Properties

Label 1150.4.a.q.1.3
Level $1150$
Weight $4$
Character 1150.1
Self dual yes
Analytic conductor $67.852$
Analytic rank $1$
Dimension $5$
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] = [1150,4,Mod(1,1150)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1150, 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("1150.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1150.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: \(67.8521965066\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - 107x^{3} - 3x^{2} + 2151x - 2916 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(1.53483\) of defining polynomial
Character \(\chi\) \(=\) 1150.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000 q^{2} +0.534830 q^{3} +4.00000 q^{4} -1.06966 q^{6} +28.9380 q^{7} -8.00000 q^{8} -26.7140 q^{9} +33.5234 q^{11} +2.13932 q^{12} -10.2917 q^{13} -57.8760 q^{14} +16.0000 q^{16} -56.5854 q^{17} +53.4279 q^{18} -5.26405 q^{19} +15.4769 q^{21} -67.0468 q^{22} -23.0000 q^{23} -4.27864 q^{24} +20.5834 q^{26} -28.7278 q^{27} +115.752 q^{28} -162.334 q^{29} -160.556 q^{31} -32.0000 q^{32} +17.9293 q^{33} +113.171 q^{34} -106.856 q^{36} +16.9178 q^{37} +10.5281 q^{38} -5.50431 q^{39} +22.7758 q^{41} -30.9538 q^{42} -333.620 q^{43} +134.094 q^{44} +46.0000 q^{46} -130.383 q^{47} +8.55728 q^{48} +494.408 q^{49} -30.2636 q^{51} -41.1668 q^{52} -673.206 q^{53} +57.4557 q^{54} -231.504 q^{56} -2.81537 q^{57} +324.669 q^{58} +291.958 q^{59} +454.587 q^{61} +321.113 q^{62} -773.048 q^{63} +64.0000 q^{64} -35.8586 q^{66} -132.389 q^{67} -226.342 q^{68} -12.3011 q^{69} +121.326 q^{71} +213.712 q^{72} -176.482 q^{73} -33.8356 q^{74} -21.0562 q^{76} +970.100 q^{77} +11.0086 q^{78} +563.082 q^{79} +705.912 q^{81} -45.5516 q^{82} -809.068 q^{83} +61.9076 q^{84} +667.241 q^{86} -86.8213 q^{87} -268.187 q^{88} -702.417 q^{89} -297.821 q^{91} -92.0000 q^{92} -85.8703 q^{93} +260.766 q^{94} -17.1146 q^{96} -342.945 q^{97} -988.815 q^{98} -895.543 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 10 q^{2} - 5 q^{3} + 20 q^{4} + 10 q^{6} + 3 q^{7} - 40 q^{8} + 84 q^{9} - 26 q^{11} - 20 q^{12} + 61 q^{13} - 6 q^{14} + 80 q^{16} - 231 q^{17} - 168 q^{18} + 74 q^{19} - 88 q^{21} + 52 q^{22} - 115 q^{23}+ \cdots + 2397 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −0.707107
\(3\) 0.534830 0.102928 0.0514640 0.998675i \(-0.483611\pi\)
0.0514640 + 0.998675i \(0.483611\pi\)
\(4\) 4.00000 0.500000
\(5\) 0 0
\(6\) −1.06966 −0.0727812
\(7\) 28.9380 1.56250 0.781252 0.624215i \(-0.214581\pi\)
0.781252 + 0.624215i \(0.214581\pi\)
\(8\) −8.00000 −0.353553
\(9\) −26.7140 −0.989406
\(10\) 0 0
\(11\) 33.5234 0.918880 0.459440 0.888209i \(-0.348050\pi\)
0.459440 + 0.888209i \(0.348050\pi\)
\(12\) 2.13932 0.0514640
\(13\) −10.2917 −0.219570 −0.109785 0.993955i \(-0.535016\pi\)
−0.109785 + 0.993955i \(0.535016\pi\)
\(14\) −57.8760 −1.10486
\(15\) 0 0
\(16\) 16.0000 0.250000
\(17\) −56.5854 −0.807293 −0.403646 0.914915i \(-0.632257\pi\)
−0.403646 + 0.914915i \(0.632257\pi\)
\(18\) 53.4279 0.699616
\(19\) −5.26405 −0.0635608 −0.0317804 0.999495i \(-0.510118\pi\)
−0.0317804 + 0.999495i \(0.510118\pi\)
\(20\) 0 0
\(21\) 15.4769 0.160826
\(22\) −67.0468 −0.649747
\(23\) −23.0000 −0.208514
\(24\) −4.27864 −0.0363906
\(25\) 0 0
\(26\) 20.5834 0.155259
\(27\) −28.7278 −0.204766
\(28\) 115.752 0.781252
\(29\) −162.334 −1.03947 −0.519737 0.854327i \(-0.673970\pi\)
−0.519737 + 0.854327i \(0.673970\pi\)
\(30\) 0 0
\(31\) −160.556 −0.930218 −0.465109 0.885253i \(-0.653985\pi\)
−0.465109 + 0.885253i \(0.653985\pi\)
\(32\) −32.0000 −0.176777
\(33\) 17.9293 0.0945786
\(34\) 113.171 0.570842
\(35\) 0 0
\(36\) −106.856 −0.494703
\(37\) 16.9178 0.0751694 0.0375847 0.999293i \(-0.488034\pi\)
0.0375847 + 0.999293i \(0.488034\pi\)
\(38\) 10.5281 0.0449443
\(39\) −5.50431 −0.0225999
\(40\) 0 0
\(41\) 22.7758 0.0867557 0.0433779 0.999059i \(-0.486188\pi\)
0.0433779 + 0.999059i \(0.486188\pi\)
\(42\) −30.9538 −0.113721
\(43\) −333.620 −1.18318 −0.591589 0.806240i \(-0.701499\pi\)
−0.591589 + 0.806240i \(0.701499\pi\)
\(44\) 134.094 0.459440
\(45\) 0 0
\(46\) 46.0000 0.147442
\(47\) −130.383 −0.404645 −0.202322 0.979319i \(-0.564849\pi\)
−0.202322 + 0.979319i \(0.564849\pi\)
\(48\) 8.55728 0.0257320
\(49\) 494.408 1.44142
\(50\) 0 0
\(51\) −30.2636 −0.0830931
\(52\) −41.1668 −0.109785
\(53\) −673.206 −1.74475 −0.872376 0.488835i \(-0.837422\pi\)
−0.872376 + 0.488835i \(0.837422\pi\)
\(54\) 57.4557 0.144791
\(55\) 0 0
\(56\) −231.504 −0.552429
\(57\) −2.81537 −0.00654219
\(58\) 324.669 0.735019
\(59\) 291.958 0.644233 0.322116 0.946700i \(-0.395606\pi\)
0.322116 + 0.946700i \(0.395606\pi\)
\(60\) 0 0
\(61\) 454.587 0.954162 0.477081 0.878859i \(-0.341695\pi\)
0.477081 + 0.878859i \(0.341695\pi\)
\(62\) 321.113 0.657764
\(63\) −773.048 −1.54595
\(64\) 64.0000 0.125000
\(65\) 0 0
\(66\) −35.8586 −0.0668772
\(67\) −132.389 −0.241401 −0.120701 0.992689i \(-0.538514\pi\)
−0.120701 + 0.992689i \(0.538514\pi\)
\(68\) −226.342 −0.403646
\(69\) −12.3011 −0.0214620
\(70\) 0 0
\(71\) 121.326 0.202799 0.101399 0.994846i \(-0.467668\pi\)
0.101399 + 0.994846i \(0.467668\pi\)
\(72\) 213.712 0.349808
\(73\) −176.482 −0.282955 −0.141477 0.989942i \(-0.545185\pi\)
−0.141477 + 0.989942i \(0.545185\pi\)
\(74\) −33.8356 −0.0531528
\(75\) 0 0
\(76\) −21.0562 −0.0317804
\(77\) 970.100 1.43576
\(78\) 11.0086 0.0159805
\(79\) 563.082 0.801920 0.400960 0.916096i \(-0.368677\pi\)
0.400960 + 0.916096i \(0.368677\pi\)
\(80\) 0 0
\(81\) 705.912 0.968330
\(82\) −45.5516 −0.0613456
\(83\) −809.068 −1.06996 −0.534981 0.844864i \(-0.679681\pi\)
−0.534981 + 0.844864i \(0.679681\pi\)
\(84\) 61.9076 0.0804128
\(85\) 0 0
\(86\) 667.241 0.836633
\(87\) −86.8213 −0.106991
\(88\) −268.187 −0.324873
\(89\) −702.417 −0.836585 −0.418293 0.908312i \(-0.637371\pi\)
−0.418293 + 0.908312i \(0.637371\pi\)
\(90\) 0 0
\(91\) −297.821 −0.343079
\(92\) −92.0000 −0.104257
\(93\) −85.8703 −0.0957456
\(94\) 260.766 0.286127
\(95\) 0 0
\(96\) −17.1146 −0.0181953
\(97\) −342.945 −0.358977 −0.179489 0.983760i \(-0.557444\pi\)
−0.179489 + 0.983760i \(0.557444\pi\)
\(98\) −988.815 −1.01924
\(99\) −895.543 −0.909146
\(100\) 0 0
\(101\) 1719.68 1.69420 0.847102 0.531431i \(-0.178345\pi\)
0.847102 + 0.531431i \(0.178345\pi\)
\(102\) 60.5272 0.0587557
\(103\) −387.872 −0.371050 −0.185525 0.982640i \(-0.559399\pi\)
−0.185525 + 0.982640i \(0.559399\pi\)
\(104\) 82.3337 0.0776296
\(105\) 0 0
\(106\) 1346.41 1.23373
\(107\) −31.3904 −0.0283610 −0.0141805 0.999899i \(-0.504514\pi\)
−0.0141805 + 0.999899i \(0.504514\pi\)
\(108\) −114.911 −0.102383
\(109\) 686.159 0.602955 0.301478 0.953473i \(-0.402520\pi\)
0.301478 + 0.953473i \(0.402520\pi\)
\(110\) 0 0
\(111\) 9.04814 0.00773704
\(112\) 463.008 0.390626
\(113\) 42.2350 0.0351605 0.0175802 0.999845i \(-0.494404\pi\)
0.0175802 + 0.999845i \(0.494404\pi\)
\(114\) 5.63074 0.00462603
\(115\) 0 0
\(116\) −649.337 −0.519737
\(117\) 274.932 0.217244
\(118\) −583.917 −0.455541
\(119\) −1637.47 −1.26140
\(120\) 0 0
\(121\) −207.182 −0.155659
\(122\) −909.173 −0.674694
\(123\) 12.1812 0.00892960
\(124\) −642.225 −0.465109
\(125\) 0 0
\(126\) 1546.10 1.09315
\(127\) −1234.48 −0.862538 −0.431269 0.902223i \(-0.641934\pi\)
−0.431269 + 0.902223i \(0.641934\pi\)
\(128\) −128.000 −0.0883883
\(129\) −178.430 −0.121782
\(130\) 0 0
\(131\) −2216.74 −1.47846 −0.739228 0.673455i \(-0.764809\pi\)
−0.739228 + 0.673455i \(0.764809\pi\)
\(132\) 71.7173 0.0472893
\(133\) −152.331 −0.0993140
\(134\) 264.778 0.170697
\(135\) 0 0
\(136\) 452.683 0.285421
\(137\) 1179.48 0.735545 0.367773 0.929916i \(-0.380120\pi\)
0.367773 + 0.929916i \(0.380120\pi\)
\(138\) 24.6022 0.0151759
\(139\) 241.224 0.147197 0.0735983 0.997288i \(-0.476552\pi\)
0.0735983 + 0.997288i \(0.476552\pi\)
\(140\) 0 0
\(141\) −69.7327 −0.0416493
\(142\) −242.651 −0.143400
\(143\) −345.013 −0.201758
\(144\) −427.423 −0.247351
\(145\) 0 0
\(146\) 352.964 0.200079
\(147\) 264.424 0.148363
\(148\) 67.6711 0.0375847
\(149\) −1028.14 −0.565294 −0.282647 0.959224i \(-0.591212\pi\)
−0.282647 + 0.959224i \(0.591212\pi\)
\(150\) 0 0
\(151\) 1511.24 0.814456 0.407228 0.913327i \(-0.366495\pi\)
0.407228 + 0.913327i \(0.366495\pi\)
\(152\) 42.1124 0.0224721
\(153\) 1511.62 0.798740
\(154\) −1940.20 −1.01523
\(155\) 0 0
\(156\) −22.0173 −0.0112999
\(157\) 2097.04 1.06600 0.532999 0.846116i \(-0.321065\pi\)
0.532999 + 0.846116i \(0.321065\pi\)
\(158\) −1126.16 −0.567043
\(159\) −360.051 −0.179584
\(160\) 0 0
\(161\) −665.574 −0.325805
\(162\) −1411.82 −0.684712
\(163\) −703.046 −0.337833 −0.168917 0.985630i \(-0.554027\pi\)
−0.168917 + 0.985630i \(0.554027\pi\)
\(164\) 91.1033 0.0433779
\(165\) 0 0
\(166\) 1618.14 0.756577
\(167\) −3063.04 −1.41931 −0.709656 0.704549i \(-0.751150\pi\)
−0.709656 + 0.704549i \(0.751150\pi\)
\(168\) −123.815 −0.0568605
\(169\) −2091.08 −0.951789
\(170\) 0 0
\(171\) 140.624 0.0628874
\(172\) −1334.48 −0.591589
\(173\) −2810.34 −1.23506 −0.617531 0.786546i \(-0.711867\pi\)
−0.617531 + 0.786546i \(0.711867\pi\)
\(174\) 173.643 0.0756541
\(175\) 0 0
\(176\) 536.374 0.229720
\(177\) 156.148 0.0663096
\(178\) 1404.83 0.591555
\(179\) −2516.53 −1.05081 −0.525403 0.850853i \(-0.676086\pi\)
−0.525403 + 0.850853i \(0.676086\pi\)
\(180\) 0 0
\(181\) 1085.01 0.445570 0.222785 0.974868i \(-0.428485\pi\)
0.222785 + 0.974868i \(0.428485\pi\)
\(182\) 595.643 0.242593
\(183\) 243.127 0.0982100
\(184\) 184.000 0.0737210
\(185\) 0 0
\(186\) 171.741 0.0677024
\(187\) −1896.94 −0.741806
\(188\) −521.532 −0.202322
\(189\) −831.326 −0.319947
\(190\) 0 0
\(191\) −2081.87 −0.788683 −0.394342 0.918964i \(-0.629027\pi\)
−0.394342 + 0.918964i \(0.629027\pi\)
\(192\) 34.2291 0.0128660
\(193\) −648.493 −0.241863 −0.120931 0.992661i \(-0.538588\pi\)
−0.120931 + 0.992661i \(0.538588\pi\)
\(194\) 685.890 0.253835
\(195\) 0 0
\(196\) 1977.63 0.720711
\(197\) 1250.92 0.452409 0.226205 0.974080i \(-0.427368\pi\)
0.226205 + 0.974080i \(0.427368\pi\)
\(198\) 1791.09 0.642863
\(199\) 3135.54 1.11695 0.558473 0.829523i \(-0.311387\pi\)
0.558473 + 0.829523i \(0.311387\pi\)
\(200\) 0 0
\(201\) −70.8056 −0.0248470
\(202\) −3439.36 −1.19798
\(203\) −4697.63 −1.62418
\(204\) −121.054 −0.0415466
\(205\) 0 0
\(206\) 775.743 0.262372
\(207\) 614.421 0.206305
\(208\) −164.667 −0.0548924
\(209\) −176.469 −0.0584048
\(210\) 0 0
\(211\) −844.189 −0.275433 −0.137716 0.990472i \(-0.543976\pi\)
−0.137716 + 0.990472i \(0.543976\pi\)
\(212\) −2692.82 −0.872376
\(213\) 64.8886 0.0208737
\(214\) 62.7808 0.0200542
\(215\) 0 0
\(216\) 229.823 0.0723956
\(217\) −4646.18 −1.45347
\(218\) −1372.32 −0.426354
\(219\) −94.3880 −0.0291240
\(220\) 0 0
\(221\) 582.360 0.177257
\(222\) −18.0963 −0.00547091
\(223\) −5648.57 −1.69622 −0.848108 0.529824i \(-0.822258\pi\)
−0.848108 + 0.529824i \(0.822258\pi\)
\(224\) −926.016 −0.276214
\(225\) 0 0
\(226\) −84.4700 −0.0248622
\(227\) 3914.91 1.14468 0.572338 0.820018i \(-0.306036\pi\)
0.572338 + 0.820018i \(0.306036\pi\)
\(228\) −11.2615 −0.00327110
\(229\) −550.992 −0.158998 −0.0794990 0.996835i \(-0.525332\pi\)
−0.0794990 + 0.996835i \(0.525332\pi\)
\(230\) 0 0
\(231\) 518.839 0.147780
\(232\) 1298.67 0.367509
\(233\) −5785.67 −1.62675 −0.813373 0.581742i \(-0.802371\pi\)
−0.813373 + 0.581742i \(0.802371\pi\)
\(234\) −549.864 −0.153614
\(235\) 0 0
\(236\) 1167.83 0.322116
\(237\) 301.153 0.0825400
\(238\) 3274.94 0.891944
\(239\) −4525.71 −1.22487 −0.612435 0.790521i \(-0.709810\pi\)
−0.612435 + 0.790521i \(0.709810\pi\)
\(240\) 0 0
\(241\) 517.292 0.138264 0.0691322 0.997608i \(-0.477977\pi\)
0.0691322 + 0.997608i \(0.477977\pi\)
\(242\) 414.363 0.110067
\(243\) 1153.19 0.304434
\(244\) 1818.35 0.477081
\(245\) 0 0
\(246\) −24.3624 −0.00631418
\(247\) 54.1760 0.0139560
\(248\) 1284.45 0.328882
\(249\) −432.714 −0.110129
\(250\) 0 0
\(251\) −7039.00 −1.77011 −0.885055 0.465486i \(-0.845879\pi\)
−0.885055 + 0.465486i \(0.845879\pi\)
\(252\) −3092.19 −0.772976
\(253\) −771.038 −0.191600
\(254\) 2468.96 0.609906
\(255\) 0 0
\(256\) 256.000 0.0625000
\(257\) 4250.94 1.03177 0.515887 0.856656i \(-0.327462\pi\)
0.515887 + 0.856656i \(0.327462\pi\)
\(258\) 356.860 0.0861130
\(259\) 489.567 0.117453
\(260\) 0 0
\(261\) 4336.59 1.02846
\(262\) 4433.49 1.04543
\(263\) −3598.83 −0.843778 −0.421889 0.906648i \(-0.638633\pi\)
−0.421889 + 0.906648i \(0.638633\pi\)
\(264\) −143.435 −0.0334386
\(265\) 0 0
\(266\) 304.662 0.0702256
\(267\) −375.674 −0.0861081
\(268\) −529.556 −0.120701
\(269\) −5062.52 −1.14746 −0.573731 0.819044i \(-0.694505\pi\)
−0.573731 + 0.819044i \(0.694505\pi\)
\(270\) 0 0
\(271\) 1854.58 0.415712 0.207856 0.978159i \(-0.433352\pi\)
0.207856 + 0.978159i \(0.433352\pi\)
\(272\) −905.366 −0.201823
\(273\) −159.284 −0.0353124
\(274\) −2358.96 −0.520109
\(275\) 0 0
\(276\) −49.2044 −0.0107310
\(277\) −8747.91 −1.89751 −0.948756 0.316009i \(-0.897657\pi\)
−0.948756 + 0.316009i \(0.897657\pi\)
\(278\) −482.447 −0.104084
\(279\) 4289.09 0.920363
\(280\) 0 0
\(281\) 4046.88 0.859134 0.429567 0.903035i \(-0.358666\pi\)
0.429567 + 0.903035i \(0.358666\pi\)
\(282\) 139.465 0.0294505
\(283\) −1598.52 −0.335766 −0.167883 0.985807i \(-0.553693\pi\)
−0.167883 + 0.985807i \(0.553693\pi\)
\(284\) 485.303 0.101399
\(285\) 0 0
\(286\) 690.026 0.142665
\(287\) 659.086 0.135556
\(288\) 854.847 0.174904
\(289\) −1711.09 −0.348278
\(290\) 0 0
\(291\) −183.417 −0.0369488
\(292\) −705.929 −0.141477
\(293\) 4542.62 0.905742 0.452871 0.891576i \(-0.350400\pi\)
0.452871 + 0.891576i \(0.350400\pi\)
\(294\) −528.848 −0.104908
\(295\) 0 0
\(296\) −135.342 −0.0265764
\(297\) −963.055 −0.188155
\(298\) 2056.29 0.399723
\(299\) 236.709 0.0457834
\(300\) 0 0
\(301\) −9654.31 −1.84872
\(302\) −3022.48 −0.575907
\(303\) 919.736 0.174381
\(304\) −84.2247 −0.0158902
\(305\) 0 0
\(306\) −3023.24 −0.564795
\(307\) 2366.39 0.439925 0.219963 0.975508i \(-0.429406\pi\)
0.219963 + 0.975508i \(0.429406\pi\)
\(308\) 3880.40 0.717878
\(309\) −207.445 −0.0381914
\(310\) 0 0
\(311\) 830.158 0.151363 0.0756816 0.997132i \(-0.475887\pi\)
0.0756816 + 0.997132i \(0.475887\pi\)
\(312\) 44.0345 0.00799027
\(313\) 7182.03 1.29697 0.648486 0.761226i \(-0.275402\pi\)
0.648486 + 0.761226i \(0.275402\pi\)
\(314\) −4194.07 −0.753775
\(315\) 0 0
\(316\) 2252.33 0.400960
\(317\) −1910.06 −0.338422 −0.169211 0.985580i \(-0.554122\pi\)
−0.169211 + 0.985580i \(0.554122\pi\)
\(318\) 720.101 0.126985
\(319\) −5442.00 −0.955152
\(320\) 0 0
\(321\) −16.7885 −0.00291914
\(322\) 1331.15 0.230379
\(323\) 297.868 0.0513122
\(324\) 2823.65 0.484165
\(325\) 0 0
\(326\) 1406.09 0.238884
\(327\) 366.979 0.0620610
\(328\) −182.207 −0.0306728
\(329\) −3773.02 −0.632260
\(330\) 0 0
\(331\) 7540.40 1.25214 0.626069 0.779767i \(-0.284663\pi\)
0.626069 + 0.779767i \(0.284663\pi\)
\(332\) −3236.27 −0.534981
\(333\) −451.941 −0.0743730
\(334\) 6126.08 1.00360
\(335\) 0 0
\(336\) 247.631 0.0402064
\(337\) 10069.4 1.62764 0.813822 0.581114i \(-0.197383\pi\)
0.813822 + 0.581114i \(0.197383\pi\)
\(338\) 4182.16 0.673017
\(339\) 22.5885 0.00361900
\(340\) 0 0
\(341\) −5382.39 −0.854759
\(342\) −281.247 −0.0444681
\(343\) 4381.43 0.689723
\(344\) 2668.96 0.418316
\(345\) 0 0
\(346\) 5620.67 0.873321
\(347\) −6031.06 −0.933039 −0.466519 0.884511i \(-0.654492\pi\)
−0.466519 + 0.884511i \(0.654492\pi\)
\(348\) −347.285 −0.0534955
\(349\) −11352.0 −1.74114 −0.870569 0.492047i \(-0.836249\pi\)
−0.870569 + 0.492047i \(0.836249\pi\)
\(350\) 0 0
\(351\) 295.659 0.0449604
\(352\) −1072.75 −0.162437
\(353\) 4864.81 0.733506 0.366753 0.930318i \(-0.380469\pi\)
0.366753 + 0.930318i \(0.380469\pi\)
\(354\) −312.296 −0.0468880
\(355\) 0 0
\(356\) −2809.67 −0.418293
\(357\) −875.767 −0.129833
\(358\) 5033.06 0.743032
\(359\) −5809.49 −0.854076 −0.427038 0.904234i \(-0.640443\pi\)
−0.427038 + 0.904234i \(0.640443\pi\)
\(360\) 0 0
\(361\) −6831.29 −0.995960
\(362\) −2170.02 −0.315066
\(363\) −110.807 −0.0160216
\(364\) −1191.29 −0.171539
\(365\) 0 0
\(366\) −486.253 −0.0694450
\(367\) −6984.38 −0.993410 −0.496705 0.867919i \(-0.665457\pi\)
−0.496705 + 0.867919i \(0.665457\pi\)
\(368\) −368.000 −0.0521286
\(369\) −608.432 −0.0858366
\(370\) 0 0
\(371\) −19481.2 −2.72618
\(372\) −343.481 −0.0478728
\(373\) −8551.53 −1.18708 −0.593541 0.804804i \(-0.702270\pi\)
−0.593541 + 0.804804i \(0.702270\pi\)
\(374\) 3793.87 0.524536
\(375\) 0 0
\(376\) 1043.06 0.143064
\(377\) 1670.70 0.228237
\(378\) 1662.65 0.226237
\(379\) 9933.40 1.34629 0.673145 0.739510i \(-0.264943\pi\)
0.673145 + 0.739510i \(0.264943\pi\)
\(380\) 0 0
\(381\) −660.236 −0.0887794
\(382\) 4163.73 0.557683
\(383\) −9748.52 −1.30059 −0.650295 0.759682i \(-0.725355\pi\)
−0.650295 + 0.759682i \(0.725355\pi\)
\(384\) −68.4582 −0.00909764
\(385\) 0 0
\(386\) 1296.99 0.171023
\(387\) 8912.32 1.17064
\(388\) −1371.78 −0.179489
\(389\) −10517.0 −1.37078 −0.685391 0.728175i \(-0.740369\pi\)
−0.685391 + 0.728175i \(0.740369\pi\)
\(390\) 0 0
\(391\) 1301.46 0.168332
\(392\) −3955.26 −0.509619
\(393\) −1185.58 −0.152175
\(394\) −2501.85 −0.319902
\(395\) 0 0
\(396\) −3582.17 −0.454573
\(397\) −4117.94 −0.520588 −0.260294 0.965529i \(-0.583819\pi\)
−0.260294 + 0.965529i \(0.583819\pi\)
\(398\) −6271.07 −0.789800
\(399\) −81.4712 −0.0102222
\(400\) 0 0
\(401\) −7374.29 −0.918340 −0.459170 0.888348i \(-0.651853\pi\)
−0.459170 + 0.888348i \(0.651853\pi\)
\(402\) 141.611 0.0175695
\(403\) 1652.40 0.204248
\(404\) 6878.72 0.847102
\(405\) 0 0
\(406\) 9395.26 1.14847
\(407\) 567.142 0.0690717
\(408\) 242.109 0.0293778
\(409\) 12941.5 1.56459 0.782296 0.622907i \(-0.214049\pi\)
0.782296 + 0.622907i \(0.214049\pi\)
\(410\) 0 0
\(411\) 630.821 0.0757083
\(412\) −1551.49 −0.185525
\(413\) 8448.69 1.00662
\(414\) −1228.84 −0.145880
\(415\) 0 0
\(416\) 329.335 0.0388148
\(417\) 129.014 0.0151507
\(418\) 352.937 0.0412984
\(419\) 5633.46 0.656832 0.328416 0.944533i \(-0.393485\pi\)
0.328416 + 0.944533i \(0.393485\pi\)
\(420\) 0 0
\(421\) −4205.49 −0.486848 −0.243424 0.969920i \(-0.578271\pi\)
−0.243424 + 0.969920i \(0.578271\pi\)
\(422\) 1688.38 0.194761
\(423\) 3483.04 0.400358
\(424\) 5385.64 0.616863
\(425\) 0 0
\(426\) −129.777 −0.0147599
\(427\) 13154.8 1.49088
\(428\) −125.562 −0.0141805
\(429\) −184.523 −0.0207666
\(430\) 0 0
\(431\) 15075.7 1.68486 0.842428 0.538809i \(-0.181125\pi\)
0.842428 + 0.538809i \(0.181125\pi\)
\(432\) −459.645 −0.0511914
\(433\) −3098.05 −0.343840 −0.171920 0.985111i \(-0.554997\pi\)
−0.171920 + 0.985111i \(0.554997\pi\)
\(434\) 9292.36 1.02776
\(435\) 0 0
\(436\) 2744.64 0.301478
\(437\) 121.073 0.0132533
\(438\) 188.776 0.0205938
\(439\) 6867.74 0.746649 0.373325 0.927701i \(-0.378218\pi\)
0.373325 + 0.927701i \(0.378218\pi\)
\(440\) 0 0
\(441\) −13207.6 −1.42615
\(442\) −1164.72 −0.125340
\(443\) 5878.29 0.630442 0.315221 0.949018i \(-0.397921\pi\)
0.315221 + 0.949018i \(0.397921\pi\)
\(444\) 36.1926 0.00386852
\(445\) 0 0
\(446\) 11297.1 1.19941
\(447\) −549.882 −0.0581846
\(448\) 1852.03 0.195313
\(449\) 13670.7 1.43689 0.718443 0.695586i \(-0.244855\pi\)
0.718443 + 0.695586i \(0.244855\pi\)
\(450\) 0 0
\(451\) 763.523 0.0797182
\(452\) 168.940 0.0175802
\(453\) 808.256 0.0838304
\(454\) −7829.81 −0.809408
\(455\) 0 0
\(456\) 22.5230 0.00231301
\(457\) 16947.2 1.73470 0.867349 0.497700i \(-0.165822\pi\)
0.867349 + 0.497700i \(0.165822\pi\)
\(458\) 1101.98 0.112429
\(459\) 1625.58 0.165306
\(460\) 0 0
\(461\) −5583.33 −0.564081 −0.282041 0.959402i \(-0.591011\pi\)
−0.282041 + 0.959402i \(0.591011\pi\)
\(462\) −1037.68 −0.104496
\(463\) 5858.02 0.588003 0.294001 0.955805i \(-0.405013\pi\)
0.294001 + 0.955805i \(0.405013\pi\)
\(464\) −2597.35 −0.259868
\(465\) 0 0
\(466\) 11571.3 1.15028
\(467\) 13949.8 1.38227 0.691136 0.722725i \(-0.257111\pi\)
0.691136 + 0.722725i \(0.257111\pi\)
\(468\) 1099.73 0.108622
\(469\) −3831.07 −0.377191
\(470\) 0 0
\(471\) 1121.56 0.109721
\(472\) −2335.67 −0.227771
\(473\) −11184.1 −1.08720
\(474\) −602.306 −0.0583646
\(475\) 0 0
\(476\) −6549.87 −0.630699
\(477\) 17984.0 1.72627
\(478\) 9051.43 0.866114
\(479\) 7154.84 0.682491 0.341245 0.939974i \(-0.389151\pi\)
0.341245 + 0.939974i \(0.389151\pi\)
\(480\) 0 0
\(481\) −174.113 −0.0165049
\(482\) −1034.58 −0.0977677
\(483\) −355.969 −0.0335345
\(484\) −828.727 −0.0778293
\(485\) 0 0
\(486\) −2306.39 −0.215267
\(487\) 14811.9 1.37821 0.689106 0.724661i \(-0.258004\pi\)
0.689106 + 0.724661i \(0.258004\pi\)
\(488\) −3636.69 −0.337347
\(489\) −376.010 −0.0347725
\(490\) 0 0
\(491\) 3092.94 0.284282 0.142141 0.989846i \(-0.454601\pi\)
0.142141 + 0.989846i \(0.454601\pi\)
\(492\) 48.7248 0.00446480
\(493\) 9185.75 0.839159
\(494\) −108.352 −0.00986840
\(495\) 0 0
\(496\) −2568.90 −0.232555
\(497\) 3510.92 0.316874
\(498\) 865.428 0.0778730
\(499\) 17250.6 1.54758 0.773790 0.633443i \(-0.218359\pi\)
0.773790 + 0.633443i \(0.218359\pi\)
\(500\) 0 0
\(501\) −1638.21 −0.146087
\(502\) 14078.0 1.25166
\(503\) 5534.20 0.490572 0.245286 0.969451i \(-0.421118\pi\)
0.245286 + 0.969451i \(0.421118\pi\)
\(504\) 6184.39 0.546576
\(505\) 0 0
\(506\) 1542.08 0.135482
\(507\) −1118.37 −0.0979658
\(508\) −4937.91 −0.431269
\(509\) 21995.5 1.91539 0.957693 0.287791i \(-0.0929208\pi\)
0.957693 + 0.287791i \(0.0929208\pi\)
\(510\) 0 0
\(511\) −5107.04 −0.442118
\(512\) −512.000 −0.0441942
\(513\) 151.225 0.0130151
\(514\) −8501.87 −0.729575
\(515\) 0 0
\(516\) −713.721 −0.0608911
\(517\) −4370.88 −0.371820
\(518\) −979.134 −0.0830515
\(519\) −1503.05 −0.127123
\(520\) 0 0
\(521\) 150.733 0.0126751 0.00633756 0.999980i \(-0.497983\pi\)
0.00633756 + 0.999980i \(0.497983\pi\)
\(522\) −8673.18 −0.727232
\(523\) 21831.2 1.82526 0.912630 0.408787i \(-0.134048\pi\)
0.912630 + 0.408787i \(0.134048\pi\)
\(524\) −8866.97 −0.739228
\(525\) 0 0
\(526\) 7197.67 0.596641
\(527\) 9085.14 0.750958
\(528\) 286.869 0.0236447
\(529\) 529.000 0.0434783
\(530\) 0 0
\(531\) −7799.36 −0.637408
\(532\) −609.324 −0.0496570
\(533\) −234.402 −0.0190489
\(534\) 751.348 0.0608877
\(535\) 0 0
\(536\) 1059.11 0.0853483
\(537\) −1345.92 −0.108158
\(538\) 10125.0 0.811379
\(539\) 16574.2 1.32449
\(540\) 0 0
\(541\) 5796.22 0.460627 0.230313 0.973117i \(-0.426025\pi\)
0.230313 + 0.973117i \(0.426025\pi\)
\(542\) −3709.16 −0.293952
\(543\) 580.297 0.0458617
\(544\) 1810.73 0.142711
\(545\) 0 0
\(546\) 318.568 0.0249697
\(547\) −9736.32 −0.761051 −0.380526 0.924770i \(-0.624257\pi\)
−0.380526 + 0.924770i \(0.624257\pi\)
\(548\) 4717.92 0.367773
\(549\) −12143.8 −0.944053
\(550\) 0 0
\(551\) 854.535 0.0660698
\(552\) 98.4087 0.00758796
\(553\) 16294.5 1.25300
\(554\) 17495.8 1.34174
\(555\) 0 0
\(556\) 964.895 0.0735983
\(557\) −5064.36 −0.385249 −0.192625 0.981273i \(-0.561700\pi\)
−0.192625 + 0.981273i \(0.561700\pi\)
\(558\) −8578.19 −0.650795
\(559\) 3433.52 0.259790
\(560\) 0 0
\(561\) −1014.54 −0.0763526
\(562\) −8093.76 −0.607499
\(563\) −3091.61 −0.231431 −0.115716 0.993282i \(-0.536916\pi\)
−0.115716 + 0.993282i \(0.536916\pi\)
\(564\) −278.931 −0.0208247
\(565\) 0 0
\(566\) 3197.03 0.237423
\(567\) 20427.7 1.51302
\(568\) −970.605 −0.0717002
\(569\) 8120.51 0.598294 0.299147 0.954207i \(-0.403298\pi\)
0.299147 + 0.954207i \(0.403298\pi\)
\(570\) 0 0
\(571\) −5547.16 −0.406552 −0.203276 0.979121i \(-0.565159\pi\)
−0.203276 + 0.979121i \(0.565159\pi\)
\(572\) −1380.05 −0.100879
\(573\) −1113.44 −0.0811777
\(574\) −1318.17 −0.0958527
\(575\) 0 0
\(576\) −1709.69 −0.123676
\(577\) −23746.0 −1.71327 −0.856636 0.515922i \(-0.827450\pi\)
−0.856636 + 0.515922i \(0.827450\pi\)
\(578\) 3422.18 0.246270
\(579\) −346.833 −0.0248945
\(580\) 0 0
\(581\) −23412.8 −1.67182
\(582\) 366.835 0.0261268
\(583\) −22568.1 −1.60322
\(584\) 1411.86 0.100040
\(585\) 0 0
\(586\) −9085.23 −0.640456
\(587\) −17023.6 −1.19700 −0.598500 0.801123i \(-0.704237\pi\)
−0.598500 + 0.801123i \(0.704237\pi\)
\(588\) 1057.70 0.0741814
\(589\) 845.176 0.0591254
\(590\) 0 0
\(591\) 669.032 0.0465656
\(592\) 270.685 0.0187923
\(593\) −2675.31 −0.185264 −0.0926321 0.995700i \(-0.529528\pi\)
−0.0926321 + 0.995700i \(0.529528\pi\)
\(594\) 1926.11 0.133046
\(595\) 0 0
\(596\) −4112.57 −0.282647
\(597\) 1676.98 0.114965
\(598\) −473.419 −0.0323738
\(599\) 15350.4 1.04708 0.523538 0.852002i \(-0.324612\pi\)
0.523538 + 0.852002i \(0.324612\pi\)
\(600\) 0 0
\(601\) −15429.3 −1.04721 −0.523604 0.851962i \(-0.675413\pi\)
−0.523604 + 0.851962i \(0.675413\pi\)
\(602\) 19308.6 1.30724
\(603\) 3536.63 0.238844
\(604\) 6044.95 0.407228
\(605\) 0 0
\(606\) −1839.47 −0.123306
\(607\) 6027.74 0.403061 0.201531 0.979482i \(-0.435408\pi\)
0.201531 + 0.979482i \(0.435408\pi\)
\(608\) 168.449 0.0112361
\(609\) −2512.43 −0.167174
\(610\) 0 0
\(611\) 1341.86 0.0888478
\(612\) 6046.48 0.399370
\(613\) 21260.9 1.40085 0.700423 0.713728i \(-0.252995\pi\)
0.700423 + 0.713728i \(0.252995\pi\)
\(614\) −4732.78 −0.311074
\(615\) 0 0
\(616\) −7760.80 −0.507616
\(617\) −20739.7 −1.35324 −0.676621 0.736332i \(-0.736556\pi\)
−0.676621 + 0.736332i \(0.736556\pi\)
\(618\) 414.891 0.0270054
\(619\) −17994.4 −1.16843 −0.584214 0.811600i \(-0.698597\pi\)
−0.584214 + 0.811600i \(0.698597\pi\)
\(620\) 0 0
\(621\) 660.740 0.0426966
\(622\) −1660.32 −0.107030
\(623\) −20326.6 −1.30717
\(624\) −88.0690 −0.00564997
\(625\) 0 0
\(626\) −14364.1 −0.917098
\(627\) −94.3808 −0.00601149
\(628\) 8388.15 0.532999
\(629\) −957.300 −0.0606837
\(630\) 0 0
\(631\) 22242.4 1.40326 0.701630 0.712542i \(-0.252456\pi\)
0.701630 + 0.712542i \(0.252456\pi\)
\(632\) −4504.65 −0.283521
\(633\) −451.498 −0.0283498
\(634\) 3820.13 0.239301
\(635\) 0 0
\(636\) −1440.20 −0.0897920
\(637\) −5088.30 −0.316492
\(638\) 10884.0 0.675394
\(639\) −3241.09 −0.200650
\(640\) 0 0
\(641\) 12480.7 0.769046 0.384523 0.923115i \(-0.374366\pi\)
0.384523 + 0.923115i \(0.374366\pi\)
\(642\) 33.5771 0.00206415
\(643\) 3063.19 0.187870 0.0939352 0.995578i \(-0.470055\pi\)
0.0939352 + 0.995578i \(0.470055\pi\)
\(644\) −2662.30 −0.162902
\(645\) 0 0
\(646\) −595.736 −0.0362832
\(647\) −20052.9 −1.21849 −0.609243 0.792984i \(-0.708526\pi\)
−0.609243 + 0.792984i \(0.708526\pi\)
\(648\) −5647.30 −0.342356
\(649\) 9787.43 0.591973
\(650\) 0 0
\(651\) −2484.92 −0.149603
\(652\) −2812.18 −0.168917
\(653\) 16978.6 1.01749 0.508746 0.860917i \(-0.330109\pi\)
0.508746 + 0.860917i \(0.330109\pi\)
\(654\) −733.957 −0.0438838
\(655\) 0 0
\(656\) 364.413 0.0216889
\(657\) 4714.54 0.279957
\(658\) 7546.04 0.447075
\(659\) −15608.4 −0.922637 −0.461319 0.887235i \(-0.652623\pi\)
−0.461319 + 0.887235i \(0.652623\pi\)
\(660\) 0 0
\(661\) 3744.26 0.220325 0.110163 0.993914i \(-0.464863\pi\)
0.110163 + 0.993914i \(0.464863\pi\)
\(662\) −15080.8 −0.885396
\(663\) 311.464 0.0182447
\(664\) 6472.55 0.378288
\(665\) 0 0
\(666\) 903.882 0.0525897
\(667\) 3733.69 0.216745
\(668\) −12252.2 −0.709656
\(669\) −3021.02 −0.174588
\(670\) 0 0
\(671\) 15239.3 0.876761
\(672\) −495.261 −0.0284302
\(673\) −8962.72 −0.513355 −0.256677 0.966497i \(-0.582628\pi\)
−0.256677 + 0.966497i \(0.582628\pi\)
\(674\) −20138.8 −1.15092
\(675\) 0 0
\(676\) −8364.32 −0.475895
\(677\) −30864.5 −1.75217 −0.876086 0.482155i \(-0.839854\pi\)
−0.876086 + 0.482155i \(0.839854\pi\)
\(678\) −45.1771 −0.00255902
\(679\) −9924.14 −0.560904
\(680\) 0 0
\(681\) 2093.81 0.117819
\(682\) 10764.8 0.604406
\(683\) −2135.02 −0.119611 −0.0598055 0.998210i \(-0.519048\pi\)
−0.0598055 + 0.998210i \(0.519048\pi\)
\(684\) 562.494 0.0314437
\(685\) 0 0
\(686\) −8762.86 −0.487708
\(687\) −294.687 −0.0163654
\(688\) −5337.93 −0.295794
\(689\) 6928.44 0.383095
\(690\) 0 0
\(691\) −14271.3 −0.785680 −0.392840 0.919607i \(-0.628507\pi\)
−0.392840 + 0.919607i \(0.628507\pi\)
\(692\) −11241.3 −0.617531
\(693\) −25915.2 −1.42054
\(694\) 12062.1 0.659758
\(695\) 0 0
\(696\) 694.570 0.0378270
\(697\) −1288.78 −0.0700373
\(698\) 22703.9 1.23117
\(699\) −3094.35 −0.167438
\(700\) 0 0
\(701\) −13473.5 −0.725945 −0.362973 0.931800i \(-0.618238\pi\)
−0.362973 + 0.931800i \(0.618238\pi\)
\(702\) −591.317 −0.0317918
\(703\) −89.0560 −0.00477782
\(704\) 2145.50 0.114860
\(705\) 0 0
\(706\) −9729.61 −0.518667
\(707\) 49764.1 2.64720
\(708\) 624.592 0.0331548
\(709\) −8117.53 −0.429986 −0.214993 0.976616i \(-0.568973\pi\)
−0.214993 + 0.976616i \(0.568973\pi\)
\(710\) 0 0
\(711\) −15042.1 −0.793424
\(712\) 5619.34 0.295778
\(713\) 3692.80 0.193964
\(714\) 1751.53 0.0918061
\(715\) 0 0
\(716\) −10066.1 −0.525403
\(717\) −2420.49 −0.126074
\(718\) 11619.0 0.603923
\(719\) −34187.5 −1.77327 −0.886634 0.462471i \(-0.846963\pi\)
−0.886634 + 0.462471i \(0.846963\pi\)
\(720\) 0 0
\(721\) −11224.2 −0.579767
\(722\) 13662.6 0.704250
\(723\) 276.663 0.0142313
\(724\) 4340.04 0.222785
\(725\) 0 0
\(726\) 221.614 0.0113290
\(727\) −26638.2 −1.35895 −0.679476 0.733698i \(-0.737793\pi\)
−0.679476 + 0.733698i \(0.737793\pi\)
\(728\) 2382.57 0.121297
\(729\) −18442.9 −0.936995
\(730\) 0 0
\(731\) 18878.0 0.955171
\(732\) 972.507 0.0491050
\(733\) 26875.8 1.35427 0.677135 0.735858i \(-0.263221\pi\)
0.677135 + 0.735858i \(0.263221\pi\)
\(734\) 13968.8 0.702447
\(735\) 0 0
\(736\) 736.000 0.0368605
\(737\) −4438.13 −0.221819
\(738\) 1216.86 0.0606957
\(739\) 5873.86 0.292386 0.146193 0.989256i \(-0.453298\pi\)
0.146193 + 0.989256i \(0.453298\pi\)
\(740\) 0 0
\(741\) 28.9750 0.00143647
\(742\) 38962.4 1.92770
\(743\) 16863.9 0.832673 0.416337 0.909210i \(-0.363314\pi\)
0.416337 + 0.909210i \(0.363314\pi\)
\(744\) 686.963 0.0338512
\(745\) 0 0
\(746\) 17103.1 0.839394
\(747\) 21613.4 1.05863
\(748\) −7587.74 −0.370903
\(749\) −908.376 −0.0443142
\(750\) 0 0
\(751\) 24885.3 1.20916 0.604578 0.796546i \(-0.293342\pi\)
0.604578 + 0.796546i \(0.293342\pi\)
\(752\) −2086.13 −0.101161
\(753\) −3764.67 −0.182194
\(754\) −3341.39 −0.161388
\(755\) 0 0
\(756\) −3325.30 −0.159974
\(757\) 14692.8 0.705442 0.352721 0.935728i \(-0.385256\pi\)
0.352721 + 0.935728i \(0.385256\pi\)
\(758\) −19866.8 −0.951971
\(759\) −412.374 −0.0197210
\(760\) 0 0
\(761\) −7531.01 −0.358737 −0.179369 0.983782i \(-0.557405\pi\)
−0.179369 + 0.983782i \(0.557405\pi\)
\(762\) 1320.47 0.0627765
\(763\) 19856.1 0.942121
\(764\) −8327.46 −0.394342
\(765\) 0 0
\(766\) 19497.0 0.919656
\(767\) −3004.75 −0.141454
\(768\) 136.916 0.00643301
\(769\) 20747.5 0.972916 0.486458 0.873704i \(-0.338289\pi\)
0.486458 + 0.873704i \(0.338289\pi\)
\(770\) 0 0
\(771\) 2273.53 0.106199
\(772\) −2593.97 −0.120931
\(773\) 940.128 0.0437439 0.0218720 0.999761i \(-0.493037\pi\)
0.0218720 + 0.999761i \(0.493037\pi\)
\(774\) −17824.6 −0.827769
\(775\) 0 0
\(776\) 2743.56 0.126918
\(777\) 261.835 0.0120892
\(778\) 21034.1 0.969290
\(779\) −119.893 −0.00551426
\(780\) 0 0
\(781\) 4067.25 0.186348
\(782\) −2602.93 −0.119029
\(783\) 4663.51 0.212849
\(784\) 7910.52 0.360355
\(785\) 0 0
\(786\) 2371.16 0.107604
\(787\) 6072.14 0.275030 0.137515 0.990500i \(-0.456088\pi\)
0.137515 + 0.990500i \(0.456088\pi\)
\(788\) 5003.70 0.226205
\(789\) −1924.76 −0.0868484
\(790\) 0 0
\(791\) 1222.20 0.0549384
\(792\) 7164.34 0.321432
\(793\) −4678.47 −0.209505
\(794\) 8235.88 0.368111
\(795\) 0 0
\(796\) 12542.1 0.558473
\(797\) −5424.76 −0.241098 −0.120549 0.992707i \(-0.538465\pi\)
−0.120549 + 0.992707i \(0.538465\pi\)
\(798\) 162.942 0.00722819
\(799\) 7377.77 0.326667
\(800\) 0 0
\(801\) 18764.4 0.827723
\(802\) 14748.6 0.649365
\(803\) −5916.28 −0.260001
\(804\) −283.223 −0.0124235
\(805\) 0 0
\(806\) −3304.80 −0.144425
\(807\) −2707.59 −0.118106
\(808\) −13757.4 −0.598991
\(809\) −13646.3 −0.593051 −0.296526 0.955025i \(-0.595828\pi\)
−0.296526 + 0.955025i \(0.595828\pi\)
\(810\) 0 0
\(811\) −10015.4 −0.433647 −0.216823 0.976211i \(-0.569570\pi\)
−0.216823 + 0.976211i \(0.569570\pi\)
\(812\) −18790.5 −0.812091
\(813\) 991.886 0.0427884
\(814\) −1134.28 −0.0488410
\(815\) 0 0
\(816\) −484.217 −0.0207733
\(817\) 1756.19 0.0752037
\(818\) −25883.1 −1.10633
\(819\) 7955.99 0.339444
\(820\) 0 0
\(821\) 6525.48 0.277394 0.138697 0.990335i \(-0.455709\pi\)
0.138697 + 0.990335i \(0.455709\pi\)
\(822\) −1261.64 −0.0535338
\(823\) −42874.0 −1.81591 −0.907954 0.419069i \(-0.862356\pi\)
−0.907954 + 0.419069i \(0.862356\pi\)
\(824\) 3102.97 0.131186
\(825\) 0 0
\(826\) −16897.4 −0.711785
\(827\) 21654.4 0.910517 0.455259 0.890359i \(-0.349547\pi\)
0.455259 + 0.890359i \(0.349547\pi\)
\(828\) 2457.68 0.103153
\(829\) −22392.7 −0.938153 −0.469077 0.883158i \(-0.655413\pi\)
−0.469077 + 0.883158i \(0.655413\pi\)
\(830\) 0 0
\(831\) −4678.64 −0.195307
\(832\) −658.669 −0.0274462
\(833\) −27976.2 −1.16365
\(834\) −258.027 −0.0107131
\(835\) 0 0
\(836\) −705.875 −0.0292024
\(837\) 4612.44 0.190477
\(838\) −11266.9 −0.464450
\(839\) 21335.4 0.877926 0.438963 0.898505i \(-0.355346\pi\)
0.438963 + 0.898505i \(0.355346\pi\)
\(840\) 0 0
\(841\) 1963.43 0.0805049
\(842\) 8410.97 0.344253
\(843\) 2164.39 0.0884290
\(844\) −3376.76 −0.137716
\(845\) 0 0
\(846\) −6966.09 −0.283096
\(847\) −5995.42 −0.243217
\(848\) −10771.3 −0.436188
\(849\) −854.934 −0.0345598
\(850\) 0 0
\(851\) −389.109 −0.0156739
\(852\) 259.554 0.0104368
\(853\) 11610.2 0.466034 0.233017 0.972473i \(-0.425140\pi\)
0.233017 + 0.972473i \(0.425140\pi\)
\(854\) −26309.7 −1.05421
\(855\) 0 0
\(856\) 251.123 0.0100271
\(857\) −27905.6 −1.11230 −0.556148 0.831084i \(-0.687721\pi\)
−0.556148 + 0.831084i \(0.687721\pi\)
\(858\) 369.047 0.0146842
\(859\) 4529.52 0.179913 0.0899565 0.995946i \(-0.471327\pi\)
0.0899565 + 0.995946i \(0.471327\pi\)
\(860\) 0 0
\(861\) 352.499 0.0139525
\(862\) −30151.5 −1.19137
\(863\) 10511.6 0.414622 0.207311 0.978275i \(-0.433529\pi\)
0.207311 + 0.978275i \(0.433529\pi\)
\(864\) 919.291 0.0361978
\(865\) 0 0
\(866\) 6196.11 0.243132
\(867\) −915.143 −0.0358476
\(868\) −18584.7 −0.726735
\(869\) 18876.4 0.736868
\(870\) 0 0
\(871\) 1362.51 0.0530044
\(872\) −5489.27 −0.213177
\(873\) 9161.42 0.355174
\(874\) −242.146 −0.00937153
\(875\) 0 0
\(876\) −377.552 −0.0145620
\(877\) −20949.8 −0.806643 −0.403321 0.915058i \(-0.632144\pi\)
−0.403321 + 0.915058i \(0.632144\pi\)
\(878\) −13735.5 −0.527961
\(879\) 2429.53 0.0932263
\(880\) 0 0
\(881\) 39907.1 1.52611 0.763057 0.646332i \(-0.223698\pi\)
0.763057 + 0.646332i \(0.223698\pi\)
\(882\) 26415.2 1.00844
\(883\) 16565.2 0.631329 0.315665 0.948871i \(-0.397773\pi\)
0.315665 + 0.948871i \(0.397773\pi\)
\(884\) 2329.44 0.0886285
\(885\) 0 0
\(886\) −11756.6 −0.445790
\(887\) −8217.44 −0.311065 −0.155532 0.987831i \(-0.549709\pi\)
−0.155532 + 0.987831i \(0.549709\pi\)
\(888\) −72.3851 −0.00273546
\(889\) −35723.3 −1.34772
\(890\) 0 0
\(891\) 23664.6 0.889779
\(892\) −22594.3 −0.848108
\(893\) 686.342 0.0257195
\(894\) 1099.76 0.0411427
\(895\) 0 0
\(896\) −3704.06 −0.138107
\(897\) 126.599 0.00471240
\(898\) −27341.5 −1.01603
\(899\) 26063.8 0.966937
\(900\) 0 0
\(901\) 38093.6 1.40853
\(902\) −1527.05 −0.0563692
\(903\) −5163.41 −0.190285
\(904\) −337.880 −0.0124311
\(905\) 0 0
\(906\) −1616.51 −0.0592770
\(907\) −25129.0 −0.919952 −0.459976 0.887931i \(-0.652142\pi\)
−0.459976 + 0.887931i \(0.652142\pi\)
\(908\) 15659.6 0.572338
\(909\) −45939.5 −1.67625
\(910\) 0 0
\(911\) −9275.75 −0.337343 −0.168671 0.985672i \(-0.553948\pi\)
−0.168671 + 0.985672i \(0.553948\pi\)
\(912\) −45.0459 −0.00163555
\(913\) −27122.7 −0.983166
\(914\) −33894.4 −1.22662
\(915\) 0 0
\(916\) −2203.97 −0.0794990
\(917\) −64148.1 −2.31010
\(918\) −3251.15 −0.116889
\(919\) −47822.1 −1.71655 −0.858273 0.513194i \(-0.828462\pi\)
−0.858273 + 0.513194i \(0.828462\pi\)
\(920\) 0 0
\(921\) 1265.62 0.0452807
\(922\) 11166.7 0.398866
\(923\) −1248.65 −0.0445285
\(924\) 2075.35 0.0738898
\(925\) 0 0
\(926\) −11716.0 −0.415781
\(927\) 10361.6 0.367119
\(928\) 5194.70 0.183755
\(929\) −447.878 −0.0158175 −0.00790873 0.999969i \(-0.502517\pi\)
−0.00790873 + 0.999969i \(0.502517\pi\)
\(930\) 0 0
\(931\) −2602.58 −0.0916179
\(932\) −23142.7 −0.813373
\(933\) 443.994 0.0155795
\(934\) −27899.6 −0.977414
\(935\) 0 0
\(936\) −2199.46 −0.0768072
\(937\) 3402.08 0.118614 0.0593069 0.998240i \(-0.481111\pi\)
0.0593069 + 0.998240i \(0.481111\pi\)
\(938\) 7662.15 0.266714
\(939\) 3841.17 0.133495
\(940\) 0 0
\(941\) 14084.0 0.487912 0.243956 0.969786i \(-0.421555\pi\)
0.243956 + 0.969786i \(0.421555\pi\)
\(942\) −2243.12 −0.0775846
\(943\) −523.844 −0.0180898
\(944\) 4671.33 0.161058
\(945\) 0 0
\(946\) 22368.2 0.768766
\(947\) 10020.6 0.343850 0.171925 0.985110i \(-0.445001\pi\)
0.171925 + 0.985110i \(0.445001\pi\)
\(948\) 1204.61 0.0412700
\(949\) 1816.30 0.0621283
\(950\) 0 0
\(951\) −1021.56 −0.0348331
\(952\) 13099.7 0.445972
\(953\) 45482.6 1.54599 0.772993 0.634415i \(-0.218759\pi\)
0.772993 + 0.634415i \(0.218759\pi\)
\(954\) −35968.0 −1.22066
\(955\) 0 0
\(956\) −18102.9 −0.612435
\(957\) −2910.54 −0.0983120
\(958\) −14309.7 −0.482594
\(959\) 34131.8 1.14929
\(960\) 0 0
\(961\) −4012.67 −0.134694
\(962\) 348.226 0.0116707
\(963\) 838.562 0.0280605
\(964\) 2069.17 0.0691322
\(965\) 0 0
\(966\) 711.938 0.0237124
\(967\) −50955.7 −1.69455 −0.847273 0.531158i \(-0.821757\pi\)
−0.847273 + 0.531158i \(0.821757\pi\)
\(968\) 1657.45 0.0550336
\(969\) 159.309 0.00528146
\(970\) 0 0
\(971\) −38192.3 −1.26226 −0.631128 0.775679i \(-0.717408\pi\)
−0.631128 + 0.775679i \(0.717408\pi\)
\(972\) 4612.78 0.152217
\(973\) 6980.53 0.229995
\(974\) −29623.7 −0.974543
\(975\) 0 0
\(976\) 7273.39 0.238540
\(977\) 28889.6 0.946018 0.473009 0.881058i \(-0.343168\pi\)
0.473009 + 0.881058i \(0.343168\pi\)
\(978\) 752.020 0.0245879
\(979\) −23547.4 −0.768722
\(980\) 0 0
\(981\) −18330.0 −0.596568
\(982\) −6185.88 −0.201018
\(983\) −51725.2 −1.67831 −0.839154 0.543894i \(-0.816949\pi\)
−0.839154 + 0.543894i \(0.816949\pi\)
\(984\) −97.4495 −0.00315709
\(985\) 0 0
\(986\) −18371.5 −0.593375
\(987\) −2017.93 −0.0650773
\(988\) 216.704 0.00697801
\(989\) 7673.27 0.246710
\(990\) 0 0
\(991\) 24851.8 0.796613 0.398307 0.917252i \(-0.369598\pi\)
0.398307 + 0.917252i \(0.369598\pi\)
\(992\) 5137.80 0.164441
\(993\) 4032.83 0.128880
\(994\) −7021.84 −0.224064
\(995\) 0 0
\(996\) −1730.86 −0.0550645
\(997\) −2537.99 −0.0806209 −0.0403104 0.999187i \(-0.512835\pi\)
−0.0403104 + 0.999187i \(0.512835\pi\)
\(998\) −34501.2 −1.09430
\(999\) −486.011 −0.0153921
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 1150.4.a.q.1.3 5
5.2 odd 4 1150.4.b.r.599.3 10
5.3 odd 4 1150.4.b.r.599.8 10
5.4 even 2 1150.4.a.v.1.3 yes 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1150.4.a.q.1.3 5 1.1 even 1 trivial
1150.4.a.v.1.3 yes 5 5.4 even 2
1150.4.b.r.599.3 10 5.2 odd 4
1150.4.b.r.599.8 10 5.3 odd 4