + 3.48764e6i) q^{44} +(-506626. + 292500. i) q^{45} +(1.27696e6 + 2.21176e6i) q^{46} +(2.78766e6 + 1.60946e6i) q^{47} +1.51304e6i q^{48} +(5.32571e6 + 2.20675e6i) q^{49} +2.16303e6 q^{50} +(-204374. + 353986. i) q^{51} +(-7.40789e6 + 4.27695e6i) q^{52} +(-7.69978e6 - 1.33364e7i) q^{53} +(600446. + 346668. i) q^{54} -5.12859e6i q^{55} +(-7.43975e6 - 1.48034e6i) q^{56} +5.80142e6 q^{57} +(3.14285e6 - 5.44358e6i) q^{58} +(-2.49651e6 + 1.44136e6i) q^{59} +(-1.31375e6 - 2.27548e6i) q^{60} +(1.44479e6 + 834148. i) q^{61} +6.55212e6i q^{62} +(3.46246e6 - 3.94769e6i) q^{63} -1.31288e6 q^{64} +(5.44667e6 - 9.43391e6i) q^{65} +(-5.26400e6 + 3.03917e6i) q^{66} +(-8.55413e6 - 1.48162e7i) q^{67} +(-1.58991e6 - 917935. i) q^{68} -1.76182e7i q^{69} +(4.12285e6 - 1.39923e6i) q^{70} +3.12574e7 q^{71} +(-3.45475e6 + 5.98380e6i) q^{72} +(-2.38356e7 + 1.37615e7i) q^{73} +(-3.12711e6 - 5.41631e6i) q^{74} +(-1.29225e7 - 7.46081e6i) q^{75} +2.60567e7i q^{76} +(1.47946e7 + 4.35923e7i) q^{77} -1.29106e7 q^{78} +(1.23733e7 - 2.14311e7i) q^{79} +(7.49488e6 - 4.32717e6i) q^{80} +(-2.39148e6 - 4.14217e6i) q^{81} +(1.45102e7 + 8.37746e6i) q^{82} +5.98657e7i q^{83} +(1.77308e7 + 1.55515e7i) q^{84} +2.33797e6 q^{85} +(-4.65450e6 + 8.06182e6i) q^{86} +(-3.75525e7 + 2.16810e7i) q^{87} +(-3.02871e7 - 5.24588e7i) q^{88} +(5.94265e7 + 3.43099e7i) q^{89} -3.96576e6i q^{90} +(-1.90817e7 + 9.58990e7i) q^{91} +7.91313e7 q^{92} +(2.25999e7 - 3.91441e7i) q^{93} +(-1.88977e7 + 1.09106e7i) q^{94} +(-1.65916e7 - 2.87374e7i) q^{95} +(-4.16389e7 - 2.40403e7i) q^{96} -1.66923e8i q^{97} +(-3.10072e7 + 2.37866e7i) q^{98} +4.19314e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{2} + 486 q^{3} - 1117 q^{4} + 1389 q^{5} - 1226 q^{7} + 3558 q^{8} + 13122 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{2} + 486 q^{3} - 1117 q^{4} + 1389 q^{5} - 1226 q^{7} + 3558 q^{8} + 13122 q^{9} - 19731 q^{10} + 18081 q^{11} - 90477 q^{12} - 175188 q^{14} + 75006 q^{15} - 298849 q^{16} + 63306 q^{17} - 6561 q^{18} + 476265 q^{19} - 154953 q^{21} + 419258 q^{22} - 66384 q^{23} + 144099 q^{24} + 792375 q^{25} + 1890762 q^{26} - 4229651 q^{28} + 671106 q^{29} - 532737 q^{30} + 717240 q^{31} + 895149 q^{32} + 1464561 q^{33} + 3454614 q^{35} - 4885758 q^{36} + 2289443 q^{37} - 6275988 q^{38} - 930933 q^{39} + 8773863 q^{40} - 4123629 q^{42} - 10119958 q^{43} + 14123901 q^{44} + 3037743 q^{45} - 19926544 q^{46} - 4198782 q^{47} + 8565642 q^{49} - 1162248 q^{50} + 1709262 q^{51} - 26384844 q^{52} - 209511 q^{53} - 531441 q^{54} + 70081743 q^{56} + 25718310 q^{57} + 1938935 q^{58} - 97052259 q^{59} - 51464727 q^{60} - 24195864 q^{61} - 9869931 q^{63} + 272849458 q^{64} + 30440562 q^{65} + 16979949 q^{66} - 57546057 q^{67} - 32476050 q^{68} - 108189027 q^{70} + 224566620 q^{71} + 3890673 q^{72} - 193344135 q^{73} - 71015400 q^{74} + 64182375 q^{75} + 92041617 q^{77} + 102101148 q^{78} - 29314488 q^{79} - 735358533 q^{80} - 28697814 q^{81} + 321118926 q^{82} - 120939804 q^{84} + 248647620 q^{85} + 127268268 q^{86} + 27179793 q^{87} - 487070897 q^{88} + 119863098 q^{89} + 100090965 q^{91} + 364039200 q^{92} + 19365480 q^{93} - 191086092 q^{94} - 95584488 q^{95} + 72507069 q^{96} + 24200217 q^{98} + 79086294 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.38954 + 5.87085i −0.211846 + 0.366928i −0.952292 0.305188i \(-0.901281\pi\)
0.740446 + 0.672116i \(0.234614\pi\)
\(3\) 40.5000 23.3827i 0.500000 0.288675i
\(4\) 105.022 + 181.904i 0.410243 + 0.710561i
\(5\) −231.653 133.745i −0.370645 0.213992i 0.303095 0.952960i \(-0.401980\pi\)
−0.673740 + 0.738968i \(0.735313\pi\)
\(6\) 317.026i 0.244619i
\(7\) 2354.84 + 468.558i 0.980773 + 0.195151i
\(8\) −3159.35 −0.771325
\(9\) 1093.50 1894.00i 0.166667 0.288675i
\(10\) 1570.39 906.668i 0.157039 0.0906668i
\(11\) 9586.51 + 16604.3i 0.654771 + 1.13410i 0.981951 + 0.189135i \(0.0605684\pi\)
−0.327180 + 0.944962i \(0.606098\pi\)
\(12\) 8506.79 + 4911.40i 0.410243 + 0.236854i
\(13\) 40724.3i 1.42587i 0.701230 + 0.712935i \(0.252634\pi\)
−0.701230 + 0.712935i \(0.747366\pi\)
\(14\) −10732.6 + 12236.7i −0.279379 + 0.318531i
\(15\) −12509.3 −0.247097
\(16\) −16176.9 + 28019.3i −0.246840 + 0.427540i
\(17\) −7569.41 + 4370.20i −0.0906288 + 0.0523246i −0.544629 0.838677i \(-0.683330\pi\)
0.454001 + 0.891001i \(0.349996\pi\)
\(18\) 7412.92 + 12839.5i 0.0706153 + 0.122309i
\(19\) 107434. + 62026.8i 0.824377 + 0.475954i 0.851923 0.523666i \(-0.175436\pi\)
−0.0275466 + 0.999621i \(0.508769\pi\)
\(20\) 56184.8i 0.351155i
\(21\) 106327. 36085.8i 0.546722 0.185549i
\(22\) −129975. −0.554843
\(23\) 188368. 326263.i 0.673126 1.16589i −0.303887 0.952708i \(-0.598285\pi\)
0.977013 0.213180i \(-0.0683820\pi\)
\(24\) −127954. + 73874.0i −0.385662 + 0.222662i
\(25\) −159537. 276326.i −0.408415 0.707395i
\(26\) −239086. 138036.i −0.523192 0.302065i
\(27\) 102276.i 0.192450i
\(28\) 162078. + 477562.i 0.263688 + 0.776958i
\(29\) −927223. −1.31097 −0.655484 0.755209i \(-0.727535\pi\)
−0.655484 + 0.755209i \(0.727535\pi\)
\(30\) 42400.6 73440.1i 0.0523465 0.0906668i
\(31\) 837032. 483261.i 0.906349 0.523281i 0.0270943 0.999633i \(-0.491375\pi\)
0.879255 + 0.476352i \(0.158041\pi\)
\(32\) −514061. 890380.i −0.490247 0.849132i
\(33\) 776507. + 448316.i 0.654771 + 0.378032i
\(34\) 59251.8i 0.0443390i
\(35\) −482838. 423491.i −0.321758 0.282210i
\(36\) 459367. 0.273495
\(37\) −461288. + 798974.i −0.246130 + 0.426310i −0.962449 0.271463i \(-0.912493\pi\)
0.716318 + 0.697774i \(0.245826\pi\)
\(38\) −728300. + 420484.i −0.349282 + 0.201658i
\(39\) 952243. + 1.64933e6i 0.411613 + 0.712935i
\(40\) 731873. + 422547.i 0.285888 + 0.165057i
\(41\) 2.47157e6i 0.874655i −0.899302 0.437327i \(-0.855925\pi\)
0.899302 0.437327i \(-0.144075\pi\)
\(42\) −148545. + 746544.i −0.0477376 + 0.239915i
\(43\) 1.37320e6 0.401660 0.200830 0.979626i \(-0.435636\pi\)
0.200830 + 0.979626i \(0.435636\pi\)
\(44\) −2.01359e6 + 3.48764e6i −0.537230 + 0.930510i
\(45\) −506626. + 292500.i −0.123548 + 0.0713307i
\(46\) 1.27696e6 + 2.21176e6i 0.285198 + 0.493977i
\(47\) 2.78766e6 + 1.60946e6i 0.571279 + 0.329828i 0.757660 0.652649i \(-0.226343\pi\)
−0.186381 + 0.982478i \(0.559676\pi\)
\(48\) 1.51304e6i 0.285027i
\(49\) 5.32571e6 + 2.20675e6i 0.923832 + 0.382798i
\(50\) 2.16303e6 0.346084
\(51\) −204374. + 353986.i −0.0302096 + 0.0523246i
\(52\) −7.40789e6 + 4.27695e6i −1.01317 + 0.584952i
\(53\) −7.69978e6 1.33364e7i −0.975832 1.69019i −0.677162 0.735834i \(-0.736790\pi\)
−0.298670 0.954356i \(-0.596543\pi\)
\(54\) 600446. + 346668.i 0.0706153 + 0.0407698i
\(55\) 5.12859e6i 0.560464i
\(56\) −7.43975e6 1.48034e6i −0.756495 0.150525i
\(57\) 5.80142e6 0.549585
\(58\) 3.14285e6 5.44358e6i 0.277723 0.481031i
\(59\) −2.49651e6 + 1.44136e6i −0.206028 + 0.118950i −0.599464 0.800402i \(-0.704620\pi\)
0.393436 + 0.919352i \(0.371286\pi\)
\(60\) −1.31375e6 2.27548e6i −0.101370 0.175577i
\(61\) 1.44479e6 + 834148.i 0.104348 + 0.0602454i 0.551266 0.834330i \(-0.314145\pi\)
−0.446918 + 0.894575i \(0.647478\pi\)
\(62\) 6.55212e6i 0.443420i
\(63\) 3.46246e6 3.94769e6i 0.219797 0.250600i
\(64\) −1.31288e6 −0.0782535
\(65\) 5.44667e6 9.43391e6i 0.305125 0.528492i
\(66\) −5.26400e6 + 3.03917e6i −0.277421 + 0.160169i
\(67\) −8.55413e6 1.48162e7i −0.424499 0.735254i 0.571874 0.820341i \(-0.306216\pi\)
−0.996374 + 0.0850872i \(0.972883\pi\)
\(68\) −1.58991e6 917935.i −0.0743596 0.0429315i
\(69\) 1.76182e7i 0.777258i
\(70\) 4.12285e6 1.39923e6i 0.171714 0.0582771i
\(71\) 3.12574e7 1.23004 0.615020 0.788511i \(-0.289148\pi\)
0.615020 + 0.788511i \(0.289148\pi\)
\(72\) −3.45475e6 + 5.98380e6i −0.128554 + 0.222662i
\(73\) −2.38356e7 + 1.37615e7i −0.839333 + 0.484589i −0.857038 0.515254i \(-0.827698\pi\)
0.0177042 + 0.999843i \(0.494364\pi\)
\(74\) −3.12711e6 5.41631e6i −0.104284 0.180624i
\(75\) −1.29225e7 7.46081e6i −0.408415 0.235798i
\(76\) 2.60567e7i 0.781027i
\(77\) 1.47946e7 + 4.35923e7i 0.420862 + 1.24007i
\(78\) −1.29106e7 −0.348794
\(79\) 1.23733e7 2.14311e7i 0.317670 0.550220i −0.662332 0.749211i \(-0.730433\pi\)
0.980001 + 0.198991i \(0.0637663\pi\)
\(80\) 7.49488e6 4.32717e6i 0.182980 0.105644i
\(81\) −2.39148e6 4.14217e6i −0.0555556 0.0962250i
\(82\) 1.45102e7 + 8.37746e6i 0.320935 + 0.185292i
\(83\) 5.98657e7i 1.26144i 0.776012 + 0.630718i \(0.217240\pi\)
−0.776012 + 0.630718i \(0.782760\pi\)
\(84\) 1.77308e7 + 1.55515e7i 0.356133 + 0.312359i
\(85\) 2.33797e6 0.0447882
\(86\) −4.65450e6 + 8.06182e6i −0.0850901 + 0.147380i
\(87\) −3.75525e7 + 2.16810e7i −0.655484 + 0.378444i
\(88\) −3.02871e7 5.24588e7i −0.505041 0.874757i
\(89\) 5.94265e7 + 3.43099e7i 0.947153 + 0.546839i 0.892195 0.451650i \(-0.149164\pi\)
0.0549574 + 0.998489i \(0.482498\pi\)
\(90\) 3.96576e6i 0.0604445i
\(91\) −1.90817e7 + 9.58990e7i −0.278260 + 1.39845i
\(92\) 7.91313e7 1.10458
\(93\) 2.25999e7 3.91441e7i 0.302116 0.523281i
\(94\) −1.88977e7 + 1.09106e7i −0.242046 + 0.139746i
\(95\) −1.65916e7 2.87374e7i −0.203701 0.352820i
\(96\) −4.16389e7 2.40403e7i −0.490247 0.283044i
\(97\) 1.66923e8i 1.88551i −0.333482 0.942757i \(-0.608224\pi\)
0.333482 0.942757i \(-0.391776\pi\)
\(98\) −3.10072e7 + 2.37866e7i −0.336169 + 0.257886i
\(99\) 4.19314e7 0.436514
\(100\) 3.35098e7 5.80407e7i 0.335098 0.580407i
\(101\) −1.23598e8 + 7.13591e7i −1.18775 + 0.685747i −0.957794 0.287454i \(-0.907191\pi\)
−0.229954 + 0.973201i \(0.573858\pi\)
\(102\) −1.38547e6 2.39970e6i −0.0127996 0.0221695i
\(103\) −5.00884e7 2.89186e7i −0.445029 0.256938i 0.260699 0.965420i \(-0.416047\pi\)
−0.705729 + 0.708482i \(0.749380\pi\)
\(104\) 1.28662e8i 1.09981i
\(105\) −2.94573e7 5.86132e6i −0.242346 0.0482212i
\(106\) 1.04395e8 0.826904
\(107\) 4.47179e7 7.74538e7i 0.341151 0.590891i −0.643496 0.765450i \(-0.722517\pi\)
0.984647 + 0.174559i \(0.0558499\pi\)
\(108\) 1.86043e7 1.07412e7i 0.136748 0.0789512i
\(109\) 1.75975e7 + 3.04797e7i 0.124665 + 0.215926i 0.921602 0.388136i \(-0.126881\pi\)
−0.796937 + 0.604062i \(0.793548\pi\)
\(110\) 3.01092e7 + 1.73835e7i 0.205650 + 0.118732i
\(111\) 4.31446e7i 0.284207i
\(112\) −5.12227e7 + 5.84010e7i −0.325529 + 0.371149i
\(113\) −6.70322e7 −0.411121 −0.205560 0.978644i \(-0.565902\pi\)
−0.205560 + 0.978644i \(0.565902\pi\)
\(114\) −1.96641e7 + 3.40592e7i −0.116427 + 0.201658i
\(115\) −8.72722e7 + 5.03866e7i −0.498982 + 0.288087i
\(116\) −9.73789e7 1.68665e8i −0.537815 0.931522i
\(117\) 7.71317e7 + 4.45320e7i 0.411613 + 0.237645i
\(118\) 1.95422e7i 0.100796i
\(119\) −1.98724e7 + 6.74440e6i −0.0990975 + 0.0336322i
\(120\) 3.95211e7 0.190592
\(121\) −7.66227e7 + 1.32714e8i −0.357451 + 0.619123i
\(122\) −9.79431e6 + 5.65475e6i −0.0442114 + 0.0255255i
\(123\) −5.77918e7 1.00098e8i −0.252491 0.437327i
\(124\) 1.75814e8 + 1.01506e8i 0.743646 + 0.429344i
\(125\) 1.89838e8i 0.777574i
\(126\) 1.14401e7 + 3.37084e7i 0.0453888 + 0.133738i
\(127\) 5.97711e7 0.229761 0.114881 0.993379i \(-0.463351\pi\)
0.114881 + 0.993379i \(0.463351\pi\)
\(128\) 1.36050e8 2.35645e8i 0.506825 0.877846i
\(129\) 5.56144e7 3.21090e7i 0.200830 0.115949i
\(130\) 3.69234e7 + 6.39531e7i 0.129279 + 0.223918i
\(131\) −1.81198e8 1.04615e8i −0.615273 0.355228i 0.159753 0.987157i \(-0.448930\pi\)
−0.775026 + 0.631929i \(0.782264\pi\)
\(132\) 1.88333e8i 0.620340i
\(133\) 2.23925e8 + 1.96402e8i 0.715644 + 0.627681i
\(134\) 1.15978e8 0.359714
\(135\) −1.36789e7 + 2.36925e7i −0.0411828 + 0.0713307i
\(136\) 2.39144e7 1.38070e7i 0.0699043 0.0403592i
\(137\) 3.50307e7 + 6.06750e7i 0.0994414 + 0.172238i 0.911454 0.411403i \(-0.134961\pi\)
−0.812012 + 0.583640i \(0.801628\pi\)
\(138\) 1.03434e8 + 5.97176e7i 0.285198 + 0.164659i
\(139\) 1.28614e7i 0.0344531i 0.999852 + 0.0172265i \(0.00548365\pi\)
−0.999852 + 0.0172265i \(0.994516\pi\)
\(140\) 2.63258e7 1.32306e8i 0.0685282 0.344403i
\(141\) 1.50534e8 0.380853
\(142\) −1.05948e8 + 1.83508e8i −0.260579 + 0.451336i
\(143\) −6.76198e8 + 3.90403e8i −1.61707 + 0.933618i
\(144\) 3.53790e7 + 6.12781e7i 0.0822801 + 0.142513i
\(145\) 2.14794e8 + 1.24011e8i 0.485904 + 0.280537i
\(146\) 1.86580e8i 0.410633i
\(147\) 2.67291e8 3.51559e7i 0.572420 0.0752885i
\(148\) −1.93782e8 −0.403893
\(149\) −4.46096e7 + 7.72661e7i −0.0905072 + 0.156763i −0.907725 0.419566i \(-0.862182\pi\)
0.817217 + 0.576329i \(0.195515\pi\)
\(150\) 8.76025e7 5.05774e7i 0.173042 0.0999059i
\(151\) −2.79390e8 4.83918e8i −0.537407 0.930816i −0.999043 0.0437467i \(-0.986071\pi\)
0.461636 0.887070i \(-0.347263\pi\)
\(152\) −3.39420e8 1.95964e8i −0.635862 0.367115i
\(153\) 1.91153e7i 0.0348830i
\(154\) −3.06070e8 6.09009e7i −0.544175 0.108278i
\(155\) −2.58535e8 −0.447912
\(156\) −2.00013e8 + 3.46433e8i −0.337722 + 0.584952i
\(157\) 9.34000e8 5.39245e8i 1.53726 0.887539i 0.538265 0.842776i \(-0.319080\pi\)
0.998998 0.0447635i \(-0.0142534\pi\)
\(158\) 8.38792e7 + 1.45283e8i 0.134594 + 0.233124i
\(159\) −6.23682e8 3.60083e8i −0.975832 0.563397i
\(160\) 2.75013e8i 0.419636i
\(161\) 5.96449e8 6.80035e8i 0.887708 1.01211i
\(162\) 3.24241e7 0.0470769
\(163\) 2.72747e8 4.72411e8i 0.386375 0.669222i −0.605584 0.795782i \(-0.707060\pi\)
0.991959 + 0.126560i \(0.0403936\pi\)
\(164\) 4.49587e8 2.59569e8i 0.621495 0.358821i
\(165\) −1.19920e8 2.07708e8i −0.161792 0.280232i
\(166\) −3.51462e8 2.02917e8i −0.462856 0.267230i
\(167\) 2.98358e7i 0.0383594i 0.999816 + 0.0191797i \(0.00610546\pi\)
−0.999816 + 0.0191797i \(0.993895\pi\)
\(168\) −3.35924e8 + 1.14008e8i −0.421700 + 0.143119i
\(169\) −8.42735e8 −1.03310
\(170\) −7.92464e6 + 1.37259e7i −0.00948820 + 0.0164340i
\(171\) 2.34957e8 1.35653e8i 0.274792 0.158651i
\(172\) 1.44216e8 + 2.49789e8i 0.164778 + 0.285404i
\(173\) 1.36675e9 + 7.89093e8i 1.52582 + 0.880935i 0.999531 + 0.0306326i \(0.00975219\pi\)
0.526294 + 0.850303i \(0.323581\pi\)
\(174\) 2.93954e8i 0.320687i
\(175\) −2.46209e8 7.25455e8i −0.262513 0.773497i
\(176\) −6.20321e8 −0.646496
\(177\) −6.74058e7 + 1.16750e8i −0.0686759 + 0.118950i
\(178\) −4.02856e8 + 2.32589e8i −0.401301 + 0.231691i
\(179\) 7.89835e8 + 1.36804e9i 0.769351 + 1.33256i 0.937915 + 0.346864i \(0.112754\pi\)
−0.168564 + 0.985691i \(0.553913\pi\)
\(180\) −1.06414e8 6.14380e7i −0.101370 0.0585258i
\(181\) 6.13370e8i 0.571490i −0.958306 0.285745i \(-0.907759\pi\)
0.958306 0.285745i \(-0.0922410\pi\)
\(182\) −4.98330e8 4.37079e8i −0.454184 0.398358i
\(183\) 7.80185e7 0.0695654
\(184\) −5.95120e8 + 1.03078e9i −0.519199 + 0.899278i
\(185\) 2.13718e8 1.23390e8i 0.182454 0.105340i
\(186\) 1.53206e8 + 2.65361e8i 0.128004 + 0.221710i
\(187\) −1.45128e8 8.37899e7i −0.118682 0.0685212i
\(188\) 6.76114e8i 0.541238i
\(189\) 4.79221e7 2.40843e8i 0.0375568 0.188750i
\(190\) 2.24951e8 0.172613
\(191\) −3.00465e8 + 5.20420e8i −0.225767 + 0.391039i −0.956549 0.291571i \(-0.905822\pi\)
0.730782 + 0.682610i \(0.239155\pi\)
\(192\) −5.31715e7 + 3.06986e7i −0.0391268 + 0.0225898i
\(193\) 9.28691e8 + 1.60854e9i 0.669332 + 1.15932i 0.978091 + 0.208177i \(0.0667531\pi\)
−0.308759 + 0.951140i \(0.599914\pi\)
\(194\) 9.79980e8 + 5.65792e8i 0.691848 + 0.399438i
\(195\) 5.09431e8i 0.352328i
\(196\) 1.57901e8 + 1.20052e9i 0.106994 + 0.813479i
\(197\) 7.08218e8 0.470221 0.235111 0.971969i \(-0.424455\pi\)
0.235111 + 0.971969i \(0.424455\pi\)
\(198\) −1.42128e8 + 2.46173e8i −0.0924738 + 0.160169i
\(199\) 1.52211e9 8.78793e8i 0.970588 0.560369i 0.0711725 0.997464i \(-0.477326\pi\)
0.899415 + 0.437095i \(0.143993\pi\)
\(200\) 5.04033e8 + 8.73010e8i 0.315020 + 0.545632i
\(201\) −6.92885e8 4.00037e8i −0.424499 0.245085i
\(202\) 9.67497e8i 0.581091i
\(203\) −2.18346e9 4.34457e8i −1.28576 0.255837i
\(204\) −8.58552e7 −0.0495731
\(205\) −3.30560e8 + 5.72546e8i −0.187169 + 0.324187i
\(206\) 3.39553e8 1.96041e8i 0.188555 0.108862i
\(207\) −4.11961e8 7.13538e8i −0.224375 0.388629i
\(208\) −1.14106e9 6.58794e8i −0.609617 0.351962i
\(209\) 2.37848e9i 1.24656i
\(210\) 1.34257e8 1.53072e8i 0.0690337 0.0787081i
\(211\) −3.43205e9 −1.73151 −0.865753 0.500472i \(-0.833160\pi\)
−0.865753 + 0.500472i \(0.833160\pi\)
\(212\) 1.61729e9 2.80124e9i 0.800656 1.38678i
\(213\) 1.26592e9 7.30882e8i 0.615020 0.355082i
\(214\) 3.03146e8 + 5.25065e8i 0.144543 + 0.250356i
\(215\) −3.18105e8 1.83658e8i −0.148873 0.0859521i
\(216\) 3.23125e8i 0.148442i
\(217\) 2.19751e9 7.45802e8i 0.991042 0.336345i
\(218\) −2.38589e8 −0.105639
\(219\) −6.43561e8 + 1.11468e9i −0.279778 + 0.484589i
\(220\) 9.32909e8 5.38615e8i 0.398243 0.229926i
\(221\) −1.77973e8 3.08259e8i −0.0746080 0.129225i
\(222\) −2.53296e8 1.46240e8i −0.104284 0.0602081i
\(223\) 1.86934e8i 0.0755907i 0.999286 + 0.0377953i \(0.0120335\pi\)
−0.999286 + 0.0377953i \(0.987967\pi\)
\(224\) −7.93335e8 2.33757e9i −0.315112 0.928478i
\(225\) −6.97815e8 −0.272276
\(226\) 2.27208e8 3.93536e8i 0.0870943 0.150852i
\(227\) 6.54720e8 3.78003e8i 0.246577 0.142361i −0.371619 0.928385i \(-0.621197\pi\)
0.618196 + 0.786024i \(0.287864\pi\)
\(228\) 6.09277e8 + 1.05530e9i 0.225463 + 0.390513i
\(229\) −2.96305e9 1.71072e9i −1.07745 0.622067i −0.147244 0.989100i \(-0.547040\pi\)
−0.930208 + 0.367034i \(0.880373\pi\)
\(230\) 6.83149e8i 0.244120i
\(231\) 1.61848e9 + 1.41955e9i 0.568409 + 0.498543i
\(232\) 2.92942e9 1.01118
\(233\) 1.27863e9 2.21466e9i 0.433833 0.751420i −0.563367 0.826207i \(-0.690494\pi\)
0.997200 + 0.0747866i \(0.0238276\pi\)
\(234\) −5.22881e8 + 3.01886e8i −0.174397 + 0.100688i
\(235\) −4.30514e8 7.45672e8i −0.141161 0.244498i
\(236\) −5.24378e8 3.02750e8i −0.169043 0.0975968i
\(237\) 1.15728e9i 0.366813i
\(238\) 2.77629e7 1.39528e8i 0.00865280 0.0434865i
\(239\) −6.23455e9 −1.91079 −0.955396 0.295328i \(-0.904571\pi\)
−0.955396 + 0.295328i \(0.904571\pi\)
\(240\) 2.02362e8 3.50501e8i 0.0609935 0.105644i
\(241\) 6.76231e8 3.90422e8i 0.200460 0.115735i −0.396410 0.918073i \(-0.629744\pi\)
0.596870 + 0.802338i \(0.296411\pi\)
\(242\) −5.19431e8 8.99681e8i −0.151449 0.262317i
\(243\) −1.93710e8 1.11839e8i −0.0555556 0.0320750i
\(244\) 3.50416e8i 0.0988608i
\(245\) −9.38575e8 1.22349e9i −0.260498 0.339575i
\(246\) 7.83550e8 0.213957
\(247\) −2.52600e9 + 4.37515e9i −0.678649 + 1.17545i
\(248\) −2.64448e9 + 1.52679e9i −0.699090 + 0.403620i
\(249\) 1.39982e9 + 2.42456e9i 0.364145 + 0.630718i
\(250\) −1.11451e9 6.43461e8i −0.285314 0.164726i
\(251\) 3.15325e9i 0.794445i 0.917722 + 0.397222i \(0.130026\pi\)
−0.917722 + 0.397222i \(0.869974\pi\)
\(252\) 1.08173e9 + 2.15240e8i 0.268237 + 0.0533728i
\(253\) 7.22317e9 1.76297
\(254\) −2.02596e8 + 3.50907e8i −0.0486740 + 0.0843058i
\(255\) 9.46878e7 5.46680e7i 0.0223941 0.0129292i
\(256\) 7.54242e8 + 1.30639e9i 0.175611 + 0.304167i
\(257\) 6.57968e9 + 3.79878e9i 1.50825 + 0.870786i 0.999954 + 0.00960166i \(0.00305635\pi\)
0.508292 + 0.861185i \(0.330277\pi\)
\(258\) 4.35339e8i 0.0982536i
\(259\) −1.46062e9 + 1.66531e9i −0.324593 + 0.370081i
\(260\) 2.28808e9 0.500701
\(261\) −1.01392e9 + 1.75616e9i −0.218495 + 0.378444i
\(262\) 1.22835e9 7.09191e8i 0.260686 0.150507i
\(263\) −3.51345e9 6.08547e9i −0.734363 1.27195i −0.955002 0.296598i \(-0.904148\pi\)
0.220640 0.975355i \(-0.429186\pi\)
\(264\) −2.45325e9 1.41639e9i −0.505041 0.291586i
\(265\) 4.11923e9i 0.835281i
\(266\) −1.91205e9 + 6.48921e8i −0.381920 + 0.129618i
\(267\) 3.20903e9 0.631435
\(268\) 1.79675e9 3.11205e9i 0.348295 0.603265i
\(269\) −7.13899e9 + 4.12170e9i −1.36341 + 0.787167i −0.990077 0.140529i \(-0.955120\pi\)
−0.373337 + 0.927696i \(0.621786\pi\)
\(270\) −9.27302e7 1.60613e8i −0.0174488 0.0302223i
\(271\) 5.99220e9 + 3.45960e9i 1.11099 + 0.641429i 0.939085 0.343685i \(-0.111675\pi\)
0.171903 + 0.985114i \(0.445009\pi\)
\(272\) 2.82786e8i 0.0516633i
\(273\) 1.46957e9 + 4.33009e9i 0.264569 + 0.779554i
\(274\) −4.74952e8 −0.0842650
\(275\) 3.05880e9 5.29801e9i 0.534836 0.926364i
\(276\) 3.20482e9 1.85030e9i 0.552289 0.318864i
\(277\) −2.83448e9 4.90947e9i −0.481454 0.833903i 0.518319 0.855187i \(-0.326558\pi\)
−0.999773 + 0.0212843i \(0.993224\pi\)
\(278\) −7.55072e7 4.35941e7i −0.0126418 0.00729875i
\(279\) 2.11378e9i 0.348854i
\(280\) 1.52545e9 + 1.33795e9i 0.248180 + 0.217675i
\(281\) −2.39953e7 −0.00384858 −0.00192429 0.999998i \(-0.500613\pi\)
−0.00192429 + 0.999998i \(0.500613\pi\)
\(282\) −5.10239e8 + 8.83760e8i −0.0806821 + 0.139746i
\(283\) −7.65100e9 + 4.41731e9i −1.19281 + 0.688671i −0.958943 0.283597i \(-0.908472\pi\)
−0.233869 + 0.972268i \(0.575139\pi\)
\(284\) 3.28272e9 + 5.68583e9i 0.504615 + 0.874019i
\(285\) −1.34392e9 7.75911e8i −0.203701 0.117607i
\(286\) 5.29315e9i 0.791133i
\(287\) 1.15807e9 5.82013e9i 0.170690 0.857838i
\(288\) −2.24850e9 −0.326831
\(289\) −3.44968e9 + 5.97502e9i −0.494524 + 0.856541i
\(290\) −1.45611e9 + 8.40683e8i −0.205874 + 0.118861i
\(291\) −3.90311e9 6.76039e9i −0.544301 0.942757i
\(292\) −5.00653e9 2.89052e9i −0.688661 0.397598i
\(293\) 8.07016e9i 1.09499i −0.836808 0.547497i \(-0.815581\pi\)
0.836808 0.547497i \(-0.184419\pi\)
\(294\) −6.99598e8 + 1.68839e9i −0.0936395 + 0.225987i
\(295\) 7.71100e8 0.101818
\(296\) 1.45737e9 2.52424e9i 0.189847 0.328824i
\(297\) 1.69822e9 9.80468e8i 0.218257 0.126011i
\(298\) −3.02412e8 5.23793e8i −0.0383472 0.0664193i
\(299\) 1.32868e10 + 7.67115e9i 1.66240 + 0.959789i
\(300\) 3.13420e9i 0.386938i
\(301\) 3.23365e9 + 6.43421e8i 0.393937 + 0.0783844i
\(302\) 3.78801e9 0.455390
\(303\) −3.33714e9 + 5.78009e9i −0.395916 + 0.685747i
\(304\) −3.47589e9 + 2.00681e9i −0.406979 + 0.234969i
\(305\) −2.23126e8 3.86466e8i −0.0257841 0.0446593i
\(306\) −1.12223e8 6.47919e7i −0.0127996 0.00738983i
\(307\) 1.00925e10i 1.13617i −0.822968 0.568087i \(-0.807684\pi\)
0.822968 0.568087i \(-0.192316\pi\)
\(308\) −6.37583e9 + 7.26934e9i −0.708491 + 0.807778i
\(309\) −2.70478e9 −0.296686
\(310\) 8.76314e8 1.51782e9i 0.0948884 0.164351i
\(311\) −6.13405e9 + 3.54149e9i −0.655701 + 0.378569i −0.790637 0.612285i \(-0.790250\pi\)
0.134936 + 0.990854i \(0.456917\pi\)
\(312\) −3.00847e9 5.21081e9i −0.317487 0.549904i
\(313\) −6.76423e9 3.90533e9i −0.704759 0.406893i 0.104358 0.994540i \(-0.466721\pi\)
−0.809118 + 0.587647i \(0.800054\pi\)
\(314\) 7.31116e9i 0.752086i
\(315\) −1.33007e9 + 4.51407e8i −0.135093 + 0.0458486i
\(316\) 5.19786e9 0.521287
\(317\) 7.52195e9 1.30284e10i 0.744892 1.29019i −0.205353 0.978688i \(-0.565834\pi\)
0.950245 0.311504i \(-0.100833\pi\)
\(318\) 4.22799e9 2.44103e9i 0.413452 0.238707i
\(319\) −8.88882e9 1.53959e10i −0.858384 1.48676i
\(320\) 3.04132e8 + 1.75591e8i 0.0290043 + 0.0167456i
\(321\) 4.18250e9i 0.393927i
\(322\) 1.97070e9 + 5.80667e9i 0.183314 + 0.540136i
\(323\) −1.08428e9 −0.0996164
\(324\) 5.02317e8 8.70039e8i 0.0455825 0.0789512i
\(325\) 1.12532e10 6.49703e9i 1.00865 0.582346i
\(326\) 1.84897e9 + 3.20251e9i 0.163704 + 0.283544i
\(327\) 1.42539e9 + 8.22952e8i 0.124665 + 0.0719753i
\(328\) 7.80853e9i 0.674643i
\(329\) 5.81036e9 + 5.09619e9i 0.495929 + 0.434972i
\(330\) 1.62590e9 0.137100
\(331\) −4.19026e9 + 7.25774e9i −0.349083 + 0.604629i −0.986087 0.166231i \(-0.946840\pi\)
0.637004 + 0.770861i \(0.280174\pi\)
\(332\) −1.08898e10 + 6.28722e9i −0.896327 + 0.517495i
\(333\) 1.00884e9 + 1.74736e9i 0.0820435 + 0.142103i
\(334\) −1.75161e8 1.01129e8i −0.0140751 0.00812628i
\(335\) 4.57629e9i 0.363358i
\(336\) −7.08947e8 + 3.56296e9i −0.0556233 + 0.279547i
\(337\) 4.79019e9 0.371392 0.185696 0.982607i \(-0.440546\pi\)
0.185696 + 0.982607i \(0.440546\pi\)
\(338\) 2.85648e9 4.94757e9i 0.218859 0.379075i
\(339\) −2.71480e9 + 1.56739e9i −0.205560 + 0.118680i
\(340\) 2.45539e8 + 4.25285e8i 0.0183740 + 0.0318247i
\(341\) 1.60484e10 + 9.26556e9i 1.18690 + 0.685258i
\(342\) 1.83920e9i 0.134439i
\(343\) 1.15072e10 + 7.69194e9i 0.831366 + 0.555725i
\(344\) −4.33840e9 −0.309810
\(345\) −2.35635e9 + 4.08132e9i −0.166327 + 0.288087i
\(346\) −9.26530e9 + 5.34932e9i −0.646480 + 0.373245i
\(347\) 2.20690e9 + 3.82247e9i 0.152218 + 0.263649i 0.932042 0.362349i \(-0.118025\pi\)
−0.779825 + 0.625998i \(0.784692\pi\)
\(348\) −7.88769e9 4.55396e9i −0.537815 0.310507i
\(349\) 1.02728e10i 0.692448i 0.938152 + 0.346224i \(0.112536\pi\)
−0.938152 + 0.346224i \(0.887464\pi\)
\(350\) 5.09357e9 + 1.01350e9i 0.339430 + 0.0675387i
\(351\) 4.16511e9 0.274409
\(352\) 9.85610e9 1.70713e10i 0.641999 1.11197i
\(353\) −1.27695e10 + 7.37247e9i −0.822385 + 0.474804i −0.851238 0.524780i \(-0.824148\pi\)
0.0288534 + 0.999584i \(0.490814\pi\)
\(354\) −4.56949e8 7.91459e8i −0.0290974 0.0503982i
\(355\) −7.24088e9 4.18052e9i −0.455909 0.263219i
\(356\) 1.44132e10i 0.897346i
\(357\) −6.47130e8 + 7.37819e8i −0.0398400 + 0.0454231i
\(358\) −1.07087e10 −0.651936
\(359\) 3.32597e9 5.76074e9i 0.200235 0.346817i −0.748369 0.663283i \(-0.769163\pi\)
0.948604 + 0.316465i \(0.102496\pi\)
\(360\) 1.60061e9 9.24111e8i 0.0952960 0.0550192i
\(361\) −7.97128e8 1.38067e9i −0.0469352 0.0812942i
\(362\) 3.60100e9 + 2.07904e9i 0.209696 + 0.121068i
\(363\) 7.16658e9i 0.412748i
\(364\) −1.94484e10 + 6.60049e9i −1.10784 + 0.375985i
\(365\) 7.36212e9 0.414793
\(366\) −2.64446e8 + 4.58035e8i −0.0147371 + 0.0255255i
\(367\) 1.59310e10 9.19776e9i 0.878169 0.507011i 0.00811490 0.999967i \(-0.497417\pi\)
0.870054 + 0.492956i \(0.164084\pi\)
\(368\) 6.09444e9 + 1.05559e10i 0.332309 + 0.575576i
\(369\) −4.68114e9 2.70266e9i −0.252491 0.145776i
\(370\) 1.67294e9i 0.0892634i
\(371\) −1.18829e10 3.50129e10i −0.627227 1.84813i
\(372\) 9.49394e9 0.495764
\(373\) −1.32605e10 + 2.29678e10i −0.685052 + 1.18655i 0.288368 + 0.957520i \(0.406887\pi\)
−0.973420 + 0.229026i \(0.926446\pi\)
\(374\) 9.83836e8 5.68018e8i 0.0502847 0.0290319i
\(375\) 4.43891e9 + 7.68842e9i 0.224466 + 0.388787i
\(376\) −8.80719e9 5.08483e9i −0.440642 0.254405i
\(377\) 3.77605e10i 1.86927i
\(378\) 1.25152e9 + 1.09769e9i 0.0613014 + 0.0537666i
\(379\) 1.90327e10 0.922454 0.461227 0.887282i \(-0.347409\pi\)
0.461227 + 0.887282i \(0.347409\pi\)
\(380\) 3.48496e9 6.03613e9i 0.167134 0.289484i
\(381\) 2.42073e9 1.39761e9i 0.114881 0.0663263i
\(382\) −2.03687e9 3.52797e9i −0.0956556 0.165680i
\(383\) −1.30082e10 7.51027e9i −0.604535 0.349028i 0.166289 0.986077i \(-0.446822\pi\)
−0.770823 + 0.637049i \(0.780155\pi\)
\(384\) 1.27248e10i 0.585231i
\(385\) 2.40304e9 1.20770e10i 0.109375 0.549688i
\(386\) −1.25913e10 −0.567182
\(387\) 1.50159e9 2.60083e9i 0.0669433 0.115949i
\(388\) 3.03639e10 1.75306e10i 1.33977 0.773518i
\(389\) −1.19641e10 2.07225e10i −0.522496 0.904989i −0.999657 0.0261734i \(-0.991668\pi\)
0.477162 0.878815i \(-0.341666\pi\)
\(390\) 2.99079e9 + 1.72674e9i 0.129279 + 0.0746393i
\(391\) 3.29283e9i 0.140884i
\(392\) −1.68258e10 6.97190e9i −0.712575 0.295262i
\(393\) −9.78469e9 −0.410182
\(394\) −2.40053e9 + 4.15784e9i −0.0996145 + 0.172537i
\(395\) −5.73261e9 + 3.30973e9i −0.235486 + 0.135958i
\(396\) 4.40372e9 + 7.62747e9i 0.179077 + 0.310170i
\(397\) 1.10835e10 + 6.39904e9i 0.446183 + 0.257604i 0.706217 0.707996i \(-0.250400\pi\)
−0.260034 + 0.965600i \(0.583734\pi\)
\(398\) 1.19148e10i 0.474848i
\(399\) 1.36614e10 + 2.71830e9i 0.539018 + 0.107252i
\(400\) 1.03233e10 0.403253
\(401\) −8.49974e9 + 1.47220e10i −0.328721 + 0.569362i −0.982258 0.187532i \(-0.939951\pi\)
0.653537 + 0.756895i \(0.273284\pi\)
\(402\) 4.69712e9 2.71188e9i 0.179857 0.103840i
\(403\) 1.96804e10 + 3.40875e10i 0.746130 + 1.29234i
\(404\) −2.59610e10 1.49886e10i −0.974530 0.562645i
\(405\) 1.27940e9i 0.0475538i
\(406\) 9.95154e9 1.13461e10i 0.366257 0.417584i
\(407\) −1.76886e10 −0.644637
\(408\) 6.45689e8 1.11837e9i 0.0233014 0.0403592i
\(409\) −4.31951e10 + 2.49387e10i −1.54362 + 0.891212i −0.545019 + 0.838424i \(0.683478\pi\)
−0.998606 + 0.0527885i \(0.983189\pi\)
\(410\) −2.24089e9 3.88133e9i −0.0793021 0.137355i
\(411\) 2.83749e9 + 1.63823e9i 0.0994414 + 0.0574125i
\(412\) 1.21484e10i 0.421627i
\(413\) −6.55424e9 + 2.22441e9i −0.225280 + 0.0764566i
\(414\) 5.58543e9 0.190132
\(415\) 8.00674e9 1.38681e10i 0.269937 0.467545i
\(416\) 3.62601e10 2.09348e10i 1.21075 0.699028i
\(417\) 3.00733e8 + 5.20885e8i 0.00994575 + 0.0172265i
\(418\) −1.39637e10 8.06195e9i −0.457399 0.264080i
\(419\) 3.21565e10i 1.04331i 0.853157 + 0.521655i \(0.174685\pi\)
−0.853157 + 0.521655i \(0.825315\pi\)
\(420\) −2.02747e9 5.97396e9i −0.0651565 0.191984i
\(421\) −5.71409e10 −1.81894 −0.909471 0.415767i \(-0.863513\pi\)
−0.909471 + 0.415767i \(0.863513\pi\)
\(422\) 1.16331e10 2.01491e10i 0.366813 0.635338i
\(423\) 6.09661e9 3.51988e9i 0.190426 0.109943i
\(424\) 2.43263e10 + 4.21344e10i 0.752684 + 1.30369i
\(425\) 2.41520e9 + 1.39442e9i 0.0740283 + 0.0427402i
\(426\) 9.90941e9i 0.300891i
\(427\) 3.01139e9 + 2.64125e9i 0.0905848 + 0.0794507i
\(428\) 1.87855e10 0.559819
\(429\) −1.82574e10 + 3.16227e10i −0.539025 + 0.933618i
\(430\) 2.15646e9 1.24503e9i 0.0630765 0.0364172i
\(431\) 1.48286e10 + 2.56839e10i 0.429726 + 0.744307i 0.996849 0.0793263i \(-0.0252769\pi\)
−0.567123 + 0.823633i \(0.691944\pi\)
\(432\) 2.86570e9 + 1.65451e9i 0.0822801 + 0.0475045i
\(433\) 3.29153e10i 0.936368i −0.883631 0.468184i \(-0.844908\pi\)
0.883631 0.468184i \(-0.155092\pi\)
\(434\) −3.07005e9 + 1.54292e10i −0.0865338 + 0.434894i
\(435\) 1.15989e10 0.323936
\(436\) −3.69625e9 + 6.40208e9i −0.102286 + 0.177164i
\(437\) 4.04741e10 2.33678e10i 1.10982 0.640754i
\(438\) −4.36275e9 7.55650e9i −0.118540 0.205317i
\(439\) 5.76158e10 + 3.32645e10i 1.55126 + 0.895619i 0.998040 + 0.0625821i \(0.0199335\pi\)
0.553218 + 0.833037i \(0.313400\pi\)
\(440\) 1.62030e10i 0.432300i
\(441\) 1.00032e10 7.67379e9i 0.264476 0.202888i
\(442\) 2.41299e9 0.0632216
\(443\) −3.44935e10 + 5.97444e10i −0.895616 + 1.55125i −0.0625754 + 0.998040i \(0.519931\pi\)
−0.833041 + 0.553212i \(0.813402\pi\)
\(444\) −7.84816e9 + 4.53114e9i −0.201946 + 0.116594i
\(445\) −9.17756e9 1.58960e10i −0.234038 0.405366i
\(446\) −1.09746e9 6.33619e8i −0.0277363 0.0160136i
\(447\) 4.17237e9i 0.104509i
\(448\) −3.09161e9 6.15158e8i −0.0767489 0.0152713i
\(449\) −4.11572e10 −1.01265 −0.506326 0.862342i \(-0.668997\pi\)
−0.506326 + 0.862342i \(0.668997\pi\)
\(450\) 2.36527e9 4.09677e9i 0.0576807 0.0999059i
\(451\) 4.10386e10 2.36937e10i 0.991943 0.572699i
\(452\) −7.03986e9 1.21934e10i −0.168659 0.292126i
\(453\) −2.26306e10 1.30658e10i −0.537407 0.310272i
\(454\) 5.12501e9i 0.120635i
\(455\) 1.72463e10 1.96632e10i 0.402394 0.458785i
\(456\) −1.83287e10 −0.423908
\(457\) −1.63130e10 + 2.82550e10i −0.373998 + 0.647784i −0.990177 0.139823i \(-0.955347\pi\)
0.616178 + 0.787607i \(0.288680\pi\)
\(458\) 2.00868e10 1.15971e10i 0.456507 0.263565i
\(459\) 4.46966e8 + 7.74168e8i 0.0100699 + 0.0174415i
\(460\) −1.83310e10 1.05834e10i −0.409407 0.236371i
\(461\) 5.26181e9i 0.116502i 0.998302 + 0.0582508i \(0.0185523\pi\)
−0.998302 + 0.0582508i \(0.981448\pi\)
\(462\) −1.38199e10 + 4.69026e9i −0.303345 + 0.102951i
\(463\) −5.12482e10 −1.11520 −0.557602 0.830108i \(-0.688278\pi\)
−0.557602 + 0.830108i \(0.688278\pi\)
\(464\) 1.49996e10 2.59801e10i 0.323600 0.560491i
\(465\) −1.04707e10 + 6.04524e9i −0.223956 + 0.129301i
\(466\) 8.66795e9 + 1.50133e10i 0.183811 + 0.318371i
\(467\) 4.94910e10 + 2.85736e10i 1.04054 + 0.600756i 0.919986 0.391951i \(-0.128200\pi\)
0.120554 + 0.992707i \(0.461533\pi\)
\(468\) 1.87074e10i 0.389968i
\(469\) −1.32013e10 3.88978e10i −0.272852 0.803959i
\(470\) 5.83697e9 0.119618
\(471\) 2.52180e10 4.36788e10i 0.512421 0.887539i
\(472\) 7.88735e9 4.55376e9i 0.158914 0.0917492i
\(473\) 1.31641e10 + 2.28010e10i 0.262995 + 0.455521i
\(474\) 6.79422e9 + 3.92264e9i 0.134594 + 0.0777080i
\(475\) 3.95823e10i 0.777547i
\(476\) −3.31387e9 2.90655e9i −0.0645518 0.0566174i
\(477\) −3.36789e10 −0.650555
\(478\) 2.11322e10 3.66021e10i 0.404794 0.701123i
\(479\) −1.22340e9 + 7.06331e8i −0.0232395 + 0.0134173i −0.511575 0.859239i \(-0.670938\pi\)
0.488335 + 0.872656i \(0.337604\pi\)
\(480\) 6.43053e9 + 1.11380e10i 0.121138 + 0.209818i
\(481\) −3.25376e10 1.87856e10i −0.607863 0.350950i
\(482\) 5.29340e9i 0.0980723i
\(483\) 8.25515e9 4.14880e10i 0.151683 0.762314i
\(484\) −3.21883e10 −0.586566
\(485\) −2.23251e10 + 3.86683e10i −0.403485 + 0.698856i
\(486\) 1.31318e9 7.58162e8i 0.0235384 0.0135899i
\(487\) −2.05546e10 3.56016e10i −0.365420 0.632926i 0.623423 0.781885i \(-0.285741\pi\)
−0.988844 + 0.148958i \(0.952408\pi\)
\(488\) −4.56458e9 2.63536e9i −0.0804862 0.0464688i
\(489\) 2.55102e10i 0.446148i
\(490\) 1.03643e10 1.36317e9i 0.179785 0.0236465i
\(491\) 7.29089e9 0.125445 0.0627226 0.998031i \(-0.480022\pi\)
0.0627226 + 0.998031i \(0.480022\pi\)
\(492\) 1.21388e10 2.10251e10i 0.207165 0.358821i
\(493\) 7.01853e9 4.05215e9i 0.118811 0.0685958i
\(494\) −1.71239e10 2.96595e10i −0.287538 0.498030i
\(495\) −9.71354e9 5.60811e9i −0.161792 0.0934106i
\(496\) 3.12707e10i 0.516667i
\(497\) 7.36061e10 + 1.46459e10i 1.20639 + 0.240044i
\(498\) −1.89790e10 −0.308571
\(499\) 1.66296e10 2.88034e10i 0.268214 0.464560i −0.700187 0.713960i \(-0.746900\pi\)
0.968401 + 0.249400i \(0.0802334\pi\)
\(500\) −3.45321e10 + 1.99371e10i −0.552514 + 0.318994i
\(501\) 6.97641e8 + 1.20835e9i 0.0110734 + 0.0191797i
\(502\) −1.85123e10 1.06881e10i −0.291504 0.168300i
\(503\) 2.23813e10i 0.349633i −0.984601 0.174817i \(-0.944067\pi\)
0.984601 0.174817i \(-0.0559332\pi\)
\(504\) −1.09391e10 + 1.24721e10i −0.169535 + 0.193294i
\(505\) 3.81757e10 0.586978
\(506\) −2.44832e10 + 4.24061e10i −0.373479 + 0.646884i
\(507\) −3.41308e10 + 1.97054e10i −0.516552 + 0.298231i
\(508\) 6.27729e9 + 1.08726e10i 0.0942578 + 0.163259i
\(509\) −5.60138e10 3.23396e10i −0.834495 0.481796i 0.0208945 0.999782i \(-0.493349\pi\)
−0.855389 + 0.517986i \(0.826682\pi\)
\(510\) 7.41197e8i 0.0109560i
\(511\) −6.25770e10 + 2.12377e10i −0.917764 + 0.311475i
\(512\) 5.94313e10 0.864839
\(513\) 6.34385e9 1.09879e10i 0.0915974 0.158651i
\(514\) −4.46041e10 + 2.57522e10i −0.639032 + 0.368945i
\(515\) 7.73543e9 + 1.33982e10i 0.109965 + 0.190466i
\(516\) 1.16815e10 + 6.74431e9i 0.164778 + 0.0951346i
\(517\) 6.17162e10i 0.863848i
\(518\) −4.82597e9 1.42197e10i −0.0670294 0.197503i
\(519\) 7.38045e10 1.01722
\(520\) −1.72079e10 + 2.98050e10i −0.235350 + 0.407639i
\(521\) 5.03381e10 2.90627e10i 0.683197 0.394444i −0.117861 0.993030i \(-0.537604\pi\)
0.801059 + 0.598586i \(0.204270\pi\)
\(522\) −6.87342e9 1.19051e10i −0.0925744 0.160344i
\(523\) 9.86806e10 + 5.69733e10i 1.31894 + 0.761491i 0.983558 0.180591i \(-0.0578012\pi\)
0.335382 + 0.942082i \(0.391134\pi\)
\(524\) 4.39474e10i 0.582919i
\(525\) −2.69346e10 2.36239e10i −0.354546 0.310967i
\(526\) 4.76358e10 0.622287
\(527\) −4.22389e9 + 7.31600e9i −0.0547609 + 0.0948486i
\(528\) −2.51230e10 + 1.45048e10i −0.323248 + 0.186627i
\(529\) −3.18096e10 5.50959e10i −0.406196 0.703552i
\(530\) −2.41834e10 1.39623e10i −0.306488 0.176951i
\(531\) 6.30451e9i 0.0793001i
\(532\) −1.22091e10 + 6.13594e10i −0.152418 + 0.766010i
\(533\) 1.00653e11 1.24714
\(534\) −1.08771e10 + 1.88397e10i −0.133767 + 0.231691i
\(535\) −2.07181e10 + 1.19616e10i −0.252892 + 0.146007i
\(536\) 2.70255e10 + 4.68095e10i 0.327427 + 0.567120i
\(537\) 6.39767e10 + 3.69370e10i 0.769351 + 0.444185i
\(538\) 5.58826e10i 0.667033i
\(539\) 1.44133e10 + 1.09585e11i 0.170769 + 1.29836i
\(540\) −5.74634e9 −0.0675798
\(541\) −6.99025e9 + 1.21075e10i −0.0816025 + 0.141340i −0.903938 0.427663i \(-0.859337\pi\)
0.822336 + 0.569002i \(0.192670\pi\)
\(542\) −4.06216e10 + 2.34529e10i −0.470717 + 0.271768i
\(543\) −1.43422e10 2.48415e10i −0.164975 0.285745i
\(544\) 7.78228e9 + 4.49310e9i 0.0888610 + 0.0513039i
\(545\) 9.41430e9i 0.106709i
\(546\) −3.04025e10 6.04938e9i −0.342088 0.0680676i
\(547\) 6.43329e10 0.718594 0.359297 0.933223i \(-0.383017\pi\)
0.359297 + 0.933223i \(0.383017\pi\)
\(548\) −7.35800e9 + 1.27444e10i −0.0815902 + 0.141318i
\(549\) 3.15975e9 1.82428e9i 0.0347827 0.0200818i
\(550\) 2.07359e10 + 3.59156e10i 0.226606 + 0.392493i
\(551\) −9.96149e10 5.75127e10i −1.08073 0.623961i
\(552\) 5.56620e10i 0.599519i
\(553\) 3.91787e10 4.46692e10i 0.418938 0.477648i
\(554\) 3.84303e10 0.407976
\(555\) 5.77038e9 9.99459e9i 0.0608181 0.105340i
\(556\) −2.33953e9 + 1.35073e9i −0.0244810 + 0.0141341i
\(557\) −2.74849e10 4.76053e10i −0.285544 0.494577i 0.687197 0.726471i \(-0.258841\pi\)
−0.972741 + 0.231894i \(0.925508\pi\)
\(558\) 1.24097e10 + 7.16474e9i 0.128004 + 0.0739033i
\(559\) 5.59224e10i 0.572715i
\(560\) 1.96767e10 6.67800e9i 0.200079 0.0679038i
\(561\) −7.83693e9 −0.0791215
\(562\) 8.13328e7 1.40873e8i 0.000815305 0.00141215i
\(563\) −7.43985e10 + 4.29540e10i −0.740509 + 0.427533i −0.822254 0.569120i \(-0.807284\pi\)
0.0817454 + 0.996653i \(0.473951\pi\)
\(564\) 1.58094e10 + 2.73826e10i 0.156242 + 0.270619i
\(565\) 1.55282e10 + 8.96522e9i 0.152380 + 0.0879766i
\(566\) 5.98905e10i 0.583569i
\(567\) −3.69071e9 1.08747e10i −0.0357090 0.105217i
\(568\) −9.87530e10 −0.948761
\(569\) 1.88137e10 3.25863e10i 0.179484 0.310875i −0.762220 0.647318i \(-0.775891\pi\)
0.941704 + 0.336443i \(0.109224\pi\)
\(570\) 9.11051e9 5.25995e9i 0.0863064 0.0498290i
\(571\) −1.88677e10 3.26798e10i −0.177490 0.307422i 0.763530 0.645772i \(-0.223464\pi\)
−0.941020 + 0.338350i \(0.890131\pi\)
\(572\) −1.42032e11 8.20020e10i −1.32679 0.766020i
\(573\) 2.81027e10i 0.260693i
\(574\) 3.02438e10 + 2.65264e10i 0.278605 + 0.244360i
\(575\) −1.20207e11 −1.09966
\(576\) −1.43563e9 + 2.48658e9i −0.0130423 + 0.0225898i
\(577\) −8.38562e10 + 4.84144e10i −0.756540 + 0.436788i −0.828052 0.560651i \(-0.810551\pi\)
0.0715123 + 0.997440i \(0.477217\pi\)
\(578\) −2.33856e10 4.05051e10i −0.209526 0.362910i
\(579\) 7.52239e10 + 4.34306e10i 0.669332 + 0.386439i
\(580\) 5.20958e10i 0.460352i
\(581\) −2.80505e10 + 1.40974e11i −0.246171 + 1.23718i
\(582\) 5.29189e10 0.461232
\(583\) 1.47628e11 2.55699e11i 1.27789 2.21338i
\(584\) 7.53049e10 4.34773e10i 0.647399 0.373776i
\(585\) −1.19119e10 2.06320e10i −0.101708 0.176164i
\(586\) 4.73787e10 + 2.73541e10i 0.401784 + 0.231970i
\(587\) 1.01539e11i 0.855223i −0.903963 0.427612i \(-0.859355\pi\)
0.903963 0.427612i \(-0.140645\pi\)
\(588\) 3.44664e10 + 4.49291e10i 0.288328 + 0.375853i
\(589\) 1.19901e11 0.996231
\(590\) −2.61367e9 + 4.52701e9i −0.0215696 + 0.0373597i
\(591\) 2.86828e10 1.65600e10i 0.235111 0.135741i
\(592\) −1.49245e10 2.58499e10i −0.121510 0.210461i
\(593\) −1.82032e10 1.05096e10i −0.147207 0.0849899i 0.424587 0.905387i \(-0.360419\pi\)
−0.571794 + 0.820397i \(0.693752\pi\)
\(594\) 1.32933e10i 0.106780i
\(595\) 5.50554e9 + 1.09547e9i 0.0439271 + 0.00874046i
\(596\) −1.87400e10 −0.148520
\(597\) 4.10971e10 7.11822e10i 0.323529 0.560369i
\(598\) −9.00724e10 + 5.20033e10i −0.704347 + 0.406655i
\(599\) −1.08341e11 1.87653e11i −0.841563 1.45763i −0.888573 0.458735i \(-0.848303\pi\)
0.0470100 0.998894i \(-0.485031\pi\)
\(600\) 4.08267e10 + 2.35713e10i 0.315020 + 0.181877i
\(601\) 3.99391e10i 0.306126i 0.988216 + 0.153063i \(0.0489138\pi\)
−0.988216 + 0.153063i \(0.951086\pi\)
\(602\) −1.47380e10 + 1.68034e10i −0.112215 + 0.127941i
\(603\) −3.74158e10 −0.282999
\(604\) 5.86843e10 1.01644e11i 0.440934 0.763721i
\(605\) 3.54998e10 2.04958e10i 0.264975 0.152983i
\(606\) −2.26227e10 3.91836e10i −0.167747 0.290546i
\(607\) −4.68557e10 2.70521e10i −0.345150 0.199272i 0.317397 0.948293i \(-0.397191\pi\)
−0.662547 + 0.749020i \(0.730524\pi\)
\(608\) 1.27542e11i 0.933340i
\(609\) −9.85888e10 + 3.34596e10i −0.716735 + 0.243249i
\(610\) 3.02518e9 0.0218490
\(611\) −6.55439e10 + 1.13525e11i −0.470292 + 0.814570i
\(612\) −3.47713e9 + 2.00752e9i −0.0247865 + 0.0143105i
\(613\) −4.75233e10 8.23128e10i −0.336562 0.582942i 0.647222 0.762302i \(-0.275931\pi\)
−0.983784 + 0.179359i \(0.942597\pi\)
\(614\) 5.92515e10 + 3.42089e10i 0.416894 + 0.240694i
\(615\) 3.09175e10i 0.216124i
\(616\) −4.67412e10 1.37723e11i −0.324621 0.956498i
\(617\) 9.30288e10 0.641914 0.320957 0.947094i \(-0.395996\pi\)
0.320957 + 0.947094i \(0.395996\pi\)
\(618\) 9.16793e9 1.58793e10i 0.0628518 0.108862i
\(619\) −6.05185e10 + 3.49403e10i −0.412216 + 0.237993i −0.691742 0.722145i \(-0.743156\pi\)
0.279525 + 0.960138i \(0.409823\pi\)
\(620\) −2.71519e10 4.70285e10i −0.183753 0.318269i
\(621\) −3.33688e10 1.92655e10i −0.224375 0.129543i
\(622\) 4.80161e10i 0.320793i
\(623\) 1.23863e11 + 1.08639e11i 0.822226 + 0.721163i
\(624\) −6.16175e10 −0.406411
\(625\) −3.69293e10 + 6.39634e10i −0.242020 + 0.419191i
\(626\) 4.58552e10 2.64745e10i 0.298601 0.172397i
\(627\) 5.56153e10 + 9.63285e10i 0.359852 + 0.623282i
\(628\) 1.96181e11 + 1.13265e11i 1.26130 + 0.728213i
\(629\) 8.06369e9i 0.0515147i
\(630\) 1.85819e9 9.33873e9i 0.0117958 0.0592824i
\(631\) −8.99980e10 −0.567695 −0.283848 0.958869i \(-0.591611\pi\)
−0.283848 + 0.958869i \(0.591611\pi\)
\(632\) −3.90914e10 + 6.77083e10i −0.245027 + 0.424399i
\(633\) −1.38998e11 + 8.02506e10i −0.865753 + 0.499843i
\(634\) 5.09919e10 + 8.83205e10i 0.315605 + 0.546644i
\(635\) −1.38462e10 7.99409e9i −0.0851599 0.0491671i
\(636\) 1.51267e11i 0.924517i
\(637\) −8.98684e10 + 2.16886e11i −0.545820 + 1.31726i
\(638\) 1.20516e11 0.727381
\(639\) 3.41800e10 5.92015e10i 0.205007 0.355082i
\(640\) −6.30327e10 + 3.63919e10i −0.375704 + 0.216913i
\(641\) 1.01466e11 + 1.75744e11i 0.601019 + 1.04100i 0.992667 + 0.120880i \(0.0385717\pi\)
−0.391648 + 0.920115i \(0.628095\pi\)
\(642\) 2.45548e10 + 1.41767e10i 0.144543 + 0.0834519i
\(643\) 1.99065e11i 1.16453i 0.812999 + 0.582265i \(0.197833\pi\)
−0.812999 + 0.582265i \(0.802167\pi\)
\(644\) 1.86341e11 + 3.70776e10i 1.08334 + 0.215560i
\(645\) −1.71777e10 −0.0992489
\(646\) 3.67520e9 6.36564e9i 0.0211033 0.0365520i
\(647\) −9.44003e10 + 5.45021e10i −0.538712 + 0.311025i −0.744557 0.667559i \(-0.767339\pi\)
0.205845 + 0.978585i \(0.434006\pi\)
\(648\) 7.55553e9 + 1.30866e10i 0.0428514 + 0.0742208i
\(649\) −4.78656e10 2.76352e10i −0.269802 0.155770i
\(650\) 8.80876e10i 0.493471i
\(651\) 7.15603e10 8.15887e10i 0.398426 0.454262i
\(652\) 1.14578e11 0.634030
\(653\) −4.34249e10 + 7.52141e10i −0.238828 + 0.413663i −0.960378 0.278700i \(-0.910097\pi\)
0.721550 + 0.692362i \(0.243430\pi\)
\(654\) −9.66285e9 + 5.57885e9i −0.0528195 + 0.0304954i
\(655\) 2.79834e10 + 4.84687e10i 0.152032 + 0.263327i
\(656\) 6.92515e10 + 3.99823e10i 0.373950 + 0.215900i
\(657\) 6.01927e10i 0.323060i
\(658\) −4.96134e10 + 1.68380e10i −0.264664 + 0.0898231i
\(659\) −1.49313e11 −0.791689 −0.395845 0.918317i \(-0.629548\pi\)
−0.395845 + 0.918317i \(0.629548\pi\)
\(660\) 2.51885e10 4.36278e10i 0.132748 0.229926i
\(661\) 2.17164e11 1.25380e11i 1.13758 0.656781i 0.191749 0.981444i \(-0.438584\pi\)
0.945830 + 0.324663i \(0.105251\pi\)
\(662\) −2.84061e10 4.92007e10i −0.147904 0.256177i
\(663\) −1.44158e10 8.32298e9i −0.0746080 0.0430750i
\(664\) 1.89136e11i 0.972977i
\(665\) −2.56053e10 7.54461e10i −0.130931 0.385789i
\(666\) −1.36780e10 −0.0695223
\(667\) −1.74659e11 + 3.02519e11i −0.882446 + 1.52844i
\(668\) −5.42724e9 + 3.13342e9i −0.0272567 + 0.0157366i
\(669\) 4.37101e9 + 7.57082e9i 0.0218211 + 0.0377953i
\(670\) −2.68667e10 1.55115e10i −0.133326 0.0769759i
\(671\) 3.19862e10i 0.157788i
\(672\) −8.67887e10 7.61211e10i −0.425585 0.373274i
\(673\) 2.52426e10 0.123048 0.0615240 0.998106i \(-0.480404\pi\)
0.0615240 + 0.998106i \(0.480404\pi\)
\(674\) −1.62365e10 + 2.81225e10i −0.0786780 + 0.136274i
\(675\) −2.82615e10 + 1.63168e10i −0.136138 + 0.0785995i
\(676\) −8.85058e10 1.53296e11i −0.423823 0.734083i
\(677\) 7.78426e10 + 4.49424e10i 0.370564 + 0.213945i 0.673705 0.739001i \(-0.264702\pi\)
−0.303141 + 0.952946i \(0.598035\pi\)
\(678\) 2.12509e10i 0.100568i
\(679\) 7.82131e10 3.93077e11i 0.367960 1.84926i
\(680\) −7.38646e9 −0.0345462
\(681\) 1.76774e10 3.06182e10i 0.0821922 0.142361i
\(682\) −1.08793e11 + 6.28119e10i −0.502881 + 0.290339i
\(683\) 3.85503e10 + 6.67711e10i 0.177152 + 0.306835i 0.940904 0.338674i \(-0.109978\pi\)
−0.763752 + 0.645510i \(0.776645\pi\)
\(684\) 4.93514e10 + 2.84931e10i 0.225463 + 0.130171i
\(685\) 1.87408e10i 0.0851187i
\(686\) −8.41622e10 + 4.14848e10i −0.380033 + 0.187324i
\(687\) −1.60005e11 −0.718301
\(688\) −2.22141e10 + 3.84759e10i −0.0991459 + 0.171726i
\(689\) 5.43116e11 3.13568e11i 2.40999 1.39141i
\(690\) −1.59739e10 2.76675e10i −0.0704715 0.122060i
\(691\) −1.52741e11 8.81853e10i −0.669954 0.386798i 0.126105 0.992017i \(-0.459752\pi\)
−0.796059 + 0.605219i \(0.793086\pi\)
\(692\) 3.31489e11i 1.44559i
\(693\) 9.87415e10 + 1.96473e10i 0.428121 + 0.0851862i
\(694\) −2.99215e10 −0.128987
\(695\) 1.72014e9 2.97938e9i 0.00737269 0.0127699i
\(696\) 1.18641e11 6.84977e10i 0.505591 0.291903i
\(697\) 1.08012e10 + 1.87083e10i 0.0457659 + 0.0792689i
\(698\) −6.03101e10 3.48200e10i −0.254079 0.146692i
\(699\) 1.19592e11i 0.500947i
\(700\) 1.06106e11 1.20975e11i 0.441922 0.503853i
\(701\) 2.37032e11 0.981599 0.490800 0.871272i \(-0.336705\pi\)
0.490800 + 0.871272i \(0.336705\pi\)
\(702\) −1.41178e10 + 2.44527e10i −0.0581324 + 0.100688i
\(703\) −9.91157e10 + 5.72245e10i −0.405808 + 0.234294i
\(704\) −1.25859e10 2.17994e10i −0.0512381 0.0887471i
\(705\) −3.48716e10 2.01331e10i −0.141161 0.0814995i
\(706\) 9.99571e10i 0.402341i
\(707\) −3.24488e11 + 1.10126e11i −1.29874 + 0.440772i
\(708\) −2.83164e10 −0.112695
\(709\) 2.97998e10 5.16148e10i 0.117931 0.204263i −0.801016 0.598642i \(-0.795707\pi\)
0.918948 + 0.394379i \(0.129040\pi\)
\(710\) 4.90865e10 2.83401e10i 0.193165 0.111524i
\(711\) −2.70603e10 4.68699e10i −0.105890 0.183407i
\(712\) −1.87749e11 1.08397e11i −0.730563 0.421790i
\(713\) 3.64124e11i 1.40893i
\(714\) −2.13815e9 6.30007e9i −0.00822707 0.0242411i
\(715\) 2.08858e11 0.799148
\(716\) −1.65900e11 + 2.87348e11i −0.631241 + 1.09334i
\(717\) −2.52499e11 + 1.45781e11i −0.955396 + 0.551598i
\(718\) 2.25470e10 + 3.90525e10i 0.0848380 + 0.146944i
\(719\) −1.65282e11 9.54254e10i −0.618456 0.357066i 0.157811 0.987469i \(-0.449556\pi\)
−0.776268 + 0.630403i \(0.782890\pi\)
\(720\) 1.89270e10i 0.0704292i
\(721\) −1.04400e11 9.15678e10i −0.386331 0.338846i
\(722\) 1.08076e10 0.0397722
\(723\) 1.82582e10 3.16242e10i 0.0668199 0.115735i
\(724\) 1.11574e11 6.44174e10i 0.406078 0.234449i
\(725\) 1.47926e11 + 2.56216e11i 0.535419 + 0.927372i
\(726\) −4.20739e10 2.42914e10i −0.151449 0.0874391i
\(727\) 8.50700e10i 0.304536i 0.988339 + 0.152268i \(0.0486577\pi\)
−0.988339 + 0.152268i \(0.951342\pi\)
\(728\) 6.02856e10 3.02978e11i 0.214629 1.07866i
\(729\) −1.04604e10 −0.0370370
\(730\) −2.49542e10 + 4.32219e10i −0.0878723 + 0.152199i
\(731\) −1.03943e10 + 6.00114e9i −0.0364020 + 0.0210167i
\(732\) 8.19366e9 + 1.41918e10i 0.0285387 + 0.0494304i
\(733\) −8.47822e9 4.89490e9i −0.0293690 0.0169562i 0.485244 0.874379i \(-0.338731\pi\)
−0.514613 + 0.857423i \(0.672064\pi\)
\(734\) 1.24704e11i 0.429633i
\(735\) −6.66208e10 2.76049e10i −0.228276 0.0945881i
\(736\) −3.87331e11 −1.31999
\(737\) 1.64008e11 2.84071e11i 0.555899 0.962846i
\(738\) 3.17338e10 1.83215e10i 0.106978 0.0617640i
\(739\) 1.64891e11 + 2.85599e11i 0.552864 + 0.957588i 0.998066 + 0.0621581i \(0.0197983\pi\)
−0.445203 + 0.895430i \(0.646868\pi\)
\(740\) 4.48902e10 + 2.59174e10i 0.149701 + 0.0864299i
\(741\) 2.36258e11i 0.783636i
\(742\) 2.45833e11 + 4.89150e10i 0.811006 + 0.161371i
\(743\) −3.93745e11 −1.29199 −0.645996 0.763341i \(-0.723558\pi\)
−0.645996 + 0.763341i \(0.723558\pi\)
\(744\) −7.14008e10 + 1.23670e11i −0.233030 + 0.403620i
\(745\) 2.06679e10 1.19326e10i 0.0670922 0.0387357i
\(746\) −8.98937e10 1.55701e11i −0.290251 0.502730i
\(747\) 1.13385e11 + 6.54631e10i 0.364145 + 0.210239i
\(748\) 3.51992e10i 0.112441i
\(749\) 1.41595e11 1.61438e11i 0.449905 0.512954i
\(750\) −6.01834e10 −0.190209
\(751\) 2.67018e11 4.62489e11i 0.839423 1.45392i −0.0509539 0.998701i \(-0.516226\pi\)
0.890377 0.455223i \(-0.150441\pi\)
\(752\) −9.01916e10 + 5.20721e10i −0.282030 + 0.162830i
\(753\) 7.37315e10 + 1.27707e11i 0.229336 + 0.397222i
\(754\) 2.21686e11 + 1.27990e11i 0.685887 + 0.395997i
\(755\) 1.49468e11i 0.460004i
\(756\) 4.88431e10 1.65766e10i 0.149526 0.0507468i
\(757\) −3.48900e11 −1.06247 −0.531236 0.847224i \(-0.678272\pi\)
−0.531236 + 0.847224i \(0.678272\pi\)
\(758\) −6.45122e10 + 1.11738e11i −0.195418 + 0.338474i
\(759\) 2.92538e11 1.68897e11i 0.881486 0.508926i
\(760\) 5.24185e10 + 9.07915e10i 0.157120 + 0.272139i
\(761\) 1.24626e11 + 7.19527e10i 0.371594 + 0.214540i 0.674155 0.738590i \(-0.264508\pi\)
−0.302561 + 0.953130i \(0.597841\pi\)
\(762\) 1.89490e10i 0.0562039i
\(763\) 2.71577e10 + 8.00201e10i 0.0801298 + 0.236103i
\(764\) −1.26222e11 −0.370476
\(765\) 2.55657e9 4.42811e9i 0.00746470 0.0129292i
\(766\) 8.81833e10 5.09127e10i 0.256136 0.147880i
\(767\) −5.86984e10 1.01669e11i −0.169607 0.293769i
\(768\) 6.10936e10 + 3.52724e10i 0.175611 + 0.101389i
\(769\) 2.83112e11i 0.809567i 0.914413 + 0.404783i \(0.132653\pi\)
−0.914413 + 0.404783i \(0.867347\pi\)
\(770\) 6.27570e10 + 5.50433e10i 0.178525 + 0.156582i
\(771\) 3.55303e11 1.00550
\(772\) −1.95066e11 + 3.37864e11i −0.549177 + 0.951203i
\(773\) 1.18891e11 6.86416e10i 0.332989 0.192251i −0.324178 0.945996i \(-0.605088\pi\)
0.657167 + 0.753745i \(0.271754\pi\)
\(774\) 1.01794e10 + 1.76312e10i 0.0283634 + 0.0491268i
\(775\) −2.67075e11 1.54196e11i −0.740333 0.427431i
\(776\) 5.27368e11i 1.45434i
\(777\) −2.02157e10 + 1.01599e11i −0.0554633 + 0.278743i
\(778\) 1.62211e11 0.442754
\(779\) 1.53303e11 2.65529e11i 0.416296 0.721045i
\(780\) 9.26673e10 5.35015e10i 0.250350 0.144540i
\(781\) 2.99649e11 + 5.19008e11i 0.805395 + 1.39499i
\(782\) −1.93317e10 1.11612e10i −0.0516943 0.0298457i
\(783\) 9.48325e10i 0.252296i
\(784\) −1.47985e11 + 1.13524e11i −0.391701 + 0.300485i
\(785\) −2.88485e11 −0.759706
\(786\) 3.31656e10 5.74444e10i 0.0868955 0.150507i
\(787\) 2.96173e11 1.70995e11i 0.772051 0.445744i −0.0615545 0.998104i \(-0.519606\pi\)
0.833606 + 0.552360i \(0.186272\pi\)
\(788\) 7.43786e10 + 1.28827e11i 0.192905 + 0.334121i
\(789\) −2.84589e11 1.64308e11i −0.734363 0.423985i
\(790\) 4.48737e10i 0.115208i
\(791\) −1.57850e11 3.14084e10i −0.403216 0.0802307i
\(792\) −1.32476e11 −0.336694
\(793\) −3.39701e10 + 5.88379e10i −0.0859020 + 0.148787i
\(794\) −7.51356e10 + 4.33795e10i −0.189044 + 0.109145i
\(795\) 9.63187e10 + 1.66829e11i 0.241125 + 0.417641i
\(796\) 3.19711e11 + 1.84585e11i 0.796353 + 0.459775i
\(797\) 5.90299e11i 1.46298i −0.681852 0.731491i \(-0.738825\pi\)
0.681852 0.731491i \(-0.261175\pi\)
\(798\) −6.22645e10 + 7.09902e10i −0.153543 + 0.175060i
\(799\) −2.81346e10 −0.0690325
\(800\) −1.64024e11 + 2.84097e11i −0.400448 + 0.693596i
\(801\) 1.29966e11 7.50357e10i 0.315718 0.182280i
\(802\) −5.76203e10 9.98013e10i −0.139277 0.241234i
\(803\) −4.57000e11 2.63849e11i −1.09914 0.634590i
\(804\) 1.68051e11i 0.402177i
\(805\) −2.29121e11 + 7.77602e10i −0.545608 + 0.185171i
\(806\) −2.66830e11 −0.632259
\(807\) −1.92753e11 + 3.33857e11i −0.454471 + 0.787167i
\(808\) 3.90488e11 2.25448e11i 0.916140 0.528934i
\(809\) 4.80422e10 + 8.32115e10i 0.112158 + 0.194263i 0.916640 0.399714i \(-0.130891\pi\)
−0.804482 + 0.593976i \(0.797557\pi\)
\(810\) −7.51115e9 4.33656e9i −0.0174488 0.0100741i
\(811\) 2.61119e11i 0.603608i 0.953370 + 0.301804i \(0.0975888\pi\)
−0.953370 + 0.301804i \(0.902411\pi\)
\(812\) −1.50282e11 4.42806e11i −0.345687 1.01857i
\(813\) 3.23579e11 0.740658
\(814\) 5.99560e10 1.03847e11i 0.136564 0.236535i
\(815\) −1.26365e11 + 7.29571e10i −0.286416 + 0.165363i
\(816\) −6.61229e9 1.14528e10i −0.0149139 0.0258316i
\(817\) 1.47527e11 + 8.51750e10i 0.331119 + 0.191172i
\(818\) 3.38123e11i 0.755199i
\(819\) 1.60767e11 + 1.41006e11i 0.357322 + 0.313403i
\(820\) −1.38864e11 −0.307139
\(821\) 1.69853e11 2.94194e11i 0.373853 0.647532i −0.616302 0.787510i \(-0.711370\pi\)
0.990155 + 0.139978i \(0.0447032\pi\)
\(822\) −1.92356e10 + 1.11057e10i −0.0421325 + 0.0243252i
\(823\) −6.89538e10 1.19432e11i −0.150300 0.260327i 0.781038 0.624484i \(-0.214691\pi\)
−0.931338 + 0.364157i \(0.881357\pi\)
\(824\) 1.58247e11 + 9.13638e10i 0.343262 + 0.198183i
\(825\) 2.86092e11i 0.617576i
\(826\) 9.15664e9 4.60187e10i 0.0196705 0.0988584i
\(827\) 1.03179e11 0.220582 0.110291 0.993899i \(-0.464822\pi\)
0.110291 + 0.993899i \(0.464822\pi\)
\(828\) 8.65300e10 1.49874e11i 0.184096 0.318864i
\(829\) −2.61446e11 + 1.50946e11i −0.553559 + 0.319598i −0.750556 0.660806i \(-0.770214\pi\)
0.196997 + 0.980404i \(0.436881\pi\)
\(830\) 5.42782e10 + 9.40127e10i 0.114370 + 0.198095i
\(831\) −2.29593e11 1.32556e11i −0.481454 0.277968i
\(832\) 5.34659e10i 0.111579i
\(833\) −4.99564e10 + 6.57060e9i −0.103756 + 0.0136466i
\(834\) −4.07739e9 −0.00842787
\(835\) 3.99039e9 6.91156e9i 0.00820860 0.0142177i
\(836\) −4.32654e11 + 2.49793e11i −0.885760 + 0.511394i
\(837\) −4.94259e10 8.56082e10i −0.100705 0.174427i
\(838\) −1.88786e11 1.08996e11i −0.382820 0.221021i
\(839\) 4.99916e11i 1.00890i −0.863440 0.504451i \(-0.831695\pi\)
0.863440 0.504451i \(-0.168305\pi\)
\(840\) 9.30658e10 + 1.85179e10i 0.186927 + 0.0371942i
\(841\) 3.59495e11 0.718636
\(842\) 1.93681e11 3.35466e11i 0.385336 0.667421i
\(843\) −9.71808e8 + 5.61073e8i −0.00192429 + 0.00111099i
\(844\) −3.60441e11 6.24302e11i −0.710337 1.23034i
\(845\) 1.95222e11 + 1.12712e11i 0.382915 + 0.221076i
\(846\) 4.77231e10i 0.0931637i
\(847\) −2.42618e11 + 2.76619e11i −0.471400 + 0.537462i
\(848\) 4.98236e11 0.963499
\(849\) −2.06577e11 + 3.57802e11i −0.397604 + 0.688671i
\(850\) −1.63728e10 + 9.45286e9i −0.0313652 + 0.0181087i
\(851\) 1.73784e11 + 3.01003e11i 0.331353 + 0.573921i
\(852\) 2.65900e11 + 1.53518e11i 0.504615 + 0.291340i
\(853\) 6.64273e11i 1.25473i −0.778725 0.627365i \(-0.784133\pi\)
0.778725 0.627365i \(-0.215867\pi\)
\(854\) −2.57136e10 + 8.72681e9i −0.0483427 + 0.0164068i
\(855\) −7.25715e10 −0.135801
\(856\) −1.41280e11 + 2.44703e11i −0.263138 + 0.455769i
\(857\) −3.73865e11 + 2.15851e11i −0.693092 + 0.400157i −0.804769 0.593587i \(-0.797711\pi\)
0.111677 + 0.993745i \(0.464378\pi\)
\(858\) −1.23768e11 2.14372e11i −0.228381 0.395567i
\(859\) −3.15583e11 1.82202e11i −0.579618 0.334642i 0.181364 0.983416i \(-0.441949\pi\)
−0.760981 + 0.648774i \(0.775282\pi\)
\(860\) 7.71527e10i 0.141045i
\(861\) −8.91884e10 2.62794e11i −0.162292 0.478193i
\(862\) −2.01048e11 −0.364143
\(863\) 3.50506e11 6.07094e11i 0.631906 1.09449i −0.355256 0.934769i \(-0.615606\pi\)
0.987162 0.159724i \(-0.0510604\pi\)
\(864\) −9.10644e10 + 5.25760e10i −0.163416 + 0.0943480i
\(865\) −2.11075e11 3.65592e11i −0.377026 0.653029i
\(866\) 1.93241e11 + 1.11568e11i 0.343580 + 0.198366i
\(867\) 3.22651e11i 0.571027i
\(868\) 3.66451e11 + 3.21409e11i 0.645561 + 0.566212i
\(869\) 4.74465e11 0.832004
\(870\) −3.93148e10 + 6.80953e10i −0.0686245 + 0.118861i
\(871\) 6.03378e11 3.48361e11i 1.04838 0.605280i
\(872\) −5.55965e10 9.62960e10i −0.0961571 0.166549i
\(873\) −3.16152e11 1.82530e11i −0.544301 0.314252i
\(874\) 3.16823e11i 0.542965i
\(875\) −8.89498e10 + 4.47036e11i −0.151744 + 0.762624i
\(876\) −2.70352e11 −0.459107
\(877\) −2.68814e11 + 4.65600e11i −0.454416 + 0.787072i −0.998654 0.0518586i \(-0.983486\pi\)
0.544238 + 0.838931i \(0.316819\pi\)
\(878\) −3.90582e11 + 2.25503e11i −0.657255 + 0.379467i
\(879\) −1.88702e11 3.26842e11i −0.316098 0.547497i
\(880\) 1.43699e11 + 8.29649e10i 0.239621 + 0.138345i
\(881\) 1.18727e12i 1.97081i 0.170220 + 0.985406i \(0.445552\pi\)
−0.170220 + 0.985406i \(0.554448\pi\)
\(882\) 1.11453e10 + 8.47382e10i 0.0184170 + 0.140025i
\(883\) 1.03398e11 0.170086 0.0850429 0.996377i \(-0.472897\pi\)
0.0850429 + 0.996377i \(0.472897\pi\)
\(884\) 3.73822e10 6.47479e10i 0.0612148 0.106027i
\(885\) 3.12295e10 1.80304e10i 0.0509088 0.0293922i
\(886\) −2.33834e11 4.05012e11i −0.379465 0.657253i
\(887\) 7.38676e11 + 4.26475e11i 1.19333 + 0.688967i 0.959059 0.283205i \(-0.0913977\pi\)
0.234267 + 0.972172i \(0.424731\pi\)
\(888\) 1.36309e11i 0.219216i
\(889\) 1.40751e11 + 2.80062e10i 0.225344 + 0.0448381i
\(890\) 1.24431e11 0.198320
\(891\) 4.58520e10 7.94179e10i 0.0727524 0.126011i
\(892\) −3.40039e10 + 1.96322e10i −0.0537118 + 0.0310105i
\(893\) 1.99659e11 + 3.45819e11i 0.313966 + 0.543805i
\(894\) −2.44954e10 1.41424e10i −0.0383472 0.0221398i
\(895\) 4.22546e11i 0.658540i
\(896\) 4.30788e11 4.91158e11i 0.668392 0.762060i
\(897\) 7.17489e11 1.10827
\(898\) 1.39504e11 2.41628e11i 0.214526 0.371571i
\(899\) −7.76115e11 + 4.48090e11i −1.18819 + 0.686004i
\(900\) −7.32860e10 1.26935e11i −0.111699 0.193469i
\(901\) 1.16566e11 + 6.72992e10i 0.176877 + 0.102120i
\(902\) 3.21242e11i 0.485296i
\(903\) 1.46008e11 4.95529e10i 0.219596 0.0745278i
\(904\) 2.11778e11 0.317108
\(905\) −8.20353e10 + 1.42089e11i −0.122294 + 0.211820i
\(906\) 1.53415e11 8.85739e10i 0.227695 0.131460i
\(907\) 1.20799e11 + 2.09230e11i 0.178498 + 0.309168i 0.941366 0.337386i \(-0.109543\pi\)
−0.762868 + 0.646554i \(0.776209\pi\)
\(908\) 1.37520e11 + 7.93973e10i 0.202313 + 0.116805i
\(909\) 3.12125e11i 0.457165i
\(910\) 5.69828e10 + 1.67900e11i 0.0830956 + 0.244841i
\(911\) −3.40518e11 −0.494386 −0.247193 0.968966i \(-0.579508\pi\)
−0.247193 + 0.968966i \(0.579508\pi\)
\(912\) −9.38491e10 + 1.62551e11i −0.135660 + 0.234969i
\(913\) −9.94028e11 + 5.73902e11i −1.43059 + 0.825952i
\(914\) −1.10587e11 1.91543e11i −0.158460 0.274461i
\(915\) −1.80732e10 1.04346e10i −0.0257841 0.0148864i
\(916\) 7.18654e11i 1.02079i
\(917\) −3.77674e11 3.31252e11i −0.534120 0.468470i
\(918\) −6.06003e9 −0.00853305
\(919\) −1.70782e11 + 2.95802e11i −0.239430 + 0.414705i −0.960551 0.278104i \(-0.910294\pi\)
0.721121 + 0.692809i \(0.243627\pi\)
\(920\) 2.75723e11 1.59189e11i 0.384877 0.222209i
\(921\) −2.35990e11 4.08746e11i −0.327985 0.568087i
\(922\) −3.08913e10 1.78351e10i −0.0427477 0.0246804i
\(923\) 1.27293e12i 1.75388i
\(924\) −8.82446e10 + 4.43492e11i −0.121060 + 0.608413i
\(925\) 2.94370e11 0.402093
\(926\) 1.73708e11 3.00870e11i 0.236252 0.409200i
\(927\) −1.09543e11 + 6.32449e10i −0.148343 + 0.0856459i
\(928\) 4.76649e11 + 8.25580e11i 0.642698 + 1.11319i
\(929\) 7.66008e11 + 4.42255e11i 1.02842 + 0.593759i 0.916532 0.399962i \(-0.130977\pi\)
0.111889 + 0.993721i \(0.464310\pi\)
\(930\) 8.19623e10i 0.109568i
\(931\) 4.35282e11 + 5.67416e11i 0.579392 + 0.755271i
\(932\) 5.37139e11 0.711907
\(933\) −1.65619e11 + 2.86861e11i −0.218567 + 0.378569i
\(934\) −3.35503e11 + 1.93703e11i −0.440868 + 0.254535i
\(935\) 2.24130e10 + 3.88204e10i 0.0293260 + 0.0507941i
\(936\) −2.43686e11 1.40692e11i −0.317487 0.183301i
\(937\) 4.85369e11i 0.629671i −0.949146 0.314836i \(-0.898051\pi\)
0.949146 0.314836i \(-0.101949\pi\)
\(938\) 2.73110e11 + 5.43424e10i 0.352798 + 0.0701985i
\(939\) −3.65268e11 −0.469840
\(940\) 9.04269e10 1.56624e11i 0.115821 0.200607i
\(941\) −7.31010e11 + 4.22049e11i −0.932320 + 0.538275i −0.887545 0.460722i \(-0.847591\pi\)
−0.0447755 + 0.998997i \(0.514257\pi\)
\(942\) 1.70955e11 + 2.96102e11i 0.217109 + 0.376043i
\(943\) −8.06381e11 4.65564e11i −1.01975 0.588752i
\(944\) 9.32672e10i 0.117447i
\(945\) −4.33129e10 + 4.93827e10i −0.0543113 + 0.0619224i
\(946\) −1.78481e11 −0.222858
\(947\) 3.11821e11 5.40090e11i 0.387709 0.671531i −0.604432 0.796656i \(-0.706600\pi\)
0.992141 + 0.125126i \(0.0399334\pi\)
\(948\) 2.10513e11 1.21540e11i 0.260643 0.150482i
\(949\) −5.60426e11 9.70687e11i −0.690961 1.19678i
\(950\) 2.32382e11 + 1.34166e11i 0.285304 + 0.164720i
\(951\) 7.03534e11i 0.860128i
\(952\) 6.27838e10 2.13079e10i 0.0764364 0.0259414i
\(953\) −5.74523e11 −0.696524 −0.348262 0.937397i \(-0.613228\pi\)
−0.348262 + 0.937397i \(0.613228\pi\)
\(954\) 1.14156e11 1.97723e11i 0.137817 0.238707i
\(955\) 1.39207e11 8.03713e10i 0.167359 0.0966246i
\(956\) −6.54765e11 1.13409e12i −0.783888 1.35773i
\(957\) −7.19995e11 4.15689e11i −0.858384 0.495588i
\(958\) 9.57653e9i 0.0113696i
\(959\) 5.40619e10 + 1.59294e11i 0.0639171 + 0.188332i
\(960\) 1.64231e10 0.0193362
\(961\) 4.06366e10 7.03846e10i 0.0476457 0.0825247i
\(962\) 2.20575e11 1.27349e11i 0.257547 0.148695i
\(963\) −9.77982e10 1.69391e11i −0.113717 0.196964i
\(964\) 1.42038e11 + 8.20059e10i 0.164474 + 0.0949592i
\(965\) 4.96831e11i 0.572927i
\(966\) 2.15589e11 + 1.89090e11i 0.247581 + 0.217150i
\(967\) 1.02285e12 1.16978 0.584892 0.811111i \(-0.301137\pi\)
0.584892 + 0.811111i \(0.301137\pi\)
\(968\) 2.42078e11 4.19291e11i 0.275711 0.477545i
\(969\) −4.39133e10 + 2.53533e10i −0.0498082 + 0.0287568i
\(970\) −1.51344e11 2.62135e11i −0.170953 0.296100i
\(971\) 1.43260e12 + 8.27112e11i 1.61157 + 0.930438i 0.989008 + 0.147864i \(0.0472397\pi\)
0.622558 + 0.782574i \(0.286094\pi\)
\(972\) 4.69821e10i 0.0526341i
\(973\) −6.02629e9 + 3.02864e10i −0.00672355 + 0.0337907i
\(974\) 2.78682e11 0.309651
\(975\) 3.03836e11 5.26259e11i 0.336218 0.582346i
\(976\) −4.67444e10 + 2.69879e10i −0.0515146 + 0.0297420i
\(977\) −7.08767e11 1.22762e12i −0.777902 1.34737i −0.933149 0.359490i \(-0.882951\pi\)
0.155247 0.987876i \(-0.450383\pi\)
\(978\) 1.49767e11 + 8.64678e10i 0.163704 + 0.0945146i
\(979\) 1.31565e12i 1.43222i
\(980\) 1.23986e11 2.99224e11i 0.134421 0.324408i
\(981\) 7.69713e10 0.0831099
\(982\) −2.47127e10 + 4.28037e10i −0.0265751 + 0.0460294i
\(983\) 6.10227e11 3.52315e11i 0.653548 0.377326i −0.136266 0.990672i \(-0.543510\pi\)
0.789814 + 0.613346i \(0.210177\pi\)
\(984\) 1.82584e11 + 3.16246e11i 0.194753 + 0.337322i
\(985\) −1.64061e11 9.47207e10i −0.174285 0.100624i
\(986\) 5.49396e10i 0.0581270i
\(987\) 3.54482e11 + 7.05337e10i 0.373530 + 0.0743238i
\(988\) −1.06114e12 −1.11364
\(989\) 2.58666e11 4.48023e11i 0.270368 0.468291i
\(990\) 6.58488e10 3.80178e10i 0.0685499 0.0395773i
\(991\) −6.48285e11 1.12286e12i −0.672158 1.16421i −0.977291 0.211902i \(-0.932034\pi\)
0.305133 0.952310i \(-0.401299\pi\)
\(992\) −8.60571e11 4.96851e11i −0.888669 0.513074i
\(993\) 3.91918e11i 0.403086i
\(994\) −3.35474e11 + 3.82487e11i −0.343648 + 0.391806i
\(995\) −4.70137e11 −0.479658
\(996\) −2.94024e11 + 5.09264e11i −0.298776 + 0.517495i
\(997\) 1.85093e11 1.06863e11i 0.187331 0.108155i −0.403402 0.915023i \(-0.632172\pi\)
0.590732 + 0.806868i \(0.298839\pi\)
\(998\) 1.12734e11 + 1.95260e11i 0.113640 + 0.196830i
\(999\) 8.17158e10 + 4.71786e10i 0.0820435 + 0.0473678i
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 21.9.f.b.19.3 yes 12
3.2 odd 2 63.9.m.d.19.4 12
7.2 even 3 147.9.d.b.97.8 12
7.3 odd 6 inner 21.9.f.b.10.3 12
7.5 odd 6 147.9.d.b.97.7 12
21.17 even 6 63.9.m.d.10.4 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.9.f.b.10.3 12 7.3 odd 6 inner
21.9.f.b.19.3 yes 12 1.1 even 1 trivial
63.9.m.d.10.4 12 21.17 even 6
63.9.m.d.19.4 12 3.2 odd 2
147.9.d.b.97.7 12 7.5 odd 6
147.9.d.b.97.8 12 7.2 even 3