Properties

Label 363.4.a.l.1.1
Level $363$
Weight $4$
Character 363.1
Self dual yes
Analytic conductor $21.418$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [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: \(2\)
Coefficient field: \(\Q(\zeta_{12})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 3 \) 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 1.1
Root \(-1.73205\) 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)
 
\(f(q)\) \(=\) \(q-5.19615 q^{2} -3.00000 q^{3} +19.0000 q^{4} +9.00000 q^{5} +15.5885 q^{6} -24.2487 q^{7} -57.1577 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-5.19615 q^{2} -3.00000 q^{3} +19.0000 q^{4} +9.00000 q^{5} +15.5885 q^{6} -24.2487 q^{7} -57.1577 q^{8} +9.00000 q^{9} -46.7654 q^{10} -57.0000 q^{12} +71.0141 q^{13} +126.000 q^{14} -27.0000 q^{15} +145.000 q^{16} +88.3346 q^{17} -46.7654 q^{18} -145.492 q^{19} +171.000 q^{20} +72.7461 q^{21} +90.0000 q^{23} +171.473 q^{24} -44.0000 q^{25} -369.000 q^{26} -27.0000 q^{27} -460.726 q^{28} -88.3346 q^{29} +140.296 q^{30} -188.000 q^{31} -296.181 q^{32} -459.000 q^{34} -218.238 q^{35} +171.000 q^{36} +133.000 q^{37} +756.000 q^{38} -213.042 q^{39} -514.419 q^{40} +36.3731 q^{41} -378.000 q^{42} -72.7461 q^{43} +81.0000 q^{45} -467.654 q^{46} +72.0000 q^{47} -435.000 q^{48} +245.000 q^{49} +228.631 q^{50} -265.004 q^{51} +1349.27 q^{52} -45.0000 q^{53} +140.296 q^{54} +1386.00 q^{56} +436.477 q^{57} +459.000 q^{58} +378.000 q^{59} -513.000 q^{60} +623.538 q^{61} +976.877 q^{62} -218.238 q^{63} +379.000 q^{64} +639.127 q^{65} -386.000 q^{67} +1678.36 q^{68} -270.000 q^{69} +1134.00 q^{70} -198.000 q^{71} -514.419 q^{72} +76.2102 q^{73} -691.088 q^{74} +132.000 q^{75} -2764.35 q^{76} +1107.00 q^{78} -152.420 q^{79} +1305.00 q^{80} +81.0000 q^{81} -189.000 q^{82} +1247.08 q^{83} +1382.18 q^{84} +795.011 q^{85} +378.000 q^{86} +265.004 q^{87} +45.0000 q^{89} -420.888 q^{90} -1722.00 q^{91} +1710.00 q^{92} +564.000 q^{93} -374.123 q^{94} -1309.43 q^{95} +888.542 q^{96} +89.0000 q^{97} -1273.06 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 6 q^{3} + 38 q^{4} + 18 q^{5} + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 6 q^{3} + 38 q^{4} + 18 q^{5} + 18 q^{9} - 114 q^{12} + 252 q^{14} - 54 q^{15} + 290 q^{16} + 342 q^{20} + 180 q^{23} - 88 q^{25} - 738 q^{26} - 54 q^{27} - 376 q^{31} - 918 q^{34} + 342 q^{36} + 266 q^{37} + 1512 q^{38} - 756 q^{42} + 162 q^{45} + 144 q^{47} - 870 q^{48} + 490 q^{49} - 90 q^{53} + 2772 q^{56} + 918 q^{58} + 756 q^{59} - 1026 q^{60} + 758 q^{64} - 772 q^{67} - 540 q^{69} + 2268 q^{70} - 396 q^{71} + 264 q^{75} + 2214 q^{78} + 2610 q^{80} + 162 q^{81} - 378 q^{82} + 756 q^{86} + 90 q^{89} - 3444 q^{91} + 3420 q^{92} + 1128 q^{93} + 178 q^{97}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.19615 −1.83712 −0.918559 0.395285i \(-0.870646\pi\)
−0.918559 + 0.395285i \(0.870646\pi\)
\(3\) −3.00000 −0.577350
\(4\) 19.0000 2.37500
\(5\) 9.00000 0.804984 0.402492 0.915423i \(-0.368144\pi\)
0.402492 + 0.915423i \(0.368144\pi\)
\(6\) 15.5885 1.06066
\(7\) −24.2487 −1.30931 −0.654654 0.755929i \(-0.727186\pi\)
−0.654654 + 0.755929i \(0.727186\pi\)
\(8\) −57.1577 −2.52604
\(9\) 9.00000 0.333333
\(10\) −46.7654 −1.47885
\(11\) 0 0
\(12\) −57.0000 −1.37121
\(13\) 71.0141 1.51506 0.757529 0.652801i \(-0.226406\pi\)
0.757529 + 0.652801i \(0.226406\pi\)
\(14\) 126.000 2.40535
\(15\) −27.0000 −0.464758
\(16\) 145.000 2.26562
\(17\) 88.3346 1.26025 0.630126 0.776493i \(-0.283003\pi\)
0.630126 + 0.776493i \(0.283003\pi\)
\(18\) −46.7654 −0.612372
\(19\) −145.492 −1.75675 −0.878374 0.477974i \(-0.841371\pi\)
−0.878374 + 0.477974i \(0.841371\pi\)
\(20\) 171.000 1.91184
\(21\) 72.7461 0.755929
\(22\) 0 0
\(23\) 90.0000 0.815926 0.407963 0.912998i \(-0.366239\pi\)
0.407963 + 0.912998i \(0.366239\pi\)
\(24\) 171.473 1.45841
\(25\) −44.0000 −0.352000
\(26\) −369.000 −2.78334
\(27\) −27.0000 −0.192450
\(28\) −460.726 −3.10960
\(29\) −88.3346 −0.565632 −0.282816 0.959174i \(-0.591269\pi\)
−0.282816 + 0.959174i \(0.591269\pi\)
\(30\) 140.296 0.853815
\(31\) −188.000 −1.08922 −0.544610 0.838690i \(-0.683322\pi\)
−0.544610 + 0.838690i \(0.683322\pi\)
\(32\) −296.181 −1.63618
\(33\) 0 0
\(34\) −459.000 −2.31523
\(35\) −218.238 −1.05397
\(36\) 171.000 0.791667
\(37\) 133.000 0.590948 0.295474 0.955351i \(-0.404522\pi\)
0.295474 + 0.955351i \(0.404522\pi\)
\(38\) 756.000 3.22735
\(39\) −213.042 −0.874720
\(40\) −514.419 −2.03342
\(41\) 36.3731 0.138549 0.0692746 0.997598i \(-0.477932\pi\)
0.0692746 + 0.997598i \(0.477932\pi\)
\(42\) −378.000 −1.38873
\(43\) −72.7461 −0.257993 −0.128996 0.991645i \(-0.541176\pi\)
−0.128996 + 0.991645i \(0.541176\pi\)
\(44\) 0 0
\(45\) 81.0000 0.268328
\(46\) −467.654 −1.49895
\(47\) 72.0000 0.223453 0.111726 0.993739i \(-0.464362\pi\)
0.111726 + 0.993739i \(0.464362\pi\)
\(48\) −435.000 −1.30806
\(49\) 245.000 0.714286
\(50\) 228.631 0.646665
\(51\) −265.004 −0.727607
\(52\) 1349.27 3.59826
\(53\) −45.0000 −0.116627 −0.0583134 0.998298i \(-0.518572\pi\)
−0.0583134 + 0.998298i \(0.518572\pi\)
\(54\) 140.296 0.353553
\(55\) 0 0
\(56\) 1386.00 3.30736
\(57\) 436.477 1.01426
\(58\) 459.000 1.03913
\(59\) 378.000 0.834092 0.417046 0.908885i \(-0.363065\pi\)
0.417046 + 0.908885i \(0.363065\pi\)
\(60\) −513.000 −1.10380
\(61\) 623.538 1.30879 0.654393 0.756155i \(-0.272924\pi\)
0.654393 + 0.756155i \(0.272924\pi\)
\(62\) 976.877 2.00102
\(63\) −218.238 −0.436436
\(64\) 379.000 0.740234
\(65\) 639.127 1.21960
\(66\) 0 0
\(67\) −386.000 −0.703842 −0.351921 0.936030i \(-0.614471\pi\)
−0.351921 + 0.936030i \(0.614471\pi\)
\(68\) 1678.36 2.99310
\(69\) −270.000 −0.471075
\(70\) 1134.00 1.93627
\(71\) −198.000 −0.330962 −0.165481 0.986213i \(-0.552918\pi\)
−0.165481 + 0.986213i \(0.552918\pi\)
\(72\) −514.419 −0.842012
\(73\) 76.2102 0.122188 0.0610941 0.998132i \(-0.480541\pi\)
0.0610941 + 0.998132i \(0.480541\pi\)
\(74\) −691.088 −1.08564
\(75\) 132.000 0.203227
\(76\) −2764.35 −4.17228
\(77\) 0 0
\(78\) 1107.00 1.60696
\(79\) −152.420 −0.217071 −0.108536 0.994093i \(-0.534616\pi\)
−0.108536 + 0.994093i \(0.534616\pi\)
\(80\) 1305.00 1.82379
\(81\) 81.0000 0.111111
\(82\) −189.000 −0.254531
\(83\) 1247.08 1.64921 0.824605 0.565709i \(-0.191397\pi\)
0.824605 + 0.565709i \(0.191397\pi\)
\(84\) 1382.18 1.79533
\(85\) 795.011 1.01448
\(86\) 378.000 0.473963
\(87\) 265.004 0.326568
\(88\) 0 0
\(89\) 45.0000 0.0535954 0.0267977 0.999641i \(-0.491469\pi\)
0.0267977 + 0.999641i \(0.491469\pi\)
\(90\) −420.888 −0.492950
\(91\) −1722.00 −1.98368
\(92\) 1710.00 1.93782
\(93\) 564.000 0.628861
\(94\) −374.123 −0.410509
\(95\) −1309.43 −1.41416
\(96\) 888.542 0.944650
\(97\) 89.0000 0.0931606 0.0465803 0.998915i \(-0.485168\pi\)
0.0465803 + 0.998915i \(0.485168\pi\)
\(98\) −1273.06 −1.31223
\(99\) 0 0
\(100\) −836.000 −0.836000
\(101\) 1288.65 1.26955 0.634777 0.772695i \(-0.281092\pi\)
0.634777 + 0.772695i \(0.281092\pi\)
\(102\) 1377.00 1.33670
\(103\) 1358.00 1.29910 0.649552 0.760317i \(-0.274956\pi\)
0.649552 + 0.760317i \(0.274956\pi\)
\(104\) −4059.00 −3.82709
\(105\) 654.715 0.608511
\(106\) 233.827 0.214257
\(107\) 1299.04 1.17367 0.586835 0.809706i \(-0.300374\pi\)
0.586835 + 0.809706i \(0.300374\pi\)
\(108\) −513.000 −0.457069
\(109\) 1203.78 1.05781 0.528903 0.848683i \(-0.322604\pi\)
0.528903 + 0.848683i \(0.322604\pi\)
\(110\) 0 0
\(111\) −399.000 −0.341184
\(112\) −3516.06 −2.96640
\(113\) 711.000 0.591905 0.295952 0.955203i \(-0.404363\pi\)
0.295952 + 0.955203i \(0.404363\pi\)
\(114\) −2268.00 −1.86331
\(115\) 810.000 0.656808
\(116\) −1678.36 −1.34338
\(117\) 639.127 0.505020
\(118\) −1964.15 −1.53232
\(119\) −2142.00 −1.65006
\(120\) 1543.26 1.17400
\(121\) 0 0
\(122\) −3240.00 −2.40439
\(123\) −109.119 −0.0799914
\(124\) −3572.00 −2.58690
\(125\) −1521.00 −1.08834
\(126\) 1134.00 0.801784
\(127\) 651.251 0.455033 0.227516 0.973774i \(-0.426939\pi\)
0.227516 + 0.973774i \(0.426939\pi\)
\(128\) 400.104 0.276285
\(129\) 218.238 0.148952
\(130\) −3321.00 −2.24055
\(131\) 2608.47 1.73972 0.869859 0.493301i \(-0.164210\pi\)
0.869859 + 0.493301i \(0.164210\pi\)
\(132\) 0 0
\(133\) 3528.00 2.30012
\(134\) 2005.71 1.29304
\(135\) −243.000 −0.154919
\(136\) −5049.00 −3.18344
\(137\) 2394.00 1.49294 0.746472 0.665417i \(-0.231746\pi\)
0.746472 + 0.665417i \(0.231746\pi\)
\(138\) 1402.96 0.865420
\(139\) 183.597 0.112033 0.0560163 0.998430i \(-0.482160\pi\)
0.0560163 + 0.998430i \(0.482160\pi\)
\(140\) −4146.53 −2.50318
\(141\) −216.000 −0.129011
\(142\) 1028.84 0.608015
\(143\) 0 0
\(144\) 1305.00 0.755208
\(145\) −795.011 −0.455325
\(146\) −396.000 −0.224474
\(147\) −735.000 −0.412393
\(148\) 2527.00 1.40350
\(149\) −3611.33 −1.98558 −0.992790 0.119869i \(-0.961753\pi\)
−0.992790 + 0.119869i \(0.961753\pi\)
\(150\) −685.892 −0.373352
\(151\) 1357.93 0.731832 0.365916 0.930648i \(-0.380756\pi\)
0.365916 + 0.930648i \(0.380756\pi\)
\(152\) 8316.00 4.43761
\(153\) 795.011 0.420084
\(154\) 0 0
\(155\) −1692.00 −0.876805
\(156\) −4047.80 −2.07746
\(157\) 1306.00 0.663886 0.331943 0.943299i \(-0.392296\pi\)
0.331943 + 0.943299i \(0.392296\pi\)
\(158\) 792.000 0.398786
\(159\) 135.000 0.0673346
\(160\) −2665.63 −1.31710
\(161\) −2182.38 −1.06830
\(162\) −420.888 −0.204124
\(163\) 2546.00 1.22342 0.611712 0.791081i \(-0.290481\pi\)
0.611712 + 0.791081i \(0.290481\pi\)
\(164\) 691.088 0.329054
\(165\) 0 0
\(166\) −6480.00 −3.02979
\(167\) −675.500 −0.313004 −0.156502 0.987678i \(-0.550022\pi\)
−0.156502 + 0.987678i \(0.550022\pi\)
\(168\) −4158.00 −1.90950
\(169\) 2846.00 1.29540
\(170\) −4131.00 −1.86372
\(171\) −1309.43 −0.585583
\(172\) −1382.18 −0.612732
\(173\) −3180.05 −1.39754 −0.698770 0.715347i \(-0.746269\pi\)
−0.698770 + 0.715347i \(0.746269\pi\)
\(174\) −1377.00 −0.599943
\(175\) 1066.94 0.460876
\(176\) 0 0
\(177\) −1134.00 −0.481563
\(178\) −233.827 −0.0984610
\(179\) −2556.00 −1.06729 −0.533644 0.845709i \(-0.679178\pi\)
−0.533644 + 0.845709i \(0.679178\pi\)
\(180\) 1539.00 0.637279
\(181\) −775.000 −0.318261 −0.159131 0.987258i \(-0.550869\pi\)
−0.159131 + 0.987258i \(0.550869\pi\)
\(182\) 8947.77 3.64425
\(183\) −1870.61 −0.755627
\(184\) −5144.19 −2.06106
\(185\) 1197.00 0.475704
\(186\) −2930.63 −1.15529
\(187\) 0 0
\(188\) 1368.00 0.530700
\(189\) 654.715 0.251976
\(190\) 6804.00 2.59797
\(191\) 2628.00 0.995578 0.497789 0.867298i \(-0.334145\pi\)
0.497789 + 0.867298i \(0.334145\pi\)
\(192\) −1137.00 −0.427375
\(193\) 2790.33 1.04069 0.520344 0.853957i \(-0.325804\pi\)
0.520344 + 0.853957i \(0.325804\pi\)
\(194\) −462.458 −0.171147
\(195\) −1917.38 −0.704136
\(196\) 4655.00 1.69643
\(197\) −3590.54 −1.29856 −0.649278 0.760551i \(-0.724929\pi\)
−0.649278 + 0.760551i \(0.724929\pi\)
\(198\) 0 0
\(199\) 1618.00 0.576367 0.288183 0.957575i \(-0.406949\pi\)
0.288183 + 0.957575i \(0.406949\pi\)
\(200\) 2514.94 0.889165
\(201\) 1158.00 0.406363
\(202\) −6696.00 −2.33232
\(203\) 2142.00 0.740586
\(204\) −5035.07 −1.72807
\(205\) 327.358 0.111530
\(206\) −7056.37 −2.38661
\(207\) 810.000 0.271975
\(208\) 10297.0 3.43255
\(209\) 0 0
\(210\) −3402.00 −1.11791
\(211\) 1860.22 0.606934 0.303467 0.952842i \(-0.401856\pi\)
0.303467 + 0.952842i \(0.401856\pi\)
\(212\) −855.000 −0.276989
\(213\) 594.000 0.191081
\(214\) −6750.00 −2.15617
\(215\) −654.715 −0.207680
\(216\) 1543.26 0.486136
\(217\) 4558.76 1.42612
\(218\) −6255.00 −1.94331
\(219\) −228.631 −0.0705453
\(220\) 0 0
\(221\) 6273.00 1.90936
\(222\) 2073.26 0.626795
\(223\) −964.000 −0.289481 −0.144740 0.989470i \(-0.546235\pi\)
−0.144740 + 0.989470i \(0.546235\pi\)
\(224\) 7182.00 2.14227
\(225\) −396.000 −0.117333
\(226\) −3694.46 −1.08740
\(227\) −2857.88 −0.835614 −0.417807 0.908536i \(-0.637201\pi\)
−0.417807 + 0.908536i \(0.637201\pi\)
\(228\) 8293.06 2.40887
\(229\) −5519.00 −1.59260 −0.796301 0.604901i \(-0.793213\pi\)
−0.796301 + 0.604901i \(0.793213\pi\)
\(230\) −4208.88 −1.20663
\(231\) 0 0
\(232\) 5049.00 1.42881
\(233\) −3611.33 −1.01539 −0.507695 0.861537i \(-0.669502\pi\)
−0.507695 + 0.861537i \(0.669502\pi\)
\(234\) −3321.00 −0.927780
\(235\) 648.000 0.179876
\(236\) 7182.00 1.98097
\(237\) 457.261 0.125326
\(238\) 11130.2 3.03135
\(239\) 3263.18 0.883171 0.441585 0.897219i \(-0.354416\pi\)
0.441585 + 0.897219i \(0.354416\pi\)
\(240\) −3915.00 −1.05297
\(241\) 3457.17 0.924050 0.462025 0.886867i \(-0.347123\pi\)
0.462025 + 0.886867i \(0.347123\pi\)
\(242\) 0 0
\(243\) −243.000 −0.0641500
\(244\) 11847.2 3.10836
\(245\) 2205.00 0.574989
\(246\) 567.000 0.146954
\(247\) −10332.0 −2.66158
\(248\) 10745.6 2.75141
\(249\) −3741.23 −0.952172
\(250\) 7903.35 1.99941
\(251\) 6714.00 1.68838 0.844191 0.536042i \(-0.180081\pi\)
0.844191 + 0.536042i \(0.180081\pi\)
\(252\) −4146.53 −1.03653
\(253\) 0 0
\(254\) −3384.00 −0.835949
\(255\) −2385.03 −0.585712
\(256\) −5111.00 −1.24780
\(257\) 1341.00 0.325484 0.162742 0.986669i \(-0.447966\pi\)
0.162742 + 0.986669i \(0.447966\pi\)
\(258\) −1134.00 −0.273642
\(259\) −3225.08 −0.773732
\(260\) 12143.4 2.89655
\(261\) −795.011 −0.188544
\(262\) −13554.0 −3.19606
\(263\) 956.092 0.224164 0.112082 0.993699i \(-0.464248\pi\)
0.112082 + 0.993699i \(0.464248\pi\)
\(264\) 0 0
\(265\) −405.000 −0.0938828
\(266\) −18332.0 −4.22560
\(267\) −135.000 −0.0309433
\(268\) −7334.00 −1.67162
\(269\) 3087.00 0.699694 0.349847 0.936807i \(-0.386234\pi\)
0.349847 + 0.936807i \(0.386234\pi\)
\(270\) 1262.67 0.284605
\(271\) 4035.68 0.904613 0.452306 0.891863i \(-0.350601\pi\)
0.452306 + 0.891863i \(0.350601\pi\)
\(272\) 12808.5 2.85526
\(273\) 5166.00 1.14528
\(274\) −12439.6 −2.74271
\(275\) 0 0
\(276\) −5130.00 −1.11880
\(277\) −3791.46 −0.822407 −0.411203 0.911544i \(-0.634891\pi\)
−0.411203 + 0.911544i \(0.634891\pi\)
\(278\) −954.000 −0.205817
\(279\) −1692.00 −0.363073
\(280\) 12474.0 2.66237
\(281\) −2722.78 −0.578034 −0.289017 0.957324i \(-0.593328\pi\)
−0.289017 + 0.957324i \(0.593328\pi\)
\(282\) 1122.37 0.237007
\(283\) −3238.94 −0.680335 −0.340167 0.940365i \(-0.610484\pi\)
−0.340167 + 0.940365i \(0.610484\pi\)
\(284\) −3762.00 −0.786034
\(285\) 3928.29 0.816463
\(286\) 0 0
\(287\) −882.000 −0.181404
\(288\) −2665.63 −0.545394
\(289\) 2890.00 0.588235
\(290\) 4131.00 0.836485
\(291\) −267.000 −0.0537863
\(292\) 1447.99 0.290197
\(293\) 4338.79 0.865101 0.432551 0.901610i \(-0.357614\pi\)
0.432551 + 0.901610i \(0.357614\pi\)
\(294\) 3819.17 0.757614
\(295\) 3402.00 0.671431
\(296\) −7601.97 −1.49276
\(297\) 0 0
\(298\) 18765.0 3.64774
\(299\) 6391.27 1.23618
\(300\) 2508.00 0.482665
\(301\) 1764.00 0.337792
\(302\) −7056.00 −1.34446
\(303\) −3865.94 −0.732978
\(304\) −21096.4 −3.98013
\(305\) 5611.84 1.05355
\(306\) −4131.00 −0.771744
\(307\) −5781.59 −1.07483 −0.537415 0.843318i \(-0.680599\pi\)
−0.537415 + 0.843318i \(0.680599\pi\)
\(308\) 0 0
\(309\) −4074.00 −0.750038
\(310\) 8791.89 1.61079
\(311\) 5220.00 0.951765 0.475883 0.879509i \(-0.342129\pi\)
0.475883 + 0.879509i \(0.342129\pi\)
\(312\) 12177.0 2.20957
\(313\) −3977.00 −0.718190 −0.359095 0.933301i \(-0.616915\pi\)
−0.359095 + 0.933301i \(0.616915\pi\)
\(314\) −6786.18 −1.21964
\(315\) −1964.15 −0.351324
\(316\) −2895.99 −0.515545
\(317\) 9918.00 1.75726 0.878628 0.477506i \(-0.158459\pi\)
0.878628 + 0.477506i \(0.158459\pi\)
\(318\) −701.481 −0.123702
\(319\) 0 0
\(320\) 3411.00 0.595877
\(321\) −3897.11 −0.677619
\(322\) 11340.0 1.96259
\(323\) −12852.0 −2.21395
\(324\) 1539.00 0.263889
\(325\) −3124.62 −0.533301
\(326\) −13229.4 −2.24757
\(327\) −3611.33 −0.610724
\(328\) −2079.00 −0.349980
\(329\) −1745.91 −0.292568
\(330\) 0 0
\(331\) 8756.00 1.45400 0.726999 0.686639i \(-0.240915\pi\)
0.726999 + 0.686639i \(0.240915\pi\)
\(332\) 23694.5 3.91687
\(333\) 1197.00 0.196983
\(334\) 3510.00 0.575026
\(335\) −3474.00 −0.566582
\(336\) 10548.2 1.71265
\(337\) 9919.45 1.60340 0.801702 0.597724i \(-0.203928\pi\)
0.801702 + 0.597724i \(0.203928\pi\)
\(338\) −14788.2 −2.37981
\(339\) −2133.00 −0.341736
\(340\) 15105.2 2.40940
\(341\) 0 0
\(342\) 6804.00 1.07578
\(343\) 2376.37 0.374088
\(344\) 4158.00 0.651699
\(345\) −2430.00 −0.379208
\(346\) 16524.0 2.56744
\(347\) −1330.22 −0.205792 −0.102896 0.994692i \(-0.532811\pi\)
−0.102896 + 0.994692i \(0.532811\pi\)
\(348\) 5035.07 0.775598
\(349\) 2842.30 0.435944 0.217972 0.975955i \(-0.430056\pi\)
0.217972 + 0.975955i \(0.430056\pi\)
\(350\) −5544.00 −0.846684
\(351\) −1917.38 −0.291573
\(352\) 0 0
\(353\) −1431.00 −0.215763 −0.107882 0.994164i \(-0.534407\pi\)
−0.107882 + 0.994164i \(0.534407\pi\)
\(354\) 5892.44 0.884688
\(355\) −1782.00 −0.266419
\(356\) 855.000 0.127289
\(357\) 6426.00 0.952661
\(358\) 13281.4 1.96073
\(359\) −5393.61 −0.792935 −0.396467 0.918049i \(-0.629764\pi\)
−0.396467 + 0.918049i \(0.629764\pi\)
\(360\) −4629.77 −0.677807
\(361\) 14309.0 2.08616
\(362\) 4027.02 0.584683
\(363\) 0 0
\(364\) −32718.0 −4.71123
\(365\) 685.892 0.0983595
\(366\) 9720.00 1.38818
\(367\) 3554.00 0.505497 0.252748 0.967532i \(-0.418666\pi\)
0.252748 + 0.967532i \(0.418666\pi\)
\(368\) 13050.0 1.84858
\(369\) 327.358 0.0461831
\(370\) −6219.79 −0.873924
\(371\) 1091.19 0.152700
\(372\) 10716.0 1.49354
\(373\) −5577.20 −0.774200 −0.387100 0.922038i \(-0.626523\pi\)
−0.387100 + 0.922038i \(0.626523\pi\)
\(374\) 0 0
\(375\) 4563.00 0.628353
\(376\) −4115.35 −0.564450
\(377\) −6273.00 −0.856965
\(378\) −3402.00 −0.462910
\(379\) −13186.0 −1.78712 −0.893561 0.448942i \(-0.851801\pi\)
−0.893561 + 0.448942i \(0.851801\pi\)
\(380\) −24879.2 −3.35862
\(381\) −1953.75 −0.262713
\(382\) −13655.5 −1.82899
\(383\) −3330.00 −0.444269 −0.222135 0.975016i \(-0.571302\pi\)
−0.222135 + 0.975016i \(0.571302\pi\)
\(384\) −1200.31 −0.159513
\(385\) 0 0
\(386\) −14499.0 −1.91186
\(387\) −654.715 −0.0859975
\(388\) 1691.00 0.221256
\(389\) 3537.00 0.461010 0.230505 0.973071i \(-0.425962\pi\)
0.230505 + 0.973071i \(0.425962\pi\)
\(390\) 9963.00 1.29358
\(391\) 7950.11 1.02827
\(392\) −14003.6 −1.80431
\(393\) −7825.41 −1.00443
\(394\) 18657.0 2.38560
\(395\) −1371.78 −0.174739
\(396\) 0 0
\(397\) −4501.00 −0.569014 −0.284507 0.958674i \(-0.591830\pi\)
−0.284507 + 0.958674i \(0.591830\pi\)
\(398\) −8407.37 −1.05885
\(399\) −10584.0 −1.32798
\(400\) −6380.00 −0.797500
\(401\) 3303.00 0.411332 0.205666 0.978622i \(-0.434064\pi\)
0.205666 + 0.978622i \(0.434064\pi\)
\(402\) −6017.14 −0.746537
\(403\) −13350.6 −1.65023
\(404\) 24484.3 3.01519
\(405\) 729.000 0.0894427
\(406\) −11130.2 −1.36054
\(407\) 0 0
\(408\) 15147.0 1.83796
\(409\) −9576.51 −1.15777 −0.578885 0.815409i \(-0.696512\pi\)
−0.578885 + 0.815409i \(0.696512\pi\)
\(410\) −1701.00 −0.204894
\(411\) −7182.00 −0.861951
\(412\) 25802.0 3.08537
\(413\) −9166.01 −1.09208
\(414\) −4208.88 −0.499651
\(415\) 11223.7 1.32759
\(416\) −21033.0 −2.47891
\(417\) −550.792 −0.0646820
\(418\) 0 0
\(419\) −6750.00 −0.787015 −0.393507 0.919322i \(-0.628738\pi\)
−0.393507 + 0.919322i \(0.628738\pi\)
\(420\) 12439.6 1.44521
\(421\) −13481.0 −1.56063 −0.780313 0.625389i \(-0.784940\pi\)
−0.780313 + 0.625389i \(0.784940\pi\)
\(422\) −9666.00 −1.11501
\(423\) 648.000 0.0744843
\(424\) 2572.10 0.294604
\(425\) −3886.72 −0.443609
\(426\) −3086.51 −0.351038
\(427\) −15120.0 −1.71360
\(428\) 24681.7 2.78747
\(429\) 0 0
\(430\) 3402.00 0.381533
\(431\) −1382.18 −0.154471 −0.0772356 0.997013i \(-0.524609\pi\)
−0.0772356 + 0.997013i \(0.524609\pi\)
\(432\) −3915.00 −0.436020
\(433\) −1531.00 −0.169920 −0.0849598 0.996384i \(-0.527076\pi\)
−0.0849598 + 0.996384i \(0.527076\pi\)
\(434\) −23688.0 −2.61995
\(435\) 2385.03 0.262882
\(436\) 22871.7 2.51229
\(437\) −13094.3 −1.43338
\(438\) 1188.00 0.129600
\(439\) 1919.11 0.208643 0.104321 0.994544i \(-0.466733\pi\)
0.104321 + 0.994544i \(0.466733\pi\)
\(440\) 0 0
\(441\) 2205.00 0.238095
\(442\) −32595.5 −3.50771
\(443\) 14598.0 1.56563 0.782813 0.622258i \(-0.213784\pi\)
0.782813 + 0.622258i \(0.213784\pi\)
\(444\) −7581.00 −0.810312
\(445\) 405.000 0.0431435
\(446\) 5009.09 0.531810
\(447\) 10834.0 1.14637
\(448\) −9190.26 −0.969194
\(449\) −12591.0 −1.32340 −0.661699 0.749769i \(-0.730164\pi\)
−0.661699 + 0.749769i \(0.730164\pi\)
\(450\) 2057.68 0.215555
\(451\) 0 0
\(452\) 13509.0 1.40577
\(453\) −4073.78 −0.422523
\(454\) 14850.0 1.53512
\(455\) −15498.0 −1.59683
\(456\) −24948.0 −2.56206
\(457\) −16778.4 −1.71742 −0.858708 0.512465i \(-0.828733\pi\)
−0.858708 + 0.512465i \(0.828733\pi\)
\(458\) 28677.6 2.92580
\(459\) −2385.03 −0.242536
\(460\) 15390.0 1.55992
\(461\) −14138.7 −1.42843 −0.714215 0.699926i \(-0.753216\pi\)
−0.714215 + 0.699926i \(0.753216\pi\)
\(462\) 0 0
\(463\) 6902.00 0.692793 0.346396 0.938088i \(-0.387405\pi\)
0.346396 + 0.938088i \(0.387405\pi\)
\(464\) −12808.5 −1.28151
\(465\) 5076.00 0.506223
\(466\) 18765.0 1.86539
\(467\) 15894.0 1.57492 0.787459 0.616367i \(-0.211396\pi\)
0.787459 + 0.616367i \(0.211396\pi\)
\(468\) 12143.4 1.19942
\(469\) 9360.00 0.921545
\(470\) −3367.11 −0.330453
\(471\) −3918.00 −0.383295
\(472\) −21605.6 −2.10695
\(473\) 0 0
\(474\) −2376.00 −0.230239
\(475\) 6401.66 0.618375
\(476\) −40698.0 −3.91889
\(477\) −405.000 −0.0388756
\(478\) −16956.0 −1.62249
\(479\) 9716.81 0.926873 0.463436 0.886130i \(-0.346616\pi\)
0.463436 + 0.886130i \(0.346616\pi\)
\(480\) 7996.88 0.760429
\(481\) 9444.87 0.895320
\(482\) −17964.0 −1.69759
\(483\) 6547.15 0.616782
\(484\) 0 0
\(485\) 801.000 0.0749929
\(486\) 1262.67 0.117851
\(487\) −7622.00 −0.709211 −0.354606 0.935016i \(-0.615385\pi\)
−0.354606 + 0.935016i \(0.615385\pi\)
\(488\) −35640.0 −3.30604
\(489\) −7638.00 −0.706344
\(490\) −11457.5 −1.05632
\(491\) −14902.6 −1.36974 −0.684871 0.728664i \(-0.740141\pi\)
−0.684871 + 0.728664i \(0.740141\pi\)
\(492\) −2073.26 −0.189980
\(493\) −7803.00 −0.712839
\(494\) 53686.6 4.88963
\(495\) 0 0
\(496\) −27260.0 −2.46776
\(497\) 4801.24 0.433331
\(498\) 19440.0 1.74925
\(499\) 13006.0 1.16679 0.583395 0.812188i \(-0.301724\pi\)
0.583395 + 0.812188i \(0.301724\pi\)
\(500\) −28899.0 −2.58481
\(501\) 2026.50 0.180713
\(502\) −34887.0 −3.10176
\(503\) 14185.5 1.25746 0.628728 0.777626i \(-0.283576\pi\)
0.628728 + 0.777626i \(0.283576\pi\)
\(504\) 12474.0 1.10245
\(505\) 11597.8 1.02197
\(506\) 0 0
\(507\) −8538.00 −0.747901
\(508\) 12373.8 1.08070
\(509\) 18234.0 1.58783 0.793917 0.608026i \(-0.208038\pi\)
0.793917 + 0.608026i \(0.208038\pi\)
\(510\) 12393.0 1.07602
\(511\) −1848.00 −0.159982
\(512\) 23356.7 2.01607
\(513\) 3928.29 0.338086
\(514\) −6968.04 −0.597952
\(515\) 12222.0 1.04576
\(516\) 4146.53 0.353761
\(517\) 0 0
\(518\) 16758.0 1.42144
\(519\) 9540.14 0.806870
\(520\) −36531.0 −3.08075
\(521\) 20502.0 1.72401 0.862005 0.506900i \(-0.169209\pi\)
0.862005 + 0.506900i \(0.169209\pi\)
\(522\) 4131.00 0.346377
\(523\) 10600.2 0.886257 0.443128 0.896458i \(-0.353869\pi\)
0.443128 + 0.896458i \(0.353869\pi\)
\(524\) 49560.9 4.13183
\(525\) −3200.83 −0.266087
\(526\) −4968.00 −0.411816
\(527\) −16606.9 −1.37269
\(528\) 0 0
\(529\) −4067.00 −0.334265
\(530\) 2104.44 0.172474
\(531\) 3402.00 0.278031
\(532\) 67032.0 5.46279
\(533\) 2583.00 0.209910
\(534\) 701.481 0.0568465
\(535\) 11691.3 0.944787
\(536\) 22062.9 1.77793
\(537\) 7668.00 0.616199
\(538\) −16040.5 −1.28542
\(539\) 0 0
\(540\) −4617.00 −0.367933
\(541\) −6082.96 −0.483414 −0.241707 0.970349i \(-0.577707\pi\)
−0.241707 + 0.970349i \(0.577707\pi\)
\(542\) −20970.0 −1.66188
\(543\) 2325.00 0.183748
\(544\) −26163.0 −2.06200
\(545\) 10834.0 0.851517
\(546\) −26843.3 −2.10401
\(547\) −19378.2 −1.51472 −0.757360 0.652998i \(-0.773511\pi\)
−0.757360 + 0.652998i \(0.773511\pi\)
\(548\) 45486.0 3.54574
\(549\) 5611.84 0.436262
\(550\) 0 0
\(551\) 12852.0 0.993673
\(552\) 15432.6 1.18995
\(553\) 3696.00 0.284213
\(554\) 19701.0 1.51086
\(555\) −3591.00 −0.274648
\(556\) 3488.35 0.266077
\(557\) 14216.7 1.08147 0.540736 0.841192i \(-0.318146\pi\)
0.540736 + 0.841192i \(0.318146\pi\)
\(558\) 8791.89 0.667008
\(559\) −5166.00 −0.390874
\(560\) −31644.6 −2.38791
\(561\) 0 0
\(562\) 14148.0 1.06192
\(563\) 2130.42 0.159479 0.0797394 0.996816i \(-0.474591\pi\)
0.0797394 + 0.996816i \(0.474591\pi\)
\(564\) −4104.00 −0.306400
\(565\) 6399.00 0.476474
\(566\) 16830.0 1.24985
\(567\) −1964.15 −0.145479
\(568\) 11317.2 0.836021
\(569\) −17251.2 −1.27102 −0.635509 0.772094i \(-0.719210\pi\)
−0.635509 + 0.772094i \(0.719210\pi\)
\(570\) −20412.0 −1.49994
\(571\) −9079.41 −0.665432 −0.332716 0.943027i \(-0.607965\pi\)
−0.332716 + 0.943027i \(0.607965\pi\)
\(572\) 0 0
\(573\) −7884.00 −0.574797
\(574\) 4583.01 0.333260
\(575\) −3960.00 −0.287206
\(576\) 3411.00 0.246745
\(577\) −7427.00 −0.535858 −0.267929 0.963439i \(-0.586339\pi\)
−0.267929 + 0.963439i \(0.586339\pi\)
\(578\) −15016.9 −1.08066
\(579\) −8371.00 −0.600841
\(580\) −15105.2 −1.08140
\(581\) −30240.0 −2.15932
\(582\) 1387.37 0.0988118
\(583\) 0 0
\(584\) −4356.00 −0.308652
\(585\) 5752.14 0.406533
\(586\) −22545.0 −1.58929
\(587\) −9972.00 −0.701173 −0.350586 0.936530i \(-0.614018\pi\)
−0.350586 + 0.936530i \(0.614018\pi\)
\(588\) −13965.0 −0.979433
\(589\) 27352.5 1.91348
\(590\) −17677.3 −1.23350
\(591\) 10771.6 0.749721
\(592\) 19285.0 1.33887
\(593\) 21922.6 1.51813 0.759066 0.651014i \(-0.225656\pi\)
0.759066 + 0.651014i \(0.225656\pi\)
\(594\) 0 0
\(595\) −19278.0 −1.32827
\(596\) −68615.2 −4.71575
\(597\) −4854.00 −0.332765
\(598\) −33210.0 −2.27100
\(599\) 576.000 0.0392900 0.0196450 0.999807i \(-0.493746\pi\)
0.0196450 + 0.999807i \(0.493746\pi\)
\(600\) −7544.81 −0.513360
\(601\) 7740.54 0.525363 0.262681 0.964883i \(-0.415393\pi\)
0.262681 + 0.964883i \(0.415393\pi\)
\(602\) −9166.01 −0.620563
\(603\) −3474.00 −0.234614
\(604\) 25800.6 1.73810
\(605\) 0 0
\(606\) 20088.0 1.34657
\(607\) 14500.7 0.969632 0.484816 0.874616i \(-0.338887\pi\)
0.484816 + 0.874616i \(0.338887\pi\)
\(608\) 43092.0 2.87436
\(609\) −6426.00 −0.427577
\(610\) −29160.0 −1.93550
\(611\) 5113.01 0.338544
\(612\) 15105.2 0.997700
\(613\) −5298.34 −0.349100 −0.174550 0.984648i \(-0.555847\pi\)
−0.174550 + 0.984648i \(0.555847\pi\)
\(614\) 30042.0 1.97459
\(615\) −982.073 −0.0643919
\(616\) 0 0
\(617\) 6939.00 0.452761 0.226381 0.974039i \(-0.427311\pi\)
0.226381 + 0.974039i \(0.427311\pi\)
\(618\) 21169.1 1.37791
\(619\) 1286.00 0.0835036 0.0417518 0.999128i \(-0.486706\pi\)
0.0417518 + 0.999128i \(0.486706\pi\)
\(620\) −32148.0 −2.08241
\(621\) −2430.00 −0.157025
\(622\) −27123.9 −1.74850
\(623\) −1091.19 −0.0701728
\(624\) −30891.1 −1.98179
\(625\) −8189.00 −0.524096
\(626\) 20665.1 1.31940
\(627\) 0 0
\(628\) 24814.0 1.57673
\(629\) 11748.5 0.744743
\(630\) 10206.0 0.645423
\(631\) −15110.0 −0.953280 −0.476640 0.879099i \(-0.658145\pi\)
−0.476640 + 0.879099i \(0.658145\pi\)
\(632\) 8712.00 0.548330
\(633\) −5580.67 −0.350413
\(634\) −51535.4 −3.22829
\(635\) 5861.26 0.366294
\(636\) 2565.00 0.159920
\(637\) 17398.5 1.08218
\(638\) 0 0
\(639\) −1782.00 −0.110321
\(640\) 3600.93 0.222405
\(641\) 13293.0 0.819098 0.409549 0.912288i \(-0.365686\pi\)
0.409549 + 0.912288i \(0.365686\pi\)
\(642\) 20250.0 1.24487
\(643\) 20528.0 1.25901 0.629506 0.776995i \(-0.283257\pi\)
0.629506 + 0.776995i \(0.283257\pi\)
\(644\) −41465.3 −2.53721
\(645\) 1964.15 0.119904
\(646\) 66781.0 4.06728
\(647\) −11124.0 −0.675934 −0.337967 0.941158i \(-0.609739\pi\)
−0.337967 + 0.941158i \(0.609739\pi\)
\(648\) −4629.77 −0.280671
\(649\) 0 0
\(650\) 16236.0 0.979736
\(651\) −13676.3 −0.823372
\(652\) 48374.0 2.90563
\(653\) 5562.00 0.333320 0.166660 0.986014i \(-0.446702\pi\)
0.166660 + 0.986014i \(0.446702\pi\)
\(654\) 18765.0 1.12197
\(655\) 23476.2 1.40045
\(656\) 5274.09 0.313901
\(657\) 685.892 0.0407294
\(658\) 9072.00 0.537482
\(659\) −16378.3 −0.968144 −0.484072 0.875028i \(-0.660843\pi\)
−0.484072 + 0.875028i \(0.660843\pi\)
\(660\) 0 0
\(661\) −28385.0 −1.67027 −0.835135 0.550045i \(-0.814611\pi\)
−0.835135 + 0.550045i \(0.814611\pi\)
\(662\) −45497.5 −2.67116
\(663\) −18819.0 −1.10237
\(664\) −71280.0 −4.16596
\(665\) 31752.0 1.85156
\(666\) −6219.79 −0.361880
\(667\) −7950.11 −0.461514
\(668\) −12834.5 −0.743386
\(669\) 2892.00 0.167132
\(670\) 18051.4 1.04088
\(671\) 0 0
\(672\) −21546.0 −1.23684
\(673\) 6948.99 0.398015 0.199007 0.979998i \(-0.436228\pi\)
0.199007 + 0.979998i \(0.436228\pi\)
\(674\) −51543.0 −2.94564
\(675\) 1188.00 0.0677424
\(676\) 54074.0 3.07658
\(677\) 3923.10 0.222713 0.111357 0.993781i \(-0.464480\pi\)
0.111357 + 0.993781i \(0.464480\pi\)
\(678\) 11083.4 0.627810
\(679\) −2158.14 −0.121976
\(680\) −45441.0 −2.56262
\(681\) 8573.65 0.482442
\(682\) 0 0
\(683\) 2034.00 0.113951 0.0569757 0.998376i \(-0.481854\pi\)
0.0569757 + 0.998376i \(0.481854\pi\)
\(684\) −24879.2 −1.39076
\(685\) 21546.0 1.20180
\(686\) −12348.0 −0.687243
\(687\) 16557.0 0.919489
\(688\) −10548.2 −0.584514
\(689\) −3195.63 −0.176697
\(690\) 12626.7 0.696650
\(691\) 4598.00 0.253135 0.126567 0.991958i \(-0.459604\pi\)
0.126567 + 0.991958i \(0.459604\pi\)
\(692\) −60420.9 −3.31916
\(693\) 0 0
\(694\) 6912.00 0.378063
\(695\) 1652.38 0.0901845
\(696\) −15147.0 −0.824922
\(697\) 3213.00 0.174607
\(698\) −14769.0 −0.800881
\(699\) 10834.0 0.586236
\(700\) 20271.9 1.09458
\(701\) 5949.59 0.320561 0.160280 0.987072i \(-0.448760\pi\)
0.160280 + 0.987072i \(0.448760\pi\)
\(702\) 9963.00 0.535654
\(703\) −19350.5 −1.03815
\(704\) 0 0
\(705\) −1944.00 −0.103851
\(706\) 7435.69 0.396382
\(707\) −31248.0 −1.66224
\(708\) −21546.0 −1.14371
\(709\) 24814.0 1.31440 0.657200 0.753716i \(-0.271741\pi\)
0.657200 + 0.753716i \(0.271741\pi\)
\(710\) 9259.54 0.489443
\(711\) −1371.78 −0.0723571
\(712\) −2572.10 −0.135384
\(713\) −16920.0 −0.888722
\(714\) −33390.5 −1.75015
\(715\) 0 0
\(716\) −48564.0 −2.53481
\(717\) −9789.55 −0.509899
\(718\) 28026.0 1.45671
\(719\) 26442.0 1.37152 0.685758 0.727829i \(-0.259471\pi\)
0.685758 + 0.727829i \(0.259471\pi\)
\(720\) 11745.0 0.607931
\(721\) −32929.7 −1.70093
\(722\) −74351.7 −3.83253
\(723\) −10371.5 −0.533501
\(724\) −14725.0 −0.755871
\(725\) 3886.72 0.199102
\(726\) 0 0
\(727\) −28370.0 −1.44730 −0.723649 0.690169i \(-0.757536\pi\)
−0.723649 + 0.690169i \(0.757536\pi\)
\(728\) 98425.5 5.01084
\(729\) 729.000 0.0370370
\(730\) −3564.00 −0.180698
\(731\) −6426.00 −0.325136
\(732\) −35541.7 −1.79462
\(733\) 20332.5 1.02456 0.512278 0.858820i \(-0.328802\pi\)
0.512278 + 0.858820i \(0.328802\pi\)
\(734\) −18467.1 −0.928657
\(735\) −6615.00 −0.331970
\(736\) −26656.3 −1.33500
\(737\) 0 0
\(738\) −1701.00 −0.0848437
\(739\) −9048.23 −0.450399 −0.225199 0.974313i \(-0.572303\pi\)
−0.225199 + 0.974313i \(0.572303\pi\)
\(740\) 22743.0 1.12980
\(741\) 30996.0 1.53666
\(742\) −5670.00 −0.280529
\(743\) −9758.37 −0.481830 −0.240915 0.970546i \(-0.577448\pi\)
−0.240915 + 0.970546i \(0.577448\pi\)
\(744\) −32236.9 −1.58853
\(745\) −32501.9 −1.59836
\(746\) 28980.0 1.42230
\(747\) 11223.7 0.549737
\(748\) 0 0
\(749\) −31500.0 −1.53670
\(750\) −23710.0 −1.15436
\(751\) −34010.0 −1.65252 −0.826260 0.563289i \(-0.809536\pi\)
−0.826260 + 0.563289i \(0.809536\pi\)
\(752\) 10440.0 0.506260
\(753\) −20142.0 −0.974788
\(754\) 32595.5 1.57435
\(755\) 12221.4 0.589113
\(756\) 12439.6 0.598444
\(757\) −5345.00 −0.256628 −0.128314 0.991734i \(-0.540957\pi\)
−0.128314 + 0.991734i \(0.540957\pi\)
\(758\) 68516.5 3.28315
\(759\) 0 0
\(760\) 74844.0 3.57221
\(761\) 22629.2 1.07794 0.538968 0.842326i \(-0.318814\pi\)
0.538968 + 0.842326i \(0.318814\pi\)
\(762\) 10152.0 0.482635
\(763\) −29190.0 −1.38499
\(764\) 49932.0 2.36450
\(765\) 7155.10 0.338161
\(766\) 17303.2 0.816174
\(767\) 26843.3 1.26370
\(768\) 15333.0 0.720419
\(769\) 34961.4 1.63946 0.819728 0.572753i \(-0.194124\pi\)
0.819728 + 0.572753i \(0.194124\pi\)
\(770\) 0 0
\(771\) −4023.00 −0.187918
\(772\) 53016.3 2.47163
\(773\) 29610.0 1.37775 0.688873 0.724882i \(-0.258106\pi\)
0.688873 + 0.724882i \(0.258106\pi\)
\(774\) 3402.00 0.157988
\(775\) 8272.00 0.383405
\(776\) −5087.03 −0.235327
\(777\) 9675.24 0.446714
\(778\) −18378.8 −0.846930
\(779\) −5292.00 −0.243396
\(780\) −36430.2 −1.67232
\(781\) 0 0
\(782\) −41310.0 −1.88906
\(783\) 2385.03 0.108856
\(784\) 35525.0 1.61830
\(785\) 11754.0 0.534418
\(786\) 40662.0 1.84525
\(787\) 5785.05 0.262026 0.131013 0.991381i \(-0.458177\pi\)
0.131013 + 0.991381i \(0.458177\pi\)
\(788\) −68220.3 −3.08407
\(789\) −2868.28 −0.129421
\(790\) 7128.00 0.321016
\(791\) −17240.8 −0.774985
\(792\) 0 0
\(793\) 44280.0 1.98289
\(794\) 23387.9 1.04535
\(795\) 1215.00 0.0542033
\(796\) 30742.0 1.36887
\(797\) −4626.00 −0.205598 −0.102799 0.994702i \(-0.532780\pi\)
−0.102799 + 0.994702i \(0.532780\pi\)
\(798\) 54996.1 2.43965
\(799\) 6360.09 0.281607
\(800\) 13032.0 0.575936
\(801\) 405.000 0.0178651
\(802\) −17162.9 −0.755664
\(803\) 0 0
\(804\) 22002.0 0.965113
\(805\) −19641.5 −0.859963
\(806\) 69372.0 3.03167
\(807\) −9261.00 −0.403969
\(808\) −73656.0 −3.20694
\(809\) −31239.3 −1.35762 −0.678810 0.734314i \(-0.737504\pi\)
−0.678810 + 0.734314i \(0.737504\pi\)
\(810\) −3788.00 −0.164317
\(811\) −44340.5 −1.91986 −0.959929 0.280242i \(-0.909585\pi\)
−0.959929 + 0.280242i \(0.909585\pi\)
\(812\) 40698.0 1.75889
\(813\) −12107.0 −0.522278
\(814\) 0 0
\(815\) 22914.0 0.984837
\(816\) −38425.5 −1.64848
\(817\) 10584.0 0.453228
\(818\) 49761.0 2.12696
\(819\) −15498.0 −0.661226
\(820\) 6219.79 0.264884
\(821\) 38493.1 1.63632 0.818160 0.574991i \(-0.194994\pi\)
0.818160 + 0.574991i \(0.194994\pi\)
\(822\) 37318.8 1.58351
\(823\) 8678.00 0.367553 0.183776 0.982968i \(-0.441168\pi\)
0.183776 + 0.982968i \(0.441168\pi\)
\(824\) −77620.1 −3.28158
\(825\) 0 0
\(826\) 47628.0 2.00628
\(827\) 27238.2 1.14530 0.572652 0.819799i \(-0.305915\pi\)
0.572652 + 0.819799i \(0.305915\pi\)
\(828\) 15390.0 0.645941
\(829\) −19789.0 −0.829072 −0.414536 0.910033i \(-0.636056\pi\)
−0.414536 + 0.910033i \(0.636056\pi\)
\(830\) −58320.0 −2.43894
\(831\) 11374.4 0.474817
\(832\) 26914.3 1.12150
\(833\) 21642.0 0.900180
\(834\) 2862.00 0.118828
\(835\) −6079.50 −0.251964
\(836\) 0 0
\(837\) 5076.00 0.209620
\(838\) 35074.0 1.44584
\(839\) −1800.00 −0.0740678 −0.0370339 0.999314i \(-0.511791\pi\)
−0.0370339 + 0.999314i \(0.511791\pi\)
\(840\) −37422.0 −1.53712
\(841\) −16586.0 −0.680061
\(842\) 70049.3 2.86705
\(843\) 8168.35 0.333728
\(844\) 35344.2 1.44147
\(845\) 25614.0 1.04278
\(846\) −3367.11 −0.136836
\(847\) 0 0
\(848\) −6525.00 −0.264233
\(849\) 9716.81 0.392791
\(850\) 20196.0 0.814961
\(851\) 11970.0 0.482170
\(852\) 11286.0 0.453817
\(853\) −33513.5 −1.34523 −0.672614 0.739994i \(-0.734828\pi\)
−0.672614 + 0.739994i \(0.734828\pi\)
\(854\) 78565.8 3.14809
\(855\) −11784.9 −0.471385
\(856\) −74250.0 −2.96473
\(857\) −26687.4 −1.06374 −0.531870 0.846826i \(-0.678511\pi\)
−0.531870 + 0.846826i \(0.678511\pi\)
\(858\) 0 0
\(859\) 46694.0 1.85469 0.927345 0.374207i \(-0.122085\pi\)
0.927345 + 0.374207i \(0.122085\pi\)
\(860\) −12439.6 −0.493240
\(861\) 2646.00 0.104733
\(862\) 7182.00 0.283782
\(863\) −36018.0 −1.42070 −0.710352 0.703847i \(-0.751464\pi\)
−0.710352 + 0.703847i \(0.751464\pi\)
\(864\) 7996.88 0.314883
\(865\) −28620.4 −1.12500
\(866\) 7955.31 0.312162
\(867\) −8670.00 −0.339618
\(868\) 86616.4 3.38704
\(869\) 0 0
\(870\) −12393.0 −0.482945
\(871\) −27411.4 −1.06636
\(872\) −68805.0 −2.67205
\(873\) 801.000 0.0310535
\(874\) 68040.0 2.63328
\(875\) 36882.3 1.42497
\(876\) −4343.98 −0.167545
\(877\) 9191.99 0.353924 0.176962 0.984218i \(-0.443373\pi\)
0.176962 + 0.984218i \(0.443373\pi\)
\(878\) −9972.00 −0.383301
\(879\) −13016.4 −0.499466
\(880\) 0 0
\(881\) −40005.0 −1.52986 −0.764928 0.644116i \(-0.777225\pi\)
−0.764928 + 0.644116i \(0.777225\pi\)
\(882\) −11457.5 −0.437409
\(883\) 4492.00 0.171198 0.0855990 0.996330i \(-0.472720\pi\)
0.0855990 + 0.996330i \(0.472720\pi\)
\(884\) 119187. 4.53472
\(885\) −10206.0 −0.387651
\(886\) −75853.4 −2.87624
\(887\) −43554.1 −1.64871 −0.824355 0.566074i \(-0.808462\pi\)
−0.824355 + 0.566074i \(0.808462\pi\)
\(888\) 22805.9 0.861843
\(889\) −15792.0 −0.595778
\(890\) −2104.44 −0.0792596
\(891\) 0 0
\(892\) −18316.0 −0.687517
\(893\) −10475.4 −0.392550
\(894\) −56295.0 −2.10603
\(895\) −23004.0 −0.859150
\(896\) −9702.00 −0.361742
\(897\) −19173.8 −0.713706
\(898\) 65424.8 2.43124
\(899\) 16606.9 0.616097
\(900\) −7524.00 −0.278667
\(901\) −3975.06 −0.146979
\(902\) 0 0
\(903\) −5292.00 −0.195024
\(904\) −40639.1 −1.49517
\(905\) −6975.00 −0.256195
\(906\) 21168.0 0.776225
\(907\) 7634.00 0.279474 0.139737 0.990189i \(-0.455374\pi\)
0.139737 + 0.990189i \(0.455374\pi\)
\(908\) −54299.8 −1.98458
\(909\) 11597.8 0.423185
\(910\) 80530.0 2.93356
\(911\) −43830.0 −1.59402 −0.797010 0.603966i \(-0.793586\pi\)
−0.797010 + 0.603966i \(0.793586\pi\)
\(912\) 63289.1 2.29793
\(913\) 0 0
\(914\) 87183.0 3.15510
\(915\) −16835.5 −0.608268
\(916\) −104861. −3.78243
\(917\) −63252.0 −2.27782
\(918\) 12393.0 0.445566
\(919\) 32531.4 1.16769 0.583847 0.811864i \(-0.301547\pi\)
0.583847 + 0.811864i \(0.301547\pi\)
\(920\) −46297.7 −1.65912
\(921\) 17344.8 0.620553
\(922\) 73467.0 2.62419
\(923\) −14060.8 −0.501426
\(924\) 0 0
\(925\) −5852.00 −0.208014
\(926\) −35863.8 −1.27274
\(927\) 12222.0 0.433035
\(928\) 26163.0 0.925477
\(929\) 15651.0 0.552737 0.276368 0.961052i \(-0.410869\pi\)
0.276368 + 0.961052i \(0.410869\pi\)
\(930\) −26375.7 −0.929992
\(931\) −35645.6 −1.25482
\(932\) −68615.2 −2.41155
\(933\) −15660.0 −0.549502
\(934\) −82587.6 −2.89331
\(935\) 0 0
\(936\) −36531.0 −1.27570
\(937\) 6337.57 0.220960 0.110480 0.993878i \(-0.464761\pi\)
0.110480 + 0.993878i \(0.464761\pi\)
\(938\) −48636.0 −1.69299
\(939\) 11931.0 0.414647
\(940\) 12312.0 0.427205
\(941\) −9846.71 −0.341120 −0.170560 0.985347i \(-0.554558\pi\)
−0.170560 + 0.985347i \(0.554558\pi\)
\(942\) 20358.5 0.704158
\(943\) 3273.58 0.113046
\(944\) 54810.0 1.88974
\(945\) 5892.44 0.202837
\(946\) 0 0
\(947\) −738.000 −0.0253239 −0.0126620 0.999920i \(-0.504031\pi\)
−0.0126620 + 0.999920i \(0.504031\pi\)
\(948\) 8687.97 0.297650
\(949\) 5412.00 0.185122
\(950\) −33264.0 −1.13603
\(951\) −29754.0 −1.01455
\(952\) 122432. 4.16810
\(953\) 15541.7 0.528274 0.264137 0.964485i \(-0.414913\pi\)
0.264137 + 0.964485i \(0.414913\pi\)
\(954\) 2104.44 0.0714191
\(955\) 23652.0 0.801425
\(956\) 62000.5 2.09753
\(957\) 0 0
\(958\) −50490.0 −1.70277
\(959\) −58051.4 −1.95472
\(960\) −10233.0 −0.344030
\(961\) 5553.00 0.186399
\(962\) −49077.0 −1.64481
\(963\) 11691.3 0.391224
\(964\) 65686.3 2.19462
\(965\) 25113.0 0.837737
\(966\) −34020.0 −1.13310
\(967\) 37692.9 1.25349 0.626743 0.779226i \(-0.284387\pi\)
0.626743 + 0.779226i \(0.284387\pi\)
\(968\) 0 0
\(969\) 38556.0 1.27822
\(970\) −4162.12 −0.137771
\(971\) −12402.0 −0.409886 −0.204943 0.978774i \(-0.565701\pi\)
−0.204943 + 0.978774i \(0.565701\pi\)
\(972\) −4617.00 −0.152356
\(973\) −4452.00 −0.146685
\(974\) 39605.1 1.30290
\(975\) 9373.86 0.307901
\(976\) 90413.1 2.96522
\(977\) 31203.0 1.02177 0.510887 0.859648i \(-0.329317\pi\)
0.510887 + 0.859648i \(0.329317\pi\)
\(978\) 39688.2 1.29764
\(979\) 0 0
\(980\) 41895.0 1.36560
\(981\) 10834.0 0.352602
\(982\) 77436.0 2.51638
\(983\) −36540.0 −1.18560 −0.592800 0.805350i \(-0.701978\pi\)
−0.592800 + 0.805350i \(0.701978\pi\)
\(984\) 6237.00 0.202061
\(985\) −32314.9 −1.04532
\(986\) 40545.6 1.30957
\(987\) 5237.72 0.168914
\(988\) −196308. −6.32124
\(989\) −6547.15 −0.210503
\(990\) 0 0
\(991\) −56888.0 −1.82352 −0.911759 0.410725i \(-0.865276\pi\)
−0.911759 + 0.410725i \(0.865276\pi\)
\(992\) 55682.0 1.78216
\(993\) −26268.0 −0.839466
\(994\) −24948.0 −0.796079
\(995\) 14562.0 0.463966
\(996\) −71083.4 −2.26141
\(997\) −15711.4 −0.499083 −0.249542 0.968364i \(-0.580280\pi\)
−0.249542 + 0.968364i \(0.580280\pi\)
\(998\) −67581.2 −2.14353
\(999\) −3591.00 −0.113728
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.l.1.1 2
3.2 odd 2 1089.4.a.s.1.2 2
11.10 odd 2 inner 363.4.a.l.1.2 yes 2
33.32 even 2 1089.4.a.s.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
363.4.a.l.1.1 2 1.1 even 1 trivial
363.4.a.l.1.2 yes 2 11.10 odd 2 inner
1089.4.a.s.1.1 2 33.32 even 2
1089.4.a.s.1.2 2 3.2 odd 2