Properties

Label 350.4.a.n.1.1
Level $350$
Weight $4$
Character 350.1
Self dual yes
Analytic conductor $20.651$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [350,4,Mod(1,350)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(350, 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("350.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 350.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: \(20.6506685020\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 350.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000 q^{2} -4.00000 q^{3} +4.00000 q^{4} -8.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} -11.0000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} -4.00000 q^{3} +4.00000 q^{4} -8.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} -11.0000 q^{9} +5.00000 q^{11} -16.0000 q^{12} +82.0000 q^{13} -14.0000 q^{14} +16.0000 q^{16} -12.0000 q^{17} -22.0000 q^{18} -42.0000 q^{19} +28.0000 q^{21} +10.0000 q^{22} +175.000 q^{23} -32.0000 q^{24} +164.000 q^{26} +152.000 q^{27} -28.0000 q^{28} +1.00000 q^{29} +226.000 q^{31} +32.0000 q^{32} -20.0000 q^{33} -24.0000 q^{34} -44.0000 q^{36} -19.0000 q^{37} -84.0000 q^{38} -328.000 q^{39} +16.0000 q^{41} +56.0000 q^{42} +281.000 q^{43} +20.0000 q^{44} +350.000 q^{46} +334.000 q^{47} -64.0000 q^{48} +49.0000 q^{49} +48.0000 q^{51} +328.000 q^{52} -398.000 q^{53} +304.000 q^{54} -56.0000 q^{56} +168.000 q^{57} +2.00000 q^{58} +106.000 q^{59} +48.0000 q^{61} +452.000 q^{62} +77.0000 q^{63} +64.0000 q^{64} -40.0000 q^{66} +483.000 q^{67} -48.0000 q^{68} -700.000 q^{69} -15.0000 q^{71} -88.0000 q^{72} +1044.00 q^{73} -38.0000 q^{74} -168.000 q^{76} -35.0000 q^{77} -656.000 q^{78} -1253.00 q^{79} -311.000 q^{81} +32.0000 q^{82} +758.000 q^{83} +112.000 q^{84} +562.000 q^{86} -4.00000 q^{87} +40.0000 q^{88} +86.0000 q^{89} -574.000 q^{91} +700.000 q^{92} -904.000 q^{93} +668.000 q^{94} -128.000 q^{96} +710.000 q^{97} +98.0000 q^{98} -55.0000 q^{99} +O(q^{100})\)

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
\(3\) −4.00000 −0.769800 −0.384900 0.922958i \(-0.625764\pi\)
−0.384900 + 0.922958i \(0.625764\pi\)
\(4\) 4.00000 0.500000
\(5\) 0 0
\(6\) −8.00000 −0.544331
\(7\) −7.00000 −0.377964
\(8\) 8.00000 0.353553
\(9\) −11.0000 −0.407407
\(10\) 0 0
\(11\) 5.00000 0.137051 0.0685253 0.997649i \(-0.478171\pi\)
0.0685253 + 0.997649i \(0.478171\pi\)
\(12\) −16.0000 −0.384900
\(13\) 82.0000 1.74944 0.874720 0.484629i \(-0.161046\pi\)
0.874720 + 0.484629i \(0.161046\pi\)
\(14\) −14.0000 −0.267261
\(15\) 0 0
\(16\) 16.0000 0.250000
\(17\) −12.0000 −0.171202 −0.0856008 0.996330i \(-0.527281\pi\)
−0.0856008 + 0.996330i \(0.527281\pi\)
\(18\) −22.0000 −0.288081
\(19\) −42.0000 −0.507130 −0.253565 0.967318i \(-0.581603\pi\)
−0.253565 + 0.967318i \(0.581603\pi\)
\(20\) 0 0
\(21\) 28.0000 0.290957
\(22\) 10.0000 0.0969094
\(23\) 175.000 1.58652 0.793261 0.608881i \(-0.208381\pi\)
0.793261 + 0.608881i \(0.208381\pi\)
\(24\) −32.0000 −0.272166
\(25\) 0 0
\(26\) 164.000 1.23704
\(27\) 152.000 1.08342
\(28\) −28.0000 −0.188982
\(29\) 1.00000 0.00640329 0.00320164 0.999995i \(-0.498981\pi\)
0.00320164 + 0.999995i \(0.498981\pi\)
\(30\) 0 0
\(31\) 226.000 1.30938 0.654690 0.755897i \(-0.272799\pi\)
0.654690 + 0.755897i \(0.272799\pi\)
\(32\) 32.0000 0.176777
\(33\) −20.0000 −0.105502
\(34\) −24.0000 −0.121058
\(35\) 0 0
\(36\) −44.0000 −0.203704
\(37\) −19.0000 −0.0844211 −0.0422106 0.999109i \(-0.513440\pi\)
−0.0422106 + 0.999109i \(0.513440\pi\)
\(38\) −84.0000 −0.358595
\(39\) −328.000 −1.34672
\(40\) 0 0
\(41\) 16.0000 0.0609459 0.0304729 0.999536i \(-0.490299\pi\)
0.0304729 + 0.999536i \(0.490299\pi\)
\(42\) 56.0000 0.205738
\(43\) 281.000 0.996560 0.498280 0.867016i \(-0.333965\pi\)
0.498280 + 0.867016i \(0.333965\pi\)
\(44\) 20.0000 0.0685253
\(45\) 0 0
\(46\) 350.000 1.12184
\(47\) 334.000 1.03657 0.518286 0.855207i \(-0.326570\pi\)
0.518286 + 0.855207i \(0.326570\pi\)
\(48\) −64.0000 −0.192450
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) 48.0000 0.131791
\(52\) 328.000 0.874720
\(53\) −398.000 −1.03150 −0.515750 0.856739i \(-0.672487\pi\)
−0.515750 + 0.856739i \(0.672487\pi\)
\(54\) 304.000 0.766096
\(55\) 0 0
\(56\) −56.0000 −0.133631
\(57\) 168.000 0.390388
\(58\) 2.00000 0.00452781
\(59\) 106.000 0.233899 0.116949 0.993138i \(-0.462688\pi\)
0.116949 + 0.993138i \(0.462688\pi\)
\(60\) 0 0
\(61\) 48.0000 0.100750 0.0503752 0.998730i \(-0.483958\pi\)
0.0503752 + 0.998730i \(0.483958\pi\)
\(62\) 452.000 0.925872
\(63\) 77.0000 0.153986
\(64\) 64.0000 0.125000
\(65\) 0 0
\(66\) −40.0000 −0.0746009
\(67\) 483.000 0.880714 0.440357 0.897823i \(-0.354852\pi\)
0.440357 + 0.897823i \(0.354852\pi\)
\(68\) −48.0000 −0.0856008
\(69\) −700.000 −1.22131
\(70\) 0 0
\(71\) −15.0000 −0.0250729 −0.0125364 0.999921i \(-0.503991\pi\)
−0.0125364 + 0.999921i \(0.503991\pi\)
\(72\) −88.0000 −0.144040
\(73\) 1044.00 1.67385 0.836924 0.547319i \(-0.184351\pi\)
0.836924 + 0.547319i \(0.184351\pi\)
\(74\) −38.0000 −0.0596947
\(75\) 0 0
\(76\) −168.000 −0.253565
\(77\) −35.0000 −0.0518003
\(78\) −656.000 −0.952274
\(79\) −1253.00 −1.78447 −0.892237 0.451567i \(-0.850865\pi\)
−0.892237 + 0.451567i \(0.850865\pi\)
\(80\) 0 0
\(81\) −311.000 −0.426612
\(82\) 32.0000 0.0430952
\(83\) 758.000 1.00243 0.501213 0.865324i \(-0.332887\pi\)
0.501213 + 0.865324i \(0.332887\pi\)
\(84\) 112.000 0.145479
\(85\) 0 0
\(86\) 562.000 0.704675
\(87\) −4.00000 −0.00492925
\(88\) 40.0000 0.0484547
\(89\) 86.0000 0.102427 0.0512134 0.998688i \(-0.483691\pi\)
0.0512134 + 0.998688i \(0.483691\pi\)
\(90\) 0 0
\(91\) −574.000 −0.661226
\(92\) 700.000 0.793261
\(93\) −904.000 −1.00796
\(94\) 668.000 0.732967
\(95\) 0 0
\(96\) −128.000 −0.136083
\(97\) 710.000 0.743192 0.371596 0.928395i \(-0.378811\pi\)
0.371596 + 0.928395i \(0.378811\pi\)
\(98\) 98.0000 0.101015
\(99\) −55.0000 −0.0558354
\(100\) 0 0
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 96.0000 0.0931904
\(103\) −838.000 −0.801656 −0.400828 0.916153i \(-0.631278\pi\)
−0.400828 + 0.916153i \(0.631278\pi\)
\(104\) 656.000 0.618520
\(105\) 0 0
\(106\) −796.000 −0.729381
\(107\) −2164.00 −1.95516 −0.977578 0.210572i \(-0.932467\pi\)
−0.977578 + 0.210572i \(0.932467\pi\)
\(108\) 608.000 0.541711
\(109\) −1827.00 −1.60546 −0.802729 0.596344i \(-0.796619\pi\)
−0.802729 + 0.596344i \(0.796619\pi\)
\(110\) 0 0
\(111\) 76.0000 0.0649874
\(112\) −112.000 −0.0944911
\(113\) −93.0000 −0.0774222 −0.0387111 0.999250i \(-0.512325\pi\)
−0.0387111 + 0.999250i \(0.512325\pi\)
\(114\) 336.000 0.276046
\(115\) 0 0
\(116\) 4.00000 0.00320164
\(117\) −902.000 −0.712734
\(118\) 212.000 0.165391
\(119\) 84.0000 0.0647081
\(120\) 0 0
\(121\) −1306.00 −0.981217
\(122\) 96.0000 0.0712412
\(123\) −64.0000 −0.0469161
\(124\) 904.000 0.654690
\(125\) 0 0
\(126\) 154.000 0.108884
\(127\) −1433.00 −1.00125 −0.500623 0.865666i \(-0.666896\pi\)
−0.500623 + 0.865666i \(0.666896\pi\)
\(128\) 128.000 0.0883883
\(129\) −1124.00 −0.767153
\(130\) 0 0
\(131\) 868.000 0.578912 0.289456 0.957191i \(-0.406526\pi\)
0.289456 + 0.957191i \(0.406526\pi\)
\(132\) −80.0000 −0.0527508
\(133\) 294.000 0.191677
\(134\) 966.000 0.622759
\(135\) 0 0
\(136\) −96.0000 −0.0605289
\(137\) −2646.00 −1.65010 −0.825048 0.565063i \(-0.808852\pi\)
−0.825048 + 0.565063i \(0.808852\pi\)
\(138\) −1400.00 −0.863594
\(139\) 896.000 0.546746 0.273373 0.961908i \(-0.411861\pi\)
0.273373 + 0.961908i \(0.411861\pi\)
\(140\) 0 0
\(141\) −1336.00 −0.797954
\(142\) −30.0000 −0.0177292
\(143\) 410.000 0.239762
\(144\) −176.000 −0.101852
\(145\) 0 0
\(146\) 2088.00 1.18359
\(147\) −196.000 −0.109971
\(148\) −76.0000 −0.0422106
\(149\) 2523.00 1.38720 0.693598 0.720362i \(-0.256024\pi\)
0.693598 + 0.720362i \(0.256024\pi\)
\(150\) 0 0
\(151\) 2433.00 1.31122 0.655612 0.755098i \(-0.272411\pi\)
0.655612 + 0.755098i \(0.272411\pi\)
\(152\) −336.000 −0.179297
\(153\) 132.000 0.0697488
\(154\) −70.0000 −0.0366283
\(155\) 0 0
\(156\) −1312.00 −0.673359
\(157\) −2572.00 −1.30744 −0.653720 0.756737i \(-0.726792\pi\)
−0.653720 + 0.756737i \(0.726792\pi\)
\(158\) −2506.00 −1.26181
\(159\) 1592.00 0.794049
\(160\) 0 0
\(161\) −1225.00 −0.599649
\(162\) −622.000 −0.301660
\(163\) 2488.00 1.19555 0.597777 0.801663i \(-0.296051\pi\)
0.597777 + 0.801663i \(0.296051\pi\)
\(164\) 64.0000 0.0304729
\(165\) 0 0
\(166\) 1516.00 0.708822
\(167\) 3054.00 1.41512 0.707562 0.706652i \(-0.249795\pi\)
0.707562 + 0.706652i \(0.249795\pi\)
\(168\) 224.000 0.102869
\(169\) 4527.00 2.06054
\(170\) 0 0
\(171\) 462.000 0.206608
\(172\) 1124.00 0.498280
\(173\) −3894.00 −1.71130 −0.855651 0.517553i \(-0.826843\pi\)
−0.855651 + 0.517553i \(0.826843\pi\)
\(174\) −8.00000 −0.00348551
\(175\) 0 0
\(176\) 80.0000 0.0342627
\(177\) −424.000 −0.180055
\(178\) 172.000 0.0724267
\(179\) −1108.00 −0.462658 −0.231329 0.972876i \(-0.574307\pi\)
−0.231329 + 0.972876i \(0.574307\pi\)
\(180\) 0 0
\(181\) −1920.00 −0.788467 −0.394233 0.919010i \(-0.628990\pi\)
−0.394233 + 0.919010i \(0.628990\pi\)
\(182\) −1148.00 −0.467557
\(183\) −192.000 −0.0775576
\(184\) 1400.00 0.560920
\(185\) 0 0
\(186\) −1808.00 −0.712737
\(187\) −60.0000 −0.0234633
\(188\) 1336.00 0.518286
\(189\) −1064.00 −0.409495
\(190\) 0 0
\(191\) −936.000 −0.354589 −0.177295 0.984158i \(-0.556735\pi\)
−0.177295 + 0.984158i \(0.556735\pi\)
\(192\) −256.000 −0.0962250
\(193\) 3163.00 1.17968 0.589839 0.807521i \(-0.299191\pi\)
0.589839 + 0.807521i \(0.299191\pi\)
\(194\) 1420.00 0.525516
\(195\) 0 0
\(196\) 196.000 0.0714286
\(197\) −349.000 −0.126219 −0.0631097 0.998007i \(-0.520102\pi\)
−0.0631097 + 0.998007i \(0.520102\pi\)
\(198\) −110.000 −0.0394816
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) −1932.00 −0.677974
\(202\) 0 0
\(203\) −7.00000 −0.00242022
\(204\) 192.000 0.0658955
\(205\) 0 0
\(206\) −1676.00 −0.566857
\(207\) −1925.00 −0.646361
\(208\) 1312.00 0.437360
\(209\) −210.000 −0.0695024
\(210\) 0 0
\(211\) 1676.00 0.546827 0.273414 0.961897i \(-0.411847\pi\)
0.273414 + 0.961897i \(0.411847\pi\)
\(212\) −1592.00 −0.515750
\(213\) 60.0000 0.0193011
\(214\) −4328.00 −1.38250
\(215\) 0 0
\(216\) 1216.00 0.383048
\(217\) −1582.00 −0.494899
\(218\) −3654.00 −1.13523
\(219\) −4176.00 −1.28853
\(220\) 0 0
\(221\) −984.000 −0.299507
\(222\) 152.000 0.0459530
\(223\) 1176.00 0.353143 0.176571 0.984288i \(-0.443499\pi\)
0.176571 + 0.984288i \(0.443499\pi\)
\(224\) −224.000 −0.0668153
\(225\) 0 0
\(226\) −186.000 −0.0547457
\(227\) 2234.00 0.653197 0.326599 0.945163i \(-0.394097\pi\)
0.326599 + 0.945163i \(0.394097\pi\)
\(228\) 672.000 0.195194
\(229\) 4274.00 1.23334 0.616668 0.787223i \(-0.288482\pi\)
0.616668 + 0.787223i \(0.288482\pi\)
\(230\) 0 0
\(231\) 140.000 0.0398759
\(232\) 8.00000 0.00226390
\(233\) −5427.00 −1.52590 −0.762950 0.646458i \(-0.776250\pi\)
−0.762950 + 0.646458i \(0.776250\pi\)
\(234\) −1804.00 −0.503979
\(235\) 0 0
\(236\) 424.000 0.116949
\(237\) 5012.00 1.37369
\(238\) 168.000 0.0457556
\(239\) 3516.00 0.951595 0.475797 0.879555i \(-0.342160\pi\)
0.475797 + 0.879555i \(0.342160\pi\)
\(240\) 0 0
\(241\) −3890.00 −1.03974 −0.519869 0.854246i \(-0.674019\pi\)
−0.519869 + 0.854246i \(0.674019\pi\)
\(242\) −2612.00 −0.693825
\(243\) −2860.00 −0.755017
\(244\) 192.000 0.0503752
\(245\) 0 0
\(246\) −128.000 −0.0331747
\(247\) −3444.00 −0.887192
\(248\) 1808.00 0.462936
\(249\) −3032.00 −0.771667
\(250\) 0 0
\(251\) 2512.00 0.631697 0.315849 0.948810i \(-0.397711\pi\)
0.315849 + 0.948810i \(0.397711\pi\)
\(252\) 308.000 0.0769928
\(253\) 875.000 0.217434
\(254\) −2866.00 −0.707988
\(255\) 0 0
\(256\) 256.000 0.0625000
\(257\) 6934.00 1.68300 0.841500 0.540257i \(-0.181673\pi\)
0.841500 + 0.540257i \(0.181673\pi\)
\(258\) −2248.00 −0.542459
\(259\) 133.000 0.0319082
\(260\) 0 0
\(261\) −11.0000 −0.00260875
\(262\) 1736.00 0.409353
\(263\) 5505.00 1.29070 0.645348 0.763889i \(-0.276713\pi\)
0.645348 + 0.763889i \(0.276713\pi\)
\(264\) −160.000 −0.0373005
\(265\) 0 0
\(266\) 588.000 0.135536
\(267\) −344.000 −0.0788482
\(268\) 1932.00 0.440357
\(269\) −8698.00 −1.97147 −0.985737 0.168294i \(-0.946174\pi\)
−0.985737 + 0.168294i \(0.946174\pi\)
\(270\) 0 0
\(271\) 2054.00 0.460412 0.230206 0.973142i \(-0.426060\pi\)
0.230206 + 0.973142i \(0.426060\pi\)
\(272\) −192.000 −0.0428004
\(273\) 2296.00 0.509012
\(274\) −5292.00 −1.16679
\(275\) 0 0
\(276\) −2800.00 −0.610653
\(277\) 8450.00 1.83289 0.916446 0.400158i \(-0.131045\pi\)
0.916446 + 0.400158i \(0.131045\pi\)
\(278\) 1792.00 0.386608
\(279\) −2486.00 −0.533451
\(280\) 0 0
\(281\) 4469.00 0.948748 0.474374 0.880323i \(-0.342674\pi\)
0.474374 + 0.880323i \(0.342674\pi\)
\(282\) −2672.00 −0.564239
\(283\) −794.000 −0.166779 −0.0833894 0.996517i \(-0.526575\pi\)
−0.0833894 + 0.996517i \(0.526575\pi\)
\(284\) −60.0000 −0.0125364
\(285\) 0 0
\(286\) 820.000 0.169537
\(287\) −112.000 −0.0230354
\(288\) −352.000 −0.0720201
\(289\) −4769.00 −0.970690
\(290\) 0 0
\(291\) −2840.00 −0.572109
\(292\) 4176.00 0.836924
\(293\) −6462.00 −1.28844 −0.644222 0.764839i \(-0.722819\pi\)
−0.644222 + 0.764839i \(0.722819\pi\)
\(294\) −392.000 −0.0777616
\(295\) 0 0
\(296\) −152.000 −0.0298474
\(297\) 760.000 0.148484
\(298\) 5046.00 0.980896
\(299\) 14350.0 2.77552
\(300\) 0 0
\(301\) −1967.00 −0.376664
\(302\) 4866.00 0.927175
\(303\) 0 0
\(304\) −672.000 −0.126782
\(305\) 0 0
\(306\) 264.000 0.0493199
\(307\) 56.0000 0.0104107 0.00520536 0.999986i \(-0.498343\pi\)
0.00520536 + 0.999986i \(0.498343\pi\)
\(308\) −140.000 −0.0259001
\(309\) 3352.00 0.617115
\(310\) 0 0
\(311\) 10656.0 1.94291 0.971457 0.237215i \(-0.0762347\pi\)
0.971457 + 0.237215i \(0.0762347\pi\)
\(312\) −2624.00 −0.476137
\(313\) −2010.00 −0.362977 −0.181489 0.983393i \(-0.558092\pi\)
−0.181489 + 0.983393i \(0.558092\pi\)
\(314\) −5144.00 −0.924499
\(315\) 0 0
\(316\) −5012.00 −0.892237
\(317\) 3903.00 0.691528 0.345764 0.938322i \(-0.387620\pi\)
0.345764 + 0.938322i \(0.387620\pi\)
\(318\) 3184.00 0.561478
\(319\) 5.00000 0.000877574 0
\(320\) 0 0
\(321\) 8656.00 1.50508
\(322\) −2450.00 −0.424016
\(323\) 504.000 0.0868214
\(324\) −1244.00 −0.213306
\(325\) 0 0
\(326\) 4976.00 0.845384
\(327\) 7308.00 1.23588
\(328\) 128.000 0.0215476
\(329\) −2338.00 −0.391788
\(330\) 0 0
\(331\) −3277.00 −0.544170 −0.272085 0.962273i \(-0.587713\pi\)
−0.272085 + 0.962273i \(0.587713\pi\)
\(332\) 3032.00 0.501213
\(333\) 209.000 0.0343938
\(334\) 6108.00 1.00064
\(335\) 0 0
\(336\) 448.000 0.0727393
\(337\) 6462.00 1.04453 0.522266 0.852782i \(-0.325087\pi\)
0.522266 + 0.852782i \(0.325087\pi\)
\(338\) 9054.00 1.45702
\(339\) 372.000 0.0595996
\(340\) 0 0
\(341\) 1130.00 0.179451
\(342\) 924.000 0.146094
\(343\) −343.000 −0.0539949
\(344\) 2248.00 0.352337
\(345\) 0 0
\(346\) −7788.00 −1.21007
\(347\) −3787.00 −0.585870 −0.292935 0.956132i \(-0.594632\pi\)
−0.292935 + 0.956132i \(0.594632\pi\)
\(348\) −16.0000 −0.00246463
\(349\) 7398.00 1.13469 0.567344 0.823481i \(-0.307971\pi\)
0.567344 + 0.823481i \(0.307971\pi\)
\(350\) 0 0
\(351\) 12464.0 1.89538
\(352\) 160.000 0.0242274
\(353\) −9654.00 −1.45561 −0.727805 0.685784i \(-0.759460\pi\)
−0.727805 + 0.685784i \(0.759460\pi\)
\(354\) −848.000 −0.127318
\(355\) 0 0
\(356\) 344.000 0.0512134
\(357\) −336.000 −0.0498123
\(358\) −2216.00 −0.327149
\(359\) −7691.00 −1.13068 −0.565342 0.824857i \(-0.691256\pi\)
−0.565342 + 0.824857i \(0.691256\pi\)
\(360\) 0 0
\(361\) −5095.00 −0.742820
\(362\) −3840.00 −0.557530
\(363\) 5224.00 0.755341
\(364\) −2296.00 −0.330613
\(365\) 0 0
\(366\) −384.000 −0.0548415
\(367\) −6836.00 −0.972306 −0.486153 0.873874i \(-0.661600\pi\)
−0.486153 + 0.873874i \(0.661600\pi\)
\(368\) 2800.00 0.396631
\(369\) −176.000 −0.0248298
\(370\) 0 0
\(371\) 2786.00 0.389870
\(372\) −3616.00 −0.503981
\(373\) 12123.0 1.68286 0.841428 0.540370i \(-0.181716\pi\)
0.841428 + 0.540370i \(0.181716\pi\)
\(374\) −120.000 −0.0165910
\(375\) 0 0
\(376\) 2672.00 0.366484
\(377\) 82.0000 0.0112022
\(378\) −2128.00 −0.289557
\(379\) 10811.0 1.46523 0.732617 0.680641i \(-0.238299\pi\)
0.732617 + 0.680641i \(0.238299\pi\)
\(380\) 0 0
\(381\) 5732.00 0.770759
\(382\) −1872.00 −0.250733
\(383\) −12778.0 −1.70477 −0.852383 0.522918i \(-0.824843\pi\)
−0.852383 + 0.522918i \(0.824843\pi\)
\(384\) −512.000 −0.0680414
\(385\) 0 0
\(386\) 6326.00 0.834158
\(387\) −3091.00 −0.406006
\(388\) 2840.00 0.371596
\(389\) −383.000 −0.0499200 −0.0249600 0.999688i \(-0.507946\pi\)
−0.0249600 + 0.999688i \(0.507946\pi\)
\(390\) 0 0
\(391\) −2100.00 −0.271615
\(392\) 392.000 0.0505076
\(393\) −3472.00 −0.445647
\(394\) −698.000 −0.0892506
\(395\) 0 0
\(396\) −220.000 −0.0279177
\(397\) 12050.0 1.52336 0.761678 0.647956i \(-0.224376\pi\)
0.761678 + 0.647956i \(0.224376\pi\)
\(398\) 0 0
\(399\) −1176.00 −0.147553
\(400\) 0 0
\(401\) −7523.00 −0.936860 −0.468430 0.883501i \(-0.655180\pi\)
−0.468430 + 0.883501i \(0.655180\pi\)
\(402\) −3864.00 −0.479400
\(403\) 18532.0 2.29068
\(404\) 0 0
\(405\) 0 0
\(406\) −14.0000 −0.00171135
\(407\) −95.0000 −0.0115700
\(408\) 384.000 0.0465952
\(409\) −4534.00 −0.548146 −0.274073 0.961709i \(-0.588371\pi\)
−0.274073 + 0.961709i \(0.588371\pi\)
\(410\) 0 0
\(411\) 10584.0 1.27024
\(412\) −3352.00 −0.400828
\(413\) −742.000 −0.0884054
\(414\) −3850.00 −0.457046
\(415\) 0 0
\(416\) 2624.00 0.309260
\(417\) −3584.00 −0.420885
\(418\) −420.000 −0.0491456
\(419\) 8494.00 0.990356 0.495178 0.868792i \(-0.335103\pi\)
0.495178 + 0.868792i \(0.335103\pi\)
\(420\) 0 0
\(421\) −8765.00 −1.01468 −0.507340 0.861746i \(-0.669371\pi\)
−0.507340 + 0.861746i \(0.669371\pi\)
\(422\) 3352.00 0.386665
\(423\) −3674.00 −0.422307
\(424\) −3184.00 −0.364690
\(425\) 0 0
\(426\) 120.000 0.0136479
\(427\) −336.000 −0.0380800
\(428\) −8656.00 −0.977578
\(429\) −1640.00 −0.184569
\(430\) 0 0
\(431\) −6696.00 −0.748341 −0.374170 0.927360i \(-0.622073\pi\)
−0.374170 + 0.927360i \(0.622073\pi\)
\(432\) 2432.00 0.270856
\(433\) −4148.00 −0.460370 −0.230185 0.973147i \(-0.573933\pi\)
−0.230185 + 0.973147i \(0.573933\pi\)
\(434\) −3164.00 −0.349947
\(435\) 0 0
\(436\) −7308.00 −0.802729
\(437\) −7350.00 −0.804572
\(438\) −8352.00 −0.911128
\(439\) 6182.00 0.672097 0.336049 0.941845i \(-0.390909\pi\)
0.336049 + 0.941845i \(0.390909\pi\)
\(440\) 0 0
\(441\) −539.000 −0.0582011
\(442\) −1968.00 −0.211783
\(443\) 616.000 0.0660656 0.0330328 0.999454i \(-0.489483\pi\)
0.0330328 + 0.999454i \(0.489483\pi\)
\(444\) 304.000 0.0324937
\(445\) 0 0
\(446\) 2352.00 0.249709
\(447\) −10092.0 −1.06786
\(448\) −448.000 −0.0472456
\(449\) −8653.00 −0.909488 −0.454744 0.890622i \(-0.650269\pi\)
−0.454744 + 0.890622i \(0.650269\pi\)
\(450\) 0 0
\(451\) 80.0000 0.00835267
\(452\) −372.000 −0.0387111
\(453\) −9732.00 −1.00938
\(454\) 4468.00 0.461880
\(455\) 0 0
\(456\) 1344.00 0.138023
\(457\) −7785.00 −0.796864 −0.398432 0.917198i \(-0.630446\pi\)
−0.398432 + 0.917198i \(0.630446\pi\)
\(458\) 8548.00 0.872100
\(459\) −1824.00 −0.185484
\(460\) 0 0
\(461\) −14718.0 −1.48695 −0.743477 0.668762i \(-0.766825\pi\)
−0.743477 + 0.668762i \(0.766825\pi\)
\(462\) 280.000 0.0281965
\(463\) 2864.00 0.287476 0.143738 0.989616i \(-0.454088\pi\)
0.143738 + 0.989616i \(0.454088\pi\)
\(464\) 16.0000 0.00160082
\(465\) 0 0
\(466\) −10854.0 −1.07897
\(467\) −1878.00 −0.186089 −0.0930444 0.995662i \(-0.529660\pi\)
−0.0930444 + 0.995662i \(0.529660\pi\)
\(468\) −3608.00 −0.356367
\(469\) −3381.00 −0.332879
\(470\) 0 0
\(471\) 10288.0 1.00647
\(472\) 848.000 0.0826957
\(473\) 1405.00 0.136579
\(474\) 10024.0 0.971345
\(475\) 0 0
\(476\) 336.000 0.0323541
\(477\) 4378.00 0.420241
\(478\) 7032.00 0.672879
\(479\) −9914.00 −0.945683 −0.472842 0.881147i \(-0.656772\pi\)
−0.472842 + 0.881147i \(0.656772\pi\)
\(480\) 0 0
\(481\) −1558.00 −0.147690
\(482\) −7780.00 −0.735206
\(483\) 4900.00 0.461610
\(484\) −5224.00 −0.490609
\(485\) 0 0
\(486\) −5720.00 −0.533878
\(487\) −12883.0 −1.19874 −0.599368 0.800474i \(-0.704581\pi\)
−0.599368 + 0.800474i \(0.704581\pi\)
\(488\) 384.000 0.0356206
\(489\) −9952.00 −0.920337
\(490\) 0 0
\(491\) −16567.0 −1.52273 −0.761363 0.648326i \(-0.775469\pi\)
−0.761363 + 0.648326i \(0.775469\pi\)
\(492\) −256.000 −0.0234581
\(493\) −12.0000 −0.00109625
\(494\) −6888.00 −0.627340
\(495\) 0 0
\(496\) 3616.00 0.327345
\(497\) 105.000 0.00947665
\(498\) −6064.00 −0.545651
\(499\) 2044.00 0.183371 0.0916854 0.995788i \(-0.470775\pi\)
0.0916854 + 0.995788i \(0.470775\pi\)
\(500\) 0 0
\(501\) −12216.0 −1.08936
\(502\) 5024.00 0.446677
\(503\) −14610.0 −1.29508 −0.647542 0.762029i \(-0.724203\pi\)
−0.647542 + 0.762029i \(0.724203\pi\)
\(504\) 616.000 0.0544421
\(505\) 0 0
\(506\) 1750.00 0.153749
\(507\) −18108.0 −1.58620
\(508\) −5732.00 −0.500623
\(509\) 18074.0 1.57390 0.786951 0.617016i \(-0.211659\pi\)
0.786951 + 0.617016i \(0.211659\pi\)
\(510\) 0 0
\(511\) −7308.00 −0.632655
\(512\) 512.000 0.0441942
\(513\) −6384.00 −0.549436
\(514\) 13868.0 1.19006
\(515\) 0 0
\(516\) −4496.00 −0.383576
\(517\) 1670.00 0.142063
\(518\) 266.000 0.0225625
\(519\) 15576.0 1.31736
\(520\) 0 0
\(521\) −13554.0 −1.13975 −0.569877 0.821730i \(-0.693009\pi\)
−0.569877 + 0.821730i \(0.693009\pi\)
\(522\) −22.0000 −0.00184466
\(523\) 11984.0 1.00196 0.500979 0.865460i \(-0.332973\pi\)
0.500979 + 0.865460i \(0.332973\pi\)
\(524\) 3472.00 0.289456
\(525\) 0 0
\(526\) 11010.0 0.912659
\(527\) −2712.00 −0.224168
\(528\) −320.000 −0.0263754
\(529\) 18458.0 1.51705
\(530\) 0 0
\(531\) −1166.00 −0.0952921
\(532\) 1176.00 0.0958385
\(533\) 1312.00 0.106621
\(534\) −688.000 −0.0557541
\(535\) 0 0
\(536\) 3864.00 0.311379
\(537\) 4432.00 0.356154
\(538\) −17396.0 −1.39404
\(539\) 245.000 0.0195787
\(540\) 0 0
\(541\) 3863.00 0.306993 0.153497 0.988149i \(-0.450947\pi\)
0.153497 + 0.988149i \(0.450947\pi\)
\(542\) 4108.00 0.325560
\(543\) 7680.00 0.606962
\(544\) −384.000 −0.0302645
\(545\) 0 0
\(546\) 4592.00 0.359926
\(547\) 19579.0 1.53042 0.765208 0.643783i \(-0.222636\pi\)
0.765208 + 0.643783i \(0.222636\pi\)
\(548\) −10584.0 −0.825048
\(549\) −528.000 −0.0410464
\(550\) 0 0
\(551\) −42.0000 −0.00324730
\(552\) −5600.00 −0.431797
\(553\) 8771.00 0.674468
\(554\) 16900.0 1.29605
\(555\) 0 0
\(556\) 3584.00 0.273373
\(557\) −7437.00 −0.565738 −0.282869 0.959159i \(-0.591286\pi\)
−0.282869 + 0.959159i \(0.591286\pi\)
\(558\) −4972.00 −0.377207
\(559\) 23042.0 1.74342
\(560\) 0 0
\(561\) 240.000 0.0180620
\(562\) 8938.00 0.670866
\(563\) −5690.00 −0.425941 −0.212971 0.977059i \(-0.568314\pi\)
−0.212971 + 0.977059i \(0.568314\pi\)
\(564\) −5344.00 −0.398977
\(565\) 0 0
\(566\) −1588.00 −0.117930
\(567\) 2177.00 0.161244
\(568\) −120.000 −0.00886459
\(569\) −24771.0 −1.82505 −0.912526 0.409019i \(-0.865871\pi\)
−0.912526 + 0.409019i \(0.865871\pi\)
\(570\) 0 0
\(571\) −8633.00 −0.632714 −0.316357 0.948640i \(-0.602460\pi\)
−0.316357 + 0.948640i \(0.602460\pi\)
\(572\) 1640.00 0.119881
\(573\) 3744.00 0.272963
\(574\) −224.000 −0.0162885
\(575\) 0 0
\(576\) −704.000 −0.0509259
\(577\) 1666.00 0.120202 0.0601009 0.998192i \(-0.480858\pi\)
0.0601009 + 0.998192i \(0.480858\pi\)
\(578\) −9538.00 −0.686381
\(579\) −12652.0 −0.908116
\(580\) 0 0
\(581\) −5306.00 −0.378881
\(582\) −5680.00 −0.404542
\(583\) −1990.00 −0.141368
\(584\) 8352.00 0.591795
\(585\) 0 0
\(586\) −12924.0 −0.911067
\(587\) −7536.00 −0.529888 −0.264944 0.964264i \(-0.585353\pi\)
−0.264944 + 0.964264i \(0.585353\pi\)
\(588\) −784.000 −0.0549857
\(589\) −9492.00 −0.664026
\(590\) 0 0
\(591\) 1396.00 0.0971637
\(592\) −304.000 −0.0211053
\(593\) 3568.00 0.247083 0.123541 0.992339i \(-0.460575\pi\)
0.123541 + 0.992339i \(0.460575\pi\)
\(594\) 1520.00 0.104994
\(595\) 0 0
\(596\) 10092.0 0.693598
\(597\) 0 0
\(598\) 28700.0 1.96259
\(599\) −24901.0 −1.69854 −0.849272 0.527956i \(-0.822958\pi\)
−0.849272 + 0.527956i \(0.822958\pi\)
\(600\) 0 0
\(601\) −23744.0 −1.61154 −0.805772 0.592226i \(-0.798249\pi\)
−0.805772 + 0.592226i \(0.798249\pi\)
\(602\) −3934.00 −0.266342
\(603\) −5313.00 −0.358809
\(604\) 9732.00 0.655612
\(605\) 0 0
\(606\) 0 0
\(607\) −22894.0 −1.53087 −0.765436 0.643513i \(-0.777476\pi\)
−0.765436 + 0.643513i \(0.777476\pi\)
\(608\) −1344.00 −0.0896487
\(609\) 28.0000 0.00186308
\(610\) 0 0
\(611\) 27388.0 1.81342
\(612\) 528.000 0.0348744
\(613\) −7811.00 −0.514655 −0.257327 0.966324i \(-0.582842\pi\)
−0.257327 + 0.966324i \(0.582842\pi\)
\(614\) 112.000 0.00736149
\(615\) 0 0
\(616\) −280.000 −0.0183142
\(617\) 11833.0 0.772089 0.386044 0.922480i \(-0.373841\pi\)
0.386044 + 0.922480i \(0.373841\pi\)
\(618\) 6704.00 0.436366
\(619\) −4186.00 −0.271809 −0.135904 0.990722i \(-0.543394\pi\)
−0.135904 + 0.990722i \(0.543394\pi\)
\(620\) 0 0
\(621\) 26600.0 1.71887
\(622\) 21312.0 1.37385
\(623\) −602.000 −0.0387137
\(624\) −5248.00 −0.336680
\(625\) 0 0
\(626\) −4020.00 −0.256664
\(627\) 840.000 0.0535030
\(628\) −10288.0 −0.653720
\(629\) 228.000 0.0144530
\(630\) 0 0
\(631\) 12079.0 0.762056 0.381028 0.924563i \(-0.375570\pi\)
0.381028 + 0.924563i \(0.375570\pi\)
\(632\) −10024.0 −0.630907
\(633\) −6704.00 −0.420948
\(634\) 7806.00 0.488984
\(635\) 0 0
\(636\) 6368.00 0.397025
\(637\) 4018.00 0.249920
\(638\) 10.0000 0.000620539 0
\(639\) 165.000 0.0102149
\(640\) 0 0
\(641\) 4017.00 0.247523 0.123761 0.992312i \(-0.460504\pi\)
0.123761 + 0.992312i \(0.460504\pi\)
\(642\) 17312.0 1.06425
\(643\) 13508.0 0.828466 0.414233 0.910171i \(-0.364050\pi\)
0.414233 + 0.910171i \(0.364050\pi\)
\(644\) −4900.00 −0.299825
\(645\) 0 0
\(646\) 1008.00 0.0613920
\(647\) −1346.00 −0.0817878 −0.0408939 0.999163i \(-0.513021\pi\)
−0.0408939 + 0.999163i \(0.513021\pi\)
\(648\) −2488.00 −0.150830
\(649\) 530.000 0.0320560
\(650\) 0 0
\(651\) 6328.00 0.380974
\(652\) 9952.00 0.597777
\(653\) −10274.0 −0.615701 −0.307850 0.951435i \(-0.599610\pi\)
−0.307850 + 0.951435i \(0.599610\pi\)
\(654\) 14616.0 0.873900
\(655\) 0 0
\(656\) 256.000 0.0152365
\(657\) −11484.0 −0.681938
\(658\) −4676.00 −0.277036
\(659\) −13116.0 −0.775306 −0.387653 0.921805i \(-0.626714\pi\)
−0.387653 + 0.921805i \(0.626714\pi\)
\(660\) 0 0
\(661\) 23070.0 1.35752 0.678759 0.734361i \(-0.262518\pi\)
0.678759 + 0.734361i \(0.262518\pi\)
\(662\) −6554.00 −0.384786
\(663\) 3936.00 0.230560
\(664\) 6064.00 0.354411
\(665\) 0 0
\(666\) 418.000 0.0243201
\(667\) 175.000 0.0101590
\(668\) 12216.0 0.707562
\(669\) −4704.00 −0.271849
\(670\) 0 0
\(671\) 240.000 0.0138079
\(672\) 896.000 0.0514344
\(673\) 24922.0 1.42745 0.713724 0.700427i \(-0.247007\pi\)
0.713724 + 0.700427i \(0.247007\pi\)
\(674\) 12924.0 0.738596
\(675\) 0 0
\(676\) 18108.0 1.03027
\(677\) 14294.0 0.811467 0.405733 0.913991i \(-0.367016\pi\)
0.405733 + 0.913991i \(0.367016\pi\)
\(678\) 744.000 0.0421433
\(679\) −4970.00 −0.280900
\(680\) 0 0
\(681\) −8936.00 −0.502832
\(682\) 2260.00 0.126891
\(683\) −4979.00 −0.278940 −0.139470 0.990226i \(-0.544540\pi\)
−0.139470 + 0.990226i \(0.544540\pi\)
\(684\) 1848.00 0.103304
\(685\) 0 0
\(686\) −686.000 −0.0381802
\(687\) −17096.0 −0.949422
\(688\) 4496.00 0.249140
\(689\) −32636.0 −1.80455
\(690\) 0 0
\(691\) 6744.00 0.371279 0.185640 0.982618i \(-0.440564\pi\)
0.185640 + 0.982618i \(0.440564\pi\)
\(692\) −15576.0 −0.855651
\(693\) 385.000 0.0211038
\(694\) −7574.00 −0.414272
\(695\) 0 0
\(696\) −32.0000 −0.00174275
\(697\) −192.000 −0.0104340
\(698\) 14796.0 0.802345
\(699\) 21708.0 1.17464
\(700\) 0 0
\(701\) −17682.0 −0.952696 −0.476348 0.879257i \(-0.658040\pi\)
−0.476348 + 0.879257i \(0.658040\pi\)
\(702\) 24928.0 1.34024
\(703\) 798.000 0.0428124
\(704\) 320.000 0.0171313
\(705\) 0 0
\(706\) −19308.0 −1.02927
\(707\) 0 0
\(708\) −1696.00 −0.0900277
\(709\) −3514.00 −0.186137 −0.0930684 0.995660i \(-0.529668\pi\)
−0.0930684 + 0.995660i \(0.529668\pi\)
\(710\) 0 0
\(711\) 13783.0 0.727008
\(712\) 688.000 0.0362133
\(713\) 39550.0 2.07736
\(714\) −672.000 −0.0352226
\(715\) 0 0
\(716\) −4432.00 −0.231329
\(717\) −14064.0 −0.732538
\(718\) −15382.0 −0.799514
\(719\) −34132.0 −1.77039 −0.885194 0.465222i \(-0.845974\pi\)
−0.885194 + 0.465222i \(0.845974\pi\)
\(720\) 0 0
\(721\) 5866.00 0.302998
\(722\) −10190.0 −0.525253
\(723\) 15560.0 0.800391
\(724\) −7680.00 −0.394233
\(725\) 0 0
\(726\) 10448.0 0.534107
\(727\) 22112.0 1.12804 0.564022 0.825759i \(-0.309253\pi\)
0.564022 + 0.825759i \(0.309253\pi\)
\(728\) −4592.00 −0.233779
\(729\) 19837.0 1.00782
\(730\) 0 0
\(731\) −3372.00 −0.170613
\(732\) −768.000 −0.0387788
\(733\) −22180.0 −1.11765 −0.558825 0.829286i \(-0.688748\pi\)
−0.558825 + 0.829286i \(0.688748\pi\)
\(734\) −13672.0 −0.687524
\(735\) 0 0
\(736\) 5600.00 0.280460
\(737\) 2415.00 0.120702
\(738\) −352.000 −0.0175573
\(739\) −16279.0 −0.810328 −0.405164 0.914244i \(-0.632786\pi\)
−0.405164 + 0.914244i \(0.632786\pi\)
\(740\) 0 0
\(741\) 13776.0 0.682961
\(742\) 5572.00 0.275680
\(743\) 29068.0 1.43526 0.717632 0.696422i \(-0.245226\pi\)
0.717632 + 0.696422i \(0.245226\pi\)
\(744\) −7232.00 −0.356368
\(745\) 0 0
\(746\) 24246.0 1.18996
\(747\) −8338.00 −0.408396
\(748\) −240.000 −0.0117316
\(749\) 15148.0 0.738980
\(750\) 0 0
\(751\) 20.0000 0.000971785 0 0.000485892 1.00000i \(-0.499845\pi\)
0.000485892 1.00000i \(0.499845\pi\)
\(752\) 5344.00 0.259143
\(753\) −10048.0 −0.486281
\(754\) 164.000 0.00792112
\(755\) 0 0
\(756\) −4256.00 −0.204748
\(757\) 22961.0 1.10242 0.551210 0.834367i \(-0.314166\pi\)
0.551210 + 0.834367i \(0.314166\pi\)
\(758\) 21622.0 1.03608
\(759\) −3500.00 −0.167381
\(760\) 0 0
\(761\) 2832.00 0.134901 0.0674507 0.997723i \(-0.478513\pi\)
0.0674507 + 0.997723i \(0.478513\pi\)
\(762\) 11464.0 0.545009
\(763\) 12789.0 0.606806
\(764\) −3744.00 −0.177295
\(765\) 0 0
\(766\) −25556.0 −1.20545
\(767\) 8692.00 0.409192
\(768\) −1024.00 −0.0481125
\(769\) −20204.0 −0.947432 −0.473716 0.880678i \(-0.657088\pi\)
−0.473716 + 0.880678i \(0.657088\pi\)
\(770\) 0 0
\(771\) −27736.0 −1.29557
\(772\) 12652.0 0.589839
\(773\) −27882.0 −1.29734 −0.648671 0.761069i \(-0.724675\pi\)
−0.648671 + 0.761069i \(0.724675\pi\)
\(774\) −6182.00 −0.287090
\(775\) 0 0
\(776\) 5680.00 0.262758
\(777\) −532.000 −0.0245629
\(778\) −766.000 −0.0352988
\(779\) −672.000 −0.0309074
\(780\) 0 0
\(781\) −75.0000 −0.00343625
\(782\) −4200.00 −0.192061
\(783\) 152.000 0.00693747
\(784\) 784.000 0.0357143
\(785\) 0 0
\(786\) −6944.00 −0.315120
\(787\) 36304.0 1.64434 0.822171 0.569240i \(-0.192762\pi\)
0.822171 + 0.569240i \(0.192762\pi\)
\(788\) −1396.00 −0.0631097
\(789\) −22020.0 −0.993578
\(790\) 0 0
\(791\) 651.000 0.0292628
\(792\) −440.000 −0.0197408
\(793\) 3936.00 0.176257
\(794\) 24100.0 1.07718
\(795\) 0 0
\(796\) 0 0
\(797\) −21096.0 −0.937589 −0.468795 0.883307i \(-0.655312\pi\)
−0.468795 + 0.883307i \(0.655312\pi\)
\(798\) −2352.00 −0.104336
\(799\) −4008.00 −0.177463
\(800\) 0 0
\(801\) −946.000 −0.0417294
\(802\) −15046.0 −0.662460
\(803\) 5220.00 0.229402
\(804\) −7728.00 −0.338987
\(805\) 0 0
\(806\) 37064.0 1.61976
\(807\) 34792.0 1.51764
\(808\) 0 0
\(809\) 15879.0 0.690081 0.345041 0.938588i \(-0.387865\pi\)
0.345041 + 0.938588i \(0.387865\pi\)
\(810\) 0 0
\(811\) 33402.0 1.44624 0.723121 0.690721i \(-0.242707\pi\)
0.723121 + 0.690721i \(0.242707\pi\)
\(812\) −28.0000 −0.00121011
\(813\) −8216.00 −0.354425
\(814\) −190.000 −0.00818120
\(815\) 0 0
\(816\) 768.000 0.0329478
\(817\) −11802.0 −0.505385
\(818\) −9068.00 −0.387598
\(819\) 6314.00 0.269388
\(820\) 0 0
\(821\) 10506.0 0.446604 0.223302 0.974749i \(-0.428316\pi\)
0.223302 + 0.974749i \(0.428316\pi\)
\(822\) 21168.0 0.898198
\(823\) 1035.00 0.0438370 0.0219185 0.999760i \(-0.493023\pi\)
0.0219185 + 0.999760i \(0.493023\pi\)
\(824\) −6704.00 −0.283428
\(825\) 0 0
\(826\) −1484.00 −0.0625121
\(827\) 30137.0 1.26719 0.633595 0.773665i \(-0.281579\pi\)
0.633595 + 0.773665i \(0.281579\pi\)
\(828\) −7700.00 −0.323181
\(829\) 35464.0 1.48578 0.742892 0.669411i \(-0.233453\pi\)
0.742892 + 0.669411i \(0.233453\pi\)
\(830\) 0 0
\(831\) −33800.0 −1.41096
\(832\) 5248.00 0.218680
\(833\) −588.000 −0.0244574
\(834\) −7168.00 −0.297611
\(835\) 0 0
\(836\) −840.000 −0.0347512
\(837\) 34352.0 1.41861
\(838\) 16988.0 0.700287
\(839\) −1492.00 −0.0613940 −0.0306970 0.999529i \(-0.509773\pi\)
−0.0306970 + 0.999529i \(0.509773\pi\)
\(840\) 0 0
\(841\) −24388.0 −0.999959
\(842\) −17530.0 −0.717487
\(843\) −17876.0 −0.730347
\(844\) 6704.00 0.273414
\(845\) 0 0
\(846\) −7348.00 −0.298616
\(847\) 9142.00 0.370865
\(848\) −6368.00 −0.257875
\(849\) 3176.00 0.128386
\(850\) 0 0
\(851\) −3325.00 −0.133936
\(852\) 240.000 0.00965055
\(853\) 19288.0 0.774219 0.387109 0.922034i \(-0.373474\pi\)
0.387109 + 0.922034i \(0.373474\pi\)
\(854\) −672.000 −0.0269267
\(855\) 0 0
\(856\) −17312.0 −0.691252
\(857\) 2656.00 0.105866 0.0529330 0.998598i \(-0.483143\pi\)
0.0529330 + 0.998598i \(0.483143\pi\)
\(858\) −3280.00 −0.130510
\(859\) 3786.00 0.150380 0.0751901 0.997169i \(-0.476044\pi\)
0.0751901 + 0.997169i \(0.476044\pi\)
\(860\) 0 0
\(861\) 448.000 0.0177326
\(862\) −13392.0 −0.529157
\(863\) −45503.0 −1.79483 −0.897416 0.441185i \(-0.854558\pi\)
−0.897416 + 0.441185i \(0.854558\pi\)
\(864\) 4864.00 0.191524
\(865\) 0 0
\(866\) −8296.00 −0.325531
\(867\) 19076.0 0.747238
\(868\) −6328.00 −0.247450
\(869\) −6265.00 −0.244563
\(870\) 0 0
\(871\) 39606.0 1.54076
\(872\) −14616.0 −0.567615
\(873\) −7810.00 −0.302782
\(874\) −14700.0 −0.568919
\(875\) 0 0
\(876\) −16704.0 −0.644265
\(877\) −32626.0 −1.25622 −0.628108 0.778126i \(-0.716170\pi\)
−0.628108 + 0.778126i \(0.716170\pi\)
\(878\) 12364.0 0.475245
\(879\) 25848.0 0.991845
\(880\) 0 0
\(881\) −25754.0 −0.984874 −0.492437 0.870348i \(-0.663894\pi\)
−0.492437 + 0.870348i \(0.663894\pi\)
\(882\) −1078.00 −0.0411544
\(883\) −9165.00 −0.349294 −0.174647 0.984631i \(-0.555878\pi\)
−0.174647 + 0.984631i \(0.555878\pi\)
\(884\) −3936.00 −0.149753
\(885\) 0 0
\(886\) 1232.00 0.0467154
\(887\) 1472.00 0.0557214 0.0278607 0.999612i \(-0.491131\pi\)
0.0278607 + 0.999612i \(0.491131\pi\)
\(888\) 608.000 0.0229765
\(889\) 10031.0 0.378435
\(890\) 0 0
\(891\) −1555.00 −0.0584674
\(892\) 4704.00 0.176571
\(893\) −14028.0 −0.525677
\(894\) −20184.0 −0.755094
\(895\) 0 0
\(896\) −896.000 −0.0334077
\(897\) −57400.0 −2.13660
\(898\) −17306.0 −0.643105
\(899\) 226.000 0.00838434
\(900\) 0 0
\(901\) 4776.00 0.176594
\(902\) 160.000 0.00590623
\(903\) 7868.00 0.289956
\(904\) −744.000 −0.0273729
\(905\) 0 0
\(906\) −19464.0 −0.713740
\(907\) 22412.0 0.820483 0.410242 0.911977i \(-0.365444\pi\)
0.410242 + 0.911977i \(0.365444\pi\)
\(908\) 8936.00 0.326599
\(909\) 0 0
\(910\) 0 0
\(911\) 15163.0 0.551452 0.275726 0.961236i \(-0.411082\pi\)
0.275726 + 0.961236i \(0.411082\pi\)
\(912\) 2688.00 0.0975971
\(913\) 3790.00 0.137383
\(914\) −15570.0 −0.563468
\(915\) 0 0
\(916\) 17096.0 0.616668
\(917\) −6076.00 −0.218808
\(918\) −3648.00 −0.131157
\(919\) −6501.00 −0.233350 −0.116675 0.993170i \(-0.537224\pi\)
−0.116675 + 0.993170i \(0.537224\pi\)
\(920\) 0 0
\(921\) −224.000 −0.00801417
\(922\) −29436.0 −1.05143
\(923\) −1230.00 −0.0438634
\(924\) 560.000 0.0199379
\(925\) 0 0
\(926\) 5728.00 0.203276
\(927\) 9218.00 0.326601
\(928\) 32.0000 0.00113195
\(929\) 1464.00 0.0517032 0.0258516 0.999666i \(-0.491770\pi\)
0.0258516 + 0.999666i \(0.491770\pi\)
\(930\) 0 0
\(931\) −2058.00 −0.0724471
\(932\) −21708.0 −0.762950
\(933\) −42624.0 −1.49566
\(934\) −3756.00 −0.131585
\(935\) 0 0
\(936\) −7216.00 −0.251990
\(937\) −14064.0 −0.490342 −0.245171 0.969480i \(-0.578844\pi\)
−0.245171 + 0.969480i \(0.578844\pi\)
\(938\) −6762.00 −0.235381
\(939\) 8040.00 0.279420
\(940\) 0 0
\(941\) −39114.0 −1.35503 −0.677513 0.735511i \(-0.736942\pi\)
−0.677513 + 0.735511i \(0.736942\pi\)
\(942\) 20576.0 0.711680
\(943\) 2800.00 0.0966920
\(944\) 1696.00 0.0584747
\(945\) 0 0
\(946\) 2810.00 0.0965761
\(947\) −15068.0 −0.517048 −0.258524 0.966005i \(-0.583236\pi\)
−0.258524 + 0.966005i \(0.583236\pi\)
\(948\) 20048.0 0.686845
\(949\) 85608.0 2.92830
\(950\) 0 0
\(951\) −15612.0 −0.532338
\(952\) 672.000 0.0228778
\(953\) 27847.0 0.946540 0.473270 0.880917i \(-0.343073\pi\)
0.473270 + 0.880917i \(0.343073\pi\)
\(954\) 8756.00 0.297155
\(955\) 0 0
\(956\) 14064.0 0.475797
\(957\) −20.0000 −0.000675557 0
\(958\) −19828.0 −0.668699
\(959\) 18522.0 0.623677
\(960\) 0 0
\(961\) 21285.0 0.714478
\(962\) −3116.00 −0.104432
\(963\) 23804.0 0.796545
\(964\) −15560.0 −0.519869
\(965\) 0 0
\(966\) 9800.00 0.326408
\(967\) −33704.0 −1.12084 −0.560418 0.828210i \(-0.689359\pi\)
−0.560418 + 0.828210i \(0.689359\pi\)
\(968\) −10448.0 −0.346913
\(969\) −2016.00 −0.0668351
\(970\) 0 0
\(971\) −30006.0 −0.991698 −0.495849 0.868409i \(-0.665143\pi\)
−0.495849 + 0.868409i \(0.665143\pi\)
\(972\) −11440.0 −0.377508
\(973\) −6272.00 −0.206651
\(974\) −25766.0 −0.847634
\(975\) 0 0
\(976\) 768.000 0.0251876
\(977\) 14457.0 0.473409 0.236704 0.971582i \(-0.423933\pi\)
0.236704 + 0.971582i \(0.423933\pi\)
\(978\) −19904.0 −0.650777
\(979\) 430.000 0.0140377
\(980\) 0 0
\(981\) 20097.0 0.654075
\(982\) −33134.0 −1.07673
\(983\) −43742.0 −1.41928 −0.709640 0.704564i \(-0.751143\pi\)
−0.709640 + 0.704564i \(0.751143\pi\)
\(984\) −512.000 −0.0165874
\(985\) 0 0
\(986\) −24.0000 −0.000775168 0
\(987\) 9352.00 0.301598
\(988\) −13776.0 −0.443596
\(989\) 49175.0 1.58107
\(990\) 0 0
\(991\) −8201.00 −0.262879 −0.131440 0.991324i \(-0.541960\pi\)
−0.131440 + 0.991324i \(0.541960\pi\)
\(992\) 7232.00 0.231468
\(993\) 13108.0 0.418902
\(994\) 210.000 0.00670100
\(995\) 0 0
\(996\) −12128.0 −0.385834
\(997\) 4274.00 0.135766 0.0678831 0.997693i \(-0.478376\pi\)
0.0678831 + 0.997693i \(0.478376\pi\)
\(998\) 4088.00 0.129663
\(999\) −2888.00 −0.0914637
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 350.4.a.n.1.1 yes 1
5.2 odd 4 350.4.c.c.99.2 2
5.3 odd 4 350.4.c.c.99.1 2
5.4 even 2 350.4.a.h.1.1 1
7.6 odd 2 2450.4.a.bk.1.1 1
35.34 odd 2 2450.4.a.e.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
350.4.a.h.1.1 1 5.4 even 2
350.4.a.n.1.1 yes 1 1.1 even 1 trivial
350.4.c.c.99.1 2 5.3 odd 4
350.4.c.c.99.2 2 5.2 odd 4
2450.4.a.e.1.1 1 35.34 odd 2
2450.4.a.bk.1.1 1 7.6 odd 2