Properties

Label 966.4.a.k.1.3
Level $966$
Weight $4$
Character 966.1
Self dual yes
Analytic conductor $56.996$
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] = [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: \(1\)
Dimension: \(4\)
Coefficient field: 4.4.9814581.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 66x^{2} + 271x - 241 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(3.60967\) 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)
 
\(f(q)\) \(=\) \(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -1.29416 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -1.29416 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -2.58831 q^{10} -49.0162 q^{11} -12.0000 q^{12} +82.4110 q^{13} +14.0000 q^{14} +3.88247 q^{15} +16.0000 q^{16} -90.3504 q^{17} +18.0000 q^{18} -80.5815 q^{19} -5.17663 q^{20} -21.0000 q^{21} -98.0324 q^{22} +23.0000 q^{23} -24.0000 q^{24} -123.325 q^{25} +164.822 q^{26} -27.0000 q^{27} +28.0000 q^{28} -141.887 q^{29} +7.76494 q^{30} +94.3956 q^{31} +32.0000 q^{32} +147.049 q^{33} -180.701 q^{34} -9.05909 q^{35} +36.0000 q^{36} +445.105 q^{37} -161.163 q^{38} -247.233 q^{39} -10.3533 q^{40} +37.5069 q^{41} -42.0000 q^{42} +256.931 q^{43} -196.065 q^{44} -11.6474 q^{45} +46.0000 q^{46} -156.166 q^{47} -48.0000 q^{48} +49.0000 q^{49} -246.650 q^{50} +271.051 q^{51} +329.644 q^{52} -518.418 q^{53} -54.0000 q^{54} +63.4346 q^{55} +56.0000 q^{56} +241.745 q^{57} -283.774 q^{58} -628.541 q^{59} +15.5299 q^{60} -396.834 q^{61} +188.791 q^{62} +63.0000 q^{63} +64.0000 q^{64} -106.653 q^{65} +294.097 q^{66} -927.524 q^{67} -361.402 q^{68} -69.0000 q^{69} -18.1182 q^{70} -857.272 q^{71} +72.0000 q^{72} -114.015 q^{73} +890.209 q^{74} +369.975 q^{75} -322.326 q^{76} -343.113 q^{77} -494.466 q^{78} +305.602 q^{79} -20.7065 q^{80} +81.0000 q^{81} +75.0138 q^{82} -1234.53 q^{83} -84.0000 q^{84} +116.928 q^{85} +513.861 q^{86} +425.662 q^{87} -392.130 q^{88} +827.954 q^{89} -23.2948 q^{90} +576.877 q^{91} +92.0000 q^{92} -283.187 q^{93} -312.332 q^{94} +104.285 q^{95} -96.0000 q^{96} -1343.90 q^{97} +98.0000 q^{98} -441.146 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 8 q^{2} - 12 q^{3} + 16 q^{4} - 15 q^{5} - 24 q^{6} + 28 q^{7} + 32 q^{8} + 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 8 q^{2} - 12 q^{3} + 16 q^{4} - 15 q^{5} - 24 q^{6} + 28 q^{7} + 32 q^{8} + 36 q^{9} - 30 q^{10} - 26 q^{11} - 48 q^{12} - 33 q^{13} + 56 q^{14} + 45 q^{15} + 64 q^{16} - 168 q^{17} + 72 q^{18} - 138 q^{19} - 60 q^{20} - 84 q^{21} - 52 q^{22} + 92 q^{23} - 96 q^{24} - 41 q^{25} - 66 q^{26} - 108 q^{27} + 112 q^{28} + 52 q^{29} + 90 q^{30} - 248 q^{31} + 128 q^{32} + 78 q^{33} - 336 q^{34} - 105 q^{35} + 144 q^{36} + 226 q^{37} - 276 q^{38} + 99 q^{39} - 120 q^{40} - 274 q^{41} - 168 q^{42} + 269 q^{43} - 104 q^{44} - 135 q^{45} + 184 q^{46} - 408 q^{47} - 192 q^{48} + 196 q^{49} - 82 q^{50} + 504 q^{51} - 132 q^{52} - 843 q^{53} - 216 q^{54} - 249 q^{55} + 224 q^{56} + 414 q^{57} + 104 q^{58} - 653 q^{59} + 180 q^{60} - 963 q^{61} - 496 q^{62} + 252 q^{63} + 256 q^{64} - 588 q^{65} + 156 q^{66} - 789 q^{67} - 672 q^{68} - 276 q^{69} - 210 q^{70} - 1697 q^{71} + 288 q^{72} - 1800 q^{73} + 452 q^{74} + 123 q^{75} - 552 q^{76} - 182 q^{77} + 198 q^{78} + 274 q^{79} - 240 q^{80} + 324 q^{81} - 548 q^{82} - 1496 q^{83} - 336 q^{84} - 435 q^{85} + 538 q^{86} - 156 q^{87} - 208 q^{88} - 1829 q^{89} - 270 q^{90} - 231 q^{91} + 368 q^{92} + 744 q^{93} - 816 q^{94} - 1767 q^{95} - 384 q^{96} - 1910 q^{97} + 392 q^{98} - 234 q^{99}+O(q^{100}) \) 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
\(5\) −1.29416 −0.115753 −0.0578764 0.998324i \(-0.518433\pi\)
−0.0578764 + 0.998324i \(0.518433\pi\)
\(6\) −6.00000 −0.408248
\(7\) 7.00000 0.377964
\(8\) 8.00000 0.353553
\(9\) 9.00000 0.333333
\(10\) −2.58831 −0.0818496
\(11\) −49.0162 −1.34354 −0.671770 0.740760i \(-0.734466\pi\)
−0.671770 + 0.740760i \(0.734466\pi\)
\(12\) −12.0000 −0.288675
\(13\) 82.4110 1.75821 0.879104 0.476631i \(-0.158142\pi\)
0.879104 + 0.476631i \(0.158142\pi\)
\(14\) 14.0000 0.267261
\(15\) 3.88247 0.0668299
\(16\) 16.0000 0.250000
\(17\) −90.3504 −1.28901 −0.644506 0.764600i \(-0.722937\pi\)
−0.644506 + 0.764600i \(0.722937\pi\)
\(18\) 18.0000 0.235702
\(19\) −80.5815 −0.972982 −0.486491 0.873685i \(-0.661723\pi\)
−0.486491 + 0.873685i \(0.661723\pi\)
\(20\) −5.17663 −0.0578764
\(21\) −21.0000 −0.218218
\(22\) −98.0324 −0.950027
\(23\) 23.0000 0.208514
\(24\) −24.0000 −0.204124
\(25\) −123.325 −0.986601
\(26\) 164.822 1.24324
\(27\) −27.0000 −0.192450
\(28\) 28.0000 0.188982
\(29\) −141.887 −0.908545 −0.454272 0.890863i \(-0.650101\pi\)
−0.454272 + 0.890863i \(0.650101\pi\)
\(30\) 7.76494 0.0472559
\(31\) 94.3956 0.546902 0.273451 0.961886i \(-0.411835\pi\)
0.273451 + 0.961886i \(0.411835\pi\)
\(32\) 32.0000 0.176777
\(33\) 147.049 0.775693
\(34\) −180.701 −0.911469
\(35\) −9.05909 −0.0437505
\(36\) 36.0000 0.166667
\(37\) 445.105 1.97770 0.988848 0.148927i \(-0.0475819\pi\)
0.988848 + 0.148927i \(0.0475819\pi\)
\(38\) −161.163 −0.688002
\(39\) −247.233 −1.01510
\(40\) −10.3533 −0.0409248
\(41\) 37.5069 0.142868 0.0714340 0.997445i \(-0.477242\pi\)
0.0714340 + 0.997445i \(0.477242\pi\)
\(42\) −42.0000 −0.154303
\(43\) 256.931 0.911199 0.455600 0.890185i \(-0.349425\pi\)
0.455600 + 0.890185i \(0.349425\pi\)
\(44\) −196.065 −0.671770
\(45\) −11.6474 −0.0385843
\(46\) 46.0000 0.147442
\(47\) −156.166 −0.484662 −0.242331 0.970194i \(-0.577912\pi\)
−0.242331 + 0.970194i \(0.577912\pi\)
\(48\) −48.0000 −0.144338
\(49\) 49.0000 0.142857
\(50\) −246.650 −0.697632
\(51\) 271.051 0.744211
\(52\) 329.644 0.879104
\(53\) −518.418 −1.34359 −0.671794 0.740738i \(-0.734476\pi\)
−0.671794 + 0.740738i \(0.734476\pi\)
\(54\) −54.0000 −0.136083
\(55\) 63.4346 0.155519
\(56\) 56.0000 0.133631
\(57\) 241.745 0.561752
\(58\) −283.774 −0.642438
\(59\) −628.541 −1.38693 −0.693467 0.720489i \(-0.743918\pi\)
−0.693467 + 0.720489i \(0.743918\pi\)
\(60\) 15.5299 0.0334150
\(61\) −396.834 −0.832941 −0.416470 0.909149i \(-0.636733\pi\)
−0.416470 + 0.909149i \(0.636733\pi\)
\(62\) 188.791 0.386718
\(63\) 63.0000 0.125988
\(64\) 64.0000 0.125000
\(65\) −106.653 −0.203518
\(66\) 294.097 0.548498
\(67\) −927.524 −1.69127 −0.845635 0.533762i \(-0.820778\pi\)
−0.845635 + 0.533762i \(0.820778\pi\)
\(68\) −361.402 −0.644506
\(69\) −69.0000 −0.120386
\(70\) −18.1182 −0.0309363
\(71\) −857.272 −1.43295 −0.716475 0.697612i \(-0.754246\pi\)
−0.716475 + 0.697612i \(0.754246\pi\)
\(72\) 72.0000 0.117851
\(73\) −114.015 −0.182801 −0.0914007 0.995814i \(-0.529134\pi\)
−0.0914007 + 0.995814i \(0.529134\pi\)
\(74\) 890.209 1.39844
\(75\) 369.975 0.569615
\(76\) −322.326 −0.486491
\(77\) −343.113 −0.507811
\(78\) −494.466 −0.717785
\(79\) 305.602 0.435227 0.217614 0.976035i \(-0.430173\pi\)
0.217614 + 0.976035i \(0.430173\pi\)
\(80\) −20.7065 −0.0289382
\(81\) 81.0000 0.111111
\(82\) 75.0138 0.101023
\(83\) −1234.53 −1.63262 −0.816308 0.577617i \(-0.803983\pi\)
−0.816308 + 0.577617i \(0.803983\pi\)
\(84\) −84.0000 −0.109109
\(85\) 116.928 0.149207
\(86\) 513.861 0.644315
\(87\) 425.662 0.524548
\(88\) −392.130 −0.475013
\(89\) 827.954 0.986100 0.493050 0.870001i \(-0.335882\pi\)
0.493050 + 0.870001i \(0.335882\pi\)
\(90\) −23.2948 −0.0272832
\(91\) 576.877 0.664540
\(92\) 92.0000 0.104257
\(93\) −283.187 −0.315754
\(94\) −312.332 −0.342708
\(95\) 104.285 0.112625
\(96\) −96.0000 −0.102062
\(97\) −1343.90 −1.40673 −0.703363 0.710831i \(-0.748319\pi\)
−0.703363 + 0.710831i \(0.748319\pi\)
\(98\) 98.0000 0.101015
\(99\) −441.146 −0.447847
\(100\) −493.301 −0.493301
\(101\) 1380.26 1.35981 0.679906 0.733299i \(-0.262020\pi\)
0.679906 + 0.733299i \(0.262020\pi\)
\(102\) 542.102 0.526237
\(103\) −1848.11 −1.76796 −0.883981 0.467523i \(-0.845147\pi\)
−0.883981 + 0.467523i \(0.845147\pi\)
\(104\) 659.288 0.621620
\(105\) 27.1773 0.0252593
\(106\) −1036.84 −0.950060
\(107\) 1595.43 1.44145 0.720727 0.693219i \(-0.243808\pi\)
0.720727 + 0.693219i \(0.243808\pi\)
\(108\) −108.000 −0.0962250
\(109\) −140.344 −0.123326 −0.0616631 0.998097i \(-0.519640\pi\)
−0.0616631 + 0.998097i \(0.519640\pi\)
\(110\) 126.869 0.109968
\(111\) −1335.31 −1.14182
\(112\) 112.000 0.0944911
\(113\) −1226.94 −1.02142 −0.510711 0.859753i \(-0.670618\pi\)
−0.510711 + 0.859753i \(0.670618\pi\)
\(114\) 483.489 0.397218
\(115\) −29.7656 −0.0241361
\(116\) −567.549 −0.454272
\(117\) 741.699 0.586069
\(118\) −1257.08 −0.980710
\(119\) −632.453 −0.487200
\(120\) 31.0598 0.0236280
\(121\) 1071.59 0.805101
\(122\) −793.668 −0.588978
\(123\) −112.521 −0.0824849
\(124\) 377.582 0.273451
\(125\) 321.372 0.229955
\(126\) 126.000 0.0890871
\(127\) −929.972 −0.649777 −0.324889 0.945752i \(-0.605327\pi\)
−0.324889 + 0.945752i \(0.605327\pi\)
\(128\) 128.000 0.0883883
\(129\) −770.792 −0.526081
\(130\) −213.305 −0.143909
\(131\) −1804.26 −1.20335 −0.601675 0.798741i \(-0.705500\pi\)
−0.601675 + 0.798741i \(0.705500\pi\)
\(132\) 588.195 0.387847
\(133\) −564.071 −0.367753
\(134\) −1855.05 −1.19591
\(135\) 34.9422 0.0222766
\(136\) −722.803 −0.455734
\(137\) 691.762 0.431396 0.215698 0.976460i \(-0.430797\pi\)
0.215698 + 0.976460i \(0.430797\pi\)
\(138\) −138.000 −0.0851257
\(139\) 1907.71 1.16410 0.582050 0.813153i \(-0.302251\pi\)
0.582050 + 0.813153i \(0.302251\pi\)
\(140\) −36.2364 −0.0218752
\(141\) 468.497 0.279820
\(142\) −1714.54 −1.01325
\(143\) −4039.47 −2.36222
\(144\) 144.000 0.0833333
\(145\) 183.624 0.105167
\(146\) −228.031 −0.129260
\(147\) −147.000 −0.0824786
\(148\) 1780.42 0.988848
\(149\) 77.3801 0.0425451 0.0212726 0.999774i \(-0.493228\pi\)
0.0212726 + 0.999774i \(0.493228\pi\)
\(150\) 739.951 0.402778
\(151\) 1693.51 0.912686 0.456343 0.889804i \(-0.349159\pi\)
0.456343 + 0.889804i \(0.349159\pi\)
\(152\) −644.652 −0.344001
\(153\) −813.154 −0.429670
\(154\) −686.227 −0.359076
\(155\) −122.163 −0.0633054
\(156\) −988.932 −0.507551
\(157\) −2761.74 −1.40389 −0.701946 0.712230i \(-0.747685\pi\)
−0.701946 + 0.712230i \(0.747685\pi\)
\(158\) 611.204 0.307752
\(159\) 1555.25 0.775721
\(160\) −41.4130 −0.0204624
\(161\) 161.000 0.0788110
\(162\) 162.000 0.0785674
\(163\) −3382.22 −1.62525 −0.812626 0.582786i \(-0.801963\pi\)
−0.812626 + 0.582786i \(0.801963\pi\)
\(164\) 150.028 0.0714340
\(165\) −190.304 −0.0897887
\(166\) −2469.06 −1.15443
\(167\) −997.598 −0.462254 −0.231127 0.972924i \(-0.574241\pi\)
−0.231127 + 0.972924i \(0.574241\pi\)
\(168\) −168.000 −0.0771517
\(169\) 4594.57 2.09129
\(170\) 233.855 0.105505
\(171\) −725.234 −0.324327
\(172\) 1027.72 0.455600
\(173\) −420.461 −0.184781 −0.0923903 0.995723i \(-0.529451\pi\)
−0.0923903 + 0.995723i \(0.529451\pi\)
\(174\) 851.323 0.370912
\(175\) −863.276 −0.372900
\(176\) −784.259 −0.335885
\(177\) 1885.62 0.800747
\(178\) 1655.91 0.697278
\(179\) −531.844 −0.222078 −0.111039 0.993816i \(-0.535418\pi\)
−0.111039 + 0.993816i \(0.535418\pi\)
\(180\) −46.5896 −0.0192921
\(181\) −497.521 −0.204312 −0.102156 0.994768i \(-0.532574\pi\)
−0.102156 + 0.994768i \(0.532574\pi\)
\(182\) 1153.75 0.469901
\(183\) 1190.50 0.480899
\(184\) 184.000 0.0737210
\(185\) −576.035 −0.228924
\(186\) −566.374 −0.223272
\(187\) 4428.63 1.73184
\(188\) −624.663 −0.242331
\(189\) −189.000 −0.0727393
\(190\) 208.570 0.0796382
\(191\) 1079.54 0.408967 0.204484 0.978870i \(-0.434448\pi\)
0.204484 + 0.978870i \(0.434448\pi\)
\(192\) −192.000 −0.0721688
\(193\) −1761.70 −0.657048 −0.328524 0.944496i \(-0.606551\pi\)
−0.328524 + 0.944496i \(0.606551\pi\)
\(194\) −2687.80 −0.994706
\(195\) 319.958 0.117501
\(196\) 196.000 0.0714286
\(197\) 2747.60 0.993698 0.496849 0.867837i \(-0.334490\pi\)
0.496849 + 0.867837i \(0.334490\pi\)
\(198\) −882.292 −0.316676
\(199\) −1910.52 −0.680569 −0.340284 0.940323i \(-0.610523\pi\)
−0.340284 + 0.940323i \(0.610523\pi\)
\(200\) −986.601 −0.348816
\(201\) 2782.57 0.976455
\(202\) 2760.52 0.961533
\(203\) −993.211 −0.343398
\(204\) 1084.20 0.372106
\(205\) −48.5398 −0.0165374
\(206\) −3696.23 −1.25014
\(207\) 207.000 0.0695048
\(208\) 1318.58 0.439552
\(209\) 3949.80 1.30724
\(210\) 54.3546 0.0178611
\(211\) 2578.90 0.841416 0.420708 0.907196i \(-0.361782\pi\)
0.420708 + 0.907196i \(0.361782\pi\)
\(212\) −2073.67 −0.671794
\(213\) 2571.82 0.827315
\(214\) 3190.85 1.01926
\(215\) −332.508 −0.105474
\(216\) −216.000 −0.0680414
\(217\) 660.769 0.206709
\(218\) −280.689 −0.0872047
\(219\) 342.046 0.105540
\(220\) 253.739 0.0777593
\(221\) −7445.87 −2.26635
\(222\) −2670.63 −0.807391
\(223\) 394.705 0.118526 0.0592632 0.998242i \(-0.481125\pi\)
0.0592632 + 0.998242i \(0.481125\pi\)
\(224\) 224.000 0.0668153
\(225\) −1109.93 −0.328867
\(226\) −2453.88 −0.722254
\(227\) −1497.44 −0.437836 −0.218918 0.975743i \(-0.570253\pi\)
−0.218918 + 0.975743i \(0.570253\pi\)
\(228\) 966.978 0.280876
\(229\) −3152.77 −0.909787 −0.454893 0.890546i \(-0.650323\pi\)
−0.454893 + 0.890546i \(0.650323\pi\)
\(230\) −59.5312 −0.0170668
\(231\) 1029.34 0.293185
\(232\) −1135.10 −0.321219
\(233\) 5529.90 1.55483 0.777416 0.628987i \(-0.216530\pi\)
0.777416 + 0.628987i \(0.216530\pi\)
\(234\) 1483.40 0.414413
\(235\) 202.103 0.0561010
\(236\) −2514.16 −0.693467
\(237\) −916.807 −0.251278
\(238\) −1264.91 −0.344503
\(239\) 5043.44 1.36499 0.682496 0.730889i \(-0.260894\pi\)
0.682496 + 0.730889i \(0.260894\pi\)
\(240\) 62.1195 0.0167075
\(241\) −986.086 −0.263566 −0.131783 0.991279i \(-0.542070\pi\)
−0.131783 + 0.991279i \(0.542070\pi\)
\(242\) 2143.18 0.569292
\(243\) −243.000 −0.0641500
\(244\) −1587.34 −0.416470
\(245\) −63.4137 −0.0165361
\(246\) −225.041 −0.0583257
\(247\) −6640.80 −1.71070
\(248\) 755.165 0.193359
\(249\) 3703.59 0.942591
\(250\) 642.743 0.162603
\(251\) −2918.07 −0.733812 −0.366906 0.930258i \(-0.619583\pi\)
−0.366906 + 0.930258i \(0.619583\pi\)
\(252\) 252.000 0.0629941
\(253\) −1127.37 −0.280148
\(254\) −1859.94 −0.459462
\(255\) −350.783 −0.0861445
\(256\) 256.000 0.0625000
\(257\) −2482.59 −0.602567 −0.301284 0.953535i \(-0.597415\pi\)
−0.301284 + 0.953535i \(0.597415\pi\)
\(258\) −1541.58 −0.371995
\(259\) 3115.73 0.747499
\(260\) −426.611 −0.101759
\(261\) −1276.98 −0.302848
\(262\) −3608.52 −0.850897
\(263\) 5568.78 1.30565 0.652825 0.757509i \(-0.273584\pi\)
0.652825 + 0.757509i \(0.273584\pi\)
\(264\) 1176.39 0.274249
\(265\) 670.914 0.155524
\(266\) −1128.14 −0.260040
\(267\) −2483.86 −0.569325
\(268\) −3710.10 −0.845635
\(269\) −2665.62 −0.604186 −0.302093 0.953278i \(-0.597685\pi\)
−0.302093 + 0.953278i \(0.597685\pi\)
\(270\) 69.8844 0.0157520
\(271\) −3635.18 −0.814840 −0.407420 0.913241i \(-0.633572\pi\)
−0.407420 + 0.913241i \(0.633572\pi\)
\(272\) −1445.61 −0.322253
\(273\) −1730.63 −0.383672
\(274\) 1383.52 0.305043
\(275\) 6044.93 1.32554
\(276\) −276.000 −0.0601929
\(277\) −3729.83 −0.809038 −0.404519 0.914529i \(-0.632561\pi\)
−0.404519 + 0.914529i \(0.632561\pi\)
\(278\) 3815.42 0.823143
\(279\) 849.560 0.182301
\(280\) −72.4728 −0.0154681
\(281\) 2095.46 0.444856 0.222428 0.974949i \(-0.428602\pi\)
0.222428 + 0.974949i \(0.428602\pi\)
\(282\) 936.995 0.197863
\(283\) 8578.79 1.80197 0.900983 0.433854i \(-0.142847\pi\)
0.900983 + 0.433854i \(0.142847\pi\)
\(284\) −3429.09 −0.716475
\(285\) −312.855 −0.0650244
\(286\) −8078.95 −1.67034
\(287\) 262.548 0.0539991
\(288\) 288.000 0.0589256
\(289\) 3250.20 0.661550
\(290\) 367.248 0.0743640
\(291\) 4031.70 0.812174
\(292\) −456.062 −0.0914007
\(293\) −3816.23 −0.760911 −0.380455 0.924799i \(-0.624233\pi\)
−0.380455 + 0.924799i \(0.624233\pi\)
\(294\) −294.000 −0.0583212
\(295\) 813.430 0.160542
\(296\) 3560.84 0.699221
\(297\) 1323.44 0.258564
\(298\) 154.760 0.0300839
\(299\) 1895.45 0.366612
\(300\) 1479.90 0.284807
\(301\) 1798.51 0.344401
\(302\) 3387.01 0.645366
\(303\) −4140.78 −0.785088
\(304\) −1289.30 −0.243246
\(305\) 513.565 0.0964153
\(306\) −1626.31 −0.303823
\(307\) 6176.53 1.14825 0.574125 0.818767i \(-0.305342\pi\)
0.574125 + 0.818767i \(0.305342\pi\)
\(308\) −1372.45 −0.253905
\(309\) 5544.34 1.02073
\(310\) −244.325 −0.0447637
\(311\) 1969.82 0.359159 0.179579 0.983743i \(-0.442526\pi\)
0.179579 + 0.983743i \(0.442526\pi\)
\(312\) −1977.86 −0.358893
\(313\) 2657.30 0.479870 0.239935 0.970789i \(-0.422874\pi\)
0.239935 + 0.970789i \(0.422874\pi\)
\(314\) −5523.49 −0.992702
\(315\) −81.5318 −0.0145835
\(316\) 1222.41 0.217614
\(317\) 3309.95 0.586453 0.293226 0.956043i \(-0.405271\pi\)
0.293226 + 0.956043i \(0.405271\pi\)
\(318\) 3110.51 0.548518
\(319\) 6954.77 1.22067
\(320\) −82.8260 −0.0144691
\(321\) −4786.28 −0.832224
\(322\) 322.000 0.0557278
\(323\) 7280.57 1.25419
\(324\) 324.000 0.0555556
\(325\) −10163.3 −1.73465
\(326\) −6764.44 −1.14923
\(327\) 421.033 0.0712024
\(328\) 300.055 0.0505115
\(329\) −1093.16 −0.183185
\(330\) −380.608 −0.0634902
\(331\) 10329.2 1.71524 0.857620 0.514284i \(-0.171942\pi\)
0.857620 + 0.514284i \(0.171942\pi\)
\(332\) −4938.11 −0.816308
\(333\) 4005.94 0.659232
\(334\) −1995.20 −0.326863
\(335\) 1200.36 0.195769
\(336\) −336.000 −0.0545545
\(337\) 8882.04 1.43571 0.717857 0.696191i \(-0.245123\pi\)
0.717857 + 0.696191i \(0.245123\pi\)
\(338\) 9189.14 1.47877
\(339\) 3680.81 0.589718
\(340\) 467.710 0.0746034
\(341\) −4626.91 −0.734784
\(342\) −1450.47 −0.229334
\(343\) 343.000 0.0539949
\(344\) 2055.45 0.322158
\(345\) 89.2968 0.0139350
\(346\) −840.921 −0.130660
\(347\) 6600.40 1.02112 0.510560 0.859842i \(-0.329438\pi\)
0.510560 + 0.859842i \(0.329438\pi\)
\(348\) 1702.65 0.262274
\(349\) 9416.49 1.44428 0.722139 0.691748i \(-0.243159\pi\)
0.722139 + 0.691748i \(0.243159\pi\)
\(350\) −1726.55 −0.263680
\(351\) −2225.10 −0.338367
\(352\) −1568.52 −0.237507
\(353\) 12937.9 1.95075 0.975374 0.220555i \(-0.0707869\pi\)
0.975374 + 0.220555i \(0.0707869\pi\)
\(354\) 3771.25 0.566213
\(355\) 1109.44 0.165868
\(356\) 3311.81 0.493050
\(357\) 1897.36 0.281285
\(358\) −1063.69 −0.157033
\(359\) 4687.95 0.689193 0.344597 0.938751i \(-0.388016\pi\)
0.344597 + 0.938751i \(0.388016\pi\)
\(360\) −93.1793 −0.0136416
\(361\) −365.621 −0.0533052
\(362\) −995.042 −0.144470
\(363\) −3214.77 −0.464825
\(364\) 2307.51 0.332270
\(365\) 147.554 0.0211598
\(366\) 2381.00 0.340047
\(367\) −10802.7 −1.53650 −0.768251 0.640149i \(-0.778873\pi\)
−0.768251 + 0.640149i \(0.778873\pi\)
\(368\) 368.000 0.0521286
\(369\) 337.562 0.0476227
\(370\) −1152.07 −0.161874
\(371\) −3628.92 −0.507829
\(372\) −1132.75 −0.157877
\(373\) 6855.89 0.951701 0.475850 0.879526i \(-0.342140\pi\)
0.475850 + 0.879526i \(0.342140\pi\)
\(374\) 8857.27 1.22459
\(375\) −964.115 −0.132764
\(376\) −1249.33 −0.171354
\(377\) −11693.1 −1.59741
\(378\) −378.000 −0.0514344
\(379\) 7348.38 0.995939 0.497969 0.867195i \(-0.334079\pi\)
0.497969 + 0.867195i \(0.334079\pi\)
\(380\) 417.140 0.0563127
\(381\) 2789.92 0.375149
\(382\) 2159.08 0.289184
\(383\) −9917.48 −1.32313 −0.661566 0.749887i \(-0.730108\pi\)
−0.661566 + 0.749887i \(0.730108\pi\)
\(384\) −384.000 −0.0510310
\(385\) 444.042 0.0587805
\(386\) −3523.41 −0.464603
\(387\) 2312.38 0.303733
\(388\) −5375.60 −0.703363
\(389\) −4781.41 −0.623205 −0.311603 0.950212i \(-0.600866\pi\)
−0.311603 + 0.950212i \(0.600866\pi\)
\(390\) 639.916 0.0830857
\(391\) −2078.06 −0.268777
\(392\) 392.000 0.0505076
\(393\) 5412.78 0.694755
\(394\) 5495.20 0.702650
\(395\) −395.497 −0.0503788
\(396\) −1764.58 −0.223923
\(397\) 5412.61 0.684260 0.342130 0.939653i \(-0.388852\pi\)
0.342130 + 0.939653i \(0.388852\pi\)
\(398\) −3821.04 −0.481235
\(399\) 1692.21 0.212322
\(400\) −1973.20 −0.246650
\(401\) −1971.06 −0.245462 −0.122731 0.992440i \(-0.539165\pi\)
−0.122731 + 0.992440i \(0.539165\pi\)
\(402\) 5565.14 0.690458
\(403\) 7779.23 0.961566
\(404\) 5521.04 0.679906
\(405\) −104.827 −0.0128614
\(406\) −1986.42 −0.242819
\(407\) −21817.3 −2.65711
\(408\) 2168.41 0.263118
\(409\) −648.731 −0.0784295 −0.0392148 0.999231i \(-0.512486\pi\)
−0.0392148 + 0.999231i \(0.512486\pi\)
\(410\) −97.0795 −0.0116937
\(411\) −2075.29 −0.249067
\(412\) −7392.46 −0.883981
\(413\) −4399.79 −0.524212
\(414\) 414.000 0.0491473
\(415\) 1597.67 0.188980
\(416\) 2637.15 0.310810
\(417\) −5723.13 −0.672094
\(418\) 7899.60 0.924359
\(419\) −13307.1 −1.55154 −0.775772 0.631014i \(-0.782639\pi\)
−0.775772 + 0.631014i \(0.782639\pi\)
\(420\) 108.709 0.0126297
\(421\) 9403.07 1.08855 0.544273 0.838908i \(-0.316806\pi\)
0.544273 + 0.838908i \(0.316806\pi\)
\(422\) 5157.80 0.594971
\(423\) −1405.49 −0.161554
\(424\) −4147.34 −0.475030
\(425\) 11142.5 1.27174
\(426\) 5143.63 0.585000
\(427\) −2777.84 −0.314822
\(428\) 6381.70 0.720727
\(429\) 12118.4 1.36383
\(430\) −665.017 −0.0745813
\(431\) −3874.55 −0.433018 −0.216509 0.976281i \(-0.569467\pi\)
−0.216509 + 0.976281i \(0.569467\pi\)
\(432\) −432.000 −0.0481125
\(433\) −9234.70 −1.02492 −0.512461 0.858711i \(-0.671266\pi\)
−0.512461 + 0.858711i \(0.671266\pi\)
\(434\) 1321.54 0.146166
\(435\) −550.873 −0.0607180
\(436\) −561.377 −0.0616631
\(437\) −1853.37 −0.202881
\(438\) 684.093 0.0746283
\(439\) −17639.5 −1.91774 −0.958872 0.283841i \(-0.908391\pi\)
−0.958872 + 0.283841i \(0.908391\pi\)
\(440\) 507.477 0.0549841
\(441\) 441.000 0.0476190
\(442\) −14891.7 −1.60255
\(443\) −17240.4 −1.84902 −0.924511 0.381155i \(-0.875526\pi\)
−0.924511 + 0.381155i \(0.875526\pi\)
\(444\) −5341.26 −0.570912
\(445\) −1071.50 −0.114144
\(446\) 789.410 0.0838109
\(447\) −232.140 −0.0245634
\(448\) 448.000 0.0472456
\(449\) −9081.43 −0.954519 −0.477260 0.878762i \(-0.658370\pi\)
−0.477260 + 0.878762i \(0.658370\pi\)
\(450\) −2219.85 −0.232544
\(451\) −1838.45 −0.191949
\(452\) −4907.75 −0.510711
\(453\) −5080.52 −0.526939
\(454\) −2994.89 −0.309597
\(455\) −746.569 −0.0769224
\(456\) 1933.96 0.198609
\(457\) 1078.59 0.110403 0.0552017 0.998475i \(-0.482420\pi\)
0.0552017 + 0.998475i \(0.482420\pi\)
\(458\) −6305.55 −0.643316
\(459\) 2439.46 0.248070
\(460\) −119.062 −0.0120681
\(461\) 8684.43 0.877384 0.438692 0.898637i \(-0.355442\pi\)
0.438692 + 0.898637i \(0.355442\pi\)
\(462\) 2058.68 0.207313
\(463\) −18900.9 −1.89719 −0.948597 0.316488i \(-0.897496\pi\)
−0.948597 + 0.316488i \(0.897496\pi\)
\(464\) −2270.20 −0.227136
\(465\) 366.488 0.0365494
\(466\) 11059.8 1.09943
\(467\) 809.992 0.0802612 0.0401306 0.999194i \(-0.487223\pi\)
0.0401306 + 0.999194i \(0.487223\pi\)
\(468\) 2966.80 0.293035
\(469\) −6492.67 −0.639240
\(470\) 404.206 0.0396694
\(471\) 8285.23 0.810538
\(472\) −5028.33 −0.490355
\(473\) −12593.8 −1.22423
\(474\) −1833.61 −0.177681
\(475\) 9937.73 0.959946
\(476\) −2529.81 −0.243600
\(477\) −4665.76 −0.447863
\(478\) 10086.9 0.965195
\(479\) −7613.75 −0.726266 −0.363133 0.931737i \(-0.618293\pi\)
−0.363133 + 0.931737i \(0.618293\pi\)
\(480\) 124.239 0.0118140
\(481\) 36681.5 3.47720
\(482\) −1972.17 −0.186369
\(483\) −483.000 −0.0455016
\(484\) 4286.36 0.402550
\(485\) 1739.22 0.162833
\(486\) −486.000 −0.0453609
\(487\) 7458.06 0.693957 0.346978 0.937873i \(-0.387208\pi\)
0.346978 + 0.937873i \(0.387208\pi\)
\(488\) −3174.67 −0.294489
\(489\) 10146.7 0.938339
\(490\) −126.827 −0.0116928
\(491\) 1914.55 0.175972 0.0879862 0.996122i \(-0.471957\pi\)
0.0879862 + 0.996122i \(0.471957\pi\)
\(492\) −450.083 −0.0412425
\(493\) 12819.6 1.17112
\(494\) −13281.6 −1.20965
\(495\) 570.912 0.0518395
\(496\) 1510.33 0.136725
\(497\) −6000.91 −0.541605
\(498\) 7407.17 0.666513
\(499\) 1798.53 0.161349 0.0806745 0.996740i \(-0.474293\pi\)
0.0806745 + 0.996740i \(0.474293\pi\)
\(500\) 1285.49 0.114977
\(501\) 2992.80 0.266883
\(502\) −5836.13 −0.518883
\(503\) 8417.12 0.746125 0.373062 0.927806i \(-0.378308\pi\)
0.373062 + 0.927806i \(0.378308\pi\)
\(504\) 504.000 0.0445435
\(505\) −1786.27 −0.157402
\(506\) −2254.75 −0.198094
\(507\) −13783.7 −1.20741
\(508\) −3719.89 −0.324889
\(509\) 9022.57 0.785695 0.392847 0.919604i \(-0.371490\pi\)
0.392847 + 0.919604i \(0.371490\pi\)
\(510\) −701.565 −0.0609134
\(511\) −798.108 −0.0690924
\(512\) 512.000 0.0441942
\(513\) 2175.70 0.187251
\(514\) −4965.18 −0.426079
\(515\) 2391.75 0.204647
\(516\) −3083.17 −0.263041
\(517\) 7654.66 0.651163
\(518\) 6231.47 0.528562
\(519\) 1261.38 0.106683
\(520\) −853.222 −0.0719543
\(521\) 17253.7 1.45086 0.725432 0.688294i \(-0.241640\pi\)
0.725432 + 0.688294i \(0.241640\pi\)
\(522\) −2553.97 −0.214146
\(523\) 14252.3 1.19160 0.595801 0.803132i \(-0.296835\pi\)
0.595801 + 0.803132i \(0.296835\pi\)
\(524\) −7217.04 −0.601675
\(525\) 2589.83 0.215294
\(526\) 11137.6 0.923234
\(527\) −8528.68 −0.704962
\(528\) 2352.78 0.193923
\(529\) 529.000 0.0434783
\(530\) 1341.83 0.109972
\(531\) −5656.87 −0.462311
\(532\) −2256.28 −0.183876
\(533\) 3090.98 0.251192
\(534\) −4967.72 −0.402574
\(535\) −2064.73 −0.166852
\(536\) −7420.19 −0.597954
\(537\) 1595.53 0.128217
\(538\) −5331.25 −0.427224
\(539\) −2401.79 −0.191934
\(540\) 139.769 0.0111383
\(541\) 2539.10 0.201783 0.100892 0.994897i \(-0.467831\pi\)
0.100892 + 0.994897i \(0.467831\pi\)
\(542\) −7270.37 −0.576179
\(543\) 1492.56 0.117960
\(544\) −2891.21 −0.227867
\(545\) 181.627 0.0142753
\(546\) −3461.26 −0.271297
\(547\) −6632.90 −0.518468 −0.259234 0.965815i \(-0.583470\pi\)
−0.259234 + 0.965815i \(0.583470\pi\)
\(548\) 2767.05 0.215698
\(549\) −3571.51 −0.277647
\(550\) 12089.9 0.937297
\(551\) 11433.5 0.883998
\(552\) −552.000 −0.0425628
\(553\) 2139.22 0.164500
\(554\) −7459.66 −0.572077
\(555\) 1728.11 0.132169
\(556\) 7630.85 0.582050
\(557\) 15215.9 1.15749 0.578743 0.815510i \(-0.303544\pi\)
0.578743 + 0.815510i \(0.303544\pi\)
\(558\) 1699.12 0.128906
\(559\) 21173.9 1.60208
\(560\) −144.946 −0.0109376
\(561\) −13285.9 −0.999878
\(562\) 4190.91 0.314560
\(563\) −5321.43 −0.398351 −0.199176 0.979964i \(-0.563826\pi\)
−0.199176 + 0.979964i \(0.563826\pi\)
\(564\) 1873.99 0.139910
\(565\) 1587.85 0.118232
\(566\) 17157.6 1.27418
\(567\) 567.000 0.0419961
\(568\) −6858.18 −0.506625
\(569\) −6120.97 −0.450974 −0.225487 0.974246i \(-0.572397\pi\)
−0.225487 + 0.974246i \(0.572397\pi\)
\(570\) −625.710 −0.0459792
\(571\) −26413.3 −1.93584 −0.967918 0.251267i \(-0.919153\pi\)
−0.967918 + 0.251267i \(0.919153\pi\)
\(572\) −16157.9 −1.18111
\(573\) −3238.62 −0.236117
\(574\) 525.096 0.0381831
\(575\) −2836.48 −0.205721
\(576\) 576.000 0.0416667
\(577\) 23548.2 1.69901 0.849503 0.527584i \(-0.176902\pi\)
0.849503 + 0.527584i \(0.176902\pi\)
\(578\) 6500.39 0.467787
\(579\) 5285.11 0.379347
\(580\) 734.497 0.0525833
\(581\) −8641.70 −0.617071
\(582\) 8063.40 0.574294
\(583\) 25410.9 1.80516
\(584\) −912.123 −0.0646300
\(585\) −959.874 −0.0678392
\(586\) −7632.47 −0.538045
\(587\) 11780.0 0.828298 0.414149 0.910209i \(-0.364079\pi\)
0.414149 + 0.910209i \(0.364079\pi\)
\(588\) −588.000 −0.0412393
\(589\) −7606.54 −0.532126
\(590\) 1626.86 0.113520
\(591\) −8242.80 −0.573712
\(592\) 7121.68 0.494424
\(593\) −6475.79 −0.448447 −0.224223 0.974538i \(-0.571985\pi\)
−0.224223 + 0.974538i \(0.571985\pi\)
\(594\) 2646.88 0.182833
\(595\) 818.493 0.0563948
\(596\) 309.520 0.0212726
\(597\) 5731.56 0.392926
\(598\) 3790.91 0.259234
\(599\) −969.373 −0.0661227 −0.0330613 0.999453i \(-0.510526\pi\)
−0.0330613 + 0.999453i \(0.510526\pi\)
\(600\) 2959.80 0.201389
\(601\) −317.461 −0.0215466 −0.0107733 0.999942i \(-0.503429\pi\)
−0.0107733 + 0.999942i \(0.503429\pi\)
\(602\) 3597.03 0.243528
\(603\) −8347.72 −0.563757
\(604\) 6774.02 0.456343
\(605\) −1386.80 −0.0931927
\(606\) −8281.57 −0.555141
\(607\) 7255.36 0.485150 0.242575 0.970133i \(-0.422008\pi\)
0.242575 + 0.970133i \(0.422008\pi\)
\(608\) −2578.61 −0.172001
\(609\) 2979.63 0.198261
\(610\) 1027.13 0.0681759
\(611\) −12869.8 −0.852137
\(612\) −3252.61 −0.214835
\(613\) 17804.6 1.17312 0.586560 0.809906i \(-0.300482\pi\)
0.586560 + 0.809906i \(0.300482\pi\)
\(614\) 12353.1 0.811936
\(615\) 145.619 0.00954787
\(616\) −2744.91 −0.179538
\(617\) −29001.0 −1.89228 −0.946139 0.323760i \(-0.895053\pi\)
−0.946139 + 0.323760i \(0.895053\pi\)
\(618\) 11088.7 0.721767
\(619\) −6442.18 −0.418309 −0.209154 0.977883i \(-0.567071\pi\)
−0.209154 + 0.977883i \(0.567071\pi\)
\(620\) −488.651 −0.0316527
\(621\) −621.000 −0.0401286
\(622\) 3939.64 0.253964
\(623\) 5795.68 0.372711
\(624\) −3955.73 −0.253775
\(625\) 14999.7 0.959983
\(626\) 5314.59 0.339319
\(627\) −11849.4 −0.754736
\(628\) −11047.0 −0.701946
\(629\) −40215.4 −2.54927
\(630\) −163.064 −0.0103121
\(631\) −21326.5 −1.34547 −0.672737 0.739882i \(-0.734881\pi\)
−0.672737 + 0.739882i \(0.734881\pi\)
\(632\) 2444.82 0.153876
\(633\) −7736.70 −0.485792
\(634\) 6619.91 0.414685
\(635\) 1203.53 0.0752136
\(636\) 6221.01 0.387860
\(637\) 4038.14 0.251172
\(638\) 13909.5 0.863141
\(639\) −7715.45 −0.477650
\(640\) −165.652 −0.0102312
\(641\) 26218.6 1.61556 0.807780 0.589484i \(-0.200669\pi\)
0.807780 + 0.589484i \(0.200669\pi\)
\(642\) −9572.55 −0.588471
\(643\) −3049.87 −0.187053 −0.0935264 0.995617i \(-0.529814\pi\)
−0.0935264 + 0.995617i \(0.529814\pi\)
\(644\) 644.000 0.0394055
\(645\) 997.525 0.0608954
\(646\) 14561.1 0.886843
\(647\) −23702.8 −1.44027 −0.720135 0.693834i \(-0.755920\pi\)
−0.720135 + 0.693834i \(0.755920\pi\)
\(648\) 648.000 0.0392837
\(649\) 30808.7 1.86340
\(650\) −20326.7 −1.22658
\(651\) −1982.31 −0.119344
\(652\) −13528.9 −0.812626
\(653\) −11241.5 −0.673681 −0.336840 0.941562i \(-0.609358\pi\)
−0.336840 + 0.941562i \(0.609358\pi\)
\(654\) 842.066 0.0503477
\(655\) 2334.99 0.139291
\(656\) 600.110 0.0357170
\(657\) −1026.14 −0.0609338
\(658\) −2186.32 −0.129531
\(659\) −119.895 −0.00708715 −0.00354357 0.999994i \(-0.501128\pi\)
−0.00354357 + 0.999994i \(0.501128\pi\)
\(660\) −761.216 −0.0448944
\(661\) −291.504 −0.0171531 −0.00857653 0.999963i \(-0.502730\pi\)
−0.00857653 + 0.999963i \(0.502730\pi\)
\(662\) 20658.4 1.21286
\(663\) 22337.6 1.30848
\(664\) −9876.23 −0.577217
\(665\) 729.995 0.0425684
\(666\) 8011.89 0.466148
\(667\) −3263.41 −0.189445
\(668\) −3990.39 −0.231127
\(669\) −1184.11 −0.0684313
\(670\) 2400.72 0.138430
\(671\) 19451.3 1.11909
\(672\) −672.000 −0.0385758
\(673\) −620.282 −0.0355277 −0.0177638 0.999842i \(-0.505655\pi\)
−0.0177638 + 0.999842i \(0.505655\pi\)
\(674\) 17764.1 1.01520
\(675\) 3329.78 0.189872
\(676\) 18378.3 1.04565
\(677\) 11632.0 0.660344 0.330172 0.943921i \(-0.392893\pi\)
0.330172 + 0.943921i \(0.392893\pi\)
\(678\) 7361.63 0.416993
\(679\) −9407.30 −0.531692
\(680\) 935.420 0.0527525
\(681\) 4492.33 0.252785
\(682\) −9253.83 −0.519571
\(683\) −7993.51 −0.447823 −0.223912 0.974609i \(-0.571883\pi\)
−0.223912 + 0.974609i \(0.571883\pi\)
\(684\) −2900.93 −0.162164
\(685\) −895.249 −0.0499353
\(686\) 686.000 0.0381802
\(687\) 9458.32 0.525266
\(688\) 4110.89 0.227800
\(689\) −42723.3 −2.36231
\(690\) 178.594 0.00985354
\(691\) −12692.5 −0.698761 −0.349381 0.936981i \(-0.613608\pi\)
−0.349381 + 0.936981i \(0.613608\pi\)
\(692\) −1681.84 −0.0923903
\(693\) −3088.02 −0.169270
\(694\) 13200.8 0.722040
\(695\) −2468.88 −0.134748
\(696\) 3405.29 0.185456
\(697\) −3388.76 −0.184159
\(698\) 18833.0 1.02126
\(699\) −16589.7 −0.897683
\(700\) −3453.10 −0.186450
\(701\) 12675.6 0.682953 0.341477 0.939890i \(-0.389073\pi\)
0.341477 + 0.939890i \(0.389073\pi\)
\(702\) −4450.19 −0.239262
\(703\) −35867.2 −1.92426
\(704\) −3137.04 −0.167943
\(705\) −606.309 −0.0323900
\(706\) 25875.8 1.37939
\(707\) 9661.83 0.513961
\(708\) 7542.49 0.400373
\(709\) 36203.0 1.91768 0.958838 0.283953i \(-0.0916460\pi\)
0.958838 + 0.283953i \(0.0916460\pi\)
\(710\) 2218.89 0.117287
\(711\) 2750.42 0.145076
\(712\) 6623.63 0.348639
\(713\) 2171.10 0.114037
\(714\) 3794.72 0.198899
\(715\) 5227.71 0.273434
\(716\) −2127.38 −0.111039
\(717\) −15130.3 −0.788079
\(718\) 9375.89 0.487333
\(719\) −5039.30 −0.261383 −0.130691 0.991423i \(-0.541720\pi\)
−0.130691 + 0.991423i \(0.541720\pi\)
\(720\) −186.359 −0.00964607
\(721\) −12936.8 −0.668227
\(722\) −731.241 −0.0376925
\(723\) 2958.26 0.152170
\(724\) −1990.08 −0.102156
\(725\) 17498.3 0.896371
\(726\) −6429.53 −0.328681
\(727\) 8312.00 0.424037 0.212019 0.977266i \(-0.431996\pi\)
0.212019 + 0.977266i \(0.431996\pi\)
\(728\) 4615.02 0.234950
\(729\) 729.000 0.0370370
\(730\) 295.108 0.0149622
\(731\) −23213.8 −1.17455
\(732\) 4762.01 0.240449
\(733\) −34034.7 −1.71501 −0.857504 0.514478i \(-0.827986\pi\)
−0.857504 + 0.514478i \(0.827986\pi\)
\(734\) −21605.4 −1.08647
\(735\) 190.241 0.00954713
\(736\) 736.000 0.0368605
\(737\) 45463.7 2.27229
\(738\) 675.124 0.0336743
\(739\) 10630.7 0.529170 0.264585 0.964362i \(-0.414765\pi\)
0.264585 + 0.964362i \(0.414765\pi\)
\(740\) −2304.14 −0.114462
\(741\) 19922.4 0.987676
\(742\) −7257.85 −0.359089
\(743\) −15072.4 −0.744216 −0.372108 0.928189i \(-0.621365\pi\)
−0.372108 + 0.928189i \(0.621365\pi\)
\(744\) −2265.49 −0.111636
\(745\) −100.142 −0.00492472
\(746\) 13711.8 0.672954
\(747\) −11110.8 −0.544205
\(748\) 17714.5 0.865919
\(749\) 11168.0 0.544819
\(750\) −1928.23 −0.0938786
\(751\) −23636.4 −1.14848 −0.574238 0.818689i \(-0.694701\pi\)
−0.574238 + 0.818689i \(0.694701\pi\)
\(752\) −2498.65 −0.121166
\(753\) 8754.20 0.423666
\(754\) −23386.1 −1.12954
\(755\) −2191.66 −0.105646
\(756\) −756.000 −0.0363696
\(757\) 31193.3 1.49768 0.748838 0.662753i \(-0.230612\pi\)
0.748838 + 0.662753i \(0.230612\pi\)
\(758\) 14696.8 0.704235
\(759\) 3382.12 0.161743
\(760\) 834.281 0.0398191
\(761\) 19915.8 0.948680 0.474340 0.880342i \(-0.342687\pi\)
0.474340 + 0.880342i \(0.342687\pi\)
\(762\) 5579.83 0.265270
\(763\) −982.410 −0.0466129
\(764\) 4318.16 0.204484
\(765\) 1052.35 0.0497356
\(766\) −19835.0 −0.935596
\(767\) −51798.7 −2.43852
\(768\) −768.000 −0.0360844
\(769\) −36684.1 −1.72024 −0.860119 0.510093i \(-0.829611\pi\)
−0.860119 + 0.510093i \(0.829611\pi\)
\(770\) 888.085 0.0415641
\(771\) 7447.77 0.347892
\(772\) −7046.82 −0.328524
\(773\) 18762.4 0.873008 0.436504 0.899702i \(-0.356217\pi\)
0.436504 + 0.899702i \(0.356217\pi\)
\(774\) 4624.75 0.214772
\(775\) −11641.4 −0.539574
\(776\) −10751.2 −0.497353
\(777\) −9347.20 −0.431569
\(778\) −9562.81 −0.440673
\(779\) −3022.36 −0.139008
\(780\) 1279.83 0.0587504
\(781\) 42020.2 1.92523
\(782\) −4156.12 −0.190054
\(783\) 3830.95 0.174849
\(784\) 784.000 0.0357143
\(785\) 3574.13 0.162505
\(786\) 10825.6 0.491266
\(787\) 8865.12 0.401534 0.200767 0.979639i \(-0.435657\pi\)
0.200767 + 0.979639i \(0.435657\pi\)
\(788\) 10990.4 0.496849
\(789\) −16706.3 −0.753817
\(790\) −790.994 −0.0356232
\(791\) −8588.56 −0.386061
\(792\) −3529.17 −0.158338
\(793\) −32703.5 −1.46448
\(794\) 10825.2 0.483845
\(795\) −2012.74 −0.0897919
\(796\) −7642.08 −0.340284
\(797\) −7271.07 −0.323155 −0.161578 0.986860i \(-0.551658\pi\)
−0.161578 + 0.986860i \(0.551658\pi\)
\(798\) 3384.42 0.150134
\(799\) 14109.6 0.624735
\(800\) −3946.41 −0.174408
\(801\) 7451.58 0.328700
\(802\) −3942.12 −0.173568
\(803\) 5588.60 0.245601
\(804\) 11130.3 0.488228
\(805\) −208.359 −0.00912260
\(806\) 15558.5 0.679930
\(807\) 7996.87 0.348827
\(808\) 11042.1 0.480766
\(809\) 4495.05 0.195349 0.0976746 0.995218i \(-0.468860\pi\)
0.0976746 + 0.995218i \(0.468860\pi\)
\(810\) −209.653 −0.00909440
\(811\) 20649.3 0.894073 0.447037 0.894516i \(-0.352479\pi\)
0.447037 + 0.894516i \(0.352479\pi\)
\(812\) −3972.84 −0.171699
\(813\) 10905.6 0.470448
\(814\) −43634.7 −1.87886
\(815\) 4377.12 0.188127
\(816\) 4336.82 0.186053
\(817\) −20703.9 −0.886581
\(818\) −1297.46 −0.0554580
\(819\) 5191.89 0.221513
\(820\) −194.159 −0.00826869
\(821\) −31424.8 −1.33585 −0.667926 0.744228i \(-0.732818\pi\)
−0.667926 + 0.744228i \(0.732818\pi\)
\(822\) −4150.57 −0.176117
\(823\) 11977.4 0.507299 0.253650 0.967296i \(-0.418369\pi\)
0.253650 + 0.967296i \(0.418369\pi\)
\(824\) −14784.9 −0.625069
\(825\) −18134.8 −0.765300
\(826\) −8799.58 −0.370674
\(827\) −21289.6 −0.895180 −0.447590 0.894239i \(-0.647718\pi\)
−0.447590 + 0.894239i \(0.647718\pi\)
\(828\) 828.000 0.0347524
\(829\) −3264.10 −0.136751 −0.0683757 0.997660i \(-0.521782\pi\)
−0.0683757 + 0.997660i \(0.521782\pi\)
\(830\) 3195.35 0.133629
\(831\) 11189.5 0.467099
\(832\) 5274.30 0.219776
\(833\) −4427.17 −0.184144
\(834\) −11446.3 −0.475242
\(835\) 1291.05 0.0535073
\(836\) 15799.2 0.653621
\(837\) −2548.68 −0.105251
\(838\) −26614.3 −1.09711
\(839\) −43345.5 −1.78361 −0.891807 0.452416i \(-0.850562\pi\)
−0.891807 + 0.452416i \(0.850562\pi\)
\(840\) 217.418 0.00893053
\(841\) −4257.02 −0.174547
\(842\) 18806.1 0.769718
\(843\) −6286.37 −0.256837
\(844\) 10315.6 0.420708
\(845\) −5946.09 −0.242073
\(846\) −2810.98 −0.114236
\(847\) 7501.12 0.304299
\(848\) −8294.69 −0.335897
\(849\) −25736.4 −1.04037
\(850\) 22285.0 0.899256
\(851\) 10237.4 0.412378
\(852\) 10287.3 0.413657
\(853\) 1295.84 0.0520148 0.0260074 0.999662i \(-0.491721\pi\)
0.0260074 + 0.999662i \(0.491721\pi\)
\(854\) −5555.68 −0.222613
\(855\) 938.566 0.0375418
\(856\) 12763.4 0.509631
\(857\) −35943.9 −1.43270 −0.716348 0.697743i \(-0.754188\pi\)
−0.716348 + 0.697743i \(0.754188\pi\)
\(858\) 24236.8 0.964373
\(859\) 14368.5 0.570718 0.285359 0.958421i \(-0.407887\pi\)
0.285359 + 0.958421i \(0.407887\pi\)
\(860\) −1330.03 −0.0527370
\(861\) −787.645 −0.0311764
\(862\) −7749.10 −0.306190
\(863\) −56.2780 −0.00221984 −0.00110992 0.999999i \(-0.500353\pi\)
−0.00110992 + 0.999999i \(0.500353\pi\)
\(864\) −864.000 −0.0340207
\(865\) 544.142 0.0213889
\(866\) −18469.4 −0.724729
\(867\) −9750.59 −0.381946
\(868\) 2643.08 0.103355
\(869\) −14979.5 −0.584745
\(870\) −1101.75 −0.0429341
\(871\) −76438.2 −2.97360
\(872\) −1122.75 −0.0436024
\(873\) −12095.1 −0.468909
\(874\) −3706.75 −0.143458
\(875\) 2249.60 0.0869147
\(876\) 1368.19 0.0527702
\(877\) 3184.12 0.122600 0.0612999 0.998119i \(-0.480475\pi\)
0.0612999 + 0.998119i \(0.480475\pi\)
\(878\) −35279.1 −1.35605
\(879\) 11448.7 0.439312
\(880\) 1014.95 0.0388797
\(881\) 33026.3 1.26298 0.631490 0.775384i \(-0.282444\pi\)
0.631490 + 0.775384i \(0.282444\pi\)
\(882\) 882.000 0.0336718
\(883\) 19095.2 0.727751 0.363875 0.931448i \(-0.381453\pi\)
0.363875 + 0.931448i \(0.381453\pi\)
\(884\) −29783.5 −1.13317
\(885\) −2440.29 −0.0926887
\(886\) −34480.8 −1.30746
\(887\) 38429.8 1.45473 0.727366 0.686250i \(-0.240744\pi\)
0.727366 + 0.686250i \(0.240744\pi\)
\(888\) −10682.5 −0.403696
\(889\) −6509.81 −0.245593
\(890\) −2143.00 −0.0807119
\(891\) −3970.31 −0.149282
\(892\) 1578.82 0.0592632
\(893\) 12584.1 0.471568
\(894\) −464.281 −0.0173690
\(895\) 688.290 0.0257061
\(896\) 896.000 0.0334077
\(897\) −5686.36 −0.211663
\(898\) −18162.9 −0.674947
\(899\) −13393.5 −0.496885
\(900\) −4439.71 −0.164434
\(901\) 46839.3 1.73190
\(902\) −3676.89 −0.135728
\(903\) −5395.54 −0.198840
\(904\) −9815.50 −0.361127
\(905\) 643.870 0.0236497
\(906\) −10161.0 −0.372602
\(907\) 461.488 0.0168946 0.00844732 0.999964i \(-0.497311\pi\)
0.00844732 + 0.999964i \(0.497311\pi\)
\(908\) −5989.77 −0.218918
\(909\) 12422.3 0.453271
\(910\) −1493.14 −0.0543923
\(911\) −11511.9 −0.418667 −0.209333 0.977844i \(-0.567129\pi\)
−0.209333 + 0.977844i \(0.567129\pi\)
\(912\) 3867.91 0.140438
\(913\) 60511.9 2.19349
\(914\) 2157.18 0.0780669
\(915\) −1540.70 −0.0556654
\(916\) −12611.1 −0.454893
\(917\) −12629.8 −0.454824
\(918\) 4878.92 0.175412
\(919\) −30932.9 −1.11032 −0.555159 0.831744i \(-0.687343\pi\)
−0.555159 + 0.831744i \(0.687343\pi\)
\(920\) −238.125 −0.00853341
\(921\) −18529.6 −0.662943
\(922\) 17368.9 0.620404
\(923\) −70648.7 −2.51942
\(924\) 4117.36 0.146592
\(925\) −54892.6 −1.95120
\(926\) −37801.9 −1.34152
\(927\) −16633.0 −0.589321
\(928\) −4540.39 −0.160610
\(929\) −37586.9 −1.32743 −0.663717 0.747984i \(-0.731022\pi\)
−0.663717 + 0.747984i \(0.731022\pi\)
\(930\) 732.976 0.0258443
\(931\) −3948.49 −0.138997
\(932\) 22119.6 0.777416
\(933\) −5909.46 −0.207360
\(934\) 1619.98 0.0567532
\(935\) −5731.35 −0.200465
\(936\) 5933.59 0.207207
\(937\) −22224.0 −0.774843 −0.387421 0.921903i \(-0.626634\pi\)
−0.387421 + 0.921903i \(0.626634\pi\)
\(938\) −12985.3 −0.452011
\(939\) −7971.89 −0.277053
\(940\) 808.412 0.0280505
\(941\) −52898.1 −1.83255 −0.916275 0.400549i \(-0.868819\pi\)
−0.916275 + 0.400549i \(0.868819\pi\)
\(942\) 16570.5 0.573137
\(943\) 862.658 0.0297901
\(944\) −10056.7 −0.346733
\(945\) 244.596 0.00841978
\(946\) −25187.5 −0.865663
\(947\) −1594.40 −0.0547107 −0.0273554 0.999626i \(-0.508709\pi\)
−0.0273554 + 0.999626i \(0.508709\pi\)
\(948\) −3667.23 −0.125639
\(949\) −9396.12 −0.321403
\(950\) 19875.5 0.678784
\(951\) −9929.86 −0.338589
\(952\) −5059.62 −0.172251
\(953\) −16262.4 −0.552769 −0.276385 0.961047i \(-0.589136\pi\)
−0.276385 + 0.961047i \(0.589136\pi\)
\(954\) −9331.52 −0.316687
\(955\) −1397.09 −0.0473391
\(956\) 20173.8 0.682496
\(957\) −20864.3 −0.704752
\(958\) −15227.5 −0.513548
\(959\) 4842.34 0.163052
\(960\) 248.478 0.00835374
\(961\) −20880.5 −0.700899
\(962\) 73363.0 2.45875
\(963\) 14358.8 0.480485
\(964\) −3944.34 −0.131783
\(965\) 2279.92 0.0760552
\(966\) −966.000 −0.0321745
\(967\) −12443.3 −0.413806 −0.206903 0.978361i \(-0.566339\pi\)
−0.206903 + 0.978361i \(0.566339\pi\)
\(968\) 8572.71 0.284646
\(969\) −21841.7 −0.724104
\(970\) 3478.43 0.115140
\(971\) 22843.1 0.754963 0.377481 0.926017i \(-0.376790\pi\)
0.377481 + 0.926017i \(0.376790\pi\)
\(972\) −972.000 −0.0320750
\(973\) 13354.0 0.439989
\(974\) 14916.1 0.490701
\(975\) 30490.0 1.00150
\(976\) −6349.34 −0.208235
\(977\) −7472.82 −0.244705 −0.122352 0.992487i \(-0.539044\pi\)
−0.122352 + 0.992487i \(0.539044\pi\)
\(978\) 20293.3 0.663506
\(979\) −40583.2 −1.32487
\(980\) −253.655 −0.00826806
\(981\) −1263.10 −0.0411087
\(982\) 3829.10 0.124431
\(983\) 6369.09 0.206655 0.103328 0.994647i \(-0.467051\pi\)
0.103328 + 0.994647i \(0.467051\pi\)
\(984\) −900.165 −0.0291628
\(985\) −3555.83 −0.115023
\(986\) 25639.1 0.828110
\(987\) 3279.48 0.105762
\(988\) −26563.2 −0.855352
\(989\) 5909.41 0.189998
\(990\) 1141.82 0.0366561
\(991\) 48476.3 1.55389 0.776943 0.629571i \(-0.216769\pi\)
0.776943 + 0.629571i \(0.216769\pi\)
\(992\) 3020.66 0.0966795
\(993\) −30987.6 −0.990294
\(994\) −12001.8 −0.382972
\(995\) 2472.51 0.0787778
\(996\) 14814.3 0.471296
\(997\) 10534.0 0.334619 0.167310 0.985904i \(-0.446492\pi\)
0.167310 + 0.985904i \(0.446492\pi\)
\(998\) 3597.06 0.114091
\(999\) −12017.8 −0.380608
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.k.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
966.4.a.k.1.3 4 1.1 even 1 trivial