Properties

Label 637.2.f.l.393.1
Level $637$
Weight $2$
Character 637.393
Analytic conductor $5.086$
Analytic rank $0$
Dimension $16$
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(295,637)]
 
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([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.295");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.f (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: 16.0.468066644398978174550016.2
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 393.1
Root \(0.756863 - 1.31093i\) of defining polynomial
Character \(\chi\) \(=\) 637.393
Dual form 637.2.f.l.295.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.21605 - 2.10626i) q^{2} +(-0.376796 - 0.652630i) q^{3} +(-1.95755 + 3.39058i) q^{4} +0.341537 q^{5} +(-0.916405 + 1.58726i) q^{6} +4.65773 q^{8} +(1.21605 - 2.10626i) q^{9} +O(q^{10})\) \(q+(-1.21605 - 2.10626i) q^{2} +(-0.376796 - 0.652630i) q^{3} +(-1.95755 + 3.39058i) q^{4} +0.341537 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} +2.95039 q^{12} +(2.50139 - 2.59674i) q^{13} +(-0.128690 - 0.222897i) q^{15} +(-1.74892 - 3.02922i) q^{16} +(0.974117 - 1.68722i) q^{17} -5.91511 q^{18} +(3.14519 - 5.44764i) q^{19} +(-0.668577 + 1.15801i) q^{20} +(2.95755 - 5.12263i) q^{22} +(1.84474 + 3.19518i) q^{23} +(-1.75501 - 3.03977i) q^{24} -4.88335 q^{25} +(-8.51122 - 2.11081i) q^{26} -4.09359 q^{27} +(-2.22068 - 3.84632i) q^{29} +(-0.312986 + 0.542108i) q^{30} -1.97532 q^{31} +(0.404180 - 0.700061i) q^{32} +(0.916405 - 1.58726i) q^{33} -4.73830 q^{34} +(4.76096 + 8.24623i) q^{36} +(4.81433 + 8.33867i) q^{37} -15.2988 q^{38} +(-2.63722 - 0.654039i) q^{39} +1.59079 q^{40} +(-6.26793 - 10.8564i) q^{41} +(4.20368 - 7.28099i) q^{43} -9.52192 q^{44} +(0.415326 - 0.719366i) q^{45} +(4.48659 - 7.77100i) q^{46} -9.00530 q^{47} +(-1.31797 + 2.28279i) q^{48} +(5.93840 + 10.2856i) q^{50} -1.46817 q^{51} +(3.90786 + 13.5644i) q^{52} +1.49226 q^{53} +(4.97800 + 8.62216i) q^{54} +(0.415326 + 0.719366i) q^{55} -4.74039 q^{57} +(-5.40090 + 9.35464i) q^{58} +(-0.313495 + 0.542990i) q^{59} +1.00767 q^{60} +(0.571597 - 0.990035i) q^{61} +(2.40209 + 4.16054i) q^{62} -8.96169 q^{64} +(0.854317 - 0.886883i) q^{65} -4.45758 q^{66} +(2.79599 + 4.84280i) q^{67} +(3.81377 + 6.60564i) q^{68} +(1.39018 - 2.40786i) q^{69} +(-4.74859 + 8.22481i) q^{71} +(5.66402 - 9.81038i) q^{72} +11.9187 q^{73} +(11.7089 - 20.2805i) q^{74} +(1.84003 + 3.18702i) q^{75} +(12.3138 + 21.3281i) q^{76} +(1.82942 + 6.35002i) q^{78} +4.47167 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} -20.4475 q^{86} +(-1.67348 + 2.89856i) q^{87} +(5.66402 + 9.81038i) q^{88} +(-6.22219 - 10.7771i) q^{89} -2.02023 q^{90} -14.4447 q^{92} +(0.744294 + 1.28915i) q^{93} +(10.9509 + 18.9675i) q^{94} +(1.07420 - 1.86057i) q^{95} -0.609174 q^{96} +(-5.13850 + 8.90014i) q^{97} +5.91511 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} - 4 q^{9} - 4 q^{11} - 8 q^{15} - 4 q^{16} - 56 q^{18} + 28 q^{22} + 12 q^{23} - 24 q^{25} + 8 q^{29} + 28 q^{30} + 4 q^{36} - 8 q^{37} - 4 q^{39} + 32 q^{43} - 8 q^{44} - 4 q^{46} + 36 q^{50} - 88 q^{51} - 8 q^{53} - 96 q^{57} - 48 q^{58} + 128 q^{60} - 64 q^{64} + 16 q^{65} + 20 q^{67} + 8 q^{71} + 28 q^{72} + 76 q^{74} + 28 q^{78} - 8 q^{79} + 56 q^{81} + 36 q^{85} + 8 q^{86} + 28 q^{88} - 160 q^{92} + 8 q^{93} + 52 q^{95} + 56 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.21605 2.10626i −0.859877 1.48935i −0.872046 0.489424i \(-0.837207\pi\)
0.0121689 0.999926i \(-0.496126\pi\)
\(3\) −0.376796 0.652630i −0.217543 0.376796i 0.736513 0.676423i \(-0.236471\pi\)
−0.954056 + 0.299627i \(0.903138\pi\)
\(4\) −1.95755 + 3.39058i −0.978776 + 1.69529i
\(5\) 0.341537 0.152740 0.0763700 0.997080i \(-0.475667\pi\)
0.0763700 + 0.997080i \(0.475667\pi\)
\(6\) −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 \(0.713837\pi\)
\(12\) 2.95039 0.851705
\(13\) 2.50139 2.59674i 0.693760 0.720206i
\(14\) 0 0
\(15\) −0.128690 0.222897i −0.0332276 0.0575518i
\(16\) −1.74892 3.02922i −0.437230 0.757304i
\(17\) 0.974117 1.68722i 0.236258 0.409211i −0.723379 0.690451i \(-0.757412\pi\)
0.959638 + 0.281240i \(0.0907456\pi\)
\(18\) −5.91511 −1.39420
\(19\) 3.14519 5.44764i 0.721557 1.24977i −0.238819 0.971064i \(-0.576760\pi\)
0.960376 0.278709i \(-0.0899065\pi\)
\(20\) −0.668577 + 1.15801i −0.149498 + 0.258939i
\(21\) 0 0
\(22\) 2.95755 5.12263i 0.630552 1.09215i
\(23\) 1.84474 + 3.19518i 0.384655 + 0.666242i 0.991721 0.128409i \(-0.0409872\pi\)
−0.607066 + 0.794651i \(0.707654\pi\)
\(24\) −1.75501 3.03977i −0.358240 0.620491i
\(25\) −4.88335 −0.976670
\(26\) −8.51122 2.11081i −1.66919 0.413963i
\(27\) −4.09359 −0.787811
\(28\) 0 0
\(29\) −2.22068 3.84632i −0.412369 0.714244i 0.582779 0.812631i \(-0.301965\pi\)
−0.995148 + 0.0983864i \(0.968632\pi\)
\(30\) −0.312986 + 0.542108i −0.0571432 + 0.0989750i
\(31\) −1.97532 −0.354778 −0.177389 0.984141i \(-0.556765\pi\)
−0.177389 + 0.984141i \(0.556765\pi\)
\(32\) 0.404180 0.700061i 0.0714496 0.123754i
\(33\) 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
\(37\) 4.81433 + 8.33867i 0.791472 + 1.37087i 0.925056 + 0.379832i \(0.124018\pi\)
−0.133584 + 0.991037i \(0.542649\pi\)
\(38\) −15.2988 −2.48180
\(39\) −2.63722 0.654039i −0.422294 0.104730i
\(40\) 1.59079 0.251525
\(41\) −6.26793 10.8564i −0.978887 1.69548i −0.666461 0.745540i \(-0.732192\pi\)
−0.312426 0.949942i \(-0.601141\pi\)
\(42\) 0 0
\(43\) 4.20368 7.28099i 0.641055 1.11034i −0.344142 0.938918i \(-0.611830\pi\)
0.985198 0.171423i \(-0.0548365\pi\)
\(44\) −9.52192 −1.43548
\(45\) 0.415326 0.719366i 0.0619131 0.107237i
\(46\) 4.48659 7.77100i 0.661511 1.14577i
\(47\) −9.00530 −1.31356 −0.656779 0.754083i \(-0.728081\pi\)
−0.656779 + 0.754083i \(0.728081\pi\)
\(48\) −1.31797 + 2.28279i −0.190233 + 0.329493i
\(49\) 0 0
\(50\) 5.93840 + 10.2856i 0.839816 + 1.45460i
\(51\) −1.46817 −0.205585
\(52\) 3.90786 + 13.5644i 0.541923 + 1.88105i
\(53\) 1.49226 0.204977 0.102489 0.994734i \(-0.467319\pi\)
0.102489 + 0.994734i \(0.467319\pi\)
\(54\) 4.97800 + 8.62216i 0.677421 + 1.17333i
\(55\) 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
\(59\) −0.313495 + 0.542990i −0.0408136 + 0.0706913i −0.885711 0.464238i \(-0.846328\pi\)
0.844897 + 0.534929i \(0.179662\pi\)
\(60\) 1.00767 0.130089
\(61\) 0.571597 0.990035i 0.0731855 0.126761i −0.827110 0.562040i \(-0.810017\pi\)
0.900296 + 0.435279i \(0.143350\pi\)
\(62\) 2.40209 + 4.16054i 0.305066 + 0.528389i
\(63\) 0 0
\(64\) −8.96169 −1.12021
\(65\) 0.854317 0.886883i 0.105965 0.110004i
\(66\) −4.45758 −0.548690
\(67\) 2.79599 + 4.84280i 0.341585 + 0.591642i 0.984727 0.174104i \(-0.0557030\pi\)
−0.643142 + 0.765747i \(0.722370\pi\)
\(68\) 3.81377 + 6.60564i 0.462488 + 0.801052i
\(69\) 1.39018 2.40786i 0.167358 0.289873i
\(70\) 0 0
\(71\) −4.74859 + 8.22481i −0.563554 + 0.976105i 0.433628 + 0.901092i \(0.357233\pi\)
−0.997183 + 0.0750130i \(0.976100\pi\)
\(72\) 5.66402 9.81038i 0.667512 1.15616i
\(73\) 11.9187 1.39498 0.697488 0.716597i \(-0.254301\pi\)
0.697488 + 0.716597i \(0.254301\pi\)
\(74\) 11.7089 20.2805i 1.36114 2.35756i
\(75\) 1.84003 + 3.18702i 0.212468 + 0.368006i
\(76\) 12.3138 + 21.3281i 1.41249 + 2.44650i
\(77\) 0 0
\(78\) 1.82942 + 6.35002i 0.207141 + 0.718998i
\(79\) 4.47167 0.503102 0.251551 0.967844i \(-0.419059\pi\)
0.251551 + 0.967844i \(0.419059\pi\)
\(80\) −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 \(-0.475303\pi\)
0.0775104 + 0.996992i \(0.475303\pi\)
\(84\) 0 0
\(85\) 0.332697 0.576248i 0.0360861 0.0625029i
\(86\) −20.4475 −2.20491
\(87\) −1.67348 + 2.89856i −0.179416 + 0.310758i
\(88\) 5.66402 + 9.81038i 0.603787 + 1.04579i
\(89\) −6.22219 10.7771i −0.659551 1.14238i −0.980732 0.195357i \(-0.937413\pi\)
0.321182 0.947018i \(-0.395920\pi\)
\(90\) −2.02023 −0.212951
\(91\) 0 0
\(92\) −14.4447 −1.50596
\(93\) 0.744294 + 1.28915i 0.0771797 + 0.133679i
\(94\) 10.9509 + 18.9675i 1.12950 + 1.95635i
\(95\) 1.07420 1.86057i 0.110211 0.190890i
\(96\) −0.609174 −0.0621736
\(97\) −5.13850 + 8.90014i −0.521736 + 0.903673i 0.477945 + 0.878390i \(0.341382\pi\)
−0.999680 + 0.0252826i \(0.991951\pi\)
\(98\) 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 \(-0.897226\pi\)
0.199380 0.979922i \(-0.436107\pi\)
\(102\) 1.78537 + 3.09235i 0.176778 + 0.306189i
\(103\) 17.6176 1.73591 0.867957 0.496639i \(-0.165433\pi\)
0.867957 + 0.496639i \(0.165433\pi\)
\(104\) 11.6508 12.0949i 1.14245 1.18600i
\(105\) 0 0
\(106\) −1.81466 3.14308i −0.176255 0.305283i
\(107\) −3.19227 5.52917i −0.308608 0.534525i 0.669450 0.742857i \(-0.266530\pi\)
−0.978058 + 0.208332i \(0.933197\pi\)
\(108\) 8.01341 13.8796i 0.771091 1.33557i
\(109\) −8.17472 −0.782996 −0.391498 0.920179i \(-0.628043\pi\)
−0.391498 + 0.920179i \(0.628043\pi\)
\(110\) 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 −0.545980 0.837798i \(-0.683843\pi\)
0.998545 + 0.0539336i \(0.0171759\pi\)
\(114\) 5.76454 + 9.98448i 0.539899 + 0.935133i
\(115\) 0.630047 + 1.09127i 0.0587522 + 0.101762i
\(116\) 17.3884 1.61447
\(117\) −2.42760 8.42634i −0.224432 0.779015i
\(118\) 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
\(122\) −2.78036 −0.251722
\(123\) −4.72347 + 8.18128i −0.425901 + 0.737681i
\(124\) 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 0.593561 0.804789i \(-0.297722\pi\)
−0.993748 + 0.111644i \(0.964388\pi\)
\(128\) 10.0895 + 17.4755i 0.891794 + 1.54463i
\(129\) −6.33572 −0.557829
\(130\) −2.90690 0.720919i −0.254952 0.0632287i
\(131\) −0.192483 −0.0168173 −0.00840867 0.999965i \(-0.502677\pi\)
−0.00840867 + 0.999965i \(0.502677\pi\)
\(132\) 3.58782 + 6.21429i 0.312280 + 0.540885i
\(133\) 0 0
\(134\) 6.80013 11.7782i 0.587442 1.01748i
\(135\) −1.39811 −0.120330
\(136\) 4.53717 7.85861i 0.389059 0.673870i
\(137\) −2.43840 + 4.22343i −0.208326 + 0.360832i −0.951187 0.308614i \(-0.900135\pi\)
0.742861 + 0.669446i \(0.233468\pi\)
\(138\) −6.76212 −0.575629
\(139\) 5.53701 9.59038i 0.469643 0.813446i −0.529755 0.848151i \(-0.677716\pi\)
0.999398 + 0.0347054i \(0.0110493\pi\)
\(140\) 0 0
\(141\) 3.39316 + 5.87713i 0.285756 + 0.494943i
\(142\) 23.0981 1.93835
\(143\) 8.51122 + 2.11081i 0.711744 + 0.176514i
\(144\) −8.50709 −0.708924
\(145\) −0.758443 1.31366i −0.0629853 0.109094i
\(146\) −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 \(0.940746\pi\)
\(150\) 4.47513 7.75115i 0.365393 0.632879i
\(151\) −10.5904 −0.861831 −0.430916 0.902392i \(-0.641809\pi\)
−0.430916 + 0.902392i \(0.641809\pi\)
\(152\) 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
\(156\) 7.38007 7.66140i 0.590879 0.613403i
\(157\) 9.12388 0.728165 0.364082 0.931367i \(-0.381383\pi\)
0.364082 + 0.931367i \(0.381383\pi\)
\(158\) −5.43777 9.41849i −0.432606 0.749295i
\(159\) −0.562277 0.973892i −0.0445915 0.0772347i
\(160\) 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 \(0.0253986\pi\)
\(164\) 49.0792 3.83245
\(165\) 0.312986 0.542108i 0.0243660 0.0422031i
\(166\) −1.71744 2.97469i −0.133299 0.230880i
\(167\) 9.13884 + 15.8289i 0.707185 + 1.22488i 0.965897 + 0.258925i \(0.0833683\pi\)
−0.258713 + 0.965954i \(0.583298\pi\)
\(168\) 0 0
\(169\) −0.486122 12.9909i −0.0373940 0.999301i
\(170\) −1.61830 −0.124118
\(171\) −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 −0.667066 0.744999i \(-0.732450\pi\)
0.978721 + 0.205197i \(0.0657835\pi\)
\(174\) 8.14015 0.617104
\(175\) 0 0
\(176\) 4.25355 7.36736i 0.320623 0.555335i
\(177\) 0.472495 0.0355149
\(178\) −15.1330 + 26.2111i −1.13426 + 1.96460i
\(179\) 7.77684 + 13.4699i 0.581268 + 1.00679i 0.995329 + 0.0965370i \(0.0307766\pi\)
−0.414061 + 0.910249i \(0.635890\pi\)
\(180\) 1.62605 + 2.81639i 0.121198 + 0.209922i
\(181\) −6.67302 −0.496001 −0.248001 0.968760i \(-0.579774\pi\)
−0.248001 + 0.968760i \(0.579774\pi\)
\(182\) 0 0
\(183\) −0.861502 −0.0636841
\(184\) 8.59229 + 14.8823i 0.633432 + 1.09714i
\(185\) 1.64427 + 2.84797i 0.120889 + 0.209387i
\(186\) 1.81020 3.13535i 0.132730 0.229895i
\(187\) 4.73830 0.346499
\(188\) 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 \(0.738295\pi\)
\(194\) 24.9947 1.79451
\(195\) −0.900710 0.223378i −0.0645012 0.0159965i
\(196\) 0 0
\(197\) −4.36006 7.55184i −0.310641 0.538047i 0.667860 0.744287i \(-0.267210\pi\)
−0.978501 + 0.206240i \(0.933877\pi\)
\(198\) −7.19306 12.4587i −0.511189 0.885405i
\(199\) 8.73332 15.1266i 0.619089 1.07229i −0.370563 0.928807i \(-0.620835\pi\)
0.989652 0.143486i \(-0.0458313\pi\)
\(200\) −22.7453 −1.60834
\(201\) 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
\(205\) −2.14073 3.70786i −0.149515 0.258968i
\(206\) −21.4239 37.1073i −1.49267 2.58539i
\(207\) 8.97318 0.623679
\(208\) −12.2408 3.03576i −0.848748 0.210492i
\(209\) 15.2988 1.05824
\(210\) 0 0
\(211\) 11.6284 + 20.1410i 0.800535 + 1.38657i 0.919265 + 0.393640i \(0.128784\pi\)
−0.118730 + 0.992927i \(0.537882\pi\)
\(212\) −2.92117 + 5.05962i −0.200627 + 0.347496i
\(213\) 7.15701 0.490390
\(214\) −7.76391 + 13.4475i −0.530730 + 0.919252i
\(215\) 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
\(219\) −4.49091 7.77848i −0.303468 0.525621i
\(220\) −3.25209 −0.219256
\(221\) −1.94463 6.74992i −0.130810 0.454049i
\(222\) −17.6475 −1.18442
\(223\) 14.6364 + 25.3510i 0.980128 + 1.69763i 0.661855 + 0.749632i \(0.269769\pi\)
0.318272 + 0.947999i \(0.396897\pi\)
\(224\) 0 0
\(225\) −5.93840 + 10.2856i −0.395893 + 0.685707i
\(226\) −23.4008 −1.55660
\(227\) −9.90551 + 17.1569i −0.657452 + 1.13874i 0.323821 + 0.946118i \(0.395032\pi\)
−0.981273 + 0.192622i \(0.938301\pi\)
\(228\) 9.27956 16.0727i 0.614554 1.06444i
\(229\) −1.32821 −0.0877709 −0.0438855 0.999037i \(-0.513974\pi\)
−0.0438855 + 0.999037i \(0.513974\pi\)
\(230\) 1.53234 2.65408i 0.101039 0.175005i
\(231\) 0 0
\(232\) −10.3433 17.9151i −0.679071 1.17618i
\(233\) 1.51634 0.0993389 0.0496695 0.998766i \(-0.484183\pi\)
0.0496695 + 0.998766i \(0.484183\pi\)
\(234\) −14.7960 + 15.3600i −0.967243 + 1.00411i
\(235\) −3.07564 −0.200633
\(236\) −1.22737 2.12586i −0.0798948 0.138382i
\(237\) −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
\(241\) −6.65528 + 11.5273i −0.428704 + 0.742538i −0.996758 0.0804535i \(-0.974363\pi\)
0.568054 + 0.822991i \(0.307696\pi\)
\(242\) −12.3670 −0.794979
\(243\) −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
\(247\) −6.27875 21.7939i −0.399507 1.38671i
\(248\) −9.20051 −0.584233
\(249\) −0.532152 0.921714i −0.0337238 0.0584113i
\(250\) 4.10481 + 7.10974i 0.259611 + 0.449660i
\(251\) −7.95169 + 13.7727i −0.501906 + 0.869327i 0.498091 + 0.867125i \(0.334034\pi\)
−0.999998 + 0.00220260i \(0.999299\pi\)
\(252\) 0 0
\(253\) −4.48659 + 7.77100i −0.282069 + 0.488559i
\(254\) −10.9685 + 18.9980i −0.688224 + 1.19204i
\(255\) −0.501436 −0.0314011
\(256\) 15.5770 26.9801i 0.973561 1.68626i
\(257\) 14.6198 + 25.3223i 0.911960 + 1.57956i 0.811292 + 0.584641i \(0.198764\pi\)
0.100667 + 0.994920i \(0.467902\pi\)
\(258\) 7.70455 + 13.3447i 0.479664 + 0.830803i
\(259\) 0 0
\(260\) 1.33468 + 4.63275i 0.0827733 + 0.287311i
\(261\) −10.8018 −0.668615
\(262\) 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
\(268\) −21.8932 −1.33734
\(269\) −4.18937 + 7.25620i −0.255430 + 0.442418i −0.965012 0.262205i \(-0.915550\pi\)
0.709582 + 0.704623i \(0.248884\pi\)
\(270\) 1.70017 + 2.94479i 0.103469 + 0.179214i
\(271\) 6.07877 + 10.5287i 0.369259 + 0.639575i 0.989450 0.144876i \(-0.0462782\pi\)
−0.620191 + 0.784451i \(0.712945\pi\)
\(272\) −6.81461 −0.413196
\(273\) 0 0
\(274\) 11.8609 0.716540
\(275\) −5.93840 10.2856i −0.358099 0.620245i
\(276\) 5.44270 + 9.42704i 0.327612 + 0.567441i
\(277\) −5.15907 + 8.93578i −0.309979 + 0.536899i −0.978357 0.206922i \(-0.933655\pi\)
0.668379 + 0.743821i \(0.266989\pi\)
\(278\) −26.9331 −1.61534
\(279\) −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 0.789465 0.613796i \(-0.210358\pi\)
−0.926295 + 0.376799i \(0.877025\pi\)
\(284\) −18.5912 32.2010i −1.10319 1.91078i
\(285\) −1.61902 −0.0959023
\(286\) −5.90416 20.4937i −0.349120 1.21182i
\(287\) 0 0
\(288\) −0.983006 1.70262i −0.0579242 0.100328i
\(289\) 6.60219 + 11.4353i 0.388364 + 0.672667i
\(290\) −1.84461 + 3.19496i −0.108319 + 0.187614i
\(291\) 7.74466 0.454000
\(292\) −23.3314 + 40.4112i −1.36537 + 2.36489i
\(293\) 0.980596 1.69844i 0.0572870 0.0992241i −0.835960 0.548791i \(-0.815088\pi\)
0.893247 + 0.449567i \(0.148422\pi\)
\(294\) 0 0
\(295\) −0.107070 + 0.185451i −0.00623388 + 0.0107974i
\(296\) 22.4238 + 38.8392i 1.30336 + 2.25749i
\(297\) −4.97800 8.62216i −0.288853 0.500308i
\(298\) 38.6915 2.24134
\(299\) 12.9115 + 3.20208i 0.746689 + 0.185181i
\(300\) −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
\(304\) −22.0028 −1.26194
\(305\) 0.195222 0.338134i 0.0111784 0.0193615i
\(306\) −5.76200 + 9.98008i −0.329392 + 0.570523i
\(307\) 7.37658 0.421004 0.210502 0.977593i \(-0.432490\pi\)
0.210502 + 0.977593i \(0.432490\pi\)
\(308\) 0 0
\(309\) −6.63825 11.4978i −0.377637 0.654086i
\(310\) 0.820403 + 1.42098i 0.0465957 + 0.0807062i
\(311\) 14.1618 0.803040 0.401520 0.915850i \(-0.368482\pi\)
0.401520 + 0.915850i \(0.368482\pi\)
\(312\) −12.2835 3.04633i −0.695414 0.172465i
\(313\) −26.7152 −1.51003 −0.755017 0.655705i \(-0.772371\pi\)
−0.755017 + 0.655705i \(0.772371\pi\)
\(314\) −11.0951 19.2173i −0.626132 1.08449i
\(315\) 0 0
\(316\) −8.75352 + 15.1615i −0.492424 + 0.852904i
\(317\) 21.4362 1.20398 0.601989 0.798504i \(-0.294375\pi\)
0.601989 + 0.798504i \(0.294375\pi\)
\(318\) −1.36751 + 2.36860i −0.0766863 + 0.132825i
\(319\) 5.40090 9.35464i 0.302392 0.523759i
\(320\) −3.06075 −0.171101
\(321\) −2.40567 + 4.16674i −0.134271 + 0.232565i
\(322\) 0 0
\(323\) −6.12757 10.6133i −0.340947 0.590538i
\(324\) 16.4881 0.916005
\(325\) −12.2152 + 12.6808i −0.677575 + 0.703404i
\(326\) −26.6654 −1.47686
\(327\) 3.08020 + 5.33507i 0.170336 + 0.295030i
\(328\) −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 \(0.260886\pi\)
\(332\) −2.76467 + 4.78854i −0.151731 + 0.262805i
\(333\) 23.4179 1.28329
\(334\) 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 \(0.441093\pi\)
\(338\) −26.7711 + 16.8215i −1.45615 + 0.914968i
\(339\) −7.25080 −0.393809
\(340\) 1.30254 + 2.25607i 0.0706404 + 0.122353i
\(341\) −2.40209 4.16054i −0.130080 0.225306i
\(342\) −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
\(346\) −19.9392 −1.07194
\(347\) 8.01021 13.8741i 0.430010 0.744800i −0.566863 0.823812i \(-0.691843\pi\)
0.996874 + 0.0790120i \(0.0251765\pi\)
\(348\) −6.55186 11.3482i −0.351217 0.608325i
\(349\) −8.01922 13.8897i −0.429259 0.743498i 0.567549 0.823340i \(-0.307892\pi\)
−0.996808 + 0.0798418i \(0.974558\pi\)
\(350\) 0 0
\(351\) −10.2396 + 10.6300i −0.546552 + 0.567386i
\(352\) 1.96601 0.104789
\(353\) −1.92156 3.32823i −0.102274 0.177144i 0.810347 0.585950i \(-0.199279\pi\)
−0.912621 + 0.408806i \(0.865945\pi\)
\(354\) −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
\(359\) −21.1335 −1.11538 −0.557692 0.830048i \(-0.688313\pi\)
−0.557692 + 0.830048i \(0.688313\pi\)
\(360\) 1.93447 3.35061i 0.101956 0.176593i
\(361\) −10.2845 17.8133i −0.541289 0.937540i
\(362\) 8.11472 + 14.0551i 0.426500 + 0.738720i
\(363\) −3.83194 −0.201125
\(364\) 0 0
\(365\) 4.07067 0.213069
\(366\) 1.04763 + 1.81455i 0.0547605 + 0.0948479i
\(367\) 7.36961 + 12.7645i 0.384690 + 0.666303i 0.991726 0.128371i \(-0.0409749\pi\)
−0.607036 + 0.794674i \(0.707642\pi\)
\(368\) 6.45260 11.1762i 0.336365 0.582601i
\(369\) −30.4885 −1.58717
\(370\) 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
\(376\) −41.9442 −2.16311
\(377\) −15.5427 3.85463i −0.800488 0.198523i
\(378\) 0 0
\(379\) 13.4179 + 23.2405i 0.689231 + 1.19378i 0.972087 + 0.234621i \(0.0753848\pi\)
−0.282856 + 0.959162i \(0.591282\pi\)
\(380\) 4.20561 + 7.28433i 0.215743 + 0.373678i
\(381\) −3.39861 + 5.88657i −0.174116 + 0.301578i
\(382\) −45.5919 −2.33269
\(383\) 1.45391 2.51825i 0.0742914 0.128677i −0.826487 0.562957i \(-0.809664\pi\)
0.900778 + 0.434280i \(0.142997\pi\)
\(384\) 7.60337 13.1694i 0.388008 0.672049i
\(385\) 0 0
\(386\) 9.93889 17.2147i 0.505876 0.876203i
\(387\) −10.2238 17.7081i −0.519703 0.900153i
\(388\) −20.1178 34.8450i −1.02132 1.76899i
\(389\) −16.7010 −0.846773 −0.423386 0.905949i \(-0.639159\pi\)
−0.423386 + 0.905949i \(0.639159\pi\)
\(390\) 0.624814 + 2.16877i 0.0316387 + 0.109820i
\(391\) 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
\(395\) 1.52724 0.0768438
\(396\) −11.5791 + 20.0556i −0.581873 + 1.00783i
\(397\) 12.0492 20.8699i 0.604733 1.04743i −0.387360 0.921928i \(-0.626613\pi\)
0.992094 0.125500i \(-0.0400536\pi\)
\(398\) −42.4806 −2.12936
\(399\) 0 0
\(400\) 8.54059 + 14.7927i 0.427030 + 0.739637i
\(401\) −0.922448 1.59773i −0.0460649 0.0797867i 0.842074 0.539363i \(-0.181335\pi\)
−0.888139 + 0.459576i \(0.848001\pi\)
\(402\) −10.2491 −0.511176
\(403\) −4.94105 + 5.12940i −0.246131 + 0.255514i
\(404\) 58.9367 2.93221
\(405\) −0.719175 1.24565i −0.0357361 0.0618967i
\(406\) 0 0
\(407\) −11.7089 + 20.2805i −0.580390 + 1.00527i
\(408\) −6.83835 −0.338549
\(409\) 12.8351 22.2311i 0.634657 1.09926i −0.351931 0.936026i \(-0.614475\pi\)
0.986588 0.163232i \(-0.0521920\pi\)
\(410\) −5.20647 + 9.01787i −0.257129 + 0.445361i
\(411\) 3.67512 0.181280
\(412\) −34.4874 + 59.7339i −1.69907 + 2.94288i
\(413\) 0 0
\(414\) −10.9118 18.8998i −0.536287 0.928876i
\(415\) 0.482355 0.0236779
\(416\) −0.806865 2.80067i −0.0395598 0.137314i
\(417\) −8.34529 −0.408671
\(418\) −18.6042 32.2233i −0.909959 1.57609i
\(419\) 13.1199 + 22.7244i 0.640950 + 1.11016i 0.985221 + 0.171288i \(0.0547928\pi\)
−0.344271 + 0.938870i \(0.611874\pi\)
\(420\) 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
\(423\) −10.9509 + 18.9675i −0.532450 + 0.922231i
\(424\) 6.95053 0.337548
\(425\) −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
\(429\) −1.82942 6.35002i −0.0883252 0.306582i
\(430\) −6.98359 −0.336779
\(431\) 11.5088 + 19.9339i 0.554361 + 0.960182i 0.997953 + 0.0639528i \(0.0203707\pi\)
−0.443592 + 0.896229i \(0.646296\pi\)
\(432\) 7.15935 + 12.4004i 0.344455 + 0.596613i
\(433\) 12.9304 22.3961i 0.621394 1.07629i −0.367832 0.929892i \(-0.619900\pi\)
0.989226 0.146394i \(-0.0467667\pi\)
\(434\) 0 0
\(435\) −0.571557 + 0.989965i −0.0274040 + 0.0474652i
\(436\) 16.0024 27.7170i 0.766378 1.32741i
\(437\) 23.2082 1.11020
\(438\) −10.9223 + 18.9180i −0.521890 + 0.903939i
\(439\) 17.8385 + 30.8973i 0.851387 + 1.47465i 0.879956 + 0.475054i \(0.157572\pi\)
−0.0285691 + 0.999592i \(0.509095\pi\)
\(440\) 1.93447 + 3.35061i 0.0922225 + 0.159734i
\(441\) 0 0
\(442\) −11.8523 + 12.3041i −0.563757 + 0.585248i
\(443\) −6.85881 −0.325872 −0.162936 0.986637i \(-0.552096\pi\)
−0.162936 + 0.986637i \(0.552096\pi\)
\(444\) 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 −0.723898 0.689907i \(-0.757651\pi\)
0.959426 + 0.281961i \(0.0909847\pi\)
\(450\) 28.8855 1.36168
\(451\) 15.2442 26.4038i 0.717823 1.24331i
\(452\) 18.8349 + 32.6230i 0.885919 + 1.53446i
\(453\) 3.99041 + 6.91159i 0.187486 + 0.324735i
\(454\) 48.1824 2.26131
\(455\) 0 0
\(456\) −22.0794 −1.03396
\(457\) 4.38656 + 7.59774i 0.205194 + 0.355407i 0.950195 0.311657i \(-0.100884\pi\)
−0.745000 + 0.667064i \(0.767551\pi\)
\(458\) 1.61518 + 2.79757i 0.0754722 + 0.130722i
\(459\) −3.98763 + 6.90678i −0.186127 + 0.322381i
\(460\) −4.93340 −0.230021
\(461\) −3.44272 + 5.96296i −0.160343 + 0.277723i −0.934992 0.354669i \(-0.884593\pi\)
0.774649 + 0.632392i \(0.217927\pi\)
\(462\) 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
\(467\) −28.8113 −1.33323 −0.666613 0.745404i \(-0.732257\pi\)
−0.666613 + 0.745404i \(0.732257\pi\)
\(468\) 33.3223 + 8.26403i 1.54032 + 0.382005i
\(469\) 0 0
\(470\) 3.74013 + 6.47810i 0.172520 + 0.298813i
\(471\) −3.43784 5.95452i −0.158407 0.274370i
\(472\) −1.46018 + 2.52910i −0.0672100 + 0.116411i
\(473\) 20.4475 0.940179
\(474\) −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
\(478\) −27.3359 47.3472i −1.25032 2.16561i
\(479\) 12.2936 + 21.2931i 0.561707 + 0.972906i 0.997348 + 0.0727849i \(0.0231887\pi\)
−0.435640 + 0.900121i \(0.643478\pi\)
\(480\) −0.208056 −0.00949639
\(481\) 33.6959 + 8.35667i 1.53640 + 0.381031i
\(482\) 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
\(486\) 37.5867 1.70497
\(487\) 1.28658 2.22842i 0.0583004 0.100979i −0.835402 0.549639i \(-0.814765\pi\)
0.893703 + 0.448660i \(0.148099\pi\)
\(488\) 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 0.663049 0.748576i \(-0.269262\pi\)
−0.979810 + 0.199929i \(0.935929\pi\)
\(492\) −18.4929 32.0306i −0.833723 1.44405i
\(493\) −8.65279 −0.389702
\(494\) −38.2683 + 39.7271i −1.72177 + 1.78741i
\(495\) 2.02023 0.0908025
\(496\) 3.45468 + 5.98368i 0.155120 + 0.268675i
\(497\) 0 0
\(498\) −1.29425 + 2.24170i −0.0579965 + 0.100453i
\(499\) 13.5345 0.605888 0.302944 0.953008i \(-0.402030\pi\)
0.302944 + 0.953008i \(0.402030\pi\)
\(500\) 6.60778 11.4450i 0.295509 0.511836i
\(501\) 6.88696 11.9286i 0.307687 0.532929i
\(502\) 38.6786 1.72631
\(503\) 4.13877 7.16856i 0.184539 0.319630i −0.758882 0.651228i \(-0.774254\pi\)
0.943421 + 0.331597i \(0.107588\pi\)
\(504\) 0 0
\(505\) −2.57069 4.45257i −0.114394 0.198137i
\(506\) 21.8237 0.970180
\(507\) −8.29509 + 5.21218i −0.368398 + 0.231481i
\(508\) 35.3133 1.56678
\(509\) 0.0831091 + 0.143949i 0.00368375 + 0.00638044i 0.867861 0.496806i \(-0.165494\pi\)
−0.864178 + 0.503187i \(0.832161\pi\)
\(510\) 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
\(514\) 35.5569 61.5863i 1.56835 2.71646i
\(515\) 6.01707 0.265144
\(516\) 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
\(520\) 3.97917 4.13086i 0.174498 0.181150i
\(521\) −7.06180 −0.309383 −0.154691 0.987963i \(-0.549438\pi\)
−0.154691 + 0.987963i \(0.549438\pi\)
\(522\) 13.1355 + 22.7514i 0.574926 + 0.995802i
\(523\) −11.6956 20.2574i −0.511414 0.885795i −0.999912 0.0132299i \(-0.995789\pi\)
0.488499 0.872565i \(-0.337545\pi\)
\(524\) 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
\(528\) −6.41088 −0.278998
\(529\) 4.69387 8.13003i 0.204081 0.353479i
\(530\) −0.619774 1.07348i −0.0269212 0.0466290i
\(531\) 0.762452 + 1.32061i 0.0330876 + 0.0573094i
\(532\) 0 0
\(533\) −43.8697 10.8798i −1.90021 0.471257i
\(534\) 22.8082 0.987006
\(535\) −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
\(541\) 26.3079 1.13107 0.565533 0.824726i \(-0.308671\pi\)
0.565533 + 0.824726i \(0.308671\pi\)
\(542\) 14.7842 25.6069i 0.635035 1.09991i
\(543\) 2.51437 + 4.35501i 0.107902 + 0.186891i
\(544\) −0.787438 1.36388i −0.0337611 0.0584760i
\(545\) −2.79197 −0.119595
\(546\) 0 0
\(547\) 41.7636 1.78568 0.892841 0.450371i \(-0.148708\pi\)
0.892841 + 0.450371i \(0.148708\pi\)
\(548\) −9.54659 16.5352i −0.407810 0.706348i
\(549\) −1.39018 2.40786i −0.0593315 0.102765i
\(550\) −14.4428 + 25.0156i −0.615842 + 1.06667i
\(551\) −27.9378 −1.19019
\(552\) 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 \(0.882827\pi\)
\(558\) 11.6842 0.494633
\(559\) −8.39181 29.1284i −0.354936 1.23200i
\(560\) 0 0
\(561\) −1.78537 3.09235i −0.0753785 0.130559i
\(562\) 3.15780 + 5.46947i 0.133204 + 0.230716i
\(563\) −22.3868 + 38.7751i −0.943493 + 1.63418i −0.184751 + 0.982785i \(0.559148\pi\)
−0.758741 + 0.651392i \(0.774185\pi\)
\(564\) −26.5692 −1.11876
\(565\) 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
\(569\) 21.2563 + 36.8171i 0.891112 + 1.54345i 0.838544 + 0.544834i \(0.183407\pi\)
0.0525679 + 0.998617i \(0.483259\pi\)
\(570\) 1.96881 + 3.41007i 0.0824642 + 0.142832i
\(571\) −40.8648 −1.71014 −0.855069 0.518515i \(-0.826485\pi\)
−0.855069 + 0.518515i \(0.826485\pi\)
\(572\) −23.8180 + 24.7260i −0.995881 + 1.03384i
\(573\) −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
\(577\) −21.7280 −0.904550 −0.452275 0.891879i \(-0.649387\pi\)
−0.452275 + 0.891879i \(0.649387\pi\)
\(578\) 16.0572 27.8119i 0.667891 1.15682i
\(579\) 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
\(583\) 1.81466 + 3.14308i 0.0751555 + 0.130173i
\(584\) 55.5139 2.29718
\(585\) −0.829115 2.87791i −0.0342797 0.118987i
\(586\) −4.76981 −0.197039
\(587\) −10.2408 17.7376i −0.422683 0.732108i 0.573518 0.819193i \(-0.305578\pi\)
−0.996201 + 0.0870851i \(0.972245\pi\)
\(588\) 0 0
\(589\) −6.21277 + 10.7608i −0.255993 + 0.443393i
\(590\) 0.520811 0.0214415
\(591\) −3.28571 + 5.69101i −0.135156 + 0.234097i
\(592\) 16.8398 29.1673i 0.692110 1.19877i
\(593\) −5.63861 −0.231550 −0.115775 0.993275i \(-0.536935\pi\)
−0.115775 + 0.993275i \(0.536935\pi\)
\(594\) −12.1070 + 20.9699i −0.496756 + 0.860407i
\(595\) 0 0
\(596\) −31.1421 53.9397i −1.27563 2.20946i
\(597\) −13.1627 −0.538715
\(598\) −8.95657 31.0888i −0.366261 1.27131i
\(599\) 39.6719 1.62095 0.810474 0.585774i \(-0.199209\pi\)
0.810474 + 0.585774i \(0.199209\pi\)
\(600\) 8.57035 + 14.8443i 0.349883 + 0.606015i
\(601\) −8.41334 14.5723i −0.343187 0.594418i 0.641836 0.766842i \(-0.278173\pi\)
−0.985023 + 0.172425i \(0.944840\pi\)
\(602\) 0 0
\(603\) 13.6003 0.553845
\(604\) 20.7312 35.9075i 0.843540 1.46105i
\(605\) 0.868340 1.50401i 0.0353030 0.0611467i
\(606\) 27.5905 1.12079
\(607\) −11.2490 + 19.4838i −0.456582 + 0.790823i −0.998778 0.0494290i \(-0.984260\pi\)
0.542196 + 0.840252i \(0.317593\pi\)
\(608\) −2.54245 4.40365i −0.103110 0.178592i
\(609\) 0 0
\(610\) −0.949597 −0.0384480
\(611\) −22.5257 + 23.3844i −0.911294 + 0.946032i
\(612\) 18.5509 0.749877
\(613\) −13.7135 23.7524i −0.553882 0.959351i −0.997990 0.0633780i \(-0.979813\pi\)
0.444108 0.895973i \(-0.353521\pi\)
\(614\) −8.97028 15.5370i −0.362011 0.627022i
\(615\) −1.61324 + 2.79421i −0.0650521 + 0.112673i
\(616\) 0 0
\(617\) −5.31896 + 9.21271i −0.214133 + 0.370890i −0.953004 0.302957i \(-0.902026\pi\)
0.738871 + 0.673847i \(0.235359\pi\)
\(618\) −16.1449 + 27.9637i −0.649442 + 1.12487i
\(619\) −45.4677 −1.82750 −0.913751 0.406274i \(-0.866828\pi\)
−0.913751 + 0.406274i \(0.866828\pi\)
\(620\) 1.32065 2.28744i 0.0530388 0.0918659i
\(621\) −7.55160 13.0798i −0.303035 0.524873i
\(622\) −17.2214 29.8283i −0.690515 1.19601i
\(623\) 0 0
\(624\) 2.63107 + 9.13258i 0.105327 + 0.365596i
\(625\) 23.2639 0.930556
\(626\) 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 0.405199 + 0.914229i \(0.367202\pi\)
−0.994345 + 0.106202i \(0.966131\pi\)
\(632\) 20.8278 0.828485
\(633\) 8.76310 15.1781i 0.348302 0.603277i
\(634\) −26.0675 45.1503i −1.03527 1.79315i
\(635\) −1.54029 2.66786i −0.0611246 0.105871i
\(636\) 4.40275 0.174580
\(637\) 0 0
\(638\) −26.2711 −1.04008
\(639\) 11.5491 + 20.0035i 0.456873 + 0.791328i
\(640\) 3.44594 + 5.96854i 0.136213 + 0.235927i
\(641\) 21.2823 36.8621i 0.840601 1.45596i −0.0487858 0.998809i \(-0.515535\pi\)
0.889387 0.457155i \(-0.151131\pi\)
\(642\) 11.7016 0.461827
\(643\) −10.9980 + 19.0492i −0.433721 + 0.751226i −0.997190 0.0749106i \(-0.976133\pi\)
0.563470 + 0.826137i \(0.309466\pi\)
\(644\) 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 \(-0.926833\pi\)
0.289533 0.957168i \(-0.406500\pi\)
\(648\) −9.80778 16.9876i −0.385286 0.667335i
\(649\) −1.52490 −0.0598577
\(650\) 41.5633 + 10.3078i 1.63025 + 0.404306i
\(651\) 0 0
\(652\) 21.4625 + 37.1741i 0.840535 + 1.45585i
\(653\) 25.4084 + 44.0086i 0.994306 + 1.72219i 0.589436 + 0.807815i \(0.299350\pi\)
0.404870 + 0.914374i \(0.367317\pi\)
\(654\) 7.49136 12.9754i 0.292935 0.507379i
\(655\) −0.0657402 −0.00256868
\(656\) −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 −0.685960 0.727639i \(-0.740618\pi\)
0.973134 + 0.230240i \(0.0739511\pi\)
\(660\) 1.22537 + 2.12241i 0.0476976 + 0.0826147i
\(661\) 9.06227 + 15.6963i 0.352481 + 0.610516i 0.986684 0.162651i \(-0.0520046\pi\)
−0.634202 + 0.773167i \(0.718671\pi\)
\(662\) 25.8139 1.00329
\(663\) −3.67247 + 3.81247i −0.142627 + 0.148064i
\(664\) 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
\(668\) −71.5590 −2.76870
\(669\) 11.0299 19.1043i 0.426440 0.738616i
\(670\) 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 0.590997 0.806674i \(-0.298735\pi\)
−0.994099 + 0.108481i \(0.965401\pi\)
\(674\) −8.21547 14.2296i −0.316448 0.548104i
\(675\) 19.9904 0.769432
\(676\) 44.9983 + 23.7821i 1.73071 + 0.914698i
\(677\) −38.2179 −1.46883 −0.734416 0.678700i \(-0.762544\pi\)
−0.734416 + 0.678700i \(0.762544\pi\)
\(678\) 8.81733 + 15.2721i 0.338628 + 0.586520i
\(679\) 0 0
\(680\) 1.54961 2.68401i 0.0594249 0.102927i
\(681\) 14.9294 0.572097
\(682\) −5.84212 + 10.1188i −0.223706 + 0.387471i
\(683\) 11.9126 20.6333i 0.455825 0.789511i −0.542911 0.839790i \(-0.682678\pi\)
0.998735 + 0.0502792i \(0.0160111\pi\)
\(684\) 59.8966 2.29020
\(685\) −0.832803 + 1.44246i −0.0318198 + 0.0551135i
\(686\) 0 0
\(687\) 0.500466 + 0.866833i 0.0190940 + 0.0330717i
\(688\) −29.4076 −1.12115
\(689\) 3.73272 3.87501i 0.142205 0.147626i
\(690\) −2.30951 −0.0879217
\(691\) 9.57063 + 16.5768i 0.364084 + 0.630612i 0.988629 0.150377i \(-0.0480488\pi\)
−0.624545 + 0.780989i \(0.714715\pi\)
\(692\) 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
\(696\) −7.79463 + 13.5007i −0.295455 + 0.511742i
\(697\) −24.4228 −0.925080
\(698\) −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 \(0.672383\pi\)
\(702\) 34.8414 + 8.64077i 1.31500 + 0.326125i
\(703\) 60.5681 2.28437
\(704\) −10.8979 18.8756i −0.410729 0.711403i
\(705\) 1.15889 + 2.00726i 0.0436463 + 0.0755977i
\(706\) −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 \(0.203639\pi\)
\(710\) 7.88886 0.296064
\(711\) 5.43777 9.41849i 0.203932 0.353221i
\(712\) −28.9812 50.1970i −1.08612 1.88121i
\(713\) −3.64395 6.31152i −0.136467 0.236368i
\(714\) 0 0
\(715\) 2.90690 + 0.720919i 0.108712 + 0.0269608i
\(716\) −60.8943 −2.27573
\(717\) −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 −0.890282 0.455410i \(-0.849493\pi\)
0.839538 + 0.543302i \(0.182826\pi\)
\(720\) −2.90549 −0.108281
\(721\) 0 0
\(722\) −25.0129 + 43.3236i −0.930883 + 1.61234i
\(723\) 10.0307 0.373047
\(724\) 13.0628 22.6254i 0.485475 0.840867i
\(725\) 10.8443 + 18.7829i 0.402749 + 0.697581i
\(726\) 4.65982 + 8.07105i 0.172942 + 0.299545i
\(727\) −9.47153 −0.351280 −0.175640 0.984455i \(-0.556199\pi\)
−0.175640 + 0.984455i \(0.556199\pi\)
\(728\) 0 0
\(729\) −0.987863 −0.0365875
\(730\) −4.95014 8.57389i −0.183213 0.317334i
\(731\) −8.18976 14.1851i −0.302909 0.524654i
\(732\) 1.68644 2.92099i 0.0623325 0.107963i
\(733\) 3.49707 0.129167 0.0645836 0.997912i \(-0.479428\pi\)
0.0645836 + 0.997912i \(0.479428\pi\)
\(734\) 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 \(-0.367195\pi\)
\(740\) −12.8750 −0.473295
\(741\) −11.8575 + 12.3096i −0.435598 + 0.452203i
\(742\) 0 0
\(743\) −17.4593 30.2404i −0.640519 1.10941i −0.985317 0.170734i \(-0.945386\pi\)
0.344798 0.938677i \(-0.387947\pi\)
\(744\) 3.46672 + 6.00453i 0.127096 + 0.220137i
\(745\) −2.71670 + 4.70547i −0.0995324 + 0.172395i
\(746\) 31.4387 1.15105
\(747\) 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
\(751\) −13.4986 23.3803i −0.492571 0.853158i 0.507392 0.861715i \(-0.330610\pi\)
−0.999963 + 0.00855684i \(0.997276\pi\)
\(752\) 15.7495 + 27.2790i 0.574327 + 0.994763i
\(753\) 11.9847 0.436745
\(754\) 10.7818 + 37.4243i 0.392651 + 1.36291i
\(755\) −3.61700 −0.131636
\(756\) 0 0
\(757\) 26.2950 + 45.5442i 0.955707 + 1.65533i 0.732742 + 0.680507i \(0.238240\pi\)
0.222965 + 0.974826i \(0.428426\pi\)
\(758\) 32.6337 56.5231i 1.18531 2.05301i
\(759\) 6.76212 0.245449
\(760\) 5.00333 8.66602i 0.181490 0.314350i
\(761\) −6.96431 + 12.0625i −0.252456 + 0.437267i −0.964201 0.265171i \(-0.914572\pi\)
0.711745 + 0.702437i \(0.247905\pi\)
\(762\) 16.5315 0.598874
\(763\) 0 0
\(764\) 36.6961 + 63.5596i 1.32762 + 2.29950i
\(765\) −0.809152 1.40149i −0.0292550 0.0506711i
\(766\) −7.07211 −0.255526
\(767\) 0.625831 + 2.17229i 0.0225974 + 0.0784370i
\(768\) −23.4774 −0.847166
\(769\) −6.89545 11.9433i −0.248656 0.430685i 0.714497 0.699639i \(-0.246656\pi\)
−0.963153 + 0.268953i \(0.913322\pi\)
\(770\) 0 0
\(771\) 11.0174 19.0827i 0.396781 0.687246i
\(772\) −31.9985 −1.15165
\(773\) −25.2435 + 43.7230i −0.907946 + 1.57261i −0.0910326 + 0.995848i \(0.529017\pi\)
−0.816913 + 0.576760i \(0.804317\pi\)
\(774\) −24.8652 + 43.0678i −0.893762 + 1.54804i
\(775\) 9.64620 0.346502
\(776\) −23.9337 + 41.4544i −0.859170 + 1.48813i
\(777\)