Properties

Label 39.3.g.a.31.4
Level $39$
Weight $3$
Character 39.31
Analytic conductor $1.063$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [39,3,Mod(31,39)]
 
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([0, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("39.31");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 39 = 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 39.g (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: \(1.06267303101\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.1579585536.10
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{7} - 4x^{6} + 28x^{5} - 38x^{4} + 8x^{3} + 200x^{2} - 352x + 484 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 31.4
Root \(2.22833 - 1.32913i\) of defining polynomial
Character \(\chi\) \(=\) 39.31
Dual form 39.3.g.a.34.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.26523 - 2.26523i) q^{2} -1.73205 q^{3} -6.26250i q^{4} +(-2.07379 + 2.07379i) q^{5} +(-3.92349 + 3.92349i) q^{6} +(7.04857 + 7.04857i) q^{7} +(-5.12509 - 5.12509i) q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+(2.26523 - 2.26523i) q^{2} -1.73205 q^{3} -6.26250i q^{4} +(-2.07379 + 2.07379i) q^{5} +(-3.92349 + 3.92349i) q^{6} +(7.04857 + 7.04857i) q^{7} +(-5.12509 - 5.12509i) q^{8} +3.00000 q^{9} +9.39521i q^{10} +(-10.8395 - 10.8395i) q^{11} +10.8470i q^{12} +(-12.9619 + 0.994555i) q^{13} +31.9332 q^{14} +(3.59191 - 3.59191i) q^{15} +1.83106 q^{16} +5.74438i q^{17} +(6.79568 - 6.79568i) q^{18} +(-7.54533 + 7.54533i) q^{19} +(12.9871 + 12.9871i) q^{20} +(-12.2085 - 12.2085i) q^{21} -49.1080 q^{22} -35.8702i q^{23} +(8.87691 + 8.87691i) q^{24} +16.3988i q^{25} +(-27.1088 + 31.6145i) q^{26} -5.19615 q^{27} +(44.1417 - 44.1417i) q^{28} -7.97423 q^{29} -16.2730i q^{30} +(37.2527 - 37.2527i) q^{31} +(24.6481 - 24.6481i) q^{32} +(18.7746 + 18.7746i) q^{33} +(13.0123 + 13.0123i) q^{34} -29.2345 q^{35} -18.7875i q^{36} +(23.0620 + 23.0620i) q^{37} +34.1838i q^{38} +(22.4507 - 1.72262i) q^{39} +21.2567 q^{40} +(-23.2376 + 23.2376i) q^{41} -55.3100 q^{42} -16.3140i q^{43} +(-67.8827 + 67.8827i) q^{44} +(-6.22137 + 6.22137i) q^{45} +(-81.2541 - 81.2541i) q^{46} +(18.9476 + 18.9476i) q^{47} -3.17148 q^{48} +50.3648i q^{49} +(37.1470 + 37.1470i) q^{50} -9.94957i q^{51} +(6.22841 + 81.1740i) q^{52} +5.50653 q^{53} +(-11.7705 + 11.7705i) q^{54} +44.9578 q^{55} -72.2491i q^{56} +(13.0689 - 13.0689i) q^{57} +(-18.0634 + 18.0634i) q^{58} +(43.2576 + 43.2576i) q^{59} +(-22.4943 - 22.4943i) q^{60} -52.1029 q^{61} -168.771i q^{62} +(21.1457 + 21.1457i) q^{63} -104.343i q^{64} +(24.8178 - 28.9428i) q^{65} +85.0576 q^{66} +(45.3282 - 45.3282i) q^{67} +35.9742 q^{68} +62.1290i q^{69} +(-66.2228 + 66.2228i) q^{70} +(-76.4801 + 76.4801i) q^{71} +(-15.3753 - 15.3753i) q^{72} +(2.46881 + 2.46881i) q^{73} +104.481 q^{74} -28.4035i q^{75} +(47.2527 + 47.2527i) q^{76} -152.807i q^{77} +(46.9537 - 54.7580i) q^{78} -98.6735 q^{79} +(-3.79723 + 3.79723i) q^{80} +9.00000 q^{81} +105.277i q^{82} +(28.1778 - 28.1778i) q^{83} +(-76.4557 + 76.4557i) q^{84} +(-11.9126 - 11.9126i) q^{85} +(-36.9550 - 36.9550i) q^{86} +13.8118 q^{87} +111.107i q^{88} +(18.8536 + 18.8536i) q^{89} +28.1856i q^{90} +(-98.3731 - 84.3527i) q^{91} -224.637 q^{92} +(-64.5235 + 64.5235i) q^{93} +85.8411 q^{94} -31.2949i q^{95} +(-42.6918 + 42.6918i) q^{96} +(34.6799 - 34.6799i) q^{97} +(114.088 + 114.088i) q^{98} +(-32.5186 - 32.5186i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} - 20 q^{5} + 8 q^{7} - 24 q^{8} + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{2} - 20 q^{5} + 8 q^{7} - 24 q^{8} + 24 q^{9} - 20 q^{11} + 8 q^{13} - 16 q^{14} + 12 q^{15} + 56 q^{16} + 12 q^{18} - 40 q^{19} + 44 q^{20} - 48 q^{21} - 128 q^{22} + 36 q^{24} - 32 q^{26} + 32 q^{28} + 56 q^{29} + 32 q^{31} + 148 q^{32} - 36 q^{33} + 96 q^{34} + 104 q^{35} - 16 q^{37} + 24 q^{39} + 48 q^{40} - 116 q^{41} - 216 q^{42} - 92 q^{44} - 60 q^{45} - 264 q^{46} + 100 q^{47} + 20 q^{50} + 72 q^{52} - 232 q^{53} - 176 q^{55} + 120 q^{57} - 104 q^{58} + 316 q^{59} + 12 q^{60} + 160 q^{61} + 24 q^{63} - 92 q^{65} + 312 q^{66} + 176 q^{67} + 168 q^{68} + 184 q^{70} + 4 q^{71} - 72 q^{72} - 64 q^{73} - 64 q^{74} + 112 q^{76} + 180 q^{78} + 208 q^{79} - 332 q^{80} + 72 q^{81} - 212 q^{83} - 240 q^{84} - 168 q^{85} - 24 q^{87} - 452 q^{89} - 400 q^{91} - 720 q^{92} - 24 q^{93} + 16 q^{94} + 24 q^{96} + 128 q^{97} + 724 q^{98} - 60 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.26523 2.26523i 1.13261 1.13261i 0.142872 0.989741i \(-0.454366\pi\)
0.989741 0.142872i \(-0.0456338\pi\)
\(3\) −1.73205 −0.577350
\(4\) 6.26250i 1.56563i
\(5\) −2.07379 + 2.07379i −0.414758 + 0.414758i −0.883392 0.468634i \(-0.844746\pi\)
0.468634 + 0.883392i \(0.344746\pi\)
\(6\) −3.92349 + 3.92349i −0.653915 + 0.653915i
\(7\) 7.04857 + 7.04857i 1.00694 + 1.00694i 0.999976 + 0.00696323i \(0.00221648\pi\)
0.00696323 + 0.999976i \(0.497784\pi\)
\(8\) −5.12509 5.12509i −0.640636 0.640636i
\(9\) 3.00000 0.333333
\(10\) 9.39521i 0.939521i
\(11\) −10.8395 10.8395i −0.985413 0.985413i 0.0144826 0.999895i \(-0.495390\pi\)
−0.999895 + 0.0144826i \(0.995390\pi\)
\(12\) 10.8470i 0.903915i
\(13\) −12.9619 + 0.994555i −0.997069 + 0.0765042i
\(14\) 31.9332 2.28095
\(15\) 3.59191 3.59191i 0.239461 0.239461i
\(16\) 1.83106 0.114441
\(17\) 5.74438i 0.337905i 0.985624 + 0.168952i \(0.0540384\pi\)
−0.985624 + 0.168952i \(0.945962\pi\)
\(18\) 6.79568 6.79568i 0.377538 0.377538i
\(19\) −7.54533 + 7.54533i −0.397123 + 0.397123i −0.877217 0.480094i \(-0.840602\pi\)
0.480094 + 0.877217i \(0.340602\pi\)
\(20\) 12.9871 + 12.9871i 0.649356 + 0.649356i
\(21\) −12.2085 12.2085i −0.581356 0.581356i
\(22\) −49.1080 −2.23218
\(23\) 35.8702i 1.55957i −0.626045 0.779787i \(-0.715328\pi\)
0.626045 0.779787i \(-0.284672\pi\)
\(24\) 8.87691 + 8.87691i 0.369871 + 0.369871i
\(25\) 16.3988i 0.655952i
\(26\) −27.1088 + 31.6145i −1.04264 + 1.21594i
\(27\) −5.19615 −0.192450
\(28\) 44.1417 44.1417i 1.57649 1.57649i
\(29\) −7.97423 −0.274974 −0.137487 0.990504i \(-0.543902\pi\)
−0.137487 + 0.990504i \(0.543902\pi\)
\(30\) 16.2730i 0.542433i
\(31\) 37.2527 37.2527i 1.20170 1.20170i 0.228049 0.973650i \(-0.426765\pi\)
0.973650 0.228049i \(-0.0732346\pi\)
\(32\) 24.6481 24.6481i 0.770253 0.770253i
\(33\) 18.7746 + 18.7746i 0.568928 + 0.568928i
\(34\) 13.0123 + 13.0123i 0.382716 + 0.382716i
\(35\) −29.2345 −0.835272
\(36\) 18.7875i 0.521875i
\(37\) 23.0620 + 23.0620i 0.623297 + 0.623297i 0.946373 0.323076i \(-0.104717\pi\)
−0.323076 + 0.946373i \(0.604717\pi\)
\(38\) 34.1838i 0.899573i
\(39\) 22.4507 1.72262i 0.575658 0.0441697i
\(40\) 21.2567 0.531417
\(41\) −23.2376 + 23.2376i −0.566772 + 0.566772i −0.931223 0.364451i \(-0.881257\pi\)
0.364451 + 0.931223i \(0.381257\pi\)
\(42\) −55.3100 −1.31690
\(43\) 16.3140i 0.379396i −0.981843 0.189698i \(-0.939249\pi\)
0.981843 0.189698i \(-0.0607509\pi\)
\(44\) −67.8827 + 67.8827i −1.54279 + 1.54279i
\(45\) −6.22137 + 6.22137i −0.138253 + 0.138253i
\(46\) −81.2541 81.2541i −1.76639 1.76639i
\(47\) 18.9476 + 18.9476i 0.403140 + 0.403140i 0.879338 0.476198i \(-0.157985\pi\)
−0.476198 + 0.879338i \(0.657985\pi\)
\(48\) −3.17148 −0.0660726
\(49\) 50.3648i 1.02785i
\(50\) 37.1470 + 37.1470i 0.742940 + 0.742940i
\(51\) 9.94957i 0.195090i
\(52\) 6.22841 + 81.1740i 0.119777 + 1.56104i
\(53\) 5.50653 0.103897 0.0519484 0.998650i \(-0.483457\pi\)
0.0519484 + 0.998650i \(0.483457\pi\)
\(54\) −11.7705 + 11.7705i −0.217972 + 0.217972i
\(55\) 44.9578 0.817415
\(56\) 72.2491i 1.29016i
\(57\) 13.0689 13.0689i 0.229279 0.229279i
\(58\) −18.0634 + 18.0634i −0.311439 + 0.311439i
\(59\) 43.2576 + 43.2576i 0.733180 + 0.733180i 0.971248 0.238069i \(-0.0765143\pi\)
−0.238069 + 0.971248i \(0.576514\pi\)
\(60\) −22.4943 22.4943i −0.374906 0.374906i
\(61\) −52.1029 −0.854146 −0.427073 0.904217i \(-0.640455\pi\)
−0.427073 + 0.904217i \(0.640455\pi\)
\(62\) 168.771i 2.72212i
\(63\) 21.1457 + 21.1457i 0.335646 + 0.335646i
\(64\) 104.343i 1.63036i
\(65\) 24.8178 28.9428i 0.381812 0.445273i
\(66\) 85.0576 1.28875
\(67\) 45.3282 45.3282i 0.676540 0.676540i −0.282676 0.959216i \(-0.591222\pi\)
0.959216 + 0.282676i \(0.0912221\pi\)
\(68\) 35.9742 0.529033
\(69\) 62.1290i 0.900420i
\(70\) −66.2228 + 66.2228i −0.946040 + 0.946040i
\(71\) −76.4801 + 76.4801i −1.07719 + 1.07719i −0.0804243 + 0.996761i \(0.525628\pi\)
−0.996761 + 0.0804243i \(0.974372\pi\)
\(72\) −15.3753 15.3753i −0.213545 0.213545i
\(73\) 2.46881 + 2.46881i 0.0338193 + 0.0338193i 0.723814 0.689995i \(-0.242387\pi\)
−0.689995 + 0.723814i \(0.742387\pi\)
\(74\) 104.481 1.41191
\(75\) 28.4035i 0.378714i
\(76\) 47.2527 + 47.2527i 0.621745 + 0.621745i
\(77\) 152.807i 1.98450i
\(78\) 46.9537 54.7580i 0.601971 0.702025i
\(79\) −98.6735 −1.24903 −0.624516 0.781012i \(-0.714704\pi\)
−0.624516 + 0.781012i \(0.714704\pi\)
\(80\) −3.79723 + 3.79723i −0.0474654 + 0.0474654i
\(81\) 9.00000 0.111111
\(82\) 105.277i 1.28387i
\(83\) 28.1778 28.1778i 0.339492 0.339492i −0.516684 0.856176i \(-0.672834\pi\)
0.856176 + 0.516684i \(0.172834\pi\)
\(84\) −76.4557 + 76.4557i −0.910187 + 0.910187i
\(85\) −11.9126 11.9126i −0.140149 0.140149i
\(86\) −36.9550 36.9550i −0.429709 0.429709i
\(87\) 13.8118 0.158756
\(88\) 111.107i 1.26258i
\(89\) 18.8536 + 18.8536i 0.211838 + 0.211838i 0.805048 0.593210i \(-0.202140\pi\)
−0.593210 + 0.805048i \(0.702140\pi\)
\(90\) 28.1856i 0.313174i
\(91\) −98.3731 84.3527i −1.08102 0.926953i
\(92\) −224.637 −2.44171
\(93\) −64.5235 + 64.5235i −0.693801 + 0.693801i
\(94\) 85.8411 0.913203
\(95\) 31.2949i 0.329420i
\(96\) −42.6918 + 42.6918i −0.444706 + 0.444706i
\(97\) 34.6799 34.6799i 0.357525 0.357525i −0.505375 0.862900i \(-0.668646\pi\)
0.862900 + 0.505375i \(0.168646\pi\)
\(98\) 114.088 + 114.088i 1.16416 + 1.16416i
\(99\) −32.5186 32.5186i −0.328471 0.328471i
\(100\) 102.698 1.02698
\(101\) 126.405i 1.25154i 0.780008 + 0.625769i \(0.215215\pi\)
−0.780008 + 0.625769i \(0.784785\pi\)
\(102\) −22.5380 22.5380i −0.220961 0.220961i
\(103\) 89.7003i 0.870877i −0.900219 0.435438i \(-0.856593\pi\)
0.900219 0.435438i \(-0.143407\pi\)
\(104\) 71.5280 + 61.3337i 0.687769 + 0.589747i
\(105\) 50.6357 0.482244
\(106\) 12.4735 12.4735i 0.117675 0.117675i
\(107\) 48.7860 0.455944 0.227972 0.973668i \(-0.426791\pi\)
0.227972 + 0.973668i \(0.426791\pi\)
\(108\) 32.5409i 0.301305i
\(109\) 29.6606 29.6606i 0.272115 0.272115i −0.557836 0.829951i \(-0.688368\pi\)
0.829951 + 0.557836i \(0.188368\pi\)
\(110\) 101.840 101.840i 0.925816 0.925816i
\(111\) −39.9445 39.9445i −0.359861 0.359861i
\(112\) 12.9063 + 12.9063i 0.115235 + 0.115235i
\(113\) −81.1492 −0.718135 −0.359067 0.933312i \(-0.616905\pi\)
−0.359067 + 0.933312i \(0.616905\pi\)
\(114\) 59.2080i 0.519369i
\(115\) 74.3872 + 74.3872i 0.646845 + 0.646845i
\(116\) 49.9387i 0.430506i
\(117\) −38.8857 + 2.98367i −0.332356 + 0.0255014i
\(118\) 195.977 1.66082
\(119\) −40.4897 + 40.4897i −0.340250 + 0.340250i
\(120\) −36.8177 −0.306814
\(121\) 113.991i 0.942076i
\(122\) −118.025 + 118.025i −0.967417 + 0.967417i
\(123\) 40.2488 40.2488i 0.327226 0.327226i
\(124\) −233.295 233.295i −1.88141 1.88141i
\(125\) −85.8524 85.8524i −0.686819 0.686819i
\(126\) 95.7997 0.760315
\(127\) 14.5872i 0.114860i −0.998350 0.0574301i \(-0.981709\pi\)
0.998350 0.0574301i \(-0.0182906\pi\)
\(128\) −137.768 137.768i −1.07631 1.07631i
\(129\) 28.2567i 0.219044i
\(130\) −9.34405 121.780i −0.0718773 0.936767i
\(131\) −88.9240 −0.678809 −0.339405 0.940640i \(-0.610226\pi\)
−0.339405 + 0.940640i \(0.610226\pi\)
\(132\) 117.576 117.576i 0.890729 0.890729i
\(133\) −106.368 −0.799756
\(134\) 205.357i 1.53252i
\(135\) 10.7757 10.7757i 0.0798202 0.0798202i
\(136\) 29.4405 29.4405i 0.216474 0.216474i
\(137\) 98.5465 + 98.5465i 0.719317 + 0.719317i 0.968465 0.249148i \(-0.0801506\pi\)
−0.249148 + 0.968465i \(0.580151\pi\)
\(138\) 140.736 + 140.736i 1.01983 + 1.01983i
\(139\) −113.610 −0.817341 −0.408670 0.912682i \(-0.634007\pi\)
−0.408670 + 0.912682i \(0.634007\pi\)
\(140\) 183.081i 1.30772i
\(141\) −32.8182 32.8182i −0.232753 0.232753i
\(142\) 346.490i 2.44007i
\(143\) 151.282 + 129.720i 1.05791 + 0.907136i
\(144\) 5.49317 0.0381470
\(145\) 16.5369 16.5369i 0.114047 0.114047i
\(146\) 11.1848 0.0766084
\(147\) 87.2343i 0.593431i
\(148\) 144.426 144.426i 0.975850 0.975850i
\(149\) 146.466 146.466i 0.982990 0.982990i −0.0168674 0.999858i \(-0.505369\pi\)
0.999858 + 0.0168674i \(0.00536932\pi\)
\(150\) −64.3405 64.3405i −0.428936 0.428936i
\(151\) 117.662 + 117.662i 0.779216 + 0.779216i 0.979698 0.200481i \(-0.0642506\pi\)
−0.200481 + 0.979698i \(0.564251\pi\)
\(152\) 77.3409 0.508822
\(153\) 17.2332i 0.112635i
\(154\) −346.141 346.141i −2.24767 2.24767i
\(155\) 154.508i 0.996828i
\(156\) −10.7879 140.597i −0.0691533 0.901265i
\(157\) −168.697 −1.07450 −0.537251 0.843423i \(-0.680537\pi\)
−0.537251 + 0.843423i \(0.680537\pi\)
\(158\) −223.518 + 223.518i −1.41467 + 1.41467i
\(159\) −9.53760 −0.0599849
\(160\) 102.230i 0.638937i
\(161\) 252.834 252.834i 1.57040 1.57040i
\(162\) 20.3870 20.3870i 0.125846 0.125846i
\(163\) 195.823 + 195.823i 1.20137 + 1.20137i 0.973751 + 0.227616i \(0.0730931\pi\)
0.227616 + 0.973751i \(0.426907\pi\)
\(164\) 145.526 + 145.526i 0.887353 + 0.887353i
\(165\) −77.8693 −0.471935
\(166\) 127.658i 0.769026i
\(167\) −23.0045 23.0045i −0.137751 0.137751i 0.634869 0.772620i \(-0.281054\pi\)
−0.772620 + 0.634869i \(0.781054\pi\)
\(168\) 125.139i 0.744875i
\(169\) 167.022 25.7826i 0.988294 0.152560i
\(170\) −53.9697 −0.317469
\(171\) −22.6360 + 22.6360i −0.132374 + 0.132374i
\(172\) −102.167 −0.593992
\(173\) 7.01149i 0.0405288i −0.999795 0.0202644i \(-0.993549\pi\)
0.999795 0.0202644i \(-0.00645081\pi\)
\(174\) 31.2868 31.2868i 0.179809 0.179809i
\(175\) −115.588 + 115.588i −0.660503 + 0.660503i
\(176\) −19.8478 19.8478i −0.112772 0.112772i
\(177\) −74.9244 74.9244i −0.423302 0.423302i
\(178\) 85.4153 0.479861
\(179\) 96.9928i 0.541859i 0.962599 + 0.270930i \(0.0873311\pi\)
−0.962599 + 0.270930i \(0.912669\pi\)
\(180\) 38.9614 + 38.9614i 0.216452 + 0.216452i
\(181\) 173.824i 0.960355i 0.877171 + 0.480177i \(0.159428\pi\)
−0.877171 + 0.480177i \(0.840572\pi\)
\(182\) −413.915 + 31.7594i −2.27426 + 0.174502i
\(183\) 90.2449 0.493142
\(184\) −183.838 + 183.838i −0.999118 + 0.999118i
\(185\) −95.6514 −0.517035
\(186\) 292.321i 1.57162i
\(187\) 62.2665 62.2665i 0.332976 0.332976i
\(188\) 118.659 118.659i 0.631166 0.631166i
\(189\) −36.6255 36.6255i −0.193785 0.193785i
\(190\) −70.8899 70.8899i −0.373105 0.373105i
\(191\) −134.906 −0.706314 −0.353157 0.935564i \(-0.614892\pi\)
−0.353157 + 0.935564i \(0.614892\pi\)
\(192\) 180.727i 0.941287i
\(193\) 4.47074 + 4.47074i 0.0231645 + 0.0231645i 0.718594 0.695430i \(-0.244786\pi\)
−0.695430 + 0.718594i \(0.744786\pi\)
\(194\) 157.116i 0.809874i
\(195\) −42.9856 + 50.1303i −0.220439 + 0.257079i
\(196\) 315.410 1.60923
\(197\) 56.6892 56.6892i 0.287763 0.287763i −0.548432 0.836195i \(-0.684775\pi\)
0.836195 + 0.548432i \(0.184775\pi\)
\(198\) −147.324 −0.744061
\(199\) 360.006i 1.80908i −0.426392 0.904539i \(-0.640216\pi\)
0.426392 0.904539i \(-0.359784\pi\)
\(200\) 84.0452 84.0452i 0.420226 0.420226i
\(201\) −78.5107 + 78.5107i −0.390600 + 0.390600i
\(202\) 286.337 + 286.337i 1.41751 + 1.41751i
\(203\) −56.2070 56.2070i −0.276882 0.276882i
\(204\) −62.3092 −0.305437
\(205\) 96.3800i 0.470146i
\(206\) −203.191 203.191i −0.986366 0.986366i
\(207\) 107.611i 0.519858i
\(208\) −23.7340 + 1.82109i −0.114106 + 0.00875523i
\(209\) 163.576 0.782659
\(210\) 114.701 114.701i 0.546197 0.546197i
\(211\) −212.166 −1.00553 −0.502763 0.864424i \(-0.667683\pi\)
−0.502763 + 0.864424i \(0.667683\pi\)
\(212\) 34.4847i 0.162664i
\(213\) 132.467 132.467i 0.621913 0.621913i
\(214\) 110.511 110.511i 0.516408 0.516408i
\(215\) 33.8318 + 33.8318i 0.157357 + 0.157357i
\(216\) 26.6307 + 26.6307i 0.123290 + 0.123290i
\(217\) 525.156 2.42007
\(218\) 134.376i 0.616403i
\(219\) −4.27610 4.27610i −0.0195256 0.0195256i
\(220\) 281.549i 1.27977i
\(221\) −5.71311 74.4581i −0.0258512 0.336915i
\(222\) −180.967 −0.815166
\(223\) −42.6102 + 42.6102i −0.191077 + 0.191077i −0.796162 0.605084i \(-0.793139\pi\)
0.605084 + 0.796162i \(0.293139\pi\)
\(224\) 347.468 1.55120
\(225\) 49.1964i 0.218651i
\(226\) −183.821 + 183.821i −0.813369 + 0.813369i
\(227\) 53.0656 53.0656i 0.233769 0.233769i −0.580495 0.814264i \(-0.697141\pi\)
0.814264 + 0.580495i \(0.197141\pi\)
\(228\) −81.8440 81.8440i −0.358965 0.358965i
\(229\) −135.376 135.376i −0.591162 0.591162i 0.346783 0.937945i \(-0.387274\pi\)
−0.937945 + 0.346783i \(0.887274\pi\)
\(230\) 337.008 1.46525
\(231\) 264.669i 1.14575i
\(232\) 40.8686 + 40.8686i 0.176158 + 0.176158i
\(233\) 31.3244i 0.134440i −0.997738 0.0672198i \(-0.978587\pi\)
0.997738 0.0672198i \(-0.0214129\pi\)
\(234\) −81.3263 + 94.8436i −0.347548 + 0.405315i
\(235\) −78.5866 −0.334411
\(236\) 270.901 270.901i 1.14789 1.14789i
\(237\) 170.908 0.721129
\(238\) 183.437i 0.770743i
\(239\) −333.688 + 333.688i −1.39618 + 1.39618i −0.585544 + 0.810641i \(0.699119\pi\)
−0.810641 + 0.585544i \(0.800881\pi\)
\(240\) 6.57699 6.57699i 0.0274041 0.0274041i
\(241\) −246.650 246.650i −1.02345 1.02345i −0.999718 0.0237276i \(-0.992447\pi\)
−0.0237276 0.999718i \(-0.507553\pi\)
\(242\) 258.216 + 258.216i 1.06701 + 1.06701i
\(243\) −15.5885 −0.0641500
\(244\) 326.295i 1.33727i
\(245\) −104.446 104.446i −0.426310 0.426310i
\(246\) 182.345i 0.741241i
\(247\) 90.2976 105.306i 0.365577 0.426340i
\(248\) −381.846 −1.53970
\(249\) −48.8054 + 48.8054i −0.196006 + 0.196006i
\(250\) −388.950 −1.55580
\(251\) 331.076i 1.31903i 0.751693 + 0.659513i \(0.229237\pi\)
−0.751693 + 0.659513i \(0.770763\pi\)
\(252\) 132.425 132.425i 0.525497 0.525497i
\(253\) −388.816 + 388.816i −1.53682 + 1.53682i
\(254\) −33.0434 33.0434i −0.130092 0.130092i
\(255\) 20.6333 + 20.6333i 0.0809149 + 0.0809149i
\(256\) −206.779 −0.807731
\(257\) 82.8095i 0.322216i −0.986937 0.161108i \(-0.948493\pi\)
0.986937 0.161108i \(-0.0515068\pi\)
\(258\) 64.0079 + 64.0079i 0.248092 + 0.248092i
\(259\) 325.108i 1.25524i
\(260\) −181.254 155.421i −0.697131 0.597774i
\(261\) −23.9227 −0.0916579
\(262\) −201.433 + 201.433i −0.768828 + 0.768828i
\(263\) 98.6102 0.374944 0.187472 0.982270i \(-0.439971\pi\)
0.187472 + 0.982270i \(0.439971\pi\)
\(264\) 192.443i 0.728951i
\(265\) −11.4194 + 11.4194i −0.0430920 + 0.0430920i
\(266\) −240.947 + 240.947i −0.905815 + 0.905815i
\(267\) −32.6554 32.6554i −0.122305 0.122305i
\(268\) −283.868 283.868i −1.05921 1.05921i
\(269\) 92.5439 0.344029 0.172015 0.985094i \(-0.444972\pi\)
0.172015 + 0.985094i \(0.444972\pi\)
\(270\) 48.8189i 0.180811i
\(271\) 197.527 + 197.527i 0.728881 + 0.728881i 0.970397 0.241516i \(-0.0776446\pi\)
−0.241516 + 0.970397i \(0.577645\pi\)
\(272\) 10.5183i 0.0386702i
\(273\) 170.387 + 146.103i 0.624129 + 0.535176i
\(274\) 446.460 1.62942
\(275\) 177.755 177.755i 0.646383 0.646383i
\(276\) 389.083 1.40972
\(277\) 389.761i 1.40708i −0.710656 0.703539i \(-0.751602\pi\)
0.710656 0.703539i \(-0.248398\pi\)
\(278\) −257.353 + 257.353i −0.925731 + 0.925731i
\(279\) 111.758 111.758i 0.400566 0.400566i
\(280\) 149.829 + 149.829i 0.535105 + 0.535105i
\(281\) 125.522 + 125.522i 0.446699 + 0.446699i 0.894256 0.447557i \(-0.147706\pi\)
−0.447557 + 0.894256i \(0.647706\pi\)
\(282\) −148.681 −0.527238
\(283\) 277.295i 0.979841i −0.871767 0.489921i \(-0.837026\pi\)
0.871767 0.489921i \(-0.162974\pi\)
\(284\) 478.957 + 478.957i 1.68647 + 1.68647i
\(285\) 54.2043i 0.190190i
\(286\) 636.533 48.8406i 2.22564 0.170771i
\(287\) −327.585 −1.14141
\(288\) 73.9443 73.9443i 0.256751 0.256751i
\(289\) 256.002 0.885820
\(290\) 74.9196i 0.258343i
\(291\) −60.0673 + 60.0673i −0.206417 + 0.206417i
\(292\) 15.4609 15.4609i 0.0529484 0.0529484i
\(293\) −327.997 327.997i −1.11944 1.11944i −0.991823 0.127620i \(-0.959266\pi\)
−0.127620 0.991823i \(-0.540734\pi\)
\(294\) −197.606 197.606i −0.672128 0.672128i
\(295\) −179.414 −0.608184
\(296\) 236.389i 0.798613i
\(297\) 56.3239 + 56.3239i 0.189643 + 0.189643i
\(298\) 663.555i 2.22670i
\(299\) 35.6749 + 464.946i 0.119314 + 1.55500i
\(300\) −177.877 −0.592924
\(301\) 114.991 114.991i 0.382028 0.382028i
\(302\) 533.061 1.76510
\(303\) 218.940i 0.722576i
\(304\) −13.8159 + 13.8159i −0.0454471 + 0.0454471i
\(305\) 108.051 108.051i 0.354264 0.354264i
\(306\) 39.0370 + 39.0370i 0.127572 + 0.127572i
\(307\) −88.7474 88.7474i −0.289080 0.289080i 0.547637 0.836716i \(-0.315528\pi\)
−0.836716 + 0.547637i \(0.815528\pi\)
\(308\) −956.952 −3.10699
\(309\) 155.365i 0.502801i
\(310\) 349.996 + 349.996i 1.12902 + 1.12902i
\(311\) 511.900i 1.64598i −0.568054 0.822991i \(-0.692304\pi\)
0.568054 0.822991i \(-0.307696\pi\)
\(312\) −123.890 106.233i −0.397084 0.340490i
\(313\) −402.205 −1.28500 −0.642500 0.766285i \(-0.722103\pi\)
−0.642500 + 0.766285i \(0.722103\pi\)
\(314\) −382.136 + 382.136i −1.21699 + 1.21699i
\(315\) −87.7035 −0.278424
\(316\) 617.943i 1.95552i
\(317\) −159.843 + 159.843i −0.504238 + 0.504238i −0.912752 0.408514i \(-0.866047\pi\)
0.408514 + 0.912752i \(0.366047\pi\)
\(318\) −21.6048 + 21.6048i −0.0679397 + 0.0679397i
\(319\) 86.4370 + 86.4370i 0.270962 + 0.270962i
\(320\) 216.385 + 216.385i 0.676203 + 0.676203i
\(321\) −84.4998 −0.263239
\(322\) 1145.45i 3.55730i
\(323\) −43.3433 43.3433i −0.134190 0.134190i
\(324\) 56.3625i 0.173958i
\(325\) −16.3095 212.560i −0.0501831 0.654029i
\(326\) 887.166 2.72137
\(327\) −51.3736 + 51.3736i −0.157106 + 0.157106i
\(328\) 238.190 0.726189
\(329\) 267.107i 0.811874i
\(330\) −176.392 + 176.392i −0.534520 + 0.534520i
\(331\) 355.451 355.451i 1.07387 1.07387i 0.0768261 0.997045i \(-0.475521\pi\)
0.997045 0.0768261i \(-0.0244786\pi\)
\(332\) −176.464 176.464i −0.531517 0.531517i
\(333\) 69.1860 + 69.1860i 0.207766 + 0.207766i
\(334\) −104.221 −0.312038
\(335\) 188.002i 0.561200i
\(336\) −22.3544 22.3544i −0.0665311 0.0665311i
\(337\) 436.012i 1.29381i 0.762573 + 0.646903i \(0.223936\pi\)
−0.762573 + 0.646903i \(0.776064\pi\)
\(338\) 319.939 436.746i 0.946564 1.29215i
\(339\) 140.555 0.414615
\(340\) −74.6030 + 74.6030i −0.219421 + 0.219421i
\(341\) −807.603 −2.36834
\(342\) 102.551i 0.299858i
\(343\) −9.61961 + 9.61961i −0.0280455 + 0.0280455i
\(344\) −83.6107 + 83.6107i −0.243054 + 0.243054i
\(345\) −128.842 128.842i −0.373456 0.373456i
\(346\) −15.8826 15.8826i −0.0459035 0.0459035i
\(347\) 327.281 0.943174 0.471587 0.881820i \(-0.343681\pi\)
0.471587 + 0.881820i \(0.343681\pi\)
\(348\) 86.4963i 0.248553i
\(349\) 156.300 + 156.300i 0.447851 + 0.447851i 0.894640 0.446788i \(-0.147432\pi\)
−0.446788 + 0.894640i \(0.647432\pi\)
\(350\) 523.666i 1.49619i
\(351\) 67.3520 5.16786i 0.191886 0.0147232i
\(352\) −534.348 −1.51803
\(353\) 301.930 301.930i 0.855327 0.855327i −0.135457 0.990783i \(-0.543250\pi\)
0.990783 + 0.135457i \(0.0432501\pi\)
\(354\) −339.441 −0.958874
\(355\) 317.207i 0.893542i
\(356\) 118.071 118.071i 0.331659 0.331659i
\(357\) 70.1302 70.1302i 0.196443 0.196443i
\(358\) 219.711 + 219.711i 0.613717 + 0.613717i
\(359\) −459.938 459.938i −1.28117 1.28117i −0.940005 0.341160i \(-0.889180\pi\)
−0.341160 0.940005i \(-0.610820\pi\)
\(360\) 63.7701 0.177139
\(361\) 247.136i 0.684587i
\(362\) 393.751 + 393.751i 1.08771 + 1.08771i
\(363\) 197.438i 0.543908i
\(364\) −528.259 + 616.062i −1.45126 + 1.69248i
\(365\) −10.2396 −0.0280537
\(366\) 204.425 204.425i 0.558539 0.558539i
\(367\) 189.697 0.516885 0.258443 0.966027i \(-0.416791\pi\)
0.258443 + 0.966027i \(0.416791\pi\)
\(368\) 65.6804i 0.178479i
\(369\) −69.7129 + 69.7129i −0.188924 + 0.188924i
\(370\) −216.672 + 216.672i −0.585601 + 0.585601i
\(371\) 38.8132 + 38.8132i 0.104618 + 0.104618i
\(372\) 404.079 + 404.079i 1.08623 + 1.08623i
\(373\) 204.386 0.547951 0.273975 0.961737i \(-0.411661\pi\)
0.273975 + 0.961737i \(0.411661\pi\)
\(374\) 282.095i 0.754266i
\(375\) 148.701 + 148.701i 0.396535 + 0.396535i
\(376\) 194.216i 0.516532i
\(377\) 103.361 7.93082i 0.274168 0.0210366i
\(378\) −165.930 −0.438968
\(379\) 18.5656 18.5656i 0.0489858 0.0489858i −0.682190 0.731175i \(-0.738972\pi\)
0.731175 + 0.682190i \(0.238972\pi\)
\(380\) −195.984 −0.515748
\(381\) 25.2658i 0.0663145i
\(382\) −305.593 + 305.593i −0.799981 + 0.799981i
\(383\) −60.2763 + 60.2763i −0.157379 + 0.157379i −0.781404 0.624025i \(-0.785496\pi\)
0.624025 + 0.781404i \(0.285496\pi\)
\(384\) 238.621 + 238.621i 0.621408 + 0.621408i
\(385\) 316.889 + 316.889i 0.823087 + 0.823087i
\(386\) 20.2545 0.0524728
\(387\) 48.9421i 0.126465i
\(388\) −217.183 217.183i −0.559750 0.559750i
\(389\) 6.81993i 0.0175320i −0.999962 0.00876598i \(-0.997210\pi\)
0.999962 0.00876598i \(-0.00279033\pi\)
\(390\) 16.1844 + 210.929i 0.0414984 + 0.540843i
\(391\) 206.052 0.526988
\(392\) 258.124 258.124i 0.658479 0.658479i
\(393\) 154.021 0.391911
\(394\) 256.828i 0.651847i
\(395\) 204.628 204.628i 0.518046 0.518046i
\(396\) −203.648 + 203.648i −0.514263 + 0.514263i
\(397\) 105.682 + 105.682i 0.266200 + 0.266200i 0.827567 0.561367i \(-0.189724\pi\)
−0.561367 + 0.827567i \(0.689724\pi\)
\(398\) −815.496 815.496i −2.04898 2.04898i
\(399\) 184.234 0.461740
\(400\) 30.0271i 0.0750678i
\(401\) 124.906 + 124.906i 0.311487 + 0.311487i 0.845486 0.533998i \(-0.179311\pi\)
−0.533998 + 0.845486i \(0.679311\pi\)
\(402\) 355.689i 0.884798i
\(403\) −445.815 + 519.915i −1.10624 + 1.29011i
\(404\) 791.614 1.95944
\(405\) −18.6641 + 18.6641i −0.0460842 + 0.0460842i
\(406\) −254.643 −0.627200
\(407\) 499.963i 1.22841i
\(408\) −50.9924 + 50.9924i −0.124981 + 0.124981i
\(409\) −341.744 + 341.744i −0.835559 + 0.835559i −0.988271 0.152712i \(-0.951199\pi\)
0.152712 + 0.988271i \(0.451199\pi\)
\(410\) −218.323 218.323i −0.532494 0.532494i
\(411\) −170.687 170.687i −0.415298 0.415298i
\(412\) −561.748 −1.36347
\(413\) 609.809i 1.47653i
\(414\) −243.762 243.762i −0.588798 0.588798i
\(415\) 116.870i 0.281614i
\(416\) −294.972 + 344.000i −0.709068 + 0.826923i
\(417\) 196.779 0.471892
\(418\) 370.536 370.536i 0.886450 0.886450i
\(419\) 347.010 0.828187 0.414093 0.910234i \(-0.364099\pi\)
0.414093 + 0.910234i \(0.364099\pi\)
\(420\) 317.106i 0.755014i
\(421\) −52.0656 + 52.0656i −0.123671 + 0.123671i −0.766233 0.642562i \(-0.777871\pi\)
0.642562 + 0.766233i \(0.277871\pi\)
\(422\) −480.604 + 480.604i −1.13887 + 1.13887i
\(423\) 56.8427 + 56.8427i 0.134380 + 0.134380i
\(424\) −28.2215 28.2215i −0.0665600 0.0665600i
\(425\) −94.2010 −0.221649
\(426\) 600.138i 1.40877i
\(427\) −367.251 367.251i −0.860073 0.860073i
\(428\) 305.523i 0.713838i
\(429\) −262.027 224.682i −0.610786 0.523735i
\(430\) 153.274 0.356450
\(431\) −26.1543 + 26.1543i −0.0606829 + 0.0606829i −0.736797 0.676114i \(-0.763663\pi\)
0.676114 + 0.736797i \(0.263663\pi\)
\(432\) −9.51445 −0.0220242
\(433\) 298.973i 0.690469i 0.938517 + 0.345234i \(0.112201\pi\)
−0.938517 + 0.345234i \(0.887799\pi\)
\(434\) 1189.60 1189.60i 2.74101 2.74101i
\(435\) −28.6427 + 28.6427i −0.0658453 + 0.0658453i
\(436\) −185.749 185.749i −0.426031 0.426031i
\(437\) 270.652 + 270.652i 0.619342 + 0.619342i
\(438\) −19.3727 −0.0442299
\(439\) 176.942i 0.403057i 0.979483 + 0.201528i \(0.0645909\pi\)
−0.979483 + 0.201528i \(0.935409\pi\)
\(440\) −230.413 230.413i −0.523665 0.523665i
\(441\) 151.094i 0.342617i
\(442\) −181.606 155.723i −0.410873 0.352315i
\(443\) 488.694 1.10315 0.551574 0.834126i \(-0.314027\pi\)
0.551574 + 0.834126i \(0.314027\pi\)
\(444\) −250.153 + 250.153i −0.563407 + 0.563407i
\(445\) −78.1967 −0.175723
\(446\) 193.044i 0.432834i
\(447\) −253.686 + 253.686i −0.567530 + 0.567530i
\(448\) 735.468 735.468i 1.64167 1.64167i
\(449\) 291.469 + 291.469i 0.649151 + 0.649151i 0.952788 0.303637i \(-0.0982010\pi\)
−0.303637 + 0.952788i \(0.598201\pi\)
\(450\) 111.441 + 111.441i 0.247647 + 0.247647i
\(451\) 503.771 1.11701
\(452\) 508.198i 1.12433i
\(453\) −203.796 203.796i −0.449881 0.449881i
\(454\) 240.411i 0.529541i
\(455\) 378.935 29.0753i 0.832824 0.0639018i
\(456\) −133.958 −0.293768
\(457\) 420.955 420.955i 0.921126 0.921126i −0.0759832 0.997109i \(-0.524210\pi\)
0.997109 + 0.0759832i \(0.0242096\pi\)
\(458\) −613.315 −1.33912
\(459\) 29.8487i 0.0650298i
\(460\) 465.850 465.850i 1.01272 1.01272i
\(461\) −209.193 + 209.193i −0.453782 + 0.453782i −0.896608 0.442826i \(-0.853976\pi\)
0.442826 + 0.896608i \(0.353976\pi\)
\(462\) 599.535 + 599.535i 1.29769 + 1.29769i
\(463\) 203.453 + 203.453i 0.439422 + 0.439422i 0.891818 0.452395i \(-0.149430\pi\)
−0.452395 + 0.891818i \(0.649430\pi\)
\(464\) −14.6013 −0.0314683
\(465\) 267.616i 0.575519i
\(466\) −70.9569 70.9569i −0.152268 0.152268i
\(467\) 110.726i 0.237101i −0.992948 0.118551i \(-0.962175\pi\)
0.992948 0.118551i \(-0.0378248\pi\)
\(468\) 18.6852 + 243.522i 0.0399257 + 0.520346i
\(469\) 638.998 1.36247
\(470\) −178.016 + 178.016i −0.378758 + 0.378758i
\(471\) 292.191 0.620363
\(472\) 443.398i 0.939402i
\(473\) −176.836 + 176.836i −0.373861 + 0.373861i
\(474\) 387.144 387.144i 0.816760 0.816760i
\(475\) −123.734 123.734i −0.260493 0.260493i
\(476\) 253.567 + 253.567i 0.532704 + 0.532704i
\(477\) 16.5196 0.0346323
\(478\) 1511.76i 3.16267i
\(479\) −652.131 652.131i −1.36144 1.36144i −0.872081 0.489361i \(-0.837230\pi\)
−0.489361 0.872081i \(-0.662770\pi\)
\(480\) 177.067i 0.368891i
\(481\) −321.864 275.991i −0.669155 0.573785i
\(482\) −1117.44 −2.31834
\(483\) −437.921 + 437.921i −0.906668 + 0.906668i
\(484\) 713.870 1.47494
\(485\) 143.838i 0.296572i
\(486\) −35.3114 + 35.3114i −0.0726572 + 0.0726572i
\(487\) 106.252 106.252i 0.218176 0.218176i −0.589553 0.807729i \(-0.700696\pi\)
0.807729 + 0.589553i \(0.200696\pi\)
\(488\) 267.032 + 267.032i 0.547197 + 0.547197i
\(489\) −339.175 339.175i −0.693610 0.693610i
\(490\) −473.187 −0.965689
\(491\) 742.581i 1.51238i −0.654350 0.756192i \(-0.727058\pi\)
0.654350 0.756192i \(-0.272942\pi\)
\(492\) −252.058 252.058i −0.512313 0.512313i
\(493\) 45.8071i 0.0929150i
\(494\) −33.9976 443.087i −0.0688211 0.896936i
\(495\) 134.874 0.272472
\(496\) 68.2118 68.2118i 0.137524 0.137524i
\(497\) −1078.15 −2.16932
\(498\) 221.111i 0.443997i
\(499\) −346.438 + 346.438i −0.694265 + 0.694265i −0.963167 0.268903i \(-0.913339\pi\)
0.268903 + 0.963167i \(0.413339\pi\)
\(500\) −537.651 + 537.651i −1.07530 + 1.07530i
\(501\) 39.8449 + 39.8449i 0.0795307 + 0.0795307i
\(502\) 749.961 + 749.961i 1.49395 + 1.49395i
\(503\) −545.549 −1.08459 −0.542295 0.840188i \(-0.682444\pi\)
−0.542295 + 0.840188i \(0.682444\pi\)
\(504\) 216.747i 0.430054i
\(505\) −262.138 262.138i −0.519085 0.519085i
\(506\) 1761.51i 3.48125i
\(507\) −289.290 + 44.6569i −0.570592 + 0.0880806i
\(508\) −91.3526 −0.179828
\(509\) −352.500 + 352.500i −0.692534 + 0.692534i −0.962789 0.270255i \(-0.912892\pi\)
0.270255 + 0.962789i \(0.412892\pi\)
\(510\) 93.4782 0.183291
\(511\) 34.8032i 0.0681080i
\(512\) 82.6694 82.6694i 0.161464 0.161464i
\(513\) 39.2067 39.2067i 0.0764263 0.0764263i
\(514\) −187.582 187.582i −0.364946 0.364946i
\(515\) 186.020 + 186.020i 0.361203 + 0.361203i
\(516\) 176.958 0.342941
\(517\) 410.766i 0.794518i
\(518\) 736.444 + 736.444i 1.42171 + 1.42171i
\(519\) 12.1443i 0.0233993i
\(520\) −275.527 + 21.1410i −0.529860 + 0.0406557i
\(521\) 604.304 1.15989 0.579947 0.814654i \(-0.303073\pi\)
0.579947 + 0.814654i \(0.303073\pi\)
\(522\) −54.1903 + 54.1903i −0.103813 + 0.103813i
\(523\) −6.78648 −0.0129761 −0.00648803 0.999979i \(-0.502065\pi\)
−0.00648803 + 0.999979i \(0.502065\pi\)
\(524\) 556.887i 1.06276i
\(525\) 200.204 200.204i 0.381342 0.381342i
\(526\) 223.375 223.375i 0.424666 0.424666i
\(527\) 213.994 + 213.994i 0.406060 + 0.406060i
\(528\) 34.3774 + 34.3774i 0.0651088 + 0.0651088i
\(529\) −757.670 −1.43227
\(530\) 51.7350i 0.0976133i
\(531\) 129.773 + 129.773i 0.244393 + 0.244393i
\(532\) 666.128i 1.25212i
\(533\) 278.093 324.315i 0.521750 0.608471i
\(534\) −147.944 −0.277048
\(535\) −101.172 + 101.172i −0.189106 + 0.189106i
\(536\) −464.621 −0.866831
\(537\) 167.996i 0.312843i
\(538\) 209.633 209.633i 0.389652 0.389652i
\(539\) 545.931 545.931i 1.01286 1.01286i
\(540\) −67.4830 67.4830i −0.124969 0.124969i
\(541\) −197.678 197.678i −0.365393 0.365393i 0.500401 0.865794i \(-0.333186\pi\)
−0.865794 + 0.500401i \(0.833186\pi\)
\(542\) 894.886 1.65108
\(543\) 301.072i 0.554461i
\(544\) 141.588 + 141.588i 0.260272 + 0.260272i
\(545\) 123.020i 0.225724i
\(546\) 716.922 55.0088i 1.31304 0.100749i
\(547\) −873.392 −1.59669 −0.798347 0.602197i \(-0.794292\pi\)
−0.798347 + 0.602197i \(0.794292\pi\)
\(548\) 617.148 617.148i 1.12618 1.12618i
\(549\) −156.309 −0.284715
\(550\) 805.312i 1.46420i
\(551\) 60.1682 60.1682i 0.109198 0.109198i
\(552\) 318.416 318.416i 0.576841 0.576841i
\(553\) −695.508 695.508i −1.25770 1.25770i
\(554\) −882.897 882.897i −1.59368 1.59368i
\(555\) 165.673 0.298510
\(556\) 711.485i 1.27965i
\(557\) 403.156 + 403.156i 0.723799 + 0.723799i 0.969377 0.245578i \(-0.0789778\pi\)
−0.245578 + 0.969377i \(0.578978\pi\)
\(558\) 506.314i 0.907373i
\(559\) 16.2252 + 211.461i 0.0290254 + 0.378284i
\(560\) −53.5301 −0.0955894
\(561\) −107.849 + 107.849i −0.192244 + 0.192244i
\(562\) 568.674 1.01187
\(563\) 956.142i 1.69830i 0.528153 + 0.849149i \(0.322885\pi\)
−0.528153 + 0.849149i \(0.677115\pi\)
\(564\) −205.524 + 205.524i −0.364404 + 0.364404i
\(565\) 168.286 168.286i 0.297852 0.297852i
\(566\) −628.136 628.136i −1.10978 1.10978i
\(567\) 63.4372 + 63.4372i 0.111882 + 0.111882i
\(568\) 783.934 1.38017
\(569\) 183.113i 0.321816i −0.986969 0.160908i \(-0.948558\pi\)
0.986969 0.160908i \(-0.0514422\pi\)
\(570\) 122.785 + 122.785i 0.215412 + 0.215412i
\(571\) 526.076i 0.921324i −0.887576 0.460662i \(-0.847612\pi\)
0.887576 0.460662i \(-0.152388\pi\)
\(572\) 812.375 947.401i 1.42024 1.65630i
\(573\) 233.664 0.407791
\(574\) −742.053 + 742.053i −1.29278 + 1.29278i
\(575\) 588.228 1.02300
\(576\) 313.029i 0.543452i
\(577\) 277.438 277.438i 0.480829 0.480829i −0.424568 0.905396i \(-0.639574\pi\)
0.905396 + 0.424568i \(0.139574\pi\)
\(578\) 579.903 579.903i 1.00329 1.00329i
\(579\) −7.74355 7.74355i −0.0133740 0.0133740i
\(580\) −103.562 103.562i −0.178556 0.178556i
\(581\) 397.227 0.683695
\(582\) 272.132i 0.467581i
\(583\) −59.6883 59.6883i −0.102381 0.102381i
\(584\) 25.3057i 0.0433317i
\(585\) 74.4533 86.8283i 0.127271 0.148424i
\(586\) −1485.97 −2.53579
\(587\) 197.192 197.192i 0.335932 0.335932i −0.518902 0.854834i \(-0.673659\pi\)
0.854834 + 0.518902i \(0.173659\pi\)
\(588\) −546.305 −0.929091
\(589\) 562.167i 0.954443i
\(590\) −406.414 + 406.414i −0.688838 + 0.688838i
\(591\) −98.1886 + 98.1886i −0.166140 + 0.166140i
\(592\) 42.2278 + 42.2278i 0.0713308 + 0.0713308i
\(593\) 318.917 + 318.917i 0.537803 + 0.537803i 0.922883 0.385080i \(-0.125826\pi\)
−0.385080 + 0.922883i \(0.625826\pi\)
\(594\) 255.173 0.429584
\(595\) 167.934i 0.282243i
\(596\) −917.241 917.241i −1.53900 1.53900i
\(597\) 623.549i 1.04447i
\(598\) 1134.02 + 972.396i 1.89635 + 1.62608i
\(599\) −587.889 −0.981451 −0.490725 0.871314i \(-0.663268\pi\)
−0.490725 + 0.871314i \(0.663268\pi\)
\(600\) −145.571 + 145.571i −0.242618 + 0.242618i
\(601\) 848.887 1.41246 0.706229 0.707984i \(-0.250395\pi\)
0.706229 + 0.707984i \(0.250395\pi\)
\(602\) 520.959i 0.865381i
\(603\) 135.984 135.984i 0.225513 0.225513i
\(604\) 736.856 736.856i 1.21996 1.21996i
\(605\) −236.394 236.394i −0.390733 0.390733i
\(606\) −495.950 495.950i −0.818399 0.818399i
\(607\) 147.750 0.243411 0.121705 0.992566i \(-0.461164\pi\)
0.121705 + 0.992566i \(0.461164\pi\)
\(608\) 371.956i 0.611770i
\(609\) 97.3533 + 97.3533i 0.159858 + 0.159858i
\(610\) 489.518i 0.802488i
\(611\) −264.441 226.752i −0.432800 0.371116i
\(612\) 107.923 0.176344
\(613\) −505.998 + 505.998i −0.825446 + 0.825446i −0.986883 0.161437i \(-0.948387\pi\)
0.161437 + 0.986883i \(0.448387\pi\)
\(614\) −402.066 −0.654831
\(615\) 166.935i 0.271439i
\(616\) −783.147 + 783.147i −1.27134 + 1.27134i
\(617\) −803.096 + 803.096i −1.30161 + 1.30161i −0.374311 + 0.927303i \(0.622121\pi\)
−0.927303 + 0.374311i \(0.877879\pi\)
\(618\) 351.938 + 351.938i 0.569479 + 0.569479i
\(619\) −67.6340 67.6340i −0.109263 0.109263i 0.650362 0.759625i \(-0.274617\pi\)
−0.759625 + 0.650362i \(0.774617\pi\)
\(620\) 967.609 1.56066
\(621\) 186.387i 0.300140i
\(622\) −1159.57 1159.57i −1.86426 1.86426i
\(623\) 265.782i 0.426616i
\(624\) 41.1085 3.15422i 0.0658790 0.00505483i
\(625\) −53.8902 −0.0862243
\(626\) −911.086 + 911.086i −1.45541 + 1.45541i
\(627\) −283.322 −0.451868
\(628\) 1056.46i 1.68227i
\(629\) −132.477 + 132.477i −0.210615 + 0.210615i
\(630\) −198.668 + 198.668i −0.315347 + 0.315347i
\(631\) 494.414 + 494.414i 0.783540 + 0.783540i 0.980426 0.196886i \(-0.0630829\pi\)
−0.196886 + 0.980426i \(0.563083\pi\)
\(632\) 505.710 + 505.710i 0.800175 + 0.800175i
\(633\) 367.482 0.580541
\(634\) 724.163i 1.14221i
\(635\) 30.2509 + 30.2509i 0.0476392 + 0.0476392i
\(636\) 59.7292i 0.0939139i
\(637\) −50.0905 652.823i −0.0786351 1.02484i
\(638\) 391.599 0.613791
\(639\) −229.440 + 229.440i −0.359062 + 0.359062i
\(640\) 571.403 0.892817
\(641\) 340.781i 0.531640i 0.964023 + 0.265820i \(0.0856427\pi\)
−0.964023 + 0.265820i \(0.914357\pi\)
\(642\) −191.411 + 191.411i −0.298148 + 0.298148i
\(643\) −3.63964 + 3.63964i −0.00566040 + 0.00566040i −0.709931 0.704271i \(-0.751274\pi\)
0.704271 + 0.709931i \(0.251274\pi\)
\(644\) −1583.37 1583.37i −2.45865 2.45865i
\(645\) −58.5985 58.5985i −0.0908504 0.0908504i
\(646\) −196.365 −0.303970
\(647\) 643.861i 0.995149i −0.867421 0.497574i \(-0.834224\pi\)
0.867421 0.497574i \(-0.165776\pi\)
\(648\) −46.1258 46.1258i −0.0711817 0.0711817i
\(649\) 937.785i 1.44497i
\(650\) −518.440 444.551i −0.797600 0.683924i
\(651\) −909.597 −1.39723
\(652\) 1226.34 1226.34i 1.88089 1.88089i
\(653\) 1033.33 1.58243 0.791215 0.611538i \(-0.209449\pi\)
0.791215 + 0.611538i \(0.209449\pi\)
\(654\) 232.746i 0.355880i
\(655\) 184.410 184.410i 0.281542 0.281542i
\(656\) −42.5495 + 42.5495i −0.0648620 + 0.0648620i
\(657\) 7.40643 + 7.40643i 0.0112731 + 0.0112731i
\(658\) 605.057 + 605.057i 0.919540 + 0.919540i
\(659\) 52.9124 0.0802919 0.0401460 0.999194i \(-0.487218\pi\)
0.0401460 + 0.999194i \(0.487218\pi\)
\(660\) 487.657i 0.738874i
\(661\) 866.525 + 866.525i 1.31093 + 1.31093i 0.920730 + 0.390201i \(0.127594\pi\)
0.390201 + 0.920730i \(0.372406\pi\)
\(662\) 1610.35i 2.43256i
\(663\) 9.89539 + 128.965i 0.0149252 + 0.194518i
\(664\) −288.827 −0.434981
\(665\) 220.584 220.584i 0.331705 0.331705i
\(666\) 313.444 0.470636
\(667\) 286.037i 0.428841i
\(668\) −144.065 + 144.065i −0.215667 + 0.215667i
\(669\) 73.8031 73.8031i 0.110319 0.110319i
\(670\) 425.867 + 425.867i 0.635623 + 0.635623i
\(671\) 564.772 + 564.772i 0.841686 + 0.841686i
\(672\) −601.832 −0.895583
\(673\) 230.740i 0.342852i 0.985197 + 0.171426i \(0.0548375\pi\)
−0.985197 + 0.171426i \(0.945162\pi\)
\(674\) 987.667 + 987.667i 1.46538 + 1.46538i
\(675\) 85.2106i 0.126238i
\(676\) −161.464 1045.97i −0.238852 1.54730i
\(677\) 799.458 1.18088 0.590441 0.807080i \(-0.298954\pi\)
0.590441 + 0.807080i \(0.298954\pi\)
\(678\) 318.388 318.388i 0.469599 0.469599i
\(679\) 488.887 0.720011
\(680\) 122.107i 0.179569i
\(681\) −91.9124 + 91.9124i −0.134967 + 0.134967i
\(682\) −1829.40 + 1829.40i −2.68241 + 2.68241i
\(683\) 750.113 + 750.113i 1.09826 + 1.09826i 0.994614 + 0.103648i \(0.0330517\pi\)
0.103648 + 0.994614i \(0.466948\pi\)
\(684\) 141.758 + 141.758i 0.207248 + 0.207248i
\(685\) −408.729 −0.596685
\(686\) 43.5812i 0.0635295i
\(687\) 234.478 + 234.478i 0.341308 + 0.341308i
\(688\) 29.8719i 0.0434185i
\(689\) −71.3751 + 5.47655i −0.103592 + 0.00794855i
\(690\) −583.715 −0.845963
\(691\) −408.357 + 408.357i −0.590965 + 0.590965i −0.937892 0.346927i \(-0.887225\pi\)
0.346927 + 0.937892i \(0.387225\pi\)
\(692\) −43.9095 −0.0634530
\(693\) 458.420i 0.661500i
\(694\) 741.366 741.366i 1.06825 1.06825i
\(695\) 235.604 235.604i 0.338998 0.338998i
\(696\) −70.7865 70.7865i −0.101705 0.101705i
\(697\) −133.486 133.486i −0.191515 0.191515i
\(698\) 708.110 1.01448
\(699\) 54.2555i 0.0776187i
\(700\) 723.871 + 723.871i 1.03410 + 1.03410i
\(701\) 1057.89i 1.50911i −0.656236 0.754556i \(-0.727852\pi\)
0.656236 0.754556i \(-0.272148\pi\)
\(702\) 140.861 164.274i 0.200657 0.234008i
\(703\) −348.021 −0.495051
\(704\) −1131.03 + 1131.03i −1.60657 + 1.60657i
\(705\) 136.116 0.193072
\(706\) 1367.88i 1.93751i
\(707\) −890.977 + 890.977i −1.26022 + 1.26022i
\(708\) −469.214 + 469.214i −0.662732 + 0.662732i
\(709\) −154.683 154.683i −0.218170 0.218170i 0.589557 0.807727i \(-0.299302\pi\)
−0.807727 + 0.589557i \(0.799302\pi\)
\(710\) −718.547 718.547i −1.01204 1.01204i
\(711\) −296.021 −0.416344
\(712\) 193.252i 0.271422i
\(713\) −1336.26 1336.26i −1.87414 1.87414i
\(714\) 317.722i 0.444989i
\(715\) −582.739 + 44.7131i −0.815020 + 0.0625357i
\(716\) 607.418 0.848349
\(717\) 577.965 577.965i 0.806088 0.806088i
\(718\) −2083.73 −2.90213
\(719\) 101.626i 0.141344i 0.997500 + 0.0706720i \(0.0225144\pi\)
−0.997500 + 0.0706720i \(0.977486\pi\)
\(720\) −11.3917 + 11.3917i −0.0158218 + 0.0158218i
\(721\) 632.259 632.259i 0.876920 0.876920i
\(722\) 559.819 + 559.819i 0.775373 + 0.775373i
\(723\) 427.211 + 427.211i 0.590887 + 0.590887i
\(724\) 1088.57 1.50356
\(725\) 130.768i 0.180369i
\(726\) −447.243 447.243i −0.616037 0.616037i
\(727\) 147.112i 0.202355i 0.994868 + 0.101177i \(0.0322610\pi\)
−0.994868 + 0.101177i \(0.967739\pi\)
\(728\) 71.8557 + 936.485i 0.0987029 + 1.28638i
\(729\) 27.0000 0.0370370
\(730\) −23.1950 + 23.1950i −0.0317740 + 0.0317740i
\(731\) 93.7140 0.128200
\(732\) 565.159i 0.772075i
\(733\) 187.854 187.854i 0.256281 0.256281i −0.567259 0.823539i \(-0.691996\pi\)
0.823539 + 0.567259i \(0.191996\pi\)
\(734\) 429.706 429.706i 0.585431 0.585431i
\(735\) 180.906 + 180.906i 0.246130 + 0.246130i
\(736\) −884.132 884.132i −1.20127 1.20127i
\(737\) −982.673 −1.33334
\(738\) 315.831i 0.427956i
\(739\) 109.296 + 109.296i 0.147898 + 0.147898i 0.777178 0.629281i \(-0.216650\pi\)
−0.629281 + 0.777178i \(0.716650\pi\)
\(740\) 599.018i 0.809483i
\(741\) −156.400 + 182.395i −0.211066 + 0.246148i
\(742\) 175.841 0.236983
\(743\) 358.323 358.323i 0.482265 0.482265i −0.423589 0.905854i \(-0.639230\pi\)
0.905854 + 0.423589i \(0.139230\pi\)
\(744\) 661.377 0.888947
\(745\) 607.478i 0.815406i
\(746\) 462.980 462.980i 0.620617 0.620617i
\(747\) 84.5334 84.5334i 0.113164 0.113164i
\(748\) −389.944 389.944i −0.521316 0.521316i
\(749\) 343.872 + 343.872i 0.459108 + 0.459108i
\(750\) 673.682 0.898242
\(751\) 185.270i 0.246698i 0.992363 + 0.123349i \(0.0393634\pi\)
−0.992363 + 0.123349i \(0.960637\pi\)
\(752\) 34.6941 + 34.6941i 0.0461358 + 0.0461358i
\(753\) 573.440i 0.761540i
\(754\) 216.172 252.102i 0.286700 0.334352i
\(755\) −488.011 −0.646372
\(756\) −229.367 + 229.367i −0.303396 + 0.303396i
\(757\) −324.887 −0.429177 −0.214588 0.976705i \(-0.568841\pi\)
−0.214588 + 0.976705i \(0.568841\pi\)
\(758\) 84.1107i 0.110964i
\(759\) 673.449 673.449i 0.887285 0.887285i
\(760\) −160.389 + 160.389i −0.211038 + 0.211038i
\(761\) −431.075 431.075i −0.566459 0.566459i 0.364676 0.931135i \(-0.381180\pi\)
−0.931135 + 0.364676i \(0.881180\pi\)
\(762\) 57.2329 + 57.2329i 0.0751087 + 0.0751087i
\(763\) 418.129 0.548007
\(764\) 844.850i 1.10582i
\(765\) −35.7379 35.7379i −0.0467163 0.0467163i
\(766\) 273.079i 0.356500i
\(767\) −603.723 517.679i −0.787122 0.674940i
\(768\) 358.152 0.466344
\(769\) −482.446 + 482.446i −0.627368 + 0.627368i −0.947405 0.320037i \(-0.896305\pi\)
0.320037 + 0.947405i \(0.396305\pi\)
\(770\) 1435.65 1.86448
\(771\) 143.430i 0.186032i
\(772\) 27.9980 27.9980i 0.0362669 0.0362669i
\(773\) −34.4442 + 34.4442i −0.0445591 + 0.0445591i −0.729035 0.684476i \(-0.760031\pi\)
0.684476 + 0.729035i \(0.260031\pi\)
\(774\) −110.865 110.865i −0.143236 0.143236i
\(775\) 610.899 + 610.899i 0.788256 + 0.788256i
\(776\) −355.475 −0.458086
\(777\) 563.104i 0.724716i
\(778\) −15.4487 15.4487i −0.0198569 0.0198569i
\(779\) 350.671i 0.450156i
\(780\) 313.941 + 269.198i 0.402489 + 0.345125i
\(781\) 1658.02 2.12294
\(782\) 466.755 466.755i 0.596873 0.596873i
\(783\) 41.4353 0.0529187
\(784\) 92.2208i 0.117629i
\(785\) 349.841 349.841i 0.445658 0.445658i
\(786\) 348.892 348.892i 0.443883 0.443883i
\(787\) −181.342 181.342i −0.230422 0.230422i 0.582447 0.812869i \(-0.302095\pi\)
−0.812869 + 0.582447i \(0.802095\pi\)
\(788\) −355.017 355.017i −0.450529 0.450529i
\(789\) −170.798 −0.216474
\(790\) 927.058i 1.17349i
\(791\) −571.986 571.986i −0.723118 0.723118i
\(792\) 333.321i 0.420860i
\(793\) 675.353 51.8192i 0.851643 0.0653458i
\(794\) 478.785 0.603004
\(795\) 19.7790 19.7790i 0.0248792 0.0248792i
\(796\) −2254.54 −2.83234
\(797\) 1091.56i 1.36959i 0.728736 + 0.684795i \(0.240108\pi\)
−0.728736 + 0.684795i \(0.759892\pi\)
\(798\) 417.332 417.332i 0.522972 0.522972i
\(799\) −108.842 + 108.842i −0.136223 + 0.136223i
\(800\) 404.199 + 404.199i 0.505249 + 0.505249i
\(801\) 56.5607 + 56.5607i 0.0706127 + 0.0706127i
\(802\) 565.882 0.705589
\(803\) 53.5215i 0.0666520i
\(804\) 491.673 + 491.673i 0.611534 + 0.611534i
\(805\) 1048.65i 1.30267i
\(806\) 167.852 + 2187.60i 0.208254 + 2.71414i
\(807\) −160.291 −0.198625
\(808\) 647.838 647.838i 0.801780 0.801780i
\(809\) −1040.75 −1.28646 −0.643230 0.765673i \(-0.722406\pi\)
−0.643230 + 0.765673i \(0.722406\pi\)
\(810\) 84.5569i 0.104391i
\(811\) −621.215 + 621.215i −0.765987 + 0.765987i −0.977397 0.211411i \(-0.932194\pi\)
0.211411 + 0.977397i \(0.432194\pi\)
\(812\) −351.996 + 351.996i −0.433493 + 0.433493i
\(813\) −342.126 342.126i −0.420820 0.420820i
\(814\) −1132.53 1132.53i −1.39131 1.39131i
\(815\) −812.191 −0.996553
\(816\) 18.2182i 0.0223263i
\(817\) 123.095 + 123.095i 0.150667 + 0.150667i
\(818\) 1548.25i 1.89273i
\(819\) −295.119 253.058i −0.360341 0.308984i
\(820\) −603.580 −0.736073
\(821\) 589.552 589.552i 0.718090 0.718090i −0.250124 0.968214i \(-0.580471\pi\)
0.968214 + 0.250124i \(0.0804713\pi\)
\(822\) −773.292 −0.940744
\(823\) 1259.69i 1.53061i −0.643668 0.765305i \(-0.722588\pi\)
0.643668 0.765305i \(-0.277412\pi\)
\(824\) −459.722 + 459.722i −0.557915 + 0.557915i
\(825\) −307.881 + 307.881i −0.373189 + 0.373189i
\(826\) 1381.36 + 1381.36i 1.67234 + 1.67234i
\(827\) 425.074 + 425.074i 0.513995 + 0.513995i 0.915748 0.401753i \(-0.131599\pi\)
−0.401753 + 0.915748i \(0.631599\pi\)
\(828\) −673.912 −0.813903
\(829\) 1094.86i 1.32069i −0.750960 0.660347i \(-0.770409\pi\)
0.750960 0.660347i \(-0.229591\pi\)
\(830\) 264.736 + 264.736i 0.318959 + 0.318959i
\(831\) 675.086i 0.812377i
\(832\) 103.775 + 1352.48i 0.124729 + 1.62558i
\(833\) −289.315 −0.347316
\(834\) 445.749 445.749i 0.534471 0.534471i
\(835\) 95.4128 0.114267
\(836\) 1024.39i 1.22535i
\(837\) −193.570 + 193.570i −0.231267 + 0.231267i
\(838\) 786.057 786.057i 0.938015 0.938015i
\(839\) 185.015 + 185.015i 0.220519 + 0.220519i 0.808717 0.588198i \(-0.200162\pi\)
−0.588198 + 0.808717i \(0.700162\pi\)
\(840\) −259.512 259.512i −0.308943 0.308943i
\(841\) −777.412 −0.924390
\(842\) 235.881i 0.280143i
\(843\) −217.411 217.411i −0.257902 0.257902i
\(844\) 1328.69i 1.57428i
\(845\) −292.900 + 399.836i −0.346627 + 0.473178i
\(846\) 257.523 0.304401
\(847\) −803.475 + 803.475i −0.948613 + 0.948613i
\(848\) 10.0828 0.0118901
\(849\) 480.289i 0.565712i
\(850\) −213.387 + 213.387i −0.251043 + 0.251043i
\(851\) 827.238 827.238i 0.972077 0.972077i
\(852\) −829.578 829.578i −0.973683 0.973683i
\(853\) −441.207 441.207i −0.517242 0.517242i 0.399494 0.916736i \(-0.369186\pi\)
−0.916736 + 0.399494i \(0.869186\pi\)
\(854\) −1663.81 −1.94826
\(855\) 93.8846i 0.109807i
\(856\) −250.032 250.032i −0.292094 0.292094i
\(857\) 1315.33i 1.53481i 0.641163 + 0.767404i \(0.278452\pi\)
−0.641163 + 0.767404i \(0.721548\pi\)
\(858\) −1102.51 + 84.5945i −1.28497 + 0.0985949i
\(859\) 1595.61 1.85752 0.928758 0.370687i \(-0.120878\pi\)
0.928758 + 0.370687i \(0.120878\pi\)
\(860\) 211.872 211.872i 0.246363 0.246363i
\(861\) 567.393 0.658993
\(862\) 118.491i 0.137461i
\(863\) −162.354 + 162.354i −0.188127 + 0.188127i −0.794886 0.606759i \(-0.792469\pi\)
0.606759 + 0.794886i \(0.292469\pi\)
\(864\) −128.075 + 128.075i −0.148235 + 0.148235i
\(865\) 14.5404 + 14.5404i 0.0168097 + 0.0168097i
\(866\) 677.242 + 677.242i 0.782034 + 0.782034i
\(867\) −443.409 −0.511429
\(868\) 3288.79i 3.78893i
\(869\) 1069.58 + 1069.58i 1.23081 + 1.23081i
\(870\) 129.765i 0.149155i
\(871\) −542.458 + 632.620i −0.622799 + 0.726315i
\(872\) −304.026 −0.348654
\(873\) 104.040 104.040i 0.119175 0.119175i
\(874\) 1226.18 1.40295
\(875\) 1210.27i 1.38317i
\(876\) −26.7791 + 26.7791i −0.0305698 + 0.0305698i
\(877\) 161.563 161.563i 0.184222 0.184222i −0.608971 0.793193i \(-0.708417\pi\)
0.793193 + 0.608971i \(0.208417\pi\)
\(878\) 400.814 + 400.814i 0.456508 + 0.456508i
\(879\) 568.107 + 568.107i 0.646311 + 0.646311i
\(880\) 82.3204 0.0935459
\(881\) 801.723i 0.910015i −0.890488 0.455008i \(-0.849637\pi\)
0.890488 0.455008i \(-0.150363\pi\)
\(882\) 342.263 + 342.263i 0.388053 + 0.388053i
\(883\) 608.168i 0.688753i 0.938832 + 0.344376i \(0.111910\pi\)
−0.938832 + 0.344376i \(0.888090\pi\)
\(884\) −466.294 + 35.7784i −0.527482 + 0.0404733i
\(885\) 310.755 0.351135
\(886\) 1107.00 1107.00i 1.24944 1.24944i
\(887\) −1169.09 −1.31802 −0.659011 0.752133i \(-0.729025\pi\)
−0.659011 + 0.752133i \(0.729025\pi\)
\(888\) 409.438i 0.461079i
\(889\) 102.819 102.819i 0.115657 0.115657i
\(890\) −177.133 + 177.133i −0.199026 + 0.199026i
\(891\) −97.5558 97.5558i −0.109490 0.109490i
\(892\) 266.847 + 266.847i 0.299156 + 0.299156i
\(893\) −285.931 −0.320192
\(894\) 1149.31i 1.28558i
\(895\) −201.143 201.143i −0.224740 0.224740i
\(896\) 1942.13i 2.16756i
\(897\) −61.7907 805.310i −0.0688859 0.897781i
\(898\) 1320.49 1.47047
\(899\) −297.061 + 297.061i −0.330435 + 0.330435i
\(900\) 308.093 0.342325
\(901\) 31.6316i 0.0351073i
\(902\) 1141.15 1141.15i 1.26514 1.26514i
\(903\) −199.170 + 199.170i −0.220564 + 0.220564i
\(904\) 415.897 + 415.897i 0.460063 + 0.460063i
\(905\) −360.475 360.475i −0.398315 0.398315i
\(906\) −923.288 −1.01908
\(907\) 420.272i 0.463364i 0.972792 + 0.231682i \(0.0744230\pi\)
−0.972792 + 0.231682i \(0.925577\pi\)
\(908\) −332.324 332.324i −0.365995 0.365995i
\(909\) 379.216i 0.417179i
\(910\) 792.511 924.236i 0.870891 1.01564i
\(911\) −1503.63 −1.65053 −0.825264 0.564747i \(-0.808974\pi\)
−0.825264 + 0.564747i \(0.808974\pi\)
\(912\) 23.9299 23.9299i 0.0262389 0.0262389i
\(913\) −610.869 −0.669079
\(914\) 1907.11i 2.08656i
\(915\) −187.149 + 187.149i −0.204534 + 0.204534i
\(916\) −847.794 + 847.794i −0.925539 + 0.925539i
\(917\) −626.787 626.787i −0.683519 0.683519i
\(918\) −67.6141 67.6141i −0.0736537 0.0736537i
\(919\) 99.7403 0.108531 0.0542657 0.998527i \(-0.482718\pi\)
0.0542657 + 0.998527i \(0.482718\pi\)
\(920\) 762.482i 0.828784i
\(921\) 153.715 + 153.715i 0.166900 + 0.166900i
\(922\) 947.740i 1.02792i
\(923\) 915.264 1067.39i 0.991619 1.15644i
\(924\) 1657.49 1.79382
\(925\) −378.189 + 378.189i −0.408853 + 0.408853i
\(926\) 921.732 0.995391
\(927\) 269.101i 0.290292i
\(928\) −196.550 + 196.550i −0.211799 + 0.211799i
\(929\) −122.462 + 122.462i −0.131821 + 0.131821i −0.769939 0.638118i \(-0.779713\pi\)
0.638118 + 0.769939i \(0.279713\pi\)
\(930\) −606.212 606.212i −0.651840 0.651840i
\(931\) −380.019 380.019i −0.408183 0.408183i
\(932\) −196.169 −0.210482
\(933\) 886.638i 0.950308i
\(934\) −250.820 250.820i −0.268544 0.268544i
\(935\) 258.255i 0.276209i
\(936\) 214.584 + 184.001i 0.229256 + 0.196582i
\(937\) 975.263 1.04084 0.520418 0.853912i \(-0.325776\pi\)
0.520418 + 0.853912i \(0.325776\pi\)
\(938\) 1447.47 1447.47i 1.54315 1.54315i
\(939\) 696.640 0.741895
\(940\) 492.149i 0.523562i
\(941\) 1188.28 1188.28i 1.26279 1.26279i 0.313052 0.949736i \(-0.398649\pi\)
0.949736 0.313052i \(-0.101351\pi\)
\(942\) 661.879 661.879i 0.702632 0.702632i
\(943\) 833.539 + 833.539i 0.883922 + 0.883922i
\(944\) 79.2072 + 79.2072i 0.0839059 + 0.0839059i
\(945\) 151.907 0.160748
\(946\) 801.149i 0.846881i
\(947\) 957.995 + 957.995i 1.01161 + 1.01161i 0.999932 + 0.0116790i \(0.00371764\pi\)
0.0116790 + 0.999932i \(0.496282\pi\)
\(948\) 1070.31i 1.12902i
\(949\) −34.4558 29.5451i −0.0363075 0.0311329i
\(950\) −560.572 −0.590076
\(951\) 276.857 276.857i 0.291122 0.291122i
\(952\) 415.026 0.435952
\(953\) 777.339i 0.815676i 0.913054 + 0.407838i \(0.133717\pi\)
−0.913054 + 0.407838i \(0.866283\pi\)
\(954\) 37.4206 37.4206i 0.0392250 0.0392250i
\(955\) 279.767 279.767i 0.292950 0.292950i
\(956\) 2089.72 + 2089.72i 2.18590 + 2.18590i
\(957\) −149.713 149.713i −0.156440 0.156440i
\(958\) −2954.45 −3.08398
\(959\) 1389.22i 1.44862i
\(960\) −374.790 374.790i −0.390406 0.390406i
\(961\) 1814.52i 1.88816i
\(962\) −1354.28 + 103.912i −1.40777 + 0.108017i
\(963\) 146.358 0.151981
\(964\) −1544.65 + 1544.65i −1.60233 + 1.60233i
\(965\) −18.5428 −0.0192153
\(966\) 1983.98i 2.05381i
\(967\) 427.468 427.468i 0.442056 0.442056i −0.450647 0.892702i \(-0.648807\pi\)
0.892702 + 0.450647i \(0.148807\pi\)
\(968\) 584.214 584.214i 0.603527 0.603527i
\(969\) 75.0728 + 75.0728i 0.0774745 + 0.0774745i
\(970\) 325.825 + 325.825i 0.335902 + 0.335902i
\(971\) 287.153 0.295729 0.147865 0.989008i \(-0.452760\pi\)
0.147865 + 0.989008i \(0.452760\pi\)
\(972\) 97.6228i 0.100435i
\(973\) −800.791 800.791i −0.823012 0.823012i
\(974\) 481.369i 0.494218i
\(975\) 28.2489 + 368.164i 0.0289732 + 0.377604i
\(976\) −95.4034 −0.0977494
\(977\) 478.694 478.694i 0.489963 0.489963i −0.418332 0.908294i \(-0.637385\pi\)
0.908294 + 0.418332i \(0.137385\pi\)
\(978\) −1536.62 −1.57118
\(979\) 408.728i 0.417496i
\(980\) −654.093 + 654.093i −0.667442 + 0.667442i
\(981\) 88.9817 88.9817i 0.0907051 0.0907051i
\(982\) −1682.11 1682.11i −1.71295 1.71295i
\(983\) −1192.12 1192.12i −1.21273 1.21273i −0.970124 0.242609i \(-0.921997\pi\)
−0.242609 0.970124i \(-0.578003\pi\)
\(984\) −412.557 −0.419265
\(985\) 235.123i 0.238704i
\(986\) −103.763 103.763i −0.105237 0.105237i
\(987\) 462.642i 0.468736i
\(988\) −659.480 565.489i −0.667489 0.572357i
\(989\) −585.187 −0.591696
\(990\) 305.519 305.519i 0.308605 0.308605i
\(991\) −1428.83 −1.44180 −0.720901 0.693038i \(-0.756272\pi\)
−0.720901 + 0.693038i \(0.756272\pi\)
\(992\) 1836.41i 1.85122i
\(993\) −615.659 + 615.659i −0.619999 + 0.619999i
\(994\) −2442.26 + 2442.26i −2.45700 + 2.45700i
\(995\) 746.577 + 746.577i 0.750329 + 0.750329i
\(996\) 305.644 + 305.644i 0.306872 + 0.306872i
\(997\) 648.361 0.650312 0.325156 0.945660i \(-0.394583\pi\)
0.325156 + 0.945660i \(0.394583\pi\)
\(998\) 1569.52i 1.57267i
\(999\) −119.834 119.834i −0.119954 0.119954i
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 39.3.g.a.31.4 8
3.2 odd 2 117.3.j.b.109.1 8
4.3 odd 2 624.3.ba.b.577.4 8
13.8 odd 4 inner 39.3.g.a.34.4 yes 8
39.8 even 4 117.3.j.b.73.1 8
52.47 even 4 624.3.ba.b.385.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.3.g.a.31.4 8 1.1 even 1 trivial
39.3.g.a.34.4 yes 8 13.8 odd 4 inner
117.3.j.b.73.1 8 39.8 even 4
117.3.j.b.109.1 8 3.2 odd 2
624.3.ba.b.385.4 8 52.47 even 4
624.3.ba.b.577.4 8 4.3 odd 2