Properties

Label 9.6.c.a.7.4
Level $9$
Weight $6$
Character 9.7
Analytic conductor $1.443$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [9,6,Mod(4,9)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("9.4");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9 = 3^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 9.c (of order \(3\), 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: \(1.44345437832\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 40x^{6} + 568x^{4} + 3363x^{2} + 7056 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 7.4
Root \(-2.56934i\) of defining polynomial
Character \(\chi\) \(=\) 9.7
Dual form 9.6.c.a.4.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.96163 - 8.59380i) q^{2} +(-3.07760 + 15.2816i) q^{3} +(-33.2356 - 57.5657i) q^{4} +(23.6560 + 40.9735i) q^{5} +(116.057 + 102.270i) q^{6} +(1.01546 - 1.75882i) q^{7} -342.066 q^{8} +(-224.057 - 94.0614i) q^{9} +O(q^{10})\) \(q+(4.96163 - 8.59380i) q^{2} +(-3.07760 + 15.2816i) q^{3} +(-33.2356 - 57.5657i) q^{4} +(23.6560 + 40.9735i) q^{5} +(116.057 + 102.270i) q^{6} +(1.01546 - 1.75882i) q^{7} -342.066 q^{8} +(-224.057 - 94.0614i) q^{9} +469.490 q^{10} +(-91.8836 + 159.147i) q^{11} +(981.984 - 330.730i) q^{12} +(-364.672 - 631.630i) q^{13} +(-10.0766 - 17.4532i) q^{14} +(-698.946 + 235.403i) q^{15} +(-633.668 + 1097.55i) q^{16} +1212.88 q^{17} +(-1920.03 + 1458.80i) q^{18} -473.092 q^{19} +(1572.44 - 2723.55i) q^{20} +(23.7525 + 20.9308i) q^{21} +(911.785 + 1579.26i) q^{22} +(1806.42 + 3128.81i) q^{23} +(1052.74 - 5227.33i) q^{24} +(443.283 - 767.788i) q^{25} -7237.47 q^{26} +(2126.97 - 3134.47i) q^{27} -134.997 q^{28} +(663.121 - 1148.56i) q^{29} +(-1444.90 + 7174.58i) q^{30} +(2590.41 + 4486.72i) q^{31} +(814.997 + 1411.62i) q^{32} +(-2149.25 - 1893.92i) q^{33} +(6017.88 - 10423.3i) q^{34} +96.0867 q^{35} +(2031.95 + 16024.2i) q^{36} -14715.2 q^{37} +(-2347.31 + 4065.65i) q^{38} +(10774.7 - 3628.88i) q^{39} +(-8091.94 - 14015.6i) q^{40} +(-3159.83 - 5472.98i) q^{41} +(297.726 - 100.273i) q^{42} +(-3067.89 + 5313.75i) q^{43} +12215.2 q^{44} +(-1446.28 - 11405.5i) q^{45} +35851.1 q^{46} +(-1584.17 + 2743.86i) q^{47} +(-14822.1 - 13061.3i) q^{48} +(8401.44 + 14551.7i) q^{49} +(-4398.81 - 7618.96i) q^{50} +(-3732.76 + 18534.8i) q^{51} +(-24240.2 + 41985.2i) q^{52} -12265.0 q^{53} +(-16383.8 - 33830.8i) q^{54} -8694.41 q^{55} +(-347.353 + 601.633i) q^{56} +(1455.98 - 7229.61i) q^{57} +(-6580.32 - 11397.5i) q^{58} +(14773.5 + 25588.5i) q^{59} +(36781.0 + 32411.5i) q^{60} +(20153.6 - 34907.1i) q^{61} +51410.7 q^{62} +(-392.957 + 298.561i) q^{63} -24379.9 q^{64} +(17253.4 - 29883.8i) q^{65} +(-26939.7 + 9073.25i) q^{66} +(-11748.9 - 20349.7i) q^{67} +(-40310.9 - 69820.5i) q^{68} +(-53372.8 + 17975.8i) q^{69} +(476.747 - 825.750i) q^{70} -123.786 q^{71} +(76642.3 + 32175.2i) q^{72} +35217.6 q^{73} +(-73011.4 + 126459. i) q^{74} +(10368.8 + 9137.03i) q^{75} +(15723.5 + 27233.8i) q^{76} +(186.607 + 323.214i) q^{77} +(22274.0 - 110600. i) q^{78} +(24072.8 - 41695.3i) q^{79} -59960.3 q^{80} +(41353.9 + 42150.2i) q^{81} -62711.6 q^{82} +(-5167.97 + 8951.18i) q^{83} +(415.466 - 2062.98i) q^{84} +(28692.0 + 49696.1i) q^{85} +(30443.5 + 52729.7i) q^{86} +(15511.0 + 13668.4i) q^{87} +(31430.3 - 54438.8i) q^{88} -42585.7 q^{89} +(-105193. - 44160.9i) q^{90} -1481.23 q^{91} +(120075. - 207976. i) q^{92} +(-76536.7 + 25777.4i) q^{93} +(15720.1 + 27228.1i) q^{94} +(-11191.5 - 19384.2i) q^{95} +(-24080.0 + 8110.10i) q^{96} +(-49347.3 + 85472.1i) q^{97} +166739. q^{98} +(35556.7 - 27015.3i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 3 q^{2} - 12 q^{3} - 49 q^{4} + 78 q^{5} + 171 q^{6} + 28 q^{7} - 750 q^{8} - 414 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 3 q^{2} - 12 q^{3} - 49 q^{4} + 78 q^{5} + 171 q^{6} + 28 q^{7} - 750 q^{8} - 414 q^{9} + 60 q^{10} + 444 q^{11} + 2724 q^{12} - 182 q^{13} + 1392 q^{14} - 2052 q^{15} - 289 q^{16} - 4356 q^{17} - 8100 q^{18} + 952 q^{19} + 6684 q^{20} + 8670 q^{21} + 1011 q^{22} + 8844 q^{23} + 549 q^{24} - 1654 q^{25} - 24888 q^{26} - 10152 q^{27} - 1604 q^{28} + 12018 q^{29} + 22104 q^{30} + 1132 q^{31} + 8703 q^{32} - 8820 q^{33} + 10125 q^{34} - 16224 q^{35} - 14589 q^{36} - 15176 q^{37} - 11145 q^{38} + 8220 q^{39} - 8736 q^{40} + 1248 q^{41} + 10098 q^{42} - 6092 q^{43} + 49530 q^{44} + 43038 q^{45} + 45960 q^{46} - 60 q^{47} - 57405 q^{48} + 9090 q^{49} - 57057 q^{50} - 9396 q^{51} - 32510 q^{52} + 20952 q^{53} + 8181 q^{54} - 36120 q^{55} - 61170 q^{56} - 104298 q^{57} + 8328 q^{58} + 2076 q^{59} + 88308 q^{60} + 48142 q^{61} + 241764 q^{62} + 133524 q^{63} - 20926 q^{64} - 13146 q^{65} - 100998 q^{66} - 7148 q^{67} - 123129 q^{68} - 125982 q^{69} - 654 q^{70} - 71856 q^{71} + 35451 q^{72} + 122452 q^{73} - 160320 q^{74} - 18732 q^{75} - 49571 q^{76} + 39534 q^{77} + 181422 q^{78} - 59516 q^{79} + 124512 q^{80} + 194562 q^{81} - 233598 q^{82} + 117696 q^{83} + 108354 q^{84} + 28836 q^{85} - 15915 q^{86} - 142956 q^{87} + 104523 q^{88} - 451728 q^{89} - 539892 q^{90} + 111392 q^{91} + 134034 q^{92} + 113898 q^{93} + 169464 q^{94} + 294888 q^{95} + 42768 q^{96} + 33976 q^{97} + 57654 q^{98} + 33696 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/9\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.96163 8.59380i 0.877101 1.51918i 0.0225929 0.999745i \(-0.492808\pi\)
0.854508 0.519438i \(-0.173859\pi\)
\(3\) −3.07760 + 15.2816i −0.197428 + 0.980317i
\(4\) −33.2356 57.5657i −1.03861 1.79893i
\(5\) 23.6560 + 40.9735i 0.423172 + 0.732956i 0.996248 0.0865467i \(-0.0275832\pi\)
−0.573076 + 0.819503i \(0.694250\pi\)
\(6\) 116.057 + 102.270i 1.31612 + 1.15977i
\(7\) 1.01546 1.75882i 0.00783278 0.0135668i −0.862082 0.506768i \(-0.830840\pi\)
0.869915 + 0.493201i \(0.164173\pi\)
\(8\) −342.066 −1.88967
\(9\) −224.057 94.0614i −0.922044 0.387084i
\(10\) 469.490 1.48466
\(11\) −91.8836 + 159.147i −0.228958 + 0.396567i −0.957500 0.288435i \(-0.906865\pi\)
0.728541 + 0.685002i \(0.240199\pi\)
\(12\) 981.984 330.730i 1.96857 0.663011i
\(13\) −364.672 631.630i −0.598472 1.03658i −0.993047 0.117720i \(-0.962441\pi\)
0.394574 0.918864i \(-0.370892\pi\)
\(14\) −10.0766 17.4532i −0.0137403 0.0237989i
\(15\) −698.946 + 235.403i −0.802075 + 0.270137i
\(16\) −633.668 + 1097.55i −0.618817 + 1.07182i
\(17\) 1212.88 1.01788 0.508940 0.860802i \(-0.330037\pi\)
0.508940 + 0.860802i \(0.330037\pi\)
\(18\) −1920.03 + 1458.80i −1.39678 + 1.06124i
\(19\) −473.092 −0.300650 −0.150325 0.988637i \(-0.548032\pi\)
−0.150325 + 0.988637i \(0.548032\pi\)
\(20\) 1572.44 2723.55i 0.879023 1.52251i
\(21\) 23.7525 + 20.9308i 0.0117533 + 0.0103571i
\(22\) 911.785 + 1579.26i 0.401639 + 0.695659i
\(23\) 1806.42 + 3128.81i 0.712031 + 1.23327i 0.964094 + 0.265563i \(0.0855578\pi\)
−0.252063 + 0.967711i \(0.581109\pi\)
\(24\) 1052.74 5227.33i 0.373073 1.85247i
\(25\) 443.283 767.788i 0.141850 0.245692i
\(26\) −7237.47 −2.09968
\(27\) 2126.97 3134.47i 0.561502 0.827475i
\(28\) −134.997 −0.0325409
\(29\) 663.121 1148.56i 0.146419 0.253605i −0.783482 0.621414i \(-0.786559\pi\)
0.929901 + 0.367809i \(0.119892\pi\)
\(30\) −1444.90 + 7174.58i −0.293113 + 1.45544i
\(31\) 2590.41 + 4486.72i 0.484133 + 0.838542i 0.999834 0.0182261i \(-0.00580186\pi\)
−0.515701 + 0.856769i \(0.672469\pi\)
\(32\) 814.997 + 1411.62i 0.140696 + 0.243692i
\(33\) −2149.25 1893.92i −0.343559 0.302745i
\(34\) 6017.88 10423.3i 0.892784 1.54635i
\(35\) 96.0867 0.0132585
\(36\) 2031.95 + 16024.2i 0.261310 + 2.06072i
\(37\) −14715.2 −1.76710 −0.883552 0.468334i \(-0.844854\pi\)
−0.883552 + 0.468334i \(0.844854\pi\)
\(38\) −2347.31 + 4065.65i −0.263700 + 0.456742i
\(39\) 10774.7 3628.88i 1.13434 0.382042i
\(40\) −8091.94 14015.6i −0.799655 1.38504i
\(41\) −3159.83 5472.98i −0.293564 0.508469i 0.681085 0.732204i \(-0.261508\pi\)
−0.974650 + 0.223735i \(0.928175\pi\)
\(42\) 297.726 100.273i 0.0260431 0.00877128i
\(43\) −3067.89 + 5313.75i −0.253028 + 0.438258i −0.964358 0.264600i \(-0.914760\pi\)
0.711330 + 0.702858i \(0.248093\pi\)
\(44\) 12215.2 0.951195
\(45\) −1446.28 11405.5i −0.106468 0.839621i
\(46\) 35851.1 2.49809
\(47\) −1584.17 + 2743.86i −0.104606 + 0.181183i −0.913577 0.406665i \(-0.866692\pi\)
0.808971 + 0.587848i \(0.200025\pi\)
\(48\) −14822.1 13061.3i −0.928554 0.818244i
\(49\) 8401.44 + 14551.7i 0.499877 + 0.865813i
\(50\) −4398.81 7618.96i −0.248834 0.430994i
\(51\) −3732.76 + 18534.8i −0.200958 + 0.997846i
\(52\) −24240.2 + 41985.2i −1.24316 + 2.15322i
\(53\) −12265.0 −0.599763 −0.299881 0.953977i \(-0.596947\pi\)
−0.299881 + 0.953977i \(0.596947\pi\)
\(54\) −16383.8 33830.8i −0.764592 1.57880i
\(55\) −8694.41 −0.387555
\(56\) −347.353 + 601.633i −0.0148013 + 0.0256367i
\(57\) 1455.98 7229.61i 0.0593567 0.294732i
\(58\) −6580.32 11397.5i −0.256849 0.444875i
\(59\) 14773.5 + 25588.5i 0.552528 + 0.957006i 0.998091 + 0.0617560i \(0.0196701\pi\)
−0.445563 + 0.895250i \(0.646997\pi\)
\(60\) 36781.0 + 32411.5i 1.31900 + 1.16231i
\(61\) 20153.6 34907.1i 0.693472 1.20113i −0.277221 0.960806i \(-0.589413\pi\)
0.970693 0.240323i \(-0.0772534\pi\)
\(62\) 51410.7 1.69853
\(63\) −392.957 + 298.561i −0.0124737 + 0.00947723i
\(64\) −24379.9 −0.744016
\(65\) 17253.4 29883.8i 0.506514 0.877308i
\(66\) −26939.7 + 9073.25i −0.761261 + 0.256391i
\(67\) −11748.9 20349.7i −0.319750 0.553823i 0.660686 0.750662i \(-0.270266\pi\)
−0.980436 + 0.196840i \(0.936932\pi\)
\(68\) −40310.9 69820.5i −1.05718 1.83109i
\(69\) −53372.8 + 17975.8i −1.34957 + 0.454534i
\(70\) 476.747 825.750i 0.0116290 0.0201420i
\(71\) −123.786 −0.00291425 −0.00145713 0.999999i \(-0.500464\pi\)
−0.00145713 + 0.999999i \(0.500464\pi\)
\(72\) 76642.3 + 32175.2i 1.74236 + 0.731460i
\(73\) 35217.6 0.773486 0.386743 0.922188i \(-0.373600\pi\)
0.386743 + 0.922188i \(0.373600\pi\)
\(74\) −73011.4 + 126459.i −1.54993 + 2.68455i
\(75\) 10368.8 + 9137.03i 0.212851 + 0.187565i
\(76\) 15723.5 + 27233.8i 0.312259 + 0.540848i
\(77\) 186.607 + 323.214i 0.00358676 + 0.00621245i
\(78\) 22274.0 110600.i 0.414536 2.05836i
\(79\) 24072.8 41695.3i 0.433969 0.751656i −0.563242 0.826292i \(-0.690446\pi\)
0.997211 + 0.0746359i \(0.0237794\pi\)
\(80\) −59960.3 −1.04746
\(81\) 41353.9 + 42150.2i 0.700332 + 0.713817i
\(82\) −62711.6 −1.02994
\(83\) −5167.97 + 8951.18i −0.0823426 + 0.142622i −0.904256 0.426991i \(-0.859574\pi\)
0.821913 + 0.569613i \(0.192907\pi\)
\(84\) 415.466 2062.98i 0.00642447 0.0319004i
\(85\) 28692.0 + 49696.1i 0.430739 + 0.746062i
\(86\) 30443.5 + 52729.7i 0.443863 + 0.768793i
\(87\) 15511.0 + 13668.4i 0.219706 + 0.193606i
\(88\) 31430.3 54438.8i 0.432655 0.749380i
\(89\) −42585.7 −0.569887 −0.284944 0.958544i \(-0.591975\pi\)
−0.284944 + 0.958544i \(0.591975\pi\)
\(90\) −105193. 44160.9i −1.36892 0.574688i
\(91\) −1481.23 −0.0187508
\(92\) 120075. 207976.i 1.47905 2.56178i
\(93\) −76536.7 + 25777.4i −0.917619 + 0.309052i
\(94\) 15720.1 + 27228.1i 0.183500 + 0.317832i
\(95\) −11191.5 19384.2i −0.127227 0.220363i
\(96\) −24080.0 + 8110.10i −0.266673 + 0.0898149i
\(97\) −49347.3 + 85472.1i −0.532518 + 0.922348i 0.466761 + 0.884383i \(0.345421\pi\)
−0.999279 + 0.0379646i \(0.987913\pi\)
\(98\) 166739. 1.75377
\(99\) 35556.7 27015.3i 0.364614 0.277027i
\(100\) −58931.0 −0.589310
\(101\) 37818.9 65504.3i 0.368898 0.638949i −0.620496 0.784210i \(-0.713069\pi\)
0.989393 + 0.145260i \(0.0464020\pi\)
\(102\) 140764. + 124042.i 1.33965 + 1.18050i
\(103\) −73869.1 127945.i −0.686072 1.18831i −0.973099 0.230389i \(-0.926000\pi\)
0.287026 0.957923i \(-0.407333\pi\)
\(104\) 124742. + 216059.i 1.13091 + 1.95880i
\(105\) −295.716 + 1468.36i −0.00261759 + 0.0129975i
\(106\) −60854.6 + 105403.i −0.526052 + 0.911149i
\(107\) −209139. −1.76594 −0.882969 0.469430i \(-0.844459\pi\)
−0.882969 + 0.469430i \(0.844459\pi\)
\(108\) −251129. 18264.4i −2.07175 0.150677i
\(109\) 115605. 0.931988 0.465994 0.884788i \(-0.345697\pi\)
0.465994 + 0.884788i \(0.345697\pi\)
\(110\) −43138.5 + 74718.0i −0.339925 + 0.588767i
\(111\) 45287.4 224872.i 0.348875 1.73232i
\(112\) 1286.92 + 2229.02i 0.00969411 + 0.0167907i
\(113\) −23415.8 40557.3i −0.172509 0.298795i 0.766787 0.641901i \(-0.221854\pi\)
−0.939296 + 0.343107i \(0.888521\pi\)
\(114\) −54905.8 48383.1i −0.395691 0.348684i
\(115\) −85465.5 + 148031.i −0.602623 + 1.04377i
\(116\) −88156.8 −0.608290
\(117\) 22295.2 + 175823.i 0.150573 + 1.18744i
\(118\) 293203. 1.93849
\(119\) 1231.63 2133.25i 0.00797283 0.0138094i
\(120\) 239086. 80523.5i 1.51566 0.510469i
\(121\) 63640.3 + 110228.i 0.395156 + 0.684431i
\(122\) −199990. 346393.i −1.21649 2.10702i
\(123\) 93360.7 31443.7i 0.556418 0.187400i
\(124\) 172188. 298238.i 1.00565 1.74184i
\(125\) 189796. 1.08645
\(126\) 616.062 + 4858.34i 0.00345699 + 0.0272622i
\(127\) −93444.5 −0.514096 −0.257048 0.966399i \(-0.582750\pi\)
−0.257048 + 0.966399i \(0.582750\pi\)
\(128\) −147044. + 254688.i −0.793273 + 1.37399i
\(129\) −71761.0 63236.0i −0.379677 0.334572i
\(130\) −171210. 296544.i −0.888527 1.53897i
\(131\) 183869. + 318470.i 0.936115 + 1.62140i 0.772634 + 0.634852i \(0.218939\pi\)
0.163481 + 0.986546i \(0.447728\pi\)
\(132\) −37593.5 + 186668.i −0.187792 + 0.932473i
\(133\) −480.404 + 832.083i −0.00235493 + 0.00407885i
\(134\) −233175. −1.12181
\(135\) 178746. + 13000.1i 0.844115 + 0.0613919i
\(136\) −414887. −1.92346
\(137\) 76809.2 133037.i 0.349632 0.605581i −0.636552 0.771234i \(-0.719640\pi\)
0.986184 + 0.165653i \(0.0529731\pi\)
\(138\) −110335. + 547864.i −0.493193 + 2.44892i
\(139\) −122213. 211679.i −0.536513 0.929268i −0.999088 0.0426878i \(-0.986408\pi\)
0.462575 0.886580i \(-0.346925\pi\)
\(140\) −3193.50 5531.30i −0.0137704 0.0238510i
\(141\) −37055.3 32653.2i −0.156965 0.138318i
\(142\) −614.183 + 1063.80i −0.00255609 + 0.00442728i
\(143\) 134029. 0.548101
\(144\) 245214. 186309.i 0.985461 0.748734i
\(145\) 62747.3 0.247842
\(146\) 174737. 302653.i 0.678425 1.17507i
\(147\) −248230. + 83603.4i −0.947461 + 0.319103i
\(148\) 489068. + 847091.i 1.83533 + 3.17889i
\(149\) 4924.61 + 8529.67i 0.0181721 + 0.0314751i 0.874968 0.484180i \(-0.160882\pi\)
−0.856796 + 0.515655i \(0.827549\pi\)
\(150\) 129968. 43772.9i 0.471637 0.158846i
\(151\) 109892. 190339.i 0.392216 0.679338i −0.600526 0.799606i \(-0.705042\pi\)
0.992741 + 0.120268i \(0.0383753\pi\)
\(152\) 161829. 0.568128
\(153\) −271755. 114086.i −0.938531 0.394005i
\(154\) 3703.51 0.0125838
\(155\) −122558. + 212276.i −0.409743 + 0.709696i
\(156\) −567001. 499643.i −1.86540 1.64380i
\(157\) −15290.5 26483.9i −0.0495077 0.0857498i 0.840210 0.542262i \(-0.182432\pi\)
−0.889717 + 0.456512i \(0.849099\pi\)
\(158\) −238881. 413753.i −0.761269 1.31856i
\(159\) 37746.8 187430.i 0.118410 0.587958i
\(160\) −38559.2 + 66786.5i −0.119077 + 0.206248i
\(161\) 7337.35 0.0223087
\(162\) 567413. 146253.i 1.69868 0.437843i
\(163\) −272367. −0.802945 −0.401472 0.915871i \(-0.631501\pi\)
−0.401472 + 0.915871i \(0.631501\pi\)
\(164\) −210037. + 363795.i −0.609799 + 1.05620i
\(165\) 26757.9 132865.i 0.0765142 0.379927i
\(166\) 51283.1 + 88824.9i 0.144445 + 0.250187i
\(167\) 99337.8 + 172058.i 0.275628 + 0.477402i 0.970293 0.241931i \(-0.0777809\pi\)
−0.694665 + 0.719333i \(0.744448\pi\)
\(168\) −8124.93 7159.71i −0.0222099 0.0195714i
\(169\) −80324.9 + 139127.i −0.216338 + 0.374709i
\(170\) 569437. 1.51121
\(171\) 105999. + 44499.6i 0.277213 + 0.116377i
\(172\) 407853. 1.05119
\(173\) −33895.9 + 58709.5i −0.0861058 + 0.149140i −0.905862 0.423573i \(-0.860776\pi\)
0.819756 + 0.572713i \(0.194109\pi\)
\(174\) 194423. 65481.3i 0.486828 0.163962i
\(175\) −900.268 1559.31i −0.00222217 0.00384891i
\(176\) −116447. 201693.i −0.283366 0.490805i
\(177\) −436501. + 147013.i −1.04725 + 0.352713i
\(178\) −211295. + 365973.i −0.499848 + 0.865763i
\(179\) 21849.0 0.0509681 0.0254840 0.999675i \(-0.491887\pi\)
0.0254840 + 0.999675i \(0.491887\pi\)
\(180\) −608498. + 462325.i −1.39984 + 1.06357i
\(181\) 188080. 0.426722 0.213361 0.976973i \(-0.431559\pi\)
0.213361 + 0.976973i \(0.431559\pi\)
\(182\) −7349.33 + 12729.4i −0.0164463 + 0.0284859i
\(183\) 471414. + 415411.i 1.04058 + 0.916959i
\(184\) −617915. 1.07026e6i −1.34550 2.33048i
\(185\) −348104. 602933.i −0.747789 1.29521i
\(186\) −158221. + 785639.i −0.335338 + 1.66510i
\(187\) −111444. + 193027.i −0.233052 + 0.403658i
\(188\) 210603. 0.434581
\(189\) −3353.13 6923.87i −0.00682804 0.0140992i
\(190\) −222112. −0.446363
\(191\) 123200. 213389.i 0.244359 0.423241i −0.717592 0.696463i \(-0.754756\pi\)
0.961951 + 0.273222i \(0.0880893\pi\)
\(192\) 75031.5 372565.i 0.146889 0.729372i
\(193\) 113565. + 196701.i 0.219459 + 0.380114i 0.954643 0.297754i \(-0.0962375\pi\)
−0.735184 + 0.677868i \(0.762904\pi\)
\(194\) 489686. + 848162.i 0.934144 + 1.61798i
\(195\) 403574. + 355630.i 0.760040 + 0.669749i
\(196\) 558453. 967269.i 1.03836 1.79849i
\(197\) −503086. −0.923584 −0.461792 0.886988i \(-0.652793\pi\)
−0.461792 + 0.886988i \(0.652793\pi\)
\(198\) −55744.4 439607.i −0.101051 0.796896i
\(199\) 4126.65 0.00738694 0.00369347 0.999993i \(-0.498824\pi\)
0.00369347 + 0.999993i \(0.498824\pi\)
\(200\) −151632. + 262634.i −0.268050 + 0.464276i
\(201\) 347135. 116914.i 0.606050 0.204116i
\(202\) −375287. 650016.i −0.647121 1.12085i
\(203\) −1346.74 2332.62i −0.00229374 0.00397287i
\(204\) 1.19103e6 401137.i 2.00377 0.674866i
\(205\) 149498. 258938.i 0.248457 0.430340i
\(206\) −1.46605e6 −2.40702
\(207\) −110440. 870945.i −0.179144 1.41275i
\(208\) 924324. 1.48138
\(209\) 43469.3 75291.1i 0.0688363 0.119228i
\(210\) 11151.6 + 9826.79i 0.0174497 + 0.0153767i
\(211\) 494954. + 857285.i 0.765347 + 1.32562i 0.940063 + 0.341001i \(0.110766\pi\)
−0.174716 + 0.984619i \(0.555901\pi\)
\(212\) 407636. + 706046.i 0.622921 + 1.07893i
\(213\) 380.965 1891.66i 0.000575355 0.00285689i
\(214\) −1.03767e6 + 1.79730e6i −1.54891 + 2.68278i
\(215\) −290297. −0.428298
\(216\) −727564. + 1.07220e6i −1.06105 + 1.56365i
\(217\) 10521.8 0.0151684
\(218\) 573589. 993485.i 0.817447 1.41586i
\(219\) −108385. + 538182.i −0.152708 + 0.758262i
\(220\) 288964. + 500500.i 0.402519 + 0.697184i
\(221\) −442305. 766094.i −0.609173 1.05512i
\(222\) −1.70781e6 1.50492e6i −2.32572 2.04943i
\(223\) 523910. 907438.i 0.705496 1.22195i −0.261017 0.965334i \(-0.584058\pi\)
0.966512 0.256620i \(-0.0826089\pi\)
\(224\) 3310.37 0.00440816
\(225\) −171540. + 130332.i −0.225896 + 0.171631i
\(226\) −464722. −0.605232
\(227\) −355537. + 615808.i −0.457952 + 0.793196i −0.998853 0.0478902i \(-0.984750\pi\)
0.540900 + 0.841087i \(0.318084\pi\)
\(228\) −464568. + 156466.i −0.591851 + 0.199334i
\(229\) −147071. 254734.i −0.185327 0.320995i 0.758360 0.651836i \(-0.226001\pi\)
−0.943687 + 0.330841i \(0.892668\pi\)
\(230\) 848096. + 1.46895e6i 1.05712 + 1.83099i
\(231\) −5513.53 + 1856.95i −0.00679830 + 0.00228965i
\(232\) −226831. + 392883.i −0.276683 + 0.479230i
\(233\) 1.56670e6 1.89059 0.945294 0.326218i \(-0.105774\pi\)
0.945294 + 0.326218i \(0.105774\pi\)
\(234\) 1.62161e6 + 680767.i 1.93600 + 0.812753i
\(235\) −149901. −0.177066
\(236\) 982013. 1.70090e6i 1.14772 1.98792i
\(237\) 563086. + 496193.i 0.651184 + 0.573825i
\(238\) −12221.8 21168.8i −0.0139860 0.0242244i
\(239\) −260961. 451998.i −0.295516 0.511849i 0.679589 0.733593i \(-0.262158\pi\)
−0.975105 + 0.221744i \(0.928825\pi\)
\(240\) 184534. 916292.i 0.206799 1.02685i
\(241\) 213855. 370407.i 0.237179 0.410806i −0.722725 0.691136i \(-0.757111\pi\)
0.959904 + 0.280330i \(0.0904439\pi\)
\(242\) 1.26304e6 1.38637
\(243\) −771394. + 502234.i −0.838032 + 0.545620i
\(244\) −2.67927e6 −2.88099
\(245\) −397490. + 688472.i −0.423068 + 0.732776i
\(246\) 193001. 958335.i 0.203339 1.00967i
\(247\) 172523. + 298819.i 0.179931 + 0.311649i
\(248\) −886092. 1.53476e6i −0.914849 1.58457i
\(249\) −120884. 106523.i −0.123558 0.108879i
\(250\) 941696. 1.63106e6i 0.952929 1.65052i
\(251\) −231914. −0.232350 −0.116175 0.993229i \(-0.537063\pi\)
−0.116175 + 0.993229i \(0.537063\pi\)
\(252\) 30247.0 + 12698.0i 0.0300041 + 0.0125960i
\(253\) −663921. −0.652101
\(254\) −463637. + 803043.i −0.450914 + 0.781006i
\(255\) −847740. + 285517.i −0.816417 + 0.274967i
\(256\) 1.06908e6 + 1.85170e6i 1.01955 + 1.76592i
\(257\) 707127. + 1.22478e6i 0.667828 + 1.15671i 0.978510 + 0.206199i \(0.0661093\pi\)
−0.310682 + 0.950514i \(0.600557\pi\)
\(258\) −899489. + 302946.i −0.841292 + 0.283345i
\(259\) −14942.6 + 25881.4i −0.0138413 + 0.0239739i
\(260\) −2.29371e6 −2.10428
\(261\) −256612. + 194968.i −0.233171 + 0.177159i
\(262\) 3.64915e6 3.28427
\(263\) 615838. 1.06666e6i 0.549006 0.950907i −0.449336 0.893363i \(-0.648340\pi\)
0.998343 0.0575445i \(-0.0183271\pi\)
\(264\) 735185. + 647847.i 0.649212 + 0.572087i
\(265\) −290143. 502542.i −0.253803 0.439600i
\(266\) 4767.17 + 8256.98i 0.00413101 + 0.00715513i
\(267\) 131062. 650779.i 0.112512 0.558670i
\(268\) −780963. + 1.35267e6i −0.664192 + 1.15041i
\(269\) 119245. 0.100475 0.0502377 0.998737i \(-0.484002\pi\)
0.0502377 + 0.998737i \(0.484002\pi\)
\(270\) 998591. 1.47160e6i 0.833639 1.22852i
\(271\) 50141.4 0.0414738 0.0207369 0.999785i \(-0.493399\pi\)
0.0207369 + 0.999785i \(0.493399\pi\)
\(272\) −768566. + 1.33120e6i −0.629881 + 1.09099i
\(273\) 4558.64 22635.7i 0.00370193 0.0183817i
\(274\) −762198. 1.32017e6i −0.613326 1.06231i
\(275\) 81460.8 + 141094.i 0.0649557 + 0.112506i
\(276\) 2.80866e6 + 2.47500e6i 2.21936 + 1.95570i
\(277\) −235820. + 408452.i −0.184663 + 0.319846i −0.943463 0.331478i \(-0.892453\pi\)
0.758800 + 0.651324i \(0.225786\pi\)
\(278\) −2.42550e6 −1.88230
\(279\) −158372. 1.24894e6i −0.121806 0.960573i
\(280\) −32868.0 −0.0250541
\(281\) −1.03652e6 + 1.79530e6i −0.783087 + 1.35635i 0.147048 + 0.989129i \(0.453023\pi\)
−0.930135 + 0.367217i \(0.880311\pi\)
\(282\) −464470. + 156432.i −0.347804 + 0.117140i
\(283\) −758046. 1.31297e6i −0.562639 0.974519i −0.997265 0.0739079i \(-0.976453\pi\)
0.434626 0.900611i \(-0.356880\pi\)
\(284\) 4114.11 + 7125.86i 0.00302678 + 0.00524253i
\(285\) 330665. 111367.i 0.241144 0.0812168i
\(286\) 665005. 1.15182e6i 0.480739 0.832665i
\(287\) −12834.7 −0.00919770
\(288\) −49827.0 392942.i −0.0353984 0.279156i
\(289\) 51229.6 0.0360808
\(290\) 311329. 539237.i 0.217382 0.376517i
\(291\) −1.15428e6 1.01716e6i −0.799060 0.704134i
\(292\) −1.17048e6 2.02733e6i −0.803352 1.39145i
\(293\) −385100. 667013.i −0.262062 0.453905i 0.704727 0.709478i \(-0.251069\pi\)
−0.966790 + 0.255573i \(0.917736\pi\)
\(294\) −513156. + 2.54805e6i −0.346243 + 1.71925i
\(295\) −698967. + 1.21065e6i −0.467629 + 0.809957i
\(296\) 5.03357e6 3.33924
\(297\) 303408. + 626507.i 0.199589 + 0.412131i
\(298\) 97736.4 0.0637552
\(299\) 1.31750e6 2.28198e6i 0.852262 1.47616i
\(300\) 181366. 900562.i 0.116346 0.577711i
\(301\) 6230.62 + 10791.8i 0.00396383 + 0.00686556i
\(302\) −1.09049e6 1.88879e6i −0.688026 1.19170i
\(303\) 884622. + 779531.i 0.553543 + 0.487783i
\(304\) 299783. 519240.i 0.186047 0.322243i
\(305\) 1.90702e6 1.17383
\(306\) −2.32878e6 + 1.76936e6i −1.42175 + 1.08022i
\(307\) 2.13559e6 1.29322 0.646610 0.762821i \(-0.276186\pi\)
0.646610 + 0.762821i \(0.276186\pi\)
\(308\) 12404.0 21484.4i 0.00745050 0.0129046i
\(309\) 2.18255e6 735078.i 1.30037 0.437963i
\(310\) 1.21617e6 + 2.10647e6i 0.718772 + 1.24495i
\(311\) 301713. + 522582.i 0.176886 + 0.306375i 0.940812 0.338928i \(-0.110064\pi\)
−0.763927 + 0.645303i \(0.776731\pi\)
\(312\) −3.68565e6 + 1.24132e6i −2.14352 + 0.721932i
\(313\) −1.08619e6 + 1.88133e6i −0.626677 + 1.08544i 0.361537 + 0.932358i \(0.382252\pi\)
−0.988214 + 0.153079i \(0.951081\pi\)
\(314\) −303463. −0.173693
\(315\) −21528.9 9038.05i −0.0122249 0.00513214i
\(316\) −3.20029e6 −1.80290
\(317\) −1.60049e6 + 2.77213e6i −0.894550 + 1.54941i −0.0601886 + 0.998187i \(0.519170\pi\)
−0.834361 + 0.551218i \(0.814163\pi\)
\(318\) −1.42345e6 1.25435e6i −0.789358 0.695585i
\(319\) 121860. + 211067.i 0.0670477 + 0.116130i
\(320\) −576732. 998930.i −0.314847 0.545331i
\(321\) 643645. 3.19599e6i 0.348646 1.73118i
\(322\) 36405.2 63055.7i 0.0195670 0.0338910i
\(323\) −573805. −0.306026
\(324\) 1.05198e6 3.78145e6i 0.556733 2.00123i
\(325\) −646611. −0.339574
\(326\) −1.35139e6 + 2.34067e6i −0.704263 + 1.21982i
\(327\) −355785. + 1.76663e6i −0.184000 + 0.913644i
\(328\) 1.08087e6 + 1.87212e6i 0.554739 + 0.960836i
\(329\) 3217.31 + 5572.54i 0.00163871 + 0.00283834i
\(330\) −1.00905e6 889178.i −0.510068 0.449473i
\(331\) −1.30413e6 + 2.25883e6i −0.654263 + 1.13322i 0.327815 + 0.944742i \(0.393688\pi\)
−0.982078 + 0.188475i \(0.939645\pi\)
\(332\) 687041. 0.342088
\(333\) 3.29704e6 + 1.38413e6i 1.62935 + 0.684017i
\(334\) 1.97151e6 0.967014
\(335\) 555865. 962787.i 0.270618 0.468725i
\(336\) −38023.7 + 12806.3i −0.0183741 + 0.00618835i
\(337\) 414934. + 718687.i 0.199024 + 0.344719i 0.948212 0.317638i \(-0.102890\pi\)
−0.749189 + 0.662357i \(0.769556\pi\)
\(338\) 797085. + 1.38059e6i 0.379501 + 0.657315i
\(339\) 691846. 233012.i 0.326972 0.110123i
\(340\) 1.90719e6 3.30335e6i 0.894741 1.54974i
\(341\) −952065. −0.443385
\(342\) 908351. 690146.i 0.419941 0.319063i
\(343\) 68258.7 0.0313273
\(344\) 1.04942e6 1.81765e6i 0.478139 0.828161i
\(345\) −1.99912e6 1.76163e6i −0.904256 0.796832i
\(346\) 336358. + 582589.i 0.151047 + 0.261621i
\(347\) −1.15930e6 2.00796e6i −0.516858 0.895224i −0.999808 0.0195761i \(-0.993768\pi\)
0.482951 0.875648i \(-0.339565\pi\)
\(348\) 271311. 1.34718e6i 0.120093 0.596318i
\(349\) 1.56680e6 2.71377e6i 0.688572 1.19264i −0.283728 0.958905i \(-0.591571\pi\)
0.972300 0.233737i \(-0.0750955\pi\)
\(350\) −17867.2 −0.00779626
\(351\) −2.75547e6 200404.i −1.19379 0.0868236i
\(352\) −299539. −0.128854
\(353\) 1.33508e6 2.31243e6i 0.570259 0.987717i −0.426280 0.904591i \(-0.640176\pi\)
0.996539 0.0831261i \(-0.0264904\pi\)
\(354\) −902361. + 4.48062e6i −0.382712 + 1.90034i
\(355\) −2928.30 5071.96i −0.00123323 0.00213602i
\(356\) 1.41536e6 + 2.45148e6i 0.591891 + 1.02519i
\(357\) 28809.0 + 25386.6i 0.0119635 + 0.0105423i
\(358\) 108407. 187766.i 0.0447041 0.0774299i
\(359\) −2.05907e6 −0.843210 −0.421605 0.906780i \(-0.638533\pi\)
−0.421605 + 0.906780i \(0.638533\pi\)
\(360\) 494722. + 3.90144e6i 0.201190 + 1.58660i
\(361\) −2.25228e6 −0.909610
\(362\) 933182. 1.61632e6i 0.374278 0.648269i
\(363\) −1.88033e6 + 633290.i −0.748974 + 0.252253i
\(364\) 49229.6 + 85268.2i 0.0194748 + 0.0337314i
\(365\) 833109. + 1.44299e6i 0.327318 + 0.566931i
\(366\) 5.90894e6 1.99012e6i 2.30572 0.776562i
\(367\) 509190. 881943.i 0.197340 0.341803i −0.750325 0.661069i \(-0.770103\pi\)
0.947665 + 0.319266i \(0.103436\pi\)
\(368\) −4.57868e6 −1.76247
\(369\) 193184. + 1.52348e6i 0.0738595 + 0.582465i
\(370\) −6.90865e6 −2.62355
\(371\) −12454.6 + 21572.0i −0.00469781 + 0.00813685i
\(372\) 4.02764e6 + 3.54916e6i 1.50901 + 1.32975i
\(373\) −2.61768e6 4.53395e6i −0.974191 1.68735i −0.682579 0.730812i \(-0.739142\pi\)
−0.291612 0.956537i \(-0.594192\pi\)
\(374\) 1.10589e6 + 1.91546e6i 0.408820 + 0.708098i
\(375\) −584114. + 2.90039e6i −0.214496 + 1.06507i
\(376\) 541891. 938583.i 0.197671 0.342376i
\(377\) −967286. −0.350511
\(378\) −76139.4 5537.57i −0.0274082 0.00199338i
\(379\) 2.73883e6 0.979417 0.489708 0.871886i \(-0.337103\pi\)
0.489708 + 0.871886i \(0.337103\pi\)
\(380\) −743910. + 1.28849e6i −0.264278 + 0.457743i
\(381\) 287584. 1.42799e6i 0.101497 0.503978i
\(382\) −1.22255e6 2.11751e6i −0.428654 0.742451i
\(383\) 2.17454e6 + 3.76641e6i 0.757478 + 1.31199i 0.944133 + 0.329564i \(0.106902\pi\)
−0.186655 + 0.982425i \(0.559765\pi\)
\(384\) −3.43950e6 3.03090e6i −1.19033 1.04892i
\(385\) −8828.79 + 15291.9i −0.00303563 + 0.00525787i
\(386\) 2.25388e6 0.769950
\(387\) 1.18720e6 902011.i 0.402946 0.306150i
\(388\) 6.56035e6 2.21232
\(389\) −1.50378e6 + 2.60462e6i −0.503860 + 0.872712i 0.496130 + 0.868248i \(0.334754\pi\)
−0.999990 + 0.00446327i \(0.998579\pi\)
\(390\) 5.05860e6 1.70373e6i 1.68410 0.567202i
\(391\) 2.19098e6 + 3.79488e6i 0.724762 + 1.25533i
\(392\) −2.87385e6 4.97765e6i −0.944602 1.63610i
\(393\) −5.43261e6 + 1.82969e6i −1.77430 + 0.597581i
\(394\) −2.49613e6 + 4.32342e6i −0.810077 + 1.40309i
\(395\) 2.27787e6 0.734574
\(396\) −2.73690e6 1.14898e6i −0.877044 0.368192i
\(397\) 2.16602e6 0.689740 0.344870 0.938650i \(-0.387923\pi\)
0.344870 + 0.938650i \(0.387923\pi\)
\(398\) 20474.9 35463.6i 0.00647910 0.0112221i
\(399\) −11237.1 9902.17i −0.00353364 0.00311385i
\(400\) 561788. + 973046.i 0.175559 + 0.304077i
\(401\) −1.76996e6 3.06566e6i −0.549670 0.952057i −0.998297 0.0583377i \(-0.981420\pi\)
0.448626 0.893719i \(-0.351913\pi\)
\(402\) 717618. 3.56329e6i 0.221477 1.09973i
\(403\) 1.88930e6 3.27236e6i 0.579480 1.00369i
\(404\) −5.02774e6 −1.53257
\(405\) −748770. + 2.69152e6i −0.226835 + 0.815380i
\(406\) −26728.1 −0.00804735
\(407\) 1.35209e6 2.34188e6i 0.404593 0.700775i
\(408\) 1.27685e6 6.34014e6i 0.379744 1.88560i
\(409\) 783644. + 1.35731e6i 0.231638 + 0.401210i 0.958290 0.285796i \(-0.0922580\pi\)
−0.726652 + 0.687006i \(0.758925\pi\)
\(410\) −1.48351e6 2.56951e6i −0.435843 0.754902i
\(411\) 1.79664e6 + 1.58321e6i 0.524635 + 0.462309i
\(412\) −4.91016e6 + 8.50465e6i −1.42513 + 2.46839i
\(413\) 60007.5 0.0173113
\(414\) −8.03269e6 3.37221e6i −2.30335 0.966971i
\(415\) −489015. −0.139380
\(416\) 594413. 1.02955e6i 0.168405 0.291686i
\(417\) 3.61092e6 1.21615e6i 1.01690 0.342490i
\(418\) −431358. 747133.i −0.120753 0.209150i
\(419\) 1.18321e6 + 2.04937e6i 0.329250 + 0.570277i 0.982363 0.186983i \(-0.0598709\pi\)
−0.653114 + 0.757260i \(0.726538\pi\)
\(420\) 94355.6 31778.8i 0.0261002 0.00879050i
\(421\) 1.84288e6 3.19196e6i 0.506747 0.877712i −0.493222 0.869903i \(-0.664181\pi\)
0.999970 0.00780885i \(-0.00248566\pi\)
\(422\) 9.82311e6 2.68515
\(423\) 613036. 465772.i 0.166585 0.126568i
\(424\) 4.19546e6 1.13335
\(425\) 537650. 931238.i 0.144387 0.250085i
\(426\) −14366.3 12659.7i −0.00383550 0.00337985i
\(427\) −40930.3 70893.3i −0.0108636 0.0188164i
\(428\) 6.95086e6 + 1.20392e7i 1.83412 + 3.17680i
\(429\) −412489. + 2.04819e6i −0.108210 + 0.537313i
\(430\) −1.44035e6 + 2.49475e6i −0.375661 + 0.650664i
\(431\) −6.78152e6 −1.75847 −0.879233 0.476391i \(-0.841945\pi\)
−0.879233 + 0.476391i \(0.841945\pi\)
\(432\) 2.09243e6 + 4.32066e6i 0.539439 + 1.11389i
\(433\) −3.20434e6 −0.821332 −0.410666 0.911786i \(-0.634704\pi\)
−0.410666 + 0.911786i \(0.634704\pi\)
\(434\) 52205.2 90422.1i 0.0133042 0.0230436i
\(435\) −193111. + 958881.i −0.0489309 + 0.242964i
\(436\) −3.84220e6 6.65488e6i −0.967973 1.67658i
\(437\) −854601. 1.48021e6i −0.214072 0.370784i
\(438\) 4.08726e6 + 3.60171e6i 1.01800 + 0.897063i
\(439\) −698435. + 1.20972e6i −0.172967 + 0.299588i −0.939456 0.342670i \(-0.888669\pi\)
0.766489 + 0.642258i \(0.222002\pi\)
\(440\) 2.97406e6 0.732350
\(441\) −513645. 4.05066e6i −0.125767 0.991812i
\(442\) −8.77821e6 −2.13723
\(443\) 2.48597e6 4.30583e6i 0.601847 1.04243i −0.390694 0.920521i \(-0.627765\pi\)
0.992541 0.121910i \(-0.0389018\pi\)
\(444\) −1.44501e7 + 4.86676e6i −3.47867 + 1.17161i
\(445\) −1.00741e6 1.74488e6i −0.241160 0.417702i
\(446\) −5.19889e6 9.00475e6i −1.23758 2.14355i
\(447\) −145503. + 49005.2i −0.0344432 + 0.0116004i
\(448\) −24756.7 + 42879.9i −0.00582771 + 0.0100939i
\(449\) 4.85114e6 1.13561 0.567804 0.823164i \(-0.307793\pi\)
0.567804 + 0.823164i \(0.307793\pi\)
\(450\) 268933. + 2.12084e6i 0.0626056 + 0.493715i
\(451\) 1.16134e6 0.268856
\(452\) −1.55647e6 + 2.69589e6i −0.358340 + 0.620663i
\(453\) 2.57049e6 + 2.26512e6i 0.588532 + 0.518616i
\(454\) 3.52809e6 + 6.11083e6i 0.803340 + 1.39143i
\(455\) −35040.1 60691.3i −0.00793482 0.0137435i
\(456\) −498043. + 2.47301e6i −0.112164 + 0.556946i
\(457\) −2.14244e6 + 3.71081e6i −0.479864 + 0.831149i −0.999733 0.0230972i \(-0.992647\pi\)
0.519869 + 0.854246i \(0.325981\pi\)
\(458\) −2.91885e6 −0.650201
\(459\) 2.57976e6 3.80175e6i 0.571542 0.842271i
\(460\) 1.13620e7 2.50357
\(461\) −11973.0 + 20737.8i −0.00262392 + 0.00454476i −0.867334 0.497726i \(-0.834169\pi\)
0.864710 + 0.502271i \(0.167502\pi\)
\(462\) −11397.9 + 56595.7i −0.00248439 + 0.0123361i
\(463\) 1.76420e6 + 3.05569e6i 0.382469 + 0.662456i 0.991415 0.130756i \(-0.0417405\pi\)
−0.608945 + 0.793212i \(0.708407\pi\)
\(464\) 840397. + 1.45561e6i 0.181213 + 0.313870i
\(465\) −2.86675e6 2.52618e6i −0.614832 0.541792i
\(466\) 7.77341e6 1.34639e7i 1.65824 2.87215i
\(467\) −4.66263e6 −0.989324 −0.494662 0.869086i \(-0.664708\pi\)
−0.494662 + 0.869086i \(0.664708\pi\)
\(468\) 9.38036e6 7.12701e6i 1.97973 1.50415i
\(469\) −47722.0 −0.0100181
\(470\) −743753. + 1.28822e6i −0.155304 + 0.268995i
\(471\) 451776. 152157.i 0.0938362 0.0316038i
\(472\) −5.05353e6 8.75296e6i −1.04409 1.80842i
\(473\) −563778. 976492.i −0.115866 0.200686i
\(474\) 7.05800e6 2.37712e6i 1.44290 0.485965i
\(475\) −209713. + 363234.i −0.0426473 + 0.0738673i
\(476\) −163736. −0.0331227
\(477\) 2.74807e6 + 1.15367e6i 0.553008 + 0.232158i
\(478\) −5.17917e6 −1.03679
\(479\) −3.27492e6 + 5.67232e6i −0.652171 + 1.12959i 0.330424 + 0.943832i \(0.392808\pi\)
−0.982595 + 0.185760i \(0.940525\pi\)
\(480\) −901938. 794790.i −0.178679 0.157452i
\(481\) 5.36622e6 + 9.29457e6i 1.05756 + 1.83175i
\(482\) −2.12214e6 3.67565e6i −0.416060 0.720637i
\(483\) −22581.4 + 112127.i −0.00440436 + 0.0218696i
\(484\) 4.23024e6 7.32700e6i 0.820828 1.42172i
\(485\) −4.66945e6 −0.901387
\(486\) 488724. + 9.12111e6i 0.0938584 + 1.75169i
\(487\) −9.23457e6 −1.76439 −0.882194 0.470886i \(-0.843934\pi\)
−0.882194 + 0.470886i \(0.843934\pi\)
\(488\) −6.89388e6 + 1.19406e7i −1.31043 + 2.26973i
\(489\) 838236. 4.16221e6i 0.158524 0.787141i
\(490\) 3.94439e6 + 6.83189e6i 0.742147 + 1.28544i
\(491\) 2.62130e6 + 4.54023e6i 0.490697 + 0.849912i 0.999943 0.0107089i \(-0.00340882\pi\)
−0.509246 + 0.860621i \(0.670075\pi\)
\(492\) −4.91298e6 4.32933e6i −0.915023 0.806320i
\(493\) 804288. 1.39307e6i 0.149037 0.258140i
\(494\) 3.42399e6 0.631269
\(495\) 1.94804e6 + 817808.i 0.357343 + 0.150016i
\(496\) −6.56584e6 −1.19836
\(497\) −125.700 + 217.718i −2.28267e−5 + 3.95370e-5i
\(498\) −1.51522e6 + 510322.i −0.273780 + 0.0922086i
\(499\) −3.23974e6 5.61140e6i −0.582451 1.00883i −0.995188 0.0979844i \(-0.968760\pi\)
0.412737 0.910850i \(-0.364573\pi\)
\(500\) −6.30796e6 1.09257e7i −1.12840 1.95445i
\(501\) −2.93505e6 + 988519.i −0.522422 + 0.175951i
\(502\) −1.15067e6 + 1.99302e6i −0.203794 + 0.352982i
\(503\) 4.42908e6 0.780538 0.390269 0.920701i \(-0.372382\pi\)
0.390269 + 0.920701i \(0.372382\pi\)
\(504\) 134417. 102128.i 0.0235710 0.0179088i
\(505\) 3.57859e6 0.624429
\(506\) −3.29413e6 + 5.70560e6i −0.571959 + 0.990661i
\(507\) −1.87888e6 1.65567e6i −0.324622 0.286058i
\(508\) 3.10568e6 + 5.37920e6i 0.533946 + 0.924822i
\(509\) −2.14026e6 3.70704e6i −0.366162 0.634210i 0.622800 0.782381i \(-0.285995\pi\)
−0.988962 + 0.148170i \(0.952662\pi\)
\(510\) −1.75250e6 + 8.70193e6i −0.298354 + 1.48146i
\(511\) 35761.9 61941.4i 0.00605855 0.0104937i
\(512\) 1.18067e7 1.99046
\(513\) −1.00625e6 + 1.48289e6i −0.168816 + 0.248780i
\(514\) 1.40340e7 2.34301
\(515\) 3.49490e6 6.05335e6i 0.580653 1.00572i
\(516\) −1.25521e6 + 6.23266e6i −0.207535 + 1.03050i
\(517\) −291118. 504232.i −0.0479009 0.0829667i
\(518\) 148280. + 256828.i 0.0242805 + 0.0420550i
\(519\) −792859. 698669.i −0.129204 0.113855i
\(520\) −5.90181e6 + 1.02222e7i −0.957142 + 1.65782i
\(521\) 8.64335e6 1.39504 0.697522 0.716564i \(-0.254286\pi\)
0.697522 + 0.716564i \(0.254286\pi\)
\(522\) 402306. + 3.17263e6i 0.0646220 + 0.509616i
\(523\) −9.11201e6 −1.45667 −0.728333 0.685224i \(-0.759704\pi\)
−0.728333 + 0.685224i \(0.759704\pi\)
\(524\) 1.22220e7 2.11690e7i 1.94452 3.36801i
\(525\) 26599.5 8958.64i 0.00421187 0.00141855i
\(526\) −6.11113e6 1.05848e7i −0.963068 1.66808i
\(527\) 3.14187e6 + 5.44187e6i 0.492789 + 0.853536i
\(528\) 3.44057e6 1.15878e6i 0.537089 0.180890i
\(529\) −3.30813e6 + 5.72984e6i −0.513976 + 0.890233i
\(530\) −5.75832e6 −0.890443
\(531\) −903220. 7.12290e6i −0.139014 1.09628i
\(532\) 63865.9 0.00978341
\(533\) −2.30460e6 + 3.99168e6i −0.351380 + 0.608609i
\(534\) −4.94239e6 4.35524e6i −0.750038 0.660936i
\(535\) −4.94740e6 8.56915e6i −0.747296 1.29436i
\(536\) 4.01890e6 + 6.96094e6i 0.604221 + 1.04654i
\(537\) −67242.3 + 333888.i −0.0100625 + 0.0499649i
\(538\) 591650. 1.02477e6i 0.0881271 0.152641i
\(539\) −3.08782e6 −0.457804
\(540\) −5.19236e6 1.07217e7i −0.766268 1.58226i
\(541\) 5.76360e6 0.846643 0.423322 0.905979i \(-0.360864\pi\)
0.423322 + 0.905979i \(0.360864\pi\)
\(542\) 248783. 430905.i 0.0363767 0.0630062i
\(543\) −578833. + 2.87416e6i −0.0842468 + 0.418323i
\(544\) 988496. + 1.71213e6i 0.143211 + 0.248050i
\(545\) 2.73476e6 + 4.73674e6i 0.394391 + 0.683106i
\(546\) −171908. 151486.i −0.0246783 0.0217466i
\(547\) 2.80744e6 4.86263e6i 0.401183 0.694869i −0.592686 0.805434i \(-0.701933\pi\)
0.993869 + 0.110564i \(0.0352659\pi\)
\(548\) −1.02112e7 −1.45253
\(549\) −7.79898e6 + 5.92550e6i −1.10435 + 0.839063i
\(550\) 1.61671e6 0.227891
\(551\) −313717. + 543374.i −0.0440209 + 0.0762464i
\(552\) 1.82570e7 6.14892e6i 2.55025 0.858917i
\(553\) −48889.7 84679.4i −0.00679837 0.0117751i
\(554\) 2.34010e6 + 4.05317e6i 0.323937 + 0.561075i
\(555\) 1.02851e7 3.46401e6i 1.41735 0.477360i
\(556\) −8.12364e6 + 1.40705e7i −1.11446 + 1.93030i
\(557\) 2.18422e6 0.298303 0.149152 0.988814i \(-0.452346\pi\)
0.149152 + 0.988814i \(0.452346\pi\)
\(558\) −1.15189e7 4.83576e6i −1.56612 0.657475i
\(559\) 4.47510e6 0.605722
\(560\) −60887.1 + 105460.i −0.00820456 + 0.0142107i
\(561\) −2.60679e6 2.29711e6i −0.349702 0.308158i
\(562\) 1.02856e7 + 1.78152e7i 1.37369 + 2.37931i
\(563\) −339673. 588330.i −0.0451637 0.0782258i 0.842560 0.538603i \(-0.181048\pi\)
−0.887724 + 0.460377i \(0.847714\pi\)
\(564\) −648152. + 3.21836e6i −0.0857983 + 0.426027i
\(565\) 1.10785e6 1.91885e6i 0.146002 0.252883i
\(566\) −1.50446e7 −1.97396
\(567\) 116128. 29932.5i 0.0151697 0.00391007i
\(568\) 42343.2 0.00550697
\(569\) 3.28195e6 5.68451e6i 0.424964 0.736059i −0.571453 0.820635i \(-0.693620\pi\)
0.996417 + 0.0845759i \(0.0269536\pi\)
\(570\) 683571. 3.39423e6i 0.0881244 0.437577i
\(571\) 952119. + 1.64912e6i 0.122208 + 0.211671i 0.920638 0.390417i \(-0.127669\pi\)
−0.798430 + 0.602088i \(0.794336\pi\)
\(572\) −4.45455e6 7.71550e6i −0.569264 0.985994i
\(573\) 2.88177e6 + 2.53942e6i 0.366668 + 0.323109i
\(574\) −63680.8 + 110298.i −0.00806731 + 0.0139730i
\(575\) 3.20302e6 0.404008
\(576\) 5.46249e6 + 2.29321e6i 0.686016 + 0.287997i
\(577\) 1.13367e7 1.41758 0.708792 0.705417i \(-0.249240\pi\)
0.708792 + 0.705417i \(0.249240\pi\)
\(578\) 254182. 440257.i 0.0316465 0.0548133i
\(579\) −3.35542e6 + 1.13010e6i −0.415959 + 0.140094i
\(580\) −2.08544e6 3.61209e6i −0.257412 0.445850i
\(581\) 10495.7 + 18179.1i 0.00128994 + 0.00223425i
\(582\) −1.44684e7 + 4.87291e6i −1.77056 + 0.596322i
\(583\) 1.12696e6 1.95195e6i 0.137321 0.237846i
\(584\) −1.20467e7 −1.46163
\(585\) −6.67665e6 + 5.07278e6i −0.806620 + 0.612853i
\(586\) −7.64290e6 −0.919420
\(587\) −6.88666e6 + 1.19280e7i −0.824923 + 1.42881i 0.0770557 + 0.997027i \(0.475448\pi\)
−0.901978 + 0.431781i \(0.857885\pi\)
\(588\) 1.30628e7 + 1.15109e7i 1.55809 + 1.37299i
\(589\) −1.22550e6 2.12263e6i −0.145554 0.252108i
\(590\) 6.93603e6 + 1.20136e7i 0.820315 + 1.42083i
\(591\) 1.54830e6 7.68798e6i 0.182341 0.905406i
\(592\) 9.32456e6 1.61506e7i 1.09351 1.89402i
\(593\) 9.94674e6 1.16157 0.580783 0.814058i \(-0.302746\pi\)
0.580783 + 0.814058i \(0.302746\pi\)
\(594\) 6.88948e6 + 501067.i 0.801162 + 0.0582679i
\(595\) 116542. 0.0134955
\(596\) 327344. 566977.i 0.0377476 0.0653807i
\(597\) −12700.2 + 63062.0i −0.00145839 + 0.00724155i
\(598\) −1.30739e7 2.26447e7i −1.49504 2.58948i
\(599\) −2.77125e6 4.79995e6i −0.315579 0.546600i 0.663981 0.747749i \(-0.268866\pi\)
−0.979561 + 0.201150i \(0.935532\pi\)
\(600\) −3.54682e6 3.12547e6i −0.402218 0.354435i
\(601\) −6.63325e6 + 1.14891e7i −0.749101 + 1.29748i 0.199153 + 0.979968i \(0.436181\pi\)
−0.948254 + 0.317513i \(0.897152\pi\)
\(602\) 123656. 0.0139067
\(603\) 718301. + 5.66461e6i 0.0804476 + 0.634419i
\(604\) −1.46093e7 −1.62944
\(605\) −3.01096e6 + 5.21513e6i −0.334438 + 0.579264i
\(606\) 1.10883e7 3.73451e6i 1.22654 0.413098i
\(607\) −3.04326e6 5.27108e6i −0.335249 0.580668i 0.648284 0.761399i \(-0.275487\pi\)
−0.983533 + 0.180731i \(0.942154\pi\)
\(608\) −385568. 667824.i −0.0423002 0.0732660i
\(609\) 39791.0 13401.5i 0.00434752 0.00146424i
\(610\) 9.46194e6 1.63886e7i 1.02957 1.78327i
\(611\) 2.31081e6 0.250416
\(612\) 2.46451e6 + 1.94355e7i 0.265982 + 2.09757i
\(613\) −4.59806e6 −0.494223 −0.247112 0.968987i \(-0.579481\pi\)
−0.247112 + 0.968987i \(0.579481\pi\)
\(614\) 1.05960e7 1.83528e7i 1.13428 1.96464i
\(615\) 3.49690e6 + 3.08148e6i 0.372817 + 0.328527i
\(616\) −63832.1 110560.i −0.00677778 0.0117395i
\(617\) −8.01311e6 1.38791e7i −0.847399 1.46774i −0.883521 0.468391i \(-0.844834\pi\)
0.0361221 0.999347i \(-0.488499\pi\)
\(618\) 4.51189e6 2.24036e7i 0.475212 2.35964i
\(619\) −1.19878e6 + 2.07634e6i −0.125751 + 0.217807i −0.922026 0.387127i \(-0.873467\pi\)
0.796275 + 0.604934i \(0.206801\pi\)
\(620\) 1.62931e7 1.70226
\(621\) 1.36494e7 + 992709.i 1.42031 + 0.103298i
\(622\) 5.98795e6 0.620587
\(623\) −43243.9 + 74900.6i −0.00446380 + 0.00773153i
\(624\) −2.84470e6 + 1.41252e7i −0.292465 + 1.45222i
\(625\) 3.10456e6 + 5.37725e6i 0.317906 + 0.550630i
\(626\) 1.07785e7 + 1.86689e7i 1.09932 + 1.90407i
\(627\) 1.01679e6 + 895998.i 0.103291 + 0.0910203i
\(628\) −1.01638e6 + 1.76042e6i −0.102839 + 0.178122i
\(629\) −1.78478e7 −1.79870
\(630\) −184490. + 140171.i −0.0185191 + 0.0140704i
\(631\) 6.25228e6 0.625122 0.312561 0.949898i \(-0.398813\pi\)
0.312561 + 0.949898i \(0.398813\pi\)
\(632\) −8.23449e6 + 1.42625e7i −0.820057 + 1.42038i
\(633\) −1.46240e7 + 4.92533e6i −1.45063 + 0.488569i
\(634\) 1.58821e7 + 2.75086e7i 1.56922 + 2.71797i
\(635\) −2.21053e6 3.82875e6i −0.217551 0.376810i
\(636\) −1.20441e7 + 4.05642e6i −1.18068 + 0.397649i
\(637\) 6.12754e6 1.06132e7i 0.598325 1.03633i
\(638\) 2.41849e6 0.235230
\(639\) 27735.2 + 11643.5i 0.00268707 + 0.00112806i
\(640\) −1.39139e7 −1.34276
\(641\) 9.48142e6 1.64223e7i 0.911440 1.57866i 0.0994090 0.995047i \(-0.468305\pi\)
0.812031 0.583614i \(-0.198362\pi\)
\(642\) −2.42721e7 2.13887e7i −2.32418 2.04808i
\(643\) 1.64962e6 + 2.85722e6i 0.157346 + 0.272532i 0.933911 0.357506i \(-0.116373\pi\)
−0.776565 + 0.630038i \(0.783039\pi\)
\(644\) −243861. 422380.i −0.0231701 0.0401318i
\(645\) 893417. 4.43621e6i 0.0845580 0.419868i
\(646\) −2.84701e6 + 4.93116e6i −0.268415 + 0.464909i
\(647\) −1.56481e7 −1.46961 −0.734805 0.678278i \(-0.762726\pi\)
−0.734805 + 0.678278i \(0.762726\pi\)
\(648\) −1.41458e7 1.44182e7i −1.32339 1.34888i
\(649\) −5.42978e6 −0.506023
\(650\) −3.20825e6 + 5.55685e6i −0.297841 + 0.515876i
\(651\) −32381.8 + 160790.i −0.00299467 + 0.0148699i
\(652\) 9.05228e6 + 1.56790e7i 0.833948 + 1.44444i
\(653\) −7.78514e6 1.34843e7i −0.714469 1.23750i −0.963164 0.268915i \(-0.913335\pi\)
0.248695 0.968582i \(-0.419998\pi\)
\(654\) 1.34168e7 + 1.18229e7i 1.22661 + 1.08089i
\(655\) −8.69921e6 + 1.50675e7i −0.792276 + 1.37226i
\(656\) 8.00912e6 0.726650
\(657\) −7.89074e6 3.31262e6i −0.713189 0.299404i
\(658\) 63852.4 0.00574927
\(659\) −6.40513e6 + 1.10940e7i −0.574532 + 0.995119i 0.421560 + 0.906800i \(0.361483\pi\)
−0.996092 + 0.0883184i \(0.971851\pi\)
\(660\) −8.53777e6 + 2.87550e6i −0.762930 + 0.256953i
\(661\) −230248. 398801.i −0.0204971 0.0355020i 0.855595 0.517646i \(-0.173192\pi\)
−0.876092 + 0.482144i \(0.839858\pi\)
\(662\) 1.29413e7 + 2.24149e7i 1.14771 + 1.98789i
\(663\) 1.30684e7 4.40141e6i 1.15462 0.388873i
\(664\) 1.76779e6 3.06190e6i 0.155600 0.269507i
\(665\) −45457.8 −0.00398616
\(666\) 2.82537e7 2.14665e7i 2.46825 1.87533i
\(667\) 4.79150e6 0.417020
\(668\) 6.60310e6 1.14369e7i 0.572541 0.991670i
\(669\) 1.22548e7 + 1.07989e7i 1.05862 + 0.932857i
\(670\) −5.51600e6 9.55399e6i −0.474719 0.822238i
\(671\) 3.70358e6 + 6.41479e6i 0.317552 + 0.550017i
\(672\) −10188.0 + 50587.9i −0.000870293 + 0.00432139i
\(673\) 4.03608e6 6.99069e6i 0.343496 0.594952i −0.641583 0.767053i \(-0.721722\pi\)
0.985079 + 0.172101i \(0.0550555\pi\)
\(674\) 8.23500e6 0.698255
\(675\) −1.46376e6 3.02252e6i −0.123655 0.255334i
\(676\) 1.06786e7 0.898766
\(677\) −1.82149e6 + 3.15491e6i −0.152741 + 0.264554i −0.932234 0.361856i \(-0.882143\pi\)
0.779493 + 0.626410i \(0.215477\pi\)
\(678\) 1.43023e6 7.10171e6i 0.119490 0.593319i
\(679\) 100220. + 173586.i 0.00834219 + 0.0144491i
\(680\) −9.81458e6 1.69993e7i −0.813953 1.40981i
\(681\) −8.31636e6 7.32839e6i −0.687172 0.605538i
\(682\) −4.72380e6 + 8.18185e6i −0.388893 + 0.673582i
\(683\) 9.57475e6 0.785373 0.392686 0.919672i \(-0.371546\pi\)
0.392686 + 0.919672i \(0.371546\pi\)
\(684\) −961297. 7.58090e6i −0.0785628 0.619556i
\(685\) 7.26801e6 0.591819
\(686\) 338674. 586601.i 0.0274772 0.0475919i
\(687\) 4.34538e6 1.46351e6i 0.351266 0.118306i
\(688\) −3.88805e6 6.73431e6i −0.313156 0.542403i
\(689\) 4.47272e6 + 7.74698e6i 0.358941 + 0.621705i
\(690\) −2.50580e7 + 8.43948e6i −2.00366 + 0.674828i
\(691\) −3.01871e6 + 5.22857e6i −0.240506 + 0.416569i −0.960859 0.277039i \(-0.910647\pi\)
0.720352 + 0.693608i \(0.243980\pi\)
\(692\) 4.50620e6 0.357722
\(693\) −11408.8 89970.8i −0.000902412 0.00711653i
\(694\) −2.30080e7 −1.81334
\(695\) 5.78215e6 1.00150e7i 0.454075 0.786481i
\(696\) −5.30580e6 4.67549e6i −0.415172 0.365851i
\(697\) −3.83250e6 6.63809e6i −0.298814 0.517560i
\(698\) −1.55478e7 2.69295e7i −1.20789 2.09213i
\(699\) −4.82168e6 + 2.39418e7i −0.373255 + 1.85338i
\(700\) −59841.8 + 103649.i −0.00461594 + 0.00799504i
\(701\) 1.37603e7 1.05763 0.528813 0.848739i \(-0.322637\pi\)
0.528813 + 0.848739i \(0.322637\pi\)
\(702\) −1.53939e7 + 2.26857e7i −1.17898 + 1.73743i
\(703\) 6.96164e6 0.531279
\(704\) 2.24011e6 3.87999e6i 0.170349 0.295052i
\(705\) 461334. 2.29073e6i 0.0349577 0.173581i
\(706\) −1.32484e7 2.29469e7i −1.00035 1.73266i
\(707\) −76806.9 133033.i −0.00577899 0.0100095i
\(708\) 2.29702e7 + 2.02414e7i 1.72220 + 1.51760i
\(709\) 809892. 1.40277e6i 0.0605078 0.104803i −0.834185 0.551485i \(-0.814061\pi\)
0.894693 + 0.446683i \(0.147395\pi\)
\(710\) −58116.6 −0.00432667
\(711\) −9.31559e6 + 7.07779e6i −0.691093 + 0.525078i
\(712\) 1.45671e7 1.07690
\(713\) −9.35873e6 + 1.62098e7i −0.689435 + 1.19414i
\(714\) 361107. 121620.i 0.0265088 0.00892811i
\(715\) 3.17061e6 + 5.49165e6i 0.231941 + 0.401734i
\(716\) −726163. 1.25775e6i −0.0529360 0.0916879i
\(717\) 7.71040e6 2.59685e6i 0.560118 0.188646i
\(718\) −1.02164e7 + 1.76953e7i −0.739580 + 1.28099i
\(719\) 1.42931e7 1.03111 0.515555 0.856856i \(-0.327586\pi\)
0.515555 + 0.856856i \(0.327586\pi\)
\(720\) 1.34345e7 + 5.63995e6i 0.965809 + 0.405457i
\(721\) −300043. −0.0214954
\(722\) −1.11750e7 + 1.93557e7i −0.797819 + 1.38186i
\(723\) 5.00227e6 + 4.40802e6i 0.355895 + 0.313615i
\(724\) −6.25093e6 1.08269e7i −0.443199 0.767643i
\(725\) −587900. 1.01827e6i −0.0415392 0.0719481i
\(726\) −3.88712e6 + 1.93013e7i −0.273708 + 1.35908i
\(727\) 1.37208e7 2.37652e7i 0.962818 1.66765i 0.247450 0.968901i \(-0.420407\pi\)
0.715367 0.698749i \(-0.246259\pi\)
\(728\) 506680. 0.0354328
\(729\) −5.30092e6 1.33338e7i −0.369430 0.929258i
\(730\) 1.65343e7 1.14836
\(731\) −3.72100e6 + 6.44496e6i −0.257553 + 0.446094i
\(732\) 8.24572e6 4.09437e7i 0.568788 2.82429i
\(733\) 2.55310e6 + 4.42209e6i 0.175512 + 0.303996i 0.940338 0.340241i \(-0.110509\pi\)
−0.764826 + 0.644237i \(0.777175\pi\)
\(734\) −5.05283e6 8.75175e6i −0.346174 0.599591i
\(735\) −9.29767e6 8.19313e6i −0.634828 0.559412i
\(736\) −2.94445e6 + 5.09994e6i −0.200359 + 0.347033i
\(737\) 4.31812e6 0.292837
\(738\) 1.40510e7 + 5.89874e6i 0.949653 + 0.398674i
\(739\) −1.34356e7 −0.904997 −0.452498 0.891765i \(-0.649467\pi\)
−0.452498 + 0.891765i \(0.649467\pi\)
\(740\) −2.31388e7 + 4.00776e7i −1.55332 + 2.69044i
\(741\) −5.09740e6 + 1.71679e6i −0.341038 + 0.114861i
\(742\) 123590. + 214065.i 0.00824091 + 0.0142737i
\(743\) 343246. + 594519.i 0.0228104 + 0.0395088i 0.877205 0.480116i \(-0.159405\pi\)
−0.854395 + 0.519624i \(0.826072\pi\)
\(744\) 2.61806e7 8.81758e6i 1.73399 0.584005i
\(745\) −232994. + 403557.i −0.0153799 + 0.0266387i
\(746\) −5.19518e7 −3.41786
\(747\) 1.99988e6 1.51947e6i 0.131130 0.0996299i
\(748\) 1.48156e7 0.968203
\(749\) −212371. + 367838.i −0.0138322 + 0.0239581i
\(750\) 2.20272e7 + 1.94104e7i 1.42990 + 1.26003i
\(751\) −5.46542e6 9.46639e6i −0.353610 0.612470i 0.633269 0.773931i \(-0.281712\pi\)
−0.986879 + 0.161462i \(0.948379\pi\)
\(752\) −2.00768e6 3.47740e6i −0.129464 0.224238i
\(753\) 713738. 3.54403e6i 0.0458724 0.227777i
\(754\) −4.79932e6 + 8.31266e6i −0.307434 + 0.532491i
\(755\) 1.03985e7 0.663900
\(756\) −287134. + 423144.i −0.0182718 + 0.0269268i
\(757\) −2.31128e7 −1.46593 −0.732966 0.680265i \(-0.761865\pi\)
−0.732966 + 0.680265i \(0.761865\pi\)
\(758\) 1.35891e7 2.35370e7i 0.859047 1.48791i
\(759\) 2.04328e6 1.01458e7i 0.128743 0.639266i
\(760\) 3.82823e6 + 6.63068e6i 0.240416 + 0.416413i
\(761\) 5.94528e6 + 1.02975e7i 0.372144 + 0.644572i 0.989895 0.141801i \(-0.0452894\pi\)
−0.617751 + 0.786374i \(0.711956\pi\)
\(762\) −1.08449e7 9.55658e6i −0.676611 0.596232i
\(763\) 117392. 203328.i 0.00730005 0.0126441i
\(764\) −1.63785e7 −1.01517
\(765\) −1.75417e6 1.38336e7i −0.108372 0.854634i
\(766\) 4.31570e7 2.65754
\(767\) 1.07750e7 1.86628e7i 0.661345 1.14548i
\(768\) −3.15872e7 + 1.06385e7i −1.93245 + 0.650844i
\(769\) −1.32545e6 2.29575e6i −0.0808253 0.139994i 0.822779 0.568361i \(-0.192422\pi\)
−0.903605 + 0.428367i \(0.859089\pi\)
\(770\) 87610.4 + 151746.i 0.00532511 + 0.00922337i
\(771\) −2.08929e7 + 7.03668e6i −1.26579 + 0.426316i
\(772\) 7.54883e6 1.30750e7i 0.455865 0.789581i
\(773\) −2.12893e7 −1.28148 −0.640742 0.767757i \(-0.721373\pi\)
−0.640742 + 0.767757i \(0.721373\pi\)
\(774\) −1.86125e6 1.46780e7i −0.111674 0.880673i
\(775\) 4.59314e6 0.274698
\(776\) 1.68801e7 2.92371e7i 1.00628 1.74293i
\(777\) −349523. 308000.i −0.0207694 0.0183020i
\(778\) 1.49224e7 + 2.58464e7i 0.883873 + 1.53091i
\(779\) 1.49489e6 + 2.58922e6i 0.0882601 + 0.152871i
\(780\) 7.05910e6 3.50516e7i 0.415444 2.06287i
\(781\) 11373.9 19700.3i 0.000667242 0.00115570i
\(782\) 4.34833e7 2.54276
\(783\) −2.18969e6 4.52148e6i −0.127637 0.263558i
\(784\) −2.12949e7 −1.23733
\(785\) 723426. 1.25301e6i 0.0419006 0.0725739i
\(786\) −1.12306e7 + 5.57650e7i −0.648406 + 3.21963i
\(787\) 1.14439e7 + 1.98214e7i 0.658623 + 1.14077i 0.980972 + 0.194148i \(0.0621942\pi\)
−0.322349 + 0.946621i \(0.604472\pi\)
\(788\) 1.67203e7 + 2.89605e7i 0.959246 + 1.66146i
\(789\) 1.44051e7 + 1.26938e7i 0.823802 + 0.725936i
\(790\) 1.13019e7 1.95755e7i 0.644296 1.11595i
\(791\) −95110.7 −0.00540491
\(792\) −1.21628e7 + 9.24102e6i −0.689000 + 0.523488i
\(793\) −2.93979e7 −1.66010
\(794\) 1.07470e7 1.86143e7i 0.604972 1.04784i
\(795\) 8.57260e6 2.88723e6i 0.481055 0.162018i
\(796\) −137152. 237553.i −0.00767217 0.0132886i
\(797\) 1.28424e7 + 2.22437e7i 0.716146 + 1.24040i 0.962516 + 0.271225i \(0.0874287\pi\)
−0.246370 + 0.969176i \(0.579238\pi\)
\(798\) −140852. + 47438.5i −0.00782987 + 0.00263708i
\(799\) −1.92141e6 + 3.32799e6i −0.106477 + 0.184423i
\(800\) 1.44510e6 0.0798310
\(801\) 9.54162e6 + 4.00567e6i 0.525461 + 0.220594i
\(802\) −3.51275e7 −1.92847
\(803\) −3.23592e6 + 5.60478e6i −0.177096 + 0.306739i
\(804\) −1.82675e7 1.60974e7i −0.996641 0.878242i
\(805\) 173573. + 300637.i 0.00944043 + 0.0163513i
\(806\) −1.87480e7 3.24725e7i −1.01652 1.76067i
\(807\) −366988. + 1.82226e6i −0.0198366 + 0.0984978i
\(808\) −1.29366e7 + 2.24068e7i −0.697094 + 1.20740i
\(809\) −5.88061e6 −0.315901 −0.157951 0.987447i \(-0.550489\pi\)
−0.157951 + 0.987447i \(0.550489\pi\)
\(810\) 1.94153e7 + 1.97891e7i 1.03975 + 1.05978i
\(811\) −2.04938e7 −1.09414 −0.547068 0.837088i \(-0.684256\pi\)
−0.547068 + 0.837088i \(0.684256\pi\)
\(812\) −89519.3 + 155052.i −0.00476460 + 0.00825254i
\(813\) −154315. + 766243.i −0.00818808 + 0.0406575i
\(814\) −1.34171e7 2.32391e7i −0.709737 1.22930i
\(815\) −6.44313e6 1.11598e7i −0.339784 0.588523i
\(816\) −1.79775e7 1.58418e7i −0.945157 0.832875i
\(817\) 1.45139e6 2.51389e6i 0.0760730 0.131762i
\(818\) 1.55526e7 0.812681
\(819\) 331880. + 139327.i 0.0172891 + 0.00725814i
\(820\) −1.98746e7 −1.03220
\(821\) 1.81711e6 3.14732e6i 0.0940855 0.162961i −0.815141 0.579263i \(-0.803341\pi\)
0.909227 + 0.416302i \(0.136674\pi\)
\(822\) 2.25200e7 7.58470e6i 1.16249 0.391524i
\(823\) 7.90337e6 + 1.36890e7i 0.406736 + 0.704488i 0.994522 0.104529i \(-0.0333335\pi\)
−0.587786 + 0.809017i \(0.700000\pi\)
\(824\) 2.52681e7 + 4.37657e7i 1.29645 + 2.24551i
\(825\) −2.40685e6 + 810623.i −0.123116 + 0.0414652i
\(826\) 297735. 515692.i 0.0151838 0.0262991i
\(827\) −1.98096e6 −0.100719 −0.0503597 0.998731i \(-0.516037\pi\)
−0.0503597 + 0.998731i \(0.516037\pi\)
\(828\) −4.64660e7 + 3.53039e7i −2.35537 + 1.78956i
\(829\) 2.56811e7 1.29786 0.648929 0.760849i \(-0.275217\pi\)
0.648929 + 0.760849i \(0.275217\pi\)
\(830\) −2.42631e6 + 4.20249e6i −0.122251 + 0.211744i
\(831\) −5.51605e6 4.86076e6i −0.277093 0.244175i
\(832\) 8.89067e6 + 1.53991e7i 0.445273 + 0.771235i
\(833\) 1.01900e7 + 1.76495e7i 0.508815 + 0.881294i
\(834\) 7.46472e6 3.70656e7i 0.371619 1.84526i
\(835\) −4.69988e6 + 8.14043e6i −0.233276 + 0.404046i
\(836\) −5.77891e6 −0.285977
\(837\) 1.95732e7 + 1.42355e6i 0.965715 + 0.0702358i
\(838\) 2.34825e7 1.15514
\(839\) −2.27342e6 + 3.93767e6i −0.111500 + 0.193123i −0.916375 0.400321i \(-0.868899\pi\)
0.804875 + 0.593444i \(0.202232\pi\)
\(840\) 101154. 502277.i 0.00494637 0.0245609i
\(841\) 9.37612e6 + 1.62399e7i 0.457123 + 0.791760i
\(842\) −1.82874e7 3.16747e7i −0.888937 1.53968i
\(843\) −2.42451e7 2.13649e7i −1.17505 1.03545i
\(844\) 3.29001e7 5.69847e7i 1.58980 2.75361i
\(845\) −7.60068e6 −0.366193
\(846\) −961093. 7.57929e6i −0.0461678 0.364085i
\(847\) 258496. 0.0123807
\(848\) 7.77197e6 1.34614e7i 0.371143 0.642839i
\(849\) 2.23974e7 7.54338e6i 1.06642 0.359167i
\(850\) −5.33525e6 9.24092e6i −0.253284 0.438700i
\(851\) −2.65818e7 4.60411e7i −1.25823 2.17932i
\(852\) −121556. + 40939.9i −0.00573692 + 0.00193218i
\(853\) −708511. + 1.22718e6i −0.0333407 + 0.0577477i −0.882214 0.470848i \(-0.843948\pi\)
0.848874 + 0.528596i \(0.177281\pi\)
\(854\) −812324. −0.0381140
\(855\) 684221. + 5.39585e6i 0.0320097 + 0.252432i
\(856\) 7.15394e7 3.33704
\(857\) 4.07200e6 7.05290e6i 0.189389 0.328032i −0.755658 0.654967i \(-0.772683\pi\)
0.945047 + 0.326935i \(0.106016\pi\)
\(858\) 1.55551e7 + 1.37072e7i 0.721365 + 0.635669i
\(859\) −5.33500e6 9.24050e6i −0.246690 0.427280i 0.715915 0.698187i \(-0.246010\pi\)
−0.962605 + 0.270907i \(0.912676\pi\)
\(860\) 9.64819e6 + 1.67111e7i 0.444836 + 0.770478i
\(861\) 39499.9 196134.i 0.00181588 0.00901667i
\(862\) −3.36474e7 + 5.82791e7i −1.54235 + 2.67143i
\(863\) −1.21144e7 −0.553701 −0.276851 0.960913i \(-0.589291\pi\)
−0.276851 + 0.960913i \(0.589291\pi\)
\(864\) 6.15814e6 + 447878.i 0.280650 + 0.0204115i
\(865\) −3.20737e6 −0.145750
\(866\) −1.58987e7 + 2.75374e7i −0.720391 + 1.24775i
\(867\) −157664. + 782872.i −0.00712335 + 0.0353706i
\(868\) −349698. 605694.i −0.0157541 0.0272869i
\(869\) 4.42379e6 + 7.66222e6i 0.198721 + 0.344196i
\(870\) 7.28229e6 + 6.41717e6i 0.326189 + 0.287439i
\(871\) −8.56899e6 + 1.48419e7i −0.382723 + 0.662895i
\(872\) −3.95445e7 −1.76115
\(873\) 1.90962e7 1.45089e7i 0.848031 0.644317i
\(874\) −1.69609e7 −0.751051
\(875\) 192729. 333816.i 0.00850995 0.0147397i
\(876\) 3.45831e7 1.16475e7i 1.52266 0.512829i
\(877\) −1.65673e7 2.86954e7i −0.727366 1.25983i −0.957993 0.286792i \(-0.907411\pi\)
0.230627 0.973042i \(-0.425922\pi\)
\(878\) 6.93075e6 + 1.20044e7i 0.303420 + 0.525538i
\(879\) 1.13782e7 3.83216e6i 0.496710 0.167291i
\(880\) 5.50937e6 9.54251e6i 0.239826 0.415390i
\(881\) 49573.7 0.00215185 0.00107592 0.999999i \(-0.499658\pi\)
0.00107592 + 0.999999i \(0.499658\pi\)
\(882\) −3.73591e7 1.56837e7i −1.61706 0.678857i
\(883\) 4.21109e7 1.81758 0.908788 0.417259i \(-0.137009\pi\)
0.908788 + 0.417259i \(0.137009\pi\)
\(884\) −2.94005e7 + 5.09232e7i −1.26539 + 2.19172i
\(885\) −1.63495e7 1.44072e7i −0.701692 0.618333i
\(886\) −2.46689e7 4.27278e7i −1.05576 1.82863i
\(887\) −550680. 953806.i −0.0235012 0.0407053i 0.854036 0.520215i \(-0.174148\pi\)
−0.877537 + 0.479509i \(0.840815\pi\)
\(888\) −1.54913e7 + 7.69212e7i −0.659258 + 3.27351i
\(889\) −94888.8 + 164352.i −0.00402680 + 0.00697463i
\(890\) −1.99936e7 −0.846088
\(891\) −1.05078e7 + 2.70844e6i −0.443423 + 0.114294i
\(892\) −6.96498e7 −2.93094
\(893\) 749458. 1.29810e6i 0.0314498 0.0544727i
\(894\) −300793. + 1.49357e6i −0.0125870 + 0.0625003i
\(895\) 516860. + 895228.i 0.0215683 + 0.0373574i
\(896\) 298633. + 517248.i 0.0124271 + 0.0215243i
\(897\) 3.08176e7 + 2.71566e7i 1.27885 + 1.12692i
\(898\) 2.40696e7 4.16898e7i 0.996042 1.72520i
\(899\) 6.87102e6 0.283545
\(900\) 1.32039e7 + 5.54313e6i 0.543370 + 0.228112i
\(901\) −1.48761e7 −0.610487
\(902\) 5.76216e6 9.98036e6i 0.235814 0.408441i
\(903\) −184091. + 62001.4i −0.00751299 + 0.00253036i
\(904\) 8.00974e6 + 1.38733e7i 0.325985 + 0.564622i
\(905\) 4.44922e6 + 7.70627e6i 0.180577 + 0.312769i
\(906\) 3.22198e7 1.08516e7i 1.30408 0.439210i
\(907\) 3.72157e6 6.44595e6i 0.150213 0.260177i −0.781093 0.624415i \(-0.785337\pi\)
0.931306 + 0.364238i \(0.118671\pi\)
\(908\) 4.72659e7 1.90254
\(909\) −1.46350e7 + 1.11194e7i −0.587467 + 0.446345i
\(910\) −695425. −0.0278386
\(911\) 1.61672e7 2.80024e7i 0.645414 1.11789i −0.338792 0.940861i \(-0.610018\pi\)
0.984206 0.177028i \(-0.0566483\pi\)
\(912\) 7.01222e6 + 6.17918e6i 0.279170 + 0.246005i
\(913\) −949703. 1.64493e6i −0.0377060 0.0653087i
\(914\) 2.12600e7 + 3.68234e7i 0.841778 + 1.45800i
\(915\) −5.86905e6 + 2.91424e7i −0.231747 + 1.15073i
\(916\) −9.77597e6 + 1.69325e7i −0.384965 + 0.666779i
\(917\) 746841. 0.0293295
\(918\) −1.98716e7 4.10329e7i −0.778263 1.60703i
\(919\) 3.18905e7 1.24558 0.622792 0.782388i \(-0.285998\pi\)
0.622792 + 0.782388i \(0.285998\pi\)
\(920\) 2.92348e7 5.06362e7i 1.13876 1.97239i
\(921\) −6.57249e6 + 3.26353e7i −0.255318 + 1.26777i
\(922\) 118811. + 205787.i 0.00460288 + 0.00797243i
\(923\) 45141.5 + 78187.3i 0.00174410 + 0.00302087i
\(924\) 290142. + 255674.i 0.0111797 + 0.00985159i
\(925\) −6.52299e6 + 1.12982e7i −0.250664 + 0.434163i
\(926\) 3.50133e7 1.34186
\(927\) 4.51619e6 + 3.56152e7i 0.172613 + 1.36124i
\(928\) 2.16177e6 0.0824022
\(929\) 7.20450e6 1.24786e7i 0.273883 0.474379i −0.695970 0.718071i \(-0.745025\pi\)
0.969853 + 0.243692i \(0.0783586\pi\)
\(930\) −3.59332e7 + 1.21022e7i −1.36235 + 0.458837i
\(931\) −3.97465e6 6.88429e6i −0.150288 0.260307i
\(932\) −5.20703e7 9.01884e7i −1.96359 3.40103i
\(933\) −8.91446e6 + 3.00237e6i −0.335267 + 0.112917i
\(934\) −2.31342e7 + 4.00697e7i −0.867737 + 1.50296i
\(935\) −1.05453e7 −0.394485
\(936\) −7.62644e6 6.01430e7i −0.284533 2.24386i
\(937\) 2.33199e7 0.867718 0.433859 0.900981i \(-0.357152\pi\)
0.433859 + 0.900981i \(0.357152\pi\)
\(938\) −236779. + 410113.i −0.00878690 + 0.0152194i
\(939\) −2.54070e7 2.23887e7i −0.940349 0.828638i
\(940\) 4.98204e6 + 8.62915e6i 0.183902 + 0.318528i
\(941\) 2.35788e7 + 4.08396e7i 0.868054 + 1.50351i 0.863982 + 0.503522i \(0.167963\pi\)
0.00407185 + 0.999992i \(0.498704\pi\)
\(942\) 933937. 4.63742e6i 0.0342918 0.170274i
\(943\) 1.14159e7 1.97730e7i 0.418054 0.724091i
\(944\) −3.74461e7 −1.36765
\(945\) 204373. 301181.i 0.00744466 0.0109710i
\(946\) −1.11890e7 −0.406504
\(947\) −1.21868e7 + 2.11081e7i −0.441585 + 0.764847i −0.997807 0.0661864i \(-0.978917\pi\)
0.556223 + 0.831033i \(0.312250\pi\)
\(948\) 9.84920e6 4.89057e7i 0.355943 1.76741i
\(949\) −1.28429e7 2.22445e7i −0.462910 0.801784i
\(950\) 2.08104e6 + 3.60447e6i 0.0748120 + 0.129578i
\(951\) −3.74370e7 3.29896e7i −1.34230 1.18284i
\(952\) −421299. + 729711.i −0.0150660 + 0.0260951i
\(953\) −4.33987e7 −1.54790 −0.773952 0.633244i \(-0.781723\pi\)
−0.773952 + 0.633244i \(0.781723\pi\)
\(954\) 2.35493e7 1.78923e7i 0.837735 0.636494i
\(955\) 1.16577e7 0.413623
\(956\) −1.73464e7 + 3.00448e7i −0.613853 + 1.06322i
\(957\) −3.60049e6 + 1.21264e6i −0.127081 + 0.0428007i
\(958\) 3.24978e7 + 5.62879e7i 1.14404 + 1.98153i
\(959\) −155993. 270187.i −0.00547719 0.00948677i
\(960\) 1.70402e7 5.73911e6i 0.596757 0.200986i
\(961\) 894119. 1.54866e6i 0.0312311 0.0540938i
\(962\) 1.06501e8 3.71035
\(963\) 4.68590e7 + 1.96719e7i 1.62827 + 0.683567i
\(964\) −2.84303e7 −0.985348
\(965\) −5.37302e6 + 9.30634e6i −0.185738 + 0.321707i
\(966\) 851554. + 750392.i 0.0293609 + 0.0258729i
\(967\) −137300. 237810.i −0.00472176 0.00817832i 0.863655 0.504084i \(-0.168170\pi\)
−0.868377 + 0.495905i \(0.834836\pi\)
\(968\) −2.17692e7 3.77054e7i −0.746714 1.29335i
\(969\) 1.76594e6 8.76868e6i 0.0604180 0.300002i
\(970\) −2.31681e7 + 4.01283e7i −0.790607 + 1.36937i
\(971\) 3.36920e7 1.14678 0.573388 0.819284i \(-0.305629\pi\)
0.573388 + 0.819284i \(0.305629\pi\)
\(972\) 5.45492e7 + 2.77138e7i 1.85192 + 0.940872i
\(973\) −496407. −0.0168096
\(974\) −4.58185e7 + 7.93600e7i −1.54755 + 2.68043i
\(975\) 1.99001e6 9.88128e6i 0.0670414 0.332891i
\(976\) 2.55415e7 + 4.42391e7i 0.858264 + 1.48656i
\(977\) −6.93084e6 1.20046e7i −0.232300 0.402356i 0.726184 0.687500i \(-0.241292\pi\)
−0.958485 + 0.285144i \(0.907959\pi\)
\(978\) −3.16102e7 2.78550e7i −1.05677 0.931228i
\(979\) 3.91293e6 6.77739e6i 0.130480 0.225999i
\(980\) 5.28432e7 1.75762
\(981\) −2.59021e7 1.08740e7i −0.859334 0.360757i
\(982\) 5.20238e7 1.72156
\(983\) 4.34952e6 7.53359e6i 0.143568 0.248667i −0.785270 0.619154i \(-0.787476\pi\)
0.928838 + 0.370487i \(0.120809\pi\)
\(984\) −3.19356e7 + 1.07558e7i −1.05145 + 0.354125i
\(985\) −1.19010e7 2.06132e7i −0.390835 0.676947i
\(986\) −7.98116e6 1.38238e7i −0.261441 0.452829i
\(987\) −95059.2 + 32015.7i −0.00310600 + 0.00104609i
\(988\) 1.14678e7 1.98628e7i 0.373756 0.647365i
\(989\) −2.21676e7 −0.720656
\(990\) 1.66935e7 1.26834e7i 0.541328 0.411290i
\(991\) −4.44501e7 −1.43777 −0.718884 0.695130i \(-0.755347\pi\)
−0.718884 + 0.695130i \(0.755347\pi\)
\(992\) −4.22235e6 + 7.31333e6i −0.136231 + 0.235959i
\(993\) −3.05050e7 2.68811e7i −0.981743 0.865114i
\(994\) 1247.35 + 2160.48i 4.00426e−5 + 6.93559e-5i
\(995\) 97620.2 + 169083.i 0.00312595 + 0.00541430i
\(996\) −2.11444e6 + 1.04991e7i −0.0675377 + 0.335355i
\(997\) 8.21072e6 1.42214e7i 0.261603 0.453110i −0.705065 0.709143i \(-0.749082\pi\)
0.966668 + 0.256033i \(0.0824154\pi\)
\(998\) −6.42977e7 −2.04347
\(999\) −3.12988e7 + 4.61244e7i −0.992232 + 1.46223i
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 9.6.c.a.7.4 yes 8
3.2 odd 2 27.6.c.a.19.1 8
4.3 odd 2 144.6.i.c.97.3 8
9.2 odd 6 81.6.a.d.1.4 4
9.4 even 3 inner 9.6.c.a.4.4 8
9.5 odd 6 27.6.c.a.10.1 8
9.7 even 3 81.6.a.c.1.1 4
12.11 even 2 432.6.i.c.289.2 8
36.23 even 6 432.6.i.c.145.2 8
36.31 odd 6 144.6.i.c.49.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
9.6.c.a.4.4 8 9.4 even 3 inner
9.6.c.a.7.4 yes 8 1.1 even 1 trivial
27.6.c.a.10.1 8 9.5 odd 6
27.6.c.a.19.1 8 3.2 odd 2
81.6.a.c.1.1 4 9.7 even 3
81.6.a.d.1.4 4 9.2 odd 6
144.6.i.c.49.3 8 36.31 odd 6
144.6.i.c.97.3 8 4.3 odd 2
432.6.i.c.145.2 8 36.23 even 6
432.6.i.c.289.2 8 12.11 even 2