Properties

Label 1859.4.a.f.1.12
Level $1859$
Weight $4$
Character 1859.1
Self dual yes
Analytic conductor $109.685$
Analytic rank $1$
Dimension $17$
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] = [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: \(1\)
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 1.12
Root \(-2.47248\) 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)
 
\(f(q)\) \(=\) \(q+2.47248 q^{2} +6.49330 q^{3} -1.88686 q^{4} +10.7576 q^{5} +16.0545 q^{6} -24.9760 q^{7} -24.4450 q^{8} +15.1629 q^{9} +O(q^{10})\) \(q+2.47248 q^{2} +6.49330 q^{3} -1.88686 q^{4} +10.7576 q^{5} +16.0545 q^{6} -24.9760 q^{7} -24.4450 q^{8} +15.1629 q^{9} +26.5979 q^{10} +11.0000 q^{11} -12.2520 q^{12} -61.7527 q^{14} +69.8523 q^{15} -45.3448 q^{16} +99.6374 q^{17} +37.4900 q^{18} -87.2296 q^{19} -20.2981 q^{20} -162.177 q^{21} +27.1972 q^{22} +95.5895 q^{23} -158.729 q^{24} -9.27403 q^{25} -76.8616 q^{27} +47.1264 q^{28} -43.7369 q^{29} +172.708 q^{30} -183.927 q^{31} +83.4462 q^{32} +71.4263 q^{33} +246.351 q^{34} -268.682 q^{35} -28.6104 q^{36} -263.861 q^{37} -215.673 q^{38} -262.970 q^{40} +61.8766 q^{41} -400.979 q^{42} -207.867 q^{43} -20.7555 q^{44} +163.117 q^{45} +236.343 q^{46} +122.424 q^{47} -294.438 q^{48} +280.803 q^{49} -22.9298 q^{50} +646.976 q^{51} -315.428 q^{53} -190.038 q^{54} +118.334 q^{55} +610.540 q^{56} -566.408 q^{57} -108.139 q^{58} -209.700 q^{59} -131.802 q^{60} +52.8547 q^{61} -454.754 q^{62} -378.710 q^{63} +569.077 q^{64} +176.600 q^{66} -286.699 q^{67} -188.002 q^{68} +620.691 q^{69} -664.311 q^{70} -777.192 q^{71} -370.659 q^{72} -824.682 q^{73} -652.389 q^{74} -60.2191 q^{75} +164.590 q^{76} -274.737 q^{77} -860.840 q^{79} -487.802 q^{80} -908.485 q^{81} +152.988 q^{82} +1424.92 q^{83} +306.006 q^{84} +1071.86 q^{85} -513.946 q^{86} -283.997 q^{87} -268.895 q^{88} -434.711 q^{89} +403.303 q^{90} -180.364 q^{92} -1194.29 q^{93} +302.690 q^{94} -938.381 q^{95} +541.841 q^{96} +1111.26 q^{97} +694.279 q^{98} +166.792 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 17 q - 4 q^{2} - 6 q^{3} + 78 q^{4} - 16 q^{5} - 14 q^{6} + 6 q^{7} - 63 q^{8} + 135 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.47248 0.874152 0.437076 0.899425i \(-0.356014\pi\)
0.437076 + 0.899425i \(0.356014\pi\)
\(3\) 6.49330 1.24964 0.624818 0.780770i \(-0.285173\pi\)
0.624818 + 0.780770i \(0.285173\pi\)
\(4\) −1.88686 −0.235858
\(5\) 10.7576 0.962189 0.481095 0.876669i \(-0.340239\pi\)
0.481095 + 0.876669i \(0.340239\pi\)
\(6\) 16.0545 1.09237
\(7\) −24.9760 −1.34858 −0.674290 0.738467i \(-0.735550\pi\)
−0.674290 + 0.738467i \(0.735550\pi\)
\(8\) −24.4450 −1.08033
\(9\) 15.1629 0.561590
\(10\) 26.5979 0.841100
\(11\) 11.0000 0.301511
\(12\) −12.2520 −0.294737
\(13\) 0 0
\(14\) −61.7527 −1.17886
\(15\) 69.8523 1.20239
\(16\) −45.3448 −0.708513
\(17\) 99.6374 1.42151 0.710754 0.703441i \(-0.248354\pi\)
0.710754 + 0.703441i \(0.248354\pi\)
\(18\) 37.4900 0.490916
\(19\) −87.2296 −1.05325 −0.526627 0.850096i \(-0.676544\pi\)
−0.526627 + 0.850096i \(0.676544\pi\)
\(20\) −20.2981 −0.226940
\(21\) −162.177 −1.68523
\(22\) 27.1972 0.263567
\(23\) 95.5895 0.866600 0.433300 0.901250i \(-0.357349\pi\)
0.433300 + 0.901250i \(0.357349\pi\)
\(24\) −158.729 −1.35002
\(25\) −9.27403 −0.0741922
\(26\) 0 0
\(27\) −76.8616 −0.547852
\(28\) 47.1264 0.318073
\(29\) −43.7369 −0.280060 −0.140030 0.990147i \(-0.544720\pi\)
−0.140030 + 0.990147i \(0.544720\pi\)
\(30\) 172.708 1.05107
\(31\) −183.927 −1.06562 −0.532810 0.846235i \(-0.678864\pi\)
−0.532810 + 0.846235i \(0.678864\pi\)
\(32\) 83.4462 0.460980
\(33\) 71.4263 0.376779
\(34\) 246.351 1.24261
\(35\) −268.682 −1.29759
\(36\) −28.6104 −0.132456
\(37\) −263.861 −1.17239 −0.586195 0.810170i \(-0.699375\pi\)
−0.586195 + 0.810170i \(0.699375\pi\)
\(38\) −215.673 −0.920705
\(39\) 0 0
\(40\) −262.970 −1.03948
\(41\) 61.8766 0.235695 0.117848 0.993032i \(-0.462401\pi\)
0.117848 + 0.993032i \(0.462401\pi\)
\(42\) −400.979 −1.47315
\(43\) −207.867 −0.737195 −0.368598 0.929589i \(-0.620162\pi\)
−0.368598 + 0.929589i \(0.620162\pi\)
\(44\) −20.7555 −0.0711138
\(45\) 163.117 0.540356
\(46\) 236.343 0.757540
\(47\) 122.424 0.379943 0.189972 0.981790i \(-0.439160\pi\)
0.189972 + 0.981790i \(0.439160\pi\)
\(48\) −294.438 −0.885384
\(49\) 280.803 0.818668
\(50\) −22.9298 −0.0648553
\(51\) 646.976 1.77637
\(52\) 0 0
\(53\) −315.428 −0.817499 −0.408749 0.912647i \(-0.634035\pi\)
−0.408749 + 0.912647i \(0.634035\pi\)
\(54\) −190.038 −0.478906
\(55\) 118.334 0.290111
\(56\) 610.540 1.45691
\(57\) −566.408 −1.31618
\(58\) −108.139 −0.244815
\(59\) −209.700 −0.462723 −0.231362 0.972868i \(-0.574318\pi\)
−0.231362 + 0.972868i \(0.574318\pi\)
\(60\) −131.802 −0.283592
\(61\) 52.8547 0.110940 0.0554700 0.998460i \(-0.482334\pi\)
0.0554700 + 0.998460i \(0.482334\pi\)
\(62\) −454.754 −0.931514
\(63\) −378.710 −0.757350
\(64\) 569.077 1.11148
\(65\) 0 0
\(66\) 176.600 0.329363
\(67\) −286.699 −0.522773 −0.261387 0.965234i \(-0.584180\pi\)
−0.261387 + 0.965234i \(0.584180\pi\)
\(68\) −188.002 −0.335274
\(69\) 620.691 1.08293
\(70\) −664.311 −1.13429
\(71\) −777.192 −1.29909 −0.649547 0.760321i \(-0.725042\pi\)
−0.649547 + 0.760321i \(0.725042\pi\)
\(72\) −370.659 −0.606702
\(73\) −824.682 −1.32222 −0.661108 0.750291i \(-0.729913\pi\)
−0.661108 + 0.750291i \(0.729913\pi\)
\(74\) −652.389 −1.02485
\(75\) −60.2191 −0.0927133
\(76\) 164.590 0.248418
\(77\) −274.737 −0.406612
\(78\) 0 0
\(79\) −860.840 −1.22598 −0.612988 0.790092i \(-0.710033\pi\)
−0.612988 + 0.790092i \(0.710033\pi\)
\(80\) −487.802 −0.681724
\(81\) −908.485 −1.24621
\(82\) 152.988 0.206033
\(83\) 1424.92 1.88440 0.942202 0.335045i \(-0.108751\pi\)
0.942202 + 0.335045i \(0.108751\pi\)
\(84\) 306.006 0.397476
\(85\) 1071.86 1.36776
\(86\) −513.946 −0.644421
\(87\) −283.997 −0.349973
\(88\) −268.895 −0.325731
\(89\) −434.711 −0.517744 −0.258872 0.965912i \(-0.583351\pi\)
−0.258872 + 0.965912i \(0.583351\pi\)
\(90\) 403.303 0.472354
\(91\) 0 0
\(92\) −180.364 −0.204394
\(93\) −1194.29 −1.33164
\(94\) 302.690 0.332128
\(95\) −938.381 −1.01343
\(96\) 541.841 0.576057
\(97\) 1111.26 1.16321 0.581606 0.813470i \(-0.302424\pi\)
0.581606 + 0.813470i \(0.302424\pi\)
\(98\) 694.279 0.715640
\(99\) 166.792 0.169326
\(100\) 17.4988 0.0174988
\(101\) −741.078 −0.730099 −0.365050 0.930988i \(-0.618948\pi\)
−0.365050 + 0.930988i \(0.618948\pi\)
\(102\) 1599.63 1.55281
\(103\) −517.376 −0.494937 −0.247469 0.968896i \(-0.579599\pi\)
−0.247469 + 0.968896i \(0.579599\pi\)
\(104\) 0 0
\(105\) −1744.64 −1.62151
\(106\) −779.889 −0.714618
\(107\) 1361.03 1.22968 0.614838 0.788653i \(-0.289221\pi\)
0.614838 + 0.788653i \(0.289221\pi\)
\(108\) 145.027 0.129215
\(109\) −1918.88 −1.68620 −0.843098 0.537759i \(-0.819271\pi\)
−0.843098 + 0.537759i \(0.819271\pi\)
\(110\) 292.577 0.253601
\(111\) −1713.33 −1.46506
\(112\) 1132.53 0.955486
\(113\) 104.069 0.0866368 0.0433184 0.999061i \(-0.486207\pi\)
0.0433184 + 0.999061i \(0.486207\pi\)
\(114\) −1400.43 −1.15055
\(115\) 1028.31 0.833833
\(116\) 82.5256 0.0660544
\(117\) 0 0
\(118\) −518.479 −0.404491
\(119\) −2488.55 −1.91702
\(120\) −1707.54 −1.29897
\(121\) 121.000 0.0909091
\(122\) 130.682 0.0969785
\(123\) 401.783 0.294533
\(124\) 347.045 0.251335
\(125\) −1444.47 −1.03358
\(126\) −936.352 −0.662039
\(127\) −2482.43 −1.73449 −0.867244 0.497883i \(-0.834111\pi\)
−0.867244 + 0.497883i \(0.834111\pi\)
\(128\) 739.461 0.510623
\(129\) −1349.74 −0.921226
\(130\) 0 0
\(131\) −915.026 −0.610276 −0.305138 0.952308i \(-0.598703\pi\)
−0.305138 + 0.952308i \(0.598703\pi\)
\(132\) −134.772 −0.0888664
\(133\) 2178.65 1.42040
\(134\) −708.856 −0.456984
\(135\) −826.846 −0.527138
\(136\) −2435.64 −1.53569
\(137\) −2936.58 −1.83131 −0.915653 0.401971i \(-0.868325\pi\)
−0.915653 + 0.401971i \(0.868325\pi\)
\(138\) 1534.64 0.946649
\(139\) 2905.10 1.77272 0.886359 0.462999i \(-0.153227\pi\)
0.886359 + 0.462999i \(0.153227\pi\)
\(140\) 506.967 0.306047
\(141\) 794.933 0.474791
\(142\) −1921.59 −1.13561
\(143\) 0 0
\(144\) −687.561 −0.397894
\(145\) −470.505 −0.269471
\(146\) −2039.01 −1.15582
\(147\) 1823.34 1.02304
\(148\) 497.869 0.276517
\(149\) 1617.42 0.889288 0.444644 0.895707i \(-0.353330\pi\)
0.444644 + 0.895707i \(0.353330\pi\)
\(150\) −148.890 −0.0810455
\(151\) −1869.40 −1.00748 −0.503741 0.863855i \(-0.668043\pi\)
−0.503741 + 0.863855i \(0.668043\pi\)
\(152\) 2132.33 1.13786
\(153\) 1510.80 0.798305
\(154\) −679.279 −0.355441
\(155\) −1978.61 −1.02533
\(156\) 0 0
\(157\) −1248.10 −0.634455 −0.317228 0.948349i \(-0.602752\pi\)
−0.317228 + 0.948349i \(0.602752\pi\)
\(158\) −2128.41 −1.07169
\(159\) −2048.17 −1.02158
\(160\) 897.681 0.443550
\(161\) −2387.45 −1.16868
\(162\) −2246.21 −1.08937
\(163\) 2868.84 1.37856 0.689278 0.724497i \(-0.257928\pi\)
0.689278 + 0.724497i \(0.257928\pi\)
\(164\) −116.753 −0.0555906
\(165\) 768.376 0.362533
\(166\) 3523.09 1.64726
\(167\) 1661.77 0.770009 0.385005 0.922915i \(-0.374200\pi\)
0.385005 + 0.922915i \(0.374200\pi\)
\(168\) 3964.42 1.82061
\(169\) 0 0
\(170\) 2650.15 1.19563
\(171\) −1322.66 −0.591498
\(172\) 392.216 0.173873
\(173\) 834.458 0.366721 0.183360 0.983046i \(-0.441302\pi\)
0.183360 + 0.983046i \(0.441302\pi\)
\(174\) −702.176 −0.305930
\(175\) 231.629 0.100054
\(176\) −498.793 −0.213625
\(177\) −1361.65 −0.578236
\(178\) −1074.81 −0.452587
\(179\) 1133.04 0.473116 0.236558 0.971617i \(-0.423981\pi\)
0.236558 + 0.971617i \(0.423981\pi\)
\(180\) −307.779 −0.127447
\(181\) 4414.26 1.81276 0.906380 0.422464i \(-0.138835\pi\)
0.906380 + 0.422464i \(0.138835\pi\)
\(182\) 0 0
\(183\) 343.201 0.138635
\(184\) −2336.69 −0.936212
\(185\) −2838.51 −1.12806
\(186\) −2952.86 −1.16405
\(187\) 1096.01 0.428600
\(188\) −230.997 −0.0896126
\(189\) 1919.70 0.738823
\(190\) −2320.12 −0.885892
\(191\) 2556.25 0.968398 0.484199 0.874958i \(-0.339111\pi\)
0.484199 + 0.874958i \(0.339111\pi\)
\(192\) 3695.19 1.38894
\(193\) −2067.33 −0.771033 −0.385516 0.922701i \(-0.625977\pi\)
−0.385516 + 0.922701i \(0.625977\pi\)
\(194\) 2747.57 1.01682
\(195\) 0 0
\(196\) −529.837 −0.193089
\(197\) 3312.55 1.19802 0.599009 0.800742i \(-0.295561\pi\)
0.599009 + 0.800742i \(0.295561\pi\)
\(198\) 412.390 0.148017
\(199\) −120.572 −0.0429503 −0.0214751 0.999769i \(-0.506836\pi\)
−0.0214751 + 0.999769i \(0.506836\pi\)
\(200\) 226.704 0.0801519
\(201\) −1861.62 −0.653277
\(202\) −1832.30 −0.638218
\(203\) 1092.38 0.377684
\(204\) −1220.75 −0.418970
\(205\) 665.644 0.226783
\(206\) −1279.20 −0.432651
\(207\) 1449.42 0.486674
\(208\) 0 0
\(209\) −959.525 −0.317568
\(210\) −4313.57 −1.41745
\(211\) 4845.63 1.58098 0.790491 0.612474i \(-0.209826\pi\)
0.790491 + 0.612474i \(0.209826\pi\)
\(212\) 595.170 0.192814
\(213\) −5046.54 −1.62340
\(214\) 3365.11 1.07492
\(215\) −2236.15 −0.709321
\(216\) 1878.88 0.591860
\(217\) 4593.76 1.43707
\(218\) −4744.39 −1.47399
\(219\) −5354.91 −1.65229
\(220\) −223.279 −0.0684250
\(221\) 0 0
\(222\) −4236.16 −1.28069
\(223\) 1683.59 0.505569 0.252784 0.967523i \(-0.418654\pi\)
0.252784 + 0.967523i \(0.418654\pi\)
\(224\) −2084.16 −0.621668
\(225\) −140.622 −0.0416657
\(226\) 257.307 0.0757338
\(227\) −1577.15 −0.461142 −0.230571 0.973056i \(-0.574059\pi\)
−0.230571 + 0.973056i \(0.574059\pi\)
\(228\) 1068.73 0.310433
\(229\) −2368.16 −0.683374 −0.341687 0.939814i \(-0.610998\pi\)
−0.341687 + 0.939814i \(0.610998\pi\)
\(230\) 2542.48 0.728897
\(231\) −1783.95 −0.508117
\(232\) 1069.15 0.302557
\(233\) 4037.46 1.13521 0.567603 0.823302i \(-0.307871\pi\)
0.567603 + 0.823302i \(0.307871\pi\)
\(234\) 0 0
\(235\) 1316.98 0.365577
\(236\) 395.676 0.109137
\(237\) −5589.69 −1.53202
\(238\) −6152.88 −1.67576
\(239\) 4072.68 1.10226 0.551129 0.834420i \(-0.314197\pi\)
0.551129 + 0.834420i \(0.314197\pi\)
\(240\) −3167.44 −0.851906
\(241\) −4726.49 −1.26332 −0.631659 0.775246i \(-0.717626\pi\)
−0.631659 + 0.775246i \(0.717626\pi\)
\(242\) 299.170 0.0794684
\(243\) −3823.80 −1.00945
\(244\) −99.7295 −0.0261661
\(245\) 3020.77 0.787713
\(246\) 993.400 0.257467
\(247\) 0 0
\(248\) 4496.09 1.15122
\(249\) 9252.45 2.35482
\(250\) −3571.41 −0.903503
\(251\) −1098.64 −0.276276 −0.138138 0.990413i \(-0.544112\pi\)
−0.138138 + 0.990413i \(0.544112\pi\)
\(252\) 714.575 0.178627
\(253\) 1051.48 0.261290
\(254\) −6137.75 −1.51621
\(255\) 6959.90 1.70920
\(256\) −2724.32 −0.665118
\(257\) 670.252 0.162682 0.0813408 0.996686i \(-0.474080\pi\)
0.0813408 + 0.996686i \(0.474080\pi\)
\(258\) −3337.20 −0.805292
\(259\) 6590.19 1.58106
\(260\) 0 0
\(261\) −663.181 −0.157279
\(262\) −2262.38 −0.533474
\(263\) −7002.52 −1.64180 −0.820900 0.571071i \(-0.806528\pi\)
−0.820900 + 0.571071i \(0.806528\pi\)
\(264\) −1746.02 −0.407045
\(265\) −3393.25 −0.786588
\(266\) 5386.66 1.24164
\(267\) −2822.71 −0.646992
\(268\) 540.961 0.123300
\(269\) −498.594 −0.113011 −0.0565053 0.998402i \(-0.517996\pi\)
−0.0565053 + 0.998402i \(0.517996\pi\)
\(270\) −2044.36 −0.460798
\(271\) 1788.15 0.400822 0.200411 0.979712i \(-0.435772\pi\)
0.200411 + 0.979712i \(0.435772\pi\)
\(272\) −4518.04 −1.00716
\(273\) 0 0
\(274\) −7260.62 −1.60084
\(275\) −102.014 −0.0223698
\(276\) −1171.16 −0.255419
\(277\) 2880.64 0.624840 0.312420 0.949944i \(-0.398860\pi\)
0.312420 + 0.949944i \(0.398860\pi\)
\(278\) 7182.80 1.54963
\(279\) −2788.87 −0.598442
\(280\) 6567.95 1.40182
\(281\) 6128.45 1.30104 0.650521 0.759489i \(-0.274551\pi\)
0.650521 + 0.759489i \(0.274551\pi\)
\(282\) 1965.45 0.415039
\(283\) 7039.28 1.47859 0.739296 0.673380i \(-0.235158\pi\)
0.739296 + 0.673380i \(0.235158\pi\)
\(284\) 1466.46 0.306402
\(285\) −6093.19 −1.26642
\(286\) 0 0
\(287\) −1545.43 −0.317854
\(288\) 1265.29 0.258882
\(289\) 5014.61 1.02068
\(290\) −1163.31 −0.235559
\(291\) 7215.76 1.45359
\(292\) 1556.06 0.311855
\(293\) −5273.69 −1.05151 −0.525755 0.850636i \(-0.676217\pi\)
−0.525755 + 0.850636i \(0.676217\pi\)
\(294\) 4508.16 0.894290
\(295\) −2255.87 −0.445227
\(296\) 6450.08 1.26656
\(297\) −845.477 −0.165184
\(298\) 3999.02 0.777373
\(299\) 0 0
\(300\) 113.625 0.0218672
\(301\) 5191.69 0.994167
\(302\) −4622.05 −0.880692
\(303\) −4812.04 −0.912358
\(304\) 3955.41 0.746245
\(305\) 568.589 0.106745
\(306\) 3735.41 0.697840
\(307\) −215.715 −0.0401026 −0.0200513 0.999799i \(-0.506383\pi\)
−0.0200513 + 0.999799i \(0.506383\pi\)
\(308\) 518.390 0.0959027
\(309\) −3359.48 −0.618492
\(310\) −4892.07 −0.896292
\(311\) 7314.80 1.33371 0.666855 0.745187i \(-0.267640\pi\)
0.666855 + 0.745187i \(0.267640\pi\)
\(312\) 0 0
\(313\) −420.725 −0.0759769 −0.0379884 0.999278i \(-0.512095\pi\)
−0.0379884 + 0.999278i \(0.512095\pi\)
\(314\) −3085.91 −0.554611
\(315\) −4074.02 −0.728713
\(316\) 1624.29 0.289156
\(317\) −7647.34 −1.35494 −0.677472 0.735548i \(-0.736925\pi\)
−0.677472 + 0.735548i \(0.736925\pi\)
\(318\) −5064.05 −0.893013
\(319\) −481.106 −0.0844413
\(320\) 6121.91 1.06945
\(321\) 8837.55 1.53665
\(322\) −5902.91 −1.02160
\(323\) −8691.33 −1.49721
\(324\) 1714.19 0.293928
\(325\) 0 0
\(326\) 7093.13 1.20507
\(327\) −12459.9 −2.10713
\(328\) −1512.58 −0.254628
\(329\) −3057.66 −0.512384
\(330\) 1899.79 0.316909
\(331\) −9264.16 −1.53838 −0.769191 0.639019i \(-0.779340\pi\)
−0.769191 + 0.639019i \(0.779340\pi\)
\(332\) −2688.63 −0.444452
\(333\) −4000.90 −0.658403
\(334\) 4108.68 0.673105
\(335\) −3084.19 −0.503007
\(336\) 7353.89 1.19401
\(337\) −3367.62 −0.544350 −0.272175 0.962248i \(-0.587743\pi\)
−0.272175 + 0.962248i \(0.587743\pi\)
\(338\) 0 0
\(339\) 675.749 0.108265
\(340\) −2022.45 −0.322597
\(341\) −2023.19 −0.321296
\(342\) −3270.24 −0.517059
\(343\) 1553.44 0.244541
\(344\) 5081.31 0.796413
\(345\) 6677.15 1.04199
\(346\) 2063.18 0.320570
\(347\) −4548.38 −0.703660 −0.351830 0.936064i \(-0.614440\pi\)
−0.351830 + 0.936064i \(0.614440\pi\)
\(348\) 535.864 0.0825440
\(349\) −11551.2 −1.77169 −0.885845 0.463980i \(-0.846421\pi\)
−0.885845 + 0.463980i \(0.846421\pi\)
\(350\) 572.696 0.0874626
\(351\) 0 0
\(352\) 917.909 0.138991
\(353\) −4656.01 −0.702024 −0.351012 0.936371i \(-0.614162\pi\)
−0.351012 + 0.936371i \(0.614162\pi\)
\(354\) −3366.64 −0.505466
\(355\) −8360.72 −1.24997
\(356\) 820.240 0.122114
\(357\) −16158.9 −2.39557
\(358\) 2801.43 0.413575
\(359\) 4795.68 0.705031 0.352516 0.935806i \(-0.385326\pi\)
0.352516 + 0.935806i \(0.385326\pi\)
\(360\) −3987.40 −0.583762
\(361\) 749.997 0.109345
\(362\) 10914.2 1.58463
\(363\) 785.689 0.113603
\(364\) 0 0
\(365\) −8871.60 −1.27222
\(366\) 848.557 0.121188
\(367\) 2731.53 0.388515 0.194257 0.980951i \(-0.437770\pi\)
0.194257 + 0.980951i \(0.437770\pi\)
\(368\) −4334.49 −0.613997
\(369\) 938.232 0.132364
\(370\) −7018.14 −0.986096
\(371\) 7878.15 1.10246
\(372\) 2253.46 0.314077
\(373\) 11335.3 1.57351 0.786757 0.617263i \(-0.211758\pi\)
0.786757 + 0.617263i \(0.211758\pi\)
\(374\) 2709.86 0.374662
\(375\) −9379.35 −1.29159
\(376\) −2992.65 −0.410463
\(377\) 0 0
\(378\) 4746.41 0.645843
\(379\) 10699.6 1.45014 0.725071 0.688674i \(-0.241807\pi\)
0.725071 + 0.688674i \(0.241807\pi\)
\(380\) 1770.60 0.239025
\(381\) −16119.2 −2.16748
\(382\) 6320.28 0.846528
\(383\) −6729.49 −0.897809 −0.448905 0.893580i \(-0.648186\pi\)
−0.448905 + 0.893580i \(0.648186\pi\)
\(384\) 4801.54 0.638092
\(385\) −2955.51 −0.391238
\(386\) −5111.41 −0.674000
\(387\) −3151.87 −0.414002
\(388\) −2096.80 −0.274353
\(389\) 8798.11 1.14674 0.573370 0.819296i \(-0.305636\pi\)
0.573370 + 0.819296i \(0.305636\pi\)
\(390\) 0 0
\(391\) 9524.29 1.23188
\(392\) −6864.24 −0.884429
\(393\) −5941.54 −0.762623
\(394\) 8190.20 1.04725
\(395\) −9260.57 −1.17962
\(396\) −314.714 −0.0399369
\(397\) −3726.62 −0.471118 −0.235559 0.971860i \(-0.575692\pi\)
−0.235559 + 0.971860i \(0.575692\pi\)
\(398\) −298.111 −0.0375451
\(399\) 14146.6 1.77498
\(400\) 420.529 0.0525662
\(401\) 7708.28 0.959932 0.479966 0.877287i \(-0.340649\pi\)
0.479966 + 0.877287i \(0.340649\pi\)
\(402\) −4602.81 −0.571063
\(403\) 0 0
\(404\) 1398.31 0.172200
\(405\) −9773.11 −1.19909
\(406\) 2700.87 0.330153
\(407\) −2902.47 −0.353489
\(408\) −15815.3 −1.91906
\(409\) −6777.35 −0.819360 −0.409680 0.912229i \(-0.634360\pi\)
−0.409680 + 0.912229i \(0.634360\pi\)
\(410\) 1645.79 0.198243
\(411\) −19068.1 −2.28847
\(412\) 976.218 0.116735
\(413\) 5237.49 0.624019
\(414\) 3583.65 0.425427
\(415\) 15328.7 1.81315
\(416\) 0 0
\(417\) 18863.7 2.21525
\(418\) −2372.40 −0.277603
\(419\) 15203.6 1.77266 0.886329 0.463055i \(-0.153247\pi\)
0.886329 + 0.463055i \(0.153247\pi\)
\(420\) 3291.89 0.382447
\(421\) 504.983 0.0584593 0.0292296 0.999573i \(-0.490695\pi\)
0.0292296 + 0.999573i \(0.490695\pi\)
\(422\) 11980.7 1.38202
\(423\) 1856.30 0.213372
\(424\) 7710.66 0.883166
\(425\) −924.040 −0.105465
\(426\) −12477.5 −1.41909
\(427\) −1320.10 −0.149612
\(428\) −2568.07 −0.290029
\(429\) 0 0
\(430\) −5528.82 −0.620055
\(431\) −6636.70 −0.741714 −0.370857 0.928690i \(-0.620936\pi\)
−0.370857 + 0.928690i \(0.620936\pi\)
\(432\) 3485.28 0.388161
\(433\) −4418.04 −0.490341 −0.245170 0.969480i \(-0.578844\pi\)
−0.245170 + 0.969480i \(0.578844\pi\)
\(434\) 11358.0 1.25622
\(435\) −3055.13 −0.336741
\(436\) 3620.67 0.397703
\(437\) −8338.23 −0.912750
\(438\) −13239.9 −1.44435
\(439\) 8127.71 0.883632 0.441816 0.897106i \(-0.354334\pi\)
0.441816 + 0.897106i \(0.354334\pi\)
\(440\) −2892.67 −0.313415
\(441\) 4257.80 0.459756
\(442\) 0 0
\(443\) −16067.6 −1.72324 −0.861620 0.507554i \(-0.830550\pi\)
−0.861620 + 0.507554i \(0.830550\pi\)
\(444\) 3232.81 0.345546
\(445\) −4676.45 −0.498168
\(446\) 4162.65 0.441944
\(447\) 10502.4 1.11129
\(448\) −14213.3 −1.49892
\(449\) −6330.96 −0.665426 −0.332713 0.943028i \(-0.607964\pi\)
−0.332713 + 0.943028i \(0.607964\pi\)
\(450\) −347.683 −0.0364221
\(451\) 680.643 0.0710648
\(452\) −196.363 −0.0204340
\(453\) −12138.6 −1.25898
\(454\) −3899.47 −0.403108
\(455\) 0 0
\(456\) 13845.9 1.42191
\(457\) −7781.66 −0.796523 −0.398261 0.917272i \(-0.630386\pi\)
−0.398261 + 0.917272i \(0.630386\pi\)
\(458\) −5855.23 −0.597373
\(459\) −7658.29 −0.778776
\(460\) −1940.29 −0.196666
\(461\) 16672.3 1.68439 0.842197 0.539171i \(-0.181262\pi\)
0.842197 + 0.539171i \(0.181262\pi\)
\(462\) −4410.76 −0.444172
\(463\) −287.484 −0.0288564 −0.0144282 0.999896i \(-0.504593\pi\)
−0.0144282 + 0.999896i \(0.504593\pi\)
\(464\) 1983.24 0.198426
\(465\) −12847.7 −1.28129
\(466\) 9982.53 0.992343
\(467\) −3349.86 −0.331934 −0.165967 0.986131i \(-0.553075\pi\)
−0.165967 + 0.986131i \(0.553075\pi\)
\(468\) 0 0
\(469\) 7160.60 0.705002
\(470\) 3256.21 0.319570
\(471\) −8104.31 −0.792838
\(472\) 5126.13 0.499893
\(473\) −2286.54 −0.222273
\(474\) −13820.4 −1.33922
\(475\) 808.970 0.0781433
\(476\) 4695.55 0.452143
\(477\) −4782.82 −0.459099
\(478\) 10069.6 0.963542
\(479\) 8197.72 0.781970 0.390985 0.920397i \(-0.372134\pi\)
0.390985 + 0.920397i \(0.372134\pi\)
\(480\) 5828.91 0.554276
\(481\) 0 0
\(482\) −11686.1 −1.10433
\(483\) −15502.4 −1.46042
\(484\) −228.310 −0.0214416
\(485\) 11954.5 1.11923
\(486\) −9454.26 −0.882415
\(487\) 10583.9 0.984806 0.492403 0.870367i \(-0.336119\pi\)
0.492403 + 0.870367i \(0.336119\pi\)
\(488\) −1292.03 −0.119852
\(489\) 18628.2 1.72269
\(490\) 7468.77 0.688581
\(491\) 7023.97 0.645596 0.322798 0.946468i \(-0.395377\pi\)
0.322798 + 0.946468i \(0.395377\pi\)
\(492\) −758.110 −0.0694680
\(493\) −4357.83 −0.398108
\(494\) 0 0
\(495\) 1794.29 0.162924
\(496\) 8340.13 0.755006
\(497\) 19411.2 1.75193
\(498\) 22876.5 2.05847
\(499\) −14779.1 −1.32586 −0.662928 0.748683i \(-0.730687\pi\)
−0.662928 + 0.748683i \(0.730687\pi\)
\(500\) 2725.51 0.243777
\(501\) 10790.4 0.962231
\(502\) −2716.35 −0.241507
\(503\) 13506.3 1.19725 0.598624 0.801030i \(-0.295714\pi\)
0.598624 + 0.801030i \(0.295714\pi\)
\(504\) 9257.59 0.818186
\(505\) −7972.22 −0.702493
\(506\) 2599.77 0.228407
\(507\) 0 0
\(508\) 4684.01 0.409093
\(509\) 9756.32 0.849590 0.424795 0.905290i \(-0.360346\pi\)
0.424795 + 0.905290i \(0.360346\pi\)
\(510\) 17208.2 1.49410
\(511\) 20597.3 1.78311
\(512\) −12651.5 −1.09204
\(513\) 6704.60 0.577028
\(514\) 1657.18 0.142209
\(515\) −5565.72 −0.476223
\(516\) 2546.78 0.217278
\(517\) 1346.66 0.114557
\(518\) 16294.1 1.38209
\(519\) 5418.39 0.458267
\(520\) 0 0
\(521\) −20113.6 −1.69135 −0.845675 0.533698i \(-0.820802\pi\)
−0.845675 + 0.533698i \(0.820802\pi\)
\(522\) −1639.70 −0.137486
\(523\) 7449.01 0.622797 0.311398 0.950279i \(-0.399203\pi\)
0.311398 + 0.950279i \(0.399203\pi\)
\(524\) 1726.53 0.143939
\(525\) 1504.03 0.125031
\(526\) −17313.6 −1.43518
\(527\) −18326.0 −1.51479
\(528\) −3238.81 −0.266953
\(529\) −3029.64 −0.249005
\(530\) −8389.74 −0.687598
\(531\) −3179.68 −0.259861
\(532\) −4110.81 −0.335012
\(533\) 0 0
\(534\) −6979.08 −0.565570
\(535\) 14641.4 1.18318
\(536\) 7008.36 0.564767
\(537\) 7357.20 0.591223
\(538\) −1232.76 −0.0987884
\(539\) 3088.83 0.246838
\(540\) 1560.15 0.124330
\(541\) −12994.4 −1.03267 −0.516335 0.856387i \(-0.672704\pi\)
−0.516335 + 0.856387i \(0.672704\pi\)
\(542\) 4421.17 0.350379
\(543\) 28663.1 2.26529
\(544\) 8314.37 0.655286
\(545\) −20642.6 −1.62244
\(546\) 0 0
\(547\) 7228.20 0.565001 0.282501 0.959267i \(-0.408836\pi\)
0.282501 + 0.959267i \(0.408836\pi\)
\(548\) 5540.92 0.431928
\(549\) 801.432 0.0623029
\(550\) −252.228 −0.0195546
\(551\) 3815.15 0.294975
\(552\) −15172.8 −1.16992
\(553\) 21500.4 1.65333
\(554\) 7122.31 0.546205
\(555\) −18431.3 −1.40966
\(556\) −5481.54 −0.418110
\(557\) −21258.3 −1.61713 −0.808565 0.588407i \(-0.799755\pi\)
−0.808565 + 0.588407i \(0.799755\pi\)
\(558\) −6895.41 −0.523129
\(559\) 0 0
\(560\) 12183.4 0.919359
\(561\) 7116.73 0.535595
\(562\) 15152.4 1.13731
\(563\) 4193.52 0.313918 0.156959 0.987605i \(-0.449831\pi\)
0.156959 + 0.987605i \(0.449831\pi\)
\(564\) −1499.93 −0.111983
\(565\) 1119.53 0.0833610
\(566\) 17404.5 1.29252
\(567\) 22690.4 1.68061
\(568\) 18998.5 1.40345
\(569\) −12696.3 −0.935427 −0.467713 0.883880i \(-0.654922\pi\)
−0.467713 + 0.883880i \(0.654922\pi\)
\(570\) −15065.3 −1.10704
\(571\) 5206.70 0.381600 0.190800 0.981629i \(-0.438892\pi\)
0.190800 + 0.981629i \(0.438892\pi\)
\(572\) 0 0
\(573\) 16598.5 1.21015
\(574\) −3821.05 −0.277853
\(575\) −886.500 −0.0642950
\(576\) 8628.89 0.624196
\(577\) −5567.86 −0.401721 −0.200860 0.979620i \(-0.564374\pi\)
−0.200860 + 0.979620i \(0.564374\pi\)
\(578\) 12398.5 0.892232
\(579\) −13423.8 −0.963510
\(580\) 887.778 0.0635568
\(581\) −35588.9 −2.54127
\(582\) 17840.8 1.27066
\(583\) −3469.71 −0.246485
\(584\) 20159.4 1.42843
\(585\) 0 0
\(586\) −13039.1 −0.919179
\(587\) −19446.1 −1.36734 −0.683669 0.729792i \(-0.739617\pi\)
−0.683669 + 0.729792i \(0.739617\pi\)
\(588\) −3440.39 −0.241291
\(589\) 16043.8 1.12237
\(590\) −5577.59 −0.389196
\(591\) 21509.4 1.49709
\(592\) 11964.7 0.830653
\(593\) −629.272 −0.0435769 −0.0217884 0.999763i \(-0.506936\pi\)
−0.0217884 + 0.999763i \(0.506936\pi\)
\(594\) −2090.42 −0.144396
\(595\) −26770.8 −1.84453
\(596\) −3051.85 −0.209746
\(597\) −782.909 −0.0536722
\(598\) 0 0
\(599\) −25701.5 −1.75315 −0.876574 0.481268i \(-0.840176\pi\)
−0.876574 + 0.481268i \(0.840176\pi\)
\(600\) 1472.06 0.100161
\(601\) 11196.3 0.759913 0.379957 0.925004i \(-0.375939\pi\)
0.379957 + 0.925004i \(0.375939\pi\)
\(602\) 12836.3 0.869053
\(603\) −4347.20 −0.293585
\(604\) 3527.30 0.237622
\(605\) 1301.67 0.0874717
\(606\) −11897.7 −0.797540
\(607\) 5856.62 0.391619 0.195810 0.980642i \(-0.437267\pi\)
0.195810 + 0.980642i \(0.437267\pi\)
\(608\) −7278.98 −0.485529
\(609\) 7093.12 0.471967
\(610\) 1405.82 0.0933117
\(611\) 0 0
\(612\) −2850.67 −0.188287
\(613\) 18626.4 1.22727 0.613633 0.789592i \(-0.289708\pi\)
0.613633 + 0.789592i \(0.289708\pi\)
\(614\) −533.350 −0.0350558
\(615\) 4322.23 0.283397
\(616\) 6715.94 0.439274
\(617\) −6014.29 −0.392425 −0.196213 0.980561i \(-0.562864\pi\)
−0.196213 + 0.980561i \(0.562864\pi\)
\(618\) −8306.23 −0.540656
\(619\) 13605.2 0.883427 0.441713 0.897156i \(-0.354371\pi\)
0.441713 + 0.897156i \(0.354371\pi\)
\(620\) 3733.37 0.241832
\(621\) −7347.16 −0.474769
\(622\) 18085.7 1.16587
\(623\) 10857.4 0.698220
\(624\) 0 0
\(625\) −14379.7 −0.920303
\(626\) −1040.23 −0.0664153
\(627\) −6230.49 −0.396845
\(628\) 2355.00 0.149641
\(629\) −26290.4 −1.66656
\(630\) −10072.9 −0.637006
\(631\) −15244.3 −0.961751 −0.480876 0.876789i \(-0.659681\pi\)
−0.480876 + 0.876789i \(0.659681\pi\)
\(632\) 21043.3 1.32446
\(633\) 31464.1 1.97565
\(634\) −18907.9 −1.18443
\(635\) −26705.0 −1.66891
\(636\) 3864.62 0.240947
\(637\) 0 0
\(638\) −1189.52 −0.0738146
\(639\) −11784.5 −0.729559
\(640\) 7954.82 0.491315
\(641\) −25338.9 −1.56135 −0.780677 0.624934i \(-0.785126\pi\)
−0.780677 + 0.624934i \(0.785126\pi\)
\(642\) 21850.6 1.34326
\(643\) 11455.3 0.702570 0.351285 0.936269i \(-0.385745\pi\)
0.351285 + 0.936269i \(0.385745\pi\)
\(644\) 4504.79 0.275642
\(645\) −14520.0 −0.886393
\(646\) −21489.1 −1.30879
\(647\) −12557.8 −0.763058 −0.381529 0.924357i \(-0.624602\pi\)
−0.381529 + 0.924357i \(0.624602\pi\)
\(648\) 22207.9 1.34631
\(649\) −2306.71 −0.139516
\(650\) 0 0
\(651\) 29828.7 1.79582
\(652\) −5413.10 −0.325143
\(653\) −3738.25 −0.224026 −0.112013 0.993707i \(-0.535730\pi\)
−0.112013 + 0.993707i \(0.535730\pi\)
\(654\) −30806.7 −1.84195
\(655\) −9843.49 −0.587201
\(656\) −2805.79 −0.166993
\(657\) −12504.6 −0.742543
\(658\) −7559.99 −0.447901
\(659\) 16091.1 0.951171 0.475586 0.879669i \(-0.342236\pi\)
0.475586 + 0.879669i \(0.342236\pi\)
\(660\) −1449.82 −0.0855063
\(661\) 13820.8 0.813265 0.406633 0.913592i \(-0.366703\pi\)
0.406633 + 0.913592i \(0.366703\pi\)
\(662\) −22905.4 −1.34478
\(663\) 0 0
\(664\) −34832.3 −2.03577
\(665\) 23437.0 1.36669
\(666\) −9892.13 −0.575544
\(667\) −4180.79 −0.242700
\(668\) −3135.53 −0.181613
\(669\) 10932.1 0.631777
\(670\) −7625.58 −0.439705
\(671\) 581.401 0.0334497
\(672\) −13533.1 −0.776859
\(673\) −20587.0 −1.17916 −0.589578 0.807712i \(-0.700706\pi\)
−0.589578 + 0.807712i \(0.700706\pi\)
\(674\) −8326.35 −0.475844
\(675\) 712.816 0.0406464
\(676\) 0 0
\(677\) −3979.12 −0.225894 −0.112947 0.993601i \(-0.536029\pi\)
−0.112947 + 0.993601i \(0.536029\pi\)
\(678\) 1670.77 0.0946397
\(679\) −27754.9 −1.56868
\(680\) −26201.6 −1.47763
\(681\) −10240.9 −0.576259
\(682\) −5002.30 −0.280862
\(683\) −26072.1 −1.46064 −0.730322 0.683103i \(-0.760630\pi\)
−0.730322 + 0.683103i \(0.760630\pi\)
\(684\) 2495.67 0.139509
\(685\) −31590.5 −1.76206
\(686\) 3840.83 0.213766
\(687\) −15377.2 −0.853969
\(688\) 9425.69 0.522312
\(689\) 0 0
\(690\) 16509.1 0.910856
\(691\) −13017.8 −0.716675 −0.358337 0.933592i \(-0.616656\pi\)
−0.358337 + 0.933592i \(0.616656\pi\)
\(692\) −1574.51 −0.0864940
\(693\) −4165.81 −0.228349
\(694\) −11245.8 −0.615106
\(695\) 31252.0 1.70569
\(696\) 6942.32 0.378086
\(697\) 6165.22 0.335042
\(698\) −28560.0 −1.54873
\(699\) 26216.5 1.41859
\(700\) −437.052 −0.0235986
\(701\) −13900.1 −0.748927 −0.374464 0.927242i \(-0.622173\pi\)
−0.374464 + 0.927242i \(0.622173\pi\)
\(702\) 0 0
\(703\) 23016.4 1.23482
\(704\) 6259.85 0.335124
\(705\) 8551.58 0.456838
\(706\) −11511.9 −0.613676
\(707\) 18509.2 0.984597
\(708\) 2569.24 0.136381
\(709\) −23353.6 −1.23704 −0.618520 0.785769i \(-0.712268\pi\)
−0.618520 + 0.785769i \(0.712268\pi\)
\(710\) −20671.7 −1.09267
\(711\) −13052.9 −0.688496
\(712\) 10626.5 0.559334
\(713\) −17581.5 −0.923466
\(714\) −39952.5 −2.09409
\(715\) 0 0
\(716\) −2137.90 −0.111588
\(717\) 26445.1 1.37742
\(718\) 11857.2 0.616305
\(719\) −18288.9 −0.948624 −0.474312 0.880357i \(-0.657303\pi\)
−0.474312 + 0.880357i \(0.657303\pi\)
\(720\) −7396.51 −0.382849
\(721\) 12922.0 0.667463
\(722\) 1854.35 0.0955842
\(723\) −30690.5 −1.57869
\(724\) −8329.11 −0.427554
\(725\) 405.618 0.0207783
\(726\) 1942.60 0.0993066
\(727\) −18378.0 −0.937555 −0.468777 0.883316i \(-0.655305\pi\)
−0.468777 + 0.883316i \(0.655305\pi\)
\(728\) 0 0
\(729\) −300.001 −0.0152416
\(730\) −21934.8 −1.11211
\(731\) −20711.3 −1.04793
\(732\) −647.574 −0.0326981
\(733\) 12956.4 0.652874 0.326437 0.945219i \(-0.394152\pi\)
0.326437 + 0.945219i \(0.394152\pi\)
\(734\) 6753.65 0.339621
\(735\) 19614.7 0.984355
\(736\) 7976.59 0.399485
\(737\) −3153.69 −0.157622
\(738\) 2319.75 0.115706
\(739\) 30833.2 1.53480 0.767400 0.641169i \(-0.221550\pi\)
0.767400 + 0.641169i \(0.221550\pi\)
\(740\) 5355.87 0.266062
\(741\) 0 0
\(742\) 19478.5 0.963720
\(743\) 28532.4 1.40882 0.704410 0.709793i \(-0.251212\pi\)
0.704410 + 0.709793i \(0.251212\pi\)
\(744\) 29194.5 1.43860
\(745\) 17399.5 0.855664
\(746\) 28026.3 1.37549
\(747\) 21606.0 1.05826
\(748\) −2068.02 −0.101089
\(749\) −33993.1 −1.65832
\(750\) −23190.2 −1.12905
\(751\) 19355.4 0.940464 0.470232 0.882543i \(-0.344170\pi\)
0.470232 + 0.882543i \(0.344170\pi\)
\(752\) −5551.28 −0.269195
\(753\) −7133.77 −0.345244
\(754\) 0 0
\(755\) −20110.3 −0.969387
\(756\) −3622.21 −0.174257
\(757\) −21781.8 −1.04580 −0.522902 0.852393i \(-0.675151\pi\)
−0.522902 + 0.852393i \(0.675151\pi\)
\(758\) 26454.6 1.26765
\(759\) 6827.61 0.326517
\(760\) 22938.7 1.09484
\(761\) 1847.78 0.0880182 0.0440091 0.999031i \(-0.485987\pi\)
0.0440091 + 0.999031i \(0.485987\pi\)
\(762\) −39854.2 −1.89471
\(763\) 47926.1 2.27397
\(764\) −4823.30 −0.228404
\(765\) 16252.5 0.768120
\(766\) −16638.5 −0.784822
\(767\) 0 0
\(768\) −17689.8 −0.831155
\(769\) −3741.48 −0.175450 −0.0877251 0.996145i \(-0.527960\pi\)
−0.0877251 + 0.996145i \(0.527960\pi\)
\(770\) −7307.42 −0.342001
\(771\) 4352.15 0.203293
\(772\) 3900.76 0.181854
\(773\) −16469.9 −0.766338 −0.383169 0.923678i \(-0.625167\pi\)
−0.383169 + 0.923678i \(0.625167\pi\)
\(774\) −7792.93 −0.361901
\(775\) 1705.74 0.0790607
\(776\) −27164.8 −1.25665
\(777\) 42792.1 1.97575
\(778\) 21753.1 1.00243
\(779\) −5397.47 −0.248247
\(780\) 0 0
\(781\) −8549.11 −0.391692
\(782\) 23548.6 1.07685
\(783\) 3361.69 0.153432
\(784\) −12733.0 −0.580037
\(785\) −13426.6 −0.610466
\(786\) −14690.3 −0.666649
\(787\) 32554.4 1.47451 0.737254 0.675616i \(-0.236122\pi\)
0.737254 + 0.675616i \(0.236122\pi\)
\(788\) −6250.33 −0.282562
\(789\) −45469.4 −2.05165
\(790\) −22896.5 −1.03117
\(791\) −2599.23 −0.116837
\(792\) −4077.24 −0.182928
\(793\) 0 0
\(794\) −9213.98 −0.411829
\(795\) −22033.4 −0.982949
\(796\) 227.502 0.0101302
\(797\) 316.849 0.0140820 0.00704101 0.999975i \(-0.497759\pi\)
0.00704101 + 0.999975i \(0.497759\pi\)
\(798\) 34977.2 1.55160
\(799\) 12198.0 0.540092
\(800\) −773.883 −0.0342011
\(801\) −6591.49 −0.290760
\(802\) 19058.5 0.839127
\(803\) −9071.50 −0.398663
\(804\) 3512.62 0.154080
\(805\) −25683.2 −1.12449
\(806\) 0 0
\(807\) −3237.52 −0.141222
\(808\) 18115.7 0.788746
\(809\) 17621.3 0.765798 0.382899 0.923790i \(-0.374926\pi\)
0.382899 + 0.923790i \(0.374926\pi\)
\(810\) −24163.8 −1.04818
\(811\) 35740.6 1.54750 0.773751 0.633490i \(-0.218378\pi\)
0.773751 + 0.633490i \(0.218378\pi\)
\(812\) −2061.16 −0.0890797
\(813\) 11611.0 0.500881
\(814\) −7176.28 −0.309003
\(815\) 30861.8 1.32643
\(816\) −29337.0 −1.25858
\(817\) 18132.1 0.776454
\(818\) −16756.8 −0.716246
\(819\) 0 0
\(820\) −1255.98 −0.0534886
\(821\) −4653.75 −0.197828 −0.0989142 0.995096i \(-0.531537\pi\)
−0.0989142 + 0.995096i \(0.531537\pi\)
\(822\) −47145.4 −2.00047
\(823\) 34143.4 1.44613 0.723065 0.690780i \(-0.242733\pi\)
0.723065 + 0.690780i \(0.242733\pi\)
\(824\) 12647.3 0.534695
\(825\) −662.410 −0.0279541
\(826\) 12949.6 0.545488
\(827\) −10628.8 −0.446914 −0.223457 0.974714i \(-0.571734\pi\)
−0.223457 + 0.974714i \(0.571734\pi\)
\(828\) −2734.85 −0.114786
\(829\) 17652.2 0.739549 0.369775 0.929122i \(-0.379435\pi\)
0.369775 + 0.929122i \(0.379435\pi\)
\(830\) 37900.0 1.58497
\(831\) 18704.8 0.780823
\(832\) 0 0
\(833\) 27978.5 1.16374
\(834\) 46640.1 1.93647
\(835\) 17876.6 0.740894
\(836\) 1810.49 0.0749010
\(837\) 14136.9 0.583802
\(838\) 37590.5 1.54957
\(839\) −31051.9 −1.27775 −0.638874 0.769312i \(-0.720599\pi\)
−0.638874 + 0.769312i \(0.720599\pi\)
\(840\) 42647.7 1.75177
\(841\) −22476.1 −0.921566
\(842\) 1248.56 0.0511023
\(843\) 39793.9 1.62583
\(844\) −9143.05 −0.372887
\(845\) 0 0
\(846\) 4589.66 0.186520
\(847\) −3022.10 −0.122598
\(848\) 14303.0 0.579208
\(849\) 45708.2 1.84770
\(850\) −2284.67 −0.0921923
\(851\) −25222.3 −1.01599
\(852\) 9522.13 0.382891
\(853\) 27998.0 1.12384 0.561918 0.827193i \(-0.310064\pi\)
0.561918 + 0.827193i \(0.310064\pi\)
\(854\) −3263.92 −0.130783
\(855\) −14228.6 −0.569133
\(856\) −33270.3 −1.32845
\(857\) −39389.9 −1.57005 −0.785025 0.619464i \(-0.787350\pi\)
−0.785025 + 0.619464i \(0.787350\pi\)
\(858\) 0 0
\(859\) 32534.3 1.29226 0.646132 0.763226i \(-0.276385\pi\)
0.646132 + 0.763226i \(0.276385\pi\)
\(860\) 4219.31 0.167299
\(861\) −10035.0 −0.397202
\(862\) −16409.1 −0.648371
\(863\) 23046.9 0.909067 0.454533 0.890730i \(-0.349806\pi\)
0.454533 + 0.890730i \(0.349806\pi\)
\(864\) −6413.81 −0.252549
\(865\) 8976.77 0.352855
\(866\) −10923.5 −0.428633
\(867\) 32561.4 1.27548
\(868\) −8667.80 −0.338945
\(869\) −9469.24 −0.369646
\(870\) −7553.73 −0.294362
\(871\) 0 0
\(872\) 46907.1 1.82165
\(873\) 16850.0 0.653249
\(874\) −20616.1 −0.797882
\(875\) 36077.1 1.39386
\(876\) 10104.0 0.389705
\(877\) −13302.0 −0.512176 −0.256088 0.966654i \(-0.582434\pi\)
−0.256088 + 0.966654i \(0.582434\pi\)
\(878\) 20095.6 0.772429
\(879\) −34243.7 −1.31400
\(880\) −5365.82 −0.205547
\(881\) −26136.9 −0.999516 −0.499758 0.866165i \(-0.666578\pi\)
−0.499758 + 0.866165i \(0.666578\pi\)
\(882\) 10527.3 0.401897
\(883\) 9479.63 0.361285 0.180643 0.983549i \(-0.442182\pi\)
0.180643 + 0.983549i \(0.442182\pi\)
\(884\) 0 0
\(885\) −14648.1 −0.556372
\(886\) −39726.8 −1.50637
\(887\) −11961.4 −0.452790 −0.226395 0.974036i \(-0.572694\pi\)
−0.226395 + 0.974036i \(0.572694\pi\)
\(888\) 41882.3 1.58275
\(889\) 62001.3 2.33910
\(890\) −11562.4 −0.435475
\(891\) −9993.33 −0.375745
\(892\) −3176.71 −0.119242
\(893\) −10679.0 −0.400177
\(894\) 25966.9 0.971434
\(895\) 12188.8 0.455227
\(896\) −18468.8 −0.688615
\(897\) 0 0
\(898\) −15653.1 −0.581684
\(899\) 8044.39 0.298438
\(900\) 265.334 0.00982717
\(901\) −31428.5 −1.16208
\(902\) 1682.87 0.0621214
\(903\) 33711.2 1.24235
\(904\) −2543.96 −0.0935962
\(905\) 47486.9 1.74422
\(906\) −30012.3 −1.10054
\(907\) −17900.5 −0.655321 −0.327661 0.944795i \(-0.606260\pi\)
−0.327661 + 0.944795i \(0.606260\pi\)
\(908\) 2975.87 0.108764
\(909\) −11236.9 −0.410017
\(910\) 0 0
\(911\) −818.497 −0.0297673 −0.0148836 0.999889i \(-0.504738\pi\)
−0.0148836 + 0.999889i \(0.504738\pi\)
\(912\) 25683.7 0.932534
\(913\) 15674.1 0.568169
\(914\) −19240.0 −0.696282
\(915\) 3692.02 0.133393
\(916\) 4468.40 0.161179
\(917\) 22853.7 0.823006
\(918\) −18934.9 −0.680769
\(919\) 43051.4 1.54531 0.772653 0.634829i \(-0.218929\pi\)
0.772653 + 0.634829i \(0.218929\pi\)
\(920\) −25137.2 −0.900813
\(921\) −1400.70 −0.0501137
\(922\) 41221.8 1.47242
\(923\) 0 0
\(924\) 3366.06 0.119843
\(925\) 2447.05 0.0869822
\(926\) −710.796 −0.0252249
\(927\) −7844.94 −0.277952
\(928\) −3649.68 −0.129102
\(929\) 42221.7 1.49112 0.745559 0.666439i \(-0.232182\pi\)
0.745559 + 0.666439i \(0.232182\pi\)
\(930\) −31765.7 −1.12004
\(931\) −24494.3 −0.862265
\(932\) −7618.14 −0.267747
\(933\) 47497.2 1.66665
\(934\) −8282.46 −0.290161
\(935\) 11790.5 0.412395
\(936\) 0 0
\(937\) 1130.59 0.0394181 0.0197091 0.999806i \(-0.493726\pi\)
0.0197091 + 0.999806i \(0.493726\pi\)
\(938\) 17704.4 0.616279
\(939\) −2731.89 −0.0949434
\(940\) −2484.97 −0.0862243
\(941\) 17108.5 0.592692 0.296346 0.955081i \(-0.404232\pi\)
0.296346 + 0.955081i \(0.404232\pi\)
\(942\) −20037.7 −0.693061
\(943\) 5914.76 0.204253
\(944\) 9508.83 0.327846
\(945\) 20651.3 0.710887
\(946\) −5653.40 −0.194300
\(947\) 2802.40 0.0961624 0.0480812 0.998843i \(-0.484689\pi\)
0.0480812 + 0.998843i \(0.484689\pi\)
\(948\) 10547.0 0.361340
\(949\) 0 0
\(950\) 2000.16 0.0683091
\(951\) −49656.5 −1.69319
\(952\) 60832.6 2.07101
\(953\) 2705.21 0.0919521 0.0459760 0.998943i \(-0.485360\pi\)
0.0459760 + 0.998943i \(0.485360\pi\)
\(954\) −11825.4 −0.401323
\(955\) 27499.2 0.931782
\(956\) −7684.59 −0.259976
\(957\) −3123.97 −0.105521
\(958\) 20268.7 0.683560
\(959\) 73344.1 2.46966
\(960\) 39751.4 1.33643
\(961\) 4038.04 0.135546
\(962\) 0 0
\(963\) 20637.2 0.690575
\(964\) 8918.24 0.297964
\(965\) −22239.5 −0.741879
\(966\) −38329.4 −1.27663
\(967\) −59777.8 −1.98792 −0.993962 0.109723i \(-0.965004\pi\)
−0.993962 + 0.109723i \(0.965004\pi\)
\(968\) −2957.85 −0.0982116
\(969\) −56435.4 −1.87097
\(970\) 29557.3 0.978378
\(971\) 25271.6 0.835224 0.417612 0.908625i \(-0.362867\pi\)
0.417612 + 0.908625i \(0.362867\pi\)
\(972\) 7214.99 0.238087
\(973\) −72558.0 −2.39065
\(974\) 26168.3 0.860870
\(975\) 0 0
\(976\) −2396.69 −0.0786025
\(977\) 50763.1 1.66229 0.831144 0.556057i \(-0.187686\pi\)
0.831144 + 0.556057i \(0.187686\pi\)
\(978\) 46057.8 1.50590
\(979\) −4781.82 −0.156106
\(980\) −5699.77 −0.185788
\(981\) −29095.9 −0.946952
\(982\) 17366.6 0.564349
\(983\) −25390.8 −0.823847 −0.411924 0.911218i \(-0.635143\pi\)
−0.411924 + 0.911218i \(0.635143\pi\)
\(984\) −9821.61 −0.318192
\(985\) 35635.1 1.15272
\(986\) −10774.6 −0.348007
\(987\) −19854.3 −0.640293
\(988\) 0 0
\(989\) −19869.9 −0.638853
\(990\) 4436.33 0.142420
\(991\) 15905.8 0.509853 0.254927 0.966960i \(-0.417949\pi\)
0.254927 + 0.966960i \(0.417949\pi\)
\(992\) −15348.0 −0.491229
\(993\) −60155.0 −1.92242
\(994\) 47993.7 1.53146
\(995\) −1297.06 −0.0413263
\(996\) −17458.1 −0.555403
\(997\) 26353.4 0.837133 0.418567 0.908186i \(-0.362533\pi\)
0.418567 + 0.908186i \(0.362533\pi\)
\(998\) −36540.9 −1.15900
\(999\) 20280.7 0.642296
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.f.1.12 17
13.4 even 6 143.4.e.a.133.12 yes 34
13.10 even 6 143.4.e.a.100.12 34
13.12 even 2 1859.4.a.i.1.6 17
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
143.4.e.a.100.12 34 13.10 even 6
143.4.e.a.133.12 yes 34 13.4 even 6
1859.4.a.f.1.12 17 1.1 even 1 trivial
1859.4.a.i.1.6 17 13.12 even 2