Properties

Label 363.4.a.q.1.4
Level $363$
Weight $4$
Character 363.1
Self dual yes
Analytic conductor $21.418$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [363,4,Mod(1,363)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(363, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("363.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 363.a (trivial)

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: yes
Analytic conductor: \(21.4176933321\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 28x^{2} - 2x + 72 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-4.40829\) of defining polynomial
Character \(\chi\) \(=\) 363.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4.40829 q^{2} +3.00000 q^{3} +11.4330 q^{4} +18.8997 q^{5} +13.2249 q^{6} +18.5994 q^{7} +15.1336 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+4.40829 q^{2} +3.00000 q^{3} +11.4330 q^{4} +18.8997 q^{5} +13.2249 q^{6} +18.5994 q^{7} +15.1336 q^{8} +9.00000 q^{9} +83.3152 q^{10} +34.2989 q^{12} -27.8331 q^{13} +81.9916 q^{14} +56.6991 q^{15} -24.7508 q^{16} -98.0301 q^{17} +39.6746 q^{18} -132.832 q^{19} +216.080 q^{20} +55.7983 q^{21} -180.964 q^{23} +45.4007 q^{24} +232.198 q^{25} -122.696 q^{26} +27.0000 q^{27} +212.647 q^{28} +132.665 q^{29} +249.946 q^{30} +68.7713 q^{31} -230.177 q^{32} -432.145 q^{34} +351.523 q^{35} +102.897 q^{36} +170.699 q^{37} -585.562 q^{38} -83.4993 q^{39} +286.020 q^{40} +259.000 q^{41} +245.975 q^{42} -49.1715 q^{43} +170.097 q^{45} -797.740 q^{46} -158.960 q^{47} -74.2523 q^{48} +2.93850 q^{49} +1023.60 q^{50} -294.090 q^{51} -318.215 q^{52} +471.067 q^{53} +119.024 q^{54} +281.476 q^{56} -398.496 q^{57} +584.824 q^{58} -30.9586 q^{59} +648.239 q^{60} -369.790 q^{61} +303.164 q^{62} +167.395 q^{63} -816.680 q^{64} -526.037 q^{65} +213.328 q^{67} -1120.78 q^{68} -542.891 q^{69} +1549.61 q^{70} +1120.64 q^{71} +136.202 q^{72} -49.4611 q^{73} +752.489 q^{74} +696.594 q^{75} -1518.67 q^{76} -368.089 q^{78} +615.958 q^{79} -467.782 q^{80} +81.0000 q^{81} +1141.75 q^{82} +100.520 q^{83} +637.941 q^{84} -1852.74 q^{85} -216.762 q^{86} +397.994 q^{87} -322.668 q^{89} +749.837 q^{90} -517.679 q^{91} -2068.95 q^{92} +206.314 q^{93} -700.740 q^{94} -2510.49 q^{95} -690.531 q^{96} +1153.20 q^{97} +12.9537 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{2} + 12 q^{3} + 25 q^{4} + 14 q^{5} - 3 q^{6} + 20 q^{7} - 75 q^{8} + 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - q^{2} + 12 q^{3} + 25 q^{4} + 14 q^{5} - 3 q^{6} + 20 q^{7} - 75 q^{8} + 36 q^{9} + 3 q^{10} + 75 q^{12} + 32 q^{13} + 62 q^{14} + 42 q^{15} + 289 q^{16} + 92 q^{17} - 9 q^{18} - 34 q^{19} + 391 q^{20} + 60 q^{21} - 26 q^{23} - 225 q^{24} + 334 q^{25} - 181 q^{26} + 108 q^{27} + 692 q^{28} + 174 q^{29} + 9 q^{30} + 422 q^{31} - 1271 q^{32} - 477 q^{34} - 82 q^{35} + 225 q^{36} + 518 q^{37} - 798 q^{38} + 96 q^{39} + 423 q^{40} + 428 q^{41} + 186 q^{42} - 550 q^{43} + 126 q^{45} - 2004 q^{46} + 556 q^{47} + 867 q^{48} + 282 q^{49} + 2074 q^{50} + 276 q^{51} + 467 q^{52} + 882 q^{53} - 27 q^{54} - 2112 q^{56} - 102 q^{57} - 225 q^{58} - 158 q^{59} + 1173 q^{60} + 290 q^{61} + 1142 q^{62} + 180 q^{63} + 3097 q^{64} - 1636 q^{65} + 992 q^{67} - 2033 q^{68} - 78 q^{69} + 948 q^{70} - 42 q^{71} - 675 q^{72} + 1274 q^{73} + 1509 q^{74} + 1002 q^{75} + 632 q^{76} - 543 q^{78} + 362 q^{79} + 1423 q^{80} + 324 q^{81} + 2403 q^{82} + 1500 q^{83} + 2076 q^{84} - 2388 q^{85} - 1272 q^{86} + 522 q^{87} + 1428 q^{89} + 27 q^{90} + 1750 q^{91} + 896 q^{92} + 1266 q^{93} - 1728 q^{94} - 4452 q^{95} - 3813 q^{96} + 1052 q^{97} - 615 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.40829 1.55856 0.779282 0.626673i \(-0.215584\pi\)
0.779282 + 0.626673i \(0.215584\pi\)
\(3\) 3.00000 0.577350
\(4\) 11.4330 1.42912
\(5\) 18.8997 1.69044 0.845220 0.534419i \(-0.179470\pi\)
0.845220 + 0.534419i \(0.179470\pi\)
\(6\) 13.2249 0.899838
\(7\) 18.5994 1.00427 0.502137 0.864788i \(-0.332547\pi\)
0.502137 + 0.864788i \(0.332547\pi\)
\(8\) 15.1336 0.668815
\(9\) 9.00000 0.333333
\(10\) 83.3152 2.63466
\(11\) 0 0
\(12\) 34.2989 0.825104
\(13\) −27.8331 −0.593808 −0.296904 0.954907i \(-0.595954\pi\)
−0.296904 + 0.954907i \(0.595954\pi\)
\(14\) 81.9916 1.56523
\(15\) 56.6991 0.975976
\(16\) −24.7508 −0.386731
\(17\) −98.0301 −1.39858 −0.699288 0.714840i \(-0.746500\pi\)
−0.699288 + 0.714840i \(0.746500\pi\)
\(18\) 39.6746 0.519521
\(19\) −132.832 −1.60388 −0.801942 0.597402i \(-0.796200\pi\)
−0.801942 + 0.597402i \(0.796200\pi\)
\(20\) 216.080 2.41585
\(21\) 55.7983 0.579818
\(22\) 0 0
\(23\) −180.964 −1.64059 −0.820294 0.571941i \(-0.806190\pi\)
−0.820294 + 0.571941i \(0.806190\pi\)
\(24\) 45.4007 0.386141
\(25\) 232.198 1.85758
\(26\) −122.696 −0.925489
\(27\) 27.0000 0.192450
\(28\) 212.647 1.43523
\(29\) 132.665 0.849490 0.424745 0.905313i \(-0.360364\pi\)
0.424745 + 0.905313i \(0.360364\pi\)
\(30\) 249.946 1.52112
\(31\) 68.7713 0.398442 0.199221 0.979955i \(-0.436159\pi\)
0.199221 + 0.979955i \(0.436159\pi\)
\(32\) −230.177 −1.27156
\(33\) 0 0
\(34\) −432.145 −2.17977
\(35\) 351.523 1.69766
\(36\) 102.897 0.476374
\(37\) 170.699 0.758452 0.379226 0.925304i \(-0.376190\pi\)
0.379226 + 0.925304i \(0.376190\pi\)
\(38\) −585.562 −2.49976
\(39\) −83.4993 −0.342835
\(40\) 286.020 1.13059
\(41\) 259.000 0.986561 0.493281 0.869870i \(-0.335798\pi\)
0.493281 + 0.869870i \(0.335798\pi\)
\(42\) 245.975 0.903684
\(43\) −49.1715 −0.174386 −0.0871928 0.996191i \(-0.527790\pi\)
−0.0871928 + 0.996191i \(0.527790\pi\)
\(44\) 0 0
\(45\) 170.097 0.563480
\(46\) −797.740 −2.55696
\(47\) −158.960 −0.493333 −0.246667 0.969100i \(-0.579335\pi\)
−0.246667 + 0.969100i \(0.579335\pi\)
\(48\) −74.2523 −0.223279
\(49\) 2.93850 0.00856706
\(50\) 1023.60 2.89517
\(51\) −294.090 −0.807469
\(52\) −318.215 −0.848625
\(53\) 471.067 1.22087 0.610434 0.792067i \(-0.290995\pi\)
0.610434 + 0.792067i \(0.290995\pi\)
\(54\) 119.024 0.299946
\(55\) 0 0
\(56\) 281.476 0.671674
\(57\) −398.496 −0.926003
\(58\) 584.824 1.32398
\(59\) −30.9586 −0.0683131 −0.0341565 0.999416i \(-0.510874\pi\)
−0.0341565 + 0.999416i \(0.510874\pi\)
\(60\) 648.239 1.39479
\(61\) −369.790 −0.776176 −0.388088 0.921622i \(-0.626864\pi\)
−0.388088 + 0.921622i \(0.626864\pi\)
\(62\) 303.164 0.620997
\(63\) 167.395 0.334758
\(64\) −816.680 −1.59508
\(65\) −526.037 −1.00380
\(66\) 0 0
\(67\) 213.328 0.388987 0.194493 0.980904i \(-0.437694\pi\)
0.194493 + 0.980904i \(0.437694\pi\)
\(68\) −1120.78 −1.99874
\(69\) −542.891 −0.947194
\(70\) 1549.61 2.64592
\(71\) 1120.64 1.87317 0.936584 0.350442i \(-0.113969\pi\)
0.936584 + 0.350442i \(0.113969\pi\)
\(72\) 136.202 0.222938
\(73\) −49.4611 −0.0793012 −0.0396506 0.999214i \(-0.512624\pi\)
−0.0396506 + 0.999214i \(0.512624\pi\)
\(74\) 752.489 1.18210
\(75\) 696.594 1.07248
\(76\) −1518.67 −2.29215
\(77\) 0 0
\(78\) −368.089 −0.534331
\(79\) 615.958 0.877224 0.438612 0.898677i \(-0.355470\pi\)
0.438612 + 0.898677i \(0.355470\pi\)
\(80\) −467.782 −0.653745
\(81\) 81.0000 0.111111
\(82\) 1141.75 1.53762
\(83\) 100.520 0.132933 0.0664667 0.997789i \(-0.478827\pi\)
0.0664667 + 0.997789i \(0.478827\pi\)
\(84\) 637.941 0.828631
\(85\) −1852.74 −2.36421
\(86\) −216.762 −0.271791
\(87\) 397.994 0.490453
\(88\) 0 0
\(89\) −322.668 −0.384301 −0.192150 0.981366i \(-0.561546\pi\)
−0.192150 + 0.981366i \(0.561546\pi\)
\(90\) 749.837 0.878219
\(91\) −517.679 −0.596347
\(92\) −2068.95 −2.34460
\(93\) 206.314 0.230041
\(94\) −700.740 −0.768891
\(95\) −2510.49 −2.71127
\(96\) −690.531 −0.734136
\(97\) 1153.20 1.20711 0.603553 0.797323i \(-0.293751\pi\)
0.603553 + 0.797323i \(0.293751\pi\)
\(98\) 12.9537 0.0133523
\(99\) 0 0
\(100\) 2654.72 2.65472
\(101\) 10.2583 0.0101063 0.00505317 0.999987i \(-0.498392\pi\)
0.00505317 + 0.999987i \(0.498392\pi\)
\(102\) −1296.43 −1.25849
\(103\) 316.066 0.302358 0.151179 0.988506i \(-0.451693\pi\)
0.151179 + 0.988506i \(0.451693\pi\)
\(104\) −421.214 −0.397148
\(105\) 1054.57 0.980147
\(106\) 2076.60 1.90280
\(107\) 303.527 0.274234 0.137117 0.990555i \(-0.456216\pi\)
0.137117 + 0.990555i \(0.456216\pi\)
\(108\) 308.691 0.275035
\(109\) −2073.65 −1.82220 −0.911099 0.412188i \(-0.864765\pi\)
−0.911099 + 0.412188i \(0.864765\pi\)
\(110\) 0 0
\(111\) 512.096 0.437892
\(112\) −460.350 −0.388384
\(113\) 1291.15 1.07488 0.537440 0.843302i \(-0.319391\pi\)
0.537440 + 0.843302i \(0.319391\pi\)
\(114\) −1756.69 −1.44323
\(115\) −3420.16 −2.77332
\(116\) 1516.75 1.21403
\(117\) −250.498 −0.197936
\(118\) −136.475 −0.106470
\(119\) −1823.30 −1.40455
\(120\) 858.059 0.652747
\(121\) 0 0
\(122\) −1630.14 −1.20972
\(123\) 777.000 0.569591
\(124\) 786.262 0.569422
\(125\) 2026.01 1.44969
\(126\) 737.924 0.521742
\(127\) −735.456 −0.513867 −0.256934 0.966429i \(-0.582712\pi\)
−0.256934 + 0.966429i \(0.582712\pi\)
\(128\) −1758.74 −1.21447
\(129\) −147.515 −0.100682
\(130\) −2318.92 −1.56448
\(131\) 1367.81 0.912258 0.456129 0.889914i \(-0.349235\pi\)
0.456129 + 0.889914i \(0.349235\pi\)
\(132\) 0 0
\(133\) −2470.60 −1.61074
\(134\) 940.409 0.606261
\(135\) 510.291 0.325325
\(136\) −1483.55 −0.935390
\(137\) −1784.08 −1.11259 −0.556294 0.830986i \(-0.687777\pi\)
−0.556294 + 0.830986i \(0.687777\pi\)
\(138\) −2393.22 −1.47626
\(139\) −577.559 −0.352431 −0.176216 0.984352i \(-0.556386\pi\)
−0.176216 + 0.984352i \(0.556386\pi\)
\(140\) 4018.96 2.42617
\(141\) −476.879 −0.284826
\(142\) 4940.08 2.91945
\(143\) 0 0
\(144\) −222.757 −0.128910
\(145\) 2507.32 1.43601
\(146\) −218.039 −0.123596
\(147\) 8.81550 0.00494619
\(148\) 1951.60 1.08392
\(149\) 257.866 0.141780 0.0708900 0.997484i \(-0.477416\pi\)
0.0708900 + 0.997484i \(0.477416\pi\)
\(150\) 3070.79 1.67152
\(151\) 656.364 0.353736 0.176868 0.984235i \(-0.443403\pi\)
0.176868 + 0.984235i \(0.443403\pi\)
\(152\) −2010.22 −1.07270
\(153\) −882.271 −0.466192
\(154\) 0 0
\(155\) 1299.76 0.673542
\(156\) −954.646 −0.489954
\(157\) 3016.25 1.53327 0.766634 0.642084i \(-0.221930\pi\)
0.766634 + 0.642084i \(0.221930\pi\)
\(158\) 2715.32 1.36721
\(159\) 1413.20 0.704868
\(160\) −4350.27 −2.14950
\(161\) −3365.82 −1.64760
\(162\) 357.071 0.173174
\(163\) 668.898 0.321424 0.160712 0.987001i \(-0.448621\pi\)
0.160712 + 0.987001i \(0.448621\pi\)
\(164\) 2961.14 1.40992
\(165\) 0 0
\(166\) 443.120 0.207185
\(167\) −293.314 −0.135912 −0.0679560 0.997688i \(-0.521648\pi\)
−0.0679560 + 0.997688i \(0.521648\pi\)
\(168\) 844.427 0.387791
\(169\) −1422.32 −0.647392
\(170\) −8167.40 −3.68477
\(171\) −1195.49 −0.534628
\(172\) −562.177 −0.249219
\(173\) −1283.75 −0.564170 −0.282085 0.959389i \(-0.591026\pi\)
−0.282085 + 0.959389i \(0.591026\pi\)
\(174\) 1754.47 0.764403
\(175\) 4318.75 1.86552
\(176\) 0 0
\(177\) −92.8759 −0.0394406
\(178\) −1422.41 −0.598957
\(179\) −1224.08 −0.511130 −0.255565 0.966792i \(-0.582261\pi\)
−0.255565 + 0.966792i \(0.582261\pi\)
\(180\) 1944.72 0.805282
\(181\) 3386.04 1.39051 0.695256 0.718763i \(-0.255291\pi\)
0.695256 + 0.718763i \(0.255291\pi\)
\(182\) −2282.08 −0.929445
\(183\) −1109.37 −0.448125
\(184\) −2738.63 −1.09725
\(185\) 3226.15 1.28212
\(186\) 909.491 0.358533
\(187\) 0 0
\(188\) −1817.38 −0.705034
\(189\) 502.184 0.193273
\(190\) −11066.9 −4.22568
\(191\) −4124.15 −1.56237 −0.781185 0.624299i \(-0.785385\pi\)
−0.781185 + 0.624299i \(0.785385\pi\)
\(192\) −2450.04 −0.920919
\(193\) 1714.28 0.639362 0.319681 0.947525i \(-0.396424\pi\)
0.319681 + 0.947525i \(0.396424\pi\)
\(194\) 5083.62 1.88135
\(195\) −1578.11 −0.579543
\(196\) 33.5958 0.0122434
\(197\) −1288.77 −0.466098 −0.233049 0.972465i \(-0.574870\pi\)
−0.233049 + 0.972465i \(0.574870\pi\)
\(198\) 0 0
\(199\) −3577.10 −1.27424 −0.637120 0.770765i \(-0.719874\pi\)
−0.637120 + 0.770765i \(0.719874\pi\)
\(200\) 3513.98 1.24238
\(201\) 639.983 0.224582
\(202\) 45.2216 0.0157514
\(203\) 2467.49 0.853121
\(204\) −3362.33 −1.15397
\(205\) 4895.02 1.66772
\(206\) 1393.31 0.471245
\(207\) −1628.67 −0.546863
\(208\) 688.891 0.229644
\(209\) 0 0
\(210\) 4648.84 1.52762
\(211\) 4130.08 1.34752 0.673760 0.738950i \(-0.264678\pi\)
0.673760 + 0.738950i \(0.264678\pi\)
\(212\) 5385.70 1.74477
\(213\) 3361.91 1.08147
\(214\) 1338.03 0.427411
\(215\) −929.326 −0.294788
\(216\) 408.606 0.128714
\(217\) 1279.11 0.400145
\(218\) −9141.24 −2.84001
\(219\) −148.383 −0.0457846
\(220\) 0 0
\(221\) 2728.48 0.830487
\(222\) 2257.47 0.682483
\(223\) 959.958 0.288267 0.144134 0.989558i \(-0.453961\pi\)
0.144134 + 0.989558i \(0.453961\pi\)
\(224\) −4281.16 −1.27700
\(225\) 2089.78 0.619195
\(226\) 5691.77 1.67527
\(227\) −480.415 −0.140468 −0.0702340 0.997531i \(-0.522375\pi\)
−0.0702340 + 0.997531i \(0.522375\pi\)
\(228\) −4556.00 −1.32337
\(229\) 4323.55 1.24763 0.623817 0.781570i \(-0.285581\pi\)
0.623817 + 0.781570i \(0.285581\pi\)
\(230\) −15077.0 −4.32239
\(231\) 0 0
\(232\) 2007.69 0.568152
\(233\) 565.768 0.159076 0.0795380 0.996832i \(-0.474655\pi\)
0.0795380 + 0.996832i \(0.474655\pi\)
\(234\) −1104.27 −0.308496
\(235\) −3004.29 −0.833950
\(236\) −353.950 −0.0976278
\(237\) 1847.87 0.506466
\(238\) −8037.65 −2.18909
\(239\) −5085.43 −1.37636 −0.688178 0.725542i \(-0.741589\pi\)
−0.688178 + 0.725542i \(0.741589\pi\)
\(240\) −1403.35 −0.377440
\(241\) 2710.26 0.724412 0.362206 0.932098i \(-0.382024\pi\)
0.362206 + 0.932098i \(0.382024\pi\)
\(242\) 0 0
\(243\) 243.000 0.0641500
\(244\) −4227.80 −1.10925
\(245\) 55.5367 0.0144821
\(246\) 3425.24 0.887745
\(247\) 3697.13 0.952400
\(248\) 1040.76 0.266484
\(249\) 301.559 0.0767492
\(250\) 8931.23 2.25944
\(251\) −5422.24 −1.36354 −0.681771 0.731566i \(-0.738790\pi\)
−0.681771 + 0.731566i \(0.738790\pi\)
\(252\) 1913.82 0.478410
\(253\) 0 0
\(254\) −3242.10 −0.800896
\(255\) −5558.22 −1.36498
\(256\) −1219.60 −0.297753
\(257\) −5600.61 −1.35936 −0.679682 0.733507i \(-0.737882\pi\)
−0.679682 + 0.733507i \(0.737882\pi\)
\(258\) −650.286 −0.156919
\(259\) 3174.90 0.761694
\(260\) −6014.17 −1.43455
\(261\) 1193.98 0.283163
\(262\) 6029.68 1.42181
\(263\) −868.505 −0.203629 −0.101814 0.994803i \(-0.532465\pi\)
−0.101814 + 0.994803i \(0.532465\pi\)
\(264\) 0 0
\(265\) 8903.01 2.06380
\(266\) −10891.1 −2.51044
\(267\) −968.004 −0.221876
\(268\) 2438.97 0.555910
\(269\) −4466.34 −1.01233 −0.506167 0.862436i \(-0.668938\pi\)
−0.506167 + 0.862436i \(0.668938\pi\)
\(270\) 2249.51 0.507040
\(271\) −6916.04 −1.55026 −0.775129 0.631803i \(-0.782315\pi\)
−0.775129 + 0.631803i \(0.782315\pi\)
\(272\) 2426.32 0.540873
\(273\) −1553.04 −0.344301
\(274\) −7864.75 −1.73404
\(275\) 0 0
\(276\) −6206.86 −1.35366
\(277\) −2896.34 −0.628247 −0.314123 0.949382i \(-0.601711\pi\)
−0.314123 + 0.949382i \(0.601711\pi\)
\(278\) −2546.04 −0.549286
\(279\) 618.942 0.132814
\(280\) 5319.80 1.13542
\(281\) 4248.88 0.902017 0.451009 0.892520i \(-0.351064\pi\)
0.451009 + 0.892520i \(0.351064\pi\)
\(282\) −2102.22 −0.443920
\(283\) −702.330 −0.147524 −0.0737618 0.997276i \(-0.523500\pi\)
−0.0737618 + 0.997276i \(0.523500\pi\)
\(284\) 12812.2 2.67699
\(285\) −7531.46 −1.56535
\(286\) 0 0
\(287\) 4817.25 0.990778
\(288\) −2071.59 −0.423853
\(289\) 4696.91 0.956017
\(290\) 11053.0 2.23812
\(291\) 3459.59 0.696923
\(292\) −565.488 −0.113331
\(293\) 2901.05 0.578434 0.289217 0.957264i \(-0.406605\pi\)
0.289217 + 0.957264i \(0.406605\pi\)
\(294\) 38.8612 0.00770896
\(295\) −585.109 −0.115479
\(296\) 2583.28 0.507264
\(297\) 0 0
\(298\) 1136.75 0.220973
\(299\) 5036.78 0.974196
\(300\) 7964.15 1.53270
\(301\) −914.561 −0.175131
\(302\) 2893.44 0.551321
\(303\) 30.7750 0.00583490
\(304\) 3287.70 0.620271
\(305\) −6988.91 −1.31208
\(306\) −3889.30 −0.726591
\(307\) 6229.17 1.15804 0.579019 0.815314i \(-0.303436\pi\)
0.579019 + 0.815314i \(0.303436\pi\)
\(308\) 0 0
\(309\) 948.198 0.174567
\(310\) 5729.70 1.04976
\(311\) 290.145 0.0529022 0.0264511 0.999650i \(-0.491579\pi\)
0.0264511 + 0.999650i \(0.491579\pi\)
\(312\) −1263.64 −0.229294
\(313\) −679.981 −0.122795 −0.0613975 0.998113i \(-0.519556\pi\)
−0.0613975 + 0.998113i \(0.519556\pi\)
\(314\) 13296.5 2.38970
\(315\) 3163.71 0.565888
\(316\) 7042.24 1.25366
\(317\) −6331.04 −1.12172 −0.560862 0.827909i \(-0.689530\pi\)
−0.560862 + 0.827909i \(0.689530\pi\)
\(318\) 6229.79 1.09858
\(319\) 0 0
\(320\) −15435.0 −2.69638
\(321\) 910.580 0.158329
\(322\) −14837.5 −2.56789
\(323\) 13021.6 2.24315
\(324\) 926.072 0.158791
\(325\) −6462.79 −1.10305
\(326\) 2948.69 0.500960
\(327\) −6220.95 −1.05205
\(328\) 3919.59 0.659827
\(329\) −2956.56 −0.495442
\(330\) 0 0
\(331\) 267.631 0.0444420 0.0222210 0.999753i \(-0.492926\pi\)
0.0222210 + 0.999753i \(0.492926\pi\)
\(332\) 1149.24 0.189978
\(333\) 1536.29 0.252817
\(334\) −1293.01 −0.211828
\(335\) 4031.82 0.657558
\(336\) −1381.05 −0.224234
\(337\) 10560.7 1.70706 0.853531 0.521042i \(-0.174457\pi\)
0.853531 + 0.521042i \(0.174457\pi\)
\(338\) −6269.99 −1.00900
\(339\) 3873.46 0.620582
\(340\) −21182.3 −3.37874
\(341\) 0 0
\(342\) −5270.06 −0.833252
\(343\) −6324.95 −0.995671
\(344\) −744.140 −0.116632
\(345\) −10260.5 −1.60117
\(346\) −5659.12 −0.879296
\(347\) 479.283 0.0741478 0.0370739 0.999313i \(-0.488196\pi\)
0.0370739 + 0.999313i \(0.488196\pi\)
\(348\) 4550.26 0.700918
\(349\) 8529.68 1.30826 0.654131 0.756381i \(-0.273035\pi\)
0.654131 + 0.756381i \(0.273035\pi\)
\(350\) 19038.3 2.90754
\(351\) −751.493 −0.114278
\(352\) 0 0
\(353\) 5098.22 0.768700 0.384350 0.923188i \(-0.374426\pi\)
0.384350 + 0.923188i \(0.374426\pi\)
\(354\) −409.424 −0.0614707
\(355\) 21179.7 3.16648
\(356\) −3689.06 −0.549213
\(357\) −5469.91 −0.810920
\(358\) −5396.10 −0.796628
\(359\) 12979.3 1.90814 0.954071 0.299581i \(-0.0968467\pi\)
0.954071 + 0.299581i \(0.0968467\pi\)
\(360\) 2574.18 0.376864
\(361\) 10785.4 1.57244
\(362\) 14926.6 2.16720
\(363\) 0 0
\(364\) −5918.62 −0.852253
\(365\) −934.800 −0.134054
\(366\) −4890.42 −0.698432
\(367\) 2113.99 0.300680 0.150340 0.988634i \(-0.451963\pi\)
0.150340 + 0.988634i \(0.451963\pi\)
\(368\) 4478.99 0.634466
\(369\) 2331.00 0.328854
\(370\) 14221.8 1.99826
\(371\) 8761.57 1.22609
\(372\) 2358.78 0.328756
\(373\) 9600.73 1.33273 0.666363 0.745627i \(-0.267850\pi\)
0.666363 + 0.745627i \(0.267850\pi\)
\(374\) 0 0
\(375\) 6078.03 0.836982
\(376\) −2405.63 −0.329949
\(377\) −3692.47 −0.504434
\(378\) 2213.77 0.301228
\(379\) −13629.6 −1.84725 −0.923623 0.383302i \(-0.874787\pi\)
−0.923623 + 0.383302i \(0.874787\pi\)
\(380\) −28702.3 −3.87473
\(381\) −2206.37 −0.296682
\(382\) −18180.4 −2.43505
\(383\) −6751.22 −0.900708 −0.450354 0.892850i \(-0.648702\pi\)
−0.450354 + 0.892850i \(0.648702\pi\)
\(384\) −5276.23 −0.701175
\(385\) 0 0
\(386\) 7557.05 0.996487
\(387\) −442.544 −0.0581286
\(388\) 13184.5 1.72510
\(389\) −10469.5 −1.36459 −0.682297 0.731075i \(-0.739019\pi\)
−0.682297 + 0.731075i \(0.739019\pi\)
\(390\) −6956.76 −0.903254
\(391\) 17739.9 2.29449
\(392\) 44.4700 0.00572978
\(393\) 4103.42 0.526693
\(394\) −5681.29 −0.726444
\(395\) 11641.4 1.48289
\(396\) 0 0
\(397\) −13399.2 −1.69392 −0.846959 0.531658i \(-0.821569\pi\)
−0.846959 + 0.531658i \(0.821569\pi\)
\(398\) −15768.9 −1.98598
\(399\) −7411.80 −0.929961
\(400\) −5747.08 −0.718385
\(401\) 5533.31 0.689079 0.344539 0.938772i \(-0.388035\pi\)
0.344539 + 0.938772i \(0.388035\pi\)
\(402\) 2821.23 0.350025
\(403\) −1914.12 −0.236598
\(404\) 117.283 0.0144432
\(405\) 1530.87 0.187827
\(406\) 10877.4 1.32964
\(407\) 0 0
\(408\) −4450.64 −0.540047
\(409\) 12995.5 1.57111 0.785556 0.618791i \(-0.212377\pi\)
0.785556 + 0.618791i \(0.212377\pi\)
\(410\) 21578.6 2.59925
\(411\) −5352.25 −0.642353
\(412\) 3613.58 0.432107
\(413\) −575.813 −0.0686051
\(414\) −7179.66 −0.852321
\(415\) 1899.79 0.224716
\(416\) 6406.54 0.755063
\(417\) −1732.68 −0.203476
\(418\) 0 0
\(419\) −9868.79 −1.15065 −0.575325 0.817925i \(-0.695124\pi\)
−0.575325 + 0.817925i \(0.695124\pi\)
\(420\) 12056.9 1.40075
\(421\) −10279.6 −1.19001 −0.595007 0.803721i \(-0.702851\pi\)
−0.595007 + 0.803721i \(0.702851\pi\)
\(422\) 18206.6 2.10020
\(423\) −1430.64 −0.164444
\(424\) 7128.92 0.816535
\(425\) −22762.4 −2.59797
\(426\) 14820.2 1.68555
\(427\) −6877.87 −0.779493
\(428\) 3470.21 0.391914
\(429\) 0 0
\(430\) −4096.73 −0.459447
\(431\) 7446.31 0.832195 0.416097 0.909320i \(-0.363398\pi\)
0.416097 + 0.909320i \(0.363398\pi\)
\(432\) −668.271 −0.0744264
\(433\) 17086.2 1.89632 0.948162 0.317788i \(-0.102940\pi\)
0.948162 + 0.317788i \(0.102940\pi\)
\(434\) 5638.67 0.623652
\(435\) 7521.96 0.829081
\(436\) −23708.0 −2.60414
\(437\) 24037.8 2.63131
\(438\) −654.116 −0.0713582
\(439\) −11144.4 −1.21160 −0.605798 0.795618i \(-0.707146\pi\)
−0.605798 + 0.795618i \(0.707146\pi\)
\(440\) 0 0
\(441\) 26.4465 0.00285569
\(442\) 12027.9 1.29437
\(443\) 1782.31 0.191151 0.0955757 0.995422i \(-0.469531\pi\)
0.0955757 + 0.995422i \(0.469531\pi\)
\(444\) 5854.79 0.625802
\(445\) −6098.32 −0.649637
\(446\) 4231.77 0.449283
\(447\) 773.599 0.0818568
\(448\) −15189.8 −1.60190
\(449\) −7635.66 −0.802559 −0.401279 0.915956i \(-0.631434\pi\)
−0.401279 + 0.915956i \(0.631434\pi\)
\(450\) 9212.36 0.965055
\(451\) 0 0
\(452\) 14761.7 1.53614
\(453\) 1969.09 0.204230
\(454\) −2117.81 −0.218929
\(455\) −9783.98 −1.00809
\(456\) −6030.67 −0.619325
\(457\) −14026.3 −1.43572 −0.717859 0.696189i \(-0.754878\pi\)
−0.717859 + 0.696189i \(0.754878\pi\)
\(458\) 19059.4 1.94452
\(459\) −2646.81 −0.269156
\(460\) −39102.6 −3.96341
\(461\) −6675.99 −0.674472 −0.337236 0.941420i \(-0.609492\pi\)
−0.337236 + 0.941420i \(0.609492\pi\)
\(462\) 0 0
\(463\) −4588.01 −0.460525 −0.230262 0.973129i \(-0.573958\pi\)
−0.230262 + 0.973129i \(0.573958\pi\)
\(464\) −3283.55 −0.328524
\(465\) 3899.27 0.388869
\(466\) 2494.07 0.247930
\(467\) 6034.02 0.597903 0.298952 0.954268i \(-0.403363\pi\)
0.298952 + 0.954268i \(0.403363\pi\)
\(468\) −2863.94 −0.282875
\(469\) 3967.77 0.390649
\(470\) −13243.8 −1.29976
\(471\) 9048.76 0.885233
\(472\) −468.515 −0.0456889
\(473\) 0 0
\(474\) 8145.96 0.789359
\(475\) −30843.4 −2.97935
\(476\) −20845.8 −2.00728
\(477\) 4239.60 0.406956
\(478\) −22418.0 −2.14514
\(479\) −3123.36 −0.297933 −0.148967 0.988842i \(-0.547595\pi\)
−0.148967 + 0.988842i \(0.547595\pi\)
\(480\) −13050.8 −1.24101
\(481\) −4751.08 −0.450375
\(482\) 11947.6 1.12904
\(483\) −10097.5 −0.951243
\(484\) 0 0
\(485\) 21795.0 2.04054
\(486\) 1071.21 0.0999819
\(487\) 3592.75 0.334298 0.167149 0.985932i \(-0.446544\pi\)
0.167149 + 0.985932i \(0.446544\pi\)
\(488\) −5596.24 −0.519118
\(489\) 2006.69 0.185574
\(490\) 244.822 0.0225713
\(491\) −2578.80 −0.237025 −0.118513 0.992953i \(-0.537813\pi\)
−0.118513 + 0.992953i \(0.537813\pi\)
\(492\) 8883.43 0.814016
\(493\) −13005.1 −1.18808
\(494\) 16298.0 1.48438
\(495\) 0 0
\(496\) −1702.14 −0.154090
\(497\) 20843.2 1.88118
\(498\) 1329.36 0.119619
\(499\) −8110.99 −0.727651 −0.363825 0.931467i \(-0.618530\pi\)
−0.363825 + 0.931467i \(0.618530\pi\)
\(500\) 23163.3 2.07179
\(501\) −879.941 −0.0784688
\(502\) −23902.8 −2.12517
\(503\) −18187.9 −1.61224 −0.806122 0.591749i \(-0.798438\pi\)
−0.806122 + 0.591749i \(0.798438\pi\)
\(504\) 2533.28 0.223891
\(505\) 193.879 0.0170842
\(506\) 0 0
\(507\) −4266.96 −0.373772
\(508\) −8408.46 −0.734380
\(509\) −14040.4 −1.22265 −0.611326 0.791379i \(-0.709364\pi\)
−0.611326 + 0.791379i \(0.709364\pi\)
\(510\) −24502.2 −2.12740
\(511\) −919.948 −0.0796402
\(512\) 8693.60 0.750403
\(513\) −3586.47 −0.308668
\(514\) −24689.1 −2.11866
\(515\) 5973.55 0.511119
\(516\) −1686.53 −0.143886
\(517\) 0 0
\(518\) 13995.9 1.18715
\(519\) −3851.24 −0.325724
\(520\) −7960.81 −0.671355
\(521\) −4484.21 −0.377076 −0.188538 0.982066i \(-0.560375\pi\)
−0.188538 + 0.982066i \(0.560375\pi\)
\(522\) 5263.41 0.441328
\(523\) −7546.44 −0.630943 −0.315471 0.948935i \(-0.602163\pi\)
−0.315471 + 0.948935i \(0.602163\pi\)
\(524\) 15638.1 1.30373
\(525\) 12956.2 1.07706
\(526\) −3828.62 −0.317368
\(527\) −6741.66 −0.557251
\(528\) 0 0
\(529\) 20580.9 1.69153
\(530\) 39247.0 3.21657
\(531\) −278.628 −0.0227710
\(532\) −28246.3 −2.30194
\(533\) −7208.77 −0.585828
\(534\) −4267.24 −0.345808
\(535\) 5736.56 0.463576
\(536\) 3228.41 0.260160
\(537\) −3672.25 −0.295101
\(538\) −19688.9 −1.57779
\(539\) 0 0
\(540\) 5834.15 0.464930
\(541\) 731.644 0.0581439 0.0290719 0.999577i \(-0.490745\pi\)
0.0290719 + 0.999577i \(0.490745\pi\)
\(542\) −30487.9 −2.41618
\(543\) 10158.1 0.802812
\(544\) 22564.3 1.77837
\(545\) −39191.3 −3.08031
\(546\) −6846.24 −0.536615
\(547\) 1251.69 0.0978398 0.0489199 0.998803i \(-0.484422\pi\)
0.0489199 + 0.998803i \(0.484422\pi\)
\(548\) −20397.4 −1.59002
\(549\) −3328.11 −0.258725
\(550\) 0 0
\(551\) −17622.1 −1.36248
\(552\) −8215.88 −0.633498
\(553\) 11456.5 0.880974
\(554\) −12767.9 −0.979163
\(555\) 9678.46 0.740230
\(556\) −6603.22 −0.503667
\(557\) 10604.2 0.806666 0.403333 0.915053i \(-0.367852\pi\)
0.403333 + 0.915053i \(0.367852\pi\)
\(558\) 2728.47 0.206999
\(559\) 1368.59 0.103552
\(560\) −8700.47 −0.656539
\(561\) 0 0
\(562\) 18730.3 1.40585
\(563\) −22493.4 −1.68381 −0.841904 0.539627i \(-0.818565\pi\)
−0.841904 + 0.539627i \(0.818565\pi\)
\(564\) −5452.15 −0.407051
\(565\) 24402.4 1.81702
\(566\) −3096.07 −0.229925
\(567\) 1506.55 0.111586
\(568\) 16959.2 1.25280
\(569\) −19837.1 −1.46154 −0.730770 0.682624i \(-0.760839\pi\)
−0.730770 + 0.682624i \(0.760839\pi\)
\(570\) −33200.8 −2.43970
\(571\) 2777.51 0.203565 0.101782 0.994807i \(-0.467545\pi\)
0.101782 + 0.994807i \(0.467545\pi\)
\(572\) 0 0
\(573\) −12372.4 −0.902035
\(574\) 21235.8 1.54419
\(575\) −42019.4 −3.04753
\(576\) −7350.12 −0.531693
\(577\) 16236.1 1.17143 0.585716 0.810516i \(-0.300813\pi\)
0.585716 + 0.810516i \(0.300813\pi\)
\(578\) 20705.3 1.49001
\(579\) 5142.85 0.369136
\(580\) 28666.1 2.05224
\(581\) 1869.61 0.133502
\(582\) 15250.9 1.08620
\(583\) 0 0
\(584\) −748.523 −0.0530379
\(585\) −4734.33 −0.334599
\(586\) 12788.7 0.901527
\(587\) −1800.96 −0.126633 −0.0633166 0.997993i \(-0.520168\pi\)
−0.0633166 + 0.997993i \(0.520168\pi\)
\(588\) 100.787 0.00706872
\(589\) −9135.04 −0.639054
\(590\) −2579.33 −0.179982
\(591\) −3866.32 −0.269102
\(592\) −4224.93 −0.293317
\(593\) 1156.37 0.0800782 0.0400391 0.999198i \(-0.487252\pi\)
0.0400391 + 0.999198i \(0.487252\pi\)
\(594\) 0 0
\(595\) −34459.9 −2.37431
\(596\) 2948.18 0.202621
\(597\) −10731.3 −0.735683
\(598\) 22203.6 1.51835
\(599\) 9085.22 0.619720 0.309860 0.950782i \(-0.399718\pi\)
0.309860 + 0.950782i \(0.399718\pi\)
\(600\) 10542.0 0.717289
\(601\) 3920.94 0.266121 0.133060 0.991108i \(-0.457520\pi\)
0.133060 + 0.991108i \(0.457520\pi\)
\(602\) −4031.65 −0.272953
\(603\) 1919.95 0.129662
\(604\) 7504.20 0.505532
\(605\) 0 0
\(606\) 135.665 0.00909407
\(607\) 2049.62 0.137054 0.0685268 0.997649i \(-0.478170\pi\)
0.0685268 + 0.997649i \(0.478170\pi\)
\(608\) 30574.9 2.03943
\(609\) 7402.46 0.492550
\(610\) −30809.1 −2.04496
\(611\) 4424.34 0.292945
\(612\) −10087.0 −0.666246
\(613\) −13468.5 −0.887418 −0.443709 0.896171i \(-0.646338\pi\)
−0.443709 + 0.896171i \(0.646338\pi\)
\(614\) 27460.0 1.80488
\(615\) 14685.1 0.962860
\(616\) 0 0
\(617\) 4767.00 0.311041 0.155520 0.987833i \(-0.450295\pi\)
0.155520 + 0.987833i \(0.450295\pi\)
\(618\) 4179.93 0.272074
\(619\) −14114.9 −0.916519 −0.458260 0.888818i \(-0.651527\pi\)
−0.458260 + 0.888818i \(0.651527\pi\)
\(620\) 14860.1 0.962574
\(621\) −4886.02 −0.315731
\(622\) 1279.04 0.0824516
\(623\) −6001.44 −0.385943
\(624\) 2066.67 0.132585
\(625\) 9266.19 0.593036
\(626\) −2997.55 −0.191384
\(627\) 0 0
\(628\) 34484.8 2.19123
\(629\) −16733.6 −1.06075
\(630\) 13946.5 0.881973
\(631\) 12693.1 0.800797 0.400398 0.916341i \(-0.368872\pi\)
0.400398 + 0.916341i \(0.368872\pi\)
\(632\) 9321.64 0.586701
\(633\) 12390.3 0.777991
\(634\) −27909.0 −1.74828
\(635\) −13899.9 −0.868662
\(636\) 16157.1 1.00734
\(637\) −81.7875 −0.00508719
\(638\) 0 0
\(639\) 10085.7 0.624390
\(640\) −33239.7 −2.05299
\(641\) 21268.0 1.31051 0.655253 0.755410i \(-0.272562\pi\)
0.655253 + 0.755410i \(0.272562\pi\)
\(642\) 4014.10 0.246766
\(643\) −17821.4 −1.09301 −0.546506 0.837455i \(-0.684042\pi\)
−0.546506 + 0.837455i \(0.684042\pi\)
\(644\) −38481.4 −2.35462
\(645\) −2787.98 −0.170196
\(646\) 57402.7 3.49610
\(647\) 10189.2 0.619134 0.309567 0.950878i \(-0.399816\pi\)
0.309567 + 0.950878i \(0.399816\pi\)
\(648\) 1225.82 0.0743128
\(649\) 0 0
\(650\) −28489.8 −1.71917
\(651\) 3837.32 0.231024
\(652\) 7647.49 0.459354
\(653\) 1296.95 0.0777236 0.0388618 0.999245i \(-0.487627\pi\)
0.0388618 + 0.999245i \(0.487627\pi\)
\(654\) −27423.7 −1.63968
\(655\) 25851.1 1.54212
\(656\) −6410.45 −0.381534
\(657\) −445.150 −0.0264337
\(658\) −13033.4 −0.772178
\(659\) 23407.1 1.38363 0.691815 0.722074i \(-0.256811\pi\)
0.691815 + 0.722074i \(0.256811\pi\)
\(660\) 0 0
\(661\) 1486.35 0.0874621 0.0437310 0.999043i \(-0.486076\pi\)
0.0437310 + 0.999043i \(0.486076\pi\)
\(662\) 1179.79 0.0692658
\(663\) 8185.45 0.479482
\(664\) 1521.22 0.0889079
\(665\) −46693.6 −2.72286
\(666\) 6772.40 0.394032
\(667\) −24007.5 −1.39366
\(668\) −3353.45 −0.194235
\(669\) 2879.87 0.166431
\(670\) 17773.4 1.02485
\(671\) 0 0
\(672\) −12843.5 −0.737274
\(673\) 26974.0 1.54498 0.772490 0.635027i \(-0.219011\pi\)
0.772490 + 0.635027i \(0.219011\pi\)
\(674\) 46554.7 2.66057
\(675\) 6269.35 0.357492
\(676\) −16261.3 −0.925202
\(677\) −27230.7 −1.54588 −0.772940 0.634479i \(-0.781215\pi\)
−0.772940 + 0.634479i \(0.781215\pi\)
\(678\) 17075.3 0.967217
\(679\) 21448.8 1.21227
\(680\) −28038.5 −1.58122
\(681\) −1441.24 −0.0810993
\(682\) 0 0
\(683\) −27178.2 −1.52261 −0.761306 0.648392i \(-0.775442\pi\)
−0.761306 + 0.648392i \(0.775442\pi\)
\(684\) −13668.0 −0.764049
\(685\) −33718.6 −1.88076
\(686\) −27882.2 −1.55182
\(687\) 12970.7 0.720322
\(688\) 1217.03 0.0674403
\(689\) −13111.2 −0.724961
\(690\) −45231.1 −2.49553
\(691\) 29234.1 1.60943 0.804716 0.593661i \(-0.202318\pi\)
0.804716 + 0.593661i \(0.202318\pi\)
\(692\) −14677.1 −0.806269
\(693\) 0 0
\(694\) 2112.82 0.115564
\(695\) −10915.7 −0.595763
\(696\) 6023.07 0.328023
\(697\) −25389.8 −1.37978
\(698\) 37601.3 2.03901
\(699\) 1697.30 0.0918426
\(700\) 49376.2 2.66606
\(701\) 36490.5 1.96609 0.983043 0.183374i \(-0.0587018\pi\)
0.983043 + 0.183374i \(0.0587018\pi\)
\(702\) −3312.80 −0.178110
\(703\) −22674.3 −1.21647
\(704\) 0 0
\(705\) −9012.87 −0.481481
\(706\) 22474.4 1.19807
\(707\) 190.799 0.0101495
\(708\) −1061.85 −0.0563654
\(709\) 17000.6 0.900524 0.450262 0.892896i \(-0.351331\pi\)
0.450262 + 0.892896i \(0.351331\pi\)
\(710\) 93366.0 4.93516
\(711\) 5543.62 0.292408
\(712\) −4883.12 −0.257026
\(713\) −12445.1 −0.653679
\(714\) −24112.9 −1.26387
\(715\) 0 0
\(716\) −13994.9 −0.730467
\(717\) −15256.3 −0.794639
\(718\) 57216.6 2.97396
\(719\) 11795.2 0.611806 0.305903 0.952063i \(-0.401042\pi\)
0.305903 + 0.952063i \(0.401042\pi\)
\(720\) −4210.04 −0.217915
\(721\) 5878.65 0.303651
\(722\) 47545.0 2.45075
\(723\) 8130.79 0.418240
\(724\) 38712.6 1.98721
\(725\) 30804.5 1.57800
\(726\) 0 0
\(727\) −23337.0 −1.19054 −0.595269 0.803526i \(-0.702955\pi\)
−0.595269 + 0.803526i \(0.702955\pi\)
\(728\) −7834.33 −0.398846
\(729\) 729.000 0.0370370
\(730\) −4120.86 −0.208932
\(731\) 4820.29 0.243892
\(732\) −12683.4 −0.640426
\(733\) 22902.2 1.15404 0.577021 0.816729i \(-0.304215\pi\)
0.577021 + 0.816729i \(0.304215\pi\)
\(734\) 9319.08 0.468629
\(735\) 166.610 0.00836124
\(736\) 41653.7 2.08611
\(737\) 0 0
\(738\) 10275.7 0.512540
\(739\) 20796.9 1.03522 0.517610 0.855617i \(-0.326822\pi\)
0.517610 + 0.855617i \(0.326822\pi\)
\(740\) 36884.6 1.83230
\(741\) 11091.4 0.549868
\(742\) 38623.5 1.91093
\(743\) −26448.0 −1.30590 −0.652948 0.757402i \(-0.726468\pi\)
−0.652948 + 0.757402i \(0.726468\pi\)
\(744\) 3122.27 0.153855
\(745\) 4873.59 0.239671
\(746\) 42322.7 2.07714
\(747\) 904.678 0.0443112
\(748\) 0 0
\(749\) 5645.42 0.275406
\(750\) 26793.7 1.30449
\(751\) −20835.8 −1.01240 −0.506199 0.862417i \(-0.668950\pi\)
−0.506199 + 0.862417i \(0.668950\pi\)
\(752\) 3934.38 0.190787
\(753\) −16266.7 −0.787241
\(754\) −16277.4 −0.786193
\(755\) 12405.1 0.597970
\(756\) 5741.47 0.276210
\(757\) 36359.3 1.74571 0.872853 0.487983i \(-0.162267\pi\)
0.872853 + 0.487983i \(0.162267\pi\)
\(758\) −60083.2 −2.87905
\(759\) 0 0
\(760\) −37992.6 −1.81334
\(761\) 16656.1 0.793409 0.396704 0.917946i \(-0.370154\pi\)
0.396704 + 0.917946i \(0.370154\pi\)
\(762\) −9726.30 −0.462397
\(763\) −38568.7 −1.82999
\(764\) −47151.3 −2.23282
\(765\) −16674.6 −0.788070
\(766\) −29761.3 −1.40381
\(767\) 861.675 0.0405649
\(768\) −3658.79 −0.171908
\(769\) −32370.5 −1.51796 −0.758979 0.651115i \(-0.774302\pi\)
−0.758979 + 0.651115i \(0.774302\pi\)
\(770\) 0 0
\(771\) −16801.8 −0.784830
\(772\) 19599.4 0.913727
\(773\) −15812.2 −0.735736 −0.367868 0.929878i \(-0.619912\pi\)
−0.367868 + 0.929878i \(0.619912\pi\)
\(774\) −1950.86 −0.0905971
\(775\) 15968.6 0.740139
\(776\) 17452.0 0.807332
\(777\) 9524.70 0.439764
\(778\) −46152.7 −2.12681
\(779\) −34403.5 −1.58233
\(780\) −18042.5 −0.828237
\(781\) 0 0
\(782\) 78202.5 3.57611
\(783\) 3581.95 0.163484
\(784\) −72.7302 −0.00331315
\(785\) 57006.2 2.59190
\(786\) 18089.1 0.820884
\(787\) 18133.5 0.821332 0.410666 0.911786i \(-0.365296\pi\)
0.410666 + 0.911786i \(0.365296\pi\)
\(788\) −14734.5 −0.666112
\(789\) −2605.52 −0.117565
\(790\) 51318.7 2.31119
\(791\) 24014.7 1.07947
\(792\) 0 0
\(793\) 10292.4 0.460900
\(794\) −59067.4 −2.64008
\(795\) 26709.0 1.19154
\(796\) −40896.9 −1.82104
\(797\) −1704.11 −0.0757375 −0.0378687 0.999283i \(-0.512057\pi\)
−0.0378687 + 0.999283i \(0.512057\pi\)
\(798\) −32673.3 −1.44940
\(799\) 15582.8 0.689964
\(800\) −53446.7 −2.36203
\(801\) −2904.01 −0.128100
\(802\) 24392.4 1.07397
\(803\) 0 0
\(804\) 7316.91 0.320955
\(805\) −63612.9 −2.78517
\(806\) −8437.98 −0.368753
\(807\) −13399.0 −0.584471
\(808\) 155.245 0.00675928
\(809\) 43338.8 1.88345 0.941726 0.336382i \(-0.109203\pi\)
0.941726 + 0.336382i \(0.109203\pi\)
\(810\) 6748.53 0.292740
\(811\) −20547.5 −0.889669 −0.444835 0.895613i \(-0.646738\pi\)
−0.444835 + 0.895613i \(0.646738\pi\)
\(812\) 28210.7 1.21921
\(813\) −20748.1 −0.895042
\(814\) 0 0
\(815\) 12642.0 0.543348
\(816\) 7278.97 0.312273
\(817\) 6531.56 0.279694
\(818\) 57287.7 2.44868
\(819\) −4659.11 −0.198782
\(820\) 55964.7 2.38338
\(821\) −14149.1 −0.601469 −0.300735 0.953708i \(-0.597232\pi\)
−0.300735 + 0.953708i \(0.597232\pi\)
\(822\) −23594.2 −1.00115
\(823\) −13944.8 −0.590628 −0.295314 0.955400i \(-0.595424\pi\)
−0.295314 + 0.955400i \(0.595424\pi\)
\(824\) 4783.21 0.202222
\(825\) 0 0
\(826\) −2538.35 −0.106925
\(827\) 20786.2 0.874012 0.437006 0.899459i \(-0.356039\pi\)
0.437006 + 0.899459i \(0.356039\pi\)
\(828\) −18620.6 −0.781534
\(829\) 19298.8 0.808534 0.404267 0.914641i \(-0.367527\pi\)
0.404267 + 0.914641i \(0.367527\pi\)
\(830\) 8374.82 0.350234
\(831\) −8689.02 −0.362718
\(832\) 22730.7 0.947171
\(833\) −288.062 −0.0119817
\(834\) −7638.13 −0.317131
\(835\) −5543.54 −0.229751
\(836\) 0 0
\(837\) 1856.83 0.0766802
\(838\) −43504.5 −1.79336
\(839\) 6221.61 0.256012 0.128006 0.991773i \(-0.459142\pi\)
0.128006 + 0.991773i \(0.459142\pi\)
\(840\) 15959.4 0.655538
\(841\) −6789.09 −0.278367
\(842\) −45315.3 −1.85471
\(843\) 12746.6 0.520780
\(844\) 47219.2 1.92577
\(845\) −26881.4 −1.09438
\(846\) −6306.66 −0.256297
\(847\) 0 0
\(848\) −11659.3 −0.472147
\(849\) −2106.99 −0.0851728
\(850\) −100343. −4.04911
\(851\) −30890.3 −1.24431
\(852\) 38436.6 1.54556
\(853\) −34035.4 −1.36618 −0.683089 0.730335i \(-0.739364\pi\)
−0.683089 + 0.730335i \(0.739364\pi\)
\(854\) −30319.6 −1.21489
\(855\) −22594.4 −0.903756
\(856\) 4593.44 0.183412
\(857\) −26507.9 −1.05658 −0.528292 0.849063i \(-0.677167\pi\)
−0.528292 + 0.849063i \(0.677167\pi\)
\(858\) 0 0
\(859\) −5714.68 −0.226988 −0.113494 0.993539i \(-0.536204\pi\)
−0.113494 + 0.993539i \(0.536204\pi\)
\(860\) −10625.0 −0.421289
\(861\) 14451.8 0.572026
\(862\) 32825.4 1.29703
\(863\) −3152.04 −0.124330 −0.0621650 0.998066i \(-0.519801\pi\)
−0.0621650 + 0.998066i \(0.519801\pi\)
\(864\) −6214.78 −0.244712
\(865\) −24262.4 −0.953696
\(866\) 75320.6 2.95554
\(867\) 14090.7 0.551956
\(868\) 14624.0 0.571856
\(869\) 0 0
\(870\) 33158.9 1.29218
\(871\) −5937.56 −0.230984
\(872\) −31381.7 −1.21871
\(873\) 10378.8 0.402369
\(874\) 105965. 4.10107
\(875\) 37682.6 1.45589
\(876\) −1696.46 −0.0654318
\(877\) 36382.0 1.40084 0.700418 0.713733i \(-0.252997\pi\)
0.700418 + 0.713733i \(0.252997\pi\)
\(878\) −49127.5 −1.88835
\(879\) 8703.16 0.333959
\(880\) 0 0
\(881\) −12985.4 −0.496581 −0.248291 0.968686i \(-0.579869\pi\)
−0.248291 + 0.968686i \(0.579869\pi\)
\(882\) 116.584 0.00445077
\(883\) −46353.7 −1.76662 −0.883311 0.468787i \(-0.844691\pi\)
−0.883311 + 0.468787i \(0.844691\pi\)
\(884\) 31194.7 1.18687
\(885\) −1755.33 −0.0666719
\(886\) 7856.93 0.297922
\(887\) −22271.7 −0.843077 −0.421538 0.906811i \(-0.638510\pi\)
−0.421538 + 0.906811i \(0.638510\pi\)
\(888\) 7749.84 0.292869
\(889\) −13679.1 −0.516064
\(890\) −26883.2 −1.01250
\(891\) 0 0
\(892\) 10975.2 0.411969
\(893\) 21115.0 0.791249
\(894\) 3410.25 0.127579
\(895\) −23134.8 −0.864033
\(896\) −32711.6 −1.21966
\(897\) 15110.3 0.562452
\(898\) −33660.2 −1.25084
\(899\) 9123.53 0.338472
\(900\) 23892.4 0.884905
\(901\) −46178.7 −1.70748
\(902\) 0 0
\(903\) −2743.68 −0.101112
\(904\) 19539.7 0.718896
\(905\) 63995.1 2.35057
\(906\) 8680.32 0.318305
\(907\) −7371.73 −0.269873 −0.134936 0.990854i \(-0.543083\pi\)
−0.134936 + 0.990854i \(0.543083\pi\)
\(908\) −5492.57 −0.200746
\(909\) 92.3249 0.00336878
\(910\) −43130.6 −1.57117
\(911\) −33107.7 −1.20407 −0.602034 0.798470i \(-0.705643\pi\)
−0.602034 + 0.798470i \(0.705643\pi\)
\(912\) 9863.10 0.358114
\(913\) 0 0
\(914\) −61832.0 −2.23766
\(915\) −20966.7 −0.757528
\(916\) 49431.1 1.78302
\(917\) 25440.4 0.916158
\(918\) −11667.9 −0.419497
\(919\) 31326.7 1.12445 0.562227 0.826983i \(-0.309945\pi\)
0.562227 + 0.826983i \(0.309945\pi\)
\(920\) −51759.2 −1.85484
\(921\) 18687.5 0.668593
\(922\) −29429.7 −1.05121
\(923\) −31190.8 −1.11230
\(924\) 0 0
\(925\) 39635.9 1.40889
\(926\) −20225.3 −0.717757
\(927\) 2844.60 0.100786
\(928\) −30536.4 −1.08018
\(929\) 45635.1 1.61167 0.805833 0.592142i \(-0.201718\pi\)
0.805833 + 0.592142i \(0.201718\pi\)
\(930\) 17189.1 0.606078
\(931\) −390.327 −0.0137406
\(932\) 6468.42 0.227339
\(933\) 870.434 0.0305431
\(934\) 26599.7 0.931871
\(935\) 0 0
\(936\) −3790.92 −0.132383
\(937\) −27388.0 −0.954883 −0.477442 0.878663i \(-0.658436\pi\)
−0.477442 + 0.878663i \(0.658436\pi\)
\(938\) 17491.1 0.608852
\(939\) −2039.94 −0.0708957
\(940\) −34348.0 −1.19182
\(941\) −3856.53 −0.133602 −0.0668009 0.997766i \(-0.521279\pi\)
−0.0668009 + 0.997766i \(0.521279\pi\)
\(942\) 39889.5 1.37969
\(943\) −46869.6 −1.61854
\(944\) 766.251 0.0264188
\(945\) 9491.13 0.326716
\(946\) 0 0
\(947\) 7585.45 0.260289 0.130145 0.991495i \(-0.458456\pi\)
0.130145 + 0.991495i \(0.458456\pi\)
\(948\) 21126.7 0.723801
\(949\) 1376.66 0.0470897
\(950\) −135966. −4.64351
\(951\) −18993.1 −0.647628
\(952\) −27593.1 −0.939388
\(953\) 16429.7 0.558457 0.279229 0.960225i \(-0.409921\pi\)
0.279229 + 0.960225i \(0.409921\pi\)
\(954\) 18689.4 0.634267
\(955\) −77945.1 −2.64109
\(956\) −58141.6 −1.96698
\(957\) 0 0
\(958\) −13768.7 −0.464348
\(959\) −33182.9 −1.11734
\(960\) −46305.0 −1.55676
\(961\) −25061.5 −0.841244
\(962\) −20944.1 −0.701938
\(963\) 2731.74 0.0914113
\(964\) 30986.4 1.03527
\(965\) 32399.4 1.08080
\(966\) −44512.5 −1.48257
\(967\) 30924.7 1.02841 0.514205 0.857668i \(-0.328087\pi\)
0.514205 + 0.857668i \(0.328087\pi\)
\(968\) 0 0
\(969\) 39064.7 1.29509
\(970\) 96078.8 3.18031
\(971\) −58367.8 −1.92906 −0.964528 0.263982i \(-0.914964\pi\)
−0.964528 + 0.263982i \(0.914964\pi\)
\(972\) 2778.21 0.0916783
\(973\) −10742.3 −0.353937
\(974\) 15837.9 0.521025
\(975\) −19388.4 −0.636846
\(976\) 9152.58 0.300171
\(977\) 36123.6 1.18290 0.591451 0.806341i \(-0.298555\pi\)
0.591451 + 0.806341i \(0.298555\pi\)
\(978\) 8846.07 0.289229
\(979\) 0 0
\(980\) 634.950 0.0206967
\(981\) −18662.8 −0.607399
\(982\) −11368.1 −0.369419
\(983\) −51520.0 −1.67165 −0.835825 0.548996i \(-0.815010\pi\)
−0.835825 + 0.548996i \(0.815010\pi\)
\(984\) 11758.8 0.380952
\(985\) −24357.4 −0.787911
\(986\) −57330.3 −1.85169
\(987\) −8869.68 −0.286043
\(988\) 42269.2 1.36110
\(989\) 8898.26 0.286095
\(990\) 0 0
\(991\) 45589.0 1.46133 0.730667 0.682734i \(-0.239209\pi\)
0.730667 + 0.682734i \(0.239209\pi\)
\(992\) −15829.6 −0.506643
\(993\) 802.892 0.0256586
\(994\) 91882.7 2.93193
\(995\) −67606.0 −2.15402
\(996\) 3447.72 0.109684
\(997\) 9651.01 0.306570 0.153285 0.988182i \(-0.451015\pi\)
0.153285 + 0.988182i \(0.451015\pi\)
\(998\) −35755.6 −1.13409
\(999\) 4608.87 0.145964
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 363.4.a.q.1.4 4
3.2 odd 2 1089.4.a.bf.1.1 4
11.10 odd 2 363.4.a.s.1.1 yes 4
33.32 even 2 1089.4.a.ba.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
363.4.a.q.1.4 4 1.1 even 1 trivial
363.4.a.s.1.1 yes 4 11.10 odd 2
1089.4.a.ba.1.4 4 33.32 even 2
1089.4.a.bf.1.1 4 3.2 odd 2