Properties

Label 637.2.e.m.79.2
Level $637$
Weight $2$
Character 637.79
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 79.2
Root \(-0.606661 + 1.05077i\) of defining polynomial
Character \(\chi\) \(=\) 637.79
Dual form 637.2.e.m.508.2

$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.10666 + 1.91679i −0.782527 + 1.35538i 0.147938 + 0.988997i \(0.452737\pi\)
−0.930465 + 0.366381i \(0.880597\pi\)
\(3\) 1.23721 + 2.14292i 0.714306 + 1.23721i 0.963227 + 0.268690i \(0.0865908\pi\)
−0.248921 + 0.968524i \(0.580076\pi\)
\(4\) −1.44940 2.51043i −0.724699 1.25521i
\(5\) −1.06140 + 1.83839i −0.474671 + 0.822155i −0.999579 0.0290040i \(-0.990766\pi\)
0.524908 + 0.851159i \(0.324100\pi\)
\(6\) −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 −0.960212 0.279272i \(-0.909907\pi\)
0.238250 0.971204i \(-0.423426\pi\)
\(12\) 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 0.540682 0.841227i \(-0.318166\pi\)
−0.998865 + 0.0476304i \(0.984833\pi\)
\(18\) −3.45588 5.98575i −0.814558 1.41086i
\(19\) −1.78362 + 3.08931i −0.409190 + 0.708737i −0.994799 0.101856i \(-0.967522\pi\)
0.585609 + 0.810593i \(0.300855\pi\)
\(20\) 6.15355 1.37597
\(21\) 0 0
\(22\) 10.5995 2.25982
\(23\) −2.23721 + 3.87497i −0.466491 + 0.807987i −0.999267 0.0382695i \(-0.987815\pi\)
0.532776 + 0.846256i \(0.321149\pi\)
\(24\) 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 0.645521 0.763743i \(-0.276640\pi\)
−0.984181 + 0.177166i \(0.943307\pi\)
\(32\) 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 −0.999081 0.0428524i \(-0.986355\pi\)
0.536652 + 0.843804i \(0.319689\pi\)
\(38\) −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 0.481311 + 0.876550i \(0.340161\pi\)
−0.999770 + 0.0214479i \(0.993172\pi\)
\(48\) 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 0.880968 + 0.473175i \(0.156892\pi\)
−0.0307027 + 0.999529i \(0.509774\pi\)
\(54\) 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 0.978738 0.205115i \(-0.0657567\pi\)
−0.667003 + 0.745055i \(0.732423\pi\)
\(60\) 7.61326 + 13.1865i 0.982867 + 1.70238i
\(61\) 1.60348 2.77732i 0.205305 0.355599i −0.744925 0.667148i \(-0.767515\pi\)
0.950230 + 0.311550i \(0.100848\pi\)
\(62\) 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 0.940892 0.338706i \(-0.109989\pi\)
−0.763774 + 0.645484i \(0.776656\pi\)
\(68\) −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 0.998426 0.0560762i \(-0.0178590\pi\)
−0.547777 + 0.836625i \(0.684526\pi\)
\(74\) −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 −0.682807 0.730598i \(-0.739241\pi\)
0.974120 + 0.226029i \(0.0725745\pi\)
\(80\) 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 −0.752432 0.658670i \(-0.771119\pi\)
0.946641 + 0.322291i \(0.104453\pi\)
\(90\) 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 0.999135 0.0415891i \(-0.0132420\pi\)
−0.535585 + 0.844482i \(0.679909\pi\)
\(102\) 10.3463 + 17.9202i 1.02443 + 1.77437i
\(103\) 3.65318 6.32749i 0.359958 0.623466i −0.627995 0.778217i \(-0.716124\pi\)
0.987953 + 0.154751i \(0.0494576\pi\)
\(104\) −1.98932 −0.195069
\(105\) 0 0
\(106\) −27.4011 −2.66143
\(107\) −3.37365 + 5.84333i −0.326143 + 0.564896i −0.981743 0.190212i \(-0.939082\pi\)
0.655600 + 0.755108i \(0.272416\pi\)
\(108\) 0.440397 + 0.762790i 0.0423772 + 0.0733995i
\(109\) −2.08822 3.61691i −0.200016 0.346437i 0.748518 0.663115i \(-0.230766\pi\)
−0.948533 + 0.316678i \(0.897433\pi\)
\(110\) −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 −0.722886 0.690967i \(-0.757185\pi\)
0.959838 + 0.280554i \(0.0905182\pi\)
\(132\) −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 −0.744886 0.667192i \(-0.767496\pi\)
−0.205363 0.978686i \(-0.565837\pi\)
\(138\) 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 −0.920174 0.391509i \(-0.871953\pi\)
0.799144 + 0.601140i \(0.205286\pi\)
\(150\) −1.35203 2.34179i −0.110393 0.191206i
\(151\) 9.27736 + 16.0689i 0.754981 + 1.30766i 0.945384 + 0.325959i \(0.105687\pi\)
−0.190403 + 0.981706i \(0.560980\pi\)
\(152\) −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 0.601540 0.798843i \(-0.294554\pi\)
−0.992588 + 0.121528i \(0.961221\pi\)
\(158\) 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 0.457013 + 0.889460i \(0.348919\pi\)
−0.998801 + 0.0489451i \(0.984414\pi\)
\(164\) 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 −0.916808 0.399329i \(-0.869243\pi\)
0.804233 + 0.594314i \(0.202576\pi\)
\(174\) 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 0.952295 0.305178i \(-0.0987159\pi\)
−0.740440 + 0.672123i \(0.765383\pi\)
\(180\) −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 −0.996861 0.0791703i \(-0.974773\pi\)
0.566994 + 0.823722i \(0.308106\pi\)
\(192\) −15.8965 27.5335i −1.14723 1.98706i
\(193\) −11.4851 19.8927i −0.826714 1.43191i −0.900602 0.434645i \(-0.856874\pi\)
0.0738876 0.997267i \(-0.476459\pi\)
\(194\) −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 0.987379 0.158374i \(-0.0506251\pi\)
−0.630845 + 0.775909i \(0.717292\pi\)
\(200\) 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 0.649044 0.760751i \(-0.275169\pi\)
−0.983352 + 0.181713i \(0.941836\pi\)
\(228\) 12.7936 + 22.1592i 0.847279 + 1.46753i
\(229\) −5.56997 + 9.64748i −0.368074 + 0.637523i −0.989264 0.146137i \(-0.953316\pi\)
0.621190 + 0.783660i \(0.286649\pi\)
\(230\) 21.0228 1.38620
\(231\) 0 0
\(232\) −11.7391 −0.770711
\(233\) 8.54166 14.7946i 0.559583 0.969226i −0.437948 0.899000i \(-0.644295\pi\)
0.997531 0.0702257i \(-0.0223720\pi\)
\(234\) 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 0.951472 0.307735i \(-0.0995709\pi\)
−0.742242 + 0.670132i \(0.766238\pi\)
\(242\) −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 −0.738891 0.673825i \(-0.764650\pi\)
0.952995 + 0.302986i \(0.0979836\pi\)
\(258\) −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 0.867970 0.496617i \(-0.165425\pi\)
−0.864068 + 0.503375i \(0.832091\pi\)
\(264\) 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 0.794073 0.607822i \(-0.207957\pi\)
−0.923426 + 0.383777i \(0.874623\pi\)
\(270\) 0.713805 + 1.23635i 0.0434408 + 0.0752417i
\(271\) 0.783616 1.35726i 0.0476013 0.0824479i −0.841243 0.540657i \(-0.818176\pi\)
0.888844 + 0.458209i \(0.151509\pi\)
\(272\) −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 0.991474 0.130302i \(-0.0415947\pi\)
−0.608582 + 0.793491i \(0.708261\pi\)
\(278\) −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 0.915136 0.403144i \(-0.132083\pi\)
−0.806701 + 0.590959i \(0.798749\pi\)
\(284\) 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 0.829653 0.558279i \(-0.188538\pi\)
−0.898311 + 0.439361i \(0.855205\pi\)
\(312\) −2.46122 4.26295i −0.139339 0.241342i
\(313\) 6.98026 12.0902i 0.394548 0.683377i −0.598496 0.801126i \(-0.704235\pi\)
0.993043 + 0.117749i \(0.0375679\pi\)
\(314\) 21.6897 1.22402
\(315\) 0 0
\(316\) −15.0114 −0.844457
\(317\) −1.53431 + 2.65750i −0.0861753 + 0.149260i −0.905891 0.423510i \(-0.860798\pi\)
0.819716 + 0.572770i \(0.194131\pi\)
\(318\) −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 −0.990162 0.139922i \(-0.955315\pi\)
0.616257 + 0.787545i \(0.288648\pi\)
\(332\) 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 0.930062 0.367404i \(-0.119753\pi\)
−0.783212 + 0.621755i \(0.786420\pi\)
\(348\) −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 0.954951 + 0.296762i \(0.0959068\pi\)
−0.220472 + 0.975393i \(0.570760\pi\)
\(354\) −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 −0.940134 0.340806i \(-0.889300\pi\)
0.765213 + 0.643777i \(0.222634\pi\)
\(360\) −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 0.909682 + 0.415305i \(0.136325\pi\)
−0.0951768 + 0.995460i \(0.530342\pi\)
\(368\) 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 −0.586321 0.810079i \(-0.699424\pi\)
0.994709 + 0.102729i \(0.0327574\pi\)
\(374\) −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 −0.663145 0.748491i \(-0.730779\pi\)
0.979785 + 0.200055i \(0.0641122\pi\)
\(384\) 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 0.987423 0.158100i \(-0.0505370\pi\)
−0.630631 + 0.776083i \(0.717204\pi\)
\(390\) −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 −0.940156 0.340745i \(-0.889321\pi\)
0.765172 + 0.643826i \(0.222654\pi\)
\(398\) −22.2639 −1.11599
\(399\) 0 0
\(400\) 0.688560 0.0344280
\(401\) −1.36841 + 2.37016i −0.0683352 + 0.118360i −0.898169 0.439651i \(-0.855102\pi\)
0.829833 + 0.558011i \(0.188435\pi\)
\(402\) −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 −0.991876 0.127208i \(-0.959398\pi\)
0.385772 0.922594i \(-0.373935\pi\)
\(410\) 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 0.998549 0.0538455i \(-0.0171478\pi\)
−0.545906 + 0.837846i \(0.683815\pi\)
\(432\) −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 −0.0865713 + 0.996246i \(0.527591\pi\)
−0.819488 + 0.573096i \(0.805742\pi\)
\(440\) 20.2234 0.964112
\(441\) 0 0
\(442\) −8.36254 −0.397766
\(443\) −17.8135 + 30.8539i −0.846344 + 1.46591i 0.0381050 + 0.999274i \(0.487868\pi\)
−0.884449 + 0.466637i \(0.845465\pi\)
\(444\) 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 −0.988746 0.149603i \(-0.952200\pi\)
0.623933 + 0.781478i \(0.285534\pi\)
\(458\) −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 −0.696186 0.717862i \(-0.745121\pi\)
0.969779 + 0.243984i \(0.0784543\pi\)
\(468\) −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 0.999792 + 0.0204092i \(0.00649690\pi\)
−0.482221 + 0.876050i \(0.660170\pi\)
\(480\) −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 0.951918 + 0.306353i \(0.0991087\pi\)
−0.210650 + 0.977562i \(0.567558\pi\)
\(488\) 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 −0.654388 0.756159i \(-0.727074\pi\)
0.982047 + 0.188637i \(0.0604071\pi\)
\(500\) 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 −0.706996 0.707217i \(-0.749950\pi\)
0.965966 + 0.258668i \(0.0832835\pi\)
\(510\) −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 0.943808 0.330495i \(-0.107216\pi\)
−0.758121 + 0.652114i \(0.773882\pi\)
\(522\) 20.3934 + 35.3224i 0.892594 + 1.54602i
\(523\) 16.3554 28.3284i 0.715172 1.23871i −0.247721 0.968831i \(-0.579682\pi\)
0.962893 0.269883i \(-0.0869849\pi\)
\(524\) −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 −0.386388 0.922336i \(-0.626277\pi\)
0.991961 0.126547i \(-0.0403893\pi\)
\(542\) 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 0.820504 0.571640i \(-0.193693\pi\)
−0.905307 + 0.424758i \(0.860359\pi\)
\(558\) −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 0.614138 0.789199i \(-0.289504\pi\)
−0.990535 + 0.137260i \(0.956170\pi\)
\(564\) 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 −0.143434 0.989660i \(-0.545815\pi\)
0.928788 0.370612i \(-0.120852\pi\)
\(570\) 20.7362 + 35.9161i 0.868544 + 1.50436i
\(571\) −8.78514 15.2163i −0.367646 0.636782i 0.621551 0.783374i \(-0.286503\pi\)
−0.989197 + 0.146592i \(0.953170\pi\)
\(572\) 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 −0.963760 0.266770i \(-0.914043\pi\)
0.250850 0.968026i \(-0.419290\pi\)
\(578\) 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 0.271013 + 0.962576i \(0.412641\pi\)
−0.969121 + 0.246584i \(0.920692\pi\)
\(594\) −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 0.559495 0.828834i \(-0.310995\pi\)
−0.997539 + 0.0701203i \(0.977662\pi\)
\(600\) −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 −0.0517636 + 0.998659i \(0.516484\pi\)
−0.838983 + 0.544158i \(0.816849\pi\)
\(608\) −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 0.973595 0.228282i \(-0.0733108\pi\)
−0.684496 + 0.729017i \(0.739977\pi\)
\(614\) −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 0.973150 0.230172i \(-0.0739288\pi\)
−0.685910 + 0.727687i \(0.740595\pi\)
\(620\) −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 −0.887695 0.460433i \(-0.847694\pi\)
0.0451008 0.998982i \(-0.485639\pi\)
\(642\) 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 −0.947514 0.319713i \(-0.896413\pi\)
0.196877 0.980428i \(-0.436920\pi\)
\(648\) 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 0.192843 + 0.981230i \(0.438229\pi\)
−0.946191 + 0.323608i \(0.895104\pi\)
\(654\) 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 −0.912638 0.408770i \(-0.865958\pi\)
0.102314 0.994752i \(-0.467375\pi\)
\(662\) −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 0.429391 + 0.903119i \(0.358728\pi\)
−0.996819 + 0.0796963i \(0.974605\pi\)
\(678\) −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 −0.826795 0.562503i \(-0.809839\pi\)
−0.0737441 0.997277i \(-0.523495\pi\)
\(684\) −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 0.407495 + 0.913207i \(0.366402\pi\)
−0.994608 + 0.103703i \(0.966931\pi\)
\(692\) 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 −0.712706 0.701463i \(-0.752531\pi\)
0.963838 + 0.266490i \(0.0858641\pi\)
\(710\) 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 −0.978831 0.204670i \(-0.934388\pi\)
0.666665 + 0.745358i \(0.267721\pi\)
\(720\) −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 −0.272830 0.962062i \(-0.587960\pi\)
0.969585 0.244754i \(-0.0787071\pi\)
\(734\) −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 0.938334 0.345729i \(-0.112368\pi\)
−0.768578 + 0.639757i \(0.779035\pi\)
\(740\) −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 −0.158561 + 0.987349i \(0.550685\pi\)
−0.775789 + 0.630992i \(0.782648\pi\)
\(752\) 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 −0.831076 0.556159i \(-0.812275\pi\)
0.897186 + 0.441653i \(0.145608\pi\)
\(762\) 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 0.992858 0.119305i \(-0.0380667\pi\)
−0.599750 + 0.800187i \(0.704733\pi\)
\(774\) −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 0.964648 + 0.263541i \(0.0848905\pi\)
−0.254091 + 0.967180i \(0.581776\pi\)
\(788\) −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 0.842851 0.538148i \(-0.180876\pi\)
−0.887475 + 0.460856i \(0.847542\pi\)
\(810\) 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 0.440541 + 0.897733i \(0.354787\pi\)
−0.997730 + 0.0673467i \(0.978547\pi\)
\(822\) 60.9140 + 105.506i 2.12462 + 3.67995i
\(823\) 17.1266 + 29.6641i 0.596995 + 1.03402i 0.993262 + 0.115890i \(0.0369720\pi\)
−0.396267 + 0.918135i \(0.629695\pi\)
\(824\) 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 0.638607 0.769533i \(-0.279511\pi\)
−0.985739 + 0.168284i \(0.946178\pi\)
\(830\) 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 −0.815182 0.579205i \(-0.803363\pi\)
−0.0940154 0.995571i \(-0.529970\pi\)
\(858\) −13.1139 22.7139i −0.447700 0.775438i
\(859\) −6.13597 + 10.6278i −0.209357 + 0.362616i −0.951512 0.307611i \(-0.900470\pi\)
0.742155 + 0.670228i \(0.233804\pi\)
\(860\) 20.9672 0.714975
\(861\) 0 0
\(862\) −41.5977 −1.41682
\(863\) −12.2226 + 21.1702i −0.416064 + 0.720643i −0.995539 0.0943460i \(-0.969924\pi\)
0.579476 + 0.814989i \(0.303257\pi\)
\(864\) −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 0.0561539 0.998422i \(-0.482116\pi\)
0.836582 0.547842i \(-0.184550\pi\)
\(878\) −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 −0.905560 0.424219i \(-0.860549\pi\)
0.820164 + 0.572128i \(0.193882\pi\)
\(888\) −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 0.976345 0.216220i \(-0.0693730\pi\)
−0.675425 + 0.737429i \(0.736040\pi\)
\(908\) −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 0.139620 + 0.990205i \(0.455412\pi\)
−0.927353 + 0.374188i \(0.877922\pi\)
\(920\) −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 −0.440267 0.897867i \(-0.645116\pi\)
0.997709 0.0676505i \(-0.0215503\pi\)
\(930\) −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 0.791005 0.611810i \(-0.209558\pi\)
−0.925345 + 0.379126i \(0.876225\pi\)
\(942\) 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 −0.981414 0.191902i \(-0.938535\pi\)
0.656899 + 0.753979i \(0.271868\pi\)
\(948\) −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 0.0403390 + 0.999186i \(0.487156\pi\)
−0.885490 + 0.464658i \(0.846177\pi\)
\(972\) 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 0.716094 0.698004i \(-0.245928\pi\)
−0.962536 + 0.271153i \(0.912595\pi\)
\(978\) 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 0.920125 0.391625i \(-0.128087\pi\)
−0.799219 + 0.601039i \(0.794754\pi\)
\(984\) −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 0.976605 0.215042i \(-0.0689888\pi\)
−0.674534 + 0.738244i \(0.735655\pi\)
\(992\) 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 0.956883 + 0.290473i \(0.0938125\pi\)
−0.226885 + 0.973922i \(0.572854\pi\)
\(998\) 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.79.2 10
7.2 even 3 637.2.a.k.1.4 5
7.3 odd 6 91.2.e.c.53.2 10
7.4 even 3 inner 637.2.e.m.508.2 10
7.5 odd 6 637.2.a.l.1.4 5
7.6 odd 2 91.2.e.c.79.2 yes 10
21.2 odd 6 5733.2.a.bm.1.2 5
21.5 even 6 5733.2.a.bl.1.2 5
21.17 even 6 819.2.j.h.235.4 10
21.20 even 2 819.2.j.h.352.4 10
28.3 even 6 1456.2.r.p.417.5 10
28.27 even 2 1456.2.r.p.625.5 10
91.12 odd 6 8281.2.a.bw.1.2 5
91.38 odd 6 1183.2.e.f.508.4 10
91.51 even 6 8281.2.a.bx.1.2 5
91.90 odd 2 1183.2.e.f.170.4 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.e.c.53.2 10 7.3 odd 6
91.2.e.c.79.2 yes 10 7.6 odd 2
637.2.a.k.1.4 5 7.2 even 3
637.2.a.l.1.4 5 7.5 odd 6
637.2.e.m.79.2 10 1.1 even 1 trivial
637.2.e.m.508.2 10 7.4 even 3 inner
819.2.j.h.235.4 10 21.17 even 6
819.2.j.h.352.4 10 21.20 even 2
1183.2.e.f.170.4 10 91.90 odd 2
1183.2.e.f.508.4 10 91.38 odd 6
1456.2.r.p.417.5 10 28.3 even 6
1456.2.r.p.625.5 10 28.27 even 2
5733.2.a.bl.1.2 5 21.5 even 6
5733.2.a.bm.1.2 5 21.2 odd 6
8281.2.a.bw.1.2 5 91.12 odd 6
8281.2.a.bx.1.2 5 91.51 even 6