Properties

Label 135.4.e.c.46.4
Level $135$
Weight $4$
Character 135.46
Analytic conductor $7.965$
Analytic rank $0$
Dimension $14$
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] = [135,4,Mod(46,135)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(135, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("135.46");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 135 = 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 135.e (of order \(3\), degree \(2\), 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: \(7.96525785077\)
Analytic rank: \(0\)
Dimension: \(14\)
Relative dimension: \(7\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{14} - 2 x^{13} + 48 x^{12} - 60 x^{11} + 1605 x^{10} - 1800 x^{9} + 23232 x^{8} - 2346 x^{7} + \cdots + 82944 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{13} \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 46.4
Root \(0.112625 + 0.195072i\) of defining polynomial
Character \(\chi\) \(=\) 135.46
Dual form 135.4.e.c.91.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.112625 + 0.195072i) q^{2} +(3.97463 + 6.88426i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(15.5970 - 27.0148i) q^{7} -3.59257 q^{8} +O(q^{10})\) \(q+(-0.112625 + 0.195072i) q^{2} +(3.97463 + 6.88426i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(15.5970 - 27.0148i) q^{7} -3.59257 q^{8} +1.12625 q^{10} +(9.06424 - 15.6997i) q^{11} +(25.0781 + 43.4366i) q^{13} +(3.51322 + 6.08508i) q^{14} +(-31.3924 + 54.3733i) q^{16} +131.631 q^{17} +23.2428 q^{19} +(19.8732 - 34.4213i) q^{20} +(2.04172 + 3.53636i) q^{22} +(-16.4928 - 28.5664i) q^{23} +(-12.5000 + 21.6506i) q^{25} -11.2977 q^{26} +247.969 q^{28} +(62.9087 - 108.961i) q^{29} +(-62.5563 - 108.351i) q^{31} +(-21.4414 - 37.1376i) q^{32} +(-14.8249 + 25.6775i) q^{34} -155.970 q^{35} +99.9894 q^{37} +(-2.61772 + 4.53402i) q^{38} +(8.98142 + 15.5563i) q^{40} +(122.663 + 212.458i) q^{41} +(-69.5882 + 120.530i) q^{43} +144.108 q^{44} +7.43001 q^{46} +(-236.480 + 409.596i) q^{47} +(-315.033 - 545.654i) q^{49} +(-2.81562 - 4.87680i) q^{50} +(-199.352 + 345.289i) q^{52} -421.529 q^{53} -90.6424 q^{55} +(-56.0333 + 97.0526i) q^{56} +(14.1702 + 24.5435i) q^{58} +(-371.207 - 642.949i) q^{59} +(-4.48868 + 7.77462i) q^{61} +28.1816 q^{62} -492.620 q^{64} +(125.391 - 217.183i) q^{65} +(-294.453 - 510.008i) q^{67} +(523.185 + 906.182i) q^{68} +(17.5661 - 30.4254i) q^{70} +48.5526 q^{71} +409.800 q^{73} +(-11.2613 + 19.5051i) q^{74} +(92.3816 + 160.010i) q^{76} +(-282.750 - 489.737i) q^{77} +(-265.263 + 459.449i) q^{79} +313.924 q^{80} -55.2595 q^{82} +(-147.295 + 255.122i) q^{83} +(-329.077 - 569.979i) q^{85} +(-15.6747 - 27.1494i) q^{86} +(-32.5639 + 56.4023i) q^{88} -852.817 q^{89} +1564.57 q^{91} +(131.106 - 227.082i) q^{92} +(-53.2672 - 92.2615i) q^{94} +(-58.1070 - 100.644i) q^{95} +(194.045 - 336.096i) q^{97} +141.922 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q - 2 q^{2} - 36 q^{4} - 35 q^{5} - 22 q^{7} + 36 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 14 q - 2 q^{2} - 36 q^{4} - 35 q^{5} - 22 q^{7} + 36 q^{8} + 20 q^{10} - 23 q^{11} - 96 q^{13} + 21 q^{14} - 324 q^{16} + 322 q^{17} + 558 q^{19} - 180 q^{20} - 311 q^{22} - 96 q^{23} - 175 q^{25} - 716 q^{26} + 674 q^{28} + 296 q^{29} - 244 q^{31} + 314 q^{32} - 125 q^{34} + 220 q^{35} + 808 q^{37} - 305 q^{38} - 90 q^{40} + 47 q^{41} - 525 q^{43} + 110 q^{44} + 1434 q^{46} - 164 q^{47} - 1225 q^{49} - 50 q^{50} - 1682 q^{52} + 1012 q^{53} + 230 q^{55} + 981 q^{56} - 1183 q^{58} + 85 q^{59} - 828 q^{61} - 1572 q^{62} + 4472 q^{64} - 480 q^{65} - 1093 q^{67} - 2473 q^{68} + 105 q^{70} + 656 q^{71} + 4170 q^{73} + 1316 q^{74} - 2789 q^{76} - 24 q^{77} - 2110 q^{79} + 3240 q^{80} - 124 q^{82} - 1290 q^{83} - 805 q^{85} + 2569 q^{86} - 2271 q^{88} - 6096 q^{89} + 6676 q^{91} - 2763 q^{92} + 517 q^{94} - 1395 q^{95} - 1787 q^{97} + 2558 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/135\mathbb{Z}\right)^\times\).

\(n\) \(56\) \(82\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.112625 + 0.195072i −0.0398189 + 0.0689684i −0.885248 0.465119i \(-0.846011\pi\)
0.845429 + 0.534088i \(0.179345\pi\)
\(3\) 0 0
\(4\) 3.97463 + 6.88426i 0.496829 + 0.860533i
\(5\) −2.50000 4.33013i −0.223607 0.387298i
\(6\) 0 0
\(7\) 15.5970 27.0148i 0.842159 1.45866i −0.0459062 0.998946i \(-0.514618\pi\)
0.888066 0.459717i \(-0.152049\pi\)
\(8\) −3.59257 −0.158771
\(9\) 0 0
\(10\) 1.12625 0.0356151
\(11\) 9.06424 15.6997i 0.248452 0.430331i −0.714645 0.699488i \(-0.753412\pi\)
0.963096 + 0.269156i \(0.0867449\pi\)
\(12\) 0 0
\(13\) 25.0781 + 43.4366i 0.535032 + 0.926702i 0.999162 + 0.0409353i \(0.0130337\pi\)
−0.464130 + 0.885767i \(0.653633\pi\)
\(14\) 3.51322 + 6.08508i 0.0670678 + 0.116165i
\(15\) 0 0
\(16\) −31.3924 + 54.3733i −0.490507 + 0.849583i
\(17\) 131.631 1.87795 0.938977 0.343981i \(-0.111776\pi\)
0.938977 + 0.343981i \(0.111776\pi\)
\(18\) 0 0
\(19\) 23.2428 0.280646 0.140323 0.990106i \(-0.455186\pi\)
0.140323 + 0.990106i \(0.455186\pi\)
\(20\) 19.8732 34.4213i 0.222189 0.384842i
\(21\) 0 0
\(22\) 2.04172 + 3.53636i 0.0197862 + 0.0342707i
\(23\) −16.4928 28.5664i −0.149521 0.258978i 0.781529 0.623868i \(-0.214440\pi\)
−0.931051 + 0.364890i \(0.881107\pi\)
\(24\) 0 0
\(25\) −12.5000 + 21.6506i −0.100000 + 0.173205i
\(26\) −11.2977 −0.0852176
\(27\) 0 0
\(28\) 247.969 1.67364
\(29\) 62.9087 108.961i 0.402823 0.697709i −0.591243 0.806494i \(-0.701363\pi\)
0.994065 + 0.108784i \(0.0346958\pi\)
\(30\) 0 0
\(31\) −62.5563 108.351i −0.362434 0.627754i 0.625927 0.779882i \(-0.284721\pi\)
−0.988361 + 0.152128i \(0.951387\pi\)
\(32\) −21.4414 37.1376i −0.118448 0.205158i
\(33\) 0 0
\(34\) −14.8249 + 25.6775i −0.0747781 + 0.129519i
\(35\) −155.970 −0.753250
\(36\) 0 0
\(37\) 99.9894 0.444274 0.222137 0.975015i \(-0.428697\pi\)
0.222137 + 0.975015i \(0.428697\pi\)
\(38\) −2.61772 + 4.53402i −0.0111750 + 0.0193557i
\(39\) 0 0
\(40\) 8.98142 + 15.5563i 0.0355022 + 0.0614916i
\(41\) 122.663 + 212.458i 0.467237 + 0.809278i 0.999299 0.0374272i \(-0.0119162\pi\)
−0.532063 + 0.846705i \(0.678583\pi\)
\(42\) 0 0
\(43\) −69.5882 + 120.530i −0.246793 + 0.427458i −0.962634 0.270805i \(-0.912710\pi\)
0.715841 + 0.698263i \(0.246043\pi\)
\(44\) 144.108 0.493752
\(45\) 0 0
\(46\) 7.43001 0.0238151
\(47\) −236.480 + 409.596i −0.733919 + 1.27119i 0.221276 + 0.975211i \(0.428978\pi\)
−0.955196 + 0.295975i \(0.904356\pi\)
\(48\) 0 0
\(49\) −315.033 545.654i −0.918465 1.59083i
\(50\) −2.81562 4.87680i −0.00796378 0.0137937i
\(51\) 0 0
\(52\) −199.352 + 345.289i −0.531639 + 0.920825i
\(53\) −421.529 −1.09248 −0.546240 0.837628i \(-0.683941\pi\)
−0.546240 + 0.837628i \(0.683941\pi\)
\(54\) 0 0
\(55\) −90.6424 −0.222222
\(56\) −56.0333 + 97.0526i −0.133710 + 0.231593i
\(57\) 0 0
\(58\) 14.1702 + 24.5435i 0.0320799 + 0.0555641i
\(59\) −371.207 642.949i −0.819101 1.41873i −0.906345 0.422538i \(-0.861139\pi\)
0.0872437 0.996187i \(-0.472194\pi\)
\(60\) 0 0
\(61\) −4.48868 + 7.77462i −0.00942158 + 0.0163187i −0.870698 0.491818i \(-0.836332\pi\)
0.861276 + 0.508137i \(0.169666\pi\)
\(62\) 28.1816 0.0577269
\(63\) 0 0
\(64\) −492.620 −0.962148
\(65\) 125.391 217.183i 0.239274 0.414434i
\(66\) 0 0
\(67\) −294.453 510.008i −0.536913 0.929960i −0.999068 0.0431613i \(-0.986257\pi\)
0.462155 0.886799i \(-0.347076\pi\)
\(68\) 523.185 + 906.182i 0.933021 + 1.61604i
\(69\) 0 0
\(70\) 17.5661 30.4254i 0.0299936 0.0519505i
\(71\) 48.5526 0.0811568 0.0405784 0.999176i \(-0.487080\pi\)
0.0405784 + 0.999176i \(0.487080\pi\)
\(72\) 0 0
\(73\) 409.800 0.657034 0.328517 0.944498i \(-0.393451\pi\)
0.328517 + 0.944498i \(0.393451\pi\)
\(74\) −11.2613 + 19.5051i −0.0176905 + 0.0306409i
\(75\) 0 0
\(76\) 92.3816 + 160.010i 0.139433 + 0.241505i
\(77\) −282.750 489.737i −0.418472 0.724815i
\(78\) 0 0
\(79\) −265.263 + 459.449i −0.377778 + 0.654330i −0.990739 0.135783i \(-0.956645\pi\)
0.612961 + 0.790113i \(0.289978\pi\)
\(80\) 313.924 0.438723
\(81\) 0 0
\(82\) −55.2595 −0.0744195
\(83\) −147.295 + 255.122i −0.194792 + 0.337389i −0.946832 0.321728i \(-0.895736\pi\)
0.752040 + 0.659117i \(0.229070\pi\)
\(84\) 0 0
\(85\) −329.077 569.979i −0.419923 0.727328i
\(86\) −15.6747 27.1494i −0.0196541 0.0340418i
\(87\) 0 0
\(88\) −32.5639 + 56.4023i −0.0394469 + 0.0683240i
\(89\) −852.817 −1.01571 −0.507856 0.861442i \(-0.669562\pi\)
−0.507856 + 0.861442i \(0.669562\pi\)
\(90\) 0 0
\(91\) 1564.57 1.80233
\(92\) 131.106 227.082i 0.148573 0.257336i
\(93\) 0 0
\(94\) −53.2672 92.2615i −0.0584478 0.101234i
\(95\) −58.1070 100.644i −0.0627543 0.108694i
\(96\) 0 0
\(97\) 194.045 336.096i 0.203117 0.351808i −0.746414 0.665481i \(-0.768226\pi\)
0.949531 + 0.313673i \(0.101560\pi\)
\(98\) 141.922 0.146289
\(99\) 0 0
\(100\) −198.732 −0.198732
\(101\) −539.997 + 935.302i −0.531997 + 0.921446i 0.467305 + 0.884096i \(0.345225\pi\)
−0.999302 + 0.0373500i \(0.988108\pi\)
\(102\) 0 0
\(103\) 297.498 + 515.282i 0.284596 + 0.492935i 0.972511 0.232856i \(-0.0748072\pi\)
−0.687915 + 0.725791i \(0.741474\pi\)
\(104\) −90.0948 156.049i −0.0849473 0.147133i
\(105\) 0 0
\(106\) 47.4747 82.2286i 0.0435014 0.0753467i
\(107\) 498.693 0.450565 0.225282 0.974293i \(-0.427670\pi\)
0.225282 + 0.974293i \(0.427670\pi\)
\(108\) 0 0
\(109\) −959.301 −0.842976 −0.421488 0.906834i \(-0.638492\pi\)
−0.421488 + 0.906834i \(0.638492\pi\)
\(110\) 10.2086 17.6818i 0.00884864 0.0153263i
\(111\) 0 0
\(112\) 979.256 + 1696.12i 0.826170 + 1.43097i
\(113\) 864.396 + 1497.18i 0.719607 + 1.24640i 0.961156 + 0.276007i \(0.0890113\pi\)
−0.241549 + 0.970389i \(0.577655\pi\)
\(114\) 0 0
\(115\) −82.4641 + 142.832i −0.0668679 + 0.115819i
\(116\) 1000.16 0.800536
\(117\) 0 0
\(118\) 167.228 0.130463
\(119\) 2053.05 3555.99i 1.58154 2.73930i
\(120\) 0 0
\(121\) 501.179 + 868.068i 0.376543 + 0.652192i
\(122\) −1.01107 1.75123i −0.000750315 0.00129958i
\(123\) 0 0
\(124\) 497.277 861.309i 0.360135 0.623773i
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) 1019.95 0.712647 0.356324 0.934363i \(-0.384030\pi\)
0.356324 + 0.934363i \(0.384030\pi\)
\(128\) 227.013 393.197i 0.156760 0.271516i
\(129\) 0 0
\(130\) 28.2442 + 48.9204i 0.0190552 + 0.0330046i
\(131\) −851.196 1474.31i −0.567705 0.983294i −0.996792 0.0800308i \(-0.974498\pi\)
0.429088 0.903263i \(-0.358835\pi\)
\(132\) 0 0
\(133\) 362.518 627.900i 0.236348 0.409367i
\(134\) 132.651 0.0855172
\(135\) 0 0
\(136\) −472.893 −0.298164
\(137\) −524.839 + 909.049i −0.327300 + 0.566900i −0.981975 0.189010i \(-0.939472\pi\)
0.654675 + 0.755910i \(0.272805\pi\)
\(138\) 0 0
\(139\) −717.411 1242.59i −0.437770 0.758240i 0.559747 0.828663i \(-0.310898\pi\)
−0.997517 + 0.0704236i \(0.977565\pi\)
\(140\) −619.924 1073.74i −0.374236 0.648197i
\(141\) 0 0
\(142\) −5.46823 + 9.47126i −0.00323158 + 0.00559726i
\(143\) 909.256 0.531719
\(144\) 0 0
\(145\) −629.087 −0.360295
\(146\) −46.1537 + 79.9406i −0.0261624 + 0.0453146i
\(147\) 0 0
\(148\) 397.421 + 688.353i 0.220728 + 0.382313i
\(149\) 609.231 + 1055.22i 0.334968 + 0.580181i 0.983479 0.181024i \(-0.0579413\pi\)
−0.648511 + 0.761205i \(0.724608\pi\)
\(150\) 0 0
\(151\) −804.751 + 1393.87i −0.433707 + 0.751202i −0.997189 0.0749258i \(-0.976128\pi\)
0.563482 + 0.826128i \(0.309461\pi\)
\(152\) −83.5014 −0.0445583
\(153\) 0 0
\(154\) 127.379 0.0666524
\(155\) −312.782 + 541.754i −0.162085 + 0.280740i
\(156\) 0 0
\(157\) −643.168 1114.00i −0.326945 0.566286i 0.654959 0.755664i \(-0.272686\pi\)
−0.981904 + 0.189379i \(0.939353\pi\)
\(158\) −59.7505 103.491i −0.0300854 0.0521095i
\(159\) 0 0
\(160\) −107.207 + 185.688i −0.0529717 + 0.0917496i
\(161\) −1028.95 −0.503683
\(162\) 0 0
\(163\) 1416.84 0.680830 0.340415 0.940275i \(-0.389432\pi\)
0.340415 + 0.940275i \(0.389432\pi\)
\(164\) −975.079 + 1688.89i −0.464273 + 0.804145i
\(165\) 0 0
\(166\) −33.1782 57.4663i −0.0155128 0.0268690i
\(167\) 447.487 + 775.071i 0.207351 + 0.359142i 0.950879 0.309562i \(-0.100182\pi\)
−0.743528 + 0.668704i \(0.766849\pi\)
\(168\) 0 0
\(169\) −159.323 + 275.955i −0.0725183 + 0.125605i
\(170\) 148.249 0.0668835
\(171\) 0 0
\(172\) −1106.35 −0.490456
\(173\) −867.548 + 1502.64i −0.381263 + 0.660367i −0.991243 0.132050i \(-0.957844\pi\)
0.609980 + 0.792417i \(0.291177\pi\)
\(174\) 0 0
\(175\) 389.925 + 675.370i 0.168432 + 0.291733i
\(176\) 569.097 + 985.705i 0.243735 + 0.422161i
\(177\) 0 0
\(178\) 96.0485 166.361i 0.0404446 0.0700521i
\(179\) −2133.37 −0.890815 −0.445408 0.895328i \(-0.646941\pi\)
−0.445408 + 0.895328i \(0.646941\pi\)
\(180\) 0 0
\(181\) −3611.98 −1.48330 −0.741648 0.670789i \(-0.765955\pi\)
−0.741648 + 0.670789i \(0.765955\pi\)
\(182\) −176.210 + 305.205i −0.0717668 + 0.124304i
\(183\) 0 0
\(184\) 59.2516 + 102.627i 0.0237396 + 0.0411182i
\(185\) −249.974 432.967i −0.0993428 0.172067i
\(186\) 0 0
\(187\) 1193.13 2066.57i 0.466581 0.808142i
\(188\) −3759.69 −1.45853
\(189\) 0 0
\(190\) 26.1772 0.00999523
\(191\) −298.495 + 517.008i −0.113080 + 0.195861i −0.917011 0.398863i \(-0.869405\pi\)
0.803930 + 0.594723i \(0.202738\pi\)
\(192\) 0 0
\(193\) 603.872 + 1045.94i 0.225221 + 0.390094i 0.956386 0.292107i \(-0.0943563\pi\)
−0.731165 + 0.682201i \(0.761023\pi\)
\(194\) 43.7087 + 75.7056i 0.0161758 + 0.0280173i
\(195\) 0 0
\(196\) 2504.28 4337.54i 0.912639 1.58074i
\(197\) 3268.56 1.18211 0.591054 0.806632i \(-0.298712\pi\)
0.591054 + 0.806632i \(0.298712\pi\)
\(198\) 0 0
\(199\) −2109.88 −0.751585 −0.375793 0.926704i \(-0.622629\pi\)
−0.375793 + 0.926704i \(0.622629\pi\)
\(200\) 44.9071 77.7814i 0.0158771 0.0274999i
\(201\) 0 0
\(202\) −121.634 210.677i −0.0423671 0.0733820i
\(203\) −1962.38 3398.93i −0.678482 1.17516i
\(204\) 0 0
\(205\) 613.314 1062.29i 0.208955 0.361920i
\(206\) −134.023 −0.0453292
\(207\) 0 0
\(208\) −3149.05 −1.04975
\(209\) 210.678 364.906i 0.0697269 0.120771i
\(210\) 0 0
\(211\) −329.321 570.400i −0.107447 0.186104i 0.807288 0.590157i \(-0.200934\pi\)
−0.914735 + 0.404053i \(0.867601\pi\)
\(212\) −1675.42 2901.92i −0.542776 0.940116i
\(213\) 0 0
\(214\) −56.1652 + 97.2810i −0.0179410 + 0.0310747i
\(215\) 695.882 0.220738
\(216\) 0 0
\(217\) −3902.77 −1.22091
\(218\) 108.041 187.133i 0.0335664 0.0581387i
\(219\) 0 0
\(220\) −360.270 624.006i −0.110406 0.191229i
\(221\) 3301.06 + 5717.60i 1.00476 + 1.74030i
\(222\) 0 0
\(223\) −609.397 + 1055.51i −0.182997 + 0.316959i −0.942900 0.333077i \(-0.891913\pi\)
0.759903 + 0.650036i \(0.225246\pi\)
\(224\) −1337.69 −0.399009
\(225\) 0 0
\(226\) −389.410 −0.114616
\(227\) −762.785 + 1321.18i −0.223030 + 0.386299i −0.955727 0.294256i \(-0.904928\pi\)
0.732697 + 0.680555i \(0.238261\pi\)
\(228\) 0 0
\(229\) 3091.33 + 5354.33i 0.892055 + 1.54508i 0.837408 + 0.546578i \(0.184070\pi\)
0.0546469 + 0.998506i \(0.482597\pi\)
\(230\) −18.5750 32.1729i −0.00532522 0.00922355i
\(231\) 0 0
\(232\) −226.004 + 391.450i −0.0639564 + 0.110776i
\(233\) 2013.82 0.566222 0.283111 0.959087i \(-0.408633\pi\)
0.283111 + 0.959087i \(0.408633\pi\)
\(234\) 0 0
\(235\) 2364.80 0.656438
\(236\) 2950.82 5110.97i 0.813906 1.40973i
\(237\) 0 0
\(238\) 462.449 + 800.985i 0.125950 + 0.218152i
\(239\) 2543.15 + 4404.87i 0.688297 + 1.19216i 0.972389 + 0.233368i \(0.0749746\pi\)
−0.284092 + 0.958797i \(0.591692\pi\)
\(240\) 0 0
\(241\) −1643.41 + 2846.47i −0.439259 + 0.760820i −0.997633 0.0687703i \(-0.978092\pi\)
0.558373 + 0.829590i \(0.311426\pi\)
\(242\) −225.781 −0.0599742
\(243\) 0 0
\(244\) −71.3634 −0.0187237
\(245\) −1575.17 + 2728.27i −0.410750 + 0.711440i
\(246\) 0 0
\(247\) 582.886 + 1009.59i 0.150154 + 0.260075i
\(248\) 224.738 + 389.258i 0.0575439 + 0.0996689i
\(249\) 0 0
\(250\) −14.0781 + 24.3840i −0.00356151 + 0.00616872i
\(251\) −3480.55 −0.875260 −0.437630 0.899155i \(-0.644182\pi\)
−0.437630 + 0.899155i \(0.644182\pi\)
\(252\) 0 0
\(253\) −597.979 −0.148595
\(254\) −114.872 + 198.964i −0.0283768 + 0.0491501i
\(255\) 0 0
\(256\) −1919.34 3324.40i −0.468590 0.811621i
\(257\) −3397.49 5884.62i −0.824628 1.42830i −0.902203 0.431312i \(-0.858051\pi\)
0.0775746 0.996987i \(-0.475282\pi\)
\(258\) 0 0
\(259\) 1559.54 2701.19i 0.374150 0.648047i
\(260\) 1993.52 0.475512
\(261\) 0 0
\(262\) 383.464 0.0904216
\(263\) 2682.12 4645.56i 0.628846 1.08919i −0.358938 0.933362i \(-0.616861\pi\)
0.987784 0.155832i \(-0.0498057\pi\)
\(264\) 0 0
\(265\) 1053.82 + 1825.27i 0.244286 + 0.423116i
\(266\) 81.6572 + 141.434i 0.0188223 + 0.0326011i
\(267\) 0 0
\(268\) 2340.68 4054.18i 0.533508 0.924062i
\(269\) −48.4985 −0.0109926 −0.00549629 0.999985i \(-0.501750\pi\)
−0.00549629 + 0.999985i \(0.501750\pi\)
\(270\) 0 0
\(271\) 7643.16 1.71324 0.856622 0.515945i \(-0.172559\pi\)
0.856622 + 0.515945i \(0.172559\pi\)
\(272\) −4132.22 + 7157.21i −0.921149 + 1.59548i
\(273\) 0 0
\(274\) −118.220 204.763i −0.0260654 0.0451467i
\(275\) 226.606 + 392.493i 0.0496904 + 0.0860663i
\(276\) 0 0
\(277\) −2573.01 + 4456.59i −0.558113 + 0.966680i 0.439541 + 0.898223i \(0.355141\pi\)
−0.997654 + 0.0684576i \(0.978192\pi\)
\(278\) 323.193 0.0697261
\(279\) 0 0
\(280\) 560.333 0.119594
\(281\) 2927.37 5070.35i 0.621467 1.07641i −0.367746 0.929926i \(-0.619870\pi\)
0.989213 0.146486i \(-0.0467963\pi\)
\(282\) 0 0
\(283\) −4696.92 8135.31i −0.986583 1.70881i −0.634679 0.772776i \(-0.718868\pi\)
−0.351904 0.936036i \(-0.614466\pi\)
\(284\) 192.979 + 334.249i 0.0403211 + 0.0698381i
\(285\) 0 0
\(286\) −102.405 + 177.370i −0.0211725 + 0.0366718i
\(287\) 7652.69 1.57395
\(288\) 0 0
\(289\) 12413.7 2.52671
\(290\) 70.8509 122.717i 0.0143466 0.0248490i
\(291\) 0 0
\(292\) 1628.81 + 2821.17i 0.326434 + 0.565400i
\(293\) −890.291 1542.03i −0.177513 0.307462i 0.763515 0.645790i \(-0.223472\pi\)
−0.941028 + 0.338328i \(0.890139\pi\)
\(294\) 0 0
\(295\) −1856.03 + 3214.74i −0.366313 + 0.634473i
\(296\) −359.219 −0.0705377
\(297\) 0 0
\(298\) −274.458 −0.0533522
\(299\) 827.217 1432.78i 0.159997 0.277123i
\(300\) 0 0
\(301\) 2170.74 + 3759.82i 0.415678 + 0.719976i
\(302\) −181.270 313.969i −0.0345395 0.0598241i
\(303\) 0 0
\(304\) −729.649 + 1263.79i −0.137659 + 0.238432i
\(305\) 44.8868 0.00842692
\(306\) 0 0
\(307\) 8480.18 1.57651 0.788256 0.615347i \(-0.210984\pi\)
0.788256 + 0.615347i \(0.210984\pi\)
\(308\) 2247.65 3893.05i 0.415818 0.720218i
\(309\) 0 0
\(310\) −70.4540 122.030i −0.0129081 0.0223575i
\(311\) −3405.40 5898.32i −0.620908 1.07544i −0.989317 0.145780i \(-0.953431\pi\)
0.368409 0.929664i \(-0.379903\pi\)
\(312\) 0 0
\(313\) −4023.41 + 6968.74i −0.726570 + 1.25846i 0.231755 + 0.972774i \(0.425553\pi\)
−0.958325 + 0.285682i \(0.907780\pi\)
\(314\) 289.747 0.0520744
\(315\) 0 0
\(316\) −4217.30 −0.750764
\(317\) 783.112 1356.39i 0.138751 0.240323i −0.788273 0.615325i \(-0.789025\pi\)
0.927024 + 0.375002i \(0.122358\pi\)
\(318\) 0 0
\(319\) −1140.44 1975.30i −0.200164 0.346694i
\(320\) 1231.55 + 2133.11i 0.215143 + 0.372638i
\(321\) 0 0
\(322\) 115.886 200.720i 0.0200561 0.0347382i
\(323\) 3059.47 0.527039
\(324\) 0 0
\(325\) −1253.91 −0.214013
\(326\) −159.571 + 276.385i −0.0271099 + 0.0469557i
\(327\) 0 0
\(328\) −440.674 763.271i −0.0741835 0.128490i
\(329\) 7376.77 + 12776.9i 1.23615 + 2.14108i
\(330\) 0 0
\(331\) −1221.28 + 2115.32i −0.202802 + 0.351264i −0.949430 0.313978i \(-0.898338\pi\)
0.746628 + 0.665242i \(0.231672\pi\)
\(332\) −2341.77 −0.387113
\(333\) 0 0
\(334\) −201.593 −0.0330260
\(335\) −1472.27 + 2550.04i −0.240115 + 0.415891i
\(336\) 0 0
\(337\) −4736.49 8203.84i −0.765617 1.32609i −0.939920 0.341396i \(-0.889100\pi\)
0.174302 0.984692i \(-0.444233\pi\)
\(338\) −35.8874 62.1588i −0.00577520 0.0100029i
\(339\) 0 0
\(340\) 2615.92 4530.91i 0.417260 0.722715i
\(341\) −2268.10 −0.360190
\(342\) 0 0
\(343\) −8954.76 −1.40966
\(344\) 250.000 433.013i 0.0391835 0.0678678i
\(345\) 0 0
\(346\) −195.415 338.469i −0.0303630 0.0525902i
\(347\) −1656.23 2868.68i −0.256229 0.443801i 0.709000 0.705209i \(-0.249147\pi\)
−0.965229 + 0.261408i \(0.915813\pi\)
\(348\) 0 0
\(349\) −2834.48 + 4909.46i −0.434745 + 0.753001i −0.997275 0.0737765i \(-0.976495\pi\)
0.562530 + 0.826777i \(0.309828\pi\)
\(350\) −175.661 −0.0268271
\(351\) 0 0
\(352\) −777.400 −0.117715
\(353\) −869.541 + 1506.09i −0.131108 + 0.227085i −0.924104 0.382142i \(-0.875187\pi\)
0.792996 + 0.609227i \(0.208520\pi\)
\(354\) 0 0
\(355\) −121.382 210.239i −0.0181472 0.0314319i
\(356\) −3389.63 5871.02i −0.504636 0.874054i
\(357\) 0 0
\(358\) 240.271 416.162i 0.0354713 0.0614381i
\(359\) −8624.58 −1.26793 −0.633966 0.773361i \(-0.718574\pi\)
−0.633966 + 0.773361i \(0.718574\pi\)
\(360\) 0 0
\(361\) −6318.77 −0.921238
\(362\) 406.799 704.597i 0.0590632 0.102301i
\(363\) 0 0
\(364\) 6218.60 + 10770.9i 0.895449 + 1.55096i
\(365\) −1024.50 1774.49i −0.146917 0.254468i
\(366\) 0 0
\(367\) 3054.59 5290.70i 0.434463 0.752513i −0.562788 0.826601i \(-0.690271\pi\)
0.997252 + 0.0740883i \(0.0236047\pi\)
\(368\) 2071.00 0.293365
\(369\) 0 0
\(370\) 112.613 0.0158229
\(371\) −6574.59 + 11387.5i −0.920043 + 1.59356i
\(372\) 0 0
\(373\) −3277.67 5677.08i −0.454990 0.788065i 0.543698 0.839281i \(-0.317024\pi\)
−0.998688 + 0.0512159i \(0.983690\pi\)
\(374\) 268.753 + 465.494i 0.0371575 + 0.0643587i
\(375\) 0 0
\(376\) 849.572 1471.50i 0.116525 0.201827i
\(377\) 6310.52 0.862092
\(378\) 0 0
\(379\) 5032.40 0.682050 0.341025 0.940054i \(-0.389226\pi\)
0.341025 + 0.940054i \(0.389226\pi\)
\(380\) 461.908 800.048i 0.0623563 0.108004i
\(381\) 0 0
\(382\) −67.2359 116.456i −0.00900547 0.0155979i
\(383\) 1831.49 + 3172.24i 0.244347 + 0.423222i 0.961948 0.273233i \(-0.0880930\pi\)
−0.717601 + 0.696455i \(0.754760\pi\)
\(384\) 0 0
\(385\) −1413.75 + 2448.69i −0.187146 + 0.324147i
\(386\) −272.044 −0.0358722
\(387\) 0 0
\(388\) 3085.03 0.403657
\(389\) −2435.48 + 4218.37i −0.317439 + 0.549820i −0.979953 0.199229i \(-0.936156\pi\)
0.662514 + 0.749049i \(0.269489\pi\)
\(390\) 0 0
\(391\) −2170.97 3760.22i −0.280794 0.486349i
\(392\) 1131.78 + 1960.30i 0.145825 + 0.252577i
\(393\) 0 0
\(394\) −368.121 + 637.605i −0.0470703 + 0.0815281i
\(395\) 2652.63 0.337895
\(396\) 0 0
\(397\) −3744.62 −0.473393 −0.236696 0.971584i \(-0.576065\pi\)
−0.236696 + 0.971584i \(0.576065\pi\)
\(398\) 237.625 411.579i 0.0299273 0.0518356i
\(399\) 0 0
\(400\) −784.811 1359.33i −0.0981014 0.169917i
\(401\) −900.435 1559.60i −0.112134 0.194221i 0.804497 0.593957i \(-0.202435\pi\)
−0.916630 + 0.399736i \(0.869102\pi\)
\(402\) 0 0
\(403\) 3137.59 5434.46i 0.387827 0.671737i
\(404\) −8585.16 −1.05725
\(405\) 0 0
\(406\) 884.049 0.108066
\(407\) 906.328 1569.81i 0.110381 0.191185i
\(408\) 0 0
\(409\) −7965.99 13797.5i −0.963064 1.66808i −0.714730 0.699401i \(-0.753450\pi\)
−0.248334 0.968675i \(-0.579883\pi\)
\(410\) 138.149 + 239.281i 0.0166407 + 0.0288225i
\(411\) 0 0
\(412\) −2364.89 + 4096.12i −0.282791 + 0.489809i
\(413\) −23158.8 −2.75926
\(414\) 0 0
\(415\) 1472.95 0.174227
\(416\) 1075.42 1862.68i 0.126747 0.219532i
\(417\) 0 0
\(418\) 47.4553 + 82.1949i 0.00555290 + 0.00961791i
\(419\) −1723.87 2985.84i −0.200995 0.348133i 0.747854 0.663863i \(-0.231084\pi\)
−0.948849 + 0.315730i \(0.897751\pi\)
\(420\) 0 0
\(421\) −2807.99 + 4863.58i −0.325066 + 0.563032i −0.981526 0.191330i \(-0.938720\pi\)
0.656459 + 0.754361i \(0.272053\pi\)
\(422\) 148.359 0.0171137
\(423\) 0 0
\(424\) 1514.37 0.173454
\(425\) −1645.39 + 2849.89i −0.187795 + 0.325271i
\(426\) 0 0
\(427\) 140.020 + 242.522i 0.0158689 + 0.0274858i
\(428\) 1982.12 + 3433.13i 0.223854 + 0.387726i
\(429\) 0 0
\(430\) −78.3737 + 135.747i −0.00878957 + 0.0152240i
\(431\) 3534.04 0.394962 0.197481 0.980307i \(-0.436724\pi\)
0.197481 + 0.980307i \(0.436724\pi\)
\(432\) 0 0
\(433\) 6674.80 0.740809 0.370405 0.928871i \(-0.379219\pi\)
0.370405 + 0.928871i \(0.379219\pi\)
\(434\) 439.549 761.321i 0.0486153 0.0842041i
\(435\) 0 0
\(436\) −3812.87 6604.08i −0.418815 0.725408i
\(437\) −383.339 663.963i −0.0419625 0.0726812i
\(438\) 0 0
\(439\) 3271.76 5666.85i 0.355700 0.616091i −0.631537 0.775346i \(-0.717576\pi\)
0.987238 + 0.159254i \(0.0509090\pi\)
\(440\) 325.639 0.0352823
\(441\) 0 0
\(442\) −1487.12 −0.160035
\(443\) 7154.86 12392.6i 0.767353 1.32909i −0.171640 0.985160i \(-0.554907\pi\)
0.938993 0.343935i \(-0.111760\pi\)
\(444\) 0 0
\(445\) 2132.04 + 3692.81i 0.227120 + 0.393384i
\(446\) −137.267 237.753i −0.0145734 0.0252420i
\(447\) 0 0
\(448\) −7683.39 + 13308.0i −0.810282 + 1.40345i
\(449\) 14587.4 1.53324 0.766618 0.642104i \(-0.221938\pi\)
0.766618 + 0.642104i \(0.221938\pi\)
\(450\) 0 0
\(451\) 4447.38 0.464343
\(452\) −6871.31 + 11901.5i −0.715043 + 1.23849i
\(453\) 0 0
\(454\) −171.817 297.596i −0.0177616 0.0307640i
\(455\) −3911.43 6774.80i −0.403013 0.698039i
\(456\) 0 0
\(457\) −1012.89 + 1754.37i −0.103678 + 0.179576i −0.913197 0.407518i \(-0.866394\pi\)
0.809519 + 0.587093i \(0.199728\pi\)
\(458\) −1392.64 −0.142083
\(459\) 0 0
\(460\) −1311.06 −0.132888
\(461\) −1778.09 + 3079.75i −0.179640 + 0.311146i −0.941757 0.336293i \(-0.890827\pi\)
0.762117 + 0.647439i \(0.224160\pi\)
\(462\) 0 0
\(463\) 5141.34 + 8905.07i 0.516066 + 0.893852i 0.999826 + 0.0186517i \(0.00593735\pi\)
−0.483760 + 0.875201i \(0.660729\pi\)
\(464\) 3949.72 + 6841.11i 0.395174 + 0.684462i
\(465\) 0 0
\(466\) −226.806 + 392.840i −0.0225464 + 0.0390514i
\(467\) −8217.44 −0.814256 −0.407128 0.913371i \(-0.633470\pi\)
−0.407128 + 0.913371i \(0.633470\pi\)
\(468\) 0 0
\(469\) −18370.3 −1.80866
\(470\) −266.336 + 461.307i −0.0261386 + 0.0452734i
\(471\) 0 0
\(472\) 1333.59 + 2309.84i 0.130049 + 0.225252i
\(473\) 1261.53 + 2185.03i 0.122632 + 0.212406i
\(474\) 0 0
\(475\) −290.535 + 503.222i −0.0280646 + 0.0486093i
\(476\) 32640.5 3.14301
\(477\) 0 0
\(478\) −1145.69 −0.109629
\(479\) 6842.59 11851.7i 0.652705 1.13052i −0.329759 0.944065i \(-0.606967\pi\)
0.982464 0.186453i \(-0.0596993\pi\)
\(480\) 0 0
\(481\) 2507.54 + 4343.19i 0.237701 + 0.411710i
\(482\) −370.178 641.168i −0.0349817 0.0605900i
\(483\) 0 0
\(484\) −3984.00 + 6900.50i −0.374155 + 0.648056i
\(485\) −1940.45 −0.181673
\(486\) 0 0
\(487\) −3239.59 −0.301437 −0.150718 0.988577i \(-0.548159\pi\)
−0.150718 + 0.988577i \(0.548159\pi\)
\(488\) 16.1259 27.9309i 0.00149587 0.00259092i
\(489\) 0 0
\(490\) −354.806 614.542i −0.0327112 0.0566575i
\(491\) 5564.04 + 9637.20i 0.511409 + 0.885786i 0.999913 + 0.0132239i \(0.00420943\pi\)
−0.488504 + 0.872562i \(0.662457\pi\)
\(492\) 0 0
\(493\) 8280.74 14342.7i 0.756482 1.31027i
\(494\) −262.590 −0.0239159
\(495\) 0 0
\(496\) 7855.18 0.711105
\(497\) 757.276 1311.64i 0.0683470 0.118380i
\(498\) 0 0
\(499\) 2713.61 + 4700.11i 0.243443 + 0.421655i 0.961693 0.274130i \(-0.0883899\pi\)
−0.718250 + 0.695785i \(0.755057\pi\)
\(500\) 496.829 + 860.533i 0.0444377 + 0.0769684i
\(501\) 0 0
\(502\) 391.997 678.958i 0.0348519 0.0603653i
\(503\) 9600.22 0.850999 0.425500 0.904959i \(-0.360098\pi\)
0.425500 + 0.904959i \(0.360098\pi\)
\(504\) 0 0
\(505\) 5399.97 0.475833
\(506\) 67.3474 116.649i 0.00591691 0.0102484i
\(507\) 0 0
\(508\) 4053.94 + 7021.62i 0.354064 + 0.613256i
\(509\) −9469.94 16402.4i −0.824652 1.42834i −0.902185 0.431349i \(-0.858038\pi\)
0.0775333 0.996990i \(-0.475296\pi\)
\(510\) 0 0
\(511\) 6391.66 11070.7i 0.553328 0.958392i
\(512\) 4496.87 0.388155
\(513\) 0 0
\(514\) 1530.57 0.131343
\(515\) 1487.49 2576.41i 0.127275 0.220447i
\(516\) 0 0
\(517\) 4287.03 + 7425.35i 0.364687 + 0.631657i
\(518\) 351.285 + 608.444i 0.0297965 + 0.0516090i
\(519\) 0 0
\(520\) −450.474 + 780.244i −0.0379896 + 0.0657999i
\(521\) −19292.6 −1.62231 −0.811155 0.584831i \(-0.801161\pi\)
−0.811155 + 0.584831i \(0.801161\pi\)
\(522\) 0 0
\(523\) 17967.5 1.50223 0.751114 0.660172i \(-0.229517\pi\)
0.751114 + 0.660172i \(0.229517\pi\)
\(524\) 6766.38 11719.7i 0.564104 0.977057i
\(525\) 0 0
\(526\) 604.147 + 1046.41i 0.0500799 + 0.0867410i
\(527\) −8234.35 14262.3i −0.680634 1.17889i
\(528\) 0 0
\(529\) 5539.47 9594.65i 0.455287 0.788580i
\(530\) −474.747 −0.0389088
\(531\) 0 0
\(532\) 5763.51 0.469699
\(533\) −6152.30 + 10656.1i −0.499973 + 0.865979i
\(534\) 0 0
\(535\) −1246.73 2159.40i −0.100749 0.174503i
\(536\) 1057.84 + 1832.24i 0.0852460 + 0.147650i
\(537\) 0 0
\(538\) 5.46214 9.46070i 0.000437713 0.000758141i
\(539\) −11422.1 −0.912777
\(540\) 0 0
\(541\) −8299.36 −0.659552 −0.329776 0.944059i \(-0.606973\pi\)
−0.329776 + 0.944059i \(0.606973\pi\)
\(542\) −860.811 + 1490.97i −0.0682195 + 0.118160i
\(543\) 0 0
\(544\) −2822.35 4888.46i −0.222440 0.385278i
\(545\) 2398.25 + 4153.89i 0.188495 + 0.326483i
\(546\) 0 0
\(547\) −42.3605 + 73.3706i −0.00331116 + 0.00573510i −0.867676 0.497130i \(-0.834387\pi\)
0.864365 + 0.502865i \(0.167721\pi\)
\(548\) −8344.17 −0.650448
\(549\) 0 0
\(550\) −102.086 −0.00791447
\(551\) 1462.18 2532.56i 0.113050 0.195809i
\(552\) 0 0
\(553\) 8274.63 + 14332.1i 0.636298 + 1.10210i
\(554\) −579.571 1003.85i −0.0444469 0.0769843i
\(555\) 0 0
\(556\) 5702.89 9877.69i 0.434994 0.753431i
\(557\) 20914.0 1.59094 0.795469 0.605994i \(-0.207224\pi\)
0.795469 + 0.605994i \(0.207224\pi\)
\(558\) 0 0
\(559\) −6980.56 −0.528169
\(560\) 4896.28 8480.61i 0.369474 0.639948i
\(561\) 0 0
\(562\) 659.389 + 1142.10i 0.0494923 + 0.0857231i
\(563\) 5520.48 + 9561.76i 0.413252 + 0.715773i 0.995243 0.0974220i \(-0.0310596\pi\)
−0.581991 + 0.813195i \(0.697726\pi\)
\(564\) 0 0
\(565\) 4321.98 7485.89i 0.321818 0.557405i
\(566\) 2115.96 0.157139
\(567\) 0 0
\(568\) −174.429 −0.0128853
\(569\) −3007.31 + 5208.81i −0.221569 + 0.383770i −0.955285 0.295688i \(-0.904451\pi\)
0.733715 + 0.679457i \(0.237785\pi\)
\(570\) 0 0
\(571\) 10968.7 + 18998.3i 0.803896 + 1.39239i 0.917034 + 0.398810i \(0.130577\pi\)
−0.113137 + 0.993579i \(0.536090\pi\)
\(572\) 3613.96 + 6259.56i 0.264173 + 0.457561i
\(573\) 0 0
\(574\) −861.884 + 1492.83i −0.0626730 + 0.108553i
\(575\) 824.641 0.0598085
\(576\) 0 0
\(577\) 473.507 0.0341635 0.0170818 0.999854i \(-0.494562\pi\)
0.0170818 + 0.999854i \(0.494562\pi\)
\(578\) −1398.09 + 2421.57i −0.100611 + 0.174263i
\(579\) 0 0
\(580\) −2500.39 4330.80i −0.179005 0.310046i
\(581\) 4594.72 + 7958.29i 0.328092 + 0.568271i
\(582\) 0 0
\(583\) −3820.84 + 6617.89i −0.271429 + 0.470129i
\(584\) −1472.24 −0.104318
\(585\) 0 0
\(586\) 401.076 0.0282735
\(587\) 6510.17 11275.9i 0.457757 0.792859i −0.541085 0.840968i \(-0.681986\pi\)
0.998842 + 0.0481093i \(0.0153196\pi\)
\(588\) 0 0
\(589\) −1453.99 2518.38i −0.101715 0.176176i
\(590\) −418.071 724.120i −0.0291724 0.0505281i
\(591\) 0 0
\(592\) −3138.91 + 5436.75i −0.217920 + 0.377448i
\(593\) 12887.3 0.892441 0.446220 0.894923i \(-0.352770\pi\)
0.446220 + 0.894923i \(0.352770\pi\)
\(594\) 0 0
\(595\) −20530.5 −1.41457
\(596\) −4842.94 + 8388.22i −0.332843 + 0.576501i
\(597\) 0 0
\(598\) 186.330 + 322.734i 0.0127418 + 0.0220695i
\(599\) −4337.24 7512.32i −0.295851 0.512429i 0.679332 0.733832i \(-0.262270\pi\)
−0.975182 + 0.221403i \(0.928937\pi\)
\(600\) 0 0
\(601\) −5467.86 + 9470.61i −0.371112 + 0.642786i −0.989737 0.142901i \(-0.954357\pi\)
0.618625 + 0.785687i \(0.287690\pi\)
\(602\) −977.916 −0.0662074
\(603\) 0 0
\(604\) −12794.4 −0.861913
\(605\) 2505.90 4340.34i 0.168395 0.291669i
\(606\) 0 0
\(607\) −10835.2 18767.1i −0.724527 1.25492i −0.959168 0.282836i \(-0.908725\pi\)
0.234641 0.972082i \(-0.424608\pi\)
\(608\) −498.359 863.183i −0.0332420 0.0575768i
\(609\) 0 0
\(610\) −5.05537 + 8.75616i −0.000335551 + 0.000581191i
\(611\) −23721.9 −1.57068
\(612\) 0 0
\(613\) −15571.2 −1.02596 −0.512982 0.858399i \(-0.671459\pi\)
−0.512982 + 0.858399i \(0.671459\pi\)
\(614\) −955.079 + 1654.25i −0.0627750 + 0.108730i
\(615\) 0 0
\(616\) 1015.80 + 1759.42i 0.0664411 + 0.115079i
\(617\) 4863.27 + 8423.43i 0.317322 + 0.549618i 0.979928 0.199350i \(-0.0638829\pi\)
−0.662606 + 0.748968i \(0.730550\pi\)
\(618\) 0 0
\(619\) −3148.79 + 5453.87i −0.204460 + 0.354135i −0.949961 0.312370i \(-0.898877\pi\)
0.745501 + 0.666505i \(0.232210\pi\)
\(620\) −4972.77 −0.322115
\(621\) 0 0
\(622\) 1534.13 0.0988955
\(623\) −13301.4 + 23038.7i −0.855392 + 1.48158i
\(624\) 0 0
\(625\) −312.500 541.266i −0.0200000 0.0346410i
\(626\) −906.272 1569.71i −0.0578625 0.100221i
\(627\) 0 0
\(628\) 5112.71 8855.47i 0.324872 0.562694i
\(629\) 13161.7 0.834327
\(630\) 0 0
\(631\) −5670.98 −0.357778 −0.178889 0.983869i \(-0.557250\pi\)
−0.178889 + 0.983869i \(0.557250\pi\)
\(632\) 952.977 1650.60i 0.0599800 0.103888i
\(633\) 0 0
\(634\) 176.396 + 305.527i 0.0110498 + 0.0191388i
\(635\) −2549.88 4416.53i −0.159353 0.276007i
\(636\) 0 0
\(637\) 15800.9 27367.9i 0.982816 1.70229i
\(638\) 513.767 0.0318813
\(639\) 0 0
\(640\) −2270.13 −0.140210
\(641\) 10832.3 18762.0i 0.667470 1.15609i −0.311140 0.950364i \(-0.600711\pi\)
0.978609 0.205727i \(-0.0659560\pi\)
\(642\) 0 0
\(643\) −3111.86 5389.90i −0.190855 0.330570i 0.754679 0.656094i \(-0.227793\pi\)
−0.945534 + 0.325524i \(0.894459\pi\)
\(644\) −4089.71 7083.59i −0.250244 0.433436i
\(645\) 0 0
\(646\) −344.573 + 596.818i −0.0209861 + 0.0363491i
\(647\) −20451.9 −1.24273 −0.621365 0.783521i \(-0.713422\pi\)
−0.621365 + 0.783521i \(0.713422\pi\)
\(648\) 0 0
\(649\) −13458.8 −0.814029
\(650\) 141.221 244.602i 0.00852176 0.0147601i
\(651\) 0 0
\(652\) 5631.41 + 9753.88i 0.338256 + 0.585876i
\(653\) 3724.22 + 6450.54i 0.223185 + 0.386568i 0.955773 0.294104i \(-0.0950211\pi\)
−0.732588 + 0.680672i \(0.761688\pi\)
\(654\) 0 0
\(655\) −4255.98 + 7371.57i −0.253885 + 0.439742i
\(656\) −15402.7 −0.916731
\(657\) 0 0
\(658\) −3323.23 −0.196889
\(659\) 413.185 715.658i 0.0244240 0.0423036i −0.853555 0.521003i \(-0.825558\pi\)
0.877979 + 0.478699i \(0.158891\pi\)
\(660\) 0 0
\(661\) 3129.11 + 5419.77i 0.184127 + 0.318918i 0.943282 0.331992i \(-0.107721\pi\)
−0.759155 + 0.650910i \(0.774387\pi\)
\(662\) −275.093 476.475i −0.0161507 0.0279739i
\(663\) 0 0
\(664\) 529.167 916.545i 0.0309272 0.0535675i
\(665\) −3625.18 −0.211396
\(666\) 0 0
\(667\) −4150.17 −0.240922
\(668\) −3557.19 + 6161.24i −0.206036 + 0.356865i
\(669\) 0 0
\(670\) −331.627 574.396i −0.0191222 0.0331207i
\(671\) 81.3729 + 140.942i 0.00468162 + 0.00810880i
\(672\) 0 0
\(673\) 5039.90 8729.36i 0.288668 0.499988i −0.684824 0.728709i \(-0.740121\pi\)
0.973492 + 0.228720i \(0.0734542\pi\)
\(674\) 2133.79 0.121944
\(675\) 0 0
\(676\) −2532.99 −0.144117
\(677\) −12855.2 + 22265.9i −0.729788 + 1.26403i 0.227185 + 0.973852i \(0.427048\pi\)
−0.956973 + 0.290178i \(0.906285\pi\)
\(678\) 0 0
\(679\) −6053.05 10484.2i −0.342113 0.592557i
\(680\) 1182.23 + 2047.69i 0.0666714 + 0.115478i
\(681\) 0 0
\(682\) 255.445 442.443i 0.0143424 0.0248417i
\(683\) 32091.0 1.79784 0.898922 0.438109i \(-0.144352\pi\)
0.898922 + 0.438109i \(0.144352\pi\)
\(684\) 0 0
\(685\) 5248.39 0.292746
\(686\) 1008.53 1746.82i 0.0561310 0.0972217i
\(687\) 0 0
\(688\) −4369.09 7567.48i −0.242107 0.419342i
\(689\) −10571.2 18309.8i −0.584512 1.01240i
\(690\) 0 0
\(691\) −5282.87 + 9150.20i −0.290839 + 0.503748i −0.974008 0.226512i \(-0.927268\pi\)
0.683169 + 0.730260i \(0.260601\pi\)
\(692\) −13792.7 −0.757690
\(693\) 0 0
\(694\) 746.133 0.0408110
\(695\) −3587.06 + 6212.96i −0.195777 + 0.339095i
\(696\) 0 0
\(697\) 16146.2 + 27966.1i 0.877449 + 1.51979i
\(698\) −638.465 1105.85i −0.0346222 0.0599673i
\(699\) 0 0
\(700\) −3099.62 + 5368.70i −0.167364 + 0.289882i
\(701\) −13081.8 −0.704837 −0.352419 0.935842i \(-0.614641\pi\)
−0.352419 + 0.935842i \(0.614641\pi\)
\(702\) 0 0
\(703\) 2324.04 0.124684
\(704\) −4465.22 + 7733.99i −0.239047 + 0.414042i
\(705\) 0 0
\(706\) −195.864 339.246i −0.0104411 0.0180846i
\(707\) 16844.7 + 29175.8i 0.896053 + 1.55201i
\(708\) 0 0
\(709\) 14110.6 24440.3i 0.747440 1.29460i −0.201606 0.979467i \(-0.564616\pi\)
0.949046 0.315137i \(-0.102051\pi\)
\(710\) 54.6823 0.00289041
\(711\) 0 0
\(712\) 3063.80 0.161265
\(713\) −2063.46 + 3574.02i −0.108383 + 0.187725i
\(714\) 0 0
\(715\) −2273.14 3937.19i −0.118896 0.205934i
\(716\) −8479.38 14686.7i −0.442583 0.766576i
\(717\) 0 0
\(718\) 971.342 1682.41i 0.0504877 0.0874473i
\(719\) 11471.4 0.595010 0.297505 0.954720i \(-0.403846\pi\)
0.297505 + 0.954720i \(0.403846\pi\)
\(720\) 0 0
\(721\) 18560.3 0.958701
\(722\) 711.651 1232.62i 0.0366827 0.0635363i
\(723\) 0 0
\(724\) −14356.3 24865.8i −0.736944 1.27642i
\(725\) 1572.72 + 2724.03i 0.0805645 + 0.139542i
\(726\) 0 0
\(727\) −10829.6 + 18757.5i −0.552475 + 0.956914i 0.445621 + 0.895222i \(0.352983\pi\)
−0.998095 + 0.0616922i \(0.980350\pi\)
\(728\) −5620.84 −0.286157
\(729\) 0 0
\(730\) 461.537 0.0234004
\(731\) −9159.96 + 15865.5i −0.463466 + 0.802746i
\(732\) 0 0
\(733\) −2840.86 4920.51i −0.143151 0.247944i 0.785531 0.618823i \(-0.212390\pi\)
−0.928682 + 0.370878i \(0.879057\pi\)
\(734\) 688.045 + 1191.73i 0.0345997 + 0.0599285i
\(735\) 0 0
\(736\) −707.259 + 1225.01i −0.0354211 + 0.0613511i
\(737\) −10676.0 −0.533588
\(738\) 0 0
\(739\) 261.324 0.0130080 0.00650402 0.999979i \(-0.497930\pi\)
0.00650402 + 0.999979i \(0.497930\pi\)
\(740\) 1987.11 3441.77i 0.0987127 0.170975i
\(741\) 0 0
\(742\) −1480.93 2565.04i −0.0732702 0.126908i
\(743\) −8202.97 14208.0i −0.405031 0.701533i 0.589294 0.807918i \(-0.299406\pi\)
−0.994325 + 0.106385i \(0.966072\pi\)
\(744\) 0 0
\(745\) 3046.16 5276.10i 0.149802 0.259465i
\(746\) 1476.59 0.0724688
\(747\) 0 0
\(748\) 18969.1 0.927244
\(749\) 7778.11 13472.1i 0.379447 0.657222i
\(750\) 0 0
\(751\) −10737.3 18597.5i −0.521716 0.903639i −0.999681 0.0252601i \(-0.991959\pi\)
0.477965 0.878379i \(-0.341375\pi\)
\(752\) −14847.4 25716.4i −0.719985 1.24705i
\(753\) 0 0
\(754\) −710.722 + 1231.01i −0.0343276 + 0.0594571i
\(755\) 8047.51 0.387919
\(756\) 0 0
\(757\) −13643.2 −0.655046 −0.327523 0.944843i \(-0.606214\pi\)
−0.327523 + 0.944843i \(0.606214\pi\)
\(758\) −566.773 + 981.680i −0.0271585 + 0.0470399i
\(759\) 0 0
\(760\) 208.754 + 361.572i 0.00996353 + 0.0172573i
\(761\) 13469.0 + 23328.9i 0.641589 + 1.11127i 0.985078 + 0.172109i \(0.0550580\pi\)
−0.343489 + 0.939157i \(0.611609\pi\)
\(762\) 0 0
\(763\) −14962.2 + 25915.3i −0.709920 + 1.22962i
\(764\) −4745.63 −0.224726
\(765\) 0 0
\(766\) −825.088 −0.0389186
\(767\) 18618.3 32247.9i 0.876491 1.51813i
\(768\) 0 0
\(769\) 14442.7 + 25015.5i 0.677265 + 1.17306i 0.975801 + 0.218659i \(0.0701683\pi\)
−0.298536 + 0.954398i \(0.596498\pi\)
\(770\) −318.447 551.566i −0.0149039 0.0258144i
\(771\) 0 0
\(772\) −4800.34 + 8314.43i −0.223793 + 0.387620i
\(773\) −3031.34 −0.141048 −0.0705238 0.997510i \(-0.522467\pi\)
−0.0705238 + 0.997510i \(0.522467\pi\)
\(774\) 0 0
\(775\) 3127.82 0.144974
\(776\) −697.121 + 1207.45i −0.0322490 + 0.0558568i
\(777\) 0 0
\(778\) −548.591 950.188i −0.0252801 0.0437865i
\(779\) 2851.03 + 4938.13i 0.131128 + 0.227120i
\(780\) 0 0
\(781\) 440.092 762.262i 0.0201636 0.0349243i
\(782\) 978.019 0.0447236
\(783\) 0 0
\(784\) 39558.7 1.80205
\(785\) −3215.84 + 5570.00i −0.146214 + 0.253251i
\(786\) 0 0
\(787\) −7577.38 13124.4i −0.343208 0.594453i 0.641819 0.766856i \(-0.278180\pi\)
−0.985026 + 0.172403i \(0.944847\pi\)
\(788\) 12991.3 + 22501.6i 0.587306 + 1.01724i
\(789\) 0 0
\(790\) −298.753 + 517.455i −0.0134546 + 0.0233041i
\(791\) 53928.0 2.42409
\(792\) 0 0
\(793\) −450.270 −0.0201634
\(794\) 421.737 730.470i 0.0188500 0.0326491i
\(795\) 0 0
\(796\) −8386.00 14525.0i −0.373409 0.646764i
\(797\) 14190.3 + 24578.3i 0.630673 + 1.09236i 0.987414 + 0.158155i \(0.0505546\pi\)
−0.356741 + 0.934203i \(0.616112\pi\)
\(798\) 0 0
\(799\) −31128.1 + 53915.5i −1.37827 + 2.38723i
\(800\) 1072.07 0.0473793
\(801\) 0 0
\(802\) 405.646 0.0178602
\(803\) 3714.53 6433.75i 0.163241 0.282742i
\(804\) 0 0
\(805\) 2572.39 + 4455.50i 0.112627 + 0.195076i
\(806\) 706.741 + 1224.11i 0.0308857 + 0.0534957i
\(807\) 0 0
\(808\) 1939.98 3360.14i 0.0844655 0.146299i
\(809\) 14569.6 0.633175 0.316588 0.948563i \(-0.397463\pi\)
0.316588 + 0.948563i \(0.397463\pi\)
\(810\) 0 0
\(811\) 27927.7 1.20921 0.604607 0.796524i \(-0.293330\pi\)
0.604607 + 0.796524i \(0.293330\pi\)
\(812\) 15599.4 27019.0i 0.674178 1.16771i
\(813\) 0 0
\(814\) 204.150 + 353.598i 0.00879049 + 0.0152256i
\(815\) −3542.09 6135.09i −0.152238 0.263684i
\(816\) 0 0
\(817\) −1617.43 + 2801.46i −0.0692614 + 0.119964i
\(818\) 3588.68 0.153393
\(819\) 0 0
\(820\) 9750.79 0.415259
\(821\) 9022.03 15626.6i 0.383521 0.664279i −0.608041 0.793905i \(-0.708045\pi\)
0.991563 + 0.129627i \(0.0413779\pi\)
\(822\) 0 0
\(823\) 16126.4 + 27931.8i 0.683028 + 1.18304i 0.974052 + 0.226323i \(0.0726705\pi\)
−0.291025 + 0.956716i \(0.593996\pi\)
\(824\) −1068.78 1851.19i −0.0451855 0.0782636i
\(825\) 0 0
\(826\) 2608.26 4517.64i 0.109871 0.190301i
\(827\) −13569.5 −0.570566 −0.285283 0.958443i \(-0.592088\pi\)
−0.285283 + 0.958443i \(0.592088\pi\)
\(828\) 0 0
\(829\) 742.559 0.0311099 0.0155550 0.999879i \(-0.495049\pi\)
0.0155550 + 0.999879i \(0.495049\pi\)
\(830\) −165.891 + 287.331i −0.00693754 + 0.0120162i
\(831\) 0 0
\(832\) −12354.0 21397.7i −0.514780 0.891625i
\(833\) −41468.1 71824.9i −1.72483 2.98750i
\(834\) 0 0
\(835\) 2237.44 3875.35i 0.0927302 0.160613i
\(836\) 3349.48 0.138569
\(837\) 0 0
\(838\) 776.605 0.0320136
\(839\) −17752.3 + 30747.9i −0.730487 + 1.26524i 0.226189 + 0.974083i \(0.427373\pi\)
−0.956675 + 0.291157i \(0.905960\pi\)
\(840\) 0 0
\(841\) 4279.49 + 7412.29i 0.175468 + 0.303919i
\(842\) −632.499 1095.52i −0.0258876 0.0448386i
\(843\) 0 0
\(844\) 2617.86 4534.26i 0.106766 0.184924i
\(845\) 1593.23 0.0648623
\(846\) 0 0
\(847\) 31267.6 1.26844
\(848\) 13232.8 22919.9i 0.535869 0.928153i
\(849\) 0 0
\(850\) −370.623 641.938i −0.0149556 0.0259039i
\(851\) −1649.11 2856.34i −0.0664285 0.115058i
\(852\) 0 0
\(853\) −187.524 + 324.801i −0.00752719 + 0.0130375i −0.869764 0.493467i \(-0.835729\pi\)
0.862237 + 0.506505i \(0.169063\pi\)
\(854\) −63.0790 −0.00252754
\(855\) 0 0
\(856\) −1791.59 −0.0715365
\(857\) 16097.4 27881.5i 0.641629 1.11133i −0.343440 0.939174i \(-0.611592\pi\)
0.985069 0.172159i \(-0.0550743\pi\)
\(858\) 0 0
\(859\) 14068.8 + 24367.8i 0.558813 + 0.967893i 0.997596 + 0.0692994i \(0.0220764\pi\)
−0.438783 + 0.898593i \(0.644590\pi\)
\(860\) 2765.87 + 4790.64i 0.109669 + 0.189953i
\(861\) 0 0
\(862\) −398.021 + 689.392i −0.0157270 + 0.0272399i
\(863\) −15724.6 −0.620244 −0.310122 0.950697i \(-0.600370\pi\)
−0.310122 + 0.950697i \(0.600370\pi\)
\(864\) 0 0
\(865\) 8675.48 0.341012
\(866\) −751.749 + 1302.07i −0.0294982 + 0.0510924i
\(867\) 0 0
\(868\) −15512.1 26867.7i −0.606583 1.05063i
\(869\) 4808.82 + 8329.12i 0.187719 + 0.325139i
\(870\) 0 0
\(871\) 14768.6 25580.0i 0.574531 0.995117i
\(872\) 3446.35 0.133840
\(873\) 0 0
\(874\) 172.694 0.00668361
\(875\) 1949.63 3376.85i 0.0753250 0.130467i
\(876\) 0 0
\(877\) −7640.23 13233.3i −0.294176 0.509528i 0.680617 0.732639i \(-0.261712\pi\)
−0.974793 + 0.223112i \(0.928378\pi\)
\(878\) 736.963 + 1276.46i 0.0283272 + 0.0490642i
\(879\) 0 0
\(880\) 2845.49 4928.52i 0.109001 0.188796i
\(881\) 24687.6 0.944092 0.472046 0.881574i \(-0.343516\pi\)
0.472046 + 0.881574i \(0.343516\pi\)
\(882\) 0 0
\(883\) 6562.59 0.250112 0.125056 0.992150i \(-0.460089\pi\)
0.125056 + 0.992150i \(0.460089\pi\)
\(884\) −26241.0 + 45450.7i −0.998392 + 1.72927i
\(885\) 0 0
\(886\) 1611.63 + 2791.43i 0.0611104 + 0.105846i
\(887\) 25255.5 + 43743.9i 0.956030 + 1.65589i 0.731994 + 0.681311i \(0.238590\pi\)
0.224035 + 0.974581i \(0.428077\pi\)
\(888\) 0 0
\(889\) 15908.2 27553.8i 0.600162 1.03951i
\(890\) −960.485 −0.0361747
\(891\) 0 0
\(892\) −9688.51 −0.363672
\(893\) −5496.47 + 9520.17i −0.205971 + 0.356753i
\(894\) 0 0
\(895\) 5333.44 + 9237.78i 0.199192 + 0.345011i
\(896\) −7081.43 12265.4i −0.264034 0.457320i
\(897\) 0 0
\(898\) −1642.91 + 2845.60i −0.0610518 + 0.105745i
\(899\) −15741.4 −0.583986
\(900\) 0 0
\(901\) −55486.3 −2.05163
\(902\) −500.886 + 867.559i −0.0184897 + 0.0320250i
\(903\) 0 0
\(904\) −3105.40 5378.72i −0.114252 0.197891i
\(905\) 9029.96 + 15640.3i 0.331675 + 0.574478i
\(906\) 0 0
\(907\) 3508.72 6077.28i 0.128451 0.222484i −0.794626 0.607100i \(-0.792333\pi\)
0.923077 + 0.384616i \(0.125666\pi\)
\(908\) −12127.2 −0.443231
\(909\) 0 0
\(910\) 1762.10 0.0641902
\(911\) −3062.30 + 5304.05i −0.111370 + 0.192899i −0.916323 0.400440i \(-0.868857\pi\)
0.804953 + 0.593339i \(0.202191\pi\)
\(912\) 0 0
\(913\) 2670.23 + 4624.98i 0.0967928 + 0.167650i
\(914\) −228.153 395.172i −0.00825669 0.0143010i
\(915\) 0 0
\(916\) −24573.8 + 42563.0i −0.886397 + 1.53528i
\(917\) −53104.4 −1.91239
\(918\) 0 0
\(919\) 23780.7 0.853594 0.426797 0.904347i \(-0.359642\pi\)
0.426797 + 0.904347i \(0.359642\pi\)
\(920\) 296.258 513.134i 0.0106167 0.0183886i
\(921\) 0 0
\(922\) −400.515 693.713i −0.0143062 0.0247790i
\(923\) 1217.61 + 2108.96i 0.0434215 + 0.0752082i
\(924\) 0 0
\(925\) −1249.87 + 2164.83i −0.0444274 + 0.0769506i
\(926\) −2316.17 −0.0821967
\(927\) 0 0
\(928\) −5395.41 −0.190854
\(929\) 5094.54 8824.01i 0.179921 0.311632i −0.761932 0.647657i \(-0.775749\pi\)
0.941853 + 0.336024i \(0.109082\pi\)
\(930\) 0 0
\(931\) −7322.26 12682.5i −0.257763 0.446459i
\(932\) 8004.19 + 13863.7i 0.281316 + 0.487253i
\(933\) 0 0
\(934\) 925.488 1602.99i 0.0324228 0.0561579i
\(935\) −11931.3 −0.417323
\(936\) 0 0
\(937\) −3880.22 −0.135284 −0.0676421 0.997710i \(-0.521548\pi\)
−0.0676421 + 0.997710i \(0.521548\pi\)
\(938\) 2068.96 3583.54i 0.0720191 0.124741i
\(939\) 0 0
\(940\) 9399.22 + 16279.9i 0.326137 + 0.564886i
\(941\) −19336.9 33492.6i −0.669890 1.16028i −0.977935 0.208911i \(-0.933008\pi\)
0.308045 0.951372i \(-0.400325\pi\)
\(942\) 0 0
\(943\) 4046.11 7008.07i 0.139724 0.242008i
\(944\) 46612.3 1.60710
\(945\) 0 0
\(946\) −568.318 −0.0195324
\(947\) −3877.44 + 6715.92i −0.133052 + 0.230452i −0.924851 0.380328i \(-0.875811\pi\)
0.791800 + 0.610781i \(0.209144\pi\)
\(948\) 0 0
\(949\) 10277.0 + 17800.3i 0.351534 + 0.608875i
\(950\) −65.4430 113.351i −0.00223500 0.00387114i
\(951\) 0 0
\(952\) −7375.72 + 12775.1i −0.251101 + 0.434920i
\(953\) 22527.9 0.765739 0.382870 0.923802i \(-0.374936\pi\)
0.382870 + 0.923802i \(0.374936\pi\)
\(954\) 0 0
\(955\) 2984.95 0.101142
\(956\) −20216.2 + 35015.5i −0.683931 + 1.18460i
\(957\) 0 0
\(958\) 1541.29 + 2669.60i 0.0519800 + 0.0900321i
\(959\) 16371.9 + 28356.9i 0.551277 + 0.954840i
\(960\) 0 0
\(961\) 7068.91 12243.7i 0.237283 0.410987i
\(962\) −1129.65 −0.0378600
\(963\) 0 0
\(964\) −26127.8 −0.872947
\(965\) 3019.36 5229.68i 0.100722 0.174455i
\(966\) 0 0
\(967\) 2826.20 + 4895.13i 0.0939861 + 0.162789i 0.909185 0.416392i \(-0.136706\pi\)
−0.815199 + 0.579181i \(0.803372\pi\)
\(968\) −1800.52 3118.59i −0.0597840 0.103549i
\(969\) 0 0
\(970\) 218.543 378.528i 0.00723402 0.0125297i
\(971\) −19612.4 −0.648188 −0.324094 0.946025i \(-0.605059\pi\)
−0.324094 + 0.946025i \(0.605059\pi\)
\(972\) 0 0
\(973\) −44757.9 −1.47469
\(974\) 364.858 631.953i 0.0120029 0.0207896i
\(975\) 0 0
\(976\) −281.821 488.129i −0.00924270 0.0160088i
\(977\) −13841.8 23974.7i −0.453264 0.785076i 0.545323 0.838226i \(-0.316407\pi\)
−0.998587 + 0.0531500i \(0.983074\pi\)
\(978\) 0 0
\(979\) −7730.14 + 13389.0i −0.252356 + 0.437093i
\(980\) −25042.8 −0.816290
\(981\) 0 0
\(982\) −2506.60 −0.0814549
\(983\) −15308.2 + 26514.6i −0.496700 + 0.860310i −0.999993 0.00380619i \(-0.998788\pi\)
0.503293 + 0.864116i \(0.332122\pi\)
\(984\) 0 0
\(985\) −8171.40 14153.3i −0.264327 0.457829i
\(986\) 1865.23 + 3230.68i 0.0602446 + 0.104347i
\(987\) 0 0
\(988\) −4633.51 + 8025.48i −0.149202 + 0.258426i
\(989\) 4590.82 0.147603
\(990\) 0 0
\(991\) −14462.4 −0.463587 −0.231793 0.972765i \(-0.574459\pi\)
−0.231793 + 0.972765i \(0.574459\pi\)
\(992\) −2682.59 + 4646.39i −0.0858593 + 0.148713i
\(993\) 0 0
\(994\) 170.576 + 295.447i 0.00544301 + 0.00942756i
\(995\) 5274.70 + 9136.05i 0.168060 + 0.291088i
\(996\) 0 0
\(997\) 3448.63 5973.20i 0.109548 0.189743i −0.806039 0.591862i \(-0.798393\pi\)
0.915587 + 0.402120i \(0.131726\pi\)
\(998\) −1222.48 −0.0387745
\(999\) 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 135.4.e.c.46.4 14
3.2 odd 2 45.4.e.c.16.4 14
9.2 odd 6 405.4.a.m.1.4 7
9.4 even 3 inner 135.4.e.c.91.4 14
9.5 odd 6 45.4.e.c.31.4 yes 14
9.7 even 3 405.4.a.n.1.4 7
15.2 even 4 225.4.k.d.124.8 28
15.8 even 4 225.4.k.d.124.7 28
15.14 odd 2 225.4.e.d.151.4 14
45.14 odd 6 225.4.e.d.76.4 14
45.23 even 12 225.4.k.d.49.8 28
45.29 odd 6 2025.4.a.bb.1.4 7
45.32 even 12 225.4.k.d.49.7 28
45.34 even 6 2025.4.a.ba.1.4 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.4.e.c.16.4 14 3.2 odd 2
45.4.e.c.31.4 yes 14 9.5 odd 6
135.4.e.c.46.4 14 1.1 even 1 trivial
135.4.e.c.91.4 14 9.4 even 3 inner
225.4.e.d.76.4 14 45.14 odd 6
225.4.e.d.151.4 14 15.14 odd 2
225.4.k.d.49.7 28 45.32 even 12
225.4.k.d.49.8 28 45.23 even 12
225.4.k.d.124.7 28 15.8 even 4
225.4.k.d.124.8 28 15.2 even 4
405.4.a.m.1.4 7 9.2 odd 6
405.4.a.n.1.4 7 9.7 even 3
2025.4.a.ba.1.4 7 45.34 even 6
2025.4.a.bb.1.4 7 45.29 odd 6