Properties

Label 15.6.e.a.2.2
Level $15$
Weight $6$
Character 15.2
Analytic conductor $2.406$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [15,6,Mod(2,15)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(15, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("15.2");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 15.e (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.40575729719\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 10768x^{12} + 16341006x^{8} + 4217167600x^{4} + 50906640625 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{9}\cdot 3^{10}\cdot 5^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 2.2
Root \(1.33460 + 1.33460i\) of defining polynomial
Character \(\chi\) \(=\) 15.2
Dual form 15.6.e.a.8.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-5.80199 + 5.80199i) q^{2} +(-7.07428 - 13.8908i) q^{3} -35.3261i q^{4} +(42.8643 - 35.8839i) q^{5} +(121.639 + 39.5494i) q^{6} +(-140.332 - 140.332i) q^{7} +(19.2981 + 19.2981i) q^{8} +(-142.909 + 196.535i) q^{9} +O(q^{10})\) \(q+(-5.80199 + 5.80199i) q^{2} +(-7.07428 - 13.8908i) q^{3} -35.3261i q^{4} +(42.8643 - 35.8839i) q^{5} +(121.639 + 39.5494i) q^{6} +(-140.332 - 140.332i) q^{7} +(19.2981 + 19.2981i) q^{8} +(-142.909 + 196.535i) q^{9} +(-40.5000 + 456.896i) q^{10} -164.276i q^{11} +(-490.708 + 249.907i) q^{12} +(32.2859 - 32.2859i) q^{13} +1628.41 q^{14} +(-801.690 - 341.567i) q^{15} +906.501 q^{16} +(-489.608 + 489.608i) q^{17} +(-311.136 - 1969.45i) q^{18} -807.175i q^{19} +(-1267.64 - 1514.23i) q^{20} +(-956.579 + 2942.08i) q^{21} +(953.126 + 953.126i) q^{22} +(136.703 + 136.703i) q^{23} +(131.546 - 404.587i) q^{24} +(549.691 - 3076.27i) q^{25} +374.645i q^{26} +(3741.01 + 594.781i) q^{27} +(-4957.39 + 4957.39i) q^{28} +4091.96 q^{29} +(6633.16 - 2669.63i) q^{30} -5188.95 q^{31} +(-5877.05 + 5877.05i) q^{32} +(-2281.92 + 1162.13i) q^{33} -5681.40i q^{34} +(-11050.9 - 979.570i) q^{35} +(6942.82 + 5048.43i) q^{36} +(6351.55 + 6351.55i) q^{37} +(4683.22 + 4683.22i) q^{38} +(-676.877 - 220.078i) q^{39} +(1519.69 + 134.708i) q^{40} -14423.5i q^{41} +(-11519.8 - 22620.0i) q^{42} +(15108.4 - 15108.4i) q^{43} -5803.23 q^{44} +(926.743 + 13552.5i) q^{45} -1586.30 q^{46} +(4527.76 - 4527.76i) q^{47} +(-6412.84 - 12592.0i) q^{48} +22579.3i q^{49} +(14659.2 + 21037.8i) q^{50} +(10264.7 + 3337.43i) q^{51} +(-1140.54 - 1140.54i) q^{52} +(582.510 + 582.510i) q^{53} +(-25156.2 + 18254.4i) q^{54} +(-5894.86 - 7041.56i) q^{55} -5416.30i q^{56} +(-11212.3 + 5710.18i) q^{57} +(-23741.5 + 23741.5i) q^{58} +6015.51 q^{59} +(-12066.2 + 28320.6i) q^{60} -19406.1 q^{61} +(30106.2 - 30106.2i) q^{62} +(47635.0 - 7525.42i) q^{63} -39189.1i q^{64} +(225.367 - 2542.46i) q^{65} +(6497.02 - 19982.4i) q^{66} +(7481.04 + 7481.04i) q^{67} +(17296.0 + 17296.0i) q^{68} +(931.840 - 2865.99i) q^{69} +(69800.7 - 58433.8i) q^{70} -8971.59i q^{71} +(-6550.64 + 1034.88i) q^{72} +(-41387.0 + 41387.0i) q^{73} -73703.3 q^{74} +(-46620.6 + 14126.8i) q^{75} -28514.4 q^{76} +(-23053.2 + 23053.2i) q^{77} +(5204.12 - 2650.34i) q^{78} -45334.9i q^{79} +(38856.5 - 32528.8i) q^{80} +(-18202.9 - 56173.3i) q^{81} +(83685.2 + 83685.2i) q^{82} +(-47307.8 - 47307.8i) q^{83} +(103932. + 33792.2i) q^{84} +(-3417.64 + 38555.8i) q^{85} +175317. i q^{86} +(-28947.7 - 56840.7i) q^{87} +(3170.22 - 3170.22i) q^{88} +64592.0 q^{89} +(-84008.2 - 73254.3i) q^{90} -9061.51 q^{91} +(4829.19 - 4829.19i) q^{92} +(36708.1 + 72078.7i) q^{93} +52540.0i q^{94} +(-28964.6 - 34599.0i) q^{95} +(123213. + 40061.1i) q^{96} +(-15396.4 - 15396.4i) q^{97} +(-131005. - 131005. i) q^{98} +(32285.9 + 23476.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 84 q^{6} - 80 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 84 q^{6} - 80 q^{7} + 1060 q^{10} + 420 q^{12} - 2120 q^{13} - 3000 q^{15} - 452 q^{16} + 6000 q^{18} + 1416 q^{21} + 3380 q^{22} + 9160 q^{25} - 12960 q^{27} - 10900 q^{28} - 13380 q^{30} - 21568 q^{31} + 5760 q^{33} + 61932 q^{36} + 55720 q^{37} + 21480 q^{40} - 103020 q^{42} - 23360 q^{43} - 21240 q^{45} - 151168 q^{46} + 74820 q^{48} + 138816 q^{51} + 204160 q^{52} + 89120 q^{55} - 163800 q^{57} - 163500 q^{58} - 217380 q^{60} - 175168 q^{61} + 143040 q^{63} + 263400 q^{66} + 140320 q^{67} + 385260 q^{70} - 328680 q^{72} - 240320 q^{73} - 199920 q^{75} - 271536 q^{76} + 429960 q^{78} + 326016 q^{81} + 431120 q^{82} + 2440 q^{85} - 331680 q^{87} - 401700 q^{88} - 348360 q^{90} - 487168 q^{91} - 22320 q^{93} + 311748 q^{96} + 440800 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).

\(n\) \(7\) \(11\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.80199 + 5.80199i −1.02566 + 1.02566i −0.0259941 + 0.999662i \(0.508275\pi\)
−0.999662 + 0.0259941i \(0.991725\pi\)
\(3\) −7.07428 13.8908i −0.453815 0.891096i
\(4\) 35.3261i 1.10394i
\(5\) 42.8643 35.8839i 0.766779 0.641911i
\(6\) 121.639 + 39.5494i 1.37942 + 0.448500i
\(7\) −140.332 140.332i −1.08246 1.08246i −0.996279 0.0861819i \(-0.972533\pi\)
−0.0861819 0.996279i \(-0.527467\pi\)
\(8\) 19.2981 + 19.2981i 0.106608 + 0.106608i
\(9\) −142.909 + 196.535i −0.588104 + 0.808786i
\(10\) −40.5000 + 456.896i −0.128072 + 1.44483i
\(11\) 164.276i 0.409347i −0.978830 0.204674i \(-0.934387\pi\)
0.978830 0.204674i \(-0.0656133\pi\)
\(12\) −490.708 + 249.907i −0.983718 + 0.500985i
\(13\) 32.2859 32.2859i 0.0529852 0.0529852i −0.680118 0.733103i \(-0.738071\pi\)
0.733103 + 0.680118i \(0.238071\pi\)
\(14\) 1628.41 2.22047
\(15\) −801.690 341.567i −0.919980 0.391965i
\(16\) 906.501 0.885255
\(17\) −489.608 + 489.608i −0.410891 + 0.410891i −0.882049 0.471158i \(-0.843836\pi\)
0.471158 + 0.882049i \(0.343836\pi\)
\(18\) −311.136 1969.45i −0.226344 1.43273i
\(19\) 807.175i 0.512960i −0.966549 0.256480i \(-0.917437\pi\)
0.966549 0.256480i \(-0.0825628\pi\)
\(20\) −1267.64 1514.23i −0.708632 0.846479i
\(21\) −956.579 + 2942.08i −0.473339 + 1.45581i
\(22\) 953.126 + 953.126i 0.419850 + 0.419850i
\(23\) 136.703 + 136.703i 0.0538838 + 0.0538838i 0.733535 0.679651i \(-0.237869\pi\)
−0.679651 + 0.733535i \(0.737869\pi\)
\(24\) 131.546 404.587i 0.0466177 0.143379i
\(25\) 549.691 3076.27i 0.175901 0.984408i
\(26\) 374.645i 0.108689i
\(27\) 3741.01 + 594.781i 0.987596 + 0.157017i
\(28\) −4957.39 + 4957.39i −1.19497 + 1.19497i
\(29\) 4091.96 0.903518 0.451759 0.892140i \(-0.350797\pi\)
0.451759 + 0.892140i \(0.350797\pi\)
\(30\) 6633.16 2669.63i 1.34560 0.541562i
\(31\) −5188.95 −0.969784 −0.484892 0.874574i \(-0.661141\pi\)
−0.484892 + 0.874574i \(0.661141\pi\)
\(32\) −5877.05 + 5877.05i −1.01458 + 1.01458i
\(33\) −2281.92 + 1162.13i −0.364768 + 0.185768i
\(34\) 5681.40i 0.842865i
\(35\) −11050.9 979.570i −1.52485 0.135165i
\(36\) 6942.82 + 5048.43i 0.892852 + 0.649232i
\(37\) 6351.55 + 6351.55i 0.762738 + 0.762738i 0.976817 0.214078i \(-0.0686747\pi\)
−0.214078 + 0.976817i \(0.568675\pi\)
\(38\) 4683.22 + 4683.22i 0.526121 + 0.526121i
\(39\) −676.877 220.078i −0.0712604 0.0231694i
\(40\) 1519.69 + 134.708i 0.150178 + 0.0133120i
\(41\) 14423.5i 1.34002i −0.742350 0.670012i \(-0.766289\pi\)
0.742350 0.670012i \(-0.233711\pi\)
\(42\) −11519.8 22620.0i −1.00768 1.97865i
\(43\) 15108.4 15108.4i 1.24608 1.24608i 0.288644 0.957436i \(-0.406795\pi\)
0.957436 0.288644i \(-0.0932045\pi\)
\(44\) −5803.23 −0.451896
\(45\) 926.743 + 13552.5i 0.0682226 + 0.997670i
\(46\) −1586.30 −0.110533
\(47\) 4527.76 4527.76i 0.298977 0.298977i −0.541636 0.840613i \(-0.682195\pi\)
0.840613 + 0.541636i \(0.182195\pi\)
\(48\) −6412.84 12592.0i −0.401742 0.788847i
\(49\) 22579.3i 1.34345i
\(50\) 14659.2 + 21037.8i 0.829250 + 1.19008i
\(51\) 10264.7 + 3337.43i 0.552612 + 0.179675i
\(52\) −1140.54 1140.54i −0.0584925 0.0584925i
\(53\) 582.510 + 582.510i 0.0284848 + 0.0284848i 0.721206 0.692721i \(-0.243588\pi\)
−0.692721 + 0.721206i \(0.743588\pi\)
\(54\) −25156.2 + 18254.4i −1.17398 + 0.851888i
\(55\) −5894.86 7041.56i −0.262764 0.313879i
\(56\) 5416.30i 0.230798i
\(57\) −11212.3 + 5710.18i −0.457097 + 0.232789i
\(58\) −23741.5 + 23741.5i −0.926699 + 0.926699i
\(59\) 6015.51 0.224979 0.112490 0.993653i \(-0.464117\pi\)
0.112490 + 0.993653i \(0.464117\pi\)
\(60\) −12066.2 + 28320.6i −0.432706 + 1.01560i
\(61\) −19406.1 −0.667751 −0.333875 0.942617i \(-0.608356\pi\)
−0.333875 + 0.942617i \(0.608356\pi\)
\(62\) 30106.2 30106.2i 0.994665 0.994665i
\(63\) 47635.0 7525.42i 1.51208 0.238880i
\(64\) 39189.1i 1.19596i
\(65\) 225.367 2542.46i 0.00661618 0.0746397i
\(66\) 6497.02 19982.4i 0.183592 0.564660i
\(67\) 7481.04 + 7481.04i 0.203599 + 0.203599i 0.801540 0.597941i \(-0.204014\pi\)
−0.597941 + 0.801540i \(0.704014\pi\)
\(68\) 17296.0 + 17296.0i 0.453599 + 0.453599i
\(69\) 931.840 2865.99i 0.0235623 0.0724689i
\(70\) 69800.7 58433.8i 1.70261 1.42534i
\(71\) 8971.59i 0.211214i −0.994408 0.105607i \(-0.966321\pi\)
0.994408 0.105607i \(-0.0336786\pi\)
\(72\) −6550.64 + 1034.88i −0.148920 + 0.0235265i
\(73\) −41387.0 + 41387.0i −0.908986 + 0.908986i −0.996190 0.0872047i \(-0.972207\pi\)
0.0872047 + 0.996190i \(0.472207\pi\)
\(74\) −73703.3 −1.56461
\(75\) −46620.6 + 14126.8i −0.957028 + 0.289995i
\(76\) −28514.4 −0.566278
\(77\) −23053.2 + 23053.2i −0.443103 + 0.443103i
\(78\) 5204.12 2650.34i 0.0968525 0.0493248i
\(79\) 45334.9i 0.817268i −0.912698 0.408634i \(-0.866005\pi\)
0.912698 0.408634i \(-0.133995\pi\)
\(80\) 38856.5 32528.8i 0.678795 0.568255i
\(81\) −18202.9 56173.3i −0.308268 0.951299i
\(82\) 83685.2 + 83685.2i 1.37440 + 1.37440i
\(83\) −47307.8 47307.8i −0.753768 0.753768i 0.221412 0.975180i \(-0.428933\pi\)
−0.975180 + 0.221412i \(0.928933\pi\)
\(84\) 103932. + 33792.2i 1.60713 + 0.522539i
\(85\) −3417.64 + 38555.8i −0.0513073 + 0.578818i
\(86\) 175317.i 2.55610i
\(87\) −28947.7 56840.7i −0.410030 0.805121i
\(88\) 3170.22 3170.22i 0.0436398 0.0436398i
\(89\) 64592.0 0.864378 0.432189 0.901783i \(-0.357741\pi\)
0.432189 + 0.901783i \(0.357741\pi\)
\(90\) −84008.2 73254.3i −1.09324 0.953294i
\(91\) −9061.51 −0.114709
\(92\) 4829.19 4829.19i 0.0594846 0.0594846i
\(93\) 36708.1 + 72078.7i 0.440103 + 0.864171i
\(94\) 52540.0i 0.613296i
\(95\) −28964.6 34599.0i −0.329275 0.393327i
\(96\) 123213. + 40061.1i 1.36451 + 0.443654i
\(97\) −15396.4 15396.4i −0.166146 0.166146i 0.619137 0.785283i \(-0.287483\pi\)
−0.785283 + 0.619137i \(0.787483\pi\)
\(98\) −131005. 131005.i −1.37791 1.37791i
\(99\) 32285.9 + 23476.5i 0.331074 + 0.240739i
\(100\) −108673. 19418.4i −1.08673 0.194184i
\(101\) 12805.3i 0.124907i −0.998048 0.0624536i \(-0.980107\pi\)
0.998048 0.0624536i \(-0.0198926\pi\)
\(102\) −78919.3 + 40191.8i −0.751074 + 0.382505i
\(103\) 78304.8 78304.8i 0.727269 0.727269i −0.242806 0.970075i \(-0.578068\pi\)
0.970075 + 0.242806i \(0.0780677\pi\)
\(104\) 1246.12 0.0112973
\(105\) 64570.2 + 160436.i 0.571556 + 1.42013i
\(106\) −6759.43 −0.0584313
\(107\) −114730. + 114730.i −0.968759 + 0.968759i −0.999527 0.0307677i \(-0.990205\pi\)
0.0307677 + 0.999527i \(0.490205\pi\)
\(108\) 21011.3 132155.i 0.173338 1.09025i
\(109\) 87202.6i 0.703013i −0.936185 0.351507i \(-0.885670\pi\)
0.936185 0.351507i \(-0.114330\pi\)
\(110\) 75057.0 + 6653.17i 0.591438 + 0.0524260i
\(111\) 43295.6 133161.i 0.333531 1.02582i
\(112\) −127211. 127211.i −0.958254 0.958254i
\(113\) 170508. + 170508.i 1.25617 + 1.25617i 0.952908 + 0.303259i \(0.0980749\pi\)
0.303259 + 0.952908i \(0.401925\pi\)
\(114\) 31923.3 98184.1i 0.230063 0.707586i
\(115\) 10765.1 + 954.236i 0.0759056 + 0.00672839i
\(116\) 144553.i 0.997431i
\(117\) 1731.36 + 10959.3i 0.0116929 + 0.0740144i
\(118\) −34901.9 + 34901.9i −0.230751 + 0.230751i
\(119\) 137416. 0.889547
\(120\) −8879.53 22062.7i −0.0562907 0.139864i
\(121\) 134064. 0.832435
\(122\) 112594. 112594.i 0.684883 0.684883i
\(123\) −200355. + 102036.i −1.19409 + 0.608123i
\(124\) 183305.i 1.07059i
\(125\) −86826.6 151587.i −0.497025 0.867736i
\(126\) −232715. + 320040.i −1.30586 + 1.79588i
\(127\) 140821. + 140821.i 0.774743 + 0.774743i 0.978932 0.204189i \(-0.0654556\pi\)
−0.204189 + 0.978932i \(0.565456\pi\)
\(128\) 39309.1 + 39309.1i 0.212065 + 0.212065i
\(129\) −316748. 102987.i −1.67587 0.544887i
\(130\) 13443.7 + 16058.9i 0.0697688 + 0.0833406i
\(131\) 97283.3i 0.495291i 0.968851 + 0.247645i \(0.0796568\pi\)
−0.968851 + 0.247645i \(0.920343\pi\)
\(132\) 41053.7 + 80611.6i 0.205077 + 0.402682i
\(133\) −113273. + 113273.i −0.555260 + 0.555260i
\(134\) −86809.8 −0.417645
\(135\) 181699. 108747.i 0.858059 0.513551i
\(136\) −18897.1 −0.0876086
\(137\) 118487. 118487.i 0.539349 0.539349i −0.383989 0.923338i \(-0.625450\pi\)
0.923338 + 0.383989i \(0.125450\pi\)
\(138\) 11221.9 + 22035.0i 0.0501613 + 0.0984951i
\(139\) 21750.2i 0.0954829i 0.998860 + 0.0477415i \(0.0152024\pi\)
−0.998860 + 0.0477415i \(0.984798\pi\)
\(140\) −34604.4 + 390386.i −0.149215 + 1.68335i
\(141\) −94924.8 30863.6i −0.402098 0.130737i
\(142\) 52053.1 + 52053.1i 0.216633 + 0.216633i
\(143\) −5303.79 5303.79i −0.0216893 0.0216893i
\(144\) −129547. + 178159.i −0.520621 + 0.715981i
\(145\) 175399. 146836.i 0.692799 0.579978i
\(146\) 480254.i 1.86461i
\(147\) 313644. 159732.i 1.19714 0.609676i
\(148\) 224376. 224376.i 0.842018 0.842018i
\(149\) 23997.2 0.0885514 0.0442757 0.999019i \(-0.485902\pi\)
0.0442757 + 0.999019i \(0.485902\pi\)
\(150\) 188529. 352456.i 0.684147 1.27902i
\(151\) −359892. −1.28449 −0.642243 0.766501i \(-0.721996\pi\)
−0.642243 + 0.766501i \(0.721996\pi\)
\(152\) 15577.0 15577.0i 0.0546858 0.0546858i
\(153\) −26255.6 166195.i −0.0906762 0.573969i
\(154\) 267509.i 0.908942i
\(155\) −222420. + 186200.i −0.743611 + 0.622515i
\(156\) −7774.50 + 23911.4i −0.0255777 + 0.0786673i
\(157\) −310096. 310096.i −1.00403 1.00403i −0.999992 0.00403898i \(-0.998714\pi\)
−0.00403898 0.999992i \(-0.501286\pi\)
\(158\) 263032. + 263032.i 0.838236 + 0.838236i
\(159\) 3970.70 12212.4i 0.0124559 0.0383096i
\(160\) −41023.9 + 462807.i −0.126689 + 1.42922i
\(161\) 38367.7i 0.116654i
\(162\) 431530. + 220303.i 1.29188 + 0.659529i
\(163\) 150586. 150586.i 0.443932 0.443932i −0.449399 0.893331i \(-0.648362\pi\)
0.893331 + 0.449399i \(0.148362\pi\)
\(164\) −509528. −1.47931
\(165\) −56111.1 + 131698.i −0.160450 + 0.376591i
\(166\) 548959. 1.54621
\(167\) −363760. + 363760.i −1.00931 + 1.00931i −0.00935065 + 0.999956i \(0.502976\pi\)
−0.999956 + 0.00935065i \(0.997024\pi\)
\(168\) −75236.8 + 38316.4i −0.205664 + 0.104740i
\(169\) 369208.i 0.994385i
\(170\) −203871. 243529.i −0.541044 0.646292i
\(171\) 158638. + 115353.i 0.414875 + 0.301674i
\(172\) −533720. 533720.i −1.37560 1.37560i
\(173\) −80605.1 80605.1i −0.204761 0.204761i 0.597275 0.802036i \(-0.296250\pi\)
−0.802036 + 0.597275i \(0.796250\pi\)
\(174\) 497743. + 161835.i 1.24633 + 0.405228i
\(175\) −508840. + 354561.i −1.25599 + 0.875177i
\(176\) 148916.i 0.362377i
\(177\) −42555.4 83560.3i −0.102099 0.200478i
\(178\) −374762. + 374762.i −0.886554 + 0.886554i
\(179\) 407767. 0.951216 0.475608 0.879657i \(-0.342228\pi\)
0.475608 + 0.879657i \(0.342228\pi\)
\(180\) 478756. 32738.2i 1.10137 0.0753137i
\(181\) 229845. 0.521481 0.260741 0.965409i \(-0.416033\pi\)
0.260741 + 0.965409i \(0.416033\pi\)
\(182\) 52574.7 52574.7i 0.117652 0.117652i
\(183\) 137284. + 269567.i 0.303035 + 0.595030i
\(184\) 5276.23i 0.0114889i
\(185\) 500173. + 44336.1i 1.07446 + 0.0952420i
\(186\) −631180. 205220.i −1.33774 0.434948i
\(187\) 80430.8 + 80430.8i 0.168197 + 0.168197i
\(188\) −159948. 159948.i −0.330054 0.330054i
\(189\) −441517. 608451.i −0.899069 1.23900i
\(190\) 368795. + 32690.6i 0.741141 + 0.0656960i
\(191\) 424327.i 0.841623i 0.907148 + 0.420812i \(0.138255\pi\)
−0.907148 + 0.420812i \(0.861745\pi\)
\(192\) −544368. + 277235.i −1.06571 + 0.542743i
\(193\) 551081. 551081.i 1.06493 1.06493i 0.0671936 0.997740i \(-0.478595\pi\)
0.997740 0.0671936i \(-0.0214045\pi\)
\(194\) 178660. 0.340818
\(195\) −36911.1 + 14855.5i −0.0695137 + 0.0279770i
\(196\) 797639. 1.48308
\(197\) 54471.1 54471.1i 0.100000 0.100000i −0.655337 0.755337i \(-0.727473\pi\)
0.755337 + 0.655337i \(0.227473\pi\)
\(198\) −323533. + 51112.1i −0.586483 + 0.0926533i
\(199\) 856506.i 1.53320i 0.642128 + 0.766598i \(0.278052\pi\)
−0.642128 + 0.766598i \(0.721948\pi\)
\(200\) 69974.4 48758.4i 0.123698 0.0861934i
\(201\) 50994.7 156841.i 0.0890298 0.273822i
\(202\) 74296.4 + 74296.4i 0.128112 + 0.128112i
\(203\) −574235. 574235.i −0.978023 0.978023i
\(204\) 117898. 362611.i 0.198350 0.610051i
\(205\) −517573. 618255.i −0.860176 1.02750i
\(206\) 908647.i 1.49186i
\(207\) −46403.0 + 7330.80i −0.0752697 + 0.0118912i
\(208\) 29267.2 29267.2i 0.0469054 0.0469054i
\(209\) −132599. −0.209979
\(210\) −1.30548e6 556211.i −2.04278 0.870345i
\(211\) −316233. −0.488992 −0.244496 0.969650i \(-0.578622\pi\)
−0.244496 + 0.969650i \(0.578622\pi\)
\(212\) 20577.8 20577.8i 0.0314456 0.0314456i
\(213\) −124623. + 63467.5i −0.188212 + 0.0958523i
\(214\) 1.33132e6i 1.98723i
\(215\) 105462. 1.18976e6i 0.155596 1.75534i
\(216\) 60716.3 + 83672.7i 0.0885465 + 0.122025i
\(217\) 728177. + 728177.i 1.04975 + 1.04975i
\(218\) 505949. + 505949.i 0.721050 + 0.721050i
\(219\) 867683. + 282116.i 1.22250 + 0.397482i
\(220\) −248751. + 208243.i −0.346504 + 0.290077i
\(221\) 31614.9i 0.0435423i
\(222\) 521397. + 1.02380e6i 0.710046 + 1.39422i
\(223\) 112517. 112517.i 0.151515 0.151515i −0.627279 0.778795i \(-0.715831\pi\)
0.778795 + 0.627279i \(0.215831\pi\)
\(224\) 1.64948e6 2.19648
\(225\) 526039. + 547661.i 0.692727 + 0.721200i
\(226\) −1.97857e6 −2.57679
\(227\) 592921. 592921.i 0.763717 0.763717i −0.213275 0.976992i \(-0.568413\pi\)
0.976992 + 0.213275i \(0.0684131\pi\)
\(228\) 201719. + 396088.i 0.256986 + 0.504608i
\(229\) 67505.7i 0.0850652i 0.999095 + 0.0425326i \(0.0135426\pi\)
−0.999095 + 0.0425326i \(0.986457\pi\)
\(230\) −67995.5 + 56922.6i −0.0847541 + 0.0709520i
\(231\) 483312. + 157143.i 0.595934 + 0.193760i
\(232\) 78967.3 + 78967.3i 0.0963224 + 0.0963224i
\(233\) −440320. 440320.i −0.531348 0.531348i 0.389625 0.920973i \(-0.372604\pi\)
−0.920973 + 0.389625i \(0.872604\pi\)
\(234\) −73630.8 53540.2i −0.0879062 0.0639205i
\(235\) 31605.4 356553.i 0.0373329 0.421167i
\(236\) 212505.i 0.248364i
\(237\) −629738. + 320711.i −0.728264 + 0.370889i
\(238\) −797284. + 797284.i −0.912369 + 0.912369i
\(239\) −1.45871e6 −1.65186 −0.825932 0.563770i \(-0.809350\pi\)
−0.825932 + 0.563770i \(0.809350\pi\)
\(240\) −726733. 309630.i −0.814417 0.346989i
\(241\) 250218. 0.277508 0.138754 0.990327i \(-0.455690\pi\)
0.138754 + 0.990327i \(0.455690\pi\)
\(242\) −777840. + 777840.i −0.853792 + 0.853792i
\(243\) −651520. + 650239.i −0.707802 + 0.706411i
\(244\) 685543.i 0.737157i
\(245\) 810233. + 967844.i 0.862372 + 1.03013i
\(246\) 570443. 1.75447e6i 0.601000 1.84845i
\(247\) −26060.4 26060.4i −0.0271793 0.0271793i
\(248\) −100137. 100137.i −0.103387 0.103387i
\(249\) −322475. + 991813.i −0.329608 + 1.01375i
\(250\) 1.38327e6 + 375741.i 1.39978 + 0.380223i
\(251\) 1.60059e6i 1.60360i 0.597590 + 0.801802i \(0.296125\pi\)
−0.597590 + 0.801802i \(0.703875\pi\)
\(252\) −265844. 1.68276e6i −0.263709 1.66925i
\(253\) 22457.0 22457.0i 0.0220572 0.0220572i
\(254\) −1.63408e6 −1.58924
\(255\) 559748. 225280.i 0.539066 0.216957i
\(256\) 797909. 0.760945
\(257\) 1.07743e6 1.07743e6i 1.01755 1.01755i 0.0177088 0.999843i \(-0.494363\pi\)
0.999843 0.0177088i \(-0.00563717\pi\)
\(258\) 2.43530e6 1.24024e6i 2.27773 1.16000i
\(259\) 1.78266e6i 1.65127i
\(260\) −89815.1 7961.35i −0.0823979 0.00730388i
\(261\) −584779. + 804214.i −0.531362 + 0.730752i
\(262\) −564437. 564437.i −0.507998 0.507998i
\(263\) 64027.4 + 64027.4i 0.0570790 + 0.0570790i 0.735070 0.677991i \(-0.237149\pi\)
−0.677991 + 0.735070i \(0.737149\pi\)
\(264\) −66463.9 21609.9i −0.0586916 0.0190828i
\(265\) 45871.6 + 4066.13i 0.0401263 + 0.00355686i
\(266\) 1.31441e6i 1.13901i
\(267\) −456942. 897235.i −0.392268 0.770243i
\(268\) 264276. 264276.i 0.224761 0.224761i
\(269\) −8993.19 −0.00757762 −0.00378881 0.999993i \(-0.501206\pi\)
−0.00378881 + 0.999993i \(0.501206\pi\)
\(270\) −423264. + 1.68516e6i −0.353347 + 1.40680i
\(271\) 1.65405e6 1.36812 0.684062 0.729423i \(-0.260212\pi\)
0.684062 + 0.729423i \(0.260212\pi\)
\(272\) −443830. + 443830.i −0.363743 + 0.363743i
\(273\) 64103.6 + 125872.i 0.0520566 + 0.102217i
\(274\) 1.37492e6i 1.10637i
\(275\) −505358. 90300.9i −0.402965 0.0720046i
\(276\) −101244. 32918.3i −0.0800015 0.0260114i
\(277\) −726549. 726549.i −0.568939 0.568939i 0.362892 0.931831i \(-0.381789\pi\)
−0.931831 + 0.362892i \(0.881789\pi\)
\(278\) −126194. 126194.i −0.0979327 0.0979327i
\(279\) 741548. 1.01981e6i 0.570334 0.784348i
\(280\) −194358. 232166.i −0.148152 0.176972i
\(281\) 2.29314e6i 1.73246i −0.499641 0.866232i \(-0.666535\pi\)
0.499641 0.866232i \(-0.333465\pi\)
\(282\) 729823. 371683.i 0.546506 0.278323i
\(283\) −562759. + 562759.i −0.417692 + 0.417692i −0.884408 0.466715i \(-0.845437\pi\)
0.466715 + 0.884408i \(0.345437\pi\)
\(284\) −316932. −0.233168
\(285\) −275704. + 647104.i −0.201062 + 0.471913i
\(286\) 61545.1 0.0444916
\(287\) −2.02409e6 + 2.02409e6i −1.45052 + 1.45052i
\(288\) −315161. 1.99493e6i −0.223899 1.41725i
\(289\) 940425.i 0.662338i
\(290\) −165724. + 1.86960e6i −0.115716 + 1.30543i
\(291\) −104950. + 322788.i −0.0726526 + 0.223452i
\(292\) 1.46204e6 + 1.46204e6i 1.00347 + 1.00347i
\(293\) 1.15765e6 + 1.15765e6i 0.787787 + 0.787787i 0.981131 0.193344i \(-0.0619332\pi\)
−0.193344 + 0.981131i \(0.561933\pi\)
\(294\) −892998. + 2.74653e6i −0.602535 + 1.85317i
\(295\) 257850. 215860.i 0.172509 0.144417i
\(296\) 245146.i 0.162628i
\(297\) 97708.2 614557.i 0.0642747 0.404270i
\(298\) −139232. + 139232.i −0.0908233 + 0.0908233i
\(299\) 8827.15 0.00571009
\(300\) 499044. + 1.64693e6i 0.320137 + 1.05650i
\(301\) −4.24038e6 −2.69767
\(302\) 2.08809e6 2.08809e6i 1.31744 1.31744i
\(303\) −177877. + 90588.5i −0.111304 + 0.0566848i
\(304\) 731705.i 0.454101i
\(305\) −831829. + 696368.i −0.512017 + 0.428636i
\(306\) 1.11659e6 + 811924.i 0.681697 + 0.495692i
\(307\) 646353. + 646353.i 0.391403 + 0.391403i 0.875187 0.483784i \(-0.160738\pi\)
−0.483784 + 0.875187i \(0.660738\pi\)
\(308\) 814380. + 814380.i 0.489159 + 0.489159i
\(309\) −1.64167e6 533767.i −0.978112 0.318021i
\(310\) 210152. 2.37081e6i 0.124202 1.40118i
\(311\) 1.76436e6i 1.03439i −0.855867 0.517197i \(-0.826976\pi\)
0.855867 0.517197i \(-0.173024\pi\)
\(312\) −8815.37 17309.6i −0.00512689 0.0100670i
\(313\) −562244. + 562244.i −0.324388 + 0.324388i −0.850447 0.526060i \(-0.823669\pi\)
0.526060 + 0.850447i \(0.323669\pi\)
\(314\) 3.59835e6 2.05958
\(315\) 1.77180e6 2.03190e6i 1.00609 1.15379i
\(316\) −1.60151e6 −0.902216
\(317\) 1.76895e6 1.76895e6i 0.988706 0.988706i −0.0112312 0.999937i \(-0.503575\pi\)
0.999937 + 0.0112312i \(0.00357507\pi\)
\(318\) 47818.1 + 93894.0i 0.0265170 + 0.0520679i
\(319\) 672211.i 0.369853i
\(320\) −1.40626e6 1.67981e6i −0.767697 0.917034i
\(321\) 2.40531e6 + 782057.i 1.30289 + 0.423619i
\(322\) 222609. + 222609.i 0.119647 + 0.119647i
\(323\) 395200. + 395200.i 0.210771 + 0.210771i
\(324\) −1.98438e6 + 643039.i −1.05018 + 0.340310i
\(325\) −81573.0 117068.i −0.0428389 0.0614792i
\(326\) 1.74740e6i 0.910642i
\(327\) −1.21132e6 + 616896.i −0.626452 + 0.319038i
\(328\) 278348. 278348.i 0.142857 0.142857i
\(329\) −1.27078e6 −0.647263
\(330\) −438556. 1.08967e6i −0.221687 0.550820i
\(331\) 723065. 0.362750 0.181375 0.983414i \(-0.441945\pi\)
0.181375 + 0.983414i \(0.441945\pi\)
\(332\) −1.67120e6 + 1.67120e6i −0.832116 + 0.832116i
\(333\) −2.15600e6 + 340607.i −1.06546 + 0.168323i
\(334\) 4.22106e6i 2.07040i
\(335\) 589118. + 52220.4i 0.286808 + 0.0254231i
\(336\) −867140. + 2.66700e6i −0.419026 + 1.28877i
\(337\) 2.49850e6 + 2.49850e6i 1.19841 + 1.19841i 0.974643 + 0.223767i \(0.0718354\pi\)
0.223767 + 0.974643i \(0.428165\pi\)
\(338\) −2.14214e6 2.14214e6i −1.01990 1.01990i
\(339\) 1.16227e6 3.57471e6i 0.549298 1.68943i
\(340\) 1.36203e6 + 120732.i 0.638981 + 0.0566403i
\(341\) 852419.i 0.396979i
\(342\) −1.58969e6 + 251141.i −0.734933 + 0.116105i
\(343\) 810037. 810037.i 0.371766 0.371766i
\(344\) 583127. 0.265685
\(345\) −62900.3 156287.i −0.0284515 0.0706926i
\(346\) 935340. 0.420029
\(347\) −1.38088e6 + 1.38088e6i −0.615648 + 0.615648i −0.944412 0.328764i \(-0.893368\pi\)
0.328764 + 0.944412i \(0.393368\pi\)
\(348\) −2.00796e6 + 1.02261e6i −0.888807 + 0.452649i
\(349\) 3.30618e6i 1.45299i 0.687172 + 0.726495i \(0.258852\pi\)
−0.687172 + 0.726495i \(0.741148\pi\)
\(350\) 895123. 5.00944e6i 0.390582 2.18584i
\(351\) 139985. 101579.i 0.0606475 0.0440084i
\(352\) 965457. + 965457.i 0.415314 + 0.415314i
\(353\) 2.37220e6 + 2.37220e6i 1.01325 + 1.01325i 0.999911 + 0.0133341i \(0.00424449\pi\)
0.0133341 + 0.999911i \(0.495756\pi\)
\(354\) 731722. + 237910.i 0.310340 + 0.100903i
\(355\) −321936. 384561.i −0.135581 0.161955i
\(356\) 2.28178e6i 0.954222i
\(357\) −972117. 1.90881e6i −0.403690 0.792671i
\(358\) −2.36586e6 + 2.36586e6i −0.975621 + 0.975621i
\(359\) 4.10333e6 1.68035 0.840177 0.542312i \(-0.182451\pi\)
0.840177 + 0.542312i \(0.182451\pi\)
\(360\) −243653. + 279422.i −0.0990867 + 0.113633i
\(361\) 1.82457e6 0.736872
\(362\) −1.33356e6 + 1.33356e6i −0.534861 + 0.534861i
\(363\) −948409. 1.86226e6i −0.377772 0.741779i
\(364\) 320108.i 0.126632i
\(365\) −288896. + 3.25915e6i −0.113504 + 1.28048i
\(366\) −2.36055e6 767501.i −0.921106 0.299486i
\(367\) −2.22211e6 2.22211e6i −0.861192 0.861192i 0.130285 0.991477i \(-0.458411\pi\)
−0.991477 + 0.130285i \(0.958411\pi\)
\(368\) 123921. + 123921.i 0.0477009 + 0.0477009i
\(369\) 2.83473e6 + 2.06126e6i 1.08379 + 0.788073i
\(370\) −3.15924e6 + 2.64476e6i −1.19971 + 1.00434i
\(371\) 163490.i 0.0616675i
\(372\) 2.54626e6 1.29675e6i 0.953994 0.485848i
\(373\) 2.77675e6 2.77675e6i 1.03339 1.03339i 0.0339689 0.999423i \(-0.489185\pi\)
0.999423 0.0339689i \(-0.0108147\pi\)
\(374\) −933317. −0.345025
\(375\) −1.49143e6 + 2.27846e6i −0.547679 + 0.836689i
\(376\) 174755. 0.0637469
\(377\) 132113. 132113.i 0.0478731 0.0478731i
\(378\) 6.09190e6 + 968549.i 2.19292 + 0.348652i
\(379\) 2.10010e6i 0.751005i 0.926821 + 0.375502i \(0.122530\pi\)
−0.926821 + 0.375502i \(0.877470\pi\)
\(380\) −1.22225e6 + 1.02321e6i −0.434210 + 0.363500i
\(381\) 959910. 2.95232e6i 0.338780 1.04196i
\(382\) −2.46194e6 2.46194e6i −0.863216 0.863216i
\(383\) −2.06770e6 2.06770e6i −0.720261 0.720261i 0.248397 0.968658i \(-0.420096\pi\)
−0.968658 + 0.248397i \(0.920096\pi\)
\(384\) 267952. 824119.i 0.0927317 0.285208i
\(385\) −160920. + 1.81540e6i −0.0553296 + 0.624194i
\(386\) 6.39474e6i 2.18451i
\(387\) 810197. + 5.12844e6i 0.274988 + 1.74064i
\(388\) −543897. + 543897.i −0.183416 + 0.183416i
\(389\) −3.49610e6 −1.17141 −0.585707 0.810523i \(-0.699183\pi\)
−0.585707 + 0.810523i \(0.699183\pi\)
\(390\) 127966. 300349.i 0.0426024 0.0999919i
\(391\) −133862. −0.0442807
\(392\) −435738. + 435738.i −0.143222 + 0.143222i
\(393\) 1.35134e6 688209.i 0.441351 0.224770i
\(394\) 632081.i 0.205131i
\(395\) −1.62679e6 1.94325e6i −0.524613 0.626664i
\(396\) 829335. 1.14054e6i 0.265761 0.365487i
\(397\) −1.81474e6 1.81474e6i −0.577879 0.577879i 0.356439 0.934319i \(-0.383991\pi\)
−0.934319 + 0.356439i \(0.883991\pi\)
\(398\) −4.96944e6 4.96944e6i −1.57253 1.57253i
\(399\) 2.37477e6 + 772127.i 0.746775 + 0.242804i
\(400\) 498295. 2.78865e6i 0.155717 0.871452i
\(401\) 209439.i 0.0650425i −0.999471 0.0325212i \(-0.989646\pi\)
0.999471 0.0325212i \(-0.0103537\pi\)
\(402\) 614117. + 1.20586e6i 0.189533 + 0.372161i
\(403\) −167530. + 167530.i −0.0513842 + 0.0513842i
\(404\) −452363. −0.137890
\(405\) −2.79597e6 1.75463e6i −0.847023 0.531556i
\(406\) 6.66340e6 2.00623
\(407\) 1.04341e6 1.04341e6i 0.312225 0.312225i
\(408\) 133683. + 262495.i 0.0397581 + 0.0780677i
\(409\) 3.63117e6i 1.07334i −0.843791 0.536672i \(-0.819681\pi\)
0.843791 0.536672i \(-0.180319\pi\)
\(410\) 6.59006e6 + 584153.i 1.93611 + 0.171620i
\(411\) −2.48410e6 807672.i −0.725377 0.235847i
\(412\) −2.76620e6 2.76620e6i −0.802863 0.802863i
\(413\) −844170. 844170.i −0.243531 0.243531i
\(414\) 226696. 311763.i 0.0650046 0.0893971i
\(415\) −3.72541e6 330226.i −1.06183 0.0941219i
\(416\) 379492.i 0.107515i
\(417\) 302128. 153867.i 0.0850845 0.0433316i
\(418\) 769340. 769340.i 0.215366 0.215366i
\(419\) −197133. −0.0548560 −0.0274280 0.999624i \(-0.508732\pi\)
−0.0274280 + 0.999624i \(0.508732\pi\)
\(420\) 5.66758e6 2.28101e6i 1.56774 0.630964i
\(421\) −3.16076e6 −0.869133 −0.434566 0.900640i \(-0.643098\pi\)
−0.434566 + 0.900640i \(0.643098\pi\)
\(422\) 1.83478e6 1.83478e6i 0.501537 0.501537i
\(423\) 242804. + 1.53692e6i 0.0659790 + 0.417638i
\(424\) 22482.7i 0.00607343i
\(425\) 1.23704e6 + 1.77530e6i 0.332208 + 0.476760i
\(426\) 354821. 1.09130e6i 0.0947296 0.291353i
\(427\) 2.72331e6 + 2.72331e6i 0.722814 + 0.722814i
\(428\) 4.05295e6 + 4.05295e6i 1.06945 + 1.06945i
\(429\) −36153.5 + 111194.i −0.00948433 + 0.0291702i
\(430\) 6.29106e6 + 7.51484e6i 1.64079 + 1.95997i
\(431\) 75464.2i 0.0195681i −0.999952 0.00978404i \(-0.996886\pi\)
0.999952 0.00978404i \(-0.00311440\pi\)
\(432\) 3.39123e6 + 539170.i 0.874274 + 0.139000i
\(433\) 2.05905e6 2.05905e6i 0.527772 0.527772i −0.392135 0.919908i \(-0.628263\pi\)
0.919908 + 0.392135i \(0.128263\pi\)
\(434\) −8.44975e6 −2.15337
\(435\) −3.28049e6 1.39768e6i −0.831219 0.354147i
\(436\) −3.08053e6 −0.776085
\(437\) 110343. 110343.i 0.0276403 0.0276403i
\(438\) −6.67112e6 + 3.39745e6i −1.66155 + 0.846190i
\(439\) 337512.i 0.0835850i 0.999126 + 0.0417925i \(0.0133068\pi\)
−0.999126 + 0.0417925i \(0.986693\pi\)
\(440\) 22129.3 249649.i 0.00544924 0.0614749i
\(441\) −4.43762e6 3.22679e6i −1.08656 0.790085i
\(442\) −183429. 183429.i −0.0446594 0.0446594i
\(443\) 4.86518e6 + 4.86518e6i 1.17785 + 1.17785i 0.980291 + 0.197559i \(0.0633014\pi\)
0.197559 + 0.980291i \(0.436699\pi\)
\(444\) −4.70406e6 1.52946e6i −1.13244 0.368198i
\(445\) 2.76869e6 2.31781e6i 0.662787 0.554853i
\(446\) 1.30565e6i 0.310806i
\(447\) −169763. 333341.i −0.0401860 0.0789078i
\(448\) −5.49949e6 + 5.49949e6i −1.29458 + 1.29458i
\(449\) −2.48941e6 −0.582747 −0.291374 0.956609i \(-0.594112\pi\)
−0.291374 + 0.956609i \(0.594112\pi\)
\(450\) −6.22960e6 125449.i −1.45020 0.0292037i
\(451\) −2.36944e6 −0.548535
\(452\) 6.02337e6 6.02337e6i 1.38674 1.38674i
\(453\) 2.54597e6 + 4.99918e6i 0.582919 + 1.14460i
\(454\) 6.88024e6i 1.56662i
\(455\) −388415. + 325162.i −0.0879564 + 0.0736328i
\(456\) −326573. 106181.i −0.0735475 0.0239130i
\(457\) 1.59204e6 + 1.59204e6i 0.356586 + 0.356586i 0.862553 0.505967i \(-0.168864\pi\)
−0.505967 + 0.862553i \(0.668864\pi\)
\(458\) −391667. 391667.i −0.0872476 0.0872476i
\(459\) −2.12284e6 + 1.54042e6i −0.470311 + 0.341277i
\(460\) 33709.5 380290.i 0.00742775 0.0837953i
\(461\) 5.78760e6i 1.26837i −0.773181 0.634185i \(-0.781336\pi\)
0.773181 0.634185i \(-0.218664\pi\)
\(462\) −3.71591e6 + 1.89243e6i −0.809955 + 0.412492i
\(463\) 1.53846e6 1.53846e6i 0.333530 0.333530i −0.520395 0.853925i \(-0.674215\pi\)
0.853925 + 0.520395i \(0.174215\pi\)
\(464\) 3.70937e6 0.799844
\(465\) 4.15993e6 + 1.77237e6i 0.892182 + 0.380122i
\(466\) 5.10947e6 1.08996
\(467\) 212015. 212015.i 0.0449858 0.0449858i −0.684256 0.729242i \(-0.739873\pi\)
0.729242 + 0.684256i \(0.239873\pi\)
\(468\) 387148. 61162.1i 0.0817076 0.0129083i
\(469\) 2.09966e6i 0.440776i
\(470\) 1.88534e6 + 2.25209e6i 0.393681 + 0.470263i
\(471\) −2.11378e6 + 6.50119e6i −0.439043 + 1.35033i
\(472\) 116088. + 116088.i 0.0239846 + 0.0239846i
\(473\) −2.48194e6 2.48194e6i −0.510080 0.510080i
\(474\) 1.79297e6 5.51450e6i 0.366544 1.12735i
\(475\) −2.48309e6 443697.i −0.504962 0.0902303i
\(476\) 4.85436e6i 0.982007i
\(477\) −197730. + 31237.5i −0.0397902 + 0.00628609i
\(478\) 8.46342e6 8.46342e6i 1.69424 1.69424i
\(479\) 8.47895e6 1.68851 0.844254 0.535943i \(-0.180044\pi\)
0.844254 + 0.535943i \(0.180044\pi\)
\(480\) 6.71897e6 2.70417e6i 1.33107 0.535711i
\(481\) 410131. 0.0808277
\(482\) −1.45176e6 + 1.45176e6i −0.284628 + 0.284628i
\(483\) −532958. + 271424.i −0.103950 + 0.0529395i
\(484\) 4.73598e6i 0.918959i
\(485\) −1.21244e6 107473.i −0.234049 0.0207465i
\(486\) 7429.91 7.55279e6i 0.00142690 1.45050i
\(487\) −1.08517e6 1.08517e6i −0.207336 0.207336i 0.595798 0.803134i \(-0.296836\pi\)
−0.803134 + 0.595798i \(0.796836\pi\)
\(488\) −374502. 374502.i −0.0711877 0.0711877i
\(489\) −3.15705e6 1.02648e6i −0.597048 0.194123i
\(490\) −1.03164e7 914461.i −1.94105 0.172058i
\(491\) 7.95104e6i 1.48840i 0.667956 + 0.744201i \(0.267170\pi\)
−0.667956 + 0.744201i \(0.732830\pi\)
\(492\) 3.60454e6 + 7.07776e6i 0.671332 + 1.31820i
\(493\) −2.00346e6 + 2.00346e6i −0.371247 + 0.371247i
\(494\) 302404. 0.0557532
\(495\) 2.22634e6 152242.i 0.408394 0.0279267i
\(496\) −4.70379e6 −0.858506
\(497\) −1.25900e6 + 1.25900e6i −0.228631 + 0.228631i
\(498\) −3.88349e6 7.62548e6i −0.701695 1.37782i
\(499\) 5.32202e6i 0.956809i 0.878140 + 0.478405i \(0.158785\pi\)
−0.878140 + 0.478405i \(0.841215\pi\)
\(500\) −5.35499e6 + 3.06725e6i −0.957930 + 0.548686i
\(501\) 7.62625e6 + 2.47958e6i 1.35743 + 0.441350i
\(502\) −9.28663e6 9.28663e6i −1.64475 1.64475i
\(503\) −6.37826e6 6.37826e6i −1.12404 1.12404i −0.991128 0.132913i \(-0.957567\pi\)
−0.132913 0.991128i \(-0.542433\pi\)
\(504\) 1.06449e6 + 774039.i 0.186667 + 0.135733i
\(505\) −459506. 548891.i −0.0801793 0.0957763i
\(506\) 260590.i 0.0452462i
\(507\) 5.12860e6 2.61188e6i 0.886092 0.451267i
\(508\) 4.97466e6 4.97466e6i 0.855271 0.855271i
\(509\) −5.79647e6 −0.991675 −0.495838 0.868415i \(-0.665139\pi\)
−0.495838 + 0.868415i \(0.665139\pi\)
\(510\) −1.94058e6 + 4.55472e6i −0.330374 + 0.775419i
\(511\) 1.16159e7 1.96788
\(512\) −5.88735e6 + 5.88735e6i −0.992533 + 0.992533i
\(513\) 480093. 3.01965e6i 0.0805437 0.506597i
\(514\) 1.25025e7i 2.08732i
\(515\) 546596. 6.16636e6i 0.0908131 1.02450i
\(516\) −3.63812e6 + 1.11895e7i −0.601523 + 1.85006i
\(517\) −743801. 743801.i −0.122386 0.122386i
\(518\) 1.03429e7 + 1.03429e7i 1.69363 + 1.69363i
\(519\) −549447. + 1.68989e6i −0.0895381 + 0.275386i
\(520\) 53413.8 44715.5i 0.00866254 0.00725187i
\(521\) 4.91868e6i 0.793880i −0.917845 0.396940i \(-0.870072\pi\)
0.917845 0.396940i \(-0.129928\pi\)
\(522\) −1.27316e6 8.05892e6i −0.204506 1.29450i
\(523\) −5.31998e6 + 5.31998e6i −0.850463 + 0.850463i −0.990190 0.139727i \(-0.955378\pi\)
0.139727 + 0.990190i \(0.455378\pi\)
\(524\) 3.43664e6 0.546772
\(525\) 8.52482e6 + 4.55993e6i 1.34985 + 0.722038i
\(526\) −742972. −0.117087
\(527\) 2.54055e6 2.54055e6i 0.398475 0.398475i
\(528\) −2.06857e6 + 1.05347e6i −0.322912 + 0.164452i
\(529\) 6.39897e6i 0.994193i
\(530\) −289738. + 242555.i −0.0448039 + 0.0375077i
\(531\) −859671. + 1.18226e6i −0.132311 + 0.181960i
\(532\) 4.00149e6 + 4.00149e6i 0.612974 + 0.612974i
\(533\) −465677. 465677.i −0.0710014 0.0710014i
\(534\) 7.85691e6 + 2.55458e6i 1.19234 + 0.387673i
\(535\) −800854. + 9.03474e6i −0.120968 + 1.36468i
\(536\) 288740.i 0.0434106i
\(537\) −2.88466e6 5.66421e6i −0.431676 0.847625i
\(538\) 52178.4 52178.4i 0.00777204 0.00777204i
\(539\) 3.70923e6 0.549936
\(540\) −3.84161e6 6.41871e6i −0.566930 0.947247i
\(541\) −399832. −0.0587334 −0.0293667 0.999569i \(-0.509349\pi\)
−0.0293667 + 0.999569i \(0.509349\pi\)
\(542\) −9.59679e6 + 9.59679e6i −1.40323 + 1.40323i
\(543\) −1.62599e6 3.19273e6i −0.236656 0.464690i
\(544\) 5.75490e6i 0.833759i
\(545\) −3.12917e6 3.73788e6i −0.451272 0.539056i
\(546\) −1.10223e6 358377.i −0.158231 0.0514469i
\(547\) 482360. + 482360.i 0.0689291 + 0.0689291i 0.740731 0.671802i \(-0.234479\pi\)
−0.671802 + 0.740731i \(0.734479\pi\)
\(548\) −4.18570e6 4.18570e6i −0.595410 0.595410i
\(549\) 2.77331e6 3.81398e6i 0.392706 0.540067i
\(550\) 3.45600e6 2.40815e6i 0.487155 0.339451i
\(551\) 3.30293e6i 0.463469i
\(552\) 73291.0 37325.5i 0.0102377 0.00521384i
\(553\) −6.36194e6 + 6.36194e6i −0.884661 + 0.884661i
\(554\) 8.43086e6 1.16707
\(555\) −2.92250e6 7.26146e6i −0.402737 1.00067i
\(556\) 768350. 0.105408
\(557\) −4.37833e6 + 4.37833e6i −0.597958 + 0.597958i −0.939769 0.341811i \(-0.888960\pi\)
0.341811 + 0.939769i \(0.388960\pi\)
\(558\) 1.61447e6 + 1.02194e7i 0.219505 + 1.38944i
\(559\) 975574.i 0.132048i
\(560\) −1.00177e7 887981.i −1.34988 0.119656i
\(561\) 548259. 1.68624e6i 0.0735493 0.226210i
\(562\) 1.33048e7 + 1.33048e7i 1.77691 + 1.77691i
\(563\) 2.52905e6 + 2.52905e6i 0.336269 + 0.336269i 0.854961 0.518692i \(-0.173581\pi\)
−0.518692 + 0.854961i \(0.673581\pi\)
\(564\) −1.09029e6 + 3.35333e6i −0.144326 + 0.443893i
\(565\) 1.34272e7 + 1.19020e6i 1.76955 + 0.156856i
\(566\) 6.53024e6i 0.856817i
\(567\) −5.32846e6 + 1.04374e7i −0.696056 + 1.36343i
\(568\) 173135. 173135.i 0.0225172 0.0225172i
\(569\) 2.05551e6 0.266157 0.133079 0.991105i \(-0.457514\pi\)
0.133079 + 0.991105i \(0.457514\pi\)
\(570\) −2.15486e6 5.35412e6i −0.277800 0.690242i
\(571\) −3.77699e6 −0.484792 −0.242396 0.970177i \(-0.577933\pi\)
−0.242396 + 0.970177i \(0.577933\pi\)
\(572\) −187362. + 187362.i −0.0239438 + 0.0239438i
\(573\) 5.89425e6 3.00181e6i 0.749967 0.381941i
\(574\) 2.34875e7i 2.97548i
\(575\) 495680. 345391.i 0.0625219 0.0435654i
\(576\) 7.70202e6 + 5.60048e6i 0.967272 + 0.703346i
\(577\) −4.37044e6 4.37044e6i −0.546494 0.546494i 0.378931 0.925425i \(-0.376292\pi\)
−0.925425 + 0.378931i \(0.876292\pi\)
\(578\) −5.45633e6 5.45633e6i −0.679331 0.679331i
\(579\) −1.15535e7 3.75646e6i −1.43224 0.465675i
\(580\) −5.18713e6 6.19617e6i −0.640262 0.764810i
\(581\) 1.32776e7i 1.63185i
\(582\) −1.26389e6 2.48173e6i −0.154668 0.303702i
\(583\) 95692.3 95692.3i 0.0116602 0.0116602i
\(584\) −1.59739e6 −0.193811
\(585\) 467474. + 407633.i 0.0564765 + 0.0492470i
\(586\) −1.34334e7 −1.61600
\(587\) −9213.49 + 9213.49i −0.00110364 + 0.00110364i −0.707658 0.706555i \(-0.750248\pi\)
0.706555 + 0.707658i \(0.250248\pi\)
\(588\) −5.64272e6 1.10798e7i −0.673046 1.32157i
\(589\) 4.18839e6i 0.497461i
\(590\) −243628. + 2.74846e6i −0.0288136 + 0.325057i
\(591\) −1.14199e6 371304.i −0.134491 0.0437281i
\(592\) 5.75769e6 + 5.75769e6i 0.675218 + 0.675218i
\(593\) 8.46827e6 + 8.46827e6i 0.988913 + 0.988913i 0.999939 0.0110261i \(-0.00350978\pi\)
−0.0110261 + 0.999939i \(0.503510\pi\)
\(594\) 2.99875e6 + 4.13256e6i 0.348718 + 0.480566i
\(595\) 5.89022e6 4.93101e6i 0.682086 0.571010i
\(596\) 847729.i 0.0977556i
\(597\) 1.18976e7 6.05916e6i 1.36622 0.695787i
\(598\) −51215.0 + 51215.0i −0.00585659 + 0.00585659i
\(599\) 73180.9 0.00833356 0.00416678 0.999991i \(-0.498674\pi\)
0.00416678 + 0.999991i \(0.498674\pi\)
\(600\) −1.17231e6 627071.i −0.132943 0.0711113i
\(601\) 1.00986e6 0.114045 0.0570223 0.998373i \(-0.481839\pi\)
0.0570223 + 0.998373i \(0.481839\pi\)
\(602\) 2.46026e7 2.46026e7i 2.76688 2.76688i
\(603\) −2.53940e6 + 401176.i −0.284405 + 0.0449306i
\(604\) 1.27136e7i 1.41800i
\(605\) 5.74657e6 4.81076e6i 0.638294 0.534349i
\(606\) 506444. 1.55763e6i 0.0560208 0.172299i
\(607\) −7.94420e6 7.94420e6i −0.875142 0.875142i 0.117885 0.993027i \(-0.462389\pi\)
−0.993027 + 0.117885i \(0.962389\pi\)
\(608\) 4.74381e6 + 4.74381e6i 0.520437 + 0.520437i
\(609\) −3.91429e6 + 1.20389e7i −0.427671 + 1.31535i
\(610\) 785948. 8.86658e6i 0.0855203 0.964787i
\(611\) 292365.i 0.0316828i
\(612\) −5.87101e6 + 927509.i −0.633628 + 0.100101i
\(613\) −6.97272e6 + 6.97272e6i −0.749465 + 0.749465i −0.974379 0.224914i \(-0.927790\pi\)
0.224914 + 0.974379i \(0.427790\pi\)
\(614\) −7.50027e6 −0.802890
\(615\) −4.92660e6 + 1.15632e7i −0.525242 + 1.23280i
\(616\) −889768. −0.0944768
\(617\) −6.05476e6 + 6.05476e6i −0.640301 + 0.640301i −0.950629 0.310329i \(-0.899561\pi\)
0.310329 + 0.950629i \(0.399561\pi\)
\(618\) 1.26218e7 6.42802e6i 1.32939 0.677027i
\(619\) 1.16405e7i 1.22108i −0.791986 0.610539i \(-0.790953\pi\)
0.791986 0.610539i \(-0.209047\pi\)
\(620\) 6.57772e6 + 7.85725e6i 0.687220 + 0.820903i
\(621\) 430098. + 592715.i 0.0447547 + 0.0616761i
\(622\) 1.02368e7 + 1.02368e7i 1.06093 + 1.06093i
\(623\) −9.06434e6 9.06434e6i −0.935655 0.935655i
\(624\) −613589. 199501.i −0.0630836 0.0205108i
\(625\) −9.16130e6 3.38200e6i −0.938118 0.346317i
\(626\) 6.52427e6i 0.665420i
\(627\) 938045. + 1.84191e6i 0.0952916 + 0.187111i
\(628\) −1.09545e7 + 1.09545e7i −1.10839 + 1.10839i
\(629\) −6.21954e6 −0.626804
\(630\) 1.50912e6 + 2.20690e7i 0.151486 + 2.21529i
\(631\) −8.66671e6 −0.866524 −0.433262 0.901268i \(-0.642638\pi\)
−0.433262 + 0.901268i \(0.642638\pi\)
\(632\) 874879. 874879.i 0.0871275 0.0871275i
\(633\) 2.23712e6 + 4.39274e6i 0.221912 + 0.435738i
\(634\) 2.05268e7i 2.02814i
\(635\) 1.10894e7 + 982981.i 1.09137 + 0.0967410i
\(636\) −431416. 140269.i −0.0422915 0.0137505i
\(637\) 728992. + 728992.i 0.0711827 + 0.0711827i
\(638\) 3.90016e6 + 3.90016e6i 0.379342 + 0.379342i
\(639\) 1.76323e6 + 1.28212e6i 0.170827 + 0.124216i
\(640\) 3.09552e6 + 274392.i 0.298733 + 0.0264802i
\(641\) 1.07773e7i 1.03601i 0.855377 + 0.518006i \(0.173326\pi\)
−0.855377 + 0.518006i \(0.826674\pi\)
\(642\) −1.84931e7 + 9.41812e6i −1.77081 + 0.901834i
\(643\) 1.37197e7 1.37197e7i 1.30864 1.30864i 0.386234 0.922401i \(-0.373776\pi\)
0.922401 0.386234i \(-0.126224\pi\)
\(644\) −1.35538e6 −0.128779
\(645\) −1.72727e7 + 6.95171e6i −1.63479 + 0.657949i
\(646\) −4.58589e6 −0.432356
\(647\) 724759. 724759.i 0.0680664 0.0680664i −0.672254 0.740321i \(-0.734674\pi\)
0.740321 + 0.672254i \(0.234674\pi\)
\(648\) 732757. 1.43532e6i 0.0685524 0.134280i
\(649\) 988203.i 0.0920946i
\(650\) 1.15251e6 + 205939.i 0.106994 + 0.0191185i
\(651\) 4.96364e6 1.52663e7i 0.459037 1.41183i
\(652\) −5.31963e6 5.31963e6i −0.490074 0.490074i
\(653\) −1.39175e7 1.39175e7i −1.27726 1.27726i −0.942197 0.335060i \(-0.891243\pi\)
−0.335060 0.942197i \(-0.608757\pi\)
\(654\) 3.44881e6 1.06073e7i 0.315301 0.969748i
\(655\) 3.49091e6 + 4.16998e6i 0.317932 + 0.379779i
\(656\) 1.30750e7i 1.18626i
\(657\) −2.21941e6 1.40486e7i −0.200597 1.26975i
\(658\) 7.37305e6 7.37305e6i 0.663869 0.663869i
\(659\) 1.09373e7 0.981064 0.490532 0.871423i \(-0.336803\pi\)
0.490532 + 0.871423i \(0.336803\pi\)
\(660\) 4.65239e6 + 1.98219e6i 0.415735 + 0.177127i
\(661\) 1.75257e7 1.56017 0.780086 0.625672i \(-0.215175\pi\)
0.780086 + 0.625672i \(0.215175\pi\)
\(662\) −4.19521e6 + 4.19521e6i −0.372057 + 0.372057i
\(663\) 439156. 223652.i 0.0388003 0.0197601i
\(664\) 1.82591e6i 0.160716i
\(665\) −790685. + 8.92002e6i −0.0693345 + 0.782189i
\(666\) 1.05329e7 1.44853e7i 0.920155 1.26544i
\(667\) 559384. + 559384.i 0.0486850 + 0.0486850i
\(668\) 1.28502e7 + 1.28502e7i 1.11422 + 1.11422i
\(669\) −2.35893e6 766977.i −0.203775 0.0662548i
\(670\) −3.72104e6 + 3.11508e6i −0.320241 + 0.268091i
\(671\) 3.18796e6i 0.273342i
\(672\) −1.16689e7 2.29126e7i −0.996795 1.95727i
\(673\) −6.38592e6 + 6.38592e6i −0.543483 + 0.543483i −0.924548 0.381065i \(-0.875557\pi\)
0.381065 + 0.924548i \(0.375557\pi\)
\(674\) −2.89926e7 −2.45831
\(675\) 3.88611e6 1.11814e7i 0.328288 0.944578i
\(676\) 1.30427e7 1.09774
\(677\) 9.27369e6 9.27369e6i 0.777644 0.777644i −0.201785 0.979430i \(-0.564674\pi\)
0.979430 + 0.201785i \(0.0646743\pi\)
\(678\) 1.39969e7 + 2.74839e7i 1.16939 + 2.29617i
\(679\) 4.32123e6i 0.359694i
\(680\) −810009. + 678100.i −0.0671765 + 0.0562369i
\(681\) −1.24306e7 4.04167e6i −1.02713 0.333959i
\(682\) −4.94572e6 4.94572e6i −0.407164 0.407164i
\(683\) 5.35197e6 + 5.35197e6i 0.438997 + 0.438997i 0.891674 0.452677i \(-0.149531\pi\)
−0.452677 + 0.891674i \(0.649531\pi\)
\(684\) 4.07496e6 5.60407e6i 0.333030 0.457998i
\(685\) 827084. 9.33065e6i 0.0673478 0.759776i
\(686\) 9.39965e6i 0.762608i
\(687\) 937709. 477554.i 0.0758012 0.0386039i
\(688\) 1.36957e7 1.36957e7i 1.10310 1.10310i
\(689\) 37613.7 0.00301855
\(690\) 1.27172e6 + 541826.i 0.101688 + 0.0433249i
\(691\) 3.50149e6 0.278970 0.139485 0.990224i \(-0.455455\pi\)
0.139485 + 0.990224i \(0.455455\pi\)
\(692\) −2.84747e6 + 2.84747e6i −0.226044 + 0.226044i
\(693\) −1.23625e6 7.82527e6i −0.0977848 0.618965i
\(694\) 1.60237e7i 1.26289i
\(695\) 780481. + 932305.i 0.0612915 + 0.0732143i
\(696\) 538283. 1.65556e6i 0.0421199 0.129545i
\(697\) 7.06189e6 + 7.06189e6i 0.550603 + 0.550603i
\(698\) −1.91824e7 1.91824e7i −1.49027 1.49027i
\(699\) −3.00146e6 + 9.23136e6i −0.232348 + 0.714616i
\(700\) 1.25253e7 + 1.79753e7i 0.966144 + 1.38654i
\(701\) 6.92867e6i 0.532543i 0.963898 + 0.266271i \(0.0857918\pi\)
−0.963898 + 0.266271i \(0.914208\pi\)
\(702\) −222832. + 1.40155e6i −0.0170661 + 0.107341i
\(703\) 5.12682e6 5.12682e6i 0.391255 0.391255i
\(704\) −6.43782e6 −0.489561
\(705\) −5.17639e6 + 2.08333e6i −0.392242 + 0.157865i
\(706\) −2.75270e7 −2.07848
\(707\) −1.79700e6 + 1.79700e6i −0.135207 + 0.135207i
\(708\) −2.95186e6 + 1.50332e6i −0.221316 + 0.112711i
\(709\) 1.88400e7i 1.40755i 0.710422 + 0.703776i \(0.248504\pi\)
−0.710422 + 0.703776i \(0.751496\pi\)
\(710\) 4.09908e6 + 363349.i 0.305169 + 0.0270507i
\(711\) 8.90988e6 + 6.47877e6i 0.660995 + 0.480638i
\(712\) 1.24651e6 + 1.24651e6i 0.0921497 + 0.0921497i
\(713\) −709345. 709345.i −0.0522557 0.0522557i
\(714\) 1.67151e7 + 5.43471e6i 1.22706 + 0.398961i
\(715\) −417664. 37022.4i −0.0305536 0.00270832i
\(716\) 1.44048e7i 1.05009i
\(717\) 1.03193e7 + 2.02627e7i 0.749641 + 1.47197i
\(718\) −2.38075e7 + 2.38075e7i −1.72347 + 1.72347i
\(719\) −2.47186e7 −1.78321 −0.891603 0.452818i \(-0.850419\pi\)
−0.891603 + 0.452818i \(0.850419\pi\)
\(720\) 840094. + 1.22853e7i 0.0603944 + 0.883192i
\(721\) −2.19774e7 −1.57448
\(722\) −1.05861e7 + 1.05861e7i −0.755777 + 0.755777i
\(723\) −1.77011e6 3.47572e6i −0.125937 0.247286i
\(724\) 8.11954e6i 0.575685i
\(725\) 2.24932e6 1.25880e7i 0.158930 0.889430i
\(726\) 1.63075e7 + 5.30217e6i 1.14827 + 0.373347i
\(727\) 3.10947e6 + 3.10947e6i 0.218198 + 0.218198i 0.807738 0.589541i \(-0.200691\pi\)
−0.589541 + 0.807738i \(0.700691\pi\)
\(728\) −174870. 174870.i −0.0122289 0.0122289i
\(729\) 1.36414e7 + 4.45016e6i 0.950691 + 0.310139i
\(730\) −1.72334e7 2.05857e7i −1.19692 1.42975i
\(731\) 1.47944e7i 1.02401i
\(732\) 9.52275e6 4.84972e6i 0.656878 0.334533i
\(733\) −2.33294e6 + 2.33294e6i −0.160377 + 0.160377i −0.782734 0.622356i \(-0.786175\pi\)
0.622356 + 0.782734i \(0.286175\pi\)
\(734\) 2.57853e7 1.76657
\(735\) 7.71233e6 1.81016e7i 0.526583 1.23594i
\(736\) −1.60682e6 −0.109338
\(737\) 1.22895e6 1.22895e6i 0.0833426 0.0833426i
\(738\) −2.84065e7 + 4.48768e6i −1.91989 + 0.303306i
\(739\) 1.73637e7i 1.16959i −0.811183 0.584793i \(-0.801176\pi\)
0.811183 0.584793i \(-0.198824\pi\)
\(740\) 1.56622e6 1.76692e7i 0.105142 1.18614i
\(741\) −177641. + 546358.i −0.0118850 + 0.0365537i
\(742\) 948566. + 948566.i 0.0632496 + 0.0632496i
\(743\) 1.00487e7 + 1.00487e7i 0.667784 + 0.667784i 0.957203 0.289419i \(-0.0934619\pi\)
−0.289419 + 0.957203i \(0.593462\pi\)
\(744\) −682587. + 2.09938e6i −0.0452091 + 0.139046i
\(745\) 1.02862e6 861114.i 0.0678994 0.0568421i
\(746\) 3.22214e7i 2.11981i
\(747\) 1.60584e7 2.53692e6i 1.05293 0.166343i
\(748\) 2.84131e6 2.84131e6i 0.185680 0.185680i
\(749\) 3.22005e7 2.09729
\(750\) −4.56633e6 2.18729e7i −0.296425 1.41989i
\(751\) 8.25367e6 0.534007 0.267004 0.963696i \(-0.413966\pi\)
0.267004 + 0.963696i \(0.413966\pi\)
\(752\) 4.10442e6 4.10442e6i 0.264671 0.264671i
\(753\) 2.22336e7 1.13231e7i 1.42896 0.727740i
\(754\) 1.53303e6i 0.0982026i
\(755\) −1.54265e7 + 1.29143e7i −0.984917 + 0.824525i
\(756\) −2.14942e7 + 1.55971e7i −1.36778 + 0.992520i
\(757\) 1.88926e7 + 1.88926e7i 1.19826 + 1.19826i 0.974687 + 0.223576i \(0.0717730\pi\)
0.223576 + 0.974687i \(0.428227\pi\)
\(758\) −1.21848e7 1.21848e7i −0.770272 0.770272i
\(759\) −470813. 153079.i −0.0296650 0.00964518i
\(760\) 108733. 1.22666e6i 0.00682853 0.0770353i
\(761\) 1.13709e7i 0.711757i −0.934532 0.355878i \(-0.884182\pi\)
0.934532 0.355878i \(-0.115818\pi\)
\(762\) 1.15599e7 + 2.26987e7i 0.721221 + 1.41617i
\(763\) −1.22373e7 + 1.22373e7i −0.760984 + 0.760984i
\(764\) 1.49898e7 0.929103
\(765\) −7.08914e6 6.18166e6i −0.437965 0.381901i
\(766\) 2.39935e7 1.47748
\(767\) 194216. 194216.i 0.0119206 0.0119206i
\(768\) −5.64463e6 1.10836e7i −0.345329 0.678075i
\(769\) 1.69819e7i 1.03555i −0.855517 0.517774i \(-0.826761\pi\)
0.855517 0.517774i \(-0.173239\pi\)
\(770\) −9.59926e6 1.14666e7i −0.583460 0.696958i
\(771\) −2.25884e7 7.34434e6i −1.36852 0.444956i
\(772\) −1.94676e7 1.94676e7i −1.17562 1.17562i
\(773\) 7.99621e6 + 7.99621e6i 0.481321 + 0.481321i 0.905554 0.424232i \(-0.139456\pi\)
−0.424232 + 0.905554i \(0.639456\pi\)
\(774\) −3.44559e7 2.50544e7i −2.06734 1.50325i
\(775\) −2.85232e6 + 1.59626e7i −0.170586 + 0.954663i
\(776\) 594245.i 0.0354251i
\(777\) −2.47625e7 + 1.26110e7i −1.47144 + 0.749371i
\(778\) 2.02843e7 2.02843e7i 1.20147 1.20147i
\(779\) −1.16423e7 −0.687379
\(780\) 524787. + 1.30393e6i 0.0308849 + 0.0767390i
\(781\) −1.47382e6 −0.0864601
\(782\) 776664. 776664.i 0.0454168 0.0454168i
\(783\) 1.53081e7 + 2.43382e6i 0.892311 + 0.141868i
\(784\) 2.04681e7i 1.18929i
\(785\) −2.44195e7 2.16458e6i −1.41437 0.125372i
\(786\) −3.84750e6 + 1.18335e7i −0.222138 + 0.683212i
\(787\) −1.65733e7 1.65733e7i −0.953833 0.953833i 0.0451470 0.998980i \(-0.485624\pi\)
−0.998980 + 0.0451470i \(0.985624\pi\)
\(788\) −1.92425e6 1.92425e6i −0.110394 0.110394i
\(789\) 436445. 1.34234e6i 0.0249596 0.0767662i
\(790\) 2.07133e7 + 1.83606e6i 1.18082 + 0.104669i
\(791\) 4.78554e7i 2.71951i
\(792\) 170005. + 1.07611e6i 0.00963052 + 0.0609599i
\(793\) −626544. + 626544.i −0.0353809 + 0.0353809i
\(794\) 2.10582e7 1.18541
\(795\) −268027. 665959.i −0.0150404 0.0373705i
\(796\) 3.02570e7 1.69256
\(797\) −6.61994e6 + 6.61994e6i −0.369154 + 0.369154i −0.867169 0.498014i \(-0.834063\pi\)
0.498014 + 0.867169i \(0.334063\pi\)
\(798\) −1.82583e7 + 9.29853e6i −1.01497 + 0.516901i
\(799\) 4.43365e6i 0.245694i
\(800\) 1.48489e7 + 2.13100e7i 0.820291 + 1.17722i
\(801\) −9.23078e6 + 1.26946e7i −0.508344 + 0.699096i
\(802\) 1.21516e6 + 1.21516e6i 0.0667112 + 0.0667112i
\(803\) 6.79889e6 + 6.79889e6i 0.372091 + 0.372091i
\(804\) −5.54057e6 1.80145e6i −0.302284 0.0982837i
\(805\) −1.37678e6 1.64460e6i −0.0748816 0.0894481i
\(806\) 1.94401e6i 0.105405i
\(807\) 63620.3 + 124923.i 0.00343884 + 0.00675239i
\(808\) 247119. 247119.i 0.0133161 0.0133161i
\(809\) 1.97653e7 1.06177 0.530887 0.847442i \(-0.321859\pi\)
0.530887 + 0.847442i \(0.321859\pi\)
\(810\) 2.64026e7 6.04183e6i 1.41395 0.323561i
\(811\) 1.15246e7 0.615281 0.307641 0.951503i \(-0.400461\pi\)
0.307641 + 0.951503i \(0.400461\pi\)
\(812\) −2.02855e7 + 2.02855e7i −1.07968 + 1.07968i
\(813\) −1.17012e7 2.29761e7i −0.620876 1.21913i
\(814\) 1.21077e7i 0.640471i
\(815\) 1.05115e6 1.18584e7i 0.0554331 0.625362i
\(816\) 9.30494e6 + 3.02538e6i 0.489202 + 0.159058i
\(817\) −1.21951e7 1.21951e7i −0.639190 0.639190i
\(818\) 2.10680e7 + 2.10680e7i 1.10088 + 1.10088i
\(819\) 1.29497e6 1.78090e6i 0.0674607 0.0927749i
\(820\) −2.18405e7 + 1.82839e7i −1.13430 + 0.949583i
\(821\) 1.02322e7i 0.529800i −0.964276 0.264900i \(-0.914661\pi\)
0.964276 0.264900i \(-0.0853390\pi\)
\(822\) 1.90988e7 9.72659e6i 0.985885 0.502089i
\(823\) −8.91119e6 + 8.91119e6i −0.458602 + 0.458602i −0.898196 0.439594i \(-0.855122\pi\)
0.439594 + 0.898196i \(0.355122\pi\)
\(824\) 3.02227e6 0.155066
\(825\) 2.32069e6 + 7.65864e6i 0.118708 + 0.391757i
\(826\) 9.79573e6 0.499559
\(827\) 7.85039e6 7.85039e6i 0.399142 0.399142i −0.478788 0.877930i \(-0.658924\pi\)
0.877930 + 0.478788i \(0.158924\pi\)
\(828\) 258969. + 1.63924e6i 0.0131272 + 0.0830934i
\(829\) 1.28382e7i 0.648813i −0.945918 0.324406i \(-0.894835\pi\)
0.945918 0.324406i \(-0.105165\pi\)
\(830\) 2.35307e7 1.96988e7i 1.18560 0.992531i
\(831\) −4.95254e6 + 1.52322e7i −0.248786 + 0.765172i
\(832\) −1.26525e6 1.26525e6i −0.0633680 0.0633680i
\(833\) −1.10550e7 1.10550e7i −0.552009 0.552009i
\(834\) −860207. + 2.64567e6i −0.0428241 + 0.131711i
\(835\) −2.53917e6 + 2.86454e7i −0.126031 + 1.42180i
\(836\) 4.68422e6i 0.231804i
\(837\) −1.94119e7 3.08629e6i −0.957755 0.152273i
\(838\) 1.14376e6 1.14376e6i 0.0562634 0.0562634i
\(839\) −1.15260e7 −0.565294 −0.282647 0.959224i \(-0.591212\pi\)
−0.282647 + 0.959224i \(0.591212\pi\)
\(840\) −1.85003e6 + 4.34220e6i −0.0904649 + 0.212330i
\(841\) −3.76698e6 −0.183655
\(842\) 1.83387e7 1.83387e7i 0.891431 0.891431i
\(843\) −3.18535e7 + 1.62223e7i −1.54379 + 0.786219i
\(844\) 1.11713e7i 0.539818i
\(845\) 1.32486e7 + 1.58258e7i 0.638307 + 0.762474i
\(846\) −1.03259e7 7.50845e6i −0.496025 0.360682i
\(847\) −1.88136e7 1.88136e7i −0.901078 0.901078i
\(848\) 528046. + 528046.i 0.0252163 + 0.0252163i
\(849\) 1.17983e7 + 3.83607e6i 0.561759 + 0.182649i
\(850\) −1.74776e7 3.12301e6i −0.829723 0.148261i
\(851\) 1.73655e6i 0.0821985i
\(852\) 2.24206e6 + 4.40244e6i 0.105815 + 0.207775i
\(853\) 1.36182e7 1.36182e7i 0.640837 0.640837i −0.309924 0.950761i \(-0.600304\pi\)
0.950761 + 0.309924i \(0.100304\pi\)
\(854\) −3.16012e7 −1.48272
\(855\) 1.09392e7 748044.i 0.511765 0.0349955i
\(856\) −4.42813e6 −0.206555
\(857\) −2.00407e7 + 2.00407e7i −0.932095 + 0.932095i −0.997837 0.0657421i \(-0.979059\pi\)
0.0657421 + 0.997837i \(0.479059\pi\)
\(858\) −435387. 854911.i −0.0201910 0.0396463i
\(859\) 3.67165e7i 1.69777i 0.528581 + 0.848883i \(0.322724\pi\)
−0.528581 + 0.848883i \(0.677276\pi\)
\(860\) −4.20295e7 3.72556e6i −1.93779 0.171769i
\(861\) 4.24352e7 + 1.37973e7i 1.95083 + 0.634286i
\(862\) 437843. + 437843.i 0.0200701 + 0.0200701i
\(863\) 9.66370e6 + 9.66370e6i 0.441689 + 0.441689i 0.892579 0.450890i \(-0.148893\pi\)
−0.450890 + 0.892579i \(0.648893\pi\)
\(864\) −2.54816e7 + 1.84905e7i −1.16130 + 0.842684i
\(865\) −6.34751e6 562653.i −0.288445 0.0255682i
\(866\) 2.38931e7i 1.08263i
\(867\) 1.30633e7 6.65283e6i 0.590206 0.300579i
\(868\) 2.57237e7 2.57237e7i 1.15887 1.15887i
\(869\) −7.44742e6 −0.334547
\(870\) 2.71427e7 1.09240e7i 1.21578 0.489311i
\(871\) 483064. 0.0215754
\(872\) 1.68285e6 1.68285e6i 0.0749469 0.0749469i
\(873\) 5.22623e6 825646.i 0.232088 0.0366655i
\(874\) 1.28042e6i 0.0566988i
\(875\) −9.08801e6 + 3.34572e7i −0.401281 + 1.47730i
\(876\) 9.96606e6 3.06519e7i 0.438797 1.34957i
\(877\) 4.25969e6 + 4.25969e6i 0.187016 + 0.187016i 0.794405 0.607389i \(-0.207783\pi\)
−0.607389 + 0.794405i \(0.707783\pi\)
\(878\) −1.95824e6 1.95824e6i −0.0857295 0.0857295i
\(879\) 7.89117e6 2.42703e7i 0.344484 1.05950i
\(880\) −5.34369e6 6.38318e6i −0.232614 0.277863i
\(881\) 2.55098e7i 1.10731i −0.832747 0.553653i \(-0.813233\pi\)
0.832747 0.553653i \(-0.186767\pi\)
\(882\) 4.44688e7 7.02523e6i 1.92479 0.304081i
\(883\) 1.00886e7 1.00886e7i 0.435442 0.435442i −0.455033 0.890475i \(-0.650372\pi\)
0.890475 + 0.455033i \(0.150372\pi\)
\(884\) 1.11683e6 0.0480681
\(885\) −4.82258e6 2.05470e6i −0.206976 0.0881840i
\(886\) −5.64555e7 −2.41614
\(887\) 1.17625e7 1.17625e7i 0.501986 0.501986i −0.410069 0.912055i \(-0.634495\pi\)
0.912055 + 0.410069i \(0.134495\pi\)
\(888\) 3.40528e6 1.73423e6i 0.144917 0.0738032i
\(889\) 3.95234e7i 1.67726i
\(890\) −2.61597e6 + 2.95118e7i −0.110703 + 1.24888i
\(891\) −9.22791e6 + 2.99030e6i −0.389412 + 0.126189i
\(892\) −3.97480e6 3.97480e6i −0.167264 0.167264i
\(893\) −3.65469e6 3.65469e6i −0.153364 0.153364i
\(894\) 2.91900e6 + 949077.i 0.122149 + 0.0397153i
\(895\) 1.74786e7 1.46323e7i 0.729373 0.610596i
\(896\) 1.10327e7i 0.459103i
\(897\) −62445.8 122616.i −0.00259132 0.00508824i
\(898\) 1.44435e7 1.44435e7i 0.597698 0.597698i
\(899\) −2.12330e7 −0.876218
\(900\) 1.93468e7 1.85829e7i 0.796163 0.764730i
\(901\) −570403. −0.0234083
\(902\) 1.37475e7 1.37475e7i 0.562608 0.562608i
\(903\) 2.99976e7 + 5.89023e7i 1.22424 + 2.40388i
\(904\) 6.58096e6i 0.267835i
\(905\) 9.85214e6 8.24774e6i 0.399861 0.334745i
\(906\) −4.37769e7 1.42335e7i −1.77184 0.576091i
\(907\) −8.33201e6 8.33201e6i −0.336304 0.336304i 0.518670 0.854974i \(-0.326427\pi\)
−0.854974 + 0.518670i \(0.826427\pi\)
\(908\) −2.09456e7 2.09456e7i −0.843099 0.843099i
\(909\) 2.51670e6 + 1.83000e6i 0.101023 + 0.0734584i
\(910\) 366991. 4.14017e6i 0.0146910 0.165735i
\(911\) 2.83077e7i 1.13008i −0.825063 0.565040i \(-0.808861\pi\)
0.825063 0.565040i \(-0.191139\pi\)
\(912\) −1.01640e7 + 5.17628e6i −0.404647 + 0.206078i
\(913\) −7.77153e6 + 7.77153e6i −0.308553 + 0.308553i
\(914\) −1.84740e7 −0.731470
\(915\) 1.55577e7 + 6.62848e6i 0.614317 + 0.261735i
\(916\) 2.38471e6 0.0939069
\(917\) 1.36520e7 1.36520e7i 0.536133 0.536133i
\(918\) 3.37919e6 2.12542e7i 0.132345 0.832410i
\(919\) 2.04193e7i 0.797540i 0.917051 + 0.398770i \(0.130563\pi\)
−0.917051 + 0.398770i \(0.869437\pi\)
\(920\) 189332. + 226162.i 0.00737486 + 0.00880946i
\(921\) 4.40589e6 1.35509e7i 0.171153 0.526402i
\(922\) 3.35796e7 + 3.35796e7i 1.30091 + 1.30091i
\(923\) −289656. 289656.i −0.0111912 0.0111912i
\(924\) 5.55125e6 1.70736e7i 0.213900 0.657876i
\(925\) 2.30305e7 1.60477e7i 0.885012 0.616679i
\(926\) 1.78523e7i 0.684174i
\(927\) 4.19915e6 + 2.65801e7i 0.160495 + 1.01591i
\(928\) −2.40487e7 + 2.40487e7i −0.916687 + 0.916687i
\(929\) 1.41172e6 0.0536674 0.0268337 0.999640i \(-0.491458\pi\)
0.0268337 + 0.999640i \(0.491458\pi\)
\(930\) −3.44191e7 + 1.38526e7i −1.30495 + 0.525198i
\(931\) 1.82254e7 0.689134
\(932\) −1.55548e7 + 1.55548e7i −0.586577 + 0.586577i
\(933\) −2.45084e7 + 1.24816e7i −0.921743 + 0.469423i
\(934\) 2.46022e6i 0.0922798i
\(935\) 6.33378e6 + 561436.i 0.236938 + 0.0210025i
\(936\) −178081. + 244905.i −0.00664399 + 0.00913710i
\(937\) 2.41503e7 + 2.41503e7i 0.898615 + 0.898615i 0.995314 0.0966989i \(-0.0308284\pi\)
−0.0966989 + 0.995314i \(0.530828\pi\)
\(938\) 1.21822e7 + 1.21822e7i 0.452084 + 0.452084i
\(939\) 1.17875e7 + 3.83255e6i 0.436272 + 0.141848i
\(940\) −1.25956e7 1.11650e6i −0.464943 0.0412133i
\(941\) 3.35812e7i 1.23629i 0.786063 + 0.618147i \(0.212116\pi\)
−0.786063 + 0.618147i \(0.787884\pi\)
\(942\) −2.54557e7 4.99839e7i −0.934669 1.83528i
\(943\) 1.97174e6 1.97174e6i 0.0722056 0.0722056i
\(944\) 5.45306e6 0.199164
\(945\) −4.07589e7 1.02375e7i −1.48471 0.372917i
\(946\) 2.88004e7 1.04633
\(947\) −1.34516e7 + 1.34516e7i −0.487413 + 0.487413i −0.907489 0.420076i \(-0.862004\pi\)
0.420076 + 0.907489i \(0.362004\pi\)
\(948\) 1.13295e7 + 2.22462e7i 0.409439 + 0.803961i
\(949\) 2.67243e6i 0.0963256i
\(950\) 1.69812e7 1.18325e7i 0.610463 0.425372i
\(951\) −3.70862e7 1.20581e7i −1.32972 0.432342i
\(952\) 2.65187e6 + 2.65187e6i 0.0948330 + 0.0948330i
\(953\) 1.40505e7 + 1.40505e7i 0.501139 + 0.501139i 0.911792 0.410653i \(-0.134699\pi\)
−0.410653 + 0.911792i \(0.634699\pi\)
\(954\) 965985. 1.32846e6i 0.0343637 0.0472584i
\(955\) 1.52265e7 + 1.81885e7i 0.540247 + 0.645339i
\(956\) 5.15306e7i 1.82356i
\(957\) −9.33755e6 + 4.75541e6i −0.329574 + 0.167845i
\(958\) −4.91948e7 + 4.91948e7i −1.73183 + 1.73183i
\(959\) −3.32552e7 −1.16765
\(960\) −1.33857e7 + 3.14175e7i −0.468773 + 1.10026i
\(961\) −1.70396e6 −0.0595183
\(962\) −2.37958e6 + 2.37958e6i −0.0829014 + 0.0829014i
\(963\) −6.15246e6 3.89443e7i −0.213788 1.35325i
\(964\) 8.83922e6i 0.306352i
\(965\) 3.84675e6 4.33967e7i 0.132977 1.50016i
\(966\) 1.51742e6 4.66701e6i 0.0523194 0.160915i
\(967\) 1.52842e6 + 1.52842e6i 0.0525624 + 0.0525624i 0.732899 0.680337i \(-0.238167\pi\)
−0.680337 + 0.732899i \(0.738167\pi\)
\(968\) 2.58719e6 + 2.58719e6i 0.0887444 + 0.0887444i
\(969\) 2.69389e6 8.28539e6i 0.0921659 0.283468i
\(970\) 7.65813e6 6.41102e6i 0.261332 0.218775i
\(971\) 4.66888e6i 0.158915i 0.996838 + 0.0794574i \(0.0253188\pi\)
−0.996838 + 0.0794574i \(0.974681\pi\)
\(972\) 2.29704e7 + 2.30157e7i 0.779836 + 0.781372i
\(973\) 3.05225e6 3.05225e6i 0.103357 0.103357i
\(974\) 1.25923e7 0.425311
\(975\) −1.04909e6 + 1.96128e6i −0.0353429 + 0.0660737i
\(976\) −1.75917e7 −0.591129
\(977\) 2.86346e7 2.86346e7i 0.959743 0.959743i −0.0394774 0.999220i \(-0.512569\pi\)
0.999220 + 0.0394774i \(0.0125693\pi\)
\(978\) 2.42728e7 1.23616e7i 0.811470 0.413263i
\(979\) 1.06109e7i 0.353831i
\(980\) 3.41902e7 2.86224e7i 1.13720 0.952008i
\(981\) 1.71384e7 + 1.24621e7i 0.568587 + 0.413444i
\(982\) −4.61318e7 4.61318e7i −1.52659 1.52659i
\(983\) −6.38514e6 6.38514e6i −0.210759 0.210759i 0.593831 0.804590i \(-0.297615\pi\)
−0.804590 + 0.593831i \(0.797615\pi\)
\(984\) −5.83558e6 1.89737e6i −0.192131 0.0624688i
\(985\) 380228. 4.28950e6i 0.0124869 0.140869i
\(986\) 2.32481e7i 0.761544i
\(987\) 8.98986e6 + 1.76522e7i 0.293738 + 0.576773i
\(988\) −920612. + 920612.i −0.0300044 + 0.0300044i
\(989\) 4.13071e6 0.134287
\(990\) −1.20339e7 + 1.38005e7i −0.390228 + 0.447515i
\(991\) −2.10467e6 −0.0680770 −0.0340385 0.999421i \(-0.510837\pi\)
−0.0340385 + 0.999421i \(0.510837\pi\)
\(992\) 3.04957e7 3.04957e7i 0.983919 0.983919i
\(993\) −5.11516e6 1.00440e7i −0.164621 0.323245i
\(994\) 1.46094e7i 0.468995i
\(995\) 3.07348e7 + 3.67135e7i 0.984175 + 1.17562i
\(996\) 3.50369e7 + 1.13918e7i 1.11912 + 0.363868i
\(997\) −2.12150e7 2.12150e7i −0.675936 0.675936i 0.283142 0.959078i \(-0.408623\pi\)
−0.959078 + 0.283142i \(0.908623\pi\)
\(998\) −3.08783e7 3.08783e7i −0.981357 0.981357i
\(999\) 1.99834e7 + 2.75390e7i 0.633514 + 0.873040i
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 15.6.e.a.2.2 16
3.2 odd 2 inner 15.6.e.a.2.7 yes 16
5.2 odd 4 75.6.e.e.68.2 16
5.3 odd 4 inner 15.6.e.a.8.7 yes 16
5.4 even 2 75.6.e.e.32.7 16
15.2 even 4 75.6.e.e.68.7 16
15.8 even 4 inner 15.6.e.a.8.2 yes 16
15.14 odd 2 75.6.e.e.32.2 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
15.6.e.a.2.2 16 1.1 even 1 trivial
15.6.e.a.2.7 yes 16 3.2 odd 2 inner
15.6.e.a.8.2 yes 16 15.8 even 4 inner
15.6.e.a.8.7 yes 16 5.3 odd 4 inner
75.6.e.e.32.2 16 15.14 odd 2
75.6.e.e.32.7 16 5.4 even 2
75.6.e.e.68.2 16 5.2 odd 4
75.6.e.e.68.7 16 15.2 even 4