Properties

Label 162.4.e.b.73.5
Level $162$
Weight $4$
Character 162.73
Analytic conductor $9.558$
Analytic rank $0$
Dimension $30$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [162,4,Mod(19,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.19");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 162.e (of order \(9\), degree \(6\), not 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: \(9.55830942093\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(5\) over \(\Q(\zeta_{9})\)
Twist minimal: no (minimal twist has level 54)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 73.5
Character \(\chi\) \(=\) 162.73
Dual form 162.4.e.b.91.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.347296 - 1.96962i) q^{2} +(-3.75877 - 1.36808i) q^{4} +(14.9069 - 12.5084i) q^{5} +(11.7781 - 4.28689i) q^{7} +(-4.00000 + 6.92820i) q^{8} +O(q^{10})\) \(q+(0.347296 - 1.96962i) q^{2} +(-3.75877 - 1.36808i) q^{4} +(14.9069 - 12.5084i) q^{5} +(11.7781 - 4.28689i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(-19.4596 - 33.7050i) q^{10} +(9.63062 + 8.08105i) q^{11} +(6.96648 + 39.5088i) q^{13} +(-4.35302 - 24.6872i) q^{14} +(12.2567 + 10.2846i) q^{16} +(-24.5383 - 42.5016i) q^{17} +(67.8741 - 117.561i) q^{19} +(-73.1441 + 26.6223i) q^{20} +(19.2612 - 16.1621i) q^{22} +(-162.928 - 59.3010i) q^{23} +(44.0502 - 249.821i) q^{25} +80.2367 q^{26} -50.1361 q^{28} +(-7.51379 + 42.6128i) q^{29} +(-18.2216 - 6.63213i) q^{31} +(24.5134 - 20.5692i) q^{32} +(-92.2339 + 33.5704i) q^{34} +(121.953 - 211.229i) q^{35} +(124.441 + 215.538i) q^{37} +(-207.978 - 174.514i) q^{38} +(27.0330 + 153.311i) q^{40} +(68.5925 + 389.008i) q^{41} +(-164.521 - 138.049i) q^{43} +(-25.1438 - 43.5503i) q^{44} +(-173.385 + 300.311i) q^{46} +(-267.360 + 97.3112i) q^{47} +(-142.406 + 119.493i) q^{49} +(-476.753 - 173.524i) q^{50} +(27.8659 - 158.035i) q^{52} +695.130 q^{53} +244.643 q^{55} +(-17.4121 + 98.7488i) q^{56} +(81.3214 + 29.5986i) q^{58} +(320.887 - 269.256i) q^{59} +(78.1126 - 28.4307i) q^{61} +(-19.3911 + 33.5863i) q^{62} +(-32.0000 - 55.4256i) q^{64} +(598.040 + 501.815i) q^{65} +(104.917 + 595.014i) q^{67} +(34.0883 + 193.324i) q^{68} +(-373.687 - 313.560i) q^{70} +(-25.4078 - 44.0076i) q^{71} +(444.921 - 770.626i) q^{73} +(467.746 - 170.246i) q^{74} +(-415.956 + 349.029i) q^{76} +(148.073 + 53.8943i) q^{77} +(-29.3386 + 166.388i) q^{79} +311.353 q^{80} +790.017 q^{82} +(-257.027 + 1457.67i) q^{83} +(-897.416 - 326.633i) q^{85} +(-329.041 + 276.099i) q^{86} +(-94.5096 + 34.3987i) q^{88} +(-401.246 + 694.978i) q^{89} +(251.422 + 435.476i) q^{91} +(531.281 + 445.798i) q^{92} +(98.8124 + 560.393i) q^{94} +(-458.709 - 2601.47i) q^{95} +(1141.18 + 957.566i) q^{97} +(185.898 + 321.985i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8} - 30 q^{10} + 39 q^{11} - 60 q^{13} + 66 q^{14} - 102 q^{17} - 171 q^{19} - 96 q^{20} + 78 q^{22} - 48 q^{23} - 432 q^{25} + 468 q^{26} + 336 q^{28} + 381 q^{29} - 801 q^{31} - 222 q^{34} - 624 q^{35} - 555 q^{37} - 606 q^{38} + 96 q^{40} - 1401 q^{41} + 648 q^{43} - 132 q^{44} - 348 q^{46} - 540 q^{47} + 15 q^{49} + 828 q^{50} - 240 q^{52} + 1794 q^{53} + 3906 q^{55} + 264 q^{56} - 444 q^{58} + 1500 q^{59} - 378 q^{61} - 744 q^{62} - 960 q^{64} - 3666 q^{65} + 3087 q^{67} + 24 q^{68} + 2118 q^{70} - 120 q^{71} - 2604 q^{73} + 1974 q^{74} - 1212 q^{76} + 6504 q^{77} - 2625 q^{79} + 480 q^{80} + 3408 q^{82} + 5211 q^{83} - 1395 q^{85} + 1296 q^{86} - 912 q^{88} - 2604 q^{89} - 3399 q^{91} - 372 q^{92} + 4500 q^{94} - 7545 q^{95} + 8940 q^{97} - 4002 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.347296 1.96962i 0.122788 0.696364i
\(3\) 0 0
\(4\) −3.75877 1.36808i −0.469846 0.171010i
\(5\) 14.9069 12.5084i 1.33331 1.11878i 0.350022 0.936741i \(-0.386174\pi\)
0.983291 0.182041i \(-0.0582705\pi\)
\(6\) 0 0
\(7\) 11.7781 4.28689i 0.635959 0.231470i −0.00386374 0.999993i \(-0.501230\pi\)
0.639823 + 0.768522i \(0.279008\pi\)
\(8\) −4.00000 + 6.92820i −0.176777 + 0.306186i
\(9\) 0 0
\(10\) −19.4596 33.7050i −0.615366 1.06584i
\(11\) 9.63062 + 8.08105i 0.263976 + 0.221503i 0.765163 0.643837i \(-0.222658\pi\)
−0.501186 + 0.865339i \(0.667103\pi\)
\(12\) 0 0
\(13\) 6.96648 + 39.5088i 0.148627 + 0.842906i 0.964383 + 0.264510i \(0.0852102\pi\)
−0.815756 + 0.578396i \(0.803679\pi\)
\(14\) −4.35302 24.6872i −0.0830996 0.471281i
\(15\) 0 0
\(16\) 12.2567 + 10.2846i 0.191511 + 0.160697i
\(17\) −24.5383 42.5016i −0.350083 0.606362i 0.636181 0.771540i \(-0.280513\pi\)
−0.986264 + 0.165178i \(0.947180\pi\)
\(18\) 0 0
\(19\) 67.8741 117.561i 0.819546 1.41950i −0.0864706 0.996254i \(-0.527559\pi\)
0.906017 0.423241i \(-0.139108\pi\)
\(20\) −73.1441 + 26.6223i −0.817775 + 0.297646i
\(21\) 0 0
\(22\) 19.2612 16.1621i 0.186660 0.156626i
\(23\) −162.928 59.3010i −1.47708 0.537614i −0.527068 0.849823i \(-0.676709\pi\)
−0.950013 + 0.312209i \(0.898931\pi\)
\(24\) 0 0
\(25\) 44.0502 249.821i 0.352401 1.99857i
\(26\) 80.2367 0.605219
\(27\) 0 0
\(28\) −50.1361 −0.338387
\(29\) −7.51379 + 42.6128i −0.0481130 + 0.272862i −0.999368 0.0355426i \(-0.988684\pi\)
0.951255 + 0.308405i \(0.0997952\pi\)
\(30\) 0 0
\(31\) −18.2216 6.63213i −0.105571 0.0384247i 0.288695 0.957421i \(-0.406779\pi\)
−0.394266 + 0.918997i \(0.629001\pi\)
\(32\) 24.5134 20.5692i 0.135419 0.113630i
\(33\) 0 0
\(34\) −92.2339 + 33.5704i −0.465235 + 0.169332i
\(35\) 121.953 211.229i 0.588968 1.02012i
\(36\) 0 0
\(37\) 124.441 + 215.538i 0.552919 + 0.957684i 0.998062 + 0.0622244i \(0.0198195\pi\)
−0.445143 + 0.895459i \(0.646847\pi\)
\(38\) −207.978 174.514i −0.887856 0.745000i
\(39\) 0 0
\(40\) 27.0330 + 153.311i 0.106857 + 0.606017i
\(41\) 68.5925 + 389.008i 0.261277 + 1.48177i 0.779431 + 0.626488i \(0.215508\pi\)
−0.518154 + 0.855287i \(0.673381\pi\)
\(42\) 0 0
\(43\) −164.521 138.049i −0.583469 0.489589i 0.302615 0.953113i \(-0.402140\pi\)
−0.886084 + 0.463524i \(0.846585\pi\)
\(44\) −25.1438 43.5503i −0.0861492 0.149215i
\(45\) 0 0
\(46\) −173.385 + 300.311i −0.555742 + 0.962574i
\(47\) −267.360 + 97.3112i −0.829756 + 0.302006i −0.721759 0.692145i \(-0.756666\pi\)
−0.107997 + 0.994151i \(0.534444\pi\)
\(48\) 0 0
\(49\) −142.406 + 119.493i −0.415179 + 0.348376i
\(50\) −476.753 173.524i −1.34846 0.490800i
\(51\) 0 0
\(52\) 27.8659 158.035i 0.0743136 0.421453i
\(53\) 695.130 1.80157 0.900787 0.434262i \(-0.142991\pi\)
0.900787 + 0.434262i \(0.142991\pi\)
\(54\) 0 0
\(55\) 244.643 0.599777
\(56\) −17.4121 + 98.7488i −0.0415498 + 0.235641i
\(57\) 0 0
\(58\) 81.3214 + 29.5986i 0.184104 + 0.0670083i
\(59\) 320.887 269.256i 0.708066 0.594138i −0.215990 0.976396i \(-0.569298\pi\)
0.924056 + 0.382258i \(0.124853\pi\)
\(60\) 0 0
\(61\) 78.1126 28.4307i 0.163956 0.0596750i −0.258738 0.965947i \(-0.583307\pi\)
0.422694 + 0.906272i \(0.361085\pi\)
\(62\) −19.3911 + 33.5863i −0.0397204 + 0.0687978i
\(63\) 0 0
\(64\) −32.0000 55.4256i −0.0625000 0.108253i
\(65\) 598.040 + 501.815i 1.14120 + 0.957577i
\(66\) 0 0
\(67\) 104.917 + 595.014i 0.191308 + 1.08496i 0.917579 + 0.397554i \(0.130141\pi\)
−0.726270 + 0.687409i \(0.758748\pi\)
\(68\) 34.0883 + 193.324i 0.0607913 + 0.344765i
\(69\) 0 0
\(70\) −373.687 313.560i −0.638059 0.535395i
\(71\) −25.4078 44.0076i −0.0424697 0.0735597i 0.844009 0.536329i \(-0.180189\pi\)
−0.886479 + 0.462769i \(0.846856\pi\)
\(72\) 0 0
\(73\) 444.921 770.626i 0.713343 1.23555i −0.250252 0.968181i \(-0.580513\pi\)
0.963595 0.267366i \(-0.0861533\pi\)
\(74\) 467.746 170.246i 0.734789 0.267441i
\(75\) 0 0
\(76\) −415.956 + 349.029i −0.627809 + 0.526794i
\(77\) 148.073 + 53.8943i 0.219150 + 0.0797639i
\(78\) 0 0
\(79\) −29.3386 + 166.388i −0.0417830 + 0.236963i −0.998546 0.0539054i \(-0.982833\pi\)
0.956763 + 0.290868i \(0.0939442\pi\)
\(80\) 311.353 0.435129
\(81\) 0 0
\(82\) 790.017 1.06394
\(83\) −257.027 + 1457.67i −0.339909 + 1.92772i 0.0320928 + 0.999485i \(0.489783\pi\)
−0.372001 + 0.928232i \(0.621328\pi\)
\(84\) 0 0
\(85\) −897.416 326.633i −1.14516 0.416803i
\(86\) −329.041 + 276.099i −0.412575 + 0.346192i
\(87\) 0 0
\(88\) −94.5096 + 34.3987i −0.114486 + 0.0416695i
\(89\) −401.246 + 694.978i −0.477887 + 0.827725i −0.999679 0.0253482i \(-0.991931\pi\)
0.521792 + 0.853073i \(0.325264\pi\)
\(90\) 0 0
\(91\) 251.422 + 435.476i 0.289629 + 0.501651i
\(92\) 531.281 + 445.798i 0.602064 + 0.505192i
\(93\) 0 0
\(94\) 98.8124 + 560.393i 0.108423 + 0.614895i
\(95\) −458.709 2601.47i −0.495395 2.80953i
\(96\) 0 0
\(97\) 1141.18 + 957.566i 1.19453 + 1.00233i 0.999769 + 0.0214809i \(0.00683810\pi\)
0.194763 + 0.980850i \(0.437606\pi\)
\(98\) 185.898 + 321.985i 0.191618 + 0.331892i
\(99\) 0 0
\(100\) −507.350 + 878.756i −0.507350 + 0.878756i
\(101\) −388.444 + 141.382i −0.382689 + 0.139287i −0.526199 0.850361i \(-0.676383\pi\)
0.143510 + 0.989649i \(0.454161\pi\)
\(102\) 0 0
\(103\) −501.504 + 420.812i −0.479754 + 0.402561i −0.850338 0.526238i \(-0.823602\pi\)
0.370583 + 0.928799i \(0.379158\pi\)
\(104\) −301.591 109.770i −0.284360 0.103499i
\(105\) 0 0
\(106\) 241.416 1369.14i 0.221211 1.25455i
\(107\) 403.828 0.364856 0.182428 0.983219i \(-0.441604\pi\)
0.182428 + 0.983219i \(0.441604\pi\)
\(108\) 0 0
\(109\) 611.461 0.537315 0.268657 0.963236i \(-0.413420\pi\)
0.268657 + 0.963236i \(0.413420\pi\)
\(110\) 84.9638 481.854i 0.0736453 0.417663i
\(111\) 0 0
\(112\) 188.450 + 68.5902i 0.158990 + 0.0578676i
\(113\) −351.359 + 294.825i −0.292505 + 0.245441i −0.777217 0.629233i \(-0.783369\pi\)
0.484711 + 0.874674i \(0.338925\pi\)
\(114\) 0 0
\(115\) −3170.51 + 1153.97i −2.57089 + 0.935726i
\(116\) 86.5404 149.892i 0.0692679 0.119976i
\(117\) 0 0
\(118\) −418.888 725.535i −0.326795 0.566025i
\(119\) −471.215 395.396i −0.362993 0.304588i
\(120\) 0 0
\(121\) −203.680 1155.13i −0.153028 0.867865i
\(122\) −28.8693 163.726i −0.0214238 0.121500i
\(123\) 0 0
\(124\) 59.4177 + 49.8573i 0.0430311 + 0.0361074i
\(125\) −1251.98 2168.49i −0.895844 1.55165i
\(126\) 0 0
\(127\) 560.448 970.724i 0.391588 0.678250i −0.601071 0.799196i \(-0.705259\pi\)
0.992659 + 0.120945i \(0.0385925\pi\)
\(128\) −120.281 + 43.7786i −0.0830579 + 0.0302306i
\(129\) 0 0
\(130\) 1196.08 1003.63i 0.806947 0.677109i
\(131\) 487.069 + 177.279i 0.324851 + 0.118236i 0.499298 0.866431i \(-0.333591\pi\)
−0.174447 + 0.984667i \(0.555814\pi\)
\(132\) 0 0
\(133\) 295.457 1675.62i 0.192627 1.09244i
\(134\) 1208.39 0.779020
\(135\) 0 0
\(136\) 392.613 0.247546
\(137\) 92.8002 526.296i 0.0578720 0.328208i −0.942103 0.335324i \(-0.891154\pi\)
0.999975 + 0.00711622i \(0.00226518\pi\)
\(138\) 0 0
\(139\) 344.110 + 125.246i 0.209979 + 0.0764260i 0.444868 0.895596i \(-0.353251\pi\)
−0.234889 + 0.972022i \(0.575473\pi\)
\(140\) −747.374 + 627.121i −0.451176 + 0.378581i
\(141\) 0 0
\(142\) −95.5020 + 34.7599i −0.0564391 + 0.0205421i
\(143\) −252.181 + 436.791i −0.147472 + 0.255429i
\(144\) 0 0
\(145\) 421.010 + 729.211i 0.241124 + 0.417639i
\(146\) −1363.32 1143.96i −0.772801 0.648457i
\(147\) 0 0
\(148\) −172.872 980.405i −0.0960134 0.544519i
\(149\) 82.0854 + 465.529i 0.0451322 + 0.255957i 0.999023 0.0441970i \(-0.0140729\pi\)
−0.953891 + 0.300154i \(0.902962\pi\)
\(150\) 0 0
\(151\) 582.736 + 488.974i 0.314056 + 0.263524i 0.786166 0.618016i \(-0.212063\pi\)
−0.472110 + 0.881540i \(0.656508\pi\)
\(152\) 542.993 + 940.491i 0.289753 + 0.501868i
\(153\) 0 0
\(154\) 157.576 272.930i 0.0824536 0.142814i
\(155\) −354.585 + 129.058i −0.183748 + 0.0668789i
\(156\) 0 0
\(157\) −102.489 + 85.9981i −0.0520986 + 0.0437159i −0.668465 0.743743i \(-0.733048\pi\)
0.616367 + 0.787459i \(0.288604\pi\)
\(158\) 317.530 + 115.572i 0.159882 + 0.0581923i
\(159\) 0 0
\(160\) 108.132 613.246i 0.0534286 0.303008i
\(161\) −2173.21 −1.06381
\(162\) 0 0
\(163\) −907.179 −0.435925 −0.217962 0.975957i \(-0.569941\pi\)
−0.217962 + 0.975957i \(0.569941\pi\)
\(164\) 274.370 1556.03i 0.130638 0.740887i
\(165\) 0 0
\(166\) 2781.79 + 1012.49i 1.30066 + 0.473400i
\(167\) −1447.22 + 1214.36i −0.670595 + 0.562696i −0.913242 0.407419i \(-0.866429\pi\)
0.242646 + 0.970115i \(0.421985\pi\)
\(168\) 0 0
\(169\) 552.088 200.943i 0.251292 0.0914627i
\(170\) −955.010 + 1654.13i −0.430858 + 0.746268i
\(171\) 0 0
\(172\) 429.533 + 743.973i 0.190416 + 0.329811i
\(173\) 426.505 + 357.880i 0.187437 + 0.157278i 0.731677 0.681651i \(-0.238738\pi\)
−0.544241 + 0.838929i \(0.683182\pi\)
\(174\) 0 0
\(175\) −552.126 3131.26i −0.238496 1.35258i
\(176\) 34.9294 + 198.094i 0.0149597 + 0.0848404i
\(177\) 0 0
\(178\) 1229.49 + 1031.66i 0.517719 + 0.434418i
\(179\) −1048.50 1816.06i −0.437814 0.758316i 0.559707 0.828691i \(-0.310914\pi\)
−0.997521 + 0.0703748i \(0.977580\pi\)
\(180\) 0 0
\(181\) −138.831 + 240.463i −0.0570124 + 0.0987484i −0.893123 0.449813i \(-0.851491\pi\)
0.836111 + 0.548561i \(0.184824\pi\)
\(182\) 945.038 343.966i 0.384895 0.140090i
\(183\) 0 0
\(184\) 1062.56 891.595i 0.425723 0.357224i
\(185\) 4551.07 + 1656.45i 1.80865 + 0.658296i
\(186\) 0 0
\(187\) 107.138 607.612i 0.0418970 0.237610i
\(188\) 1138.08 0.441504
\(189\) 0 0
\(190\) −5283.20 −2.01728
\(191\) 250.820 1422.47i 0.0950195 0.538882i −0.899722 0.436464i \(-0.856231\pi\)
0.994741 0.102419i \(-0.0326582\pi\)
\(192\) 0 0
\(193\) −2350.57 855.537i −0.876671 0.319082i −0.135806 0.990735i \(-0.543362\pi\)
−0.740866 + 0.671653i \(0.765585\pi\)
\(194\) 2282.37 1915.13i 0.844662 0.708755i
\(195\) 0 0
\(196\) 698.749 254.324i 0.254646 0.0926836i
\(197\) 538.794 933.218i 0.194860 0.337508i −0.751994 0.659169i \(-0.770908\pi\)
0.946855 + 0.321662i \(0.104241\pi\)
\(198\) 0 0
\(199\) −1890.89 3275.12i −0.673577 1.16667i −0.976883 0.213776i \(-0.931424\pi\)
0.303306 0.952893i \(-0.401909\pi\)
\(200\) 1554.61 + 1304.47i 0.549638 + 0.461201i
\(201\) 0 0
\(202\) 143.563 + 814.186i 0.0500052 + 0.283594i
\(203\) 94.1781 + 534.110i 0.0325616 + 0.184666i
\(204\) 0 0
\(205\) 5888.35 + 4940.91i 2.00615 + 1.68336i
\(206\) 654.667 + 1133.92i 0.221421 + 0.383513i
\(207\) 0 0
\(208\) −320.947 + 555.896i −0.106989 + 0.185310i
\(209\) 1603.69 583.695i 0.530763 0.193182i
\(210\) 0 0
\(211\) −2722.62 + 2284.55i −0.888308 + 0.745379i −0.967870 0.251451i \(-0.919092\pi\)
0.0795624 + 0.996830i \(0.474648\pi\)
\(212\) −2612.83 950.993i −0.846463 0.308087i
\(213\) 0 0
\(214\) 140.248 795.386i 0.0447998 0.254072i
\(215\) −4179.27 −1.32569
\(216\) 0 0
\(217\) −243.048 −0.0760331
\(218\) 212.358 1204.34i 0.0659757 0.374167i
\(219\) 0 0
\(220\) −919.559 334.692i −0.281803 0.102568i
\(221\) 1508.24 1265.57i 0.459074 0.385209i
\(222\) 0 0
\(223\) −1852.55 + 674.273i −0.556305 + 0.202478i −0.604845 0.796343i \(-0.706765\pi\)
0.0485408 + 0.998821i \(0.484543\pi\)
\(224\) 200.544 347.353i 0.0598189 0.103609i
\(225\) 0 0
\(226\) 458.667 + 794.434i 0.135000 + 0.233827i
\(227\) −1475.96 1238.48i −0.431555 0.362118i 0.400983 0.916086i \(-0.368669\pi\)
−0.832538 + 0.553968i \(0.813113\pi\)
\(228\) 0 0
\(229\) 1123.91 + 6374.01i 0.324323 + 1.83933i 0.514388 + 0.857557i \(0.328019\pi\)
−0.190065 + 0.981772i \(0.560870\pi\)
\(230\) 1171.77 + 6645.46i 0.335933 + 1.90517i
\(231\) 0 0
\(232\) −265.175 222.508i −0.0750414 0.0629672i
\(233\) 1709.54 + 2961.01i 0.480668 + 0.832542i 0.999754 0.0221805i \(-0.00706086\pi\)
−0.519086 + 0.854722i \(0.673728\pi\)
\(234\) 0 0
\(235\) −2768.31 + 4794.85i −0.768445 + 1.33099i
\(236\) −1574.50 + 573.072i −0.434286 + 0.158067i
\(237\) 0 0
\(238\) −942.430 + 790.793i −0.256675 + 0.215376i
\(239\) 1160.72 + 422.466i 0.314144 + 0.114339i 0.494280 0.869303i \(-0.335432\pi\)
−0.180136 + 0.983642i \(0.557654\pi\)
\(240\) 0 0
\(241\) −504.392 + 2860.55i −0.134816 + 0.764581i 0.840171 + 0.542321i \(0.182454\pi\)
−0.974987 + 0.222260i \(0.928657\pi\)
\(242\) −2345.90 −0.623140
\(243\) 0 0
\(244\) −332.503 −0.0872390
\(245\) −628.172 + 3562.54i −0.163806 + 0.928990i
\(246\) 0 0
\(247\) 5117.56 + 1862.64i 1.31831 + 0.479825i
\(248\) 118.835 99.7147i 0.0304276 0.0255318i
\(249\) 0 0
\(250\) −4705.90 + 1712.81i −1.19051 + 0.433310i
\(251\) −1023.72 + 1773.14i −0.257438 + 0.445895i −0.965555 0.260200i \(-0.916211\pi\)
0.708117 + 0.706095i \(0.249545\pi\)
\(252\) 0 0
\(253\) −1089.88 1887.74i −0.270832 0.469095i
\(254\) −1717.31 1441.00i −0.424227 0.355969i
\(255\) 0 0
\(256\) 44.4539 + 252.111i 0.0108530 + 0.0615505i
\(257\) 1055.49 + 5986.00i 0.256186 + 1.45290i 0.793009 + 0.609210i \(0.208513\pi\)
−0.536823 + 0.843695i \(0.680376\pi\)
\(258\) 0 0
\(259\) 2389.67 + 2005.17i 0.573309 + 0.481064i
\(260\) −1561.37 2704.37i −0.372431 0.645070i
\(261\) 0 0
\(262\) 518.328 897.771i 0.122223 0.211697i
\(263\) 1749.34 636.706i 0.410147 0.149281i −0.128703 0.991683i \(-0.541081\pi\)
0.538850 + 0.842402i \(0.318859\pi\)
\(264\) 0 0
\(265\) 10362.2 8694.94i 2.40206 2.01557i
\(266\) −3197.72 1163.87i −0.737085 0.268277i
\(267\) 0 0
\(268\) 419.668 2380.06i 0.0956541 0.542482i
\(269\) 6473.01 1.46716 0.733580 0.679603i \(-0.237848\pi\)
0.733580 + 0.679603i \(0.237848\pi\)
\(270\) 0 0
\(271\) −2770.56 −0.621032 −0.310516 0.950568i \(-0.600502\pi\)
−0.310516 + 0.950568i \(0.600502\pi\)
\(272\) 136.353 773.296i 0.0303957 0.172382i
\(273\) 0 0
\(274\) −1004.37 365.562i −0.221446 0.0805999i
\(275\) 2443.05 2049.96i 0.535714 0.449517i
\(276\) 0 0
\(277\) −4974.34 + 1810.51i −1.07899 + 0.392719i −0.819530 0.573036i \(-0.805765\pi\)
−0.259456 + 0.965755i \(0.583543\pi\)
\(278\) 366.194 634.267i 0.0790031 0.136837i
\(279\) 0 0
\(280\) 975.627 + 1689.84i 0.208232 + 0.360668i
\(281\) −3448.49 2893.63i −0.732098 0.614303i 0.198605 0.980080i \(-0.436359\pi\)
−0.930703 + 0.365776i \(0.880803\pi\)
\(282\) 0 0
\(283\) −1580.95 8966.03i −0.332077 1.88330i −0.454374 0.890811i \(-0.650137\pi\)
0.122297 0.992494i \(-0.460974\pi\)
\(284\) 35.2961 + 200.174i 0.00737479 + 0.0418245i
\(285\) 0 0
\(286\) 772.729 + 648.396i 0.159764 + 0.134058i
\(287\) 2475.52 + 4287.73i 0.509148 + 0.881871i
\(288\) 0 0
\(289\) 1252.24 2168.95i 0.254884 0.441471i
\(290\) 1582.48 575.976i 0.320436 0.116629i
\(291\) 0 0
\(292\) −2726.63 + 2287.92i −0.546453 + 0.458528i
\(293\) 1645.06 + 598.754i 0.328005 + 0.119384i 0.500774 0.865578i \(-0.333049\pi\)
−0.172768 + 0.984963i \(0.555271\pi\)
\(294\) 0 0
\(295\) 1415.47 8027.54i 0.279363 1.58434i
\(296\) −1991.06 −0.390973
\(297\) 0 0
\(298\) 945.422 0.183781
\(299\) 1207.88 6850.22i 0.233624 1.32495i
\(300\) 0 0
\(301\) −2529.55 920.681i −0.484388 0.176303i
\(302\) 1165.47 977.948i 0.222071 0.186340i
\(303\) 0 0
\(304\) 2040.98 742.858i 0.385061 0.140151i
\(305\) 808.795 1400.87i 0.151841 0.262996i
\(306\) 0 0
\(307\) 395.713 + 685.395i 0.0735652 + 0.127419i 0.900461 0.434936i \(-0.143229\pi\)
−0.826896 + 0.562355i \(0.809896\pi\)
\(308\) −482.842 405.152i −0.0893262 0.0749536i
\(309\) 0 0
\(310\) 131.049 + 743.218i 0.0240100 + 0.136168i
\(311\) −725.349 4113.66i −0.132253 0.750046i −0.976733 0.214458i \(-0.931201\pi\)
0.844480 0.535587i \(-0.179910\pi\)
\(312\) 0 0
\(313\) −1032.97 866.763i −0.186539 0.156525i 0.544736 0.838608i \(-0.316630\pi\)
−0.731275 + 0.682083i \(0.761074\pi\)
\(314\) 133.789 + 231.730i 0.0240451 + 0.0416474i
\(315\) 0 0
\(316\) 337.909 585.275i 0.0601546 0.104191i
\(317\) −4882.25 + 1776.99i −0.865030 + 0.314845i −0.736153 0.676815i \(-0.763360\pi\)
−0.128877 + 0.991661i \(0.541137\pi\)
\(318\) 0 0
\(319\) −416.719 + 349.669i −0.0731404 + 0.0613721i
\(320\) −1170.30 425.956i −0.204444 0.0744115i
\(321\) 0 0
\(322\) −754.747 + 4280.38i −0.130622 + 0.740796i
\(323\) −6662.06 −1.14764
\(324\) 0 0
\(325\) 10177.0 1.73698
\(326\) −315.060 + 1786.79i −0.0535263 + 0.303562i
\(327\) 0 0
\(328\) −2969.49 1080.81i −0.499887 0.181944i
\(329\) −2731.84 + 2292.29i −0.457785 + 0.384128i
\(330\) 0 0
\(331\) −336.280 + 122.396i −0.0558417 + 0.0203247i −0.369790 0.929115i \(-0.620570\pi\)
0.313948 + 0.949440i \(0.398348\pi\)
\(332\) 2960.32 5127.43i 0.489364 0.847603i
\(333\) 0 0
\(334\) 1889.21 + 3272.22i 0.309501 + 0.536071i
\(335\) 9006.64 + 7557.47i 1.46891 + 1.23256i
\(336\) 0 0
\(337\) 215.613 + 1222.80i 0.0348523 + 0.197657i 0.997262 0.0739431i \(-0.0235583\pi\)
−0.962410 + 0.271600i \(0.912447\pi\)
\(338\) −204.043 1157.19i −0.0328358 0.186221i
\(339\) 0 0
\(340\) 2926.32 + 2455.47i 0.466771 + 0.391667i
\(341\) −121.891 211.121i −0.0193571 0.0335275i
\(342\) 0 0
\(343\) −3314.61 + 5741.08i −0.521785 + 0.903758i
\(344\) 1614.52 587.636i 0.253049 0.0921024i
\(345\) 0 0
\(346\) 853.010 715.760i 0.132538 0.111212i
\(347\) −6499.67 2365.69i −1.00554 0.365985i −0.213818 0.976873i \(-0.568590\pi\)
−0.791717 + 0.610889i \(0.790812\pi\)
\(348\) 0 0
\(349\) 1406.21 7974.99i 0.215680 1.22318i −0.664042 0.747696i \(-0.731160\pi\)
0.879722 0.475488i \(-0.157729\pi\)
\(350\) −6359.14 −0.971172
\(351\) 0 0
\(352\) 402.300 0.0609167
\(353\) −78.4710 + 445.031i −0.0118317 + 0.0671009i −0.990152 0.139997i \(-0.955291\pi\)
0.978320 + 0.207098i \(0.0664018\pi\)
\(354\) 0 0
\(355\) −929.214 338.206i −0.138923 0.0505637i
\(356\) 2458.98 2063.33i 0.366083 0.307180i
\(357\) 0 0
\(358\) −3941.08 + 1434.43i −0.581822 + 0.211766i
\(359\) 1390.92 2409.15i 0.204485 0.354178i −0.745484 0.666524i \(-0.767781\pi\)
0.949968 + 0.312346i \(0.101115\pi\)
\(360\) 0 0
\(361\) −5784.28 10018.7i −0.843312 1.46066i
\(362\) 425.404 + 356.956i 0.0617644 + 0.0518265i
\(363\) 0 0
\(364\) −349.272 1980.82i −0.0502935 0.285228i
\(365\) −3006.88 17052.9i −0.431198 2.44545i
\(366\) 0 0
\(367\) 1856.61 + 1557.88i 0.264072 + 0.221583i 0.765204 0.643788i \(-0.222638\pi\)
−0.501132 + 0.865371i \(0.667083\pi\)
\(368\) −1387.08 2402.49i −0.196485 0.340321i
\(369\) 0 0
\(370\) 4843.14 8388.57i 0.680495 1.17865i
\(371\) 8187.33 2979.94i 1.14573 0.417011i
\(372\) 0 0
\(373\) −9923.42 + 8326.74i −1.37752 + 1.15588i −0.407402 + 0.913249i \(0.633565\pi\)
−0.970119 + 0.242628i \(0.921990\pi\)
\(374\) −1159.55 422.043i −0.160318 0.0583511i
\(375\) 0 0
\(376\) 395.250 2241.57i 0.0542113 0.307448i
\(377\) −1735.93 −0.237148
\(378\) 0 0
\(379\) 5632.80 0.763423 0.381711 0.924282i \(-0.375335\pi\)
0.381711 + 0.924282i \(0.375335\pi\)
\(380\) −1834.84 + 10405.9i −0.247698 + 1.40476i
\(381\) 0 0
\(382\) −2714.62 988.039i −0.363591 0.132336i
\(383\) −10225.1 + 8579.85i −1.36417 + 1.14467i −0.389498 + 0.921027i \(0.627352\pi\)
−0.974670 + 0.223646i \(0.928204\pi\)
\(384\) 0 0
\(385\) 2881.44 1048.76i 0.381434 0.138830i
\(386\) −2501.42 + 4332.59i −0.329842 + 0.571303i
\(387\) 0 0
\(388\) −2979.42 5160.50i −0.389838 0.675219i
\(389\) 1941.59 + 1629.18i 0.253065 + 0.212347i 0.760491 0.649349i \(-0.224958\pi\)
−0.507426 + 0.861696i \(0.669403\pi\)
\(390\) 0 0
\(391\) 1477.59 + 8379.85i 0.191113 + 1.08386i
\(392\) −258.247 1464.59i −0.0332741 0.188707i
\(393\) 0 0
\(394\) −1650.96 1385.32i −0.211102 0.177136i
\(395\) 1643.89 + 2847.30i 0.209400 + 0.362692i
\(396\) 0 0
\(397\) 6531.29 11312.5i 0.825683 1.43013i −0.0757128 0.997130i \(-0.524123\pi\)
0.901396 0.432996i \(-0.142543\pi\)
\(398\) −7107.43 + 2586.89i −0.895133 + 0.325802i
\(399\) 0 0
\(400\) 3109.22 2608.95i 0.388653 0.326118i
\(401\) 5401.76 + 1966.08i 0.672696 + 0.244841i 0.655708 0.755015i \(-0.272370\pi\)
0.0169875 + 0.999856i \(0.494592\pi\)
\(402\) 0 0
\(403\) 135.087 766.118i 0.0166977 0.0946974i
\(404\) 1653.49 0.203625
\(405\) 0 0
\(406\) 1084.70 0.132593
\(407\) −543.331 + 3081.38i −0.0661718 + 0.375279i
\(408\) 0 0
\(409\) −4723.52 1719.22i −0.571059 0.207848i 0.0403195 0.999187i \(-0.487162\pi\)
−0.611378 + 0.791338i \(0.709385\pi\)
\(410\) 11776.7 9881.83i 1.41856 1.19031i
\(411\) 0 0
\(412\) 2460.74 895.637i 0.294253 0.107099i
\(413\) 2625.18 4546.94i 0.312776 0.541744i
\(414\) 0 0
\(415\) 14401.6 + 24944.4i 1.70349 + 2.95053i
\(416\) 983.438 + 825.202i 0.115906 + 0.0972569i
\(417\) 0 0
\(418\) −592.699 3361.36i −0.0693538 0.393325i
\(419\) −1510.39 8565.82i −0.176103 0.998730i −0.936863 0.349697i \(-0.886285\pi\)
0.760760 0.649033i \(-0.224826\pi\)
\(420\) 0 0
\(421\) −9129.88 7660.87i −1.05692 0.886860i −0.0631149 0.998006i \(-0.520103\pi\)
−0.993804 + 0.111146i \(0.964548\pi\)
\(422\) 3554.13 + 6155.93i 0.409982 + 0.710109i
\(423\) 0 0
\(424\) −2780.52 + 4816.00i −0.318476 + 0.551617i
\(425\) −11698.7 + 4257.98i −1.33523 + 0.485982i
\(426\) 0 0
\(427\) 798.141 669.720i 0.0904561 0.0759017i
\(428\) −1517.90 552.469i −0.171426 0.0623940i
\(429\) 0 0
\(430\) −1451.44 + 8231.55i −0.162779 + 0.923164i
\(431\) 2409.07 0.269236 0.134618 0.990898i \(-0.457019\pi\)
0.134618 + 0.990898i \(0.457019\pi\)
\(432\) 0 0
\(433\) −14299.0 −1.58699 −0.793496 0.608575i \(-0.791742\pi\)
−0.793496 + 0.608575i \(0.791742\pi\)
\(434\) −84.4097 + 478.711i −0.00933593 + 0.0529467i
\(435\) 0 0
\(436\) −2298.34 836.527i −0.252455 0.0918862i
\(437\) −18030.1 + 15129.1i −1.97368 + 1.65611i
\(438\) 0 0
\(439\) −1498.70 + 545.482i −0.162936 + 0.0593039i −0.422200 0.906502i \(-0.638742\pi\)
0.259264 + 0.965806i \(0.416520\pi\)
\(440\) −978.574 + 1694.94i −0.106027 + 0.183643i
\(441\) 0 0
\(442\) −1968.87 3410.19i −0.211877 0.366982i
\(443\) −9206.21 7724.93i −0.987360 0.828493i −0.00217624 0.999998i \(-0.500693\pi\)
−0.985183 + 0.171505i \(0.945137\pi\)
\(444\) 0 0
\(445\) 2711.71 + 15378.9i 0.288871 + 1.63827i
\(446\) 684.675 + 3882.98i 0.0726912 + 0.412253i
\(447\) 0 0
\(448\) −614.504 515.630i −0.0648048 0.0543777i
\(449\) 422.329 + 731.495i 0.0443896 + 0.0768850i 0.887367 0.461065i \(-0.152532\pi\)
−0.842977 + 0.537950i \(0.819199\pi\)
\(450\) 0 0
\(451\) −2483.00 + 4300.68i −0.259246 + 0.449027i
\(452\) 1724.02 627.493i 0.179405 0.0652982i
\(453\) 0 0
\(454\) −2951.93 + 2476.96i −0.305156 + 0.256056i
\(455\) 9195.02 + 3346.71i 0.947404 + 0.344827i
\(456\) 0 0
\(457\) −1531.06 + 8683.08i −0.156718 + 0.888791i 0.800481 + 0.599359i \(0.204578\pi\)
−0.957199 + 0.289432i \(0.906534\pi\)
\(458\) 12944.7 1.32067
\(459\) 0 0
\(460\) 13496.0 1.36794
\(461\) 288.993 1638.96i 0.0291969 0.165584i −0.966723 0.255825i \(-0.917653\pi\)
0.995920 + 0.0902416i \(0.0287639\pi\)
\(462\) 0 0
\(463\) 15794.8 + 5748.83i 1.58541 + 0.577043i 0.976372 0.216096i \(-0.0693326\pi\)
0.609040 + 0.793139i \(0.291555\pi\)
\(464\) −530.351 + 445.017i −0.0530623 + 0.0445246i
\(465\) 0 0
\(466\) 6425.77 2338.79i 0.638772 0.232494i
\(467\) 3752.00 6498.66i 0.371781 0.643944i −0.618058 0.786132i \(-0.712080\pi\)
0.989840 + 0.142188i \(0.0454138\pi\)
\(468\) 0 0
\(469\) 3786.49 + 6558.39i 0.372801 + 0.645710i
\(470\) 8482.59 + 7117.74i 0.832495 + 0.698546i
\(471\) 0 0
\(472\) 581.913 + 3300.19i 0.0567473 + 0.321830i
\(473\) −468.854 2659.00i −0.0455770 0.258480i
\(474\) 0 0
\(475\) −26379.4 22135.0i −2.54815 2.13815i
\(476\) 1230.25 + 2130.86i 0.118464 + 0.205185i
\(477\) 0 0
\(478\) 1235.21 2139.44i 0.118195 0.204719i
\(479\) 9907.76 3606.13i 0.945088 0.343984i 0.176915 0.984226i \(-0.443388\pi\)
0.768173 + 0.640242i \(0.221166\pi\)
\(480\) 0 0
\(481\) −7648.76 + 6418.07i −0.725059 + 0.608397i
\(482\) 5459.01 + 1986.92i 0.515873 + 0.187763i
\(483\) 0 0
\(484\) −814.721 + 4620.51i −0.0765140 + 0.433932i
\(485\) 28989.1 2.71408
\(486\) 0 0
\(487\) −7526.48 −0.700323 −0.350161 0.936689i \(-0.613873\pi\)
−0.350161 + 0.936689i \(0.613873\pi\)
\(488\) −115.477 + 654.903i −0.0107119 + 0.0607501i
\(489\) 0 0
\(490\) 6798.68 + 2474.52i 0.626802 + 0.228137i
\(491\) −4344.46 + 3645.44i −0.399313 + 0.335064i −0.820228 0.572036i \(-0.806154\pi\)
0.420915 + 0.907100i \(0.361709\pi\)
\(492\) 0 0
\(493\) 1995.49 726.299i 0.182297 0.0663506i
\(494\) 5445.99 9432.73i 0.496005 0.859106i
\(495\) 0 0
\(496\) −155.128 268.690i −0.0140433 0.0243237i
\(497\) −487.912 409.406i −0.0440359 0.0369505i
\(498\) 0 0
\(499\) −1147.63 6508.52i −0.102956 0.583890i −0.992017 0.126103i \(-0.959753\pi\)
0.889062 0.457788i \(-0.151358\pi\)
\(500\) 1739.23 + 9863.67i 0.155562 + 0.882234i
\(501\) 0 0
\(502\) 3136.87 + 2632.15i 0.278895 + 0.234021i
\(503\) 5921.08 + 10255.6i 0.524866 + 0.909095i 0.999581 + 0.0289553i \(0.00921805\pi\)
−0.474714 + 0.880140i \(0.657449\pi\)
\(504\) 0 0
\(505\) −4022.03 + 6966.37i −0.354412 + 0.613860i
\(506\) −4096.63 + 1491.05i −0.359916 + 0.130999i
\(507\) 0 0
\(508\) −3434.62 + 2881.99i −0.299974 + 0.251708i
\(509\) −5319.30 1936.07i −0.463210 0.168594i 0.0998643 0.995001i \(-0.468159\pi\)
−0.563074 + 0.826407i \(0.690381\pi\)
\(510\) 0 0
\(511\) 1936.75 10983.9i 0.167665 0.950875i
\(512\) 512.000 0.0441942
\(513\) 0 0
\(514\) 12156.7 1.04321
\(515\) −2212.20 + 12546.0i −0.189284 + 1.07348i
\(516\) 0 0
\(517\) −3361.22 1223.39i −0.285931 0.104070i
\(518\) 4779.35 4010.35i 0.405391 0.340163i
\(519\) 0 0
\(520\) −5868.84 + 2136.08i −0.494934 + 0.180141i
\(521\) 3673.26 6362.28i 0.308884 0.535003i −0.669235 0.743051i \(-0.733378\pi\)
0.978119 + 0.208049i \(0.0667112\pi\)
\(522\) 0 0
\(523\) −5484.53 9499.49i −0.458550 0.794233i 0.540334 0.841450i \(-0.318298\pi\)
−0.998885 + 0.0472179i \(0.984964\pi\)
\(524\) −1588.25 1332.70i −0.132410 0.111106i
\(525\) 0 0
\(526\) −646.528 3666.64i −0.0535931 0.303942i
\(527\) 165.252 + 937.190i 0.0136594 + 0.0774661i
\(528\) 0 0
\(529\) 13708.5 + 11502.8i 1.12670 + 0.945411i
\(530\) −13526.9 23429.3i −1.10863 1.92020i
\(531\) 0 0
\(532\) −3402.94 + 5894.07i −0.277324 + 0.480339i
\(533\) −14891.4 + 5420.02i −1.21016 + 0.440464i
\(534\) 0 0
\(535\) 6019.82 5051.23i 0.486467 0.408194i
\(536\) −4542.05 1653.17i −0.366020 0.133220i
\(537\) 0 0
\(538\) 2248.05 12749.3i 0.180149 1.02168i
\(539\) −2337.09 −0.186764
\(540\) 0 0
\(541\) −6254.50 −0.497046 −0.248523 0.968626i \(-0.579945\pi\)
−0.248523 + 0.968626i \(0.579945\pi\)
\(542\) −962.206 + 5456.94i −0.0762552 + 0.432465i
\(543\) 0 0
\(544\) −1475.74 537.126i −0.116309 0.0423329i
\(545\) 9114.98 7648.38i 0.716409 0.601138i
\(546\) 0 0
\(547\) 9564.08 3481.04i 0.747588 0.272100i 0.0599974 0.998199i \(-0.480891\pi\)
0.687590 + 0.726099i \(0.258669\pi\)
\(548\) −1068.83 + 1851.27i −0.0833178 + 0.144311i
\(549\) 0 0
\(550\) −3189.17 5523.81i −0.247249 0.428247i
\(551\) 4499.63 + 3775.64i 0.347896 + 0.291919i
\(552\) 0 0
\(553\) 367.731 + 2085.51i 0.0282776 + 0.160370i
\(554\) 1838.44 + 10426.3i 0.140989 + 0.799588i
\(555\) 0 0
\(556\) −1122.08 941.540i −0.0855881 0.0718169i
\(557\) −2682.97 4647.04i −0.204095 0.353503i 0.745749 0.666227i \(-0.232092\pi\)
−0.949844 + 0.312724i \(0.898759\pi\)
\(558\) 0 0
\(559\) 4308.04 7461.74i 0.325958 0.564576i
\(560\) 3667.16 1334.74i 0.276724 0.100719i
\(561\) 0 0
\(562\) −6896.98 + 5787.25i −0.517672 + 0.434378i
\(563\) −13974.5 5086.31i −1.04610 0.380750i −0.238912 0.971041i \(-0.576791\pi\)
−0.807190 + 0.590291i \(0.799013\pi\)
\(564\) 0 0
\(565\) −1549.89 + 8789.86i −0.115406 + 0.654500i
\(566\) −18208.7 −1.35224
\(567\) 0 0
\(568\) 406.524 0.0300306
\(569\) 4185.50 23737.2i 0.308375 1.74888i −0.298803 0.954315i \(-0.596587\pi\)
0.607178 0.794566i \(-0.292302\pi\)
\(570\) 0 0
\(571\) 14252.4 + 5187.44i 1.04456 + 0.380188i 0.806607 0.591089i \(-0.201302\pi\)
0.237952 + 0.971277i \(0.423524\pi\)
\(572\) 1545.46 1296.79i 0.112970 0.0947931i
\(573\) 0 0
\(574\) 9304.93 3386.72i 0.676620 0.246270i
\(575\) −21991.7 + 38090.7i −1.59498 + 2.76259i
\(576\) 0 0
\(577\) −1471.56 2548.82i −0.106173 0.183897i 0.808044 0.589122i \(-0.200526\pi\)
−0.914217 + 0.405225i \(0.867193\pi\)
\(578\) −3837.10 3219.71i −0.276128 0.231699i
\(579\) 0 0
\(580\) −584.861 3316.91i −0.0418707 0.237461i
\(581\) 3221.59 + 18270.5i 0.230041 + 1.30463i
\(582\) 0 0
\(583\) 6694.53 + 5617.38i 0.475573 + 0.399053i
\(584\) 3559.37 + 6165.01i 0.252205 + 0.436832i
\(585\) 0 0
\(586\) 1750.64 3032.20i 0.123410 0.213752i
\(587\) 11897.8 4330.46i 0.836586 0.304492i 0.112027 0.993705i \(-0.464266\pi\)
0.724559 + 0.689213i \(0.242043\pi\)
\(588\) 0 0
\(589\) −2016.46 + 1692.01i −0.141064 + 0.118367i
\(590\) −15319.6 5575.87i −1.06898 0.389076i
\(591\) 0 0
\(592\) −691.488 + 3921.62i −0.0480067 + 0.272259i
\(593\) −27302.9 −1.89071 −0.945357 0.326036i \(-0.894287\pi\)
−0.945357 + 0.326036i \(0.894287\pi\)
\(594\) 0 0
\(595\) −11970.1 −0.824751
\(596\) 328.342 1862.12i 0.0225661 0.127979i
\(597\) 0 0
\(598\) −13072.8 4758.11i −0.893958 0.325374i
\(599\) 18405.2 15443.8i 1.25545 1.05345i 0.259300 0.965797i \(-0.416508\pi\)
0.996151 0.0876521i \(-0.0279364\pi\)
\(600\) 0 0
\(601\) 16283.0 5926.53i 1.10515 0.402243i 0.275941 0.961175i \(-0.411011\pi\)
0.829214 + 0.558931i \(0.188788\pi\)
\(602\) −2691.89 + 4662.49i −0.182248 + 0.315663i
\(603\) 0 0
\(604\) −1521.42 2635.17i −0.102493 0.177522i
\(605\) −17485.0 14671.7i −1.17499 0.985931i
\(606\) 0 0
\(607\) −2979.50 16897.6i −0.199233 1.12990i −0.906261 0.422719i \(-0.861076\pi\)
0.707028 0.707186i \(-0.250035\pi\)
\(608\) −754.317 4277.95i −0.0503151 0.285351i
\(609\) 0 0
\(610\) −2478.29 2079.53i −0.164497 0.138029i
\(611\) −5707.21 9885.19i −0.377887 0.654520i
\(612\) 0 0
\(613\) −936.810 + 1622.60i −0.0617249 + 0.106911i −0.895237 0.445591i \(-0.852993\pi\)
0.833512 + 0.552502i \(0.186327\pi\)
\(614\) 1487.39 541.367i 0.0977627 0.0355827i
\(615\) 0 0
\(616\) −965.683 + 810.305i −0.0631631 + 0.0530002i
\(617\) 14311.7 + 5209.04i 0.933822 + 0.339884i 0.763724 0.645543i \(-0.223369\pi\)
0.170099 + 0.985427i \(0.445591\pi\)
\(618\) 0 0
\(619\) −3287.30 + 18643.2i −0.213453 + 1.21055i 0.670117 + 0.742256i \(0.266244\pi\)
−0.883570 + 0.468299i \(0.844867\pi\)
\(620\) 1509.37 0.0977704
\(621\) 0 0
\(622\) −8354.24 −0.538544
\(623\) −1746.63 + 9905.64i −0.112323 + 0.637016i
\(624\) 0 0
\(625\) −15990.4 5820.02i −1.02338 0.372481i
\(626\) −2065.94 + 1733.53i −0.131903 + 0.110680i
\(627\) 0 0
\(628\) 502.883 183.034i 0.0319542 0.0116304i
\(629\) 6107.15 10577.9i 0.387135 0.670538i
\(630\) 0 0
\(631\) −5557.83 9626.44i −0.350640 0.607326i 0.635722 0.771918i \(-0.280702\pi\)
−0.986362 + 0.164592i \(0.947369\pi\)
\(632\) −1035.41 868.815i −0.0651685 0.0546829i
\(633\) 0 0
\(634\) 1804.41 + 10233.3i 0.113032 + 0.641035i
\(635\) −3787.64 21480.8i −0.236705 1.34242i
\(636\) 0 0
\(637\) −5713.10 4793.86i −0.355355 0.298179i
\(638\) 543.988 + 942.215i 0.0337566 + 0.0584681i
\(639\) 0 0
\(640\) −1245.41 + 2157.12i −0.0769207 + 0.133231i
\(641\) 7179.60 2613.16i 0.442398 0.161020i −0.111210 0.993797i \(-0.535473\pi\)
0.553608 + 0.832777i \(0.313250\pi\)
\(642\) 0 0
\(643\) 13997.5 11745.3i 0.858489 0.720358i −0.103153 0.994665i \(-0.532893\pi\)
0.961642 + 0.274308i \(0.0884487\pi\)
\(644\) 8168.58 + 2973.12i 0.499825 + 0.181921i
\(645\) 0 0
\(646\) −2313.71 + 13121.7i −0.140916 + 0.799174i
\(647\) 25312.2 1.53806 0.769031 0.639211i \(-0.220739\pi\)
0.769031 + 0.639211i \(0.220739\pi\)
\(648\) 0 0
\(649\) 5266.21 0.318516
\(650\) 3534.44 20044.8i 0.213280 1.20957i
\(651\) 0 0
\(652\) 3409.88 + 1241.09i 0.204818 + 0.0745475i
\(653\) −6698.10 + 5620.37i −0.401404 + 0.336818i −0.821036 0.570876i \(-0.806604\pi\)
0.419632 + 0.907694i \(0.362159\pi\)
\(654\) 0 0
\(655\) 9478.16 3449.77i 0.565408 0.205792i
\(656\) −3160.07 + 5473.40i −0.188079 + 0.325763i
\(657\) 0 0
\(658\) 3566.17 + 6176.79i 0.211282 + 0.365952i
\(659\) 5256.35 + 4410.60i 0.310711 + 0.260717i 0.784786 0.619767i \(-0.212773\pi\)
−0.474075 + 0.880484i \(0.657217\pi\)
\(660\) 0 0
\(661\) −3401.50 19290.9i −0.200156 1.13514i −0.904883 0.425661i \(-0.860042\pi\)
0.704727 0.709479i \(-0.251070\pi\)
\(662\) 124.284 + 704.849i 0.00729673 + 0.0413818i
\(663\) 0 0
\(664\) −9070.95 7611.43i −0.530152 0.444851i
\(665\) −16554.9 28674.0i −0.965373 1.67208i
\(666\) 0 0
\(667\) 3751.19 6497.26i 0.217761 0.377174i
\(668\) 7101.12 2584.60i 0.411304 0.149702i
\(669\) 0 0
\(670\) 18013.3 15114.9i 1.03868 0.871554i
\(671\) 982.022 + 357.427i 0.0564986 + 0.0205638i
\(672\) 0 0
\(673\) −4940.53 + 28019.1i −0.282977 + 1.60484i 0.429448 + 0.903092i \(0.358708\pi\)
−0.712425 + 0.701749i \(0.752403\pi\)
\(674\) 2483.34 0.141921
\(675\) 0 0
\(676\) −2350.08 −0.133709
\(677\) 2864.92 16247.8i 0.162641 0.922383i −0.788822 0.614621i \(-0.789309\pi\)
0.951463 0.307762i \(-0.0995800\pi\)
\(678\) 0 0
\(679\) 17546.0 + 6386.22i 0.991684 + 0.360943i
\(680\) 5852.64 4910.95i 0.330057 0.276950i
\(681\) 0 0
\(682\) −458.160 + 166.757i −0.0257242 + 0.00936283i
\(683\) −6611.99 + 11452.3i −0.370426 + 0.641596i −0.989631 0.143633i \(-0.954122\pi\)
0.619205 + 0.785229i \(0.287455\pi\)
\(684\) 0 0
\(685\) −5199.75 9006.22i −0.290032 0.502351i
\(686\) 10156.6 + 8522.37i 0.565276 + 0.474323i
\(687\) 0 0
\(688\) −596.701 3384.06i −0.0330654 0.187523i
\(689\) 4842.60 + 27463.8i 0.267763 + 1.51856i
\(690\) 0 0
\(691\) −22845.9 19170.0i −1.25774 1.05537i −0.995919 0.0902562i \(-0.971231\pi\)
−0.261824 0.965116i \(-0.584324\pi\)
\(692\) −1113.52 1928.68i −0.0611703 0.105950i
\(693\) 0 0
\(694\) −6916.81 + 11980.3i −0.378326 + 0.655280i
\(695\) 6696.23 2437.23i 0.365471 0.133021i
\(696\) 0 0
\(697\) 14850.3 12460.9i 0.807023 0.677173i
\(698\) −15219.3 5539.37i −0.825299 0.300384i
\(699\) 0 0
\(700\) −2208.50 + 12525.1i −0.119248 + 0.676289i
\(701\) −21101.1 −1.13692 −0.568459 0.822712i \(-0.692460\pi\)
−0.568459 + 0.822712i \(0.692460\pi\)
\(702\) 0 0
\(703\) 33785.3 1.81257
\(704\) 139.717 792.377i 0.00747983 0.0424202i
\(705\) 0 0
\(706\) 849.288 + 309.116i 0.0452739 + 0.0164784i
\(707\) −3969.05 + 3330.43i −0.211134 + 0.177162i
\(708\) 0 0
\(709\) 18874.2 6869.65i 0.999769 0.363886i 0.210273 0.977643i \(-0.432565\pi\)
0.789495 + 0.613756i \(0.210342\pi\)
\(710\) −988.849 + 1712.74i −0.0522688 + 0.0905322i
\(711\) 0 0
\(712\) −3209.97 5559.82i −0.168959 0.292645i
\(713\) 2575.53 + 2161.12i 0.135279 + 0.113513i
\(714\) 0 0
\(715\) 1704.30 + 9665.58i 0.0891431 + 0.505555i
\(716\) 1456.56 + 8260.58i 0.0760256 + 0.431163i
\(717\) 0 0
\(718\) −4262.03 3576.27i −0.221529 0.185885i
\(719\) 7845.00 + 13587.9i 0.406911 + 0.704791i 0.994542 0.104338i \(-0.0332724\pi\)
−0.587630 + 0.809129i \(0.699939\pi\)
\(720\) 0 0
\(721\) −4102.81 + 7106.27i −0.211923 + 0.367062i
\(722\) −21741.8 + 7913.36i −1.12070 + 0.407901i
\(723\) 0 0
\(724\) 850.807 713.912i 0.0436740 0.0366469i
\(725\) 10314.6 + 3754.21i 0.528379 + 0.192314i
\(726\) 0 0
\(727\) −3384.34 + 19193.5i −0.172652 + 0.979160i 0.768167 + 0.640250i \(0.221169\pi\)
−0.940819 + 0.338910i \(0.889942\pi\)
\(728\) −4022.75 −0.204798
\(729\) 0 0
\(730\) −34631.9 −1.75587
\(731\) −1830.25 + 10379.9i −0.0926052 + 0.525190i
\(732\) 0 0
\(733\) −32670.0 11890.9i −1.64624 0.599182i −0.658126 0.752908i \(-0.728651\pi\)
−0.988114 + 0.153725i \(0.950873\pi\)
\(734\) 3713.23 3115.77i 0.186727 0.156683i
\(735\) 0 0
\(736\) −5213.70 + 1897.63i −0.261114 + 0.0950376i
\(737\) −3797.92 + 6578.19i −0.189821 + 0.328780i
\(738\) 0 0
\(739\) 10087.7 + 17472.4i 0.502141 + 0.869735i 0.999997 + 0.00247455i \(0.000787673\pi\)
−0.497855 + 0.867260i \(0.665879\pi\)
\(740\) −14840.3 12452.5i −0.737214 0.618596i
\(741\) 0 0
\(742\) −3025.91 17160.8i −0.149710 0.849047i
\(743\) 2895.63 + 16422.0i 0.142975 + 0.810852i 0.968971 + 0.247175i \(0.0795024\pi\)
−0.825996 + 0.563676i \(0.809386\pi\)
\(744\) 0 0
\(745\) 7046.65 + 5912.84i 0.346536 + 0.290778i
\(746\) 12954.1 + 22437.2i 0.635769 + 1.10118i
\(747\) 0 0
\(748\) −1233.97 + 2137.30i −0.0603188 + 0.104475i
\(749\) 4756.34 1731.17i 0.232033 0.0844532i
\(750\) 0 0
\(751\) 12359.7 10371.0i 0.600547 0.503919i −0.291074 0.956700i \(-0.594013\pi\)
0.891621 + 0.452782i \(0.149568\pi\)
\(752\) −4277.77 1556.98i −0.207439 0.0755016i
\(753\) 0 0
\(754\) −602.882 + 3419.11i −0.0291189 + 0.165142i
\(755\) 14803.1 0.713561
\(756\) 0 0
\(757\) −198.559 −0.00953334 −0.00476667 0.999989i \(-0.501517\pi\)
−0.00476667 + 0.999989i \(0.501517\pi\)
\(758\) 1956.25 11094.4i 0.0937390 0.531620i
\(759\) 0 0
\(760\) 19858.3 + 7227.85i 0.947813 + 0.344976i
\(761\) 7147.26 5997.26i 0.340457 0.285677i −0.456488 0.889730i \(-0.650893\pi\)
0.796945 + 0.604052i \(0.206448\pi\)
\(762\) 0 0
\(763\) 7201.86 2621.26i 0.341710 0.124372i
\(764\) −2888.83 + 5003.61i −0.136799 + 0.236943i
\(765\) 0 0
\(766\) 13347.9 + 23119.2i 0.629606 + 1.09051i
\(767\) 12873.4 + 10802.1i 0.606040 + 0.508528i
\(768\) 0 0
\(769\) −1495.36 8480.61i −0.0701223 0.397683i −0.999586 0.0287700i \(-0.990841\pi\)
0.929464 0.368914i \(-0.120270\pi\)
\(770\) −1064.94 6039.56i −0.0498412 0.282663i
\(771\) 0 0
\(772\) 7664.80 + 6431.53i 0.357335 + 0.299839i
\(773\) 3744.86 + 6486.29i 0.174247 + 0.301805i 0.939901 0.341448i \(-0.110917\pi\)
−0.765653 + 0.643254i \(0.777584\pi\)
\(774\) 0 0
\(775\) −2459.51 + 4260.00i −0.113998 + 0.197450i
\(776\) −11198.9 + 4076.08i −0.518065 + 0.188560i
\(777\) 0 0
\(778\) 3883.17 3258.37i 0.178944 0.150152i
\(779\) 50387.9 + 18339.7i 2.31750 + 0.843502i
\(780\) 0 0
\(781\) 110.935 629.142i 0.00508266 0.0288252i
\(782\) 17018.3 0.778224
\(783\) 0 0
\(784\) −2974.37 −0.135494
\(785\) −452.090 + 2563.93i −0.0205551 + 0.116574i
\(786\) 0 0
\(787\) −13257.6 4825.38i −0.600487 0.218560i 0.0238484 0.999716i \(-0.492408\pi\)
−0.624336 + 0.781156i \(0.714630\pi\)
\(788\) −3301.92 + 2770.64i −0.149272 + 0.125254i
\(789\) 0 0
\(790\) 6179.01 2248.97i 0.278277 0.101285i
\(791\) −2874.47 + 4978.73i −0.129209 + 0.223797i
\(792\) 0 0
\(793\) 1667.43 + 2888.08i 0.0746687 + 0.129330i
\(794\) −20013.0 16792.9i −0.894504 0.750578i
\(795\) 0 0
\(796\) 2626.80 + 14897.3i 0.116965 + 0.663343i
\(797\) −3950.90 22406.6i −0.175593 0.995839i −0.937457 0.348102i \(-0.886826\pi\)
0.761863 0.647738i \(-0.224285\pi\)
\(798\) 0 0
\(799\) 10696.5 + 8975.39i 0.473609 + 0.397405i
\(800\) −4058.80 7030.05i −0.179375 0.310687i
\(801\) 0 0
\(802\) 5748.43 9956.57i 0.253097 0.438378i
\(803\) 10512.3 3826.18i 0.461983 0.168148i
\(804\) 0 0
\(805\) −32395.8 + 27183.3i −1.41839 + 1.19017i
\(806\) −1462.04 532.140i −0.0638936 0.0232554i
\(807\) 0 0
\(808\) 574.252 3256.75i 0.0250026 0.141797i
\(809\) −19598.1 −0.851708 −0.425854 0.904792i \(-0.640026\pi\)
−0.425854 + 0.904792i \(0.640026\pi\)
\(810\) 0 0
\(811\) −26568.7 −1.15038 −0.575188 0.818022i \(-0.695071\pi\)
−0.575188 + 0.818022i \(0.695071\pi\)
\(812\) 376.712 2136.44i 0.0162808 0.0923330i
\(813\) 0 0
\(814\) 5880.45 + 2140.31i 0.253206 + 0.0921594i
\(815\) −13523.2 + 11347.3i −0.581224 + 0.487705i
\(816\) 0 0
\(817\) −27396.0 + 9971.31i −1.17315 + 0.426991i
\(818\) −5026.67 + 8706.44i −0.214857 + 0.372144i
\(819\) 0 0
\(820\) −15373.4 26627.5i −0.654710 1.13399i
\(821\) 32503.4 + 27273.6i 1.38170 + 1.15938i 0.968578 + 0.248708i \(0.0800060\pi\)
0.413122 + 0.910676i \(0.364438\pi\)
\(822\) 0 0
\(823\) 3848.66 + 21826.8i 0.163008 + 0.924466i 0.951094 + 0.308901i \(0.0999611\pi\)
−0.788086 + 0.615565i \(0.788928\pi\)
\(824\) −909.454 5157.77i −0.0384494 0.218058i
\(825\) 0 0
\(826\) −8044.01 6749.72i −0.338846 0.284325i
\(827\) −6584.87 11405.3i −0.276878 0.479567i 0.693729 0.720236i \(-0.255967\pi\)
−0.970607 + 0.240669i \(0.922633\pi\)
\(828\) 0 0
\(829\) 13106.3 22700.8i 0.549097 0.951065i −0.449239 0.893411i \(-0.648305\pi\)
0.998337 0.0576531i \(-0.0183617\pi\)
\(830\) 54132.5 19702.6i 2.26381 0.823961i
\(831\) 0 0
\(832\) 1966.88 1650.40i 0.0819581 0.0687710i
\(833\) 8573.06 + 3120.34i 0.356589 + 0.129788i
\(834\) 0 0
\(835\) −6383.88 + 36204.8i −0.264579 + 1.50050i
\(836\) −6826.44 −0.282413
\(837\) 0 0
\(838\) −17395.9 −0.717103
\(839\) 1196.65 6786.56i 0.0492408 0.279259i −0.950239 0.311523i \(-0.899161\pi\)
0.999479 + 0.0322647i \(0.0102719\pi\)
\(840\) 0 0
\(841\) 21158.8 + 7701.16i 0.867554 + 0.315764i
\(842\) −18259.8 + 15321.7i −0.747355 + 0.627105i
\(843\) 0 0
\(844\) 13359.2 4862.33i 0.544835 0.198304i
\(845\) 5716.44 9901.16i 0.232724 0.403089i
\(846\) 0 0
\(847\) −7350.88 12732.1i −0.298204 0.516505i
\(848\) 8520.00 + 7149.13i 0.345021 + 0.289507i
\(849\) 0 0
\(850\) 4323.67 + 24520.7i 0.174471 + 0.989476i
\(851\) −7493.33 42496.8i −0.301842 1.71183i
\(852\) 0 0
\(853\) 14085.2 + 11818.9i 0.565379 + 0.474409i 0.880109 0.474772i \(-0.157470\pi\)
−0.314730 + 0.949181i \(0.601914\pi\)
\(854\) −1041.90 1804.62i −0.0417483 0.0723102i
\(855\) 0 0
\(856\) −1615.31 + 2797.80i −0.0644980 + 0.111714i
\(857\) −28034.0 + 10203.6i −1.11742 + 0.406706i −0.833708 0.552205i \(-0.813786\pi\)
−0.283707 + 0.958911i \(0.591564\pi\)
\(858\) 0 0
\(859\) −10061.0 + 8442.15i −0.399623 + 0.335323i −0.820348 0.571865i \(-0.806220\pi\)
0.420725 + 0.907188i \(0.361776\pi\)
\(860\) 15708.9 + 5717.57i 0.622871 + 0.226707i
\(861\) 0 0
\(862\) 836.660 4744.94i 0.0330589 0.187486i
\(863\) −26268.6 −1.03615 −0.518074 0.855336i \(-0.673351\pi\)
−0.518074 + 0.855336i \(0.673351\pi\)
\(864\) 0 0
\(865\) 10834.4 0.425872
\(866\) −4966.00 + 28163.6i −0.194863 + 1.10513i
\(867\) 0 0
\(868\) 913.562 + 332.509i 0.0357239 + 0.0130024i
\(869\) −1627.14 + 1365.33i −0.0635176 + 0.0532976i
\(870\) 0 0
\(871\) −22777.4 + 8290.30i −0.886089 + 0.322510i
\(872\) −2445.84 + 4236.32i −0.0949847 + 0.164518i
\(873\) 0 0
\(874\) 23536.6 + 40766.6i 0.910913 + 1.57775i
\(875\) −24042.1 20173.7i −0.928880 0.779423i
\(876\) 0 0
\(877\) −2217.19 12574.3i −0.0853696 0.484155i −0.997276 0.0737574i \(-0.976501\pi\)
0.911907 0.410398i \(-0.134610\pi\)
\(878\) 553.897 + 3141.30i 0.0212906 + 0.120745i
\(879\) 0 0
\(880\) 2998.52 + 2516.06i 0.114864 + 0.0963822i
\(881\) −3774.21 6537.12i −0.144332 0.249990i 0.784792 0.619760i \(-0.212770\pi\)
−0.929123 + 0.369770i \(0.879437\pi\)
\(882\) 0 0
\(883\) −20359.5 + 35263.7i −0.775938 + 1.34396i 0.158328 + 0.987387i \(0.449390\pi\)
−0.934266 + 0.356577i \(0.883944\pi\)
\(884\) −7400.54 + 2693.58i −0.281569 + 0.102483i
\(885\) 0 0
\(886\) −18412.4 + 15449.9i −0.698169 + 0.585833i
\(887\) −30952.9 11265.9i −1.17170 0.426464i −0.318436 0.947944i \(-0.603158\pi\)
−0.853263 + 0.521481i \(0.825380\pi\)
\(888\) 0 0
\(889\) 2439.64 13835.9i 0.0920393 0.521981i
\(890\) 31232.3 1.17630
\(891\) 0 0
\(892\) 7885.77 0.296004
\(893\) −6706.80 + 38036.2i −0.251326 + 1.42534i
\(894\) 0 0
\(895\) −38345.8 13956.7i −1.43213 0.521254i
\(896\) −1229.01 + 1031.26i −0.0458239 + 0.0384509i
\(897\) 0 0
\(898\) 1587.44 577.780i 0.0589905 0.0214708i
\(899\) 419.528 726.643i 0.0155640 0.0269576i
\(900\) 0 0
\(901\) −17057.3 29544.1i −0.630700 1.09241i
\(902\) 7608.36 + 6384.17i 0.280854 + 0.235665i
\(903\) 0 0
\(904\) −637.173 3613.59i −0.0234426 0.132949i
\(905\) 938.255 + 5321.11i 0.0344626 + 0.195447i
\(906\) 0 0
\(907\) −5243.98 4400.22i −0.191977 0.161088i 0.541733 0.840551i \(-0.317768\pi\)
−0.733710 + 0.679463i \(0.762213\pi\)
\(908\) 3853.47 + 6674.40i 0.140839 + 0.243940i
\(909\) 0 0
\(910\) 9785.13 16948.3i 0.356455 0.617398i
\(911\) −13894.1 + 5057.05i −0.505306 + 0.183916i −0.582079 0.813132i \(-0.697761\pi\)
0.0767731 + 0.997049i \(0.475538\pi\)
\(912\) 0 0
\(913\) −14254.9 + 11961.3i −0.516722 + 0.433581i
\(914\) 16570.6 + 6031.20i 0.599679 + 0.218265i
\(915\) 0 0
\(916\) 4495.64 25496.0i 0.162162 0.919664i
\(917\) 6496.74 0.233960
\(918\) 0 0
\(919\) 40416.4 1.45072 0.725361 0.688369i \(-0.241673\pi\)
0.725361 + 0.688369i \(0.241673\pi\)
\(920\) 4687.10 26581.8i 0.167966 0.952584i
\(921\) 0 0
\(922\) −3127.76 1138.41i −0.111721 0.0406633i
\(923\) 1561.69 1310.41i 0.0556918 0.0467309i
\(924\) 0 0
\(925\) 59327.7 21593.5i 2.10885 0.767557i
\(926\) 16808.5 29113.1i 0.596501 1.03317i
\(927\) 0 0
\(928\) 692.323 + 1199.14i 0.0244899 + 0.0424178i
\(929\) −14171.4 11891.2i −0.500482 0.419955i 0.357283 0.933996i \(-0.383703\pi\)
−0.857765 + 0.514042i \(0.828148\pi\)
\(930\) 0 0
\(931\) 4382.07 + 24852.0i 0.154261 + 0.874855i
\(932\) −2374.87 13468.5i −0.0834671 0.473366i
\(933\) 0 0
\(934\) −11496.8 9646.96i −0.402770 0.337964i
\(935\) −6003.14 10397.7i −0.209972 0.363682i
\(936\) 0 0
\(937\) −1797.36 + 3113.11i −0.0626650 + 0.108539i −0.895656 0.444748i \(-0.853293\pi\)
0.832991 + 0.553287i \(0.186627\pi\)
\(938\) 14232.5 5180.22i 0.495425 0.180320i
\(939\) 0 0
\(940\) 16965.2 14235.5i 0.588663 0.493947i
\(941\) 17243.5 + 6276.11i 0.597366 + 0.217423i 0.622966 0.782249i \(-0.285927\pi\)
−0.0256002 + 0.999672i \(0.508150\pi\)
\(942\) 0 0
\(943\) 11892.9 67447.9i 0.410695 2.32917i
\(944\) 6702.21 0.231079
\(945\) 0 0
\(946\) −5400.04 −0.185592
\(947\) 3245.48 18406.1i 0.111366 0.631591i −0.877119 0.480273i \(-0.840537\pi\)
0.988485 0.151317i \(-0.0483515\pi\)
\(948\) 0 0
\(949\) 33546.1 + 12209.8i 1.14747 + 0.417646i
\(950\) −52758.9 + 44269.9i −1.80181 + 1.51190i
\(951\) 0 0
\(952\) 4624.25 1683.09i 0.157429 0.0572996i
\(953\) 15425.8 26718.3i 0.524335 0.908175i −0.475263 0.879844i \(-0.657647\pi\)
0.999599 0.0283318i \(-0.00901950\pi\)
\(954\) 0 0
\(955\) −14053.9 24342.0i −0.476202 0.824805i
\(956\) −3784.90 3175.91i −0.128046 0.107444i
\(957\) 0 0
\(958\) −3661.76 20766.9i −0.123493 0.700362i
\(959\) −1163.16 6596.61i −0.0391662 0.222123i
\(960\) 0 0
\(961\) −22533.2 18907.6i −0.756376 0.634675i
\(962\) 9984.75 + 17294.1i 0.334637 + 0.579609i
\(963\) 0 0
\(964\) 5809.35 10062.1i 0.194094 0.336181i
\(965\) −45741.0 + 16648.4i −1.52586 + 0.555368i
\(966\) 0 0
\(967\) 32906.2 27611.6i 1.09430 0.918230i 0.0972745 0.995258i \(-0.468988\pi\)
0.997029 + 0.0770280i \(0.0245431\pi\)
\(968\) 8817.68 + 3209.37i 0.292780 + 0.106563i
\(969\) 0 0
\(970\) 10067.8 57097.4i 0.333255 1.88999i
\(971\) −29429.6 −0.972647 −0.486324 0.873779i \(-0.661662\pi\)
−0.486324 + 0.873779i \(0.661662\pi\)
\(972\) 0 0
\(973\) 4589.89 0.151228
\(974\) −2613.92 + 14824.3i −0.0859911 + 0.487680i
\(975\) 0 0
\(976\) 1249.80 + 454.891i 0.0409889 + 0.0149187i
\(977\) 23965.6 20109.5i 0.784776 0.658505i −0.159670 0.987170i \(-0.551043\pi\)
0.944447 + 0.328665i \(0.106599\pi\)
\(978\) 0 0
\(979\) −9480.40 + 3450.58i −0.309494 + 0.112647i
\(980\) 7235.00 12531.4i 0.235830 0.408470i
\(981\) 0 0
\(982\) 5671.29 + 9822.97i 0.184296 + 0.319209i
\(983\) −20050.0 16823.9i −0.650555 0.545880i 0.256685 0.966495i \(-0.417370\pi\)
−0.907239 + 0.420615i \(0.861814\pi\)
\(984\) 0 0
\(985\) −3641.30 20650.8i −0.117788 0.668010i
\(986\) −737.503 4182.59i −0.0238204 0.135092i
\(987\) 0 0
\(988\) −16687.5 14002.5i −0.537348 0.450888i
\(989\) 18618.6 + 32248.4i 0.598622 + 1.03684i
\(990\) 0 0
\(991\) 4608.89 7982.83i 0.147736 0.255886i −0.782654 0.622456i \(-0.786135\pi\)
0.930390 + 0.366570i \(0.119468\pi\)
\(992\) −583.092 + 212.228i −0.0186625 + 0.00679259i
\(993\) 0 0
\(994\) −975.823 + 818.813i −0.0311381 + 0.0261279i
\(995\) −69153.7 25169.9i −2.20334 0.801949i
\(996\) 0 0
\(997\) −7954.93 + 45114.7i −0.252693 + 1.43310i 0.549231 + 0.835670i \(0.314921\pi\)
−0.801925 + 0.597425i \(0.796191\pi\)
\(998\) −13217.8 −0.419242
\(999\) 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 162.4.e.b.73.5 30
3.2 odd 2 54.4.e.b.25.5 yes 30
27.11 odd 18 1458.4.a.i.1.1 15
27.13 even 9 inner 162.4.e.b.91.5 30
27.14 odd 18 54.4.e.b.13.5 30
27.16 even 9 1458.4.a.j.1.15 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
54.4.e.b.13.5 30 27.14 odd 18
54.4.e.b.25.5 yes 30 3.2 odd 2
162.4.e.b.73.5 30 1.1 even 1 trivial
162.4.e.b.91.5 30 27.13 even 9 inner
1458.4.a.i.1.1 15 27.11 odd 18
1458.4.a.j.1.15 15 27.16 even 9