Properties

Label 20.6.e.b.7.8
Level $20$
Weight $6$
Character 20.7
Analytic conductor $3.208$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [20,6,Mod(3,20)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(20, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("20.3");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 20.e (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.20767639626\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 7.8
Character \(\chi\) \(=\) 20.7
Dual form 20.6.e.b.3.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.294699 + 5.64917i) q^{2} +(20.2176 + 20.2176i) q^{3} +(-31.8263 + 3.32961i) q^{4} +(16.5333 - 53.4008i) q^{5} +(-108.255 + 120.171i) q^{6} +(-9.02060 + 9.02060i) q^{7} +(-28.1887 - 178.811i) q^{8} +574.502i q^{9} +O(q^{10})\) \(q+(0.294699 + 5.64917i) q^{2} +(20.2176 + 20.2176i) q^{3} +(-31.8263 + 3.32961i) q^{4} +(16.5333 - 53.4008i) q^{5} +(-108.255 + 120.171i) q^{6} +(-9.02060 + 9.02060i) q^{7} +(-28.1887 - 178.811i) q^{8} +574.502i q^{9} +(306.543 + 77.6625i) q^{10} -200.964i q^{11} +(-710.768 - 576.134i) q^{12} +(362.922 - 362.922i) q^{13} +(-53.6173 - 48.3006i) q^{14} +(1413.90 - 745.372i) q^{15} +(1001.83 - 211.938i) q^{16} +(465.936 + 465.936i) q^{17} +(-3245.46 + 169.305i) q^{18} -582.013 q^{19} +(-348.391 + 1754.60i) q^{20} -364.749 q^{21} +(1135.28 - 59.2240i) q^{22} +(285.210 + 285.210i) q^{23} +(3045.22 - 4185.04i) q^{24} +(-2578.30 - 1765.79i) q^{25} +(2157.16 + 1943.25i) q^{26} +(-6702.16 + 6702.16i) q^{27} +(257.057 - 317.127i) q^{28} +1272.50i q^{29} +(4627.41 + 7767.71i) q^{30} -4269.21i q^{31} +(1492.51 + 5597.04i) q^{32} +(4063.02 - 4063.02i) q^{33} +(-2494.84 + 2769.46i) q^{34} +(332.567 + 630.848i) q^{35} +(-1912.87 - 18284.3i) q^{36} +(-6272.71 - 6272.71i) q^{37} +(-171.519 - 3287.89i) q^{38} +14674.8 q^{39} +(-10014.7 - 1451.04i) q^{40} -11615.1 q^{41} +(-107.491 - 2060.53i) q^{42} +(-11992.8 - 11992.8i) q^{43} +(669.133 + 6395.96i) q^{44} +(30678.9 + 9498.43i) q^{45} +(-1527.15 + 1695.25i) q^{46} +(4131.72 - 4131.72i) q^{47} +(24539.4 + 15969.7i) q^{48} +16644.3i q^{49} +(9215.42 - 15085.6i) q^{50} +18840.2i q^{51} +(-10342.1 + 12758.8i) q^{52} +(-13795.5 + 13795.5i) q^{53} +(-39836.8 - 35886.6i) q^{54} +(-10731.7 - 3322.61i) q^{55} +(1867.26 + 1358.70i) q^{56} +(-11766.9 - 11766.9i) q^{57} +(-7188.60 + 375.006i) q^{58} +38121.2 q^{59} +(-42517.4 + 28430.2i) q^{60} +30096.6 q^{61} +(24117.5 - 1258.13i) q^{62} +(-5182.35 - 5182.35i) q^{63} +(-31178.8 + 10080.9i) q^{64} +(-13380.0 - 25380.6i) q^{65} +(24150.0 + 21755.3i) q^{66} +(3078.23 - 3078.23i) q^{67} +(-16380.4 - 13277.6i) q^{68} +11532.5i q^{69} +(-3465.76 + 2064.64i) q^{70} +49490.1i q^{71} +(102727. - 16194.5i) q^{72} +(25457.2 - 25457.2i) q^{73} +(33587.1 - 37284.2i) q^{74} +(-16427.0 - 87826.9i) q^{75} +(18523.3 - 1937.88i) q^{76} +(1812.82 + 1812.82i) q^{77} +(4324.65 + 82900.5i) q^{78} -99053.4 q^{79} +(5245.86 - 57002.5i) q^{80} -131399. q^{81} +(-3422.94 - 65615.5i) q^{82} +(39858.9 + 39858.9i) q^{83} +(11608.6 - 1214.47i) q^{84} +(32584.9 - 17177.9i) q^{85} +(64215.0 - 71283.5i) q^{86} +(-25727.0 + 25727.0i) q^{87} +(-35934.7 + 5664.93i) q^{88} +65188.8i q^{89} +(-44617.2 + 176109. i) q^{90} +6547.54i q^{91} +(-10026.8 - 8127.55i) q^{92} +(86313.2 - 86313.2i) q^{93} +(24558.4 + 22123.2i) q^{94} +(-9622.61 + 31080.0i) q^{95} +(-82983.6 + 143334. i) q^{96} +(-44621.3 - 44621.3i) q^{97} +(-94026.3 + 4905.04i) q^{98} +115454. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 10 q^{2} - 80 q^{5} - 184 q^{6} + 500 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 10 q^{2} - 80 q^{5} - 184 q^{6} + 500 q^{8} + 590 q^{10} - 1280 q^{12} - 1320 q^{13} + 4024 q^{16} + 2440 q^{17} - 5190 q^{18} + 1260 q^{20} + 1632 q^{21} - 2440 q^{22} - 7320 q^{25} - 4668 q^{26} + 5920 q^{28} + 8600 q^{30} + 25800 q^{32} + 10400 q^{33} - 43460 q^{36} + 14120 q^{37} - 22160 q^{38} - 11220 q^{40} - 19552 q^{41} - 39400 q^{42} + 7960 q^{45} + 29416 q^{46} + 108160 q^{48} + 141010 q^{50} - 7540 q^{52} - 106520 q^{53} - 85984 q^{56} + 40320 q^{57} - 115160 q^{58} - 263840 q^{60} + 206048 q^{61} - 109400 q^{62} - 181800 q^{65} + 186000 q^{66} + 268100 q^{68} + 364240 q^{70} + 247620 q^{72} + 107960 q^{73} - 297600 q^{76} - 53280 q^{77} - 586200 q^{78} - 390000 q^{80} - 66744 q^{81} - 498360 q^{82} - 31880 q^{85} + 545416 q^{86} + 690080 q^{88} + 791790 q^{90} + 576800 q^{92} + 182240 q^{93} - 841984 q^{96} + 60760 q^{97} - 902450 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(17\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.294699 + 5.64917i 0.0520959 + 0.998642i
\(3\) 20.2176 + 20.2176i 1.29696 + 1.29696i 0.930392 + 0.366567i \(0.119467\pi\)
0.366567 + 0.930392i \(0.380533\pi\)
\(4\) −31.8263 + 3.32961i −0.994572 + 0.104050i
\(5\) 16.5333 53.4008i 0.295757 0.955263i
\(6\) −108.255 + 120.171i −1.22763 + 1.36276i
\(7\) −9.02060 + 9.02060i −0.0695809 + 0.0695809i −0.741041 0.671460i \(-0.765668\pi\)
0.671460 + 0.741041i \(0.265668\pi\)
\(8\) −28.1887 178.811i −0.155722 0.987801i
\(9\) 574.502i 2.36420i
\(10\) 306.543 + 77.6625i 0.969374 + 0.245590i
\(11\) 200.964i 0.500769i −0.968146 0.250385i \(-0.919443\pi\)
0.968146 0.250385i \(-0.0805570\pi\)
\(12\) −710.768 576.134i −1.42487 1.15497i
\(13\) 362.922 362.922i 0.595600 0.595600i −0.343539 0.939139i \(-0.611626\pi\)
0.939139 + 0.343539i \(0.111626\pi\)
\(14\) −53.6173 48.3006i −0.0731113 0.0658616i
\(15\) 1413.90 745.372i 1.62252 0.855352i
\(16\) 1001.83 211.938i 0.978347 0.206971i
\(17\) 465.936 + 465.936i 0.391025 + 0.391025i 0.875053 0.484028i \(-0.160827\pi\)
−0.484028 + 0.875053i \(0.660827\pi\)
\(18\) −3245.46 + 169.305i −2.36099 + 0.123165i
\(19\) −582.013 −0.369870 −0.184935 0.982751i \(-0.559207\pi\)
−0.184935 + 0.982751i \(0.559207\pi\)
\(20\) −348.391 + 1754.60i −0.194756 + 0.980852i
\(21\) −364.749 −0.180487
\(22\) 1135.28 59.2240i 0.500089 0.0260880i
\(23\) 285.210 + 285.210i 0.112421 + 0.112421i 0.761079 0.648659i \(-0.224670\pi\)
−0.648659 + 0.761079i \(0.724670\pi\)
\(24\) 3045.22 4185.04i 1.07917 1.48310i
\(25\) −2578.30 1765.79i −0.825055 0.565052i
\(26\) 2157.16 + 1943.25i 0.625819 + 0.563763i
\(27\) −6702.16 + 6702.16i −1.76932 + 1.76932i
\(28\) 257.057 317.127i 0.0619633 0.0764432i
\(29\) 1272.50i 0.280973i 0.990083 + 0.140486i \(0.0448666\pi\)
−0.990083 + 0.140486i \(0.955133\pi\)
\(30\) 4627.41 + 7767.71i 0.938717 + 1.57576i
\(31\) 4269.21i 0.797891i −0.916975 0.398946i \(-0.869376\pi\)
0.916975 0.398946i \(-0.130624\pi\)
\(32\) 1492.51 + 5597.04i 0.257658 + 0.966236i
\(33\) 4063.02 4063.02i 0.649477 0.649477i
\(34\) −2494.84 + 2769.46i −0.370123 + 0.410864i
\(35\) 332.567 + 630.848i 0.0458890 + 0.0870472i
\(36\) −1912.87 18284.3i −0.245996 2.35137i
\(37\) −6272.71 6272.71i −0.753271 0.753271i 0.221817 0.975088i \(-0.428801\pi\)
−0.975088 + 0.221817i \(0.928801\pi\)
\(38\) −171.519 3287.89i −0.0192687 0.369367i
\(39\) 14674.8 1.54494
\(40\) −10014.7 1451.04i −0.989666 0.143394i
\(41\) −11615.1 −1.07910 −0.539550 0.841954i \(-0.681406\pi\)
−0.539550 + 0.841954i \(0.681406\pi\)
\(42\) −107.491 2060.53i −0.00940264 0.180242i
\(43\) −11992.8 11992.8i −0.989119 0.989119i 0.0108221 0.999941i \(-0.496555\pi\)
−0.999941 + 0.0108221i \(0.996555\pi\)
\(44\) 669.133 + 6395.96i 0.0521052 + 0.498051i
\(45\) 30678.9 + 9498.43i 2.25844 + 0.699231i
\(46\) −1527.15 + 1695.25i −0.106411 + 0.118125i
\(47\) 4131.72 4131.72i 0.272826 0.272826i −0.557411 0.830237i \(-0.688205\pi\)
0.830237 + 0.557411i \(0.188205\pi\)
\(48\) 24539.4 + 15969.7i 1.53731 + 1.00044i
\(49\) 16644.3i 0.990317i
\(50\) 9215.42 15085.6i 0.521303 0.853372i
\(51\) 18840.2i 1.01429i
\(52\) −10342.1 + 12758.8i −0.530395 + 0.654339i
\(53\) −13795.5 + 13795.5i −0.674602 + 0.674602i −0.958773 0.284172i \(-0.908281\pi\)
0.284172 + 0.958773i \(0.408281\pi\)
\(54\) −39836.8 35886.6i −1.85909 1.67474i
\(55\) −10731.7 3322.61i −0.478366 0.148106i
\(56\) 1867.26 + 1358.70i 0.0795674 + 0.0578968i
\(57\) −11766.9 11766.9i −0.479706 0.479706i
\(58\) −7188.60 + 375.006i −0.280591 + 0.0146375i
\(59\) 38121.2 1.42573 0.712863 0.701303i \(-0.247398\pi\)
0.712863 + 0.701303i \(0.247398\pi\)
\(60\) −42517.4 + 28430.2i −1.52472 + 1.01953i
\(61\) 30096.6 1.03560 0.517801 0.855501i \(-0.326751\pi\)
0.517801 + 0.855501i \(0.326751\pi\)
\(62\) 24117.5 1258.13i 0.796808 0.0415669i
\(63\) −5182.35 5182.35i −0.164504 0.164504i
\(64\) −31178.8 + 10080.9i −0.951501 + 0.307645i
\(65\) −13380.0 25380.6i −0.392802 0.745107i
\(66\) 24150.0 + 21755.3i 0.682430 + 0.614760i
\(67\) 3078.23 3078.23i 0.0837750 0.0837750i −0.663978 0.747753i \(-0.731133\pi\)
0.747753 + 0.663978i \(0.231133\pi\)
\(68\) −16380.4 13277.6i −0.429588 0.348216i
\(69\) 11532.5i 0.291610i
\(70\) −3465.76 + 2064.64i −0.0845383 + 0.0503615i
\(71\) 49490.1i 1.16513i 0.812786 + 0.582563i \(0.197950\pi\)
−0.812786 + 0.582563i \(0.802050\pi\)
\(72\) 102727. 16194.5i 2.33536 0.368159i
\(73\) 25457.2 25457.2i 0.559117 0.559117i −0.369939 0.929056i \(-0.620621\pi\)
0.929056 + 0.369939i \(0.120621\pi\)
\(74\) 33587.1 37284.2i 0.713006 0.791490i
\(75\) −16427.0 87826.9i −0.337214 1.80291i
\(76\) 18523.3 1937.88i 0.367862 0.0384850i
\(77\) 1812.82 + 1812.82i 0.0348440 + 0.0348440i
\(78\) 4324.65 + 82900.5i 0.0804849 + 1.54284i
\(79\) −99053.4 −1.78567 −0.892836 0.450382i \(-0.851288\pi\)
−0.892836 + 0.450382i \(0.851288\pi\)
\(80\) 5245.86 57002.5i 0.0916414 0.995792i
\(81\) −131399. −2.22526
\(82\) −3422.94 65615.5i −0.0562167 1.07763i
\(83\) 39858.9 + 39858.9i 0.635083 + 0.635083i 0.949338 0.314256i \(-0.101755\pi\)
−0.314256 + 0.949338i \(0.601755\pi\)
\(84\) 11608.6 1214.47i 0.179508 0.0187797i
\(85\) 32584.9 17177.9i 0.489180 0.257883i
\(86\) 64215.0 71283.5i 0.936247 1.03931i
\(87\) −25727.0 + 25727.0i −0.364410 + 0.364410i
\(88\) −35934.7 + 5664.93i −0.494660 + 0.0779808i
\(89\) 65188.8i 0.872365i 0.899858 + 0.436182i \(0.143670\pi\)
−0.899858 + 0.436182i \(0.856330\pi\)
\(90\) −44617.2 + 176109.i −0.580626 + 2.29180i
\(91\) 6547.54i 0.0828848i
\(92\) −10026.8 8127.55i −0.123508 0.100113i
\(93\) 86313.2 86313.2i 1.03483 1.03483i
\(94\) 24558.4 + 22123.2i 0.286669 + 0.258242i
\(95\) −9622.61 + 31080.0i −0.109392 + 0.353323i
\(96\) −82983.6 + 143334.i −0.918997 + 1.58734i
\(97\) −44621.3 44621.3i −0.481518 0.481518i 0.424098 0.905616i \(-0.360591\pi\)
−0.905616 + 0.424098i \(0.860591\pi\)
\(98\) −94026.3 + 4905.04i −0.988972 + 0.0515914i
\(99\) 115454. 1.18392
\(100\) 87937.1 + 47613.8i 0.879371 + 0.476138i
\(101\) 69462.4 0.677558 0.338779 0.940866i \(-0.389986\pi\)
0.338779 + 0.940866i \(0.389986\pi\)
\(102\) −106432. + 5552.19i −1.01291 + 0.0528401i
\(103\) 74405.5 + 74405.5i 0.691054 + 0.691054i 0.962464 0.271410i \(-0.0874900\pi\)
−0.271410 + 0.962464i \(0.587490\pi\)
\(104\) −75124.7 54664.1i −0.681082 0.495586i
\(105\) −6030.52 + 19477.9i −0.0533804 + 0.172413i
\(106\) −81998.6 73867.6i −0.708830 0.638542i
\(107\) −34940.2 + 34940.2i −0.295030 + 0.295030i −0.839063 0.544034i \(-0.816896\pi\)
0.544034 + 0.839063i \(0.316896\pi\)
\(108\) 190990. 235621.i 1.57562 1.94381i
\(109\) 49187.7i 0.396543i 0.980147 + 0.198272i \(0.0635328\pi\)
−0.980147 + 0.198272i \(0.936467\pi\)
\(110\) 15607.4 61604.2i 0.122984 0.485432i
\(111\) 253638.i 1.95392i
\(112\) −7125.27 + 10948.9i −0.0536731 + 0.0824755i
\(113\) −161701. + 161701.i −1.19129 + 1.19129i −0.214581 + 0.976706i \(0.568839\pi\)
−0.976706 + 0.214581i \(0.931161\pi\)
\(114\) 63005.5 69940.9i 0.454063 0.504045i
\(115\) 19945.9 10515.0i 0.140640 0.0741420i
\(116\) −4236.94 40499.1i −0.0292353 0.279448i
\(117\) 208499. + 208499.i 1.40812 + 1.40812i
\(118\) 11234.3 + 215353.i 0.0742744 + 1.42379i
\(119\) −8406.05 −0.0544157
\(120\) −173137. 231810.i −1.09758 1.46953i
\(121\) 120664. 0.749230
\(122\) 8869.44 + 170021.i 0.0539507 + 1.03420i
\(123\) −234828. 234828.i −1.39955 1.39955i
\(124\) 14214.8 + 135873.i 0.0830208 + 0.793560i
\(125\) −136922. + 108489.i −0.783789 + 0.621027i
\(126\) 27748.8 30803.2i 0.155710 0.172850i
\(127\) 204895. 204895.i 1.12725 1.12725i 0.136630 0.990622i \(-0.456373\pi\)
0.990622 0.136630i \(-0.0436272\pi\)
\(128\) −66137.1 173164.i −0.356796 0.934182i
\(129\) 484930.i 2.56569i
\(130\) 139436. 83065.7i 0.723632 0.431085i
\(131\) 291964.i 1.48645i 0.669041 + 0.743226i \(0.266705\pi\)
−0.669041 + 0.743226i \(0.733295\pi\)
\(132\) −115783. + 142839.i −0.578373 + 0.713530i
\(133\) 5250.10 5250.10i 0.0257359 0.0257359i
\(134\) 18296.6 + 16482.3i 0.0880256 + 0.0792969i
\(135\) 247092. + 468710.i 1.16688 + 2.21345i
\(136\) 70180.4 96448.7i 0.325363 0.447146i
\(137\) −213117. 213117.i −0.970102 0.970102i 0.0294634 0.999566i \(-0.490620\pi\)
−0.999566 + 0.0294634i \(0.990620\pi\)
\(138\) −65149.3 + 3398.62i −0.291214 + 0.0151917i
\(139\) −10045.0 −0.0440972 −0.0220486 0.999757i \(-0.507019\pi\)
−0.0220486 + 0.999757i \(0.507019\pi\)
\(140\) −12684.9 18970.2i −0.0546972 0.0817999i
\(141\) 167067. 0.707688
\(142\) −279578. + 14584.7i −1.16354 + 0.0606982i
\(143\) −72934.3 72934.3i −0.298258 0.298258i
\(144\) 121759. + 575552.i 0.489322 + 2.31301i
\(145\) 67952.8 + 21038.7i 0.268403 + 0.0830997i
\(146\) 151314. + 136310.i 0.587486 + 0.529230i
\(147\) −336507. + 336507.i −1.28440 + 1.28440i
\(148\) 220523. + 178752.i 0.827560 + 0.670804i
\(149\) 46622.5i 0.172040i 0.996293 + 0.0860201i \(0.0274149\pi\)
−0.996293 + 0.0860201i \(0.972585\pi\)
\(150\) 491308. 118681.i 1.78290 0.430680i
\(151\) 233568.i 0.833625i −0.908992 0.416813i \(-0.863147\pi\)
0.908992 0.416813i \(-0.136853\pi\)
\(152\) 16406.2 + 104070.i 0.0575969 + 0.365357i
\(153\) −267681. + 267681.i −0.924462 + 0.924462i
\(154\) −9706.69 + 10775.2i −0.0329814 + 0.0366119i
\(155\) −227980. 70584.3i −0.762196 0.235982i
\(156\) −467045. + 48861.4i −1.53655 + 0.160751i
\(157\) −146024. 146024.i −0.472799 0.472799i 0.430020 0.902819i \(-0.358506\pi\)
−0.902819 + 0.430020i \(0.858506\pi\)
\(158\) −29190.9 559570.i −0.0930262 1.78325i
\(159\) −557823. −1.74986
\(160\) 323563. + 12836.2i 0.999214 + 0.0396403i
\(161\) −5145.54 −0.0156447
\(162\) −38723.2 742297.i −0.115927 2.22224i
\(163\) 191971. + 191971.i 0.565936 + 0.565936i 0.930987 0.365051i \(-0.118949\pi\)
−0.365051 + 0.930987i \(0.618949\pi\)
\(164\) 369664. 38673.6i 1.07324 0.112281i
\(165\) −149793. 284144.i −0.428334 0.812509i
\(166\) −213423. + 236916.i −0.601135 + 0.667305i
\(167\) 403364. 403364.i 1.11920 1.11920i 0.127336 0.991860i \(-0.459357\pi\)
0.991860 0.127336i \(-0.0406428\pi\)
\(168\) 10281.8 + 65221.2i 0.0281059 + 0.178285i
\(169\) 107869.i 0.290522i
\(170\) 106644. + 179015.i 0.283017 + 0.475081i
\(171\) 334367.i 0.874447i
\(172\) 421617. + 341755.i 1.08667 + 0.880832i
\(173\) 355811. 355811.i 0.903867 0.903867i −0.0919008 0.995768i \(-0.529294\pi\)
0.995768 + 0.0919008i \(0.0292943\pi\)
\(174\) −152918. 137754.i −0.382900 0.344931i
\(175\) 39186.2 7329.33i 0.0967250 0.0180913i
\(176\) −42592.1 201332.i −0.103645 0.489926i
\(177\) 770718. + 770718.i 1.84911 + 1.84911i
\(178\) −368263. + 19211.1i −0.871180 + 0.0454466i
\(179\) 423056. 0.986882 0.493441 0.869779i \(-0.335739\pi\)
0.493441 + 0.869779i \(0.335739\pi\)
\(180\) −1.00802e6 200151.i −2.31893 0.460444i
\(181\) −286397. −0.649788 −0.324894 0.945750i \(-0.605329\pi\)
−0.324894 + 0.945750i \(0.605329\pi\)
\(182\) −36988.2 + 1929.55i −0.0827722 + 0.00431796i
\(183\) 608481. + 608481.i 1.34313 + 1.34313i
\(184\) 42959.1 59038.5i 0.0935428 0.128555i
\(185\) −438677. + 231259.i −0.942357 + 0.496787i
\(186\) 513035. + 462162.i 1.08734 + 0.979516i
\(187\) 93636.6 93636.6i 0.195813 0.195813i
\(188\) −117740. + 145254.i −0.242958 + 0.299733i
\(189\) 120915.i 0.246221i
\(190\) −178412. 45200.6i −0.358542 0.0908364i
\(191\) 16778.2i 0.0332784i −0.999862 0.0166392i \(-0.994703\pi\)
0.999862 0.0166392i \(-0.00529667\pi\)
\(192\) −834172. 426548.i −1.63306 0.835055i
\(193\) 457652. 457652.i 0.884386 0.884386i −0.109591 0.993977i \(-0.534954\pi\)
0.993977 + 0.109591i \(0.0349540\pi\)
\(194\) 238923. 265223.i 0.455779 0.505949i
\(195\) 242623. 783647.i 0.456926 1.47582i
\(196\) −55418.9 529725.i −0.103043 0.984942i
\(197\) 40421.4 + 40421.4i 0.0742072 + 0.0742072i 0.743236 0.669029i \(-0.233290\pi\)
−0.669029 + 0.743236i \(0.733290\pi\)
\(198\) 34024.3 + 652222.i 0.0616774 + 1.18231i
\(199\) −1.00700e6 −1.80260 −0.901298 0.433200i \(-0.857384\pi\)
−0.901298 + 0.433200i \(0.857384\pi\)
\(200\) −243063. + 510803.i −0.429679 + 0.902981i
\(201\) 124469. 0.217306
\(202\) 20470.5 + 392405.i 0.0352980 + 0.676638i
\(203\) −11478.8 11478.8i −0.0195503 0.0195503i
\(204\) −62730.5 599614.i −0.105537 1.00878i
\(205\) −192036. + 620254.i −0.319152 + 1.03082i
\(206\) −398402. + 442256.i −0.654114 + 0.726116i
\(207\) −163854. + 163854.i −0.265785 + 0.265785i
\(208\) 286668. 440502.i 0.459431 0.705975i
\(209\) 116964.i 0.185219i
\(210\) −111811. 28327.3i −0.174960 0.0443259i
\(211\) 769943.i 1.19056i 0.803517 + 0.595281i \(0.202959\pi\)
−0.803517 + 0.595281i \(0.797041\pi\)
\(212\) 393126. 484993.i 0.600747 0.741133i
\(213\) −1.00057e6 + 1.00057e6i −1.51112 + 1.51112i
\(214\) −207680. 187086.i −0.309999 0.279259i
\(215\) −838705. + 442144.i −1.23741 + 0.652330i
\(216\) 1.38735e6 + 1.00950e6i 2.02325 + 1.47221i
\(217\) 38510.9 + 38510.9i 0.0555180 + 0.0555180i
\(218\) −277870. + 14495.6i −0.396005 + 0.0206583i
\(219\) 1.02936e6 1.45030
\(220\) 352612. + 70014.2i 0.491180 + 0.0975280i
\(221\) 338197. 0.465788
\(222\) 1.43285e6 74746.9i 1.95127 0.101791i
\(223\) −128914. 128914.i −0.173595 0.173595i 0.614962 0.788557i \(-0.289171\pi\)
−0.788557 + 0.614962i \(0.789171\pi\)
\(224\) −63952.0 37025.3i −0.0851597 0.0493035i
\(225\) 1.01445e6 1.48124e6i 1.33590 1.95060i
\(226\) −961130. 865824.i −1.25173 1.12761i
\(227\) 342980. 342980.i 0.441778 0.441778i −0.450831 0.892609i \(-0.648872\pi\)
0.892609 + 0.450831i \(0.148872\pi\)
\(228\) 413676. + 335318.i 0.527015 + 0.427188i
\(229\) 189890.i 0.239284i −0.992817 0.119642i \(-0.961825\pi\)
0.992817 0.119642i \(-0.0381746\pi\)
\(230\) 65279.1 + 109579.i 0.0813681 + 0.136587i
\(231\) 73301.7i 0.0903824i
\(232\) 227538. 35870.3i 0.277545 0.0437537i
\(233\) 519010. 519010.i 0.626305 0.626305i −0.320831 0.947136i \(-0.603962\pi\)
0.947136 + 0.320831i \(0.103962\pi\)
\(234\) −1.11640e6 + 1.23929e6i −1.33285 + 1.47956i
\(235\) −152326. 288948.i −0.179930 0.341311i
\(236\) −1.21326e6 + 126929.i −1.41799 + 0.148347i
\(237\) −2.00262e6 2.00262e6i −2.31594 2.31594i
\(238\) −2477.25 47487.2i −0.00283483 0.0543418i
\(239\) 283416. 0.320945 0.160472 0.987040i \(-0.448698\pi\)
0.160472 + 0.987040i \(0.448698\pi\)
\(240\) 1.25851e6 1.04639e6i 1.41036 1.17265i
\(241\) −715522. −0.793562 −0.396781 0.917913i \(-0.629873\pi\)
−0.396781 + 0.917913i \(0.629873\pi\)
\(242\) 35559.6 + 681653.i 0.0390318 + 0.748213i
\(243\) −1.02795e6 1.02795e6i −1.11675 1.11675i
\(244\) −957865. + 100210.i −1.02998 + 0.107755i
\(245\) 888817. + 275185.i 0.946013 + 0.292893i
\(246\) 1.25738e6 1.39579e6i 1.32474 1.47056i
\(247\) −211225. + 211225.i −0.220294 + 0.220294i
\(248\) −763383. + 120344.i −0.788158 + 0.124249i
\(249\) 1.61170e6i 1.64735i
\(250\) −653223. 741527.i −0.661016 0.750372i
\(251\) 729075.i 0.730446i 0.930920 + 0.365223i \(0.119007\pi\)
−0.930920 + 0.365223i \(0.880993\pi\)
\(252\) 182190. + 147680.i 0.180727 + 0.146494i
\(253\) 57317.1 57317.1i 0.0562967 0.0562967i
\(254\) 1.21787e6 + 1.09710e6i 1.18445 + 1.06700i
\(255\) 1.00608e6 + 311491.i 0.968910 + 0.299982i
\(256\) 958740. 424651.i 0.914326 0.404979i
\(257\) 354126. + 354126.i 0.334445 + 0.334445i 0.854272 0.519827i \(-0.174004\pi\)
−0.519827 + 0.854272i \(0.674004\pi\)
\(258\) 2.73945e6 142908.i 2.56221 0.133662i
\(259\) 113167. 0.104827
\(260\) 510344. + 763221.i 0.468198 + 0.700192i
\(261\) −731056. −0.664277
\(262\) −1.64935e6 + 86041.4i −1.48443 + 0.0774380i
\(263\) −1.27436e6 1.27436e6i −1.13606 1.13606i −0.989150 0.146911i \(-0.953067\pi\)
−0.146911 0.989150i \(-0.546933\pi\)
\(264\) −841043. 611981.i −0.742692 0.540416i
\(265\) 508605. + 964776.i 0.444904 + 0.843940i
\(266\) 31205.9 + 28111.5i 0.0270417 + 0.0243602i
\(267\) −1.31796e6 + 1.31796e6i −1.13142 + 1.13142i
\(268\) −87719.5 + 108218.i −0.0746035 + 0.0920371i
\(269\) 433722.i 0.365452i −0.983164 0.182726i \(-0.941508\pi\)
0.983164 0.182726i \(-0.0584921\pi\)
\(270\) −2.57501e6 + 1.53399e6i −2.14966 + 1.28060i
\(271\) 496087.i 0.410331i 0.978727 + 0.205165i \(0.0657733\pi\)
−0.978727 + 0.205165i \(0.934227\pi\)
\(272\) 565537. + 368038.i 0.463489 + 0.301627i
\(273\) −132375. + 132375.i −0.107498 + 0.107498i
\(274\) 1.14113e6 1.26674e6i 0.918247 1.01932i
\(275\) −354860. + 518146.i −0.282961 + 0.413162i
\(276\) −38398.8 367038.i −0.0303421 0.290027i
\(277\) 176095. + 176095.i 0.137894 + 0.137894i 0.772685 0.634790i \(-0.218913\pi\)
−0.634790 + 0.772685i \(0.718913\pi\)
\(278\) −2960.24 56745.7i −0.00229728 0.0440373i
\(279\) 2.45267e6 1.88638
\(280\) 103428. 77249.4i 0.0788393 0.0588844i
\(281\) 882746. 0.666914 0.333457 0.942765i \(-0.391785\pi\)
0.333457 + 0.942765i \(0.391785\pi\)
\(282\) 49234.4 + 943789.i 0.0368677 + 0.706727i
\(283\) 879056. + 879056.i 0.652455 + 0.652455i 0.953584 0.301128i \(-0.0973633\pi\)
−0.301128 + 0.953584i \(0.597363\pi\)
\(284\) −164783. 1.57509e6i −0.121232 1.15880i
\(285\) −822908. + 433816.i −0.600121 + 0.316369i
\(286\) 390525. 433512.i 0.282315 0.313391i
\(287\) 104775. 104775.i 0.0750848 0.0750848i
\(288\) −3.21551e6 + 857452.i −2.28438 + 0.609156i
\(289\) 985664.i 0.694199i
\(290\) −98825.8 + 390077.i −0.0690042 + 0.272368i
\(291\) 1.80427e6i 1.24902i
\(292\) −725445. + 894970.i −0.497906 + 0.614259i
\(293\) 371593. 371593.i 0.252871 0.252871i −0.569276 0.822147i \(-0.692776\pi\)
0.822147 + 0.569276i \(0.192776\pi\)
\(294\) −2.00015e6 1.80182e6i −1.34957 1.21574i
\(295\) 630270. 2.03570e6i 0.421669 1.36194i
\(296\) −944811. + 1.29845e6i −0.626781 + 0.861382i
\(297\) 1.34690e6 + 1.34690e6i 0.886019 + 0.886019i
\(298\) −263379. + 13739.6i −0.171807 + 0.00896259i
\(299\) 207018. 0.133915
\(300\) 815240. + 2.74051e6i 0.522977 + 1.75804i
\(301\) 216364. 0.137648
\(302\) 1.31947e6 68832.2i 0.832493 0.0434285i
\(303\) 1.40436e6 + 1.40436e6i 0.878765 + 0.878765i
\(304\) −583076. + 123351.i −0.361861 + 0.0765523i
\(305\) 497598. 1.60719e6i 0.306287 0.989273i
\(306\) −1.59106e6 1.43329e6i −0.971368 0.875046i
\(307\) −547759. + 547759.i −0.331699 + 0.331699i −0.853231 0.521533i \(-0.825360\pi\)
0.521533 + 0.853231i \(0.325360\pi\)
\(308\) −63731.3 51659.4i −0.0382804 0.0310293i
\(309\) 3.00860e6i 1.79254i
\(310\) 331558. 1.30870e6i 0.195954 0.773455i
\(311\) 2.66010e6i 1.55954i −0.626065 0.779771i \(-0.715336\pi\)
0.626065 0.779771i \(-0.284664\pi\)
\(312\) −413664. 2.62402e6i −0.240581 1.52609i
\(313\) −455775. + 455775.i −0.262960 + 0.262960i −0.826256 0.563295i \(-0.809533\pi\)
0.563295 + 0.826256i \(0.309533\pi\)
\(314\) 781884. 867950.i 0.447526 0.496788i
\(315\) −362423. + 191060.i −0.205797 + 0.108491i
\(316\) 3.15250e6 329809.i 1.77598 0.185800i
\(317\) −752475. 752475.i −0.420575 0.420575i 0.464826 0.885402i \(-0.346117\pi\)
−0.885402 + 0.464826i \(0.846117\pi\)
\(318\) −164390. 3.15124e6i −0.0911606 1.74749i
\(319\) 255728. 0.140702
\(320\) 22839.5 + 1.83164e6i 0.0124685 + 0.999922i
\(321\) −1.41281e6 −0.765283
\(322\) −1516.38 29068.0i −0.000815022 0.0156234i
\(323\) −271181. 271181.i −0.144628 0.144628i
\(324\) 4.18195e6 437508.i 2.21318 0.231539i
\(325\) −1.57656e6 + 294878.i −0.827948 + 0.154858i
\(326\) −1.02791e6 + 1.14105e6i −0.535685 + 0.594651i
\(327\) −994457. + 994457.i −0.514300 + 0.514300i
\(328\) 327414. + 2.07690e6i 0.168040 + 1.06594i
\(329\) 74541.1i 0.0379670i
\(330\) 1.56103e6 929945.i 0.789091 0.470081i
\(331\) 1.14555e6i 0.574704i 0.957825 + 0.287352i \(0.0927749\pi\)
−0.957825 + 0.287352i \(0.907225\pi\)
\(332\) −1.40128e6 1.13585e6i −0.697716 0.565555i
\(333\) 3.60368e6 3.60368e6i 1.78089 1.78089i
\(334\) 2.39754e6 + 2.15980e6i 1.17598 + 1.05937i
\(335\) −113487. 215274.i −0.0552501 0.104804i
\(336\) −365416. + 77304.4i −0.176579 + 0.0373556i
\(337\) −347364. 347364.i −0.166614 0.166614i 0.618876 0.785489i \(-0.287589\pi\)
−0.785489 + 0.618876i \(0.787589\pi\)
\(338\) −609369. + 31788.8i −0.290127 + 0.0151350i
\(339\) −6.53841e6 −3.09010
\(340\) −979860. + 655204.i −0.459692 + 0.307383i
\(341\) −857960. −0.399559
\(342\) 1.88890e6 98537.7i 0.873260 0.0455551i
\(343\) −301750. 301750.i −0.138488 0.138488i
\(344\) −1.80638e6 + 2.48250e6i −0.823025 + 1.13108i
\(345\) 615847. + 190671.i 0.278564 + 0.0862457i
\(346\) 2.11490e6 + 1.90518e6i 0.949728 + 0.855552i
\(347\) 1.61941e6 1.61941e6i 0.721994 0.721994i −0.247017 0.969011i \(-0.579450\pi\)
0.969011 + 0.247017i \(0.0794503\pi\)
\(348\) 733134. 904455.i 0.324515 0.400349i
\(349\) 75542.7i 0.0331993i 0.999862 + 0.0165996i \(0.00528407\pi\)
−0.999862 + 0.0165996i \(0.994716\pi\)
\(350\) 52952.8 + 219210.i 0.0231057 + 0.0956511i
\(351\) 4.86472e6i 2.10761i
\(352\) 1.12481e6 299942.i 0.483861 0.129027i
\(353\) −2.12610e6 + 2.12610e6i −0.908128 + 0.908128i −0.996121 0.0879935i \(-0.971955\pi\)
0.0879935 + 0.996121i \(0.471955\pi\)
\(354\) −4.12679e6 + 4.58105e6i −1.75027 + 1.94293i
\(355\) 2.64281e6 + 818236.i 1.11300 + 0.344594i
\(356\) −217053. 2.07472e6i −0.0907698 0.867630i
\(357\) −169950. 169950.i −0.0705749 0.0705749i
\(358\) 124674. + 2.38992e6i 0.0514125 + 0.985542i
\(359\) 269278. 0.110272 0.0551360 0.998479i \(-0.482441\pi\)
0.0551360 + 0.998479i \(0.482441\pi\)
\(360\) 833626. 5.75347e6i 0.339012 2.33977i
\(361\) −2.13736e6 −0.863197
\(362\) −84400.9 1.61791e6i −0.0338513 0.648906i
\(363\) 2.43954e6 + 2.43954e6i 0.971721 + 0.971721i
\(364\) −21800.8 208384.i −0.00862418 0.0824349i
\(365\) −938542. 1.78033e6i −0.368741 0.699467i
\(366\) −3.25810e6 + 3.61673e6i −1.27134 + 1.41128i
\(367\) 173595. 173595.i 0.0672778 0.0672778i −0.672667 0.739945i \(-0.734851\pi\)
0.739945 + 0.672667i \(0.234851\pi\)
\(368\) 346179. + 225285.i 0.133254 + 0.0867185i
\(369\) 6.67287e6i 2.55121i
\(370\) −1.43570e6 2.41001e6i −0.545205 0.915197i
\(371\) 248887.i 0.0938788i
\(372\) −2.45964e6 + 3.03442e6i −0.921541 + 1.13689i
\(373\) −790591. + 790591.i −0.294225 + 0.294225i −0.838747 0.544522i \(-0.816711\pi\)
0.544522 + 0.838747i \(0.316711\pi\)
\(374\) 556564. + 501375.i 0.205748 + 0.185346i
\(375\) −4.96162e6 574856.i −1.82199 0.211096i
\(376\) −855264. 622329.i −0.311983 0.227013i
\(377\) 461819. + 461819.i 0.167347 + 0.167347i
\(378\) 683070. 35633.5i 0.245887 0.0128271i
\(379\) 1.00878e6 0.360743 0.180371 0.983599i \(-0.442270\pi\)
0.180371 + 0.983599i \(0.442270\pi\)
\(380\) 202768. 1.02120e6i 0.0720345 0.362787i
\(381\) 8.28495e6 2.92400
\(382\) 94783.1 4944.52i 0.0332332 0.00173367i
\(383\) −2.32173e6 2.32173e6i −0.808751 0.808751i 0.175693 0.984445i \(-0.443783\pi\)
−0.984445 + 0.175693i \(0.943783\pi\)
\(384\) 2.16382e6 4.83808e6i 0.748846 1.67435i
\(385\) 126778. 66834.1i 0.0435905 0.0229798i
\(386\) 2.72022e6 + 2.45048e6i 0.929258 + 0.837112i
\(387\) 6.88987e6 6.88987e6i 2.33848 2.33848i
\(388\) 1.56870e6 + 1.27156e6i 0.529007 + 0.428802i
\(389\) 2.08733e6i 0.699388i 0.936864 + 0.349694i \(0.113714\pi\)
−0.936864 + 0.349694i \(0.886286\pi\)
\(390\) 4.49846e6 + 1.13968e6i 1.49762 + 0.379422i
\(391\) 265780.i 0.0879184i
\(392\) 2.97618e6 469180.i 0.978236 0.154214i
\(393\) −5.90280e6 + 5.90280e6i −1.92787 + 1.92787i
\(394\) −216435. + 240260.i −0.0702406 + 0.0779723i
\(395\) −1.63768e6 + 5.28953e6i −0.528125 + 1.70579i
\(396\) −3.67449e6 + 384418.i −1.17749 + 0.123187i
\(397\) 2.49759e6 + 2.49759e6i 0.795324 + 0.795324i 0.982354 0.187030i \(-0.0598861\pi\)
−0.187030 + 0.982354i \(0.559886\pi\)
\(398\) −296763. 5.68874e6i −0.0939078 1.80015i
\(399\) 212289. 0.0667567
\(400\) −2.95725e6 1.22257e6i −0.924140 0.382054i
\(401\) 2.71283e6 0.842484 0.421242 0.906948i \(-0.361594\pi\)
0.421242 + 0.906948i \(0.361594\pi\)
\(402\) 36680.8 + 703146.i 0.0113207 + 0.217010i
\(403\) −1.54939e6 1.54939e6i −0.475224 0.475224i
\(404\) −2.21073e6 + 231283.i −0.673880 + 0.0705001i
\(405\) −2.17247e6 + 7.01683e6i −0.658136 + 2.12571i
\(406\) 61462.7 68228.2i 0.0185053 0.0205423i
\(407\) −1.26059e6 + 1.26059e6i −0.377215 + 0.377215i
\(408\) 3.36884e6 531081.i 1.00191 0.157947i
\(409\) 4.13491e6i 1.22224i −0.791536 0.611122i \(-0.790718\pi\)
0.791536 0.611122i \(-0.209282\pi\)
\(410\) −3.56051e6 902054.i −1.04605 0.265017i
\(411\) 8.61744e6i 2.51637i
\(412\) −2.61579e6 2.12031e6i −0.759207 0.615398i
\(413\) −343876. + 343876.i −0.0992033 + 0.0992033i
\(414\) −973926. 877351.i −0.279271 0.251578i
\(415\) 2.78750e6 1.46950e6i 0.794501 0.418841i
\(416\) 2.57295e6 + 1.48962e6i 0.728951 + 0.422029i
\(417\) −203085. 203085.i −0.0571923 0.0571923i
\(418\) −660749. + 34469.1i −0.184968 + 0.00964916i
\(419\) 2.03570e6 0.566473 0.283236 0.959050i \(-0.408592\pi\)
0.283236 + 0.959050i \(0.408592\pi\)
\(420\) 127075. 639990.i 0.0351511 0.177031i
\(421\) 1.23458e6 0.339481 0.169740 0.985489i \(-0.445707\pi\)
0.169740 + 0.985489i \(0.445707\pi\)
\(422\) −4.34954e6 + 226901.i −1.18895 + 0.0620234i
\(423\) 2.37368e6 + 2.37368e6i 0.645017 + 0.645017i
\(424\) 2.85566e6 + 2.07791e6i 0.771423 + 0.561322i
\(425\) −378578. 2.02407e6i −0.101668 0.543566i
\(426\) −5.94726e6 5.35753e6i −1.58779 1.43034i
\(427\) −271490. + 271490.i −0.0720582 + 0.0720582i
\(428\) 995680. 1.22835e6i 0.262730 0.324126i
\(429\) 2.94911e6i 0.773657i
\(430\) −2.74491e6 4.60769e6i −0.715908 1.20174i
\(431\) 4.57789e6i 1.18706i 0.804813 + 0.593529i \(0.202266\pi\)
−0.804813 + 0.593529i \(0.797734\pi\)
\(432\) −5.29397e6 + 8.13486e6i −1.36481 + 2.09720i
\(433\) 4.05050e6 4.05050e6i 1.03822 1.03822i 0.0389784 0.999240i \(-0.487590\pi\)
0.999240 0.0389784i \(-0.0124104\pi\)
\(434\) −206205. + 228904.i −0.0525504 + 0.0583349i
\(435\) 948489. + 1.79919e6i 0.240331 + 0.455885i
\(436\) −163776. 1.56546e6i −0.0412604 0.394391i
\(437\) −165996. 165996.i −0.0415809 0.0415809i
\(438\) 303353. + 5.81506e6i 0.0755549 + 1.44833i
\(439\) −724011. −0.179301 −0.0896507 0.995973i \(-0.528575\pi\)
−0.0896507 + 0.995973i \(0.528575\pi\)
\(440\) −291608. + 2.01260e6i −0.0718071 + 0.495594i
\(441\) −9.56215e6 −2.34131
\(442\) 99666.2 + 1.91053e6i 0.0242657 + 0.465156i
\(443\) 3.59442e6 + 3.59442e6i 0.870201 + 0.870201i 0.992494 0.122293i \(-0.0390249\pi\)
−0.122293 + 0.992494i \(0.539025\pi\)
\(444\) 844516. + 8.07237e6i 0.203306 + 1.94332i
\(445\) 3.48114e6 + 1.07779e6i 0.833338 + 0.258008i
\(446\) 690267. 766248.i 0.164316 0.182403i
\(447\) −942595. + 942595.i −0.223129 + 0.223129i
\(448\) 190316. 372187.i 0.0448001 0.0876126i
\(449\) 5.25803e6i 1.23086i 0.788193 + 0.615428i \(0.211017\pi\)
−0.788193 + 0.615428i \(0.788983\pi\)
\(450\) 8.66672e6 + 5.29427e6i 2.01755 + 1.23247i
\(451\) 2.33421e6i 0.540380i
\(452\) 4.60794e6 5.68475e6i 1.06087 1.30878i
\(453\) 4.72218e6 4.72218e6i 1.08118 1.08118i
\(454\) 2.03863e6 + 1.83648e6i 0.464193 + 0.418164i
\(455\) 349644. + 108253.i 0.0791768 + 0.0245138i
\(456\) −1.77236e6 + 2.43574e6i −0.399153 + 0.548554i
\(457\) 4.48090e6 + 4.48090e6i 1.00363 + 1.00363i 0.999993 + 0.00363922i \(0.00115840\pi\)
0.00363922 + 0.999993i \(0.498842\pi\)
\(458\) 1.07272e6 55960.3i 0.238959 0.0124657i
\(459\) −6.24556e6 −1.38369
\(460\) −599795. + 401066.i −0.132163 + 0.0883733i
\(461\) −451870. −0.0990286 −0.0495143 0.998773i \(-0.515767\pi\)
−0.0495143 + 0.998773i \(0.515767\pi\)
\(462\) −414094. + 21601.9i −0.0902597 + 0.00470855i
\(463\) −5.17841e6 5.17841e6i −1.12265 1.12265i −0.991342 0.131308i \(-0.958082\pi\)
−0.131308 0.991342i \(-0.541918\pi\)
\(464\) 269692. + 1.27483e6i 0.0581532 + 0.274889i
\(465\) −3.18215e6 6.03624e6i −0.682478 1.29460i
\(466\) 3.08493e6 + 2.77903e6i 0.658083 + 0.592827i
\(467\) −6.07751e6 + 6.07751e6i −1.28954 + 1.28954i −0.354468 + 0.935068i \(0.615338\pi\)
−0.935068 + 0.354468i \(0.884662\pi\)
\(468\) −7.32998e6 5.94154e6i −1.54699 1.25396i
\(469\) 55535.0i 0.0116583i
\(470\) 1.58743e6 945669.i 0.331474 0.197467i
\(471\) 5.90452e6i 1.22640i
\(472\) −1.07459e6 6.81648e6i −0.222017 1.40833i
\(473\) −2.41012e6 + 2.41012e6i −0.495320 + 0.495320i
\(474\) 1.07230e7 1.19033e7i 2.19215 2.43345i
\(475\) 1.50060e6 + 1.02771e6i 0.305163 + 0.208995i
\(476\) 267533. 27988.8i 0.0541203 0.00566197i
\(477\) −7.92553e6 7.92553e6i −1.59490 1.59490i
\(478\) 83522.5 + 1.60107e6i 0.0167199 + 0.320509i
\(479\) 4.32290e6 0.860867 0.430434 0.902622i \(-0.358361\pi\)
0.430434 + 0.902622i \(0.358361\pi\)
\(480\) 6.28214e6 + 6.80117e6i 1.24453 + 1.34735i
\(481\) −4.55301e6 −0.897296
\(482\) −210864. 4.04211e6i −0.0413413 0.792484i
\(483\) −104030. 104030.i −0.0202905 0.0202905i
\(484\) −3.84030e6 + 401765.i −0.745164 + 0.0779576i
\(485\) −3.12055e6 + 1.64507e6i −0.602389 + 0.317564i
\(486\) 5.50413e6 6.11001e6i 1.05706 1.17341i
\(487\) −3.00888e6 + 3.00888e6i −0.574888 + 0.574888i −0.933490 0.358602i \(-0.883253\pi\)
0.358602 + 0.933490i \(0.383253\pi\)
\(488\) −848385. 5.38161e6i −0.161266 1.02297i
\(489\) 7.76240e6i 1.46799i
\(490\) −1.29263e6 + 5.10218e6i −0.243212 + 0.959987i
\(491\) 7.96829e6i 1.49163i −0.666153 0.745815i \(-0.732060\pi\)
0.666153 0.745815i \(-0.267940\pi\)
\(492\) 8.25561e6 + 6.69184e6i 1.53758 + 1.24633i
\(493\) −592906. + 592906.i −0.109867 + 0.109867i
\(494\) −1.25549e6 1.13100e6i −0.231471 0.208519i
\(495\) 1.90885e6 6.16536e6i 0.350153 1.13096i
\(496\) −904810. 4.27702e6i −0.165140 0.780615i
\(497\) −446430. 446430.i −0.0810705 0.0810705i
\(498\) −9.10478e6 + 474967.i −1.64511 + 0.0858203i
\(499\) −8.28416e6 −1.48935 −0.744675 0.667427i \(-0.767396\pi\)
−0.744675 + 0.667427i \(0.767396\pi\)
\(500\) 3.99651e6 3.90870e6i 0.714917 0.699209i
\(501\) 1.63101e7 2.90310
\(502\) −4.11867e6 + 214858.i −0.729454 + 0.0380532i
\(503\) 5.69632e6 + 5.69632e6i 1.00386 + 1.00386i 0.999993 + 0.00386994i \(0.00123184\pi\)
0.00386994 + 0.999993i \(0.498768\pi\)
\(504\) −780578. + 1.07275e6i −0.136880 + 0.188114i
\(505\) 1.14845e6 3.70935e6i 0.200393 0.647246i
\(506\) 340686. + 306903.i 0.0591531 + 0.0532875i
\(507\) −2.18085e6 + 2.18085e6i −0.376795 + 0.376795i
\(508\) −5.83882e6 + 7.20326e6i −1.00384 + 1.23842i
\(509\) 3.73663e6i 0.639272i −0.947540 0.319636i \(-0.896439\pi\)
0.947540 0.319636i \(-0.103561\pi\)
\(510\) −1.46318e6 + 5.77533e6i −0.249099 + 0.983222i
\(511\) 459278.i 0.0778078i
\(512\) 2.68147e6 + 5.29095e6i 0.452062 + 0.891987i
\(513\) 3.90075e6 3.90075e6i 0.654416 0.654416i
\(514\) −1.89616e6 + 2.10488e6i −0.316568 + 0.351414i
\(515\) 5.20348e6 2.74314e6i 0.864522 0.455754i
\(516\) 1.61463e6 + 1.54335e7i 0.266961 + 2.55177i
\(517\) −830328. 830328.i −0.136623 0.136623i
\(518\) 33350.3 + 639301.i 0.00546103 + 0.104684i
\(519\) 1.43873e7 2.34456
\(520\) −4.16117e6 + 3.10794e6i −0.674850 + 0.504039i
\(521\) −4.16069e6 −0.671538 −0.335769 0.941944i \(-0.608996\pi\)
−0.335769 + 0.941944i \(0.608996\pi\)
\(522\) −215441. 4.12986e6i −0.0346061 0.663375i
\(523\) −4.46268e6 4.46268e6i −0.713413 0.713413i 0.253835 0.967248i \(-0.418308\pi\)
−0.967248 + 0.253835i \(0.918308\pi\)
\(524\) −972125. 9.29213e6i −0.154666 1.47838i
\(525\) 940433. + 644070.i 0.148912 + 0.101985i
\(526\) 6.82351e6 7.57461e6i 1.07533 1.19370i
\(527\) 1.98918e6 1.98918e6i 0.311995 0.311995i
\(528\) 3.20933e6 4.93155e6i 0.500991 0.769837i
\(529\) 6.27365e6i 0.974723i
\(530\) −5.30030e6 + 3.15752e6i −0.819617 + 0.488266i
\(531\) 2.19007e7i 3.37071i
\(532\) −149611. + 184572.i −0.0229183 + 0.0282740i
\(533\) −4.21536e6 + 4.21536e6i −0.642712 + 0.642712i
\(534\) −7.83379e6 7.05699e6i −1.18883 1.07094i
\(535\) 1.28816e6 + 2.44351e6i 0.194574 + 0.369088i
\(536\) −637194. 463651.i −0.0957987 0.0697074i
\(537\) 8.55317e6 + 8.55317e6i 1.27995 + 1.27995i
\(538\) 2.45017e6 127817.i 0.364956 0.0190386i
\(539\) 3.34490e6 0.495920
\(540\) −9.42465e6 1.40946e7i −1.39085 2.08002i
\(541\) −1.24455e7 −1.82818 −0.914090 0.405511i \(-0.867094\pi\)
−0.914090 + 0.405511i \(0.867094\pi\)
\(542\) −2.80248e6 + 146196.i −0.409774 + 0.0213766i
\(543\) −5.79026e6 5.79026e6i −0.842749 0.842749i
\(544\) −1.91245e6 + 3.30328e6i −0.277072 + 0.478573i
\(545\) 2.62666e6 + 813237.i 0.378803 + 0.117280i
\(546\) −786823. 708801.i −0.112952 0.101752i
\(547\) 5.69241e6 5.69241e6i 0.813444 0.813444i −0.171705 0.985148i \(-0.554927\pi\)
0.985148 + 0.171705i \(0.0549274\pi\)
\(548\) 7.49234e6 + 6.07314e6i 1.06578 + 0.863897i
\(549\) 1.72906e7i 2.44838i
\(550\) −3.03167e6 1.85197e6i −0.427342 0.261052i
\(551\) 740614.i 0.103923i
\(552\) 2.06214e6 325087.i 0.288052 0.0454101i
\(553\) 893521. 893521.i 0.124249 0.124249i
\(554\) −942894. + 1.04668e6i −0.130523 + 0.144891i
\(555\) −1.35445e7 4.19349e6i −1.86651 0.577887i
\(556\) 319694. 33445.8i 0.0438579 0.00458833i
\(557\) −1.81645e6 1.81645e6i −0.248076 0.248076i 0.572104 0.820181i \(-0.306127\pi\)
−0.820181 + 0.572104i \(0.806127\pi\)
\(558\) 722799. + 1.38556e7i 0.0982725 + 1.88382i
\(559\) −8.70488e6 −1.17824
\(560\) 466876. + 561517.i 0.0629116 + 0.0756646i
\(561\) 3.78621e6 0.507923
\(562\) 260144. + 4.98678e6i 0.0347435 + 0.666008i
\(563\) −309147. 309147.i −0.0411049 0.0411049i 0.686256 0.727360i \(-0.259253\pi\)
−0.727360 + 0.686256i \(0.759253\pi\)
\(564\) −5.31711e6 + 556267.i −0.703847 + 0.0736352i
\(565\) 5.96151e6 + 1.13084e7i 0.785661 + 1.49033i
\(566\) −4.70688e6 + 5.22500e6i −0.617579 + 0.685559i
\(567\) 1.18530e6 1.18530e6i 0.154836 0.154836i
\(568\) 8.84938e6 1.39506e6i 1.15091 0.181436i
\(569\) 2.96189e6i 0.383521i −0.981442 0.191760i \(-0.938580\pi\)
0.981442 0.191760i \(-0.0614197\pi\)
\(570\) −2.69321e6 4.52090e6i −0.347203 0.582825i
\(571\) 5.02769e6i 0.645325i −0.946514 0.322662i \(-0.895422\pi\)
0.946514 0.322662i \(-0.104578\pi\)
\(572\) 2.56407e6 + 2.07839e6i 0.327673 + 0.265605i
\(573\) 339215. 339215.i 0.0431607 0.0431607i
\(574\) 622768. + 561014.i 0.0788944 + 0.0710712i
\(575\) −231736. 1.23898e6i −0.0292297 0.156277i
\(576\) −5.79150e6 1.79123e7i −0.727335 2.24954i
\(577\) −3.54316e6 3.54316e6i −0.443048 0.443048i 0.449987 0.893035i \(-0.351429\pi\)
−0.893035 + 0.449987i \(0.851429\pi\)
\(578\) 5.56819e6 290474.i 0.693257 0.0361649i
\(579\) 1.85052e7 2.29402
\(580\) −2.23274e6 443329.i −0.275593 0.0547213i
\(581\) −719102. −0.0883793
\(582\) 1.01926e7 531716.i 1.24732 0.0650687i
\(583\) 2.77240e6 + 2.77240e6i 0.337820 + 0.337820i
\(584\) −5.26963e6 3.83442e6i −0.639363 0.465230i
\(585\) 1.45812e7 7.68684e6i 1.76159 0.928663i
\(586\) 2.20870e6 + 1.98968e6i 0.265701 + 0.239354i
\(587\) −2.07615e6 + 2.07615e6i −0.248693 + 0.248693i −0.820434 0.571741i \(-0.806268\pi\)
0.571741 + 0.820434i \(0.306268\pi\)
\(588\) 9.58933e6 1.18302e7i 1.14379 1.41107i
\(589\) 2.48474e6i 0.295116i
\(590\) 1.16858e7 + 2.96058e6i 1.38206 + 0.350144i
\(591\) 1.63445e6i 0.192487i
\(592\) −7.61360e6 4.95475e6i −0.892865 0.581055i
\(593\) −2.80426e6 + 2.80426e6i −0.327477 + 0.327477i −0.851627 0.524149i \(-0.824383\pi\)
0.524149 + 0.851627i \(0.324383\pi\)
\(594\) −7.21192e6 + 8.00578e6i −0.838658 + 0.930974i
\(595\) −138980. + 448890.i −0.0160938 + 0.0519813i
\(596\) −155235. 1.48382e6i −0.0179008 0.171106i
\(597\) −2.03592e7 2.03592e7i −2.33789 2.33789i
\(598\) 61008.0 + 1.16948e6i 0.00697644 + 0.133733i
\(599\) −2.22073e6 −0.252888 −0.126444 0.991974i \(-0.540356\pi\)
−0.126444 + 0.991974i \(0.540356\pi\)
\(600\) −1.52414e7 + 5.41306e6i −1.72841 + 0.613853i
\(601\) −1.51711e6 −0.171329 −0.0856646 0.996324i \(-0.527301\pi\)
−0.0856646 + 0.996324i \(0.527301\pi\)
\(602\) 63762.2 + 1.22228e6i 0.00717088 + 0.137461i
\(603\) 1.76845e6 + 1.76845e6i 0.198061 + 0.198061i
\(604\) 777690. + 7.43361e6i 0.0867390 + 0.829100i
\(605\) 1.99498e6 6.44357e6i 0.221590 0.715712i
\(606\) −7.51962e6 + 8.34735e6i −0.831792 + 0.923352i
\(607\) 7.42339e6 7.42339e6i 0.817768 0.817768i −0.168016 0.985784i \(-0.553736\pi\)
0.985784 + 0.168016i \(0.0537360\pi\)
\(608\) −868662. 3.25755e6i −0.0952998 0.357381i
\(609\) 464145.i 0.0507120i
\(610\) 9.22591e6 + 2.33738e6i 1.00389 + 0.254334i
\(611\) 2.99898e6i 0.324990i
\(612\) 7.62803e6 9.41057e6i 0.823254 1.01563i
\(613\) 9.06287e6 9.06287e6i 0.974125 0.974125i −0.0255484 0.999674i \(-0.508133\pi\)
0.999674 + 0.0255484i \(0.00813318\pi\)
\(614\) −3.25581e6 2.93296e6i −0.348528 0.313968i
\(615\) −1.64225e7 + 8.65754e6i −1.75086 + 0.923011i
\(616\) 273051. 375253.i 0.0289929 0.0398449i
\(617\) 3.71664e6 + 3.71664e6i 0.393041 + 0.393041i 0.875770 0.482729i \(-0.160354\pi\)
−0.482729 + 0.875770i \(0.660354\pi\)
\(618\) −1.69961e7 + 886630.i −1.79010 + 0.0933838i
\(619\) 1.38492e7 1.45277 0.726386 0.687287i \(-0.241199\pi\)
0.726386 + 0.687287i \(0.241199\pi\)
\(620\) 7.49077e6 + 1.48736e6i 0.782613 + 0.155394i
\(621\) −3.82305e6 −0.397815
\(622\) 1.50274e7 783928.i 1.55742 0.0812457i
\(623\) −588042. 588042.i −0.0606999 0.0606999i
\(624\) 1.47016e7 3.11015e6i 1.51148 0.319757i
\(625\) 3.52962e6 + 9.10545e6i 0.361433 + 0.932398i
\(626\) −2.70907e6 2.44044e6i −0.276302 0.248904i
\(627\) −2.36473e6 + 2.36473e6i −0.240222 + 0.240222i
\(628\) 5.13362e6 + 4.16121e6i 0.519427 + 0.421038i
\(629\) 5.84537e6i 0.589095i
\(630\) −1.18614e6 1.99109e6i −0.119065 0.199866i
\(631\) 1.34462e7i 1.34439i 0.740372 + 0.672197i \(0.234649\pi\)
−0.740372 + 0.672197i \(0.765351\pi\)
\(632\) 2.79219e6 + 1.77118e7i 0.278069 + 1.76389i
\(633\) −1.55664e7 + 1.55664e7i −1.54411 + 1.54411i
\(634\) 4.02911e6 4.47261e6i 0.398094 0.441915i
\(635\) −7.55395e6 1.43291e7i −0.743430 1.41022i
\(636\) 1.77534e7 1.85733e6i 1.74036 0.182074i
\(637\) 6.04056e6 + 6.04056e6i 0.589833 + 0.589833i
\(638\) 75362.8 + 1.44465e6i 0.00733002 + 0.140511i
\(639\) −2.84322e7 −2.75459
\(640\) −1.03405e7 + 668808.i −0.997915 + 0.0645434i
\(641\) 4.22833e6 0.406465 0.203233 0.979130i \(-0.434855\pi\)
0.203233 + 0.979130i \(0.434855\pi\)
\(642\) −416354. 7.98122e6i −0.0398681 0.764244i
\(643\) −3.02277e6 3.02277e6i −0.288322 0.288322i 0.548095 0.836416i \(-0.315353\pi\)
−0.836416 + 0.548095i \(0.815353\pi\)
\(644\) 163763. 17132.6i 0.0155597 0.00162783i
\(645\) −2.58957e7 8.01751e6i −2.45091 0.758823i
\(646\) 1.45203e6 1.61186e6i 0.136897 0.151966i
\(647\) −1.00207e7 + 1.00207e7i −0.941103 + 0.941103i −0.998360 0.0572562i \(-0.981765\pi\)
0.0572562 + 0.998360i \(0.481765\pi\)
\(648\) 3.70398e6 + 2.34956e7i 0.346522 + 2.19811i
\(649\) 7.66100e6i 0.713959i
\(650\) −2.13043e6 8.81937e6i −0.197780 0.818756i
\(651\) 1.55719e6i 0.144009i
\(652\) −6.74893e6 5.47055e6i −0.621750 0.503978i
\(653\) 8.18950e6 8.18950e6i 0.751578 0.751578i −0.223195 0.974774i \(-0.571649\pi\)
0.974774 + 0.223195i \(0.0716488\pi\)
\(654\) −5.91092e6 5.32479e6i −0.540395 0.486809i
\(655\) 1.55911e7 + 4.82713e6i 1.41995 + 0.439629i
\(656\) −1.16363e7 + 2.46168e6i −1.05573 + 0.223342i
\(657\) 1.46252e7 + 1.46252e7i 1.32187 + 1.32187i
\(658\) −421096. + 21967.2i −0.0379154 + 0.00197792i
\(659\) −1.48071e7 −1.32817 −0.664087 0.747655i \(-0.731180\pi\)
−0.664087 + 0.747655i \(0.731180\pi\)
\(660\) 5.71345e6 + 8.54449e6i 0.510551 + 0.763530i
\(661\) −1.38435e7 −1.23237 −0.616187 0.787600i \(-0.711324\pi\)
−0.616187 + 0.787600i \(0.711324\pi\)
\(662\) −6.47141e6 + 337592.i −0.573923 + 0.0299397i
\(663\) 6.83752e6 + 6.83752e6i 0.604108 + 0.604108i
\(664\) 6.00364e6 8.25078e6i 0.528439 0.726231i
\(665\) −193558. 367162.i −0.0169730 0.0321961i
\(666\) 2.14198e7 + 1.92958e7i 1.87124 + 1.68569i
\(667\) −362931. + 362931.i −0.0315871 + 0.0315871i
\(668\) −1.14945e7 + 1.41806e7i −0.996668 + 1.22957i
\(669\) 5.21266e6i 0.450292i
\(670\) 1.18267e6 704547.i 0.101784 0.0606350i
\(671\) 6.04835e6i 0.518598i
\(672\) −544394. 2.04152e6i −0.0465039 0.174393i
\(673\) 9.85470e6 9.85470e6i 0.838699 0.838699i −0.149989 0.988688i \(-0.547924\pi\)
0.988688 + 0.149989i \(0.0479238\pi\)
\(674\) 1.85995e6 2.06469e6i 0.157707 0.175067i
\(675\) 2.91148e7 5.44558e6i 2.45954 0.460028i
\(676\) −359161. 3.43306e6i −0.0302289 0.288945i
\(677\) 4.40570e6 + 4.40570e6i 0.369439 + 0.369439i 0.867273 0.497833i \(-0.165871\pi\)
−0.497833 + 0.867273i \(0.665871\pi\)
\(678\) −1.92686e6 3.69366e7i −0.160982 3.08591i
\(679\) 805021. 0.0670090
\(680\) −3.99012e6 5.34231e6i −0.330913 0.443054i
\(681\) 1.38685e7 1.14594
\(682\) −252840. 4.84677e6i −0.0208154 0.399017i
\(683\) 4.65818e6 + 4.65818e6i 0.382089 + 0.382089i 0.871854 0.489765i \(-0.162918\pi\)
−0.489765 + 0.871854i \(0.662918\pi\)
\(684\) 1.11331e6 + 1.06417e7i 0.0909865 + 0.869701i
\(685\) −1.49042e7 + 7.85711e6i −1.21362 + 0.639788i
\(686\) 1.61571e6 1.79357e6i 0.131085 0.145515i
\(687\) 3.83912e6 3.83912e6i 0.310341 0.310341i
\(688\) −1.45564e7 9.47297e6i −1.17242 0.762983i
\(689\) 1.00134e7i 0.803585i
\(690\) −895645. + 3.53522e6i −0.0716165 + 0.282679i
\(691\) 1.22079e7i 0.972623i 0.873785 + 0.486312i \(0.161658\pi\)
−0.873785 + 0.486312i \(0.838342\pi\)
\(692\) −1.01395e7 + 1.25089e7i −0.804914 + 0.993009i
\(693\) −1.04147e6 + 1.04147e6i −0.0823783 + 0.0823783i
\(694\) 9.62558e6 + 8.67110e6i 0.758627 + 0.683401i
\(695\) −166077. + 536409.i −0.0130421 + 0.0421244i
\(696\) 5.32548e6 + 3.87506e6i 0.416711 + 0.303218i
\(697\) −5.41188e6 5.41188e6i −0.421955 0.421955i
\(698\) −426753. + 22262.3i −0.0331542 + 0.00172955i
\(699\) 2.09863e7 1.62458
\(700\) −1.22275e6 + 363740.i −0.0943175 + 0.0280573i
\(701\) 1.97541e7 1.51832 0.759158 0.650907i \(-0.225611\pi\)
0.759158 + 0.650907i \(0.225611\pi\)
\(702\) −2.74817e7 + 1.43363e6i −2.10475 + 0.109798i
\(703\) 3.65080e6 + 3.65080e6i 0.278612 + 0.278612i
\(704\) 2.02590e6 + 6.26583e6i 0.154059 + 0.476482i
\(705\) 2.76217e6 8.92150e6i 0.209304 0.676029i
\(706\) −1.26373e7 1.13841e7i −0.954204 0.859585i
\(707\) −626593. + 626593.i −0.0471451 + 0.0471451i
\(708\) −2.70953e7 2.19629e7i −2.03147 1.64667i
\(709\) 2.01172e7i 1.50297i 0.659749 + 0.751486i \(0.270663\pi\)
−0.659749 + 0.751486i \(0.729337\pi\)
\(710\) −3.84353e6 + 1.51708e7i −0.286143 + 1.12944i
\(711\) 5.69064e7i 4.22169i
\(712\) 1.16565e7 1.83759e6i 0.861723 0.135846i
\(713\) 1.21762e6 1.21762e6i 0.0896994 0.0896994i
\(714\) 909993. 1.01016e6i 0.0668024 0.0741558i
\(715\) −5.10060e6 + 2.68891e6i −0.373127 + 0.196703i
\(716\) −1.34643e7 + 1.40861e6i −0.981525 + 0.102685i
\(717\) 5.73000e6 + 5.73000e6i 0.416252 + 0.416252i
\(718\) 79356.1 + 1.52120e6i 0.00574472 + 0.110122i
\(719\) −8.94896e6 −0.645580 −0.322790 0.946471i \(-0.604621\pi\)
−0.322790 + 0.946471i \(0.604621\pi\)
\(720\) 3.27480e7 + 3.01376e6i 2.35426 + 0.216659i
\(721\) −1.34236e6 −0.0961683
\(722\) −629878. 1.20743e7i −0.0449690 0.862024i
\(723\) −1.44661e7 1.44661e7i −1.02922 1.02922i
\(724\) 9.11496e6 953590.i 0.646261 0.0676107i
\(725\) 2.24697e6 3.28090e6i 0.158764 0.231818i
\(726\) −1.30625e7 + 1.45003e7i −0.919779 + 1.02102i
\(727\) 1.20635e7 1.20635e7i 0.846522 0.846522i −0.143176 0.989697i \(-0.545731\pi\)
0.989697 + 0.143176i \(0.0457314\pi\)
\(728\) 1.17077e6 184567.i 0.0818737 0.0129070i
\(729\) 9.63534e6i 0.671503i
\(730\) 9.78078e6 5.82665e6i 0.679307 0.404680i
\(731\) 1.11757e7i 0.773540i
\(732\) −2.13917e7 1.73397e7i −1.47560 1.19609i
\(733\) −1.21578e7 + 1.21578e7i −0.835786 + 0.835786i −0.988301 0.152515i \(-0.951263\pi\)
0.152515 + 0.988301i \(0.451263\pi\)
\(734\) 1.03183e6 + 929509.i 0.0706913 + 0.0636815i
\(735\) 1.24062e7 + 2.35333e7i 0.847070 + 1.60681i
\(736\) −1.17065e6 + 2.02201e6i −0.0796588 + 0.137591i
\(737\) −618615. 618615.i −0.0419519 0.0419519i
\(738\) 3.76962e7 1.96649e6i 2.54775 0.132908i
\(739\) −1.34461e7 −0.905699 −0.452849 0.891587i \(-0.649592\pi\)
−0.452849 + 0.891587i \(0.649592\pi\)
\(740\) 1.31915e7 8.82075e6i 0.885551 0.592143i
\(741\) −8.54092e6 −0.571425
\(742\) 1.40601e6 73346.8i 0.0937514 0.00489070i
\(743\) 1.01421e7 + 1.01421e7i 0.673994 + 0.673994i 0.958634 0.284640i \(-0.0918741\pi\)
−0.284640 + 0.958634i \(0.591874\pi\)
\(744\) −1.78668e7 1.30007e7i −1.18335 0.861062i
\(745\) 2.48968e6 + 770826.i 0.164344 + 0.0508821i
\(746\) −4.69917e6 4.23320e6i −0.309154 0.278498i
\(747\) −2.28990e7 + 2.28990e7i −1.50146 + 1.50146i
\(748\) −2.66833e6 + 3.29188e6i −0.174376 + 0.215125i
\(749\) 630363.i 0.0410569i
\(750\) 1.78528e6 2.81985e7i 0.115892 1.83051i
\(751\) 2.32212e7i 1.50240i 0.660075 + 0.751199i \(0.270524\pi\)
−0.660075 + 0.751199i \(0.729476\pi\)
\(752\) 3.26360e6 5.01494e6i 0.210451 0.323386i
\(753\) −1.47401e7 + 1.47401e7i −0.947358 + 0.947358i
\(754\) −2.47280e6 + 2.74500e6i −0.158402 + 0.175838i
\(755\) −1.24727e7 3.86166e6i −0.796332 0.246551i
\(756\) 402600. + 3.84828e6i 0.0256194 + 0.244885i
\(757\) −360441. 360441.i −0.0228609 0.0228609i 0.695584 0.718445i \(-0.255146\pi\)
−0.718445 + 0.695584i \(0.755146\pi\)
\(758\) 297286. + 5.69876e6i 0.0187932 + 0.360253i
\(759\) 2.31763e6 0.146029
\(760\) 5.82869e6 + 844525.i 0.366047 + 0.0530369i
\(761\) 3.99873e6 0.250300 0.125150 0.992138i \(-0.460059\pi\)
0.125150 + 0.992138i \(0.460059\pi\)
\(762\) 2.44156e6 + 4.68031e7i 0.152328 + 2.92003i
\(763\) −443703. 443703.i −0.0275918 0.0275918i
\(764\) 55864.9 + 533989.i 0.00346263 + 0.0330978i
\(765\) 9.86873e6 + 1.87201e7i 0.609688 + 1.15652i
\(766\) 1.24317e7 1.38001e7i 0.765521 0.849786i
\(767\) 1.38350e7 1.38350e7i 0.849162 0.849162i
\(768\) 2.79688e7 + 1.07980e7i 1.71108 + 0.660602i
\(769\) 1.73617e7i 1.05871i −0.848401 0.529354i \(-0.822434\pi\)
0.848401 0.529354i \(-0.177566\pi\)
\(770\) 414919. + 696495.i 0.0252195 + 0.0423342i
\(771\) 1.43191e7i 0.867523i
\(772\) −1.30416e7 + 1.60892e7i −0.787565 + 0.971606i
\(773\) 1.00187e7 1.00187e7i 0.603064 0.603064i −0.338061 0.941124i \(-0.609771\pi\)
0.941124 + 0.338061i \(0.109771\pi\)
\(774\) 4.09525e7 + 3.68916e7i 2.45713 + 2.21348i
\(775\) −7.53852e6 + 1.10073e7i −0.450850 + 0.658304i
\(776\) −6.72096e6 + 9.23659e6i −0.400661 + 0.550627i
\(777\) 2.28797e6 + 2.28797e6i 0.135956 + 0.135956i
\(778\) −1.17917e7 + 615135.i −0.698438 + 0.0364352i
\(779\) 6.76011e6 0.399126
\(780\) −5.11257e6 + 2.57484e7i −0.300886 + 1.51535i
\(781\) 9.94575e6 0.583459
\(782\) −1.50144e6 + 78325.0i −0.0877990 + 0.00458019i
\(783\) −8.52853e6 8.52853e6i −0.497130 0.497130i
\(784\) 3.52756e6 + 1.66747e7i 0.204967 + 0.968874i
\(785\) −1.02121e7 + 5.38355e6i −0.591481 + 0.311814i
\(786\) −3.50855e7 3.16064e7i −2.02568 1.82481i
\(787\) −3.84520e6 + 3.84520e6i −0.221300 + 0.221300i −0.809046 0.587746i \(-0.800016\pi\)
0.587746 + 0.809046i \(0.300016\pi\)
\(788\) −1.42105e6 1.15188e6i −0.0815257 0.0660831i
\(789\) 5.15288e7i 2.94685i
\(790\) −3.03641e7 7.69273e6i −1.73098 0.438544i
\(791\) 2.91728e6i 0.165782i
\(792\) −3.25451e6 2.06445e7i −0.184363 1.16948i
\(793\) 1.09227e7 1.09227e7i 0.616805 0.616805i
\(794\) −1.33733e7 + 1.48453e7i −0.752811 + 0.835677i
\(795\) −9.22267e6 + 2.97882e7i −0.517534 + 1.67158i
\(796\) 3.20492e7 3.35293e6i 1.79281 0.187561i
\(797\) −2.16302e7 2.16302e7i −1.20618 1.20618i −0.972253 0.233932i \(-0.924841\pi\)
−0.233932 0.972253i \(-0.575159\pi\)
\(798\) 62561.3 + 1.19926e6i 0.00347775 + 0.0666661i
\(799\) 3.85023e6 0.213363
\(800\) 6.03503e6 1.70663e7i 0.333392 0.942788i
\(801\) −3.74511e7 −2.06245
\(802\) 799468. + 1.53252e7i 0.0438899 + 0.841340i
\(803\) −5.11598e6 5.11598e6i −0.279989 0.279989i
\(804\) −3.96139e6 + 414433.i −0.216126 + 0.0226107i
\(805\) −85072.9 + 274776.i −0.00462702 + 0.0149448i
\(806\) 8.29617e6 9.20938e6i 0.449821 0.499336i
\(807\) 8.76881e6 8.76881e6i 0.473976 0.473976i
\(808\) −1.95806e6 1.24207e7i −0.105511 0.669293i
\(809\) 9.05916e6i 0.486650i −0.969945 0.243325i \(-0.921762\pi\)
0.969945 0.243325i \(-0.0782382\pi\)
\(810\) −4.02795e7 1.02048e7i −2.15711 0.546502i
\(811\) 4.21486e6i 0.225025i −0.993650 0.112513i \(-0.964110\pi\)
0.993650 0.112513i \(-0.0358899\pi\)
\(812\) 403546. + 327106.i 0.0214785 + 0.0174100i
\(813\) −1.00297e7 + 1.00297e7i −0.532182 + 0.532182i
\(814\) −7.49280e6 6.74981e6i −0.396354 0.357051i
\(815\) 1.34254e7 7.07750e6i 0.707998 0.373238i
\(816\) 3.99296e6 + 1.88746e7i 0.209928 + 0.992323i
\(817\) 6.97995e6 + 6.97995e6i 0.365845 + 0.365845i
\(818\) 2.33588e7 1.21855e6i 1.22058 0.0636739i
\(819\) −3.76157e6 −0.195957
\(820\) 4.04658e6 2.03798e7i 0.210162 1.05844i
\(821\) 3.30523e7 1.71137 0.855684 0.517499i \(-0.173137\pi\)
0.855684 + 0.517499i \(0.173137\pi\)
\(822\) 4.86814e7 2.53955e6i 2.51295 0.131092i
\(823\) −1.25085e7 1.25085e7i −0.643733 0.643733i 0.307738 0.951471i \(-0.400428\pi\)
−0.951471 + 0.307738i \(0.900428\pi\)
\(824\) 1.12071e7 1.54019e7i 0.575011 0.790236i
\(825\) −1.76501e7 + 3.30124e6i −0.902842 + 0.168866i
\(826\) −2.04395e6 1.84127e6i −0.104237 0.0939005i
\(827\) 6.75582e6 6.75582e6i 0.343490 0.343490i −0.514188 0.857678i \(-0.671906\pi\)
0.857678 + 0.514188i \(0.171906\pi\)
\(828\) 4.66929e6 5.76043e6i 0.236687 0.291998i
\(829\) 3.56246e6i 0.180038i 0.995940 + 0.0900188i \(0.0286927\pi\)
−0.995940 + 0.0900188i \(0.971307\pi\)
\(830\) 9.12292e6 + 1.53140e7i 0.459662 + 0.771602i
\(831\) 7.12042e6i 0.357687i
\(832\) −7.65688e6 + 1.49740e7i −0.383481 + 0.749947i
\(833\) −7.75516e6 + 7.75516e6i −0.387238 + 0.387238i
\(834\) 1.08741e6 1.20711e6i 0.0541351 0.0600941i
\(835\) −1.48710e7 2.82089e7i −0.738116 1.40014i
\(836\) −389444. 3.72253e6i −0.0192721 0.184214i
\(837\) 2.86130e7 + 2.86130e7i 1.41172 + 1.41172i
\(838\) 599919. + 1.15000e7i 0.0295109 + 0.565704i
\(839\) −1.61087e7 −0.790050 −0.395025 0.918670i \(-0.629264\pi\)
−0.395025 + 0.918670i \(0.629264\pi\)
\(840\) 3.65286e6 + 529267.i 0.178622 + 0.0258807i
\(841\) 1.88919e7 0.921054
\(842\) 363830. + 6.97437e6i 0.0176856 + 0.339020i
\(843\) 1.78470e7 + 1.78470e7i 0.864960 + 0.864960i
\(844\) −2.56361e6 2.45044e7i −0.123878 1.18410i
\(845\) 5.76028e6 + 1.78343e6i 0.277525 + 0.0859239i
\(846\) −1.27098e7 + 1.41088e7i −0.610538 + 0.677743i
\(847\) −1.08846e6 + 1.08846e6i −0.0521321 + 0.0521321i
\(848\) −1.08969e7 + 1.67445e7i −0.520372 + 0.799618i
\(849\) 3.55448e7i 1.69241i
\(850\) 1.13227e7 2.73514e6i 0.537532 0.129847i
\(851\) 3.57809e6i 0.169366i
\(852\) 2.85130e7 3.51760e7i 1.34568 1.66015i
\(853\) −2.22837e7 + 2.22837e7i −1.04861 + 1.04861i −0.0498570 + 0.998756i \(0.515877\pi\)
−0.998756 + 0.0498570i \(0.984123\pi\)
\(854\) −1.61370e6 1.45368e6i −0.0757143 0.0682064i
\(855\) −1.78555e7 5.52821e6i −0.835327 0.258624i
\(856\) 7.23261e6 + 5.26277e6i 0.337373 + 0.245488i
\(857\) −1.51501e7 1.51501e7i −0.704635 0.704635i 0.260767 0.965402i \(-0.416025\pi\)
−0.965402 + 0.260767i \(0.916025\pi\)
\(858\) 1.66600e7 869100.i 0.772606 0.0403043i
\(859\) 4.63842e6 0.214480 0.107240 0.994233i \(-0.465799\pi\)
0.107240 + 0.994233i \(0.465799\pi\)
\(860\) 2.52207e7 1.68644e7i 1.16282 0.777542i
\(861\) 4.23659e6 0.194764
\(862\) −2.58613e7 + 1.34910e6i −1.18545 + 0.0618408i
\(863\) 1.61594e7 + 1.61594e7i 0.738581 + 0.738581i 0.972303 0.233723i \(-0.0750907\pi\)
−0.233723 + 0.972303i \(0.575091\pi\)
\(864\) −4.75153e7 2.75092e7i −2.16546 1.25370i
\(865\) −1.31179e7 2.48834e7i −0.596106 1.13076i
\(866\) 2.40756e7 + 2.16883e7i 1.09090 + 0.982722i
\(867\) 1.99277e7 1.99277e7i 0.900348 0.900348i
\(868\) −1.35388e6 1.09743e6i −0.0609933 0.0494400i
\(869\) 1.99062e7i 0.894209i
\(870\) −9.88444e6 + 5.88840e6i −0.442745 + 0.263754i
\(871\) 2.23432e6i 0.0997928i
\(872\) 8.79531e6 1.38654e6i 0.391706 0.0617505i
\(873\) 2.56350e7 2.56350e7i 1.13841 1.13841i
\(874\) 888822. 986659.i 0.0393583 0.0436907i
\(875\) 256487. 2.21376e6i 0.0113252 0.0977484i
\(876\) −3.27609e7 + 3.42738e6i −1.44243 + 0.150905i
\(877\) −3.59530e6 3.59530e6i −0.157847 0.157847i 0.623765 0.781612i \(-0.285602\pi\)
−0.781612 + 0.623765i \(0.785602\pi\)
\(878\) −213365. 4.09006e6i −0.00934087 0.179058i
\(879\) 1.50254e7 0.655925
\(880\) −1.14555e7 1.05423e6i −0.498662 0.0458912i
\(881\) −2.22543e7 −0.965994 −0.482997 0.875622i \(-0.660452\pi\)
−0.482997 + 0.875622i \(0.660452\pi\)
\(882\) −2.81796e6 5.40183e7i −0.121973 2.33813i
\(883\) −4.96533e6 4.96533e6i −0.214312 0.214312i 0.591784 0.806096i \(-0.298424\pi\)
−0.806096 + 0.591784i \(0.798424\pi\)
\(884\) −1.07635e7 + 1.12606e6i −0.463260 + 0.0484654i
\(885\) 5.38995e7 2.84144e7i 2.31327 1.21950i
\(886\) −1.92462e7 + 2.13648e7i −0.823685 + 0.914353i
\(887\) −7.10684e6 + 7.10684e6i −0.303297 + 0.303297i −0.842302 0.539005i \(-0.818800\pi\)
0.539005 + 0.842302i \(0.318800\pi\)
\(888\) −4.53533e7 + 7.14974e6i −1.93009 + 0.304269i
\(889\) 3.69654e6i 0.156871i
\(890\) −5.06273e6 + 1.99832e7i −0.214244 + 0.845647i
\(891\) 2.64066e7i 1.11434i
\(892\) 4.53209e6 + 3.67362e6i 0.190716 + 0.154590i
\(893\) −2.40471e6 + 2.40471e6i −0.100910 + 0.100910i
\(894\) −5.60266e6 5.04710e6i −0.234450 0.211202i
\(895\) 6.99452e6 2.25915e7i 0.291877 0.942732i
\(896\) 2.15864e6 + 965442.i 0.0898275 + 0.0401750i
\(897\) 4.18541e6 + 4.18541e6i 0.173683 + 0.173683i
\(898\) −2.97035e7 + 1.54954e6i −1.22918 + 0.0641225i
\(899\) 5.43259e6 0.224186
\(900\) −2.73542e7 + 5.05200e7i −1.12569 + 2.07901i
\(901\) −1.28556e7 −0.527572
\(902\) −1.31864e7 + 687890.i −0.539646 + 0.0281516i
\(903\) 4.37436e6 + 4.37436e6i 0.178523 + 0.178523i
\(904\) 3.34721e7 + 2.43558e7i 1.36226 + 0.991245i
\(905\) −4.73510e6 + 1.52938e7i −0.192180 + 0.620719i
\(906\) 2.80680e7 + 2.52848e7i 1.13603 + 1.02338i
\(907\) 1.52216e7 1.52216e7i 0.614389 0.614389i −0.329698 0.944086i \(-0.606947\pi\)
0.944086 + 0.329698i \(0.106947\pi\)
\(908\) −9.77380e6 + 1.20578e7i −0.393413 + 0.485347i
\(909\) 3.99063e7i 1.60189i
\(910\) −508498. + 2.00710e6i −0.0203557 + 0.0803463i
\(911\) 3.88800e7i 1.55214i 0.630648 + 0.776069i \(0.282789\pi\)
−0.630648 + 0.776069i \(0.717211\pi\)
\(912\) −1.42823e7 9.29454e6i −0.568604 0.370033i
\(913\) 8.01022e6 8.01022e6i 0.318030 0.318030i
\(914\) −2.39929e7 + 2.66339e7i −0.949985 + 1.05455i
\(915\) 4.25536e7 2.24332e7i 1.68029 0.885805i
\(916\) 632259. + 6.04350e6i 0.0248975 + 0.237985i
\(917\) −2.63369e6 2.63369e6i −0.103429 0.103429i
\(918\) −1.84056e6 3.52823e7i −0.0720847 1.38181i
\(919\) −1.59381e7 −0.622512 −0.311256 0.950326i \(-0.600750\pi\)
−0.311256 + 0.950326i \(0.600750\pi\)
\(920\) −2.44245e6 3.27015e6i −0.0951384 0.127379i
\(921\) −2.21487e7 −0.860399
\(922\) −133165. 2.55269e6i −0.00515898 0.0988942i
\(923\) 1.79610e7 + 1.79610e7i 0.693948 + 0.693948i
\(924\) −244066. 2.33292e6i −0.00940432 0.0898918i
\(925\) 5.09665e6 + 2.72492e7i 0.195853 + 1.04713i
\(926\) 2.77277e7 3.07798e7i 1.06264 1.17961i
\(927\) −4.27461e7 + 4.27461e7i −1.63379 + 1.63379i
\(928\) −7.12226e6 + 1.89923e6i −0.271486 + 0.0723948i
\(929\) 3.83803e7i 1.45905i 0.683957 + 0.729523i \(0.260258\pi\)
−0.683957 + 0.729523i \(0.739742\pi\)
\(930\) 3.31620e7 1.97554e7i 1.25728 0.748994i
\(931\) 9.68717e6i 0.366288i
\(932\) −1.47901e7 + 1.82463e7i −0.557739 + 0.688073i
\(933\) 5.37808e7 5.37808e7i 2.02266 2.02266i
\(934\) −3.61239e7 3.25419e7i −1.35496 1.22061i
\(935\) −3.45215e6 6.54840e6i −0.129140 0.244966i
\(936\) 3.14046e7 4.31593e7i 1.17167 1.61022i
\(937\) −2.55035e7 2.55035e7i −0.948965 0.948965i 0.0497944 0.998759i \(-0.484143\pi\)
−0.998759 + 0.0497944i \(0.984143\pi\)
\(938\) −313727. + 16366.1i −0.0116425 + 0.000607349i
\(939\) −1.84294e7 −0.682097
\(940\) 5.81006e6 + 8.68897e6i 0.214467 + 0.320737i
\(941\) −1.60209e7 −0.589810 −0.294905 0.955527i \(-0.595288\pi\)
−0.294905 + 0.955527i \(0.595288\pi\)
\(942\) 3.33557e7 1.74006e6i 1.22474 0.0638904i
\(943\) −3.31274e6 3.31274e6i −0.121313 0.121313i
\(944\) 3.81908e7 8.07933e6i 1.39485 0.295084i
\(945\) −6.45697e6 1.99913e6i −0.235206 0.0728218i
\(946\) −1.43255e7 1.29049e7i −0.520452 0.468844i
\(947\) 3.20367e6 3.20367e6i 0.116084 0.116084i −0.646679 0.762763i \(-0.723842\pi\)
0.762763 + 0.646679i \(0.223842\pi\)
\(948\) 7.04040e7 + 5.70681e7i 2.54435 + 2.06240i
\(949\) 1.84779e7i 0.666020i
\(950\) −5.36349e6 + 8.78003e6i −0.192814 + 0.315636i
\(951\) 3.04265e7i 1.09094i
\(952\) 236956. + 1.50309e6i 0.00847373 + 0.0537519i
\(953\) −1.23052e7 + 1.23052e7i −0.438891 + 0.438891i −0.891639 0.452748i \(-0.850444\pi\)
0.452748 + 0.891639i \(0.350444\pi\)
\(954\) 4.24371e7 4.71083e7i 1.50964 1.67582i
\(955\) −895971. 277400.i −0.0317896 0.00984233i
\(956\) −9.02010e6 + 943666.i −0.319203 + 0.0333944i
\(957\) 5.17021e6 + 5.17021e6i 0.182485 + 0.182485i
\(958\) 1.27395e6 + 2.44208e7i 0.0448476 + 0.859698i
\(959\) 3.84489e6 0.135001
\(960\) −3.65697e7 + 3.74932e7i −1.28069 + 1.31303i
\(961\) 1.04030e7 0.363369
\(962\) −1.34177e6 2.57207e7i −0.0467454 0.896077i
\(963\) −2.00732e7 2.00732e7i −0.697511 0.697511i
\(964\) 2.27724e7 2.38241e6i 0.789254 0.0825703i
\(965\) −1.68725e7 3.20055e7i −0.583258 1.10638i
\(966\) 557028. 618343.i 0.0192059 0.0213200i
\(967\) −2.91509e7 + 2.91509e7i −1.00250 + 1.00250i −0.00250756 + 0.999997i \(0.500798\pi\)
−0.999997 + 0.00250756i \(0.999202\pi\)
\(968\) −3.40137e6 2.15761e7i −0.116672 0.740090i
\(969\) 1.09652e7i 0.375153i
\(970\) −1.02129e7 1.71437e7i −0.348515 0.585027i
\(971\) 3.24023e7i 1.10288i −0.834215 0.551439i \(-0.814079\pi\)
0.834215 0.551439i \(-0.185921\pi\)
\(972\) 3.61385e7 + 2.92932e7i 1.22689 + 0.994492i
\(973\) 90611.5 90611.5i 0.00306833 0.00306833i
\(974\) −1.78844e7 1.61110e7i −0.604057 0.544158i
\(975\) −3.78360e7 2.59126e7i −1.27466 0.872970i
\(976\) 3.01516e7 6.37863e6i 1.01318 0.214340i
\(977\) 1.41425e7 + 1.41425e7i 0.474012 + 0.474012i 0.903210 0.429198i \(-0.141204\pi\)
−0.429198 + 0.903210i \(0.641204\pi\)
\(978\) −4.38511e7 + 2.28757e6i −1.46600 + 0.0764763i
\(979\) 1.31006e7 0.436853
\(980\) −2.92040e7 5.79871e6i −0.971354 0.192871i
\(981\) −2.82584e7 −0.937509
\(982\) 4.50142e7 2.34824e6i 1.48960 0.0777078i
\(983\) −2.67228e7 2.67228e7i −0.882061 0.882061i 0.111683 0.993744i \(-0.464376\pi\)
−0.993744 + 0.111683i \(0.964376\pi\)
\(984\) −3.53704e7 + 4.86094e7i −1.16453 + 1.60042i
\(985\) 2.82684e6 1.49024e6i 0.0928347 0.0489401i
\(986\) −3.52416e6 3.17470e6i −0.115442 0.103994i
\(987\) −1.50704e6 + 1.50704e6i −0.0492416 + 0.0492416i
\(988\) 6.01922e6 7.42581e6i 0.196177 0.242020i
\(989\) 6.84093e6i 0.222395i
\(990\) 3.53917e7 + 8.96648e6i 1.14766 + 0.290759i
\(991\) 2.55747e7i 0.827231i 0.910452 + 0.413616i \(0.135734\pi\)
−0.910452 + 0.413616i \(0.864266\pi\)
\(992\) 2.38950e7 6.37186e6i 0.770951 0.205583i
\(993\) −2.31603e7 + 2.31603e7i −0.745367 + 0.745367i
\(994\) 2.39040e6 2.65353e6i 0.0767370 0.0851838i
\(995\) −1.66491e7 + 5.37748e7i −0.533131 + 1.72195i
\(996\) −5.36634e6 5.12945e7i −0.171407 1.63841i
\(997\) 3.17239e7 + 3.17239e7i 1.01076 + 1.01076i 0.999941 + 0.0108201i \(0.00344422\pi\)
0.0108201 + 0.999941i \(0.496556\pi\)
\(998\) −2.44133e6 4.67986e7i −0.0775890 1.48733i
\(999\) 8.40815e7 2.66555
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 20.6.e.b.7.8 yes 24
4.3 odd 2 inner 20.6.e.b.7.11 yes 24
5.2 odd 4 100.6.e.e.43.2 24
5.3 odd 4 inner 20.6.e.b.3.11 yes 24
5.4 even 2 100.6.e.e.7.5 24
20.3 even 4 inner 20.6.e.b.3.8 24
20.7 even 4 100.6.e.e.43.5 24
20.19 odd 2 100.6.e.e.7.2 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
20.6.e.b.3.8 24 20.3 even 4 inner
20.6.e.b.3.11 yes 24 5.3 odd 4 inner
20.6.e.b.7.8 yes 24 1.1 even 1 trivial
20.6.e.b.7.11 yes 24 4.3 odd 2 inner
100.6.e.e.7.2 24 20.19 odd 2
100.6.e.e.7.5 24 5.4 even 2
100.6.e.e.43.2 24 5.2 odd 4
100.6.e.e.43.5 24 20.7 even 4