Properties

Label 1134.2.e.t.865.2
Level $1134$
Weight $2$
Character 1134.865
Analytic conductor $9.055$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1134,2,Mod(865,1134)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1134.865");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.05503558921\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{7})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 7x^{2} + 49 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 378)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 865.2
Root \(1.32288 - 2.29129i\) of defining polynomial
Character \(\chi\) \(=\) 1134.865
Dual form 1134.2.e.t.919.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} +(1.82288 - 3.15731i) q^{5} +(1.32288 - 2.29129i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} +(1.82288 - 3.15731i) q^{5} +(1.32288 - 2.29129i) q^{7} +1.00000 q^{8} +(1.82288 - 3.15731i) q^{10} +(-1.82288 - 3.15731i) q^{11} +(2.32288 + 4.02334i) q^{13} +(1.32288 - 2.29129i) q^{14} +1.00000 q^{16} +(-1.82288 + 3.15731i) q^{17} +(-1.00000 - 1.73205i) q^{19} +(1.82288 - 3.15731i) q^{20} +(-1.82288 - 3.15731i) q^{22} +(0.645751 - 1.11847i) q^{23} +(-4.14575 - 7.18065i) q^{25} +(2.32288 + 4.02334i) q^{26} +(1.32288 - 2.29129i) q^{28} +(-1.17712 + 2.03884i) q^{29} -4.64575 q^{31} +1.00000 q^{32} +(-1.82288 + 3.15731i) q^{34} +(-4.82288 - 8.35347i) q^{35} +(5.96863 + 10.3380i) q^{37} +(-1.00000 - 1.73205i) q^{38} +(1.82288 - 3.15731i) q^{40} +(-5.46863 - 9.47194i) q^{41} +(-2.50000 + 4.33013i) q^{43} +(-1.82288 - 3.15731i) q^{44} +(0.645751 - 1.11847i) q^{46} +4.93725 q^{47} +(-3.50000 - 6.06218i) q^{49} +(-4.14575 - 7.18065i) q^{50} +(2.32288 + 4.02334i) q^{52} +(-3.00000 + 5.19615i) q^{53} -13.2915 q^{55} +(1.32288 - 2.29129i) q^{56} +(-1.17712 + 2.03884i) q^{58} +8.35425 q^{59} +7.35425 q^{61} -4.64575 q^{62} +1.00000 q^{64} +16.9373 q^{65} -2.29150 q^{67} +(-1.82288 + 3.15731i) q^{68} +(-4.82288 - 8.35347i) q^{70} +15.6458 q^{71} +(-5.29150 + 9.16515i) q^{73} +(5.96863 + 10.3380i) q^{74} +(-1.00000 - 1.73205i) q^{76} -9.64575 q^{77} +11.2288 q^{79} +(1.82288 - 3.15731i) q^{80} +(-5.46863 - 9.47194i) q^{82} +(6.64575 - 11.5108i) q^{83} +(6.64575 + 11.5108i) q^{85} +(-2.50000 + 4.33013i) q^{86} +(-1.82288 - 3.15731i) q^{88} +(-2.46863 - 4.27579i) q^{89} +12.2915 q^{91} +(0.645751 - 1.11847i) q^{92} +4.93725 q^{94} -7.29150 q^{95} +(-6.79150 + 11.7632i) q^{97} +(-3.50000 - 6.06218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} + 4 q^{4} + 2 q^{5} + 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{2} + 4 q^{4} + 2 q^{5} + 4 q^{8} + 2 q^{10} - 2 q^{11} + 4 q^{13} + 4 q^{16} - 2 q^{17} - 4 q^{19} + 2 q^{20} - 2 q^{22} - 8 q^{23} - 6 q^{25} + 4 q^{26} - 10 q^{29} - 8 q^{31} + 4 q^{32} - 2 q^{34} - 14 q^{35} + 8 q^{37} - 4 q^{38} + 2 q^{40} - 6 q^{41} - 10 q^{43} - 2 q^{44} - 8 q^{46} - 12 q^{47} - 14 q^{49} - 6 q^{50} + 4 q^{52} - 12 q^{53} - 32 q^{55} - 10 q^{58} + 44 q^{59} + 40 q^{61} - 8 q^{62} + 4 q^{64} + 36 q^{65} + 12 q^{67} - 2 q^{68} - 14 q^{70} + 52 q^{71} + 8 q^{74} - 4 q^{76} - 28 q^{77} - 8 q^{79} + 2 q^{80} - 6 q^{82} + 16 q^{83} + 16 q^{85} - 10 q^{86} - 2 q^{88} + 6 q^{89} + 28 q^{91} - 8 q^{92} - 12 q^{94} - 8 q^{95} - 6 q^{97} - 14 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 1.82288 3.15731i 0.815215 1.41199i −0.0939588 0.995576i \(-0.529952\pi\)
0.909174 0.416417i \(-0.136714\pi\)
\(6\) 0 0
\(7\) 1.32288 2.29129i 0.500000 0.866025i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 1.82288 3.15731i 0.576444 0.998430i
\(11\) −1.82288 3.15731i −0.549618 0.951966i −0.998301 0.0582747i \(-0.981440\pi\)
0.448683 0.893691i \(-0.351893\pi\)
\(12\) 0 0
\(13\) 2.32288 + 4.02334i 0.644250 + 1.11587i 0.984474 + 0.175529i \(0.0561636\pi\)
−0.340224 + 0.940344i \(0.610503\pi\)
\(14\) 1.32288 2.29129i 0.353553 0.612372i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −1.82288 + 3.15731i −0.442112 + 0.765761i −0.997846 0.0655994i \(-0.979104\pi\)
0.555734 + 0.831360i \(0.312437\pi\)
\(18\) 0 0
\(19\) −1.00000 1.73205i −0.229416 0.397360i 0.728219 0.685344i \(-0.240348\pi\)
−0.957635 + 0.287984i \(0.907015\pi\)
\(20\) 1.82288 3.15731i 0.407607 0.705997i
\(21\) 0 0
\(22\) −1.82288 3.15731i −0.388638 0.673141i
\(23\) 0.645751 1.11847i 0.134648 0.233218i −0.790815 0.612056i \(-0.790343\pi\)
0.925463 + 0.378838i \(0.123676\pi\)
\(24\) 0 0
\(25\) −4.14575 7.18065i −0.829150 1.43613i
\(26\) 2.32288 + 4.02334i 0.455553 + 0.789042i
\(27\) 0 0
\(28\) 1.32288 2.29129i 0.250000 0.433013i
\(29\) −1.17712 + 2.03884i −0.218587 + 0.378603i −0.954376 0.298607i \(-0.903478\pi\)
0.735790 + 0.677210i \(0.236811\pi\)
\(30\) 0 0
\(31\) −4.64575 −0.834402 −0.417201 0.908814i \(-0.636989\pi\)
−0.417201 + 0.908814i \(0.636989\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −1.82288 + 3.15731i −0.312621 + 0.541475i
\(35\) −4.82288 8.35347i −0.815215 1.41199i
\(36\) 0 0
\(37\) 5.96863 + 10.3380i 0.981236 + 1.69955i 0.657596 + 0.753371i \(0.271573\pi\)
0.323640 + 0.946180i \(0.395093\pi\)
\(38\) −1.00000 1.73205i −0.162221 0.280976i
\(39\) 0 0
\(40\) 1.82288 3.15731i 0.288222 0.499215i
\(41\) −5.46863 9.47194i −0.854056 1.47927i −0.877518 0.479544i \(-0.840802\pi\)
0.0234619 0.999725i \(-0.492531\pi\)
\(42\) 0 0
\(43\) −2.50000 + 4.33013i −0.381246 + 0.660338i −0.991241 0.132068i \(-0.957838\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) −1.82288 3.15731i −0.274809 0.475983i
\(45\) 0 0
\(46\) 0.645751 1.11847i 0.0952108 0.164910i
\(47\) 4.93725 0.720173 0.360086 0.932919i \(-0.382747\pi\)
0.360086 + 0.932919i \(0.382747\pi\)
\(48\) 0 0
\(49\) −3.50000 6.06218i −0.500000 0.866025i
\(50\) −4.14575 7.18065i −0.586298 1.01550i
\(51\) 0 0
\(52\) 2.32288 + 4.02334i 0.322125 + 0.557937i
\(53\) −3.00000 + 5.19615i −0.412082 + 0.713746i −0.995117 0.0987002i \(-0.968532\pi\)
0.583036 + 0.812447i \(0.301865\pi\)
\(54\) 0 0
\(55\) −13.2915 −1.79223
\(56\) 1.32288 2.29129i 0.176777 0.306186i
\(57\) 0 0
\(58\) −1.17712 + 2.03884i −0.154564 + 0.267713i
\(59\) 8.35425 1.08763 0.543815 0.839205i \(-0.316979\pi\)
0.543815 + 0.839205i \(0.316979\pi\)
\(60\) 0 0
\(61\) 7.35425 0.941615 0.470808 0.882236i \(-0.343963\pi\)
0.470808 + 0.882236i \(0.343963\pi\)
\(62\) −4.64575 −0.590011
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 16.9373 2.10081
\(66\) 0 0
\(67\) −2.29150 −0.279952 −0.139976 0.990155i \(-0.544702\pi\)
−0.139976 + 0.990155i \(0.544702\pi\)
\(68\) −1.82288 + 3.15731i −0.221056 + 0.382880i
\(69\) 0 0
\(70\) −4.82288 8.35347i −0.576444 0.998430i
\(71\) 15.6458 1.85681 0.928405 0.371571i \(-0.121181\pi\)
0.928405 + 0.371571i \(0.121181\pi\)
\(72\) 0 0
\(73\) −5.29150 + 9.16515i −0.619324 + 1.07270i 0.370286 + 0.928918i \(0.379260\pi\)
−0.989609 + 0.143782i \(0.954074\pi\)
\(74\) 5.96863 + 10.3380i 0.693839 + 1.20176i
\(75\) 0 0
\(76\) −1.00000 1.73205i −0.114708 0.198680i
\(77\) −9.64575 −1.09924
\(78\) 0 0
\(79\) 11.2288 1.26333 0.631667 0.775240i \(-0.282371\pi\)
0.631667 + 0.775240i \(0.282371\pi\)
\(80\) 1.82288 3.15731i 0.203804 0.352998i
\(81\) 0 0
\(82\) −5.46863 9.47194i −0.603909 1.04600i
\(83\) 6.64575 11.5108i 0.729466 1.26347i −0.227643 0.973745i \(-0.573102\pi\)
0.957109 0.289728i \(-0.0935647\pi\)
\(84\) 0 0
\(85\) 6.64575 + 11.5108i 0.720833 + 1.24852i
\(86\) −2.50000 + 4.33013i −0.269582 + 0.466930i
\(87\) 0 0
\(88\) −1.82288 3.15731i −0.194319 0.336571i
\(89\) −2.46863 4.27579i −0.261674 0.453233i 0.705013 0.709194i \(-0.250941\pi\)
−0.966687 + 0.255962i \(0.917608\pi\)
\(90\) 0 0
\(91\) 12.2915 1.28850
\(92\) 0.645751 1.11847i 0.0673242 0.116609i
\(93\) 0 0
\(94\) 4.93725 0.509239
\(95\) −7.29150 −0.748092
\(96\) 0 0
\(97\) −6.79150 + 11.7632i −0.689573 + 1.19437i 0.282404 + 0.959296i \(0.408868\pi\)
−0.971976 + 0.235079i \(0.924465\pi\)
\(98\) −3.50000 6.06218i −0.353553 0.612372i
\(99\) 0 0
\(100\) −4.14575 7.18065i −0.414575 0.718065i
\(101\) −4.17712 7.23499i −0.415639 0.719909i 0.579856 0.814719i \(-0.303109\pi\)
−0.995495 + 0.0948105i \(0.969775\pi\)
\(102\) 0 0
\(103\) −1.96863 + 3.40976i −0.193975 + 0.335974i −0.946564 0.322516i \(-0.895471\pi\)
0.752589 + 0.658490i \(0.228805\pi\)
\(104\) 2.32288 + 4.02334i 0.227777 + 0.394521i
\(105\) 0 0
\(106\) −3.00000 + 5.19615i −0.291386 + 0.504695i
\(107\) 3.00000 + 5.19615i 0.290021 + 0.502331i 0.973814 0.227345i \(-0.0730044\pi\)
−0.683793 + 0.729676i \(0.739671\pi\)
\(108\) 0 0
\(109\) 1.67712 2.90486i 0.160639 0.278236i −0.774459 0.632624i \(-0.781978\pi\)
0.935098 + 0.354389i \(0.115311\pi\)
\(110\) −13.2915 −1.26730
\(111\) 0 0
\(112\) 1.32288 2.29129i 0.125000 0.216506i
\(113\) −1.17712 2.03884i −0.110735 0.191798i 0.805332 0.592824i \(-0.201987\pi\)
−0.916067 + 0.401026i \(0.868654\pi\)
\(114\) 0 0
\(115\) −2.35425 4.07768i −0.219535 0.380245i
\(116\) −1.17712 + 2.03884i −0.109293 + 0.189301i
\(117\) 0 0
\(118\) 8.35425 0.769071
\(119\) 4.82288 + 8.35347i 0.442112 + 0.765761i
\(120\) 0 0
\(121\) −1.14575 + 1.98450i −0.104159 + 0.180409i
\(122\) 7.35425 0.665822
\(123\) 0 0
\(124\) −4.64575 −0.417201
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) 1.35425 0.120170 0.0600851 0.998193i \(-0.480863\pi\)
0.0600851 + 0.998193i \(0.480863\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) 16.9373 1.48550
\(131\) 7.29150 12.6293i 0.637062 1.10342i −0.349013 0.937118i \(-0.613483\pi\)
0.986074 0.166305i \(-0.0531836\pi\)
\(132\) 0 0
\(133\) −5.29150 −0.458831
\(134\) −2.29150 −0.197956
\(135\) 0 0
\(136\) −1.82288 + 3.15731i −0.156310 + 0.270737i
\(137\) −0.645751 1.11847i −0.0551703 0.0955577i 0.837121 0.547017i \(-0.184237\pi\)
−0.892292 + 0.451460i \(0.850903\pi\)
\(138\) 0 0
\(139\) −0.791503 1.37092i −0.0671344 0.116280i 0.830504 0.557012i \(-0.188052\pi\)
−0.897639 + 0.440732i \(0.854719\pi\)
\(140\) −4.82288 8.35347i −0.407607 0.705997i
\(141\) 0 0
\(142\) 15.6458 1.31296
\(143\) 8.46863 14.6681i 0.708182 1.22661i
\(144\) 0 0
\(145\) 4.29150 + 7.43310i 0.356390 + 0.617285i
\(146\) −5.29150 + 9.16515i −0.437928 + 0.758513i
\(147\) 0 0
\(148\) 5.96863 + 10.3380i 0.490618 + 0.849776i
\(149\) −11.4686 + 19.8642i −0.939547 + 1.62734i −0.173228 + 0.984882i \(0.555420\pi\)
−0.766319 + 0.642461i \(0.777914\pi\)
\(150\) 0 0
\(151\) 9.61438 + 16.6526i 0.782407 + 1.35517i 0.930536 + 0.366201i \(0.119342\pi\)
−0.148129 + 0.988968i \(0.547325\pi\)
\(152\) −1.00000 1.73205i −0.0811107 0.140488i
\(153\) 0 0
\(154\) −9.64575 −0.777277
\(155\) −8.46863 + 14.6681i −0.680216 + 1.17817i
\(156\) 0 0
\(157\) −4.00000 −0.319235 −0.159617 0.987179i \(-0.551026\pi\)
−0.159617 + 0.987179i \(0.551026\pi\)
\(158\) 11.2288 0.893312
\(159\) 0 0
\(160\) 1.82288 3.15731i 0.144111 0.249608i
\(161\) −1.70850 2.95920i −0.134648 0.233218i
\(162\) 0 0
\(163\) 0.500000 + 0.866025i 0.0391630 + 0.0678323i 0.884943 0.465700i \(-0.154198\pi\)
−0.845780 + 0.533533i \(0.820864\pi\)
\(164\) −5.46863 9.47194i −0.427028 0.739634i
\(165\) 0 0
\(166\) 6.64575 11.5108i 0.515810 0.893410i
\(167\) 4.29150 + 7.43310i 0.332086 + 0.575191i 0.982921 0.184029i \(-0.0589141\pi\)
−0.650834 + 0.759220i \(0.725581\pi\)
\(168\) 0 0
\(169\) −4.29150 + 7.43310i −0.330116 + 0.571777i
\(170\) 6.64575 + 11.5108i 0.509706 + 0.882836i
\(171\) 0 0
\(172\) −2.50000 + 4.33013i −0.190623 + 0.330169i
\(173\) −14.5830 −1.10873 −0.554363 0.832275i \(-0.687038\pi\)
−0.554363 + 0.832275i \(0.687038\pi\)
\(174\) 0 0
\(175\) −21.9373 −1.65830
\(176\) −1.82288 3.15731i −0.137404 0.237991i
\(177\) 0 0
\(178\) −2.46863 4.27579i −0.185031 0.320484i
\(179\) −8.46863 + 14.6681i −0.632975 + 1.09634i 0.353965 + 0.935259i \(0.384833\pi\)
−0.986940 + 0.161086i \(0.948500\pi\)
\(180\) 0 0
\(181\) −2.70850 −0.201321 −0.100661 0.994921i \(-0.532096\pi\)
−0.100661 + 0.994921i \(0.532096\pi\)
\(182\) 12.2915 0.911107
\(183\) 0 0
\(184\) 0.645751 1.11847i 0.0476054 0.0824550i
\(185\) 43.5203 3.19967
\(186\) 0 0
\(187\) 13.2915 0.971971
\(188\) 4.93725 0.360086
\(189\) 0 0
\(190\) −7.29150 −0.528981
\(191\) −20.8118 −1.50589 −0.752943 0.658086i \(-0.771366\pi\)
−0.752943 + 0.658086i \(0.771366\pi\)
\(192\) 0 0
\(193\) −7.00000 −0.503871 −0.251936 0.967744i \(-0.581067\pi\)
−0.251936 + 0.967744i \(0.581067\pi\)
\(194\) −6.79150 + 11.7632i −0.487601 + 0.844551i
\(195\) 0 0
\(196\) −3.50000 6.06218i −0.250000 0.433013i
\(197\) 4.70850 0.335467 0.167733 0.985832i \(-0.446355\pi\)
0.167733 + 0.985832i \(0.446355\pi\)
\(198\) 0 0
\(199\) −3.03137 + 5.25049i −0.214888 + 0.372198i −0.953238 0.302221i \(-0.902272\pi\)
0.738350 + 0.674418i \(0.235605\pi\)
\(200\) −4.14575 7.18065i −0.293149 0.507749i
\(201\) 0 0
\(202\) −4.17712 7.23499i −0.293901 0.509052i
\(203\) 3.11438 + 5.39426i 0.218587 + 0.378603i
\(204\) 0 0
\(205\) −39.8745 −2.78496
\(206\) −1.96863 + 3.40976i −0.137161 + 0.237569i
\(207\) 0 0
\(208\) 2.32288 + 4.02334i 0.161062 + 0.278968i
\(209\) −3.64575 + 6.31463i −0.252182 + 0.436792i
\(210\) 0 0
\(211\) −7.43725 12.8817i −0.512002 0.886813i −0.999903 0.0139142i \(-0.995571\pi\)
0.487902 0.872899i \(-0.337763\pi\)
\(212\) −3.00000 + 5.19615i −0.206041 + 0.356873i
\(213\) 0 0
\(214\) 3.00000 + 5.19615i 0.205076 + 0.355202i
\(215\) 9.11438 + 15.7866i 0.621595 + 1.07663i
\(216\) 0 0
\(217\) −6.14575 + 10.6448i −0.417201 + 0.722613i
\(218\) 1.67712 2.90486i 0.113589 0.196742i
\(219\) 0 0
\(220\) −13.2915 −0.896113
\(221\) −16.9373 −1.13932
\(222\) 0 0
\(223\) 6.93725 12.0157i 0.464553 0.804629i −0.534628 0.845087i \(-0.679548\pi\)
0.999181 + 0.0404581i \(0.0128817\pi\)
\(224\) 1.32288 2.29129i 0.0883883 0.153093i
\(225\) 0 0
\(226\) −1.17712 2.03884i −0.0783011 0.135622i
\(227\) −3.00000 5.19615i −0.199117 0.344881i 0.749125 0.662428i \(-0.230474\pi\)
−0.948242 + 0.317547i \(0.897141\pi\)
\(228\) 0 0
\(229\) 4.67712 8.10102i 0.309073 0.535330i −0.669087 0.743184i \(-0.733315\pi\)
0.978160 + 0.207854i \(0.0666479\pi\)
\(230\) −2.35425 4.07768i −0.155235 0.268874i
\(231\) 0 0
\(232\) −1.17712 + 2.03884i −0.0772820 + 0.133856i
\(233\) 9.64575 + 16.7069i 0.631914 + 1.09451i 0.987160 + 0.159735i \(0.0510638\pi\)
−0.355246 + 0.934773i \(0.615603\pi\)
\(234\) 0 0
\(235\) 9.00000 15.5885i 0.587095 1.01688i
\(236\) 8.35425 0.543815
\(237\) 0 0
\(238\) 4.82288 + 8.35347i 0.312621 + 0.541475i
\(239\) 5.46863 + 9.47194i 0.353736 + 0.612689i 0.986901 0.161328i \(-0.0515778\pi\)
−0.633165 + 0.774017i \(0.718244\pi\)
\(240\) 0 0
\(241\) −2.50000 4.33013i −0.161039 0.278928i 0.774202 0.632938i \(-0.218151\pi\)
−0.935242 + 0.354010i \(0.884818\pi\)
\(242\) −1.14575 + 1.98450i −0.0736517 + 0.127568i
\(243\) 0 0
\(244\) 7.35425 0.470808
\(245\) −25.5203 −1.63043
\(246\) 0 0
\(247\) 4.64575 8.04668i 0.295602 0.511998i
\(248\) −4.64575 −0.295006
\(249\) 0 0
\(250\) −12.0000 −0.758947
\(251\) −18.0000 −1.13615 −0.568075 0.822977i \(-0.692312\pi\)
−0.568075 + 0.822977i \(0.692312\pi\)
\(252\) 0 0
\(253\) −4.70850 −0.296021
\(254\) 1.35425 0.0849731
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −7.93725 + 13.7477i −0.495112 + 0.857560i −0.999984 0.00563467i \(-0.998206\pi\)
0.504872 + 0.863194i \(0.331540\pi\)
\(258\) 0 0
\(259\) 31.5830 1.96247
\(260\) 16.9373 1.05040
\(261\) 0 0
\(262\) 7.29150 12.6293i 0.450471 0.780238i
\(263\) 2.46863 + 4.27579i 0.152222 + 0.263656i 0.932044 0.362345i \(-0.118024\pi\)
−0.779822 + 0.626001i \(0.784690\pi\)
\(264\) 0 0
\(265\) 10.9373 + 18.9439i 0.671870 + 1.16371i
\(266\) −5.29150 −0.324443
\(267\) 0 0
\(268\) −2.29150 −0.139976
\(269\) 8.35425 14.4700i 0.509368 0.882250i −0.490574 0.871400i \(-0.663213\pi\)
0.999941 0.0108507i \(-0.00345395\pi\)
\(270\) 0 0
\(271\) −2.61438 4.52824i −0.158812 0.275071i 0.775628 0.631190i \(-0.217433\pi\)
−0.934441 + 0.356119i \(0.884100\pi\)
\(272\) −1.82288 + 3.15731i −0.110528 + 0.191440i
\(273\) 0 0
\(274\) −0.645751 1.11847i −0.0390113 0.0675695i
\(275\) −15.1144 + 26.1789i −0.911431 + 1.57865i
\(276\) 0 0
\(277\) 1.03137 + 1.78639i 0.0619692 + 0.107334i 0.895346 0.445372i \(-0.146929\pi\)
−0.833376 + 0.552706i \(0.813595\pi\)
\(278\) −0.791503 1.37092i −0.0474712 0.0822225i
\(279\) 0 0
\(280\) −4.82288 8.35347i −0.288222 0.499215i
\(281\) −9.76013 + 16.9050i −0.582241 + 1.00847i 0.412973 + 0.910743i \(0.364490\pi\)
−0.995213 + 0.0977268i \(0.968843\pi\)
\(282\) 0 0
\(283\) −2.29150 −0.136216 −0.0681078 0.997678i \(-0.521696\pi\)
−0.0681078 + 0.997678i \(0.521696\pi\)
\(284\) 15.6458 0.928405
\(285\) 0 0
\(286\) 8.46863 14.6681i 0.500760 0.867342i
\(287\) −28.9373 −1.70811
\(288\) 0 0
\(289\) 1.85425 + 3.21165i 0.109073 + 0.188921i
\(290\) 4.29150 + 7.43310i 0.252006 + 0.436487i
\(291\) 0 0
\(292\) −5.29150 + 9.16515i −0.309662 + 0.536350i
\(293\) −3.53137 6.11652i −0.206305 0.357331i 0.744243 0.667909i \(-0.232811\pi\)
−0.950548 + 0.310578i \(0.899477\pi\)
\(294\) 0 0
\(295\) 15.2288 26.3770i 0.886652 1.53573i
\(296\) 5.96863 + 10.3380i 0.346919 + 0.600882i
\(297\) 0 0
\(298\) −11.4686 + 19.8642i −0.664360 + 1.15070i
\(299\) 6.00000 0.346989
\(300\) 0 0
\(301\) 6.61438 + 11.4564i 0.381246 + 0.660338i
\(302\) 9.61438 + 16.6526i 0.553245 + 0.958249i
\(303\) 0 0
\(304\) −1.00000 1.73205i −0.0573539 0.0993399i
\(305\) 13.4059 23.2197i 0.767619 1.32955i
\(306\) 0 0
\(307\) 7.58301 0.432785 0.216392 0.976306i \(-0.430571\pi\)
0.216392 + 0.976306i \(0.430571\pi\)
\(308\) −9.64575 −0.549618
\(309\) 0 0
\(310\) −8.46863 + 14.6681i −0.480986 + 0.833092i
\(311\) −13.5203 −0.766664 −0.383332 0.923611i \(-0.625223\pi\)
−0.383332 + 0.923611i \(0.625223\pi\)
\(312\) 0 0
\(313\) 12.7085 0.718327 0.359163 0.933275i \(-0.383062\pi\)
0.359163 + 0.933275i \(0.383062\pi\)
\(314\) −4.00000 −0.225733
\(315\) 0 0
\(316\) 11.2288 0.631667
\(317\) 26.8118 1.50590 0.752949 0.658079i \(-0.228631\pi\)
0.752949 + 0.658079i \(0.228631\pi\)
\(318\) 0 0
\(319\) 8.58301 0.480556
\(320\) 1.82288 3.15731i 0.101902 0.176499i
\(321\) 0 0
\(322\) −1.70850 2.95920i −0.0952108 0.164910i
\(323\) 7.29150 0.405710
\(324\) 0 0
\(325\) 19.2601 33.3595i 1.06836 1.85045i
\(326\) 0.500000 + 0.866025i 0.0276924 + 0.0479647i
\(327\) 0 0
\(328\) −5.46863 9.47194i −0.301954 0.523000i
\(329\) 6.53137 11.3127i 0.360086 0.623688i
\(330\) 0 0
\(331\) −31.8745 −1.75198 −0.875991 0.482328i \(-0.839791\pi\)
−0.875991 + 0.482328i \(0.839791\pi\)
\(332\) 6.64575 11.5108i 0.364733 0.631736i
\(333\) 0 0
\(334\) 4.29150 + 7.43310i 0.234821 + 0.406721i
\(335\) −4.17712 + 7.23499i −0.228221 + 0.395290i
\(336\) 0 0
\(337\) 15.2915 + 26.4857i 0.832981 + 1.44277i 0.895664 + 0.444732i \(0.146701\pi\)
−0.0626823 + 0.998034i \(0.519965\pi\)
\(338\) −4.29150 + 7.43310i −0.233427 + 0.404307i
\(339\) 0 0
\(340\) 6.64575 + 11.5108i 0.360416 + 0.624260i
\(341\) 8.46863 + 14.6681i 0.458602 + 0.794322i
\(342\) 0 0
\(343\) −18.5203 −1.00000
\(344\) −2.50000 + 4.33013i −0.134791 + 0.233465i
\(345\) 0 0
\(346\) −14.5830 −0.783987
\(347\) −12.0000 −0.644194 −0.322097 0.946707i \(-0.604388\pi\)
−0.322097 + 0.946707i \(0.604388\pi\)
\(348\) 0 0
\(349\) 0.614378 1.06413i 0.0328869 0.0569618i −0.849113 0.528210i \(-0.822863\pi\)
0.882000 + 0.471249i \(0.156197\pi\)
\(350\) −21.9373 −1.17260
\(351\) 0 0
\(352\) −1.82288 3.15731i −0.0971596 0.168285i
\(353\) 6.00000 + 10.3923i 0.319348 + 0.553127i 0.980352 0.197256i \(-0.0632029\pi\)
−0.661004 + 0.750382i \(0.729870\pi\)
\(354\) 0 0
\(355\) 28.5203 49.3985i 1.51370 2.62180i
\(356\) −2.46863 4.27579i −0.130837 0.226616i
\(357\) 0 0
\(358\) −8.46863 + 14.6681i −0.447581 + 0.775233i
\(359\) −5.58301 9.67005i −0.294660 0.510366i 0.680246 0.732984i \(-0.261873\pi\)
−0.974906 + 0.222618i \(0.928540\pi\)
\(360\) 0 0
\(361\) 7.50000 12.9904i 0.394737 0.683704i
\(362\) −2.70850 −0.142355
\(363\) 0 0
\(364\) 12.2915 0.644250
\(365\) 19.2915 + 33.4139i 1.00976 + 1.74896i
\(366\) 0 0
\(367\) −14.9373 25.8721i −0.779718 1.35051i −0.932104 0.362191i \(-0.882029\pi\)
0.152386 0.988321i \(-0.451304\pi\)
\(368\) 0.645751 1.11847i 0.0336621 0.0583045i
\(369\) 0 0
\(370\) 43.5203 2.26251
\(371\) 7.93725 + 13.7477i 0.412082 + 0.713746i
\(372\) 0 0
\(373\) −2.29150 + 3.96900i −0.118650 + 0.205507i −0.919233 0.393715i \(-0.871190\pi\)
0.800583 + 0.599222i \(0.204523\pi\)
\(374\) 13.2915 0.687287
\(375\) 0 0
\(376\) 4.93725 0.254619
\(377\) −10.9373 −0.563297
\(378\) 0 0
\(379\) 25.5830 1.31411 0.657055 0.753842i \(-0.271802\pi\)
0.657055 + 0.753842i \(0.271802\pi\)
\(380\) −7.29150 −0.374046
\(381\) 0 0
\(382\) −20.8118 −1.06482
\(383\) −10.2915 + 17.8254i −0.525871 + 0.910836i 0.473675 + 0.880700i \(0.342927\pi\)
−0.999546 + 0.0301357i \(0.990406\pi\)
\(384\) 0 0
\(385\) −17.5830 + 30.4547i −0.896113 + 1.55211i
\(386\) −7.00000 −0.356291
\(387\) 0 0
\(388\) −6.79150 + 11.7632i −0.344786 + 0.597187i
\(389\) −9.64575 16.7069i −0.489059 0.847075i 0.510862 0.859663i \(-0.329326\pi\)
−0.999921 + 0.0125878i \(0.995993\pi\)
\(390\) 0 0
\(391\) 2.35425 + 4.07768i 0.119059 + 0.206217i
\(392\) −3.50000 6.06218i −0.176777 0.306186i
\(393\) 0 0
\(394\) 4.70850 0.237211
\(395\) 20.4686 35.4527i 1.02989 1.78382i
\(396\) 0 0
\(397\) 8.32288 + 14.4156i 0.417713 + 0.723500i 0.995709 0.0925393i \(-0.0294984\pi\)
−0.577996 + 0.816040i \(0.696165\pi\)
\(398\) −3.03137 + 5.25049i −0.151949 + 0.263183i
\(399\) 0 0
\(400\) −4.14575 7.18065i −0.207288 0.359033i
\(401\) 10.4059 18.0235i 0.519645 0.900051i −0.480094 0.877217i \(-0.659398\pi\)
0.999739 0.0228345i \(-0.00726908\pi\)
\(402\) 0 0
\(403\) −10.7915 18.6914i −0.537563 0.931086i
\(404\) −4.17712 7.23499i −0.207820 0.359954i
\(405\) 0 0
\(406\) 3.11438 + 5.39426i 0.154564 + 0.267713i
\(407\) 21.7601 37.6897i 1.07861 1.86821i
\(408\) 0 0
\(409\) 14.8745 0.735497 0.367749 0.929925i \(-0.380129\pi\)
0.367749 + 0.929925i \(0.380129\pi\)
\(410\) −39.8745 −1.96926
\(411\) 0 0
\(412\) −1.96863 + 3.40976i −0.0969873 + 0.167987i
\(413\) 11.0516 19.1420i 0.543815 0.941916i
\(414\) 0 0
\(415\) −24.2288 41.9654i −1.18934 2.06000i
\(416\) 2.32288 + 4.02334i 0.113888 + 0.197260i
\(417\) 0 0
\(418\) −3.64575 + 6.31463i −0.178320 + 0.308858i
\(419\) −14.4686 25.0604i −0.706839 1.22428i −0.966024 0.258453i \(-0.916787\pi\)
0.259185 0.965828i \(-0.416546\pi\)
\(420\) 0 0
\(421\) 7.35425 12.7379i 0.358424 0.620809i −0.629274 0.777184i \(-0.716648\pi\)
0.987698 + 0.156375i \(0.0499808\pi\)
\(422\) −7.43725 12.8817i −0.362040 0.627071i
\(423\) 0 0
\(424\) −3.00000 + 5.19615i −0.145693 + 0.252347i
\(425\) 30.2288 1.46631
\(426\) 0 0
\(427\) 9.72876 16.8507i 0.470808 0.815463i
\(428\) 3.00000 + 5.19615i 0.145010 + 0.251166i
\(429\) 0 0
\(430\) 9.11438 + 15.7866i 0.439534 + 0.761296i
\(431\) −19.4059 + 33.6120i −0.934748 + 1.61903i −0.159666 + 0.987171i \(0.551042\pi\)
−0.775082 + 0.631861i \(0.782291\pi\)
\(432\) 0 0
\(433\) −19.0000 −0.913082 −0.456541 0.889702i \(-0.650912\pi\)
−0.456541 + 0.889702i \(0.650912\pi\)
\(434\) −6.14575 + 10.6448i −0.295006 + 0.510965i
\(435\) 0 0
\(436\) 1.67712 2.90486i 0.0803197 0.139118i
\(437\) −2.58301 −0.123562
\(438\) 0 0
\(439\) 25.1660 1.20111 0.600554 0.799584i \(-0.294947\pi\)
0.600554 + 0.799584i \(0.294947\pi\)
\(440\) −13.2915 −0.633648
\(441\) 0 0
\(442\) −16.9373 −0.805623
\(443\) −19.2915 −0.916567 −0.458283 0.888806i \(-0.651536\pi\)
−0.458283 + 0.888806i \(0.651536\pi\)
\(444\) 0 0
\(445\) −18.0000 −0.853282
\(446\) 6.93725 12.0157i 0.328488 0.568959i
\(447\) 0 0
\(448\) 1.32288 2.29129i 0.0625000 0.108253i
\(449\) 2.35425 0.111104 0.0555519 0.998456i \(-0.482308\pi\)
0.0555519 + 0.998456i \(0.482308\pi\)
\(450\) 0 0
\(451\) −19.9373 + 34.5323i −0.938809 + 1.62606i
\(452\) −1.17712 2.03884i −0.0553673 0.0958989i
\(453\) 0 0
\(454\) −3.00000 5.19615i −0.140797 0.243868i
\(455\) 22.4059 38.8081i 1.05040 1.81935i
\(456\) 0 0
\(457\) −8.29150 −0.387860 −0.193930 0.981015i \(-0.562123\pi\)
−0.193930 + 0.981015i \(0.562123\pi\)
\(458\) 4.67712 8.10102i 0.218548 0.378536i
\(459\) 0 0
\(460\) −2.35425 4.07768i −0.109767 0.190123i
\(461\) −12.1144 + 20.9827i −0.564223 + 0.977263i 0.432899 + 0.901443i \(0.357491\pi\)
−0.997122 + 0.0758200i \(0.975843\pi\)
\(462\) 0 0
\(463\) −9.35425 16.2020i −0.434729 0.752972i 0.562545 0.826767i \(-0.309822\pi\)
−0.997273 + 0.0737945i \(0.976489\pi\)
\(464\) −1.17712 + 2.03884i −0.0546466 + 0.0946507i
\(465\) 0 0
\(466\) 9.64575 + 16.7069i 0.446831 + 0.773934i
\(467\) −0.114378 0.198109i −0.00529280 0.00916739i 0.863367 0.504577i \(-0.168351\pi\)
−0.868660 + 0.495409i \(0.835018\pi\)
\(468\) 0 0
\(469\) −3.03137 + 5.25049i −0.139976 + 0.242445i
\(470\) 9.00000 15.5885i 0.415139 0.719042i
\(471\) 0 0
\(472\) 8.35425 0.384535
\(473\) 18.2288 0.838159
\(474\) 0 0
\(475\) −8.29150 + 14.3613i −0.380440 + 0.658942i
\(476\) 4.82288 + 8.35347i 0.221056 + 0.382880i
\(477\) 0 0
\(478\) 5.46863 + 9.47194i 0.250129 + 0.433236i
\(479\) −1.82288 3.15731i −0.0832893 0.144261i 0.821372 0.570393i \(-0.193209\pi\)
−0.904661 + 0.426132i \(0.859876\pi\)
\(480\) 0 0
\(481\) −27.7288 + 48.0276i −1.26432 + 2.18987i
\(482\) −2.50000 4.33013i −0.113872 0.197232i
\(483\) 0 0
\(484\) −1.14575 + 1.98450i −0.0520796 + 0.0902045i
\(485\) 24.7601 + 42.8858i 1.12430 + 1.94734i
\(486\) 0 0
\(487\) −11.9373 + 20.6759i −0.540929 + 0.936916i 0.457922 + 0.888992i \(0.348594\pi\)
−0.998851 + 0.0479237i \(0.984740\pi\)
\(488\) 7.35425 0.332911
\(489\) 0 0
\(490\) −25.5203 −1.15289
\(491\) −12.8745 22.2993i −0.581018 1.00635i −0.995359 0.0962315i \(-0.969321\pi\)
0.414341 0.910122i \(-0.364012\pi\)
\(492\) 0 0
\(493\) −4.29150 7.43310i −0.193280 0.334770i
\(494\) 4.64575 8.04668i 0.209022 0.362037i
\(495\) 0 0
\(496\) −4.64575 −0.208600
\(497\) 20.6974 35.8489i 0.928405 1.60804i
\(498\) 0 0
\(499\) 3.08301 5.33992i 0.138014 0.239048i −0.788731 0.614739i \(-0.789261\pi\)
0.926745 + 0.375691i \(0.122595\pi\)
\(500\) −12.0000 −0.536656
\(501\) 0 0
\(502\) −18.0000 −0.803379
\(503\) 3.87451 0.172756 0.0863779 0.996262i \(-0.472471\pi\)
0.0863779 + 0.996262i \(0.472471\pi\)
\(504\) 0 0
\(505\) −30.4575 −1.35534
\(506\) −4.70850 −0.209318
\(507\) 0 0
\(508\) 1.35425 0.0600851
\(509\) −4.06275 + 7.03688i −0.180078 + 0.311904i −0.941907 0.335874i \(-0.890968\pi\)
0.761829 + 0.647778i \(0.224302\pi\)
\(510\) 0 0
\(511\) 14.0000 + 24.2487i 0.619324 + 1.07270i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −7.93725 + 13.7477i −0.350097 + 0.606386i
\(515\) 7.17712 + 12.4311i 0.316262 + 0.547782i
\(516\) 0 0
\(517\) −9.00000 15.5885i −0.395820 0.685580i
\(518\) 31.5830 1.38768
\(519\) 0 0
\(520\) 16.9373 0.742748
\(521\) 4.06275 7.03688i 0.177992 0.308291i −0.763201 0.646162i \(-0.776373\pi\)
0.941193 + 0.337870i \(0.109707\pi\)
\(522\) 0 0
\(523\) 0.500000 + 0.866025i 0.0218635 + 0.0378686i 0.876750 0.480946i \(-0.159707\pi\)
−0.854887 + 0.518815i \(0.826373\pi\)
\(524\) 7.29150 12.6293i 0.318531 0.551711i
\(525\) 0 0
\(526\) 2.46863 + 4.27579i 0.107637 + 0.186433i
\(527\) 8.46863 14.6681i 0.368899 0.638952i
\(528\) 0 0
\(529\) 10.6660 + 18.4741i 0.463740 + 0.803221i
\(530\) 10.9373 + 18.9439i 0.475084 + 0.822870i
\(531\) 0 0
\(532\) −5.29150 −0.229416
\(533\) 25.4059 44.0043i 1.10045 1.90604i
\(534\) 0 0
\(535\) 21.8745 0.945717
\(536\) −2.29150 −0.0989778
\(537\) 0 0
\(538\) 8.35425 14.4700i 0.360177 0.623845i
\(539\) −12.7601 + 22.1012i −0.549618 + 0.951966i
\(540\) 0 0
\(541\) −0.583005 1.00979i −0.0250654 0.0434145i 0.853221 0.521550i \(-0.174646\pi\)
−0.878286 + 0.478136i \(0.841313\pi\)
\(542\) −2.61438 4.52824i −0.112297 0.194504i
\(543\) 0 0
\(544\) −1.82288 + 3.15731i −0.0781551 + 0.135369i
\(545\) −6.11438 10.5904i −0.261911 0.453643i
\(546\) 0 0
\(547\) −9.14575 + 15.8409i −0.391044 + 0.677308i −0.992588 0.121532i \(-0.961219\pi\)
0.601543 + 0.798840i \(0.294553\pi\)
\(548\) −0.645751 1.11847i −0.0275851 0.0477788i
\(549\) 0 0
\(550\) −15.1144 + 26.1789i −0.644479 + 1.11627i
\(551\) 4.70850 0.200589
\(552\) 0 0
\(553\) 14.8542 25.7283i 0.631667 1.09408i
\(554\) 1.03137 + 1.78639i 0.0438188 + 0.0758965i
\(555\) 0 0
\(556\) −0.791503 1.37092i −0.0335672 0.0581401i
\(557\) 2.88562 4.99804i 0.122268 0.211774i −0.798394 0.602136i \(-0.794317\pi\)
0.920662 + 0.390362i \(0.127650\pi\)
\(558\) 0 0
\(559\) −23.2288 −0.982472
\(560\) −4.82288 8.35347i −0.203804 0.352998i
\(561\) 0 0
\(562\) −9.76013 + 16.9050i −0.411706 + 0.713096i
\(563\) 18.4575 0.777891 0.388946 0.921261i \(-0.372839\pi\)
0.388946 + 0.921261i \(0.372839\pi\)
\(564\) 0 0
\(565\) −8.58301 −0.361090
\(566\) −2.29150 −0.0963190
\(567\) 0 0
\(568\) 15.6458 0.656481
\(569\) −16.9373 −0.710047 −0.355023 0.934857i \(-0.615527\pi\)
−0.355023 + 0.934857i \(0.615527\pi\)
\(570\) 0 0
\(571\) 9.29150 0.388837 0.194419 0.980919i \(-0.437718\pi\)
0.194419 + 0.980919i \(0.437718\pi\)
\(572\) 8.46863 14.6681i 0.354091 0.613304i
\(573\) 0 0
\(574\) −28.9373 −1.20782
\(575\) −10.7085 −0.446575
\(576\) 0 0
\(577\) 16.1458 27.9653i 0.672156 1.16421i −0.305135 0.952309i \(-0.598702\pi\)
0.977291 0.211900i \(-0.0679651\pi\)
\(578\) 1.85425 + 3.21165i 0.0771266 + 0.133587i
\(579\) 0 0
\(580\) 4.29150 + 7.43310i 0.178195 + 0.308643i
\(581\) −17.5830 30.4547i −0.729466 1.26347i
\(582\) 0 0
\(583\) 21.8745 0.905950
\(584\) −5.29150 + 9.16515i −0.218964 + 0.379257i
\(585\) 0 0
\(586\) −3.53137 6.11652i −0.145880 0.252671i
\(587\) −5.88562 + 10.1942i −0.242926 + 0.420759i −0.961546 0.274643i \(-0.911440\pi\)
0.718621 + 0.695402i \(0.244774\pi\)
\(588\) 0 0
\(589\) 4.64575 + 8.04668i 0.191425 + 0.331558i
\(590\) 15.2288 26.3770i 0.626958 1.08592i
\(591\) 0 0
\(592\) 5.96863 + 10.3380i 0.245309 + 0.424888i
\(593\) −20.4686 35.4527i −0.840546 1.45587i −0.889434 0.457064i \(-0.848901\pi\)
0.0488882 0.998804i \(-0.484432\pi\)
\(594\) 0 0
\(595\) 35.1660 1.44167
\(596\) −11.4686 + 19.8642i −0.469773 + 0.813671i
\(597\) 0 0
\(598\) 6.00000 0.245358
\(599\) 9.87451 0.403461 0.201731 0.979441i \(-0.435343\pi\)
0.201731 + 0.979441i \(0.435343\pi\)
\(600\) 0 0
\(601\) −13.4373 + 23.2740i −0.548117 + 0.949367i 0.450287 + 0.892884i \(0.351322\pi\)
−0.998404 + 0.0564824i \(0.982012\pi\)
\(602\) 6.61438 + 11.4564i 0.269582 + 0.466930i
\(603\) 0 0
\(604\) 9.61438 + 16.6526i 0.391204 + 0.677584i
\(605\) 4.17712 + 7.23499i 0.169824 + 0.294144i
\(606\) 0 0
\(607\) −2.70850 + 4.69126i −0.109935 + 0.190412i −0.915744 0.401763i \(-0.868397\pi\)
0.805809 + 0.592176i \(0.201731\pi\)
\(608\) −1.00000 1.73205i −0.0405554 0.0702439i
\(609\) 0 0
\(610\) 13.4059 23.2197i 0.542788 0.940137i
\(611\) 11.4686 + 19.8642i 0.463971 + 0.803621i
\(612\) 0 0
\(613\) 21.1974 36.7149i 0.856154 1.48290i −0.0194158 0.999811i \(-0.506181\pi\)
0.875570 0.483091i \(-0.160486\pi\)
\(614\) 7.58301 0.306025
\(615\) 0 0
\(616\) −9.64575 −0.388638
\(617\) −0.760130 1.31658i −0.0306017 0.0530036i 0.850319 0.526268i \(-0.176409\pi\)
−0.880921 + 0.473264i \(0.843076\pi\)
\(618\) 0 0
\(619\) 4.14575 + 7.18065i 0.166632 + 0.288615i 0.937234 0.348702i \(-0.113378\pi\)
−0.770602 + 0.637317i \(0.780044\pi\)
\(620\) −8.46863 + 14.6681i −0.340108 + 0.589085i
\(621\) 0 0
\(622\) −13.5203 −0.542113
\(623\) −13.0627 −0.523348
\(624\) 0 0
\(625\) −1.14575 + 1.98450i −0.0458301 + 0.0793800i
\(626\) 12.7085 0.507934
\(627\) 0 0
\(628\) −4.00000 −0.159617
\(629\) −43.5203 −1.73527
\(630\) 0 0
\(631\) 6.06275 0.241354 0.120677 0.992692i \(-0.461493\pi\)
0.120677 + 0.992692i \(0.461493\pi\)
\(632\) 11.2288 0.446656
\(633\) 0 0
\(634\) 26.8118 1.06483
\(635\) 2.46863 4.27579i 0.0979645 0.169679i
\(636\) 0 0
\(637\) 16.2601 28.1634i 0.644250 1.11587i
\(638\) 8.58301 0.339804
\(639\) 0 0
\(640\) 1.82288 3.15731i 0.0720555 0.124804i
\(641\) 9.11438 + 15.7866i 0.359996 + 0.623532i 0.987960 0.154711i \(-0.0494446\pi\)
−0.627963 + 0.778243i \(0.716111\pi\)
\(642\) 0 0
\(643\) 1.56275 + 2.70676i 0.0616287 + 0.106744i 0.895194 0.445678i \(-0.147037\pi\)
−0.833565 + 0.552422i \(0.813704\pi\)
\(644\) −1.70850 2.95920i −0.0673242 0.116609i
\(645\) 0 0
\(646\) 7.29150 0.286880
\(647\) −4.93725 + 8.55157i −0.194103 + 0.336197i −0.946606 0.322392i \(-0.895513\pi\)
0.752503 + 0.658589i \(0.228846\pi\)
\(648\) 0 0
\(649\) −15.2288 26.3770i −0.597781 1.03539i
\(650\) 19.2601 33.3595i 0.755444 1.30847i
\(651\) 0 0
\(652\) 0.500000 + 0.866025i 0.0195815 + 0.0339162i
\(653\) 3.00000 5.19615i 0.117399 0.203341i −0.801337 0.598213i \(-0.795878\pi\)
0.918736 + 0.394872i \(0.129211\pi\)
\(654\) 0 0
\(655\) −26.5830 46.0431i −1.03868 1.79905i
\(656\) −5.46863 9.47194i −0.213514 0.369817i
\(657\) 0 0
\(658\) 6.53137 11.3127i 0.254619 0.441014i
\(659\) 12.1144 20.9827i 0.471909 0.817371i −0.527574 0.849509i \(-0.676898\pi\)
0.999483 + 0.0321382i \(0.0102317\pi\)
\(660\) 0 0
\(661\) −3.16601 −0.123144 −0.0615718 0.998103i \(-0.519611\pi\)
−0.0615718 + 0.998103i \(0.519611\pi\)
\(662\) −31.8745 −1.23884
\(663\) 0 0
\(664\) 6.64575 11.5108i 0.257905 0.446705i
\(665\) −9.64575 + 16.7069i −0.374046 + 0.647867i
\(666\) 0 0
\(667\) 1.52026 + 2.63317i 0.0588647 + 0.101957i
\(668\) 4.29150 + 7.43310i 0.166043 + 0.287595i
\(669\) 0 0
\(670\) −4.17712 + 7.23499i −0.161376 + 0.279512i
\(671\) −13.4059 23.2197i −0.517528 0.896385i
\(672\) 0 0
\(673\) −7.87451 + 13.6390i −0.303540 + 0.525747i −0.976935 0.213536i \(-0.931502\pi\)
0.673395 + 0.739283i \(0.264835\pi\)
\(674\) 15.2915 + 26.4857i 0.589007 + 1.02019i
\(675\) 0 0
\(676\) −4.29150 + 7.43310i −0.165058 + 0.285888i
\(677\) −45.8745 −1.76310 −0.881550 0.472090i \(-0.843500\pi\)
−0.881550 + 0.472090i \(0.843500\pi\)
\(678\) 0 0
\(679\) 17.9686 + 31.1226i 0.689573 + 1.19437i
\(680\) 6.64575 + 11.5108i 0.254853 + 0.441418i
\(681\) 0 0
\(682\) 8.46863 + 14.6681i 0.324280 + 0.561670i
\(683\) 13.4059 23.2197i 0.512962 0.888476i −0.486925 0.873444i \(-0.661882\pi\)
0.999887 0.0150322i \(-0.00478508\pi\)
\(684\) 0 0
\(685\) −4.70850 −0.179902
\(686\) −18.5203 −0.707107
\(687\) 0 0
\(688\) −2.50000 + 4.33013i −0.0953116 + 0.165085i
\(689\) −27.8745 −1.06193
\(690\) 0 0
\(691\) −38.7490 −1.47408 −0.737041 0.675848i \(-0.763778\pi\)
−0.737041 + 0.675848i \(0.763778\pi\)
\(692\) −14.5830 −0.554363
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) −5.77124 −0.218916
\(696\) 0 0
\(697\) 39.8745 1.51035
\(698\) 0.614378 1.06413i 0.0232546 0.0402781i
\(699\) 0 0
\(700\) −21.9373 −0.829150
\(701\) −26.5830 −1.00403 −0.502013 0.864860i \(-0.667407\pi\)
−0.502013 + 0.864860i \(0.667407\pi\)
\(702\) 0 0
\(703\) 11.9373 20.6759i 0.450222 0.779807i
\(704\) −1.82288 3.15731i −0.0687022 0.118996i
\(705\) 0 0
\(706\) 6.00000 + 10.3923i 0.225813 + 0.391120i
\(707\) −22.1033 −0.831279
\(708\) 0 0
\(709\) 37.8118 1.42005 0.710025 0.704176i \(-0.248683\pi\)
0.710025 + 0.704176i \(0.248683\pi\)
\(710\) 28.5203 49.3985i 1.07035 1.85389i
\(711\) 0 0
\(712\) −2.46863 4.27579i −0.0925157 0.160242i
\(713\) −3.00000 + 5.19615i −0.112351 + 0.194597i
\(714\) 0 0
\(715\) −30.8745 53.4762i −1.15464 1.99990i
\(716\) −8.46863 + 14.6681i −0.316487 + 0.548172i
\(717\) 0 0
\(718\) −5.58301 9.67005i −0.208356 0.360883i
\(719\) −11.4686 19.8642i −0.427708 0.740811i 0.568961 0.822364i \(-0.307345\pi\)
−0.996669 + 0.0815529i \(0.974012\pi\)
\(720\) 0 0
\(721\) 5.20850 + 9.02138i 0.193975 + 0.335974i
\(722\) 7.50000 12.9904i 0.279121 0.483452i
\(723\) 0 0
\(724\) −2.70850 −0.100661
\(725\) 19.5203 0.724964
\(726\) 0 0
\(727\) 0.614378 1.06413i 0.0227860 0.0394666i −0.854408 0.519603i \(-0.826080\pi\)
0.877194 + 0.480137i \(0.159413\pi\)
\(728\) 12.2915 0.455553
\(729\) 0 0
\(730\) 19.2915 + 33.4139i 0.714011 + 1.23670i
\(731\) −9.11438 15.7866i −0.337107 0.583887i
\(732\) 0 0
\(733\) −17.6144 + 30.5090i −0.650602 + 1.12688i 0.332375 + 0.943147i \(0.392150\pi\)
−0.982977 + 0.183728i \(0.941183\pi\)
\(734\) −14.9373 25.8721i −0.551344 0.954956i
\(735\) 0 0
\(736\) 0.645751 1.11847i 0.0238027 0.0412275i
\(737\) 4.17712 + 7.23499i 0.153866 + 0.266504i
\(738\) 0 0
\(739\) 15.7288 27.2430i 0.578592 1.00215i −0.417050 0.908884i \(-0.636936\pi\)
0.995641 0.0932664i \(-0.0297308\pi\)
\(740\) 43.5203 1.59984
\(741\) 0 0
\(742\) 7.93725 + 13.7477i 0.291386 + 0.504695i
\(743\) 14.4686 + 25.0604i 0.530802 + 0.919377i 0.999354 + 0.0359406i \(0.0114427\pi\)
−0.468551 + 0.883436i \(0.655224\pi\)
\(744\) 0 0
\(745\) 41.8118 + 72.4201i 1.53186 + 2.65327i
\(746\) −2.29150 + 3.96900i −0.0838979 + 0.145315i
\(747\) 0 0
\(748\) 13.2915 0.485985
\(749\) 15.8745 0.580042
\(750\) 0 0
\(751\) 26.2288 45.4295i 0.957101 1.65775i 0.227615 0.973751i \(-0.426907\pi\)
0.729485 0.683996i \(-0.239760\pi\)
\(752\) 4.93725 0.180043
\(753\) 0 0
\(754\) −10.9373 −0.398311
\(755\) 70.1033 2.55132
\(756\) 0 0
\(757\) 48.9778 1.78013 0.890064 0.455836i \(-0.150660\pi\)
0.890064 + 0.455836i \(0.150660\pi\)
\(758\) 25.5830 0.929217
\(759\) 0 0
\(760\) −7.29150 −0.264491
\(761\) −1.29150 + 2.23695i −0.0468169 + 0.0810893i −0.888484 0.458907i \(-0.848241\pi\)
0.841667 + 0.539996i \(0.181574\pi\)
\(762\) 0 0
\(763\) −4.43725 7.68555i −0.160639 0.278236i
\(764\) −20.8118 −0.752943
\(765\) 0 0
\(766\) −10.2915 + 17.8254i −0.371847 + 0.644058i
\(767\) 19.4059 + 33.6120i 0.700706 + 1.21366i
\(768\) 0 0
\(769\) −20.2915 35.1459i −0.731730 1.26739i −0.956143 0.292900i \(-0.905380\pi\)
0.224413 0.974494i \(-0.427954\pi\)
\(770\) −17.5830 + 30.4547i −0.633648 + 1.09751i
\(771\) 0 0
\(772\) −7.00000 −0.251936
\(773\) 23.1660 40.1247i 0.833223 1.44319i −0.0622452 0.998061i \(-0.519826\pi\)
0.895469 0.445125i \(-0.146841\pi\)
\(774\) 0 0
\(775\) 19.2601 + 33.3595i 0.691844 + 1.19831i
\(776\) −6.79150 + 11.7632i −0.243801 + 0.422275i
\(777\) 0 0
\(778\) −9.64575 16.7069i −0.345817 0.598973i
\(779\) −10.9373 + 18.9439i −0.391868 + 0.678735i
\(780\) 0 0
\(781\) −28.5203 49.3985i −1.02054 1.76762i
\(782\) 2.35425 + 4.07768i 0.0841878 + 0.145817i
\(783\) 0 0
\(784\) −3.50000 6.06218i −0.125000 0.216506i
\(785\) −7.29150 + 12.6293i −0.260245 + 0.450757i
\(786\) 0 0
\(787\) −11.7085 −0.417363 −0.208681 0.977984i \(-0.566917\pi\)
−0.208681 + 0.977984i \(0.566917\pi\)
\(788\) 4.70850 0.167733
\(789\) 0 0
\(790\) 20.4686 35.4527i 0.728241 1.26135i
\(791\) −6.22876 −0.221469
\(792\) 0 0
\(793\) 17.0830 + 29.5886i 0.606635 + 1.05072i
\(794\) 8.32288 + 14.4156i 0.295368 + 0.511592i
\(795\) 0 0
\(796\) −3.03137 + 5.25049i −0.107444 + 0.186099i
\(797\) 7.40588 + 12.8274i 0.262330 + 0.454368i 0.966861 0.255305i \(-0.0821759\pi\)
−0.704531 + 0.709673i \(0.748843\pi\)
\(798\) 0 0
\(799\) −9.00000 + 15.5885i −0.318397 + 0.551480i
\(800\) −4.14575 7.18065i −0.146574 0.253874i
\(801\) 0 0
\(802\) 10.4059 18.0235i 0.367444 0.636432i
\(803\) 38.5830 1.36156
\(804\) 0 0
\(805\) −12.4575 −0.439070
\(806\) −10.7915 18.6914i −0.380114 0.658378i
\(807\) 0 0
\(808\) −4.17712 7.23499i −0.146951 0.254526i
\(809\) −7.70850 + 13.3515i −0.271016 + 0.469414i −0.969122 0.246580i \(-0.920693\pi\)
0.698106 + 0.715994i \(0.254026\pi\)
\(810\) 0 0
\(811\) −29.2915 −1.02856 −0.514282 0.857621i \(-0.671941\pi\)
−0.514282 + 0.857621i \(0.671941\pi\)
\(812\) 3.11438 + 5.39426i 0.109293 + 0.189301i
\(813\) 0 0
\(814\) 21.7601 37.6897i 0.762692 1.32102i
\(815\) 3.64575 0.127705
\(816\) 0 0
\(817\) 10.0000 0.349856
\(818\) 14.8745 0.520075
\(819\) 0 0
\(820\) −39.8745 −1.39248
\(821\) 20.5830 0.718352 0.359176 0.933270i \(-0.383058\pi\)
0.359176 + 0.933270i \(0.383058\pi\)
\(822\) 0 0
\(823\) −35.1033 −1.22362 −0.611811 0.791004i \(-0.709559\pi\)
−0.611811 + 0.791004i \(0.709559\pi\)
\(824\) −1.96863 + 3.40976i −0.0685804 + 0.118785i
\(825\) 0 0
\(826\) 11.0516 19.1420i 0.384535 0.666035i
\(827\) −43.7490 −1.52130 −0.760651 0.649161i \(-0.775120\pi\)
−0.760651 + 0.649161i \(0.775120\pi\)
\(828\) 0 0
\(829\) 14.6458 25.3672i 0.508668 0.881039i −0.491282 0.871001i \(-0.663471\pi\)
0.999950 0.0100380i \(-0.00319525\pi\)
\(830\) −24.2288 41.9654i −0.840992 1.45664i
\(831\) 0 0
\(832\) 2.32288 + 4.02334i 0.0805312 + 0.139484i
\(833\) 25.5203 0.884225
\(834\) 0 0
\(835\) 31.2915 1.08289
\(836\) −3.64575 + 6.31463i −0.126091 + 0.218396i
\(837\) 0 0
\(838\) −14.4686 25.0604i −0.499810 0.865697i
\(839\) 24.6458 42.6877i 0.850866 1.47374i −0.0295622 0.999563i \(-0.509411\pi\)
0.880428 0.474180i \(-0.157255\pi\)
\(840\) 0 0
\(841\) 11.7288 + 20.3148i 0.404440 + 0.700510i
\(842\) 7.35425 12.7379i 0.253444 0.438978i
\(843\) 0 0
\(844\) −7.43725 12.8817i −0.256001 0.443406i
\(845\) 15.6458 + 27.0992i 0.538230 + 0.932242i
\(846\) 0 0
\(847\) 3.03137 + 5.25049i 0.104159 + 0.180409i
\(848\) −3.00000 + 5.19615i −0.103020 + 0.178437i
\(849\) 0 0
\(850\) 30.2288 1.03684
\(851\) 15.4170 0.528488
\(852\) 0 0
\(853\) −23.9373 + 41.4605i −0.819596 + 1.41958i 0.0863843 + 0.996262i \(0.472469\pi\)
−0.905980 + 0.423320i \(0.860865\pi\)
\(854\) 9.72876 16.8507i 0.332911 0.576619i
\(855\) 0 0
\(856\) 3.00000 + 5.19615i 0.102538 + 0.177601i
\(857\) 13.4059 + 23.2197i 0.457936 + 0.793169i 0.998852 0.0479082i \(-0.0152555\pi\)
−0.540916 + 0.841077i \(0.681922\pi\)
\(858\) 0 0
\(859\) 3.50000 6.06218i 0.119418 0.206839i −0.800119 0.599841i \(-0.795230\pi\)
0.919537 + 0.393003i \(0.128564\pi\)
\(860\) 9.11438 + 15.7866i 0.310798 + 0.538317i
\(861\) 0 0
\(862\) −19.4059 + 33.6120i −0.660967 + 1.14483i
\(863\) −14.5830 25.2585i −0.496411 0.859810i 0.503580 0.863949i \(-0.332016\pi\)
−0.999991 + 0.00413896i \(0.998683\pi\)
\(864\) 0 0
\(865\) −26.5830 + 46.0431i −0.903849 + 1.56551i
\(866\) −19.0000 −0.645646
\(867\) 0 0
\(868\) −6.14575 + 10.6448i −0.208600 + 0.361306i
\(869\) −20.4686 35.4527i −0.694351 1.20265i
\(870\) 0 0
\(871\) −5.32288 9.21949i −0.180359 0.312391i
\(872\) 1.67712 2.90486i 0.0567946 0.0983711i
\(873\) 0 0
\(874\) −2.58301 −0.0873715
\(875\) −15.8745 + 27.4955i −0.536656 + 0.929516i
\(876\) 0 0
\(877\) −13.3229 + 23.0759i −0.449882 + 0.779218i −0.998378 0.0569353i \(-0.981867\pi\)
0.548496 + 0.836153i \(0.315200\pi\)
\(878\) 25.1660 0.849312
\(879\) 0 0
\(880\) −13.2915 −0.448056
\(881\) −3.87451 −0.130535 −0.0652677 0.997868i \(-0.520790\pi\)
−0.0652677 + 0.997868i \(0.520790\pi\)
\(882\) 0 0
\(883\) −19.8745 −0.668830 −0.334415 0.942426i \(-0.608539\pi\)
−0.334415 + 0.942426i \(0.608539\pi\)
\(884\) −16.9373 −0.569661
\(885\) 0 0
\(886\) −19.2915 −0.648111
\(887\) −7.93725 + 13.7477i −0.266507 + 0.461603i −0.967957 0.251115i \(-0.919203\pi\)
0.701450 + 0.712718i \(0.252536\pi\)
\(888\) 0 0
\(889\) 1.79150 3.10297i 0.0600851 0.104070i
\(890\) −18.0000 −0.603361
\(891\) 0 0
\(892\) 6.93725 12.0157i 0.232276 0.402315i
\(893\) −4.93725 8.55157i −0.165219 0.286168i
\(894\) 0 0
\(895\) 30.8745 + 53.4762i 1.03202 + 1.78751i
\(896\) 1.32288 2.29129i 0.0441942 0.0765466i
\(897\) 0 0
\(898\) 2.35425 0.0785623
\(899\) 5.46863 9.47194i 0.182389 0.315907i
\(900\) 0 0
\(901\) −10.9373 18.9439i −0.364373 0.631112i
\(902\) −19.9373 + 34.5323i −0.663838 + 1.14980i
\(903\) 0 0
\(904\) −1.17712 2.03884i −0.0391506 0.0678108i
\(905\) −4.93725 + 8.55157i −0.164120 + 0.284264i
\(906\) 0 0
\(907\) −18.1458 31.4294i −0.602520 1.04359i −0.992438 0.122745i \(-0.960830\pi\)
0.389918 0.920849i \(-0.372503\pi\)
\(908\) −3.00000 5.19615i −0.0995585 0.172440i
\(909\) 0 0
\(910\) 22.4059 38.8081i 0.742748 1.28648i
\(911\) −14.4686 + 25.0604i −0.479367 + 0.830288i −0.999720 0.0236633i \(-0.992467\pi\)
0.520353 + 0.853951i \(0.325800\pi\)
\(912\) 0 0
\(913\) −48.4575 −1.60371
\(914\) −8.29150 −0.274259
\(915\) 0 0
\(916\) 4.67712 8.10102i 0.154537 0.267665i
\(917\) −19.2915 33.4139i −0.637062 1.10342i
\(918\) 0 0
\(919\) −14.3856 24.9166i −0.474538 0.821924i 0.525037 0.851079i \(-0.324051\pi\)
−0.999575 + 0.0291557i \(0.990718\pi\)
\(920\) −2.35425 4.07768i −0.0776173 0.134437i
\(921\) 0 0
\(922\) −12.1144 + 20.9827i −0.398966 + 0.691029i
\(923\) 36.3431 + 62.9482i 1.19625 + 2.07196i
\(924\) 0 0
\(925\) 49.4889 85.7173i 1.62718 2.81837i
\(926\) −9.35425 16.2020i −0.307400 0.532432i
\(927\) 0 0
\(928\) −1.17712 + 2.03884i −0.0386410 + 0.0669282i
\(929\) −16.9373 −0.555693 −0.277847 0.960625i \(-0.589621\pi\)
−0.277847 + 0.960625i \(0.589621\pi\)
\(930\) 0 0
\(931\) −7.00000 + 12.1244i −0.229416 + 0.397360i
\(932\) 9.64575 + 16.7069i 0.315957 + 0.547254i
\(933\) 0 0
\(934\) −0.114378 0.198109i −0.00374257 0.00648232i
\(935\) 24.2288 41.9654i 0.792365 1.37242i
\(936\) 0 0
\(937\) −44.7490 −1.46189 −0.730943 0.682438i \(-0.760920\pi\)
−0.730943 + 0.682438i \(0.760920\pi\)
\(938\) −3.03137 + 5.25049i −0.0989778 + 0.171435i
\(939\) 0 0
\(940\) 9.00000 15.5885i 0.293548 0.508439i
\(941\) −53.3948 −1.74062 −0.870310 0.492505i \(-0.836081\pi\)
−0.870310 + 0.492505i \(0.836081\pi\)
\(942\) 0 0
\(943\) −14.1255 −0.459989
\(944\) 8.35425 0.271908
\(945\) 0 0
\(946\) 18.2288 0.592668
\(947\) 10.4797 0.340546 0.170273 0.985397i \(-0.445535\pi\)
0.170273 + 0.985397i \(0.445535\pi\)
\(948\) 0 0
\(949\) −49.1660 −1.59600
\(950\) −8.29150 + 14.3613i −0.269012 + 0.465942i
\(951\) 0 0
\(952\) 4.82288 + 8.35347i 0.156310 + 0.270737i
\(953\) 52.3320 1.69520 0.847600 0.530635i \(-0.178047\pi\)
0.847600 + 0.530635i \(0.178047\pi\)
\(954\) 0 0
\(955\) −37.9373 + 65.7093i −1.22762 + 2.12630i
\(956\) 5.46863 + 9.47194i 0.176868 + 0.306344i
\(957\) 0 0
\(958\) −1.82288 3.15731i −0.0588944 0.102008i
\(959\) −3.41699 −0.110341
\(960\) 0 0
\(961\) −9.41699 −0.303774
\(962\) −27.7288 + 48.0276i −0.894011 + 1.54847i
\(963\) 0 0
\(964\) −2.50000 4.33013i −0.0805196 0.139464i
\(965\) −12.7601 + 22.1012i −0.410763 + 0.711463i
\(966\) 0 0
\(967\) −18.0314 31.2313i −0.579850 1.00433i −0.995496 0.0948030i \(-0.969778\pi\)
0.415646 0.909526i \(-0.363555\pi\)
\(968\) −1.14575 + 1.98450i −0.0368258 + 0.0637842i
\(969\) 0 0
\(970\) 24.7601 + 42.8858i 0.795000 + 1.37698i
\(971\) 4.93725 + 8.55157i 0.158444 + 0.274433i 0.934308 0.356467i \(-0.116019\pi\)
−0.775864 + 0.630901i \(0.782686\pi\)
\(972\) 0 0
\(973\) −4.18824 −0.134269
\(974\) −11.9373 + 20.6759i −0.382494 + 0.662500i
\(975\) 0 0
\(976\) 7.35425 0.235404
\(977\) −51.8745 −1.65961 −0.829806 0.558052i \(-0.811549\pi\)
−0.829806 + 0.558052i \(0.811549\pi\)
\(978\) 0 0
\(979\) −9.00000 + 15.5885i −0.287641 + 0.498209i
\(980\) −25.5203 −0.815215
\(981\) 0 0
\(982\) −12.8745 22.2993i −0.410842 0.711599i
\(983\) −10.4059 18.0235i −0.331896 0.574861i 0.650988 0.759088i \(-0.274355\pi\)
−0.982884 + 0.184228i \(0.941022\pi\)
\(984\) 0 0
\(985\) 8.58301 14.8662i 0.273477 0.473677i
\(986\) −4.29150 7.43310i −0.136669 0.236718i
\(987\) 0 0
\(988\) 4.64575 8.04668i 0.147801 0.255999i
\(989\) 3.22876 + 5.59237i 0.102668 + 0.177827i
\(990\) 0 0
\(991\) 13.0314 22.5710i 0.413955 0.716991i −0.581363 0.813644i \(-0.697480\pi\)
0.995318 + 0.0966529i \(0.0308137\pi\)
\(992\) −4.64575 −0.147503
\(993\) 0 0
\(994\) 20.6974 35.8489i 0.656481 1.13706i
\(995\) 11.0516 + 19.1420i 0.350360 + 0.606842i
\(996\) 0 0
\(997\) −11.8431 20.5129i −0.375076 0.649650i 0.615263 0.788322i \(-0.289050\pi\)
−0.990338 + 0.138672i \(0.955717\pi\)
\(998\) 3.08301 5.33992i 0.0975908 0.169032i
\(999\) 0 0
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 1134.2.e.t.865.2 4
3.2 odd 2 1134.2.e.q.865.1 4
7.2 even 3 1134.2.h.q.541.1 4
9.2 odd 6 378.2.g.h.109.1 yes 4
9.4 even 3 1134.2.h.q.109.1 4
9.5 odd 6 1134.2.h.t.109.2 4
9.7 even 3 378.2.g.g.109.2 4
21.2 odd 6 1134.2.h.t.541.2 4
63.2 odd 6 378.2.g.h.163.1 yes 4
63.11 odd 6 2646.2.a.bi.1.2 2
63.16 even 3 378.2.g.g.163.2 yes 4
63.23 odd 6 1134.2.e.q.919.1 4
63.25 even 3 2646.2.a.bl.1.1 2
63.38 even 6 2646.2.a.bf.1.1 2
63.52 odd 6 2646.2.a.bo.1.2 2
63.58 even 3 inner 1134.2.e.t.919.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
378.2.g.g.109.2 4 9.7 even 3
378.2.g.g.163.2 yes 4 63.16 even 3
378.2.g.h.109.1 yes 4 9.2 odd 6
378.2.g.h.163.1 yes 4 63.2 odd 6
1134.2.e.q.865.1 4 3.2 odd 2
1134.2.e.q.919.1 4 63.23 odd 6
1134.2.e.t.865.2 4 1.1 even 1 trivial
1134.2.e.t.919.2 4 63.58 even 3 inner
1134.2.h.q.109.1 4 9.4 even 3
1134.2.h.q.541.1 4 7.2 even 3
1134.2.h.t.109.2 4 9.5 odd 6
1134.2.h.t.541.2 4 21.2 odd 6
2646.2.a.bf.1.1 2 63.38 even 6
2646.2.a.bi.1.2 2 63.11 odd 6
2646.2.a.bl.1.1 2 63.25 even 3
2646.2.a.bo.1.2 2 63.52 odd 6