Properties

Label 39.4.f.b.5.3
Level $39$
Weight $4$
Character 39.5
Analytic conductor $2.301$
Analytic rank $0$
Dimension $20$
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] = [39,4,Mod(5,39)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(39, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("39.5");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 39 = 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 39.f (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: \(2.30107449022\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 1316x^{16} + 520390x^{12} + 64668772x^{8} + 2536036097x^{4} + 8509693504 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{12}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 5.3
Root \(-2.26335 + 2.26335i\) of defining polynomial
Character \(\chi\) \(=\) 39.5
Dual form 39.4.f.b.8.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.26335 - 2.26335i) q^{2} +(2.15347 - 4.72891i) q^{3} +2.24555i q^{4} +(0.350510 + 0.350510i) q^{5} +(-15.5773 + 5.82912i) q^{6} +(-7.24142 - 7.24142i) q^{7} +(-13.0244 + 13.0244i) q^{8} +(-17.7251 - 20.3671i) q^{9} +O(q^{10})\) \(q+(-2.26335 - 2.26335i) q^{2} +(2.15347 - 4.72891i) q^{3} +2.24555i q^{4} +(0.350510 + 0.350510i) q^{5} +(-15.5773 + 5.82912i) q^{6} +(-7.24142 - 7.24142i) q^{7} +(-13.0244 + 13.0244i) q^{8} +(-17.7251 - 20.3671i) q^{9} -1.58666i q^{10} +(-0.0601824 + 0.0601824i) q^{11} +(10.6190 + 4.83573i) q^{12} +(38.0081 - 27.4297i) q^{13} +32.7798i q^{14} +(2.41234 - 0.902716i) q^{15} +76.9219 q^{16} +58.1275 q^{17} +(-5.97982 + 86.2163i) q^{18} +(20.4339 - 20.4339i) q^{19} +(-0.787088 + 0.787088i) q^{20} +(-49.8382 + 18.6498i) q^{21} +0.272428 q^{22} +93.7819 q^{23} +(33.5434 + 89.6386i) q^{24} -124.754i q^{25} +(-148.109 - 23.9426i) q^{26} +(-134.485 + 39.9604i) q^{27} +(16.2610 - 16.2610i) q^{28} -189.233i q^{29} +(-7.50315 - 3.41682i) q^{30} +(-173.538 + 173.538i) q^{31} +(-69.9066 - 69.9066i) q^{32} +(0.154996 + 0.414198i) q^{33} +(-131.563 - 131.563i) q^{34} -5.07638i q^{35} +(45.7354 - 39.8026i) q^{36} +(247.149 + 247.149i) q^{37} -92.4984 q^{38} +(-47.8631 - 238.806i) q^{39} -9.13034 q^{40} +(132.516 + 132.516i) q^{41} +(155.013 + 70.5903i) q^{42} +277.604i q^{43} +(-0.135143 - 0.135143i) q^{44} +(0.926053 - 13.3517i) q^{45} +(-212.262 - 212.262i) q^{46} +(219.429 - 219.429i) q^{47} +(165.649 - 363.757i) q^{48} -238.124i q^{49} +(-282.363 + 282.363i) q^{50} +(125.176 - 274.879i) q^{51} +(61.5947 + 85.3490i) q^{52} +582.835i q^{53} +(394.831 + 213.942i) q^{54} -0.0421891 q^{55} +188.630 q^{56} +(-52.6262 - 140.634i) q^{57} +(-428.301 + 428.301i) q^{58} +(-396.700 + 396.700i) q^{59} +(2.02709 + 5.41704i) q^{60} -244.208 q^{61} +785.556 q^{62} +(-19.1319 + 275.842i) q^{63} -298.928i q^{64} +(22.9366 + 3.70783i) q^{65} +(0.586667 - 1.28829i) q^{66} +(-44.4298 + 44.4298i) q^{67} +130.528i q^{68} +(201.957 - 443.486i) q^{69} +(-11.4896 + 11.4896i) q^{70} +(-454.877 - 454.877i) q^{71} +(496.127 + 34.4106i) q^{72} +(430.182 + 430.182i) q^{73} -1118.77i q^{74} +(-589.951 - 268.655i) q^{75} +(45.8854 + 45.8854i) q^{76} +0.871612 q^{77} +(-432.171 + 648.833i) q^{78} +637.325 q^{79} +(26.9619 + 26.9619i) q^{80} +(-100.640 + 722.020i) q^{81} -599.860i q^{82} +(-868.087 - 868.087i) q^{83} +(-41.8790 - 111.914i) q^{84} +(20.3743 + 20.3743i) q^{85} +(628.317 - 628.317i) q^{86} +(-894.865 - 407.508i) q^{87} -1.56768i q^{88} +(-477.014 + 477.014i) q^{89} +(-32.3157 + 28.1237i) q^{90} +(-473.862 - 76.6025i) q^{91} +210.592i q^{92} +(446.936 + 1194.35i) q^{93} -993.294 q^{94} +14.3246 q^{95} +(-481.124 + 180.040i) q^{96} +(168.184 - 168.184i) q^{97} +(-538.959 + 538.959i) q^{98} +(2.29248 + 0.159003i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 4 q^{3} + 44 q^{6} + 44 q^{7} - 112 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 4 q^{3} + 44 q^{6} + 44 q^{7} - 112 q^{9} - 76 q^{13} - 76 q^{15} - 16 q^{16} + 296 q^{18} + 260 q^{19} - 532 q^{21} - 224 q^{22} + 36 q^{24} - 592 q^{27} + 584 q^{28} - 700 q^{31} + 872 q^{33} + 816 q^{34} - 1660 q^{37} + 1016 q^{39} + 3288 q^{40} + 124 q^{42} + 260 q^{45} - 1560 q^{46} - 1084 q^{48} - 3456 q^{52} - 232 q^{54} - 872 q^{55} + 2648 q^{57} - 1352 q^{58} - 1064 q^{60} + 1960 q^{61} + 428 q^{63} - 7664 q^{66} - 916 q^{67} + 1192 q^{70} + 6984 q^{72} + 1964 q^{73} + 1816 q^{76} + 728 q^{78} + 6544 q^{79} + 200 q^{81} + 2612 q^{84} - 8304 q^{85} + 3136 q^{87} + 4580 q^{91} - 2536 q^{93} - 6056 q^{94} - 5956 q^{96} - 2572 q^{97} + 1700 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).

\(n\) \(14\) \(28\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.26335 2.26335i −0.800217 0.800217i 0.182912 0.983129i \(-0.441448\pi\)
−0.983129 + 0.182912i \(0.941448\pi\)
\(3\) 2.15347 4.72891i 0.414436 0.910079i
\(4\) 2.24555i 0.280694i
\(5\) 0.350510 + 0.350510i 0.0313506 + 0.0313506i 0.722608 0.691258i \(-0.242943\pi\)
−0.691258 + 0.722608i \(0.742943\pi\)
\(6\) −15.5773 + 5.82912i −1.05990 + 0.396622i
\(7\) −7.24142 7.24142i −0.391000 0.391000i 0.484044 0.875044i \(-0.339167\pi\)
−0.875044 + 0.484044i \(0.839167\pi\)
\(8\) −13.0244 + 13.0244i −0.575601 + 0.575601i
\(9\) −17.7251 20.3671i −0.656486 0.754338i
\(10\) 1.58666i 0.0501745i
\(11\) −0.0601824 + 0.0601824i −0.00164961 + 0.00164961i −0.707931 0.706281i \(-0.750371\pi\)
0.706281 + 0.707931i \(0.250371\pi\)
\(12\) 10.6190 + 4.83573i 0.255453 + 0.116330i
\(13\) 38.0081 27.4297i 0.810888 0.585202i
\(14\) 32.7798i 0.625769i
\(15\) 2.41234 0.902716i 0.0415243 0.0155387i
\(16\) 76.9219 1.20190
\(17\) 58.1275 0.829293 0.414647 0.909982i \(-0.363905\pi\)
0.414647 + 0.909982i \(0.363905\pi\)
\(18\) −5.97982 + 86.2163i −0.0783032 + 1.12897i
\(19\) 20.4339 20.4339i 0.246730 0.246730i −0.572897 0.819627i \(-0.694181\pi\)
0.819627 + 0.572897i \(0.194181\pi\)
\(20\) −0.787088 + 0.787088i −0.00879991 + 0.00879991i
\(21\) −49.8382 + 18.6498i −0.517885 + 0.193796i
\(22\) 0.272428 0.00264009
\(23\) 93.7819 0.850212 0.425106 0.905143i \(-0.360237\pi\)
0.425106 + 0.905143i \(0.360237\pi\)
\(24\) 33.5434 + 89.6386i 0.285292 + 0.762392i
\(25\) 124.754i 0.998034i
\(26\) −148.109 23.9426i −1.11717 0.180598i
\(27\) −134.485 + 39.9604i −0.958578 + 0.284829i
\(28\) 16.2610 16.2610i 0.109751 0.109751i
\(29\) 189.233i 1.21171i −0.795574 0.605856i \(-0.792831\pi\)
0.795574 0.605856i \(-0.207169\pi\)
\(30\) −7.50315 3.41682i −0.0456627 0.0207941i
\(31\) −173.538 + 173.538i −1.00543 + 1.00543i −0.00544479 + 0.999985i \(0.501733\pi\)
−0.999985 + 0.00544479i \(0.998267\pi\)
\(32\) −69.9066 69.9066i −0.386183 0.386183i
\(33\) 0.154996 + 0.414198i 0.000817616 + 0.00218493i
\(34\) −131.563 131.563i −0.663614 0.663614i
\(35\) 5.07638i 0.0245161i
\(36\) 45.7354 39.8026i 0.211738 0.184271i
\(37\) 247.149 + 247.149i 1.09813 + 1.09813i 0.994629 + 0.103506i \(0.0330060\pi\)
0.103506 + 0.994629i \(0.466994\pi\)
\(38\) −92.4984 −0.394874
\(39\) −47.8631 238.806i −0.196519 0.980500i
\(40\) −9.13034 −0.0360908
\(41\) 132.516 + 132.516i 0.504767 + 0.504767i 0.912916 0.408148i \(-0.133825\pi\)
−0.408148 + 0.912916i \(0.633825\pi\)
\(42\) 155.013 + 70.5903i 0.569499 + 0.259341i
\(43\) 277.604i 0.984517i 0.870449 + 0.492259i \(0.163829\pi\)
−0.870449 + 0.492259i \(0.836171\pi\)
\(44\) −0.135143 0.135143i −0.000463034 0.000463034i
\(45\) 0.926053 13.3517i 0.00306773 0.0442302i
\(46\) −212.262 212.262i −0.680354 0.680354i
\(47\) 219.429 219.429i 0.681002 0.681002i −0.279224 0.960226i \(-0.590077\pi\)
0.960226 + 0.279224i \(0.0900773\pi\)
\(48\) 165.649 363.757i 0.498112 1.09383i
\(49\) 238.124i 0.694238i
\(50\) −282.363 + 282.363i −0.798644 + 0.798644i
\(51\) 125.176 274.879i 0.343689 0.754722i
\(52\) 61.5947 + 85.3490i 0.164262 + 0.227611i
\(53\) 582.835i 1.51054i 0.655414 + 0.755270i \(0.272494\pi\)
−0.655414 + 0.755270i \(0.727506\pi\)
\(54\) 394.831 + 213.942i 0.994995 + 0.539146i
\(55\) −0.0421891 −0.000103432
\(56\) 188.630 0.450120
\(57\) −52.6262 140.634i −0.122290 0.326797i
\(58\) −428.301 + 428.301i −0.969633 + 0.969633i
\(59\) −396.700 + 396.700i −0.875356 + 0.875356i −0.993050 0.117694i \(-0.962450\pi\)
0.117694 + 0.993050i \(0.462450\pi\)
\(60\) 2.02709 + 5.41704i 0.00436161 + 0.0116556i
\(61\) −244.208 −0.512585 −0.256293 0.966599i \(-0.582501\pi\)
−0.256293 + 0.966599i \(0.582501\pi\)
\(62\) 785.556 1.60912
\(63\) −19.1319 + 275.842i −0.0382603 + 0.551632i
\(64\) 298.928i 0.583844i
\(65\) 22.9366 + 3.70783i 0.0437682 + 0.00707539i
\(66\) 0.586667 1.28829i 0.00109415 0.00240269i
\(67\) −44.4298 + 44.4298i −0.0810145 + 0.0810145i −0.746453 0.665438i \(-0.768245\pi\)
0.665438 + 0.746453i \(0.268245\pi\)
\(68\) 130.528i 0.232777i
\(69\) 201.957 443.486i 0.352359 0.773760i
\(70\) −11.4896 + 11.4896i −0.0196182 + 0.0196182i
\(71\) −454.877 454.877i −0.760338 0.760338i 0.216046 0.976383i \(-0.430684\pi\)
−0.976383 + 0.216046i \(0.930684\pi\)
\(72\) 496.127 + 34.4106i 0.812072 + 0.0563240i
\(73\) 430.182 + 430.182i 0.689712 + 0.689712i 0.962168 0.272456i \(-0.0878361\pi\)
−0.272456 + 0.962168i \(0.587836\pi\)
\(74\) 1118.77i 1.75749i
\(75\) −589.951 268.655i −0.908290 0.413621i
\(76\) 45.8854 + 45.8854i 0.0692555 + 0.0692555i
\(77\) 0.871612 0.00128999
\(78\) −432.171 + 648.833i −0.627355 + 0.941870i
\(79\) 637.325 0.907653 0.453827 0.891090i \(-0.350059\pi\)
0.453827 + 0.891090i \(0.350059\pi\)
\(80\) 26.9619 + 26.9619i 0.0376804 + 0.0376804i
\(81\) −100.640 + 722.020i −0.138053 + 0.990425i
\(82\) 599.860i 0.807846i
\(83\) −868.087 868.087i −1.14801 1.14801i −0.986943 0.161068i \(-0.948506\pi\)
−0.161068 0.986943i \(-0.551494\pi\)
\(84\) −41.8790 111.914i −0.0543974 0.145367i
\(85\) 20.3743 + 20.3743i 0.0259988 + 0.0259988i
\(86\) 628.317 628.317i 0.787827 0.787827i
\(87\) −894.865 407.508i −1.10275 0.502177i
\(88\) 1.56768i 0.00189903i
\(89\) −477.014 + 477.014i −0.568128 + 0.568128i −0.931604 0.363476i \(-0.881590\pi\)
0.363476 + 0.931604i \(0.381590\pi\)
\(90\) −32.3157 + 28.1237i −0.0378486 + 0.0329389i
\(91\) −473.862 76.6025i −0.545871 0.0882431i
\(92\) 210.592i 0.238649i
\(93\) 446.936 + 1194.35i 0.498334 + 1.33171i
\(94\) −993.294 −1.08990
\(95\) 14.3246 0.0154702
\(96\) −481.124 + 180.040i −0.511505 + 0.191409i
\(97\) 168.184 168.184i 0.176046 0.176046i −0.613584 0.789630i \(-0.710273\pi\)
0.789630 + 0.613584i \(0.210273\pi\)
\(98\) −538.959 + 538.959i −0.555541 + 0.555541i
\(99\) 2.29248 + 0.159003i 0.00232731 + 0.000161418i
\(100\) 280.142 0.280142
\(101\) 1773.86 1.74758 0.873791 0.486301i \(-0.161654\pi\)
0.873791 + 0.486301i \(0.161654\pi\)
\(102\) −905.467 + 338.832i −0.878967 + 0.328916i
\(103\) 1309.11i 1.25233i 0.779689 + 0.626167i \(0.215377\pi\)
−0.779689 + 0.626167i \(0.784623\pi\)
\(104\) −137.777 + 852.285i −0.129905 + 0.803590i
\(105\) −24.0057 10.9318i −0.0223116 0.0101604i
\(106\) 1319.16 1319.16i 1.20876 1.20876i
\(107\) 373.388i 0.337353i −0.985671 0.168677i \(-0.946051\pi\)
0.985671 0.168677i \(-0.0539494\pi\)
\(108\) −89.7330 301.992i −0.0799497 0.269067i
\(109\) 1439.45 1439.45i 1.26490 1.26490i 0.316214 0.948688i \(-0.397588\pi\)
0.948688 0.316214i \(-0.102412\pi\)
\(110\) 0.0954889 + 0.0954889i 8.27682e−5 + 8.27682e-5i
\(111\) 1700.97 636.515i 1.45449 0.544282i
\(112\) −557.023 557.023i −0.469944 0.469944i
\(113\) 1299.74i 1.08203i 0.841013 + 0.541014i \(0.181960\pi\)
−0.841013 + 0.541014i \(0.818040\pi\)
\(114\) −199.193 + 437.416i −0.163650 + 0.359367i
\(115\) 32.8715 + 32.8715i 0.0266547 + 0.0266547i
\(116\) 424.932 0.340120
\(117\) −1232.36 287.921i −0.973776 0.227507i
\(118\) 1795.75 1.40095
\(119\) −420.925 420.925i −0.324253 0.324253i
\(120\) −19.6619 + 43.1765i −0.0149573 + 0.0328455i
\(121\) 1330.99i 0.999995i
\(122\) 552.730 + 552.730i 0.410179 + 0.410179i
\(123\) 912.022 341.285i 0.668572 0.250184i
\(124\) −389.688 389.688i −0.282218 0.282218i
\(125\) 87.5414 87.5414i 0.0626395 0.0626395i
\(126\) 667.630 581.026i 0.472042 0.410809i
\(127\) 825.698i 0.576920i −0.957492 0.288460i \(-0.906857\pi\)
0.957492 0.288460i \(-0.0931432\pi\)
\(128\) −1235.83 + 1235.83i −0.853385 + 0.853385i
\(129\) 1312.76 + 597.813i 0.895988 + 0.408019i
\(130\) −43.5215 60.3058i −0.0293622 0.0406859i
\(131\) 276.713i 0.184554i 0.995733 + 0.0922768i \(0.0294144\pi\)
−0.995733 + 0.0922768i \(0.970586\pi\)
\(132\) −0.930102 + 0.348051i −0.000613296 + 0.000229500i
\(133\) −295.941 −0.192942
\(134\) 201.121 0.129658
\(135\) −61.1448 33.1318i −0.0389815 0.0211224i
\(136\) −757.074 + 757.074i −0.477342 + 0.477342i
\(137\) 144.788 144.788i 0.0902925 0.0902925i −0.660518 0.750810i \(-0.729663\pi\)
0.750810 + 0.660518i \(0.229663\pi\)
\(138\) −1460.87 + 546.666i −0.901139 + 0.337213i
\(139\) −2444.55 −1.49168 −0.745841 0.666124i \(-0.767952\pi\)
−0.745841 + 0.666124i \(0.767952\pi\)
\(140\) 11.3993 0.00688152
\(141\) −565.126 1510.20i −0.337534 0.901997i
\(142\) 2059.10i 1.21687i
\(143\) −0.636633 + 3.93820i −0.000372293 + 0.00230300i
\(144\) −1363.45 1566.68i −0.789033 0.906643i
\(145\) 66.3280 66.3280i 0.0379879 0.0379879i
\(146\) 1947.31i 1.10384i
\(147\) −1126.07 512.793i −0.631812 0.287717i
\(148\) −554.984 + 554.984i −0.308239 + 0.308239i
\(149\) −934.262 934.262i −0.513676 0.513676i 0.401975 0.915651i \(-0.368324\pi\)
−0.915651 + 0.401975i \(0.868324\pi\)
\(150\) 727.208 + 1943.33i 0.395842 + 1.05782i
\(151\) −683.199 683.199i −0.368198 0.368198i 0.498621 0.866820i \(-0.333840\pi\)
−0.866820 + 0.498621i \(0.833840\pi\)
\(152\) 532.278i 0.284036i
\(153\) −1030.32 1183.89i −0.544419 0.625568i
\(154\) −1.97277 1.97277i −0.00103227 0.00103227i
\(155\) −121.654 −0.0630416
\(156\) 536.250 107.479i 0.275220 0.0551615i
\(157\) −116.097 −0.0590160 −0.0295080 0.999565i \(-0.509394\pi\)
−0.0295080 + 0.999565i \(0.509394\pi\)
\(158\) −1442.49 1442.49i −0.726319 0.726319i
\(159\) 2756.17 + 1255.12i 1.37471 + 0.626022i
\(160\) 49.0060i 0.0242141i
\(161\) −679.114 679.114i −0.332433 0.332433i
\(162\) 1861.97 1406.40i 0.903027 0.682083i
\(163\) −267.153 267.153i −0.128374 0.128374i 0.640000 0.768375i \(-0.278934\pi\)
−0.768375 + 0.640000i \(0.778934\pi\)
\(164\) −297.570 + 297.570i −0.141685 + 0.141685i
\(165\) −0.0908530 + 0.199508i −4.28660e−5 + 9.41315e-5i
\(166\) 3929.58i 1.83732i
\(167\) 2454.42 2454.42i 1.13730 1.13730i 0.148366 0.988932i \(-0.452598\pi\)
0.988932 0.148366i \(-0.0474015\pi\)
\(168\) 406.209 892.012i 0.186546 0.409644i
\(169\) 692.226 2085.10i 0.315078 0.949066i
\(170\) 92.2284i 0.0416094i
\(171\) −778.374 53.9868i −0.348092 0.0241431i
\(172\) −623.374 −0.276348
\(173\) 702.152 0.308576 0.154288 0.988026i \(-0.450692\pi\)
0.154288 + 0.988026i \(0.450692\pi\)
\(174\) 1103.06 + 2947.73i 0.480591 + 1.28429i
\(175\) −903.398 + 903.398i −0.390231 + 0.390231i
\(176\) −4.62935 + 4.62935i −0.00198267 + 0.00198267i
\(177\) 1021.68 + 2730.24i 0.433864 + 1.15942i
\(178\) 2159.30 0.909251
\(179\) 343.109 0.143269 0.0716345 0.997431i \(-0.477178\pi\)
0.0716345 + 0.997431i \(0.477178\pi\)
\(180\) 29.9819 + 2.07950i 0.0124151 + 0.000861093i
\(181\) 2707.33i 1.11179i −0.831252 0.555895i \(-0.812376\pi\)
0.831252 0.555895i \(-0.187624\pi\)
\(182\) 899.139 + 1245.90i 0.366201 + 0.507428i
\(183\) −525.896 + 1154.84i −0.212434 + 0.466493i
\(184\) −1221.45 + 1221.45i −0.489383 + 0.489383i
\(185\) 173.256i 0.0688543i
\(186\) 1691.67 3714.82i 0.666879 1.46443i
\(187\) −3.49825 + 3.49825i −0.00136801 + 0.00136801i
\(188\) 492.740 + 492.740i 0.191153 + 0.191153i
\(189\) 1263.23 + 684.491i 0.486172 + 0.263436i
\(190\) −32.4216 32.4216i −0.0123795 0.0123795i
\(191\) 3556.56i 1.34735i 0.739029 + 0.673674i \(0.235285\pi\)
−0.739029 + 0.673674i \(0.764715\pi\)
\(192\) −1413.60 643.733i −0.531344 0.241966i
\(193\) −59.4885 59.4885i −0.0221869 0.0221869i 0.695926 0.718113i \(-0.254994\pi\)
−0.718113 + 0.695926i \(0.754994\pi\)
\(194\) −761.319 −0.281750
\(195\) 66.9273 100.480i 0.0245783 0.0369002i
\(196\) 534.719 0.194868
\(197\) 229.292 + 229.292i 0.0829258 + 0.0829258i 0.747353 0.664427i \(-0.231324\pi\)
−0.664427 + 0.747353i \(0.731324\pi\)
\(198\) −4.82882 5.54858i −0.00173318 0.00199152i
\(199\) 4289.02i 1.52784i 0.645310 + 0.763921i \(0.276728\pi\)
−0.645310 + 0.763921i \(0.723272\pi\)
\(200\) 1624.85 + 1624.85i 0.574469 + 0.574469i
\(201\) 114.426 + 305.783i 0.0401542 + 0.107305i
\(202\) −4014.88 4014.88i −1.39844 1.39844i
\(203\) −1370.31 + 1370.31i −0.473779 + 0.473779i
\(204\) 617.255 + 281.089i 0.211846 + 0.0964713i
\(205\) 92.8961i 0.0316495i
\(206\) 2962.98 2962.98i 1.00214 1.00214i
\(207\) −1662.30 1910.07i −0.558152 0.641348i
\(208\) 2923.65 2109.94i 0.974610 0.703357i
\(209\) 2.45953i 0.000814014i
\(210\) 29.5908 + 79.0761i 0.00972363 + 0.0259846i
\(211\) −927.050 −0.302468 −0.151234 0.988498i \(-0.548325\pi\)
−0.151234 + 0.988498i \(0.548325\pi\)
\(212\) −1308.79 −0.423999
\(213\) −3130.64 + 1171.51i −1.00708 + 0.376856i
\(214\) −845.110 + 845.110i −0.269956 + 0.269956i
\(215\) −97.3031 + 97.3031i −0.0308652 + 0.0308652i
\(216\) 1231.12 2272.04i 0.387811 0.715706i
\(217\) 2513.32 0.786246
\(218\) −6515.97 −2.02439
\(219\) 2960.67 1107.90i 0.913533 0.341851i
\(220\) 0.0947377i 2.90328e-5i
\(221\) 2209.31 1594.42i 0.672464 0.485304i
\(222\) −5290.56 2409.24i −1.59946 0.728367i
\(223\) −287.402 + 287.402i −0.0863043 + 0.0863043i −0.748941 0.662637i \(-0.769437\pi\)
0.662637 + 0.748941i \(0.269437\pi\)
\(224\) 1012.45i 0.301995i
\(225\) −2540.89 + 2211.28i −0.752856 + 0.655195i
\(226\) 2941.77 2941.77i 0.865858 0.865858i
\(227\) 3982.28 + 3982.28i 1.16438 + 1.16438i 0.983507 + 0.180869i \(0.0578910\pi\)
0.180869 + 0.983507i \(0.442109\pi\)
\(228\) 315.801 118.175i 0.0917298 0.0343260i
\(229\) 1178.36 + 1178.36i 0.340035 + 0.340035i 0.856380 0.516346i \(-0.172708\pi\)
−0.516346 + 0.856380i \(0.672708\pi\)
\(230\) 148.800i 0.0426590i
\(231\) 1.87699 4.12177i 0.000534619 0.00117399i
\(232\) 2464.64 + 2464.64i 0.697463 + 0.697463i
\(233\) −5811.46 −1.63400 −0.816999 0.576639i \(-0.804364\pi\)
−0.816999 + 0.576639i \(0.804364\pi\)
\(234\) 2137.60 + 3440.94i 0.597177 + 0.961287i
\(235\) 153.825 0.0426996
\(236\) −890.810 890.810i −0.245707 0.245707i
\(237\) 1372.46 3013.85i 0.376164 0.826036i
\(238\) 1905.41i 0.518946i
\(239\) −521.832 521.832i −0.141232 0.141232i 0.632956 0.774188i \(-0.281841\pi\)
−0.774188 + 0.632956i \(0.781841\pi\)
\(240\) 185.562 69.4386i 0.0499082 0.0186760i
\(241\) −2758.93 2758.93i −0.737421 0.737421i 0.234657 0.972078i \(-0.424603\pi\)
−0.972078 + 0.234657i \(0.924603\pi\)
\(242\) 3012.51 3012.51i 0.800212 0.800212i
\(243\) 3197.64 + 2030.77i 0.844150 + 0.536106i
\(244\) 548.382i 0.143879i
\(245\) 83.4648 83.4648i 0.0217648 0.0217648i
\(246\) −2836.68 1291.78i −0.735204 0.334801i
\(247\) 216.158 1337.15i 0.0556834 0.344457i
\(248\) 4520.44i 1.15745i
\(249\) −5974.50 + 2235.70i −1.52056 + 0.569003i
\(250\) −396.274 −0.100250
\(251\) −2175.12 −0.546981 −0.273491 0.961875i \(-0.588178\pi\)
−0.273491 + 0.961875i \(0.588178\pi\)
\(252\) −619.416 42.9617i −0.154840 0.0107394i
\(253\) −5.64402 + 5.64402i −0.00140252 + 0.00140252i
\(254\) −1868.85 + 1868.85i −0.461661 + 0.461661i
\(255\) 140.223 52.4726i 0.0344358 0.0128861i
\(256\) 3202.83 0.781942
\(257\) 1163.64 0.282436 0.141218 0.989979i \(-0.454898\pi\)
0.141218 + 0.989979i \(0.454898\pi\)
\(258\) −1618.19 4324.31i −0.390481 1.04349i
\(259\) 3579.41i 0.858741i
\(260\) −8.32612 + 51.5052i −0.00198602 + 0.0122855i
\(261\) −3854.13 + 3354.18i −0.914041 + 0.795472i
\(262\) 626.299 626.299i 0.147683 0.147683i
\(263\) 1652.99i 0.387559i 0.981045 + 0.193779i \(0.0620746\pi\)
−0.981045 + 0.193779i \(0.937925\pi\)
\(264\) −7.41339 3.37594i −0.00172827 0.000787027i
\(265\) −204.290 + 204.290i −0.0473563 + 0.0473563i
\(266\) 669.820 + 669.820i 0.154396 + 0.154396i
\(267\) 1228.52 + 3282.99i 0.281588 + 0.752494i
\(268\) −99.7694 99.7694i −0.0227402 0.0227402i
\(269\) 3584.47i 0.812449i −0.913773 0.406225i \(-0.866845\pi\)
0.913773 0.406225i \(-0.133155\pi\)
\(270\) 63.4034 + 213.381i 0.0142911 + 0.0480962i
\(271\) −220.676 220.676i −0.0494653 0.0494653i 0.681941 0.731407i \(-0.261136\pi\)
−0.731407 + 0.681941i \(0.761136\pi\)
\(272\) 4471.28 0.996732
\(273\) −1382.69 + 2075.89i −0.306537 + 0.460214i
\(274\) −655.413 −0.144507
\(275\) 7.50801 + 7.50801i 0.00164636 + 0.00164636i
\(276\) 995.870 + 453.504i 0.217190 + 0.0989048i
\(277\) 550.383i 0.119384i 0.998217 + 0.0596919i \(0.0190118\pi\)
−0.998217 + 0.0596919i \(0.980988\pi\)
\(278\) 5532.88 + 5532.88i 1.19367 + 1.19367i
\(279\) 6610.45 + 458.490i 1.41848 + 0.0983838i
\(280\) 66.1166 + 66.1166i 0.0141115 + 0.0141115i
\(281\) −4713.18 + 4713.18i −1.00059 + 1.00059i −0.000586773 1.00000i \(0.500187\pi\)
−1.00000 0.000586773i \(0.999813\pi\)
\(282\) −2139.03 + 4697.19i −0.451693 + 0.991893i
\(283\) 1465.49i 0.307824i −0.988085 0.153912i \(-0.950813\pi\)
0.988085 0.153912i \(-0.0491872\pi\)
\(284\) 1021.45 1021.45i 0.213422 0.213422i
\(285\) 30.8476 67.7397i 0.00641142 0.0140791i
\(286\) 10.3545 7.47262i 0.00214081 0.00154498i
\(287\) 1919.20i 0.394728i
\(288\) −184.695 + 2662.90i −0.0377890 + 0.544837i
\(289\) −1534.19 −0.312272
\(290\) −300.248 −0.0607971
\(291\) −433.147 1157.50i −0.0872560 0.233176i
\(292\) −965.994 + 965.994i −0.193598 + 0.193598i
\(293\) 4976.72 4976.72i 0.992297 0.992297i −0.00767353 0.999971i \(-0.502443\pi\)
0.999971 + 0.00767353i \(0.00244258\pi\)
\(294\) 1388.05 + 3709.32i 0.275350 + 0.735822i
\(295\) −278.095 −0.0548858
\(296\) −6437.91 −1.26417
\(297\) 5.68871 10.4985i 0.00111142 0.00205113i
\(298\) 4229.13i 0.822105i
\(299\) 3564.47 2572.41i 0.689427 0.497546i
\(300\) 603.278 1324.76i 0.116101 0.254951i
\(301\) 2010.25 2010.25i 0.384946 0.384946i
\(302\) 3092.64i 0.589277i
\(303\) 3819.96 8388.43i 0.724261 1.59044i
\(304\) 1571.82 1571.82i 0.296546 0.296546i
\(305\) −85.5975 85.5975i −0.0160698 0.0160698i
\(306\) −347.592 + 5011.54i −0.0649363 + 0.936243i
\(307\) 1119.82 + 1119.82i 0.208181 + 0.208181i 0.803494 0.595313i \(-0.202972\pi\)
−0.595313 + 0.803494i \(0.702972\pi\)
\(308\) 1.95725i 0.000362093i
\(309\) 6190.66 + 2819.13i 1.13972 + 0.519013i
\(310\) 275.345 + 275.345i 0.0504470 + 0.0504470i
\(311\) 1793.81 0.327067 0.163534 0.986538i \(-0.447711\pi\)
0.163534 + 0.986538i \(0.447711\pi\)
\(312\) 3733.68 + 2486.91i 0.677493 + 0.451260i
\(313\) 7542.23 1.36202 0.681010 0.732274i \(-0.261541\pi\)
0.681010 + 0.732274i \(0.261541\pi\)
\(314\) 262.768 + 262.768i 0.0472256 + 0.0472256i
\(315\) −103.391 + 89.9794i −0.0184935 + 0.0160945i
\(316\) 1431.14i 0.254773i
\(317\) −3785.41 3785.41i −0.670693 0.670693i 0.287183 0.957876i \(-0.407281\pi\)
−0.957876 + 0.287183i \(0.907281\pi\)
\(318\) −3397.42 9078.98i −0.599112 1.60102i
\(319\) 11.3885 + 11.3885i 0.00199885 + 0.00199885i
\(320\) 104.777 104.777i 0.0183038 0.0183038i
\(321\) −1765.72 804.081i −0.307018 0.139811i
\(322\) 3074.15i 0.532037i
\(323\) 1187.77 1187.77i 0.204611 0.204611i
\(324\) −1621.33 225.993i −0.278006 0.0387505i
\(325\) −3421.97 4741.67i −0.584051 0.809294i
\(326\) 1209.32i 0.205455i
\(327\) −3707.21 9906.84i −0.626939 1.67538i
\(328\) −3451.86 −0.581089
\(329\) −3177.96 −0.532543
\(330\) 0.657191 0.245925i 0.000109628 4.10235e-5i
\(331\) −3829.32 + 3829.32i −0.635886 + 0.635886i −0.949538 0.313652i \(-0.898447\pi\)
0.313652 + 0.949538i \(0.398447\pi\)
\(332\) 1949.33 1949.33i 0.322240 0.322240i
\(333\) 652.971 9414.45i 0.107455 1.54927i
\(334\) −11110.5 −1.82017
\(335\) −31.1462 −0.00507970
\(336\) −3833.65 + 1434.58i −0.622448 + 0.232925i
\(337\) 9715.03i 1.57036i 0.619268 + 0.785180i \(0.287429\pi\)
−0.619268 + 0.785180i \(0.712571\pi\)
\(338\) −6286.07 + 3152.56i −1.01159 + 0.507328i
\(339\) 6146.35 + 2798.95i 0.984731 + 0.448432i
\(340\) −45.7514 + 45.7514i −0.00729771 + 0.00729771i
\(341\) 20.8879i 0.00331713i
\(342\) 1639.55 + 1883.93i 0.259229 + 0.297869i
\(343\) −4208.16 + 4208.16i −0.662447 + 0.662447i
\(344\) −3615.62 3615.62i −0.566689 0.566689i
\(345\) 226.234 84.6585i 0.0353045 0.0132112i
\(346\) −1589.22 1589.22i −0.246928 0.246928i
\(347\) 703.045i 0.108765i 0.998520 + 0.0543825i \(0.0173190\pi\)
−0.998520 + 0.0543825i \(0.982681\pi\)
\(348\) 915.079 2009.46i 0.140958 0.309536i
\(349\) −6231.70 6231.70i −0.955802 0.955802i 0.0432615 0.999064i \(-0.486225\pi\)
−0.999064 + 0.0432615i \(0.986225\pi\)
\(350\) 4089.42 0.624539
\(351\) −4015.41 + 5207.69i −0.610617 + 0.791926i
\(352\) 8.41430 0.00127410
\(353\) 4606.02 + 4606.02i 0.694486 + 0.694486i 0.963216 0.268729i \(-0.0866038\pi\)
−0.268729 + 0.963216i \(0.586604\pi\)
\(354\) 3867.09 8491.92i 0.580603 1.27497i
\(355\) 318.878i 0.0476740i
\(356\) −1071.16 1071.16i −0.159470 0.159470i
\(357\) −2896.97 + 1084.07i −0.429478 + 0.160714i
\(358\) −776.577 776.577i −0.114646 0.114646i
\(359\) −8688.79 + 8688.79i −1.27737 + 1.27737i −0.335240 + 0.942133i \(0.608818\pi\)
−0.942133 + 0.335240i \(0.891182\pi\)
\(360\) 161.836 + 185.959i 0.0236931 + 0.0272247i
\(361\) 6023.91i 0.878249i
\(362\) −6127.64 + 6127.64i −0.889674 + 0.889674i
\(363\) 6294.14 + 2866.26i 0.910074 + 0.414434i
\(364\) 172.015 1064.08i 0.0247693 0.153222i
\(365\) 301.566i 0.0432457i
\(366\) 3804.10 1423.52i 0.543288 0.203302i
\(367\) −3039.03 −0.432251 −0.216125 0.976366i \(-0.569342\pi\)
−0.216125 + 0.976366i \(0.569342\pi\)
\(368\) 7213.89 1.02187
\(369\) 350.108 5047.82i 0.0493927 0.712138i
\(370\) 392.140 392.140i 0.0550984 0.0550984i
\(371\) 4220.55 4220.55i 0.590620 0.590620i
\(372\) −2681.98 + 1003.62i −0.373802 + 0.139879i
\(373\) 4113.21 0.570975 0.285488 0.958382i \(-0.407844\pi\)
0.285488 + 0.958382i \(0.407844\pi\)
\(374\) 15.8356 0.00218941
\(375\) −225.457 602.493i −0.0310468 0.0829670i
\(376\) 5715.86i 0.783970i
\(377\) −5190.60 7192.38i −0.709096 0.982563i
\(378\) −1309.89 4408.38i −0.178237 0.599849i
\(379\) 3541.54 3541.54i 0.479992 0.479992i −0.425137 0.905129i \(-0.639774\pi\)
0.905129 + 0.425137i \(0.139774\pi\)
\(380\) 32.1666i 0.00434240i
\(381\) −3904.65 1778.12i −0.525042 0.239096i
\(382\) 8049.75 8049.75i 1.07817 1.07817i
\(383\) −495.148 495.148i −0.0660598 0.0660598i 0.673305 0.739365i \(-0.264874\pi\)
−0.739365 + 0.673305i \(0.764874\pi\)
\(384\) 3182.81 + 8505.47i 0.422974 + 1.13032i
\(385\) 0.305509 + 0.305509i 4.04420e−5 + 4.04420e-5i
\(386\) 269.287i 0.0355087i
\(387\) 5654.00 4920.57i 0.742659 0.646322i
\(388\) 377.665 + 377.665i 0.0494151 + 0.0494151i
\(389\) 7976.07 1.03960 0.519798 0.854289i \(-0.326007\pi\)
0.519798 + 0.854289i \(0.326007\pi\)
\(390\) −378.903 + 75.9423i −0.0491961 + 0.00986023i
\(391\) 5451.31 0.705076
\(392\) 3101.41 + 3101.41i 0.399604 + 0.399604i
\(393\) 1308.55 + 595.893i 0.167958 + 0.0764856i
\(394\) 1037.94i 0.132717i
\(395\) 223.389 + 223.389i 0.0284555 + 0.0284555i
\(396\) −0.357049 + 5.14789i −4.53090e−5 + 0.000653260i
\(397\) 3273.29 + 3273.29i 0.413807 + 0.413807i 0.883063 0.469255i \(-0.155478\pi\)
−0.469255 + 0.883063i \(0.655478\pi\)
\(398\) 9707.57 9707.57i 1.22260 1.22260i
\(399\) −637.301 + 1399.48i −0.0799623 + 0.175593i
\(400\) 9596.34i 1.19954i
\(401\) −8314.24 + 8314.24i −1.03539 + 1.03539i −0.0360441 + 0.999350i \(0.511476\pi\)
−0.999350 + 0.0360441i \(0.988524\pi\)
\(402\) 433.108 951.082i 0.0537350 0.117999i
\(403\) −1835.75 + 11355.9i −0.226911 + 1.40367i
\(404\) 3983.29i 0.490535i
\(405\) −288.351 + 217.800i −0.0353784 + 0.0267224i
\(406\) 6203.01 0.758252
\(407\) −29.7480 −0.00362298
\(408\) 1949.79 + 5210.47i 0.236591 + 0.632246i
\(409\) 7048.05 7048.05i 0.852087 0.852087i −0.138303 0.990390i \(-0.544165\pi\)
0.990390 + 0.138303i \(0.0441646\pi\)
\(410\) 210.257 210.257i 0.0253265 0.0253265i
\(411\) −372.892 996.486i −0.0447528 0.119594i
\(412\) −2939.67 −0.351523
\(413\) 5745.35 0.684528
\(414\) −560.799 + 8085.53i −0.0665743 + 0.959860i
\(415\) 608.547i 0.0719816i
\(416\) −4574.53 739.500i −0.539146 0.0871562i
\(417\) −5264.27 + 11560.0i −0.618207 + 1.35755i
\(418\) 5.56678 5.56678i 0.000651388 0.000651388i
\(419\) 7049.75i 0.821963i 0.911644 + 0.410982i \(0.134814\pi\)
−0.911644 + 0.410982i \(0.865186\pi\)
\(420\) 24.5480 53.9060i 0.00285195 0.00626273i
\(421\) −3428.49 + 3428.49i −0.396899 + 0.396899i −0.877138 0.480239i \(-0.840550\pi\)
0.480239 + 0.877138i \(0.340550\pi\)
\(422\) 2098.24 + 2098.24i 0.242040 + 0.242040i
\(423\) −8358.56 579.736i −0.960774 0.0666377i
\(424\) −7591.06 7591.06i −0.869468 0.869468i
\(425\) 7251.65i 0.827663i
\(426\) 9737.27 + 4434.21i 1.10745 + 0.504314i
\(427\) 1768.41 + 1768.41i 0.200421 + 0.200421i
\(428\) 838.462 0.0946930
\(429\) 17.2524 + 11.4914i 0.00194162 + 0.00129326i
\(430\) 440.463 0.0493977
\(431\) 5002.08 + 5002.08i 0.559029 + 0.559029i 0.929031 0.370002i \(-0.120643\pi\)
−0.370002 + 0.929031i \(0.620643\pi\)
\(432\) −10344.8 + 3073.83i −1.15212 + 0.342337i
\(433\) 3256.29i 0.361402i 0.983538 + 0.180701i \(0.0578367\pi\)
−0.983538 + 0.180701i \(0.942163\pi\)
\(434\) −5688.54 5688.54i −0.629167 0.629167i
\(435\) −170.824 456.495i −0.0188284 0.0503155i
\(436\) 3232.36 + 3232.36i 0.355050 + 0.355050i
\(437\) 1916.33 1916.33i 0.209773 0.209773i
\(438\) −9208.63 4193.47i −1.00458 0.457470i
\(439\) 6361.30i 0.691591i −0.938310 0.345795i \(-0.887609\pi\)
0.938310 0.345795i \(-0.112391\pi\)
\(440\) 0.549486 0.549486i 5.95357e−5 5.95357e-5i
\(441\) −4849.90 + 4220.77i −0.523691 + 0.455758i
\(442\) −8609.19 1391.73i −0.926465 0.149768i
\(443\) 11204.8i 1.20171i −0.799359 0.600854i \(-0.794827\pi\)
0.799359 0.600854i \(-0.205173\pi\)
\(444\) 1429.33 + 3819.61i 0.152777 + 0.408268i
\(445\) −334.396 −0.0356223
\(446\) 1300.99 0.138124
\(447\) −6429.95 + 2406.13i −0.680372 + 0.254600i
\(448\) −2164.66 + 2164.66i −0.228283 + 0.228283i
\(449\) −4510.62 + 4510.62i −0.474096 + 0.474096i −0.903237 0.429141i \(-0.858816\pi\)
0.429141 + 0.903237i \(0.358816\pi\)
\(450\) 10755.9 + 746.008i 1.12675 + 0.0781493i
\(451\) −15.9502 −0.00166534
\(452\) −2918.63 −0.303719
\(453\) −4702.04 + 1759.54i −0.487684 + 0.182495i
\(454\) 18026.6i 1.86351i
\(455\) −139.243 192.943i −0.0143469 0.0198798i
\(456\) 2517.09 + 1146.24i 0.258495 + 0.117715i
\(457\) 6380.62 6380.62i 0.653113 0.653113i −0.300628 0.953741i \(-0.597196\pi\)
0.953741 + 0.300628i \(0.0971963\pi\)
\(458\) 5334.07i 0.544203i
\(459\) −7817.27 + 2322.80i −0.794943 + 0.236207i
\(460\) −73.8146 + 73.8146i −0.00748179 + 0.00748179i
\(461\) −5380.50 5380.50i −0.543590 0.543590i 0.380990 0.924579i \(-0.375583\pi\)
−0.924579 + 0.380990i \(0.875583\pi\)
\(462\) −13.5773 + 5.08073i −0.00136726 + 0.000511639i
\(463\) 5694.54 + 5694.54i 0.571594 + 0.571594i 0.932574 0.360980i \(-0.117558\pi\)
−0.360980 + 0.932574i \(0.617558\pi\)
\(464\) 14556.2i 1.45636i
\(465\) −261.978 + 575.288i −0.0261267 + 0.0573728i
\(466\) 13153.4 + 13153.4i 1.30755 + 1.30755i
\(467\) −13135.9 −1.30162 −0.650811 0.759240i \(-0.725571\pi\)
−0.650811 + 0.759240i \(0.725571\pi\)
\(468\) 646.541 2767.33i 0.0638598 0.273333i
\(469\) 643.470 0.0633533
\(470\) −348.159 348.159i −0.0341689 0.0341689i
\(471\) −250.011 + 549.010i −0.0244583 + 0.0537092i
\(472\) 10333.5i 1.00771i
\(473\) −16.7069 16.7069i −0.00162407 0.00162407i
\(474\) −9927.77 + 3715.04i −0.962021 + 0.359995i
\(475\) −2549.22 2549.22i −0.246245 0.246245i
\(476\) 945.209 945.209i 0.0910159 0.0910159i
\(477\) 11870.7 10330.8i 1.13946 0.991648i
\(478\) 2362.18i 0.226033i
\(479\) 1999.71 1999.71i 0.190749 0.190749i −0.605270 0.796020i \(-0.706935\pi\)
0.796020 + 0.605270i \(0.206935\pi\)
\(480\) −231.745 105.533i −0.0220368 0.0100352i
\(481\) 16172.8 + 2614.43i 1.53309 + 0.247834i
\(482\) 12488.9i 1.18019i
\(483\) −4673.92 + 1749.01i −0.440312 + 0.164768i
\(484\) −2988.81 −0.280692
\(485\) 117.900 0.0110383
\(486\) −2641.04 11833.7i −0.246502 1.10450i
\(487\) −7192.22 + 7192.22i −0.669220 + 0.669220i −0.957536 0.288315i \(-0.906905\pi\)
0.288315 + 0.957536i \(0.406905\pi\)
\(488\) 3180.66 3180.66i 0.295044 0.295044i
\(489\) −1838.65 + 688.034i −0.170034 + 0.0636278i
\(490\) −377.821 −0.0348331
\(491\) 8860.19 0.814368 0.407184 0.913346i \(-0.366511\pi\)
0.407184 + 0.913346i \(0.366511\pi\)
\(492\) 766.373 + 2047.99i 0.0702251 + 0.187664i
\(493\) 10999.6i 1.00487i
\(494\) −3515.69 + 2537.20i −0.320199 + 0.231081i
\(495\) 0.747807 + 0.859271i 6.79018e−5 + 7.80229e-5i
\(496\) −13348.9 + 13348.9i −1.20843 + 1.20843i
\(497\) 6587.91i 0.594584i
\(498\) 18582.6 + 8462.24i 1.67210 + 0.761450i
\(499\) −3607.76 + 3607.76i −0.323659 + 0.323659i −0.850169 0.526510i \(-0.823500\pi\)
0.526510 + 0.850169i \(0.323500\pi\)
\(500\) 196.579 + 196.579i 0.0175825 + 0.0175825i
\(501\) −6321.21 16892.3i −0.563694 1.50637i
\(502\) 4923.07 + 4923.07i 0.437704 + 0.437704i
\(503\) 6518.68i 0.577840i −0.957353 0.288920i \(-0.906704\pi\)
0.957353 0.288920i \(-0.0932962\pi\)
\(504\) −3343.48 3841.85i −0.295497 0.339542i
\(505\) 621.756 + 621.756i 0.0547877 + 0.0547877i
\(506\) 25.5489 0.00224463
\(507\) −8369.54 7763.67i −0.733145 0.680072i
\(508\) 1854.14 0.161938
\(509\) 8689.49 + 8689.49i 0.756689 + 0.756689i 0.975718 0.219029i \(-0.0702890\pi\)
−0.219029 + 0.975718i \(0.570289\pi\)
\(510\) −436.140 198.611i −0.0378678 0.0172444i
\(511\) 6230.25i 0.539354i
\(512\) 2637.52 + 2637.52i 0.227662 + 0.227662i
\(513\) −1931.51 + 3564.60i −0.166234 + 0.306785i
\(514\) −2633.74 2633.74i −0.226010 0.226010i
\(515\) −458.856 + 458.856i −0.0392614 + 0.0392614i
\(516\) −1342.42 + 2947.88i −0.114528 + 0.251498i
\(517\) 26.4116i 0.00224677i
\(518\) −8101.48 + 8101.48i −0.687179 + 0.687179i
\(519\) 1512.06 3320.41i 0.127885 0.280828i
\(520\) −347.027 + 250.442i −0.0292656 + 0.0211204i
\(521\) 21252.3i 1.78710i 0.448963 + 0.893550i \(0.351793\pi\)
−0.448963 + 0.893550i \(0.648207\pi\)
\(522\) 16315.0 + 1131.58i 1.36798 + 0.0948810i
\(523\) 3719.30 0.310963 0.155481 0.987839i \(-0.450307\pi\)
0.155481 + 0.987839i \(0.450307\pi\)
\(524\) −621.372 −0.0518030
\(525\) 2326.64 + 6217.52i 0.193415 + 0.516867i
\(526\) 3741.31 3741.31i 0.310131 0.310131i
\(527\) −10087.3 + 10087.3i −0.833796 + 0.833796i
\(528\) 11.9226 + 31.8609i 0.000982696 + 0.00262608i
\(529\) −3371.95 −0.277139
\(530\) 924.760 0.0757906
\(531\) 15111.2 + 1048.09i 1.23497 + 0.0856557i
\(532\) 664.550i 0.0541577i
\(533\) 8671.52 + 1401.80i 0.704700 + 0.113919i
\(534\) 4650.00 10211.1i 0.376826 0.827490i
\(535\) 130.876 130.876i 0.0105762 0.0105762i
\(536\) 1157.34i 0.0932640i
\(537\) 738.875 1622.53i 0.0593758 0.130386i
\(538\) −8112.92 + 8112.92i −0.650136 + 0.650136i
\(539\) 14.3309 + 14.3309i 0.00114522 + 0.00114522i
\(540\) 74.3990 137.304i 0.00592893 0.0109419i
\(541\) −935.454 935.454i −0.0743407 0.0743407i 0.668959 0.743299i \(-0.266740\pi\)
−0.743299 + 0.668959i \(0.766740\pi\)
\(542\) 998.935i 0.0791660i
\(543\) −12802.7 5830.15i −1.01182 0.460766i
\(544\) −4063.50 4063.50i −0.320259 0.320259i
\(545\) 1009.08 0.0793108
\(546\) 7828.00 1568.94i 0.613567 0.122975i
\(547\) −24246.7 −1.89528 −0.947638 0.319348i \(-0.896536\pi\)
−0.947638 + 0.319348i \(0.896536\pi\)
\(548\) 325.129 + 325.129i 0.0253445 + 0.0253445i
\(549\) 4328.62 + 4973.83i 0.336505 + 0.386663i
\(550\) 33.9866i 0.00263490i
\(551\) −3866.77 3866.77i −0.298965 0.298965i
\(552\) 3145.77 + 8406.48i 0.242559 + 0.648195i
\(553\) −4615.13 4615.13i −0.354892 0.354892i
\(554\) 1245.71 1245.71i 0.0955330 0.0955330i
\(555\) 819.312 + 373.102i 0.0626628 + 0.0285357i
\(556\) 5489.35i 0.418706i
\(557\) 7890.32 7890.32i 0.600222 0.600222i −0.340150 0.940371i \(-0.610478\pi\)
0.940371 + 0.340150i \(0.110478\pi\)
\(558\) −13924.1 15999.5i −1.05637 1.21382i
\(559\) 7614.59 + 10551.2i 0.576141 + 0.798333i
\(560\) 390.485i 0.0294661i
\(561\) 9.00952 + 24.0763i 0.000678043 + 0.00181195i
\(562\) 21335.2 1.60137
\(563\) 9586.10 0.717595 0.358798 0.933415i \(-0.383187\pi\)
0.358798 + 0.933415i \(0.383187\pi\)
\(564\) 3391.22 1269.02i 0.253185 0.0947435i
\(565\) −455.572 + 455.572i −0.0339222 + 0.0339222i
\(566\) −3316.92 + 3316.92i −0.246326 + 0.246326i
\(567\) 5957.22 4499.67i 0.441234 0.333277i
\(568\) 11849.0 0.875302
\(569\) 12552.5 0.924831 0.462415 0.886663i \(-0.346983\pi\)
0.462415 + 0.886663i \(0.346983\pi\)
\(570\) −223.138 + 83.4998i −0.0163969 + 0.00613583i
\(571\) 276.603i 0.0202723i −0.999949 0.0101361i \(-0.996774\pi\)
0.999949 0.0101361i \(-0.00322649\pi\)
\(572\) −8.84342 1.42959i −0.000646437 0.000104500i
\(573\) 16818.6 + 7658.94i 1.22619 + 0.558389i
\(574\) −4343.83 + 4343.83i −0.315868 + 0.315868i
\(575\) 11699.7i 0.848541i
\(576\) −6088.31 + 5298.54i −0.440416 + 0.383285i
\(577\) −6032.82 + 6032.82i −0.435268 + 0.435268i −0.890416 0.455148i \(-0.849586\pi\)
0.455148 + 0.890416i \(0.349586\pi\)
\(578\) 3472.43 + 3472.43i 0.249886 + 0.249886i
\(579\) −409.422 + 153.209i −0.0293869 + 0.0109968i
\(580\) 148.943 + 148.943i 0.0106630 + 0.0106630i
\(581\) 12572.4i 0.897744i
\(582\) −1639.48 + 3600.21i −0.116767 + 0.256415i
\(583\) −35.0764 35.0764i −0.00249180 0.00249180i
\(584\) −11205.7 −0.793997
\(585\) −331.036 532.874i −0.0233960 0.0376609i
\(586\) −22528.2 −1.58811
\(587\) −16607.1 16607.1i −1.16772 1.16772i −0.982743 0.184975i \(-0.940780\pi\)
−0.184975 0.982743i \(-0.559220\pi\)
\(588\) 1151.50 2528.64i 0.0807604 0.177345i
\(589\) 7092.12i 0.496139i
\(590\) 629.428 + 629.428i 0.0439206 + 0.0439206i
\(591\) 1578.07 590.527i 0.109836 0.0411016i
\(592\) 19011.1 + 19011.1i 1.31985 + 1.31985i
\(593\) 7681.48 7681.48i 0.531941 0.531941i −0.389209 0.921149i \(-0.627252\pi\)
0.921149 + 0.389209i \(0.127252\pi\)
\(594\) −36.6375 + 10.8863i −0.00253073 + 0.000751973i
\(595\) 295.077i 0.0203311i
\(596\) 2097.93 2097.93i 0.144186 0.144186i
\(597\) 20282.4 + 9236.28i 1.39046 + 0.633192i
\(598\) −13889.9 2245.39i −0.949835 0.153546i
\(599\) 19722.5i 1.34531i −0.739956 0.672655i \(-0.765154\pi\)
0.739956 0.672655i \(-0.234846\pi\)
\(600\) 11182.8 4184.68i 0.760893 0.284732i
\(601\) −6532.58 −0.443377 −0.221689 0.975118i \(-0.571157\pi\)
−0.221689 + 0.975118i \(0.571157\pi\)
\(602\) −9099.81 −0.616080
\(603\) 1692.43 + 117.384i 0.114297 + 0.00792746i
\(604\) 1534.16 1534.16i 0.103351 0.103351i
\(605\) −466.526 + 466.526i −0.0313504 + 0.0313504i
\(606\) −27631.9 + 10340.1i −1.85226 + 0.693129i
\(607\) 2988.34 0.199824 0.0999120 0.994996i \(-0.468144\pi\)
0.0999120 + 0.994996i \(0.468144\pi\)
\(608\) −2856.93 −0.190566
\(609\) 3529.16 + 9431.02i 0.234825 + 0.627528i
\(610\) 387.475i 0.0257187i
\(611\) 2321.21 14359.0i 0.153693 0.950739i
\(612\) 2658.48 2313.63i 0.175593 0.152815i
\(613\) −3030.04 + 3030.04i −0.199645 + 0.199645i −0.799848 0.600203i \(-0.795086\pi\)
0.600203 + 0.799848i \(0.295086\pi\)
\(614\) 5069.10i 0.333179i
\(615\) 439.297 + 200.049i 0.0288035 + 0.0131167i
\(616\) −11.3522 + 11.3522i −0.000742521 + 0.000742521i
\(617\) −11141.2 11141.2i −0.726948 0.726948i 0.243062 0.970011i \(-0.421848\pi\)
−0.970011 + 0.243062i \(0.921848\pi\)
\(618\) −7630.97 20392.4i −0.496703 1.32735i
\(619\) −11973.1 11973.1i −0.777444 0.777444i 0.201951 0.979396i \(-0.435272\pi\)
−0.979396 + 0.201951i \(0.935272\pi\)
\(620\) 273.179i 0.0176954i
\(621\) −12612.2 + 3747.56i −0.814995 + 0.242165i
\(622\) −4060.04 4060.04i −0.261725 0.261725i
\(623\) 6908.51 0.444276
\(624\) −3681.72 18369.4i −0.236197 1.17847i
\(625\) −15532.9 −0.994107
\(626\) −17070.7 17070.7i −1.08991 1.08991i
\(627\) 11.6309 + 5.29652i 0.000740817 + 0.000337357i
\(628\) 260.701i 0.0165654i
\(629\) 14366.1 + 14366.1i 0.910676 + 0.910676i
\(630\) 437.666 + 30.3558i 0.0276779 + 0.00191969i
\(631\) 10462.6 + 10462.6i 0.660079 + 0.660079i 0.955398 0.295320i \(-0.0954262\pi\)
−0.295320 + 0.955398i \(0.595426\pi\)
\(632\) −8300.75 + 8300.75i −0.522446 + 0.522446i
\(633\) −1996.38 + 4383.93i −0.125354 + 0.275270i
\(634\) 17135.4i 1.07340i
\(635\) 289.415 289.415i 0.0180868 0.0180868i
\(636\) −2818.43 + 6189.12i −0.175720 + 0.385872i
\(637\) −6531.66 9050.62i −0.406270 0.562949i
\(638\) 51.5524i 0.00319903i
\(639\) −1201.79 + 17327.3i −0.0744009 + 1.07270i
\(640\) −866.344 −0.0535082
\(641\) −11375.1 −0.700922 −0.350461 0.936577i \(-0.613975\pi\)
−0.350461 + 0.936577i \(0.613975\pi\)
\(642\) 2176.53 + 5816.37i 0.133802 + 0.357560i
\(643\) 20708.6 20708.6i 1.27009 1.27009i 0.324054 0.946039i \(-0.394954\pi\)
0.946039 0.324054i \(-0.105046\pi\)
\(644\) 1524.98 1524.98i 0.0933118 0.0933118i
\(645\) 250.598 + 669.677i 0.0152981 + 0.0408814i
\(646\) −5376.70 −0.327467
\(647\) −4586.05 −0.278665 −0.139333 0.990246i \(-0.544496\pi\)
−0.139333 + 0.990246i \(0.544496\pi\)
\(648\) −8093.07 10714.6i −0.490626 0.649553i
\(649\) 47.7488i 0.00288799i
\(650\) −2986.95 + 18477.2i −0.180243 + 1.11498i
\(651\) 5412.36 11885.3i 0.325848 0.715545i
\(652\) 599.905 599.905i 0.0360339 0.0360339i
\(653\) 21589.3i 1.29380i −0.762573 0.646902i \(-0.776064\pi\)
0.762573 0.646902i \(-0.223936\pi\)
\(654\) −14032.0 + 30813.4i −0.838980 + 1.84236i
\(655\) −96.9906 + 96.9906i −0.00578586 + 0.00578586i
\(656\) 10193.4 + 10193.4i 0.606682 + 0.606682i
\(657\) 1136.55 16386.6i 0.0674900 0.973062i
\(658\) 7192.85 + 7192.85i 0.426150 + 0.426150i
\(659\) 32017.7i 1.89261i 0.323271 + 0.946306i \(0.395218\pi\)
−0.323271 + 0.946306i \(0.604782\pi\)
\(660\) −0.448006 0.204015i −2.64221e−5 1.20322e-5i
\(661\) −5903.99 5903.99i −0.347411 0.347411i 0.511733 0.859144i \(-0.329004\pi\)
−0.859144 + 0.511733i \(0.829004\pi\)
\(662\) 17334.2 1.01769
\(663\) −2782.16 13881.2i −0.162972 0.813122i
\(664\) 22612.6 1.32159
\(665\) −103.730 103.730i −0.00604886 0.00604886i
\(666\) −22786.1 + 19830.3i −1.32574 + 1.15377i
\(667\) 17746.6i 1.03021i
\(668\) 5511.53 + 5511.53i 0.319233 + 0.319233i
\(669\) 740.185 + 1978.01i 0.0427761 + 0.114311i
\(670\) 70.4949 + 70.4949i 0.00406486 + 0.00406486i
\(671\) 14.6971 14.6971i 0.000845564 0.000845564i
\(672\) 4787.76 + 2180.27i 0.274839 + 0.125158i
\(673\) 4597.39i 0.263323i −0.991295 0.131662i \(-0.957969\pi\)
0.991295 0.131662i \(-0.0420312\pi\)
\(674\) 21988.5 21988.5i 1.25663 1.25663i
\(675\) 4985.23 + 16777.6i 0.284269 + 0.956694i
\(676\) 4682.19 + 1554.43i 0.266397 + 0.0884403i
\(677\) 4282.28i 0.243104i −0.992585 0.121552i \(-0.961213\pi\)
0.992585 0.121552i \(-0.0387871\pi\)
\(678\) −7576.34 20246.4i −0.429156 1.14684i
\(679\) −2435.78 −0.137668
\(680\) −530.724 −0.0299299
\(681\) 27407.6 10256.1i 1.54223 0.577115i
\(682\) −47.2766 + 47.2766i −0.00265442 + 0.00265442i
\(683\) −20404.1 + 20404.1i −1.14310 + 1.14310i −0.155224 + 0.987879i \(0.549610\pi\)
−0.987879 + 0.155224i \(0.950390\pi\)
\(684\) 121.230 1747.88i 0.00677682 0.0977073i
\(685\) 101.499 0.00566144
\(686\) 19049.1 1.06020
\(687\) 8109.89 3034.78i 0.450381 0.168536i
\(688\) 21353.8i 1.18330i
\(689\) 15987.0 + 22152.4i 0.883970 + 1.22488i
\(690\) −703.660 320.436i −0.0388230 0.0176794i
\(691\) 10715.7 10715.7i 0.589936 0.589936i −0.347678 0.937614i \(-0.613030\pi\)
0.937614 + 0.347678i \(0.113030\pi\)
\(692\) 1576.72i 0.0866153i
\(693\) −15.4494 17.7522i −0.000846861 0.000973090i
\(694\) 1591.24 1591.24i 0.0870356 0.0870356i
\(695\) −856.839 856.839i −0.0467651 0.0467651i
\(696\) 16962.6 6347.52i 0.923800 0.345692i
\(697\) 7702.80 + 7702.80i 0.418600 + 0.418600i
\(698\) 28209.1i 1.52970i
\(699\) −12514.8 + 27481.9i −0.677187 + 1.48707i
\(700\) −2028.62 2028.62i −0.109535 0.109535i
\(701\) −22279.2 −1.20039 −0.600195 0.799854i \(-0.704910\pi\)
−0.600195 + 0.799854i \(0.704910\pi\)
\(702\) 20875.1 2698.56i 1.12234 0.145086i
\(703\) 10100.4 0.541885
\(704\) 17.9902 + 17.9902i 0.000963113 + 0.000963113i
\(705\) 331.257 727.422i 0.0176962 0.0388600i
\(706\) 20850.1i 1.11148i
\(707\) −12845.3 12845.3i −0.683304 0.683304i
\(708\) −6130.89 + 2294.22i −0.325442 + 0.121783i
\(709\) 10387.2 + 10387.2i 0.550213 + 0.550213i 0.926502 0.376289i \(-0.122800\pi\)
−0.376289 + 0.926502i \(0.622800\pi\)
\(710\) −721.734 + 721.734i −0.0381496 + 0.0381496i
\(711\) −11296.7 12980.5i −0.595862 0.684678i
\(712\) 12425.6i 0.654030i
\(713\) −16274.7 + 16274.7i −0.854829 + 0.854829i
\(714\) 9010.49 + 4103.24i 0.472282 + 0.215070i
\(715\) −1.60353 + 1.15723i −8.38720e−5 + 6.05287e-5i
\(716\) 770.468i 0.0402147i
\(717\) −3591.44 + 1343.94i −0.187064 + 0.0700007i
\(718\) 39331.6 2.04435
\(719\) 29006.9 1.50455 0.752276 0.658848i \(-0.228956\pi\)
0.752276 + 0.658848i \(0.228956\pi\)
\(720\) 71.2338 1027.04i 0.00368712 0.0531604i
\(721\) 9479.81 9479.81i 0.489663 0.489663i
\(722\) 13634.2 13634.2i 0.702790 0.702790i
\(723\) −18988.0 + 7105.46i −0.976725 + 0.365498i
\(724\) 6079.44 0.312073
\(725\) −23607.6 −1.20933
\(726\) −7758.52 20733.2i −0.396619 1.05989i
\(727\) 1301.34i 0.0663881i 0.999449 + 0.0331941i \(0.0105679\pi\)
−0.999449 + 0.0331941i \(0.989432\pi\)
\(728\) 7169.45 5174.05i 0.364996 0.263411i
\(729\) 16489.3 10748.1i 0.837745 0.546062i
\(730\) 682.551 682.551i 0.0346059 0.0346059i
\(731\) 16136.4i 0.816454i
\(732\) −2593.25 1180.93i −0.130942 0.0596288i
\(733\) 7575.76 7575.76i 0.381742 0.381742i −0.489987 0.871730i \(-0.662999\pi\)
0.871730 + 0.489987i \(0.162999\pi\)
\(734\) 6878.40 + 6878.40i 0.345894 + 0.345894i
\(735\) −214.958 574.436i −0.0107876 0.0288278i
\(736\) −6555.98 6555.98i −0.328338 0.328338i
\(737\) 5.34779i 0.000267284i
\(738\) −12217.4 + 10632.6i −0.609390 + 0.530340i
\(739\) −26362.3 26362.3i −1.31225 1.31225i −0.919752 0.392500i \(-0.871610\pi\)
−0.392500 0.919752i \(-0.628390\pi\)
\(740\) −389.055 −0.0193270
\(741\) −5857.77 3901.71i −0.290405 0.193431i
\(742\) −19105.2 −0.945249
\(743\) −14985.2 14985.2i −0.739913 0.739913i 0.232648 0.972561i \(-0.425261\pi\)
−0.972561 + 0.232648i \(0.925261\pi\)
\(744\) −21376.7 9734.64i −1.05337 0.479690i
\(745\) 654.937i 0.0322081i
\(746\) −9309.65 9309.65i −0.456904 0.456904i
\(747\) −2293.50 + 33067.4i −0.112336 + 1.61964i
\(748\) −7.85550 7.85550i −0.000383991 0.000383991i
\(749\) −2703.86 + 2703.86i −0.131905 + 0.131905i
\(750\) −853.366 + 1873.95i −0.0415474 + 0.0912357i
\(751\) 349.933i 0.0170030i 0.999964 + 0.00850149i \(0.00270614\pi\)
−0.999964 + 0.00850149i \(0.997294\pi\)
\(752\) 16878.9 16878.9i 0.818499 0.818499i
\(753\) −4684.06 + 10285.9i −0.226689 + 0.497796i
\(754\) −4530.74 + 28027.1i −0.218833 + 1.35369i
\(755\) 478.936i 0.0230865i
\(756\) −1537.06 + 2836.65i −0.0739448 + 0.136465i
\(757\) −24519.0 −1.17722 −0.588612 0.808416i \(-0.700325\pi\)
−0.588612 + 0.808416i \(0.700325\pi\)
\(758\) −16031.5 −0.768195
\(759\) 14.5358 + 38.8443i 0.000695147 + 0.00185765i
\(760\) −186.569 + 186.569i −0.00890468 + 0.00890468i
\(761\) 20497.4 20497.4i 0.976387 0.976387i −0.0233407 0.999728i \(-0.507430\pi\)
0.999728 + 0.0233407i \(0.00743024\pi\)
\(762\) 4813.09 + 12862.1i 0.228819 + 0.611476i
\(763\) −20847.3 −0.989153
\(764\) −7986.42 −0.378192
\(765\) 53.8292 776.102i 0.00254405 0.0366798i
\(766\) 2241.39i 0.105724i
\(767\) −4196.45 + 25959.2i −0.197556 + 1.22208i
\(768\) 6897.21 15145.9i 0.324065 0.711629i
\(769\) −16748.3 + 16748.3i −0.785381 + 0.785381i −0.980733 0.195352i \(-0.937415\pi\)
0.195352 + 0.980733i \(0.437415\pi\)
\(770\) 1.38295i 6.47247e-5i
\(771\) 2505.87 5502.76i 0.117052 0.257039i
\(772\) 133.584 133.584i 0.00622772 0.00622772i
\(773\) −3346.88 3346.88i −0.155730 0.155730i 0.624942 0.780671i \(-0.285123\pi\)
−0.780671 + 0.624942i \(0.785123\pi\)
\(774\) −23934.0 1660.02i −1.11149 0.0770908i
\(775\) 21649.6 + 21649.6i 1.00345 + 1.00345i
\(776\) 4380.97i 0.202665i
\(777\) −16926.7 7708.16i −0.781521 0.355893i
\(778\) −18052.7 18052.7i −0.831902 0.831902i
\(779\) 5415.63 0.249082
\(780\) 225.633 + 150.289i 0.0103577 + 0.00689897i
\(781\) 54.7512 0.00250852
\(782\) −12338.2 12338.2i −0.564213 0.564213i
\(783\) 7561.82 + 25449.0i 0.345131 + 1.16152i
\(784\) 18316.9i 0.834409i
\(785\) −40.6930 40.6930i −0.00185019 0.00185019i
\(786\) −1612.99 4310.43i −0.0731979 0.195608i
\(787\) 24752.5 + 24752.5i 1.12113 + 1.12113i 0.991572 + 0.129559i \(0.0413561\pi\)
0.129559 + 0.991572i \(0.458644\pi\)
\(788\) −514.887 + 514.887i −0.0232768 + 0.0232768i
\(789\) 7816.85 + 3559.68i 0.352709 + 0.160618i
\(790\) 1011.22i 0.0455411i
\(791\) 9411.96 9411.96i 0.423073 0.423073i
\(792\) −31.9291 + 27.7872i −0.00143251 + 0.00124669i
\(793\) −9281.89 + 6698.56i −0.415649 + 0.299966i
\(794\) 14817.2i 0.662271i
\(795\) 526.135 + 1406.00i 0.0234718 + 0.0627241i
\(796\) −9631.20 −0.428855
\(797\) −15529.1 −0.690176 −0.345088 0.938570i \(-0.612151\pi\)
−0.345088 + 0.938570i \(0.612151\pi\)
\(798\) 4609.95 1725.08i 0.204499 0.0765251i
\(799\) 12754.9 12754.9i 0.564750 0.564750i
\(800\) −8721.15 + 8721.15i −0.385424 + 0.385424i
\(801\) 18170.5 + 1260.28i 0.801529 + 0.0555927i
\(802\) 37636.1 1.65708
\(803\) −51.7787 −0.00227551
\(804\) −686.651 + 256.950i −0.0301198 + 0.0112710i
\(805\) 476.073i 0.0208439i
\(806\) 29857.5 21547.5i 1.30482 0.941662i
\(807\) −16950.6 7719.05i −0.739393 0.336708i
\(808\) −23103.4 + 23103.4i −1.00591 + 1.00591i
\(809\) 37192.7i 1.61635i −0.588943 0.808175i \(-0.700456\pi\)
0.588943 0.808175i \(-0.299544\pi\)
\(810\) 1145.60 + 159.682i 0.0496941 + 0.00692672i
\(811\) 12080.9 12080.9i 0.523080 0.523080i −0.395420 0.918500i \(-0.629401\pi\)
0.918500 + 0.395420i \(0.129401\pi\)
\(812\) −3077.11 3077.11i −0.132987 0.132987i
\(813\) −1518.77 + 568.336i −0.0655175 + 0.0245171i
\(814\) 67.3303 + 67.3303i 0.00289917 + 0.00289917i
\(815\) 187.279i 0.00804922i
\(816\) 9628.77 21144.3i 0.413081 0.907104i
\(817\) 5672.54 + 5672.54i 0.242910 + 0.242910i
\(818\) −31904.5 −1.36371
\(819\) 6839.08 + 11009.0i 0.291791 + 0.469701i
\(820\) −208.603 −0.00888381
\(821\) 4210.80 + 4210.80i 0.178999 + 0.178999i 0.790919 0.611921i \(-0.209603\pi\)
−0.611921 + 0.790919i \(0.709603\pi\)
\(822\) −1411.41 + 3099.39i −0.0598889 + 0.131513i
\(823\) 30867.3i 1.30737i 0.756766 + 0.653686i \(0.226778\pi\)
−0.756766 + 0.653686i \(0.773222\pi\)
\(824\) −17050.3 17050.3i −0.720845 0.720845i
\(825\) 51.6730 19.3364i 0.00218063 0.000816009i
\(826\) −13003.8 13003.8i −0.547771 0.547771i
\(827\) 15143.3 15143.3i 0.636739 0.636739i −0.313010 0.949750i \(-0.601337\pi\)
0.949750 + 0.313010i \(0.101337\pi\)
\(828\) 4289.16 3732.77i 0.180022 0.156670i
\(829\) 23785.9i 0.996525i 0.867026 + 0.498263i \(0.166028\pi\)
−0.867026 + 0.498263i \(0.833972\pi\)
\(830\) −1377.36 + 1377.36i −0.0576009 + 0.0576009i
\(831\) 2602.71 + 1185.24i 0.108649 + 0.0494770i
\(832\) −8199.50 11361.7i −0.341667 0.473432i
\(833\) 13841.5i 0.575727i
\(834\) 38079.4 14249.6i 1.58103 0.591634i
\(835\) 1720.60 0.0713100
\(836\) −5.52299 −0.000228489
\(837\) 16403.6 30272.9i 0.677408 1.25016i
\(838\) 15956.1 15956.1i 0.657749 0.657749i
\(839\) −5042.71 + 5042.71i −0.207501 + 0.207501i −0.803205 0.595703i \(-0.796873\pi\)
0.595703 + 0.803205i \(0.296873\pi\)
\(840\) 455.039 170.279i 0.0186909 0.00699427i
\(841\) −11420.1 −0.468248
\(842\) 15519.8 0.635210
\(843\) 12138.5 + 32437.9i 0.495933 + 1.32529i
\(844\) 2081.74i 0.0849008i
\(845\) 973.480 488.216i 0.0396316 0.0198759i
\(846\) 17606.2 + 20230.5i 0.715503 + 0.822152i
\(847\) 9638.27 9638.27i 0.390998 0.390998i
\(848\) 44832.8i 1.81552i
\(849\) −6930.16 3155.89i −0.280144 0.127573i
\(850\) −16413.1 + 16413.1i −0.662310 + 0.662310i
\(851\) 23178.1 + 23178.1i 0.933648 + 0.933648i
\(852\) −2630.67 7030.00i −0.105781 0.282680i
\(853\) −6010.39 6010.39i −0.241257 0.241257i 0.576113 0.817370i \(-0.304569\pi\)
−0.817370 + 0.576113i \(0.804569\pi\)
\(854\) 8005.10i 0.320760i
\(855\) −253.905 291.751i −0.0101560 0.0116698i
\(856\) 4863.15 + 4863.15i 0.194181 + 0.194181i
\(857\) 3348.20 0.133457 0.0667284 0.997771i \(-0.478744\pi\)
0.0667284 + 0.997771i \(0.478744\pi\)
\(858\) −13.0393 65.0574i −0.000518826 0.00258861i
\(859\) −19432.4 −0.771858 −0.385929 0.922529i \(-0.626119\pi\)
−0.385929 + 0.922529i \(0.626119\pi\)
\(860\) −218.499 218.499i −0.00866366 0.00866366i
\(861\) −9075.72 4132.95i −0.359233 0.163589i
\(862\) 22642.9i 0.894689i
\(863\) 32959.0 + 32959.0i 1.30004 + 1.30004i 0.928359 + 0.371685i \(0.121220\pi\)
0.371685 + 0.928359i \(0.378780\pi\)
\(864\) 12194.9 + 6607.89i 0.480183 + 0.260191i
\(865\) 246.111 + 246.111i 0.00967403 + 0.00967403i
\(866\) 7370.13 7370.13i 0.289200 0.289200i
\(867\) −3303.85 + 7255.06i −0.129417 + 0.284192i
\(868\) 5643.78i 0.220694i
\(869\) −38.3557 + 38.3557i −0.00149727 + 0.00149727i
\(870\) −646.575 + 1419.84i −0.0251965 + 0.0553301i
\(871\) −469.996 + 2907.39i −0.0182838 + 0.113103i
\(872\) 37495.8i 1.45616i
\(873\) −6406.50 444.344i −0.248370 0.0172266i
\(874\) −8674.68 −0.335727
\(875\) −1267.85 −0.0489841
\(876\) 2487.85 + 6648.34i 0.0959553 + 0.256423i
\(877\) −28070.1 + 28070.1i −1.08080 + 1.08080i −0.0843650 + 0.996435i \(0.526886\pi\)
−0.996435 + 0.0843650i \(0.973114\pi\)
\(878\) −14397.9 + 14397.9i −0.553423 + 0.553423i
\(879\) −12817.2 34251.7i −0.491825 1.31431i
\(880\) −3.24526 −0.000124316
\(881\) −16588.0 −0.634353 −0.317176 0.948367i \(-0.602735\pi\)
−0.317176 + 0.948367i \(0.602735\pi\)
\(882\) 20530.1 + 1423.94i 0.783771 + 0.0543611i
\(883\) 45423.1i 1.73115i −0.500776 0.865577i \(-0.666952\pi\)
0.500776 0.865577i \(-0.333048\pi\)
\(884\) 3580.34 + 4961.12i 0.136222 + 0.188756i
\(885\) −598.870 + 1315.09i −0.0227467 + 0.0499504i
\(886\) −25360.5 + 25360.5i −0.961627 + 0.961627i
\(887\) 21141.8i 0.800308i 0.916448 + 0.400154i \(0.131043\pi\)
−0.916448 + 0.400154i \(0.868957\pi\)
\(888\) −13863.8 + 30444.3i −0.523919 + 1.15050i
\(889\) −5979.22 + 5979.22i −0.225575 + 0.225575i
\(890\) 756.858 + 756.858i 0.0285055 + 0.0285055i
\(891\) −37.3961 49.5097i −0.00140608 0.00186154i
\(892\) −645.376 645.376i −0.0242251 0.0242251i
\(893\) 8967.61i 0.336047i
\(894\) 19999.2 + 9107.32i 0.748180 + 0.340710i
\(895\) 120.263 + 120.263i 0.00449157 + 0.00449157i
\(896\) 17898.4 0.667347
\(897\) −4488.69 22395.7i −0.167083 0.833633i
\(898\) 20418.3 0.758759
\(899\) 32839.1 + 32839.1i 1.21829 + 1.21829i
\(900\) −4965.55 5705.69i −0.183909 0.211322i
\(901\) 33878.8i 1.25268i
\(902\) 36.1010 + 36.1010i 0.00133263 + 0.00133263i
\(903\) −5177.26 13835.3i −0.190796 0.509866i
\(904\) −16928.3 16928.3i −0.622817 0.622817i
\(905\) 948.946 948.946i 0.0348553 0.0348553i
\(906\) 14624.8 + 6659.92i 0.536288 + 0.244218i
\(907\) 31242.6i 1.14376i −0.820336 0.571881i \(-0.806214\pi\)
0.820336 0.571881i \(-0.193786\pi\)
\(908\) −8942.41 + 8942.41i −0.326833 + 0.326833i
\(909\) −31441.9 36128.5i −1.14726 1.31827i
\(910\) −121.542 + 751.856i −0.00442756 + 0.0273888i
\(911\) 28667.7i 1.04260i −0.853375 0.521298i \(-0.825448\pi\)
0.853375 0.521298i \(-0.174552\pi\)
\(912\) −4048.11 10817.8i −0.146981 0.392779i
\(913\) 104.487 0.00378754
\(914\) −28883.2 −1.04526
\(915\) −589.115 + 220.451i −0.0212847 + 0.00796490i
\(916\) −2646.06 + 2646.06i −0.0954456 + 0.0954456i
\(917\) 2003.79 2003.79i 0.0721604 0.0721604i
\(918\) 22950.6 + 12435.9i 0.825143 + 0.447110i
\(919\) 16605.4 0.596040 0.298020 0.954560i \(-0.403674\pi\)
0.298020 + 0.954560i \(0.403674\pi\)
\(920\) −856.261 −0.0306849
\(921\) 7707.02 2884.02i 0.275738 0.103183i
\(922\) 24355.9i 0.869979i
\(923\) −29766.1 4811.87i −1.06150 0.171598i
\(924\) 9.25564 + 4.21488i 0.000329533 + 0.000150064i
\(925\) 30832.8 30832.8i 1.09598 1.09598i
\(926\) 25777.5i 0.914798i
\(927\) 26662.8 23204.1i 0.944684 0.822140i
\(928\) −13228.6 + 13228.6i −0.467943 + 0.467943i
\(929\) −18663.1 18663.1i −0.659112 0.659112i 0.296058 0.955170i \(-0.404328\pi\)
−0.955170 + 0.296058i \(0.904328\pi\)
\(930\) 1895.03 709.134i 0.0668177 0.0250037i
\(931\) −4865.80 4865.80i −0.171289 0.171289i
\(932\) 13049.9i 0.458653i
\(933\) 3862.93 8482.78i 0.135548 0.297657i
\(934\) 29731.2 + 29731.2i 1.04158 + 1.04158i
\(935\) −2.45235 −8.57757e−5
\(936\) 19800.7 12300.7i 0.691460 0.429553i
\(937\) −24863.9 −0.866881 −0.433440 0.901182i \(-0.642701\pi\)
−0.433440 + 0.901182i \(0.642701\pi\)
\(938\) −1456.40 1456.40i −0.0506963 0.0506963i
\(939\) 16242.0 35666.5i 0.564470 1.23954i
\(940\) 345.421i 0.0119855i
\(941\) 10173.1 + 10173.1i 0.352426 + 0.352426i 0.861011 0.508586i \(-0.169831\pi\)
−0.508586 + 0.861011i \(0.669831\pi\)
\(942\) 1808.47 676.741i 0.0625510 0.0234070i
\(943\) 12427.6 + 12427.6i 0.429159 + 0.429159i
\(944\) −30515.0 + 30515.0i −1.05209 + 1.05209i
\(945\) 202.854 + 682.696i 0.00698290 + 0.0235006i
\(946\) 75.6272i 0.00259921i
\(947\) −6473.47 + 6473.47i −0.222132 + 0.222132i −0.809396 0.587263i \(-0.800205\pi\)
0.587263 + 0.809396i \(0.300205\pi\)
\(948\) 6767.75 + 3081.93i 0.231863 + 0.105587i
\(949\) 28150.1 + 4550.63i 0.962899 + 0.155658i
\(950\) 11539.6i 0.394098i
\(951\) −26052.6 + 9749.07i −0.888343 + 0.332424i
\(952\) 10964.6 0.373281
\(953\) 28943.0 0.983793 0.491897 0.870654i \(-0.336304\pi\)
0.491897 + 0.870654i \(0.336304\pi\)
\(954\) −50249.9 3485.25i −1.70535 0.118280i
\(955\) −1246.61 + 1246.61i −0.0422401 + 0.0422401i
\(956\) 1171.80 1171.80i 0.0396430 0.0396430i
\(957\) 78.3799 29.3303i 0.00264751 0.000990715i
\(958\) −9052.09 −0.305282
\(959\) −2096.94 −0.0706087
\(960\) −269.847 721.117i −0.00907217 0.0242437i
\(961\) 30439.8i 1.02178i
\(962\) −30687.5 42522.3i −1.02849 1.42513i
\(963\) −7604.85 + 6618.35i −0.254479 + 0.221468i
\(964\) 6195.32 6195.32i 0.206990 0.206990i
\(965\) 41.7026i 0.00139114i
\(966\) 14537.4 + 6620.10i 0.484195 + 0.220495i
\(967\) −6194.98 + 6194.98i −0.206016 + 0.206016i −0.802572 0.596556i \(-0.796535\pi\)
0.596556 + 0.802572i \(0.296535\pi\)
\(968\) −17335.3 17335.3i −0.575598 0.575598i
\(969\) −3059.03 8174.70i −0.101414 0.271011i
\(970\) −266.850 266.850i −0.00883303 0.00883303i
\(971\) 47616.7i 1.57373i −0.617124 0.786866i \(-0.711702\pi\)
0.617124 0.786866i \(-0.288298\pi\)
\(972\) −4560.19 + 7180.45i −0.150482 + 0.236948i
\(973\) 17702.0 + 17702.0i 0.583248 + 0.583248i
\(974\) 32557.1 1.07104
\(975\) −29792.0 + 5971.12i −0.978573 + 0.196132i
\(976\) −18785.0 −0.616078
\(977\) 1901.80 + 1901.80i 0.0622764 + 0.0622764i 0.737559 0.675283i \(-0.235978\pi\)
−0.675283 + 0.737559i \(0.735978\pi\)
\(978\) 5718.77 + 2604.24i 0.186980 + 0.0851477i
\(979\) 57.4157i 0.00187438i
\(980\) 187.424 + 187.424i 0.00610923 + 0.00610923i
\(981\) −54831.9 3803.05i −1.78455 0.123774i
\(982\) −20053.7 20053.7i −0.651671 0.651671i
\(983\) 9735.99 9735.99i 0.315900 0.315900i −0.531290 0.847190i \(-0.678293\pi\)
0.847190 + 0.531290i \(0.178293\pi\)
\(984\) −7433.49 + 16323.5i −0.240824 + 0.528837i
\(985\) 160.738i 0.00519954i
\(986\) −24896.1 + 24896.1i −0.804110 + 0.804110i
\(987\) −6843.65 + 15028.3i −0.220705 + 0.484656i
\(988\) 3002.64 + 485.393i 0.0966868 + 0.0156300i
\(989\) 26034.3i 0.837049i
\(990\) 0.252283 3.63739i 8.09908e−6 0.000116771i
\(991\) 62313.0 1.99741 0.998707 0.0508357i \(-0.0161885\pi\)
0.998707 + 0.0508357i \(0.0161885\pi\)
\(992\) 24262.9 0.776561
\(993\) 9862.16 + 26354.8i 0.315172 + 0.842240i
\(994\) 14910.8 14910.8i 0.475796 0.475796i
\(995\) −1503.34 + 1503.34i −0.0478987 + 0.0478987i
\(996\) −5020.38 13416.0i −0.159716 0.426811i
\(997\) −40277.8 −1.27945 −0.639725 0.768604i \(-0.720952\pi\)
−0.639725 + 0.768604i \(0.720952\pi\)
\(998\) 16331.3 0.517994
\(999\) −43113.9 23361.6i −1.36543 0.739868i
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 39.4.f.b.5.3 20
3.2 odd 2 inner 39.4.f.b.5.8 yes 20
13.8 odd 4 inner 39.4.f.b.8.8 yes 20
39.8 even 4 inner 39.4.f.b.8.3 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.4.f.b.5.3 20 1.1 even 1 trivial
39.4.f.b.5.8 yes 20 3.2 odd 2 inner
39.4.f.b.8.3 yes 20 39.8 even 4 inner
39.4.f.b.8.8 yes 20 13.8 odd 4 inner