Properties

Label 475.2.l.c.176.3
Level $475$
Weight $2$
Character 475.176
Analytic conductor $3.793$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [475,2,Mod(101,475)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(475, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("475.101");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.l (of order \(9\), degree \(6\), 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: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(3\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} - 3 x^{17} + 15 x^{16} - 14 x^{15} + 72 x^{14} - 51 x^{13} + 231 x^{12} - 93 x^{11} + 438 x^{10} - 156 x^{9} + 582 x^{8} - 138 x^{7} + 437 x^{6} - 132 x^{5} + 198 x^{4} - 16 x^{3} + \cdots + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 176.3
Root \(-0.791558 - 1.37102i\) of defining polynomial
Character \(\chi\) \(=\) 475.176
Dual form 475.2.l.c.251.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.42733 - 0.883478i) q^{2} +(0.0430161 - 0.243956i) q^{3} +(3.57933 - 3.00342i) q^{4} +(-0.111115 - 0.630167i) q^{6} +(-0.200820 - 0.347830i) q^{7} +(3.45167 - 5.97847i) q^{8} +(2.76141 + 1.00507i) q^{9} +O(q^{10})\) \(q+(2.42733 - 0.883478i) q^{2} +(0.0430161 - 0.243956i) q^{3} +(3.57933 - 3.00342i) q^{4} +(-0.111115 - 0.630167i) q^{6} +(-0.200820 - 0.347830i) q^{7} +(3.45167 - 5.97847i) q^{8} +(2.76141 + 1.00507i) q^{9} +(-2.59530 + 4.49520i) q^{11} +(-0.578733 - 1.00240i) q^{12} +(-0.501737 - 2.84549i) q^{13} +(-0.794758 - 0.666881i) q^{14} +(1.47378 - 8.35823i) q^{16} +(-3.89339 + 1.41708i) q^{17} +7.59083 q^{18} +(0.386682 - 4.34171i) q^{19} +(-0.0934938 + 0.0340290i) q^{21} +(-2.32827 + 13.2043i) q^{22} +(-2.57278 + 2.15882i) q^{23} +(-1.31001 - 1.09923i) q^{24} +(-3.73181 - 6.46368i) q^{26} +(0.735558 - 1.27402i) q^{27} +(-1.76348 - 0.641855i) q^{28} +(-6.18683 - 2.25182i) q^{29} +(3.13119 + 5.42339i) q^{31} +(-1.40944 - 7.99334i) q^{32} +(0.984992 + 0.826506i) q^{33} +(-8.19861 + 6.87945i) q^{34} +(12.9027 - 4.69619i) q^{36} -1.14106 q^{37} +(-2.89720 - 10.8804i) q^{38} -0.715757 q^{39} +(0.496543 - 2.81603i) q^{41} +(-0.196877 + 0.165199i) q^{42} +(9.52394 + 7.99153i) q^{43} +(4.21150 + 23.8846i) q^{44} +(-4.33773 + 7.51317i) q^{46} +(6.35381 + 2.31260i) q^{47} +(-1.97565 - 0.719076i) q^{48} +(3.41934 - 5.92248i) q^{49} +(0.178227 + 1.01077i) q^{51} +(-10.3421 - 8.67803i) q^{52} +(-9.42382 + 7.90752i) q^{53} +(0.659874 - 3.74233i) q^{54} -2.77266 q^{56} +(-1.04255 - 0.281097i) q^{57} -17.0069 q^{58} +(1.42380 - 0.518220i) q^{59} +(-5.35269 + 4.49144i) q^{61} +(12.3919 + 10.3980i) q^{62} +(-0.204952 - 1.16234i) q^{63} +(-1.99595 - 3.45709i) q^{64} +(3.12111 + 1.13599i) q^{66} +(-0.711451 - 0.258947i) q^{67} +(-9.67967 + 16.7657i) q^{68} +(0.415986 + 0.720510i) q^{69} +(-6.38582 - 5.35834i) q^{71} +(15.5403 - 13.0399i) q^{72} +(1.72232 - 9.76776i) q^{73} +(-2.76974 + 1.00810i) q^{74} +(-11.6559 - 16.7018i) q^{76} +2.08476 q^{77} +(-1.73738 + 0.632356i) q^{78} +(0.553655 - 3.13994i) q^{79} +(6.47421 + 5.43251i) q^{81} +(-1.28263 - 7.27414i) q^{82} +(2.75971 + 4.77995i) q^{83} +(-0.232442 + 0.402602i) q^{84} +(30.1781 + 10.9839i) q^{86} +(-0.815478 + 1.41245i) q^{87} +(17.9163 + 31.0319i) q^{88} +(-2.17478 - 12.3338i) q^{89} +(-0.888989 + 0.745950i) q^{91} +(-2.72500 + 15.4543i) q^{92} +(1.45776 - 0.530581i) q^{93} +17.4660 q^{94} -2.01065 q^{96} +(-8.35815 + 3.04212i) q^{97} +(3.06752 - 17.3967i) q^{98} +(-11.6847 + 9.80464i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9} + 18 q^{12} + 3 q^{13} - 12 q^{14} - 3 q^{16} - 24 q^{17} - 48 q^{18} - 21 q^{21} - 9 q^{22} + 9 q^{23} - 15 q^{24} + 3 q^{26} + 24 q^{27} + 12 q^{28} + 15 q^{29} - 18 q^{31} - 15 q^{32} + 33 q^{33} - 12 q^{34} + 75 q^{36} - 36 q^{37} + 33 q^{38} + 36 q^{39} - 30 q^{41} + 9 q^{42} + 36 q^{43} + 42 q^{44} + 9 q^{46} - 21 q^{47} - 33 q^{48} + 9 q^{49} - 45 q^{51} + 39 q^{52} + 12 q^{53} - 66 q^{54} - 72 q^{57} - 12 q^{58} + 18 q^{59} - 30 q^{61} + 24 q^{62} - 54 q^{63} + 36 q^{64} + 39 q^{66} - 51 q^{68} + 15 q^{69} - 12 q^{71} + 66 q^{72} - 24 q^{73} - 15 q^{74} - 33 q^{76} + 60 q^{77} + 48 q^{78} - 51 q^{79} + 27 q^{81} + 15 q^{82} + 48 q^{84} + 63 q^{86} + 15 q^{87} + 27 q^{88} - 54 q^{89} + 30 q^{91} + 42 q^{92} - 72 q^{93} + 30 q^{94} - 66 q^{96} - 27 q^{97} + 3 q^{98} - 93 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{8}{9}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.42733 0.883478i 1.71639 0.624713i 0.718869 0.695146i \(-0.244660\pi\)
0.997517 + 0.0704330i \(0.0224381\pi\)
\(3\) 0.0430161 0.243956i 0.0248353 0.140848i −0.969869 0.243628i \(-0.921663\pi\)
0.994704 + 0.102780i \(0.0327736\pi\)
\(4\) 3.57933 3.00342i 1.78967 1.50171i
\(5\) 0 0
\(6\) −0.111115 0.630167i −0.0453627 0.257265i
\(7\) −0.200820 0.347830i −0.0759028 0.131468i 0.825576 0.564291i \(-0.190851\pi\)
−0.901479 + 0.432824i \(0.857517\pi\)
\(8\) 3.45167 5.97847i 1.22035 2.11371i
\(9\) 2.76141 + 1.00507i 0.920471 + 0.335024i
\(10\) 0 0
\(11\) −2.59530 + 4.49520i −0.782514 + 1.35535i 0.147959 + 0.988993i \(0.452730\pi\)
−0.930473 + 0.366360i \(0.880604\pi\)
\(12\) −0.578733 1.00240i −0.167066 0.289367i
\(13\) −0.501737 2.84549i −0.139157 0.789197i −0.971875 0.235499i \(-0.924327\pi\)
0.832718 0.553698i \(-0.186784\pi\)
\(14\) −0.794758 0.666881i −0.212408 0.178231i
\(15\) 0 0
\(16\) 1.47378 8.35823i 0.368445 2.08956i
\(17\) −3.89339 + 1.41708i −0.944286 + 0.343692i −0.767857 0.640621i \(-0.778677\pi\)
−0.176429 + 0.984313i \(0.556455\pi\)
\(18\) 7.59083 1.78918
\(19\) 0.386682 4.34171i 0.0887110 0.996057i
\(20\) 0 0
\(21\) −0.0934938 + 0.0340290i −0.0204020 + 0.00742573i
\(22\) −2.32827 + 13.2043i −0.496388 + 2.81516i
\(23\) −2.57278 + 2.15882i −0.536462 + 0.450145i −0.870326 0.492476i \(-0.836092\pi\)
0.333864 + 0.942621i \(0.391647\pi\)
\(24\) −1.31001 1.09923i −0.267404 0.224379i
\(25\) 0 0
\(26\) −3.73181 6.46368i −0.731868 1.26763i
\(27\) 0.735558 1.27402i 0.141558 0.245186i
\(28\) −1.76348 0.641855i −0.333267 0.121299i
\(29\) −6.18683 2.25182i −1.14887 0.418153i −0.303758 0.952749i \(-0.598241\pi\)
−0.845107 + 0.534597i \(0.820464\pi\)
\(30\) 0 0
\(31\) 3.13119 + 5.42339i 0.562379 + 0.974069i 0.997288 + 0.0735948i \(0.0234472\pi\)
−0.434909 + 0.900474i \(0.643220\pi\)
\(32\) −1.40944 7.99334i −0.249156 1.41304i
\(33\) 0.984992 + 0.826506i 0.171465 + 0.143876i
\(34\) −8.19861 + 6.87945i −1.40605 + 1.17982i
\(35\) 0 0
\(36\) 12.9027 4.69619i 2.15045 0.782698i
\(37\) −1.14106 −0.187590 −0.0937949 0.995592i \(-0.529900\pi\)
−0.0937949 + 0.995592i \(0.529900\pi\)
\(38\) −2.89720 10.8804i −0.469988 1.76504i
\(39\) −0.715757 −0.114613
\(40\) 0 0
\(41\) 0.496543 2.81603i 0.0775469 0.439790i −0.921171 0.389159i \(-0.872766\pi\)
0.998717 0.0506312i \(-0.0161233\pi\)
\(42\) −0.196877 + 0.165199i −0.0303788 + 0.0254908i
\(43\) 9.52394 + 7.99153i 1.45239 + 1.21870i 0.930815 + 0.365491i \(0.119099\pi\)
0.521572 + 0.853207i \(0.325346\pi\)
\(44\) 4.21150 + 23.8846i 0.634908 + 3.60074i
\(45\) 0 0
\(46\) −4.33773 + 7.51317i −0.639564 + 1.10776i
\(47\) 6.35381 + 2.31260i 0.926798 + 0.337327i 0.760940 0.648822i \(-0.224738\pi\)
0.165859 + 0.986150i \(0.446960\pi\)
\(48\) −1.97565 0.719076i −0.285160 0.103790i
\(49\) 3.41934 5.92248i 0.488478 0.846068i
\(50\) 0 0
\(51\) 0.178227 + 1.01077i 0.0249567 + 0.141537i
\(52\) −10.3421 8.67803i −1.43419 1.20343i
\(53\) −9.42382 + 7.90752i −1.29446 + 1.08618i −0.303387 + 0.952867i \(0.598117\pi\)
−0.991074 + 0.133314i \(0.957438\pi\)
\(54\) 0.659874 3.74233i 0.0897975 0.509267i
\(55\) 0 0
\(56\) −2.77266 −0.370512
\(57\) −1.04255 0.281097i −0.138090 0.0372322i
\(58\) −17.0069 −2.23312
\(59\) 1.42380 0.518220i 0.185363 0.0674665i −0.247671 0.968844i \(-0.579665\pi\)
0.433034 + 0.901378i \(0.357443\pi\)
\(60\) 0 0
\(61\) −5.35269 + 4.49144i −0.685342 + 0.575070i −0.917562 0.397593i \(-0.869845\pi\)
0.232220 + 0.972663i \(0.425401\pi\)
\(62\) 12.3919 + 10.3980i 1.57377 + 1.32055i
\(63\) −0.204952 1.16234i −0.0258216 0.146441i
\(64\) −1.99595 3.45709i −0.249494 0.432136i
\(65\) 0 0
\(66\) 3.12111 + 1.13599i 0.384182 + 0.139831i
\(67\) −0.711451 0.258947i −0.0869175 0.0316354i 0.298195 0.954505i \(-0.403615\pi\)
−0.385113 + 0.922869i \(0.625838\pi\)
\(68\) −9.67967 + 16.7657i −1.17383 + 2.03314i
\(69\) 0.415986 + 0.720510i 0.0500789 + 0.0867392i
\(70\) 0 0
\(71\) −6.38582 5.35834i −0.757857 0.635918i 0.179711 0.983719i \(-0.442484\pi\)
−0.937568 + 0.347802i \(0.886928\pi\)
\(72\) 15.5403 13.0399i 1.83144 1.53676i
\(73\) 1.72232 9.76776i 0.201582 1.14323i −0.701146 0.713018i \(-0.747328\pi\)
0.902728 0.430212i \(-0.141561\pi\)
\(74\) −2.76974 + 1.00810i −0.321976 + 0.117190i
\(75\) 0 0
\(76\) −11.6559 16.7018i −1.33702 1.91583i
\(77\) 2.08476 0.237580
\(78\) −1.73738 + 0.632356i −0.196720 + 0.0716002i
\(79\) 0.553655 3.13994i 0.0622911 0.353270i −0.937692 0.347467i \(-0.887042\pi\)
0.999983 0.00580301i \(-0.00184717\pi\)
\(80\) 0 0
\(81\) 6.47421 + 5.43251i 0.719357 + 0.603612i
\(82\) −1.28263 7.27414i −0.141642 0.803294i
\(83\) 2.75971 + 4.77995i 0.302917 + 0.524668i 0.976795 0.214174i \(-0.0687061\pi\)
−0.673878 + 0.738842i \(0.735373\pi\)
\(84\) −0.232442 + 0.402602i −0.0253615 + 0.0439275i
\(85\) 0 0
\(86\) 30.1781 + 10.9839i 3.25419 + 1.18443i
\(87\) −0.815478 + 1.41245i −0.0874285 + 0.151431i
\(88\) 17.9163 + 31.0319i 1.90988 + 3.30801i
\(89\) −2.17478 12.3338i −0.230527 1.30738i −0.851833 0.523814i \(-0.824509\pi\)
0.621306 0.783568i \(-0.286602\pi\)
\(90\) 0 0
\(91\) −0.888989 + 0.745950i −0.0931914 + 0.0781968i
\(92\) −2.72500 + 15.4543i −0.284101 + 1.61122i
\(93\) 1.45776 0.530581i 0.151163 0.0550187i
\(94\) 17.4660 1.80148
\(95\) 0 0
\(96\) −2.01065 −0.205211
\(97\) −8.35815 + 3.04212i −0.848642 + 0.308880i −0.729487 0.683995i \(-0.760241\pi\)
−0.119155 + 0.992876i \(0.538019\pi\)
\(98\) 3.06752 17.3967i 0.309866 1.75734i
\(99\) −11.6847 + 9.80464i −1.17436 + 0.985403i
\(100\) 0 0
\(101\) 0.233727 + 1.32553i 0.0232567 + 0.131895i 0.994226 0.107311i \(-0.0342240\pi\)
−0.970969 + 0.239206i \(0.923113\pi\)
\(102\) 1.32561 + 2.29603i 0.131255 + 0.227341i
\(103\) 6.21391 10.7628i 0.612275 1.06049i −0.378581 0.925568i \(-0.623588\pi\)
0.990856 0.134923i \(-0.0430787\pi\)
\(104\) −18.7435 6.82208i −1.83795 0.668960i
\(105\) 0 0
\(106\) −15.8886 + 27.5199i −1.54324 + 2.67297i
\(107\) −7.28110 12.6112i −0.703890 1.21917i −0.967091 0.254432i \(-0.918111\pi\)
0.263200 0.964741i \(-0.415222\pi\)
\(108\) −1.19362 6.76934i −0.114856 0.651380i
\(109\) 3.38582 + 2.84104i 0.324303 + 0.272122i 0.790374 0.612625i \(-0.209886\pi\)
−0.466071 + 0.884747i \(0.654331\pi\)
\(110\) 0 0
\(111\) −0.0490841 + 0.278370i −0.00465885 + 0.0264217i
\(112\) −3.20321 + 1.16587i −0.302675 + 0.110165i
\(113\) −8.08453 −0.760528 −0.380264 0.924878i \(-0.624167\pi\)
−0.380264 + 0.924878i \(0.624167\pi\)
\(114\) −2.77897 + 0.238757i −0.260274 + 0.0223616i
\(115\) 0 0
\(116\) −28.9079 + 10.5216i −2.68403 + 0.976907i
\(117\) 1.47442 8.36186i 0.136310 0.773054i
\(118\) 2.99820 2.51579i 0.276006 0.231597i
\(119\) 1.27477 + 1.06966i 0.116858 + 0.0980557i
\(120\) 0 0
\(121\) −7.97122 13.8065i −0.724656 1.25514i
\(122\) −9.02468 + 15.6312i −0.817056 + 1.41518i
\(123\) −0.665629 0.242269i −0.0600178 0.0218447i
\(124\) 27.4963 + 10.0078i 2.46924 + 0.898730i
\(125\) 0 0
\(126\) −1.52439 2.64032i −0.135804 0.235219i
\(127\) 0.0974458 + 0.552642i 0.00864691 + 0.0490391i 0.988826 0.149075i \(-0.0476295\pi\)
−0.980179 + 0.198114i \(0.936518\pi\)
\(128\) 4.53632 + 3.80642i 0.400958 + 0.336444i
\(129\) 2.35927 1.97966i 0.207722 0.174299i
\(130\) 0 0
\(131\) 9.28037 3.37778i 0.810830 0.295118i 0.0968634 0.995298i \(-0.469119\pi\)
0.713967 + 0.700180i \(0.246897\pi\)
\(132\) 6.00796 0.522926
\(133\) −1.58783 + 0.737403i −0.137683 + 0.0639409i
\(134\) −1.95570 −0.168947
\(135\) 0 0
\(136\) −4.96675 + 28.1678i −0.425895 + 2.41537i
\(137\) 6.86600 5.76126i 0.586602 0.492217i −0.300506 0.953780i \(-0.597155\pi\)
0.887108 + 0.461563i \(0.152711\pi\)
\(138\) 1.64629 + 1.38140i 0.140142 + 0.117593i
\(139\) −2.28639 12.9668i −0.193929 1.09983i −0.913935 0.405860i \(-0.866972\pi\)
0.720006 0.693968i \(-0.244139\pi\)
\(140\) 0 0
\(141\) 0.837488 1.45057i 0.0705292 0.122160i
\(142\) −20.2345 7.36475i −1.69804 0.618036i
\(143\) 14.0932 + 5.12951i 1.17853 + 0.428951i
\(144\) 12.4703 21.5993i 1.03920 1.79994i
\(145\) 0 0
\(146\) −4.44895 25.2313i −0.368198 2.08815i
\(147\) −1.29774 1.08893i −0.107036 0.0898135i
\(148\) −4.08425 + 3.42709i −0.335723 + 0.281705i
\(149\) −1.42107 + 8.05930i −0.116419 + 0.660243i 0.869619 + 0.493723i \(0.164364\pi\)
−0.986038 + 0.166520i \(0.946747\pi\)
\(150\) 0 0
\(151\) 7.60636 0.618997 0.309498 0.950900i \(-0.399839\pi\)
0.309498 + 0.950900i \(0.399839\pi\)
\(152\) −24.6221 17.2979i −1.99712 1.40305i
\(153\) −12.1755 −0.984333
\(154\) 5.06040 1.84184i 0.407779 0.148419i
\(155\) 0 0
\(156\) −2.56193 + 2.14972i −0.205119 + 0.172115i
\(157\) 9.62566 + 8.07689i 0.768212 + 0.644606i 0.940250 0.340484i \(-0.110591\pi\)
−0.172039 + 0.985090i \(0.555035\pi\)
\(158\) −1.43016 8.11082i −0.113777 0.645262i
\(159\) 1.52371 + 2.63915i 0.120838 + 0.209298i
\(160\) 0 0
\(161\) 1.26757 + 0.461357i 0.0998984 + 0.0363600i
\(162\) 20.5146 + 7.46669i 1.61178 + 0.586639i
\(163\) −1.64175 + 2.84359i −0.128591 + 0.222727i −0.923131 0.384485i \(-0.874379\pi\)
0.794540 + 0.607212i \(0.207712\pi\)
\(164\) −6.68043 11.5708i −0.521654 0.903531i
\(165\) 0 0
\(166\) 10.9217 + 9.16441i 0.847689 + 0.711296i
\(167\) 4.00460 3.36026i 0.309885 0.260025i −0.474559 0.880224i \(-0.657393\pi\)
0.784445 + 0.620199i \(0.212948\pi\)
\(168\) −0.119269 + 0.676407i −0.00920179 + 0.0521860i
\(169\) 4.37093 1.59089i 0.336226 0.122376i
\(170\) 0 0
\(171\) 5.43153 11.6006i 0.415359 0.887122i
\(172\) 58.0913 4.42942
\(173\) 4.23385 1.54100i 0.321894 0.117160i −0.176019 0.984387i \(-0.556322\pi\)
0.497913 + 0.867227i \(0.334100\pi\)
\(174\) −0.731571 + 4.14895i −0.0554603 + 0.314531i
\(175\) 0 0
\(176\) 33.7470 + 28.3171i 2.54378 + 2.13448i
\(177\) −0.0651768 0.369636i −0.00489899 0.0277835i
\(178\) −16.1756 28.0169i −1.21241 2.09996i
\(179\) 1.88583 3.26636i 0.140954 0.244139i −0.786902 0.617078i \(-0.788316\pi\)
0.927856 + 0.372939i \(0.121650\pi\)
\(180\) 0 0
\(181\) −17.9437 6.53096i −1.33374 0.485442i −0.425906 0.904767i \(-0.640045\pi\)
−0.907836 + 0.419325i \(0.862267\pi\)
\(182\) −1.49884 + 2.59607i −0.111102 + 0.192434i
\(183\) 0.865463 + 1.49903i 0.0639768 + 0.110811i
\(184\) 4.02605 + 22.8328i 0.296804 + 1.68326i
\(185\) 0 0
\(186\) 3.06972 2.57580i 0.225082 0.188867i
\(187\) 3.73449 21.1793i 0.273093 1.54879i
\(188\) 29.6881 10.8056i 2.16523 0.788078i
\(189\) −0.590859 −0.0429787
\(190\) 0 0
\(191\) 2.89599 0.209547 0.104773 0.994496i \(-0.466588\pi\)
0.104773 + 0.994496i \(0.466588\pi\)
\(192\) −0.929236 + 0.338214i −0.0670619 + 0.0244085i
\(193\) −1.97618 + 11.2075i −0.142249 + 0.806733i 0.827286 + 0.561781i \(0.189883\pi\)
−0.969535 + 0.244952i \(0.921228\pi\)
\(194\) −17.6004 + 14.7685i −1.26363 + 1.06032i
\(195\) 0 0
\(196\) −5.54870 31.4682i −0.396336 2.24773i
\(197\) −5.07545 8.79093i −0.361610 0.626328i 0.626616 0.779329i \(-0.284440\pi\)
−0.988226 + 0.153001i \(0.951106\pi\)
\(198\) −19.7005 + 34.1223i −1.40006 + 2.42497i
\(199\) 2.75352 + 1.00220i 0.195192 + 0.0710440i 0.437766 0.899089i \(-0.355770\pi\)
−0.242575 + 0.970133i \(0.577992\pi\)
\(200\) 0 0
\(201\) −0.0937755 + 0.162424i −0.00661441 + 0.0114565i
\(202\) 1.73841 + 3.01101i 0.122314 + 0.211854i
\(203\) 0.459187 + 2.60418i 0.0322286 + 0.182777i
\(204\) 3.67371 + 3.08261i 0.257211 + 0.215826i
\(205\) 0 0
\(206\) 5.57454 31.6148i 0.388397 2.20271i
\(207\) −9.27428 + 3.37556i −0.644607 + 0.234618i
\(208\) −24.5227 −1.70034
\(209\) 18.5133 + 13.0063i 1.28059 + 0.899664i
\(210\) 0 0
\(211\) 5.17374 1.88309i 0.356175 0.129637i −0.157734 0.987482i \(-0.550419\pi\)
0.513909 + 0.857845i \(0.328197\pi\)
\(212\) −9.98140 + 56.6073i −0.685525 + 3.88781i
\(213\) −1.58189 + 1.32737i −0.108389 + 0.0909496i
\(214\) −28.8154 24.1790i −1.96978 1.65284i
\(215\) 0 0
\(216\) −5.07781 8.79503i −0.345501 0.598426i
\(217\) 1.25761 2.17825i 0.0853723 0.147869i
\(218\) 10.7285 + 3.90486i 0.726626 + 0.264470i
\(219\) −2.30882 0.840341i −0.156015 0.0567850i
\(220\) 0 0
\(221\) 5.98574 + 10.3676i 0.402644 + 0.697400i
\(222\) 0.126790 + 0.719061i 0.00850958 + 0.0482602i
\(223\) −6.09836 5.11713i −0.408376 0.342669i 0.415344 0.909664i \(-0.363661\pi\)
−0.823721 + 0.566996i \(0.808106\pi\)
\(224\) −2.49728 + 2.09547i −0.166857 + 0.140009i
\(225\) 0 0
\(226\) −19.6239 + 7.14250i −1.30536 + 0.475112i
\(227\) −8.02439 −0.532597 −0.266299 0.963891i \(-0.585801\pi\)
−0.266299 + 0.963891i \(0.585801\pi\)
\(228\) −4.57590 + 2.12509i −0.303046 + 0.140737i
\(229\) −28.2466 −1.86659 −0.933295 0.359111i \(-0.883080\pi\)
−0.933295 + 0.359111i \(0.883080\pi\)
\(230\) 0 0
\(231\) 0.0896780 0.508589i 0.00590038 0.0334627i
\(232\) −34.8174 + 29.2152i −2.28587 + 1.91807i
\(233\) −7.23338 6.06953i −0.473875 0.397628i 0.374331 0.927295i \(-0.377872\pi\)
−0.848206 + 0.529667i \(0.822317\pi\)
\(234\) −3.80860 21.5996i −0.248976 1.41201i
\(235\) 0 0
\(236\) 3.53981 6.13114i 0.230422 0.399103i
\(237\) −0.742191 0.270135i −0.0482105 0.0175472i
\(238\) 4.03932 + 1.47019i 0.261831 + 0.0952985i
\(239\) −5.89638 + 10.2128i −0.381405 + 0.660613i −0.991263 0.131897i \(-0.957893\pi\)
0.609858 + 0.792511i \(0.291226\pi\)
\(240\) 0 0
\(241\) −2.22273 12.6057i −0.143179 0.812007i −0.968811 0.247799i \(-0.920293\pi\)
0.825633 0.564208i \(-0.190818\pi\)
\(242\) −31.5466 26.4707i −2.02789 1.70160i
\(243\) 4.98461 4.18258i 0.319763 0.268313i
\(244\) −5.66939 + 32.1527i −0.362946 + 2.05837i
\(245\) 0 0
\(246\) −1.82974 −0.116660
\(247\) −12.5483 + 1.07810i −0.798430 + 0.0685976i
\(248\) 43.2314 2.74520
\(249\) 1.28481 0.467633i 0.0814216 0.0296350i
\(250\) 0 0
\(251\) 1.83823 1.54246i 0.116028 0.0973590i −0.582928 0.812524i \(-0.698093\pi\)
0.698956 + 0.715165i \(0.253648\pi\)
\(252\) −4.22459 3.54485i −0.266124 0.223305i
\(253\) −3.02717 17.1680i −0.190317 1.07934i
\(254\) 0.724781 + 1.25536i 0.0454768 + 0.0787681i
\(255\) 0 0
\(256\) 21.8764 + 7.96235i 1.36727 + 0.497647i
\(257\) 16.1772 + 5.88802i 1.00911 + 0.367285i 0.793090 0.609105i \(-0.208471\pi\)
0.216017 + 0.976390i \(0.430693\pi\)
\(258\) 3.97774 6.88966i 0.247644 0.428931i
\(259\) 0.229148 + 0.396897i 0.0142386 + 0.0246620i
\(260\) 0 0
\(261\) −14.8211 12.4364i −0.917406 0.769795i
\(262\) 19.5424 16.3980i 1.20733 1.01307i
\(263\) −2.54981 + 14.4607i −0.157228 + 0.891685i 0.799492 + 0.600677i \(0.205102\pi\)
−0.956720 + 0.291009i \(0.906009\pi\)
\(264\) 8.34112 3.03592i 0.513360 0.186848i
\(265\) 0 0
\(266\) −3.20272 + 3.19274i −0.196372 + 0.195759i
\(267\) −3.10246 −0.189868
\(268\) −3.32424 + 1.20993i −0.203061 + 0.0739080i
\(269\) −3.89891 + 22.1118i −0.237721 + 1.34818i 0.599086 + 0.800685i \(0.295531\pi\)
−0.836807 + 0.547498i \(0.815580\pi\)
\(270\) 0 0
\(271\) 10.1742 + 8.53716i 0.618038 + 0.518596i 0.897186 0.441652i \(-0.145608\pi\)
−0.279148 + 0.960248i \(0.590052\pi\)
\(272\) 6.10626 + 34.6303i 0.370246 + 2.09977i
\(273\) 0.143738 + 0.248962i 0.00869944 + 0.0150679i
\(274\) 11.5761 20.0505i 0.699340 1.21129i
\(275\) 0 0
\(276\) 3.65294 + 1.32956i 0.219881 + 0.0800303i
\(277\) 1.67963 2.90921i 0.100919 0.174797i −0.811144 0.584846i \(-0.801155\pi\)
0.912064 + 0.410049i \(0.134488\pi\)
\(278\) −17.0057 29.4548i −1.01993 1.76658i
\(279\) 3.19563 + 18.1233i 0.191317 + 1.08501i
\(280\) 0 0
\(281\) 15.3380 12.8702i 0.914991 0.767769i −0.0580707 0.998312i \(-0.518495\pi\)
0.973062 + 0.230544i \(0.0740504\pi\)
\(282\) 0.751316 4.26093i 0.0447402 0.253735i
\(283\) 0.498021 0.181265i 0.0296043 0.0107751i −0.327176 0.944964i \(-0.606097\pi\)
0.356780 + 0.934188i \(0.383875\pi\)
\(284\) −38.9503 −2.31127
\(285\) 0 0
\(286\) 38.7407 2.29079
\(287\) −1.07922 + 0.392803i −0.0637042 + 0.0231864i
\(288\) 4.14183 23.4895i 0.244060 1.38413i
\(289\) 0.127626 0.107091i 0.00750741 0.00629946i
\(290\) 0 0
\(291\) 0.382609 + 2.16988i 0.0224289 + 0.127201i
\(292\) −23.1719 40.1349i −1.35603 2.34872i
\(293\) 15.8074 27.3793i 0.923480 1.59951i 0.129492 0.991580i \(-0.458665\pi\)
0.793988 0.607934i \(-0.208001\pi\)
\(294\) −4.11209 1.49668i −0.239822 0.0872881i
\(295\) 0 0
\(296\) −3.93858 + 6.82182i −0.228925 + 0.396510i
\(297\) 3.81799 + 6.61296i 0.221543 + 0.383723i
\(298\) 3.67079 + 20.8181i 0.212643 + 1.20596i
\(299\) 7.43376 + 6.23766i 0.429905 + 0.360733i
\(300\) 0 0
\(301\) 0.867101 4.91757i 0.0499789 0.283444i
\(302\) 18.4632 6.72005i 1.06244 0.386695i
\(303\) 0.333425 0.0191548
\(304\) −35.7192 9.63072i −2.04863 0.552359i
\(305\) 0 0
\(306\) −29.5541 + 10.7568i −1.68949 + 0.614926i
\(307\) −1.59262 + 9.03222i −0.0908958 + 0.515496i 0.905032 + 0.425343i \(0.139847\pi\)
−0.995928 + 0.0901527i \(0.971264\pi\)
\(308\) 7.46204 6.26139i 0.425189 0.356776i
\(309\) −2.35836 1.97890i −0.134162 0.112575i
\(310\) 0 0
\(311\) 12.0255 + 20.8288i 0.681906 + 1.18110i 0.974399 + 0.224828i \(0.0721819\pi\)
−0.292493 + 0.956268i \(0.594485\pi\)
\(312\) −2.47056 + 4.27914i −0.139868 + 0.242258i
\(313\) −2.31124 0.841224i −0.130639 0.0475488i 0.275873 0.961194i \(-0.411033\pi\)
−0.406512 + 0.913645i \(0.633255\pi\)
\(314\) 30.5005 + 11.1013i 1.72124 + 0.626480i
\(315\) 0 0
\(316\) −7.44882 12.9017i −0.419029 0.725779i
\(317\) −1.21940 6.91555i −0.0684882 0.388416i −0.999713 0.0239697i \(-0.992369\pi\)
0.931225 0.364446i \(-0.118742\pi\)
\(318\) 6.03019 + 5.05993i 0.338156 + 0.283747i
\(319\) 26.1791 21.9669i 1.46575 1.22991i
\(320\) 0 0
\(321\) −3.38979 + 1.23378i −0.189200 + 0.0688631i
\(322\) 3.48441 0.194179
\(323\) 4.64704 + 17.4519i 0.258568 + 0.971052i
\(324\) 39.4894 2.19386
\(325\) 0 0
\(326\) −1.47282 + 8.35278i −0.0815720 + 0.462618i
\(327\) 0.838733 0.703781i 0.0463821 0.0389192i
\(328\) −15.1217 12.6886i −0.834955 0.700610i
\(329\) −0.471580 2.67446i −0.0259991 0.147448i
\(330\) 0 0
\(331\) −8.70524 + 15.0779i −0.478483 + 0.828758i −0.999696 0.0246694i \(-0.992147\pi\)
0.521212 + 0.853427i \(0.325480\pi\)
\(332\) 24.2341 + 8.82049i 1.33002 + 0.484087i
\(333\) −3.15095 1.14685i −0.172671 0.0628471i
\(334\) 6.75180 11.6945i 0.369442 0.639892i
\(335\) 0 0
\(336\) 0.146632 + 0.831594i 0.00799946 + 0.0453672i
\(337\) 25.0326 + 21.0048i 1.36361 + 1.14420i 0.974849 + 0.222866i \(0.0715413\pi\)
0.388761 + 0.921339i \(0.372903\pi\)
\(338\) 9.20420 7.72324i 0.500643 0.420089i
\(339\) −0.347764 + 1.97227i −0.0188880 + 0.107119i
\(340\) 0 0
\(341\) −32.5056 −1.76028
\(342\) 2.93524 32.9572i 0.158720 1.78212i
\(343\) −5.55817 −0.300113
\(344\) 80.6507 29.3545i 4.34839 1.58269i
\(345\) 0 0
\(346\) 8.91554 7.48102i 0.479302 0.402182i
\(347\) −5.46153 4.58277i −0.293191 0.246016i 0.484313 0.874895i \(-0.339070\pi\)
−0.777503 + 0.628879i \(0.783514\pi\)
\(348\) 1.32331 + 7.50485i 0.0709368 + 0.402302i
\(349\) −11.3504 19.6595i −0.607575 1.05235i −0.991639 0.129044i \(-0.958809\pi\)
0.384064 0.923307i \(-0.374524\pi\)
\(350\) 0 0
\(351\) −3.99428 1.45380i −0.213199 0.0775980i
\(352\) 39.5896 + 14.4094i 2.11013 + 0.768025i
\(353\) −2.24694 + 3.89182i −0.119593 + 0.207141i −0.919606 0.392841i \(-0.871492\pi\)
0.800014 + 0.599982i \(0.204826\pi\)
\(354\) −0.484771 0.839648i −0.0257653 0.0446268i
\(355\) 0 0
\(356\) −44.8279 37.6151i −2.37587 1.99359i
\(357\) 0.315786 0.264976i 0.0167132 0.0140240i
\(358\) 1.69179 9.59464i 0.0894140 0.507092i
\(359\) −9.94626 + 3.62014i −0.524943 + 0.191064i −0.590879 0.806760i \(-0.701219\pi\)
0.0659357 + 0.997824i \(0.478997\pi\)
\(360\) 0 0
\(361\) −18.7010 3.35773i −0.984261 0.176723i
\(362\) −49.3252 −2.59248
\(363\) −3.71108 + 1.35072i −0.194781 + 0.0708946i
\(364\) −0.941588 + 5.34001i −0.0493526 + 0.279893i
\(365\) 0 0
\(366\) 3.42512 + 2.87402i 0.179034 + 0.150227i
\(367\) 0.313391 + 1.77733i 0.0163589 + 0.0927759i 0.991894 0.127067i \(-0.0405565\pi\)
−0.975535 + 0.219843i \(0.929445\pi\)
\(368\) 14.2522 + 24.6855i 0.742947 + 1.28682i
\(369\) 4.20148 7.27717i 0.218720 0.378834i
\(370\) 0 0
\(371\) 4.64297 + 1.68990i 0.241051 + 0.0877353i
\(372\) 3.62425 6.27739i 0.187909 0.325468i
\(373\) −6.48193 11.2270i −0.335622 0.581314i 0.647982 0.761655i \(-0.275613\pi\)
−0.983604 + 0.180342i \(0.942280\pi\)
\(374\) −9.64661 54.7086i −0.498814 2.82892i
\(375\) 0 0
\(376\) 35.7571 30.0038i 1.84403 1.54733i
\(377\) −3.30338 + 18.7344i −0.170132 + 0.964869i
\(378\) −1.43421 + 0.522011i −0.0737679 + 0.0268493i
\(379\) 33.1372 1.70214 0.851071 0.525051i \(-0.175954\pi\)
0.851071 + 0.525051i \(0.175954\pi\)
\(380\) 0 0
\(381\) 0.139012 0.00712181
\(382\) 7.02955 2.55855i 0.359663 0.130907i
\(383\) −3.50654 + 19.8866i −0.179176 + 1.01616i 0.754037 + 0.656832i \(0.228104\pi\)
−0.933213 + 0.359324i \(0.883007\pi\)
\(384\) 1.12374 0.942926i 0.0573454 0.0481185i
\(385\) 0 0
\(386\) 5.10471 + 28.9503i 0.259823 + 1.47353i
\(387\) 18.2675 + 31.6402i 0.928588 + 1.60836i
\(388\) −20.7799 + 35.9918i −1.05494 + 1.82721i
\(389\) 1.90648 + 0.693903i 0.0966625 + 0.0351823i 0.389899 0.920858i \(-0.372510\pi\)
−0.293236 + 0.956040i \(0.594732\pi\)
\(390\) 0 0
\(391\) 6.95762 12.0510i 0.351862 0.609443i
\(392\) −23.6049 40.8849i −1.19223 2.06500i
\(393\) −0.424825 2.40930i −0.0214296 0.121533i
\(394\) −20.0864 16.8545i −1.01194 0.849117i
\(395\) 0 0
\(396\) −12.3761 + 70.1881i −0.621920 + 3.52709i
\(397\) 7.54838 2.74738i 0.378842 0.137887i −0.145578 0.989347i \(-0.546504\pi\)
0.524420 + 0.851459i \(0.324282\pi\)
\(398\) 7.56914 0.379406
\(399\) 0.111592 + 0.419082i 0.00558657 + 0.0209803i
\(400\) 0 0
\(401\) 13.5128 4.91825i 0.674796 0.245606i 0.0181845 0.999835i \(-0.494211\pi\)
0.656611 + 0.754229i \(0.271989\pi\)
\(402\) −0.0841266 + 0.477106i −0.00419585 + 0.0237959i
\(403\) 13.8612 11.6309i 0.690473 0.579376i
\(404\) 4.81770 + 4.04253i 0.239690 + 0.201124i
\(405\) 0 0
\(406\) 3.41533 + 5.91553i 0.169500 + 0.293583i
\(407\) 2.96141 5.12931i 0.146792 0.254250i
\(408\) 6.65806 + 2.42334i 0.329623 + 0.119973i
\(409\) −0.227020 0.0826284i −0.0112254 0.00408571i 0.336401 0.941719i \(-0.390790\pi\)
−0.347627 + 0.937633i \(0.613012\pi\)
\(410\) 0 0
\(411\) −1.11015 1.92283i −0.0547595 0.0948462i
\(412\) −10.0835 57.1867i −0.496781 2.81738i
\(413\) −0.466179 0.391171i −0.0229392 0.0192483i
\(414\) −19.5296 + 16.3872i −0.959825 + 0.805389i
\(415\) 0 0
\(416\) −22.0378 + 8.02110i −1.08049 + 0.393267i
\(417\) −3.26168 −0.159725
\(418\) 56.4288 + 15.2145i 2.76002 + 0.744166i
\(419\) −22.7086 −1.10939 −0.554693 0.832055i \(-0.687164\pi\)
−0.554693 + 0.832055i \(0.687164\pi\)
\(420\) 0 0
\(421\) −4.33685 + 24.5955i −0.211365 + 1.19871i 0.675738 + 0.737142i \(0.263825\pi\)
−0.887103 + 0.461571i \(0.847286\pi\)
\(422\) 10.8947 9.14177i 0.530347 0.445014i
\(423\) 15.2212 + 12.7721i 0.740079 + 0.621000i
\(424\) 14.7470 + 83.6342i 0.716176 + 4.06164i
\(425\) 0 0
\(426\) −2.66708 + 4.61953i −0.129221 + 0.223817i
\(427\) 2.63719 + 0.959857i 0.127622 + 0.0464507i
\(428\) −63.9383 23.2716i −3.09057 1.12488i
\(429\) 1.85761 3.21747i 0.0896862 0.155341i
\(430\) 0 0
\(431\) 3.10128 + 17.5883i 0.149384 + 0.847196i 0.963742 + 0.266835i \(0.0859777\pi\)
−0.814359 + 0.580362i \(0.802911\pi\)
\(432\) −9.56453 8.02560i −0.460174 0.386132i
\(433\) 29.9613 25.1405i 1.43985 1.20818i 0.500257 0.865877i \(-0.333239\pi\)
0.939591 0.342299i \(-0.111206\pi\)
\(434\) 1.12821 6.39841i 0.0541559 0.307134i
\(435\) 0 0
\(436\) 20.6518 0.989042
\(437\) 8.37813 + 12.0051i 0.400780 + 0.574280i
\(438\) −6.34670 −0.303257
\(439\) −17.6050 + 6.40768i −0.840239 + 0.305822i −0.726054 0.687638i \(-0.758648\pi\)
−0.114185 + 0.993460i \(0.536426\pi\)
\(440\) 0 0
\(441\) 15.3947 12.9177i 0.733083 0.615129i
\(442\) 23.6889 + 19.8774i 1.12677 + 0.945471i
\(443\) −2.96093 16.7923i −0.140678 0.797826i −0.970736 0.240149i \(-0.922804\pi\)
0.830058 0.557677i \(-0.188307\pi\)
\(444\) 0.660372 + 1.14380i 0.0313399 + 0.0542822i
\(445\) 0 0
\(446\) −19.3236 7.03323i −0.915001 0.333033i
\(447\) 1.90499 + 0.693358i 0.0901028 + 0.0327947i
\(448\) −0.801654 + 1.38851i −0.0378746 + 0.0656007i
\(449\) −6.10161 10.5683i −0.287953 0.498749i 0.685368 0.728197i \(-0.259641\pi\)
−0.973321 + 0.229448i \(0.926308\pi\)
\(450\) 0 0
\(451\) 11.3700 + 9.54052i 0.535390 + 0.449246i
\(452\) −28.9372 + 24.2812i −1.36109 + 1.14209i
\(453\) 0.327195 1.85562i 0.0153730 0.0871845i
\(454\) −19.4779 + 7.08937i −0.914142 + 0.332721i
\(455\) 0 0
\(456\) −5.27909 + 5.26263i −0.247216 + 0.246445i
\(457\) 13.4079 0.627193 0.313596 0.949556i \(-0.398466\pi\)
0.313596 + 0.949556i \(0.398466\pi\)
\(458\) −68.5640 + 24.9553i −3.20379 + 1.16608i
\(459\) −1.05842 + 6.00262i −0.0494030 + 0.280178i
\(460\) 0 0
\(461\) −10.7371 9.00946i −0.500075 0.419613i 0.357546 0.933896i \(-0.383614\pi\)
−0.857621 + 0.514283i \(0.828058\pi\)
\(462\) −0.231649 1.31374i −0.0107773 0.0611209i
\(463\) 13.0889 + 22.6706i 0.608292 + 1.05359i 0.991522 + 0.129940i \(0.0414785\pi\)
−0.383230 + 0.923653i \(0.625188\pi\)
\(464\) −27.9393 + 48.3922i −1.29705 + 2.24655i
\(465\) 0 0
\(466\) −22.9201 8.34225i −1.06175 0.386447i
\(467\) −19.7941 + 34.2843i −0.915960 + 1.58649i −0.110470 + 0.993879i \(0.535236\pi\)
−0.805490 + 0.592609i \(0.798098\pi\)
\(468\) −19.8367 34.3582i −0.916952 1.58821i
\(469\) 0.0528039 + 0.299466i 0.00243826 + 0.0138280i
\(470\) 0 0
\(471\) 2.38447 2.00080i 0.109870 0.0921922i
\(472\) 1.81632 10.3009i 0.0836029 0.474135i
\(473\) −60.6411 + 22.0715i −2.78828 + 1.01485i
\(474\) −2.04020 −0.0937097
\(475\) 0 0
\(476\) 7.77548 0.356389
\(477\) −33.9707 + 12.3643i −1.55541 + 0.566123i
\(478\) −5.28968 + 29.9993i −0.241944 + 1.37214i
\(479\) 2.89476 2.42899i 0.132265 0.110983i −0.574255 0.818676i \(-0.694708\pi\)
0.706520 + 0.707693i \(0.250264\pi\)
\(480\) 0 0
\(481\) 0.572514 + 3.24689i 0.0261044 + 0.148045i
\(482\) −16.5322 28.6346i −0.753022 1.30427i
\(483\) 0.167077 0.289385i 0.00760225 0.0131675i
\(484\) −69.9985 25.4774i −3.18175 1.15806i
\(485\) 0 0
\(486\) 8.40410 14.5563i 0.381218 0.660288i
\(487\) 3.49493 + 6.05339i 0.158370 + 0.274305i 0.934281 0.356537i \(-0.116043\pi\)
−0.775911 + 0.630843i \(0.782709\pi\)
\(488\) 8.37622 + 47.5039i 0.379174 + 2.15040i
\(489\) 0.623089 + 0.522834i 0.0281771 + 0.0236434i
\(490\) 0 0
\(491\) −5.66765 + 32.1428i −0.255777 + 1.45059i 0.538292 + 0.842758i \(0.319070\pi\)
−0.794069 + 0.607827i \(0.792041\pi\)
\(492\) −3.11014 + 1.13200i −0.140216 + 0.0510345i
\(493\) 27.2787 1.22857
\(494\) −29.5065 + 13.7031i −1.32756 + 0.616530i
\(495\) 0 0
\(496\) 49.9446 18.1784i 2.24258 0.816232i
\(497\) −0.581393 + 3.29724i −0.0260790 + 0.147902i
\(498\) 2.70552 2.27020i 0.121237 0.101730i
\(499\) 21.2906 + 17.8650i 0.953100 + 0.799746i 0.979817 0.199897i \(-0.0640608\pi\)
−0.0267168 + 0.999643i \(0.508505\pi\)
\(500\) 0 0
\(501\) −0.647494 1.12149i −0.0289279 0.0501046i
\(502\) 3.09927 5.36809i 0.138327 0.239590i
\(503\) 15.3827 + 5.59886i 0.685883 + 0.249641i 0.661371 0.750059i \(-0.269975\pi\)
0.0245113 + 0.999700i \(0.492197\pi\)
\(504\) −7.65646 2.78672i −0.341046 0.124131i
\(505\) 0 0
\(506\) −22.5155 38.9979i −1.00093 1.73367i
\(507\) −0.200087 1.13475i −0.00888618 0.0503960i
\(508\) 2.00861 + 1.68542i 0.0891175 + 0.0747785i
\(509\) −27.2953 + 22.9034i −1.20984 + 1.01518i −0.210548 + 0.977584i \(0.567525\pi\)
−0.999293 + 0.0375938i \(0.988031\pi\)
\(510\) 0 0
\(511\) −3.74340 + 1.36249i −0.165598 + 0.0602728i
\(512\) 48.2924 2.13424
\(513\) −5.24702 3.68622i −0.231662 0.162751i
\(514\) 44.4694 1.96146
\(515\) 0 0
\(516\) 2.49886 14.1717i 0.110006 0.623875i
\(517\) −26.8857 + 22.5598i −1.18243 + 0.992177i
\(518\) 0.906869 + 0.760954i 0.0398455 + 0.0334344i
\(519\) −0.193812 1.09916i −0.00850739 0.0482478i
\(520\) 0 0
\(521\) −17.4659 + 30.2518i −0.765194 + 1.32536i 0.174950 + 0.984577i \(0.444024\pi\)
−0.940144 + 0.340778i \(0.889310\pi\)
\(522\) −46.9632 17.0932i −2.05552 0.748149i
\(523\) −12.7730 4.64899i −0.558524 0.203286i 0.0473057 0.998880i \(-0.484936\pi\)
−0.605830 + 0.795594i \(0.707159\pi\)
\(524\) 23.0727 39.9630i 1.00793 1.74579i
\(525\) 0 0
\(526\) 6.58646 + 37.3537i 0.287183 + 1.62870i
\(527\) −19.8763 16.6782i −0.865826 0.726515i
\(528\) 8.35979 7.01470i 0.363813 0.305276i
\(529\) −2.03521 + 11.5422i −0.0884873 + 0.501837i
\(530\) 0 0
\(531\) 4.45254 0.193224
\(532\) −3.46866 + 7.40834i −0.150385 + 0.321192i
\(533\) −8.26213 −0.357872
\(534\) −7.53071 + 2.74096i −0.325886 + 0.118613i
\(535\) 0 0
\(536\) −4.00380 + 3.35959i −0.172938 + 0.145112i
\(537\) −0.715727 0.600566i −0.0308859 0.0259163i
\(538\) 10.0713 + 57.1174i 0.434206 + 2.46251i
\(539\) 17.7485 + 30.7413i 0.764481 + 1.32412i
\(540\) 0 0
\(541\) 7.38859 + 2.68923i 0.317660 + 0.115619i 0.495929 0.868363i \(-0.334828\pi\)
−0.178269 + 0.983982i \(0.557050\pi\)
\(542\) 32.2386 + 11.7339i 1.38476 + 0.504013i
\(543\) −2.36513 + 4.09653i −0.101498 + 0.175799i
\(544\) 16.8147 + 29.1239i 0.720924 + 1.24868i
\(545\) 0 0
\(546\) 0.568854 + 0.477325i 0.0243447 + 0.0204276i
\(547\) −20.3369 + 17.0647i −0.869544 + 0.729634i −0.964002 0.265895i \(-0.914333\pi\)
0.0944579 + 0.995529i \(0.469888\pi\)
\(548\) 7.27224 41.2429i 0.310655 1.76181i
\(549\) −19.2952 + 7.02288i −0.823500 + 0.299729i
\(550\) 0 0
\(551\) −12.1691 + 25.9907i −0.518421 + 1.10724i
\(552\) 5.74340 0.244455
\(553\) −1.20335 + 0.437984i −0.0511717 + 0.0186250i
\(554\) 1.50681 8.54554i 0.0640182 0.363065i
\(555\) 0 0
\(556\) −47.1284 39.5455i −1.99869 1.67710i
\(557\) −0.661630 3.75229i −0.0280342 0.158990i 0.967577 0.252576i \(-0.0812779\pi\)
−0.995611 + 0.0935867i \(0.970167\pi\)
\(558\) 23.7684 + 41.1680i 1.00620 + 1.74278i
\(559\) 17.9613 31.1099i 0.759683 1.31581i
\(560\) 0 0
\(561\) −5.00618 1.82210i −0.211361 0.0769292i
\(562\) 25.8601 44.7910i 1.09084 1.88939i
\(563\) −6.08960 10.5475i −0.256646 0.444524i 0.708695 0.705515i \(-0.249284\pi\)
−0.965341 + 0.260991i \(0.915951\pi\)
\(564\) −1.35902 7.70741i −0.0572252 0.324540i
\(565\) 0 0
\(566\) 1.04872 0.879981i 0.0440810 0.0369884i
\(567\) 0.589440 3.34288i 0.0247542 0.140388i
\(568\) −54.0764 + 19.6822i −2.26900 + 0.825847i
\(569\) 22.8626 0.958451 0.479226 0.877692i \(-0.340918\pi\)
0.479226 + 0.877692i \(0.340918\pi\)
\(570\) 0 0
\(571\) 40.3908 1.69030 0.845152 0.534527i \(-0.179510\pi\)
0.845152 + 0.534527i \(0.179510\pi\)
\(572\) 65.8503 23.9676i 2.75334 1.00213i
\(573\) 0.124574 0.706496i 0.00520416 0.0295143i
\(574\) −2.27259 + 1.90693i −0.0948560 + 0.0795937i
\(575\) 0 0
\(576\) −2.03702 11.5525i −0.0848760 0.481355i
\(577\) −3.93190 6.81026i −0.163687 0.283515i 0.772501 0.635013i \(-0.219005\pi\)
−0.936188 + 0.351499i \(0.885672\pi\)
\(578\) 0.215179 0.372700i 0.00895025 0.0155023i
\(579\) 2.64913 + 0.964204i 0.110094 + 0.0400710i
\(580\) 0 0
\(581\) 1.10841 1.91982i 0.0459845 0.0796475i
\(582\) 2.84576 + 4.92901i 0.117961 + 0.204314i
\(583\) −11.0882 62.8844i −0.459227 2.60440i
\(584\) −52.4514 44.0120i −2.17045 1.82123i
\(585\) 0 0
\(586\) 14.1810 80.4242i 0.585810 3.32229i
\(587\) 37.7961 13.7566i 1.56001 0.567797i 0.589271 0.807935i \(-0.299415\pi\)
0.970739 + 0.240138i \(0.0771927\pi\)
\(588\) −7.91555 −0.326432
\(589\) 24.7576 11.4976i 1.02012 0.473751i
\(590\) 0 0
\(591\) −2.36293 + 0.860035i −0.0971978 + 0.0353771i
\(592\) −1.68168 + 9.53727i −0.0691166 + 0.391980i
\(593\) −26.1035 + 21.9034i −1.07194 + 0.899466i −0.995227 0.0975874i \(-0.968887\pi\)
−0.0767145 + 0.997053i \(0.524443\pi\)
\(594\) 15.1100 + 12.6788i 0.619969 + 0.520216i
\(595\) 0 0
\(596\) 19.1189 + 33.1150i 0.783142 + 1.35644i
\(597\) 0.362938 0.628627i 0.0148541 0.0257280i
\(598\) 23.5551 + 8.57334i 0.963238 + 0.350590i
\(599\) −16.8047 6.11643i −0.686623 0.249910i −0.0249346 0.999689i \(-0.507938\pi\)
−0.661689 + 0.749779i \(0.730160\pi\)
\(600\) 0 0
\(601\) −0.355966 0.616551i −0.0145201 0.0251496i 0.858674 0.512522i \(-0.171289\pi\)
−0.873194 + 0.487372i \(0.837955\pi\)
\(602\) −2.23982 12.7027i −0.0912884 0.517722i
\(603\) −1.70435 1.43012i −0.0694065 0.0582389i
\(604\) 27.2257 22.8451i 1.10780 0.929553i
\(605\) 0 0
\(606\) 0.809335 0.294574i 0.0328770 0.0119662i
\(607\) 34.3415 1.39388 0.696940 0.717129i \(-0.254544\pi\)
0.696940 + 0.717129i \(0.254544\pi\)
\(608\) −35.2498 + 3.02851i −1.42957 + 0.122822i
\(609\) 0.655057 0.0265443
\(610\) 0 0
\(611\) 3.39253 19.2400i 0.137247 0.778368i
\(612\) −43.5803 + 36.5682i −1.76163 + 1.47818i
\(613\) −22.9647 19.2696i −0.927534 0.778293i 0.0478390 0.998855i \(-0.484767\pi\)
−0.975373 + 0.220562i \(0.929211\pi\)
\(614\) 4.11393 + 23.3313i 0.166025 + 0.941573i
\(615\) 0 0
\(616\) 7.19590 12.4637i 0.289931 0.502175i
\(617\) 20.7677 + 7.55883i 0.836076 + 0.304307i 0.724350 0.689432i \(-0.242140\pi\)
0.111726 + 0.993739i \(0.464362\pi\)
\(618\) −7.47283 2.71989i −0.300601 0.109410i
\(619\) −9.72359 + 16.8417i −0.390824 + 0.676927i −0.992558 0.121769i \(-0.961143\pi\)
0.601734 + 0.798696i \(0.294477\pi\)
\(620\) 0 0
\(621\) 0.857958 + 4.86572i 0.0344287 + 0.195255i
\(622\) 47.5918 + 39.9343i 1.90826 + 1.60122i
\(623\) −3.85334 + 3.23333i −0.154381 + 0.129541i
\(624\) −1.05487 + 5.98246i −0.0422286 + 0.239490i
\(625\) 0 0
\(626\) −6.35337 −0.253932
\(627\) 3.96933 3.95696i 0.158520 0.158026i
\(628\) 58.7117 2.34285
\(629\) 4.44261 1.61698i 0.177138 0.0644731i
\(630\) 0 0
\(631\) 3.39379 2.84773i 0.135105 0.113366i −0.572731 0.819743i \(-0.694116\pi\)
0.707836 + 0.706377i \(0.249672\pi\)
\(632\) −16.8610 14.1480i −0.670694 0.562779i
\(633\) −0.236837 1.34317i −0.00941342 0.0533862i
\(634\) −9.06962 15.7090i −0.360201 0.623886i
\(635\) 0 0
\(636\) 13.3803 + 4.87005i 0.530565 + 0.193110i
\(637\) −18.5680 6.75818i −0.735689 0.267769i
\(638\) 44.1382 76.4496i 1.74745 3.02667i
\(639\) −12.2484 21.2148i −0.484538 0.839244i
\(640\) 0 0
\(641\) 19.6593 + 16.4961i 0.776496 + 0.651558i 0.942364 0.334590i \(-0.108598\pi\)
−0.165867 + 0.986148i \(0.553042\pi\)
\(642\) −7.13814 + 5.98961i −0.281720 + 0.236391i
\(643\) −6.45413 + 36.6032i −0.254526 + 1.44349i 0.542761 + 0.839887i \(0.317379\pi\)
−0.797287 + 0.603601i \(0.793732\pi\)
\(644\) 5.92270 2.15569i 0.233387 0.0849459i
\(645\) 0 0
\(646\) 26.6983 + 38.2562i 1.05043 + 1.50517i
\(647\) −20.6750 −0.812819 −0.406409 0.913691i \(-0.633219\pi\)
−0.406409 + 0.913691i \(0.633219\pi\)
\(648\) 54.8250 19.9547i 2.15373 0.783893i
\(649\) −1.36569 + 7.74519i −0.0536079 + 0.304025i
\(650\) 0 0
\(651\) −0.477300 0.400502i −0.0187068 0.0156969i
\(652\) 2.66412 + 15.1090i 0.104335 + 0.591714i
\(653\) 17.0168 + 29.4740i 0.665919 + 1.15341i 0.979035 + 0.203691i \(0.0652939\pi\)
−0.313116 + 0.949715i \(0.601373\pi\)
\(654\) 1.41411 2.44931i 0.0552962 0.0957758i
\(655\) 0 0
\(656\) −22.8053 8.30043i −0.890395 0.324077i
\(657\) 14.5733 25.2418i 0.568560 0.984775i
\(658\) −3.50751 6.07519i −0.136737 0.236836i
\(659\) −5.38526 30.5413i −0.209780 1.18972i −0.889739 0.456470i \(-0.849114\pi\)
0.679959 0.733250i \(-0.261998\pi\)
\(660\) 0 0
\(661\) −13.9912 + 11.7400i −0.544195 + 0.456634i −0.872970 0.487775i \(-0.837809\pi\)
0.328775 + 0.944408i \(0.393364\pi\)
\(662\) −7.80953 + 44.2901i −0.303526 + 1.72138i
\(663\) 2.78672 1.01428i 0.108227 0.0393915i
\(664\) 38.1024 1.47866
\(665\) 0 0
\(666\) −8.66163 −0.335631
\(667\) 20.7786 7.56280i 0.804552 0.292833i
\(668\) 4.24154 24.0550i 0.164110 0.930715i
\(669\) −1.51068 + 1.26761i −0.0584064 + 0.0490088i
\(670\) 0 0
\(671\) −6.29806 35.7181i −0.243134 1.37888i
\(672\) 0.403779 + 0.699366i 0.0155761 + 0.0269786i
\(673\) 13.0160 22.5444i 0.501731 0.869023i −0.498267 0.867024i \(-0.666030\pi\)
0.999998 0.00199979i \(-0.000636552\pi\)
\(674\) 79.3197 + 28.8700i 3.05528 + 1.11203i
\(675\) 0 0
\(676\) 10.8669 18.8221i 0.417958 0.723925i
\(677\) −0.0300638 0.0520720i −0.00115545 0.00200129i 0.865447 0.501000i \(-0.167034\pi\)
−0.866603 + 0.498999i \(0.833701\pi\)
\(678\) 0.898316 + 5.09460i 0.0344996 + 0.195657i
\(679\) 2.73663 + 2.29630i 0.105022 + 0.0881240i
\(680\) 0 0
\(681\) −0.345178 + 1.95760i −0.0132272 + 0.0750154i
\(682\) −78.9020 + 28.7180i −3.02131 + 1.09967i
\(683\) 31.5145 1.20587 0.602935 0.797790i \(-0.293998\pi\)
0.602935 + 0.797790i \(0.293998\pi\)
\(684\) −15.4003 57.8356i −0.588844 2.21140i
\(685\) 0 0
\(686\) −13.4915 + 4.91052i −0.515109 + 0.187484i
\(687\) −1.21506 + 6.89094i −0.0463574 + 0.262906i
\(688\) 80.8313 67.8255i 3.08166 2.58582i
\(689\) 27.2290 + 22.8479i 1.03734 + 0.870435i
\(690\) 0 0
\(691\) −4.69765 8.13657i −0.178707 0.309530i 0.762731 0.646716i \(-0.223858\pi\)
−0.941438 + 0.337186i \(0.890525\pi\)
\(692\) 10.5261 18.2318i 0.400143 0.693067i
\(693\) 5.75687 + 2.09533i 0.218686 + 0.0795950i
\(694\) −17.3057 6.29878i −0.656917 0.239098i
\(695\) 0 0
\(696\) 5.62953 + 9.75063i 0.213387 + 0.369597i
\(697\) 2.05730 + 11.6676i 0.0779260 + 0.441940i
\(698\) −44.9201 37.6924i −1.70025 1.42668i
\(699\) −1.79185 + 1.50354i −0.0677740 + 0.0568691i
\(700\) 0 0
\(701\) 6.95262 2.53055i 0.262597 0.0955775i −0.207367 0.978263i \(-0.566489\pi\)
0.469964 + 0.882686i \(0.344267\pi\)
\(702\) −10.9798 −0.414408
\(703\) −0.441229 + 4.95417i −0.0166413 + 0.186850i
\(704\) 20.7204 0.780930
\(705\) 0 0
\(706\) −2.01575 + 11.4319i −0.0758637 + 0.430245i
\(707\) 0.414122 0.347490i 0.0155747 0.0130687i
\(708\) −1.34346 1.12730i −0.0504903 0.0423664i
\(709\) −7.51502 42.6198i −0.282233 1.60062i −0.715006 0.699118i \(-0.753576\pi\)
0.432774 0.901502i \(-0.357535\pi\)
\(710\) 0 0
\(711\) 4.68474 8.11420i 0.175691 0.304306i
\(712\) −81.2440 29.5704i −3.04475 1.10820i
\(713\) −19.7640 7.19350i −0.740167 0.269399i
\(714\) 0.532419 0.922176i 0.0199253 0.0345116i
\(715\) 0 0
\(716\) −3.06021 17.3553i −0.114366 0.648599i
\(717\) 2.23784 + 1.87777i 0.0835738 + 0.0701268i
\(718\) −20.9446 + 17.5746i −0.781645 + 0.655878i
\(719\) 5.61767 31.8594i 0.209504 1.18815i −0.680690 0.732572i \(-0.738320\pi\)
0.890193 0.455583i \(-0.150569\pi\)
\(720\) 0 0
\(721\) −4.99151 −0.185894
\(722\) −48.3600 + 8.37154i −1.79977 + 0.311557i
\(723\) −3.17086 −0.117926
\(724\) −83.8416 + 30.5158i −3.11595 + 1.13411i
\(725\) 0 0
\(726\) −7.81471 + 6.55732i −0.290031 + 0.243365i
\(727\) −38.0516 31.9291i −1.41125 1.18418i −0.955834 0.293907i \(-0.905044\pi\)
−0.455421 0.890276i \(-0.650511\pi\)
\(728\) 1.39114 + 7.88957i 0.0515592 + 0.292407i
\(729\) 11.8713 + 20.5616i 0.439677 + 0.761542i
\(730\) 0 0
\(731\) −48.4051 17.6180i −1.79033 0.651625i
\(732\) 7.59998 + 2.76617i 0.280903 + 0.102240i
\(733\) 0.684201 1.18507i 0.0252715 0.0437716i −0.853113 0.521726i \(-0.825288\pi\)
0.878385 + 0.477955i \(0.158622\pi\)
\(734\) 2.33094 + 4.03730i 0.0860365 + 0.149020i
\(735\) 0 0
\(736\) 20.8824 + 17.5224i 0.769734 + 0.645883i
\(737\) 3.01045 2.52607i 0.110891 0.0930489i
\(738\) 3.76917 21.3760i 0.138745 0.786863i
\(739\) −16.6998 + 6.07823i −0.614312 + 0.223591i −0.630389 0.776279i \(-0.717105\pi\)
0.0160769 + 0.999871i \(0.494882\pi\)
\(740\) 0 0
\(741\) −0.276771 + 3.10761i −0.0101674 + 0.114161i
\(742\) 12.7630 0.468545
\(743\) 36.2978 13.2113i 1.33164 0.484676i 0.424469 0.905443i \(-0.360461\pi\)
0.907169 + 0.420766i \(0.138239\pi\)
\(744\) 1.85965 10.5466i 0.0681779 0.386656i
\(745\) 0 0
\(746\) −25.6526 21.5251i −0.939210 0.788091i
\(747\) 2.81649 + 15.9731i 0.103050 + 0.584426i
\(748\) −50.2434 87.0241i −1.83708 3.18192i
\(749\) −2.92438 + 5.06517i −0.106854 + 0.185077i
\(750\) 0 0
\(751\) −15.0160 5.46539i −0.547943 0.199435i 0.0531894 0.998584i \(-0.483061\pi\)
−0.601132 + 0.799150i \(0.705284\pi\)
\(752\) 28.6933 49.6983i 1.04634 1.81231i
\(753\) −0.297218 0.514797i −0.0108312 0.0187603i
\(754\) 8.53300 + 48.3931i 0.310754 + 1.76237i
\(755\) 0 0
\(756\) −2.11488 + 1.77460i −0.0769175 + 0.0645414i
\(757\) −0.338466 + 1.91954i −0.0123018 + 0.0697668i −0.990341 0.138656i \(-0.955722\pi\)
0.978039 + 0.208423i \(0.0668329\pi\)
\(758\) 80.4350 29.2759i 2.92153 1.06335i
\(759\) −4.31845 −0.156750
\(760\) 0 0
\(761\) −48.1168 −1.74423 −0.872115 0.489300i \(-0.837252\pi\)
−0.872115 + 0.489300i \(0.837252\pi\)
\(762\) 0.337429 0.122814i 0.0122238 0.00444909i
\(763\) 0.308260 1.74823i 0.0111597 0.0632901i
\(764\) 10.3657 8.69788i 0.375019 0.314678i
\(765\) 0 0
\(766\) 9.05780 + 51.3693i 0.327272 + 1.85605i
\(767\) −2.18896 3.79139i −0.0790388 0.136899i
\(768\) 2.88350 4.99437i 0.104049 0.180219i
\(769\) 6.00593 + 2.18598i 0.216579 + 0.0788284i 0.448031 0.894018i \(-0.352125\pi\)
−0.231452 + 0.972846i \(0.574348\pi\)
\(770\) 0 0
\(771\) 2.13230 3.69325i 0.0767929 0.133009i
\(772\) 26.5874 + 46.0507i 0.956900 + 1.65740i
\(773\) 6.20576 + 35.1946i 0.223206 + 1.26586i 0.866086 + 0.499895i \(0.166628\pi\)
−0.642880 + 0.765967i \(0.722261\pi\)
\(774\) 72.2947 + 60.6624i 2.59858 + 2.18047i
\(775\) 0 0
\(776\) −10.6624 + 60.4694i −0.382757 + 2.17073i
\(777\) 0.106682 0.0388292i 0.00382721 0.00139299i
\(778\) 5.24072 0.187889
\(779\) −12.0344 3.24476i −0.431177 0.116255i
\(780\) 0 0
\(781\) 40.6599 14.7990i 1.45493 0.529550i
\(782\) 6.24173 35.3986i 0.223204 1.26585i
\(783\) −7.41964 + 6.22582i −0.265156 + 0.222493i
\(784\) −44.4620 37.3081i −1.58793 1.33243i
\(785\) 0 0
\(786\) −3.15976 5.47286i −0.112705 0.195211i
\(787\) 0.970153 1.68035i 0.0345822 0.0598982i −0.848216 0.529650i \(-0.822323\pi\)
0.882799 + 0.469752i \(0.155657\pi\)
\(788\) −44.5695 16.2220i −1.58772 0.577884i
\(789\) 3.41810 + 1.24409i 0.121687 + 0.0442906i
\(790\) 0 0
\(791\) 1.62353 + 2.81204i 0.0577262 + 0.0999848i
\(792\) 18.2850 + 103.699i 0.649728 + 3.68479i
\(793\) 15.4660 + 12.9775i 0.549213 + 0.460845i
\(794\) 15.8952 13.3376i 0.564099 0.473335i
\(795\) 0 0
\(796\) 12.8658 4.68276i 0.456016 0.165976i
\(797\) −44.3436 −1.57073 −0.785365 0.619033i \(-0.787525\pi\)
−0.785365 + 0.619033i \(0.787525\pi\)
\(798\) 0.641120 + 0.918663i 0.0226954 + 0.0325203i
\(799\) −28.0150 −0.991099
\(800\) 0 0
\(801\) 6.39090 36.2446i 0.225811 1.28064i
\(802\) 28.4549 23.8765i 1.00478 0.843108i
\(803\) 39.4381 + 33.0925i 1.39174 + 1.16781i
\(804\) 0.152173 + 0.863016i 0.00536673 + 0.0304362i
\(805\) 0 0
\(806\) 23.3700 40.4781i 0.823175 1.42578i
\(807\) 5.22660 + 1.90233i 0.183985 + 0.0669651i
\(808\) 8.73139 + 3.17797i 0.307169 + 0.111800i
\(809\) 13.9319 24.1307i 0.489819 0.848392i −0.510112 0.860108i \(-0.670396\pi\)
0.999931 + 0.0117160i \(0.00372940\pi\)
\(810\) 0 0
\(811\) 5.29449 + 30.0265i 0.185915 + 1.05437i 0.924775 + 0.380515i \(0.124253\pi\)
−0.738860 + 0.673859i \(0.764636\pi\)
\(812\) 9.46501 + 7.94209i 0.332157 + 0.278713i
\(813\) 2.52035 2.11482i 0.0883924 0.0741700i
\(814\) 2.65670 15.0669i 0.0931173 0.528094i
\(815\) 0 0
\(816\) 8.71095 0.304944
\(817\) 38.3797 38.2600i 1.34274 1.33855i
\(818\) −0.624053 −0.0218195
\(819\) −3.20460 + 1.16638i −0.111978 + 0.0407566i
\(820\) 0 0
\(821\) 38.4716 32.2815i 1.34267 1.12663i 0.361738 0.932280i \(-0.382184\pi\)
0.980932 0.194354i \(-0.0622609\pi\)
\(822\) −4.39347 3.68656i −0.153240 0.128584i
\(823\) −7.55147 42.8265i −0.263228 1.49284i −0.774035 0.633143i \(-0.781765\pi\)
0.510807 0.859695i \(-0.329347\pi\)
\(824\) −42.8968 74.2994i −1.49438 2.58834i
\(825\) 0 0
\(826\) −1.47716 0.537644i −0.0513971 0.0187070i
\(827\) −0.559803 0.203752i −0.0194663 0.00708514i 0.332269 0.943185i \(-0.392186\pi\)
−0.351735 + 0.936100i \(0.614408\pi\)
\(828\) −23.0575 + 39.9368i −0.801304 + 1.38790i
\(829\) −9.62397 16.6692i −0.334254 0.578946i 0.649087 0.760714i \(-0.275151\pi\)
−0.983341 + 0.181769i \(0.941818\pi\)
\(830\) 0 0
\(831\) −0.637468 0.534900i −0.0221135 0.0185555i
\(832\) −8.83567 + 7.41401i −0.306322 + 0.257035i
\(833\) −4.92023 + 27.9040i −0.170476 + 0.966816i
\(834\) −7.91719 + 2.88162i −0.274150 + 0.0997824i
\(835\) 0 0
\(836\) 105.329 9.04937i 3.64287 0.312979i
\(837\) 9.21270 0.318438
\(838\) −55.1213 + 20.0625i −1.90413 + 0.693048i
\(839\) −8.84381 + 50.1557i −0.305322 + 1.73157i 0.316662 + 0.948539i \(0.397438\pi\)
−0.621984 + 0.783030i \(0.713673\pi\)
\(840\) 0 0
\(841\) 10.9908 + 9.22242i 0.378995 + 0.318014i
\(842\) 11.2026 + 63.5331i 0.386067 + 2.18949i
\(843\) −2.47997 4.29543i −0.0854147 0.147943i
\(844\) 12.8628 22.2791i 0.442757 0.766878i
\(845\) 0 0
\(846\) 48.2307 + 17.5545i 1.65821 + 0.603538i
\(847\) −3.20156 + 5.54526i −0.110007 + 0.190537i
\(848\) 52.2042 + 90.4204i 1.79270 + 3.10505i
\(849\) −0.0227978 0.129293i −0.000782418 0.00443731i
\(850\) 0 0
\(851\) 2.93571 2.46335i 0.100635 0.0844426i
\(852\) −1.67549 + 9.50216i −0.0574013 + 0.325539i
\(853\) −2.44273 + 0.889082i −0.0836375 + 0.0304416i −0.383500 0.923541i \(-0.625281\pi\)
0.299863 + 0.953982i \(0.403059\pi\)
\(854\) 7.24935 0.248067
\(855\) 0 0
\(856\) −100.528 −3.43597
\(857\) 37.7972 13.7570i 1.29113 0.469932i 0.397030 0.917806i \(-0.370041\pi\)
0.894097 + 0.447874i \(0.147819\pi\)
\(858\) 1.66647 9.45104i 0.0568925 0.322653i
\(859\) −21.5150 + 18.0532i −0.734083 + 0.615969i −0.931241 0.364403i \(-0.881273\pi\)
0.197159 + 0.980372i \(0.436829\pi\)
\(860\) 0 0
\(861\) 0.0494030 + 0.280179i 0.00168365 + 0.00954846i
\(862\) 23.0667 + 39.9527i 0.785654 + 1.36079i
\(863\) −14.9698 + 25.9284i −0.509577 + 0.882613i 0.490362 + 0.871519i \(0.336865\pi\)
−0.999938 + 0.0110937i \(0.996469\pi\)
\(864\) −11.2204 4.08390i −0.381727 0.138937i
\(865\) 0 0
\(866\) 50.5150 87.4946i 1.71657 2.97319i
\(867\) −0.0206355 0.0357418i −0.000700819 0.00121385i
\(868\) −2.04078 11.5738i −0.0692684 0.392841i
\(869\) 12.6777 + 10.6379i 0.430063 + 0.360866i
\(870\) 0 0
\(871\) −0.379870 + 2.15435i −0.0128714 + 0.0729973i
\(872\) 28.6718 10.4357i 0.970950 0.353397i
\(873\) −26.1379 −0.884633
\(874\) 30.9427 + 21.7384i 1.04665 + 0.735312i
\(875\) 0 0
\(876\) −10.7879 + 3.92648i −0.364490 + 0.132664i
\(877\) 1.40747 7.98213i 0.0475267 0.269537i −0.951779 0.306783i \(-0.900747\pi\)
0.999306 + 0.0372458i \(0.0118584\pi\)
\(878\) −37.0721 + 31.1072i −1.25112 + 1.04982i
\(879\) −5.99937 5.03407i −0.202354 0.169795i
\(880\) 0 0
\(881\) −4.46598 7.73530i −0.150463 0.260609i 0.780935 0.624612i \(-0.214743\pi\)
−0.931398 + 0.364003i \(0.881410\pi\)
\(882\) 25.9557 44.9565i 0.873973 1.51377i
\(883\) −1.42061 0.517061i −0.0478074 0.0174005i 0.318006 0.948089i \(-0.396987\pi\)
−0.365813 + 0.930688i \(0.619209\pi\)
\(884\) 52.5632 + 19.1314i 1.76789 + 0.643460i
\(885\) 0 0
\(886\) −22.0228 38.1446i −0.739870 1.28149i
\(887\) −4.83393 27.4146i −0.162307 0.920491i −0.951797 0.306728i \(-0.900766\pi\)
0.789490 0.613764i \(-0.210345\pi\)
\(888\) 1.49480 + 1.25429i 0.0501623 + 0.0420912i
\(889\) 0.172657 0.144876i 0.00579072 0.00485899i
\(890\) 0 0
\(891\) −41.2228 + 15.0039i −1.38101 + 0.502648i
\(892\) −37.1970 −1.24545
\(893\) 12.4975 26.6922i 0.418214 0.893220i
\(894\) 5.23661 0.175138
\(895\) 0 0
\(896\) 0.413006 2.34228i 0.0137976 0.0782499i
\(897\) 1.84149 1.54519i 0.0614855 0.0515924i
\(898\) −24.1475 20.2622i −0.805813 0.676157i
\(899\) −7.15966 40.6045i −0.238788 1.35423i
\(900\) 0 0
\(901\) 25.4850 44.1414i 0.849029 1.47056i
\(902\) 36.0275 + 13.1129i 1.19959 + 0.436613i
\(903\) −1.16237 0.423069i −0.0386814 0.0140789i
\(904\) −27.9051 + 48.3331i −0.928111 + 1.60754i
\(905\) 0 0
\(906\) −0.845184 4.79328i −0.0280794 0.159246i
\(907\) −24.2585 20.3553i −0.805492 0.675888i 0.144036 0.989573i \(-0.453992\pi\)
−0.949527 + 0.313685i \(0.898436\pi\)
\(908\) −28.7220 + 24.1006i −0.953172 + 0.799806i
\(909\) −0.686837 + 3.89525i −0.0227810 + 0.129197i
\(910\) 0 0
\(911\) 10.4766 0.347104 0.173552 0.984825i \(-0.444476\pi\)
0.173552 + 0.984825i \(0.444476\pi\)
\(912\) −3.88597 + 8.29963i −0.128677 + 0.274828i
\(913\) −28.6491 −0.948148
\(914\) 32.5454 11.8455i 1.07650 0.391816i
\(915\) 0 0
\(916\) −101.104 + 84.8364i −3.34057 + 2.80307i
\(917\) −3.03858 2.54967i −0.100343 0.0841975i
\(918\) 2.73403 + 15.5055i 0.0902364 + 0.511756i
\(919\) 5.30464 + 9.18791i 0.174984 + 0.303081i 0.940156 0.340745i \(-0.110679\pi\)
−0.765172 + 0.643826i \(0.777346\pi\)
\(920\) 0 0
\(921\) 2.13496 + 0.777061i 0.0703492 + 0.0256050i
\(922\) −34.0221 12.3830i −1.12046 0.407814i
\(923\) −12.0431 + 20.8593i −0.396403 + 0.686591i
\(924\) −1.20652 2.08975i −0.0396915 0.0687477i
\(925\) 0 0
\(926\) 51.8001 + 43.4655i 1.70226 + 1.42836i
\(927\) 27.9766 23.4751i 0.918871 0.771025i
\(928\) −9.27960 + 52.6272i −0.304618 + 1.72757i
\(929\) 13.3285 4.85116i 0.437293 0.159162i −0.113987 0.993482i \(-0.536362\pi\)
0.551279 + 0.834321i \(0.314140\pi\)
\(930\) 0 0
\(931\) −24.3915 17.1359i −0.799399 0.561607i
\(932\) −44.1200 −1.44520
\(933\) 5.59862 2.03773i 0.183290 0.0667123i
\(934\) −17.7574 + 100.707i −0.581039 + 3.29524i
\(935\) 0 0
\(936\) −44.9019 37.6772i −1.46766 1.23152i
\(937\) −7.73465 43.8654i −0.252680 1.43302i −0.801958 0.597380i \(-0.796208\pi\)
0.549278 0.835640i \(-0.314903\pi\)
\(938\) 0.392744 + 0.680253i 0.0128235 + 0.0222110i
\(939\) −0.304642 + 0.527656i −0.00994163 + 0.0172194i
\(940\) 0 0
\(941\) 28.5593 + 10.3947i 0.931006 + 0.338859i 0.762608 0.646860i \(-0.223918\pi\)
0.168398 + 0.985719i \(0.446141\pi\)
\(942\) 4.02023 6.96324i 0.130986 0.226875i
\(943\) 4.80181 + 8.31698i 0.156368 + 0.270838i
\(944\) −2.23303 12.6642i −0.0726791 0.412183i
\(945\) 0 0
\(946\) −127.696 + 107.150i −4.15177 + 3.48375i
\(947\) 5.37877 30.5045i 0.174787 0.991264i −0.763603 0.645686i \(-0.776572\pi\)
0.938390 0.345578i \(-0.112317\pi\)
\(948\) −3.46788 + 1.26220i −0.112631 + 0.0409945i
\(949\) −28.6582 −0.930285
\(950\) 0 0
\(951\) −1.73954 −0.0564086
\(952\) 10.7950 3.92908i 0.349869 0.127342i
\(953\) 3.86599 21.9251i 0.125232 0.710224i −0.855938 0.517078i \(-0.827020\pi\)
0.981170 0.193146i \(-0.0618691\pi\)
\(954\) −71.5346 + 60.0247i −2.31602 + 1.94337i
\(955\) 0 0
\(956\) 9.56828 + 54.2644i 0.309460 + 1.75504i
\(957\) −4.23283 7.33148i −0.136828 0.236993i
\(958\) 4.88059 8.45343i 0.157685 0.273118i
\(959\) −3.38277 1.23123i −0.109235 0.0397584i
\(960\) 0 0
\(961\) −4.10876 + 7.11657i −0.132540 + 0.229567i
\(962\) 4.25823 + 7.37548i 0.137291 + 0.237795i
\(963\) −7.43092 42.1428i −0.239458 1.35803i
\(964\) −45.8162 38.4444i −1.47564 1.23821i
\(965\) 0 0
\(966\) 0.149886 0.850044i 0.00482249 0.0273497i
\(967\) −16.4816 + 5.99883i −0.530014 + 0.192909i −0.593145 0.805096i \(-0.702114\pi\)
0.0631307 + 0.998005i \(0.479892\pi\)
\(968\) −110.056 −3.53734
\(969\) 4.45741 0.382961i 0.143193 0.0123025i
\(970\) 0 0
\(971\) 15.7599 5.73614i 0.505759 0.184081i −0.0765232 0.997068i \(-0.524382\pi\)
0.582283 + 0.812986i \(0.302160\pi\)
\(972\) 5.27953 29.9417i 0.169341 0.960381i
\(973\) −4.05109 + 3.39927i −0.129872 + 0.108975i
\(974\) 13.8314 + 11.6059i 0.443187 + 0.371878i
\(975\) 0 0
\(976\) 29.6518 + 51.3584i 0.949131 + 1.64394i
\(977\) −14.3920 + 24.9276i −0.460440 + 0.797506i −0.998983 0.0450925i \(-0.985642\pi\)
0.538543 + 0.842598i \(0.318975\pi\)
\(978\) 1.97436 + 0.718608i 0.0631330 + 0.0229785i
\(979\) 61.0872 + 22.2339i 1.95236 + 0.710599i
\(980\) 0 0
\(981\) 6.49419 + 11.2483i 0.207344 + 0.359130i
\(982\) 14.6402 + 83.0287i 0.467187 + 2.64955i
\(983\) 22.9176 + 19.2302i 0.730959 + 0.613348i 0.930393 0.366564i \(-0.119466\pi\)
−0.199434 + 0.979911i \(0.563910\pi\)
\(984\) −3.74593 + 3.14321i −0.119416 + 0.100202i
\(985\) 0 0
\(986\) 66.2147 24.1002i 2.10870 0.767506i
\(987\) −0.672737 −0.0214135
\(988\) −41.6766 + 41.5467i −1.32591 + 1.32178i
\(989\) −41.7553 −1.32774
\(990\) 0 0
\(991\) 7.97273 45.2156i 0.253262 1.43632i −0.547232 0.836981i \(-0.684319\pi\)
0.800495 0.599340i \(-0.204570\pi\)
\(992\) 38.9377 32.6726i 1.23627 1.03736i
\(993\) 3.30389 + 2.77229i 0.104846 + 0.0879760i
\(994\) 1.50181 + 8.51716i 0.0476344 + 0.270148i
\(995\) 0 0
\(996\) 3.19427 5.53264i 0.101214 0.175308i
\(997\) −50.6964 18.4520i −1.60557 0.584380i −0.625014 0.780614i \(-0.714907\pi\)
−0.980557 + 0.196234i \(0.937129\pi\)
\(998\) 67.4628 + 24.5545i 2.13550 + 0.777258i
\(999\) −0.839319 + 1.45374i −0.0265549 + 0.0459944i
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 475.2.l.c.176.3 18
5.2 odd 4 475.2.u.b.24.6 36
5.3 odd 4 475.2.u.b.24.1 36
5.4 even 2 95.2.k.a.81.1 yes 18
15.14 odd 2 855.2.bs.c.271.3 18
19.2 odd 18 9025.2.a.cf.1.9 9
19.4 even 9 inner 475.2.l.c.251.3 18
19.17 even 9 9025.2.a.cc.1.1 9
95.4 even 18 95.2.k.a.61.1 18
95.23 odd 36 475.2.u.b.99.6 36
95.42 odd 36 475.2.u.b.99.1 36
95.59 odd 18 1805.2.a.s.1.1 9
95.74 even 18 1805.2.a.v.1.9 9
285.194 odd 18 855.2.bs.c.631.3 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.k.a.61.1 18 95.4 even 18
95.2.k.a.81.1 yes 18 5.4 even 2
475.2.l.c.176.3 18 1.1 even 1 trivial
475.2.l.c.251.3 18 19.4 even 9 inner
475.2.u.b.24.1 36 5.3 odd 4
475.2.u.b.24.6 36 5.2 odd 4
475.2.u.b.99.1 36 95.42 odd 36
475.2.u.b.99.6 36 95.23 odd 36
855.2.bs.c.271.3 18 15.14 odd 2
855.2.bs.c.631.3 18 285.194 odd 18
1805.2.a.s.1.1 9 95.59 odd 18
1805.2.a.v.1.9 9 95.74 even 18
9025.2.a.cc.1.1 9 19.17 even 9
9025.2.a.cf.1.9 9 19.2 odd 18