Properties

Label 1386.2.bk.d.901.2
Level $1386$
Weight $2$
Character 1386.901
Analytic conductor $11.067$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1386,2,Mod(703,1386)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 1, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1386.703");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.bk (of order \(6\), 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: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 901.2
Character \(\chi\) \(=\) 1386.901
Dual form 1386.2.bk.d.703.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.194145 + 0.112089i) q^{5} +(-2.62785 + 0.307218i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.194145 + 0.112089i) q^{5} +(-2.62785 + 0.307218i) q^{7} -1.00000i q^{8} +(-0.112089 - 0.194145i) q^{10} +(-1.73915 + 2.82407i) q^{11} -5.03153 q^{13} +(2.42940 + 1.04787i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.92826 + 6.80394i) q^{17} +(3.66573 - 6.34924i) q^{19} +0.224179i q^{20} +(2.91818 - 1.57614i) q^{22} +(2.42940 - 4.20784i) q^{23} +(-2.47487 - 4.28660i) q^{25} +(4.35743 + 2.51576i) q^{26} +(-1.57999 - 2.12218i) q^{28} -5.65814i q^{29} +(3.73996 - 2.15927i) q^{31} +(0.866025 - 0.500000i) q^{32} -7.85652i q^{34} +(-0.544620 - 0.234910i) q^{35} +(-0.0891097 + 0.154343i) q^{37} +(-6.34924 + 3.66573i) q^{38} +(0.112089 - 0.194145i) q^{40} -0.568932 q^{41} -6.39391i q^{43} +(-3.31529 - 0.0941129i) q^{44} +(-4.20784 + 2.42940i) q^{46} +(-2.93076 - 1.69208i) q^{47} +(6.81123 - 1.61465i) q^{49} +4.94974i q^{50} +(-2.51576 - 4.35743i) q^{52} +(1.07478 + 1.86157i) q^{53} +(-0.654195 + 0.353338i) q^{55} +(0.307218 + 2.62785i) q^{56} +(-2.82907 + 4.90010i) q^{58} +(2.00911 - 1.15996i) q^{59} +(2.19784 - 3.80677i) q^{61} -4.31854 q^{62} -1.00000 q^{64} +(-0.976845 - 0.563982i) q^{65} +(4.32907 + 7.49817i) q^{67} +(-3.92826 + 6.80394i) q^{68} +(0.354200 + 0.475748i) q^{70} +11.6958 q^{71} +(-5.25571 - 9.10315i) q^{73} +(0.154343 - 0.0891097i) q^{74} +7.33147 q^{76} +(3.70262 - 7.95554i) q^{77} +(-8.75195 - 5.05294i) q^{79} +(-0.194145 + 0.112089i) q^{80} +(0.492709 + 0.284466i) q^{82} +14.2897 q^{83} +1.76127i q^{85} +(-3.19696 + 5.53729i) q^{86} +(2.82407 + 1.73915i) q^{88} +(-9.10315 - 5.25571i) q^{89} +(13.2221 - 1.54578i) q^{91} +4.85879 q^{92} +(1.69208 + 2.93076i) q^{94} +(1.42337 - 0.821781i) q^{95} -3.96123i q^{97} +(-6.70603 - 2.00729i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 16 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 16 q^{4} - 16 q^{16} + 20 q^{22} + 36 q^{25} + 12 q^{31} - 20 q^{37} - 44 q^{49} - 32 q^{64} + 48 q^{67} + 36 q^{70} + 72 q^{82} + 10 q^{88} + 144 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0.194145 + 0.112089i 0.0868242 + 0.0501279i 0.542783 0.839873i \(-0.317370\pi\)
−0.455959 + 0.890001i \(0.650704\pi\)
\(6\) 0 0
\(7\) −2.62785 + 0.307218i −0.993235 + 0.116117i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −0.112089 0.194145i −0.0354458 0.0613939i
\(11\) −1.73915 + 2.82407i −0.524373 + 0.851489i
\(12\) 0 0
\(13\) −5.03153 −1.39550 −0.697748 0.716344i \(-0.745814\pi\)
−0.697748 + 0.716344i \(0.745814\pi\)
\(14\) 2.42940 + 1.04787i 0.649284 + 0.280055i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.92826 + 6.80394i 0.952743 + 1.65020i 0.739451 + 0.673210i \(0.235085\pi\)
0.213291 + 0.976989i \(0.431582\pi\)
\(18\) 0 0
\(19\) 3.66573 6.34924i 0.840977 1.45662i −0.0480924 0.998843i \(-0.515314\pi\)
0.889070 0.457772i \(-0.151352\pi\)
\(20\) 0.224179i 0.0501279i
\(21\) 0 0
\(22\) 2.91818 1.57614i 0.622158 0.336034i
\(23\) 2.42940 4.20784i 0.506564 0.877395i −0.493407 0.869799i \(-0.664249\pi\)
0.999971 0.00759654i \(-0.00241808\pi\)
\(24\) 0 0
\(25\) −2.47487 4.28660i −0.494974 0.857321i
\(26\) 4.35743 + 2.51576i 0.854563 + 0.493382i
\(27\) 0 0
\(28\) −1.57999 2.12218i −0.298589 0.401054i
\(29\) 5.65814i 1.05069i −0.850889 0.525345i \(-0.823936\pi\)
0.850889 0.525345i \(-0.176064\pi\)
\(30\) 0 0
\(31\) 3.73996 2.15927i 0.671717 0.387816i −0.125010 0.992155i \(-0.539896\pi\)
0.796727 + 0.604340i \(0.206563\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0 0
\(34\) 7.85652i 1.34738i
\(35\) −0.544620 0.234910i −0.0920576 0.0397071i
\(36\) 0 0
\(37\) −0.0891097 + 0.154343i −0.0146495 + 0.0253738i −0.873257 0.487259i \(-0.837997\pi\)
0.858608 + 0.512633i \(0.171330\pi\)
\(38\) −6.34924 + 3.66573i −1.02998 + 0.594661i
\(39\) 0 0
\(40\) 0.112089 0.194145i 0.0177229 0.0306970i
\(41\) −0.568932 −0.0888522 −0.0444261 0.999013i \(-0.514146\pi\)
−0.0444261 + 0.999013i \(0.514146\pi\)
\(42\) 0 0
\(43\) 6.39391i 0.975063i −0.873105 0.487531i \(-0.837897\pi\)
0.873105 0.487531i \(-0.162103\pi\)
\(44\) −3.31529 0.0941129i −0.499799 0.0141881i
\(45\) 0 0
\(46\) −4.20784 + 2.42940i −0.620412 + 0.358195i
\(47\) −2.93076 1.69208i −0.427495 0.246815i 0.270784 0.962640i \(-0.412717\pi\)
−0.698279 + 0.715826i \(0.746051\pi\)
\(48\) 0 0
\(49\) 6.81123 1.61465i 0.973033 0.230664i
\(50\) 4.94974i 0.699999i
\(51\) 0 0
\(52\) −2.51576 4.35743i −0.348874 0.604267i
\(53\) 1.07478 + 1.86157i 0.147632 + 0.255706i 0.930352 0.366668i \(-0.119502\pi\)
−0.782720 + 0.622374i \(0.786168\pi\)
\(54\) 0 0
\(55\) −0.654195 + 0.353338i −0.0882116 + 0.0476440i
\(56\) 0.307218 + 2.62785i 0.0410537 + 0.351162i
\(57\) 0 0
\(58\) −2.82907 + 4.90010i −0.371475 + 0.643414i
\(59\) 2.00911 1.15996i 0.261563 0.151014i −0.363484 0.931600i \(-0.618413\pi\)
0.625048 + 0.780587i \(0.285080\pi\)
\(60\) 0 0
\(61\) 2.19784 3.80677i 0.281404 0.487407i −0.690327 0.723498i \(-0.742533\pi\)
0.971731 + 0.236091i \(0.0758665\pi\)
\(62\) −4.31854 −0.548455
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −0.976845 0.563982i −0.121163 0.0699533i
\(66\) 0 0
\(67\) 4.32907 + 7.49817i 0.528880 + 0.916047i 0.999433 + 0.0336755i \(0.0107213\pi\)
−0.470553 + 0.882372i \(0.655945\pi\)
\(68\) −3.92826 + 6.80394i −0.476371 + 0.825099i
\(69\) 0 0
\(70\) 0.354200 + 0.475748i 0.0423349 + 0.0568628i
\(71\) 11.6958 1.38803 0.694015 0.719960i \(-0.255840\pi\)
0.694015 + 0.719960i \(0.255840\pi\)
\(72\) 0 0
\(73\) −5.25571 9.10315i −0.615134 1.06544i −0.990361 0.138511i \(-0.955769\pi\)
0.375227 0.926933i \(-0.377565\pi\)
\(74\) 0.154343 0.0891097i 0.0179420 0.0103588i
\(75\) 0 0
\(76\) 7.33147 0.840977
\(77\) 3.70262 7.95554i 0.421953 0.906618i
\(78\) 0 0
\(79\) −8.75195 5.05294i −0.984671 0.568500i −0.0809939 0.996715i \(-0.525809\pi\)
−0.903677 + 0.428214i \(0.859143\pi\)
\(80\) −0.194145 + 0.112089i −0.0217060 + 0.0125320i
\(81\) 0 0
\(82\) 0.492709 + 0.284466i 0.0544106 + 0.0314140i
\(83\) 14.2897 1.56849 0.784247 0.620448i \(-0.213049\pi\)
0.784247 + 0.620448i \(0.213049\pi\)
\(84\) 0 0
\(85\) 1.76127i 0.191036i
\(86\) −3.19696 + 5.53729i −0.344737 + 0.597102i
\(87\) 0 0
\(88\) 2.82407 + 1.73915i 0.301047 + 0.185394i
\(89\) −9.10315 5.25571i −0.964932 0.557104i −0.0672448 0.997737i \(-0.521421\pi\)
−0.897688 + 0.440633i \(0.854754\pi\)
\(90\) 0 0
\(91\) 13.2221 1.54578i 1.38606 0.162041i
\(92\) 4.85879 0.506564
\(93\) 0 0
\(94\) 1.69208 + 2.93076i 0.174524 + 0.302285i
\(95\) 1.42337 0.821781i 0.146034 0.0843129i
\(96\) 0 0
\(97\) 3.96123i 0.402202i −0.979571 0.201101i \(-0.935548\pi\)
0.979571 0.201101i \(-0.0644519\pi\)
\(98\) −6.70603 2.00729i −0.677411 0.202767i
\(99\) 0 0
\(100\) 2.47487 4.28660i 0.247487 0.428660i
\(101\) −3.38364 5.86063i −0.336685 0.583155i 0.647122 0.762386i \(-0.275972\pi\)
−0.983807 + 0.179231i \(0.942639\pi\)
\(102\) 0 0
\(103\) −12.4945 7.21371i −1.23112 0.710788i −0.263857 0.964562i \(-0.584995\pi\)
−0.967263 + 0.253774i \(0.918328\pi\)
\(104\) 5.03153i 0.493382i
\(105\) 0 0
\(106\) 2.14956i 0.208783i
\(107\) 14.9528 + 8.63301i 1.44554 + 0.834585i 0.998211 0.0597828i \(-0.0190408\pi\)
0.447332 + 0.894368i \(0.352374\pi\)
\(108\) 0 0
\(109\) 2.87038 1.65721i 0.274932 0.158732i −0.356195 0.934412i \(-0.615926\pi\)
0.631127 + 0.775680i \(0.282593\pi\)
\(110\) 0.743218 + 0.0210981i 0.0708631 + 0.00201163i
\(111\) 0 0
\(112\) 1.04787 2.42940i 0.0990143 0.229556i
\(113\) −17.4297 −1.63965 −0.819825 0.572613i \(-0.805930\pi\)
−0.819825 + 0.572613i \(0.805930\pi\)
\(114\) 0 0
\(115\) 0.943309 0.544620i 0.0879640 0.0507861i
\(116\) 4.90010 2.82907i 0.454962 0.262673i
\(117\) 0 0
\(118\) −2.31992 −0.213566
\(119\) −12.4132 16.6729i −1.13791 1.52841i
\(120\) 0 0
\(121\) −4.95072 9.82295i −0.450066 0.892995i
\(122\) −3.80677 + 2.19784i −0.344649 + 0.198983i
\(123\) 0 0
\(124\) 3.73996 + 2.15927i 0.335858 + 0.193908i
\(125\) 2.23052i 0.199504i
\(126\) 0 0
\(127\) 8.23722i 0.730935i 0.930824 + 0.365468i \(0.119091\pi\)
−0.930824 + 0.365468i \(0.880909\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 0.563982 + 0.976845i 0.0494645 + 0.0856750i
\(131\) 1.07003 1.85334i 0.0934888 0.161927i −0.815488 0.578774i \(-0.803531\pi\)
0.908977 + 0.416846i \(0.136865\pi\)
\(132\) 0 0
\(133\) −7.68241 + 17.8111i −0.666150 + 1.54441i
\(134\) 8.65814i 0.747950i
\(135\) 0 0
\(136\) 6.80394 3.92826i 0.583433 0.336845i
\(137\) −5.69013 9.85559i −0.486140 0.842020i 0.513733 0.857950i \(-0.328262\pi\)
−0.999873 + 0.0159306i \(0.994929\pi\)
\(138\) 0 0
\(139\) 14.0998 1.19593 0.597963 0.801523i \(-0.295977\pi\)
0.597963 + 0.801523i \(0.295977\pi\)
\(140\) −0.0688718 0.589110i −0.00582073 0.0497889i
\(141\) 0 0
\(142\) −10.1288 5.84788i −0.849991 0.490743i
\(143\) 8.75058 14.2094i 0.731760 1.18825i
\(144\) 0 0
\(145\) 0.634218 1.09850i 0.0526690 0.0912253i
\(146\) 10.5114i 0.869931i
\(147\) 0 0
\(148\) −0.178219 −0.0146495
\(149\) −11.8830 6.86063i −0.973491 0.562045i −0.0731920 0.997318i \(-0.523319\pi\)
−0.900299 + 0.435273i \(0.856652\pi\)
\(150\) 0 0
\(151\) −15.1576 + 8.75126i −1.23351 + 0.712167i −0.967760 0.251875i \(-0.918953\pi\)
−0.265750 + 0.964042i \(0.585620\pi\)
\(152\) −6.34924 3.66573i −0.514991 0.297330i
\(153\) 0 0
\(154\) −7.18434 + 5.03838i −0.578930 + 0.406005i
\(155\) 0.968125 0.0777617
\(156\) 0 0
\(157\) −2.73267 + 1.57771i −0.218091 + 0.125915i −0.605066 0.796175i \(-0.706853\pi\)
0.386975 + 0.922090i \(0.373520\pi\)
\(158\) 5.05294 + 8.75195i 0.401990 + 0.696268i
\(159\) 0 0
\(160\) 0.224179 0.0177229
\(161\) −5.09138 + 11.8039i −0.401257 + 0.930281i
\(162\) 0 0
\(163\) −6.07127 + 10.5158i −0.475539 + 0.823657i −0.999607 0.0280187i \(-0.991080\pi\)
0.524069 + 0.851676i \(0.324414\pi\)
\(164\) −0.284466 0.492709i −0.0222130 0.0384741i
\(165\) 0 0
\(166\) −12.3752 7.14483i −0.960503 0.554547i
\(167\) 14.4274 1.11643 0.558213 0.829697i \(-0.311487\pi\)
0.558213 + 0.829697i \(0.311487\pi\)
\(168\) 0 0
\(169\) 12.3163 0.947407
\(170\) 0.880633 1.52530i 0.0675415 0.116985i
\(171\) 0 0
\(172\) 5.53729 3.19696i 0.422215 0.243766i
\(173\) −1.80593 + 3.12796i −0.137302 + 0.237815i −0.926475 0.376357i \(-0.877177\pi\)
0.789172 + 0.614172i \(0.210510\pi\)
\(174\) 0 0
\(175\) 7.82052 + 10.5042i 0.591176 + 0.794046i
\(176\) −1.57614 2.91818i −0.118806 0.219966i
\(177\) 0 0
\(178\) 5.25571 + 9.10315i 0.393932 + 0.682310i
\(179\) −1.27355 2.20585i −0.0951895 0.164873i 0.814498 0.580166i \(-0.197012\pi\)
−0.909688 + 0.415293i \(0.863679\pi\)
\(180\) 0 0
\(181\) 6.92820i 0.514969i −0.966282 0.257485i \(-0.917106\pi\)
0.966282 0.257485i \(-0.0828937\pi\)
\(182\) −12.2236 5.27238i −0.906072 0.390815i
\(183\) 0 0
\(184\) −4.20784 2.42940i −0.310206 0.179098i
\(185\) −0.0346003 + 0.0199765i −0.00254387 + 0.00146870i
\(186\) 0 0
\(187\) −26.0466 0.739400i −1.90472 0.0540703i
\(188\) 3.38415i 0.246815i
\(189\) 0 0
\(190\) −1.64356 −0.119236
\(191\) −0.339220 + 0.587546i −0.0245451 + 0.0425133i −0.878037 0.478593i \(-0.841147\pi\)
0.853492 + 0.521106i \(0.174480\pi\)
\(192\) 0 0
\(193\) 20.7803 11.9975i 1.49580 0.863600i 0.495811 0.868430i \(-0.334871\pi\)
0.999988 + 0.00483004i \(0.00153746\pi\)
\(194\) −1.98061 + 3.43052i −0.142200 + 0.246297i
\(195\) 0 0
\(196\) 4.80394 + 5.09138i 0.343139 + 0.363670i
\(197\) 13.4945i 0.961444i −0.876873 0.480722i \(-0.840375\pi\)
0.876873 0.480722i \(-0.159625\pi\)
\(198\) 0 0
\(199\) 15.6225 9.01964i 1.10745 0.639385i 0.169280 0.985568i \(-0.445856\pi\)
0.938167 + 0.346183i \(0.112522\pi\)
\(200\) −4.28660 + 2.47487i −0.303109 + 0.175000i
\(201\) 0 0
\(202\) 6.76728i 0.476144i
\(203\) 1.73828 + 14.8688i 0.122004 + 1.04358i
\(204\) 0 0
\(205\) −0.110455 0.0637712i −0.00771451 0.00445398i
\(206\) 7.21371 + 12.4945i 0.502603 + 0.870533i
\(207\) 0 0
\(208\) 2.51576 4.35743i 0.174437 0.302134i
\(209\) 11.5554 + 21.3946i 0.799305 + 1.47989i
\(210\) 0 0
\(211\) 10.1699i 0.700124i −0.936727 0.350062i \(-0.886161\pi\)
0.936727 0.350062i \(-0.113839\pi\)
\(212\) −1.07478 + 1.86157i −0.0738160 + 0.127853i
\(213\) 0 0
\(214\) −8.63301 14.9528i −0.590141 1.02215i
\(215\) 0.716691 1.24134i 0.0488779 0.0846590i
\(216\) 0 0
\(217\) −9.16471 + 6.82322i −0.622141 + 0.463191i
\(218\) −3.31442 −0.224481
\(219\) 0 0
\(220\) −0.633097 0.389881i −0.0426834 0.0262857i
\(221\) −19.7651 34.2342i −1.32955 2.30284i
\(222\) 0 0
\(223\) 20.6489i 1.38276i −0.722494 0.691378i \(-0.757004\pi\)
0.722494 0.691378i \(-0.242996\pi\)
\(224\) −2.12218 + 1.57999i −0.141794 + 0.105567i
\(225\) 0 0
\(226\) 15.0946 + 8.71486i 1.00408 + 0.579704i
\(227\) 1.61465 + 2.79665i 0.107168 + 0.185620i 0.914622 0.404310i \(-0.132488\pi\)
−0.807454 + 0.589931i \(0.799155\pi\)
\(228\) 0 0
\(229\) −6.90120 3.98441i −0.456044 0.263297i 0.254335 0.967116i \(-0.418143\pi\)
−0.710379 + 0.703819i \(0.751477\pi\)
\(230\) −1.08924 −0.0718223
\(231\) 0 0
\(232\) −5.65814 −0.371475
\(233\) 9.88963 + 5.70978i 0.647891 + 0.374060i 0.787648 0.616126i \(-0.211299\pi\)
−0.139757 + 0.990186i \(0.544632\pi\)
\(234\) 0 0
\(235\) −0.379328 0.657015i −0.0247446 0.0428589i
\(236\) 2.00911 + 1.15996i 0.130782 + 0.0755068i
\(237\) 0 0
\(238\) 2.41366 + 20.6458i 0.156455 + 1.33827i
\(239\) 3.67272i 0.237569i −0.992920 0.118784i \(-0.962100\pi\)
0.992920 0.118784i \(-0.0378997\pi\)
\(240\) 0 0
\(241\) 10.4731 + 18.1399i 0.674632 + 1.16850i 0.976576 + 0.215171i \(0.0690308\pi\)
−0.301945 + 0.953325i \(0.597636\pi\)
\(242\) −0.624023 + 10.9823i −0.0401137 + 0.705968i
\(243\) 0 0
\(244\) 4.39568 0.281404
\(245\) 1.50335 + 0.449992i 0.0960455 + 0.0287490i
\(246\) 0 0
\(247\) −18.4442 + 31.9464i −1.17358 + 2.03270i
\(248\) −2.15927 3.73996i −0.137114 0.237488i
\(249\) 0 0
\(250\) −1.11526 + 1.93169i −0.0705353 + 0.122171i
\(251\) 20.8713i 1.31739i −0.752411 0.658694i \(-0.771109\pi\)
0.752411 0.658694i \(-0.228891\pi\)
\(252\) 0 0
\(253\) 7.65814 + 14.1788i 0.481463 + 0.891416i
\(254\) 4.11861 7.13364i 0.258425 0.447605i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 17.0414 + 9.83888i 1.06302 + 0.613732i 0.926265 0.376873i \(-0.123001\pi\)
0.136751 + 0.990605i \(0.456334\pi\)
\(258\) 0 0
\(259\) 0.186750 0.432966i 0.0116041 0.0269032i
\(260\) 1.12796i 0.0699533i
\(261\) 0 0
\(262\) −1.85334 + 1.07003i −0.114500 + 0.0661066i
\(263\) −18.4604 + 10.6581i −1.13832 + 0.657209i −0.946014 0.324126i \(-0.894930\pi\)
−0.192306 + 0.981335i \(0.561597\pi\)
\(264\) 0 0
\(265\) 0.481885i 0.0296020i
\(266\) 15.5587 11.5836i 0.953965 0.710237i
\(267\) 0 0
\(268\) −4.32907 + 7.49817i −0.264440 + 0.458024i
\(269\) −13.6201 + 7.86359i −0.830434 + 0.479451i −0.854001 0.520271i \(-0.825831\pi\)
0.0235673 + 0.999722i \(0.492498\pi\)
\(270\) 0 0
\(271\) 8.18151 14.1708i 0.496991 0.860814i −0.503003 0.864285i \(-0.667771\pi\)
0.999994 + 0.00347047i \(0.00110469\pi\)
\(272\) −7.85652 −0.476371
\(273\) 0 0
\(274\) 11.3803i 0.687506i
\(275\) 16.4098 + 0.465835i 0.989550 + 0.0280909i
\(276\) 0 0
\(277\) −6.09136 + 3.51685i −0.365994 + 0.211307i −0.671707 0.740817i \(-0.734439\pi\)
0.305713 + 0.952124i \(0.401105\pi\)
\(278\) −12.2108 7.04988i −0.732353 0.422824i
\(279\) 0 0
\(280\) −0.234910 + 0.544620i −0.0140386 + 0.0325473i
\(281\) 17.9643i 1.07166i −0.844325 0.535831i \(-0.819998\pi\)
0.844325 0.535831i \(-0.180002\pi\)
\(282\) 0 0
\(283\) 10.3239 + 17.8816i 0.613693 + 1.06295i 0.990612 + 0.136702i \(0.0436502\pi\)
−0.376919 + 0.926246i \(0.623016\pi\)
\(284\) 5.84788 + 10.1288i 0.347008 + 0.601035i
\(285\) 0 0
\(286\) −14.6829 + 7.93040i −0.868219 + 0.468934i
\(287\) 1.49507 0.174786i 0.0882511 0.0103173i
\(288\) 0 0
\(289\) −22.3624 + 38.7329i −1.31544 + 2.27840i
\(290\) −1.09850 + 0.634218i −0.0645061 + 0.0372426i
\(291\) 0 0
\(292\) 5.25571 9.10315i 0.307567 0.532722i
\(293\) 5.05047 0.295051 0.147526 0.989058i \(-0.452869\pi\)
0.147526 + 0.989058i \(0.452869\pi\)
\(294\) 0 0
\(295\) 0.520076 0.0302800
\(296\) 0.154343 + 0.0891097i 0.00897098 + 0.00517940i
\(297\) 0 0
\(298\) 6.86063 + 11.8830i 0.397426 + 0.688362i
\(299\) −12.2236 + 21.1719i −0.706908 + 1.22440i
\(300\) 0 0
\(301\) 1.96433 + 16.8023i 0.113222 + 0.968467i
\(302\) 17.5025 1.00716
\(303\) 0 0
\(304\) 3.66573 + 6.34924i 0.210244 + 0.364154i
\(305\) 0.853397 0.492709i 0.0488654 0.0282124i
\(306\) 0 0
\(307\) 2.61678 0.149348 0.0746738 0.997208i \(-0.476208\pi\)
0.0746738 + 0.997208i \(0.476208\pi\)
\(308\) 8.74101 0.771201i 0.498065 0.0439433i
\(309\) 0 0
\(310\) −0.838421 0.484063i −0.0476191 0.0274929i
\(311\) 15.6292 9.02354i 0.886253 0.511678i 0.0135378 0.999908i \(-0.495691\pi\)
0.872715 + 0.488230i \(0.162357\pi\)
\(312\) 0 0
\(313\) 6.23405 + 3.59923i 0.352370 + 0.203441i 0.665728 0.746194i \(-0.268121\pi\)
−0.313359 + 0.949635i \(0.601454\pi\)
\(314\) 3.15542 0.178070
\(315\) 0 0
\(316\) 10.1059i 0.568500i
\(317\) −15.5781 + 26.9821i −0.874955 + 1.51547i −0.0181453 + 0.999835i \(0.505776\pi\)
−0.856810 + 0.515632i \(0.827557\pi\)
\(318\) 0 0
\(319\) 15.9790 + 9.84035i 0.894651 + 0.550954i
\(320\) −0.194145 0.112089i −0.0108530 0.00626599i
\(321\) 0 0
\(322\) 10.3112 7.67683i 0.574623 0.427813i
\(323\) 57.5998 3.20494
\(324\) 0 0
\(325\) 12.4524 + 21.5682i 0.690734 + 1.19639i
\(326\) 10.5158 6.07127i 0.582414 0.336257i
\(327\) 0 0
\(328\) 0.568932i 0.0314140i
\(329\) 8.22145 + 3.54614i 0.453263 + 0.195505i
\(330\) 0 0
\(331\) 5.87847 10.1818i 0.323110 0.559643i −0.658018 0.753002i \(-0.728605\pi\)
0.981128 + 0.193359i \(0.0619383\pi\)
\(332\) 7.14483 + 12.3752i 0.392124 + 0.679178i
\(333\) 0 0
\(334\) −12.4945 7.21371i −0.683669 0.394716i
\(335\) 1.94097i 0.106047i
\(336\) 0 0
\(337\) 23.0213i 1.25405i 0.779000 + 0.627024i \(0.215727\pi\)
−0.779000 + 0.627024i \(0.784273\pi\)
\(338\) −10.6662 6.15814i −0.580166 0.334959i
\(339\) 0 0
\(340\) −1.52530 + 0.880633i −0.0827211 + 0.0477590i
\(341\) −0.406430 + 14.3172i −0.0220094 + 0.775320i
\(342\) 0 0
\(343\) −17.4029 + 6.33559i −0.939667 + 0.342090i
\(344\) −6.39391 −0.344737
\(345\) 0 0
\(346\) 3.12796 1.80593i 0.168160 0.0970874i
\(347\) −25.6752 + 14.8236i −1.37832 + 0.795771i −0.991957 0.126577i \(-0.959601\pi\)
−0.386360 + 0.922348i \(0.626268\pi\)
\(348\) 0 0
\(349\) 8.53049 0.456627 0.228313 0.973588i \(-0.426679\pi\)
0.228313 + 0.973588i \(0.426679\pi\)
\(350\) −1.52065 13.0072i −0.0812822 0.695264i
\(351\) 0 0
\(352\) −0.0941129 + 3.31529i −0.00501624 + 0.176706i
\(353\) −23.5882 + 13.6187i −1.25548 + 0.724849i −0.972192 0.234187i \(-0.924757\pi\)
−0.283284 + 0.959036i \(0.591424\pi\)
\(354\) 0 0
\(355\) 2.27067 + 1.31097i 0.120515 + 0.0695791i
\(356\) 10.5114i 0.557104i
\(357\) 0 0
\(358\) 2.54710i 0.134618i
\(359\) −15.2798 8.82178i −0.806436 0.465596i 0.0392810 0.999228i \(-0.487493\pi\)
−0.845717 + 0.533632i \(0.820827\pi\)
\(360\) 0 0
\(361\) −17.3752 30.0948i −0.914485 1.58393i
\(362\) −3.46410 + 6.00000i −0.182069 + 0.315353i
\(363\) 0 0
\(364\) 7.94974 + 10.6778i 0.416680 + 0.559669i
\(365\) 2.35644i 0.123342i
\(366\) 0 0
\(367\) 6.03328 3.48331i 0.314934 0.181827i −0.334198 0.942503i \(-0.608465\pi\)
0.649132 + 0.760675i \(0.275132\pi\)
\(368\) 2.42940 + 4.20784i 0.126641 + 0.219349i
\(369\) 0 0
\(370\) 0.0399530 0.00207706
\(371\) −3.39627 4.56174i −0.176325 0.236834i
\(372\) 0 0
\(373\) 25.1206 + 14.5034i 1.30069 + 0.750956i 0.980523 0.196404i \(-0.0629265\pi\)
0.320170 + 0.947360i \(0.396260\pi\)
\(374\) 22.1873 + 13.6637i 1.14728 + 0.706531i
\(375\) 0 0
\(376\) −1.69208 + 2.93076i −0.0872621 + 0.151142i
\(377\) 28.4691i 1.46623i
\(378\) 0 0
\(379\) −11.7569 −0.603914 −0.301957 0.953322i \(-0.597640\pi\)
−0.301957 + 0.953322i \(0.597640\pi\)
\(380\) 1.42337 + 0.821781i 0.0730171 + 0.0421565i
\(381\) 0 0
\(382\) 0.587546 0.339220i 0.0300615 0.0173560i
\(383\) −24.8948 14.3730i −1.27206 0.734426i −0.296687 0.954975i \(-0.595882\pi\)
−0.975376 + 0.220549i \(0.929215\pi\)
\(384\) 0 0
\(385\) 1.61058 1.12950i 0.0820826 0.0575647i
\(386\) −23.9950 −1.22132
\(387\) 0 0
\(388\) 3.43052 1.98061i 0.174158 0.100550i
\(389\) 15.4023 + 26.6775i 0.780926 + 1.35260i 0.931403 + 0.363990i \(0.118586\pi\)
−0.150477 + 0.988613i \(0.548081\pi\)
\(390\) 0 0
\(391\) 38.1732 1.93050
\(392\) −1.61465 6.81123i −0.0815520 0.344019i
\(393\) 0 0
\(394\) −6.74725 + 11.6866i −0.339922 + 0.588762i
\(395\) −1.13276 1.96200i −0.0569955 0.0987191i
\(396\) 0 0
\(397\) −30.8496 17.8111i −1.54830 0.893911i −0.998272 0.0587644i \(-0.981284\pi\)
−0.550027 0.835147i \(-0.685383\pi\)
\(398\) −18.0393 −0.904227
\(399\) 0 0
\(400\) 4.94974 0.247487
\(401\) 1.53512 2.65891i 0.0766602 0.132779i −0.825147 0.564918i \(-0.808908\pi\)
0.901807 + 0.432139i \(0.142241\pi\)
\(402\) 0 0
\(403\) −18.8177 + 10.8644i −0.937378 + 0.541195i
\(404\) 3.38364 5.86063i 0.168342 0.291577i
\(405\) 0 0
\(406\) 5.92899 13.7459i 0.294251 0.682196i
\(407\) −0.280899 0.520076i −0.0139236 0.0257792i
\(408\) 0 0
\(409\) −1.51423 2.62272i −0.0748737 0.129685i 0.826158 0.563439i \(-0.190522\pi\)
−0.901031 + 0.433754i \(0.857189\pi\)
\(410\) 0.0637712 + 0.110455i 0.00314944 + 0.00545499i
\(411\) 0 0
\(412\) 14.4274i 0.710788i
\(413\) −4.92328 + 3.66543i −0.242259 + 0.180364i
\(414\) 0 0
\(415\) 2.77426 + 1.60172i 0.136183 + 0.0786254i
\(416\) −4.35743 + 2.51576i −0.213641 + 0.123346i
\(417\) 0 0
\(418\) 0.689986 24.3059i 0.0337483 1.18884i
\(419\) 0.668585i 0.0326625i −0.999867 0.0163312i \(-0.994801\pi\)
0.999867 0.0163312i \(-0.00519863\pi\)
\(420\) 0 0
\(421\) −8.07771 −0.393683 −0.196842 0.980435i \(-0.563068\pi\)
−0.196842 + 0.980435i \(0.563068\pi\)
\(422\) −5.08494 + 8.80738i −0.247531 + 0.428736i
\(423\) 0 0
\(424\) 1.86157 1.07478i 0.0904058 0.0521958i
\(425\) 19.4439 33.6778i 0.943166 1.63361i
\(426\) 0 0
\(427\) −4.60609 + 10.6788i −0.222904 + 0.516786i
\(428\) 17.2660i 0.834585i
\(429\) 0 0
\(430\) −1.24134 + 0.716691i −0.0598630 + 0.0345619i
\(431\) 8.26452 4.77152i 0.398088 0.229836i −0.287571 0.957759i \(-0.592848\pi\)
0.685659 + 0.727923i \(0.259514\pi\)
\(432\) 0 0
\(433\) 0.729857i 0.0350747i 0.999846 + 0.0175374i \(0.00558260\pi\)
−0.999846 + 0.0175374i \(0.994417\pi\)
\(434\) 11.3485 1.32673i 0.544745 0.0636852i
\(435\) 0 0
\(436\) 2.87038 + 1.65721i 0.137466 + 0.0793661i
\(437\) −17.8111 30.8496i −0.852018 1.47574i
\(438\) 0 0
\(439\) 12.9809 22.4835i 0.619542 1.07308i −0.370027 0.929021i \(-0.620652\pi\)
0.989569 0.144058i \(-0.0460151\pi\)
\(440\) 0.353338 + 0.654195i 0.0168447 + 0.0311875i
\(441\) 0 0
\(442\) 39.5303i 1.88026i
\(443\) 8.80056 15.2430i 0.418127 0.724218i −0.577624 0.816303i \(-0.696020\pi\)
0.995751 + 0.0920854i \(0.0293533\pi\)
\(444\) 0 0
\(445\) −1.17822 2.04074i −0.0558530 0.0967402i
\(446\) −10.3245 + 17.8825i −0.488878 + 0.846761i
\(447\) 0 0
\(448\) 2.62785 0.307218i 0.124154 0.0145147i
\(449\) −8.92251 −0.421079 −0.210540 0.977585i \(-0.567522\pi\)
−0.210540 + 0.977585i \(0.567522\pi\)
\(450\) 0 0
\(451\) 0.989457 1.60670i 0.0465917 0.0756566i
\(452\) −8.71486 15.0946i −0.409913 0.709990i
\(453\) 0 0
\(454\) 3.22930i 0.151558i
\(455\) 2.74027 + 1.18196i 0.128466 + 0.0554110i
\(456\) 0 0
\(457\) −24.3327 14.0485i −1.13823 0.657160i −0.192241 0.981348i \(-0.561576\pi\)
−0.945993 + 0.324188i \(0.894909\pi\)
\(458\) 3.98441 + 6.90120i 0.186179 + 0.322472i
\(459\) 0 0
\(460\) 0.943309 + 0.544620i 0.0439820 + 0.0253930i
\(461\) 18.7712 0.874262 0.437131 0.899398i \(-0.355995\pi\)
0.437131 + 0.899398i \(0.355995\pi\)
\(462\) 0 0
\(463\) 7.57221 0.351911 0.175955 0.984398i \(-0.443699\pi\)
0.175955 + 0.984398i \(0.443699\pi\)
\(464\) 4.90010 + 2.82907i 0.227481 + 0.131336i
\(465\) 0 0
\(466\) −5.70978 9.88963i −0.264501 0.458128i
\(467\) 34.4353 + 19.8812i 1.59347 + 0.919993i 0.992705 + 0.120571i \(0.0384725\pi\)
0.600770 + 0.799422i \(0.294861\pi\)
\(468\) 0 0
\(469\) −13.6797 18.3741i −0.631672 0.848439i
\(470\) 0.758655i 0.0349942i
\(471\) 0 0
\(472\) −1.15996 2.00911i −0.0533914 0.0924766i
\(473\) 18.0569 + 11.1200i 0.830255 + 0.511297i
\(474\) 0 0
\(475\) −36.2889 −1.66505
\(476\) 8.23260 19.0866i 0.377340 0.874833i
\(477\) 0 0
\(478\) −1.83636 + 3.18067i −0.0839933 + 0.145481i
\(479\) 9.30307 + 16.1134i 0.425068 + 0.736239i 0.996427 0.0844611i \(-0.0269169\pi\)
−0.571359 + 0.820700i \(0.693584\pi\)
\(480\) 0 0
\(481\) 0.448358 0.776579i 0.0204434 0.0354089i
\(482\) 20.9462i 0.954073i
\(483\) 0 0
\(484\) 6.03156 9.19893i 0.274162 0.418133i
\(485\) 0.444012 0.769051i 0.0201615 0.0349208i
\(486\) 0 0
\(487\) −10.2345 17.7266i −0.463768 0.803270i 0.535377 0.844613i \(-0.320170\pi\)
−0.999145 + 0.0413435i \(0.986836\pi\)
\(488\) −3.80677 2.19784i −0.172324 0.0994915i
\(489\) 0 0
\(490\) −1.07694 1.14138i −0.0486513 0.0515623i
\(491\) 29.5933i 1.33553i 0.744373 + 0.667764i \(0.232748\pi\)
−0.744373 + 0.667764i \(0.767252\pi\)
\(492\) 0 0
\(493\) 38.4977 22.2266i 1.73385 1.00104i
\(494\) 31.9464 18.4442i 1.43734 0.829846i
\(495\) 0 0
\(496\) 4.31854i 0.193908i
\(497\) −30.7347 + 3.59314i −1.37864 + 0.161175i
\(498\) 0 0
\(499\) −3.72298 + 6.44839i −0.166664 + 0.288670i −0.937245 0.348672i \(-0.886633\pi\)
0.770581 + 0.637342i \(0.219966\pi\)
\(500\) 1.93169 1.11526i 0.0863878 0.0498760i
\(501\) 0 0
\(502\) −10.4357 + 18.0751i −0.465767 + 0.806732i
\(503\) −8.83120 −0.393764 −0.196882 0.980427i \(-0.563082\pi\)
−0.196882 + 0.980427i \(0.563082\pi\)
\(504\) 0 0
\(505\) 1.51708i 0.0675092i
\(506\) 0.457275 16.1083i 0.0203284 0.716102i
\(507\) 0 0
\(508\) −7.13364 + 4.11861i −0.316504 + 0.182734i
\(509\) −2.15760 1.24569i −0.0956341 0.0552144i 0.451420 0.892311i \(-0.350918\pi\)
−0.547054 + 0.837097i \(0.684251\pi\)
\(510\) 0 0
\(511\) 16.6079 + 22.3071i 0.734690 + 0.986809i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −9.83888 17.0414i −0.433974 0.751666i
\(515\) −1.61716 2.80101i −0.0712606 0.123427i
\(516\) 0 0
\(517\) 9.87556 5.33390i 0.434327 0.234584i
\(518\) −0.378213 + 0.281584i −0.0166177 + 0.0123721i
\(519\) 0 0
\(520\) −0.563982 + 0.976845i −0.0247322 + 0.0428375i
\(521\) 8.03642 4.63983i 0.352082 0.203275i −0.313520 0.949582i \(-0.601508\pi\)
0.665602 + 0.746307i \(0.268175\pi\)
\(522\) 0 0
\(523\) −4.35899 + 7.55000i −0.190605 + 0.330138i −0.945451 0.325764i \(-0.894378\pi\)
0.754846 + 0.655903i \(0.227712\pi\)
\(524\) 2.14006 0.0934888
\(525\) 0 0
\(526\) 21.3163 0.929434
\(527\) 29.3831 + 16.9643i 1.27995 + 0.738978i
\(528\) 0 0
\(529\) −0.303943 0.526445i −0.0132149 0.0228889i
\(530\) 0.240943 0.417325i 0.0104659 0.0181274i
\(531\) 0 0
\(532\) −19.2660 + 2.25236i −0.835288 + 0.0976521i
\(533\) 2.86260 0.123993
\(534\) 0 0
\(535\) 1.93534 + 3.35211i 0.0836721 + 0.144924i
\(536\) 7.49817 4.32907i 0.323872 0.186987i
\(537\) 0 0
\(538\) 15.7272 0.678047
\(539\) −7.28587 + 22.0435i −0.313825 + 0.949481i
\(540\) 0 0
\(541\) −38.5195 22.2392i −1.65608 0.956139i −0.974497 0.224398i \(-0.927958\pi\)
−0.681583 0.731740i \(-0.738708\pi\)
\(542\) −14.1708 + 8.18151i −0.608688 + 0.351426i
\(543\) 0 0
\(544\) 6.80394 + 3.92826i 0.291717 + 0.168423i
\(545\) 0.743024 0.0318277
\(546\) 0 0
\(547\) 22.6133i 0.966874i 0.875379 + 0.483437i \(0.160612\pi\)
−0.875379 + 0.483437i \(0.839388\pi\)
\(548\) 5.69013 9.85559i 0.243070 0.421010i
\(549\) 0 0
\(550\) −13.9784 8.60834i −0.596042 0.367061i
\(551\) −35.9249 20.7412i −1.53045 0.883607i
\(552\) 0 0
\(553\) 24.5512 + 10.5896i 1.04402 + 0.450317i
\(554\) 7.03370 0.298833
\(555\) 0 0
\(556\) 7.04988 + 12.2108i 0.298982 + 0.517851i
\(557\) −19.8094 + 11.4370i −0.839351 + 0.484599i −0.857044 0.515244i \(-0.827701\pi\)
0.0176926 + 0.999843i \(0.494368\pi\)
\(558\) 0 0
\(559\) 32.1712i 1.36070i
\(560\) 0.475748 0.354200i 0.0201040 0.0149677i
\(561\) 0 0
\(562\) −8.98216 + 15.5576i −0.378890 + 0.656256i
\(563\) −16.6837 28.8971i −0.703136 1.21787i −0.967360 0.253406i \(-0.918449\pi\)
0.264224 0.964461i \(-0.414884\pi\)
\(564\) 0 0
\(565\) −3.38389 1.95369i −0.142361 0.0821923i
\(566\) 20.6478i 0.867894i
\(567\) 0 0
\(568\) 11.6958i 0.490743i
\(569\) −31.7920 18.3551i −1.33279 0.769487i −0.347065 0.937841i \(-0.612822\pi\)
−0.985727 + 0.168354i \(0.946155\pi\)
\(570\) 0 0
\(571\) 14.9063 8.60618i 0.623811 0.360158i −0.154540 0.987987i \(-0.549390\pi\)
0.778351 + 0.627829i \(0.216056\pi\)
\(572\) 16.6810 + 0.473532i 0.697467 + 0.0197994i
\(573\) 0 0
\(574\) −1.38216 0.596165i −0.0576903 0.0248835i
\(575\) −24.0498 −1.00295
\(576\) 0 0
\(577\) 34.1924 19.7410i 1.42345 0.821827i 0.426855 0.904320i \(-0.359622\pi\)
0.996592 + 0.0824929i \(0.0262882\pi\)
\(578\) 38.7329 22.3624i 1.61107 0.930154i
\(579\) 0 0
\(580\) 1.26844 0.0526690
\(581\) −37.5512 + 4.39004i −1.55788 + 0.182130i
\(582\) 0 0
\(583\) −7.12640 0.202301i −0.295145 0.00837845i
\(584\) −9.10315 + 5.25571i −0.376691 + 0.217483i
\(585\) 0 0
\(586\) −4.37383 2.52523i −0.180681 0.104316i
\(587\) 33.2111i 1.37077i 0.728182 + 0.685384i \(0.240366\pi\)
−0.728182 + 0.685384i \(0.759634\pi\)
\(588\) 0 0
\(589\) 31.6612i 1.30458i
\(590\) −0.450399 0.260038i −0.0185426 0.0107056i
\(591\) 0 0
\(592\) −0.0891097 0.154343i −0.00366239 0.00634344i
\(593\) −7.18187 + 12.4394i −0.294924 + 0.510823i −0.974967 0.222349i \(-0.928628\pi\)
0.680043 + 0.733172i \(0.261961\pi\)
\(594\) 0 0
\(595\) −0.541093 4.62835i −0.0221826 0.189744i
\(596\) 13.7213i 0.562045i
\(597\) 0 0
\(598\) 21.1719 12.2236i 0.865782 0.499860i
\(599\) 7.17073 + 12.4201i 0.292988 + 0.507470i 0.974515 0.224323i \(-0.0720171\pi\)
−0.681527 + 0.731793i \(0.738684\pi\)
\(600\) 0 0
\(601\) −10.9630 −0.447192 −0.223596 0.974682i \(-0.571780\pi\)
−0.223596 + 0.974682i \(0.571780\pi\)
\(602\) 6.69998 15.5334i 0.273071 0.633092i
\(603\) 0 0
\(604\) −15.1576 8.75126i −0.616755 0.356084i
\(605\) 0.139893 2.46200i 0.00568745 0.100094i
\(606\) 0 0
\(607\) 3.89629 6.74857i 0.158146 0.273916i −0.776054 0.630666i \(-0.782782\pi\)
0.934200 + 0.356750i \(0.116115\pi\)
\(608\) 7.33147i 0.297330i
\(609\) 0 0
\(610\) −0.985418 −0.0398984
\(611\) 14.7462 + 8.51373i 0.596568 + 0.344428i
\(612\) 0 0
\(613\) 21.9788 12.6895i 0.887715 0.512522i 0.0145204 0.999895i \(-0.495378\pi\)
0.873194 + 0.487372i \(0.162045\pi\)
\(614\) −2.26620 1.30839i −0.0914563 0.0528023i
\(615\) 0 0
\(616\) −7.95554 3.70262i −0.320538 0.149183i
\(617\) −41.0360 −1.65205 −0.826024 0.563635i \(-0.809402\pi\)
−0.826024 + 0.563635i \(0.809402\pi\)
\(618\) 0 0
\(619\) 7.48172 4.31957i 0.300716 0.173618i −0.342049 0.939682i \(-0.611121\pi\)
0.642764 + 0.766064i \(0.277787\pi\)
\(620\) 0.484063 + 0.838421i 0.0194404 + 0.0336718i
\(621\) 0 0
\(622\) −18.0471 −0.723622
\(623\) 25.5364 + 11.0146i 1.02309 + 0.441290i
\(624\) 0 0
\(625\) −12.1243 + 21.0000i −0.484974 + 0.839999i
\(626\) −3.59923 6.23405i −0.143854 0.249163i
\(627\) 0 0
\(628\) −2.73267 1.57771i −0.109045 0.0629574i
\(629\) −1.40018 −0.0558290
\(630\) 0 0
\(631\) −1.12348 −0.0447252 −0.0223626 0.999750i \(-0.507119\pi\)
−0.0223626 + 0.999750i \(0.507119\pi\)
\(632\) −5.05294 + 8.75195i −0.200995 + 0.348134i
\(633\) 0 0
\(634\) 26.9821 15.5781i 1.07160 0.618687i
\(635\) −0.923306 + 1.59921i −0.0366403 + 0.0634628i
\(636\) 0 0
\(637\) −34.2709 + 8.12415i −1.35786 + 0.321891i
\(638\) −8.91803 16.5115i −0.353068 0.653696i
\(639\) 0 0
\(640\) 0.112089 + 0.194145i 0.00443073 + 0.00767424i
\(641\) −4.29911 7.44628i −0.169805 0.294110i 0.768546 0.639794i \(-0.220980\pi\)
−0.938351 + 0.345684i \(0.887647\pi\)
\(642\) 0 0
\(643\) 21.6511i 0.853837i −0.904290 0.426919i \(-0.859599\pi\)
0.904290 0.426919i \(-0.140401\pi\)
\(644\) −12.7682 + 1.49271i −0.503138 + 0.0588210i
\(645\) 0 0
\(646\) −49.8829 28.7999i −1.96262 1.13312i
\(647\) 2.74766 1.58636i 0.108022 0.0623664i −0.445016 0.895523i \(-0.646802\pi\)
0.553038 + 0.833156i \(0.313469\pi\)
\(648\) 0 0
\(649\) −0.218334 + 7.69119i −0.00857036 + 0.301906i
\(650\) 24.9048i 0.976846i
\(651\) 0 0
\(652\) −12.1425 −0.475539
\(653\) −14.7215 + 25.4983i −0.576095 + 0.997826i 0.419826 + 0.907604i \(0.362091\pi\)
−0.995922 + 0.0902218i \(0.971242\pi\)
\(654\) 0 0
\(655\) 0.415481 0.239878i 0.0162342 0.00937280i
\(656\) 0.284466 0.492709i 0.0111065 0.0192371i
\(657\) 0 0
\(658\) −5.34691 7.18177i −0.208444 0.279975i
\(659\) 0.469820i 0.0183016i −0.999958 0.00915080i \(-0.997087\pi\)
0.999958 0.00915080i \(-0.00291283\pi\)
\(660\) 0 0
\(661\) −6.13937 + 3.54456i −0.238794 + 0.137868i −0.614622 0.788822i \(-0.710692\pi\)
0.375829 + 0.926689i \(0.377358\pi\)
\(662\) −10.1818 + 5.87847i −0.395727 + 0.228473i
\(663\) 0 0
\(664\) 14.2897i 0.554547i
\(665\) −3.48793 + 2.59680i −0.135256 + 0.100700i
\(666\) 0 0
\(667\) −23.8086 13.7459i −0.921871 0.532243i
\(668\) 7.21371 + 12.4945i 0.279107 + 0.483427i
\(669\) 0 0
\(670\) 0.970487 1.68093i 0.0374932 0.0649401i
\(671\) 6.92820 + 12.8274i 0.267460 + 0.495196i
\(672\) 0 0
\(673\) 43.2330i 1.66651i −0.552889 0.833255i \(-0.686475\pi\)
0.552889 0.833255i \(-0.313525\pi\)
\(674\) 11.5106 19.9370i 0.443373 0.767944i
\(675\) 0 0
\(676\) 6.15814 + 10.6662i 0.236852 + 0.410239i
\(677\) 10.8282 18.7550i 0.416161 0.720812i −0.579389 0.815051i \(-0.696709\pi\)
0.995550 + 0.0942398i \(0.0300420\pi\)
\(678\) 0 0
\(679\) 1.21696 + 10.4095i 0.0467027 + 0.399481i
\(680\) 1.76127 0.0675415
\(681\) 0 0
\(682\) 7.51058 12.1958i 0.287595 0.467003i
\(683\) −8.93736 15.4800i −0.341978 0.592324i 0.642822 0.766016i \(-0.277764\pi\)
−0.984800 + 0.173692i \(0.944430\pi\)
\(684\) 0 0
\(685\) 2.55121i 0.0974769i
\(686\) 18.2391 + 3.21466i 0.696373 + 0.122736i
\(687\) 0 0
\(688\) 5.53729 + 3.19696i 0.211107 + 0.121883i
\(689\) −5.40778 9.36654i −0.206020 0.356837i
\(690\) 0 0
\(691\) −15.7085 9.06930i −0.597579 0.345012i 0.170510 0.985356i \(-0.445459\pi\)
−0.768089 + 0.640344i \(0.778792\pi\)
\(692\) −3.61186 −0.137302
\(693\) 0 0
\(694\) 29.6472 1.12539
\(695\) 2.73740 + 1.58044i 0.103835 + 0.0599494i
\(696\) 0 0
\(697\) −2.23491 3.87098i −0.0846533 0.146624i
\(698\) −7.38762 4.26524i −0.279626 0.161442i
\(699\) 0 0
\(700\) −5.18668 + 12.0249i −0.196038 + 0.454498i
\(701\) 37.5868i 1.41963i 0.704386 + 0.709817i \(0.251222\pi\)
−0.704386 + 0.709817i \(0.748778\pi\)
\(702\) 0 0
\(703\) 0.653305 + 1.13156i 0.0246399 + 0.0426775i
\(704\) 1.73915 2.82407i 0.0655466 0.106436i
\(705\) 0 0
\(706\) 27.2374 1.02509
\(707\) 10.6922 + 14.3614i 0.402122 + 0.540115i
\(708\) 0 0
\(709\) 7.63216 13.2193i 0.286632 0.496461i −0.686372 0.727251i \(-0.740798\pi\)
0.973004 + 0.230790i \(0.0741311\pi\)
\(710\) −1.31097 2.27067i −0.0491999 0.0852167i
\(711\) 0 0
\(712\) −5.25571 + 9.10315i −0.196966 + 0.341155i
\(713\) 20.9829i 0.785815i
\(714\) 0 0
\(715\) 3.29160 1.77783i 0.123099 0.0664870i
\(716\) 1.27355 2.20585i 0.0475947 0.0824365i
\(717\) 0 0
\(718\) 8.82178 + 15.2798i 0.329226 + 0.570236i
\(719\) 30.5794 + 17.6550i 1.14042 + 0.658422i 0.946535 0.322602i \(-0.104557\pi\)
0.193886 + 0.981024i \(0.437891\pi\)
\(720\) 0 0
\(721\) 35.0499 + 15.1180i 1.30533 + 0.563025i
\(722\) 34.7504i 1.29328i
\(723\) 0 0
\(724\) 6.00000 3.46410i 0.222988 0.128742i
\(725\) −24.2542 + 14.0032i −0.900779 + 0.520065i
\(726\) 0 0
\(727\) 17.0371i 0.631870i −0.948781 0.315935i \(-0.897682\pi\)
0.948781 0.315935i \(-0.102318\pi\)
\(728\) −1.54578 13.2221i −0.0572903 0.490045i
\(729\) 0 0
\(730\) −1.17822 + 2.04074i −0.0436079 + 0.0755310i
\(731\) 43.5038 25.1169i 1.60905 0.928984i
\(732\) 0 0
\(733\) 21.3208 36.9287i 0.787501 1.36399i −0.139992 0.990153i \(-0.544708\pi\)
0.927493 0.373839i \(-0.121959\pi\)
\(734\) −6.96663 −0.257143
\(735\) 0 0
\(736\) 4.85879i 0.179098i
\(737\) −28.7042 0.814843i −1.05733 0.0300151i
\(738\) 0 0
\(739\) 27.8460 16.0769i 1.02433 0.591398i 0.108976 0.994044i \(-0.465243\pi\)
0.915356 + 0.402646i \(0.131909\pi\)
\(740\) −0.0346003 0.0199765i −0.00127193 0.000734351i
\(741\) 0 0
\(742\) 0.660382 + 5.64872i 0.0242434 + 0.207371i
\(743\) 52.5029i 1.92614i −0.269243 0.963072i \(-0.586774\pi\)
0.269243 0.963072i \(-0.413226\pi\)
\(744\) 0 0
\(745\) −1.53801 2.66391i −0.0563483 0.0975982i
\(746\) −14.5034 25.1206i −0.531006 0.919729i
\(747\) 0 0
\(748\) −12.3830 22.9267i −0.452766 0.838285i
\(749\) −41.9460 18.0925i −1.53268 0.661087i
\(750\) 0 0
\(751\) 12.3478 21.3871i 0.450579 0.780426i −0.547843 0.836581i \(-0.684551\pi\)
0.998422 + 0.0561550i \(0.0178841\pi\)
\(752\) 2.93076 1.69208i 0.106874 0.0617036i
\(753\) 0 0
\(754\) 14.2346 24.6550i 0.518392 0.897881i
\(755\) −3.92370 −0.142798
\(756\) 0 0
\(757\) 40.8108 1.48329 0.741647 0.670791i \(-0.234045\pi\)
0.741647 + 0.670791i \(0.234045\pi\)
\(758\) 10.1818 + 5.87847i 0.369820 + 0.213516i
\(759\) 0 0
\(760\) −0.821781 1.42337i −0.0298091 0.0516309i
\(761\) 21.0095 36.3894i 0.761592 1.31912i −0.180438 0.983586i \(-0.557751\pi\)
0.942030 0.335530i \(-0.108915\pi\)
\(762\) 0 0
\(763\) −7.03380 + 5.23674i −0.254641 + 0.189583i
\(764\) −0.678440 −0.0245451
\(765\) 0 0
\(766\) 14.3730 + 24.8948i 0.519318 + 0.899484i
\(767\) −10.1089 + 5.83636i −0.365010 + 0.210739i
\(768\) 0 0
\(769\) −15.6284 −0.563574 −0.281787 0.959477i \(-0.590927\pi\)
−0.281787 + 0.959477i \(0.590927\pi\)
\(770\) −1.95955 + 0.172887i −0.0706173 + 0.00623042i
\(771\) 0 0
\(772\) 20.7803 + 11.9975i 0.747900 + 0.431800i
\(773\) −2.74004 + 1.58196i −0.0985523 + 0.0568992i −0.548466 0.836173i \(-0.684788\pi\)
0.449914 + 0.893072i \(0.351455\pi\)
\(774\) 0 0
\(775\) −18.5119 10.6878i −0.664965 0.383918i
\(776\) −3.96123 −0.142200
\(777\) 0 0
\(778\) 30.8045i 1.10440i
\(779\) −2.08555 + 3.61228i −0.0747226 + 0.129423i
\(780\) 0 0
\(781\) −20.3407 + 33.0296i −0.727846 + 1.18189i
\(782\) −33.0590 19.0866i −1.18219 0.682535i
\(783\) 0 0
\(784\) −2.00729 + 6.70603i −0.0716890 + 0.239501i
\(785\) −0.707378 −0.0252474
\(786\) 0 0
\(787\) −18.2920 31.6827i −0.652039 1.12936i −0.982627 0.185590i \(-0.940581\pi\)
0.330588 0.943775i \(-0.392753\pi\)
\(788\) 11.6866 6.74725i 0.416317 0.240361i
\(789\) 0 0
\(790\) 2.26553i 0.0806038i
\(791\) 45.8028 5.35473i 1.62856 0.190392i
\(792\) 0 0
\(793\) −11.0585 + 19.1539i −0.392698 + 0.680174i
\(794\) 17.8111 + 30.8496i 0.632091 + 1.09481i
\(795\) 0 0
\(796\) 15.6225 + 9.01964i 0.553724 + 0.319693i
\(797\) 8.72925i 0.309206i 0.987977 + 0.154603i \(0.0494098\pi\)
−0.987977 + 0.154603i \(0.950590\pi\)
\(798\) 0 0
\(799\) 26.5876i 0.940603i
\(800\) −4.28660 2.47487i −0.151554 0.0874999i
\(801\) 0 0
\(802\) −2.65891 + 1.53512i −0.0938892 + 0.0542070i
\(803\) 34.8484 + 0.989260i 1.22977 + 0.0349102i
\(804\) 0 0
\(805\) −2.31156 + 1.72098i −0.0814719 + 0.0606567i
\(806\) 21.7288 0.765366
\(807\) 0 0
\(808\) −5.86063 + 3.38364i −0.206176 + 0.119036i
\(809\) −25.2367 + 14.5704i −0.887275 + 0.512269i −0.873050 0.487630i \(-0.837861\pi\)
−0.0142249 + 0.999899i \(0.504528\pi\)
\(810\) 0 0
\(811\) −32.7260 −1.14917 −0.574583 0.818446i \(-0.694836\pi\)
−0.574583 + 0.818446i \(0.694836\pi\)
\(812\) −12.0076 + 8.93978i −0.421384 + 0.313725i
\(813\) 0 0
\(814\) −0.0167727 + 0.590849i −0.000587884 + 0.0207092i
\(815\) −2.35741 + 1.36105i −0.0825765 + 0.0476756i
\(816\) 0 0
\(817\) −40.5965 23.4384i −1.42029 0.820006i
\(818\) 3.02845i 0.105887i
\(819\) 0 0
\(820\) 0.127542i 0.00445398i
\(821\) −10.8680 6.27462i −0.379294 0.218986i 0.298217 0.954498i \(-0.403608\pi\)
−0.677511 + 0.735512i \(0.736941\pi\)
\(822\) 0 0
\(823\) −2.32728 4.03096i −0.0811237 0.140510i 0.822609 0.568607i \(-0.192518\pi\)
−0.903733 + 0.428097i \(0.859184\pi\)
\(824\) −7.21371 + 12.4945i −0.251301 + 0.435267i
\(825\) 0 0
\(826\) 6.09640 0.712720i 0.212121 0.0247987i
\(827\) 1.60601i 0.0558463i −0.999610 0.0279232i \(-0.991111\pi\)
0.999610 0.0279232i \(-0.00888938\pi\)
\(828\) 0 0
\(829\) 30.6111 17.6733i 1.06317 0.613819i 0.136860 0.990590i \(-0.456299\pi\)
0.926306 + 0.376771i \(0.122966\pi\)
\(830\) −1.60172 2.77426i −0.0555966 0.0962961i
\(831\) 0 0
\(832\) 5.03153 0.174437
\(833\) 37.7423 + 40.0005i 1.30769 + 1.38594i
\(834\) 0 0
\(835\) 2.80101 + 1.61716i 0.0969328 + 0.0559642i
\(836\) −12.7505 + 20.7046i −0.440986 + 0.716082i
\(837\) 0 0
\(838\) −0.334292 + 0.579011i −0.0115479 + 0.0200016i
\(839\) 20.3870i 0.703837i −0.936031 0.351918i \(-0.885529\pi\)
0.936031 0.351918i \(-0.114471\pi\)
\(840\) 0 0
\(841\) −3.01458 −0.103951
\(842\) 6.99550 + 4.03885i 0.241081 + 0.139188i
\(843\) 0 0
\(844\) 8.80738 5.08494i 0.303162 0.175031i
\(845\) 2.39114 + 1.38053i 0.0822578 + 0.0474915i
\(846\) 0 0
\(847\) 16.0276 + 24.2923i 0.550714 + 0.834694i
\(848\) −2.14956 −0.0738160
\(849\) 0 0
\(850\) −33.6778 + 19.4439i −1.15514 + 0.666919i
\(851\) 0.432966 + 0.749919i 0.0148419 + 0.0257069i
\(852\) 0 0
\(853\) −13.6020 −0.465723 −0.232861 0.972510i \(-0.574809\pi\)
−0.232861 + 0.972510i \(0.574809\pi\)
\(854\) 9.32841 6.94511i 0.319212 0.237657i
\(855\) 0 0
\(856\) 8.63301 14.9528i 0.295070 0.511077i
\(857\) −14.5169 25.1439i −0.495886 0.858900i 0.504102 0.863644i \(-0.331823\pi\)
−0.999989 + 0.00474364i \(0.998490\pi\)
\(858\) 0 0
\(859\) 17.6354 + 10.1818i 0.601713 + 0.347399i 0.769715 0.638388i \(-0.220398\pi\)
−0.168002 + 0.985787i \(0.553732\pi\)
\(860\) 1.43338 0.0488779
\(861\) 0 0
\(862\) −9.54305 −0.325038
\(863\) −3.55527 + 6.15791i −0.121023 + 0.209618i −0.920171 0.391516i \(-0.871951\pi\)
0.799148 + 0.601134i \(0.205284\pi\)
\(864\) 0 0
\(865\) −0.701224 + 0.404852i −0.0238423 + 0.0137654i
\(866\) 0.364929 0.632075i 0.0124008 0.0214788i
\(867\) 0 0
\(868\) −10.4914 4.52526i −0.356103 0.153597i
\(869\) 29.4908 15.9283i 1.00041 0.540330i
\(870\) 0 0
\(871\) −21.7818 37.7273i −0.738050 1.27834i
\(872\) −1.65721 2.87038i −0.0561203 0.0972032i
\(873\) 0 0
\(874\) 35.6221i 1.20494i
\(875\) 0.685257 + 5.86149i 0.0231659 + 0.198155i
\(876\) 0 0
\(877\) 19.7715 + 11.4151i 0.667636 + 0.385460i 0.795180 0.606373i \(-0.207376\pi\)
−0.127544 + 0.991833i \(0.540709\pi\)
\(878\) −22.4835 + 12.9809i −0.758781 + 0.438082i
\(879\) 0 0
\(880\) 0.0210981 0.743218i 0.000711218 0.0250539i
\(881\) 28.5824i 0.962967i 0.876455 + 0.481483i \(0.159902\pi\)
−0.876455 + 0.481483i \(0.840098\pi\)
\(882\) 0 0
\(883\) 40.1298 1.35048 0.675238 0.737600i \(-0.264041\pi\)
0.675238 + 0.737600i \(0.264041\pi\)
\(884\) 19.7651 34.2342i 0.664774 1.15142i
\(885\) 0 0
\(886\) −15.2430 + 8.80056i −0.512099 + 0.295661i
\(887\) 8.30087 14.3775i 0.278716 0.482750i −0.692350 0.721562i \(-0.743425\pi\)
0.971066 + 0.238812i \(0.0767579\pi\)
\(888\) 0 0
\(889\) −2.53062 21.6462i −0.0848744 0.725991i
\(890\) 2.35644i 0.0789880i
\(891\) 0 0
\(892\) 17.8825 10.3245i 0.598751 0.345689i
\(893\) −21.4868 + 12.4054i −0.719028 + 0.415131i
\(894\) 0 0
\(895\) 0.571006i 0.0190866i
\(896\) −2.42940 1.04787i −0.0811605 0.0350068i
\(897\) 0 0
\(898\) 7.72712 + 4.46125i 0.257857 + 0.148874i
\(899\) −12.2174 21.1612i −0.407475 0.705767i
\(900\) 0 0
\(901\) −8.44401 + 14.6255i −0.281311 + 0.487245i
\(902\) −1.66025 + 0.896716i −0.0552801 + 0.0298574i
\(903\) 0 0
\(904\) 17.4297i 0.579704i
\(905\) 0.776579 1.34507i 0.0258144 0.0447118i
\(906\) 0 0
\(907\) −12.6308 21.8771i −0.419398 0.726419i 0.576481 0.817111i \(-0.304425\pi\)
−0.995879 + 0.0906919i \(0.971092\pi\)
\(908\) −1.61465 + 2.79665i −0.0535840 + 0.0928102i
\(909\) 0 0
\(910\) −1.78217 2.39374i −0.0590782 0.0793517i
\(911\) −0.530745 −0.0175844 −0.00879219 0.999961i \(-0.502799\pi\)
−0.00879219 + 0.999961i \(0.502799\pi\)
\(912\) 0 0
\(913\) −24.8519 + 40.3550i −0.822477 + 1.33556i
\(914\) 14.0485 + 24.3327i 0.464682 + 0.804853i
\(915\) 0 0
\(916\) 7.96882i 0.263297i
\(917\) −2.24250 + 5.19905i −0.0740538 + 0.171688i
\(918\) 0 0
\(919\) −21.2350 12.2601i −0.700480 0.404422i 0.107046 0.994254i \(-0.465861\pi\)
−0.807526 + 0.589832i \(0.799194\pi\)
\(920\) −0.544620 0.943309i −0.0179556 0.0311000i
\(921\) 0 0
\(922\) −16.2563 9.38560i −0.535374 0.309098i
\(923\) −58.8475 −1.93699
\(924\) 0 0
\(925\) 0.882140 0.0290046
\(926\) −6.55773 3.78611i −0.215500 0.124419i
\(927\) 0 0
\(928\) −2.82907 4.90010i −0.0928688 0.160854i
\(929\) 20.0150 + 11.5557i 0.656671 + 0.379129i 0.791008 0.611806i \(-0.209557\pi\)
−0.134336 + 0.990936i \(0.542890\pi\)
\(930\) 0 0
\(931\) 14.7164 49.1650i 0.482310 1.61132i
\(932\) 11.4196i 0.374060i
\(933\) 0 0
\(934\) −19.8812 34.4353i −0.650533 1.12676i
\(935\) −4.97394 3.06310i −0.162665 0.100174i
\(936\) 0 0
\(937\) 21.7695 0.711180 0.355590 0.934642i \(-0.384280\pi\)
0.355590 + 0.934642i \(0.384280\pi\)
\(938\) 2.65994 + 22.7523i 0.0868500 + 0.742890i
\(939\) 0 0
\(940\) 0.379328 0.657015i 0.0123723 0.0214295i
\(941\) 5.39515 + 9.34467i 0.175877 + 0.304628i 0.940464 0.339892i \(-0.110391\pi\)
−0.764588 + 0.644520i \(0.777057\pi\)
\(942\) 0 0
\(943\) −1.38216 + 2.39397i −0.0450093 + 0.0779585i
\(944\) 2.31992i 0.0755068i
\(945\) 0 0
\(946\) −10.0777 18.6586i −0.327655 0.606643i
\(947\) −4.56068 + 7.89933i −0.148202 + 0.256694i −0.930563 0.366132i \(-0.880682\pi\)
0.782361 + 0.622825i \(0.214015\pi\)
\(948\) 0 0
\(949\) 26.4442 + 45.8028i 0.858417 + 1.48682i
\(950\) 31.4271 + 18.1444i 1.01963 + 0.588684i
\(951\) 0 0
\(952\) −16.6729 + 12.4132i −0.540373 + 0.402314i
\(953\) 48.6873i 1.57714i 0.614947 + 0.788568i \(0.289177\pi\)
−0.614947 + 0.788568i \(0.710823\pi\)
\(954\) 0 0
\(955\) −0.131715 + 0.0760460i −0.00426221 + 0.00246079i
\(956\) 3.18067 1.83636i 0.102870 0.0593922i
\(957\) 0 0
\(958\) 18.6061i 0.601137i
\(959\) 17.9806 + 24.1509i 0.580625 + 0.779874i
\(960\) 0 0
\(961\) −6.17512 + 10.6956i −0.199198 + 0.345020i
\(962\) −0.776579 + 0.448358i −0.0250379 + 0.0144556i
\(963\) 0 0
\(964\) −10.4731 + 18.1399i −0.337316 + 0.584248i
\(965\) 5.37918 0.173162
\(966\) 0 0
\(967\) 38.8957i 1.25080i 0.780304 + 0.625401i \(0.215065\pi\)
−0.780304 + 0.625401i \(0.784935\pi\)
\(968\) −9.82295 + 4.95072i −0.315722 + 0.159122i
\(969\) 0 0
\(970\) −0.769051 + 0.444012i −0.0246928 + 0.0142564i
\(971\) 15.1953 + 8.77301i 0.487640 + 0.281539i 0.723595 0.690225i \(-0.242488\pi\)
−0.235955 + 0.971764i \(0.575822\pi\)
\(972\) 0 0
\(973\) −37.0521 + 4.33170i −1.18784 + 0.138868i
\(974\) 20.4689i 0.655867i
\(975\) 0 0
\(976\) 2.19784 + 3.80677i 0.0703511 + 0.121852i
\(977\) −30.2650 52.4205i −0.968263 1.67708i −0.700580 0.713574i \(-0.747075\pi\)
−0.267683 0.963507i \(-0.586258\pi\)
\(978\) 0 0
\(979\) 30.6742 16.5675i 0.980352 0.529499i
\(980\) 0.361970 + 1.52694i 0.0115627 + 0.0487762i
\(981\) 0 0
\(982\) 14.7967 25.6286i 0.472180 0.817840i
\(983\) 33.6952 19.4539i 1.07471 0.620484i 0.145245 0.989396i \(-0.453603\pi\)
0.929464 + 0.368912i \(0.120270\pi\)
\(984\) 0 0
\(985\) 1.51259 2.61989i 0.0481952 0.0834765i
\(986\) −44.4533 −1.41568
\(987\) 0 0
\(988\) −36.8885 −1.17358
\(989\) −26.9046 15.5334i −0.855515 0.493932i
\(990\) 0 0
\(991\) −7.41269 12.8391i −0.235472 0.407849i 0.723938 0.689865i \(-0.242330\pi\)
−0.959410 + 0.282016i \(0.908997\pi\)
\(992\) 2.15927 3.73996i 0.0685568 0.118744i
\(993\) 0 0
\(994\) 28.4136 + 12.2556i 0.901225 + 0.388724i
\(995\) 4.04403 0.128204
\(996\) 0 0
\(997\) 2.94741 + 5.10507i 0.0933456 + 0.161679i 0.908917 0.416977i \(-0.136911\pi\)
−0.815571 + 0.578657i \(0.803577\pi\)
\(998\) 6.44839 3.72298i 0.204120 0.117849i
\(999\) 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 1386.2.bk.d.901.2 yes 32
3.2 odd 2 inner 1386.2.bk.d.901.9 yes 32
7.3 odd 6 inner 1386.2.bk.d.703.10 yes 32
11.10 odd 2 inner 1386.2.bk.d.901.10 yes 32
21.17 even 6 inner 1386.2.bk.d.703.1 32
33.32 even 2 inner 1386.2.bk.d.901.1 yes 32
77.10 even 6 inner 1386.2.bk.d.703.2 yes 32
231.164 odd 6 inner 1386.2.bk.d.703.9 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1386.2.bk.d.703.1 32 21.17 even 6 inner
1386.2.bk.d.703.2 yes 32 77.10 even 6 inner
1386.2.bk.d.703.9 yes 32 231.164 odd 6 inner
1386.2.bk.d.703.10 yes 32 7.3 odd 6 inner
1386.2.bk.d.901.1 yes 32 33.32 even 2 inner
1386.2.bk.d.901.2 yes 32 1.1 even 1 trivial
1386.2.bk.d.901.9 yes 32 3.2 odd 2 inner
1386.2.bk.d.901.10 yes 32 11.10 odd 2 inner