Properties

Label 231.2.g.a.197.9
Level $231$
Weight $2$
Character 231.197
Analytic conductor $1.845$
Analytic rank $0$
Dimension $24$
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] = [231,2,Mod(197,231)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(231, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("231.197");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 231 = 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 231.g (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.84454428669\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 197.9
Character \(\chi\) \(=\) 231.197
Dual form 231.2.g.a.197.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.858468 q^{2} +(1.60964 - 0.639565i) q^{3} -1.26303 q^{4} -2.44714i q^{5} +(-1.38183 + 0.549047i) q^{6} +1.00000i q^{7} +2.80121 q^{8} +(2.18191 - 2.05895i) q^{9} +O(q^{10})\) \(q-0.858468 q^{2} +(1.60964 - 0.639565i) q^{3} -1.26303 q^{4} -2.44714i q^{5} +(-1.38183 + 0.549047i) q^{6} +1.00000i q^{7} +2.80121 q^{8} +(2.18191 - 2.05895i) q^{9} +2.10079i q^{10} +(-3.19676 - 0.883578i) q^{11} +(-2.03303 + 0.807792i) q^{12} -5.20778i q^{13} -0.858468i q^{14} +(-1.56511 - 3.93903i) q^{15} +0.121314 q^{16} +0.151573 q^{17} +(-1.87310 + 1.76754i) q^{18} -3.38435i q^{19} +3.09082i q^{20} +(0.639565 + 1.60964i) q^{21} +(2.74432 + 0.758524i) q^{22} +5.75973i q^{23} +(4.50895 - 1.79156i) q^{24} -0.988494 q^{25} +4.47072i q^{26} +(2.19527 - 4.70965i) q^{27} -1.26303i q^{28} +6.48993 q^{29} +(1.34359 + 3.38153i) q^{30} -5.46192 q^{31} -5.70656 q^{32} +(-5.71076 + 0.622291i) q^{33} -0.130121 q^{34} +2.44714 q^{35} +(-2.75583 + 2.60052i) q^{36} +7.70173 q^{37} +2.90535i q^{38} +(-3.33072 - 8.38268i) q^{39} -6.85495i q^{40} +2.83876 q^{41} +(-0.549047 - 1.38183i) q^{42} +9.44759i q^{43} +(4.03761 + 1.11599i) q^{44} +(-5.03853 - 5.33944i) q^{45} -4.94454i q^{46} +0.242178i q^{47} +(0.195273 - 0.0775883i) q^{48} -1.00000 q^{49} +0.848591 q^{50} +(0.243979 - 0.0969411i) q^{51} +6.57760i q^{52} +11.3416i q^{53} +(-1.88457 + 4.04308i) q^{54} +(-2.16224 + 7.82293i) q^{55} +2.80121i q^{56} +(-2.16451 - 5.44759i) q^{57} -5.57140 q^{58} -2.22046i q^{59} +(1.97678 + 4.97512i) q^{60} +11.1592i q^{61} +4.68888 q^{62} +(2.05895 + 2.18191i) q^{63} +4.65628 q^{64} -12.7442 q^{65} +(4.90250 - 0.534218i) q^{66} -1.94205 q^{67} -0.191442 q^{68} +(3.68372 + 9.27111i) q^{69} -2.10079 q^{70} +7.57130i q^{71} +(6.11199 - 5.76754i) q^{72} -3.49122i q^{73} -6.61169 q^{74} +(-1.59112 + 0.632207i) q^{75} +4.27454i q^{76} +(0.883578 - 3.19676i) q^{77} +(2.85932 + 7.19627i) q^{78} -11.6311i q^{79} -0.296873i q^{80} +(0.521482 - 8.98488i) q^{81} -2.43699 q^{82} +15.6670 q^{83} +(-0.807792 - 2.03303i) q^{84} -0.370921i q^{85} -8.11046i q^{86} +(10.4465 - 4.15073i) q^{87} +(-8.95480 - 2.47509i) q^{88} +2.58238i q^{89} +(4.32542 + 4.58374i) q^{90} +5.20778 q^{91} -7.27472i q^{92} +(-8.79175 + 3.49325i) q^{93} -0.207902i q^{94} -8.28197 q^{95} +(-9.18554 + 3.64972i) q^{96} -5.06076 q^{97} +0.858468 q^{98} +(-8.79429 + 4.65407i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 6 q^{3} + 24 q^{4} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 6 q^{3} + 24 q^{4} + 10 q^{9} - 20 q^{12} - 10 q^{15} - 8 q^{16} - 12 q^{25} - 20 q^{31} + 14 q^{33} - 8 q^{34} - 12 q^{36} + 4 q^{37} + 6 q^{45} - 48 q^{48} - 24 q^{49} - 28 q^{55} + 44 q^{58} + 32 q^{60} - 52 q^{64} + 12 q^{66} - 4 q^{67} + 54 q^{69} - 20 q^{70} + 68 q^{75} - 20 q^{78} + 2 q^{81} + 16 q^{82} - 44 q^{88} + 24 q^{91} + 26 q^{93} - 12 q^{97} - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/231\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.858468 −0.607029 −0.303514 0.952827i \(-0.598160\pi\)
−0.303514 + 0.952827i \(0.598160\pi\)
\(3\) 1.60964 0.639565i 0.929329 0.369253i
\(4\) −1.26303 −0.631516
\(5\) 2.44714i 1.09439i −0.837004 0.547197i \(-0.815695\pi\)
0.837004 0.547197i \(-0.184305\pi\)
\(6\) −1.38183 + 0.549047i −0.564129 + 0.224147i
\(7\) 1.00000i 0.377964i
\(8\) 2.80121 0.990377
\(9\) 2.18191 2.05895i 0.727304 0.686315i
\(10\) 2.10079i 0.664329i
\(11\) −3.19676 0.883578i −0.963860 0.266409i
\(12\) −2.03303 + 0.807792i −0.586886 + 0.233189i
\(13\) 5.20778i 1.44438i −0.691695 0.722190i \(-0.743136\pi\)
0.691695 0.722190i \(-0.256864\pi\)
\(14\) 0.858468i 0.229435i
\(15\) −1.56511 3.93903i −0.404109 1.01705i
\(16\) 0.121314 0.0303285
\(17\) 0.151573 0.0367619 0.0183810 0.999831i \(-0.494149\pi\)
0.0183810 + 0.999831i \(0.494149\pi\)
\(18\) −1.87310 + 1.76754i −0.441495 + 0.416613i
\(19\) 3.38435i 0.776422i −0.921570 0.388211i \(-0.873093\pi\)
0.921570 0.388211i \(-0.126907\pi\)
\(20\) 3.09082i 0.691128i
\(21\) 0.639565 + 1.60964i 0.139565 + 0.351253i
\(22\) 2.74432 + 0.758524i 0.585091 + 0.161718i
\(23\) 5.75973i 1.20099i 0.799630 + 0.600493i \(0.205029\pi\)
−0.799630 + 0.600493i \(0.794971\pi\)
\(24\) 4.50895 1.79156i 0.920386 0.365700i
\(25\) −0.988494 −0.197699
\(26\) 4.47072i 0.876780i
\(27\) 2.19527 4.70965i 0.422480 0.906372i
\(28\) 1.26303i 0.238691i
\(29\) 6.48993 1.20515 0.602575 0.798062i \(-0.294142\pi\)
0.602575 + 0.798062i \(0.294142\pi\)
\(30\) 1.34359 + 3.38153i 0.245306 + 0.617380i
\(31\) −5.46192 −0.980989 −0.490495 0.871444i \(-0.663184\pi\)
−0.490495 + 0.871444i \(0.663184\pi\)
\(32\) −5.70656 −1.00879
\(33\) −5.71076 + 0.622291i −0.994115 + 0.108327i
\(34\) −0.130121 −0.0223156
\(35\) 2.44714 0.413642
\(36\) −2.75583 + 2.60052i −0.459304 + 0.433419i
\(37\) 7.70173 1.26616 0.633078 0.774088i \(-0.281791\pi\)
0.633078 + 0.774088i \(0.281791\pi\)
\(38\) 2.90535i 0.471311i
\(39\) −3.33072 8.38268i −0.533342 1.34230i
\(40\) 6.85495i 1.08386i
\(41\) 2.83876 0.443340 0.221670 0.975122i \(-0.428849\pi\)
0.221670 + 0.975122i \(0.428849\pi\)
\(42\) −0.549047 1.38183i −0.0847197 0.213221i
\(43\) 9.44759i 1.44074i 0.693588 + 0.720372i \(0.256029\pi\)
−0.693588 + 0.720372i \(0.743971\pi\)
\(44\) 4.03761 + 1.11599i 0.608693 + 0.168241i
\(45\) −5.03853 5.33944i −0.751100 0.795957i
\(46\) 4.94454i 0.729033i
\(47\) 0.242178i 0.0353252i 0.999844 + 0.0176626i \(0.00562248\pi\)
−0.999844 + 0.0176626i \(0.994378\pi\)
\(48\) 0.195273 0.0775883i 0.0281852 0.0111989i
\(49\) −1.00000 −0.142857
\(50\) 0.848591 0.120009
\(51\) 0.243979 0.0969411i 0.0341639 0.0135745i
\(52\) 6.57760i 0.912149i
\(53\) 11.3416i 1.55789i 0.627091 + 0.778946i \(0.284246\pi\)
−0.627091 + 0.778946i \(0.715754\pi\)
\(54\) −1.88457 + 4.04308i −0.256458 + 0.550194i
\(55\) −2.16224 + 7.82293i −0.291556 + 1.05484i
\(56\) 2.80121i 0.374327i
\(57\) −2.16451 5.44759i −0.286696 0.721552i
\(58\) −5.57140 −0.731560
\(59\) 2.22046i 0.289080i −0.989499 0.144540i \(-0.953830\pi\)
0.989499 0.144540i \(-0.0461702\pi\)
\(60\) 1.97678 + 4.97512i 0.255201 + 0.642285i
\(61\) 11.1592i 1.42879i 0.699741 + 0.714397i \(0.253299\pi\)
−0.699741 + 0.714397i \(0.746701\pi\)
\(62\) 4.68888 0.595489
\(63\) 2.05895 + 2.18191i 0.259403 + 0.274895i
\(64\) 4.65628 0.582035
\(65\) −12.7442 −1.58072
\(66\) 4.90250 0.534218i 0.603457 0.0657576i
\(67\) −1.94205 −0.237259 −0.118630 0.992939i \(-0.537850\pi\)
−0.118630 + 0.992939i \(0.537850\pi\)
\(68\) −0.191442 −0.0232157
\(69\) 3.68372 + 9.27111i 0.443468 + 1.11611i
\(70\) −2.10079 −0.251093
\(71\) 7.57130i 0.898548i 0.893394 + 0.449274i \(0.148317\pi\)
−0.893394 + 0.449274i \(0.851683\pi\)
\(72\) 6.11199 5.76754i 0.720305 0.679711i
\(73\) 3.49122i 0.408616i −0.978907 0.204308i \(-0.934506\pi\)
0.978907 0.204308i \(-0.0654945\pi\)
\(74\) −6.61169 −0.768593
\(75\) −1.59112 + 0.632207i −0.183727 + 0.0730009i
\(76\) 4.27454i 0.490323i
\(77\) 0.883578 3.19676i 0.100693 0.364305i
\(78\) 2.85932 + 7.19627i 0.323754 + 0.814817i
\(79\) 11.6311i 1.30861i −0.756232 0.654303i \(-0.772962\pi\)
0.756232 0.654303i \(-0.227038\pi\)
\(80\) 0.296873i 0.0331914i
\(81\) 0.521482 8.98488i 0.0579424 0.998320i
\(82\) −2.43699 −0.269120
\(83\) 15.6670 1.71968 0.859841 0.510562i \(-0.170563\pi\)
0.859841 + 0.510562i \(0.170563\pi\)
\(84\) −0.807792 2.03303i −0.0881373 0.221822i
\(85\) 0.370921i 0.0402320i
\(86\) 8.11046i 0.874574i
\(87\) 10.4465 4.15073i 1.11998 0.445005i
\(88\) −8.95480 2.47509i −0.954585 0.263845i
\(89\) 2.58238i 0.273732i 0.990590 + 0.136866i \(0.0437030\pi\)
−0.990590 + 0.136866i \(0.956297\pi\)
\(90\) 4.32542 + 4.58374i 0.455939 + 0.483169i
\(91\) 5.20778 0.545924
\(92\) 7.27472i 0.758442i
\(93\) −8.79175 + 3.49325i −0.911662 + 0.362234i
\(94\) 0.207902i 0.0214434i
\(95\) −8.28197 −0.849712
\(96\) −9.18554 + 3.64972i −0.937495 + 0.372498i
\(97\) −5.06076 −0.513842 −0.256921 0.966432i \(-0.582708\pi\)
−0.256921 + 0.966432i \(0.582708\pi\)
\(98\) 0.858468 0.0867184
\(99\) −8.79429 + 4.65407i −0.883860 + 0.467752i
\(100\) 1.24850 0.124850
\(101\) 2.97195 0.295720 0.147860 0.989008i \(-0.452762\pi\)
0.147860 + 0.989008i \(0.452762\pi\)
\(102\) −0.209448 + 0.0832208i −0.0207385 + 0.00824009i
\(103\) 2.10711 0.207620 0.103810 0.994597i \(-0.466897\pi\)
0.103810 + 0.994597i \(0.466897\pi\)
\(104\) 14.5881i 1.43048i
\(105\) 3.93903 1.56511i 0.384410 0.152739i
\(106\) 9.73643i 0.945686i
\(107\) −15.5706 −1.50527 −0.752635 0.658438i \(-0.771218\pi\)
−0.752635 + 0.658438i \(0.771218\pi\)
\(108\) −2.77270 + 5.94844i −0.266803 + 0.572388i
\(109\) 4.19595i 0.401899i 0.979602 + 0.200950i \(0.0644027\pi\)
−0.979602 + 0.200950i \(0.935597\pi\)
\(110\) 1.85621 6.71573i 0.176983 0.640320i
\(111\) 12.3970 4.92576i 1.17668 0.467532i
\(112\) 0.121314i 0.0114631i
\(113\) 18.7645i 1.76521i −0.470113 0.882606i \(-0.655787\pi\)
0.470113 0.882606i \(-0.344213\pi\)
\(114\) 1.85816 + 4.67659i 0.174033 + 0.438003i
\(115\) 14.0949 1.31435
\(116\) −8.19699 −0.761071
\(117\) −10.7225 11.3629i −0.991300 1.05050i
\(118\) 1.90620i 0.175480i
\(119\) 0.151573i 0.0138947i
\(120\) −4.38419 11.0340i −0.400220 1.00727i
\(121\) 9.43858 + 5.64918i 0.858053 + 0.513562i
\(122\) 9.57985i 0.867319i
\(123\) 4.56940 1.81557i 0.412009 0.163705i
\(124\) 6.89858 0.619511
\(125\) 9.81672i 0.878034i
\(126\) −1.76754 1.87310i −0.157465 0.166869i
\(127\) 0.108701i 0.00964569i −0.999988 0.00482284i \(-0.998465\pi\)
0.999988 0.00482284i \(-0.00153516\pi\)
\(128\) 7.41586 0.655476
\(129\) 6.04235 + 15.2073i 0.532000 + 1.33893i
\(130\) 10.9405 0.959543
\(131\) 12.8269 1.12069 0.560347 0.828258i \(-0.310668\pi\)
0.560347 + 0.828258i \(0.310668\pi\)
\(132\) 7.21287 0.785974i 0.627800 0.0684103i
\(133\) 3.38435 0.293460
\(134\) 1.66719 0.144023
\(135\) −11.5252 5.37214i −0.991928 0.462360i
\(136\) 0.424589 0.0364082
\(137\) 17.6915i 1.51149i −0.654868 0.755743i \(-0.727276\pi\)
0.654868 0.755743i \(-0.272724\pi\)
\(138\) −3.16236 7.95896i −0.269198 0.677511i
\(139\) 2.19619i 0.186278i −0.995653 0.0931391i \(-0.970310\pi\)
0.995653 0.0931391i \(-0.0296901\pi\)
\(140\) −3.09082 −0.261222
\(141\) 0.154888 + 0.389820i 0.0130440 + 0.0328287i
\(142\) 6.49972i 0.545445i
\(143\) −4.60148 + 16.6480i −0.384795 + 1.39218i
\(144\) 0.264697 0.249779i 0.0220581 0.0208149i
\(145\) 15.8818i 1.31891i
\(146\) 2.99710i 0.248042i
\(147\) −1.60964 + 0.639565i −0.132761 + 0.0527505i
\(148\) −9.72753 −0.799598
\(149\) −7.83843 −0.642149 −0.321075 0.947054i \(-0.604044\pi\)
−0.321075 + 0.947054i \(0.604044\pi\)
\(150\) 1.36593 0.542729i 0.111528 0.0443137i
\(151\) 8.21629i 0.668632i 0.942461 + 0.334316i \(0.108505\pi\)
−0.942461 + 0.334316i \(0.891495\pi\)
\(152\) 9.48026i 0.768951i
\(153\) 0.330720 0.312081i 0.0267371 0.0252303i
\(154\) −0.758524 + 2.74432i −0.0611236 + 0.221144i
\(155\) 13.3661i 1.07359i
\(156\) 4.20680 + 10.5876i 0.336814 + 0.847686i
\(157\) 9.44050 0.753434 0.376717 0.926328i \(-0.377053\pi\)
0.376717 + 0.926328i \(0.377053\pi\)
\(158\) 9.98497i 0.794362i
\(159\) 7.25371 + 18.2560i 0.575257 + 1.44779i
\(160\) 13.9648i 1.10401i
\(161\) −5.75973 −0.453930
\(162\) −0.447675 + 7.71323i −0.0351727 + 0.606009i
\(163\) −8.13501 −0.637183 −0.318591 0.947892i \(-0.603210\pi\)
−0.318591 + 0.947892i \(0.603210\pi\)
\(164\) −3.58545 −0.279976
\(165\) 1.52283 + 13.9750i 0.118552 + 1.08795i
\(166\) −13.4497 −1.04390
\(167\) 2.64732 0.204856 0.102428 0.994740i \(-0.467339\pi\)
0.102428 + 0.994740i \(0.467339\pi\)
\(168\) 1.79156 + 4.50895i 0.138222 + 0.347873i
\(169\) −14.1210 −1.08623
\(170\) 0.318424i 0.0244220i
\(171\) −6.96819 7.38435i −0.532871 0.564695i
\(172\) 11.9326i 0.909853i
\(173\) −3.03157 −0.230486 −0.115243 0.993337i \(-0.536765\pi\)
−0.115243 + 0.993337i \(0.536765\pi\)
\(174\) −8.96797 + 3.56327i −0.679860 + 0.270131i
\(175\) 0.988494i 0.0747231i
\(176\) −0.387812 0.107191i −0.0292325 0.00807979i
\(177\) −1.42013 3.57416i −0.106744 0.268650i
\(178\) 2.21689i 0.166163i
\(179\) 9.79967i 0.732462i 0.930524 + 0.366231i \(0.119352\pi\)
−0.930524 + 0.366231i \(0.880648\pi\)
\(180\) 6.36382 + 6.74389i 0.474331 + 0.502660i
\(181\) −8.03062 −0.596911 −0.298456 0.954424i \(-0.596471\pi\)
−0.298456 + 0.954424i \(0.596471\pi\)
\(182\) −4.47072 −0.331392
\(183\) 7.13706 + 17.9624i 0.527587 + 1.32782i
\(184\) 16.1342i 1.18943i
\(185\) 18.8472i 1.38567i
\(186\) 7.54744 2.99885i 0.553405 0.219886i
\(187\) −0.484544 0.133927i −0.0354334 0.00979370i
\(188\) 0.305878i 0.0223084i
\(189\) 4.70965 + 2.19527i 0.342576 + 0.159683i
\(190\) 7.10981 0.515800
\(191\) 19.1519i 1.38578i 0.721042 + 0.692892i \(0.243664\pi\)
−0.721042 + 0.692892i \(0.756336\pi\)
\(192\) 7.49495 2.97799i 0.540901 0.214918i
\(193\) 0.410169i 0.0295246i −0.999891 0.0147623i \(-0.995301\pi\)
0.999891 0.0147623i \(-0.00469916\pi\)
\(194\) 4.34450 0.311917
\(195\) −20.5136 + 8.15073i −1.46901 + 0.583686i
\(196\) 1.26303 0.0902166
\(197\) 14.6387 1.04297 0.521483 0.853262i \(-0.325379\pi\)
0.521483 + 0.853262i \(0.325379\pi\)
\(198\) 7.54962 3.99537i 0.536528 0.283939i
\(199\) −25.7403 −1.82468 −0.912342 0.409430i \(-0.865728\pi\)
−0.912342 + 0.409430i \(0.865728\pi\)
\(200\) −2.76898 −0.195796
\(201\) −3.12601 + 1.24207i −0.220492 + 0.0876088i
\(202\) −2.55132 −0.179510
\(203\) 6.48993i 0.455504i
\(204\) −0.308154 + 0.122440i −0.0215751 + 0.00857249i
\(205\) 6.94685i 0.485189i
\(206\) −1.80889 −0.126031
\(207\) 11.8590 + 12.5672i 0.824255 + 0.873482i
\(208\) 0.631778i 0.0438059i
\(209\) −2.99033 + 10.8190i −0.206846 + 0.748362i
\(210\) −3.38153 + 1.34359i −0.233348 + 0.0927168i
\(211\) 15.4265i 1.06200i −0.847371 0.531001i \(-0.821816\pi\)
0.847371 0.531001i \(-0.178184\pi\)
\(212\) 14.3248i 0.983834i
\(213\) 4.84234 + 12.1871i 0.331792 + 0.835047i
\(214\) 13.3669 0.913743
\(215\) 23.1196 1.57674
\(216\) 6.14942 13.1927i 0.418415 0.897650i
\(217\) 5.46192i 0.370779i
\(218\) 3.60209i 0.243964i
\(219\) −2.23286 5.61962i −0.150883 0.379739i
\(220\) 2.73098 9.88061i 0.184123 0.666150i
\(221\) 0.789361i 0.0530982i
\(222\) −10.6425 + 4.22861i −0.714276 + 0.283806i
\(223\) −17.9823 −1.20419 −0.602094 0.798426i \(-0.705667\pi\)
−0.602094 + 0.798426i \(0.705667\pi\)
\(224\) 5.70656i 0.381286i
\(225\) −2.15681 + 2.03526i −0.143787 + 0.135684i
\(226\) 16.1087i 1.07153i
\(227\) 13.2902 0.882102 0.441051 0.897482i \(-0.354606\pi\)
0.441051 + 0.897482i \(0.354606\pi\)
\(228\) 2.73385 + 6.88049i 0.181053 + 0.455671i
\(229\) 19.3202 1.27671 0.638356 0.769741i \(-0.279615\pi\)
0.638356 + 0.769741i \(0.279615\pi\)
\(230\) −12.1000 −0.797850
\(231\) −0.622291 5.71076i −0.0409438 0.375740i
\(232\) 18.1797 1.19355
\(233\) −4.43936 −0.290832 −0.145416 0.989371i \(-0.546452\pi\)
−0.145416 + 0.989371i \(0.546452\pi\)
\(234\) 9.20497 + 9.75471i 0.601747 + 0.637686i
\(235\) 0.592642 0.0386597
\(236\) 2.80452i 0.182558i
\(237\) −7.43888 18.7220i −0.483207 1.21613i
\(238\) 0.130121i 0.00843449i
\(239\) 1.39522 0.0902494 0.0451247 0.998981i \(-0.485631\pi\)
0.0451247 + 0.998981i \(0.485631\pi\)
\(240\) −0.189869 0.477860i −0.0122560 0.0308457i
\(241\) 15.3983i 0.991894i 0.868353 + 0.495947i \(0.165179\pi\)
−0.868353 + 0.495947i \(0.834821\pi\)
\(242\) −8.10272 4.84964i −0.520863 0.311747i
\(243\) −4.90702 14.7960i −0.314785 0.949163i
\(244\) 14.0945i 0.902306i
\(245\) 2.44714i 0.156342i
\(246\) −3.92268 + 1.55861i −0.250101 + 0.0993735i
\(247\) −17.6249 −1.12145
\(248\) −15.3000 −0.971550
\(249\) 25.2184 10.0201i 1.59815 0.634998i
\(250\) 8.42734i 0.532992i
\(251\) 20.8877i 1.31842i 0.751958 + 0.659211i \(0.229110\pi\)
−0.751958 + 0.659211i \(0.770890\pi\)
\(252\) −2.60052 2.75583i −0.163817 0.173601i
\(253\) 5.08917 18.4125i 0.319953 1.15758i
\(254\) 0.0933167i 0.00585521i
\(255\) −0.237228 0.597051i −0.0148558 0.0373888i
\(256\) −15.6788 −0.979927
\(257\) 7.35614i 0.458863i −0.973325 0.229432i \(-0.926313\pi\)
0.973325 0.229432i \(-0.0736867\pi\)
\(258\) −5.18717 13.0550i −0.322939 0.812766i
\(259\) 7.70173i 0.478562i
\(260\) 16.0963 0.998250
\(261\) 14.1605 13.3624i 0.876510 0.827113i
\(262\) −11.0115 −0.680293
\(263\) 0.993296 0.0612493 0.0306246 0.999531i \(-0.490250\pi\)
0.0306246 + 0.999531i \(0.490250\pi\)
\(264\) −15.9970 + 1.74317i −0.984549 + 0.107285i
\(265\) 27.7546 1.70495
\(266\) −2.90535 −0.178139
\(267\) 1.65160 + 4.15672i 0.101076 + 0.254387i
\(268\) 2.45287 0.149833
\(269\) 13.9465i 0.850333i 0.905115 + 0.425167i \(0.139785\pi\)
−0.905115 + 0.425167i \(0.860215\pi\)
\(270\) 9.89399 + 4.61181i 0.602129 + 0.280666i
\(271\) 31.1174i 1.89025i 0.326709 + 0.945125i \(0.394060\pi\)
−0.326709 + 0.945125i \(0.605940\pi\)
\(272\) 0.0183880 0.00111494
\(273\) 8.38268 3.33072i 0.507343 0.201584i
\(274\) 15.1876i 0.917516i
\(275\) 3.15998 + 0.873412i 0.190554 + 0.0526687i
\(276\) −4.65266 11.7097i −0.280057 0.704842i
\(277\) 8.65778i 0.520195i 0.965582 + 0.260098i \(0.0837548\pi\)
−0.965582 + 0.260098i \(0.916245\pi\)
\(278\) 1.88536i 0.113076i
\(279\) −11.9174 + 11.2458i −0.713478 + 0.673268i
\(280\) 6.85495 0.409662
\(281\) −26.3528 −1.57208 −0.786038 0.618178i \(-0.787871\pi\)
−0.786038 + 0.618178i \(0.787871\pi\)
\(282\) −0.132967 0.334648i −0.00791806 0.0199280i
\(283\) 26.5449i 1.57793i −0.614436 0.788966i \(-0.710617\pi\)
0.614436 0.788966i \(-0.289383\pi\)
\(284\) 9.56280i 0.567448i
\(285\) −13.3310 + 5.29686i −0.789662 + 0.313759i
\(286\) 3.95023 14.2918i 0.233582 0.845093i
\(287\) 2.83876i 0.167567i
\(288\) −12.4512 + 11.7495i −0.733695 + 0.692346i
\(289\) −16.9770 −0.998649
\(290\) 13.6340i 0.800616i
\(291\) −8.14602 + 3.23669i −0.477528 + 0.189738i
\(292\) 4.40952i 0.258048i
\(293\) −32.2722 −1.88536 −0.942682 0.333694i \(-0.891705\pi\)
−0.942682 + 0.333694i \(0.891705\pi\)
\(294\) 1.38183 0.549047i 0.0805899 0.0320211i
\(295\) −5.43378 −0.316367
\(296\) 21.5742 1.25397
\(297\) −11.1791 + 13.1159i −0.648678 + 0.761063i
\(298\) 6.72904 0.389803
\(299\) 29.9954 1.73468
\(300\) 2.00964 0.798497i 0.116027 0.0461013i
\(301\) −9.44759 −0.544550
\(302\) 7.05342i 0.405879i
\(303\) 4.78378 1.90075i 0.274821 0.109195i
\(304\) 0.410569i 0.0235477i
\(305\) 27.3082 1.56366
\(306\) −0.283912 + 0.267912i −0.0162302 + 0.0153155i
\(307\) 1.71093i 0.0976479i −0.998807 0.0488240i \(-0.984453\pi\)
0.998807 0.0488240i \(-0.0155473\pi\)
\(308\) −1.11599 + 4.03761i −0.0635893 + 0.230064i
\(309\) 3.39170 1.34763i 0.192947 0.0766642i
\(310\) 11.4744i 0.651700i
\(311\) 7.97842i 0.452415i 0.974079 + 0.226207i \(0.0726327\pi\)
−0.974079 + 0.226207i \(0.927367\pi\)
\(312\) −9.33004 23.4816i −0.528210 1.32939i
\(313\) 7.94955 0.449335 0.224668 0.974435i \(-0.427870\pi\)
0.224668 + 0.974435i \(0.427870\pi\)
\(314\) −8.10437 −0.457356
\(315\) 5.33944 5.03853i 0.300844 0.283889i
\(316\) 14.6905i 0.826406i
\(317\) 9.99277i 0.561250i −0.959817 0.280625i \(-0.909458\pi\)
0.959817 0.280625i \(-0.0905417\pi\)
\(318\) −6.22708 15.6722i −0.349197 0.878853i
\(319\) −20.7468 5.73436i −1.16160 0.321063i
\(320\) 11.3946i 0.636975i
\(321\) −25.0632 + 9.95844i −1.39889 + 0.555826i
\(322\) 4.94454 0.275549
\(323\) 0.512977i 0.0285428i
\(324\) −0.658648 + 11.3482i −0.0365915 + 0.630455i
\(325\) 5.14786i 0.285552i
\(326\) 6.98365 0.386788
\(327\) 2.68358 + 6.75399i 0.148403 + 0.373496i
\(328\) 7.95197 0.439074
\(329\) −0.242178 −0.0133517
\(330\) −1.30731 11.9971i −0.0719648 0.660419i
\(331\) 33.5249 1.84270 0.921348 0.388738i \(-0.127089\pi\)
0.921348 + 0.388738i \(0.127089\pi\)
\(332\) −19.7880 −1.08601
\(333\) 16.8045 15.8574i 0.920881 0.868983i
\(334\) −2.27264 −0.124353
\(335\) 4.75247i 0.259655i
\(336\) 0.0775883 + 0.195273i 0.00423279 + 0.0106530i
\(337\) 12.1898i 0.664019i 0.943276 + 0.332009i \(0.107727\pi\)
−0.943276 + 0.332009i \(0.892273\pi\)
\(338\) 12.1224 0.659374
\(339\) −12.0011 30.2041i −0.651810 1.64046i
\(340\) 0.468485i 0.0254072i
\(341\) 17.4605 + 4.82603i 0.945537 + 0.261344i
\(342\) 5.98197 + 6.33923i 0.323468 + 0.342786i
\(343\) 1.00000i 0.0539949i
\(344\) 26.4647i 1.42688i
\(345\) 22.6877 9.01458i 1.22147 0.485329i
\(346\) 2.60251 0.139912
\(347\) −2.32869 −0.125011 −0.0625054 0.998045i \(-0.519909\pi\)
−0.0625054 + 0.998045i \(0.519909\pi\)
\(348\) −13.1942 + 5.24251i −0.707285 + 0.281028i
\(349\) 18.9275i 1.01317i −0.862191 0.506584i \(-0.830908\pi\)
0.862191 0.506584i \(-0.169092\pi\)
\(350\) 0.848591i 0.0453591i
\(351\) −24.5268 11.4325i −1.30915 0.610222i
\(352\) 18.2425 + 5.04220i 0.972330 + 0.268750i
\(353\) 21.8920i 1.16519i −0.812761 0.582597i \(-0.802036\pi\)
0.812761 0.582597i \(-0.197964\pi\)
\(354\) 1.21914 + 3.06830i 0.0647965 + 0.163078i
\(355\) 18.5280 0.983366
\(356\) 3.26163i 0.172866i
\(357\) 0.0969411 + 0.243979i 0.00513066 + 0.0129127i
\(358\) 8.41271i 0.444626i
\(359\) −27.6170 −1.45757 −0.728786 0.684742i \(-0.759915\pi\)
−0.728786 + 0.684742i \(0.759915\pi\)
\(360\) −14.1140 14.9569i −0.743872 0.788298i
\(361\) 7.54620 0.397168
\(362\) 6.89403 0.362342
\(363\) 18.8058 + 3.05658i 0.987047 + 0.160429i
\(364\) −6.57760 −0.344760
\(365\) −8.54350 −0.447187
\(366\) −6.12694 15.4202i −0.320260 0.806025i
\(367\) 21.0812 1.10043 0.550214 0.835024i \(-0.314546\pi\)
0.550214 + 0.835024i \(0.314546\pi\)
\(368\) 0.698736i 0.0364241i
\(369\) 6.19393 5.84486i 0.322443 0.304271i
\(370\) 16.1797i 0.841144i
\(371\) −11.3416 −0.588828
\(372\) 11.1043 4.41209i 0.575729 0.228756i
\(373\) 31.1830i 1.61459i 0.590145 + 0.807297i \(0.299071\pi\)
−0.590145 + 0.807297i \(0.700929\pi\)
\(374\) 0.415966 + 0.114972i 0.0215091 + 0.00594506i
\(375\) −6.27843 15.8014i −0.324217 0.815982i
\(376\) 0.678390i 0.0349853i
\(377\) 33.7981i 1.74069i
\(378\) −4.04308 1.88457i −0.207954 0.0969319i
\(379\) −11.2956 −0.580219 −0.290109 0.956994i \(-0.593692\pi\)
−0.290109 + 0.956994i \(0.593692\pi\)
\(380\) 10.4604 0.536607
\(381\) −0.0695216 0.174971i −0.00356170 0.00896402i
\(382\) 16.4413i 0.841210i
\(383\) 2.15474i 0.110102i −0.998484 0.0550511i \(-0.982468\pi\)
0.998484 0.0550511i \(-0.0175322\pi\)
\(384\) 11.9369 4.74293i 0.609153 0.242037i
\(385\) −7.82293 2.16224i −0.398693 0.110198i
\(386\) 0.352118i 0.0179223i
\(387\) 19.4521 + 20.6138i 0.988805 + 1.04786i
\(388\) 6.39190 0.324500
\(389\) 10.8798i 0.551626i 0.961211 + 0.275813i \(0.0889471\pi\)
−0.961211 + 0.275813i \(0.911053\pi\)
\(390\) 17.6103 6.99715i 0.891731 0.354314i
\(391\) 0.873021i 0.0441506i
\(392\) −2.80121 −0.141482
\(393\) 20.6468 8.20365i 1.04149 0.413820i
\(394\) −12.5669 −0.633110
\(395\) −28.4630 −1.43213
\(396\) 11.1075 5.87824i 0.558172 0.295393i
\(397\) −33.3972 −1.67616 −0.838079 0.545549i \(-0.816321\pi\)
−0.838079 + 0.545549i \(0.816321\pi\)
\(398\) 22.0973 1.10764
\(399\) 5.44759 2.16451i 0.272721 0.108361i
\(400\) −0.119918 −0.00599592
\(401\) 2.29520i 0.114617i 0.998357 + 0.0573085i \(0.0182518\pi\)
−0.998357 + 0.0573085i \(0.981748\pi\)
\(402\) 2.68358 1.06628i 0.133845 0.0531811i
\(403\) 28.4445i 1.41692i
\(404\) −3.75366 −0.186752
\(405\) −21.9873 1.27614i −1.09256 0.0634118i
\(406\) 5.57140i 0.276504i
\(407\) −24.6206 6.80508i −1.22040 0.337315i
\(408\) 0.683437 0.271552i 0.0338352 0.0134438i
\(409\) 0.487637i 0.0241121i 0.999927 + 0.0120561i \(0.00383765\pi\)
−0.999927 + 0.0120561i \(0.996162\pi\)
\(410\) 5.96365i 0.294524i
\(411\) −11.3149 28.4770i −0.558121 1.40467i
\(412\) −2.66135 −0.131115
\(413\) 2.22046 0.109262
\(414\) −10.1805 10.7886i −0.500347 0.530229i
\(415\) 38.3395i 1.88201i
\(416\) 29.7186i 1.45707i
\(417\) −1.40461 3.53508i −0.0687838 0.173114i
\(418\) 2.56711 9.28773i 0.125561 0.454278i
\(419\) 16.5555i 0.808788i 0.914585 + 0.404394i \(0.132517\pi\)
−0.914585 + 0.404394i \(0.867483\pi\)
\(420\) −4.97512 + 1.97678i −0.242761 + 0.0964569i
\(421\) −1.95797 −0.0954255 −0.0477127 0.998861i \(-0.515193\pi\)
−0.0477127 + 0.998861i \(0.515193\pi\)
\(422\) 13.2431i 0.644666i
\(423\) 0.498631 + 0.528410i 0.0242442 + 0.0256922i
\(424\) 31.7703i 1.54290i
\(425\) −0.149829 −0.00726779
\(426\) −4.15700 10.4622i −0.201407 0.506897i
\(427\) −11.1592 −0.540033
\(428\) 19.6662 0.950603
\(429\) 3.24076 + 29.7404i 0.156465 + 1.43588i
\(430\) −19.8474 −0.957128
\(431\) 15.3532 0.739536 0.369768 0.929124i \(-0.379437\pi\)
0.369768 + 0.929124i \(0.379437\pi\)
\(432\) 0.266318 0.571347i 0.0128132 0.0274889i
\(433\) 9.06597 0.435683 0.217841 0.975984i \(-0.430098\pi\)
0.217841 + 0.975984i \(0.430098\pi\)
\(434\) 4.68888i 0.225074i
\(435\) −10.1574 25.5640i −0.487011 1.22570i
\(436\) 5.29962i 0.253806i
\(437\) 19.4929 0.932472
\(438\) 1.91684 + 4.82427i 0.0915903 + 0.230512i
\(439\) 3.83456i 0.183014i 0.995804 + 0.0915069i \(0.0291683\pi\)
−0.995804 + 0.0915069i \(0.970832\pi\)
\(440\) −6.05689 + 21.9137i −0.288751 + 1.04469i
\(441\) −2.18191 + 2.05895i −0.103901 + 0.0980451i
\(442\) 0.677642i 0.0322321i
\(443\) 7.53453i 0.357976i −0.983851 0.178988i \(-0.942718\pi\)
0.983851 0.178988i \(-0.0572824\pi\)
\(444\) −15.6579 + 6.22139i −0.743090 + 0.295254i
\(445\) 6.31945 0.299571
\(446\) 15.4373 0.730976
\(447\) −12.6171 + 5.01319i −0.596768 + 0.237116i
\(448\) 4.65628i 0.219988i
\(449\) 11.0420i 0.521102i 0.965460 + 0.260551i \(0.0839042\pi\)
−0.965460 + 0.260551i \(0.916096\pi\)
\(450\) 1.85155 1.74720i 0.0872830 0.0823640i
\(451\) −9.07485 2.50827i −0.427318 0.118110i
\(452\) 23.7001i 1.11476i
\(453\) 5.25485 + 13.2253i 0.246895 + 0.621379i
\(454\) −11.4092 −0.535462
\(455\) 12.7442i 0.597456i
\(456\) −6.06325 15.2599i −0.283938 0.714608i
\(457\) 6.31005i 0.295172i −0.989049 0.147586i \(-0.952850\pi\)
0.989049 0.147586i \(-0.0471503\pi\)
\(458\) −16.5857 −0.775001
\(459\) 0.332745 0.713857i 0.0155312 0.0333200i
\(460\) −17.8023 −0.830034
\(461\) 3.42269 0.159411 0.0797053 0.996818i \(-0.474602\pi\)
0.0797053 + 0.996818i \(0.474602\pi\)
\(462\) 0.534218 + 4.90250i 0.0248541 + 0.228085i
\(463\) 4.98281 0.231571 0.115785 0.993274i \(-0.463062\pi\)
0.115785 + 0.993274i \(0.463062\pi\)
\(464\) 0.787320 0.0365504
\(465\) 8.54848 + 21.5146i 0.396426 + 0.997717i
\(466\) 3.81105 0.176543
\(467\) 1.41768i 0.0656026i −0.999462 0.0328013i \(-0.989557\pi\)
0.999462 0.0328013i \(-0.0104429\pi\)
\(468\) 13.5429 + 14.3517i 0.626022 + 0.663409i
\(469\) 1.94205i 0.0896757i
\(470\) −0.508765 −0.0234676
\(471\) 15.1958 6.03782i 0.700188 0.278208i
\(472\) 6.21998i 0.286298i
\(473\) 8.34769 30.2017i 0.383827 1.38868i
\(474\) 6.38604 + 16.0723i 0.293321 + 0.738223i
\(475\) 3.34541i 0.153498i
\(476\) 0.191442i 0.00877473i
\(477\) 23.3518 + 24.7464i 1.06921 + 1.13306i
\(478\) −1.19775 −0.0547840
\(479\) 23.8833 1.09126 0.545628 0.838028i \(-0.316291\pi\)
0.545628 + 0.838028i \(0.316291\pi\)
\(480\) 8.93138 + 22.4783i 0.407660 + 1.02599i
\(481\) 40.1089i 1.82881i
\(482\) 13.2190i 0.602108i
\(483\) −9.27111 + 3.68372i −0.421850 + 0.167615i
\(484\) −11.9212 7.13509i −0.541874 0.324322i
\(485\) 12.3844i 0.562346i
\(486\) 4.21252 + 12.7019i 0.191084 + 0.576169i
\(487\) 24.6191 1.11560 0.557799 0.829976i \(-0.311646\pi\)
0.557799 + 0.829976i \(0.311646\pi\)
\(488\) 31.2594i 1.41505i
\(489\) −13.0945 + 5.20287i −0.592152 + 0.235282i
\(490\) 2.10079i 0.0949041i
\(491\) −4.71511 −0.212790 −0.106395 0.994324i \(-0.533931\pi\)
−0.106395 + 0.994324i \(0.533931\pi\)
\(492\) −5.77130 + 2.29313i −0.260190 + 0.103382i
\(493\) 0.983700 0.0443036
\(494\) 15.1305 0.680751
\(495\) 11.3892 + 21.5209i 0.511905 + 0.967291i
\(496\) −0.662608 −0.0297520
\(497\) −7.57130 −0.339619
\(498\) −21.6492 + 8.60194i −0.970123 + 0.385462i
\(499\) 13.8960 0.622070 0.311035 0.950399i \(-0.399324\pi\)
0.311035 + 0.950399i \(0.399324\pi\)
\(500\) 12.3988i 0.554492i
\(501\) 4.26124 1.69313i 0.190378 0.0756436i
\(502\) 17.9315i 0.800321i
\(503\) 21.4181 0.954987 0.477494 0.878635i \(-0.341545\pi\)
0.477494 + 0.878635i \(0.341545\pi\)
\(504\) 5.76754 + 6.11199i 0.256907 + 0.272250i
\(505\) 7.27277i 0.323634i
\(506\) −4.36889 + 15.8065i −0.194221 + 0.702686i
\(507\) −22.7298 + 9.03131i −1.00947 + 0.401095i
\(508\) 0.137293i 0.00609141i
\(509\) 1.52865i 0.0677564i 0.999426 + 0.0338782i \(0.0107858\pi\)
−0.999426 + 0.0338782i \(0.989214\pi\)
\(510\) 0.203653 + 0.512550i 0.00901791 + 0.0226961i
\(511\) 3.49122 0.154442
\(512\) −1.37194 −0.0606317
\(513\) −15.9391 7.42956i −0.703727 0.328023i
\(514\) 6.31501i 0.278543i
\(515\) 5.15639i 0.227218i
\(516\) −7.63169 19.2073i −0.335966 0.845553i
\(517\) 0.213983 0.774184i 0.00941095 0.0340486i
\(518\) 6.61169i 0.290501i
\(519\) −4.87975 + 1.93889i −0.214197 + 0.0851077i
\(520\) −35.6991 −1.56551
\(521\) 14.5996i 0.639621i −0.947481 0.319811i \(-0.896381\pi\)
0.947481 0.319811i \(-0.103619\pi\)
\(522\) −12.1563 + 11.4712i −0.532067 + 0.502081i
\(523\) 7.63979i 0.334065i −0.985951 0.167032i \(-0.946582\pi\)
0.985951 0.167032i \(-0.0534184\pi\)
\(524\) −16.2008 −0.707736
\(525\) −0.632207 1.59112i −0.0275918 0.0694424i
\(526\) −0.852713 −0.0371801
\(527\) −0.827881 −0.0360631
\(528\) −0.692796 + 0.0754928i −0.0301501 + 0.00328540i
\(529\) −10.1744 −0.442367
\(530\) −23.8264 −1.03495
\(531\) −4.57181 4.84486i −0.198400 0.210249i
\(532\) −4.27454 −0.185325
\(533\) 14.7837i 0.640351i
\(534\) −1.41785 3.56841i −0.0613563 0.154420i
\(535\) 38.1035i 1.64736i
\(536\) −5.44010 −0.234976
\(537\) 6.26753 + 15.7740i 0.270464 + 0.680698i
\(538\) 11.9726i 0.516177i
\(539\) 3.19676 + 0.883578i 0.137694 + 0.0380584i
\(540\) 14.5567 + 6.78518i 0.626419 + 0.291988i
\(541\) 23.4249i 1.00711i 0.863962 + 0.503557i \(0.167975\pi\)
−0.863962 + 0.503557i \(0.832025\pi\)
\(542\) 26.7133i 1.14744i
\(543\) −12.9264 + 5.13611i −0.554727 + 0.220411i
\(544\) −0.864963 −0.0370850
\(545\) 10.2681 0.439836
\(546\) −7.19627 + 2.85932i −0.307972 + 0.122367i
\(547\) 14.5891i 0.623785i −0.950117 0.311893i \(-0.899037\pi\)
0.950117 0.311893i \(-0.100963\pi\)
\(548\) 22.3449i 0.954528i
\(549\) 22.9763 + 24.3485i 0.980603 + 1.03917i
\(550\) −2.71274 0.749797i −0.115672 0.0319714i
\(551\) 21.9642i 0.935705i
\(552\) 10.3189 + 25.9703i 0.439201 + 1.10537i
\(553\) 11.6311 0.494607
\(554\) 7.43243i 0.315774i
\(555\) −12.0540 30.3373i −0.511665 1.28775i
\(556\) 2.77385i 0.117638i
\(557\) −1.76892 −0.0749516 −0.0374758 0.999298i \(-0.511932\pi\)
−0.0374758 + 0.999298i \(0.511932\pi\)
\(558\) 10.2307 9.65416i 0.433101 0.408693i
\(559\) 49.2010 2.08098
\(560\) 0.296873 0.0125452
\(561\) −0.865599 + 0.0943228i −0.0365456 + 0.00398231i
\(562\) 22.6231 0.954296
\(563\) −34.9625 −1.47349 −0.736747 0.676168i \(-0.763639\pi\)
−0.736747 + 0.676168i \(0.763639\pi\)
\(564\) −0.195629 0.492355i −0.00823747 0.0207319i
\(565\) −45.9193 −1.93184
\(566\) 22.7880i 0.957851i
\(567\) 8.98488 + 0.521482i 0.377329 + 0.0219002i
\(568\) 21.2088i 0.889902i
\(569\) −27.1063 −1.13636 −0.568178 0.822906i \(-0.692351\pi\)
−0.568178 + 0.822906i \(0.692351\pi\)
\(570\) 11.4443 4.54719i 0.479348 0.190461i
\(571\) 7.51053i 0.314306i 0.987574 + 0.157153i \(0.0502316\pi\)
−0.987574 + 0.157153i \(0.949768\pi\)
\(572\) 5.81182 21.0270i 0.243005 0.879184i
\(573\) 12.2489 + 30.8278i 0.511705 + 1.28785i
\(574\) 2.43699i 0.101718i
\(575\) 5.69346i 0.237434i
\(576\) 10.1596 9.58702i 0.423316 0.399459i
\(577\) 38.1511 1.58825 0.794126 0.607753i \(-0.207929\pi\)
0.794126 + 0.607753i \(0.207929\pi\)
\(578\) 14.5742 0.606208
\(579\) −0.262330 0.660227i −0.0109021 0.0274381i
\(580\) 20.0592i 0.832912i
\(581\) 15.6670i 0.649979i
\(582\) 6.99310 2.77859i 0.289873 0.115176i
\(583\) 10.0212 36.2565i 0.415036 1.50159i
\(584\) 9.77964i 0.404684i
\(585\) −27.8067 + 26.2396i −1.14966 + 1.08487i
\(586\) 27.7047 1.14447
\(587\) 21.8338i 0.901177i −0.892732 0.450589i \(-0.851214\pi\)
0.892732 0.450589i \(-0.148786\pi\)
\(588\) 2.03303 0.807792i 0.0838409 0.0333128i
\(589\) 18.4850i 0.761662i
\(590\) 4.66473 0.192044
\(591\) 23.5631 9.36241i 0.969258 0.385118i
\(592\) 0.934329 0.0384007
\(593\) −41.3070 −1.69627 −0.848137 0.529777i \(-0.822276\pi\)
−0.848137 + 0.529777i \(0.822276\pi\)
\(594\) 9.59691 11.2596i 0.393766 0.461987i
\(595\) 0.370921 0.0152063
\(596\) 9.90019 0.405528
\(597\) −41.4328 + 16.4626i −1.69573 + 0.673770i
\(598\) −25.7501 −1.05300
\(599\) 19.0163i 0.776986i −0.921452 0.388493i \(-0.872996\pi\)
0.921452 0.388493i \(-0.127004\pi\)
\(600\) −4.45707 + 1.77094i −0.181959 + 0.0722985i
\(601\) 27.9294i 1.13927i −0.821899 0.569633i \(-0.807086\pi\)
0.821899 0.569633i \(-0.192914\pi\)
\(602\) 8.11046 0.330558
\(603\) −4.23739 + 3.99858i −0.172560 + 0.162835i
\(604\) 10.3774i 0.422252i
\(605\) 13.8243 23.0975i 0.562039 0.939048i
\(606\) −4.10672 + 1.63174i −0.166824 + 0.0662848i
\(607\) 45.3889i 1.84228i 0.389231 + 0.921140i \(0.372741\pi\)
−0.389231 + 0.921140i \(0.627259\pi\)
\(608\) 19.3130i 0.783245i
\(609\) 4.15073 + 10.4465i 0.168196 + 0.423313i
\(610\) −23.4432 −0.949189
\(611\) 1.26121 0.0510230
\(612\) −0.417710 + 0.394169i −0.0168849 + 0.0159333i
\(613\) 21.9987i 0.888521i −0.895898 0.444260i \(-0.853467\pi\)
0.895898 0.444260i \(-0.146533\pi\)
\(614\) 1.46878i 0.0592751i
\(615\) −4.44296 11.1820i −0.179158 0.450900i
\(616\) 2.47509 8.95480i 0.0997241 0.360799i
\(617\) 9.86433i 0.397123i 0.980088 + 0.198562i \(0.0636270\pi\)
−0.980088 + 0.198562i \(0.936373\pi\)
\(618\) −2.91167 + 1.15690i −0.117124 + 0.0465374i
\(619\) 28.5296 1.14670 0.573351 0.819310i \(-0.305643\pi\)
0.573351 + 0.819310i \(0.305643\pi\)
\(620\) 16.8818i 0.677989i
\(621\) 27.1263 + 12.6442i 1.08854 + 0.507393i
\(622\) 6.84922i 0.274629i
\(623\) −2.58238 −0.103461
\(624\) −0.404063 1.01694i −0.0161755 0.0407101i
\(625\) −28.9654 −1.15861
\(626\) −6.82444 −0.272760
\(627\) 2.10605 + 19.3272i 0.0841075 + 0.771853i
\(628\) −11.9237 −0.475806
\(629\) 1.16738 0.0465464
\(630\) −4.58374 + 4.32542i −0.182621 + 0.172329i
\(631\) 4.84996 0.193074 0.0965369 0.995329i \(-0.469223\pi\)
0.0965369 + 0.995329i \(0.469223\pi\)
\(632\) 32.5813i 1.29601i
\(633\) −9.86624 24.8311i −0.392148 0.986949i
\(634\) 8.57848i 0.340695i
\(635\) −0.266007 −0.0105562
\(636\) −9.16167 23.0579i −0.363284 0.914305i
\(637\) 5.20778i 0.206340i
\(638\) 17.8104 + 4.92277i 0.705122 + 0.194894i
\(639\) 15.5889 + 16.5199i 0.616687 + 0.653518i
\(640\) 18.1477i 0.717349i
\(641\) 31.4366i 1.24167i 0.783940 + 0.620836i \(0.213207\pi\)
−0.783940 + 0.620836i \(0.786793\pi\)
\(642\) 21.5160 8.54901i 0.849167 0.337402i
\(643\) −17.5992 −0.694045 −0.347023 0.937857i \(-0.612807\pi\)
−0.347023 + 0.937857i \(0.612807\pi\)
\(644\) 7.27472 0.286664
\(645\) 37.2143 14.7865i 1.46531 0.582217i
\(646\) 0.440374i 0.0173263i
\(647\) 5.27548i 0.207400i 0.994609 + 0.103700i \(0.0330682\pi\)
−0.994609 + 0.103700i \(0.966932\pi\)
\(648\) 1.46078 25.1685i 0.0573848 0.988713i
\(649\) −1.96195 + 7.09829i −0.0770134 + 0.278632i
\(650\) 4.41928i 0.173338i
\(651\) −3.49325 8.79175i −0.136911 0.344576i
\(652\) 10.2748 0.402391
\(653\) 20.2731i 0.793348i −0.917959 0.396674i \(-0.870164\pi\)
0.917959 0.396674i \(-0.129836\pi\)
\(654\) −2.30377 5.79809i −0.0900846 0.226723i
\(655\) 31.3893i 1.22648i
\(656\) 0.344382 0.0134459
\(657\) −7.18823 7.61753i −0.280440 0.297188i
\(658\) 0.207902 0.00810485
\(659\) −4.30970 −0.167882 −0.0839410 0.996471i \(-0.526751\pi\)
−0.0839410 + 0.996471i \(0.526751\pi\)
\(660\) −1.92339 17.6509i −0.0748678 0.687060i
\(661\) −15.5035 −0.603018 −0.301509 0.953463i \(-0.597490\pi\)
−0.301509 + 0.953463i \(0.597490\pi\)
\(662\) −28.7801 −1.11857
\(663\) −0.504848 1.27059i −0.0196067 0.0493457i
\(664\) 43.8867 1.70313
\(665\) 8.28197i 0.321161i
\(666\) −14.4261 + 13.6131i −0.559001 + 0.527497i
\(667\) 37.3802i 1.44737i
\(668\) −3.34365 −0.129370
\(669\) −28.9452 + 11.5009i −1.11909 + 0.444650i
\(670\) 4.07985i 0.157618i
\(671\) 9.86006 35.6734i 0.380643 1.37716i
\(672\) −3.64972 9.18554i −0.140791 0.354340i
\(673\) 43.5361i 1.67819i 0.543982 + 0.839097i \(0.316916\pi\)
−0.543982 + 0.839097i \(0.683084\pi\)
\(674\) 10.4645i 0.403079i
\(675\) −2.17001 + 4.65546i −0.0835239 + 0.179189i
\(676\) 17.8353 0.685973
\(677\) −45.1287 −1.73444 −0.867219 0.497928i \(-0.834094\pi\)
−0.867219 + 0.497928i \(0.834094\pi\)
\(678\) 10.3026 + 25.9293i 0.395668 + 0.995808i
\(679\) 5.06076i 0.194214i
\(680\) 1.03903i 0.0398449i
\(681\) 21.3925 8.49996i 0.819763 0.325719i
\(682\) −14.9892 4.14300i −0.573968 0.158644i
\(683\) 15.5761i 0.596004i −0.954565 0.298002i \(-0.903680\pi\)
0.954565 0.298002i \(-0.0963202\pi\)
\(684\) 8.80104 + 9.32667i 0.336516 + 0.356614i
\(685\) −43.2936 −1.65416
\(686\) 0.858468i 0.0327765i
\(687\) 31.0986 12.3565i 1.18649 0.471430i
\(688\) 1.14613i 0.0436957i
\(689\) 59.0647 2.25019
\(690\) −19.4767 + 7.73873i −0.741465 + 0.294609i
\(691\) 4.54246 0.172803 0.0864016 0.996260i \(-0.472463\pi\)
0.0864016 + 0.996260i \(0.472463\pi\)
\(692\) 3.82897 0.145556
\(693\) −4.65407 8.79429i −0.176794 0.334068i
\(694\) 1.99911 0.0758851
\(695\) −5.37438 −0.203862
\(696\) 29.2628 11.6271i 1.10920 0.440723i
\(697\) 0.430281 0.0162980
\(698\) 16.2487i 0.615022i
\(699\) −7.14579 + 2.83926i −0.270279 + 0.107391i
\(700\) 1.24850i 0.0471889i
\(701\) 35.4949 1.34062 0.670312 0.742080i \(-0.266160\pi\)
0.670312 + 0.742080i \(0.266160\pi\)
\(702\) 21.0555 + 9.81444i 0.794689 + 0.370422i
\(703\) 26.0653i 0.983072i
\(704\) −14.8850 4.11418i −0.561000 0.155059i
\(705\) 0.953944 0.379034i 0.0359276 0.0142752i
\(706\) 18.7936i 0.707307i
\(707\) 2.97195i 0.111772i
\(708\) 1.79367 + 4.51427i 0.0674103 + 0.169657i
\(709\) −39.3543 −1.47798 −0.738990 0.673716i \(-0.764697\pi\)
−0.738990 + 0.673716i \(0.764697\pi\)
\(710\) −15.9057 −0.596932
\(711\) −23.9479 25.3781i −0.898117 0.951755i
\(712\) 7.23379i 0.271098i
\(713\) 31.4591i 1.17815i
\(714\) −0.0832208 0.209448i −0.00311446 0.00783841i
\(715\) 40.7401 + 11.2605i 1.52359 + 0.421118i
\(716\) 12.3773i 0.462562i
\(717\) 2.24581 0.892336i 0.0838714 0.0333249i
\(718\) 23.7083 0.884788
\(719\) 24.1882i 0.902068i −0.892507 0.451034i \(-0.851055\pi\)
0.892507 0.451034i \(-0.148945\pi\)
\(720\) −0.611245 0.647750i −0.0227798 0.0241402i
\(721\) 2.10711i 0.0784729i
\(722\) −6.47817 −0.241093
\(723\) 9.84824 + 24.7859i 0.366260 + 0.921796i
\(724\) 10.1429 0.376959
\(725\) −6.41526 −0.238257
\(726\) −16.1442 2.62398i −0.599166 0.0973850i
\(727\) −27.5666 −1.02239 −0.511195 0.859465i \(-0.670797\pi\)
−0.511195 + 0.859465i \(0.670797\pi\)
\(728\) 14.5881 0.540671
\(729\) −17.3616 20.6779i −0.643021 0.765849i
\(730\) 7.33433 0.271456
\(731\) 1.43200i 0.0529646i
\(732\) −9.01434 22.6871i −0.333180 0.838539i
\(733\) 20.8387i 0.769695i −0.922980 0.384848i \(-0.874254\pi\)
0.922980 0.384848i \(-0.125746\pi\)
\(734\) −18.0975 −0.667991
\(735\) 1.56511 + 3.93903i 0.0577298 + 0.145293i
\(736\) 32.8682i 1.21154i
\(737\) 6.20828 + 1.71596i 0.228685 + 0.0632080i
\(738\) −5.31729 + 5.01762i −0.195732 + 0.184701i
\(739\) 39.4845i 1.45246i −0.687452 0.726230i \(-0.741271\pi\)
0.687452 0.726230i \(-0.258729\pi\)
\(740\) 23.8046i 0.875076i
\(741\) −28.3699 + 11.2723i −1.04219 + 0.414098i
\(742\) 9.73643 0.357436
\(743\) −18.3829 −0.674405 −0.337202 0.941432i \(-0.609481\pi\)
−0.337202 + 0.941432i \(0.609481\pi\)
\(744\) −24.6275 + 9.78534i −0.902889 + 0.358748i
\(745\) 19.1817i 0.702764i
\(746\) 26.7696i 0.980105i
\(747\) 34.1841 32.2576i 1.25073 1.18024i
\(748\) 0.611994 + 0.169154i 0.0223767 + 0.00618488i
\(749\) 15.5706i 0.568939i
\(750\) 5.38984 + 13.5650i 0.196809 + 0.495325i
\(751\) −45.7526 −1.66954 −0.834768 0.550601i \(-0.814399\pi\)
−0.834768 + 0.550601i \(0.814399\pi\)
\(752\) 0.0293796i 0.00107136i
\(753\) 13.3591 + 33.6218i 0.486832 + 1.22525i
\(754\) 29.0146i 1.05665i
\(755\) 20.1064 0.731747
\(756\) −5.94844 2.77270i −0.216343 0.100842i
\(757\) −25.8349 −0.938986 −0.469493 0.882936i \(-0.655563\pi\)
−0.469493 + 0.882936i \(0.655563\pi\)
\(758\) 9.69696 0.352209
\(759\) −3.58423 32.8924i −0.130099 1.19392i
\(760\) −23.1995 −0.841536
\(761\) −33.4984 −1.21432 −0.607158 0.794581i \(-0.707690\pi\)
−0.607158 + 0.794581i \(0.707690\pi\)
\(762\) 0.0596821 + 0.150207i 0.00216206 + 0.00544142i
\(763\) −4.19595 −0.151904
\(764\) 24.1895i 0.875144i
\(765\) −0.763707 0.809317i −0.0276119 0.0292609i
\(766\) 1.84978i 0.0668352i
\(767\) −11.5637 −0.417541
\(768\) −25.2374 + 10.0276i −0.910675 + 0.361841i
\(769\) 35.1763i 1.26849i 0.773132 + 0.634245i \(0.218689\pi\)
−0.773132 + 0.634245i \(0.781311\pi\)
\(770\) 6.71573 + 1.85621i 0.242018 + 0.0668933i
\(771\) −4.70473 11.8408i −0.169437 0.426435i
\(772\) 0.518057i 0.0186453i
\(773\) 41.0079i 1.47495i 0.675374 + 0.737475i \(0.263982\pi\)
−0.675374 + 0.737475i \(0.736018\pi\)
\(774\) −16.6990 17.6963i −0.600233 0.636081i
\(775\) 5.39907 0.193940
\(776\) −14.1762 −0.508898
\(777\) 4.92576 + 12.3970i 0.176711 + 0.444742i
\(778\) 9.33994i 0.334853i
\(779\) 9.60735i 0.344219i
\(780\) 25.9093 10.2946i 0.927703 0.368607i
\(781\) 6.68984 24.2037i 0.239381 0.866075i
\(782\) 0.749461i 0.0268007i
\(783\) 14.2472 30.5653i 0.509152 1.09231i
\(784\) −0.121314 −0.00433265
\(785\) 23.1022i 0.824554i
\(786\) −17.7246 + 7.04258i −0.632216 + 0.251200i
\(787\) 14.3616i 0.511937i 0.966685 + 0.255968i \(0.0823943\pi\)
−0.966685 + 0.255968i \(0.917606\pi\)
\(788\) −18.4892 −0.658649
\(789\) 1.59885 0.635278i 0.0569207 0.0226165i
\(790\) 24.4346 0.869345
\(791\) 18.7645 0.667188
\(792\) −24.6347 + 13.0370i −0.875355 + 0.463251i
\(793\) 58.1149 2.06372
\(794\) 28.6705 1.01748
\(795\) 44.6750 17.7509i 1.58446 0.629558i
\(796\) 32.5109 1.15232
\(797\) 37.2339i 1.31889i 0.751752 + 0.659446i \(0.229209\pi\)
−0.751752 + 0.659446i \(0.770791\pi\)
\(798\) −4.67659 + 1.85816i −0.165549 + 0.0657783i
\(799\) 0.0367077i 0.00129862i
\(800\) 5.64091 0.199436
\(801\) 5.31699 + 5.63453i 0.187866 + 0.199086i
\(802\) 1.97036i 0.0695758i
\(803\) −3.08477 + 11.1606i −0.108859 + 0.393849i
\(804\) 3.94826 1.56877i 0.139244 0.0553264i
\(805\) 14.0949i 0.496778i
\(806\) 24.4187i 0.860112i
\(807\) 8.91970 + 22.4489i 0.313988 + 0.790239i
\(808\) 8.32505 0.292874
\(809\) −10.4350 −0.366876 −0.183438 0.983031i \(-0.558723\pi\)
−0.183438 + 0.983031i \(0.558723\pi\)
\(810\) 18.8754 + 1.09552i 0.663213 + 0.0384928i
\(811\) 22.1974i 0.779458i −0.920930 0.389729i \(-0.872569\pi\)
0.920930 0.389729i \(-0.127431\pi\)
\(812\) 8.19699i 0.287658i
\(813\) 19.9016 + 50.0880i 0.697981 + 1.75666i
\(814\) 21.1360 + 5.84195i 0.740817 + 0.204760i
\(815\) 19.9075i 0.697329i
\(816\) 0.0295981 0.0117603i 0.00103614 0.000411694i
\(817\) 31.9739 1.11863
\(818\) 0.418621i 0.0146367i
\(819\) 11.3629 10.7225i 0.397053 0.374676i
\(820\) 8.77409i 0.306405i
\(821\) 29.0050 1.01228 0.506140 0.862451i \(-0.331072\pi\)
0.506140 + 0.862451i \(0.331072\pi\)
\(822\) 9.71346 + 24.4466i 0.338796 + 0.852674i
\(823\) −9.36373 −0.326399 −0.163199 0.986593i \(-0.552181\pi\)
−0.163199 + 0.986593i \(0.552181\pi\)
\(824\) 5.90246 0.205622
\(825\) 5.64505 0.615132i 0.196535 0.0214161i
\(826\) −1.90620 −0.0663251
\(827\) −9.70831 −0.337591 −0.168795 0.985651i \(-0.553988\pi\)
−0.168795 + 0.985651i \(0.553988\pi\)
\(828\) −14.9783 15.8728i −0.520530 0.551618i
\(829\) 7.91149 0.274777 0.137389 0.990517i \(-0.456129\pi\)
0.137389 + 0.990517i \(0.456129\pi\)
\(830\) 32.9132i 1.14243i
\(831\) 5.53721 + 13.9359i 0.192084 + 0.483433i
\(832\) 24.2489i 0.840679i
\(833\) −0.151573 −0.00525170
\(834\) 1.20581 + 3.03475i 0.0417538 + 0.105085i
\(835\) 6.47836i 0.224193i
\(836\) 3.77689 13.6647i 0.130626 0.472603i
\(837\) −11.9904 + 25.7237i −0.414449 + 0.889141i
\(838\) 14.2123i 0.490957i
\(839\) 25.0777i 0.865779i −0.901447 0.432890i \(-0.857494\pi\)
0.901447 0.432890i \(-0.142506\pi\)
\(840\) 11.0340 4.38419i 0.380710 0.151269i
\(841\) 13.1192 0.452385
\(842\) 1.68085 0.0579260
\(843\) −42.4187 + 16.8543i −1.46098 + 0.580495i
\(844\) 19.4841i 0.670671i
\(845\) 34.5561i 1.18877i
\(846\) −0.428059 0.453623i −0.0147170 0.0155959i
\(847\) −5.64918 + 9.43858i −0.194108 + 0.324313i
\(848\) 1.37590i 0.0472486i
\(849\) −16.9772 42.7279i −0.582657 1.46642i
\(850\) 0.128624 0.00441176
\(851\) 44.3598i 1.52064i
\(852\) −6.11603 15.3927i −0.209532 0.527345i
\(853\) 30.3301i 1.03848i 0.854628 + 0.519241i \(0.173785\pi\)
−0.854628 + 0.519241i \(0.826215\pi\)
\(854\) 9.57985 0.327816
\(855\) −18.0705 + 17.0521i −0.617999 + 0.583170i
\(856\) −43.6166 −1.49079
\(857\) 12.8728 0.439726 0.219863 0.975531i \(-0.429439\pi\)
0.219863 + 0.975531i \(0.429439\pi\)
\(858\) −2.78209 25.5312i −0.0949790 0.871620i
\(859\) 22.0184 0.751259 0.375629 0.926770i \(-0.377427\pi\)
0.375629 + 0.926770i \(0.377427\pi\)
\(860\) −29.2008 −0.995738
\(861\) 1.81557 + 4.56940i 0.0618746 + 0.155725i
\(862\) −13.1802 −0.448920
\(863\) 41.5594i 1.41470i −0.706865 0.707349i \(-0.749891\pi\)
0.706865 0.707349i \(-0.250109\pi\)
\(864\) −12.5275 + 26.8759i −0.426193 + 0.914337i
\(865\) 7.41868i 0.252243i
\(866\) −7.78285 −0.264472
\(867\) −27.3270 + 10.8579i −0.928073 + 0.368754i
\(868\) 6.89858i 0.234153i
\(869\) −10.2770 + 37.1820i −0.348624 + 1.26131i
\(870\) 8.71983 + 21.9459i 0.295630 + 0.744035i
\(871\) 10.1138i 0.342693i
\(872\) 11.7537i 0.398032i
\(873\) −11.0421 + 10.4198i −0.373720 + 0.352658i
\(874\) −16.7340 −0.566037
\(875\) 9.81672 0.331866
\(876\) 2.82018 + 7.09776i 0.0952850 + 0.239811i
\(877\) 25.0341i 0.845341i 0.906283 + 0.422671i \(0.138907\pi\)
−0.906283 + 0.422671i \(0.861093\pi\)
\(878\) 3.29185i 0.111095i
\(879\) −51.9468 + 20.6402i −1.75212 + 0.696177i
\(880\) −0.262310 + 0.949031i −0.00884248 + 0.0319918i
\(881\) 17.9254i 0.603923i 0.953320 + 0.301961i \(0.0976414\pi\)
−0.953320 + 0.301961i \(0.902359\pi\)
\(882\) 1.87310 1.76754i 0.0630706 0.0595162i
\(883\) −34.8036 −1.17123 −0.585617 0.810588i \(-0.699148\pi\)
−0.585617 + 0.810588i \(0.699148\pi\)
\(884\) 0.996988i 0.0335323i
\(885\) −8.74646 + 3.47526i −0.294009 + 0.116820i
\(886\) 6.46815i 0.217302i
\(887\) −24.3669 −0.818159 −0.409079 0.912499i \(-0.634150\pi\)
−0.409079 + 0.912499i \(0.634150\pi\)
\(888\) 34.7267 13.7981i 1.16535 0.463033i
\(889\) 0.108701 0.00364573
\(890\) −5.42505 −0.181848
\(891\) −9.60590 + 28.2618i −0.321810 + 0.946804i
\(892\) 22.7123 0.760463
\(893\) 0.819613 0.0274273
\(894\) 10.8314 4.30366i 0.362255 0.143936i
\(895\) 23.9812 0.801602
\(896\) 7.41586i 0.247747i
\(897\) 48.2819 19.1840i 1.61209 0.640536i
\(898\) 9.47917i 0.316324i
\(899\) −35.4475 −1.18224
\(900\) 2.72412 2.57059i 0.0908039 0.0856865i
\(901\) 1.71909i 0.0572711i
\(902\) 7.79047 + 2.15327i 0.259394 + 0.0716960i
\(903\) −15.2073 + 6.04235i −0.506066 + 0.201077i
\(904\) 52.5632i 1.74823i
\(905\) 19.6520i 0.653256i
\(906\) −4.51113 11.3535i −0.149872 0.377195i
\(907\) −5.80381 −0.192712 −0.0963562 0.995347i \(-0.530719\pi\)
−0.0963562 + 0.995347i \(0.530719\pi\)
\(908\) −16.7860 −0.557062
\(909\) 6.48453 6.11908i 0.215078 0.202957i
\(910\) 10.9405i 0.362673i
\(911\) 36.4746i 1.20846i 0.796812 + 0.604228i \(0.206518\pi\)
−0.796812 + 0.604228i \(0.793482\pi\)
\(912\) −0.262586 0.660870i −0.00869508 0.0218836i
\(913\) −50.0838 13.8431i −1.65753 0.458138i
\(914\) 5.41698i 0.179178i
\(915\) 43.9565 17.4654i 1.45316 0.577388i
\(916\) −24.4020 −0.806264
\(917\) 12.8269i 0.423582i
\(918\) −0.285651 + 0.612824i −0.00942788 + 0.0202262i
\(919\) 14.9130i 0.491934i 0.969278 + 0.245967i \(0.0791055\pi\)
−0.969278 + 0.245967i \(0.920895\pi\)
\(920\) 39.4826 1.30170
\(921\) −1.09425 2.75399i −0.0360568 0.0907470i
\(922\) −2.93827 −0.0967669
\(923\) 39.4297 1.29784
\(924\) 0.785974 + 7.21287i 0.0258567 + 0.237286i
\(925\) −7.61312 −0.250318
\(926\) −4.27758 −0.140570
\(927\) 4.59753 4.33842i 0.151003 0.142493i
\(928\) −37.0352 −1.21574
\(929\) 26.1737i 0.858730i −0.903131 0.429365i \(-0.858737\pi\)
0.903131 0.429365i \(-0.141263\pi\)
\(930\) −7.33860 18.4696i −0.240642 0.605643i
\(931\) 3.38435i 0.110917i
\(932\) 5.60705 0.183665
\(933\) 5.10272 + 12.8424i 0.167056 + 0.420442i
\(934\) 1.21704i 0.0398227i
\(935\) −0.327738 + 1.18575i −0.0107182 + 0.0387781i
\(936\) −30.0361 31.8299i −0.981761 1.04039i
\(937\) 35.6941i 1.16607i 0.812445 + 0.583037i \(0.198136\pi\)
−0.812445 + 0.583037i \(0.801864\pi\)
\(938\) 1.66719i 0.0544357i
\(939\) 12.7960 5.08426i 0.417580 0.165919i
\(940\) −0.748526 −0.0244142
\(941\) 33.7819 1.10126 0.550629 0.834750i \(-0.314388\pi\)
0.550629 + 0.834750i \(0.314388\pi\)
\(942\) −13.0452 + 5.18327i −0.425034 + 0.168880i
\(943\) 16.3505i 0.532445i
\(944\) 0.269374i 0.00876736i
\(945\) 5.37214 11.5252i 0.174756 0.374914i
\(946\) −7.16623 + 25.9272i −0.232994 + 0.842967i
\(947\) 31.3380i 1.01835i 0.860664 + 0.509174i \(0.170049\pi\)
−0.860664 + 0.509174i \(0.829951\pi\)
\(948\) 9.39554 + 23.6465i 0.305153 + 0.768003i
\(949\) −18.1815 −0.590197
\(950\) 2.87193i 0.0931776i
\(951\) −6.39103 16.0848i −0.207243 0.521586i
\(952\) 0.424589i 0.0137610i
\(953\) 10.9252 0.353901 0.176951 0.984220i \(-0.443377\pi\)
0.176951 + 0.984220i \(0.443377\pi\)
\(954\) −20.0468 21.2440i −0.649039 0.687801i
\(955\) 46.8674 1.51659
\(956\) −1.76221 −0.0569940
\(957\) −37.0624 + 4.03863i −1.19806 + 0.130550i
\(958\) −20.5031 −0.662424
\(959\) 17.6915 0.571288
\(960\) −7.28757 18.3412i −0.235205 0.591959i
\(961\) −1.16746 −0.0376598
\(962\) 34.4323i 1.11014i
\(963\) −33.9738 + 32.0591i −1.09479 + 1.03309i
\(964\) 19.4486i 0.626397i
\(965\) −1.00374 −0.0323116
\(966\) 7.95896 3.16236i 0.256075 0.101747i
\(967\) 24.1608i 0.776959i −0.921457 0.388480i \(-0.873000\pi\)
0.921457 0.388480i \(-0.127000\pi\)
\(968\) 26.4394 + 15.8245i 0.849796 + 0.508620i
\(969\) −0.328082 0.825710i −0.0105395 0.0265256i
\(970\) 10.6316i 0.341360i
\(971\) 55.1411i 1.76956i 0.466006 + 0.884781i \(0.345692\pi\)
−0.466006 + 0.884781i \(0.654308\pi\)
\(972\) 6.19772 + 18.6878i 0.198792 + 0.599412i
\(973\) 2.19619 0.0704065
\(974\) −21.1347 −0.677201
\(975\) 3.29240 + 8.28623i 0.105441 + 0.265372i
\(976\) 1.35377i 0.0433332i
\(977\) 14.5912i 0.466815i −0.972379 0.233408i \(-0.925012\pi\)
0.972379 0.233408i \(-0.0749877\pi\)
\(978\) 11.2412 4.46650i 0.359454 0.142823i
\(979\) 2.28174 8.25526i 0.0729246 0.263839i
\(980\) 3.09082i 0.0987325i
\(981\) 8.63924 + 9.15520i 0.275830 + 0.292303i
\(982\) 4.04778 0.129170
\(983\) 57.8582i 1.84539i −0.385530 0.922695i \(-0.625981\pi\)
0.385530 0.922695i \(-0.374019\pi\)
\(984\) 12.7998 5.08580i 0.408044 0.162129i
\(985\) 35.8230i 1.14142i
\(986\) −0.844475 −0.0268936
\(987\) −0.389820 + 0.154888i −0.0124081 + 0.00493015i
\(988\) 22.2609 0.708213
\(989\) −54.4156 −1.73031
\(990\) −9.77724 18.4750i −0.310741 0.587174i
\(991\) −16.5692 −0.526337 −0.263168 0.964750i \(-0.584767\pi\)
−0.263168 + 0.964750i \(0.584767\pi\)
\(992\) 31.1688 0.989610
\(993\) 53.9632 21.4414i 1.71247 0.680422i
\(994\) 6.49972 0.206159
\(995\) 62.9902i 1.99692i
\(996\) −31.8516 + 12.6557i −1.00926 + 0.401011i
\(997\) 54.6399i 1.73046i −0.501373 0.865231i \(-0.667172\pi\)
0.501373 0.865231i \(-0.332828\pi\)
\(998\) −11.9293 −0.377614
\(999\) 16.9074 36.2724i 0.534926 1.14761i
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 231.2.g.a.197.9 24
3.2 odd 2 inner 231.2.g.a.197.16 yes 24
11.10 odd 2 inner 231.2.g.a.197.15 yes 24
33.32 even 2 inner 231.2.g.a.197.10 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
231.2.g.a.197.9 24 1.1 even 1 trivial
231.2.g.a.197.10 yes 24 33.32 even 2 inner
231.2.g.a.197.15 yes 24 11.10 odd 2 inner
231.2.g.a.197.16 yes 24 3.2 odd 2 inner