Properties

Label 1638.2.p.h.919.2
Level $1638$
Weight $2$
Character 1638.919
Analytic conductor $13.079$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1638,2,Mod(919,1638)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1638, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1638.919");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1638.p (of order \(3\), 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: \(13.0794958511\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.447703281.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 546)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 919.2
Root \(1.26359 + 0.635098i\) of defining polynomial
Character \(\chi\) \(=\) 1638.919
Dual form 1638.2.p.h.991.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.611519 + 1.05918i) q^{5} +(1.48662 + 2.18860i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.611519 + 1.05918i) q^{5} +(1.48662 + 2.18860i) q^{7} -1.00000 q^{8} -1.22304 q^{10} -0.140571 q^{11} +(2.39335 + 2.69665i) q^{13} +(-1.15207 + 2.38175i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.0932782 - 0.161563i) q^{17} +0.895909 q^{19} +(-0.611519 - 1.05918i) q^{20} +(-0.0702857 - 0.121738i) q^{22} +(0.0182404 + 0.0315933i) q^{23} +(1.75209 + 3.03471i) q^{25} +(-1.13869 + 3.42102i) q^{26} +(-2.63869 + 0.193156i) q^{28} +(-2.99337 + 5.18466i) q^{29} +(-1.82050 - 3.15319i) q^{31} +(0.500000 - 0.866025i) q^{32} +0.186556 q^{34} +(-3.22722 + 0.236237i) q^{35} +(0.181804 + 0.314894i) q^{37} +(0.447955 + 0.775880i) q^{38} +(0.611519 - 1.05918i) q^{40} +(-1.70480 + 2.95279i) q^{41} +(-2.06841 - 3.58258i) q^{43} +(0.0702857 - 0.121738i) q^{44} +(-0.0182404 + 0.0315933i) q^{46} +(-0.358745 + 0.621364i) q^{47} +(-2.57990 + 6.50724i) q^{49} +(-1.75209 + 3.03471i) q^{50} +(-3.53204 + 0.724375i) q^{52} +(-3.49556 - 6.05448i) q^{53} +(0.0859621 - 0.148891i) q^{55} +(-1.48662 - 2.18860i) q^{56} -5.98674 q^{58} +(-3.49812 + 6.05892i) q^{59} +0.373113 q^{61} +(1.82050 - 3.15319i) q^{62} +1.00000 q^{64} +(-4.31981 + 0.885937i) q^{65} -4.85806 q^{67} +(0.0932782 + 0.161563i) q^{68} +(-1.81820 - 2.67673i) q^{70} +(5.31198 + 9.20062i) q^{71} +(-4.80900 - 8.32943i) q^{73} +(-0.181804 + 0.314894i) q^{74} +(-0.447955 + 0.775880i) q^{76} +(-0.208977 - 0.307654i) q^{77} +(-2.94837 + 5.10673i) q^{79} +1.22304 q^{80} -3.40959 q^{82} +9.14057 q^{83} +(0.114083 + 0.197597i) q^{85} +(2.06841 - 3.58258i) q^{86} +0.140571 q^{88} +(-3.17736 - 5.50335i) q^{89} +(-2.34386 + 9.24696i) q^{91} -0.0364808 q^{92} -0.717490 q^{94} +(-0.547865 + 0.948930i) q^{95} +(3.24059 + 5.61287i) q^{97} +(-6.92538 + 1.01936i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} - 4 q^{4} - 2 q^{5} - 3 q^{7} - 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{2} - 4 q^{4} - 2 q^{5} - 3 q^{7} - 8 q^{8} - 4 q^{10} + 8 q^{11} + 3 q^{13} - 3 q^{14} - 4 q^{16} + 2 q^{17} + 8 q^{19} - 2 q^{20} + 4 q^{22} - 4 q^{23} + 2 q^{25} + 12 q^{26} - 2 q^{29} + 14 q^{31} + 4 q^{32} + 4 q^{34} + 4 q^{35} - 6 q^{37} + 4 q^{38} + 2 q^{40} - 12 q^{41} - 4 q^{44} + 4 q^{46} - 7 q^{47} - 7 q^{49} - 2 q^{50} + 9 q^{52} + q^{53} - 25 q^{55} + 3 q^{56} - 4 q^{58} - 16 q^{59} + 8 q^{61} - 14 q^{62} + 8 q^{64} - q^{65} - 38 q^{67} + 2 q^{68} - 22 q^{70} - 20 q^{71} - 7 q^{73} + 6 q^{74} - 4 q^{76} + 24 q^{77} + 24 q^{79} + 4 q^{80} - 24 q^{82} + 64 q^{83} + 15 q^{85} - 8 q^{88} + 11 q^{89} - 20 q^{91} + 8 q^{92} - 14 q^{94} - 28 q^{95} + 11 q^{97} - 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).

\(n\) \(379\) \(703\) \(911\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.611519 + 1.05918i −0.273479 + 0.473680i −0.969750 0.244099i \(-0.921508\pi\)
0.696271 + 0.717779i \(0.254841\pi\)
\(6\) 0 0
\(7\) 1.48662 + 2.18860i 0.561891 + 0.827211i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −1.22304 −0.386758
\(11\) −0.140571 −0.0423839 −0.0211919 0.999775i \(-0.506746\pi\)
−0.0211919 + 0.999775i \(0.506746\pi\)
\(12\) 0 0
\(13\) 2.39335 + 2.69665i 0.663795 + 0.747915i
\(14\) −1.15207 + 2.38175i −0.307903 + 0.636550i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0.0932782 0.161563i 0.0226233 0.0391847i −0.854492 0.519464i \(-0.826132\pi\)
0.877115 + 0.480280i \(0.159465\pi\)
\(18\) 0 0
\(19\) 0.895909 0.205536 0.102768 0.994705i \(-0.467230\pi\)
0.102768 + 0.994705i \(0.467230\pi\)
\(20\) −0.611519 1.05918i −0.136740 0.236840i
\(21\) 0 0
\(22\) −0.0702857 0.121738i −0.0149850 0.0259547i
\(23\) 0.0182404 + 0.0315933i 0.00380339 + 0.00658766i 0.867921 0.496703i \(-0.165456\pi\)
−0.864117 + 0.503290i \(0.832123\pi\)
\(24\) 0 0
\(25\) 1.75209 + 3.03471i 0.350418 + 0.606942i
\(26\) −1.13869 + 3.42102i −0.223316 + 0.670917i
\(27\) 0 0
\(28\) −2.63869 + 0.193156i −0.498666 + 0.0365030i
\(29\) −2.99337 + 5.18466i −0.555854 + 0.962768i 0.441982 + 0.897024i \(0.354275\pi\)
−0.997837 + 0.0657442i \(0.979058\pi\)
\(30\) 0 0
\(31\) −1.82050 3.15319i −0.326971 0.566330i 0.654939 0.755682i \(-0.272694\pi\)
−0.981909 + 0.189352i \(0.939361\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 0.186556 0.0319941
\(35\) −3.22722 + 0.236237i −0.545499 + 0.0399313i
\(36\) 0 0
\(37\) 0.181804 + 0.314894i 0.0298884 + 0.0517683i 0.880583 0.473892i \(-0.157151\pi\)
−0.850694 + 0.525661i \(0.823818\pi\)
\(38\) 0.447955 + 0.775880i 0.0726678 + 0.125864i
\(39\) 0 0
\(40\) 0.611519 1.05918i 0.0966896 0.167471i
\(41\) −1.70480 + 2.95279i −0.266245 + 0.461149i −0.967889 0.251378i \(-0.919116\pi\)
0.701644 + 0.712527i \(0.252450\pi\)
\(42\) 0 0
\(43\) −2.06841 3.58258i −0.315429 0.546339i 0.664100 0.747644i \(-0.268815\pi\)
−0.979529 + 0.201305i \(0.935482\pi\)
\(44\) 0.0702857 0.121738i 0.0105960 0.0183528i
\(45\) 0 0
\(46\) −0.0182404 + 0.0315933i −0.00268940 + 0.00465818i
\(47\) −0.358745 + 0.621364i −0.0523283 + 0.0906353i −0.891003 0.453997i \(-0.849998\pi\)
0.838675 + 0.544633i \(0.183331\pi\)
\(48\) 0 0
\(49\) −2.57990 + 6.50724i −0.368557 + 0.929605i
\(50\) −1.75209 + 3.03471i −0.247783 + 0.429173i
\(51\) 0 0
\(52\) −3.53204 + 0.724375i −0.489805 + 0.100453i
\(53\) −3.49556 6.05448i −0.480151 0.831647i 0.519589 0.854416i \(-0.326085\pi\)
−0.999741 + 0.0227694i \(0.992752\pi\)
\(54\) 0 0
\(55\) 0.0859621 0.148891i 0.0115911 0.0200764i
\(56\) −1.48662 2.18860i −0.198658 0.292463i
\(57\) 0 0
\(58\) −5.98674 −0.786097
\(59\) −3.49812 + 6.05892i −0.455416 + 0.788804i −0.998712 0.0507371i \(-0.983843\pi\)
0.543296 + 0.839541i \(0.317176\pi\)
\(60\) 0 0
\(61\) 0.373113 0.0477722 0.0238861 0.999715i \(-0.492396\pi\)
0.0238861 + 0.999715i \(0.492396\pi\)
\(62\) 1.82050 3.15319i 0.231203 0.400456i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −4.31981 + 0.885937i −0.535807 + 0.109887i
\(66\) 0 0
\(67\) −4.85806 −0.593507 −0.296753 0.954954i \(-0.595904\pi\)
−0.296753 + 0.954954i \(0.595904\pi\)
\(68\) 0.0932782 + 0.161563i 0.0113116 + 0.0195923i
\(69\) 0 0
\(70\) −1.81820 2.67673i −0.217316 0.319931i
\(71\) 5.31198 + 9.20062i 0.630416 + 1.09191i 0.987467 + 0.157828i \(0.0504492\pi\)
−0.357050 + 0.934085i \(0.616218\pi\)
\(72\) 0 0
\(73\) −4.80900 8.32943i −0.562851 0.974886i −0.997246 0.0741638i \(-0.976371\pi\)
0.434395 0.900722i \(-0.356962\pi\)
\(74\) −0.181804 + 0.314894i −0.0211343 + 0.0366057i
\(75\) 0 0
\(76\) −0.447955 + 0.775880i −0.0513839 + 0.0889996i
\(77\) −0.208977 0.307654i −0.0238151 0.0350604i
\(78\) 0 0
\(79\) −2.94837 + 5.10673i −0.331718 + 0.574552i −0.982849 0.184413i \(-0.940962\pi\)
0.651131 + 0.758966i \(0.274295\pi\)
\(80\) 1.22304 0.136740
\(81\) 0 0
\(82\) −3.40959 −0.376527
\(83\) 9.14057 1.00331 0.501654 0.865068i \(-0.332725\pi\)
0.501654 + 0.865068i \(0.332725\pi\)
\(84\) 0 0
\(85\) 0.114083 + 0.197597i 0.0123740 + 0.0214324i
\(86\) 2.06841 3.58258i 0.223042 0.386320i
\(87\) 0 0
\(88\) 0.140571 0.0149850
\(89\) −3.17736 5.50335i −0.336799 0.583354i 0.647029 0.762465i \(-0.276011\pi\)
−0.983829 + 0.179111i \(0.942678\pi\)
\(90\) 0 0
\(91\) −2.34386 + 9.24696i −0.245704 + 0.969345i
\(92\) −0.0364808 −0.00380339
\(93\) 0 0
\(94\) −0.717490 −0.0740034
\(95\) −0.547865 + 0.948930i −0.0562098 + 0.0973582i
\(96\) 0 0
\(97\) 3.24059 + 5.61287i 0.329032 + 0.569901i 0.982320 0.187209i \(-0.0599441\pi\)
−0.653288 + 0.757110i \(0.726611\pi\)
\(98\) −6.92538 + 1.01936i −0.699569 + 0.102971i
\(99\) 0 0
\(100\) −3.50418 −0.350418
\(101\) 3.00460 0.298969 0.149484 0.988764i \(-0.452239\pi\)
0.149484 + 0.988764i \(0.452239\pi\)
\(102\) 0 0
\(103\) −4.12788 + 7.14970i −0.406732 + 0.704480i −0.994521 0.104534i \(-0.966665\pi\)
0.587789 + 0.809014i \(0.299998\pi\)
\(104\) −2.39335 2.69665i −0.234687 0.264428i
\(105\) 0 0
\(106\) 3.49556 6.05448i 0.339518 0.588063i
\(107\) −2.23641 3.87358i −0.216202 0.374473i 0.737442 0.675411i \(-0.236034\pi\)
−0.953644 + 0.300938i \(0.902700\pi\)
\(108\) 0 0
\(109\) −3.83686 6.64563i −0.367504 0.636536i 0.621671 0.783279i \(-0.286454\pi\)
−0.989175 + 0.146743i \(0.953121\pi\)
\(110\) 0.171924 0.0163923
\(111\) 0 0
\(112\) 1.15207 2.38175i 0.108860 0.225054i
\(113\) 6.18222 + 10.7079i 0.581575 + 1.00732i 0.995293 + 0.0969119i \(0.0308965\pi\)
−0.413718 + 0.910405i \(0.635770\pi\)
\(114\) 0 0
\(115\) −0.0446174 −0.00416059
\(116\) −2.99337 5.18466i −0.277927 0.481384i
\(117\) 0 0
\(118\) −6.99624 −0.644056
\(119\) 0.492265 0.0360344i 0.0451258 0.00330327i
\(120\) 0 0
\(121\) −10.9802 −0.998204
\(122\) 0.186556 + 0.323125i 0.0168900 + 0.0292544i
\(123\) 0 0
\(124\) 3.64099 0.326971
\(125\) −10.4009 −0.930287
\(126\) 0 0
\(127\) −5.45432 + 9.44716i −0.483993 + 0.838300i −0.999831 0.0183858i \(-0.994147\pi\)
0.515838 + 0.856686i \(0.327481\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −2.92715 3.29810i −0.256728 0.289262i
\(131\) 10.9715 19.0032i 0.958583 1.66031i 0.232634 0.972564i \(-0.425265\pi\)
0.725948 0.687749i \(-0.241401\pi\)
\(132\) 0 0
\(133\) 1.33188 + 1.96078i 0.115489 + 0.170021i
\(134\) −2.42903 4.20720i −0.209836 0.363447i
\(135\) 0 0
\(136\) −0.0932782 + 0.161563i −0.00799854 + 0.0138539i
\(137\) 1.34605 2.33143i 0.115001 0.199188i −0.802779 0.596276i \(-0.796646\pi\)
0.917780 + 0.397089i \(0.129980\pi\)
\(138\) 0 0
\(139\) 5.28925 + 9.16126i 0.448629 + 0.777048i 0.998297 0.0583352i \(-0.0185792\pi\)
−0.549668 + 0.835383i \(0.685246\pi\)
\(140\) 1.40902 2.91297i 0.119084 0.246191i
\(141\) 0 0
\(142\) −5.31198 + 9.20062i −0.445772 + 0.772099i
\(143\) −0.336436 0.379071i −0.0281342 0.0316996i
\(144\) 0 0
\(145\) −3.66100 6.34104i −0.304029 0.526595i
\(146\) 4.80900 8.32943i 0.397996 0.689349i
\(147\) 0 0
\(148\) −0.363609 −0.0298884
\(149\) 11.9049 0.975286 0.487643 0.873043i \(-0.337857\pi\)
0.487643 + 0.873043i \(0.337857\pi\)
\(150\) 0 0
\(151\) −3.66774 6.35272i −0.298477 0.516977i 0.677311 0.735697i \(-0.263145\pi\)
−0.975788 + 0.218720i \(0.929812\pi\)
\(152\) −0.895909 −0.0726678
\(153\) 0 0
\(154\) 0.161948 0.334806i 0.0130501 0.0269795i
\(155\) 4.45307 0.357679
\(156\) 0 0
\(157\) 5.15138 + 8.92246i 0.411125 + 0.712090i 0.995013 0.0997446i \(-0.0318026\pi\)
−0.583888 + 0.811834i \(0.698469\pi\)
\(158\) −5.89675 −0.469120
\(159\) 0 0
\(160\) 0.611519 + 1.05918i 0.0483448 + 0.0837356i
\(161\) −0.0420284 + 0.0868883i −0.00331230 + 0.00684775i
\(162\) 0 0
\(163\) −10.1370 −0.793994 −0.396997 0.917820i \(-0.629948\pi\)
−0.396997 + 0.917820i \(0.629948\pi\)
\(164\) −1.70480 2.95279i −0.133122 0.230575i
\(165\) 0 0
\(166\) 4.57029 + 7.91597i 0.354723 + 0.614398i
\(167\) 4.28857 7.42802i 0.331860 0.574798i −0.651017 0.759063i \(-0.725657\pi\)
0.982876 + 0.184266i \(0.0589906\pi\)
\(168\) 0 0
\(169\) −1.54380 + 12.9080i −0.118754 + 0.992924i
\(170\) −0.114083 + 0.197597i −0.00874974 + 0.0151550i
\(171\) 0 0
\(172\) 4.13681 0.315429
\(173\) 10.6788 0.811897 0.405949 0.913896i \(-0.366941\pi\)
0.405949 + 0.913896i \(0.366941\pi\)
\(174\) 0 0
\(175\) −4.03705 + 8.34609i −0.305173 + 0.630905i
\(176\) 0.0702857 + 0.121738i 0.00529799 + 0.00917638i
\(177\) 0 0
\(178\) 3.17736 5.50335i 0.238153 0.412493i
\(179\) 12.9792 0.970112 0.485056 0.874483i \(-0.338799\pi\)
0.485056 + 0.874483i \(0.338799\pi\)
\(180\) 0 0
\(181\) 23.7327 1.76403 0.882017 0.471217i \(-0.156185\pi\)
0.882017 + 0.471217i \(0.156185\pi\)
\(182\) −9.18004 + 2.59364i −0.680470 + 0.192253i
\(183\) 0 0
\(184\) −0.0182404 0.0315933i −0.00134470 0.00232909i
\(185\) −0.444707 −0.0326955
\(186\) 0 0
\(187\) −0.0131122 + 0.0227111i −0.000958863 + 0.00166080i
\(188\) −0.358745 0.621364i −0.0261642 0.0453176i
\(189\) 0 0
\(190\) −1.09573 −0.0794926
\(191\) 19.9778 1.44555 0.722773 0.691085i \(-0.242867\pi\)
0.722773 + 0.691085i \(0.242867\pi\)
\(192\) 0 0
\(193\) −6.22388 −0.448004 −0.224002 0.974589i \(-0.571912\pi\)
−0.224002 + 0.974589i \(0.571912\pi\)
\(194\) −3.24059 + 5.61287i −0.232661 + 0.402981i
\(195\) 0 0
\(196\) −4.34548 5.48788i −0.310391 0.391991i
\(197\) −12.2503 + 21.2182i −0.872799 + 1.51173i −0.0137105 + 0.999906i \(0.504364\pi\)
−0.859089 + 0.511827i \(0.828969\pi\)
\(198\) 0 0
\(199\) 9.80754 16.9872i 0.695238 1.20419i −0.274862 0.961484i \(-0.588632\pi\)
0.970100 0.242704i \(-0.0780343\pi\)
\(200\) −1.75209 3.03471i −0.123891 0.214586i
\(201\) 0 0
\(202\) 1.50230 + 2.60206i 0.105701 + 0.183080i
\(203\) −15.7971 + 1.15637i −1.10874 + 0.0811615i
\(204\) 0 0
\(205\) −2.08503 3.61138i −0.145625 0.252230i
\(206\) −8.25576 −0.575206
\(207\) 0 0
\(208\) 1.13869 3.42102i 0.0789540 0.237205i
\(209\) −0.125939 −0.00871140
\(210\) 0 0
\(211\) −2.99635 + 5.18983i −0.206277 + 0.357283i −0.950539 0.310605i \(-0.899468\pi\)
0.744262 + 0.667888i \(0.232802\pi\)
\(212\) 6.99111 0.480151
\(213\) 0 0
\(214\) 2.23641 3.87358i 0.152878 0.264793i
\(215\) 5.05947 0.345053
\(216\) 0 0
\(217\) 4.19467 8.67194i 0.284753 0.588689i
\(218\) 3.83686 6.64563i 0.259865 0.450099i
\(219\) 0 0
\(220\) 0.0859621 + 0.148891i 0.00579556 + 0.0100382i
\(221\) 0.658924 0.135137i 0.0443240 0.00909028i
\(222\) 0 0
\(223\) 13.8098 23.9193i 0.924775 1.60176i 0.132853 0.991136i \(-0.457586\pi\)
0.791922 0.610622i \(-0.209080\pi\)
\(224\) 2.63869 0.193156i 0.176305 0.0129058i
\(225\) 0 0
\(226\) −6.18222 + 10.7079i −0.411235 + 0.712281i
\(227\) −0.895645 + 1.55130i −0.0594460 + 0.102964i −0.894217 0.447634i \(-0.852267\pi\)
0.834771 + 0.550598i \(0.185600\pi\)
\(228\) 0 0
\(229\) 12.6142 21.8485i 0.833572 1.44379i −0.0616153 0.998100i \(-0.519625\pi\)
0.895188 0.445690i \(-0.147041\pi\)
\(230\) −0.0223087 0.0386398i −0.00147099 0.00254783i
\(231\) 0 0
\(232\) 2.99337 5.18466i 0.196524 0.340390i
\(233\) −14.1852 + 24.5695i −0.929304 + 1.60960i −0.144815 + 0.989459i \(0.546259\pi\)
−0.784489 + 0.620143i \(0.787075\pi\)
\(234\) 0 0
\(235\) −0.438758 0.759952i −0.0286214 0.0495738i
\(236\) −3.49812 6.05892i −0.227708 0.394402i
\(237\) 0 0
\(238\) 0.277339 + 0.408296i 0.0179772 + 0.0264659i
\(239\) 28.9654 1.87362 0.936809 0.349842i \(-0.113765\pi\)
0.936809 + 0.349842i \(0.113765\pi\)
\(240\) 0 0
\(241\) 6.59757 11.4273i 0.424987 0.736099i −0.571432 0.820649i \(-0.693612\pi\)
0.996419 + 0.0845504i \(0.0269454\pi\)
\(242\) −5.49012 9.50917i −0.352918 0.611272i
\(243\) 0 0
\(244\) −0.186556 + 0.323125i −0.0119430 + 0.0206860i
\(245\) −5.31468 6.71188i −0.339543 0.428806i
\(246\) 0 0
\(247\) 2.14422 + 2.41595i 0.136433 + 0.153723i
\(248\) 1.82050 + 3.15319i 0.115602 + 0.200228i
\(249\) 0 0
\(250\) −5.20046 9.00747i −0.328906 0.569682i
\(251\) −4.73276 8.19739i −0.298729 0.517415i 0.677116 0.735876i \(-0.263229\pi\)
−0.975846 + 0.218462i \(0.929896\pi\)
\(252\) 0 0
\(253\) −0.00256408 0.00444112i −0.000161202 0.000279211i
\(254\) −10.9086 −0.684469
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −5.11789 8.86444i −0.319245 0.552949i 0.661086 0.750310i \(-0.270096\pi\)
−0.980331 + 0.197362i \(0.936763\pi\)
\(258\) 0 0
\(259\) −0.418902 + 0.866025i −0.0260293 + 0.0538122i
\(260\) 1.39266 4.18404i 0.0863692 0.259483i
\(261\) 0 0
\(262\) 21.9430 1.35564
\(263\) 4.84616 0.298827 0.149414 0.988775i \(-0.452261\pi\)
0.149414 + 0.988775i \(0.452261\pi\)
\(264\) 0 0
\(265\) 8.55039 0.525246
\(266\) −1.03215 + 2.13383i −0.0632851 + 0.130834i
\(267\) 0 0
\(268\) 2.42903 4.20720i 0.148377 0.256996i
\(269\) −0.448638 + 0.777064i −0.0273540 + 0.0473785i −0.879378 0.476124i \(-0.842041\pi\)
0.852024 + 0.523502i \(0.175375\pi\)
\(270\) 0 0
\(271\) −6.93756 12.0162i −0.421427 0.729933i 0.574652 0.818398i \(-0.305137\pi\)
−0.996079 + 0.0884648i \(0.971804\pi\)
\(272\) −0.186556 −0.0113116
\(273\) 0 0
\(274\) 2.69210 0.162636
\(275\) −0.246294 0.426594i −0.0148521 0.0257246i
\(276\) 0 0
\(277\) 10.2369 17.7309i 0.615078 1.06535i −0.375292 0.926907i \(-0.622458\pi\)
0.990371 0.138441i \(-0.0442090\pi\)
\(278\) −5.28925 + 9.16126i −0.317228 + 0.549456i
\(279\) 0 0
\(280\) 3.22722 0.236237i 0.192863 0.0141178i
\(281\) −5.11819 −0.305326 −0.152663 0.988278i \(-0.548785\pi\)
−0.152663 + 0.988278i \(0.548785\pi\)
\(282\) 0 0
\(283\) 9.08132 0.539829 0.269914 0.962884i \(-0.413005\pi\)
0.269914 + 0.962884i \(0.413005\pi\)
\(284\) −10.6240 −0.630416
\(285\) 0 0
\(286\) 0.160068 0.480898i 0.00946499 0.0284361i
\(287\) −8.99686 + 0.658583i −0.531068 + 0.0388749i
\(288\) 0 0
\(289\) 8.48260 + 14.6923i 0.498976 + 0.864252i
\(290\) 3.66100 6.34104i 0.214981 0.372359i
\(291\) 0 0
\(292\) 9.61800 0.562851
\(293\) −3.13195 5.42469i −0.182970 0.316914i 0.759920 0.650016i \(-0.225238\pi\)
−0.942891 + 0.333102i \(0.891905\pi\)
\(294\) 0 0
\(295\) −4.27833 7.41029i −0.249094 0.431443i
\(296\) −0.181804 0.314894i −0.0105672 0.0183029i
\(297\) 0 0
\(298\) 5.95244 + 10.3099i 0.344816 + 0.597238i
\(299\) −0.0415404 + 0.124802i −0.00240234 + 0.00721747i
\(300\) 0 0
\(301\) 4.76589 9.85286i 0.274701 0.567909i
\(302\) 3.66774 6.35272i 0.211055 0.365558i
\(303\) 0 0
\(304\) −0.447955 0.775880i −0.0256920 0.0444998i
\(305\) −0.228165 + 0.395194i −0.0130647 + 0.0226287i
\(306\) 0 0
\(307\) 30.0806 1.71679 0.858395 0.512989i \(-0.171462\pi\)
0.858395 + 0.512989i \(0.171462\pi\)
\(308\) 0.370925 0.0271522i 0.0211354 0.00154714i
\(309\) 0 0
\(310\) 2.22653 + 3.85647i 0.126459 + 0.219033i
\(311\) 13.8292 + 23.9528i 0.784180 + 1.35824i 0.929488 + 0.368853i \(0.120249\pi\)
−0.145308 + 0.989386i \(0.546417\pi\)
\(312\) 0 0
\(313\) −3.43002 + 5.94097i −0.193876 + 0.335804i −0.946532 0.322611i \(-0.895439\pi\)
0.752655 + 0.658415i \(0.228773\pi\)
\(314\) −5.15138 + 8.92246i −0.290709 + 0.503523i
\(315\) 0 0
\(316\) −2.94837 5.10673i −0.165859 0.287276i
\(317\) −3.37146 + 5.83953i −0.189360 + 0.327981i −0.945037 0.326963i \(-0.893975\pi\)
0.755677 + 0.654944i \(0.227308\pi\)
\(318\) 0 0
\(319\) 0.420782 0.728816i 0.0235593 0.0408059i
\(320\) −0.611519 + 1.05918i −0.0341849 + 0.0592100i
\(321\) 0 0
\(322\) −0.0962616 + 0.00704648i −0.00536445 + 0.000392685i
\(323\) 0.0835688 0.144745i 0.00464989 0.00805385i
\(324\) 0 0
\(325\) −3.99018 + 11.9879i −0.221335 + 0.664968i
\(326\) −5.06852 8.77893i −0.280719 0.486220i
\(327\) 0 0
\(328\) 1.70480 2.95279i 0.0941317 0.163041i
\(329\) −1.89323 + 0.138587i −0.104377 + 0.00764057i
\(330\) 0 0
\(331\) −11.0982 −0.610010 −0.305005 0.952351i \(-0.598658\pi\)
−0.305005 + 0.952351i \(0.598658\pi\)
\(332\) −4.57029 + 7.91597i −0.250827 + 0.434445i
\(333\) 0 0
\(334\) 8.57714 0.469320
\(335\) 2.97079 5.14557i 0.162312 0.281132i
\(336\) 0 0
\(337\) 21.6470 1.17918 0.589592 0.807701i \(-0.299288\pi\)
0.589592 + 0.807701i \(0.299288\pi\)
\(338\) −11.9506 + 5.11704i −0.650025 + 0.278330i
\(339\) 0 0
\(340\) −0.228165 −0.0123740
\(341\) 0.255910 + 0.443249i 0.0138583 + 0.0240033i
\(342\) 0 0
\(343\) −18.0770 + 4.02745i −0.976069 + 0.217462i
\(344\) 2.06841 + 3.58258i 0.111521 + 0.193160i
\(345\) 0 0
\(346\) 5.33942 + 9.24815i 0.287049 + 0.497183i
\(347\) 14.9337 25.8660i 0.801685 1.38856i −0.116821 0.993153i \(-0.537270\pi\)
0.918506 0.395407i \(-0.129396\pi\)
\(348\) 0 0
\(349\) −6.47690 + 11.2183i −0.346700 + 0.600503i −0.985661 0.168737i \(-0.946031\pi\)
0.638961 + 0.769239i \(0.279365\pi\)
\(350\) −9.24645 + 0.676853i −0.494243 + 0.0361793i
\(351\) 0 0
\(352\) −0.0702857 + 0.121738i −0.00374624 + 0.00648868i
\(353\) −6.15707 −0.327708 −0.163854 0.986485i \(-0.552393\pi\)
−0.163854 + 0.986485i \(0.552393\pi\)
\(354\) 0 0
\(355\) −12.9935 −0.689624
\(356\) 6.35472 0.336799
\(357\) 0 0
\(358\) 6.48961 + 11.2403i 0.342986 + 0.594070i
\(359\) −12.4203 + 21.5125i −0.655516 + 1.13539i 0.326248 + 0.945284i \(0.394215\pi\)
−0.981764 + 0.190103i \(0.939118\pi\)
\(360\) 0 0
\(361\) −18.1973 −0.957755
\(362\) 11.8663 + 20.5531i 0.623680 + 1.08025i
\(363\) 0 0
\(364\) −6.83617 6.65333i −0.358313 0.348729i
\(365\) 11.7632 0.615712
\(366\) 0 0
\(367\) 36.0612 1.88238 0.941188 0.337882i \(-0.109711\pi\)
0.941188 + 0.337882i \(0.109711\pi\)
\(368\) 0.0182404 0.0315933i 0.000950847 0.00164692i
\(369\) 0 0
\(370\) −0.222353 0.385127i −0.0115596 0.0200218i
\(371\) 8.05423 16.6511i 0.418155 0.864481i
\(372\) 0 0
\(373\) −14.7418 −0.763304 −0.381652 0.924306i \(-0.624645\pi\)
−0.381652 + 0.924306i \(0.624645\pi\)
\(374\) −0.0262245 −0.00135604
\(375\) 0 0
\(376\) 0.358745 0.621364i 0.0185009 0.0320444i
\(377\) −21.1454 + 4.33664i −1.08904 + 0.223348i
\(378\) 0 0
\(379\) 5.33674 9.24351i 0.274130 0.474807i −0.695785 0.718250i \(-0.744943\pi\)
0.969915 + 0.243443i \(0.0782768\pi\)
\(380\) −0.547865 0.948930i −0.0281049 0.0486791i
\(381\) 0 0
\(382\) 9.98892 + 17.3013i 0.511078 + 0.885213i
\(383\) 20.4033 1.04256 0.521281 0.853385i \(-0.325455\pi\)
0.521281 + 0.853385i \(0.325455\pi\)
\(384\) 0 0
\(385\) 0.453655 0.0332082i 0.0231204 0.00169244i
\(386\) −3.11194 5.39003i −0.158393 0.274346i
\(387\) 0 0
\(388\) −6.48119 −0.329032
\(389\) 15.8455 + 27.4453i 0.803400 + 1.39153i 0.917366 + 0.398045i \(0.130311\pi\)
−0.113966 + 0.993485i \(0.536356\pi\)
\(390\) 0 0
\(391\) 0.00680573 0.000344181
\(392\) 2.57990 6.50724i 0.130305 0.328665i
\(393\) 0 0
\(394\) −24.5006 −1.23432
\(395\) −3.60597 6.24573i −0.181436 0.314257i
\(396\) 0 0
\(397\) −2.61048 −0.131016 −0.0655080 0.997852i \(-0.520867\pi\)
−0.0655080 + 0.997852i \(0.520867\pi\)
\(398\) 19.6151 0.983215
\(399\) 0 0
\(400\) 1.75209 3.03471i 0.0876045 0.151735i
\(401\) −8.18479 14.1765i −0.408729 0.707939i 0.586019 0.810297i \(-0.300694\pi\)
−0.994748 + 0.102358i \(0.967361\pi\)
\(402\) 0 0
\(403\) 4.14596 12.4559i 0.206525 0.620473i
\(404\) −1.50230 + 2.60206i −0.0747422 + 0.129457i
\(405\) 0 0
\(406\) −8.90002 13.1025i −0.441701 0.650268i
\(407\) −0.0255565 0.0442652i −0.00126679 0.00219414i
\(408\) 0 0
\(409\) −11.3653 + 19.6853i −0.561980 + 0.973377i 0.435344 + 0.900264i \(0.356627\pi\)
−0.997324 + 0.0731132i \(0.976707\pi\)
\(410\) 2.08503 3.61138i 0.102972 0.178353i
\(411\) 0 0
\(412\) −4.12788 7.14970i −0.203366 0.352240i
\(413\) −18.4609 + 1.35136i −0.908402 + 0.0664963i
\(414\) 0 0
\(415\) −5.58963 + 9.68152i −0.274384 + 0.475247i
\(416\) 3.53204 0.724375i 0.173172 0.0355154i
\(417\) 0 0
\(418\) −0.0629697 0.109067i −0.00307995 0.00533462i
\(419\) 11.4491 19.8303i 0.559323 0.968776i −0.438230 0.898863i \(-0.644394\pi\)
0.997553 0.0699131i \(-0.0222722\pi\)
\(420\) 0 0
\(421\) 8.33173 0.406064 0.203032 0.979172i \(-0.434921\pi\)
0.203032 + 0.979172i \(0.434921\pi\)
\(422\) −5.99270 −0.291720
\(423\) 0 0
\(424\) 3.49556 + 6.05448i 0.169759 + 0.294032i
\(425\) 0.653727 0.0317104
\(426\) 0 0
\(427\) 0.554678 + 0.816593i 0.0268428 + 0.0395177i
\(428\) 4.47283 0.216202
\(429\) 0 0
\(430\) 2.52974 + 4.38163i 0.121995 + 0.211301i
\(431\) 27.5866 1.32880 0.664401 0.747376i \(-0.268687\pi\)
0.664401 + 0.747376i \(0.268687\pi\)
\(432\) 0 0
\(433\) −15.7254 27.2372i −0.755714 1.30893i −0.945019 0.327016i \(-0.893957\pi\)
0.189305 0.981918i \(-0.439376\pi\)
\(434\) 9.60745 0.703279i 0.461172 0.0337585i
\(435\) 0 0
\(436\) 7.67371 0.367504
\(437\) 0.0163418 + 0.0283048i 0.000781732 + 0.00135400i
\(438\) 0 0
\(439\) 7.62301 + 13.2034i 0.363827 + 0.630166i 0.988587 0.150650i \(-0.0481367\pi\)
−0.624760 + 0.780816i \(0.714803\pi\)
\(440\) −0.0859621 + 0.148891i −0.00409808 + 0.00709808i
\(441\) 0 0
\(442\) 0.446494 + 0.503076i 0.0212375 + 0.0239289i
\(443\) −10.7666 + 18.6482i −0.511535 + 0.886005i 0.488375 + 0.872634i \(0.337590\pi\)
−0.999911 + 0.0133713i \(0.995744\pi\)
\(444\) 0 0
\(445\) 7.77206 0.368431
\(446\) 27.6197 1.30783
\(447\) 0 0
\(448\) 1.48662 + 2.18860i 0.0702364 + 0.103401i
\(449\) −2.76290 4.78549i −0.130389 0.225841i 0.793437 0.608652i \(-0.208289\pi\)
−0.923827 + 0.382811i \(0.874956\pi\)
\(450\) 0 0
\(451\) 0.239646 0.415079i 0.0112845 0.0195453i
\(452\) −12.3644 −0.581575
\(453\) 0 0
\(454\) −1.79129 −0.0840694
\(455\) −8.36089 8.13727i −0.391965 0.381481i
\(456\) 0 0
\(457\) 16.0187 + 27.7451i 0.749321 + 1.29786i 0.948148 + 0.317828i \(0.102953\pi\)
−0.198827 + 0.980035i \(0.563713\pi\)
\(458\) 25.2285 1.17885
\(459\) 0 0
\(460\) 0.0223087 0.0386398i 0.00104015 0.00180159i
\(461\) 6.48516 + 11.2326i 0.302044 + 0.523156i 0.976599 0.215069i \(-0.0689977\pi\)
−0.674555 + 0.738225i \(0.735664\pi\)
\(462\) 0 0
\(463\) −11.6453 −0.541202 −0.270601 0.962692i \(-0.587222\pi\)
−0.270601 + 0.962692i \(0.587222\pi\)
\(464\) 5.98674 0.277927
\(465\) 0 0
\(466\) −28.3704 −1.31423
\(467\) −2.99029 + 5.17934i −0.138374 + 0.239671i −0.926881 0.375354i \(-0.877521\pi\)
0.788507 + 0.615026i \(0.210854\pi\)
\(468\) 0 0
\(469\) −7.22211 10.6323i −0.333486 0.490955i
\(470\) 0.438758 0.759952i 0.0202384 0.0350539i
\(471\) 0 0
\(472\) 3.49812 6.05892i 0.161014 0.278884i
\(473\) 0.290759 + 0.503609i 0.0133691 + 0.0231560i
\(474\) 0 0
\(475\) 1.56971 + 2.71882i 0.0720234 + 0.124748i
\(476\) −0.214926 + 0.444331i −0.00985109 + 0.0203659i
\(477\) 0 0
\(478\) 14.4827 + 25.0848i 0.662424 + 1.14735i
\(479\) −6.66159 −0.304376 −0.152188 0.988352i \(-0.548632\pi\)
−0.152188 + 0.988352i \(0.548632\pi\)
\(480\) 0 0
\(481\) −0.414038 + 1.24391i −0.0188785 + 0.0567175i
\(482\) 13.1951 0.601022
\(483\) 0 0
\(484\) 5.49012 9.50917i 0.249551 0.432235i
\(485\) −7.92673 −0.359934
\(486\) 0 0
\(487\) 9.46808 16.3992i 0.429039 0.743118i −0.567749 0.823202i \(-0.692185\pi\)
0.996788 + 0.0800838i \(0.0255188\pi\)
\(488\) −0.373113 −0.0168900
\(489\) 0 0
\(490\) 3.15532 7.95859i 0.142543 0.359532i
\(491\) 19.5234 33.8155i 0.881079 1.52607i 0.0309367 0.999521i \(-0.490151\pi\)
0.850143 0.526553i \(-0.176516\pi\)
\(492\) 0 0
\(493\) 0.558432 + 0.967232i 0.0251505 + 0.0435619i
\(494\) −1.02016 + 3.06492i −0.0458993 + 0.137897i
\(495\) 0 0
\(496\) −1.82050 + 3.15319i −0.0817427 + 0.141582i
\(497\) −12.2395 + 25.3036i −0.549018 + 1.13502i
\(498\) 0 0
\(499\) −16.6602 + 28.8563i −0.745812 + 1.29178i 0.204002 + 0.978970i \(0.434605\pi\)
−0.949814 + 0.312814i \(0.898728\pi\)
\(500\) 5.20046 9.00747i 0.232572 0.402826i
\(501\) 0 0
\(502\) 4.73276 8.19739i 0.211234 0.365867i
\(503\) −5.86768 10.1631i −0.261627 0.453151i 0.705048 0.709160i \(-0.250926\pi\)
−0.966674 + 0.256009i \(0.917592\pi\)
\(504\) 0 0
\(505\) −1.83737 + 3.18242i −0.0817618 + 0.141616i
\(506\) 0.00256408 0.00444112i 0.000113987 0.000197432i
\(507\) 0 0
\(508\) −5.45432 9.44716i −0.241996 0.419150i
\(509\) −17.3265 30.0103i −0.767982 1.33018i −0.938656 0.344856i \(-0.887928\pi\)
0.170674 0.985328i \(-0.445406\pi\)
\(510\) 0 0
\(511\) 11.0806 22.9077i 0.490176 1.01338i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 5.11789 8.86444i 0.225740 0.390994i
\(515\) −5.04855 8.74434i −0.222466 0.385322i
\(516\) 0 0
\(517\) 0.0504293 0.0873461i 0.00221788 0.00384148i
\(518\) −0.959451 + 0.0702331i −0.0421559 + 0.00308587i
\(519\) 0 0
\(520\) 4.31981 0.885937i 0.189436 0.0388509i
\(521\) −2.62165 4.54083i −0.114856 0.198937i 0.802866 0.596160i \(-0.203307\pi\)
−0.917722 + 0.397222i \(0.869974\pi\)
\(522\) 0 0
\(523\) 7.99001 + 13.8391i 0.349379 + 0.605142i 0.986139 0.165920i \(-0.0530594\pi\)
−0.636761 + 0.771062i \(0.719726\pi\)
\(524\) 10.9715 + 19.0032i 0.479291 + 0.830157i
\(525\) 0 0
\(526\) 2.42308 + 4.19690i 0.105651 + 0.182994i
\(527\) −0.679250 −0.0295886
\(528\) 0 0
\(529\) 11.4993 19.9174i 0.499971 0.865975i
\(530\) 4.27519 + 7.40485i 0.185703 + 0.321646i
\(531\) 0 0
\(532\) −2.36403 + 0.173050i −0.102494 + 0.00750267i
\(533\) −12.0428 + 2.46982i −0.521632 + 0.106980i
\(534\) 0 0
\(535\) 5.47043 0.236507
\(536\) 4.85806 0.209836
\(537\) 0 0
\(538\) −0.897277 −0.0386843
\(539\) 0.362661 0.914732i 0.0156209 0.0394003i
\(540\) 0 0
\(541\) −0.886405 + 1.53530i −0.0381095 + 0.0660077i −0.884451 0.466633i \(-0.845467\pi\)
0.846342 + 0.532641i \(0.178800\pi\)
\(542\) 6.93756 12.0162i 0.297994 0.516140i
\(543\) 0 0
\(544\) −0.0932782 0.161563i −0.00399927 0.00692694i
\(545\) 9.38523 0.402019
\(546\) 0 0
\(547\) 9.88287 0.422561 0.211280 0.977425i \(-0.432237\pi\)
0.211280 + 0.977425i \(0.432237\pi\)
\(548\) 1.34605 + 2.33143i 0.0575005 + 0.0995938i
\(549\) 0 0
\(550\) 0.246294 0.426594i 0.0105020 0.0181900i
\(551\) −2.68179 + 4.64499i −0.114248 + 0.197883i
\(552\) 0 0
\(553\) −15.5597 + 1.13899i −0.661666 + 0.0484348i
\(554\) 20.4739 0.869852
\(555\) 0 0
\(556\) −10.5785 −0.448629
\(557\) −20.1731 −0.854760 −0.427380 0.904072i \(-0.640563\pi\)
−0.427380 + 0.904072i \(0.640563\pi\)
\(558\) 0 0
\(559\) 4.71055 14.1521i 0.199235 0.598571i
\(560\) 1.81820 + 2.67673i 0.0768328 + 0.113113i
\(561\) 0 0
\(562\) −2.55910 4.43249i −0.107949 0.186973i
\(563\) −0.0531484 + 0.0920558i −0.00223994 + 0.00387969i −0.867143 0.498059i \(-0.834046\pi\)
0.864903 + 0.501939i \(0.167380\pi\)
\(564\) 0 0
\(565\) −15.1222 −0.636195
\(566\) 4.54066 + 7.86466i 0.190858 + 0.330576i
\(567\) 0 0
\(568\) −5.31198 9.20062i −0.222886 0.386050i
\(569\) −3.83091 6.63533i −0.160600 0.278167i 0.774484 0.632593i \(-0.218010\pi\)
−0.935084 + 0.354426i \(0.884676\pi\)
\(570\) 0 0
\(571\) −1.44075 2.49545i −0.0602935 0.104431i 0.834303 0.551306i \(-0.185870\pi\)
−0.894597 + 0.446875i \(0.852537\pi\)
\(572\) 0.496504 0.101826i 0.0207599 0.00425758i
\(573\) 0 0
\(574\) −5.06878 7.46222i −0.211567 0.311467i
\(575\) −0.0639177 + 0.110709i −0.00266555 + 0.00461687i
\(576\) 0 0
\(577\) 17.3055 + 29.9740i 0.720438 + 1.24783i 0.960825 + 0.277157i \(0.0893923\pi\)
−0.240387 + 0.970677i \(0.577274\pi\)
\(578\) −8.48260 + 14.6923i −0.352830 + 0.611119i
\(579\) 0 0
\(580\) 7.32200 0.304029
\(581\) 13.5886 + 20.0050i 0.563750 + 0.829948i
\(582\) 0 0
\(583\) 0.491375 + 0.851087i 0.0203507 + 0.0352484i
\(584\) 4.80900 + 8.32943i 0.198998 + 0.344674i
\(585\) 0 0
\(586\) 3.13195 5.42469i 0.129380 0.224092i
\(587\) 5.21346 9.02999i 0.215183 0.372707i −0.738146 0.674641i \(-0.764299\pi\)
0.953329 + 0.301933i \(0.0976320\pi\)
\(588\) 0 0
\(589\) −1.63100 2.82497i −0.0672041 0.116401i
\(590\) 4.27833 7.41029i 0.176136 0.305077i
\(591\) 0 0
\(592\) 0.181804 0.314894i 0.00747211 0.0129421i
\(593\) −10.9551 + 18.9748i −0.449873 + 0.779203i −0.998377 0.0569451i \(-0.981864\pi\)
0.548505 + 0.836148i \(0.315197\pi\)
\(594\) 0 0
\(595\) −0.262862 + 0.543433i −0.0107763 + 0.0222786i
\(596\) −5.95244 + 10.3099i −0.243822 + 0.422311i
\(597\) 0 0
\(598\) −0.128852 + 0.0264258i −0.00526913 + 0.00108063i
\(599\) 7.67924 + 13.3008i 0.313765 + 0.543457i 0.979174 0.203022i \(-0.0650762\pi\)
−0.665409 + 0.746479i \(0.731743\pi\)
\(600\) 0 0
\(601\) 1.63801 2.83711i 0.0668157 0.115728i −0.830682 0.556747i \(-0.812049\pi\)
0.897498 + 0.441019i \(0.145383\pi\)
\(602\) 10.9158 0.799049i 0.444893 0.0325668i
\(603\) 0 0
\(604\) 7.33549 0.298477
\(605\) 6.71462 11.6301i 0.272988 0.472829i
\(606\) 0 0
\(607\) 33.1535 1.34566 0.672830 0.739797i \(-0.265078\pi\)
0.672830 + 0.739797i \(0.265078\pi\)
\(608\) 0.447955 0.775880i 0.0181670 0.0314661i
\(609\) 0 0
\(610\) −0.456331 −0.0184763
\(611\) −2.53420 + 0.519731i −0.102523 + 0.0210261i
\(612\) 0 0
\(613\) −34.3585 −1.38773 −0.693863 0.720107i \(-0.744093\pi\)
−0.693863 + 0.720107i \(0.744093\pi\)
\(614\) 15.0403 + 26.0506i 0.606977 + 1.05132i
\(615\) 0 0
\(616\) 0.208977 + 0.307654i 0.00841992 + 0.0123957i
\(617\) 10.2155 + 17.6938i 0.411261 + 0.712325i 0.995028 0.0995961i \(-0.0317551\pi\)
−0.583767 + 0.811921i \(0.698422\pi\)
\(618\) 0 0
\(619\) −6.14114 10.6368i −0.246833 0.427528i 0.715812 0.698293i \(-0.246057\pi\)
−0.962645 + 0.270765i \(0.912723\pi\)
\(620\) −2.22653 + 3.85647i −0.0894197 + 0.154880i
\(621\) 0 0
\(622\) −13.8292 + 23.9528i −0.554499 + 0.960420i
\(623\) 7.32107 15.1354i 0.293312 0.606386i
\(624\) 0 0
\(625\) −2.40009 + 4.15708i −0.0960036 + 0.166283i
\(626\) −6.86004 −0.274182
\(627\) 0 0
\(628\) −10.3028 −0.411125
\(629\) 0.0678335 0.00270470
\(630\) 0 0
\(631\) −0.272895 0.472667i −0.0108638 0.0188166i 0.860542 0.509379i \(-0.170125\pi\)
−0.871406 + 0.490562i \(0.836791\pi\)
\(632\) 2.94837 5.10673i 0.117280 0.203135i
\(633\) 0 0
\(634\) −6.74291 −0.267795
\(635\) −6.67084 11.5542i −0.264724 0.458516i
\(636\) 0 0
\(637\) −23.7223 + 8.61698i −0.939912 + 0.341417i
\(638\) 0.841564 0.0333178
\(639\) 0 0
\(640\) −1.22304 −0.0483448
\(641\) −18.0298 + 31.2286i −0.712136 + 1.23346i 0.251918 + 0.967749i \(0.418939\pi\)
−0.964054 + 0.265707i \(0.914395\pi\)
\(642\) 0 0
\(643\) 13.7343 + 23.7885i 0.541627 + 0.938125i 0.998811 + 0.0487529i \(0.0155247\pi\)
−0.457184 + 0.889372i \(0.651142\pi\)
\(644\) −0.0542333 0.0798418i −0.00213709 0.00314621i
\(645\) 0 0
\(646\) 0.167138 0.00657594
\(647\) −6.14160 −0.241451 −0.120726 0.992686i \(-0.538522\pi\)
−0.120726 + 0.992686i \(0.538522\pi\)
\(648\) 0 0
\(649\) 0.491736 0.851712i 0.0193023 0.0334326i
\(650\) −12.3769 + 2.53834i −0.485462 + 0.0995619i
\(651\) 0 0
\(652\) 5.06852 8.77893i 0.198498 0.343809i
\(653\) −12.1803 21.0969i −0.476652 0.825585i 0.522990 0.852339i \(-0.324816\pi\)
−0.999642 + 0.0267533i \(0.991483\pi\)
\(654\) 0 0
\(655\) 13.4185 + 23.2416i 0.524305 + 0.908123i
\(656\) 3.40959 0.133122
\(657\) 0 0
\(658\) −1.06664 1.57029i −0.0415818 0.0612165i
\(659\) −5.44539 9.43169i −0.212122 0.367407i 0.740256 0.672325i \(-0.234704\pi\)
−0.952379 + 0.304918i \(0.901371\pi\)
\(660\) 0 0
\(661\) −37.2725 −1.44973 −0.724866 0.688889i \(-0.758099\pi\)
−0.724866 + 0.688889i \(0.758099\pi\)
\(662\) −5.54908 9.61129i −0.215671 0.373553i
\(663\) 0 0
\(664\) −9.14057 −0.354723
\(665\) −2.89129 + 0.211647i −0.112120 + 0.00820731i
\(666\) 0 0
\(667\) −0.218401 −0.00845652
\(668\) 4.28857 + 7.42802i 0.165930 + 0.287399i
\(669\) 0 0
\(670\) 5.94159 0.229544
\(671\) −0.0524490 −0.00202477
\(672\) 0 0
\(673\) −21.9417 + 38.0042i −0.845792 + 1.46495i 0.0391397 + 0.999234i \(0.487538\pi\)
−0.884932 + 0.465721i \(0.845795\pi\)
\(674\) 10.8235 + 18.7468i 0.416905 + 0.722100i
\(675\) 0 0
\(676\) −10.4068 7.79097i −0.400260 0.299653i
\(677\) 20.6518 35.7700i 0.793713 1.37475i −0.129940 0.991522i \(-0.541478\pi\)
0.923653 0.383230i \(-0.125188\pi\)
\(678\) 0 0
\(679\) −7.46677 + 15.4366i −0.286548 + 0.592402i
\(680\) −0.114083 0.197597i −0.00437487 0.00757750i
\(681\) 0 0
\(682\) −0.255910 + 0.443249i −0.00979929 + 0.0169729i
\(683\) 13.7908 23.8864i 0.527690 0.913987i −0.471789 0.881712i \(-0.656391\pi\)
0.999479 0.0322749i \(-0.0102752\pi\)
\(684\) 0 0
\(685\) 1.64627 + 2.85143i 0.0629008 + 0.108947i
\(686\) −12.5264 13.6415i −0.478260 0.520833i
\(687\) 0 0
\(688\) −2.06841 + 3.58258i −0.0788572 + 0.136585i
\(689\) 7.96072 23.9167i 0.303279 0.911155i
\(690\) 0 0
\(691\) −14.6997 25.4606i −0.559202 0.968566i −0.997563 0.0697671i \(-0.977774\pi\)
0.438362 0.898799i \(-0.355559\pi\)
\(692\) −5.33942 + 9.24815i −0.202974 + 0.351562i
\(693\) 0 0
\(694\) 29.8675 1.13375
\(695\) −12.9379 −0.490763
\(696\) 0 0
\(697\) 0.318041 + 0.550863i 0.0120466 + 0.0208654i
\(698\) −12.9538 −0.490308
\(699\) 0 0
\(700\) −5.20940 7.66923i −0.196897 0.289870i
\(701\) −19.0498 −0.719500 −0.359750 0.933049i \(-0.617138\pi\)
−0.359750 + 0.933049i \(0.617138\pi\)
\(702\) 0 0
\(703\) 0.162880 + 0.282117i 0.00614314 + 0.0106402i
\(704\) −0.140571 −0.00529799
\(705\) 0 0
\(706\) −3.07853 5.33218i −0.115862 0.200679i
\(707\) 4.46671 + 6.57585i 0.167988 + 0.247310i
\(708\) 0 0
\(709\) 17.9056 0.672460 0.336230 0.941780i \(-0.390848\pi\)
0.336230 + 0.941780i \(0.390848\pi\)
\(710\) −6.49675 11.2527i −0.243819 0.422306i
\(711\) 0 0
\(712\) 3.17736 + 5.50335i 0.119077 + 0.206247i
\(713\) 0.0664132 0.115031i 0.00248719 0.00430794i
\(714\) 0 0
\(715\) 0.607242 0.124538i 0.0227096 0.00465744i
\(716\) −6.48961 + 11.2403i −0.242528 + 0.420071i
\(717\) 0 0
\(718\) −24.8405 −0.927039
\(719\) −34.3166 −1.27979 −0.639897 0.768461i \(-0.721023\pi\)
−0.639897 + 0.768461i \(0.721023\pi\)
\(720\) 0 0
\(721\) −21.7844 + 1.59465i −0.811293 + 0.0593878i
\(722\) −9.09867 15.7594i −0.338618 0.586503i
\(723\) 0 0
\(724\) −11.8663 + 20.5531i −0.441009 + 0.763849i
\(725\) −20.9786 −0.779126
\(726\) 0 0
\(727\) 20.6482 0.765800 0.382900 0.923790i \(-0.374925\pi\)
0.382900 + 0.923790i \(0.374925\pi\)
\(728\) 2.34386 9.24696i 0.0868694 0.342715i
\(729\) 0 0
\(730\) 5.88158 + 10.1872i 0.217687 + 0.377045i
\(731\) −0.771748 −0.0285441
\(732\) 0 0
\(733\) 14.5834 25.2592i 0.538650 0.932969i −0.460327 0.887749i \(-0.652268\pi\)
0.998977 0.0452199i \(-0.0143988\pi\)
\(734\) 18.0306 + 31.2299i 0.665521 + 1.15272i
\(735\) 0 0
\(736\) 0.0364808 0.00134470
\(737\) 0.682905 0.0251551
\(738\) 0 0
\(739\) −42.2160 −1.55294 −0.776471 0.630153i \(-0.782992\pi\)
−0.776471 + 0.630153i \(0.782992\pi\)
\(740\) 0.222353 0.385127i 0.00817387 0.0141576i
\(741\) 0 0
\(742\) 18.4474 1.35037i 0.677225 0.0495738i
\(743\) −8.87311 + 15.3687i −0.325523 + 0.563822i −0.981618 0.190856i \(-0.938874\pi\)
0.656095 + 0.754678i \(0.272207\pi\)
\(744\) 0 0
\(745\) −7.28006 + 12.6094i −0.266721 + 0.461974i
\(746\) −7.37092 12.7668i −0.269869 0.467426i
\(747\) 0 0
\(748\) −0.0131122 0.0227111i −0.000479431 0.000830399i
\(749\) 5.15300 10.6532i 0.188287 0.389258i
\(750\) 0 0
\(751\) −15.6637 27.1303i −0.571576 0.989998i −0.996404 0.0847243i \(-0.972999\pi\)
0.424829 0.905274i \(-0.360334\pi\)
\(752\) 0.717490 0.0261642
\(753\) 0 0
\(754\) −14.3283 16.1441i −0.521807 0.587934i
\(755\) 8.97157 0.326509
\(756\) 0 0
\(757\) 12.9370 22.4076i 0.470204 0.814417i −0.529216 0.848487i \(-0.677514\pi\)
0.999419 + 0.0340705i \(0.0108471\pi\)
\(758\) 10.6735 0.387679
\(759\) 0 0
\(760\) 0.547865 0.948930i 0.0198732 0.0344213i
\(761\) 0.955383 0.0346326 0.0173163 0.999850i \(-0.494488\pi\)
0.0173163 + 0.999850i \(0.494488\pi\)
\(762\) 0 0
\(763\) 8.84063 18.2769i 0.320052 0.661667i
\(764\) −9.98892 + 17.3013i −0.361387 + 0.625940i
\(765\) 0 0
\(766\) 10.2017 + 17.6698i 0.368601 + 0.638436i
\(767\) −24.7110 + 5.06790i −0.892261 + 0.182991i
\(768\) 0 0
\(769\) 0.0702857 0.121738i 0.00253457 0.00439000i −0.864755 0.502193i \(-0.832527\pi\)
0.867290 + 0.497803i \(0.165860\pi\)
\(770\) 0.255586 + 0.376272i 0.00921070 + 0.0135599i
\(771\) 0 0
\(772\) 3.11194 5.39003i 0.112001 0.193992i
\(773\) 8.17360 14.1571i 0.293984 0.509195i −0.680764 0.732503i \(-0.738352\pi\)
0.974748 + 0.223308i \(0.0716854\pi\)
\(774\) 0 0
\(775\) 6.37934 11.0493i 0.229153 0.396904i
\(776\) −3.24059 5.61287i −0.116331 0.201490i
\(777\) 0 0
\(778\) −15.8455 + 27.4453i −0.568090 + 0.983960i
\(779\) −1.52734 + 2.64544i −0.0547228 + 0.0947826i
\(780\) 0 0
\(781\) −0.746713 1.29335i −0.0267195 0.0462795i
\(782\) 0.00340286 + 0.00589393i 0.000121686 + 0.000210767i
\(783\) 0 0
\(784\) 6.92538 1.01936i 0.247335 0.0364056i
\(785\) −12.6007 −0.449737
\(786\) 0 0
\(787\) −17.8553 + 30.9262i −0.636471 + 1.10240i 0.349730 + 0.936850i \(0.386273\pi\)
−0.986201 + 0.165550i \(0.947060\pi\)
\(788\) −12.2503 21.2182i −0.436400 0.755866i
\(789\) 0 0
\(790\) 3.60597 6.24573i 0.128295 0.222213i
\(791\) −14.2447 + 29.4490i −0.506483 + 1.04709i
\(792\) 0 0
\(793\) 0.892987 + 1.00615i 0.0317109 + 0.0357295i
\(794\) −1.30524 2.26074i −0.0463212 0.0802306i
\(795\) 0 0
\(796\) 9.80754 + 16.9872i 0.347619 + 0.602094i
\(797\) −2.01756 3.49451i −0.0714655 0.123782i 0.828078 0.560612i \(-0.189434\pi\)
−0.899544 + 0.436831i \(0.856101\pi\)
\(798\) 0 0
\(799\) 0.0669261 + 0.115919i 0.00236768 + 0.00410093i
\(800\) 3.50418 0.123891
\(801\) 0 0
\(802\) 8.18479 14.1765i 0.289015 0.500588i
\(803\) 0.676008 + 1.17088i 0.0238558 + 0.0413195i
\(804\) 0 0
\(805\) −0.0663293 0.0976495i −0.00233780 0.00344169i
\(806\) 12.8601 2.63744i 0.452978 0.0928999i
\(807\) 0 0
\(808\) −3.00460 −0.105701
\(809\) 27.9567 0.982904 0.491452 0.870905i \(-0.336466\pi\)
0.491452 + 0.870905i \(0.336466\pi\)
\(810\) 0 0
\(811\) 49.6578 1.74372 0.871861 0.489754i \(-0.162913\pi\)
0.871861 + 0.489754i \(0.162913\pi\)
\(812\) 6.89712 14.2589i 0.242042 0.500390i
\(813\) 0 0
\(814\) 0.0255565 0.0442652i 0.000895755 0.00155149i
\(815\) 6.19898 10.7370i 0.217141 0.376099i
\(816\) 0 0
\(817\) −1.85310 3.20967i −0.0648319 0.112292i
\(818\) −22.7307 −0.794759
\(819\) 0 0
\(820\) 4.17006 0.145625
\(821\) −20.3635 35.2705i −0.710690 1.23095i −0.964599 0.263722i \(-0.915050\pi\)
0.253909 0.967228i \(-0.418284\pi\)
\(822\) 0 0
\(823\) 26.8315 46.4735i 0.935288 1.61997i 0.161167 0.986927i \(-0.448474\pi\)
0.774120 0.633038i \(-0.218192\pi\)
\(824\) 4.12788 7.14970i 0.143801 0.249071i
\(825\) 0 0
\(826\) −10.4008 15.3119i −0.361889 0.532770i
\(827\) −55.5393 −1.93129 −0.965646 0.259862i \(-0.916323\pi\)
−0.965646 + 0.259862i \(0.916323\pi\)
\(828\) 0 0
\(829\) −33.2943 −1.15636 −0.578180 0.815909i \(-0.696237\pi\)
−0.578180 + 0.815909i \(0.696237\pi\)
\(830\) −11.1793 −0.388038
\(831\) 0 0
\(832\) 2.39335 + 2.69665i 0.0829743 + 0.0934894i
\(833\) 0.810677 + 1.02380i 0.0280883 + 0.0354725i
\(834\) 0 0
\(835\) 5.24508 + 9.08475i 0.181514 + 0.314391i
\(836\) 0.0629697 0.109067i 0.00217785 0.00377215i
\(837\) 0 0
\(838\) 22.8981 0.791002
\(839\) −2.98552 5.17107i −0.103072 0.178525i 0.809877 0.586600i \(-0.199534\pi\)
−0.912949 + 0.408074i \(0.866200\pi\)
\(840\) 0 0
\(841\) −3.42050 5.92448i −0.117948 0.204292i
\(842\) 4.16586 + 7.21549i 0.143565 + 0.248662i
\(843\) 0 0
\(844\) −2.99635 5.18983i −0.103139 0.178641i
\(845\) −12.7279 9.52865i −0.437852 0.327795i
\(846\) 0 0
\(847\) −16.3235 24.0313i −0.560881 0.825725i
\(848\) −3.49556 + 6.05448i −0.120038 + 0.207912i
\(849\) 0 0
\(850\) 0.326863 + 0.566144i 0.0112113 + 0.0194186i
\(851\) −0.00663237 + 0.0114876i −0.000227355 + 0.000393790i
\(852\) 0 0
\(853\) −24.0993 −0.825143 −0.412572 0.910925i \(-0.635369\pi\)
−0.412572 + 0.910925i \(0.635369\pi\)
\(854\) −0.429851 + 0.888662i −0.0147092 + 0.0304094i
\(855\) 0 0
\(856\) 2.23641 + 3.87358i 0.0764390 + 0.132396i
\(857\) −0.639263 1.10724i −0.0218368 0.0378225i 0.854900 0.518792i \(-0.173618\pi\)
−0.876737 + 0.480970i \(0.840285\pi\)
\(858\) 0 0
\(859\) −3.92591 + 6.79988i −0.133950 + 0.232009i −0.925196 0.379490i \(-0.876100\pi\)
0.791246 + 0.611498i \(0.209433\pi\)
\(860\) −2.52974 + 4.38163i −0.0862633 + 0.149412i
\(861\) 0 0
\(862\) 13.7933 + 23.8907i 0.469802 + 0.813722i
\(863\) −19.2024 + 33.2595i −0.653656 + 1.13217i 0.328573 + 0.944479i \(0.393432\pi\)
−0.982229 + 0.187687i \(0.939901\pi\)
\(864\) 0 0
\(865\) −6.53031 + 11.3108i −0.222037 + 0.384580i
\(866\) 15.7254 27.2372i 0.534370 0.925556i
\(867\) 0 0
\(868\) 5.41278 + 7.96866i 0.183722 + 0.270474i
\(869\) 0.414457 0.717861i 0.0140595 0.0243518i
\(870\) 0 0
\(871\) −11.6270 13.1005i −0.393966 0.443892i
\(872\) 3.83686 + 6.64563i 0.129932 + 0.225049i
\(873\) 0 0
\(874\) −0.0163418 + 0.0283048i −0.000552768 + 0.000957423i
\(875\) −15.4623 22.7634i −0.522720 0.769544i
\(876\) 0 0
\(877\) 19.1059 0.645161 0.322580 0.946542i \(-0.395450\pi\)
0.322580 + 0.946542i \(0.395450\pi\)
\(878\) −7.62301 + 13.2034i −0.257264 + 0.445595i
\(879\) 0 0
\(880\) −0.171924 −0.00579556
\(881\) −13.6438 + 23.6317i −0.459671 + 0.796173i −0.998943 0.0459583i \(-0.985366\pi\)
0.539273 + 0.842131i \(0.318699\pi\)
\(882\) 0 0
\(883\) 35.8526 1.20654 0.603268 0.797538i \(-0.293865\pi\)
0.603268 + 0.797538i \(0.293865\pi\)
\(884\) −0.212430 + 0.638213i −0.00714480 + 0.0214654i
\(885\) 0 0
\(886\) −21.5331 −0.723420
\(887\) −3.71928 6.44198i −0.124881 0.216300i 0.796805 0.604236i \(-0.206522\pi\)
−0.921686 + 0.387936i \(0.873188\pi\)
\(888\) 0 0
\(889\) −28.7845 + 2.10707i −0.965403 + 0.0706688i
\(890\) 3.88603 + 6.73080i 0.130260 + 0.225617i
\(891\) 0 0
\(892\) 13.8098 + 23.9193i 0.462388 + 0.800879i
\(893\) −0.321403 + 0.556686i −0.0107553 + 0.0186288i
\(894\) 0 0
\(895\) −7.93703 + 13.7473i −0.265306 + 0.459523i
\(896\) −1.15207 + 2.38175i −0.0384879 + 0.0795687i
\(897\) 0 0
\(898\) 2.76290 4.78549i 0.0921993 0.159694i
\(899\) 21.7976 0.726992
\(900\) 0 0
\(901\) −1.30424 −0.0434504
\(902\) 0.479292 0.0159587
\(903\) 0 0
\(904\) −6.18222 10.7079i −0.205618 0.356140i
\(905\) −14.5130 + 25.1372i −0.482427 + 0.835588i
\(906\) 0 0
\(907\) 7.29048 0.242076 0.121038 0.992648i \(-0.461378\pi\)
0.121038 + 0.992648i \(0.461378\pi\)
\(908\) −0.895645 1.55130i −0.0297230 0.0514818i
\(909\) 0 0
\(910\) 2.86663 11.3094i 0.0950280 0.374902i
\(911\) −8.89914 −0.294842 −0.147421 0.989074i \(-0.547097\pi\)
−0.147421 + 0.989074i \(0.547097\pi\)
\(912\) 0 0
\(913\) −1.28490 −0.0425241
\(914\) −16.0187 + 27.7451i −0.529850 + 0.917727i
\(915\) 0 0
\(916\) 12.6142 + 21.8485i 0.416786 + 0.721895i
\(917\) 57.9007 4.23841i 1.91205 0.139965i
\(918\) 0 0
\(919\) −7.26977 −0.239808 −0.119904 0.992786i \(-0.538259\pi\)
−0.119904 + 0.992786i \(0.538259\pi\)
\(920\) 0.0446174 0.00147099
\(921\) 0 0
\(922\) −6.48516 + 11.2326i −0.213577 + 0.369927i
\(923\) −12.0974 + 36.3448i −0.398191 + 1.19630i
\(924\) 0 0
\(925\) −0.637075 + 1.10345i −0.0209469 + 0.0362811i
\(926\) −5.82264 10.0851i −0.191344 0.331417i
\(927\) 0 0
\(928\) 2.99337 + 5.18466i 0.0982621 + 0.170195i
\(929\) −6.60933 −0.216845 −0.108423 0.994105i \(-0.534580\pi\)
−0.108423 + 0.994105i \(0.534580\pi\)
\(930\) 0 0
\(931\) −2.31136 + 5.82989i −0.0757517 + 0.191067i
\(932\) −14.1852 24.5695i −0.464652 0.804801i
\(933\) 0 0
\(934\) −5.98058 −0.195691
\(935\) −0.0160368 0.0277765i −0.000524458 0.000908389i
\(936\) 0 0
\(937\) −44.3217 −1.44793 −0.723963 0.689838i \(-0.757682\pi\)
−0.723963 + 0.689838i \(0.757682\pi\)
\(938\) 5.59682 11.5707i 0.182742 0.377797i
\(939\) 0 0
\(940\) 0.877516 0.0286214
\(941\) −8.06612 13.9709i −0.262948 0.455440i 0.704076 0.710125i \(-0.251361\pi\)
−0.967024 + 0.254685i \(0.918028\pi\)
\(942\) 0 0
\(943\) −0.124385 −0.00405053
\(944\) 6.99624 0.227708
\(945\) 0 0
\(946\) −0.290759 + 0.503609i −0.00945338 + 0.0163737i
\(947\) 3.98244 + 6.89779i 0.129412 + 0.224148i 0.923449 0.383721i \(-0.125358\pi\)
−0.794037 + 0.607870i \(0.792024\pi\)
\(948\) 0 0
\(949\) 10.9519 32.9034i 0.355515 1.06809i
\(950\) −1.56971 + 2.71882i −0.0509282 + 0.0882103i
\(951\) 0 0
\(952\) −0.492265 + 0.0360344i −0.0159544 + 0.00116788i
\(953\) −21.7224 37.6243i −0.703658 1.21877i −0.967174 0.254116i \(-0.918215\pi\)
0.263516 0.964655i \(-0.415118\pi\)
\(954\) 0 0
\(955\) −12.2168 + 21.1602i −0.395327 + 0.684727i
\(956\) −14.4827 + 25.0848i −0.468404 + 0.811300i
\(957\) 0 0
\(958\) −3.33079 5.76911i −0.107613 0.186391i
\(959\) 7.10363 0.519996i 0.229388 0.0167915i
\(960\) 0 0
\(961\) 8.87159 15.3660i 0.286180 0.495679i
\(962\) −1.28428 + 0.263389i −0.0414068 + 0.00849200i
\(963\) 0 0
\(964\) 6.59757 + 11.4273i 0.212493 + 0.368049i
\(965\) 3.80602 6.59221i 0.122520 0.212211i
\(966\) 0 0
\(967\) −8.68636 −0.279335 −0.139667 0.990198i \(-0.544603\pi\)
−0.139667 + 0.990198i \(0.544603\pi\)
\(968\) 10.9802 0.352918
\(969\) 0 0
\(970\) −3.96337 6.86475i −0.127256 0.220414i
\(971\) −27.8030 −0.892241 −0.446120 0.894973i \(-0.647195\pi\)
−0.446120 + 0.894973i \(0.647195\pi\)
\(972\) 0 0
\(973\) −12.1872 + 25.1954i −0.390702 + 0.807727i
\(974\) 18.9362 0.606753
\(975\) 0 0
\(976\) −0.186556 0.323125i −0.00597152 0.0103430i
\(977\) 42.2796 1.35264 0.676322 0.736606i \(-0.263573\pi\)
0.676322 + 0.736606i \(0.263573\pi\)
\(978\) 0 0
\(979\) 0.446646 + 0.773614i 0.0142749 + 0.0247248i
\(980\) 8.47000 1.24671i 0.270564 0.0398247i
\(981\) 0 0
\(982\) 39.0468 1.24603
\(983\) 20.5285 + 35.5564i 0.654757 + 1.13407i 0.981955 + 0.189117i \(0.0605626\pi\)
−0.327197 + 0.944956i \(0.606104\pi\)
\(984\) 0 0
\(985\) −14.9826 25.9506i −0.477385 0.826856i
\(986\) −0.558432 + 0.967232i −0.0177841 + 0.0308029i
\(987\) 0 0
\(988\) −3.16438 + 0.648974i −0.100672 + 0.0206466i
\(989\) 0.0754571 0.130696i 0.00239940 0.00415588i
\(990\) 0 0
\(991\) −27.5175 −0.874122 −0.437061 0.899432i \(-0.643981\pi\)
−0.437061 + 0.899432i \(0.643981\pi\)
\(992\) −3.64099 −0.115602
\(993\) 0 0
\(994\) −28.0334 + 2.05208i −0.889164 + 0.0650881i
\(995\) 11.9950 + 20.7759i 0.380267 + 0.658641i
\(996\) 0 0
\(997\) −18.4340 + 31.9286i −0.583810 + 1.01119i 0.411213 + 0.911539i \(0.365105\pi\)
−0.995023 + 0.0996486i \(0.968228\pi\)
\(998\) −33.3204 −1.05474
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1638.2.p.h.919.2 8
3.2 odd 2 546.2.k.c.373.3 yes 8
7.4 even 3 1638.2.m.h.1621.2 8
13.3 even 3 1638.2.m.h.289.2 8
21.11 odd 6 546.2.j.c.529.3 yes 8
39.29 odd 6 546.2.j.c.289.3 8
91.81 even 3 inner 1638.2.p.h.991.2 8
273.263 odd 6 546.2.k.c.445.3 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.j.c.289.3 8 39.29 odd 6
546.2.j.c.529.3 yes 8 21.11 odd 6
546.2.k.c.373.3 yes 8 3.2 odd 2
546.2.k.c.445.3 yes 8 273.263 odd 6
1638.2.m.h.289.2 8 13.3 even 3
1638.2.m.h.1621.2 8 7.4 even 3
1638.2.p.h.919.2 8 1.1 even 1 trivial
1638.2.p.h.991.2 8 91.81 even 3 inner