Properties

Label 196.2.f.d.19.1
Level $196$
Weight $2$
Character 196.19
Analytic conductor $1.565$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [196,2,Mod(19,196)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(196, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("196.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 196 = 2^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 196.f (of order \(6\), 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: \(1.56506787962\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 4x^{14} + 6x^{12} + 8x^{10} + 20x^{8} + 32x^{6} + 96x^{4} + 256x^{2} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.1
Root \(0.264742 - 1.38921i\) of defining polynomial
Character \(\chi\) \(=\) 196.19
Dual form 196.2.f.d.31.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.31509 - 0.520123i) q^{2} +(-1.07072 - 1.85455i) q^{3} +(1.45894 + 1.36802i) q^{4} +(-2.26303 - 1.30656i) q^{5} +(0.443508 + 2.99581i) q^{6} +(-1.20711 - 2.55791i) q^{8} +(-0.792893 + 1.37333i) q^{9} +O(q^{10})\) \(q+(-1.31509 - 0.520123i) q^{2} +(-1.07072 - 1.85455i) q^{3} +(1.45894 + 1.36802i) q^{4} +(-2.26303 - 1.30656i) q^{5} +(0.443508 + 2.99581i) q^{6} +(-1.20711 - 2.55791i) q^{8} +(-0.792893 + 1.37333i) q^{9} +(2.29653 + 2.89531i) q^{10} +(-3.42675 + 1.97844i) q^{11} +(0.974936 - 4.17045i) q^{12} +1.08239i q^{13} +5.59587i q^{15} +(0.257031 + 3.99173i) q^{16} +(0.274552 - 0.158513i) q^{17} +(1.75703 - 1.39366i) q^{18} +(-2.58495 + 4.47727i) q^{19} +(-1.51423 - 5.00208i) q^{20} +(5.53553 - 0.819496i) q^{22} +(2.00735 + 1.15894i) q^{23} +(-3.45128 + 4.97744i) q^{24} +(0.914214 + 1.58346i) q^{25} +(0.562978 - 1.42345i) q^{26} -3.02846 q^{27} -6.82843 q^{29} +(2.91054 - 7.35909i) q^{30} +(-3.02846 - 5.24545i) q^{31} +(1.73817 - 5.38319i) q^{32} +(7.33820 + 4.23671i) q^{33} +(-0.443508 + 0.0656581i) q^{34} +(-3.03553 + 0.918917i) q^{36} +(2.00000 - 3.46410i) q^{37} +(5.72819 - 4.54353i) q^{38} +(2.00735 - 1.15894i) q^{39} +(-0.610345 + 7.36579i) q^{40} -2.29610i q^{41} -7.23486i q^{43} +(-7.70598 - 1.80145i) q^{44} +(3.58869 - 2.07193i) q^{45} +(-2.03706 - 2.56818i) q^{46} +(2.14144 - 3.70909i) q^{47} +(7.12764 - 4.75071i) q^{48} +(-0.378680 - 2.55791i) q^{50} +(-0.587938 - 0.339446i) q^{51} +(-1.48074 + 1.57915i) q^{52} +(-5.24264 - 9.08052i) q^{53} +(3.98271 + 1.57517i) q^{54} +10.3398 q^{55} +11.0711 q^{57} +(8.98002 + 3.55162i) q^{58} +(5.61341 + 9.72272i) q^{59} +(-7.65527 + 8.16405i) q^{60} +(-4.68690 - 2.70598i) q^{61} +(1.25443 + 8.47343i) q^{62} +(-5.08579 + 6.17534i) q^{64} +(1.41421 - 2.44949i) q^{65} +(-7.44681 - 9.38845i) q^{66} +(2.83882 - 1.63899i) q^{67} +(0.617405 + 0.144332i) q^{68} -4.96362i q^{69} +(4.46996 + 0.370390i) q^{72} +(-12.1388 + 7.00835i) q^{73} +(-4.43195 + 3.51537i) q^{74} +(1.95774 - 3.39090i) q^{75} +(-9.89630 + 2.99581i) q^{76} +(-3.24264 + 0.480049i) q^{78} +(-6.85351 - 3.95687i) q^{79} +(4.63378 - 9.36925i) q^{80} +(5.62132 + 9.73641i) q^{81} +(-1.19426 + 3.01959i) q^{82} -9.45280 q^{83} -0.828427 q^{85} +(-3.76302 + 9.51451i) q^{86} +(7.31135 + 12.6636i) q^{87} +(9.19712 + 6.37714i) q^{88} +(-5.18889 - 2.99581i) q^{89} +(-5.79712 + 0.858221i) q^{90} +(1.34315 + 4.43692i) q^{92} +(-6.48528 + 11.2328i) q^{93} +(-4.74539 + 3.76399i) q^{94} +(11.6997 - 6.75481i) q^{95} +(-11.8445 + 2.54038i) q^{96} +9.23880i q^{97} -6.27476i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{2} + 4 q^{4} - 8 q^{8} - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 4 q^{2} + 4 q^{4} - 8 q^{8} - 24 q^{9} - 4 q^{16} + 20 q^{18} + 32 q^{22} - 8 q^{25} - 64 q^{29} + 40 q^{30} - 36 q^{32} + 8 q^{36} + 32 q^{37} - 24 q^{44} + 8 q^{46} - 40 q^{50} - 16 q^{53} + 64 q^{57} - 8 q^{60} - 104 q^{64} + 4 q^{72} - 16 q^{74} + 16 q^{78} + 56 q^{81} + 32 q^{85} - 64 q^{86} + 64 q^{88} + 112 q^{92} + 32 q^{93}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/196\mathbb{Z}\right)^\times\).

\(n\) \(99\) \(101\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.31509 0.520123i −0.929912 0.367783i
\(3\) −1.07072 1.85455i −0.618182 1.07072i −0.989817 0.142344i \(-0.954536\pi\)
0.371635 0.928379i \(-0.378797\pi\)
\(4\) 1.45894 + 1.36802i 0.729472 + 0.684011i
\(5\) −2.26303 1.30656i −1.01206 0.584313i −0.100265 0.994961i \(-0.531969\pi\)
−0.911794 + 0.410648i \(0.865303\pi\)
\(6\) 0.443508 + 2.99581i 0.181061 + 1.22303i
\(7\) 0 0
\(8\) −1.20711 2.55791i −0.426777 0.904357i
\(9\) −0.792893 + 1.37333i −0.264298 + 0.457777i
\(10\) 2.29653 + 2.89531i 0.726226 + 0.915577i
\(11\) −3.42675 + 1.97844i −1.03321 + 0.596521i −0.917901 0.396809i \(-0.870118\pi\)
−0.115304 + 0.993330i \(0.536784\pi\)
\(12\) 0.974936 4.17045i 0.281440 1.20390i
\(13\) 1.08239i 0.300202i 0.988671 + 0.150101i \(0.0479598\pi\)
−0.988671 + 0.150101i \(0.952040\pi\)
\(14\) 0 0
\(15\) 5.59587i 1.44485i
\(16\) 0.257031 + 3.99173i 0.0642577 + 0.997933i
\(17\) 0.274552 0.158513i 0.0665886 0.0384450i −0.466336 0.884608i \(-0.654426\pi\)
0.532925 + 0.846163i \(0.321093\pi\)
\(18\) 1.75703 1.39366i 0.414136 0.328488i
\(19\) −2.58495 + 4.47727i −0.593029 + 1.02716i 0.400793 + 0.916169i \(0.368735\pi\)
−0.993822 + 0.110987i \(0.964599\pi\)
\(20\) −1.51423 5.00208i −0.338592 1.11850i
\(21\) 0 0
\(22\) 5.53553 0.819496i 1.18018 0.174717i
\(23\) 2.00735 + 1.15894i 0.418561 + 0.241656i 0.694461 0.719530i \(-0.255643\pi\)
−0.275901 + 0.961186i \(0.588976\pi\)
\(24\) −3.45128 + 4.97744i −0.704490 + 1.01602i
\(25\) 0.914214 + 1.58346i 0.182843 + 0.316693i
\(26\) 0.562978 1.42345i 0.110409 0.279161i
\(27\) −3.02846 −0.582827
\(28\) 0 0
\(29\) −6.82843 −1.26801 −0.634004 0.773330i \(-0.718590\pi\)
−0.634004 + 0.773330i \(0.718590\pi\)
\(30\) 2.91054 7.35909i 0.531390 1.34358i
\(31\) −3.02846 5.24545i −0.543928 0.942110i −0.998674 0.0514890i \(-0.983603\pi\)
0.454746 0.890621i \(-0.349730\pi\)
\(32\) 1.73817 5.38319i 0.307269 0.951623i
\(33\) 7.33820 + 4.23671i 1.27742 + 0.737517i
\(34\) −0.443508 + 0.0656581i −0.0760610 + 0.0112603i
\(35\) 0 0
\(36\) −3.03553 + 0.918917i −0.505922 + 0.153153i
\(37\) 2.00000 3.46410i 0.328798 0.569495i −0.653476 0.756948i \(-0.726690\pi\)
0.982274 + 0.187453i \(0.0600231\pi\)
\(38\) 5.72819 4.54353i 0.929235 0.737059i
\(39\) 2.00735 1.15894i 0.321433 0.185579i
\(40\) −0.610345 + 7.36579i −0.0965040 + 1.16463i
\(41\) 2.29610i 0.358591i −0.983795 0.179295i \(-0.942618\pi\)
0.983795 0.179295i \(-0.0573818\pi\)
\(42\) 0 0
\(43\) 7.23486i 1.10331i −0.834074 0.551653i \(-0.813997\pi\)
0.834074 0.551653i \(-0.186003\pi\)
\(44\) −7.70598 1.80145i −1.16172 0.271578i
\(45\) 3.58869 2.07193i 0.534970 0.308865i
\(46\) −2.03706 2.56818i −0.300347 0.378658i
\(47\) 2.14144 3.70909i 0.312362 0.541027i −0.666511 0.745495i \(-0.732213\pi\)
0.978873 + 0.204468i \(0.0655465\pi\)
\(48\) 7.12764 4.75071i 1.02879 0.685706i
\(49\) 0 0
\(50\) −0.378680 2.55791i −0.0535534 0.361743i
\(51\) −0.587938 0.339446i −0.0823278 0.0475320i
\(52\) −1.48074 + 1.57915i −0.205341 + 0.218989i
\(53\) −5.24264 9.08052i −0.720132 1.24731i −0.960947 0.276734i \(-0.910748\pi\)
0.240814 0.970571i \(-0.422585\pi\)
\(54\) 3.98271 + 1.57517i 0.541978 + 0.214354i
\(55\) 10.3398 1.39422
\(56\) 0 0
\(57\) 11.0711 1.46640
\(58\) 8.98002 + 3.55162i 1.17913 + 0.466351i
\(59\) 5.61341 + 9.72272i 0.730804 + 1.26579i 0.956540 + 0.291601i \(0.0941881\pi\)
−0.225736 + 0.974189i \(0.572479\pi\)
\(60\) −7.65527 + 8.16405i −0.988291 + 1.05397i
\(61\) −4.68690 2.70598i −0.600096 0.346465i 0.168984 0.985619i \(-0.445951\pi\)
−0.769079 + 0.639154i \(0.779285\pi\)
\(62\) 1.25443 + 8.47343i 0.159313 + 1.07613i
\(63\) 0 0
\(64\) −5.08579 + 6.17534i −0.635723 + 0.771917i
\(65\) 1.41421 2.44949i 0.175412 0.303822i
\(66\) −7.44681 9.38845i −0.916639 1.15564i
\(67\) 2.83882 1.63899i 0.346817 0.200235i −0.316466 0.948604i \(-0.602496\pi\)
0.663282 + 0.748369i \(0.269163\pi\)
\(68\) 0.617405 + 0.144332i 0.0748713 + 0.0175029i
\(69\) 4.96362i 0.597550i
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 4.46996 + 0.370390i 0.526790 + 0.0436509i
\(73\) −12.1388 + 7.00835i −1.42074 + 0.820266i −0.996362 0.0852188i \(-0.972841\pi\)
−0.424380 + 0.905484i \(0.639508\pi\)
\(74\) −4.43195 + 3.51537i −0.515203 + 0.408654i
\(75\) 1.95774 3.39090i 0.226060 0.391548i
\(76\) −9.89630 + 2.99581i −1.13518 + 0.343643i
\(77\) 0 0
\(78\) −3.24264 + 0.480049i −0.367157 + 0.0543549i
\(79\) −6.85351 3.95687i −0.771080 0.445183i 0.0621799 0.998065i \(-0.480195\pi\)
−0.833260 + 0.552882i \(0.813528\pi\)
\(80\) 4.63378 9.36925i 0.518073 1.04751i
\(81\) 5.62132 + 9.73641i 0.624591 + 1.08182i
\(82\) −1.19426 + 3.01959i −0.131883 + 0.333458i
\(83\) −9.45280 −1.03758 −0.518790 0.854902i \(-0.673617\pi\)
−0.518790 + 0.854902i \(0.673617\pi\)
\(84\) 0 0
\(85\) −0.828427 −0.0898555
\(86\) −3.76302 + 9.51451i −0.405777 + 1.02598i
\(87\) 7.31135 + 12.6636i 0.783859 + 1.35768i
\(88\) 9.19712 + 6.37714i 0.980416 + 0.679805i
\(89\) −5.18889 2.99581i −0.550022 0.317555i 0.199109 0.979977i \(-0.436195\pi\)
−0.749131 + 0.662422i \(0.769529\pi\)
\(90\) −5.79712 + 0.858221i −0.611070 + 0.0904645i
\(91\) 0 0
\(92\) 1.34315 + 4.43692i 0.140033 + 0.462581i
\(93\) −6.48528 + 11.2328i −0.672492 + 1.16479i
\(94\) −4.74539 + 3.76399i −0.489449 + 0.388226i
\(95\) 11.6997 6.75481i 1.20036 0.693029i
\(96\) −11.8445 + 2.54038i −1.20887 + 0.259276i
\(97\) 9.23880i 0.938058i 0.883183 + 0.469029i \(0.155396\pi\)
−0.883183 + 0.469029i \(0.844604\pi\)
\(98\) 0 0
\(99\) 6.27476i 0.630637i
\(100\) −0.832429 + 3.56085i −0.0832429 + 0.356085i
\(101\) 13.1899 7.61521i 1.31245 0.757741i 0.329946 0.944000i \(-0.392970\pi\)
0.982501 + 0.186258i \(0.0596362\pi\)
\(102\) 0.596640 + 0.752204i 0.0590761 + 0.0744793i
\(103\) 6.05692 10.4909i 0.596806 1.03370i −0.396483 0.918042i \(-0.629769\pi\)
0.993289 0.115657i \(-0.0368972\pi\)
\(104\) 2.76866 1.30656i 0.271489 0.128119i
\(105\) 0 0
\(106\) 2.17157 + 14.6686i 0.210922 + 1.42474i
\(107\) 2.00735 + 1.15894i 0.194057 + 0.112039i 0.593881 0.804553i \(-0.297595\pi\)
−0.399823 + 0.916592i \(0.630928\pi\)
\(108\) −4.41835 4.14300i −0.425156 0.398660i
\(109\) 2.82843 + 4.89898i 0.270914 + 0.469237i 0.969096 0.246683i \(-0.0793407\pi\)
−0.698182 + 0.715920i \(0.746007\pi\)
\(110\) −13.5978 5.37798i −1.29650 0.512770i
\(111\) −8.56578 −0.813028
\(112\) 0 0
\(113\) −4.24264 −0.399114 −0.199557 0.979886i \(-0.563950\pi\)
−0.199557 + 0.979886i \(0.563950\pi\)
\(114\) −14.5595 5.75832i −1.36362 0.539316i
\(115\) −3.02846 5.24545i −0.282405 0.489140i
\(116\) −9.96229 9.34144i −0.924975 0.867331i
\(117\) −1.48648 0.858221i −0.137425 0.0793426i
\(118\) −2.32515 15.7060i −0.214048 1.44585i
\(119\) 0 0
\(120\) 14.3137 6.75481i 1.30666 0.616627i
\(121\) 2.32843 4.03295i 0.211675 0.366632i
\(122\) 4.75626 + 5.99638i 0.430612 + 0.542887i
\(123\) −4.25822 + 2.45849i −0.383951 + 0.221674i
\(124\) 2.75754 11.7958i 0.247634 1.05930i
\(125\) 8.28772i 0.741276i
\(126\) 0 0
\(127\) 10.2316i 0.907911i −0.891024 0.453955i \(-0.850013\pi\)
0.891024 0.453955i \(-0.149987\pi\)
\(128\) 9.90022 5.47591i 0.875064 0.484007i
\(129\) −13.4174 + 7.74652i −1.18133 + 0.682043i
\(130\) −3.13386 + 2.48574i −0.274858 + 0.218014i
\(131\) 0.183707 0.318190i 0.0160505 0.0278004i −0.857889 0.513836i \(-0.828224\pi\)
0.873939 + 0.486035i \(0.161557\pi\)
\(132\) 4.91010 + 16.2200i 0.427370 + 1.41177i
\(133\) 0 0
\(134\) −4.58579 + 0.678892i −0.396152 + 0.0586474i
\(135\) 6.85351 + 3.95687i 0.589856 + 0.340554i
\(136\) −0.736874 0.510937i −0.0631865 0.0438125i
\(137\) 4.12132 + 7.13834i 0.352108 + 0.609869i 0.986619 0.163045i \(-0.0521316\pi\)
−0.634510 + 0.772914i \(0.718798\pi\)
\(138\) −2.58169 + 6.52763i −0.219768 + 0.555668i
\(139\) 22.8211 1.93566 0.967829 0.251610i \(-0.0809599\pi\)
0.967829 + 0.251610i \(0.0809599\pi\)
\(140\) 0 0
\(141\) −9.17157 −0.772386
\(142\) 0 0
\(143\) −2.14144 3.70909i −0.179077 0.310170i
\(144\) −5.68577 2.81203i −0.473814 0.234336i
\(145\) 15.4530 + 8.92177i 1.28330 + 0.740913i
\(146\) 19.6089 2.90295i 1.62284 0.240250i
\(147\) 0 0
\(148\) 7.65685 2.31788i 0.629390 0.190529i
\(149\) −2.41421 + 4.18154i −0.197780 + 0.342565i −0.947808 0.318841i \(-0.896707\pi\)
0.750028 + 0.661406i \(0.230040\pi\)
\(150\) −4.33830 + 3.44109i −0.354220 + 0.280964i
\(151\) −18.5532 + 10.7117i −1.50984 + 0.871704i −0.509902 + 0.860233i \(0.670318\pi\)
−0.999934 + 0.0114717i \(0.996348\pi\)
\(152\) 14.5728 + 1.20753i 1.18201 + 0.0979435i
\(153\) 0.502734i 0.0406437i
\(154\) 0 0
\(155\) 15.8275i 1.27130i
\(156\) 4.51406 + 1.05526i 0.361414 + 0.0844887i
\(157\) 16.6178 9.59428i 1.32624 0.765707i 0.341527 0.939872i \(-0.389056\pi\)
0.984717 + 0.174165i \(0.0557226\pi\)
\(158\) 6.95494 + 8.76833i 0.553305 + 0.697571i
\(159\) −11.2268 + 19.4454i −0.890345 + 1.54212i
\(160\) −10.9670 + 9.91131i −0.867019 + 0.783558i
\(161\) 0 0
\(162\) −2.32843 15.7281i −0.182939 1.23571i
\(163\) −13.1191 7.57430i −1.02757 0.593265i −0.111279 0.993789i \(-0.535495\pi\)
−0.916286 + 0.400524i \(0.868828\pi\)
\(164\) 3.14112 3.34988i 0.245280 0.261582i
\(165\) −11.0711 19.1757i −0.861881 1.49282i
\(166\) 12.4313 + 4.91662i 0.964857 + 0.381604i
\(167\) −7.83095 −0.605977 −0.302989 0.952994i \(-0.597984\pi\)
−0.302989 + 0.952994i \(0.597984\pi\)
\(168\) 0 0
\(169\) 11.8284 0.909879
\(170\) 1.08946 + 0.430884i 0.0835577 + 0.0330473i
\(171\) −4.09918 7.09999i −0.313472 0.542950i
\(172\) 9.89744 10.5552i 0.754673 0.804830i
\(173\) −5.69089 3.28564i −0.432671 0.249802i 0.267813 0.963471i \(-0.413699\pi\)
−0.700484 + 0.713668i \(0.747032\pi\)
\(174\) −3.02846 20.4567i −0.229587 1.55082i
\(175\) 0 0
\(176\) −8.77817 13.1702i −0.661680 0.992739i
\(177\) 12.0208 20.8207i 0.903540 1.56498i
\(178\) 5.26569 + 6.63864i 0.394680 + 0.497587i
\(179\) 11.6997 6.75481i 0.874474 0.504878i 0.00564179 0.999984i \(-0.498204\pi\)
0.868833 + 0.495106i \(0.164871\pi\)
\(180\) 8.07014 + 1.88658i 0.601513 + 0.140617i
\(181\) 21.9874i 1.63431i −0.576418 0.817155i \(-0.695550\pi\)
0.576418 0.817155i \(-0.304450\pi\)
\(182\) 0 0
\(183\) 11.5894i 0.856714i
\(184\) 0.541385 6.53357i 0.0399115 0.481661i
\(185\) −9.05213 + 5.22625i −0.665526 + 0.384242i
\(186\) 14.3712 11.3991i 1.05375 0.835822i
\(187\) −0.627215 + 1.08637i −0.0458665 + 0.0794431i
\(188\) 8.19837 2.48181i 0.597927 0.181005i
\(189\) 0 0
\(190\) −18.8995 + 2.79793i −1.37111 + 0.202983i
\(191\) 5.67763 + 3.27798i 0.410819 + 0.237186i 0.691142 0.722719i \(-0.257108\pi\)
−0.280323 + 0.959906i \(0.590441\pi\)
\(192\) 16.8979 + 2.81975i 1.21950 + 0.203498i
\(193\) −7.29289 12.6317i −0.524954 0.909247i −0.999578 0.0290581i \(-0.990749\pi\)
0.474624 0.880189i \(-0.342584\pi\)
\(194\) 4.80531 12.1499i 0.345001 0.872311i
\(195\) −6.05692 −0.433745
\(196\) 0 0
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) −3.26365 + 8.25189i −0.231937 + 0.586437i
\(199\) −8.56578 14.8364i −0.607212 1.05172i −0.991698 0.128591i \(-0.958955\pi\)
0.384486 0.923131i \(-0.374379\pi\)
\(200\) 2.94680 4.24988i 0.208370 0.300512i
\(201\) −6.07917 3.50981i −0.428791 0.247563i
\(202\) −21.3068 + 3.15432i −1.49914 + 0.221937i
\(203\) 0 0
\(204\) −0.393398 1.29954i −0.0275434 0.0909863i
\(205\) −3.00000 + 5.19615i −0.209529 + 0.362915i
\(206\) −13.4220 + 10.6462i −0.935154 + 0.741753i
\(207\) −3.18322 + 1.83783i −0.221249 + 0.127738i
\(208\) −4.32062 + 0.278208i −0.299581 + 0.0192903i
\(209\) 20.4567i 1.41502i
\(210\) 0 0
\(211\) 14.4697i 0.996136i 0.867138 + 0.498068i \(0.165957\pi\)
−0.867138 + 0.498068i \(0.834043\pi\)
\(212\) 4.77364 20.4200i 0.327855 1.40245i
\(213\) 0 0
\(214\) −2.03706 2.56818i −0.139250 0.175557i
\(215\) −9.45280 + 16.3727i −0.644675 + 1.11661i
\(216\) 3.65568 + 7.74652i 0.248737 + 0.527084i
\(217\) 0 0
\(218\) −1.17157 7.91375i −0.0793489 0.535987i
\(219\) 25.9946 + 15.0080i 1.75655 + 1.01415i
\(220\) 15.0852 + 14.1451i 1.01704 + 0.953662i
\(221\) 0.171573 + 0.297173i 0.0115412 + 0.0199900i
\(222\) 11.2648 + 4.45526i 0.756044 + 0.299018i
\(223\) −7.83095 −0.524399 −0.262200 0.965014i \(-0.584448\pi\)
−0.262200 + 0.965014i \(0.584448\pi\)
\(224\) 0 0
\(225\) −2.89949 −0.193300
\(226\) 5.57947 + 2.20670i 0.371141 + 0.146787i
\(227\) −4.98620 8.63635i −0.330946 0.573215i 0.651752 0.758432i \(-0.274034\pi\)
−0.982698 + 0.185218i \(0.940701\pi\)
\(228\) 16.1521 + 15.1455i 1.06970 + 1.00303i
\(229\) 1.16483 + 0.672512i 0.0769738 + 0.0444409i 0.537993 0.842949i \(-0.319183\pi\)
−0.461019 + 0.887390i \(0.652516\pi\)
\(230\) 1.25443 + 8.47343i 0.0827146 + 0.558721i
\(231\) 0 0
\(232\) 8.24264 + 17.4665i 0.541156 + 1.14673i
\(233\) −8.12132 + 14.0665i −0.532045 + 0.921530i 0.467255 + 0.884123i \(0.345243\pi\)
−0.999300 + 0.0374069i \(0.988090\pi\)
\(234\) 1.50848 + 1.90180i 0.0986127 + 0.124324i
\(235\) −9.69232 + 5.59587i −0.632257 + 0.365034i
\(236\) −5.11124 + 21.8642i −0.332713 + 1.42324i
\(237\) 16.9469i 1.10082i
\(238\) 0 0
\(239\) 10.2316i 0.661829i −0.943661 0.330915i \(-0.892643\pi\)
0.943661 0.330915i \(-0.107357\pi\)
\(240\) −22.3372 + 1.43831i −1.44186 + 0.0928425i
\(241\) 4.41234 2.54747i 0.284224 0.164097i −0.351110 0.936334i \(-0.614196\pi\)
0.635334 + 0.772237i \(0.280862\pi\)
\(242\) −5.15973 + 4.09264i −0.331680 + 0.263085i
\(243\) 7.49506 12.9818i 0.480808 0.832784i
\(244\) −3.13607 10.3596i −0.200767 0.663209i
\(245\) 0 0
\(246\) 6.87868 1.01834i 0.438569 0.0649269i
\(247\) −4.84616 2.79793i −0.308354 0.178028i
\(248\) −9.76170 + 14.0783i −0.619868 + 0.893975i
\(249\) 10.1213 + 17.5306i 0.641413 + 1.11096i
\(250\) 4.31064 10.8991i 0.272629 0.689321i
\(251\) 3.91548 0.247143 0.123571 0.992336i \(-0.460565\pi\)
0.123571 + 0.992336i \(0.460565\pi\)
\(252\) 0 0
\(253\) −9.17157 −0.576612
\(254\) −5.32171 + 13.4556i −0.333914 + 0.844277i
\(255\) 0.887016 + 1.53636i 0.0555471 + 0.0962103i
\(256\) −15.8679 + 2.05200i −0.991742 + 0.128250i
\(257\) 16.5041 + 9.52862i 1.02950 + 0.594379i 0.916840 0.399255i \(-0.130731\pi\)
0.112655 + 0.993634i \(0.464064\pi\)
\(258\) 21.6743 3.20871i 1.34938 0.199766i
\(259\) 0 0
\(260\) 5.41421 1.63899i 0.335775 0.101646i
\(261\) 5.41421 9.37769i 0.335131 0.580465i
\(262\) −0.407090 + 0.322899i −0.0251501 + 0.0199488i
\(263\) −22.2235 + 12.8307i −1.37036 + 0.791176i −0.990973 0.134063i \(-0.957198\pi\)
−0.379385 + 0.925239i \(0.623864\pi\)
\(264\) 1.97913 23.8846i 0.121807 1.47000i
\(265\) 27.3994i 1.68313i
\(266\) 0 0
\(267\) 12.8307i 0.785227i
\(268\) 6.38385 + 1.49237i 0.389956 + 0.0911609i
\(269\) −4.36524 + 2.52027i −0.266153 + 0.153664i −0.627138 0.778908i \(-0.715774\pi\)
0.360985 + 0.932572i \(0.382441\pi\)
\(270\) −6.95494 8.76833i −0.423264 0.533624i
\(271\) 2.14144 3.70909i 0.130084 0.225311i −0.793625 0.608407i \(-0.791809\pi\)
0.923709 + 0.383096i \(0.125142\pi\)
\(272\) 0.703309 + 1.05520i 0.0426443 + 0.0639806i
\(273\) 0 0
\(274\) −1.70711 11.5312i −0.103130 0.696624i
\(275\) −6.26557 3.61743i −0.377828 0.218139i
\(276\) 6.79034 7.24164i 0.408731 0.435895i
\(277\) 2.07107 + 3.58719i 0.124438 + 0.215534i 0.921513 0.388347i \(-0.126954\pi\)
−0.797075 + 0.603880i \(0.793620\pi\)
\(278\) −30.0118 11.8698i −1.79999 0.711902i
\(279\) 9.60498 0.575035
\(280\) 0 0
\(281\) 10.3848 0.619504 0.309752 0.950817i \(-0.399754\pi\)
0.309752 + 0.950817i \(0.399754\pi\)
\(282\) 12.0615 + 4.77035i 0.718251 + 0.284070i
\(283\) 1.69794 + 2.94091i 0.100932 + 0.174819i 0.912069 0.410037i \(-0.134484\pi\)
−0.811137 + 0.584856i \(0.801151\pi\)
\(284\) 0 0
\(285\) −25.0542 14.4650i −1.48408 0.856835i
\(286\) 0.887016 + 5.99162i 0.0524503 + 0.354292i
\(287\) 0 0
\(288\) 6.01472 + 6.65539i 0.354421 + 0.392172i
\(289\) −8.44975 + 14.6354i −0.497044 + 0.860905i
\(290\) −15.6817 19.7704i −0.920859 1.16096i
\(291\) 17.1338 9.89219i 1.00440 0.579890i
\(292\) −27.2974 6.38139i −1.59746 0.373443i
\(293\) 11.7975i 0.689219i 0.938746 + 0.344609i \(0.111989\pi\)
−0.938746 + 0.344609i \(0.888011\pi\)
\(294\) 0 0
\(295\) 29.3371i 1.70807i
\(296\) −11.2751 0.934275i −0.655350 0.0543037i
\(297\) 10.3778 5.99162i 0.602180 0.347669i
\(298\) 5.34983 4.24343i 0.309908 0.245815i
\(299\) −1.25443 + 2.17274i −0.0725455 + 0.125653i
\(300\) 7.49506 2.26890i 0.432727 0.130995i
\(301\) 0 0
\(302\) 29.9706 4.43692i 1.72461 0.255316i
\(303\) −28.2455 16.3075i −1.62266 0.936844i
\(304\) −18.5365 9.16765i −1.06314 0.525801i
\(305\) 7.07107 + 12.2474i 0.404888 + 0.701287i
\(306\) 0.261484 0.661143i 0.0149480 0.0377950i
\(307\) 3.91548 0.223468 0.111734 0.993738i \(-0.464360\pi\)
0.111734 + 0.993738i \(0.464360\pi\)
\(308\) 0 0
\(309\) −25.9411 −1.47574
\(310\) 8.23225 20.8146i 0.467561 1.18219i
\(311\) 10.3398 + 17.9091i 0.586317 + 1.01553i 0.994710 + 0.102724i \(0.0327560\pi\)
−0.408393 + 0.912806i \(0.633911\pi\)
\(312\) −5.38755 3.73564i −0.305010 0.211489i
\(313\) −11.0406 6.37430i −0.624052 0.360297i 0.154393 0.988010i \(-0.450658\pi\)
−0.778445 + 0.627713i \(0.783991\pi\)
\(314\) −26.8442 + 3.97408i −1.51490 + 0.224270i
\(315\) 0 0
\(316\) −4.58579 15.1486i −0.257971 0.852176i
\(317\) 2.75736 4.77589i 0.154869 0.268241i −0.778142 0.628088i \(-0.783838\pi\)
0.933011 + 0.359847i \(0.117171\pi\)
\(318\) 24.8784 19.7332i 1.39511 1.10658i
\(319\) 23.3993 13.5096i 1.31011 0.756393i
\(320\) 19.5778 7.33009i 1.09443 0.409765i
\(321\) 4.96362i 0.277042i
\(322\) 0 0
\(323\) 1.63899i 0.0911959i
\(324\) −5.11844 + 21.8950i −0.284358 + 1.21639i
\(325\) −1.71393 + 0.989538i −0.0950717 + 0.0548897i
\(326\) 13.3132 + 16.7845i 0.737352 + 0.929605i
\(327\) 6.05692 10.4909i 0.334948 0.580148i
\(328\) −5.87321 + 2.77164i −0.324294 + 0.153038i
\(329\) 0 0
\(330\) 4.58579 + 30.9761i 0.252439 + 1.70518i
\(331\) −13.1191 7.57430i −0.721090 0.416321i 0.0940639 0.995566i \(-0.470014\pi\)
−0.815154 + 0.579245i \(0.803348\pi\)
\(332\) −13.7911 12.9316i −0.756884 0.709716i
\(333\) 3.17157 + 5.49333i 0.173801 + 0.301032i
\(334\) 10.2984 + 4.07306i 0.563505 + 0.222868i
\(335\) −8.56578 −0.467999
\(336\) 0 0
\(337\) 10.8284 0.589862 0.294931 0.955519i \(-0.404703\pi\)
0.294931 + 0.955519i \(0.404703\pi\)
\(338\) −15.5555 6.15224i −0.846107 0.334638i
\(339\) 4.54269 + 7.86817i 0.246725 + 0.427340i
\(340\) −1.20863 1.13331i −0.0655471 0.0614622i
\(341\) 20.7556 + 11.9832i 1.12398 + 0.648929i
\(342\) 1.69794 + 11.4692i 0.0918139 + 0.620185i
\(343\) 0 0
\(344\) −18.5061 + 8.73324i −0.997782 + 0.470865i
\(345\) −6.48528 + 11.2328i −0.349156 + 0.604756i
\(346\) 5.77512 + 7.28089i 0.310472 + 0.391423i
\(347\) −3.42675 + 1.97844i −0.183958 + 0.106208i −0.589151 0.808023i \(-0.700538\pi\)
0.405193 + 0.914231i \(0.367204\pi\)
\(348\) −6.65728 + 28.4776i −0.356868 + 1.52656i
\(349\) 8.47343i 0.453572i −0.973945 0.226786i \(-0.927178\pi\)
0.973945 0.226786i \(-0.0728218\pi\)
\(350\) 0 0
\(351\) 3.27798i 0.174966i
\(352\) 4.69401 + 21.8857i 0.250192 + 1.16651i
\(353\) −8.71096 + 5.02928i −0.463638 + 0.267681i −0.713573 0.700581i \(-0.752924\pi\)
0.249935 + 0.968263i \(0.419591\pi\)
\(354\) −26.6378 + 21.1288i −1.41578 + 1.12298i
\(355\) 0 0
\(356\) −3.47197 11.4692i −0.184014 0.607868i
\(357\) 0 0
\(358\) −18.8995 + 2.79793i −0.998869 + 0.147875i
\(359\) 27.0696 + 15.6287i 1.42868 + 0.824849i 0.997017 0.0771860i \(-0.0245935\pi\)
0.431663 + 0.902035i \(0.357927\pi\)
\(360\) −9.63174 6.67849i −0.507637 0.351987i
\(361\) −3.86396 6.69258i −0.203366 0.352241i
\(362\) −11.4362 + 28.9155i −0.601071 + 1.51976i
\(363\) −9.97240 −0.523415
\(364\) 0 0
\(365\) 36.6274 1.91717
\(366\) 6.02793 15.2412i 0.315085 0.796669i
\(367\) 6.42433 + 11.1273i 0.335348 + 0.580839i 0.983552 0.180628i \(-0.0578129\pi\)
−0.648204 + 0.761467i \(0.724480\pi\)
\(368\) −4.11024 + 8.31067i −0.214261 + 0.433224i
\(369\) 3.15331 + 1.82056i 0.164155 + 0.0947747i
\(370\) 14.6227 2.16478i 0.760198 0.112542i
\(371\) 0 0
\(372\) −24.8284 + 7.51606i −1.28729 + 0.389690i
\(373\) 10.0711 17.4436i 0.521460 0.903195i −0.478228 0.878236i \(-0.658721\pi\)
0.999688 0.0249599i \(-0.00794580\pi\)
\(374\) 1.38989 1.10245i 0.0718696 0.0570061i
\(375\) 15.3700 8.87385i 0.793701 0.458244i
\(376\) −12.0725 1.00035i −0.622590 0.0515891i
\(377\) 7.39104i 0.380658i
\(378\) 0 0
\(379\) 21.7046i 1.11489i −0.830214 0.557444i \(-0.811782\pi\)
0.830214 0.557444i \(-0.188218\pi\)
\(380\) 26.3099 + 6.15053i 1.34967 + 0.315515i
\(381\) −18.9750 + 10.9552i −0.972120 + 0.561254i
\(382\) −5.76166 7.26392i −0.294792 0.371655i
\(383\) 15.5097 26.8636i 0.792509 1.37267i −0.131899 0.991263i \(-0.542108\pi\)
0.924409 0.381404i \(-0.124559\pi\)
\(384\) −20.7557 12.4972i −1.05919 0.637747i
\(385\) 0 0
\(386\) 3.02082 + 20.4050i 0.153755 + 1.03859i
\(387\) 9.93585 + 5.73647i 0.505068 + 0.291601i
\(388\) −12.6389 + 13.4789i −0.641642 + 0.684286i
\(389\) −7.07107 12.2474i −0.358517 0.620970i 0.629196 0.777247i \(-0.283384\pi\)
−0.987713 + 0.156276i \(0.950051\pi\)
\(390\) 7.96542 + 3.15035i 0.403345 + 0.159524i
\(391\) 0.734828 0.0371618
\(392\) 0 0
\(393\) −0.786797 −0.0396886
\(394\) −2.63019 1.04025i −0.132507 0.0524069i
\(395\) 10.3398 + 17.9091i 0.520252 + 0.901103i
\(396\) 8.58401 9.15452i 0.431363 0.460032i
\(397\) −13.9665 8.06355i −0.700957 0.404698i 0.106747 0.994286i \(-0.465957\pi\)
−0.807704 + 0.589588i \(0.799290\pi\)
\(398\) 3.54806 + 23.9665i 0.177848 + 1.20133i
\(399\) 0 0
\(400\) −6.08579 + 4.05630i −0.304289 + 0.202815i
\(401\) 6.41421 11.1097i 0.320311 0.554794i −0.660242 0.751053i \(-0.729546\pi\)
0.980552 + 0.196259i \(0.0628794\pi\)
\(402\) 6.16914 + 7.77765i 0.307689 + 0.387914i
\(403\) 5.67763 3.27798i 0.282823 0.163288i
\(404\) 29.6611 + 6.93396i 1.47570 + 0.344977i
\(405\) 29.3784i 1.45983i
\(406\) 0 0
\(407\) 15.8275i 0.784540i
\(408\) −0.158568 + 1.91364i −0.00785029 + 0.0947392i
\(409\) 11.9780 6.91550i 0.592274 0.341949i −0.173722 0.984795i \(-0.555580\pi\)
0.765996 + 0.642845i \(0.222246\pi\)
\(410\) 6.64792 5.27306i 0.328317 0.260418i
\(411\) 8.82558 15.2864i 0.435334 0.754020i
\(412\) 23.1885 7.01962i 1.14241 0.345832i
\(413\) 0 0
\(414\) 5.14214 0.761256i 0.252722 0.0374137i
\(415\) 21.3920 + 12.3507i 1.05009 + 0.606271i
\(416\) 5.82672 + 1.88139i 0.285679 + 0.0922426i
\(417\) −24.4350 42.3227i −1.19659 2.07255i
\(418\) −10.6400 + 26.9024i −0.520419 + 1.31584i
\(419\) 17.2837 0.844366 0.422183 0.906511i \(-0.361264\pi\)
0.422183 + 0.906511i \(0.361264\pi\)
\(420\) 0 0
\(421\) −10.4853 −0.511021 −0.255511 0.966806i \(-0.582244\pi\)
−0.255511 + 0.966806i \(0.582244\pi\)
\(422\) 7.52604 19.0290i 0.366362 0.926319i
\(423\) 3.39587 + 5.88183i 0.165113 + 0.285984i
\(424\) −16.8987 + 24.3713i −0.820674 + 1.18358i
\(425\) 0.501998 + 0.289829i 0.0243505 + 0.0140588i
\(426\) 0 0
\(427\) 0 0
\(428\) 1.34315 + 4.43692i 0.0649234 + 0.214467i
\(429\) −4.58579 + 7.94282i −0.221404 + 0.383483i
\(430\) 20.9471 16.6150i 1.01016 0.801249i
\(431\) −0.831470 + 0.480049i −0.0400505 + 0.0231232i −0.519892 0.854232i \(-0.674028\pi\)
0.479841 + 0.877355i \(0.340694\pi\)
\(432\) −0.778407 12.0888i −0.0374511 0.581623i
\(433\) 26.1857i 1.25840i −0.777243 0.629201i \(-0.783382\pi\)
0.777243 0.629201i \(-0.216618\pi\)
\(434\) 0 0
\(435\) 38.2110i 1.83208i
\(436\) −2.57540 + 11.0167i −0.123339 + 0.527603i
\(437\) −10.3778 + 5.99162i −0.496437 + 0.286618i
\(438\) −26.3794 33.2573i −1.26045 1.58910i
\(439\) −11.2268 + 19.4454i −0.535827 + 0.928080i 0.463296 + 0.886204i \(0.346667\pi\)
−0.999123 + 0.0418761i \(0.986667\pi\)
\(440\) −12.4813 26.4483i −0.595021 1.26087i
\(441\) 0 0
\(442\) −0.0710678 0.480049i −0.00338035 0.0228336i
\(443\) −24.5752 14.1885i −1.16760 0.674116i −0.214489 0.976726i \(-0.568809\pi\)
−0.953114 + 0.302610i \(0.902142\pi\)
\(444\) −12.4970 11.7182i −0.593081 0.556120i
\(445\) 7.82843 + 13.5592i 0.371103 + 0.642769i
\(446\) 10.2984 + 4.07306i 0.487645 + 0.192865i
\(447\) 10.3398 0.489056
\(448\) 0 0
\(449\) −16.2843 −0.768502 −0.384251 0.923229i \(-0.625540\pi\)
−0.384251 + 0.923229i \(0.625540\pi\)
\(450\) 3.81311 + 1.50810i 0.179752 + 0.0710923i
\(451\) 4.54269 + 7.86817i 0.213907 + 0.370498i
\(452\) −6.18977 5.80403i −0.291142 0.272998i
\(453\) 39.7306 + 22.9385i 1.86671 + 1.07774i
\(454\) 2.06535 + 13.9510i 0.0969317 + 0.654755i
\(455\) 0 0
\(456\) −13.3640 28.3188i −0.625825 1.32615i
\(457\) −0.363961 + 0.630399i −0.0170254 + 0.0294888i −0.874413 0.485183i \(-0.838753\pi\)
0.857387 + 0.514672i \(0.172086\pi\)
\(458\) −1.18207 1.49027i −0.0552343 0.0696357i
\(459\) −0.831470 + 0.480049i −0.0388097 + 0.0224068i
\(460\) 2.75754 11.7958i 0.128571 0.549983i
\(461\) 29.7499i 1.38559i 0.721135 + 0.692794i \(0.243621\pi\)
−0.721135 + 0.692794i \(0.756379\pi\)
\(462\) 0 0
\(463\) 34.9330i 1.62347i 0.584024 + 0.811737i \(0.301477\pi\)
−0.584024 + 0.811737i \(0.698523\pi\)
\(464\) −1.75512 27.2573i −0.0814792 1.26539i
\(465\) 29.3528 16.9469i 1.36120 0.785892i
\(466\) 17.9966 14.2747i 0.833678 0.661264i
\(467\) −12.0377 + 20.8500i −0.557041 + 0.964823i 0.440701 + 0.897654i \(0.354730\pi\)
−0.997742 + 0.0671686i \(0.978603\pi\)
\(468\) −0.994629 3.28564i −0.0459767 0.151879i
\(469\) 0 0
\(470\) 15.6569 2.31788i 0.722197 0.106916i
\(471\) −35.5861 20.5456i −1.63972 0.946693i
\(472\) 18.0938 26.0950i 0.832836 1.20112i
\(473\) 14.3137 + 24.7921i 0.658145 + 1.13994i
\(474\) 8.81446 22.2867i 0.404861 1.02366i
\(475\) −9.45280 −0.433724
\(476\) 0 0
\(477\) 16.6274 0.761317
\(478\) −5.32171 + 13.4556i −0.243409 + 0.615443i
\(479\) −16.3967 28.4000i −0.749186 1.29763i −0.948213 0.317634i \(-0.897112\pi\)
0.199028 0.979994i \(-0.436222\pi\)
\(480\) 30.1236 + 9.72659i 1.37495 + 0.443956i
\(481\) 3.74952 + 2.16478i 0.170963 + 0.0987057i
\(482\) −7.12764 + 1.05520i −0.324655 + 0.0480628i
\(483\) 0 0
\(484\) 8.91421 2.69851i 0.405192 0.122660i
\(485\) 12.0711 20.9077i 0.548119 0.949370i
\(486\) −16.6089 + 13.1740i −0.753393 + 0.597583i
\(487\) 16.8902 9.75158i 0.765370 0.441886i −0.0658507 0.997829i \(-0.520976\pi\)
0.831220 + 0.555943i \(0.187643\pi\)
\(488\) −1.26407 + 15.2551i −0.0572216 + 0.690564i
\(489\) 32.4399i 1.46698i
\(490\) 0 0
\(491\) 14.4697i 0.653009i −0.945196 0.326504i \(-0.894129\pi\)
0.945196 0.326504i \(-0.105871\pi\)
\(492\) −9.57577 2.23855i −0.431709 0.100922i
\(493\) −1.87476 + 1.08239i −0.0844349 + 0.0487485i
\(494\) 4.91789 + 6.20015i 0.221266 + 0.278958i
\(495\) −8.19837 + 14.2000i −0.368489 + 0.638242i
\(496\) 20.1600 13.4370i 0.905212 0.603341i
\(497\) 0 0
\(498\) −4.19239 28.3188i −0.187865 1.26899i
\(499\) 10.8682 + 6.27476i 0.486527 + 0.280897i 0.723133 0.690709i \(-0.242701\pi\)
−0.236605 + 0.971606i \(0.576035\pi\)
\(500\) −11.3378 + 12.0913i −0.507041 + 0.540740i
\(501\) 8.38478 + 14.5229i 0.374604 + 0.648833i
\(502\) −5.14922 2.03653i −0.229821 0.0908948i
\(503\) 7.83095 0.349165 0.174582 0.984643i \(-0.444142\pi\)
0.174582 + 0.984643i \(0.444142\pi\)
\(504\) 0 0
\(505\) −39.7990 −1.77103
\(506\) 12.0615 + 4.77035i 0.536198 + 0.212068i
\(507\) −12.6650 21.9364i −0.562471 0.974228i
\(508\) 13.9971 14.9274i 0.621021 0.662295i
\(509\) −5.69089 3.28564i −0.252244 0.145633i 0.368547 0.929609i \(-0.379855\pi\)
−0.620791 + 0.783976i \(0.713189\pi\)
\(510\) −0.367414 2.48181i −0.0162694 0.109896i
\(511\) 0 0
\(512\) 21.9350 + 5.55468i 0.969400 + 0.245485i
\(513\) 7.82843 13.5592i 0.345634 0.598655i
\(514\) −16.7483 21.1152i −0.738737 0.931351i
\(515\) −27.4140 + 15.8275i −1.20801 + 0.697443i
\(516\) −30.1726 7.05352i −1.32827 0.310514i
\(517\) 16.9469i 0.745322i
\(518\) 0 0
\(519\) 14.0720i 0.617693i
\(520\) −7.97268 0.660632i −0.349625 0.0289707i
\(521\) −10.4249 + 6.01882i −0.456723 + 0.263689i −0.710665 0.703530i \(-0.751606\pi\)
0.253942 + 0.967219i \(0.418273\pi\)
\(522\) −11.9978 + 9.51649i −0.525128 + 0.416525i
\(523\) −3.73177 + 6.46361i −0.163179 + 0.282634i −0.936007 0.351981i \(-0.885508\pi\)
0.772828 + 0.634615i \(0.218841\pi\)
\(524\) 0.703309 0.212906i 0.0307242 0.00930083i
\(525\) 0 0
\(526\) 35.8995 5.31466i 1.56529 0.231730i
\(527\) −1.66294 0.960099i −0.0724388 0.0418226i
\(528\) −15.0257 + 30.3811i −0.653909 + 1.32217i
\(529\) −8.81371 15.2658i −0.383205 0.663730i
\(530\) 14.2510 36.0327i 0.619026 1.56516i
\(531\) −17.8033 −0.772600
\(532\) 0 0
\(533\) 2.48528 0.107649
\(534\) 6.67356 16.8736i 0.288793 0.730192i
\(535\) −3.02846 5.24545i −0.130932 0.226780i
\(536\) −7.61914 5.28299i −0.329097 0.228191i
\(537\) −25.0542 14.4650i −1.08117 0.624213i
\(538\) 7.05155 1.04393i 0.304014 0.0450070i
\(539\) 0 0
\(540\) 4.58579 + 15.1486i 0.197341 + 0.651892i
\(541\) −22.6569 + 39.2428i −0.974094 + 1.68718i −0.291202 + 0.956662i \(0.594055\pi\)
−0.682892 + 0.730519i \(0.739278\pi\)
\(542\) −4.74539 + 3.76399i −0.203832 + 0.161677i
\(543\) −40.7766 + 23.5424i −1.74989 + 1.01030i
\(544\) −0.376085 1.75349i −0.0161245 0.0751802i
\(545\) 14.7821i 0.633194i
\(546\) 0 0
\(547\) 27.6981i 1.18429i 0.805833 + 0.592143i \(0.201718\pi\)
−0.805833 + 0.592143i \(0.798282\pi\)
\(548\) −3.75263 + 16.0525i −0.160304 + 0.685728i
\(549\) 7.43242 4.29111i 0.317208 0.183140i
\(550\) 6.35830 + 8.01613i 0.271119 + 0.341809i
\(551\) 17.6512 30.5727i 0.751965 1.30244i
\(552\) −12.6965 + 5.99162i −0.540398 + 0.255020i
\(553\) 0 0
\(554\) −0.857864 5.79471i −0.0364472 0.246194i
\(555\) 19.3846 + 11.1917i 0.822832 + 0.475063i
\(556\) 33.2946 + 31.2197i 1.41201 + 1.32401i
\(557\) 9.82843 + 17.0233i 0.416444 + 0.721302i 0.995579 0.0939298i \(-0.0299429\pi\)
−0.579135 + 0.815232i \(0.696610\pi\)
\(558\) −12.6315 4.99578i −0.534732 0.211488i
\(559\) 7.83095 0.331214
\(560\) 0 0
\(561\) 2.68629 0.113415
\(562\) −13.6570 5.40137i −0.576084 0.227843i
\(563\) −10.5235 18.2273i −0.443513 0.768188i 0.554434 0.832228i \(-0.312935\pi\)
−0.997947 + 0.0640400i \(0.979601\pi\)
\(564\) −13.3808 12.5469i −0.563433 0.528320i
\(565\) 9.60124 + 5.54328i 0.403927 + 0.233207i
\(566\) −0.703309 4.75071i −0.0295623 0.199687i
\(567\) 0 0
\(568\) 0 0
\(569\) −9.41421 + 16.3059i −0.394664 + 0.683579i −0.993058 0.117623i \(-0.962472\pi\)
0.598394 + 0.801202i \(0.295806\pi\)
\(570\) 25.4250 + 32.0542i 1.06494 + 1.34260i
\(571\) −8.61732 + 4.97521i −0.360624 + 0.208206i −0.669354 0.742943i \(-0.733429\pi\)
0.308731 + 0.951150i \(0.400096\pi\)
\(572\) 1.94987 8.34090i 0.0815283 0.348750i
\(573\) 14.0392i 0.586497i
\(574\) 0 0
\(575\) 4.23808i 0.176740i
\(576\) −4.44830 11.8809i −0.185346 0.495036i
\(577\) −0.729445 + 0.421145i −0.0303672 + 0.0175325i −0.515107 0.857126i \(-0.672248\pi\)
0.484740 + 0.874659i \(0.338914\pi\)
\(578\) 18.7244 14.8520i 0.778833 0.617762i
\(579\) −15.6173 + 27.0500i −0.649034 + 1.12416i
\(580\) 10.3398 + 34.1563i 0.429337 + 1.41827i
\(581\) 0 0
\(582\) −27.6777 + 4.09748i −1.14728 + 0.169846i
\(583\) 35.9305 + 20.7445i 1.48809 + 0.859148i
\(584\) 32.5796 + 22.5902i 1.34815 + 0.934788i
\(585\) 2.24264 + 3.88437i 0.0927218 + 0.160599i
\(586\) 6.13617 15.5149i 0.253483 0.640913i
\(587\) −22.8211 −0.941926 −0.470963 0.882153i \(-0.656094\pi\)
−0.470963 + 0.882153i \(0.656094\pi\)
\(588\) 0 0
\(589\) 31.3137 1.29026
\(590\) −15.2589 + 38.5811i −0.628200 + 1.58836i
\(591\) −2.14144 3.70909i −0.0880873 0.152572i
\(592\) 14.3418 + 7.09309i 0.589446 + 0.291524i
\(593\) −32.4395 18.7290i −1.33213 0.769106i −0.346505 0.938048i \(-0.612632\pi\)
−0.985626 + 0.168942i \(0.945965\pi\)
\(594\) −16.7641 + 2.48181i −0.687841 + 0.101830i
\(595\) 0 0
\(596\) −9.24264 + 2.79793i −0.378593 + 0.114608i
\(597\) −18.3431 + 31.7713i −0.750735 + 1.30031i
\(598\) 2.77978 2.20489i 0.113674 0.0901648i
\(599\) 27.9011 16.1087i 1.14001 0.658184i 0.193575 0.981085i \(-0.437992\pi\)
0.946433 + 0.322902i \(0.104658\pi\)
\(600\) −11.0368 0.914533i −0.450576 0.0373357i
\(601\) 25.5516i 1.04227i 0.853474 + 0.521136i \(0.174491\pi\)
−0.853474 + 0.521136i \(0.825509\pi\)
\(602\) 0 0
\(603\) 5.19818i 0.211686i
\(604\) −41.7218 9.75342i −1.69764 0.396861i
\(605\) −10.5386 + 6.08447i −0.428456 + 0.247369i
\(606\) 28.6635 + 36.1371i 1.16438 + 1.46797i
\(607\) 6.05692 10.4909i 0.245843 0.425812i −0.716525 0.697561i \(-0.754269\pi\)
0.962368 + 0.271749i \(0.0876020\pi\)
\(608\) 19.6089 + 21.6976i 0.795246 + 0.879953i
\(609\) 0 0
\(610\) −2.92893 19.7844i −0.118589 0.801046i
\(611\) 4.01469 + 2.31788i 0.162417 + 0.0937715i
\(612\) −0.687752 + 0.733461i −0.0278007 + 0.0296484i
\(613\) 4.34315 + 7.52255i 0.175418 + 0.303833i 0.940306 0.340331i \(-0.110539\pi\)
−0.764888 + 0.644163i \(0.777206\pi\)
\(614\) −5.14922 2.03653i −0.207806 0.0821877i
\(615\) 12.8487 0.518108
\(616\) 0 0
\(617\) −35.4558 −1.42740 −0.713699 0.700452i \(-0.752982\pi\)
−0.713699 + 0.700452i \(0.752982\pi\)
\(618\) 34.1150 + 13.4926i 1.37231 + 0.542751i
\(619\) 6.76023 + 11.7091i 0.271717 + 0.470627i 0.969301 0.245875i \(-0.0790753\pi\)
−0.697585 + 0.716502i \(0.745742\pi\)
\(620\) −21.6524 + 23.0914i −0.869580 + 0.927374i
\(621\) −6.07917 3.50981i −0.243949 0.140844i
\(622\) −4.28289 28.9301i −0.171728 1.15999i
\(623\) 0 0
\(624\) 5.14214 + 7.71491i 0.205850 + 0.308843i
\(625\) 15.3995 26.6727i 0.615980 1.06691i
\(626\) 11.2040 + 14.1253i 0.447803 + 0.564560i
\(627\) −37.9378 + 21.9034i −1.51509 + 0.874738i
\(628\) 37.3696 + 8.73598i 1.49121 + 0.348604i
\(629\) 1.26810i 0.0505625i
\(630\) 0 0
\(631\) 20.4633i 0.814630i 0.913288 + 0.407315i \(0.133535\pi\)
−0.913288 + 0.407315i \(0.866465\pi\)
\(632\) −1.84841 + 22.3070i −0.0735256 + 0.887325i
\(633\) 26.8347 15.4930i 1.06659 0.615793i
\(634\) −6.11024 + 4.84657i −0.242668 + 0.192482i
\(635\) −13.3683 + 23.1545i −0.530504 + 0.918859i
\(636\) −42.9811 + 13.0112i −1.70431 + 0.515929i
\(637\) 0 0
\(638\) −37.7990 + 5.59587i −1.49648 + 0.221542i
\(639\) 0 0
\(640\) −29.5592 0.543099i −1.16843 0.0214679i
\(641\) −24.7279 42.8300i −0.976694 1.69168i −0.674227 0.738524i \(-0.735523\pi\)
−0.302467 0.953160i \(-0.597810\pi\)
\(642\) −2.58169 + 6.52763i −0.101891 + 0.257625i
\(643\) −41.7267 −1.64554 −0.822769 0.568375i \(-0.807572\pi\)
−0.822769 + 0.568375i \(0.807572\pi\)
\(644\) 0 0
\(645\) 40.4853 1.59411
\(646\) 0.852478 2.15543i 0.0335403 0.0848041i
\(647\) −21.9341 37.9909i −0.862317 1.49358i −0.869687 0.493603i \(-0.835680\pi\)
0.00737070 0.999973i \(-0.497654\pi\)
\(648\) 18.1193 26.1317i 0.711794 1.02655i
\(649\) −38.4716 22.2116i −1.51014 0.871880i
\(650\) 2.76866 0.409880i 0.108596 0.0160768i
\(651\) 0 0
\(652\) −8.77817 28.9977i −0.343780 1.13564i
\(653\) 11.8995 20.6105i 0.465663 0.806552i −0.533568 0.845757i \(-0.679149\pi\)
0.999231 + 0.0392048i \(0.0124825\pi\)
\(654\) −13.4220 + 10.6462i −0.524841 + 0.416298i
\(655\) −0.831470 + 0.480049i −0.0324882 + 0.0187571i
\(656\) 9.16542 0.590168i 0.357850 0.0230422i
\(657\) 22.2275i 0.867177i
\(658\) 0 0
\(659\) 13.2284i 0.515306i 0.966238 + 0.257653i \(0.0829491\pi\)
−0.966238 + 0.257653i \(0.917051\pi\)
\(660\) 10.0807 43.1217i 0.392389 1.67851i
\(661\) −32.6198 + 18.8331i −1.26877 + 0.732522i −0.974754 0.223280i \(-0.928323\pi\)
−0.294011 + 0.955802i \(0.594990\pi\)
\(662\) 13.3132 + 16.7845i 0.517434 + 0.652346i
\(663\) 0.367414 0.636379i 0.0142692 0.0247149i
\(664\) 11.4105 + 24.1794i 0.442815 + 0.938342i
\(665\) 0 0
\(666\) −1.31371 8.87385i −0.0509052 0.343855i
\(667\) −13.7070 7.91375i −0.530738 0.306422i
\(668\) −11.4249 10.7129i −0.442043 0.414495i
\(669\) 8.38478 + 14.5229i 0.324174 + 0.561486i
\(670\) 11.2648 + 4.45526i 0.435197 + 0.172122i
\(671\) 21.4144 0.826696
\(672\) 0 0
\(673\) 10.3848 0.400304 0.200152 0.979765i \(-0.435856\pi\)
0.200152 + 0.979765i \(0.435856\pi\)
\(674\) −14.2404 5.63212i −0.548520 0.216941i
\(675\) −2.76866 4.79546i −0.106566 0.184577i
\(676\) 17.2570 + 16.1816i 0.663731 + 0.622367i
\(677\) 24.9876 + 14.4266i 0.960351 + 0.554459i 0.896281 0.443487i \(-0.146259\pi\)
0.0640697 + 0.997945i \(0.479592\pi\)
\(678\) −1.88164 12.7101i −0.0722641 0.488130i
\(679\) 0 0
\(680\) 1.00000 + 2.11904i 0.0383482 + 0.0812615i
\(681\) −10.6777 + 18.4943i −0.409169 + 0.708702i
\(682\) −21.0628 26.5545i −0.806535 1.01683i
\(683\) 27.9011 16.1087i 1.06761 0.616382i 0.140079 0.990140i \(-0.455264\pi\)
0.927526 + 0.373758i \(0.121931\pi\)
\(684\) 3.73247 15.9663i 0.142715 0.610485i
\(685\) 21.5391i 0.822965i
\(686\) 0 0
\(687\) 2.88030i 0.109890i
\(688\) 28.8796 1.85958i 1.10103 0.0708958i
\(689\) 9.82868 5.67459i 0.374443 0.216185i
\(690\) 14.3712 11.3991i 0.547103 0.433956i
\(691\) 4.09918 7.09999i 0.155940 0.270096i −0.777461 0.628931i \(-0.783493\pi\)
0.933401 + 0.358835i \(0.116826\pi\)
\(692\) −3.80786 12.5788i −0.144753 0.478175i
\(693\) 0 0
\(694\) 5.53553 0.819496i 0.210126 0.0311076i
\(695\) −51.6448 29.8172i −1.95900 1.13103i
\(696\) 23.5668 33.9881i 0.893298 1.28832i
\(697\) −0.363961 0.630399i −0.0137860 0.0238781i
\(698\) −4.40723 + 11.1434i −0.166816 + 0.421782i
\(699\) 34.7827 1.31560
\(700\) 0 0
\(701\) 16.0000 0.604312 0.302156 0.953259i \(-0.402294\pi\)
0.302156 + 0.953259i \(0.402294\pi\)
\(702\) −1.70496 + 4.31085i −0.0643494 + 0.162703i
\(703\) 10.3398 + 17.9091i 0.389973 + 0.675454i
\(704\) 5.21022 31.2233i 0.196368 1.17677i
\(705\) 20.7556 + 11.9832i 0.781700 + 0.451315i
\(706\) 14.0716 2.08319i 0.529591 0.0784021i
\(707\) 0 0
\(708\) 46.0208 13.9314i 1.72957 0.523575i
\(709\) 23.3137 40.3805i 0.875565 1.51652i 0.0194047 0.999812i \(-0.493823\pi\)
0.856160 0.516711i \(-0.172844\pi\)
\(710\) 0 0
\(711\) 10.8682 6.27476i 0.407589 0.235322i
\(712\) −1.39946 + 16.8890i −0.0524468 + 0.632941i
\(713\) 14.0392i 0.525774i
\(714\) 0 0
\(715\) 11.1917i 0.418547i
\(716\) 26.3099 + 6.15053i 0.983246 + 0.229856i
\(717\) −18.9750 + 10.9552i −0.708635 + 0.409131i
\(718\) −27.4703 34.6327i −1.02518 1.29248i
\(719\) −16.7641 + 29.0364i −0.625197 + 1.08287i 0.363306 + 0.931670i \(0.381648\pi\)
−0.988503 + 0.151203i \(0.951685\pi\)
\(720\) 9.19299 + 13.7925i 0.342603 + 0.514017i
\(721\) 0 0
\(722\) 1.60051 + 10.8111i 0.0595646 + 0.402348i
\(723\) −9.44879 5.45526i −0.351404 0.202883i
\(724\) 30.0792 32.0784i 1.11789 1.19218i
\(725\) −6.24264 10.8126i −0.231846 0.401569i
\(726\) 13.1146 + 5.18688i 0.486730 + 0.192503i
\(727\) −29.9802 −1.11191 −0.555953 0.831214i \(-0.687646\pi\)
−0.555953 + 0.831214i \(0.687646\pi\)
\(728\) 0 0
\(729\) 1.62742 0.0602747
\(730\) −48.1685 19.0508i −1.78280 0.705101i
\(731\) −1.14682 1.98634i −0.0424165 0.0734676i
\(732\) −15.8546 + 16.9083i −0.586002 + 0.624949i
\(733\) 17.7160 + 10.2283i 0.654355 + 0.377792i 0.790123 0.612949i \(-0.210017\pi\)
−0.135768 + 0.990741i \(0.543350\pi\)
\(734\) −2.66105 17.9749i −0.0982210 0.663464i
\(735\) 0 0
\(736\) 9.72792 8.79148i 0.358576 0.324058i
\(737\) −6.48528 + 11.2328i −0.238888 + 0.413767i
\(738\) −3.19998 4.03432i −0.117793 0.148505i
\(739\) −10.7673 + 6.21652i −0.396082 + 0.228678i −0.684792 0.728738i \(-0.740107\pi\)
0.288710 + 0.957417i \(0.406774\pi\)
\(740\) −20.3562 4.75871i −0.748308 0.174934i
\(741\) 11.9832i 0.440215i
\(742\) 0 0
\(743\) 45.1646i 1.65693i −0.560042 0.828464i \(-0.689215\pi\)
0.560042 0.828464i \(-0.310785\pi\)
\(744\) 36.5610 + 3.02952i 1.34039 + 0.111068i
\(745\) 10.9269 6.30864i 0.400330 0.231131i
\(746\) −22.3172 + 17.7018i −0.817092 + 0.648108i
\(747\) 7.49506 12.9818i 0.274230 0.474980i
\(748\) −2.40125 + 0.726905i −0.0877982 + 0.0265783i
\(749\) 0 0
\(750\) −24.8284 + 3.67567i −0.906606 + 0.134216i
\(751\) 32.2602 + 18.6254i 1.17719 + 0.679652i 0.955363 0.295434i \(-0.0954643\pi\)
0.221828 + 0.975086i \(0.428798\pi\)
\(752\) 15.3561 + 7.59473i 0.559980 + 0.276951i
\(753\) −4.19239 7.26143i −0.152779 0.264621i
\(754\) −3.84425 + 9.71991i −0.139999 + 0.353978i
\(755\) 55.9819 2.03739
\(756\) 0 0
\(757\) −44.2843 −1.60954 −0.804770 0.593587i \(-0.797711\pi\)
−0.804770 + 0.593587i \(0.797711\pi\)
\(758\) −11.2891 + 28.5435i −0.410037 + 1.03675i
\(759\) 9.82021 + 17.0091i 0.356451 + 0.617391i
\(760\) −31.4009 21.7729i −1.13903 0.789786i
\(761\) −0.0471057 0.0271965i −0.00170758 0.000985871i 0.499146 0.866518i \(-0.333647\pi\)
−0.500854 + 0.865532i \(0.666980\pi\)
\(762\) 30.6520 4.53781i 1.11041 0.164387i
\(763\) 0 0
\(764\) 3.79899 + 12.5495i 0.137443 + 0.454026i
\(765\) 0.656854 1.13770i 0.0237486 0.0411338i
\(766\) −34.3691 + 27.2612i −1.24181 + 0.984987i
\(767\) −10.5238 + 6.07591i −0.379992 + 0.219389i
\(768\) 20.7956 + 27.2306i 0.750397 + 0.982599i
\(769\) 19.1342i 0.689996i 0.938603 + 0.344998i \(0.112120\pi\)
−0.938603 + 0.344998i \(0.887880\pi\)
\(770\) 0 0
\(771\) 40.8100i 1.46974i
\(772\) 6.64048 28.4057i 0.238996 1.02234i
\(773\) 42.8644 24.7478i 1.54173 0.890116i 0.542995 0.839736i \(-0.317290\pi\)
0.998730 0.0503797i \(-0.0160432\pi\)
\(774\) −10.0829 12.7119i −0.362423 0.456919i
\(775\) 5.53732 9.59092i 0.198906 0.344516i
\(776\) 23.6320 11.1522i 0.848339 0.400341i
\(777\) 0 0
\(778\) 2.92893 + 19.7844i 0.105007 + 0.709304i
\(779\) 10.2803 + 5.93531i 0.368329 + 0.212655i
\(780\) −8.83670 8.28600i −0.316405 0.296686i
\(781\) 0 0
\(782\) −0.966367 0.382201i −0.0345572 0.0136675i
\(783\) 20.6796 0.739029
\(784\) 0 0
\(785\) −50.1421 −1.78965
\(786\) 1.03471 + 0.409231i 0.0369069 + 0.0145968i
\(787\) 20.6035 + 35.6864i 0.734436 + 1.27208i 0.954970 + 0.296702i \(0.0958868\pi\)
−0.220534 + 0.975379i \(0.570780\pi\)
\(788\) 2.91789 + 2.73604i 0.103945 + 0.0974675i
\(789\) 47.5903 + 27.4763i 1.69426 + 0.978182i
\(790\) −4.28289 28.9301i −0.152378 1.02929i
\(791\) 0 0
\(792\) −16.0503 + 7.57430i −0.570321 + 0.269141i
\(793\) 2.92893 5.07306i 0.104009 0.180150i
\(794\) 14.1732 + 17.8686i 0.502988 + 0.634133i
\(795\) 50.8134 29.3371i 1.80216 1.04048i
\(796\) 7.79949 33.3636i 0.276446 1.18254i
\(797\) 20.1940i 0.715309i 0.933854 + 0.357655i \(0.116424\pi\)
−0.933854 + 0.357655i \(0.883576\pi\)
\(798\) 0 0
\(799\) 1.35778i 0.0480350i
\(800\) 10.1132 2.16905i 0.357554 0.0766875i
\(801\) 8.22848 4.75071i 0.290739 0.167858i
\(802\) −14.2137 + 11.2742i −0.501904 + 0.398105i
\(803\) 27.7312 48.0318i 0.978612 1.69501i
\(804\) −4.06766 13.4370i −0.143455 0.473888i
\(805\) 0 0
\(806\) −9.17157 + 1.35778i −0.323055 + 0.0478259i
\(807\) 9.34792 + 5.39702i 0.329062 + 0.189984i
\(808\) −35.4006 24.5462i −1.24539 0.863534i
\(809\) 0.0208153 + 0.0360531i 0.000731826 + 0.00126756i 0.866391 0.499366i \(-0.166434\pi\)
−0.865659 + 0.500634i \(0.833100\pi\)
\(810\) −15.2804 + 38.6354i −0.536899 + 1.35751i
\(811\) −39.4330 −1.38468 −0.692340 0.721571i \(-0.743420\pi\)
−0.692340 + 0.721571i \(0.743420\pi\)
\(812\) 0 0
\(813\) −9.17157 −0.321661
\(814\) 8.23225 20.8146i 0.288540 0.729553i
\(815\) 19.7926 + 34.2818i 0.693305 + 1.20084i
\(816\) 1.20386 2.43414i 0.0421435 0.0852119i
\(817\) 32.3924 + 18.7018i 1.13327 + 0.654292i
\(818\) −19.3491 + 2.86449i −0.676525 + 0.100155i
\(819\) 0 0
\(820\) −11.4853 + 3.47682i −0.401083 + 0.121416i
\(821\) 9.00000 15.5885i 0.314102 0.544041i −0.665144 0.746715i \(-0.731630\pi\)
0.979246 + 0.202674i \(0.0649632\pi\)
\(822\) −19.5573 + 15.5126i −0.682138 + 0.541064i
\(823\) −14.8829 + 8.59264i −0.518785 + 0.299521i −0.736437 0.676506i \(-0.763493\pi\)
0.217652 + 0.976026i \(0.430160\pi\)
\(824\) −34.1461 2.82942i −1.18954 0.0985674i
\(825\) 15.4930i 0.539399i
\(826\) 0 0
\(827\) 45.1646i 1.57053i −0.619162 0.785264i \(-0.712527\pi\)
0.619162 0.785264i \(-0.287473\pi\)
\(828\) −7.15834 1.67342i −0.248769 0.0581555i
\(829\) −40.8954 + 23.6110i −1.42036 + 0.820044i −0.996329 0.0856056i \(-0.972717\pi\)
−0.424028 + 0.905649i \(0.639384\pi\)
\(830\) −21.7086 27.3688i −0.753517 0.949984i
\(831\) 4.43508 7.68178i 0.153851 0.266478i
\(832\) −6.68414 5.50482i −0.231731 0.190845i
\(833\) 0 0
\(834\) 10.1213 + 68.3676i 0.350473 + 2.36738i
\(835\) 17.7217 + 10.2316i 0.613285 + 0.354080i
\(836\) 27.9852 29.8451i 0.967887 1.03221i
\(837\) 9.17157 + 15.8856i 0.317016 + 0.549088i
\(838\) −22.7297 8.98968i −0.785186 0.310543i
\(839\) −42.3984 −1.46376 −0.731878 0.681435i \(-0.761356\pi\)
−0.731878 + 0.681435i \(0.761356\pi\)
\(840\) 0 0
\(841\) 17.6274 0.607842
\(842\) 13.7891 + 5.45364i 0.475205 + 0.187945i
\(843\) −11.1192 19.2590i −0.382966 0.663317i
\(844\) −19.7949 + 21.1105i −0.681368 + 0.726653i
\(845\) −26.7681 15.4546i −0.920852 0.531654i
\(846\) −1.40662 9.50143i −0.0483605 0.326666i
\(847\) 0 0
\(848\) 34.8995 23.2612i 1.19845 0.798793i
\(849\) 3.63604 6.29780i 0.124789 0.216140i
\(850\) −0.509428 0.642253i −0.0174732 0.0220291i
\(851\) 8.02938 4.63577i 0.275244 0.158912i
\(852\) 0 0
\(853\) 38.3002i 1.31137i −0.755033 0.655687i \(-0.772379\pi\)
0.755033 0.655687i \(-0.227621\pi\)
\(854\) 0 0
\(855\) 21.4234i 0.732664i
\(856\) 0.541385 6.53357i 0.0185042 0.223313i
\(857\) 2.99248 1.72771i 0.102221 0.0590174i −0.448018 0.894025i \(-0.647870\pi\)
0.550239 + 0.835007i \(0.314537\pi\)
\(858\) 10.1620 8.06037i 0.346924 0.275177i
\(859\) 1.33052 2.30453i 0.0453969 0.0786297i −0.842434 0.538799i \(-0.818878\pi\)
0.887831 + 0.460170i \(0.152211\pi\)
\(860\) −36.1893 + 10.9552i −1.23405 + 0.373571i
\(861\) 0 0
\(862\) 1.34315 0.198843i 0.0457477 0.00677262i
\(863\) 10.8682 + 6.27476i 0.369958 + 0.213595i 0.673440 0.739242i \(-0.264816\pi\)
−0.303482 + 0.952837i \(0.598149\pi\)
\(864\) −5.26399 + 16.3028i −0.179085 + 0.554632i
\(865\) 8.58579 + 14.8710i 0.291925 + 0.505630i
\(866\) −13.6198 + 34.4366i −0.462819 + 1.17020i
\(867\) 36.1893 1.22905
\(868\) 0 0
\(869\) 31.3137 1.06224
\(870\) −19.8744 + 50.2510i −0.673806 + 1.70367i
\(871\) 1.77403 + 3.07271i 0.0601107 + 0.104115i
\(872\) 9.11693 13.1484i 0.308738 0.445263i
\(873\) −12.6879 7.32538i −0.429421 0.247926i
\(874\) 16.7641 2.48181i 0.567056 0.0839485i
\(875\) 0 0
\(876\) 17.3934 + 57.4570i 0.587668 + 1.94129i
\(877\) −15.2132 + 26.3500i −0.513713 + 0.889778i 0.486160 + 0.873870i \(0.338397\pi\)
−0.999873 + 0.0159079i \(0.994936\pi\)
\(878\) 24.8784 19.7332i 0.839604 0.665964i
\(879\) 21.8791 12.6319i 0.737962 0.426063i
\(880\) 2.65765 + 41.2738i 0.0895893 + 1.39134i
\(881\) 26.1857i 0.882217i −0.897454 0.441109i \(-0.854585\pi\)
0.897454 0.441109i \(-0.145415\pi\)
\(882\) 0 0
\(883\) 24.7013i 0.831266i 0.909532 + 0.415633i \(0.136440\pi\)
−0.909532 + 0.415633i \(0.863560\pi\)
\(884\) −0.156224 + 0.668274i −0.00525438 + 0.0224765i
\(885\) −54.4070 + 31.4119i −1.82887 + 1.05590i
\(886\) 24.9389 + 31.4414i 0.837840 + 1.05629i
\(887\) −11.2268 + 19.4454i −0.376960 + 0.652914i −0.990618 0.136658i \(-0.956364\pi\)
0.613658 + 0.789572i \(0.289697\pi\)
\(888\) 10.3398 + 21.9105i 0.346981 + 0.735267i
\(889\) 0 0
\(890\) −3.24264 21.9034i −0.108694 0.734204i
\(891\) −38.5258 22.2429i −1.29066 0.745164i
\(892\) −11.4249 10.7129i −0.382534 0.358695i
\(893\) 11.0711 + 19.1757i 0.370479 + 0.641689i
\(894\) −13.5978 5.37798i −0.454779 0.179866i
\(895\) −35.3023 −1.18003
\(896\) 0 0
\(897\) 5.37258 0.179385
\(898\) 21.4153 + 8.46983i 0.714639 + 0.282642i
\(899\) 20.6796 + 35.8182i 0.689704 + 1.19460i
\(900\) −4.23020 3.96657i −0.141007 0.132219i
\(901\) −2.87875 1.66205i −0.0959052 0.0553709i
\(902\) −1.88164 12.7101i −0.0626519 0.423201i
\(903\) 0 0
\(904\) 5.12132 + 10.8523i 0.170333 + 0.360942i
\(905\) −28.7279 + 49.7582i −0.954948 + 1.65402i
\(906\) −40.3186 50.8311i −1.33950 1.68875i
\(907\) 29.4214 16.9864i 0.976921 0.564025i 0.0755817 0.997140i \(-0.475919\pi\)
0.901339 + 0.433114i \(0.142585\pi\)
\(908\) 4.54014 19.4212i 0.150670 0.644514i
\(909\) 24.1522i 0.801077i
\(910\) 0 0
\(911\) 18.7078i 0.619817i −0.950766 0.309908i \(-0.899702\pi\)
0.950766 0.309908i \(-0.100298\pi\)
\(912\) 2.84560 + 44.1928i 0.0942274 + 1.46337i
\(913\) 32.3924 18.7018i 1.07203 0.618938i
\(914\) 0.806528 0.639729i 0.0266776 0.0211604i
\(915\) 15.1423 26.2272i 0.500589 0.867046i
\(916\) 0.779403 + 2.57466i 0.0257522 + 0.0850693i
\(917\) 0 0
\(918\) 1.34315 0.198843i 0.0443304 0.00656280i
\(919\) −42.2969 24.4201i −1.39525 0.805546i −0.401357 0.915922i \(-0.631461\pi\)
−0.993890 + 0.110376i \(0.964795\pi\)
\(920\) −9.76170 + 14.0783i −0.321834 + 0.464149i
\(921\) −4.19239 7.26143i −0.138144 0.239272i
\(922\) 15.4736 39.1238i 0.509596 1.28848i
\(923\) 0 0
\(924\) 0 0
\(925\) 7.31371 0.240473
\(926\) 18.1695 45.9401i 0.597085 1.50969i
\(927\) 9.60498 + 16.6363i 0.315469 + 0.546408i
\(928\) −11.8690 + 36.7587i −0.389619 + 1.20666i
\(929\) −25.8779 14.9406i −0.849025 0.490185i 0.0112969 0.999936i \(-0.496404\pi\)
−0.860322 + 0.509751i \(0.829737\pi\)
\(930\) −47.4162 + 7.01962i −1.55484 + 0.230182i
\(931\) 0 0
\(932\) −31.0919 + 9.41214i −1.01845 + 0.308305i
\(933\) 22.1421 38.3513i 0.724901 1.25557i
\(934\) 26.6753 21.1586i 0.872844 0.692330i
\(935\) 2.83882 1.63899i 0.0928392 0.0536007i
\(936\) −0.400908 + 4.83825i −0.0131041 + 0.158143i
\(937\) 29.8042i 0.973662i −0.873496 0.486831i \(-0.838153\pi\)
0.873496 0.486831i \(-0.161847\pi\)
\(938\) 0 0
\(939\) 27.3004i 0.890916i
\(940\) −21.7958 5.09526i −0.710901 0.166189i
\(941\) 21.4655 12.3931i 0.699756 0.404004i −0.107501 0.994205i \(-0.534285\pi\)
0.807256 + 0.590201i \(0.200951\pi\)
\(942\) 36.1128 + 45.5286i 1.17662 + 1.48340i
\(943\) 2.66105 4.60907i 0.0866556 0.150092i
\(944\) −37.3677 + 24.9063i −1.21621 + 0.810631i
\(945\) 0 0
\(946\) −5.92893 40.0488i −0.192766 1.30210i
\(947\) −7.92851 4.57753i −0.257642 0.148750i 0.365616 0.930766i \(-0.380858\pi\)
−0.623258 + 0.782016i \(0.714192\pi\)
\(948\) −23.1837 + 24.7245i −0.752971 + 0.803015i
\(949\) −7.58579 13.1390i −0.246245 0.426509i
\(950\) 12.4313 + 4.91662i 0.403325 + 0.159516i
\(951\) −11.8095 −0.382948
\(952\) 0 0
\(953\) 26.3431 0.853338 0.426669 0.904408i \(-0.359687\pi\)
0.426669 + 0.904408i \(0.359687\pi\)
\(954\) −21.8666 8.64831i −0.707958 0.279999i
\(955\) −8.56578 14.8364i −0.277182 0.480094i
\(956\) 13.9971 14.9274i 0.452699 0.482786i
\(957\) −50.1084 28.9301i −1.61977 0.935177i
\(958\) 6.79175 + 45.8770i 0.219431 + 1.48222i
\(959\) 0 0
\(960\) −34.5563 28.4594i −1.11530 0.918522i
\(961\) −2.84315 + 4.92447i −0.0917144 + 0.158854i
\(962\) −3.80501 4.79711i −0.122678 0.154665i
\(963\) −3.18322 + 1.83783i −0.102578 + 0.0592234i
\(964\) 9.92235 + 2.31957i 0.319577 + 0.0747084i
\(965\) 38.1145i 1.22695i
\(966\) 0 0
\(967\) 45.1646i 1.45240i −0.687486 0.726198i \(-0.741286\pi\)
0.687486 0.726198i \(-0.258714\pi\)
\(968\) −13.1266 1.08770i −0.421904 0.0349599i
\(969\) 3.03958 1.75490i 0.0976455 0.0563757i
\(970\) −26.7492 + 21.2171i −0.858864 + 0.681241i
\(971\) −6.50043 + 11.2591i −0.208609 + 0.361321i −0.951276 0.308339i \(-0.900227\pi\)
0.742668 + 0.669660i \(0.233560\pi\)
\(972\) 28.6943 8.68633i 0.920369 0.278614i
\(973\) 0 0
\(974\) −27.2843 + 4.03924i −0.874244 + 0.129426i
\(975\) 3.67029 + 2.11904i 0.117543 + 0.0678636i
\(976\) 9.59688 19.4044i 0.307189 0.621118i
\(977\) −8.80761 15.2552i −0.281780 0.488058i 0.690043 0.723768i \(-0.257592\pi\)
−0.971823 + 0.235710i \(0.924258\pi\)
\(978\) 16.8728 42.6615i 0.539531 1.36416i
\(979\) 23.7081 0.757714
\(980\) 0 0
\(981\) −8.97056 −0.286408
\(982\) −7.52604 + 19.0290i −0.240165 + 0.607241i
\(983\) 4.80249 + 8.31816i 0.153176 + 0.265308i 0.932393 0.361445i \(-0.117717\pi\)
−0.779218 + 0.626754i \(0.784383\pi\)
\(984\) 11.4287 + 7.92449i 0.364334 + 0.252623i
\(985\) −4.52607 2.61313i −0.144212 0.0832611i
\(986\) 3.02846 0.448342i 0.0964458 0.0142781i
\(987\) 0 0
\(988\) −3.24264 10.7117i −0.103162 0.340784i
\(989\) 8.38478 14.5229i 0.266620 0.461800i
\(990\) 18.1674 14.4102i 0.577397 0.457985i
\(991\) −22.2235 + 12.8307i −0.705952 + 0.407581i −0.809560 0.587037i \(-0.800294\pi\)
0.103609 + 0.994618i \(0.466961\pi\)
\(992\) −33.5012 + 7.18528i −1.06367 + 0.228133i
\(993\) 32.4399i 1.02945i
\(994\) 0 0
\(995\) 44.7669i 1.41921i
\(996\) −9.21587 + 39.4224i −0.292016 + 1.24915i
\(997\) −26.7681 + 15.4546i −0.847755 + 0.489452i −0.859893 0.510475i \(-0.829470\pi\)
0.0121377 + 0.999926i \(0.496136\pi\)
\(998\) −11.0291 13.9047i −0.349119 0.440146i
\(999\) −6.05692 + 10.4909i −0.191632 + 0.331917i
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 196.2.f.d.19.1 16
4.3 odd 2 inner 196.2.f.d.19.6 16
7.2 even 3 196.2.d.c.195.8 yes 8
7.3 odd 6 inner 196.2.f.d.31.6 16
7.4 even 3 inner 196.2.f.d.31.5 16
7.5 odd 6 196.2.d.c.195.7 yes 8
7.6 odd 2 inner 196.2.f.d.19.2 16
21.2 odd 6 1764.2.b.k.1567.1 8
21.5 even 6 1764.2.b.k.1567.2 8
28.3 even 6 inner 196.2.f.d.31.1 16
28.11 odd 6 inner 196.2.f.d.31.2 16
28.19 even 6 196.2.d.c.195.6 yes 8
28.23 odd 6 196.2.d.c.195.5 8
28.27 even 2 inner 196.2.f.d.19.5 16
56.5 odd 6 3136.2.f.i.3135.6 8
56.19 even 6 3136.2.f.i.3135.4 8
56.37 even 6 3136.2.f.i.3135.3 8
56.51 odd 6 3136.2.f.i.3135.5 8
84.23 even 6 1764.2.b.k.1567.3 8
84.47 odd 6 1764.2.b.k.1567.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
196.2.d.c.195.5 8 28.23 odd 6
196.2.d.c.195.6 yes 8 28.19 even 6
196.2.d.c.195.7 yes 8 7.5 odd 6
196.2.d.c.195.8 yes 8 7.2 even 3
196.2.f.d.19.1 16 1.1 even 1 trivial
196.2.f.d.19.2 16 7.6 odd 2 inner
196.2.f.d.19.5 16 28.27 even 2 inner
196.2.f.d.19.6 16 4.3 odd 2 inner
196.2.f.d.31.1 16 28.3 even 6 inner
196.2.f.d.31.2 16 28.11 odd 6 inner
196.2.f.d.31.5 16 7.4 even 3 inner
196.2.f.d.31.6 16 7.3 odd 6 inner
1764.2.b.k.1567.1 8 21.2 odd 6
1764.2.b.k.1567.2 8 21.5 even 6
1764.2.b.k.1567.3 8 84.23 even 6
1764.2.b.k.1567.4 8 84.47 odd 6
3136.2.f.i.3135.3 8 56.37 even 6
3136.2.f.i.3135.4 8 56.19 even 6
3136.2.f.i.3135.5 8 56.51 odd 6
3136.2.f.i.3135.6 8 56.5 odd 6