Properties

Label 15.3.f.a.13.2
Level $15$
Weight $3$
Character 15.13
Analytic conductor $0.409$
Analytic rank $0$
Dimension $4$
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] = [15,3,Mod(7,15)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(15, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("15.7");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 15.f (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.408720396540\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 13.2
Root \(1.22474 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 15.13
Dual form 15.3.f.a.7.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.224745 - 0.224745i) q^{2} +(-1.22474 - 1.22474i) q^{3} +3.89898i q^{4} +(-4.67423 - 1.77526i) q^{5} -0.550510 q^{6} +(3.44949 - 3.44949i) q^{7} +(1.77526 + 1.77526i) q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+(0.224745 - 0.224745i) q^{2} +(-1.22474 - 1.22474i) q^{3} +3.89898i q^{4} +(-4.67423 - 1.77526i) q^{5} -0.550510 q^{6} +(3.44949 - 3.44949i) q^{7} +(1.77526 + 1.77526i) q^{8} +3.00000i q^{9} +(-1.44949 + 0.651531i) q^{10} +11.3485 q^{11} +(4.77526 - 4.77526i) q^{12} +(-5.55051 - 5.55051i) q^{13} -1.55051i q^{14} +(3.55051 + 7.89898i) q^{15} -14.7980 q^{16} +(-17.3485 + 17.3485i) q^{17} +(0.674235 + 0.674235i) q^{18} -8.69694i q^{19} +(6.92168 - 18.2247i) q^{20} -8.44949 q^{21} +(2.55051 - 2.55051i) q^{22} +(11.5505 + 11.5505i) q^{23} -4.34847i q^{24} +(18.6969 + 16.5959i) q^{25} -2.49490 q^{26} +(3.67423 - 3.67423i) q^{27} +(13.4495 + 13.4495i) q^{28} -35.1464i q^{29} +(2.57321 + 0.977296i) q^{30} +10.6969 q^{31} +(-10.4268 + 10.4268i) q^{32} +(-13.8990 - 13.8990i) q^{33} +7.79796i q^{34} +(-22.2474 + 10.0000i) q^{35} -11.6969 q^{36} +(-6.04541 + 6.04541i) q^{37} +(-1.95459 - 1.95459i) q^{38} +13.5959i q^{39} +(-5.14643 - 11.4495i) q^{40} +0.696938 q^{41} +(-1.89898 + 1.89898i) q^{42} +(-26.4949 - 26.4949i) q^{43} +44.2474i q^{44} +(5.32577 - 14.0227i) q^{45} +5.19184 q^{46} +(44.2474 - 44.2474i) q^{47} +(18.1237 + 18.1237i) q^{48} +25.2020i q^{49} +(7.93189 - 0.472194i) q^{50} +42.4949 q^{51} +(21.6413 - 21.6413i) q^{52} +(-0.696938 - 0.696938i) q^{53} -1.65153i q^{54} +(-53.0454 - 20.1464i) q^{55} +12.2474 q^{56} +(-10.6515 + 10.6515i) q^{57} +(-7.89898 - 7.89898i) q^{58} +39.9342i q^{59} +(-30.7980 + 13.8434i) q^{60} +5.90918 q^{61} +(2.40408 - 2.40408i) q^{62} +(10.3485 + 10.3485i) q^{63} -54.5051i q^{64} +(16.0908 + 35.7980i) q^{65} -6.24745 q^{66} +(-45.1010 + 45.1010i) q^{67} +(-67.6413 - 67.6413i) q^{68} -28.2929i q^{69} +(-2.75255 + 7.24745i) q^{70} -68.0000 q^{71} +(-5.32577 + 5.32577i) q^{72} +(77.7878 + 77.7878i) q^{73} +2.71735i q^{74} +(-2.57321 - 43.2247i) q^{75} +33.9092 q^{76} +(39.1464 - 39.1464i) q^{77} +(3.05561 + 3.05561i) q^{78} +24.4949i q^{79} +(69.1691 + 26.2702i) q^{80} -9.00000 q^{81} +(0.156633 - 0.156633i) q^{82} +(13.1464 + 13.1464i) q^{83} -32.9444i q^{84} +(111.889 - 50.2929i) q^{85} -11.9092 q^{86} +(-43.0454 + 43.0454i) q^{87} +(20.1464 + 20.1464i) q^{88} -82.1816i q^{89} +(-1.95459 - 4.34847i) q^{90} -38.2929 q^{91} +(-45.0352 + 45.0352i) q^{92} +(-13.1010 - 13.1010i) q^{93} -19.8888i q^{94} +(-15.4393 + 40.6515i) q^{95} +25.5403 q^{96} +(-24.5959 + 24.5959i) q^{97} +(5.66403 + 5.66403i) q^{98} +34.0454i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} - 4 q^{5} - 12 q^{6} + 4 q^{7} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{2} - 4 q^{5} - 12 q^{6} + 4 q^{7} + 12 q^{8} + 4 q^{10} + 16 q^{11} + 24 q^{12} - 32 q^{13} + 24 q^{15} - 20 q^{16} - 40 q^{17} - 12 q^{18} - 36 q^{20} - 24 q^{21} + 20 q^{22} + 56 q^{23} + 16 q^{25} + 88 q^{26} + 44 q^{28} - 24 q^{30} - 16 q^{31} - 76 q^{32} - 36 q^{33} - 40 q^{35} + 12 q^{36} + 64 q^{37} - 96 q^{38} + 48 q^{40} - 56 q^{41} + 12 q^{42} - 8 q^{43} + 36 q^{45} - 136 q^{46} + 128 q^{47} + 48 q^{48} + 164 q^{50} + 72 q^{51} - 80 q^{52} + 56 q^{53} - 124 q^{55} - 72 q^{57} - 12 q^{58} - 84 q^{60} + 200 q^{61} + 88 q^{62} + 12 q^{63} - 112 q^{65} + 24 q^{66} - 200 q^{67} - 104 q^{68} - 60 q^{70} - 272 q^{71} - 36 q^{72} + 76 q^{73} + 24 q^{75} + 312 q^{76} + 88 q^{77} + 120 q^{78} + 164 q^{80} - 36 q^{81} + 128 q^{82} - 16 q^{83} + 232 q^{85} - 224 q^{86} - 84 q^{87} + 12 q^{88} - 96 q^{90} - 16 q^{91} + 104 q^{92} - 72 q^{93} + 144 q^{95} - 84 q^{96} - 20 q^{97} - 188 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(7\) \(11\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.224745 0.224745i 0.112372 0.112372i −0.648685 0.761057i \(-0.724681\pi\)
0.761057 + 0.648685i \(0.224681\pi\)
\(3\) −1.22474 1.22474i −0.408248 0.408248i
\(4\) 3.89898i 0.974745i
\(5\) −4.67423 1.77526i −0.934847 0.355051i
\(6\) −0.550510 −0.0917517
\(7\) 3.44949 3.44949i 0.492784 0.492784i −0.416398 0.909182i \(-0.636708\pi\)
0.909182 + 0.416398i \(0.136708\pi\)
\(8\) 1.77526 + 1.77526i 0.221907 + 0.221907i
\(9\) 3.00000i 0.333333i
\(10\) −1.44949 + 0.651531i −0.144949 + 0.0651531i
\(11\) 11.3485 1.03168 0.515840 0.856685i \(-0.327480\pi\)
0.515840 + 0.856685i \(0.327480\pi\)
\(12\) 4.77526 4.77526i 0.397938 0.397938i
\(13\) −5.55051 5.55051i −0.426962 0.426962i 0.460630 0.887592i \(-0.347624\pi\)
−0.887592 + 0.460630i \(0.847624\pi\)
\(14\) 1.55051i 0.110751i
\(15\) 3.55051 + 7.89898i 0.236701 + 0.526599i
\(16\) −14.7980 −0.924872
\(17\) −17.3485 + 17.3485i −1.02050 + 1.02050i −0.0207127 + 0.999785i \(0.506594\pi\)
−0.999785 + 0.0207127i \(0.993406\pi\)
\(18\) 0.674235 + 0.674235i 0.0374575 + 0.0374575i
\(19\) 8.69694i 0.457734i −0.973458 0.228867i \(-0.926498\pi\)
0.973458 0.228867i \(-0.0735020\pi\)
\(20\) 6.92168 18.2247i 0.346084 0.911237i
\(21\) −8.44949 −0.402357
\(22\) 2.55051 2.55051i 0.115932 0.115932i
\(23\) 11.5505 + 11.5505i 0.502196 + 0.502196i 0.912120 0.409924i \(-0.134445\pi\)
−0.409924 + 0.912120i \(0.634445\pi\)
\(24\) 4.34847i 0.181186i
\(25\) 18.6969 + 16.5959i 0.747878 + 0.663837i
\(26\) −2.49490 −0.0959576
\(27\) 3.67423 3.67423i 0.136083 0.136083i
\(28\) 13.4495 + 13.4495i 0.480339 + 0.480339i
\(29\) 35.1464i 1.21195i −0.795485 0.605973i \(-0.792784\pi\)
0.795485 0.605973i \(-0.207216\pi\)
\(30\) 2.57321 + 0.977296i 0.0857738 + 0.0325765i
\(31\) 10.6969 0.345063 0.172531 0.985004i \(-0.444805\pi\)
0.172531 + 0.985004i \(0.444805\pi\)
\(32\) −10.4268 + 10.4268i −0.325837 + 0.325837i
\(33\) −13.8990 13.8990i −0.421181 0.421181i
\(34\) 7.79796i 0.229352i
\(35\) −22.2474 + 10.0000i −0.635641 + 0.285714i
\(36\) −11.6969 −0.324915
\(37\) −6.04541 + 6.04541i −0.163389 + 0.163389i −0.784066 0.620677i \(-0.786858\pi\)
0.620677 + 0.784066i \(0.286858\pi\)
\(38\) −1.95459 1.95459i −0.0514366 0.0514366i
\(39\) 13.5959i 0.348613i
\(40\) −5.14643 11.4495i −0.128661 0.286237i
\(41\) 0.696938 0.0169985 0.00849925 0.999964i \(-0.497295\pi\)
0.00849925 + 0.999964i \(0.497295\pi\)
\(42\) −1.89898 + 1.89898i −0.0452138 + 0.0452138i
\(43\) −26.4949 26.4949i −0.616160 0.616160i 0.328384 0.944544i \(-0.393496\pi\)
−0.944544 + 0.328384i \(0.893496\pi\)
\(44\) 44.2474i 1.00562i
\(45\) 5.32577 14.0227i 0.118350 0.311616i
\(46\) 5.19184 0.112866
\(47\) 44.2474 44.2474i 0.941435 0.941435i −0.0569424 0.998377i \(-0.518135\pi\)
0.998377 + 0.0569424i \(0.0181351\pi\)
\(48\) 18.1237 + 18.1237i 0.377578 + 0.377578i
\(49\) 25.2020i 0.514327i
\(50\) 7.93189 0.472194i 0.158638 0.00944387i
\(51\) 42.4949 0.833233
\(52\) 21.6413 21.6413i 0.416179 0.416179i
\(53\) −0.696938 0.696938i −0.0131498 0.0131498i 0.700501 0.713651i \(-0.252960\pi\)
−0.713651 + 0.700501i \(0.752960\pi\)
\(54\) 1.65153i 0.0305839i
\(55\) −53.0454 20.1464i −0.964462 0.366299i
\(56\) 12.2474 0.218704
\(57\) −10.6515 + 10.6515i −0.186869 + 0.186869i
\(58\) −7.89898 7.89898i −0.136189 0.136189i
\(59\) 39.9342i 0.676851i 0.940993 + 0.338425i \(0.109894\pi\)
−0.940993 + 0.338425i \(0.890106\pi\)
\(60\) −30.7980 + 13.8434i −0.513299 + 0.230723i
\(61\) 5.90918 0.0968719 0.0484359 0.998826i \(-0.484576\pi\)
0.0484359 + 0.998826i \(0.484576\pi\)
\(62\) 2.40408 2.40408i 0.0387755 0.0387755i
\(63\) 10.3485 + 10.3485i 0.164261 + 0.164261i
\(64\) 54.5051i 0.851642i
\(65\) 16.0908 + 35.7980i 0.247551 + 0.550738i
\(66\) −6.24745 −0.0946583
\(67\) −45.1010 + 45.1010i −0.673150 + 0.673150i −0.958441 0.285291i \(-0.907910\pi\)
0.285291 + 0.958441i \(0.407910\pi\)
\(68\) −67.6413 67.6413i −0.994725 0.994725i
\(69\) 28.2929i 0.410041i
\(70\) −2.75255 + 7.24745i −0.0393222 + 0.103535i
\(71\) −68.0000 −0.957746 −0.478873 0.877884i \(-0.658955\pi\)
−0.478873 + 0.877884i \(0.658955\pi\)
\(72\) −5.32577 + 5.32577i −0.0739690 + 0.0739690i
\(73\) 77.7878 + 77.7878i 1.06559 + 1.06559i 0.997693 + 0.0678931i \(0.0216277\pi\)
0.0678931 + 0.997693i \(0.478372\pi\)
\(74\) 2.71735i 0.0367209i
\(75\) −2.57321 43.2247i −0.0343095 0.576330i
\(76\) 33.9092 0.446173
\(77\) 39.1464 39.1464i 0.508395 0.508395i
\(78\) 3.05561 + 3.05561i 0.0391745 + 0.0391745i
\(79\) 24.4949i 0.310062i 0.987910 + 0.155031i \(0.0495477\pi\)
−0.987910 + 0.155031i \(0.950452\pi\)
\(80\) 69.1691 + 26.2702i 0.864614 + 0.328377i
\(81\) −9.00000 −0.111111
\(82\) 0.156633 0.156633i 0.00191016 0.00191016i
\(83\) 13.1464 + 13.1464i 0.158391 + 0.158391i 0.781853 0.623463i \(-0.214275\pi\)
−0.623463 + 0.781853i \(0.714275\pi\)
\(84\) 32.9444i 0.392195i
\(85\) 111.889 50.2929i 1.31634 0.591681i
\(86\) −11.9092 −0.138479
\(87\) −43.0454 + 43.0454i −0.494775 + 0.494775i
\(88\) 20.1464 + 20.1464i 0.228937 + 0.228937i
\(89\) 82.1816i 0.923389i −0.887039 0.461695i \(-0.847242\pi\)
0.887039 0.461695i \(-0.152758\pi\)
\(90\) −1.95459 4.34847i −0.0217177 0.0483163i
\(91\) −38.2929 −0.420801
\(92\) −45.0352 + 45.0352i −0.489513 + 0.489513i
\(93\) −13.1010 13.1010i −0.140871 0.140871i
\(94\) 19.8888i 0.211583i
\(95\) −15.4393 + 40.6515i −0.162519 + 0.427911i
\(96\) 25.5403 0.266045
\(97\) −24.5959 + 24.5959i −0.253566 + 0.253566i −0.822431 0.568865i \(-0.807383\pi\)
0.568865 + 0.822431i \(0.307383\pi\)
\(98\) 5.66403 + 5.66403i 0.0577962 + 0.0577962i
\(99\) 34.0454i 0.343893i
\(100\) −64.7071 + 72.8990i −0.647071 + 0.728990i
\(101\) −105.621 −1.04575 −0.522876 0.852409i \(-0.675141\pi\)
−0.522876 + 0.852409i \(0.675141\pi\)
\(102\) 9.55051 9.55051i 0.0936325 0.0936325i
\(103\) −89.2474 89.2474i −0.866480 0.866480i 0.125601 0.992081i \(-0.459914\pi\)
−0.992081 + 0.125601i \(0.959914\pi\)
\(104\) 19.7071i 0.189492i
\(105\) 39.4949 + 15.0000i 0.376142 + 0.142857i
\(106\) −0.313267 −0.00295535
\(107\) 68.7423 68.7423i 0.642452 0.642452i −0.308706 0.951158i \(-0.599896\pi\)
0.951158 + 0.308706i \(0.0998958\pi\)
\(108\) 14.3258 + 14.3258i 0.132646 + 0.132646i
\(109\) 68.6969i 0.630247i −0.949051 0.315124i \(-0.897954\pi\)
0.949051 0.315124i \(-0.102046\pi\)
\(110\) −16.4495 + 7.39388i −0.149541 + 0.0672171i
\(111\) 14.8082 0.133407
\(112\) −51.0454 + 51.0454i −0.455763 + 0.455763i
\(113\) 97.6413 + 97.6413i 0.864083 + 0.864083i 0.991809 0.127727i \(-0.0407681\pi\)
−0.127727 + 0.991809i \(0.540768\pi\)
\(114\) 4.78775i 0.0419978i
\(115\) −33.4847 74.4949i −0.291171 0.647782i
\(116\) 137.035 1.18134
\(117\) 16.6515 16.6515i 0.142321 0.142321i
\(118\) 8.97500 + 8.97500i 0.0760593 + 0.0760593i
\(119\) 119.687i 1.00577i
\(120\) −7.71964 + 20.3258i −0.0643304 + 0.169381i
\(121\) 7.78775 0.0643616
\(122\) 1.32806 1.32806i 0.0108857 0.0108857i
\(123\) −0.853572 0.853572i −0.00693961 0.00693961i
\(124\) 41.7071i 0.336348i
\(125\) −57.9319 110.765i −0.463455 0.886120i
\(126\) 4.65153 0.0369169
\(127\) 164.621 164.621i 1.29623 1.29623i 0.365362 0.930865i \(-0.380945\pi\)
0.930865 0.365362i \(-0.119055\pi\)
\(128\) −53.9569 53.9569i −0.421538 0.421538i
\(129\) 64.8990i 0.503093i
\(130\) 11.6617 + 4.42908i 0.0897057 + 0.0340698i
\(131\) 106.136 0.810200 0.405100 0.914272i \(-0.367237\pi\)
0.405100 + 0.914272i \(0.367237\pi\)
\(132\) 54.1918 54.1918i 0.410544 0.410544i
\(133\) −30.0000 30.0000i −0.225564 0.225564i
\(134\) 20.2724i 0.151287i
\(135\) −23.6969 + 10.6515i −0.175533 + 0.0789002i
\(136\) −61.5959 −0.452911
\(137\) −166.631 + 166.631i −1.21629 + 1.21629i −0.247363 + 0.968923i \(0.579564\pi\)
−0.968923 + 0.247363i \(0.920436\pi\)
\(138\) −6.35867 6.35867i −0.0460774 0.0460774i
\(139\) 191.171i 1.37533i 0.726026 + 0.687667i \(0.241365\pi\)
−0.726026 + 0.687667i \(0.758635\pi\)
\(140\) −38.9898 86.7423i −0.278499 0.619588i
\(141\) −108.384 −0.768679
\(142\) −15.2827 + 15.2827i −0.107624 + 0.107624i
\(143\) −62.9898 62.9898i −0.440488 0.440488i
\(144\) 44.3939i 0.308291i
\(145\) −62.3939 + 164.283i −0.430303 + 1.13298i
\(146\) 34.9648 0.239485
\(147\) 30.8661 30.8661i 0.209973 0.209973i
\(148\) −23.5709 23.5709i −0.159263 0.159263i
\(149\) 84.8536i 0.569487i −0.958604 0.284744i \(-0.908092\pi\)
0.958604 0.284744i \(-0.0919084\pi\)
\(150\) −10.2929 9.13622i −0.0686190 0.0609082i
\(151\) 148.969 0.986552 0.493276 0.869873i \(-0.335799\pi\)
0.493276 + 0.869873i \(0.335799\pi\)
\(152\) 15.4393 15.4393i 0.101574 0.101574i
\(153\) −52.0454 52.0454i −0.340166 0.340166i
\(154\) 17.5959i 0.114259i
\(155\) −50.0000 18.9898i −0.322581 0.122515i
\(156\) −53.0102 −0.339809
\(157\) 16.8536 16.8536i 0.107348 0.107348i −0.651393 0.758741i \(-0.725815\pi\)
0.758741 + 0.651393i \(0.225815\pi\)
\(158\) 5.50510 + 5.50510i 0.0348424 + 0.0348424i
\(159\) 1.70714i 0.0107368i
\(160\) 67.2474 30.2270i 0.420297 0.188919i
\(161\) 79.6867 0.494949
\(162\) −2.02270 + 2.02270i −0.0124858 + 0.0124858i
\(163\) 130.606 + 130.606i 0.801265 + 0.801265i 0.983293 0.182029i \(-0.0582664\pi\)
−0.182029 + 0.983293i \(0.558266\pi\)
\(164\) 2.71735i 0.0165692i
\(165\) 40.2929 + 89.6413i 0.244199 + 0.543281i
\(166\) 5.90918 0.0355975
\(167\) −45.0352 + 45.0352i −0.269672 + 0.269672i −0.828968 0.559296i \(-0.811071\pi\)
0.559296 + 0.828968i \(0.311071\pi\)
\(168\) −15.0000 15.0000i −0.0892857 0.0892857i
\(169\) 107.384i 0.635406i
\(170\) 13.8434 36.4495i 0.0814316 0.214409i
\(171\) 26.0908 0.152578
\(172\) 103.303 103.303i 0.600599 0.600599i
\(173\) 146.631 + 146.631i 0.847579 + 0.847579i 0.989831 0.142252i \(-0.0454343\pi\)
−0.142252 + 0.989831i \(0.545434\pi\)
\(174\) 19.3485i 0.111198i
\(175\) 121.742 7.24745i 0.695671 0.0414140i
\(176\) −167.934 −0.954171
\(177\) 48.9092 48.9092i 0.276323 0.276323i
\(178\) −18.4699 18.4699i −0.103763 0.103763i
\(179\) 183.712i 1.02632i −0.858292 0.513161i \(-0.828474\pi\)
0.858292 0.513161i \(-0.171526\pi\)
\(180\) 54.6742 + 20.7650i 0.303746 + 0.115361i
\(181\) −286.272 −1.58162 −0.790808 0.612064i \(-0.790339\pi\)
−0.790808 + 0.612064i \(0.790339\pi\)
\(182\) −8.60612 + 8.60612i −0.0472864 + 0.0472864i
\(183\) −7.23724 7.23724i −0.0395478 0.0395478i
\(184\) 41.0102i 0.222882i
\(185\) 38.9898 17.5255i 0.210756 0.0947325i
\(186\) −5.88877 −0.0316601
\(187\) −196.879 + 196.879i −1.05283 + 1.05283i
\(188\) 172.520 + 172.520i 0.917659 + 0.917659i
\(189\) 25.3485i 0.134119i
\(190\) 5.66632 + 12.6061i 0.0298228 + 0.0663480i
\(191\) 48.0908 0.251784 0.125892 0.992044i \(-0.459821\pi\)
0.125892 + 0.992044i \(0.459821\pi\)
\(192\) −66.7548 + 66.7548i −0.347681 + 0.347681i
\(193\) −255.565 255.565i −1.32417 1.32417i −0.910364 0.413809i \(-0.864198\pi\)
−0.413809 0.910364i \(-0.635802\pi\)
\(194\) 11.0556i 0.0569877i
\(195\) 24.1362 63.5505i 0.123776 0.325900i
\(196\) −98.2622 −0.501338
\(197\) −96.6969 + 96.6969i −0.490847 + 0.490847i −0.908573 0.417726i \(-0.862827\pi\)
0.417726 + 0.908573i \(0.362827\pi\)
\(198\) 7.65153 + 7.65153i 0.0386441 + 0.0386441i
\(199\) 192.606i 0.967870i −0.875104 0.483935i \(-0.839207\pi\)
0.875104 0.483935i \(-0.160793\pi\)
\(200\) 3.72985 + 62.6538i 0.0186492 + 0.313269i
\(201\) 110.474 0.549624
\(202\) −23.7378 + 23.7378i −0.117514 + 0.117514i
\(203\) −121.237 121.237i −0.597228 0.597228i
\(204\) 165.687i 0.812190i
\(205\) −3.25765 1.23724i −0.0158910 0.00603533i
\(206\) −40.1158 −0.194737
\(207\) −34.6515 + 34.6515i −0.167399 + 0.167399i
\(208\) 82.1362 + 82.1362i 0.394886 + 0.394886i
\(209\) 98.6969i 0.472234i
\(210\) 12.2474 5.50510i 0.0583212 0.0262148i
\(211\) 147.212 0.697688 0.348844 0.937181i \(-0.386574\pi\)
0.348844 + 0.937181i \(0.386574\pi\)
\(212\) 2.71735 2.71735i 0.0128177 0.0128177i
\(213\) 83.2827 + 83.2827i 0.390998 + 0.390998i
\(214\) 30.8990i 0.144388i
\(215\) 76.8082 + 170.879i 0.357247 + 0.794784i
\(216\) 13.0454 0.0603954
\(217\) 36.8990 36.8990i 0.170041 0.170041i
\(218\) −15.4393 15.4393i −0.0708224 0.0708224i
\(219\) 190.540i 0.870047i
\(220\) 78.5505 206.823i 0.357048 0.940104i
\(221\) 192.586 0.871429
\(222\) 3.32806 3.32806i 0.0149913 0.0149913i
\(223\) 167.429 + 167.429i 0.750803 + 0.750803i 0.974629 0.223826i \(-0.0718548\pi\)
−0.223826 + 0.974629i \(0.571855\pi\)
\(224\) 71.9342i 0.321135i
\(225\) −49.7878 + 56.0908i −0.221279 + 0.249293i
\(226\) 43.8888 0.194198
\(227\) 253.171 253.171i 1.11529 1.11529i 0.122870 0.992423i \(-0.460790\pi\)
0.992423 0.122870i \(-0.0392098\pi\)
\(228\) −41.5301 41.5301i −0.182150 0.182150i
\(229\) 224.202i 0.979048i 0.871990 + 0.489524i \(0.162829\pi\)
−0.871990 + 0.489524i \(0.837171\pi\)
\(230\) −24.2679 9.21683i −0.105512 0.0400732i
\(231\) −95.8888 −0.415103
\(232\) 62.3939 62.3939i 0.268939 0.268939i
\(233\) −205.712 205.712i −0.882883 0.882883i 0.110944 0.993827i \(-0.464613\pi\)
−0.993827 + 0.110944i \(0.964613\pi\)
\(234\) 7.48469i 0.0319859i
\(235\) −285.373 + 128.272i −1.21436 + 0.545840i
\(236\) −155.703 −0.659757
\(237\) 30.0000 30.0000i 0.126582 0.126582i
\(238\) 26.8990 + 26.8990i 0.113021 + 0.113021i
\(239\) 345.798i 1.44685i 0.690401 + 0.723427i \(0.257434\pi\)
−0.690401 + 0.723427i \(0.742566\pi\)
\(240\) −52.5403 116.889i −0.218918 0.487037i
\(241\) 101.576 0.421475 0.210738 0.977543i \(-0.432413\pi\)
0.210738 + 0.977543i \(0.432413\pi\)
\(242\) 1.75026 1.75026i 0.00723247 0.00723247i
\(243\) 11.0227 + 11.0227i 0.0453609 + 0.0453609i
\(244\) 23.0398i 0.0944254i
\(245\) 44.7401 117.800i 0.182612 0.480817i
\(246\) −0.383672 −0.00155964
\(247\) −48.2724 + 48.2724i −0.195435 + 0.195435i
\(248\) 18.9898 + 18.9898i 0.0765718 + 0.0765718i
\(249\) 32.2020i 0.129325i
\(250\) −37.9138 11.8740i −0.151655 0.0474959i
\(251\) −331.258 −1.31975 −0.659876 0.751375i \(-0.729391\pi\)
−0.659876 + 0.751375i \(0.729391\pi\)
\(252\) −40.3485 + 40.3485i −0.160113 + 0.160113i
\(253\) 131.081 + 131.081i 0.518105 + 0.518105i
\(254\) 73.9954i 0.291321i
\(255\) −198.631 75.4393i −0.778946 0.295840i
\(256\) 193.767 0.756904
\(257\) 33.2372 33.2372i 0.129328 0.129328i −0.639480 0.768808i \(-0.720850\pi\)
0.768808 + 0.639480i \(0.220850\pi\)
\(258\) 14.5857 + 14.5857i 0.0565338 + 0.0565338i
\(259\) 41.7071i 0.161031i
\(260\) −139.576 + 62.7378i −0.536829 + 0.241299i
\(261\) 105.439 0.403982
\(262\) 23.8536 23.8536i 0.0910442 0.0910442i
\(263\) −278.157 278.157i −1.05763 1.05763i −0.998235 0.0593952i \(-0.981083\pi\)
−0.0593952 0.998235i \(-0.518917\pi\)
\(264\) 49.3485i 0.186926i
\(265\) 2.02041 + 4.49490i 0.00762419 + 0.0169619i
\(266\) −13.4847 −0.0506943
\(267\) −100.652 + 100.652i −0.376972 + 0.376972i
\(268\) −175.848 175.848i −0.656149 0.656149i
\(269\) 488.499i 1.81598i 0.418988 + 0.907992i \(0.362385\pi\)
−0.418988 + 0.907992i \(0.637615\pi\)
\(270\) −2.93189 + 7.71964i −0.0108588 + 0.0285913i
\(271\) 131.576 0.485518 0.242759 0.970087i \(-0.421947\pi\)
0.242759 + 0.970087i \(0.421947\pi\)
\(272\) 256.722 256.722i 0.943831 0.943831i
\(273\) 46.8990 + 46.8990i 0.171791 + 0.171791i
\(274\) 74.8990i 0.273354i
\(275\) 212.182 + 188.338i 0.771570 + 0.684866i
\(276\) 110.313 0.399686
\(277\) 101.510 101.510i 0.366461 0.366461i −0.499724 0.866185i \(-0.666565\pi\)
0.866185 + 0.499724i \(0.166565\pi\)
\(278\) 42.9648 + 42.9648i 0.154550 + 0.154550i
\(279\) 32.0908i 0.115021i
\(280\) −57.2474 21.7423i −0.204455 0.0776512i
\(281\) 343.303 1.22172 0.610860 0.791739i \(-0.290824\pi\)
0.610860 + 0.791739i \(0.290824\pi\)
\(282\) −24.3587 + 24.3587i −0.0863783 + 0.0863783i
\(283\) 1.19184 + 1.19184i 0.00421143 + 0.00421143i 0.709209 0.704998i \(-0.249052\pi\)
−0.704998 + 0.709209i \(0.749052\pi\)
\(284\) 265.131i 0.933558i
\(285\) 68.6969 30.8786i 0.241042 0.108346i
\(286\) −28.3133 −0.0989974
\(287\) 2.40408 2.40408i 0.00837659 0.00837659i
\(288\) −31.2804 31.2804i −0.108612 0.108612i
\(289\) 312.939i 1.08283i
\(290\) 22.8990 + 50.9444i 0.0789620 + 0.175670i
\(291\) 60.2474 0.207036
\(292\) −303.293 + 303.293i −1.03867 + 1.03867i
\(293\) 96.5653 + 96.5653i 0.329574 + 0.329574i 0.852425 0.522850i \(-0.175131\pi\)
−0.522850 + 0.852425i \(0.675131\pi\)
\(294\) 13.8740i 0.0471904i
\(295\) 70.8934 186.662i 0.240316 0.632752i
\(296\) −21.4643 −0.0725145
\(297\) 41.6969 41.6969i 0.140394 0.140394i
\(298\) −19.0704 19.0704i −0.0639946 0.0639946i
\(299\) 128.222i 0.428838i
\(300\) 168.532 10.0329i 0.561775 0.0334430i
\(301\) −182.788 −0.607268
\(302\) 33.4801 33.4801i 0.110861 0.110861i
\(303\) 129.359 + 129.359i 0.426926 + 0.426926i
\(304\) 128.697i 0.423345i
\(305\) −27.6209 10.4903i −0.0905604 0.0343945i
\(306\) −23.3939 −0.0764506
\(307\) −124.969 + 124.969i −0.407066 + 0.407066i −0.880714 0.473648i \(-0.842937\pi\)
0.473648 + 0.880714i \(0.342937\pi\)
\(308\) 152.631 + 152.631i 0.495556 + 0.495556i
\(309\) 218.611i 0.707478i
\(310\) −15.5051 + 6.96938i −0.0500165 + 0.0224819i
\(311\) −586.302 −1.88522 −0.942608 0.333902i \(-0.891635\pi\)
−0.942608 + 0.333902i \(0.891635\pi\)
\(312\) −24.1362 + 24.1362i −0.0773597 + 0.0773597i
\(313\) −102.373 102.373i −0.327072 0.327072i 0.524400 0.851472i \(-0.324290\pi\)
−0.851472 + 0.524400i \(0.824290\pi\)
\(314\) 7.57551i 0.0241258i
\(315\) −30.0000 66.7423i −0.0952381 0.211880i
\(316\) −95.5051 −0.302231
\(317\) −108.783 + 108.783i −0.343165 + 0.343165i −0.857556 0.514391i \(-0.828018\pi\)
0.514391 + 0.857556i \(0.328018\pi\)
\(318\) 0.383672 + 0.383672i 0.00120651 + 0.00120651i
\(319\) 398.858i 1.25034i
\(320\) −96.7605 + 254.770i −0.302376 + 0.796155i
\(321\) −168.384 −0.524560
\(322\) 17.9092 17.9092i 0.0556186 0.0556186i
\(323\) 150.879 + 150.879i 0.467116 + 0.467116i
\(324\) 35.0908i 0.108305i
\(325\) −11.6617 195.893i −0.0358823 0.602749i
\(326\) 58.7061 0.180080
\(327\) −84.1362 + 84.1362i −0.257297 + 0.257297i
\(328\) 1.23724 + 1.23724i 0.00377208 + 0.00377208i
\(329\) 305.262i 0.927849i
\(330\) 29.2020 + 11.0908i 0.0884910 + 0.0336085i
\(331\) −245.423 −0.741461 −0.370730 0.928741i \(-0.620893\pi\)
−0.370730 + 0.928741i \(0.620893\pi\)
\(332\) −51.2577 + 51.2577i −0.154391 + 0.154391i
\(333\) −18.1362 18.1362i −0.0544631 0.0544631i
\(334\) 20.2429i 0.0606074i
\(335\) 290.879 130.747i 0.868294 0.390289i
\(336\) 125.035 0.372129
\(337\) 213.808 213.808i 0.634446 0.634446i −0.314734 0.949180i \(-0.601915\pi\)
0.949180 + 0.314734i \(0.101915\pi\)
\(338\) −24.1339 24.1339i −0.0714022 0.0714022i
\(339\) 239.171i 0.705520i
\(340\) 196.091 + 436.252i 0.576738 + 1.28309i
\(341\) 121.394 0.355994
\(342\) 5.86378 5.86378i 0.0171455 0.0171455i
\(343\) 255.959 + 255.959i 0.746237 + 0.746237i
\(344\) 94.0704i 0.273460i
\(345\) −50.2270 + 132.247i −0.145586 + 0.383326i
\(346\) 65.9092 0.190489
\(347\) −160.050 + 160.050i −0.461239 + 0.461239i −0.899062 0.437822i \(-0.855750\pi\)
0.437822 + 0.899062i \(0.355750\pi\)
\(348\) −167.833 167.833i −0.482279 0.482279i
\(349\) 298.009i 0.853894i 0.904277 + 0.426947i \(0.140411\pi\)
−0.904277 + 0.426947i \(0.859589\pi\)
\(350\) 25.7321 28.9898i 0.0735204 0.0828280i
\(351\) −40.7878 −0.116204
\(352\) −118.328 + 118.328i −0.336159 + 0.336159i
\(353\) −22.5199 22.5199i −0.0637957 0.0637957i 0.674489 0.738285i \(-0.264364\pi\)
−0.738285 + 0.674489i \(0.764364\pi\)
\(354\) 21.9842i 0.0621022i
\(355\) 317.848 + 120.717i 0.895346 + 0.340049i
\(356\) 320.424 0.900069
\(357\) 146.586 146.586i 0.410604 0.410604i
\(358\) −41.2883 41.2883i −0.115330 0.115330i
\(359\) 48.2724i 0.134464i −0.997737 0.0672318i \(-0.978583\pi\)
0.997737 0.0672318i \(-0.0214167\pi\)
\(360\) 34.3485 15.4393i 0.0954124 0.0428869i
\(361\) 285.363 0.790480
\(362\) −64.3383 + 64.3383i −0.177730 + 0.177730i
\(363\) −9.53801 9.53801i −0.0262755 0.0262755i
\(364\) 149.303i 0.410173i
\(365\) −225.505 501.691i −0.617822 1.37450i
\(366\) −3.25307 −0.00888816
\(367\) 146.510 146.510i 0.399209 0.399209i −0.478745 0.877954i \(-0.658908\pi\)
0.877954 + 0.478745i \(0.158908\pi\)
\(368\) −170.924 170.924i −0.464467 0.464467i
\(369\) 2.09082i 0.00566617i
\(370\) 4.82399 12.7015i 0.0130378 0.0343284i
\(371\) −4.80816 −0.0129600
\(372\) 51.0806 51.0806i 0.137313 0.137313i
\(373\) 86.2066 + 86.2066i 0.231117 + 0.231117i 0.813159 0.582042i \(-0.197746\pi\)
−0.582042 + 0.813159i \(0.697746\pi\)
\(374\) 88.4949i 0.236617i
\(375\) −64.7071 + 206.611i −0.172552 + 0.550962i
\(376\) 157.101 0.417822
\(377\) −195.081 + 195.081i −0.517455 + 0.517455i
\(378\) −5.69694 5.69694i −0.0150713 0.0150713i
\(379\) 210.000i 0.554090i 0.960857 + 0.277045i \(0.0893551\pi\)
−0.960857 + 0.277045i \(0.910645\pi\)
\(380\) −158.499 60.1975i −0.417104 0.158414i
\(381\) −403.237 −1.05837
\(382\) 10.8082 10.8082i 0.0282936 0.0282936i
\(383\) −10.6311 10.6311i −0.0277575 0.0277575i 0.693092 0.720849i \(-0.256248\pi\)
−0.720849 + 0.693092i \(0.756248\pi\)
\(384\) 132.167i 0.344184i
\(385\) −252.474 + 113.485i −0.655778 + 0.294765i
\(386\) −114.874 −0.297601
\(387\) 79.4847 79.4847i 0.205387 0.205387i
\(388\) −95.8990 95.8990i −0.247162 0.247162i
\(389\) 535.337i 1.37619i 0.725621 + 0.688094i \(0.241552\pi\)
−0.725621 + 0.688094i \(0.758448\pi\)
\(390\) −8.85816 19.7071i −0.0227132 0.0505311i
\(391\) −400.767 −1.02498
\(392\) −44.7401 + 44.7401i −0.114133 + 0.114133i
\(393\) −129.990 129.990i −0.330763 0.330763i
\(394\) 43.4643i 0.110315i
\(395\) 43.4847 114.495i 0.110088 0.289860i
\(396\) −132.742 −0.335208
\(397\) 118.742 118.742i 0.299099 0.299099i −0.541562 0.840661i \(-0.682167\pi\)
0.840661 + 0.541562i \(0.182167\pi\)
\(398\) −43.2872 43.2872i −0.108762 0.108762i
\(399\) 73.4847i 0.184172i
\(400\) −276.677 245.586i −0.691691 0.613964i
\(401\) 420.302 1.04813 0.524067 0.851677i \(-0.324414\pi\)
0.524067 + 0.851677i \(0.324414\pi\)
\(402\) 24.8286 24.8286i 0.0617626 0.0617626i
\(403\) −59.3735 59.3735i −0.147329 0.147329i
\(404\) 411.814i 1.01934i
\(405\) 42.0681 + 15.9773i 0.103872 + 0.0394501i
\(406\) −54.4949 −0.134224
\(407\) −68.6061 + 68.6061i −0.168565 + 0.168565i
\(408\) 75.4393 + 75.4393i 0.184900 + 0.184900i
\(409\) 515.110i 1.25944i 0.776823 + 0.629719i \(0.216830\pi\)
−0.776823 + 0.629719i \(0.783170\pi\)
\(410\) −1.01021 + 0.454077i −0.00246391 + 0.00110750i
\(411\) 408.161 0.993093
\(412\) 347.974 347.974i 0.844597 0.844597i
\(413\) 137.753 + 137.753i 0.333541 + 0.333541i
\(414\) 15.5755i 0.0376220i
\(415\) −38.1112 84.7878i −0.0918343 0.204308i
\(416\) 115.748 0.278240
\(417\) 234.136 234.136i 0.561478 0.561478i
\(418\) −22.1816 22.1816i −0.0530661 0.0530661i
\(419\) 88.6015i 0.211460i 0.994395 + 0.105730i \(0.0337178\pi\)
−0.994395 + 0.105730i \(0.966282\pi\)
\(420\) −58.4847 + 153.990i −0.139249 + 0.366642i
\(421\) −257.151 −0.610810 −0.305405 0.952223i \(-0.598792\pi\)
−0.305405 + 0.952223i \(0.598792\pi\)
\(422\) 33.0852 33.0852i 0.0784009 0.0784009i
\(423\) 132.742 + 132.742i 0.313812 + 0.313812i
\(424\) 2.47449i 0.00583605i
\(425\) −612.277 + 36.4495i −1.44065 + 0.0857635i
\(426\) 37.4347 0.0878749
\(427\) 20.3837 20.3837i 0.0477369 0.0477369i
\(428\) 268.025 + 268.025i 0.626227 + 0.626227i
\(429\) 154.293i 0.359657i
\(430\) 55.6663 + 21.1418i 0.129457 + 0.0491671i
\(431\) 804.636 1.86690 0.933452 0.358702i \(-0.116781\pi\)
0.933452 + 0.358702i \(0.116781\pi\)
\(432\) −54.3712 + 54.3712i −0.125859 + 0.125859i
\(433\) −344.848 344.848i −0.796416 0.796416i 0.186113 0.982528i \(-0.440411\pi\)
−0.982528 + 0.186113i \(0.940411\pi\)
\(434\) 16.5857i 0.0382159i
\(435\) 277.621 124.788i 0.638209 0.286868i
\(436\) 267.848 0.614330
\(437\) 100.454 100.454i 0.229872 0.229872i
\(438\) −42.8230 42.8230i −0.0977693 0.0977693i
\(439\) 432.929i 0.986170i −0.869981 0.493085i \(-0.835869\pi\)
0.869981 0.493085i \(-0.164131\pi\)
\(440\) −58.4041 129.934i −0.132737 0.295305i
\(441\) −75.6061 −0.171442
\(442\) 43.2827 43.2827i 0.0979246 0.0979246i
\(443\) 245.131 + 245.131i 0.553342 + 0.553342i 0.927404 0.374062i \(-0.122035\pi\)
−0.374062 + 0.927404i \(0.622035\pi\)
\(444\) 57.7367i 0.130038i
\(445\) −145.893 + 384.136i −0.327850 + 0.863227i
\(446\) 75.2577 0.168739
\(447\) −103.924 + 103.924i −0.232492 + 0.232492i
\(448\) −188.015 188.015i −0.419676 0.419676i
\(449\) 386.091i 0.859890i −0.902855 0.429945i \(-0.858533\pi\)
0.902855 0.429945i \(-0.141467\pi\)
\(450\) 1.41658 + 23.7957i 0.00314796 + 0.0528793i
\(451\) 7.90918 0.0175370
\(452\) −380.702 + 380.702i −0.842260 + 0.842260i
\(453\) −182.449 182.449i −0.402758 0.402758i
\(454\) 113.798i 0.250656i
\(455\) 178.990 + 67.9796i 0.393384 + 0.149406i
\(456\) −37.8184 −0.0829350
\(457\) −223.747 + 223.747i −0.489599 + 0.489599i −0.908180 0.418580i \(-0.862528\pi\)
0.418580 + 0.908180i \(0.362528\pi\)
\(458\) 50.3883 + 50.3883i 0.110018 + 0.110018i
\(459\) 127.485i 0.277744i
\(460\) 290.454 130.556i 0.631422 0.283818i
\(461\) −722.620 −1.56751 −0.783753 0.621073i \(-0.786697\pi\)
−0.783753 + 0.621073i \(0.786697\pi\)
\(462\) −21.5505 + 21.5505i −0.0466461 + 0.0466461i
\(463\) −129.702 129.702i −0.280133 0.280133i 0.553029 0.833162i \(-0.313472\pi\)
−0.833162 + 0.553029i \(0.813472\pi\)
\(464\) 520.095i 1.12090i
\(465\) 37.9796 + 84.4949i 0.0816765 + 0.181709i
\(466\) −92.4653 −0.198423
\(467\) 415.258 415.258i 0.889203 0.889203i −0.105244 0.994446i \(-0.533562\pi\)
0.994446 + 0.105244i \(0.0335623\pi\)
\(468\) 64.9240 + 64.9240i 0.138726 + 0.138726i
\(469\) 311.151i 0.663435i
\(470\) −35.3076 + 92.9648i −0.0751227 + 0.197797i
\(471\) −41.2827 −0.0876489
\(472\) −70.8934 + 70.8934i −0.150198 + 0.150198i
\(473\) −300.677 300.677i −0.635680 0.635680i
\(474\) 13.4847i 0.0284487i
\(475\) 144.334 162.606i 0.303860 0.342329i
\(476\) −466.656 −0.980370
\(477\) 2.09082 2.09082i 0.00438326 0.00438326i
\(478\) 77.7163 + 77.7163i 0.162586 + 0.162586i
\(479\) 304.949i 0.636637i −0.947984 0.318318i \(-0.896882\pi\)
0.947984 0.318318i \(-0.103118\pi\)
\(480\) −119.381 45.3406i −0.248711 0.0944595i
\(481\) 67.1102 0.139522
\(482\) 22.8286 22.8286i 0.0473622 0.0473622i
\(483\) −97.5959 97.5959i −0.202062 0.202062i
\(484\) 30.3643i 0.0627361i
\(485\) 158.631 71.3031i 0.327074 0.147017i
\(486\) 4.95459 0.0101946
\(487\) −429.318 + 429.318i −0.881556 + 0.881556i −0.993693 0.112137i \(-0.964231\pi\)
0.112137 + 0.993693i \(0.464231\pi\)
\(488\) 10.4903 + 10.4903i 0.0214965 + 0.0214965i
\(489\) 319.918i 0.654230i
\(490\) −16.4199 36.5301i −0.0335100 0.0745512i
\(491\) −414.318 −0.843825 −0.421912 0.906637i \(-0.638641\pi\)
−0.421912 + 0.906637i \(0.638641\pi\)
\(492\) 3.32806 3.32806i 0.00676435 0.00676435i
\(493\) 609.737 + 609.737i 1.23679 + 1.23679i
\(494\) 21.6980i 0.0439230i
\(495\) 60.4393 159.136i 0.122100 0.321487i
\(496\) −158.293 −0.319139
\(497\) −234.565 + 234.565i −0.471962 + 0.471962i
\(498\) −7.23724 7.23724i −0.0145326 0.0145326i
\(499\) 367.585i 0.736643i −0.929699 0.368321i \(-0.879933\pi\)
0.929699 0.368321i \(-0.120067\pi\)
\(500\) 431.871 225.875i 0.863741 0.451750i
\(501\) 110.313 0.220186
\(502\) −74.4485 + 74.4485i −0.148304 + 0.148304i
\(503\) −9.59133 9.59133i −0.0190683 0.0190683i 0.697508 0.716577i \(-0.254292\pi\)
−0.716577 + 0.697508i \(0.754292\pi\)
\(504\) 36.7423i 0.0729015i
\(505\) 493.697 + 187.504i 0.977618 + 0.371295i
\(506\) 58.9194 0.116441
\(507\) −131.518 + 131.518i −0.259404 + 0.259404i
\(508\) 641.854 + 641.854i 1.26349 + 1.26349i
\(509\) 777.489i 1.52748i −0.645522 0.763742i \(-0.723360\pi\)
0.645522 0.763742i \(-0.276640\pi\)
\(510\) −61.5959 + 27.6867i −0.120776 + 0.0542877i
\(511\) 536.656 1.05021
\(512\) 259.376 259.376i 0.506593 0.506593i
\(513\) −31.9546 31.9546i −0.0622897 0.0622897i
\(514\) 14.9398i 0.0290658i
\(515\) 258.727 + 575.601i 0.502382 + 1.11767i
\(516\) −253.040 −0.490387
\(517\) 502.141 502.141i 0.971259 0.971259i
\(518\) 9.37347 + 9.37347i 0.0180955 + 0.0180955i
\(519\) 359.171i 0.692045i
\(520\) −34.9852 + 92.1158i −0.0672792 + 0.177146i
\(521\) 321.605 0.617284 0.308642 0.951178i \(-0.400125\pi\)
0.308642 + 0.951178i \(0.400125\pi\)
\(522\) 23.6969 23.6969i 0.0453964 0.0453964i
\(523\) −582.454 582.454i −1.11368 1.11368i −0.992649 0.121030i \(-0.961380\pi\)
−0.121030 0.992649i \(-0.538620\pi\)
\(524\) 413.823i 0.789738i
\(525\) −157.980 140.227i −0.300914 0.267099i
\(526\) −125.029 −0.237697
\(527\) −185.576 + 185.576i −0.352136 + 0.352136i
\(528\) 205.677 + 205.677i 0.389539 + 0.389539i
\(529\) 262.171i 0.495598i
\(530\) 1.46428 + 0.556128i 0.00276280 + 0.00104930i
\(531\) −119.803 −0.225617
\(532\) 116.969 116.969i 0.219867 0.219867i
\(533\) −3.86836 3.86836i −0.00725772 0.00725772i
\(534\) 45.2418i 0.0847225i
\(535\) −443.353 + 199.283i −0.828697 + 0.372491i
\(536\) −160.132 −0.298753
\(537\) −225.000 + 225.000i −0.418994 + 0.418994i
\(538\) 109.788 + 109.788i 0.204066 + 0.204066i
\(539\) 286.005i 0.530621i
\(540\) −41.5301 92.3939i −0.0769076 0.171100i
\(541\) 460.697 0.851566 0.425783 0.904825i \(-0.359999\pi\)
0.425783 + 0.904825i \(0.359999\pi\)
\(542\) 29.5709 29.5709i 0.0545589 0.0545589i
\(543\) 350.611 + 350.611i 0.645692 + 0.645692i
\(544\) 361.778i 0.665032i
\(545\) −121.955 + 321.106i −0.223770 + 0.589185i
\(546\) 21.0806 0.0386092
\(547\) −661.778 + 661.778i −1.20983 + 1.20983i −0.238750 + 0.971081i \(0.576738\pi\)
−0.971081 + 0.238750i \(0.923262\pi\)
\(548\) −649.691 649.691i −1.18557 1.18557i
\(549\) 17.7276i 0.0322906i
\(550\) 90.0148 5.35867i 0.163663 0.00974304i
\(551\) −305.666 −0.554748
\(552\) 50.2270 50.2270i 0.0909910 0.0909910i
\(553\) 84.4949 + 84.4949i 0.152794 + 0.152794i
\(554\) 45.6276i 0.0823602i
\(555\) −69.2168 26.2883i −0.124715 0.0473663i
\(556\) −745.373 −1.34060
\(557\) 125.909 125.909i 0.226049 0.226049i −0.584991 0.811040i \(-0.698902\pi\)
0.811040 + 0.584991i \(0.198902\pi\)
\(558\) 7.21225 + 7.21225i 0.0129252 + 0.0129252i
\(559\) 294.120i 0.526155i
\(560\) 329.217 147.980i 0.587887 0.264249i
\(561\) 482.252 0.859629
\(562\) 77.1556 77.1556i 0.137288 0.137288i
\(563\) −200.009 200.009i −0.355256 0.355256i 0.506805 0.862061i \(-0.330826\pi\)
−0.862061 + 0.506805i \(0.830826\pi\)
\(564\) 422.586i 0.749265i
\(565\) −283.060 629.737i −0.500992 1.11458i
\(566\) 0.535718 0.000946498
\(567\) −31.0454 + 31.0454i −0.0547538 + 0.0547538i
\(568\) −120.717 120.717i −0.212531 0.212531i
\(569\) 599.839i 1.05420i 0.849804 + 0.527099i \(0.176720\pi\)
−0.849804 + 0.527099i \(0.823280\pi\)
\(570\) 8.49948 22.3791i 0.0149114 0.0392616i
\(571\) −247.970 −0.434274 −0.217137 0.976141i \(-0.569672\pi\)
−0.217137 + 0.976141i \(0.569672\pi\)
\(572\) 245.596 245.596i 0.429363 0.429363i
\(573\) −58.8990 58.8990i −0.102791 0.102791i
\(574\) 1.08061i 0.00188260i
\(575\) 24.2679 + 407.650i 0.0422050 + 0.708957i
\(576\) 163.515 0.283881
\(577\) −292.121 + 292.121i −0.506276 + 0.506276i −0.913381 0.407105i \(-0.866538\pi\)
0.407105 + 0.913381i \(0.366538\pi\)
\(578\) −70.3314 70.3314i −0.121681 0.121681i
\(579\) 626.005i 1.08118i
\(580\) −640.535 243.272i −1.10437 0.419435i
\(581\) 90.6969 0.156105
\(582\) 13.5403 13.5403i 0.0232651 0.0232651i
\(583\) −7.90918 7.90918i −0.0135664 0.0135664i
\(584\) 276.186i 0.472922i
\(585\) −107.394 + 48.2724i −0.183579 + 0.0825170i
\(586\) 43.4051 0.0740702
\(587\) 611.217 611.217i 1.04126 1.04126i 0.0421437 0.999112i \(-0.486581\pi\)
0.999112 0.0421437i \(-0.0134187\pi\)
\(588\) 120.346 + 120.346i 0.204670 + 0.204670i
\(589\) 93.0306i 0.157947i
\(590\) −26.0183 57.8842i −0.0440989 0.0981088i
\(591\) 236.858 0.400775
\(592\) 89.4597 89.4597i 0.151114 0.151114i
\(593\) 524.742 + 524.742i 0.884894 + 0.884894i 0.994027 0.109133i \(-0.0348074\pi\)
−0.109133 + 0.994027i \(0.534807\pi\)
\(594\) 18.7423i 0.0315528i
\(595\) 212.474 559.444i 0.357100 0.940242i
\(596\) 330.842 0.555105
\(597\) −235.893 + 235.893i −0.395131 + 0.395131i
\(598\) −28.8173 28.8173i −0.0481895 0.0481895i
\(599\) 368.858i 0.615790i 0.951420 + 0.307895i \(0.0996245\pi\)
−0.951420 + 0.307895i \(0.900375\pi\)
\(600\) 72.1668 81.3031i 0.120278 0.135505i
\(601\) 932.484 1.55155 0.775777 0.631007i \(-0.217358\pi\)
0.775777 + 0.631007i \(0.217358\pi\)
\(602\) −41.0806 + 41.0806i −0.0682402 + 0.0682402i
\(603\) −135.303 135.303i −0.224383 0.224383i
\(604\) 580.829i 0.961637i
\(605\) −36.4018 13.8252i −0.0601682 0.0228517i
\(606\) 58.1454 0.0959495
\(607\) 513.611 513.611i 0.846146 0.846146i −0.143504 0.989650i \(-0.545837\pi\)
0.989650 + 0.143504i \(0.0458369\pi\)
\(608\) 90.6811 + 90.6811i 0.149147 + 0.149147i
\(609\) 296.969i 0.487634i
\(610\) −8.56530 + 3.85002i −0.0140415 + 0.00631150i
\(611\) −491.192 −0.803915
\(612\) 202.924 202.924i 0.331575 0.331575i
\(613\) −615.287 615.287i −1.00373 1.00373i −0.999993 0.00373821i \(-0.998810\pi\)
−0.00373821 0.999993i \(-0.501190\pi\)
\(614\) 56.1725i 0.0914861i
\(615\) 2.47449 + 5.50510i 0.00402356 + 0.00895139i
\(616\) 138.990 0.225633
\(617\) 546.752 546.752i 0.886145 0.886145i −0.108005 0.994150i \(-0.534446\pi\)
0.994150 + 0.108005i \(0.0344463\pi\)
\(618\) 49.1316 + 49.1316i 0.0795010 + 0.0795010i
\(619\) 152.869i 0.246962i −0.992347 0.123481i \(-0.960594\pi\)
0.992347 0.123481i \(-0.0394058\pi\)
\(620\) 74.0408 194.949i 0.119421 0.314434i
\(621\) 84.8786 0.136680
\(622\) −131.768 + 131.768i −0.211846 + 0.211846i
\(623\) −283.485 283.485i −0.455032 0.455032i
\(624\) 201.192i 0.322423i
\(625\) 74.1510 + 620.586i 0.118642 + 0.992937i
\(626\) −46.0158 −0.0735077
\(627\) −120.879 + 120.879i −0.192789 + 0.192789i
\(628\) 65.7117 + 65.7117i 0.104637 + 0.104637i
\(629\) 209.757i 0.333477i
\(630\) −21.7423 8.25765i −0.0345117 0.0131074i
\(631\) −41.4847 −0.0657444 −0.0328722 0.999460i \(-0.510465\pi\)
−0.0328722 + 0.999460i \(0.510465\pi\)
\(632\) −43.4847 + 43.4847i −0.0688049 + 0.0688049i
\(633\) −180.297 180.297i −0.284830 0.284830i
\(634\) 48.8969i 0.0771245i
\(635\) −1061.72 + 477.233i −1.67200 + 0.751547i
\(636\) −6.65612 −0.0104656
\(637\) 139.884 139.884i 0.219598 0.219598i
\(638\) −89.6413 89.6413i −0.140504 0.140504i
\(639\) 204.000i 0.319249i
\(640\) 156.420 + 347.994i 0.244406 + 0.543741i
\(641\) 47.2122 0.0736541 0.0368270 0.999322i \(-0.488275\pi\)
0.0368270 + 0.999322i \(0.488275\pi\)
\(642\) −37.8434 + 37.8434i −0.0589461 + 0.0589461i
\(643\) 460.372 + 460.372i 0.715976 + 0.715976i 0.967779 0.251803i \(-0.0810234\pi\)
−0.251803 + 0.967779i \(0.581023\pi\)
\(644\) 310.697i 0.482449i
\(645\) 115.212 303.353i 0.178624 0.470315i
\(646\) 67.8184 0.104982
\(647\) −281.287 + 281.287i −0.434756 + 0.434756i −0.890243 0.455487i \(-0.849465\pi\)
0.455487 + 0.890243i \(0.349465\pi\)
\(648\) −15.9773 15.9773i −0.0246563 0.0246563i
\(649\) 453.192i 0.698293i
\(650\) −46.6469 41.4051i −0.0717645 0.0637002i
\(651\) −90.3837 −0.138838
\(652\) −509.231 + 509.231i −0.781029 + 0.781029i
\(653\) 89.8230 + 89.8230i 0.137554 + 0.137554i 0.772531 0.634977i \(-0.218990\pi\)
−0.634977 + 0.772531i \(0.718990\pi\)
\(654\) 37.8184i 0.0578263i
\(655\) −496.106 188.419i −0.757413 0.287662i
\(656\) −10.3133 −0.0157214
\(657\) −233.363 + 233.363i −0.355195 + 0.355195i
\(658\) −68.6061 68.6061i −0.104265 0.104265i
\(659\) 1081.24i 1.64072i −0.571844 0.820362i \(-0.693772\pi\)
0.571844 0.820362i \(-0.306228\pi\)
\(660\) −349.510 + 157.101i −0.529560 + 0.238032i
\(661\) −632.393 −0.956721 −0.478361 0.878163i \(-0.658769\pi\)
−0.478361 + 0.878163i \(0.658769\pi\)
\(662\) −55.1577 + 55.1577i −0.0833197 + 0.0833197i
\(663\) −235.868 235.868i −0.355759 0.355759i
\(664\) 46.6765i 0.0702960i
\(665\) 86.9694 + 193.485i 0.130781 + 0.290954i
\(666\) −8.15205 −0.0122403
\(667\) 405.959 405.959i 0.608634 0.608634i
\(668\) −175.591 175.591i −0.262861 0.262861i
\(669\) 410.116i 0.613028i
\(670\) 35.9888 94.7582i 0.0537146 0.141430i
\(671\) 67.0602 0.0999407
\(672\) 88.1010 88.1010i 0.131103 0.131103i
\(673\) 233.293 + 233.293i 0.346646 + 0.346646i 0.858859 0.512213i \(-0.171174\pi\)
−0.512213 + 0.858859i \(0.671174\pi\)
\(674\) 96.1046i 0.142588i
\(675\) 129.674 7.71964i 0.192110 0.0114365i
\(676\) 418.687 0.619359
\(677\) −48.3883 + 48.3883i −0.0714745 + 0.0714745i −0.741940 0.670466i \(-0.766094\pi\)
0.670466 + 0.741940i \(0.266094\pi\)
\(678\) −53.7526 53.7526i −0.0792810 0.0792810i
\(679\) 169.687i 0.249907i
\(680\) 287.914 + 109.348i 0.423403 + 0.160807i
\(681\) −620.141 −0.910633
\(682\) 27.2827 27.2827i 0.0400039 0.0400039i
\(683\) 213.410 + 213.410i 0.312459 + 0.312459i 0.845862 0.533402i \(-0.179087\pi\)
−0.533402 + 0.845862i \(0.679087\pi\)
\(684\) 101.728i 0.148724i
\(685\) 1074.69 483.060i 1.56888 0.705197i
\(686\) 115.051 0.167713
\(687\) 274.590 274.590i 0.399695 0.399695i
\(688\) 392.070 + 392.070i 0.569870 + 0.569870i
\(689\) 7.73673i 0.0112289i
\(690\) 18.4337 + 41.0102i 0.0267155 + 0.0594351i
\(691\) 151.121 0.218700 0.109350 0.994003i \(-0.465123\pi\)
0.109350 + 0.994003i \(0.465123\pi\)
\(692\) −571.712 + 571.712i −0.826173 + 0.826173i
\(693\) 117.439 + 117.439i 0.169465 + 0.169465i
\(694\) 71.9408i 0.103661i
\(695\) 339.378 893.580i 0.488314 1.28573i
\(696\) −152.833 −0.219588
\(697\) −12.0908 + 12.0908i −0.0173469 + 0.0173469i
\(698\) 66.9760 + 66.9760i 0.0959542 + 0.0959542i
\(699\) 503.889i 0.720871i
\(700\) 28.2577 + 474.671i 0.0403681 + 0.678101i
\(701\) −745.680 −1.06374 −0.531869 0.846827i \(-0.678510\pi\)
−0.531869 + 0.846827i \(0.678510\pi\)
\(702\) −9.16684 + 9.16684i −0.0130582 + 0.0130582i
\(703\) 52.5765 + 52.5765i 0.0747888 + 0.0747888i
\(704\) 618.549i 0.878621i
\(705\) 506.611 + 192.409i 0.718597 + 0.272920i
\(706\) −10.1225 −0.0143378
\(707\) −364.338 + 364.338i −0.515330 + 0.515330i
\(708\) 190.696 + 190.696i 0.269345 + 0.269345i
\(709\) 719.049i 1.01417i −0.861895 0.507087i \(-0.830722\pi\)
0.861895 0.507087i \(-0.169278\pi\)
\(710\) 98.5653 44.3041i 0.138824 0.0624001i
\(711\) −73.4847 −0.103354
\(712\) 145.893 145.893i 0.204906 0.204906i
\(713\) 123.555 + 123.555i 0.173289 + 0.173289i
\(714\) 65.8888i 0.0922812i
\(715\) 182.606 + 406.252i 0.255393 + 0.568185i
\(716\) 716.288 1.00040
\(717\) 423.514 423.514i 0.590675 0.590675i
\(718\) −10.8490 10.8490i −0.0151100 0.0151100i
\(719\) 605.271i 0.841824i 0.907101 + 0.420912i \(0.138290\pi\)
−0.907101 + 0.420912i \(0.861710\pi\)
\(720\) −78.8105 + 207.507i −0.109459 + 0.288205i
\(721\) −615.716 −0.853975
\(722\) 64.1339 64.1339i 0.0888282 0.0888282i
\(723\) −124.404 124.404i −0.172067 0.172067i
\(724\) 1116.17i 1.54167i
\(725\) 583.287 657.131i 0.804534 0.906387i
\(726\) −4.28724 −0.00590529
\(727\) −246.126 + 246.126i −0.338550 + 0.338550i −0.855821 0.517271i \(-0.826948\pi\)
0.517271 + 0.855821i \(0.326948\pi\)
\(728\) −67.9796 67.9796i −0.0933786 0.0933786i
\(729\) 27.0000i 0.0370370i
\(730\) −163.434 62.0714i −0.223882 0.0850294i
\(731\) 919.292 1.25758
\(732\) 28.2179 28.2179i 0.0385490 0.0385490i
\(733\) −270.763 270.763i −0.369390 0.369390i 0.497865 0.867255i \(-0.334118\pi\)
−0.867255 + 0.497865i \(0.834118\pi\)
\(734\) 65.8546i 0.0897202i
\(735\) −199.070 + 89.4801i −0.270844 + 0.121742i
\(736\) −240.869 −0.327268
\(737\) −511.828 + 511.828i −0.694474 + 0.694474i
\(738\) 0.469900 + 0.469900i 0.000636721 + 0.000636721i
\(739\) 515.666i 0.697789i 0.937162 + 0.348895i \(0.113443\pi\)
−0.937162 + 0.348895i \(0.886557\pi\)
\(740\) 68.3316 + 152.020i 0.0923400 + 0.205433i
\(741\) 118.243 0.159572
\(742\) −1.08061 + 1.08061i −0.00145635 + 0.00145635i
\(743\) 420.702 + 420.702i 0.566220 + 0.566220i 0.931067 0.364847i \(-0.118879\pi\)
−0.364847 + 0.931067i \(0.618879\pi\)
\(744\) 46.5153i 0.0625206i
\(745\) −150.637 + 396.626i −0.202197 + 0.532383i
\(746\) 38.7490 0.0519424
\(747\) −39.4393 + 39.4393i −0.0527969 + 0.0527969i
\(748\) −767.626 767.626i −1.02624 1.02624i
\(749\) 474.252i 0.633180i
\(750\) 31.8921 + 60.9773i 0.0425228 + 0.0813031i
\(751\) −859.787 −1.14486 −0.572428 0.819955i \(-0.693998\pi\)
−0.572428 + 0.819955i \(0.693998\pi\)
\(752\) −654.772 + 654.772i −0.870707 + 0.870707i
\(753\) 405.706 + 405.706i 0.538786 + 0.538786i
\(754\) 87.6867i 0.116295i
\(755\) −696.318 264.459i −0.922275 0.350276i
\(756\) 98.8332 0.130732
\(757\) −956.075 + 956.075i −1.26298 + 1.26298i −0.313337 + 0.949642i \(0.601447\pi\)
−0.949642 + 0.313337i \(0.898553\pi\)
\(758\) 47.1964 + 47.1964i 0.0622644 + 0.0622644i
\(759\) 321.081i 0.423031i
\(760\) −99.5755 + 44.7582i −0.131020 + 0.0588923i
\(761\) −322.758 −0.424124 −0.212062 0.977256i \(-0.568018\pi\)
−0.212062 + 0.977256i \(0.568018\pi\)
\(762\) −90.6255 + 90.6255i −0.118931 + 0.118931i
\(763\) −236.969 236.969i −0.310576 0.310576i
\(764\) 187.505i 0.245426i
\(765\) 150.879 + 335.666i 0.197227 + 0.438780i
\(766\) −4.77858 −0.00623835
\(767\) 221.655 221.655i 0.288990 0.288990i
\(768\) −237.316 237.316i −0.309005 0.309005i
\(769\) 692.402i 0.900393i −0.892930 0.450196i \(-0.851354\pi\)
0.892930 0.450196i \(-0.148646\pi\)
\(770\) −31.2372 + 82.2474i −0.0405678 + 0.106815i
\(771\) −81.4143 −0.105596
\(772\) 996.444 996.444i 1.29073 1.29073i
\(773\) 375.226 + 375.226i 0.485415 + 0.485415i 0.906856 0.421441i \(-0.138475\pi\)
−0.421441 + 0.906856i \(0.638475\pi\)
\(774\) 35.7276i 0.0461596i
\(775\) 200.000 + 177.526i 0.258065 + 0.229065i
\(776\) −87.3281 −0.112536
\(777\) 51.0806 51.0806i 0.0657408 0.0657408i
\(778\) 120.314 + 120.314i 0.154646 + 0.154646i
\(779\) 6.06123i 0.00778078i
\(780\) 247.782 + 94.1066i 0.317669 + 0.120650i
\(781\) −771.696 −0.988087
\(782\) −90.0704 + 90.0704i −0.115180 + 0.115180i
\(783\) −129.136 129.136i −0.164925 0.164925i
\(784\) 372.939i 0.475687i
\(785\) −108.697 + 48.8582i −0.138467 + 0.0622397i
\(786\) −58.4291 −0.0743373
\(787\) 910.990 910.990i 1.15755 1.15755i 0.172546 0.985001i \(-0.444801\pi\)
0.985001 0.172546i \(-0.0551993\pi\)
\(788\) −377.019 377.019i −0.478451 0.478451i
\(789\) 681.342i 0.863551i
\(790\) −15.9592 35.5051i −0.0202015 0.0449432i
\(791\) 673.626 0.851613
\(792\) −60.4393 + 60.4393i −0.0763122 + 0.0763122i
\(793\) −32.7990 32.7990i −0.0413606 0.0413606i
\(794\) 53.3735i 0.0672210i
\(795\) 3.03062 7.97959i 0.00381209 0.0100372i
\(796\) 750.967 0.943426
\(797\) −7.21683 + 7.21683i −0.00905500 + 0.00905500i −0.711620 0.702565i \(-0.752038\pi\)
0.702565 + 0.711620i \(0.252038\pi\)
\(798\) 16.5153 + 16.5153i 0.0206959 + 0.0206959i
\(799\) 1535.25i 1.92147i
\(800\) −367.991 + 21.9069i −0.459989 + 0.0273836i
\(801\) 246.545 0.307796
\(802\) 94.4607 94.4607i 0.117781 0.117781i
\(803\) 882.772 + 882.772i 1.09934 + 1.09934i
\(804\) 430.738i 0.535743i
\(805\) −372.474 141.464i −0.462701 0.175732i
\(806\) −26.6878 −0.0331114
\(807\) 598.287 598.287i 0.741372 0.741372i
\(808\) −187.504 187.504i −0.232059 0.232059i
\(809\) 150.000i 0.185414i 0.995693 + 0.0927070i \(0.0295520\pi\)
−0.995693 + 0.0927070i \(0.970448\pi\)
\(810\) 13.0454 5.86378i 0.0161054 0.00723923i
\(811\) 1336.85 1.64839 0.824197 0.566304i \(-0.191627\pi\)
0.824197 + 0.566304i \(0.191627\pi\)
\(812\) 472.702 472.702i 0.582145 0.582145i
\(813\) −161.146 161.146i −0.198212 0.198212i
\(814\) 30.8377i 0.0378842i
\(815\) −378.624 842.343i −0.464570 1.03355i
\(816\) −628.838 −0.770634
\(817\) −230.424 + 230.424i −0.282037 + 0.282037i
\(818\) 115.768 + 115.768i 0.141526 + 0.141526i
\(819\) 114.879i 0.140267i
\(820\) 4.82399 12.7015i 0.00588291 0.0154897i
\(821\) −33.8934 −0.0412830 −0.0206415 0.999787i \(-0.506571\pi\)
−0.0206415 + 0.999787i \(0.506571\pi\)
\(822\) 91.7321 91.7321i 0.111596 0.111596i
\(823\) 481.631 + 481.631i 0.585214 + 0.585214i 0.936331 0.351117i \(-0.114198\pi\)
−0.351117 + 0.936331i \(0.614198\pi\)
\(824\) 316.874i 0.384556i
\(825\) −29.2020 490.535i −0.0353964 0.594587i
\(826\) 61.9184 0.0749617
\(827\) 350.756 350.756i 0.424131 0.424131i −0.462492 0.886623i \(-0.653045\pi\)
0.886623 + 0.462492i \(0.153045\pi\)
\(828\) −135.106 135.106i −0.163171 0.163171i
\(829\) 697.423i 0.841283i 0.907227 + 0.420641i \(0.138195\pi\)
−0.907227 + 0.420641i \(0.861805\pi\)
\(830\) −27.6209 10.4903i −0.0332782 0.0126389i
\(831\) −248.647 −0.299214
\(832\) −302.531 + 302.531i −0.363619 + 0.363619i
\(833\) −437.217 437.217i −0.524870 0.524870i
\(834\) 105.242i 0.126189i
\(835\) 290.454 130.556i 0.347849 0.156355i
\(836\) 384.817 0.460308
\(837\) 39.3031 39.3031i 0.0469571 0.0469571i
\(838\) 19.9127 + 19.9127i 0.0237622 + 0.0237622i
\(839\) 72.3724i 0.0862604i −0.999069 0.0431302i \(-0.986267\pi\)
0.999069 0.0431302i \(-0.0137330\pi\)
\(840\) 43.4847 + 96.7423i 0.0517675 + 0.115169i
\(841\) −394.271 −0.468813
\(842\) −57.7934 + 57.7934i −0.0686382 + 0.0686382i
\(843\) −420.459 420.459i −0.498765 0.498765i
\(844\) 573.978i 0.680068i
\(845\) −190.633 + 501.936i −0.225602 + 0.594008i
\(846\) 59.6663 0.0705276
\(847\) 26.8638 26.8638i 0.0317164 0.0317164i
\(848\) 10.3133 + 10.3133i 0.0121619 + 0.0121619i
\(849\) 2.91939i 0.00343862i
\(850\) −129.414 + 145.798i −0.152252 + 0.171527i
\(851\) −139.655 −0.164107
\(852\) −324.717 + 324.717i −0.381124 + 0.381124i
\(853\) −74.5699 74.5699i −0.0874207 0.0874207i 0.662044 0.749465i \(-0.269689\pi\)
−0.749465 + 0.662044i \(0.769689\pi\)
\(854\) 9.16225i 0.0107286i
\(855\) −121.955 46.3179i −0.142637 0.0541729i
\(856\) 244.070 0.285129
\(857\) −293.176 + 293.176i −0.342096 + 0.342096i −0.857155 0.515059i \(-0.827770\pi\)
0.515059 + 0.857155i \(0.327770\pi\)
\(858\) 34.6765 + 34.6765i 0.0404155 + 0.0404155i
\(859\) 786.867i 0.916027i 0.888945 + 0.458014i \(0.151439\pi\)
−0.888945 + 0.458014i \(0.848561\pi\)
\(860\) −666.252 + 299.473i −0.774712 + 0.348225i
\(861\) −5.88877 −0.00683946
\(862\) 180.838 180.838i 0.209789 0.209789i
\(863\) −1072.68 1072.68i −1.24297 1.24297i −0.958764 0.284204i \(-0.908271\pi\)
−0.284204 0.958764i \(-0.591729\pi\)
\(864\) 76.6209i 0.0886816i
\(865\) −425.081 945.696i −0.491423 1.09329i
\(866\) −155.006 −0.178990
\(867\) −383.270 + 383.270i −0.442065 + 0.442065i
\(868\) 143.868 + 143.868i 0.165747 + 0.165747i
\(869\) 277.980i 0.319884i
\(870\) 34.3485 90.4393i 0.0394810 0.103953i
\(871\) 500.667 0.574819
\(872\) 121.955 121.955i 0.139856 0.139856i
\(873\) −73.7878 73.7878i −0.0845221 0.0845221i
\(874\) 45.1531i 0.0516626i
\(875\) −581.918 182.247i −0.665050 0.208283i
\(876\) 742.913 0.848074
\(877\) 239.460 239.460i 0.273044 0.273044i −0.557280 0.830324i \(-0.688155\pi\)
0.830324 + 0.557280i \(0.188155\pi\)
\(878\) −97.2985 97.2985i −0.110818 0.110818i
\(879\) 236.536i 0.269096i
\(880\) 784.964 + 298.126i 0.892004 + 0.338780i
\(881\) 62.8490 0.0713382 0.0356691 0.999364i \(-0.488644\pi\)
0.0356691 + 0.999364i \(0.488644\pi\)
\(882\) −16.9921 + 16.9921i −0.0192654 + 0.0192654i
\(883\) −158.061 158.061i −0.179005 0.179005i 0.611917 0.790922i \(-0.290399\pi\)
−0.790922 + 0.611917i \(0.790399\pi\)
\(884\) 750.888i 0.849421i
\(885\) −315.439 + 141.787i −0.356429 + 0.160211i
\(886\) 110.184 0.124361
\(887\) 30.2066 30.2066i 0.0340548 0.0340548i −0.689874 0.723929i \(-0.742334\pi\)
0.723929 + 0.689874i \(0.242334\pi\)
\(888\) 26.2883 + 26.2883i 0.0296039 + 0.0296039i
\(889\) 1135.72i 1.27752i
\(890\) 53.5439 + 119.121i 0.0601616 + 0.133844i
\(891\) −102.136 −0.114631
\(892\) −652.803 + 652.803i −0.731841 + 0.731841i
\(893\) −384.817 384.817i −0.430926 0.430926i
\(894\) 46.7128i 0.0522514i
\(895\) −326.135 + 858.712i −0.364397 + 0.959454i
\(896\) −372.247 −0.415455
\(897\) −157.040 + 157.040i −0.175072 + 0.175072i
\(898\) −86.7719 86.7719i −0.0966280 0.0966280i
\(899\) 375.959i 0.418197i
\(900\) −218.697 194.121i −0.242997 0.215690i
\(901\) 24.1816 0.0268387
\(902\) 1.77755 1.77755i 0.00197067 0.00197067i
\(903\) 223.868 + 223.868i 0.247916 + 0.247916i
\(904\) 346.677i 0.383492i
\(905\) 1338.10 + 508.207i 1.47857 + 0.561554i
\(906\) −82.0092 −0.0905179
\(907\) 571.342 571.342i 0.629925 0.629925i −0.318124 0.948049i \(-0.603053\pi\)
0.948049 + 0.318124i \(0.103053\pi\)
\(908\) 987.110 + 987.110i 1.08713 + 1.08713i
\(909\) 316.863i 0.348584i
\(910\) 55.5051 24.9490i 0.0609946 0.0274165i
\(911\) 173.362 0.190299 0.0951494 0.995463i \(-0.469667\pi\)
0.0951494 + 0.995463i \(0.469667\pi\)
\(912\) 157.621 157.621i 0.172830 0.172830i
\(913\) 149.192 + 149.192i 0.163408 + 0.163408i
\(914\) 100.572i 0.110035i
\(915\) 20.9806 + 46.6765i 0.0229296 + 0.0510126i
\(916\) −874.159 −0.954322
\(917\) 366.116 366.116i 0.399254 0.399254i
\(918\) 28.6515 + 28.6515i 0.0312108 + 0.0312108i
\(919\) 1147.42i 1.24856i −0.781202 0.624278i \(-0.785393\pi\)
0.781202 0.624278i \(-0.214607\pi\)
\(920\) 72.8036 191.691i 0.0791343 0.208360i
\(921\) 306.111 0.332368
\(922\) −162.405 + 162.405i −0.176144 + 0.176144i
\(923\) 377.435 + 377.435i 0.408922 + 0.408922i
\(924\) 373.868i 0.404619i
\(925\) −213.360 + 12.7015i −0.230659 + 0.0137314i
\(926\) −58.2995 −0.0629584
\(927\) 267.742 267.742i 0.288827 0.288827i
\(928\) 366.464 + 366.464i 0.394897 + 0.394897i
\(929\) 220.293i 0.237129i 0.992946 + 0.118565i \(0.0378292\pi\)
−0.992946 + 0.118565i \(0.962171\pi\)
\(930\) 27.5255 + 10.4541i 0.0295973 + 0.0112409i
\(931\) 219.181 0.235425
\(932\) 802.066 802.066i 0.860586 0.860586i
\(933\) 718.070 + 718.070i 0.769636 + 0.769636i
\(934\) 186.654i 0.199844i
\(935\) 1269.77 570.747i 1.35804 0.610425i
\(936\) 59.1214 0.0631639
\(937\) −396.090 + 396.090i −0.422721 + 0.422721i −0.886140 0.463418i \(-0.846623\pi\)
0.463418 + 0.886140i \(0.346623\pi\)
\(938\) 69.9296 + 69.9296i 0.0745518 + 0.0745518i
\(939\) 250.763i 0.267053i
\(940\) −500.132 1112.67i −0.532055 1.18369i
\(941\) 185.771 0.197419 0.0987093 0.995116i \(-0.468529\pi\)
0.0987093 + 0.995116i \(0.468529\pi\)
\(942\) −9.27806 + 9.27806i −0.00984932 + 0.00984932i
\(943\) 8.04999 + 8.04999i 0.00853658 + 0.00853658i
\(944\) 590.944i 0.626000i
\(945\) −45.0000 + 118.485i −0.0476190 + 0.125381i
\(946\) −135.151 −0.142866
\(947\) −845.190 + 845.190i −0.892492 + 0.892492i −0.994757 0.102265i \(-0.967391\pi\)
0.102265 + 0.994757i \(0.467391\pi\)
\(948\) 116.969 + 116.969i 0.123385 + 0.123385i
\(949\) 863.523i 0.909930i
\(950\) −4.10664 68.9831i −0.00432278 0.0726138i
\(951\) 266.463 0.280193
\(952\) −212.474 + 212.474i −0.223187 + 0.223187i
\(953\) −630.499 630.499i −0.661594 0.661594i 0.294161 0.955756i \(-0.404960\pi\)
−0.955756 + 0.294161i \(0.904960\pi\)
\(954\) 0.939800i 0.000985115i
\(955\) −224.788 85.3735i −0.235380 0.0893963i
\(956\) −1348.26 −1.41031
\(957\) −488.499 + 488.499i −0.510449 + 0.510449i
\(958\) −68.5357 68.5357i −0.0715404 0.0715404i
\(959\) 1149.58i 1.19873i
\(960\) 430.535 193.521i 0.448474 0.201584i
\(961\) −846.576 −0.880932
\(962\) 15.0827 15.0827i 0.0156785 0.0156785i
\(963\) 206.227 + 206.227i 0.214151 + 0.214151i
\(964\) 396.041i 0.410831i
\(965\) 740.879 + 1648.27i 0.767750 + 1.70805i
\(966\) −43.8684 −0.0454124
\(967\) −381.690 + 381.690i −0.394716 + 0.394716i −0.876364 0.481649i \(-0.840038\pi\)
0.481649 + 0.876364i \(0.340038\pi\)
\(968\) 13.8252 + 13.8252i 0.0142823 + 0.0142823i
\(969\) 369.576i 0.381399i
\(970\) 19.6265 51.6765i 0.0202335 0.0532748i
\(971\) −1000.44 −1.03032 −0.515159 0.857095i \(-0.672267\pi\)
−0.515159 + 0.857095i \(0.672267\pi\)
\(972\) −42.9773 + 42.9773i −0.0442153 + 0.0442153i
\(973\) 659.444 + 659.444i 0.677743 + 0.677743i
\(974\) 192.974i 0.198125i
\(975\) −225.637 + 254.202i −0.231422 + 0.260720i
\(976\) −87.4439 −0.0895941
\(977\) 593.662 593.662i 0.607637 0.607637i −0.334691 0.942328i \(-0.608632\pi\)
0.942328 + 0.334691i \(0.108632\pi\)
\(978\) −71.9000 71.9000i −0.0735174 0.0735174i
\(979\) 932.636i 0.952641i
\(980\) 459.301 + 174.441i 0.468674 + 0.178001i
\(981\) 206.091 0.210082
\(982\) −93.1158 + 93.1158i −0.0948226 + 0.0948226i
\(983\) −1217.34 1217.34i −1.23839 1.23839i −0.960659 0.277731i \(-0.910418\pi\)
−0.277731 0.960659i \(-0.589582\pi\)
\(984\) 3.03062i 0.00307989i
\(985\) 623.646 280.322i 0.633143 0.284591i
\(986\) 274.070 0.277962
\(987\) −373.868 + 373.868i −0.378793 + 0.378793i
\(988\) −188.213 188.213i −0.190499 0.190499i
\(989\) 612.059i 0.618867i
\(990\) −22.1816 49.3485i −0.0224057 0.0498469i
\(991\) −544.061 −0.549002 −0.274501 0.961587i \(-0.588513\pi\)
−0.274501 + 0.961587i \(0.588513\pi\)
\(992\) −111.535 + 111.535i −0.112434 + 0.112434i
\(993\) 300.581 + 300.581i 0.302700 + 0.302700i
\(994\) 105.435i 0.106071i
\(995\) −341.925 + 900.286i −0.343643 + 0.904810i
\(996\) 125.555 0.126059
\(997\) −316.733 + 316.733i −0.317686 + 0.317686i −0.847878 0.530192i \(-0.822120\pi\)
0.530192 + 0.847878i \(0.322120\pi\)
\(998\) −82.6128 82.6128i −0.0827783 0.0827783i
\(999\) 44.4245i 0.0444690i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 15.3.f.a.13.2 yes 4
3.2 odd 2 45.3.g.b.28.1 4
4.3 odd 2 240.3.bg.a.193.2 4
5.2 odd 4 inner 15.3.f.a.7.2 4
5.3 odd 4 75.3.f.c.7.1 4
5.4 even 2 75.3.f.c.43.1 4
8.3 odd 2 960.3.bg.h.193.1 4
8.5 even 2 960.3.bg.i.193.2 4
9.2 odd 6 405.3.l.f.28.2 8
9.4 even 3 405.3.l.h.298.2 8
9.5 odd 6 405.3.l.f.298.1 8
9.7 even 3 405.3.l.h.28.1 8
12.11 even 2 720.3.bh.k.433.2 4
15.2 even 4 45.3.g.b.37.1 4
15.8 even 4 225.3.g.a.82.2 4
15.14 odd 2 225.3.g.a.118.2 4
20.3 even 4 1200.3.bg.k.1057.1 4
20.7 even 4 240.3.bg.a.97.2 4
20.19 odd 2 1200.3.bg.k.193.1 4
40.27 even 4 960.3.bg.h.577.1 4
40.37 odd 4 960.3.bg.i.577.2 4
45.2 even 12 405.3.l.f.352.1 8
45.7 odd 12 405.3.l.h.352.2 8
45.22 odd 12 405.3.l.h.217.1 8
45.32 even 12 405.3.l.f.217.2 8
60.47 odd 4 720.3.bh.k.577.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
15.3.f.a.7.2 4 5.2 odd 4 inner
15.3.f.a.13.2 yes 4 1.1 even 1 trivial
45.3.g.b.28.1 4 3.2 odd 2
45.3.g.b.37.1 4 15.2 even 4
75.3.f.c.7.1 4 5.3 odd 4
75.3.f.c.43.1 4 5.4 even 2
225.3.g.a.82.2 4 15.8 even 4
225.3.g.a.118.2 4 15.14 odd 2
240.3.bg.a.97.2 4 20.7 even 4
240.3.bg.a.193.2 4 4.3 odd 2
405.3.l.f.28.2 8 9.2 odd 6
405.3.l.f.217.2 8 45.32 even 12
405.3.l.f.298.1 8 9.5 odd 6
405.3.l.f.352.1 8 45.2 even 12
405.3.l.h.28.1 8 9.7 even 3
405.3.l.h.217.1 8 45.22 odd 12
405.3.l.h.298.2 8 9.4 even 3
405.3.l.h.352.2 8 45.7 odd 12
720.3.bh.k.433.2 4 12.11 even 2
720.3.bh.k.577.2 4 60.47 odd 4
960.3.bg.h.193.1 4 8.3 odd 2
960.3.bg.h.577.1 4 40.27 even 4
960.3.bg.i.193.2 4 8.5 even 2
960.3.bg.i.577.2 4 40.37 odd 4
1200.3.bg.k.193.1 4 20.19 odd 2
1200.3.bg.k.1057.1 4 20.3 even 4