Properties

Label 1859.4.a.i.1.2
Level $1859$
Weight $4$
Character 1859.1
Self dual yes
Analytic conductor $109.685$
Analytic rank $0$
Dimension $17$
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] = [1859,4,Mod(1,1859)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1859, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1859.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1859.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: \(109.684550701\)
Analytic rank: \(0\)
Dimension: \(17\)
Coefficient field: \(\mathbb{Q}[x]/(x^{17} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{17} - 4 x^{16} - 99 x^{15} + 375 x^{14} + 3949 x^{13} - 13998 x^{12} - 81750 x^{11} + 267574 x^{10} + 941923 x^{9} - 2799440 x^{8} - 6021311 x^{7} + 15765187 x^{6} + \cdots + 2596992 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{8}\cdot 3\cdot 5 \)
Twist minimal: no (minimal twist has level 143)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-4.61453\) of defining polynomial
Character \(\chi\) \(=\) 1859.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.61453 q^{2} +3.68758 q^{3} +13.2939 q^{4} +19.7910 q^{5} -17.0165 q^{6} -18.7869 q^{7} -24.4287 q^{8} -13.4017 q^{9} +O(q^{10})\) \(q-4.61453 q^{2} +3.68758 q^{3} +13.2939 q^{4} +19.7910 q^{5} -17.0165 q^{6} -18.7869 q^{7} -24.4287 q^{8} -13.4017 q^{9} -91.3259 q^{10} -11.0000 q^{11} +49.0223 q^{12} +86.6927 q^{14} +72.9808 q^{15} +6.37610 q^{16} +67.7750 q^{17} +61.8427 q^{18} +129.430 q^{19} +263.099 q^{20} -69.2783 q^{21} +50.7598 q^{22} -103.682 q^{23} -90.0830 q^{24} +266.682 q^{25} -148.985 q^{27} -249.751 q^{28} +269.826 q^{29} -336.772 q^{30} +75.1728 q^{31} +166.007 q^{32} -40.5634 q^{33} -312.750 q^{34} -371.811 q^{35} -178.161 q^{36} -9.87062 q^{37} -597.258 q^{38} -483.468 q^{40} +162.811 q^{41} +319.687 q^{42} -231.244 q^{43} -146.233 q^{44} -265.233 q^{45} +478.444 q^{46} +42.7253 q^{47} +23.5124 q^{48} +9.94786 q^{49} -1230.61 q^{50} +249.926 q^{51} -717.060 q^{53} +687.494 q^{54} -217.701 q^{55} +458.940 q^{56} +477.283 q^{57} -1245.12 q^{58} +583.309 q^{59} +970.198 q^{60} -341.669 q^{61} -346.887 q^{62} +251.777 q^{63} -817.054 q^{64} +187.181 q^{66} -697.923 q^{67} +900.993 q^{68} -382.336 q^{69} +1715.73 q^{70} +620.263 q^{71} +327.387 q^{72} +790.345 q^{73} +45.5483 q^{74} +983.412 q^{75} +1720.62 q^{76} +206.656 q^{77} -119.274 q^{79} +126.189 q^{80} -187.547 q^{81} -751.298 q^{82} +98.6344 q^{83} -920.977 q^{84} +1341.33 q^{85} +1067.08 q^{86} +995.007 q^{87} +268.716 q^{88} +455.102 q^{89} +1223.93 q^{90} -1378.34 q^{92} +277.206 q^{93} -197.157 q^{94} +2561.54 q^{95} +612.165 q^{96} +346.559 q^{97} -45.9047 q^{98} +147.419 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 17 q + 4 q^{2} - 6 q^{3} + 78 q^{4} + 16 q^{5} + 14 q^{6} - 6 q^{7} + 63 q^{8} + 135 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 17 q + 4 q^{2} - 6 q^{3} + 78 q^{4} + 16 q^{5} + 14 q^{6} - 6 q^{7} + 63 q^{8} + 135 q^{9} + 2 q^{10} - 187 q^{11} - 95 q^{12} - 60 q^{14} - 28 q^{15} + 350 q^{16} + 118 q^{17} + 478 q^{18} + 403 q^{19} + 98 q^{20} + 220 q^{21} - 44 q^{22} - 215 q^{23} + 26 q^{24} + 319 q^{25} - 384 q^{27} - 396 q^{28} - 7 q^{29} - 1269 q^{30} + 682 q^{31} + 813 q^{32} + 66 q^{33} + 738 q^{34} + 10 q^{35} + 560 q^{36} + 1084 q^{37} + 410 q^{38} + 95 q^{40} + 240 q^{41} + 393 q^{42} - 435 q^{43} - 858 q^{44} + 1242 q^{45} + 1671 q^{46} + 549 q^{47} + 894 q^{48} + 403 q^{49} - 651 q^{50} + 1552 q^{51} - 566 q^{53} + 311 q^{54} - 176 q^{55} - 1925 q^{56} - 534 q^{57} + 618 q^{58} + 2010 q^{59} - 411 q^{60} + 460 q^{61} - 823 q^{62} + 820 q^{63} + 3171 q^{64} - 154 q^{66} - 232 q^{67} + 1795 q^{68} - 1608 q^{69} + 207 q^{70} + 489 q^{71} + 2556 q^{72} + 290 q^{73} + 2653 q^{74} - 2852 q^{75} + 2421 q^{76} + 66 q^{77} - 732 q^{79} + 4915 q^{80} + 2393 q^{81} - 1772 q^{82} - 117 q^{83} + 4161 q^{84} + 4858 q^{85} + 1034 q^{86} + 3032 q^{87} - 693 q^{88} + 4113 q^{89} + 15145 q^{90} - 3554 q^{92} + 802 q^{93} + 2325 q^{94} - 3924 q^{95} + 2601 q^{96} + 2793 q^{97} + 533 q^{98} - 1485 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.61453 −1.63148 −0.815741 0.578417i \(-0.803671\pi\)
−0.815741 + 0.578417i \(0.803671\pi\)
\(3\) 3.68758 0.709676 0.354838 0.934928i \(-0.384536\pi\)
0.354838 + 0.934928i \(0.384536\pi\)
\(4\) 13.2939 1.66173
\(5\) 19.7910 1.77016 0.885079 0.465442i \(-0.154104\pi\)
0.885079 + 0.465442i \(0.154104\pi\)
\(6\) −17.0165 −1.15782
\(7\) −18.7869 −1.01440 −0.507199 0.861829i \(-0.669319\pi\)
−0.507199 + 0.861829i \(0.669319\pi\)
\(8\) −24.4287 −1.07961
\(9\) −13.4017 −0.496360
\(10\) −91.3259 −2.88798
\(11\) −11.0000 −0.301511
\(12\) 49.0223 1.17929
\(13\) 0 0
\(14\) 86.6927 1.65497
\(15\) 72.9808 1.25624
\(16\) 6.37610 0.0996265
\(17\) 67.7750 0.966933 0.483466 0.875363i \(-0.339378\pi\)
0.483466 + 0.875363i \(0.339378\pi\)
\(18\) 61.8427 0.809803
\(19\) 129.430 1.56280 0.781401 0.624029i \(-0.214505\pi\)
0.781401 + 0.624029i \(0.214505\pi\)
\(20\) 263.099 2.94153
\(21\) −69.2783 −0.719893
\(22\) 50.7598 0.491910
\(23\) −103.682 −0.939966 −0.469983 0.882676i \(-0.655740\pi\)
−0.469983 + 0.882676i \(0.655740\pi\)
\(24\) −90.0830 −0.766171
\(25\) 266.682 2.13346
\(26\) 0 0
\(27\) −148.985 −1.06193
\(28\) −249.751 −1.68566
\(29\) 269.826 1.72778 0.863888 0.503684i \(-0.168022\pi\)
0.863888 + 0.503684i \(0.168022\pi\)
\(30\) −336.772 −2.04953
\(31\) 75.1728 0.435530 0.217765 0.976001i \(-0.430123\pi\)
0.217765 + 0.976001i \(0.430123\pi\)
\(32\) 166.007 0.917069
\(33\) −40.5634 −0.213975
\(34\) −312.750 −1.57753
\(35\) −371.811 −1.79564
\(36\) −178.161 −0.824819
\(37\) −9.87062 −0.0438573 −0.0219286 0.999760i \(-0.506981\pi\)
−0.0219286 + 0.999760i \(0.506981\pi\)
\(38\) −597.258 −2.54968
\(39\) 0 0
\(40\) −483.468 −1.91108
\(41\) 162.811 0.620168 0.310084 0.950709i \(-0.399643\pi\)
0.310084 + 0.950709i \(0.399643\pi\)
\(42\) 319.687 1.17449
\(43\) −231.244 −0.820101 −0.410051 0.912063i \(-0.634489\pi\)
−0.410051 + 0.912063i \(0.634489\pi\)
\(44\) −146.233 −0.501032
\(45\) −265.233 −0.878636
\(46\) 478.444 1.53354
\(47\) 42.7253 0.132598 0.0662991 0.997800i \(-0.478881\pi\)
0.0662991 + 0.997800i \(0.478881\pi\)
\(48\) 23.5124 0.0707025
\(49\) 9.94786 0.0290025
\(50\) −1230.61 −3.48070
\(51\) 249.926 0.686209
\(52\) 0 0
\(53\) −717.060 −1.85841 −0.929205 0.369564i \(-0.879507\pi\)
−0.929205 + 0.369564i \(0.879507\pi\)
\(54\) 687.494 1.73252
\(55\) −217.701 −0.533722
\(56\) 458.940 1.09515
\(57\) 477.283 1.10908
\(58\) −1245.12 −2.81884
\(59\) 583.309 1.28712 0.643562 0.765394i \(-0.277456\pi\)
0.643562 + 0.765394i \(0.277456\pi\)
\(60\) 970.198 2.08753
\(61\) −341.669 −0.717152 −0.358576 0.933501i \(-0.616738\pi\)
−0.358576 + 0.933501i \(0.616738\pi\)
\(62\) −346.887 −0.710559
\(63\) 251.777 0.503507
\(64\) −817.054 −1.59581
\(65\) 0 0
\(66\) 187.181 0.349097
\(67\) −697.923 −1.27261 −0.636305 0.771438i \(-0.719538\pi\)
−0.636305 + 0.771438i \(0.719538\pi\)
\(68\) 900.993 1.60679
\(69\) −382.336 −0.667071
\(70\) 1715.73 2.92956
\(71\) 620.263 1.03678 0.518392 0.855143i \(-0.326531\pi\)
0.518392 + 0.855143i \(0.326531\pi\)
\(72\) 327.387 0.535875
\(73\) 790.345 1.26716 0.633581 0.773676i \(-0.281584\pi\)
0.633581 + 0.773676i \(0.281584\pi\)
\(74\) 45.5483 0.0715524
\(75\) 983.412 1.51406
\(76\) 1720.62 2.59696
\(77\) 206.656 0.305852
\(78\) 0 0
\(79\) −119.274 −0.169866 −0.0849328 0.996387i \(-0.527068\pi\)
−0.0849328 + 0.996387i \(0.527068\pi\)
\(80\) 126.189 0.176355
\(81\) −187.547 −0.257266
\(82\) −751.298 −1.01179
\(83\) 98.6344 0.130440 0.0652201 0.997871i \(-0.479225\pi\)
0.0652201 + 0.997871i \(0.479225\pi\)
\(84\) −920.977 −1.19627
\(85\) 1341.33 1.71162
\(86\) 1067.08 1.33798
\(87\) 995.007 1.22616
\(88\) 268.716 0.325514
\(89\) 455.102 0.542030 0.271015 0.962575i \(-0.412641\pi\)
0.271015 + 0.962575i \(0.412641\pi\)
\(90\) 1223.93 1.43348
\(91\) 0 0
\(92\) −1378.34 −1.56197
\(93\) 277.206 0.309085
\(94\) −197.157 −0.216332
\(95\) 2561.54 2.76641
\(96\) 612.165 0.650821
\(97\) 346.559 0.362761 0.181380 0.983413i \(-0.441943\pi\)
0.181380 + 0.983413i \(0.441943\pi\)
\(98\) −45.9047 −0.0473171
\(99\) 147.419 0.149658
\(100\) 3545.24 3.54524
\(101\) 1584.30 1.56083 0.780414 0.625264i \(-0.215009\pi\)
0.780414 + 0.625264i \(0.215009\pi\)
\(102\) −1153.29 −1.11954
\(103\) −430.743 −0.412062 −0.206031 0.978546i \(-0.566055\pi\)
−0.206031 + 0.978546i \(0.566055\pi\)
\(104\) 0 0
\(105\) −1371.08 −1.27432
\(106\) 3308.89 3.03196
\(107\) 446.381 0.403302 0.201651 0.979457i \(-0.435369\pi\)
0.201651 + 0.979457i \(0.435369\pi\)
\(108\) −1980.58 −1.76465
\(109\) −1219.62 −1.07173 −0.535865 0.844303i \(-0.680015\pi\)
−0.535865 + 0.844303i \(0.680015\pi\)
\(110\) 1004.59 0.870759
\(111\) −36.3987 −0.0311245
\(112\) −119.787 −0.101061
\(113\) −509.751 −0.424366 −0.212183 0.977230i \(-0.568057\pi\)
−0.212183 + 0.977230i \(0.568057\pi\)
\(114\) −2202.44 −1.80945
\(115\) −2051.97 −1.66389
\(116\) 3587.04 2.87110
\(117\) 0 0
\(118\) −2691.69 −2.09992
\(119\) −1273.28 −0.980854
\(120\) −1782.83 −1.35624
\(121\) 121.000 0.0909091
\(122\) 1576.64 1.17002
\(123\) 600.381 0.440118
\(124\) 999.337 0.723735
\(125\) 2804.02 2.00640
\(126\) −1161.83 −0.821463
\(127\) 796.850 0.556764 0.278382 0.960470i \(-0.410202\pi\)
0.278382 + 0.960470i \(0.410202\pi\)
\(128\) 2442.26 1.68646
\(129\) −852.731 −0.582006
\(130\) 0 0
\(131\) 1834.53 1.22354 0.611770 0.791035i \(-0.290458\pi\)
0.611770 + 0.791035i \(0.290458\pi\)
\(132\) −539.245 −0.355570
\(133\) −2431.59 −1.58530
\(134\) 3220.58 2.07624
\(135\) −2948.55 −1.87978
\(136\) −1655.66 −1.04391
\(137\) −387.717 −0.241788 −0.120894 0.992665i \(-0.538576\pi\)
−0.120894 + 0.992665i \(0.538576\pi\)
\(138\) 1764.30 1.08831
\(139\) −2736.11 −1.66960 −0.834798 0.550556i \(-0.814416\pi\)
−0.834798 + 0.550556i \(0.814416\pi\)
\(140\) −4942.81 −2.98388
\(141\) 157.553 0.0941018
\(142\) −2862.22 −1.69149
\(143\) 0 0
\(144\) −85.4508 −0.0494507
\(145\) 5340.12 3.05843
\(146\) −3647.07 −2.06735
\(147\) 36.6835 0.0205824
\(148\) −131.219 −0.0728792
\(149\) 1496.72 0.822929 0.411465 0.911426i \(-0.365017\pi\)
0.411465 + 0.911426i \(0.365017\pi\)
\(150\) −4537.98 −2.47017
\(151\) −2527.52 −1.36216 −0.681080 0.732209i \(-0.738490\pi\)
−0.681080 + 0.732209i \(0.738490\pi\)
\(152\) −3161.81 −1.68721
\(153\) −908.303 −0.479947
\(154\) −953.620 −0.498993
\(155\) 1487.74 0.770956
\(156\) 0 0
\(157\) 1946.37 0.989408 0.494704 0.869061i \(-0.335276\pi\)
0.494704 + 0.869061i \(0.335276\pi\)
\(158\) 550.394 0.277133
\(159\) −2644.22 −1.31887
\(160\) 3285.44 1.62336
\(161\) 1947.87 0.953499
\(162\) 865.440 0.419725
\(163\) 962.612 0.462562 0.231281 0.972887i \(-0.425708\pi\)
0.231281 + 0.972887i \(0.425708\pi\)
\(164\) 2164.40 1.03055
\(165\) −802.789 −0.378770
\(166\) −455.151 −0.212811
\(167\) −1302.91 −0.603727 −0.301863 0.953351i \(-0.597609\pi\)
−0.301863 + 0.953351i \(0.597609\pi\)
\(168\) 1692.38 0.777202
\(169\) 0 0
\(170\) −6189.62 −2.79248
\(171\) −1734.58 −0.775713
\(172\) −3074.13 −1.36279
\(173\) 1703.21 0.748514 0.374257 0.927325i \(-0.377898\pi\)
0.374257 + 0.927325i \(0.377898\pi\)
\(174\) −4591.49 −2.00046
\(175\) −5010.13 −2.16417
\(176\) −70.1371 −0.0300385
\(177\) 2151.00 0.913441
\(178\) −2100.08 −0.884313
\(179\) 959.537 0.400666 0.200333 0.979728i \(-0.435798\pi\)
0.200333 + 0.979728i \(0.435798\pi\)
\(180\) −3525.98 −1.46006
\(181\) 3296.59 1.35378 0.676888 0.736086i \(-0.263328\pi\)
0.676888 + 0.736086i \(0.263328\pi\)
\(182\) 0 0
\(183\) −1259.93 −0.508945
\(184\) 2532.82 1.01479
\(185\) −195.349 −0.0776343
\(186\) −1279.17 −0.504267
\(187\) −745.525 −0.291541
\(188\) 567.984 0.220343
\(189\) 2798.96 1.07722
\(190\) −11820.3 −4.51334
\(191\) 1052.02 0.398543 0.199271 0.979944i \(-0.436143\pi\)
0.199271 + 0.979944i \(0.436143\pi\)
\(192\) −3012.95 −1.13251
\(193\) 1543.16 0.575540 0.287770 0.957700i \(-0.407086\pi\)
0.287770 + 0.957700i \(0.407086\pi\)
\(194\) −1599.21 −0.591838
\(195\) 0 0
\(196\) 132.246 0.0481944
\(197\) −2564.36 −0.927427 −0.463713 0.885985i \(-0.653483\pi\)
−0.463713 + 0.885985i \(0.653483\pi\)
\(198\) −680.269 −0.244165
\(199\) 618.993 0.220499 0.110249 0.993904i \(-0.464835\pi\)
0.110249 + 0.993904i \(0.464835\pi\)
\(200\) −6514.70 −2.30330
\(201\) −2573.65 −0.903140
\(202\) −7310.79 −2.54646
\(203\) −5069.20 −1.75265
\(204\) 3322.49 1.14030
\(205\) 3222.20 1.09779
\(206\) 1987.68 0.672271
\(207\) 1389.52 0.466562
\(208\) 0 0
\(209\) −1423.73 −0.471203
\(210\) 6326.90 2.07904
\(211\) −102.673 −0.0334990 −0.0167495 0.999860i \(-0.505332\pi\)
−0.0167495 + 0.999860i \(0.505332\pi\)
\(212\) −9532.51 −3.08818
\(213\) 2287.27 0.735780
\(214\) −2059.84 −0.657980
\(215\) −4576.54 −1.45171
\(216\) 3639.51 1.14647
\(217\) −1412.26 −0.441800
\(218\) 5627.98 1.74851
\(219\) 2914.46 0.899274
\(220\) −2894.08 −0.886905
\(221\) 0 0
\(222\) 167.963 0.0507790
\(223\) 4471.33 1.34270 0.671350 0.741140i \(-0.265715\pi\)
0.671350 + 0.741140i \(0.265715\pi\)
\(224\) −3118.76 −0.930272
\(225\) −3574.00 −1.05896
\(226\) 2352.26 0.692345
\(227\) 310.802 0.0908752 0.0454376 0.998967i \(-0.485532\pi\)
0.0454376 + 0.998967i \(0.485532\pi\)
\(228\) 6344.94 1.84300
\(229\) 4163.95 1.20158 0.600789 0.799408i \(-0.294853\pi\)
0.600789 + 0.799408i \(0.294853\pi\)
\(230\) 9468.86 2.71460
\(231\) 762.061 0.217056
\(232\) −6591.52 −1.86532
\(233\) −1678.18 −0.471849 −0.235925 0.971771i \(-0.575812\pi\)
−0.235925 + 0.971771i \(0.575812\pi\)
\(234\) 0 0
\(235\) 845.574 0.234720
\(236\) 7754.43 2.13886
\(237\) −439.833 −0.120549
\(238\) 5875.60 1.60025
\(239\) 6855.31 1.85537 0.927685 0.373364i \(-0.121796\pi\)
0.927685 + 0.373364i \(0.121796\pi\)
\(240\) 465.333 0.125155
\(241\) 2819.47 0.753602 0.376801 0.926294i \(-0.377024\pi\)
0.376801 + 0.926294i \(0.377024\pi\)
\(242\) −558.358 −0.148317
\(243\) 3330.99 0.879355
\(244\) −4542.11 −1.19172
\(245\) 196.878 0.0513390
\(246\) −2770.47 −0.718045
\(247\) 0 0
\(248\) −1836.38 −0.470201
\(249\) 363.723 0.0925702
\(250\) −12939.2 −3.27340
\(251\) −2693.44 −0.677325 −0.338662 0.940908i \(-0.609974\pi\)
−0.338662 + 0.940908i \(0.609974\pi\)
\(252\) 3347.09 0.836695
\(253\) 1140.50 0.283410
\(254\) −3677.09 −0.908351
\(255\) 4946.28 1.21470
\(256\) −4733.45 −1.15563
\(257\) 1225.71 0.297500 0.148750 0.988875i \(-0.452475\pi\)
0.148750 + 0.988875i \(0.452475\pi\)
\(258\) 3934.95 0.949532
\(259\) 185.438 0.0444887
\(260\) 0 0
\(261\) −3616.14 −0.857600
\(262\) −8465.50 −1.99619
\(263\) 2300.15 0.539291 0.269646 0.962960i \(-0.413093\pi\)
0.269646 + 0.962960i \(0.413093\pi\)
\(264\) 990.913 0.231009
\(265\) −14191.3 −3.28968
\(266\) 11220.6 2.58639
\(267\) 1678.23 0.384666
\(268\) −9278.10 −2.11474
\(269\) −4183.92 −0.948321 −0.474160 0.880438i \(-0.657248\pi\)
−0.474160 + 0.880438i \(0.657248\pi\)
\(270\) 13606.2 3.06683
\(271\) −3308.84 −0.741689 −0.370845 0.928695i \(-0.620932\pi\)
−0.370845 + 0.928695i \(0.620932\pi\)
\(272\) 432.140 0.0963322
\(273\) 0 0
\(274\) 1789.13 0.394473
\(275\) −2933.50 −0.643261
\(276\) −5082.73 −1.10849
\(277\) 656.952 0.142500 0.0712499 0.997458i \(-0.477301\pi\)
0.0712499 + 0.997458i \(0.477301\pi\)
\(278\) 12625.9 2.72392
\(279\) −1007.45 −0.216180
\(280\) 9082.87 1.93859
\(281\) 7566.29 1.60629 0.803144 0.595785i \(-0.203159\pi\)
0.803144 + 0.595785i \(0.203159\pi\)
\(282\) −727.033 −0.153525
\(283\) 2773.07 0.582479 0.291240 0.956650i \(-0.405932\pi\)
0.291240 + 0.956650i \(0.405932\pi\)
\(284\) 8245.70 1.72286
\(285\) 9445.89 1.96325
\(286\) 0 0
\(287\) −3058.72 −0.629097
\(288\) −2224.78 −0.455197
\(289\) −319.546 −0.0650409
\(290\) −24642.1 −4.98978
\(291\) 1277.97 0.257442
\(292\) 10506.7 2.10569
\(293\) 4758.11 0.948709 0.474354 0.880334i \(-0.342682\pi\)
0.474354 + 0.880334i \(0.342682\pi\)
\(294\) −169.277 −0.0335798
\(295\) 11544.2 2.27841
\(296\) 241.127 0.0473487
\(297\) 1638.83 0.320184
\(298\) −6906.68 −1.34259
\(299\) 0 0
\(300\) 13073.4 2.51597
\(301\) 4344.36 0.831909
\(302\) 11663.3 2.22234
\(303\) 5842.23 1.10768
\(304\) 825.257 0.155697
\(305\) −6761.96 −1.26947
\(306\) 4191.39 0.783025
\(307\) 769.035 0.142968 0.0714840 0.997442i \(-0.477227\pi\)
0.0714840 + 0.997442i \(0.477227\pi\)
\(308\) 2747.26 0.508245
\(309\) −1588.40 −0.292430
\(310\) −6865.22 −1.25780
\(311\) 804.126 0.146617 0.0733084 0.997309i \(-0.476644\pi\)
0.0733084 + 0.997309i \(0.476644\pi\)
\(312\) 0 0
\(313\) 7233.90 1.30634 0.653170 0.757211i \(-0.273439\pi\)
0.653170 + 0.757211i \(0.273439\pi\)
\(314\) −8981.57 −1.61420
\(315\) 4982.91 0.891286
\(316\) −1585.61 −0.282271
\(317\) −2161.28 −0.382932 −0.191466 0.981499i \(-0.561324\pi\)
−0.191466 + 0.981499i \(0.561324\pi\)
\(318\) 12201.8 2.15171
\(319\) −2968.09 −0.520944
\(320\) −16170.3 −2.82483
\(321\) 1646.07 0.286214
\(322\) −8988.48 −1.55562
\(323\) 8772.11 1.51112
\(324\) −2493.22 −0.427507
\(325\) 0 0
\(326\) −4442.00 −0.754661
\(327\) −4497.46 −0.760581
\(328\) −3977.28 −0.669538
\(329\) −802.675 −0.134507
\(330\) 3704.49 0.617956
\(331\) −3564.76 −0.591955 −0.295978 0.955195i \(-0.595645\pi\)
−0.295978 + 0.955195i \(0.595645\pi\)
\(332\) 1311.23 0.216757
\(333\) 132.283 0.0217690
\(334\) 6012.33 0.984970
\(335\) −13812.6 −2.25272
\(336\) −441.725 −0.0717205
\(337\) 9469.23 1.53063 0.765315 0.643656i \(-0.222583\pi\)
0.765315 + 0.643656i \(0.222583\pi\)
\(338\) 0 0
\(339\) −1879.75 −0.301162
\(340\) 17831.5 2.84426
\(341\) −826.900 −0.131317
\(342\) 8004.29 1.26556
\(343\) 6257.02 0.984978
\(344\) 5648.99 0.885388
\(345\) −7566.80 −1.18082
\(346\) −7859.53 −1.22119
\(347\) 3030.03 0.468763 0.234381 0.972145i \(-0.424694\pi\)
0.234381 + 0.972145i \(0.424694\pi\)
\(348\) 13227.5 2.03755
\(349\) 11320.6 1.73633 0.868165 0.496276i \(-0.165300\pi\)
0.868165 + 0.496276i \(0.165300\pi\)
\(350\) 23119.4 3.53081
\(351\) 0 0
\(352\) −1826.08 −0.276507
\(353\) −9960.80 −1.50187 −0.750935 0.660376i \(-0.770397\pi\)
−0.750935 + 0.660376i \(0.770397\pi\)
\(354\) −9925.85 −1.49026
\(355\) 12275.6 1.83527
\(356\) 6050.07 0.900710
\(357\) −4695.34 −0.696088
\(358\) −4427.81 −0.653679
\(359\) −9822.94 −1.44411 −0.722054 0.691837i \(-0.756802\pi\)
−0.722054 + 0.691837i \(0.756802\pi\)
\(360\) 6479.31 0.948582
\(361\) 9893.08 1.44235
\(362\) −15212.2 −2.20866
\(363\) 446.198 0.0645160
\(364\) 0 0
\(365\) 15641.7 2.24308
\(366\) 5814.00 0.830335
\(367\) −2451.62 −0.348701 −0.174351 0.984684i \(-0.555783\pi\)
−0.174351 + 0.984684i \(0.555783\pi\)
\(368\) −661.087 −0.0936455
\(369\) −2181.96 −0.307827
\(370\) 901.444 0.126659
\(371\) 13471.3 1.88517
\(372\) 3685.14 0.513617
\(373\) 7431.12 1.03155 0.515776 0.856724i \(-0.327504\pi\)
0.515776 + 0.856724i \(0.327504\pi\)
\(374\) 3440.25 0.475644
\(375\) 10340.1 1.42389
\(376\) −1043.72 −0.143154
\(377\) 0 0
\(378\) −12915.9 −1.75747
\(379\) −6225.63 −0.843771 −0.421886 0.906649i \(-0.638632\pi\)
−0.421886 + 0.906649i \(0.638632\pi\)
\(380\) 34052.8 4.59703
\(381\) 2938.45 0.395122
\(382\) −4854.58 −0.650215
\(383\) 5098.87 0.680261 0.340131 0.940378i \(-0.389529\pi\)
0.340131 + 0.940378i \(0.389529\pi\)
\(384\) 9006.04 1.19684
\(385\) 4089.92 0.541407
\(386\) −7120.96 −0.938983
\(387\) 3099.07 0.407066
\(388\) 4607.12 0.602812
\(389\) −2672.32 −0.348308 −0.174154 0.984718i \(-0.555719\pi\)
−0.174154 + 0.984718i \(0.555719\pi\)
\(390\) 0 0
\(391\) −7027.06 −0.908884
\(392\) −243.014 −0.0313113
\(393\) 6764.99 0.868317
\(394\) 11833.3 1.51308
\(395\) −2360.55 −0.300689
\(396\) 1959.77 0.248692
\(397\) −400.284 −0.0506038 −0.0253019 0.999680i \(-0.508055\pi\)
−0.0253019 + 0.999680i \(0.508055\pi\)
\(398\) −2856.36 −0.359740
\(399\) −8966.68 −1.12505
\(400\) 1700.39 0.212549
\(401\) −8939.46 −1.11325 −0.556627 0.830762i \(-0.687905\pi\)
−0.556627 + 0.830762i \(0.687905\pi\)
\(402\) 11876.2 1.47346
\(403\) 0 0
\(404\) 21061.5 2.59368
\(405\) −3711.73 −0.455401
\(406\) 23392.0 2.85942
\(407\) 108.577 0.0132235
\(408\) −6105.38 −0.740836
\(409\) −9481.18 −1.14624 −0.573122 0.819470i \(-0.694268\pi\)
−0.573122 + 0.819470i \(0.694268\pi\)
\(410\) −14868.9 −1.79103
\(411\) −1429.74 −0.171591
\(412\) −5726.24 −0.684737
\(413\) −10958.6 −1.30566
\(414\) −6411.98 −0.761187
\(415\) 1952.07 0.230900
\(416\) 0 0
\(417\) −10089.6 −1.18487
\(418\) 6569.83 0.768759
\(419\) 12413.7 1.44737 0.723687 0.690128i \(-0.242446\pi\)
0.723687 + 0.690128i \(0.242446\pi\)
\(420\) −18227.0 −2.11759
\(421\) 13243.0 1.53307 0.766536 0.642201i \(-0.221979\pi\)
0.766536 + 0.642201i \(0.221979\pi\)
\(422\) 473.786 0.0546529
\(423\) −572.592 −0.0658165
\(424\) 17516.9 2.00635
\(425\) 18074.4 2.06291
\(426\) −10554.7 −1.20041
\(427\) 6418.91 0.727477
\(428\) 5934.14 0.670181
\(429\) 0 0
\(430\) 21118.6 2.36844
\(431\) −6005.50 −0.671171 −0.335585 0.942010i \(-0.608934\pi\)
−0.335585 + 0.942010i \(0.608934\pi\)
\(432\) −949.941 −0.105796
\(433\) −9921.49 −1.10115 −0.550573 0.834787i \(-0.685591\pi\)
−0.550573 + 0.834787i \(0.685591\pi\)
\(434\) 6516.93 0.720790
\(435\) 19692.1 2.17050
\(436\) −16213.5 −1.78093
\(437\) −13419.6 −1.46898
\(438\) −13448.9 −1.46715
\(439\) −4889.28 −0.531555 −0.265777 0.964034i \(-0.585629\pi\)
−0.265777 + 0.964034i \(0.585629\pi\)
\(440\) 5318.15 0.576211
\(441\) −133.319 −0.0143957
\(442\) 0 0
\(443\) −10568.8 −1.13349 −0.566747 0.823892i \(-0.691798\pi\)
−0.566747 + 0.823892i \(0.691798\pi\)
\(444\) −483.880 −0.0517206
\(445\) 9006.90 0.959479
\(446\) −20633.1 −2.19059
\(447\) 5519.30 0.584013
\(448\) 15349.9 1.61878
\(449\) −15760.7 −1.65656 −0.828280 0.560315i \(-0.810680\pi\)
−0.828280 + 0.560315i \(0.810680\pi\)
\(450\) 16492.3 1.72768
\(451\) −1790.93 −0.186988
\(452\) −6776.56 −0.705183
\(453\) −9320.42 −0.966692
\(454\) −1434.21 −0.148261
\(455\) 0 0
\(456\) −11659.4 −1.19737
\(457\) 1098.13 0.112404 0.0562018 0.998419i \(-0.482101\pi\)
0.0562018 + 0.998419i \(0.482101\pi\)
\(458\) −19214.7 −1.96035
\(459\) −10097.4 −1.02682
\(460\) −27278.6 −2.76494
\(461\) −257.041 −0.0259687 −0.0129843 0.999916i \(-0.504133\pi\)
−0.0129843 + 0.999916i \(0.504133\pi\)
\(462\) −3516.55 −0.354123
\(463\) −14489.1 −1.45435 −0.727177 0.686450i \(-0.759168\pi\)
−0.727177 + 0.686450i \(0.759168\pi\)
\(464\) 1720.44 0.172132
\(465\) 5486.17 0.547129
\(466\) 7743.99 0.769814
\(467\) 8855.29 0.877461 0.438730 0.898619i \(-0.355428\pi\)
0.438730 + 0.898619i \(0.355428\pi\)
\(468\) 0 0
\(469\) 13111.8 1.29093
\(470\) −3901.92 −0.382941
\(471\) 7177.40 0.702159
\(472\) −14249.5 −1.38959
\(473\) 2543.68 0.247270
\(474\) 2029.62 0.196674
\(475\) 34516.6 3.33417
\(476\) −16926.9 −1.62992
\(477\) 9609.85 0.922442
\(478\) −31634.0 −3.02700
\(479\) 13509.7 1.28867 0.644336 0.764743i \(-0.277134\pi\)
0.644336 + 0.764743i \(0.277134\pi\)
\(480\) 12115.3 1.15206
\(481\) 0 0
\(482\) −13010.5 −1.22949
\(483\) 7182.92 0.676675
\(484\) 1608.56 0.151067
\(485\) 6858.74 0.642143
\(486\) −15371.0 −1.43465
\(487\) 16750.5 1.55860 0.779298 0.626654i \(-0.215576\pi\)
0.779298 + 0.626654i \(0.215576\pi\)
\(488\) 8346.55 0.774243
\(489\) 3549.71 0.328269
\(490\) −908.497 −0.0837586
\(491\) 4829.42 0.443888 0.221944 0.975059i \(-0.428760\pi\)
0.221944 + 0.975059i \(0.428760\pi\)
\(492\) 7981.39 0.731359
\(493\) 18287.5 1.67064
\(494\) 0 0
\(495\) 2917.56 0.264919
\(496\) 479.309 0.0433903
\(497\) −11652.8 −1.05171
\(498\) −1678.41 −0.151027
\(499\) 8964.56 0.804226 0.402113 0.915590i \(-0.368276\pi\)
0.402113 + 0.915590i \(0.368276\pi\)
\(500\) 37276.3 3.33410
\(501\) −4804.60 −0.428450
\(502\) 12429.0 1.10504
\(503\) 12006.7 1.06432 0.532158 0.846645i \(-0.321381\pi\)
0.532158 + 0.846645i \(0.321381\pi\)
\(504\) −6150.60 −0.543590
\(505\) 31354.8 2.76291
\(506\) −5262.88 −0.462379
\(507\) 0 0
\(508\) 10593.2 0.925194
\(509\) 13634.7 1.18733 0.593663 0.804714i \(-0.297681\pi\)
0.593663 + 0.804714i \(0.297681\pi\)
\(510\) −22824.7 −1.98176
\(511\) −14848.1 −1.28541
\(512\) 2304.56 0.198922
\(513\) −19283.1 −1.65959
\(514\) −5656.06 −0.485366
\(515\) −8524.81 −0.729414
\(516\) −11336.1 −0.967139
\(517\) −469.978 −0.0399799
\(518\) −855.711 −0.0725826
\(519\) 6280.74 0.531202
\(520\) 0 0
\(521\) 16044.5 1.34918 0.674591 0.738192i \(-0.264320\pi\)
0.674591 + 0.738192i \(0.264320\pi\)
\(522\) 16686.8 1.39916
\(523\) −6594.48 −0.551351 −0.275675 0.961251i \(-0.588901\pi\)
−0.275675 + 0.961251i \(0.588901\pi\)
\(524\) 24388.0 2.03320
\(525\) −18475.3 −1.53586
\(526\) −10614.1 −0.879844
\(527\) 5094.84 0.421128
\(528\) −258.636 −0.0213176
\(529\) −1417.03 −0.116465
\(530\) 65486.2 5.36705
\(531\) −7817.35 −0.638878
\(532\) −32325.2 −2.63435
\(533\) 0 0
\(534\) −7744.22 −0.627575
\(535\) 8834.31 0.713908
\(536\) 17049.4 1.37392
\(537\) 3538.37 0.284343
\(538\) 19306.8 1.54717
\(539\) −109.426 −0.00874458
\(540\) −39197.7 −3.12370
\(541\) −6092.77 −0.484193 −0.242097 0.970252i \(-0.577835\pi\)
−0.242097 + 0.970252i \(0.577835\pi\)
\(542\) 15268.7 1.21005
\(543\) 12156.4 0.960742
\(544\) 11251.1 0.886744
\(545\) −24137.5 −1.89713
\(546\) 0 0
\(547\) 1980.28 0.154791 0.0773954 0.997000i \(-0.475340\pi\)
0.0773954 + 0.997000i \(0.475340\pi\)
\(548\) −5154.27 −0.401787
\(549\) 4578.96 0.355966
\(550\) 13536.7 1.04947
\(551\) 34923.6 2.70017
\(552\) 9339.99 0.720175
\(553\) 2240.79 0.172311
\(554\) −3031.52 −0.232486
\(555\) −720.366 −0.0550952
\(556\) −36373.5 −2.77442
\(557\) 4042.44 0.307511 0.153756 0.988109i \(-0.450863\pi\)
0.153756 + 0.988109i \(0.450863\pi\)
\(558\) 4648.88 0.352694
\(559\) 0 0
\(560\) −2370.70 −0.178894
\(561\) −2749.19 −0.206900
\(562\) −34914.8 −2.62063
\(563\) 195.731 0.0146520 0.00732601 0.999973i \(-0.497668\pi\)
0.00732601 + 0.999973i \(0.497668\pi\)
\(564\) 2094.49 0.156372
\(565\) −10088.5 −0.751194
\(566\) −12796.4 −0.950305
\(567\) 3523.42 0.260970
\(568\) −15152.2 −1.11932
\(569\) −5398.85 −0.397771 −0.198885 0.980023i \(-0.563732\pi\)
−0.198885 + 0.980023i \(0.563732\pi\)
\(570\) −43588.3 −3.20301
\(571\) −11551.6 −0.846618 −0.423309 0.905985i \(-0.639132\pi\)
−0.423309 + 0.905985i \(0.639132\pi\)
\(572\) 0 0
\(573\) 3879.42 0.282836
\(574\) 14114.6 1.02636
\(575\) −27650.1 −2.00538
\(576\) 10949.9 0.792096
\(577\) 4928.61 0.355599 0.177800 0.984067i \(-0.443102\pi\)
0.177800 + 0.984067i \(0.443102\pi\)
\(578\) 1474.55 0.106113
\(579\) 5690.54 0.408447
\(580\) 70990.9 5.08231
\(581\) −1853.04 −0.132318
\(582\) −5897.21 −0.420013
\(583\) 7887.66 0.560332
\(584\) −19307.1 −1.36804
\(585\) 0 0
\(586\) −21956.4 −1.54780
\(587\) −22142.3 −1.55692 −0.778459 0.627696i \(-0.783998\pi\)
−0.778459 + 0.627696i \(0.783998\pi\)
\(588\) 487.666 0.0342024
\(589\) 9729.60 0.680647
\(590\) −53271.2 −3.71719
\(591\) −9456.29 −0.658172
\(592\) −62.9361 −0.00436935
\(593\) 6962.36 0.482141 0.241071 0.970508i \(-0.422501\pi\)
0.241071 + 0.970508i \(0.422501\pi\)
\(594\) −7562.44 −0.522375
\(595\) −25199.5 −1.73627
\(596\) 19897.3 1.36749
\(597\) 2282.59 0.156482
\(598\) 0 0
\(599\) −4050.44 −0.276288 −0.138144 0.990412i \(-0.544114\pi\)
−0.138144 + 0.990412i \(0.544114\pi\)
\(600\) −24023.5 −1.63459
\(601\) 5193.94 0.352521 0.176261 0.984344i \(-0.443600\pi\)
0.176261 + 0.984344i \(0.443600\pi\)
\(602\) −20047.2 −1.35724
\(603\) 9353.37 0.631673
\(604\) −33600.5 −2.26355
\(605\) 2394.71 0.160923
\(606\) −26959.1 −1.80716
\(607\) −11147.8 −0.745428 −0.372714 0.927946i \(-0.621573\pi\)
−0.372714 + 0.927946i \(0.621573\pi\)
\(608\) 21486.3 1.43320
\(609\) −18693.1 −1.24381
\(610\) 31203.3 2.07112
\(611\) 0 0
\(612\) −12074.9 −0.797545
\(613\) 26142.9 1.72251 0.861257 0.508170i \(-0.169678\pi\)
0.861257 + 0.508170i \(0.169678\pi\)
\(614\) −3548.73 −0.233250
\(615\) 11882.1 0.779078
\(616\) −5048.34 −0.330201
\(617\) 8866.64 0.578537 0.289269 0.957248i \(-0.406588\pi\)
0.289269 + 0.957248i \(0.406588\pi\)
\(618\) 7329.72 0.477095
\(619\) 14375.9 0.933464 0.466732 0.884399i \(-0.345431\pi\)
0.466732 + 0.884399i \(0.345431\pi\)
\(620\) 19777.8 1.28112
\(621\) 15447.0 0.998178
\(622\) −3710.66 −0.239203
\(623\) −8549.96 −0.549834
\(624\) 0 0
\(625\) 22159.1 1.41818
\(626\) −33381.1 −2.13127
\(627\) −5250.12 −0.334401
\(628\) 25874.8 1.64413
\(629\) −668.982 −0.0424071
\(630\) −22993.8 −1.45412
\(631\) −16861.7 −1.06379 −0.531897 0.846809i \(-0.678521\pi\)
−0.531897 + 0.846809i \(0.678521\pi\)
\(632\) 2913.71 0.183388
\(633\) −378.614 −0.0237734
\(634\) 9973.28 0.624747
\(635\) 15770.4 0.985560
\(636\) −35151.9 −2.19161
\(637\) 0 0
\(638\) 13696.3 0.849911
\(639\) −8312.60 −0.514618
\(640\) 48334.7 2.98531
\(641\) 17281.8 1.06488 0.532442 0.846467i \(-0.321275\pi\)
0.532442 + 0.846467i \(0.321275\pi\)
\(642\) −7595.83 −0.466952
\(643\) −5058.54 −0.310248 −0.155124 0.987895i \(-0.549578\pi\)
−0.155124 + 0.987895i \(0.549578\pi\)
\(644\) 25894.7 1.58446
\(645\) −16876.4 −1.03024
\(646\) −40479.2 −2.46537
\(647\) 4595.03 0.279211 0.139605 0.990207i \(-0.455417\pi\)
0.139605 + 0.990207i \(0.455417\pi\)
\(648\) 4581.53 0.277746
\(649\) −6416.40 −0.388083
\(650\) 0 0
\(651\) −5207.84 −0.313535
\(652\) 12796.8 0.768655
\(653\) −11986.5 −0.718326 −0.359163 0.933275i \(-0.616938\pi\)
−0.359163 + 0.933275i \(0.616938\pi\)
\(654\) 20753.7 1.24088
\(655\) 36307.2 2.16586
\(656\) 1038.10 0.0617852
\(657\) −10592.0 −0.628969
\(658\) 3703.97 0.219446
\(659\) −27151.2 −1.60495 −0.802475 0.596686i \(-0.796484\pi\)
−0.802475 + 0.596686i \(0.796484\pi\)
\(660\) −10672.2 −0.629415
\(661\) 9477.81 0.557707 0.278853 0.960334i \(-0.410046\pi\)
0.278853 + 0.960334i \(0.410046\pi\)
\(662\) 16449.7 0.965765
\(663\) 0 0
\(664\) −2409.51 −0.140824
\(665\) −48123.4 −2.80623
\(666\) −610.426 −0.0355158
\(667\) −27976.2 −1.62405
\(668\) −17320.8 −1.00323
\(669\) 16488.4 0.952882
\(670\) 63738.4 3.67527
\(671\) 3758.36 0.216229
\(672\) −11500.7 −0.660192
\(673\) −12835.8 −0.735192 −0.367596 0.929986i \(-0.619819\pi\)
−0.367596 + 0.929986i \(0.619819\pi\)
\(674\) −43696.1 −2.49719
\(675\) −39731.6 −2.26558
\(676\) 0 0
\(677\) −25666.5 −1.45708 −0.728541 0.685002i \(-0.759801\pi\)
−0.728541 + 0.685002i \(0.759801\pi\)
\(678\) 8674.15 0.491340
\(679\) −6510.78 −0.367984
\(680\) −32767.1 −1.84788
\(681\) 1146.11 0.0644919
\(682\) 3815.76 0.214242
\(683\) −34230.6 −1.91771 −0.958856 0.283892i \(-0.908374\pi\)
−0.958856 + 0.283892i \(0.908374\pi\)
\(684\) −23059.3 −1.28903
\(685\) −7673.30 −0.428003
\(686\) −28873.2 −1.60697
\(687\) 15354.9 0.852731
\(688\) −1474.43 −0.0817039
\(689\) 0 0
\(690\) 34917.2 1.92649
\(691\) 31496.4 1.73398 0.866988 0.498328i \(-0.166053\pi\)
0.866988 + 0.498328i \(0.166053\pi\)
\(692\) 22642.3 1.24383
\(693\) −2769.55 −0.151813
\(694\) −13982.2 −0.764778
\(695\) −54150.2 −2.95545
\(696\) −24306.8 −1.32377
\(697\) 11034.6 0.599661
\(698\) −52239.3 −2.83279
\(699\) −6188.41 −0.334860
\(700\) −66604.0 −3.59628
\(701\) −27292.4 −1.47050 −0.735249 0.677797i \(-0.762935\pi\)
−0.735249 + 0.677797i \(0.762935\pi\)
\(702\) 0 0
\(703\) −1277.55 −0.0685403
\(704\) 8987.59 0.481154
\(705\) 3118.12 0.166575
\(706\) 45964.4 2.45027
\(707\) −29764.1 −1.58330
\(708\) 28595.1 1.51790
\(709\) −9950.79 −0.527094 −0.263547 0.964647i \(-0.584892\pi\)
−0.263547 + 0.964647i \(0.584892\pi\)
\(710\) −56646.1 −2.99421
\(711\) 1598.48 0.0843146
\(712\) −11117.6 −0.585180
\(713\) −7794.07 −0.409383
\(714\) 21666.8 1.13566
\(715\) 0 0
\(716\) 12756.0 0.665800
\(717\) 25279.5 1.31671
\(718\) 45328.2 2.35604
\(719\) 18426.3 0.955753 0.477876 0.878427i \(-0.341407\pi\)
0.477876 + 0.878427i \(0.341407\pi\)
\(720\) −1691.15 −0.0875355
\(721\) 8092.32 0.417994
\(722\) −45651.9 −2.35317
\(723\) 10397.0 0.534813
\(724\) 43824.4 2.24962
\(725\) 71957.8 3.68613
\(726\) −2058.99 −0.105257
\(727\) −18460.9 −0.941781 −0.470891 0.882192i \(-0.656067\pi\)
−0.470891 + 0.882192i \(0.656067\pi\)
\(728\) 0 0
\(729\) 17347.1 0.881323
\(730\) −72179.0 −3.65954
\(731\) −15672.6 −0.792983
\(732\) −16749.4 −0.845732
\(733\) 24975.1 1.25849 0.629247 0.777205i \(-0.283363\pi\)
0.629247 + 0.777205i \(0.283363\pi\)
\(734\) 11313.1 0.568900
\(735\) 726.003 0.0364340
\(736\) −17212.0 −0.862013
\(737\) 7677.15 0.383706
\(738\) 10068.7 0.502214
\(739\) −8876.13 −0.441832 −0.220916 0.975293i \(-0.570905\pi\)
−0.220916 + 0.975293i \(0.570905\pi\)
\(740\) −2596.95 −0.129008
\(741\) 0 0
\(742\) −62163.9 −3.07562
\(743\) −35601.7 −1.75788 −0.878938 0.476937i \(-0.841747\pi\)
−0.878938 + 0.476937i \(0.841747\pi\)
\(744\) −6771.79 −0.333691
\(745\) 29621.6 1.45671
\(746\) −34291.1 −1.68296
\(747\) −1321.87 −0.0647454
\(748\) −9910.92 −0.484464
\(749\) −8386.12 −0.409109
\(750\) −47714.5 −2.32305
\(751\) 37294.6 1.81212 0.906058 0.423153i \(-0.139077\pi\)
0.906058 + 0.423153i \(0.139077\pi\)
\(752\) 272.420 0.0132103
\(753\) −9932.29 −0.480681
\(754\) 0 0
\(755\) −50021.9 −2.41124
\(756\) 37209.1 1.79005
\(757\) 2656.35 0.127538 0.0637692 0.997965i \(-0.479688\pi\)
0.0637692 + 0.997965i \(0.479688\pi\)
\(758\) 28728.4 1.37660
\(759\) 4205.70 0.201129
\(760\) −62575.2 −2.98663
\(761\) 13669.7 0.651152 0.325576 0.945516i \(-0.394442\pi\)
0.325576 + 0.945516i \(0.394442\pi\)
\(762\) −13559.6 −0.644634
\(763\) 22912.9 1.08716
\(764\) 13985.4 0.662272
\(765\) −17976.2 −0.849582
\(766\) −23528.9 −1.10983
\(767\) 0 0
\(768\) −17455.0 −0.820121
\(769\) 624.543 0.0292868 0.0146434 0.999893i \(-0.495339\pi\)
0.0146434 + 0.999893i \(0.495339\pi\)
\(770\) −18873.1 −0.883296
\(771\) 4519.89 0.211128
\(772\) 20514.6 0.956394
\(773\) −17576.4 −0.817826 −0.408913 0.912573i \(-0.634092\pi\)
−0.408913 + 0.912573i \(0.634092\pi\)
\(774\) −14300.7 −0.664121
\(775\) 20047.2 0.929184
\(776\) −8466.01 −0.391639
\(777\) 683.820 0.0315726
\(778\) 12331.5 0.568259
\(779\) 21072.7 0.969200
\(780\) 0 0
\(781\) −6822.89 −0.312602
\(782\) 32426.5 1.48283
\(783\) −40200.0 −1.83478
\(784\) 63.4285 0.00288942
\(785\) 38520.5 1.75141
\(786\) −31217.2 −1.41664
\(787\) 21207.3 0.960557 0.480279 0.877116i \(-0.340536\pi\)
0.480279 + 0.877116i \(0.340536\pi\)
\(788\) −34090.3 −1.54114
\(789\) 8482.01 0.382722
\(790\) 10892.8 0.490568
\(791\) 9576.64 0.430475
\(792\) −3601.26 −0.161572
\(793\) 0 0
\(794\) 1847.12 0.0825591
\(795\) −52331.6 −2.33461
\(796\) 8228.81 0.366410
\(797\) 21481.3 0.954712 0.477356 0.878710i \(-0.341595\pi\)
0.477356 + 0.878710i \(0.341595\pi\)
\(798\) 41377.0 1.83550
\(799\) 2895.71 0.128214
\(800\) 44271.1 1.95653
\(801\) −6099.15 −0.269042
\(802\) 41251.4 1.81626
\(803\) −8693.79 −0.382064
\(804\) −34213.7 −1.50078
\(805\) 38550.1 1.68784
\(806\) 0 0
\(807\) −15428.6 −0.673000
\(808\) −38702.4 −1.68508
\(809\) −4674.16 −0.203133 −0.101566 0.994829i \(-0.532385\pi\)
−0.101566 + 0.994829i \(0.532385\pi\)
\(810\) 17127.9 0.742979
\(811\) 10381.5 0.449499 0.224749 0.974417i \(-0.427844\pi\)
0.224749 + 0.974417i \(0.427844\pi\)
\(812\) −67389.3 −2.91244
\(813\) −12201.6 −0.526359
\(814\) −501.031 −0.0215739
\(815\) 19051.0 0.818807
\(816\) 1593.55 0.0683646
\(817\) −29929.8 −1.28166
\(818\) 43751.2 1.87008
\(819\) 0 0
\(820\) 42835.5 1.82424
\(821\) 41246.0 1.75335 0.876673 0.481087i \(-0.159758\pi\)
0.876673 + 0.481087i \(0.159758\pi\)
\(822\) 6597.58 0.279948
\(823\) −22899.1 −0.969882 −0.484941 0.874547i \(-0.661159\pi\)
−0.484941 + 0.874547i \(0.661159\pi\)
\(824\) 10522.5 0.444865
\(825\) −10817.5 −0.456507
\(826\) 50568.6 2.13015
\(827\) 18630.2 0.783358 0.391679 0.920102i \(-0.371894\pi\)
0.391679 + 0.920102i \(0.371894\pi\)
\(828\) 18472.1 0.775302
\(829\) −17105.3 −0.716638 −0.358319 0.933599i \(-0.616650\pi\)
−0.358319 + 0.933599i \(0.616650\pi\)
\(830\) −9007.88 −0.376709
\(831\) 2422.57 0.101129
\(832\) 0 0
\(833\) 674.216 0.0280435
\(834\) 46558.9 1.93310
\(835\) −25785.9 −1.06869
\(836\) −18926.9 −0.783013
\(837\) −11199.6 −0.462503
\(838\) −57283.5 −2.36137
\(839\) −16211.0 −0.667065 −0.333532 0.942739i \(-0.608241\pi\)
−0.333532 + 0.942739i \(0.608241\pi\)
\(840\) 33493.8 1.37577
\(841\) 48417.3 1.98521
\(842\) −61110.1 −2.50118
\(843\) 27901.3 1.13994
\(844\) −1364.92 −0.0556664
\(845\) 0 0
\(846\) 2642.24 0.107379
\(847\) −2273.22 −0.0922180
\(848\) −4572.05 −0.185147
\(849\) 10225.9 0.413371
\(850\) −83404.8 −3.36560
\(851\) 1023.41 0.0412244
\(852\) 30406.7 1.22267
\(853\) 25403.3 1.01969 0.509843 0.860267i \(-0.329703\pi\)
0.509843 + 0.860267i \(0.329703\pi\)
\(854\) −29620.2 −1.18687
\(855\) −34329.1 −1.37313
\(856\) −10904.5 −0.435408
\(857\) 26314.5 1.04887 0.524437 0.851449i \(-0.324276\pi\)
0.524437 + 0.851449i \(0.324276\pi\)
\(858\) 0 0
\(859\) 37876.6 1.50446 0.752231 0.658900i \(-0.228978\pi\)
0.752231 + 0.658900i \(0.228978\pi\)
\(860\) −60839.9 −2.41235
\(861\) −11279.3 −0.446455
\(862\) 27712.5 1.09500
\(863\) −7130.65 −0.281263 −0.140632 0.990062i \(-0.544913\pi\)
−0.140632 + 0.990062i \(0.544913\pi\)
\(864\) −24732.5 −0.973863
\(865\) 33708.2 1.32499
\(866\) 45783.0 1.79650
\(867\) −1178.35 −0.0461579
\(868\) −18774.5 −0.734155
\(869\) 1312.01 0.0512164
\(870\) −90870.0 −3.54113
\(871\) 0 0
\(872\) 29793.8 1.15705
\(873\) −4644.50 −0.180060
\(874\) 61924.9 2.39661
\(875\) −52678.9 −2.03528
\(876\) 38744.5 1.49435
\(877\) 498.556 0.0191962 0.00959809 0.999954i \(-0.496945\pi\)
0.00959809 + 0.999954i \(0.496945\pi\)
\(878\) 22561.7 0.867222
\(879\) 17545.9 0.673275
\(880\) −1388.08 −0.0531729
\(881\) 2371.51 0.0906903 0.0453452 0.998971i \(-0.485561\pi\)
0.0453452 + 0.998971i \(0.485561\pi\)
\(882\) 615.202 0.0234863
\(883\) −32108.2 −1.22370 −0.611849 0.790974i \(-0.709574\pi\)
−0.611849 + 0.790974i \(0.709574\pi\)
\(884\) 0 0
\(885\) 42570.3 1.61693
\(886\) 48769.9 1.84927
\(887\) −24899.9 −0.942566 −0.471283 0.881982i \(-0.656209\pi\)
−0.471283 + 0.881982i \(0.656209\pi\)
\(888\) 889.175 0.0336022
\(889\) −14970.4 −0.564780
\(890\) −41562.6 −1.56537
\(891\) 2063.01 0.0775686
\(892\) 59441.3 2.23121
\(893\) 5529.92 0.207225
\(894\) −25469.0 −0.952807
\(895\) 18990.1 0.709241
\(896\) −45882.5 −1.71074
\(897\) 0 0
\(898\) 72728.4 2.70265
\(899\) 20283.6 0.752498
\(900\) −47512.3 −1.75972
\(901\) −48598.8 −1.79696
\(902\) 8264.28 0.305067
\(903\) 16020.2 0.590385
\(904\) 12452.6 0.458148
\(905\) 65242.7 2.39640
\(906\) 43009.4 1.57714
\(907\) −15807.4 −0.578696 −0.289348 0.957224i \(-0.593438\pi\)
−0.289348 + 0.957224i \(0.593438\pi\)
\(908\) 4131.77 0.151011
\(909\) −21232.3 −0.774733
\(910\) 0 0
\(911\) 6529.29 0.237459 0.118729 0.992927i \(-0.462118\pi\)
0.118729 + 0.992927i \(0.462118\pi\)
\(912\) 3043.21 0.110494
\(913\) −1084.98 −0.0393292
\(914\) −5067.36 −0.183385
\(915\) −24935.3 −0.900913
\(916\) 55355.0 1.99670
\(917\) −34465.2 −1.24116
\(918\) 46594.9 1.67523
\(919\) −592.657 −0.0212731 −0.0106365 0.999943i \(-0.503386\pi\)
−0.0106365 + 0.999943i \(0.503386\pi\)
\(920\) 50127.0 1.79634
\(921\) 2835.88 0.101461
\(922\) 1186.12 0.0423675
\(923\) 0 0
\(924\) 10130.7 0.360689
\(925\) −2632.32 −0.0935676
\(926\) 66860.4 2.37275
\(927\) 5772.70 0.204531
\(928\) 44793.1 1.58449
\(929\) 6338.23 0.223843 0.111922 0.993717i \(-0.464299\pi\)
0.111922 + 0.993717i \(0.464299\pi\)
\(930\) −25316.1 −0.892631
\(931\) 1287.55 0.0453252
\(932\) −22309.4 −0.784088
\(933\) 2965.28 0.104050
\(934\) −40863.0 −1.43156
\(935\) −14754.7 −0.516074
\(936\) 0 0
\(937\) −19414.2 −0.676877 −0.338438 0.940989i \(-0.609899\pi\)
−0.338438 + 0.940989i \(0.609899\pi\)
\(938\) −60504.8 −2.10613
\(939\) 26675.6 0.927078
\(940\) 11241.0 0.390042
\(941\) 29467.4 1.02084 0.510419 0.859926i \(-0.329490\pi\)
0.510419 + 0.859926i \(0.329490\pi\)
\(942\) −33120.3 −1.14556
\(943\) −16880.6 −0.582936
\(944\) 3719.23 0.128232
\(945\) 55394.1 1.90685
\(946\) −11737.9 −0.403416
\(947\) 36382.4 1.24844 0.624218 0.781250i \(-0.285418\pi\)
0.624218 + 0.781250i \(0.285418\pi\)
\(948\) −5847.08 −0.200321
\(949\) 0 0
\(950\) −159278. −5.43964
\(951\) −7969.90 −0.271758
\(952\) 31104.7 1.05894
\(953\) 15865.6 0.539284 0.269642 0.962961i \(-0.413095\pi\)
0.269642 + 0.962961i \(0.413095\pi\)
\(954\) −44344.9 −1.50495
\(955\) 20820.5 0.705483
\(956\) 91133.7 3.08313
\(957\) −10945.1 −0.369701
\(958\) −62340.9 −2.10245
\(959\) 7284.01 0.245269
\(960\) −59629.2 −2.00471
\(961\) −24140.1 −0.810314
\(962\) 0 0
\(963\) −5982.28 −0.200183
\(964\) 37481.7 1.25229
\(965\) 30540.6 1.01880
\(966\) −33145.8 −1.10398
\(967\) −54819.1 −1.82302 −0.911512 0.411273i \(-0.865084\pi\)
−0.911512 + 0.411273i \(0.865084\pi\)
\(968\) −2955.88 −0.0981462
\(969\) 32347.9 1.07241
\(970\) −31649.9 −1.04765
\(971\) 18825.3 0.622177 0.311088 0.950381i \(-0.399306\pi\)
0.311088 + 0.950381i \(0.399306\pi\)
\(972\) 44281.8 1.46125
\(973\) 51403.0 1.69363
\(974\) −77295.5 −2.54282
\(975\) 0 0
\(976\) −2178.52 −0.0714474
\(977\) −33592.0 −1.10000 −0.550002 0.835163i \(-0.685373\pi\)
−0.550002 + 0.835163i \(0.685373\pi\)
\(978\) −16380.2 −0.535565
\(979\) −5006.12 −0.163428
\(980\) 2617.27 0.0853117
\(981\) 16345.1 0.531965
\(982\) −22285.5 −0.724195
\(983\) −52254.5 −1.69548 −0.847741 0.530411i \(-0.822038\pi\)
−0.847741 + 0.530411i \(0.822038\pi\)
\(984\) −14666.5 −0.475155
\(985\) −50751.2 −1.64169
\(986\) −84388.1 −2.72562
\(987\) −2959.93 −0.0954566
\(988\) 0 0
\(989\) 23975.8 0.770867
\(990\) −13463.2 −0.432210
\(991\) −11333.3 −0.363285 −0.181642 0.983365i \(-0.558141\pi\)
−0.181642 + 0.983365i \(0.558141\pi\)
\(992\) 12479.2 0.399411
\(993\) −13145.4 −0.420096
\(994\) 53772.3 1.71585
\(995\) 12250.5 0.390317
\(996\) 4835.28 0.153827
\(997\) 2785.34 0.0884781 0.0442390 0.999021i \(-0.485914\pi\)
0.0442390 + 0.999021i \(0.485914\pi\)
\(998\) −41367.2 −1.31208
\(999\) 1470.57 0.0465734
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 1859.4.a.i.1.2 17
13.3 even 3 143.4.e.a.100.16 34
13.9 even 3 143.4.e.a.133.16 yes 34
13.12 even 2 1859.4.a.f.1.16 17
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
143.4.e.a.100.16 34 13.3 even 3
143.4.e.a.133.16 yes 34 13.9 even 3
1859.4.a.f.1.16 17 13.12 even 2
1859.4.a.i.1.2 17 1.1 even 1 trivial