Properties

Label 99.2.j.a.62.2
Level $99$
Weight $2$
Character 99.62
Analytic conductor $0.791$
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] = [99,2,Mod(8,99)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(99, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("99.8");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 99.j (of order \(10\), degree \(4\), 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: \(0.790518980011\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 2x^{14} - 16x^{12} - 72x^{10} + 26x^{8} + 360x^{6} + 725x^{4} + 1000x^{2} + 625 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 62.2
Root \(-0.752864 - 0.902863i\) of defining polynomial
Character \(\chi\) \(=\) 99.62
Dual form 99.2.j.a.8.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.205228 - 0.149107i) q^{2} +(-0.598148 - 1.84091i) q^{4} +(-1.71735 - 2.36373i) q^{5} +(2.58586 - 0.840196i) q^{7} +(-0.308515 + 0.949513i) q^{8} +O(q^{10})\) \(q+(-0.205228 - 0.149107i) q^{2} +(-0.598148 - 1.84091i) q^{4} +(-1.71735 - 2.36373i) q^{5} +(2.58586 - 0.840196i) q^{7} +(-0.308515 + 0.949513i) q^{8} +0.741170i q^{10} +(2.71994 + 1.89788i) q^{11} +(-1.67869 + 2.31052i) q^{13} +(-0.655969 - 0.213137i) q^{14} +(-2.92705 + 2.12663i) q^{16} +(3.60998 - 2.62280i) q^{17} +(-1.81761 - 0.590579i) q^{19} +(-3.32418 + 4.57534i) q^{20} +(-0.275220 - 0.795058i) q^{22} -0.816370i q^{23} +(-1.09283 + 3.36340i) q^{25} +(0.689029 - 0.223879i) q^{26} +(-3.09345 - 4.25777i) q^{28} +(2.95006 + 9.07936i) q^{29} +(4.84281 + 3.51851i) q^{31} +2.91456 q^{32} -1.13195 q^{34} +(-6.42681 - 4.66935i) q^{35} +(1.83750 + 5.65524i) q^{37} +(0.284966 + 0.392222i) q^{38} +(2.77422 - 0.901398i) q^{40} +(2.60604 - 8.02058i) q^{41} -11.8763i q^{43} +(1.86690 - 6.14238i) q^{44} +(-0.121726 + 0.167542i) q^{46} +(-7.34041 - 2.38504i) q^{47} +(0.317615 - 0.230761i) q^{49} +(0.725785 - 0.527314i) q^{50} +(5.25758 + 1.70829i) q^{52} +(-6.14564 + 8.45874i) q^{53} +(-0.185009 - 9.68851i) q^{55} +2.71452i q^{56} +(0.748358 - 2.30321i) q^{58} +(0.0887332 - 0.0288312i) q^{59} +(1.26024 + 1.73457i) q^{61} +(-0.469246 - 1.44419i) q^{62} +(5.25595 + 3.81867i) q^{64} +8.34434 q^{65} -1.40778 q^{67} +(-6.98766 - 5.07683i) q^{68} +(0.622728 + 1.91656i) q^{70} +(-2.12141 - 2.91987i) q^{71} +(-1.67338 + 0.543714i) q^{73} +(0.466129 - 1.43460i) q^{74} +3.69932i q^{76} +(8.62796 + 2.62237i) q^{77} +(-4.19260 + 5.77063i) q^{79} +(10.0535 + 3.26659i) q^{80} +(-1.73075 + 1.25747i) q^{82} +(-6.33808 + 4.60488i) q^{83} +(-12.3992 - 4.02874i) q^{85} +(-1.77084 + 2.43735i) q^{86} +(-2.64120 + 1.99709i) q^{88} +2.06830i q^{89} +(-2.39957 + 7.38512i) q^{91} +(-1.50286 + 0.488310i) q^{92} +(1.15083 + 1.58398i) q^{94} +(1.72551 + 5.31057i) q^{95} +(-1.35141 - 0.981858i) q^{97} -0.0995913 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{4} - 20 q^{16} - 48 q^{22} - 32 q^{25} + 40 q^{28} + 16 q^{31} + 40 q^{34} - 12 q^{37} + 60 q^{40} - 40 q^{46} - 24 q^{49} - 40 q^{52} + 16 q^{55} + 12 q^{58} + 36 q^{64} + 96 q^{67} + 76 q^{70} - 20 q^{73} - 12 q^{82} - 100 q^{85} - 12 q^{88} - 72 q^{91} - 80 q^{94} + 60 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{7}{10}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.205228 0.149107i −0.145118 0.105434i 0.512857 0.858474i \(-0.328587\pi\)
−0.657975 + 0.753039i \(0.728587\pi\)
\(3\) 0 0
\(4\) −0.598148 1.84091i −0.299074 0.920456i
\(5\) −1.71735 2.36373i −0.768021 1.05709i −0.996504 0.0835427i \(-0.973376\pi\)
0.228483 0.973548i \(-0.426624\pi\)
\(6\) 0 0
\(7\) 2.58586 0.840196i 0.977363 0.317564i 0.223578 0.974686i \(-0.428226\pi\)
0.753785 + 0.657122i \(0.228226\pi\)
\(8\) −0.308515 + 0.949513i −0.109077 + 0.335704i
\(9\) 0 0
\(10\) 0.741170i 0.234379i
\(11\) 2.71994 + 1.89788i 0.820092 + 0.572232i
\(12\) 0 0
\(13\) −1.67869 + 2.31052i −0.465586 + 0.640824i −0.975655 0.219309i \(-0.929620\pi\)
0.510070 + 0.860133i \(0.329620\pi\)
\(14\) −0.655969 0.213137i −0.175315 0.0569633i
\(15\) 0 0
\(16\) −2.92705 + 2.12663i −0.731763 + 0.531657i
\(17\) 3.60998 2.62280i 0.875549 0.636124i −0.0565211 0.998401i \(-0.518001\pi\)
0.932070 + 0.362278i \(0.118001\pi\)
\(18\) 0 0
\(19\) −1.81761 0.590579i −0.416989 0.135488i 0.0930053 0.995666i \(-0.470353\pi\)
−0.509995 + 0.860178i \(0.670353\pi\)
\(20\) −3.32418 + 4.57534i −0.743310 + 1.02308i
\(21\) 0 0
\(22\) −0.275220 0.795058i −0.0586771 0.169507i
\(23\) 0.816370i 0.170225i −0.996371 0.0851124i \(-0.972875\pi\)
0.996371 0.0851124i \(-0.0271249\pi\)
\(24\) 0 0
\(25\) −1.09283 + 3.36340i −0.218567 + 0.672680i
\(26\) 0.689029 0.223879i 0.135130 0.0439063i
\(27\) 0 0
\(28\) −3.09345 4.25777i −0.584608 0.804644i
\(29\) 2.95006 + 9.07936i 0.547813 + 1.68599i 0.714207 + 0.699935i \(0.246788\pi\)
−0.166394 + 0.986059i \(0.553212\pi\)
\(30\) 0 0
\(31\) 4.84281 + 3.51851i 0.869795 + 0.631943i 0.930532 0.366211i \(-0.119345\pi\)
−0.0607369 + 0.998154i \(0.519345\pi\)
\(32\) 2.91456 0.515226
\(33\) 0 0
\(34\) −1.13195 −0.194127
\(35\) −6.42681 4.66935i −1.08633 0.789265i
\(36\) 0 0
\(37\) 1.83750 + 5.65524i 0.302083 + 0.929717i 0.980750 + 0.195270i \(0.0625583\pi\)
−0.678666 + 0.734447i \(0.737442\pi\)
\(38\) 0.284966 + 0.392222i 0.0462275 + 0.0636267i
\(39\) 0 0
\(40\) 2.77422 0.901398i 0.438642 0.142524i
\(41\) 2.60604 8.02058i 0.406996 1.25260i −0.512221 0.858853i \(-0.671177\pi\)
0.919217 0.393751i \(-0.128823\pi\)
\(42\) 0 0
\(43\) 11.8763i 1.81112i −0.424214 0.905562i \(-0.639450\pi\)
0.424214 0.905562i \(-0.360550\pi\)
\(44\) 1.86690 6.14238i 0.281446 0.925998i
\(45\) 0 0
\(46\) −0.121726 + 0.167542i −0.0179475 + 0.0247027i
\(47\) −7.34041 2.38504i −1.07071 0.347894i −0.279945 0.960016i \(-0.590316\pi\)
−0.790764 + 0.612122i \(0.790316\pi\)
\(48\) 0 0
\(49\) 0.317615 0.230761i 0.0453735 0.0329658i
\(50\) 0.725785 0.527314i 0.102641 0.0745734i
\(51\) 0 0
\(52\) 5.25758 + 1.70829i 0.729094 + 0.236897i
\(53\) −6.14564 + 8.45874i −0.844168 + 1.16190i 0.140950 + 0.990017i \(0.454984\pi\)
−0.985118 + 0.171881i \(0.945016\pi\)
\(54\) 0 0
\(55\) −0.185009 9.68851i −0.0249466 1.30640i
\(56\) 2.71452i 0.362743i
\(57\) 0 0
\(58\) 0.748358 2.30321i 0.0982642 0.302426i
\(59\) 0.0887332 0.0288312i 0.0115521 0.00375350i −0.303235 0.952916i \(-0.598067\pi\)
0.314787 + 0.949162i \(0.398067\pi\)
\(60\) 0 0
\(61\) 1.26024 + 1.73457i 0.161357 + 0.222089i 0.882038 0.471177i \(-0.156171\pi\)
−0.720681 + 0.693267i \(0.756171\pi\)
\(62\) −0.469246 1.44419i −0.0595943 0.183412i
\(63\) 0 0
\(64\) 5.25595 + 3.81867i 0.656994 + 0.477334i
\(65\) 8.34434 1.03499
\(66\) 0 0
\(67\) −1.40778 −0.171988 −0.0859941 0.996296i \(-0.527407\pi\)
−0.0859941 + 0.996296i \(0.527407\pi\)
\(68\) −6.98766 5.07683i −0.847378 0.615656i
\(69\) 0 0
\(70\) 0.622728 + 1.91656i 0.0744303 + 0.229073i
\(71\) −2.12141 2.91987i −0.251765 0.346525i 0.664363 0.747410i \(-0.268703\pi\)
−0.916128 + 0.400885i \(0.868703\pi\)
\(72\) 0 0
\(73\) −1.67338 + 0.543714i −0.195854 + 0.0636369i −0.405302 0.914183i \(-0.632833\pi\)
0.209447 + 0.977820i \(0.432833\pi\)
\(74\) 0.466129 1.43460i 0.0541863 0.166768i
\(75\) 0 0
\(76\) 3.69932i 0.424341i
\(77\) 8.62796 + 2.62237i 0.983247 + 0.298846i
\(78\) 0 0
\(79\) −4.19260 + 5.77063i −0.471705 + 0.649246i −0.976884 0.213768i \(-0.931426\pi\)
0.505180 + 0.863014i \(0.331426\pi\)
\(80\) 10.0535 + 3.26659i 1.12402 + 0.365216i
\(81\) 0 0
\(82\) −1.73075 + 1.25747i −0.191130 + 0.138864i
\(83\) −6.33808 + 4.60488i −0.695695 + 0.505452i −0.878527 0.477692i \(-0.841473\pi\)
0.182833 + 0.983144i \(0.441473\pi\)
\(84\) 0 0
\(85\) −12.3992 4.02874i −1.34488 0.436978i
\(86\) −1.77084 + 2.43735i −0.190955 + 0.262826i
\(87\) 0 0
\(88\) −2.64120 + 1.99709i −0.281553 + 0.212890i
\(89\) 2.06830i 0.219240i 0.993974 + 0.109620i \(0.0349633\pi\)
−0.993974 + 0.109620i \(0.965037\pi\)
\(90\) 0 0
\(91\) −2.39957 + 7.38512i −0.251543 + 0.774171i
\(92\) −1.50286 + 0.488310i −0.156684 + 0.0509099i
\(93\) 0 0
\(94\) 1.15083 + 1.58398i 0.118699 + 0.163375i
\(95\) 1.72551 + 5.31057i 0.177034 + 0.544853i
\(96\) 0 0
\(97\) −1.35141 0.981858i −0.137215 0.0996926i 0.517060 0.855949i \(-0.327026\pi\)
−0.654275 + 0.756256i \(0.727026\pi\)
\(98\) −0.0995913 −0.0100602
\(99\) 0 0
\(100\) 6.84540 0.684540
\(101\) 7.31972 + 5.31809i 0.728339 + 0.529170i 0.889038 0.457834i \(-0.151375\pi\)
−0.160698 + 0.987004i \(0.551375\pi\)
\(102\) 0 0
\(103\) −5.12132 15.7618i −0.504618 1.55306i −0.801411 0.598114i \(-0.795917\pi\)
0.296793 0.954942i \(-0.404083\pi\)
\(104\) −1.67597 2.30677i −0.164342 0.226198i
\(105\) 0 0
\(106\) 2.52251 0.819613i 0.245008 0.0796079i
\(107\) −2.19803 + 6.76484i −0.212492 + 0.653982i 0.786830 + 0.617169i \(0.211721\pi\)
−0.999322 + 0.0368130i \(0.988279\pi\)
\(108\) 0 0
\(109\) 8.62045i 0.825690i 0.910801 + 0.412845i \(0.135465\pi\)
−0.910801 + 0.412845i \(0.864535\pi\)
\(110\) −1.40665 + 2.01594i −0.134119 + 0.192212i
\(111\) 0 0
\(112\) −5.78216 + 7.95845i −0.546362 + 0.752003i
\(113\) −10.8495 3.52523i −1.02064 0.331626i −0.249556 0.968360i \(-0.580285\pi\)
−0.771083 + 0.636735i \(0.780285\pi\)
\(114\) 0 0
\(115\) −1.92967 + 1.40199i −0.179943 + 0.130736i
\(116\) 14.9497 10.8616i 1.38805 1.00847i
\(117\) 0 0
\(118\) −0.0225094 0.00731376i −0.00207216 0.000673286i
\(119\) 7.13123 9.81529i 0.653719 0.899767i
\(120\) 0 0
\(121\) 3.79611 + 10.3242i 0.345101 + 0.938566i
\(122\) 0.543892i 0.0492417i
\(123\) 0 0
\(124\) 3.58054 11.0198i 0.321542 0.989606i
\(125\) −4.06670 + 1.32135i −0.363737 + 0.118185i
\(126\) 0 0
\(127\) −1.69463 2.33246i −0.150374 0.206973i 0.727184 0.686443i \(-0.240829\pi\)
−0.877558 + 0.479470i \(0.840829\pi\)
\(128\) −2.31057 7.11122i −0.204228 0.628549i
\(129\) 0 0
\(130\) −1.71249 1.24420i −0.150195 0.109123i
\(131\) −2.10155 −0.183613 −0.0918067 0.995777i \(-0.529264\pi\)
−0.0918067 + 0.995777i \(0.529264\pi\)
\(132\) 0 0
\(133\) −5.19630 −0.450576
\(134\) 0.288916 + 0.209910i 0.0249586 + 0.0181335i
\(135\) 0 0
\(136\) 1.37665 + 4.23690i 0.118047 + 0.363311i
\(137\) −2.98245 4.10498i −0.254808 0.350712i 0.662380 0.749168i \(-0.269546\pi\)
−0.917188 + 0.398455i \(0.869546\pi\)
\(138\) 0 0
\(139\) 16.6282 5.40283i 1.41039 0.458262i 0.497852 0.867262i \(-0.334122\pi\)
0.912535 + 0.409000i \(0.134122\pi\)
\(140\) −4.75168 + 14.6242i −0.401590 + 1.23597i
\(141\) 0 0
\(142\) 0.915555i 0.0768317i
\(143\) −8.95103 + 3.09852i −0.748523 + 0.259111i
\(144\) 0 0
\(145\) 16.3948 22.5656i 1.36152 1.87397i
\(146\) 0.424495 + 0.137927i 0.0351315 + 0.0114149i
\(147\) 0 0
\(148\) 9.31171 6.76535i 0.765418 0.556108i
\(149\) −4.57623 + 3.32483i −0.374900 + 0.272381i −0.759240 0.650811i \(-0.774429\pi\)
0.384340 + 0.923192i \(0.374429\pi\)
\(150\) 0 0
\(151\) 8.72640 + 2.83538i 0.710145 + 0.230740i 0.641745 0.766918i \(-0.278211\pi\)
0.0683995 + 0.997658i \(0.478211\pi\)
\(152\) 1.12152 1.54365i 0.0909677 0.125206i
\(153\) 0 0
\(154\) −1.37968 1.82467i −0.111178 0.147036i
\(155\) 17.4896i 1.40480i
\(156\) 0 0
\(157\) −0.943653 + 2.90426i −0.0753117 + 0.231785i −0.981625 0.190821i \(-0.938885\pi\)
0.906313 + 0.422607i \(0.138885\pi\)
\(158\) 1.72088 0.559147i 0.136906 0.0444833i
\(159\) 0 0
\(160\) −5.00531 6.88922i −0.395705 0.544641i
\(161\) −0.685911 2.11102i −0.0540573 0.166371i
\(162\) 0 0
\(163\) −6.39488 4.64615i −0.500885 0.363914i 0.308470 0.951234i \(-0.400183\pi\)
−0.809355 + 0.587320i \(0.800183\pi\)
\(164\) −16.3240 −1.27469
\(165\) 0 0
\(166\) 1.98737 0.154250
\(167\) 13.3065 + 9.66777i 1.02969 + 0.748115i 0.968247 0.249996i \(-0.0804292\pi\)
0.0614446 + 0.998110i \(0.480429\pi\)
\(168\) 0 0
\(169\) 1.49672 + 4.60642i 0.115132 + 0.354340i
\(170\) 1.94394 + 2.67561i 0.149094 + 0.205210i
\(171\) 0 0
\(172\) −21.8633 + 7.10381i −1.66706 + 0.541660i
\(173\) 4.79669 14.7627i 0.364686 1.12239i −0.585492 0.810678i \(-0.699099\pi\)
0.950178 0.311709i \(-0.100901\pi\)
\(174\) 0 0
\(175\) 9.61547i 0.726861i
\(176\) −11.9975 + 0.229100i −0.904344 + 0.0172691i
\(177\) 0 0
\(178\) 0.308398 0.424473i 0.0231154 0.0318156i
\(179\) 4.93538 + 1.60360i 0.368888 + 0.119859i 0.487594 0.873071i \(-0.337875\pi\)
−0.118706 + 0.992929i \(0.537875\pi\)
\(180\) 0 0
\(181\) −4.29773 + 3.12248i −0.319448 + 0.232092i −0.735940 0.677047i \(-0.763259\pi\)
0.416492 + 0.909139i \(0.363259\pi\)
\(182\) 1.59363 1.15784i 0.118128 0.0858247i
\(183\) 0 0
\(184\) 0.775154 + 0.251863i 0.0571451 + 0.0185676i
\(185\) 10.2118 14.0554i 0.750788 1.03337i
\(186\) 0 0
\(187\) 14.7967 0.282553i 1.08204 0.0206624i
\(188\) 14.9396i 1.08959i
\(189\) 0 0
\(190\) 0.437719 1.34716i 0.0317555 0.0977334i
\(191\) 10.3662 3.36817i 0.750069 0.243712i 0.0910582 0.995846i \(-0.470975\pi\)
0.659011 + 0.752133i \(0.270975\pi\)
\(192\) 0 0
\(193\) 9.03216 + 12.4317i 0.650149 + 0.894853i 0.999106 0.0422855i \(-0.0134639\pi\)
−0.348956 + 0.937139i \(0.613464\pi\)
\(194\) 0.130946 + 0.403009i 0.00940134 + 0.0289344i
\(195\) 0 0
\(196\) −0.614791 0.446672i −0.0439136 0.0319051i
\(197\) −7.24149 −0.515935 −0.257967 0.966154i \(-0.583053\pi\)
−0.257967 + 0.966154i \(0.583053\pi\)
\(198\) 0 0
\(199\) −11.3726 −0.806181 −0.403090 0.915160i \(-0.632064\pi\)
−0.403090 + 0.915160i \(0.632064\pi\)
\(200\) −2.85643 2.07532i −0.201980 0.146747i
\(201\) 0 0
\(202\) −0.709247 2.18284i −0.0499024 0.153584i
\(203\) 15.2569 + 20.9993i 1.07082 + 1.47386i
\(204\) 0 0
\(205\) −23.4339 + 7.61415i −1.63670 + 0.531795i
\(206\) −1.29915 + 3.99838i −0.0905162 + 0.278580i
\(207\) 0 0
\(208\) 10.3330i 0.716463i
\(209\) −3.82295 5.05595i −0.264439 0.349727i
\(210\) 0 0
\(211\) −2.17376 + 2.99193i −0.149648 + 0.205973i −0.877259 0.480017i \(-0.840631\pi\)
0.727611 + 0.685990i \(0.240631\pi\)
\(212\) 19.2478 + 6.25399i 1.32194 + 0.429526i
\(213\) 0 0
\(214\) 1.45978 1.06059i 0.0997885 0.0725006i
\(215\) −28.0724 + 20.3958i −1.91452 + 1.39098i
\(216\) 0 0
\(217\) 15.4791 + 5.02946i 1.05079 + 0.341422i
\(218\) 1.28537 1.76916i 0.0870560 0.119822i
\(219\) 0 0
\(220\) −17.7250 + 6.13575i −1.19502 + 0.413672i
\(221\) 12.7438i 0.857243i
\(222\) 0 0
\(223\) −0.0875209 + 0.269362i −0.00586083 + 0.0180378i −0.953944 0.299984i \(-0.903019\pi\)
0.948083 + 0.318022i \(0.103019\pi\)
\(224\) 7.53664 2.44880i 0.503563 0.163618i
\(225\) 0 0
\(226\) 1.70099 + 2.34121i 0.113148 + 0.155735i
\(227\) −5.64140 17.3625i −0.374433 1.15239i −0.943860 0.330345i \(-0.892835\pi\)
0.569427 0.822042i \(-0.307165\pi\)
\(228\) 0 0
\(229\) −21.3385 15.5033i −1.41009 1.02449i −0.993310 0.115479i \(-0.963160\pi\)
−0.416777 0.909009i \(-0.636840\pi\)
\(230\) 0.605069 0.0398971
\(231\) 0 0
\(232\) −9.53111 −0.625748
\(233\) 8.73916 + 6.34937i 0.572521 + 0.415961i 0.836020 0.548699i \(-0.184877\pi\)
−0.263499 + 0.964660i \(0.584877\pi\)
\(234\) 0 0
\(235\) 6.96844 + 21.4467i 0.454571 + 1.39903i
\(236\) −0.106151 0.146105i −0.00690986 0.00951060i
\(237\) 0 0
\(238\) −2.92705 + 0.951057i −0.189733 + 0.0616478i
\(239\) 2.29393 7.06000i 0.148382 0.456673i −0.849048 0.528315i \(-0.822824\pi\)
0.997430 + 0.0716420i \(0.0228239\pi\)
\(240\) 0 0
\(241\) 2.66873i 0.171908i 0.996299 + 0.0859539i \(0.0273938\pi\)
−0.996299 + 0.0859539i \(0.972606\pi\)
\(242\) 0.760344 2.68484i 0.0488767 0.172588i
\(243\) 0 0
\(244\) 2.43938 3.35752i 0.156165 0.214943i
\(245\) −1.09091 0.354458i −0.0696957 0.0226455i
\(246\) 0 0
\(247\) 4.41576 3.20824i 0.280968 0.204135i
\(248\) −4.83495 + 3.51280i −0.307020 + 0.223063i
\(249\) 0 0
\(250\) 1.03162 + 0.335194i 0.0652455 + 0.0211996i
\(251\) 14.2630 19.6313i 0.900271 1.23912i −0.0701107 0.997539i \(-0.522335\pi\)
0.970382 0.241577i \(-0.0776647\pi\)
\(252\) 0 0
\(253\) 1.54937 2.22047i 0.0974081 0.139600i
\(254\) 0.731367i 0.0458901i
\(255\) 0 0
\(256\) 3.42906 10.5535i 0.214316 0.659597i
\(257\) −15.9360 + 5.17791i −0.994059 + 0.322989i −0.760489 0.649351i \(-0.775041\pi\)
−0.233570 + 0.972340i \(0.575041\pi\)
\(258\) 0 0
\(259\) 9.50303 + 13.0798i 0.590490 + 0.812739i
\(260\) −4.99116 15.3612i −0.309538 0.952661i
\(261\) 0 0
\(262\) 0.431296 + 0.313355i 0.0266456 + 0.0193591i
\(263\) 10.9146 0.673021 0.336511 0.941680i \(-0.390753\pi\)
0.336511 + 0.941680i \(0.390753\pi\)
\(264\) 0 0
\(265\) 30.5484 1.87657
\(266\) 1.06642 + 0.774802i 0.0653866 + 0.0475062i
\(267\) 0 0
\(268\) 0.842064 + 2.59161i 0.0514373 + 0.158308i
\(269\) 9.22041 + 12.6908i 0.562178 + 0.773772i 0.991601 0.129331i \(-0.0412830\pi\)
−0.429423 + 0.903103i \(0.641283\pi\)
\(270\) 0 0
\(271\) −2.76289 + 0.897717i −0.167834 + 0.0545324i −0.391728 0.920081i \(-0.628123\pi\)
0.223895 + 0.974613i \(0.428123\pi\)
\(272\) −4.98887 + 15.3542i −0.302495 + 0.930983i
\(273\) 0 0
\(274\) 1.28716i 0.0777601i
\(275\) −9.35577 + 7.07416i −0.564174 + 0.426588i
\(276\) 0 0
\(277\) 12.4111 17.0824i 0.745709 1.02638i −0.252561 0.967581i \(-0.581273\pi\)
0.998270 0.0587992i \(-0.0187272\pi\)
\(278\) −4.21817 1.37057i −0.252989 0.0822011i
\(279\) 0 0
\(280\) 6.41638 4.66177i 0.383452 0.278594i
\(281\) −2.50015 + 1.81647i −0.149147 + 0.108361i −0.659856 0.751392i \(-0.729383\pi\)
0.510709 + 0.859753i \(0.329383\pi\)
\(282\) 0 0
\(283\) −21.3272 6.92961i −1.26777 0.411923i −0.403512 0.914975i \(-0.632211\pi\)
−0.864256 + 0.503052i \(0.832211\pi\)
\(284\) −4.10631 + 5.65185i −0.243664 + 0.335375i
\(285\) 0 0
\(286\) 2.29901 + 0.698757i 0.135943 + 0.0413183i
\(287\) 22.9297i 1.35350i
\(288\) 0 0
\(289\) 0.899570 2.76859i 0.0529159 0.162858i
\(290\) −6.72935 + 2.18650i −0.395161 + 0.128396i
\(291\) 0 0
\(292\) 2.00186 + 2.75532i 0.117150 + 0.161243i
\(293\) −6.40930 19.7258i −0.374435 1.15239i −0.943859 0.330349i \(-0.892833\pi\)
0.569423 0.822044i \(-0.307167\pi\)
\(294\) 0 0
\(295\) −0.220535 0.160228i −0.0128400 0.00932883i
\(296\) −5.93663 −0.345059
\(297\) 0 0
\(298\) 1.43492 0.0831229
\(299\) 1.88624 + 1.37043i 0.109084 + 0.0792543i
\(300\) 0 0
\(301\) −9.97845 30.7105i −0.575148 1.77012i
\(302\) −1.36813 1.88306i −0.0787268 0.108358i
\(303\) 0 0
\(304\) 6.57619 2.13673i 0.377170 0.122550i
\(305\) 1.93578 5.95772i 0.110843 0.341138i
\(306\) 0 0
\(307\) 15.0077i 0.856533i −0.903652 0.428267i \(-0.859124\pi\)
0.903652 0.428267i \(-0.140876\pi\)
\(308\) −0.333256 17.4519i −0.0189890 0.994413i
\(309\) 0 0
\(310\) −2.60781 + 3.58935i −0.148114 + 0.203861i
\(311\) 1.95824 + 0.636270i 0.111042 + 0.0360796i 0.364011 0.931395i \(-0.381407\pi\)
−0.252969 + 0.967474i \(0.581407\pi\)
\(312\) 0 0
\(313\) 20.1223 14.6197i 1.13738 0.826355i 0.150628 0.988591i \(-0.451870\pi\)
0.986752 + 0.162236i \(0.0518705\pi\)
\(314\) 0.626709 0.455330i 0.0353672 0.0256958i
\(315\) 0 0
\(316\) 13.1310 + 4.26652i 0.738677 + 0.240011i
\(317\) −0.254351 + 0.350085i −0.0142858 + 0.0196627i −0.816100 0.577910i \(-0.803868\pi\)
0.801814 + 0.597573i \(0.203868\pi\)
\(318\) 0 0
\(319\) −9.20754 + 30.2941i −0.515523 + 1.69615i
\(320\) 18.9816i 1.06111i
\(321\) 0 0
\(322\) −0.173999 + 0.535513i −0.00969657 + 0.0298430i
\(323\) −8.11053 + 2.63527i −0.451282 + 0.146630i
\(324\) 0 0
\(325\) −5.93668 8.17113i −0.329308 0.453253i
\(326\) 0.619634 + 1.90704i 0.0343183 + 0.105621i
\(327\) 0 0
\(328\) 6.81164 + 4.94895i 0.376110 + 0.273260i
\(329\) −20.9852 −1.15695
\(330\) 0 0
\(331\) −17.3090 −0.951391 −0.475696 0.879610i \(-0.657804\pi\)
−0.475696 + 0.879610i \(0.657804\pi\)
\(332\) 12.2683 + 8.91344i 0.673310 + 0.489189i
\(333\) 0 0
\(334\) −1.28934 3.96819i −0.0705497 0.217130i
\(335\) 2.41766 + 3.32762i 0.132091 + 0.181807i
\(336\) 0 0
\(337\) 23.8381 7.74548i 1.29855 0.421923i 0.423471 0.905910i \(-0.360812\pi\)
0.875076 + 0.483986i \(0.160812\pi\)
\(338\) 0.379680 1.16853i 0.0206519 0.0635599i
\(339\) 0 0
\(340\) 25.2356i 1.36859i
\(341\) 6.49444 + 18.7612i 0.351694 + 1.01598i
\(342\) 0 0
\(343\) −10.5596 + 14.5341i −0.570166 + 0.784766i
\(344\) 11.2767 + 3.66403i 0.608001 + 0.197551i
\(345\) 0 0
\(346\) −3.18563 + 2.31449i −0.171260 + 0.124428i
\(347\) 16.8866 12.2688i 0.906519 0.658625i −0.0336127 0.999435i \(-0.510701\pi\)
0.940132 + 0.340810i \(0.110701\pi\)
\(348\) 0 0
\(349\) −17.1385 5.56865i −0.917405 0.298083i −0.188003 0.982168i \(-0.560202\pi\)
−0.729402 + 0.684085i \(0.760202\pi\)
\(350\) 1.43373 1.97336i 0.0766361 0.105481i
\(351\) 0 0
\(352\) 7.92742 + 5.53148i 0.422533 + 0.294829i
\(353\) 16.2953i 0.867313i 0.901078 + 0.433656i \(0.142777\pi\)
−0.901078 + 0.433656i \(0.857223\pi\)
\(354\) 0 0
\(355\) −3.25858 + 10.0289i −0.172947 + 0.532277i
\(356\) 3.80756 1.23715i 0.201800 0.0655689i
\(357\) 0 0
\(358\) −0.773769 1.06500i −0.0408949 0.0562871i
\(359\) 7.65875 + 23.5712i 0.404213 + 1.24404i 0.921550 + 0.388259i \(0.126923\pi\)
−0.517337 + 0.855782i \(0.673077\pi\)
\(360\) 0 0
\(361\) −12.4164 9.02103i −0.653494 0.474791i
\(362\) 1.34760 0.0708281
\(363\) 0 0
\(364\) 15.0306 0.787820
\(365\) 4.15897 + 3.02167i 0.217690 + 0.158161i
\(366\) 0 0
\(367\) 2.76683 + 8.51544i 0.144428 + 0.444502i 0.996937 0.0782097i \(-0.0249204\pi\)
−0.852509 + 0.522712i \(0.824920\pi\)
\(368\) 1.73611 + 2.38956i 0.0905012 + 0.124564i
\(369\) 0 0
\(370\) −4.19150 + 1.36190i −0.217906 + 0.0708018i
\(371\) −8.78474 + 27.0367i −0.456081 + 1.40367i
\(372\) 0 0
\(373\) 16.9007i 0.875088i 0.899197 + 0.437544i \(0.144152\pi\)
−0.899197 + 0.437544i \(0.855848\pi\)
\(374\) −3.07882 2.14830i −0.159202 0.111086i
\(375\) 0 0
\(376\) 4.52926 6.23399i 0.233579 0.321493i
\(377\) −25.9303 8.42527i −1.33548 0.433923i
\(378\) 0 0
\(379\) −15.9625 + 11.5975i −0.819940 + 0.595722i −0.916695 0.399587i \(-0.869154\pi\)
0.0967550 + 0.995308i \(0.469154\pi\)
\(380\) 8.74419 6.35302i 0.448567 0.325903i
\(381\) 0 0
\(382\) −2.62964 0.854422i −0.134544 0.0437160i
\(383\) −2.93889 + 4.04503i −0.150170 + 0.206691i −0.877474 0.479624i \(-0.840773\pi\)
0.727304 + 0.686315i \(0.240773\pi\)
\(384\) 0 0
\(385\) −8.61865 24.8977i −0.439247 1.26890i
\(386\) 3.89808i 0.198407i
\(387\) 0 0
\(388\) −0.999169 + 3.07513i −0.0507251 + 0.156116i
\(389\) 9.37115 3.04487i 0.475136 0.154381i −0.0616527 0.998098i \(-0.519637\pi\)
0.536789 + 0.843716i \(0.319637\pi\)
\(390\) 0 0
\(391\) −2.14118 2.94708i −0.108284 0.149040i
\(392\) 0.121121 + 0.372773i 0.00611754 + 0.0188279i
\(393\) 0 0
\(394\) 1.48615 + 1.07975i 0.0748714 + 0.0543972i
\(395\) 20.8403 1.04859
\(396\) 0 0
\(397\) −19.0245 −0.954812 −0.477406 0.878683i \(-0.658423\pi\)
−0.477406 + 0.878683i \(0.658423\pi\)
\(398\) 2.33397 + 1.69573i 0.116991 + 0.0849991i
\(399\) 0 0
\(400\) −3.95391 12.1689i −0.197696 0.608445i
\(401\) −18.0482 24.8413i −0.901286 1.24051i −0.970056 0.242881i \(-0.921907\pi\)
0.0687699 0.997633i \(-0.478093\pi\)
\(402\) 0 0
\(403\) −16.2592 + 5.28293i −0.809928 + 0.263162i
\(404\) 5.41185 16.6560i 0.269250 0.828665i
\(405\) 0 0
\(406\) 6.58454i 0.326785i
\(407\) −5.73509 + 18.8693i −0.284278 + 0.935315i
\(408\) 0 0
\(409\) −6.97905 + 9.60583i −0.345092 + 0.474978i −0.945920 0.324400i \(-0.894838\pi\)
0.600828 + 0.799378i \(0.294838\pi\)
\(410\) 5.94461 + 1.93152i 0.293584 + 0.0953911i
\(411\) 0 0
\(412\) −25.9528 + 18.8558i −1.27860 + 0.928958i
\(413\) 0.205228 0.149107i 0.0100986 0.00733706i
\(414\) 0 0
\(415\) 21.7694 + 7.07330i 1.06862 + 0.347215i
\(416\) −4.89265 + 6.73416i −0.239882 + 0.330169i
\(417\) 0 0
\(418\) 0.0306992 + 1.60765i 0.00150155 + 0.0786326i
\(419\) 10.0629i 0.491606i 0.969320 + 0.245803i \(0.0790516\pi\)
−0.969320 + 0.245803i \(0.920948\pi\)
\(420\) 0 0
\(421\) −1.93337 + 5.95029i −0.0942265 + 0.289999i −0.987051 0.160405i \(-0.948720\pi\)
0.892825 + 0.450404i \(0.148720\pi\)
\(422\) 0.892232 0.289904i 0.0434332 0.0141123i
\(423\) 0 0
\(424\) −6.13566 8.44502i −0.297974 0.410126i
\(425\) 4.87643 + 15.0081i 0.236541 + 0.728000i
\(426\) 0 0
\(427\) 4.71618 + 3.42651i 0.228232 + 0.165820i
\(428\) 13.7682 0.665512
\(429\) 0 0
\(430\) 8.80238 0.424489
\(431\) −15.8885 11.5436i −0.765321 0.556038i 0.135217 0.990816i \(-0.456827\pi\)
−0.900538 + 0.434778i \(0.856827\pi\)
\(432\) 0 0
\(433\) 9.66882 + 29.7576i 0.464654 + 1.43006i 0.859418 + 0.511274i \(0.170826\pi\)
−0.394764 + 0.918783i \(0.629174\pi\)
\(434\) −2.42681 3.34022i −0.116491 0.160335i
\(435\) 0 0
\(436\) 15.8695 5.15631i 0.760011 0.246942i
\(437\) −0.482131 + 1.48385i −0.0230634 + 0.0709820i
\(438\) 0 0
\(439\) 20.1935i 0.963782i −0.876231 0.481891i \(-0.839950\pi\)
0.876231 0.481891i \(-0.160050\pi\)
\(440\) 9.25644 + 2.81339i 0.441283 + 0.134123i
\(441\) 0 0
\(442\) 1.90019 2.61539i 0.0903828 0.124401i
\(443\) 23.1752 + 7.53009i 1.10109 + 0.357765i 0.802521 0.596624i \(-0.203491\pi\)
0.298567 + 0.954389i \(0.403491\pi\)
\(444\) 0 0
\(445\) 4.88890 3.55199i 0.231756 0.168381i
\(446\) 0.0581253 0.0422305i 0.00275231 0.00199967i
\(447\) 0 0
\(448\) 16.7996 + 5.45852i 0.793706 + 0.257891i
\(449\) 1.94082 2.67131i 0.0915930 0.126067i −0.760761 0.649032i \(-0.775174\pi\)
0.852354 + 0.522965i \(0.175174\pi\)
\(450\) 0 0
\(451\) 22.3104 16.8695i 1.05055 0.794354i
\(452\) 22.0817i 1.03863i
\(453\) 0 0
\(454\) −1.43109 + 4.40443i −0.0671642 + 0.206710i
\(455\) 21.5773 7.01089i 1.01156 0.328675i
\(456\) 0 0
\(457\) −9.17968 12.6347i −0.429407 0.591028i 0.538410 0.842683i \(-0.319025\pi\)
−0.967817 + 0.251655i \(0.919025\pi\)
\(458\) 2.06760 + 6.36342i 0.0966126 + 0.297343i
\(459\) 0 0
\(460\) 3.73517 + 2.71376i 0.174153 + 0.126530i
\(461\) −36.5685 −1.70316 −0.851582 0.524221i \(-0.824356\pi\)
−0.851582 + 0.524221i \(0.824356\pi\)
\(462\) 0 0
\(463\) 4.45531 0.207056 0.103528 0.994627i \(-0.466987\pi\)
0.103528 + 0.994627i \(0.466987\pi\)
\(464\) −27.9434 20.3021i −1.29724 0.942499i
\(465\) 0 0
\(466\) −0.846784 2.60613i −0.0392265 0.120727i
\(467\) −24.4676 33.6768i −1.13223 1.55838i −0.783769 0.621052i \(-0.786706\pi\)
−0.348458 0.937325i \(-0.613294\pi\)
\(468\) 0 0
\(469\) −3.64033 + 1.18282i −0.168095 + 0.0546173i
\(470\) 1.76772 5.44049i 0.0815390 0.250951i
\(471\) 0 0
\(472\) 0.0931482i 0.00428749i
\(473\) 22.5398 32.3029i 1.03638 1.48529i
\(474\) 0 0
\(475\) 3.97270 5.46796i 0.182280 0.250887i
\(476\) −22.3346 7.25696i −1.02371 0.332622i
\(477\) 0 0
\(478\) −1.52347 + 1.10687i −0.0696819 + 0.0506269i
\(479\) 2.84896 2.06989i 0.130172 0.0945756i −0.520794 0.853682i \(-0.674364\pi\)
0.650966 + 0.759107i \(0.274364\pi\)
\(480\) 0 0
\(481\) −16.1512 5.24783i −0.736430 0.239281i
\(482\) 0.397925 0.547696i 0.0181250 0.0249469i
\(483\) 0 0
\(484\) 16.7353 13.1637i 0.760697 0.598351i
\(485\) 4.88056i 0.221615i
\(486\) 0 0
\(487\) 9.85775 30.3390i 0.446697 1.37479i −0.433914 0.900954i \(-0.642868\pi\)
0.880611 0.473839i \(-0.157132\pi\)
\(488\) −2.03580 + 0.661472i −0.0921564 + 0.0299434i
\(489\) 0 0
\(490\) 0.171033 + 0.235407i 0.00772648 + 0.0106346i
\(491\) 7.54595 + 23.2241i 0.340544 + 1.04809i 0.963926 + 0.266170i \(0.0857581\pi\)
−0.623382 + 0.781917i \(0.714242\pi\)
\(492\) 0 0
\(493\) 34.4630 + 25.0389i 1.55214 + 1.12769i
\(494\) −1.38461 −0.0622964
\(495\) 0 0
\(496\) −21.6577 −0.972460
\(497\) −7.93893 5.76797i −0.356110 0.258729i
\(498\) 0 0
\(499\) −7.19057 22.1303i −0.321894 0.990689i −0.972823 0.231550i \(-0.925620\pi\)
0.650929 0.759139i \(-0.274380\pi\)
\(500\) 4.86498 + 6.69608i 0.217569 + 0.299458i
\(501\) 0 0
\(502\) −5.85431 + 1.90218i −0.261291 + 0.0848985i
\(503\) 11.2856 34.7334i 0.503199 1.54869i −0.300579 0.953757i \(-0.597180\pi\)
0.803778 0.594930i \(-0.202820\pi\)
\(504\) 0 0
\(505\) 26.4348i 1.17633i
\(506\) −0.649061 + 0.224681i −0.0288543 + 0.00998829i
\(507\) 0 0
\(508\) −3.28022 + 4.51483i −0.145536 + 0.200313i
\(509\) −23.6347 7.67938i −1.04759 0.340383i −0.265868 0.964009i \(-0.585659\pi\)
−0.781722 + 0.623627i \(0.785659\pi\)
\(510\) 0 0
\(511\) −3.87030 + 2.81193i −0.171212 + 0.124393i
\(512\) −14.3757 + 10.4445i −0.635321 + 0.461588i
\(513\) 0 0
\(514\) 4.04257 + 1.31351i 0.178310 + 0.0579364i
\(515\) −28.4615 + 39.1739i −1.25416 + 1.72621i
\(516\) 0 0
\(517\) −15.4389 20.4184i −0.679003 0.897999i
\(518\) 4.10130i 0.180201i
\(519\) 0 0
\(520\) −2.57436 + 7.92306i −0.112893 + 0.347449i
\(521\) 9.26334 3.00984i 0.405834 0.131864i −0.0989844 0.995089i \(-0.531559\pi\)
0.504819 + 0.863225i \(0.331559\pi\)
\(522\) 0 0
\(523\) 19.5526 + 26.9118i 0.854975 + 1.17677i 0.982744 + 0.184968i \(0.0592182\pi\)
−0.127769 + 0.991804i \(0.540782\pi\)
\(524\) 1.25704 + 3.86877i 0.0549140 + 0.169008i
\(525\) 0 0
\(526\) −2.23997 1.62743i −0.0976674 0.0709595i
\(527\) 26.7108 1.16354
\(528\) 0 0
\(529\) 22.3335 0.971023
\(530\) −6.26937 4.55496i −0.272324 0.197855i
\(531\) 0 0
\(532\) 3.10816 + 9.56592i 0.134756 + 0.414735i
\(533\) 14.1570 + 19.4854i 0.613207 + 0.844007i
\(534\) 0 0
\(535\) 19.7650 6.42205i 0.854517 0.277649i
\(536\) 0.434323 1.33671i 0.0187599 0.0577371i
\(537\) 0 0
\(538\) 3.97933i 0.171561i
\(539\) 1.30185 0.0248597i 0.0560746 0.00107078i
\(540\) 0 0
\(541\) −6.85075 + 9.42925i −0.294537 + 0.405395i −0.930481 0.366340i \(-0.880611\pi\)
0.635944 + 0.771735i \(0.280611\pi\)
\(542\) 0.700877 + 0.227729i 0.0301052 + 0.00978178i
\(543\) 0 0
\(544\) 10.5215 7.64432i 0.451106 0.327748i
\(545\) 20.3764 14.8043i 0.872829 0.634147i
\(546\) 0 0
\(547\) 0.773004 + 0.251164i 0.0330513 + 0.0107390i 0.325496 0.945543i \(-0.394469\pi\)
−0.292445 + 0.956282i \(0.594469\pi\)
\(548\) −5.77297 + 7.94581i −0.246609 + 0.339428i
\(549\) 0 0
\(550\) 2.97487 0.0568072i 0.126849 0.00242227i
\(551\) 18.2450i 0.777264i
\(552\) 0 0
\(553\) −5.99302 + 18.4446i −0.254849 + 0.784345i
\(554\) −5.09419 + 1.65520i −0.216431 + 0.0703228i
\(555\) 0 0
\(556\) −19.8923 27.3794i −0.843620 1.16114i
\(557\) 2.14843 + 6.61219i 0.0910320 + 0.280168i 0.986199 0.165563i \(-0.0529440\pi\)
−0.895167 + 0.445730i \(0.852944\pi\)
\(558\) 0 0
\(559\) 27.4405 + 19.9367i 1.16061 + 0.843233i
\(560\) 28.7416 1.21455
\(561\) 0 0
\(562\) 0.783948 0.0330689
\(563\) −23.2654 16.9033i −0.980519 0.712388i −0.0226941 0.999742i \(-0.507224\pi\)
−0.957824 + 0.287354i \(0.907224\pi\)
\(564\) 0 0
\(565\) 10.2998 + 31.6994i 0.433314 + 1.33360i
\(566\) 3.34367 + 4.60217i 0.140545 + 0.193444i
\(567\) 0 0
\(568\) 3.42694 1.11348i 0.143791 0.0467207i
\(569\) −3.22890 + 9.93752i −0.135362 + 0.416602i −0.995646 0.0932129i \(-0.970286\pi\)
0.860284 + 0.509815i \(0.170286\pi\)
\(570\) 0 0
\(571\) 21.2530i 0.889409i 0.895677 + 0.444704i \(0.146691\pi\)
−0.895677 + 0.444704i \(0.853309\pi\)
\(572\) 11.0581 + 14.6247i 0.462364 + 0.611489i
\(573\) 0 0
\(574\) −3.41897 + 4.70580i −0.142705 + 0.196416i
\(575\) 2.74578 + 0.892157i 0.114507 + 0.0372055i
\(576\) 0 0
\(577\) −12.6856 + 9.21665i −0.528110 + 0.383694i −0.819650 0.572864i \(-0.805832\pi\)
0.291541 + 0.956558i \(0.405832\pi\)
\(578\) −0.597432 + 0.434060i −0.0248499 + 0.0180545i
\(579\) 0 0
\(580\) −51.3477 16.6839i −2.13210 0.692761i
\(581\) −12.5204 + 17.2328i −0.519432 + 0.714937i
\(582\) 0 0
\(583\) −32.7694 + 11.3436i −1.35717 + 0.469803i
\(584\) 1.75664i 0.0726903i
\(585\) 0 0
\(586\) −1.62588 + 5.00395i −0.0671646 + 0.206711i
\(587\) −19.1691 + 6.22843i −0.791195 + 0.257075i −0.676613 0.736339i \(-0.736553\pi\)
−0.114582 + 0.993414i \(0.536553\pi\)
\(588\) 0 0
\(589\) −6.72441 9.25536i −0.277075 0.381360i
\(590\) 0.0213688 + 0.0657664i 0.000879739 + 0.00270756i
\(591\) 0 0
\(592\) −17.4051 12.6455i −0.715343 0.519727i
\(593\) 40.5694 1.66599 0.832993 0.553284i \(-0.186626\pi\)
0.832993 + 0.553284i \(0.186626\pi\)
\(594\) 0 0
\(595\) −35.4475 −1.45320
\(596\) 8.85798 + 6.43570i 0.362837 + 0.263617i
\(597\) 0 0
\(598\) −0.182768 0.562502i −0.00747394 0.0230024i
\(599\) −6.42889 8.84861i −0.262678 0.361545i 0.657223 0.753696i \(-0.271731\pi\)
−0.919901 + 0.392151i \(0.871731\pi\)
\(600\) 0 0
\(601\) 15.5556 5.05433i 0.634527 0.206170i 0.0259478 0.999663i \(-0.491740\pi\)
0.608580 + 0.793493i \(0.291740\pi\)
\(602\) −2.53129 + 7.79050i −0.103168 + 0.317517i
\(603\) 0 0
\(604\) 17.7605i 0.722665i
\(605\) 17.8844 26.7032i 0.727104 1.08564i
\(606\) 0 0
\(607\) −14.0272 + 19.3068i −0.569348 + 0.783641i −0.992477 0.122429i \(-0.960932\pi\)
0.423129 + 0.906069i \(0.360932\pi\)
\(608\) −5.29755 1.72128i −0.214844 0.0698070i
\(609\) 0 0
\(610\) −1.28561 + 0.934052i −0.0520529 + 0.0378187i
\(611\) 17.8330 12.9564i 0.721445 0.524161i
\(612\) 0 0
\(613\) 0.0461533 + 0.0149961i 0.00186411 + 0.000605687i 0.309949 0.950753i \(-0.399688\pi\)
−0.308085 + 0.951359i \(0.599688\pi\)
\(614\) −2.23774 + 3.07999i −0.0903080 + 0.124298i
\(615\) 0 0
\(616\) −5.15183 + 7.38332i −0.207573 + 0.297482i
\(617\) 8.24561i 0.331956i 0.986129 + 0.165978i \(0.0530780\pi\)
−0.986129 + 0.165978i \(0.946922\pi\)
\(618\) 0 0
\(619\) −0.537464 + 1.65414i −0.0216025 + 0.0664857i −0.961277 0.275585i \(-0.911128\pi\)
0.939674 + 0.342071i \(0.111128\pi\)
\(620\) −32.1968 + 10.4614i −1.29305 + 0.420139i
\(621\) 0 0
\(622\) −0.307013 0.422567i −0.0123101 0.0169434i
\(623\) 1.73778 + 5.34834i 0.0696227 + 0.214277i
\(624\) 0 0
\(625\) 24.4126 + 17.7368i 0.976506 + 0.709473i
\(626\) −6.30955 −0.252180
\(627\) 0 0
\(628\) 5.91094 0.235872
\(629\) 21.4659 + 15.5959i 0.855903 + 0.621850i
\(630\) 0 0
\(631\) −8.14182 25.0580i −0.324121 0.997541i −0.971836 0.235659i \(-0.924275\pi\)
0.647715 0.761883i \(-0.275725\pi\)
\(632\) −4.18580 5.76126i −0.166502 0.229171i
\(633\) 0 0
\(634\) 0.104400 0.0339216i 0.00414625 0.00134720i
\(635\) −2.60303 + 8.01130i −0.103298 + 0.317919i
\(636\) 0 0
\(637\) 1.12123i 0.0444249i
\(638\) 6.40670 4.84429i 0.253644 0.191787i
\(639\) 0 0
\(640\) −12.8409 + 17.6740i −0.507582 + 0.698626i
\(641\) −8.27017 2.68714i −0.326652 0.106136i 0.141100 0.989995i \(-0.454936\pi\)
−0.467752 + 0.883860i \(0.654936\pi\)
\(642\) 0 0
\(643\) 17.4877 12.7055i 0.689646 0.501057i −0.186897 0.982379i \(-0.559843\pi\)
0.876544 + 0.481322i \(0.159843\pi\)
\(644\) −3.47592 + 2.52540i −0.136970 + 0.0995148i
\(645\) 0 0
\(646\) 2.05744 + 0.668503i 0.0809489 + 0.0263019i
\(647\) −17.2616 + 23.7586i −0.678625 + 0.934048i −0.999916 0.0129330i \(-0.995883\pi\)
0.321291 + 0.946980i \(0.395883\pi\)
\(648\) 0 0
\(649\) 0.296067 + 0.0899860i 0.0116216 + 0.00353226i
\(650\) 2.56214i 0.100495i
\(651\) 0 0
\(652\) −4.72806 + 14.5515i −0.185165 + 0.569880i
\(653\) −22.5339 + 7.32170i −0.881818 + 0.286520i −0.714712 0.699419i \(-0.753442\pi\)
−0.167106 + 0.985939i \(0.553442\pi\)
\(654\) 0 0
\(655\) 3.60909 + 4.96749i 0.141019 + 0.194096i
\(656\) 9.42876 + 29.0187i 0.368131 + 1.13299i
\(657\) 0 0
\(658\) 4.30674 + 3.12903i 0.167894 + 0.121982i
\(659\) 34.5941 1.34759 0.673797 0.738916i \(-0.264662\pi\)
0.673797 + 0.738916i \(0.264662\pi\)
\(660\) 0 0
\(661\) 35.4913 1.38045 0.690225 0.723595i \(-0.257512\pi\)
0.690225 + 0.723595i \(0.257512\pi\)
\(662\) 3.55229 + 2.58089i 0.138064 + 0.100309i
\(663\) 0 0
\(664\) −2.41700 7.43877i −0.0937979 0.288680i
\(665\) 8.92385 + 12.2826i 0.346052 + 0.476300i
\(666\) 0 0
\(667\) 7.41211 2.40834i 0.286998 0.0932513i
\(668\) 9.83822 30.2789i 0.380652 1.17153i
\(669\) 0 0
\(670\) 1.04341i 0.0403104i
\(671\) 0.135765 + 7.10971i 0.00524115 + 0.274467i
\(672\) 0 0
\(673\) −12.2854 + 16.9095i −0.473569 + 0.651812i −0.977253 0.212076i \(-0.931978\pi\)
0.503684 + 0.863888i \(0.331978\pi\)
\(674\) −6.04715 1.96484i −0.232928 0.0756827i
\(675\) 0 0
\(676\) 7.58475 5.51064i 0.291721 0.211948i
\(677\) 19.6090 14.2468i 0.753634 0.547547i −0.143317 0.989677i \(-0.545777\pi\)
0.896951 + 0.442130i \(0.145777\pi\)
\(678\) 0 0
\(679\) −4.31951 1.40350i −0.165768 0.0538612i
\(680\) 7.65068 10.5303i 0.293390 0.403817i
\(681\) 0 0
\(682\) 1.46458 4.81868i 0.0560817 0.184517i
\(683\) 17.6311i 0.674636i −0.941391 0.337318i \(-0.890480\pi\)
0.941391 0.337318i \(-0.109520\pi\)
\(684\) 0 0
\(685\) −4.58116 + 14.0994i −0.175037 + 0.538709i
\(686\) 4.33425 1.40828i 0.165482 0.0537685i
\(687\) 0 0
\(688\) 25.2565 + 34.7626i 0.962896 + 1.32531i
\(689\) −9.22748 28.3993i −0.351539 1.08193i
\(690\) 0 0
\(691\) −23.5718 17.1259i −0.896713 0.651500i 0.0409063 0.999163i \(-0.486976\pi\)
−0.937620 + 0.347663i \(0.886976\pi\)
\(692\) −30.0459 −1.14218
\(693\) 0 0
\(694\) −5.29496 −0.200994
\(695\) −41.3272 30.0260i −1.56763 1.13895i
\(696\) 0 0
\(697\) −11.6286 35.7893i −0.440466 1.35562i
\(698\) 2.68698 + 3.69831i 0.101704 + 0.139983i
\(699\) 0 0
\(700\) 17.7012 5.75148i 0.669044 0.217385i
\(701\) −4.54301 + 13.9820i −0.171587 + 0.528091i −0.999461 0.0328229i \(-0.989550\pi\)
0.827874 + 0.560914i \(0.189550\pi\)
\(702\) 0 0
\(703\) 11.3642i 0.428611i
\(704\) 7.04848 + 20.3617i 0.265649 + 0.767411i
\(705\) 0 0
\(706\) 2.42974 3.34425i 0.0914445 0.125863i
\(707\) 23.3960 + 7.60182i 0.879897 + 0.285896i
\(708\) 0 0
\(709\) −8.72312 + 6.33772i −0.327604 + 0.238018i −0.739413 0.673252i \(-0.764897\pi\)
0.411810 + 0.911270i \(0.364897\pi\)
\(710\) 2.16412 1.57233i 0.0812180 0.0590083i
\(711\) 0 0
\(712\) −1.96388 0.638103i −0.0735995 0.0239139i
\(713\) 2.87241 3.95353i 0.107572 0.148061i
\(714\) 0 0
\(715\) 22.6961 + 15.8366i 0.848785 + 0.592254i
\(716\) 10.0448i 0.375391i
\(717\) 0 0
\(718\) 1.94284 5.97944i 0.0725060 0.223151i
\(719\) 30.1960 9.81128i 1.12612 0.365899i 0.314020 0.949416i \(-0.398324\pi\)
0.812101 + 0.583517i \(0.198324\pi\)
\(720\) 0 0
\(721\) −26.4860 36.4549i −0.986390 1.35765i
\(722\) 1.20309 + 3.70273i 0.0447744 + 0.137801i
\(723\) 0 0
\(724\) 8.31889 + 6.04403i 0.309169 + 0.224625i
\(725\) −33.7614 −1.25387
\(726\) 0 0
\(727\) 23.6418 0.876828 0.438414 0.898773i \(-0.355540\pi\)
0.438414 + 0.898773i \(0.355540\pi\)
\(728\) −6.27196 4.55685i −0.232454 0.168888i
\(729\) 0 0
\(730\) −0.402984 1.24026i −0.0149151 0.0459040i
\(731\) −31.1493 42.8733i −1.15210 1.58573i
\(732\) 0 0
\(733\) 15.6206 5.07543i 0.576959 0.187465i −0.00597872 0.999982i \(-0.501903\pi\)
0.582938 + 0.812517i \(0.301903\pi\)
\(734\) 0.701877 2.16016i 0.0259068 0.0797328i
\(735\) 0 0
\(736\) 2.37936i 0.0877043i
\(737\) −3.82908 2.67181i −0.141046 0.0984172i
\(738\) 0 0
\(739\) 20.4813 28.1901i 0.753417 1.03699i −0.244316 0.969696i \(-0.578563\pi\)
0.997733 0.0672942i \(-0.0214366\pi\)
\(740\) −31.9829 10.3919i −1.17571 0.382013i
\(741\) 0 0
\(742\) 5.83422 4.23881i 0.214181 0.155611i
\(743\) −42.7101 + 31.0307i −1.56688 + 1.13841i −0.636813 + 0.771019i \(0.719748\pi\)
−0.930068 + 0.367387i \(0.880252\pi\)
\(744\) 0 0
\(745\) 15.7180 + 5.10708i 0.575862 + 0.187109i
\(746\) 2.52001 3.46850i 0.0922643 0.126991i
\(747\) 0 0
\(748\) −9.37077 27.0704i −0.342629 0.989791i
\(749\) 19.3397i 0.706657i
\(750\) 0 0
\(751\) 15.8766 48.8631i 0.579345 1.78304i −0.0415382 0.999137i \(-0.513226\pi\)
0.620883 0.783903i \(-0.286774\pi\)
\(752\) 26.5578 8.62917i 0.968465 0.314673i
\(753\) 0 0
\(754\) 4.06535 + 5.59548i 0.148051 + 0.203775i
\(755\) −8.28421 25.4962i −0.301493 0.927900i
\(756\) 0 0
\(757\) 5.71877 + 4.15493i 0.207852 + 0.151013i 0.686841 0.726807i \(-0.258997\pi\)
−0.478989 + 0.877821i \(0.658997\pi\)
\(758\) 5.00521 0.181797
\(759\) 0 0
\(760\) −5.57481 −0.202219
\(761\) 23.5688 + 17.1238i 0.854370 + 0.620736i 0.926347 0.376670i \(-0.122931\pi\)
−0.0719775 + 0.997406i \(0.522931\pi\)
\(762\) 0 0
\(763\) 7.24287 + 22.2913i 0.262210 + 0.806998i
\(764\) −12.4010 17.0685i −0.448653 0.617517i
\(765\) 0 0
\(766\) 1.20628 0.391945i 0.0435847 0.0141615i
\(767\) −0.0823407 + 0.253419i −0.00297315 + 0.00915042i
\(768\) 0 0
\(769\) 44.2408i 1.59536i 0.603079 + 0.797682i \(0.293940\pi\)
−0.603079 + 0.797682i \(0.706060\pi\)
\(770\) −1.94362 + 6.39479i −0.0700432 + 0.230452i
\(771\) 0 0
\(772\) 17.4831 24.0634i 0.629230 0.866061i
\(773\) 38.0786 + 12.3725i 1.36959 + 0.445007i 0.899234 0.437468i \(-0.144125\pi\)
0.470358 + 0.882476i \(0.344125\pi\)
\(774\) 0 0
\(775\) −17.1266 + 12.4432i −0.615204 + 0.446972i
\(776\) 1.34922 0.980265i 0.0484341 0.0351895i
\(777\) 0 0
\(778\) −2.37723 0.772409i −0.0852279 0.0276922i
\(779\) −9.47357 + 13.0393i −0.339426 + 0.467180i
\(780\) 0 0
\(781\) −0.228538 11.9680i −0.00817775 0.428250i
\(782\) 0.924086i 0.0330453i
\(783\) 0 0
\(784\) −0.438933 + 1.35090i −0.0156762 + 0.0482463i
\(785\) 8.48547 2.75709i 0.302859 0.0984049i
\(786\) 0 0
\(787\) −16.6720 22.9470i −0.594292 0.817973i 0.400878 0.916131i \(-0.368705\pi\)
−0.995171 + 0.0981579i \(0.968705\pi\)
\(788\) 4.33149 + 13.3309i 0.154303 + 0.474895i
\(789\) 0 0
\(790\) −4.27701 3.10743i −0.152169 0.110558i
\(791\) −31.0173 −1.10285
\(792\) 0 0
\(793\) −6.12332 −0.217446
\(794\) 3.90435 + 2.83668i 0.138560 + 0.100670i
\(795\) 0 0
\(796\) 6.80249 + 20.9359i 0.241108 + 0.742054i
\(797\) 8.78371 + 12.0897i 0.311135 + 0.428241i 0.935735 0.352704i \(-0.114738\pi\)
−0.624600 + 0.780945i \(0.714738\pi\)
\(798\) 0 0
\(799\) −32.7542 + 10.6425i −1.15876 + 0.376504i
\(800\) −3.18513 + 9.80283i −0.112611 + 0.346582i
\(801\) 0 0
\(802\) 7.78923i 0.275047i
\(803\) −5.58339 1.69700i −0.197034 0.0598860i
\(804\) 0 0
\(805\) −3.81192 + 5.24666i −0.134352 + 0.184920i
\(806\) 4.12456 + 1.34015i 0.145281 + 0.0472048i
\(807\) 0 0
\(808\) −7.30784 + 5.30946i −0.257089 + 0.186786i
\(809\) 24.0892 17.5019i 0.846933 0.615333i −0.0773660 0.997003i \(-0.524651\pi\)
0.924299 + 0.381670i \(0.124651\pi\)
\(810\) 0 0
\(811\) 41.9856 + 13.6420i 1.47432 + 0.479034i 0.932409 0.361405i \(-0.117703\pi\)
0.541906 + 0.840439i \(0.317703\pi\)
\(812\) 29.5320 40.6473i 1.03637 1.42644i
\(813\) 0 0
\(814\) 3.99053 3.01735i 0.139868 0.105758i
\(815\) 23.0948i 0.808975i
\(816\) 0 0
\(817\) −7.01391 + 21.5866i −0.245386 + 0.755220i
\(818\) 2.86459 0.930761i 0.100158 0.0325433i
\(819\) 0 0
\(820\) 28.0340 + 38.5854i 0.978988 + 1.34746i
\(821\) −1.23760 3.80893i −0.0431924 0.132933i 0.927135 0.374728i \(-0.122264\pi\)
−0.970327 + 0.241795i \(0.922264\pi\)
\(822\) 0 0
\(823\) −34.1262 24.7941i −1.18956 0.864268i −0.196345 0.980535i \(-0.562907\pi\)
−0.993218 + 0.116266i \(0.962907\pi\)
\(824\) 16.5460 0.576409
\(825\) 0 0
\(826\) −0.0643512 −0.00223906
\(827\) −21.5183 15.6340i −0.748266 0.543647i 0.147023 0.989133i \(-0.453031\pi\)
−0.895289 + 0.445486i \(0.853031\pi\)
\(828\) 0 0
\(829\) 3.77976 + 11.6329i 0.131276 + 0.404027i 0.994992 0.0999518i \(-0.0318689\pi\)
−0.863716 + 0.503979i \(0.831869\pi\)
\(830\) −3.41300 4.69759i −0.118467 0.163056i
\(831\) 0 0
\(832\) −17.6463 + 5.73362i −0.611774 + 0.198777i
\(833\) 0.541343 1.66608i 0.0187564 0.0577264i
\(834\) 0 0
\(835\) 48.0560i 1.66305i
\(836\) −7.02087 + 10.0619i −0.242822 + 0.347999i
\(837\) 0 0
\(838\) 1.50045 2.06519i 0.0518321 0.0713408i
\(839\) −9.17434 2.98092i −0.316733 0.102913i 0.146336 0.989235i \(-0.453252\pi\)
−0.463069 + 0.886322i \(0.653252\pi\)
\(840\) 0 0
\(841\) −50.2704 + 36.5236i −1.73346 + 1.25943i
\(842\) 1.28401 0.932887i 0.0442498 0.0321494i
\(843\) 0 0
\(844\) 6.80810 + 2.21209i 0.234345 + 0.0761432i
\(845\) 8.31793 11.4486i 0.286146 0.393846i
\(846\) 0 0
\(847\) 18.4906 + 23.5075i 0.635344 + 0.807727i
\(848\) 37.8287i 1.29904i
\(849\) 0 0
\(850\) 1.23703 3.80718i 0.0424298 0.130585i
\(851\) 4.61677 1.50008i 0.158261 0.0514221i
\(852\) 0 0
\(853\) −6.89976 9.49670i −0.236243 0.325161i 0.674391 0.738374i \(-0.264406\pi\)
−0.910634 + 0.413214i \(0.864406\pi\)
\(854\) −0.456976 1.40643i −0.0156374 0.0481270i
\(855\) 0 0
\(856\) −5.74518 4.17412i −0.196366 0.142668i
\(857\) −48.7738 −1.66608 −0.833041 0.553212i \(-0.813402\pi\)
−0.833041 + 0.553212i \(0.813402\pi\)
\(858\) 0 0
\(859\) −31.0880 −1.06071 −0.530355 0.847776i \(-0.677941\pi\)
−0.530355 + 0.847776i \(0.677941\pi\)
\(860\) 54.3383 + 39.4791i 1.85292 + 1.34623i
\(861\) 0 0
\(862\) 1.53952 + 4.73815i 0.0524362 + 0.161382i
\(863\) 30.6459 + 42.1805i 1.04320 + 1.43584i 0.894559 + 0.446950i \(0.147490\pi\)
0.148641 + 0.988891i \(0.452510\pi\)
\(864\) 0 0
\(865\) −43.1325 + 14.0146i −1.46655 + 0.476511i
\(866\) 2.45274 7.54876i 0.0833475 0.256517i
\(867\) 0 0
\(868\) 31.5040i 1.06931i
\(869\) −22.3556 + 7.73868i −0.758361 + 0.262517i
\(870\) 0 0
\(871\) 2.36324 3.25272i 0.0800753 0.110214i
\(872\) −8.18523 2.65954i −0.277187 0.0900635i
\(873\) 0 0
\(874\) 0.320198 0.232637i 0.0108309 0.00786907i
\(875\) −9.40572 + 6.83366i −0.317971 + 0.231020i
\(876\) 0 0
\(877\) 16.1564 + 5.24952i 0.545561 + 0.177264i 0.568814 0.822466i \(-0.307402\pi\)
−0.0232530 + 0.999730i \(0.507402\pi\)
\(878\) −3.01098 + 4.14426i −0.101616 + 0.139862i
\(879\) 0 0
\(880\) 21.1454 + 27.9653i 0.712810 + 0.942710i
\(881\) 50.3115i 1.69504i 0.530765 + 0.847519i \(0.321905\pi\)
−0.530765 + 0.847519i \(0.678095\pi\)
\(882\) 0 0
\(883\) 4.44037 13.6660i 0.149430 0.459899i −0.848124 0.529798i \(-0.822268\pi\)
0.997554 + 0.0698990i \(0.0222677\pi\)
\(884\) 23.4603 7.62270i 0.789054 0.256379i
\(885\) 0 0
\(886\) −3.63341 5.00096i −0.122067 0.168011i
\(887\) 12.7625 + 39.2790i 0.428523 + 1.31886i 0.899580 + 0.436756i \(0.143873\pi\)
−0.471057 + 0.882103i \(0.656127\pi\)
\(888\) 0 0
\(889\) −6.34181 4.60760i −0.212698 0.154534i
\(890\) −1.53296 −0.0513851
\(891\) 0 0
\(892\) 0.548221 0.0183558
\(893\) 11.9335 + 8.67018i 0.399339 + 0.290136i
\(894\) 0 0
\(895\) −4.68529 14.4198i −0.156612 0.482002i
\(896\) −11.9496 16.4473i −0.399209 0.549465i
\(897\) 0 0
\(898\) −0.796620 + 0.258838i −0.0265836 + 0.00863752i
\(899\) −17.6592 + 54.3495i −0.588968 + 1.81266i
\(900\) 0 0
\(901\) 46.6547i 1.55429i
\(902\) −7.09406 + 0.135466i −0.236206 + 0.00451053i
\(903\) 0 0
\(904\) 6.69450 9.21419i 0.222656 0.306460i
\(905\) 14.7614 + 4.79627i 0.490685 + 0.159433i
\(906\) 0 0
\(907\) 21.1288 15.3510i 0.701571 0.509721i −0.178872 0.983872i \(-0.557245\pi\)
0.880444 + 0.474151i \(0.157245\pi\)
\(908\) −28.5883 + 20.7706i −0.948738 + 0.689298i
\(909\) 0 0
\(910\) −5.47363 1.77849i −0.181449 0.0589563i
\(911\) 26.6929 36.7397i 0.884377 1.21724i −0.0908128 0.995868i \(-0.528946\pi\)
0.975189 0.221372i \(-0.0710535\pi\)
\(912\) 0 0
\(913\) −25.9787 + 0.496082i −0.859769 + 0.0164179i
\(914\) 3.96175i 0.131043i
\(915\) 0 0
\(916\) −15.7767 + 48.5555i −0.521275 + 1.60432i
\(917\) −5.43431 + 1.76572i −0.179457 + 0.0583091i
\(918\) 0 0
\(919\) −16.3737 22.5365i −0.540119 0.743410i 0.448511 0.893777i \(-0.351954\pi\)
−0.988630 + 0.150367i \(0.951954\pi\)
\(920\) −0.735874 2.26479i −0.0242610 0.0746678i
\(921\) 0 0
\(922\) 7.50486 + 5.45260i 0.247160 + 0.179572i
\(923\) 10.3076 0.339280
\(924\) 0 0
\(925\) −21.0289 −0.691427
\(926\) −0.914353 0.664317i −0.0300475 0.0218308i
\(927\) 0 0
\(928\) 8.59813 + 26.4623i 0.282248 + 0.868669i
\(929\) 29.2450 + 40.2523i 0.959497 + 1.32063i 0.947178 + 0.320710i \(0.103921\pi\)
0.0123191 + 0.999924i \(0.496079\pi\)
\(930\) 0 0
\(931\) −0.713584 + 0.231857i −0.0233868 + 0.00759882i
\(932\) 6.46131 19.8859i 0.211647 0.651384i
\(933\) 0 0
\(934\) 10.5597i 0.345524i
\(935\) −26.0789 34.4901i −0.852872 1.12795i
\(936\) 0 0
\(937\) 11.9943 16.5087i 0.391837 0.539317i −0.566835 0.823831i \(-0.691832\pi\)
0.958672 + 0.284514i \(0.0918323\pi\)
\(938\) 0.923462 + 0.300051i 0.0301521 + 0.00979702i
\(939\) 0 0
\(940\) 35.3132 25.6566i 1.15179 0.836825i
\(941\) 14.1929 10.3117i 0.462675 0.336153i −0.331904 0.943313i \(-0.607691\pi\)
0.794580 + 0.607160i \(0.207691\pi\)
\(942\) 0 0
\(943\) −6.54776 2.12750i −0.213224 0.0692808i
\(944\) −0.198413 + 0.273093i −0.00645781 + 0.00888841i
\(945\) 0 0
\(946\) −9.44237 + 3.26860i −0.306998 + 0.106271i
\(947\) 47.0672i 1.52948i −0.644340 0.764739i \(-0.722868\pi\)
0.644340 0.764739i \(-0.277132\pi\)
\(948\) 0 0
\(949\) 1.55283 4.77911i 0.0504069 0.155136i
\(950\) −1.63062 + 0.529820i −0.0529042 + 0.0171896i
\(951\) 0 0
\(952\) 7.11966 + 9.79937i 0.230749 + 0.317599i
\(953\) −15.9545 49.1029i −0.516817 1.59060i −0.779952 0.625839i \(-0.784757\pi\)
0.263136 0.964759i \(-0.415243\pi\)
\(954\) 0 0
\(955\) −25.7637 18.7185i −0.833695 0.605715i
\(956\) −14.3689 −0.464725
\(957\) 0 0
\(958\) −0.893318 −0.0288618
\(959\) −11.1612 8.10907i −0.360413 0.261855i
\(960\) 0 0
\(961\) 1.49341 + 4.59623i 0.0481744 + 0.148266i
\(962\) 2.53218 + 3.48525i 0.0816408 + 0.112369i
\(963\) 0 0
\(964\) 4.91289 1.59629i 0.158233 0.0514132i
\(965\) 13.8738 42.6991i 0.446613 1.37453i
\(966\) 0 0
\(967\) 33.6964i 1.08360i 0.840506 + 0.541802i \(0.182258\pi\)
−0.840506 + 0.541802i \(0.817742\pi\)
\(968\) −10.9741 + 0.419271i −0.352722 + 0.0134759i
\(969\) 0 0
\(970\) 0.727724 1.00163i 0.0233658 0.0321603i
\(971\) 53.1467 + 17.2684i 1.70556 + 0.554170i 0.989584 0.143955i \(-0.0459822\pi\)
0.715976 + 0.698125i \(0.245982\pi\)
\(972\) 0 0
\(973\) 38.4588 27.9419i 1.23293 0.895777i
\(974\) −6.54684 + 4.75656i −0.209774 + 0.152410i
\(975\) 0 0
\(976\) −7.37757 2.39712i −0.236150 0.0767299i
\(977\) 12.1432 16.7137i 0.388496 0.534719i −0.569314 0.822120i \(-0.692791\pi\)
0.957810 + 0.287401i \(0.0927912\pi\)
\(978\) 0 0
\(979\) −3.92539 + 5.62565i −0.125456 + 0.179797i
\(980\) 2.22029i 0.0709245i
\(981\) 0 0
\(982\) 1.91422 5.89137i 0.0610853 0.188001i
\(983\) −47.6740 + 15.4902i −1.52056 + 0.494061i −0.945936 0.324354i \(-0.894853\pi\)
−0.574628 + 0.818415i \(0.694853\pi\)
\(984\) 0 0
\(985\) 12.4362 + 17.1169i 0.396249 + 0.545390i
\(986\) −3.33931 10.2773i −0.106345 0.327297i
\(987\) 0 0
\(988\) −8.54737 6.21003i −0.271928 0.197567i
\(989\) −9.69548 −0.308298
\(990\) 0 0
\(991\) 45.3068 1.43922 0.719609 0.694379i \(-0.244321\pi\)
0.719609 + 0.694379i \(0.244321\pi\)
\(992\) 14.1147 + 10.2549i 0.448141 + 0.325594i
\(993\) 0 0
\(994\) 0.769246 + 2.36750i 0.0243990 + 0.0750924i
\(995\) 19.5307 + 26.8817i 0.619164 + 0.852206i
\(996\) 0 0
\(997\) 9.77676 3.17666i 0.309633 0.100606i −0.150079 0.988674i \(-0.547953\pi\)
0.459712 + 0.888068i \(0.347953\pi\)
\(998\) −1.82407 + 5.61392i −0.0577400 + 0.177705i
\(999\) 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 99.2.j.a.62.2 yes 16
3.2 odd 2 inner 99.2.j.a.62.3 yes 16
4.3 odd 2 1584.2.cd.c.161.2 16
9.2 odd 6 891.2.u.c.458.3 32
9.4 even 3 891.2.u.c.755.3 32
9.5 odd 6 891.2.u.c.755.2 32
9.7 even 3 891.2.u.c.458.2 32
11.5 even 5 1089.2.d.g.1088.10 16
11.6 odd 10 1089.2.d.g.1088.8 16
11.8 odd 10 inner 99.2.j.a.8.3 yes 16
12.11 even 2 1584.2.cd.c.161.3 16
33.5 odd 10 1089.2.d.g.1088.7 16
33.8 even 10 inner 99.2.j.a.8.2 16
33.17 even 10 1089.2.d.g.1088.9 16
44.19 even 10 1584.2.cd.c.305.3 16
99.41 even 30 891.2.u.c.107.2 32
99.52 odd 30 891.2.u.c.701.2 32
99.74 even 30 891.2.u.c.701.3 32
99.85 odd 30 891.2.u.c.107.3 32
132.107 odd 10 1584.2.cd.c.305.2 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.j.a.8.2 16 33.8 even 10 inner
99.2.j.a.8.3 yes 16 11.8 odd 10 inner
99.2.j.a.62.2 yes 16 1.1 even 1 trivial
99.2.j.a.62.3 yes 16 3.2 odd 2 inner
891.2.u.c.107.2 32 99.41 even 30
891.2.u.c.107.3 32 99.85 odd 30
891.2.u.c.458.2 32 9.7 even 3
891.2.u.c.458.3 32 9.2 odd 6
891.2.u.c.701.2 32 99.52 odd 30
891.2.u.c.701.3 32 99.74 even 30
891.2.u.c.755.2 32 9.5 odd 6
891.2.u.c.755.3 32 9.4 even 3
1089.2.d.g.1088.7 16 33.5 odd 10
1089.2.d.g.1088.8 16 11.6 odd 10
1089.2.d.g.1088.9 16 33.17 even 10
1089.2.d.g.1088.10 16 11.5 even 5
1584.2.cd.c.161.2 16 4.3 odd 2
1584.2.cd.c.161.3 16 12.11 even 2
1584.2.cd.c.305.2 16 132.107 odd 10
1584.2.cd.c.305.3 16 44.19 even 10