Properties

Label 637.2.e.m.508.2
Level $637$
Weight $2$
Character 637.508
Analytic conductor $5.086$
Analytic rank $0$
Dimension $10$
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] = [637,2,Mod(79,637)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(637, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.79");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.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: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + 8x^{8} + 7x^{7} + 41x^{6} + 18x^{5} + 58x^{4} + 28x^{3} + 64x^{2} + 16x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 508.2
Root \(-0.606661 - 1.05077i\) of defining polynomial
Character \(\chi\) \(=\) 637.508
Dual form 637.2.e.m.79.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.10666 - 1.91679i) q^{2} +(1.23721 - 2.14292i) q^{3} +(-1.44940 + 2.51043i) q^{4} +(-1.06140 - 1.83839i) q^{5} -5.47671 q^{6} +1.98932 q^{8} +(-1.56140 - 2.70442i) q^{9} +O(q^{10})\) \(q+(-1.10666 - 1.91679i) q^{2} +(1.23721 - 2.14292i) q^{3} +(-1.44940 + 2.51043i) q^{4} +(-1.06140 - 1.83839i) q^{5} -5.47671 q^{6} +1.98932 q^{8} +(-1.56140 - 2.70442i) q^{9} +(-2.34921 + 4.06896i) q^{10} +(-2.39448 + 4.14736i) q^{11} +(3.58643 + 6.21188i) q^{12} -1.00000 q^{13} -5.25271 q^{15} +(0.697291 + 1.20774i) q^{16} +(-1.88914 + 3.27208i) q^{17} +(-3.45588 + 5.98575i) q^{18} +(-1.78362 - 3.08931i) q^{19} +6.15355 q^{20} +10.5995 q^{22} +(-2.23721 - 3.87497i) q^{23} +(2.46122 - 4.26295i) q^{24} +(0.246870 - 0.427591i) q^{25} +(1.10666 + 1.91679i) q^{26} -0.303848 q^{27} -5.90107 q^{29} +(5.81296 + 10.0683i) q^{30} +(-1.88558 + 3.26592i) q^{31} +(3.53265 - 6.11873i) q^{32} +(5.92496 + 10.2623i) q^{33} +8.36254 q^{34} +9.05234 q^{36} +(-2.81285 - 4.87200i) q^{37} +(-3.94772 + 6.83765i) q^{38} +(-1.23721 + 2.14292i) q^{39} +(-2.11146 - 3.65716i) q^{40} -10.3948 q^{41} +3.40733 q^{43} +(-6.94110 - 12.0223i) q^{44} +(-3.31453 + 5.74093i) q^{45} +(-4.95168 + 8.57655i) q^{46} +(-3.55438 - 6.15636i) q^{47} +3.45079 q^{48} -1.09280 q^{50} +(4.67454 + 8.09654i) q^{51} +(1.44940 - 2.51043i) q^{52} +(6.19003 - 10.7214i) q^{53} +(0.336257 + 0.582415i) q^{54} +10.1660 q^{55} -8.82686 q^{57} +(6.53049 + 11.3111i) q^{58} +(2.39448 - 4.14736i) q^{59} +(7.61326 - 13.1865i) q^{60} +(1.60348 + 2.77732i) q^{61} +8.34680 q^{62} -12.8486 q^{64} +(1.06140 + 1.83839i) q^{65} +(13.1139 - 22.7139i) q^{66} +(1.44978 - 2.51109i) q^{67} +(-5.47622 - 9.48510i) q^{68} -11.0717 q^{69} -2.53876 q^{71} +(-3.10612 - 5.37996i) q^{72} +(3.85035 - 6.66901i) q^{73} +(-6.22574 + 10.7833i) q^{74} +(-0.610862 - 1.05804i) q^{75} +10.3407 q^{76} +5.47671 q^{78} +(2.58925 + 4.48471i) q^{79} +(1.48021 - 2.56379i) q^{80} +(4.30827 - 7.46214i) q^{81} +(11.5035 + 19.9247i) q^{82} -3.46731 q^{83} +8.02051 q^{85} +(-3.77076 - 6.53115i) q^{86} +(-7.30089 + 12.6455i) q^{87} +(-4.76338 + 8.25042i) q^{88} +(1.83216 + 3.17339i) q^{89} +14.6722 q^{90} +12.9704 q^{92} +(4.66574 + 8.08129i) q^{93} +(-7.86698 + 13.6260i) q^{94} +(-3.78625 + 6.55798i) q^{95} +(-8.74129 - 15.1404i) q^{96} +5.40733 q^{97} +14.9549 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 4 q^{2} - 8 q^{4} + 2 q^{5} + 10 q^{6} + 18 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 4 q^{2} - 8 q^{4} + 2 q^{5} + 10 q^{6} + 18 q^{8} - 3 q^{9} - 5 q^{10} - 11 q^{11} + 5 q^{12} - 10 q^{13} - 10 q^{16} - 5 q^{17} - 9 q^{18} + 9 q^{19} - 2 q^{20} + 16 q^{22} - 10 q^{23} - 9 q^{25} + 4 q^{26} - 6 q^{29} + 13 q^{30} - 6 q^{31} - 22 q^{32} + 8 q^{33} + 44 q^{34} + 14 q^{36} - 4 q^{37} - 10 q^{38} + 28 q^{40} - 28 q^{41} + 4 q^{43} - 32 q^{45} - 3 q^{46} + q^{47} + 46 q^{48} + 18 q^{50} + 8 q^{51} + 8 q^{52} - 17 q^{53} + 23 q^{54} - 32 q^{57} + 27 q^{58} + 11 q^{59} + 29 q^{60} - 11 q^{61} + 46 q^{62} + 18 q^{64} - 2 q^{65} + 21 q^{66} - 13 q^{67} - 32 q^{68} - 36 q^{69} + 30 q^{71} + 19 q^{72} + 33 q^{74} - 20 q^{75} - 16 q^{76} - 10 q^{78} - 2 q^{79} + 55 q^{80} + 19 q^{81} + 34 q^{82} - 12 q^{83} - 44 q^{85} - 28 q^{86} - 8 q^{87} + 3 q^{88} - 4 q^{89} + 68 q^{90} + 42 q^{92} - 18 q^{93} + 20 q^{94} + 12 q^{95} - 37 q^{96} + 24 q^{97} + 22 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.10666 1.91679i −0.782527 1.35538i −0.930465 0.366381i \(-0.880597\pi\)
0.147938 0.988997i \(-0.452737\pi\)
\(3\) 1.23721 2.14292i 0.714306 1.23721i −0.248921 0.968524i \(-0.580076\pi\)
0.963227 0.268690i \(-0.0865908\pi\)
\(4\) −1.44940 + 2.51043i −0.724699 + 1.25521i
\(5\) −1.06140 1.83839i −0.474671 0.822155i 0.524908 0.851159i \(-0.324100\pi\)
−0.999579 + 0.0290040i \(0.990766\pi\)
\(6\) −5.47671 −2.23586
\(7\) 0 0
\(8\) 1.98932 0.703331
\(9\) −1.56140 2.70442i −0.520466 0.901473i
\(10\) −2.34921 + 4.06896i −0.742887 + 1.28672i
\(11\) −2.39448 + 4.14736i −0.721962 + 1.25048i 0.238250 + 0.971204i \(0.423426\pi\)
−0.960212 + 0.279272i \(0.909907\pi\)
\(12\) 3.58643 + 6.21188i 1.03531 + 1.79321i
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −5.25271 −1.35624
\(16\) 0.697291 + 1.20774i 0.174323 + 0.301936i
\(17\) −1.88914 + 3.27208i −0.458183 + 0.793597i −0.998865 0.0476304i \(-0.984833\pi\)
0.540682 + 0.841227i \(0.318166\pi\)
\(18\) −3.45588 + 5.98575i −0.814558 + 1.41086i
\(19\) −1.78362 3.08931i −0.409190 0.708737i 0.585609 0.810593i \(-0.300855\pi\)
−0.994799 + 0.101856i \(0.967522\pi\)
\(20\) 6.15355 1.37597
\(21\) 0 0
\(22\) 10.5995 2.25982
\(23\) −2.23721 3.87497i −0.466491 0.807987i 0.532776 0.846256i \(-0.321149\pi\)
−0.999267 + 0.0382695i \(0.987815\pi\)
\(24\) 2.46122 4.26295i 0.502394 0.870171i
\(25\) 0.246870 0.427591i 0.0493740 0.0855182i
\(26\) 1.10666 + 1.91679i 0.217034 + 0.375914i
\(27\) −0.303848 −0.0584757
\(28\) 0 0
\(29\) −5.90107 −1.09580 −0.547901 0.836543i \(-0.684573\pi\)
−0.547901 + 0.836543i \(0.684573\pi\)
\(30\) 5.81296 + 10.0683i 1.06130 + 1.83822i
\(31\) −1.88558 + 3.26592i −0.338660 + 0.586577i −0.984181 0.177166i \(-0.943307\pi\)
0.645521 + 0.763743i \(0.276640\pi\)
\(32\) 3.53265 6.11873i 0.624490 1.08165i
\(33\) 5.92496 + 10.2623i 1.03140 + 1.78644i
\(34\) 8.36254 1.43416
\(35\) 0 0
\(36\) 9.05234 1.50872
\(37\) −2.81285 4.87200i −0.462429 0.800951i 0.536652 0.843804i \(-0.319689\pi\)
−0.999081 + 0.0428524i \(0.986355\pi\)
\(38\) −3.94772 + 6.83765i −0.640404 + 1.10921i
\(39\) −1.23721 + 2.14292i −0.198113 + 0.343141i
\(40\) −2.11146 3.65716i −0.333851 0.578247i
\(41\) −10.3948 −1.62340 −0.811698 0.584077i \(-0.801457\pi\)
−0.811698 + 0.584077i \(0.801457\pi\)
\(42\) 0 0
\(43\) 3.40733 0.519613 0.259807 0.965661i \(-0.416341\pi\)
0.259807 + 0.965661i \(0.416341\pi\)
\(44\) −6.94110 12.0223i −1.04641 1.81244i
\(45\) −3.31453 + 5.74093i −0.494101 + 0.855807i
\(46\) −4.95168 + 8.57655i −0.730085 + 1.26454i
\(47\) −3.55438 6.15636i −0.518459 0.897998i −0.999770 0.0214479i \(-0.993172\pi\)
0.481311 0.876550i \(-0.340161\pi\)
\(48\) 3.45079 0.498079
\(49\) 0 0
\(50\) −1.09280 −0.154546
\(51\) 4.67454 + 8.09654i 0.654566 + 1.13374i
\(52\) 1.44940 2.51043i 0.200995 0.348134i
\(53\) 6.19003 10.7214i 0.850266 1.47270i −0.0307027 0.999529i \(-0.509774\pi\)
0.880968 0.473175i \(-0.156892\pi\)
\(54\) 0.336257 + 0.582415i 0.0457588 + 0.0792566i
\(55\) 10.1660 1.37078
\(56\) 0 0
\(57\) −8.82686 −1.16915
\(58\) 6.53049 + 11.3111i 0.857495 + 1.48522i
\(59\) 2.39448 4.14736i 0.311734 0.539940i −0.667003 0.745055i \(-0.732423\pi\)
0.978738 + 0.205115i \(0.0657567\pi\)
\(60\) 7.61326 13.1865i 0.982867 1.70238i
\(61\) 1.60348 + 2.77732i 0.205305 + 0.355599i 0.950230 0.311550i \(-0.100848\pi\)
−0.744925 + 0.667148i \(0.767515\pi\)
\(62\) 8.34680 1.06004
\(63\) 0 0
\(64\) −12.8486 −1.60608
\(65\) 1.06140 + 1.83839i 0.131650 + 0.228025i
\(66\) 13.1139 22.7139i 1.61420 2.79588i
\(67\) 1.44978 2.51109i 0.177118 0.306778i −0.763774 0.645484i \(-0.776656\pi\)
0.940892 + 0.338706i \(0.109989\pi\)
\(68\) −5.47622 9.48510i −0.664090 1.15024i
\(69\) −11.0717 −1.33287
\(70\) 0 0
\(71\) −2.53876 −0.301295 −0.150648 0.988588i \(-0.548136\pi\)
−0.150648 + 0.988588i \(0.548136\pi\)
\(72\) −3.10612 5.37996i −0.366060 0.634034i
\(73\) 3.85035 6.66901i 0.450650 0.780548i −0.547777 0.836625i \(-0.684526\pi\)
0.998426 + 0.0560762i \(0.0178590\pi\)
\(74\) −6.22574 + 10.7833i −0.723727 + 1.25353i
\(75\) −0.610862 1.05804i −0.0705362 0.122172i
\(76\) 10.3407 1.18616
\(77\) 0 0
\(78\) 5.47671 0.620115
\(79\) 2.58925 + 4.48471i 0.291313 + 0.504569i 0.974120 0.226029i \(-0.0725745\pi\)
−0.682807 + 0.730598i \(0.739241\pi\)
\(80\) 1.48021 2.56379i 0.165492 0.286641i
\(81\) 4.30827 7.46214i 0.478696 0.829126i
\(82\) 11.5035 + 19.9247i 1.27035 + 2.20032i
\(83\) −3.46731 −0.380587 −0.190294 0.981727i \(-0.560944\pi\)
−0.190294 + 0.981727i \(0.560944\pi\)
\(84\) 0 0
\(85\) 8.02051 0.869946
\(86\) −3.77076 6.53115i −0.406612 0.704272i
\(87\) −7.30089 + 12.6455i −0.782738 + 1.35574i
\(88\) −4.76338 + 8.25042i −0.507778 + 0.879498i
\(89\) 1.83216 + 3.17339i 0.194209 + 0.336379i 0.946641 0.322291i \(-0.104453\pi\)
−0.752432 + 0.658670i \(0.771119\pi\)
\(90\) 14.6722 1.54659
\(91\) 0 0
\(92\) 12.9704 1.35226
\(93\) 4.66574 + 8.08129i 0.483814 + 0.837991i
\(94\) −7.86698 + 13.6260i −0.811417 + 1.40542i
\(95\) −3.78625 + 6.55798i −0.388461 + 0.672835i
\(96\) −8.74129 15.1404i −0.892154 1.54526i
\(97\) 5.40733 0.549031 0.274516 0.961583i \(-0.411482\pi\)
0.274516 + 0.961583i \(0.411482\pi\)
\(98\) 0 0
\(99\) 14.9549 1.50303
\(100\) 0.715625 + 1.23950i 0.0715625 + 0.123950i
\(101\) 4.65862 8.06897i 0.463550 0.802892i −0.535585 0.844482i \(-0.679909\pi\)
0.999135 + 0.0415891i \(0.0132420\pi\)
\(102\) 10.3463 17.9202i 1.02443 1.77437i
\(103\) 3.65318 + 6.32749i 0.359958 + 0.623466i 0.987953 0.154751i \(-0.0494576\pi\)
−0.627995 + 0.778217i \(0.716124\pi\)
\(104\) −1.98932 −0.195069
\(105\) 0 0
\(106\) −27.4011 −2.66143
\(107\) −3.37365 5.84333i −0.326143 0.564896i 0.655600 0.755108i \(-0.272416\pi\)
−0.981743 + 0.190212i \(0.939082\pi\)
\(108\) 0.440397 0.762790i 0.0423772 0.0733995i
\(109\) −2.08822 + 3.61691i −0.200016 + 0.346437i −0.948533 0.316678i \(-0.897433\pi\)
0.748518 + 0.663115i \(0.230766\pi\)
\(110\) −11.2503 19.4861i −1.07267 1.85792i
\(111\) −13.9204 −1.32126
\(112\) 0 0
\(113\) 5.90107 0.555126 0.277563 0.960707i \(-0.410473\pi\)
0.277563 + 0.960707i \(0.410473\pi\)
\(114\) 9.76834 + 16.9193i 0.914889 + 1.58463i
\(115\) −4.74915 + 8.22577i −0.442860 + 0.767057i
\(116\) 8.55300 14.8142i 0.794126 1.37547i
\(117\) 1.56140 + 2.70442i 0.144351 + 0.250024i
\(118\) −10.5995 −0.975763
\(119\) 0 0
\(120\) −10.4493 −0.953888
\(121\) −5.96705 10.3352i −0.542459 0.939567i
\(122\) 3.54903 6.14709i 0.321314 0.556532i
\(123\) −12.8606 + 22.2752i −1.15960 + 2.00849i
\(124\) −5.46591 9.46724i −0.490853 0.850183i
\(125\) −11.6621 −1.04309
\(126\) 0 0
\(127\) −10.5268 −0.934100 −0.467050 0.884231i \(-0.654683\pi\)
−0.467050 + 0.884231i \(0.654683\pi\)
\(128\) 7.15377 + 12.3907i 0.632309 + 1.09519i
\(129\) 4.21560 7.30163i 0.371163 0.642873i
\(130\) 2.34921 4.06896i 0.206040 0.356871i
\(131\) 2.71204 + 4.69740i 0.236952 + 0.410413i 0.959838 0.280554i \(-0.0905182\pi\)
−0.722886 + 0.690967i \(0.757185\pi\)
\(132\) −34.3505 −2.98983
\(133\) 0 0
\(134\) −6.41765 −0.554400
\(135\) 0.322504 + 0.558593i 0.0277567 + 0.0480761i
\(136\) −3.75810 + 6.50922i −0.322255 + 0.558161i
\(137\) −11.1224 + 19.2645i −0.950248 + 1.64588i −0.205363 + 0.978686i \(0.565837\pi\)
−0.744886 + 0.667192i \(0.767496\pi\)
\(138\) 12.2526 + 21.2221i 1.04301 + 1.80654i
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) −17.5901 −1.48135
\(142\) 2.80955 + 4.86628i 0.235772 + 0.408369i
\(143\) 2.39448 4.14736i 0.200236 0.346819i
\(144\) 2.17750 3.77153i 0.181458 0.314294i
\(145\) 6.26338 + 10.8485i 0.520146 + 0.900919i
\(146\) −17.0441 −1.41058
\(147\) 0 0
\(148\) 16.3077 1.34049
\(149\) −1.47736 2.55887i −0.121030 0.209630i 0.799144 0.601140i \(-0.205286\pi\)
−0.920174 + 0.391509i \(0.871953\pi\)
\(150\) −1.35203 + 2.34179i −0.110393 + 0.191206i
\(151\) 9.27736 16.0689i 0.754981 1.30766i −0.190403 0.981706i \(-0.560980\pi\)
0.945384 0.325959i \(-0.105687\pi\)
\(152\) −3.54818 6.14564i −0.287796 0.498477i
\(153\) 11.7988 0.953875
\(154\) 0 0
\(155\) 8.00541 0.643010
\(156\) −3.58643 6.21188i −0.287144 0.497348i
\(157\) −4.89982 + 8.48673i −0.391048 + 0.677315i −0.992588 0.121528i \(-0.961221\pi\)
0.601540 + 0.798843i \(0.294554\pi\)
\(158\) 5.73084 9.92610i 0.455921 0.789678i
\(159\) −15.3168 26.5294i −1.21470 2.10392i
\(160\) −14.9982 −1.18571
\(161\) 0 0
\(162\) −19.0712 −1.49837
\(163\) −6.91709 11.9808i −0.541788 0.938405i −0.998801 0.0489451i \(-0.984414\pi\)
0.457013 0.889460i \(-0.348919\pi\)
\(164\) 15.0662 26.0954i 1.17647 2.03771i
\(165\) 12.5775 21.7848i 0.979156 1.69595i
\(166\) 3.83714 + 6.64612i 0.297820 + 0.515839i
\(167\) −17.3534 −1.34285 −0.671424 0.741073i \(-0.734317\pi\)
−0.671424 + 0.741073i \(0.734317\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) −8.87598 15.3737i −0.680757 1.17911i
\(171\) −5.56987 + 9.64730i −0.425939 + 0.737747i
\(172\) −4.93858 + 8.55387i −0.376563 + 0.652226i
\(173\) −1.48069 2.56463i −0.112575 0.194985i 0.804233 0.594314i \(-0.202576\pi\)
−0.916808 + 0.399329i \(0.869243\pi\)
\(174\) 32.3184 2.45005
\(175\) 0 0
\(176\) −6.67859 −0.503418
\(177\) −5.92496 10.2623i −0.445348 0.771365i
\(178\) 4.05516 7.02374i 0.303947 0.526452i
\(179\) 2.83444 4.90939i 0.211856 0.366945i −0.740440 0.672123i \(-0.765383\pi\)
0.952295 + 0.305178i \(0.0987159\pi\)
\(180\) −9.60813 16.6418i −0.716148 1.24040i
\(181\) −7.17645 −0.533421 −0.266711 0.963777i \(-0.585937\pi\)
−0.266711 + 0.963777i \(0.585937\pi\)
\(182\) 0 0
\(183\) 7.93541 0.586603
\(184\) −4.45054 7.70855i −0.328098 0.568282i
\(185\) −5.97110 + 10.3423i −0.439004 + 0.760377i
\(186\) 10.3268 17.8865i 0.757196 1.31150i
\(187\) −9.04700 15.6699i −0.661582 1.14589i
\(188\) 20.6068 1.50291
\(189\) 0 0
\(190\) 16.7604 1.21593
\(191\) −5.94088 10.2899i −0.429867 0.744552i 0.566994 0.823722i \(-0.308106\pi\)
−0.996861 + 0.0791703i \(0.974773\pi\)
\(192\) −15.8965 + 27.5335i −1.14723 + 1.98706i
\(193\) −11.4851 + 19.8927i −0.826714 + 1.43191i 0.0738876 + 0.997267i \(0.476459\pi\)
−0.900602 + 0.434645i \(0.856874\pi\)
\(194\) −5.98408 10.3647i −0.429632 0.744145i
\(195\) 5.25271 0.376154
\(196\) 0 0
\(197\) 16.9216 1.20561 0.602806 0.797888i \(-0.294049\pi\)
0.602806 + 0.797888i \(0.294049\pi\)
\(198\) −16.5500 28.6655i −1.17616 2.03717i
\(199\) 5.02953 8.71140i 0.356534 0.617535i −0.630845 0.775909i \(-0.717292\pi\)
0.987379 + 0.158374i \(0.0506251\pi\)
\(200\) 0.491103 0.850616i 0.0347262 0.0601476i
\(201\) −3.58737 6.21351i −0.253034 0.438267i
\(202\) −20.6221 −1.45096
\(203\) 0 0
\(204\) −27.1010 −1.89745
\(205\) 11.0330 + 19.1098i 0.770580 + 1.33468i
\(206\) 8.08566 14.0048i 0.563355 0.975759i
\(207\) −6.98636 + 12.1007i −0.485586 + 0.841059i
\(208\) −0.697291 1.20774i −0.0483484 0.0837419i
\(209\) 17.0833 1.18168
\(210\) 0 0
\(211\) −24.4609 −1.68396 −0.841978 0.539512i \(-0.818609\pi\)
−0.841978 + 0.539512i \(0.818609\pi\)
\(212\) 17.9436 + 31.0793i 1.23237 + 2.13453i
\(213\) −3.14099 + 5.44035i −0.215217 + 0.372767i
\(214\) −7.46697 + 12.9332i −0.510431 + 0.884093i
\(215\) −3.61654 6.26402i −0.246646 0.427203i
\(216\) −0.604452 −0.0411277
\(217\) 0 0
\(218\) 9.24382 0.626071
\(219\) −9.52742 16.5020i −0.643804 1.11510i
\(220\) −14.7345 + 25.5210i −0.993402 + 1.72062i
\(221\) 1.88914 3.27208i 0.127077 0.220104i
\(222\) 15.4051 + 26.6825i 1.03393 + 1.79081i
\(223\) 29.2625 1.95956 0.979780 0.200076i \(-0.0641188\pi\)
0.979780 + 0.200076i \(0.0641188\pi\)
\(224\) 0 0
\(225\) −1.54185 −0.102790
\(226\) −6.53049 11.3111i −0.434401 0.752405i
\(227\) −5.03685 + 8.72408i −0.334307 + 0.579038i −0.983352 0.181713i \(-0.941836\pi\)
0.649044 + 0.760751i \(0.275169\pi\)
\(228\) 12.7936 22.1592i 0.847279 1.46753i
\(229\) −5.56997 9.64748i −0.368074 0.637523i 0.621190 0.783660i \(-0.286649\pi\)
−0.989264 + 0.146137i \(0.953316\pi\)
\(230\) 21.0228 1.38620
\(231\) 0 0
\(232\) −11.7391 −0.770711
\(233\) 8.54166 + 14.7946i 0.559583 + 0.969226i 0.997531 + 0.0702257i \(0.0223720\pi\)
−0.437948 + 0.899000i \(0.644295\pi\)
\(234\) 3.45588 5.98575i 0.225918 0.391301i
\(235\) −7.54522 + 13.0687i −0.492196 + 0.852508i
\(236\) 6.94110 + 12.0223i 0.451827 + 0.782587i
\(237\) 12.8138 0.832347
\(238\) 0 0
\(239\) 6.92142 0.447710 0.223855 0.974622i \(-0.428136\pi\)
0.223855 + 0.974622i \(0.428136\pi\)
\(240\) −3.66266 6.34392i −0.236424 0.409498i
\(241\) 3.24812 5.62592i 0.209230 0.362397i −0.742242 0.670132i \(-0.766238\pi\)
0.951472 + 0.307735i \(0.0995709\pi\)
\(242\) −13.2070 + 22.8752i −0.848978 + 1.47047i
\(243\) −11.1163 19.2539i −0.713109 1.23514i
\(244\) −9.29634 −0.595137
\(245\) 0 0
\(246\) 56.9293 3.62968
\(247\) 1.78362 + 3.08931i 0.113489 + 0.196568i
\(248\) −3.75103 + 6.49697i −0.238190 + 0.412558i
\(249\) −4.28981 + 7.43017i −0.271856 + 0.470868i
\(250\) 12.9060 + 22.3538i 0.816246 + 1.41378i
\(251\) 9.86804 0.622865 0.311433 0.950268i \(-0.399191\pi\)
0.311433 + 0.950268i \(0.399191\pi\)
\(252\) 0 0
\(253\) 21.4278 1.34716
\(254\) 11.6496 + 20.1776i 0.730959 + 1.26606i
\(255\) 9.92309 17.1873i 0.621408 1.07631i
\(256\) 2.98497 5.17012i 0.186560 0.323132i
\(257\) 3.43234 + 5.94499i 0.214104 + 0.370838i 0.952995 0.302986i \(-0.0979836\pi\)
−0.738891 + 0.673825i \(0.764650\pi\)
\(258\) −18.6610 −1.16178
\(259\) 0 0
\(260\) −6.15355 −0.381627
\(261\) 9.21392 + 15.9590i 0.570327 + 0.987836i
\(262\) 6.00262 10.3969i 0.370843 0.642320i
\(263\) 0.0632753 0.109596i 0.00390172 0.00675798i −0.864068 0.503375i \(-0.832091\pi\)
0.867970 + 0.496617i \(0.165425\pi\)
\(264\) 11.7867 + 20.4151i 0.725418 + 1.25646i
\(265\) −26.2803 −1.61439
\(266\) 0 0
\(267\) 9.06710 0.554897
\(268\) 4.20261 + 7.27913i 0.256715 + 0.444643i
\(269\) −2.12154 + 3.67462i −0.129353 + 0.224045i −0.923426 0.383777i \(-0.874623\pi\)
0.794073 + 0.607822i \(0.207957\pi\)
\(270\) 0.713805 1.23635i 0.0434408 0.0752417i
\(271\) 0.783616 + 1.35726i 0.0476013 + 0.0824479i 0.888844 0.458209i \(-0.151509\pi\)
−0.841243 + 0.540657i \(0.818176\pi\)
\(272\) −5.26911 −0.319487
\(273\) 0 0
\(274\) 49.2348 2.97438
\(275\) 1.18225 + 2.04771i 0.0712923 + 0.123482i
\(276\) 16.0472 27.7946i 0.965929 1.67304i
\(277\) 6.37260 11.0377i 0.382892 0.663189i −0.608582 0.793491i \(-0.708261\pi\)
0.991474 + 0.130302i \(0.0415947\pi\)
\(278\) −4.42664 7.66717i −0.265492 0.459846i
\(279\) 11.7766 0.705045
\(280\) 0 0
\(281\) 4.62986 0.276194 0.138097 0.990419i \(-0.455901\pi\)
0.138097 + 0.990419i \(0.455901\pi\)
\(282\) 19.4663 + 33.7166i 1.15920 + 2.00779i
\(283\) 1.82416 3.15954i 0.108435 0.187815i −0.806701 0.590959i \(-0.798749\pi\)
0.915136 + 0.403144i \(0.132083\pi\)
\(284\) 3.67967 6.37338i 0.218348 0.378190i
\(285\) 9.36881 + 16.2273i 0.554960 + 0.961220i
\(286\) −10.5995 −0.626762
\(287\) 0 0
\(288\) −22.0635 −1.30010
\(289\) 1.36231 + 2.35959i 0.0801360 + 0.138800i
\(290\) 13.8629 24.0112i 0.814057 1.40999i
\(291\) 6.69003 11.5875i 0.392176 0.679269i
\(292\) 11.1614 + 19.3321i 0.653171 + 1.13132i
\(293\) 21.0415 1.22926 0.614630 0.788816i \(-0.289305\pi\)
0.614630 + 0.788816i \(0.289305\pi\)
\(294\) 0 0
\(295\) −10.1660 −0.591886
\(296\) −5.59566 9.69196i −0.325241 0.563334i
\(297\) 0.727559 1.26017i 0.0422172 0.0731224i
\(298\) −3.26988 + 5.66359i −0.189419 + 0.328083i
\(299\) 2.23721 + 3.87497i 0.129381 + 0.224095i
\(300\) 3.54152 0.204470
\(301\) 0 0
\(302\) −41.0676 −2.36317
\(303\) −11.5274 19.9661i −0.662233 1.14702i
\(304\) 2.48740 4.30830i 0.142662 0.247098i
\(305\) 3.40387 5.89567i 0.194905 0.337585i
\(306\) −13.0573 22.6158i −0.746434 1.29286i
\(307\) 4.95861 0.283003 0.141502 0.989938i \(-0.454807\pi\)
0.141502 + 0.989938i \(0.454807\pi\)
\(308\) 0 0
\(309\) 18.0791 1.02848
\(310\) −8.85927 15.3447i −0.503173 0.871521i
\(311\) −1.21079 + 2.09715i −0.0686575 + 0.118918i −0.898311 0.439361i \(-0.855205\pi\)
0.829653 + 0.558279i \(0.188538\pi\)
\(312\) −2.46122 + 4.26295i −0.139339 + 0.241342i
\(313\) 6.98026 + 12.0902i 0.394548 + 0.683377i 0.993043 0.117749i \(-0.0375679\pi\)
−0.598496 + 0.801126i \(0.704235\pi\)
\(314\) 21.6897 1.22402
\(315\) 0 0
\(316\) −15.0114 −0.844457
\(317\) −1.53431 2.65750i −0.0861753 0.149260i 0.819716 0.572770i \(-0.194131\pi\)
−0.905891 + 0.423510i \(0.860798\pi\)
\(318\) −33.9010 + 58.7182i −1.90107 + 3.29275i
\(319\) 14.1300 24.4739i 0.791127 1.37027i
\(320\) 13.6375 + 23.6208i 0.762359 + 1.32044i
\(321\) −16.6957 −0.931863
\(322\) 0 0
\(323\) 13.4780 0.749936
\(324\) 12.4888 + 21.6312i 0.693821 + 1.20173i
\(325\) −0.246870 + 0.427591i −0.0136939 + 0.0237185i
\(326\) −15.3098 + 26.5173i −0.847929 + 1.46866i
\(327\) 5.16716 + 8.94978i 0.285745 + 0.494924i
\(328\) −20.6786 −1.14179
\(329\) 0 0
\(330\) −55.6761 −3.06487
\(331\) −6.80261 11.7825i −0.373905 0.647623i 0.616257 0.787545i \(-0.288648\pi\)
−0.990162 + 0.139922i \(0.955315\pi\)
\(332\) 5.02551 8.70445i 0.275811 0.477719i
\(333\) −8.78395 + 15.2142i −0.481358 + 0.833736i
\(334\) 19.2044 + 33.2629i 1.05082 + 1.82007i
\(335\) −6.15516 −0.336292
\(336\) 0 0
\(337\) −35.1646 −1.91554 −0.957769 0.287538i \(-0.907163\pi\)
−0.957769 + 0.287538i \(0.907163\pi\)
\(338\) −1.10666 1.91679i −0.0601944 0.104260i
\(339\) 7.30089 12.6455i 0.396530 0.686810i
\(340\) −11.6249 + 20.1349i −0.630449 + 1.09197i
\(341\) −9.02997 15.6404i −0.489000 0.846973i
\(342\) 24.6558 1.33323
\(343\) 0 0
\(344\) 6.77828 0.365460
\(345\) 11.7514 + 20.3541i 0.632676 + 1.09583i
\(346\) −3.27724 + 5.67635i −0.176186 + 0.305162i
\(347\) 2.73551 4.73804i 0.146850 0.254351i −0.783212 0.621755i \(-0.786420\pi\)
0.930062 + 0.367404i \(0.119753\pi\)
\(348\) −21.1638 36.6567i −1.13450 1.96501i
\(349\) −4.34196 −0.232420 −0.116210 0.993225i \(-0.537075\pi\)
−0.116210 + 0.993225i \(0.537075\pi\)
\(350\) 0 0
\(351\) 0.303848 0.0162182
\(352\) 16.9177 + 29.3023i 0.901717 + 1.56182i
\(353\) 13.7996 23.9016i 0.734479 1.27216i −0.220472 0.975393i \(-0.570760\pi\)
0.954951 0.296762i \(-0.0959068\pi\)
\(354\) −13.1139 + 22.7139i −0.696993 + 1.20723i
\(355\) 2.69463 + 4.66724i 0.143016 + 0.247712i
\(356\) −10.6221 −0.562971
\(357\) 0 0
\(358\) −12.5470 −0.663132
\(359\) −3.31427 5.74049i −0.174921 0.302971i 0.765213 0.643777i \(-0.222634\pi\)
−0.940134 + 0.340806i \(0.889300\pi\)
\(360\) −6.59366 + 11.4206i −0.347516 + 0.601916i
\(361\) 3.13742 5.43418i 0.165128 0.286009i
\(362\) 7.94189 + 13.7558i 0.417417 + 0.722987i
\(363\) −29.5301 −1.54993
\(364\) 0 0
\(365\) −16.3470 −0.855643
\(366\) −8.78181 15.2105i −0.459033 0.795068i
\(367\) 15.6037 27.0264i 0.814506 1.41077i −0.0951768 0.995460i \(-0.530342\pi\)
0.909682 0.415305i \(-0.136325\pi\)
\(368\) 3.11998 5.40396i 0.162640 0.281701i
\(369\) 16.2304 + 28.1119i 0.844923 + 1.46345i
\(370\) 26.4319 1.37413
\(371\) 0 0
\(372\) −27.0500 −1.40248
\(373\) 7.88730 + 13.6612i 0.408389 + 0.707350i 0.994709 0.102729i \(-0.0327574\pi\)
−0.586321 + 0.810079i \(0.699424\pi\)
\(374\) −20.0239 + 34.6825i −1.03541 + 1.79339i
\(375\) −14.4285 + 24.9909i −0.745084 + 1.29052i
\(376\) −7.07080 12.2470i −0.364649 0.631590i
\(377\) 5.90107 0.303921
\(378\) 0 0
\(379\) 31.6512 1.62581 0.812907 0.582393i \(-0.197884\pi\)
0.812907 + 0.582393i \(0.197884\pi\)
\(380\) −10.9756 19.0102i −0.563035 0.975205i
\(381\) −13.0239 + 22.5580i −0.667233 + 1.15568i
\(382\) −13.1491 + 22.7749i −0.672766 + 1.16526i
\(383\) 6.19675 + 10.7331i 0.316639 + 0.548435i 0.979785 0.200055i \(-0.0641122\pi\)
−0.663145 + 0.748491i \(0.730779\pi\)
\(384\) 35.4030 1.80665
\(385\) 0 0
\(386\) 50.8404 2.58771
\(387\) −5.32020 9.21486i −0.270441 0.468418i
\(388\) −7.83737 + 13.5747i −0.397882 + 0.689152i
\(389\) 7.03705 12.1885i 0.356792 0.617983i −0.630631 0.776083i \(-0.717204\pi\)
0.987423 + 0.158100i \(0.0505370\pi\)
\(390\) −5.81296 10.0683i −0.294351 0.509831i
\(391\) 16.9056 0.854954
\(392\) 0 0
\(393\) 13.4215 0.677026
\(394\) −18.7265 32.4352i −0.943425 1.63406i
\(395\) 5.49644 9.52012i 0.276556 0.479009i
\(396\) −21.6756 + 37.5433i −1.08924 + 1.88662i
\(397\) −3.48652 6.03884i −0.174984 0.303081i 0.765172 0.643826i \(-0.222654\pi\)
−0.940156 + 0.340745i \(0.889321\pi\)
\(398\) −22.2639 −1.11599
\(399\) 0 0
\(400\) 0.688560 0.0344280
\(401\) −1.36841 2.37016i −0.0683352 0.118360i 0.829833 0.558011i \(-0.188435\pi\)
−0.898169 + 0.439651i \(0.855102\pi\)
\(402\) −7.94000 + 13.7525i −0.396011 + 0.685912i
\(403\) 1.88558 3.26592i 0.0939275 0.162687i
\(404\) 13.5044 + 23.3903i 0.671868 + 1.16371i
\(405\) −18.2911 −0.908894
\(406\) 0 0
\(407\) 26.9412 1.33543
\(408\) 9.29915 + 16.1066i 0.460377 + 0.797396i
\(409\) −12.2577 + 21.2309i −0.606104 + 1.04980i 0.385772 + 0.922594i \(0.373935\pi\)
−0.991876 + 0.127208i \(0.959398\pi\)
\(410\) 24.4196 42.2961i 1.20600 2.08885i
\(411\) 27.5215 + 47.6686i 1.35754 + 2.35132i
\(412\) −21.1796 −1.04345
\(413\) 0 0
\(414\) 30.9261 1.51994
\(415\) 3.68020 + 6.37429i 0.180654 + 0.312902i
\(416\) −3.53265 + 6.11873i −0.173202 + 0.299995i
\(417\) 4.94886 8.57167i 0.242347 0.419757i
\(418\) −18.9054 32.7452i −0.924696 1.60162i
\(419\) 3.01252 0.147171 0.0735856 0.997289i \(-0.476556\pi\)
0.0735856 + 0.997289i \(0.476556\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 27.0699 + 46.8864i 1.31774 + 2.28240i
\(423\) −11.0996 + 19.2251i −0.539681 + 0.934755i
\(424\) 12.3140 21.3284i 0.598018 1.03580i
\(425\) 0.932742 + 1.61556i 0.0452447 + 0.0783660i
\(426\) 13.9040 0.673653
\(427\) 0 0
\(428\) 19.5590 0.945421
\(429\) −5.92496 10.2623i −0.286060 0.495470i
\(430\) −8.00456 + 13.8643i −0.386014 + 0.668596i
\(431\) 9.39711 16.2763i 0.452643 0.784001i −0.545906 0.837846i \(-0.683815\pi\)
0.998549 + 0.0538455i \(0.0171478\pi\)
\(432\) −0.211871 0.366971i −0.0101936 0.0176559i
\(433\) 7.76911 0.373360 0.186680 0.982421i \(-0.440227\pi\)
0.186680 + 0.982421i \(0.440227\pi\)
\(434\) 0 0
\(435\) 30.9966 1.48617
\(436\) −6.05333 10.4847i −0.289902 0.502125i
\(437\) −7.98066 + 13.8229i −0.381767 + 0.661240i
\(438\) −21.0873 + 36.5242i −1.00759 + 1.74519i
\(439\) −18.9841 32.8814i −0.906060 1.56934i −0.819488 0.573096i \(-0.805742\pi\)
−0.0865713 0.996246i \(-0.527591\pi\)
\(440\) 20.2234 0.964112
\(441\) 0 0
\(442\) −8.36254 −0.397766
\(443\) −17.8135 30.8539i −0.846344 1.46591i −0.884449 0.466637i \(-0.845465\pi\)
0.0381050 0.999274i \(-0.487868\pi\)
\(444\) 20.1762 34.9461i 0.957518 1.65847i
\(445\) 3.88930 6.73647i 0.184371 0.319339i
\(446\) −32.3837 56.0901i −1.53341 2.65594i
\(447\) −7.31125 −0.345810
\(448\) 0 0
\(449\) −8.05285 −0.380038 −0.190019 0.981780i \(-0.560855\pi\)
−0.190019 + 0.981780i \(0.560855\pi\)
\(450\) 1.70630 + 2.95540i 0.0804359 + 0.139319i
\(451\) 24.8901 43.1110i 1.17203 2.03002i
\(452\) −8.55300 + 14.8142i −0.402299 + 0.696803i
\(453\) −22.9562 39.7612i −1.07857 1.86815i
\(454\) 22.2963 1.04642
\(455\) 0 0
\(456\) −17.5595 −0.822297
\(457\) −7.79881 13.5079i −0.364813 0.631875i 0.623933 0.781478i \(-0.285534\pi\)
−0.988746 + 0.149603i \(0.952200\pi\)
\(458\) −12.3281 + 21.3530i −0.576056 + 0.997759i
\(459\) 0.574012 0.994218i 0.0267926 0.0464061i
\(460\) −13.7668 23.8448i −0.641880 1.11177i
\(461\) 25.6991 1.19692 0.598462 0.801151i \(-0.295779\pi\)
0.598462 + 0.801151i \(0.295779\pi\)
\(462\) 0 0
\(463\) −20.5209 −0.953685 −0.476842 0.878989i \(-0.658219\pi\)
−0.476842 + 0.878989i \(0.658219\pi\)
\(464\) −4.11476 7.12698i −0.191023 0.330862i
\(465\) 9.90440 17.1549i 0.459306 0.795541i
\(466\) 18.9054 32.7452i 0.875778 1.51689i
\(467\) 5.91241 + 10.2406i 0.273594 + 0.473878i 0.969779 0.243984i \(-0.0784543\pi\)
−0.696186 + 0.717862i \(0.745121\pi\)
\(468\) −9.05234 −0.418445
\(469\) 0 0
\(470\) 33.4000 1.54063
\(471\) 12.1242 + 20.9998i 0.558656 + 0.967620i
\(472\) 4.76338 8.25042i 0.219253 0.379757i
\(473\) −8.15878 + 14.1314i −0.375141 + 0.649764i
\(474\) −14.1805 24.5614i −0.651334 1.12814i
\(475\) −1.76128 −0.0808133
\(476\) 0 0
\(477\) −38.6604 −1.77014
\(478\) −7.65967 13.2669i −0.350345 0.606816i
\(479\) 11.3276 19.6200i 0.517571 0.896459i −0.482221 0.876050i \(-0.660170\pi\)
0.999792 0.0204092i \(-0.00649690\pi\)
\(480\) −18.5560 + 32.1399i −0.846960 + 1.46698i
\(481\) 2.81285 + 4.87200i 0.128255 + 0.222144i
\(482\) −14.3783 −0.654913
\(483\) 0 0
\(484\) 34.5945 1.57248
\(485\) −5.73933 9.94081i −0.260610 0.451389i
\(486\) −24.6039 + 42.6152i −1.11606 + 1.93306i
\(487\) 16.3584 28.3335i 0.741268 1.28391i −0.210650 0.977562i \(-0.567558\pi\)
0.951918 0.306353i \(-0.0991087\pi\)
\(488\) 3.18984 + 5.52497i 0.144397 + 0.250104i
\(489\) −34.2317 −1.54801
\(490\) 0 0
\(491\) 6.17281 0.278575 0.139288 0.990252i \(-0.455519\pi\)
0.139288 + 0.990252i \(0.455519\pi\)
\(492\) −37.2803 64.5713i −1.68072 2.91110i
\(493\) 11.1479 19.3088i 0.502078 0.869625i
\(494\) 3.94772 6.83765i 0.177616 0.307640i
\(495\) −15.8731 27.4931i −0.713444 1.23572i
\(496\) −5.25919 −0.236145
\(497\) 0 0
\(498\) 18.9895 0.850938
\(499\) 7.31934 + 12.6775i 0.327659 + 0.567521i 0.982047 0.188637i \(-0.0604071\pi\)
−0.654388 + 0.756159i \(0.727074\pi\)
\(500\) 16.9030 29.2768i 0.755925 1.30930i
\(501\) −21.4699 + 37.1870i −0.959205 + 1.66139i
\(502\) −10.9206 18.9150i −0.487409 0.844218i
\(503\) −12.7787 −0.569774 −0.284887 0.958561i \(-0.591956\pi\)
−0.284887 + 0.958561i \(0.591956\pi\)
\(504\) 0 0
\(505\) −19.7786 −0.880136
\(506\) −23.7134 41.0727i −1.05419 1.82591i
\(507\) 1.23721 2.14292i 0.0549466 0.0951703i
\(508\) 15.2575 26.4267i 0.676941 1.17250i
\(509\) 5.84263 + 10.1197i 0.258970 + 0.448549i 0.965966 0.258668i \(-0.0832835\pi\)
−0.706996 + 0.707217i \(0.749950\pi\)
\(510\) −43.9260 −1.94507
\(511\) 0 0
\(512\) 15.4017 0.680664
\(513\) 0.541949 + 0.938683i 0.0239276 + 0.0414439i
\(514\) 7.59688 13.1582i 0.335084 0.580382i
\(515\) 7.75495 13.4320i 0.341724 0.591883i
\(516\) 12.2202 + 21.1659i 0.537962 + 0.931778i
\(517\) 34.0435 1.49723
\(518\) 0 0
\(519\) −7.32772 −0.321651
\(520\) 2.11146 + 3.65716i 0.0925937 + 0.160377i
\(521\) 4.23838 7.34108i 0.185687 0.321619i −0.758121 0.652114i \(-0.773882\pi\)
0.943808 + 0.330495i \(0.107216\pi\)
\(522\) 20.3934 35.3224i 0.892594 1.54602i
\(523\) 16.3554 + 28.3284i 0.715172 + 1.23871i 0.962893 + 0.269883i \(0.0869849\pi\)
−0.247721 + 0.968831i \(0.579682\pi\)
\(524\) −15.7233 −0.686876
\(525\) 0 0
\(526\) −0.280097 −0.0122128
\(527\) −7.12425 12.3396i −0.310337 0.537520i
\(528\) −8.26284 + 14.3117i −0.359594 + 0.622835i
\(529\) 1.48975 2.58032i 0.0647716 0.112188i
\(530\) 29.0834 + 50.3739i 1.26330 + 2.18810i
\(531\) −14.9549 −0.648989
\(532\) 0 0
\(533\) 10.3948 0.450249
\(534\) −10.0342 17.3797i −0.434222 0.752095i
\(535\) −7.16156 + 12.4042i −0.309621 + 0.536280i
\(536\) 2.88407 4.99536i 0.124573 0.215767i
\(537\) −7.01361 12.1479i −0.302660 0.524222i
\(538\) 9.39131 0.404888
\(539\) 0 0
\(540\) −1.86975 −0.0804610
\(541\) 14.0853 + 24.3964i 0.605573 + 1.04888i 0.991961 + 0.126547i \(0.0403893\pi\)
−0.386388 + 0.922336i \(0.626277\pi\)
\(542\) 1.73440 3.00406i 0.0744987 0.129035i
\(543\) −8.87880 + 15.3785i −0.381026 + 0.659956i
\(544\) 13.3473 + 23.1182i 0.572262 + 0.991187i
\(545\) 8.86574 0.379767
\(546\) 0 0
\(547\) −18.5377 −0.792615 −0.396307 0.918118i \(-0.629709\pi\)
−0.396307 + 0.918118i \(0.629709\pi\)
\(548\) −32.2415 55.8438i −1.37729 2.38553i
\(549\) 5.00735 8.67299i 0.213709 0.370154i
\(550\) 2.61670 4.53225i 0.111576 0.193256i
\(551\) 10.5252 + 18.2303i 0.448391 + 0.776635i
\(552\) −22.0251 −0.937449
\(553\) 0 0
\(554\) −28.2092 −1.19850
\(555\) 14.7751 + 25.5912i 0.627167 + 1.08628i
\(556\) −5.79759 + 10.0417i −0.245873 + 0.425864i
\(557\) −2.00142 + 3.46655i −0.0848027 + 0.146883i −0.905307 0.424758i \(-0.860359\pi\)
0.820504 + 0.571640i \(0.193693\pi\)
\(558\) −13.0327 22.5732i −0.551717 0.955602i
\(559\) −3.40733 −0.144115
\(560\) 0 0
\(561\) −44.7723 −1.89029
\(562\) −5.12368 8.87448i −0.216129 0.374347i
\(563\) −8.93100 + 15.4689i −0.376397 + 0.651938i −0.990535 0.137260i \(-0.956170\pi\)
0.614138 + 0.789199i \(0.289504\pi\)
\(564\) 25.4951 44.1587i 1.07354 1.85942i
\(565\) −6.26338 10.8485i −0.263503 0.456400i
\(566\) −8.07490 −0.339413
\(567\) 0 0
\(568\) −5.05041 −0.211910
\(569\) 18.7336 + 32.4475i 0.785353 + 1.36027i 0.928788 + 0.370612i \(0.120852\pi\)
−0.143434 + 0.989660i \(0.545815\pi\)
\(570\) 20.7362 35.9161i 0.868544 1.50436i
\(571\) −8.78514 + 15.2163i −0.367646 + 0.636782i −0.989197 0.146592i \(-0.953170\pi\)
0.621551 + 0.783374i \(0.286503\pi\)
\(572\) 6.94110 + 12.0223i 0.290222 + 0.502679i
\(573\) −29.4006 −1.22823
\(574\) 0 0
\(575\) −2.20920 −0.0921301
\(576\) 20.0618 + 34.7481i 0.835908 + 1.44784i
\(577\) −17.1247 + 29.6608i −0.712910 + 1.23480i 0.250850 + 0.968026i \(0.419290\pi\)
−0.963760 + 0.266770i \(0.914043\pi\)
\(578\) 3.01524 5.22254i 0.125417 0.217229i
\(579\) 28.4190 + 49.2232i 1.18105 + 2.04565i
\(580\) −36.3125 −1.50780
\(581\) 0 0
\(582\) −29.6144 −1.22756
\(583\) 29.6438 + 51.3445i 1.22772 + 2.12647i
\(584\) 7.65959 13.2668i 0.316956 0.548984i
\(585\) 3.31453 5.74093i 0.137039 0.237358i
\(586\) −23.2859 40.3323i −0.961930 1.66611i
\(587\) 29.4494 1.21551 0.607754 0.794126i \(-0.292071\pi\)
0.607754 + 0.794126i \(0.292071\pi\)
\(588\) 0 0
\(589\) 13.4526 0.554305
\(590\) 11.2503 + 19.4861i 0.463167 + 0.802229i
\(591\) 20.9356 36.2616i 0.861176 1.49160i
\(592\) 3.92275 6.79439i 0.161224 0.279248i
\(593\) −17.0001 29.4450i −0.698109 1.20916i −0.969121 0.246584i \(-0.920692\pi\)
0.271013 0.962576i \(-0.412641\pi\)
\(594\) −3.22064 −0.132145
\(595\) 0 0
\(596\) 8.56514 0.350842
\(597\) −12.4452 21.5557i −0.509349 0.882218i
\(598\) 4.95168 8.57655i 0.202489 0.350721i
\(599\) −10.7209 + 18.5691i −0.438043 + 0.758713i −0.997539 0.0701203i \(-0.977662\pi\)
0.559495 + 0.828834i \(0.310995\pi\)
\(600\) −1.21520 2.10479i −0.0496103 0.0859276i
\(601\) −40.4039 −1.64811 −0.824054 0.566511i \(-0.808293\pi\)
−0.824054 + 0.566511i \(0.808293\pi\)
\(602\) 0 0
\(603\) −9.05472 −0.368737
\(604\) 26.8931 + 46.5803i 1.09427 + 1.89533i
\(605\) −12.6668 + 21.9396i −0.514980 + 0.891971i
\(606\) −25.5139 + 44.1914i −1.03643 + 1.79515i
\(607\) −21.9456 38.0110i −0.890746 1.54282i −0.838983 0.544158i \(-0.816849\pi\)
−0.0517636 0.998659i \(-0.516484\pi\)
\(608\) −25.2036 −1.02214
\(609\) 0 0
\(610\) −15.0677 −0.610074
\(611\) 3.55438 + 6.15636i 0.143795 + 0.249060i
\(612\) −17.1011 + 29.6200i −0.691272 + 1.19732i
\(613\) 7.15777 12.3976i 0.289100 0.500735i −0.684496 0.729017i \(-0.739977\pi\)
0.973595 + 0.228282i \(0.0733108\pi\)
\(614\) −5.48750 9.50464i −0.221458 0.383576i
\(615\) 54.6009 2.20172
\(616\) 0 0
\(617\) −36.9097 −1.48593 −0.742965 0.669330i \(-0.766581\pi\)
−0.742965 + 0.669330i \(0.766581\pi\)
\(618\) −20.0074 34.6538i −0.804815 1.39398i
\(619\) 7.14646 12.3780i 0.287240 0.497515i −0.685910 0.727687i \(-0.740595\pi\)
0.973150 + 0.230172i \(0.0739288\pi\)
\(620\) −11.6030 + 20.0970i −0.465988 + 0.807115i
\(621\) 0.679774 + 1.17740i 0.0272784 + 0.0472476i
\(622\) 5.35973 0.214906
\(623\) 0 0
\(624\) −3.45079 −0.138142
\(625\) 11.1438 + 19.3016i 0.445750 + 0.772062i
\(626\) 15.4496 26.7594i 0.617489 1.06952i
\(627\) 21.1357 36.6082i 0.844080 1.46199i
\(628\) −14.2036 24.6013i −0.566784 0.981698i
\(629\) 21.2554 0.847510
\(630\) 0 0
\(631\) −0.0431064 −0.00171604 −0.000858019 1.00000i \(-0.500273\pi\)
−0.000858019 1.00000i \(0.500273\pi\)
\(632\) 5.15084 + 8.92152i 0.204890 + 0.354879i
\(633\) −30.2633 + 52.4176i −1.20286 + 2.08341i
\(634\) −3.39592 + 5.88190i −0.134869 + 0.233600i
\(635\) 11.1731 + 19.3524i 0.443390 + 0.767975i
\(636\) 88.8004 3.52116
\(637\) 0 0
\(638\) −62.5484 −2.47632
\(639\) 3.96401 + 6.86587i 0.156814 + 0.271610i
\(640\) 15.1860 26.3029i 0.600279 1.03971i
\(641\) −21.3328 + 36.9494i −0.842594 + 1.45942i 0.0451008 + 0.998982i \(0.485639\pi\)
−0.887695 + 0.460433i \(0.847694\pi\)
\(642\) 18.4765 + 32.0022i 0.729208 + 1.26303i
\(643\) 5.49737 0.216795 0.108398 0.994108i \(-0.465428\pi\)
0.108398 + 0.994108i \(0.465428\pi\)
\(644\) 0 0
\(645\) −17.8977 −0.704722
\(646\) −14.9156 25.8345i −0.586845 1.01645i
\(647\) −19.0933 + 33.0706i −0.750637 + 1.30014i 0.196877 + 0.980428i \(0.436920\pi\)
−0.947514 + 0.319713i \(0.896413\pi\)
\(648\) 8.57053 14.8446i 0.336682 0.583150i
\(649\) 11.4671 + 19.8615i 0.450121 + 0.779633i
\(650\) 1.09280 0.0428633
\(651\) 0 0
\(652\) 40.1024 1.57053
\(653\) −19.2510 33.3437i −0.753349 1.30484i −0.946191 0.323608i \(-0.895104\pi\)
0.192843 0.981230i \(-0.438229\pi\)
\(654\) 11.4366 19.8088i 0.447206 0.774584i
\(655\) 5.75711 9.97161i 0.224949 0.389623i
\(656\) −7.24820 12.5543i −0.282995 0.490161i
\(657\) −24.0477 −0.938192
\(658\) 0 0
\(659\) 19.4843 0.759002 0.379501 0.925191i \(-0.376096\pi\)
0.379501 + 0.925191i \(0.376096\pi\)
\(660\) 36.4595 + 63.1498i 1.41919 + 2.45810i
\(661\) −20.8334 + 36.0844i −0.810324 + 1.40352i 0.102314 + 0.994752i \(0.467375\pi\)
−0.912638 + 0.408770i \(0.865958\pi\)
\(662\) −15.0564 + 26.0784i −0.585182 + 1.01356i
\(663\) −4.67454 8.09654i −0.181544 0.314443i
\(664\) −6.89760 −0.267679
\(665\) 0 0
\(666\) 38.8834 1.50670
\(667\) 13.2020 + 22.8665i 0.511182 + 0.885393i
\(668\) 25.1520 43.5645i 0.973160 1.68556i
\(669\) 36.2040 62.7071i 1.39973 2.42440i
\(670\) 6.81168 + 11.7982i 0.263158 + 0.455803i
\(671\) −15.3580 −0.592890
\(672\) 0 0
\(673\) −14.3157 −0.551830 −0.275915 0.961182i \(-0.588981\pi\)
−0.275915 + 0.961182i \(0.588981\pi\)
\(674\) 38.9153 + 67.4033i 1.49896 + 2.59628i
\(675\) −0.0750110 + 0.129923i −0.00288718 + 0.00500073i
\(676\) −1.44940 + 2.51043i −0.0557460 + 0.0965550i
\(677\) −14.7641 25.5721i −0.567429 0.982815i −0.996819 0.0796963i \(-0.974605\pi\)
0.429391 0.903119i \(-0.358728\pi\)
\(678\) −32.3184 −1.24118
\(679\) 0 0
\(680\) 15.9554 0.611860
\(681\) 12.4633 + 21.5871i 0.477596 + 0.827220i
\(682\) −19.9862 + 34.6172i −0.765312 + 1.32556i
\(683\) −23.5349 + 40.7637i −0.900539 + 1.55978i −0.0737441 + 0.997277i \(0.523495\pi\)
−0.826795 + 0.562503i \(0.809839\pi\)
\(684\) −16.1459 27.9655i −0.617354 1.06929i
\(685\) 47.2210 1.80422
\(686\) 0 0
\(687\) −27.5650 −1.05167
\(688\) 2.37590 + 4.11518i 0.0905804 + 0.156890i
\(689\) −6.19003 + 10.7214i −0.235821 + 0.408454i
\(690\) 26.0097 45.0501i 0.990172 1.71503i
\(691\) −15.4334 26.7314i −0.587113 1.01691i −0.994608 0.103703i \(-0.966931\pi\)
0.407495 0.913207i \(-0.366402\pi\)
\(692\) 8.58442 0.326331
\(693\) 0 0
\(694\) −12.1091 −0.459656
\(695\) −4.24559 7.35358i −0.161044 0.278937i
\(696\) −14.5238 + 25.1560i −0.550524 + 0.953535i
\(697\) 19.6372 34.0127i 0.743813 1.28832i
\(698\) 4.80508 + 8.32264i 0.181875 + 0.315017i
\(699\) 42.2715 1.59885
\(700\) 0 0
\(701\) 6.48958 0.245108 0.122554 0.992462i \(-0.460892\pi\)
0.122554 + 0.992462i \(0.460892\pi\)
\(702\) −0.336257 0.582415i −0.0126912 0.0219818i
\(703\) −10.0341 + 17.3795i −0.378443 + 0.655482i
\(704\) 30.7657 53.2878i 1.15953 2.00836i
\(705\) 18.6701 + 32.3376i 0.703157 + 1.21790i
\(706\) −61.0860 −2.29900
\(707\) 0 0
\(708\) 34.3505 1.29097
\(709\) 6.68689 + 11.5820i 0.251131 + 0.434972i 0.963838 0.266490i \(-0.0858641\pi\)
−0.712706 + 0.701463i \(0.752531\pi\)
\(710\) 5.96409 10.3301i 0.223828 0.387682i
\(711\) 8.08569 14.0048i 0.303237 0.525222i
\(712\) 3.64475 + 6.31290i 0.136593 + 0.236586i
\(713\) 16.8738 0.631929
\(714\) 0 0
\(715\) −10.1660 −0.380186
\(716\) 8.21645 + 14.2313i 0.307063 + 0.531849i
\(717\) 8.56328 14.8320i 0.319802 0.553913i
\(718\) −7.33555 + 12.7055i −0.273760 + 0.474167i
\(719\) −8.37048 14.4981i −0.312166 0.540688i 0.666665 0.745358i \(-0.267721\pi\)
−0.978831 + 0.204670i \(0.934388\pi\)
\(720\) −9.24476 −0.344532
\(721\) 0 0
\(722\) −13.8883 −0.516868
\(723\) −8.03725 13.9209i −0.298909 0.517725i
\(724\) 10.4015 18.0160i 0.386570 0.669558i
\(725\) −1.45680 + 2.52325i −0.0541041 + 0.0937110i
\(726\) 32.6798 + 56.6030i 1.21286 + 2.10074i
\(727\) −38.8138 −1.43952 −0.719761 0.694221i \(-0.755749\pi\)
−0.719761 + 0.694221i \(0.755749\pi\)
\(728\) 0 0
\(729\) −29.1632 −1.08012
\(730\) 18.0906 + 31.3339i 0.669564 + 1.15972i
\(731\) −6.43692 + 11.1491i −0.238078 + 0.412364i
\(732\) −11.5016 + 19.9213i −0.425110 + 0.736312i
\(733\) 18.8639 + 32.6733i 0.696756 + 1.20682i 0.969585 + 0.244754i \(0.0787071\pi\)
−0.272830 + 0.962062i \(0.587960\pi\)
\(734\) −69.0719 −2.54949
\(735\) 0 0
\(736\) −31.6132 −1.16528
\(737\) 6.94292 + 12.0255i 0.255746 + 0.442965i
\(738\) 35.9232 62.2208i 1.32235 2.29038i
\(739\) 4.61476 7.99300i 0.169757 0.294027i −0.768578 0.639757i \(-0.779035\pi\)
0.938334 + 0.345729i \(0.112368\pi\)
\(740\) −17.3090 29.9801i −0.636291 1.10209i
\(741\) 8.82686 0.324263
\(742\) 0 0
\(743\) −3.56327 −0.130724 −0.0653619 0.997862i \(-0.520820\pi\)
−0.0653619 + 0.997862i \(0.520820\pi\)
\(744\) 9.28164 + 16.0763i 0.340282 + 0.589385i
\(745\) −3.13614 + 5.43195i −0.114899 + 0.199011i
\(746\) 17.4571 30.2366i 0.639151 1.10704i
\(747\) 5.41386 + 9.37707i 0.198083 + 0.343089i
\(748\) 52.4508 1.91779
\(749\) 0 0
\(750\) 63.8698 2.33220
\(751\) −25.6053 44.3496i −0.934350 1.61834i −0.775789 0.630992i \(-0.782648\pi\)
−0.158561 0.987349i \(-0.550685\pi\)
\(752\) 4.95687 8.58555i 0.180758 0.313083i
\(753\) 12.2089 21.1464i 0.444916 0.770618i
\(754\) −6.53049 11.3111i −0.237826 0.411927i
\(755\) −39.3879 −1.43347
\(756\) 0 0
\(757\) 25.2305 0.917019 0.458509 0.888690i \(-0.348384\pi\)
0.458509 + 0.888690i \(0.348384\pi\)
\(758\) −35.0272 60.6688i −1.27224 2.20359i
\(759\) 26.5108 45.9181i 0.962282 1.66672i
\(760\) −7.53207 + 13.0459i −0.273217 + 0.473226i
\(761\) 1.82372 + 3.15878i 0.0661099 + 0.114506i 0.897186 0.441653i \(-0.145608\pi\)
−0.831076 + 0.556159i \(0.812275\pi\)
\(762\) 57.6520 2.08851
\(763\) 0 0
\(764\) 34.4428 1.24610
\(765\) −12.5232 21.6908i −0.452777 0.784233i
\(766\) 13.7154 23.7558i 0.495558 0.858331i
\(767\) −2.39448 + 4.14736i −0.0864596 + 0.149752i
\(768\) −7.38609 12.7931i −0.266523 0.461631i
\(769\) −21.9882 −0.792914 −0.396457 0.918053i \(-0.629760\pi\)
−0.396457 + 0.918053i \(0.629760\pi\)
\(770\) 0 0
\(771\) 16.9862 0.611742
\(772\) −33.2929 57.6650i −1.19824 2.07541i
\(773\) 10.9295 18.9305i 0.393108 0.680882i −0.599750 0.800187i \(-0.704733\pi\)
0.992858 + 0.119305i \(0.0380667\pi\)
\(774\) −11.7753 + 20.3954i −0.423255 + 0.733099i
\(775\) 0.930986 + 1.61252i 0.0334420 + 0.0579233i
\(776\) 10.7569 0.386151
\(777\) 0 0
\(778\) −31.1505 −1.11680
\(779\) 18.5404 + 32.1128i 0.664277 + 1.15056i
\(780\) −7.61326 + 13.1865i −0.272598 + 0.472154i
\(781\) 6.07900 10.5291i 0.217524 0.376762i
\(782\) −18.7088 32.4046i −0.669025 1.15879i
\(783\) 1.79303 0.0640777
\(784\) 0 0
\(785\) 20.8026 0.742477
\(786\) −14.8531 25.7263i −0.529791 0.917625i
\(787\) 19.9336 34.5261i 0.710557 1.23072i −0.254091 0.967180i \(-0.581776\pi\)
0.964648 0.263541i \(-0.0848905\pi\)
\(788\) −24.5261 + 42.4804i −0.873706 + 1.51330i
\(789\) −0.156570 0.271188i −0.00557405 0.00965454i
\(790\) −24.3308 −0.865651
\(791\) 0 0
\(792\) 29.7502 1.05713
\(793\) −1.60348 2.77732i −0.0569414 0.0986254i
\(794\) −7.71680 + 13.3659i −0.273859 + 0.474338i
\(795\) −32.5144 + 56.3166i −1.15317 + 1.99734i
\(796\) 14.5796 + 25.2526i 0.516759 + 0.895053i
\(797\) 40.1971 1.42385 0.711927 0.702253i \(-0.247822\pi\)
0.711927 + 0.702253i \(0.247822\pi\)
\(798\) 0 0
\(799\) 26.8589 0.950198
\(800\) −1.74421 3.02106i −0.0616671 0.106811i
\(801\) 5.72146 9.90986i 0.202158 0.350148i
\(802\) −3.02873 + 5.24592i −0.106948 + 0.185240i
\(803\) 18.4392 + 31.9376i 0.650704 + 1.12705i
\(804\) 20.7981 0.733492
\(805\) 0 0
\(806\) −8.34680 −0.294003
\(807\) 5.24960 + 9.09258i 0.184795 + 0.320074i
\(808\) 9.26749 16.0518i 0.326029 0.564699i
\(809\) −1.26924 + 2.19840i −0.0446243 + 0.0772915i −0.887475 0.460856i \(-0.847542\pi\)
0.842851 + 0.538148i \(0.180876\pi\)
\(810\) 20.2421 + 35.0603i 0.711235 + 1.23189i
\(811\) 41.7062 1.46450 0.732251 0.681035i \(-0.238470\pi\)
0.732251 + 0.681035i \(0.238470\pi\)
\(812\) 0 0
\(813\) 3.87801 0.136008
\(814\) −29.8148 51.6407i −1.04501 1.81001i
\(815\) −14.6836 + 25.4327i −0.514343 + 0.890868i
\(816\) −6.51902 + 11.2913i −0.228211 + 0.395274i
\(817\) −6.07737 10.5263i −0.212620 0.368269i
\(818\) 54.2604 1.89717
\(819\) 0 0
\(820\) −63.9650 −2.23375
\(821\) −15.9652 27.6525i −0.557189 0.965079i −0.997730 0.0673467i \(-0.978547\pi\)
0.440541 0.897733i \(-0.354787\pi\)
\(822\) 60.9140 105.506i 2.12462 3.67995i
\(823\) 17.1266 29.6641i 0.596995 1.03402i −0.396267 0.918135i \(-0.629695\pi\)
0.993262 0.115890i \(-0.0369720\pi\)
\(824\) 7.26734 + 12.5874i 0.253170 + 0.438503i
\(825\) 5.85078 0.203698
\(826\) 0 0
\(827\) 36.9755 1.28576 0.642882 0.765965i \(-0.277739\pi\)
0.642882 + 0.765965i \(0.277739\pi\)
\(828\) −20.2520 35.0775i −0.703807 1.21903i
\(829\) −9.99473 + 17.3114i −0.347131 + 0.601249i −0.985739 0.168284i \(-0.946178\pi\)
0.638607 + 0.769533i \(0.279511\pi\)
\(830\) 8.14547 14.1084i 0.282733 0.489708i
\(831\) −15.7685 27.3119i −0.547005 0.947440i
\(832\) 12.8486 0.445446
\(833\) 0 0
\(834\) −21.9068 −0.758571
\(835\) 18.4189 + 31.9024i 0.637412 + 1.10403i
\(836\) −24.7605 + 42.8865i −0.856360 + 1.48326i
\(837\) 0.572931 0.992346i 0.0198034 0.0343005i
\(838\) −3.33384 5.77438i −0.115166 0.199473i
\(839\) −12.8147 −0.442411 −0.221206 0.975227i \(-0.570999\pi\)
−0.221206 + 0.975227i \(0.570999\pi\)
\(840\) 0 0
\(841\) 5.82265 0.200781
\(842\) 11.0666 + 19.1679i 0.381381 + 0.660571i
\(843\) 5.72812 9.92140i 0.197287 0.341711i
\(844\) 35.4535 61.4073i 1.22036 2.11373i
\(845\) −1.06140 1.83839i −0.0365132 0.0632427i
\(846\) 49.1340 1.68926
\(847\) 0 0
\(848\) 17.2650 0.592882
\(849\) −4.51375 7.81805i −0.154912 0.268315i
\(850\) 2.06446 3.57575i 0.0708104 0.122647i
\(851\) −12.5859 + 21.7994i −0.431439 + 0.747274i
\(852\) −9.10508 15.7705i −0.311935 0.540287i
\(853\) 30.1839 1.03348 0.516739 0.856143i \(-0.327146\pi\)
0.516739 + 0.856143i \(0.327146\pi\)
\(854\) 0 0
\(855\) 23.6474 0.808724
\(856\) −6.71127 11.6243i −0.229386 0.397309i
\(857\) −26.6164 + 46.1009i −0.909197 + 1.57478i −0.0940154 + 0.995571i \(0.529970\pi\)
−0.815182 + 0.579205i \(0.803363\pi\)
\(858\) −13.1139 + 22.7139i −0.447700 + 0.775438i
\(859\) −6.13597 10.6278i −0.209357 0.362616i 0.742155 0.670228i \(-0.233804\pi\)
−0.951512 + 0.307611i \(0.900470\pi\)
\(860\) 20.9672 0.714975
\(861\) 0 0
\(862\) −41.5977 −1.41682
\(863\) −12.2226 21.1702i −0.416064 0.720643i 0.579476 0.814989i \(-0.303257\pi\)
−0.995539 + 0.0943460i \(0.969924\pi\)
\(864\) −1.07339 + 1.85917i −0.0365175 + 0.0632501i
\(865\) −3.14320 + 5.44418i −0.106872 + 0.185108i
\(866\) −8.59778 14.8918i −0.292164 0.506043i
\(867\) 6.74189 0.228967
\(868\) 0 0
\(869\) −24.7996 −0.841268
\(870\) −34.3027 59.4141i −1.16297 2.01432i
\(871\) −1.44978 + 2.51109i −0.0491238 + 0.0850850i
\(872\) −4.15415 + 7.19519i −0.140677 + 0.243660i
\(873\) −8.44300 14.6237i −0.285752 0.494937i
\(874\) 35.3276 1.19497
\(875\) 0 0
\(876\) 55.2361 1.86625
\(877\) 26.4376 + 45.7913i 0.892736 + 1.54626i 0.836582 + 0.547842i \(0.184550\pi\)
0.0561539 + 0.998422i \(0.482116\pi\)
\(878\) −42.0178 + 72.7770i −1.41803 + 2.45611i
\(879\) 26.0329 45.0903i 0.878068 1.52086i
\(880\) 7.08864 + 12.2779i 0.238958 + 0.413887i
\(881\) −55.0118 −1.85339 −0.926697 0.375809i \(-0.877365\pi\)
−0.926697 + 0.375809i \(0.877365\pi\)
\(882\) 0 0
\(883\) 44.1730 1.48654 0.743269 0.668992i \(-0.233274\pi\)
0.743269 + 0.668992i \(0.233274\pi\)
\(884\) 5.47622 + 9.48510i 0.184185 + 0.319018i
\(885\) −12.5775 + 21.7848i −0.422788 + 0.732290i
\(886\) −39.4270 + 68.2895i −1.32457 + 2.29423i
\(887\) −2.54330 4.40512i −0.0853955 0.147909i 0.820164 0.572128i \(-0.193882\pi\)
−0.905560 + 0.424219i \(0.860549\pi\)
\(888\) −27.6921 −0.929286
\(889\) 0 0
\(890\) −17.2165 −0.577100
\(891\) 20.6321 + 35.7359i 0.691202 + 1.19720i
\(892\) −42.4130 + 73.4614i −1.42009 + 2.45967i
\(893\) −12.6793 + 21.9612i −0.424296 + 0.734903i
\(894\) 8.09108 + 14.0142i 0.270606 + 0.468704i
\(895\) −12.0339 −0.402248
\(896\) 0 0
\(897\) 11.0717 0.369672
\(898\) 8.91178 + 15.4356i 0.297390 + 0.515094i
\(899\) 11.1270 19.2724i 0.371105 0.642772i
\(900\) 2.23475 3.87070i 0.0744917 0.129023i
\(901\) 23.3876 + 40.5086i 0.779155 + 1.34954i
\(902\) −110.180 −3.66859
\(903\) 0 0
\(904\) 11.7391 0.390437
\(905\) 7.61706 + 13.1931i 0.253200 + 0.438555i
\(906\) −50.8094 + 88.0044i −1.68803 + 2.92375i
\(907\) 9.06264 15.6969i 0.300920 0.521209i −0.675425 0.737429i \(-0.736040\pi\)
0.976345 + 0.216220i \(0.0693730\pi\)
\(908\) −14.6008 25.2893i −0.484544 0.839255i
\(909\) −29.0958 −0.965048
\(910\) 0 0
\(911\) −9.65804 −0.319985 −0.159993 0.987118i \(-0.551147\pi\)
−0.159993 + 0.987118i \(0.551147\pi\)
\(912\) −6.15489 10.6606i −0.203809 0.353007i
\(913\) 8.30241 14.3802i 0.274770 0.475915i
\(914\) −17.2613 + 29.8974i −0.570952 + 0.988918i
\(915\) −8.42263 14.5884i −0.278444 0.482278i
\(916\) 32.2924 1.06697
\(917\) 0 0
\(918\) −2.54095 −0.0838637
\(919\) −23.8801 41.3616i −0.787733 1.36439i −0.927353 0.374188i \(-0.877922\pi\)
0.139620 0.990205i \(-0.455412\pi\)
\(920\) −9.44758 + 16.3637i −0.311477 + 0.539495i
\(921\) 6.13487 10.6259i 0.202151 0.350135i
\(922\) −28.4401 49.2598i −0.936626 1.62228i
\(923\) 2.53876 0.0835643
\(924\) 0 0
\(925\) −2.77763 −0.0913279
\(926\) 22.7096 + 39.3342i 0.746285 + 1.29260i
\(927\) 11.4081 19.7595i 0.374692 0.648986i
\(928\) −20.8464 + 36.1071i −0.684317 + 1.18527i
\(929\) 16.9905 + 29.4285i 0.557442 + 0.965517i 0.997709 + 0.0676505i \(0.0215503\pi\)
−0.440267 + 0.897867i \(0.645116\pi\)
\(930\) −43.8433 −1.43768
\(931\) 0 0
\(932\) −49.5210 −1.62212
\(933\) 2.99601 + 5.18924i 0.0980850 + 0.169888i
\(934\) 13.0861 22.6657i 0.428189 0.741645i
\(935\) −19.2049 + 33.2639i −0.628068 + 1.08785i
\(936\) 3.10612 + 5.37996i 0.101527 + 0.175849i
\(937\) 24.7948 0.810012 0.405006 0.914314i \(-0.367269\pi\)
0.405006 + 0.914314i \(0.367269\pi\)
\(938\) 0 0
\(939\) 34.5443 1.12731
\(940\) −21.8720 37.8835i −0.713387 1.23562i
\(941\) −4.12098 + 7.13774i −0.134340 + 0.232684i −0.925345 0.379126i \(-0.876225\pi\)
0.791005 + 0.611810i \(0.209558\pi\)
\(942\) 26.8349 46.4793i 0.874327 1.51438i
\(943\) 23.2554 + 40.2796i 0.757301 + 1.31168i
\(944\) 6.67859 0.217370
\(945\) 0 0
\(946\) 36.1160 1.17423
\(947\) −9.98643 17.2970i −0.324515 0.562077i 0.656899 0.753979i \(-0.271868\pi\)
−0.981414 + 0.191902i \(0.938535\pi\)
\(948\) −18.5723 + 32.1682i −0.603200 + 1.04477i
\(949\) −3.85035 + 6.66901i −0.124988 + 0.216485i
\(950\) 1.94914 + 3.37602i 0.0632386 + 0.109532i
\(951\) −7.59307 −0.246222
\(952\) 0 0
\(953\) −21.5341 −0.697557 −0.348778 0.937205i \(-0.613403\pi\)
−0.348778 + 0.937205i \(0.613403\pi\)
\(954\) 42.7839 + 74.1040i 1.38518 + 2.39920i
\(955\) −12.6113 + 21.8434i −0.408091 + 0.706835i
\(956\) −10.0319 + 17.3757i −0.324455 + 0.561972i
\(957\) −34.9636 60.5588i −1.13021 1.95759i
\(958\) −50.1432 −1.62005
\(959\) 0 0
\(960\) 67.4900 2.17823
\(961\) 8.38917 + 14.5305i 0.270618 + 0.468725i
\(962\) 6.22574 10.7833i 0.200726 0.347667i
\(963\) −10.5352 + 18.2475i −0.339492 + 0.588018i
\(964\) 9.41564 + 16.3084i 0.303257 + 0.525257i
\(965\) 48.7610 1.56967
\(966\) 0 0
\(967\) 43.2887 1.39207 0.696036 0.718007i \(-0.254945\pi\)
0.696036 + 0.718007i \(0.254945\pi\)
\(968\) −11.8704 20.5601i −0.381528 0.660827i
\(969\) 16.6752 28.8822i 0.535683 0.927831i
\(970\) −12.7030 + 22.0022i −0.407868 + 0.706449i
\(971\) −26.3356 45.6147i −0.845151 1.46384i −0.885490 0.464658i \(-0.846177\pi\)
0.0403390 0.999186i \(-0.487156\pi\)
\(972\) 64.4476 2.06716
\(973\) 0 0
\(974\) −72.4127 −2.32025
\(975\) 0.610862 + 1.05804i 0.0195632 + 0.0338845i
\(976\) −2.23619 + 3.87319i −0.0715787 + 0.123978i
\(977\) −7.70305 + 13.3421i −0.246442 + 0.426851i −0.962536 0.271153i \(-0.912595\pi\)
0.716094 + 0.698004i \(0.245928\pi\)
\(978\) 37.8829 + 65.6151i 1.21136 + 2.09814i
\(979\) −17.5483 −0.560845
\(980\) 0 0
\(981\) 13.0422 0.416405
\(982\) −6.83121 11.8320i −0.217993 0.377575i
\(983\) 3.79073 6.56574i 0.120906 0.209415i −0.799219 0.601039i \(-0.794754\pi\)
0.920125 + 0.391625i \(0.128087\pi\)
\(984\) −25.5839 + 44.3126i −0.815584 + 1.41263i
\(985\) −17.9605 31.1085i −0.572270 0.991201i
\(986\) −49.3480 −1.57156
\(987\) 0 0
\(988\) −10.3407 −0.328981
\(989\) −7.62293 13.2033i −0.242395 0.419841i
\(990\) −35.1323 + 60.8510i −1.11658 + 1.93397i
\(991\) 9.50923 16.4705i 0.302071 0.523202i −0.674534 0.738244i \(-0.735655\pi\)
0.976605 + 0.215042i \(0.0689888\pi\)
\(992\) 13.3222 + 23.0747i 0.422980 + 0.732623i
\(993\) −33.6651 −1.06833
\(994\) 0 0
\(995\) −21.3533 −0.676946
\(996\) −12.4353 21.5385i −0.394027 0.682474i
\(997\) 23.0499 39.9236i 0.729998 1.26439i −0.226885 0.973922i \(-0.572854\pi\)
0.956883 0.290473i \(-0.0938125\pi\)
\(998\) 16.2001 28.0593i 0.512804 0.888202i
\(999\) 0.854680 + 1.48035i 0.0270409 + 0.0468362i
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 637.2.e.m.508.2 10
7.2 even 3 inner 637.2.e.m.79.2 10
7.3 odd 6 637.2.a.l.1.4 5
7.4 even 3 637.2.a.k.1.4 5
7.5 odd 6 91.2.e.c.79.2 yes 10
7.6 odd 2 91.2.e.c.53.2 10
21.5 even 6 819.2.j.h.352.4 10
21.11 odd 6 5733.2.a.bm.1.2 5
21.17 even 6 5733.2.a.bl.1.2 5
21.20 even 2 819.2.j.h.235.4 10
28.19 even 6 1456.2.r.p.625.5 10
28.27 even 2 1456.2.r.p.417.5 10
91.12 odd 6 1183.2.e.f.170.4 10
91.25 even 6 8281.2.a.bx.1.2 5
91.38 odd 6 8281.2.a.bw.1.2 5
91.90 odd 2 1183.2.e.f.508.4 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.e.c.53.2 10 7.6 odd 2
91.2.e.c.79.2 yes 10 7.5 odd 6
637.2.a.k.1.4 5 7.4 even 3
637.2.a.l.1.4 5 7.3 odd 6
637.2.e.m.79.2 10 7.2 even 3 inner
637.2.e.m.508.2 10 1.1 even 1 trivial
819.2.j.h.235.4 10 21.20 even 2
819.2.j.h.352.4 10 21.5 even 6
1183.2.e.f.170.4 10 91.12 odd 6
1183.2.e.f.508.4 10 91.90 odd 2
1456.2.r.p.417.5 10 28.27 even 2
1456.2.r.p.625.5 10 28.19 even 6
5733.2.a.bl.1.2 5 21.17 even 6
5733.2.a.bm.1.2 5 21.11 odd 6
8281.2.a.bw.1.2 5 91.38 odd 6
8281.2.a.bx.1.2 5 91.25 even 6