Properties

Label 1710.2.l.k.1261.1
Level $1710$
Weight $2$
Character 1710.1261
Analytic conductor $13.654$
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] = [1710,2,Mod(1261,1710)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1710, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1710.1261");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1710.l (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(13.6544187456\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{19})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 19x^{2} + 361 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 570)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1261.1
Root \(2.17945 + 3.77492i\) of defining polynomial
Character \(\chi\) \(=\) 1710.1261
Dual form 1710.2.l.k.1531.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -4.35890 q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -4.35890 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +3.00000 q^{11} +(2.00000 - 3.46410i) q^{13} +(2.17945 + 3.77492i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.67945 + 2.90889i) q^{17} +(-2.17945 - 3.77492i) q^{19} +1.00000 q^{20} +(-1.50000 - 2.59808i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{25} -4.00000 q^{26} +(2.17945 - 3.77492i) q^{28} +(4.67945 - 8.10504i) q^{29} -10.7178 q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.67945 - 2.90889i) q^{34} +(2.17945 + 3.77492i) q^{35} -7.00000 q^{37} +(-2.17945 + 3.77492i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(-3.17945 - 5.50697i) q^{41} +(5.00000 + 8.66025i) q^{43} +(-1.50000 + 2.59808i) q^{44} +3.00000 q^{46} +(-3.00000 + 5.19615i) q^{47} +12.0000 q^{49} +1.00000 q^{50} +(2.00000 + 3.46410i) q^{52} +(-6.53835 + 11.3248i) q^{53} +(-1.50000 - 2.59808i) q^{55} -4.35890 q^{56} -9.35890 q^{58} +(6.35890 + 11.0139i) q^{59} +(-2.67945 + 4.64094i) q^{61} +(5.35890 + 9.28189i) q^{62} +1.00000 q^{64} -4.00000 q^{65} +(-5.67945 + 9.83710i) q^{67} -3.35890 q^{68} +(2.17945 - 3.77492i) q^{70} +(-5.03835 - 8.72668i) q^{71} +(-2.32055 - 4.01931i) q^{73} +(3.50000 + 6.06218i) q^{74} +4.35890 q^{76} -13.0767 q^{77} +(2.35890 + 4.08573i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-3.17945 + 5.50697i) q^{82} +6.00000 q^{83} +(1.67945 - 2.90889i) q^{85} +(5.00000 - 8.66025i) q^{86} +3.00000 q^{88} +(0.179449 - 0.310816i) q^{89} +(-8.71780 + 15.0997i) q^{91} +(-1.50000 - 2.59808i) q^{92} +6.00000 q^{94} +(-2.17945 + 3.77492i) q^{95} +(7.03835 + 12.1908i) q^{97} +(-6.00000 - 10.3923i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 4 q^{8} - 2 q^{10} + 12 q^{11} + 8 q^{13} - 2 q^{16} - 2 q^{17} + 4 q^{20} - 6 q^{22} - 6 q^{23} - 2 q^{25} - 16 q^{26} + 10 q^{29} - 8 q^{31} - 2 q^{32} - 2 q^{34} - 28 q^{37} - 2 q^{40} - 4 q^{41} + 20 q^{43} - 6 q^{44} + 12 q^{46} - 12 q^{47} + 48 q^{49} + 4 q^{50} + 8 q^{52} - 6 q^{55} - 20 q^{58} + 8 q^{59} - 2 q^{61} + 4 q^{62} + 4 q^{64} - 16 q^{65} - 14 q^{67} + 4 q^{68} + 6 q^{71} - 18 q^{73} + 14 q^{74} - 8 q^{79} - 2 q^{80} - 4 q^{82} + 24 q^{83} - 2 q^{85} + 20 q^{86} + 12 q^{88} - 8 q^{89} - 6 q^{92} + 24 q^{94} + 2 q^{97} - 24 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(1027\) \(1351\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 0 0
\(7\) −4.35890 −1.64751 −0.823754 0.566947i \(-0.808125\pi\)
−0.823754 + 0.566947i \(0.808125\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −0.500000 + 0.866025i −0.158114 + 0.273861i
\(11\) 3.00000 0.904534 0.452267 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) 0 0
\(13\) 2.00000 3.46410i 0.554700 0.960769i −0.443227 0.896410i \(-0.646166\pi\)
0.997927 0.0643593i \(-0.0205004\pi\)
\(14\) 2.17945 + 3.77492i 0.582482 + 1.00889i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.67945 + 2.90889i 0.407326 + 0.705510i 0.994589 0.103886i \(-0.0331278\pi\)
−0.587263 + 0.809396i \(0.699795\pi\)
\(18\) 0 0
\(19\) −2.17945 3.77492i −0.500000 0.866025i
\(20\) 1.00000 0.223607
\(21\) 0 0
\(22\) −1.50000 2.59808i −0.319801 0.553912i
\(23\) −1.50000 + 2.59808i −0.312772 + 0.541736i −0.978961 0.204046i \(-0.934591\pi\)
0.666190 + 0.745782i \(0.267924\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −4.00000 −0.784465
\(27\) 0 0
\(28\) 2.17945 3.77492i 0.411877 0.713392i
\(29\) 4.67945 8.10504i 0.868952 1.50507i 0.00588307 0.999983i \(-0.498127\pi\)
0.863069 0.505086i \(-0.168539\pi\)
\(30\) 0 0
\(31\) −10.7178 −1.92497 −0.962487 0.271329i \(-0.912537\pi\)
−0.962487 + 0.271329i \(0.912537\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 1.67945 2.90889i 0.288023 0.498871i
\(35\) 2.17945 + 3.77492i 0.368394 + 0.638077i
\(36\) 0 0
\(37\) −7.00000 −1.15079 −0.575396 0.817875i \(-0.695152\pi\)
−0.575396 + 0.817875i \(0.695152\pi\)
\(38\) −2.17945 + 3.77492i −0.353553 + 0.612372i
\(39\) 0 0
\(40\) −0.500000 0.866025i −0.0790569 0.136931i
\(41\) −3.17945 5.50697i −0.496547 0.860044i 0.503445 0.864027i \(-0.332065\pi\)
−0.999992 + 0.00398308i \(0.998732\pi\)
\(42\) 0 0
\(43\) 5.00000 + 8.66025i 0.762493 + 1.32068i 0.941562 + 0.336840i \(0.109358\pi\)
−0.179069 + 0.983836i \(0.557309\pi\)
\(44\) −1.50000 + 2.59808i −0.226134 + 0.391675i
\(45\) 0 0
\(46\) 3.00000 0.442326
\(47\) −3.00000 + 5.19615i −0.437595 + 0.757937i −0.997503 0.0706177i \(-0.977503\pi\)
0.559908 + 0.828554i \(0.310836\pi\)
\(48\) 0 0
\(49\) 12.0000 1.71429
\(50\) 1.00000 0.141421
\(51\) 0 0
\(52\) 2.00000 + 3.46410i 0.277350 + 0.480384i
\(53\) −6.53835 + 11.3248i −0.898111 + 1.55557i −0.0682050 + 0.997671i \(0.521727\pi\)
−0.829906 + 0.557903i \(0.811606\pi\)
\(54\) 0 0
\(55\) −1.50000 2.59808i −0.202260 0.350325i
\(56\) −4.35890 −0.582482
\(57\) 0 0
\(58\) −9.35890 −1.22888
\(59\) 6.35890 + 11.0139i 0.827858 + 1.43389i 0.899715 + 0.436477i \(0.143774\pi\)
−0.0718571 + 0.997415i \(0.522893\pi\)
\(60\) 0 0
\(61\) −2.67945 + 4.64094i −0.343068 + 0.594212i −0.985001 0.172549i \(-0.944800\pi\)
0.641933 + 0.766761i \(0.278133\pi\)
\(62\) 5.35890 + 9.28189i 0.680581 + 1.17880i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −4.00000 −0.496139
\(66\) 0 0
\(67\) −5.67945 + 9.83710i −0.693855 + 1.20179i 0.276710 + 0.960953i \(0.410756\pi\)
−0.970565 + 0.240839i \(0.922577\pi\)
\(68\) −3.35890 −0.407326
\(69\) 0 0
\(70\) 2.17945 3.77492i 0.260494 0.451189i
\(71\) −5.03835 8.72668i −0.597942 1.03567i −0.993124 0.117063i \(-0.962652\pi\)
0.395183 0.918603i \(-0.370681\pi\)
\(72\) 0 0
\(73\) −2.32055 4.01931i −0.271600 0.470425i 0.697672 0.716418i \(-0.254219\pi\)
−0.969272 + 0.245993i \(0.920886\pi\)
\(74\) 3.50000 + 6.06218i 0.406867 + 0.704714i
\(75\) 0 0
\(76\) 4.35890 0.500000
\(77\) −13.0767 −1.49023
\(78\) 0 0
\(79\) 2.35890 + 4.08573i 0.265397 + 0.459681i 0.967668 0.252229i \(-0.0811637\pi\)
−0.702271 + 0.711910i \(0.747830\pi\)
\(80\) −0.500000 + 0.866025i −0.0559017 + 0.0968246i
\(81\) 0 0
\(82\) −3.17945 + 5.50697i −0.351111 + 0.608143i
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 0 0
\(85\) 1.67945 2.90889i 0.182162 0.315514i
\(86\) 5.00000 8.66025i 0.539164 0.933859i
\(87\) 0 0
\(88\) 3.00000 0.319801
\(89\) 0.179449 0.310816i 0.0190216 0.0329464i −0.856358 0.516383i \(-0.827278\pi\)
0.875380 + 0.483436i \(0.160612\pi\)
\(90\) 0 0
\(91\) −8.71780 + 15.0997i −0.913874 + 1.58288i
\(92\) −1.50000 2.59808i −0.156386 0.270868i
\(93\) 0 0
\(94\) 6.00000 0.618853
\(95\) −2.17945 + 3.77492i −0.223607 + 0.387298i
\(96\) 0 0
\(97\) 7.03835 + 12.1908i 0.714636 + 1.23779i 0.963100 + 0.269145i \(0.0867410\pi\)
−0.248464 + 0.968641i \(0.579926\pi\)
\(98\) −6.00000 10.3923i −0.606092 1.04978i
\(99\) 0 0
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) −6.35890 + 11.0139i −0.632734 + 1.09593i 0.354256 + 0.935148i \(0.384734\pi\)
−0.986990 + 0.160779i \(0.948599\pi\)
\(102\) 0 0
\(103\) −10.3589 −1.02069 −0.510346 0.859969i \(-0.670483\pi\)
−0.510346 + 0.859969i \(0.670483\pi\)
\(104\) 2.00000 3.46410i 0.196116 0.339683i
\(105\) 0 0
\(106\) 13.0767 1.27012
\(107\) −9.35890 −0.904759 −0.452379 0.891826i \(-0.649425\pi\)
−0.452379 + 0.891826i \(0.649425\pi\)
\(108\) 0 0
\(109\) −5.32055 9.21546i −0.509616 0.882681i −0.999938 0.0111398i \(-0.996454\pi\)
0.490322 0.871542i \(-0.336879\pi\)
\(110\) −1.50000 + 2.59808i −0.143019 + 0.247717i
\(111\) 0 0
\(112\) 2.17945 + 3.77492i 0.205939 + 0.356696i
\(113\) −3.35890 −0.315979 −0.157989 0.987441i \(-0.550501\pi\)
−0.157989 + 0.987441i \(0.550501\pi\)
\(114\) 0 0
\(115\) 3.00000 0.279751
\(116\) 4.67945 + 8.10504i 0.434476 + 0.752534i
\(117\) 0 0
\(118\) 6.35890 11.0139i 0.585384 1.01391i
\(119\) −7.32055 12.6796i −0.671074 1.16233i
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 5.35890 0.485172
\(123\) 0 0
\(124\) 5.35890 9.28189i 0.481243 0.833538i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 5.17945 8.97107i 0.459602 0.796054i −0.539338 0.842089i \(-0.681325\pi\)
0.998940 + 0.0460357i \(0.0146588\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) 2.00000 + 3.46410i 0.175412 + 0.303822i
\(131\) −1.50000 2.59808i −0.131056 0.226995i 0.793028 0.609185i \(-0.208503\pi\)
−0.924084 + 0.382190i \(0.875170\pi\)
\(132\) 0 0
\(133\) 9.50000 + 16.4545i 0.823754 + 1.42678i
\(134\) 11.3589 0.981259
\(135\) 0 0
\(136\) 1.67945 + 2.90889i 0.144012 + 0.249435i
\(137\) 6.00000 10.3923i 0.512615 0.887875i −0.487278 0.873247i \(-0.662010\pi\)
0.999893 0.0146279i \(-0.00465636\pi\)
\(138\) 0 0
\(139\) −0.641101 + 1.11042i −0.0543775 + 0.0941846i −0.891933 0.452168i \(-0.850651\pi\)
0.837555 + 0.546353i \(0.183984\pi\)
\(140\) −4.35890 −0.368394
\(141\) 0 0
\(142\) −5.03835 + 8.72668i −0.422809 + 0.732326i
\(143\) 6.00000 10.3923i 0.501745 0.869048i
\(144\) 0 0
\(145\) −9.35890 −0.777214
\(146\) −2.32055 + 4.01931i −0.192050 + 0.332641i
\(147\) 0 0
\(148\) 3.50000 6.06218i 0.287698 0.498308i
\(149\) −5.03835 8.72668i −0.412758 0.714917i 0.582433 0.812879i \(-0.302101\pi\)
−0.995190 + 0.0979619i \(0.968768\pi\)
\(150\) 0 0
\(151\) −2.07670 −0.168999 −0.0844996 0.996424i \(-0.526929\pi\)
−0.0844996 + 0.996424i \(0.526929\pi\)
\(152\) −2.17945 3.77492i −0.176777 0.306186i
\(153\) 0 0
\(154\) 6.53835 + 11.3248i 0.526875 + 0.912574i
\(155\) 5.35890 + 9.28189i 0.430437 + 0.745539i
\(156\) 0 0
\(157\) −2.50000 4.33013i −0.199522 0.345582i 0.748852 0.662738i \(-0.230606\pi\)
−0.948373 + 0.317156i \(0.897272\pi\)
\(158\) 2.35890 4.08573i 0.187664 0.325043i
\(159\) 0 0
\(160\) 1.00000 0.0790569
\(161\) 6.53835 11.3248i 0.515294 0.892515i
\(162\) 0 0
\(163\) −4.71780 −0.369526 −0.184763 0.982783i \(-0.559152\pi\)
−0.184763 + 0.982783i \(0.559152\pi\)
\(164\) 6.35890 0.496547
\(165\) 0 0
\(166\) −3.00000 5.19615i −0.232845 0.403300i
\(167\) −11.2178 + 19.4298i −0.868059 + 1.50352i −0.00408215 + 0.999992i \(0.501299\pi\)
−0.863977 + 0.503531i \(0.832034\pi\)
\(168\) 0 0
\(169\) −1.50000 2.59808i −0.115385 0.199852i
\(170\) −3.35890 −0.257616
\(171\) 0 0
\(172\) −10.0000 −0.762493
\(173\) 9.17945 + 15.8993i 0.697901 + 1.20880i 0.969193 + 0.246302i \(0.0792156\pi\)
−0.271292 + 0.962497i \(0.587451\pi\)
\(174\) 0 0
\(175\) 2.17945 3.77492i 0.164751 0.285357i
\(176\) −1.50000 2.59808i −0.113067 0.195837i
\(177\) 0 0
\(178\) −0.358899 −0.0269006
\(179\) −15.7178 −1.17480 −0.587402 0.809296i \(-0.699849\pi\)
−0.587402 + 0.809296i \(0.699849\pi\)
\(180\) 0 0
\(181\) −9.03835 + 15.6549i −0.671815 + 1.16362i 0.305574 + 0.952168i \(0.401152\pi\)
−0.977389 + 0.211450i \(0.932182\pi\)
\(182\) 17.4356 1.29241
\(183\) 0 0
\(184\) −1.50000 + 2.59808i −0.110581 + 0.191533i
\(185\) 3.50000 + 6.06218i 0.257325 + 0.445700i
\(186\) 0 0
\(187\) 5.03835 + 8.72668i 0.368441 + 0.638158i
\(188\) −3.00000 5.19615i −0.218797 0.378968i
\(189\) 0 0
\(190\) 4.35890 0.316228
\(191\) 19.4356 1.40631 0.703155 0.711036i \(-0.251774\pi\)
0.703155 + 0.711036i \(0.251774\pi\)
\(192\) 0 0
\(193\) −12.0383 20.8510i −0.866539 1.50089i −0.865511 0.500891i \(-0.833006\pi\)
−0.00102867 0.999999i \(-0.500327\pi\)
\(194\) 7.03835 12.1908i 0.505324 0.875247i
\(195\) 0 0
\(196\) −6.00000 + 10.3923i −0.428571 + 0.742307i
\(197\) 5.64110 0.401912 0.200956 0.979600i \(-0.435595\pi\)
0.200956 + 0.979600i \(0.435595\pi\)
\(198\) 0 0
\(199\) −8.32055 + 14.4116i −0.589828 + 1.02161i 0.404426 + 0.914571i \(0.367471\pi\)
−0.994255 + 0.107042i \(0.965862\pi\)
\(200\) −0.500000 + 0.866025i −0.0353553 + 0.0612372i
\(201\) 0 0
\(202\) 12.7178 0.894821
\(203\) −20.3972 + 35.3291i −1.43161 + 2.47961i
\(204\) 0 0
\(205\) −3.17945 + 5.50697i −0.222062 + 0.384623i
\(206\) 5.17945 + 8.97107i 0.360869 + 0.625044i
\(207\) 0 0
\(208\) −4.00000 −0.277350
\(209\) −6.53835 11.3248i −0.452267 0.783349i
\(210\) 0 0
\(211\) −7.53835 13.0568i −0.518961 0.898867i −0.999757 0.0220348i \(-0.992986\pi\)
0.480796 0.876833i \(-0.340348\pi\)
\(212\) −6.53835 11.3248i −0.449056 0.777787i
\(213\) 0 0
\(214\) 4.67945 + 8.10504i 0.319881 + 0.554049i
\(215\) 5.00000 8.66025i 0.340997 0.590624i
\(216\) 0 0
\(217\) 46.7178 3.17141
\(218\) −5.32055 + 9.21546i −0.360353 + 0.624150i
\(219\) 0 0
\(220\) 3.00000 0.202260
\(221\) 13.4356 0.903776
\(222\) 0 0
\(223\) −10.1794 17.6313i −0.681666 1.18068i −0.974472 0.224509i \(-0.927922\pi\)
0.292806 0.956172i \(-0.405411\pi\)
\(224\) 2.17945 3.77492i 0.145621 0.252222i
\(225\) 0 0
\(226\) 1.67945 + 2.90889i 0.111715 + 0.193497i
\(227\) 3.35890 0.222938 0.111469 0.993768i \(-0.464444\pi\)
0.111469 + 0.993768i \(0.464444\pi\)
\(228\) 0 0
\(229\) 8.71780 0.576088 0.288044 0.957617i \(-0.406995\pi\)
0.288044 + 0.957617i \(0.406995\pi\)
\(230\) −1.50000 2.59808i −0.0989071 0.171312i
\(231\) 0 0
\(232\) 4.67945 8.10504i 0.307221 0.532122i
\(233\) 3.00000 + 5.19615i 0.196537 + 0.340411i 0.947403 0.320043i \(-0.103697\pi\)
−0.750867 + 0.660454i \(0.770364\pi\)
\(234\) 0 0
\(235\) 6.00000 0.391397
\(236\) −12.7178 −0.827858
\(237\) 0 0
\(238\) −7.32055 + 12.6796i −0.474521 + 0.821894i
\(239\) 13.4356 0.869076 0.434538 0.900653i \(-0.356912\pi\)
0.434538 + 0.900653i \(0.356912\pi\)
\(240\) 0 0
\(241\) 2.00000 3.46410i 0.128831 0.223142i −0.794393 0.607404i \(-0.792211\pi\)
0.923224 + 0.384262i \(0.125544\pi\)
\(242\) 1.00000 + 1.73205i 0.0642824 + 0.111340i
\(243\) 0 0
\(244\) −2.67945 4.64094i −0.171534 0.297106i
\(245\) −6.00000 10.3923i −0.383326 0.663940i
\(246\) 0 0
\(247\) −17.4356 −1.10940
\(248\) −10.7178 −0.680581
\(249\) 0 0
\(250\) −0.500000 0.866025i −0.0316228 0.0547723i
\(251\) −6.00000 + 10.3923i −0.378717 + 0.655956i −0.990876 0.134778i \(-0.956968\pi\)
0.612159 + 0.790735i \(0.290301\pi\)
\(252\) 0 0
\(253\) −4.50000 + 7.79423i −0.282913 + 0.490019i
\(254\) −10.3589 −0.649975
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −3.71780 + 6.43941i −0.231910 + 0.401680i −0.958370 0.285529i \(-0.907831\pi\)
0.726460 + 0.687208i \(0.241164\pi\)
\(258\) 0 0
\(259\) 30.5123 1.89594
\(260\) 2.00000 3.46410i 0.124035 0.214834i
\(261\) 0 0
\(262\) −1.50000 + 2.59808i −0.0926703 + 0.160510i
\(263\) −4.14110 7.17260i −0.255351 0.442281i 0.709640 0.704565i \(-0.248858\pi\)
−0.964991 + 0.262284i \(0.915524\pi\)
\(264\) 0 0
\(265\) 13.0767 0.803295
\(266\) 9.50000 16.4545i 0.582482 1.00889i
\(267\) 0 0
\(268\) −5.67945 9.83710i −0.346928 0.600896i
\(269\) 1.67945 + 2.90889i 0.102398 + 0.177358i 0.912672 0.408693i \(-0.134015\pi\)
−0.810274 + 0.586051i \(0.800682\pi\)
\(270\) 0 0
\(271\) 2.35890 + 4.08573i 0.143293 + 0.248191i 0.928735 0.370745i \(-0.120898\pi\)
−0.785442 + 0.618935i \(0.787564\pi\)
\(272\) 1.67945 2.90889i 0.101832 0.176377i
\(273\) 0 0
\(274\) −12.0000 −0.724947
\(275\) −1.50000 + 2.59808i −0.0904534 + 0.156670i
\(276\) 0 0
\(277\) −4.00000 −0.240337 −0.120168 0.992754i \(-0.538343\pi\)
−0.120168 + 0.992754i \(0.538343\pi\)
\(278\) 1.28220 0.0769014
\(279\) 0 0
\(280\) 2.17945 + 3.77492i 0.130247 + 0.225594i
\(281\) 0.538348 0.932447i 0.0321152 0.0556251i −0.849521 0.527555i \(-0.823109\pi\)
0.881636 + 0.471930i \(0.156442\pi\)
\(282\) 0 0
\(283\) −4.35890 7.54983i −0.259110 0.448791i 0.706894 0.707319i \(-0.250096\pi\)
−0.966004 + 0.258528i \(0.916762\pi\)
\(284\) 10.0767 0.597942
\(285\) 0 0
\(286\) −12.0000 −0.709575
\(287\) 13.8589 + 24.0043i 0.818065 + 1.41693i
\(288\) 0 0
\(289\) 2.85890 4.95176i 0.168171 0.291280i
\(290\) 4.67945 + 8.10504i 0.274787 + 0.475945i
\(291\) 0 0
\(292\) 4.64110 0.271600
\(293\) −5.64110 −0.329557 −0.164778 0.986331i \(-0.552691\pi\)
−0.164778 + 0.986331i \(0.552691\pi\)
\(294\) 0 0
\(295\) 6.35890 11.0139i 0.370229 0.641256i
\(296\) −7.00000 −0.406867
\(297\) 0 0
\(298\) −5.03835 + 8.72668i −0.291864 + 0.505523i
\(299\) 6.00000 + 10.3923i 0.346989 + 0.601003i
\(300\) 0 0
\(301\) −21.7945 37.7492i −1.25621 2.17583i
\(302\) 1.03835 + 1.79847i 0.0597502 + 0.103490i
\(303\) 0 0
\(304\) −2.17945 + 3.77492i −0.125000 + 0.216506i
\(305\) 5.35890 0.306850
\(306\) 0 0
\(307\) 0.679449 + 1.17684i 0.0387782 + 0.0671659i 0.884763 0.466041i \(-0.154320\pi\)
−0.845985 + 0.533207i \(0.820987\pi\)
\(308\) 6.53835 11.3248i 0.372557 0.645288i
\(309\) 0 0
\(310\) 5.35890 9.28189i 0.304365 0.527176i
\(311\) −1.43560 −0.0814052 −0.0407026 0.999171i \(-0.512960\pi\)
−0.0407026 + 0.999171i \(0.512960\pi\)
\(312\) 0 0
\(313\) 8.71780 15.0997i 0.492759 0.853484i −0.507206 0.861825i \(-0.669322\pi\)
0.999965 + 0.00834102i \(0.00265506\pi\)
\(314\) −2.50000 + 4.33013i −0.141083 + 0.244363i
\(315\) 0 0
\(316\) −4.71780 −0.265397
\(317\) 9.53835 16.5209i 0.535727 0.927906i −0.463401 0.886149i \(-0.653371\pi\)
0.999128 0.0417576i \(-0.0132957\pi\)
\(318\) 0 0
\(319\) 14.0383 24.3151i 0.785997 1.36139i
\(320\) −0.500000 0.866025i −0.0279508 0.0484123i
\(321\) 0 0
\(322\) −13.0767 −0.728736
\(323\) 7.32055 12.6796i 0.407326 0.705510i
\(324\) 0 0
\(325\) 2.00000 + 3.46410i 0.110940 + 0.192154i
\(326\) 2.35890 + 4.08573i 0.130647 + 0.226288i
\(327\) 0 0
\(328\) −3.17945 5.50697i −0.175556 0.304071i
\(329\) 13.0767 22.6495i 0.720942 1.24871i
\(330\) 0 0
\(331\) 14.3589 0.789236 0.394618 0.918845i \(-0.370877\pi\)
0.394618 + 0.918845i \(0.370877\pi\)
\(332\) −3.00000 + 5.19615i −0.164646 + 0.285176i
\(333\) 0 0
\(334\) 22.4356 1.22762
\(335\) 11.3589 0.620603
\(336\) 0 0
\(337\) −11.0767 19.1854i −0.603386 1.04510i −0.992304 0.123823i \(-0.960484\pi\)
0.388918 0.921272i \(-0.372849\pi\)
\(338\) −1.50000 + 2.59808i −0.0815892 + 0.141317i
\(339\) 0 0
\(340\) 1.67945 + 2.90889i 0.0910809 + 0.157757i
\(341\) −32.1534 −1.74120
\(342\) 0 0
\(343\) −21.7945 −1.17679
\(344\) 5.00000 + 8.66025i 0.269582 + 0.466930i
\(345\) 0 0
\(346\) 9.17945 15.8993i 0.493490 0.854750i
\(347\) −3.71780 6.43941i −0.199582 0.345686i 0.748811 0.662784i \(-0.230625\pi\)
−0.948393 + 0.317098i \(0.897292\pi\)
\(348\) 0 0
\(349\) 0.0766968 0.00410549 0.00205274 0.999998i \(-0.499347\pi\)
0.00205274 + 0.999998i \(0.499347\pi\)
\(350\) −4.35890 −0.232993
\(351\) 0 0
\(352\) −1.50000 + 2.59808i −0.0799503 + 0.138478i
\(353\) 10.0767 0.536328 0.268164 0.963373i \(-0.413583\pi\)
0.268164 + 0.963373i \(0.413583\pi\)
\(354\) 0 0
\(355\) −5.03835 + 8.72668i −0.267408 + 0.463164i
\(356\) 0.179449 + 0.310816i 0.00951080 + 0.0164732i
\(357\) 0 0
\(358\) 7.85890 + 13.6120i 0.415356 + 0.719417i
\(359\) 7.67945 + 13.3012i 0.405306 + 0.702010i 0.994357 0.106085i \(-0.0338317\pi\)
−0.589051 + 0.808096i \(0.700498\pi\)
\(360\) 0 0
\(361\) −9.50000 + 16.4545i −0.500000 + 0.866025i
\(362\) 18.0767 0.950090
\(363\) 0 0
\(364\) −8.71780 15.0997i −0.456937 0.791438i
\(365\) −2.32055 + 4.01931i −0.121463 + 0.210380i
\(366\) 0 0
\(367\) −7.35890 + 12.7460i −0.384131 + 0.665335i −0.991648 0.128972i \(-0.958832\pi\)
0.607517 + 0.794307i \(0.292166\pi\)
\(368\) 3.00000 0.156386
\(369\) 0 0
\(370\) 3.50000 6.06218i 0.181956 0.315158i
\(371\) 28.5000 49.3634i 1.47965 2.56282i
\(372\) 0 0
\(373\) 11.0000 0.569558 0.284779 0.958593i \(-0.408080\pi\)
0.284779 + 0.958593i \(0.408080\pi\)
\(374\) 5.03835 8.72668i 0.260527 0.451246i
\(375\) 0 0
\(376\) −3.00000 + 5.19615i −0.154713 + 0.267971i
\(377\) −18.7178 32.4202i −0.964016 1.66972i
\(378\) 0 0
\(379\) 14.7178 0.756002 0.378001 0.925805i \(-0.376611\pi\)
0.378001 + 0.925805i \(0.376611\pi\)
\(380\) −2.17945 3.77492i −0.111803 0.193649i
\(381\) 0 0
\(382\) −9.71780 16.8317i −0.497206 0.861186i
\(383\) 3.00000 + 5.19615i 0.153293 + 0.265511i 0.932436 0.361335i \(-0.117679\pi\)
−0.779143 + 0.626846i \(0.784346\pi\)
\(384\) 0 0
\(385\) 6.53835 + 11.3248i 0.333225 + 0.577163i
\(386\) −12.0383 + 20.8510i −0.612736 + 1.06129i
\(387\) 0 0
\(388\) −14.0767 −0.714636
\(389\) 2.03835 3.53052i 0.103348 0.179005i −0.809714 0.586825i \(-0.800378\pi\)
0.913062 + 0.407820i \(0.133711\pi\)
\(390\) 0 0
\(391\) −10.0767 −0.509600
\(392\) 12.0000 0.606092
\(393\) 0 0
\(394\) −2.82055 4.88534i −0.142097 0.246120i
\(395\) 2.35890 4.08573i 0.118689 0.205576i
\(396\) 0 0
\(397\) −3.21780 5.57339i −0.161497 0.279720i 0.773909 0.633297i \(-0.218299\pi\)
−0.935406 + 0.353576i \(0.884965\pi\)
\(398\) 16.6411 0.834143
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) −9.00000 15.5885i −0.449439 0.778450i 0.548911 0.835881i \(-0.315043\pi\)
−0.998350 + 0.0574304i \(0.981709\pi\)
\(402\) 0 0
\(403\) −21.4356 + 37.1275i −1.06778 + 1.84945i
\(404\) −6.35890 11.0139i −0.316367 0.547964i
\(405\) 0 0
\(406\) 40.7945 2.02460
\(407\) −21.0000 −1.04093
\(408\) 0 0
\(409\) −5.50000 + 9.52628i −0.271957 + 0.471044i −0.969363 0.245633i \(-0.921004\pi\)
0.697406 + 0.716677i \(0.254338\pi\)
\(410\) 6.35890 0.314044
\(411\) 0 0
\(412\) 5.17945 8.97107i 0.255173 0.441973i
\(413\) −27.7178 48.0086i −1.36390 2.36235i
\(414\) 0 0
\(415\) −3.00000 5.19615i −0.147264 0.255069i
\(416\) 2.00000 + 3.46410i 0.0980581 + 0.169842i
\(417\) 0 0
\(418\) −6.53835 + 11.3248i −0.319801 + 0.553912i
\(419\) −15.7178 −0.767865 −0.383932 0.923361i \(-0.625430\pi\)
−0.383932 + 0.923361i \(0.625430\pi\)
\(420\) 0 0
\(421\) −18.0383 31.2433i −0.879135 1.52271i −0.852291 0.523067i \(-0.824788\pi\)
−0.0268440 0.999640i \(-0.508546\pi\)
\(422\) −7.53835 + 13.0568i −0.366961 + 0.635595i
\(423\) 0 0
\(424\) −6.53835 + 11.3248i −0.317530 + 0.549979i
\(425\) −3.35890 −0.162931
\(426\) 0 0
\(427\) 11.6794 20.2294i 0.565208 0.978969i
\(428\) 4.67945 8.10504i 0.226190 0.391772i
\(429\) 0 0
\(430\) −10.0000 −0.482243
\(431\) 5.39725 9.34831i 0.259976 0.450292i −0.706259 0.707954i \(-0.749619\pi\)
0.966235 + 0.257661i \(0.0829519\pi\)
\(432\) 0 0
\(433\) −18.3972 + 31.8650i −0.884115 + 1.53133i −0.0373910 + 0.999301i \(0.511905\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(434\) −23.3589 40.4588i −1.12126 1.94208i
\(435\) 0 0
\(436\) 10.6411 0.509616
\(437\) 13.0767 0.625543
\(438\) 0 0
\(439\) −11.6794 20.2294i −0.557430 0.965497i −0.997710 0.0676362i \(-0.978454\pi\)
0.440280 0.897860i \(-0.354879\pi\)
\(440\) −1.50000 2.59808i −0.0715097 0.123858i
\(441\) 0 0
\(442\) −6.71780 11.6356i −0.319533 0.553447i
\(443\) −1.32055 + 2.28726i −0.0627412 + 0.108671i −0.895690 0.444679i \(-0.853318\pi\)
0.832949 + 0.553350i \(0.186651\pi\)
\(444\) 0 0
\(445\) −0.358899 −0.0170134
\(446\) −10.1794 + 17.6313i −0.482011 + 0.834867i
\(447\) 0 0
\(448\) −4.35890 −0.205939
\(449\) −0.358899 −0.0169375 −0.00846874 0.999964i \(-0.502696\pi\)
−0.00846874 + 0.999964i \(0.502696\pi\)
\(450\) 0 0
\(451\) −9.53835 16.5209i −0.449143 0.777939i
\(452\) 1.67945 2.90889i 0.0789947 0.136823i
\(453\) 0 0
\(454\) −1.67945 2.90889i −0.0788205 0.136521i
\(455\) 17.4356 0.817393
\(456\) 0 0
\(457\) −30.6411 −1.43333 −0.716665 0.697417i \(-0.754332\pi\)
−0.716665 + 0.697417i \(0.754332\pi\)
\(458\) −4.35890 7.54983i −0.203678 0.352781i
\(459\) 0 0
\(460\) −1.50000 + 2.59808i −0.0699379 + 0.121136i
\(461\) 9.00000 + 15.5885i 0.419172 + 0.726027i 0.995856 0.0909401i \(-0.0289872\pi\)
−0.576685 + 0.816967i \(0.695654\pi\)
\(462\) 0 0
\(463\) −17.7945 −0.826980 −0.413490 0.910509i \(-0.635690\pi\)
−0.413490 + 0.910509i \(0.635690\pi\)
\(464\) −9.35890 −0.434476
\(465\) 0 0
\(466\) 3.00000 5.19615i 0.138972 0.240707i
\(467\) −28.7945 −1.33245 −0.666225 0.745751i \(-0.732091\pi\)
−0.666225 + 0.745751i \(0.732091\pi\)
\(468\) 0 0
\(469\) 24.7561 42.8789i 1.14313 1.97996i
\(470\) −3.00000 5.19615i −0.138380 0.239681i
\(471\) 0 0
\(472\) 6.35890 + 11.0139i 0.292692 + 0.506957i
\(473\) 15.0000 + 25.9808i 0.689701 + 1.19460i
\(474\) 0 0
\(475\) 4.35890 0.200000
\(476\) 14.6411 0.671074
\(477\) 0 0
\(478\) −6.71780 11.6356i −0.307265 0.532198i
\(479\) −11.0383 + 19.1190i −0.504355 + 0.873569i 0.495632 + 0.868532i \(0.334936\pi\)
−0.999987 + 0.00503606i \(0.998397\pi\)
\(480\) 0 0
\(481\) −14.0000 + 24.2487i −0.638345 + 1.10565i
\(482\) −4.00000 −0.182195
\(483\) 0 0
\(484\) 1.00000 1.73205i 0.0454545 0.0787296i
\(485\) 7.03835 12.1908i 0.319595 0.553555i
\(486\) 0 0
\(487\) −9.64110 −0.436880 −0.218440 0.975850i \(-0.570097\pi\)
−0.218440 + 0.975850i \(0.570097\pi\)
\(488\) −2.67945 + 4.64094i −0.121293 + 0.210086i
\(489\) 0 0
\(490\) −6.00000 + 10.3923i −0.271052 + 0.469476i
\(491\) 7.50000 + 12.9904i 0.338470 + 0.586248i 0.984145 0.177365i \(-0.0567572\pi\)
−0.645675 + 0.763612i \(0.723424\pi\)
\(492\) 0 0
\(493\) 31.4356 1.41579
\(494\) 8.71780 + 15.0997i 0.392232 + 0.679366i
\(495\) 0 0
\(496\) 5.35890 + 9.28189i 0.240622 + 0.416769i
\(497\) 21.9617 + 38.0387i 0.985115 + 1.70627i
\(498\) 0 0
\(499\) 7.82055 + 13.5456i 0.350096 + 0.606384i 0.986266 0.165165i \(-0.0528157\pi\)
−0.636170 + 0.771549i \(0.719482\pi\)
\(500\) −0.500000 + 0.866025i −0.0223607 + 0.0387298i
\(501\) 0 0
\(502\) 12.0000 0.535586
\(503\) 14.9356 25.8692i 0.665945 1.15345i −0.313083 0.949726i \(-0.601362\pi\)
0.979028 0.203725i \(-0.0653049\pi\)
\(504\) 0 0
\(505\) 12.7178 0.565935
\(506\) 9.00000 0.400099
\(507\) 0 0
\(508\) 5.17945 + 8.97107i 0.229801 + 0.398027i
\(509\) 12.3589 21.4062i 0.547799 0.948815i −0.450626 0.892713i \(-0.648799\pi\)
0.998425 0.0561023i \(-0.0178673\pi\)
\(510\) 0 0
\(511\) 10.1150 + 17.5198i 0.447463 + 0.775029i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 7.43560 0.327970
\(515\) 5.17945 + 8.97107i 0.228234 + 0.395313i
\(516\) 0 0
\(517\) −9.00000 + 15.5885i −0.395820 + 0.685580i
\(518\) −15.2561 26.4244i −0.670317 1.16102i
\(519\) 0 0
\(520\) −4.00000 −0.175412
\(521\) −23.2822 −1.02001 −0.510006 0.860171i \(-0.670357\pi\)
−0.510006 + 0.860171i \(0.670357\pi\)
\(522\) 0 0
\(523\) 19.3972 33.5970i 0.848182 1.46910i −0.0346461 0.999400i \(-0.511030\pi\)
0.882829 0.469695i \(-0.155636\pi\)
\(524\) 3.00000 0.131056
\(525\) 0 0
\(526\) −4.14110 + 7.17260i −0.180561 + 0.312740i
\(527\) −18.0000 31.1769i −0.784092 1.35809i
\(528\) 0 0
\(529\) 7.00000 + 12.1244i 0.304348 + 0.527146i
\(530\) −6.53835 11.3248i −0.284008 0.491916i
\(531\) 0 0
\(532\) −19.0000 −0.823754
\(533\) −25.4356 −1.10174
\(534\) 0 0
\(535\) 4.67945 + 8.10504i 0.202310 + 0.350412i
\(536\) −5.67945 + 9.83710i −0.245315 + 0.424898i
\(537\) 0 0
\(538\) 1.67945 2.90889i 0.0724062 0.125411i
\(539\) 36.0000 1.55063
\(540\) 0 0
\(541\) 4.64110 8.03862i 0.199537 0.345607i −0.748842 0.662749i \(-0.769390\pi\)
0.948378 + 0.317142i \(0.102723\pi\)
\(542\) 2.35890 4.08573i 0.101323 0.175497i
\(543\) 0 0
\(544\) −3.35890 −0.144012
\(545\) −5.32055 + 9.21546i −0.227907 + 0.394747i
\(546\) 0 0
\(547\) 3.07670 5.32900i 0.131550 0.227851i −0.792724 0.609580i \(-0.791338\pi\)
0.924274 + 0.381729i \(0.124671\pi\)
\(548\) 6.00000 + 10.3923i 0.256307 + 0.443937i
\(549\) 0 0
\(550\) 3.00000 0.127920
\(551\) −40.7945 −1.73790
\(552\) 0 0
\(553\) −10.2822 17.8093i −0.437244 0.757328i
\(554\) 2.00000 + 3.46410i 0.0849719 + 0.147176i
\(555\) 0 0
\(556\) −0.641101 1.11042i −0.0271887 0.0470923i
\(557\) −5.46165 + 9.45986i −0.231418 + 0.400827i −0.958226 0.286014i \(-0.907670\pi\)
0.726808 + 0.686841i \(0.241003\pi\)
\(558\) 0 0
\(559\) 40.0000 1.69182
\(560\) 2.17945 3.77492i 0.0920985 0.159519i
\(561\) 0 0
\(562\) −1.07670 −0.0454177
\(563\) −12.0000 −0.505740 −0.252870 0.967500i \(-0.581374\pi\)
−0.252870 + 0.967500i \(0.581374\pi\)
\(564\) 0 0
\(565\) 1.67945 + 2.90889i 0.0706550 + 0.122378i
\(566\) −4.35890 + 7.54983i −0.183218 + 0.317343i
\(567\) 0 0
\(568\) −5.03835 8.72668i −0.211404 0.366163i
\(569\) 37.7945 1.58443 0.792214 0.610244i \(-0.208928\pi\)
0.792214 + 0.610244i \(0.208928\pi\)
\(570\) 0 0
\(571\) 34.1534 1.42928 0.714638 0.699495i \(-0.246592\pi\)
0.714638 + 0.699495i \(0.246592\pi\)
\(572\) 6.00000 + 10.3923i 0.250873 + 0.434524i
\(573\) 0 0
\(574\) 13.8589 24.0043i 0.578459 1.00192i
\(575\) −1.50000 2.59808i −0.0625543 0.108347i
\(576\) 0 0
\(577\) 18.7945 0.782425 0.391213 0.920300i \(-0.372056\pi\)
0.391213 + 0.920300i \(0.372056\pi\)
\(578\) −5.71780 −0.237829
\(579\) 0 0
\(580\) 4.67945 8.10504i 0.194304 0.336544i
\(581\) −26.1534 −1.08503
\(582\) 0 0
\(583\) −19.6150 + 33.9743i −0.812372 + 1.40707i
\(584\) −2.32055 4.01931i −0.0960251 0.166320i
\(585\) 0 0
\(586\) 2.82055 + 4.88534i 0.116516 + 0.201811i
\(587\) −21.3589 36.9947i −0.881576 1.52693i −0.849588 0.527446i \(-0.823150\pi\)
−0.0319878 0.999488i \(-0.510184\pi\)
\(588\) 0 0
\(589\) 23.3589 + 40.4588i 0.962487 + 1.66708i
\(590\) −12.7178 −0.523583
\(591\) 0 0
\(592\) 3.50000 + 6.06218i 0.143849 + 0.249154i
\(593\) 3.96165 6.86178i 0.162686 0.281780i −0.773145 0.634229i \(-0.781318\pi\)
0.935831 + 0.352449i \(0.114651\pi\)
\(594\) 0 0
\(595\) −7.32055 + 12.6796i −0.300113 + 0.519812i
\(596\) 10.0767 0.412758
\(597\) 0 0
\(598\) 6.00000 10.3923i 0.245358 0.424973i
\(599\) 13.3206 23.0719i 0.544263 0.942691i −0.454390 0.890803i \(-0.650143\pi\)
0.998653 0.0518882i \(-0.0165239\pi\)
\(600\) 0 0
\(601\) 5.71780 0.233234 0.116617 0.993177i \(-0.462795\pi\)
0.116617 + 0.993177i \(0.462795\pi\)
\(602\) −21.7945 + 37.7492i −0.888277 + 1.53854i
\(603\) 0 0
\(604\) 1.03835 1.79847i 0.0422498 0.0731788i
\(605\) 1.00000 + 1.73205i 0.0406558 + 0.0704179i
\(606\) 0 0
\(607\) −35.7945 −1.45285 −0.726427 0.687244i \(-0.758820\pi\)
−0.726427 + 0.687244i \(0.758820\pi\)
\(608\) 4.35890 0.176777
\(609\) 0 0
\(610\) −2.67945 4.64094i −0.108488 0.187906i
\(611\) 12.0000 + 20.7846i 0.485468 + 0.840855i
\(612\) 0 0
\(613\) −3.21780 5.57339i −0.129966 0.225107i 0.793697 0.608313i \(-0.208153\pi\)
−0.923663 + 0.383206i \(0.874820\pi\)
\(614\) 0.679449 1.17684i 0.0274203 0.0474934i
\(615\) 0 0
\(616\) −13.0767 −0.526875
\(617\) −0.717798 + 1.24326i −0.0288975 + 0.0500519i −0.880112 0.474765i \(-0.842533\pi\)
0.851215 + 0.524817i \(0.175866\pi\)
\(618\) 0 0
\(619\) −3.64110 −0.146348 −0.0731741 0.997319i \(-0.523313\pi\)
−0.0731741 + 0.997319i \(0.523313\pi\)
\(620\) −10.7178 −0.430437
\(621\) 0 0
\(622\) 0.717798 + 1.24326i 0.0287811 + 0.0498503i
\(623\) −0.782202 + 1.35481i −0.0313383 + 0.0542795i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −17.4356 −0.696867
\(627\) 0 0
\(628\) 5.00000 0.199522
\(629\) −11.7561 20.3622i −0.468748 0.811896i
\(630\) 0 0
\(631\) −20.6794 + 35.8179i −0.823236 + 1.42589i 0.0800242 + 0.996793i \(0.474500\pi\)
−0.903260 + 0.429093i \(0.858833\pi\)
\(632\) 2.35890 + 4.08573i 0.0938320 + 0.162522i
\(633\) 0 0
\(634\) −19.0767 −0.757632
\(635\) −10.3589 −0.411080
\(636\) 0 0
\(637\) 24.0000 41.5692i 0.950915 1.64703i
\(638\) −28.0767 −1.11157
\(639\) 0 0
\(640\) −0.500000 + 0.866025i −0.0197642 + 0.0342327i
\(641\) −5.64110 9.77067i −0.222810 0.385918i 0.732850 0.680390i \(-0.238190\pi\)
−0.955660 + 0.294472i \(0.904856\pi\)
\(642\) 0 0
\(643\) 19.7561 + 34.2186i 0.779106 + 1.34945i 0.932457 + 0.361280i \(0.117660\pi\)
−0.153351 + 0.988172i \(0.549007\pi\)
\(644\) 6.53835 + 11.3248i 0.257647 + 0.446258i
\(645\) 0 0
\(646\) −14.6411 −0.576046
\(647\) 17.1534 0.674369 0.337185 0.941438i \(-0.390525\pi\)
0.337185 + 0.941438i \(0.390525\pi\)
\(648\) 0 0
\(649\) 19.0767 + 33.0418i 0.748826 + 1.29700i
\(650\) 2.00000 3.46410i 0.0784465 0.135873i
\(651\) 0 0
\(652\) 2.35890 4.08573i 0.0923816 0.160010i
\(653\) 25.0767 0.981327 0.490663 0.871349i \(-0.336754\pi\)
0.490663 + 0.871349i \(0.336754\pi\)
\(654\) 0 0
\(655\) −1.50000 + 2.59808i −0.0586098 + 0.101515i
\(656\) −3.17945 + 5.50697i −0.124137 + 0.215011i
\(657\) 0 0
\(658\) −26.1534 −1.01957
\(659\) −19.8589 + 34.3966i −0.773593 + 1.33990i 0.161989 + 0.986793i \(0.448209\pi\)
−0.935582 + 0.353110i \(0.885124\pi\)
\(660\) 0 0
\(661\) 8.71780 15.0997i 0.339083 0.587309i −0.645177 0.764033i \(-0.723217\pi\)
0.984261 + 0.176724i \(0.0565499\pi\)
\(662\) −7.17945 12.4352i −0.279037 0.483307i
\(663\) 0 0
\(664\) 6.00000 0.232845
\(665\) 9.50000 16.4545i 0.368394 0.638077i
\(666\) 0 0
\(667\) 14.0383 + 24.3151i 0.543567 + 0.941486i
\(668\) −11.2178 19.4298i −0.434030 0.751761i
\(669\) 0 0
\(670\) −5.67945 9.83710i −0.219416 0.380040i
\(671\) −8.03835 + 13.9228i −0.310317 + 0.537485i
\(672\) 0 0
\(673\) −21.2822 −0.820369 −0.410184 0.912003i \(-0.634536\pi\)
−0.410184 + 0.912003i \(0.634536\pi\)
\(674\) −11.0767 + 19.1854i −0.426658 + 0.738994i
\(675\) 0 0
\(676\) 3.00000 0.115385
\(677\) −7.07670 −0.271980 −0.135990 0.990710i \(-0.543421\pi\)
−0.135990 + 0.990710i \(0.543421\pi\)
\(678\) 0 0
\(679\) −30.6794 53.1384i −1.17737 2.03926i
\(680\) 1.67945 2.90889i 0.0644039 0.111551i
\(681\) 0 0
\(682\) 16.0767 + 27.8457i 0.615609 + 1.06627i
\(683\) 22.7945 0.872207 0.436104 0.899896i \(-0.356358\pi\)
0.436104 + 0.899896i \(0.356358\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) 10.8972 + 18.8746i 0.416059 + 0.720635i
\(687\) 0 0
\(688\) 5.00000 8.66025i 0.190623 0.330169i
\(689\) 26.1534 + 45.2990i 0.996365 + 1.72575i
\(690\) 0 0
\(691\) 31.6411 1.20368 0.601842 0.798615i \(-0.294434\pi\)
0.601842 + 0.798615i \(0.294434\pi\)
\(692\) −18.3589 −0.697901
\(693\) 0 0
\(694\) −3.71780 + 6.43941i −0.141126 + 0.244437i
\(695\) 1.28220 0.0486367
\(696\) 0 0
\(697\) 10.6794 18.4973i 0.404513 0.700637i
\(698\) −0.0383484 0.0664214i −0.00145151 0.00251409i
\(699\) 0 0
\(700\) 2.17945 + 3.77492i 0.0823754 + 0.142678i
\(701\) 9.00000 + 15.5885i 0.339925 + 0.588768i 0.984418 0.175842i \(-0.0562649\pi\)
−0.644493 + 0.764610i \(0.722932\pi\)
\(702\) 0 0
\(703\) 15.2561 + 26.4244i 0.575396 + 0.996616i
\(704\) 3.00000 0.113067
\(705\) 0 0
\(706\) −5.03835 8.72668i −0.189621 0.328433i
\(707\) 27.7178 48.0086i 1.04244 1.80555i
\(708\) 0 0
\(709\) 13.3972 23.2047i 0.503144 0.871471i −0.496849 0.867837i \(-0.665510\pi\)
0.999993 0.00363441i \(-0.00115687\pi\)
\(710\) 10.0767 0.378172
\(711\) 0 0
\(712\) 0.179449 0.310816i 0.00672515 0.0116483i
\(713\) 16.0767 27.8457i 0.602077 1.04283i
\(714\) 0 0
\(715\) −12.0000 −0.448775
\(716\) 7.85890 13.6120i 0.293701 0.508705i
\(717\) 0 0
\(718\) 7.67945 13.3012i 0.286595 0.496396i
\(719\) −8.64110 14.9668i −0.322259 0.558168i 0.658695 0.752410i \(-0.271109\pi\)
−0.980954 + 0.194242i \(0.937775\pi\)
\(720\) 0 0
\(721\) 45.1534 1.68160
\(722\) 19.0000 0.707107
\(723\) 0 0
\(724\) −9.03835 15.6549i −0.335908 0.581809i
\(725\) 4.67945 + 8.10504i 0.173790 + 0.301014i
\(726\) 0 0
\(727\) 15.0767 + 26.1136i 0.559164 + 0.968500i 0.997567 + 0.0697214i \(0.0222110\pi\)
−0.438403 + 0.898779i \(0.644456\pi\)
\(728\) −8.71780 + 15.0997i −0.323103 + 0.559631i
\(729\) 0 0
\(730\) 4.64110 0.171775
\(731\) −16.7945 + 29.0889i −0.621167 + 1.07589i
\(732\) 0 0
\(733\) 9.56440 0.353269 0.176635 0.984276i \(-0.443479\pi\)
0.176635 + 0.984276i \(0.443479\pi\)
\(734\) 14.7178 0.543244
\(735\) 0 0
\(736\) −1.50000 2.59808i −0.0552907 0.0957664i
\(737\) −17.0383 + 29.5113i −0.627616 + 1.08706i
\(738\) 0 0
\(739\) 8.17945 + 14.1672i 0.300886 + 0.521150i 0.976337 0.216255i \(-0.0693843\pi\)
−0.675451 + 0.737405i \(0.736051\pi\)
\(740\) −7.00000 −0.257325
\(741\) 0 0
\(742\) −57.0000 −2.09254
\(743\) 4.50000 + 7.79423i 0.165089 + 0.285943i 0.936687 0.350168i \(-0.113876\pi\)
−0.771598 + 0.636111i \(0.780542\pi\)
\(744\) 0 0
\(745\) −5.03835 + 8.72668i −0.184591 + 0.319721i
\(746\) −5.50000 9.52628i −0.201369 0.348782i
\(747\) 0 0
\(748\) −10.0767 −0.368441
\(749\) 40.7945 1.49060
\(750\) 0 0
\(751\) −11.4356 + 19.8070i −0.417291 + 0.722769i −0.995666 0.0930021i \(-0.970354\pi\)
0.578375 + 0.815771i \(0.303687\pi\)
\(752\) 6.00000 0.218797
\(753\) 0 0
\(754\) −18.7178 + 32.4202i −0.681662 + 1.18067i
\(755\) 1.03835 + 1.79847i 0.0377894 + 0.0654531i
\(756\) 0 0
\(757\) −24.9356 43.1897i −0.906300 1.56976i −0.819163 0.573561i \(-0.805562\pi\)
−0.0871365 0.996196i \(-0.527772\pi\)
\(758\) −7.35890 12.7460i −0.267287 0.462955i
\(759\) 0 0
\(760\) −2.17945 + 3.77492i −0.0790569 + 0.136931i
\(761\) 7.07670 0.256530 0.128265 0.991740i \(-0.459059\pi\)
0.128265 + 0.991740i \(0.459059\pi\)
\(762\) 0 0
\(763\) 23.1917 + 40.1693i 0.839597 + 1.45423i
\(764\) −9.71780 + 16.8317i −0.351578 + 0.608950i
\(765\) 0 0
\(766\) 3.00000 5.19615i 0.108394 0.187745i
\(767\) 50.8712 1.83685
\(768\) 0 0
\(769\) −1.35890 + 2.35368i −0.0490031 + 0.0848759i −0.889487 0.456961i \(-0.848938\pi\)
0.840483 + 0.541837i \(0.182271\pi\)
\(770\) 6.53835 11.3248i 0.235626 0.408116i
\(771\) 0 0
\(772\) 24.0767 0.866539
\(773\) −0.897247 + 1.55408i −0.0322717 + 0.0558963i −0.881710 0.471791i \(-0.843608\pi\)
0.849438 + 0.527688i \(0.176941\pi\)
\(774\) 0 0
\(775\) 5.35890 9.28189i 0.192497 0.333415i
\(776\) 7.03835 + 12.1908i 0.252662 + 0.437623i
\(777\) 0 0
\(778\) −4.07670 −0.146157
\(779\) −13.8589 + 24.0043i −0.496547 + 0.860044i
\(780\) 0 0
\(781\) −15.1150 26.1800i −0.540859 0.936795i
\(782\) 5.03835 + 8.72668i 0.180171 + 0.312065i
\(783\) 0 0
\(784\) −6.00000 10.3923i −0.214286 0.371154i
\(785\) −2.50000 + 4.33013i −0.0892288 + 0.154549i
\(786\) 0 0
\(787\) −20.0767 −0.715657 −0.357828 0.933787i \(-0.616483\pi\)
−0.357828 + 0.933787i \(0.616483\pi\)
\(788\) −2.82055 + 4.88534i −0.100478 + 0.174033i
\(789\) 0 0
\(790\) −4.71780 −0.167852
\(791\) 14.6411 0.520578
\(792\) 0 0
\(793\) 10.7178 + 18.5638i 0.380600 + 0.659219i
\(794\) −3.21780 + 5.57339i −0.114195 + 0.197792i
\(795\) 0 0
\(796\) −8.32055 14.4116i −0.294914 0.510806i
\(797\) −1.07670 −0.0381386 −0.0190693 0.999818i \(-0.506070\pi\)
−0.0190693 + 0.999818i \(0.506070\pi\)
\(798\) 0 0
\(799\) −20.1534 −0.712976
\(800\) −0.500000 0.866025i −0.0176777 0.0306186i
\(801\) 0 0
\(802\) −9.00000 + 15.5885i −0.317801 + 0.550448i
\(803\) −6.96165 12.0579i −0.245671 0.425515i
\(804\) 0 0
\(805\) −13.0767 −0.460893
\(806\) 42.8712 1.51007
\(807\) 0 0
\(808\) −6.35890 + 11.0139i −0.223705 + 0.387469i
\(809\) 1.43560 0.0504729 0.0252364 0.999682i \(-0.491966\pi\)
0.0252364 + 0.999682i \(0.491966\pi\)
\(810\) 0 0
\(811\) 14.5383 25.1812i 0.510510 0.884230i −0.489415 0.872051i \(-0.662790\pi\)
0.999926 0.0121793i \(-0.00387687\pi\)
\(812\) −20.3972 35.3291i −0.715803 1.23981i
\(813\) 0 0
\(814\) 10.5000 + 18.1865i 0.368025 + 0.637438i
\(815\) 2.35890 + 4.08573i 0.0826286 + 0.143117i
\(816\) 0 0
\(817\) 21.7945 37.7492i 0.762493 1.32068i
\(818\) 11.0000 0.384606
\(819\) 0 0
\(820\) −3.17945 5.50697i −0.111031 0.192312i
\(821\) −9.71780 + 16.8317i −0.339153 + 0.587431i −0.984274 0.176650i \(-0.943474\pi\)
0.645120 + 0.764081i \(0.276807\pi\)
\(822\) 0 0
\(823\) −19.1794 + 33.2198i −0.668554 + 1.15797i 0.309755 + 0.950816i \(0.399753\pi\)
−0.978309 + 0.207152i \(0.933580\pi\)
\(824\) −10.3589 −0.360869
\(825\) 0 0
\(826\) −27.7178 + 48.0086i −0.964426 + 1.67043i
\(827\) −19.6794 + 34.0858i −0.684322 + 1.18528i 0.289328 + 0.957230i \(0.406568\pi\)
−0.973650 + 0.228050i \(0.926765\pi\)
\(828\) 0 0
\(829\) −0.153394 −0.00532758 −0.00266379 0.999996i \(-0.500848\pi\)
−0.00266379 + 0.999996i \(0.500848\pi\)
\(830\) −3.00000 + 5.19615i −0.104132 + 0.180361i
\(831\) 0 0
\(832\) 2.00000 3.46410i 0.0693375 0.120096i
\(833\) 20.1534 + 34.9067i 0.698274 + 1.20945i
\(834\) 0 0
\(835\) 22.4356 0.776416
\(836\) 13.0767 0.452267
\(837\) 0 0
\(838\) 7.85890 + 13.6120i 0.271481 + 0.470219i
\(839\) −0.358899 0.621631i −0.0123906 0.0214611i 0.859764 0.510692i \(-0.170611\pi\)
−0.872154 + 0.489231i \(0.837277\pi\)
\(840\) 0 0
\(841\) −29.2945 50.7396i −1.01015 1.74964i
\(842\) −18.0383 + 31.2433i −0.621643 + 1.07672i
\(843\) 0 0
\(844\) 15.0767 0.518961
\(845\) −1.50000 + 2.59808i −0.0516016 + 0.0893765i
\(846\) 0 0
\(847\) 8.71780 0.299547
\(848\) 13.0767 0.449056
\(849\) 0 0
\(850\) 1.67945 + 2.90889i 0.0576046 + 0.0997742i
\(851\) 10.5000 18.1865i 0.359935 0.623426i
\(852\) 0 0
\(853\) −7.71780 13.3676i −0.264252 0.457699i 0.703115 0.711076i \(-0.251792\pi\)
−0.967367 + 0.253378i \(0.918459\pi\)
\(854\) −23.3589 −0.799325
\(855\) 0 0
\(856\) −9.35890 −0.319881
\(857\) −12.7178 22.0279i −0.434432 0.752458i 0.562817 0.826581i \(-0.309717\pi\)
−0.997249 + 0.0741235i \(0.976384\pi\)
\(858\) 0 0
\(859\) 1.46165 2.53165i 0.0498709 0.0863789i −0.840012 0.542567i \(-0.817452\pi\)
0.889883 + 0.456188i \(0.150786\pi\)
\(860\) 5.00000 + 8.66025i 0.170499 + 0.295312i
\(861\) 0 0
\(862\) −10.7945 −0.367662
\(863\) 21.0000 0.714848 0.357424 0.933942i \(-0.383655\pi\)
0.357424 + 0.933942i \(0.383655\pi\)
\(864\) 0 0
\(865\) 9.17945 15.8993i 0.312111 0.540591i
\(866\) 36.7945 1.25033
\(867\) 0 0
\(868\) −23.3589 + 40.4588i −0.792853 + 1.37326i
\(869\) 7.07670 + 12.2572i 0.240060 + 0.415797i
\(870\) 0 0
\(871\) 22.7178 + 39.3484i 0.769763 + 1.33327i
\(872\) −5.32055 9.21546i −0.180177 0.312075i
\(873\) 0 0
\(874\) −6.53835 11.3248i −0.221163 0.383065i
\(875\) −4.35890 −0.147358
\(876\) 0 0
\(877\) 6.50000 + 11.2583i 0.219489 + 0.380167i 0.954652 0.297724i \(-0.0962275\pi\)
−0.735163 + 0.677891i \(0.762894\pi\)
\(878\) −11.6794 + 20.2294i −0.394162 + 0.682709i
\(879\) 0 0
\(880\) −1.50000 + 2.59808i −0.0505650 + 0.0875811i
\(881\) 19.0767 0.642710 0.321355 0.946959i \(-0.395862\pi\)
0.321355 + 0.946959i \(0.395862\pi\)
\(882\) 0 0
\(883\) 8.96165 15.5220i 0.301584 0.522358i −0.674911 0.737899i \(-0.735818\pi\)
0.976495 + 0.215541i \(0.0691514\pi\)
\(884\) −6.71780 + 11.6356i −0.225944 + 0.391346i
\(885\) 0 0
\(886\) 2.64110 0.0887295
\(887\) 1.07670 1.86489i 0.0361519 0.0626170i −0.847383 0.530982i \(-0.821823\pi\)
0.883535 + 0.468365i \(0.155157\pi\)
\(888\) 0 0
\(889\) −22.5767 + 39.1040i −0.757198 + 1.31151i
\(890\) 0.179449 + 0.310816i 0.00601516 + 0.0104186i
\(891\) 0 0
\(892\) 20.3589 0.681666
\(893\) 26.1534 0.875190
\(894\) 0 0
\(895\) 7.85890 + 13.6120i 0.262694 + 0.454999i
\(896\) 2.17945 + 3.77492i 0.0728103 + 0.126111i
\(897\) 0 0
\(898\) 0.179449 + 0.310816i 0.00598831 + 0.0103721i
\(899\) −50.1534 + 86.8682i −1.67271 + 2.89722i
\(900\) 0 0
\(901\) −43.9233 −1.46330
\(902\) −9.53835 + 16.5209i −0.317592 + 0.550086i
\(903\) 0 0
\(904\) −3.35890 −0.111715
\(905\) 18.0767 0.600890
\(906\) 0 0
\(907\) 11.7178 + 20.2958i 0.389083 + 0.673912i 0.992326 0.123645i \(-0.0394586\pi\)
−0.603243 + 0.797557i \(0.706125\pi\)
\(908\) −1.67945 + 2.90889i −0.0557345 + 0.0965350i
\(909\) 0 0
\(910\) −8.71780 15.0997i −0.288992 0.500549i
\(911\) −35.2822 −1.16895 −0.584476 0.811411i \(-0.698700\pi\)
−0.584476 + 0.811411i \(0.698700\pi\)
\(912\) 0 0
\(913\) 18.0000 0.595713
\(914\) 15.3206 + 26.5360i 0.506759 + 0.877732i
\(915\) 0 0
\(916\) −4.35890 + 7.54983i −0.144022 + 0.249454i
\(917\) 6.53835 + 11.3248i 0.215915 + 0.373976i
\(918\) 0 0
\(919\) −37.3589 −1.23236 −0.616178 0.787607i \(-0.711320\pi\)
−0.616178 + 0.787607i \(0.711320\pi\)
\(920\) 3.00000 0.0989071
\(921\) 0 0
\(922\) 9.00000 15.5885i 0.296399 0.513378i
\(923\) −40.3068 −1.32671
\(924\) 0 0
\(925\) 3.50000 6.06218i 0.115079 0.199323i
\(926\) 8.89725 + 15.4105i 0.292382 + 0.506420i
\(927\) 0 0
\(928\) 4.67945 + 8.10504i 0.153610 + 0.266061i
\(929\) −13.2561 22.9603i −0.434920 0.753304i 0.562369 0.826886i \(-0.309890\pi\)
−0.997289 + 0.0735827i \(0.976557\pi\)
\(930\) 0 0
\(931\) −26.1534 45.2990i −0.857143 1.48461i
\(932\) −6.00000 −0.196537
\(933\) 0 0
\(934\) 14.3972 + 24.9368i 0.471092 + 0.815956i
\(935\) 5.03835 8.72668i 0.164772 0.285393i
\(936\) 0 0
\(937\) −18.3972 + 31.8650i −0.601012 + 1.04098i 0.391656 + 0.920112i \(0.371902\pi\)
−0.992668 + 0.120872i \(0.961431\pi\)
\(938\) −49.5123 −1.61663
\(939\) 0 0
\(940\) −3.00000 + 5.19615i −0.0978492 + 0.169480i
\(941\) −12.1150 + 20.9839i −0.394939 + 0.684055i −0.993093 0.117326i \(-0.962568\pi\)
0.598154 + 0.801381i \(0.295901\pi\)
\(942\) 0 0
\(943\) 19.0767 0.621223
\(944\) 6.35890 11.0139i 0.206965 0.358473i
\(945\) 0 0
\(946\) 15.0000 25.9808i 0.487692 0.844707i
\(947\) −8.03835 13.9228i −0.261211 0.452431i 0.705353 0.708856i \(-0.250789\pi\)
−0.966564 + 0.256425i \(0.917455\pi\)
\(948\) 0 0
\(949\) −18.5644 −0.602626
\(950\) −2.17945 3.77492i −0.0707107 0.122474i
\(951\) 0 0
\(952\) −7.32055 12.6796i −0.237260 0.410947i
\(953\) 6.71780 + 11.6356i 0.217611 + 0.376913i 0.954077 0.299561i \(-0.0968403\pi\)
−0.736466 + 0.676474i \(0.763507\pi\)
\(954\) 0 0
\(955\) −9.71780 16.8317i −0.314461 0.544662i
\(956\) −6.71780 + 11.6356i −0.217269 + 0.376321i
\(957\) 0 0
\(958\) 22.0767 0.713266
\(959\) −26.1534 + 45.2990i −0.844537 + 1.46278i
\(960\) 0 0
\(961\) 83.8712 2.70552
\(962\) 28.0000 0.902756
\(963\) 0 0
\(964\) 2.00000 + 3.46410i 0.0644157 + 0.111571i
\(965\) −12.0383 + 20.8510i −0.387528 + 0.671218i
\(966\) 0 0
\(967\) −2.07670 3.59694i −0.0667821 0.115670i 0.830701 0.556719i \(-0.187940\pi\)
−0.897483 + 0.441049i \(0.854607\pi\)
\(968\) −2.00000 −0.0642824
\(969\) 0 0
\(970\) −14.0767 −0.451975
\(971\) −10.4356 18.0750i −0.334894 0.580054i 0.648570 0.761155i \(-0.275367\pi\)
−0.983465 + 0.181101i \(0.942034\pi\)
\(972\) 0 0
\(973\) 2.79449 4.84021i 0.0895874 0.155170i
\(974\) 4.82055 + 8.34944i 0.154460 + 0.267533i
\(975\) 0 0
\(976\) 5.35890 0.171534
\(977\) −9.35890 −0.299418 −0.149709 0.988730i \(-0.547834\pi\)
−0.149709 + 0.988730i \(0.547834\pi\)
\(978\) 0 0
\(979\) 0.538348 0.932447i 0.0172057 0.0298011i
\(980\) 12.0000 0.383326
\(981\) 0 0
\(982\) 7.50000 12.9904i 0.239335 0.414540i
\(983\) 27.2945 + 47.2755i 0.870559 + 1.50785i 0.861419 + 0.507895i \(0.169576\pi\)
0.00913990 + 0.999958i \(0.497091\pi\)
\(984\) 0 0
\(985\) −2.82055 4.88534i −0.0898702 0.155660i
\(986\) −15.7178 27.2240i −0.500557 0.866990i
\(987\) 0 0
\(988\) 8.71780 15.0997i 0.277350 0.480384i
\(989\) −30.0000 −0.953945
\(990\) 0 0
\(991\) −26.6794 46.2102i −0.847501 1.46791i −0.883432 0.468560i \(-0.844773\pi\)
0.0359311 0.999354i \(-0.488560\pi\)
\(992\) 5.35890 9.28189i 0.170145 0.294700i
\(993\) 0 0
\(994\) 21.9617 38.0387i 0.696581 1.20651i
\(995\) 16.6411 0.527558
\(996\) 0 0
\(997\) −14.8589 + 25.7364i −0.470586 + 0.815079i −0.999434 0.0336376i \(-0.989291\pi\)
0.528848 + 0.848717i \(0.322624\pi\)
\(998\) 7.82055 13.5456i 0.247555 0.428778i
\(999\) 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 1710.2.l.k.1261.1 4
3.2 odd 2 570.2.i.h.121.1 4
19.11 even 3 inner 1710.2.l.k.1531.1 4
57.11 odd 6 570.2.i.h.391.1 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.2.i.h.121.1 4 3.2 odd 2
570.2.i.h.391.1 yes 4 57.11 odd 6
1710.2.l.k.1261.1 4 1.1 even 1 trivial
1710.2.l.k.1531.1 4 19.11 even 3 inner