Properties

Label 1815.4.a.w.1.2
Level $1815$
Weight $4$
Character 1815.1
Self dual yes
Analytic conductor $107.088$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1815,4,Mod(1,1815)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1815, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("1815.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1815.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: \(107.088466660\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 28x^{2} + 18x + 132 \) 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 1.2
Root \(-2.09331\) of defining polynomial
Character \(\chi\) \(=\) 1815.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.09331 q^{2} -3.00000 q^{3} -3.61805 q^{4} -5.00000 q^{5} +6.27993 q^{6} +3.55562 q^{7} +24.3202 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-2.09331 q^{2} -3.00000 q^{3} -3.61805 q^{4} -5.00000 q^{5} +6.27993 q^{6} +3.55562 q^{7} +24.3202 q^{8} +9.00000 q^{9} +10.4666 q^{10} +10.8541 q^{12} -10.2397 q^{13} -7.44301 q^{14} +15.0000 q^{15} -21.9654 q^{16} +45.8819 q^{17} -18.8398 q^{18} -97.1404 q^{19} +18.0902 q^{20} -10.6668 q^{21} -15.7760 q^{23} -72.9606 q^{24} +25.0000 q^{25} +21.4348 q^{26} -27.0000 q^{27} -12.8644 q^{28} -179.522 q^{29} -31.3997 q^{30} +79.6764 q^{31} -148.581 q^{32} -96.0452 q^{34} -17.7781 q^{35} -32.5624 q^{36} +235.295 q^{37} +203.345 q^{38} +30.7190 q^{39} -121.601 q^{40} -144.425 q^{41} +22.3290 q^{42} +229.458 q^{43} -45.0000 q^{45} +33.0241 q^{46} -138.515 q^{47} +65.8961 q^{48} -330.358 q^{49} -52.3328 q^{50} -137.646 q^{51} +37.0476 q^{52} -1.77711 q^{53} +56.5194 q^{54} +86.4733 q^{56} +291.421 q^{57} +375.795 q^{58} +95.7448 q^{59} -54.2707 q^{60} +527.720 q^{61} -166.787 q^{62} +32.0005 q^{63} +486.750 q^{64} +51.1984 q^{65} +6.52540 q^{67} -166.003 q^{68} +47.3281 q^{69} +37.2151 q^{70} +361.209 q^{71} +218.882 q^{72} +505.985 q^{73} -492.546 q^{74} -75.0000 q^{75} +351.458 q^{76} -64.3045 q^{78} -587.149 q^{79} +109.827 q^{80} +81.0000 q^{81} +302.327 q^{82} +907.928 q^{83} +38.5931 q^{84} -229.410 q^{85} -480.327 q^{86} +538.565 q^{87} +1541.60 q^{89} +94.1990 q^{90} -36.4084 q^{91} +57.0784 q^{92} -239.029 q^{93} +289.954 q^{94} +485.702 q^{95} +445.744 q^{96} -913.677 q^{97} +691.541 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{2} - 12 q^{3} + 25 q^{4} - 20 q^{5} - 3 q^{6} + 45 q^{7} + 15 q^{8} + 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + q^{2} - 12 q^{3} + 25 q^{4} - 20 q^{5} - 3 q^{6} + 45 q^{7} + 15 q^{8} + 36 q^{9} - 5 q^{10} - 75 q^{12} - 67 q^{13} - 23 q^{14} + 60 q^{15} - 31 q^{16} - 62 q^{17} + 9 q^{18} + 61 q^{19} - 125 q^{20} - 135 q^{21} + 21 q^{23} - 45 q^{24} + 100 q^{25} + 489 q^{26} - 108 q^{27} + 123 q^{28} - 31 q^{29} + 15 q^{30} - 173 q^{31} - 9 q^{32} - 167 q^{34} - 225 q^{35} + 225 q^{36} + 117 q^{37} - 147 q^{38} + 201 q^{39} - 75 q^{40} + 138 q^{41} + 69 q^{42} - 230 q^{43} - 180 q^{45} - 1484 q^{46} - 321 q^{47} + 93 q^{48} - 153 q^{49} + 25 q^{50} + 186 q^{51} - 237 q^{52} - 477 q^{53} - 27 q^{54} - 1167 q^{56} - 183 q^{57} - 495 q^{58} + 572 q^{59} + 375 q^{60} - 775 q^{61} + 738 q^{62} + 405 q^{63} - 423 q^{64} + 335 q^{65} - 732 q^{67} - 2427 q^{68} - 63 q^{69} + 115 q^{70} + 1833 q^{71} + 135 q^{72} + 626 q^{73} + 149 q^{74} - 300 q^{75} + 2527 q^{76} - 1467 q^{78} - 1443 q^{79} + 155 q^{80} + 324 q^{81} - 528 q^{82} + 1395 q^{83} - 369 q^{84} + 310 q^{85} + 1428 q^{86} + 93 q^{87} - 812 q^{89} - 45 q^{90} - 2295 q^{91} + 1654 q^{92} + 519 q^{93} + 692 q^{94} - 305 q^{95} + 27 q^{96} - 2082 q^{97} + 1080 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.09331 −0.740097 −0.370049 0.929012i \(-0.620659\pi\)
−0.370049 + 0.929012i \(0.620659\pi\)
\(3\) −3.00000 −0.577350
\(4\) −3.61805 −0.452256
\(5\) −5.00000 −0.447214
\(6\) 6.27993 0.427295
\(7\) 3.55562 0.191985 0.0959926 0.995382i \(-0.469397\pi\)
0.0959926 + 0.995382i \(0.469397\pi\)
\(8\) 24.3202 1.07481
\(9\) 9.00000 0.333333
\(10\) 10.4666 0.330982
\(11\) 0 0
\(12\) 10.8541 0.261110
\(13\) −10.2397 −0.218460 −0.109230 0.994017i \(-0.534838\pi\)
−0.109230 + 0.994017i \(0.534838\pi\)
\(14\) −7.44301 −0.142088
\(15\) 15.0000 0.258199
\(16\) −21.9654 −0.343209
\(17\) 45.8819 0.654589 0.327294 0.944922i \(-0.393863\pi\)
0.327294 + 0.944922i \(0.393863\pi\)
\(18\) −18.8398 −0.246699
\(19\) −97.1404 −1.17292 −0.586461 0.809977i \(-0.699479\pi\)
−0.586461 + 0.809977i \(0.699479\pi\)
\(20\) 18.0902 0.202255
\(21\) −10.6668 −0.110843
\(22\) 0 0
\(23\) −15.7760 −0.143023 −0.0715115 0.997440i \(-0.522782\pi\)
−0.0715115 + 0.997440i \(0.522782\pi\)
\(24\) −72.9606 −0.620542
\(25\) 25.0000 0.200000
\(26\) 21.4348 0.161681
\(27\) −27.0000 −0.192450
\(28\) −12.8644 −0.0868264
\(29\) −179.522 −1.14953 −0.574765 0.818319i \(-0.694906\pi\)
−0.574765 + 0.818319i \(0.694906\pi\)
\(30\) −31.3997 −0.191092
\(31\) 79.6764 0.461622 0.230811 0.972999i \(-0.425862\pi\)
0.230811 + 0.972999i \(0.425862\pi\)
\(32\) −148.581 −0.820803
\(33\) 0 0
\(34\) −96.0452 −0.484459
\(35\) −17.7781 −0.0858584
\(36\) −32.5624 −0.150752
\(37\) 235.295 1.04547 0.522733 0.852496i \(-0.324912\pi\)
0.522733 + 0.852496i \(0.324912\pi\)
\(38\) 203.345 0.868077
\(39\) 30.7190 0.126128
\(40\) −121.601 −0.480670
\(41\) −144.425 −0.550133 −0.275067 0.961425i \(-0.588700\pi\)
−0.275067 + 0.961425i \(0.588700\pi\)
\(42\) 22.3290 0.0820344
\(43\) 229.458 0.813767 0.406884 0.913480i \(-0.366615\pi\)
0.406884 + 0.913480i \(0.366615\pi\)
\(44\) 0 0
\(45\) −45.0000 −0.149071
\(46\) 33.0241 0.105851
\(47\) −138.515 −0.429882 −0.214941 0.976627i \(-0.568956\pi\)
−0.214941 + 0.976627i \(0.568956\pi\)
\(48\) 65.8961 0.198152
\(49\) −330.358 −0.963142
\(50\) −52.3328 −0.148019
\(51\) −137.646 −0.377927
\(52\) 37.0476 0.0987997
\(53\) −1.77711 −0.00460575 −0.00230288 0.999997i \(-0.500733\pi\)
−0.00230288 + 0.999997i \(0.500733\pi\)
\(54\) 56.5194 0.142432
\(55\) 0 0
\(56\) 86.4733 0.206348
\(57\) 291.421 0.677187
\(58\) 375.795 0.850764
\(59\) 95.7448 0.211270 0.105635 0.994405i \(-0.466313\pi\)
0.105635 + 0.994405i \(0.466313\pi\)
\(60\) −54.2707 −0.116772
\(61\) 527.720 1.10767 0.553833 0.832628i \(-0.313165\pi\)
0.553833 + 0.832628i \(0.313165\pi\)
\(62\) −166.787 −0.341646
\(63\) 32.0005 0.0639951
\(64\) 486.750 0.950683
\(65\) 51.1984 0.0976981
\(66\) 0 0
\(67\) 6.52540 0.0118986 0.00594929 0.999982i \(-0.498106\pi\)
0.00594929 + 0.999982i \(0.498106\pi\)
\(68\) −166.003 −0.296041
\(69\) 47.3281 0.0825744
\(70\) 37.2151 0.0635436
\(71\) 361.209 0.603769 0.301885 0.953344i \(-0.402384\pi\)
0.301885 + 0.953344i \(0.402384\pi\)
\(72\) 218.882 0.358270
\(73\) 505.985 0.811248 0.405624 0.914040i \(-0.367054\pi\)
0.405624 + 0.914040i \(0.367054\pi\)
\(74\) −492.546 −0.773747
\(75\) −75.0000 −0.115470
\(76\) 351.458 0.530461
\(77\) 0 0
\(78\) −64.3045 −0.0933468
\(79\) −587.149 −0.836195 −0.418098 0.908402i \(-0.637303\pi\)
−0.418098 + 0.908402i \(0.637303\pi\)
\(80\) 109.827 0.153488
\(81\) 81.0000 0.111111
\(82\) 302.327 0.407152
\(83\) 907.928 1.20070 0.600350 0.799738i \(-0.295028\pi\)
0.600350 + 0.799738i \(0.295028\pi\)
\(84\) 38.5931 0.0501293
\(85\) −229.410 −0.292741
\(86\) −480.327 −0.602267
\(87\) 538.565 0.663681
\(88\) 0 0
\(89\) 1541.60 1.83606 0.918030 0.396510i \(-0.129779\pi\)
0.918030 + 0.396510i \(0.129779\pi\)
\(90\) 94.1990 0.110327
\(91\) −36.4084 −0.0419410
\(92\) 57.0784 0.0646830
\(93\) −239.029 −0.266518
\(94\) 289.954 0.318154
\(95\) 485.702 0.524547
\(96\) 445.744 0.473891
\(97\) −913.677 −0.956390 −0.478195 0.878254i \(-0.658709\pi\)
−0.478195 + 0.878254i \(0.658709\pi\)
\(98\) 691.541 0.712819
\(99\) 0 0
\(100\) −90.4512 −0.0904512
\(101\) −419.835 −0.413615 −0.206808 0.978382i \(-0.566307\pi\)
−0.206808 + 0.978382i \(0.566307\pi\)
\(102\) 288.136 0.279703
\(103\) 481.611 0.460724 0.230362 0.973105i \(-0.426009\pi\)
0.230362 + 0.973105i \(0.426009\pi\)
\(104\) −249.031 −0.234803
\(105\) 53.3342 0.0495704
\(106\) 3.72005 0.00340870
\(107\) −141.219 −0.127590 −0.0637949 0.997963i \(-0.520320\pi\)
−0.0637949 + 0.997963i \(0.520320\pi\)
\(108\) 97.6873 0.0870367
\(109\) 876.420 0.770145 0.385072 0.922886i \(-0.374177\pi\)
0.385072 + 0.922886i \(0.374177\pi\)
\(110\) 0 0
\(111\) −705.885 −0.603600
\(112\) −78.1004 −0.0658910
\(113\) −1079.39 −0.898585 −0.449292 0.893385i \(-0.648324\pi\)
−0.449292 + 0.893385i \(0.648324\pi\)
\(114\) −610.035 −0.501184
\(115\) 78.8801 0.0639618
\(116\) 649.518 0.519881
\(117\) −92.1571 −0.0728199
\(118\) −200.424 −0.156360
\(119\) 163.139 0.125671
\(120\) 364.803 0.277515
\(121\) 0 0
\(122\) −1104.68 −0.819781
\(123\) 433.276 0.317620
\(124\) −288.273 −0.208771
\(125\) −125.000 −0.0894427
\(126\) −66.9871 −0.0473626
\(127\) 1542.46 1.07773 0.538863 0.842394i \(-0.318854\pi\)
0.538863 + 0.842394i \(0.318854\pi\)
\(128\) 169.731 0.117205
\(129\) −688.373 −0.469829
\(130\) −107.174 −0.0723061
\(131\) 1491.30 0.994623 0.497311 0.867572i \(-0.334321\pi\)
0.497311 + 0.867572i \(0.334321\pi\)
\(132\) 0 0
\(133\) −345.394 −0.225184
\(134\) −13.6597 −0.00880610
\(135\) 135.000 0.0860663
\(136\) 1115.86 0.703559
\(137\) 1735.30 1.08217 0.541084 0.840969i \(-0.318014\pi\)
0.541084 + 0.840969i \(0.318014\pi\)
\(138\) −99.0724 −0.0611131
\(139\) −815.237 −0.497464 −0.248732 0.968572i \(-0.580014\pi\)
−0.248732 + 0.968572i \(0.580014\pi\)
\(140\) 64.3219 0.0388300
\(141\) 415.544 0.248192
\(142\) −756.123 −0.446848
\(143\) 0 0
\(144\) −197.688 −0.114403
\(145\) 897.609 0.514085
\(146\) −1059.18 −0.600402
\(147\) 991.073 0.556070
\(148\) −851.308 −0.472818
\(149\) 2493.44 1.37095 0.685473 0.728098i \(-0.259595\pi\)
0.685473 + 0.728098i \(0.259595\pi\)
\(150\) 156.998 0.0854591
\(151\) −1102.20 −0.594010 −0.297005 0.954876i \(-0.595988\pi\)
−0.297005 + 0.954876i \(0.595988\pi\)
\(152\) −2362.47 −1.26067
\(153\) 412.937 0.218196
\(154\) 0 0
\(155\) −398.382 −0.206444
\(156\) −111.143 −0.0570420
\(157\) −2485.15 −1.26329 −0.631646 0.775257i \(-0.717620\pi\)
−0.631646 + 0.775257i \(0.717620\pi\)
\(158\) 1229.09 0.618866
\(159\) 5.33133 0.00265913
\(160\) 742.906 0.367074
\(161\) −56.0935 −0.0274583
\(162\) −169.558 −0.0822330
\(163\) −688.813 −0.330994 −0.165497 0.986210i \(-0.552923\pi\)
−0.165497 + 0.986210i \(0.552923\pi\)
\(164\) 522.538 0.248801
\(165\) 0 0
\(166\) −1900.58 −0.888635
\(167\) 2216.01 1.02683 0.513414 0.858141i \(-0.328381\pi\)
0.513414 + 0.858141i \(0.328381\pi\)
\(168\) −259.420 −0.119135
\(169\) −2092.15 −0.952275
\(170\) 480.226 0.216657
\(171\) −874.263 −0.390974
\(172\) −830.189 −0.368031
\(173\) −2710.23 −1.19107 −0.595534 0.803330i \(-0.703060\pi\)
−0.595534 + 0.803330i \(0.703060\pi\)
\(174\) −1127.39 −0.491189
\(175\) 88.8904 0.0383970
\(176\) 0 0
\(177\) −287.235 −0.121977
\(178\) −3227.05 −1.35886
\(179\) −1629.13 −0.680263 −0.340131 0.940378i \(-0.610472\pi\)
−0.340131 + 0.940378i \(0.610472\pi\)
\(180\) 162.812 0.0674183
\(181\) −1735.36 −0.712644 −0.356322 0.934363i \(-0.615969\pi\)
−0.356322 + 0.934363i \(0.615969\pi\)
\(182\) 76.2140 0.0310404
\(183\) −1583.16 −0.639511
\(184\) −383.676 −0.153723
\(185\) −1176.47 −0.467547
\(186\) 500.362 0.197249
\(187\) 0 0
\(188\) 501.152 0.194416
\(189\) −96.0016 −0.0369476
\(190\) −1016.73 −0.388216
\(191\) −1890.92 −0.716348 −0.358174 0.933655i \(-0.616600\pi\)
−0.358174 + 0.933655i \(0.616600\pi\)
\(192\) −1460.25 −0.548877
\(193\) 235.046 0.0876631 0.0438315 0.999039i \(-0.486044\pi\)
0.0438315 + 0.999039i \(0.486044\pi\)
\(194\) 1912.61 0.707822
\(195\) −153.595 −0.0564060
\(196\) 1195.25 0.435586
\(197\) 2336.24 0.844923 0.422462 0.906381i \(-0.361166\pi\)
0.422462 + 0.906381i \(0.361166\pi\)
\(198\) 0 0
\(199\) −4000.38 −1.42502 −0.712512 0.701660i \(-0.752442\pi\)
−0.712512 + 0.701660i \(0.752442\pi\)
\(200\) 608.005 0.214962
\(201\) −19.5762 −0.00686964
\(202\) 878.846 0.306116
\(203\) −638.310 −0.220693
\(204\) 498.009 0.170920
\(205\) 722.127 0.246027
\(206\) −1008.16 −0.340980
\(207\) −141.984 −0.0476743
\(208\) 224.918 0.0749773
\(209\) 0 0
\(210\) −111.645 −0.0366869
\(211\) −626.154 −0.204295 −0.102147 0.994769i \(-0.532571\pi\)
−0.102147 + 0.994769i \(0.532571\pi\)
\(212\) 6.42967 0.00208298
\(213\) −1083.63 −0.348586
\(214\) 295.615 0.0944289
\(215\) −1147.29 −0.363928
\(216\) −656.645 −0.206847
\(217\) 283.298 0.0886247
\(218\) −1834.62 −0.569982
\(219\) −1517.96 −0.468374
\(220\) 0 0
\(221\) −469.816 −0.143001
\(222\) 1477.64 0.446723
\(223\) −296.977 −0.0891795 −0.0445897 0.999005i \(-0.514198\pi\)
−0.0445897 + 0.999005i \(0.514198\pi\)
\(224\) −528.298 −0.157582
\(225\) 225.000 0.0666667
\(226\) 2259.49 0.665040
\(227\) 1216.15 0.355590 0.177795 0.984068i \(-0.443104\pi\)
0.177795 + 0.984068i \(0.443104\pi\)
\(228\) −1054.38 −0.306262
\(229\) 4475.00 1.29134 0.645669 0.763617i \(-0.276579\pi\)
0.645669 + 0.763617i \(0.276579\pi\)
\(230\) −165.121 −0.0473380
\(231\) 0 0
\(232\) −4366.00 −1.23553
\(233\) −5653.07 −1.58946 −0.794732 0.606961i \(-0.792388\pi\)
−0.794732 + 0.606961i \(0.792388\pi\)
\(234\) 192.914 0.0538938
\(235\) 692.573 0.192249
\(236\) −346.409 −0.0955480
\(237\) 1761.45 0.482778
\(238\) −341.500 −0.0930090
\(239\) −3769.86 −1.02030 −0.510151 0.860085i \(-0.670411\pi\)
−0.510151 + 0.860085i \(0.670411\pi\)
\(240\) −329.481 −0.0886162
\(241\) 3873.99 1.03546 0.517730 0.855544i \(-0.326777\pi\)
0.517730 + 0.855544i \(0.326777\pi\)
\(242\) 0 0
\(243\) −243.000 −0.0641500
\(244\) −1909.32 −0.500949
\(245\) 1651.79 0.430730
\(246\) −906.982 −0.235069
\(247\) 994.686 0.256236
\(248\) 1937.74 0.496157
\(249\) −2723.78 −0.693224
\(250\) 261.664 0.0661963
\(251\) 3579.50 0.900144 0.450072 0.892992i \(-0.351398\pi\)
0.450072 + 0.892992i \(0.351398\pi\)
\(252\) −115.779 −0.0289421
\(253\) 0 0
\(254\) −3228.85 −0.797622
\(255\) 688.229 0.169014
\(256\) −4249.30 −1.03743
\(257\) −7366.86 −1.78806 −0.894031 0.448005i \(-0.852135\pi\)
−0.894031 + 0.448005i \(0.852135\pi\)
\(258\) 1440.98 0.347719
\(259\) 836.618 0.200714
\(260\) −185.238 −0.0441845
\(261\) −1615.70 −0.383177
\(262\) −3121.76 −0.736118
\(263\) 1407.41 0.329978 0.164989 0.986295i \(-0.447241\pi\)
0.164989 + 0.986295i \(0.447241\pi\)
\(264\) 0 0
\(265\) 8.88555 0.00205975
\(266\) 723.017 0.166658
\(267\) −4624.80 −1.06005
\(268\) −23.6092 −0.00538120
\(269\) −2679.07 −0.607233 −0.303617 0.952794i \(-0.598194\pi\)
−0.303617 + 0.952794i \(0.598194\pi\)
\(270\) −282.597 −0.0636974
\(271\) 4830.77 1.08284 0.541418 0.840754i \(-0.317888\pi\)
0.541418 + 0.840754i \(0.317888\pi\)
\(272\) −1007.81 −0.224661
\(273\) 109.225 0.0242147
\(274\) −3632.53 −0.800910
\(275\) 0 0
\(276\) −171.235 −0.0373447
\(277\) −2302.39 −0.499413 −0.249706 0.968322i \(-0.580334\pi\)
−0.249706 + 0.968322i \(0.580334\pi\)
\(278\) 1706.54 0.368172
\(279\) 717.087 0.153874
\(280\) −432.366 −0.0922815
\(281\) −813.238 −0.172647 −0.0863234 0.996267i \(-0.527512\pi\)
−0.0863234 + 0.996267i \(0.527512\pi\)
\(282\) −869.863 −0.183686
\(283\) −6164.30 −1.29480 −0.647402 0.762149i \(-0.724144\pi\)
−0.647402 + 0.762149i \(0.724144\pi\)
\(284\) −1306.87 −0.273058
\(285\) −1457.11 −0.302847
\(286\) 0 0
\(287\) −513.521 −0.105617
\(288\) −1337.23 −0.273601
\(289\) −2807.85 −0.571514
\(290\) −1878.98 −0.380473
\(291\) 2741.03 0.552172
\(292\) −1830.68 −0.366892
\(293\) 4264.64 0.850317 0.425158 0.905119i \(-0.360218\pi\)
0.425158 + 0.905119i \(0.360218\pi\)
\(294\) −2074.62 −0.411546
\(295\) −478.724 −0.0944827
\(296\) 5722.42 1.12368
\(297\) 0 0
\(298\) −5219.56 −1.01463
\(299\) 161.541 0.0312448
\(300\) 271.353 0.0522220
\(301\) 815.864 0.156231
\(302\) 2307.24 0.439625
\(303\) 1259.51 0.238801
\(304\) 2133.72 0.402557
\(305\) −2638.60 −0.495363
\(306\) −864.407 −0.161486
\(307\) 1442.87 0.268238 0.134119 0.990965i \(-0.457180\pi\)
0.134119 + 0.990965i \(0.457180\pi\)
\(308\) 0 0
\(309\) −1444.83 −0.265999
\(310\) 833.937 0.152789
\(311\) 6754.23 1.23150 0.615751 0.787940i \(-0.288853\pi\)
0.615751 + 0.787940i \(0.288853\pi\)
\(312\) 747.093 0.135563
\(313\) 760.144 0.137271 0.0686356 0.997642i \(-0.478135\pi\)
0.0686356 + 0.997642i \(0.478135\pi\)
\(314\) 5202.20 0.934959
\(315\) −160.003 −0.0286195
\(316\) 2124.33 0.378174
\(317\) −3391.25 −0.600856 −0.300428 0.953804i \(-0.597130\pi\)
−0.300428 + 0.953804i \(0.597130\pi\)
\(318\) −11.1601 −0.00196802
\(319\) 0 0
\(320\) −2433.75 −0.425158
\(321\) 423.656 0.0736640
\(322\) 117.421 0.0203218
\(323\) −4456.99 −0.767782
\(324\) −293.062 −0.0502506
\(325\) −255.992 −0.0436919
\(326\) 1441.90 0.244968
\(327\) −2629.26 −0.444643
\(328\) −3512.45 −0.591289
\(329\) −492.505 −0.0825309
\(330\) 0 0
\(331\) −3220.55 −0.534797 −0.267398 0.963586i \(-0.586164\pi\)
−0.267398 + 0.963586i \(0.586164\pi\)
\(332\) −3284.93 −0.543023
\(333\) 2117.65 0.348489
\(334\) −4638.81 −0.759953
\(335\) −32.6270 −0.00532120
\(336\) 234.301 0.0380422
\(337\) −4386.18 −0.708992 −0.354496 0.935058i \(-0.615348\pi\)
−0.354496 + 0.935058i \(0.615348\pi\)
\(338\) 4379.52 0.704777
\(339\) 3238.16 0.518798
\(340\) 830.015 0.132394
\(341\) 0 0
\(342\) 1830.11 0.289359
\(343\) −2394.20 −0.376894
\(344\) 5580.46 0.874646
\(345\) −236.640 −0.0369284
\(346\) 5673.35 0.881507
\(347\) 6501.60 1.00583 0.502916 0.864335i \(-0.332260\pi\)
0.502916 + 0.864335i \(0.332260\pi\)
\(348\) −1948.55 −0.300154
\(349\) −1943.01 −0.298014 −0.149007 0.988836i \(-0.547608\pi\)
−0.149007 + 0.988836i \(0.547608\pi\)
\(350\) −186.075 −0.0284176
\(351\) 276.471 0.0420426
\(352\) 0 0
\(353\) 2124.76 0.320367 0.160183 0.987087i \(-0.448791\pi\)
0.160183 + 0.987087i \(0.448791\pi\)
\(354\) 601.271 0.0902746
\(355\) −1806.05 −0.270014
\(356\) −5577.58 −0.830369
\(357\) −489.416 −0.0725564
\(358\) 3410.28 0.503461
\(359\) 6163.44 0.906112 0.453056 0.891482i \(-0.350334\pi\)
0.453056 + 0.891482i \(0.350334\pi\)
\(360\) −1094.41 −0.160223
\(361\) 2577.25 0.375747
\(362\) 3632.66 0.527426
\(363\) 0 0
\(364\) 131.727 0.0189681
\(365\) −2529.93 −0.362801
\(366\) 3314.05 0.473301
\(367\) −12573.5 −1.78837 −0.894184 0.447699i \(-0.852244\pi\)
−0.894184 + 0.447699i \(0.852244\pi\)
\(368\) 346.526 0.0490868
\(369\) −1299.83 −0.183378
\(370\) 2462.73 0.346030
\(371\) −6.31872 −0.000884236 0
\(372\) 864.818 0.120534
\(373\) −6379.88 −0.885624 −0.442812 0.896614i \(-0.646019\pi\)
−0.442812 + 0.896614i \(0.646019\pi\)
\(374\) 0 0
\(375\) 375.000 0.0516398
\(376\) −3368.70 −0.462041
\(377\) 1838.25 0.251126
\(378\) 200.961 0.0273448
\(379\) 6409.71 0.868720 0.434360 0.900739i \(-0.356975\pi\)
0.434360 + 0.900739i \(0.356975\pi\)
\(380\) −1757.29 −0.237229
\(381\) −4627.38 −0.622225
\(382\) 3958.29 0.530167
\(383\) −6122.43 −0.816818 −0.408409 0.912799i \(-0.633916\pi\)
−0.408409 + 0.912799i \(0.633916\pi\)
\(384\) −509.192 −0.0676682
\(385\) 0 0
\(386\) −492.024 −0.0648792
\(387\) 2065.12 0.271256
\(388\) 3305.72 0.432533
\(389\) −7544.33 −0.983323 −0.491662 0.870786i \(-0.663610\pi\)
−0.491662 + 0.870786i \(0.663610\pi\)
\(390\) 321.523 0.0417460
\(391\) −723.835 −0.0936212
\(392\) −8034.36 −1.03520
\(393\) −4473.90 −0.574246
\(394\) −4890.47 −0.625326
\(395\) 2935.74 0.373958
\(396\) 0 0
\(397\) −5341.07 −0.675216 −0.337608 0.941287i \(-0.609618\pi\)
−0.337608 + 0.941287i \(0.609618\pi\)
\(398\) 8374.05 1.05466
\(399\) 1036.18 0.130010
\(400\) −549.134 −0.0686418
\(401\) 14413.2 1.79492 0.897458 0.441100i \(-0.145412\pi\)
0.897458 + 0.441100i \(0.145412\pi\)
\(402\) 40.9791 0.00508421
\(403\) −815.860 −0.100846
\(404\) 1518.98 0.187060
\(405\) −405.000 −0.0496904
\(406\) 1336.18 0.163334
\(407\) 0 0
\(408\) −3347.57 −0.406200
\(409\) −13192.8 −1.59496 −0.797482 0.603342i \(-0.793835\pi\)
−0.797482 + 0.603342i \(0.793835\pi\)
\(410\) −1511.64 −0.182084
\(411\) −5205.91 −0.624790
\(412\) −1742.49 −0.208365
\(413\) 340.432 0.0405607
\(414\) 297.217 0.0352837
\(415\) −4539.64 −0.536969
\(416\) 1521.42 0.179312
\(417\) 2445.71 0.287211
\(418\) 0 0
\(419\) −4648.27 −0.541964 −0.270982 0.962584i \(-0.587348\pi\)
−0.270982 + 0.962584i \(0.587348\pi\)
\(420\) −192.966 −0.0224185
\(421\) −14885.8 −1.72326 −0.861628 0.507541i \(-0.830555\pi\)
−0.861628 + 0.507541i \(0.830555\pi\)
\(422\) 1310.74 0.151198
\(423\) −1246.63 −0.143294
\(424\) −43.2197 −0.00495031
\(425\) 1147.05 0.130918
\(426\) 2268.37 0.257988
\(427\) 1876.37 0.212656
\(428\) 510.935 0.0577033
\(429\) 0 0
\(430\) 2401.63 0.269342
\(431\) −1795.56 −0.200671 −0.100336 0.994954i \(-0.531992\pi\)
−0.100336 + 0.994954i \(0.531992\pi\)
\(432\) 593.065 0.0660506
\(433\) 14633.7 1.62414 0.812069 0.583561i \(-0.198341\pi\)
0.812069 + 0.583561i \(0.198341\pi\)
\(434\) −593.032 −0.0655909
\(435\) −2692.83 −0.296807
\(436\) −3170.93 −0.348302
\(437\) 1532.49 0.167755
\(438\) 3177.55 0.346642
\(439\) −7081.49 −0.769889 −0.384944 0.922940i \(-0.625779\pi\)
−0.384944 + 0.922940i \(0.625779\pi\)
\(440\) 0 0
\(441\) −2973.22 −0.321047
\(442\) 983.472 0.105835
\(443\) 14206.1 1.52360 0.761798 0.647815i \(-0.224317\pi\)
0.761798 + 0.647815i \(0.224317\pi\)
\(444\) 2553.92 0.272982
\(445\) −7708.00 −0.821111
\(446\) 621.664 0.0660015
\(447\) −7480.33 −0.791516
\(448\) 1730.69 0.182517
\(449\) 4005.28 0.420982 0.210491 0.977596i \(-0.432494\pi\)
0.210491 + 0.977596i \(0.432494\pi\)
\(450\) −470.995 −0.0493398
\(451\) 0 0
\(452\) 3905.27 0.406390
\(453\) 3306.59 0.342952
\(454\) −2545.79 −0.263171
\(455\) 182.042 0.0187566
\(456\) 7087.42 0.727848
\(457\) −18169.7 −1.85983 −0.929916 0.367771i \(-0.880121\pi\)
−0.929916 + 0.367771i \(0.880121\pi\)
\(458\) −9367.57 −0.955716
\(459\) −1238.81 −0.125976
\(460\) −285.392 −0.0289271
\(461\) −2485.00 −0.251059 −0.125529 0.992090i \(-0.540063\pi\)
−0.125529 + 0.992090i \(0.540063\pi\)
\(462\) 0 0
\(463\) −16228.3 −1.62893 −0.814463 0.580215i \(-0.802969\pi\)
−0.814463 + 0.580215i \(0.802969\pi\)
\(464\) 3943.26 0.394529
\(465\) 1195.15 0.119190
\(466\) 11833.6 1.17636
\(467\) −10523.4 −1.04275 −0.521376 0.853327i \(-0.674581\pi\)
−0.521376 + 0.853327i \(0.674581\pi\)
\(468\) 333.429 0.0329332
\(469\) 23.2018 0.00228435
\(470\) −1449.77 −0.142283
\(471\) 7455.46 0.729362
\(472\) 2328.53 0.227075
\(473\) 0 0
\(474\) −3687.26 −0.357302
\(475\) −2428.51 −0.234585
\(476\) −590.243 −0.0568356
\(477\) −15.9940 −0.00153525
\(478\) 7891.50 0.755123
\(479\) 3980.01 0.379648 0.189824 0.981818i \(-0.439208\pi\)
0.189824 + 0.981818i \(0.439208\pi\)
\(480\) −2228.72 −0.211930
\(481\) −2409.34 −0.228392
\(482\) −8109.47 −0.766341
\(483\) 168.280 0.0158531
\(484\) 0 0
\(485\) 4568.38 0.427711
\(486\) 508.675 0.0474773
\(487\) −1101.38 −0.102481 −0.0512406 0.998686i \(-0.516318\pi\)
−0.0512406 + 0.998686i \(0.516318\pi\)
\(488\) 12834.3 1.19053
\(489\) 2066.44 0.191099
\(490\) −3457.71 −0.318782
\(491\) 2319.62 0.213204 0.106602 0.994302i \(-0.466003\pi\)
0.106602 + 0.994302i \(0.466003\pi\)
\(492\) −1567.61 −0.143645
\(493\) −8236.81 −0.752469
\(494\) −2082.19 −0.189640
\(495\) 0 0
\(496\) −1750.12 −0.158433
\(497\) 1284.32 0.115915
\(498\) 5701.73 0.513053
\(499\) −3583.35 −0.321469 −0.160734 0.986998i \(-0.551386\pi\)
−0.160734 + 0.986998i \(0.551386\pi\)
\(500\) 452.256 0.0404510
\(501\) −6648.04 −0.592839
\(502\) −7493.01 −0.666194
\(503\) −11119.5 −0.985674 −0.492837 0.870122i \(-0.664040\pi\)
−0.492837 + 0.870122i \(0.664040\pi\)
\(504\) 778.259 0.0687826
\(505\) 2099.18 0.184974
\(506\) 0 0
\(507\) 6276.45 0.549796
\(508\) −5580.69 −0.487408
\(509\) 8984.01 0.782336 0.391168 0.920319i \(-0.372071\pi\)
0.391168 + 0.920319i \(0.372071\pi\)
\(510\) −1440.68 −0.125087
\(511\) 1799.09 0.155748
\(512\) 7537.26 0.650591
\(513\) 2622.79 0.225729
\(514\) 15421.1 1.32334
\(515\) −2408.06 −0.206042
\(516\) 2490.57 0.212483
\(517\) 0 0
\(518\) −1751.30 −0.148548
\(519\) 8130.68 0.687664
\(520\) 1245.15 0.105007
\(521\) −16931.5 −1.42376 −0.711882 0.702299i \(-0.752157\pi\)
−0.711882 + 0.702299i \(0.752157\pi\)
\(522\) 3382.16 0.283588
\(523\) −18323.2 −1.53197 −0.765983 0.642861i \(-0.777747\pi\)
−0.765983 + 0.642861i \(0.777747\pi\)
\(524\) −5395.60 −0.449824
\(525\) −266.671 −0.0221685
\(526\) −2946.14 −0.244216
\(527\) 3655.71 0.302173
\(528\) 0 0
\(529\) −11918.1 −0.979544
\(530\) −18.6002 −0.00152442
\(531\) 861.704 0.0704233
\(532\) 1249.65 0.101841
\(533\) 1478.87 0.120182
\(534\) 9681.15 0.784540
\(535\) 706.093 0.0570599
\(536\) 158.699 0.0127887
\(537\) 4887.39 0.392750
\(538\) 5608.13 0.449412
\(539\) 0 0
\(540\) −488.436 −0.0389240
\(541\) 13422.3 1.06667 0.533335 0.845904i \(-0.320939\pi\)
0.533335 + 0.845904i \(0.320939\pi\)
\(542\) −10112.3 −0.801404
\(543\) 5206.09 0.411445
\(544\) −6817.19 −0.537288
\(545\) −4382.10 −0.344419
\(546\) −228.642 −0.0179212
\(547\) 13824.7 1.08063 0.540314 0.841463i \(-0.318305\pi\)
0.540314 + 0.841463i \(0.318305\pi\)
\(548\) −6278.41 −0.489417
\(549\) 4749.48 0.369222
\(550\) 0 0
\(551\) 17438.8 1.34831
\(552\) 1151.03 0.0887518
\(553\) −2087.68 −0.160537
\(554\) 4819.63 0.369614
\(555\) 3529.42 0.269938
\(556\) 2949.56 0.224981
\(557\) −5443.20 −0.414067 −0.207034 0.978334i \(-0.566381\pi\)
−0.207034 + 0.978334i \(0.566381\pi\)
\(558\) −1501.09 −0.113882
\(559\) −2349.57 −0.177775
\(560\) 390.502 0.0294674
\(561\) 0 0
\(562\) 1702.36 0.127775
\(563\) −16823.2 −1.25935 −0.629675 0.776858i \(-0.716812\pi\)
−0.629675 + 0.776858i \(0.716812\pi\)
\(564\) −1503.46 −0.112246
\(565\) 5396.93 0.401859
\(566\) 12903.8 0.958281
\(567\) 288.005 0.0213317
\(568\) 8784.67 0.648938
\(569\) 19196.0 1.41430 0.707151 0.707063i \(-0.249980\pi\)
0.707151 + 0.707063i \(0.249980\pi\)
\(570\) 3050.18 0.224137
\(571\) 17350.0 1.27159 0.635794 0.771859i \(-0.280673\pi\)
0.635794 + 0.771859i \(0.280673\pi\)
\(572\) 0 0
\(573\) 5672.77 0.413583
\(574\) 1074.96 0.0781672
\(575\) −394.401 −0.0286046
\(576\) 4380.75 0.316894
\(577\) −19192.4 −1.38473 −0.692367 0.721545i \(-0.743432\pi\)
−0.692367 + 0.721545i \(0.743432\pi\)
\(578\) 5877.70 0.422976
\(579\) −705.138 −0.0506123
\(580\) −3247.59 −0.232498
\(581\) 3228.24 0.230517
\(582\) −5737.83 −0.408661
\(583\) 0 0
\(584\) 12305.7 0.871938
\(585\) 460.786 0.0325660
\(586\) −8927.22 −0.629317
\(587\) −11943.4 −0.839789 −0.419895 0.907573i \(-0.637933\pi\)
−0.419895 + 0.907573i \(0.637933\pi\)
\(588\) −3585.75 −0.251486
\(589\) −7739.79 −0.541447
\(590\) 1002.12 0.0699264
\(591\) −7008.71 −0.487817
\(592\) −5168.34 −0.358813
\(593\) −13925.2 −0.964315 −0.482158 0.876085i \(-0.660147\pi\)
−0.482158 + 0.876085i \(0.660147\pi\)
\(594\) 0 0
\(595\) −815.693 −0.0562019
\(596\) −9021.40 −0.620018
\(597\) 12001.1 0.822738
\(598\) −338.157 −0.0231242
\(599\) 9438.13 0.643792 0.321896 0.946775i \(-0.395680\pi\)
0.321896 + 0.946775i \(0.395680\pi\)
\(600\) −1824.01 −0.124108
\(601\) 18515.0 1.25664 0.628321 0.777954i \(-0.283742\pi\)
0.628321 + 0.777954i \(0.283742\pi\)
\(602\) −1707.86 −0.115626
\(603\) 58.7286 0.00396619
\(604\) 3987.80 0.268644
\(605\) 0 0
\(606\) −2636.54 −0.176736
\(607\) −22935.8 −1.53366 −0.766832 0.641848i \(-0.778168\pi\)
−0.766832 + 0.641848i \(0.778168\pi\)
\(608\) 14433.2 0.962738
\(609\) 1914.93 0.127417
\(610\) 5523.41 0.366617
\(611\) 1418.35 0.0939118
\(612\) −1494.03 −0.0986805
\(613\) 5076.32 0.334471 0.167235 0.985917i \(-0.446516\pi\)
0.167235 + 0.985917i \(0.446516\pi\)
\(614\) −3020.38 −0.198522
\(615\) −2166.38 −0.142044
\(616\) 0 0
\(617\) 11305.1 0.737643 0.368822 0.929500i \(-0.379761\pi\)
0.368822 + 0.929500i \(0.379761\pi\)
\(618\) 3024.49 0.196865
\(619\) −13500.7 −0.876638 −0.438319 0.898819i \(-0.644426\pi\)
−0.438319 + 0.898819i \(0.644426\pi\)
\(620\) 1441.36 0.0933654
\(621\) 425.953 0.0275248
\(622\) −14138.7 −0.911432
\(623\) 5481.34 0.352496
\(624\) −674.755 −0.0432882
\(625\) 625.000 0.0400000
\(626\) −1591.22 −0.101594
\(627\) 0 0
\(628\) 8991.40 0.571331
\(629\) 10795.8 0.684350
\(630\) 334.936 0.0211812
\(631\) 7201.91 0.454364 0.227182 0.973852i \(-0.427049\pi\)
0.227182 + 0.973852i \(0.427049\pi\)
\(632\) −14279.6 −0.898752
\(633\) 1878.46 0.117950
\(634\) 7098.93 0.444692
\(635\) −7712.30 −0.481973
\(636\) −19.2890 −0.00120261
\(637\) 3382.76 0.210408
\(638\) 0 0
\(639\) 3250.88 0.201256
\(640\) −848.653 −0.0524156
\(641\) −10896.8 −0.671446 −0.335723 0.941961i \(-0.608981\pi\)
−0.335723 + 0.941961i \(0.608981\pi\)
\(642\) −886.844 −0.0545186
\(643\) −24156.4 −1.48155 −0.740774 0.671754i \(-0.765541\pi\)
−0.740774 + 0.671754i \(0.765541\pi\)
\(644\) 202.949 0.0124182
\(645\) 3441.87 0.210114
\(646\) 9329.87 0.568233
\(647\) 6293.32 0.382405 0.191202 0.981551i \(-0.438761\pi\)
0.191202 + 0.981551i \(0.438761\pi\)
\(648\) 1969.94 0.119423
\(649\) 0 0
\(650\) 535.871 0.0323363
\(651\) −849.895 −0.0511675
\(652\) 2492.16 0.149694
\(653\) 900.311 0.0539539 0.0269770 0.999636i \(-0.491412\pi\)
0.0269770 + 0.999636i \(0.491412\pi\)
\(654\) 5503.86 0.329079
\(655\) −7456.50 −0.444809
\(656\) 3172.36 0.188811
\(657\) 4553.87 0.270416
\(658\) 1030.97 0.0610809
\(659\) −24626.9 −1.45573 −0.727865 0.685720i \(-0.759487\pi\)
−0.727865 + 0.685720i \(0.759487\pi\)
\(660\) 0 0
\(661\) 30979.4 1.82293 0.911467 0.411373i \(-0.134951\pi\)
0.911467 + 0.411373i \(0.134951\pi\)
\(662\) 6741.62 0.395802
\(663\) 1409.45 0.0825618
\(664\) 22081.0 1.29052
\(665\) 1726.97 0.100705
\(666\) −4432.91 −0.257916
\(667\) 2832.14 0.164409
\(668\) −8017.64 −0.464389
\(669\) 890.930 0.0514878
\(670\) 68.2985 0.00393821
\(671\) 0 0
\(672\) 1584.89 0.0909800
\(673\) 1125.07 0.0644402 0.0322201 0.999481i \(-0.489742\pi\)
0.0322201 + 0.999481i \(0.489742\pi\)
\(674\) 9181.63 0.524723
\(675\) −675.000 −0.0384900
\(676\) 7569.49 0.430672
\(677\) 16409.3 0.931551 0.465776 0.884903i \(-0.345775\pi\)
0.465776 + 0.884903i \(0.345775\pi\)
\(678\) −6778.47 −0.383961
\(679\) −3248.68 −0.183613
\(680\) −5579.29 −0.314641
\(681\) −3648.46 −0.205300
\(682\) 0 0
\(683\) 24830.7 1.39110 0.695548 0.718479i \(-0.255161\pi\)
0.695548 + 0.718479i \(0.255161\pi\)
\(684\) 3163.13 0.176820
\(685\) −8676.52 −0.483960
\(686\) 5011.81 0.278938
\(687\) −13425.0 −0.745554
\(688\) −5040.13 −0.279292
\(689\) 18.1970 0.00100617
\(690\) 495.362 0.0273306
\(691\) 33267.5 1.83148 0.915741 0.401768i \(-0.131604\pi\)
0.915741 + 0.401768i \(0.131604\pi\)
\(692\) 9805.73 0.538668
\(693\) 0 0
\(694\) −13609.9 −0.744414
\(695\) 4076.18 0.222473
\(696\) 13098.0 0.713332
\(697\) −6626.52 −0.360111
\(698\) 4067.33 0.220560
\(699\) 16959.2 0.917677
\(700\) −321.610 −0.0173653
\(701\) 15590.4 0.840000 0.420000 0.907524i \(-0.362030\pi\)
0.420000 + 0.907524i \(0.362030\pi\)
\(702\) −578.741 −0.0311156
\(703\) −22856.6 −1.22625
\(704\) 0 0
\(705\) −2077.72 −0.110995
\(706\) −4447.78 −0.237103
\(707\) −1492.77 −0.0794080
\(708\) 1039.23 0.0551647
\(709\) −33594.5 −1.77950 −0.889752 0.456443i \(-0.849123\pi\)
−0.889752 + 0.456443i \(0.849123\pi\)
\(710\) 3780.62 0.199837
\(711\) −5284.34 −0.278732
\(712\) 37492.0 1.97342
\(713\) −1256.98 −0.0660226
\(714\) 1024.50 0.0536988
\(715\) 0 0
\(716\) 5894.27 0.307653
\(717\) 11309.6 0.589072
\(718\) −12902.0 −0.670611
\(719\) 9329.98 0.483935 0.241968 0.970284i \(-0.422207\pi\)
0.241968 + 0.970284i \(0.422207\pi\)
\(720\) 988.442 0.0511626
\(721\) 1712.42 0.0884521
\(722\) −5394.99 −0.278090
\(723\) −11622.0 −0.597823
\(724\) 6278.62 0.322297
\(725\) −4488.04 −0.229906
\(726\) 0 0
\(727\) −7667.73 −0.391170 −0.195585 0.980687i \(-0.562660\pi\)
−0.195585 + 0.980687i \(0.562660\pi\)
\(728\) −885.458 −0.0450787
\(729\) 729.000 0.0370370
\(730\) 5295.92 0.268508
\(731\) 10528.0 0.532683
\(732\) 5727.95 0.289223
\(733\) 27923.5 1.40706 0.703531 0.710664i \(-0.251606\pi\)
0.703531 + 0.710664i \(0.251606\pi\)
\(734\) 26320.2 1.32357
\(735\) −4955.36 −0.248682
\(736\) 2344.02 0.117394
\(737\) 0 0
\(738\) 2720.95 0.135717
\(739\) −8329.33 −0.414614 −0.207307 0.978276i \(-0.566470\pi\)
−0.207307 + 0.978276i \(0.566470\pi\)
\(740\) 4256.54 0.211451
\(741\) −2984.06 −0.147938
\(742\) 13.2271 0.000654421 0
\(743\) −10423.0 −0.514646 −0.257323 0.966325i \(-0.582841\pi\)
−0.257323 + 0.966325i \(0.582841\pi\)
\(744\) −5813.23 −0.286456
\(745\) −12467.2 −0.613106
\(746\) 13355.1 0.655448
\(747\) 8171.35 0.400233
\(748\) 0 0
\(749\) −502.119 −0.0244954
\(750\) −784.992 −0.0382185
\(751\) −36541.4 −1.77552 −0.887760 0.460307i \(-0.847739\pi\)
−0.887760 + 0.460307i \(0.847739\pi\)
\(752\) 3042.52 0.147539
\(753\) −10738.5 −0.519698
\(754\) −3848.02 −0.185858
\(755\) 5510.98 0.265649
\(756\) 347.338 0.0167098
\(757\) −17114.6 −0.821718 −0.410859 0.911699i \(-0.634771\pi\)
−0.410859 + 0.911699i \(0.634771\pi\)
\(758\) −13417.5 −0.642937
\(759\) 0 0
\(760\) 11812.4 0.563789
\(761\) 23597.4 1.12405 0.562027 0.827119i \(-0.310022\pi\)
0.562027 + 0.827119i \(0.310022\pi\)
\(762\) 9686.54 0.460507
\(763\) 3116.21 0.147856
\(764\) 6841.45 0.323972
\(765\) −2064.69 −0.0975803
\(766\) 12816.2 0.604525
\(767\) −980.396 −0.0461539
\(768\) 12747.9 0.598958
\(769\) −9769.32 −0.458116 −0.229058 0.973413i \(-0.573564\pi\)
−0.229058 + 0.973413i \(0.573564\pi\)
\(770\) 0 0
\(771\) 22100.6 1.03234
\(772\) −850.407 −0.0396461
\(773\) 4933.64 0.229561 0.114781 0.993391i \(-0.463384\pi\)
0.114781 + 0.993391i \(0.463384\pi\)
\(774\) −4322.94 −0.200756
\(775\) 1991.91 0.0923245
\(776\) −22220.8 −1.02794
\(777\) −2509.85 −0.115882
\(778\) 15792.6 0.727755
\(779\) 14029.5 0.645264
\(780\) 555.714 0.0255100
\(781\) 0 0
\(782\) 1515.21 0.0692888
\(783\) 4847.09 0.221227
\(784\) 7256.43 0.330559
\(785\) 12425.8 0.564961
\(786\) 9365.27 0.424998
\(787\) 5524.93 0.250245 0.125122 0.992141i \(-0.460068\pi\)
0.125122 + 0.992141i \(0.460068\pi\)
\(788\) −8452.61 −0.382121
\(789\) −4222.22 −0.190513
\(790\) −6145.43 −0.276765
\(791\) −3837.88 −0.172515
\(792\) 0 0
\(793\) −5403.68 −0.241980
\(794\) 11180.5 0.499725
\(795\) −26.6567 −0.00118920
\(796\) 14473.6 0.644475
\(797\) −29994.7 −1.33308 −0.666541 0.745468i \(-0.732226\pi\)
−0.666541 + 0.745468i \(0.732226\pi\)
\(798\) −2169.05 −0.0962200
\(799\) −6355.32 −0.281396
\(800\) −3714.53 −0.164161
\(801\) 13874.4 0.612020
\(802\) −30171.3 −1.32841
\(803\) 0 0
\(804\) 70.8276 0.00310684
\(805\) 280.467 0.0122797
\(806\) 1707.85 0.0746358
\(807\) 8037.21 0.350586
\(808\) −10210.5 −0.444558
\(809\) −6020.90 −0.261661 −0.130830 0.991405i \(-0.541764\pi\)
−0.130830 + 0.991405i \(0.541764\pi\)
\(810\) 847.791 0.0367757
\(811\) 25351.3 1.09766 0.548831 0.835933i \(-0.315073\pi\)
0.548831 + 0.835933i \(0.315073\pi\)
\(812\) 2309.44 0.0998095
\(813\) −14492.3 −0.625176
\(814\) 0 0
\(815\) 3444.07 0.148025
\(816\) 3023.44 0.129708
\(817\) −22289.6 −0.954486
\(818\) 27616.6 1.18043
\(819\) −327.675 −0.0139803
\(820\) −2612.69 −0.111267
\(821\) 16072.6 0.683238 0.341619 0.939839i \(-0.389025\pi\)
0.341619 + 0.939839i \(0.389025\pi\)
\(822\) 10897.6 0.462405
\(823\) −19242.3 −0.815000 −0.407500 0.913205i \(-0.633599\pi\)
−0.407500 + 0.913205i \(0.633599\pi\)
\(824\) 11712.9 0.495191
\(825\) 0 0
\(826\) −712.630 −0.0300188
\(827\) 40811.2 1.71602 0.858008 0.513636i \(-0.171702\pi\)
0.858008 + 0.513636i \(0.171702\pi\)
\(828\) 513.706 0.0215610
\(829\) −3445.06 −0.144333 −0.0721663 0.997393i \(-0.522991\pi\)
−0.0721663 + 0.997393i \(0.522991\pi\)
\(830\) 9502.88 0.397410
\(831\) 6907.18 0.288336
\(832\) −4984.16 −0.207686
\(833\) −15157.4 −0.630461
\(834\) −5119.63 −0.212564
\(835\) −11080.1 −0.459211
\(836\) 0 0
\(837\) −2151.26 −0.0888393
\(838\) 9730.28 0.401106
\(839\) 18299.8 0.753015 0.376508 0.926414i \(-0.377125\pi\)
0.376508 + 0.926414i \(0.377125\pi\)
\(840\) 1297.10 0.0532788
\(841\) 7839.07 0.321418
\(842\) 31160.7 1.27538
\(843\) 2439.72 0.0996776
\(844\) 2265.46 0.0923936
\(845\) 10460.7 0.425870
\(846\) 2609.59 0.106051
\(847\) 0 0
\(848\) 39.0349 0.00158073
\(849\) 18492.9 0.747555
\(850\) −2401.13 −0.0968919
\(851\) −3712.02 −0.149526
\(852\) 3920.61 0.157650
\(853\) 13253.4 0.531990 0.265995 0.963974i \(-0.414299\pi\)
0.265995 + 0.963974i \(0.414299\pi\)
\(854\) −3927.83 −0.157386
\(855\) 4371.32 0.174849
\(856\) −3434.46 −0.137135
\(857\) −14698.3 −0.585862 −0.292931 0.956134i \(-0.594631\pi\)
−0.292931 + 0.956134i \(0.594631\pi\)
\(858\) 0 0
\(859\) 28131.1 1.11737 0.558685 0.829380i \(-0.311306\pi\)
0.558685 + 0.829380i \(0.311306\pi\)
\(860\) 4150.95 0.164588
\(861\) 1540.56 0.0609783
\(862\) 3758.68 0.148516
\(863\) −38137.0 −1.50429 −0.752144 0.658999i \(-0.770980\pi\)
−0.752144 + 0.658999i \(0.770980\pi\)
\(864\) 4011.69 0.157964
\(865\) 13551.1 0.532662
\(866\) −30632.9 −1.20202
\(867\) 8423.54 0.329964
\(868\) −1024.99 −0.0400810
\(869\) 0 0
\(870\) 5636.93 0.219666
\(871\) −66.8180 −0.00259936
\(872\) 21314.7 0.827760
\(873\) −8223.09 −0.318797
\(874\) −3207.98 −0.124155
\(875\) −444.452 −0.0171717
\(876\) 5492.03 0.211825
\(877\) 23653.1 0.910728 0.455364 0.890305i \(-0.349509\pi\)
0.455364 + 0.890305i \(0.349509\pi\)
\(878\) 14823.8 0.569793
\(879\) −12793.9 −0.490931
\(880\) 0 0
\(881\) 4181.89 0.159922 0.0799612 0.996798i \(-0.474520\pi\)
0.0799612 + 0.996798i \(0.474520\pi\)
\(882\) 6223.87 0.237606
\(883\) −20102.5 −0.766142 −0.383071 0.923719i \(-0.625134\pi\)
−0.383071 + 0.923719i \(0.625134\pi\)
\(884\) 1699.82 0.0646731
\(885\) 1436.17 0.0545496
\(886\) −29737.8 −1.12761
\(887\) −7941.42 −0.300617 −0.150308 0.988639i \(-0.548027\pi\)
−0.150308 + 0.988639i \(0.548027\pi\)
\(888\) −17167.3 −0.648756
\(889\) 5484.39 0.206907
\(890\) 16135.3 0.607702
\(891\) 0 0
\(892\) 1074.47 0.0403319
\(893\) 13455.4 0.504218
\(894\) 15658.7 0.585799
\(895\) 8145.66 0.304223
\(896\) 603.497 0.0225016
\(897\) −484.624 −0.0180392
\(898\) −8384.30 −0.311568
\(899\) −14303.6 −0.530649
\(900\) −814.060 −0.0301504
\(901\) −81.5373 −0.00301487
\(902\) 0 0
\(903\) −2447.59 −0.0902002
\(904\) −26250.9 −0.965808
\(905\) 8676.82 0.318704
\(906\) −6921.72 −0.253818
\(907\) −9541.21 −0.349295 −0.174647 0.984631i \(-0.555879\pi\)
−0.174647 + 0.984631i \(0.555879\pi\)
\(908\) −4400.10 −0.160818
\(909\) −3778.52 −0.137872
\(910\) −381.070 −0.0138817
\(911\) 54124.8 1.96842 0.984212 0.176993i \(-0.0566369\pi\)
0.984212 + 0.176993i \(0.0566369\pi\)
\(912\) −6401.17 −0.232417
\(913\) 0 0
\(914\) 38034.9 1.37646
\(915\) 7915.80 0.285998
\(916\) −16190.8 −0.584015
\(917\) 5302.49 0.190953
\(918\) 2593.22 0.0932342
\(919\) 4785.90 0.171787 0.0858935 0.996304i \(-0.472626\pi\)
0.0858935 + 0.996304i \(0.472626\pi\)
\(920\) 1918.38 0.0687469
\(921\) −4328.62 −0.154867
\(922\) 5201.88 0.185808
\(923\) −3698.66 −0.131899
\(924\) 0 0
\(925\) 5882.37 0.209093
\(926\) 33970.9 1.20556
\(927\) 4334.50 0.153575
\(928\) 26673.6 0.943537
\(929\) −42417.2 −1.49802 −0.749011 0.662558i \(-0.769471\pi\)
−0.749011 + 0.662558i \(0.769471\pi\)
\(930\) −2501.81 −0.0882125
\(931\) 32091.1 1.12969
\(932\) 20453.1 0.718844
\(933\) −20262.7 −0.711008
\(934\) 22028.8 0.771738
\(935\) 0 0
\(936\) −2241.28 −0.0782676
\(937\) 43632.1 1.52124 0.760618 0.649200i \(-0.224896\pi\)
0.760618 + 0.649200i \(0.224896\pi\)
\(938\) −48.5686 −0.00169064
\(939\) −2280.43 −0.0792536
\(940\) −2505.76 −0.0869457
\(941\) −41150.7 −1.42558 −0.712792 0.701376i \(-0.752570\pi\)
−0.712792 + 0.701376i \(0.752570\pi\)
\(942\) −15606.6 −0.539799
\(943\) 2278.46 0.0786817
\(944\) −2103.07 −0.0725097
\(945\) 480.008 0.0165235
\(946\) 0 0
\(947\) −40605.3 −1.39334 −0.696671 0.717390i \(-0.745336\pi\)
−0.696671 + 0.717390i \(0.745336\pi\)
\(948\) −6373.00 −0.218339
\(949\) −5181.13 −0.177225
\(950\) 5083.63 0.173615
\(951\) 10173.7 0.346904
\(952\) 3967.56 0.135073
\(953\) −18063.2 −0.613981 −0.306990 0.951713i \(-0.599322\pi\)
−0.306990 + 0.951713i \(0.599322\pi\)
\(954\) 33.4804 0.00113623
\(955\) 9454.61 0.320360
\(956\) 13639.5 0.461438
\(957\) 0 0
\(958\) −8331.41 −0.280977
\(959\) 6170.07 0.207760
\(960\) 7301.24 0.245465
\(961\) −23442.7 −0.786905
\(962\) 5043.51 0.169032
\(963\) −1270.97 −0.0425300
\(964\) −14016.3 −0.468293
\(965\) −1175.23 −0.0392041
\(966\) −352.263 −0.0117328
\(967\) −39800.2 −1.32357 −0.661783 0.749696i \(-0.730200\pi\)
−0.661783 + 0.749696i \(0.730200\pi\)
\(968\) 0 0
\(969\) 13371.0 0.443279
\(970\) −9563.05 −0.316547
\(971\) −27405.4 −0.905748 −0.452874 0.891575i \(-0.649601\pi\)
−0.452874 + 0.891575i \(0.649601\pi\)
\(972\) 879.185 0.0290122
\(973\) −2898.67 −0.0955057
\(974\) 2305.53 0.0758461
\(975\) 767.976 0.0252256
\(976\) −11591.6 −0.380161
\(977\) 6513.88 0.213303 0.106652 0.994296i \(-0.465987\pi\)
0.106652 + 0.994296i \(0.465987\pi\)
\(978\) −4325.70 −0.141432
\(979\) 0 0
\(980\) −5976.25 −0.194800
\(981\) 7887.78 0.256715
\(982\) −4855.69 −0.157792
\(983\) −2650.01 −0.0859838 −0.0429919 0.999075i \(-0.513689\pi\)
−0.0429919 + 0.999075i \(0.513689\pi\)
\(984\) 10537.4 0.341381
\(985\) −11681.2 −0.377861
\(986\) 17242.2 0.556900
\(987\) 1477.51 0.0476492
\(988\) −3598.82 −0.115884
\(989\) −3619.93 −0.116387
\(990\) 0 0
\(991\) −10091.7 −0.323486 −0.161743 0.986833i \(-0.551712\pi\)
−0.161743 + 0.986833i \(0.551712\pi\)
\(992\) −11838.4 −0.378901
\(993\) 9661.66 0.308765
\(994\) −2688.48 −0.0857882
\(995\) 20001.9 0.637290
\(996\) 9854.78 0.313515
\(997\) −3007.33 −0.0955297 −0.0477648 0.998859i \(-0.515210\pi\)
−0.0477648 + 0.998859i \(0.515210\pi\)
\(998\) 7501.07 0.237918
\(999\) −6352.96 −0.201200
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 1815.4.a.w.1.2 yes 4
11.10 odd 2 1815.4.a.u.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1815.4.a.u.1.3 4 11.10 odd 2
1815.4.a.w.1.2 yes 4 1.1 even 1 trivial