Properties

Label 891.2.f.b.163.1
Level $891$
Weight $2$
Character 891.163
Analytic conductor $7.115$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [891,2,Mod(82,891)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(891, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("891.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 891 = 3^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 891.f (of order \(5\), 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: \(7.11467082010\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 99)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 163.1
Root \(-0.309017 - 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 891.163
Dual form 891.2.f.b.82.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.118034 + 0.363271i) q^{2} +(1.50000 + 1.08981i) q^{4} +(-0.381966 - 1.17557i) q^{5} +(0.809017 + 0.587785i) q^{7} +(-1.19098 + 0.865300i) q^{8} +0.472136 q^{10} +(0.309017 - 3.30220i) q^{11} +(-2.00000 + 6.15537i) q^{13} +(-0.309017 + 0.224514i) q^{14} +(0.972136 + 2.99193i) q^{16} +(1.50000 + 4.61653i) q^{17} +(-0.809017 + 0.587785i) q^{19} +(0.708204 - 2.17963i) q^{20} +(1.16312 + 0.502029i) q^{22} +4.61803 q^{23} +(2.80902 - 2.04087i) q^{25} +(-2.00000 - 1.45309i) q^{26} +(0.572949 + 1.76336i) q^{28} +(3.92705 + 2.85317i) q^{29} +(0.190983 - 0.587785i) q^{31} -4.14590 q^{32} -1.85410 q^{34} +(0.381966 - 1.17557i) q^{35} +(4.11803 + 2.99193i) q^{37} +(-0.118034 - 0.363271i) q^{38} +(1.47214 + 1.06957i) q^{40} +(2.04508 - 1.48584i) q^{41} +1.85410 q^{43} +(4.06231 - 4.61653i) q^{44} +(-0.545085 + 1.67760i) q^{46} +(-9.66312 + 7.02067i) q^{47} +(-1.85410 - 5.70634i) q^{49} +(0.409830 + 1.26133i) q^{50} +(-9.70820 + 7.05342i) q^{52} +(1.26393 - 3.88998i) q^{53} +(-4.00000 + 0.898056i) q^{55} -1.47214 q^{56} +(-1.50000 + 1.08981i) q^{58} +(-1.30902 - 0.951057i) q^{59} +(3.35410 + 10.3229i) q^{61} +(0.190983 + 0.138757i) q^{62} +(-1.45492 + 4.47777i) q^{64} +8.00000 q^{65} +6.00000 q^{67} +(-2.78115 + 8.55951i) q^{68} +(0.381966 + 0.277515i) q^{70} +(-0.899187 - 2.76741i) q^{71} +(0.118034 + 0.0857567i) q^{73} +(-1.57295 + 1.14281i) q^{74} -1.85410 q^{76} +(2.19098 - 2.48990i) q^{77} +(3.26393 - 10.0453i) q^{79} +(3.14590 - 2.28563i) q^{80} +(0.298374 + 0.918300i) q^{82} +(-3.01722 - 9.28605i) q^{83} +(4.85410 - 3.52671i) q^{85} +(-0.218847 + 0.673542i) q^{86} +(2.48936 + 4.20025i) q^{88} -6.76393 q^{89} +(-5.23607 + 3.80423i) q^{91} +(6.92705 + 5.03280i) q^{92} +(-1.40983 - 4.33901i) q^{94} +(1.00000 + 0.726543i) q^{95} +(1.85410 - 5.70634i) q^{97} +2.29180 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} + 6 q^{4} - 6 q^{5} + q^{7} - 7 q^{8} - 16 q^{10} - q^{11} - 8 q^{13} + q^{14} - 14 q^{16} + 6 q^{17} - q^{19} - 24 q^{20} - 11 q^{22} + 14 q^{23} + 9 q^{25} - 8 q^{26} + 9 q^{28} + 9 q^{29}+ \cdots + 36 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).

\(n\) \(244\) \(650\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.118034 + 0.363271i −0.0834626 + 0.256872i −0.984076 0.177750i \(-0.943118\pi\)
0.900613 + 0.434622i \(0.143118\pi\)
\(3\) 0 0
\(4\) 1.50000 + 1.08981i 0.750000 + 0.544907i
\(5\) −0.381966 1.17557i −0.170820 0.525731i 0.828598 0.559845i \(-0.189139\pi\)
−0.999418 + 0.0341136i \(0.989139\pi\)
\(6\) 0 0
\(7\) 0.809017 + 0.587785i 0.305780 + 0.222162i 0.730084 0.683358i \(-0.239481\pi\)
−0.424304 + 0.905520i \(0.639481\pi\)
\(8\) −1.19098 + 0.865300i −0.421076 + 0.305930i
\(9\) 0 0
\(10\) 0.472136 0.149302
\(11\) 0.309017 3.30220i 0.0931721 0.995650i
\(12\) 0 0
\(13\) −2.00000 + 6.15537i −0.554700 + 1.70719i 0.142034 + 0.989862i \(0.454636\pi\)
−0.696734 + 0.717330i \(0.745364\pi\)
\(14\) −0.309017 + 0.224514i −0.0825883 + 0.0600039i
\(15\) 0 0
\(16\) 0.972136 + 2.99193i 0.243034 + 0.747982i
\(17\) 1.50000 + 4.61653i 0.363803 + 1.11967i 0.950727 + 0.310029i \(0.100339\pi\)
−0.586924 + 0.809642i \(0.699661\pi\)
\(18\) 0 0
\(19\) −0.809017 + 0.587785i −0.185601 + 0.134847i −0.676706 0.736253i \(-0.736593\pi\)
0.491105 + 0.871100i \(0.336593\pi\)
\(20\) 0.708204 2.17963i 0.158359 0.487380i
\(21\) 0 0
\(22\) 1.16312 + 0.502029i 0.247978 + 0.107033i
\(23\) 4.61803 0.962927 0.481463 0.876466i \(-0.340105\pi\)
0.481463 + 0.876466i \(0.340105\pi\)
\(24\) 0 0
\(25\) 2.80902 2.04087i 0.561803 0.408174i
\(26\) −2.00000 1.45309i −0.392232 0.284973i
\(27\) 0 0
\(28\) 0.572949 + 1.76336i 0.108277 + 0.333243i
\(29\) 3.92705 + 2.85317i 0.729235 + 0.529820i 0.889321 0.457283i \(-0.151177\pi\)
−0.160086 + 0.987103i \(0.551177\pi\)
\(30\) 0 0
\(31\) 0.190983 0.587785i 0.0343016 0.105569i −0.932440 0.361325i \(-0.882324\pi\)
0.966741 + 0.255756i \(0.0823244\pi\)
\(32\) −4.14590 −0.732898
\(33\) 0 0
\(34\) −1.85410 −0.317976
\(35\) 0.381966 1.17557i 0.0645640 0.198708i
\(36\) 0 0
\(37\) 4.11803 + 2.99193i 0.677001 + 0.491870i 0.872361 0.488862i \(-0.162588\pi\)
−0.195361 + 0.980731i \(0.562588\pi\)
\(38\) −0.118034 0.363271i −0.0191476 0.0589304i
\(39\) 0 0
\(40\) 1.47214 + 1.06957i 0.232765 + 0.169114i
\(41\) 2.04508 1.48584i 0.319389 0.232049i −0.416526 0.909124i \(-0.636752\pi\)
0.735915 + 0.677074i \(0.236752\pi\)
\(42\) 0 0
\(43\) 1.85410 0.282748 0.141374 0.989956i \(-0.454848\pi\)
0.141374 + 0.989956i \(0.454848\pi\)
\(44\) 4.06231 4.61653i 0.612416 0.695967i
\(45\) 0 0
\(46\) −0.545085 + 1.67760i −0.0803684 + 0.247348i
\(47\) −9.66312 + 7.02067i −1.40951 + 1.02407i −0.416117 + 0.909311i \(0.636609\pi\)
−0.993393 + 0.114759i \(0.963391\pi\)
\(48\) 0 0
\(49\) −1.85410 5.70634i −0.264872 0.815191i
\(50\) 0.409830 + 1.26133i 0.0579587 + 0.178379i
\(51\) 0 0
\(52\) −9.70820 + 7.05342i −1.34629 + 0.978134i
\(53\) 1.26393 3.88998i 0.173614 0.534330i −0.825953 0.563739i \(-0.809362\pi\)
0.999567 + 0.0294087i \(0.00936242\pi\)
\(54\) 0 0
\(55\) −4.00000 + 0.898056i −0.539360 + 0.121094i
\(56\) −1.47214 −0.196722
\(57\) 0 0
\(58\) −1.50000 + 1.08981i −0.196960 + 0.143100i
\(59\) −1.30902 0.951057i −0.170419 0.123817i 0.499306 0.866426i \(-0.333588\pi\)
−0.669726 + 0.742609i \(0.733588\pi\)
\(60\) 0 0
\(61\) 3.35410 + 10.3229i 0.429449 + 1.32171i 0.898669 + 0.438626i \(0.144535\pi\)
−0.469221 + 0.883081i \(0.655465\pi\)
\(62\) 0.190983 + 0.138757i 0.0242549 + 0.0176222i
\(63\) 0 0
\(64\) −1.45492 + 4.47777i −0.181864 + 0.559721i
\(65\) 8.00000 0.992278
\(66\) 0 0
\(67\) 6.00000 0.733017 0.366508 0.930415i \(-0.380553\pi\)
0.366508 + 0.930415i \(0.380553\pi\)
\(68\) −2.78115 + 8.55951i −0.337264 + 1.03799i
\(69\) 0 0
\(70\) 0.381966 + 0.277515i 0.0456537 + 0.0331693i
\(71\) −0.899187 2.76741i −0.106714 0.328431i 0.883415 0.468591i \(-0.155238\pi\)
−0.990129 + 0.140160i \(0.955238\pi\)
\(72\) 0 0
\(73\) 0.118034 + 0.0857567i 0.0138148 + 0.0100371i 0.594671 0.803969i \(-0.297282\pi\)
−0.580856 + 0.814006i \(0.697282\pi\)
\(74\) −1.57295 + 1.14281i −0.182852 + 0.132849i
\(75\) 0 0
\(76\) −1.85410 −0.212680
\(77\) 2.19098 2.48990i 0.249686 0.283750i
\(78\) 0 0
\(79\) 3.26393 10.0453i 0.367221 1.13019i −0.581357 0.813648i \(-0.697478\pi\)
0.948579 0.316542i \(-0.102522\pi\)
\(80\) 3.14590 2.28563i 0.351722 0.255541i
\(81\) 0 0
\(82\) 0.298374 + 0.918300i 0.0329499 + 0.101409i
\(83\) −3.01722 9.28605i −0.331183 1.01928i −0.968572 0.248734i \(-0.919985\pi\)
0.637389 0.770542i \(-0.280015\pi\)
\(84\) 0 0
\(85\) 4.85410 3.52671i 0.526501 0.382526i
\(86\) −0.218847 + 0.673542i −0.0235989 + 0.0726299i
\(87\) 0 0
\(88\) 2.48936 + 4.20025i 0.265366 + 0.447749i
\(89\) −6.76393 −0.716975 −0.358488 0.933534i \(-0.616707\pi\)
−0.358488 + 0.933534i \(0.616707\pi\)
\(90\) 0 0
\(91\) −5.23607 + 3.80423i −0.548889 + 0.398791i
\(92\) 6.92705 + 5.03280i 0.722195 + 0.524705i
\(93\) 0 0
\(94\) −1.40983 4.33901i −0.145413 0.447535i
\(95\) 1.00000 + 0.726543i 0.102598 + 0.0745417i
\(96\) 0 0
\(97\) 1.85410 5.70634i 0.188256 0.579391i −0.811734 0.584028i \(-0.801476\pi\)
0.999989 + 0.00463676i \(0.00147593\pi\)
\(98\) 2.29180 0.231506
\(99\) 0 0
\(100\) 6.43769 0.643769
\(101\) −2.61803 + 8.05748i −0.260504 + 0.801749i 0.732191 + 0.681099i \(0.238498\pi\)
−0.992695 + 0.120650i \(0.961502\pi\)
\(102\) 0 0
\(103\) 8.28115 + 6.01661i 0.815966 + 0.592834i 0.915554 0.402195i \(-0.131752\pi\)
−0.0995880 + 0.995029i \(0.531752\pi\)
\(104\) −2.94427 9.06154i −0.288710 0.888557i
\(105\) 0 0
\(106\) 1.26393 + 0.918300i 0.122764 + 0.0891932i
\(107\) −11.3541 + 8.24924i −1.09764 + 0.797484i −0.980673 0.195652i \(-0.937318\pi\)
−0.116969 + 0.993136i \(0.537318\pi\)
\(108\) 0 0
\(109\) 7.14590 0.684453 0.342226 0.939618i \(-0.388819\pi\)
0.342226 + 0.939618i \(0.388819\pi\)
\(110\) 0.145898 1.55909i 0.0139108 0.148653i
\(111\) 0 0
\(112\) −0.972136 + 2.99193i −0.0918582 + 0.282711i
\(113\) −13.9443 + 10.1311i −1.31177 + 0.953054i −0.311771 + 0.950157i \(0.600922\pi\)
−0.999996 + 0.00289705i \(0.999078\pi\)
\(114\) 0 0
\(115\) −1.76393 5.42882i −0.164488 0.506240i
\(116\) 2.78115 + 8.55951i 0.258224 + 0.794730i
\(117\) 0 0
\(118\) 0.500000 0.363271i 0.0460287 0.0334418i
\(119\) −1.50000 + 4.61653i −0.137505 + 0.423196i
\(120\) 0 0
\(121\) −10.8090 2.04087i −0.982638 0.185534i
\(122\) −4.14590 −0.375352
\(123\) 0 0
\(124\) 0.927051 0.673542i 0.0832516 0.0604859i
\(125\) −8.47214 6.15537i −0.757771 0.550553i
\(126\) 0 0
\(127\) −3.26393 10.0453i −0.289627 0.891381i −0.984973 0.172706i \(-0.944749\pi\)
0.695346 0.718675i \(-0.255251\pi\)
\(128\) −8.16312 5.93085i −0.721525 0.524218i
\(129\) 0 0
\(130\) −0.944272 + 2.90617i −0.0828181 + 0.254888i
\(131\) 21.2361 1.85540 0.927702 0.373322i \(-0.121781\pi\)
0.927702 + 0.373322i \(0.121781\pi\)
\(132\) 0 0
\(133\) −1.00000 −0.0867110
\(134\) −0.708204 + 2.17963i −0.0611795 + 0.188291i
\(135\) 0 0
\(136\) −5.78115 4.20025i −0.495730 0.360169i
\(137\) −2.66312 8.19624i −0.227526 0.700252i −0.998025 0.0628116i \(-0.979993\pi\)
0.770500 0.637440i \(-0.220007\pi\)
\(138\) 0 0
\(139\) −7.85410 5.70634i −0.666176 0.484005i 0.202567 0.979268i \(-0.435072\pi\)
−0.868743 + 0.495263i \(0.835072\pi\)
\(140\) 1.85410 1.34708i 0.156700 0.113849i
\(141\) 0 0
\(142\) 1.11146 0.0932713
\(143\) 19.7082 + 8.50651i 1.64808 + 0.711350i
\(144\) 0 0
\(145\) 1.85410 5.70634i 0.153975 0.473886i
\(146\) −0.0450850 + 0.0327561i −0.00373126 + 0.00271092i
\(147\) 0 0
\(148\) 2.91641 + 8.97578i 0.239727 + 0.737805i
\(149\) −4.69098 14.4374i −0.384300 1.18275i −0.936987 0.349365i \(-0.886397\pi\)
0.552686 0.833389i \(-0.313603\pi\)
\(150\) 0 0
\(151\) −3.50000 + 2.54290i −0.284826 + 0.206938i −0.721020 0.692915i \(-0.756326\pi\)
0.436194 + 0.899853i \(0.356326\pi\)
\(152\) 0.454915 1.40008i 0.0368985 0.113562i
\(153\) 0 0
\(154\) 0.645898 + 1.08981i 0.0520479 + 0.0878197i
\(155\) −0.763932 −0.0613605
\(156\) 0 0
\(157\) −5.78115 + 4.20025i −0.461386 + 0.335217i −0.794075 0.607820i \(-0.792044\pi\)
0.332689 + 0.943037i \(0.392044\pi\)
\(158\) 3.26393 + 2.37139i 0.259664 + 0.188657i
\(159\) 0 0
\(160\) 1.58359 + 4.87380i 0.125194 + 0.385307i
\(161\) 3.73607 + 2.71441i 0.294443 + 0.213926i
\(162\) 0 0
\(163\) 6.39919 19.6947i 0.501223 1.54261i −0.305806 0.952094i \(-0.598926\pi\)
0.807029 0.590512i \(-0.201074\pi\)
\(164\) 4.68692 0.365987
\(165\) 0 0
\(166\) 3.72949 0.289465
\(167\) −1.78115 + 5.48183i −0.137830 + 0.424196i −0.996019 0.0891363i \(-0.971589\pi\)
0.858190 + 0.513333i \(0.171589\pi\)
\(168\) 0 0
\(169\) −23.3713 16.9803i −1.79779 1.30617i
\(170\) 0.708204 + 2.17963i 0.0543168 + 0.167170i
\(171\) 0 0
\(172\) 2.78115 + 2.02063i 0.212061 + 0.154071i
\(173\) 18.6803 13.5721i 1.42024 1.03186i 0.428508 0.903538i \(-0.359039\pi\)
0.991732 0.128327i \(-0.0409606\pi\)
\(174\) 0 0
\(175\) 3.47214 0.262469
\(176\) 10.1803 2.28563i 0.767372 0.172286i
\(177\) 0 0
\(178\) 0.798374 2.45714i 0.0598407 0.184171i
\(179\) 4.09017 2.97168i 0.305714 0.222114i −0.424341 0.905502i \(-0.639494\pi\)
0.730055 + 0.683388i \(0.239494\pi\)
\(180\) 0 0
\(181\) −3.06231 9.42481i −0.227619 0.700540i −0.998015 0.0629745i \(-0.979941\pi\)
0.770396 0.637566i \(-0.220059\pi\)
\(182\) −0.763932 2.35114i −0.0566264 0.174278i
\(183\) 0 0
\(184\) −5.50000 + 3.99598i −0.405465 + 0.294588i
\(185\) 1.94427 5.98385i 0.142946 0.439942i
\(186\) 0 0
\(187\) 15.7082 3.52671i 1.14870 0.257899i
\(188\) −22.1459 −1.61516
\(189\) 0 0
\(190\) −0.381966 + 0.277515i −0.0277107 + 0.0201330i
\(191\) −4.80902 3.49396i −0.347968 0.252814i 0.400048 0.916494i \(-0.368993\pi\)
−0.748016 + 0.663680i \(0.768993\pi\)
\(192\) 0 0
\(193\) −3.39919 10.4616i −0.244679 0.753044i −0.995689 0.0927535i \(-0.970433\pi\)
0.751010 0.660291i \(-0.229567\pi\)
\(194\) 1.85410 + 1.34708i 0.133117 + 0.0967150i
\(195\) 0 0
\(196\) 3.43769 10.5801i 0.245550 0.755724i
\(197\) 8.23607 0.586796 0.293398 0.955990i \(-0.405214\pi\)
0.293398 + 0.955990i \(0.405214\pi\)
\(198\) 0 0
\(199\) −7.14590 −0.506559 −0.253280 0.967393i \(-0.581509\pi\)
−0.253280 + 0.967393i \(0.581509\pi\)
\(200\) −1.57953 + 4.86128i −0.111689 + 0.343745i
\(201\) 0 0
\(202\) −2.61803 1.90211i −0.184204 0.133832i
\(203\) 1.50000 + 4.61653i 0.105279 + 0.324017i
\(204\) 0 0
\(205\) −2.52786 1.83660i −0.176554 0.128274i
\(206\) −3.16312 + 2.29814i −0.220385 + 0.160119i
\(207\) 0 0
\(208\) −20.3607 −1.41176
\(209\) 1.69098 + 2.85317i 0.116968 + 0.197358i
\(210\) 0 0
\(211\) 6.32624 19.4702i 0.435516 1.34038i −0.457041 0.889446i \(-0.651091\pi\)
0.892557 0.450935i \(-0.148909\pi\)
\(212\) 6.13525 4.45752i 0.421371 0.306144i
\(213\) 0 0
\(214\) −1.65654 5.09831i −0.113239 0.348513i
\(215\) −0.708204 2.17963i −0.0482991 0.148649i
\(216\) 0 0
\(217\) 0.500000 0.363271i 0.0339422 0.0246605i
\(218\) −0.843459 + 2.59590i −0.0571262 + 0.175816i
\(219\) 0 0
\(220\) −6.97871 3.01217i −0.470505 0.203081i
\(221\) −31.4164 −2.11330
\(222\) 0 0
\(223\) 12.5451 9.11454i 0.840081 0.610355i −0.0823123 0.996607i \(-0.526230\pi\)
0.922393 + 0.386252i \(0.126230\pi\)
\(224\) −3.35410 2.43690i −0.224105 0.162822i
\(225\) 0 0
\(226\) −2.03444 6.26137i −0.135329 0.416500i
\(227\) 13.4443 + 9.76784i 0.892328 + 0.648314i 0.936484 0.350711i \(-0.114060\pi\)
−0.0441562 + 0.999025i \(0.514060\pi\)
\(228\) 0 0
\(229\) 3.14590 9.68208i 0.207887 0.639810i −0.791696 0.610916i \(-0.790801\pi\)
0.999582 0.0288941i \(-0.00919856\pi\)
\(230\) 2.18034 0.143767
\(231\) 0 0
\(232\) −7.14590 −0.469151
\(233\) −3.43769 + 10.5801i −0.225211 + 0.693128i 0.773059 + 0.634334i \(0.218725\pi\)
−0.998270 + 0.0587939i \(0.981275\pi\)
\(234\) 0 0
\(235\) 11.9443 + 8.67802i 0.779158 + 0.566092i
\(236\) −0.927051 2.85317i −0.0603459 0.185726i
\(237\) 0 0
\(238\) −1.50000 1.08981i −0.0972306 0.0706421i
\(239\) −8.47214 + 6.15537i −0.548017 + 0.398158i −0.827054 0.562123i \(-0.809985\pi\)
0.279037 + 0.960280i \(0.409985\pi\)
\(240\) 0 0
\(241\) −26.8328 −1.72845 −0.864227 0.503102i \(-0.832192\pi\)
−0.864227 + 0.503102i \(0.832192\pi\)
\(242\) 2.01722 3.68571i 0.129672 0.236927i
\(243\) 0 0
\(244\) −6.21885 + 19.1396i −0.398121 + 1.22529i
\(245\) −6.00000 + 4.35926i −0.383326 + 0.278503i
\(246\) 0 0
\(247\) −2.00000 6.15537i −0.127257 0.391657i
\(248\) 0.281153 + 0.865300i 0.0178532 + 0.0549466i
\(249\) 0 0
\(250\) 3.23607 2.35114i 0.204667 0.148699i
\(251\) 6.35410 19.5559i 0.401067 1.23436i −0.523067 0.852291i \(-0.675212\pi\)
0.924135 0.382067i \(-0.124788\pi\)
\(252\) 0 0
\(253\) 1.42705 15.2497i 0.0897179 0.958738i
\(254\) 4.03444 0.253143
\(255\) 0 0
\(256\) −4.50000 + 3.26944i −0.281250 + 0.204340i
\(257\) 12.0623 + 8.76378i 0.752426 + 0.546669i 0.896578 0.442886i \(-0.146045\pi\)
−0.144152 + 0.989556i \(0.546045\pi\)
\(258\) 0 0
\(259\) 1.57295 + 4.84104i 0.0977383 + 0.300808i
\(260\) 12.0000 + 8.71851i 0.744208 + 0.540699i
\(261\) 0 0
\(262\) −2.50658 + 7.71445i −0.154857 + 0.476601i
\(263\) −12.7082 −0.783621 −0.391811 0.920046i \(-0.628151\pi\)
−0.391811 + 0.920046i \(0.628151\pi\)
\(264\) 0 0
\(265\) −5.05573 −0.310571
\(266\) 0.118034 0.363271i 0.00723713 0.0222736i
\(267\) 0 0
\(268\) 9.00000 + 6.53888i 0.549762 + 0.399426i
\(269\) −6.57295 20.2295i −0.400760 1.23341i −0.924384 0.381463i \(-0.875421\pi\)
0.523625 0.851949i \(-0.324579\pi\)
\(270\) 0 0
\(271\) −8.70820 6.32688i −0.528986 0.384331i 0.290993 0.956725i \(-0.406015\pi\)
−0.819978 + 0.572395i \(0.806015\pi\)
\(272\) −12.3541 + 8.97578i −0.749077 + 0.544237i
\(273\) 0 0
\(274\) 3.29180 0.198865
\(275\) −5.87132 9.90659i −0.354054 0.597390i
\(276\) 0 0
\(277\) −5.94427 + 18.2946i −0.357157 + 1.09922i 0.597592 + 0.801801i \(0.296124\pi\)
−0.954748 + 0.297415i \(0.903876\pi\)
\(278\) 3.00000 2.17963i 0.179928 0.130725i
\(279\) 0 0
\(280\) 0.562306 + 1.73060i 0.0336042 + 0.103423i
\(281\) −2.88197 8.86978i −0.171924 0.529127i 0.827556 0.561383i \(-0.189731\pi\)
−0.999480 + 0.0322566i \(0.989731\pi\)
\(282\) 0 0
\(283\) 13.7533 9.99235i 0.817548 0.593984i −0.0984610 0.995141i \(-0.531392\pi\)
0.916009 + 0.401157i \(0.131392\pi\)
\(284\) 1.66718 5.13107i 0.0989292 0.304473i
\(285\) 0 0
\(286\) −5.41641 + 6.15537i −0.320279 + 0.363974i
\(287\) 2.52786 0.149215
\(288\) 0 0
\(289\) −5.30902 + 3.85723i −0.312295 + 0.226896i
\(290\) 1.85410 + 1.34708i 0.108877 + 0.0791035i
\(291\) 0 0
\(292\) 0.0835921 + 0.257270i 0.00489186 + 0.0150556i
\(293\) 23.6074 + 17.1518i 1.37916 + 1.00202i 0.996958 + 0.0779378i \(0.0248336\pi\)
0.382200 + 0.924080i \(0.375166\pi\)
\(294\) 0 0
\(295\) −0.618034 + 1.90211i −0.0359833 + 0.110745i
\(296\) −7.49342 −0.435546
\(297\) 0 0
\(298\) 5.79837 0.335891
\(299\) −9.23607 + 28.4257i −0.534136 + 1.64390i
\(300\) 0 0
\(301\) 1.50000 + 1.08981i 0.0864586 + 0.0628158i
\(302\) −0.510643 1.57160i −0.0293842 0.0904353i
\(303\) 0 0
\(304\) −2.54508 1.84911i −0.145971 0.106054i
\(305\) 10.8541 7.88597i 0.621504 0.451549i
\(306\) 0 0
\(307\) 7.85410 0.448257 0.224129 0.974560i \(-0.428046\pi\)
0.224129 + 0.974560i \(0.428046\pi\)
\(308\) 6.00000 1.34708i 0.341882 0.0767572i
\(309\) 0 0
\(310\) 0.0901699 0.277515i 0.00512131 0.0157618i
\(311\) −12.2812 + 8.92278i −0.696400 + 0.505964i −0.878758 0.477268i \(-0.841627\pi\)
0.182358 + 0.983232i \(0.441627\pi\)
\(312\) 0 0
\(313\) 1.07295 + 3.30220i 0.0606467 + 0.186651i 0.976790 0.214200i \(-0.0687144\pi\)
−0.916143 + 0.400851i \(0.868714\pi\)
\(314\) −0.843459 2.59590i −0.0475991 0.146495i
\(315\) 0 0
\(316\) 15.8435 11.5109i 0.891264 0.647541i
\(317\) 6.47214 19.9192i 0.363511 1.11877i −0.587397 0.809299i \(-0.699847\pi\)
0.950908 0.309474i \(-0.100153\pi\)
\(318\) 0 0
\(319\) 10.6353 12.0862i 0.595460 0.676698i
\(320\) 5.81966 0.325329
\(321\) 0 0
\(322\) −1.42705 + 1.03681i −0.0795264 + 0.0577793i
\(323\) −3.92705 2.85317i −0.218507 0.158755i
\(324\) 0 0
\(325\) 6.94427 + 21.3723i 0.385199 + 1.18552i
\(326\) 6.39919 + 4.64928i 0.354418 + 0.257500i
\(327\) 0 0
\(328\) −1.14996 + 3.53922i −0.0634961 + 0.195421i
\(329\) −11.9443 −0.658509
\(330\) 0 0
\(331\) 14.4164 0.792397 0.396199 0.918165i \(-0.370329\pi\)
0.396199 + 0.918165i \(0.370329\pi\)
\(332\) 5.59424 17.2173i 0.307024 0.944921i
\(333\) 0 0
\(334\) −1.78115 1.29408i −0.0974604 0.0708091i
\(335\) −2.29180 7.05342i −0.125214 0.385370i
\(336\) 0 0
\(337\) 9.28115 + 6.74315i 0.505577 + 0.367323i 0.811143 0.584848i \(-0.198846\pi\)
−0.305566 + 0.952171i \(0.598846\pi\)
\(338\) 8.92705 6.48588i 0.485568 0.352785i
\(339\) 0 0
\(340\) 11.1246 0.603317
\(341\) −1.88197 0.812299i −0.101914 0.0439885i
\(342\) 0 0
\(343\) 4.01722 12.3637i 0.216910 0.667579i
\(344\) −2.20820 + 1.60435i −0.119058 + 0.0865010i
\(345\) 0 0
\(346\) 2.72542 + 8.38800i 0.146520 + 0.450941i
\(347\) −2.74671 8.45351i −0.147451 0.453808i 0.849867 0.526997i \(-0.176682\pi\)
−0.997318 + 0.0731894i \(0.976682\pi\)
\(348\) 0 0
\(349\) 3.35410 2.43690i 0.179541 0.130444i −0.494385 0.869243i \(-0.664607\pi\)
0.673926 + 0.738799i \(0.264607\pi\)
\(350\) −0.409830 + 1.26133i −0.0219063 + 0.0674208i
\(351\) 0 0
\(352\) −1.28115 + 13.6906i −0.0682857 + 0.729710i
\(353\) −16.4164 −0.873757 −0.436879 0.899520i \(-0.643916\pi\)
−0.436879 + 0.899520i \(0.643916\pi\)
\(354\) 0 0
\(355\) −2.90983 + 2.11412i −0.154438 + 0.112206i
\(356\) −10.1459 7.37143i −0.537732 0.390685i
\(357\) 0 0
\(358\) 0.596748 + 1.83660i 0.0315391 + 0.0970674i
\(359\) 18.4894 + 13.4333i 0.975831 + 0.708983i 0.956773 0.290836i \(-0.0939333\pi\)
0.0190579 + 0.999818i \(0.493933\pi\)
\(360\) 0 0
\(361\) −5.56231 + 17.1190i −0.292753 + 0.901001i
\(362\) 3.78522 0.198947
\(363\) 0 0
\(364\) −12.0000 −0.628971
\(365\) 0.0557281 0.171513i 0.00291694 0.00897742i
\(366\) 0 0
\(367\) 10.2812 + 7.46969i 0.536672 + 0.389915i 0.822847 0.568262i \(-0.192384\pi\)
−0.286176 + 0.958177i \(0.592384\pi\)
\(368\) 4.48936 + 13.8168i 0.234024 + 0.720252i
\(369\) 0 0
\(370\) 1.94427 + 1.41260i 0.101078 + 0.0734374i
\(371\) 3.30902 2.40414i 0.171796 0.124817i
\(372\) 0 0
\(373\) −5.65248 −0.292674 −0.146337 0.989235i \(-0.546748\pi\)
−0.146337 + 0.989235i \(0.546748\pi\)
\(374\) −0.572949 + 6.12261i −0.0296265 + 0.316593i
\(375\) 0 0
\(376\) 5.43363 16.7230i 0.280218 0.862422i
\(377\) −25.4164 + 18.4661i −1.30901 + 0.951053i
\(378\) 0 0
\(379\) 4.88197 + 15.0251i 0.250770 + 0.771790i 0.994634 + 0.103459i \(0.0329910\pi\)
−0.743864 + 0.668331i \(0.767009\pi\)
\(380\) 0.708204 + 2.17963i 0.0363301 + 0.111813i
\(381\) 0 0
\(382\) 1.83688 1.33457i 0.0939830 0.0682827i
\(383\) 6.13525 18.8824i 0.313497 0.964844i −0.662872 0.748733i \(-0.730663\pi\)
0.976369 0.216111i \(-0.0693374\pi\)
\(384\) 0 0
\(385\) −3.76393 1.62460i −0.191828 0.0827972i
\(386\) 4.20163 0.213857
\(387\) 0 0
\(388\) 9.00000 6.53888i 0.456906 0.331961i
\(389\) 18.3262 + 13.3148i 0.929177 + 0.675087i 0.945791 0.324775i \(-0.105289\pi\)
−0.0166141 + 0.999862i \(0.505289\pi\)
\(390\) 0 0
\(391\) 6.92705 + 21.3193i 0.350316 + 1.07816i
\(392\) 7.14590 + 5.19180i 0.360922 + 0.262225i
\(393\) 0 0
\(394\) −0.972136 + 2.99193i −0.0489755 + 0.150731i
\(395\) −13.0557 −0.656905
\(396\) 0 0
\(397\) −2.12461 −0.106631 −0.0533156 0.998578i \(-0.516979\pi\)
−0.0533156 + 0.998578i \(0.516979\pi\)
\(398\) 0.843459 2.59590i 0.0422788 0.130121i
\(399\) 0 0
\(400\) 8.83688 + 6.42037i 0.441844 + 0.321018i
\(401\) 4.50000 + 13.8496i 0.224719 + 0.691615i 0.998320 + 0.0579414i \(0.0184537\pi\)
−0.773601 + 0.633673i \(0.781546\pi\)
\(402\) 0 0
\(403\) 3.23607 + 2.35114i 0.161200 + 0.117119i
\(404\) −12.7082 + 9.23305i −0.632257 + 0.459361i
\(405\) 0 0
\(406\) −1.85410 −0.0920175
\(407\) 11.1525 12.6740i 0.552808 0.628227i
\(408\) 0 0
\(409\) −10.4271 + 32.0912i −0.515584 + 1.58681i 0.266631 + 0.963799i \(0.414089\pi\)
−0.782216 + 0.623007i \(0.785911\pi\)
\(410\) 0.965558 0.701519i 0.0476855 0.0346456i
\(411\) 0 0
\(412\) 5.86475 + 18.0498i 0.288935 + 0.889251i
\(413\) −0.500000 1.53884i −0.0246034 0.0757215i
\(414\) 0 0
\(415\) −9.76393 + 7.09391i −0.479293 + 0.348226i
\(416\) 8.29180 25.5195i 0.406539 1.25120i
\(417\) 0 0
\(418\) −1.23607 + 0.277515i −0.0604581 + 0.0135737i
\(419\) 8.09017 0.395231 0.197615 0.980280i \(-0.436680\pi\)
0.197615 + 0.980280i \(0.436680\pi\)
\(420\) 0 0
\(421\) −8.28115 + 6.01661i −0.403599 + 0.293232i −0.771005 0.636829i \(-0.780246\pi\)
0.367407 + 0.930060i \(0.380246\pi\)
\(422\) 6.32624 + 4.59628i 0.307956 + 0.223743i
\(423\) 0 0
\(424\) 1.86068 + 5.72658i 0.0903626 + 0.278107i
\(425\) 13.6353 + 9.90659i 0.661407 + 0.480540i
\(426\) 0 0
\(427\) −3.35410 + 10.3229i −0.162316 + 0.499558i
\(428\) −26.0213 −1.25779
\(429\) 0 0
\(430\) 0.875388 0.0422150
\(431\) −10.5279 + 32.4014i −0.507109 + 1.56072i 0.290086 + 0.957001i \(0.406316\pi\)
−0.797195 + 0.603722i \(0.793684\pi\)
\(432\) 0 0
\(433\) −11.9271 8.66551i −0.573177 0.416438i 0.263081 0.964774i \(-0.415261\pi\)
−0.836258 + 0.548336i \(0.815261\pi\)
\(434\) 0.0729490 + 0.224514i 0.00350166 + 0.0107770i
\(435\) 0 0
\(436\) 10.7188 + 7.78770i 0.513340 + 0.372963i
\(437\) −3.73607 + 2.71441i −0.178720 + 0.129848i
\(438\) 0 0
\(439\) −0.708204 −0.0338007 −0.0169004 0.999857i \(-0.505380\pi\)
−0.0169004 + 0.999857i \(0.505380\pi\)
\(440\) 3.98684 4.53077i 0.190065 0.215996i
\(441\) 0 0
\(442\) 3.70820 11.4127i 0.176381 0.542846i
\(443\) 1.00000 0.726543i 0.0475114 0.0345191i −0.563776 0.825928i \(-0.690652\pi\)
0.611288 + 0.791409i \(0.290652\pi\)
\(444\) 0 0
\(445\) 2.58359 + 7.95148i 0.122474 + 0.376936i
\(446\) 1.83030 + 5.63309i 0.0866674 + 0.266735i
\(447\) 0 0
\(448\) −3.80902 + 2.76741i −0.179959 + 0.130748i
\(449\) 2.30902 7.10642i 0.108969 0.335373i −0.881672 0.471862i \(-0.843582\pi\)
0.990642 + 0.136489i \(0.0435820\pi\)
\(450\) 0 0
\(451\) −4.27458 7.21242i −0.201282 0.339620i
\(452\) −31.9574 −1.50315
\(453\) 0 0
\(454\) −5.13525 + 3.73098i −0.241009 + 0.175104i
\(455\) 6.47214 + 4.70228i 0.303418 + 0.220446i
\(456\) 0 0
\(457\) −0.309017 0.951057i −0.0144552 0.0444885i 0.943569 0.331177i \(-0.107446\pi\)
−0.958024 + 0.286688i \(0.907446\pi\)
\(458\) 3.14590 + 2.28563i 0.146998 + 0.106800i
\(459\) 0 0
\(460\) 3.27051 10.0656i 0.152488 0.469311i
\(461\) −16.1459 −0.751989 −0.375995 0.926622i \(-0.622699\pi\)
−0.375995 + 0.926622i \(0.622699\pi\)
\(462\) 0 0
\(463\) 17.0000 0.790057 0.395029 0.918669i \(-0.370735\pi\)
0.395029 + 0.918669i \(0.370735\pi\)
\(464\) −4.71885 + 14.5231i −0.219067 + 0.674219i
\(465\) 0 0
\(466\) −3.43769 2.49763i −0.159248 0.115701i
\(467\) −0.236068 0.726543i −0.0109239 0.0336204i 0.945446 0.325779i \(-0.105627\pi\)
−0.956370 + 0.292159i \(0.905627\pi\)
\(468\) 0 0
\(469\) 4.85410 + 3.52671i 0.224142 + 0.162848i
\(470\) −4.56231 + 3.31471i −0.210443 + 0.152896i
\(471\) 0 0
\(472\) 2.38197 0.109639
\(473\) 0.572949 6.12261i 0.0263442 0.281518i
\(474\) 0 0
\(475\) −1.07295 + 3.30220i −0.0492303 + 0.151515i
\(476\) −7.28115 + 5.29007i −0.333731 + 0.242470i
\(477\) 0 0
\(478\) −1.23607 3.80423i −0.0565364 0.174001i
\(479\) −3.63525 11.1882i −0.166099 0.511200i 0.833017 0.553248i \(-0.186612\pi\)
−0.999116 + 0.0420478i \(0.986612\pi\)
\(480\) 0 0
\(481\) −26.6525 + 19.3642i −1.21525 + 0.882930i
\(482\) 3.16718 9.74759i 0.144261 0.443991i
\(483\) 0 0
\(484\) −13.9894 14.8411i −0.635880 0.674596i
\(485\) −7.41641 −0.336762
\(486\) 0 0
\(487\) 10.5000 7.62870i 0.475800 0.345689i −0.323897 0.946092i \(-0.604993\pi\)
0.799698 + 0.600403i \(0.204993\pi\)
\(488\) −12.9271 9.39205i −0.585180 0.425158i
\(489\) 0 0
\(490\) −0.875388 2.69417i −0.0395460 0.121710i
\(491\) −5.92705 4.30625i −0.267484 0.194339i 0.445956 0.895055i \(-0.352864\pi\)
−0.713440 + 0.700716i \(0.752864\pi\)
\(492\) 0 0
\(493\) −7.28115 + 22.4091i −0.327927 + 1.00925i
\(494\) 2.47214 0.111227
\(495\) 0 0
\(496\) 1.94427 0.0873004
\(497\) 0.899187 2.76741i 0.0403340 0.124135i
\(498\) 0 0
\(499\) −31.0795 22.5806i −1.39131 1.01085i −0.995720 0.0924194i \(-0.970540\pi\)
−0.395591 0.918427i \(-0.629460\pi\)
\(500\) −6.00000 18.4661i −0.268328 0.825829i
\(501\) 0 0
\(502\) 6.35410 + 4.61653i 0.283597 + 0.206046i
\(503\) 7.70820 5.60034i 0.343692 0.249707i −0.402526 0.915409i \(-0.631868\pi\)
0.746218 + 0.665702i \(0.231868\pi\)
\(504\) 0 0
\(505\) 10.4721 0.466004
\(506\) 5.37132 + 2.31838i 0.238784 + 0.103065i
\(507\) 0 0
\(508\) 6.05166 18.6251i 0.268499 0.826355i
\(509\) 21.9894 15.9762i 0.974661 0.708133i 0.0181520 0.999835i \(-0.494222\pi\)
0.956509 + 0.291702i \(0.0942217\pi\)
\(510\) 0 0
\(511\) 0.0450850 + 0.138757i 0.00199444 + 0.00613826i
\(512\) −6.89261 21.2133i −0.304613 0.937503i
\(513\) 0 0
\(514\) −4.60739 + 3.34747i −0.203223 + 0.147650i
\(515\) 3.90983 12.0332i 0.172288 0.530247i
\(516\) 0 0
\(517\) 20.1976 + 34.0790i 0.888288 + 1.49879i
\(518\) −1.94427 −0.0854264
\(519\) 0 0
\(520\) −9.52786 + 6.92240i −0.417824 + 0.303567i
\(521\) 32.6525 + 23.7234i 1.43053 + 1.03934i 0.989918 + 0.141645i \(0.0452390\pi\)
0.440613 + 0.897697i \(0.354761\pi\)
\(522\) 0 0
\(523\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(524\) 31.8541 + 23.1434i 1.39155 + 1.01102i
\(525\) 0 0
\(526\) 1.50000 4.61653i 0.0654031 0.201290i
\(527\) 3.00000 0.130682
\(528\) 0 0
\(529\) −1.67376 −0.0727723
\(530\) 0.596748 1.83660i 0.0259211 0.0797768i
\(531\) 0 0
\(532\) −1.50000 1.08981i −0.0650332 0.0472494i
\(533\) 5.05573 + 15.5599i 0.218988 + 0.673975i
\(534\) 0 0
\(535\) 14.0344 + 10.1966i 0.606762 + 0.440838i
\(536\) −7.14590 + 5.19180i −0.308656 + 0.224252i
\(537\) 0 0
\(538\) 8.12461 0.350277
\(539\) −19.4164 + 4.35926i −0.836324 + 0.187766i
\(540\) 0 0
\(541\) −3.68034 + 11.3269i −0.158230 + 0.486982i −0.998474 0.0552266i \(-0.982412\pi\)
0.840244 + 0.542209i \(0.182412\pi\)
\(542\) 3.32624 2.41665i 0.142874 0.103804i
\(543\) 0 0
\(544\) −6.21885 19.1396i −0.266631 0.820605i
\(545\) −2.72949 8.40051i −0.116919 0.359838i
\(546\) 0 0
\(547\) 26.1525 19.0009i 1.11820 0.812419i 0.134264 0.990946i \(-0.457133\pi\)
0.983935 + 0.178526i \(0.0571330\pi\)
\(548\) 4.93769 15.1967i 0.210928 0.649169i
\(549\) 0 0
\(550\) 4.29180 0.963568i 0.183003 0.0410867i
\(551\) −4.85410 −0.206792
\(552\) 0 0
\(553\) 8.54508 6.20837i 0.363374 0.264007i
\(554\) −5.94427 4.31877i −0.252548 0.183487i
\(555\) 0 0
\(556\) −5.56231 17.1190i −0.235894 0.726008i
\(557\) 0.527864 + 0.383516i 0.0223663 + 0.0162501i 0.598912 0.800815i \(-0.295600\pi\)
−0.576546 + 0.817065i \(0.695600\pi\)
\(558\) 0 0
\(559\) −3.70820 + 11.4127i −0.156840 + 0.482705i
\(560\) 3.88854 0.164321
\(561\) 0 0
\(562\) 3.56231 0.150267
\(563\) −6.27458 + 19.3112i −0.264442 + 0.813868i 0.727380 + 0.686235i \(0.240738\pi\)
−0.991821 + 0.127633i \(0.959262\pi\)
\(564\) 0 0
\(565\) 17.2361 + 12.5227i 0.725127 + 0.526835i
\(566\) 2.00658 + 6.17561i 0.0843428 + 0.259580i
\(567\) 0 0
\(568\) 3.46556 + 2.51788i 0.145412 + 0.105648i
\(569\) −31.3885 + 22.8051i −1.31588 + 0.956040i −0.315902 + 0.948792i \(0.602307\pi\)
−0.999974 + 0.00724836i \(0.997693\pi\)
\(570\) 0 0
\(571\) −18.5279 −0.775367 −0.387683 0.921793i \(-0.626725\pi\)
−0.387683 + 0.921793i \(0.626725\pi\)
\(572\) 20.2918 + 34.2380i 0.848443 + 1.43156i
\(573\) 0 0
\(574\) −0.298374 + 0.918300i −0.0124539 + 0.0383291i
\(575\) 12.9721 9.42481i 0.540975 0.393042i
\(576\) 0 0
\(577\) 10.9443 + 33.6830i 0.455616 + 1.40224i 0.870410 + 0.492327i \(0.163853\pi\)
−0.414794 + 0.909915i \(0.636147\pi\)
\(578\) −0.774575 2.38390i −0.0322181 0.0991570i
\(579\) 0 0
\(580\) 9.00000 6.53888i 0.373705 0.271512i
\(581\) 3.01722 9.28605i 0.125175 0.385250i
\(582\) 0 0
\(583\) −12.4549 5.37582i −0.515830 0.222644i
\(584\) −0.214782 −0.00888773
\(585\) 0 0
\(586\) −9.01722 + 6.55139i −0.372498 + 0.270636i
\(587\) −10.8541 7.88597i −0.447997 0.325489i 0.340808 0.940133i \(-0.389300\pi\)
−0.788804 + 0.614644i \(0.789300\pi\)
\(588\) 0 0
\(589\) 0.190983 + 0.587785i 0.00786932 + 0.0242193i
\(590\) −0.618034 0.449028i −0.0254441 0.0184862i
\(591\) 0 0
\(592\) −4.94834 + 15.2294i −0.203375 + 0.625925i
\(593\) −10.9443 −0.449427 −0.224714 0.974425i \(-0.572145\pi\)
−0.224714 + 0.974425i \(0.572145\pi\)
\(594\) 0 0
\(595\) 6.00000 0.245976
\(596\) 8.69756 26.7683i 0.356266 1.09647i
\(597\) 0 0
\(598\) −9.23607 6.71040i −0.377691 0.274409i
\(599\) −4.12868 12.7068i −0.168693 0.519184i 0.830596 0.556875i \(-0.188000\pi\)
−0.999289 + 0.0376909i \(0.988000\pi\)
\(600\) 0 0
\(601\) 14.1353 + 10.2699i 0.576589 + 0.418916i 0.837493 0.546448i \(-0.184021\pi\)
−0.260904 + 0.965365i \(0.584021\pi\)
\(602\) −0.572949 + 0.416272i −0.0233517 + 0.0169660i
\(603\) 0 0
\(604\) −8.02129 −0.326382
\(605\) 1.72949 + 13.4863i 0.0703138 + 0.548296i
\(606\) 0 0
\(607\) −1.10739 + 3.40820i −0.0449476 + 0.138335i −0.971012 0.239031i \(-0.923170\pi\)
0.926064 + 0.377366i \(0.123170\pi\)
\(608\) 3.35410 2.43690i 0.136027 0.0988293i
\(609\) 0 0
\(610\) 1.58359 + 4.87380i 0.0641178 + 0.197334i
\(611\) −23.8885 73.5214i −0.966427 2.97436i
\(612\) 0 0
\(613\) −16.0623 + 11.6699i −0.648750 + 0.471345i −0.862845 0.505468i \(-0.831320\pi\)
0.214095 + 0.976813i \(0.431320\pi\)
\(614\) −0.927051 + 2.85317i −0.0374127 + 0.115145i
\(615\) 0 0
\(616\) −0.454915 + 4.86128i −0.0183290 + 0.195867i
\(617\) −27.1591 −1.09338 −0.546691 0.837334i \(-0.684113\pi\)
−0.546691 + 0.837334i \(0.684113\pi\)
\(618\) 0 0
\(619\) −22.2984 + 16.2007i −0.896247 + 0.651162i −0.937499 0.347987i \(-0.886865\pi\)
0.0412520 + 0.999149i \(0.486865\pi\)
\(620\) −1.14590 0.832544i −0.0460204 0.0334358i
\(621\) 0 0
\(622\) −1.79180 5.51458i −0.0718445 0.221115i
\(623\) −5.47214 3.97574i −0.219236 0.159285i
\(624\) 0 0
\(625\) 1.36475 4.20025i 0.0545898 0.168010i
\(626\) −1.32624 −0.0530071
\(627\) 0 0
\(628\) −13.2492 −0.528702
\(629\) −7.63525 + 23.4989i −0.304438 + 0.936962i
\(630\) 0 0
\(631\) 8.80902 + 6.40013i 0.350681 + 0.254785i 0.749155 0.662395i \(-0.230460\pi\)
−0.398473 + 0.917180i \(0.630460\pi\)
\(632\) 4.80495 + 14.7881i 0.191131 + 0.588240i
\(633\) 0 0
\(634\) 6.47214 + 4.70228i 0.257041 + 0.186751i
\(635\) −10.5623 + 7.67396i −0.419152 + 0.304532i
\(636\) 0 0
\(637\) 38.8328 1.53861
\(638\) 3.13525 + 5.29007i 0.124126 + 0.209436i
\(639\) 0 0
\(640\) −3.85410 + 11.8617i −0.152347 + 0.468875i
\(641\) 16.5451 12.0207i 0.653492 0.474789i −0.210967 0.977493i \(-0.567661\pi\)
0.864459 + 0.502704i \(0.167661\pi\)
\(642\) 0 0
\(643\) −2.11803 6.51864i −0.0835271 0.257070i 0.900567 0.434717i \(-0.143152\pi\)
−0.984094 + 0.177647i \(0.943152\pi\)
\(644\) 2.64590 + 8.14324i 0.104263 + 0.320888i
\(645\) 0 0
\(646\) 1.50000 1.08981i 0.0590167 0.0428782i
\(647\) −1.29180 + 3.97574i −0.0507857 + 0.156302i −0.973233 0.229821i \(-0.926186\pi\)
0.922447 + 0.386123i \(0.126186\pi\)
\(648\) 0 0
\(649\) −3.54508 + 4.02874i −0.139157 + 0.158142i
\(650\) −8.58359 −0.336676
\(651\) 0 0
\(652\) 31.0623 22.5681i 1.21649 0.883834i
\(653\) 1.10081 + 0.799788i 0.0430781 + 0.0312981i 0.609116 0.793081i \(-0.291524\pi\)
−0.566038 + 0.824379i \(0.691524\pi\)
\(654\) 0 0
\(655\) −8.11146 24.9645i −0.316941 0.975444i
\(656\) 6.43363 + 4.67430i 0.251191 + 0.182501i
\(657\) 0 0
\(658\) 1.40983 4.33901i 0.0549609 0.169152i
\(659\) 9.97871 0.388715 0.194358 0.980931i \(-0.437738\pi\)
0.194358 + 0.980931i \(0.437738\pi\)
\(660\) 0 0
\(661\) −4.29180 −0.166932 −0.0834658 0.996511i \(-0.526599\pi\)
−0.0834658 + 0.996511i \(0.526599\pi\)
\(662\) −1.70163 + 5.23707i −0.0661356 + 0.203544i
\(663\) 0 0
\(664\) 11.6287 + 8.44873i 0.451280 + 0.327874i
\(665\) 0.381966 + 1.17557i 0.0148120 + 0.0455867i
\(666\) 0 0
\(667\) 18.1353 + 13.1760i 0.702200 + 0.510178i
\(668\) −8.64590 + 6.28161i −0.334520 + 0.243043i
\(669\) 0 0
\(670\) 2.83282 0.109441
\(671\) 35.1246 7.88597i 1.35597 0.304434i
\(672\) 0 0
\(673\) −9.13525 + 28.1154i −0.352138 + 1.08377i 0.605512 + 0.795836i \(0.292968\pi\)
−0.957650 + 0.287934i \(0.907032\pi\)
\(674\) −3.54508 + 2.57565i −0.136552 + 0.0992105i
\(675\) 0 0
\(676\) −16.5517 50.9408i −0.636602 1.95926i
\(677\) 1.87132 + 5.75934i 0.0719208 + 0.221349i 0.980555 0.196243i \(-0.0628741\pi\)
−0.908635 + 0.417592i \(0.862874\pi\)
\(678\) 0 0
\(679\) 4.85410 3.52671i 0.186283 0.135343i
\(680\) −2.72949 + 8.40051i −0.104671 + 0.322145i
\(681\) 0 0
\(682\) 0.517221 0.587785i 0.0198054 0.0225075i
\(683\) −5.52786 −0.211518 −0.105759 0.994392i \(-0.533727\pi\)
−0.105759 + 0.994392i \(0.533727\pi\)
\(684\) 0 0
\(685\) −8.61803 + 6.26137i −0.329278 + 0.239235i
\(686\) 4.01722 + 2.91868i 0.153378 + 0.111436i
\(687\) 0 0
\(688\) 1.80244 + 5.54734i 0.0687173 + 0.211490i
\(689\) 21.4164 + 15.5599i 0.815900 + 0.592786i
\(690\) 0 0
\(691\) 4.51064 13.8823i 0.171593 0.528109i −0.827869 0.560922i \(-0.810447\pi\)
0.999461 + 0.0328134i \(0.0104467\pi\)
\(692\) 42.8115 1.62745
\(693\) 0 0
\(694\) 3.39512 0.128877
\(695\) −3.70820 + 11.4127i −0.140660 + 0.432908i
\(696\) 0 0
\(697\) 9.92705 + 7.21242i 0.376014 + 0.273190i
\(698\) 0.489357 + 1.50609i 0.0185224 + 0.0570062i
\(699\) 0 0
\(700\) 5.20820 + 3.78398i 0.196852 + 0.143021i
\(701\) 38.6074 28.0499i 1.45818 1.05943i 0.474349 0.880337i \(-0.342683\pi\)
0.983832 0.179094i \(-0.0573165\pi\)
\(702\) 0 0
\(703\) −5.09017 −0.191979
\(704\) 14.3369 + 6.18812i 0.540342 + 0.233224i
\(705\) 0 0
\(706\) 1.93769 5.96361i 0.0729261 0.224443i
\(707\) −6.85410 + 4.97980i −0.257775 + 0.187285i
\(708\) 0 0
\(709\) −7.96149 24.5030i −0.299000 0.920228i −0.981848 0.189668i \(-0.939259\pi\)
0.682848 0.730560i \(-0.260741\pi\)
\(710\) −0.424538 1.30660i −0.0159326 0.0490356i
\(711\) 0 0
\(712\) 8.05573 5.85283i 0.301901 0.219344i
\(713\) 0.881966 2.71441i 0.0330299 0.101656i
\(714\) 0 0
\(715\) 2.47214 26.4176i 0.0924526 0.987961i
\(716\) 9.37384 0.350317
\(717\) 0 0
\(718\) −7.06231 + 5.13107i −0.263563 + 0.191490i
\(719\) 15.8541 + 11.5187i 0.591258 + 0.429574i 0.842765 0.538281i \(-0.180926\pi\)
−0.251507 + 0.967855i \(0.580926\pi\)
\(720\) 0 0
\(721\) 3.16312 + 9.73508i 0.117801 + 0.362553i
\(722\) −5.56231 4.04125i −0.207008 0.150400i
\(723\) 0 0
\(724\) 5.67783 17.4746i 0.211015 0.649437i
\(725\) 16.8541 0.625946
\(726\) 0 0
\(727\) 18.8328 0.698470 0.349235 0.937035i \(-0.386441\pi\)
0.349235 + 0.937035i \(0.386441\pi\)
\(728\) 2.94427 9.06154i 0.109122 0.335843i
\(729\) 0 0
\(730\) 0.0557281 + 0.0404888i 0.00206259 + 0.00149856i
\(731\) 2.78115 + 8.55951i 0.102865 + 0.316585i
\(732\) 0 0
\(733\) −39.2148 28.4912i −1.44843 1.05235i −0.986195 0.165590i \(-0.947047\pi\)
−0.462236 0.886757i \(-0.652953\pi\)
\(734\) −3.92705 + 2.85317i −0.144950 + 0.105312i
\(735\) 0 0
\(736\) −19.1459 −0.705727
\(737\) 1.85410 19.8132i 0.0682967 0.729828i
\(738\) 0 0
\(739\) 13.1459 40.4589i 0.483580 1.48831i −0.350448 0.936582i \(-0.613971\pi\)
0.834027 0.551723i \(-0.186029\pi\)
\(740\) 9.43769 6.85689i 0.346937 0.252064i
\(741\) 0 0
\(742\) 0.482779 + 1.48584i 0.0177234 + 0.0545469i
\(743\) −13.0902 40.2874i −0.480232 1.47800i −0.838770 0.544486i \(-0.816725\pi\)
0.358538 0.933515i \(-0.383275\pi\)
\(744\) 0 0
\(745\) −15.1803 + 11.0292i −0.556165 + 0.404077i
\(746\) 0.667184 2.05338i 0.0244274 0.0751797i
\(747\) 0 0
\(748\) 27.4058 + 11.8290i 1.00205 + 0.432509i
\(749\) −14.0344 −0.512807
\(750\) 0 0
\(751\) 25.2812 18.3678i 0.922522 0.670252i −0.0216282 0.999766i \(-0.506885\pi\)
0.944151 + 0.329514i \(0.106885\pi\)
\(752\) −30.3992 22.0863i −1.10854 0.805405i
\(753\) 0 0
\(754\) −3.70820 11.4127i −0.135045 0.415625i
\(755\) 4.32624 + 3.14320i 0.157448 + 0.114393i
\(756\) 0 0
\(757\) 3.39919 10.4616i 0.123546 0.380234i −0.870088 0.492897i \(-0.835938\pi\)
0.993633 + 0.112663i \(0.0359380\pi\)
\(758\) −6.03444 −0.219181
\(759\) 0 0
\(760\) −1.81966 −0.0660060
\(761\) 2.15654 6.63715i 0.0781746 0.240597i −0.904330 0.426833i \(-0.859629\pi\)
0.982505 + 0.186237i \(0.0596291\pi\)
\(762\) 0 0
\(763\) 5.78115 + 4.20025i 0.209292 + 0.152059i
\(764\) −3.40576 10.4819i −0.123216 0.379221i
\(765\) 0 0
\(766\) 6.13525 + 4.45752i 0.221676 + 0.161057i
\(767\) 8.47214 6.15537i 0.305911 0.222257i
\(768\) 0 0
\(769\) −15.7984 −0.569704 −0.284852 0.958572i \(-0.591944\pi\)
−0.284852 + 0.958572i \(0.591944\pi\)
\(770\) 1.03444 1.17557i 0.0372787 0.0423646i
\(771\) 0 0
\(772\) 6.30244 19.3969i 0.226830 0.698110i
\(773\) −19.1353 + 13.9026i −0.688247 + 0.500041i −0.876083 0.482159i \(-0.839853\pi\)
0.187836 + 0.982200i \(0.439853\pi\)
\(774\) 0 0
\(775\) −0.663119 2.04087i −0.0238199 0.0733102i
\(776\) 2.72949 + 8.40051i 0.0979830 + 0.301561i
\(777\) 0 0
\(778\) −7.00000 + 5.08580i −0.250962 + 0.182335i
\(779\) −0.781153 + 2.40414i −0.0279877 + 0.0861373i
\(780\) 0 0
\(781\) −9.41641 + 2.11412i −0.336946 + 0.0756490i
\(782\) −8.56231 −0.306187
\(783\) 0 0
\(784\) 15.2705 11.0947i 0.545375 0.396238i
\(785\) 7.14590 + 5.19180i 0.255048 + 0.185303i
\(786\) 0 0
\(787\) 11.1246 + 34.2380i 0.396550 + 1.22045i 0.927748 + 0.373207i \(0.121742\pi\)
−0.531199 + 0.847247i \(0.678258\pi\)
\(788\) 12.3541 + 8.97578i 0.440097 + 0.319749i
\(789\) 0 0
\(790\) 1.54102 4.74277i 0.0548270 0.168740i
\(791\) −17.2361 −0.612844
\(792\) 0 0
\(793\) −70.2492 −2.49462
\(794\) 0.250776 0.771810i 0.00889972 0.0273905i
\(795\) 0 0
\(796\) −10.7188 7.78770i −0.379919 0.276028i
\(797\) 7.50000 + 23.0826i 0.265664 + 0.817629i 0.991540 + 0.129803i \(0.0414345\pi\)
−0.725876 + 0.687825i \(0.758565\pi\)
\(798\) 0 0
\(799\) −46.9058 34.0790i −1.65941 1.20563i
\(800\) −11.6459 + 8.46124i −0.411745 + 0.299150i
\(801\) 0 0
\(802\) −5.56231 −0.196412
\(803\) 0.319660 0.363271i 0.0112806 0.0128196i
\(804\) 0 0
\(805\) 1.76393 5.42882i 0.0621704 0.191341i
\(806\) −1.23607 + 0.898056i −0.0435386 + 0.0316327i
\(807\) 0 0
\(808\) −3.85410 11.8617i −0.135587 0.417293i
\(809\) −5.59017 17.2048i −0.196540 0.604888i −0.999955 0.00946853i \(-0.996986\pi\)
0.803415 0.595419i \(-0.203014\pi\)
\(810\) 0 0
\(811\) −7.02786 + 5.10604i −0.246782 + 0.179297i −0.704299 0.709903i \(-0.748739\pi\)
0.457518 + 0.889201i \(0.348739\pi\)
\(812\) −2.78115 + 8.55951i −0.0975993 + 0.300380i
\(813\) 0 0
\(814\) 3.28773 + 5.54734i 0.115235 + 0.194434i
\(815\) −25.5967 −0.896615
\(816\) 0 0
\(817\) −1.50000 + 1.08981i −0.0524784 + 0.0381278i
\(818\) −10.4271 7.57570i −0.364573 0.264878i
\(819\) 0 0
\(820\) −1.79024 5.50980i −0.0625180 0.192411i
\(821\) −30.9164 22.4621i −1.07899 0.783932i −0.101484 0.994837i \(-0.532359\pi\)
−0.977507 + 0.210905i \(0.932359\pi\)
\(822\) 0 0
\(823\) −13.0689 + 40.2219i −0.455553 + 1.40205i 0.414932 + 0.909852i \(0.363805\pi\)
−0.870485 + 0.492195i \(0.836195\pi\)
\(824\) −15.0689 −0.524949
\(825\) 0 0
\(826\) 0.618034 0.0215042
\(827\) −17.6246 + 54.2430i −0.612868 + 1.88621i −0.183721 + 0.982978i \(0.558814\pi\)
−0.429147 + 0.903235i \(0.641186\pi\)
\(828\) 0 0
\(829\) −35.2254 25.5928i −1.22343 0.888874i −0.227049 0.973883i \(-0.572908\pi\)
−0.996380 + 0.0850096i \(0.972908\pi\)
\(830\) −1.42454 4.38428i −0.0494465 0.152181i
\(831\) 0 0
\(832\) −24.6525 17.9111i −0.854671 0.620955i
\(833\) 23.5623 17.1190i 0.816386 0.593139i
\(834\) 0 0
\(835\) 7.12461 0.246557
\(836\) −0.572949 + 6.12261i −0.0198159 + 0.211755i
\(837\) 0 0
\(838\) −0.954915 + 2.93893i −0.0329870 + 0.101524i
\(839\) 13.9894 10.1639i 0.482966 0.350896i −0.319507 0.947584i \(-0.603517\pi\)
0.802473 + 0.596689i \(0.203517\pi\)
\(840\) 0 0
\(841\) −1.68034 5.17155i −0.0579428 0.178329i
\(842\) −1.20820 3.71847i −0.0416375 0.128147i
\(843\) 0 0
\(844\) 30.7082 22.3108i 1.05702 0.767970i
\(845\) −11.0344 + 33.9605i −0.379596 + 1.16828i
\(846\) 0 0
\(847\) −7.54508 8.00448i −0.259252 0.275037i
\(848\) 12.8673 0.441863
\(849\) 0 0
\(850\) −5.20820 + 3.78398i −0.178640 + 0.129789i
\(851\) 19.0172 + 13.8168i 0.651902 + 0.473634i
\(852\) 0 0
\(853\) −10.9508 33.7032i −0.374950 1.15398i −0.943512 0.331337i \(-0.892500\pi\)
0.568562 0.822640i \(-0.307500\pi\)
\(854\) −3.35410 2.43690i −0.114775 0.0833889i
\(855\) 0 0
\(856\) 6.38448 19.6494i 0.218217 0.671603i
\(857\) 25.3607 0.866304 0.433152 0.901321i \(-0.357401\pi\)
0.433152 + 0.901321i \(0.357401\pi\)
\(858\) 0 0
\(859\) −32.5623 −1.11101 −0.555506 0.831513i \(-0.687475\pi\)
−0.555506 + 0.831513i \(0.687475\pi\)
\(860\) 1.31308 4.04125i 0.0447757 0.137806i
\(861\) 0 0
\(862\) −10.5279 7.64894i −0.358580 0.260524i
\(863\) 4.46556 + 13.7436i 0.152009 + 0.467837i 0.997846 0.0656059i \(-0.0208980\pi\)
−0.845836 + 0.533443i \(0.820898\pi\)
\(864\) 0 0
\(865\) −23.0902 16.7760i −0.785089 0.570401i
\(866\) 4.55573 3.30993i 0.154810 0.112476i
\(867\) 0 0
\(868\) 1.14590 0.0388943
\(869\) −32.1631 13.8823i −1.09106 0.470926i
\(870\) 0 0
\(871\) −12.0000 + 36.9322i −0.406604 + 1.25140i
\(872\) −8.51064 + 6.18334i −0.288207 + 0.209394i
\(873\) 0 0
\(874\) −0.545085 1.67760i −0.0184378 0.0567456i
\(875\) −3.23607 9.95959i −0.109399 0.336696i
\(876\) 0 0
\(877\) −9.38197 + 6.81640i −0.316806 + 0.230173i −0.734812 0.678271i \(-0.762729\pi\)
0.418005 + 0.908445i \(0.362729\pi\)
\(878\) 0.0835921 0.257270i 0.00282110 0.00868245i
\(879\) 0 0
\(880\) −6.57546 11.0947i −0.221659 0.374001i
\(881\) 1.81966 0.0613059 0.0306530 0.999530i \(-0.490241\pi\)
0.0306530 + 0.999530i \(0.490241\pi\)
\(882\) 0 0
\(883\) 28.8435 20.9560i 0.970660 0.705226i 0.0150579 0.999887i \(-0.495207\pi\)
0.955602 + 0.294661i \(0.0952068\pi\)
\(884\) −47.1246 34.2380i −1.58497 1.15155i
\(885\) 0 0
\(886\) 0.145898 + 0.449028i 0.00490154 + 0.0150854i
\(887\) 3.26393 + 2.37139i 0.109592 + 0.0796233i 0.641232 0.767347i \(-0.278424\pi\)
−0.531639 + 0.846971i \(0.678424\pi\)
\(888\) 0 0
\(889\) 3.26393 10.0453i 0.109469 0.336910i
\(890\) −3.19350 −0.107046
\(891\) 0 0
\(892\) 28.7508 0.962647
\(893\) 3.69098 11.3597i 0.123514 0.380137i
\(894\) 0 0
\(895\) −5.05573 3.67320i −0.168994 0.122782i
\(896\) −3.11803 9.59632i −0.104166 0.320591i
\(897\) 0 0
\(898\) 2.30902 + 1.67760i 0.0770529 + 0.0559822i
\(899\) 2.42705 1.76336i 0.0809467 0.0588112i
\(900\) 0 0
\(901\) 19.8541 0.661436
\(902\) 3.12461 0.701519i 0.104038 0.0233580i
\(903\) 0 0
\(904\) 7.84095 24.1320i 0.260786 0.802617i
\(905\) −9.90983 + 7.19991i −0.329414 + 0.239333i
\(906\) 0 0
\(907\) −4.50658 13.8698i −0.149638 0.460540i 0.847940 0.530093i \(-0.177843\pi\)
−0.997578 + 0.0695527i \(0.977843\pi\)
\(908\) 9.52129 + 29.3035i 0.315975 + 0.972471i
\(909\) 0 0
\(910\) −2.47214 + 1.79611i −0.0819505 + 0.0595405i
\(911\) −5.92705 + 18.2416i −0.196372 + 0.604371i 0.803586 + 0.595189i \(0.202923\pi\)
−0.999958 + 0.00918193i \(0.997077\pi\)
\(912\) 0 0
\(913\) −31.5967 + 7.09391i −1.04570 + 0.234774i
\(914\) 0.381966 0.0126343
\(915\) 0 0
\(916\) 15.2705 11.0947i 0.504552 0.366578i
\(917\) 17.1803 + 12.4822i 0.567345 + 0.412200i
\(918\) 0 0
\(919\) −8.30244 25.5523i −0.273872 0.842892i −0.989516 0.144426i \(-0.953866\pi\)
0.715643 0.698466i \(-0.246134\pi\)
\(920\) 6.79837 + 4.93931i 0.224136 + 0.162844i
\(921\) 0 0
\(922\) 1.90576 5.86534i 0.0627630 0.193165i
\(923\) 18.8328 0.619890
\(924\) 0 0
\(925\) 17.6738 0.581110
\(926\) −2.00658 + 6.17561i −0.0659402 + 0.202943i
\(927\) 0 0
\(928\) −16.2812 11.8290i −0.534455 0.388304i
\(929\) −14.9164 45.9080i −0.489391 1.50619i −0.825518 0.564375i \(-0.809117\pi\)
0.336127 0.941817i \(-0.390883\pi\)
\(930\) 0 0
\(931\) 4.85410 + 3.52671i 0.159087 + 0.115583i
\(932\) −16.6869 + 12.1238i −0.546598 + 0.397127i
\(933\) 0 0
\(934\) 0.291796 0.00954786
\(935\) −10.1459 17.1190i −0.331806 0.559852i
\(936\) 0 0
\(937\) −7.11803 + 21.9071i −0.232536 + 0.715672i 0.764903 + 0.644146i \(0.222787\pi\)
−0.997439 + 0.0715265i \(0.977213\pi\)
\(938\) −1.85410 + 1.34708i −0.0605386 + 0.0439838i
\(939\) 0 0
\(940\) 8.45898 + 26.0341i 0.275902 + 0.849138i
\(941\) 8.39261 + 25.8298i 0.273591 + 0.842027i 0.989589 + 0.143924i \(0.0459722\pi\)
−0.715997 + 0.698103i \(0.754028\pi\)
\(942\) 0 0
\(943\) 9.44427 6.86167i 0.307548 0.223447i
\(944\) 1.57295 4.84104i 0.0511951 0.157562i
\(945\) 0 0
\(946\) 2.15654 + 0.930812i 0.0701152 + 0.0302633i
\(947\) 36.7082 1.19286 0.596428 0.802666i \(-0.296586\pi\)
0.596428 + 0.802666i \(0.296586\pi\)
\(948\) 0 0
\(949\) −0.763932 + 0.555029i −0.0247983 + 0.0180170i
\(950\) −1.07295 0.779543i −0.0348111 0.0252917i
\(951\) 0 0
\(952\) −2.20820 6.79615i −0.0715683 0.220265i
\(953\) 7.68034 + 5.58009i 0.248791 + 0.180757i 0.705191 0.709018i \(-0.250861\pi\)
−0.456400 + 0.889775i \(0.650861\pi\)
\(954\) 0 0
\(955\) −2.27051 + 6.98791i −0.0734720 + 0.226123i
\(956\) −19.4164 −0.627972
\(957\) 0 0
\(958\) 4.49342 0.145176
\(959\) 2.66312 8.19624i 0.0859966 0.264670i
\(960\) 0 0
\(961\) 24.7705 + 17.9968i 0.799049 + 0.580543i
\(962\) −3.88854 11.9677i −0.125372 0.385854i
\(963\) 0 0
\(964\) −40.2492 29.2428i −1.29634 0.941846i
\(965\) −11.0000 + 7.99197i −0.354103 + 0.257271i
\(966\) 0 0
\(967\) 52.4853 1.68781 0.843907 0.536490i \(-0.180250\pi\)
0.843907 + 0.536490i \(0.180250\pi\)
\(968\) 14.6393 6.92240i 0.470526 0.222494i
\(969\) 0 0
\(970\) 0.875388 2.69417i 0.0281070 0.0865045i
\(971\) −7.50000 + 5.44907i −0.240686 + 0.174869i −0.701589 0.712582i \(-0.747526\pi\)
0.460903 + 0.887451i \(0.347526\pi\)
\(972\) 0 0
\(973\) −3.00000 9.23305i −0.0961756 0.295998i
\(974\) 1.53193 + 4.71479i 0.0490862 + 0.151072i
\(975\) 0 0
\(976\) −27.6246 + 20.0705i −0.884242 + 0.642440i
\(977\) 4.87132 14.9924i 0.155847 0.479649i −0.842398 0.538855i \(-0.818857\pi\)
0.998246 + 0.0592062i \(0.0188570\pi\)
\(978\) 0 0
\(979\) −2.09017 + 22.3358i −0.0668021 + 0.713857i
\(980\) −13.7508 −0.439252
\(981\) 0 0
\(982\) 2.26393 1.64484i 0.0722450 0.0524890i
\(983\) −7.48936 5.44134i −0.238873 0.173552i 0.461908 0.886928i \(-0.347165\pi\)
−0.700781 + 0.713376i \(0.747165\pi\)
\(984\) 0 0
\(985\) −3.14590 9.68208i −0.100237 0.308497i
\(986\) −7.28115 5.29007i −0.231879 0.168470i
\(987\) 0 0
\(988\) 3.70820 11.4127i 0.117974 0.363086i
\(989\) 8.56231 0.272265
\(990\) 0 0
\(991\) 20.5967 0.654277 0.327139 0.944976i \(-0.393916\pi\)
0.327139 + 0.944976i \(0.393916\pi\)
\(992\) −0.791796 + 2.43690i −0.0251396 + 0.0773716i
\(993\) 0 0
\(994\) 0.899187 + 0.653298i 0.0285205 + 0.0207213i
\(995\) 2.72949 + 8.40051i 0.0865307 + 0.266314i
\(996\) 0 0
\(997\) −5.97214 4.33901i −0.189139 0.137418i 0.489186 0.872180i \(-0.337294\pi\)
−0.678325 + 0.734762i \(0.737294\pi\)
\(998\) 11.8713 8.62502i 0.375780 0.273020i
\(999\) 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 891.2.f.b.163.1 4
3.2 odd 2 891.2.f.a.163.1 4
9.2 odd 6 297.2.n.a.64.1 8
9.4 even 3 99.2.m.a.97.1 yes 8
9.5 odd 6 297.2.n.a.262.1 8
9.7 even 3 99.2.m.a.31.1 yes 8
11.4 even 5 9801.2.a.n.1.2 2
11.5 even 5 inner 891.2.f.b.82.1 4
11.7 odd 10 9801.2.a.bc.1.1 2
33.5 odd 10 891.2.f.a.82.1 4
33.26 odd 10 9801.2.a.bb.1.1 2
33.29 even 10 9801.2.a.m.1.2 2
99.4 even 15 1089.2.e.g.727.1 4
99.5 odd 30 297.2.n.a.181.1 8
99.7 odd 30 1089.2.e.d.364.2 4
99.16 even 15 99.2.m.a.49.1 yes 8
99.38 odd 30 297.2.n.a.280.1 8
99.40 odd 30 1089.2.e.d.727.2 4
99.49 even 15 99.2.m.a.16.1 8
99.70 even 15 1089.2.e.g.364.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.m.a.16.1 8 99.49 even 15
99.2.m.a.31.1 yes 8 9.7 even 3
99.2.m.a.49.1 yes 8 99.16 even 15
99.2.m.a.97.1 yes 8 9.4 even 3
297.2.n.a.64.1 8 9.2 odd 6
297.2.n.a.181.1 8 99.5 odd 30
297.2.n.a.262.1 8 9.5 odd 6
297.2.n.a.280.1 8 99.38 odd 30
891.2.f.a.82.1 4 33.5 odd 10
891.2.f.a.163.1 4 3.2 odd 2
891.2.f.b.82.1 4 11.5 even 5 inner
891.2.f.b.163.1 4 1.1 even 1 trivial
1089.2.e.d.364.2 4 99.7 odd 30
1089.2.e.d.727.2 4 99.40 odd 30
1089.2.e.g.364.1 4 99.70 even 15
1089.2.e.g.727.1 4 99.4 even 15
9801.2.a.m.1.2 2 33.29 even 10
9801.2.a.n.1.2 2 11.4 even 5
9801.2.a.bb.1.1 2 33.26 odd 10
9801.2.a.bc.1.1 2 11.7 odd 10