Properties

Label 1050.2.b.f.251.14
Level $1050$
Weight $2$
Character 1050.251
Analytic conductor $8.384$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1050,2,Mod(251,1050)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1050.251");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.b (of order \(2\), degree \(1\), 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: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: 16.0.101415451701035401216.7
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 18x^{12} + 145x^{8} - 72x^{4} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{16} \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 251.14
Root \(-0.752908 - 0.137538i\) of defining polynomial
Character \(\chi\) \(=\) 1050.251
Dual form 1050.2.b.f.251.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} +(0.420861 + 1.68014i) q^{3} -1.00000 q^{4} +(-1.68014 + 0.420861i) q^{6} +(2.57794 + 0.595188i) q^{7} -1.00000i q^{8} +(-2.64575 + 1.41421i) q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(0.420861 + 1.68014i) q^{3} -1.00000 q^{4} +(-1.68014 + 0.420861i) q^{6} +(2.57794 + 0.595188i) q^{7} -1.00000i q^{8} +(-2.64575 + 1.41421i) q^{9} +2.82843i q^{11} +(-0.420861 - 1.68014i) q^{12} -3.36028i q^{13} +(-0.595188 + 2.57794i) q^{14} +1.00000 q^{16} -4.75216 q^{17} +(-1.41421 - 2.64575i) q^{18} +5.59388i q^{19} +(0.0849536 + 4.58179i) q^{21} -2.82843 q^{22} +7.29150i q^{23} +(1.68014 - 0.420861i) q^{24} +3.36028 q^{26} +(-3.48957 - 3.85005i) q^{27} +(-2.57794 - 0.595188i) q^{28} +0.500983i q^{29} +3.06871i q^{31} +1.00000i q^{32} +(-4.75216 + 1.19038i) q^{33} -4.75216i q^{34} +(2.64575 - 1.41421i) q^{36} -3.32941 q^{37} -5.59388 q^{38} +(5.64575 - 1.41421i) q^{39} -4.33981 q^{41} +(-4.58179 + 0.0849536i) q^{42} +10.3117 q^{43} -2.82843i q^{44} -7.29150 q^{46} -7.82087 q^{47} +(0.420861 + 1.68014i) q^{48} +(6.29150 + 3.06871i) q^{49} +(-2.00000 - 7.98430i) q^{51} +3.36028i q^{52} -8.58301i q^{53} +(3.85005 - 3.48957i) q^{54} +(0.595188 - 2.57794i) q^{56} +(-9.39851 + 2.35425i) q^{57} -0.500983 q^{58} -2.16991 q^{59} +2.52517i q^{61} -3.06871 q^{62} +(-7.66230 + 2.07103i) q^{63} -1.00000 q^{64} +(-1.19038 - 4.75216i) q^{66} +10.3117 q^{67} +4.75216 q^{68} +(-12.2508 + 3.06871i) q^{69} +9.81076i q^{71} +(1.41421 + 2.64575i) q^{72} -5.53019i q^{73} -3.32941i q^{74} -5.59388i q^{76} +(-1.68345 + 7.29150i) q^{77} +(1.41421 + 5.64575i) q^{78} -3.29150 q^{79} +(5.00000 - 7.48331i) q^{81} -4.33981i q^{82} -6.97915 q^{83} +(-0.0849536 - 4.58179i) q^{84} +10.3117i q^{86} +(-0.841723 + 0.210845i) q^{87} +2.82843 q^{88} +15.8219 q^{89} +(2.00000 - 8.66259i) q^{91} -7.29150i q^{92} +(-5.15587 + 1.29150i) q^{93} -7.82087i q^{94} +(-1.68014 + 0.420861i) q^{96} -14.6315i q^{97} +(-3.06871 + 6.29150i) q^{98} +(-4.00000 - 7.48331i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{4} + 16 q^{16} - 16 q^{21} + 48 q^{39} - 32 q^{46} + 16 q^{49} - 32 q^{51} - 16 q^{64} + 32 q^{79} + 80 q^{81} + 16 q^{84} + 32 q^{91} - 64 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0.420861 + 1.68014i 0.242984 + 0.970030i
\(4\) −1.00000 −0.500000
\(5\) 0 0
\(6\) −1.68014 + 0.420861i −0.685915 + 0.171816i
\(7\) 2.57794 + 0.595188i 0.974368 + 0.224960i
\(8\) 1.00000i 0.353553i
\(9\) −2.64575 + 1.41421i −0.881917 + 0.471405i
\(10\) 0 0
\(11\) 2.82843i 0.852803i 0.904534 + 0.426401i \(0.140219\pi\)
−0.904534 + 0.426401i \(0.859781\pi\)
\(12\) −0.420861 1.68014i −0.121492 0.485015i
\(13\) 3.36028i 0.931975i −0.884791 0.465987i \(-0.845699\pi\)
0.884791 0.465987i \(-0.154301\pi\)
\(14\) −0.595188 + 2.57794i −0.159071 + 0.688982i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −4.75216 −1.15257 −0.576284 0.817250i \(-0.695498\pi\)
−0.576284 + 0.817250i \(0.695498\pi\)
\(18\) −1.41421 2.64575i −0.333333 0.623610i
\(19\) 5.59388i 1.28332i 0.766987 + 0.641662i \(0.221755\pi\)
−0.766987 + 0.641662i \(0.778245\pi\)
\(20\) 0 0
\(21\) 0.0849536 + 4.58179i 0.0185384 + 0.999828i
\(22\) −2.82843 −0.603023
\(23\) 7.29150i 1.52038i 0.649699 + 0.760192i \(0.274895\pi\)
−0.649699 + 0.760192i \(0.725105\pi\)
\(24\) 1.68014 0.420861i 0.342957 0.0859080i
\(25\) 0 0
\(26\) 3.36028 0.659006
\(27\) −3.48957 3.85005i −0.671569 0.740942i
\(28\) −2.57794 0.595188i −0.487184 0.112480i
\(29\) 0.500983i 0.0930303i 0.998918 + 0.0465151i \(0.0148116\pi\)
−0.998918 + 0.0465151i \(0.985188\pi\)
\(30\) 0 0
\(31\) 3.06871i 0.551157i 0.961279 + 0.275578i \(0.0888694\pi\)
−0.961279 + 0.275578i \(0.911131\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −4.75216 + 1.19038i −0.827245 + 0.207218i
\(34\) 4.75216i 0.814988i
\(35\) 0 0
\(36\) 2.64575 1.41421i 0.440959 0.235702i
\(37\) −3.32941 −0.547352 −0.273676 0.961822i \(-0.588240\pi\)
−0.273676 + 0.961822i \(0.588240\pi\)
\(38\) −5.59388 −0.907447
\(39\) 5.64575 1.41421i 0.904044 0.226455i
\(40\) 0 0
\(41\) −4.33981 −0.677765 −0.338883 0.940829i \(-0.610049\pi\)
−0.338883 + 0.940829i \(0.610049\pi\)
\(42\) −4.58179 + 0.0849536i −0.706985 + 0.0131086i
\(43\) 10.3117 1.57253 0.786263 0.617892i \(-0.212013\pi\)
0.786263 + 0.617892i \(0.212013\pi\)
\(44\) 2.82843i 0.426401i
\(45\) 0 0
\(46\) −7.29150 −1.07507
\(47\) −7.82087 −1.14079 −0.570396 0.821370i \(-0.693210\pi\)
−0.570396 + 0.821370i \(0.693210\pi\)
\(48\) 0.420861 + 1.68014i 0.0607461 + 0.242508i
\(49\) 6.29150 + 3.06871i 0.898786 + 0.438387i
\(50\) 0 0
\(51\) −2.00000 7.98430i −0.280056 1.11803i
\(52\) 3.36028i 0.465987i
\(53\) 8.58301i 1.17897i −0.807781 0.589483i \(-0.799331\pi\)
0.807781 0.589483i \(-0.200669\pi\)
\(54\) 3.85005 3.48957i 0.523925 0.474871i
\(55\) 0 0
\(56\) 0.595188 2.57794i 0.0795353 0.344491i
\(57\) −9.39851 + 2.35425i −1.24486 + 0.311828i
\(58\) −0.500983 −0.0657823
\(59\) −2.16991 −0.282498 −0.141249 0.989974i \(-0.545112\pi\)
−0.141249 + 0.989974i \(0.545112\pi\)
\(60\) 0 0
\(61\) 2.52517i 0.323315i 0.986847 + 0.161657i \(0.0516839\pi\)
−0.986847 + 0.161657i \(0.948316\pi\)
\(62\) −3.06871 −0.389727
\(63\) −7.66230 + 2.07103i −0.965359 + 0.260926i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −1.19038 4.75216i −0.146525 0.584950i
\(67\) 10.3117 1.25978 0.629890 0.776684i \(-0.283100\pi\)
0.629890 + 0.776684i \(0.283100\pi\)
\(68\) 4.75216 0.576284
\(69\) −12.2508 + 3.06871i −1.47482 + 0.369430i
\(70\) 0 0
\(71\) 9.81076i 1.16432i 0.813073 + 0.582161i \(0.197793\pi\)
−0.813073 + 0.582161i \(0.802207\pi\)
\(72\) 1.41421 + 2.64575i 0.166667 + 0.311805i
\(73\) 5.53019i 0.647260i −0.946184 0.323630i \(-0.895097\pi\)
0.946184 0.323630i \(-0.104903\pi\)
\(74\) 3.32941i 0.387036i
\(75\) 0 0
\(76\) 5.59388i 0.641662i
\(77\) −1.68345 + 7.29150i −0.191846 + 0.830944i
\(78\) 1.41421 + 5.64575i 0.160128 + 0.639255i
\(79\) −3.29150 −0.370323 −0.185161 0.982708i \(-0.559281\pi\)
−0.185161 + 0.982708i \(0.559281\pi\)
\(80\) 0 0
\(81\) 5.00000 7.48331i 0.555556 0.831479i
\(82\) 4.33981i 0.479252i
\(83\) −6.97915 −0.766061 −0.383030 0.923736i \(-0.625120\pi\)
−0.383030 + 0.923736i \(0.625120\pi\)
\(84\) −0.0849536 4.58179i −0.00926920 0.499914i
\(85\) 0 0
\(86\) 10.3117i 1.11194i
\(87\) −0.841723 + 0.210845i −0.0902422 + 0.0226049i
\(88\) 2.82843 0.301511
\(89\) 15.8219 1.67712 0.838558 0.544812i \(-0.183399\pi\)
0.838558 + 0.544812i \(0.183399\pi\)
\(90\) 0 0
\(91\) 2.00000 8.66259i 0.209657 0.908086i
\(92\) 7.29150i 0.760192i
\(93\) −5.15587 + 1.29150i −0.534639 + 0.133923i
\(94\) 7.82087i 0.806661i
\(95\) 0 0
\(96\) −1.68014 + 0.420861i −0.171479 + 0.0429540i
\(97\) 14.6315i 1.48560i −0.669511 0.742802i \(-0.733496\pi\)
0.669511 0.742802i \(-0.266504\pi\)
\(98\) −3.06871 + 6.29150i −0.309987 + 0.635538i
\(99\) −4.00000 7.48331i −0.402015 0.752101i
\(100\) 0 0
\(101\) −2.16991 −0.215914 −0.107957 0.994156i \(-0.534431\pi\)
−0.107957 + 0.994156i \(0.534431\pi\)
\(102\) 7.98430 2.00000i 0.790563 0.198030i
\(103\) 3.14944i 0.310323i 0.987889 + 0.155162i \(0.0495899\pi\)
−0.987889 + 0.155162i \(0.950410\pi\)
\(104\) −3.36028 −0.329503
\(105\) 0 0
\(106\) 8.58301 0.833655
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 3.48957 + 3.85005i 0.335784 + 0.370471i
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) 0 0
\(111\) −1.40122 5.59388i −0.132998 0.530948i
\(112\) 2.57794 + 0.595188i 0.243592 + 0.0562400i
\(113\) 6.00000i 0.564433i −0.959351 0.282216i \(-0.908930\pi\)
0.959351 0.282216i \(-0.0910696\pi\)
\(114\) −2.35425 9.39851i −0.220496 0.880251i
\(115\) 0 0
\(116\) 0.500983i 0.0465151i
\(117\) 4.75216 + 8.89047i 0.439337 + 0.821925i
\(118\) 2.16991i 0.199756i
\(119\) −12.2508 2.82843i −1.12303 0.259281i
\(120\) 0 0
\(121\) 3.00000 0.272727
\(122\) −2.52517 −0.228618
\(123\) −1.82646 7.29150i −0.164686 0.657453i
\(124\) 3.06871i 0.275578i
\(125\) 0 0
\(126\) −2.07103 7.66230i −0.184502 0.682612i
\(127\) 3.32941 0.295437 0.147719 0.989029i \(-0.452807\pi\)
0.147719 + 0.989029i \(0.452807\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 4.33981 + 17.3252i 0.382099 + 1.52540i
\(130\) 0 0
\(131\) 17.9918 1.57195 0.785975 0.618258i \(-0.212161\pi\)
0.785975 + 0.618258i \(0.212161\pi\)
\(132\) 4.75216 1.19038i 0.413622 0.103609i
\(133\) −3.32941 + 14.4207i −0.288696 + 1.25043i
\(134\) 10.3117i 0.890799i
\(135\) 0 0
\(136\) 4.75216i 0.407494i
\(137\) 1.29150i 0.110341i −0.998477 0.0551703i \(-0.982430\pi\)
0.998477 0.0551703i \(-0.0175702\pi\)
\(138\) −3.06871 12.2508i −0.261226 1.04285i
\(139\) 0.543544i 0.0461028i 0.999734 + 0.0230514i \(0.00733813\pi\)
−0.999734 + 0.0230514i \(0.992662\pi\)
\(140\) 0 0
\(141\) −3.29150 13.1402i −0.277195 1.10660i
\(142\) −9.81076 −0.823301
\(143\) 9.50432 0.794791
\(144\) −2.64575 + 1.41421i −0.220479 + 0.117851i
\(145\) 0 0
\(146\) 5.53019 0.457682
\(147\) −2.50802 + 11.8621i −0.206858 + 0.978371i
\(148\) 3.32941 0.273676
\(149\) 10.8127i 0.885813i 0.896568 + 0.442906i \(0.146053\pi\)
−0.896568 + 0.442906i \(0.853947\pi\)
\(150\) 0 0
\(151\) −1.41699 −0.115313 −0.0576567 0.998336i \(-0.518363\pi\)
−0.0576567 + 0.998336i \(0.518363\pi\)
\(152\) 5.59388 0.453724
\(153\) 12.5730 6.72057i 1.01647 0.543326i
\(154\) −7.29150 1.68345i −0.587566 0.135656i
\(155\) 0 0
\(156\) −5.64575 + 1.41421i −0.452022 + 0.113228i
\(157\) 16.3797i 1.30724i 0.756821 + 0.653622i \(0.226751\pi\)
−0.756821 + 0.653622i \(0.773249\pi\)
\(158\) 3.29150i 0.261858i
\(159\) 14.4207 3.61226i 1.14363 0.286471i
\(160\) 0 0
\(161\) −4.33981 + 18.7970i −0.342025 + 1.48141i
\(162\) 7.48331 + 5.00000i 0.587945 + 0.392837i
\(163\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(164\) 4.33981 0.338883
\(165\) 0 0
\(166\) 6.97915i 0.541687i
\(167\) 20.6921 1.60120 0.800601 0.599198i \(-0.204514\pi\)
0.800601 + 0.599198i \(0.204514\pi\)
\(168\) 4.58179 0.0849536i 0.353493 0.00655431i
\(169\) 1.70850 0.131423
\(170\) 0 0
\(171\) −7.91094 14.8000i −0.604965 1.13179i
\(172\) −10.3117 −0.786263
\(173\) 2.22699 0.169315 0.0846574 0.996410i \(-0.473020\pi\)
0.0846574 + 0.996410i \(0.473020\pi\)
\(174\) −0.210845 0.841723i −0.0159841 0.0638108i
\(175\) 0 0
\(176\) 2.82843i 0.213201i
\(177\) −0.913230 3.64575i −0.0686426 0.274031i
\(178\) 15.8219i 1.18590i
\(179\) 24.4539i 1.82777i 0.405975 + 0.913884i \(0.366932\pi\)
−0.405975 + 0.913884i \(0.633068\pi\)
\(180\) 0 0
\(181\) 14.8000i 1.10008i 0.835139 + 0.550038i \(0.185387\pi\)
−0.835139 + 0.550038i \(0.814613\pi\)
\(182\) 8.66259 + 2.00000i 0.642114 + 0.148250i
\(183\) −4.24264 + 1.06275i −0.313625 + 0.0785604i
\(184\) 7.29150 0.537537
\(185\) 0 0
\(186\) −1.29150 5.15587i −0.0946976 0.378047i
\(187\) 13.4411i 0.982913i
\(188\) 7.82087 0.570396
\(189\) −6.70439 12.0021i −0.487673 0.873026i
\(190\) 0 0
\(191\) 0.500983i 0.0362499i −0.999836 0.0181249i \(-0.994230\pi\)
0.999836 0.0181249i \(-0.00576966\pi\)
\(192\) −0.420861 1.68014i −0.0303731 0.121254i
\(193\) 8.48528 0.610784 0.305392 0.952227i \(-0.401213\pi\)
0.305392 + 0.952227i \(0.401213\pi\)
\(194\) 14.6315 1.05048
\(195\) 0 0
\(196\) −6.29150 3.06871i −0.449393 0.219194i
\(197\) 18.0000i 1.28245i −0.767354 0.641223i \(-0.778427\pi\)
0.767354 0.641223i \(-0.221573\pi\)
\(198\) 7.48331 4.00000i 0.531816 0.284268i
\(199\) 9.20614i 0.652606i −0.945265 0.326303i \(-0.894197\pi\)
0.945265 0.326303i \(-0.105803\pi\)
\(200\) 0 0
\(201\) 4.33981 + 17.3252i 0.306107 + 1.22202i
\(202\) 2.16991i 0.152674i
\(203\) −0.298179 + 1.29150i −0.0209281 + 0.0906457i
\(204\) 2.00000 + 7.98430i 0.140028 + 0.559013i
\(205\) 0 0
\(206\) −3.14944 −0.219432
\(207\) −10.3117 19.2915i −0.716716 1.34085i
\(208\) 3.36028i 0.232994i
\(209\) −15.8219 −1.09442
\(210\) 0 0
\(211\) −21.1660 −1.45713 −0.728564 0.684978i \(-0.759812\pi\)
−0.728564 + 0.684978i \(0.759812\pi\)
\(212\) 8.58301i 0.589483i
\(213\) −16.4835 + 4.12897i −1.12943 + 0.282912i
\(214\) 0 0
\(215\) 0 0
\(216\) −3.85005 + 3.48957i −0.261963 + 0.237435i
\(217\) −1.82646 + 7.91094i −0.123988 + 0.537030i
\(218\) 2.00000i 0.135457i
\(219\) 9.29150 2.32744i 0.627862 0.157274i
\(220\) 0 0
\(221\) 15.9686i 1.07416i
\(222\) 5.59388 1.40122i 0.375437 0.0940438i
\(223\) 1.19038i 0.0797135i −0.999205 0.0398567i \(-0.987310\pi\)
0.999205 0.0398567i \(-0.0126902\pi\)
\(224\) −0.595188 + 2.57794i −0.0397677 + 0.172246i
\(225\) 0 0
\(226\) 6.00000 0.399114
\(227\) 18.1669 1.20578 0.602890 0.797824i \(-0.294016\pi\)
0.602890 + 0.797824i \(0.294016\pi\)
\(228\) 9.39851 2.35425i 0.622432 0.155914i
\(229\) 24.9007i 1.64548i 0.568415 + 0.822742i \(0.307557\pi\)
−0.568415 + 0.822742i \(0.692443\pi\)
\(230\) 0 0
\(231\) −12.9593 + 0.240285i −0.852656 + 0.0158096i
\(232\) 0.500983 0.0328912
\(233\) 13.2915i 0.870755i 0.900248 + 0.435378i \(0.143385\pi\)
−0.900248 + 0.435378i \(0.856615\pi\)
\(234\) −8.89047 + 4.75216i −0.581188 + 0.310658i
\(235\) 0 0
\(236\) 2.16991 0.141249
\(237\) −1.38527 5.53019i −0.0899827 0.359224i
\(238\) 2.82843 12.2508i 0.183340 0.794099i
\(239\) 14.6431i 0.947185i −0.880744 0.473592i \(-0.842957\pi\)
0.880744 0.473592i \(-0.157043\pi\)
\(240\) 0 0
\(241\) 17.3252i 1.11601i 0.829836 + 0.558007i \(0.188434\pi\)
−0.829836 + 0.558007i \(0.811566\pi\)
\(242\) 3.00000i 0.192847i
\(243\) 14.6773 + 5.25127i 0.941551 + 0.336869i
\(244\) 2.52517i 0.161657i
\(245\) 0 0
\(246\) 7.29150 1.82646i 0.464889 0.116451i
\(247\) 18.7970 1.19603
\(248\) 3.06871 0.194863
\(249\) −2.93725 11.7260i −0.186141 0.743102i
\(250\) 0 0
\(251\) −6.50972 −0.410890 −0.205445 0.978669i \(-0.565864\pi\)
−0.205445 + 0.978669i \(0.565864\pi\)
\(252\) 7.66230 2.07103i 0.482679 0.130463i
\(253\) −20.6235 −1.29659
\(254\) 3.32941i 0.208906i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 18.7105 1.16713 0.583563 0.812068i \(-0.301658\pi\)
0.583563 + 0.812068i \(0.301658\pi\)
\(258\) −17.3252 + 4.33981i −1.07862 + 0.270185i
\(259\) −8.58301 1.98162i −0.533322 0.123132i
\(260\) 0 0
\(261\) −0.708497 1.32548i −0.0438549 0.0820450i
\(262\) 17.9918i 1.11154i
\(263\) 14.5830i 0.899227i 0.893223 + 0.449613i \(0.148438\pi\)
−0.893223 + 0.449613i \(0.851562\pi\)
\(264\) 1.19038 + 4.75216i 0.0732626 + 0.292475i
\(265\) 0 0
\(266\) −14.4207 3.32941i −0.884188 0.204139i
\(267\) 6.65882 + 26.5830i 0.407513 + 1.62685i
\(268\) −10.3117 −0.629890
\(269\) 9.31216 0.567773 0.283886 0.958858i \(-0.408376\pi\)
0.283886 + 0.958858i \(0.408376\pi\)
\(270\) 0 0
\(271\) 20.3939i 1.23884i −0.785059 0.619421i \(-0.787368\pi\)
0.785059 0.619421i \(-0.212632\pi\)
\(272\) −4.75216 −0.288142
\(273\) 15.3961 0.285468i 0.931815 0.0172773i
\(274\) 1.29150 0.0780225
\(275\) 0 0
\(276\) 12.2508 3.06871i 0.737409 0.184715i
\(277\) −6.98233 −0.419528 −0.209764 0.977752i \(-0.567270\pi\)
−0.209764 + 0.977752i \(0.567270\pi\)
\(278\) −0.543544 −0.0325996
\(279\) −4.33981 8.11905i −0.259818 0.486075i
\(280\) 0 0
\(281\) 9.30978i 0.555375i −0.960672 0.277687i \(-0.910432\pi\)
0.960672 0.277687i \(-0.0895679\pi\)
\(282\) 13.1402 3.29150i 0.782486 0.196006i
\(283\) 32.2016i 1.91419i −0.289779 0.957094i \(-0.593582\pi\)
0.289779 0.957094i \(-0.406418\pi\)
\(284\) 9.81076i 0.582161i
\(285\) 0 0
\(286\) 9.50432i 0.562002i
\(287\) −11.1878 2.58301i −0.660393 0.152470i
\(288\) −1.41421 2.64575i −0.0833333 0.155902i
\(289\) 5.58301 0.328412
\(290\) 0 0
\(291\) 24.5830 6.15784i 1.44108 0.360979i
\(292\) 5.53019i 0.323630i
\(293\) 7.27733 0.425146 0.212573 0.977145i \(-0.431816\pi\)
0.212573 + 0.977145i \(0.431816\pi\)
\(294\) −11.8621 2.50802i −0.691813 0.146271i
\(295\) 0 0
\(296\) 3.32941i 0.193518i
\(297\) 10.8896 9.87000i 0.631878 0.572716i
\(298\) −10.8127 −0.626364
\(299\) 24.5015 1.41696
\(300\) 0 0
\(301\) 26.5830 + 6.13742i 1.53222 + 0.353755i
\(302\) 1.41699i 0.0815389i
\(303\) −0.913230 3.64575i −0.0524637 0.209443i
\(304\) 5.59388i 0.320831i
\(305\) 0 0
\(306\) 6.72057 + 12.5730i 0.384189 + 0.718752i
\(307\) 12.0399i 0.687154i 0.939124 + 0.343577i \(0.111639\pi\)
−0.939124 + 0.343577i \(0.888361\pi\)
\(308\) 1.68345 7.29150i 0.0959232 0.415472i
\(309\) −5.29150 + 1.32548i −0.301023 + 0.0754038i
\(310\) 0 0
\(311\) 24.5015 1.38935 0.694677 0.719322i \(-0.255547\pi\)
0.694677 + 0.719322i \(0.255547\pi\)
\(312\) −1.41421 5.64575i −0.0800641 0.319628i
\(313\) 14.6315i 0.827022i 0.910499 + 0.413511i \(0.135698\pi\)
−0.910499 + 0.413511i \(0.864302\pi\)
\(314\) −16.3797 −0.924361
\(315\) 0 0
\(316\) 3.29150 0.185161
\(317\) 6.00000i 0.336994i −0.985702 0.168497i \(-0.946109\pi\)
0.985702 0.168497i \(-0.0538913\pi\)
\(318\) 3.61226 + 14.4207i 0.202565 + 0.808671i
\(319\) −1.41699 −0.0793365
\(320\) 0 0
\(321\) 0 0
\(322\) −18.7970 4.33981i −1.04752 0.241848i
\(323\) 26.5830i 1.47912i
\(324\) −5.00000 + 7.48331i −0.277778 + 0.415740i
\(325\) 0 0
\(326\) 0 0
\(327\) −0.841723 3.36028i −0.0465474 0.185824i
\(328\) 4.33981i 0.239626i
\(329\) −20.1617 4.65489i −1.11155 0.256632i
\(330\) 0 0
\(331\) 8.00000 0.439720 0.219860 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) 6.97915 0.383030
\(333\) 8.80879 4.70850i 0.482719 0.258024i
\(334\) 20.6921i 1.13222i
\(335\) 0 0
\(336\) 0.0849536 + 4.58179i 0.00463460 + 0.249957i
\(337\) 22.4499 1.22293 0.611463 0.791273i \(-0.290581\pi\)
0.611463 + 0.791273i \(0.290581\pi\)
\(338\) 1.70850i 0.0929300i
\(339\) 10.0808 2.52517i 0.547517 0.137148i
\(340\) 0 0
\(341\) −8.67963 −0.470028
\(342\) 14.8000 7.91094i 0.800293 0.427775i
\(343\) 14.3926 + 11.6556i 0.777129 + 0.629342i
\(344\) 10.3117i 0.555972i
\(345\) 0 0
\(346\) 2.22699i 0.119724i
\(347\) 24.0000i 1.28839i 0.764862 + 0.644194i \(0.222807\pi\)
−0.764862 + 0.644194i \(0.777193\pi\)
\(348\) 0.841723 0.210845i 0.0451211 0.0113025i
\(349\) 13.7129i 0.734036i −0.930214 0.367018i \(-0.880379\pi\)
0.930214 0.367018i \(-0.119621\pi\)
\(350\) 0 0
\(351\) −12.9373 + 11.7260i −0.690540 + 0.625885i
\(352\) −2.82843 −0.150756
\(353\) 9.80250 0.521734 0.260867 0.965375i \(-0.415992\pi\)
0.260867 + 0.965375i \(0.415992\pi\)
\(354\) 3.64575 0.913230i 0.193769 0.0485376i
\(355\) 0 0
\(356\) −15.8219 −0.838558
\(357\) −0.403713 21.7734i −0.0213668 1.15237i
\(358\) −24.4539 −1.29243
\(359\) 4.33138i 0.228601i −0.993446 0.114301i \(-0.963537\pi\)
0.993446 0.114301i \(-0.0364627\pi\)
\(360\) 0 0
\(361\) −12.2915 −0.646921
\(362\) −14.8000 −0.777872
\(363\) 1.26258 + 5.04042i 0.0662685 + 0.264554i
\(364\) −2.00000 + 8.66259i −0.104828 + 0.454043i
\(365\) 0 0
\(366\) −1.06275 4.24264i −0.0555506 0.221766i
\(367\) 14.6315i 0.763759i −0.924212 0.381879i \(-0.875277\pi\)
0.924212 0.381879i \(-0.124723\pi\)
\(368\) 7.29150i 0.380096i
\(369\) 11.4821 6.13742i 0.597733 0.319502i
\(370\) 0 0
\(371\) 5.10850 22.1264i 0.265220 1.14875i
\(372\) 5.15587 1.29150i 0.267319 0.0669613i
\(373\) −6.98233 −0.361531 −0.180766 0.983526i \(-0.557858\pi\)
−0.180766 + 0.983526i \(0.557858\pi\)
\(374\) 13.4411 0.695024
\(375\) 0 0
\(376\) 7.82087i 0.403331i
\(377\) 1.68345 0.0867019
\(378\) 12.0021 6.70439i 0.617323 0.344837i
\(379\) 6.58301 0.338146 0.169073 0.985604i \(-0.445923\pi\)
0.169073 + 0.985604i \(0.445923\pi\)
\(380\) 0 0
\(381\) 1.40122 + 5.59388i 0.0717867 + 0.286583i
\(382\) 0.500983 0.0256325
\(383\) −20.6921 −1.05732 −0.528658 0.848835i \(-0.677305\pi\)
−0.528658 + 0.848835i \(0.677305\pi\)
\(384\) 1.68014 0.420861i 0.0857394 0.0214770i
\(385\) 0 0
\(386\) 8.48528i 0.431889i
\(387\) −27.2823 + 14.5830i −1.38684 + 0.741296i
\(388\) 14.6315i 0.742802i
\(389\) 37.0931i 1.88069i −0.340218 0.940346i \(-0.610501\pi\)
0.340218 0.940346i \(-0.389499\pi\)
\(390\) 0 0
\(391\) 34.6504i 1.75234i
\(392\) 3.06871 6.29150i 0.154993 0.317769i
\(393\) 7.57205 + 30.2288i 0.381959 + 1.52484i
\(394\) 18.0000 0.906827
\(395\) 0 0
\(396\) 4.00000 + 7.48331i 0.201008 + 0.376051i
\(397\) 14.8424i 0.744916i 0.928049 + 0.372458i \(0.121485\pi\)
−0.928049 + 0.372458i \(0.878515\pi\)
\(398\) 9.20614 0.461462
\(399\) −25.6300 + 0.475220i −1.28310 + 0.0237908i
\(400\) 0 0
\(401\) 7.48331i 0.373699i −0.982389 0.186849i \(-0.940172\pi\)
0.982389 0.186849i \(-0.0598277\pi\)
\(402\) −17.3252 + 4.33981i −0.864102 + 0.216450i
\(403\) 10.3117 0.513664
\(404\) 2.16991 0.107957
\(405\) 0 0
\(406\) −1.29150 0.298179i −0.0640962 0.0147984i
\(407\) 9.41699i 0.466783i
\(408\) −7.98430 + 2.00000i −0.395282 + 0.0990148i
\(409\) 23.4626i 1.16015i −0.814563 0.580076i \(-0.803023\pi\)
0.814563 0.580076i \(-0.196977\pi\)
\(410\) 0 0
\(411\) 2.16991 0.543544i 0.107034 0.0268110i
\(412\) 3.14944i 0.155162i
\(413\) −5.59388 1.29150i −0.275257 0.0635507i
\(414\) 19.2915 10.3117i 0.948126 0.506794i
\(415\) 0 0
\(416\) 3.36028 0.164751
\(417\) −0.913230 + 0.228757i −0.0447211 + 0.0112023i
\(418\) 15.8219i 0.773874i
\(419\) −33.8137 −1.65191 −0.825953 0.563739i \(-0.809362\pi\)
−0.825953 + 0.563739i \(0.809362\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 21.1660i 1.03035i
\(423\) 20.6921 11.0604i 1.00608 0.537774i
\(424\) −8.58301 −0.416828
\(425\) 0 0
\(426\) −4.12897 16.4835i −0.200049 0.798626i
\(427\) −1.50295 + 6.50972i −0.0727328 + 0.315028i
\(428\) 0 0
\(429\) 4.00000 + 15.9686i 0.193122 + 0.770971i
\(430\) 0 0
\(431\) 8.98626i 0.432853i −0.976299 0.216427i \(-0.930560\pi\)
0.976299 0.216427i \(-0.0694402\pi\)
\(432\) −3.48957 3.85005i −0.167892 0.185236i
\(433\) 18.5496i 0.891439i −0.895173 0.445719i \(-0.852948\pi\)
0.895173 0.445719i \(-0.147052\pi\)
\(434\) −7.91094 1.82646i −0.379737 0.0876729i
\(435\) 0 0
\(436\) 2.00000 0.0957826
\(437\) −40.7878 −1.95114
\(438\) 2.32744 + 9.29150i 0.111210 + 0.443965i
\(439\) 26.5313i 1.26627i −0.774041 0.633135i \(-0.781768\pi\)
0.774041 0.633135i \(-0.218232\pi\)
\(440\) 0 0
\(441\) −20.9856 + 0.778479i −0.999313 + 0.0370704i
\(442\) −15.9686 −0.759549
\(443\) 29.1660i 1.38572i −0.721073 0.692859i \(-0.756351\pi\)
0.721073 0.692859i \(-0.243649\pi\)
\(444\) 1.40122 + 5.59388i 0.0664990 + 0.265474i
\(445\) 0 0
\(446\) 1.19038 0.0563659
\(447\) −18.1669 + 4.55066i −0.859265 + 0.215239i
\(448\) −2.57794 0.595188i −0.121796 0.0281200i
\(449\) 36.5921i 1.72689i 0.504446 + 0.863444i \(0.331697\pi\)
−0.504446 + 0.863444i \(0.668303\pi\)
\(450\) 0 0
\(451\) 12.2748i 0.578000i
\(452\) 6.00000i 0.282216i
\(453\) −0.596358 2.38075i −0.0280194 0.111857i
\(454\) 18.1669i 0.852615i
\(455\) 0 0
\(456\) 2.35425 + 9.39851i 0.110248 + 0.440126i
\(457\) 8.48528 0.396925 0.198462 0.980109i \(-0.436405\pi\)
0.198462 + 0.980109i \(0.436405\pi\)
\(458\) −24.9007 −1.16353
\(459\) 16.5830 + 18.2960i 0.774028 + 0.853986i
\(460\) 0 0
\(461\) −17.9918 −0.837961 −0.418981 0.907995i \(-0.637612\pi\)
−0.418981 + 0.907995i \(0.637612\pi\)
\(462\) −0.240285 12.9593i −0.0111791 0.602919i
\(463\) −1.50295 −0.0698480 −0.0349240 0.999390i \(-0.511119\pi\)
−0.0349240 + 0.999390i \(0.511119\pi\)
\(464\) 0.500983i 0.0232576i
\(465\) 0 0
\(466\) −13.2915 −0.615717
\(467\) 0.841723 0.0389503 0.0194751 0.999810i \(-0.493800\pi\)
0.0194751 + 0.999810i \(0.493800\pi\)
\(468\) −4.75216 8.89047i −0.219669 0.410962i
\(469\) 26.5830 + 6.13742i 1.22749 + 0.283400i
\(470\) 0 0
\(471\) −27.5203 + 6.89360i −1.26807 + 0.317640i
\(472\) 2.16991i 0.0998781i
\(473\) 29.1660i 1.34105i
\(474\) 5.53019 1.38527i 0.254010 0.0636274i
\(475\) 0 0
\(476\) 12.2508 + 2.82843i 0.561513 + 0.129641i
\(477\) 12.1382 + 22.7085i 0.555770 + 1.03975i
\(478\) 14.6431 0.669761
\(479\) 21.6991 0.991456 0.495728 0.868478i \(-0.334901\pi\)
0.495728 + 0.868478i \(0.334901\pi\)
\(480\) 0 0
\(481\) 11.1878i 0.510118i
\(482\) −17.3252 −0.789141
\(483\) −33.4081 + 0.619439i −1.52012 + 0.0281855i
\(484\) −3.00000 −0.136364
\(485\) 0 0
\(486\) −5.25127 + 14.6773i −0.238202 + 0.665777i
\(487\) −9.98823 −0.452610 −0.226305 0.974056i \(-0.572665\pi\)
−0.226305 + 0.974056i \(0.572665\pi\)
\(488\) 2.52517 0.114309
\(489\) 0 0
\(490\) 0 0
\(491\) 14.1421i 0.638226i −0.947717 0.319113i \(-0.896615\pi\)
0.947717 0.319113i \(-0.103385\pi\)
\(492\) 1.82646 + 7.29150i 0.0823432 + 0.328726i
\(493\) 2.38075i 0.107224i
\(494\) 18.7970i 0.845718i
\(495\) 0 0
\(496\) 3.06871i 0.137789i
\(497\) −5.83925 + 25.2915i −0.261926 + 1.13448i
\(498\) 11.7260 2.93725i 0.525453 0.131621i
\(499\) −22.5830 −1.01095 −0.505477 0.862840i \(-0.668683\pi\)
−0.505477 + 0.862840i \(0.668683\pi\)
\(500\) 0 0
\(501\) 8.70850 + 34.7656i 0.389067 + 1.55321i
\(502\) 6.50972i 0.290543i
\(503\) −15.6417 −0.697431 −0.348715 0.937229i \(-0.613382\pi\)
−0.348715 + 0.937229i \(0.613382\pi\)
\(504\) 2.07103 + 7.66230i 0.0922511 + 0.341306i
\(505\) 0 0
\(506\) 20.6235i 0.916826i
\(507\) 0.719041 + 2.87052i 0.0319337 + 0.127484i
\(508\) −3.32941 −0.147719
\(509\) 39.6909 1.75927 0.879633 0.475652i \(-0.157788\pi\)
0.879633 + 0.475652i \(0.157788\pi\)
\(510\) 0 0
\(511\) 3.29150 14.2565i 0.145608 0.630669i
\(512\) 1.00000i 0.0441942i
\(513\) 21.5367 19.5203i 0.950869 0.861840i
\(514\) 18.7105i 0.825283i
\(515\) 0 0
\(516\) −4.33981 17.3252i −0.191050 0.762699i
\(517\) 22.1208i 0.972870i
\(518\) 1.98162 8.58301i 0.0870676 0.377116i
\(519\) 0.937254 + 3.74166i 0.0411409 + 0.164241i
\(520\) 0 0
\(521\) 13.0194 0.570392 0.285196 0.958469i \(-0.407941\pi\)
0.285196 + 0.958469i \(0.407941\pi\)
\(522\) 1.32548 0.708497i 0.0580146 0.0310101i
\(523\) 16.8014i 0.734675i 0.930088 + 0.367337i \(0.119731\pi\)
−0.930088 + 0.367337i \(0.880269\pi\)
\(524\) −17.9918 −0.785975
\(525\) 0 0
\(526\) −14.5830 −0.635849
\(527\) 14.5830i 0.635246i
\(528\) −4.75216 + 1.19038i −0.206811 + 0.0518045i
\(529\) −30.1660 −1.31157
\(530\) 0 0
\(531\) 5.74103 3.06871i 0.249140 0.133171i
\(532\) 3.32941 14.4207i 0.144348 0.625215i
\(533\) 14.5830i 0.631660i
\(534\) −26.5830 + 6.65882i −1.15036 + 0.288155i
\(535\) 0 0
\(536\) 10.3117i 0.445399i
\(537\) −41.0860 + 10.2917i −1.77299 + 0.444119i
\(538\) 9.31216i 0.401476i
\(539\) −8.67963 + 17.7951i −0.373858 + 0.766487i
\(540\) 0 0
\(541\) 2.00000 0.0859867 0.0429934 0.999075i \(-0.486311\pi\)
0.0429934 + 0.999075i \(0.486311\pi\)
\(542\) 20.3939 0.875993
\(543\) −24.8661 + 6.22876i −1.06711 + 0.267302i
\(544\) 4.75216i 0.203747i
\(545\) 0 0
\(546\) 0.285468 + 15.3961i 0.0122169 + 0.658892i
\(547\) −16.9706 −0.725609 −0.362804 0.931865i \(-0.618181\pi\)
−0.362804 + 0.931865i \(0.618181\pi\)
\(548\) 1.29150i 0.0551703i
\(549\) −3.57113 6.68097i −0.152412 0.285137i
\(550\) 0 0
\(551\) −2.80244 −0.119388
\(552\) 3.06871 + 12.2508i 0.130613 + 0.521427i
\(553\) −8.48528 1.95906i −0.360831 0.0833078i
\(554\) 6.98233i 0.296651i
\(555\) 0 0
\(556\) 0.543544i 0.0230514i
\(557\) 35.1660i 1.49003i 0.667047 + 0.745016i \(0.267558\pi\)
−0.667047 + 0.745016i \(0.732442\pi\)
\(558\) 8.11905 4.33981i 0.343707 0.183719i
\(559\) 34.6504i 1.46555i
\(560\) 0 0
\(561\) 22.5830 5.65685i 0.953455 0.238833i
\(562\) 9.30978 0.392709
\(563\) −13.1166 −0.552798 −0.276399 0.961043i \(-0.589141\pi\)
−0.276399 + 0.961043i \(0.589141\pi\)
\(564\) 3.29150 + 13.1402i 0.138597 + 0.553301i
\(565\) 0 0
\(566\) 32.2016 1.35353
\(567\) 17.3437 16.3156i 0.728365 0.685189i
\(568\) 9.81076 0.411650
\(569\) 33.7637i 1.41545i −0.706490 0.707723i \(-0.749722\pi\)
0.706490 0.707723i \(-0.250278\pi\)
\(570\) 0 0
\(571\) −13.4170 −0.561484 −0.280742 0.959783i \(-0.590580\pi\)
−0.280742 + 0.959783i \(0.590580\pi\)
\(572\) −9.50432 −0.397395
\(573\) 0.841723 0.210845i 0.0351635 0.00880816i
\(574\) 2.58301 11.1878i 0.107813 0.466968i
\(575\) 0 0
\(576\) 2.64575 1.41421i 0.110240 0.0589256i
\(577\) 36.3306i 1.51246i −0.654305 0.756231i \(-0.727039\pi\)
0.654305 0.756231i \(-0.272961\pi\)
\(578\) 5.58301i 0.232222i
\(579\) 3.57113 + 14.2565i 0.148411 + 0.592479i
\(580\) 0 0
\(581\) −17.9918 4.15390i −0.746425 0.172333i
\(582\) 6.15784 + 24.5830i 0.255251 + 1.01900i
\(583\) 24.2764 1.00543
\(584\) −5.53019 −0.228841
\(585\) 0 0
\(586\) 7.27733i 0.300624i
\(587\) −37.7719 −1.55901 −0.779507 0.626394i \(-0.784530\pi\)
−0.779507 + 0.626394i \(0.784530\pi\)
\(588\) 2.50802 11.8621i 0.103429 0.489185i
\(589\) −17.1660 −0.707313
\(590\) 0 0
\(591\) 30.2425 7.57551i 1.24401 0.311615i
\(592\) −3.32941 −0.136838
\(593\) −6.43560 −0.264279 −0.132139 0.991231i \(-0.542185\pi\)
−0.132139 + 0.991231i \(0.542185\pi\)
\(594\) 9.87000 + 10.8896i 0.404971 + 0.446805i
\(595\) 0 0
\(596\) 10.8127i 0.442906i
\(597\) 15.4676 3.87451i 0.633047 0.158573i
\(598\) 24.5015i 1.00194i
\(599\) 4.15390i 0.169724i 0.996393 + 0.0848620i \(0.0270449\pi\)
−0.996393 + 0.0848620i \(0.972955\pi\)
\(600\) 0 0
\(601\) 6.13742i 0.250351i 0.992135 + 0.125175i \(0.0399494\pi\)
−0.992135 + 0.125175i \(0.960051\pi\)
\(602\) −6.13742 + 26.5830i −0.250143 + 1.08344i
\(603\) −27.2823 + 14.5830i −1.11102 + 0.593866i
\(604\) 1.41699 0.0576567
\(605\) 0 0
\(606\) 3.64575 0.913230i 0.148099 0.0370974i
\(607\) 5.95188i 0.241579i −0.992678 0.120790i \(-0.961457\pi\)
0.992678 0.120790i \(-0.0385427\pi\)
\(608\) −5.59388 −0.226862
\(609\) −2.29540 + 0.0425603i −0.0930143 + 0.00172463i
\(610\) 0 0
\(611\) 26.2803i 1.06319i
\(612\) −12.5730 + 6.72057i −0.508235 + 0.271663i
\(613\) −47.5823 −1.92183 −0.960915 0.276843i \(-0.910712\pi\)
−0.960915 + 0.276843i \(0.910712\pi\)
\(614\) −12.0399 −0.485891
\(615\) 0 0
\(616\) 7.29150 + 1.68345i 0.293783 + 0.0678280i
\(617\) 47.1660i 1.89883i −0.314021 0.949416i \(-0.601676\pi\)
0.314021 0.949416i \(-0.398324\pi\)
\(618\) −1.32548 5.29150i −0.0533185 0.212855i
\(619\) 40.2443i 1.61755i 0.588116 + 0.808777i \(0.299870\pi\)
−0.588116 + 0.808777i \(0.700130\pi\)
\(620\) 0 0
\(621\) 28.0726 25.4442i 1.12652 1.02104i
\(622\) 24.5015i 0.982421i
\(623\) 40.7878 + 9.41699i 1.63413 + 0.377284i
\(624\) 5.64575 1.41421i 0.226011 0.0566139i
\(625\) 0 0
\(626\) −14.6315 −0.584793
\(627\) −6.65882 26.5830i −0.265928 1.06162i
\(628\) 16.3797i 0.653622i
\(629\) 15.8219 0.630860
\(630\) 0 0
\(631\) 32.4575 1.29211 0.646057 0.763290i \(-0.276417\pi\)
0.646057 + 0.763290i \(0.276417\pi\)
\(632\) 3.29150i 0.130929i
\(633\) −8.90796 35.5619i −0.354060 1.41346i
\(634\) 6.00000 0.238290
\(635\) 0 0
\(636\) −14.4207 + 3.61226i −0.571817 + 0.143235i
\(637\) 10.3117 21.1412i 0.408566 0.837646i
\(638\) 1.41699i 0.0560994i
\(639\) −13.8745 25.9568i −0.548867 1.02684i
\(640\) 0 0
\(641\) 28.1068i 1.11015i −0.831800 0.555076i \(-0.812689\pi\)
0.831800 0.555076i \(-0.187311\pi\)
\(642\) 0 0
\(643\) 22.6786i 0.894357i 0.894445 + 0.447178i \(0.147571\pi\)
−0.894445 + 0.447178i \(0.852429\pi\)
\(644\) 4.33981 18.7970i 0.171013 0.740706i
\(645\) 0 0
\(646\) 26.5830 1.04589
\(647\) −13.9583 −0.548757 −0.274379 0.961622i \(-0.588472\pi\)
−0.274379 + 0.961622i \(0.588472\pi\)
\(648\) −7.48331 5.00000i −0.293972 0.196419i
\(649\) 6.13742i 0.240915i
\(650\) 0 0
\(651\) −14.0602 + 0.260698i −0.551062 + 0.0102176i
\(652\) 0 0
\(653\) 23.1660i 0.906556i −0.891369 0.453278i \(-0.850254\pi\)
0.891369 0.453278i \(-0.149746\pi\)
\(654\) 3.36028 0.841723i 0.131397 0.0329140i
\(655\) 0 0
\(656\) −4.33981 −0.169441
\(657\) 7.82087 + 14.6315i 0.305121 + 0.570830i
\(658\) 4.65489 20.1617i 0.181466 0.785985i
\(659\) 27.1048i 1.05585i −0.849290 0.527927i \(-0.822969\pi\)
0.849290 0.527927i \(-0.177031\pi\)
\(660\) 0 0
\(661\) 8.66259i 0.336936i 0.985707 + 0.168468i \(0.0538820\pi\)
−0.985707 + 0.168468i \(0.946118\pi\)
\(662\) 8.00000i 0.310929i
\(663\) −26.8295 + 6.72057i −1.04197 + 0.261005i
\(664\) 6.97915i 0.270843i
\(665\) 0 0
\(666\) 4.70850 + 8.80879i 0.182451 + 0.341334i
\(667\) −3.65292 −0.141442
\(668\) −20.6921 −0.800601
\(669\) 2.00000 0.500983i 0.0773245 0.0193691i
\(670\) 0 0
\(671\) −7.14226 −0.275724
\(672\) −4.58179 + 0.0849536i −0.176746 + 0.00327716i
\(673\) 23.6294 0.910846 0.455423 0.890275i \(-0.349488\pi\)
0.455423 + 0.890275i \(0.349488\pi\)
\(674\) 22.4499i 0.864740i
\(675\) 0 0
\(676\) −1.70850 −0.0657114
\(677\) −6.19024 −0.237910 −0.118955 0.992900i \(-0.537954\pi\)
−0.118955 + 0.992900i \(0.537954\pi\)
\(678\) 2.52517 + 10.0808i 0.0969785 + 0.387153i
\(679\) 8.70850 37.7191i 0.334201 1.44753i
\(680\) 0 0
\(681\) 7.64575 + 30.5230i 0.292986 + 1.16964i
\(682\) 8.67963i 0.332360i
\(683\) 26.5830i 1.01717i 0.861012 + 0.508585i \(0.169831\pi\)
−0.861012 + 0.508585i \(0.830169\pi\)
\(684\) 7.91094 + 14.8000i 0.302482 + 0.565893i
\(685\) 0 0
\(686\) −11.6556 + 14.3926i −0.445012 + 0.549513i
\(687\) −41.8367 + 10.4797i −1.59617 + 0.399827i
\(688\) 10.3117 0.393131
\(689\) −28.8413 −1.09877
\(690\) 0 0
\(691\) 11.7313i 0.446280i 0.974786 + 0.223140i \(0.0716307\pi\)
−0.974786 + 0.223140i \(0.928369\pi\)
\(692\) −2.22699 −0.0846574
\(693\) −5.85776 21.6723i −0.222518 0.823261i
\(694\) −24.0000 −0.911028
\(695\) 0 0
\(696\) 0.210845 + 0.841723i 0.00799204 + 0.0319054i
\(697\) 20.6235 0.781170
\(698\) 13.7129 0.519042
\(699\) −22.3316 + 5.59388i −0.844659 + 0.211580i
\(700\) 0 0
\(701\) 21.1245i 0.797860i −0.916981 0.398930i \(-0.869382\pi\)
0.916981 0.398930i \(-0.130618\pi\)
\(702\) −11.7260 12.9373i −0.442568 0.488285i
\(703\) 18.6243i 0.702430i
\(704\) 2.82843i 0.106600i
\(705\) 0 0
\(706\) 9.80250i 0.368922i
\(707\) −5.59388 1.29150i −0.210380 0.0485720i
\(708\) 0.913230 + 3.64575i 0.0343213 + 0.137016i
\(709\) 0.583005 0.0218952 0.0109476 0.999940i \(-0.496515\pi\)
0.0109476 + 0.999940i \(0.496515\pi\)
\(710\) 0 0
\(711\) 8.70850 4.65489i 0.326594 0.174572i
\(712\) 15.8219i 0.592950i
\(713\) −22.3755 −0.837970
\(714\) 21.7734 0.403713i 0.814848 0.0151086i
\(715\) 0 0
\(716\) 24.4539i 0.913884i
\(717\) 24.6025 6.16272i 0.918798 0.230151i
\(718\) 4.33138 0.161646
\(719\) 2.80244 0.104513 0.0522567 0.998634i \(-0.483359\pi\)
0.0522567 + 0.998634i \(0.483359\pi\)
\(720\) 0 0
\(721\) −1.87451 + 8.11905i −0.0698103 + 0.302369i
\(722\) 12.2915i 0.457442i
\(723\) −29.1088 + 7.29150i −1.08257 + 0.271174i
\(724\) 14.8000i 0.550038i
\(725\) 0 0
\(726\) −5.04042 + 1.26258i −0.187068 + 0.0468589i
\(727\) 45.8536i 1.70062i 0.526286 + 0.850308i \(0.323584\pi\)
−0.526286 + 0.850308i \(0.676416\pi\)
\(728\) −8.66259 2.00000i −0.321057 0.0741249i
\(729\) −2.64575 + 26.8701i −0.0979908 + 0.995187i
\(730\) 0 0
\(731\) −49.0030 −1.81244
\(732\) 4.24264 1.06275i 0.156813 0.0392802i
\(733\) 28.2835i 1.04467i 0.852739 + 0.522337i \(0.174940\pi\)
−0.852739 + 0.522337i \(0.825060\pi\)
\(734\) 14.6315 0.540059
\(735\) 0 0
\(736\) −7.29150 −0.268768
\(737\) 29.1660i 1.07434i
\(738\) 6.13742 + 11.4821i 0.225922 + 0.422661i
\(739\) 33.1660 1.22003 0.610016 0.792389i \(-0.291163\pi\)
0.610016 + 0.792389i \(0.291163\pi\)
\(740\) 0 0
\(741\) 7.91094 + 31.5817i 0.290616 + 1.16018i
\(742\) 22.1264 + 5.10850i 0.812287 + 0.187539i
\(743\) 2.12549i 0.0779767i −0.999240 0.0389884i \(-0.987586\pi\)
0.999240 0.0389884i \(-0.0124135\pi\)
\(744\) 1.29150 + 5.15587i 0.0473488 + 0.189023i
\(745\) 0 0
\(746\) 6.98233i 0.255641i
\(747\) 18.4651 9.87000i 0.675602 0.361125i
\(748\) 13.4411i 0.491456i
\(749\) 0 0
\(750\) 0 0
\(751\) −21.1660 −0.772359 −0.386179 0.922424i \(-0.626205\pi\)
−0.386179 + 0.922424i \(0.626205\pi\)
\(752\) −7.82087 −0.285198
\(753\) −2.73969 10.9373i −0.0998399 0.398576i
\(754\) 1.68345i 0.0613075i
\(755\) 0 0
\(756\) 6.70439 + 12.0021i 0.243836 + 0.436513i
\(757\) −34.2646 −1.24537 −0.622685 0.782473i \(-0.713958\pi\)
−0.622685 + 0.782473i \(0.713958\pi\)
\(758\) 6.58301i 0.239106i
\(759\) −8.67963 34.6504i −0.315051 1.25773i
\(760\) 0 0
\(761\) 11.4821 0.416225 0.208112 0.978105i \(-0.433268\pi\)
0.208112 + 0.978105i \(0.433268\pi\)
\(762\) −5.59388 + 1.40122i −0.202645 + 0.0507609i
\(763\) −5.15587 1.19038i −0.186655 0.0430945i
\(764\) 0.500983i 0.0181249i
\(765\) 0 0
\(766\) 20.6921i 0.747635i
\(767\) 7.29150i 0.263281i
\(768\) 0.420861 + 1.68014i 0.0151865 + 0.0606269i
\(769\) 35.7375i 1.28873i 0.764720 + 0.644363i \(0.222877\pi\)
−0.764720 + 0.644363i \(0.777123\pi\)
\(770\) 0 0
\(771\) 7.87451 + 31.4362i 0.283593 + 1.13215i
\(772\) −8.48528 −0.305392
\(773\) 41.9277 1.50803 0.754017 0.656855i \(-0.228113\pi\)
0.754017 + 0.656855i \(0.228113\pi\)
\(774\) −14.5830 27.2823i −0.524175 0.980642i
\(775\) 0 0
\(776\) −14.6315 −0.525241
\(777\) −0.282845 15.2547i −0.0101470 0.547258i
\(778\) 37.0931 1.32985
\(779\) 24.2764i 0.869792i
\(780\) 0 0
\(781\) −27.7490 −0.992938
\(782\) 34.6504 1.23909
\(783\) 1.92881 1.74822i 0.0689301 0.0624762i
\(784\) 6.29150 + 3.06871i 0.224697 + 0.109597i
\(785\) 0 0
\(786\) −30.2288 + 7.57205i −1.07822 + 0.270086i
\(787\) 28.2835i 1.00820i −0.863646 0.504099i \(-0.831825\pi\)
0.863646 0.504099i \(-0.168175\pi\)
\(788\) 18.0000i 0.641223i
\(789\) −24.5015 + 6.13742i −0.872277 + 0.218498i
\(790\) 0 0
\(791\) 3.57113 15.4676i 0.126975 0.549965i
\(792\) −7.48331 + 4.00000i −0.265908 + 0.142134i
\(793\) 8.48528 0.301321
\(794\) −14.8424 −0.526735
\(795\) 0 0
\(796\) 9.20614i 0.326303i
\(797\) 15.0982 0.534806 0.267403 0.963585i \(-0.413835\pi\)
0.267403 + 0.963585i \(0.413835\pi\)
\(798\) −0.475220 25.6300i −0.0168226 0.907291i
\(799\) 37.1660 1.31484
\(800\) 0 0
\(801\) −41.8608 + 22.3755i −1.47908 + 0.790600i
\(802\) 7.48331 0.264245
\(803\) 15.6417 0.551985
\(804\) −4.33981 17.3252i −0.153053 0.611012i
\(805\) 0 0
\(806\) 10.3117i 0.363216i
\(807\) 3.91913 + 15.6458i 0.137960 + 0.550757i
\(808\) 2.16991i 0.0763371i
\(809\) 11.1362i 0.391529i 0.980651 + 0.195765i \(0.0627188\pi\)
−0.980651 + 0.195765i \(0.937281\pi\)
\(810\) 0 0
\(811\) 24.0062i 0.842970i 0.906835 + 0.421485i \(0.138491\pi\)
−0.906835 + 0.421485i \(0.861509\pi\)
\(812\) 0.298179 1.29150i 0.0104640 0.0453229i
\(813\) 34.2646 8.58301i 1.20171 0.301019i
\(814\) 9.41699 0.330065
\(815\) 0 0
\(816\) −2.00000 7.98430i −0.0700140 0.279506i
\(817\) 57.6827i 2.01806i
\(818\) 23.4626 0.820351
\(819\) 6.95925 + 25.7475i 0.243176 + 0.899690i
\(820\) 0 0
\(821\) 31.4362i 1.09713i −0.836107 0.548566i \(-0.815174\pi\)
0.836107 0.548566i \(-0.184826\pi\)
\(822\) 0.543544 + 2.16991i 0.0189583 + 0.0756842i
\(823\) 11.8147 0.411834 0.205917 0.978569i \(-0.433982\pi\)
0.205917 + 0.978569i \(0.433982\pi\)
\(824\) 3.14944 0.109716
\(825\) 0 0
\(826\) 1.29150 5.59388i 0.0449371 0.194636i
\(827\) 36.0000i 1.25184i −0.779886 0.625921i \(-0.784723\pi\)
0.779886 0.625921i \(-0.215277\pi\)
\(828\) 10.3117 + 19.2915i 0.358358 + 0.670426i
\(829\) 33.2123i 1.15351i 0.816917 + 0.576755i \(0.195681\pi\)
−0.816917 + 0.576755i \(0.804319\pi\)
\(830\) 0 0
\(831\) −2.93859 11.7313i −0.101939 0.406954i
\(832\) 3.36028i 0.116497i
\(833\) −29.8982 14.5830i −1.03591 0.505271i
\(834\) −0.228757 0.913230i −0.00792119 0.0316226i
\(835\) 0 0
\(836\) 15.8219 0.547211
\(837\) 11.8147 10.7085i 0.408375 0.370140i
\(838\) 33.8137i 1.16807i
\(839\) 37.5210 1.29537 0.647684 0.761909i \(-0.275738\pi\)
0.647684 + 0.761909i \(0.275738\pi\)
\(840\) 0 0
\(841\) 28.7490 0.991345
\(842\) 10.0000i 0.344623i
\(843\) 15.6417 3.91813i 0.538730 0.134947i
\(844\) 21.1660 0.728564
\(845\) 0 0
\(846\) 11.0604 + 20.6921i 0.380264 + 0.711408i
\(847\) 7.73381 + 1.78556i 0.265737 + 0.0613527i
\(848\) 8.58301i 0.294742i
\(849\) 54.1033 13.5524i 1.85682 0.465118i
\(850\) 0 0
\(851\) 24.2764i 0.832184i
\(852\) 16.4835 4.12897i 0.564714 0.141456i
\(853\) 23.5220i 0.805377i −0.915337 0.402689i \(-0.868076\pi\)
0.915337 0.402689i \(-0.131924\pi\)
\(854\) −6.50972 1.50295i −0.222758 0.0514299i
\(855\) 0 0
\(856\) 0 0
\(857\) 46.1363 1.57599 0.787993 0.615684i \(-0.211120\pi\)
0.787993 + 0.615684i \(0.211120\pi\)
\(858\) −15.9686 + 4.00000i −0.545159 + 0.136558i
\(859\) 22.9191i 0.781988i 0.920393 + 0.390994i \(0.127869\pi\)
−0.920393 + 0.390994i \(0.872131\pi\)
\(860\) 0 0
\(861\) −0.368683 19.8841i −0.0125647 0.677649i
\(862\) 8.98626 0.306073
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 3.85005 3.48957i 0.130981 0.118718i
\(865\) 0 0
\(866\) 18.5496 0.630342
\(867\) 2.34967 + 9.38024i 0.0797990 + 0.318570i
\(868\) 1.82646 7.91094i 0.0619941 0.268515i
\(869\) 9.30978i 0.315812i
\(870\) 0 0
\(871\) 34.6504i 1.17408i
\(872\) 2.00000i 0.0677285i
\(873\) 20.6921 + 38.7113i 0.700321 + 1.31018i
\(874\) 40.7878i 1.37967i
\(875\) 0 0
\(876\) −9.29150 + 2.32744i −0.313931 + 0.0786370i
\(877\) −23.9529 −0.808832 −0.404416 0.914575i \(-0.632525\pi\)
−0.404416 + 0.914575i \(0.632525\pi\)
\(878\) 26.5313 0.895389
\(879\) 3.06275 + 12.2269i 0.103304 + 0.412404i
\(880\) 0 0
\(881\) 15.8219 0.533053 0.266526 0.963828i \(-0.414124\pi\)
0.266526 + 0.963828i \(0.414124\pi\)
\(882\) −0.778479 20.9856i −0.0262127 0.706621i
\(883\) 30.9352 1.04105 0.520527 0.853845i \(-0.325736\pi\)
0.520527 + 0.853845i \(0.325736\pi\)
\(884\) 15.9686i 0.537082i
\(885\) 0 0
\(886\) 29.1660 0.979851
\(887\) 2.27980 0.0765483 0.0382742 0.999267i \(-0.487814\pi\)
0.0382742 + 0.999267i \(0.487814\pi\)
\(888\) −5.59388 + 1.40122i −0.187718 + 0.0470219i
\(889\) 8.58301 + 1.98162i 0.287865 + 0.0664616i
\(890\) 0 0
\(891\) 21.1660 + 14.1421i 0.709088 + 0.473779i
\(892\) 1.19038i 0.0398567i
\(893\) 43.7490i 1.46400i
\(894\) −4.55066 18.1669i −0.152197 0.607592i
\(895\) 0 0
\(896\) 0.595188 2.57794i 0.0198838 0.0861228i
\(897\) 10.3117 + 41.1660i 0.344299 + 1.37449i
\(898\) −36.5921 −1.22109
\(899\) −1.53737 −0.0512743
\(900\) 0 0
\(901\) 40.7878i 1.35884i
\(902\) 12.2748 0.408708
\(903\) 0.876020 + 47.2462i 0.0291521 + 1.57226i
\(904\) −6.00000 −0.199557
\(905\) 0 0
\(906\) 2.38075 0.596358i 0.0790952 0.0198127i
\(907\) 33.9411 1.12700 0.563498 0.826117i \(-0.309455\pi\)
0.563498 + 0.826117i \(0.309455\pi\)
\(908\) −18.1669 −0.602890
\(909\) 5.74103 3.06871i 0.190418 0.101783i
\(910\) 0 0
\(911\) 18.2960i 0.606175i 0.952963 + 0.303087i \(0.0980174\pi\)
−0.952963 + 0.303087i \(0.901983\pi\)
\(912\) −9.39851 + 2.35425i −0.311216 + 0.0779570i
\(913\) 19.7400i 0.653299i
\(914\) 8.48528i 0.280668i
\(915\) 0 0
\(916\) 24.9007i 0.822742i
\(917\) 46.3817 + 10.7085i 1.53166 + 0.353626i
\(918\) −18.2960 + 16.5830i −0.603859 + 0.547321i
\(919\) −41.8745 −1.38131 −0.690656 0.723183i \(-0.742678\pi\)
−0.690656 + 0.723183i \(0.742678\pi\)
\(920\) 0 0
\(921\) −20.2288 + 5.06713i −0.666560 + 0.166968i
\(922\) 17.9918i 0.592528i
\(923\) 32.9669 1.08512
\(924\) 12.9593 0.240285i 0.426328 0.00790480i
\(925\) 0 0
\(926\) 1.50295i 0.0493900i
\(927\) −4.45398 8.33263i −0.146288 0.273680i
\(928\) −0.500983 −0.0164456
\(929\) −51.8055 −1.69968 −0.849841 0.527039i \(-0.823302\pi\)
−0.849841 + 0.527039i \(0.823302\pi\)
\(930\) 0 0
\(931\) −17.1660 + 35.1939i −0.562593 + 1.15343i
\(932\) 13.2915i 0.435378i
\(933\) 10.3117 + 41.1660i 0.337591 + 1.34771i
\(934\) 0.841723i 0.0275420i
\(935\) 0 0
\(936\) 8.89047 4.75216i 0.290594 0.155329i
\(937\) 5.53019i 0.180663i 0.995912 + 0.0903317i \(0.0287927\pi\)
−0.995912 + 0.0903317i \(0.971207\pi\)
\(938\) −6.13742 + 26.5830i −0.200394 + 0.867966i
\(939\) −24.5830 + 6.15784i −0.802236 + 0.200953i
\(940\) 0 0
\(941\) −0.632534 −0.0206200 −0.0103100 0.999947i \(-0.503282\pi\)
−0.0103100 + 0.999947i \(0.503282\pi\)
\(942\) −6.89360 27.5203i −0.224605 0.896658i
\(943\) 31.6438i 1.03046i
\(944\) −2.16991 −0.0706245
\(945\) 0 0
\(946\) −29.1660 −0.948269
\(947\) 24.0000i 0.779895i −0.920837 0.389948i \(-0.872493\pi\)
0.920837 0.389948i \(-0.127507\pi\)
\(948\) 1.38527 + 5.53019i 0.0449914 + 0.179612i
\(949\) −18.5830 −0.603230
\(950\) 0 0
\(951\) 10.0808 2.52517i 0.326894 0.0818842i
\(952\) −2.82843 + 12.2508i −0.0916698 + 0.397049i
\(953\) 3.87451i 0.125508i 0.998029 + 0.0627538i \(0.0199883\pi\)
−0.998029 + 0.0627538i \(0.980012\pi\)
\(954\) −22.7085 + 12.1382i −0.735215 + 0.392989i
\(955\) 0 0
\(956\) 14.6431i 0.473592i
\(957\) −0.596358 2.38075i −0.0192775 0.0769588i
\(958\) 21.6991i 0.701065i
\(959\) 0.768687 3.32941i 0.0248222 0.107512i
\(960\) 0 0
\(961\) 21.5830 0.696226
\(962\) −11.1878 −0.360708
\(963\) 0 0
\(964\) 17.3252i 0.558007i
\(965\) 0 0
\(966\) −0.619439 33.4081i −0.0199301 1.07489i
\(967\) 26.9588 0.866936 0.433468 0.901169i \(-0.357290\pi\)
0.433468 + 0.901169i \(0.357290\pi\)
\(968\) 3.00000i 0.0964237i
\(969\) 44.6632 11.1878i 1.43479 0.359403i
\(970\) 0 0
\(971\) −9.31216 −0.298842 −0.149421 0.988774i \(-0.547741\pi\)
−0.149421 + 0.988774i \(0.547741\pi\)
\(972\) −14.6773 5.25127i −0.470776 0.168435i
\(973\) −0.323511 + 1.40122i −0.0103713 + 0.0449211i
\(974\) 9.98823i 0.320044i
\(975\) 0 0
\(976\) 2.52517i 0.0808287i
\(977\) 20.1255i 0.643872i 0.946762 + 0.321936i \(0.104334\pi\)
−0.946762 + 0.321936i \(0.895666\pi\)
\(978\) 0 0
\(979\) 44.7510i 1.43025i
\(980\) 0 0
\(981\) 5.29150 2.82843i 0.168945 0.0903047i
\(982\) 14.1421 0.451294
\(983\) −29.0037 −0.925074 −0.462537 0.886600i \(-0.653061\pi\)
−0.462537 + 0.886600i \(0.653061\pi\)
\(984\) −7.29150 + 1.82646i −0.232445 + 0.0582254i
\(985\) 0 0
\(986\) 2.38075 0.0758186
\(987\) −0.664411 35.8336i −0.0211484 1.14060i
\(988\) −18.7970 −0.598013
\(989\) 75.1881i 2.39084i
\(990\) 0 0
\(991\) −11.2915 −0.358686 −0.179343 0.983787i \(-0.557397\pi\)
−0.179343 + 0.983787i \(0.557397\pi\)
\(992\) −3.06871 −0.0974317
\(993\) 3.36689 + 13.4411i 0.106845 + 0.426541i
\(994\) −25.2915 5.83925i −0.802198 0.185210i
\(995\) 0 0
\(996\) 2.93725 + 11.7260i 0.0930705 + 0.371551i
\(997\) 26.3244i 0.833703i 0.908975 + 0.416851i \(0.136866\pi\)
−0.908975 + 0.416851i \(0.863134\pi\)
\(998\) 22.5830i 0.714853i
\(999\) 11.6182 + 12.8184i 0.367584 + 0.405556i
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 1050.2.b.f.251.14 16
3.2 odd 2 inner 1050.2.b.f.251.4 16
5.2 odd 4 210.2.d.a.209.7 yes 8
5.3 odd 4 210.2.d.b.209.2 yes 8
5.4 even 2 inner 1050.2.b.f.251.3 16
7.6 odd 2 inner 1050.2.b.f.251.11 16
15.2 even 4 210.2.d.b.209.8 yes 8
15.8 even 4 210.2.d.a.209.1 8
15.14 odd 2 inner 1050.2.b.f.251.13 16
20.3 even 4 1680.2.k.f.209.7 8
20.7 even 4 1680.2.k.e.209.2 8
21.20 even 2 inner 1050.2.b.f.251.5 16
35.13 even 4 210.2.d.b.209.7 yes 8
35.27 even 4 210.2.d.a.209.2 yes 8
35.34 odd 2 inner 1050.2.b.f.251.6 16
60.23 odd 4 1680.2.k.e.209.8 8
60.47 odd 4 1680.2.k.f.209.1 8
105.62 odd 4 210.2.d.b.209.1 yes 8
105.83 odd 4 210.2.d.a.209.8 yes 8
105.104 even 2 inner 1050.2.b.f.251.12 16
140.27 odd 4 1680.2.k.e.209.7 8
140.83 odd 4 1680.2.k.f.209.2 8
420.83 even 4 1680.2.k.e.209.1 8
420.167 even 4 1680.2.k.f.209.8 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.d.a.209.1 8 15.8 even 4
210.2.d.a.209.2 yes 8 35.27 even 4
210.2.d.a.209.7 yes 8 5.2 odd 4
210.2.d.a.209.8 yes 8 105.83 odd 4
210.2.d.b.209.1 yes 8 105.62 odd 4
210.2.d.b.209.2 yes 8 5.3 odd 4
210.2.d.b.209.7 yes 8 35.13 even 4
210.2.d.b.209.8 yes 8 15.2 even 4
1050.2.b.f.251.3 16 5.4 even 2 inner
1050.2.b.f.251.4 16 3.2 odd 2 inner
1050.2.b.f.251.5 16 21.20 even 2 inner
1050.2.b.f.251.6 16 35.34 odd 2 inner
1050.2.b.f.251.11 16 7.6 odd 2 inner
1050.2.b.f.251.12 16 105.104 even 2 inner
1050.2.b.f.251.13 16 15.14 odd 2 inner
1050.2.b.f.251.14 16 1.1 even 1 trivial
1680.2.k.e.209.1 8 420.83 even 4
1680.2.k.e.209.2 8 20.7 even 4
1680.2.k.e.209.7 8 140.27 odd 4
1680.2.k.e.209.8 8 60.23 odd 4
1680.2.k.f.209.1 8 60.47 odd 4
1680.2.k.f.209.2 8 140.83 odd 4
1680.2.k.f.209.7 8 20.3 even 4
1680.2.k.f.209.8 8 420.167 even 4