Properties

Label 1014.2.i.g.823.3
Level $1014$
Weight $2$
Character 1014.823
Analytic conductor $8.097$
Analytic rank $0$
Dimension $12$
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] = [1014,2,Mod(361,1014)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1014, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1014.361");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1014.i (of order \(6\), degree \(2\), not 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: \(8.09683076496\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.17213603549184.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 823.3
Root \(-1.07992 + 0.623490i\) of defining polynomial
Character \(\chi\) \(=\) 1014.823
Dual form 1014.2.i.g.361.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +0.692021i q^{5} +(0.866025 - 0.500000i) q^{6} +(0.309081 - 0.178448i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +0.692021i q^{5} +(0.866025 - 0.500000i) q^{6} +(0.309081 - 0.178448i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.346011 - 0.599308i) q^{10} +(-2.54525 - 1.46950i) q^{11} -1.00000 q^{12} -0.356896 q^{14} +(-0.599308 - 0.346011i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.35690 + 5.81431i) q^{17} +1.00000i q^{18} +(6.24210 - 3.60388i) q^{19} +(-0.599308 + 0.346011i) q^{20} +0.356896i q^{21} +(1.46950 + 2.54525i) q^{22} +(1.19806 - 2.07510i) q^{23} +(0.866025 + 0.500000i) q^{24} +4.52111 q^{25} +1.00000 q^{27} +(0.309081 + 0.178448i) q^{28} +(-3.91454 + 6.78019i) q^{29} +(0.346011 + 0.599308i) q^{30} +2.76271i q^{31} +(0.866025 - 0.500000i) q^{32} +(2.54525 - 1.46950i) q^{33} -6.71379i q^{34} +(0.123490 + 0.213891i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-8.74498 - 5.04892i) q^{37} -7.20775 q^{38} +0.692021 q^{40} +(4.23494 + 2.44504i) q^{41} +(0.178448 - 0.309081i) q^{42} +(3.29590 + 5.70866i) q^{43} -2.93900i q^{44} +(0.599308 - 0.346011i) q^{45} +(-2.07510 + 1.19806i) q^{46} +4.98792i q^{47} +(-0.500000 - 0.866025i) q^{48} +(-3.43631 + 5.95187i) q^{49} +(-3.91539 - 2.26055i) q^{50} -6.71379 q^{51} -8.88769 q^{53} +(-0.866025 - 0.500000i) q^{54} +(1.01693 - 1.76137i) q^{55} +(-0.178448 - 0.309081i) q^{56} +7.20775i q^{57} +(6.78019 - 3.91454i) q^{58} +(1.42297 - 0.821552i) q^{59} -0.692021i q^{60} +(3.24698 + 5.62393i) q^{61} +(1.38135 - 2.39258i) q^{62} +(-0.309081 - 0.178448i) q^{63} -1.00000 q^{64} -2.93900 q^{66} +(11.7134 + 6.76271i) q^{67} +(-3.35690 + 5.81431i) q^{68} +(1.19806 + 2.07510i) q^{69} -0.246980i q^{70} +(-5.89904 + 3.40581i) q^{71} +(-0.866025 + 0.500000i) q^{72} +3.18598i q^{73} +(5.04892 + 8.74498i) q^{74} +(-2.26055 + 3.91539i) q^{75} +(6.24210 + 3.60388i) q^{76} -1.04892 q^{77} +15.0465 q^{79} +(-0.599308 - 0.346011i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.44504 - 4.23494i) q^{82} +14.8267i q^{83} +(-0.309081 + 0.178448i) q^{84} +(-4.02363 + 2.32304i) q^{85} -6.59179i q^{86} +(-3.91454 - 6.78019i) q^{87} +(-1.46950 + 2.54525i) q^{88} +(-0.343054 - 0.198062i) q^{89} -0.692021 q^{90} +2.39612 q^{92} +(-2.39258 - 1.38135i) q^{93} +(2.49396 - 4.31966i) q^{94} +(2.49396 + 4.31966i) q^{95} +1.00000i q^{96} +(0.361908 - 0.208947i) q^{97} +(5.95187 - 3.43631i) q^{98} +2.93900i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 6 q^{3} + 6 q^{4} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 6 q^{3} + 6 q^{4} - 6 q^{9} - 6 q^{10} - 12 q^{12} + 12 q^{14} - 6 q^{16} + 24 q^{17} - 2 q^{22} + 32 q^{23} - 8 q^{25} + 12 q^{27} - 26 q^{29} - 6 q^{30} - 8 q^{35} + 6 q^{36} - 16 q^{38} - 12 q^{40} - 6 q^{42} - 16 q^{43} - 6 q^{48} - 8 q^{49} - 48 q^{51} + 60 q^{53} + 44 q^{55} + 6 q^{56} + 20 q^{61} - 18 q^{62} - 12 q^{64} + 4 q^{66} - 24 q^{68} + 32 q^{69} + 24 q^{74} + 4 q^{75} + 24 q^{77} - 20 q^{79} - 6 q^{81} - 28 q^{82} - 26 q^{87} + 2 q^{88} + 12 q^{90} + 64 q^{92} - 8 q^{94} - 8 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).

\(n\) \(677\) \(847\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0.692021i 0.309481i 0.987955 + 0.154741i \(0.0494542\pi\)
−0.987955 + 0.154741i \(0.950546\pi\)
\(6\) 0.866025 0.500000i 0.353553 0.204124i
\(7\) 0.309081 0.178448i 0.116822 0.0674470i −0.440451 0.897777i \(-0.645181\pi\)
0.557272 + 0.830330i \(0.311848\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0.346011 0.599308i 0.109418 0.189518i
\(11\) −2.54525 1.46950i −0.767422 0.443071i 0.0645324 0.997916i \(-0.479444\pi\)
−0.831954 + 0.554845i \(0.812778\pi\)
\(12\) −1.00000 −0.288675
\(13\) 0 0
\(14\) −0.356896 −0.0953844
\(15\) −0.599308 0.346011i −0.154741 0.0893396i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.35690 + 5.81431i 0.814167 + 1.41018i 0.909925 + 0.414774i \(0.136139\pi\)
−0.0957578 + 0.995405i \(0.530527\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 6.24210 3.60388i 1.43203 0.826786i 0.434759 0.900547i \(-0.356834\pi\)
0.997276 + 0.0737611i \(0.0235002\pi\)
\(20\) −0.599308 + 0.346011i −0.134009 + 0.0773704i
\(21\) 0.356896i 0.0778811i
\(22\) 1.46950 + 2.54525i 0.313299 + 0.542649i
\(23\) 1.19806 2.07510i 0.249813 0.432689i −0.713661 0.700492i \(-0.752964\pi\)
0.963474 + 0.267802i \(0.0862974\pi\)
\(24\) 0.866025 + 0.500000i 0.176777 + 0.102062i
\(25\) 4.52111 0.904221
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0.309081 + 0.178448i 0.0584108 + 0.0337235i
\(29\) −3.91454 + 6.78019i −0.726912 + 1.25905i 0.231270 + 0.972890i \(0.425712\pi\)
−0.958182 + 0.286159i \(0.907621\pi\)
\(30\) 0.346011 + 0.599308i 0.0631726 + 0.109418i
\(31\) 2.76271i 0.496197i 0.968735 + 0.248099i \(0.0798057\pi\)
−0.968735 + 0.248099i \(0.920194\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 2.54525 1.46950i 0.443071 0.255807i
\(34\) 6.71379i 1.15141i
\(35\) 0.123490 + 0.213891i 0.0208736 + 0.0361541i
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) −8.74498 5.04892i −1.43767 0.830037i −0.439979 0.898008i \(-0.645014\pi\)
−0.997687 + 0.0679713i \(0.978347\pi\)
\(38\) −7.20775 −1.16925
\(39\) 0 0
\(40\) 0.692021 0.109418
\(41\) 4.23494 + 2.44504i 0.661386 + 0.381851i 0.792805 0.609476i \(-0.208620\pi\)
−0.131419 + 0.991327i \(0.541953\pi\)
\(42\) 0.178448 0.309081i 0.0275351 0.0476922i
\(43\) 3.29590 + 5.70866i 0.502620 + 0.870563i 0.999995 + 0.00302747i \(0.000963674\pi\)
−0.497376 + 0.867535i \(0.665703\pi\)
\(44\) 2.93900i 0.443071i
\(45\) 0.599308 0.346011i 0.0893396 0.0515802i
\(46\) −2.07510 + 1.19806i −0.305957 + 0.176645i
\(47\) 4.98792i 0.727563i 0.931484 + 0.363781i \(0.118514\pi\)
−0.931484 + 0.363781i \(0.881486\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) −3.43631 + 5.95187i −0.490902 + 0.850267i
\(50\) −3.91539 2.26055i −0.553720 0.319690i
\(51\) −6.71379 −0.940119
\(52\) 0 0
\(53\) −8.88769 −1.22082 −0.610409 0.792086i \(-0.708995\pi\)
−0.610409 + 0.792086i \(0.708995\pi\)
\(54\) −0.866025 0.500000i −0.117851 0.0680414i
\(55\) 1.01693 1.76137i 0.137122 0.237503i
\(56\) −0.178448 0.309081i −0.0238461 0.0413027i
\(57\) 7.20775i 0.954690i
\(58\) 6.78019 3.91454i 0.890282 0.514005i
\(59\) 1.42297 0.821552i 0.185255 0.106957i −0.404504 0.914536i \(-0.632556\pi\)
0.589759 + 0.807579i \(0.299223\pi\)
\(60\) 0.692021i 0.0893396i
\(61\) 3.24698 + 5.62393i 0.415733 + 0.720071i 0.995505 0.0947079i \(-0.0301917\pi\)
−0.579772 + 0.814779i \(0.696858\pi\)
\(62\) 1.38135 2.39258i 0.175432 0.303857i
\(63\) −0.309081 0.178448i −0.0389405 0.0224823i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −2.93900 −0.361766
\(67\) 11.7134 + 6.76271i 1.43101 + 0.826196i 0.997198 0.0748051i \(-0.0238335\pi\)
0.433816 + 0.901001i \(0.357167\pi\)
\(68\) −3.35690 + 5.81431i −0.407083 + 0.705089i
\(69\) 1.19806 + 2.07510i 0.144230 + 0.249813i
\(70\) 0.246980i 0.0295197i
\(71\) −5.89904 + 3.40581i −0.700087 + 0.404196i −0.807380 0.590032i \(-0.799115\pi\)
0.107293 + 0.994227i \(0.465782\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) 3.18598i 0.372891i 0.982465 + 0.186445i \(0.0596968\pi\)
−0.982465 + 0.186445i \(0.940303\pi\)
\(74\) 5.04892 + 8.74498i 0.586925 + 1.01658i
\(75\) −2.26055 + 3.91539i −0.261026 + 0.452111i
\(76\) 6.24210 + 3.60388i 0.716017 + 0.413393i
\(77\) −1.04892 −0.119535
\(78\) 0 0
\(79\) 15.0465 1.69287 0.846433 0.532495i \(-0.178745\pi\)
0.846433 + 0.532495i \(0.178745\pi\)
\(80\) −0.599308 0.346011i −0.0670047 0.0386852i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −2.44504 4.23494i −0.270010 0.467671i
\(83\) 14.8267i 1.62744i 0.581256 + 0.813720i \(0.302561\pi\)
−0.581256 + 0.813720i \(0.697439\pi\)
\(84\) −0.309081 + 0.178448i −0.0337235 + 0.0194703i
\(85\) −4.02363 + 2.32304i −0.436424 + 0.251970i
\(86\) 6.59179i 0.710811i
\(87\) −3.91454 6.78019i −0.419683 0.726912i
\(88\) −1.46950 + 2.54525i −0.156649 + 0.271325i
\(89\) −0.343054 0.198062i −0.0363636 0.0209946i 0.481708 0.876332i \(-0.340017\pi\)
−0.518072 + 0.855337i \(0.673350\pi\)
\(90\) −0.692021 −0.0729455
\(91\) 0 0
\(92\) 2.39612 0.249813
\(93\) −2.39258 1.38135i −0.248099 0.143240i
\(94\) 2.49396 4.31966i 0.257232 0.445539i
\(95\) 2.49396 + 4.31966i 0.255875 + 0.443188i
\(96\) 1.00000i 0.102062i
\(97\) 0.361908 0.208947i 0.0367461 0.0212154i −0.481514 0.876438i \(-0.659913\pi\)
0.518261 + 0.855223i \(0.326580\pi\)
\(98\) 5.95187 3.43631i 0.601229 0.347120i
\(99\) 2.93900i 0.295381i
\(100\) 2.26055 + 3.91539i 0.226055 + 0.391539i
\(101\) 5.00753 8.67330i 0.498268 0.863026i −0.501730 0.865024i \(-0.667303\pi\)
0.999998 + 0.00199864i \(0.000636186\pi\)
\(102\) 5.81431 + 3.35690i 0.575703 + 0.332382i
\(103\) 9.62565 0.948443 0.474222 0.880406i \(-0.342730\pi\)
0.474222 + 0.880406i \(0.342730\pi\)
\(104\) 0 0
\(105\) −0.246980 −0.0241027
\(106\) 7.69697 + 4.44385i 0.747595 + 0.431624i
\(107\) 3.31551 5.74263i 0.320523 0.555161i −0.660073 0.751201i \(-0.729475\pi\)
0.980596 + 0.196040i \(0.0628082\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) 12.9879i 1.24402i −0.783011 0.622008i \(-0.786317\pi\)
0.783011 0.622008i \(-0.213683\pi\)
\(110\) −1.76137 + 1.01693i −0.167940 + 0.0969601i
\(111\) 8.74498 5.04892i 0.830037 0.479222i
\(112\) 0.356896i 0.0337235i
\(113\) −0.396125 0.686108i −0.0372643 0.0645436i 0.846792 0.531925i \(-0.178531\pi\)
−0.884056 + 0.467381i \(0.845198\pi\)
\(114\) 3.60388 6.24210i 0.337534 0.584626i
\(115\) 1.43602 + 0.829085i 0.133909 + 0.0773126i
\(116\) −7.82908 −0.726912
\(117\) 0 0
\(118\) −1.64310 −0.151260
\(119\) 2.07510 + 1.19806i 0.190225 + 0.109826i
\(120\) −0.346011 + 0.599308i −0.0315863 + 0.0547091i
\(121\) −1.18114 2.04579i −0.107376 0.185981i
\(122\) 6.49396i 0.587935i
\(123\) −4.23494 + 2.44504i −0.381851 + 0.220462i
\(124\) −2.39258 + 1.38135i −0.214860 + 0.124049i
\(125\) 6.58881i 0.589321i
\(126\) 0.178448 + 0.309081i 0.0158974 + 0.0275351i
\(127\) −9.10872 + 15.7768i −0.808268 + 1.39996i 0.105794 + 0.994388i \(0.466262\pi\)
−0.914062 + 0.405574i \(0.867072\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) −6.59179 −0.580375
\(130\) 0 0
\(131\) 2.73556 0.239007 0.119504 0.992834i \(-0.461870\pi\)
0.119504 + 0.992834i \(0.461870\pi\)
\(132\) 2.54525 + 1.46950i 0.221536 + 0.127904i
\(133\) 1.28621 2.22778i 0.111528 0.193173i
\(134\) −6.76271 11.7134i −0.584209 1.01188i
\(135\) 0.692021i 0.0595597i
\(136\) 5.81431 3.35690i 0.498573 0.287851i
\(137\) −6.62286 + 3.82371i −0.565829 + 0.326681i −0.755482 0.655170i \(-0.772597\pi\)
0.189653 + 0.981851i \(0.439264\pi\)
\(138\) 2.39612i 0.203972i
\(139\) −1.69202 2.93067i −0.143515 0.248576i 0.785303 0.619112i \(-0.212507\pi\)
−0.928818 + 0.370536i \(0.879174\pi\)
\(140\) −0.123490 + 0.213891i −0.0104368 + 0.0180771i
\(141\) −4.31966 2.49396i −0.363781 0.210029i
\(142\) 6.81163 0.571619
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −4.69203 2.70895i −0.389652 0.224966i
\(146\) 1.59299 2.75914i 0.131837 0.228348i
\(147\) −3.43631 5.95187i −0.283422 0.490902i
\(148\) 10.0978i 0.830037i
\(149\) −18.0281 + 10.4085i −1.47692 + 0.852698i −0.999660 0.0260669i \(-0.991702\pi\)
−0.477255 + 0.878765i \(0.658368\pi\)
\(150\) 3.91539 2.26055i 0.319690 0.184573i
\(151\) 0.895461i 0.0728715i 0.999336 + 0.0364358i \(0.0116004\pi\)
−0.999336 + 0.0364358i \(0.988400\pi\)
\(152\) −3.60388 6.24210i −0.292313 0.506301i
\(153\) 3.35690 5.81431i 0.271389 0.470059i
\(154\) 0.908389 + 0.524459i 0.0732001 + 0.0422621i
\(155\) −1.91185 −0.153564
\(156\) 0 0
\(157\) 8.59179 0.685700 0.342850 0.939390i \(-0.388608\pi\)
0.342850 + 0.939390i \(0.388608\pi\)
\(158\) −13.0307 7.52326i −1.03666 0.598519i
\(159\) 4.44385 7.69697i 0.352420 0.610409i
\(160\) 0.346011 + 0.599308i 0.0273546 + 0.0473795i
\(161\) 0.855167i 0.0673966i
\(162\) 0.866025 0.500000i 0.0680414 0.0392837i
\(163\) −1.49465 + 0.862937i −0.117070 + 0.0675904i −0.557392 0.830250i \(-0.688198\pi\)
0.440322 + 0.897840i \(0.354864\pi\)
\(164\) 4.89008i 0.381851i
\(165\) 1.01693 + 1.76137i 0.0791676 + 0.137122i
\(166\) 7.41335 12.8403i 0.575387 0.996600i
\(167\) 18.3078 + 10.5700i 1.41670 + 0.817933i 0.996007 0.0892696i \(-0.0284533\pi\)
0.420694 + 0.907203i \(0.361787\pi\)
\(168\) 0.356896 0.0275351
\(169\) 0 0
\(170\) 4.64609 0.356339
\(171\) −6.24210 3.60388i −0.477345 0.275595i
\(172\) −3.29590 + 5.70866i −0.251310 + 0.435281i
\(173\) 4.67725 + 8.10124i 0.355605 + 0.615926i 0.987221 0.159355i \(-0.0509416\pi\)
−0.631616 + 0.775281i \(0.717608\pi\)
\(174\) 7.82908i 0.593521i
\(175\) 1.39739 0.806782i 0.105633 0.0609870i
\(176\) 2.54525 1.46950i 0.191855 0.110768i
\(177\) 1.64310i 0.123503i
\(178\) 0.198062 + 0.343054i 0.0148454 + 0.0257130i
\(179\) 1.58761 2.74983i 0.118664 0.205532i −0.800575 0.599233i \(-0.795472\pi\)
0.919238 + 0.393701i \(0.128806\pi\)
\(180\) 0.599308 + 0.346011i 0.0446698 + 0.0257901i
\(181\) 19.7995 1.47169 0.735844 0.677151i \(-0.236786\pi\)
0.735844 + 0.677151i \(0.236786\pi\)
\(182\) 0 0
\(183\) −6.49396 −0.480047
\(184\) −2.07510 1.19806i −0.152979 0.0883223i
\(185\) 3.49396 6.05171i 0.256881 0.444931i
\(186\) 1.38135 + 2.39258i 0.101286 + 0.175432i
\(187\) 19.7318i 1.44294i
\(188\) −4.31966 + 2.49396i −0.315044 + 0.181891i
\(189\) 0.309081 0.178448i 0.0224823 0.0129802i
\(190\) 4.98792i 0.361862i
\(191\) −7.63102 13.2173i −0.552161 0.956372i −0.998118 0.0613172i \(-0.980470\pi\)
0.445957 0.895054i \(-0.352863\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 4.12928 + 2.38404i 0.297232 + 0.171607i 0.641199 0.767375i \(-0.278437\pi\)
−0.343967 + 0.938982i \(0.611771\pi\)
\(194\) −0.417895 −0.0300031
\(195\) 0 0
\(196\) −6.87263 −0.490902
\(197\) −10.5957 6.11745i −0.754915 0.435850i 0.0725523 0.997365i \(-0.476886\pi\)
−0.827467 + 0.561514i \(0.810219\pi\)
\(198\) 1.46950 2.54525i 0.104433 0.180883i
\(199\) −5.92423 10.2611i −0.419958 0.727388i 0.575977 0.817466i \(-0.304622\pi\)
−0.995935 + 0.0900779i \(0.971288\pi\)
\(200\) 4.52111i 0.319690i
\(201\) −11.7134 + 6.76271i −0.826196 + 0.477005i
\(202\) −8.67330 + 5.00753i −0.610251 + 0.352329i
\(203\) 2.79417i 0.196112i
\(204\) −3.35690 5.81431i −0.235030 0.407083i
\(205\) −1.69202 + 2.93067i −0.118176 + 0.204687i
\(206\) −8.33605 4.81282i −0.580800 0.335325i
\(207\) −2.39612 −0.166542
\(208\) 0 0
\(209\) −21.1836 −1.46530
\(210\) 0.213891 + 0.123490i 0.0147599 + 0.00852161i
\(211\) 8.63102 14.9494i 0.594184 1.02916i −0.399477 0.916743i \(-0.630808\pi\)
0.993661 0.112414i \(-0.0358583\pi\)
\(212\) −4.44385 7.69697i −0.305205 0.528630i
\(213\) 6.81163i 0.466725i
\(214\) −5.74263 + 3.31551i −0.392558 + 0.226644i
\(215\) −3.95052 + 2.28083i −0.269423 + 0.155551i
\(216\) 1.00000i 0.0680414i
\(217\) 0.493000 + 0.853901i 0.0334670 + 0.0579665i
\(218\) −6.49396 + 11.2479i −0.439826 + 0.761802i
\(219\) −2.75914 1.59299i −0.186445 0.107644i
\(220\) 2.03385 0.137122
\(221\) 0 0
\(222\) −10.0978 −0.677722
\(223\) −5.86133 3.38404i −0.392504 0.226612i 0.290741 0.956802i \(-0.406098\pi\)
−0.683245 + 0.730190i \(0.739432\pi\)
\(224\) 0.178448 0.309081i 0.0119231 0.0206513i
\(225\) −2.26055 3.91539i −0.150704 0.261026i
\(226\) 0.792249i 0.0526996i
\(227\) 20.5074 11.8400i 1.36113 0.785846i 0.371352 0.928492i \(-0.378894\pi\)
0.989774 + 0.142646i \(0.0455610\pi\)
\(228\) −6.24210 + 3.60388i −0.413393 + 0.238672i
\(229\) 8.29829i 0.548366i 0.961677 + 0.274183i \(0.0884075\pi\)
−0.961677 + 0.274183i \(0.911593\pi\)
\(230\) −0.829085 1.43602i −0.0546682 0.0946882i
\(231\) 0.524459 0.908389i 0.0345068 0.0597676i
\(232\) 6.78019 + 3.91454i 0.445141 + 0.257002i
\(233\) 23.9651 1.57000 0.785002 0.619493i \(-0.212662\pi\)
0.785002 + 0.619493i \(0.212662\pi\)
\(234\) 0 0
\(235\) −3.45175 −0.225167
\(236\) 1.42297 + 0.821552i 0.0926275 + 0.0534785i
\(237\) −7.52326 + 13.0307i −0.488688 + 0.846433i
\(238\) −1.19806 2.07510i −0.0776588 0.134509i
\(239\) 12.6160i 0.816058i 0.912969 + 0.408029i \(0.133784\pi\)
−0.912969 + 0.408029i \(0.866216\pi\)
\(240\) 0.599308 0.346011i 0.0386852 0.0223349i
\(241\) −22.8576 + 13.1969i −1.47239 + 0.850085i −0.999518 0.0310462i \(-0.990116\pi\)
−0.472872 + 0.881131i \(0.656783\pi\)
\(242\) 2.36227i 0.151853i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −3.24698 + 5.62393i −0.207867 + 0.360035i
\(245\) −4.11882 2.37800i −0.263142 0.151925i
\(246\) 4.89008 0.311780
\(247\) 0 0
\(248\) 2.76271 0.175432
\(249\) −12.8403 7.41335i −0.813720 0.469802i
\(250\) 3.29440 5.70608i 0.208356 0.360884i
\(251\) −15.0172 26.0106i −0.947879 1.64177i −0.749882 0.661571i \(-0.769890\pi\)
−0.197996 0.980203i \(-0.563443\pi\)
\(252\) 0.356896i 0.0224823i
\(253\) −6.09873 + 3.52111i −0.383424 + 0.221370i
\(254\) 15.7768 9.10872i 0.989922 0.571532i
\(255\) 4.64609i 0.290949i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 5.63102 9.75322i 0.351254 0.608389i −0.635216 0.772335i \(-0.719089\pi\)
0.986469 + 0.163946i \(0.0524222\pi\)
\(258\) 5.70866 + 3.29590i 0.355406 + 0.205194i
\(259\) −3.60388 −0.223934
\(260\) 0 0
\(261\) 7.82908 0.484608
\(262\) −2.36907 1.36778i −0.146361 0.0845018i
\(263\) 2.77479 4.80608i 0.171101 0.296355i −0.767704 0.640804i \(-0.778601\pi\)
0.938805 + 0.344449i \(0.111934\pi\)
\(264\) −1.46950 2.54525i −0.0904415 0.156649i
\(265\) 6.15047i 0.377821i
\(266\) −2.22778 + 1.28621i −0.136594 + 0.0788625i
\(267\) 0.343054 0.198062i 0.0209946 0.0121212i
\(268\) 13.5254i 0.826196i
\(269\) −8.34362 14.4516i −0.508719 0.881128i −0.999949 0.0100977i \(-0.996786\pi\)
0.491230 0.871030i \(-0.336548\pi\)
\(270\) 0.346011 0.599308i 0.0210575 0.0364727i
\(271\) −5.72751 3.30678i −0.347922 0.200873i 0.315848 0.948810i \(-0.397711\pi\)
−0.663770 + 0.747937i \(0.731044\pi\)
\(272\) −6.71379 −0.407083
\(273\) 0 0
\(274\) 7.64742 0.461997
\(275\) −11.5073 6.64377i −0.693919 0.400634i
\(276\) −1.19806 + 2.07510i −0.0721149 + 0.124907i
\(277\) −10.8998 18.8790i −0.654904 1.13433i −0.981918 0.189307i \(-0.939376\pi\)
0.327014 0.945019i \(-0.393958\pi\)
\(278\) 3.38404i 0.202961i
\(279\) 2.39258 1.38135i 0.143240 0.0826995i
\(280\) 0.213891 0.123490i 0.0127824 0.00737993i
\(281\) 20.5918i 1.22840i −0.789149 0.614202i \(-0.789478\pi\)
0.789149 0.614202i \(-0.210522\pi\)
\(282\) 2.49396 + 4.31966i 0.148513 + 0.257232i
\(283\) −6.50604 + 11.2688i −0.386744 + 0.669860i −0.992009 0.126163i \(-0.959734\pi\)
0.605265 + 0.796024i \(0.293067\pi\)
\(284\) −5.89904 3.40581i −0.350044 0.202098i
\(285\) −4.98792 −0.295459
\(286\) 0 0
\(287\) 1.74525 0.103019
\(288\) −0.866025 0.500000i −0.0510310 0.0294628i
\(289\) −14.0375 + 24.3137i −0.825735 + 1.43022i
\(290\) 2.70895 + 4.69203i 0.159075 + 0.275526i
\(291\) 0.417895i 0.0244974i
\(292\) −2.75914 + 1.59299i −0.161466 + 0.0932227i
\(293\) 12.9376 7.46950i 0.755820 0.436373i −0.0719730 0.997407i \(-0.522930\pi\)
0.827793 + 0.561034i \(0.189596\pi\)
\(294\) 6.87263i 0.400820i
\(295\) 0.568532 + 0.984726i 0.0331012 + 0.0573329i
\(296\) −5.04892 + 8.74498i −0.293462 + 0.508292i
\(297\) −2.54525 1.46950i −0.147690 0.0852691i
\(298\) 20.8170 1.20590
\(299\) 0 0
\(300\) −4.52111 −0.261026
\(301\) 2.03740 + 1.17629i 0.117434 + 0.0678003i
\(302\) 0.447730 0.775492i 0.0257640 0.0446245i
\(303\) 5.00753 + 8.67330i 0.287675 + 0.498268i
\(304\) 7.20775i 0.413393i
\(305\) −3.89188 + 2.24698i −0.222849 + 0.128662i
\(306\) −5.81431 + 3.35690i −0.332382 + 0.191901i
\(307\) 26.0301i 1.48562i −0.669503 0.742809i \(-0.733493\pi\)
0.669503 0.742809i \(-0.266507\pi\)
\(308\) −0.524459 0.908389i −0.0298838 0.0517603i
\(309\) −4.81282 + 8.33605i −0.273792 + 0.474222i
\(310\) 1.65571 + 0.955927i 0.0940382 + 0.0542930i
\(311\) 4.81163 0.272842 0.136421 0.990651i \(-0.456440\pi\)
0.136421 + 0.990651i \(0.456440\pi\)
\(312\) 0 0
\(313\) −26.0411 −1.47193 −0.735966 0.677018i \(-0.763272\pi\)
−0.735966 + 0.677018i \(0.763272\pi\)
\(314\) −7.44071 4.29590i −0.419904 0.242431i
\(315\) 0.123490 0.213891i 0.00695786 0.0120514i
\(316\) 7.52326 + 13.0307i 0.423217 + 0.733033i
\(317\) 11.5211i 0.647090i −0.946213 0.323545i \(-0.895125\pi\)
0.946213 0.323545i \(-0.104875\pi\)
\(318\) −7.69697 + 4.44385i −0.431624 + 0.249198i
\(319\) 19.9270 11.5048i 1.11570 0.644148i
\(320\) 0.692021i 0.0386852i
\(321\) 3.31551 + 5.74263i 0.185054 + 0.320523i
\(322\) −0.427583 + 0.740596i −0.0238283 + 0.0412718i
\(323\) 41.9081 + 24.1957i 2.33183 + 1.34628i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) 1.72587 0.0955873
\(327\) 11.2479 + 6.49396i 0.622008 + 0.359117i
\(328\) 2.44504 4.23494i 0.135005 0.233835i
\(329\) 0.890084 + 1.54167i 0.0490719 + 0.0849950i
\(330\) 2.03385i 0.111960i
\(331\) 2.97769 1.71917i 0.163668 0.0944940i −0.415928 0.909397i \(-0.636543\pi\)
0.579597 + 0.814903i \(0.303210\pi\)
\(332\) −12.8403 + 7.41335i −0.704703 + 0.406860i
\(333\) 10.0978i 0.553358i
\(334\) −10.5700 18.3078i −0.578366 1.00176i
\(335\) −4.67994 + 8.10589i −0.255692 + 0.442872i
\(336\) −0.309081 0.178448i −0.0168617 0.00973513i
\(337\) −8.20105 −0.446739 −0.223370 0.974734i \(-0.571706\pi\)
−0.223370 + 0.974734i \(0.571706\pi\)
\(338\) 0 0
\(339\) 0.792249 0.0430291
\(340\) −4.02363 2.32304i −0.218212 0.125985i
\(341\) 4.05980 7.03178i 0.219851 0.380792i
\(342\) 3.60388 + 6.24210i 0.194875 + 0.337534i
\(343\) 4.95108i 0.267333i
\(344\) 5.70866 3.29590i 0.307790 0.177703i
\(345\) −1.43602 + 0.829085i −0.0773126 + 0.0446364i
\(346\) 9.35450i 0.502901i
\(347\) −3.93147 6.80950i −0.211052 0.365553i 0.740992 0.671514i \(-0.234356\pi\)
−0.952044 + 0.305961i \(0.901022\pi\)
\(348\) 3.91454 6.78019i 0.209841 0.363456i
\(349\) −16.2159 9.36227i −0.868019 0.501151i −0.00132953 0.999999i \(-0.500423\pi\)
−0.866689 + 0.498848i \(0.833757\pi\)
\(350\) −1.61356 −0.0862486
\(351\) 0 0
\(352\) −2.93900 −0.156649
\(353\) 27.3186 + 15.7724i 1.45402 + 0.839480i 0.998706 0.0508500i \(-0.0161930\pi\)
0.455316 + 0.890330i \(0.349526\pi\)
\(354\) 0.821552 1.42297i 0.0436650 0.0756300i
\(355\) −2.35690 4.08226i −0.125091 0.216664i
\(356\) 0.396125i 0.0209946i
\(357\) −2.07510 + 1.19806i −0.109826 + 0.0634082i
\(358\) −2.74983 + 1.58761i −0.145333 + 0.0839080i
\(359\) 2.39612i 0.126463i −0.997999 0.0632313i \(-0.979859\pi\)
0.997999 0.0632313i \(-0.0201406\pi\)
\(360\) −0.346011 0.599308i −0.0182364 0.0315863i
\(361\) 16.4758 28.5370i 0.867149 1.50195i
\(362\) −17.1469 9.89977i −0.901222 0.520320i
\(363\) 2.36227 0.123987
\(364\) 0 0
\(365\) −2.20477 −0.115403
\(366\) 5.62393 + 3.24698i 0.293968 + 0.169722i
\(367\) 0.00215593 0.00373419i 0.000112539 0.000194923i −0.865969 0.500097i \(-0.833298\pi\)
0.866082 + 0.499903i \(0.166631\pi\)
\(368\) 1.19806 + 2.07510i 0.0624533 + 0.108172i
\(369\) 4.89008i 0.254568i
\(370\) −6.05171 + 3.49396i −0.314614 + 0.181642i
\(371\) −2.74702 + 1.58599i −0.142618 + 0.0823405i
\(372\) 2.76271i 0.143240i
\(373\) 16.1564 + 27.9838i 0.836549 + 1.44895i 0.892763 + 0.450526i \(0.148764\pi\)
−0.0562144 + 0.998419i \(0.517903\pi\)
\(374\) −9.86592 + 17.0883i −0.510155 + 0.883614i
\(375\) −5.70608 3.29440i −0.294661 0.170122i
\(376\) 4.98792 0.257232
\(377\) 0 0
\(378\) −0.356896 −0.0183567
\(379\) −17.1092 9.87800i −0.878841 0.507399i −0.00856468 0.999963i \(-0.502726\pi\)
−0.870276 + 0.492564i \(0.836060\pi\)
\(380\) −2.49396 + 4.31966i −0.127937 + 0.221594i
\(381\) −9.10872 15.7768i −0.466654 0.808268i
\(382\) 15.2620i 0.780874i
\(383\) 24.9516 14.4058i 1.27497 0.736103i 0.299049 0.954238i \(-0.403331\pi\)
0.975919 + 0.218135i \(0.0699974\pi\)
\(384\) −0.866025 + 0.500000i −0.0441942 + 0.0255155i
\(385\) 0.725873i 0.0369939i
\(386\) −2.38404 4.12928i −0.121345 0.210175i
\(387\) 3.29590 5.70866i 0.167540 0.290188i
\(388\) 0.361908 + 0.208947i 0.0183731 + 0.0106077i
\(389\) −34.7821 −1.76352 −0.881761 0.471697i \(-0.843642\pi\)
−0.881761 + 0.471697i \(0.843642\pi\)
\(390\) 0 0
\(391\) 16.0871 0.813559
\(392\) 5.95187 + 3.43631i 0.300615 + 0.173560i
\(393\) −1.36778 + 2.36907i −0.0689954 + 0.119504i
\(394\) 6.11745 + 10.5957i 0.308193 + 0.533805i
\(395\) 10.4125i 0.523911i
\(396\) −2.54525 + 1.46950i −0.127904 + 0.0738452i
\(397\) 4.46302 2.57673i 0.223993 0.129322i −0.383805 0.923414i \(-0.625386\pi\)
0.607798 + 0.794092i \(0.292053\pi\)
\(398\) 11.8485i 0.593910i
\(399\) 1.28621 + 2.22778i 0.0643910 + 0.111528i
\(400\) −2.26055 + 3.91539i −0.113028 + 0.195770i
\(401\) 11.5398 + 6.66248i 0.576268 + 0.332708i 0.759649 0.650333i \(-0.225371\pi\)
−0.183381 + 0.983042i \(0.558704\pi\)
\(402\) 13.5254 0.674587
\(403\) 0 0
\(404\) 10.0151 0.498268
\(405\) −0.599308 0.346011i −0.0297799 0.0171934i
\(406\) 1.39708 2.41982i 0.0693361 0.120094i
\(407\) 14.8388 + 25.7015i 0.735531 + 1.27398i
\(408\) 6.71379i 0.332382i
\(409\) −20.8051 + 12.0118i −1.02875 + 0.593947i −0.916626 0.399747i \(-0.869098\pi\)
−0.112122 + 0.993694i \(0.535765\pi\)
\(410\) 2.93067 1.69202i 0.144735 0.0835630i
\(411\) 7.64742i 0.377219i
\(412\) 4.81282 + 8.33605i 0.237111 + 0.410688i
\(413\) 0.293209 0.507852i 0.0144278 0.0249898i
\(414\) 2.07510 + 1.19806i 0.101986 + 0.0588815i
\(415\) −10.2604 −0.503663
\(416\) 0 0
\(417\) 3.38404 0.165717
\(418\) 18.3455 + 10.5918i 0.897309 + 0.518062i
\(419\) −6.90246 + 11.9554i −0.337207 + 0.584060i −0.983906 0.178685i \(-0.942816\pi\)
0.646699 + 0.762745i \(0.276149\pi\)
\(420\) −0.123490 0.213891i −0.00602569 0.0104368i
\(421\) 7.72587i 0.376536i 0.982118 + 0.188268i \(0.0602874\pi\)
−0.982118 + 0.188268i \(0.939713\pi\)
\(422\) −14.9494 + 8.63102i −0.727724 + 0.420152i
\(423\) 4.31966 2.49396i 0.210029 0.121260i
\(424\) 8.88769i 0.431624i
\(425\) 15.1769 + 26.2871i 0.736187 + 1.27511i
\(426\) −3.40581 + 5.89904i −0.165012 + 0.285809i
\(427\) 2.00716 + 1.15883i 0.0971332 + 0.0560799i
\(428\) 6.63102 0.320523
\(429\) 0 0
\(430\) 4.56166 0.219983
\(431\) −0.554360 0.320060i −0.0267026 0.0154168i 0.486589 0.873631i \(-0.338241\pi\)
−0.513292 + 0.858214i \(0.671574\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) 10.6380 + 18.4256i 0.511231 + 0.885478i 0.999915 + 0.0130171i \(0.00414358\pi\)
−0.488685 + 0.872461i \(0.662523\pi\)
\(434\) 0.985999i 0.0473295i
\(435\) 4.69203 2.70895i 0.224966 0.129884i
\(436\) 11.2479 6.49396i 0.538675 0.311004i
\(437\) 17.2707i 0.826168i
\(438\) 1.59299 + 2.75914i 0.0761160 + 0.131837i
\(439\) 6.35905 11.0142i 0.303501 0.525679i −0.673425 0.739255i \(-0.735178\pi\)
0.976926 + 0.213576i \(0.0685111\pi\)
\(440\) −1.76137 1.01693i −0.0839699 0.0484800i
\(441\) 6.87263 0.327268
\(442\) 0 0
\(443\) 22.5972 1.07362 0.536812 0.843702i \(-0.319628\pi\)
0.536812 + 0.843702i \(0.319628\pi\)
\(444\) 8.74498 + 5.04892i 0.415018 + 0.239611i
\(445\) 0.137063 0.237401i 0.00649743 0.0112539i
\(446\) 3.38404 + 5.86133i 0.160239 + 0.277542i
\(447\) 20.8170i 0.984610i
\(448\) −0.309081 + 0.178448i −0.0146027 + 0.00843087i
\(449\) −10.0870 + 5.82371i −0.476033 + 0.274838i −0.718762 0.695256i \(-0.755291\pi\)
0.242729 + 0.970094i \(0.421957\pi\)
\(450\) 4.52111i 0.213127i
\(451\) −7.18598 12.4465i −0.338375 0.586082i
\(452\) 0.396125 0.686108i 0.0186321 0.0322718i
\(453\) −0.775492 0.447730i −0.0364358 0.0210362i
\(454\) −23.6799 −1.11135
\(455\) 0 0
\(456\) 7.20775 0.337534
\(457\) 18.3502 + 10.5945i 0.858385 + 0.495589i 0.863471 0.504398i \(-0.168286\pi\)
−0.00508594 + 0.999987i \(0.501619\pi\)
\(458\) 4.14914 7.18653i 0.193877 0.335804i
\(459\) 3.35690 + 5.81431i 0.156686 + 0.271389i
\(460\) 1.65817i 0.0773126i
\(461\) 20.8447 12.0347i 0.970833 0.560511i 0.0713432 0.997452i \(-0.477271\pi\)
0.899490 + 0.436941i \(0.143938\pi\)
\(462\) −0.908389 + 0.524459i −0.0422621 + 0.0244000i
\(463\) 18.1715i 0.844502i 0.906479 + 0.422251i \(0.138760\pi\)
−0.906479 + 0.422251i \(0.861240\pi\)
\(464\) −3.91454 6.78019i −0.181728 0.314762i
\(465\) 0.955927 1.65571i 0.0443301 0.0767819i
\(466\) −20.7544 11.9825i −0.961428 0.555081i
\(467\) 2.93123 0.135641 0.0678206 0.997698i \(-0.478395\pi\)
0.0678206 + 0.997698i \(0.478395\pi\)
\(468\) 0 0
\(469\) 4.82717 0.222898
\(470\) 2.98930 + 1.72587i 0.137886 + 0.0796086i
\(471\) −4.29590 + 7.44071i −0.197944 + 0.342850i
\(472\) −0.821552 1.42297i −0.0378150 0.0654975i
\(473\) 19.3733i 0.890785i
\(474\) 13.0307 7.52326i 0.598519 0.345555i
\(475\) 28.2212 16.2935i 1.29488 0.747597i
\(476\) 2.39612i 0.109826i
\(477\) 4.44385 + 7.69697i 0.203470 + 0.352420i
\(478\) 6.30798 10.9257i 0.288520 0.499732i
\(479\) −26.5948 15.3545i −1.21515 0.701565i −0.251271 0.967917i \(-0.580848\pi\)
−0.963876 + 0.266352i \(0.914182\pi\)
\(480\) −0.692021 −0.0315863
\(481\) 0 0
\(482\) 26.3937 1.20220
\(483\) 0.740596 + 0.427583i 0.0336983 + 0.0194557i
\(484\) 1.18114 2.04579i 0.0536880 0.0929904i
\(485\) 0.144596 + 0.250448i 0.00656577 + 0.0113722i
\(486\) 1.00000i 0.0453609i
\(487\) 20.9143 12.0749i 0.947717 0.547164i 0.0553458 0.998467i \(-0.482374\pi\)
0.892371 + 0.451303i \(0.149041\pi\)
\(488\) 5.62393 3.24698i 0.254584 0.146984i
\(489\) 1.72587i 0.0780467i
\(490\) 2.37800 + 4.11882i 0.107427 + 0.186069i
\(491\) 7.29859 12.6415i 0.329381 0.570504i −0.653009 0.757351i \(-0.726493\pi\)
0.982389 + 0.186847i \(0.0598268\pi\)
\(492\) −4.23494 2.44504i −0.190926 0.110231i
\(493\) −52.5628 −2.36731
\(494\) 0 0
\(495\) −2.03385 −0.0914148
\(496\) −2.39258 1.38135i −0.107430 0.0620246i
\(497\) −1.21552 + 2.10534i −0.0545236 + 0.0944376i
\(498\) 7.41335 + 12.8403i 0.332200 + 0.575387i
\(499\) 6.85517i 0.306879i 0.988158 + 0.153440i \(0.0490351\pi\)
−0.988158 + 0.153440i \(0.950965\pi\)
\(500\) −5.70608 + 3.29440i −0.255184 + 0.147330i
\(501\) −18.3078 + 10.5700i −0.817933 + 0.472234i
\(502\) 30.0344i 1.34050i
\(503\) 13.3666 + 23.1516i 0.595987 + 1.03228i 0.993407 + 0.114642i \(0.0365722\pi\)
−0.397420 + 0.917637i \(0.630094\pi\)
\(504\) −0.178448 + 0.309081i −0.00794870 + 0.0137676i
\(505\) 6.00211 + 3.46532i 0.267090 + 0.154205i
\(506\) 7.04221 0.313065
\(507\) 0 0
\(508\) −18.2174 −0.808268
\(509\) 17.8916 + 10.3297i 0.793033 + 0.457858i 0.841029 0.540989i \(-0.181950\pi\)
−0.0479959 + 0.998848i \(0.515283\pi\)
\(510\) −2.32304 + 4.02363i −0.102866 + 0.178169i
\(511\) 0.568532 + 0.984726i 0.0251504 + 0.0435617i
\(512\) 1.00000i 0.0441942i
\(513\) 6.24210 3.60388i 0.275595 0.159115i
\(514\) −9.75322 + 5.63102i −0.430196 + 0.248374i
\(515\) 6.66115i 0.293525i
\(516\) −3.29590 5.70866i −0.145094 0.251310i
\(517\) 7.32975 12.6955i 0.322362 0.558347i
\(518\) 3.12105 + 1.80194i 0.137131 + 0.0791726i
\(519\) −9.35450 −0.410617
\(520\) 0 0
\(521\) −15.0965 −0.661390 −0.330695 0.943738i \(-0.607283\pi\)
−0.330695 + 0.943738i \(0.607283\pi\)
\(522\) −6.78019 3.91454i −0.296761 0.171335i
\(523\) −0.0174584 + 0.0302388i −0.000763402 + 0.00132225i −0.866407 0.499339i \(-0.833576\pi\)
0.865643 + 0.500661i \(0.166910\pi\)
\(524\) 1.36778 + 2.36907i 0.0597518 + 0.103493i
\(525\) 1.61356i 0.0704217i
\(526\) −4.80608 + 2.77479i −0.209555 + 0.120987i
\(527\) −16.0633 + 9.27413i −0.699727 + 0.403987i
\(528\) 2.93900i 0.127904i
\(529\) 8.62929 + 14.9464i 0.375187 + 0.649842i
\(530\) −3.07524 + 5.32647i −0.133580 + 0.231367i
\(531\) −1.42297 0.821552i −0.0617516 0.0356523i
\(532\) 2.57242 0.111528
\(533\) 0 0
\(534\) −0.396125 −0.0171420
\(535\) 3.97403 + 2.29440i 0.171812 + 0.0991958i
\(536\) 6.76271 11.7134i 0.292105 0.505940i
\(537\) 1.58761 + 2.74983i 0.0685106 + 0.118664i
\(538\) 16.6872i 0.719438i
\(539\) 17.4925 10.0993i 0.753457 0.435009i
\(540\) −0.599308 + 0.346011i −0.0257901 + 0.0148899i
\(541\) 13.0858i 0.562600i −0.959620 0.281300i \(-0.909234\pi\)
0.959620 0.281300i \(-0.0907657\pi\)
\(542\) 3.30678 + 5.72751i 0.142038 + 0.246018i
\(543\) −9.89977 + 17.1469i −0.424840 + 0.735844i
\(544\) 5.81431 + 3.35690i 0.249287 + 0.143926i
\(545\) 8.98792 0.385000
\(546\) 0 0
\(547\) −5.97584 −0.255508 −0.127754 0.991806i \(-0.540777\pi\)
−0.127754 + 0.991806i \(0.540777\pi\)
\(548\) −6.62286 3.82371i −0.282914 0.163341i
\(549\) 3.24698 5.62393i 0.138578 0.240024i
\(550\) 6.64377 + 11.5073i 0.283291 + 0.490675i
\(551\) 56.4301i 2.40400i
\(552\) 2.07510 1.19806i 0.0883223 0.0509929i
\(553\) 4.65059 2.68502i 0.197763 0.114179i
\(554\) 21.7995i 0.926174i
\(555\) 3.49396 + 6.05171i 0.148310 + 0.256881i
\(556\) 1.69202 2.93067i 0.0717577 0.124288i
\(557\) −9.04102 5.21983i −0.383080 0.221171i 0.296077 0.955164i \(-0.404321\pi\)
−0.679158 + 0.733993i \(0.737655\pi\)
\(558\) −2.76271 −0.116955
\(559\) 0 0
\(560\) −0.246980 −0.0104368
\(561\) 17.0883 + 9.86592i 0.721468 + 0.416539i
\(562\) −10.2959 + 17.8330i −0.434306 + 0.752240i
\(563\) −2.83028 4.90219i −0.119282 0.206603i 0.800201 0.599732i \(-0.204726\pi\)
−0.919483 + 0.393129i \(0.871393\pi\)
\(564\) 4.98792i 0.210029i
\(565\) 0.474801 0.274127i 0.0199750 0.0115326i
\(566\) 11.2688 6.50604i 0.473663 0.273469i
\(567\) 0.356896i 0.0149882i
\(568\) 3.40581 + 5.89904i 0.142905 + 0.247518i
\(569\) 10.3284 17.8893i 0.432990 0.749961i −0.564139 0.825680i \(-0.690792\pi\)
0.997129 + 0.0757191i \(0.0241252\pi\)
\(570\) 4.31966 + 2.49396i 0.180931 + 0.104460i
\(571\) −44.3672 −1.85671 −0.928354 0.371697i \(-0.878776\pi\)
−0.928354 + 0.371697i \(0.878776\pi\)
\(572\) 0 0
\(573\) 15.2620 0.637581
\(574\) −1.51143 0.872625i −0.0630859 0.0364227i
\(575\) 5.41657 9.38177i 0.225886 0.391247i
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 29.4426i 1.22571i 0.790194 + 0.612857i \(0.209980\pi\)
−0.790194 + 0.612857i \(0.790020\pi\)
\(578\) 24.3137 14.0375i 1.01132 0.583883i
\(579\) −4.12928 + 2.38404i −0.171607 + 0.0990774i
\(580\) 5.41789i 0.224966i
\(581\) 2.64579 + 4.58265i 0.109766 + 0.190120i
\(582\) 0.208947 0.361908i 0.00866115 0.0150015i
\(583\) 22.6214 + 13.0605i 0.936882 + 0.540909i
\(584\) 3.18598 0.131837
\(585\) 0 0
\(586\) −14.9390 −0.617124
\(587\) 16.9426 + 9.78179i 0.699294 + 0.403738i 0.807085 0.590436i \(-0.201044\pi\)
−0.107790 + 0.994174i \(0.534377\pi\)
\(588\) 3.43631 5.95187i 0.141711 0.245451i
\(589\) 9.95646 + 17.2451i 0.410249 + 0.710572i
\(590\) 1.13706i 0.0468122i
\(591\) 10.5957 6.11745i 0.435850 0.251638i
\(592\) 8.74498 5.04892i 0.359417 0.207509i
\(593\) 10.8793i 0.446761i 0.974731 + 0.223380i \(0.0717092\pi\)
−0.974731 + 0.223380i \(0.928291\pi\)
\(594\) 1.46950 + 2.54525i 0.0602943 + 0.104433i
\(595\) −0.829085 + 1.43602i −0.0339892 + 0.0588710i
\(596\) −18.0281 10.4085i −0.738458 0.426349i
\(597\) 11.8485 0.484925
\(598\) 0 0
\(599\) 16.0543 0.655961 0.327980 0.944685i \(-0.393632\pi\)
0.327980 + 0.944685i \(0.393632\pi\)
\(600\) 3.91539 + 2.26055i 0.159845 + 0.0922867i
\(601\) −6.44773 + 11.1678i −0.263008 + 0.455544i −0.967040 0.254625i \(-0.918048\pi\)
0.704032 + 0.710169i \(0.251381\pi\)
\(602\) −1.17629 2.03740i −0.0479421 0.0830381i
\(603\) 13.5254i 0.550798i
\(604\) −0.775492 + 0.447730i −0.0315543 + 0.0182179i
\(605\) 1.41573 0.817372i 0.0575576 0.0332309i
\(606\) 10.0151i 0.406834i
\(607\) −22.2371 38.5157i −0.902574 1.56330i −0.824141 0.566385i \(-0.808342\pi\)
−0.0784334 0.996919i \(-0.524992\pi\)
\(608\) 3.60388 6.24210i 0.146156 0.253150i
\(609\) −2.41982 1.39708i −0.0980561 0.0566127i
\(610\) 4.49396 0.181955
\(611\) 0 0
\(612\) 6.71379 0.271389
\(613\) −36.3950 21.0127i −1.46998 0.848694i −0.470548 0.882374i \(-0.655944\pi\)
−0.999433 + 0.0336804i \(0.989277\pi\)
\(614\) −13.0151 + 22.5428i −0.525245 + 0.909752i
\(615\) −1.69202 2.93067i −0.0682289 0.118176i
\(616\) 1.04892i 0.0422621i
\(617\) −14.4327 + 8.33273i −0.581039 + 0.335463i −0.761546 0.648111i \(-0.775559\pi\)
0.180507 + 0.983574i \(0.442226\pi\)
\(618\) 8.33605 4.81282i 0.335325 0.193600i
\(619\) 39.7512i 1.59774i −0.601506 0.798868i \(-0.705432\pi\)
0.601506 0.798868i \(-0.294568\pi\)
\(620\) −0.955927 1.65571i −0.0383910 0.0664951i
\(621\) 1.19806 2.07510i 0.0480766 0.0832711i
\(622\) −4.16699 2.40581i −0.167081 0.0964643i
\(623\) −0.141375 −0.00566408
\(624\) 0 0
\(625\) 18.0459 0.721837
\(626\) 22.5523 + 13.0206i 0.901371 + 0.520407i
\(627\) 10.5918 18.3455i 0.422996 0.732650i
\(628\) 4.29590 + 7.44071i 0.171425 + 0.296917i
\(629\) 67.7948i 2.70315i
\(630\) −0.213891 + 0.123490i −0.00852161 + 0.00491995i
\(631\) −12.6238 + 7.28836i −0.502546 + 0.290145i −0.729764 0.683699i \(-0.760370\pi\)
0.227218 + 0.973844i \(0.427037\pi\)
\(632\) 15.0465i 0.598519i
\(633\) 8.63102 + 14.9494i 0.343052 + 0.594184i
\(634\) −5.76055 + 9.97757i −0.228781 + 0.396260i
\(635\) −10.9179 6.30343i −0.433262 0.250144i
\(636\) 8.88769 0.352420
\(637\) 0 0
\(638\) −23.0097 −0.910962
\(639\) 5.89904 + 3.40581i 0.233362 + 0.134732i
\(640\) −0.346011 + 0.599308i −0.0136773 + 0.0236897i
\(641\) 19.2174 + 33.2856i 0.759043 + 1.31470i 0.943339 + 0.331831i \(0.107666\pi\)
−0.184296 + 0.982871i \(0.559000\pi\)
\(642\) 6.63102i 0.261706i
\(643\) −0.902583 + 0.521106i −0.0355944 + 0.0205504i −0.517692 0.855567i \(-0.673209\pi\)
0.482097 + 0.876118i \(0.339875\pi\)
\(644\) 0.740596 0.427583i 0.0291836 0.0168491i
\(645\) 4.56166i 0.179615i
\(646\) −24.1957 41.9081i −0.951966 1.64885i
\(647\) −14.0804 + 24.3879i −0.553557 + 0.958788i 0.444458 + 0.895800i \(0.353396\pi\)
−0.998014 + 0.0629884i \(0.979937\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) −4.82908 −0.189558
\(650\) 0 0
\(651\) −0.985999 −0.0386444
\(652\) −1.49465 0.862937i −0.0585350 0.0337952i
\(653\) −5.31013 + 9.19742i −0.207802 + 0.359923i −0.951022 0.309124i \(-0.899964\pi\)
0.743220 + 0.669047i \(0.233298\pi\)
\(654\) −6.49396 11.2479i −0.253934 0.439826i
\(655\) 1.89307i 0.0739683i
\(656\) −4.23494 + 2.44504i −0.165347 + 0.0954628i
\(657\) 2.75914 1.59299i 0.107644 0.0621485i
\(658\) 1.78017i 0.0693982i
\(659\) 20.1814 + 34.9553i 0.786157 + 1.36166i 0.928305 + 0.371818i \(0.121266\pi\)
−0.142148 + 0.989845i \(0.545401\pi\)
\(660\) −1.01693 + 1.76137i −0.0395838 + 0.0685611i
\(661\) −27.6407 15.9584i −1.07510 0.620709i −0.145529 0.989354i \(-0.546488\pi\)
−0.929570 + 0.368645i \(0.879822\pi\)
\(662\) −3.43834 −0.133635
\(663\) 0 0
\(664\) 14.8267 0.575387
\(665\) 1.54167 + 0.890084i 0.0597834 + 0.0345160i
\(666\) 5.04892 8.74498i 0.195642 0.338861i
\(667\) 9.37973 + 16.2462i 0.363185 + 0.629054i
\(668\) 21.1400i 0.817933i
\(669\) 5.86133 3.38404i 0.226612 0.130835i
\(670\) 8.10589 4.67994i 0.313158 0.180802i
\(671\) 19.0858i 0.736797i
\(672\) 0.178448 + 0.309081i 0.00688378 + 0.0119231i
\(673\) 1.91401 3.31516i 0.0737797 0.127790i −0.826775 0.562532i \(-0.809827\pi\)
0.900555 + 0.434742i \(0.143161\pi\)
\(674\) 7.10231 + 4.10052i 0.273571 + 0.157946i
\(675\) 4.52111 0.174017
\(676\) 0 0
\(677\) 1.78927 0.0687670 0.0343835 0.999409i \(-0.489053\pi\)
0.0343835 + 0.999409i \(0.489053\pi\)
\(678\) −0.686108 0.396125i −0.0263498 0.0152131i
\(679\) 0.0745725 0.129163i 0.00286183 0.00495683i
\(680\) 2.32304 + 4.02363i 0.0890847 + 0.154299i
\(681\) 23.6799i 0.907417i
\(682\) −7.03178 + 4.05980i −0.269261 + 0.155458i
\(683\) −0.657941 + 0.379863i −0.0251754 + 0.0145350i −0.512535 0.858666i \(-0.671293\pi\)
0.487359 + 0.873201i \(0.337960\pi\)
\(684\) 7.20775i 0.275595i
\(685\) −2.64609 4.58316i −0.101102 0.175114i
\(686\) 2.47554 4.28776i 0.0945166 0.163708i
\(687\) −7.18653 4.14914i −0.274183 0.158300i
\(688\) −6.59179 −0.251310
\(689\) 0 0
\(690\) 1.65817 0.0631254
\(691\) −4.03524 2.32975i −0.153508 0.0886278i 0.421278 0.906931i \(-0.361582\pi\)
−0.574786 + 0.818304i \(0.694915\pi\)
\(692\) −4.67725 + 8.10124i −0.177802 + 0.307963i
\(693\) 0.524459 + 0.908389i 0.0199225 + 0.0345068i
\(694\) 7.86294i 0.298473i
\(695\) 2.02808 1.17092i 0.0769296 0.0444153i
\(696\) −6.78019 + 3.91454i −0.257002 + 0.148380i
\(697\) 32.8310i 1.24356i
\(698\) 9.36227 + 16.2159i 0.354367 + 0.613782i
\(699\) −11.9825 + 20.7544i −0.453221 + 0.785002i
\(700\) 1.39739 + 0.806782i 0.0528163 + 0.0304935i
\(701\) 24.3284 0.918872 0.459436 0.888211i \(-0.348052\pi\)
0.459436 + 0.888211i \(0.348052\pi\)
\(702\) 0 0
\(703\) −72.7827 −2.74505
\(704\) 2.54525 + 1.46950i 0.0959277 + 0.0553839i
\(705\) 1.72587 2.98930i 0.0650001 0.112584i
\(706\) −15.7724 27.3186i −0.593602 1.02815i
\(707\) 3.57434i 0.134427i
\(708\) −1.42297 + 0.821552i −0.0534785 + 0.0308758i
\(709\) 25.4548 14.6963i 0.955975 0.551932i 0.0610430 0.998135i \(-0.480557\pi\)
0.894932 + 0.446203i \(0.147224\pi\)
\(710\) 4.71379i 0.176905i
\(711\) −7.52326 13.0307i −0.282144 0.488688i
\(712\) −0.198062 + 0.343054i −0.00742270 + 0.0128565i
\(713\) 5.73291 + 3.30990i 0.214699 + 0.123957i
\(714\) 2.39612 0.0896727
\(715\) 0 0
\(716\) 3.17523 0.118664
\(717\) −10.9257 6.30798i −0.408029 0.235576i
\(718\) −1.19806 + 2.07510i −0.0447113 + 0.0774422i
\(719\) −25.7439 44.5898i −0.960086 1.66292i −0.722274 0.691607i \(-0.756903\pi\)
−0.237812 0.971311i \(-0.576430\pi\)
\(720\) 0.692021i 0.0257901i
\(721\) 2.97510 1.71768i 0.110799 0.0639696i
\(722\) −28.5370 + 16.4758i −1.06204 + 0.613167i
\(723\) 26.3937i 0.981593i
\(724\) 9.89977 + 17.1469i 0.367922 + 0.637260i
\(725\) −17.6981 + 30.6539i −0.657290 + 1.13846i
\(726\) −2.04579 1.18114i −0.0759263 0.0438361i
\(727\) 3.67324 0.136233 0.0681164 0.997677i \(-0.478301\pi\)
0.0681164 + 0.997677i \(0.478301\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 1.90938 + 1.10238i 0.0706695 + 0.0408010i
\(731\) −22.1280 + 38.3268i −0.818432 + 1.41757i
\(732\) −3.24698 5.62393i −0.120012 0.207867i
\(733\) 18.3612i 0.678187i 0.940753 + 0.339093i \(0.110120\pi\)
−0.940753 + 0.339093i \(0.889880\pi\)
\(734\) −0.00373419 + 0.00215593i −0.000137831 + 7.95770e-5i
\(735\) 4.11882 2.37800i 0.151925 0.0877139i
\(736\) 2.39612i 0.0883223i
\(737\) −19.8756 34.4256i −0.732127 1.26808i
\(738\) −2.44504 + 4.23494i −0.0900032 + 0.155890i
\(739\) 1.45694 + 0.841166i 0.0535945 + 0.0309428i 0.526558 0.850139i \(-0.323482\pi\)
−0.472963 + 0.881082i \(0.656816\pi\)
\(740\) 6.98792 0.256881
\(741\) 0 0
\(742\) 3.17198 0.116447
\(743\) −41.8234 24.1468i −1.53435 0.885858i −0.999154 0.0411318i \(-0.986904\pi\)
−0.535198 0.844727i \(-0.679763\pi\)
\(744\) −1.38135 + 2.39258i −0.0506429 + 0.0877161i
\(745\) −7.20291 12.4758i −0.263894 0.457078i
\(746\) 32.3129i 1.18306i
\(747\) 12.8403 7.41335i 0.469802 0.271240i
\(748\) 17.0883 9.86592i 0.624809 0.360734i
\(749\) 2.36658i 0.0864731i
\(750\) 3.29440 + 5.70608i 0.120295 + 0.208356i
\(751\) 5.85056 10.1335i 0.213490 0.369775i −0.739314 0.673360i \(-0.764850\pi\)
0.952804 + 0.303585i \(0.0981836\pi\)
\(752\) −4.31966 2.49396i −0.157522 0.0909453i
\(753\) 30.0344 1.09452
\(754\) 0 0
\(755\) −0.619678 −0.0225524
\(756\) 0.309081 + 0.178448i 0.0112412 + 0.00649009i
\(757\) −12.5918 + 21.8096i −0.457657 + 0.792684i −0.998837 0.0482223i \(-0.984644\pi\)
0.541180 + 0.840907i \(0.317978\pi\)
\(758\) 9.87800 + 17.1092i 0.358785 + 0.621434i
\(759\) 7.04221i 0.255616i
\(760\) 4.31966 2.49396i 0.156691 0.0904654i
\(761\) −19.4124 + 11.2078i −0.703699 + 0.406281i −0.808724 0.588189i \(-0.799841\pi\)
0.105025 + 0.994470i \(0.466508\pi\)
\(762\) 18.2174i 0.659948i
\(763\) −2.31767 4.01432i −0.0839052 0.145328i
\(764\) 7.63102 13.2173i 0.276081 0.478186i
\(765\) 4.02363 + 2.32304i 0.145475 + 0.0839898i
\(766\) −28.8116 −1.04101
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) 0.114966 + 0.0663757i 0.00414579 + 0.00239357i 0.502071 0.864826i \(-0.332571\pi\)
−0.497926 + 0.867220i \(0.665905\pi\)
\(770\) −0.362937 + 0.628625i −0.0130793 + 0.0226541i
\(771\) 5.63102 + 9.75322i 0.202796 + 0.351254i
\(772\) 4.76809i 0.171607i
\(773\) −41.6293 + 24.0347i −1.49730 + 0.864467i −0.999995 0.00310775i \(-0.999011\pi\)
−0.497306 + 0.867575i \(0.665677\pi\)
\(774\) −5.70866 + 3.29590i −0.205194 + 0.118469i
\(775\) 12.4905i 0.448672i
\(776\) −0.208947 0.361908i −0.00750077 0.0129917i
\(777\) 1.80194 3.12105i 0.0646442 0.111967i
\(778\) 30.1222 + 17.3910i 1.07993 + 0.623499i
\(779\) 35.2465 1.26284
\(780\) 0 0
\(781\) 20.0194 0.716350
\(782\) −13.9318 8.04354i −0.498201 0.287636i
\(783\) −3.91454 + 6.78019i −0.139894 + 0.242304i
\(784\) −3.43631 5.95187i −0.122725 0.212567i
\(785\) 5.94571i 0.212211i
\(786\) 2.36907 1.36778i 0.0845018 0.0487871i
\(787\) −5.37722 + 3.10454i −0.191677 + 0.110665i −0.592767 0.805374i \(-0.701965\pi\)
0.401090 + 0.916039i \(0.368631\pi\)
\(788\) 12.2349i 0.435850i
\(789\) 2.77479 + 4.80608i 0.0987852 + 0.171101i
\(790\) 5.20626 9.01751i 0.185230 0.320828i
\(791\) −0.244869 0.141375i −0.00870654 0.00502672i
\(792\) 2.93900 0.104433
\(793\) 0 0
\(794\) −5.15346 −0.182889
\(795\) 5.32647 + 3.07524i 0.188910 + 0.109067i
\(796\) 5.92423 10.2611i 0.209979 0.363694i
\(797\) 0.163915 + 0.283909i 0.00580616 + 0.0100566i 0.868914 0.494963i \(-0.164818\pi\)
−0.863108 + 0.505020i \(0.831485\pi\)
\(798\) 2.57242i 0.0910626i
\(799\) −29.0013 + 16.7439i −1.02599 + 0.592357i
\(800\) 3.91539 2.26055i 0.138430 0.0799226i
\(801\) 0.396125i 0.0139964i
\(802\) −6.66248 11.5398i −0.235260 0.407483i
\(803\) 4.68180 8.10912i 0.165217 0.286164i
\(804\) −11.7134 6.76271i −0.413098 0.238502i
\(805\) 0.591794 0.0208580
\(806\) 0 0
\(807\) 16.6872 0.587419
\(808\) −8.67330 5.00753i −0.305126 0.176164i
\(809\) 18.7192 32.4226i 0.658131 1.13992i −0.322968 0.946410i \(-0.604681\pi\)
0.981099 0.193506i \(-0.0619860\pi\)
\(810\) 0.346011 + 0.599308i 0.0121576 + 0.0210575i
\(811\) 17.1448i 0.602037i 0.953618 + 0.301018i \(0.0973265\pi\)
−0.953618 + 0.301018i \(0.902673\pi\)
\(812\) −2.41982 + 1.39708i −0.0849191 + 0.0490280i
\(813\) 5.72751 3.30678i 0.200873 0.115974i
\(814\) 29.6775i 1.04020i
\(815\) −0.597171 1.03433i −0.0209180 0.0362310i
\(816\) 3.35690 5.81431i 0.117515 0.203542i
\(817\) 41.1466 + 23.7560i 1.43954 + 0.831117i
\(818\) 24.0237 0.839969
\(819\) 0 0
\(820\) −3.38404 −0.118176
\(821\) 15.4053 + 8.89426i 0.537649 + 0.310412i 0.744126 0.668040i \(-0.232866\pi\)
−0.206476 + 0.978452i \(0.566200\pi\)
\(822\) −3.82371 + 6.62286i −0.133367 + 0.230999i
\(823\) 6.11506 + 10.5916i 0.213157 + 0.369200i 0.952701 0.303909i \(-0.0982919\pi\)
−0.739544 + 0.673109i \(0.764959\pi\)
\(824\) 9.62565i 0.335325i
\(825\) 11.5073 6.64377i 0.400634 0.231306i
\(826\) −0.507852 + 0.293209i −0.0176704 + 0.0102020i
\(827\) 20.5623i 0.715020i −0.933909 0.357510i \(-0.883626\pi\)
0.933909 0.357510i \(-0.116374\pi\)
\(828\) −1.19806 2.07510i −0.0416355 0.0721149i
\(829\) −12.7235 + 22.0377i −0.441905 + 0.765401i −0.997831 0.0658303i \(-0.979030\pi\)
0.555926 + 0.831232i \(0.312364\pi\)
\(830\) 8.88576 + 5.13019i 0.308429 + 0.178072i
\(831\) 21.7995 0.756218
\(832\) 0 0
\(833\) −46.1414 −1.59870
\(834\) −2.93067 1.69202i −0.101481 0.0585899i
\(835\) −7.31468 + 12.6694i −0.253135 + 0.438443i
\(836\) −10.5918 18.3455i −0.366325 0.634493i
\(837\) 2.76271i 0.0954932i
\(838\) 11.9554 6.90246i 0.412993 0.238442i
\(839\) −4.99416 + 2.88338i −0.172418 + 0.0995453i −0.583725 0.811951i \(-0.698405\pi\)
0.411308 + 0.911497i \(0.365072\pi\)
\(840\) 0.246980i 0.00852161i
\(841\) −16.1473 27.9679i −0.556803 0.964411i
\(842\) 3.86294 6.69080i 0.133126 0.230580i
\(843\) 17.8330 + 10.2959i 0.614202 + 0.354610i
\(844\) 17.2620 0.594184
\(845\) 0 0
\(846\) −4.98792 −0.171488
\(847\) −0.730133 0.421543i −0.0250877 0.0144844i
\(848\) 4.44385 7.69697i 0.152602 0.264315i
\(849\) −6.50604 11.2688i −0.223287 0.386744i
\(850\) 30.3538i 1.04113i
\(851\) −20.9541 + 12.0978i −0.718296 + 0.414708i
\(852\) 5.89904 3.40581i 0.202098 0.116681i
\(853\) 21.1728i 0.724944i 0.931995 + 0.362472i \(0.118067\pi\)
−0.931995 + 0.362472i \(0.881933\pi\)
\(854\) −1.15883 2.00716i −0.0396545 0.0686836i
\(855\) 2.49396 4.31966i 0.0852916 0.147729i
\(856\) −5.74263 3.31551i −0.196279 0.113322i
\(857\) −12.0086 −0.410207 −0.205103 0.978740i \(-0.565753\pi\)
−0.205103 + 0.978740i \(0.565753\pi\)
\(858\) 0 0
\(859\) −1.66296 −0.0567393 −0.0283697 0.999598i \(-0.509032\pi\)
−0.0283697 + 0.999598i \(0.509032\pi\)
\(860\) −3.95052 2.28083i −0.134711 0.0777757i
\(861\) −0.872625 + 1.51143i −0.0297390 + 0.0515094i
\(862\) 0.320060 + 0.554360i 0.0109013 + 0.0188816i
\(863\) 23.8323i 0.811262i −0.914037 0.405631i \(-0.867052\pi\)
0.914037 0.405631i \(-0.132948\pi\)
\(864\) 0.866025 0.500000i 0.0294628 0.0170103i
\(865\) −5.60623 + 3.23676i −0.190618 + 0.110053i
\(866\) 21.2760i 0.722989i
\(867\) −14.0375 24.3137i −0.476738 0.825735i
\(868\) −0.493000 + 0.853901i −0.0167335 + 0.0289833i
\(869\) −38.2972 22.1109i −1.29914 0.750060i
\(870\) −5.41789 −0.183684
\(871\) 0 0
\(872\) −12.9879 −0.439826
\(873\) −0.361908 0.208947i −0.0122487 0.00707180i
\(874\) −8.63533 + 14.9568i −0.292095 + 0.505923i
\(875\) 1.17576 + 2.03648i 0.0397479 + 0.0688454i
\(876\) 3.18598i 0.107644i
\(877\) −36.6482 + 21.1588i −1.23752 + 0.714483i −0.968587 0.248676i \(-0.920005\pi\)
−0.268934 + 0.963159i \(0.586671\pi\)
\(878\) −11.0142 + 6.35905i −0.371711 + 0.214608i
\(879\) 14.9390i 0.503880i
\(880\) 1.01693 + 1.76137i 0.0342806 + 0.0593757i
\(881\) 11.1371 19.2900i 0.375217 0.649895i −0.615142 0.788416i \(-0.710901\pi\)
0.990360 + 0.138521i \(0.0442348\pi\)
\(882\) −5.95187 3.43631i −0.200410 0.115707i
\(883\) 8.54229 0.287471 0.143735 0.989616i \(-0.454089\pi\)
0.143735 + 0.989616i \(0.454089\pi\)
\(884\) 0 0
\(885\) −1.13706 −0.0382220
\(886\) −19.5697 11.2986i −0.657458 0.379583i
\(887\) 9.45712 16.3802i 0.317539 0.549994i −0.662435 0.749120i \(-0.730477\pi\)
0.979974 + 0.199126i \(0.0638102\pi\)
\(888\) −5.04892 8.74498i −0.169431 0.293462i
\(889\) 6.50173i 0.218061i
\(890\) −0.237401 + 0.137063i −0.00795769 + 0.00459437i
\(891\) 2.54525 1.46950i 0.0852691 0.0492301i
\(892\) 6.76809i 0.226612i
\(893\) 17.9758 + 31.1351i 0.601538 + 1.04190i
\(894\) −10.4085 + 18.0281i −0.348112 + 0.602948i
\(895\) 1.90294 + 1.09866i 0.0636083 + 0.0367242i
\(896\) 0.356896 0.0119231
\(897\) 0 0
\(898\) 11.6474 0.388679
\(899\) −18.7317 10.8147i −0.624737 0.360692i
\(900\) 2.26055 3.91539i 0.0753518 0.130513i
\(901\) −29.8351 51.6758i −0.993950 1.72157i
\(902\) 14.3720i 0.478534i
\(903\) −2.03740 + 1.17629i −0.0678003 + 0.0391445i
\(904\) −0.686108 + 0.396125i −0.0228196 + 0.0131749i
\(905\) 13.7017i 0.455460i
\(906\) 0.447730 + 0.775492i 0.0148748 + 0.0257640i
\(907\) 6.97584 12.0825i 0.231629 0.401193i −0.726659 0.686999i \(-0.758928\pi\)
0.958288 + 0.285806i \(0.0922612\pi\)
\(908\) 20.5074 + 11.8400i 0.680563 + 0.392923i
\(909\) −10.0151 −0.332179
\(910\) 0 0
\(911\) 45.0422 1.49232 0.746158 0.665769i \(-0.231897\pi\)
0.746158 + 0.665769i \(0.231897\pi\)
\(912\) −6.24210 3.60388i −0.206696 0.119336i
\(913\) 21.7878 37.7376i 0.721072 1.24893i
\(914\) −10.5945 18.3502i −0.350434 0.606970i
\(915\) 4.49396i 0.148566i
\(916\) −7.18653 + 4.14914i −0.237450 + 0.137092i
\(917\) 0.845510 0.488155i 0.0279212 0.0161203i
\(918\) 6.71379i 0.221588i
\(919\) −19.9988 34.6389i −0.659700 1.14263i −0.980693 0.195552i \(-0.937350\pi\)
0.320994 0.947081i \(-0.395983\pi\)
\(920\) 0.829085 1.43602i 0.0273341 0.0473441i
\(921\) 22.5428 + 13.0151i 0.742809 + 0.428861i
\(922\) −24.0694 −0.792682
\(923\) 0 0
\(924\) 1.04892 0.0345068
\(925\) −39.5370 22.8267i −1.29997 0.750537i
\(926\) 9.08575 15.7370i 0.298576 0.517149i
\(927\) −4.81282 8.33605i −0.158074 0.273792i
\(928\) 7.82908i 0.257002i
\(929\) 30.0380 17.3424i 0.985513 0.568986i 0.0815832 0.996667i \(-0.474002\pi\)
0.903930 + 0.427680i \(0.140669\pi\)
\(930\) −1.65571 + 0.955927i −0.0542930 + 0.0313461i
\(931\) 49.5362i 1.62348i
\(932\) 11.9825 + 20.7544i 0.392501 + 0.679832i
\(933\) −2.40581 + 4.16699i −0.0787628 + 0.136421i
\(934\) −2.53852 1.46562i −0.0830629 0.0479564i
\(935\) 13.6549 0.446562
\(936\) 0 0
\(937\) −19.1260 −0.624821 −0.312410 0.949947i \(-0.601136\pi\)
−0.312410 + 0.949947i \(0.601136\pi\)
\(938\) −4.18045 2.41358i −0.136496 0.0788063i
\(939\) 13.0206 22.5523i 0.424910 0.735966i
\(940\) −1.72587 2.98930i −0.0562918 0.0975002i
\(941\) 22.5972i 0.736647i −0.929698 0.368323i \(-0.879932\pi\)
0.929698 0.368323i \(-0.120068\pi\)
\(942\) 7.44071 4.29590i 0.242431 0.139968i
\(943\) 10.1474 5.85862i 0.330446 0.190783i
\(944\) 1.64310i 0.0534785i
\(945\) 0.123490 + 0.213891i 0.00401712 + 0.00695786i
\(946\) −9.68664 + 16.7778i −0.314940 + 0.545492i
\(947\) −23.7602 13.7180i −0.772104 0.445774i 0.0615209 0.998106i \(-0.480405\pi\)
−0.833625 + 0.552332i \(0.813738\pi\)
\(948\) −15.0465 −0.488688
\(949\) 0 0
\(950\) −32.5870 −1.05726
\(951\) 9.97757 + 5.76055i 0.323545 + 0.186799i
\(952\) 1.19806 2.07510i 0.0388294 0.0672545i
\(953\) −0.923936 1.60030i −0.0299292 0.0518389i 0.850673 0.525695i \(-0.176195\pi\)
−0.880602 + 0.473857i \(0.842862\pi\)
\(954\) 8.88769i 0.287750i
\(955\) 9.14667 5.28083i 0.295979 0.170884i
\(956\) −10.9257 + 6.30798i −0.353364 + 0.204015i
\(957\) 23.0097i 0.743798i
\(958\) 15.3545 + 26.5948i 0.496081 + 0.859238i
\(959\) −1.36467 + 2.36367i −0.0440674 + 0.0763269i
\(960\) 0.599308 + 0.346011i 0.0193426 + 0.0111674i
\(961\) 23.3674 0.753788
\(962\) 0 0
\(963\) −6.63102 −0.213682
\(964\) −22.8576 13.1969i −0.736195 0.425042i
\(965\) −1.64981 + 2.85755i −0.0531092 + 0.0919879i
\(966\) −0.427583 0.740596i −0.0137573 0.0238283i
\(967\) 8.88471i 0.285713i −0.989743 0.142856i \(-0.954371\pi\)
0.989743 0.142856i \(-0.0456287\pi\)
\(968\) −2.04579 + 1.18114i −0.0657541 + 0.0379632i
\(969\) −41.9081 + 24.1957i −1.34628 + 0.777277i
\(970\) 0.289192i 0.00928540i
\(971\) −17.5432 30.3857i −0.562987 0.975122i −0.997234 0.0743284i \(-0.976319\pi\)
0.434247 0.900794i \(-0.357015\pi\)
\(972\) 0.500000 0.866025i 0.0160375 0.0277778i
\(973\) −1.04594 0.603875i −0.0335314 0.0193594i
\(974\) −24.1497 −0.773807
\(975\) 0 0
\(976\) −6.49396 −0.207867
\(977\) 7.22009 + 4.16852i 0.230991 + 0.133363i 0.611029 0.791608i \(-0.290756\pi\)
−0.380038 + 0.924971i \(0.624089\pi\)
\(978\) −0.862937 + 1.49465i −0.0275937 + 0.0477936i
\(979\) 0.582105 + 1.00824i 0.0186042 + 0.0322234i
\(980\) 4.75600i 0.151925i
\(981\) −11.2479 + 6.49396i −0.359117 + 0.207336i
\(982\) −12.6415 + 7.29859i −0.403407 + 0.232907i
\(983\) 55.6051i 1.77353i 0.462224 + 0.886763i \(0.347051\pi\)
−0.462224 + 0.886763i \(0.652949\pi\)
\(984\) 2.44504 + 4.23494i 0.0779451 + 0.135005i
\(985\) 4.23341 7.33247i 0.134888 0.233632i
\(986\) 45.5208 + 26.2814i 1.44968 + 0.836971i
\(987\) −1.78017 −0.0566634
\(988\) 0 0
\(989\) 15.7948 0.502244
\(990\) 1.76137 + 1.01693i 0.0559799 + 0.0323200i
\(991\) 21.7983 37.7558i 0.692447 1.19935i −0.278586 0.960411i \(-0.589866\pi\)
0.971034 0.238943i \(-0.0768008\pi\)
\(992\) 1.38135 + 2.39258i 0.0438581 + 0.0759644i
\(993\) 3.43834i 0.109112i
\(994\) 2.10534 1.21552i 0.0667774 0.0385540i
\(995\) 7.10088 4.09970i 0.225113 0.129969i
\(996\) 14.8267i 0.469802i
\(997\) −11.2295 19.4501i −0.355643 0.615991i 0.631585 0.775306i \(-0.282405\pi\)
−0.987228 + 0.159316i \(0.949071\pi\)
\(998\) 3.42758 5.93675i 0.108498 0.187924i
\(999\) −8.74498 5.04892i −0.276679 0.159741i
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 1014.2.i.g.823.3 12
13.2 odd 12 1014.2.e.k.991.3 6
13.3 even 3 inner 1014.2.i.g.361.6 12
13.4 even 6 1014.2.b.g.337.1 6
13.5 odd 4 1014.2.e.k.529.3 6
13.6 odd 12 1014.2.a.o.1.3 yes 3
13.7 odd 12 1014.2.a.m.1.1 3
13.8 odd 4 1014.2.e.m.529.1 6
13.9 even 3 1014.2.b.g.337.6 6
13.10 even 6 inner 1014.2.i.g.361.1 12
13.11 odd 12 1014.2.e.m.991.1 6
13.12 even 2 inner 1014.2.i.g.823.4 12
39.17 odd 6 3042.2.b.r.1351.6 6
39.20 even 12 3042.2.a.be.1.3 3
39.32 even 12 3042.2.a.bd.1.1 3
39.35 odd 6 3042.2.b.r.1351.1 6
52.7 even 12 8112.2.a.ce.1.1 3
52.19 even 12 8112.2.a.bz.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1014.2.a.m.1.1 3 13.7 odd 12
1014.2.a.o.1.3 yes 3 13.6 odd 12
1014.2.b.g.337.1 6 13.4 even 6
1014.2.b.g.337.6 6 13.9 even 3
1014.2.e.k.529.3 6 13.5 odd 4
1014.2.e.k.991.3 6 13.2 odd 12
1014.2.e.m.529.1 6 13.8 odd 4
1014.2.e.m.991.1 6 13.11 odd 12
1014.2.i.g.361.1 12 13.10 even 6 inner
1014.2.i.g.361.6 12 13.3 even 3 inner
1014.2.i.g.823.3 12 1.1 even 1 trivial
1014.2.i.g.823.4 12 13.12 even 2 inner
3042.2.a.bd.1.1 3 39.32 even 12
3042.2.a.be.1.3 3 39.20 even 12
3042.2.b.r.1351.1 6 39.35 odd 6
3042.2.b.r.1351.6 6 39.17 odd 6
8112.2.a.bz.1.3 3 52.19 even 12
8112.2.a.ce.1.1 3 52.7 even 12