Properties

Label 294.4.e.d.79.1
Level $294$
Weight $4$
Character 294.79
Analytic conductor $17.347$
Analytic rank $0$
Dimension $2$
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] = [294,4,Mod(67,294)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(294, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("294.67");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 294.e (of order \(3\), 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: \(17.3465615417\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 294.79
Dual form 294.4.e.d.67.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(1.00000 - 1.73205i) q^{5} -6.00000 q^{6} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(1.00000 - 1.73205i) q^{5} -6.00000 q^{6} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(2.00000 + 3.46410i) q^{10} +(4.00000 + 6.92820i) q^{11} +(6.00000 - 10.3923i) q^{12} +42.0000 q^{13} +6.00000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(-1.00000 - 1.73205i) q^{17} +(-9.00000 - 15.5885i) q^{18} +(-62.0000 + 107.387i) q^{19} -8.00000 q^{20} -16.0000 q^{22} +(-38.0000 + 65.8179i) q^{23} +(12.0000 + 20.7846i) q^{24} +(60.5000 + 104.789i) q^{25} +(-42.0000 + 72.7461i) q^{26} -27.0000 q^{27} +254.000 q^{29} +(-6.00000 + 10.3923i) q^{30} +(-36.0000 - 62.3538i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(-12.0000 + 20.7846i) q^{33} +4.00000 q^{34} +36.0000 q^{36} +(-199.000 + 344.678i) q^{37} +(-124.000 - 214.774i) q^{38} +(63.0000 + 109.119i) q^{39} +(8.00000 - 13.8564i) q^{40} -462.000 q^{41} +212.000 q^{43} +(16.0000 - 27.7128i) q^{44} +(9.00000 + 15.5885i) q^{45} +(-76.0000 - 131.636i) q^{46} +(-132.000 + 228.631i) q^{47} -48.0000 q^{48} -242.000 q^{50} +(3.00000 - 5.19615i) q^{51} +(-84.0000 - 145.492i) q^{52} +(81.0000 + 140.296i) q^{53} +(27.0000 - 46.7654i) q^{54} +16.0000 q^{55} -372.000 q^{57} +(-254.000 + 439.941i) q^{58} +(-386.000 - 668.572i) q^{59} +(-12.0000 - 20.7846i) q^{60} +(15.0000 - 25.9808i) q^{61} +144.000 q^{62} +64.0000 q^{64} +(42.0000 - 72.7461i) q^{65} +(-24.0000 - 41.5692i) q^{66} +(382.000 + 661.643i) q^{67} +(-4.00000 + 6.92820i) q^{68} -228.000 q^{69} -236.000 q^{71} +(-36.0000 + 62.3538i) q^{72} +(209.000 + 361.999i) q^{73} +(-398.000 - 689.356i) q^{74} +(-181.500 + 314.367i) q^{75} +496.000 q^{76} -252.000 q^{78} +(-276.000 + 478.046i) q^{79} +(16.0000 + 27.7128i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(462.000 - 800.207i) q^{82} -1036.00 q^{83} -4.00000 q^{85} +(-212.000 + 367.195i) q^{86} +(381.000 + 659.911i) q^{87} +(32.0000 + 55.4256i) q^{88} +(15.0000 - 25.9808i) q^{89} -36.0000 q^{90} +304.000 q^{92} +(108.000 - 187.061i) q^{93} +(-264.000 - 457.261i) q^{94} +(124.000 + 214.774i) q^{95} +(48.0000 - 83.1384i) q^{96} +1190.00 q^{97} -72.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} + 3 q^{3} - 4 q^{4} + 2 q^{5} - 12 q^{6} + 16 q^{8} - 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{2} + 3 q^{3} - 4 q^{4} + 2 q^{5} - 12 q^{6} + 16 q^{8} - 9 q^{9} + 4 q^{10} + 8 q^{11} + 12 q^{12} + 84 q^{13} + 12 q^{15} - 16 q^{16} - 2 q^{17} - 18 q^{18} - 124 q^{19} - 16 q^{20} - 32 q^{22} - 76 q^{23} + 24 q^{24} + 121 q^{25} - 84 q^{26} - 54 q^{27} + 508 q^{29} - 12 q^{30} - 72 q^{31} - 32 q^{32} - 24 q^{33} + 8 q^{34} + 72 q^{36} - 398 q^{37} - 248 q^{38} + 126 q^{39} + 16 q^{40} - 924 q^{41} + 424 q^{43} + 32 q^{44} + 18 q^{45} - 152 q^{46} - 264 q^{47} - 96 q^{48} - 484 q^{50} + 6 q^{51} - 168 q^{52} + 162 q^{53} + 54 q^{54} + 32 q^{55} - 744 q^{57} - 508 q^{58} - 772 q^{59} - 24 q^{60} + 30 q^{61} + 288 q^{62} + 128 q^{64} + 84 q^{65} - 48 q^{66} + 764 q^{67} - 8 q^{68} - 456 q^{69} - 472 q^{71} - 72 q^{72} + 418 q^{73} - 796 q^{74} - 363 q^{75} + 992 q^{76} - 504 q^{78} - 552 q^{79} + 32 q^{80} - 81 q^{81} + 924 q^{82} - 2072 q^{83} - 8 q^{85} - 424 q^{86} + 762 q^{87} + 64 q^{88} + 30 q^{89} - 72 q^{90} + 608 q^{92} + 216 q^{93} - 528 q^{94} + 248 q^{95} + 96 q^{96} + 2380 q^{97} - 144 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(199\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.73205i −0.353553 + 0.612372i
\(3\) 1.50000 + 2.59808i 0.288675 + 0.500000i
\(4\) −2.00000 3.46410i −0.250000 0.433013i
\(5\) 1.00000 1.73205i 0.0894427 0.154919i −0.817833 0.575456i \(-0.804825\pi\)
0.907276 + 0.420536i \(0.138158\pi\)
\(6\) −6.00000 −0.408248
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) 2.00000 + 3.46410i 0.0632456 + 0.109545i
\(11\) 4.00000 + 6.92820i 0.109640 + 0.189903i 0.915625 0.402034i \(-0.131697\pi\)
−0.805984 + 0.591937i \(0.798363\pi\)
\(12\) 6.00000 10.3923i 0.144338 0.250000i
\(13\) 42.0000 0.896054 0.448027 0.894020i \(-0.352127\pi\)
0.448027 + 0.894020i \(0.352127\pi\)
\(14\) 0 0
\(15\) 6.00000 0.103280
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) −1.00000 1.73205i −0.0142668 0.0247108i 0.858804 0.512305i \(-0.171208\pi\)
−0.873071 + 0.487594i \(0.837875\pi\)
\(18\) −9.00000 15.5885i −0.117851 0.204124i
\(19\) −62.0000 + 107.387i −0.748620 + 1.29665i 0.199865 + 0.979824i \(0.435950\pi\)
−0.948484 + 0.316824i \(0.897384\pi\)
\(20\) −8.00000 −0.0894427
\(21\) 0 0
\(22\) −16.0000 −0.155055
\(23\) −38.0000 + 65.8179i −0.344502 + 0.596695i −0.985263 0.171045i \(-0.945286\pi\)
0.640761 + 0.767740i \(0.278619\pi\)
\(24\) 12.0000 + 20.7846i 0.102062 + 0.176777i
\(25\) 60.5000 + 104.789i 0.484000 + 0.838313i
\(26\) −42.0000 + 72.7461i −0.316803 + 0.548719i
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) 254.000 1.62644 0.813218 0.581960i \(-0.197714\pi\)
0.813218 + 0.581960i \(0.197714\pi\)
\(30\) −6.00000 + 10.3923i −0.0365148 + 0.0632456i
\(31\) −36.0000 62.3538i −0.208574 0.361261i 0.742692 0.669634i \(-0.233549\pi\)
−0.951266 + 0.308373i \(0.900216\pi\)
\(32\) −16.0000 27.7128i −0.0883883 0.153093i
\(33\) −12.0000 + 20.7846i −0.0633010 + 0.109640i
\(34\) 4.00000 0.0201763
\(35\) 0 0
\(36\) 36.0000 0.166667
\(37\) −199.000 + 344.678i −0.884200 + 1.53148i −0.0375721 + 0.999294i \(0.511962\pi\)
−0.846628 + 0.532185i \(0.821371\pi\)
\(38\) −124.000 214.774i −0.529354 0.916868i
\(39\) 63.0000 + 109.119i 0.258669 + 0.448027i
\(40\) 8.00000 13.8564i 0.0316228 0.0547723i
\(41\) −462.000 −1.75981 −0.879906 0.475148i \(-0.842394\pi\)
−0.879906 + 0.475148i \(0.842394\pi\)
\(42\) 0 0
\(43\) 212.000 0.751853 0.375927 0.926649i \(-0.377324\pi\)
0.375927 + 0.926649i \(0.377324\pi\)
\(44\) 16.0000 27.7128i 0.0548202 0.0949514i
\(45\) 9.00000 + 15.5885i 0.0298142 + 0.0516398i
\(46\) −76.0000 131.636i −0.243600 0.421927i
\(47\) −132.000 + 228.631i −0.409663 + 0.709558i −0.994852 0.101339i \(-0.967687\pi\)
0.585189 + 0.810897i \(0.301021\pi\)
\(48\) −48.0000 −0.144338
\(49\) 0 0
\(50\) −242.000 −0.684479
\(51\) 3.00000 5.19615i 0.00823694 0.0142668i
\(52\) −84.0000 145.492i −0.224014 0.388003i
\(53\) 81.0000 + 140.296i 0.209928 + 0.363607i 0.951692 0.307055i \(-0.0993436\pi\)
−0.741763 + 0.670662i \(0.766010\pi\)
\(54\) 27.0000 46.7654i 0.0680414 0.117851i
\(55\) 16.0000 0.0392262
\(56\) 0 0
\(57\) −372.000 −0.864432
\(58\) −254.000 + 439.941i −0.575032 + 0.995984i
\(59\) −386.000 668.572i −0.851744 1.47526i −0.879633 0.475654i \(-0.842212\pi\)
0.0278883 0.999611i \(-0.491122\pi\)
\(60\) −12.0000 20.7846i −0.0258199 0.0447214i
\(61\) 15.0000 25.9808i 0.0314845 0.0545327i −0.849854 0.527018i \(-0.823310\pi\)
0.881338 + 0.472486i \(0.156643\pi\)
\(62\) 144.000 0.294968
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 42.0000 72.7461i 0.0801455 0.138816i
\(66\) −24.0000 41.5692i −0.0447605 0.0775275i
\(67\) 382.000 + 661.643i 0.696548 + 1.20646i 0.969656 + 0.244473i \(0.0786151\pi\)
−0.273108 + 0.961983i \(0.588052\pi\)
\(68\) −4.00000 + 6.92820i −0.00713340 + 0.0123554i
\(69\) −228.000 −0.397797
\(70\) 0 0
\(71\) −236.000 −0.394480 −0.197240 0.980355i \(-0.563198\pi\)
−0.197240 + 0.980355i \(0.563198\pi\)
\(72\) −36.0000 + 62.3538i −0.0589256 + 0.102062i
\(73\) 209.000 + 361.999i 0.335090 + 0.580394i 0.983502 0.180896i \(-0.0578998\pi\)
−0.648412 + 0.761290i \(0.724566\pi\)
\(74\) −398.000 689.356i −0.625224 1.08292i
\(75\) −181.500 + 314.367i −0.279438 + 0.484000i
\(76\) 496.000 0.748620
\(77\) 0 0
\(78\) −252.000 −0.365813
\(79\) −276.000 + 478.046i −0.393069 + 0.680815i −0.992853 0.119347i \(-0.961920\pi\)
0.599784 + 0.800162i \(0.295253\pi\)
\(80\) 16.0000 + 27.7128i 0.0223607 + 0.0387298i
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) 462.000 800.207i 0.622187 1.07766i
\(83\) −1036.00 −1.37007 −0.685035 0.728510i \(-0.740213\pi\)
−0.685035 + 0.728510i \(0.740213\pi\)
\(84\) 0 0
\(85\) −4.00000 −0.00510425
\(86\) −212.000 + 367.195i −0.265820 + 0.460414i
\(87\) 381.000 + 659.911i 0.469511 + 0.813218i
\(88\) 32.0000 + 55.4256i 0.0387638 + 0.0671408i
\(89\) 15.0000 25.9808i 0.0178651 0.0309433i −0.856955 0.515392i \(-0.827646\pi\)
0.874820 + 0.484449i \(0.160980\pi\)
\(90\) −36.0000 −0.0421637
\(91\) 0 0
\(92\) 304.000 0.344502
\(93\) 108.000 187.061i 0.120420 0.208574i
\(94\) −264.000 457.261i −0.289676 0.501733i
\(95\) 124.000 + 214.774i 0.133917 + 0.231951i
\(96\) 48.0000 83.1384i 0.0510310 0.0883883i
\(97\) 1190.00 1.24563 0.622815 0.782369i \(-0.285989\pi\)
0.622815 + 0.782369i \(0.285989\pi\)
\(98\) 0 0
\(99\) −72.0000 −0.0730937
\(100\) 242.000 419.156i 0.242000 0.419156i
\(101\) 685.000 + 1186.45i 0.674852 + 1.16888i 0.976512 + 0.215462i \(0.0691259\pi\)
−0.301660 + 0.953416i \(0.597541\pi\)
\(102\) 6.00000 + 10.3923i 0.00582440 + 0.0100882i
\(103\) 232.000 401.836i 0.221938 0.384408i −0.733458 0.679735i \(-0.762095\pi\)
0.955396 + 0.295326i \(0.0954283\pi\)
\(104\) 336.000 0.316803
\(105\) 0 0
\(106\) −324.000 −0.296884
\(107\) 1068.00 1849.83i 0.964930 1.67131i 0.255125 0.966908i \(-0.417883\pi\)
0.709804 0.704399i \(-0.248783\pi\)
\(108\) 54.0000 + 93.5307i 0.0481125 + 0.0833333i
\(109\) 613.000 + 1061.75i 0.538667 + 0.932999i 0.998976 + 0.0452405i \(0.0144054\pi\)
−0.460309 + 0.887759i \(0.652261\pi\)
\(110\) −16.0000 + 27.7128i −0.0138685 + 0.0240210i
\(111\) −1194.00 −1.02099
\(112\) 0 0
\(113\) 338.000 0.281384 0.140692 0.990053i \(-0.455067\pi\)
0.140692 + 0.990053i \(0.455067\pi\)
\(114\) 372.000 644.323i 0.305623 0.529354i
\(115\) 76.0000 + 131.636i 0.0616264 + 0.106740i
\(116\) −508.000 879.882i −0.406609 0.704267i
\(117\) −189.000 + 327.358i −0.149342 + 0.258669i
\(118\) 1544.00 1.20455
\(119\) 0 0
\(120\) 48.0000 0.0365148
\(121\) 633.500 1097.25i 0.475958 0.824383i
\(122\) 30.0000 + 51.9615i 0.0222629 + 0.0385605i
\(123\) −693.000 1200.31i −0.508014 0.879906i
\(124\) −144.000 + 249.415i −0.104287 + 0.180630i
\(125\) 492.000 0.352047
\(126\) 0 0
\(127\) 2088.00 1.45890 0.729449 0.684035i \(-0.239777\pi\)
0.729449 + 0.684035i \(0.239777\pi\)
\(128\) −64.0000 + 110.851i −0.0441942 + 0.0765466i
\(129\) 318.000 + 550.792i 0.217041 + 0.375927i
\(130\) 84.0000 + 145.492i 0.0566714 + 0.0981578i
\(131\) −146.000 + 252.879i −0.0973747 + 0.168658i −0.910597 0.413295i \(-0.864378\pi\)
0.813223 + 0.581953i \(0.197711\pi\)
\(132\) 96.0000 0.0633010
\(133\) 0 0
\(134\) −1528.00 −0.985068
\(135\) −27.0000 + 46.7654i −0.0172133 + 0.0298142i
\(136\) −8.00000 13.8564i −0.00504408 0.00873660i
\(137\) −409.000 708.409i −0.255060 0.441777i 0.709852 0.704351i \(-0.248762\pi\)
−0.964912 + 0.262574i \(0.915429\pi\)
\(138\) 228.000 394.908i 0.140642 0.243600i
\(139\) 2156.00 1.31561 0.657804 0.753189i \(-0.271485\pi\)
0.657804 + 0.753189i \(0.271485\pi\)
\(140\) 0 0
\(141\) −792.000 −0.473039
\(142\) 236.000 408.764i 0.139470 0.241568i
\(143\) 168.000 + 290.985i 0.0982438 + 0.170163i
\(144\) −72.0000 124.708i −0.0416667 0.0721688i
\(145\) 254.000 439.941i 0.145473 0.251966i
\(146\) −836.000 −0.473889
\(147\) 0 0
\(148\) 1592.00 0.884200
\(149\) 1425.00 2468.17i 0.783494 1.35705i −0.146401 0.989225i \(-0.546769\pi\)
0.929895 0.367825i \(-0.119898\pi\)
\(150\) −363.000 628.734i −0.197592 0.342240i
\(151\) −836.000 1447.99i −0.450548 0.780372i 0.547872 0.836562i \(-0.315438\pi\)
−0.998420 + 0.0561903i \(0.982105\pi\)
\(152\) −496.000 + 859.097i −0.264677 + 0.458434i
\(153\) 18.0000 0.00951120
\(154\) 0 0
\(155\) −144.000 −0.0746217
\(156\) 252.000 436.477i 0.129334 0.224014i
\(157\) 223.000 + 386.247i 0.113359 + 0.196343i 0.917123 0.398605i \(-0.130506\pi\)
−0.803764 + 0.594949i \(0.797172\pi\)
\(158\) −552.000 956.092i −0.277942 0.481409i
\(159\) −243.000 + 420.888i −0.121202 + 0.209928i
\(160\) −64.0000 −0.0316228
\(161\) 0 0
\(162\) 162.000 0.0785674
\(163\) −1354.00 + 2345.20i −0.650635 + 1.12693i 0.332334 + 0.943162i \(0.392164\pi\)
−0.982969 + 0.183771i \(0.941170\pi\)
\(164\) 924.000 + 1600.41i 0.439953 + 0.762021i
\(165\) 24.0000 + 41.5692i 0.0113236 + 0.0196131i
\(166\) 1036.00 1794.40i 0.484393 0.838993i
\(167\) −896.000 −0.415177 −0.207589 0.978216i \(-0.566561\pi\)
−0.207589 + 0.978216i \(0.566561\pi\)
\(168\) 0 0
\(169\) −433.000 −0.197087
\(170\) 4.00000 6.92820i 0.00180462 0.00312570i
\(171\) −558.000 966.484i −0.249540 0.432216i
\(172\) −424.000 734.390i −0.187963 0.325562i
\(173\) 2017.00 3493.55i 0.886414 1.53531i 0.0423302 0.999104i \(-0.486522\pi\)
0.844084 0.536211i \(-0.180145\pi\)
\(174\) −1524.00 −0.663989
\(175\) 0 0
\(176\) −128.000 −0.0548202
\(177\) 1158.00 2005.71i 0.491755 0.851744i
\(178\) 30.0000 + 51.9615i 0.0126326 + 0.0218802i
\(179\) 1740.00 + 3013.77i 0.726557 + 1.25843i 0.958330 + 0.285664i \(0.0922140\pi\)
−0.231773 + 0.972770i \(0.574453\pi\)
\(180\) 36.0000 62.3538i 0.0149071 0.0258199i
\(181\) 2898.00 1.19009 0.595046 0.803692i \(-0.297134\pi\)
0.595046 + 0.803692i \(0.297134\pi\)
\(182\) 0 0
\(183\) 90.0000 0.0363551
\(184\) −304.000 + 526.543i −0.121800 + 0.210964i
\(185\) 398.000 + 689.356i 0.158170 + 0.273959i
\(186\) 216.000 + 374.123i 0.0851499 + 0.147484i
\(187\) 8.00000 13.8564i 0.00312844 0.00541861i
\(188\) 1056.00 0.409663
\(189\) 0 0
\(190\) −496.000 −0.189387
\(191\) −1326.00 + 2296.70i −0.502335 + 0.870070i 0.497661 + 0.867371i \(0.334192\pi\)
−0.999996 + 0.00269837i \(0.999141\pi\)
\(192\) 96.0000 + 166.277i 0.0360844 + 0.0625000i
\(193\) −73.0000 126.440i −0.0272262 0.0471571i 0.852091 0.523393i \(-0.175334\pi\)
−0.879317 + 0.476236i \(0.842001\pi\)
\(194\) −1190.00 + 2061.14i −0.440397 + 0.762790i
\(195\) 252.000 0.0925441
\(196\) 0 0
\(197\) −2546.00 −0.920787 −0.460393 0.887715i \(-0.652292\pi\)
−0.460393 + 0.887715i \(0.652292\pi\)
\(198\) 72.0000 124.708i 0.0258425 0.0447605i
\(199\) −1268.00 2196.24i −0.451689 0.782349i 0.546802 0.837262i \(-0.315845\pi\)
−0.998491 + 0.0549134i \(0.982512\pi\)
\(200\) 484.000 + 838.313i 0.171120 + 0.296388i
\(201\) −1146.00 + 1984.93i −0.402152 + 0.696548i
\(202\) −2740.00 −0.954385
\(203\) 0 0
\(204\) −24.0000 −0.00823694
\(205\) −462.000 + 800.207i −0.157402 + 0.272629i
\(206\) 464.000 + 803.672i 0.156934 + 0.271818i
\(207\) −342.000 592.361i −0.114834 0.198898i
\(208\) −336.000 + 581.969i −0.112007 + 0.194001i
\(209\) −992.000 −0.328316
\(210\) 0 0
\(211\) −1300.00 −0.424150 −0.212075 0.977253i \(-0.568022\pi\)
−0.212075 + 0.977253i \(0.568022\pi\)
\(212\) 324.000 561.184i 0.104964 0.181803i
\(213\) −354.000 613.146i −0.113876 0.197240i
\(214\) 2136.00 + 3699.66i 0.682308 + 1.18179i
\(215\) 212.000 367.195i 0.0672478 0.116477i
\(216\) −216.000 −0.0680414
\(217\) 0 0
\(218\) −2452.00 −0.761791
\(219\) −627.000 + 1086.00i −0.193465 + 0.335090i
\(220\) −32.0000 55.4256i −0.00980654 0.0169854i
\(221\) −42.0000 72.7461i −0.0127838 0.0221422i
\(222\) 1194.00 2068.07i 0.360973 0.625224i
\(223\) −2576.00 −0.773550 −0.386775 0.922174i \(-0.626411\pi\)
−0.386775 + 0.922174i \(0.626411\pi\)
\(224\) 0 0
\(225\) −1089.00 −0.322667
\(226\) −338.000 + 585.433i −0.0994842 + 0.172312i
\(227\) −918.000 1590.02i −0.268413 0.464905i 0.700039 0.714105i \(-0.253166\pi\)
−0.968452 + 0.249199i \(0.919833\pi\)
\(228\) 744.000 + 1288.65i 0.216108 + 0.374310i
\(229\) −937.000 + 1622.93i −0.270387 + 0.468325i −0.968961 0.247213i \(-0.920485\pi\)
0.698574 + 0.715538i \(0.253818\pi\)
\(230\) −304.000 −0.0871529
\(231\) 0 0
\(232\) 2032.00 0.575032
\(233\) −1865.00 + 3230.27i −0.524379 + 0.908250i 0.475219 + 0.879868i \(0.342369\pi\)
−0.999597 + 0.0283826i \(0.990964\pi\)
\(234\) −378.000 654.715i −0.105601 0.182906i
\(235\) 264.000 + 457.261i 0.0732828 + 0.126930i
\(236\) −1544.00 + 2674.29i −0.425872 + 0.737632i
\(237\) −1656.00 −0.453877
\(238\) 0 0
\(239\) 2004.00 0.542377 0.271188 0.962526i \(-0.412583\pi\)
0.271188 + 0.962526i \(0.412583\pi\)
\(240\) −48.0000 + 83.1384i −0.0129099 + 0.0223607i
\(241\) −323.000 559.452i −0.0863330 0.149533i 0.819625 0.572900i \(-0.194182\pi\)
−0.905958 + 0.423367i \(0.860848\pi\)
\(242\) 1267.00 + 2194.51i 0.336553 + 0.582927i
\(243\) 121.500 210.444i 0.0320750 0.0555556i
\(244\) −120.000 −0.0314845
\(245\) 0 0
\(246\) 2772.00 0.718440
\(247\) −2604.00 + 4510.26i −0.670804 + 1.16187i
\(248\) −288.000 498.831i −0.0737420 0.127725i
\(249\) −1554.00 2691.61i −0.395505 0.685035i
\(250\) −492.000 + 852.169i −0.124467 + 0.215584i
\(251\) −1260.00 −0.316855 −0.158427 0.987371i \(-0.550642\pi\)
−0.158427 + 0.987371i \(0.550642\pi\)
\(252\) 0 0
\(253\) −608.000 −0.151086
\(254\) −2088.00 + 3616.52i −0.515798 + 0.893389i
\(255\) −6.00000 10.3923i −0.00147347 0.00255212i
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) 2955.00 5118.21i 0.717229 1.24228i −0.244865 0.969557i \(-0.578744\pi\)
0.962094 0.272720i \(-0.0879232\pi\)
\(258\) −1272.00 −0.306943
\(259\) 0 0
\(260\) −336.000 −0.0801455
\(261\) −1143.00 + 1979.73i −0.271073 + 0.469511i
\(262\) −292.000 505.759i −0.0688543 0.119259i
\(263\) −1494.00 2587.68i −0.350281 0.606705i 0.636017 0.771675i \(-0.280581\pi\)
−0.986299 + 0.164970i \(0.947247\pi\)
\(264\) −96.0000 + 166.277i −0.0223803 + 0.0387638i
\(265\) 324.000 0.0751063
\(266\) 0 0
\(267\) 90.0000 0.0206289
\(268\) 1528.00 2646.57i 0.348274 0.603228i
\(269\) −659.000 1141.42i −0.149368 0.258713i 0.781626 0.623747i \(-0.214391\pi\)
−0.930994 + 0.365035i \(0.881057\pi\)
\(270\) −54.0000 93.5307i −0.0121716 0.0210819i
\(271\) −2820.00 + 4884.38i −0.632114 + 1.09485i 0.355005 + 0.934864i \(0.384479\pi\)
−0.987119 + 0.159989i \(0.948854\pi\)
\(272\) 32.0000 0.00713340
\(273\) 0 0
\(274\) 1636.00 0.360709
\(275\) −484.000 + 838.313i −0.106132 + 0.183826i
\(276\) 456.000 + 789.815i 0.0994492 + 0.172251i
\(277\) −3223.00 5582.40i −0.699102 1.21088i −0.968778 0.247929i \(-0.920250\pi\)
0.269676 0.962951i \(-0.413083\pi\)
\(278\) −2156.00 + 3734.30i −0.465138 + 0.805642i
\(279\) 648.000 0.139049
\(280\) 0 0
\(281\) 4930.00 1.04662 0.523308 0.852144i \(-0.324698\pi\)
0.523308 + 0.852144i \(0.324698\pi\)
\(282\) 792.000 1371.78i 0.167244 0.289676i
\(283\) −3130.00 5421.32i −0.657453 1.13874i −0.981273 0.192623i \(-0.938301\pi\)
0.323820 0.946119i \(-0.395033\pi\)
\(284\) 472.000 + 817.528i 0.0986199 + 0.170815i
\(285\) −372.000 + 644.323i −0.0773171 + 0.133917i
\(286\) −672.000 −0.138938
\(287\) 0 0
\(288\) 288.000 0.0589256
\(289\) 2454.50 4251.32i 0.499593 0.865320i
\(290\) 508.000 + 879.882i 0.102865 + 0.178167i
\(291\) 1785.00 + 3091.71i 0.359583 + 0.622815i
\(292\) 836.000 1447.99i 0.167545 0.290197i
\(293\) 2310.00 0.460586 0.230293 0.973121i \(-0.426032\pi\)
0.230293 + 0.973121i \(0.426032\pi\)
\(294\) 0 0
\(295\) −1544.00 −0.304729
\(296\) −1592.00 + 2757.42i −0.312612 + 0.541460i
\(297\) −108.000 187.061i −0.0211003 0.0365468i
\(298\) 2850.00 + 4936.34i 0.554014 + 0.959580i
\(299\) −1596.00 + 2764.35i −0.308693 + 0.534671i
\(300\) 1452.00 0.279438
\(301\) 0 0
\(302\) 3344.00 0.637171
\(303\) −2055.00 + 3559.36i −0.389626 + 0.674852i
\(304\) −992.000 1718.19i −0.187155 0.324162i
\(305\) −30.0000 51.9615i −0.00563211 0.00975511i
\(306\) −18.0000 + 31.1769i −0.00336272 + 0.00582440i
\(307\) −196.000 −0.0364375 −0.0182187 0.999834i \(-0.505800\pi\)
−0.0182187 + 0.999834i \(0.505800\pi\)
\(308\) 0 0
\(309\) 1392.00 0.256272
\(310\) 144.000 249.415i 0.0263827 0.0456963i
\(311\) −3368.00 5833.55i −0.614089 1.06363i −0.990544 0.137199i \(-0.956190\pi\)
0.376454 0.926435i \(-0.377143\pi\)
\(312\) 504.000 + 872.954i 0.0914531 + 0.158401i
\(313\) 197.000 341.214i 0.0355754 0.0616184i −0.847690 0.530493i \(-0.822007\pi\)
0.883265 + 0.468874i \(0.155340\pi\)
\(314\) −892.000 −0.160314
\(315\) 0 0
\(316\) 2208.00 0.393069
\(317\) 3357.00 5814.49i 0.594788 1.03020i −0.398788 0.917043i \(-0.630569\pi\)
0.993577 0.113161i \(-0.0360975\pi\)
\(318\) −486.000 841.777i −0.0857029 0.148442i
\(319\) 1016.00 + 1759.76i 0.178323 + 0.308865i
\(320\) 64.0000 110.851i 0.0111803 0.0193649i
\(321\) 6408.00 1.11420
\(322\) 0 0
\(323\) 248.000 0.0427216
\(324\) −162.000 + 280.592i −0.0277778 + 0.0481125i
\(325\) 2541.00 + 4401.14i 0.433690 + 0.751173i
\(326\) −2708.00 4690.39i −0.460068 0.796862i
\(327\) −1839.00 + 3185.24i −0.311000 + 0.538667i
\(328\) −3696.00 −0.622187
\(329\) 0 0
\(330\) −96.0000 −0.0160140
\(331\) −346.000 + 599.290i −0.0574558 + 0.0995164i −0.893323 0.449416i \(-0.851632\pi\)
0.835867 + 0.548932i \(0.184966\pi\)
\(332\) 2072.00 + 3588.81i 0.342517 + 0.593258i
\(333\) −1791.00 3102.10i −0.294733 0.510493i
\(334\) 896.000 1551.92i 0.146787 0.254243i
\(335\) 1528.00 0.249205
\(336\) 0 0
\(337\) −1566.00 −0.253132 −0.126566 0.991958i \(-0.540396\pi\)
−0.126566 + 0.991958i \(0.540396\pi\)
\(338\) 433.000 749.978i 0.0696808 0.120691i
\(339\) 507.000 + 878.150i 0.0812285 + 0.140692i
\(340\) 8.00000 + 13.8564i 0.00127606 + 0.00221020i
\(341\) 288.000 498.831i 0.0457363 0.0792176i
\(342\) 2232.00 0.352903
\(343\) 0 0
\(344\) 1696.00 0.265820
\(345\) −228.000 + 394.908i −0.0355800 + 0.0616264i
\(346\) 4034.00 + 6987.09i 0.626790 + 1.08563i
\(347\) 2664.00 + 4614.18i 0.412135 + 0.713840i 0.995123 0.0986415i \(-0.0314497\pi\)
−0.582988 + 0.812481i \(0.698116\pi\)
\(348\) 1524.00 2639.65i 0.234756 0.406609i
\(349\) −11326.0 −1.73715 −0.868577 0.495554i \(-0.834965\pi\)
−0.868577 + 0.495554i \(0.834965\pi\)
\(350\) 0 0
\(351\) −1134.00 −0.172446
\(352\) 128.000 221.703i 0.0193819 0.0335704i
\(353\) −1065.00 1844.63i −0.160579 0.278130i 0.774498 0.632577i \(-0.218003\pi\)
−0.935076 + 0.354446i \(0.884669\pi\)
\(354\) 2316.00 + 4011.43i 0.347723 + 0.602274i
\(355\) −236.000 + 408.764i −0.0352833 + 0.0611125i
\(356\) −120.000 −0.0178651
\(357\) 0 0
\(358\) −6960.00 −1.02751
\(359\) −1522.00 + 2636.18i −0.223755 + 0.387555i −0.955945 0.293545i \(-0.905165\pi\)
0.732190 + 0.681100i \(0.238498\pi\)
\(360\) 72.0000 + 124.708i 0.0105409 + 0.0182574i
\(361\) −4258.50 7375.94i −0.620863 1.07537i
\(362\) −2898.00 + 5019.48i −0.420761 + 0.728780i
\(363\) 3801.00 0.549589
\(364\) 0 0
\(365\) 836.000 0.119886
\(366\) −90.0000 + 155.885i −0.0128535 + 0.0222629i
\(367\) 6208.00 + 10752.6i 0.882984 + 1.52937i 0.848008 + 0.529984i \(0.177802\pi\)
0.0349760 + 0.999388i \(0.488865\pi\)
\(368\) −608.000 1053.09i −0.0861255 0.149174i
\(369\) 2079.00 3600.93i 0.293302 0.508014i
\(370\) −1592.00 −0.223687
\(371\) 0 0
\(372\) −864.000 −0.120420
\(373\) 3721.00 6444.96i 0.516531 0.894658i −0.483285 0.875463i \(-0.660556\pi\)
0.999816 0.0191948i \(-0.00611026\pi\)
\(374\) 16.0000 + 27.7128i 0.00221214 + 0.00383154i
\(375\) 738.000 + 1278.25i 0.101627 + 0.176023i
\(376\) −1056.00 + 1829.05i −0.144838 + 0.250867i
\(377\) 10668.0 1.45737
\(378\) 0 0
\(379\) 100.000 0.0135532 0.00677659 0.999977i \(-0.497843\pi\)
0.00677659 + 0.999977i \(0.497843\pi\)
\(380\) 496.000 859.097i 0.0669586 0.115976i
\(381\) 3132.00 + 5424.78i 0.421148 + 0.729449i
\(382\) −2652.00 4593.40i −0.355205 0.615232i
\(383\) 4040.00 6997.49i 0.538993 0.933563i −0.459965 0.887937i \(-0.652138\pi\)
0.998959 0.0456266i \(-0.0145284\pi\)
\(384\) −384.000 −0.0510310
\(385\) 0 0
\(386\) 292.000 0.0385036
\(387\) −954.000 + 1652.38i −0.125309 + 0.217041i
\(388\) −2380.00 4122.28i −0.311408 0.539374i
\(389\) 2741.00 + 4747.55i 0.357260 + 0.618793i 0.987502 0.157606i \(-0.0503776\pi\)
−0.630242 + 0.776399i \(0.717044\pi\)
\(390\) −252.000 + 436.477i −0.0327193 + 0.0566714i
\(391\) 152.000 0.0196598
\(392\) 0 0
\(393\) −876.000 −0.112439
\(394\) 2546.00 4409.80i 0.325547 0.563864i
\(395\) 552.000 + 956.092i 0.0703143 + 0.121788i
\(396\) 144.000 + 249.415i 0.0182734 + 0.0316505i
\(397\) 5223.00 9046.50i 0.660289 1.14365i −0.320250 0.947333i \(-0.603767\pi\)
0.980540 0.196322i \(-0.0628997\pi\)
\(398\) 5072.00 0.638785
\(399\) 0 0
\(400\) −1936.00 −0.242000
\(401\) 5667.00 9815.53i 0.705727 1.22235i −0.260702 0.965419i \(-0.583954\pi\)
0.966429 0.256935i \(-0.0827128\pi\)
\(402\) −2292.00 3969.86i −0.284365 0.492534i
\(403\) −1512.00 2618.86i −0.186894 0.323709i
\(404\) 2740.00 4745.82i 0.337426 0.584439i
\(405\) −162.000 −0.0198762
\(406\) 0 0
\(407\) −3184.00 −0.387776
\(408\) 24.0000 41.5692i 0.00291220 0.00504408i
\(409\) 4297.00 + 7442.62i 0.519494 + 0.899790i 0.999743 + 0.0226578i \(0.00721280\pi\)
−0.480249 + 0.877132i \(0.659454\pi\)
\(410\) −924.000 1600.41i −0.111300 0.192778i
\(411\) 1227.00 2125.23i 0.147259 0.255060i
\(412\) −1856.00 −0.221938
\(413\) 0 0
\(414\) 1368.00 0.162400
\(415\) −1036.00 + 1794.40i −0.122543 + 0.212250i
\(416\) −672.000 1163.94i −0.0792007 0.137180i
\(417\) 3234.00 + 5601.45i 0.379783 + 0.657804i
\(418\) 992.000 1718.19i 0.116077 0.201052i
\(419\) −10500.0 −1.22424 −0.612122 0.790763i \(-0.709684\pi\)
−0.612122 + 0.790763i \(0.709684\pi\)
\(420\) 0 0
\(421\) −12066.0 −1.39682 −0.698410 0.715698i \(-0.746109\pi\)
−0.698410 + 0.715698i \(0.746109\pi\)
\(422\) 1300.00 2251.67i 0.149960 0.259738i
\(423\) −1188.00 2057.68i −0.136554 0.236519i
\(424\) 648.000 + 1122.37i 0.0742209 + 0.128554i
\(425\) 121.000 209.578i 0.0138103 0.0239201i
\(426\) 1416.00 0.161046
\(427\) 0 0
\(428\) −8544.00 −0.964930
\(429\) −504.000 + 872.954i −0.0567211 + 0.0982438i
\(430\) 424.000 + 734.390i 0.0475514 + 0.0823614i
\(431\) −2166.00 3751.62i −0.242071 0.419279i 0.719233 0.694769i \(-0.244493\pi\)
−0.961304 + 0.275490i \(0.911160\pi\)
\(432\) 216.000 374.123i 0.0240563 0.0416667i
\(433\) 1918.00 0.212871 0.106436 0.994320i \(-0.466056\pi\)
0.106436 + 0.994320i \(0.466056\pi\)
\(434\) 0 0
\(435\) 1524.00 0.167977
\(436\) 2452.00 4246.99i 0.269334 0.466500i
\(437\) −4712.00 8161.42i −0.515802 0.893395i
\(438\) −1254.00 2171.99i −0.136800 0.236945i
\(439\) −3996.00 + 6921.28i −0.434439 + 0.752470i −0.997250 0.0741155i \(-0.976387\pi\)
0.562811 + 0.826586i \(0.309720\pi\)
\(440\) 128.000 0.0138685
\(441\) 0 0
\(442\) 168.000 0.0180791
\(443\) −1592.00 + 2757.42i −0.170741 + 0.295732i −0.938679 0.344792i \(-0.887949\pi\)
0.767938 + 0.640524i \(0.221283\pi\)
\(444\) 2388.00 + 4136.14i 0.255247 + 0.442100i
\(445\) −30.0000 51.9615i −0.00319581 0.00553531i
\(446\) 2576.00 4461.76i 0.273491 0.473701i
\(447\) 8550.00 0.904700
\(448\) 0 0
\(449\) 11426.0 1.20095 0.600475 0.799644i \(-0.294978\pi\)
0.600475 + 0.799644i \(0.294978\pi\)
\(450\) 1089.00 1886.20i 0.114080 0.197592i
\(451\) −1848.00 3200.83i −0.192947 0.334193i
\(452\) −676.000 1170.87i −0.0703459 0.121843i
\(453\) 2508.00 4343.98i 0.260124 0.450548i
\(454\) 3672.00 0.379594
\(455\) 0 0
\(456\) −2976.00 −0.305623
\(457\) 8467.00 14665.3i 0.866673 1.50112i 0.00129662 0.999999i \(-0.499587\pi\)
0.865376 0.501122i \(-0.167079\pi\)
\(458\) −1874.00 3245.86i −0.191193 0.331156i
\(459\) 27.0000 + 46.7654i 0.00274565 + 0.00475560i
\(460\) 304.000 526.543i 0.0308132 0.0533700i
\(461\) 17038.0 1.72134 0.860671 0.509161i \(-0.170044\pi\)
0.860671 + 0.509161i \(0.170044\pi\)
\(462\) 0 0
\(463\) −13592.0 −1.36431 −0.682153 0.731209i \(-0.738956\pi\)
−0.682153 + 0.731209i \(0.738956\pi\)
\(464\) −2032.00 + 3519.53i −0.203304 + 0.352134i
\(465\) −216.000 374.123i −0.0215414 0.0373108i
\(466\) −3730.00 6460.55i −0.370792 0.642230i
\(467\) 4306.00 7458.21i 0.426676 0.739025i −0.569899 0.821715i \(-0.693018\pi\)
0.996575 + 0.0826895i \(0.0263510\pi\)
\(468\) 1512.00 0.149342
\(469\) 0 0
\(470\) −1056.00 −0.103638
\(471\) −669.000 + 1158.74i −0.0654478 + 0.113359i
\(472\) −3088.00 5348.57i −0.301137 0.521585i
\(473\) 848.000 + 1468.78i 0.0824336 + 0.142779i
\(474\) 1656.00 2868.28i 0.160470 0.277942i
\(475\) −15004.0 −1.44933
\(476\) 0 0
\(477\) −1458.00 −0.139952
\(478\) −2004.00 + 3471.03i −0.191759 + 0.332136i
\(479\) 3716.00 + 6436.30i 0.354464 + 0.613950i 0.987026 0.160560i \(-0.0513299\pi\)
−0.632562 + 0.774510i \(0.717997\pi\)
\(480\) −96.0000 166.277i −0.00912871 0.0158114i
\(481\) −8358.00 + 14476.5i −0.792291 + 1.37229i
\(482\) 1292.00 0.122093
\(483\) 0 0
\(484\) −5068.00 −0.475958
\(485\) 1190.00 2061.14i 0.111413 0.192972i
\(486\) 243.000 + 420.888i 0.0226805 + 0.0392837i
\(487\) 3308.00 + 5729.62i 0.307802 + 0.533129i 0.977881 0.209160i \(-0.0670731\pi\)
−0.670079 + 0.742290i \(0.733740\pi\)
\(488\) 120.000 207.846i 0.0111314 0.0192802i
\(489\) −8124.00 −0.751288
\(490\) 0 0
\(491\) 17040.0 1.56620 0.783100 0.621896i \(-0.213637\pi\)
0.783100 + 0.621896i \(0.213637\pi\)
\(492\) −2772.00 + 4801.24i −0.254007 + 0.439953i
\(493\) −254.000 439.941i −0.0232040 0.0401906i
\(494\) −5208.00 9020.52i −0.474330 0.821564i
\(495\) −72.0000 + 124.708i −0.00653770 + 0.0113236i
\(496\) 1152.00 0.104287
\(497\) 0 0
\(498\) 6216.00 0.559329
\(499\) 1474.00 2553.04i 0.132235 0.229038i −0.792303 0.610128i \(-0.791118\pi\)
0.924538 + 0.381090i \(0.124451\pi\)
\(500\) −984.000 1704.34i −0.0880116 0.152441i
\(501\) −1344.00 2327.88i −0.119851 0.207589i
\(502\) 1260.00 2182.38i 0.112025 0.194033i
\(503\) −17304.0 −1.53389 −0.766946 0.641712i \(-0.778224\pi\)
−0.766946 + 0.641712i \(0.778224\pi\)
\(504\) 0 0
\(505\) 2740.00 0.241442
\(506\) 608.000 1053.09i 0.0534168 0.0925206i
\(507\) −649.500 1124.97i −0.0568941 0.0985435i
\(508\) −4176.00 7233.04i −0.364724 0.631721i
\(509\) 2325.00 4027.02i 0.202463 0.350677i −0.746858 0.664983i \(-0.768439\pi\)
0.949322 + 0.314307i \(0.101772\pi\)
\(510\) 24.0000 0.00208380
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) 1674.00 2899.45i 0.144072 0.249540i
\(514\) 5910.00 + 10236.4i 0.507157 + 0.878422i
\(515\) −464.000 803.672i −0.0397015 0.0687651i
\(516\) 1272.00 2203.17i 0.108521 0.187963i
\(517\) −2112.00 −0.179663
\(518\) 0 0
\(519\) 12102.0 1.02354
\(520\) 336.000 581.969i 0.0283357 0.0490789i
\(521\) 8427.00 + 14596.0i 0.708625 + 1.22737i 0.965367 + 0.260894i \(0.0840175\pi\)
−0.256742 + 0.966480i \(0.582649\pi\)
\(522\) −2286.00 3959.47i −0.191677 0.331995i
\(523\) −62.0000 + 107.387i −0.00518369 + 0.00897842i −0.868606 0.495504i \(-0.834983\pi\)
0.863422 + 0.504482i \(0.168317\pi\)
\(524\) 1168.00 0.0973747
\(525\) 0 0
\(526\) 5976.00 0.495373
\(527\) −72.0000 + 124.708i −0.00595136 + 0.0103081i
\(528\) −192.000 332.554i −0.0158252 0.0274101i
\(529\) 3195.50 + 5534.77i 0.262637 + 0.454900i
\(530\) −324.000 + 561.184i −0.0265541 + 0.0459930i
\(531\) 6948.00 0.567830
\(532\) 0 0
\(533\) −19404.0 −1.57689
\(534\) −90.0000 + 155.885i −0.00729341 + 0.0126326i
\(535\) −2136.00 3699.66i −0.172612 0.298972i
\(536\) 3056.00 + 5293.15i 0.246267 + 0.426547i
\(537\) −5220.00 + 9041.31i −0.419478 + 0.726557i
\(538\) 2636.00 0.211238
\(539\) 0 0
\(540\) 216.000 0.0172133
\(541\) −2691.00 + 4660.95i −0.213854 + 0.370406i −0.952918 0.303230i \(-0.901935\pi\)
0.739063 + 0.673636i \(0.235268\pi\)
\(542\) −5640.00 9768.77i −0.446972 0.774178i
\(543\) 4347.00 + 7529.22i 0.343550 + 0.595046i
\(544\) −32.0000 + 55.4256i −0.00252204 + 0.00436830i
\(545\) 2452.00 0.192720
\(546\) 0 0
\(547\) 17460.0 1.36478 0.682391 0.730987i \(-0.260940\pi\)
0.682391 + 0.730987i \(0.260940\pi\)
\(548\) −1636.00 + 2833.64i −0.127530 + 0.220888i
\(549\) 135.000 + 233.827i 0.0104948 + 0.0181776i
\(550\) −968.000 1676.63i −0.0750467 0.129985i
\(551\) −15748.0 + 27276.3i −1.21758 + 2.10891i
\(552\) −1824.00 −0.140642
\(553\) 0 0
\(554\) 12892.0 0.988680
\(555\) −1194.00 + 2068.07i −0.0913198 + 0.158170i
\(556\) −4312.00 7468.60i −0.328902 0.569675i
\(557\) 4757.00 + 8239.37i 0.361868 + 0.626774i 0.988268 0.152728i \(-0.0488057\pi\)
−0.626400 + 0.779502i \(0.715472\pi\)
\(558\) −648.000 + 1122.37i −0.0491613 + 0.0851499i
\(559\) 8904.00 0.673701
\(560\) 0 0
\(561\) 48.0000 0.00361241
\(562\) −4930.00 + 8539.01i −0.370035 + 0.640919i
\(563\) 1994.00 + 3453.71i 0.149267 + 0.258537i 0.930957 0.365130i \(-0.118975\pi\)
−0.781690 + 0.623667i \(0.785642\pi\)
\(564\) 1584.00 + 2743.57i 0.118260 + 0.204832i
\(565\) 338.000 585.433i 0.0251677 0.0435918i
\(566\) 12520.0 0.929779
\(567\) 0 0
\(568\) −1888.00 −0.139470
\(569\) −5673.00 + 9825.92i −0.417969 + 0.723944i −0.995735 0.0922585i \(-0.970591\pi\)
0.577766 + 0.816203i \(0.303925\pi\)
\(570\) −744.000 1288.65i −0.0546715 0.0946937i
\(571\) 4218.00 + 7305.79i 0.309138 + 0.535443i 0.978174 0.207787i \(-0.0666262\pi\)
−0.669036 + 0.743230i \(0.733293\pi\)
\(572\) 672.000 1163.94i 0.0491219 0.0850816i
\(573\) −7956.00 −0.580047
\(574\) 0 0
\(575\) −9196.00 −0.666956
\(576\) −288.000 + 498.831i −0.0208333 + 0.0360844i
\(577\) 1049.00 + 1816.92i 0.0756853 + 0.131091i 0.901384 0.433020i \(-0.142552\pi\)
−0.825699 + 0.564111i \(0.809219\pi\)
\(578\) 4909.00 + 8502.64i 0.353266 + 0.611874i
\(579\) 219.000 379.319i 0.0157190 0.0272262i
\(580\) −2032.00 −0.145473
\(581\) 0 0
\(582\) −7140.00 −0.508527
\(583\) −648.000 + 1122.37i −0.0460333 + 0.0797320i
\(584\) 1672.00 + 2895.99i 0.118472 + 0.205200i
\(585\) 378.000 + 654.715i 0.0267152 + 0.0462720i
\(586\) −2310.00 + 4001.04i −0.162842 + 0.282050i
\(587\) −9436.00 −0.663484 −0.331742 0.943370i \(-0.607636\pi\)
−0.331742 + 0.943370i \(0.607636\pi\)
\(588\) 0 0
\(589\) 8928.00 0.624570
\(590\) 1544.00 2674.29i 0.107738 0.186608i
\(591\) −3819.00 6614.70i −0.265808 0.460393i
\(592\) −3184.00 5514.85i −0.221050 0.382870i
\(593\) −657.000 + 1137.96i −0.0454971 + 0.0788032i −0.887877 0.460081i \(-0.847820\pi\)
0.842380 + 0.538884i \(0.181154\pi\)
\(594\) 432.000 0.0298404
\(595\) 0 0
\(596\) −11400.0 −0.783494
\(597\) 3804.00 6588.72i 0.260783 0.451689i
\(598\) −3192.00 5528.71i −0.218279 0.378070i
\(599\) 4470.00 + 7742.27i 0.304907 + 0.528114i 0.977241 0.212134i \(-0.0680413\pi\)
−0.672334 + 0.740248i \(0.734708\pi\)
\(600\) −1452.00 + 2514.94i −0.0987961 + 0.171120i
\(601\) −16058.0 −1.08988 −0.544941 0.838474i \(-0.683448\pi\)
−0.544941 + 0.838474i \(0.683448\pi\)
\(602\) 0 0
\(603\) −6876.00 −0.464365
\(604\) −3344.00 + 5791.98i −0.225274 + 0.390186i
\(605\) −1267.00 2194.51i −0.0851419 0.147470i
\(606\) −4110.00 7118.73i −0.275507 0.477192i
\(607\) 1968.00 3408.68i 0.131596 0.227931i −0.792696 0.609617i \(-0.791323\pi\)
0.924292 + 0.381686i \(0.124657\pi\)
\(608\) 3968.00 0.264677
\(609\) 0 0
\(610\) 120.000 0.00796501
\(611\) −5544.00 + 9602.49i −0.367081 + 0.635802i
\(612\) −36.0000 62.3538i −0.00237780 0.00411847i
\(613\) −87.0000 150.688i −0.00573230 0.00992863i 0.863145 0.504956i \(-0.168491\pi\)
−0.868877 + 0.495027i \(0.835158\pi\)
\(614\) 196.000 339.482i 0.0128826 0.0223133i
\(615\) −2772.00 −0.181753
\(616\) 0 0
\(617\) 16018.0 1.04515 0.522577 0.852592i \(-0.324971\pi\)
0.522577 + 0.852592i \(0.324971\pi\)
\(618\) −1392.00 + 2411.01i −0.0906059 + 0.156934i
\(619\) −1534.00 2656.97i −0.0996069 0.172524i 0.811915 0.583776i \(-0.198425\pi\)
−0.911522 + 0.411251i \(0.865092\pi\)
\(620\) 288.000 + 498.831i 0.0186554 + 0.0323121i
\(621\) 1026.00 1777.08i 0.0662995 0.114834i
\(622\) 13472.0 0.868453
\(623\) 0 0
\(624\) −2016.00 −0.129334
\(625\) −7070.50 + 12246.5i −0.452512 + 0.783774i
\(626\) 394.000 + 682.428i 0.0251556 + 0.0435708i
\(627\) −1488.00 2577.29i −0.0947767 0.164158i
\(628\) 892.000 1544.99i 0.0566794 0.0981716i
\(629\) 796.000 0.0504588
\(630\) 0 0
\(631\) 24656.0 1.55553 0.777765 0.628555i \(-0.216353\pi\)
0.777765 + 0.628555i \(0.216353\pi\)
\(632\) −2208.00 + 3824.37i −0.138971 + 0.240704i
\(633\) −1950.00 3377.50i −0.122442 0.212075i
\(634\) 6714.00 + 11629.0i 0.420579 + 0.728464i
\(635\) 2088.00 3616.52i 0.130488 0.226011i
\(636\) 1944.00 0.121202
\(637\) 0 0
\(638\) −4064.00 −0.252187
\(639\) 1062.00 1839.44i 0.0657466 0.113876i
\(640\) 128.000 + 221.703i 0.00790569 + 0.0136931i
\(641\) −3797.00 6576.60i −0.233966 0.405242i 0.725005 0.688743i \(-0.241837\pi\)
−0.958972 + 0.283501i \(0.908504\pi\)
\(642\) −6408.00 + 11099.0i −0.393931 + 0.682308i
\(643\) 3724.00 0.228398 0.114199 0.993458i \(-0.463570\pi\)
0.114199 + 0.993458i \(0.463570\pi\)
\(644\) 0 0
\(645\) 1272.00 0.0776511
\(646\) −248.000 + 429.549i −0.0151044 + 0.0261616i
\(647\) 1896.00 + 3283.97i 0.115208 + 0.199546i 0.917863 0.396898i \(-0.129913\pi\)
−0.802655 + 0.596444i \(0.796580\pi\)
\(648\) −324.000 561.184i −0.0196419 0.0340207i
\(649\) 3088.00 5348.57i 0.186771 0.323497i
\(650\) −10164.0 −0.613331
\(651\) 0 0
\(652\) 10832.0 0.650635
\(653\) −12351.0 + 21392.6i −0.740171 + 1.28201i 0.212245 + 0.977216i \(0.431922\pi\)
−0.952417 + 0.304798i \(0.901411\pi\)
\(654\) −3678.00 6370.48i −0.219910 0.380895i
\(655\) 292.000 + 505.759i 0.0174189 + 0.0301704i
\(656\) 3696.00 6401.66i 0.219976 0.381010i
\(657\) −3762.00 −0.223394
\(658\) 0 0
\(659\) −20144.0 −1.19074 −0.595371 0.803451i \(-0.702995\pi\)
−0.595371 + 0.803451i \(0.702995\pi\)
\(660\) 96.0000 166.277i 0.00566181 0.00980654i
\(661\) −1261.00 2184.12i −0.0742015 0.128521i 0.826537 0.562882i \(-0.190307\pi\)
−0.900739 + 0.434361i \(0.856974\pi\)
\(662\) −692.000 1198.58i −0.0406274 0.0703687i
\(663\) 126.000 218.238i 0.00738075 0.0127838i
\(664\) −8288.00 −0.484393
\(665\) 0 0
\(666\) 7164.00 0.416816
\(667\) −9652.00 + 16717.8i −0.560310 + 0.970486i
\(668\) 1792.00 + 3103.84i 0.103794 + 0.179777i
\(669\) −3864.00 6692.64i −0.223305 0.386775i
\(670\) −1528.00 + 2646.57i −0.0881071 + 0.152606i
\(671\) 240.000 0.0138079
\(672\) 0 0
\(673\) −10414.0 −0.596479 −0.298239 0.954491i \(-0.596399\pi\)
−0.298239 + 0.954491i \(0.596399\pi\)
\(674\) 1566.00 2712.39i 0.0894956 0.155011i
\(675\) −1633.50 2829.30i −0.0931458 0.161333i
\(676\) 866.000 + 1499.96i 0.0492717 + 0.0853411i
\(677\) −11115.0 + 19251.7i −0.630996 + 1.09292i 0.356353 + 0.934352i \(0.384020\pi\)
−0.987348 + 0.158565i \(0.949313\pi\)
\(678\) −2028.00 −0.114874
\(679\) 0 0
\(680\) −32.0000 −0.00180462
\(681\) 2754.00 4770.07i 0.154968 0.268413i
\(682\) 576.000 + 997.661i 0.0323404 + 0.0560153i
\(683\) −9096.00 15754.7i −0.509588 0.882633i −0.999938 0.0111072i \(-0.996464\pi\)
0.490350 0.871526i \(-0.336869\pi\)
\(684\) −2232.00 + 3865.94i −0.124770 + 0.216108i
\(685\) −1636.00 −0.0912531
\(686\) 0 0
\(687\) −5622.00 −0.312216
\(688\) −1696.00 + 2937.56i −0.0939817 + 0.162781i
\(689\) 3402.00 + 5892.44i 0.188107 + 0.325811i
\(690\) −456.000 789.815i −0.0251589 0.0435764i
\(691\) 4054.00 7021.73i 0.223186 0.386569i −0.732588 0.680673i \(-0.761688\pi\)
0.955774 + 0.294103i \(0.0950210\pi\)
\(692\) −16136.0 −0.886414
\(693\) 0 0
\(694\) −10656.0 −0.582848
\(695\) 2156.00 3734.30i 0.117672 0.203813i
\(696\) 3048.00 + 5279.29i 0.165997 + 0.287516i
\(697\) 462.000 + 800.207i 0.0251069 + 0.0434864i
\(698\) 11326.0 19617.2i 0.614177 1.06379i
\(699\) −11190.0 −0.605500
\(700\) 0 0
\(701\) −5794.00 −0.312177 −0.156089 0.987743i \(-0.549889\pi\)
−0.156089 + 0.987743i \(0.549889\pi\)
\(702\) 1134.00 1964.15i 0.0609688 0.105601i
\(703\) −24676.0 42740.1i −1.32386 2.29299i
\(704\) 256.000 + 443.405i 0.0137051 + 0.0237379i
\(705\) −792.000 + 1371.78i −0.0423099 + 0.0732828i
\(706\) 4260.00 0.227092
\(707\) 0 0
\(708\) −9264.00 −0.491755
\(709\) 977.000 1692.21i 0.0517518 0.0896367i −0.838989 0.544148i \(-0.816853\pi\)
0.890741 + 0.454512i \(0.150186\pi\)
\(710\) −472.000 817.528i −0.0249491 0.0432131i
\(711\) −2484.00 4302.41i −0.131023 0.226938i
\(712\) 120.000 207.846i 0.00631628 0.0109401i
\(713\) 5472.00 0.287417
\(714\) 0 0
\(715\) 672.000 0.0351488
\(716\) 6960.00 12055.1i 0.363279 0.629217i
\(717\) 3006.00 + 5206.54i 0.156571 + 0.271188i
\(718\) −3044.00 5272.36i −0.158219 0.274043i
\(719\) −16008.0 + 27726.7i −0.830317 + 1.43815i 0.0674706 + 0.997721i \(0.478507\pi\)
−0.897787 + 0.440429i \(0.854826\pi\)
\(720\) −288.000 −0.0149071
\(721\) 0 0
\(722\) 17034.0 0.878033
\(723\) 969.000 1678.36i 0.0498444 0.0863330i
\(724\) −5796.00 10039.0i −0.297523 0.515325i
\(725\) 15367.0 + 26616.4i 0.787195 + 1.36346i
\(726\) −3801.00 + 6583.53i −0.194309 + 0.336553i
\(727\) 23072.0 1.17702 0.588510 0.808490i \(-0.299715\pi\)
0.588510 + 0.808490i \(0.299715\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) −836.000 + 1447.99i −0.0423860 + 0.0734146i
\(731\) −212.000 367.195i −0.0107265 0.0185789i
\(732\) −180.000 311.769i −0.00908879 0.0157422i
\(733\) 15891.0 27524.0i 0.800747 1.38693i −0.118378 0.992969i \(-0.537770\pi\)
0.919125 0.393966i \(-0.128897\pi\)
\(734\) −24832.0 −1.24873
\(735\) 0 0
\(736\) 2432.00 0.121800
\(737\) −3056.00 + 5293.15i −0.152740 + 0.264553i
\(738\) 4158.00 + 7201.87i 0.207396 + 0.359220i
\(739\) 12198.0 + 21127.6i 0.607186 + 1.05168i 0.991702 + 0.128559i \(0.0410352\pi\)
−0.384516 + 0.923119i \(0.625631\pi\)
\(740\) 1592.00 2757.42i 0.0790852 0.136980i
\(741\) −15624.0 −0.774578
\(742\) 0 0
\(743\) −32604.0 −1.60986 −0.804929 0.593371i \(-0.797797\pi\)
−0.804929 + 0.593371i \(0.797797\pi\)
\(744\) 864.000 1496.49i 0.0425750 0.0737420i
\(745\) −2850.00 4936.34i −0.140156 0.242757i
\(746\) 7442.00 + 12889.9i 0.365243 + 0.632619i
\(747\) 4662.00 8074.82i 0.228345 0.395505i
\(748\) −64.0000 −0.00312844
\(749\) 0 0
\(750\) −2952.00 −0.143722
\(751\) 3840.00 6651.08i 0.186583 0.323171i −0.757526 0.652805i \(-0.773592\pi\)
0.944109 + 0.329634i \(0.106925\pi\)
\(752\) −2112.00 3658.09i −0.102416 0.177389i
\(753\) −1890.00 3273.58i −0.0914680 0.158427i
\(754\) −10668.0 + 18477.5i −0.515259 + 0.892456i
\(755\) −3344.00 −0.161193
\(756\) 0 0
\(757\) 366.000 0.0175727 0.00878633 0.999961i \(-0.497203\pi\)
0.00878633 + 0.999961i \(0.497203\pi\)
\(758\) −100.000 + 173.205i −0.00479177 + 0.00829959i
\(759\) −912.000 1579.63i −0.0436146 0.0755428i
\(760\) 992.000 + 1718.19i 0.0473469 + 0.0820072i
\(761\) 14687.0 25438.6i 0.699610 1.21176i −0.268992 0.963143i \(-0.586690\pi\)
0.968602 0.248618i \(-0.0799763\pi\)
\(762\) −12528.0 −0.595593
\(763\) 0 0
\(764\) 10608.0 0.502335
\(765\) 18.0000 31.1769i 0.000850708 0.00147347i
\(766\) 8080.00 + 13995.0i 0.381126 + 0.660129i
\(767\) −16212.0 28080.0i −0.763209 1.32192i
\(768\) 384.000 665.108i 0.0180422 0.0312500i
\(769\) 38990.0 1.82837 0.914184 0.405299i \(-0.132833\pi\)
0.914184 + 0.405299i \(0.132833\pi\)
\(770\) 0 0
\(771\) 17730.0 0.828185
\(772\) −292.000 + 505.759i −0.0136131 + 0.0235786i
\(773\) −10235.0 17727.5i −0.476232 0.824858i 0.523397 0.852089i \(-0.324664\pi\)
−0.999629 + 0.0272308i \(0.991331\pi\)
\(774\) −1908.00 3304.75i −0.0886068 0.153471i
\(775\) 4356.00 7544.81i 0.201900 0.349700i
\(776\) 9520.00 0.440397
\(777\) 0 0
\(778\) −10964.0 −0.505242
\(779\) 28644.0 49612.9i 1.31743 2.28186i
\(780\) −504.000 872.954i −0.0231360 0.0400728i
\(781\) −944.000 1635.06i −0.0432509 0.0749128i
\(782\) −152.000 + 263.272i −0.00695078 + 0.0120391i
\(783\) −6858.00 −0.313008
\(784\) 0 0
\(785\) 892.000 0.0405565
\(786\) 876.000 1517.28i 0.0397530 0.0688543i
\(787\) 14958.0 + 25908.0i 0.677503 + 1.17347i 0.975730 + 0.218975i \(0.0702714\pi\)
−0.298227 + 0.954495i \(0.596395\pi\)
\(788\) 5092.00 + 8819.60i 0.230197 + 0.398712i
\(789\) 4482.00 7763.05i 0.202235 0.350281i
\(790\) −2208.00 −0.0994394
\(791\) 0 0
\(792\) −576.000 −0.0258425
\(793\) 630.000 1091.19i 0.0282118 0.0488643i
\(794\) 10446.0 + 18093.0i 0.466895 + 0.808686i
\(795\) 486.000 + 841.777i 0.0216813 + 0.0375531i
\(796\) −5072.00 + 8784.96i −0.225845 + 0.391174i
\(797\) −4914.00 −0.218398 −0.109199 0.994020i \(-0.534828\pi\)
−0.109199 + 0.994020i \(0.534828\pi\)
\(798\) 0 0
\(799\) 528.000 0.0233783
\(800\) 1936.00 3353.25i 0.0855599 0.148194i
\(801\) 135.000 + 233.827i 0.00595504 + 0.0103144i
\(802\) 11334.0 + 19631.1i 0.499024 + 0.864335i
\(803\) −1672.00 + 2895.99i −0.0734790 + 0.127269i
\(804\) 9168.00 0.402152
\(805\) 0 0
\(806\) 6048.00 0.264307
\(807\) 1977.00 3424.26i 0.0862375 0.149368i
\(808\) 5480.00 + 9491.64i 0.238596 + 0.413261i
\(809\) −17125.0 29661.4i −0.744231 1.28905i −0.950553 0.310562i \(-0.899483\pi\)
0.206322 0.978484i \(-0.433851\pi\)
\(810\) 162.000 280.592i 0.00702728 0.0121716i
\(811\) 41804.0 1.81003 0.905017 0.425376i \(-0.139858\pi\)
0.905017 + 0.425376i \(0.139858\pi\)
\(812\) 0 0
\(813\) −16920.0 −0.729902
\(814\) 3184.00 5514.85i 0.137100 0.237464i
\(815\) 2708.00 + 4690.39i 0.116389 + 0.201592i
\(816\) 48.0000 + 83.1384i 0.00205924 + 0.00356670i
\(817\) −13144.0 + 22766.1i −0.562852 + 0.974889i
\(818\) −17188.0 −0.734675
\(819\) 0 0
\(820\) 3696.00 0.157402
\(821\) −15431.0 + 26727.3i −0.655963 + 1.13616i 0.325688 + 0.945477i \(0.394404\pi\)
−0.981651 + 0.190684i \(0.938929\pi\)
\(822\) 2454.00 + 4250.45i 0.104128 + 0.180355i
\(823\) −5288.00 9159.08i −0.223971 0.387929i 0.732039 0.681262i \(-0.238569\pi\)
−0.956010 + 0.293333i \(0.905235\pi\)
\(824\) 1856.00 3214.69i 0.0784670 0.135909i
\(825\) −2904.00 −0.122551
\(826\) 0 0
\(827\) −10680.0 −0.449069 −0.224534 0.974466i \(-0.572086\pi\)
−0.224534 + 0.974466i \(0.572086\pi\)
\(828\) −1368.00 + 2369.45i −0.0574170 + 0.0994492i
\(829\) −589.000 1020.18i −0.0246765 0.0427409i 0.853423 0.521218i \(-0.174522\pi\)
−0.878100 + 0.478477i \(0.841189\pi\)
\(830\) −2072.00 3588.81i −0.0866508 0.150084i
\(831\) 9669.00 16747.2i 0.403627 0.699102i
\(832\) 2688.00 0.112007
\(833\) 0 0
\(834\) −12936.0 −0.537095
\(835\) −896.000 + 1551.92i −0.0371346 + 0.0643189i
\(836\) 1984.00 + 3436.39i 0.0820790 + 0.142165i
\(837\) 972.000 + 1683.55i 0.0401401 + 0.0695246i
\(838\) 10500.0 18186.5i 0.432836 0.749694i
\(839\) 5600.00 0.230433 0.115217 0.993340i \(-0.463244\pi\)
0.115217 + 0.993340i \(0.463244\pi\)
\(840\) 0 0
\(841\) 40127.0 1.64529
\(842\) 12066.0 20898.9i 0.493850 0.855374i
\(843\) 7395.00 + 12808.5i 0.302132 + 0.523308i
\(844\) 2600.00 + 4503.33i 0.106038 + 0.183662i
\(845\) −433.000 + 749.978i −0.0176280 + 0.0305326i
\(846\) 4752.00 0.193117
\(847\) 0 0
\(848\) −2592.00 −0.104964
\(849\) 9390.00 16264.0i 0.379581 0.657453i
\(850\) 242.000 + 419.156i 0.00976533 + 0.0169140i
\(851\) −15124.0 26195.5i −0.609217 1.05520i
\(852\) −1416.00 + 2452.58i −0.0569382 + 0.0986199i
\(853\) 826.000 0.0331556 0.0165778 0.999863i \(-0.494723\pi\)
0.0165778 + 0.999863i \(0.494723\pi\)
\(854\) 0 0
\(855\) −2232.00 −0.0892781
\(856\) 8544.00 14798.6i 0.341154 0.590896i
\(857\) 22959.0 + 39766.2i 0.915128 + 1.58505i 0.806714 + 0.590942i \(0.201244\pi\)
0.108414 + 0.994106i \(0.465423\pi\)
\(858\) −1008.00 1745.91i −0.0401079 0.0694689i
\(859\) 21190.0 36702.2i 0.841669 1.45781i −0.0468143 0.998904i \(-0.514907\pi\)
0.888483 0.458909i \(-0.151760\pi\)
\(860\) −1696.00 −0.0672478
\(861\) 0 0
\(862\) 8664.00 0.342340
\(863\) 13262.0 22970.5i 0.523110 0.906053i −0.476529 0.879159i \(-0.658105\pi\)
0.999638 0.0268937i \(-0.00856156\pi\)
\(864\) 432.000 + 748.246i 0.0170103 + 0.0294628i
\(865\) −4034.00 6987.09i −0.158567 0.274645i
\(866\) −1918.00 + 3322.07i −0.0752613 + 0.130356i
\(867\) 14727.0 0.576880
\(868\) 0 0
\(869\) −4416.00 −0.172385
\(870\) −1524.00 + 2639.65i −0.0593890 + 0.102865i
\(871\) 16044.0 + 27789.0i 0.624145 + 1.08105i
\(872\) 4904.00 + 8493.98i 0.190448 + 0.329865i
\(873\) −5355.00 + 9275.13i −0.207605 + 0.359583i
\(874\) 18848.0 0.729454
\(875\) 0 0
\(876\) 5016.00 0.193465
\(877\) −10307.0 + 17852.2i −0.396856 + 0.687375i −0.993336 0.115253i \(-0.963232\pi\)
0.596480 + 0.802628i \(0.296565\pi\)
\(878\) −7992.00 13842.6i −0.307195 0.532077i
\(879\) 3465.00 + 6001.56i 0.132960 + 0.230293i
\(880\) −128.000 + 221.703i −0.00490327 + 0.00849272i
\(881\) 23730.0 0.907473 0.453737 0.891136i \(-0.350091\pi\)
0.453737 + 0.891136i \(0.350091\pi\)
\(882\) 0 0
\(883\) −9028.00 −0.344073 −0.172036 0.985091i \(-0.555035\pi\)
−0.172036 + 0.985091i \(0.555035\pi\)
\(884\) −168.000 + 290.985i −0.00639191 + 0.0110711i
\(885\) −2316.00 4011.43i −0.0879678 0.152365i
\(886\) −3184.00 5514.85i −0.120732 0.209114i
\(887\) 18600.0 32216.1i 0.704089 1.21952i −0.262930 0.964815i \(-0.584689\pi\)
0.967019 0.254703i \(-0.0819777\pi\)
\(888\) −9552.00 −0.360973
\(889\) 0 0
\(890\) 120.000 0.00451956
\(891\) 324.000 561.184i 0.0121823 0.0211003i
\(892\) 5152.00 + 8923.53i 0.193388 + 0.334957i
\(893\) −16368.0 28350.2i −0.613364 1.06238i
\(894\) −8550.00 + 14809.0i −0.319860 + 0.554014i
\(895\) 6960.00 0.259941
\(896\) 0 0
\(897\) −9576.00 −0.356447
\(898\) −11426.0 + 19790.4i −0.424600 + 0.735428i
\(899\) −9144.00 15837.9i −0.339232 0.587567i
\(900\) 2178.00 + 3772.41i 0.0806667 + 0.139719i
\(901\) 162.000 280.592i 0.00599001 0.0103750i
\(902\) 7392.00 0.272868
\(903\) 0 0
\(904\) 2704.00 0.0994842
\(905\) 2898.00 5019.48i 0.106445 0.184368i
\(906\) 5016.00 + 8687.97i 0.183935 + 0.318585i
\(907\) −11994.0 20774.2i −0.439090 0.760525i 0.558530 0.829484i \(-0.311366\pi\)
−0.997619 + 0.0689589i \(0.978032\pi\)
\(908\) −3672.00 + 6360.09i −0.134207 + 0.232453i
\(909\) −12330.0 −0.449901
\(910\) 0 0
\(911\) 15276.0 0.555561 0.277781 0.960645i \(-0.410401\pi\)
0.277781 + 0.960645i \(0.410401\pi\)
\(912\) 2976.00 5154.58i 0.108054 0.187155i
\(913\) −4144.00 7177.62i −0.150215 0.260180i
\(914\) 16934.0 + 29330.5i 0.612830 + 1.06145i
\(915\) 90.0000 155.885i 0.00325170 0.00563211i
\(916\) 7496.00 0.270387
\(917\) 0 0
\(918\) −108.000 −0.00388293
\(919\) 5380.00 9318.43i 0.193112 0.334480i −0.753168 0.657828i \(-0.771475\pi\)
0.946280 + 0.323349i \(0.104809\pi\)
\(920\) 608.000 + 1053.09i 0.0217882 + 0.0377383i
\(921\) −294.000 509.223i −0.0105186 0.0182187i
\(922\) −17038.0 + 29510.7i −0.608586 + 1.05410i
\(923\) −9912.00 −0.353475
\(924\) 0 0
\(925\) −48158.0 −1.71181
\(926\) 13592.0 23542.0i 0.482355 0.835464i
\(927\) 2088.00 + 3616.52i 0.0739794 + 0.128136i
\(928\) −4064.00 7039.05i −0.143758 0.248996i
\(929\) −26445.0 + 45804.1i −0.933942 + 1.61764i −0.157433 + 0.987530i \(0.550322\pi\)
−0.776509 + 0.630106i \(0.783012\pi\)
\(930\) 864.000 0.0304642
\(931\) 0 0
\(932\) 14920.0 0.524379
\(933\) 10104.0 17500.6i 0.354545 0.614089i
\(934\) 8612.00 + 14916.4i 0.301706 + 0.522570i
\(935\) −16.0000 27.7128i −0.000559632 0.000969311i
\(936\) −1512.00 + 2618.86i −0.0528005 + 0.0914531i
\(937\) 6118.00 0.213305 0.106652 0.994296i \(-0.465987\pi\)
0.106652 + 0.994296i \(0.465987\pi\)
\(938\) 0 0
\(939\) 1182.00 0.0410789
\(940\) 1056.00 1829.05i 0.0366414 0.0634648i
\(941\) −16115.0 27912.0i −0.558272 0.966956i −0.997641 0.0686488i \(-0.978131\pi\)
0.439369 0.898307i \(-0.355202\pi\)
\(942\) −1338.00 2317.48i −0.0462786 0.0801568i
\(943\) 17556.0 30407.9i 0.606259 1.05007i
\(944\) 12352.0 0.425872
\(945\) 0 0
\(946\) −3392.00 −0.116579
\(947\) 9272.00 16059.6i 0.318162 0.551073i −0.661942 0.749555i \(-0.730268\pi\)
0.980105 + 0.198482i \(0.0636010\pi\)
\(948\) 3312.00 + 5736.55i 0.113469 + 0.196534i
\(949\) 8778.00 + 15203.9i 0.300259 + 0.520064i
\(950\) 15004.0 25987.7i 0.512415 0.887528i
\(951\) 20142.0 0.686802
\(952\) 0 0
\(953\) 25930.0 0.881380 0.440690 0.897659i \(-0.354734\pi\)
0.440690 + 0.897659i \(0.354734\pi\)
\(954\) 1458.00 2525.33i 0.0494806 0.0857029i
\(955\) 2652.00 + 4593.40i 0.0898604 + 0.155643i
\(956\) −4008.00 6942.06i −0.135594 0.234856i
\(957\) −3048.00 + 5279.29i −0.102955 + 0.178323i
\(958\) −14864.0 −0.501288
\(959\) 0 0
\(960\) 384.000 0.0129099
\(961\) 12303.5 21310.3i 0.412994 0.715326i
\(962\) −16716.0 28953.0i −0.560234 0.970354i
\(963\) 9612.00 + 16648.5i 0.321643 + 0.557102i
\(964\) −1292.00 + 2237.81i −0.0431665 + 0.0747666i
\(965\) −292.000 −0.00974074
\(966\) 0 0
\(967\) 8192.00 0.272427 0.136214 0.990680i \(-0.456507\pi\)
0.136214 + 0.990680i \(0.456507\pi\)
\(968\) 5068.00 8778.03i 0.168277 0.291464i
\(969\) 372.000 + 644.323i 0.0123327 + 0.0213608i
\(970\) 2380.00 + 4122.28i 0.0787806 + 0.136452i
\(971\) −27222.0 + 47149.9i −0.899686 + 1.55830i −0.0717914 + 0.997420i \(0.522872\pi\)
−0.827895 + 0.560883i \(0.810462\pi\)
\(972\) −972.000 −0.0320750
\(973\) 0 0
\(974\) −13232.0 −0.435298
\(975\) −7623.00 + 13203.4i −0.250391 + 0.433690i
\(976\) 240.000 + 415.692i 0.00787112 + 0.0136332i
\(977\) 12723.0 + 22036.9i 0.416627 + 0.721620i 0.995598 0.0937289i \(-0.0298787\pi\)
−0.578970 + 0.815348i \(0.696545\pi\)
\(978\) 8124.00 14071.2i 0.265621 0.460068i
\(979\) 240.000 0.00783497
\(980\) 0 0
\(981\) −11034.0 −0.359112
\(982\) −17040.0 + 29514.1i −0.553735 + 0.959098i
\(983\) 16596.0 + 28745.1i 0.538484 + 0.932682i 0.998986 + 0.0450235i \(0.0143363\pi\)
−0.460502 + 0.887659i \(0.652330\pi\)
\(984\) −5544.00 9602.49i −0.179610 0.311094i
\(985\) −2546.00 + 4409.80i −0.0823577 + 0.142648i
\(986\) 1016.00 0.0328154
\(987\) 0 0
\(988\) 20832.0 0.670804
\(989\) −8056.00 + 13953.4i −0.259015 + 0.448627i
\(990\) −144.000 249.415i −0.00462285 0.00800701i
\(991\) −5512.00 9547.06i −0.176685 0.306027i 0.764058 0.645147i \(-0.223204\pi\)
−0.940743 + 0.339120i \(0.889871\pi\)
\(992\) −1152.00 + 1995.32i −0.0368710 + 0.0638625i
\(993\) −2076.00 −0.0663443
\(994\) 0 0
\(995\) −5072.00 −0.161601
\(996\) −6216.00 + 10766.4i −0.197753 + 0.342517i
\(997\) −20357.0 35259.4i −0.646653 1.12004i −0.983917 0.178625i \(-0.942835\pi\)
0.337265 0.941410i \(-0.390498\pi\)
\(998\) 2948.00 + 5106.09i 0.0935043 + 0.161954i
\(999\) 5373.00 9306.31i 0.170164 0.294733i
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 294.4.e.d.79.1 2
3.2 odd 2 882.4.g.r.667.1 2
7.2 even 3 294.4.a.h.1.1 1
7.3 odd 6 294.4.e.a.67.1 2
7.4 even 3 inner 294.4.e.d.67.1 2
7.5 odd 6 42.4.a.b.1.1 1
7.6 odd 2 294.4.e.a.79.1 2
21.2 odd 6 882.4.a.d.1.1 1
21.5 even 6 126.4.a.c.1.1 1
21.11 odd 6 882.4.g.r.361.1 2
21.17 even 6 882.4.g.s.361.1 2
21.20 even 2 882.4.g.s.667.1 2
28.19 even 6 336.4.a.d.1.1 1
28.23 odd 6 2352.4.a.ba.1.1 1
35.12 even 12 1050.4.g.n.799.2 2
35.19 odd 6 1050.4.a.d.1.1 1
35.33 even 12 1050.4.g.n.799.1 2
56.5 odd 6 1344.4.a.f.1.1 1
56.19 even 6 1344.4.a.t.1.1 1
84.47 odd 6 1008.4.a.j.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.4.a.b.1.1 1 7.5 odd 6
126.4.a.c.1.1 1 21.5 even 6
294.4.a.h.1.1 1 7.2 even 3
294.4.e.a.67.1 2 7.3 odd 6
294.4.e.a.79.1 2 7.6 odd 2
294.4.e.d.67.1 2 7.4 even 3 inner
294.4.e.d.79.1 2 1.1 even 1 trivial
336.4.a.d.1.1 1 28.19 even 6
882.4.a.d.1.1 1 21.2 odd 6
882.4.g.r.361.1 2 21.11 odd 6
882.4.g.r.667.1 2 3.2 odd 2
882.4.g.s.361.1 2 21.17 even 6
882.4.g.s.667.1 2 21.20 even 2
1008.4.a.j.1.1 1 84.47 odd 6
1050.4.a.d.1.1 1 35.19 odd 6
1050.4.g.n.799.1 2 35.33 even 12
1050.4.g.n.799.2 2 35.12 even 12
1344.4.a.f.1.1 1 56.5 odd 6
1344.4.a.t.1.1 1 56.19 even 6
2352.4.a.ba.1.1 1 28.23 odd 6