Properties

Label 966.4.a.q.1.2
Level $966$
Weight $4$
Character 966.1
Self dual yes
Analytic conductor $56.996$
Analytic rank $0$
Dimension $5$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [966,4,Mod(1,966)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(966, 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("966.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 966.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: \(56.9958450655\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - 570x^{3} - 189x^{2} + 63838x + 254320 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(15.0684\) of defining polynomial
Character \(\chi\) \(=\) 966.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -17.0684 q^{5} +6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -17.0684 q^{5} +6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -34.1369 q^{10} -63.2891 q^{11} +12.0000 q^{12} +22.2563 q^{13} -14.0000 q^{14} -51.2053 q^{15} +16.0000 q^{16} +53.5635 q^{17} +18.0000 q^{18} +40.5028 q^{19} -68.2738 q^{20} -21.0000 q^{21} -126.578 q^{22} -23.0000 q^{23} +24.0000 q^{24} +166.332 q^{25} +44.5126 q^{26} +27.0000 q^{27} -28.0000 q^{28} +151.616 q^{29} -102.411 q^{30} +181.258 q^{31} +32.0000 q^{32} -189.867 q^{33} +107.127 q^{34} +119.479 q^{35} +36.0000 q^{36} +346.839 q^{37} +81.0056 q^{38} +66.7688 q^{39} -136.548 q^{40} -83.1893 q^{41} -42.0000 q^{42} +61.9979 q^{43} -253.156 q^{44} -153.616 q^{45} -46.0000 q^{46} +401.068 q^{47} +48.0000 q^{48} +49.0000 q^{49} +332.663 q^{50} +160.691 q^{51} +89.0251 q^{52} -354.475 q^{53} +54.0000 q^{54} +1080.25 q^{55} -56.0000 q^{56} +121.508 q^{57} +303.232 q^{58} +159.553 q^{59} -204.821 q^{60} -438.025 q^{61} +362.515 q^{62} -63.0000 q^{63} +64.0000 q^{64} -379.880 q^{65} -379.735 q^{66} +41.8010 q^{67} +214.254 q^{68} -69.0000 q^{69} +238.958 q^{70} +479.166 q^{71} +72.0000 q^{72} +584.054 q^{73} +693.679 q^{74} +498.995 q^{75} +162.011 q^{76} +443.024 q^{77} +133.538 q^{78} +555.934 q^{79} -273.095 q^{80} +81.0000 q^{81} -166.379 q^{82} -815.363 q^{83} -84.0000 q^{84} -914.246 q^{85} +123.996 q^{86} +454.848 q^{87} -506.313 q^{88} -422.496 q^{89} -307.232 q^{90} -155.794 q^{91} -92.0000 q^{92} +543.773 q^{93} +802.137 q^{94} -691.320 q^{95} +96.0000 q^{96} -124.121 q^{97} +98.0000 q^{98} -569.602 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q + 10 q^{2} + 15 q^{3} + 20 q^{4} - 10 q^{5} + 30 q^{6} - 35 q^{7} + 40 q^{8} + 45 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 5 q + 10 q^{2} + 15 q^{3} + 20 q^{4} - 10 q^{5} + 30 q^{6} - 35 q^{7} + 40 q^{8} + 45 q^{9} - 20 q^{10} + 47 q^{11} + 60 q^{12} + 74 q^{13} - 70 q^{14} - 30 q^{15} + 80 q^{16} - 4 q^{17} + 90 q^{18} + 215 q^{19} - 40 q^{20} - 105 q^{21} + 94 q^{22} - 115 q^{23} + 120 q^{24} + 535 q^{25} + 148 q^{26} + 135 q^{27} - 140 q^{28} + 273 q^{29} - 60 q^{30} + 660 q^{31} + 160 q^{32} + 141 q^{33} - 8 q^{34} + 70 q^{35} + 180 q^{36} - 71 q^{37} + 430 q^{38} + 222 q^{39} - 80 q^{40} + 428 q^{41} - 210 q^{42} + 606 q^{43} + 188 q^{44} - 90 q^{45} - 230 q^{46} + 514 q^{47} + 240 q^{48} + 245 q^{49} + 1070 q^{50} - 12 q^{51} + 296 q^{52} + 376 q^{53} + 270 q^{54} - 395 q^{55} - 280 q^{56} + 645 q^{57} + 546 q^{58} + 1062 q^{59} - 120 q^{60} + 60 q^{61} + 1320 q^{62} - 315 q^{63} + 320 q^{64} + 1755 q^{65} + 282 q^{66} + 671 q^{67} - 16 q^{68} - 345 q^{69} + 140 q^{70} + 1885 q^{71} + 360 q^{72} + 790 q^{73} - 142 q^{74} + 1605 q^{75} + 860 q^{76} - 329 q^{77} + 444 q^{78} + 738 q^{79} - 160 q^{80} + 405 q^{81} + 856 q^{82} + 774 q^{83} - 420 q^{84} + 781 q^{85} + 1212 q^{86} + 819 q^{87} + 376 q^{88} + 131 q^{89} - 180 q^{90} - 518 q^{91} - 460 q^{92} + 1980 q^{93} + 1028 q^{94} + 625 q^{95} + 480 q^{96} - 51 q^{97} + 490 q^{98} + 423 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 0.707107
\(3\) 3.00000 0.577350
\(4\) 4.00000 0.500000
\(5\) −17.0684 −1.52665 −0.763324 0.646016i \(-0.776434\pi\)
−0.763324 + 0.646016i \(0.776434\pi\)
\(6\) 6.00000 0.408248
\(7\) −7.00000 −0.377964
\(8\) 8.00000 0.353553
\(9\) 9.00000 0.333333
\(10\) −34.1369 −1.07950
\(11\) −63.2891 −1.73476 −0.867381 0.497644i \(-0.834198\pi\)
−0.867381 + 0.497644i \(0.834198\pi\)
\(12\) 12.0000 0.288675
\(13\) 22.2563 0.474829 0.237415 0.971408i \(-0.423700\pi\)
0.237415 + 0.971408i \(0.423700\pi\)
\(14\) −14.0000 −0.267261
\(15\) −51.2053 −0.881411
\(16\) 16.0000 0.250000
\(17\) 53.5635 0.764181 0.382090 0.924125i \(-0.375204\pi\)
0.382090 + 0.924125i \(0.375204\pi\)
\(18\) 18.0000 0.235702
\(19\) 40.5028 0.489051 0.244526 0.969643i \(-0.421368\pi\)
0.244526 + 0.969643i \(0.421368\pi\)
\(20\) −68.2738 −0.763324
\(21\) −21.0000 −0.218218
\(22\) −126.578 −1.22666
\(23\) −23.0000 −0.208514
\(24\) 24.0000 0.204124
\(25\) 166.332 1.33065
\(26\) 44.5126 0.335755
\(27\) 27.0000 0.192450
\(28\) −28.0000 −0.188982
\(29\) 151.616 0.970841 0.485420 0.874281i \(-0.338667\pi\)
0.485420 + 0.874281i \(0.338667\pi\)
\(30\) −102.411 −0.623251
\(31\) 181.258 1.05016 0.525078 0.851054i \(-0.324036\pi\)
0.525078 + 0.851054i \(0.324036\pi\)
\(32\) 32.0000 0.176777
\(33\) −189.867 −1.00157
\(34\) 107.127 0.540357
\(35\) 119.479 0.577019
\(36\) 36.0000 0.166667
\(37\) 346.839 1.54108 0.770541 0.637390i \(-0.219986\pi\)
0.770541 + 0.637390i \(0.219986\pi\)
\(38\) 81.0056 0.345812
\(39\) 66.7688 0.274143
\(40\) −136.548 −0.539752
\(41\) −83.1893 −0.316878 −0.158439 0.987369i \(-0.550646\pi\)
−0.158439 + 0.987369i \(0.550646\pi\)
\(42\) −42.0000 −0.154303
\(43\) 61.9979 0.219874 0.109937 0.993939i \(-0.464935\pi\)
0.109937 + 0.993939i \(0.464935\pi\)
\(44\) −253.156 −0.867381
\(45\) −153.616 −0.508883
\(46\) −46.0000 −0.147442
\(47\) 401.068 1.24472 0.622360 0.782731i \(-0.286174\pi\)
0.622360 + 0.782731i \(0.286174\pi\)
\(48\) 48.0000 0.144338
\(49\) 49.0000 0.142857
\(50\) 332.663 0.940914
\(51\) 160.691 0.441200
\(52\) 89.0251 0.237415
\(53\) −354.475 −0.918696 −0.459348 0.888256i \(-0.651917\pi\)
−0.459348 + 0.888256i \(0.651917\pi\)
\(54\) 54.0000 0.136083
\(55\) 1080.25 2.64837
\(56\) −56.0000 −0.133631
\(57\) 121.508 0.282354
\(58\) 303.232 0.686488
\(59\) 159.553 0.352068 0.176034 0.984384i \(-0.443673\pi\)
0.176034 + 0.984384i \(0.443673\pi\)
\(60\) −204.821 −0.440705
\(61\) −438.025 −0.919398 −0.459699 0.888075i \(-0.652043\pi\)
−0.459699 + 0.888075i \(0.652043\pi\)
\(62\) 362.515 0.742573
\(63\) −63.0000 −0.125988
\(64\) 64.0000 0.125000
\(65\) −379.880 −0.724897
\(66\) −379.735 −0.708214
\(67\) 41.8010 0.0762210 0.0381105 0.999274i \(-0.487866\pi\)
0.0381105 + 0.999274i \(0.487866\pi\)
\(68\) 214.254 0.382090
\(69\) −69.0000 −0.120386
\(70\) 238.958 0.408014
\(71\) 479.166 0.800938 0.400469 0.916310i \(-0.368847\pi\)
0.400469 + 0.916310i \(0.368847\pi\)
\(72\) 72.0000 0.117851
\(73\) 584.054 0.936416 0.468208 0.883618i \(-0.344900\pi\)
0.468208 + 0.883618i \(0.344900\pi\)
\(74\) 693.679 1.08971
\(75\) 498.995 0.768253
\(76\) 162.011 0.244526
\(77\) 443.024 0.655679
\(78\) 133.538 0.193848
\(79\) 555.934 0.791740 0.395870 0.918307i \(-0.370443\pi\)
0.395870 + 0.918307i \(0.370443\pi\)
\(80\) −273.095 −0.381662
\(81\) 81.0000 0.111111
\(82\) −166.379 −0.224066
\(83\) −815.363 −1.07829 −0.539143 0.842215i \(-0.681252\pi\)
−0.539143 + 0.842215i \(0.681252\pi\)
\(84\) −84.0000 −0.109109
\(85\) −914.246 −1.16663
\(86\) 123.996 0.155475
\(87\) 454.848 0.560515
\(88\) −506.313 −0.613331
\(89\) −422.496 −0.503196 −0.251598 0.967832i \(-0.580956\pi\)
−0.251598 + 0.967832i \(0.580956\pi\)
\(90\) −307.232 −0.359834
\(91\) −155.794 −0.179469
\(92\) −92.0000 −0.104257
\(93\) 543.773 0.606308
\(94\) 802.137 0.880150
\(95\) −691.320 −0.746609
\(96\) 96.0000 0.102062
\(97\) −124.121 −0.129924 −0.0649620 0.997888i \(-0.520693\pi\)
−0.0649620 + 0.997888i \(0.520693\pi\)
\(98\) 98.0000 0.101015
\(99\) −569.602 −0.578254
\(100\) 665.327 0.665327
\(101\) −544.113 −0.536052 −0.268026 0.963412i \(-0.586371\pi\)
−0.268026 + 0.963412i \(0.586371\pi\)
\(102\) 321.381 0.311975
\(103\) 924.598 0.884498 0.442249 0.896892i \(-0.354181\pi\)
0.442249 + 0.896892i \(0.354181\pi\)
\(104\) 178.050 0.167878
\(105\) 358.437 0.333142
\(106\) −708.950 −0.649616
\(107\) 1931.47 1.74506 0.872532 0.488557i \(-0.162477\pi\)
0.872532 + 0.488557i \(0.162477\pi\)
\(108\) 108.000 0.0962250
\(109\) 604.510 0.531207 0.265603 0.964082i \(-0.414429\pi\)
0.265603 + 0.964082i \(0.414429\pi\)
\(110\) 2160.49 1.87268
\(111\) 1040.52 0.889744
\(112\) −112.000 −0.0944911
\(113\) −770.432 −0.641382 −0.320691 0.947184i \(-0.603915\pi\)
−0.320691 + 0.947184i \(0.603915\pi\)
\(114\) 243.017 0.199654
\(115\) 392.574 0.318328
\(116\) 606.464 0.485420
\(117\) 200.306 0.158276
\(118\) 319.106 0.248950
\(119\) −374.945 −0.288833
\(120\) −409.643 −0.311626
\(121\) 2674.51 2.00940
\(122\) −876.049 −0.650113
\(123\) −249.568 −0.182949
\(124\) 725.031 0.525078
\(125\) −705.468 −0.504792
\(126\) −126.000 −0.0890871
\(127\) −205.742 −0.143753 −0.0718764 0.997414i \(-0.522899\pi\)
−0.0718764 + 0.997414i \(0.522899\pi\)
\(128\) 128.000 0.0883883
\(129\) 185.994 0.126944
\(130\) −759.760 −0.512580
\(131\) −338.187 −0.225554 −0.112777 0.993620i \(-0.535975\pi\)
−0.112777 + 0.993620i \(0.535975\pi\)
\(132\) −759.469 −0.500783
\(133\) −283.520 −0.184844
\(134\) 83.6021 0.0538964
\(135\) −460.848 −0.293804
\(136\) 428.508 0.270179
\(137\) 303.650 0.189362 0.0946810 0.995508i \(-0.469817\pi\)
0.0946810 + 0.995508i \(0.469817\pi\)
\(138\) −138.000 −0.0851257
\(139\) −1159.68 −0.707644 −0.353822 0.935313i \(-0.615118\pi\)
−0.353822 + 0.935313i \(0.615118\pi\)
\(140\) 477.916 0.288509
\(141\) 1203.21 0.718639
\(142\) 958.333 0.566348
\(143\) −1408.58 −0.823716
\(144\) 144.000 0.0833333
\(145\) −2587.85 −1.48213
\(146\) 1168.11 0.662146
\(147\) 147.000 0.0824786
\(148\) 1387.36 0.770541
\(149\) 1537.19 0.845178 0.422589 0.906322i \(-0.361121\pi\)
0.422589 + 0.906322i \(0.361121\pi\)
\(150\) 997.990 0.543237
\(151\) −392.585 −0.211577 −0.105789 0.994389i \(-0.533737\pi\)
−0.105789 + 0.994389i \(0.533737\pi\)
\(152\) 324.022 0.172906
\(153\) 482.072 0.254727
\(154\) 886.048 0.463635
\(155\) −3093.79 −1.60322
\(156\) 267.075 0.137071
\(157\) 1364.03 0.693387 0.346694 0.937978i \(-0.387304\pi\)
0.346694 + 0.937978i \(0.387304\pi\)
\(158\) 1111.87 0.559845
\(159\) −1063.42 −0.530409
\(160\) −546.190 −0.269876
\(161\) 161.000 0.0788110
\(162\) 162.000 0.0785674
\(163\) 1131.18 0.543566 0.271783 0.962359i \(-0.412387\pi\)
0.271783 + 0.962359i \(0.412387\pi\)
\(164\) −332.757 −0.158439
\(165\) 3240.74 1.52904
\(166\) −1630.73 −0.762463
\(167\) −1753.41 −0.812473 −0.406236 0.913768i \(-0.633159\pi\)
−0.406236 + 0.913768i \(0.633159\pi\)
\(168\) −168.000 −0.0771517
\(169\) −1701.66 −0.774537
\(170\) −1828.49 −0.824935
\(171\) 364.525 0.163017
\(172\) 247.992 0.109937
\(173\) −3851.07 −1.69244 −0.846218 0.532837i \(-0.821126\pi\)
−0.846218 + 0.532837i \(0.821126\pi\)
\(174\) 909.696 0.396344
\(175\) −1164.32 −0.502940
\(176\) −1012.63 −0.433691
\(177\) 478.659 0.203267
\(178\) −844.992 −0.355814
\(179\) 2028.12 0.846865 0.423433 0.905928i \(-0.360825\pi\)
0.423433 + 0.905928i \(0.360825\pi\)
\(180\) −614.464 −0.254441
\(181\) −3136.57 −1.28806 −0.644031 0.764999i \(-0.722739\pi\)
−0.644031 + 0.764999i \(0.722739\pi\)
\(182\) −311.588 −0.126903
\(183\) −1314.07 −0.530815
\(184\) −184.000 −0.0737210
\(185\) −5920.01 −2.35269
\(186\) 1087.55 0.428725
\(187\) −3389.99 −1.32567
\(188\) 1604.27 0.622360
\(189\) −189.000 −0.0727393
\(190\) −1382.64 −0.527933
\(191\) −995.461 −0.377115 −0.188558 0.982062i \(-0.560381\pi\)
−0.188558 + 0.982062i \(0.560381\pi\)
\(192\) 192.000 0.0721688
\(193\) 3334.74 1.24373 0.621864 0.783125i \(-0.286376\pi\)
0.621864 + 0.783125i \(0.286376\pi\)
\(194\) −248.243 −0.0918701
\(195\) −1139.64 −0.418520
\(196\) 196.000 0.0714286
\(197\) 801.347 0.289815 0.144908 0.989445i \(-0.453712\pi\)
0.144908 + 0.989445i \(0.453712\pi\)
\(198\) −1139.20 −0.408887
\(199\) 2231.55 0.794926 0.397463 0.917618i \(-0.369891\pi\)
0.397463 + 0.917618i \(0.369891\pi\)
\(200\) 1330.65 0.470457
\(201\) 125.403 0.0440062
\(202\) −1088.23 −0.379046
\(203\) −1061.31 −0.366943
\(204\) 642.763 0.220600
\(205\) 1419.91 0.483761
\(206\) 1849.20 0.625435
\(207\) −207.000 −0.0695048
\(208\) 356.100 0.118707
\(209\) −2563.39 −0.848388
\(210\) 716.875 0.235567
\(211\) 4649.81 1.51709 0.758546 0.651620i \(-0.225910\pi\)
0.758546 + 0.651620i \(0.225910\pi\)
\(212\) −1417.90 −0.459348
\(213\) 1437.50 0.462422
\(214\) 3862.93 1.23395
\(215\) −1058.21 −0.335671
\(216\) 216.000 0.0680414
\(217\) −1268.80 −0.396922
\(218\) 1209.02 0.375620
\(219\) 1752.16 0.540640
\(220\) 4320.99 1.32419
\(221\) 1192.13 0.362855
\(222\) 2081.04 0.629144
\(223\) −3620.90 −1.08732 −0.543662 0.839304i \(-0.682963\pi\)
−0.543662 + 0.839304i \(0.682963\pi\)
\(224\) −224.000 −0.0668153
\(225\) 1496.99 0.443551
\(226\) −1540.86 −0.453525
\(227\) 2189.52 0.640192 0.320096 0.947385i \(-0.396285\pi\)
0.320096 + 0.947385i \(0.396285\pi\)
\(228\) 486.033 0.141177
\(229\) −5748.77 −1.65891 −0.829453 0.558577i \(-0.811348\pi\)
−0.829453 + 0.558577i \(0.811348\pi\)
\(230\) 785.148 0.225092
\(231\) 1329.07 0.378556
\(232\) 1212.93 0.343244
\(233\) 5231.77 1.47101 0.735504 0.677521i \(-0.236946\pi\)
0.735504 + 0.677521i \(0.236946\pi\)
\(234\) 400.613 0.111918
\(235\) −6845.61 −1.90025
\(236\) 638.212 0.176034
\(237\) 1667.80 0.457111
\(238\) −749.890 −0.204236
\(239\) −3242.68 −0.877620 −0.438810 0.898580i \(-0.644600\pi\)
−0.438810 + 0.898580i \(0.644600\pi\)
\(240\) −819.285 −0.220353
\(241\) 6571.09 1.75635 0.878177 0.478336i \(-0.158760\pi\)
0.878177 + 0.478336i \(0.158760\pi\)
\(242\) 5349.02 1.42086
\(243\) 243.000 0.0641500
\(244\) −1752.10 −0.459699
\(245\) −836.354 −0.218093
\(246\) −499.136 −0.129365
\(247\) 901.441 0.232216
\(248\) 1450.06 0.371286
\(249\) −2446.09 −0.622548
\(250\) −1410.94 −0.356942
\(251\) 5874.34 1.47723 0.738616 0.674127i \(-0.235480\pi\)
0.738616 + 0.674127i \(0.235480\pi\)
\(252\) −252.000 −0.0629941
\(253\) 1455.65 0.361723
\(254\) −411.483 −0.101649
\(255\) −2742.74 −0.673557
\(256\) 256.000 0.0625000
\(257\) 2618.66 0.635593 0.317797 0.948159i \(-0.397057\pi\)
0.317797 + 0.948159i \(0.397057\pi\)
\(258\) 371.988 0.0897633
\(259\) −2427.88 −0.582474
\(260\) −1519.52 −0.362449
\(261\) 1364.54 0.323614
\(262\) −676.375 −0.159491
\(263\) 3280.34 0.769105 0.384553 0.923103i \(-0.374356\pi\)
0.384553 + 0.923103i \(0.374356\pi\)
\(264\) −1518.94 −0.354107
\(265\) 6050.33 1.40252
\(266\) −567.039 −0.130704
\(267\) −1267.49 −0.290521
\(268\) 167.204 0.0381105
\(269\) 2482.84 0.562755 0.281378 0.959597i \(-0.409209\pi\)
0.281378 + 0.959597i \(0.409209\pi\)
\(270\) −921.696 −0.207750
\(271\) −4847.56 −1.08660 −0.543299 0.839539i \(-0.682825\pi\)
−0.543299 + 0.839539i \(0.682825\pi\)
\(272\) 857.017 0.191045
\(273\) −467.382 −0.103616
\(274\) 607.301 0.133899
\(275\) −10527.0 −2.30837
\(276\) −276.000 −0.0601929
\(277\) 3012.01 0.653336 0.326668 0.945139i \(-0.394074\pi\)
0.326668 + 0.945139i \(0.394074\pi\)
\(278\) −2319.36 −0.500380
\(279\) 1631.32 0.350052
\(280\) 955.833 0.204007
\(281\) 5944.23 1.26193 0.630966 0.775810i \(-0.282659\pi\)
0.630966 + 0.775810i \(0.282659\pi\)
\(282\) 2406.41 0.508155
\(283\) −50.5291 −0.0106136 −0.00530679 0.999986i \(-0.501689\pi\)
−0.00530679 + 0.999986i \(0.501689\pi\)
\(284\) 1916.67 0.400469
\(285\) −2073.96 −0.431055
\(286\) −2817.16 −0.582455
\(287\) 582.325 0.119768
\(288\) 288.000 0.0589256
\(289\) −2043.95 −0.416028
\(290\) −5175.70 −1.04803
\(291\) −372.364 −0.0750116
\(292\) 2336.22 0.468208
\(293\) −8282.29 −1.65139 −0.825694 0.564118i \(-0.809216\pi\)
−0.825694 + 0.564118i \(0.809216\pi\)
\(294\) 294.000 0.0583212
\(295\) −2723.32 −0.537484
\(296\) 2774.72 0.544855
\(297\) −1708.81 −0.333855
\(298\) 3074.38 0.597631
\(299\) −511.894 −0.0990087
\(300\) 1995.98 0.384127
\(301\) −433.985 −0.0831047
\(302\) −785.171 −0.149608
\(303\) −1632.34 −0.309490
\(304\) 648.045 0.122263
\(305\) 7476.40 1.40360
\(306\) 964.144 0.180119
\(307\) 6900.46 1.28283 0.641417 0.767193i \(-0.278347\pi\)
0.641417 + 0.767193i \(0.278347\pi\)
\(308\) 1772.10 0.327839
\(309\) 2773.79 0.510665
\(310\) −6187.57 −1.13365
\(311\) 4412.27 0.804492 0.402246 0.915532i \(-0.368230\pi\)
0.402246 + 0.915532i \(0.368230\pi\)
\(312\) 534.151 0.0969241
\(313\) 246.414 0.0444989 0.0222495 0.999752i \(-0.492917\pi\)
0.0222495 + 0.999752i \(0.492917\pi\)
\(314\) 2728.07 0.490299
\(315\) 1075.31 0.192340
\(316\) 2223.74 0.395870
\(317\) 7944.22 1.40754 0.703772 0.710426i \(-0.251498\pi\)
0.703772 + 0.710426i \(0.251498\pi\)
\(318\) −2126.85 −0.375056
\(319\) −9595.64 −1.68418
\(320\) −1092.38 −0.190831
\(321\) 5794.40 1.00751
\(322\) 322.000 0.0557278
\(323\) 2169.47 0.373724
\(324\) 324.000 0.0555556
\(325\) 3701.93 0.631833
\(326\) 2262.37 0.384359
\(327\) 1813.53 0.306693
\(328\) −665.514 −0.112033
\(329\) −2807.48 −0.470460
\(330\) 6481.48 1.08119
\(331\) −2485.12 −0.412673 −0.206336 0.978481i \(-0.566154\pi\)
−0.206336 + 0.978481i \(0.566154\pi\)
\(332\) −3261.45 −0.539143
\(333\) 3121.55 0.513694
\(334\) −3506.82 −0.574505
\(335\) −713.479 −0.116363
\(336\) −336.000 −0.0545545
\(337\) 4701.99 0.760041 0.380021 0.924978i \(-0.375917\pi\)
0.380021 + 0.924978i \(0.375917\pi\)
\(338\) −3403.32 −0.547680
\(339\) −2311.30 −0.370302
\(340\) −3656.99 −0.583317
\(341\) −11471.6 −1.82177
\(342\) 729.050 0.115271
\(343\) −343.000 −0.0539949
\(344\) 495.983 0.0777373
\(345\) 1177.72 0.183787
\(346\) −7702.14 −1.19673
\(347\) −1405.56 −0.217448 −0.108724 0.994072i \(-0.534677\pi\)
−0.108724 + 0.994072i \(0.534677\pi\)
\(348\) 1819.39 0.280258
\(349\) 252.056 0.0386598 0.0193299 0.999813i \(-0.493847\pi\)
0.0193299 + 0.999813i \(0.493847\pi\)
\(350\) −2328.64 −0.355632
\(351\) 600.919 0.0913809
\(352\) −2025.25 −0.306666
\(353\) −1075.60 −0.162177 −0.0810886 0.996707i \(-0.525840\pi\)
−0.0810886 + 0.996707i \(0.525840\pi\)
\(354\) 957.318 0.143731
\(355\) −8178.62 −1.22275
\(356\) −1689.98 −0.251598
\(357\) −1124.83 −0.166758
\(358\) 4056.24 0.598824
\(359\) −7098.48 −1.04357 −0.521787 0.853076i \(-0.674735\pi\)
−0.521787 + 0.853076i \(0.674735\pi\)
\(360\) −1228.93 −0.179917
\(361\) −5218.52 −0.760829
\(362\) −6273.13 −0.910797
\(363\) 8023.54 1.16013
\(364\) −623.176 −0.0897343
\(365\) −9968.89 −1.42958
\(366\) −2628.15 −0.375343
\(367\) 4081.79 0.580566 0.290283 0.956941i \(-0.406251\pi\)
0.290283 + 0.956941i \(0.406251\pi\)
\(368\) −368.000 −0.0521286
\(369\) −748.703 −0.105626
\(370\) −11840.0 −1.66360
\(371\) 2481.32 0.347234
\(372\) 2175.09 0.303154
\(373\) −2285.49 −0.317260 −0.158630 0.987338i \(-0.550708\pi\)
−0.158630 + 0.987338i \(0.550708\pi\)
\(374\) −6779.98 −0.937391
\(375\) −2116.41 −0.291442
\(376\) 3208.55 0.440075
\(377\) 3374.41 0.460984
\(378\) −378.000 −0.0514344
\(379\) −9978.10 −1.35235 −0.676175 0.736741i \(-0.736364\pi\)
−0.676175 + 0.736741i \(0.736364\pi\)
\(380\) −2765.28 −0.373305
\(381\) −617.225 −0.0829958
\(382\) −1990.92 −0.266661
\(383\) 2054.78 0.274136 0.137068 0.990562i \(-0.456232\pi\)
0.137068 + 0.990562i \(0.456232\pi\)
\(384\) 384.000 0.0510310
\(385\) −7561.73 −1.00099
\(386\) 6669.47 0.879449
\(387\) 557.981 0.0732914
\(388\) −496.486 −0.0649620
\(389\) 7183.55 0.936300 0.468150 0.883649i \(-0.344921\pi\)
0.468150 + 0.883649i \(0.344921\pi\)
\(390\) −2279.28 −0.295938
\(391\) −1231.96 −0.159343
\(392\) 392.000 0.0505076
\(393\) −1014.56 −0.130224
\(394\) 1602.69 0.204930
\(395\) −9488.92 −1.20871
\(396\) −2278.41 −0.289127
\(397\) −9361.01 −1.18341 −0.591707 0.806153i \(-0.701546\pi\)
−0.591707 + 0.806153i \(0.701546\pi\)
\(398\) 4463.10 0.562097
\(399\) −850.559 −0.106720
\(400\) 2661.31 0.332663
\(401\) 908.583 0.113148 0.0565741 0.998398i \(-0.481982\pi\)
0.0565741 + 0.998398i \(0.481982\pi\)
\(402\) 250.806 0.0311171
\(403\) 4034.12 0.498645
\(404\) −2176.45 −0.268026
\(405\) −1382.54 −0.169628
\(406\) −2122.62 −0.259468
\(407\) −21951.2 −2.67341
\(408\) 1285.53 0.155988
\(409\) 6063.62 0.733073 0.366536 0.930404i \(-0.380544\pi\)
0.366536 + 0.930404i \(0.380544\pi\)
\(410\) 2839.82 0.342070
\(411\) 910.951 0.109328
\(412\) 3698.39 0.442249
\(413\) −1116.87 −0.133069
\(414\) −414.000 −0.0491473
\(415\) 13917.0 1.64616
\(416\) 712.201 0.0839388
\(417\) −3479.03 −0.408559
\(418\) −5126.77 −0.599901
\(419\) −11669.9 −1.36064 −0.680322 0.732913i \(-0.738160\pi\)
−0.680322 + 0.732913i \(0.738160\pi\)
\(420\) 1433.75 0.166571
\(421\) −14906.4 −1.72564 −0.862821 0.505509i \(-0.831305\pi\)
−0.862821 + 0.505509i \(0.831305\pi\)
\(422\) 9299.63 1.07275
\(423\) 3609.62 0.414907
\(424\) −2835.80 −0.324808
\(425\) 8909.32 1.01686
\(426\) 2875.00 0.326981
\(427\) 3066.17 0.347500
\(428\) 7725.86 0.872532
\(429\) −4225.74 −0.475573
\(430\) −2116.42 −0.237355
\(431\) −9659.56 −1.07955 −0.539773 0.841811i \(-0.681490\pi\)
−0.539773 + 0.841811i \(0.681490\pi\)
\(432\) 432.000 0.0481125
\(433\) 1441.23 0.159956 0.0799782 0.996797i \(-0.474515\pi\)
0.0799782 + 0.996797i \(0.474515\pi\)
\(434\) −2537.61 −0.280666
\(435\) −7763.55 −0.855709
\(436\) 2418.04 0.265603
\(437\) −931.564 −0.101974
\(438\) 3504.32 0.382290
\(439\) 14116.1 1.53468 0.767339 0.641242i \(-0.221581\pi\)
0.767339 + 0.641242i \(0.221581\pi\)
\(440\) 8641.97 0.936341
\(441\) 441.000 0.0476190
\(442\) 2384.25 0.256577
\(443\) −2529.67 −0.271306 −0.135653 0.990756i \(-0.543313\pi\)
−0.135653 + 0.990756i \(0.543313\pi\)
\(444\) 4162.07 0.444872
\(445\) 7211.35 0.768204
\(446\) −7241.79 −0.768854
\(447\) 4611.57 0.487964
\(448\) −448.000 −0.0472456
\(449\) −13297.6 −1.39767 −0.698833 0.715285i \(-0.746297\pi\)
−0.698833 + 0.715285i \(0.746297\pi\)
\(450\) 2993.97 0.313638
\(451\) 5264.98 0.549707
\(452\) −3081.73 −0.320691
\(453\) −1177.76 −0.122154
\(454\) 4379.04 0.452684
\(455\) 2659.16 0.273985
\(456\) 972.067 0.0998272
\(457\) 12384.0 1.26762 0.633808 0.773490i \(-0.281491\pi\)
0.633808 + 0.773490i \(0.281491\pi\)
\(458\) −11497.5 −1.17302
\(459\) 1446.22 0.147067
\(460\) 1570.30 0.159164
\(461\) −15167.2 −1.53234 −0.766168 0.642641i \(-0.777839\pi\)
−0.766168 + 0.642641i \(0.777839\pi\)
\(462\) 2658.14 0.267680
\(463\) 2425.65 0.243477 0.121738 0.992562i \(-0.461153\pi\)
0.121738 + 0.992562i \(0.461153\pi\)
\(464\) 2425.86 0.242710
\(465\) −9281.36 −0.925619
\(466\) 10463.5 1.04016
\(467\) −2348.70 −0.232730 −0.116365 0.993207i \(-0.537124\pi\)
−0.116365 + 0.993207i \(0.537124\pi\)
\(468\) 801.226 0.0791382
\(469\) −292.607 −0.0288088
\(470\) −13691.2 −1.34368
\(471\) 4092.10 0.400327
\(472\) 1276.42 0.124475
\(473\) −3923.79 −0.381430
\(474\) 3335.60 0.323226
\(475\) 6736.90 0.650758
\(476\) −1499.78 −0.144417
\(477\) −3190.27 −0.306232
\(478\) −6485.35 −0.620571
\(479\) −10710.7 −1.02168 −0.510838 0.859677i \(-0.670665\pi\)
−0.510838 + 0.859677i \(0.670665\pi\)
\(480\) −1638.57 −0.155813
\(481\) 7719.35 0.731751
\(482\) 13142.2 1.24193
\(483\) 483.000 0.0455016
\(484\) 10698.0 1.00470
\(485\) 2118.56 0.198348
\(486\) 486.000 0.0453609
\(487\) 14462.9 1.34574 0.672871 0.739760i \(-0.265061\pi\)
0.672871 + 0.739760i \(0.265061\pi\)
\(488\) −3504.20 −0.325056
\(489\) 3393.55 0.313828
\(490\) −1672.71 −0.154215
\(491\) −5583.57 −0.513204 −0.256602 0.966517i \(-0.582603\pi\)
−0.256602 + 0.966517i \(0.582603\pi\)
\(492\) −998.271 −0.0914747
\(493\) 8121.09 0.741897
\(494\) 1802.88 0.164201
\(495\) 9722.22 0.882790
\(496\) 2900.12 0.262539
\(497\) −3354.16 −0.302726
\(498\) −4892.18 −0.440208
\(499\) 1670.76 0.149887 0.0749434 0.997188i \(-0.476122\pi\)
0.0749434 + 0.997188i \(0.476122\pi\)
\(500\) −2821.87 −0.252396
\(501\) −5260.23 −0.469081
\(502\) 11748.7 1.04456
\(503\) 105.819 0.00938020 0.00469010 0.999989i \(-0.498507\pi\)
0.00469010 + 0.999989i \(0.498507\pi\)
\(504\) −504.000 −0.0445435
\(505\) 9287.16 0.818363
\(506\) 2911.30 0.255777
\(507\) −5104.97 −0.447179
\(508\) −822.966 −0.0718764
\(509\) −4456.71 −0.388095 −0.194048 0.980992i \(-0.562162\pi\)
−0.194048 + 0.980992i \(0.562162\pi\)
\(510\) −5485.48 −0.476277
\(511\) −4088.38 −0.353932
\(512\) 512.000 0.0441942
\(513\) 1093.58 0.0941180
\(514\) 5237.32 0.449432
\(515\) −15781.4 −1.35032
\(516\) 743.975 0.0634722
\(517\) −25383.3 −2.15929
\(518\) −4855.75 −0.411872
\(519\) −11553.2 −0.977129
\(520\) −3039.04 −0.256290
\(521\) 12970.8 1.09071 0.545355 0.838205i \(-0.316395\pi\)
0.545355 + 0.838205i \(0.316395\pi\)
\(522\) 2729.09 0.228829
\(523\) 20645.8 1.72615 0.863076 0.505074i \(-0.168535\pi\)
0.863076 + 0.505074i \(0.168535\pi\)
\(524\) −1352.75 −0.112777
\(525\) −3492.97 −0.290372
\(526\) 6560.69 0.543839
\(527\) 9708.81 0.802509
\(528\) −3037.88 −0.250391
\(529\) 529.000 0.0434783
\(530\) 12100.7 0.991735
\(531\) 1435.98 0.117356
\(532\) −1134.08 −0.0924220
\(533\) −1851.48 −0.150463
\(534\) −2534.98 −0.205429
\(535\) −32967.1 −2.66410
\(536\) 334.408 0.0269482
\(537\) 6084.36 0.488938
\(538\) 4965.67 0.397928
\(539\) −3101.17 −0.247823
\(540\) −1843.39 −0.146902
\(541\) −16727.0 −1.32930 −0.664650 0.747155i \(-0.731419\pi\)
−0.664650 + 0.747155i \(0.731419\pi\)
\(542\) −9695.12 −0.768341
\(543\) −9409.70 −0.743663
\(544\) 1714.03 0.135089
\(545\) −10318.0 −0.810966
\(546\) −934.764 −0.0732677
\(547\) 19711.6 1.54078 0.770392 0.637570i \(-0.220061\pi\)
0.770392 + 0.637570i \(0.220061\pi\)
\(548\) 1214.60 0.0946810
\(549\) −3942.22 −0.306466
\(550\) −21054.0 −1.63226
\(551\) 6140.87 0.474791
\(552\) −552.000 −0.0425628
\(553\) −3891.54 −0.299249
\(554\) 6024.02 0.461978
\(555\) −17760.0 −1.35833
\(556\) −4638.71 −0.353822
\(557\) −21814.7 −1.65946 −0.829728 0.558168i \(-0.811504\pi\)
−0.829728 + 0.558168i \(0.811504\pi\)
\(558\) 3262.64 0.247524
\(559\) 1379.84 0.104403
\(560\) 1911.67 0.144255
\(561\) −10170.0 −0.765377
\(562\) 11888.5 0.892321
\(563\) −20280.8 −1.51818 −0.759090 0.650986i \(-0.774356\pi\)
−0.759090 + 0.650986i \(0.774356\pi\)
\(564\) 4812.82 0.359320
\(565\) 13150.1 0.979164
\(566\) −101.058 −0.00750494
\(567\) −567.000 −0.0419961
\(568\) 3833.33 0.283174
\(569\) −21214.3 −1.56300 −0.781502 0.623902i \(-0.785546\pi\)
−0.781502 + 0.623902i \(0.785546\pi\)
\(570\) −4147.92 −0.304802
\(571\) 23364.1 1.71236 0.856179 0.516680i \(-0.172832\pi\)
0.856179 + 0.516680i \(0.172832\pi\)
\(572\) −5634.32 −0.411858
\(573\) −2986.38 −0.217728
\(574\) 1164.65 0.0846891
\(575\) −3825.63 −0.277461
\(576\) 576.000 0.0416667
\(577\) 2069.97 0.149348 0.0746741 0.997208i \(-0.476208\pi\)
0.0746741 + 0.997208i \(0.476208\pi\)
\(578\) −4087.89 −0.294176
\(579\) 10004.2 0.718067
\(580\) −10351.4 −0.741066
\(581\) 5707.54 0.407553
\(582\) −744.729 −0.0530412
\(583\) 22434.4 1.59372
\(584\) 4672.43 0.331073
\(585\) −3418.92 −0.241632
\(586\) −16564.6 −1.16771
\(587\) −14726.0 −1.03545 −0.517724 0.855547i \(-0.673221\pi\)
−0.517724 + 0.855547i \(0.673221\pi\)
\(588\) 588.000 0.0412393
\(589\) 7341.44 0.513580
\(590\) −5446.64 −0.380059
\(591\) 2404.04 0.167325
\(592\) 5549.43 0.385271
\(593\) 10601.6 0.734157 0.367079 0.930190i \(-0.380358\pi\)
0.367079 + 0.930190i \(0.380358\pi\)
\(594\) −3417.61 −0.236071
\(595\) 6399.72 0.440946
\(596\) 6148.76 0.422589
\(597\) 6694.64 0.458951
\(598\) −1023.79 −0.0700098
\(599\) 18715.5 1.27662 0.638310 0.769779i \(-0.279634\pi\)
0.638310 + 0.769779i \(0.279634\pi\)
\(600\) 3991.96 0.271619
\(601\) −23578.4 −1.60031 −0.800154 0.599795i \(-0.795249\pi\)
−0.800154 + 0.599795i \(0.795249\pi\)
\(602\) −867.971 −0.0587639
\(603\) 376.209 0.0254070
\(604\) −1570.34 −0.105789
\(605\) −45649.8 −3.06765
\(606\) −3264.68 −0.218842
\(607\) 18198.4 1.21688 0.608442 0.793598i \(-0.291795\pi\)
0.608442 + 0.793598i \(0.291795\pi\)
\(608\) 1296.09 0.0864529
\(609\) −3183.94 −0.211855
\(610\) 14952.8 0.992493
\(611\) 8926.29 0.591030
\(612\) 1928.29 0.127363
\(613\) 24455.2 1.61131 0.805657 0.592383i \(-0.201813\pi\)
0.805657 + 0.592383i \(0.201813\pi\)
\(614\) 13800.9 0.907100
\(615\) 4259.73 0.279299
\(616\) 3544.19 0.231817
\(617\) 11449.5 0.747069 0.373534 0.927616i \(-0.378146\pi\)
0.373534 + 0.927616i \(0.378146\pi\)
\(618\) 5547.59 0.361095
\(619\) −8695.71 −0.564637 −0.282318 0.959321i \(-0.591103\pi\)
−0.282318 + 0.959321i \(0.591103\pi\)
\(620\) −12375.1 −0.801610
\(621\) −621.000 −0.0401286
\(622\) 8824.55 0.568862
\(623\) 2957.47 0.190190
\(624\) 1068.30 0.0685357
\(625\) −8750.22 −0.560014
\(626\) 492.829 0.0314655
\(627\) −7690.16 −0.489817
\(628\) 5456.14 0.346694
\(629\) 18578.0 1.17767
\(630\) 2150.62 0.136005
\(631\) 4645.27 0.293067 0.146534 0.989206i \(-0.453188\pi\)
0.146534 + 0.989206i \(0.453188\pi\)
\(632\) 4447.47 0.279922
\(633\) 13949.4 0.875893
\(634\) 15888.4 0.995284
\(635\) 3511.69 0.219460
\(636\) −4253.70 −0.265205
\(637\) 1090.56 0.0678328
\(638\) −19191.3 −1.19089
\(639\) 4312.50 0.266979
\(640\) −2184.76 −0.134938
\(641\) 11438.8 0.704847 0.352424 0.935841i \(-0.385358\pi\)
0.352424 + 0.935841i \(0.385358\pi\)
\(642\) 11588.8 0.712419
\(643\) 17370.6 1.06536 0.532681 0.846316i \(-0.321184\pi\)
0.532681 + 0.846316i \(0.321184\pi\)
\(644\) 644.000 0.0394055
\(645\) −3174.62 −0.193800
\(646\) 4338.95 0.264262
\(647\) −7601.36 −0.461886 −0.230943 0.972967i \(-0.574181\pi\)
−0.230943 + 0.972967i \(0.574181\pi\)
\(648\) 648.000 0.0392837
\(649\) −10098.0 −0.610755
\(650\) 7403.85 0.446774
\(651\) −3806.41 −0.229163
\(652\) 4524.74 0.271783
\(653\) −9187.39 −0.550582 −0.275291 0.961361i \(-0.588774\pi\)
−0.275291 + 0.961361i \(0.588774\pi\)
\(654\) 3627.06 0.216864
\(655\) 5772.33 0.344341
\(656\) −1331.03 −0.0792194
\(657\) 5256.49 0.312139
\(658\) −5614.96 −0.332665
\(659\) 28617.3 1.69161 0.845804 0.533493i \(-0.179121\pi\)
0.845804 + 0.533493i \(0.179121\pi\)
\(660\) 12963.0 0.764519
\(661\) 6987.83 0.411188 0.205594 0.978637i \(-0.434087\pi\)
0.205594 + 0.978637i \(0.434087\pi\)
\(662\) −4970.24 −0.291804
\(663\) 3576.38 0.209495
\(664\) −6522.90 −0.381231
\(665\) 4839.24 0.282192
\(666\) 6243.11 0.363237
\(667\) −3487.17 −0.202434
\(668\) −7013.64 −0.406236
\(669\) −10862.7 −0.627767
\(670\) −1426.96 −0.0822808
\(671\) 27722.2 1.59494
\(672\) −672.000 −0.0385758
\(673\) −16988.1 −0.973020 −0.486510 0.873675i \(-0.661730\pi\)
−0.486510 + 0.873675i \(0.661730\pi\)
\(674\) 9403.99 0.537430
\(675\) 4490.96 0.256084
\(676\) −6806.63 −0.387269
\(677\) −17446.1 −0.990412 −0.495206 0.868776i \(-0.664907\pi\)
−0.495206 + 0.868776i \(0.664907\pi\)
\(678\) −4622.59 −0.261843
\(679\) 868.850 0.0491066
\(680\) −7313.97 −0.412468
\(681\) 6568.56 0.369615
\(682\) −22943.3 −1.28819
\(683\) −15659.5 −0.877296 −0.438648 0.898659i \(-0.644543\pi\)
−0.438648 + 0.898659i \(0.644543\pi\)
\(684\) 1458.10 0.0815086
\(685\) −5182.84 −0.289089
\(686\) −686.000 −0.0381802
\(687\) −17246.3 −0.957770
\(688\) 991.967 0.0549686
\(689\) −7889.29 −0.436224
\(690\) 2355.45 0.129957
\(691\) 9537.41 0.525066 0.262533 0.964923i \(-0.415442\pi\)
0.262533 + 0.964923i \(0.415442\pi\)
\(692\) −15404.3 −0.846218
\(693\) 3987.21 0.218560
\(694\) −2811.12 −0.153759
\(695\) 19793.9 1.08032
\(696\) 3638.78 0.198172
\(697\) −4455.91 −0.242152
\(698\) 504.112 0.0273366
\(699\) 15695.3 0.849287
\(700\) −4657.29 −0.251470
\(701\) 10884.0 0.586424 0.293212 0.956048i \(-0.405276\pi\)
0.293212 + 0.956048i \(0.405276\pi\)
\(702\) 1201.84 0.0646161
\(703\) 14048.0 0.753669
\(704\) −4050.50 −0.216845
\(705\) −20536.8 −1.09711
\(706\) −2151.20 −0.114677
\(707\) 3808.79 0.202609
\(708\) 1914.64 0.101633
\(709\) 31200.7 1.65270 0.826352 0.563154i \(-0.190412\pi\)
0.826352 + 0.563154i \(0.190412\pi\)
\(710\) −16357.2 −0.864615
\(711\) 5003.40 0.263913
\(712\) −3379.97 −0.177907
\(713\) −4168.93 −0.218973
\(714\) −2249.67 −0.117916
\(715\) 24042.3 1.25752
\(716\) 8112.48 0.423433
\(717\) −9728.03 −0.506694
\(718\) −14197.0 −0.737919
\(719\) 13774.6 0.714473 0.357236 0.934014i \(-0.383719\pi\)
0.357236 + 0.934014i \(0.383719\pi\)
\(720\) −2457.86 −0.127221
\(721\) −6472.18 −0.334309
\(722\) −10437.0 −0.537987
\(723\) 19713.3 1.01403
\(724\) −12546.3 −0.644031
\(725\) 25218.5 1.29185
\(726\) 16047.1 0.820334
\(727\) −14858.9 −0.758027 −0.379014 0.925391i \(-0.623737\pi\)
−0.379014 + 0.925391i \(0.623737\pi\)
\(728\) −1246.35 −0.0634517
\(729\) 729.000 0.0370370
\(730\) −19937.8 −1.01086
\(731\) 3320.83 0.168024
\(732\) −5256.29 −0.265407
\(733\) −35179.1 −1.77267 −0.886336 0.463043i \(-0.846757\pi\)
−0.886336 + 0.463043i \(0.846757\pi\)
\(734\) 8163.57 0.410522
\(735\) −2509.06 −0.125916
\(736\) −736.000 −0.0368605
\(737\) −2645.55 −0.132225
\(738\) −1497.41 −0.0746888
\(739\) 5814.21 0.289417 0.144708 0.989474i \(-0.453776\pi\)
0.144708 + 0.989474i \(0.453776\pi\)
\(740\) −23680.0 −1.17635
\(741\) 2704.32 0.134070
\(742\) 4962.65 0.245532
\(743\) −32551.6 −1.60727 −0.803637 0.595120i \(-0.797104\pi\)
−0.803637 + 0.595120i \(0.797104\pi\)
\(744\) 4350.19 0.214362
\(745\) −26237.4 −1.29029
\(746\) −4570.97 −0.224337
\(747\) −7338.26 −0.359428
\(748\) −13560.0 −0.662836
\(749\) −13520.3 −0.659572
\(750\) −4232.81 −0.206081
\(751\) 24224.1 1.17703 0.588515 0.808486i \(-0.299713\pi\)
0.588515 + 0.808486i \(0.299713\pi\)
\(752\) 6417.10 0.311180
\(753\) 17623.0 0.852880
\(754\) 6748.81 0.325965
\(755\) 6700.82 0.323004
\(756\) −756.000 −0.0363696
\(757\) −22180.9 −1.06497 −0.532483 0.846441i \(-0.678741\pi\)
−0.532483 + 0.846441i \(0.678741\pi\)
\(758\) −19956.2 −0.956256
\(759\) 4366.95 0.208841
\(760\) −5530.56 −0.263966
\(761\) 34512.3 1.64398 0.821990 0.569502i \(-0.192864\pi\)
0.821990 + 0.569502i \(0.192864\pi\)
\(762\) −1234.45 −0.0586869
\(763\) −4231.57 −0.200777
\(764\) −3981.84 −0.188558
\(765\) −8228.22 −0.388878
\(766\) 4109.55 0.193844
\(767\) 3551.06 0.167172
\(768\) 768.000 0.0360844
\(769\) −30867.8 −1.44749 −0.723746 0.690067i \(-0.757581\pi\)
−0.723746 + 0.690067i \(0.757581\pi\)
\(770\) −15123.5 −0.707807
\(771\) 7855.98 0.366960
\(772\) 13338.9 0.621864
\(773\) 25543.7 1.18854 0.594271 0.804265i \(-0.297441\pi\)
0.594271 + 0.804265i \(0.297441\pi\)
\(774\) 1115.96 0.0518249
\(775\) 30148.9 1.39739
\(776\) −992.971 −0.0459350
\(777\) −7283.63 −0.336292
\(778\) 14367.1 0.662064
\(779\) −3369.40 −0.154969
\(780\) −4558.56 −0.209260
\(781\) −30326.0 −1.38944
\(782\) −2463.92 −0.112672
\(783\) 4093.63 0.186838
\(784\) 784.000 0.0357143
\(785\) −23281.9 −1.05856
\(786\) −2029.12 −0.0920820
\(787\) −26008.6 −1.17803 −0.589013 0.808123i \(-0.700483\pi\)
−0.589013 + 0.808123i \(0.700483\pi\)
\(788\) 3205.39 0.144908
\(789\) 9841.03 0.444043
\(790\) −18977.8 −0.854685
\(791\) 5393.02 0.242419
\(792\) −4556.82 −0.204444
\(793\) −9748.80 −0.436557
\(794\) −18722.0 −0.836801
\(795\) 18151.0 0.809748
\(796\) 8926.19 0.397463
\(797\) 40066.1 1.78070 0.890348 0.455281i \(-0.150461\pi\)
0.890348 + 0.455281i \(0.150461\pi\)
\(798\) −1701.12 −0.0754623
\(799\) 21482.6 0.951191
\(800\) 5322.62 0.235229
\(801\) −3802.46 −0.167732
\(802\) 1817.17 0.0800079
\(803\) −36964.3 −1.62446
\(804\) 501.612 0.0220031
\(805\) −2748.02 −0.120317
\(806\) 8068.24 0.352595
\(807\) 7448.51 0.324907
\(808\) −4352.90 −0.189523
\(809\) 31655.4 1.37570 0.687851 0.725852i \(-0.258554\pi\)
0.687851 + 0.725852i \(0.258554\pi\)
\(810\) −2765.09 −0.119945
\(811\) −18907.1 −0.818640 −0.409320 0.912391i \(-0.634234\pi\)
−0.409320 + 0.912391i \(0.634234\pi\)
\(812\) −4245.25 −0.183472
\(813\) −14542.7 −0.627348
\(814\) −43902.3 −1.89039
\(815\) −19307.6 −0.829833
\(816\) 2571.05 0.110300
\(817\) 2511.09 0.107530
\(818\) 12127.2 0.518361
\(819\) −1402.15 −0.0598229
\(820\) 5679.65 0.241880
\(821\) −1227.03 −0.0521604 −0.0260802 0.999660i \(-0.508303\pi\)
−0.0260802 + 0.999660i \(0.508303\pi\)
\(822\) 1821.90 0.0773067
\(823\) 13362.2 0.565951 0.282976 0.959127i \(-0.408678\pi\)
0.282976 + 0.959127i \(0.408678\pi\)
\(824\) 7396.78 0.312717
\(825\) −31581.0 −1.33274
\(826\) −2233.74 −0.0940942
\(827\) 30313.1 1.27459 0.637297 0.770618i \(-0.280053\pi\)
0.637297 + 0.770618i \(0.280053\pi\)
\(828\) −828.000 −0.0347524
\(829\) −6416.41 −0.268819 −0.134410 0.990926i \(-0.542914\pi\)
−0.134410 + 0.990926i \(0.542914\pi\)
\(830\) 27833.9 1.16401
\(831\) 9036.03 0.377204
\(832\) 1424.40 0.0593537
\(833\) 2624.61 0.109169
\(834\) −6958.07 −0.288895
\(835\) 29928.0 1.24036
\(836\) −10253.5 −0.424194
\(837\) 4893.96 0.202103
\(838\) −23339.7 −0.962121
\(839\) −21333.8 −0.877858 −0.438929 0.898522i \(-0.644642\pi\)
−0.438929 + 0.898522i \(0.644642\pi\)
\(840\) 2867.50 0.117783
\(841\) −1401.60 −0.0574685
\(842\) −29812.9 −1.22021
\(843\) 17832.7 0.728577
\(844\) 18599.3 0.758546
\(845\) 29044.7 1.18245
\(846\) 7219.23 0.293383
\(847\) −18721.6 −0.759482
\(848\) −5671.60 −0.229674
\(849\) −151.587 −0.00612776
\(850\) 17818.6 0.719028
\(851\) −7977.31 −0.321338
\(852\) 5750.00 0.231211
\(853\) 44204.3 1.77436 0.887178 0.461428i \(-0.152663\pi\)
0.887178 + 0.461428i \(0.152663\pi\)
\(854\) 6132.34 0.245720
\(855\) −6221.88 −0.248870
\(856\) 15451.7 0.616973
\(857\) −24525.9 −0.977585 −0.488792 0.872400i \(-0.662562\pi\)
−0.488792 + 0.872400i \(0.662562\pi\)
\(858\) −8451.48 −0.336281
\(859\) 23934.9 0.950695 0.475348 0.879798i \(-0.342322\pi\)
0.475348 + 0.879798i \(0.342322\pi\)
\(860\) −4232.83 −0.167835
\(861\) 1746.97 0.0691484
\(862\) −19319.1 −0.763354
\(863\) −27472.0 −1.08361 −0.541807 0.840503i \(-0.682260\pi\)
−0.541807 + 0.840503i \(0.682260\pi\)
\(864\) 864.000 0.0340207
\(865\) 65731.8 2.58375
\(866\) 2882.46 0.113106
\(867\) −6131.84 −0.240194
\(868\) −5075.22 −0.198461
\(869\) −35184.6 −1.37348
\(870\) −15527.1 −0.605078
\(871\) 930.335 0.0361920
\(872\) 4836.08 0.187810
\(873\) −1117.09 −0.0433080
\(874\) −1863.13 −0.0721067
\(875\) 4938.28 0.190793
\(876\) 7008.65 0.270320
\(877\) 14503.1 0.558420 0.279210 0.960230i \(-0.409927\pi\)
0.279210 + 0.960230i \(0.409927\pi\)
\(878\) 28232.1 1.08518
\(879\) −24846.9 −0.953429
\(880\) 17283.9 0.662093
\(881\) −10198.5 −0.390008 −0.195004 0.980802i \(-0.562472\pi\)
−0.195004 + 0.980802i \(0.562472\pi\)
\(882\) 882.000 0.0336718
\(883\) 366.578 0.0139709 0.00698546 0.999976i \(-0.497776\pi\)
0.00698546 + 0.999976i \(0.497776\pi\)
\(884\) 4768.50 0.181428
\(885\) −8169.97 −0.310317
\(886\) −5059.35 −0.191842
\(887\) 26509.7 1.00350 0.501752 0.865012i \(-0.332689\pi\)
0.501752 + 0.865012i \(0.332689\pi\)
\(888\) 8324.15 0.314572
\(889\) 1440.19 0.0543335
\(890\) 14422.7 0.543202
\(891\) −5126.42 −0.192751
\(892\) −14483.6 −0.543662
\(893\) 16244.4 0.608732
\(894\) 9223.14 0.345042
\(895\) −34616.9 −1.29286
\(896\) −896.000 −0.0334077
\(897\) −1535.68 −0.0571627
\(898\) −26595.2 −0.988299
\(899\) 27481.6 1.01953
\(900\) 5987.94 0.221776
\(901\) −18986.9 −0.702049
\(902\) 10530.0 0.388702
\(903\) −1301.96 −0.0479805
\(904\) −6163.45 −0.226763
\(905\) 53536.3 1.96642
\(906\) −2355.51 −0.0863760
\(907\) −3179.92 −0.116414 −0.0582071 0.998305i \(-0.518538\pi\)
−0.0582071 + 0.998305i \(0.518538\pi\)
\(908\) 8758.08 0.320096
\(909\) −4897.02 −0.178684
\(910\) 5318.32 0.193737
\(911\) −7517.86 −0.273411 −0.136706 0.990612i \(-0.543651\pi\)
−0.136706 + 0.990612i \(0.543651\pi\)
\(912\) 1944.13 0.0705885
\(913\) 51603.6 1.87057
\(914\) 24768.1 0.896340
\(915\) 22429.2 0.810367
\(916\) −22995.1 −0.829453
\(917\) 2367.31 0.0852514
\(918\) 2892.43 0.103992
\(919\) 20848.6 0.748347 0.374173 0.927359i \(-0.377926\pi\)
0.374173 + 0.927359i \(0.377926\pi\)
\(920\) 3140.59 0.112546
\(921\) 20701.4 0.740644
\(922\) −30334.4 −1.08352
\(923\) 10664.5 0.380309
\(924\) 5316.29 0.189278
\(925\) 57690.4 2.05065
\(926\) 4851.31 0.172164
\(927\) 8321.38 0.294833
\(928\) 4851.71 0.171622
\(929\) −5293.99 −0.186965 −0.0934824 0.995621i \(-0.529800\pi\)
−0.0934824 + 0.995621i \(0.529800\pi\)
\(930\) −18562.7 −0.654511
\(931\) 1984.64 0.0698645
\(932\) 20927.1 0.735504
\(933\) 13236.8 0.464474
\(934\) −4697.40 −0.164565
\(935\) 57861.8 2.02383
\(936\) 1602.45 0.0559592
\(937\) 32372.2 1.12866 0.564329 0.825550i \(-0.309135\pi\)
0.564329 + 0.825550i \(0.309135\pi\)
\(938\) −585.215 −0.0203709
\(939\) 739.243 0.0256915
\(940\) −27382.5 −0.950125
\(941\) 14785.0 0.512196 0.256098 0.966651i \(-0.417563\pi\)
0.256098 + 0.966651i \(0.417563\pi\)
\(942\) 8184.21 0.283074
\(943\) 1913.35 0.0660736
\(944\) 2552.85 0.0880171
\(945\) 3225.94 0.111047
\(946\) −7847.59 −0.269711
\(947\) 29711.4 1.01952 0.509762 0.860315i \(-0.329733\pi\)
0.509762 + 0.860315i \(0.329733\pi\)
\(948\) 6671.21 0.228556
\(949\) 12998.9 0.444638
\(950\) 13473.8 0.460156
\(951\) 23832.6 0.812646
\(952\) −2999.56 −0.102118
\(953\) 10740.6 0.365082 0.182541 0.983198i \(-0.441568\pi\)
0.182541 + 0.983198i \(0.441568\pi\)
\(954\) −6380.55 −0.216539
\(955\) 16991.0 0.575722
\(956\) −12970.7 −0.438810
\(957\) −28786.9 −0.972360
\(958\) −21421.3 −0.722433
\(959\) −2125.55 −0.0715721
\(960\) −3277.14 −0.110176
\(961\) 3063.36 0.102828
\(962\) 15438.7 0.517426
\(963\) 17383.2 0.581688
\(964\) 26284.4 0.878177
\(965\) −56918.8 −1.89874
\(966\) 966.000 0.0321745
\(967\) 24542.7 0.816175 0.408087 0.912943i \(-0.366196\pi\)
0.408087 + 0.912943i \(0.366196\pi\)
\(968\) 21396.1 0.710430
\(969\) 6508.42 0.215769
\(970\) 4237.12 0.140253
\(971\) 45866.8 1.51590 0.757948 0.652315i \(-0.226202\pi\)
0.757948 + 0.652315i \(0.226202\pi\)
\(972\) 972.000 0.0320750
\(973\) 8117.74 0.267464
\(974\) 28925.8 0.951583
\(975\) 11105.8 0.364789
\(976\) −7008.39 −0.229850
\(977\) 11048.0 0.361779 0.180890 0.983503i \(-0.442102\pi\)
0.180890 + 0.983503i \(0.442102\pi\)
\(978\) 6787.11 0.221910
\(979\) 26739.4 0.872926
\(980\) −3345.41 −0.109046
\(981\) 5440.59 0.177069
\(982\) −11167.1 −0.362890
\(983\) 44742.5 1.45174 0.725872 0.687830i \(-0.241437\pi\)
0.725872 + 0.687830i \(0.241437\pi\)
\(984\) −1996.54 −0.0646824
\(985\) −13677.7 −0.442446
\(986\) 16242.2 0.524601
\(987\) −8422.44 −0.271620
\(988\) 3605.77 0.116108
\(989\) −1425.95 −0.0458470
\(990\) 19444.4 0.624227
\(991\) 53711.0 1.72168 0.860841 0.508874i \(-0.169938\pi\)
0.860841 + 0.508874i \(0.169938\pi\)
\(992\) 5800.25 0.185643
\(993\) −7455.37 −0.238257
\(994\) −6708.33 −0.214060
\(995\) −38089.0 −1.21357
\(996\) −9784.35 −0.311274
\(997\) −60393.5 −1.91844 −0.959218 0.282667i \(-0.908781\pi\)
−0.959218 + 0.282667i \(0.908781\pi\)
\(998\) 3341.52 0.105986
\(999\) 9364.66 0.296581
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 966.4.a.q.1.2 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
966.4.a.q.1.2 5 1.1 even 1 trivial