Properties

Label 475.2.u.b.24.1
Level $475$
Weight $2$
Character 475.24
Analytic conductor $3.793$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [475,2,Mod(24,475)]
 
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([9, 16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("475.24");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.u (of order \(18\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 24.1
Character \(\chi\) \(=\) 475.24
Dual form 475.2.u.b.99.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.883478 - 2.42733i) q^{2} +(0.243956 + 0.0430161i) q^{3} +(-3.57933 + 3.00342i) q^{4} +(-0.111115 - 0.630167i) q^{6} +(-0.347830 + 0.200820i) q^{7} +(5.97847 + 3.45167i) q^{8} +(-2.76141 - 1.00507i) q^{9} +O(q^{10})\) \(q+(-0.883478 - 2.42733i) q^{2} +(0.243956 + 0.0430161i) q^{3} +(-3.57933 + 3.00342i) q^{4} +(-0.111115 - 0.630167i) q^{6} +(-0.347830 + 0.200820i) q^{7} +(5.97847 + 3.45167i) q^{8} +(-2.76141 - 1.00507i) q^{9} +(-2.59530 + 4.49520i) q^{11} +(-1.00240 + 0.578733i) q^{12} +(2.84549 - 0.501737i) q^{13} +(0.794758 + 0.666881i) q^{14} +(1.47378 - 8.35823i) q^{16} +(1.41708 + 3.89339i) q^{17} +7.59083i q^{18} +(-0.386682 + 4.34171i) q^{19} +(-0.0934938 + 0.0340290i) q^{21} +(13.2043 + 2.32827i) q^{22} +(-2.15882 - 2.57278i) q^{23} +(1.31001 + 1.09923i) q^{24} +(-3.73181 - 6.46368i) q^{26} +(-1.27402 - 0.735558i) q^{27} +(0.641855 - 1.76348i) q^{28} +(6.18683 + 2.25182i) q^{29} +(3.13119 + 5.42339i) q^{31} +(-7.99334 + 1.40944i) q^{32} +(-0.826506 + 0.984992i) q^{33} +(8.19861 - 6.87945i) q^{34} +(12.9027 - 4.69619i) q^{36} +1.14106i q^{37} +(10.8804 - 2.89720i) q^{38} +0.715757 q^{39} +(0.496543 - 2.81603i) q^{41} +(0.165199 + 0.196877i) q^{42} +(-7.99153 + 9.52394i) q^{43} +(-4.21150 - 23.8846i) q^{44} +(-4.33773 + 7.51317i) q^{46} +(2.31260 - 6.35381i) q^{47} +(0.719076 - 1.97565i) q^{48} +(-3.41934 + 5.92248i) q^{49} +(0.178227 + 1.01077i) q^{51} +(-8.67803 + 10.3421i) q^{52} +(-7.90752 - 9.42382i) q^{53} +(-0.659874 + 3.74233i) q^{54} -2.77266 q^{56} +(-0.281097 + 1.04255i) q^{57} -17.0069i q^{58} +(-1.42380 + 0.518220i) q^{59} +(-5.35269 + 4.49144i) q^{61} +(10.3980 - 12.3919i) q^{62} +(1.16234 - 0.204952i) q^{63} +(1.99595 + 3.45709i) q^{64} +(3.12111 + 1.13599i) q^{66} +(-0.258947 + 0.711451i) q^{67} +(-16.7657 - 9.67967i) q^{68} +(-0.415986 - 0.720510i) q^{69} +(-6.38582 - 5.35834i) q^{71} +(-13.0399 - 15.5403i) q^{72} +(9.76776 + 1.72232i) q^{73} +(2.76974 - 1.00810i) q^{74} +(-11.6559 - 16.7018i) q^{76} -2.08476i q^{77} +(-0.632356 - 1.73738i) q^{78} +(-0.553655 + 3.13994i) q^{79} +(6.47421 + 5.43251i) q^{81} +(-7.27414 + 1.28263i) q^{82} +(-4.77995 + 2.75971i) q^{83} +(0.232442 - 0.402602i) q^{84} +(30.1781 + 10.9839i) q^{86} +(1.41245 + 0.815478i) q^{87} +(-31.0319 + 17.9163i) q^{88} +(2.17478 + 12.3338i) q^{89} +(-0.888989 + 0.745950i) q^{91} +(15.4543 + 2.72500i) q^{92} +(0.530581 + 1.45776i) q^{93} -17.4660 q^{94} -2.01065 q^{96} +(3.04212 + 8.35815i) q^{97} +(17.3967 + 3.06752i) q^{98} +(11.6847 - 9.80464i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 6 q^{4} - 12 q^{6} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 6 q^{4} - 12 q^{6} - 6 q^{9} + 24 q^{14} - 6 q^{16} - 42 q^{21} + 30 q^{24} + 6 q^{26} - 30 q^{29} - 36 q^{31} + 24 q^{34} + 150 q^{36} - 72 q^{39} - 60 q^{41} - 84 q^{44} + 18 q^{46} - 18 q^{49} - 90 q^{51} + 132 q^{54} - 36 q^{59} - 60 q^{61} - 72 q^{64} + 78 q^{66} - 30 q^{69} - 24 q^{71} + 30 q^{74} - 66 q^{76} + 102 q^{79} + 54 q^{81} - 96 q^{84} + 126 q^{86} + 108 q^{89} + 60 q^{91} - 60 q^{94} - 132 q^{96} + 186 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.883478 2.42733i −0.624713 1.71639i −0.695146 0.718869i \(-0.744660\pi\)
0.0704330 0.997517i \(-0.477562\pi\)
\(3\) 0.243956 + 0.0430161i 0.140848 + 0.0248353i 0.243628 0.969869i \(-0.421663\pi\)
−0.102780 + 0.994704i \(0.532774\pi\)
\(4\) −3.57933 + 3.00342i −1.78967 + 1.50171i
\(5\) 0 0
\(6\) −0.111115 0.630167i −0.0453627 0.257265i
\(7\) −0.347830 + 0.200820i −0.131468 + 0.0759028i −0.564291 0.825576i \(-0.690851\pi\)
0.432824 + 0.901479i \(0.357517\pi\)
\(8\) 5.97847 + 3.45167i 2.11371 + 1.22035i
\(9\) −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 \(0.880604\pi\)
\(12\) −1.00240 + 0.578733i −0.289367 + 0.167066i
\(13\) 2.84549 0.501737i 0.789197 0.139157i 0.235499 0.971875i \(-0.424327\pi\)
0.553698 + 0.832718i \(0.313216\pi\)
\(14\) 0.794758 + 0.666881i 0.212408 + 0.178231i
\(15\) 0 0
\(16\) 1.47378 8.35823i 0.368445 2.08956i
\(17\) 1.41708 + 3.89339i 0.343692 + 0.944286i 0.984313 + 0.176429i \(0.0564546\pi\)
−0.640621 + 0.767857i \(0.721323\pi\)
\(18\) 7.59083i 1.78918i
\(19\) −0.386682 + 4.34171i −0.0887110 + 0.996057i
\(20\) 0 0
\(21\) −0.0934938 + 0.0340290i −0.0204020 + 0.00742573i
\(22\) 13.2043 + 2.32827i 2.81516 + 0.496388i
\(23\) −2.15882 2.57278i −0.450145 0.536462i 0.492476 0.870326i \(-0.336092\pi\)
−0.942621 + 0.333864i \(0.891647\pi\)
\(24\) 1.31001 + 1.09923i 0.267404 + 0.224379i
\(25\) 0 0
\(26\) −3.73181 6.46368i −0.731868 1.26763i
\(27\) −1.27402 0.735558i −0.245186 0.141558i
\(28\) 0.641855 1.76348i 0.121299 0.333267i
\(29\) 6.18683 + 2.25182i 1.14887 + 0.418153i 0.845107 0.534597i \(-0.179536\pi\)
0.303758 + 0.952749i \(0.401759\pi\)
\(30\) 0 0
\(31\) 3.13119 + 5.42339i 0.562379 + 0.974069i 0.997288 + 0.0735948i \(0.0234472\pi\)
−0.434909 + 0.900474i \(0.643220\pi\)
\(32\) −7.99334 + 1.40944i −1.41304 + 0.249156i
\(33\) −0.826506 + 0.984992i −0.143876 + 0.171465i
\(34\) 8.19861 6.87945i 1.40605 1.17982i
\(35\) 0 0
\(36\) 12.9027 4.69619i 2.15045 0.782698i
\(37\) 1.14106i 0.187590i 0.995592 + 0.0937949i \(0.0298998\pi\)
−0.995592 + 0.0937949i \(0.970100\pi\)
\(38\) 10.8804 2.89720i 1.76504 0.469988i
\(39\) 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 \(-0.0161233\pi\)
\(42\) 0.165199 + 0.196877i 0.0254908 + 0.0303788i
\(43\) −7.99153 + 9.52394i −1.21870 + 1.45239i −0.365491 + 0.930815i \(0.619099\pi\)
−0.853207 + 0.521572i \(0.825346\pi\)
\(44\) −4.21150 23.8846i −0.634908 3.60074i
\(45\) 0 0
\(46\) −4.33773 + 7.51317i −0.639564 + 1.10776i
\(47\) 2.31260 6.35381i 0.337327 0.926798i −0.648822 0.760940i \(-0.724738\pi\)
0.986150 0.165859i \(-0.0530395\pi\)
\(48\) 0.719076 1.97565i 0.103790 0.285160i
\(49\) −3.41934 + 5.92248i −0.488478 + 0.846068i
\(50\) 0 0
\(51\) 0.178227 + 1.01077i 0.0249567 + 0.141537i
\(52\) −8.67803 + 10.3421i −1.20343 + 1.43419i
\(53\) −7.90752 9.42382i −1.08618 1.29446i −0.952867 0.303387i \(-0.901883\pi\)
−0.133314 0.991074i \(-0.542562\pi\)
\(54\) −0.659874 + 3.74233i −0.0897975 + 0.509267i
\(55\) 0 0
\(56\) −2.77266 −0.370512
\(57\) −0.281097 + 1.04255i −0.0372322 + 0.138090i
\(58\) 17.0069i 2.23312i
\(59\) −1.42380 + 0.518220i −0.185363 + 0.0674665i −0.433034 0.901378i \(-0.642557\pi\)
0.247671 + 0.968844i \(0.420335\pi\)
\(60\) 0 0
\(61\) −5.35269 + 4.49144i −0.685342 + 0.575070i −0.917562 0.397593i \(-0.869845\pi\)
0.232220 + 0.972663i \(0.425401\pi\)
\(62\) 10.3980 12.3919i 1.32055 1.57377i
\(63\) 1.16234 0.204952i 0.146441 0.0258216i
\(64\) 1.99595 + 3.45709i 0.249494 + 0.432136i
\(65\) 0 0
\(66\) 3.12111 + 1.13599i 0.384182 + 0.139831i
\(67\) −0.258947 + 0.711451i −0.0316354 + 0.0869175i −0.954505 0.298195i \(-0.903615\pi\)
0.922869 + 0.385113i \(0.125838\pi\)
\(68\) −16.7657 9.67967i −2.03314 1.17383i
\(69\) −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 \(0.886928\pi\)
\(72\) −13.0399 15.5403i −1.53676 1.83144i
\(73\) 9.76776 + 1.72232i 1.14323 + 0.201582i 0.713018 0.701146i \(-0.247328\pi\)
0.430212 + 0.902728i \(0.358439\pi\)
\(74\) 2.76974 1.00810i 0.321976 0.117190i
\(75\) 0 0
\(76\) −11.6559 16.7018i −1.33702 1.91583i
\(77\) 2.08476i 0.237580i
\(78\) −0.632356 1.73738i −0.0716002 0.196720i
\(79\) −0.553655 + 3.13994i −0.0622911 + 0.353270i 0.937692 + 0.347467i \(0.112958\pi\)
−0.999983 + 0.00580301i \(0.998153\pi\)
\(80\) 0 0
\(81\) 6.47421 + 5.43251i 0.719357 + 0.603612i
\(82\) −7.27414 + 1.28263i −0.803294 + 0.141642i
\(83\) −4.77995 + 2.75971i −0.524668 + 0.302917i −0.738842 0.673878i \(-0.764627\pi\)
0.214174 + 0.976795i \(0.431294\pi\)
\(84\) 0.232442 0.402602i 0.0253615 0.0439275i
\(85\) 0 0
\(86\) 30.1781 + 10.9839i 3.25419 + 1.18443i
\(87\) 1.41245 + 0.815478i 0.151431 + 0.0874285i
\(88\) −31.0319 + 17.9163i −3.30801 + 1.90988i
\(89\) 2.17478 + 12.3338i 0.230527 + 1.30738i 0.851833 + 0.523814i \(0.175491\pi\)
−0.621306 + 0.783568i \(0.713398\pi\)
\(90\) 0 0
\(91\) −0.888989 + 0.745950i −0.0931914 + 0.0781968i
\(92\) 15.4543 + 2.72500i 1.61122 + 0.284101i
\(93\) 0.530581 + 1.45776i 0.0550187 + 0.151163i
\(94\) −17.4660 −1.80148
\(95\) 0 0
\(96\) −2.01065 −0.205211
\(97\) 3.04212 + 8.35815i 0.308880 + 0.848642i 0.992876 + 0.119155i \(0.0380187\pi\)
−0.683995 + 0.729487i \(0.739759\pi\)
\(98\) 17.3967 + 3.06752i 1.75734 + 0.309866i
\(99\) 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 \(0.923113\pi\)
\(102\) 2.29603 1.32561i 0.227341 0.131255i
\(103\) 10.7628 + 6.21391i 1.06049 + 0.612275i 0.925568 0.378581i \(-0.123588\pi\)
0.134923 + 0.990856i \(0.456921\pi\)
\(104\) 18.7435 + 6.82208i 1.83795 + 0.668960i
\(105\) 0 0
\(106\) −15.8886 + 27.5199i −1.54324 + 2.67297i
\(107\) −12.6112 + 7.28110i −1.21917 + 0.703890i −0.964741 0.263200i \(-0.915222\pi\)
−0.254432 + 0.967091i \(0.581889\pi\)
\(108\) 6.76934 1.19362i 0.651380 0.114856i
\(109\) −3.38582 2.84104i −0.324303 0.272122i 0.466071 0.884747i \(-0.345669\pi\)
−0.790374 + 0.612625i \(0.790114\pi\)
\(110\) 0 0
\(111\) −0.0490841 + 0.278370i −0.00465885 + 0.0264217i
\(112\) 1.16587 + 3.20321i 0.110165 + 0.302675i
\(113\) 8.08453i 0.760528i −0.924878 0.380264i \(-0.875833\pi\)
0.924878 0.380264i \(-0.124167\pi\)
\(114\) 2.77897 0.238757i 0.260274 0.0223616i
\(115\) 0 0
\(116\) −28.9079 + 10.5216i −2.68403 + 0.976907i
\(117\) −8.36186 1.47442i −0.773054 0.136310i
\(118\) 2.51579 + 2.99820i 0.231597 + 0.276006i
\(119\) −1.27477 1.06966i −0.116858 0.0980557i
\(120\) 0 0
\(121\) −7.97122 13.8065i −0.724656 1.25514i
\(122\) 15.6312 + 9.02468i 1.41518 + 0.817056i
\(123\) 0.242269 0.665629i 0.0218447 0.0600178i
\(124\) −27.4963 10.0078i −2.46924 0.898730i
\(125\) 0 0
\(126\) −1.52439 2.64032i −0.135804 0.235219i
\(127\) 0.552642 0.0974458i 0.0490391 0.00864691i −0.149075 0.988826i \(-0.547630\pi\)
0.198114 + 0.980179i \(0.436518\pi\)
\(128\) −3.80642 + 4.53632i −0.336444 + 0.400958i
\(129\) −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 \(0.246897\pi\)
\(132\) 6.00796i 0.522926i
\(133\) −0.737403 1.58783i −0.0639409 0.137683i
\(134\) 1.95570 0.168947
\(135\) 0 0
\(136\) −4.96675 + 28.1678i −0.425895 + 2.41537i
\(137\) −5.76126 6.86600i −0.492217 0.586602i 0.461563 0.887108i \(-0.347289\pi\)
−0.953780 + 0.300506i \(0.902845\pi\)
\(138\) −1.38140 + 1.64629i −0.117593 + 0.140142i
\(139\) 2.28639 + 12.9668i 0.193929 + 1.09983i 0.913935 + 0.405860i \(0.133028\pi\)
−0.720006 + 0.693968i \(0.755861\pi\)
\(140\) 0 0
\(141\) 0.837488 1.45057i 0.0705292 0.122160i
\(142\) −7.36475 + 20.2345i −0.618036 + 1.69804i
\(143\) −5.12951 + 14.0932i −0.428951 + 1.17853i
\(144\) −12.4703 + 21.5993i −1.03920 + 1.79994i
\(145\) 0 0
\(146\) −4.44895 25.2313i −0.368198 2.08815i
\(147\) −1.08893 + 1.29774i −0.0898135 + 0.107036i
\(148\) −3.42709 4.08425i −0.281705 0.335723i
\(149\) 1.42107 8.05930i 0.116419 0.660243i −0.869619 0.493723i \(-0.835636\pi\)
0.986038 0.166520i \(-0.0532532\pi\)
\(150\) 0 0
\(151\) 7.60636 0.618997 0.309498 0.950900i \(-0.399839\pi\)
0.309498 + 0.950900i \(0.399839\pi\)
\(152\) −17.2979 + 24.6221i −1.40305 + 1.99712i
\(153\) 12.1755i 0.984333i
\(154\) −5.06040 + 1.84184i −0.407779 + 0.148419i
\(155\) 0 0
\(156\) −2.56193 + 2.14972i −0.205119 + 0.172115i
\(157\) 8.07689 9.62566i 0.644606 0.768212i −0.340484 0.940250i \(-0.610591\pi\)
0.985090 + 0.172039i \(0.0550354\pi\)
\(158\) 8.11082 1.43016i 0.645262 0.113777i
\(159\) −1.52371 2.63915i −0.120838 0.209298i
\(160\) 0 0
\(161\) 1.26757 + 0.461357i 0.0998984 + 0.0363600i
\(162\) 7.46669 20.5146i 0.586639 1.61178i
\(163\) −2.84359 1.64175i −0.222727 0.128591i 0.384485 0.923131i \(-0.374379\pi\)
−0.607212 + 0.794540i \(0.707712\pi\)
\(164\) 6.68043 + 11.5708i 0.521654 + 0.903531i
\(165\) 0 0
\(166\) 10.9217 + 9.16441i 0.847689 + 0.711296i
\(167\) −3.36026 4.00460i −0.260025 0.309885i 0.620199 0.784445i \(-0.287052\pi\)
−0.880224 + 0.474559i \(0.842607\pi\)
\(168\) −0.676407 0.119269i −0.0521860 0.00920179i
\(169\) −4.37093 + 1.59089i −0.336226 + 0.122376i
\(170\) 0 0
\(171\) 5.43153 11.6006i 0.415359 0.887122i
\(172\) 58.0913i 4.42942i
\(173\) 1.54100 + 4.23385i 0.117160 + 0.321894i 0.984387 0.176019i \(-0.0563221\pi\)
−0.867227 + 0.497913i \(0.834100\pi\)
\(174\) 0.731571 4.14895i 0.0554603 0.314531i
\(175\) 0 0
\(176\) 33.7470 + 28.3171i 2.54378 + 2.13448i
\(177\) −0.369636 + 0.0651768i −0.0277835 + 0.00489899i
\(178\) 28.0169 16.1756i 2.09996 1.21241i
\(179\) −1.88583 + 3.26636i −0.140954 + 0.244139i −0.927856 0.372939i \(-0.878350\pi\)
0.786902 + 0.617078i \(0.211684\pi\)
\(180\) 0 0
\(181\) −17.9437 6.53096i −1.33374 0.485442i −0.425906 0.904767i \(-0.640045\pi\)
−0.907836 + 0.419325i \(0.862267\pi\)
\(182\) 2.59607 + 1.49884i 0.192434 + 0.111102i
\(183\) −1.49903 + 0.865463i −0.110811 + 0.0639768i
\(184\) −4.02605 22.8328i −0.296804 1.68326i
\(185\) 0 0
\(186\) 3.06972 2.57580i 0.225082 0.188867i
\(187\) −21.1793 3.73449i −1.54879 0.273093i
\(188\) 10.8056 + 29.6881i 0.788078 + 2.16523i
\(189\) 0.590859 0.0429787
\(190\) 0 0
\(191\) 2.89599 0.209547 0.104773 0.994496i \(-0.466588\pi\)
0.104773 + 0.994496i \(0.466588\pi\)
\(192\) 0.338214 + 0.929236i 0.0244085 + 0.0670619i
\(193\) −11.2075 1.97618i −0.806733 0.142249i −0.244952 0.969535i \(-0.578772\pi\)
−0.561781 + 0.827286i \(0.689883\pi\)
\(194\) 17.6004 14.7685i 1.26363 1.06032i
\(195\) 0 0
\(196\) −5.54870 31.4682i −0.396336 2.24773i
\(197\) −8.79093 + 5.07545i −0.626328 + 0.361610i −0.779329 0.626616i \(-0.784440\pi\)
0.153001 + 0.988226i \(0.451106\pi\)
\(198\) −34.1223 19.7005i −2.42497 1.40006i
\(199\) −2.75352 1.00220i −0.195192 0.0710440i 0.242575 0.970133i \(-0.422008\pi\)
−0.437766 + 0.899089i \(0.644230\pi\)
\(200\) 0 0
\(201\) −0.0937755 + 0.162424i −0.00661441 + 0.0114565i
\(202\) 3.01101 1.73841i 0.211854 0.122314i
\(203\) −2.60418 + 0.459187i −0.182777 + 0.0322286i
\(204\) −3.67371 3.08261i −0.257211 0.215826i
\(205\) 0 0
\(206\) 5.57454 31.6148i 0.388397 2.20271i
\(207\) 3.37556 + 9.27428i 0.234618 + 0.644607i
\(208\) 24.5227i 1.70034i
\(209\) −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 \(0.328197\pi\)
\(212\) 56.6073 + 9.98140i 3.88781 + 0.685525i
\(213\) −1.32737 1.58189i −0.0909496 0.108389i
\(214\) 28.8154 + 24.1790i 1.96978 + 1.65284i
\(215\) 0 0
\(216\) −5.07781 8.79503i −0.345501 0.598426i
\(217\) −2.17825 1.25761i −0.147869 0.0853723i
\(218\) −3.90486 + 10.7285i −0.264470 + 0.726626i
\(219\) 2.30882 + 0.840341i 0.156015 + 0.0567850i
\(220\) 0 0
\(221\) 5.98574 + 10.3676i 0.402644 + 0.697400i
\(222\) 0.719061 0.126790i 0.0482602 0.00850958i
\(223\) 5.11713 6.09836i 0.342669 0.408376i −0.566996 0.823721i \(-0.691894\pi\)
0.909664 + 0.415344i \(0.136339\pi\)
\(224\) 2.49728 2.09547i 0.166857 0.140009i
\(225\) 0 0
\(226\) −19.6239 + 7.14250i −1.30536 + 0.475112i
\(227\) 8.02439i 0.532597i 0.963891 + 0.266299i \(0.0858008\pi\)
−0.963891 + 0.266299i \(0.914199\pi\)
\(228\) −2.12509 4.57590i −0.140737 0.303046i
\(229\) 28.2466 1.86659 0.933295 0.359111i \(-0.116920\pi\)
0.933295 + 0.359111i \(0.116920\pi\)
\(230\) 0 0
\(231\) 0.0896780 0.508589i 0.00590038 0.0334627i
\(232\) 29.2152 + 34.8174i 1.91807 + 2.28587i
\(233\) 6.06953 7.23338i 0.397628 0.473875i −0.529667 0.848206i \(-0.677683\pi\)
0.927295 + 0.374331i \(0.122128\pi\)
\(234\) 3.80860 + 21.5996i 0.248976 + 1.41201i
\(235\) 0 0
\(236\) 3.53981 6.13114i 0.230422 0.399103i
\(237\) −0.270135 + 0.742191i −0.0175472 + 0.0482105i
\(238\) −1.47019 + 4.03932i −0.0952985 + 0.261831i
\(239\) 5.89638 10.2128i 0.381405 0.660613i −0.609858 0.792511i \(-0.708774\pi\)
0.991263 + 0.131897i \(0.0421069\pi\)
\(240\) 0 0
\(241\) −2.22273 12.6057i −0.143179 0.812007i −0.968811 0.247799i \(-0.920293\pi\)
0.825633 0.564208i \(-0.190818\pi\)
\(242\) −26.4707 + 31.5466i −1.70160 + 2.02789i
\(243\) 4.18258 + 4.98461i 0.268313 + 0.319763i
\(244\) 5.66939 32.1527i 0.362946 2.05837i
\(245\) 0 0
\(246\) −1.82974 −0.116660
\(247\) 1.07810 + 12.5483i 0.0685976 + 0.798430i
\(248\) 43.2314i 2.74520i
\(249\) −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 \(0.253648\pi\)
\(252\) −3.54485 + 4.22459i −0.223305 + 0.266124i
\(253\) 17.1680 3.02717i 1.07934 0.190317i
\(254\) −0.724781 1.25536i −0.0454768 0.0787681i
\(255\) 0 0
\(256\) 21.8764 + 7.96235i 1.36727 + 0.497647i
\(257\) 5.88802 16.1772i 0.367285 1.00911i −0.609105 0.793090i \(-0.708471\pi\)
0.976390 0.216017i \(-0.0693066\pi\)
\(258\) 6.88966 + 3.97774i 0.428931 + 0.247644i
\(259\) −0.229148 0.396897i −0.0142386 0.0246620i
\(260\) 0 0
\(261\) −14.8211 12.4364i −0.917406 0.769795i
\(262\) −16.3980 19.5424i −1.01307 1.20733i
\(263\) −14.4607 2.54981i −0.891685 0.157228i −0.291009 0.956720i \(-0.593991\pi\)
−0.600677 + 0.799492i \(0.705102\pi\)
\(264\) −8.34112 + 3.03592i −0.513360 + 0.186848i
\(265\) 0 0
\(266\) −3.20272 + 3.19274i −0.196372 + 0.195759i
\(267\) 3.10246i 0.189868i
\(268\) −1.20993 3.32424i −0.0739080 0.203061i
\(269\) 3.89891 22.1118i 0.237721 1.34818i −0.599086 0.800685i \(-0.704469\pi\)
0.836807 0.547498i \(-0.184420\pi\)
\(270\) 0 0
\(271\) 10.1742 + 8.53716i 0.618038 + 0.518596i 0.897186 0.441652i \(-0.145608\pi\)
−0.279148 + 0.960248i \(0.590052\pi\)
\(272\) 34.6303 6.10626i 2.09977 0.370246i
\(273\) −0.248962 + 0.143738i −0.0150679 + 0.00869944i
\(274\) −11.5761 + 20.0505i −0.699340 + 1.21129i
\(275\) 0 0
\(276\) 3.65294 + 1.32956i 0.219881 + 0.0800303i
\(277\) −2.90921 1.67963i −0.174797 0.100919i 0.410049 0.912064i \(-0.365512\pi\)
−0.584846 + 0.811144i \(0.698845\pi\)
\(278\) 29.4548 17.0057i 1.76658 1.01993i
\(279\) −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 \(0.0740504\pi\)
\(282\) −4.26093 0.751316i −0.253735 0.0447402i
\(283\) 0.181265 + 0.498021i 0.0107751 + 0.0296043i 0.944964 0.327176i \(-0.106097\pi\)
−0.934188 + 0.356780i \(0.883875\pi\)
\(284\) 38.9503 2.31127
\(285\) 0 0
\(286\) 38.7407 2.29079
\(287\) 0.392803 + 1.07922i 0.0231864 + 0.0637042i
\(288\) 23.4895 + 4.14183i 1.38413 + 0.244060i
\(289\) −0.127626 + 0.107091i −0.00750741 + 0.00629946i
\(290\) 0 0
\(291\) 0.382609 + 2.16988i 0.0224289 + 0.127201i
\(292\) −40.1349 + 23.1719i −2.34872 + 1.35603i
\(293\) 27.3793 + 15.8074i 1.59951 + 0.923480i 0.991580 + 0.129492i \(0.0413348\pi\)
0.607934 + 0.793988i \(0.291999\pi\)
\(294\) 4.11209 + 1.49668i 0.239822 + 0.0872881i
\(295\) 0 0
\(296\) −3.93858 + 6.82182i −0.228925 + 0.396510i
\(297\) 6.61296 3.81799i 0.383723 0.221543i
\(298\) −20.8181 + 3.67079i −1.20596 + 0.212643i
\(299\) −7.43376 6.23766i −0.429905 0.360733i
\(300\) 0 0
\(301\) 0.867101 4.91757i 0.0499789 0.283444i
\(302\) −6.72005 18.4632i −0.386695 1.06244i
\(303\) 0.333425i 0.0191548i
\(304\) 35.7192 + 9.63072i 2.04863 + 0.552359i
\(305\) 0 0
\(306\) −29.5541 + 10.7568i −1.68949 + 0.614926i
\(307\) 9.03222 + 1.59262i 0.515496 + 0.0908958i 0.425343 0.905032i \(-0.360153\pi\)
0.0901527 + 0.995928i \(0.471264\pi\)
\(308\) 6.26139 + 7.46204i 0.356776 + 0.425189i
\(309\) 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 \(0.594485\pi\)
\(312\) 4.27914 + 2.47056i 0.242258 + 0.139868i
\(313\) 0.841224 2.31124i 0.0475488 0.130639i −0.913645 0.406512i \(-0.866745\pi\)
0.961194 + 0.275873i \(0.0889670\pi\)
\(314\) −30.5005 11.1013i −1.72124 0.626480i
\(315\) 0 0
\(316\) −7.44882 12.9017i −0.419029 0.725779i
\(317\) −6.91555 + 1.21940i −0.388416 + 0.0684882i −0.364446 0.931225i \(-0.618742\pi\)
−0.0239697 + 0.999713i \(0.507631\pi\)
\(318\) −5.05993 + 6.03019i −0.283747 + 0.338156i
\(319\) −26.1791 + 21.9669i −1.46575 + 1.22991i
\(320\) 0 0
\(321\) −3.38979 + 1.23378i −0.189200 + 0.0688631i
\(322\) 3.48441i 0.194179i
\(323\) −17.4519 + 4.64704i −0.971052 + 0.258568i
\(324\) −39.4894 −2.19386
\(325\) 0 0
\(326\) −1.47282 + 8.35278i −0.0815720 + 0.462618i
\(327\) −0.703781 0.838733i −0.0389192 0.0463821i
\(328\) 12.6886 15.1217i 0.700610 0.834955i
\(329\) 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 \(0.325480\pi\)
\(332\) 8.82049 24.2341i 0.484087 1.33002i
\(333\) 1.14685 3.15095i 0.0628471 0.172671i
\(334\) −6.75180 + 11.6945i −0.369442 + 0.639892i
\(335\) 0 0
\(336\) 0.146632 + 0.831594i 0.00799946 + 0.0453672i
\(337\) 21.0048 25.0326i 1.14420 1.36361i 0.222866 0.974849i \(-0.428459\pi\)
0.921339 0.388761i \(-0.127097\pi\)
\(338\) 7.72324 + 9.20420i 0.420089 + 0.500643i
\(339\) 0.347764 1.97227i 0.0188880 0.107119i
\(340\) 0 0
\(341\) −32.5056 −1.76028
\(342\) −32.9572 2.93524i −1.78212 0.158720i
\(343\) 5.55817i 0.300113i
\(344\) −80.6507 + 29.3545i −4.34839 + 1.58269i
\(345\) 0 0
\(346\) 8.91554 7.48102i 0.479302 0.402182i
\(347\) −4.58277 + 5.46153i −0.246016 + 0.293191i −0.874895 0.484313i \(-0.839070\pi\)
0.628879 + 0.777503i \(0.283514\pi\)
\(348\) −7.50485 + 1.32331i −0.402302 + 0.0709368i
\(349\) 11.3504 + 19.6595i 0.607575 + 1.05235i 0.991639 + 0.129044i \(0.0411909\pi\)
−0.384064 + 0.923307i \(0.625476\pi\)
\(350\) 0 0
\(351\) −3.99428 1.45380i −0.213199 0.0775980i
\(352\) 14.4094 39.5896i 0.768025 2.11013i
\(353\) −3.89182 2.24694i −0.207141 0.119593i 0.392841 0.919606i \(-0.371492\pi\)
−0.599982 + 0.800014i \(0.704826\pi\)
\(354\) 0.484771 + 0.839648i 0.0257653 + 0.0446268i
\(355\) 0 0
\(356\) −44.8279 37.6151i −2.37587 1.99359i
\(357\) −0.264976 0.315786i −0.0140240 0.0167132i
\(358\) 9.59464 + 1.69179i 0.507092 + 0.0894140i
\(359\) 9.94626 3.62014i 0.524943 0.191064i −0.0659357 0.997824i \(-0.521003\pi\)
0.590879 + 0.806760i \(0.298781\pi\)
\(360\) 0 0
\(361\) −18.7010 3.35773i −0.984261 0.176723i
\(362\) 49.3252i 2.59248i
\(363\) −1.35072 3.71108i −0.0708946 0.194781i
\(364\) 0.941588 5.34001i 0.0493526 0.279893i
\(365\) 0 0
\(366\) 3.42512 + 2.87402i 0.179034 + 0.150227i
\(367\) 1.77733 0.313391i 0.0927759 0.0163589i −0.127067 0.991894i \(-0.540556\pi\)
0.219843 + 0.975535i \(0.429445\pi\)
\(368\) −24.6855 + 14.2522i −1.28682 + 0.742947i
\(369\) −4.20148 + 7.27717i −0.218720 + 0.378834i
\(370\) 0 0
\(371\) 4.64297 + 1.68990i 0.241051 + 0.0877353i
\(372\) −6.27739 3.62425i −0.325468 0.187909i
\(373\) 11.2270 6.48193i 0.581314 0.335622i −0.180342 0.983604i \(-0.557720\pi\)
0.761655 + 0.647982i \(0.224387\pi\)
\(374\) 9.64661 + 54.7086i 0.498814 + 2.82892i
\(375\) 0 0
\(376\) 35.7571 30.0038i 1.84403 1.54733i
\(377\) 18.7344 + 3.30338i 0.964869 + 0.170132i
\(378\) −0.522011 1.43421i −0.0268493 0.0737679i
\(379\) −33.1372 −1.70214 −0.851071 0.525051i \(-0.824046\pi\)
−0.851071 + 0.525051i \(0.824046\pi\)
\(380\) 0 0
\(381\) 0.139012 0.00712181
\(382\) −2.55855 7.02955i −0.130907 0.359663i
\(383\) −19.8866 3.50654i −1.01616 0.179176i −0.359324 0.933213i \(-0.616993\pi\)
−0.656832 + 0.754037i \(0.728104\pi\)
\(384\) −1.12374 + 0.942926i −0.0573454 + 0.0481185i
\(385\) 0 0
\(386\) 5.10471 + 28.9503i 0.259823 + 1.47353i
\(387\) 31.6402 18.2675i 1.60836 0.928588i
\(388\) −35.9918 20.7799i −1.82721 1.05494i
\(389\) −1.90648 0.693903i −0.0966625 0.0351823i 0.293236 0.956040i \(-0.405268\pi\)
−0.389899 + 0.920858i \(0.627490\pi\)
\(390\) 0 0
\(391\) 6.95762 12.0510i 0.351862 0.609443i
\(392\) −40.8849 + 23.6049i −2.06500 + 1.19223i
\(393\) 2.40930 0.424825i 0.121533 0.0214296i
\(394\) 20.0864 + 16.8545i 1.01194 + 0.849117i
\(395\) 0 0
\(396\) −12.3761 + 70.1881i −0.621920 + 3.52709i
\(397\) −2.74738 7.54838i −0.137887 0.378842i 0.851459 0.524420i \(-0.175718\pi\)
−0.989347 + 0.145578i \(0.953496\pi\)
\(398\) 7.56914i 0.379406i
\(399\) −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 \(0.271989\pi\)
\(402\) 0.477106 + 0.0841266i 0.0237959 + 0.00419585i
\(403\) 11.6309 + 13.8612i 0.579376 + 0.690473i
\(404\) −4.81770 4.04253i −0.239690 0.201124i
\(405\) 0 0
\(406\) 3.41533 + 5.91553i 0.169500 + 0.293583i
\(407\) −5.12931 2.96141i −0.254250 0.146792i
\(408\) −2.42334 + 6.65806i −0.119973 + 0.329623i
\(409\) 0.227020 + 0.0826284i 0.0112254 + 0.00408571i 0.347627 0.937633i \(-0.386988\pi\)
−0.336401 + 0.941719i \(0.609210\pi\)
\(410\) 0 0
\(411\) −1.11015 1.92283i −0.0547595 0.0948462i
\(412\) −57.1867 + 10.0835i −2.81738 + 0.496781i
\(413\) 0.391171 0.466179i 0.0192483 0.0229392i
\(414\) 19.5296 16.3872i 0.959825 0.805389i
\(415\) 0 0
\(416\) −22.0378 + 8.02110i −1.08049 + 0.393267i
\(417\) 3.26168i 0.159725i
\(418\) −15.2145 + 56.4288i −0.744166 + 2.76002i
\(419\) 22.7086 1.10939 0.554693 0.832055i \(-0.312836\pi\)
0.554693 + 0.832055i \(0.312836\pi\)
\(420\) 0 0
\(421\) −4.33685 + 24.5955i −0.211365 + 1.19871i 0.675738 + 0.737142i \(0.263825\pi\)
−0.887103 + 0.461571i \(0.847286\pi\)
\(422\) −9.14177 10.8947i −0.445014 0.530347i
\(423\) −12.7721 + 15.2212i −0.621000 + 0.740079i
\(424\) −14.7470 83.6342i −0.716176 4.06164i
\(425\) 0 0
\(426\) −2.66708 + 4.61953i −0.129221 + 0.223817i
\(427\) 0.959857 2.63719i 0.0464507 0.127622i
\(428\) 23.2716 63.9383i 1.12488 3.09057i
\(429\) −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 \(0.802911\pi\)
\(432\) −8.02560 + 9.56453i −0.386132 + 0.460174i
\(433\) 25.1405 + 29.9613i 1.20818 + 1.43985i 0.865877 + 0.500257i \(0.166761\pi\)
0.342299 + 0.939591i \(0.388794\pi\)
\(434\) −1.12821 + 6.39841i −0.0541559 + 0.307134i
\(435\) 0 0
\(436\) 20.6518 0.989042
\(437\) 12.0051 8.37813i 0.574280 0.400780i
\(438\) 6.34670i 0.303257i
\(439\) 17.6050 6.40768i 0.840239 0.305822i 0.114185 0.993460i \(-0.463574\pi\)
0.726054 + 0.687638i \(0.241352\pi\)
\(440\) 0 0
\(441\) 15.3947 12.9177i 0.733083 0.615129i
\(442\) 19.8774 23.6889i 0.945471 1.12677i
\(443\) 16.7923 2.96093i 0.797826 0.140678i 0.240149 0.970736i \(-0.422804\pi\)
0.557677 + 0.830058i \(0.311693\pi\)
\(444\) −0.660372 1.14380i −0.0313399 0.0542822i
\(445\) 0 0
\(446\) −19.3236 7.03323i −0.915001 0.333033i
\(447\) 0.693358 1.90499i 0.0327947 0.0901028i
\(448\) −1.38851 0.801654i −0.0656007 0.0378746i
\(449\) 6.10161 + 10.5683i 0.287953 + 0.498749i 0.973321 0.229448i \(-0.0736920\pi\)
−0.685368 + 0.728197i \(0.740359\pi\)
\(450\) 0 0
\(451\) 11.3700 + 9.54052i 0.535390 + 0.449246i
\(452\) 24.2812 + 28.9372i 1.14209 + 1.36109i
\(453\) 1.85562 + 0.327195i 0.0871845 + 0.0153730i
\(454\) 19.4779 7.08937i 0.914142 0.332721i
\(455\) 0 0
\(456\) −5.27909 + 5.26263i −0.247216 + 0.246445i
\(457\) 13.4079i 0.627193i −0.949556 0.313596i \(-0.898466\pi\)
0.949556 0.313596i \(-0.101534\pi\)
\(458\) −24.9553 68.5640i −1.16608 3.20379i
\(459\) 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 \(0.828058\pi\)
\(462\) −1.31374 + 0.231649i −0.0611209 + 0.0107773i
\(463\) −22.6706 + 13.0889i −1.05359 + 0.608292i −0.923653 0.383230i \(-0.874812\pi\)
−0.129940 + 0.991522i \(0.541478\pi\)
\(464\) 27.9393 48.3922i 1.29705 2.24655i
\(465\) 0 0
\(466\) −22.9201 8.34225i −1.06175 0.386447i
\(467\) 34.2843 + 19.7941i 1.58649 + 0.915960i 0.993879 + 0.110470i \(0.0352355\pi\)
0.592609 + 0.805490i \(0.298098\pi\)
\(468\) 34.3582 19.8367i 1.58821 0.916952i
\(469\) −0.0528039 0.299466i −0.00243826 0.0138280i
\(470\) 0 0
\(471\) 2.38447 2.00080i 0.109870 0.0921922i
\(472\) −10.3009 1.81632i −0.474135 0.0836029i
\(473\) −22.0715 60.6411i −1.01485 2.78828i
\(474\) 2.04020 0.0937097
\(475\) 0 0
\(476\) 7.77548 0.356389
\(477\) 12.3643 + 33.9707i 0.566123 + 1.55541i
\(478\) −29.9993 5.28968i −1.37214 0.241944i
\(479\) −2.89476 + 2.42899i −0.132265 + 0.110983i −0.706520 0.707693i \(-0.749736\pi\)
0.574255 + 0.818676i \(0.305292\pi\)
\(480\) 0 0
\(481\) 0.572514 + 3.24689i 0.0261044 + 0.148045i
\(482\) −28.6346 + 16.5322i −1.30427 + 0.753022i
\(483\) 0.289385 + 0.167077i 0.0131675 + 0.00760225i
\(484\) 69.9985 + 25.4774i 3.18175 + 1.15806i
\(485\) 0 0
\(486\) 8.40410 14.5563i 0.381218 0.660288i
\(487\) 6.05339 3.49493i 0.274305 0.158370i −0.356537 0.934281i \(-0.616043\pi\)
0.630843 + 0.775911i \(0.282709\pi\)
\(488\) −47.5039 + 8.37622i −2.15040 + 0.379174i
\(489\) −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 \(0.792041\pi\)
\(492\) 1.13200 + 3.11014i 0.0510345 + 0.140216i
\(493\) 27.2787i 1.22857i
\(494\) 29.5065 13.7031i 1.32756 0.616530i
\(495\) 0 0
\(496\) 49.9446 18.1784i 2.24258 0.816232i
\(497\) 3.29724 + 0.581393i 0.147902 + 0.0260790i
\(498\) 2.27020 + 2.70552i 0.101730 + 0.121237i
\(499\) −21.2906 17.8650i −0.953100 0.799746i 0.0267168 0.999643i \(-0.491495\pi\)
−0.979817 + 0.199897i \(0.935939\pi\)
\(500\) 0 0
\(501\) −0.647494 1.12149i −0.0289279 0.0501046i
\(502\) −5.36809 3.09927i −0.239590 0.138327i
\(503\) −5.59886 + 15.3827i −0.249641 + 0.685883i 0.750059 + 0.661371i \(0.230025\pi\)
−0.999700 + 0.0245113i \(0.992197\pi\)
\(504\) 7.65646 + 2.78672i 0.341046 + 0.124131i
\(505\) 0 0
\(506\) −22.5155 38.9979i −1.00093 1.73367i
\(507\) −1.13475 + 0.200087i −0.0503960 + 0.00888618i
\(508\) −1.68542 + 2.00861i −0.0747785 + 0.0891175i
\(509\) 27.2953 22.9034i 1.20984 1.01518i 0.210548 0.977584i \(-0.432475\pi\)
0.999293 0.0375938i \(-0.0119693\pi\)
\(510\) 0 0
\(511\) −3.74340 + 1.36249i −0.165598 + 0.0602728i
\(512\) 48.2924i 2.13424i
\(513\) 3.68622 5.24702i 0.162751 0.231662i
\(514\) −44.4694 −1.96146
\(515\) 0 0
\(516\) 2.49886 14.1717i 0.110006 0.623875i
\(517\) 22.5598 + 26.8857i 0.992177 + 1.18243i
\(518\) −0.760954 + 0.906869i −0.0334344 + 0.0398455i
\(519\) 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 \(0.889310\pi\)
\(522\) −17.0932 + 46.9632i −0.748149 + 2.05552i
\(523\) 4.64899 12.7730i 0.203286 0.558524i −0.795594 0.605830i \(-0.792841\pi\)
0.998880 + 0.0473057i \(0.0150635\pi\)
\(524\) −23.0727 + 39.9630i −1.00793 + 1.74579i
\(525\) 0 0
\(526\) 6.58646 + 37.3537i 0.287183 + 1.62870i
\(527\) −16.6782 + 19.8763i −0.726515 + 0.865826i
\(528\) 7.01470 + 8.35979i 0.305276 + 0.363813i
\(529\) 2.03521 11.5422i 0.0884873 0.501837i
\(530\) 0 0
\(531\) 4.45254 0.193224
\(532\) 7.40834 + 3.46866i 0.321192 + 0.150385i
\(533\) 8.26213i 0.357872i
\(534\) 7.53071 2.74096i 0.325886 0.118613i
\(535\) 0 0
\(536\) −4.00380 + 3.35959i −0.172938 + 0.145112i
\(537\) −0.600566 + 0.715727i −0.0259163 + 0.0308859i
\(538\) −57.1174 + 10.0713i −2.46251 + 0.434206i
\(539\) −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 \(0.557050\pi\)
\(542\) 11.7339 32.2386i 0.504013 1.38476i
\(543\) −4.09653 2.36513i −0.175799 0.101498i
\(544\) −16.8147 29.1239i −0.720924 1.24868i
\(545\) 0 0
\(546\) 0.568854 + 0.477325i 0.0243447 + 0.0204276i
\(547\) 17.0647 + 20.3369i 0.729634 + 0.869544i 0.995529 0.0944579i \(-0.0301118\pi\)
−0.265895 + 0.964002i \(0.585667\pi\)
\(548\) 41.2429 + 7.27224i 1.76181 + 0.310655i
\(549\) 19.2952 7.02288i 0.823500 0.299729i
\(550\) 0 0
\(551\) −12.1691 + 25.9907i −0.518421 + 1.10724i
\(552\) 5.74340i 0.244455i
\(553\) −0.437984 1.20335i −0.0186250 0.0511717i
\(554\) −1.50681 + 8.54554i −0.0640182 + 0.363065i
\(555\) 0 0
\(556\) −47.1284 39.5455i −1.99869 1.67710i
\(557\) −3.75229 + 0.661630i −0.158990 + 0.0280342i −0.252576 0.967577i \(-0.581278\pi\)
0.0935867 + 0.995611i \(0.470167\pi\)
\(558\) −41.1680 + 23.7684i −1.74278 + 1.00620i
\(559\) −17.9613 + 31.1099i −0.759683 + 1.31581i
\(560\) 0 0
\(561\) −5.00618 1.82210i −0.211361 0.0769292i
\(562\) −44.7910 25.8601i −1.88939 1.09084i
\(563\) 10.5475 6.08960i 0.444524 0.256646i −0.260991 0.965341i \(-0.584049\pi\)
0.705515 + 0.708695i \(0.250716\pi\)
\(564\) 1.35902 + 7.70741i 0.0572252 + 0.324540i
\(565\) 0 0
\(566\) 1.04872 0.879981i 0.0440810 0.0369884i
\(567\) −3.34288 0.589440i −0.140388 0.0247542i
\(568\) −19.6822 54.0764i −0.825847 2.26900i
\(569\) −22.8626 −0.958451 −0.479226 0.877692i \(-0.659082\pi\)
−0.479226 + 0.877692i \(0.659082\pi\)
\(570\) 0 0
\(571\) 40.3908 1.69030 0.845152 0.534527i \(-0.179510\pi\)
0.845152 + 0.534527i \(0.179510\pi\)
\(572\) −23.9676 65.8503i −1.00213 2.75334i
\(573\) 0.706496 + 0.124574i 0.0295143 + 0.00520416i
\(574\) 2.27259 1.90693i 0.0948560 0.0795937i
\(575\) 0 0
\(576\) −2.03702 11.5525i −0.0848760 0.481355i
\(577\) −6.81026 + 3.93190i −0.283515 + 0.163687i −0.635013 0.772501i \(-0.719005\pi\)
0.351499 + 0.936188i \(0.385672\pi\)
\(578\) 0.372700 + 0.215179i 0.0155023 + 0.00895025i
\(579\) −2.64913 0.964204i −0.110094 0.0400710i
\(580\) 0 0
\(581\) 1.10841 1.91982i 0.0459845 0.0796475i
\(582\) 4.92901 2.84576i 0.204314 0.117961i
\(583\) 62.8844 11.0882i 2.60440 0.459227i
\(584\) 52.4514 + 44.0120i 2.17045 + 1.82123i
\(585\) 0 0
\(586\) 14.1810 80.4242i 0.585810 3.32229i
\(587\) −13.7566 37.7961i −0.567797 1.56001i −0.807935 0.589271i \(-0.799415\pi\)
0.240138 0.970739i \(-0.422807\pi\)
\(588\) 7.91555i 0.326432i
\(589\) −24.7576 + 11.4976i −1.02012 + 0.473751i
\(590\) 0 0
\(591\) −2.36293 + 0.860035i −0.0971978 + 0.0353771i
\(592\) 9.53727 + 1.68168i 0.391980 + 0.0691166i
\(593\) −21.9034 26.1035i −0.899466 1.07194i −0.997053 0.0767145i \(-0.975557\pi\)
0.0975874 0.995227i \(-0.468887\pi\)
\(594\) −15.1100 12.6788i −0.619969 0.520216i
\(595\) 0 0
\(596\) 19.1189 + 33.1150i 0.783142 + 1.35644i
\(597\) −0.628627 0.362938i −0.0257280 0.0148541i
\(598\) −8.57334 + 23.5551i −0.350590 + 0.963238i
\(599\) 16.8047 + 6.11643i 0.686623 + 0.249910i 0.661689 0.749779i \(-0.269840\pi\)
0.0249346 + 0.999689i \(0.492062\pi\)
\(600\) 0 0
\(601\) −0.355966 0.616551i −0.0145201 0.0251496i 0.858674 0.512522i \(-0.171289\pi\)
−0.873194 + 0.487372i \(0.837955\pi\)
\(602\) −12.7027 + 2.23982i −0.517722 + 0.0912884i
\(603\) 1.43012 1.70435i 0.0582389 0.0694065i
\(604\) −27.2257 + 22.8451i −1.10780 + 0.929553i
\(605\) 0 0
\(606\) 0.809335 0.294574i 0.0328770 0.0119662i
\(607\) 34.3415i 1.39388i −0.717129 0.696940i \(-0.754544\pi\)
0.717129 0.696940i \(-0.245456\pi\)
\(608\) −3.02851 35.2498i −0.122822 1.42957i
\(609\) −0.655057 −0.0265443
\(610\) 0 0
\(611\) 3.39253 19.2400i 0.137247 0.778368i
\(612\) 36.5682 + 43.5803i 1.47818 + 1.76163i
\(613\) 19.2696 22.9647i 0.778293 0.927534i −0.220562 0.975373i \(-0.570789\pi\)
0.998855 + 0.0478390i \(0.0152334\pi\)
\(614\) −4.11393 23.3313i −0.166025 0.941573i
\(615\) 0 0
\(616\) 7.19590 12.4637i 0.289931 0.502175i
\(617\) 7.55883 20.7677i 0.304307 0.836076i −0.689432 0.724350i \(-0.742140\pi\)
0.993739 0.111726i \(-0.0356379\pi\)
\(618\) 2.71989 7.47283i 0.109410 0.300601i
\(619\) 9.72359 16.8417i 0.390824 0.676927i −0.601734 0.798696i \(-0.705523\pi\)
0.992558 + 0.121769i \(0.0388568\pi\)
\(620\) 0 0
\(621\) 0.857958 + 4.86572i 0.0344287 + 0.195255i
\(622\) 39.9343 47.5918i 1.60122 1.90826i
\(623\) −3.23333 3.85334i −0.129541 0.154381i
\(624\) 1.05487 5.98246i 0.0422286 0.239490i
\(625\) 0 0
\(626\) −6.35337 −0.253932
\(627\) −3.95696 3.96933i −0.158026 0.158520i
\(628\) 58.7117i 2.34285i
\(629\) −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 \(0.249672\pi\)
\(632\) −14.1480 + 16.8610i −0.562779 + 0.670694i
\(633\) 1.34317 0.236837i 0.0533862 0.00941342i
\(634\) 9.06962 + 15.7090i 0.360201 + 0.623886i
\(635\) 0 0
\(636\) 13.3803 + 4.87005i 0.530565 + 0.193110i
\(637\) −6.75818 + 18.5680i −0.267769 + 0.735689i
\(638\) 76.4496 + 44.1382i 3.02667 + 1.74745i
\(639\) 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 \(0.553042\pi\)
\(642\) 5.98961 + 7.13814i 0.236391 + 0.281720i
\(643\) −36.6032 6.45413i −1.44349 0.254526i −0.603601 0.797287i \(-0.706268\pi\)
−0.839887 + 0.542761i \(0.817379\pi\)
\(644\) −5.92270 + 2.15569i −0.233387 + 0.0849459i
\(645\) 0 0
\(646\) 26.6983 + 38.2562i 1.05043 + 1.50517i
\(647\) 20.6750i 0.812819i 0.913691 + 0.406409i \(0.133219\pi\)
−0.913691 + 0.406409i \(0.866781\pi\)
\(648\) 19.9547 + 54.8250i 0.783893 + 2.15373i
\(649\) 1.36569 7.74519i 0.0536079 0.304025i
\(650\) 0 0
\(651\) −0.477300 0.400502i −0.0187068 0.0156969i
\(652\) 15.1090 2.66412i 0.591714 0.104335i
\(653\) −29.4740 + 17.0168i −1.15341 + 0.665919i −0.949715 0.313116i \(-0.898627\pi\)
−0.203691 + 0.979035i \(0.565294\pi\)
\(654\) −1.41411 + 2.44931i −0.0552962 + 0.0957758i
\(655\) 0 0
\(656\) −22.8053 8.30043i −0.890395 0.324077i
\(657\) −25.2418 14.5733i −0.984775 0.568560i
\(658\) 6.07519 3.50751i 0.236836 0.136737i
\(659\) 5.38526 + 30.5413i 0.209780 + 1.18972i 0.889739 + 0.456470i \(0.150886\pi\)
−0.679959 + 0.733250i \(0.738002\pi\)
\(660\) 0 0
\(661\) −13.9912 + 11.7400i −0.544195 + 0.456634i −0.872970 0.487775i \(-0.837809\pi\)
0.328775 + 0.944408i \(0.393364\pi\)
\(662\) 44.2901 + 7.80953i 1.72138 + 0.303526i
\(663\) 1.01428 + 2.78672i 0.0393915 + 0.108227i
\(664\) −38.1024 −1.47866
\(665\) 0 0
\(666\) −8.66163 −0.335631
\(667\) −7.56280 20.7786i −0.292833 0.804552i
\(668\) 24.0550 + 4.24154i 0.930715 + 0.164110i
\(669\) 1.51068 1.26761i 0.0584064 0.0490088i
\(670\) 0 0
\(671\) −6.29806 35.7181i −0.243134 1.37888i
\(672\) 0.699366 0.403779i 0.0269786 0.0155761i
\(673\) 22.5444 + 13.0160i 0.869023 + 0.501731i 0.867024 0.498267i \(-0.166030\pi\)
0.00199979 + 0.999998i \(0.499363\pi\)
\(674\) −79.3197 28.8700i −3.05528 1.11203i
\(675\) 0 0
\(676\) 10.8669 18.8221i 0.417958 0.723925i
\(677\) −0.0520720 + 0.0300638i −0.00200129 + 0.00115545i −0.501000 0.865447i \(-0.667034\pi\)
0.498999 + 0.866603i \(0.333701\pi\)
\(678\) −5.09460 + 0.898316i −0.195657 + 0.0344996i
\(679\) −2.73663 2.29630i −0.105022 0.0881240i
\(680\) 0 0
\(681\) −0.345178 + 1.95760i −0.0132272 + 0.0750154i
\(682\) 28.7180 + 78.9020i 1.09967 + 3.02131i
\(683\) 31.5145i 1.20587i 0.797790 + 0.602935i \(0.206002\pi\)
−0.797790 + 0.602935i \(0.793998\pi\)
\(684\) 15.4003 + 57.8356i 0.588844 + 2.21140i
\(685\) 0 0
\(686\) −13.4915 + 4.91052i −0.515109 + 0.187484i
\(687\) 6.89094 + 1.21506i 0.262906 + 0.0463574i
\(688\) 67.8255 + 80.8313i 2.58582 + 3.08166i
\(689\) −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 \(0.890525\pi\)
\(692\) −18.2318 10.5261i −0.693067 0.400143i
\(693\) −2.09533 + 5.75687i −0.0795950 + 0.218686i
\(694\) 17.3057 + 6.29878i 0.656917 + 0.239098i
\(695\) 0 0
\(696\) 5.62953 + 9.75063i 0.213387 + 0.369597i
\(697\) 11.6676 2.05730i 0.441940 0.0779260i
\(698\) 37.6924 44.9201i 1.42668 1.70025i
\(699\) 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 \(0.344267\pi\)
\(702\) 10.9798i 0.414408i
\(703\) −4.95417 0.441229i −0.186850 0.0166413i
\(704\) −20.7204 −0.780930
\(705\) 0 0
\(706\) −2.01575 + 11.4319i −0.0758637 + 0.430245i
\(707\) −0.347490 0.414122i −0.0130687 0.0155747i
\(708\) 1.12730 1.34346i 0.0423664 0.0504903i
\(709\) 7.51502 + 42.6198i 0.282233 + 1.60062i 0.715006 + 0.699118i \(0.246424\pi\)
−0.432774 + 0.901502i \(0.642465\pi\)
\(710\) 0 0
\(711\) 4.68474 8.11420i 0.175691 0.304306i
\(712\) −29.5704 + 81.2440i −1.10820 + 3.04475i
\(713\) 7.19350 19.7640i 0.269399 0.740167i
\(714\) −0.532419 + 0.922176i −0.0199253 + 0.0345116i
\(715\) 0 0
\(716\) −3.06021 17.3553i −0.114366 0.648599i
\(717\) 1.87777 2.23784i 0.0701268 0.0835738i
\(718\) −17.5746 20.9446i −0.655878 0.781645i
\(719\) −5.61767 + 31.8594i −0.209504 + 1.18815i 0.680690 + 0.732572i \(0.261680\pi\)
−0.890193 + 0.455583i \(0.849431\pi\)
\(720\) 0 0
\(721\) −4.99151 −0.185894
\(722\) 8.37154 + 48.3600i 0.311557 + 1.79977i
\(723\) 3.17086i 0.117926i
\(724\) 83.8416 30.5158i 3.11595 1.13411i
\(725\) 0 0
\(726\) −7.81471 + 6.55732i −0.290031 + 0.243365i
\(727\) −31.9291 + 38.0516i −1.18418 + 1.41125i −0.293907 + 0.955834i \(0.594956\pi\)
−0.890276 + 0.455421i \(0.849489\pi\)
\(728\) −7.88957 + 1.39114i −0.292407 + 0.0515592i
\(729\) −11.8713 20.5616i −0.439677 0.761542i
\(730\) 0 0
\(731\) −48.4051 17.6180i −1.79033 0.651625i
\(732\) 2.76617 7.59998i 0.102240 0.280903i
\(733\) 1.18507 + 0.684201i 0.0437716 + 0.0252715i 0.521726 0.853113i \(-0.325288\pi\)
−0.477955 + 0.878385i \(0.658622\pi\)
\(734\) −2.33094 4.03730i −0.0860365 0.149020i
\(735\) 0 0
\(736\) 20.8824 + 17.5224i 0.769734 + 0.645883i
\(737\) −2.52607 3.01045i −0.0930489 0.110891i
\(738\) 21.3760 + 3.76917i 0.786863 + 0.138745i
\(739\) 16.6998 6.07823i 0.614312 0.223591i −0.0160769 0.999871i \(-0.505118\pi\)
0.630389 + 0.776279i \(0.282895\pi\)
\(740\) 0 0
\(741\) −0.276771 + 3.10761i −0.0101674 + 0.114161i
\(742\) 12.7630i 0.468545i
\(743\) 13.2113 + 36.2978i 0.484676 + 1.33164i 0.905443 + 0.424469i \(0.139539\pi\)
−0.420766 + 0.907169i \(0.638239\pi\)
\(744\) −1.85965 + 10.5466i −0.0681779 + 0.386656i
\(745\) 0 0
\(746\) −25.6526 21.5251i −0.939210 0.788091i
\(747\) 15.9731 2.81649i 0.584426 0.103050i
\(748\) 87.0241 50.2434i 3.18192 1.83708i
\(749\) 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 \(0.705284\pi\)
\(752\) −49.6983 28.6933i −1.81231 1.04634i
\(753\) 0.514797 0.297218i 0.0187603 0.0108312i
\(754\) −8.53300 48.3931i −0.310754 1.76237i
\(755\) 0 0
\(756\) −2.11488 + 1.77460i −0.0769175 + 0.0645414i
\(757\) 1.91954 + 0.338466i 0.0697668 + 0.0123018i 0.208423 0.978039i \(-0.433167\pi\)
−0.138656 + 0.990341i \(0.544278\pi\)
\(758\) 29.2759 + 80.4350i 1.06335 + 2.92153i
\(759\) 4.31845 0.156750
\(760\) 0 0
\(761\) −48.1168 −1.74423 −0.872115 0.489300i \(-0.837252\pi\)
−0.872115 + 0.489300i \(0.837252\pi\)
\(762\) −0.122814 0.337429i −0.00444909 0.0122238i
\(763\) 1.74823 + 0.308260i 0.0632901 + 0.0111597i
\(764\) −10.3657 + 8.69788i −0.375019 + 0.314678i
\(765\) 0 0
\(766\) 9.05780 + 51.3693i 0.327272 + 1.85605i
\(767\) −3.79139 + 2.18896i −0.136899 + 0.0790388i
\(768\) 4.99437 + 2.88350i 0.180219 + 0.104049i
\(769\) −6.00593 2.18598i −0.216579 0.0788284i 0.231452 0.972846i \(-0.425652\pi\)
−0.448031 + 0.894018i \(0.647875\pi\)
\(770\) 0 0
\(771\) 2.13230 3.69325i 0.0767929 0.133009i
\(772\) 46.0507 26.5874i 1.65740 0.956900i
\(773\) −35.1946 + 6.20576i −1.26586 + 0.223206i −0.765967 0.642880i \(-0.777739\pi\)
−0.499895 + 0.866086i \(0.666628\pi\)
\(774\) −72.2947 60.6624i −2.59858 2.18047i
\(775\) 0 0
\(776\) −10.6624 + 60.4694i −0.382757 + 2.17073i
\(777\) −0.0388292 0.106682i −0.00139299 0.00382721i
\(778\) 5.24072i 0.187889i
\(779\) 12.0344 + 3.24476i 0.431177 + 0.116255i
\(780\) 0 0
\(781\) 40.6599 14.7990i 1.45493 0.529550i
\(782\) −35.3986 6.24173i −1.26585 0.223204i
\(783\) −6.22582 7.41964i −0.222493 0.265156i
\(784\) 44.4620 + 37.3081i 1.58793 + 1.33243i
\(785\) 0 0
\(786\) −3.15976 5.47286i −0.112705 0.195211i
\(787\) −1.68035 0.970153i −0.0598982 0.0345822i 0.469752 0.882799i \(-0.344343\pi\)
−0.529650 + 0.848216i \(0.677677\pi\)
\(788\) 16.2220 44.5695i 0.577884 1.58772i
\(789\) −3.41810 1.24409i −0.121687 0.0442906i
\(790\) 0 0
\(791\) 1.62353 + 2.81204i 0.0577262 + 0.0999848i
\(792\) 103.699 18.2850i 3.68479 0.649728i
\(793\) −12.9775 + 15.4660i −0.460845 + 0.549213i
\(794\) −15.8952 + 13.3376i −0.564099 + 0.473335i
\(795\) 0 0
\(796\) 12.8658 4.68276i 0.456016 0.165976i
\(797\) 44.3436i 1.57073i 0.619033 + 0.785365i \(0.287525\pi\)
−0.619033 + 0.785365i \(0.712475\pi\)
\(798\) −0.918663 + 0.641120i −0.0325203 + 0.0226954i
\(799\) 28.0150 0.991099
\(800\) 0 0
\(801\) 6.39090 36.2446i 0.225811 1.28064i
\(802\) −23.8765 28.4549i −0.843108 1.00478i
\(803\) −33.0925 + 39.4381i −1.16781 + 1.39174i
\(804\) −0.152173 0.863016i −0.00536673 0.0304362i
\(805\) 0 0
\(806\) 23.3700 40.4781i 0.823175 1.42578i
\(807\) 1.90233 5.22660i 0.0669651 0.183985i
\(808\) −3.17797 + 8.73139i −0.111800 + 0.307169i
\(809\) −13.9319 + 24.1307i −0.489819 + 0.848392i −0.999931 0.0117160i \(-0.996271\pi\)
0.510112 + 0.860108i \(0.329604\pi\)
\(810\) 0 0
\(811\) 5.29449 + 30.0265i 0.185915 + 1.05437i 0.924775 + 0.380515i \(0.124253\pi\)
−0.738860 + 0.673859i \(0.764636\pi\)
\(812\) 7.94209 9.46501i 0.278713 0.332157i
\(813\) 2.11482 + 2.52035i 0.0741700 + 0.0883924i
\(814\) −2.65670 + 15.0669i −0.0931173 + 0.528094i
\(815\) 0 0
\(816\) 8.71095 0.304944
\(817\) −38.2600 38.3797i −1.33855 1.34274i
\(818\) 0.624053i 0.0218195i
\(819\) 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 \(-0.0622609\pi\)
\(822\) −3.68656 + 4.39347i −0.128584 + 0.153240i
\(823\) 42.8265 7.55147i 1.49284 0.263228i 0.633143 0.774035i \(-0.281765\pi\)
0.859695 + 0.510807i \(0.170653\pi\)
\(824\) 42.8968 + 74.2994i 1.49438 + 2.58834i
\(825\) 0 0
\(826\) −1.47716 0.537644i −0.0513971 0.0187070i
\(827\) −0.203752 + 0.559803i −0.00708514 + 0.0194663i −0.943185 0.332269i \(-0.892186\pi\)
0.936100 + 0.351735i \(0.114408\pi\)
\(828\) −39.9368 23.0575i −1.38790 0.801304i
\(829\) 9.62397 + 16.6692i 0.334254 + 0.578946i 0.983341 0.181769i \(-0.0581822\pi\)
−0.649087 + 0.760714i \(0.724849\pi\)
\(830\) 0 0
\(831\) −0.637468 0.534900i −0.0221135 0.0185555i
\(832\) 7.41401 + 8.83567i 0.257035 + 0.306322i
\(833\) −27.9040 4.92023i −0.966816 0.170476i
\(834\) 7.91719 2.88162i 0.274150 0.0997824i
\(835\) 0 0
\(836\) 105.329 9.04937i 3.64287 0.312979i
\(837\) 9.21270i 0.318438i
\(838\) −20.0625 55.1213i −0.693048 1.90413i
\(839\) 8.84381 50.1557i 0.305322 1.73157i −0.316662 0.948539i \(-0.602562\pi\)
0.621984 0.783030i \(-0.286327\pi\)
\(840\) 0 0
\(841\) 10.9908 + 9.22242i 0.378995 + 0.318014i
\(842\) 63.5331 11.2026i 2.18949 0.386067i
\(843\) 4.29543 2.47997i 0.147943 0.0854147i
\(844\) −12.8628 + 22.2791i −0.442757 + 0.766878i
\(845\) 0 0
\(846\) 48.2307 + 17.5545i 1.65821 + 0.603538i
\(847\) 5.54526 + 3.20156i 0.190537 + 0.110007i
\(848\) −90.4204 + 52.2042i −3.10505 + 1.79270i
\(849\) 0.0227978 + 0.129293i 0.000782418 + 0.00443731i
\(850\) 0 0
\(851\) 2.93571 2.46335i 0.100635 0.0844426i
\(852\) 9.50216 + 1.67549i 0.325539 + 0.0574013i
\(853\) −0.889082 2.44273i −0.0304416 0.0836375i 0.923541 0.383500i \(-0.125281\pi\)
−0.953982 + 0.299863i \(0.903059\pi\)
\(854\) −7.24935 −0.248067
\(855\) 0 0
\(856\) −100.528 −3.43597
\(857\) −13.7570 37.7972i −0.469932 1.29113i −0.917806 0.397030i \(-0.870041\pi\)
0.447874 0.894097i \(-0.352181\pi\)
\(858\) 9.45104 + 1.66647i 0.322653 + 0.0568925i
\(859\) 21.5150 18.0532i 0.734083 0.615969i −0.197159 0.980372i \(-0.563171\pi\)
0.931241 + 0.364403i \(0.118727\pi\)
\(860\) 0 0
\(861\) 0.0494030 + 0.280179i 0.00168365 + 0.00954846i
\(862\) 39.9527 23.0667i 1.36079 0.785654i
\(863\) −25.9284 14.9698i −0.882613 0.509577i −0.0110937 0.999938i \(-0.503531\pi\)
−0.871519 + 0.490362i \(0.836865\pi\)
\(864\) 11.2204 + 4.08390i 0.381727 + 0.138937i
\(865\) 0 0
\(866\) 50.5150 87.4946i 1.71657 2.97319i
\(867\) −0.0357418 + 0.0206355i −0.00121385 + 0.000700819i
\(868\) 11.5738 2.04078i 0.392841 0.0692684i
\(869\) −12.6777 10.6379i −0.430063 0.360866i
\(870\) 0 0
\(871\) −0.379870 + 2.15435i −0.0128714 + 0.0729973i
\(872\) −10.4357 28.6718i −0.353397 0.970950i
\(873\) 26.1379i 0.884633i
\(874\) −30.9427 21.7384i −1.04665 0.735312i
\(875\) 0 0
\(876\) −10.7879 + 3.92648i −0.364490 + 0.132664i
\(877\) −7.98213 1.40747i −0.269537 0.0475267i 0.0372458 0.999306i \(-0.488142\pi\)
−0.306783 + 0.951779i \(0.599253\pi\)
\(878\) −31.1072 37.0721i −1.04982 1.25112i
\(879\) 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 \(0.881410\pi\)
\(882\) −44.9565 25.9557i −1.51377 0.873973i
\(883\) 0.517061 1.42061i 0.0174005 0.0478074i −0.930688 0.365813i \(-0.880791\pi\)
0.948089 + 0.318006i \(0.103013\pi\)
\(884\) −52.5632 19.1314i −1.76789 0.643460i
\(885\) 0 0
\(886\) −22.0228 38.1446i −0.739870 1.28149i
\(887\) −27.4146 + 4.83393i −0.920491 + 0.162307i −0.613764 0.789490i \(-0.710345\pi\)
−0.306728 + 0.951797i \(0.599234\pi\)
\(888\) −1.25429 + 1.49480i −0.0420912 + 0.0501623i
\(889\) −0.172657 + 0.144876i −0.00579072 + 0.00485899i
\(890\) 0 0
\(891\) −41.2228 + 15.0039i −1.38101 + 0.502648i
\(892\) 37.1970i 1.24545i
\(893\) 26.6922 + 12.4975i 0.893220 + 0.418214i
\(894\) −5.23661 −0.175138
\(895\) 0 0
\(896\) 0.413006 2.34228i 0.0137976 0.0782499i
\(897\) −1.54519 1.84149i −0.0515924 0.0614855i
\(898\) 20.2622 24.1475i 0.676157 0.805813i
\(899\) 7.15966 + 40.6045i 0.238788 + 1.35423i
\(900\) 0 0
\(901\) 25.4850 44.1414i 0.849029 1.47056i
\(902\) 13.1129 36.0275i 0.436613 1.19959i
\(903\) 0.423069 1.16237i 0.0140789 0.0386814i
\(904\) 27.9051 48.3331i 0.928111 1.60754i
\(905\) 0 0
\(906\) −0.845184 4.79328i −0.0280794 0.159246i
\(907\) −20.3553 + 24.2585i −0.675888 + 0.805492i −0.989573 0.144036i \(-0.953992\pi\)
0.313685 + 0.949527i \(0.398436\pi\)
\(908\) −24.1006 28.7220i −0.799806 0.953172i
\(909\) 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 \(0.444476\pi\)
\(912\) 8.29963 + 3.88597i 0.274828 + 0.128677i
\(913\) 28.6491i 0.948148i
\(914\) −32.5454 + 11.8455i −1.07650 + 0.391816i
\(915\) 0 0
\(916\) −101.104 + 84.8364i −3.34057 + 2.80307i
\(917\) −2.54967 + 3.03858i −0.0841975 + 0.100343i
\(918\) −15.5055 + 2.73403i −0.511756 + 0.0902364i
\(919\) −5.30464 9.18791i −0.174984 0.303081i 0.765172 0.643826i \(-0.222654\pi\)
−0.940156 + 0.340745i \(0.889321\pi\)
\(920\) 0 0
\(921\) 2.13496 + 0.777061i 0.0703492 + 0.0256050i
\(922\) −12.3830 + 34.0221i −0.407814 + 1.12046i
\(923\) −20.8593 12.0431i −0.686591 0.396403i
\(924\) 1.20652 + 2.08975i 0.0396915 + 0.0687477i
\(925\) 0 0
\(926\) 51.8001 + 43.4655i 1.70226 + 1.42836i
\(927\) −23.4751 27.9766i −0.771025 0.918871i
\(928\) −52.6272 9.27960i −1.72757 0.304618i
\(929\) −13.3285 + 4.85116i −0.437293 + 0.159162i −0.551279 0.834321i \(-0.685860\pi\)
0.113987 + 0.993482i \(0.463638\pi\)
\(930\) 0 0
\(931\) −24.3915 17.1359i −0.799399 0.561607i
\(932\) 44.1200i 1.44520i
\(933\) 2.03773 + 5.59862i 0.0667123 + 0.183290i
\(934\) 17.7574 100.707i 0.581039 3.29524i
\(935\) 0 0
\(936\) −44.9019 37.6772i −1.46766 1.23152i
\(937\) −43.8654 + 7.73465i −1.43302 + 0.252680i −0.835640 0.549278i \(-0.814903\pi\)
−0.597380 + 0.801958i \(0.703792\pi\)
\(938\) −0.680253 + 0.392744i −0.0222110 + 0.0128235i
\(939\) 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 \(0.446141\pi\)
\(942\) −6.96324 4.02023i −0.226875 0.130986i
\(943\) −8.31698 + 4.80181i −0.270838 + 0.156368i
\(944\) 2.23303 + 12.6642i 0.0726791 + 0.412183i
\(945\) 0 0
\(946\) −127.696 + 107.150i −4.15177 + 3.48375i
\(947\) −30.5045 5.37877i −0.991264 0.174787i −0.345578 0.938390i \(-0.612317\pi\)
−0.645686 + 0.763603i \(0.723428\pi\)
\(948\) −1.26220 3.46788i −0.0409945 0.112631i
\(949\) 28.6582 0.930285
\(950\) 0 0
\(951\) −1.73954 −0.0564086
\(952\) −3.92908 10.7950i −0.127342 0.349869i
\(953\) 21.9251 + 3.86599i 0.710224 + 0.125232i 0.517078 0.855938i \(-0.327020\pi\)
0.193146 + 0.981170i \(0.438131\pi\)
\(954\) 71.5346 60.0247i 2.31602 1.94337i
\(955\) 0 0
\(956\) 9.56828 + 54.2644i 0.309460 + 1.75504i
\(957\) −7.33148 + 4.23283i −0.236993 + 0.136828i
\(958\) 8.45343 + 4.88059i 0.273118 + 0.157685i
\(959\) 3.38277 + 1.23123i 0.109235 + 0.0397584i
\(960\) 0 0
\(961\) −4.10876 + 7.11657i −0.132540 + 0.229567i
\(962\) 7.37548 4.25823i 0.237795 0.137291i
\(963\) 42.1428 7.43092i 1.35803 0.239458i
\(964\) 45.8162 + 38.4444i 1.47564 + 1.23821i
\(965\) 0 0
\(966\) 0.149886 0.850044i 0.00482249 0.0273497i
\(967\) 5.99883 + 16.4816i 0.192909 + 0.530014i 0.998005 0.0631307i \(-0.0201085\pi\)
−0.805096 + 0.593145i \(0.797886\pi\)
\(968\) 110.056i 3.53734i
\(969\) −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 \(0.302160\pi\)
\(972\) −29.9417 5.27953i −0.960381 0.169341i
\(973\) −3.39927 4.05109i −0.108975 0.129872i
\(974\) −13.8314 11.6059i −0.443187 0.371878i
\(975\) 0 0
\(976\) 29.6518 + 51.3584i 0.949131 + 1.64394i
\(977\) 24.9276 + 14.3920i 0.797506 + 0.460440i 0.842598 0.538543i \(-0.181025\pi\)
−0.0450925 + 0.998983i \(0.514358\pi\)
\(978\) −0.718608 + 1.97436i −0.0229785 + 0.0631330i
\(979\) −61.0872 22.2339i −1.95236 0.710599i
\(980\) 0 0
\(981\) 6.49419 + 11.2483i 0.207344 + 0.359130i
\(982\) 83.0287 14.6402i 2.64955 0.467187i
\(983\) −19.2302 + 22.9176i −0.613348 + 0.730959i −0.979911 0.199434i \(-0.936090\pi\)
0.366564 + 0.930393i \(0.380534\pi\)
\(984\) 3.74593 3.14321i 0.119416 0.100202i
\(985\) 0 0
\(986\) 66.2147 24.1002i 2.10870 0.767506i
\(987\) 0.672737i 0.0214135i
\(988\) −41.5467 41.6766i −1.32178 1.32591i
\(989\) 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 \(-0.204570\pi\)
\(992\) −32.6726 38.9377i −1.03736 1.23627i
\(993\) −2.77229 + 3.30389i −0.0879760 + 0.104846i
\(994\) −1.50181 8.51716i −0.0476344 0.270148i
\(995\) 0 0
\(996\) 3.19427 5.53264i 0.101214 0.175308i
\(997\) −18.4520 + 50.6964i −0.584380 + 1.60557i 0.196234 + 0.980557i \(0.437129\pi\)
−0.780614 + 0.625014i \(0.785093\pi\)
\(998\) −24.5545 + 67.4628i −0.777258 + 2.13550i
\(999\) 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.u.b.24.1 36
5.2 odd 4 475.2.l.c.176.3 18
5.3 odd 4 95.2.k.a.81.1 yes 18
5.4 even 2 inner 475.2.u.b.24.6 36
15.8 even 4 855.2.bs.c.271.3 18
19.4 even 9 inner 475.2.u.b.99.6 36
95.2 even 36 9025.2.a.cf.1.9 9
95.4 even 18 inner 475.2.u.b.99.1 36
95.17 odd 36 9025.2.a.cc.1.1 9
95.23 odd 36 95.2.k.a.61.1 18
95.42 odd 36 475.2.l.c.251.3 18
95.78 even 36 1805.2.a.s.1.1 9
95.93 odd 36 1805.2.a.v.1.9 9
285.23 even 36 855.2.bs.c.631.3 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.k.a.61.1 18 95.23 odd 36
95.2.k.a.81.1 yes 18 5.3 odd 4
475.2.l.c.176.3 18 5.2 odd 4
475.2.l.c.251.3 18 95.42 odd 36
475.2.u.b.24.1 36 1.1 even 1 trivial
475.2.u.b.24.6 36 5.4 even 2 inner
475.2.u.b.99.1 36 95.4 even 18 inner
475.2.u.b.99.6 36 19.4 even 9 inner
855.2.bs.c.271.3 18 15.8 even 4
855.2.bs.c.631.3 18 285.23 even 36
1805.2.a.s.1.1 9 95.78 even 36
1805.2.a.v.1.9 9 95.93 odd 36
9025.2.a.cc.1.1 9 95.17 odd 36
9025.2.a.cf.1.9 9 95.2 even 36