Properties

Label 2070.2.j.i.323.4
Level $2070$
Weight $2$
Character 2070.323
Analytic conductor $16.529$
Analytic rank $0$
Dimension $16$
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] = [2070,2,Mod(323,2070)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2070, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2070.323");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2070.j (of order \(4\), 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: \(16.5290332184\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 28x^{14} + 290x^{12} + 1396x^{10} + 3263x^{8} + 3508x^{6} + 1442x^{4} + 128x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 323.4
Root \(-0.328628i\) of defining polynomial
Character \(\chi\) \(=\) 2070.323
Dual form 2070.2.j.i.737.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(1.80260 - 1.32312i) q^{5} +(0.949464 - 0.949464i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(1.80260 - 1.32312i) q^{5} +(0.949464 - 0.949464i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.21021 - 0.339045i) q^{10} -2.64623i q^{11} +(2.00000 + 2.00000i) q^{13} -1.34274 q^{14} -1.00000 q^{16} +(-4.94794 - 4.94794i) q^{17} -2.42043i q^{19} +(1.32312 + 1.80260i) q^{20} +(-1.87117 + 1.87117i) q^{22} +(-0.707107 + 0.707107i) q^{23} +(1.49872 - 4.77010i) q^{25} -2.82843i q^{26} +(0.949464 + 0.949464i) q^{28} +0.383781 q^{29} -6.99745 q^{31} +(0.707107 + 0.707107i) q^{32} +6.99745i q^{34} +(0.455250 - 2.96775i) q^{35} +(-0.820634 + 0.820634i) q^{37} +(-1.71150 + 1.71150i) q^{38} +(0.339045 - 2.21021i) q^{40} -5.41240i q^{41} +(-2.82063 - 2.82063i) q^{43} +2.64623 q^{44} +1.00000 q^{46} +(2.19098 + 2.19098i) q^{47} +5.19704i q^{49} +(-4.43273 + 2.31321i) q^{50} +(-2.00000 + 2.00000i) q^{52} +(7.11469 - 7.11469i) q^{53} +(-3.50128 - 4.77010i) q^{55} -1.34274i q^{56} +(-0.271374 - 0.271374i) q^{58} +1.93732 q^{59} -8.31936 q^{61} +(4.94794 + 4.94794i) q^{62} -1.00000i q^{64} +(6.25143 + 0.958963i) q^{65} +(-2.59724 + 2.59724i) q^{67} +(4.94794 - 4.94794i) q^{68} +(-2.42043 + 1.77661i) q^{70} -8.76755i q^{71} +(8.26882 + 8.26882i) q^{73} +1.16055 q^{74} +2.42043 q^{76} +(-2.51250 - 2.51250i) q^{77} +12.2526i q^{79} +(-1.80260 + 1.32312i) q^{80} +(-3.82714 + 3.82714i) q^{82} +(5.56115 - 5.56115i) q^{83} +(-15.4659 - 2.37245i) q^{85} +3.98898i q^{86} +(-1.87117 - 1.87117i) q^{88} -5.34093 q^{89} +3.79785 q^{91} +(-0.707107 - 0.707107i) q^{92} -3.09852i q^{94} +(-3.20251 - 4.36306i) q^{95} +(4.46841 - 4.46841i) q^{97} +(3.67486 - 3.67486i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{10} + 32 q^{13} - 16 q^{16} - 24 q^{25} - 16 q^{31} + 32 q^{37} + 4 q^{40} + 16 q^{46} - 32 q^{52} - 104 q^{55} + 8 q^{58} - 40 q^{61} + 72 q^{67} + 24 q^{70} + 24 q^{73} - 24 q^{76} - 8 q^{82} - 8 q^{85} - 72 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times\).

\(n\) \(461\) \(1657\) \(1891\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 0.707107i −0.500000 0.500000i
\(3\) 0 0
\(4\) 1.00000i 0.500000i
\(5\) 1.80260 1.32312i 0.806147 0.591716i
\(6\) 0 0
\(7\) 0.949464 0.949464i 0.358864 0.358864i −0.504530 0.863394i \(-0.668334\pi\)
0.863394 + 0.504530i \(0.168334\pi\)
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 0 0
\(10\) −2.21021 0.339045i −0.698931 0.107215i
\(11\) 2.64623i 0.797870i −0.916979 0.398935i \(-0.869380\pi\)
0.916979 0.398935i \(-0.130620\pi\)
\(12\) 0 0
\(13\) 2.00000 + 2.00000i 0.554700 + 0.554700i 0.927794 0.373094i \(-0.121703\pi\)
−0.373094 + 0.927794i \(0.621703\pi\)
\(14\) −1.34274 −0.358864
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) −4.94794 4.94794i −1.20005 1.20005i −0.974150 0.225902i \(-0.927467\pi\)
−0.225902 0.974150i \(-0.572533\pi\)
\(18\) 0 0
\(19\) 2.42043i 0.555285i −0.960685 0.277642i \(-0.910447\pi\)
0.960685 0.277642i \(-0.0895530\pi\)
\(20\) 1.32312 + 1.80260i 0.295858 + 0.403073i
\(21\) 0 0
\(22\) −1.87117 + 1.87117i −0.398935 + 0.398935i
\(23\) −0.707107 + 0.707107i −0.147442 + 0.147442i
\(24\) 0 0
\(25\) 1.49872 4.77010i 0.299745 0.954019i
\(26\) 2.82843i 0.554700i
\(27\) 0 0
\(28\) 0.949464 + 0.949464i 0.179432 + 0.179432i
\(29\) 0.383781 0.0712664 0.0356332 0.999365i \(-0.488655\pi\)
0.0356332 + 0.999365i \(0.488655\pi\)
\(30\) 0 0
\(31\) −6.99745 −1.25678 −0.628389 0.777899i \(-0.716285\pi\)
−0.628389 + 0.777899i \(0.716285\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) 0 0
\(34\) 6.99745i 1.20005i
\(35\) 0.455250 2.96775i 0.0769514 0.501642i
\(36\) 0 0
\(37\) −0.820634 + 0.820634i −0.134911 + 0.134911i −0.771338 0.636426i \(-0.780412\pi\)
0.636426 + 0.771338i \(0.280412\pi\)
\(38\) −1.71150 + 1.71150i −0.277642 + 0.277642i
\(39\) 0 0
\(40\) 0.339045 2.21021i 0.0536077 0.349466i
\(41\) 5.41240i 0.845275i −0.906299 0.422637i \(-0.861104\pi\)
0.906299 0.422637i \(-0.138896\pi\)
\(42\) 0 0
\(43\) −2.82063 2.82063i −0.430143 0.430143i 0.458534 0.888677i \(-0.348375\pi\)
−0.888677 + 0.458534i \(0.848375\pi\)
\(44\) 2.64623 0.398935
\(45\) 0 0
\(46\) 1.00000 0.147442
\(47\) 2.19098 + 2.19098i 0.319588 + 0.319588i 0.848609 0.529021i \(-0.177441\pi\)
−0.529021 + 0.848609i \(0.677441\pi\)
\(48\) 0 0
\(49\) 5.19704i 0.742434i
\(50\) −4.43273 + 2.31321i −0.626882 + 0.327137i
\(51\) 0 0
\(52\) −2.00000 + 2.00000i −0.277350 + 0.277350i
\(53\) 7.11469 7.11469i 0.977278 0.977278i −0.0224692 0.999748i \(-0.507153\pi\)
0.999748 + 0.0224692i \(0.00715276\pi\)
\(54\) 0 0
\(55\) −3.50128 4.77010i −0.472112 0.643200i
\(56\) 1.34274i 0.179432i
\(57\) 0 0
\(58\) −0.271374 0.271374i −0.0356332 0.0356332i
\(59\) 1.93732 0.252218 0.126109 0.992016i \(-0.459751\pi\)
0.126109 + 0.992016i \(0.459751\pi\)
\(60\) 0 0
\(61\) −8.31936 −1.06518 −0.532592 0.846372i \(-0.678782\pi\)
−0.532592 + 0.846372i \(0.678782\pi\)
\(62\) 4.94794 + 4.94794i 0.628389 + 0.628389i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) 6.25143 + 0.958963i 0.775395 + 0.118945i
\(66\) 0 0
\(67\) −2.59724 + 2.59724i −0.317304 + 0.317304i −0.847731 0.530427i \(-0.822032\pi\)
0.530427 + 0.847731i \(0.322032\pi\)
\(68\) 4.94794 4.94794i 0.600026 0.600026i
\(69\) 0 0
\(70\) −2.42043 + 1.77661i −0.289297 + 0.212345i
\(71\) 8.76755i 1.04052i −0.854009 0.520258i \(-0.825836\pi\)
0.854009 0.520258i \(-0.174164\pi\)
\(72\) 0 0
\(73\) 8.26882 + 8.26882i 0.967792 + 0.967792i 0.999497 0.0317050i \(-0.0100937\pi\)
−0.0317050 + 0.999497i \(0.510094\pi\)
\(74\) 1.16055 0.134911
\(75\) 0 0
\(76\) 2.42043 0.277642
\(77\) −2.51250 2.51250i −0.286326 0.286326i
\(78\) 0 0
\(79\) 12.2526i 1.37852i 0.724514 + 0.689260i \(0.242064\pi\)
−0.724514 + 0.689260i \(0.757936\pi\)
\(80\) −1.80260 + 1.32312i −0.201537 + 0.147929i
\(81\) 0 0
\(82\) −3.82714 + 3.82714i −0.422637 + 0.422637i
\(83\) 5.56115 5.56115i 0.610416 0.610416i −0.332638 0.943054i \(-0.607939\pi\)
0.943054 + 0.332638i \(0.107939\pi\)
\(84\) 0 0
\(85\) −15.4659 2.37245i −1.67751 0.257328i
\(86\) 3.98898i 0.430143i
\(87\) 0 0
\(88\) −1.87117 1.87117i −0.199467 0.199467i
\(89\) −5.34093 −0.566137 −0.283069 0.959100i \(-0.591352\pi\)
−0.283069 + 0.959100i \(0.591352\pi\)
\(90\) 0 0
\(91\) 3.79785 0.398123
\(92\) −0.707107 0.707107i −0.0737210 0.0737210i
\(93\) 0 0
\(94\) 3.09852i 0.319588i
\(95\) −3.20251 4.36306i −0.328571 0.447641i
\(96\) 0 0
\(97\) 4.46841 4.46841i 0.453698 0.453698i −0.442882 0.896580i \(-0.646044\pi\)
0.896580 + 0.442882i \(0.146044\pi\)
\(98\) 3.67486 3.67486i 0.371217 0.371217i
\(99\) 0 0
\(100\) 4.77010 + 1.49872i 0.477010 + 0.149872i
\(101\) 4.62281i 0.459987i 0.973192 + 0.229993i \(0.0738705\pi\)
−0.973192 + 0.229993i \(0.926130\pi\)
\(102\) 0 0
\(103\) −0.949464 0.949464i −0.0935534 0.0935534i 0.658781 0.752335i \(-0.271072\pi\)
−0.752335 + 0.658781i \(0.771072\pi\)
\(104\) 2.82843 0.277350
\(105\) 0 0
\(106\) −10.0617 −0.977278
\(107\) 1.18839 + 1.18839i 0.114886 + 0.114886i 0.762213 0.647326i \(-0.224113\pi\)
−0.647326 + 0.762213i \(0.724113\pi\)
\(108\) 0 0
\(109\) 13.5138i 1.29439i −0.762324 0.647196i \(-0.775942\pi\)
0.762324 0.647196i \(-0.224058\pi\)
\(110\) −0.897192 + 5.84874i −0.0855439 + 0.557656i
\(111\) 0 0
\(112\) −0.949464 + 0.949464i −0.0897159 + 0.0897159i
\(113\) 3.74814 3.74814i 0.352595 0.352595i −0.508479 0.861074i \(-0.669792\pi\)
0.861074 + 0.508479i \(0.169792\pi\)
\(114\) 0 0
\(115\) −0.339045 + 2.21021i −0.0316161 + 0.206104i
\(116\) 0.383781i 0.0356332i
\(117\) 0 0
\(118\) −1.36989 1.36989i −0.126109 0.126109i
\(119\) −9.39578 −0.861310
\(120\) 0 0
\(121\) 3.99745 0.363404
\(122\) 5.88267 + 5.88267i 0.532592 + 0.532592i
\(123\) 0 0
\(124\) 6.99745i 0.628389i
\(125\) −3.60980 10.5816i −0.322870 0.946443i
\(126\) 0 0
\(127\) −6.79785 + 6.79785i −0.603212 + 0.603212i −0.941164 0.337951i \(-0.890266\pi\)
0.337951 + 0.941164i \(0.390266\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) 0 0
\(130\) −3.74234 5.09852i −0.328225 0.447170i
\(131\) 3.08769i 0.269772i 0.990861 + 0.134886i \(0.0430669\pi\)
−0.990861 + 0.134886i \(0.956933\pi\)
\(132\) 0 0
\(133\) −2.29811 2.29811i −0.199271 0.199271i
\(134\) 3.67305 0.317304
\(135\) 0 0
\(136\) −6.99745 −0.600026
\(137\) 2.43544 + 2.43544i 0.208074 + 0.208074i 0.803448 0.595375i \(-0.202996\pi\)
−0.595375 + 0.803448i \(0.702996\pi\)
\(138\) 0 0
\(139\) 20.9368i 1.77584i −0.460000 0.887919i \(-0.652150\pi\)
0.460000 0.887919i \(-0.347850\pi\)
\(140\) 2.96775 + 0.455250i 0.250821 + 0.0384757i
\(141\) 0 0
\(142\) −6.19959 + 6.19959i −0.520258 + 0.520258i
\(143\) 5.29247 5.29247i 0.442578 0.442578i
\(144\) 0 0
\(145\) 0.691804 0.507788i 0.0574512 0.0421695i
\(146\) 11.6939i 0.967792i
\(147\) 0 0
\(148\) −0.820634 0.820634i −0.0674557 0.0674557i
\(149\) −13.0494 −1.06905 −0.534526 0.845152i \(-0.679510\pi\)
−0.534526 + 0.845152i \(0.679510\pi\)
\(150\) 0 0
\(151\) −11.9394 −0.971613 −0.485806 0.874066i \(-0.661474\pi\)
−0.485806 + 0.874066i \(0.661474\pi\)
\(152\) −1.71150 1.71150i −0.138821 0.138821i
\(153\) 0 0
\(154\) 3.55322i 0.286326i
\(155\) −12.6136 + 9.25844i −1.01315 + 0.743656i
\(156\) 0 0
\(157\) 15.4593 15.4593i 1.23379 1.23379i 0.271294 0.962497i \(-0.412549\pi\)
0.962497 0.271294i \(-0.0874514\pi\)
\(158\) 8.66386 8.66386i 0.689260 0.689260i
\(159\) 0 0
\(160\) 2.21021 + 0.339045i 0.174733 + 0.0268038i
\(161\) 1.34274i 0.105823i
\(162\) 0 0
\(163\) −2.19704 2.19704i −0.172085 0.172085i 0.615810 0.787895i \(-0.288829\pi\)
−0.787895 + 0.615810i \(0.788829\pi\)
\(164\) 5.41240 0.422637
\(165\) 0 0
\(166\) −7.86466 −0.610416
\(167\) 2.05166 + 2.05166i 0.158762 + 0.158762i 0.782018 0.623256i \(-0.214191\pi\)
−0.623256 + 0.782018i \(0.714191\pi\)
\(168\) 0 0
\(169\) 5.00000i 0.384615i
\(170\) 9.25844 + 12.6136i 0.710090 + 0.967418i
\(171\) 0 0
\(172\) 2.82063 2.82063i 0.215071 0.215071i
\(173\) −2.75696 + 2.75696i −0.209608 + 0.209608i −0.804101 0.594493i \(-0.797353\pi\)
0.594493 + 0.804101i \(0.297353\pi\)
\(174\) 0 0
\(175\) −3.10605 5.95202i −0.234795 0.449930i
\(176\) 2.64623i 0.199467i
\(177\) 0 0
\(178\) 3.77661 + 3.77661i 0.283069 + 0.283069i
\(179\) −12.2620 −0.916506 −0.458253 0.888822i \(-0.651525\pi\)
−0.458253 + 0.888822i \(0.651525\pi\)
\(180\) 0 0
\(181\) 3.77661 0.280713 0.140357 0.990101i \(-0.455175\pi\)
0.140357 + 0.990101i \(0.455175\pi\)
\(182\) −2.68549 2.68549i −0.199062 0.199062i
\(183\) 0 0
\(184\) 1.00000i 0.0737210i
\(185\) −0.393479 + 2.56507i −0.0289291 + 0.188588i
\(186\) 0 0
\(187\) −13.0934 + 13.0934i −0.957485 + 0.957485i
\(188\) −2.19098 + 2.19098i −0.159794 + 0.159794i
\(189\) 0 0
\(190\) −0.820634 + 5.34967i −0.0595350 + 0.388106i
\(191\) 17.0094i 1.23075i −0.788233 0.615377i \(-0.789004\pi\)
0.788233 0.615377i \(-0.210996\pi\)
\(192\) 0 0
\(193\) 17.8964 + 17.8964i 1.28821 + 1.28821i 0.935874 + 0.352335i \(0.114612\pi\)
0.352335 + 0.935874i \(0.385388\pi\)
\(194\) −6.31929 −0.453698
\(195\) 0 0
\(196\) −5.19704 −0.371217
\(197\) −2.70850 2.70850i −0.192972 0.192972i 0.604007 0.796979i \(-0.293570\pi\)
−0.796979 + 0.604007i \(0.793570\pi\)
\(198\) 0 0
\(199\) 7.19448i 0.510003i 0.966941 + 0.255002i \(0.0820760\pi\)
−0.966941 + 0.255002i \(0.917924\pi\)
\(200\) −2.31321 4.43273i −0.163569 0.313441i
\(201\) 0 0
\(202\) 3.26882 3.26882i 0.229993 0.229993i
\(203\) 0.364386 0.364386i 0.0255749 0.0255749i
\(204\) 0 0
\(205\) −7.16124 9.75638i −0.500163 0.681415i
\(206\) 1.34274i 0.0935534i
\(207\) 0 0
\(208\) −2.00000 2.00000i −0.138675 0.138675i
\(209\) −6.40502 −0.443045
\(210\) 0 0
\(211\) −0.0685362 −0.00471823 −0.00235911 0.999997i \(-0.500751\pi\)
−0.00235911 + 0.999997i \(0.500751\pi\)
\(212\) 7.11469 + 7.11469i 0.488639 + 0.488639i
\(213\) 0 0
\(214\) 1.68064i 0.114886i
\(215\) −8.81650 1.35244i −0.601280 0.0922358i
\(216\) 0 0
\(217\) −6.64382 + 6.64382i −0.451012 + 0.451012i
\(218\) −9.55573 + 9.55573i −0.647196 + 0.647196i
\(219\) 0 0
\(220\) 4.77010 3.50128i 0.321600 0.236056i
\(221\) 19.7918i 1.33134i
\(222\) 0 0
\(223\) −19.6524 19.6524i −1.31602 1.31602i −0.916895 0.399129i \(-0.869312\pi\)
−0.399129 0.916895i \(-0.630688\pi\)
\(224\) 1.34274 0.0897159
\(225\) 0 0
\(226\) −5.30066 −0.352595
\(227\) −2.83984 2.83984i −0.188487 0.188487i 0.606555 0.795042i \(-0.292551\pi\)
−0.795042 + 0.606555i \(0.792551\pi\)
\(228\) 0 0
\(229\) 4.42554i 0.292448i 0.989252 + 0.146224i \(0.0467120\pi\)
−0.989252 + 0.146224i \(0.953288\pi\)
\(230\) 1.80260 1.32312i 0.118860 0.0872437i
\(231\) 0 0
\(232\) 0.271374 0.271374i 0.0178166 0.0178166i
\(233\) 0.799777 0.799777i 0.0523951 0.0523951i −0.680424 0.732819i \(-0.738204\pi\)
0.732819 + 0.680424i \(0.238204\pi\)
\(234\) 0 0
\(235\) 6.84839 + 1.05054i 0.446740 + 0.0685294i
\(236\) 1.93732i 0.126109i
\(237\) 0 0
\(238\) 6.64382 + 6.64382i 0.430655 + 0.430655i
\(239\) −17.2078 −1.11308 −0.556540 0.830821i \(-0.687871\pi\)
−0.556540 + 0.830821i \(0.687871\pi\)
\(240\) 0 0
\(241\) 5.25511 0.338511 0.169256 0.985572i \(-0.445864\pi\)
0.169256 + 0.985572i \(0.445864\pi\)
\(242\) −2.82662 2.82662i −0.181702 0.181702i
\(243\) 0 0
\(244\) 8.31936i 0.532592i
\(245\) 6.87629 + 9.36817i 0.439310 + 0.598511i
\(246\) 0 0
\(247\) 4.84086 4.84086i 0.308016 0.308016i
\(248\) −4.94794 + 4.94794i −0.314195 + 0.314195i
\(249\) 0 0
\(250\) −4.92978 + 10.0348i −0.311786 + 0.634657i
\(251\) 16.1381i 1.01863i −0.860581 0.509314i \(-0.829899\pi\)
0.860581 0.509314i \(-0.170101\pi\)
\(252\) 0 0
\(253\) 1.87117 + 1.87117i 0.117639 + 0.117639i
\(254\) 9.61362 0.603212
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 21.8720 + 21.8720i 1.36434 + 1.36434i 0.868300 + 0.496040i \(0.165213\pi\)
0.496040 + 0.868300i \(0.334787\pi\)
\(258\) 0 0
\(259\) 1.55832i 0.0968295i
\(260\) −0.958963 + 6.25143i −0.0594724 + 0.387697i
\(261\) 0 0
\(262\) 2.18332 2.18332i 0.134886 0.134886i
\(263\) −19.9541 + 19.9541i −1.23042 + 1.23042i −0.266621 + 0.963801i \(0.585907\pi\)
−0.963801 + 0.266621i \(0.914093\pi\)
\(264\) 0 0
\(265\) 3.41136 22.2385i 0.209558 1.36610i
\(266\) 3.25002i 0.199271i
\(267\) 0 0
\(268\) −2.59724 2.59724i −0.158652 0.158652i
\(269\) −28.0750 −1.71176 −0.855881 0.517172i \(-0.826985\pi\)
−0.855881 + 0.517172i \(0.826985\pi\)
\(270\) 0 0
\(271\) 23.6766 1.43825 0.719126 0.694880i \(-0.244542\pi\)
0.719126 + 0.694880i \(0.244542\pi\)
\(272\) 4.94794 + 4.94794i 0.300013 + 0.300013i
\(273\) 0 0
\(274\) 3.44423i 0.208074i
\(275\) −12.6228 3.96597i −0.761183 0.239157i
\(276\) 0 0
\(277\) −6.55577 + 6.55577i −0.393898 + 0.393898i −0.876074 0.482176i \(-0.839846\pi\)
0.482176 + 0.876074i \(0.339846\pi\)
\(278\) −14.8046 + 14.8046i −0.887919 + 0.887919i
\(279\) 0 0
\(280\) −1.77661 2.42043i −0.106173 0.144648i
\(281\) 20.6150i 1.22979i −0.788610 0.614894i \(-0.789199\pi\)
0.788610 0.614894i \(-0.210801\pi\)
\(282\) 0 0
\(283\) 5.59980 + 5.59980i 0.332873 + 0.332873i 0.853677 0.520803i \(-0.174368\pi\)
−0.520803 + 0.853677i \(0.674368\pi\)
\(284\) 8.76755 0.520258
\(285\) 0 0
\(286\) −7.48468 −0.442578
\(287\) −5.13888 5.13888i −0.303338 0.303338i
\(288\) 0 0
\(289\) 31.9643i 1.88025i
\(290\) −0.848239 0.130119i −0.0498103 0.00764085i
\(291\) 0 0
\(292\) −8.26882 + 8.26882i −0.483896 + 0.483896i
\(293\) 15.4662 15.4662i 0.903548 0.903548i −0.0921935 0.995741i \(-0.529388\pi\)
0.995741 + 0.0921935i \(0.0293878\pi\)
\(294\) 0 0
\(295\) 3.49221 2.56330i 0.203324 0.149241i
\(296\) 1.16055i 0.0674557i
\(297\) 0 0
\(298\) 9.22735 + 9.22735i 0.534526 + 0.534526i
\(299\) −2.82843 −0.163572
\(300\) 0 0
\(301\) −5.35618 −0.308725
\(302\) 8.44241 + 8.44241i 0.485806 + 0.485806i
\(303\) 0 0
\(304\) 2.42043i 0.138821i
\(305\) −14.9965 + 11.0075i −0.858695 + 0.630287i
\(306\) 0 0
\(307\) 7.58575 7.58575i 0.432942 0.432942i −0.456686 0.889628i \(-0.650964\pi\)
0.889628 + 0.456686i \(0.150964\pi\)
\(308\) 2.51250 2.51250i 0.143163 0.143163i
\(309\) 0 0
\(310\) 15.4659 + 2.37245i 0.878402 + 0.134746i
\(311\) 3.89765i 0.221015i 0.993875 + 0.110508i \(0.0352477\pi\)
−0.993875 + 0.110508i \(0.964752\pi\)
\(312\) 0 0
\(313\) 14.9231 + 14.9231i 0.843504 + 0.843504i 0.989313 0.145809i \(-0.0465784\pi\)
−0.145809 + 0.989313i \(0.546578\pi\)
\(314\) −21.8628 −1.23379
\(315\) 0 0
\(316\) −12.2526 −0.689260
\(317\) 19.2202 + 19.2202i 1.07951 + 1.07951i 0.996553 + 0.0829610i \(0.0264377\pi\)
0.0829610 + 0.996553i \(0.473562\pi\)
\(318\) 0 0
\(319\) 1.01558i 0.0568613i
\(320\) −1.32312 1.80260i −0.0739645 0.100768i
\(321\) 0 0
\(322\) 0.949464 0.949464i 0.0529115 0.0529115i
\(323\) −11.9761 + 11.9761i −0.666370 + 0.666370i
\(324\) 0 0
\(325\) 12.5376 6.54275i 0.695463 0.362926i
\(326\) 3.10708i 0.172085i
\(327\) 0 0
\(328\) −3.82714 3.82714i −0.211319 0.211319i
\(329\) 4.16052 0.229377
\(330\) 0 0
\(331\) 20.0960 1.10457 0.552287 0.833654i \(-0.313755\pi\)
0.552287 + 0.833654i \(0.313755\pi\)
\(332\) 5.56115 + 5.56115i 0.305208 + 0.305208i
\(333\) 0 0
\(334\) 2.90148i 0.158762i
\(335\) −1.24533 + 8.11824i −0.0680396 + 0.443547i
\(336\) 0 0
\(337\) 10.6706 10.6706i 0.581262 0.581262i −0.353988 0.935250i \(-0.615175\pi\)
0.935250 + 0.353988i \(0.115175\pi\)
\(338\) −3.53553 + 3.53553i −0.192308 + 0.192308i
\(339\) 0 0
\(340\) 2.37245 15.4659i 0.128664 0.838754i
\(341\) 18.5169i 1.00275i
\(342\) 0 0
\(343\) 11.5806 + 11.5806i 0.625296 + 0.625296i
\(344\) −3.98898 −0.215071
\(345\) 0 0
\(346\) 3.89893 0.209608
\(347\) 25.3808 + 25.3808i 1.36251 + 1.36251i 0.870705 + 0.491806i \(0.163663\pi\)
0.491806 + 0.870705i \(0.336337\pi\)
\(348\) 0 0
\(349\) 1.45725i 0.0780049i 0.999239 + 0.0390024i \(0.0124180\pi\)
−0.999239 + 0.0390024i \(0.987582\pi\)
\(350\) −2.01240 + 6.40502i −0.107567 + 0.342363i
\(351\) 0 0
\(352\) 1.87117 1.87117i 0.0997337 0.0997337i
\(353\) 6.53153 6.53153i 0.347638 0.347638i −0.511591 0.859229i \(-0.670944\pi\)
0.859229 + 0.511591i \(0.170944\pi\)
\(354\) 0 0
\(355\) −11.6005 15.8044i −0.615690 0.838809i
\(356\) 5.34093i 0.283069i
\(357\) 0 0
\(358\) 8.67056 + 8.67056i 0.458253 + 0.458253i
\(359\) −13.9135 −0.734325 −0.367162 0.930157i \(-0.619671\pi\)
−0.367162 + 0.930157i \(0.619671\pi\)
\(360\) 0 0
\(361\) 13.1415 0.691659
\(362\) −2.67047 2.67047i −0.140357 0.140357i
\(363\) 0 0
\(364\) 3.79785i 0.199062i
\(365\) 25.8460 + 3.96475i 1.35284 + 0.207524i
\(366\) 0 0
\(367\) −5.87837 + 5.87837i −0.306849 + 0.306849i −0.843686 0.536837i \(-0.819619\pi\)
0.536837 + 0.843686i \(0.319619\pi\)
\(368\) 0.707107 0.707107i 0.0368605 0.0368605i
\(369\) 0 0
\(370\) 2.09201 1.53555i 0.108758 0.0798292i
\(371\) 13.5103i 0.701419i
\(372\) 0 0
\(373\) 13.5049 + 13.5049i 0.699257 + 0.699257i 0.964250 0.264993i \(-0.0853696\pi\)
−0.264993 + 0.964250i \(0.585370\pi\)
\(374\) 18.5169 0.957485
\(375\) 0 0
\(376\) 3.09852 0.159794
\(377\) 0.767563 + 0.767563i 0.0395315 + 0.0395315i
\(378\) 0 0
\(379\) 21.2692i 1.09253i −0.837614 0.546263i \(-0.816050\pi\)
0.837614 0.546263i \(-0.183950\pi\)
\(380\) 4.36306 3.20251i 0.223820 0.164285i
\(381\) 0 0
\(382\) −12.0274 + 12.0274i −0.615377 + 0.615377i
\(383\) 13.5403 13.5403i 0.691879 0.691879i −0.270766 0.962645i \(-0.587277\pi\)
0.962645 + 0.270766i \(0.0872771\pi\)
\(384\) 0 0
\(385\) −7.85337 1.20470i −0.400245 0.0613971i
\(386\) 25.3093i 1.28821i
\(387\) 0 0
\(388\) 4.46841 + 4.46841i 0.226849 + 0.226849i
\(389\) 21.2504 1.07744 0.538718 0.842486i \(-0.318909\pi\)
0.538718 + 0.842486i \(0.318909\pi\)
\(390\) 0 0
\(391\) 6.99745 0.353876
\(392\) 3.67486 + 3.67486i 0.185608 + 0.185608i
\(393\) 0 0
\(394\) 3.83039i 0.192972i
\(395\) 16.2116 + 22.0864i 0.815692 + 1.11129i
\(396\) 0 0
\(397\) −3.48468 + 3.48468i −0.174891 + 0.174891i −0.789124 0.614233i \(-0.789465\pi\)
0.614233 + 0.789124i \(0.289465\pi\)
\(398\) 5.08727 5.08727i 0.255002 0.255002i
\(399\) 0 0
\(400\) −1.49872 + 4.77010i −0.0749362 + 0.238505i
\(401\) 31.1927i 1.55769i −0.627216 0.778845i \(-0.715806\pi\)
0.627216 0.778845i \(-0.284194\pi\)
\(402\) 0 0
\(403\) −13.9949 13.9949i −0.697135 0.697135i
\(404\) −4.62281 −0.229993
\(405\) 0 0
\(406\) −0.515320 −0.0255749
\(407\) 2.17159 + 2.17159i 0.107642 + 0.107642i
\(408\) 0 0
\(409\) 4.57529i 0.226233i 0.993582 + 0.113117i \(0.0360834\pi\)
−0.993582 + 0.113117i \(0.963917\pi\)
\(410\) −1.83505 + 11.9626i −0.0906264 + 0.590789i
\(411\) 0 0
\(412\) 0.949464 0.949464i 0.0467767 0.0467767i
\(413\) 1.83942 1.83942i 0.0905118 0.0905118i
\(414\) 0 0
\(415\) 2.66647 17.3826i 0.130892 0.853278i
\(416\) 2.82843i 0.138675i
\(417\) 0 0
\(418\) 4.52903 + 4.52903i 0.221522 + 0.221522i
\(419\) 9.80817 0.479160 0.239580 0.970877i \(-0.422990\pi\)
0.239580 + 0.970877i \(0.422990\pi\)
\(420\) 0 0
\(421\) 17.0512 0.831026 0.415513 0.909587i \(-0.363602\pi\)
0.415513 + 0.909587i \(0.363602\pi\)
\(422\) 0.0484624 + 0.0484624i 0.00235911 + 0.00235911i
\(423\) 0 0
\(424\) 10.0617i 0.488639i
\(425\) −31.0178 + 16.1866i −1.50458 + 0.785164i
\(426\) 0 0
\(427\) −7.89893 + 7.89893i −0.382256 + 0.382256i
\(428\) −1.18839 + 1.18839i −0.0574432 + 0.0574432i
\(429\) 0 0
\(430\) 5.27788 + 7.19053i 0.254522 + 0.346758i
\(431\) 2.20380i 0.106153i 0.998590 + 0.0530767i \(0.0169028\pi\)
−0.998590 + 0.0530767i \(0.983097\pi\)
\(432\) 0 0
\(433\) 11.8571 + 11.8571i 0.569817 + 0.569817i 0.932077 0.362260i \(-0.117995\pi\)
−0.362260 + 0.932077i \(0.617995\pi\)
\(434\) 9.39578 0.451012
\(435\) 0 0
\(436\) 13.5138 0.647196
\(437\) 1.71150 + 1.71150i 0.0818722 + 0.0818722i
\(438\) 0 0
\(439\) 13.0255i 0.621675i 0.950463 + 0.310837i \(0.100609\pi\)
−0.950463 + 0.310837i \(0.899391\pi\)
\(440\) −5.84874 0.897192i −0.278828 0.0427719i
\(441\) 0 0
\(442\) −13.9949 + 13.9949i −0.665669 + 0.665669i
\(443\) −16.5990 + 16.5990i −0.788640 + 0.788640i −0.981271 0.192631i \(-0.938298\pi\)
0.192631 + 0.981271i \(0.438298\pi\)
\(444\) 0 0
\(445\) −9.62755 + 7.06668i −0.456390 + 0.334993i
\(446\) 27.7927i 1.31602i
\(447\) 0 0
\(448\) −0.949464 0.949464i −0.0448579 0.0448579i
\(449\) 13.8119 0.651826 0.325913 0.945400i \(-0.394328\pi\)
0.325913 + 0.945400i \(0.394328\pi\)
\(450\) 0 0
\(451\) −14.3225 −0.674419
\(452\) 3.74814 + 3.74814i 0.176297 + 0.176297i
\(453\) 0 0
\(454\) 4.01614i 0.188487i
\(455\) 6.84601 5.02501i 0.320946 0.235576i
\(456\) 0 0
\(457\) 0.0822505 0.0822505i 0.00384751 0.00384751i −0.705180 0.709028i \(-0.749134\pi\)
0.709028 + 0.705180i \(0.249134\pi\)
\(458\) 3.12933 3.12933i 0.146224 0.146224i
\(459\) 0 0
\(460\) −2.21021 0.339045i −0.103052 0.0158080i
\(461\) 31.1893i 1.45263i 0.687362 + 0.726315i \(0.258769\pi\)
−0.687362 + 0.726315i \(0.741231\pi\)
\(462\) 0 0
\(463\) −9.05552 9.05552i −0.420845 0.420845i 0.464649 0.885495i \(-0.346180\pi\)
−0.885495 + 0.464649i \(0.846180\pi\)
\(464\) −0.383781 −0.0178166
\(465\) 0 0
\(466\) −1.13105 −0.0523951
\(467\) −9.87526 9.87526i −0.456973 0.456973i 0.440688 0.897660i \(-0.354735\pi\)
−0.897660 + 0.440688i \(0.854735\pi\)
\(468\) 0 0
\(469\) 4.93197i 0.227737i
\(470\) −4.09970 5.58539i −0.189105 0.257635i
\(471\) 0 0
\(472\) 1.36989 1.36989i 0.0630544 0.0630544i
\(473\) −7.46406 + 7.46406i −0.343198 + 0.343198i
\(474\) 0 0
\(475\) −11.5457 3.62755i −0.529752 0.166444i
\(476\) 9.39578i 0.430655i
\(477\) 0 0
\(478\) 12.1677 + 12.1677i 0.556540 + 0.556540i
\(479\) −21.3913 −0.977394 −0.488697 0.872453i \(-0.662528\pi\)
−0.488697 + 0.872453i \(0.662528\pi\)
\(480\) 0 0
\(481\) −3.28253 −0.149671
\(482\) −3.71592 3.71592i −0.169256 0.169256i
\(483\) 0 0
\(484\) 3.99745i 0.181702i
\(485\) 2.14252 13.9670i 0.0972869 0.634208i
\(486\) 0 0
\(487\) 25.6336 25.6336i 1.16157 1.16157i 0.177437 0.984132i \(-0.443219\pi\)
0.984132 0.177437i \(-0.0567808\pi\)
\(488\) −5.88267 + 5.88267i −0.266296 + 0.266296i
\(489\) 0 0
\(490\) 1.76203 11.4866i 0.0796003 0.518910i
\(491\) 32.3925i 1.46185i 0.682455 + 0.730927i \(0.260912\pi\)
−0.682455 + 0.730927i \(0.739088\pi\)
\(492\) 0 0
\(493\) −1.89893 1.89893i −0.0855234 0.0855234i
\(494\) −6.84601 −0.308016
\(495\) 0 0
\(496\) 6.99745 0.314195
\(497\) −8.32447 8.32447i −0.373403 0.373403i
\(498\) 0 0
\(499\) 15.0379i 0.673189i 0.941650 + 0.336594i \(0.109275\pi\)
−0.941650 + 0.336594i \(0.890725\pi\)
\(500\) 10.5816 3.60980i 0.473222 0.161435i
\(501\) 0 0
\(502\) −11.4114 + 11.4114i −0.509314 + 0.509314i
\(503\) 17.7115 17.7115i 0.789717 0.789717i −0.191731 0.981448i \(-0.561410\pi\)
0.981448 + 0.191731i \(0.0614100\pi\)
\(504\) 0 0
\(505\) 6.11652 + 8.33307i 0.272182 + 0.370817i
\(506\) 2.64623i 0.117639i
\(507\) 0 0
\(508\) −6.79785 6.79785i −0.301606 0.301606i
\(509\) 40.5779 1.79858 0.899291 0.437351i \(-0.144083\pi\)
0.899291 + 0.437351i \(0.144083\pi\)
\(510\) 0 0
\(511\) 15.7019 0.694611
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 0 0
\(514\) 30.9317i 1.36434i
\(515\) −2.96775 0.455250i −0.130775 0.0200607i
\(516\) 0 0
\(517\) 5.79785 5.79785i 0.254989 0.254989i
\(518\) 1.10190 1.10190i 0.0484148 0.0484148i
\(519\) 0 0
\(520\) 5.09852 3.74234i 0.223585 0.164112i
\(521\) 17.7938i 0.779561i −0.920908 0.389781i \(-0.872551\pi\)
0.920908 0.389781i \(-0.127449\pi\)
\(522\) 0 0
\(523\) −13.7300 13.7300i −0.600372 0.600372i 0.340039 0.940411i \(-0.389560\pi\)
−0.940411 + 0.340039i \(0.889560\pi\)
\(524\) −3.08769 −0.134886
\(525\) 0 0
\(526\) 28.2194 1.23042
\(527\) 34.6230 + 34.6230i 1.50820 + 1.50820i
\(528\) 0 0
\(529\) 1.00000i 0.0434783i
\(530\) −18.1372 + 13.3128i −0.787830 + 0.578271i
\(531\) 0 0
\(532\) 2.29811 2.29811i 0.0996357 0.0996357i
\(533\) 10.8248 10.8248i 0.468874 0.468874i
\(534\) 0 0
\(535\) 3.71458 + 0.569813i 0.160595 + 0.0246352i
\(536\) 3.67305i 0.158652i
\(537\) 0 0
\(538\) 19.8520 + 19.8520i 0.855881 + 0.855881i
\(539\) 13.7526 0.592365
\(540\) 0 0
\(541\) 22.0000 0.945854 0.472927 0.881102i \(-0.343197\pi\)
0.472927 + 0.881102i \(0.343197\pi\)
\(542\) −16.7419 16.7419i −0.719126 0.719126i
\(543\) 0 0
\(544\) 6.99745i 0.300013i
\(545\) −17.8804 24.3600i −0.765912 1.04347i
\(546\) 0 0
\(547\) 21.1894 21.1894i 0.905992 0.905992i −0.0899537 0.995946i \(-0.528672\pi\)
0.995946 + 0.0899537i \(0.0286719\pi\)
\(548\) −2.43544 + 2.43544i −0.104037 + 0.104037i
\(549\) 0 0
\(550\) 6.12130 + 11.7300i 0.261013 + 0.500170i
\(551\) 0.928915i 0.0395731i
\(552\) 0 0
\(553\) 11.6334 + 11.6334i 0.494701 + 0.494701i
\(554\) 9.27126 0.393898
\(555\) 0 0
\(556\) 20.9368 0.887919
\(557\) −10.8857 10.8857i −0.461240 0.461240i 0.437822 0.899062i \(-0.355750\pi\)
−0.899062 + 0.437822i \(0.855750\pi\)
\(558\) 0 0
\(559\) 11.2825i 0.477200i
\(560\) −0.455250 + 2.96775i −0.0192378 + 0.125410i
\(561\) 0 0
\(562\) −14.5770 + 14.5770i −0.614894 + 0.614894i
\(563\) 2.95418 2.95418i 0.124504 0.124504i −0.642109 0.766613i \(-0.721941\pi\)
0.766613 + 0.642109i \(0.221941\pi\)
\(564\) 0 0
\(565\) 1.79716 11.7156i 0.0756072 0.492879i
\(566\) 7.91931i 0.332873i
\(567\) 0 0
\(568\) −6.19959 6.19959i −0.260129 0.260129i
\(569\) −29.1503 −1.22204 −0.611022 0.791614i \(-0.709241\pi\)
−0.611022 + 0.791614i \(0.709241\pi\)
\(570\) 0 0
\(571\) 41.2706 1.72712 0.863560 0.504246i \(-0.168229\pi\)
0.863560 + 0.504246i \(0.168229\pi\)
\(572\) 5.29247 + 5.29247i 0.221289 + 0.221289i
\(573\) 0 0
\(574\) 7.26747i 0.303338i
\(575\) 2.31321 + 4.43273i 0.0964676 + 0.184857i
\(576\) 0 0
\(577\) −16.0061 + 16.0061i −0.666341 + 0.666341i −0.956867 0.290526i \(-0.906170\pi\)
0.290526 + 0.956867i \(0.406170\pi\)
\(578\) 22.6021 22.6021i 0.940125 0.940125i
\(579\) 0 0
\(580\) 0.507788 + 0.691804i 0.0210847 + 0.0287256i
\(581\) 10.5602i 0.438112i
\(582\) 0 0
\(583\) −18.8271 18.8271i −0.779741 0.779741i
\(584\) 11.6939 0.483896
\(585\) 0 0
\(586\) −21.8726 −0.903548
\(587\) 18.5920 + 18.5920i 0.767372 + 0.767372i 0.977643 0.210271i \(-0.0674346\pi\)
−0.210271 + 0.977643i \(0.567435\pi\)
\(588\) 0 0
\(589\) 16.9368i 0.697870i
\(590\) −4.28190 0.656838i −0.176283 0.0270416i
\(591\) 0 0
\(592\) 0.820634 0.820634i 0.0337278 0.0337278i
\(593\) 5.19456 5.19456i 0.213315 0.213315i −0.592359 0.805674i \(-0.701803\pi\)
0.805674 + 0.592359i \(0.201803\pi\)
\(594\) 0 0
\(595\) −16.9368 + 12.4317i −0.694342 + 0.509651i
\(596\) 13.0494i 0.534526i
\(597\) 0 0
\(598\) 2.00000 + 2.00000i 0.0817861 + 0.0817861i
\(599\) −4.12632 −0.168597 −0.0842985 0.996441i \(-0.526865\pi\)
−0.0842985 + 0.996441i \(0.526865\pi\)
\(600\) 0 0
\(601\) 18.1364 0.739800 0.369900 0.929072i \(-0.379392\pi\)
0.369900 + 0.929072i \(0.379392\pi\)
\(602\) 3.78739 + 3.78739i 0.154363 + 0.154363i
\(603\) 0 0
\(604\) 11.9394i 0.485806i
\(605\) 7.20579 5.28909i 0.292957 0.215032i
\(606\) 0 0
\(607\) 7.70794 7.70794i 0.312856 0.312856i −0.533159 0.846015i \(-0.678995\pi\)
0.846015 + 0.533159i \(0.178995\pi\)
\(608\) 1.71150 1.71150i 0.0694106 0.0694106i
\(609\) 0 0
\(610\) 18.3876 + 2.82063i 0.744491 + 0.114204i
\(611\) 8.76393i 0.354551i
\(612\) 0 0
\(613\) 14.8073 + 14.8073i 0.598061 + 0.598061i 0.939796 0.341735i \(-0.111015\pi\)
−0.341735 + 0.939796i \(0.611015\pi\)
\(614\) −10.7279 −0.432942
\(615\) 0 0
\(616\) −3.55322 −0.143163
\(617\) 8.08164 + 8.08164i 0.325355 + 0.325355i 0.850817 0.525462i \(-0.176108\pi\)
−0.525462 + 0.850817i \(0.676108\pi\)
\(618\) 0 0
\(619\) 23.4100i 0.940926i 0.882420 + 0.470463i \(0.155913\pi\)
−0.882420 + 0.470463i \(0.844087\pi\)
\(620\) −9.25844 12.6136i −0.371828 0.506574i
\(621\) 0 0
\(622\) 2.75605 2.75605i 0.110508 0.110508i
\(623\) −5.07102 + 5.07102i −0.203166 + 0.203166i
\(624\) 0 0
\(625\) −20.5077 14.2981i −0.820306 0.571924i
\(626\) 21.1045i 0.843504i
\(627\) 0 0
\(628\) 15.4593 + 15.4593i 0.616895 + 0.616895i
\(629\) 8.12089 0.323801
\(630\) 0 0
\(631\) 33.4977 1.33352 0.666761 0.745271i \(-0.267680\pi\)
0.666761 + 0.745271i \(0.267680\pi\)
\(632\) 8.66386 + 8.66386i 0.344630 + 0.344630i
\(633\) 0 0
\(634\) 27.1815i 1.07951i
\(635\) −3.25945 + 21.2482i −0.129347 + 0.843208i
\(636\) 0 0
\(637\) −10.3941 + 10.3941i −0.411828 + 0.411828i
\(638\) −0.718120 + 0.718120i −0.0284306 + 0.0284306i
\(639\) 0 0
\(640\) −0.339045 + 2.21021i −0.0134019 + 0.0873664i
\(641\) 6.17292i 0.243816i −0.992541 0.121908i \(-0.961099\pi\)
0.992541 0.121908i \(-0.0389012\pi\)
\(642\) 0 0
\(643\) 21.5947 + 21.5947i 0.851611 + 0.851611i 0.990332 0.138720i \(-0.0442989\pi\)
−0.138720 + 0.990332i \(0.544299\pi\)
\(644\) −1.34274 −0.0529115
\(645\) 0 0
\(646\) 16.9368 0.666370
\(647\) 16.9863 + 16.9863i 0.667802 + 0.667802i 0.957207 0.289405i \(-0.0934573\pi\)
−0.289405 + 0.957207i \(0.593457\pi\)
\(648\) 0 0
\(649\) 5.12661i 0.201237i
\(650\) −13.4919 4.23903i −0.529195 0.166268i
\(651\) 0 0
\(652\) 2.19704 2.19704i 0.0860426 0.0860426i
\(653\) 34.5321 34.5321i 1.35135 1.35135i 0.467186 0.884159i \(-0.345268\pi\)
0.884159 0.467186i \(-0.154732\pi\)
\(654\) 0 0
\(655\) 4.08537 + 5.56586i 0.159629 + 0.217476i
\(656\) 5.41240i 0.211319i
\(657\) 0 0
\(658\) −2.94193 2.94193i −0.114688 0.114688i
\(659\) −44.6066 −1.73762 −0.868812 0.495142i \(-0.835116\pi\)
−0.868812 + 0.495142i \(0.835116\pi\)
\(660\) 0 0
\(661\) 17.6200 0.685339 0.342670 0.939456i \(-0.388669\pi\)
0.342670 + 0.939456i \(0.388669\pi\)
\(662\) −14.2100 14.2100i −0.552287 0.552287i
\(663\) 0 0
\(664\) 7.86466i 0.305208i
\(665\) −7.18324 1.10190i −0.278554 0.0427299i
\(666\) 0 0
\(667\) −0.271374 + 0.271374i −0.0105077 + 0.0105077i
\(668\) −2.05166 + 2.05166i −0.0793810 + 0.0793810i
\(669\) 0 0
\(670\) 6.62104 4.85988i 0.255793 0.187754i
\(671\) 22.0150i 0.849878i
\(672\) 0 0
\(673\) 3.66545 + 3.66545i 0.141293 + 0.141293i 0.774215 0.632922i \(-0.218145\pi\)
−0.632922 + 0.774215i \(0.718145\pi\)
\(674\) −15.0904 −0.581262
\(675\) 0 0
\(676\) 5.00000 0.192308
\(677\) 12.1377 + 12.1377i 0.466490 + 0.466490i 0.900775 0.434285i \(-0.142999\pi\)
−0.434285 + 0.900775i \(0.642999\pi\)
\(678\) 0 0
\(679\) 8.48519i 0.325632i
\(680\) −12.6136 + 9.25844i −0.483709 + 0.355045i
\(681\) 0 0
\(682\) 13.0934 13.0934i 0.501373 0.501373i
\(683\) −27.4988 + 27.4988i −1.05221 + 1.05221i −0.0536540 + 0.998560i \(0.517087\pi\)
−0.998560 + 0.0536540i \(0.982913\pi\)
\(684\) 0 0
\(685\) 7.61249 + 1.16775i 0.290858 + 0.0446174i
\(686\) 16.3775i 0.625296i
\(687\) 0 0
\(688\) 2.82063 + 2.82063i 0.107536 + 0.107536i
\(689\) 28.4588 1.08419
\(690\) 0 0
\(691\) −5.04300 −0.191845 −0.0959224 0.995389i \(-0.530580\pi\)
−0.0959224 + 0.995389i \(0.530580\pi\)
\(692\) −2.75696 2.75696i −0.104804 0.104804i
\(693\) 0 0
\(694\) 35.8938i 1.36251i
\(695\) −27.7019 37.7407i −1.05079 1.43159i
\(696\) 0 0
\(697\) −26.7802 + 26.7802i −1.01437 + 1.01437i
\(698\) 1.03043 1.03043i 0.0390024 0.0390024i
\(699\) 0 0
\(700\) 5.95202 3.10605i 0.224965 0.117398i
\(701\) 35.4022i 1.33712i 0.743657 + 0.668561i \(0.233089\pi\)
−0.743657 + 0.668561i \(0.766911\pi\)
\(702\) 0 0
\(703\) 1.98629 + 1.98629i 0.0749142 + 0.0749142i
\(704\) −2.64623 −0.0997337
\(705\) 0 0
\(706\) −9.23698 −0.347638
\(707\) 4.38919 + 4.38919i 0.165073 + 0.165073i
\(708\) 0 0
\(709\) 32.8245i 1.23275i 0.787453 + 0.616374i \(0.211399\pi\)
−0.787453 + 0.616374i \(0.788601\pi\)
\(710\) −2.97259 + 19.3782i −0.111559 + 0.727249i
\(711\) 0 0
\(712\) −3.77661 + 3.77661i −0.141534 + 0.141534i
\(713\) 4.94794 4.94794i 0.185302 0.185302i
\(714\) 0 0
\(715\) 2.53764 16.5427i 0.0949024 0.618664i
\(716\) 12.2620i 0.458253i
\(717\) 0 0
\(718\) 9.83830 + 9.83830i 0.367162 + 0.367162i
\(719\) −6.08304 −0.226859 −0.113430 0.993546i \(-0.536184\pi\)
−0.113430 + 0.993546i \(0.536184\pi\)
\(720\) 0 0
\(721\) −1.80296 −0.0671458
\(722\) −9.29246 9.29246i −0.345830 0.345830i
\(723\) 0 0
\(724\) 3.77661i 0.140357i
\(725\) 0.575182 1.83067i 0.0213617 0.0679895i
\(726\) 0 0
\(727\) −35.6416 + 35.6416i −1.32188 + 1.32188i −0.409619 + 0.912257i \(0.634338\pi\)
−0.912257 + 0.409619i \(0.865662\pi\)
\(728\) 2.68549 2.68549i 0.0995308 0.0995308i
\(729\) 0 0
\(730\) −15.4724 21.0794i −0.572658 0.780182i
\(731\) 27.9127i 1.03239i
\(732\) 0 0
\(733\) −12.6247 12.6247i −0.466303 0.466303i 0.434412 0.900714i \(-0.356956\pi\)
−0.900714 + 0.434412i \(0.856956\pi\)
\(734\) 8.31328 0.306849
\(735\) 0 0
\(736\) −1.00000 −0.0368605
\(737\) 6.87291 + 6.87291i 0.253167 + 0.253167i
\(738\) 0 0
\(739\) 26.0758i 0.959213i 0.877484 + 0.479607i \(0.159221\pi\)
−0.877484 + 0.479607i \(0.840779\pi\)
\(740\) −2.56507 0.393479i −0.0942938 0.0144646i
\(741\) 0 0
\(742\) −9.55322 + 9.55322i −0.350710 + 0.350710i
\(743\) −37.8958 + 37.8958i −1.39026 + 1.39026i −0.565543 + 0.824719i \(0.691334\pi\)
−0.824719 + 0.565543i \(0.808666\pi\)
\(744\) 0 0
\(745\) −23.5229 + 17.2659i −0.861813 + 0.632575i
\(746\) 19.0988i 0.699257i
\(747\) 0 0
\(748\) −13.0934 13.0934i −0.478743 0.478743i
\(749\) 2.25667 0.0824571
\(750\) 0 0
\(751\) −21.0249 −0.767209 −0.383604 0.923498i \(-0.625317\pi\)
−0.383604 + 0.923498i \(0.625317\pi\)
\(752\) −2.19098 2.19098i −0.0798969 0.0798969i
\(753\) 0 0
\(754\) 1.08550i 0.0395315i
\(755\) −21.5219 + 15.7972i −0.783262 + 0.574919i
\(756\) 0 0
\(757\) 23.8472 23.8472i 0.866743 0.866743i −0.125368 0.992110i \(-0.540011\pi\)
0.992110 + 0.125368i \(0.0400110\pi\)
\(758\) −15.0396 + 15.0396i −0.546263 + 0.546263i
\(759\) 0 0
\(760\) −5.34967 0.820634i −0.194053 0.0297675i
\(761\) 25.7309i 0.932744i −0.884589 0.466372i \(-0.845561\pi\)
0.884589 0.466372i \(-0.154439\pi\)
\(762\) 0 0
\(763\) −12.8309 12.8309i −0.464510 0.464510i
\(764\) 17.0094 0.615377
\(765\) 0 0
\(766\) −19.1489 −0.691879
\(767\) 3.87464 + 3.87464i 0.139905 + 0.139905i
\(768\) 0 0
\(769\) 1.80807i 0.0652007i −0.999468 0.0326003i \(-0.989621\pi\)
0.999468 0.0326003i \(-0.0103789\pi\)
\(770\) 4.70132 + 6.40502i 0.169424 + 0.230821i
\(771\) 0 0
\(772\) −17.8964 + 17.8964i −0.644105 + 0.644105i
\(773\) −10.6612 + 10.6612i −0.383458 + 0.383458i −0.872346 0.488888i \(-0.837403\pi\)
0.488888 + 0.872346i \(0.337403\pi\)
\(774\) 0 0
\(775\) −10.4872 + 33.3785i −0.376713 + 1.19899i
\(776\) 6.31929i 0.226849i
\(777\) 0 0
\(778\) −15.0263 15.0263i −0.538718 0.538718i
\(779\) −13.1003 −0.469368
\(780\) 0 0
\(781\) −23.2010 −0.830196
\(782\) −4.94794 4.94794i −0.176938 0.176938i
\(783\) 0 0
\(784\) 5.19704i 0.185608i
\(785\) 7.41247 48.3215i 0.264562 1.72467i
\(786\) 0 0
\(787\) −4.39510 + 4.39510i −0.156668 + 0.156668i −0.781089 0.624420i \(-0.785335\pi\)
0.624420 + 0.781089i \(0.285335\pi\)
\(788\) 2.70850 2.70850i 0.0964862 0.0964862i
\(789\) 0 0
\(790\) 4.15416 27.0808i 0.147798 0.963491i
\(791\) 7.11744i 0.253067i
\(792\) 0 0
\(793\) −16.6387 16.6387i −0.590858 0.590858i
\(794\) 4.92808 0.174891
\(795\) 0 0
\(796\) −7.19448 −0.255002
\(797\) 29.1863 + 29.1863i 1.03383 + 1.03383i 0.999407 + 0.0344254i \(0.0109601\pi\)
0.0344254 + 0.999407i \(0.489040\pi\)
\(798\) 0 0
\(799\) 21.6817i 0.767044i
\(800\) 4.43273 2.31321i 0.156721 0.0817844i
\(801\) 0 0
\(802\) −22.0566 + 22.0566i −0.778845 + 0.778845i
\(803\) 21.8812 21.8812i 0.772172 0.772172i
\(804\) 0 0
\(805\) 1.77661 + 2.42043i 0.0626172 + 0.0853089i
\(806\) 19.7918i 0.697135i
\(807\) 0 0
\(808\) 3.26882 + 3.26882i 0.114997 + 0.114997i
\(809\) −28.8768 −1.01525 −0.507626 0.861577i \(-0.669477\pi\)
−0.507626 + 0.861577i \(0.669477\pi\)
\(810\) 0 0
\(811\) −33.9696 −1.19283 −0.596417 0.802675i \(-0.703410\pi\)
−0.596417 + 0.802675i \(0.703410\pi\)
\(812\) 0.364386 + 0.364386i 0.0127875 + 0.0127875i
\(813\) 0 0
\(814\) 3.07109i 0.107642i
\(815\) −6.86731 1.05344i −0.240551 0.0369004i
\(816\) 0 0
\(817\) −6.82714 + 6.82714i −0.238852 + 0.238852i
\(818\) 3.23522 3.23522i 0.113117 0.113117i
\(819\) 0 0
\(820\) 9.75638 7.16124i 0.340708 0.250081i
\(821\) 43.0419i 1.50217i −0.660204 0.751086i \(-0.729530\pi\)
0.660204 0.751086i \(-0.270470\pi\)
\(822\) 0 0
\(823\) 17.7261 + 17.7261i 0.617892 + 0.617892i 0.944990 0.327098i \(-0.106071\pi\)
−0.327098 + 0.944990i \(0.606071\pi\)
\(824\) −1.34274 −0.0467767
\(825\) 0 0
\(826\) −2.60133 −0.0905118
\(827\) −9.45223 9.45223i −0.328686 0.328686i 0.523401 0.852087i \(-0.324663\pi\)
−0.852087 + 0.523401i \(0.824663\pi\)
\(828\) 0 0
\(829\) 17.1064i 0.594131i 0.954857 + 0.297065i \(0.0960080\pi\)
−0.954857 + 0.297065i \(0.903992\pi\)
\(830\) −14.1768 + 10.4059i −0.492085 + 0.361193i
\(831\) 0 0
\(832\) 2.00000 2.00000i 0.0693375 0.0693375i
\(833\) 25.7146 25.7146i 0.890959 0.890959i
\(834\) 0 0
\(835\) 6.41290 + 0.983732i 0.221927 + 0.0340434i
\(836\) 6.40502i 0.221522i
\(837\) 0 0
\(838\) −6.93542 6.93542i −0.239580 0.239580i
\(839\) −40.4615 −1.39689 −0.698444 0.715665i \(-0.746124\pi\)
−0.698444 + 0.715665i \(0.746124\pi\)
\(840\) 0 0
\(841\) −28.8527 −0.994921
\(842\) −12.0570 12.0570i −0.415513 0.415513i
\(843\) 0 0
\(844\) 0.0685362i 0.00235911i
\(845\) −6.61558 9.01299i −0.227583 0.310056i
\(846\) 0 0
\(847\) 3.79543 3.79543i 0.130413 0.130413i
\(848\) −7.11469 + 7.11469i −0.244320 + 0.244320i
\(849\) 0 0
\(850\) 33.3785 + 10.4872i 1.14487 + 0.359709i
\(851\) 1.16055i 0.0397832i
\(852\) 0 0
\(853\) −24.0274 24.0274i −0.822683 0.822683i 0.163809 0.986492i \(-0.447622\pi\)
−0.986492 + 0.163809i \(0.947622\pi\)
\(854\) 11.1708 0.382256
\(855\) 0 0
\(856\) 1.68064 0.0574432
\(857\) 18.0066 + 18.0066i 0.615093 + 0.615093i 0.944269 0.329175i \(-0.106771\pi\)
−0.329175 + 0.944269i \(0.606771\pi\)
\(858\) 0 0
\(859\) 56.2742i 1.92005i −0.279912 0.960026i \(-0.590305\pi\)
0.279912 0.960026i \(-0.409695\pi\)
\(860\) 1.35244 8.81650i 0.0461179 0.300640i
\(861\) 0 0
\(862\) 1.55832 1.55832i 0.0530767 0.0530767i
\(863\) 34.5743 34.5743i 1.17692 1.17692i 0.196399 0.980524i \(-0.437075\pi\)
0.980524 0.196399i \(-0.0629248\pi\)
\(864\) 0 0
\(865\) −1.32191 + 8.61747i −0.0449463 + 0.293003i
\(866\) 16.7685i 0.569817i
\(867\) 0 0
\(868\) −6.64382 6.64382i −0.225506 0.225506i
\(869\) 32.4231 1.09988
\(870\) 0 0
\(871\) −10.3890 −0.352017
\(872\) −9.55573 9.55573i −0.323598 0.323598i
\(873\) 0 0
\(874\) 2.42043i 0.0818722i
\(875\) −13.4742 6.61943i −0.455510 0.223778i
\(876\) 0 0
\(877\) 7.46516 7.46516i 0.252081 0.252081i −0.569743 0.821823i \(-0.692957\pi\)
0.821823 + 0.569743i \(0.192957\pi\)
\(878\) 9.21044 9.21044i 0.310837 0.310837i
\(879\) 0 0
\(880\) 3.50128 + 4.77010i 0.118028 + 0.160800i
\(881\) 6.96179i 0.234549i 0.993100 + 0.117274i \(0.0374157\pi\)
−0.993100 + 0.117274i \(0.962584\pi\)
\(882\) 0 0
\(883\) 11.4066 + 11.4066i 0.383862 + 0.383862i 0.872491 0.488629i \(-0.162503\pi\)
−0.488629 + 0.872491i \(0.662503\pi\)
\(884\) 19.7918 0.665669
\(885\) 0 0
\(886\) 23.4745 0.788640
\(887\) 4.39479 + 4.39479i 0.147562 + 0.147562i 0.777028 0.629466i \(-0.216726\pi\)
−0.629466 + 0.777028i \(0.716726\pi\)
\(888\) 0 0
\(889\) 12.9086i 0.432942i
\(890\) 11.8046 + 1.81081i 0.395691 + 0.0606986i
\(891\) 0 0
\(892\) 19.6524 19.6524i 0.658012 0.658012i
\(893\) 5.30312 5.30312i 0.177462 0.177462i
\(894\) 0 0
\(895\) −22.1035 + 16.2241i −0.738838 + 0.542311i
\(896\) 1.34274i 0.0448579i
\(897\) 0 0
\(898\) −9.76652 9.76652i −0.325913 0.325913i
\(899\) −2.68549 −0.0895661
\(900\) 0 0
\(901\) −70.4062 −2.34557
\(902\) 10.1275 + 10.1275i 0.337209 + 0.337209i
\(903\) 0 0
\(904\) 5.30066i 0.176297i
\(905\) 6.80771 4.99689i 0.226296 0.166102i
\(906\) 0 0
\(907\) −32.6034 + 32.6034i −1.08258 + 1.08258i −0.0863106 + 0.996268i \(0.527508\pi\)
−0.996268 + 0.0863106i \(0.972492\pi\)
\(908\) 2.83984 2.83984i 0.0942434 0.0942434i
\(909\) 0 0
\(910\) −8.39407 1.28764i −0.278261 0.0426849i
\(911\) 54.2830i 1.79848i 0.437461 + 0.899238i \(0.355878\pi\)
−0.437461 + 0.899238i \(0.644122\pi\)
\(912\) 0 0
\(913\) −14.7161 14.7161i −0.487032 0.487032i
\(914\) −0.116320 −0.00384751
\(915\) 0 0
\(916\) −4.42554 −0.146224
\(917\) 2.93164 + 2.93164i 0.0968114 + 0.0968114i
\(918\) 0 0
\(919\) 52.6590i 1.73706i 0.495637 + 0.868530i \(0.334935\pi\)
−0.495637 + 0.868530i \(0.665065\pi\)
\(920\) 1.32312 + 1.80260i 0.0436219 + 0.0594299i
\(921\) 0 0
\(922\) 22.0542 22.0542i 0.726315 0.726315i
\(923\) 17.5351 17.5351i 0.577175 0.577175i
\(924\) 0 0
\(925\) 2.68460 + 5.14441i 0.0882691 + 0.169147i
\(926\) 12.8064i 0.420845i
\(927\) 0 0
\(928\) 0.271374 + 0.271374i 0.00890830 + 0.00890830i
\(929\) −13.6515 −0.447892 −0.223946 0.974602i \(-0.571894\pi\)
−0.223946 + 0.974602i \(0.571894\pi\)
\(930\) 0 0
\(931\) 12.5791 0.412262
\(932\) 0.799777 + 0.799777i 0.0261976 + 0.0261976i
\(933\) 0 0
\(934\) 13.9657i 0.456973i
\(935\) −6.27805 + 40.9263i −0.205314 + 1.33843i
\(936\) 0 0
\(937\) 28.6980 28.6980i 0.937522 0.937522i −0.0606375 0.998160i \(-0.519313\pi\)
0.998160 + 0.0606375i \(0.0193134\pi\)
\(938\) 3.48743 3.48743i 0.113869 0.113869i
\(939\) 0 0
\(940\) −1.05054 + 6.84839i −0.0342647 + 0.223370i
\(941\) 9.58042i 0.312313i −0.987732 0.156156i \(-0.950090\pi\)
0.987732 0.156156i \(-0.0499104\pi\)
\(942\) 0 0
\(943\) 3.82714 + 3.82714i 0.124629 + 0.124629i
\(944\) −1.93732 −0.0630544
\(945\) 0 0
\(946\) 10.5558 0.343198
\(947\) −21.3347 21.3347i −0.693283 0.693283i 0.269670 0.962953i \(-0.413085\pi\)
−0.962953 + 0.269670i \(0.913085\pi\)
\(948\) 0 0
\(949\) 33.0753i 1.07367i
\(950\) 5.59896 + 10.7291i 0.181654 + 0.348098i
\(951\) 0 0
\(952\) −6.64382 + 6.64382i −0.215327 + 0.215327i
\(953\) −17.9775 + 17.9775i −0.582349 + 0.582349i −0.935548 0.353199i \(-0.885094\pi\)
0.353199 + 0.935548i \(0.385094\pi\)
\(954\) 0 0
\(955\) −22.5054 30.6610i −0.728256 0.992168i
\(956\) 17.2078i 0.556540i
\(957\) 0 0
\(958\) 15.1259 + 15.1259i 0.488697 + 0.488697i
\(959\) 4.62472 0.149340
\(960\) 0 0
\(961\) 17.9643 0.579492
\(962\) 2.32110 + 2.32110i 0.0748353 + 0.0748353i
\(963\) 0 0
\(964\) 5.25511i 0.169256i
\(965\) 55.9390 + 8.58098i 1.80074 + 0.276232i
\(966\) 0 0
\(967\) 14.2356 14.2356i 0.457787 0.457787i −0.440142 0.897928i \(-0.645072\pi\)
0.897928 + 0.440142i \(0.145072\pi\)
\(968\) 2.82662 2.82662i 0.0908510 0.0908510i
\(969\) 0 0
\(970\) −11.3911 + 8.36116i −0.365747 + 0.268461i
\(971\) 14.5361i 0.466486i 0.972419 + 0.233243i \(0.0749337\pi\)
−0.972419 + 0.233243i \(0.925066\pi\)
\(972\) 0 0
\(973\) −19.8788 19.8788i −0.637284 0.637284i
\(974\) −36.2514 −1.16157
\(975\) 0 0
\(976\) 8.31936 0.266296
\(977\) −3.29748 3.29748i −0.105496 0.105496i 0.652389 0.757884i \(-0.273767\pi\)
−0.757884 + 0.652389i \(0.773767\pi\)
\(978\) 0 0
\(979\) 14.1334i 0.451704i
\(980\) −9.36817 + 6.87629i −0.299255 + 0.219655i
\(981\) 0 0
\(982\) 22.9050 22.9050i 0.730927 0.730927i
\(983\) 16.4632 16.4632i 0.525096 0.525096i −0.394010 0.919106i \(-0.628913\pi\)
0.919106 + 0.394010i \(0.128913\pi\)
\(984\) 0 0
\(985\) −8.46599 1.29867i −0.269749 0.0413792i
\(986\) 2.68549i 0.0855234i
\(987\) 0 0
\(988\) 4.84086 + 4.84086i 0.154008 + 0.154008i
\(989\) 3.98898 0.126842
\(990\) 0 0
\(991\) −46.1262 −1.46525 −0.732623 0.680634i \(-0.761704\pi\)
−0.732623 + 0.680634i \(0.761704\pi\)
\(992\) −4.94794 4.94794i −0.157097 0.157097i
\(993\) 0 0
\(994\) 11.7726i 0.373403i
\(995\) 9.51914 + 12.9688i 0.301777 + 0.411137i
\(996\) 0 0
\(997\) −2.42727 + 2.42727i −0.0768724 + 0.0768724i −0.744498 0.667625i \(-0.767311\pi\)
0.667625 + 0.744498i \(0.267311\pi\)
\(998\) 10.6334 10.6334i 0.336594 0.336594i
\(999\) 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 2070.2.j.i.323.4 16
3.2 odd 2 inner 2070.2.j.i.323.5 yes 16
5.2 odd 4 inner 2070.2.j.i.737.5 yes 16
15.2 even 4 inner 2070.2.j.i.737.4 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2070.2.j.i.323.4 16 1.1 even 1 trivial
2070.2.j.i.323.5 yes 16 3.2 odd 2 inner
2070.2.j.i.737.4 yes 16 15.2 even 4 inner
2070.2.j.i.737.5 yes 16 5.2 odd 4 inner