Properties

Label 605.2.e.b.483.4
Level $605$
Weight $2$
Character 605.483
Analytic conductor $4.831$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [605,2,Mod(362,605)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(605, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("605.362");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.e (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.83094932229\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 55)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 483.4
Character \(\chi\) \(=\) 605.483
Dual form 605.2.e.b.362.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.03659 - 1.03659i) q^{2} +(0.588647 + 0.588647i) q^{3} +0.149021i q^{4} +(-2.18706 - 0.465567i) q^{5} -1.22037i q^{6} +(2.98069 + 2.98069i) q^{7} +(-1.91870 + 1.91870i) q^{8} -2.30699i q^{9} +O(q^{10})\) \(q+(-1.03659 - 1.03659i) q^{2} +(0.588647 + 0.588647i) q^{3} +0.149021i q^{4} +(-2.18706 - 0.465567i) q^{5} -1.22037i q^{6} +(2.98069 + 2.98069i) q^{7} +(-1.91870 + 1.91870i) q^{8} -2.30699i q^{9} +(1.78448 + 2.74968i) q^{10} +(-0.0877208 + 0.0877208i) q^{12} +(-0.654555 + 0.654555i) q^{13} -6.17948i q^{14} +(-1.01335 - 1.56146i) q^{15} +4.27583 q^{16} +(1.36314 + 1.36314i) q^{17} +(-2.39139 + 2.39139i) q^{18} +5.43176 q^{19} +(0.0693793 - 0.325918i) q^{20} +3.50915i q^{21} +(1.95998 + 1.95998i) q^{23} -2.25887 q^{24} +(4.56649 + 2.03645i) q^{25} +1.35700 q^{26} +(3.12394 - 3.12394i) q^{27} +(-0.444185 + 0.444185i) q^{28} -1.00183 q^{29} +(-0.568163 + 2.66902i) q^{30} +0.423945 q^{31} +(-0.594873 - 0.594873i) q^{32} -2.82602i q^{34} +(-5.13124 - 7.90666i) q^{35} +0.343790 q^{36} +(3.48815 - 3.48815i) q^{37} +(-5.63049 - 5.63049i) q^{38} -0.770604 q^{39} +(5.08960 - 3.30303i) q^{40} +0.577469i q^{41} +(3.63753 - 3.63753i) q^{42} +(5.05373 - 5.05373i) q^{43} +(-1.07406 + 5.04553i) q^{45} -4.06339i q^{46} +(0.841173 - 0.841173i) q^{47} +(2.51696 + 2.51696i) q^{48} +10.7690i q^{49} +(-2.62261 - 6.84452i) q^{50} +1.60481i q^{51} +(-0.0975424 - 0.0975424i) q^{52} +(6.42164 + 6.42164i) q^{53} -6.47647 q^{54} -11.4381 q^{56} +(3.19739 + 3.19739i) q^{57} +(1.03848 + 1.03848i) q^{58} -9.30975i q^{59} +(0.232691 - 0.151011i) q^{60} +7.78179i q^{61} +(-0.439456 - 0.439456i) q^{62} +(6.87641 - 6.87641i) q^{63} -7.31840i q^{64} +(1.73629 - 1.12681i) q^{65} +(-3.05526 + 3.05526i) q^{67} +(-0.203136 + 0.203136i) q^{68} +2.30748i q^{69} +(-2.87696 + 13.5149i) q^{70} +8.59135 q^{71} +(4.42642 + 4.42642i) q^{72} +(3.86109 - 3.86109i) q^{73} -7.23154 q^{74} +(1.48930 + 3.88681i) q^{75} +0.809447i q^{76} +(0.798797 + 0.798797i) q^{78} -2.28422 q^{79} +(-9.35152 - 1.99069i) q^{80} -3.24316 q^{81} +(0.598596 - 0.598596i) q^{82} +(-1.40622 + 1.40622i) q^{83} -0.522937 q^{84} +(-2.34664 - 3.61590i) q^{85} -10.4773 q^{86} +(-0.589724 - 0.589724i) q^{87} -13.9313i q^{89} +(6.34348 - 4.11677i) q^{90} -3.90204 q^{91} +(-0.292079 + 0.292079i) q^{92} +(0.249554 + 0.249554i) q^{93} -1.74390 q^{94} +(-11.8796 - 2.52885i) q^{95} -0.700340i q^{96} +(-2.35066 + 2.35066i) q^{97} +(11.1630 - 11.1630i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 4 q^{3} + 8 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 4 q^{3} + 8 q^{5} + 12 q^{12} - 36 q^{15} - 8 q^{16} - 64 q^{20} - 24 q^{23} + 16 q^{25} - 16 q^{27} - 8 q^{31} + 24 q^{36} + 32 q^{37} - 40 q^{38} + 60 q^{42} - 28 q^{45} - 28 q^{47} + 56 q^{48} + 116 q^{53} - 80 q^{56} - 80 q^{58} + 104 q^{60} - 8 q^{67} - 80 q^{70} + 24 q^{71} - 76 q^{75} + 60 q^{78} + 8 q^{80} + 8 q^{81} - 20 q^{82} - 40 q^{86} + 80 q^{91} + 52 q^{92} + 32 q^{93} + 92 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.03659 1.03659i −0.732977 0.732977i 0.238231 0.971208i \(-0.423432\pi\)
−0.971208 + 0.238231i \(0.923432\pi\)
\(3\) 0.588647 + 0.588647i 0.339856 + 0.339856i 0.856313 0.516457i \(-0.172750\pi\)
−0.516457 + 0.856313i \(0.672750\pi\)
\(4\) 0.149021i 0.0745105i
\(5\) −2.18706 0.465567i −0.978085 0.208208i
\(6\) 1.22037i 0.498213i
\(7\) 2.98069 + 2.98069i 1.12659 + 1.12659i 0.990727 + 0.135866i \(0.0433818\pi\)
0.135866 + 0.990727i \(0.456618\pi\)
\(8\) −1.91870 + 1.91870i −0.678362 + 0.678362i
\(9\) 2.30699i 0.768996i
\(10\) 1.78448 + 2.74968i 0.564302 + 0.869525i
\(11\) 0 0
\(12\) −0.0877208 + 0.0877208i −0.0253228 + 0.0253228i
\(13\) −0.654555 + 0.654555i −0.181541 + 0.181541i −0.792027 0.610486i \(-0.790974\pi\)
0.610486 + 0.792027i \(0.290974\pi\)
\(14\) 6.17948i 1.65153i
\(15\) −1.01335 1.56146i −0.261647 0.403168i
\(16\) 4.27583 1.06896
\(17\) 1.36314 + 1.36314i 0.330609 + 0.330609i 0.852818 0.522209i \(-0.174892\pi\)
−0.522209 + 0.852818i \(0.674892\pi\)
\(18\) −2.39139 + 2.39139i −0.563657 + 0.563657i
\(19\) 5.43176 1.24613 0.623066 0.782170i \(-0.285887\pi\)
0.623066 + 0.782170i \(0.285887\pi\)
\(20\) 0.0693793 0.325918i 0.0155137 0.0728776i
\(21\) 3.50915i 0.765758i
\(22\) 0 0
\(23\) 1.95998 + 1.95998i 0.408685 + 0.408685i 0.881280 0.472595i \(-0.156683\pi\)
−0.472595 + 0.881280i \(0.656683\pi\)
\(24\) −2.25887 −0.461091
\(25\) 4.56649 + 2.03645i 0.913299 + 0.407290i
\(26\) 1.35700 0.266130
\(27\) 3.12394 3.12394i 0.601203 0.601203i
\(28\) −0.444185 + 0.444185i −0.0839431 + 0.0839431i
\(29\) −1.00183 −0.186035 −0.0930175 0.995664i \(-0.529651\pi\)
−0.0930175 + 0.995664i \(0.529651\pi\)
\(30\) −0.568163 + 2.66902i −0.103732 + 0.487294i
\(31\) 0.423945 0.0761428 0.0380714 0.999275i \(-0.487879\pi\)
0.0380714 + 0.999275i \(0.487879\pi\)
\(32\) −0.594873 0.594873i −0.105160 0.105160i
\(33\) 0 0
\(34\) 2.82602i 0.484658i
\(35\) −5.13124 7.90666i −0.867338 1.33647i
\(36\) 0.343790 0.0572983
\(37\) 3.48815 3.48815i 0.573449 0.573449i −0.359642 0.933091i \(-0.617101\pi\)
0.933091 + 0.359642i \(0.117101\pi\)
\(38\) −5.63049 5.63049i −0.913386 0.913386i
\(39\) −0.770604 −0.123395
\(40\) 5.08960 3.30303i 0.804736 0.522255i
\(41\) 0.577469i 0.0901854i 0.998983 + 0.0450927i \(0.0143583\pi\)
−0.998983 + 0.0450927i \(0.985642\pi\)
\(42\) 3.63753 3.63753i 0.561283 0.561283i
\(43\) 5.05373 5.05373i 0.770687 0.770687i −0.207540 0.978227i \(-0.566546\pi\)
0.978227 + 0.207540i \(0.0665456\pi\)
\(44\) 0 0
\(45\) −1.07406 + 5.04553i −0.160111 + 0.752143i
\(46\) 4.06339i 0.599113i
\(47\) 0.841173 0.841173i 0.122698 0.122698i −0.643092 0.765789i \(-0.722349\pi\)
0.765789 + 0.643092i \(0.222349\pi\)
\(48\) 2.51696 + 2.51696i 0.363292 + 0.363292i
\(49\) 10.7690i 1.53843i
\(50\) −2.62261 6.84452i −0.370893 0.967961i
\(51\) 1.60481i 0.224719i
\(52\) −0.0975424 0.0975424i −0.0135267 0.0135267i
\(53\) 6.42164 + 6.42164i 0.882080 + 0.882080i 0.993746 0.111666i \(-0.0356188\pi\)
−0.111666 + 0.993746i \(0.535619\pi\)
\(54\) −6.47647 −0.881337
\(55\) 0 0
\(56\) −11.4381 −1.52848
\(57\) 3.19739 + 3.19739i 0.423505 + 0.423505i
\(58\) 1.03848 + 1.03848i 0.136359 + 0.136359i
\(59\) 9.30975i 1.21203i −0.795455 0.606013i \(-0.792768\pi\)
0.795455 0.606013i \(-0.207232\pi\)
\(60\) 0.232691 0.151011i 0.0300403 0.0194954i
\(61\) 7.78179i 0.996357i 0.867075 + 0.498178i \(0.165998\pi\)
−0.867075 + 0.498178i \(0.834002\pi\)
\(62\) −0.439456 0.439456i −0.0558109 0.0558109i
\(63\) 6.87641 6.87641i 0.866346 0.866346i
\(64\) 7.31840i 0.914800i
\(65\) 1.73629 1.12681i 0.215361 0.139764i
\(66\) 0 0
\(67\) −3.05526 + 3.05526i −0.373259 + 0.373259i −0.868663 0.495404i \(-0.835020\pi\)
0.495404 + 0.868663i \(0.335020\pi\)
\(68\) −0.203136 + 0.203136i −0.0246339 + 0.0246339i
\(69\) 2.30748i 0.277788i
\(70\) −2.87696 + 13.5149i −0.343863 + 1.61534i
\(71\) 8.59135 1.01961 0.509803 0.860291i \(-0.329718\pi\)
0.509803 + 0.860291i \(0.329718\pi\)
\(72\) 4.42642 + 4.42642i 0.521658 + 0.521658i
\(73\) 3.86109 3.86109i 0.451906 0.451906i −0.444081 0.895987i \(-0.646470\pi\)
0.895987 + 0.444081i \(0.146470\pi\)
\(74\) −7.23154 −0.840650
\(75\) 1.48930 + 3.88681i 0.171970 + 0.448810i
\(76\) 0.809447i 0.0928499i
\(77\) 0 0
\(78\) 0.798797 + 0.798797i 0.0904460 + 0.0904460i
\(79\) −2.28422 −0.256994 −0.128497 0.991710i \(-0.541015\pi\)
−0.128497 + 0.991710i \(0.541015\pi\)
\(80\) −9.35152 1.99069i −1.04553 0.222566i
\(81\) −3.24316 −0.360351
\(82\) 0.598596 0.598596i 0.0661039 0.0661039i
\(83\) −1.40622 + 1.40622i −0.154352 + 0.154352i −0.780059 0.625706i \(-0.784811\pi\)
0.625706 + 0.780059i \(0.284811\pi\)
\(84\) −0.522937 −0.0570571
\(85\) −2.34664 3.61590i −0.254528 0.392199i
\(86\) −10.4773 −1.12979
\(87\) −0.589724 0.589724i −0.0632250 0.0632250i
\(88\) 0 0
\(89\) 13.9313i 1.47671i −0.674410 0.738357i \(-0.735602\pi\)
0.674410 0.738357i \(-0.264398\pi\)
\(90\) 6.34348 4.11677i 0.668662 0.433946i
\(91\) −3.90204 −0.409045
\(92\) −0.292079 + 0.292079i −0.0304513 + 0.0304513i
\(93\) 0.249554 + 0.249554i 0.0258776 + 0.0258776i
\(94\) −1.74390 −0.179869
\(95\) −11.8796 2.52885i −1.21882 0.259454i
\(96\) 0.700340i 0.0714782i
\(97\) −2.35066 + 2.35066i −0.238673 + 0.238673i −0.816301 0.577627i \(-0.803979\pi\)
0.577627 + 0.816301i \(0.303979\pi\)
\(98\) 11.1630 11.1630i 1.12763 1.12763i
\(99\) 0 0
\(100\) −0.303474 + 0.680504i −0.0303474 + 0.0680504i
\(101\) 13.2909i 1.32249i 0.750168 + 0.661247i \(0.229973\pi\)
−0.750168 + 0.661247i \(0.770027\pi\)
\(102\) 1.66353 1.66353i 0.164714 0.164714i
\(103\) 7.12932 + 7.12932i 0.702472 + 0.702472i 0.964941 0.262468i \(-0.0845365\pi\)
−0.262468 + 0.964941i \(0.584536\pi\)
\(104\) 2.51179i 0.246301i
\(105\) 1.63374 7.67473i 0.159437 0.748977i
\(106\) 13.3132i 1.29309i
\(107\) −4.36050 4.36050i −0.421546 0.421546i 0.464190 0.885736i \(-0.346346\pi\)
−0.885736 + 0.464190i \(0.846346\pi\)
\(108\) 0.465533 + 0.465533i 0.0447960 + 0.0447960i
\(109\) −19.9193 −1.90793 −0.953964 0.299922i \(-0.903039\pi\)
−0.953964 + 0.299922i \(0.903039\pi\)
\(110\) 0 0
\(111\) 4.10659 0.389780
\(112\) 12.7449 + 12.7449i 1.20428 + 1.20428i
\(113\) 8.57166 + 8.57166i 0.806354 + 0.806354i 0.984080 0.177726i \(-0.0568741\pi\)
−0.177726 + 0.984080i \(0.556874\pi\)
\(114\) 6.62874i 0.620839i
\(115\) −3.37411 5.19912i −0.314637 0.484820i
\(116\) 0.149294i 0.0138616i
\(117\) 1.51005 + 1.51005i 0.139604 + 0.139604i
\(118\) −9.65036 + 9.65036i −0.888388 + 0.888388i
\(119\) 8.12617i 0.744925i
\(120\) 4.94030 + 1.05166i 0.450986 + 0.0960028i
\(121\) 0 0
\(122\) 8.06650 8.06650i 0.730306 0.730306i
\(123\) −0.339925 + 0.339925i −0.0306500 + 0.0306500i
\(124\) 0.0631767i 0.00567344i
\(125\) −9.03911 6.57985i −0.808483 0.588520i
\(126\) −14.2560 −1.27002
\(127\) −0.819912 0.819912i −0.0727554 0.0727554i 0.669793 0.742548i \(-0.266383\pi\)
−0.742548 + 0.669793i \(0.766383\pi\)
\(128\) −8.77589 + 8.77589i −0.775687 + 0.775687i
\(129\) 5.94973 0.523845
\(130\) −2.96786 0.631777i −0.260298 0.0554105i
\(131\) 14.4532i 1.26278i 0.775465 + 0.631390i \(0.217515\pi\)
−0.775465 + 0.631390i \(0.782485\pi\)
\(132\) 0 0
\(133\) 16.1904 + 16.1904i 1.40388 + 1.40388i
\(134\) 6.33408 0.547181
\(135\) −8.28667 + 5.37786i −0.713203 + 0.462852i
\(136\) −5.23090 −0.448546
\(137\) −8.74810 + 8.74810i −0.747401 + 0.747401i −0.973990 0.226590i \(-0.927242\pi\)
0.226590 + 0.973990i \(0.427242\pi\)
\(138\) 2.39190 2.39190i 0.203612 0.203612i
\(139\) 1.00938 0.0856145 0.0428073 0.999083i \(-0.486370\pi\)
0.0428073 + 0.999083i \(0.486370\pi\)
\(140\) 1.17826 0.764663i 0.0995810 0.0646258i
\(141\) 0.990308 0.0833990
\(142\) −8.90567 8.90567i −0.747347 0.747347i
\(143\) 0 0
\(144\) 9.86430i 0.822025i
\(145\) 2.19106 + 0.466419i 0.181958 + 0.0387340i
\(146\) −8.00470 −0.662474
\(147\) −6.33913 + 6.33913i −0.522843 + 0.522843i
\(148\) 0.519808 + 0.519808i 0.0427280 + 0.0427280i
\(149\) 1.22057 0.0999930 0.0499965 0.998749i \(-0.484079\pi\)
0.0499965 + 0.998749i \(0.484079\pi\)
\(150\) 2.48522 5.57280i 0.202917 0.455017i
\(151\) 1.58675i 0.129128i 0.997914 + 0.0645639i \(0.0205656\pi\)
−0.997914 + 0.0645639i \(0.979434\pi\)
\(152\) −10.4219 + 10.4219i −0.845329 + 0.845329i
\(153\) 3.14474 3.14474i 0.254237 0.254237i
\(154\) 0 0
\(155\) −0.927195 0.197375i −0.0744741 0.0158535i
\(156\) 0.114836i 0.00919425i
\(157\) −5.24615 + 5.24615i −0.418688 + 0.418688i −0.884751 0.466063i \(-0.845672\pi\)
0.466063 + 0.884751i \(0.345672\pi\)
\(158\) 2.36779 + 2.36779i 0.188371 + 0.188371i
\(159\) 7.56016i 0.599560i
\(160\) 1.02407 + 1.57798i 0.0809599 + 0.124750i
\(161\) 11.6842i 0.920844i
\(162\) 3.36182 + 3.36182i 0.264129 + 0.264129i
\(163\) −10.8957 10.8957i −0.853416 0.853416i 0.137136 0.990552i \(-0.456210\pi\)
−0.990552 + 0.137136i \(0.956210\pi\)
\(164\) −0.0860550 −0.00671976
\(165\) 0 0
\(166\) 2.91533 0.226273
\(167\) 2.93461 + 2.93461i 0.227087 + 0.227087i 0.811475 0.584388i \(-0.198665\pi\)
−0.584388 + 0.811475i \(0.698665\pi\)
\(168\) −6.73299 6.73299i −0.519462 0.519462i
\(169\) 12.1431i 0.934086i
\(170\) −1.31570 + 6.18068i −0.100910 + 0.474037i
\(171\) 12.5310i 0.958270i
\(172\) 0.753112 + 0.753112i 0.0574243 + 0.0574243i
\(173\) 3.06159 3.06159i 0.232768 0.232768i −0.581079 0.813847i \(-0.697369\pi\)
0.813847 + 0.581079i \(0.197369\pi\)
\(174\) 1.22260i 0.0926850i
\(175\) 7.54127 + 19.6813i 0.570066 + 1.48777i
\(176\) 0 0
\(177\) 5.48016 5.48016i 0.411914 0.411914i
\(178\) −14.4410 + 14.4410i −1.08240 + 1.08240i
\(179\) 3.71960i 0.278016i −0.990291 0.139008i \(-0.955609\pi\)
0.990291 0.139008i \(-0.0443913\pi\)
\(180\) −0.751890 0.160057i −0.0560426 0.0119300i
\(181\) 6.04656 0.449437 0.224719 0.974424i \(-0.427854\pi\)
0.224719 + 0.974424i \(0.427854\pi\)
\(182\) 4.04481 + 4.04481i 0.299821 + 0.299821i
\(183\) −4.58073 + 4.58073i −0.338617 + 0.338617i
\(184\) −7.52124 −0.554473
\(185\) −9.25279 + 6.00485i −0.680278 + 0.441485i
\(186\) 0.517369i 0.0379353i
\(187\) 0 0
\(188\) 0.125352 + 0.125352i 0.00914227 + 0.00914227i
\(189\) 18.6230 1.35462
\(190\) 9.69286 + 14.9356i 0.703194 + 1.08354i
\(191\) −16.5546 −1.19785 −0.598926 0.800805i \(-0.704405\pi\)
−0.598926 + 0.800805i \(0.704405\pi\)
\(192\) 4.30795 4.30795i 0.310900 0.310900i
\(193\) −11.9954 + 11.9954i −0.863451 + 0.863451i −0.991737 0.128286i \(-0.959052\pi\)
0.128286 + 0.991737i \(0.459052\pi\)
\(194\) 4.87332 0.349884
\(195\) 1.68536 + 0.358768i 0.120691 + 0.0256919i
\(196\) −1.60480 −0.114629
\(197\) −9.63624 9.63624i −0.686554 0.686554i 0.274915 0.961469i \(-0.411350\pi\)
−0.961469 + 0.274915i \(0.911350\pi\)
\(198\) 0 0
\(199\) 19.4166i 1.37640i 0.725519 + 0.688202i \(0.241600\pi\)
−0.725519 + 0.688202i \(0.758400\pi\)
\(200\) −12.6691 + 4.85439i −0.895838 + 0.343257i
\(201\) −3.59694 −0.253709
\(202\) 13.7772 13.7772i 0.969358 0.969358i
\(203\) −2.98614 2.98614i −0.209586 0.209586i
\(204\) −0.239151 −0.0167439
\(205\) 0.268850 1.26296i 0.0187773 0.0882090i
\(206\) 14.7803i 1.02979i
\(207\) 4.52166 4.52166i 0.314277 0.314277i
\(208\) −2.79877 + 2.79877i −0.194060 + 0.194060i
\(209\) 0 0
\(210\) −9.64903 + 6.26200i −0.665846 + 0.432119i
\(211\) 6.39095i 0.439971i −0.975503 0.219986i \(-0.929399\pi\)
0.975503 0.219986i \(-0.0706010\pi\)
\(212\) −0.956959 + 0.956959i −0.0657242 + 0.0657242i
\(213\) 5.05727 + 5.05727i 0.346519 + 0.346519i
\(214\) 9.04007i 0.617967i
\(215\) −13.4057 + 8.69998i −0.914260 + 0.593334i
\(216\) 11.9878i 0.815668i
\(217\) 1.26365 + 1.26365i 0.0857820 + 0.0857820i
\(218\) 20.6481 + 20.6481i 1.39847 + 1.39847i
\(219\) 4.54564 0.307166
\(220\) 0 0
\(221\) −1.78450 −0.120038
\(222\) −4.25683 4.25683i −0.285700 0.285700i
\(223\) 10.0373 + 10.0373i 0.672150 + 0.672150i 0.958211 0.286062i \(-0.0923462\pi\)
−0.286062 + 0.958211i \(0.592346\pi\)
\(224\) 3.54626i 0.236944i
\(225\) 4.69807 10.5349i 0.313204 0.702323i
\(226\) 17.7705i 1.18208i
\(227\) −5.85353 5.85353i −0.388512 0.388512i 0.485644 0.874156i \(-0.338585\pi\)
−0.874156 + 0.485644i \(0.838585\pi\)
\(228\) −0.476479 + 0.476479i −0.0315556 + 0.0315556i
\(229\) 19.5994i 1.29517i −0.761995 0.647583i \(-0.775780\pi\)
0.761995 0.647583i \(-0.224220\pi\)
\(230\) −1.89178 + 8.88688i −0.124740 + 0.585984i
\(231\) 0 0
\(232\) 1.92221 1.92221i 0.126199 0.126199i
\(233\) 2.62559 2.62559i 0.172008 0.172008i −0.615853 0.787861i \(-0.711188\pi\)
0.787861 + 0.615853i \(0.211188\pi\)
\(234\) 3.13059i 0.204653i
\(235\) −2.23132 + 1.44808i −0.145555 + 0.0944621i
\(236\) 1.38735 0.0903087
\(237\) −1.34460 1.34460i −0.0873410 0.0873410i
\(238\) 8.42347 8.42347i 0.546013 0.546013i
\(239\) 3.21291 0.207826 0.103913 0.994586i \(-0.466864\pi\)
0.103913 + 0.994586i \(0.466864\pi\)
\(240\) −4.33294 6.67656i −0.279690 0.430970i
\(241\) 25.4119i 1.63693i −0.574559 0.818463i \(-0.694826\pi\)
0.574559 0.818463i \(-0.305174\pi\)
\(242\) 0 0
\(243\) −11.2809 11.2809i −0.723671 0.723671i
\(244\) −1.15965 −0.0742390
\(245\) 5.01368 23.5524i 0.320313 1.50471i
\(246\) 0.704724 0.0449315
\(247\) −3.55538 + 3.55538i −0.226224 + 0.226224i
\(248\) −0.813423 + 0.813423i −0.0516524 + 0.0516524i
\(249\) −1.65553 −0.104915
\(250\) 2.54923 + 16.1904i 0.161227 + 1.02397i
\(251\) 16.3055 1.02919 0.514596 0.857433i \(-0.327942\pi\)
0.514596 + 0.857433i \(0.327942\pi\)
\(252\) 1.02473 + 1.02473i 0.0645519 + 0.0645519i
\(253\) 0 0
\(254\) 1.69982i 0.106656i
\(255\) 0.747149 3.50983i 0.0467883 0.219794i
\(256\) 3.55714 0.222321
\(257\) 11.4580 11.4580i 0.714729 0.714729i −0.252792 0.967521i \(-0.581349\pi\)
0.967521 + 0.252792i \(0.0813487\pi\)
\(258\) −6.16741 6.16741i −0.383966 0.383966i
\(259\) 20.7942 1.29209
\(260\) 0.167919 + 0.258744i 0.0104139 + 0.0160466i
\(261\) 2.31121i 0.143060i
\(262\) 14.9820 14.9820i 0.925589 0.925589i
\(263\) −0.677874 + 0.677874i −0.0417995 + 0.0417995i −0.727698 0.685898i \(-0.759410\pi\)
0.685898 + 0.727698i \(0.259410\pi\)
\(264\) 0 0
\(265\) −11.0548 17.0342i −0.679092 1.04640i
\(266\) 33.5654i 2.05803i
\(267\) 8.20062 8.20062i 0.501870 0.501870i
\(268\) −0.455298 0.455298i −0.0278117 0.0278117i
\(269\) 28.4238i 1.73303i −0.499149 0.866516i \(-0.666354\pi\)
0.499149 0.866516i \(-0.333646\pi\)
\(270\) 14.1645 + 3.01523i 0.862022 + 0.183501i
\(271\) 30.7500i 1.86793i −0.357369 0.933963i \(-0.616326\pi\)
0.357369 0.933963i \(-0.383674\pi\)
\(272\) 5.82855 + 5.82855i 0.353408 + 0.353408i
\(273\) −2.29693 2.29693i −0.139016 0.139016i
\(274\) 18.1363 1.09565
\(275\) 0 0
\(276\) −0.343863 −0.0206981
\(277\) −21.3182 21.3182i −1.28089 1.28089i −0.940165 0.340720i \(-0.889329\pi\)
−0.340720 0.940165i \(-0.610671\pi\)
\(278\) −1.04631 1.04631i −0.0627535 0.0627535i
\(279\) 0.978036i 0.0585535i
\(280\) 25.0158 + 5.32519i 1.49498 + 0.318241i
\(281\) 8.51905i 0.508204i 0.967177 + 0.254102i \(0.0817799\pi\)
−0.967177 + 0.254102i \(0.918220\pi\)
\(282\) −1.02654 1.02654i −0.0611295 0.0611295i
\(283\) −6.74707 + 6.74707i −0.401071 + 0.401071i −0.878611 0.477539i \(-0.841529\pi\)
0.477539 + 0.878611i \(0.341529\pi\)
\(284\) 1.28029i 0.0759713i
\(285\) −5.50430 8.48150i −0.326046 0.502401i
\(286\) 0 0
\(287\) −1.72125 + 1.72125i −0.101602 + 0.101602i
\(288\) −1.37236 + 1.37236i −0.0808674 + 0.0808674i
\(289\) 13.2837i 0.781395i
\(290\) −1.78774 2.75471i −0.104980 0.161762i
\(291\) −2.76742 −0.162229
\(292\) 0.575383 + 0.575383i 0.0336718 + 0.0336718i
\(293\) 1.63161 1.63161i 0.0953199 0.0953199i −0.657839 0.753159i \(-0.728529\pi\)
0.753159 + 0.657839i \(0.228529\pi\)
\(294\) 13.1421 0.766464
\(295\) −4.33431 + 20.3610i −0.252354 + 1.18546i
\(296\) 13.3854i 0.778013i
\(297\) 0 0
\(298\) −1.26523 1.26523i −0.0732926 0.0732926i
\(299\) −2.56583 −0.148386
\(300\) −0.579216 + 0.221938i −0.0334410 + 0.0128136i
\(301\) 30.1272 1.73650
\(302\) 1.64480 1.64480i 0.0946478 0.0946478i
\(303\) −7.82366 + 7.82366i −0.449457 + 0.449457i
\(304\) 23.2253 1.33206
\(305\) 3.62295 17.0193i 0.207449 0.974521i
\(306\) −6.51959 −0.372700
\(307\) 12.4635 + 12.4635i 0.711327 + 0.711327i 0.966813 0.255486i \(-0.0822353\pi\)
−0.255486 + 0.966813i \(0.582235\pi\)
\(308\) 0 0
\(309\) 8.39331i 0.477479i
\(310\) 0.756521 + 1.16571i 0.0429675 + 0.0662081i
\(311\) 15.1136 0.857011 0.428506 0.903539i \(-0.359040\pi\)
0.428506 + 0.903539i \(0.359040\pi\)
\(312\) 1.47856 1.47856i 0.0837068 0.0837068i
\(313\) 18.4669 + 18.4669i 1.04381 + 1.04381i 0.998995 + 0.0448178i \(0.0142707\pi\)
0.0448178 + 0.998995i \(0.485729\pi\)
\(314\) 10.8762 0.613777
\(315\) −18.2406 + 11.8377i −1.02774 + 0.666980i
\(316\) 0.340396i 0.0191488i
\(317\) 20.0304 20.0304i 1.12502 1.12502i 0.134045 0.990975i \(-0.457203\pi\)
0.990975 0.134045i \(-0.0427965\pi\)
\(318\) 7.83675 7.83675i 0.439463 0.439463i
\(319\) 0 0
\(320\) −3.40720 + 16.0058i −0.190469 + 0.894751i
\(321\) 5.13360i 0.286529i
\(322\) 12.1117 12.1117i 0.674957 0.674957i
\(323\) 7.40423 + 7.40423i 0.411983 + 0.411983i
\(324\) 0.483299i 0.0268500i
\(325\) −4.32199 + 1.65605i −0.239741 + 0.0918613i
\(326\) 22.5886i 1.25107i
\(327\) −11.7255 11.7255i −0.648420 0.648420i
\(328\) −1.10799 1.10799i −0.0611784 0.0611784i
\(329\) 5.01454 0.276461
\(330\) 0 0
\(331\) −24.6455 −1.35464 −0.677319 0.735690i \(-0.736858\pi\)
−0.677319 + 0.735690i \(0.736858\pi\)
\(332\) −0.209556 0.209556i −0.0115009 0.0115009i
\(333\) −8.04713 8.04713i −0.440980 0.440980i
\(334\) 6.08395i 0.332899i
\(335\) 8.10448 5.25962i 0.442795 0.287364i
\(336\) 15.0045i 0.818564i
\(337\) 21.9315 + 21.9315i 1.19469 + 1.19469i 0.975736 + 0.218949i \(0.0702628\pi\)
0.218949 + 0.975736i \(0.429737\pi\)
\(338\) 12.5874 12.5874i 0.684663 0.684663i
\(339\) 10.0914i 0.548088i
\(340\) 0.538845 0.349698i 0.0292230 0.0189650i
\(341\) 0 0
\(342\) −12.9895 + 12.9895i −0.702390 + 0.702390i
\(343\) −11.2342 + 11.2342i −0.606587 + 0.606587i
\(344\) 19.3932i 1.04561i
\(345\) 1.07429 5.04660i 0.0578376 0.271700i
\(346\) −6.34720 −0.341227
\(347\) −21.3446 21.3446i −1.14584 1.14584i −0.987363 0.158473i \(-0.949343\pi\)
−0.158473 0.987363i \(-0.550657\pi\)
\(348\) 0.0878813 0.0878813i 0.00471093 0.00471093i
\(349\) −21.3672 −1.14376 −0.571881 0.820336i \(-0.693786\pi\)
−0.571881 + 0.820336i \(0.693786\pi\)
\(350\) 12.5842 28.2185i 0.672653 1.50834i
\(351\) 4.08959i 0.218286i
\(352\) 0 0
\(353\) −2.82626 2.82626i −0.150427 0.150427i 0.627882 0.778309i \(-0.283922\pi\)
−0.778309 + 0.627882i \(0.783922\pi\)
\(354\) −11.3613 −0.603847
\(355\) −18.7898 3.99985i −0.997260 0.212290i
\(356\) 2.07606 0.110031
\(357\) −4.78345 + 4.78345i −0.253167 + 0.253167i
\(358\) −3.85568 + 3.85568i −0.203779 + 0.203779i
\(359\) 10.7403 0.566851 0.283425 0.958994i \(-0.408529\pi\)
0.283425 + 0.958994i \(0.408529\pi\)
\(360\) −7.62006 11.7416i −0.401612 0.618839i
\(361\) 10.5040 0.552843
\(362\) −6.26778 6.26778i −0.329427 0.329427i
\(363\) 0 0
\(364\) 0.581487i 0.0304782i
\(365\) −10.2420 + 6.64685i −0.536093 + 0.347912i
\(366\) 9.49665 0.496398
\(367\) −24.4690 + 24.4690i −1.27727 + 1.27727i −0.335079 + 0.942190i \(0.608763\pi\)
−0.942190 + 0.335079i \(0.891237\pi\)
\(368\) 8.38057 + 8.38057i 0.436867 + 0.436867i
\(369\) 1.33221 0.0693523
\(370\) 15.8158 + 3.36677i 0.822227 + 0.175030i
\(371\) 38.2818i 1.98749i
\(372\) −0.0371888 + 0.0371888i −0.00192815 + 0.00192815i
\(373\) −9.90454 + 9.90454i −0.512838 + 0.512838i −0.915395 0.402557i \(-0.868121\pi\)
0.402557 + 0.915395i \(0.368121\pi\)
\(374\) 0 0
\(375\) −1.44763 9.19406i −0.0747555 0.474779i
\(376\) 3.22791i 0.166467i
\(377\) 0.655752 0.655752i 0.0337729 0.0337729i
\(378\) −19.3043 19.3043i −0.992908 0.992908i
\(379\) 26.5008i 1.36125i −0.732630 0.680627i \(-0.761708\pi\)
0.732630 0.680627i \(-0.238292\pi\)
\(380\) 0.376852 1.77031i 0.0193321 0.0908150i
\(381\) 0.965278i 0.0494527i
\(382\) 17.1603 + 17.1603i 0.877997 + 0.877997i
\(383\) −16.9972 16.9972i −0.868516 0.868516i 0.123792 0.992308i \(-0.460495\pi\)
−0.992308 + 0.123792i \(0.960495\pi\)
\(384\) −10.3318 −0.527243
\(385\) 0 0
\(386\) 24.8686 1.26578
\(387\) −11.6589 11.6589i −0.592655 0.592655i
\(388\) −0.350298 0.350298i −0.0177837 0.0177837i
\(389\) 7.54543i 0.382569i −0.981535 0.191284i \(-0.938735\pi\)
0.981535 0.191284i \(-0.0612652\pi\)
\(390\) −1.37513 2.11891i −0.0696322 0.107295i
\(391\) 5.34346i 0.270230i
\(392\) −20.6624 20.6624i −1.04361 1.04361i
\(393\) −8.50783 + 8.50783i −0.429163 + 0.429163i
\(394\) 19.9776i 1.00646i
\(395\) 4.99573 + 1.06346i 0.251362 + 0.0535083i
\(396\) 0 0
\(397\) 16.0995 16.0995i 0.808008 0.808008i −0.176324 0.984332i \(-0.556421\pi\)
0.984332 + 0.176324i \(0.0564206\pi\)
\(398\) 20.1269 20.1269i 1.00887 1.00887i
\(399\) 19.0608i 0.954236i
\(400\) 19.5256 + 8.70752i 0.976279 + 0.435376i
\(401\) −24.1420 −1.20560 −0.602798 0.797894i \(-0.705947\pi\)
−0.602798 + 0.797894i \(0.705947\pi\)
\(402\) 3.72854 + 3.72854i 0.185963 + 0.185963i
\(403\) −0.277495 + 0.277495i −0.0138230 + 0.0138230i
\(404\) −1.98062 −0.0985397
\(405\) 7.09300 + 1.50991i 0.352454 + 0.0750280i
\(406\) 6.19078i 0.307243i
\(407\) 0 0
\(408\) −3.07915 3.07915i −0.152441 0.152441i
\(409\) 5.85586 0.289553 0.144777 0.989464i \(-0.453754\pi\)
0.144777 + 0.989464i \(0.453754\pi\)
\(410\) −1.58785 + 1.03048i −0.0784185 + 0.0508918i
\(411\) −10.2991 −0.508017
\(412\) −1.06242 + 1.06242i −0.0523416 + 0.0523416i
\(413\) 27.7495 27.7495i 1.36546 1.36546i
\(414\) −9.37418 −0.460716
\(415\) 3.73017 2.42079i 0.183107 0.118832i
\(416\) 0.778754 0.0381815
\(417\) 0.594169 + 0.594169i 0.0290966 + 0.0290966i
\(418\) 0 0
\(419\) 11.0599i 0.540311i 0.962817 + 0.270155i \(0.0870751\pi\)
−0.962817 + 0.270155i \(0.912925\pi\)
\(420\) 1.14370 + 0.243462i 0.0558066 + 0.0118797i
\(421\) 7.87306 0.383710 0.191855 0.981423i \(-0.438550\pi\)
0.191855 + 0.981423i \(0.438550\pi\)
\(422\) −6.62477 + 6.62477i −0.322489 + 0.322489i
\(423\) −1.94058 1.94058i −0.0943540 0.0943540i
\(424\) −24.6424 −1.19674
\(425\) 3.44880 + 9.00072i 0.167291 + 0.436599i
\(426\) 10.4846i 0.507980i
\(427\) −23.1951 + 23.1951i −1.12249 + 1.12249i
\(428\) 0.649807 0.649807i 0.0314096 0.0314096i
\(429\) 0 0
\(430\) 22.9144 + 4.87787i 1.10503 + 0.235232i
\(431\) 7.30295i 0.351771i 0.984411 + 0.175885i \(0.0562788\pi\)
−0.984411 + 0.175885i \(0.943721\pi\)
\(432\) 13.3575 13.3575i 0.642662 0.642662i
\(433\) −3.56913 3.56913i −0.171521 0.171521i 0.616126 0.787647i \(-0.288701\pi\)
−0.787647 + 0.616126i \(0.788701\pi\)
\(434\) 2.61976i 0.125752i
\(435\) 1.01521 + 1.56432i 0.0486755 + 0.0750034i
\(436\) 2.96840i 0.142161i
\(437\) 10.6462 + 10.6462i 0.509275 + 0.509275i
\(438\) −4.71194 4.71194i −0.225145 0.225145i
\(439\) 1.29778 0.0619394 0.0309697 0.999520i \(-0.490140\pi\)
0.0309697 + 0.999520i \(0.490140\pi\)
\(440\) 0 0
\(441\) 24.8439 1.18304
\(442\) 1.84978 + 1.84978i 0.0879852 + 0.0879852i
\(443\) −10.8900 10.8900i −0.517401 0.517401i 0.399383 0.916784i \(-0.369224\pi\)
−0.916784 + 0.399383i \(0.869224\pi\)
\(444\) 0.611968i 0.0290427i
\(445\) −6.48595 + 30.4686i −0.307464 + 1.44435i
\(446\) 20.8091i 0.985341i
\(447\) 0.718486 + 0.718486i 0.0339832 + 0.0339832i
\(448\) 21.8138 21.8138i 1.03061 1.03061i
\(449\) 12.1228i 0.572110i −0.958213 0.286055i \(-0.907656\pi\)
0.958213 0.286055i \(-0.0923440\pi\)
\(450\) −15.7902 + 6.05033i −0.744359 + 0.285215i
\(451\) 0 0
\(452\) −1.27736 + 1.27736i −0.0600818 + 0.0600818i
\(453\) −0.934036 + 0.934036i −0.0438848 + 0.0438848i
\(454\) 12.1354i 0.569541i
\(455\) 8.53402 + 1.81666i 0.400081 + 0.0851665i
\(456\) −12.2697 −0.574580
\(457\) 2.48245 + 2.48245i 0.116124 + 0.116124i 0.762781 0.646657i \(-0.223833\pi\)
−0.646657 + 0.762781i \(0.723833\pi\)
\(458\) −20.3165 + 20.3165i −0.949326 + 0.949326i
\(459\) 8.51673 0.397527
\(460\) 0.774778 0.502813i 0.0361242 0.0234438i
\(461\) 5.45336i 0.253988i −0.991903 0.126994i \(-0.959467\pi\)
0.991903 0.126994i \(-0.0405329\pi\)
\(462\) 0 0
\(463\) 15.3996 + 15.3996i 0.715681 + 0.715681i 0.967718 0.252037i \(-0.0811005\pi\)
−0.252037 + 0.967718i \(0.581100\pi\)
\(464\) −4.28365 −0.198864
\(465\) −0.429607 0.661975i −0.0199225 0.0306984i
\(466\) −5.44330 −0.252156
\(467\) −10.3830 + 10.3830i −0.480470 + 0.480470i −0.905282 0.424812i \(-0.860340\pi\)
0.424812 + 0.905282i \(0.360340\pi\)
\(468\) −0.225029 + 0.225029i −0.0104020 + 0.0104020i
\(469\) −18.2135 −0.841023
\(470\) 3.81401 + 0.811900i 0.175927 + 0.0374502i
\(471\) −6.17626 −0.284587
\(472\) 17.8626 + 17.8626i 0.822193 + 0.822193i
\(473\) 0 0
\(474\) 2.78758i 0.128038i
\(475\) 24.8041 + 11.0615i 1.13809 + 0.507537i
\(476\) −1.21097 −0.0555047
\(477\) 14.8146 14.8146i 0.678316 0.678316i
\(478\) −3.33046 3.33046i −0.152332 0.152332i
\(479\) 4.91370 0.224513 0.112256 0.993679i \(-0.464192\pi\)
0.112256 + 0.993679i \(0.464192\pi\)
\(480\) −0.326055 + 1.53169i −0.0148823 + 0.0699117i
\(481\) 4.56638i 0.208209i
\(482\) −26.3416 + 26.3416i −1.19983 + 1.19983i
\(483\) −6.87787 + 6.87787i −0.312954 + 0.312954i
\(484\) 0 0
\(485\) 6.23543 4.04665i 0.283136 0.183749i
\(486\) 23.3873i 1.06087i
\(487\) −7.59259 + 7.59259i −0.344053 + 0.344053i −0.857889 0.513836i \(-0.828224\pi\)
0.513836 + 0.857889i \(0.328224\pi\)
\(488\) −14.9309 14.9309i −0.675891 0.675891i
\(489\) 12.8274i 0.580077i
\(490\) −29.6113 + 19.2170i −1.33770 + 0.868137i
\(491\) 3.25606i 0.146944i −0.997297 0.0734720i \(-0.976592\pi\)
0.997297 0.0734720i \(-0.0234080\pi\)
\(492\) −0.0506560 0.0506560i −0.00228375 0.00228375i
\(493\) −1.36563 1.36563i −0.0615049 0.0615049i
\(494\) 7.37092 0.331634
\(495\) 0 0
\(496\) 1.81272 0.0813935
\(497\) 25.6081 + 25.6081i 1.14868 + 1.14868i
\(498\) 1.71610 + 1.71610i 0.0769002 + 0.0769002i
\(499\) 8.94183i 0.400291i 0.979766 + 0.200146i \(0.0641416\pi\)
−0.979766 + 0.200146i \(0.935858\pi\)
\(500\) 0.980537 1.34702i 0.0438509 0.0602405i
\(501\) 3.45490i 0.154353i
\(502\) −16.9020 16.9020i −0.754374 0.754374i
\(503\) −13.6708 + 13.6708i −0.609550 + 0.609550i −0.942828 0.333278i \(-0.891845\pi\)
0.333278 + 0.942828i \(0.391845\pi\)
\(504\) 26.3875i 1.17539i
\(505\) 6.18781 29.0681i 0.275354 1.29351i
\(506\) 0 0
\(507\) −7.14801 + 7.14801i −0.317454 + 0.317454i
\(508\) 0.122184 0.122184i 0.00542104 0.00542104i
\(509\) 2.82153i 0.125062i −0.998043 0.0625311i \(-0.980083\pi\)
0.998043 0.0625311i \(-0.0199173\pi\)
\(510\) −4.41272 + 2.86376i −0.195399 + 0.126809i
\(511\) 23.0174 1.01823
\(512\) 13.8645 + 13.8645i 0.612730 + 0.612730i
\(513\) 16.9685 16.9685i 0.749178 0.749178i
\(514\) −23.7544 −1.04776
\(515\) −12.2731 18.9114i −0.540817 0.833338i
\(516\) 0.886635i 0.0390319i
\(517\) 0 0
\(518\) −21.5550 21.5550i −0.947071 0.947071i
\(519\) 3.60439 0.158215
\(520\) −1.16941 + 5.49344i −0.0512818 + 0.240903i
\(521\) 9.50337 0.416350 0.208175 0.978092i \(-0.433248\pi\)
0.208175 + 0.978092i \(0.433248\pi\)
\(522\) 2.39577 2.39577i 0.104860 0.104860i
\(523\) 10.4910 10.4910i 0.458739 0.458739i −0.439503 0.898241i \(-0.644845\pi\)
0.898241 + 0.439503i \(0.144845\pi\)
\(524\) −2.15383 −0.0940904
\(525\) −7.14620 + 16.0245i −0.311886 + 0.699366i
\(526\) 1.40535 0.0612761
\(527\) 0.577895 + 0.577895i 0.0251735 + 0.0251735i
\(528\) 0 0
\(529\) 15.3169i 0.665953i
\(530\) −6.19817 + 29.1167i −0.269231 + 1.26475i
\(531\) −21.4775 −0.932044
\(532\) −2.41271 + 2.41271i −0.104604 + 0.104604i
\(533\) −0.377985 0.377985i −0.0163723 0.0163723i
\(534\) −17.0013 −0.735718
\(535\) 7.50659 + 11.5668i 0.324538 + 0.500077i
\(536\) 11.7242i 0.506410i
\(537\) 2.18953 2.18953i 0.0944853 0.0944853i
\(538\) −29.4638 + 29.4638i −1.27027 + 1.27027i
\(539\) 0 0
\(540\) −0.801414 1.23489i −0.0344874 0.0531411i
\(541\) 31.2654i 1.34420i 0.740459 + 0.672101i \(0.234608\pi\)
−0.740459 + 0.672101i \(0.765392\pi\)
\(542\) −31.8750 + 31.8750i −1.36915 + 1.36915i
\(543\) 3.55929 + 3.55929i 0.152744 + 0.152744i
\(544\) 1.62179i 0.0695335i
\(545\) 43.5649 + 9.27379i 1.86611 + 0.397246i
\(546\) 4.76193i 0.203792i
\(547\) −22.3204 22.3204i −0.954353 0.954353i 0.0446500 0.999003i \(-0.485783\pi\)
−0.999003 + 0.0446500i \(0.985783\pi\)
\(548\) −1.30365 1.30365i −0.0556892 0.0556892i
\(549\) 17.9525 0.766194
\(550\) 0 0
\(551\) −5.44169 −0.231824
\(552\) −4.42736 4.42736i −0.188441 0.188441i
\(553\) −6.80853 6.80853i −0.289528 0.289528i
\(554\) 44.1962i 1.87772i
\(555\) −8.98136 1.91189i −0.381238 0.0811553i
\(556\) 0.150419i 0.00637918i
\(557\) 9.37798 + 9.37798i 0.397358 + 0.397358i 0.877300 0.479942i \(-0.159342\pi\)
−0.479942 + 0.877300i \(0.659342\pi\)
\(558\) −1.01382 + 1.01382i −0.0429184 + 0.0429184i
\(559\) 6.61589i 0.279822i
\(560\) −21.9403 33.8076i −0.927149 1.42863i
\(561\) 0 0
\(562\) 8.83073 8.83073i 0.372502 0.372502i
\(563\) 20.7685 20.7685i 0.875286 0.875286i −0.117756 0.993043i \(-0.537570\pi\)
0.993043 + 0.117756i \(0.0375702\pi\)
\(564\) 0.147577i 0.00621410i
\(565\) −14.7561 22.7374i −0.620793 0.956572i
\(566\) 13.9878 0.587952
\(567\) −9.66685 9.66685i −0.405970 0.405970i
\(568\) −16.4842 + 16.4842i −0.691662 + 0.691662i
\(569\) 21.4507 0.899262 0.449631 0.893214i \(-0.351555\pi\)
0.449631 + 0.893214i \(0.351555\pi\)
\(570\) −3.08612 + 14.4975i −0.129264 + 0.607233i
\(571\) 28.7176i 1.20179i −0.799326 0.600897i \(-0.794810\pi\)
0.799326 0.600897i \(-0.205190\pi\)
\(572\) 0 0
\(573\) −9.74484 9.74484i −0.407097 0.407097i
\(574\) 3.56845 0.148944
\(575\) 4.95885 + 12.9417i 0.206798 + 0.539705i
\(576\) −16.8835 −0.703477
\(577\) −4.73218 + 4.73218i −0.197003 + 0.197003i −0.798714 0.601711i \(-0.794486\pi\)
0.601711 + 0.798714i \(0.294486\pi\)
\(578\) −13.7697 + 13.7697i −0.572745 + 0.572745i
\(579\) −14.1222 −0.586898
\(580\) −0.0695062 + 0.326514i −0.00288609 + 0.0135578i
\(581\) −8.38297 −0.347784
\(582\) 2.86867 + 2.86867i 0.118910 + 0.118910i
\(583\) 0 0
\(584\) 14.8165i 0.613112i
\(585\) −2.59955 4.00561i −0.107478 0.165611i
\(586\) −3.38262 −0.139735
\(587\) −25.8079 + 25.8079i −1.06520 + 1.06520i −0.0674846 + 0.997720i \(0.521497\pi\)
−0.997720 + 0.0674846i \(0.978503\pi\)
\(588\) −0.944664 0.944664i −0.0389573 0.0389573i
\(589\) 2.30277 0.0948839
\(590\) 25.5988 16.6131i 1.05389 0.683949i
\(591\) 11.3447i 0.466659i
\(592\) 14.9148 14.9148i 0.612993 0.612993i
\(593\) −26.6656 + 26.6656i −1.09502 + 1.09502i −0.100040 + 0.994983i \(0.531897\pi\)
−0.994983 + 0.100040i \(0.968103\pi\)
\(594\) 0 0
\(595\) 3.78328 17.7724i 0.155099 0.728599i
\(596\) 0.181891i 0.00745053i
\(597\) −11.4295 + 11.4295i −0.467779 + 0.467779i
\(598\) 2.65971 + 2.65971i 0.108764 + 0.108764i
\(599\) 38.6017i 1.57722i 0.614892 + 0.788611i \(0.289199\pi\)
−0.614892 + 0.788611i \(0.710801\pi\)
\(600\) −10.3151 4.60008i −0.421114 0.187798i
\(601\) 38.1177i 1.55485i −0.628974 0.777427i \(-0.716525\pi\)
0.628974 0.777427i \(-0.283475\pi\)
\(602\) −31.2294 31.2294i −1.27282 1.27282i
\(603\) 7.04845 + 7.04845i 0.287035 + 0.287035i
\(604\) −0.236459 −0.00962138
\(605\) 0 0
\(606\) 16.2198 0.658884
\(607\) −25.6202 25.6202i −1.03989 1.03989i −0.999170 0.0407231i \(-0.987034\pi\)
−0.0407231 0.999170i \(-0.512966\pi\)
\(608\) −3.23121 3.23121i −0.131043 0.131043i
\(609\) 3.51556i 0.142458i
\(610\) −21.3974 + 13.8864i −0.866357 + 0.562246i
\(611\) 1.10119i 0.0445493i
\(612\) 0.468633 + 0.468633i 0.0189434 + 0.0189434i
\(613\) −1.70361 + 1.70361i −0.0688081 + 0.0688081i −0.740673 0.671865i \(-0.765493\pi\)
0.671865 + 0.740673i \(0.265493\pi\)
\(614\) 25.8389i 1.04277i
\(615\) 0.901696 0.585180i 0.0363599 0.0235967i
\(616\) 0 0
\(617\) −25.5598 + 25.5598i −1.02900 + 1.02900i −0.0294325 + 0.999567i \(0.509370\pi\)
−0.999567 + 0.0294325i \(0.990630\pi\)
\(618\) 8.70038 8.70038i 0.349981 0.349981i
\(619\) 0.913846i 0.0367306i −0.999831 0.0183653i \(-0.994154\pi\)
0.999831 0.0183653i \(-0.00584618\pi\)
\(620\) 0.0294130 0.138172i 0.00118125 0.00554910i
\(621\) 12.2458 0.491406
\(622\) −15.6665 15.6665i −0.628170 0.628170i
\(623\) 41.5248 41.5248i 1.66366 1.66366i
\(624\) −3.29497 −0.131905
\(625\) 16.7057 + 18.5989i 0.668230 + 0.743955i
\(626\) 38.2851i 1.53018i
\(627\) 0 0
\(628\) −0.781786 0.781786i −0.0311967 0.0311967i
\(629\) 9.50966 0.379175
\(630\) 31.1787 + 6.63712i 1.24219 + 0.264429i
\(631\) 23.1071 0.919881 0.459940 0.887950i \(-0.347871\pi\)
0.459940 + 0.887950i \(0.347871\pi\)
\(632\) 4.38272 4.38272i 0.174335 0.174335i
\(633\) 3.76201 3.76201i 0.149527 0.149527i
\(634\) −41.5265 −1.64923
\(635\) 1.41148 + 2.17492i 0.0560127 + 0.0863092i
\(636\) −1.12662 −0.0446735
\(637\) −7.04889 7.04889i −0.279287 0.279287i
\(638\) 0 0
\(639\) 19.8201i 0.784072i
\(640\) 23.2792 15.1077i 0.920191 0.597183i
\(641\) 8.72877 0.344766 0.172383 0.985030i \(-0.444853\pi\)
0.172383 + 0.985030i \(0.444853\pi\)
\(642\) −5.32141 + 5.32141i −0.210019 + 0.210019i
\(643\) −22.3017 22.3017i −0.879494 0.879494i 0.113988 0.993482i \(-0.463638\pi\)
−0.993482 + 0.113988i \(0.963638\pi\)
\(644\) −1.74119 −0.0686126
\(645\) −13.0124 2.77000i −0.512364 0.109069i
\(646\) 15.3503i 0.603948i
\(647\) −9.71662 + 9.71662i −0.382000 + 0.382000i −0.871822 0.489823i \(-0.837062\pi\)
0.489823 + 0.871822i \(0.337062\pi\)
\(648\) 6.22265 6.22265i 0.244449 0.244449i
\(649\) 0 0
\(650\) 6.19675 + 2.76347i 0.243057 + 0.108392i
\(651\) 1.48769i 0.0583070i
\(652\) 1.62369 1.62369i 0.0635885 0.0635885i
\(653\) 3.84746 + 3.84746i 0.150563 + 0.150563i 0.778369 0.627807i \(-0.216047\pi\)
−0.627807 + 0.778369i \(0.716047\pi\)
\(654\) 24.3089i 0.950554i
\(655\) 6.72893 31.6100i 0.262921 1.23511i
\(656\) 2.46916i 0.0964045i
\(657\) −8.90749 8.90749i −0.347514 0.347514i
\(658\) −5.19801 5.19801i −0.202639 0.202639i
\(659\) 42.1160 1.64061 0.820304 0.571928i \(-0.193805\pi\)
0.820304 + 0.571928i \(0.193805\pi\)
\(660\) 0 0
\(661\) −19.5844 −0.761745 −0.380872 0.924628i \(-0.624376\pi\)
−0.380872 + 0.924628i \(0.624376\pi\)
\(662\) 25.5472 + 25.5472i 0.992918 + 0.992918i
\(663\) −1.05044 1.05044i −0.0407957 0.0407957i
\(664\) 5.39621i 0.209413i
\(665\) −27.8717 42.9471i −1.08082 1.66542i
\(666\) 16.6831i 0.646457i
\(667\) −1.96357 1.96357i −0.0760297 0.0760297i
\(668\) −0.437318 + 0.437318i −0.0169204 + 0.0169204i
\(669\) 11.8169i 0.456868i
\(670\) −13.8530 2.94894i −0.535189 0.113927i
\(671\) 0 0
\(672\) 2.08750 2.08750i 0.0805269 0.0805269i
\(673\) −3.92182 + 3.92182i −0.151175 + 0.151175i −0.778643 0.627468i \(-0.784092\pi\)
0.627468 + 0.778643i \(0.284092\pi\)
\(674\) 45.4678i 1.75135i
\(675\) 20.6272 7.90372i 0.793943 0.304214i
\(676\) −1.80958 −0.0695992
\(677\) −1.64985 1.64985i −0.0634089 0.0634089i 0.674691 0.738100i \(-0.264277\pi\)
−0.738100 + 0.674691i \(0.764277\pi\)
\(678\) 10.4606 10.4606i 0.401736 0.401736i
\(679\) −14.0132 −0.537776
\(680\) 11.4403 + 2.43533i 0.438716 + 0.0933908i
\(681\) 6.89132i 0.264076i
\(682\) 0 0
\(683\) −25.0400 25.0400i −0.958127 0.958127i 0.0410307 0.999158i \(-0.486936\pi\)
−0.999158 + 0.0410307i \(0.986936\pi\)
\(684\) 1.86738 0.0714012
\(685\) 23.2055 15.0598i 0.886636 0.575406i
\(686\) 23.2903 0.889229
\(687\) 11.5371 11.5371i 0.440169 0.440169i
\(688\) 21.6089 21.6089i 0.823832 0.823832i
\(689\) −8.40662 −0.320267
\(690\) −6.34483 + 4.11765i −0.241544 + 0.156756i
\(691\) −1.79981 −0.0684681 −0.0342340 0.999414i \(-0.510899\pi\)
−0.0342340 + 0.999414i \(0.510899\pi\)
\(692\) 0.456241 + 0.456241i 0.0173437 + 0.0173437i
\(693\) 0 0
\(694\) 44.2510i 1.67974i
\(695\) −2.20758 0.469934i −0.0837382 0.0178256i
\(696\) 2.26301 0.0857790
\(697\) −0.787169 + 0.787169i −0.0298161 + 0.0298161i
\(698\) 22.1490 + 22.1490i 0.838351 + 0.838351i
\(699\) 3.09109 0.116916
\(700\) −2.93293 + 1.12381i −0.110854 + 0.0424759i
\(701\) 17.8151i 0.672869i 0.941707 + 0.336434i \(0.109221\pi\)
−0.941707 + 0.336434i \(0.890779\pi\)
\(702\) 4.23921 4.23921i 0.159999 0.159999i
\(703\) 18.9468 18.9468i 0.714593 0.714593i
\(704\) 0 0
\(705\) −2.16587 0.461055i −0.0815713 0.0173643i
\(706\) 5.85933i 0.220519i
\(707\) −39.6160 + 39.6160i −1.48991 + 1.48991i
\(708\) 0.816659 + 0.816659i 0.0306919 + 0.0306919i
\(709\) 10.0474i 0.377339i 0.982041 + 0.188670i \(0.0604175\pi\)
−0.982041 + 0.188670i \(0.939583\pi\)
\(710\) 15.3311 + 23.6234i 0.575365 + 0.886572i
\(711\) 5.26966i 0.197628i
\(712\) 26.7300 + 26.7300i 1.00175 + 1.00175i
\(713\) 0.830926 + 0.830926i 0.0311184 + 0.0311184i
\(714\) 9.91691 0.371131
\(715\) 0 0
\(716\) 0.554298 0.0207151
\(717\) 1.89127 + 1.89127i 0.0706309 + 0.0706309i
\(718\) −11.1332 11.1332i −0.415489 0.415489i
\(719\) 6.85933i 0.255810i 0.991786 + 0.127905i \(0.0408252\pi\)
−0.991786 + 0.127905i \(0.959175\pi\)
\(720\) −4.59249 + 21.5739i −0.171152 + 0.804010i
\(721\) 42.5005i 1.58280i
\(722\) −10.8883 10.8883i −0.405221 0.405221i
\(723\) 14.9587 14.9587i 0.556319 0.556319i
\(724\) 0.901065i 0.0334878i
\(725\) −4.57485 2.04017i −0.169906 0.0757702i
\(726\) 0 0
\(727\) −25.2212 + 25.2212i −0.935401 + 0.935401i −0.998036 0.0626351i \(-0.980050\pi\)
0.0626351 + 0.998036i \(0.480050\pi\)
\(728\) 7.48685 7.48685i 0.277481 0.277481i
\(729\) 3.55147i 0.131536i
\(730\) 17.5068 + 3.72672i 0.647955 + 0.137932i
\(731\) 13.7779 0.509592
\(732\) −0.682625 0.682625i −0.0252306 0.0252306i
\(733\) −5.45218 + 5.45218i −0.201381 + 0.201381i −0.800591 0.599211i \(-0.795481\pi\)
0.599211 + 0.800591i \(0.295481\pi\)
\(734\) 50.7284 1.87242
\(735\) 16.8154 10.9128i 0.620245 0.402525i
\(736\) 2.33188i 0.0859543i
\(737\) 0 0
\(738\) −1.38095 1.38095i −0.0508336 0.0508336i
\(739\) −40.8032 −1.50097 −0.750485 0.660887i \(-0.770180\pi\)
−0.750485 + 0.660887i \(0.770180\pi\)
\(740\) −0.894848 1.37886i −0.0328953 0.0506879i
\(741\) −4.18574 −0.153767
\(742\) 39.6823 39.6823i 1.45678 1.45678i
\(743\) −31.3704 + 31.3704i −1.15087 + 1.15087i −0.164491 + 0.986379i \(0.552598\pi\)
−0.986379 + 0.164491i \(0.947402\pi\)
\(744\) −0.957638 −0.0351087
\(745\) −2.66947 0.568258i −0.0978017 0.0208193i
\(746\) 20.5338 0.751796
\(747\) 3.24412 + 3.24412i 0.118696 + 0.118696i
\(748\) 0 0
\(749\) 25.9946i 0.949821i
\(750\) −8.02984 + 11.0310i −0.293208 + 0.402796i
\(751\) −13.1663 −0.480445 −0.240223 0.970718i \(-0.577220\pi\)
−0.240223 + 0.970718i \(0.577220\pi\)
\(752\) 3.59672 3.59672i 0.131159 0.131159i
\(753\) 9.59817 + 9.59817i 0.349777 + 0.349777i
\(754\) −1.35949 −0.0495096
\(755\) 0.738739 3.47032i 0.0268854 0.126298i
\(756\) 2.77522i 0.100934i
\(757\) −14.0516 + 14.0516i −0.510713 + 0.510713i −0.914745 0.404032i \(-0.867608\pi\)
0.404032 + 0.914745i \(0.367608\pi\)
\(758\) −27.4703 + 27.4703i −0.997768 + 0.997768i
\(759\) 0 0
\(760\) 27.6455 17.9413i 1.00281 0.650799i
\(761\) 17.7388i 0.643030i −0.946904 0.321515i \(-0.895808\pi\)
0.946904 0.321515i \(-0.104192\pi\)
\(762\) −1.00059 + 1.00059i −0.0362477 + 0.0362477i
\(763\) −59.3733 59.3733i −2.14946 2.14946i
\(764\) 2.46699i 0.0892525i
\(765\) −8.34184 + 5.41366i −0.301600 + 0.195731i
\(766\) 35.2381i 1.27321i
\(767\) 6.09374 + 6.09374i 0.220032 + 0.220032i
\(768\) 2.09390 + 2.09390i 0.0755572 + 0.0755572i
\(769\) −33.4001 −1.20444 −0.602218 0.798331i \(-0.705716\pi\)
−0.602218 + 0.798331i \(0.705716\pi\)
\(770\) 0 0
\(771\) 13.4894 0.485810
\(772\) −1.78757 1.78757i −0.0643362 0.0643362i
\(773\) 26.9841 + 26.9841i 0.970551 + 0.970551i 0.999579 0.0290274i \(-0.00924101\pi\)
−0.0290274 + 0.999579i \(0.509241\pi\)
\(774\) 24.1709i 0.868805i
\(775\) 1.93594 + 0.863343i 0.0695411 + 0.0310122i
\(776\) 9.02042i 0.323814i
\(777\) 12.2404 + 12.2404i 0.439123 + 0.439123i
\(778\) −7.82149 + 7.82149i −0.280414 + 0.280414i
\(779\) 3.13667i 0.112383i
\(780\) −0.0534639 + 0.251154i −0.00191432 + 0.00899276i
\(781\) 0 0
\(782\) 5.53895 5.53895i 0.198072 0.198072i
\(783\) −3.12966 + 3.12966i −0.111845 + 0.111845i
\(784\) 46.0464i 1.64451i
\(785\) 13.9161 9.03122i 0.496687 0.322338i
\(786\) 17.6382 0.629133
\(787\) 25.9828 + 25.9828i 0.926187 + 0.926187i 0.997457 0.0712698i \(-0.0227051\pi\)
−0.0712698 + 0.997457i \(0.522705\pi\)
\(788\) 1.43600 1.43600i 0.0511555 0.0511555i
\(789\) −0.798057 −0.0284116
\(790\) −4.07614 6.28086i −0.145022 0.223463i
\(791\) 51.0989i 1.81687i
\(792\) 0 0
\(793\) −5.09361 5.09361i −0.180879 0.180879i
\(794\) −33.3769 −1.18450
\(795\) 3.51976 16.5345i 0.124833 0.586420i
\(796\) −2.89348 −0.102557
\(797\) 14.2420 14.2420i 0.504479 0.504479i −0.408348 0.912827i \(-0.633895\pi\)
0.912827 + 0.408348i \(0.133895\pi\)
\(798\) 19.7582 19.7582i 0.699433 0.699433i
\(799\) 2.29327 0.0811300
\(800\) −1.50505 3.92791i −0.0532117 0.138873i
\(801\) −32.1393 −1.13559
\(802\) 25.0253 + 25.0253i 0.883674 + 0.883674i
\(803\) 0 0
\(804\) 0.536020i 0.0189040i
\(805\) 5.43978 25.5541i 0.191727 0.900663i
\(806\) 0.575295 0.0202639
\(807\) 16.7316 16.7316i 0.588981 0.588981i
\(808\) −25.5012 25.5012i −0.897131 0.897131i
\(809\) −51.9338 −1.82590 −0.912948 0.408076i \(-0.866200\pi\)
−0.912948 + 0.408076i \(0.866200\pi\)
\(810\) −5.78736 8.91766i −0.203347 0.313335i
\(811\) 39.1727i 1.37554i −0.725928 0.687770i \(-0.758590\pi\)
0.725928 0.687770i \(-0.241410\pi\)
\(812\) 0.444997 0.444997i 0.0156163 0.0156163i
\(813\) 18.1009 18.1009i 0.634826 0.634826i
\(814\) 0 0
\(815\) 18.7569 + 28.9022i 0.657025 + 1.01240i
\(816\) 6.86192i 0.240215i
\(817\) 27.4507 27.4507i 0.960377 0.960377i
\(818\) −6.07010 6.07010i −0.212236 0.212236i
\(819\) 9.00197i 0.314554i
\(820\) 0.188208 + 0.0400644i 0.00657250 + 0.00139911i
\(821\) 24.9965i 0.872384i 0.899854 + 0.436192i \(0.143673\pi\)
−0.899854 + 0.436192i \(0.856327\pi\)
\(822\) 10.6759 + 10.6759i 0.372365 + 0.372365i
\(823\) −16.2466 16.2466i −0.566321 0.566321i 0.364775 0.931096i \(-0.381146\pi\)
−0.931096 + 0.364775i \(0.881146\pi\)
\(824\) −27.3580 −0.953062
\(825\) 0 0
\(826\) −57.5294 −2.00170
\(827\) 3.91550 + 3.91550i 0.136155 + 0.136155i 0.771900 0.635744i \(-0.219307\pi\)
−0.635744 + 0.771900i \(0.719307\pi\)
\(828\) 0.673823 + 0.673823i 0.0234170 + 0.0234170i
\(829\) 14.9736i 0.520054i −0.965601 0.260027i \(-0.916268\pi\)
0.965601 0.260027i \(-0.0837315\pi\)
\(830\) −6.37600 1.35728i −0.221314 0.0471119i
\(831\) 25.0978i 0.870632i
\(832\) 4.79029 + 4.79029i 0.166073 + 0.166073i
\(833\) −14.6796 + 14.6796i −0.508618 + 0.508618i
\(834\) 1.23181i 0.0426542i
\(835\) −5.05192 7.78443i −0.174829 0.269391i
\(836\) 0 0
\(837\) 1.32438 1.32438i 0.0457773 0.0457773i
\(838\) 11.4645 11.4645i 0.396035 0.396035i
\(839\) 12.5957i 0.434851i −0.976077 0.217426i \(-0.930234\pi\)
0.976077 0.217426i \(-0.0697660\pi\)
\(840\) 11.5908 + 17.8601i 0.399922 + 0.616234i
\(841\) −27.9963 −0.965391
\(842\) −8.16111 8.16111i −0.281250 0.281250i
\(843\) −5.01472 + 5.01472i −0.172716 + 0.172716i
\(844\) 0.952386 0.0327825
\(845\) 5.65344 26.5578i 0.194484 0.913615i
\(846\) 4.02315i 0.138319i
\(847\) 0 0
\(848\) 27.4579 + 27.4579i 0.942907 + 0.942907i
\(849\) −7.94329 −0.272613
\(850\) 5.75504 12.9050i 0.197396 0.442638i
\(851\) 13.6735 0.468720
\(852\) −0.753640 + 0.753640i −0.0258193 + 0.0258193i
\(853\) 35.1948 35.1948i 1.20505 1.20505i 0.232437 0.972611i \(-0.425330\pi\)
0.972611 0.232437i \(-0.0746700\pi\)
\(854\) 48.0874 1.64552
\(855\) −5.83403 + 27.4061i −0.199519 + 0.937269i
\(856\) 16.7330 0.571922
\(857\) 21.2860 + 21.2860i 0.727117 + 0.727117i 0.970044 0.242927i \(-0.0781077\pi\)
−0.242927 + 0.970044i \(0.578108\pi\)
\(858\) 0 0
\(859\) 9.31402i 0.317790i 0.987295 + 0.158895i \(0.0507932\pi\)
−0.987295 + 0.158895i \(0.949207\pi\)
\(860\) −1.29648 1.99773i −0.0442096 0.0681220i
\(861\) −2.02642 −0.0690603
\(862\) 7.57014 7.57014i 0.257840 0.257840i
\(863\) 25.0239 + 25.0239i 0.851825 + 0.851825i 0.990358 0.138533i \(-0.0442387\pi\)
−0.138533 + 0.990358i \(0.544239\pi\)
\(864\) −3.71670 −0.126445
\(865\) −8.12126 + 5.27051i −0.276131 + 0.179203i
\(866\) 7.39941i 0.251442i
\(867\) 7.81942 7.81942i 0.265562 0.265562i
\(868\) −0.188310 + 0.188310i −0.00639166 + 0.00639166i
\(869\) 0 0
\(870\) 0.569202 2.67390i 0.0192978 0.0906538i
\(871\) 3.99967i 0.135524i
\(872\) 38.2192 38.2192i 1.29427 1.29427i
\(873\) 5.42295 + 5.42295i 0.183539 + 0.183539i
\(874\) 22.0713i 0.746574i
\(875\) −7.33027 46.5552i −0.247808 1.57385i
\(876\) 0.677396i 0.0228871i
\(877\) 15.4569 + 15.4569i 0.521941 + 0.521941i 0.918157 0.396216i \(-0.129677\pi\)
−0.396216 + 0.918157i \(0.629677\pi\)
\(878\) −1.34526 1.34526i −0.0454002 0.0454002i
\(879\) 1.92089 0.0647901
\(880\) 0 0
\(881\) 46.4810 1.56599 0.782993 0.622031i \(-0.213692\pi\)
0.782993 + 0.622031i \(0.213692\pi\)
\(882\) −25.7529 25.7529i −0.867144 0.867144i
\(883\) −19.7450 19.7450i −0.664471 0.664471i 0.291959 0.956431i \(-0.405693\pi\)
−0.956431 + 0.291959i \(0.905693\pi\)
\(884\) 0.265927i 0.00894411i
\(885\) −14.5368 + 9.43408i −0.488651 + 0.317123i
\(886\) 22.5769i 0.758486i
\(887\) 4.97816 + 4.97816i 0.167150 + 0.167150i 0.785726 0.618575i \(-0.212290\pi\)
−0.618575 + 0.785726i \(0.712290\pi\)
\(888\) −7.87930 + 7.87930i −0.264412 + 0.264412i
\(889\) 4.88780i 0.163932i
\(890\) 38.3066 24.8601i 1.28404 0.833313i
\(891\) 0 0
\(892\) −1.49577 + 1.49577i −0.0500822 + 0.0500822i
\(893\) 4.56905 4.56905i 0.152897 0.152897i
\(894\) 1.48954i 0.0498178i
\(895\) −1.73172 + 8.13500i −0.0578851 + 0.271923i
\(896\) −52.3164 −1.74777
\(897\) −1.51037 1.51037i −0.0504298 0.0504298i
\(898\) −12.5663 + 12.5663i −0.419344 + 0.419344i
\(899\) −0.424720 −0.0141652
\(900\) 1.56991 + 0.700111i 0.0523305 + 0.0233370i
\(901\) 17.5071i 0.583247i
\(902\) 0 0
\(903\) 17.7343 + 17.7343i 0.590160 + 0.590160i
\(904\) −32.8929 −1.09400
\(905\) −13.2242 2.81508i −0.439588 0.0935764i
\(906\) 1.93642 0.0643332
\(907\) −20.8941 + 20.8941i −0.693777 + 0.693777i −0.963061 0.269283i \(-0.913213\pi\)
0.269283 + 0.963061i \(0.413213\pi\)
\(908\) 0.872298 0.872298i 0.0289482 0.0289482i
\(909\) 30.6620 1.01699
\(910\) −6.96312 10.7294i −0.230825 0.355675i
\(911\) 16.9533 0.561689 0.280844 0.959753i \(-0.409386\pi\)
0.280844 + 0.959753i \(0.409386\pi\)
\(912\) 13.6715 + 13.6715i 0.452709 + 0.452709i
\(913\) 0 0
\(914\) 5.14655i 0.170233i
\(915\) 12.1510 7.88571i 0.401699 0.260694i
\(916\) 2.92072 0.0965034
\(917\) −43.0804 + 43.0804i −1.42264 + 1.42264i
\(918\) −8.82832 8.82832i −0.291378 0.291378i
\(919\) −5.02309 −0.165697 −0.0828483 0.996562i \(-0.526402\pi\)
−0.0828483 + 0.996562i \(0.526402\pi\)
\(920\) 16.4494 + 3.50164i 0.542322 + 0.115446i
\(921\) 14.6732i 0.483497i
\(922\) −5.65287 + 5.65287i −0.186167 + 0.186167i
\(923\) −5.62351 + 5.62351i −0.185100 + 0.185100i
\(924\) 0 0
\(925\) 23.0321 8.82519i 0.757290 0.290170i
\(926\) 31.9260i 1.04915i
\(927\) 16.4473 16.4473i 0.540199 0.540199i
\(928\) 0.595961 + 0.595961i 0.0195634 + 0.0195634i
\(929\) 11.8130i 0.387572i 0.981044 + 0.193786i \(0.0620767\pi\)
−0.981044 + 0.193786i \(0.937923\pi\)
\(930\) −0.240870 + 1.13152i −0.00789843 + 0.0371039i
\(931\) 58.4945i 1.91708i
\(932\) 0.391268 + 0.391268i 0.0128164 + 0.0128164i
\(933\) 8.89656 + 8.89656i 0.291260 + 0.291260i
\(934\) 21.5258 0.704346
\(935\) 0 0
\(936\) −5.79466 −0.189405
\(937\) 1.62077 + 1.62077i 0.0529483 + 0.0529483i 0.733085 0.680137i \(-0.238080\pi\)
−0.680137 + 0.733085i \(0.738080\pi\)
\(938\) 18.8799 + 18.8799i 0.616451 + 0.616451i
\(939\) 21.7410i 0.709492i
\(940\) −0.215794 0.332514i −0.00703842 0.0108454i
\(941\) 1.77332i 0.0578087i 0.999582 + 0.0289044i \(0.00920183\pi\)
−0.999582 + 0.0289044i \(0.990798\pi\)
\(942\) 6.40223 + 6.40223i 0.208596 + 0.208596i
\(943\) −1.13183 + 1.13183i −0.0368574 + 0.0368574i
\(944\) 39.8070i 1.29561i
\(945\) −40.7297 8.67026i −1.32494 0.282043i
\(946\) 0 0
\(947\) −8.63289 + 8.63289i −0.280531 + 0.280531i −0.833321 0.552790i \(-0.813563\pi\)
0.552790 + 0.833321i \(0.313563\pi\)
\(948\) 0.200373 0.200373i 0.00650782 0.00650782i
\(949\) 5.05459i 0.164079i
\(950\) −14.2454 37.1778i −0.462181 1.20621i
\(951\) 23.5817 0.764689
\(952\) −15.5917 15.5917i −0.505329 0.505329i
\(953\) −13.0350 + 13.0350i −0.422246 + 0.422246i −0.885976 0.463730i \(-0.846511\pi\)
0.463730 + 0.885976i \(0.346511\pi\)
\(954\) −30.7133 −0.994380
\(955\) 36.2060 + 7.70729i 1.17160 + 0.249402i
\(956\) 0.478792i 0.0154852i
\(957\) 0 0
\(958\) −5.09348 5.09348i −0.164563 0.164563i
\(959\) −52.1507 −1.68403
\(960\) −11.4274 + 7.41613i −0.368818 + 0.239355i
\(961\) −30.8203 −0.994202
\(962\) 4.73344 4.73344i 0.152612 0.152612i
\(963\) −10.0596 + 10.0596i −0.324167 + 0.324167i
\(964\) 3.78691 0.121968
\(965\) 31.8195 20.6501i 1.02431 0.664751i
\(966\) 14.2590 0.458776
\(967\) 9.49113 + 9.49113i 0.305214 + 0.305214i 0.843050 0.537836i \(-0.180758\pi\)
−0.537836 + 0.843050i \(0.680758\pi\)
\(968\) 0 0
\(969\) 8.71697i 0.280029i
\(970\) −10.6583 2.26886i −0.342216 0.0728487i
\(971\) 51.2201 1.64373 0.821865 0.569682i \(-0.192933\pi\)
0.821865 + 0.569682i \(0.192933\pi\)
\(972\) 1.68109 1.68109i 0.0539211 0.0539211i
\(973\) 3.00865 + 3.00865i 0.0964527 + 0.0964527i
\(974\) 15.7408 0.504366
\(975\) −3.51896 1.56930i −0.112697 0.0502577i
\(976\) 33.2737i 1.06506i
\(977\) 10.2391 10.2391i 0.327578 0.327578i −0.524087 0.851665i \(-0.675593\pi\)
0.851665 + 0.524087i \(0.175593\pi\)
\(978\) −13.2967 + 13.2967i −0.425183 + 0.425183i
\(979\) 0 0
\(980\) 3.50981 + 0.747144i 0.112117 + 0.0238666i
\(981\) 45.9537i 1.46719i
\(982\) −3.37519 + 3.37519i −0.107707 + 0.107707i
\(983\) 40.6921 + 40.6921i 1.29788 + 1.29788i 0.929793 + 0.368083i \(0.119986\pi\)
0.368083 + 0.929793i \(0.380014\pi\)
\(984\) 1.30443i 0.0415837i
\(985\) 16.5888 + 25.5614i 0.528562 + 0.814454i
\(986\) 2.83119i 0.0901633i
\(987\) 2.95180 + 2.95180i 0.0939568 + 0.0939568i
\(988\) −0.529827 0.529827i −0.0168560 0.0168560i
\(989\) 19.8105 0.629936
\(990\) 0 0
\(991\) 13.1102 0.416458 0.208229 0.978080i \(-0.433230\pi\)
0.208229 + 0.978080i \(0.433230\pi\)
\(992\) −0.252193 0.252193i −0.00800715 0.00800715i
\(993\) −14.5075 14.5075i −0.460381 0.460381i
\(994\) 53.0900i 1.68391i
\(995\) 9.03971 42.4653i 0.286578 1.34624i
\(996\) 0.246709i 0.00781726i
\(997\) −1.59446 1.59446i −0.0504969 0.0504969i 0.681407 0.731904i \(-0.261368\pi\)
−0.731904 + 0.681407i \(0.761368\pi\)
\(998\) 9.26898 9.26898i 0.293404 0.293404i
\(999\) 21.7936i 0.689519i
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 605.2.e.b.483.4 32
5.2 odd 4 inner 605.2.e.b.362.13 32
11.2 odd 10 605.2.m.d.403.1 32
11.3 even 5 605.2.m.e.233.1 32
11.4 even 5 55.2.l.a.28.4 yes 32
11.5 even 5 605.2.m.d.118.4 32
11.6 odd 10 605.2.m.c.118.1 32
11.7 odd 10 605.2.m.e.578.1 32
11.8 odd 10 55.2.l.a.13.4 yes 32
11.9 even 5 605.2.m.c.403.4 32
11.10 odd 2 inner 605.2.e.b.483.13 32
33.8 even 10 495.2.bj.a.343.1 32
33.26 odd 10 495.2.bj.a.28.1 32
44.15 odd 10 880.2.cm.a.193.3 32
44.19 even 10 880.2.cm.a.673.3 32
55.2 even 20 605.2.m.d.282.4 32
55.4 even 10 275.2.bm.b.193.1 32
55.7 even 20 605.2.m.e.457.1 32
55.8 even 20 275.2.bm.b.57.1 32
55.17 even 20 605.2.m.c.602.4 32
55.19 odd 10 275.2.bm.b.68.1 32
55.27 odd 20 605.2.m.d.602.1 32
55.32 even 4 inner 605.2.e.b.362.4 32
55.37 odd 20 55.2.l.a.17.4 yes 32
55.42 odd 20 605.2.m.c.282.1 32
55.47 odd 20 605.2.m.e.112.1 32
55.48 odd 20 275.2.bm.b.182.1 32
55.52 even 20 55.2.l.a.2.4 32
165.92 even 20 495.2.bj.a.127.1 32
165.107 odd 20 495.2.bj.a.442.1 32
220.107 odd 20 880.2.cm.a.497.3 32
220.147 even 20 880.2.cm.a.17.3 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.2.l.a.2.4 32 55.52 even 20
55.2.l.a.13.4 yes 32 11.8 odd 10
55.2.l.a.17.4 yes 32 55.37 odd 20
55.2.l.a.28.4 yes 32 11.4 even 5
275.2.bm.b.57.1 32 55.8 even 20
275.2.bm.b.68.1 32 55.19 odd 10
275.2.bm.b.182.1 32 55.48 odd 20
275.2.bm.b.193.1 32 55.4 even 10
495.2.bj.a.28.1 32 33.26 odd 10
495.2.bj.a.127.1 32 165.92 even 20
495.2.bj.a.343.1 32 33.8 even 10
495.2.bj.a.442.1 32 165.107 odd 20
605.2.e.b.362.4 32 55.32 even 4 inner
605.2.e.b.362.13 32 5.2 odd 4 inner
605.2.e.b.483.4 32 1.1 even 1 trivial
605.2.e.b.483.13 32 11.10 odd 2 inner
605.2.m.c.118.1 32 11.6 odd 10
605.2.m.c.282.1 32 55.42 odd 20
605.2.m.c.403.4 32 11.9 even 5
605.2.m.c.602.4 32 55.17 even 20
605.2.m.d.118.4 32 11.5 even 5
605.2.m.d.282.4 32 55.2 even 20
605.2.m.d.403.1 32 11.2 odd 10
605.2.m.d.602.1 32 55.27 odd 20
605.2.m.e.112.1 32 55.47 odd 20
605.2.m.e.233.1 32 11.3 even 5
605.2.m.e.457.1 32 55.7 even 20
605.2.m.e.578.1 32 11.7 odd 10
880.2.cm.a.17.3 32 220.147 even 20
880.2.cm.a.193.3 32 44.15 odd 10
880.2.cm.a.497.3 32 220.107 odd 20
880.2.cm.a.673.3 32 44.19 even 10