Properties

Label 637.2.h.m.165.8
Level $637$
Weight $2$
Character 637.165
Analytic conductor $5.086$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [637,2,Mod(165,637)]
 
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([4, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.165");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.h (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: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 8x^{14} + 45x^{12} + 124x^{10} + 248x^{8} + 250x^{6} + 177x^{4} + 14x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 165.8
Root \(0.756863 + 1.31093i\) of defining polynomial
Character \(\chi\) \(=\) 637.165
Dual form 637.2.h.m.471.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.43210 q^{2} +(0.376796 + 0.652630i) q^{3} +3.91511 q^{4} +(0.170769 + 0.295780i) q^{5} +(0.916405 + 1.58726i) q^{6} +4.65773 q^{8} +(1.21605 - 2.10626i) q^{9} +O(q^{10})\) \(q+2.43210 q^{2} +(0.376796 + 0.652630i) q^{3} +3.91511 q^{4} +(0.170769 + 0.295780i) q^{5} +(0.916405 + 1.58726i) q^{6} +4.65773 q^{8} +(1.21605 - 2.10626i) q^{9} +(0.415326 + 0.719366i) q^{10} +(1.21605 + 2.10626i) q^{11} +(1.47520 + 2.55511i) q^{12} +(-2.50139 - 2.59674i) q^{13} +(-0.128690 + 0.222897i) q^{15} +3.49784 q^{16} +1.94823 q^{17} +(2.95755 - 5.12263i) q^{18} +(-3.14519 + 5.44764i) q^{19} +(0.668577 + 1.15801i) q^{20} +(2.95755 + 5.12263i) q^{22} -3.68948 q^{23} +(1.75501 + 3.03977i) q^{24} +(2.44168 - 4.22911i) q^{25} +(-6.08362 - 6.31553i) q^{26} +4.09359 q^{27} +(-2.22068 + 3.84632i) q^{29} +(-0.312986 + 0.542108i) q^{30} +(-0.987661 + 1.71068i) q^{31} -0.808361 q^{32} +(-0.916405 + 1.58726i) q^{33} +4.73830 q^{34} +(4.76096 - 8.24623i) q^{36} -9.62867 q^{37} +(-7.64942 + 13.2492i) q^{38} +(0.752198 - 2.61092i) q^{39} +(0.795393 + 1.37766i) q^{40} +(6.26793 - 10.8564i) q^{41} +(4.20368 + 7.28099i) q^{43} +(4.76096 + 8.24623i) q^{44} +0.830652 q^{45} -8.97318 q^{46} +(-4.50265 - 7.79882i) q^{47} +(1.31797 + 2.28279i) q^{48} +(5.93840 - 10.2856i) q^{50} +(0.734087 + 1.27148i) q^{51} +(-9.79320 - 10.1665i) q^{52} +(-0.746129 + 1.29233i) q^{53} +9.95601 q^{54} +(-0.415326 + 0.719366i) q^{55} -4.74039 q^{57} +(-5.40090 + 9.35464i) q^{58} -0.626991 q^{59} +(-0.503834 + 0.872666i) q^{60} +(-0.571597 + 0.990035i) q^{61} +(-2.40209 + 4.16054i) q^{62} -8.96169 q^{64} +(0.340905 - 1.18330i) q^{65} +(-2.22879 + 3.86037i) q^{66} +(2.79599 + 4.84280i) q^{67} +7.62754 q^{68} +(-1.39018 - 2.40786i) q^{69} +(-4.74859 - 8.22481i) q^{71} +(5.66402 - 9.81038i) q^{72} +(5.95934 - 10.3219i) q^{73} -23.4179 q^{74} +3.68006 q^{75} +(-12.3138 + 21.3281i) q^{76} +(1.82942 - 6.35002i) q^{78} +(-2.23583 - 3.87258i) q^{79} +(0.597321 + 1.03459i) q^{80} +(-2.10570 - 3.64718i) q^{81} +(15.2442 - 26.4038i) q^{82} -1.41231 q^{83} +(0.332697 + 0.576248i) q^{85} +(10.2238 + 17.7081i) q^{86} -3.34697 q^{87} +(5.66402 + 9.81038i) q^{88} -12.4444 q^{89} +2.02023 q^{90} -14.4447 q^{92} -1.48859 q^{93} +(-10.9509 - 18.9675i) q^{94} -2.14840 q^{95} +(-0.304587 - 0.527560i) q^{96} +(5.13850 + 8.90014i) q^{97} +5.91511 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 8 q^{2} + 24 q^{4} + 24 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 8 q^{2} + 24 q^{4} + 24 q^{8} - 4 q^{9} - 4 q^{11} - 8 q^{15} + 8 q^{16} + 28 q^{18} + 28 q^{22} - 24 q^{23} + 12 q^{25} + 8 q^{29} + 28 q^{30} + 4 q^{36} + 16 q^{37} + 20 q^{39} + 32 q^{43} + 4 q^{44} + 8 q^{46} + 36 q^{50} + 44 q^{51} + 4 q^{53} - 96 q^{57} - 48 q^{58} - 64 q^{60} - 64 q^{64} - 68 q^{65} + 20 q^{67} + 8 q^{71} + 28 q^{72} - 152 q^{74} + 28 q^{78} + 4 q^{79} + 56 q^{81} + 36 q^{85} - 4 q^{86} + 28 q^{88} - 160 q^{92} - 16 q^{93} - 104 q^{95} + 56 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.43210 1.71975 0.859877 0.510502i \(-0.170540\pi\)
0.859877 + 0.510502i \(0.170540\pi\)
\(3\) 0.376796 + 0.652630i 0.217543 + 0.376796i 0.954056 0.299627i \(-0.0968623\pi\)
−0.736513 + 0.676423i \(0.763529\pi\)
\(4\) 3.91511 1.95755
\(5\) 0.170769 + 0.295780i 0.0763700 + 0.132277i 0.901681 0.432401i \(-0.142334\pi\)
−0.825311 + 0.564678i \(0.809000\pi\)
\(6\) 0.916405 + 1.58726i 0.374121 + 0.647996i
\(7\) 0 0
\(8\) 4.65773 1.64675
\(9\) 1.21605 2.10626i 0.405350 0.702086i
\(10\) 0.415326 + 0.719366i 0.131338 + 0.227483i
\(11\) 1.21605 + 2.10626i 0.366653 + 0.635061i 0.989040 0.147648i \(-0.0471704\pi\)
−0.622387 + 0.782710i \(0.713837\pi\)
\(12\) 1.47520 + 2.55511i 0.425852 + 0.737598i
\(13\) −2.50139 2.59674i −0.693760 0.720206i
\(14\) 0 0
\(15\) −0.128690 + 0.222897i −0.0332276 + 0.0575518i
\(16\) 3.49784 0.874460
\(17\) 1.94823 0.472516 0.236258 0.971690i \(-0.424079\pi\)
0.236258 + 0.971690i \(0.424079\pi\)
\(18\) 2.95755 5.12263i 0.697102 1.20742i
\(19\) −3.14519 + 5.44764i −0.721557 + 1.24977i 0.238819 + 0.971064i \(0.423240\pi\)
−0.960376 + 0.278709i \(0.910093\pi\)
\(20\) 0.668577 + 1.15801i 0.149498 + 0.258939i
\(21\) 0 0
\(22\) 2.95755 + 5.12263i 0.630552 + 1.09215i
\(23\) −3.68948 −0.769309 −0.384655 0.923061i \(-0.625679\pi\)
−0.384655 + 0.923061i \(0.625679\pi\)
\(24\) 1.75501 + 3.03977i 0.358240 + 0.620491i
\(25\) 2.44168 4.22911i 0.488335 0.845821i
\(26\) −6.08362 6.31553i −1.19310 1.23858i
\(27\) 4.09359 0.787811
\(28\) 0 0
\(29\) −2.22068 + 3.84632i −0.412369 + 0.714244i −0.995148 0.0983864i \(-0.968632\pi\)
0.582779 + 0.812631i \(0.301965\pi\)
\(30\) −0.312986 + 0.542108i −0.0571432 + 0.0989750i
\(31\) −0.987661 + 1.71068i −0.177389 + 0.307247i −0.940986 0.338447i \(-0.890098\pi\)
0.763596 + 0.645694i \(0.223432\pi\)
\(32\) −0.808361 −0.142899
\(33\) −0.916405 + 1.58726i −0.159526 + 0.276307i
\(34\) 4.73830 0.812611
\(35\) 0 0
\(36\) 4.76096 8.24623i 0.793494 1.37437i
\(37\) −9.62867 −1.58294 −0.791472 0.611206i \(-0.790685\pi\)
−0.791472 + 0.611206i \(0.790685\pi\)
\(38\) −7.64942 + 13.2492i −1.24090 + 2.14930i
\(39\) 0.752198 2.61092i 0.120448 0.418082i
\(40\) 0.795393 + 1.37766i 0.125763 + 0.217827i
\(41\) 6.26793 10.8564i 0.978887 1.69548i 0.312426 0.949942i \(-0.398859\pi\)
0.666461 0.745540i \(-0.267808\pi\)
\(42\) 0 0
\(43\) 4.20368 + 7.28099i 0.641055 + 1.11034i 0.985198 + 0.171423i \(0.0548365\pi\)
−0.344142 + 0.938918i \(0.611830\pi\)
\(44\) 4.76096 + 8.24623i 0.717742 + 1.24317i
\(45\) 0.830652 0.123826
\(46\) −8.97318 −1.32302
\(47\) −4.50265 7.79882i −0.656779 1.13757i −0.981445 0.191745i \(-0.938585\pi\)
0.324666 0.945829i \(-0.394748\pi\)
\(48\) 1.31797 + 2.28279i 0.190233 + 0.329493i
\(49\) 0 0
\(50\) 5.93840 10.2856i 0.839816 1.45460i
\(51\) 0.734087 + 1.27148i 0.102793 + 0.178042i
\(52\) −9.79320 10.1665i −1.35807 1.40984i
\(53\) −0.746129 + 1.29233i −0.102489 + 0.177516i −0.912709 0.408609i \(-0.866014\pi\)
0.810221 + 0.586125i \(0.199347\pi\)
\(54\) 9.95601 1.35484
\(55\) −0.415326 + 0.719366i −0.0560025 + 0.0969993i
\(56\) 0 0
\(57\) −4.74039 −0.627879
\(58\) −5.40090 + 9.35464i −0.709173 + 1.22832i
\(59\) −0.626991 −0.0816273 −0.0408136 0.999167i \(-0.512995\pi\)
−0.0408136 + 0.999167i \(0.512995\pi\)
\(60\) −0.503834 + 0.872666i −0.0650447 + 0.112661i
\(61\) −0.571597 + 0.990035i −0.0731855 + 0.126761i −0.900296 0.435279i \(-0.856650\pi\)
0.827110 + 0.562040i \(0.189983\pi\)
\(62\) −2.40209 + 4.16054i −0.305066 + 0.528389i
\(63\) 0 0
\(64\) −8.96169 −1.12021
\(65\) 0.340905 1.18330i 0.0422841 0.146770i
\(66\) −2.22879 + 3.86037i −0.274345 + 0.475179i
\(67\) 2.79599 + 4.84280i 0.341585 + 0.591642i 0.984727 0.174104i \(-0.0557030\pi\)
−0.643142 + 0.765747i \(0.722370\pi\)
\(68\) 7.62754 0.924975
\(69\) −1.39018 2.40786i −0.167358 0.289873i
\(70\) 0 0
\(71\) −4.74859 8.22481i −0.563554 0.976105i −0.997183 0.0750130i \(-0.976100\pi\)
0.433628 0.901092i \(-0.357233\pi\)
\(72\) 5.66402 9.81038i 0.667512 1.15616i
\(73\) 5.95934 10.3219i 0.697488 1.20808i −0.271847 0.962340i \(-0.587634\pi\)
0.969335 0.245744i \(-0.0790322\pi\)
\(74\) −23.4179 −2.72227
\(75\) 3.68006 0.424936
\(76\) −12.3138 + 21.3281i −1.41249 + 2.44650i
\(77\) 0 0
\(78\) 1.82942 6.35002i 0.207141 0.718998i
\(79\) −2.23583 3.87258i −0.251551 0.435699i 0.712402 0.701772i \(-0.247607\pi\)
−0.963953 + 0.266073i \(0.914274\pi\)
\(80\) 0.597321 + 1.03459i 0.0667825 + 0.115671i
\(81\) −2.10570 3.64718i −0.233967 0.405242i
\(82\) 15.2442 26.4038i 1.68344 2.91581i
\(83\) −1.41231 −0.155021 −0.0775104 0.996992i \(-0.524697\pi\)
−0.0775104 + 0.996992i \(0.524697\pi\)
\(84\) 0 0
\(85\) 0.332697 + 0.576248i 0.0360861 + 0.0625029i
\(86\) 10.2238 + 17.7081i 1.10246 + 1.90951i
\(87\) −3.34697 −0.358833
\(88\) 5.66402 + 9.81038i 0.603787 + 1.04579i
\(89\) −12.4444 −1.31910 −0.659551 0.751660i \(-0.729253\pi\)
−0.659551 + 0.751660i \(0.729253\pi\)
\(90\) 2.02023 0.212951
\(91\) 0 0
\(92\) −14.4447 −1.50596
\(93\) −1.48859 −0.154359
\(94\) −10.9509 18.9675i −1.12950 1.95635i
\(95\) −2.14840 −0.220421
\(96\) −0.304587 0.527560i −0.0310868 0.0538439i
\(97\) 5.13850 + 8.90014i 0.521736 + 0.903673i 0.999680 + 0.0252826i \(0.00804857\pi\)
−0.477945 + 0.878390i \(0.658618\pi\)
\(98\) 0 0
\(99\) 5.91511 0.594490
\(100\) 9.55942 16.5574i 0.955942 1.65574i
\(101\) 7.52683 + 13.0369i 0.748948 + 1.29722i 0.948328 + 0.317293i \(0.102774\pi\)
−0.199380 + 0.979922i \(0.563893\pi\)
\(102\) 1.78537 + 3.09235i 0.176778 + 0.306189i
\(103\) 8.80880 + 15.2573i 0.867957 + 1.50335i 0.864080 + 0.503354i \(0.167901\pi\)
0.00387687 + 0.999992i \(0.498766\pi\)
\(104\) −11.6508 12.0949i −1.14245 1.18600i
\(105\) 0 0
\(106\) −1.81466 + 3.14308i −0.176255 + 0.305283i
\(107\) 6.38454 0.617217 0.308608 0.951189i \(-0.400137\pi\)
0.308608 + 0.951189i \(0.400137\pi\)
\(108\) 16.0268 1.54218
\(109\) 4.08736 7.07951i 0.391498 0.678095i −0.601149 0.799137i \(-0.705290\pi\)
0.992647 + 0.121042i \(0.0386236\pi\)
\(110\) −1.01011 + 1.74957i −0.0963106 + 0.166815i
\(111\) −3.62804 6.28396i −0.344359 0.596447i
\(112\) 0 0
\(113\) 4.81083 + 8.33259i 0.452564 + 0.783865i 0.998545 0.0539336i \(-0.0171759\pi\)
−0.545980 + 0.837798i \(0.683843\pi\)
\(114\) −11.5291 −1.07980
\(115\) −0.630047 1.09127i −0.0587522 0.101762i
\(116\) −8.69418 + 15.0588i −0.807234 + 1.39817i
\(117\) −8.51122 + 2.11081i −0.786863 + 0.195144i
\(118\) −1.52490 −0.140379
\(119\) 0 0
\(120\) −0.599402 + 1.03819i −0.0547177 + 0.0947738i
\(121\) 2.54245 4.40365i 0.231132 0.400332i
\(122\) −1.39018 + 2.40786i −0.125861 + 0.217998i
\(123\) 9.44693 0.851801
\(124\) −3.86680 + 6.69749i −0.347249 + 0.601452i
\(125\) 3.37553 0.301917
\(126\) 0 0
\(127\) −4.50988 + 7.81134i −0.400187 + 0.693145i −0.993748 0.111644i \(-0.964388\pi\)
0.593561 + 0.804789i \(0.297722\pi\)
\(128\) −20.1790 −1.78359
\(129\) −3.16786 + 5.48690i −0.278915 + 0.483094i
\(130\) 0.829115 2.87791i 0.0727182 0.252409i
\(131\) −0.0962416 0.166695i −0.00840867 0.0145642i 0.861790 0.507264i \(-0.169343\pi\)
−0.870199 + 0.492700i \(0.836010\pi\)
\(132\) −3.58782 + 6.21429i −0.312280 + 0.540885i
\(133\) 0 0
\(134\) 6.80013 + 11.7782i 0.587442 + 1.01748i
\(135\) 0.699056 + 1.21080i 0.0601651 + 0.104209i
\(136\) 9.07434 0.778118
\(137\) 4.87680 0.416653 0.208326 0.978059i \(-0.433198\pi\)
0.208326 + 0.978059i \(0.433198\pi\)
\(138\) −3.38106 5.85616i −0.287815 0.498510i
\(139\) −5.53701 9.59038i −0.469643 0.813446i 0.529755 0.848151i \(-0.322284\pi\)
−0.999398 + 0.0347054i \(0.988951\pi\)
\(140\) 0 0
\(141\) 3.39316 5.87713i 0.285756 0.494943i
\(142\) −11.5491 20.0035i −0.969175 1.67866i
\(143\) 2.42760 8.42634i 0.203006 0.704646i
\(144\) 4.25355 7.36736i 0.354462 0.613946i
\(145\) −1.51689 −0.125971
\(146\) 14.4937 25.1038i 1.19951 2.07761i
\(147\) 0 0
\(148\) −37.6973 −3.09869
\(149\) −7.95435 + 13.7773i −0.651646 + 1.12868i 0.331078 + 0.943603i \(0.392588\pi\)
−0.982723 + 0.185080i \(0.940746\pi\)
\(150\) 8.95026 0.730786
\(151\) 5.29518 9.17152i 0.430916 0.746368i −0.566037 0.824380i \(-0.691524\pi\)
0.996952 + 0.0780122i \(0.0248573\pi\)
\(152\) −14.6494 + 25.3736i −1.18823 + 2.05807i
\(153\) 2.36915 4.10349i 0.191534 0.331747i
\(154\) 0 0
\(155\) −0.674646 −0.0541889
\(156\) 2.94493 10.2220i 0.235783 0.818418i
\(157\) 4.56194 7.90151i 0.364082 0.630609i −0.624546 0.780988i \(-0.714716\pi\)
0.988628 + 0.150379i \(0.0480493\pi\)
\(158\) −5.43777 9.41849i −0.432606 0.749295i
\(159\) −1.12455 −0.0891829
\(160\) −0.138043 0.239097i −0.0109132 0.0189023i
\(161\) 0 0
\(162\) −5.12127 8.87031i −0.402365 0.696917i
\(163\) 5.48196 9.49504i 0.429380 0.743709i −0.567438 0.823416i \(-0.692065\pi\)
0.996818 + 0.0797075i \(0.0253986\pi\)
\(164\) 24.5396 42.5039i 1.91622 3.31900i
\(165\) −0.625973 −0.0487319
\(166\) −3.43487 −0.266598
\(167\) −9.13884 + 15.8289i −0.707185 + 1.22488i 0.258713 + 0.965954i \(0.416702\pi\)
−0.965897 + 0.258925i \(0.916632\pi\)
\(168\) 0 0
\(169\) −0.486122 + 12.9909i −0.0373940 + 0.999301i
\(170\) 0.809152 + 1.40149i 0.0620591 + 0.107490i
\(171\) 7.64942 + 13.2492i 0.584966 + 1.01319i
\(172\) 16.4579 + 28.5058i 1.25490 + 2.17355i
\(173\) −4.09918 + 7.09998i −0.311655 + 0.539802i −0.978721 0.205197i \(-0.934217\pi\)
0.667066 + 0.744999i \(0.267550\pi\)
\(174\) −8.14015 −0.617104
\(175\) 0 0
\(176\) 4.25355 + 7.36736i 0.320623 + 0.555335i
\(177\) −0.236248 0.409193i −0.0177575 0.0307568i
\(178\) −30.2659 −2.26853
\(179\) 7.77684 + 13.4699i 0.581268 + 1.00679i 0.995329 + 0.0965370i \(0.0307766\pi\)
−0.414061 + 0.910249i \(0.635890\pi\)
\(180\) 3.25209 0.242396
\(181\) 6.67302 0.496001 0.248001 0.968760i \(-0.420226\pi\)
0.248001 + 0.968760i \(0.420226\pi\)
\(182\) 0 0
\(183\) −0.861502 −0.0636841
\(184\) −17.1846 −1.26686
\(185\) −1.64427 2.84797i −0.120889 0.209387i
\(186\) −3.62039 −0.265460
\(187\) 2.36915 + 4.10349i 0.173249 + 0.300077i
\(188\) −17.6283 30.5332i −1.28568 2.22686i
\(189\) 0 0
\(190\) −5.22512 −0.379070
\(191\) 9.37296 16.2344i 0.678204 1.17468i −0.297318 0.954779i \(-0.596092\pi\)
0.975521 0.219905i \(-0.0705746\pi\)
\(192\) −3.37673 5.84867i −0.243694 0.422091i
\(193\) 4.08655 + 7.07811i 0.294156 + 0.509493i 0.974788 0.223132i \(-0.0716281\pi\)
−0.680632 + 0.732625i \(0.738295\pi\)
\(194\) 12.4973 + 21.6460i 0.897257 + 1.55409i
\(195\) 0.900710 0.223378i 0.0645012 0.0159965i
\(196\) 0 0
\(197\) −4.36006 + 7.55184i −0.310641 + 0.538047i −0.978501 0.206240i \(-0.933877\pi\)
0.667860 + 0.744287i \(0.267210\pi\)
\(198\) 14.3861 1.02238
\(199\) 17.4666 1.23818 0.619089 0.785321i \(-0.287502\pi\)
0.619089 + 0.785321i \(0.287502\pi\)
\(200\) 11.3727 19.6980i 0.804168 1.39286i
\(201\) −2.10704 + 3.64950i −0.148619 + 0.257416i
\(202\) 18.3060 + 31.7069i 1.28801 + 2.23089i
\(203\) 0 0
\(204\) 2.87403 + 4.97796i 0.201222 + 0.348527i
\(205\) 4.28146 0.299030
\(206\) 21.4239 + 37.1073i 1.49267 + 2.58539i
\(207\) −4.48659 + 7.77100i −0.311839 + 0.540122i
\(208\) −8.74945 9.08298i −0.606665 0.629791i
\(209\) −15.2988 −1.05824
\(210\) 0 0
\(211\) 11.6284 20.1410i 0.800535 1.38657i −0.118730 0.992927i \(-0.537882\pi\)
0.919265 0.393640i \(-0.128784\pi\)
\(212\) −2.92117 + 5.05962i −0.200627 + 0.347496i
\(213\) 3.57850 6.19815i 0.245195 0.424690i
\(214\) 15.5278 1.06146
\(215\) −1.43571 + 2.48673i −0.0979148 + 0.169593i
\(216\) 19.0668 1.29733
\(217\) 0 0
\(218\) 9.94086 17.2181i 0.673280 1.16616i
\(219\) 8.98182 0.606935
\(220\) −1.62605 + 2.81639i −0.109628 + 0.189881i
\(221\) −4.87329 5.05906i −0.327813 0.340309i
\(222\) −8.82376 15.2832i −0.592212 1.02574i
\(223\) −14.6364 + 25.3510i −0.980128 + 1.69763i −0.318272 + 0.947999i \(0.603103\pi\)
−0.661855 + 0.749632i \(0.730231\pi\)
\(224\) 0 0
\(225\) −5.93840 10.2856i −0.395893 0.685707i
\(226\) 11.7004 + 20.2657i 0.778299 + 1.34805i
\(227\) −19.8110 −1.31490 −0.657452 0.753496i \(-0.728366\pi\)
−0.657452 + 0.753496i \(0.728366\pi\)
\(228\) −18.5591 −1.22911
\(229\) −0.664107 1.15027i −0.0438855 0.0760118i 0.843248 0.537524i \(-0.180640\pi\)
−0.887134 + 0.461512i \(0.847307\pi\)
\(230\) −1.53234 2.65408i −0.101039 0.175005i
\(231\) 0 0
\(232\) −10.3433 + 17.9151i −0.679071 + 1.17618i
\(233\) −0.758171 1.31319i −0.0496695 0.0860300i 0.840122 0.542398i \(-0.182483\pi\)
−0.889791 + 0.456368i \(0.849150\pi\)
\(234\) −20.7001 + 5.13369i −1.35321 + 0.335600i
\(235\) 1.53782 2.66358i 0.100316 0.173753i
\(236\) −2.45474 −0.159790
\(237\) 1.68491 2.91834i 0.109446 0.189567i
\(238\) 0 0
\(239\) 22.4793 1.45406 0.727032 0.686603i \(-0.240899\pi\)
0.727032 + 0.686603i \(0.240899\pi\)
\(240\) −0.450136 + 0.779659i −0.0290562 + 0.0503268i
\(241\) −13.3106 −0.857409 −0.428704 0.903445i \(-0.641030\pi\)
−0.428704 + 0.903445i \(0.641030\pi\)
\(242\) 6.18348 10.7101i 0.397489 0.688472i
\(243\) 7.72722 13.3839i 0.495701 0.858580i
\(244\) −2.23786 + 3.87609i −0.143265 + 0.248141i
\(245\) 0 0
\(246\) 22.9759 1.46489
\(247\) 22.0134 5.45939i 1.40068 0.347373i
\(248\) −4.60026 + 7.96788i −0.292116 + 0.505961i
\(249\) −0.532152 0.921714i −0.0337238 0.0584113i
\(250\) 8.20963 0.519222
\(251\) 7.95169 + 13.7727i 0.501906 + 0.869327i 0.999998 + 0.00220260i \(0.000701110\pi\)
−0.498091 + 0.867125i \(0.665966\pi\)
\(252\) 0 0
\(253\) −4.48659 7.77100i −0.282069 0.488559i
\(254\) −10.9685 + 18.9980i −0.688224 + 1.19204i
\(255\) −0.250718 + 0.434256i −0.0157006 + 0.0271942i
\(256\) −31.1539 −1.94712
\(257\) 29.2397 1.82392 0.911960 0.410280i \(-0.134569\pi\)
0.911960 + 0.410280i \(0.134569\pi\)
\(258\) −7.70455 + 13.3447i −0.479664 + 0.830803i
\(259\) 0 0
\(260\) 1.33468 4.63275i 0.0827733 0.287311i
\(261\) 5.40090 + 9.35464i 0.334307 + 0.579037i
\(262\) −0.234069 0.405420i −0.0144608 0.0250469i
\(263\) 0.852177 + 1.47601i 0.0525475 + 0.0910149i 0.891103 0.453802i \(-0.149933\pi\)
−0.838555 + 0.544817i \(0.816599\pi\)
\(264\) −4.26836 + 7.39302i −0.262700 + 0.455009i
\(265\) −0.509661 −0.0313083
\(266\) 0 0
\(267\) −4.68899 8.12157i −0.286962 0.497032i
\(268\) 10.9466 + 18.9601i 0.668670 + 1.15817i
\(269\) −8.37874 −0.510861 −0.255430 0.966827i \(-0.582217\pi\)
−0.255430 + 0.966827i \(0.582217\pi\)
\(270\) 1.70017 + 2.94479i 0.103469 + 0.179214i
\(271\) 12.1575 0.738518 0.369259 0.929327i \(-0.379612\pi\)
0.369259 + 0.929327i \(0.379612\pi\)
\(272\) 6.81461 0.413196
\(273\) 0 0
\(274\) 11.8609 0.716540
\(275\) 11.8768 0.716198
\(276\) −5.44270 9.42704i −0.327612 0.567441i
\(277\) 10.3181 0.619957 0.309979 0.950744i \(-0.399678\pi\)
0.309979 + 0.950744i \(0.399678\pi\)
\(278\) −13.4666 23.3248i −0.807670 1.39893i
\(279\) 2.40209 + 4.16054i 0.143809 + 0.249085i
\(280\) 0 0
\(281\) −2.59677 −0.154910 −0.0774551 0.996996i \(-0.524679\pi\)
−0.0774551 + 0.996996i \(0.524679\pi\)
\(282\) 8.25250 14.2938i 0.491429 0.851181i
\(283\) 2.30184 + 3.98690i 0.136830 + 0.236997i 0.926295 0.376799i \(-0.122975\pi\)
−0.789465 + 0.613796i \(0.789642\pi\)
\(284\) −18.5912 32.2010i −1.10319 1.91078i
\(285\) −0.809509 1.40211i −0.0479512 0.0830539i
\(286\) 5.90416 20.4937i 0.349120 1.21182i
\(287\) 0 0
\(288\) −0.983006 + 1.70262i −0.0579242 + 0.100328i
\(289\) −13.2044 −0.776729
\(290\) −3.68922 −0.216638
\(291\) −3.87233 + 6.70708i −0.227000 + 0.393176i
\(292\) 23.3314 40.4112i 1.36537 2.36489i
\(293\) −0.980596 1.69844i −0.0572870 0.0992241i 0.835960 0.548791i \(-0.184912\pi\)
−0.893247 + 0.449567i \(0.851578\pi\)
\(294\) 0 0
\(295\) −0.107070 0.185451i −0.00623388 0.0107974i
\(296\) −44.8477 −2.60672
\(297\) 4.97800 + 8.62216i 0.288853 + 0.500308i
\(298\) −19.3458 + 33.5078i −1.12067 + 1.94106i
\(299\) 9.22882 + 9.58062i 0.533716 + 0.554061i
\(300\) 14.4078 0.831835
\(301\) 0 0
\(302\) 12.8784 22.3060i 0.741069 1.28357i
\(303\) −5.67216 + 9.82447i −0.325857 + 0.564401i
\(304\) −11.0014 + 19.0550i −0.630972 + 1.09288i
\(305\) −0.390443 −0.0223567
\(306\) 5.76200 9.98008i 0.329392 0.570523i
\(307\) −7.37658 −0.421004 −0.210502 0.977593i \(-0.567510\pi\)
−0.210502 + 0.977593i \(0.567510\pi\)
\(308\) 0 0
\(309\) −6.63825 + 11.4978i −0.377637 + 0.654086i
\(310\) −1.64081 −0.0931915
\(311\) 7.08088 12.2644i 0.401520 0.695453i −0.592390 0.805652i \(-0.701815\pi\)
0.993910 + 0.110199i \(0.0351487\pi\)
\(312\) 3.50353 12.1610i 0.198348 0.688479i
\(313\) −13.3576 23.1361i −0.755017 1.30773i −0.945366 0.326011i \(-0.894295\pi\)
0.190349 0.981716i \(-0.439038\pi\)
\(314\) 11.0951 19.2173i 0.626132 1.08449i
\(315\) 0 0
\(316\) −8.75352 15.1615i −0.492424 0.852904i
\(317\) −10.7181 18.5643i −0.601989 1.04268i −0.992520 0.122086i \(-0.961042\pi\)
0.390530 0.920590i \(-0.372292\pi\)
\(318\) −2.73503 −0.153373
\(319\) −10.8018 −0.604785
\(320\) −1.53037 2.65069i −0.0855506 0.148178i
\(321\) 2.40567 + 4.16674i 0.134271 + 0.232565i
\(322\) 0 0
\(323\) −6.12757 + 10.6133i −0.340947 + 0.590538i
\(324\) −8.24404 14.2791i −0.458002 0.793283i
\(325\) −17.0895 + 4.23824i −0.947953 + 0.235095i
\(326\) 13.3327 23.0929i 0.738429 1.27900i
\(327\) 6.16040 0.340671
\(328\) 29.1943 50.5660i 1.61199 2.79204i
\(329\) 0 0
\(330\) −1.52243 −0.0838069
\(331\) −5.30692 + 9.19185i −0.291695 + 0.505230i −0.974211 0.225641i \(-0.927552\pi\)
0.682516 + 0.730871i \(0.260886\pi\)
\(332\) −5.52933 −0.303462
\(333\) −11.7089 + 20.2805i −0.641646 + 1.11136i
\(334\) −22.2266 + 38.4975i −1.21618 + 2.10649i
\(335\) −0.954935 + 1.65400i −0.0521737 + 0.0903675i
\(336\) 0 0
\(337\) 6.75587 0.368016 0.184008 0.982925i \(-0.441093\pi\)
0.184008 + 0.982925i \(0.441093\pi\)
\(338\) −1.18230 + 31.5952i −0.0643085 + 1.71855i
\(339\) −3.62540 + 6.27938i −0.196905 + 0.341049i
\(340\) 1.30254 + 2.25607i 0.0706404 + 0.122353i
\(341\) −4.80418 −0.260161
\(342\) 18.6042 + 32.2233i 1.00600 + 1.74244i
\(343\) 0 0
\(344\) 19.5796 + 33.9129i 1.05566 + 1.82846i
\(345\) 0.474798 0.822375i 0.0255623 0.0442752i
\(346\) −9.96960 + 17.2679i −0.535969 + 0.928326i
\(347\) −16.0204 −0.860021 −0.430010 0.902824i \(-0.641490\pi\)
−0.430010 + 0.902824i \(0.641490\pi\)
\(348\) −13.1037 −0.702434
\(349\) 8.01922 13.8897i 0.429259 0.743498i −0.567549 0.823340i \(-0.692108\pi\)
0.996808 + 0.0798418i \(0.0254415\pi\)
\(350\) 0 0
\(351\) −10.2396 10.6300i −0.546552 0.567386i
\(352\) −0.983006 1.70262i −0.0523944 0.0907498i
\(353\) 1.92156 + 3.32823i 0.102274 + 0.177144i 0.912621 0.408806i \(-0.134055\pi\)
−0.810347 + 0.585950i \(0.800721\pi\)
\(354\) −0.574578 0.995198i −0.0305385 0.0528942i
\(355\) 1.62182 2.80908i 0.0860773 0.149090i
\(356\) −48.7210 −2.58221
\(357\) 0 0
\(358\) 18.9140 + 32.7601i 0.999638 + 1.73142i
\(359\) 10.5668 + 18.3022i 0.557692 + 0.965952i 0.997689 + 0.0679519i \(0.0216465\pi\)
−0.439996 + 0.898000i \(0.645020\pi\)
\(360\) 3.86895 0.203912
\(361\) −10.2845 17.8133i −0.541289 0.937540i
\(362\) 16.2294 0.853000
\(363\) 3.83194 0.201125
\(364\) 0 0
\(365\) 4.07067 0.213069
\(366\) −2.09526 −0.109521
\(367\) −7.36961 12.7645i −0.384690 0.666303i 0.607036 0.794674i \(-0.292358\pi\)
−0.991726 + 0.128371i \(0.959025\pi\)
\(368\) −12.9052 −0.672730
\(369\) −15.2442 26.4038i −0.793583 1.37453i
\(370\) −3.99904 6.92653i −0.207900 0.360093i
\(371\) 0 0
\(372\) −5.82798 −0.302166
\(373\) −6.46330 + 11.1948i −0.334657 + 0.579643i −0.983419 0.181349i \(-0.941954\pi\)
0.648762 + 0.760991i \(0.275287\pi\)
\(374\) 5.76200 + 9.98008i 0.297946 + 0.516058i
\(375\) 1.27189 + 2.20297i 0.0656800 + 0.113761i
\(376\) −20.9721 36.3247i −1.08155 1.87331i
\(377\) 15.5427 3.85463i 0.800488 0.198523i
\(378\) 0 0
\(379\) 13.4179 23.2405i 0.689231 1.19378i −0.282856 0.959162i \(-0.591282\pi\)
0.972087 0.234621i \(-0.0753848\pi\)
\(380\) −8.41121 −0.431486
\(381\) −6.79722 −0.348232
\(382\) 22.7960 39.4838i 1.16634 2.02017i
\(383\) −1.45391 + 2.51825i −0.0742914 + 0.128677i −0.900778 0.434280i \(-0.857003\pi\)
0.826487 + 0.562957i \(0.190336\pi\)
\(384\) −7.60337 13.1694i −0.388008 0.672049i
\(385\) 0 0
\(386\) 9.93889 + 17.2147i 0.505876 + 0.876203i
\(387\) 20.4475 1.03941
\(388\) 20.1178 + 34.8450i 1.02132 + 1.76899i
\(389\) 8.35048 14.4635i 0.423386 0.733327i −0.572882 0.819638i \(-0.694175\pi\)
0.996268 + 0.0863114i \(0.0275080\pi\)
\(390\) 2.19061 0.543278i 0.110926 0.0275100i
\(391\) −7.18797 −0.363511
\(392\) 0 0
\(393\) 0.0725269 0.125620i 0.00365850 0.00633671i
\(394\) −10.6041 + 18.3668i −0.534227 + 0.925308i
\(395\) 0.763620 1.32263i 0.0384219 0.0665487i
\(396\) 23.1583 1.16375
\(397\) −12.0492 + 20.8699i −0.604733 + 1.04743i 0.387360 + 0.921928i \(0.373387\pi\)
−0.992094 + 0.125500i \(0.959946\pi\)
\(398\) 42.4806 2.12936
\(399\) 0 0
\(400\) 8.54059 14.7927i 0.427030 0.739637i
\(401\) 1.84490 0.0921297 0.0460649 0.998938i \(-0.485332\pi\)
0.0460649 + 0.998938i \(0.485332\pi\)
\(402\) −5.12453 + 8.87594i −0.255588 + 0.442692i
\(403\) 6.91271 1.71437i 0.344347 0.0853990i
\(404\) 29.4683 + 51.0406i 1.46610 + 2.53937i
\(405\) 0.719175 1.24565i 0.0357361 0.0618967i
\(406\) 0 0
\(407\) −11.7089 20.2805i −0.580390 1.00527i
\(408\) 3.41918 + 5.92218i 0.169274 + 0.293192i
\(409\) 25.6703 1.26931 0.634657 0.772794i \(-0.281141\pi\)
0.634657 + 0.772794i \(0.281141\pi\)
\(410\) 10.4129 0.514259
\(411\) 1.83756 + 3.18274i 0.0906400 + 0.156993i
\(412\) 34.4874 + 59.7339i 1.69907 + 2.94288i
\(413\) 0 0
\(414\) −10.9118 + 18.8998i −0.536287 + 0.928876i
\(415\) −0.241178 0.417732i −0.0118389 0.0205057i
\(416\) 2.02202 + 2.09910i 0.0991378 + 0.102917i
\(417\) 4.17265 7.22724i 0.204335 0.353919i
\(418\) −37.2083 −1.81992
\(419\) −13.1199 + 22.7244i −0.640950 + 1.11016i 0.344271 + 0.938870i \(0.388126\pi\)
−0.985221 + 0.171288i \(0.945207\pi\)
\(420\) 0 0
\(421\) 23.6637 1.15330 0.576650 0.816992i \(-0.304360\pi\)
0.576650 + 0.816992i \(0.304360\pi\)
\(422\) 28.2815 48.9850i 1.37672 2.38455i
\(423\) −21.9018 −1.06490
\(424\) −3.47526 + 6.01933i −0.168774 + 0.292325i
\(425\) 4.75696 8.23929i 0.230746 0.399664i
\(426\) 8.70327 15.0745i 0.421675 0.730362i
\(427\) 0 0
\(428\) 24.9961 1.20823
\(429\) 6.41399 1.59069i 0.309670 0.0767991i
\(430\) −3.49180 + 6.04797i −0.168389 + 0.291659i
\(431\) 11.5088 + 19.9339i 0.554361 + 0.960182i 0.997953 + 0.0639528i \(0.0203707\pi\)
−0.443592 + 0.896229i \(0.646296\pi\)
\(432\) 14.3187 0.688909
\(433\) −12.9304 22.3961i −0.621394 1.07629i −0.989226 0.146394i \(-0.953233\pi\)
0.367832 0.929892i \(-0.380100\pi\)
\(434\) 0 0
\(435\) −0.571557 0.989965i −0.0274040 0.0474652i
\(436\) 16.0024 27.7170i 0.766378 1.32741i
\(437\) 11.6041 20.0989i 0.555101 0.961462i
\(438\) 21.8447 1.04378
\(439\) 35.6771 1.70277 0.851387 0.524537i \(-0.175762\pi\)
0.851387 + 0.524537i \(0.175762\pi\)
\(440\) −1.93447 + 3.35061i −0.0922225 + 0.159734i
\(441\) 0 0
\(442\) −11.8523 12.3041i −0.563757 0.585248i
\(443\) 3.42940 + 5.93990i 0.162936 + 0.282213i 0.935920 0.352212i \(-0.114570\pi\)
−0.772984 + 0.634425i \(0.781237\pi\)
\(444\) −14.2042 24.6024i −0.674100 1.16758i
\(445\) −2.12511 3.68079i −0.100740 0.174486i
\(446\) −35.5972 + 61.6562i −1.68558 + 2.91951i
\(447\) −11.9887 −0.567045
\(448\) 0 0
\(449\) 4.99075 + 8.64423i 0.235528 + 0.407946i 0.959426 0.281961i \(-0.0909847\pi\)
−0.723898 + 0.689907i \(0.757651\pi\)
\(450\) −14.4428 25.0156i −0.680839 1.17925i
\(451\) 30.4885 1.43565
\(452\) 18.8349 + 32.6230i 0.885919 + 1.53446i
\(453\) 7.98081 0.374971
\(454\) −48.1824 −2.26131
\(455\) 0 0
\(456\) −22.0794 −1.03396
\(457\) −8.77311 −0.410389 −0.205194 0.978721i \(-0.565783\pi\)
−0.205194 + 0.978721i \(0.565783\pi\)
\(458\) −1.61518 2.79757i −0.0754722 0.130722i
\(459\) 7.97526 0.372253
\(460\) −2.46670 4.27245i −0.115010 0.199204i
\(461\) 3.44272 + 5.96296i 0.160343 + 0.277723i 0.934992 0.354669i \(-0.115407\pi\)
−0.774649 + 0.632392i \(0.782073\pi\)
\(462\) 0 0
\(463\) −13.9526 −0.648432 −0.324216 0.945983i \(-0.605100\pi\)
−0.324216 + 0.945983i \(0.605100\pi\)
\(464\) −7.76757 + 13.4538i −0.360600 + 0.624578i
\(465\) −0.254204 0.440294i −0.0117884 0.0204181i
\(466\) −1.84395 3.19381i −0.0854192 0.147950i
\(467\) −14.4056 24.9513i −0.666613 1.15461i −0.978845 0.204602i \(-0.934410\pi\)
0.312232 0.950006i \(-0.398923\pi\)
\(468\) −33.3223 + 8.26403i −1.54032 + 0.382005i
\(469\) 0 0
\(470\) 3.74013 6.47810i 0.172520 0.298813i
\(471\) 6.87568 0.316815
\(472\) −2.92035 −0.134420
\(473\) −10.2238 + 17.7081i −0.470089 + 0.814219i
\(474\) 4.09786 7.09770i 0.188221 0.326008i
\(475\) 15.3591 + 26.6027i 0.704723 + 1.22062i
\(476\) 0 0
\(477\) 1.81466 + 3.14308i 0.0830876 + 0.143912i
\(478\) 54.6719 2.50063
\(479\) −12.2936 21.2931i −0.561707 0.972906i −0.997348 0.0727849i \(-0.976811\pi\)
0.435640 0.900121i \(-0.356522\pi\)
\(480\) 0.104028 0.180181i 0.00474820 0.00822412i
\(481\) 24.0850 + 25.0032i 1.09818 + 1.14005i
\(482\) −32.3726 −1.47453
\(483\) 0 0
\(484\) 9.95395 17.2407i 0.452452 0.783670i
\(485\) −1.75499 + 3.03973i −0.0796899 + 0.138027i
\(486\) 18.7934 32.5511i 0.852484 1.47655i
\(487\) −2.57316 −0.116601 −0.0583004 0.998299i \(-0.518568\pi\)
−0.0583004 + 0.998299i \(0.518568\pi\)
\(488\) −2.66234 + 4.61131i −0.120519 + 0.208744i
\(489\) 8.26233 0.373635
\(490\) 0 0
\(491\) −7.01897 + 12.1572i −0.316762 + 0.548647i −0.979810 0.199929i \(-0.935929\pi\)
0.663049 + 0.748576i \(0.269262\pi\)
\(492\) 36.9857 1.66745
\(493\) −4.32639 + 7.49354i −0.194851 + 0.337492i
\(494\) 53.5389 13.2778i 2.40883 0.597396i
\(495\) 1.01011 + 1.74957i 0.0454012 + 0.0786373i
\(496\) −3.45468 + 5.98368i −0.155120 + 0.268675i
\(497\) 0 0
\(498\) −1.29425 2.24170i −0.0579965 0.100453i
\(499\) −6.76726 11.7212i −0.302944 0.524715i 0.673857 0.738862i \(-0.264636\pi\)
−0.976801 + 0.214147i \(0.931303\pi\)
\(500\) 13.2156 0.591018
\(501\) −13.7739 −0.615373
\(502\) 19.3393 + 33.4966i 0.863155 + 1.49503i
\(503\) −4.13877 7.16856i −0.184539 0.319630i 0.758882 0.651228i \(-0.225746\pi\)
−0.943421 + 0.331597i \(0.892412\pi\)
\(504\) 0 0
\(505\) −2.57069 + 4.45257i −0.114394 + 0.198137i
\(506\) −10.9118 18.8998i −0.485090 0.840200i
\(507\) −8.66142 + 4.57766i −0.384667 + 0.203301i
\(508\) −17.6567 + 30.5822i −0.783388 + 1.35687i
\(509\) 0.166218 0.00736750 0.00368375 0.999993i \(-0.498827\pi\)
0.00368375 + 0.999993i \(0.498827\pi\)
\(510\) −0.609771 + 1.05615i −0.0270011 + 0.0467673i
\(511\) 0 0
\(512\) −35.4115 −1.56498
\(513\) −12.8751 + 22.3004i −0.568451 + 0.984585i
\(514\) 71.1137 3.13669
\(515\) −3.00853 + 5.21093i −0.132572 + 0.229621i
\(516\) −12.4025 + 21.4818i −0.545990 + 0.945683i
\(517\) 10.9509 18.9675i 0.481619 0.834189i
\(518\) 0 0
\(519\) −6.17821 −0.271193
\(520\) 1.58784 5.51149i 0.0696315 0.241695i
\(521\) −3.53090 + 6.11569i −0.154691 + 0.267933i −0.932947 0.360015i \(-0.882772\pi\)
0.778255 + 0.627948i \(0.216105\pi\)
\(522\) 13.1355 + 22.7514i 0.574926 + 0.995802i
\(523\) −23.3912 −1.02283 −0.511414 0.859335i \(-0.670878\pi\)
−0.511414 + 0.859335i \(0.670878\pi\)
\(524\) −0.376796 0.652630i −0.0164604 0.0285103i
\(525\) 0 0
\(526\) 2.07258 + 3.58981i 0.0903687 + 0.156523i
\(527\) −1.92420 + 3.33280i −0.0838193 + 0.145179i
\(528\) −3.20544 + 5.55198i −0.139499 + 0.241619i
\(529\) −9.38775 −0.408163
\(530\) −1.23955 −0.0538425
\(531\) −0.762452 + 1.32061i −0.0330876 + 0.0573094i
\(532\) 0 0
\(533\) −43.8697 + 10.8798i −1.90021 + 0.471257i
\(534\) −11.4041 19.7525i −0.493503 0.854773i
\(535\) 1.09028 + 1.88842i 0.0471368 + 0.0816434i
\(536\) 13.0230 + 22.5564i 0.562507 + 0.974290i
\(537\) −5.86056 + 10.1508i −0.252902 + 0.438039i
\(538\) −20.3779 −0.878554
\(539\) 0 0
\(540\) 2.73688 + 4.74041i 0.117776 + 0.203995i
\(541\) −13.1540 22.7833i −0.565533 0.979532i −0.997000 0.0774030i \(-0.975337\pi\)
0.431467 0.902129i \(-0.357996\pi\)
\(542\) 29.5683 1.27007
\(543\) 2.51437 + 4.35501i 0.107902 + 0.186891i
\(544\) −1.57488 −0.0675222
\(545\) 2.79197 0.119595
\(546\) 0 0
\(547\) 41.7636 1.78568 0.892841 0.450371i \(-0.148708\pi\)
0.892841 + 0.450371i \(0.148708\pi\)
\(548\) 19.0932 0.815620
\(549\) 1.39018 + 2.40786i 0.0593315 + 0.102765i
\(550\) 28.8855 1.23168
\(551\) −13.9689 24.1949i −0.595095 1.03074i
\(552\) −6.47508 11.2152i −0.275598 0.477349i
\(553\) 0 0
\(554\) 25.0948 1.06617
\(555\) 1.23911 2.14620i 0.0525974 0.0911013i
\(556\) −21.6780 37.5474i −0.919351 1.59236i
\(557\) −3.65494 6.33053i −0.154865 0.268233i 0.778145 0.628085i \(-0.216161\pi\)
−0.933010 + 0.359851i \(0.882827\pi\)
\(558\) 5.84212 + 10.1188i 0.247317 + 0.428365i
\(559\) 8.39181 29.1284i 0.354936 1.23200i
\(560\) 0 0
\(561\) −1.78537 + 3.09235i −0.0753785 + 0.130559i
\(562\) −6.31560 −0.266407
\(563\) −44.7737 −1.88699 −0.943493 0.331393i \(-0.892481\pi\)
−0.943493 + 0.331393i \(0.892481\pi\)
\(564\) 13.2846 23.0096i 0.559382 0.968878i
\(565\) −1.64308 + 2.84589i −0.0691247 + 0.119727i
\(566\) 5.59830 + 9.69654i 0.235314 + 0.407576i
\(567\) 0 0
\(568\) −22.1176 38.3089i −0.928036 1.60741i
\(569\) −42.5127 −1.78222 −0.891112 0.453784i \(-0.850074\pi\)
−0.891112 + 0.453784i \(0.850074\pi\)
\(570\) −1.96881 3.41007i −0.0824642 0.142832i
\(571\) 20.4324 35.3899i 0.855069 1.48102i −0.0215128 0.999769i \(-0.506848\pi\)
0.876581 0.481254i \(-0.159818\pi\)
\(572\) 9.50430 32.9900i 0.397395 1.37938i
\(573\) 14.1268 0.590155
\(574\) 0 0
\(575\) −9.00851 + 15.6032i −0.375681 + 0.650698i
\(576\) −10.8979 + 18.8756i −0.454077 + 0.786485i
\(577\) −10.8640 + 18.8170i −0.452275 + 0.783363i −0.998527 0.0542578i \(-0.982721\pi\)
0.546252 + 0.837621i \(0.316054\pi\)
\(578\) −32.1144 −1.33578
\(579\) −3.07959 + 5.33400i −0.127983 + 0.221674i
\(580\) −5.93877 −0.246594
\(581\) 0 0
\(582\) −9.41790 + 16.3123i −0.390384 + 0.676166i
\(583\) −3.62932 −0.150311
\(584\) 27.7570 48.0765i 1.14859 1.98942i
\(585\) −2.07778 2.15699i −0.0859057 0.0891805i
\(586\) −2.38491 4.13078i −0.0985196 0.170641i
\(587\) 10.2408 17.7376i 0.422683 0.732108i −0.573518 0.819193i \(-0.694422\pi\)
0.996201 + 0.0870851i \(0.0277552\pi\)
\(588\) 0 0
\(589\) −6.21277 10.7608i −0.255993 0.443393i
\(590\) −0.260406 0.451036i −0.0107207 0.0185688i
\(591\) −6.57141 −0.270312
\(592\) −33.6795 −1.38422
\(593\) −2.81930 4.88318i −0.115775 0.200528i 0.802314 0.596902i \(-0.203602\pi\)
−0.918089 + 0.396374i \(0.870268\pi\)
\(594\) 12.1070 + 20.9699i 0.496756 + 0.860407i
\(595\) 0 0
\(596\) −31.1421 + 53.9397i −1.27563 + 2.20946i
\(597\) 6.58136 + 11.3993i 0.269357 + 0.466541i
\(598\) 22.4454 + 23.3010i 0.917860 + 0.952849i
\(599\) −19.8359 + 34.3568i −0.810474 + 1.40378i 0.102058 + 0.994778i \(0.467457\pi\)
−0.912533 + 0.409004i \(0.865876\pi\)
\(600\) 17.1407 0.699766
\(601\) 8.41334 14.5723i 0.343187 0.594418i −0.641836 0.766842i \(-0.721827\pi\)
0.985023 + 0.172425i \(0.0551602\pi\)
\(602\) 0 0
\(603\) 13.6003 0.553845
\(604\) 20.7312 35.9075i 0.843540 1.46105i
\(605\) 1.73668 0.0706061
\(606\) −13.7953 + 23.8941i −0.560394 + 0.970631i
\(607\) 11.2490 19.4838i 0.456582 0.790823i −0.542196 0.840252i \(-0.682407\pi\)
0.998778 + 0.0494290i \(0.0157402\pi\)
\(608\) 2.54245 4.40365i 0.103110 0.178592i
\(609\) 0 0
\(610\) −0.949597 −0.0384480
\(611\) −8.98863 + 31.2001i −0.363641 + 1.26222i
\(612\) 9.27547 16.0656i 0.374939 0.649413i
\(613\) −13.7135 23.7524i −0.553882 0.959351i −0.997990 0.0633780i \(-0.979813\pi\)
0.444108 0.895973i \(-0.353521\pi\)
\(614\) −17.9406 −0.724022
\(615\) 1.61324 + 2.79421i 0.0650521 + 0.112673i
\(616\) 0 0
\(617\) −5.31896 9.21271i −0.214133 0.370890i 0.738871 0.673847i \(-0.235359\pi\)
−0.953004 + 0.302957i \(0.902026\pi\)
\(618\) −16.1449 + 27.9637i −0.649442 + 1.12487i
\(619\) −22.7339 + 39.3762i −0.913751 + 1.58266i −0.105032 + 0.994469i \(0.533495\pi\)
−0.808719 + 0.588195i \(0.799839\pi\)
\(620\) −2.64131 −0.106078
\(621\) −15.1032 −0.606071
\(622\) 17.2214 29.8283i 0.690515 1.19601i
\(623\) 0 0
\(624\) 2.63107 9.13258i 0.105327 0.365596i
\(625\) −11.6319 20.1471i −0.465278 0.805885i
\(626\) −32.4870 56.2692i −1.29844 2.24897i
\(627\) −5.76454 9.98448i −0.230214 0.398742i
\(628\) 17.8605 30.9353i 0.712711 1.23445i
\(629\) −18.7589 −0.747966
\(630\) 0 0
\(631\) −14.7992 25.6329i −0.589146 1.02043i −0.994345 0.106202i \(-0.966131\pi\)
0.405199 0.914229i \(-0.367202\pi\)
\(632\) −10.4139 18.0374i −0.414243 0.717489i
\(633\) 17.5262 0.696604
\(634\) −26.0675 45.1503i −1.03527 1.79315i
\(635\) −3.08058 −0.122249
\(636\) −4.40275 −0.174580
\(637\) 0 0
\(638\) −26.2711 −1.04008
\(639\) −23.0981 −0.913747
\(640\) −3.44594 5.96854i −0.136213 0.235927i
\(641\) −42.5646 −1.68120 −0.840601 0.541654i \(-0.817798\pi\)
−0.840601 + 0.541654i \(0.817798\pi\)
\(642\) 5.85082 + 10.1339i 0.230914 + 0.399954i
\(643\) 10.9980 + 19.0492i 0.433721 + 0.751226i 0.997190 0.0749106i \(-0.0238671\pi\)
−0.563470 + 0.826137i \(0.690534\pi\)
\(644\) 0 0
\(645\) −2.16388 −0.0852029
\(646\) −14.9029 + 25.8125i −0.586345 + 1.01558i
\(647\) 17.4026 + 30.1421i 0.684166 + 1.18501i 0.973698 + 0.227841i \(0.0731668\pi\)
−0.289533 + 0.957168i \(0.593500\pi\)
\(648\) −9.80778 16.9876i −0.385286 0.667335i
\(649\) −0.762452 1.32061i −0.0299289 0.0518383i
\(650\) −41.5633 + 10.3078i −1.63025 + 0.404306i
\(651\) 0 0
\(652\) 21.4625 37.1741i 0.840535 1.45585i
\(653\) −50.8167 −1.98861 −0.994306 0.106559i \(-0.966017\pi\)
−0.994306 + 0.106559i \(0.966017\pi\)
\(654\) 14.9827 0.585870
\(655\) 0.0328701 0.0569326i 0.00128434 0.00222454i
\(656\) 21.9242 37.9739i 0.855997 1.48263i
\(657\) −14.4937 25.1038i −0.565453 0.979394i
\(658\) 0 0
\(659\) 7.37203 + 12.7687i 0.287173 + 0.497399i 0.973134 0.230240i \(-0.0739511\pi\)
−0.685960 + 0.727639i \(0.740618\pi\)
\(660\) −2.45075 −0.0953953
\(661\) −9.06227 15.6963i −0.352481 0.610516i 0.634202 0.773167i \(-0.281329\pi\)
−0.986684 + 0.162651i \(0.947995\pi\)
\(662\) −12.9069 + 22.3555i −0.501643 + 0.868871i
\(663\) 1.46546 5.08669i 0.0569136 0.197551i
\(664\) −6.57814 −0.255281
\(665\) 0 0
\(666\) −28.4773 + 49.3241i −1.10347 + 1.91127i
\(667\) 8.19313 14.1909i 0.317239 0.549475i
\(668\) −35.7795 + 61.9719i −1.38435 + 2.39777i
\(669\) −22.0598 −0.852881
\(670\) −2.32250 + 4.02268i −0.0897259 + 0.155410i
\(671\) −2.78036 −0.107335
\(672\) 0 0
\(673\) −10.4574 + 18.1127i −0.403102 + 0.698193i −0.994099 0.108481i \(-0.965401\pi\)
0.590997 + 0.806674i \(0.298735\pi\)
\(674\) 16.4309 0.632896
\(675\) 9.99521 17.3122i 0.384716 0.666348i
\(676\) −1.90322 + 50.8608i −0.0732008 + 1.95618i
\(677\) −19.1089 33.0976i −0.734416 1.27205i −0.954979 0.296673i \(-0.904123\pi\)
0.220563 0.975373i \(-0.429210\pi\)
\(678\) −8.81733 + 15.2721i −0.338628 + 0.586520i
\(679\) 0 0
\(680\) 1.54961 + 2.68401i 0.0594249 + 0.102927i
\(681\) −7.46472 12.9293i −0.286049 0.495451i
\(682\) −11.6842 −0.447413
\(683\) −23.8253 −0.911649 −0.455825 0.890070i \(-0.650656\pi\)
−0.455825 + 0.890070i \(0.650656\pi\)
\(684\) 29.9483 + 51.8720i 1.14510 + 1.98337i
\(685\) 0.832803 + 1.44246i 0.0318198 + 0.0551135i
\(686\) 0 0
\(687\) 0.500466 0.866833i 0.0190940 0.0330717i
\(688\) 14.7038 + 25.4677i 0.560577 + 0.970948i
\(689\) 5.22221 1.29512i 0.198950 0.0493403i
\(690\) 1.15476 2.00010i 0.0439608 0.0761424i
\(691\) 19.1413 0.728168 0.364084 0.931366i \(-0.381382\pi\)
0.364084 + 0.931366i \(0.381382\pi\)
\(692\) −16.0487 + 27.7972i −0.610080 + 1.05669i
\(693\) 0 0
\(694\) −38.9632 −1.47902
\(695\) 1.89109 3.27547i 0.0717333 0.124246i
\(696\) −15.5893 −0.590909
\(697\) 12.2114 21.1508i 0.462540 0.801143i
\(698\) 19.5035 33.7811i 0.738219 1.27863i
\(699\) 0.571352 0.989611i 0.0216105 0.0374305i
\(700\) 0 0
\(701\) −27.2956 −1.03094 −0.515471 0.856907i \(-0.672383\pi\)
−0.515471 + 0.856907i \(0.672383\pi\)
\(702\) −24.9038 25.8532i −0.939935 0.975765i
\(703\) 30.2840 52.4535i 1.14218 1.97832i
\(704\) −10.8979 18.8756i −0.410729 0.711403i
\(705\) 2.31778 0.0872927
\(706\) 4.67342 + 8.09460i 0.175886 + 0.304644i
\(707\) 0 0
\(708\) −0.924935 1.60203i −0.0347612 0.0602081i
\(709\) −3.08583 + 5.34481i −0.115891 + 0.200729i −0.918135 0.396267i \(-0.870306\pi\)
0.802245 + 0.596995i \(0.203639\pi\)
\(710\) 3.94443 6.83195i 0.148032 0.256399i
\(711\) −10.8755 −0.407865
\(712\) −57.9625 −2.17224
\(713\) 3.64395 6.31152i 0.136467 0.236368i
\(714\) 0 0
\(715\) 2.90690 0.720919i 0.108712 0.0269608i
\(716\) 30.4471 + 52.7360i 1.13786 + 1.97084i
\(717\) 8.47011 + 14.6707i 0.316322 + 0.547886i
\(718\) 25.6994 + 44.5127i 0.959094 + 1.66120i
\(719\) 1.36066 2.35674i 0.0507442 0.0878915i −0.839538 0.543302i \(-0.817174\pi\)
0.890282 + 0.455410i \(0.150507\pi\)
\(720\) 2.90549 0.108281
\(721\) 0 0
\(722\) −25.0129 43.3236i −0.930883 1.61234i
\(723\) −5.01537 8.68687i −0.186524 0.323068i
\(724\) 26.1256 0.970949
\(725\) 10.8443 + 18.7829i 0.402749 + 0.697581i
\(726\) 9.31965 0.345885
\(727\) 9.47153 0.351280 0.175640 0.984455i \(-0.443801\pi\)
0.175640 + 0.984455i \(0.443801\pi\)
\(728\) 0 0
\(729\) −0.987863 −0.0365875
\(730\) 9.90027 0.366426
\(731\) 8.18976 + 14.1851i 0.302909 + 0.524654i
\(732\) −3.37287 −0.124665
\(733\) 1.74853 + 3.02855i 0.0645836 + 0.111862i 0.896509 0.443025i \(-0.146095\pi\)
−0.831926 + 0.554887i \(0.812761\pi\)
\(734\) −17.9236 31.0446i −0.661573 1.14588i
\(735\) 0 0
\(736\) 2.98243 0.109934
\(737\) −6.80013 + 11.7782i −0.250486 + 0.433855i
\(738\) −37.0755 64.2166i −1.36477 2.36385i
\(739\) −16.0151 27.7390i −0.589126 1.02040i −0.994347 0.106178i \(-0.966139\pi\)
0.405221 0.914219i \(-0.367195\pi\)
\(740\) −6.43750 11.1501i −0.236647 0.409885i
\(741\) 11.8575 + 12.3096i 0.435598 + 0.452203i
\(742\) 0 0
\(743\) −17.4593 + 30.2404i −0.640519 + 1.10941i 0.344798 + 0.938677i \(0.387947\pi\)
−0.985317 + 0.170734i \(0.945386\pi\)
\(744\) −6.93343 −0.254192
\(745\) −5.43341 −0.199065
\(746\) −15.7194 + 27.2268i −0.575527 + 0.996842i
\(747\) −1.71744 + 2.97469i −0.0628377 + 0.108838i
\(748\) 9.27547 + 16.0656i 0.339145 + 0.587416i
\(749\) 0 0
\(750\) 3.09335 + 5.35785i 0.112953 + 0.195641i
\(751\) 26.9972 0.985143 0.492571 0.870272i \(-0.336057\pi\)
0.492571 + 0.870272i \(0.336057\pi\)
\(752\) −15.7495 27.2790i −0.574327 0.994763i
\(753\) −5.99233 + 10.3790i −0.218373 + 0.378233i
\(754\) 37.8013 9.37483i 1.37664 0.341411i
\(755\) 3.61700 0.131636
\(756\) 0 0
\(757\) 26.2950 45.5442i 0.955707 1.65533i 0.222965 0.974826i \(-0.428426\pi\)
0.732742 0.680507i \(-0.238240\pi\)
\(758\) 32.6337 56.5231i 1.18531 2.05301i
\(759\) 3.38106 5.85616i 0.122725 0.212565i
\(760\) −10.0067 −0.362980
\(761\) 6.96431 12.0625i 0.252456 0.437267i −0.711745 0.702437i \(-0.752095\pi\)
0.964201 + 0.265171i \(0.0854284\pi\)
\(762\) −16.5315 −0.598874
\(763\) 0 0
\(764\) 36.6961 63.5596i 1.32762 2.29950i
\(765\) 1.61830 0.0585099
\(766\) −3.53606 + 6.12463i −0.127763 + 0.221292i
\(767\) 1.56835 + 1.62813i 0.0566297 + 0.0587885i
\(768\) −11.7387 20.3320i −0.423583 0.733668i
\(769\) 6.89545 11.9433i 0.248656 0.430685i −0.714497 0.699639i \(-0.753344\pi\)
0.963153 + 0.268953i \(0.0866777\pi\)
\(770\) 0 0
\(771\) 11.0174 + 19.0827i 0.396781 + 0.687246i
\(772\) 15.9993 + 27.7115i 0.575826 + 0.997360i
\(773\) −50.4870 −1.81589 −0.907946 0.419087i \(-0.862350\pi\)
−0.907946 + 0.419087i \(0.862350\pi\)
\(774\) 49.7304 1.78752
\(775\) 4.82310 + 8.35385i 0.173251 + 0.300079i
\(776\) 23.9337 + 41.4544i 0.859170 + 1.48813i
\(777\) 0 0
\(778\) 20.3092 35.1766i 0.728120 1.26114i
\(779\) 39.4277 + 68.2908i 1.41265 + 2.44677i
\(780\) 3.52637 0.874550i 0.126264 0.0313139i
\(781\) 11.5491 20.0035i 0.413258 0.715783i
\(782\) −17.4818 −0.625150
\(783\) −9.09053 + 15.7453i −0.324869 + 0.562690i
\(784\) 0 0
\(785\) 3.11614 0.111220
\(786\) 0.176393 0.305521i 0.00629172 0.0108976i
\(787\) −10.8638 −0.387252 −0.193626 0.981075i \(-0.562025\pi\)
−0.193626 + 0.981075i \(0.562025\pi\)
\(788\) −17.0701 + 29.5663i −0.608097 + 1.05325i
\(789\) −0.642194 + 1.11231i −0.0228627 + 0.0395994i
\(790\) 1.85720 3.21676i 0.0660762 0.114447i
\(791\) 0 0
\(792\) 27.5509 0.978980
\(793\) 4.00065 0.992172i 0.142067 0.0352331i
\(794\) −29.3049 + 50.7576i −1.03999 + 1.80132i
\(795\) −0.192038 0.332620i −0.00681090 0.0117968i
\(796\) 68.3838 2.42380
\(797\) −3.95840 6.85616i −0.140214 0.242858i 0.787363 0.616489i \(-0.211446\pi\)
−0.927577 + 0.373632i \(0.878112\pi\)
\(798\) 0 0
\(799\) −8.77221 15.1939i −0.310339 0.537522i
\(800\) −1.97375 + 3.41864i −0.0697828 + 0.120867i
\(801\) −15.1330 + 26.2111i −0.534697 + 0.926123i
\(802\) 4.48697 0.158440
\(803\) 28.9874 1.02294
\(804\) −8.24928 + 14.2882i −0.290930 + 0.503905i
\(805\) 0 0
\(806\) 16.8124 4.16952i 0.592192 0.146865i
\(807\) −3.15707 5.46821i −0.111134 0.192490i
\(808\) 35.0579 + 60.7221i 1.23333 + 2.13620i
\(809\) 14.8194 + 25.6680i 0.521023 + 0.902439i 0.999701 + 0.0244482i \(0.00778287\pi\)
−0.478678 + 0.877991i \(0.658884\pi\)
\(810\) 1.74910 3.02954i 0.0614573 0.106447i
\(811\) −15.8344 −0.556022 −0.278011 0.960578i \(-0.589675\pi\)
−0.278011 + 0.960578i \(0.589675\pi\)
\(812\) 0 0
\(813\) 4.58091 + 7.93438i 0.160660 + 0.278271i
\(814\) −28.4773 49.3241i −0.998129 1.72881i
\(815\) 3.74459 0.131167
\(816\) 2.56772 + 4.44742i 0.0898881 + 0.155691i
\(817\) −52.8856 −1.85023
\(818\) 62.4327 2.18291
\(819\) 0 0
\(820\) 16.7624 0.585368
\(821\) 17.7394 0.619110 0.309555 0.950882i \(-0.399820\pi\)
0.309555 + 0.950882i \(0.399820\pi\)
\(822\) 4.46912 + 7.74075i 0.155879 + 0.269990i
\(823\) −8.68200 −0.302635 −0.151318 0.988485i \(-0.548352\pi\)
−0.151318 + 0.988485i \(0.548352\pi\)
\(824\) 41.0290 + 71.0643i 1.42931 + 2.47564i
\(825\) 4.47513 + 7.75115i 0.155804 + 0.269860i
\(826\) 0 0
\(827\) 14.3121 0.497681 0.248840 0.968545i \(-0.419951\pi\)
0.248840 + 0.968545i \(0.419951\pi\)
\(828\) −17.5655 + 30.4243i −0.610442 + 1.05732i
\(829\) 12.6533 + 21.9161i 0.439467 + 0.761179i 0.997648 0.0685401i \(-0.0218341\pi\)
−0.558182 + 0.829719i \(0.688501\pi\)
\(830\) −0.586568 1.01597i −0.0203601 0.0352647i
\(831\) 3.88784 + 6.73393i 0.134868 + 0.233597i
\(832\) 22.4167 + 23.2712i 0.777158 + 0.806783i
\(833\) 0 0
\(834\) 10.1483 17.5774i 0.351407 0.608654i
\(835\) −6.24250 −0.216031
\(836\) −59.8966 −2.07157
\(837\) −4.04308 + 7.00281i −0.139749 + 0.242053i
\(838\) −31.9090 + 55.2679i −1.10228 + 1.90920i
\(839\) 6.52129 + 11.2952i 0.225140 + 0.389954i 0.956361 0.292186i \(-0.0943827\pi\)
−0.731222 + 0.682140i \(0.761049\pi\)
\(840\) 0 0
\(841\) 4.63720 + 8.03187i 0.159904 + 0.276961i
\(842\) 57.5525 1.98339
\(843\) −0.978452 1.69473i −0.0336997 0.0583696i
\(844\) 45.5266 78.8543i 1.56709 2.71428i
\(845\) −3.92546 + 2.07465i −0.135040 + 0.0713702i
\(846\) −53.2673 −1.83137
\(847\) 0 0
\(848\) −2.60984 + 4.52037i −0.0896223 + 0.155230i
\(849\) −1.73465 + 3.00450i −0.0595330 + 0.103114i
\(850\) 11.5694 20.0388i 0.396827 0.687324i
\(851\) 35.5248 1.21777
\(852\) 14.0102 24.2664i 0.479982 0.831353i
\(853\) −18.8926 −0.646869 −0.323435 0.946251i \(-0.604838\pi\)
−0.323435 + 0.946251i \(0.604838\pi\)
\(854\) 0 0
\(855\) −2.61256 + 4.52509i −0.0893477 + 0.154755i
\(856\) 29.7374 1.01640
\(857\) 12.3219 21.3422i 0.420909 0.729036i −0.575119 0.818069i \(-0.695044\pi\)
0.996029 + 0.0890333i \(0.0283777\pi\)
\(858\) 15.5995 3.86871i 0.532557 0.132075i
\(859\) 1.28571 + 2.22691i 0.0438677 + 0.0759811i 0.887126 0.461528i \(-0.152699\pi\)
−0.843258 + 0.537509i \(0.819365\pi\)
\(860\) −5.62097 + 9.73580i −0.191673 + 0.331988i
\(861\) 0 0
\(862\) 27.9906 + 48.4812i 0.953365 + 1.65128i
\(863\) −19.7704 34.2433i −0.672991 1.16565i −0.977052 0.213002i \(-0.931676\pi\)
0.304061 0.952653i \(-0.401657\pi\)
\(864\) −3.30909 −0.112578
\(865\) −2.80004 −0.0952043
\(866\) −31.4479 54.4694i −1.06864 1.85095i
\(867\) −4.97536 8.61758i −0.168972 0.292668i
\(868\) 0 0
\(869\) 5.43777 9.41849i 0.184464 0.319500i
\(870\) −1.39008 2.40769i −0.0471282 0.0816284i
\(871\) 5.58164 19.3742i 0.189127 0.656469i
\(872\) 19.0378 32.9744i 0.644701 1.11666i
\(873\) 24.9947 0.845942
\(874\) 28.2224 48.8826i 0.954636 1.65348i
\(875\) 0 0
\(876\) 35.1648 1.18811
\(877\) −10.5227 + 18.2259i −0.355328 + 0.615445i −0.987174 0.159648i \(-0.948964\pi\)
0.631846 + 0.775094i \(0.282297\pi\)
\(878\) 86.7702 2.92835
\(879\) 0.738970 1.27993i 0.0249248 0.0431711i
\(880\) −1.45274 + 2.51623i −0.0489720 + 0.0848219i
\(881\) −2.50592 + 4.34038i −0.0844266 + 0.146231i −0.905147 0.425099i \(-0.860239\pi\)
0.820720 + 0.571330i \(0.193573\pi\)
\(882\) 0 0
\(883\) −7.13079 −0.239970 −0.119985 0.992776i \(-0.538285\pi\)
−0.119985 + 0.992776i \(0.538285\pi\)
\(884\) −19.0794 19.8067i −0.641711 0.666173i
\(885\) 0.0806874 0.139755i 0.00271228 0.00469780i
\(886\) 8.34065 + 14.4464i 0.280210 + 0.485337i
\(887\) −6.72602 −0.225838 −0.112919 0.993604i \(-0.536020\pi\)
−0.112919 + 0.993604i \(0.536020\pi\)
\(888\) −16.8984 29.2689i −0.567074 0.982202i
\(889\) 0 0
\(890\) −5.16847 8.95206i −0.173248 0.300074i
\(891\) 5.12127 8.87031i 0.171569 0.297166i
\(892\) −57.3032 + 99.2520i −1.91865 + 3.32320i
\(893\) 56.6468 1.89561
\(894\) −29.1576 −0.975177
\(895\) −2.65608 + 4.60046i −0.0887829 + 0.153777i
\(896\) 0 0
\(897\) −2.77522 + 9.63294i −0.0926618 + 0.321635i
\(898\) 12.1380 + 21.0236i 0.405050 + 0.701567i
\(899\) −4.38655 7.59773i −0.146300 0.253398i
\(900\) −23.2495 40.2692i −0.774982 1.34231i
\(901\) −1.45363 + 2.51777i −0.0484276 + 0.0838790i
\(902\) 74.1510 2.46896
\(903\) 0 0
\(904\) 22.4075 + 38.8109i 0.745263 + 1.29083i
\(905\) 1.13954 + 1.97374i 0.0378796 + 0.0656095i
\(906\) 19.4101 0.644858
\(907\) −14.7862 25.6105i −0.490969 0.850383i 0.508977 0.860780i \(-0.330024\pi\)
−0.999946 + 0.0103972i \(0.996690\pi\)
\(908\) −77.5623 −2.57399
\(909\) 36.6120 1.21434
\(910\) 0 0
\(911\) −20.6132 −0.682947 −0.341473 0.939891i \(-0.610926\pi\)
−0.341473 + 0.939891i \(0.610926\pi\)
\(912\) −16.5811 −0.549055
\(913\) −1.71744 2.97469i −0.0568388 0.0984477i
\(914\) −21.3371 −0.705768
\(915\) −0.147117 0.254815i −0.00486355 0.00842392i
\(916\) −2.60005 4.50342i −0.0859081 0.148797i
\(917\) 0 0
\(918\) 19.3966 0.640184
\(919\) 2.08952 3.61916i 0.0689269 0.119385i −0.829502 0.558503i \(-0.811376\pi\)
0.898429 + 0.439118i \(0.144709\pi\)
\(920\) −2.93459 5.08285i −0.0967504 0.167577i
\(921\) −2.77947 4.81418i −0.0915865 0.158632i
\(922\) 8.37303 + 14.5025i 0.275751 + 0.477615i
\(923\) −9.47961 + 32.9043i −0.312025 + 1.08306i
\(924\) 0 0
\(925\) −23.5101 + 40.7207i −0.773007 + 1.33889i
\(926\) −33.9341 −1.11514
\(927\) 42.8478 1.40731
\(928\) 1.79511 3.10922i 0.0589273 0.102065i
\(929\) −24.0456 + 41.6482i −0.788910 + 1.36643i 0.137725 + 0.990470i \(0.456021\pi\)
−0.926635 + 0.375962i \(0.877312\pi\)
\(930\) −0.618249 1.07084i −0.0202732 0.0351142i
\(931\) 0 0
\(932\) −2.96832 5.14128i −0.0972306 0.168408i
\(933\) 10.6722 0.349392
\(934\) −35.0359 60.6840i −1.14641 1.98564i
\(935\) −0.809152 + 1.40149i −0.0264621 + 0.0458337i
\(936\) −39.6429 + 9.83156i −1.29577 + 0.321354i
\(937\) −12.5441 −0.409798 −0.204899 0.978783i \(-0.565687\pi\)
−0.204899 + 0.978783i \(0.565687\pi\)
\(938\) 0 0
\(939\) 10.0662 17.4352i 0.328498 0.568975i
\(940\) 6.02073 10.4282i 0.196375 0.340131i
\(941\) −15.2944 + 26.4907i −0.498583 + 0.863572i −0.999999 0.00163503i \(-0.999480\pi\)
0.501415 + 0.865207i \(0.332813\pi\)
\(942\) 16.7223 0.544843
\(943\) −23.1254 + 40.0544i −0.753067 + 1.30435i
\(944\) −2.19311 −0.0713798
\(945\) 0 0
\(946\) −24.8652 + 43.0678i −0.808438 + 1.40026i
\(947\) −7.78348 −0.252929 −0.126465 0.991971i \(-0.540363\pi\)
−0.126465 + 0.991971i \(0.540363\pi\)
\(948\) 6.59659 11.4256i 0.214247 0.371087i
\(949\) −41.7098 + 10.3442i −1.35396 + 0.335786i
\(950\) 37.3548 + 64.7005i 1.21195 + 2.09916i
\(951\) 8.07709 13.9899i 0.261917 0.453654i
\(952\) 0 0
\(953\) 19.2152 + 33.2817i 0.622442 + 1.07810i 0.989030 + 0.147717i \(0.0471926\pi\)
−0.366588 + 0.930383i \(0.619474\pi\)
\(954\) 4.41343 + 7.64429i 0.142890 + 0.247493i
\(955\) 6.40243 0.207178
\(956\) 88.0088 2.84641
\(957\) −4.07008 7.04958i −0.131567 0.227881i
\(958\) −29.8992 51.7869i −0.965998 1.67316i
\(959\) 0 0
\(960\) 1.15328 1.99754i 0.0372219 0.0644702i
\(961\) 13.5491 + 23.4676i 0.437066 + 0.757021i
\(962\) 58.5772 + 60.8101i 1.88860 + 1.96060i
\(963\) 7.76391 13.4475i 0.250189 0.433339i
\(964\) −52.1123 −1.67842
\(965\) −1.39571 + 2.41744i −0.0449294 + 0.0778200i
\(966\) 0 0
\(967\) 7.80008 0.250834 0.125417 0.992104i \(-0.459973\pi\)
0.125417 + 0.992104i \(0.459973\pi\)
\(968\) 11.8420 20.5110i 0.380617 0.659248i
\(969\) −9.23538 −0.296683
\(970\) −4.26830 + 7.39292i −0.137047 + 0.237372i
\(971\) 28.8957 50.0489i 0.927308 1.60614i 0.139501 0.990222i \(-0.455450\pi\)
0.787807 0.615922i \(-0.211216\pi\)
\(972\) 30.2529 52.3995i 0.970362 1.68072i
\(973\) 0 0
\(974\) −6.25817 −0.200525
\(975\) −9.20525 9.55615i −0.294804 0.306042i
\(976\) −1.99936 + 3.46298i −0.0639978 + 0.110847i
\(977\) −4.33707 7.51203i −0.138755 0.240331i 0.788270 0.615329i \(-0.210977\pi\)
−0.927026 + 0.374998i \(0.877643\pi\)
\(978\) 20.0948 0.642561
\(979\) −15.1330 26.2111i −0.483652 0.837710i
\(980\) 0 0
\(981\) −9.94086 17.2181i −0.317387 0.549731i
\(982\) −17.0708 + 29.5675i −0.544752 + 0.943538i
\(983\) 18.5560 32.1400i 0.591846 1.02511i −0.402138 0.915579i \(-0.631733\pi\)
0.993984 0.109528i \(-0.0349339\pi\)
\(984\) 44.0012 1.40271
\(985\) −2.97824 −0.0948947
\(986\) −10.5222 + 18.2250i −0.335096 + 0.580403i
\(987\) 0 0
\(988\) 86.1849 21.3741i 2.74191 0.680001i
\(989\) −15.5094 26.8631i −0.493170 0.854196i
\(990\) 2.45670 + 4.25512i 0.0780790 + 0.135237i
\(991\) 22.6318 + 39.1995i 0.718924 + 1.24521i 0.961426 + 0.275062i \(0.0886984\pi\)
−0.242502 + 0.970151i \(0.577968\pi\)
\(992\) 0.798386 1.38285i 0.0253488 0.0439054i
\(993\) −7.99850 −0.253825
\(994\) 0 0
\(995\) 2.98275 + 5.16628i 0.0945597 + 0.163782i
\(996\) −2.08343 3.60861i −0.0660160 0.114343i
\(997\) 44.2554 1.40158 0.700791 0.713367i \(-0.252831\pi\)
0.700791 + 0.713367i \(0.252831\pi\)
\(998\) −16.4586 28.5072i −0.520989 0.902380i
\(999\) −39.4158 −1.24706
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.h.m.165.8 16
7.2 even 3 637.2.g.m.373.1 16
7.3 odd 6 637.2.f.l.295.1 16
7.4 even 3 637.2.f.l.295.2 yes 16
7.5 odd 6 637.2.g.m.373.2 16
7.6 odd 2 inner 637.2.h.m.165.7 16
13.3 even 3 637.2.g.m.263.1 16
91.3 odd 6 637.2.f.l.393.1 yes 16
91.4 even 6 8281.2.a.cl.1.1 8
91.16 even 3 inner 637.2.h.m.471.8 16
91.17 odd 6 8281.2.a.cl.1.2 8
91.55 odd 6 637.2.g.m.263.2 16
91.68 odd 6 inner 637.2.h.m.471.7 16
91.74 even 3 8281.2.a.ci.1.7 8
91.81 even 3 637.2.f.l.393.2 yes 16
91.87 odd 6 8281.2.a.ci.1.8 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
637.2.f.l.295.1 16 7.3 odd 6
637.2.f.l.295.2 yes 16 7.4 even 3
637.2.f.l.393.1 yes 16 91.3 odd 6
637.2.f.l.393.2 yes 16 91.81 even 3
637.2.g.m.263.1 16 13.3 even 3
637.2.g.m.263.2 16 91.55 odd 6
637.2.g.m.373.1 16 7.2 even 3
637.2.g.m.373.2 16 7.5 odd 6
637.2.h.m.165.7 16 7.6 odd 2 inner
637.2.h.m.165.8 16 1.1 even 1 trivial
637.2.h.m.471.7 16 91.68 odd 6 inner
637.2.h.m.471.8 16 91.16 even 3 inner
8281.2.a.ci.1.7 8 91.74 even 3
8281.2.a.ci.1.8 8 91.87 odd 6
8281.2.a.cl.1.1 8 91.4 even 6
8281.2.a.cl.1.2 8 91.17 odd 6