Properties

Label 80.6.s.a.3.9
Level $80$
Weight $6$
Character 80.3
Analytic conductor $12.831$
Analytic rank $0$
Dimension $116$
CM no
Inner twists $2$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [80,6,Mod(3,80)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(80, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 3]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("80.3");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 80.s (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: \(12.8307055850\)
Analytic rank: \(0\)
Dimension: \(116\)
Relative dimension: \(58\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 3.9
Character \(\chi\) \(=\) 80.3
Dual form 80.6.s.a.27.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.99964 + 2.64643i) q^{2} -25.1055 q^{3} +(17.9928 - 26.4624i) q^{4} +(-17.6043 + 53.0574i) q^{5} +(125.519 - 66.4399i) q^{6} +(92.6452 - 92.6452i) q^{7} +(-19.9271 + 179.919i) q^{8} +387.286 q^{9} +O(q^{10})\) \(q+(-4.99964 + 2.64643i) q^{2} -25.1055 q^{3} +(17.9928 - 26.4624i) q^{4} +(-17.6043 + 53.0574i) q^{5} +(125.519 - 66.4399i) q^{6} +(92.6452 - 92.6452i) q^{7} +(-19.9271 + 179.919i) q^{8} +387.286 q^{9} +(-52.3971 - 311.857i) q^{10} +(482.653 + 482.653i) q^{11} +(-451.719 + 664.351i) q^{12} -671.517i q^{13} +(-218.014 + 708.372i) q^{14} +(441.966 - 1332.03i) q^{15} +(-376.515 - 952.267i) q^{16} +(-1000.38 + 1000.38i) q^{17} +(-1936.29 + 1024.92i) q^{18} +(865.564 + 865.564i) q^{19} +(1087.27 + 1420.51i) q^{20} +(-2325.90 + 2325.90i) q^{21} +(-3690.40 - 1135.79i) q^{22} +(-1455.06 - 1455.06i) q^{23} +(500.279 - 4516.96i) q^{24} +(-2505.17 - 1868.08i) q^{25} +(1777.12 + 3357.35i) q^{26} -3622.38 q^{27} +(-784.661 - 4118.56i) q^{28} +(-2099.15 + 2099.15i) q^{29} +(1315.46 + 7829.32i) q^{30} -770.875i q^{31} +(4402.54 + 3764.58i) q^{32} +(-12117.3 - 12117.3i) q^{33} +(2354.12 - 7649.00i) q^{34} +(3284.56 + 6546.47i) q^{35} +(6968.38 - 10248.5i) q^{36} +2437.11i q^{37} +(-6618.16 - 2036.86i) q^{38} +16858.8i q^{39} +(-9195.24 - 4224.64i) q^{40} -6655.36i q^{41} +(5473.35 - 17784.0i) q^{42} +23688.4i q^{43} +(21456.5 - 4087.85i) q^{44} +(-6817.92 + 20548.4i) q^{45} +(11125.5 + 3424.07i) q^{46} +(5228.89 + 5228.89i) q^{47} +(9452.59 + 23907.1i) q^{48} -359.269i q^{49} +(17468.7 + 2709.97i) q^{50} +(25115.1 - 25115.1i) q^{51} +(-17769.9 - 12082.5i) q^{52} -26072.6 q^{53} +(18110.6 - 9586.36i) q^{54} +(-34105.1 + 17111.5i) q^{55} +(14822.5 + 18514.8i) q^{56} +(-21730.4 - 21730.4i) q^{57} +(4939.75 - 16050.2i) q^{58} +(11299.2 - 11299.2i) q^{59} +(-27296.5 - 35662.5i) q^{60} +(-8005.46 - 8005.46i) q^{61} +(2040.06 + 3854.10i) q^{62} +(35880.2 - 35880.2i) q^{63} +(-31973.8 - 7170.52i) q^{64} +(35628.9 + 11821.6i) q^{65} +(92649.4 + 28514.5i) q^{66} -3184.75i q^{67} +(8472.77 + 44472.3i) q^{68} +(36530.0 + 36530.0i) q^{69} +(-33746.4 - 24037.7i) q^{70} -81684.8 q^{71} +(-7717.48 + 69680.2i) q^{72} +(7753.75 - 7753.75i) q^{73} +(-6449.64 - 12184.7i) q^{74} +(62893.7 + 46899.1i) q^{75} +(38478.8 - 7330.92i) q^{76} +89431.0 q^{77} +(-44615.5 - 84287.8i) q^{78} +45940.1 q^{79} +(57153.1 - 3212.86i) q^{80} -3168.95 q^{81} +(17612.9 + 33274.4i) q^{82} -76566.0 q^{83} +(19699.3 + 103399. i) q^{84} +(-35466.6 - 70688.8i) q^{85} +(-62689.5 - 118433. i) q^{86} +(52700.2 - 52700.2i) q^{87} +(-96456.5 + 77220.7i) q^{88} -116308. q^{89} +(-20292.7 - 120778. i) q^{90} +(-62212.8 - 62212.8i) q^{91} +(-64685.1 + 12323.7i) q^{92} +19353.2i q^{93} +(-39980.5 - 12304.7i) q^{94} +(-61162.2 + 30686.9i) q^{95} +(-110528. - 94511.6i) q^{96} +(-50590.4 + 50590.4i) q^{97} +(950.778 + 1796.21i) q^{98} +(186925. + 186925. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 116 q - 2 q^{2} - 4 q^{3} + 20 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{7} - 248 q^{8} + 8748 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 116 q - 2 q^{2} - 4 q^{3} + 20 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{7} - 248 q^{8} + 8748 q^{9} + 62 q^{10} - 4 q^{11} - 1280 q^{12} - 972 q^{15} - 1224 q^{16} - 4 q^{17} - 4346 q^{18} + 2360 q^{19} + 832 q^{20} - 4 q^{21} - 3148 q^{22} - 4 q^{23} - 972 q^{24} - 884 q^{26} - 976 q^{27} + 16508 q^{28} + 19836 q^{30} - 7972 q^{32} - 4 q^{33} + 12520 q^{34} + 3860 q^{35} + 2380 q^{36} - 12256 q^{38} + 16192 q^{40} + 38424 q^{42} - 8200 q^{44} - 6738 q^{45} - 35924 q^{46} - 65256 q^{47} + 17620 q^{48} + 24194 q^{50} + 10436 q^{51} - 34384 q^{52} - 4 q^{53} - 33820 q^{54} - 4 q^{55} - 64684 q^{56} - 972 q^{57} - 30632 q^{58} + 14480 q^{59} + 1200 q^{60} + 48076 q^{61} - 6116 q^{62} - 972 q^{63} - 71920 q^{64} - 4 q^{65} + 72436 q^{66} + 119464 q^{68} + 21348 q^{69} - 141252 q^{70} - 143848 q^{71} - 130864 q^{72} + 10072 q^{73} + 82508 q^{74} + 160004 q^{75} - 128004 q^{76} - 67232 q^{77} - 253108 q^{78} - 171436 q^{80} + 551116 q^{81} - 152200 q^{82} + 126436 q^{83} + 80928 q^{84} + 6248 q^{85} - 85324 q^{86} - 282188 q^{87} - 247536 q^{88} + 275094 q^{90} - 164724 q^{91} + 336476 q^{92} + 106060 q^{94} - 204760 q^{95} - 62264 q^{96} - 4 q^{97} + 110122 q^{98} + 168788 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(21\) \(31\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.99964 + 2.64643i −0.883820 + 0.467827i
\(3\) −25.1055 −1.61052 −0.805259 0.592923i \(-0.797974\pi\)
−0.805259 + 0.592923i \(0.797974\pi\)
\(4\) 17.9928 26.4624i 0.562277 0.826949i
\(5\) −17.6043 + 53.0574i −0.314916 + 0.949120i
\(6\) 125.519 66.4399i 1.42341 0.753443i
\(7\) 92.6452 92.6452i 0.714624 0.714624i −0.252875 0.967499i \(-0.581376\pi\)
0.967499 + 0.252875i \(0.0813760\pi\)
\(8\) −19.9271 + 179.919i −0.110083 + 0.993922i
\(9\) 387.286 1.59377
\(10\) −52.3971 311.857i −0.165694 0.986177i
\(11\) 482.653 + 482.653i 1.20269 + 1.20269i 0.973345 + 0.229344i \(0.0736582\pi\)
0.229344 + 0.973345i \(0.426342\pi\)
\(12\) −451.719 + 664.351i −0.905557 + 1.33182i
\(13\) 671.517i 1.10204i −0.834491 0.551022i \(-0.814238\pi\)
0.834491 0.551022i \(-0.185762\pi\)
\(14\) −218.014 + 708.372i −0.297279 + 0.965920i
\(15\) 441.966 1332.03i 0.507178 1.52857i
\(16\) −376.515 952.267i −0.367690 0.929948i
\(17\) −1000.38 + 1000.38i −0.839545 + 0.839545i −0.988799 0.149254i \(-0.952313\pi\)
0.149254 + 0.988799i \(0.452313\pi\)
\(18\) −1936.29 + 1024.92i −1.40861 + 0.745608i
\(19\) 865.564 + 865.564i 0.550066 + 0.550066i 0.926460 0.376394i \(-0.122836\pi\)
−0.376394 + 0.926460i \(0.622836\pi\)
\(20\) 1087.27 + 1420.51i 0.607804 + 0.794087i
\(21\) −2325.90 + 2325.90i −1.15092 + 1.15092i
\(22\) −3690.40 1135.79i −1.62561 0.500311i
\(23\) −1455.06 1455.06i −0.573537 0.573537i 0.359578 0.933115i \(-0.382921\pi\)
−0.933115 + 0.359578i \(0.882921\pi\)
\(24\) 500.279 4516.96i 0.177290 1.60073i
\(25\) −2505.17 1868.08i −0.801656 0.597786i
\(26\) 1777.12 + 3357.35i 0.515565 + 0.974008i
\(27\) −3622.38 −0.956278
\(28\) −784.661 4118.56i −0.189142 0.992775i
\(29\) −2099.15 + 2099.15i −0.463498 + 0.463498i −0.899800 0.436302i \(-0.856288\pi\)
0.436302 + 0.899800i \(0.356288\pi\)
\(30\) 1315.46 + 7829.32i 0.266854 + 1.58826i
\(31\) 770.875i 0.144072i −0.997402 0.0720360i \(-0.977050\pi\)
0.997402 0.0720360i \(-0.0229497\pi\)
\(32\) 4402.54 + 3764.58i 0.760027 + 0.649892i
\(33\) −12117.3 12117.3i −1.93695 1.93695i
\(34\) 2354.12 7649.00i 0.349246 1.13477i
\(35\) 3284.56 + 6546.47i 0.453217 + 0.903311i
\(36\) 6968.38 10248.5i 0.896140 1.31797i
\(37\) 2437.11i 0.292665i 0.989235 + 0.146333i \(0.0467470\pi\)
−0.989235 + 0.146333i \(0.953253\pi\)
\(38\) −6618.16 2036.86i −0.743495 0.228824i
\(39\) 16858.8i 1.77486i
\(40\) −9195.24 4224.64i −0.908685 0.417483i
\(41\) 6655.36i 0.618318i −0.951010 0.309159i \(-0.899952\pi\)
0.951010 0.309159i \(-0.100048\pi\)
\(42\) 5473.35 17784.0i 0.478774 1.55563i
\(43\) 23688.4i 1.95373i 0.213862 + 0.976864i \(0.431396\pi\)
−0.213862 + 0.976864i \(0.568604\pi\)
\(44\) 21456.5 4087.85i 1.67081 0.318319i
\(45\) −6817.92 + 20548.4i −0.501904 + 1.51268i
\(46\) 11125.5 + 3424.07i 0.775220 + 0.238588i
\(47\) 5228.89 + 5228.89i 0.345275 + 0.345275i 0.858346 0.513071i \(-0.171492\pi\)
−0.513071 + 0.858346i \(0.671492\pi\)
\(48\) 9452.59 + 23907.1i 0.592172 + 1.49770i
\(49\) 359.269i 0.0213761i
\(50\) 17468.7 + 2709.97i 0.988180 + 0.153299i
\(51\) 25115.1 25115.1i 1.35210 1.35210i
\(52\) −17769.9 12082.5i −0.911334 0.619653i
\(53\) −26072.6 −1.27495 −0.637477 0.770470i \(-0.720022\pi\)
−0.637477 + 0.770470i \(0.720022\pi\)
\(54\) 18110.6 9586.36i 0.845178 0.447372i
\(55\) −34105.1 + 17111.5i −1.52024 + 0.762750i
\(56\) 14822.5 + 18514.8i 0.631614 + 0.788949i
\(57\) −21730.4 21730.4i −0.885892 0.885892i
\(58\) 4939.75 16050.2i 0.192812 0.626486i
\(59\) 11299.2 11299.2i 0.422588 0.422588i −0.463506 0.886094i \(-0.653409\pi\)
0.886094 + 0.463506i \(0.153409\pi\)
\(60\) −27296.5 35662.5i −0.978880 1.27889i
\(61\) −8005.46 8005.46i −0.275462 0.275462i 0.555832 0.831294i \(-0.312400\pi\)
−0.831294 + 0.555832i \(0.812400\pi\)
\(62\) 2040.06 + 3854.10i 0.0674007 + 0.127334i
\(63\) 35880.2 35880.2i 1.13895 1.13895i
\(64\) −31973.8 7170.52i −0.975764 0.218827i
\(65\) 35628.9 + 11821.6i 1.04597 + 0.347051i
\(66\) 92649.4 + 28514.5i 2.61808 + 0.805761i
\(67\) 3184.75i 0.0866739i −0.999061 0.0433370i \(-0.986201\pi\)
0.999061 0.0433370i \(-0.0137989\pi\)
\(68\) 8472.77 + 44472.3i 0.222205 + 1.16632i
\(69\) 36530.0 + 36530.0i 0.923693 + 0.923693i
\(70\) −33746.4 24037.7i −0.823155 0.586337i
\(71\) −81684.8 −1.92307 −0.961536 0.274680i \(-0.911428\pi\)
−0.961536 + 0.274680i \(0.911428\pi\)
\(72\) −7717.48 + 69680.2i −0.175446 + 1.58408i
\(73\) 7753.75 7753.75i 0.170296 0.170296i −0.616813 0.787109i \(-0.711577\pi\)
0.787109 + 0.616813i \(0.211577\pi\)
\(74\) −6449.64 12184.7i −0.136917 0.258664i
\(75\) 62893.7 + 46899.1i 1.29108 + 0.962745i
\(76\) 38478.8 7330.92i 0.764166 0.145588i
\(77\) 89431.0 1.71894
\(78\) −44615.5 84287.8i −0.830327 1.56866i
\(79\) 45940.1 0.828178 0.414089 0.910236i \(-0.364100\pi\)
0.414089 + 0.910236i \(0.364100\pi\)
\(80\) 57153.1 3212.86i 0.998424 0.0561264i
\(81\) −3168.95 −0.0536665
\(82\) 17612.9 + 33274.4i 0.289266 + 0.546482i
\(83\) −76566.0 −1.21995 −0.609973 0.792422i \(-0.708820\pi\)
−0.609973 + 0.792422i \(0.708820\pi\)
\(84\) 19699.3 + 103399.i 0.304616 + 1.59888i
\(85\) −35466.6 70688.8i −0.532443 1.06122i
\(86\) −62689.5 118433.i −0.914006 1.72674i
\(87\) 52700.2 52700.2i 0.746473 0.746473i
\(88\) −96456.5 + 77220.7i −1.32778 + 1.06299i
\(89\) −116308. −1.55645 −0.778224 0.627986i \(-0.783879\pi\)
−0.778224 + 0.627986i \(0.783879\pi\)
\(90\) −20292.7 120778.i −0.264079 1.57174i
\(91\) −62212.8 62212.8i −0.787547 0.787547i
\(92\) −64685.1 + 12323.7i −0.796773 + 0.151800i
\(93\) 19353.2i 0.232031i
\(94\) −39980.5 12304.7i −0.466690 0.143632i
\(95\) −61162.2 + 30686.9i −0.695303 + 0.348854i
\(96\) −110528. 94511.6i −1.22404 1.04666i
\(97\) −50590.4 + 50590.4i −0.545932 + 0.545932i −0.925262 0.379329i \(-0.876155\pi\)
0.379329 + 0.925262i \(0.376155\pi\)
\(98\) 950.778 + 1796.21i 0.0100003 + 0.0188927i
\(99\) 186925. + 186925.i 1.91681 + 1.91681i
\(100\) −94509.1 + 32680.8i −0.945091 + 0.326808i
\(101\) −69613.2 + 69613.2i −0.679029 + 0.679029i −0.959781 0.280751i \(-0.909416\pi\)
0.280751 + 0.959781i \(0.409416\pi\)
\(102\) −59101.3 + 192032.i −0.562466 + 1.82757i
\(103\) −58748.3 58748.3i −0.545635 0.545635i 0.379540 0.925175i \(-0.376082\pi\)
−0.925175 + 0.379540i \(0.876082\pi\)
\(104\) 120819. + 13381.4i 1.09535 + 0.121316i
\(105\) −82460.4 164352.i −0.729915 1.45480i
\(106\) 130354. 68999.2i 1.12683 0.596457i
\(107\) 119609. 1.00996 0.504980 0.863131i \(-0.331500\pi\)
0.504980 + 0.863131i \(0.331500\pi\)
\(108\) −65176.9 + 95856.7i −0.537693 + 0.790794i
\(109\) −103725. + 103725.i −0.836214 + 0.836214i −0.988358 0.152144i \(-0.951382\pi\)
0.152144 + 0.988358i \(0.451382\pi\)
\(110\) 125229. 175808.i 0.986786 1.38534i
\(111\) 61185.0i 0.471343i
\(112\) −123105. 53340.7i −0.927324 0.401803i
\(113\) −40203.4 40203.4i −0.296188 0.296188i 0.543331 0.839519i \(-0.317163\pi\)
−0.839519 + 0.543331i \(0.817163\pi\)
\(114\) 166152. + 51136.3i 1.19741 + 0.368525i
\(115\) 102817. 51586.4i 0.724972 0.363740i
\(116\) 17778.8 + 93318.2i 0.122675 + 0.643904i
\(117\) 260069.i 1.75640i
\(118\) −26589.4 + 86394.4i −0.175794 + 0.571190i
\(119\) 185361.i 1.19992i
\(120\) 230851. + 106062.i 1.46345 + 0.672365i
\(121\) 304858.i 1.89293i
\(122\) 61210.3 + 18838.6i 0.372327 + 0.114590i
\(123\) 167086.i 0.995813i
\(124\) −20399.2 13870.2i −0.119140 0.0810083i
\(125\) 143217. 100032.i 0.819824 0.572615i
\(126\) −84433.9 + 274343.i −0.473795 + 1.53945i
\(127\) 77147.2 + 77147.2i 0.424435 + 0.424435i 0.886727 0.462293i \(-0.152973\pi\)
−0.462293 + 0.886727i \(0.652973\pi\)
\(128\) 178834. 48766.3i 0.964773 0.263084i
\(129\) 594708.i 3.14651i
\(130\) −209417. + 35185.6i −1.08681 + 0.182602i
\(131\) 52748.3 52748.3i 0.268553 0.268553i −0.559964 0.828517i \(-0.689185\pi\)
0.828517 + 0.559964i \(0.189185\pi\)
\(132\) −538675. + 102627.i −2.69087 + 0.512659i
\(133\) 160381. 0.786182
\(134\) 8428.21 + 15922.6i 0.0405484 + 0.0766042i
\(135\) 63769.5 192194.i 0.301147 0.907622i
\(136\) −160053. 199923.i −0.742024 0.926862i
\(137\) 280215. + 280215.i 1.27553 + 1.27553i 0.943145 + 0.332382i \(0.107852\pi\)
0.332382 + 0.943145i \(0.392148\pi\)
\(138\) −279311. 85963.1i −1.24851 0.384250i
\(139\) −131444. + 131444.i −0.577036 + 0.577036i −0.934085 0.357050i \(-0.883783\pi\)
0.357050 + 0.934085i \(0.383783\pi\)
\(140\) 232334. + 30872.5i 1.00183 + 0.133123i
\(141\) −131274. 131274.i −0.556072 0.556072i
\(142\) 408395. 216173.i 1.69965 0.899664i
\(143\) 324110. 324110.i 1.32542 1.32542i
\(144\) −145819. 368800.i −0.586014 1.48212i
\(145\) −74421.3 148330.i −0.293952 0.585879i
\(146\) −18246.3 + 59285.7i −0.0708421 + 0.230180i
\(147\) 9019.62i 0.0344266i
\(148\) 64491.8 + 43850.6i 0.242020 + 0.164559i
\(149\) −35800.1 35800.1i −0.132105 0.132105i 0.637962 0.770067i \(-0.279777\pi\)
−0.770067 + 0.637962i \(0.779777\pi\)
\(150\) −438561. 68035.2i −1.59148 0.246891i
\(151\) 387107. 1.38162 0.690810 0.723037i \(-0.257254\pi\)
0.690810 + 0.723037i \(0.257254\pi\)
\(152\) −172980. + 138483.i −0.607276 + 0.486171i
\(153\) −387435. + 387435.i −1.33804 + 1.33804i
\(154\) −447123. + 236673.i −1.51924 + 0.804167i
\(155\) 40900.6 + 13570.7i 0.136742 + 0.0453706i
\(156\) 446123. + 303337.i 1.46772 + 0.997963i
\(157\) −184722. −0.598094 −0.299047 0.954238i \(-0.596669\pi\)
−0.299047 + 0.954238i \(0.596669\pi\)
\(158\) −229684. + 121577.i −0.731961 + 0.387444i
\(159\) 654565. 2.05334
\(160\) −277242. + 167315.i −0.856170 + 0.516695i
\(161\) −269609. −0.819728
\(162\) 15843.6 8386.40i 0.0474315 0.0251066i
\(163\) −581645. −1.71470 −0.857351 0.514732i \(-0.827892\pi\)
−0.857351 + 0.514732i \(0.827892\pi\)
\(164\) −176117. 119749.i −0.511318 0.347666i
\(165\) 856226. 429594.i 2.44838 1.22842i
\(166\) 382803. 202626.i 1.07821 0.570724i
\(167\) 23980.1 23980.1i 0.0665364 0.0665364i −0.673056 0.739592i \(-0.735019\pi\)
0.739592 + 0.673056i \(0.235019\pi\)
\(168\) −372126. 464823.i −1.01723 1.27062i
\(169\) −79642.2 −0.214500
\(170\) 364393. + 259559.i 0.967048 + 0.688833i
\(171\) 335221. + 335221.i 0.876679 + 0.876679i
\(172\) 626851. + 426221.i 1.61563 + 1.09854i
\(173\) 261526.i 0.664353i −0.943217 0.332176i \(-0.892217\pi\)
0.943217 0.332176i \(-0.107783\pi\)
\(174\) −124015. + 402949.i −0.310528 + 1.00897i
\(175\) −405161. + 59023.7i −1.00008 + 0.145691i
\(176\) 277889. 641341.i 0.676222 1.56066i
\(177\) −283672. + 283672.i −0.680586 + 0.680586i
\(178\) 581499. 307801.i 1.37562 0.728148i
\(179\) 264737. + 264737.i 0.617564 + 0.617564i 0.944906 0.327342i \(-0.106153\pi\)
−0.327342 + 0.944906i \(0.606153\pi\)
\(180\) 421086. + 550142.i 0.968700 + 1.26559i
\(181\) 26818.5 26818.5i 0.0608469 0.0608469i −0.676029 0.736875i \(-0.736300\pi\)
0.736875 + 0.676029i \(0.236300\pi\)
\(182\) 475684. + 146400.i 1.06449 + 0.327615i
\(183\) 200981. + 200981.i 0.443637 + 0.443637i
\(184\) 290789. 232798.i 0.633188 0.506915i
\(185\) −129307. 42903.8i −0.277775 0.0921650i
\(186\) −51216.8 96759.1i −0.108550 0.205073i
\(187\) −965677. −2.01943
\(188\) 232452. 44286.3i 0.479665 0.0913849i
\(189\) −335596. + 335596.i −0.683380 + 0.683380i
\(190\) 224579. 315285.i 0.451320 0.633606i
\(191\) 366189.i 0.726310i −0.931729 0.363155i \(-0.881700\pi\)
0.931729 0.363155i \(-0.118300\pi\)
\(192\) 802719. + 180020.i 1.57149 + 0.352425i
\(193\) 266658. + 266658.i 0.515302 + 0.515302i 0.916146 0.400845i \(-0.131283\pi\)
−0.400845 + 0.916146i \(0.631283\pi\)
\(194\) 119050. 386818.i 0.227104 0.737908i
\(195\) −894483. 296788.i −1.68456 0.558932i
\(196\) −9507.10 6464.26i −0.0176770 0.0120193i
\(197\) 965894.i 1.77323i 0.462513 + 0.886613i \(0.346948\pi\)
−0.462513 + 0.886613i \(0.653052\pi\)
\(198\) −1.42924e6 439875.i −2.59085 0.797381i
\(199\) 656094.i 1.17445i −0.809425 0.587224i \(-0.800221\pi\)
0.809425 0.587224i \(-0.199779\pi\)
\(200\) 386024. 413504.i 0.682401 0.730978i
\(201\) 79954.8i 0.139590i
\(202\) 163815. 532268.i 0.282472 0.917808i
\(203\) 388952.i 0.662455i
\(204\) −212713. 1.11650e6i −0.357865 1.87838i
\(205\) 353116. + 117163.i 0.586858 + 0.194718i
\(206\) 449194. + 138247.i 0.737506 + 0.226981i
\(207\) −563525. 563525.i −0.914087 0.914087i
\(208\) −639464. + 252836.i −1.02484 + 0.405211i
\(209\) 835534.i 1.32312i
\(210\) 847219. + 603478.i 1.32571 + 0.944307i
\(211\) −410221. + 410221.i −0.634326 + 0.634326i −0.949150 0.314824i \(-0.898054\pi\)
0.314824 + 0.949150i \(0.398054\pi\)
\(212\) −469120. + 689943.i −0.716877 + 1.05432i
\(213\) 2.05074e6 3.09714
\(214\) −598002. + 316536.i −0.892623 + 0.472486i
\(215\) −1.25684e6 417018.i −1.85432 0.615260i
\(216\) 72183.3 651735.i 0.105270 0.950466i
\(217\) −71417.9 71417.9i −0.102957 0.102957i
\(218\) 244087. 793089.i 0.347860 1.13027i
\(219\) −194662. + 194662.i −0.274265 + 0.274265i
\(220\) −160836. + 1.21039e6i −0.224041 + 1.68604i
\(221\) 671774. + 671774.i 0.925215 + 0.925215i
\(222\) 161922. + 305903.i 0.220507 + 0.416583i
\(223\) 31988.3 31988.3i 0.0430754 0.0430754i −0.685241 0.728316i \(-0.740303\pi\)
0.728316 + 0.685241i \(0.240303\pi\)
\(224\) 756645. 59104.7i 1.00756 0.0787049i
\(225\) −970220. 723482.i −1.27766 0.952733i
\(226\) 307398. + 94607.3i 0.400341 + 0.123212i
\(227\) 231846.i 0.298630i −0.988790 0.149315i \(-0.952293\pi\)
0.988790 0.149315i \(-0.0477069\pi\)
\(228\) −966030. + 184046.i −1.23070 + 0.234471i
\(229\) 42412.5 + 42412.5i 0.0534448 + 0.0534448i 0.733324 0.679879i \(-0.237968\pi\)
−0.679879 + 0.733324i \(0.737968\pi\)
\(230\) −377529. + 530012.i −0.470578 + 0.660641i
\(231\) −2.24521e6 −2.76839
\(232\) −335847. 419507.i −0.409658 0.511705i
\(233\) −511086. + 511086.i −0.616743 + 0.616743i −0.944695 0.327951i \(-0.893642\pi\)
0.327951 + 0.944695i \(0.393642\pi\)
\(234\) 688254. + 1.30025e6i 0.821693 + 1.55235i
\(235\) −369483. + 185380.i −0.436440 + 0.218975i
\(236\) −95698.8 502308.i −0.111848 0.587070i
\(237\) −1.15335e6 −1.33380
\(238\) −490545. 926741.i −0.561354 1.06051i
\(239\) −948373. −1.07395 −0.536976 0.843598i \(-0.680433\pi\)
−0.536976 + 0.843598i \(0.680433\pi\)
\(240\) −1.43486e6 + 80660.6i −1.60798 + 0.0903926i
\(241\) −1.24537e6 −1.38120 −0.690598 0.723238i \(-0.742653\pi\)
−0.690598 + 0.723238i \(0.742653\pi\)
\(242\) −806783. 1.52418e6i −0.885561 1.67301i
\(243\) 959796. 1.04271
\(244\) −355885. + 67802.5i −0.382679 + 0.0729073i
\(245\) 19061.9 + 6324.68i 0.0202885 + 0.00673168i
\(246\) −442181. 835371.i −0.465868 0.880120i
\(247\) 581241. 581241.i 0.606197 0.606197i
\(248\) 138695. + 15361.3i 0.143196 + 0.0158598i
\(249\) 1.92223e6 1.96475
\(250\) −451309. + 879137.i −0.456693 + 0.889624i
\(251\) 213309. + 213309.i 0.213710 + 0.213710i 0.805841 0.592131i \(-0.201713\pi\)
−0.592131 + 0.805841i \(0.701713\pi\)
\(252\) −303888. 1.59506e6i −0.301448 1.58225i
\(253\) 1.40458e6i 1.37958i
\(254\) −589873. 181544.i −0.573686 0.176562i
\(255\) 890408. + 1.77468e6i 0.857509 + 1.70911i
\(256\) −765049. + 717085.i −0.729608 + 0.683866i
\(257\) 1.15322e6 1.15322e6i 1.08913 1.08913i 0.0935136 0.995618i \(-0.470190\pi\)
0.995618 0.0935136i \(-0.0298099\pi\)
\(258\) 1.57385e6 + 2.97333e6i 1.47202 + 2.78095i
\(259\) 225787. + 225787.i 0.209146 + 0.209146i
\(260\) 953894. 730122.i 0.875119 0.669826i
\(261\) −812972. + 812972.i −0.738710 + 0.738710i
\(262\) −124128. + 403317.i −0.111716 + 0.362989i
\(263\) 256503. + 256503.i 0.228667 + 0.228667i 0.812136 0.583469i \(-0.198305\pi\)
−0.583469 + 0.812136i \(0.698305\pi\)
\(264\) 2.42159e6 1.93867e6i 2.13841 1.71196i
\(265\) 458991. 1.38334e6i 0.401503 1.21008i
\(266\) −801846. + 424436.i −0.694843 + 0.367797i
\(267\) 2.91997e6 2.50669
\(268\) −84276.1 57302.7i −0.0716749 0.0487347i
\(269\) −267940. + 267940.i −0.225765 + 0.225765i −0.810921 0.585156i \(-0.801033\pi\)
0.585156 + 0.810921i \(0.301033\pi\)
\(270\) 189802. + 1.12966e6i 0.158450 + 0.943060i
\(271\) 1.19567e6i 0.988981i −0.869183 0.494490i \(-0.835355\pi\)
0.869183 0.494490i \(-0.164645\pi\)
\(272\) 1.32929e6 + 575973.i 1.08943 + 0.472041i
\(273\) 1.56188e6 + 1.56188e6i 1.26836 + 1.26836i
\(274\) −2.14254e6 659406.i −1.72406 0.530611i
\(275\) −307496. 2.11077e6i −0.245193 1.68309i
\(276\) 1.62395e6 309392.i 1.28322 0.244476i
\(277\) 549225.i 0.430082i −0.976605 0.215041i \(-0.931012\pi\)
0.976605 0.215041i \(-0.0689884\pi\)
\(278\) 309315. 1.00503e6i 0.240043 0.779949i
\(279\) 298549.i 0.229618i
\(280\) −1.24329e6 + 460503.i −0.947712 + 0.351024i
\(281\) 555458.i 0.419648i 0.977739 + 0.209824i \(0.0672891\pi\)
−0.977739 + 0.209824i \(0.932711\pi\)
\(282\) 1.00373e6 + 308916.i 0.751613 + 0.231322i
\(283\) 1.41093e6i 1.04722i 0.851957 + 0.523611i \(0.175416\pi\)
−0.851957 + 0.523611i \(0.824584\pi\)
\(284\) −1.46974e6 + 2.16157e6i −1.08130 + 1.59028i
\(285\) 1.53551e6 770409.i 1.11980 0.561836i
\(286\) −762701. + 2.47817e6i −0.551365 + 1.79149i
\(287\) −616587. 616587.i −0.441865 0.441865i
\(288\) 1.70504e6 + 1.45797e6i 1.21131 + 1.03578i
\(289\) 581676.i 0.409673i
\(290\) 764623. + 544644.i 0.533891 + 0.380293i
\(291\) 1.27010e6 1.27010e6i 0.879234 0.879234i
\(292\) −65670.6 344695.i −0.0450727 0.236580i
\(293\) −1.36398e6 −0.928192 −0.464096 0.885785i \(-0.653621\pi\)
−0.464096 + 0.885785i \(0.653621\pi\)
\(294\) −23869.8 45094.9i −0.0161057 0.0304270i
\(295\) 400591. + 798420.i 0.268007 + 0.534166i
\(296\) −438484. 48564.5i −0.290887 0.0322174i
\(297\) −1.74835e6 1.74835e6i −1.15011 1.15011i
\(298\) 273730. + 84245.4i 0.178559 + 0.0549548i
\(299\) −977099. + 977099.i −0.632063 + 0.632063i
\(300\) 2.37270e6 820468.i 1.52209 0.526330i
\(301\) 2.19461e6 + 2.19461e6i 1.39618 + 1.39618i
\(302\) −1.93540e6 + 1.02445e6i −1.22110 + 0.646358i
\(303\) 1.74768e6 1.74768e6i 1.09359 1.09359i
\(304\) 498350. 1.15015e6i 0.309279 0.713787i
\(305\) 565680. 283818.i 0.348194 0.174699i
\(306\) 911717. 2.96235e6i 0.556617 1.80856i
\(307\) 445674.i 0.269880i 0.990854 + 0.134940i \(0.0430842\pi\)
−0.990854 + 0.134940i \(0.956916\pi\)
\(308\) 1.60912e6 2.36656e6i 0.966521 1.42148i
\(309\) 1.47491e6 + 1.47491e6i 0.878755 + 0.878755i
\(310\) −240402. + 40391.7i −0.142081 + 0.0238719i
\(311\) −1.74804e6 −1.02483 −0.512415 0.858738i \(-0.671249\pi\)
−0.512415 + 0.858738i \(0.671249\pi\)
\(312\) −3.03322e6 335946.i −1.76407 0.195381i
\(313\) −121953. + 121953.i −0.0703607 + 0.0703607i −0.741411 0.671051i \(-0.765843\pi\)
0.671051 + 0.741411i \(0.265843\pi\)
\(314\) 923544. 488853.i 0.528608 0.279804i
\(315\) 1.27206e6 + 2.53536e6i 0.722324 + 1.43967i
\(316\) 826593. 1.21568e6i 0.465665 0.684861i
\(317\) −755171. −0.422083 −0.211041 0.977477i \(-0.567685\pi\)
−0.211041 + 0.977477i \(0.567685\pi\)
\(318\) −3.27259e6 + 1.73226e6i −1.81478 + 0.960606i
\(319\) −2.02632e6 −1.11489
\(320\) 943327. 1.57022e6i 0.514976 0.857204i
\(321\) −3.00284e6 −1.62656
\(322\) 1.34795e6 713500.i 0.724492 0.383490i
\(323\) −1.73179e6 −0.923611
\(324\) −57018.5 + 83858.0i −0.0301754 + 0.0443795i
\(325\) −1.25445e6 + 1.68227e6i −0.658786 + 0.883460i
\(326\) 2.90802e6 1.53928e6i 1.51549 0.802184i
\(327\) 2.60407e6 2.60407e6i 1.34674 1.34674i
\(328\) 1.19743e6 + 132622.i 0.614560 + 0.0680660i
\(329\) 968864. 0.493484
\(330\) −3.14394e6 + 4.41376e6i −1.58924 + 2.23112i
\(331\) −315540. 315540.i −0.158301 0.158301i 0.623512 0.781814i \(-0.285705\pi\)
−0.781814 + 0.623512i \(0.785705\pi\)
\(332\) −1.37764e6 + 2.02612e6i −0.685948 + 1.00883i
\(333\) 943860.i 0.466442i
\(334\) −56430.2 + 183353.i −0.0276787 + 0.0899337i
\(335\) 168975. + 56065.4i 0.0822639 + 0.0272950i
\(336\) 3.09062e6 + 1.33914e6i 1.49347 + 0.647112i
\(337\) 1.15408e6 1.15408e6i 0.553557 0.553557i −0.373909 0.927466i \(-0.621983\pi\)
0.927466 + 0.373909i \(0.121983\pi\)
\(338\) 398183. 210767.i 0.189579 0.100349i
\(339\) 1.00933e6 + 1.00933e6i 0.477016 + 0.477016i
\(340\) −2.50874e6 333361.i −1.17695 0.156393i
\(341\) 372065. 372065.i 0.173274 0.173274i
\(342\) −2.56312e6 788847.i −1.18496 0.364693i
\(343\) 1.52380e6 + 1.52380e6i 0.699349 + 0.699349i
\(344\) −4.26199e6 472040.i −1.94185 0.215071i
\(345\) −2.58128e6 + 1.29510e6i −1.16758 + 0.585809i
\(346\) 692108. + 1.30753e6i 0.310802 + 0.587169i
\(347\) 53935.7 0.0240466 0.0120233 0.999928i \(-0.496173\pi\)
0.0120233 + 0.999928i \(0.496173\pi\)
\(348\) −446346. 2.34280e6i −0.197571 1.03702i
\(349\) 1.47955e6 1.47955e6i 0.650228 0.650228i −0.302820 0.953048i \(-0.597928\pi\)
0.953048 + 0.302820i \(0.0979281\pi\)
\(350\) 1.86946e6 1.36733e6i 0.815729 0.596626i
\(351\) 2.43249e6i 1.05386i
\(352\) 307918. + 3.94189e6i 0.132458 + 1.69569i
\(353\) −869684. 869684.i −0.371471 0.371471i 0.496542 0.868013i \(-0.334603\pi\)
−0.868013 + 0.496542i \(0.834603\pi\)
\(354\) 667541. 2.16897e6i 0.283119 0.919912i
\(355\) 1.43801e6 4.33398e6i 0.605606 1.82522i
\(356\) −2.09271e6 + 3.07779e6i −0.875154 + 1.28710i
\(357\) 4.65359e6i 1.93249i
\(358\) −2.02420e6 622983.i −0.834729 0.256903i
\(359\) 573999.i 0.235058i −0.993069 0.117529i \(-0.962503\pi\)
0.993069 0.117529i \(-0.0374973\pi\)
\(360\) −3.56119e6 1.63614e6i −1.44823 0.665373i
\(361\) 977698.i 0.394854i
\(362\) −63109.8 + 205056.i −0.0253119 + 0.0822436i
\(363\) 7.65360e6i 3.04859i
\(364\) −2.76569e6 + 526913.i −1.09408 + 0.208442i
\(365\) 274894. + 547894.i 0.108002 + 0.215260i
\(366\) −1.53672e6 472952.i −0.599640 0.184550i
\(367\) 3.37171e6 + 3.37171e6i 1.30673 + 1.30673i 0.923763 + 0.382966i \(0.125097\pi\)
0.382966 + 0.923763i \(0.374903\pi\)
\(368\) −837755. + 1.93346e6i −0.322476 + 0.744244i
\(369\) 2.57753e6i 0.985457i
\(370\) 760030. 127698.i 0.288620 0.0484930i
\(371\) −2.41550e6 + 2.41550e6i −0.911113 + 0.911113i
\(372\) 512132. + 348219.i 0.191878 + 0.130465i
\(373\) 1.60011e6 0.595496 0.297748 0.954645i \(-0.403765\pi\)
0.297748 + 0.954645i \(0.403765\pi\)
\(374\) 4.82804e6 2.55559e6i 1.78481 0.944741i
\(375\) −3.59555e6 + 2.51135e6i −1.32034 + 0.922207i
\(376\) −1.04497e6 + 836582.i −0.381185 + 0.305168i
\(377\) 1.40961e6 + 1.40961e6i 0.510795 + 0.510795i
\(378\) 789729. 2.56599e6i 0.284282 0.923688i
\(379\) 793057. 793057.i 0.283600 0.283600i −0.550943 0.834543i \(-0.685732\pi\)
0.834543 + 0.550943i \(0.185732\pi\)
\(380\) −288435. + 2.17064e6i −0.102468 + 0.771133i
\(381\) −1.93682e6 1.93682e6i −0.683560 0.683560i
\(382\) 969093. + 1.83081e6i 0.339787 + 0.641927i
\(383\) 2.83292e6 2.83292e6i 0.986819 0.986819i −0.0130949 0.999914i \(-0.504168\pi\)
0.999914 + 0.0130949i \(0.00416835\pi\)
\(384\) −4.48972e6 + 1.22430e6i −1.55378 + 0.423702i
\(385\) −1.57437e6 + 4.74498e6i −0.541323 + 1.63148i
\(386\) −2.03889e6 627504.i −0.696506 0.214362i
\(387\) 9.17418e6i 3.11379i
\(388\) 428477. + 2.24901e6i 0.144493 + 0.758423i
\(389\) −1.80262e6 1.80262e6i −0.603989 0.603989i 0.337380 0.941369i \(-0.390459\pi\)
−0.941369 + 0.337380i \(0.890459\pi\)
\(390\) 5.25752e6 883351.i 1.75033 0.294084i
\(391\) 2.91124e6 0.963021
\(392\) 64639.3 + 7159.17i 0.0212462 + 0.00235314i
\(393\) −1.32427e6 + 1.32427e6i −0.432510 + 0.432510i
\(394\) −2.55617e6 4.82912e6i −0.829562 1.56721i
\(395\) −808744. + 2.43746e6i −0.260807 + 0.786040i
\(396\) 8.30979e6 1.58317e6i 2.66288 0.507328i
\(397\) −2.51260e6 −0.800105 −0.400052 0.916492i \(-0.631008\pi\)
−0.400052 + 0.916492i \(0.631008\pi\)
\(398\) 1.73631e6 + 3.28024e6i 0.549438 + 1.03800i
\(399\) −4.02644e6 −1.26616
\(400\) −835676. + 3.08896e6i −0.261149 + 0.965299i
\(401\) 3.84983e6 1.19559 0.597793 0.801650i \(-0.296044\pi\)
0.597793 + 0.801650i \(0.296044\pi\)
\(402\) −211594. 399745.i −0.0653039 0.123372i
\(403\) −517656. −0.158774
\(404\) 589591. + 3.09467e6i 0.179721 + 0.943325i
\(405\) 55787.3 168136.i 0.0169004 0.0509359i
\(406\) −1.02933e6 1.94462e6i −0.309914 0.585491i
\(407\) −1.17628e6 + 1.17628e6i −0.351986 + 0.351986i
\(408\) 4.01822e6 + 5.01916e6i 1.19504 + 1.49273i
\(409\) 1.32841e6 0.392665 0.196333 0.980537i \(-0.437097\pi\)
0.196333 + 0.980537i \(0.437097\pi\)
\(410\) −2.07552e6 + 348722.i −0.609771 + 0.102452i
\(411\) −7.03493e6 7.03493e6i −2.05426 2.05426i
\(412\) −2.61167e6 + 497570.i −0.758010 + 0.144415i
\(413\) 2.09363e6i 0.603983i
\(414\) 4.30875e6 + 1.32610e6i 1.23552 + 0.380254i
\(415\) 1.34789e6 4.06239e6i 0.384181 1.15788i
\(416\) 2.52798e6 2.95638e6i 0.716209 0.837582i
\(417\) 3.29996e6 3.29996e6i 0.929327 0.929327i
\(418\) −2.21118e6 4.17737e6i −0.618990 1.16940i
\(419\) −3.14320e6 3.14320e6i −0.874655 0.874655i 0.118320 0.992975i \(-0.462249\pi\)
−0.992975 + 0.118320i \(0.962249\pi\)
\(420\) −5.83285e6 775070.i −1.61346 0.214396i
\(421\) −1.87662e6 + 1.87662e6i −0.516025 + 0.516025i −0.916366 0.400341i \(-0.868892\pi\)
0.400341 + 0.916366i \(0.368892\pi\)
\(422\) 965340. 3.13658e6i 0.263875 0.857384i
\(423\) 2.02508e6 + 2.02508e6i 0.550289 + 0.550289i
\(424\) 519550. 4.69096e6i 0.140350 1.26721i
\(425\) 4.37493e6 637338.i 1.17489 0.171158i
\(426\) −1.02530e7 + 5.42713e6i −2.73732 + 1.44893i
\(427\) −1.48334e6 −0.393704
\(428\) 2.15210e6 3.16514e6i 0.567877 0.835185i
\(429\) −8.13694e6 + 8.13694e6i −2.13461 + 2.13461i
\(430\) 7.38737e6 1.24120e6i 1.92672 0.323722i
\(431\) 6.77381e6i 1.75647i 0.478233 + 0.878233i \(0.341278\pi\)
−0.478233 + 0.878233i \(0.658722\pi\)
\(432\) 1.36388e6 + 3.44947e6i 0.351614 + 0.889289i
\(433\) 2.95385e6 + 2.95385e6i 0.757127 + 0.757127i 0.975799 0.218671i \(-0.0701723\pi\)
−0.218671 + 0.975799i \(0.570172\pi\)
\(434\) 546066. + 168062.i 0.139162 + 0.0428296i
\(435\) 1.86838e6 + 3.72389e6i 0.473416 + 0.943568i
\(436\) 878502. + 4.61112e6i 0.221323 + 1.16169i
\(437\) 2.51890e6i 0.630967i
\(438\) 458081. 1.48840e6i 0.114093 0.370710i
\(439\) 2.92559e6i 0.724522i 0.932077 + 0.362261i \(0.117995\pi\)
−0.932077 + 0.362261i \(0.882005\pi\)
\(440\) −2.39908e6 6.47715e6i −0.590762 1.59497i
\(441\) 139140.i 0.0340686i
\(442\) −5.13643e6 1.58083e6i −1.25056 0.384884i
\(443\) 3.15699e6i 0.764299i 0.924100 + 0.382150i \(0.124816\pi\)
−0.924100 + 0.382150i \(0.875184\pi\)
\(444\) −1.61910e6 1.10089e6i −0.389777 0.265025i
\(445\) 2.04753e6 6.17100e6i 0.490150 1.47726i
\(446\) −75275.5 + 244585.i −0.0179191 + 0.0582228i
\(447\) 898780. + 898780.i 0.212757 + 0.212757i
\(448\) −3.62654e6 + 2.29791e6i −0.853684 + 0.540925i
\(449\) 5.16573e6i 1.20925i 0.796510 + 0.604625i \(0.206677\pi\)
−0.796510 + 0.604625i \(0.793323\pi\)
\(450\) 6.76539e6 + 1.04953e6i 1.57493 + 0.244324i
\(451\) 3.21223e6 3.21223e6i 0.743645 0.743645i
\(452\) −1.78725e6 + 340504.i −0.411472 + 0.0783928i
\(453\) −9.71851e6 −2.22512
\(454\) 613562. + 1.15914e6i 0.139707 + 0.263936i
\(455\) 4.39607e6 2.20564e6i 0.995488 0.499465i
\(456\) 4.34274e6 3.47669e6i 0.978029 0.782987i
\(457\) −3.53914e6 3.53914e6i −0.792697 0.792697i 0.189235 0.981932i \(-0.439399\pi\)
−0.981932 + 0.189235i \(0.939399\pi\)
\(458\) −324289. 99805.8i −0.0722385 0.0222327i
\(459\) 3.62377e6 3.62377e6i 0.802839 0.802839i
\(460\) 484875. 3.64897e6i 0.106840 0.804037i
\(461\) 3.14250e6 + 3.14250e6i 0.688689 + 0.688689i 0.961942 0.273253i \(-0.0880996\pi\)
−0.273253 + 0.961942i \(0.588100\pi\)
\(462\) 1.12253e7 5.94179e6i 2.44676 1.29513i
\(463\) 443323. 443323.i 0.0961098 0.0961098i −0.657417 0.753527i \(-0.728351\pi\)
0.753527 + 0.657417i \(0.228351\pi\)
\(464\) 2.78931e6 + 1.20859e6i 0.601454 + 0.260606i
\(465\) −1.02683e6 340700.i −0.220225 0.0730702i
\(466\) 1.20270e6 3.90780e6i 0.256561 0.833619i
\(467\) 4.52407e6i 0.959924i 0.877289 + 0.479962i \(0.159350\pi\)
−0.877289 + 0.479962i \(0.840650\pi\)
\(468\) −6.88205e6 4.67939e6i −1.45246 0.987585i
\(469\) −295052. 295052.i −0.0619393 0.0619393i
\(470\) 1.35669e6 1.90464e6i 0.283292 0.397712i
\(471\) 4.63754e6 0.963242
\(472\) 1.80778e6 + 2.25810e6i 0.373500 + 0.466539i
\(473\) −1.14333e7 + 1.14333e7i −2.34973 + 2.34973i
\(474\) 5.76633e6 3.05225e6i 1.17884 0.623985i
\(475\) −551446. 3.78533e6i −0.112142 0.769786i
\(476\) 4.90510e6 + 3.33518e6i 0.992272 + 0.674686i
\(477\) −1.00976e7 −2.03198
\(478\) 4.74153e6 2.50980e6i 0.949180 0.502423i
\(479\) −4.34987e6 −0.866239 −0.433120 0.901336i \(-0.642587\pi\)
−0.433120 + 0.901336i \(0.642587\pi\)
\(480\) 6.96031e6 4.20052e6i 1.37888 0.832147i
\(481\) 1.63656e6 0.322530
\(482\) 6.22640e6 3.29578e6i 1.22073 0.646161i
\(483\) 6.76867e6 1.32019
\(484\) 8.06726e6 + 5.48526e6i 1.56535 + 1.06435i
\(485\) −1.79358e6 3.57481e6i −0.346232 0.690078i
\(486\) −4.79864e6 + 2.54003e6i −0.921567 + 0.487807i
\(487\) 2.46757e6 2.46757e6i 0.471463 0.471463i −0.430925 0.902388i \(-0.641813\pi\)
0.902388 + 0.430925i \(0.141813\pi\)
\(488\) 1.59986e6 1.28081e6i 0.304112 0.243464i
\(489\) 1.46025e7 2.76156
\(490\) −112040. + 18824.6i −0.0210806 + 0.00354190i
\(491\) −2.98282e6 2.98282e6i −0.558371 0.558371i 0.370473 0.928843i \(-0.379196\pi\)
−0.928843 + 0.370473i \(0.879196\pi\)
\(492\) 4.42150e6 + 3.00636e6i 0.823487 + 0.559922i
\(493\) 4.19991e6i 0.778256i
\(494\) −1.36778e6 + 4.44421e6i −0.252174 + 0.819364i
\(495\) −1.32084e7 + 6.62706e6i −2.42292 + 1.21565i
\(496\) −734079. + 290246.i −0.133980 + 0.0529739i
\(497\) −7.56771e6 + 7.56771e6i −1.37427 + 1.37427i
\(498\) −9.61046e6 + 5.08704e6i −1.73648 + 0.919161i
\(499\) 1.13593e6 + 1.13593e6i 0.204221 + 0.204221i 0.801806 0.597585i \(-0.203873\pi\)
−0.597585 + 0.801806i \(0.703873\pi\)
\(500\) −70187.9 5.58973e6i −0.0125556 0.999921i
\(501\) −602031. + 602031.i −0.107158 + 0.107158i
\(502\) −1.63098e6 501962.i −0.288861 0.0889020i
\(503\) 3.98673e6 + 3.98673e6i 0.702581 + 0.702581i 0.964964 0.262383i \(-0.0845082\pi\)
−0.262383 + 0.964964i \(0.584508\pi\)
\(504\) 5.74055e6 + 7.17053e6i 1.00665 + 1.25740i
\(505\) −2.46800e6 4.91899e6i −0.430643 0.858317i
\(506\) 3.71712e6 + 7.02240e6i 0.645402 + 1.21930i
\(507\) 1.99946e6 0.345456
\(508\) 3.42960e6 653401.i 0.589636 0.112336i
\(509\) 6.10895e6 6.10895e6i 1.04513 1.04513i 0.0462016 0.998932i \(-0.485288\pi\)
0.998932 0.0462016i \(-0.0147117\pi\)
\(510\) −9.14828e6 6.51636e6i −1.55745 1.10938i
\(511\) 1.43670e6i 0.243396i
\(512\) 1.92726e6 5.60982e6i 0.324912 0.945744i
\(513\) −3.13540e6 3.13540e6i −0.526016 0.526016i
\(514\) −2.71378e6 + 8.81762e6i −0.453072 + 1.47212i
\(515\) 4.15126e6 2.08281e6i 0.689702 0.346044i
\(516\) −1.57374e7 1.07005e7i −2.60201 1.76921i
\(517\) 5.04749e6i 0.830518i
\(518\) −1.72638e6 531325.i −0.282691 0.0870034i
\(519\) 6.56573e6i 1.06995i
\(520\) −2.83692e6 + 6.17476e6i −0.460085 + 1.00141i
\(521\) 7.42883e6i 1.19902i −0.800368 0.599509i \(-0.795362\pi\)
0.800368 0.599509i \(-0.204638\pi\)
\(522\) 1.91310e6 6.21604e6i 0.307299 0.998475i
\(523\) 5.17846e6i 0.827840i −0.910313 0.413920i \(-0.864159\pi\)
0.910313 0.413920i \(-0.135841\pi\)
\(524\) −446753. 2.34494e6i −0.0710787 0.373081i
\(525\) 1.01718e7 1.48182e6i 1.61064 0.234637i
\(526\) −1.96124e6 603608.i −0.309077 0.0951241i
\(527\) 771171. + 771171.i 0.120955 + 0.120955i
\(528\) −6.97654e6 + 1.61012e7i −1.08907 + 2.51347i
\(529\) 2.20193e6i 0.342110i
\(530\) 1.36613e6 + 8.13091e6i 0.211253 + 1.25733i
\(531\) 4.37602e6 4.37602e6i 0.673508 0.673508i
\(532\) 2.88570e6 4.24405e6i 0.442051 0.650132i
\(533\) −4.46919e6 −0.681413
\(534\) −1.45988e7 + 7.72749e6i −2.21546 + 1.17270i
\(535\) −2.10564e6 + 6.34614e6i −0.318052 + 0.958572i
\(536\) 572998. + 63462.7i 0.0861472 + 0.00954128i
\(537\) −6.64636e6 6.64636e6i −0.994599 0.994599i
\(538\) 630522. 2.04869e6i 0.0939170 0.305155i
\(539\) 173402. 173402.i 0.0257088 0.0257088i
\(540\) −3.93851e6 5.14561e6i −0.581230 0.759368i
\(541\) 1.49348e6 + 1.49348e6i 0.219384 + 0.219384i 0.808239 0.588855i \(-0.200421\pi\)
−0.588855 + 0.808239i \(0.700421\pi\)
\(542\) 3.16425e6 + 5.97792e6i 0.462672 + 0.874081i
\(543\) −673293. + 673293.i −0.0979951 + 0.0979951i
\(544\) −8.17025e6 + 638213.i −1.18369 + 0.0924631i
\(545\) −3.67737e6 7.32939e6i −0.530330 1.05700i
\(546\) −1.19423e7 3.67545e6i −1.71437 0.527629i
\(547\) 4.77308e6i 0.682073i 0.940050 + 0.341036i \(0.110778\pi\)
−0.940050 + 0.341036i \(0.889222\pi\)
\(548\) 1.24570e7 2.37329e6i 1.77199 0.337597i
\(549\) −3.10040e6 3.10040e6i −0.439023 0.439023i
\(550\) 7.12336e6 + 9.73931e6i 1.00410 + 1.37285i
\(551\) −3.63389e6 −0.509910
\(552\) −7.30039e6 + 5.84452e6i −1.01976 + 0.816397i
\(553\) 4.25613e6 4.25613e6i 0.591836 0.591836i
\(554\) 1.45348e6 + 2.74593e6i 0.201204 + 0.380115i
\(555\) 3.24631e6 + 1.07712e6i 0.447361 + 0.148433i
\(556\) 1.11327e6 + 5.84336e6i 0.152726 + 0.801633i
\(557\) 1.05045e7 1.43463 0.717313 0.696751i \(-0.245372\pi\)
0.717313 + 0.696751i \(0.245372\pi\)
\(558\) 790089. + 1.49264e6i 0.107421 + 0.202941i
\(559\) 1.59071e7 2.15309
\(560\) 4.99730e6 5.59262e6i 0.673389 0.753607i
\(561\) 2.42438e7 3.25232
\(562\) −1.46998e6 2.77709e6i −0.196322 0.370893i
\(563\) −1.02868e7 −1.36776 −0.683878 0.729596i \(-0.739708\pi\)
−0.683878 + 0.729596i \(0.739708\pi\)
\(564\) −5.83582e6 + 1.11183e6i −0.772509 + 0.147177i
\(565\) 2.84084e6 1.42533e6i 0.374392 0.187843i
\(566\) −3.73392e6 7.05414e6i −0.489919 0.925556i
\(567\) −293588. + 293588.i −0.0383514 + 0.0383514i
\(568\) 1.62774e6 1.46967e7i 0.211697 1.91138i
\(569\) 1.03508e6 0.134028 0.0670138 0.997752i \(-0.478653\pi\)
0.0670138 + 0.997752i \(0.478653\pi\)
\(570\) −5.63816e6 + 7.91538e6i −0.726859 + 1.02043i
\(571\) 7.97599e6 + 7.97599e6i 1.02375 + 1.02375i 0.999711 + 0.0240393i \(0.00765270\pi\)
0.0240393 + 0.999711i \(0.492347\pi\)
\(572\) −2.74506e6 1.44084e7i −0.350802 1.84130i
\(573\) 9.19336e6i 1.16974i
\(574\) 4.71447e6 + 1.45096e6i 0.597246 + 0.183813i
\(575\) 927011. + 6.36336e6i 0.116927 + 0.802632i
\(576\) −1.23830e7 2.77704e6i −1.55514 0.348760i
\(577\) −5.12608e6 + 5.12608e6i −0.640982 + 0.640982i −0.950797 0.309815i \(-0.899733\pi\)
0.309815 + 0.950797i \(0.399733\pi\)
\(578\) 1.53936e6 + 2.90817e6i 0.191656 + 0.362077i
\(579\) −6.69458e6 6.69458e6i −0.829903 0.829903i
\(580\) −5.26420e6 699507.i −0.649774 0.0863420i
\(581\) −7.09348e6 + 7.09348e6i −0.871804 + 0.871804i
\(582\) −2.98881e6 + 9.71125e6i −0.365756 + 1.18841i
\(583\) −1.25840e7 1.25840e7i −1.53337 1.53337i
\(584\) 1.24054e6 + 1.54956e6i 0.150515 + 0.188008i
\(585\) 1.37986e7 + 4.57835e6i 1.66704 + 0.553120i
\(586\) 6.81940e6 3.60966e6i 0.820355 0.434233i
\(587\) 2.04239e6 0.244649 0.122324 0.992490i \(-0.460965\pi\)
0.122324 + 0.992490i \(0.460965\pi\)
\(588\) 238680. + 162289.i 0.0284691 + 0.0193573i
\(589\) 667241. 667241.i 0.0792492 0.0792492i
\(590\) −4.11577e6 2.93168e6i −0.486767 0.346726i
\(591\) 2.42493e7i 2.85581i
\(592\) 2.32078e6 917609.i 0.272164 0.107610i
\(593\) 8.11262e6 + 8.11262e6i 0.947381 + 0.947381i 0.998683 0.0513023i \(-0.0163372\pi\)
−0.0513023 + 0.998683i \(0.516337\pi\)
\(594\) 1.33680e7 + 4.11425e6i 1.55454 + 0.478437i
\(595\) −9.83480e6 3.26316e6i −1.13887 0.377874i
\(596\) −1.59150e6 + 303210.i −0.183524 + 0.0349646i
\(597\) 1.64716e7i 1.89147i
\(598\) 2.29932e6 7.47096e6i 0.262934 0.854326i
\(599\) 7.22533e6i 0.822793i −0.911456 0.411397i \(-0.865041\pi\)
0.911456 0.411397i \(-0.134959\pi\)
\(600\) −9.69133e6 + 1.03812e7i −1.09902 + 1.17725i
\(601\) 1.37926e6i 0.155762i −0.996963 0.0778809i \(-0.975185\pi\)
0.996963 0.0778809i \(-0.0248154\pi\)
\(602\) −1.67802e7 5.16440e6i −1.88714 0.580803i
\(603\) 1.23341e6i 0.138138i
\(604\) 6.96515e6 1.02438e7i 0.776852 1.14253i
\(605\) −1.61749e7 5.36681e6i −1.79661 0.596112i
\(606\) −4.11266e6 + 1.33628e7i −0.454926 + 1.47815i
\(607\) 9.96172e6 + 9.96172e6i 1.09739 + 1.09739i 0.994714 + 0.102680i \(0.0327417\pi\)
0.102680 + 0.994714i \(0.467258\pi\)
\(608\) 552202. + 7.06916e6i 0.0605814 + 0.775549i
\(609\) 9.76484e6i 1.06690i
\(610\) −2.07709e6 + 2.91602e6i −0.226012 + 0.317297i
\(611\) 3.51129e6 3.51129e6i 0.380508 0.380508i
\(612\) 3.28139e6 + 1.72235e7i 0.354143 + 1.85884i
\(613\) −6.72623e6 −0.722970 −0.361485 0.932378i \(-0.617730\pi\)
−0.361485 + 0.932378i \(0.617730\pi\)
\(614\) −1.17944e6 2.22821e6i −0.126257 0.238526i
\(615\) −8.86516e6 2.94144e6i −0.945145 0.313597i
\(616\) −1.78210e6 + 1.60904e7i −0.189226 + 1.70850i
\(617\) −8.50888e6 8.50888e6i −0.899828 0.899828i 0.0955928 0.995421i \(-0.469525\pi\)
−0.995421 + 0.0955928i \(0.969525\pi\)
\(618\) −1.12772e7 3.47077e6i −1.18777 0.365557i
\(619\) −3.48483e6 + 3.48483e6i −0.365557 + 0.365557i −0.865854 0.500297i \(-0.833224\pi\)
0.500297 + 0.865854i \(0.333224\pi\)
\(620\) 1.09503e6 838151.i 0.114406 0.0875676i
\(621\) 5.27078e6 + 5.27078e6i 0.548461 + 0.548461i
\(622\) 8.73960e6 4.62607e6i 0.905765 0.479442i
\(623\) −1.07754e7 + 1.07754e7i −1.11228 + 1.11228i
\(624\) 1.60541e7 6.34758e6i 1.65053 0.652599i
\(625\) 2.78618e6 + 9.35974e6i 0.285304 + 0.958437i
\(626\) 286981. 932458.i 0.0292696 0.0951028i
\(627\) 2.09765e7i 2.13091i
\(628\) −3.32368e6 + 4.88819e6i −0.336294 + 0.494594i
\(629\) −2.43805e6 2.43805e6i −0.245706 0.245706i
\(630\) −1.30695e7 9.30946e6i −1.31192 0.934487i
\(631\) 1.53607e7 1.53581 0.767905 0.640564i \(-0.221299\pi\)
0.767905 + 0.640564i \(0.221299\pi\)
\(632\) −915451. + 8.26550e6i −0.0911679 + 0.823145i
\(633\) 1.02988e7 1.02988e7i 1.02159 1.02159i
\(634\) 3.77559e6 1.99851e6i 0.373045 0.197461i
\(635\) −5.45136e6 + 2.73511e6i −0.536501 + 0.269178i
\(636\) 1.17775e7 1.73214e7i 1.15454 1.69801i
\(637\) −241255. −0.0235574
\(638\) 1.01309e7 5.36252e6i 0.985362 0.521575i
\(639\) −3.16354e7 −3.06493
\(640\) −560838. + 1.03470e7i −0.0541237 + 0.998534i
\(641\) −7.40305e6 −0.711648 −0.355824 0.934553i \(-0.615800\pi\)
−0.355824 + 0.934553i \(0.615800\pi\)
\(642\) 1.50131e7 7.94680e6i 1.43759 0.760947i
\(643\) −8.59023e6 −0.819365 −0.409683 0.912228i \(-0.634361\pi\)
−0.409683 + 0.912228i \(0.634361\pi\)
\(644\) −4.85103e6 + 7.13449e6i −0.460914 + 0.677873i
\(645\) 3.15537e7 + 1.04694e7i 2.98642 + 0.990888i
\(646\) 8.65833e6 4.58306e6i 0.816306 0.432090i
\(647\) −7.30612e6 + 7.30612e6i −0.686162 + 0.686162i −0.961381 0.275220i \(-0.911249\pi\)
0.275220 + 0.961381i \(0.411249\pi\)
\(648\) 63147.9 570156.i 0.00590774 0.0533403i
\(649\) 1.09072e7 1.01648
\(650\) 1.81979e6 1.17305e7i 0.168942 1.08902i
\(651\) 1.79298e6 + 1.79298e6i 0.165815 + 0.165815i
\(652\) −1.04654e7 + 1.53917e7i −0.964137 + 1.41797i
\(653\) 1.00355e7i 0.920997i 0.887661 + 0.460498i \(0.152329\pi\)
−0.887661 + 0.460498i \(0.847671\pi\)
\(654\) −6.12794e6 + 1.99109e7i −0.560235 + 1.82031i
\(655\) 1.87009e6 + 3.72729e6i 0.170317 + 0.339461i
\(656\) −6.33768e6 + 2.50584e6i −0.575004 + 0.227350i
\(657\) 3.00292e6 3.00292e6i 0.271413 0.271413i
\(658\) −4.84397e6 + 2.56403e6i −0.436151 + 0.230865i
\(659\) −8.40660e6 8.40660e6i −0.754062 0.754062i 0.221173 0.975235i \(-0.429011\pi\)
−0.975235 + 0.221173i \(0.929011\pi\)
\(660\) 4.03788e6 3.03874e7i 0.360822 2.71540i
\(661\) 2.85949e6 2.85949e6i 0.254557 0.254557i −0.568279 0.822836i \(-0.692390\pi\)
0.822836 + 0.568279i \(0.192390\pi\)
\(662\) 2.41264e6 + 742533.i 0.213967 + 0.0658523i
\(663\) −1.68652e7 1.68652e7i −1.49008 1.49008i
\(664\) 1.52574e6 1.37757e7i 0.134295 1.21253i
\(665\) −2.82339e6 + 8.50938e6i −0.247581 + 0.746180i
\(666\) −2.49786e6 4.71896e6i −0.218214 0.412250i
\(667\) 6.10878e6 0.531667
\(668\) −203100. 1.06604e6i −0.0176104 0.0924340i
\(669\) −803084. + 803084.i −0.0693738 + 0.0693738i
\(670\) −993186. + 166872.i −0.0854759 + 0.0143614i
\(671\) 7.72773e6i 0.662591i
\(672\) −1.89959e7 + 1.48385e6i −1.62270 + 0.126756i
\(673\) −1.08674e7 1.08674e7i −0.924881 0.924881i 0.0724878 0.997369i \(-0.476906\pi\)
−0.997369 + 0.0724878i \(0.976906\pi\)
\(674\) −2.71581e6 + 8.82420e6i −0.230276 + 0.748213i
\(675\) 9.07469e6 + 6.76689e6i 0.766606 + 0.571649i
\(676\) −1.43299e6 + 2.10752e6i −0.120608 + 0.177380i
\(677\) 7.82331e6i 0.656023i −0.944674 0.328011i \(-0.893622\pi\)
0.944674 0.328011i \(-0.106378\pi\)
\(678\) −7.71739e6 2.37516e6i −0.644757 0.198436i
\(679\) 9.37392e6i 0.780273i
\(680\) 1.34250e7 4.97251e6i 1.11338 0.412385i
\(681\) 5.82060e6i 0.480950i
\(682\) −875550. + 2.84484e6i −0.0720809 + 0.234205i
\(683\) 2.47066e6i 0.202657i 0.994853 + 0.101328i \(0.0323093\pi\)
−0.994853 + 0.101328i \(0.967691\pi\)
\(684\) 1.49023e7 2.83916e6i 1.21791 0.232033i
\(685\) −1.98005e7 + 9.93447e6i −1.61231 + 0.808944i
\(686\) −1.16511e7 3.58584e6i −0.945272 0.290925i
\(687\) −1.06479e6 1.06479e6i −0.0860739 0.0860739i
\(688\) 2.25577e7 8.91902e6i 1.81687 0.718366i
\(689\) 1.75082e7i 1.40505i
\(690\) 9.47807e6 1.33062e7i 0.757874 1.06398i
\(691\) −1.81233e6 + 1.81233e6i −0.144391 + 0.144391i −0.775607 0.631216i \(-0.782556\pi\)
0.631216 + 0.775607i \(0.282556\pi\)
\(692\) −6.92059e6 4.70559e6i −0.549386 0.373550i
\(693\) 3.46354e7 2.73960
\(694\) −269659. + 142737.i −0.0212528 + 0.0112496i
\(695\) −4.66008e6 9.28804e6i −0.365958 0.729394i
\(696\) 8.43162e6 + 1.05319e7i 0.659763 + 0.824110i
\(697\) 6.65791e6 + 6.65791e6i 0.519106 + 0.519106i
\(698\) −3.48170e6 + 1.13127e7i −0.270491 + 0.878879i
\(699\) 1.28311e7 1.28311e7i 0.993277 0.993277i
\(700\) −5.72809e6 + 1.17835e7i −0.441840 + 0.908930i
\(701\) 1.67107e7 + 1.67107e7i 1.28440 + 1.28440i 0.938140 + 0.346256i \(0.112547\pi\)
0.346256 + 0.938140i \(0.387453\pi\)
\(702\) −6.43740e6 1.21616e7i −0.493024 0.931423i
\(703\) −2.10948e6 + 2.10948e6i −0.160985 + 0.160985i
\(704\) −1.19714e7 1.88932e7i −0.910360 1.43672i
\(705\) 9.27605e6 4.65407e6i 0.702895 0.352663i
\(706\) 6.64967e6 + 2.04655e6i 0.502098 + 0.154530i
\(707\) 1.28987e7i 0.970502i
\(708\) 2.40257e6 + 1.26107e7i 0.180133 + 0.945487i
\(709\) −1.75606e7 1.75606e7i −1.31197 1.31197i −0.919963 0.392006i \(-0.871781\pi\)
−0.392006 0.919963i \(-0.628219\pi\)
\(710\) 4.28005e6 + 2.54739e7i 0.318642 + 1.89649i
\(711\) 1.77919e7 1.31993
\(712\) 2.31768e6 2.09260e7i 0.171338 1.54699i
\(713\) −1.12167e6 + 1.12167e6i −0.0826307 + 0.0826307i
\(714\) 1.23154e7 + 2.32663e7i 0.904071 + 1.70798i
\(715\) 1.14907e7 + 2.29022e7i 0.840584 + 1.67537i
\(716\) 1.17689e7 2.24220e6i 0.857936 0.163452i
\(717\) 2.38094e7 1.72962
\(718\) 1.51905e6 + 2.86979e6i 0.109966 + 0.207749i
\(719\) 2.39129e7 1.72509 0.862543 0.505984i \(-0.168871\pi\)
0.862543 + 0.505984i \(0.168871\pi\)
\(720\) 2.21346e7 1.24430e6i 1.59126 0.0894526i
\(721\) −1.08855e7 −0.779848
\(722\) 2.58741e6 + 4.88814e6i 0.184723 + 0.348980i
\(723\) 3.12656e7 2.22444
\(724\) −227140. 1.19222e6i −0.0161045 0.0845301i
\(725\) 9.18012e6 1.33736e6i 0.648639 0.0944935i
\(726\) 2.02547e7 + 3.82653e7i 1.42621 + 2.69441i
\(727\) 1.87769e7 1.87769e7i 1.31761 1.31761i 0.401952 0.915661i \(-0.368332\pi\)
0.915661 0.401952i \(-0.131668\pi\)
\(728\) 1.24330e7 9.95356e6i 0.869456 0.696066i
\(729\) −2.33261e7 −1.62564
\(730\) −2.82433e6 2.01178e6i −0.196159 0.139725i
\(731\) −2.36974e7 2.36974e7i −1.64024 1.64024i
\(732\) 8.93466e6 1.70222e6i 0.616312 0.117419i
\(733\) 2.58736e7i 1.77868i −0.457247 0.889340i \(-0.651164\pi\)
0.457247 0.889340i \(-0.348836\pi\)
\(734\) −2.57803e7 7.93436e6i −1.76624 0.543591i
\(735\) −478557. 158784.i −0.0326750 0.0108415i
\(736\) −928283. 1.18837e7i −0.0631664 0.808641i
\(737\) 1.53713e6 1.53713e6i 0.104242 0.104242i
\(738\) 6.82124e6 + 1.28867e7i 0.461023 + 0.870967i
\(739\) 1.01373e7 + 1.01373e7i 0.682828 + 0.682828i 0.960637 0.277808i \(-0.0896080\pi\)
−0.277808 + 0.960637i \(0.589608\pi\)
\(740\) −3.46194e6 + 2.64981e6i −0.232402 + 0.177883i
\(741\) −1.45923e7 + 1.45923e7i −0.976291 + 0.976291i
\(742\) 5.68419e6 1.84691e7i 0.379017 1.23150i
\(743\) 329492. + 329492.i 0.0218964 + 0.0218964i 0.717970 0.696074i \(-0.245071\pi\)
−0.696074 + 0.717970i \(0.745071\pi\)
\(744\) −3.48201e6 385653.i −0.230621 0.0255425i
\(745\) 2.52970e6 1.26922e6i 0.166985 0.0837814i
\(746\) −7.99999e6 + 4.23458e6i −0.526311 + 0.278589i
\(747\) −2.96530e7 −1.94432
\(748\) −1.73753e7 + 2.55541e7i −1.13548 + 1.66996i
\(749\) 1.10812e7 1.10812e7i 0.721742 0.721742i
\(750\) 1.13303e7 2.20712e7i 0.735512 1.43276i
\(751\) 8.03777e6i 0.520039i −0.965603 0.260019i \(-0.916271\pi\)
0.965603 0.260019i \(-0.0837290\pi\)
\(752\) 3.01055e6 6.94806e6i 0.194134 0.448042i
\(753\) −5.35523e6 5.35523e6i −0.344184 0.344184i
\(754\) −1.07780e7 3.31713e6i −0.690415 0.212488i
\(755\) −6.81476e6 + 2.05389e7i −0.435094 + 1.31132i
\(756\) 2.84234e6 + 1.49190e7i 0.180872 + 0.949369i
\(757\) 8.16444e6i 0.517830i 0.965900 + 0.258915i \(0.0833649\pi\)
−0.965900 + 0.258915i \(0.916635\pi\)
\(758\) −1.86623e6 + 6.06377e6i −0.117976 + 0.383327i
\(759\) 3.52627e7i 2.22183i
\(760\) −4.30237e6 1.16158e7i −0.270193 0.729480i
\(761\) 1.38961e7i 0.869821i 0.900474 + 0.434911i \(0.143220\pi\)
−0.900474 + 0.434911i \(0.856780\pi\)
\(762\) 1.48091e7 + 4.55775e6i 0.923932 + 0.284357i
\(763\) 1.92193e7i 1.19516i
\(764\) −9.69023e6 6.58878e6i −0.600621 0.408387i
\(765\) −1.37357e7 2.73768e7i −0.848591 1.69133i
\(766\) −6.66648e6 + 2.16607e7i −0.410511 + 1.33383i
\(767\) −7.58760e6 7.58760e6i −0.465710 0.465710i
\(768\) 1.92069e7 1.80028e7i 1.17505 1.10138i
\(769\) 8.21340e6i 0.500850i 0.968136 + 0.250425i \(0.0805703\pi\)
−0.968136 + 0.250425i \(0.919430\pi\)
\(770\) −4.68593e6 2.78897e7i −0.284819 1.69518i
\(771\) −2.89522e7 + 2.89522e7i −1.75407 + 1.75407i
\(772\) 1.18543e7 2.25847e6i 0.715870 0.136386i
\(773\) −1.32249e7 −0.796055 −0.398028 0.917373i \(-0.630305\pi\)
−0.398028 + 0.917373i \(0.630305\pi\)
\(774\) −2.42788e7 4.58676e7i −1.45672 2.75203i
\(775\) −1.44006e6 + 1.93118e6i −0.0861242 + 0.115496i
\(776\) −8.09407e6 1.01103e7i −0.482517 0.602712i
\(777\) −5.66849e6 5.66849e6i −0.336833 0.336833i
\(778\) 1.37829e7 + 4.24194e6i 0.816380 + 0.251256i
\(779\) 5.76064e6 5.76064e6i 0.340116 0.340116i
\(780\) −2.39480e7 + 1.83301e7i −1.40939 + 1.07877i
\(781\) −3.94254e7 3.94254e7i −2.31286 2.31286i
\(782\) −1.45552e7 + 7.70438e6i −0.851138 + 0.450527i
\(783\) 7.60391e6 7.60391e6i 0.443233 0.443233i
\(784\) −342120. + 135270.i −0.0198787 + 0.00785979i
\(785\) 3.25191e6 9.80087e6i 0.188349 0.567663i
\(786\) 3.11630e6 1.01255e7i 0.179921 0.584601i
\(787\) 2.08463e7i 1.19975i −0.800093 0.599876i \(-0.795216\pi\)
0.800093 0.599876i \(-0.204784\pi\)
\(788\) 2.55599e7 + 1.73792e7i 1.46637 + 0.997043i
\(789\) −6.43965e6 6.43965e6i −0.368273 0.368273i
\(790\) −2.40713e6 1.43267e7i −0.137224 0.816730i
\(791\) −7.44931e6 −0.423326
\(792\) −3.73563e7 + 2.99065e7i −2.11617 + 1.69415i
\(793\) −5.37580e6 + 5.37580e6i −0.303571 + 0.303571i
\(794\) 1.25621e7 6.64941e6i 0.707149 0.374310i
\(795\) −1.15232e7 + 3.47295e7i −0.646628 + 1.94886i
\(796\) −1.73618e7 1.18050e7i −0.971208 0.660364i
\(797\) −4.61598e6 −0.257406 −0.128703 0.991683i \(-0.541081\pi\)
−0.128703 + 0.991683i \(0.541081\pi\)
\(798\) 2.01307e7 1.06557e7i 1.11906 0.592343i
\(799\) −1.04618e7 −0.579748
\(800\) −3.99661e6 1.76552e7i −0.220784 0.975323i
\(801\) −4.50445e7 −2.48062
\(802\) −1.92478e7 + 1.01883e7i −1.05668 + 0.559327i
\(803\) 7.48475e6 0.409627
\(804\) 2.11579e6 + 1.43861e6i 0.115434 + 0.0784882i
\(805\) 4.74629e6 1.43047e7i 0.258145 0.778020i
\(806\) 2.58809e6 1.36994e6i 0.140327 0.0742785i
\(807\) 6.72678e6 6.72678e6i 0.363600 0.363600i
\(808\) −1.11376e7 1.39119e7i −0.600153 0.749652i
\(809\) −2.51403e7 −1.35052 −0.675258 0.737582i \(-0.735968\pi\)
−0.675258 + 0.737582i \(0.735968\pi\)
\(810\) 166044. + 988259.i 0.00889223 + 0.0529247i
\(811\) 5.83568e6 + 5.83568e6i 0.311558 + 0.311558i 0.845513 0.533955i \(-0.179295\pi\)
−0.533955 + 0.845513i \(0.679295\pi\)
\(812\) 1.02926e7 + 6.99836e6i 0.547816 + 0.372483i
\(813\) 3.00179e7i 1.59277i
\(814\) 2.76804e6 8.99393e6i 0.146424 0.475760i
\(815\) 1.02395e7 3.08606e7i 0.539987 1.62746i
\(816\) −3.33725e7 1.44601e7i −1.75454 0.760231i
\(817\) −2.05038e7 + 2.05038e7i −1.07468 + 1.07468i
\(818\) −6.64155e6 + 3.51553e6i −0.347045 + 0.183699i
\(819\) −2.40942e7 2.40942e7i −1.25517 1.25517i
\(820\) 9.45398e6 7.23619e6i 0.490998 0.375816i
\(821\) 2.20349e7 2.20349e7i 1.14091 1.14091i 0.152630 0.988283i \(-0.451226\pi\)
0.988283 0.152630i \(-0.0487743\pi\)
\(822\) 5.37896e7 + 1.65547e7i 2.77663 + 0.854559i
\(823\) 1.08933e7 + 1.08933e7i 0.560609 + 0.560609i 0.929480 0.368871i \(-0.120256\pi\)
−0.368871 + 0.929480i \(0.620256\pi\)
\(824\) 1.17406e7 9.39927e6i 0.602384 0.482254i
\(825\) 7.71983e6 + 5.29918e7i 0.394887 + 2.71065i
\(826\) 5.54064e6 + 1.04674e7i 0.282559 + 0.533813i
\(827\) −9.44717e6 −0.480328 −0.240164 0.970732i \(-0.577201\pi\)
−0.240164 + 0.970732i \(0.577201\pi\)
\(828\) −2.50516e7 + 4.77279e6i −1.26987 + 0.241934i
\(829\) −1.49221e7 + 1.49221e7i −0.754123 + 0.754123i −0.975246 0.221123i \(-0.929028\pi\)
0.221123 + 0.975246i \(0.429028\pi\)
\(830\) 4.01184e6 + 2.38776e7i 0.202138 + 1.20308i
\(831\) 1.37886e7i 0.692654i
\(832\) −4.81513e6 + 2.14710e7i −0.241157 + 1.07533i
\(833\) 359406. + 359406.i 0.0179462 + 0.0179462i
\(834\) −7.76552e6 + 2.52317e7i −0.386594 + 1.25612i
\(835\) 850167. + 1.69447e6i 0.0421976 + 0.0841043i
\(836\) 2.21102e7 + 1.50336e7i 1.09415 + 0.743958i
\(837\) 2.79240e6i 0.137773i
\(838\) 2.40331e7 + 7.39662e6i 1.18222 + 0.363851i
\(839\) 1.84777e7i 0.906239i 0.891450 + 0.453120i \(0.149689\pi\)
−0.891450 + 0.453120i \(0.850311\pi\)
\(840\) 3.12133e7 1.15612e7i 1.52631 0.565331i
\(841\) 1.16983e7i 0.570338i
\(842\) 4.41609e6 1.43487e7i 0.214663 0.697483i
\(843\) 1.39450e7i 0.675851i
\(844\) 3.47438e6 + 1.82365e7i 0.167889 + 0.881221i
\(845\) 1.40205e6 4.22561e6i 0.0675494 0.203586i
\(846\) −1.54839e7 4.76545e6i −0.743797 0.228917i
\(847\) 2.82436e7 + 2.82436e7i 1.35273 + 1.35273i
\(848\) 9.81671e6 + 2.48281e7i 0.468788 + 1.18564i
\(849\) 3.54221e7i 1.68657i
\(850\) −2.01864e7 + 1.47644e7i −0.958323 + 0.700920i
\(851\) 3.54615e6 3.54615e6i 0.167855 0.167855i
\(852\) 3.68986e7 5.42674e7i 1.74145 2.56118i
\(853\) 8.67132e6 0.408049 0.204025 0.978966i \(-0.434598\pi\)
0.204025 + 0.978966i \(0.434598\pi\)
\(854\) 7.41615e6 3.92554e6i 0.347963 0.184185i
\(855\) −2.36873e7 + 1.18846e7i −1.10815 + 0.555993i
\(856\) −2.38345e6 + 2.15199e7i −0.111179 + 1.00382i
\(857\) −7.50854e6 7.50854e6i −0.349223 0.349223i 0.510597 0.859820i \(-0.329424\pi\)
−0.859820 + 0.510597i \(0.829424\pi\)
\(858\) 1.91480e7 6.22156e7i 0.887983 2.88524i
\(859\) 397645. 397645.i 0.0183871 0.0183871i −0.697853 0.716241i \(-0.745861\pi\)
0.716241 + 0.697853i \(0.245861\pi\)
\(860\) −3.36495e7 + 2.57557e7i −1.55143 + 1.18748i
\(861\) 1.54797e7 + 1.54797e7i 0.711632 + 0.711632i
\(862\) −1.79264e7 3.38666e7i −0.821722 1.55240i
\(863\) 1.86871e7 1.86871e7i 0.854114 0.854114i −0.136523 0.990637i \(-0.543593\pi\)
0.990637 + 0.136523i \(0.0435927\pi\)
\(864\) −1.59477e7 1.36367e7i −0.726797 0.621477i
\(865\) 1.38759e7 + 4.60398e6i 0.630550 + 0.209215i
\(866\) −2.25853e7 6.95105e6i −1.02337 0.314960i
\(867\) 1.46033e7i 0.659785i
\(868\) −3.17490e6 + 604876.i −0.143031 + 0.0272500i
\(869\) 2.21731e7 + 2.21731e7i 0.996042 + 0.996042i
\(870\) −1.91962e7 1.36736e7i −0.859841 0.612468i
\(871\) −2.13861e6 −0.0955184
\(872\) −1.65952e7 2.07291e7i −0.739079 0.923184i
\(873\) −1.95930e7 + 1.95930e7i −0.870091 + 0.870091i
\(874\) 6.66608e6 + 1.25936e7i 0.295183 + 0.557662i
\(875\) 4.00095e6 2.25359e7i 0.176662 0.995071i
\(876\) 1.64869e6 + 8.65374e6i 0.0725905 + 0.381016i
\(877\) −1.01382e7 −0.445103 −0.222551 0.974921i \(-0.571438\pi\)
−0.222551 + 0.974921i \(0.571438\pi\)
\(878\) −7.74235e6 1.46269e7i −0.338951 0.640347i
\(879\) 3.42433e7 1.49487
\(880\) 2.91358e7 + 2.60344e7i 1.26830 + 1.13329i
\(881\) 2.56971e7 1.11543 0.557717 0.830031i \(-0.311677\pi\)
0.557717 + 0.830031i \(0.311677\pi\)
\(882\) 368223. + 695649.i 0.0159382 + 0.0301105i
\(883\) 3.71032e7 1.60144 0.800719 0.599041i \(-0.204451\pi\)
0.800719 + 0.599041i \(0.204451\pi\)
\(884\) 2.98639e7 5.68961e6i 1.28533 0.244879i
\(885\) −1.00570e7 2.00447e7i −0.431630 0.860285i
\(886\) −8.35474e6 1.57838e7i −0.357560 0.675503i
\(887\) 2.13398e7 2.13398e7i 0.910714 0.910714i −0.0856141 0.996328i \(-0.527285\pi\)
0.996328 + 0.0856141i \(0.0272852\pi\)
\(888\) 1.10083e7 + 1.21924e6i 0.468479 + 0.0518866i
\(889\) 1.42946e7 0.606623
\(890\) 6.09421e6 + 3.62714e7i 0.257895 + 1.53493i
\(891\) −1.52951e6 1.52951e6i −0.0645442 0.0645442i
\(892\) −270926. 1.42205e6i −0.0114009 0.0598415i
\(893\) 9.05188e6i 0.379848i
\(894\) −6.87214e6 2.11502e6i −0.287573 0.0885058i
\(895\) −1.87068e7 + 9.38574e6i −0.780623 + 0.391662i
\(896\) 1.20501e7 2.10861e7i 0.501444 0.877457i
\(897\) 2.45306e7 2.45306e7i 1.01795 1.01795i
\(898\) −1.36707e7 2.58268e7i −0.565719 1.06876i
\(899\) 1.61818e6 + 1.61818e6i 0.0667772 + 0.0667772i
\(900\) −3.66021e7 + 1.26568e7i −1.50626 + 0.520857i
\(901\) 2.60826e7 2.60826e7i 1.07038 1.07038i
\(902\) −7.55908e6 + 2.45610e7i −0.309352 + 1.00515i
\(903\) −5.50969e7 5.50969e7i −2.24858 2.24858i
\(904\) 8.03450e6 6.43223e6i 0.326993 0.261782i
\(905\) 950800. + 1.89504e6i 0.0385894 + 0.0769127i
\(906\) 4.85891e7 2.57193e7i 1.96661 1.04097i
\(907\) 3.55838e7 1.43626 0.718132 0.695907i \(-0.244997\pi\)
0.718132 + 0.695907i \(0.244997\pi\)
\(908\) −6.13518e6 4.17156e6i −0.246952 0.167913i
\(909\) −2.69602e7 + 2.69602e7i −1.08222 + 1.08222i
\(910\) −1.61417e7 + 2.26613e7i −0.646169 + 0.907153i
\(911\) 156152.i 0.00623380i 0.999995 + 0.00311690i \(0.000992141\pi\)
−0.999995 + 0.00311690i \(0.999008\pi\)
\(912\) −1.25113e7 + 2.88750e7i −0.498100 + 1.14957i
\(913\) −3.69549e7 3.69549e7i −1.46722 1.46722i
\(914\) 2.70605e7 + 8.32836e6i 1.07145 + 0.329757i
\(915\) −1.42017e7 + 7.12540e6i −0.560773 + 0.281356i
\(916\) 1.88546e6 359214.i 0.0742469 0.0141454i
\(917\) 9.77376e6i 0.383829i
\(918\) −8.52750e6 + 2.77076e7i −0.333976 + 1.08515i
\(919\) 1.28715e7i 0.502737i 0.967892 + 0.251368i \(0.0808805\pi\)
−0.967892 + 0.251368i \(0.919119\pi\)
\(920\) 7.23254e6 + 1.95267e7i 0.281722 + 0.760607i
\(921\) 1.11889e7i 0.434647i
\(922\) −2.40278e7 7.39499e6i −0.930865 0.286490i
\(923\) 5.48527e7i 2.11931i
\(924\) −4.03977e7 + 5.94136e7i −1.55660 + 2.28932i
\(925\) 4.55272e6 6.10540e6i 0.174951 0.234617i
\(926\) −1.04323e6 + 3.38968e6i −0.0399810 + 0.129906i
\(927\) −2.27524e7 2.27524e7i −0.869617 0.869617i
\(928\) −1.71440e7 + 1.33919e6i −0.653495 + 0.0510473i
\(929\) 1.72862e6i 0.0657145i 0.999460 + 0.0328573i \(0.0104607\pi\)
−0.999460 + 0.0328573i \(0.989539\pi\)
\(930\) 6.03543e6 1.01405e6i 0.228823 0.0384462i
\(931\) 310970. 310970.i 0.0117583 0.0117583i
\(932\) 4.32866e6 + 2.27205e7i 0.163235 + 0.856796i
\(933\) 4.38855e7 1.65051
\(934\) −1.19726e7 2.26187e7i −0.449078 0.848401i
\(935\) 1.70001e7 5.12363e7i 0.635949 1.91668i
\(936\) 4.67915e7 + 5.18242e6i 1.74573 + 0.193349i
\(937\) −2.72025e7 2.72025e7i −1.01219 1.01219i −0.999925 0.0122612i \(-0.996097\pi\)
−0.0122612 0.999925i \(-0.503903\pi\)
\(938\) 2.25599e6 + 694321.i 0.0837201 + 0.0257664i
\(939\) 3.06168e6 3.06168e6i 0.113317 0.113317i
\(940\) −1.74244e6 + 1.31129e7i −0.0643190 + 0.484038i
\(941\) 2.81852e7 + 2.81852e7i 1.03764 + 1.03764i 0.999263 + 0.0383766i \(0.0122186\pi\)
0.0383766 + 0.999263i \(0.487781\pi\)
\(942\) −2.31860e7 + 1.22729e7i −0.851333 + 0.450630i
\(943\) −9.68396e6 + 9.68396e6i −0.354629 + 0.354629i
\(944\) −1.50142e7 6.50553e6i −0.548366 0.237604i
\(945\) −1.18979e7 2.37138e7i −0.433402 0.863816i
\(946\) 2.69049e7 8.74196e7i 0.977472 3.17600i
\(947\) 2.89380e7i 1.04856i 0.851546 + 0.524280i \(0.175665\pi\)
−0.851546 + 0.524280i \(0.824335\pi\)
\(948\) −2.07520e7 + 3.05203e7i −0.749962 + 1.10298i
\(949\) −5.20678e6 5.20678e6i −0.187674 0.187674i
\(950\) 1.27746e7 + 1.74659e7i 0.459240 + 0.627889i
\(951\) 1.89590e7 0.679772
\(952\) −3.33501e7 3.69371e6i −1.19263 0.132090i
\(953\) 2.59461e7 2.59461e7i 0.925422 0.925422i −0.0719834 0.997406i \(-0.522933\pi\)
0.997406 + 0.0719834i \(0.0229328\pi\)
\(954\) 5.04841e7 2.67224e7i 1.79591 0.950616i
\(955\) 1.94290e7 + 6.44652e6i 0.689355 + 0.228727i
\(956\) −1.70639e7 + 2.50962e7i −0.603857 + 0.888103i
\(957\) 5.08719e7 1.79555
\(958\) 2.17478e7 1.15116e7i 0.765600 0.405250i
\(959\) 5.19211e7 1.82304
\(960\) −2.36827e7 + 3.94210e7i −0.829379 + 1.38054i
\(961\) 2.80349e7 0.979243
\(962\) −8.18223e6 + 4.33105e6i −0.285059 + 0.150888i
\(963\) 4.63229e7 1.60964
\(964\) −2.24077e7 + 3.29554e7i −0.776615 + 1.14218i
\(965\) −1.88425e7 + 9.45384e6i −0.651359 + 0.326806i
\(966\) −3.38409e7 + 1.79128e7i −1.16681 + 0.617619i
\(967\) −2.86643e7 + 2.86643e7i −0.985769 + 0.985769i −0.999900 0.0141312i \(-0.995502\pi\)
0.0141312 + 0.999900i \(0.495502\pi\)
\(968\) −5.48497e7 6.07492e6i −1.88142 0.208378i
\(969\) 4.34775e7 1.48749
\(970\) 1.84277e7 + 1.31262e7i 0.628844 + 0.447928i
\(971\) 1.75400e7 + 1.75400e7i 0.597009 + 0.597009i 0.939516 0.342506i \(-0.111276\pi\)
−0.342506 + 0.939516i \(0.611276\pi\)
\(972\) 1.72695e7 2.53985e7i 0.586291 0.862268i
\(973\) 2.43553e7i 0.824728i
\(974\) −5.80673e6 + 1.88672e7i −0.196125 + 0.637251i
\(975\) 3.14935e7 4.22342e7i 1.06099 1.42283i
\(976\) −4.60916e6 + 1.06375e7i −0.154881 + 0.357450i
\(977\) −3.59646e6 + 3.59646e6i −0.120542 + 0.120542i −0.764805 0.644262i \(-0.777164\pi\)
0.644262 + 0.764805i \(0.277164\pi\)
\(978\) −7.30072e7 + 3.86444e7i −2.44072 + 1.29193i
\(979\) −5.61365e7 5.61365e7i −1.87192 1.87192i
\(980\) 510343. 390623.i 0.0169745 0.0129925i
\(981\) −4.01713e7 + 4.01713e7i −1.33273 + 1.33273i
\(982\) 2.28068e7 + 7.01921e6i 0.754720 + 0.232279i
\(983\) 1.41813e6 + 1.41813e6i 0.0468092 + 0.0468092i 0.730124 0.683315i \(-0.239462\pi\)
−0.683315 + 0.730124i \(0.739462\pi\)
\(984\) −3.00620e7 3.32954e6i −0.989761 0.109622i
\(985\) −5.12478e7 1.70039e7i −1.68300 0.558417i
\(986\) 1.11147e7 + 2.09980e7i 0.364089 + 0.687838i
\(987\) −2.43238e7 −0.794765
\(988\) −4.92283e6 2.58392e7i −0.160444 0.842144i
\(989\) 3.44680e7 3.44680e7i 1.12054 1.12054i
\(990\) 4.84995e7 6.80881e7i 1.57271 2.20792i
\(991\) 1.94713e7i 0.629813i 0.949123 + 0.314906i \(0.101973\pi\)
−0.949123 + 0.314906i \(0.898027\pi\)
\(992\) 2.90202e6 3.39381e6i 0.0936313 0.109499i
\(993\) 7.92179e6 + 7.92179e6i 0.254947 + 0.254947i
\(994\) 1.78084e7 5.78632e7i 0.571689 1.85753i
\(995\) 3.48106e7 + 1.15501e7i 1.11469 + 0.369852i
\(996\) 3.45864e7 5.08667e7i 1.10473 1.62475i
\(997\) 2.24649e7i 0.715757i 0.933768 + 0.357879i \(0.116500\pi\)
−0.933768 + 0.357879i \(0.883500\pi\)
\(998\) −8.68540e6 2.67309e6i −0.276035 0.0849546i
\(999\) 8.82814e6i 0.279870i
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 80.6.s.a.3.9 yes 116
5.2 odd 4 80.6.j.a.67.23 yes 116
16.11 odd 4 80.6.j.a.43.23 116
80.27 even 4 inner 80.6.s.a.27.9 yes 116
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
80.6.j.a.43.23 116 16.11 odd 4
80.6.j.a.67.23 yes 116 5.2 odd 4
80.6.s.a.3.9 yes 116 1.1 even 1 trivial
80.6.s.a.27.9 yes 116 80.27 even 4 inner