Properties

Label 1386.2.ba.b.989.2
Level $1386$
Weight $2$
Character 1386.989
Analytic conductor $11.067$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1386,2,Mod(989,1386)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1386.989");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.ba (of order \(6\), 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: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 989.2
Character \(\chi\) \(=\) 1386.989
Dual form 1386.2.ba.b.1187.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.42143 - 1.39801i) q^{5} +(-2.62875 - 0.299420i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.42143 - 1.39801i) q^{5} +(-2.62875 - 0.299420i) q^{7} -1.00000 q^{8} +(-2.42143 + 1.39801i) q^{10} +(1.36985 + 3.02052i) q^{11} +3.20191i q^{13} +(-1.57368 + 2.12686i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.05881 - 3.56596i) q^{17} +(1.82770 + 1.05522i) q^{19} +2.79602i q^{20} +(3.30077 + 0.323937i) q^{22} +(-0.902766 - 0.521212i) q^{23} +(1.40887 + 2.44023i) q^{25} +(2.77293 + 1.60095i) q^{26} +(1.05507 + 2.42628i) q^{28} +9.40956 q^{29} +(3.58777 + 6.21420i) q^{31} +(0.500000 + 0.866025i) q^{32} -4.11761 q^{34} +(5.94674 + 4.40005i) q^{35} +(-4.60502 + 7.97612i) q^{37} +(1.82770 - 1.05522i) q^{38} +(2.42143 + 1.39801i) q^{40} -0.110771 q^{41} +4.20415i q^{43} +(1.93092 - 2.69658i) q^{44} +(-0.902766 + 0.521212i) q^{46} +(-7.27267 - 4.19888i) q^{47} +(6.82070 + 1.57420i) q^{49} +2.81773 q^{50} +(2.77293 - 1.60095i) q^{52} +(10.3301 - 5.96410i) q^{53} +(0.905736 - 9.22901i) q^{55} +(2.62875 + 0.299420i) q^{56} +(4.70478 - 8.14891i) q^{58} +(-6.34962 + 3.66595i) q^{59} +(9.21987 + 5.32310i) q^{61} +7.17555 q^{62} +1.00000 q^{64} +(4.47630 - 7.75318i) q^{65} +(-3.97143 - 6.87872i) q^{67} +(-2.05881 + 3.56596i) q^{68} +(6.78392 - 2.95000i) q^{70} +11.0925i q^{71} +(-5.46860 + 3.15730i) q^{73} +(4.60502 + 7.97612i) q^{74} -2.11045i q^{76} +(-2.69658 - 8.35036i) q^{77} +(12.4344 + 7.17899i) q^{79} +(2.42143 - 1.39801i) q^{80} +(-0.0553856 + 0.0959306i) q^{82} +14.2335 q^{83} +11.5129i q^{85} +(3.64090 + 2.10208i) q^{86} +(-1.36985 - 3.02052i) q^{88} +(-10.3472 - 5.97394i) q^{89} +(0.958715 - 8.41703i) q^{91} +1.04242i q^{92} +(-7.27267 + 4.19888i) q^{94} +(-2.95043 - 5.11029i) q^{95} -17.6911 q^{97} +(4.77365 - 5.11979i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 2 q^{11} - 16 q^{16} + 4 q^{17} + 4 q^{22} + 4 q^{25} + 16 q^{29} + 4 q^{31} + 16 q^{32} + 8 q^{34} + 16 q^{35} + 4 q^{37} - 32 q^{41} + 2 q^{44} + 20 q^{49} + 8 q^{50} - 12 q^{55} + 8 q^{58} + 8 q^{62} + 32 q^{64} - 8 q^{67} + 4 q^{68} - 4 q^{70} - 4 q^{74} + 14 q^{77} - 16 q^{82} + 88 q^{83} - 2 q^{88} - 24 q^{95} - 32 q^{97} - 8 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −2.42143 1.39801i −1.08289 0.625209i −0.151219 0.988500i \(-0.548320\pi\)
−0.931676 + 0.363291i \(0.881653\pi\)
\(6\) 0 0
\(7\) −2.62875 0.299420i −0.993576 0.113170i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −2.42143 + 1.39801i −0.765722 + 0.442090i
\(11\) 1.36985 + 3.02052i 0.413024 + 0.910720i
\(12\) 0 0
\(13\) 3.20191i 0.888050i 0.896015 + 0.444025i \(0.146450\pi\)
−0.896015 + 0.444025i \(0.853550\pi\)
\(14\) −1.57368 + 2.12686i −0.420584 + 0.568427i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.05881 3.56596i −0.499334 0.864872i 0.500666 0.865641i \(-0.333089\pi\)
−1.00000 0.000768905i \(0.999755\pi\)
\(18\) 0 0
\(19\) 1.82770 + 1.05522i 0.419304 + 0.242085i 0.694779 0.719223i \(-0.255502\pi\)
−0.275476 + 0.961308i \(0.588835\pi\)
\(20\) 2.79602i 0.625209i
\(21\) 0 0
\(22\) 3.30077 + 0.323937i 0.703726 + 0.0690637i
\(23\) −0.902766 0.521212i −0.188240 0.108680i 0.402919 0.915236i \(-0.367996\pi\)
−0.591158 + 0.806556i \(0.701329\pi\)
\(24\) 0 0
\(25\) 1.40887 + 2.44023i 0.281773 + 0.488046i
\(26\) 2.77293 + 1.60095i 0.543817 + 0.313973i
\(27\) 0 0
\(28\) 1.05507 + 2.42628i 0.199390 + 0.458523i
\(29\) 9.40956 1.74731 0.873655 0.486545i \(-0.161743\pi\)
0.873655 + 0.486545i \(0.161743\pi\)
\(30\) 0 0
\(31\) 3.58777 + 6.21420i 0.644383 + 1.11610i 0.984444 + 0.175701i \(0.0562191\pi\)
−0.340061 + 0.940404i \(0.610448\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −4.11761 −0.706165
\(35\) 5.94674 + 4.40005i 1.00518 + 0.743744i
\(36\) 0 0
\(37\) −4.60502 + 7.97612i −0.757060 + 1.31127i 0.187284 + 0.982306i \(0.440032\pi\)
−0.944344 + 0.328961i \(0.893302\pi\)
\(38\) 1.82770 1.05522i 0.296492 0.171180i
\(39\) 0 0
\(40\) 2.42143 + 1.39801i 0.382861 + 0.221045i
\(41\) −0.110771 −0.0172995 −0.00864977 0.999963i \(-0.502753\pi\)
−0.00864977 + 0.999963i \(0.502753\pi\)
\(42\) 0 0
\(43\) 4.20415i 0.641127i 0.947227 + 0.320564i \(0.103872\pi\)
−0.947227 + 0.320564i \(0.896128\pi\)
\(44\) 1.93092 2.69658i 0.291097 0.406525i
\(45\) 0 0
\(46\) −0.902766 + 0.521212i −0.133106 + 0.0768485i
\(47\) −7.27267 4.19888i −1.06083 0.612469i −0.135167 0.990823i \(-0.543157\pi\)
−0.925661 + 0.378353i \(0.876490\pi\)
\(48\) 0 0
\(49\) 6.82070 + 1.57420i 0.974385 + 0.224886i
\(50\) 2.81773 0.398488
\(51\) 0 0
\(52\) 2.77293 1.60095i 0.384537 0.222012i
\(53\) 10.3301 5.96410i 1.41895 0.819232i 0.422745 0.906249i \(-0.361067\pi\)
0.996207 + 0.0870162i \(0.0277332\pi\)
\(54\) 0 0
\(55\) 0.905736 9.22901i 0.122129 1.24444i
\(56\) 2.62875 + 0.299420i 0.351282 + 0.0400117i
\(57\) 0 0
\(58\) 4.70478 8.14891i 0.617768 1.07000i
\(59\) −6.34962 + 3.66595i −0.826650 + 0.477266i −0.852704 0.522394i \(-0.825039\pi\)
0.0260545 + 0.999661i \(0.491706\pi\)
\(60\) 0 0
\(61\) 9.21987 + 5.32310i 1.18048 + 0.681553i 0.956126 0.292954i \(-0.0946383\pi\)
0.224357 + 0.974507i \(0.427972\pi\)
\(62\) 7.17555 0.911295
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 4.47630 7.75318i 0.555217 0.961664i
\(66\) 0 0
\(67\) −3.97143 6.87872i −0.485188 0.840370i 0.514667 0.857390i \(-0.327915\pi\)
−0.999855 + 0.0170201i \(0.994582\pi\)
\(68\) −2.05881 + 3.56596i −0.249667 + 0.432436i
\(69\) 0 0
\(70\) 6.78392 2.95000i 0.810834 0.352593i
\(71\) 11.0925i 1.31643i 0.752828 + 0.658217i \(0.228689\pi\)
−0.752828 + 0.658217i \(0.771311\pi\)
\(72\) 0 0
\(73\) −5.46860 + 3.15730i −0.640052 + 0.369534i −0.784634 0.619959i \(-0.787149\pi\)
0.144583 + 0.989493i \(0.453816\pi\)
\(74\) 4.60502 + 7.97612i 0.535322 + 0.927205i
\(75\) 0 0
\(76\) 2.11045i 0.242085i
\(77\) −2.69658 8.35036i −0.307304 0.951611i
\(78\) 0 0
\(79\) 12.4344 + 7.17899i 1.39898 + 0.807700i 0.994286 0.106753i \(-0.0340455\pi\)
0.404692 + 0.914453i \(0.367379\pi\)
\(80\) 2.42143 1.39801i 0.270724 0.156302i
\(81\) 0 0
\(82\) −0.0553856 + 0.0959306i −0.00611631 + 0.0105938i
\(83\) 14.2335 1.56234 0.781168 0.624321i \(-0.214624\pi\)
0.781168 + 0.624321i \(0.214624\pi\)
\(84\) 0 0
\(85\) 11.5129i 1.24875i
\(86\) 3.64090 + 2.10208i 0.392609 + 0.226673i
\(87\) 0 0
\(88\) −1.36985 3.02052i −0.146026 0.321988i
\(89\) −10.3472 5.97394i −1.09680 0.633236i −0.161419 0.986886i \(-0.551607\pi\)
−0.935378 + 0.353650i \(0.884940\pi\)
\(90\) 0 0
\(91\) 0.958715 8.41703i 0.100501 0.882344i
\(92\) 1.04242i 0.108680i
\(93\) 0 0
\(94\) −7.27267 + 4.19888i −0.750119 + 0.433081i
\(95\) −2.95043 5.11029i −0.302708 0.524305i
\(96\) 0 0
\(97\) −17.6911 −1.79626 −0.898129 0.439733i \(-0.855073\pi\)
−0.898129 + 0.439733i \(0.855073\pi\)
\(98\) 4.77365 5.11979i 0.482211 0.517177i
\(99\) 0 0
\(100\) 1.40887 2.44023i 0.140887 0.244023i
\(101\) 0.117005 + 0.202659i 0.0116425 + 0.0201653i 0.871788 0.489883i \(-0.162961\pi\)
−0.860145 + 0.510049i \(0.829627\pi\)
\(102\) 0 0
\(103\) −6.27192 + 10.8633i −0.617991 + 1.07039i 0.371861 + 0.928288i \(0.378720\pi\)
−0.989852 + 0.142103i \(0.954614\pi\)
\(104\) 3.20191i 0.313973i
\(105\) 0 0
\(106\) 11.9282i 1.15857i
\(107\) −6.54545 + 11.3370i −0.632772 + 1.09599i 0.354210 + 0.935166i \(0.384750\pi\)
−0.986982 + 0.160828i \(0.948584\pi\)
\(108\) 0 0
\(109\) −5.63480 + 3.25325i −0.539716 + 0.311605i −0.744964 0.667105i \(-0.767533\pi\)
0.205248 + 0.978710i \(0.434200\pi\)
\(110\) −7.53969 5.39890i −0.718881 0.514765i
\(111\) 0 0
\(112\) 1.57368 2.12686i 0.148699 0.200969i
\(113\) 0.871772i 0.0820094i 0.999159 + 0.0410047i \(0.0130559\pi\)
−0.999159 + 0.0410047i \(0.986944\pi\)
\(114\) 0 0
\(115\) 1.45732 + 2.52415i 0.135896 + 0.235378i
\(116\) −4.70478 8.14891i −0.436828 0.756608i
\(117\) 0 0
\(118\) 7.33191i 0.674957i
\(119\) 4.34438 + 9.99047i 0.398248 + 0.915825i
\(120\) 0 0
\(121\) −7.24705 + 8.27528i −0.658822 + 0.752299i
\(122\) 9.21987 5.32310i 0.834728 0.481931i
\(123\) 0 0
\(124\) 3.58777 6.21420i 0.322192 0.558052i
\(125\) 6.10167i 0.545750i
\(126\) 0 0
\(127\) 9.15849i 0.812685i 0.913721 + 0.406342i \(0.133196\pi\)
−0.913721 + 0.406342i \(0.866804\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) −4.47630 7.75318i −0.392598 0.679999i
\(131\) 3.87340 6.70892i 0.338420 0.586161i −0.645716 0.763578i \(-0.723441\pi\)
0.984136 + 0.177417i \(0.0567741\pi\)
\(132\) 0 0
\(133\) −4.48862 3.32118i −0.389213 0.287982i
\(134\) −7.94287 −0.686159
\(135\) 0 0
\(136\) 2.05881 + 3.56596i 0.176541 + 0.305778i
\(137\) 6.78091 3.91496i 0.579333 0.334478i −0.181536 0.983384i \(-0.558107\pi\)
0.760868 + 0.648907i \(0.224773\pi\)
\(138\) 0 0
\(139\) 3.11030i 0.263812i 0.991262 + 0.131906i \(0.0421097\pi\)
−0.991262 + 0.131906i \(0.957890\pi\)
\(140\) 0.837184 7.35005i 0.0707550 0.621193i
\(141\) 0 0
\(142\) 9.60636 + 5.54624i 0.806148 + 0.465430i
\(143\) −9.67142 + 4.38612i −0.808765 + 0.366786i
\(144\) 0 0
\(145\) −22.7845 13.1547i −1.89215 1.09243i
\(146\) 6.31460i 0.522600i
\(147\) 0 0
\(148\) 9.21003 0.757060
\(149\) −4.08541 + 7.07613i −0.334690 + 0.579699i −0.983425 0.181314i \(-0.941965\pi\)
0.648736 + 0.761014i \(0.275298\pi\)
\(150\) 0 0
\(151\) −5.93139 + 3.42449i −0.482690 + 0.278681i −0.721537 0.692376i \(-0.756564\pi\)
0.238847 + 0.971057i \(0.423231\pi\)
\(152\) −1.82770 1.05522i −0.148246 0.0855900i
\(153\) 0 0
\(154\) −8.57991 1.83987i −0.691389 0.148261i
\(155\) 20.0630i 1.61150i
\(156\) 0 0
\(157\) 4.04332 + 7.00324i 0.322692 + 0.558920i 0.981043 0.193792i \(-0.0620787\pi\)
−0.658350 + 0.752712i \(0.728745\pi\)
\(158\) 12.4344 7.17899i 0.989226 0.571130i
\(159\) 0 0
\(160\) 2.79602i 0.221045i
\(161\) 2.21709 + 1.64044i 0.174731 + 0.129285i
\(162\) 0 0
\(163\) −0.682357 + 1.18188i −0.0534463 + 0.0925717i −0.891511 0.453000i \(-0.850354\pi\)
0.838064 + 0.545571i \(0.183687\pi\)
\(164\) 0.0553856 + 0.0959306i 0.00432489 + 0.00749092i
\(165\) 0 0
\(166\) 7.11677 12.3266i 0.552369 0.956731i
\(167\) −7.34655 −0.568493 −0.284247 0.958751i \(-0.591743\pi\)
−0.284247 + 0.958751i \(0.591743\pi\)
\(168\) 0 0
\(169\) 2.74778 0.211368
\(170\) 9.97049 + 5.75647i 0.764702 + 0.441501i
\(171\) 0 0
\(172\) 3.64090 2.10208i 0.277616 0.160282i
\(173\) 0.327674 0.567548i 0.0249126 0.0431498i −0.853300 0.521420i \(-0.825403\pi\)
0.878213 + 0.478270i \(0.158736\pi\)
\(174\) 0 0
\(175\) −2.97291 6.83660i −0.224731 0.516799i
\(176\) −3.30077 0.323937i −0.248805 0.0244177i
\(177\) 0 0
\(178\) −10.3472 + 5.97394i −0.775553 + 0.447765i
\(179\) −3.55106 + 2.05021i −0.265419 + 0.153240i −0.626804 0.779177i \(-0.715637\pi\)
0.361385 + 0.932417i \(0.382304\pi\)
\(180\) 0 0
\(181\) −11.0064 −0.818102 −0.409051 0.912511i \(-0.634140\pi\)
−0.409051 + 0.912511i \(0.634140\pi\)
\(182\) −6.81000 5.03879i −0.504791 0.373500i
\(183\) 0 0
\(184\) 0.902766 + 0.521212i 0.0665528 + 0.0384243i
\(185\) 22.3014 12.8757i 1.63963 0.946642i
\(186\) 0 0
\(187\) 7.95079 11.1035i 0.581419 0.811966i
\(188\) 8.39776i 0.612469i
\(189\) 0 0
\(190\) −5.90086 −0.428093
\(191\) 18.8331 + 10.8733i 1.36271 + 0.786763i 0.989984 0.141178i \(-0.0450890\pi\)
0.372728 + 0.927940i \(0.378422\pi\)
\(192\) 0 0
\(193\) 19.3131 11.1504i 1.39019 0.802625i 0.396852 0.917882i \(-0.370102\pi\)
0.993336 + 0.115257i \(0.0367692\pi\)
\(194\) −8.84554 + 15.3209i −0.635073 + 1.09998i
\(195\) 0 0
\(196\) −2.04705 6.69400i −0.146218 0.478143i
\(197\) −11.0036 −0.783972 −0.391986 0.919971i \(-0.628212\pi\)
−0.391986 + 0.919971i \(0.628212\pi\)
\(198\) 0 0
\(199\) −8.22506 14.2462i −0.583059 1.00989i −0.995114 0.0987290i \(-0.968522\pi\)
0.412055 0.911159i \(-0.364811\pi\)
\(200\) −1.40887 2.44023i −0.0996219 0.172550i
\(201\) 0 0
\(202\) 0.234010 0.0164649
\(203\) −24.7354 2.81741i −1.73609 0.197743i
\(204\) 0 0
\(205\) 0.268224 + 0.154859i 0.0187336 + 0.0108158i
\(206\) 6.27192 + 10.8633i 0.436986 + 0.756881i
\(207\) 0 0
\(208\) −2.77293 1.60095i −0.192268 0.111006i
\(209\) −0.683653 + 6.96610i −0.0472893 + 0.481855i
\(210\) 0 0
\(211\) 0.618822i 0.0426015i −0.999773 0.0213007i \(-0.993219\pi\)
0.999773 0.0213007i \(-0.00678075\pi\)
\(212\) −10.3301 5.96410i −0.709476 0.409616i
\(213\) 0 0
\(214\) 6.54545 + 11.3370i 0.447438 + 0.774985i
\(215\) 5.87745 10.1800i 0.400839 0.694273i
\(216\) 0 0
\(217\) −7.57072 17.4099i −0.513934 1.18186i
\(218\) 6.50650i 0.440676i
\(219\) 0 0
\(220\) −8.44543 + 3.83012i −0.569391 + 0.258226i
\(221\) 11.4179 6.59211i 0.768049 0.443433i
\(222\) 0 0
\(223\) 10.3553 0.693443 0.346722 0.937968i \(-0.387295\pi\)
0.346722 + 0.937968i \(0.387295\pi\)
\(224\) −1.05507 2.42628i −0.0704949 0.162112i
\(225\) 0 0
\(226\) 0.754977 + 0.435886i 0.0502203 + 0.0289947i
\(227\) −6.46564 11.1988i −0.429140 0.743292i 0.567657 0.823265i \(-0.307850\pi\)
−0.996797 + 0.0799731i \(0.974517\pi\)
\(228\) 0 0
\(229\) −2.73849 + 4.74320i −0.180964 + 0.313439i −0.942209 0.335025i \(-0.891255\pi\)
0.761245 + 0.648465i \(0.224589\pi\)
\(230\) 2.91464 0.192186
\(231\) 0 0
\(232\) −9.40956 −0.617768
\(233\) −13.7588 + 23.8310i −0.901372 + 1.56122i −0.0756568 + 0.997134i \(0.524105\pi\)
−0.825715 + 0.564088i \(0.809228\pi\)
\(234\) 0 0
\(235\) 11.7402 + 20.3345i 0.765843 + 1.32648i
\(236\) 6.34962 + 3.66595i 0.413325 + 0.238633i
\(237\) 0 0
\(238\) 10.8242 + 1.23290i 0.701628 + 0.0799167i
\(239\) −13.3339 −0.862499 −0.431249 0.902233i \(-0.641927\pi\)
−0.431249 + 0.902233i \(0.641927\pi\)
\(240\) 0 0
\(241\) 15.7035 9.06641i 1.01155 0.584019i 0.0999053 0.994997i \(-0.468146\pi\)
0.911645 + 0.410978i \(0.134813\pi\)
\(242\) 3.54308 + 10.4138i 0.227758 + 0.669422i
\(243\) 0 0
\(244\) 10.6462i 0.681553i
\(245\) −14.3151 13.3472i −0.914555 0.852722i
\(246\) 0 0
\(247\) −3.37873 + 5.85213i −0.214984 + 0.372362i
\(248\) −3.58777 6.21420i −0.227824 0.394602i
\(249\) 0 0
\(250\) 5.28420 + 3.05083i 0.334202 + 0.192952i
\(251\) 18.5540i 1.17112i 0.810630 + 0.585559i \(0.199125\pi\)
−0.810630 + 0.585559i \(0.800875\pi\)
\(252\) 0 0
\(253\) 0.337680 3.44080i 0.0212298 0.216321i
\(254\) 7.93149 + 4.57925i 0.497666 + 0.287327i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −23.4582 13.5436i −1.46328 0.844826i −0.464120 0.885773i \(-0.653629\pi\)
−0.999161 + 0.0409470i \(0.986963\pi\)
\(258\) 0 0
\(259\) 14.4937 19.5884i 0.900593 1.21717i
\(260\) −8.95260 −0.555217
\(261\) 0 0
\(262\) −3.87340 6.70892i −0.239299 0.414478i
\(263\) 5.53418 + 9.58548i 0.341252 + 0.591066i 0.984665 0.174453i \(-0.0558157\pi\)
−0.643414 + 0.765519i \(0.722482\pi\)
\(264\) 0 0
\(265\) −33.3515 −2.04877
\(266\) −5.12053 + 2.22667i −0.313960 + 0.136526i
\(267\) 0 0
\(268\) −3.97143 + 6.87872i −0.242594 + 0.420185i
\(269\) −8.44523 + 4.87586i −0.514915 + 0.297286i −0.734852 0.678228i \(-0.762748\pi\)
0.219937 + 0.975514i \(0.429415\pi\)
\(270\) 0 0
\(271\) −2.91324 1.68196i −0.176967 0.102172i 0.408900 0.912579i \(-0.365912\pi\)
−0.585867 + 0.810407i \(0.699246\pi\)
\(272\) 4.11761 0.249667
\(273\) 0 0
\(274\) 7.82992i 0.473023i
\(275\) −5.44082 + 7.59824i −0.328094 + 0.458191i
\(276\) 0 0
\(277\) 14.3722 8.29777i 0.863539 0.498564i −0.00165684 0.999999i \(-0.500527\pi\)
0.865196 + 0.501434i \(0.167194\pi\)
\(278\) 2.69360 + 1.55515i 0.161551 + 0.0932716i
\(279\) 0 0
\(280\) −5.94674 4.40005i −0.355386 0.262953i
\(281\) −5.58641 −0.333257 −0.166629 0.986020i \(-0.553288\pi\)
−0.166629 + 0.986020i \(0.553288\pi\)
\(282\) 0 0
\(283\) 2.33852 1.35014i 0.139010 0.0802577i −0.428882 0.903361i \(-0.641092\pi\)
0.567892 + 0.823103i \(0.307759\pi\)
\(284\) 9.60636 5.54624i 0.570033 0.329109i
\(285\) 0 0
\(286\) −1.03722 + 10.5688i −0.0613320 + 0.624944i
\(287\) 0.291190 + 0.0331671i 0.0171884 + 0.00195779i
\(288\) 0 0
\(289\) 0.0226302 0.0391967i 0.00133119 0.00230569i
\(290\) −22.7845 + 13.1547i −1.33795 + 0.772468i
\(291\) 0 0
\(292\) 5.46860 + 3.15730i 0.320026 + 0.184767i
\(293\) −15.8185 −0.924125 −0.462062 0.886847i \(-0.652890\pi\)
−0.462062 + 0.886847i \(0.652890\pi\)
\(294\) 0 0
\(295\) 20.5002 1.19357
\(296\) 4.60502 7.97612i 0.267661 0.463603i
\(297\) 0 0
\(298\) 4.08541 + 7.07613i 0.236661 + 0.409909i
\(299\) 1.66887 2.89057i 0.0965134 0.167166i
\(300\) 0 0
\(301\) 1.25881 11.0517i 0.0725564 0.637008i
\(302\) 6.84898i 0.394115i
\(303\) 0 0
\(304\) −1.82770 + 1.05522i −0.104826 + 0.0605213i
\(305\) −14.8835 25.7790i −0.852226 1.47610i
\(306\) 0 0
\(307\) 12.2813i 0.700932i −0.936575 0.350466i \(-0.886023\pi\)
0.936575 0.350466i \(-0.113977\pi\)
\(308\) −5.88333 + 6.51049i −0.335234 + 0.370969i
\(309\) 0 0
\(310\) −17.3750 10.0315i −0.986836 0.569750i
\(311\) 17.6592 10.1956i 1.00136 0.578137i 0.0927112 0.995693i \(-0.470447\pi\)
0.908651 + 0.417556i \(0.137113\pi\)
\(312\) 0 0
\(313\) 1.62210 2.80957i 0.0916867 0.158806i −0.816534 0.577297i \(-0.804108\pi\)
0.908221 + 0.418491i \(0.137441\pi\)
\(314\) 8.08665 0.456356
\(315\) 0 0
\(316\) 14.3580i 0.807700i
\(317\) −9.57584 5.52861i −0.537833 0.310518i 0.206368 0.978475i \(-0.433836\pi\)
−0.744200 + 0.667957i \(0.767169\pi\)
\(318\) 0 0
\(319\) 12.8896 + 28.4217i 0.721681 + 1.59131i
\(320\) −2.42143 1.39801i −0.135362 0.0781512i
\(321\) 0 0
\(322\) 2.52921 1.09983i 0.140947 0.0612913i
\(323\) 8.69001i 0.483525i
\(324\) 0 0
\(325\) −7.81339 + 4.51106i −0.433409 + 0.250229i
\(326\) 0.682357 + 1.18188i 0.0377922 + 0.0654581i
\(327\) 0 0
\(328\) 0.110771 0.00611631
\(329\) 17.8608 + 13.2154i 0.984700 + 0.728589i
\(330\) 0 0
\(331\) 7.27038 12.5927i 0.399616 0.692156i −0.594062 0.804419i \(-0.702477\pi\)
0.993678 + 0.112263i \(0.0358100\pi\)
\(332\) −7.11677 12.3266i −0.390584 0.676511i
\(333\) 0 0
\(334\) −3.67328 + 6.36230i −0.200993 + 0.348130i
\(335\) 22.2084i 1.21338i
\(336\) 0 0
\(337\) 20.0460i 1.09198i 0.837793 + 0.545988i \(0.183846\pi\)
−0.837793 + 0.545988i \(0.816154\pi\)
\(338\) 1.37389 2.37965i 0.0747299 0.129436i
\(339\) 0 0
\(340\) 9.97049 5.75647i 0.540726 0.312188i
\(341\) −13.8554 + 19.3494i −0.750313 + 1.04783i
\(342\) 0 0
\(343\) −17.4586 6.18044i −0.942675 0.333713i
\(344\) 4.20415i 0.226673i
\(345\) 0 0
\(346\) −0.327674 0.567548i −0.0176158 0.0305115i
\(347\) −6.04444 10.4693i −0.324482 0.562020i 0.656925 0.753956i \(-0.271857\pi\)
−0.981407 + 0.191936i \(0.938523\pi\)
\(348\) 0 0
\(349\) 4.92511i 0.263635i −0.991274 0.131818i \(-0.957919\pi\)
0.991274 0.131818i \(-0.0420813\pi\)
\(350\) −7.40713 0.843685i −0.395928 0.0450969i
\(351\) 0 0
\(352\) −1.93092 + 2.69658i −0.102918 + 0.143728i
\(353\) 8.28001 4.78047i 0.440700 0.254438i −0.263194 0.964743i \(-0.584776\pi\)
0.703895 + 0.710304i \(0.251443\pi\)
\(354\) 0 0
\(355\) 15.5074 26.8596i 0.823047 1.42556i
\(356\) 11.9479i 0.633236i
\(357\) 0 0
\(358\) 4.10041i 0.216714i
\(359\) 4.14103 7.17248i 0.218555 0.378549i −0.735811 0.677187i \(-0.763199\pi\)
0.954366 + 0.298638i \(0.0965323\pi\)
\(360\) 0 0
\(361\) −7.27300 12.5972i −0.382790 0.663011i
\(362\) −5.50322 + 9.53186i −0.289243 + 0.500983i
\(363\) 0 0
\(364\) −7.76872 + 3.37824i −0.407191 + 0.177068i
\(365\) 17.6558 0.924144
\(366\) 0 0
\(367\) 18.6919 + 32.3753i 0.975710 + 1.68998i 0.677572 + 0.735457i \(0.263032\pi\)
0.298138 + 0.954523i \(0.403634\pi\)
\(368\) 0.902766 0.521212i 0.0470599 0.0271701i
\(369\) 0 0
\(370\) 25.7514i 1.33875i
\(371\) −28.9411 + 12.5851i −1.50255 + 0.653386i
\(372\) 0 0
\(373\) 20.6889 + 11.9447i 1.07123 + 0.618475i 0.928517 0.371289i \(-0.121084\pi\)
0.142713 + 0.989764i \(0.454417\pi\)
\(374\) −5.64049 12.4373i −0.291663 0.643119i
\(375\) 0 0
\(376\) 7.27267 + 4.19888i 0.375059 + 0.216541i
\(377\) 30.1285i 1.55170i
\(378\) 0 0
\(379\) 17.9926 0.924217 0.462109 0.886823i \(-0.347093\pi\)
0.462109 + 0.886823i \(0.347093\pi\)
\(380\) −2.95043 + 5.11029i −0.151354 + 0.262153i
\(381\) 0 0
\(382\) 18.8331 10.8733i 0.963583 0.556325i
\(383\) 14.6369 + 8.45064i 0.747913 + 0.431808i 0.824939 0.565221i \(-0.191209\pi\)
−0.0770265 + 0.997029i \(0.524543\pi\)
\(384\) 0 0
\(385\) −5.14431 + 23.9896i −0.262178 + 1.22262i
\(386\) 22.3009i 1.13508i
\(387\) 0 0
\(388\) 8.84554 + 15.3209i 0.449064 + 0.777802i
\(389\) −9.20118 + 5.31230i −0.466518 + 0.269344i −0.714781 0.699348i \(-0.753474\pi\)
0.248263 + 0.968693i \(0.420140\pi\)
\(390\) 0 0
\(391\) 4.29230i 0.217071i
\(392\) −6.82070 1.57420i −0.344497 0.0795092i
\(393\) 0 0
\(394\) −5.50179 + 9.52937i −0.277176 + 0.480083i
\(395\) −20.0726 34.7668i −1.00996 1.74931i
\(396\) 0 0
\(397\) 11.4791 19.8824i 0.576120 0.997870i −0.419799 0.907617i \(-0.637899\pi\)
0.995919 0.0902525i \(-0.0287674\pi\)
\(398\) −16.4501 −0.824570
\(399\) 0 0
\(400\) −2.81773 −0.140887
\(401\) −8.28001 4.78047i −0.413484 0.238725i 0.278802 0.960349i \(-0.410063\pi\)
−0.692286 + 0.721624i \(0.743396\pi\)
\(402\) 0 0
\(403\) −19.8973 + 11.4877i −0.991156 + 0.572244i
\(404\) 0.117005 0.202659i 0.00582123 0.0100827i
\(405\) 0 0
\(406\) −14.8077 + 20.0128i −0.734891 + 0.993218i
\(407\) −30.4002 2.98347i −1.50688 0.147885i
\(408\) 0 0
\(409\) −11.3509 + 6.55346i −0.561267 + 0.324048i −0.753654 0.657271i \(-0.771711\pi\)
0.192387 + 0.981319i \(0.438377\pi\)
\(410\) 0.268224 0.154859i 0.0132466 0.00764795i
\(411\) 0 0
\(412\) 12.5438 0.617991
\(413\) 17.7892 7.73569i 0.875351 0.380648i
\(414\) 0 0
\(415\) −34.4655 19.8987i −1.69184 0.976786i
\(416\) −2.77293 + 1.60095i −0.135954 + 0.0784932i
\(417\) 0 0
\(418\) 5.69099 + 4.07511i 0.278356 + 0.199320i
\(419\) 4.51379i 0.220513i 0.993903 + 0.110256i \(0.0351672\pi\)
−0.993903 + 0.110256i \(0.964833\pi\)
\(420\) 0 0
\(421\) −37.3188 −1.81881 −0.909403 0.415917i \(-0.863461\pi\)
−0.909403 + 0.415917i \(0.863461\pi\)
\(422\) −0.535916 0.309411i −0.0260880 0.0150619i
\(423\) 0 0
\(424\) −10.3301 + 5.96410i −0.501675 + 0.289642i
\(425\) 5.80117 10.0479i 0.281398 0.487395i
\(426\) 0 0
\(427\) −22.6429 16.7537i −1.09577 0.810770i
\(428\) 13.0909 0.632772
\(429\) 0 0
\(430\) −5.87745 10.1800i −0.283436 0.490925i
\(431\) 13.8494 + 23.9878i 0.667100 + 1.15545i 0.978711 + 0.205242i \(0.0657981\pi\)
−0.311611 + 0.950210i \(0.600869\pi\)
\(432\) 0 0
\(433\) 8.18187 0.393196 0.196598 0.980484i \(-0.437011\pi\)
0.196598 + 0.980484i \(0.437011\pi\)
\(434\) −18.8627 2.14850i −0.905441 0.103131i
\(435\) 0 0
\(436\) 5.63480 + 3.25325i 0.269858 + 0.155802i
\(437\) −1.09999 1.90524i −0.0526197 0.0911400i
\(438\) 0 0
\(439\) 1.16163 + 0.670668i 0.0554416 + 0.0320092i 0.527465 0.849577i \(-0.323143\pi\)
−0.472023 + 0.881586i \(0.656476\pi\)
\(440\) −0.905736 + 9.22901i −0.0431793 + 0.439976i
\(441\) 0 0
\(442\) 13.1842i 0.627109i
\(443\) 23.5122 + 13.5748i 1.11710 + 0.644958i 0.940659 0.339354i \(-0.110208\pi\)
0.176441 + 0.984311i \(0.443542\pi\)
\(444\) 0 0
\(445\) 16.7033 + 28.9309i 0.791810 + 1.37146i
\(446\) 5.17766 8.96797i 0.245169 0.424646i
\(447\) 0 0
\(448\) −2.62875 0.299420i −0.124197 0.0141463i
\(449\) 37.3766i 1.76391i −0.471334 0.881955i \(-0.656227\pi\)
0.471334 0.881955i \(-0.343773\pi\)
\(450\) 0 0
\(451\) −0.151739 0.334586i −0.00714513 0.0157550i
\(452\) 0.754977 0.435886i 0.0355111 0.0205024i
\(453\) 0 0
\(454\) −12.9313 −0.606895
\(455\) −14.0886 + 19.0409i −0.660481 + 0.892652i
\(456\) 0 0
\(457\) 20.4149 + 11.7865i 0.954967 + 0.551350i 0.894620 0.446827i \(-0.147446\pi\)
0.0603464 + 0.998177i \(0.480779\pi\)
\(458\) 2.73849 + 4.74320i 0.127961 + 0.221635i
\(459\) 0 0
\(460\) 1.45732 2.52415i 0.0679479 0.117689i
\(461\) −38.3140 −1.78446 −0.892231 0.451580i \(-0.850861\pi\)
−0.892231 + 0.451580i \(0.850861\pi\)
\(462\) 0 0
\(463\) −9.80424 −0.455642 −0.227821 0.973703i \(-0.573160\pi\)
−0.227821 + 0.973703i \(0.573160\pi\)
\(464\) −4.70478 + 8.14891i −0.218414 + 0.378304i
\(465\) 0 0
\(466\) 13.7588 + 23.8310i 0.637366 + 1.10395i
\(467\) −10.8457 6.26175i −0.501878 0.289759i 0.227611 0.973752i \(-0.426909\pi\)
−0.729489 + 0.683993i \(0.760242\pi\)
\(468\) 0 0
\(469\) 8.38029 + 19.2716i 0.386966 + 0.889880i
\(470\) 23.4803 1.08307
\(471\) 0 0
\(472\) 6.34962 3.66595i 0.292265 0.168739i
\(473\) −12.6987 + 5.75904i −0.583887 + 0.264801i
\(474\) 0 0
\(475\) 5.94668i 0.272852i
\(476\) 6.47982 8.75758i 0.297002 0.401403i
\(477\) 0 0
\(478\) −6.66695 + 11.5475i −0.304939 + 0.528170i
\(479\) 7.84197 + 13.5827i 0.358309 + 0.620609i 0.987678 0.156497i \(-0.0500202\pi\)
−0.629370 + 0.777106i \(0.716687\pi\)
\(480\) 0 0
\(481\) −25.5388 14.7448i −1.16447 0.672307i
\(482\) 18.1328i 0.825928i
\(483\) 0 0
\(484\) 10.7901 + 2.13848i 0.490460 + 0.0972038i
\(485\) 42.8376 + 24.7323i 1.94516 + 1.12304i
\(486\) 0 0
\(487\) 19.0262 + 32.9544i 0.862161 + 1.49331i 0.869839 + 0.493336i \(0.164223\pi\)
−0.00767777 + 0.999971i \(0.502444\pi\)
\(488\) −9.21987 5.32310i −0.417364 0.240965i
\(489\) 0 0
\(490\) −18.7166 + 5.72359i −0.845528 + 0.258565i
\(491\) −3.63565 −0.164075 −0.0820373 0.996629i \(-0.526143\pi\)
−0.0820373 + 0.996629i \(0.526143\pi\)
\(492\) 0 0
\(493\) −19.3725 33.5541i −0.872492 1.51120i
\(494\) 3.37873 + 5.85213i 0.152016 + 0.263300i
\(495\) 0 0
\(496\) −7.17555 −0.322192
\(497\) 3.32131 29.1594i 0.148981 1.30798i
\(498\) 0 0
\(499\) 9.18656 15.9116i 0.411247 0.712301i −0.583779 0.811912i \(-0.698427\pi\)
0.995026 + 0.0996117i \(0.0317601\pi\)
\(500\) 5.28420 3.05083i 0.236316 0.136437i
\(501\) 0 0
\(502\) 16.0682 + 9.27699i 0.717160 + 0.414053i
\(503\) 34.2342 1.52643 0.763213 0.646146i \(-0.223620\pi\)
0.763213 + 0.646146i \(0.223620\pi\)
\(504\) 0 0
\(505\) 0.654298i 0.0291159i
\(506\) −2.81098 2.01284i −0.124963 0.0894816i
\(507\) 0 0
\(508\) 7.93149 4.57925i 0.351903 0.203171i
\(509\) 9.23009 + 5.32899i 0.409116 + 0.236203i 0.690410 0.723418i \(-0.257430\pi\)
−0.281294 + 0.959622i \(0.590763\pi\)
\(510\) 0 0
\(511\) 15.3210 6.66236i 0.677760 0.294725i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −23.4582 + 13.5436i −1.03470 + 0.597382i
\(515\) 30.3740 17.5364i 1.33844 0.772747i
\(516\) 0 0
\(517\) 2.72035 27.7190i 0.119641 1.21908i
\(518\) −9.71725 22.3461i −0.426951 0.981831i
\(519\) 0 0
\(520\) −4.47630 + 7.75318i −0.196299 + 0.339999i
\(521\) −18.3680 + 10.6048i −0.804716 + 0.464603i −0.845118 0.534581i \(-0.820470\pi\)
0.0404016 + 0.999184i \(0.487136\pi\)
\(522\) 0 0
\(523\) −18.1257 10.4649i −0.792583 0.457598i 0.0482882 0.998833i \(-0.484623\pi\)
−0.840871 + 0.541236i \(0.817957\pi\)
\(524\) −7.74679 −0.338420
\(525\) 0 0
\(526\) 11.0684 0.482603
\(527\) 14.7731 25.5877i 0.643525 1.11462i
\(528\) 0 0
\(529\) −10.9567 18.9775i −0.476377 0.825110i
\(530\) −16.6758 + 28.8833i −0.724348 + 1.25461i
\(531\) 0 0
\(532\) −0.631910 + 5.54785i −0.0273968 + 0.240530i
\(533\) 0.354679i 0.0153629i
\(534\) 0 0
\(535\) 31.6986 18.3012i 1.37045 0.791230i
\(536\) 3.97143 + 6.87872i 0.171540 + 0.297116i
\(537\) 0 0
\(538\) 9.75172i 0.420426i
\(539\) 4.58839 + 22.7584i 0.197636 + 0.980275i
\(540\) 0 0
\(541\) 0.708020 + 0.408775i 0.0304402 + 0.0175746i 0.515143 0.857104i \(-0.327739\pi\)
−0.484703 + 0.874679i \(0.661072\pi\)
\(542\) −2.91324 + 1.68196i −0.125134 + 0.0722463i
\(543\) 0 0
\(544\) 2.05881 3.56596i 0.0882706 0.152889i
\(545\) 18.1923 0.779273
\(546\) 0 0
\(547\) 16.2530i 0.694930i −0.937693 0.347465i \(-0.887043\pi\)
0.937693 0.347465i \(-0.112957\pi\)
\(548\) −6.78091 3.91496i −0.289666 0.167239i
\(549\) 0 0
\(550\) 3.85986 + 8.51101i 0.164585 + 0.362911i
\(551\) 17.1979 + 9.92919i 0.732654 + 0.422998i
\(552\) 0 0
\(553\) −30.5374 22.5949i −1.29858 0.960833i
\(554\) 16.5955i 0.705077i
\(555\) 0 0
\(556\) 2.69360 1.55515i 0.114234 0.0659530i
\(557\) −3.81751 6.61212i −0.161753 0.280165i 0.773744 0.633498i \(-0.218381\pi\)
−0.935498 + 0.353333i \(0.885048\pi\)
\(558\) 0 0
\(559\) −13.4613 −0.569353
\(560\) −6.78392 + 2.95000i −0.286673 + 0.124660i
\(561\) 0 0
\(562\) −2.79320 + 4.83797i −0.117824 + 0.204078i
\(563\) 22.5824 + 39.1138i 0.951734 + 1.64845i 0.741672 + 0.670763i \(0.234033\pi\)
0.210061 + 0.977688i \(0.432634\pi\)
\(564\) 0 0
\(565\) 1.21875 2.11093i 0.0512731 0.0888075i
\(566\) 2.70029i 0.113502i
\(567\) 0 0
\(568\) 11.0925i 0.465430i
\(569\) −16.3937 + 28.3948i −0.687261 + 1.19037i 0.285459 + 0.958391i \(0.407854\pi\)
−0.972720 + 0.231981i \(0.925479\pi\)
\(570\) 0 0
\(571\) 4.58774 2.64873i 0.191991 0.110846i −0.400923 0.916112i \(-0.631311\pi\)
0.592914 + 0.805266i \(0.297977\pi\)
\(572\) 8.63420 + 6.18263i 0.361014 + 0.258509i
\(573\) 0 0
\(574\) 0.174319 0.235594i 0.00727592 0.00983352i
\(575\) 2.93727i 0.122493i
\(576\) 0 0
\(577\) −6.83877 11.8451i −0.284702 0.493118i 0.687835 0.725867i \(-0.258561\pi\)
−0.972537 + 0.232749i \(0.925228\pi\)
\(578\) −0.0226302 0.0391967i −0.000941294 0.00163037i
\(579\) 0 0
\(580\) 26.3093i 1.09243i
\(581\) −37.4165 4.26181i −1.55230 0.176810i
\(582\) 0 0
\(583\) 32.1653 + 23.0324i 1.33215 + 0.953906i
\(584\) 5.46860 3.15730i 0.226292 0.130650i
\(585\) 0 0
\(586\) −7.90923 + 13.6992i −0.326727 + 0.565909i
\(587\) 24.5620i 1.01378i 0.862011 + 0.506890i \(0.169205\pi\)
−0.862011 + 0.506890i \(0.830795\pi\)
\(588\) 0 0
\(589\) 15.1436i 0.623982i
\(590\) 10.2501 17.7537i 0.421989 0.730907i
\(591\) 0 0
\(592\) −4.60502 7.97612i −0.189265 0.327817i
\(593\) −2.76466 + 4.78853i −0.113531 + 0.196641i −0.917192 0.398447i \(-0.869549\pi\)
0.803661 + 0.595088i \(0.202883\pi\)
\(594\) 0 0
\(595\) 3.44720 30.2647i 0.141321 1.24073i
\(596\) 8.17082 0.334690
\(597\) 0 0
\(598\) −1.66887 2.89057i −0.0682453 0.118204i
\(599\) 20.9741 12.1094i 0.856977 0.494776i −0.00602174 0.999982i \(-0.501917\pi\)
0.862999 + 0.505206i \(0.168583\pi\)
\(600\) 0 0
\(601\) 16.7793i 0.684443i 0.939619 + 0.342222i \(0.111179\pi\)
−0.939619 + 0.342222i \(0.888821\pi\)
\(602\) −8.94163 6.61600i −0.364434 0.269648i
\(603\) 0 0
\(604\) 5.93139 + 3.42449i 0.241345 + 0.139341i
\(605\) 29.1171 9.90653i 1.18378 0.402758i
\(606\) 0 0
\(607\) 30.9524 + 17.8704i 1.25632 + 0.725337i 0.972357 0.233498i \(-0.0750174\pi\)
0.283963 + 0.958835i \(0.408351\pi\)
\(608\) 2.11045i 0.0855900i
\(609\) 0 0
\(610\) −29.7670 −1.20523
\(611\) 13.4444 23.2864i 0.543903 0.942068i
\(612\) 0 0
\(613\) 7.82971 4.52049i 0.316239 0.182581i −0.333476 0.942759i \(-0.608222\pi\)
0.649715 + 0.760178i \(0.274888\pi\)
\(614\) −10.6359 6.14066i −0.429231 0.247817i
\(615\) 0 0
\(616\) 2.69658 + 8.35036i 0.108648 + 0.336445i
\(617\) 11.5919i 0.466672i 0.972396 + 0.233336i \(0.0749643\pi\)
−0.972396 + 0.233336i \(0.925036\pi\)
\(618\) 0 0
\(619\) 0.200558 + 0.347377i 0.00806111 + 0.0139622i 0.870028 0.493003i \(-0.164101\pi\)
−0.861967 + 0.506965i \(0.830767\pi\)
\(620\) −17.3750 + 10.0315i −0.697799 + 0.402874i
\(621\) 0 0
\(622\) 20.3911i 0.817609i
\(623\) 25.4114 + 18.8022i 1.01809 + 0.753292i
\(624\) 0 0
\(625\) 15.5745 26.9759i 0.622981 1.07903i
\(626\) −1.62210 2.80957i −0.0648323 0.112293i
\(627\) 0 0
\(628\) 4.04332 7.00324i 0.161346 0.279460i
\(629\) 37.9234 1.51210
\(630\) 0 0
\(631\) 32.7927 1.30546 0.652728 0.757592i \(-0.273624\pi\)
0.652728 + 0.757592i \(0.273624\pi\)
\(632\) −12.4344 7.17899i −0.494613 0.285565i
\(633\) 0 0
\(634\) −9.57584 + 5.52861i −0.380305 + 0.219569i
\(635\) 12.8037 22.1766i 0.508098 0.880052i
\(636\) 0 0
\(637\) −5.04045 + 21.8392i −0.199710 + 0.865302i
\(638\) 31.0588 + 3.04811i 1.22963 + 0.120676i
\(639\) 0 0
\(640\) −2.42143 + 1.39801i −0.0957152 + 0.0552612i
\(641\) 27.3662 15.7999i 1.08090 0.624058i 0.149761 0.988722i \(-0.452150\pi\)
0.931139 + 0.364664i \(0.118816\pi\)
\(642\) 0 0
\(643\) −4.86178 −0.191730 −0.0958650 0.995394i \(-0.530562\pi\)
−0.0958650 + 0.995394i \(0.530562\pi\)
\(644\) 0.312123 2.74028i 0.0122994 0.107982i
\(645\) 0 0
\(646\) −7.52577 4.34501i −0.296098 0.170952i
\(647\) −18.9738 + 10.9545i −0.745937 + 0.430667i −0.824224 0.566264i \(-0.808388\pi\)
0.0782867 + 0.996931i \(0.475055\pi\)
\(648\) 0 0
\(649\) −19.7711 14.1573i −0.776082 0.555724i
\(650\) 9.02212i 0.353877i
\(651\) 0 0
\(652\) 1.36471 0.0534463
\(653\) −31.4813 18.1757i −1.23196 0.711271i −0.264520 0.964380i \(-0.585214\pi\)
−0.967438 + 0.253109i \(0.918547\pi\)
\(654\) 0 0
\(655\) −18.7583 + 10.8301i −0.732947 + 0.423167i
\(656\) 0.0553856 0.0959306i 0.00216244 0.00374546i
\(657\) 0 0
\(658\) 20.3753 8.86024i 0.794312 0.345408i
\(659\) 1.25809 0.0490083 0.0245041 0.999700i \(-0.492199\pi\)
0.0245041 + 0.999700i \(0.492199\pi\)
\(660\) 0 0
\(661\) −19.0453 32.9875i −0.740778 1.28307i −0.952141 0.305658i \(-0.901124\pi\)
0.211363 0.977408i \(-0.432210\pi\)
\(662\) −7.27038 12.5927i −0.282571 0.489428i
\(663\) 0 0
\(664\) −14.2335 −0.552369
\(665\) 6.22583 + 14.3171i 0.241427 + 0.555194i
\(666\) 0 0
\(667\) −8.49463 4.90437i −0.328913 0.189898i
\(668\) 3.67328 + 6.36230i 0.142123 + 0.246165i
\(669\) 0 0
\(670\) 19.2331 + 11.1042i 0.743038 + 0.428993i
\(671\) −3.44870 + 35.1406i −0.133136 + 1.35659i
\(672\) 0 0
\(673\) 19.4116i 0.748263i 0.927376 + 0.374131i \(0.122059\pi\)
−0.927376 + 0.374131i \(0.877941\pi\)
\(674\) 17.3604 + 10.0230i 0.668696 + 0.386072i
\(675\) 0 0
\(676\) −1.37389 2.37965i −0.0528420 0.0915250i
\(677\) 5.25697 9.10535i 0.202042 0.349947i −0.747144 0.664662i \(-0.768576\pi\)
0.949186 + 0.314715i \(0.101909\pi\)
\(678\) 0 0
\(679\) 46.5055 + 5.29706i 1.78472 + 0.203283i
\(680\) 11.5129i 0.441501i
\(681\) 0 0
\(682\) 9.82939 + 21.6739i 0.376387 + 0.829935i
\(683\) 37.1706 21.4605i 1.42230 0.821163i 0.425800 0.904817i \(-0.359993\pi\)
0.996495 + 0.0836546i \(0.0266593\pi\)
\(684\) 0 0
\(685\) −21.8926 −0.836474
\(686\) −14.0817 + 12.0294i −0.537642 + 0.459283i
\(687\) 0 0
\(688\) −3.64090 2.10208i −0.138808 0.0801409i
\(689\) 19.0965 + 33.0761i 0.727519 + 1.26010i
\(690\) 0 0
\(691\) 23.5279 40.7515i 0.895043 1.55026i 0.0612926 0.998120i \(-0.480478\pi\)
0.833751 0.552141i \(-0.186189\pi\)
\(692\) −0.655347 −0.0249126
\(693\) 0 0
\(694\) −12.0889 −0.458887
\(695\) 4.34823 7.53135i 0.164938 0.285680i
\(696\) 0 0
\(697\) 0.228056 + 0.395005i 0.00863825 + 0.0149619i
\(698\) −4.26527 2.46255i −0.161443 0.0932091i
\(699\) 0 0
\(700\) −4.43422 + 5.99292i −0.167598 + 0.226511i
\(701\) −1.94709 −0.0735406 −0.0367703 0.999324i \(-0.511707\pi\)
−0.0367703 + 0.999324i \(0.511707\pi\)
\(702\) 0 0
\(703\) −16.8332 + 9.71865i −0.634876 + 0.366546i
\(704\) 1.36985 + 3.02052i 0.0516280 + 0.113840i
\(705\) 0 0
\(706\) 9.56093i 0.359830i
\(707\) −0.246898 0.567774i −0.00928555 0.0213534i
\(708\) 0 0
\(709\) −11.4549 + 19.8405i −0.430199 + 0.745126i −0.996890 0.0788042i \(-0.974890\pi\)
0.566691 + 0.823930i \(0.308223\pi\)
\(710\) −15.5074 26.8596i −0.581982 1.00802i
\(711\) 0 0
\(712\) 10.3472 + 5.97394i 0.387776 + 0.223883i
\(713\) 7.47996i 0.280127i
\(714\) 0 0
\(715\) 29.5505 + 2.90008i 1.10512 + 0.108457i
\(716\) 3.55106 + 2.05021i 0.132709 + 0.0766199i
\(717\) 0 0
\(718\) −4.14103 7.17248i −0.154542 0.267674i
\(719\) 1.87531 + 1.08271i 0.0699372 + 0.0403782i 0.534561 0.845130i \(-0.320477\pi\)
−0.464624 + 0.885508i \(0.653810\pi\)
\(720\) 0 0
\(721\) 19.7400 26.6790i 0.735157 0.993577i
\(722\) −14.5460 −0.541346
\(723\) 0 0
\(724\) 5.50322 + 9.53186i 0.204526 + 0.354249i
\(725\) 13.2568 + 22.9615i 0.492345 + 0.852767i
\(726\) 0 0
\(727\) 19.8670 0.736825 0.368412 0.929662i \(-0.379901\pi\)
0.368412 + 0.929662i \(0.379901\pi\)
\(728\) −0.958715 + 8.41703i −0.0355323 + 0.311956i
\(729\) 0 0
\(730\) 8.82788 15.2903i 0.326734 0.565921i
\(731\) 14.9918 8.65553i 0.554493 0.320137i
\(732\) 0 0
\(733\) −31.7695 18.3421i −1.17343 0.677483i −0.218948 0.975737i \(-0.570262\pi\)
−0.954487 + 0.298254i \(0.903596\pi\)
\(734\) 37.3838 1.37986
\(735\) 0 0
\(736\) 1.04242i 0.0384243i
\(737\) 15.3371 21.4186i 0.564948 0.788963i
\(738\) 0 0
\(739\) −31.5162 + 18.1959i −1.15934 + 0.669346i −0.951146 0.308742i \(-0.900092\pi\)
−0.208195 + 0.978087i \(0.566759\pi\)
\(740\) −22.3014 12.8757i −0.819816 0.473321i
\(741\) 0 0
\(742\) −3.57154 + 31.3563i −0.131115 + 1.15113i
\(743\) 0.143528 0.00526553 0.00263276 0.999997i \(-0.499162\pi\)
0.00263276 + 0.999997i \(0.499162\pi\)
\(744\) 0 0
\(745\) 19.7850 11.4229i 0.724867 0.418502i
\(746\) 20.6889 11.9447i 0.757474 0.437328i
\(747\) 0 0
\(748\) −13.5913 1.33385i −0.496947 0.0487704i
\(749\) 20.6009 27.8425i 0.752741 1.01734i
\(750\) 0 0
\(751\) 2.63144 4.55779i 0.0960226 0.166316i −0.814012 0.580848i \(-0.802721\pi\)
0.910035 + 0.414532i \(0.136055\pi\)
\(752\) 7.27267 4.19888i 0.265207 0.153117i
\(753\) 0 0
\(754\) 26.0921 + 15.0643i 0.950217 + 0.548608i
\(755\) 19.1499 0.696936
\(756\) 0 0
\(757\) −13.6449 −0.495932 −0.247966 0.968769i \(-0.579762\pi\)
−0.247966 + 0.968769i \(0.579762\pi\)
\(758\) 8.99630 15.5820i 0.326760 0.565965i
\(759\) 0 0
\(760\) 2.95043 + 5.11029i 0.107023 + 0.185370i
\(761\) 14.3603 24.8727i 0.520559 0.901635i −0.479155 0.877730i \(-0.659057\pi\)
0.999714 0.0239048i \(-0.00760986\pi\)
\(762\) 0 0
\(763\) 15.7866 6.86483i 0.571513 0.248523i
\(764\) 21.7465i 0.786763i
\(765\) 0 0
\(766\) 14.6369 8.45064i 0.528854 0.305334i
\(767\) −11.7380 20.3309i −0.423836 0.734106i
\(768\) 0 0
\(769\) 40.9742i 1.47757i 0.673943 + 0.738783i \(0.264599\pi\)
−0.673943 + 0.738783i \(0.735401\pi\)
\(770\) 18.2035 + 16.4499i 0.656007 + 0.592814i
\(771\) 0 0
\(772\) −19.3131 11.1504i −0.695094 0.401313i
\(773\) 9.44578 5.45352i 0.339741 0.196150i −0.320416 0.947277i \(-0.603823\pi\)
0.660158 + 0.751127i \(0.270490\pi\)
\(774\) 0 0
\(775\) −10.1094 + 17.5100i −0.363140 + 0.628977i
\(776\) 17.6911 0.635073
\(777\) 0 0
\(778\) 10.6246i 0.380911i
\(779\) −0.202457 0.116888i −0.00725376 0.00418796i
\(780\) 0 0
\(781\) −33.5050 + 15.1950i −1.19890 + 0.543719i
\(782\) 3.71724 + 2.14615i 0.132928 + 0.0767462i
\(783\) 0 0
\(784\) −4.77365 + 5.11979i −0.170487 + 0.182850i
\(785\) 22.6104i 0.807001i
\(786\) 0 0
\(787\) −16.7122 + 9.64880i −0.595726 + 0.343943i −0.767358 0.641219i \(-0.778429\pi\)
0.171632 + 0.985161i \(0.445096\pi\)
\(788\) 5.50179 + 9.52937i 0.195993 + 0.339470i
\(789\) 0 0
\(790\) −40.1452 −1.42830
\(791\) 0.261026 2.29167i 0.00928102 0.0814826i
\(792\) 0 0
\(793\) −17.0441 + 29.5212i −0.605253 + 1.04833i
\(794\) −11.4791 19.8824i −0.407379 0.705600i
\(795\) 0 0
\(796\) −8.22506 + 14.2462i −0.291529 + 0.504944i
\(797\) 23.8010i 0.843075i −0.906811 0.421538i \(-0.861491\pi\)
0.906811 0.421538i \(-0.138509\pi\)
\(798\) 0 0
\(799\) 34.5787i 1.22331i
\(800\) −1.40887 + 2.44023i −0.0498109 + 0.0862751i
\(801\) 0 0
\(802\) −8.28001 + 4.78047i −0.292377 + 0.168804i
\(803\) −17.0278 12.1930i −0.600899 0.430282i
\(804\) 0 0
\(805\) −3.07515 7.07173i −0.108385 0.249246i
\(806\) 22.9754i 0.809275i
\(807\) 0 0
\(808\) −0.117005 0.202659i −0.00411623 0.00712952i
\(809\) −10.7545 18.6274i −0.378109 0.654905i 0.612678 0.790333i \(-0.290092\pi\)
−0.990787 + 0.135428i \(0.956759\pi\)
\(810\) 0 0
\(811\) 52.4205i 1.84073i 0.391059 + 0.920366i \(0.372109\pi\)
−0.391059 + 0.920366i \(0.627891\pi\)
\(812\) 9.92776 + 22.8302i 0.348396 + 0.801183i
\(813\) 0 0
\(814\) −17.7839 + 24.8356i −0.623324 + 0.870487i
\(815\) 3.30455 1.90788i 0.115753 0.0668302i
\(816\) 0 0
\(817\) −4.43632 + 7.68394i −0.155207 + 0.268827i
\(818\) 13.1069i 0.458273i
\(819\) 0 0
\(820\) 0.309718i 0.0108158i
\(821\) 24.4907 42.4191i 0.854731 1.48044i −0.0221630 0.999754i \(-0.507055\pi\)
0.876894 0.480683i \(-0.159611\pi\)
\(822\) 0 0
\(823\) −3.61437 6.26027i −0.125989 0.218219i 0.796130 0.605126i \(-0.206877\pi\)
−0.922119 + 0.386906i \(0.873544\pi\)
\(824\) 6.27192 10.8633i 0.218493 0.378441i
\(825\) 0 0
\(826\) 2.19532 19.2738i 0.0763849 0.670620i
\(827\) −45.2699 −1.57419 −0.787095 0.616832i \(-0.788416\pi\)
−0.787095 + 0.616832i \(0.788416\pi\)
\(828\) 0 0
\(829\) 24.5067 + 42.4468i 0.851152 + 1.47424i 0.880169 + 0.474660i \(0.157429\pi\)
−0.0290174 + 0.999579i \(0.509238\pi\)
\(830\) −34.4655 + 19.8987i −1.19631 + 0.690692i
\(831\) 0 0
\(832\) 3.20191i 0.111006i
\(833\) −8.42895 27.5633i −0.292046 0.955011i
\(834\) 0 0
\(835\) 17.7891 + 10.2706i 0.615618 + 0.355427i
\(836\) 6.37465 2.89099i 0.220472 0.0999869i
\(837\) 0 0
\(838\) 3.90905 + 2.25689i 0.135036 + 0.0779631i
\(839\) 2.44258i 0.0843273i 0.999111 + 0.0421637i \(0.0134251\pi\)
−0.999111 + 0.0421637i \(0.986575\pi\)
\(840\) 0 0
\(841\) 59.5398 2.05309
\(842\) −18.6594 + 32.3190i −0.643045 + 1.11379i
\(843\) 0 0
\(844\) −0.535916 + 0.309411i −0.0184470 + 0.0106504i
\(845\) −6.65355 3.84143i −0.228889 0.132149i
\(846\) 0 0
\(847\) 21.5285 19.5838i 0.739728 0.672906i
\(848\) 11.9282i 0.409616i
\(849\) 0 0
\(850\) −5.80117 10.0479i −0.198978 0.344641i
\(851\) 8.31450 4.80038i 0.285017 0.164555i
\(852\) 0 0
\(853\) 37.5500i 1.28569i 0.765997 + 0.642844i \(0.222246\pi\)
−0.765997 + 0.642844i \(0.777754\pi\)
\(854\) −25.8306 + 11.2325i −0.883906 + 0.384368i
\(855\) 0 0
\(856\) 6.54545 11.3370i 0.223719 0.387492i
\(857\) 21.4068 + 37.0777i 0.731243 + 1.26655i 0.956352 + 0.292217i \(0.0943929\pi\)
−0.225109 + 0.974334i \(0.572274\pi\)
\(858\) 0 0
\(859\) −5.43313 + 9.41045i −0.185376 + 0.321080i −0.943703 0.330794i \(-0.892684\pi\)
0.758327 + 0.651874i \(0.226017\pi\)
\(860\) −11.7549 −0.400839
\(861\) 0 0
\(862\) 27.6987 0.943422
\(863\) 0.401363 + 0.231727i 0.0136626 + 0.00788808i 0.506816 0.862054i \(-0.330822\pi\)
−0.493153 + 0.869943i \(0.664156\pi\)
\(864\) 0 0
\(865\) −1.58687 + 0.916183i −0.0539554 + 0.0311511i
\(866\) 4.09094 7.08571i 0.139016 0.240782i
\(867\) 0 0
\(868\) −11.2920 + 15.2614i −0.383276 + 0.518005i
\(869\) −4.65109 + 47.3924i −0.157777 + 1.60768i
\(870\) 0 0
\(871\) 22.0250 12.7162i 0.746290 0.430871i
\(872\) 5.63480 3.25325i 0.190818 0.110169i
\(873\) 0 0
\(874\) −2.19998 −0.0744155
\(875\) 1.82696 16.0398i 0.0617625 0.542243i
\(876\) 0 0
\(877\) −15.8492 9.15055i −0.535190 0.308992i 0.207937 0.978142i \(-0.433325\pi\)
−0.743127 + 0.669150i \(0.766658\pi\)
\(878\) 1.16163 0.670668i 0.0392031 0.0226339i
\(879\) 0 0
\(880\) 7.53969 + 5.39890i 0.254163 + 0.181997i
\(881\) 26.3700i 0.888426i −0.895921 0.444213i \(-0.853483\pi\)
0.895921 0.444213i \(-0.146517\pi\)
\(882\) 0 0
\(883\) −10.2737 −0.345738 −0.172869 0.984945i \(-0.555304\pi\)
−0.172869 + 0.984945i \(0.555304\pi\)
\(884\) −11.4179 6.59211i −0.384024 0.221717i
\(885\) 0 0
\(886\) 23.5122 13.5748i 0.789909 0.456054i
\(887\) 8.89664 15.4094i 0.298720 0.517398i −0.677123 0.735870i \(-0.736774\pi\)
0.975843 + 0.218471i \(0.0701070\pi\)
\(888\) 0 0
\(889\) 2.74224 24.0754i 0.0919716 0.807464i
\(890\) 33.4065 1.11979
\(891\) 0 0
\(892\) −5.17766 8.96797i −0.173361 0.300270i
\(893\) −8.86152 15.3486i −0.296539 0.513621i
\(894\) 0 0
\(895\) 11.4648 0.383228
\(896\) −1.57368 + 2.12686i −0.0525730 + 0.0710533i
\(897\) 0 0
\(898\) −32.3691 18.6883i −1.08017 0.623636i
\(899\) 33.7594 + 58.4729i 1.12594 + 1.95018i
\(900\) 0 0
\(901\) −42.5355 24.5579i −1.41706 0.818141i
\(902\) −0.365630 0.0358829i −0.0121741 0.00119477i
\(903\) 0 0
\(904\) 0.871772i 0.0289947i
\(905\) 26.6513 + 15.3871i 0.885918 + 0.511485i
\(906\) 0 0
\(907\) −16.7926 29.0857i −0.557590 0.965775i −0.997697 0.0678291i \(-0.978393\pi\)
0.440107 0.897945i \(-0.354941\pi\)
\(908\) −6.46564 + 11.1988i −0.214570 + 0.371646i
\(909\) 0 0
\(910\) 9.44564 + 21.7215i 0.313120 + 0.720061i
\(911\) 2.04771i 0.0678437i −0.999424 0.0339218i \(-0.989200\pi\)
0.999424 0.0339218i \(-0.0107997\pi\)
\(912\) 0 0
\(913\) 19.4978 + 42.9927i 0.645282 + 1.42285i
\(914\) 20.4149 11.7865i 0.675263 0.389864i
\(915\) 0 0
\(916\) 5.47697 0.180964
\(917\) −12.1910 + 16.4763i −0.402582 + 0.544096i
\(918\) 0 0
\(919\) −37.2849 21.5264i −1.22992 0.710092i −0.262903 0.964822i \(-0.584680\pi\)
−0.967012 + 0.254731i \(0.918013\pi\)
\(920\) −1.45732 2.52415i −0.0480464 0.0832188i
\(921\) 0 0
\(922\) −19.1570 + 33.1809i −0.630902 + 1.09275i
\(923\) −35.5171 −1.16906
\(924\) 0 0
\(925\) −25.9514 −0.853277
\(926\) −4.90212 + 8.49072i −0.161094 + 0.279022i
\(927\) 0 0
\(928\) 4.70478 + 8.14891i 0.154442 + 0.267501i
\(929\) −11.1033 6.41047i −0.364286 0.210321i 0.306673 0.951815i \(-0.400784\pi\)
−0.670959 + 0.741494i \(0.734117\pi\)
\(930\) 0 0
\(931\) 10.8051 + 10.0745i 0.354122 + 0.330180i
\(932\) 27.5177 0.901372
\(933\) 0 0
\(934\) −10.8457 + 6.26175i −0.354881 + 0.204891i
\(935\) −34.7750 + 15.7709i −1.13726 + 0.515765i
\(936\) 0 0
\(937\) 47.4540i 1.55025i 0.631805 + 0.775127i \(0.282314\pi\)
−0.631805 + 0.775127i \(0.717686\pi\)
\(938\) 20.8798 + 2.37825i 0.681751 + 0.0776527i
\(939\) 0 0
\(940\) 11.7402 20.3345i 0.382922 0.663240i
\(941\) 5.71859 + 9.90490i 0.186421 + 0.322890i 0.944054 0.329790i \(-0.106978\pi\)
−0.757634 + 0.652680i \(0.773645\pi\)
\(942\) 0 0
\(943\) 0.100000 + 0.0577353i 0.00325646 + 0.00188012i
\(944\) 7.33191i 0.238633i
\(945\) 0 0
\(946\) −1.36188 + 13.8769i −0.0442786 + 0.451178i
\(947\) 4.81239 + 2.77843i 0.156382 + 0.0902869i 0.576149 0.817345i \(-0.304555\pi\)
−0.419767 + 0.907632i \(0.637888\pi\)
\(948\) 0 0
\(949\) −10.1094 17.5100i −0.328165 0.568398i
\(950\) 5.14998 + 2.97334i 0.167087 + 0.0964679i
\(951\) 0 0
\(952\) −4.34438 9.99047i −0.140802 0.323793i
\(953\) 25.6550 0.831045 0.415523 0.909583i \(-0.363599\pi\)
0.415523 + 0.909583i \(0.363599\pi\)
\(954\) 0 0
\(955\) −30.4019 52.6576i −0.983782 1.70396i
\(956\) 6.66695 + 11.5475i 0.215625 + 0.373473i
\(957\) 0 0
\(958\) 15.6839 0.506725
\(959\) −18.9976 + 8.26113i −0.613464 + 0.266766i
\(960\) 0 0
\(961\) −10.2442 + 17.7435i −0.330459 + 0.572372i
\(962\) −25.5388 + 14.7448i −0.823404 + 0.475393i
\(963\) 0 0
\(964\) −15.7035 9.06641i −0.505775 0.292009i
\(965\) −62.3537 −2.00724
\(966\) 0 0
\(967\) 44.1653i 1.42026i −0.704071 0.710130i \(-0.748636\pi\)
0.704071 0.710130i \(-0.251364\pi\)
\(968\) 7.24705 8.27528i 0.232929 0.265978i
\(969\) 0 0
\(970\) 42.8376 24.7323i 1.37543 0.794107i
\(971\) −47.3097 27.3143i −1.51824 0.876557i −0.999770 0.0214630i \(-0.993168\pi\)
−0.518472 0.855094i \(-0.673499\pi\)
\(972\) 0 0
\(973\) 0.931285 8.17621i 0.0298556 0.262117i
\(974\) 38.0525 1.21928
\(975\) 0 0
\(976\) −9.21987 + 5.32310i −0.295121 + 0.170388i
\(977\) 0.164978 0.0952499i 0.00527810 0.00304731i −0.497359 0.867545i \(-0.665697\pi\)
0.502637 + 0.864498i \(0.332363\pi\)
\(978\) 0 0
\(979\) 3.87036 39.4371i 0.123697 1.26042i
\(980\) −4.40150 + 19.0708i −0.140601 + 0.609195i
\(981\) 0 0
\(982\) −1.81783 + 3.14857i −0.0580091 + 0.100475i
\(983\) −37.5517 + 21.6805i −1.19771 + 0.691500i −0.960045 0.279847i \(-0.909716\pi\)
−0.237668 + 0.971346i \(0.576383\pi\)
\(984\) 0 0
\(985\) 26.6443 + 15.3831i 0.848959 + 0.490147i
\(986\) −38.7449 −1.23389
\(987\) 0 0
\(988\) 6.75746 0.214984
\(989\) 2.19125 3.79536i 0.0696778 0.120686i
\(990\) 0 0
\(991\) −14.8052 25.6433i −0.470302 0.814588i 0.529121 0.848546i \(-0.322522\pi\)
−0.999423 + 0.0339589i \(0.989188\pi\)
\(992\) −3.58777 + 6.21420i −0.113912 + 0.197301i
\(993\) 0 0
\(994\) −23.5921 17.4560i −0.748296 0.553672i
\(995\) 45.9949i 1.45814i
\(996\) 0 0
\(997\) 48.9359 28.2531i 1.54981 0.894786i 0.551659 0.834070i \(-0.313995\pi\)
0.998155 0.0607158i \(-0.0193383\pi\)
\(998\) −9.18656 15.9116i −0.290795 0.503673i
\(999\) 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 1386.2.ba.b.989.2 yes 32
3.2 odd 2 1386.2.ba.a.989.15 yes 32
7.4 even 3 inner 1386.2.ba.b.1187.15 yes 32
11.10 odd 2 1386.2.ba.a.989.2 32
21.11 odd 6 1386.2.ba.a.1187.2 yes 32
33.32 even 2 inner 1386.2.ba.b.989.15 yes 32
77.32 odd 6 1386.2.ba.a.1187.15 yes 32
231.32 even 6 inner 1386.2.ba.b.1187.2 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1386.2.ba.a.989.2 32 11.10 odd 2
1386.2.ba.a.989.15 yes 32 3.2 odd 2
1386.2.ba.a.1187.2 yes 32 21.11 odd 6
1386.2.ba.a.1187.15 yes 32 77.32 odd 6
1386.2.ba.b.989.2 yes 32 1.1 even 1 trivial
1386.2.ba.b.989.15 yes 32 33.32 even 2 inner
1386.2.ba.b.1187.2 yes 32 231.32 even 6 inner
1386.2.ba.b.1187.15 yes 32 7.4 even 3 inner