Properties

Label 1859.2.a.t.1.10
Level $1859$
Weight $2$
Character 1859.1
Self dual yes
Analytic conductor $14.844$
Analytic rank $0$
Dimension $21$
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] = [1859,2,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, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1859.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
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: \(14.8441897358\)
Analytic rank: \(0\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
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)
 
\(f(q)\) \(=\) \(q-0.392741 q^{2} +1.69948 q^{3} -1.84575 q^{4} +1.18432 q^{5} -0.667456 q^{6} +5.07600 q^{7} +1.51039 q^{8} -0.111771 q^{9} +O(q^{10})\) \(q-0.392741 q^{2} +1.69948 q^{3} -1.84575 q^{4} +1.18432 q^{5} -0.667456 q^{6} +5.07600 q^{7} +1.51039 q^{8} -0.111771 q^{9} -0.465133 q^{10} +1.00000 q^{11} -3.13682 q^{12} -1.99356 q^{14} +2.01273 q^{15} +3.09832 q^{16} +7.48561 q^{17} +0.0438972 q^{18} -3.99272 q^{19} -2.18597 q^{20} +8.62655 q^{21} -0.392741 q^{22} +3.36585 q^{23} +2.56687 q^{24} -3.59738 q^{25} -5.28839 q^{27} -9.36905 q^{28} +8.64322 q^{29} -0.790483 q^{30} -7.64123 q^{31} -4.23761 q^{32} +1.69948 q^{33} -2.93991 q^{34} +6.01162 q^{35} +0.206302 q^{36} -0.696141 q^{37} +1.56811 q^{38} +1.78879 q^{40} +6.07962 q^{41} -3.38800 q^{42} -9.18013 q^{43} -1.84575 q^{44} -0.132373 q^{45} -1.32191 q^{46} -3.26831 q^{47} +5.26552 q^{48} +18.7658 q^{49} +1.41284 q^{50} +12.7216 q^{51} +2.06811 q^{53} +2.07697 q^{54} +1.18432 q^{55} +7.66672 q^{56} -6.78555 q^{57} -3.39455 q^{58} -3.29281 q^{59} -3.71501 q^{60} +3.96312 q^{61} +3.00103 q^{62} -0.567351 q^{63} -4.53235 q^{64} -0.667456 q^{66} +5.18488 q^{67} -13.8166 q^{68} +5.72019 q^{69} -2.36101 q^{70} -4.07910 q^{71} -0.168818 q^{72} +4.57498 q^{73} +0.273403 q^{74} -6.11367 q^{75} +7.36958 q^{76} +5.07600 q^{77} +2.93846 q^{79} +3.66941 q^{80} -8.65219 q^{81} -2.38772 q^{82} -1.47741 q^{83} -15.9225 q^{84} +8.86538 q^{85} +3.60542 q^{86} +14.6890 q^{87} +1.51039 q^{88} -17.0055 q^{89} +0.0519884 q^{90} -6.21253 q^{92} -12.9861 q^{93} +1.28360 q^{94} -4.72867 q^{95} -7.20173 q^{96} +12.7271 q^{97} -7.37009 q^{98} -0.111771 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9} + 18 q^{10} + 21 q^{11} + 23 q^{12} + 20 q^{14} + 16 q^{15} + 50 q^{16} + 16 q^{17} + 3 q^{18} - 11 q^{19} + 24 q^{20} - 5 q^{21} - 9 q^{23} - 54 q^{24} + 36 q^{25} - 11 q^{28} + 28 q^{29} + 21 q^{30} + 15 q^{31} - 61 q^{32} + 6 q^{33} - 6 q^{34} - 3 q^{35} + 45 q^{36} - 12 q^{37} + q^{38} + 55 q^{40} - 4 q^{41} - 34 q^{42} + 17 q^{43} + 32 q^{44} + 9 q^{45} + 11 q^{46} + 36 q^{47} + 24 q^{48} + 72 q^{49} - 9 q^{50} + 2 q^{51} + 19 q^{53} + q^{54} + 7 q^{55} + 44 q^{56} - 4 q^{57} - 33 q^{58} + 54 q^{59} + 64 q^{60} + 98 q^{61} - 29 q^{62} - 81 q^{63} + 63 q^{64} - 19 q^{66} + 25 q^{67} + 4 q^{68} + 89 q^{69} + 65 q^{70} + 37 q^{71} + 55 q^{72} + 8 q^{73} - 11 q^{74} + 24 q^{75} + 13 q^{76} + q^{77} + 24 q^{79} + 26 q^{80} + 81 q^{81} + 26 q^{82} - 34 q^{83} - 103 q^{84} - 11 q^{85} + 30 q^{86} + 32 q^{87} - 3 q^{88} + 6 q^{89} + 47 q^{90} - 80 q^{92} + 41 q^{93} + 40 q^{94} + 20 q^{95} - 98 q^{96} - 5 q^{98} + 33 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.392741 −0.277710 −0.138855 0.990313i \(-0.544342\pi\)
−0.138855 + 0.990313i \(0.544342\pi\)
\(3\) 1.69948 0.981195 0.490597 0.871386i \(-0.336779\pi\)
0.490597 + 0.871386i \(0.336779\pi\)
\(4\) −1.84575 −0.922877
\(5\) 1.18432 0.529645 0.264823 0.964297i \(-0.414687\pi\)
0.264823 + 0.964297i \(0.414687\pi\)
\(6\) −0.667456 −0.272488
\(7\) 5.07600 1.91855 0.959274 0.282478i \(-0.0911565\pi\)
0.959274 + 0.282478i \(0.0911565\pi\)
\(8\) 1.51039 0.534002
\(9\) −0.111771 −0.0372571
\(10\) −0.465133 −0.147088
\(11\) 1.00000 0.301511
\(12\) −3.13682 −0.905522
\(13\) 0 0
\(14\) −1.99356 −0.532800
\(15\) 2.01273 0.519685
\(16\) 3.09832 0.774579
\(17\) 7.48561 1.81553 0.907763 0.419483i \(-0.137789\pi\)
0.907763 + 0.419483i \(0.137789\pi\)
\(18\) 0.0438972 0.0103467
\(19\) −3.99272 −0.915993 −0.457997 0.888954i \(-0.651433\pi\)
−0.457997 + 0.888954i \(0.651433\pi\)
\(20\) −2.18597 −0.488798
\(21\) 8.62655 1.88247
\(22\) −0.392741 −0.0837327
\(23\) 3.36585 0.701828 0.350914 0.936408i \(-0.385871\pi\)
0.350914 + 0.936408i \(0.385871\pi\)
\(24\) 2.56687 0.523960
\(25\) −3.59738 −0.719476
\(26\) 0 0
\(27\) −5.28839 −1.01775
\(28\) −9.36905 −1.77058
\(29\) 8.64322 1.60501 0.802503 0.596648i \(-0.203501\pi\)
0.802503 + 0.596648i \(0.203501\pi\)
\(30\) −0.790483 −0.144322
\(31\) −7.64123 −1.37240 −0.686202 0.727411i \(-0.740724\pi\)
−0.686202 + 0.727411i \(0.740724\pi\)
\(32\) −4.23761 −0.749111
\(33\) 1.69948 0.295841
\(34\) −2.93991 −0.504190
\(35\) 6.01162 1.01615
\(36\) 0.206302 0.0343837
\(37\) −0.696141 −0.114445 −0.0572224 0.998361i \(-0.518224\pi\)
−0.0572224 + 0.998361i \(0.518224\pi\)
\(38\) 1.56811 0.254381
\(39\) 0 0
\(40\) 1.78879 0.282832
\(41\) 6.07962 0.949477 0.474738 0.880127i \(-0.342543\pi\)
0.474738 + 0.880127i \(0.342543\pi\)
\(42\) −3.38800 −0.522781
\(43\) −9.18013 −1.39996 −0.699979 0.714164i \(-0.746807\pi\)
−0.699979 + 0.714164i \(0.746807\pi\)
\(44\) −1.84575 −0.278258
\(45\) −0.132373 −0.0197330
\(46\) −1.32191 −0.194905
\(47\) −3.26831 −0.476732 −0.238366 0.971175i \(-0.576612\pi\)
−0.238366 + 0.971175i \(0.576612\pi\)
\(48\) 5.26552 0.760013
\(49\) 18.7658 2.68082
\(50\) 1.41284 0.199806
\(51\) 12.7216 1.78138
\(52\) 0 0
\(53\) 2.06811 0.284077 0.142039 0.989861i \(-0.454634\pi\)
0.142039 + 0.989861i \(0.454634\pi\)
\(54\) 2.07697 0.282640
\(55\) 1.18432 0.159694
\(56\) 7.66672 1.02451
\(57\) −6.78555 −0.898768
\(58\) −3.39455 −0.445726
\(59\) −3.29281 −0.428687 −0.214343 0.976758i \(-0.568761\pi\)
−0.214343 + 0.976758i \(0.568761\pi\)
\(60\) −3.71501 −0.479606
\(61\) 3.96312 0.507426 0.253713 0.967280i \(-0.418348\pi\)
0.253713 + 0.967280i \(0.418348\pi\)
\(62\) 3.00103 0.381131
\(63\) −0.567351 −0.0714794
\(64\) −4.53235 −0.566544
\(65\) 0 0
\(66\) −0.667456 −0.0821581
\(67\) 5.18488 0.633433 0.316717 0.948520i \(-0.397420\pi\)
0.316717 + 0.948520i \(0.397420\pi\)
\(68\) −13.8166 −1.67551
\(69\) 5.72019 0.688629
\(70\) −2.36101 −0.282195
\(71\) −4.07910 −0.484100 −0.242050 0.970264i \(-0.577820\pi\)
−0.242050 + 0.970264i \(0.577820\pi\)
\(72\) −0.168818 −0.0198954
\(73\) 4.57498 0.535461 0.267731 0.963494i \(-0.413726\pi\)
0.267731 + 0.963494i \(0.413726\pi\)
\(74\) 0.273403 0.0317825
\(75\) −6.11367 −0.705946
\(76\) 7.36958 0.845349
\(77\) 5.07600 0.578464
\(78\) 0 0
\(79\) 2.93846 0.330602 0.165301 0.986243i \(-0.447140\pi\)
0.165301 + 0.986243i \(0.447140\pi\)
\(80\) 3.66941 0.410252
\(81\) −8.65219 −0.961355
\(82\) −2.38772 −0.263679
\(83\) −1.47741 −0.162167 −0.0810834 0.996707i \(-0.525838\pi\)
−0.0810834 + 0.996707i \(0.525838\pi\)
\(84\) −15.9225 −1.73729
\(85\) 8.86538 0.961585
\(86\) 3.60542 0.388782
\(87\) 14.6890 1.57482
\(88\) 1.51039 0.161008
\(89\) −17.0055 −1.80258 −0.901289 0.433219i \(-0.857378\pi\)
−0.901289 + 0.433219i \(0.857378\pi\)
\(90\) 0.0519884 0.00548006
\(91\) 0 0
\(92\) −6.21253 −0.647701
\(93\) −12.9861 −1.34660
\(94\) 1.28360 0.132393
\(95\) −4.72867 −0.485152
\(96\) −7.20173 −0.735024
\(97\) 12.7271 1.29224 0.646120 0.763236i \(-0.276391\pi\)
0.646120 + 0.763236i \(0.276391\pi\)
\(98\) −7.37009 −0.744492
\(99\) −0.111771 −0.0112334
\(100\) 6.63988 0.663988
\(101\) −5.42290 −0.539599 −0.269799 0.962917i \(-0.586957\pi\)
−0.269799 + 0.962917i \(0.586957\pi\)
\(102\) −4.99631 −0.494708
\(103\) −10.4956 −1.03416 −0.517080 0.855937i \(-0.672981\pi\)
−0.517080 + 0.855937i \(0.672981\pi\)
\(104\) 0 0
\(105\) 10.2166 0.997041
\(106\) −0.812233 −0.0788911
\(107\) 9.23601 0.892879 0.446439 0.894814i \(-0.352692\pi\)
0.446439 + 0.894814i \(0.352692\pi\)
\(108\) 9.76107 0.939259
\(109\) 6.34139 0.607395 0.303698 0.952768i \(-0.401779\pi\)
0.303698 + 0.952768i \(0.401779\pi\)
\(110\) −0.465133 −0.0443487
\(111\) −1.18308 −0.112293
\(112\) 15.7271 1.48607
\(113\) 2.26788 0.213344 0.106672 0.994294i \(-0.465980\pi\)
0.106672 + 0.994294i \(0.465980\pi\)
\(114\) 2.66497 0.249597
\(115\) 3.98625 0.371720
\(116\) −15.9533 −1.48122
\(117\) 0 0
\(118\) 1.29322 0.119051
\(119\) 37.9969 3.48317
\(120\) 3.04000 0.277513
\(121\) 1.00000 0.0909091
\(122\) −1.55648 −0.140917
\(123\) 10.3322 0.931622
\(124\) 14.1038 1.26656
\(125\) −10.1821 −0.910712
\(126\) 0.222822 0.0198506
\(127\) 8.46799 0.751412 0.375706 0.926739i \(-0.377400\pi\)
0.375706 + 0.926739i \(0.377400\pi\)
\(128\) 10.2553 0.906446
\(129\) −15.6014 −1.37363
\(130\) 0 0
\(131\) 3.07651 0.268796 0.134398 0.990927i \(-0.457090\pi\)
0.134398 + 0.990927i \(0.457090\pi\)
\(132\) −3.13682 −0.273025
\(133\) −20.2671 −1.75738
\(134\) −2.03632 −0.175911
\(135\) −6.26316 −0.539047
\(136\) 11.3062 0.969495
\(137\) 6.42662 0.549063 0.274532 0.961578i \(-0.411477\pi\)
0.274532 + 0.961578i \(0.411477\pi\)
\(138\) −2.24655 −0.191239
\(139\) 11.2711 0.956001 0.478001 0.878359i \(-0.341362\pi\)
0.478001 + 0.878359i \(0.341362\pi\)
\(140\) −11.0960 −0.937781
\(141\) −5.55442 −0.467767
\(142\) 1.60203 0.134439
\(143\) 0 0
\(144\) −0.346303 −0.0288585
\(145\) 10.2364 0.850084
\(146\) −1.79678 −0.148703
\(147\) 31.8920 2.63041
\(148\) 1.28490 0.105619
\(149\) −15.9762 −1.30882 −0.654410 0.756140i \(-0.727083\pi\)
−0.654410 + 0.756140i \(0.727083\pi\)
\(150\) 2.40109 0.196048
\(151\) −4.79638 −0.390324 −0.195162 0.980771i \(-0.562523\pi\)
−0.195162 + 0.980771i \(0.562523\pi\)
\(152\) −6.03056 −0.489143
\(153\) −0.836675 −0.0676412
\(154\) −1.99356 −0.160645
\(155\) −9.04968 −0.726888
\(156\) 0 0
\(157\) 19.3688 1.54580 0.772898 0.634530i \(-0.218806\pi\)
0.772898 + 0.634530i \(0.218806\pi\)
\(158\) −1.15405 −0.0918115
\(159\) 3.51471 0.278735
\(160\) −5.01870 −0.396763
\(161\) 17.0850 1.34649
\(162\) 3.39807 0.266978
\(163\) 9.41218 0.737219 0.368610 0.929584i \(-0.379834\pi\)
0.368610 + 0.929584i \(0.379834\pi\)
\(164\) −11.2215 −0.876251
\(165\) 2.01273 0.156691
\(166\) 0.580240 0.0450354
\(167\) 0.355939 0.0275434 0.0137717 0.999905i \(-0.495616\pi\)
0.0137717 + 0.999905i \(0.495616\pi\)
\(168\) 13.0294 1.00524
\(169\) 0 0
\(170\) −3.48180 −0.267042
\(171\) 0.446271 0.0341272
\(172\) 16.9443 1.29199
\(173\) 9.60710 0.730414 0.365207 0.930926i \(-0.380998\pi\)
0.365207 + 0.930926i \(0.380998\pi\)
\(174\) −5.76897 −0.437344
\(175\) −18.2603 −1.38035
\(176\) 3.09832 0.233544
\(177\) −5.59606 −0.420625
\(178\) 6.67876 0.500594
\(179\) −2.06020 −0.153987 −0.0769933 0.997032i \(-0.524532\pi\)
−0.0769933 + 0.997032i \(0.524532\pi\)
\(180\) 0.244328 0.0182112
\(181\) 16.4734 1.22446 0.612231 0.790679i \(-0.290272\pi\)
0.612231 + 0.790679i \(0.290272\pi\)
\(182\) 0 0
\(183\) 6.73524 0.497883
\(184\) 5.08373 0.374778
\(185\) −0.824456 −0.0606152
\(186\) 5.10018 0.373963
\(187\) 7.48561 0.547402
\(188\) 6.03249 0.439965
\(189\) −26.8439 −1.95260
\(190\) 1.85715 0.134732
\(191\) −5.30591 −0.383922 −0.191961 0.981403i \(-0.561485\pi\)
−0.191961 + 0.981403i \(0.561485\pi\)
\(192\) −7.70263 −0.555890
\(193\) −14.0769 −1.01327 −0.506637 0.862159i \(-0.669112\pi\)
−0.506637 + 0.862159i \(0.669112\pi\)
\(194\) −4.99845 −0.358868
\(195\) 0 0
\(196\) −34.6370 −2.47407
\(197\) −21.9002 −1.56032 −0.780161 0.625579i \(-0.784863\pi\)
−0.780161 + 0.625579i \(0.784863\pi\)
\(198\) 0.0438972 0.00311964
\(199\) −21.3859 −1.51601 −0.758004 0.652250i \(-0.773825\pi\)
−0.758004 + 0.652250i \(0.773825\pi\)
\(200\) −5.43343 −0.384202
\(201\) 8.81159 0.621521
\(202\) 2.12980 0.149852
\(203\) 43.8730 3.07928
\(204\) −23.4810 −1.64400
\(205\) 7.20023 0.502886
\(206\) 4.12205 0.287197
\(207\) −0.376205 −0.0261480
\(208\) 0 0
\(209\) −3.99272 −0.276182
\(210\) −4.01249 −0.276888
\(211\) −6.02049 −0.414468 −0.207234 0.978291i \(-0.566446\pi\)
−0.207234 + 0.978291i \(0.566446\pi\)
\(212\) −3.81723 −0.262168
\(213\) −6.93234 −0.474996
\(214\) −3.62736 −0.247961
\(215\) −10.8722 −0.741481
\(216\) −7.98751 −0.543482
\(217\) −38.7869 −2.63302
\(218\) −2.49053 −0.168680
\(219\) 7.77508 0.525391
\(220\) −2.18597 −0.147378
\(221\) 0 0
\(222\) 0.464643 0.0311848
\(223\) 3.83948 0.257110 0.128555 0.991702i \(-0.458966\pi\)
0.128555 + 0.991702i \(0.458966\pi\)
\(224\) −21.5101 −1.43720
\(225\) 0.402083 0.0268056
\(226\) −0.890690 −0.0592478
\(227\) −2.57539 −0.170935 −0.0854674 0.996341i \(-0.527238\pi\)
−0.0854674 + 0.996341i \(0.527238\pi\)
\(228\) 12.5245 0.829452
\(229\) −5.21467 −0.344595 −0.172297 0.985045i \(-0.555119\pi\)
−0.172297 + 0.985045i \(0.555119\pi\)
\(230\) −1.56557 −0.103230
\(231\) 8.62655 0.567586
\(232\) 13.0546 0.857077
\(233\) 4.87965 0.319676 0.159838 0.987143i \(-0.448903\pi\)
0.159838 + 0.987143i \(0.448903\pi\)
\(234\) 0 0
\(235\) −3.87073 −0.252499
\(236\) 6.07771 0.395625
\(237\) 4.99384 0.324385
\(238\) −14.9230 −0.967312
\(239\) −22.5400 −1.45799 −0.728997 0.684517i \(-0.760013\pi\)
−0.728997 + 0.684517i \(0.760013\pi\)
\(240\) 6.23608 0.402537
\(241\) −10.5543 −0.679860 −0.339930 0.940451i \(-0.610403\pi\)
−0.339930 + 0.940451i \(0.610403\pi\)
\(242\) −0.392741 −0.0252464
\(243\) 1.16095 0.0744748
\(244\) −7.31495 −0.468291
\(245\) 22.2247 1.41989
\(246\) −4.05788 −0.258721
\(247\) 0 0
\(248\) −11.5412 −0.732867
\(249\) −2.51083 −0.159117
\(250\) 3.99892 0.252914
\(251\) −7.45436 −0.470515 −0.235258 0.971933i \(-0.575593\pi\)
−0.235258 + 0.971933i \(0.575593\pi\)
\(252\) 1.04719 0.0659667
\(253\) 3.36585 0.211609
\(254\) −3.32573 −0.208675
\(255\) 15.0665 0.943502
\(256\) 5.03703 0.314814
\(257\) 15.7723 0.983850 0.491925 0.870638i \(-0.336294\pi\)
0.491925 + 0.870638i \(0.336294\pi\)
\(258\) 6.12733 0.381471
\(259\) −3.53361 −0.219568
\(260\) 0 0
\(261\) −0.966063 −0.0597978
\(262\) −1.20827 −0.0746473
\(263\) −1.63664 −0.100920 −0.0504598 0.998726i \(-0.516069\pi\)
−0.0504598 + 0.998726i \(0.516069\pi\)
\(264\) 2.56687 0.157980
\(265\) 2.44931 0.150460
\(266\) 7.95971 0.488041
\(267\) −28.9005 −1.76868
\(268\) −9.57001 −0.584581
\(269\) −6.30640 −0.384508 −0.192254 0.981345i \(-0.561580\pi\)
−0.192254 + 0.981345i \(0.561580\pi\)
\(270\) 2.45980 0.149699
\(271\) −2.90187 −0.176276 −0.0881381 0.996108i \(-0.528092\pi\)
−0.0881381 + 0.996108i \(0.528092\pi\)
\(272\) 23.1928 1.40627
\(273\) 0 0
\(274\) −2.52400 −0.152480
\(275\) −3.59738 −0.216930
\(276\) −10.5581 −0.635520
\(277\) −3.44417 −0.206940 −0.103470 0.994633i \(-0.532995\pi\)
−0.103470 + 0.994633i \(0.532995\pi\)
\(278\) −4.42662 −0.265491
\(279\) 0.854069 0.0511318
\(280\) 9.07988 0.542626
\(281\) −23.7653 −1.41772 −0.708858 0.705351i \(-0.750789\pi\)
−0.708858 + 0.705351i \(0.750789\pi\)
\(282\) 2.18145 0.129904
\(283\) 10.7805 0.640835 0.320418 0.947276i \(-0.396177\pi\)
0.320418 + 0.947276i \(0.396177\pi\)
\(284\) 7.52901 0.446765
\(285\) −8.03628 −0.476028
\(286\) 0 0
\(287\) 30.8601 1.82162
\(288\) 0.473643 0.0279097
\(289\) 39.0343 2.29614
\(290\) −4.02025 −0.236077
\(291\) 21.6294 1.26794
\(292\) −8.44429 −0.494165
\(293\) −4.75683 −0.277897 −0.138948 0.990300i \(-0.544372\pi\)
−0.138948 + 0.990300i \(0.544372\pi\)
\(294\) −12.5253 −0.730492
\(295\) −3.89975 −0.227052
\(296\) −1.05144 −0.0611138
\(297\) −5.28839 −0.306863
\(298\) 6.27451 0.363473
\(299\) 0 0
\(300\) 11.2843 0.651501
\(301\) −46.5983 −2.68588
\(302\) 1.88374 0.108397
\(303\) −9.21610 −0.529451
\(304\) −12.3707 −0.709509
\(305\) 4.69361 0.268756
\(306\) 0.328597 0.0187846
\(307\) 8.88281 0.506969 0.253485 0.967339i \(-0.418423\pi\)
0.253485 + 0.967339i \(0.418423\pi\)
\(308\) −9.36905 −0.533851
\(309\) −17.8370 −1.01471
\(310\) 3.55418 0.201864
\(311\) −2.93727 −0.166557 −0.0832785 0.996526i \(-0.526539\pi\)
−0.0832785 + 0.996526i \(0.526539\pi\)
\(312\) 0 0
\(313\) −33.9051 −1.91643 −0.958213 0.286054i \(-0.907656\pi\)
−0.958213 + 0.286054i \(0.907656\pi\)
\(314\) −7.60692 −0.429283
\(315\) −0.671926 −0.0378588
\(316\) −5.42367 −0.305105
\(317\) 16.1586 0.907556 0.453778 0.891115i \(-0.350076\pi\)
0.453778 + 0.891115i \(0.350076\pi\)
\(318\) −1.38037 −0.0774075
\(319\) 8.64322 0.483928
\(320\) −5.36777 −0.300067
\(321\) 15.6964 0.876088
\(322\) −6.71000 −0.373934
\(323\) −29.8879 −1.66301
\(324\) 15.9698 0.887212
\(325\) 0 0
\(326\) −3.69655 −0.204733
\(327\) 10.7771 0.595973
\(328\) 9.18258 0.507023
\(329\) −16.5899 −0.914632
\(330\) −0.790483 −0.0435147
\(331\) −33.8869 −1.86259 −0.931296 0.364264i \(-0.881321\pi\)
−0.931296 + 0.364264i \(0.881321\pi\)
\(332\) 2.72694 0.149660
\(333\) 0.0778085 0.00426388
\(334\) −0.139792 −0.00764907
\(335\) 6.14057 0.335495
\(336\) 26.7278 1.45812
\(337\) 25.3127 1.37887 0.689437 0.724346i \(-0.257858\pi\)
0.689437 + 0.724346i \(0.257858\pi\)
\(338\) 0 0
\(339\) 3.85421 0.209332
\(340\) −16.3633 −0.887425
\(341\) −7.64123 −0.413796
\(342\) −0.175269 −0.00947747
\(343\) 59.7230 3.22474
\(344\) −13.8656 −0.747580
\(345\) 6.77455 0.364729
\(346\) −3.77310 −0.202843
\(347\) 9.64590 0.517819 0.258909 0.965902i \(-0.416637\pi\)
0.258909 + 0.965902i \(0.416637\pi\)
\(348\) −27.1122 −1.45337
\(349\) −6.16293 −0.329894 −0.164947 0.986302i \(-0.552745\pi\)
−0.164947 + 0.986302i \(0.552745\pi\)
\(350\) 7.17157 0.383337
\(351\) 0 0
\(352\) −4.23761 −0.225865
\(353\) −15.5957 −0.830077 −0.415039 0.909804i \(-0.636232\pi\)
−0.415039 + 0.909804i \(0.636232\pi\)
\(354\) 2.19780 0.116812
\(355\) −4.83097 −0.256401
\(356\) 31.3879 1.66356
\(357\) 64.5750 3.41767
\(358\) 0.809126 0.0427636
\(359\) −29.8672 −1.57633 −0.788164 0.615465i \(-0.788968\pi\)
−0.788164 + 0.615465i \(0.788968\pi\)
\(360\) −0.199935 −0.0105375
\(361\) −3.05817 −0.160956
\(362\) −6.46980 −0.340045
\(363\) 1.69948 0.0891995
\(364\) 0 0
\(365\) 5.41826 0.283604
\(366\) −2.64521 −0.138267
\(367\) 11.1888 0.584053 0.292026 0.956410i \(-0.405671\pi\)
0.292026 + 0.956410i \(0.405671\pi\)
\(368\) 10.4285 0.543621
\(369\) −0.679526 −0.0353747
\(370\) 0.323798 0.0168335
\(371\) 10.4977 0.545015
\(372\) 23.9692 1.24274
\(373\) −18.9915 −0.983341 −0.491670 0.870781i \(-0.663613\pi\)
−0.491670 + 0.870781i \(0.663613\pi\)
\(374\) −2.93991 −0.152019
\(375\) −17.3042 −0.893586
\(376\) −4.93641 −0.254576
\(377\) 0 0
\(378\) 10.5427 0.542258
\(379\) 1.95187 0.100261 0.0501303 0.998743i \(-0.484036\pi\)
0.0501303 + 0.998743i \(0.484036\pi\)
\(380\) 8.72797 0.447735
\(381\) 14.3912 0.737282
\(382\) 2.08385 0.106619
\(383\) 21.5371 1.10049 0.550247 0.835002i \(-0.314533\pi\)
0.550247 + 0.835002i \(0.314533\pi\)
\(384\) 17.4286 0.889400
\(385\) 6.01162 0.306381
\(386\) 5.52856 0.281396
\(387\) 1.02607 0.0521583
\(388\) −23.4911 −1.19258
\(389\) −8.59364 −0.435715 −0.217858 0.975981i \(-0.569907\pi\)
−0.217858 + 0.975981i \(0.569907\pi\)
\(390\) 0 0
\(391\) 25.1954 1.27419
\(392\) 28.3436 1.43157
\(393\) 5.22846 0.263741
\(394\) 8.60110 0.433317
\(395\) 3.48008 0.175102
\(396\) 0.206302 0.0103671
\(397\) −17.7313 −0.889911 −0.444955 0.895553i \(-0.646780\pi\)
−0.444955 + 0.895553i \(0.646780\pi\)
\(398\) 8.39914 0.421011
\(399\) −34.4434 −1.72433
\(400\) −11.1458 −0.557291
\(401\) 0.312092 0.0155851 0.00779256 0.999970i \(-0.497520\pi\)
0.00779256 + 0.999970i \(0.497520\pi\)
\(402\) −3.46067 −0.172603
\(403\) 0 0
\(404\) 10.0093 0.497983
\(405\) −10.2470 −0.509177
\(406\) −17.2307 −0.855147
\(407\) −0.696141 −0.0345064
\(408\) 19.2146 0.951264
\(409\) −6.60890 −0.326789 −0.163394 0.986561i \(-0.552244\pi\)
−0.163394 + 0.986561i \(0.552244\pi\)
\(410\) −2.82783 −0.139657
\(411\) 10.9219 0.538738
\(412\) 19.3723 0.954402
\(413\) −16.7143 −0.822456
\(414\) 0.147751 0.00726157
\(415\) −1.74973 −0.0858909
\(416\) 0 0
\(417\) 19.1550 0.938023
\(418\) 1.56811 0.0766986
\(419\) 23.8929 1.16724 0.583622 0.812025i \(-0.301635\pi\)
0.583622 + 0.812025i \(0.301635\pi\)
\(420\) −18.8574 −0.920146
\(421\) 1.81207 0.0883148 0.0441574 0.999025i \(-0.485940\pi\)
0.0441574 + 0.999025i \(0.485940\pi\)
\(422\) 2.36450 0.115102
\(423\) 0.365303 0.0177616
\(424\) 3.12365 0.151698
\(425\) −26.9286 −1.30623
\(426\) 2.72262 0.131911
\(427\) 20.1168 0.973520
\(428\) −17.0474 −0.824017
\(429\) 0 0
\(430\) 4.26998 0.205917
\(431\) −30.9597 −1.49128 −0.745639 0.666350i \(-0.767856\pi\)
−0.745639 + 0.666350i \(0.767856\pi\)
\(432\) −16.3851 −0.788329
\(433\) −14.4440 −0.694135 −0.347067 0.937840i \(-0.612823\pi\)
−0.347067 + 0.937840i \(0.612823\pi\)
\(434\) 15.2332 0.731217
\(435\) 17.3965 0.834098
\(436\) −11.7047 −0.560551
\(437\) −13.4389 −0.642869
\(438\) −3.05360 −0.145907
\(439\) −17.5001 −0.835234 −0.417617 0.908623i \(-0.637135\pi\)
−0.417617 + 0.908623i \(0.637135\pi\)
\(440\) 1.78879 0.0852770
\(441\) −2.09747 −0.0998796
\(442\) 0 0
\(443\) −38.1706 −1.81354 −0.906769 0.421627i \(-0.861459\pi\)
−0.906769 + 0.421627i \(0.861459\pi\)
\(444\) 2.18367 0.103632
\(445\) −20.1400 −0.954727
\(446\) −1.50792 −0.0714022
\(447\) −27.1512 −1.28421
\(448\) −23.0062 −1.08694
\(449\) 15.8627 0.748609 0.374304 0.927306i \(-0.377882\pi\)
0.374304 + 0.927306i \(0.377882\pi\)
\(450\) −0.157915 −0.00744417
\(451\) 6.07962 0.286278
\(452\) −4.18595 −0.196890
\(453\) −8.15135 −0.382984
\(454\) 1.01146 0.0474703
\(455\) 0 0
\(456\) −10.2488 −0.479944
\(457\) −10.1022 −0.472563 −0.236281 0.971685i \(-0.575929\pi\)
−0.236281 + 0.971685i \(0.575929\pi\)
\(458\) 2.04801 0.0956975
\(459\) −39.5868 −1.84775
\(460\) −7.35764 −0.343052
\(461\) 20.7276 0.965380 0.482690 0.875791i \(-0.339660\pi\)
0.482690 + 0.875791i \(0.339660\pi\)
\(462\) −3.38800 −0.157624
\(463\) −6.34630 −0.294938 −0.147469 0.989067i \(-0.547113\pi\)
−0.147469 + 0.989067i \(0.547113\pi\)
\(464\) 26.7794 1.24320
\(465\) −15.3797 −0.713218
\(466\) −1.91644 −0.0887773
\(467\) −30.6350 −1.41762 −0.708809 0.705401i \(-0.750767\pi\)
−0.708809 + 0.705401i \(0.750767\pi\)
\(468\) 0 0
\(469\) 26.3184 1.21527
\(470\) 1.52020 0.0701215
\(471\) 32.9168 1.51673
\(472\) −4.97341 −0.228920
\(473\) −9.18013 −0.422103
\(474\) −1.96129 −0.0900850
\(475\) 14.3633 0.659035
\(476\) −70.1330 −3.21454
\(477\) −0.231155 −0.0105839
\(478\) 8.85240 0.404899
\(479\) −25.8557 −1.18137 −0.590687 0.806900i \(-0.701143\pi\)
−0.590687 + 0.806900i \(0.701143\pi\)
\(480\) −8.52918 −0.389302
\(481\) 0 0
\(482\) 4.14510 0.188804
\(483\) 29.0357 1.32117
\(484\) −1.84575 −0.0838979
\(485\) 15.0730 0.684429
\(486\) −0.455952 −0.0206824
\(487\) −15.3630 −0.696165 −0.348082 0.937464i \(-0.613167\pi\)
−0.348082 + 0.937464i \(0.613167\pi\)
\(488\) 5.98584 0.270966
\(489\) 15.9958 0.723355
\(490\) −8.72857 −0.394317
\(491\) −21.8812 −0.987483 −0.493742 0.869609i \(-0.664371\pi\)
−0.493742 + 0.869609i \(0.664371\pi\)
\(492\) −19.0707 −0.859772
\(493\) 64.6998 2.91393
\(494\) 0 0
\(495\) −0.132373 −0.00594973
\(496\) −23.6749 −1.06304
\(497\) −20.7055 −0.928768
\(498\) 0.986106 0.0441885
\(499\) 23.9077 1.07026 0.535128 0.844771i \(-0.320263\pi\)
0.535128 + 0.844771i \(0.320263\pi\)
\(500\) 18.7936 0.840476
\(501\) 0.604911 0.0270254
\(502\) 2.92764 0.130667
\(503\) −36.3671 −1.62153 −0.810764 0.585374i \(-0.800948\pi\)
−0.810764 + 0.585374i \(0.800948\pi\)
\(504\) −0.856919 −0.0381702
\(505\) −6.42246 −0.285796
\(506\) −1.32191 −0.0587660
\(507\) 0 0
\(508\) −15.6298 −0.693461
\(509\) 37.9752 1.68322 0.841610 0.540086i \(-0.181608\pi\)
0.841610 + 0.540086i \(0.181608\pi\)
\(510\) −5.91725 −0.262020
\(511\) 23.2226 1.02731
\(512\) −22.4888 −0.993873
\(513\) 21.1151 0.932253
\(514\) −6.19444 −0.273225
\(515\) −12.4302 −0.547738
\(516\) 28.7964 1.26769
\(517\) −3.26831 −0.143740
\(518\) 1.38780 0.0609762
\(519\) 16.3271 0.716678
\(520\) 0 0
\(521\) −35.7131 −1.56462 −0.782309 0.622890i \(-0.785958\pi\)
−0.782309 + 0.622890i \(0.785958\pi\)
\(522\) 0.379413 0.0166065
\(523\) −12.4494 −0.544373 −0.272187 0.962244i \(-0.587747\pi\)
−0.272187 + 0.962244i \(0.587747\pi\)
\(524\) −5.67848 −0.248065
\(525\) −31.0330 −1.35439
\(526\) 0.642776 0.0280264
\(527\) −57.1992 −2.49164
\(528\) 5.26552 0.229153
\(529\) −11.6711 −0.507438
\(530\) −0.961947 −0.0417843
\(531\) 0.368041 0.0159716
\(532\) 37.4080 1.62184
\(533\) 0 0
\(534\) 11.3504 0.491180
\(535\) 10.9384 0.472909
\(536\) 7.83117 0.338255
\(537\) −3.50127 −0.151091
\(538\) 2.47678 0.106782
\(539\) 18.7658 0.808299
\(540\) 11.5603 0.497474
\(541\) 32.1150 1.38073 0.690365 0.723461i \(-0.257450\pi\)
0.690365 + 0.723461i \(0.257450\pi\)
\(542\) 1.13969 0.0489537
\(543\) 27.9963 1.20143
\(544\) −31.7211 −1.36003
\(545\) 7.51026 0.321704
\(546\) 0 0
\(547\) −9.83396 −0.420470 −0.210235 0.977651i \(-0.567423\pi\)
−0.210235 + 0.977651i \(0.567423\pi\)
\(548\) −11.8620 −0.506718
\(549\) −0.442963 −0.0189052
\(550\) 1.41284 0.0602437
\(551\) −34.5100 −1.47018
\(552\) 8.63969 0.367730
\(553\) 14.9156 0.634276
\(554\) 1.35267 0.0574694
\(555\) −1.40115 −0.0594753
\(556\) −20.8037 −0.882272
\(557\) −17.7820 −0.753448 −0.376724 0.926326i \(-0.622950\pi\)
−0.376724 + 0.926326i \(0.622950\pi\)
\(558\) −0.335428 −0.0141998
\(559\) 0 0
\(560\) 18.6259 0.787089
\(561\) 12.7216 0.537108
\(562\) 9.33360 0.393714
\(563\) −12.4588 −0.525076 −0.262538 0.964922i \(-0.584559\pi\)
−0.262538 + 0.964922i \(0.584559\pi\)
\(564\) 10.2521 0.431691
\(565\) 2.68590 0.112997
\(566\) −4.23395 −0.177966
\(567\) −43.9185 −1.84440
\(568\) −6.16101 −0.258510
\(569\) −26.1052 −1.09439 −0.547194 0.837006i \(-0.684304\pi\)
−0.547194 + 0.837006i \(0.684304\pi\)
\(570\) 3.15618 0.132198
\(571\) 25.9415 1.08562 0.542808 0.839857i \(-0.317361\pi\)
0.542808 + 0.839857i \(0.317361\pi\)
\(572\) 0 0
\(573\) −9.01728 −0.376702
\(574\) −12.1201 −0.505881
\(575\) −12.1082 −0.504948
\(576\) 0.506586 0.0211078
\(577\) −3.87306 −0.161238 −0.0806188 0.996745i \(-0.525690\pi\)
−0.0806188 + 0.996745i \(0.525690\pi\)
\(578\) −15.3304 −0.637660
\(579\) −23.9233 −0.994219
\(580\) −18.8938 −0.784523
\(581\) −7.49933 −0.311125
\(582\) −8.49477 −0.352120
\(583\) 2.06811 0.0856525
\(584\) 6.90999 0.285937
\(585\) 0 0
\(586\) 1.86820 0.0771748
\(587\) 25.8064 1.06514 0.532571 0.846385i \(-0.321226\pi\)
0.532571 + 0.846385i \(0.321226\pi\)
\(588\) −58.8649 −2.42755
\(589\) 30.5093 1.25711
\(590\) 1.53159 0.0630547
\(591\) −37.2189 −1.53098
\(592\) −2.15687 −0.0886466
\(593\) 20.2687 0.832336 0.416168 0.909288i \(-0.363373\pi\)
0.416168 + 0.909288i \(0.363373\pi\)
\(594\) 2.07697 0.0852191
\(595\) 45.0006 1.84485
\(596\) 29.4881 1.20788
\(597\) −36.3449 −1.48750
\(598\) 0 0
\(599\) −11.0704 −0.452324 −0.226162 0.974090i \(-0.572618\pi\)
−0.226162 + 0.974090i \(0.572618\pi\)
\(600\) −9.23401 −0.376977
\(601\) −15.0016 −0.611926 −0.305963 0.952043i \(-0.598978\pi\)
−0.305963 + 0.952043i \(0.598978\pi\)
\(602\) 18.3011 0.745897
\(603\) −0.579520 −0.0235999
\(604\) 8.85294 0.360221
\(605\) 1.18432 0.0481496
\(606\) 3.61954 0.147034
\(607\) −23.6370 −0.959395 −0.479697 0.877434i \(-0.659254\pi\)
−0.479697 + 0.877434i \(0.659254\pi\)
\(608\) 16.9196 0.686181
\(609\) 74.5612 3.02137
\(610\) −1.84338 −0.0746361
\(611\) 0 0
\(612\) 1.54430 0.0624245
\(613\) 18.5235 0.748158 0.374079 0.927397i \(-0.377959\pi\)
0.374079 + 0.927397i \(0.377959\pi\)
\(614\) −3.48865 −0.140790
\(615\) 12.2366 0.493429
\(616\) 7.66672 0.308901
\(617\) 35.3078 1.42144 0.710719 0.703476i \(-0.248370\pi\)
0.710719 + 0.703476i \(0.248370\pi\)
\(618\) 7.00533 0.281796
\(619\) 9.29917 0.373765 0.186883 0.982382i \(-0.440162\pi\)
0.186883 + 0.982382i \(0.440162\pi\)
\(620\) 16.7035 0.670828
\(621\) −17.7999 −0.714286
\(622\) 1.15359 0.0462546
\(623\) −86.3198 −3.45833
\(624\) 0 0
\(625\) 5.92803 0.237121
\(626\) 13.3159 0.532211
\(627\) −6.78555 −0.270989
\(628\) −35.7500 −1.42658
\(629\) −5.21104 −0.207778
\(630\) 0.263893 0.0105138
\(631\) −40.3206 −1.60514 −0.802569 0.596559i \(-0.796534\pi\)
−0.802569 + 0.596559i \(0.796534\pi\)
\(632\) 4.43820 0.176542
\(633\) −10.2317 −0.406674
\(634\) −6.34614 −0.252037
\(635\) 10.0288 0.397982
\(636\) −6.48730 −0.257238
\(637\) 0 0
\(638\) −3.39455 −0.134392
\(639\) 0.455926 0.0180361
\(640\) 12.1455 0.480095
\(641\) −34.3899 −1.35832 −0.679160 0.733991i \(-0.737656\pi\)
−0.679160 + 0.733991i \(0.737656\pi\)
\(642\) −6.16463 −0.243298
\(643\) 13.2767 0.523582 0.261791 0.965125i \(-0.415687\pi\)
0.261791 + 0.965125i \(0.415687\pi\)
\(644\) −31.5348 −1.24264
\(645\) −18.4772 −0.727537
\(646\) 11.7382 0.461835
\(647\) 49.6984 1.95385 0.976923 0.213594i \(-0.0685170\pi\)
0.976923 + 0.213594i \(0.0685170\pi\)
\(648\) −13.0682 −0.513366
\(649\) −3.29281 −0.129254
\(650\) 0 0
\(651\) −65.9174 −2.58351
\(652\) −17.3726 −0.680363
\(653\) 43.2439 1.69226 0.846131 0.532974i \(-0.178926\pi\)
0.846131 + 0.532974i \(0.178926\pi\)
\(654\) −4.23260 −0.165508
\(655\) 3.64358 0.142366
\(656\) 18.8366 0.735445
\(657\) −0.511351 −0.0199497
\(658\) 6.51555 0.254003
\(659\) 23.2059 0.903975 0.451987 0.892024i \(-0.350715\pi\)
0.451987 + 0.892024i \(0.350715\pi\)
\(660\) −3.71501 −0.144607
\(661\) 24.5835 0.956188 0.478094 0.878309i \(-0.341328\pi\)
0.478094 + 0.878309i \(0.341328\pi\)
\(662\) 13.3088 0.517260
\(663\) 0 0
\(664\) −2.23146 −0.0865975
\(665\) −24.0027 −0.930787
\(666\) −0.0305586 −0.00118412
\(667\) 29.0918 1.12644
\(668\) −0.656976 −0.0254191
\(669\) 6.52511 0.252275
\(670\) −2.41166 −0.0931704
\(671\) 3.96312 0.152995
\(672\) −36.5560 −1.41018
\(673\) 44.6671 1.72179 0.860895 0.508782i \(-0.169904\pi\)
0.860895 + 0.508782i \(0.169904\pi\)
\(674\) −9.94136 −0.382927
\(675\) 19.0243 0.732247
\(676\) 0 0
\(677\) 28.7385 1.10451 0.552255 0.833675i \(-0.313767\pi\)
0.552255 + 0.833675i \(0.313767\pi\)
\(678\) −1.51371 −0.0581336
\(679\) 64.6027 2.47922
\(680\) 13.3901 0.513489
\(681\) −4.37683 −0.167720
\(682\) 3.00103 0.114915
\(683\) 41.4598 1.58642 0.793208 0.608951i \(-0.208410\pi\)
0.793208 + 0.608951i \(0.208410\pi\)
\(684\) −0.823707 −0.0314952
\(685\) 7.61120 0.290809
\(686\) −23.4557 −0.895543
\(687\) −8.86221 −0.338115
\(688\) −28.4430 −1.08438
\(689\) 0 0
\(690\) −2.66065 −0.101289
\(691\) −15.9472 −0.606662 −0.303331 0.952885i \(-0.598099\pi\)
−0.303331 + 0.952885i \(0.598099\pi\)
\(692\) −17.7323 −0.674082
\(693\) −0.567351 −0.0215519
\(694\) −3.78834 −0.143804
\(695\) 13.3486 0.506342
\(696\) 22.1860 0.840960
\(697\) 45.5096 1.72380
\(698\) 2.42044 0.0916150
\(699\) 8.29285 0.313665
\(700\) 33.7040 1.27389
\(701\) −31.6321 −1.19473 −0.597364 0.801970i \(-0.703785\pi\)
−0.597364 + 0.801970i \(0.703785\pi\)
\(702\) 0 0
\(703\) 2.77950 0.104831
\(704\) −4.53235 −0.170819
\(705\) −6.57823 −0.247750
\(706\) 6.12509 0.230521
\(707\) −27.5266 −1.03525
\(708\) 10.3289 0.388185
\(709\) −23.8506 −0.895728 −0.447864 0.894102i \(-0.647815\pi\)
−0.447864 + 0.894102i \(0.647815\pi\)
\(710\) 1.89732 0.0712052
\(711\) −0.328435 −0.0123173
\(712\) −25.6849 −0.962580
\(713\) −25.7192 −0.963191
\(714\) −25.3613 −0.949122
\(715\) 0 0
\(716\) 3.80262 0.142111
\(717\) −38.3063 −1.43058
\(718\) 11.7301 0.437762
\(719\) −1.19250 −0.0444727 −0.0222363 0.999753i \(-0.507079\pi\)
−0.0222363 + 0.999753i \(0.507079\pi\)
\(720\) −0.410134 −0.0152848
\(721\) −53.2755 −1.98408
\(722\) 1.20107 0.0446991
\(723\) −17.9368 −0.667075
\(724\) −30.4059 −1.13003
\(725\) −31.0929 −1.15476
\(726\) −0.667456 −0.0247716
\(727\) 6.56110 0.243338 0.121669 0.992571i \(-0.461175\pi\)
0.121669 + 0.992571i \(0.461175\pi\)
\(728\) 0 0
\(729\) 27.9296 1.03443
\(730\) −2.12797 −0.0787598
\(731\) −68.7189 −2.54166
\(732\) −12.4316 −0.459485
\(733\) −33.7942 −1.24822 −0.624108 0.781338i \(-0.714538\pi\)
−0.624108 + 0.781338i \(0.714538\pi\)
\(734\) −4.39432 −0.162197
\(735\) 37.7705 1.39318
\(736\) −14.2631 −0.525747
\(737\) 5.18488 0.190987
\(738\) 0.266878 0.00982392
\(739\) −27.5257 −1.01255 −0.506275 0.862372i \(-0.668978\pi\)
−0.506275 + 0.862372i \(0.668978\pi\)
\(740\) 1.52174 0.0559404
\(741\) 0 0
\(742\) −4.12290 −0.151356
\(743\) 35.6938 1.30948 0.654740 0.755854i \(-0.272778\pi\)
0.654740 + 0.755854i \(0.272778\pi\)
\(744\) −19.6140 −0.719086
\(745\) −18.9210 −0.693211
\(746\) 7.45873 0.273084
\(747\) 0.165132 0.00604186
\(748\) −13.8166 −0.505185
\(749\) 46.8820 1.71303
\(750\) 6.79608 0.248158
\(751\) −37.4060 −1.36496 −0.682481 0.730903i \(-0.739099\pi\)
−0.682481 + 0.730903i \(0.739099\pi\)
\(752\) −10.1263 −0.369267
\(753\) −12.6685 −0.461667
\(754\) 0 0
\(755\) −5.68047 −0.206733
\(756\) 49.5472 1.80201
\(757\) 37.7065 1.37047 0.685233 0.728324i \(-0.259701\pi\)
0.685233 + 0.728324i \(0.259701\pi\)
\(758\) −0.766579 −0.0278434
\(759\) 5.72019 0.207630
\(760\) −7.14213 −0.259072
\(761\) 8.45318 0.306428 0.153214 0.988193i \(-0.451038\pi\)
0.153214 + 0.988193i \(0.451038\pi\)
\(762\) −5.65201 −0.204751
\(763\) 32.1889 1.16532
\(764\) 9.79340 0.354313
\(765\) −0.990894 −0.0358258
\(766\) −8.45851 −0.305618
\(767\) 0 0
\(768\) 8.56033 0.308894
\(769\) 6.42082 0.231541 0.115770 0.993276i \(-0.463066\pi\)
0.115770 + 0.993276i \(0.463066\pi\)
\(770\) −2.36101 −0.0850850
\(771\) 26.8047 0.965348
\(772\) 25.9824 0.935127
\(773\) −31.3080 −1.12607 −0.563035 0.826433i \(-0.690366\pi\)
−0.563035 + 0.826433i \(0.690366\pi\)
\(774\) −0.402982 −0.0144849
\(775\) 27.4884 0.987412
\(776\) 19.2228 0.690059
\(777\) −6.00530 −0.215439
\(778\) 3.37508 0.121002
\(779\) −24.2742 −0.869715
\(780\) 0 0
\(781\) −4.07910 −0.145962
\(782\) −9.89528 −0.353854
\(783\) −45.7087 −1.63350
\(784\) 58.1423 2.07651
\(785\) 22.9389 0.818724
\(786\) −2.05343 −0.0732435
\(787\) 42.1141 1.50121 0.750603 0.660754i \(-0.229763\pi\)
0.750603 + 0.660754i \(0.229763\pi\)
\(788\) 40.4223 1.43999
\(789\) −2.78143 −0.0990217
\(790\) −1.36677 −0.0486276
\(791\) 11.5118 0.409311
\(792\) −0.168818 −0.00599868
\(793\) 0 0
\(794\) 6.96383 0.247137
\(795\) 4.16256 0.147631
\(796\) 39.4732 1.39909
\(797\) 10.5972 0.375374 0.187687 0.982229i \(-0.439901\pi\)
0.187687 + 0.982229i \(0.439901\pi\)
\(798\) 13.5274 0.478863
\(799\) −24.4653 −0.865519
\(800\) 15.2443 0.538967
\(801\) 1.90072 0.0671587
\(802\) −0.122571 −0.00432814
\(803\) 4.57498 0.161448
\(804\) −16.2640 −0.573588
\(805\) 20.2342 0.713162
\(806\) 0 0
\(807\) −10.7176 −0.377277
\(808\) −8.19067 −0.288147
\(809\) 5.29034 0.185998 0.0929992 0.995666i \(-0.470355\pi\)
0.0929992 + 0.995666i \(0.470355\pi\)
\(810\) 4.02442 0.141404
\(811\) 13.4655 0.472837 0.236419 0.971651i \(-0.424026\pi\)
0.236419 + 0.971651i \(0.424026\pi\)
\(812\) −80.9788 −2.84180
\(813\) −4.93167 −0.172961
\(814\) 0.273403 0.00958278
\(815\) 11.1471 0.390465
\(816\) 39.4156 1.37982
\(817\) 36.6537 1.28235
\(818\) 2.59559 0.0907526
\(819\) 0 0
\(820\) −13.2899 −0.464102
\(821\) 23.1787 0.808941 0.404470 0.914551i \(-0.367456\pi\)
0.404470 + 0.914551i \(0.367456\pi\)
\(822\) −4.28949 −0.149613
\(823\) −9.64680 −0.336266 −0.168133 0.985764i \(-0.553774\pi\)
−0.168133 + 0.985764i \(0.553774\pi\)
\(824\) −15.8524 −0.552244
\(825\) −6.11367 −0.212851
\(826\) 6.56439 0.228404
\(827\) 20.8985 0.726710 0.363355 0.931651i \(-0.381631\pi\)
0.363355 + 0.931651i \(0.381631\pi\)
\(828\) 0.694381 0.0241314
\(829\) 30.1544 1.04730 0.523652 0.851932i \(-0.324569\pi\)
0.523652 + 0.851932i \(0.324569\pi\)
\(830\) 0.687192 0.0238528
\(831\) −5.85330 −0.203049
\(832\) 0 0
\(833\) 140.473 4.86711
\(834\) −7.52295 −0.260499
\(835\) 0.421547 0.0145882
\(836\) 7.36958 0.254882
\(837\) 40.4098 1.39677
\(838\) −9.38373 −0.324156
\(839\) −18.9148 −0.653010 −0.326505 0.945196i \(-0.605871\pi\)
−0.326505 + 0.945196i \(0.605871\pi\)
\(840\) 15.4311 0.532422
\(841\) 45.7053 1.57605
\(842\) −0.711674 −0.0245259
\(843\) −40.3886 −1.39106
\(844\) 11.1123 0.382503
\(845\) 0 0
\(846\) −0.143469 −0.00493258
\(847\) 5.07600 0.174413
\(848\) 6.40767 0.220040
\(849\) 18.3213 0.628784
\(850\) 10.5760 0.362752
\(851\) −2.34310 −0.0803206
\(852\) 12.7954 0.438363
\(853\) −22.4051 −0.767137 −0.383568 0.923512i \(-0.625305\pi\)
−0.383568 + 0.923512i \(0.625305\pi\)
\(854\) −7.90070 −0.270356
\(855\) 0.528530 0.0180753
\(856\) 13.9499 0.476799
\(857\) 26.9098 0.919221 0.459611 0.888121i \(-0.347989\pi\)
0.459611 + 0.888121i \(0.347989\pi\)
\(858\) 0 0
\(859\) −30.0689 −1.02594 −0.512969 0.858407i \(-0.671455\pi\)
−0.512969 + 0.858407i \(0.671455\pi\)
\(860\) 20.0675 0.684296
\(861\) 52.4462 1.78736
\(862\) 12.1592 0.414143
\(863\) −23.4958 −0.799805 −0.399902 0.916558i \(-0.630956\pi\)
−0.399902 + 0.916558i \(0.630956\pi\)
\(864\) 22.4101 0.762408
\(865\) 11.3779 0.386860
\(866\) 5.67276 0.192768
\(867\) 66.3380 2.25296
\(868\) 71.5910 2.42996
\(869\) 2.93846 0.0996803
\(870\) −6.83232 −0.231637
\(871\) 0 0
\(872\) 9.57796 0.324351
\(873\) −1.42252 −0.0481451
\(874\) 5.27801 0.178531
\(875\) −51.6842 −1.74725
\(876\) −14.3509 −0.484872
\(877\) −11.2925 −0.381322 −0.190661 0.981656i \(-0.561063\pi\)
−0.190661 + 0.981656i \(0.561063\pi\)
\(878\) 6.87301 0.231953
\(879\) −8.08413 −0.272671
\(880\) 3.66941 0.123696
\(881\) −38.5640 −1.29925 −0.649627 0.760253i \(-0.725075\pi\)
−0.649627 + 0.760253i \(0.725075\pi\)
\(882\) 0.823764 0.0277376
\(883\) −7.19873 −0.242257 −0.121128 0.992637i \(-0.538651\pi\)
−0.121128 + 0.992637i \(0.538651\pi\)
\(884\) 0 0
\(885\) −6.62754 −0.222782
\(886\) 14.9912 0.503638
\(887\) 15.9910 0.536925 0.268462 0.963290i \(-0.413485\pi\)
0.268462 + 0.963290i \(0.413485\pi\)
\(888\) −1.78690 −0.0599646
\(889\) 42.9835 1.44162
\(890\) 7.90980 0.265137
\(891\) −8.65219 −0.289859
\(892\) −7.08673 −0.237281
\(893\) 13.0494 0.436683
\(894\) 10.6634 0.356637
\(895\) −2.43994 −0.0815583
\(896\) 52.0557 1.73906
\(897\) 0 0
\(898\) −6.22995 −0.207896
\(899\) −66.0448 −2.20272
\(900\) −0.742147 −0.0247382
\(901\) 15.4811 0.515749
\(902\) −2.38772 −0.0795023
\(903\) −79.1929 −2.63538
\(904\) 3.42538 0.113926
\(905\) 19.5099 0.648530
\(906\) 3.20137 0.106359
\(907\) 40.5290 1.34574 0.672871 0.739760i \(-0.265061\pi\)
0.672871 + 0.739760i \(0.265061\pi\)
\(908\) 4.75354 0.157752
\(909\) 0.606124 0.0201039
\(910\) 0 0
\(911\) −40.3365 −1.33641 −0.668204 0.743978i \(-0.732937\pi\)
−0.668204 + 0.743978i \(0.732937\pi\)
\(912\) −21.0238 −0.696167
\(913\) −1.47741 −0.0488951
\(914\) 3.96757 0.131236
\(915\) 7.97670 0.263702
\(916\) 9.62499 0.318019
\(917\) 15.6164 0.515697
\(918\) 15.5474 0.513140
\(919\) 28.3729 0.935937 0.467969 0.883745i \(-0.344986\pi\)
0.467969 + 0.883745i \(0.344986\pi\)
\(920\) 6.02078 0.198499
\(921\) 15.0962 0.497435
\(922\) −8.14058 −0.268096
\(923\) 0 0
\(924\) −15.9225 −0.523812
\(925\) 2.50428 0.0823403
\(926\) 2.49246 0.0819072
\(927\) 1.17310 0.0385298
\(928\) −36.6266 −1.20233
\(929\) 41.0810 1.34782 0.673912 0.738812i \(-0.264613\pi\)
0.673912 + 0.738812i \(0.264613\pi\)
\(930\) 6.04026 0.198068
\(931\) −74.9265 −2.45562
\(932\) −9.00663 −0.295022
\(933\) −4.99182 −0.163425
\(934\) 12.0316 0.393687
\(935\) 8.86538 0.289929
\(936\) 0 0
\(937\) −14.8078 −0.483749 −0.241875 0.970307i \(-0.577762\pi\)
−0.241875 + 0.970307i \(0.577762\pi\)
\(938\) −10.3363 −0.337493
\(939\) −57.6209 −1.88039
\(940\) 7.14442 0.233025
\(941\) −20.6634 −0.673607 −0.336804 0.941575i \(-0.609346\pi\)
−0.336804 + 0.941575i \(0.609346\pi\)
\(942\) −12.9278 −0.421211
\(943\) 20.4631 0.666369
\(944\) −10.2022 −0.332052
\(945\) −31.7918 −1.03419
\(946\) 3.60542 0.117222
\(947\) 57.5188 1.86911 0.934554 0.355820i \(-0.115798\pi\)
0.934554 + 0.355820i \(0.115798\pi\)
\(948\) −9.21741 −0.299367
\(949\) 0 0
\(950\) −5.64108 −0.183021
\(951\) 27.4612 0.890489
\(952\) 57.3901 1.86002
\(953\) 9.74354 0.315624 0.157812 0.987469i \(-0.449556\pi\)
0.157812 + 0.987469i \(0.449556\pi\)
\(954\) 0.0907843 0.00293925
\(955\) −6.28391 −0.203343
\(956\) 41.6034 1.34555
\(957\) 14.6890 0.474827
\(958\) 10.1546 0.328080
\(959\) 32.6215 1.05340
\(960\) −9.12240 −0.294424
\(961\) 27.3883 0.883495
\(962\) 0 0
\(963\) −1.03232 −0.0332660
\(964\) 19.4806 0.627428
\(965\) −16.6715 −0.536676
\(966\) −11.4035 −0.366902
\(967\) −0.920789 −0.0296106 −0.0148053 0.999890i \(-0.504713\pi\)
−0.0148053 + 0.999890i \(0.504713\pi\)
\(968\) 1.51039 0.0485457
\(969\) −50.7939 −1.63174
\(970\) −5.91979 −0.190073
\(971\) −35.6324 −1.14350 −0.571749 0.820429i \(-0.693735\pi\)
−0.571749 + 0.820429i \(0.693735\pi\)
\(972\) −2.14282 −0.0687311
\(973\) 57.2120 1.83413
\(974\) 6.03369 0.193332
\(975\) 0 0
\(976\) 12.2790 0.393041
\(977\) −12.6314 −0.404113 −0.202056 0.979374i \(-0.564762\pi\)
−0.202056 + 0.979374i \(0.564762\pi\)
\(978\) −6.28222 −0.200883
\(979\) −17.0055 −0.543497
\(980\) −41.0214 −1.31038
\(981\) −0.708785 −0.0226298
\(982\) 8.59364 0.274234
\(983\) 15.5464 0.495854 0.247927 0.968779i \(-0.420251\pi\)
0.247927 + 0.968779i \(0.420251\pi\)
\(984\) 15.6056 0.497488
\(985\) −25.9369 −0.826418
\(986\) −25.4103 −0.809228
\(987\) −28.1942 −0.897432
\(988\) 0 0
\(989\) −30.8989 −0.982529
\(990\) 0.0519884 0.00165230
\(991\) 26.1068 0.829310 0.414655 0.909979i \(-0.363902\pi\)
0.414655 + 0.909979i \(0.363902\pi\)
\(992\) 32.3805 1.02808
\(993\) −57.5900 −1.82756
\(994\) 8.13190 0.257928
\(995\) −25.3279 −0.802947
\(996\) 4.63437 0.146846
\(997\) −14.2428 −0.451076 −0.225538 0.974234i \(-0.572414\pi\)
−0.225538 + 0.974234i \(0.572414\pi\)
\(998\) −9.38955 −0.297221
\(999\) 3.68146 0.116476
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 1859.2.a.t.1.10 yes 21
13.12 even 2 1859.2.a.s.1.12 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1859.2.a.s.1.12 21 13.12 even 2
1859.2.a.t.1.10 yes 21 1.1 even 1 trivial