Properties

Label 21.7.b.a.8.4
Level $21$
Weight $7$
Character 21.8
Analytic conductor $4.831$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [21,7,Mod(8,21)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(21, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("21.8");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 21.b (of order \(2\), degree \(1\), 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: \(4.83113575602\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 642x^{10} + 155265x^{8} + 17813036x^{6} + 1003321428x^{4} + 26369892864x^{2} + 256461520896 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{8}\cdot 7^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 8.4
Root \(-7.64160i\) of defining polynomial
Character \(\chi\) \(=\) 21.8
Dual form 21.7.b.a.8.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-7.64160i q^{2} +(-4.69404 + 26.5888i) q^{3} +5.60598 q^{4} -237.150i q^{5} +(203.181 + 35.8700i) q^{6} +129.642 q^{7} -531.901i q^{8} +(-684.932 - 249.618i) q^{9} +O(q^{10})\) \(q-7.64160i q^{2} +(-4.69404 + 26.5888i) q^{3} +5.60598 q^{4} -237.150i q^{5} +(203.181 + 35.8700i) q^{6} +129.642 q^{7} -531.901i q^{8} +(-684.932 - 249.618i) q^{9} -1812.21 q^{10} -371.126i q^{11} +(-26.3147 + 149.056i) q^{12} +1997.63 q^{13} -990.671i q^{14} +(6305.54 + 1113.19i) q^{15} -3705.79 q^{16} +1254.26i q^{17} +(-1907.48 + 5233.97i) q^{18} +3949.99 q^{19} -1329.46i q^{20} +(-608.544 + 3447.02i) q^{21} -2836.00 q^{22} +17116.2i q^{23} +(14142.6 + 2496.77i) q^{24} -40615.1 q^{25} -15265.1i q^{26} +(9852.16 - 17039.8i) q^{27} +726.769 q^{28} +25218.4i q^{29} +(8506.57 - 48184.4i) q^{30} +28673.2 q^{31} -5723.49i q^{32} +(9867.81 + 1742.08i) q^{33} +9584.53 q^{34} -30744.6i q^{35} +(-3839.71 - 1399.35i) q^{36} -29150.0 q^{37} -30184.2i q^{38} +(-9376.96 + 53114.6i) q^{39} -126140. q^{40} +3976.24i q^{41} +(26340.8 + 4650.25i) q^{42} +84540.1 q^{43} -2080.52i q^{44} +(-59197.0 + 162432. i) q^{45} +130795. q^{46} -73138.8i q^{47} +(17395.1 - 98532.6i) q^{48} +16807.0 q^{49} +310365. i q^{50} +(-33349.2 - 5887.54i) q^{51} +11198.7 q^{52} -40559.3i q^{53} +(-130211. - 75286.2i) q^{54} -88012.6 q^{55} -68956.6i q^{56} +(-18541.4 + 105026. i) q^{57} +192709. q^{58} +37762.5i q^{59} +(35348.7 + 6240.53i) q^{60} +403748. q^{61} -219109. i q^{62} +(-88795.8 - 32361.0i) q^{63} -280907. q^{64} -473738. i q^{65} +(13312.3 - 75405.8i) q^{66} -1923.98 q^{67} +7031.33i q^{68} +(-455100. - 80344.2i) q^{69} -234938. q^{70} +337786. i q^{71} +(-132772. + 364316. i) q^{72} +169672. q^{73} +222753. i q^{74} +(190649. - 1.07991e6i) q^{75} +22143.6 q^{76} -48113.5i q^{77} +(405881. + 71655.0i) q^{78} -158380. q^{79} +878828. i q^{80} +(406822. + 341943. i) q^{81} +30384.8 q^{82} -32502.2i q^{83} +(-3411.48 + 19323.9i) q^{84} +297447. q^{85} -646021. i q^{86} +(-670528. - 118376. i) q^{87} -197402. q^{88} +1.05963e6i q^{89} +(1.24124e6 + 452360. i) q^{90} +258976. q^{91} +95953.0i q^{92} +(-134593. + 762388. i) q^{93} -558897. q^{94} -936741. i q^{95} +(152181. + 26866.3i) q^{96} -748094. q^{97} -128432. i q^{98} +(-92639.8 + 254196. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 52 q^{3} - 516 q^{4} + 350 q^{6} - 644 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 52 q^{3} - 516 q^{4} + 350 q^{6} - 644 q^{9} - 1092 q^{10} - 1726 q^{12} + 384 q^{13} - 632 q^{15} + 5892 q^{16} - 40 q^{18} + 11304 q^{19} - 5488 q^{21} + 15312 q^{22} + 12138 q^{24} - 77292 q^{25} + 114796 q^{27} + 41160 q^{28} - 101908 q^{30} - 9360 q^{31} - 65744 q^{33} - 169008 q^{34} - 195652 q^{36} + 212016 q^{37} + 159544 q^{39} + 196644 q^{40} - 37730 q^{42} + 28080 q^{43} - 4760 q^{45} - 418512 q^{46} + 865742 q^{48} + 201684 q^{49} - 371880 q^{51} - 138300 q^{52} - 254170 q^{54} - 732144 q^{55} - 440624 q^{57} + 1164240 q^{58} + 677660 q^{60} + 926736 q^{61} + 2744 q^{63} - 1380108 q^{64} - 1414588 q^{66} - 223104 q^{67} + 153048 q^{69} - 382788 q^{70} - 540192 q^{72} + 600984 q^{73} + 594716 q^{75} + 604596 q^{76} + 1866140 q^{78} - 276864 q^{79} + 617596 q^{81} + 1138200 q^{82} + 1398754 q^{84} - 3002472 q^{85} - 3372824 q^{87} - 1599048 q^{88} - 788032 q^{90} - 1243032 q^{91} + 408168 q^{93} + 8059296 q^{94} - 1141658 q^{96} + 1621416 q^{97} + 5211904 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(8\) \(10\)
\(\chi(n)\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.64160i 0.955200i −0.878577 0.477600i \(-0.841507\pi\)
0.878577 0.477600i \(-0.158493\pi\)
\(3\) −4.69404 + 26.5888i −0.173853 + 0.984772i
\(4\) 5.60598 0.0875934
\(5\) 237.150i 1.89720i −0.316477 0.948600i \(-0.602500\pi\)
0.316477 0.948600i \(-0.397500\pi\)
\(6\) 203.181 + 35.8700i 0.940654 + 0.166065i
\(7\) 129.642 0.377964
\(8\) 531.901i 1.03887i
\(9\) −684.932 249.618i −0.939550 0.342412i
\(10\) −1812.21 −1.81221
\(11\) 371.126i 0.278833i −0.990234 0.139416i \(-0.955477\pi\)
0.990234 0.139416i \(-0.0445226\pi\)
\(12\) −26.3147 + 149.056i −0.0152284 + 0.0862595i
\(13\) 1997.63 0.909253 0.454627 0.890682i \(-0.349773\pi\)
0.454627 + 0.890682i \(0.349773\pi\)
\(14\) 990.671i 0.361032i
\(15\) 6305.54 + 1113.19i 1.86831 + 0.329835i
\(16\) −3705.79 −0.904734
\(17\) 1254.26i 0.255294i 0.991820 + 0.127647i \(0.0407424\pi\)
−0.991820 + 0.127647i \(0.959258\pi\)
\(18\) −1907.48 + 5233.97i −0.327072 + 0.897458i
\(19\) 3949.99 0.575884 0.287942 0.957648i \(-0.407029\pi\)
0.287942 + 0.957648i \(0.407029\pi\)
\(20\) 1329.46i 0.166182i
\(21\) −608.544 + 3447.02i −0.0657104 + 0.372209i
\(22\) −2836.00 −0.266341
\(23\) 17116.2i 1.40677i 0.710808 + 0.703386i \(0.248330\pi\)
−0.710808 + 0.703386i \(0.751670\pi\)
\(24\) 14142.6 + 2496.77i 1.02305 + 0.180611i
\(25\) −40615.1 −2.59937
\(26\) 15265.1i 0.868519i
\(27\) 9852.16 17039.8i 0.500541 0.865713i
\(28\) 726.769 0.0331072
\(29\) 25218.4i 1.03401i 0.855983 + 0.517003i \(0.172953\pi\)
−0.855983 + 0.517003i \(0.827047\pi\)
\(30\) 8506.57 48184.4i 0.315058 1.78461i
\(31\) 28673.2 0.962480 0.481240 0.876589i \(-0.340187\pi\)
0.481240 + 0.876589i \(0.340187\pi\)
\(32\) 5723.49i 0.174667i
\(33\) 9867.81 + 1742.08i 0.274586 + 0.0484760i
\(34\) 9584.53 0.243856
\(35\) 30744.6i 0.717074i
\(36\) −3839.71 1399.35i −0.0822983 0.0299930i
\(37\) −29150.0 −0.575484 −0.287742 0.957708i \(-0.592905\pi\)
−0.287742 + 0.957708i \(0.592905\pi\)
\(38\) 30184.2i 0.550085i
\(39\) −9376.96 + 53114.6i −0.158077 + 0.895407i
\(40\) −126140. −1.97094
\(41\) 3976.24i 0.0576927i 0.999584 + 0.0288463i \(0.00918335\pi\)
−0.999584 + 0.0288463i \(0.990817\pi\)
\(42\) 26340.8 + 4650.25i 0.355534 + 0.0627666i
\(43\) 84540.1 1.06330 0.531652 0.846963i \(-0.321572\pi\)
0.531652 + 0.846963i \(0.321572\pi\)
\(44\) 2080.52i 0.0244239i
\(45\) −59197.0 + 162432.i −0.649624 + 1.78251i
\(46\) 130795. 1.34375
\(47\) 73138.8i 0.704457i −0.935914 0.352228i \(-0.885424\pi\)
0.935914 0.352228i \(-0.114576\pi\)
\(48\) 17395.1 98532.6i 0.157291 0.890956i
\(49\) 16807.0 0.142857
\(50\) 310365.i 2.48292i
\(51\) −33349.2 5887.54i −0.251406 0.0443837i
\(52\) 11198.7 0.0796446
\(53\) 40559.3i 0.272435i −0.990679 0.136218i \(-0.956505\pi\)
0.990679 0.136218i \(-0.0434946\pi\)
\(54\) −130211. 75286.2i −0.826928 0.478117i
\(55\) −88012.6 −0.529001
\(56\) 68956.6i 0.392656i
\(57\) −18541.4 + 105026.i −0.100120 + 0.567115i
\(58\) 192709. 0.987683
\(59\) 37762.5i 0.183867i 0.995765 + 0.0919336i \(0.0293047\pi\)
−0.995765 + 0.0919336i \(0.970695\pi\)
\(60\) 35348.7 + 6240.53i 0.163651 + 0.0288913i
\(61\) 403748. 1.77877 0.889387 0.457154i \(-0.151131\pi\)
0.889387 + 0.457154i \(0.151131\pi\)
\(62\) 219109.i 0.919360i
\(63\) −88795.8 32361.0i −0.355117 0.129420i
\(64\) −280907. −1.07158
\(65\) 473738.i 1.72504i
\(66\) 13312.3 75405.8i 0.0463043 0.262285i
\(67\) −1923.98 −0.00639701 −0.00319850 0.999995i \(-0.501018\pi\)
−0.00319850 + 0.999995i \(0.501018\pi\)
\(68\) 7031.33i 0.0223620i
\(69\) −455100. 80344.2i −1.38535 0.244572i
\(70\) −234938. −0.684949
\(71\) 337786.i 0.943772i 0.881660 + 0.471886i \(0.156427\pi\)
−0.881660 + 0.471886i \(0.843573\pi\)
\(72\) −132772. + 364316.i −0.355721 + 0.976069i
\(73\) 169672. 0.436155 0.218077 0.975931i \(-0.430021\pi\)
0.218077 + 0.975931i \(0.430021\pi\)
\(74\) 222753.i 0.549702i
\(75\) 190649. 1.07991e6i 0.451909 2.55978i
\(76\) 22143.6 0.0504437
\(77\) 48113.5i 0.105389i
\(78\) 405881. + 71655.0i 0.855292 + 0.150995i
\(79\) −158380. −0.321233 −0.160617 0.987017i \(-0.551348\pi\)
−0.160617 + 0.987017i \(0.551348\pi\)
\(80\) 878828.i 1.71646i
\(81\) 406822. + 341943.i 0.765508 + 0.643426i
\(82\) 30384.8 0.0551081
\(83\) 32502.2i 0.0568432i −0.999596 0.0284216i \(-0.990952\pi\)
0.999596 0.0284216i \(-0.00904810\pi\)
\(84\) −3411.48 + 19323.9i −0.00575580 + 0.0326030i
\(85\) 297447. 0.484343
\(86\) 646021.i 1.01567i
\(87\) −670528. 118376.i −1.01826 0.179766i
\(88\) −197402. −0.289670
\(89\) 1.05963e6i 1.50308i 0.659685 + 0.751542i \(0.270690\pi\)
−0.659685 + 0.751542i \(0.729310\pi\)
\(90\) 1.24124e6 + 452360.i 1.70266 + 0.620521i
\(91\) 258976. 0.343665
\(92\) 95953.0i 0.123224i
\(93\) −134593. + 762388.i −0.167330 + 0.947822i
\(94\) −558897. −0.672897
\(95\) 936741.i 1.09257i
\(96\) 152181. + 26866.3i 0.172007 + 0.0303665i
\(97\) −748094. −0.819673 −0.409837 0.912159i \(-0.634414\pi\)
−0.409837 + 0.912159i \(0.634414\pi\)
\(98\) 128432.i 0.136457i
\(99\) −92639.8 + 254196.i −0.0954756 + 0.261977i
\(100\) −227687. −0.227687
\(101\) 896754.i 0.870381i −0.900338 0.435190i \(-0.856681\pi\)
0.900338 0.435190i \(-0.143319\pi\)
\(102\) −44990.2 + 254841.i −0.0423953 + 0.240143i
\(103\) −1.29201e6 −1.18237 −0.591185 0.806536i \(-0.701340\pi\)
−0.591185 + 0.806536i \(0.701340\pi\)
\(104\) 1.06254e6i 0.944595i
\(105\) 817462. + 144316.i 0.706154 + 0.124666i
\(106\) −309938. −0.260230
\(107\) 78533.2i 0.0641065i −0.999486 0.0320532i \(-0.989795\pi\)
0.999486 0.0320532i \(-0.0102046\pi\)
\(108\) 55231.0 95524.8i 0.0438441 0.0758307i
\(109\) −828451. −0.639716 −0.319858 0.947465i \(-0.603635\pi\)
−0.319858 + 0.947465i \(0.603635\pi\)
\(110\) 672557.i 0.505302i
\(111\) 136831. 775064.i 0.100050 0.566720i
\(112\) −480425. −0.341957
\(113\) 1.02476e6i 0.710211i −0.934826 0.355106i \(-0.884445\pi\)
0.934826 0.355106i \(-0.115555\pi\)
\(114\) 802564. + 141686.i 0.541708 + 0.0956341i
\(115\) 4.05911e6 2.66893
\(116\) 141374.i 0.0905721i
\(117\) −1.36824e6 498645.i −0.854289 0.311339i
\(118\) 288565. 0.175630
\(119\) 162604.i 0.0964919i
\(120\) 592108. 3.35392e6i 0.342655 1.94093i
\(121\) 1.63383e6 0.922252
\(122\) 3.08528e6i 1.69909i
\(123\) −105724. 18664.6i −0.0568141 0.0100301i
\(124\) 160741. 0.0843068
\(125\) 5.92641e6i 3.03432i
\(126\) −247289. + 678542.i −0.123622 + 0.339207i
\(127\) −2.83860e6 −1.38577 −0.692887 0.721046i \(-0.743661\pi\)
−0.692887 + 0.721046i \(0.743661\pi\)
\(128\) 1.78028e6i 0.848902i
\(129\) −396835. + 2.24782e6i −0.184859 + 1.04711i
\(130\) −3.62011e6 −1.64775
\(131\) 1.90031e6i 0.845298i 0.906293 + 0.422649i \(0.138900\pi\)
−0.906293 + 0.422649i \(0.861100\pi\)
\(132\) 55318.7 + 9766.07i 0.0240519 + 0.00424618i
\(133\) 512084. 0.217664
\(134\) 14702.3i 0.00611042i
\(135\) −4.04099e6 2.33644e6i −1.64243 0.949627i
\(136\) 667140. 0.265217
\(137\) 1.83112e6i 0.712122i −0.934463 0.356061i \(-0.884120\pi\)
0.934463 0.356061i \(-0.115880\pi\)
\(138\) −613958. + 3.47769e6i −0.233615 + 1.32329i
\(139\) 1.55745e6 0.579922 0.289961 0.957038i \(-0.406358\pi\)
0.289961 + 0.957038i \(0.406358\pi\)
\(140\) 172353.i 0.0628110i
\(141\) 1.94468e6 + 343317.i 0.693729 + 0.122472i
\(142\) 2.58123e6 0.901491
\(143\) 741372.i 0.253529i
\(144\) 2.53821e6 + 925033.i 0.850043 + 0.309792i
\(145\) 5.98054e6 1.96172
\(146\) 1.29656e6i 0.416615i
\(147\) −78892.8 + 446878.i −0.0248362 + 0.140682i
\(148\) −163414. −0.0504086
\(149\) 5.41574e6i 1.63719i 0.574371 + 0.818595i \(0.305247\pi\)
−0.574371 + 0.818595i \(0.694753\pi\)
\(150\) −8.25223e6 1.45686e6i −2.44511 0.431664i
\(151\) 3.62504e6 1.05289 0.526444 0.850210i \(-0.323525\pi\)
0.526444 + 0.850210i \(0.323525\pi\)
\(152\) 2.10100e6i 0.598268i
\(153\) 313085. 859081.i 0.0874155 0.239861i
\(154\) −367664. −0.100667
\(155\) 6.79986e6i 1.82602i
\(156\) −52567.0 + 297759.i −0.0138465 + 0.0784317i
\(157\) −2.59178e6 −0.669728 −0.334864 0.942266i \(-0.608690\pi\)
−0.334864 + 0.942266i \(0.608690\pi\)
\(158\) 1.21028e6i 0.306842i
\(159\) 1.07843e6 + 190387.i 0.268286 + 0.0473638i
\(160\) −1.35733e6 −0.331379
\(161\) 2.21898e6i 0.531710i
\(162\) 2.61299e6 3.10877e6i 0.614600 0.731213i
\(163\) −3.68028e6 −0.849802 −0.424901 0.905240i \(-0.639691\pi\)
−0.424901 + 0.905240i \(0.639691\pi\)
\(164\) 22290.7i 0.00505350i
\(165\) 413135. 2.34015e6i 0.0919687 0.520945i
\(166\) −248369. −0.0542966
\(167\) 2.43800e6i 0.523460i −0.965141 0.261730i \(-0.915707\pi\)
0.965141 0.261730i \(-0.0842930\pi\)
\(168\) 1.83348e6 + 323685.i 0.386676 + 0.0682645i
\(169\) −836286. −0.173259
\(170\) 2.27297e6i 0.462644i
\(171\) −2.70548e6 985990.i −0.541072 0.197190i
\(172\) 473930. 0.0931383
\(173\) 3.19047e6i 0.616192i −0.951355 0.308096i \(-0.900308\pi\)
0.951355 0.308096i \(-0.0996917\pi\)
\(174\) −904584. + 5.12390e6i −0.171712 + 0.972642i
\(175\) −5.26542e6 −0.982469
\(176\) 1.37532e6i 0.252269i
\(177\) −1.00406e6 177259.i −0.181067 0.0319659i
\(178\) 8.09725e6 1.43575
\(179\) 6.29592e6i 1.09774i −0.835907 0.548871i \(-0.815058\pi\)
0.835907 0.548871i \(-0.184942\pi\)
\(180\) −331857. + 910588.i −0.0569027 + 0.156136i
\(181\) −9.15543e6 −1.54398 −0.771992 0.635632i \(-0.780740\pi\)
−0.771992 + 0.635632i \(0.780740\pi\)
\(182\) 1.97899e6i 0.328269i
\(183\) −1.89521e6 + 1.07352e7i −0.309246 + 1.75169i
\(184\) 9.10412e6 1.46145
\(185\) 6.91292e6i 1.09181i
\(186\) 5.82586e6 + 1.02851e6i 0.905360 + 0.159834i
\(187\) 465488. 0.0711841
\(188\) 410014.i 0.0617057i
\(189\) 1.27725e6 2.20907e6i 0.189187 0.327209i
\(190\) −7.15820e6 −1.04362
\(191\) 5.98114e6i 0.858388i −0.903212 0.429194i \(-0.858798\pi\)
0.903212 0.429194i \(-0.141202\pi\)
\(192\) 1.31859e6 7.46900e6i 0.186297 1.05526i
\(193\) −6.89082e6 −0.958515 −0.479257 0.877674i \(-0.659094\pi\)
−0.479257 + 0.877674i \(0.659094\pi\)
\(194\) 5.71663e6i 0.782952i
\(195\) 1.25961e7 + 2.22375e6i 1.69877 + 0.299903i
\(196\) 94219.6 0.0125133
\(197\) 2.96448e6i 0.387748i 0.981026 + 0.193874i \(0.0621052\pi\)
−0.981026 + 0.193874i \(0.937895\pi\)
\(198\) 1.94246e6 + 707916.i 0.250240 + 0.0911982i
\(199\) 1.22422e7 1.55346 0.776732 0.629831i \(-0.216876\pi\)
0.776732 + 0.629831i \(0.216876\pi\)
\(200\) 2.16032e7i 2.70040i
\(201\) 9031.26 51156.5i 0.00111214 0.00629959i
\(202\) −6.85263e6 −0.831387
\(203\) 3.26936e6i 0.390818i
\(204\) −186955. 33005.4i −0.0220215 0.00388771i
\(205\) 942965. 0.109455
\(206\) 9.87300e6i 1.12940i
\(207\) 4.27252e6 1.17234e7i 0.481696 1.32173i
\(208\) −7.40280e6 −0.822632
\(209\) 1.46594e6i 0.160575i
\(210\) 1.10281e6 6.24672e6i 0.119081 0.674518i
\(211\) −9.10854e6 −0.969620 −0.484810 0.874619i \(-0.661111\pi\)
−0.484810 + 0.874619i \(0.661111\pi\)
\(212\) 227375.i 0.0238635i
\(213\) −8.98135e6 1.58558e6i −0.929400 0.164078i
\(214\) −600119. −0.0612345
\(215\) 2.00487e7i 2.01730i
\(216\) −9.06350e6 5.24037e6i −0.899362 0.519997i
\(217\) 3.71725e6 0.363783
\(218\) 6.33069e6i 0.611057i
\(219\) −796446. + 4.51137e6i −0.0758270 + 0.429513i
\(220\) −493396. −0.0463370
\(221\) 2.50554e6i 0.232126i
\(222\) −5.92273e6 1.04561e6i −0.541331 0.0955676i
\(223\) 1.63703e7 1.47619 0.738093 0.674699i \(-0.235727\pi\)
0.738093 + 0.674699i \(0.235727\pi\)
\(224\) 742004.i 0.0660180i
\(225\) 2.78186e7 + 1.01383e7i 2.44224 + 0.890055i
\(226\) −7.83082e6 −0.678393
\(227\) 1.15150e6i 0.0984431i 0.998788 + 0.0492216i \(0.0156740\pi\)
−0.998788 + 0.0492216i \(0.984326\pi\)
\(228\) −103943. + 588771.i −0.00876980 + 0.0496755i
\(229\) −1.53167e7 −1.27544 −0.637719 0.770269i \(-0.720122\pi\)
−0.637719 + 0.770269i \(0.720122\pi\)
\(230\) 3.10181e7i 2.54936i
\(231\) 1.27928e6 + 225847.i 0.103784 + 0.0183222i
\(232\) 1.34137e7 1.07420
\(233\) 1.61419e7i 1.27611i −0.769992 0.638053i \(-0.779740\pi\)
0.769992 0.638053i \(-0.220260\pi\)
\(234\) −3.81044e6 + 1.04555e7i −0.297391 + 0.816017i
\(235\) −1.73449e7 −1.33650
\(236\) 211695.i 0.0161055i
\(237\) 743445. 4.21115e6i 0.0558475 0.316341i
\(238\) 1.24256e6 0.0921690
\(239\) 1.41807e7i 1.03874i 0.854551 + 0.519368i \(0.173832\pi\)
−0.854551 + 0.519368i \(0.826168\pi\)
\(240\) −2.33670e7 4.12526e6i −1.69032 0.298413i
\(241\) 685364. 0.0489633 0.0244816 0.999700i \(-0.492206\pi\)
0.0244816 + 0.999700i \(0.492206\pi\)
\(242\) 1.24850e7i 0.880935i
\(243\) −1.10015e7 + 9.21184e6i −0.766714 + 0.641989i
\(244\) 2.26340e6 0.155809
\(245\) 3.98578e6i 0.271029i
\(246\) −142628. + 807897.i −0.00958073 + 0.0542688i
\(247\) 7.89062e6 0.523625
\(248\) 1.52513e7i 0.999890i
\(249\) 864196. + 152567.i 0.0559776 + 0.00988239i
\(250\) 4.52873e7 2.89838
\(251\) 2.46524e7i 1.55897i 0.626422 + 0.779484i \(0.284519\pi\)
−0.626422 + 0.779484i \(0.715481\pi\)
\(252\) −497787. 181415.i −0.0311058 0.0113363i
\(253\) 6.35227e6 0.392254
\(254\) 2.16914e7i 1.32369i
\(255\) −1.39623e6 + 7.90877e6i −0.0842047 + 0.476967i
\(256\) −4.37390e6 −0.260705
\(257\) 1.72290e7i 1.01499i −0.861656 0.507493i \(-0.830572\pi\)
0.861656 0.507493i \(-0.169428\pi\)
\(258\) 1.71769e7 + 3.03245e6i 1.00020 + 0.176577i
\(259\) −3.77906e6 −0.217512
\(260\) 2.65576e6i 0.151102i
\(261\) 6.29497e6 1.72729e7i 0.354056 0.971501i
\(262\) 1.45214e7 0.807428
\(263\) 2.08769e7i 1.14762i 0.818988 + 0.573810i \(0.194535\pi\)
−0.818988 + 0.573810i \(0.805465\pi\)
\(264\) 926615. 5.24870e6i 0.0503602 0.285259i
\(265\) −9.61865e6 −0.516864
\(266\) 3.91314e6i 0.207912i
\(267\) −2.81743e7 4.97394e6i −1.48019 0.261316i
\(268\) −10785.8 −0.000560336
\(269\) 3.16115e7i 1.62401i 0.583653 + 0.812003i \(0.301623\pi\)
−0.583653 + 0.812003i \(0.698377\pi\)
\(270\) −1.78541e7 + 3.08797e7i −0.907084 + 1.56885i
\(271\) −1.14722e7 −0.576419 −0.288209 0.957567i \(-0.593060\pi\)
−0.288209 + 0.957567i \(0.593060\pi\)
\(272\) 4.64801e6i 0.230973i
\(273\) −1.21565e6 + 6.88588e6i −0.0597474 + 0.338432i
\(274\) −1.39927e7 −0.680218
\(275\) 1.50733e7i 0.724789i
\(276\) −2.55128e6 450408.i −0.121347 0.0214229i
\(277\) 6.88096e6 0.323750 0.161875 0.986811i \(-0.448246\pi\)
0.161875 + 0.986811i \(0.448246\pi\)
\(278\) 1.19014e7i 0.553941i
\(279\) −1.96392e7 7.15736e6i −0.904298 0.329564i
\(280\) −1.63531e7 −0.744946
\(281\) 7.25799e6i 0.327112i 0.986534 + 0.163556i \(0.0522965\pi\)
−0.986534 + 0.163556i \(0.947703\pi\)
\(282\) 2.62349e6 1.48604e7i 0.116985 0.662650i
\(283\) 1.25835e7 0.555192 0.277596 0.960698i \(-0.410462\pi\)
0.277596 + 0.960698i \(0.410462\pi\)
\(284\) 1.89362e6i 0.0826682i
\(285\) 2.49068e7 + 4.39710e6i 1.07593 + 0.189947i
\(286\) −5.66527e6 −0.242171
\(287\) 515487.i 0.0218058i
\(288\) −1.42869e6 + 3.92020e6i −0.0598081 + 0.164109i
\(289\) 2.25644e7 0.934825
\(290\) 4.57009e7i 1.87383i
\(291\) 3.51158e6 1.98909e7i 0.142503 0.807191i
\(292\) 951175. 0.0382043
\(293\) 1.89052e7i 0.751584i 0.926704 + 0.375792i \(0.122629\pi\)
−0.926704 + 0.375792i \(0.877371\pi\)
\(294\) 3.41487e6 + 602867.i 0.134379 + 0.0237235i
\(295\) 8.95537e6 0.348833
\(296\) 1.55049e7i 0.597852i
\(297\) −6.32392e6 3.65639e6i −0.241389 0.139567i
\(298\) 4.13849e7 1.56384
\(299\) 3.41918e7i 1.27911i
\(300\) 1.06877e6 6.05394e6i 0.0395843 0.224220i
\(301\) 1.09599e7 0.401891
\(302\) 2.77011e7i 1.00572i
\(303\) 2.38436e7 + 4.20940e6i 0.857126 + 0.151319i
\(304\) −1.46378e7 −0.521022
\(305\) 9.57489e7i 3.37469i
\(306\) −6.56475e6 2.39247e6i −0.229115 0.0834993i
\(307\) −1.81640e7 −0.627766 −0.313883 0.949462i \(-0.601630\pi\)
−0.313883 + 0.949462i \(0.601630\pi\)
\(308\) 269723.i 0.00923136i
\(309\) 6.06473e6 3.43529e7i 0.205559 1.16436i
\(310\) −5.19618e7 −1.74421
\(311\) 467133.i 0.0155296i 0.999970 + 0.00776479i \(0.00247163\pi\)
−0.999970 + 0.00776479i \(0.997528\pi\)
\(312\) 2.82517e7 + 4.98761e6i 0.930210 + 0.164221i
\(313\) −3.52717e7 −1.15025 −0.575127 0.818064i \(-0.695047\pi\)
−0.575127 + 0.818064i \(0.695047\pi\)
\(314\) 1.98053e7i 0.639724i
\(315\) −7.67440e6 + 2.10579e7i −0.245535 + 0.673727i
\(316\) −887877. −0.0281379
\(317\) 2.19049e7i 0.687644i −0.939035 0.343822i \(-0.888278\pi\)
0.939035 0.343822i \(-0.111722\pi\)
\(318\) 1.45486e6 8.24089e6i 0.0452419 0.256267i
\(319\) 9.35920e6 0.288315
\(320\) 6.66172e7i 2.03299i
\(321\) 2.08811e6 + 368638.i 0.0631302 + 0.0111451i
\(322\) 1.69565e7 0.507889
\(323\) 4.95430e6i 0.147020i
\(324\) 2.28064e6 + 1.91692e6i 0.0670534 + 0.0563599i
\(325\) −8.11340e7 −2.36348
\(326\) 2.81232e7i 0.811730i
\(327\) 3.88878e6 2.20275e7i 0.111217 0.629974i
\(328\) 2.11496e6 0.0599351
\(329\) 9.48185e6i 0.266260i
\(330\) −1.78825e7 3.15701e6i −0.497607 0.0878485i
\(331\) 4.37918e7 1.20756 0.603780 0.797151i \(-0.293661\pi\)
0.603780 + 0.797151i \(0.293661\pi\)
\(332\) 182207.i 0.00497909i
\(333\) 1.99658e7 + 7.27637e6i 0.540696 + 0.197053i
\(334\) −1.86302e7 −0.500009
\(335\) 456273.i 0.0121364i
\(336\) 2.25514e6 1.27740e7i 0.0594505 0.336750i
\(337\) −1.47909e7 −0.386461 −0.193231 0.981153i \(-0.561897\pi\)
−0.193231 + 0.981153i \(0.561897\pi\)
\(338\) 6.39056e6i 0.165497i
\(339\) 2.72472e7 + 4.81027e6i 0.699396 + 0.123473i
\(340\) 1.66748e6 0.0424252
\(341\) 1.06414e7i 0.268371i
\(342\) −7.53454e6 + 2.06742e7i −0.188356 + 0.516832i
\(343\) 2.17889e6 0.0539949
\(344\) 4.49669e7i 1.10463i
\(345\) −1.90536e7 + 1.07927e8i −0.464003 + 2.62829i
\(346\) −2.43803e7 −0.588586
\(347\) 5.20260e7i 1.24518i 0.782548 + 0.622590i \(0.213920\pi\)
−0.782548 + 0.622590i \(0.786080\pi\)
\(348\) −3.75896e6 663614.i −0.0891929 0.0157463i
\(349\) 4.15549e7 0.977565 0.488782 0.872406i \(-0.337441\pi\)
0.488782 + 0.872406i \(0.337441\pi\)
\(350\) 4.02362e7i 0.938454i
\(351\) 1.96810e7 3.40392e7i 0.455119 0.787152i
\(352\) −2.12414e6 −0.0487029
\(353\) 3.86041e7i 0.877626i −0.898578 0.438813i \(-0.855399\pi\)
0.898578 0.438813i \(-0.144601\pi\)
\(354\) −1.35454e6 + 7.67262e6i −0.0305339 + 0.172955i
\(355\) 8.01061e7 1.79052
\(356\) 5.94025e6i 0.131660i
\(357\) −4.32345e6 763271.i −0.0950225 0.0167754i
\(358\) −4.81109e7 −1.04856
\(359\) 8.70557e7i 1.88154i −0.339044 0.940771i \(-0.610103\pi\)
0.339044 0.940771i \(-0.389897\pi\)
\(360\) 8.63975e7 + 3.14869e7i 1.85180 + 0.674874i
\(361\) −3.14434e7 −0.668357
\(362\) 6.99621e7i 1.47481i
\(363\) −7.66925e6 + 4.34415e7i −0.160337 + 0.908208i
\(364\) 1.45181e6 0.0301028
\(365\) 4.02376e7i 0.827473i
\(366\) 8.20340e7 + 1.44824e7i 1.67321 + 0.295392i
\(367\) 4.56054e7 0.922609 0.461305 0.887242i \(-0.347382\pi\)
0.461305 + 0.887242i \(0.347382\pi\)
\(368\) 6.34291e7i 1.27275i
\(369\) 992542. 2.72345e6i 0.0197547 0.0542052i
\(370\) 5.28258e7 1.04290
\(371\) 5.25819e6i 0.102971i
\(372\) −754527. + 4.27393e6i −0.0146570 + 0.0830230i
\(373\) −9.15611e7 −1.76435 −0.882174 0.470923i \(-0.843921\pi\)
−0.882174 + 0.470923i \(0.843921\pi\)
\(374\) 3.55707e6i 0.0679951i
\(375\) −1.57576e8 2.78188e7i −2.98812 0.527528i
\(376\) −3.89026e7 −0.731838
\(377\) 5.03770e7i 0.940174i
\(378\) −1.68809e7 9.76024e6i −0.312550 0.180711i
\(379\) 5.53674e7 1.01704 0.508518 0.861051i \(-0.330193\pi\)
0.508518 + 0.861051i \(0.330193\pi\)
\(380\) 5.25134e6i 0.0957017i
\(381\) 1.33245e7 7.54749e7i 0.240922 1.36467i
\(382\) −4.57055e7 −0.819932
\(383\) 1.49962e7i 0.266923i 0.991054 + 0.133461i \(0.0426092\pi\)
−0.991054 + 0.133461i \(0.957391\pi\)
\(384\) −4.73355e7 8.35670e6i −0.835975 0.147585i
\(385\) −1.14101e7 −0.199944
\(386\) 5.26569e7i 0.915573i
\(387\) −5.79042e7 2.11027e7i −0.999027 0.364088i
\(388\) −4.19379e6 −0.0717979
\(389\) 3.89798e7i 0.662202i 0.943595 + 0.331101i \(0.107420\pi\)
−0.943595 + 0.331101i \(0.892580\pi\)
\(390\) 1.69930e7 9.62546e7i 0.286468 1.62266i
\(391\) −2.14681e7 −0.359140
\(392\) 8.93966e6i 0.148410i
\(393\) −5.05269e7 8.92012e6i −0.832425 0.146958i
\(394\) 2.26533e7 0.370377
\(395\) 3.75599e7i 0.609444i
\(396\) −519337. + 1.42502e6i −0.00836303 + 0.0229475i
\(397\) −1.53003e7 −0.244528 −0.122264 0.992498i \(-0.539015\pi\)
−0.122264 + 0.992498i \(0.539015\pi\)
\(398\) 9.35502e7i 1.48387i
\(399\) −2.40374e6 + 1.36157e7i −0.0378416 + 0.214349i
\(400\) 1.50511e8 2.35174
\(401\) 1.70287e7i 0.264088i 0.991244 + 0.132044i \(0.0421540\pi\)
−0.991244 + 0.132044i \(0.957846\pi\)
\(402\) −390917. 69013.3i −0.00601737 0.00106232i
\(403\) 5.72785e7 0.875138
\(404\) 5.02718e6i 0.0762396i
\(405\) 8.10918e7 9.64780e7i 1.22071 1.45232i
\(406\) 2.49831e7 0.373309
\(407\) 1.08183e7i 0.160464i
\(408\) −3.13159e6 + 1.77385e7i −0.0461088 + 0.261178i
\(409\) −1.18550e7 −0.173274 −0.0866368 0.996240i \(-0.527612\pi\)
−0.0866368 + 0.996240i \(0.527612\pi\)
\(410\) 7.20576e6i 0.104551i
\(411\) 4.86872e7 + 8.59534e6i 0.701277 + 0.123805i
\(412\) −7.24296e6 −0.103568
\(413\) 4.89559e6i 0.0694953i
\(414\) −8.95858e7 3.26488e7i −1.26252 0.460115i
\(415\) −7.70790e6 −0.107843
\(416\) 1.14334e7i 0.158817i
\(417\) −7.31074e6 + 4.14108e7i −0.100821 + 0.571091i
\(418\) −1.12022e7 −0.153382
\(419\) 4.26289e7i 0.579511i −0.957101 0.289755i \(-0.906426\pi\)
0.957101 0.289755i \(-0.0935740\pi\)
\(420\) 4.58267e6 + 809034.i 0.0618544 + 0.0109199i
\(421\) 5.55519e7 0.744479 0.372239 0.928137i \(-0.378590\pi\)
0.372239 + 0.928137i \(0.378590\pi\)
\(422\) 6.96038e7i 0.926181i
\(423\) −1.82568e7 + 5.00951e7i −0.241214 + 0.661872i
\(424\) −2.15735e7 −0.283025
\(425\) 5.09418e7i 0.663602i
\(426\) −1.21164e7 + 6.86318e7i −0.156727 + 0.887763i
\(427\) 5.23426e7 0.672314
\(428\) 440255.i 0.00561530i
\(429\) 1.97122e7 + 3.48003e6i 0.249669 + 0.0440770i
\(430\) −1.53204e8 −1.92692
\(431\) 2.33322e7i 0.291423i 0.989327 + 0.145711i \(0.0465471\pi\)
−0.989327 + 0.145711i \(0.953453\pi\)
\(432\) −3.65100e7 + 6.31460e7i −0.452857 + 0.783240i
\(433\) 9.98905e7 1.23044 0.615220 0.788356i \(-0.289067\pi\)
0.615220 + 0.788356i \(0.289067\pi\)
\(434\) 2.84057e7i 0.347486i
\(435\) −2.80729e7 + 1.59016e8i −0.341052 + 1.93184i
\(436\) −4.64427e6 −0.0560349
\(437\) 6.76088e7i 0.810138i
\(438\) 3.44741e7 + 6.08612e6i 0.410271 + 0.0724300i
\(439\) −7.98773e7 −0.944126 −0.472063 0.881565i \(-0.656490\pi\)
−0.472063 + 0.881565i \(0.656490\pi\)
\(440\) 4.68140e7i 0.549563i
\(441\) −1.15117e7 4.19533e6i −0.134221 0.0489160i
\(442\) 1.91463e7 0.221727
\(443\) 1.57447e7i 0.181102i 0.995892 + 0.0905512i \(0.0288629\pi\)
−0.995892 + 0.0905512i \(0.971137\pi\)
\(444\) 767073. 4.34499e6i 0.00876371 0.0496409i
\(445\) 2.51291e8 2.85165
\(446\) 1.25095e8i 1.41005i
\(447\) −1.43998e8 2.54217e7i −1.61226 0.284631i
\(448\) −3.64173e7 −0.405018
\(449\) 9.89524e7i 1.09317i 0.837404 + 0.546584i \(0.184072\pi\)
−0.837404 + 0.546584i \(0.815928\pi\)
\(450\) 7.74727e7 2.12579e8i 0.850180 2.33282i
\(451\) 1.47569e6 0.0160866
\(452\) 5.74479e6i 0.0622098i
\(453\) −1.70161e7 + 9.63856e7i −0.183048 + 1.03685i
\(454\) 8.79928e6 0.0940328
\(455\) 6.14162e7i 0.652002i
\(456\) 5.58632e7 + 9.86220e6i 0.589158 + 0.104011i
\(457\) −1.16996e8 −1.22581 −0.612904 0.790157i \(-0.709999\pi\)
−0.612904 + 0.790157i \(0.709999\pi\)
\(458\) 1.17044e8i 1.21830i
\(459\) 2.13723e7 + 1.23571e7i 0.221011 + 0.127785i
\(460\) 2.27553e7 0.233780
\(461\) 2.65404e7i 0.270897i 0.990784 + 0.135449i \(0.0432476\pi\)
−0.990784 + 0.135449i \(0.956752\pi\)
\(462\) 1.72583e6 9.77575e6i 0.0175014 0.0991343i
\(463\) −1.32352e8 −1.33349 −0.666743 0.745288i \(-0.732312\pi\)
−0.666743 + 0.745288i \(0.732312\pi\)
\(464\) 9.34541e7i 0.935501i
\(465\) 1.80800e8 + 3.19188e7i 1.79821 + 0.317459i
\(466\) −1.23350e8 −1.21894
\(467\) 3.83535e7i 0.376578i −0.982114 0.188289i \(-0.939706\pi\)
0.982114 0.188289i \(-0.0602941\pi\)
\(468\) −7.67032e6 2.79539e6i −0.0748300 0.0272712i
\(469\) −249429. −0.00241784
\(470\) 1.32543e8i 1.27662i
\(471\) 1.21659e7 6.89123e7i 0.116435 0.659529i
\(472\) 2.00859e7 0.191014
\(473\) 3.13750e7i 0.296484i
\(474\) −3.21799e7 5.68111e6i −0.302169 0.0533455i
\(475\) −1.60429e8 −1.49694
\(476\) 911555.i 0.00845205i
\(477\) −1.01244e7 + 2.77804e7i −0.0932851 + 0.255967i
\(478\) 1.08363e8 0.992200
\(479\) 2.06135e8i 1.87562i −0.347149 0.937810i \(-0.612850\pi\)
0.347149 0.937810i \(-0.387150\pi\)
\(480\) 6.37135e6 3.60897e7i 0.0576113 0.326332i
\(481\) −5.82309e7 −0.523261
\(482\) 5.23728e6i 0.0467697i
\(483\) −5.90000e7 1.04160e7i −0.523613 0.0924396i
\(484\) 9.15919e6 0.0807832
\(485\) 1.77410e8i 1.55508i
\(486\) 7.03932e7 + 8.40691e7i 0.613228 + 0.732365i
\(487\) 1.13519e8 0.982835 0.491418 0.870924i \(-0.336479\pi\)
0.491418 + 0.870924i \(0.336479\pi\)
\(488\) 2.14754e8i 1.84791i
\(489\) 1.72754e7 9.78543e7i 0.147741 0.836861i
\(490\) −3.04577e7 −0.258886
\(491\) 1.17371e8i 0.991555i −0.868450 0.495777i \(-0.834883\pi\)
0.868450 0.495777i \(-0.165117\pi\)
\(492\) −592683. 104633.i −0.00497654 0.000878568i
\(493\) −3.16304e7 −0.263975
\(494\) 6.02969e7i 0.500166i
\(495\) 6.02826e7 + 2.19695e7i 0.497023 + 0.181136i
\(496\) −1.06257e8 −0.870788
\(497\) 4.37912e7i 0.356712i
\(498\) 1.16585e6 6.60384e6i 0.00943965 0.0534698i
\(499\) 1.90289e8 1.53148 0.765741 0.643149i \(-0.222372\pi\)
0.765741 + 0.643149i \(0.222372\pi\)
\(500\) 3.32233e7i 0.265787i
\(501\) 6.48235e7 + 1.14441e7i 0.515489 + 0.0910053i
\(502\) 1.88383e8 1.48913
\(503\) 1.97076e8i 1.54857i −0.632839 0.774284i \(-0.718110\pi\)
0.632839 0.774284i \(-0.281890\pi\)
\(504\) −1.72128e7 + 4.72306e7i −0.134450 + 0.368920i
\(505\) −2.12665e8 −1.65129
\(506\) 4.85415e7i 0.374681i
\(507\) 3.92556e6 2.22359e7i 0.0301216 0.170620i
\(508\) −1.59131e7 −0.121385
\(509\) 4.63513e7i 0.351486i −0.984436 0.175743i \(-0.943767\pi\)
0.984436 0.175743i \(-0.0562328\pi\)
\(510\) 6.04357e7 + 1.06694e7i 0.455599 + 0.0804323i
\(511\) 2.19965e7 0.164851
\(512\) 1.47361e8i 1.09793i
\(513\) 3.89159e7 6.73071e7i 0.288254 0.498550i
\(514\) −1.31657e8 −0.969514
\(515\) 3.06399e8i 2.24319i
\(516\) −2.22465e6 + 1.26012e7i −0.0161924 + 0.0917200i
\(517\) −2.71437e7 −0.196425
\(518\) 2.88780e7i 0.207768i
\(519\) 8.48308e7 + 1.49762e7i 0.606808 + 0.107127i
\(520\) −2.51982e8 −1.79209
\(521\) 6.26964e7i 0.443332i 0.975123 + 0.221666i \(0.0711495\pi\)
−0.975123 + 0.221666i \(0.928850\pi\)
\(522\) −1.31992e8 4.81036e7i −0.927978 0.338194i
\(523\) −3.94364e7 −0.275672 −0.137836 0.990455i \(-0.544015\pi\)
−0.137836 + 0.990455i \(0.544015\pi\)
\(524\) 1.06531e7i 0.0740425i
\(525\) 2.47161e7 1.40001e8i 0.170806 0.967508i
\(526\) 1.59533e8 1.09621
\(527\) 3.59636e7i 0.245715i
\(528\) −3.65680e7 6.45579e6i −0.248428 0.0438579i
\(529\) −1.44928e8 −0.979008
\(530\) 7.35019e7i 0.493709i
\(531\) 9.42620e6 2.58647e7i 0.0629583 0.172752i
\(532\) 2.87073e6 0.0190659
\(533\) 7.94305e6i 0.0524573i
\(534\) −3.80088e7 + 2.15296e8i −0.249609 + 1.41388i
\(535\) −1.86242e7 −0.121623
\(536\) 1.02337e6i 0.00664565i
\(537\) 1.67401e8 + 2.95533e7i 1.08103 + 0.190846i
\(538\) 2.41562e8 1.55125
\(539\) 6.23752e6i 0.0398332i
\(540\) −2.26537e7 1.30980e7i −0.143866 0.0831811i
\(541\) −1.29534e8 −0.818070 −0.409035 0.912519i \(-0.634135\pi\)
−0.409035 + 0.912519i \(0.634135\pi\)
\(542\) 8.76658e7i 0.550595i
\(543\) 4.29760e7 2.43432e8i 0.268427 1.52047i
\(544\) 7.17873e6 0.0445914
\(545\) 1.96467e8i 1.21367i
\(546\) 5.26191e7 + 9.28948e6i 0.323270 + 0.0570707i
\(547\) 2.17338e8 1.32792 0.663962 0.747766i \(-0.268874\pi\)
0.663962 + 0.747766i \(0.268874\pi\)
\(548\) 1.02652e7i 0.0623771i
\(549\) −2.76540e8 1.00783e8i −1.67125 0.609074i
\(550\) 1.15184e8 0.692318
\(551\) 9.96125e7i 0.595469i
\(552\) −4.27351e7 + 2.42068e8i −0.254079 + 1.43920i
\(553\) −2.05327e7 −0.121415
\(554\) 5.25816e7i 0.309246i
\(555\) −1.83806e8 3.24495e7i −1.07518 0.189815i
\(556\) 8.73102e6 0.0507973
\(557\) 3.69027e7i 0.213546i 0.994283 + 0.106773i \(0.0340519\pi\)
−0.994283 + 0.106773i \(0.965948\pi\)
\(558\) −5.46937e7 + 1.50075e8i −0.314800 + 0.863785i
\(559\) 1.68880e8 0.966812
\(560\) 1.13933e8i 0.648762i
\(561\) −2.18502e6 + 1.23768e7i −0.0123756 + 0.0701001i
\(562\) 5.54626e7 0.312458
\(563\) 1.54676e8i 0.866758i 0.901212 + 0.433379i \(0.142679\pi\)
−0.901212 + 0.433379i \(0.857321\pi\)
\(564\) 1.09018e7 + 1.92463e6i 0.0607661 + 0.0107278i
\(565\) −2.43022e8 −1.34741
\(566\) 9.61583e7i 0.530319i
\(567\) 5.27412e7 + 4.43301e7i 0.289335 + 0.243192i
\(568\) 1.79669e8 0.980456
\(569\) 9.86395e7i 0.535444i −0.963496 0.267722i \(-0.913729\pi\)
0.963496 0.267722i \(-0.0862709\pi\)
\(570\) 3.36009e7 1.90328e8i 0.181437 1.02773i
\(571\) −3.30878e8 −1.77729 −0.888647 0.458591i \(-0.848354\pi\)
−0.888647 + 0.458591i \(0.848354\pi\)
\(572\) 4.15612e6i 0.0222075i
\(573\) 1.59032e8 + 2.80757e7i 0.845316 + 0.149234i
\(574\) 3.93914e6 0.0208289
\(575\) 6.95177e8i 3.65672i
\(576\) 1.92402e8 + 7.01196e7i 1.00680 + 0.366920i
\(577\) 3.52498e8 1.83497 0.917485 0.397769i \(-0.130216\pi\)
0.917485 + 0.397769i \(0.130216\pi\)
\(578\) 1.72428e8i 0.892945i
\(579\) 3.23458e7 1.83219e8i 0.166641 0.943918i
\(580\) 3.35268e7 0.171834
\(581\) 4.21364e6i 0.0214847i
\(582\) −1.51999e8 2.68341e7i −0.771029 0.136119i
\(583\) −1.50526e7 −0.0759638
\(584\) 9.02485e7i 0.453108i
\(585\) −1.18254e8 + 3.24478e8i −0.590673 + 1.62076i
\(586\) 1.44466e8 0.717913
\(587\) 2.05064e7i 0.101386i −0.998714 0.0506928i \(-0.983857\pi\)
0.998714 0.0506928i \(-0.0161429\pi\)
\(588\) −442271. + 2.50519e6i −0.00217549 + 0.0123228i
\(589\) 1.13259e8 0.554277
\(590\) 6.84333e7i 0.333205i
\(591\) −7.88219e7 1.39154e7i −0.381843 0.0674113i
\(592\) 1.08024e8 0.520660
\(593\) 1.11156e8i 0.533049i 0.963828 + 0.266525i \(0.0858753\pi\)
−0.963828 + 0.266525i \(0.914125\pi\)
\(594\) −2.79407e7 + 4.83249e7i −0.133315 + 0.230575i
\(595\) 3.85616e7 0.183064
\(596\) 3.03605e7i 0.143407i
\(597\) −5.74656e7 + 3.25507e8i −0.270075 + 1.52981i
\(598\) 2.61280e8 1.22181
\(599\) 8.38505e7i 0.390144i 0.980789 + 0.195072i \(0.0624941\pi\)
−0.980789 + 0.195072i \(0.937506\pi\)
\(600\) −5.74405e8 1.01406e8i −2.65928 0.469475i
\(601\) −3.34851e8 −1.54251 −0.771254 0.636527i \(-0.780370\pi\)
−0.771254 + 0.636527i \(0.780370\pi\)
\(602\) 8.37514e7i 0.383886i
\(603\) 1.31780e6 + 480262.i 0.00601031 + 0.00219041i
\(604\) 2.03219e7 0.0922260
\(605\) 3.87462e8i 1.74970i
\(606\) 3.21666e7 1.82204e8i 0.144540 0.818727i
\(607\) 1.44195e8 0.644737 0.322369 0.946614i \(-0.395521\pi\)
0.322369 + 0.946614i \(0.395521\pi\)
\(608\) 2.26078e7i 0.100588i
\(609\) −8.69284e7 1.53465e7i −0.384866 0.0679450i
\(610\) −7.31674e8 −3.22351
\(611\) 1.46104e8i 0.640530i
\(612\) 1.75515e6 4.81599e6i 0.00765702 0.0210102i
\(613\) −1.68868e8 −0.733103 −0.366552 0.930398i \(-0.619462\pi\)
−0.366552 + 0.930398i \(0.619462\pi\)
\(614\) 1.38802e8i 0.599641i
\(615\) −4.42632e6 + 2.50723e7i −0.0190291 + 0.107788i
\(616\) −2.55916e7 −0.109485
\(617\) 5.46510e6i 0.0232671i −0.999932 0.0116336i \(-0.996297\pi\)
0.999932 0.0116336i \(-0.00370316\pi\)
\(618\) −2.62511e8 4.63443e7i −1.11220 0.196350i
\(619\) −5.43333e6 −0.0229084 −0.0114542 0.999934i \(-0.503646\pi\)
−0.0114542 + 0.999934i \(0.503646\pi\)
\(620\) 3.81198e7i 0.159947i
\(621\) 2.91657e8 + 1.68631e8i 1.21786 + 0.704148i
\(622\) 3.56964e6 0.0148338
\(623\) 1.37372e8i 0.568112i
\(624\) 3.47490e7 1.96832e8i 0.143017 0.810105i
\(625\) 7.70837e8 3.15735
\(626\) 2.69532e8i 1.09872i
\(627\) 3.89778e7 + 6.88121e6i 0.158130 + 0.0279166i
\(628\) −1.45294e7 −0.0586637
\(629\) 3.65616e7i 0.146917i
\(630\) 1.60916e8 + 5.86447e7i 0.643544 + 0.234535i
\(631\) −3.34903e8 −1.33300 −0.666502 0.745504i \(-0.732209\pi\)
−0.666502 + 0.745504i \(0.732209\pi\)
\(632\) 8.42427e7i 0.333719i
\(633\) 4.27559e7 2.42186e8i 0.168572 0.954854i
\(634\) −1.67389e8 −0.656837
\(635\) 6.73173e8i 2.62909i
\(636\) 6.04563e6 + 1.06731e6i 0.0235001 + 0.00414876i
\(637\) 3.35742e7 0.129893
\(638\) 7.15193e7i 0.275398i
\(639\) 8.43177e7 2.31361e8i 0.323159 0.886721i
\(640\) 4.22193e8 1.61054
\(641\) 2.97951e8i 1.13128i −0.824652 0.565640i \(-0.808629\pi\)
0.824652 0.565640i \(-0.191371\pi\)
\(642\) 2.81699e6 1.59565e7i 0.0106458 0.0603020i
\(643\) 1.78960e8 0.673168 0.336584 0.941653i \(-0.390728\pi\)
0.336584 + 0.941653i \(0.390728\pi\)
\(644\) 1.24395e7i 0.0465743i
\(645\) 5.33071e8 + 9.41094e7i 1.98658 + 0.350714i
\(646\) 3.78588e7 0.140433
\(647\) 1.91354e8i 0.706519i −0.935525 0.353260i \(-0.885073\pi\)
0.935525 0.353260i \(-0.114927\pi\)
\(648\) 1.81880e8 2.16389e8i 0.668435 0.795263i
\(649\) 1.40146e7 0.0512681
\(650\) 6.19993e8i 2.25760i
\(651\) −1.74489e7 + 9.88373e7i −0.0632449 + 0.358243i
\(652\) −2.06315e7 −0.0744370
\(653\) 5.09898e8i 1.83123i 0.402053 + 0.915616i \(0.368297\pi\)
−0.402053 + 0.915616i \(0.631703\pi\)
\(654\) −1.68326e8 2.97165e7i −0.601751 0.106234i
\(655\) 4.50658e8 1.60370
\(656\) 1.47351e7i 0.0521965i
\(657\) −1.16214e8 4.23531e7i −0.409789 0.149345i
\(658\) −7.24565e7 −0.254331
\(659\) 3.97006e8i 1.38720i 0.720358 + 0.693602i \(0.243978\pi\)
−0.720358 + 0.693602i \(0.756022\pi\)
\(660\) 2.31602e6 1.31188e7i 0.00805585 0.0456313i
\(661\) −5.00309e8 −1.73234 −0.866172 0.499746i \(-0.833427\pi\)
−0.866172 + 0.499746i \(0.833427\pi\)
\(662\) 3.34639e8i 1.15346i
\(663\) −6.66194e7 1.17611e7i −0.228592 0.0403560i
\(664\) −1.72880e7 −0.0590526
\(665\) 1.21441e8i 0.412952i
\(666\) 5.56031e7 1.52570e8i 0.188225 0.516473i
\(667\) −4.31643e8 −1.45461
\(668\) 1.36673e7i 0.0458516i
\(669\) −7.68427e7 + 4.35266e8i −0.256640 + 1.45371i
\(670\) 3.48665e6 0.0115927
\(671\) 1.49841e8i 0.495980i
\(672\) 1.97290e7 + 3.48300e6i 0.0650126 + 0.0114775i
\(673\) −7.53490e7 −0.247191 −0.123595 0.992333i \(-0.539442\pi\)
−0.123595 + 0.992333i \(0.539442\pi\)
\(674\) 1.13026e8i 0.369148i
\(675\) −4.00147e8 + 6.92075e8i −1.30109 + 2.25031i
\(676\) −4.68820e6 −0.0151763
\(677\) 5.23910e8i 1.68846i −0.535982 0.844229i \(-0.680059\pi\)
0.535982 0.844229i \(-0.319941\pi\)
\(678\) 3.67582e7 2.08212e8i 0.117941 0.668063i
\(679\) −9.69842e7 −0.309807
\(680\) 1.58212e8i 0.503169i
\(681\) −3.06170e7 5.40518e6i −0.0969440 0.0171147i
\(682\) −8.13172e7 −0.256348
\(683\) 4.41828e8i 1.38673i 0.720588 + 0.693363i \(0.243872\pi\)
−0.720588 + 0.693363i \(0.756128\pi\)
\(684\) −1.51668e7 5.52744e6i −0.0473943 0.0172725i
\(685\) −4.34249e8 −1.35104
\(686\) 1.66502e7i 0.0515759i
\(687\) 7.18974e7 4.07254e8i 0.221739 1.25602i
\(688\) −3.13288e8 −0.962007
\(689\) 8.10225e7i 0.247713i
\(690\) 8.24734e8 + 1.45600e8i 2.51054 + 0.443215i
\(691\) −8.95199e7 −0.271322 −0.135661 0.990755i \(-0.543316\pi\)
−0.135661 + 0.990755i \(0.543316\pi\)
\(692\) 1.78857e7i 0.0539743i
\(693\) −1.20100e7 + 3.29544e7i −0.0360864 + 0.0990180i
\(694\) 3.97562e8 1.18940
\(695\) 3.69349e8i 1.10023i
\(696\) −6.29644e7 + 3.56654e8i −0.186753 + 1.05784i
\(697\) −4.98722e6 −0.0147286
\(698\) 3.17546e8i 0.933770i
\(699\) 4.29194e8 + 7.57708e7i 1.25667 + 0.221856i
\(700\) −2.95178e7 −0.0860578
\(701\) 1.38394e8i 0.401758i 0.979616 + 0.200879i \(0.0643798\pi\)
−0.979616 + 0.200879i \(0.935620\pi\)
\(702\) −2.60114e8 1.50394e8i −0.751887 0.434730i
\(703\) −1.15142e8 −0.331412
\(704\) 1.04252e8i 0.298790i
\(705\) 8.14176e7 4.61180e8i 0.232354 1.31614i
\(706\) −2.94997e8 −0.838308
\(707\) 1.16257e8i 0.328973i
\(708\) −5.62873e6 993707.i −0.0158603 0.00280000i
\(709\) 5.08724e8 1.42739 0.713697 0.700455i \(-0.247019\pi\)
0.713697 + 0.700455i \(0.247019\pi\)
\(710\) 6.12138e8i 1.71031i
\(711\) 1.08480e8 + 3.95347e7i 0.301815 + 0.109994i
\(712\) 5.63617e8 1.56151
\(713\) 4.90777e8i 1.35399i
\(714\) −5.83261e6 + 3.30381e7i −0.0160239 + 0.0907654i
\(715\) −1.75816e8 −0.480996
\(716\) 3.52948e7i 0.0961549i
\(717\) −3.77049e8 6.65650e7i −1.02292 0.180588i
\(718\) −6.65244e8 −1.79725
\(719\) 3.91102e8i 1.05221i 0.850419 + 0.526106i \(0.176349\pi\)
−0.850419 + 0.526106i \(0.823651\pi\)
\(720\) 2.19372e8 6.01938e8i 0.587737 1.61270i
\(721\) −1.67498e8 −0.446893
\(722\) 2.40278e8i 0.638415i
\(723\) −3.21713e6 + 1.82230e7i −0.00851243 + 0.0482176i
\(724\) −5.13251e7 −0.135243
\(725\) 1.02425e9i 2.68777i
\(726\) 3.31963e8 + 5.86053e7i 0.867520 + 0.153154i
\(727\) 8.62324e7 0.224423 0.112211 0.993684i \(-0.464207\pi\)
0.112211 + 0.993684i \(0.464207\pi\)
\(728\) 1.37750e8i 0.357023i
\(729\) −1.93290e8 3.35758e8i −0.498916 0.866650i
\(730\) −3.07480e8 −0.790402
\(731\) 1.06035e8i 0.271454i
\(732\) −1.06245e7 + 6.01812e7i −0.0270879 + 0.153436i
\(733\) −4.58012e7 −0.116296 −0.0581481 0.998308i \(-0.518520\pi\)
−0.0581481 + 0.998308i \(0.518520\pi\)
\(734\) 3.48498e8i 0.881276i
\(735\) 1.05977e8 + 1.87094e7i 0.266901 + 0.0471193i
\(736\) 9.79645e7 0.245717
\(737\) 714041.i 0.00178369i
\(738\) −2.08115e7 7.58460e6i −0.0517768 0.0188697i
\(739\) 2.96288e8 0.734143 0.367071 0.930193i \(-0.380360\pi\)
0.367071 + 0.930193i \(0.380360\pi\)
\(740\) 3.87537e7i 0.0956352i
\(741\) −3.70389e7 + 2.09802e8i −0.0910340 + 0.515651i
\(742\) −4.01809e7 −0.0983577
\(743\) 6.59062e8i 1.60679i 0.595444 + 0.803397i \(0.296976\pi\)
−0.595444 + 0.803397i \(0.703024\pi\)
\(744\) 4.05515e8 + 7.15903e7i 0.984663 + 0.173834i
\(745\) 1.28434e9 3.10608
\(746\) 6.99673e8i 1.68531i
\(747\) −8.11314e6 + 2.22618e7i −0.0194638 + 0.0534070i
\(748\) 2.60951e6 0.00623526
\(749\) 1.01812e7i 0.0242300i
\(750\) −2.12580e8 + 1.20414e9i −0.503894 + 2.85425i
\(751\) 1.44730e8 0.341694 0.170847 0.985298i \(-0.445350\pi\)
0.170847 + 0.985298i \(0.445350\pi\)
\(752\) 2.71037e8i 0.637346i
\(753\) −6.55478e8 1.15719e8i −1.53523 0.271032i
\(754\) 3.84961e8 0.898054
\(755\) 8.59679e8i 1.99754i
\(756\) 7.16024e6 1.23840e7i 0.0165715 0.0286613i
\(757\) −4.17266e8 −0.961890 −0.480945 0.876751i \(-0.659706\pi\)
−0.480945 + 0.876751i \(0.659706\pi\)
\(758\) 4.23096e8i 0.971473i
\(759\) −2.98178e7 + 1.68899e8i −0.0681947 + 0.386280i
\(760\) −4.98253e8 −1.13504
\(761\) 5.60980e8i 1.27290i −0.771319 0.636448i \(-0.780403\pi\)
0.771319 0.636448i \(-0.219597\pi\)
\(762\) −5.76749e8 1.01820e8i −1.30353 0.230128i
\(763\) −1.07402e8 −0.241790
\(764\) 3.35301e7i 0.0751891i
\(765\) −2.03731e8 7.42482e7i −0.455064 0.165845i
\(766\) 1.14595e8 0.254965
\(767\) 7.54354e7i 0.167182i
\(768\) 2.05313e7 1.16297e8i 0.0453245 0.256735i
\(769\) −3.01884e8 −0.663836 −0.331918 0.943308i \(-0.607696\pi\)
−0.331918 + 0.943308i \(0.607696\pi\)
\(770\) 8.71915e7i 0.190986i
\(771\) 4.58098e8 + 8.08735e7i 0.999529 + 0.176459i
\(772\) −3.86298e7 −0.0839595
\(773\) 5.60059e8i 1.21254i 0.795260 + 0.606268i \(0.207334\pi\)
−0.795260 + 0.606268i \(0.792666\pi\)
\(774\) −1.61259e8 + 4.42481e8i −0.347776 + 0.954270i
\(775\) −1.16457e9 −2.50184
\(776\) 3.97912e8i 0.851533i
\(777\) 1.77391e7 1.00481e8i 0.0378153 0.214200i
\(778\) 2.97868e8 0.632535
\(779\) 1.57061e7i 0.0332243i
\(780\) 7.06136e7 + 1.24663e7i 0.148801 + 0.0262695i
\(781\) 1.25361e8 0.263154
\(782\) 1.64051e8i 0.343050i
\(783\) 4.29717e8 + 2.48456e8i 0.895153 + 0.517563i
\(784\) −6.22832e7 −0.129248
\(785\) 6.14640e8i 1.27061i
\(786\) −6.81640e7 + 3.86107e8i −0.140374 + 0.795133i
\(787\) 6.20839e8 1.27366 0.636832 0.771003i \(-0.280245\pi\)
0.636832 + 0.771003i \(0.280245\pi\)
\(788\) 1.66188e7i 0.0339641i
\(789\) −5.55092e8 9.79969e7i −1.13014 0.199518i
\(790\) 2.87018e8 0.582140
\(791\) 1.32852e8i 0.268435i
\(792\) 1.35207e8 + 4.92752e7i 0.272160 + 0.0991866i
\(793\) 8.06539e8 1.61736
\(794\) 1.16919e8i 0.233573i
\(795\) 4.51504e7 2.55749e8i 0.0898586 0.508993i
\(796\) 6.86297e7 0.136073
\(797\) 4.34439e8i 0.858131i −0.903273 0.429066i \(-0.858843\pi\)
0.903273 0.429066i \(-0.141157\pi\)
\(798\) 1.04046e8 + 1.83685e7i 0.204746 + 0.0361463i
\(799\) 9.17349e7 0.179843
\(800\) 2.32461e8i 0.454024i
\(801\) 2.64502e8 7.25773e8i 0.514674 1.41222i
\(802\) 1.30127e8 0.252257
\(803\) 6.29696e7i 0.121614i
\(804\) 50629.0 286782.i 9.74163e−5 0.000551803i
\(805\) 5.26230e8 1.00876
\(806\) 4.37699e8i 0.835931i
\(807\) −8.40512e8 1.48386e8i −1.59928 0.282339i
\(808\) −4.76984e8 −0.904211
\(809\) 5.94722e8i 1.12323i 0.827399 + 0.561615i \(0.189820\pi\)
−0.827399 + 0.561615i \(0.810180\pi\)
\(810\) −7.37246e8 6.19671e8i −1.38726 1.16602i
\(811\) 6.85167e8 1.28450 0.642250 0.766495i \(-0.278001\pi\)
0.642250 + 0.766495i \(0.278001\pi\)
\(812\) 1.83279e7i 0.0342331i
\(813\) 5.38509e7 3.05032e8i 0.100212 0.567641i
\(814\) 8.26693e7 0.153275
\(815\) 8.72778e8i 1.61224i
\(816\) 1.23585e8 + 2.18180e7i 0.227455 + 0.0401554i
\(817\) 3.33933e8 0.612340
\(818\) 9.05914e7i 0.165511i
\(819\) −1.77381e8 6.46452e7i −0.322891 0.117675i
\(820\) 5.28624e6 0.00958750
\(821\) 7.16117e8i 1.29406i −0.762465 0.647030i \(-0.776011\pi\)
0.762465 0.647030i \(-0.223989\pi\)
\(822\) 6.56821e7 3.72048e8i 0.118258 0.669860i
\(823\) 3.75859e8 0.674257 0.337129 0.941459i \(-0.390544\pi\)
0.337129 + 0.941459i \(0.390544\pi\)
\(824\) 6.87219e8i 1.22833i
\(825\) −4.00782e8 7.07549e7i −0.713751 0.126007i
\(826\) 3.74102e7 0.0663818
\(827\) 1.04498e8i 0.184752i −0.995724 0.0923761i \(-0.970554\pi\)
0.995724 0.0923761i \(-0.0294462\pi\)
\(828\) 2.39516e7 6.57213e7i 0.0421933 0.115775i
\(829\) −4.87724e8 −0.856073 −0.428036 0.903761i \(-0.640795\pi\)
−0.428036 + 0.903761i \(0.640795\pi\)
\(830\) 5.89007e7i 0.103012i
\(831\) −3.22995e7 + 1.82957e8i −0.0562851 + 0.318820i
\(832\) −5.61149e8 −0.974334
\(833\) 2.10803e7i 0.0364705i
\(834\) 3.16444e8 + 5.58657e7i 0.545506 + 0.0963046i
\(835\) −5.78171e8 −0.993109
\(836\) 8.21805e6i 0.0140653i
\(837\) 2.82493e8 4.88587e8i 0.481761 0.833231i
\(838\) −3.25753e8 −0.553549
\(839\) 6.05421e8i 1.02511i −0.858654 0.512556i \(-0.828699\pi\)
0.858654 0.512556i \(-0.171301\pi\)
\(840\) 7.67620e7 4.34809e8i 0.129511 0.733602i
\(841\) −4.11442e7 −0.0691704
\(842\) 4.24505e8i 0.711126i
\(843\) −1.92981e8 3.40693e7i −0.322131 0.0568696i
\(844\) −5.10623e7 −0.0849323
\(845\) 1.98325e8i 0.328706i
\(846\) 3.82807e8 + 1.39511e8i 0.632220 + 0.230408i
\(847\) 2.11812e8 0.348579
\(848\) 1.50304e8i 0.246481i
\(849\) −5.90677e7 + 3.34581e8i −0.0965221 + 0.546737i
\(850\) −3.89277e8 −0.633873
\(851\) 4.98937e8i 0.809575i
\(852\) −5.03492e7 8.88875e6i −0.0814093 0.0143721i
\(853\) 1.02486e9 1.65126 0.825630 0.564212i \(-0.190820\pi\)
0.825630 + 0.564212i \(0.190820\pi\)
\(854\) 3.99981e8i 0.642194i
\(855\) −2.33828e8 + 6.41604e8i −0.374108 + 1.02652i
\(856\) −4.17719e7 −0.0665982
\(857\) 8.50926e8i 1.35191i −0.736941 0.675957i \(-0.763730\pi\)
0.736941 0.675957i \(-0.236270\pi\)
\(858\) 2.65930e7 1.50633e8i 0.0421023 0.238483i
\(859\) −4.93728e7 −0.0778947 −0.0389474 0.999241i \(-0.512400\pi\)
−0.0389474 + 0.999241i \(0.512400\pi\)
\(860\) 1.12392e8i 0.176702i
\(861\) −1.37062e7 2.41972e6i −0.0214737 0.00379101i
\(862\) 1.78295e8 0.278367
\(863\) 2.86202e8i 0.445288i −0.974900 0.222644i \(-0.928531\pi\)
0.974900 0.222644i \(-0.0714687\pi\)
\(864\) −9.75273e7 5.63888e7i −0.151212 0.0874282i
\(865\) −7.56619e8 −1.16904
\(866\) 7.63323e8i 1.17532i
\(867\) −1.05918e8 + 5.99961e8i −0.162523 + 0.920589i
\(868\) 2.08388e7 0.0318650
\(869\) 5.87791e7i 0.0895702i
\(870\) 1.21513e9 + 2.14522e8i 1.84530 + 0.325772i
\(871\) −3.84341e6 −0.00581650
\(872\) 4.40654e8i 0.664581i
\(873\) 5.12393e8 + 1.86738e8i 0.770124 + 0.280666i
\(874\) 5.16640e8 0.773844
\(875\) 7.68311e8i 1.14687i
\(876\) −4.46486e6 + 2.52906e7i −0.00664194 + 0.0376225i
\(877\) −1.10070e9 −1.63181 −0.815907 0.578183i \(-0.803762\pi\)
−0.815907 + 0.578183i \(0.803762\pi\)
\(878\) 6.10390e8i 0.901829i
\(879\) −5.02666e8 8.87416e7i −0.740138 0.130665i
\(880\) 3.26156e8 0.478605
\(881\) 4.55028e8i 0.665442i 0.943025 + 0.332721i \(0.107967\pi\)
−0.943025 + 0.332721i \(0.892033\pi\)
\(882\) −3.20591e7 + 8.79674e7i −0.0467245 + 0.128208i
\(883\) −1.13638e7 −0.0165059 −0.00825297 0.999966i \(-0.502627\pi\)
−0.00825297 + 0.999966i \(0.502627\pi\)
\(884\) 1.40460e7i 0.0203327i
\(885\) −4.20369e7 + 2.38113e8i −0.0606458 + 0.343521i
\(886\) 1.20315e8 0.172989
\(887\) 7.74742e8i 1.11016i −0.831796 0.555081i \(-0.812687\pi\)
0.831796 0.555081i \(-0.187313\pi\)
\(888\) −4.12257e8 7.27807e7i −0.588748 0.103939i
\(889\) −3.68001e8 −0.523773
\(890\) 1.92026e9i 2.72390i
\(891\) 1.26904e8 1.50982e8i 0.179408 0.213449i
\(892\) 9.17713e7 0.129304
\(893\) 2.88898e8i 0.405686i
\(894\) −1.94263e8 + 1.10038e9i −0.271880 + 1.54003i
\(895\) −1.49308e9 −2.08264
\(896\) 2.30798e8i 0.320855i
\(897\) −9.09121e8 1.60498e8i −1.25963 0.222378i
\(898\) 7.56154e8 1.04419
\(899\) 7.23093e8i 0.995211i
\(900\) 1.55950e8 + 5.68349e7i 0.213924 + 0.0779629i
\(901\) 5.08718e7 0.0695509
\(902\) 1.12766e7i 0.0153659i
\(903\) −5.14464e7 + 2.91412e8i −0.0698701 + 0.395771i
\(904\) −5.45072e8 −0.737816
\(905\) 2.17121e9i 2.92925i
\(906\) 7.36540e8 + 1.30030e8i 0.990403 + 0.174848i
\(907\) 5.02274e8 0.673161 0.336581 0.941655i \(-0.390730\pi\)
0.336581 + 0.941655i \(0.390730\pi\)
\(908\) 6.45527e6i 0.00862296i
\(909\) −2.23846e8 + 6.14215e8i −0.298029 + 0.817766i
\(910\) −4.69318e8 −0.622792
\(911\) 4.84534e8i 0.640869i 0.947271 + 0.320434i \(0.103829\pi\)
−0.947271 + 0.320434i \(0.896171\pi\)
\(912\) 6.87107e7 3.89203e8i 0.0905815 0.513088i
\(913\) −1.20624e7 −0.0158497
\(914\) 8.94036e8i 1.17089i
\(915\) 2.54585e9 + 4.49449e8i 3.32330 + 0.586702i
\(916\) −8.58652e7 −0.111720
\(917\) 2.46359e8i 0.319493i
\(918\) 9.44283e7 1.63319e8i 0.122060 0.211109i
\(919\) −6.90401e7 −0.0889518 −0.0444759 0.999010i \(-0.514162\pi\)
−0.0444759 + 0.999010i \(0.514162\pi\)
\(920\) 2.15904e9i 2.77267i
\(921\) 8.52628e7 4.82961e8i 0.109139 0.618206i
\(922\) 2.02811e8 0.258761
\(923\) 6.74772e8i 0.858128i
\(924\) 7.17162e6 + 1.26609e6i 0.00909078 + 0.00160490i
\(925\) 1.18393e9 1.49590
\(926\) 1.01138e9i 1.27374i
\(927\) 8.84937e8 + 3.22508e8i 1.11089 + 0.404857i
\(928\) 1.44337e8 0.180607
\(929\) 6.54937e8i 0.816868i −0.912788 0.408434i \(-0.866075\pi\)
0.912788 0.408434i \(-0.133925\pi\)
\(930\) 2.43911e8 1.38160e9i 0.303237 1.71765i
\(931\) 6.63875e7 0.0822692
\(932\) 9.04911e7i 0.111778i
\(933\) −1.24205e7 2.19274e6i −0.0152931 0.00269987i
\(934\) −2.93082e8 −0.359707
\(935\) 1.10390e8i 0.135051i
\(936\) −2.65230e8 + 7.27768e8i −0.323441 + 0.887494i
\(937\) −9.35425e6 −0.0113708 −0.00568539 0.999984i \(-0.501810\pi\)
−0.00568539 + 0.999984i \(0.501810\pi\)
\(938\) 1.90603e6i 0.00230952i
\(939\) 1.65567e8 9.37834e8i 0.199976 1.13274i
\(940\) −9.72349e7 −0.117068
\(941\) 6.78408e8i 0.814184i −0.913387 0.407092i \(-0.866543\pi\)
0.913387 0.407092i \(-0.133457\pi\)
\(942\) −5.26600e8 9.29670e7i −0.629982 0.111218i
\(943\) −6.80581e7 −0.0811605
\(944\) 1.39940e8i 0.166351i
\(945\) −5.23882e8 3.02900e8i −0.620780 0.358925i
\(946\) −2.39755e8 −0.283201
\(947\) 5.91553e8i 0.696536i −0.937395 0.348268i \(-0.886770\pi\)
0.937395 0.348268i \(-0.113230\pi\)
\(948\) 4.16773e6 2.36076e7i 0.00489187 0.0277094i
\(949\) 3.38941e8 0.396575
\(950\) 1.22594e9i 1.42987i
\(951\) 5.82426e8 + 1.02823e8i 0.677172 + 0.119549i
\(952\) 8.64893e7 0.100242
\(953\) 2.85033e8i 0.329319i 0.986350 + 0.164659i \(0.0526525\pi\)
−0.986350 + 0.164659i \(0.947348\pi\)
\(954\) 2.12287e8 + 7.73662e7i 0.244499 + 0.0891059i
\(955\) −1.41843e9 −1.62853
\(956\) 7.94968e7i 0.0909863i
\(957\) −4.39325e7 + 2.48850e8i −0.0501245 + 0.283924i
\(958\) −1.57520e9 −1.79159
\(959\) 2.37389e8i 0.269157i
\(960\) −1.77127e9 3.12704e8i −2.00204 0.353443i
\(961\) −6.53497e7 −0.0736331
\(962\) 4.44977e8i 0.499818i
\(963\) −1.96033e7 + 5.37899e7i −0.0219508 + 0.0602313i
\(964\) 3.84213e6 0.00428886
\(965\) 1.63416e9i 1.81849i
\(966\) −7.95946e7 + 4.50854e8i −0.0882983 + 0.500155i
\(967\) −4.63129e7 −0.0512180 −0.0256090 0.999672i \(-0.508152\pi\)
−0.0256090 + 0.999672i \(0.508152\pi\)
\(968\) 8.69034e8i 0.958099i
\(969\) −1.31729e8 2.32557e7i −0.144781 0.0255599i
\(970\) 1.35570e9 1.48542
\(971\) 2.13841e8i 0.233578i −0.993157 0.116789i \(-0.962740\pi\)
0.993157 0.116789i \(-0.0372602\pi\)
\(972\) −6.16742e7 + 5.16413e7i −0.0671591 + 0.0562340i
\(973\) 2.01911e8 0.219190
\(974\) 8.67465e8i 0.938804i
\(975\) 3.80846e8 2.15726e9i 0.410900 2.32749i
\(976\) −1.49621e9 −1.60932
\(977\) 1.17477e9i 1.25971i −0.776715 0.629853i \(-0.783115\pi\)
0.776715 0.629853i \(-0.216885\pi\)
\(978\) −7.47763e8 1.32011e8i −0.799369 0.141122i
\(979\) 3.93255e8 0.419109
\(980\) 2.23442e7i 0.0237403i
\(981\) 5.67432e8 + 2.06796e8i 0.601045 + 0.219046i
\(982\) −8.96903e8 −0.947133
\(983\) 1.03034e8i 0.108473i 0.998528 + 0.0542364i \(0.0172725\pi\)
−0.998528 + 0.0542364i \(0.982728\pi\)
\(984\) −9.92774e6 + 5.62344e7i −0.0104199 + 0.0590224i
\(985\) 7.03026e8 0.735635
\(986\) 2.41706e8i 0.252149i
\(987\) 2.52111e8 + 4.45082e7i 0.262205 + 0.0462902i
\(988\) 4.42346e7 0.0458661
\(989\) 1.44700e9i 1.49583i
\(990\) 1.67882e8 4.60656e8i 0.173021 0.474756i
\(991\) 7.91671e7 0.0813437 0.0406718 0.999173i \(-0.487050\pi\)
0.0406718 + 0.999173i \(0.487050\pi\)
\(992\) 1.64111e8i 0.168114i
\(993\) −2.05561e8 + 1.16437e9i −0.209939 + 1.18917i
\(994\) 3.34635e8 0.340732
\(995\) 2.90325e9i 2.94723i
\(996\) 4.84466e6 + 855286.i 0.00490326 + 0.000865632i
\(997\) −3.55491e8 −0.358709 −0.179355 0.983784i \(-0.557401\pi\)
−0.179355 + 0.983784i \(0.557401\pi\)
\(998\) 1.45411e9i 1.46287i
\(999\) −2.87190e8 + 4.96711e8i −0.288054 + 0.498204i
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 21.7.b.a.8.4 12
3.2 odd 2 inner 21.7.b.a.8.9 yes 12
4.3 odd 2 336.7.d.a.113.7 12
7.6 odd 2 147.7.b.b.50.4 12
12.11 even 2 336.7.d.a.113.8 12
21.20 even 2 147.7.b.b.50.9 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.7.b.a.8.4 12 1.1 even 1 trivial
21.7.b.a.8.9 yes 12 3.2 odd 2 inner
147.7.b.b.50.4 12 7.6 odd 2
147.7.b.b.50.9 12 21.20 even 2
336.7.d.a.113.7 12 4.3 odd 2
336.7.d.a.113.8 12 12.11 even 2