Properties

Label 99.3.l.a.71.6
Level $99$
Weight $3$
Character 99.71
Analytic conductor $2.698$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [99,3,Mod(26,99)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(99, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 2]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("99.26");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 99.l (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.69755461717\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 71.6
Character \(\chi\) \(=\) 99.71
Dual form 99.3.l.a.53.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.28527 - 0.417608i) q^{2} +(-1.75856 + 1.27767i) q^{4} +(4.85485 + 1.57744i) q^{5} +(10.6531 - 7.73991i) q^{7} +(-4.90400 + 6.74978i) q^{8} +O(q^{10})\) \(q+(1.28527 - 0.417608i) q^{2} +(-1.75856 + 1.27767i) q^{4} +(4.85485 + 1.57744i) q^{5} +(10.6531 - 7.73991i) q^{7} +(-4.90400 + 6.74978i) q^{8} +6.89852 q^{10} +(4.16151 + 10.1824i) q^{11} +(-0.825159 - 2.53958i) q^{13} +(10.4598 - 14.3966i) q^{14} +(-0.797348 + 2.45398i) q^{16} +(-16.3735 - 5.32007i) q^{17} +(-24.7742 - 17.9995i) q^{19} +(-10.5530 + 3.42886i) q^{20} +(9.60091 + 11.3492i) q^{22} +15.5309i q^{23} +(0.855829 + 0.621796i) q^{25} +(-2.12110 - 2.91944i) q^{26} +(-8.84500 + 27.2221i) q^{28} +(-6.10287 - 8.39987i) q^{29} +(5.21245 + 16.0423i) q^{31} -29.8857i q^{32} -23.2660 q^{34} +(63.9282 - 20.7715i) q^{35} +(-15.1698 + 11.0215i) q^{37} +(-39.3582 - 12.7883i) q^{38} +(-34.4555 + 25.0334i) q^{40} +(7.85173 - 10.8070i) q^{41} +10.5356 q^{43} +(-20.3280 - 12.5893i) q^{44} +(6.48583 + 19.9613i) q^{46} +(-48.3198 + 66.5065i) q^{47} +(38.4399 - 118.306i) q^{49} +(1.35963 + 0.441772i) q^{50} +(4.69582 + 3.41171i) q^{52} +(59.9022 - 19.4634i) q^{53} +(4.14138 + 55.9987i) q^{55} +109.862i q^{56} +(-11.3517 - 8.24747i) q^{58} +(-38.7385 - 53.3189i) q^{59} +(11.2965 - 34.7670i) q^{61} +(13.3988 + 18.4418i) q^{62} +(-15.6699 - 48.2271i) q^{64} -13.6309i q^{65} +60.5815 q^{67} +(35.5909 - 11.5642i) q^{68} +(73.4904 - 53.3939i) q^{70} +(-46.7818 - 15.2003i) q^{71} +(-5.15593 + 3.74600i) q^{73} +(-14.8946 + 20.5007i) q^{74} +66.5643 q^{76} +(123.144 + 76.2644i) q^{77} +(35.5533 + 109.422i) q^{79} +(-7.74201 + 10.6560i) q^{80} +(5.57848 - 17.1688i) q^{82} +(38.5111 + 12.5130i) q^{83} +(-71.0987 - 51.6562i) q^{85} +(13.5411 - 4.39977i) q^{86} +(-89.1372 - 21.8454i) q^{88} +71.1308i q^{89} +(-28.4466 - 20.6676i) q^{91} +(-19.8433 - 27.3120i) q^{92} +(-34.3301 + 105.657i) q^{94} +(-91.8821 - 126.465i) q^{95} +(5.76879 + 17.7545i) q^{97} -168.107i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 16 q^{4} - 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 16 q^{4} - 16 q^{7} + 48 q^{10} + 8 q^{13} + 96 q^{16} - 40 q^{19} - 60 q^{22} - 188 q^{25} - 348 q^{28} - 164 q^{31} + 296 q^{34} - 36 q^{37} + 48 q^{40} + 544 q^{43} + 296 q^{46} + 196 q^{49} - 640 q^{52} - 440 q^{55} - 208 q^{58} - 432 q^{61} - 328 q^{64} + 48 q^{67} + 112 q^{70} + 712 q^{73} + 2104 q^{76} + 432 q^{79} + 676 q^{82} - 68 q^{85} - 176 q^{88} + 64 q^{91} - 1360 q^{94} + 132 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.28527 0.417608i 0.642633 0.208804i 0.0304699 0.999536i \(-0.490300\pi\)
0.612163 + 0.790732i \(0.290300\pi\)
\(3\) 0 0
\(4\) −1.75856 + 1.27767i −0.439639 + 0.319416i
\(5\) 4.85485 + 1.57744i 0.970970 + 0.315487i 0.751207 0.660066i \(-0.229472\pi\)
0.219762 + 0.975553i \(0.429472\pi\)
\(6\) 0 0
\(7\) 10.6531 7.73991i 1.52187 1.10570i 0.561314 0.827603i \(-0.310296\pi\)
0.960553 0.278098i \(-0.0897040\pi\)
\(8\) −4.90400 + 6.74978i −0.613000 + 0.843722i
\(9\) 0 0
\(10\) 6.89852 0.689852
\(11\) 4.16151 + 10.1824i 0.378319 + 0.925675i
\(12\) 0 0
\(13\) −0.825159 2.53958i −0.0634737 0.195352i 0.914291 0.405059i \(-0.132749\pi\)
−0.977764 + 0.209707i \(0.932749\pi\)
\(14\) 10.4598 14.3966i 0.747127 1.02833i
\(15\) 0 0
\(16\) −0.797348 + 2.45398i −0.0498342 + 0.153374i
\(17\) −16.3735 5.32007i −0.963146 0.312945i −0.215100 0.976592i \(-0.569008\pi\)
−0.748046 + 0.663647i \(0.769008\pi\)
\(18\) 0 0
\(19\) −24.7742 17.9995i −1.30391 0.947344i −0.303922 0.952697i \(-0.598296\pi\)
−0.999986 + 0.00535276i \(0.998296\pi\)
\(20\) −10.5530 + 3.42886i −0.527648 + 0.171443i
\(21\) 0 0
\(22\) 9.60091 + 11.3492i 0.436405 + 0.515875i
\(23\) 15.5309i 0.675257i 0.941279 + 0.337628i \(0.109625\pi\)
−0.941279 + 0.337628i \(0.890375\pi\)
\(24\) 0 0
\(25\) 0.855829 + 0.621796i 0.0342332 + 0.0248718i
\(26\) −2.12110 2.91944i −0.0815806 0.112286i
\(27\) 0 0
\(28\) −8.84500 + 27.2221i −0.315893 + 0.972218i
\(29\) −6.10287 8.39987i −0.210444 0.289651i 0.690727 0.723116i \(-0.257291\pi\)
−0.901170 + 0.433465i \(0.857291\pi\)
\(30\) 0 0
\(31\) 5.21245 + 16.0423i 0.168144 + 0.517493i 0.999254 0.0386144i \(-0.0122944\pi\)
−0.831111 + 0.556107i \(0.812294\pi\)
\(32\) 29.8857i 0.933929i
\(33\) 0 0
\(34\) −23.2660 −0.684294
\(35\) 63.9282 20.7715i 1.82652 0.593473i
\(36\) 0 0
\(37\) −15.1698 + 11.0215i −0.409996 + 0.297879i −0.773600 0.633674i \(-0.781546\pi\)
0.363604 + 0.931553i \(0.381546\pi\)
\(38\) −39.3582 12.7883i −1.03574 0.336533i
\(39\) 0 0
\(40\) −34.4555 + 25.0334i −0.861388 + 0.625835i
\(41\) 7.85173 10.8070i 0.191506 0.263585i −0.702457 0.711726i \(-0.747914\pi\)
0.893963 + 0.448141i \(0.147914\pi\)
\(42\) 0 0
\(43\) 10.5356 0.245015 0.122507 0.992468i \(-0.460907\pi\)
0.122507 + 0.992468i \(0.460907\pi\)
\(44\) −20.3280 12.5893i −0.462000 0.286122i
\(45\) 0 0
\(46\) 6.48583 + 19.9613i 0.140996 + 0.433942i
\(47\) −48.3198 + 66.5065i −1.02808 + 1.41503i −0.121700 + 0.992567i \(0.538835\pi\)
−0.906380 + 0.422464i \(0.861165\pi\)
\(48\) 0 0
\(49\) 38.4399 118.306i 0.784487 2.41440i
\(50\) 1.35963 + 0.441772i 0.0271927 + 0.00883544i
\(51\) 0 0
\(52\) 4.69582 + 3.41171i 0.0903042 + 0.0656098i
\(53\) 59.9022 19.4634i 1.13023 0.367234i 0.316567 0.948570i \(-0.397470\pi\)
0.813663 + 0.581336i \(0.197470\pi\)
\(54\) 0 0
\(55\) 4.14138 + 55.9987i 0.0752978 + 1.01816i
\(56\) 109.862i 1.96183i
\(57\) 0 0
\(58\) −11.3517 8.24747i −0.195718 0.142198i
\(59\) −38.7385 53.3189i −0.656584 0.903711i 0.342778 0.939416i \(-0.388632\pi\)
−0.999362 + 0.0357057i \(0.988632\pi\)
\(60\) 0 0
\(61\) 11.2965 34.7670i 0.185188 0.569951i −0.814763 0.579794i \(-0.803133\pi\)
0.999952 + 0.00984300i \(0.00313318\pi\)
\(62\) 13.3988 + 18.4418i 0.216109 + 0.297449i
\(63\) 0 0
\(64\) −15.6699 48.2271i −0.244843 0.753548i
\(65\) 13.6309i 0.209706i
\(66\) 0 0
\(67\) 60.5815 0.904202 0.452101 0.891967i \(-0.350675\pi\)
0.452101 + 0.891967i \(0.350675\pi\)
\(68\) 35.5909 11.5642i 0.523396 0.170062i
\(69\) 0 0
\(70\) 73.4904 53.3939i 1.04986 0.762770i
\(71\) −46.7818 15.2003i −0.658899 0.214089i −0.0395649 0.999217i \(-0.512597\pi\)
−0.619334 + 0.785128i \(0.712597\pi\)
\(72\) 0 0
\(73\) −5.15593 + 3.74600i −0.0706291 + 0.0513151i −0.622540 0.782588i \(-0.713899\pi\)
0.551910 + 0.833903i \(0.313899\pi\)
\(74\) −14.8946 + 20.5007i −0.201278 + 0.277036i
\(75\) 0 0
\(76\) 66.5643 0.875846
\(77\) 123.144 + 76.2644i 1.59927 + 0.990447i
\(78\) 0 0
\(79\) 35.5533 + 109.422i 0.450042 + 1.38509i 0.876859 + 0.480748i \(0.159635\pi\)
−0.426817 + 0.904338i \(0.640365\pi\)
\(80\) −7.74201 + 10.6560i −0.0967751 + 0.133199i
\(81\) 0 0
\(82\) 5.57848 17.1688i 0.0680302 0.209375i
\(83\) 38.5111 + 12.5130i 0.463989 + 0.150759i 0.531677 0.846947i \(-0.321562\pi\)
−0.0676879 + 0.997707i \(0.521562\pi\)
\(84\) 0 0
\(85\) −71.0987 51.6562i −0.836455 0.607720i
\(86\) 13.5411 4.39977i 0.157454 0.0511601i
\(87\) 0 0
\(88\) −89.1372 21.8454i −1.01292 0.248243i
\(89\) 71.1308i 0.799222i 0.916685 + 0.399611i \(0.130855\pi\)
−0.916685 + 0.399611i \(0.869145\pi\)
\(90\) 0 0
\(91\) −28.4466 20.6676i −0.312600 0.227117i
\(92\) −19.8433 27.3120i −0.215688 0.296869i
\(93\) 0 0
\(94\) −34.3301 + 105.657i −0.365214 + 1.12401i
\(95\) −91.8821 126.465i −0.967180 1.33121i
\(96\) 0 0
\(97\) 5.76879 + 17.7545i 0.0594721 + 0.183036i 0.976379 0.216065i \(-0.0693223\pi\)
−0.916907 + 0.399101i \(0.869322\pi\)
\(98\) 168.107i 1.71538i
\(99\) 0 0
\(100\) −2.29947 −0.0229947
\(101\) 44.7592 14.5432i 0.443161 0.143992i −0.0789326 0.996880i \(-0.525151\pi\)
0.522093 + 0.852888i \(0.325151\pi\)
\(102\) 0 0
\(103\) −90.1550 + 65.5015i −0.875292 + 0.635937i −0.932002 0.362454i \(-0.881939\pi\)
0.0567100 + 0.998391i \(0.481939\pi\)
\(104\) 21.1882 + 6.88445i 0.203732 + 0.0661966i
\(105\) 0 0
\(106\) 68.8622 50.0313i 0.649643 0.471993i
\(107\) −65.1737 + 89.7039i −0.609100 + 0.838354i −0.996503 0.0835565i \(-0.973372\pi\)
0.387403 + 0.921910i \(0.373372\pi\)
\(108\) 0 0
\(109\) 118.337 1.08566 0.542832 0.839841i \(-0.317352\pi\)
0.542832 + 0.839841i \(0.317352\pi\)
\(110\) 28.7083 + 70.2437i 0.260984 + 0.638579i
\(111\) 0 0
\(112\) 10.4994 + 32.3139i 0.0937447 + 0.288517i
\(113\) 40.7594 56.1005i 0.360702 0.496464i −0.589642 0.807665i \(-0.700731\pi\)
0.950344 + 0.311200i \(0.100731\pi\)
\(114\) 0 0
\(115\) −24.4990 + 75.4002i −0.213035 + 0.655654i
\(116\) 21.4645 + 6.97423i 0.185038 + 0.0601226i
\(117\) 0 0
\(118\) −72.0557 52.3515i −0.610641 0.443657i
\(119\) −215.605 + 70.0542i −1.81180 + 0.588691i
\(120\) 0 0
\(121\) −86.3637 + 84.7486i −0.713749 + 0.700401i
\(122\) 49.4023i 0.404937i
\(123\) 0 0
\(124\) −29.6630 21.5515i −0.239218 0.173802i
\(125\) −71.8375 98.8758i −0.574700 0.791006i
\(126\) 0 0
\(127\) 3.32960 10.2475i 0.0262174 0.0806887i −0.937092 0.349083i \(-0.886493\pi\)
0.963309 + 0.268394i \(0.0864931\pi\)
\(128\) 29.9855 + 41.2716i 0.234262 + 0.322434i
\(129\) 0 0
\(130\) −5.69237 17.5193i −0.0437875 0.134764i
\(131\) 92.0724i 0.702843i −0.936217 0.351421i \(-0.885698\pi\)
0.936217 0.351421i \(-0.114302\pi\)
\(132\) 0 0
\(133\) −403.236 −3.03185
\(134\) 77.8633 25.2993i 0.581070 0.188801i
\(135\) 0 0
\(136\) 116.205 84.4277i 0.854447 0.620792i
\(137\) −188.928 61.3865i −1.37904 0.448077i −0.476685 0.879074i \(-0.658162\pi\)
−0.902353 + 0.430998i \(0.858162\pi\)
\(138\) 0 0
\(139\) 48.1649 34.9938i 0.346510 0.251754i −0.400894 0.916125i \(-0.631300\pi\)
0.747403 + 0.664371i \(0.231300\pi\)
\(140\) −85.8823 + 118.207i −0.613445 + 0.844335i
\(141\) 0 0
\(142\) −66.4748 −0.468133
\(143\) 22.4252 18.9706i 0.156819 0.132661i
\(144\) 0 0
\(145\) −16.3782 50.4070i −0.112953 0.347634i
\(146\) −5.06238 + 6.96776i −0.0346738 + 0.0477244i
\(147\) 0 0
\(148\) 12.5952 38.7640i 0.0851025 0.261919i
\(149\) 13.8516 + 4.50065i 0.0929636 + 0.0302057i 0.355129 0.934817i \(-0.384437\pi\)
−0.262166 + 0.965023i \(0.584437\pi\)
\(150\) 0 0
\(151\) 197.075 + 143.183i 1.30513 + 0.948234i 0.999992 0.00407377i \(-0.00129672\pi\)
0.305140 + 0.952307i \(0.401297\pi\)
\(152\) 242.986 78.9509i 1.59859 0.519414i
\(153\) 0 0
\(154\) 190.121 + 46.5941i 1.23455 + 0.302559i
\(155\) 86.1051i 0.555517i
\(156\) 0 0
\(157\) 89.8278 + 65.2637i 0.572151 + 0.415692i 0.835886 0.548903i \(-0.184954\pi\)
−0.263735 + 0.964595i \(0.584954\pi\)
\(158\) 91.3909 + 125.789i 0.578423 + 0.796131i
\(159\) 0 0
\(160\) 47.1428 145.091i 0.294643 0.906817i
\(161\) 120.208 + 165.452i 0.746632 + 1.02765i
\(162\) 0 0
\(163\) 38.0567 + 117.126i 0.233477 + 0.718567i 0.997320 + 0.0731653i \(0.0233101\pi\)
−0.763843 + 0.645402i \(0.776690\pi\)
\(164\) 29.0365i 0.177052i
\(165\) 0 0
\(166\) 54.7225 0.329654
\(167\) 217.801 70.7679i 1.30420 0.423760i 0.427159 0.904177i \(-0.359515\pi\)
0.877040 + 0.480417i \(0.159515\pi\)
\(168\) 0 0
\(169\) 130.955 95.1446i 0.774883 0.562986i
\(170\) −112.953 36.7006i −0.664428 0.215886i
\(171\) 0 0
\(172\) −18.5275 + 13.4610i −0.107718 + 0.0782617i
\(173\) 101.498 139.699i 0.586691 0.807511i −0.407718 0.913108i \(-0.633675\pi\)
0.994409 + 0.105597i \(0.0336754\pi\)
\(174\) 0 0
\(175\) 13.9298 0.0795991
\(176\) −28.3057 + 2.09335i −0.160828 + 0.0118940i
\(177\) 0 0
\(178\) 29.7048 + 91.4220i 0.166881 + 0.513607i
\(179\) −107.266 + 147.639i −0.599252 + 0.824800i −0.995640 0.0932832i \(-0.970264\pi\)
0.396387 + 0.918083i \(0.370264\pi\)
\(180\) 0 0
\(181\) 37.6199 115.782i 0.207845 0.639680i −0.791740 0.610858i \(-0.790824\pi\)
0.999585 0.0288218i \(-0.00917553\pi\)
\(182\) −45.1924 14.6839i −0.248310 0.0806807i
\(183\) 0 0
\(184\) −104.830 76.1636i −0.569729 0.413932i
\(185\) −91.0330 + 29.5784i −0.492071 + 0.159883i
\(186\) 0 0
\(187\) −13.9672 188.861i −0.0746910 1.00995i
\(188\) 178.692i 0.950488i
\(189\) 0 0
\(190\) −170.906 124.170i −0.899503 0.653528i
\(191\) 184.809 + 254.368i 0.967588 + 1.33177i 0.943256 + 0.332067i \(0.107746\pi\)
0.0243324 + 0.999704i \(0.492254\pi\)
\(192\) 0 0
\(193\) 38.4388 118.302i 0.199165 0.612966i −0.800738 0.599015i \(-0.795559\pi\)
0.999903 0.0139512i \(-0.00444094\pi\)
\(194\) 14.8289 + 20.4102i 0.0764374 + 0.105207i
\(195\) 0 0
\(196\) 83.5565 + 257.161i 0.426309 + 1.31204i
\(197\) 193.993i 0.984738i 0.870387 + 0.492369i \(0.163869\pi\)
−0.870387 + 0.492369i \(0.836131\pi\)
\(198\) 0 0
\(199\) −67.6934 −0.340168 −0.170084 0.985430i \(-0.554404\pi\)
−0.170084 + 0.985430i \(0.554404\pi\)
\(200\) −8.39397 + 2.72737i −0.0419699 + 0.0136368i
\(201\) 0 0
\(202\) 51.4542 37.3837i 0.254724 0.185068i
\(203\) −130.028 42.2488i −0.640534 0.208122i
\(204\) 0 0
\(205\) 55.1663 40.0806i 0.269104 0.195515i
\(206\) −88.5193 + 121.836i −0.429705 + 0.591438i
\(207\) 0 0
\(208\) 6.89002 0.0331251
\(209\) 80.1807 327.167i 0.383640 1.56539i
\(210\) 0 0
\(211\) 23.1912 + 71.3752i 0.109911 + 0.338271i 0.990852 0.134955i \(-0.0430891\pi\)
−0.880941 + 0.473227i \(0.843089\pi\)
\(212\) −80.4736 + 110.762i −0.379593 + 0.522464i
\(213\) 0 0
\(214\) −46.3044 + 142.510i −0.216376 + 0.665936i
\(215\) 51.1489 + 16.6193i 0.237902 + 0.0772990i
\(216\) 0 0
\(217\) 179.694 + 130.556i 0.828084 + 0.601638i
\(218\) 152.095 49.4187i 0.697684 0.226691i
\(219\) 0 0
\(220\) −78.8304 93.1855i −0.358320 0.423570i
\(221\) 45.9716i 0.208016i
\(222\) 0 0
\(223\) 4.83651 + 3.51393i 0.0216884 + 0.0157575i 0.598577 0.801066i \(-0.295733\pi\)
−0.576888 + 0.816823i \(0.695733\pi\)
\(224\) −231.313 318.375i −1.03265 1.42132i
\(225\) 0 0
\(226\) 28.9586 89.1255i 0.128136 0.394361i
\(227\) −98.9713 136.222i −0.435997 0.600098i 0.533320 0.845914i \(-0.320944\pi\)
−0.969317 + 0.245815i \(0.920944\pi\)
\(228\) 0 0
\(229\) −108.832 334.950i −0.475249 1.46267i −0.845622 0.533782i \(-0.820770\pi\)
0.370373 0.928883i \(-0.379230\pi\)
\(230\) 107.140i 0.465827i
\(231\) 0 0
\(232\) 86.6257 0.373387
\(233\) −338.664 + 110.039i −1.45349 + 0.472268i −0.926076 0.377338i \(-0.876840\pi\)
−0.527417 + 0.849606i \(0.676840\pi\)
\(234\) 0 0
\(235\) −339.495 + 246.657i −1.44466 + 1.04961i
\(236\) 136.248 + 44.2695i 0.577320 + 0.187583i
\(237\) 0 0
\(238\) −247.854 + 180.077i −1.04140 + 0.756624i
\(239\) 10.2500 14.1079i 0.0428871 0.0590290i −0.787035 0.616908i \(-0.788385\pi\)
0.829922 + 0.557879i \(0.188385\pi\)
\(240\) 0 0
\(241\) −98.6722 −0.409428 −0.204714 0.978822i \(-0.565626\pi\)
−0.204714 + 0.978822i \(0.565626\pi\)
\(242\) −75.6086 + 144.991i −0.312432 + 0.599135i
\(243\) 0 0
\(244\) 24.5551 + 75.5728i 0.100636 + 0.309725i
\(245\) 373.239 513.720i 1.52343 2.09682i
\(246\) 0 0
\(247\) −25.2685 + 77.7686i −0.102302 + 0.314852i
\(248\) −133.844 43.4884i −0.539692 0.175357i
\(249\) 0 0
\(250\) −133.622 97.0818i −0.534486 0.388327i
\(251\) −168.627 + 54.7903i −0.671821 + 0.218288i −0.625011 0.780616i \(-0.714906\pi\)
−0.0468100 + 0.998904i \(0.514906\pi\)
\(252\) 0 0
\(253\) −158.142 + 64.6320i −0.625068 + 0.255463i
\(254\) 14.5612i 0.0573275i
\(255\) 0 0
\(256\) 219.872 + 159.747i 0.858876 + 0.624010i
\(257\) 67.7862 + 93.2997i 0.263760 + 0.363034i 0.920271 0.391283i \(-0.127968\pi\)
−0.656511 + 0.754316i \(0.727968\pi\)
\(258\) 0 0
\(259\) −76.2997 + 234.826i −0.294593 + 0.906665i
\(260\) 17.4157 + 23.9707i 0.0669836 + 0.0921950i
\(261\) 0 0
\(262\) −38.4502 118.338i −0.146756 0.451670i
\(263\) 236.953i 0.900964i −0.892786 0.450482i \(-0.851252\pi\)
0.892786 0.450482i \(-0.148748\pi\)
\(264\) 0 0
\(265\) 321.518 1.21328
\(266\) −518.266 + 168.395i −1.94837 + 0.633063i
\(267\) 0 0
\(268\) −106.536 + 77.4029i −0.397522 + 0.288817i
\(269\) 502.614 + 163.309i 1.86845 + 0.607097i 0.992104 + 0.125419i \(0.0400275\pi\)
0.876348 + 0.481678i \(0.159973\pi\)
\(270\) 0 0
\(271\) 144.762 105.176i 0.534178 0.388103i −0.287740 0.957708i \(-0.592904\pi\)
0.821918 + 0.569606i \(0.192904\pi\)
\(272\) 26.1107 35.9383i 0.0959953 0.132126i
\(273\) 0 0
\(274\) −268.458 −0.979775
\(275\) −2.76985 + 11.3020i −0.0100722 + 0.0410983i
\(276\) 0 0
\(277\) −88.4454 272.207i −0.319297 0.982696i −0.973949 0.226766i \(-0.927185\pi\)
0.654652 0.755930i \(-0.272815\pi\)
\(278\) 47.2910 65.0904i 0.170111 0.234138i
\(279\) 0 0
\(280\) −173.301 + 533.365i −0.618932 + 1.90488i
\(281\) 241.030 + 78.3155i 0.857760 + 0.278703i 0.704693 0.709513i \(-0.251085\pi\)
0.153067 + 0.988216i \(0.451085\pi\)
\(282\) 0 0
\(283\) 229.170 + 166.502i 0.809788 + 0.588346i 0.913769 0.406234i \(-0.133158\pi\)
−0.103981 + 0.994579i \(0.533158\pi\)
\(284\) 101.689 33.0409i 0.358061 0.116341i
\(285\) 0 0
\(286\) 20.9000 33.7472i 0.0730769 0.117997i
\(287\) 175.899i 0.612889i
\(288\) 0 0
\(289\) 5.98182 + 4.34605i 0.0206983 + 0.0150382i
\(290\) −42.1008 57.9467i −0.145175 0.199816i
\(291\) 0 0
\(292\) 4.28085 13.1751i 0.0146604 0.0451202i
\(293\) −175.920 242.133i −0.600409 0.826393i 0.395336 0.918536i \(-0.370628\pi\)
−0.995746 + 0.0921437i \(0.970628\pi\)
\(294\) 0 0
\(295\) −103.962 319.963i −0.352414 1.08462i
\(296\) 156.443i 0.528523i
\(297\) 0 0
\(298\) 19.6825 0.0660485
\(299\) 39.4419 12.8155i 0.131913 0.0428611i
\(300\) 0 0
\(301\) 112.237 81.5448i 0.372880 0.270913i
\(302\) 313.088 + 101.729i 1.03672 + 0.336849i
\(303\) 0 0
\(304\) 63.9243 46.4437i 0.210277 0.152775i
\(305\) 109.685 150.969i 0.359624 0.494980i
\(306\) 0 0
\(307\) 111.839 0.364296 0.182148 0.983271i \(-0.441695\pi\)
0.182148 + 0.983271i \(0.441695\pi\)
\(308\) −313.996 + 23.2215i −1.01947 + 0.0753946i
\(309\) 0 0
\(310\) 35.9582 + 110.668i 0.115994 + 0.356993i
\(311\) −209.419 + 288.240i −0.673372 + 0.926817i −0.999831 0.0183943i \(-0.994145\pi\)
0.326459 + 0.945211i \(0.394145\pi\)
\(312\) 0 0
\(313\) 104.677 322.163i 0.334431 1.02927i −0.632570 0.774503i \(-0.718000\pi\)
0.967001 0.254771i \(-0.0820000\pi\)
\(314\) 142.707 + 46.3684i 0.454482 + 0.147670i
\(315\) 0 0
\(316\) −202.327 146.999i −0.640275 0.465187i
\(317\) −384.837 + 125.041i −1.21400 + 0.394452i −0.844893 0.534936i \(-0.820336\pi\)
−0.369105 + 0.929388i \(0.620336\pi\)
\(318\) 0 0
\(319\) 60.1340 97.0982i 0.188508 0.304383i
\(320\) 258.853i 0.808917i
\(321\) 0 0
\(322\) 223.593 + 162.450i 0.694388 + 0.504502i
\(323\) 309.882 + 426.516i 0.959386 + 1.32048i
\(324\) 0 0
\(325\) 0.872904 2.68652i 0.00268586 0.00826623i
\(326\) 97.8259 + 134.646i 0.300080 + 0.413024i
\(327\) 0 0
\(328\) 34.4398 + 105.995i 0.104999 + 0.323155i
\(329\) 1082.49i 3.29024i
\(330\) 0 0
\(331\) 634.065 1.91561 0.957803 0.287426i \(-0.0927995\pi\)
0.957803 + 0.287426i \(0.0927995\pi\)
\(332\) −83.7113 + 27.1994i −0.252142 + 0.0819260i
\(333\) 0 0
\(334\) 250.379 181.911i 0.749639 0.544644i
\(335\) 294.114 + 95.5634i 0.877952 + 0.285264i
\(336\) 0 0
\(337\) −192.071 + 139.547i −0.569942 + 0.414087i −0.835084 0.550122i \(-0.814581\pi\)
0.265142 + 0.964209i \(0.414581\pi\)
\(338\) 128.579 176.974i 0.380412 0.523592i
\(339\) 0 0
\(340\) 191.030 0.561854
\(341\) −141.658 + 119.835i −0.415418 + 0.351424i
\(342\) 0 0
\(343\) −306.786 944.192i −0.894421 2.75275i
\(344\) −51.6667 + 71.1132i −0.150194 + 0.206724i
\(345\) 0 0
\(346\) 72.1117 221.937i 0.208415 0.641436i
\(347\) −463.624 150.641i −1.33609 0.434123i −0.448102 0.893983i \(-0.647900\pi\)
−0.887992 + 0.459859i \(0.847900\pi\)
\(348\) 0 0
\(349\) −30.7829 22.3651i −0.0882033 0.0640834i 0.542810 0.839856i \(-0.317361\pi\)
−0.631013 + 0.775772i \(0.717361\pi\)
\(350\) 17.9036 5.81722i 0.0511530 0.0166206i
\(351\) 0 0
\(352\) 304.309 124.370i 0.864515 0.353323i
\(353\) 90.5379i 0.256481i −0.991743 0.128241i \(-0.959067\pi\)
0.991743 0.128241i \(-0.0409330\pi\)
\(354\) 0 0
\(355\) −203.141 147.591i −0.572228 0.415748i
\(356\) −90.8813 125.087i −0.255285 0.351369i
\(357\) 0 0
\(358\) −76.2102 + 234.551i −0.212878 + 0.655170i
\(359\) −65.8242 90.5992i −0.183354 0.252366i 0.707439 0.706775i \(-0.249850\pi\)
−0.890793 + 0.454409i \(0.849850\pi\)
\(360\) 0 0
\(361\) 178.224 + 548.519i 0.493697 + 1.51944i
\(362\) 164.521i 0.454478i
\(363\) 0 0
\(364\) 76.4312 0.209976
\(365\) −30.9403 + 10.0531i −0.0847680 + 0.0275428i
\(366\) 0 0
\(367\) −274.088 + 199.136i −0.746833 + 0.542606i −0.894844 0.446380i \(-0.852713\pi\)
0.148010 + 0.988986i \(0.452713\pi\)
\(368\) −38.1126 12.3835i −0.103567 0.0336509i
\(369\) 0 0
\(370\) −104.649 + 76.0323i −0.282836 + 0.205493i
\(371\) 487.497 670.982i 1.31401 1.80858i
\(372\) 0 0
\(373\) −554.596 −1.48685 −0.743427 0.668818i \(-0.766801\pi\)
−0.743427 + 0.668818i \(0.766801\pi\)
\(374\) −96.8216 236.904i −0.258881 0.633434i
\(375\) 0 0
\(376\) −211.944 652.295i −0.563680 1.73483i
\(377\) −16.2963 + 22.4299i −0.0432262 + 0.0594958i
\(378\) 0 0
\(379\) −77.6587 + 239.009i −0.204904 + 0.630631i 0.794813 + 0.606854i \(0.207569\pi\)
−0.999717 + 0.0237762i \(0.992431\pi\)
\(380\) 323.160 + 105.001i 0.850420 + 0.276318i
\(381\) 0 0
\(382\) 343.755 + 249.753i 0.899883 + 0.653804i
\(383\) 489.046 158.901i 1.27688 0.414885i 0.409402 0.912354i \(-0.365737\pi\)
0.867481 + 0.497470i \(0.165737\pi\)
\(384\) 0 0
\(385\) 477.543 + 564.504i 1.24037 + 1.46624i
\(386\) 168.102i 0.435499i
\(387\) 0 0
\(388\) −32.8291 23.8517i −0.0846110 0.0614735i
\(389\) −114.119 157.071i −0.293365 0.403782i 0.636739 0.771080i \(-0.280283\pi\)
−0.930103 + 0.367298i \(0.880283\pi\)
\(390\) 0 0
\(391\) 82.6254 254.295i 0.211318 0.650371i
\(392\) 610.028 + 839.632i 1.55619 + 2.14192i
\(393\) 0 0
\(394\) 81.0132 + 249.333i 0.205617 + 0.632825i
\(395\) 587.309i 1.48686i
\(396\) 0 0
\(397\) −260.248 −0.655537 −0.327769 0.944758i \(-0.606297\pi\)
−0.327769 + 0.944758i \(0.606297\pi\)
\(398\) −87.0041 + 28.2693i −0.218603 + 0.0710285i
\(399\) 0 0
\(400\) −2.20827 + 1.60440i −0.00552068 + 0.00401101i
\(401\) −360.802 117.232i −0.899755 0.292348i −0.177619 0.984099i \(-0.556840\pi\)
−0.722136 + 0.691751i \(0.756840\pi\)
\(402\) 0 0
\(403\) 36.4395 26.4748i 0.0904206 0.0656944i
\(404\) −60.1303 + 82.7623i −0.148837 + 0.204857i
\(405\) 0 0
\(406\) −184.765 −0.455085
\(407\) −175.355 108.600i −0.430849 0.266829i
\(408\) 0 0
\(409\) 210.768 + 648.678i 0.515326 + 1.58601i 0.782688 + 0.622415i \(0.213848\pi\)
−0.267362 + 0.963596i \(0.586152\pi\)
\(410\) 54.1653 74.5522i 0.132111 0.181835i
\(411\) 0 0
\(412\) 74.8537 230.376i 0.181684 0.559165i
\(413\) −825.367 268.178i −1.99847 0.649342i
\(414\) 0 0
\(415\) 167.227 + 121.497i 0.402956 + 0.292765i
\(416\) −75.8971 + 24.6605i −0.182445 + 0.0592800i
\(417\) 0 0
\(418\) −33.5741 453.981i −0.0803209 1.08608i
\(419\) 275.319i 0.657085i −0.944489 0.328543i \(-0.893443\pi\)
0.944489 0.328543i \(-0.106557\pi\)
\(420\) 0 0
\(421\) −98.2710 71.3981i −0.233423 0.169592i 0.464925 0.885350i \(-0.346081\pi\)
−0.698348 + 0.715758i \(0.746081\pi\)
\(422\) 59.6138 + 82.0513i 0.141265 + 0.194434i
\(423\) 0 0
\(424\) −162.387 + 499.775i −0.382988 + 1.17871i
\(425\) −10.7049 14.7340i −0.0251880 0.0346683i
\(426\) 0 0
\(427\) −148.751 457.809i −0.348363 1.07215i
\(428\) 241.019i 0.563130i
\(429\) 0 0
\(430\) 72.6803 0.169024
\(431\) −93.9131 + 30.5142i −0.217896 + 0.0707987i −0.415931 0.909396i \(-0.636544\pi\)
0.198035 + 0.980195i \(0.436544\pi\)
\(432\) 0 0
\(433\) −453.043 + 329.155i −1.04629 + 0.760173i −0.971503 0.237027i \(-0.923827\pi\)
−0.0747851 + 0.997200i \(0.523827\pi\)
\(434\) 285.476 + 92.7568i 0.657779 + 0.213725i
\(435\) 0 0
\(436\) −208.103 + 151.196i −0.477301 + 0.346779i
\(437\) 279.549 384.766i 0.639701 0.880472i
\(438\) 0 0
\(439\) −577.439 −1.31535 −0.657676 0.753301i \(-0.728460\pi\)
−0.657676 + 0.753301i \(0.728460\pi\)
\(440\) −398.288 246.664i −0.905200 0.560600i
\(441\) 0 0
\(442\) 19.1981 + 59.0857i 0.0434347 + 0.133678i
\(443\) 51.3607 70.6919i 0.115938 0.159575i −0.747104 0.664707i \(-0.768556\pi\)
0.863042 + 0.505132i \(0.168556\pi\)
\(444\) 0 0
\(445\) −112.204 + 345.329i −0.252144 + 0.776021i
\(446\) 7.68364 + 2.49657i 0.0172279 + 0.00559768i
\(447\) 0 0
\(448\) −540.206 392.482i −1.20582 0.876077i
\(449\) −91.5004 + 29.7303i −0.203787 + 0.0662145i −0.409132 0.912475i \(-0.634168\pi\)
0.205345 + 0.978690i \(0.434168\pi\)
\(450\) 0 0
\(451\) 142.716 + 34.9763i 0.316444 + 0.0775528i
\(452\) 150.733i 0.333479i
\(453\) 0 0
\(454\) −184.092 133.751i −0.405489 0.294605i
\(455\) −105.502 145.211i −0.231872 0.319145i
\(456\) 0 0
\(457\) −213.774 + 657.929i −0.467777 + 1.43967i 0.387679 + 0.921794i \(0.373277\pi\)
−0.855456 + 0.517875i \(0.826723\pi\)
\(458\) −279.756 385.051i −0.610821 0.840723i
\(459\) 0 0
\(460\) −53.2534 163.897i −0.115768 0.356298i
\(461\) 70.5491i 0.153035i −0.997068 0.0765175i \(-0.975620\pi\)
0.997068 0.0765175i \(-0.0243801\pi\)
\(462\) 0 0
\(463\) 248.292 0.536267 0.268134 0.963382i \(-0.413593\pi\)
0.268134 + 0.963382i \(0.413593\pi\)
\(464\) 25.4793 8.27872i 0.0549122 0.0178421i
\(465\) 0 0
\(466\) −389.320 + 282.858i −0.835451 + 0.606991i
\(467\) 241.718 + 78.5391i 0.517598 + 0.168178i 0.556155 0.831078i \(-0.312276\pi\)
−0.0385567 + 0.999256i \(0.512276\pi\)
\(468\) 0 0
\(469\) 645.379 468.895i 1.37607 0.999776i
\(470\) −333.335 + 458.796i −0.709223 + 0.976162i
\(471\) 0 0
\(472\) 549.864 1.16497
\(473\) 43.8441 + 107.278i 0.0926937 + 0.226804i
\(474\) 0 0
\(475\) −10.0105 30.8091i −0.0210747 0.0648612i
\(476\) 289.647 398.665i 0.608502 0.837531i
\(477\) 0 0
\(478\) 7.28241 22.4129i 0.0152352 0.0468890i
\(479\) 17.3840 + 5.64840i 0.0362922 + 0.0117921i 0.327107 0.944987i \(-0.393926\pi\)
−0.290815 + 0.956779i \(0.593926\pi\)
\(480\) 0 0
\(481\) 40.5076 + 29.4305i 0.0842153 + 0.0611860i
\(482\) −126.820 + 41.2063i −0.263112 + 0.0854903i
\(483\) 0 0
\(484\) 43.5950 259.379i 0.0900723 0.535907i
\(485\) 95.2954i 0.196485i
\(486\) 0 0
\(487\) 196.895 + 143.052i 0.404302 + 0.293742i 0.771291 0.636483i \(-0.219611\pi\)
−0.366989 + 0.930225i \(0.619611\pi\)
\(488\) 179.272 + 246.746i 0.367360 + 0.505627i
\(489\) 0 0
\(490\) 265.178 816.135i 0.541180 1.66558i
\(491\) −185.960 255.952i −0.378738 0.521288i 0.576512 0.817089i \(-0.304413\pi\)
−0.955250 + 0.295801i \(0.904413\pi\)
\(492\) 0 0
\(493\) 55.2373 + 170.003i 0.112043 + 0.344833i
\(494\) 110.506i 0.223696i
\(495\) 0 0
\(496\) −43.5236 −0.0877493
\(497\) −616.019 + 200.157i −1.23947 + 0.402730i
\(498\) 0 0
\(499\) −21.6847 + 15.7549i −0.0434563 + 0.0315728i −0.609301 0.792939i \(-0.708550\pi\)
0.565845 + 0.824512i \(0.308550\pi\)
\(500\) 252.660 + 82.0943i 0.505321 + 0.164189i
\(501\) 0 0
\(502\) −193.850 + 140.840i −0.386155 + 0.280558i
\(503\) −107.344 + 147.746i −0.213408 + 0.293730i −0.902278 0.431154i \(-0.858107\pi\)
0.688871 + 0.724884i \(0.258107\pi\)
\(504\) 0 0
\(505\) 240.240 0.475723
\(506\) −176.264 + 149.111i −0.348348 + 0.294686i
\(507\) 0 0
\(508\) 7.23754 + 22.2749i 0.0142471 + 0.0438482i
\(509\) 127.165 175.027i 0.249832 0.343864i −0.665620 0.746290i \(-0.731833\pi\)
0.915452 + 0.402426i \(0.131833\pi\)
\(510\) 0 0
\(511\) −25.9327 + 79.8128i −0.0507490 + 0.156189i
\(512\) 155.235 + 50.4390i 0.303194 + 0.0985137i
\(513\) 0 0
\(514\) 126.086 + 91.6069i 0.245304 + 0.178223i
\(515\) −541.013 + 175.786i −1.05051 + 0.341332i
\(516\) 0 0
\(517\) −878.280 215.245i −1.69880 0.416335i
\(518\) 333.678i 0.644165i
\(519\) 0 0
\(520\) 92.0055 + 66.8459i 0.176934 + 0.128550i
\(521\) 335.736 + 462.102i 0.644408 + 0.886951i 0.998841 0.0481300i \(-0.0153262\pi\)
−0.354433 + 0.935081i \(0.615326\pi\)
\(522\) 0 0
\(523\) 237.156 729.890i 0.453453 1.39558i −0.419490 0.907760i \(-0.637791\pi\)
0.872942 0.487824i \(-0.162209\pi\)
\(524\) 117.638 + 161.914i 0.224500 + 0.308997i
\(525\) 0 0
\(526\) −98.9537 304.548i −0.188125 0.578989i
\(527\) 290.398i 0.551041i
\(528\) 0 0
\(529\) 287.791 0.544028
\(530\) 413.237 134.269i 0.779692 0.253337i
\(531\) 0 0
\(532\) 709.114 515.201i 1.33292 0.968424i
\(533\) −33.9241 11.0226i −0.0636474 0.0206803i
\(534\) 0 0
\(535\) −457.910 + 332.691i −0.855907 + 0.621853i
\(536\) −297.092 + 408.912i −0.554276 + 0.762895i
\(537\) 0 0
\(538\) 714.191 1.32749
\(539\) 1364.61 100.919i 2.53174 0.187235i
\(540\) 0 0
\(541\) 63.5980 + 195.735i 0.117556 + 0.361801i 0.992472 0.122475i \(-0.0390830\pi\)
−0.874915 + 0.484276i \(0.839083\pi\)
\(542\) 142.136 195.633i 0.262243 0.360946i
\(543\) 0 0
\(544\) −158.994 + 489.333i −0.292269 + 0.899510i
\(545\) 574.510 + 186.670i 1.05415 + 0.342513i
\(546\) 0 0
\(547\) −352.204 255.891i −0.643883 0.467808i 0.217299 0.976105i \(-0.430275\pi\)
−0.861182 + 0.508297i \(0.830275\pi\)
\(548\) 410.672 133.435i 0.749402 0.243495i
\(549\) 0 0
\(550\) 1.15982 + 15.6828i 0.00210877 + 0.0285142i
\(551\) 317.949i 0.577040i
\(552\) 0 0
\(553\) 1225.67 + 890.498i 2.21639 + 1.61030i
\(554\) −227.352 312.923i −0.410382 0.564842i
\(555\) 0 0
\(556\) −39.9902 + 123.077i −0.0719248 + 0.221362i
\(557\) −434.244 597.686i −0.779612 1.07304i −0.995325 0.0965873i \(-0.969207\pi\)
0.215712 0.976457i \(-0.430793\pi\)
\(558\) 0 0
\(559\) −8.69356 26.7560i −0.0155520 0.0478641i
\(560\) 173.441i 0.309716i
\(561\) 0 0
\(562\) 342.493 0.609419
\(563\) 62.6356 20.3515i 0.111253 0.0361484i −0.252861 0.967503i \(-0.581372\pi\)
0.364115 + 0.931354i \(0.381372\pi\)
\(564\) 0 0
\(565\) 286.376 208.064i 0.506859 0.368255i
\(566\) 364.077 + 118.296i 0.643246 + 0.209003i
\(567\) 0 0
\(568\) 332.017 241.224i 0.584537 0.424691i
\(569\) −410.063 + 564.404i −0.720673 + 0.991922i 0.278828 + 0.960341i \(0.410054\pi\)
−0.999501 + 0.0315808i \(0.989946\pi\)
\(570\) 0 0
\(571\) −256.388 −0.449017 −0.224508 0.974472i \(-0.572078\pi\)
−0.224508 + 0.974472i \(0.572078\pi\)
\(572\) −15.1978 + 62.0127i −0.0265696 + 0.108414i
\(573\) 0 0
\(574\) −73.4569 226.077i −0.127974 0.393862i
\(575\) −9.65705 + 13.2918i −0.0167949 + 0.0231162i
\(576\) 0 0
\(577\) 140.575 432.646i 0.243631 0.749819i −0.752227 0.658903i \(-0.771021\pi\)
0.995859 0.0909159i \(-0.0289794\pi\)
\(578\) 9.50317 + 3.08777i 0.0164415 + 0.00534216i
\(579\) 0 0
\(580\) 93.2053 + 67.7176i 0.160699 + 0.116755i
\(581\) 507.110 164.770i 0.872823 0.283598i
\(582\) 0 0
\(583\) 447.468 + 528.952i 0.767527 + 0.907294i
\(584\) 53.1718i 0.0910475i
\(585\) 0 0
\(586\) −327.221 237.740i −0.558397 0.405699i
\(587\) 64.8291 + 89.2295i 0.110441 + 0.152009i 0.860660 0.509181i \(-0.170052\pi\)
−0.750218 + 0.661190i \(0.770052\pi\)
\(588\) 0 0
\(589\) 159.619 491.257i 0.271000 0.834052i
\(590\) −267.238 367.822i −0.452946 0.623427i
\(591\) 0 0
\(592\) −14.9510 46.0146i −0.0252551 0.0777273i
\(593\) 250.416i 0.422287i −0.977455 0.211144i \(-0.932281\pi\)
0.977455 0.211144i \(-0.0677188\pi\)
\(594\) 0 0
\(595\) −1157.23 −1.94493
\(596\) −30.1091 + 9.78303i −0.0505186 + 0.0164145i
\(597\) 0 0
\(598\) 45.3415 32.9425i 0.0758219 0.0550879i
\(599\) −271.473 88.2069i −0.453210 0.147257i 0.0735122 0.997294i \(-0.476579\pi\)
−0.526722 + 0.850037i \(0.676579\pi\)
\(600\) 0 0
\(601\) 180.803 131.361i 0.300836 0.218570i −0.427118 0.904196i \(-0.640471\pi\)
0.727954 + 0.685625i \(0.240471\pi\)
\(602\) 110.200 151.678i 0.183057 0.251956i
\(603\) 0 0
\(604\) −529.508 −0.876668
\(605\) −552.968 + 275.208i −0.913997 + 0.454890i
\(606\) 0 0
\(607\) 295.069 + 908.129i 0.486110 + 1.49609i 0.830367 + 0.557218i \(0.188131\pi\)
−0.344256 + 0.938876i \(0.611869\pi\)
\(608\) −537.929 + 740.396i −0.884752 + 1.21776i
\(609\) 0 0
\(610\) 77.9290 239.841i 0.127752 0.393182i
\(611\) 208.770 + 67.8334i 0.341685 + 0.111020i
\(612\) 0 0
\(613\) 275.176 + 199.927i 0.448901 + 0.326146i 0.789162 0.614185i \(-0.210515\pi\)
−0.340261 + 0.940331i \(0.610515\pi\)
\(614\) 143.743 46.7048i 0.234108 0.0760664i
\(615\) 0 0
\(616\) −1118.67 + 457.193i −1.81602 + 0.742197i
\(617\) 812.456i 1.31678i −0.752675 0.658392i \(-0.771237\pi\)
0.752675 0.658392i \(-0.228763\pi\)
\(618\) 0 0
\(619\) −739.304 537.136i −1.19435 0.867748i −0.200635 0.979666i \(-0.564301\pi\)
−0.993717 + 0.111918i \(0.964301\pi\)
\(620\) −110.014 151.421i −0.177441 0.244227i
\(621\) 0 0
\(622\) −148.787 + 457.920i −0.239208 + 0.736206i
\(623\) 550.546 + 757.761i 0.883701 + 1.21631i
\(624\) 0 0
\(625\) −200.962 618.498i −0.321540 0.989597i
\(626\) 457.779i 0.731276i
\(627\) 0 0
\(628\) −241.352 −0.384319
\(629\) 307.018 99.7563i 0.488105 0.158595i
\(630\) 0 0
\(631\) 488.541 354.946i 0.774233 0.562513i −0.129010 0.991643i \(-0.541180\pi\)
0.903243 + 0.429130i \(0.141180\pi\)
\(632\) −912.926 296.628i −1.44450 0.469348i
\(633\) 0 0
\(634\) −442.400 + 321.423i −0.697792 + 0.506976i
\(635\) 32.3295 44.4977i 0.0509125 0.0700751i
\(636\) 0 0
\(637\) −332.165 −0.521453
\(638\) 36.7392 149.909i 0.0575849 0.234968i
\(639\) 0 0
\(640\) 80.4720 + 247.667i 0.125738 + 0.386980i
\(641\) −633.628 + 872.114i −0.988499 + 1.36055i −0.0563769 + 0.998410i \(0.517955\pi\)
−0.932122 + 0.362143i \(0.882045\pi\)
\(642\) 0 0
\(643\) 118.832 365.726i 0.184808 0.568781i −0.815137 0.579268i \(-0.803338\pi\)
0.999945 + 0.0104874i \(0.00333831\pi\)
\(644\) −422.784 137.371i −0.656497 0.213309i
\(645\) 0 0
\(646\) 576.397 + 418.777i 0.892255 + 0.648262i
\(647\) −566.074 + 183.929i −0.874921 + 0.284279i −0.711847 0.702335i \(-0.752141\pi\)
−0.163074 + 0.986614i \(0.552141\pi\)
\(648\) 0 0
\(649\) 381.706 616.339i 0.588144 0.949675i
\(650\) 3.81743i 0.00587297i
\(651\) 0 0
\(652\) −216.573 157.350i −0.332168 0.241334i
\(653\) 246.058 + 338.670i 0.376812 + 0.518637i 0.954736 0.297453i \(-0.0961372\pi\)
−0.577924 + 0.816090i \(0.696137\pi\)
\(654\) 0 0
\(655\) 145.238 446.998i 0.221738 0.682439i
\(656\) 20.2596 + 27.8849i 0.0308835 + 0.0425075i
\(657\) 0 0
\(658\) 452.056 + 1391.29i 0.687015 + 2.11442i
\(659\) 1112.39i 1.68800i −0.536347 0.843998i \(-0.680196\pi\)
0.536347 0.843998i \(-0.319804\pi\)
\(660\) 0 0
\(661\) −736.025 −1.11350 −0.556751 0.830679i \(-0.687952\pi\)
−0.556751 + 0.830679i \(0.687952\pi\)
\(662\) 814.943 264.791i 1.23103 0.399986i
\(663\) 0 0
\(664\) −273.318 + 198.577i −0.411624 + 0.299062i
\(665\) −1957.65 636.080i −2.94384 0.956511i
\(666\) 0 0
\(667\) 130.458 94.7830i 0.195589 0.142103i
\(668\) −292.598 + 402.727i −0.438021 + 0.602884i
\(669\) 0 0
\(670\) 417.923 0.623765
\(671\) 401.023 29.6576i 0.597649 0.0441991i
\(672\) 0 0
\(673\) 168.609 + 518.924i 0.250533 + 0.771061i 0.994677 + 0.103042i \(0.0328576\pi\)
−0.744144 + 0.668019i \(0.767142\pi\)
\(674\) −188.586 + 259.566i −0.279801 + 0.385113i
\(675\) 0 0
\(676\) −108.729 + 334.634i −0.160842 + 0.495021i
\(677\) 936.672 + 304.343i 1.38356 + 0.449547i 0.903839 0.427873i \(-0.140737\pi\)
0.479724 + 0.877420i \(0.340737\pi\)
\(678\) 0 0
\(679\) 198.874 + 144.490i 0.292892 + 0.212798i
\(680\) 697.336 226.578i 1.02549 0.333203i
\(681\) 0 0
\(682\) −132.023 + 213.178i −0.193583 + 0.312578i
\(683\) 924.817i 1.35405i 0.735959 + 0.677026i \(0.236731\pi\)
−0.735959 + 0.677026i \(0.763269\pi\)
\(684\) 0 0
\(685\) −820.385 596.044i −1.19764 0.870138i
\(686\) −788.604 1085.42i −1.14957 1.58225i
\(687\) 0 0
\(688\) −8.40056 + 25.8543i −0.0122101 + 0.0375789i
\(689\) −98.8576 136.066i −0.143480 0.197483i
\(690\) 0 0
\(691\) −24.4525 75.2570i −0.0353871 0.108910i 0.931803 0.362965i \(-0.118236\pi\)
−0.967190 + 0.254055i \(0.918236\pi\)
\(692\) 375.349i 0.542412i
\(693\) 0 0
\(694\) −658.790 −0.949265
\(695\) 289.034 93.9127i 0.415876 0.135126i
\(696\) 0 0
\(697\) −186.054 + 135.176i −0.266935 + 0.193940i
\(698\) −48.9041 15.8899i −0.0700632 0.0227649i
\(699\) 0 0
\(700\) −24.4964 + 17.7977i −0.0349949 + 0.0254253i
\(701\) 724.322 996.943i 1.03327 1.42217i 0.130805 0.991408i \(-0.458244\pi\)
0.902464 0.430765i \(-0.141756\pi\)
\(702\) 0 0
\(703\) 574.204 0.816791
\(704\) 425.858 360.255i 0.604912 0.511726i
\(705\) 0 0
\(706\) −37.8094 116.365i −0.0535544 0.164823i
\(707\) 364.261 501.362i 0.515220 0.709140i
\(708\) 0 0
\(709\) −82.6830 + 254.472i −0.116619 + 0.358917i −0.992281 0.124007i \(-0.960425\pi\)
0.875662 + 0.482924i \(0.160425\pi\)
\(710\) −322.725 104.860i −0.454543 0.147690i
\(711\) 0 0
\(712\) −480.117 348.825i −0.674322 0.489923i
\(713\) −249.151 + 80.9541i −0.349440 + 0.113540i
\(714\) 0 0
\(715\) 138.796 56.7251i 0.194120 0.0793358i
\(716\) 396.682i 0.554025i
\(717\) 0 0
\(718\) −122.437 88.9554i −0.170525 0.123893i
\(719\) −403.585 555.487i −0.561314 0.772583i 0.430179 0.902744i \(-0.358451\pi\)
−0.991493 + 0.130161i \(0.958451\pi\)
\(720\) 0 0
\(721\) −453.452 + 1395.58i −0.628922 + 1.93562i
\(722\) 458.132 + 630.564i 0.634531 + 0.873358i
\(723\) 0 0
\(724\) 81.7742 + 251.675i 0.112948 + 0.347617i
\(725\) 10.9836i 0.0151498i
\(726\) 0 0
\(727\) −1265.58 −1.74082 −0.870410 0.492327i \(-0.836146\pi\)
−0.870410 + 0.492327i \(0.836146\pi\)
\(728\) 279.004 90.6539i 0.383247 0.124525i
\(729\) 0 0
\(730\) −35.5683 + 25.8419i −0.0487237 + 0.0353998i
\(731\) −172.505 56.0502i −0.235985 0.0766761i
\(732\) 0 0
\(733\) −80.5752 + 58.5413i −0.109925 + 0.0798654i −0.641390 0.767215i \(-0.721642\pi\)
0.531465 + 0.847081i \(0.321642\pi\)
\(734\) −269.115 + 370.405i −0.366641 + 0.504638i
\(735\) 0 0
\(736\) 464.152 0.630642
\(737\) 252.111 + 616.867i 0.342077 + 0.836997i
\(738\) 0 0
\(739\) −99.0512 304.848i −0.134034 0.412515i 0.861404 0.507920i \(-0.169585\pi\)
−0.995439 + 0.0954052i \(0.969585\pi\)
\(740\) 122.295 168.325i 0.165264 0.227466i
\(741\) 0 0
\(742\) 346.356 1065.97i 0.466787 1.43662i
\(743\) 51.9858 + 16.8912i 0.0699674 + 0.0227338i 0.343792 0.939046i \(-0.388289\pi\)
−0.273824 + 0.961780i \(0.588289\pi\)
\(744\) 0 0
\(745\) 60.1478 + 43.6999i 0.0807353 + 0.0586576i
\(746\) −712.804 + 231.604i −0.955501 + 0.310461i
\(747\) 0 0
\(748\) 265.864 + 314.278i 0.355433 + 0.420157i
\(749\) 1460.06i 1.94935i
\(750\) 0 0
\(751\) −117.339 85.2520i −0.156244 0.113518i 0.506916 0.861995i \(-0.330785\pi\)
−0.663160 + 0.748477i \(0.730785\pi\)
\(752\) −124.678 171.605i −0.165795 0.228198i
\(753\) 0 0
\(754\) −11.5782 + 35.6339i −0.0153556 + 0.0472598i
\(755\) 730.906 + 1006.01i 0.968088 + 1.33246i
\(756\) 0 0
\(757\) 80.8537 + 248.842i 0.106808 + 0.328721i 0.990151 0.140007i \(-0.0447124\pi\)
−0.883343 + 0.468728i \(0.844712\pi\)
\(758\) 339.621i 0.448049i
\(759\) 0 0
\(760\) 1304.20 1.71605
\(761\) 955.456 310.446i 1.25553 0.407945i 0.395629 0.918411i \(-0.370527\pi\)
0.859898 + 0.510465i \(0.170527\pi\)
\(762\) 0 0
\(763\) 1260.66 915.921i 1.65224 1.20042i
\(764\) −649.995 211.196i −0.850779 0.276435i
\(765\) 0 0
\(766\) 562.196 408.460i 0.733938 0.533237i
\(767\) −103.442 + 142.376i −0.134866 + 0.185627i
\(768\) 0 0
\(769\) 1067.91 1.38869 0.694347 0.719641i \(-0.255693\pi\)
0.694347 + 0.719641i \(0.255693\pi\)
\(770\) 849.511 + 526.112i 1.10326 + 0.683262i
\(771\) 0 0
\(772\) 83.5542 + 257.153i 0.108231 + 0.333100i
\(773\) 104.322 143.587i 0.134957 0.185753i −0.736190 0.676775i \(-0.763377\pi\)
0.871147 + 0.491023i \(0.163377\pi\)
\(774\) 0 0
\(775\) −5.51406 + 16.9705i −0.00711491 + 0.0218974i
\(776\) −148.129 48.1301i −0.190888 0.0620233i
\(777\) 0 0
\(778\) −212.267 154.221i −0.272837 0.198228i
\(779\) −389.041 + 126.407i −0.499411 + 0.162268i
\(780\) 0 0
\(781\) −39.9067 539.609i −0.0510970 0.690920i
\(782\) 361.342i 0.462074i
\(783\) 0 0
\(784\) 259.670 + 188.662i 0.331212 + 0.240640i
\(785\) 333.151 + 458.543i 0.424396 + 0.584131i
\(786\) 0 0
\(787\) 204.108 628.179i 0.259349 0.798194i −0.733592 0.679590i \(-0.762158\pi\)
0.992942 0.118605i \(-0.0378421\pi\)
\(788\) −247.859 341.148i −0.314541 0.432929i
\(789\) 0 0
\(790\) 245.265 + 754.849i 0.310462 + 0.955505i
\(791\) 913.116i 1.15438i
\(792\) 0 0
\(793\) −97.6148 −0.123096
\(794\) −334.488 + 108.682i −0.421270 + 0.136879i
\(795\) 0 0
\(796\) 119.043 86.4896i 0.149551 0.108655i
\(797\) 379.061 + 123.164i 0.475610 + 0.154535i 0.537006 0.843578i \(-0.319555\pi\)
−0.0613960 + 0.998113i \(0.519555\pi\)
\(798\) 0 0
\(799\) 1144.98 831.878i 1.43302 1.04115i
\(800\) 18.5828 25.5771i 0.0232285 0.0319713i
\(801\) 0 0
\(802\) −512.683 −0.639256
\(803\) −59.5998 36.9108i −0.0742215 0.0459662i
\(804\) 0 0
\(805\) 322.601 + 992.863i 0.400746 + 1.23337i
\(806\) 35.7783 49.2446i 0.0443900 0.0610976i
\(807\) 0 0
\(808\) −121.336 + 373.435i −0.150169 + 0.462172i
\(809\) 716.122 + 232.682i 0.885194 + 0.287617i 0.716112 0.697985i \(-0.245920\pi\)
0.169082 + 0.985602i \(0.445920\pi\)
\(810\) 0 0
\(811\) −811.310 589.451i −1.00038 0.726820i −0.0382118 0.999270i \(-0.512166\pi\)
−0.962170 + 0.272450i \(0.912166\pi\)
\(812\) 282.642 91.8360i 0.348082 0.113099i
\(813\) 0 0
\(814\) −270.730 66.3495i −0.332593 0.0815104i
\(815\) 628.663i 0.771366i
\(816\) 0 0
\(817\) −261.012 189.636i −0.319476 0.232113i
\(818\) 541.787 + 745.706i 0.662331 + 0.911621i
\(819\) 0 0
\(820\) −45.8033 + 140.968i −0.0558577 + 0.171912i
\(821\) −804.527 1107.34i −0.979936 1.34877i −0.936864 0.349694i \(-0.886286\pi\)
−0.0430718 0.999072i \(-0.513714\pi\)
\(822\) 0 0
\(823\) −431.321 1327.47i −0.524084 1.61296i −0.766120 0.642697i \(-0.777815\pi\)
0.242037 0.970267i \(-0.422185\pi\)
\(824\) 929.746i 1.12833i
\(825\) 0 0
\(826\) −1172.81 −1.41987
\(827\) −192.907 + 62.6792i −0.233261 + 0.0757910i −0.423315 0.905983i \(-0.639134\pi\)
0.190054 + 0.981774i \(0.439134\pi\)
\(828\) 0 0
\(829\) −461.108 + 335.015i −0.556222 + 0.404119i −0.830074 0.557653i \(-0.811702\pi\)
0.273852 + 0.961772i \(0.411702\pi\)
\(830\) 265.669 + 86.3212i 0.320084 + 0.104001i
\(831\) 0 0
\(832\) −109.546 + 79.5899i −0.131666 + 0.0956610i
\(833\) −1258.79 + 1732.57i −1.51115 + 2.07992i
\(834\) 0 0
\(835\) 1169.02 1.40003
\(836\) 277.008 + 677.786i 0.331349 + 0.810749i
\(837\) 0 0
\(838\) −114.975 353.858i −0.137202 0.422265i
\(839\) 76.3914 105.144i 0.0910505 0.125320i −0.761062 0.648680i \(-0.775321\pi\)
0.852112 + 0.523359i \(0.175321\pi\)
\(840\) 0 0
\(841\) 226.570 697.312i 0.269406 0.829146i
\(842\) −156.121 50.7267i −0.185417 0.0602455i
\(843\) 0 0
\(844\) −131.977 95.8867i −0.156371 0.113610i
\(845\) 785.853 255.339i 0.930003 0.302176i
\(846\) 0 0
\(847\) −264.092 + 1571.28i −0.311797 + 1.85511i
\(848\) 162.518i 0.191649i
\(849\) 0 0
\(850\) −19.9117 14.4667i −0.0234255 0.0170196i
\(851\) −171.174 235.601i −0.201145 0.276852i
\(852\) 0 0
\(853\) 99.5966 306.527i 0.116760 0.359351i −0.875550 0.483128i \(-0.839501\pi\)
0.992310 + 0.123777i \(0.0395006\pi\)
\(854\) −382.369 526.286i −0.447739 0.616260i
\(855\) 0 0
\(856\) −285.869 879.816i −0.333960 1.02782i
\(857\) 634.845i 0.740776i −0.928877 0.370388i \(-0.879225\pi\)
0.928877 0.370388i \(-0.120775\pi\)
\(858\) 0 0
\(859\) 1658.25 1.93044 0.965219 0.261443i \(-0.0841984\pi\)
0.965219 + 0.261443i \(0.0841984\pi\)
\(860\) −111.182 + 36.1252i −0.129281 + 0.0420061i
\(861\) 0 0
\(862\) −107.960 + 78.4378i −0.125244 + 0.0909951i
\(863\) 820.127 + 266.475i 0.950321 + 0.308778i 0.742846 0.669462i \(-0.233475\pi\)
0.207475 + 0.978240i \(0.433475\pi\)
\(864\) 0 0
\(865\) 713.122 518.113i 0.824418 0.598975i
\(866\) −444.823 + 612.246i −0.513652 + 0.706981i
\(867\) 0 0
\(868\) −482.809 −0.556231
\(869\) −966.224 + 817.379i −1.11188 + 0.940597i
\(870\) 0 0
\(871\) −49.9893 153.851i −0.0573930 0.176638i
\(872\) −580.327 + 798.752i −0.665513 + 0.916000i
\(873\) 0 0
\(874\) 198.613 611.269i 0.227246 0.699393i
\(875\) −1530.58 497.315i −1.74923 0.568360i
\(876\) 0 0
\(877\) −554.481 402.854i −0.632247 0.459354i 0.224931 0.974375i \(-0.427784\pi\)
−0.857178 + 0.515020i \(0.827784\pi\)
\(878\) −742.163 + 241.143i −0.845288 + 0.274651i
\(879\) 0 0
\(880\) −140.722 34.4875i −0.159911 0.0391904i
\(881\) 551.003i 0.625429i −0.949847 0.312715i \(-0.898762\pi\)
0.949847 0.312715i \(-0.101238\pi\)
\(882\) 0 0
\(883\) 1288.51 + 936.160i 1.45924 + 1.06020i 0.983559 + 0.180588i \(0.0578002\pi\)
0.475686 + 0.879615i \(0.342200\pi\)
\(884\) −58.7363 80.8436i −0.0664438 0.0914521i
\(885\) 0 0
\(886\) 36.4906 112.307i 0.0411858 0.126757i
\(887\) −225.726 310.686i −0.254483 0.350266i 0.662592 0.748981i \(-0.269456\pi\)
−0.917075 + 0.398715i \(0.869456\pi\)
\(888\) 0 0
\(889\) −43.8439 134.938i −0.0493183 0.151786i
\(890\) 490.697i 0.551345i
\(891\) 0 0
\(892\) −12.9949 −0.0145683
\(893\) 2394.17 777.913i 2.68104 0.871124i
\(894\) 0 0
\(895\) −753.653 + 547.561i −0.842070 + 0.611800i
\(896\) 638.876 + 207.583i 0.713031 + 0.231678i
\(897\) 0 0
\(898\) −105.187 + 76.4227i −0.117134 + 0.0851032i
\(899\) 102.942 141.688i 0.114507 0.157606i
\(900\) 0 0
\(901\) −1084.35 −1.20350
\(902\) 198.035 14.6456i 0.219551 0.0162369i
\(903\) 0 0
\(904\) 178.782 + 550.234i 0.197767 + 0.608665i
\(905\) 365.278 502.762i 0.403622 0.555538i
\(906\) 0 0
\(907\) −438.054 + 1348.19i −0.482970 + 1.48643i 0.351929 + 0.936027i \(0.385526\pi\)
−0.834899 + 0.550403i \(0.814474\pi\)
\(908\) 348.093 + 113.102i 0.383363 + 0.124562i
\(909\) 0 0
\(910\) −196.239 142.576i −0.215647 0.156677i
\(911\) 831.997 270.332i 0.913279 0.296742i 0.185572 0.982631i \(-0.440586\pi\)
0.727707 + 0.685888i \(0.240586\pi\)
\(912\) 0 0
\(913\) 32.8515 + 444.209i 0.0359819 + 0.486538i
\(914\) 934.888i 1.02285i
\(915\) 0 0
\(916\) 619.342 + 449.978i 0.676137 + 0.491242i
\(917\) −712.632 980.854i −0.777134 1.06963i
\(918\) 0 0
\(919\) −359.359 + 1105.99i −0.391033 + 1.20348i 0.540975 + 0.841039i \(0.318055\pi\)
−0.932008 + 0.362437i \(0.881945\pi\)
\(920\) −388.791 535.125i −0.422599 0.581658i
\(921\) 0 0
\(922\) −29.4619 90.6744i −0.0319543 0.0983453i
\(923\) 131.349i 0.142306i
\(924\) 0 0
\(925\) −19.8359 −0.0214443
\(926\) 319.121 103.689i 0.344623 0.111975i
\(927\) 0 0
\(928\) −251.036 + 182.389i −0.270513 + 0.196539i
\(929\) −527.156 171.283i −0.567444 0.184374i 0.0112238 0.999937i \(-0.496427\pi\)
−0.578668 + 0.815563i \(0.696427\pi\)
\(930\) 0 0
\(931\) −3081.77 + 2239.03i −3.31017 + 2.40498i
\(932\) 454.967 626.208i 0.488162 0.671897i
\(933\) 0 0
\(934\) 343.471 0.367742
\(935\) 230.108 938.925i 0.246105 1.00420i
\(936\) 0 0
\(937\) −265.097 815.885i −0.282921 0.870742i −0.987014 0.160634i \(-0.948646\pi\)
0.704093 0.710108i \(-0.251354\pi\)
\(938\) 633.669 872.170i 0.675553 0.929819i
\(939\) 0 0
\(940\) 281.875 867.522i 0.299867 0.922896i
\(941\) 320.582 + 104.163i 0.340682 + 0.110694i 0.474361 0.880330i \(-0.342679\pi\)
−0.133679 + 0.991025i \(0.542679\pi\)
\(942\) 0 0
\(943\) 167.842 + 121.944i 0.177987 + 0.129315i
\(944\) 161.732 52.5499i 0.171326 0.0556672i
\(945\) 0 0
\(946\) 101.152 + 119.571i 0.106926 + 0.126397i
\(947\) 405.388i 0.428076i −0.976825 0.214038i \(-0.931338\pi\)
0.976825 0.214038i \(-0.0686616\pi\)
\(948\) 0 0
\(949\) 13.7677 + 10.0028i 0.0145076 + 0.0105404i
\(950\) −25.7322 35.4174i −0.0270866 0.0372814i
\(951\) 0 0
\(952\) 584.475 1798.83i 0.613944 1.88953i
\(953\) −439.632 605.102i −0.461314 0.634944i 0.513467 0.858109i \(-0.328361\pi\)
−0.974781 + 0.223166i \(0.928361\pi\)
\(954\) 0 0
\(955\) 495.972 + 1526.44i 0.519342 + 1.59837i
\(956\) 37.9057i 0.0396503i
\(957\) 0 0
\(958\) 24.7019 0.0257848
\(959\) −2487.79 + 808.332i −2.59415 + 0.842891i
\(960\) 0 0
\(961\) 547.280 397.623i 0.569491 0.413759i
\(962\) 64.3534 + 20.9097i 0.0668954 + 0.0217356i
\(963\) 0 0
\(964\) 173.521 126.070i 0.180001 0.130778i
\(965\) 373.229 513.706i 0.386766 0.532338i
\(966\) 0 0
\(967\) −284.479 −0.294187 −0.147094 0.989123i \(-0.546992\pi\)
−0.147094 + 0.989123i \(0.546992\pi\)
\(968\) −148.507 998.543i −0.153416 1.03155i
\(969\) 0 0
\(970\) 39.7961 + 122.480i 0.0410269 + 0.126268i
\(971\) −693.245 + 954.170i −0.713949 + 0.982667i 0.285754 + 0.958303i \(0.407756\pi\)
−0.999703 + 0.0243639i \(0.992244\pi\)
\(972\) 0 0
\(973\) 242.255 745.583i 0.248977 0.766272i
\(974\) 312.802 + 101.636i 0.321152 + 0.104349i
\(975\) 0 0
\(976\) 76.3104 + 55.4428i 0.0781869 + 0.0568061i
\(977\) −12.9784 + 4.21695i −0.0132840 + 0.00431622i −0.315651 0.948875i \(-0.602223\pi\)
0.302367 + 0.953191i \(0.402223\pi\)
\(978\) 0 0
\(979\) −724.284 + 296.011i −0.739820 + 0.302361i
\(980\) 1380.28i 1.40845i
\(981\) 0 0
\(982\) −345.896 251.308i −0.352236 0.255915i
\(983\) 294.641 + 405.539i 0.299737 + 0.412552i 0.932146 0.362082i \(-0.117934\pi\)
−0.632409 + 0.774634i \(0.717934\pi\)
\(984\) 0 0
\(985\) −306.012 + 941.808i −0.310672 + 0.956151i
\(986\) 141.989 + 195.431i 0.144005 + 0.198206i
\(987\) 0 0
\(988\) −54.9261 169.045i −0.0555932 0.171098i
\(989\) 163.628i 0.165448i
\(990\) 0 0
\(991\) 118.253 0.119327 0.0596635 0.998219i \(-0.480997\pi\)
0.0596635 + 0.998219i \(0.480997\pi\)
\(992\) 479.435 155.778i 0.483302 0.157034i
\(993\) 0 0
\(994\) −708.161 + 514.509i −0.712436 + 0.517615i
\(995\) −328.641 106.782i −0.330293 0.107319i
\(996\) 0 0
\(997\) −401.180 + 291.474i −0.402387 + 0.292351i −0.770512 0.637425i \(-0.780000\pi\)
0.368126 + 0.929776i \(0.380000\pi\)
\(998\) −21.2912 + 29.3049i −0.0213339 + 0.0293636i
\(999\) 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 99.3.l.a.71.6 yes 32
3.2 odd 2 inner 99.3.l.a.71.3 yes 32
11.3 even 5 1089.3.b.i.485.6 16
11.8 odd 10 1089.3.b.j.485.11 16
11.9 even 5 inner 99.3.l.a.53.3 32
33.8 even 10 1089.3.b.j.485.6 16
33.14 odd 10 1089.3.b.i.485.11 16
33.20 odd 10 inner 99.3.l.a.53.6 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.3.l.a.53.3 32 11.9 even 5 inner
99.3.l.a.53.6 yes 32 33.20 odd 10 inner
99.3.l.a.71.3 yes 32 3.2 odd 2 inner
99.3.l.a.71.6 yes 32 1.1 even 1 trivial
1089.3.b.i.485.6 16 11.3 even 5
1089.3.b.i.485.11 16 33.14 odd 10
1089.3.b.j.485.6 16 33.8 even 10
1089.3.b.j.485.11 16 11.8 odd 10