Properties

Label 6034.2.a.m.1.5
Level $6034$
Weight $2$
Character 6034.1
Self dual yes
Analytic conductor $48.182$
Analytic rank $1$
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] = [6034,2,Mod(1,6034)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6034, 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("6034.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6034.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: \(48.1817325796\)
Analytic rank: \(1\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) \(=\) 6034.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.23488 q^{3} +1.00000 q^{4} +0.812592 q^{5} -2.23488 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.99468 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.23488 q^{3} +1.00000 q^{4} +0.812592 q^{5} -2.23488 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.99468 q^{9} +0.812592 q^{10} +3.26531 q^{11} -2.23488 q^{12} +2.96305 q^{13} +1.00000 q^{14} -1.81604 q^{15} +1.00000 q^{16} -2.78329 q^{17} +1.99468 q^{18} -4.32376 q^{19} +0.812592 q^{20} -2.23488 q^{21} +3.26531 q^{22} -8.63879 q^{23} -2.23488 q^{24} -4.33969 q^{25} +2.96305 q^{26} +2.24677 q^{27} +1.00000 q^{28} -9.37575 q^{29} -1.81604 q^{30} +5.70390 q^{31} +1.00000 q^{32} -7.29758 q^{33} -2.78329 q^{34} +0.812592 q^{35} +1.99468 q^{36} +7.34378 q^{37} -4.32376 q^{38} -6.62204 q^{39} +0.812592 q^{40} +1.76139 q^{41} -2.23488 q^{42} -1.70416 q^{43} +3.26531 q^{44} +1.62086 q^{45} -8.63879 q^{46} -9.53234 q^{47} -2.23488 q^{48} +1.00000 q^{49} -4.33969 q^{50} +6.22031 q^{51} +2.96305 q^{52} -11.7502 q^{53} +2.24677 q^{54} +2.65337 q^{55} +1.00000 q^{56} +9.66307 q^{57} -9.37575 q^{58} -8.71482 q^{59} -1.81604 q^{60} -4.63923 q^{61} +5.70390 q^{62} +1.99468 q^{63} +1.00000 q^{64} +2.40775 q^{65} -7.29758 q^{66} +9.29319 q^{67} -2.78329 q^{68} +19.3066 q^{69} +0.812592 q^{70} -16.1273 q^{71} +1.99468 q^{72} -11.0969 q^{73} +7.34378 q^{74} +9.69869 q^{75} -4.32376 q^{76} +3.26531 q^{77} -6.62204 q^{78} +9.75479 q^{79} +0.812592 q^{80} -11.0053 q^{81} +1.76139 q^{82} +10.2662 q^{83} -2.23488 q^{84} -2.26168 q^{85} -1.70416 q^{86} +20.9537 q^{87} +3.26531 q^{88} +6.52666 q^{89} +1.62086 q^{90} +2.96305 q^{91} -8.63879 q^{92} -12.7475 q^{93} -9.53234 q^{94} -3.51345 q^{95} -2.23488 q^{96} -1.25240 q^{97} +1.00000 q^{98} +6.51325 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9} - 11 q^{10} - 34 q^{11} - 6 q^{12} - 19 q^{13} + 21 q^{14} - 24 q^{15} + 21 q^{16} - 17 q^{17} + 5 q^{18} - 15 q^{19} - 11 q^{20} - 6 q^{21} - 34 q^{22} - 32 q^{23} - 6 q^{24} + 6 q^{25} - 19 q^{26} - 3 q^{27} + 21 q^{28} - 46 q^{29} - 24 q^{30} + 7 q^{31} + 21 q^{32} - 13 q^{33} - 17 q^{34} - 11 q^{35} + 5 q^{36} - 34 q^{37} - 15 q^{38} - 25 q^{39} - 11 q^{40} - 27 q^{41} - 6 q^{42} - 47 q^{43} - 34 q^{44} - 13 q^{45} - 32 q^{46} - 7 q^{47} - 6 q^{48} + 21 q^{49} + 6 q^{50} - 29 q^{51} - 19 q^{52} - 57 q^{53} - 3 q^{54} + 17 q^{55} + 21 q^{56} - 28 q^{57} - 46 q^{58} - 30 q^{59} - 24 q^{60} - 17 q^{61} + 7 q^{62} + 5 q^{63} + 21 q^{64} - 40 q^{65} - 13 q^{66} - 38 q^{67} - 17 q^{68} - 13 q^{69} - 11 q^{70} - 66 q^{71} + 5 q^{72} - 15 q^{73} - 34 q^{74} + 15 q^{75} - 15 q^{76} - 34 q^{77} - 25 q^{78} - 17 q^{79} - 11 q^{80} - 11 q^{81} - 27 q^{82} - 19 q^{83} - 6 q^{84} - 28 q^{85} - 47 q^{86} + 45 q^{87} - 34 q^{88} - 39 q^{89} - 13 q^{90} - 19 q^{91} - 32 q^{92} - 25 q^{93} - 7 q^{94} - 35 q^{95} - 6 q^{96} + 21 q^{98} - 52 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −2.23488 −1.29031 −0.645154 0.764053i \(-0.723207\pi\)
−0.645154 + 0.764053i \(0.723207\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.812592 0.363402 0.181701 0.983354i \(-0.441840\pi\)
0.181701 + 0.983354i \(0.441840\pi\)
\(6\) −2.23488 −0.912385
\(7\) 1.00000 0.377964
\(8\) 1.00000 0.353553
\(9\) 1.99468 0.664893
\(10\) 0.812592 0.256964
\(11\) 3.26531 0.984529 0.492265 0.870446i \(-0.336169\pi\)
0.492265 + 0.870446i \(0.336169\pi\)
\(12\) −2.23488 −0.645154
\(13\) 2.96305 0.821801 0.410900 0.911680i \(-0.365214\pi\)
0.410900 + 0.911680i \(0.365214\pi\)
\(14\) 1.00000 0.267261
\(15\) −1.81604 −0.468900
\(16\) 1.00000 0.250000
\(17\) −2.78329 −0.675047 −0.337523 0.941317i \(-0.609589\pi\)
−0.337523 + 0.941317i \(0.609589\pi\)
\(18\) 1.99468 0.470150
\(19\) −4.32376 −0.991938 −0.495969 0.868340i \(-0.665187\pi\)
−0.495969 + 0.868340i \(0.665187\pi\)
\(20\) 0.812592 0.181701
\(21\) −2.23488 −0.487690
\(22\) 3.26531 0.696167
\(23\) −8.63879 −1.80131 −0.900656 0.434533i \(-0.856913\pi\)
−0.900656 + 0.434533i \(0.856913\pi\)
\(24\) −2.23488 −0.456193
\(25\) −4.33969 −0.867939
\(26\) 2.96305 0.581101
\(27\) 2.24677 0.432391
\(28\) 1.00000 0.188982
\(29\) −9.37575 −1.74103 −0.870517 0.492139i \(-0.836215\pi\)
−0.870517 + 0.492139i \(0.836215\pi\)
\(30\) −1.81604 −0.331563
\(31\) 5.70390 1.02445 0.512226 0.858851i \(-0.328821\pi\)
0.512226 + 0.858851i \(0.328821\pi\)
\(32\) 1.00000 0.176777
\(33\) −7.29758 −1.27035
\(34\) −2.78329 −0.477330
\(35\) 0.812592 0.137353
\(36\) 1.99468 0.332446
\(37\) 7.34378 1.20731 0.603655 0.797246i \(-0.293710\pi\)
0.603655 + 0.797246i \(0.293710\pi\)
\(38\) −4.32376 −0.701406
\(39\) −6.62204 −1.06038
\(40\) 0.812592 0.128482
\(41\) 1.76139 0.275083 0.137541 0.990496i \(-0.456080\pi\)
0.137541 + 0.990496i \(0.456080\pi\)
\(42\) −2.23488 −0.344849
\(43\) −1.70416 −0.259882 −0.129941 0.991522i \(-0.541479\pi\)
−0.129941 + 0.991522i \(0.541479\pi\)
\(44\) 3.26531 0.492265
\(45\) 1.62086 0.241624
\(46\) −8.63879 −1.27372
\(47\) −9.53234 −1.39043 −0.695217 0.718800i \(-0.744692\pi\)
−0.695217 + 0.718800i \(0.744692\pi\)
\(48\) −2.23488 −0.322577
\(49\) 1.00000 0.142857
\(50\) −4.33969 −0.613725
\(51\) 6.22031 0.871018
\(52\) 2.96305 0.410900
\(53\) −11.7502 −1.61401 −0.807007 0.590541i \(-0.798914\pi\)
−0.807007 + 0.590541i \(0.798914\pi\)
\(54\) 2.24677 0.305747
\(55\) 2.65337 0.357780
\(56\) 1.00000 0.133631
\(57\) 9.66307 1.27990
\(58\) −9.37575 −1.23110
\(59\) −8.71482 −1.13457 −0.567287 0.823520i \(-0.692007\pi\)
−0.567287 + 0.823520i \(0.692007\pi\)
\(60\) −1.81604 −0.234450
\(61\) −4.63923 −0.593992 −0.296996 0.954879i \(-0.595985\pi\)
−0.296996 + 0.954879i \(0.595985\pi\)
\(62\) 5.70390 0.724396
\(63\) 1.99468 0.251306
\(64\) 1.00000 0.125000
\(65\) 2.40775 0.298644
\(66\) −7.29758 −0.898270
\(67\) 9.29319 1.13534 0.567672 0.823255i \(-0.307844\pi\)
0.567672 + 0.823255i \(0.307844\pi\)
\(68\) −2.78329 −0.337523
\(69\) 19.3066 2.32425
\(70\) 0.812592 0.0971233
\(71\) −16.1273 −1.91396 −0.956979 0.290156i \(-0.906293\pi\)
−0.956979 + 0.290156i \(0.906293\pi\)
\(72\) 1.99468 0.235075
\(73\) −11.0969 −1.29879 −0.649397 0.760450i \(-0.724979\pi\)
−0.649397 + 0.760450i \(0.724979\pi\)
\(74\) 7.34378 0.853697
\(75\) 9.69869 1.11991
\(76\) −4.32376 −0.495969
\(77\) 3.26531 0.372117
\(78\) −6.62204 −0.749799
\(79\) 9.75479 1.09750 0.548750 0.835987i \(-0.315104\pi\)
0.548750 + 0.835987i \(0.315104\pi\)
\(80\) 0.812592 0.0908505
\(81\) −11.0053 −1.22281
\(82\) 1.76139 0.194513
\(83\) 10.2662 1.12686 0.563432 0.826163i \(-0.309481\pi\)
0.563432 + 0.826163i \(0.309481\pi\)
\(84\) −2.23488 −0.243845
\(85\) −2.26168 −0.245313
\(86\) −1.70416 −0.183764
\(87\) 20.9537 2.24647
\(88\) 3.26531 0.348084
\(89\) 6.52666 0.691825 0.345912 0.938267i \(-0.387569\pi\)
0.345912 + 0.938267i \(0.387569\pi\)
\(90\) 1.62086 0.170854
\(91\) 2.96305 0.310612
\(92\) −8.63879 −0.900656
\(93\) −12.7475 −1.32186
\(94\) −9.53234 −0.983186
\(95\) −3.51345 −0.360472
\(96\) −2.23488 −0.228096
\(97\) −1.25240 −0.127162 −0.0635812 0.997977i \(-0.520252\pi\)
−0.0635812 + 0.997977i \(0.520252\pi\)
\(98\) 1.00000 0.101015
\(99\) 6.51325 0.654607
\(100\) −4.33969 −0.433969
\(101\) 13.8258 1.37572 0.687859 0.725845i \(-0.258551\pi\)
0.687859 + 0.725845i \(0.258551\pi\)
\(102\) 6.22031 0.615903
\(103\) 3.59568 0.354293 0.177147 0.984184i \(-0.443313\pi\)
0.177147 + 0.984184i \(0.443313\pi\)
\(104\) 2.96305 0.290551
\(105\) −1.81604 −0.177228
\(106\) −11.7502 −1.14128
\(107\) −0.761019 −0.0735705 −0.0367852 0.999323i \(-0.511712\pi\)
−0.0367852 + 0.999323i \(0.511712\pi\)
\(108\) 2.24677 0.216196
\(109\) 8.13333 0.779031 0.389516 0.921020i \(-0.372642\pi\)
0.389516 + 0.921020i \(0.372642\pi\)
\(110\) 2.65337 0.252989
\(111\) −16.4125 −1.55780
\(112\) 1.00000 0.0944911
\(113\) −5.97693 −0.562262 −0.281131 0.959669i \(-0.590710\pi\)
−0.281131 + 0.959669i \(0.590710\pi\)
\(114\) 9.66307 0.905029
\(115\) −7.01981 −0.654601
\(116\) −9.37575 −0.870517
\(117\) 5.91032 0.546410
\(118\) −8.71482 −0.802265
\(119\) −2.78329 −0.255144
\(120\) −1.81604 −0.165781
\(121\) −0.337724 −0.0307022
\(122\) −4.63923 −0.420016
\(123\) −3.93649 −0.354942
\(124\) 5.70390 0.512226
\(125\) −7.58936 −0.678813
\(126\) 1.99468 0.177700
\(127\) 6.98647 0.619949 0.309974 0.950745i \(-0.399680\pi\)
0.309974 + 0.950745i \(0.399680\pi\)
\(128\) 1.00000 0.0883883
\(129\) 3.80859 0.335327
\(130\) 2.40775 0.211173
\(131\) −0.0906462 −0.00791980 −0.00395990 0.999992i \(-0.501260\pi\)
−0.00395990 + 0.999992i \(0.501260\pi\)
\(132\) −7.29758 −0.635173
\(133\) −4.32376 −0.374917
\(134\) 9.29319 0.802809
\(135\) 1.82571 0.157132
\(136\) −2.78329 −0.238665
\(137\) −12.7735 −1.09131 −0.545655 0.838010i \(-0.683719\pi\)
−0.545655 + 0.838010i \(0.683719\pi\)
\(138\) 19.3066 1.64349
\(139\) 14.4342 1.22429 0.612146 0.790745i \(-0.290307\pi\)
0.612146 + 0.790745i \(0.290307\pi\)
\(140\) 0.812592 0.0686766
\(141\) 21.3036 1.79409
\(142\) −16.1273 −1.35337
\(143\) 9.67527 0.809087
\(144\) 1.99468 0.166223
\(145\) −7.61866 −0.632695
\(146\) −11.0969 −0.918386
\(147\) −2.23488 −0.184330
\(148\) 7.34378 0.603655
\(149\) −16.3307 −1.33786 −0.668931 0.743324i \(-0.733248\pi\)
−0.668931 + 0.743324i \(0.733248\pi\)
\(150\) 9.69869 0.791894
\(151\) −4.18363 −0.340459 −0.170230 0.985404i \(-0.554451\pi\)
−0.170230 + 0.985404i \(0.554451\pi\)
\(152\) −4.32376 −0.350703
\(153\) −5.55177 −0.448834
\(154\) 3.26531 0.263127
\(155\) 4.63495 0.372288
\(156\) −6.62204 −0.530188
\(157\) 22.1358 1.76663 0.883314 0.468782i \(-0.155307\pi\)
0.883314 + 0.468782i \(0.155307\pi\)
\(158\) 9.75479 0.776050
\(159\) 26.2603 2.08257
\(160\) 0.812592 0.0642410
\(161\) −8.63879 −0.680832
\(162\) −11.0053 −0.864657
\(163\) 0.335627 0.0262884 0.0131442 0.999914i \(-0.495816\pi\)
0.0131442 + 0.999914i \(0.495816\pi\)
\(164\) 1.76139 0.137541
\(165\) −5.92995 −0.461646
\(166\) 10.2662 0.796813
\(167\) 11.5237 0.891727 0.445864 0.895101i \(-0.352897\pi\)
0.445864 + 0.895101i \(0.352897\pi\)
\(168\) −2.23488 −0.172425
\(169\) −4.22036 −0.324643
\(170\) −2.26168 −0.173463
\(171\) −8.62451 −0.659532
\(172\) −1.70416 −0.129941
\(173\) −9.73755 −0.740332 −0.370166 0.928966i \(-0.620699\pi\)
−0.370166 + 0.928966i \(0.620699\pi\)
\(174\) 20.9537 1.58849
\(175\) −4.33969 −0.328050
\(176\) 3.26531 0.246132
\(177\) 19.4766 1.46395
\(178\) 6.52666 0.489194
\(179\) −23.6562 −1.76815 −0.884075 0.467346i \(-0.845210\pi\)
−0.884075 + 0.467346i \(0.845210\pi\)
\(180\) 1.62086 0.120812
\(181\) −14.9888 −1.11411 −0.557053 0.830477i \(-0.688068\pi\)
−0.557053 + 0.830477i \(0.688068\pi\)
\(182\) 2.96305 0.219636
\(183\) 10.3681 0.766433
\(184\) −8.63879 −0.636860
\(185\) 5.96750 0.438739
\(186\) −12.7475 −0.934694
\(187\) −9.08831 −0.664603
\(188\) −9.53234 −0.695217
\(189\) 2.24677 0.163428
\(190\) −3.51345 −0.254892
\(191\) −9.26422 −0.670335 −0.335168 0.942158i \(-0.608793\pi\)
−0.335168 + 0.942158i \(0.608793\pi\)
\(192\) −2.23488 −0.161288
\(193\) 23.5608 1.69594 0.847971 0.530043i \(-0.177824\pi\)
0.847971 + 0.530043i \(0.177824\pi\)
\(194\) −1.25240 −0.0899174
\(195\) −5.38102 −0.385343
\(196\) 1.00000 0.0714286
\(197\) −24.7432 −1.76288 −0.881438 0.472299i \(-0.843424\pi\)
−0.881438 + 0.472299i \(0.843424\pi\)
\(198\) 6.51325 0.462877
\(199\) −9.00585 −0.638408 −0.319204 0.947686i \(-0.603415\pi\)
−0.319204 + 0.947686i \(0.603415\pi\)
\(200\) −4.33969 −0.306863
\(201\) −20.7691 −1.46494
\(202\) 13.8258 0.972779
\(203\) −9.37575 −0.658049
\(204\) 6.22031 0.435509
\(205\) 1.43129 0.0999657
\(206\) 3.59568 0.250523
\(207\) −17.2316 −1.19768
\(208\) 2.96305 0.205450
\(209\) −14.1184 −0.976592
\(210\) −1.81604 −0.125319
\(211\) −9.99153 −0.687845 −0.343923 0.938998i \(-0.611756\pi\)
−0.343923 + 0.938998i \(0.611756\pi\)
\(212\) −11.7502 −0.807007
\(213\) 36.0426 2.46960
\(214\) −0.761019 −0.0520222
\(215\) −1.38479 −0.0944416
\(216\) 2.24677 0.152873
\(217\) 5.70390 0.387206
\(218\) 8.13333 0.550858
\(219\) 24.8002 1.67584
\(220\) 2.65337 0.178890
\(221\) −8.24701 −0.554754
\(222\) −16.4125 −1.10153
\(223\) −18.8022 −1.25909 −0.629546 0.776964i \(-0.716759\pi\)
−0.629546 + 0.776964i \(0.716759\pi\)
\(224\) 1.00000 0.0668153
\(225\) −8.65630 −0.577086
\(226\) −5.97693 −0.397579
\(227\) 4.48248 0.297513 0.148756 0.988874i \(-0.452473\pi\)
0.148756 + 0.988874i \(0.452473\pi\)
\(228\) 9.66307 0.639952
\(229\) 12.8191 0.847110 0.423555 0.905870i \(-0.360782\pi\)
0.423555 + 0.905870i \(0.360782\pi\)
\(230\) −7.01981 −0.462872
\(231\) −7.29758 −0.480145
\(232\) −9.37575 −0.615548
\(233\) −5.91773 −0.387683 −0.193842 0.981033i \(-0.562095\pi\)
−0.193842 + 0.981033i \(0.562095\pi\)
\(234\) 5.91032 0.386370
\(235\) −7.74590 −0.505287
\(236\) −8.71482 −0.567287
\(237\) −21.8008 −1.41611
\(238\) −2.78329 −0.180414
\(239\) 18.0461 1.16731 0.583654 0.812003i \(-0.301623\pi\)
0.583654 + 0.812003i \(0.301623\pi\)
\(240\) −1.81604 −0.117225
\(241\) −29.1393 −1.87703 −0.938513 0.345243i \(-0.887796\pi\)
−0.938513 + 0.345243i \(0.887796\pi\)
\(242\) −0.337724 −0.0217097
\(243\) 17.8552 1.14541
\(244\) −4.63923 −0.296996
\(245\) 0.812592 0.0519146
\(246\) −3.93649 −0.250982
\(247\) −12.8115 −0.815175
\(248\) 5.70390 0.362198
\(249\) −22.9437 −1.45400
\(250\) −7.58936 −0.479993
\(251\) 20.6603 1.30407 0.652034 0.758190i \(-0.273916\pi\)
0.652034 + 0.758190i \(0.273916\pi\)
\(252\) 1.99468 0.125653
\(253\) −28.2084 −1.77344
\(254\) 6.98647 0.438370
\(255\) 5.05457 0.316530
\(256\) 1.00000 0.0625000
\(257\) −2.83777 −0.177015 −0.0885075 0.996076i \(-0.528210\pi\)
−0.0885075 + 0.996076i \(0.528210\pi\)
\(258\) 3.80859 0.237112
\(259\) 7.34378 0.456320
\(260\) 2.40775 0.149322
\(261\) −18.7016 −1.15760
\(262\) −0.0906462 −0.00560014
\(263\) 18.9655 1.16947 0.584733 0.811226i \(-0.301199\pi\)
0.584733 + 0.811226i \(0.301199\pi\)
\(264\) −7.29758 −0.449135
\(265\) −9.54812 −0.586536
\(266\) −4.32376 −0.265107
\(267\) −14.5863 −0.892666
\(268\) 9.29319 0.567672
\(269\) 21.4827 1.30982 0.654912 0.755705i \(-0.272706\pi\)
0.654912 + 0.755705i \(0.272706\pi\)
\(270\) 1.82571 0.111109
\(271\) −31.6824 −1.92457 −0.962284 0.272047i \(-0.912299\pi\)
−0.962284 + 0.272047i \(0.912299\pi\)
\(272\) −2.78329 −0.168762
\(273\) −6.62204 −0.400784
\(274\) −12.7735 −0.771673
\(275\) −14.1705 −0.854511
\(276\) 19.3066 1.16212
\(277\) −13.8100 −0.829763 −0.414882 0.909875i \(-0.636177\pi\)
−0.414882 + 0.909875i \(0.636177\pi\)
\(278\) 14.4342 0.865705
\(279\) 11.3775 0.681150
\(280\) 0.812592 0.0485617
\(281\) −4.97958 −0.297057 −0.148528 0.988908i \(-0.547454\pi\)
−0.148528 + 0.988908i \(0.547454\pi\)
\(282\) 21.3036 1.26861
\(283\) −20.3586 −1.21019 −0.605096 0.796153i \(-0.706865\pi\)
−0.605096 + 0.796153i \(0.706865\pi\)
\(284\) −16.1273 −0.956979
\(285\) 7.85213 0.465120
\(286\) 9.67527 0.572111
\(287\) 1.76139 0.103972
\(288\) 1.99468 0.117538
\(289\) −9.25330 −0.544312
\(290\) −7.61866 −0.447383
\(291\) 2.79897 0.164079
\(292\) −11.0969 −0.649397
\(293\) −6.82559 −0.398755 −0.199377 0.979923i \(-0.563892\pi\)
−0.199377 + 0.979923i \(0.563892\pi\)
\(294\) −2.23488 −0.130341
\(295\) −7.08160 −0.412306
\(296\) 7.34378 0.426849
\(297\) 7.33641 0.425702
\(298\) −16.3307 −0.946012
\(299\) −25.5971 −1.48032
\(300\) 9.69869 0.559954
\(301\) −1.70416 −0.0982261
\(302\) −4.18363 −0.240741
\(303\) −30.8989 −1.77510
\(304\) −4.32376 −0.247984
\(305\) −3.76980 −0.215858
\(306\) −5.55177 −0.317373
\(307\) 20.6120 1.17639 0.588194 0.808720i \(-0.299839\pi\)
0.588194 + 0.808720i \(0.299839\pi\)
\(308\) 3.26531 0.186059
\(309\) −8.03591 −0.457147
\(310\) 4.63495 0.263247
\(311\) 1.90679 0.108124 0.0540620 0.998538i \(-0.482783\pi\)
0.0540620 + 0.998538i \(0.482783\pi\)
\(312\) −6.62204 −0.374899
\(313\) −23.7618 −1.34309 −0.671547 0.740962i \(-0.734370\pi\)
−0.671547 + 0.740962i \(0.734370\pi\)
\(314\) 22.1358 1.24919
\(315\) 1.62086 0.0913251
\(316\) 9.75479 0.548750
\(317\) −7.97081 −0.447685 −0.223843 0.974625i \(-0.571860\pi\)
−0.223843 + 0.974625i \(0.571860\pi\)
\(318\) 26.2603 1.47260
\(319\) −30.6148 −1.71410
\(320\) 0.812592 0.0454253
\(321\) 1.70078 0.0949285
\(322\) −8.63879 −0.481421
\(323\) 12.0343 0.669604
\(324\) −11.0053 −0.611405
\(325\) −12.8587 −0.713273
\(326\) 0.335627 0.0185887
\(327\) −18.1770 −1.00519
\(328\) 1.76139 0.0972565
\(329\) −9.53234 −0.525535
\(330\) −5.92995 −0.326433
\(331\) −20.3369 −1.11782 −0.558908 0.829230i \(-0.688779\pi\)
−0.558908 + 0.829230i \(0.688779\pi\)
\(332\) 10.2662 0.563432
\(333\) 14.6485 0.802732
\(334\) 11.5237 0.630546
\(335\) 7.55157 0.412586
\(336\) −2.23488 −0.121923
\(337\) 25.4833 1.38817 0.694083 0.719895i \(-0.255810\pi\)
0.694083 + 0.719895i \(0.255810\pi\)
\(338\) −4.22036 −0.229557
\(339\) 13.3577 0.725491
\(340\) −2.26168 −0.122657
\(341\) 18.6250 1.00860
\(342\) −8.62451 −0.466360
\(343\) 1.00000 0.0539949
\(344\) −1.70416 −0.0918821
\(345\) 15.6884 0.844636
\(346\) −9.73755 −0.523494
\(347\) −25.6592 −1.37746 −0.688728 0.725020i \(-0.741831\pi\)
−0.688728 + 0.725020i \(0.741831\pi\)
\(348\) 20.9537 1.12323
\(349\) 20.7876 1.11274 0.556368 0.830936i \(-0.312194\pi\)
0.556368 + 0.830936i \(0.312194\pi\)
\(350\) −4.33969 −0.231966
\(351\) 6.65728 0.355339
\(352\) 3.26531 0.174042
\(353\) −6.60536 −0.351568 −0.175784 0.984429i \(-0.556246\pi\)
−0.175784 + 0.984429i \(0.556246\pi\)
\(354\) 19.4766 1.03517
\(355\) −13.1049 −0.695537
\(356\) 6.52666 0.345912
\(357\) 6.22031 0.329214
\(358\) −23.6562 −1.25027
\(359\) −5.63025 −0.297153 −0.148577 0.988901i \(-0.547469\pi\)
−0.148577 + 0.988901i \(0.547469\pi\)
\(360\) 1.62086 0.0854268
\(361\) −0.305127 −0.0160593
\(362\) −14.9888 −0.787792
\(363\) 0.754771 0.0396152
\(364\) 2.96305 0.155306
\(365\) −9.01725 −0.471985
\(366\) 10.3681 0.541950
\(367\) 6.20611 0.323956 0.161978 0.986794i \(-0.448213\pi\)
0.161978 + 0.986794i \(0.448213\pi\)
\(368\) −8.63879 −0.450328
\(369\) 3.51341 0.182901
\(370\) 5.96750 0.310235
\(371\) −11.7502 −0.610040
\(372\) −12.7475 −0.660928
\(373\) −11.4320 −0.591927 −0.295964 0.955199i \(-0.595641\pi\)
−0.295964 + 0.955199i \(0.595641\pi\)
\(374\) −9.08831 −0.469945
\(375\) 16.9613 0.875877
\(376\) −9.53234 −0.491593
\(377\) −27.7808 −1.43078
\(378\) 2.24677 0.115561
\(379\) 25.5794 1.31393 0.656963 0.753923i \(-0.271841\pi\)
0.656963 + 0.753923i \(0.271841\pi\)
\(380\) −3.51345 −0.180236
\(381\) −15.6139 −0.799924
\(382\) −9.26422 −0.473999
\(383\) 22.9519 1.17279 0.586394 0.810026i \(-0.300547\pi\)
0.586394 + 0.810026i \(0.300547\pi\)
\(384\) −2.23488 −0.114048
\(385\) 2.65337 0.135228
\(386\) 23.5608 1.19921
\(387\) −3.39925 −0.172794
\(388\) −1.25240 −0.0635812
\(389\) −20.9052 −1.05994 −0.529969 0.848017i \(-0.677796\pi\)
−0.529969 + 0.848017i \(0.677796\pi\)
\(390\) −5.38102 −0.272479
\(391\) 24.0442 1.21597
\(392\) 1.00000 0.0505076
\(393\) 0.202583 0.0102190
\(394\) −24.7432 −1.24654
\(395\) 7.92667 0.398834
\(396\) 6.51325 0.327303
\(397\) 14.8338 0.744489 0.372244 0.928135i \(-0.378588\pi\)
0.372244 + 0.928135i \(0.378588\pi\)
\(398\) −9.00585 −0.451422
\(399\) 9.66307 0.483758
\(400\) −4.33969 −0.216985
\(401\) −1.99975 −0.0998630 −0.0499315 0.998753i \(-0.515900\pi\)
−0.0499315 + 0.998753i \(0.515900\pi\)
\(402\) −20.7691 −1.03587
\(403\) 16.9009 0.841895
\(404\) 13.8258 0.687859
\(405\) −8.94281 −0.444372
\(406\) −9.37575 −0.465311
\(407\) 23.9798 1.18863
\(408\) 6.22031 0.307951
\(409\) −38.6230 −1.90978 −0.954892 0.296953i \(-0.904029\pi\)
−0.954892 + 0.296953i \(0.904029\pi\)
\(410\) 1.43129 0.0706865
\(411\) 28.5471 1.40812
\(412\) 3.59568 0.177147
\(413\) −8.71482 −0.428828
\(414\) −17.2316 −0.846887
\(415\) 8.34224 0.409505
\(416\) 2.96305 0.145275
\(417\) −32.2586 −1.57971
\(418\) −14.1184 −0.690555
\(419\) 2.18635 0.106810 0.0534051 0.998573i \(-0.482993\pi\)
0.0534051 + 0.998573i \(0.482993\pi\)
\(420\) −1.81604 −0.0886139
\(421\) 10.6823 0.520624 0.260312 0.965525i \(-0.416175\pi\)
0.260312 + 0.965525i \(0.416175\pi\)
\(422\) −9.99153 −0.486380
\(423\) −19.0140 −0.924490
\(424\) −11.7502 −0.570640
\(425\) 12.0786 0.585899
\(426\) 36.0426 1.74627
\(427\) −4.63923 −0.224508
\(428\) −0.761019 −0.0367852
\(429\) −21.6231 −1.04397
\(430\) −1.38479 −0.0667803
\(431\) −1.00000 −0.0481683
\(432\) 2.24677 0.108098
\(433\) 8.63850 0.415140 0.207570 0.978220i \(-0.433445\pi\)
0.207570 + 0.978220i \(0.433445\pi\)
\(434\) 5.70390 0.273796
\(435\) 17.0268 0.816371
\(436\) 8.13333 0.389516
\(437\) 37.3520 1.78679
\(438\) 24.8002 1.18500
\(439\) 12.0109 0.573248 0.286624 0.958043i \(-0.407467\pi\)
0.286624 + 0.958043i \(0.407467\pi\)
\(440\) 2.65337 0.126494
\(441\) 1.99468 0.0949847
\(442\) −8.24701 −0.392270
\(443\) 17.0802 0.811505 0.405752 0.913983i \(-0.367010\pi\)
0.405752 + 0.913983i \(0.367010\pi\)
\(444\) −16.4125 −0.778901
\(445\) 5.30351 0.251411
\(446\) −18.8022 −0.890312
\(447\) 36.4971 1.72625
\(448\) 1.00000 0.0472456
\(449\) −22.2276 −1.04899 −0.524493 0.851415i \(-0.675745\pi\)
−0.524493 + 0.851415i \(0.675745\pi\)
\(450\) −8.65630 −0.408062
\(451\) 5.75149 0.270827
\(452\) −5.97693 −0.281131
\(453\) 9.34991 0.439297
\(454\) 4.48248 0.210373
\(455\) 2.40775 0.112877
\(456\) 9.66307 0.452515
\(457\) −37.6890 −1.76302 −0.881508 0.472169i \(-0.843471\pi\)
−0.881508 + 0.472169i \(0.843471\pi\)
\(458\) 12.8191 0.598997
\(459\) −6.25341 −0.291884
\(460\) −7.01981 −0.327300
\(461\) −4.33600 −0.201948 −0.100974 0.994889i \(-0.532196\pi\)
−0.100974 + 0.994889i \(0.532196\pi\)
\(462\) −7.29758 −0.339514
\(463\) 29.7916 1.38453 0.692265 0.721643i \(-0.256613\pi\)
0.692265 + 0.721643i \(0.256613\pi\)
\(464\) −9.37575 −0.435258
\(465\) −10.3585 −0.480366
\(466\) −5.91773 −0.274134
\(467\) −27.6527 −1.27962 −0.639808 0.768535i \(-0.720986\pi\)
−0.639808 + 0.768535i \(0.720986\pi\)
\(468\) 5.91032 0.273205
\(469\) 9.29319 0.429119
\(470\) −7.74590 −0.357292
\(471\) −49.4708 −2.27949
\(472\) −8.71482 −0.401132
\(473\) −5.56461 −0.255861
\(474\) −21.8008 −1.00134
\(475\) 18.7638 0.860941
\(476\) −2.78329 −0.127572
\(477\) −23.4379 −1.07315
\(478\) 18.0461 0.825411
\(479\) 4.07882 0.186366 0.0931830 0.995649i \(-0.470296\pi\)
0.0931830 + 0.995649i \(0.470296\pi\)
\(480\) −1.81604 −0.0828907
\(481\) 21.7600 0.992169
\(482\) −29.1393 −1.32726
\(483\) 19.3066 0.878482
\(484\) −0.337724 −0.0153511
\(485\) −1.01769 −0.0462111
\(486\) 17.8552 0.809927
\(487\) 27.6331 1.25217 0.626087 0.779753i \(-0.284655\pi\)
0.626087 + 0.779753i \(0.284655\pi\)
\(488\) −4.63923 −0.210008
\(489\) −0.750086 −0.0339201
\(490\) 0.812592 0.0367092
\(491\) 20.9329 0.944691 0.472345 0.881414i \(-0.343408\pi\)
0.472345 + 0.881414i \(0.343408\pi\)
\(492\) −3.93649 −0.177471
\(493\) 26.0954 1.17528
\(494\) −12.8115 −0.576416
\(495\) 5.29262 0.237885
\(496\) 5.70390 0.256113
\(497\) −16.1273 −0.723408
\(498\) −22.9437 −1.02813
\(499\) −28.6722 −1.28354 −0.641771 0.766896i \(-0.721800\pi\)
−0.641771 + 0.766896i \(0.721800\pi\)
\(500\) −7.58936 −0.339407
\(501\) −25.7540 −1.15060
\(502\) 20.6603 0.922116
\(503\) −5.59086 −0.249284 −0.124642 0.992202i \(-0.539778\pi\)
−0.124642 + 0.992202i \(0.539778\pi\)
\(504\) 1.99468 0.0888501
\(505\) 11.2347 0.499939
\(506\) −28.2084 −1.25401
\(507\) 9.43199 0.418890
\(508\) 6.98647 0.309974
\(509\) 4.78285 0.211996 0.105998 0.994366i \(-0.466196\pi\)
0.105998 + 0.994366i \(0.466196\pi\)
\(510\) 5.05457 0.223820
\(511\) −11.0969 −0.490898
\(512\) 1.00000 0.0441942
\(513\) −9.71449 −0.428905
\(514\) −2.83777 −0.125169
\(515\) 2.92182 0.128751
\(516\) 3.80859 0.167664
\(517\) −31.1261 −1.36892
\(518\) 7.34378 0.322667
\(519\) 21.7622 0.955256
\(520\) 2.40775 0.105587
\(521\) 30.0690 1.31734 0.658672 0.752430i \(-0.271118\pi\)
0.658672 + 0.752430i \(0.271118\pi\)
\(522\) −18.7016 −0.818547
\(523\) −3.59089 −0.157018 −0.0785092 0.996913i \(-0.525016\pi\)
−0.0785092 + 0.996913i \(0.525016\pi\)
\(524\) −0.0906462 −0.00395990
\(525\) 9.69869 0.423285
\(526\) 18.9655 0.826937
\(527\) −15.8756 −0.691552
\(528\) −7.29758 −0.317586
\(529\) 51.6286 2.24472
\(530\) −9.54812 −0.414744
\(531\) −17.3833 −0.754370
\(532\) −4.32376 −0.187459
\(533\) 5.21908 0.226063
\(534\) −14.5863 −0.631210
\(535\) −0.618398 −0.0267357
\(536\) 9.29319 0.401404
\(537\) 52.8688 2.28146
\(538\) 21.4827 0.926185
\(539\) 3.26531 0.140647
\(540\) 1.82571 0.0785659
\(541\) −28.5645 −1.22808 −0.614041 0.789274i \(-0.710457\pi\)
−0.614041 + 0.789274i \(0.710457\pi\)
\(542\) −31.6824 −1.36087
\(543\) 33.4981 1.43754
\(544\) −2.78329 −0.119333
\(545\) 6.60907 0.283102
\(546\) −6.62204 −0.283397
\(547\) −41.4043 −1.77032 −0.885160 0.465287i \(-0.845951\pi\)
−0.885160 + 0.465287i \(0.845951\pi\)
\(548\) −12.7735 −0.545655
\(549\) −9.25377 −0.394941
\(550\) −14.1705 −0.604231
\(551\) 40.5385 1.72700
\(552\) 19.3066 0.821745
\(553\) 9.75479 0.414816
\(554\) −13.8100 −0.586731
\(555\) −13.3366 −0.566108
\(556\) 14.4342 0.612146
\(557\) −10.5996 −0.449119 −0.224559 0.974460i \(-0.572094\pi\)
−0.224559 + 0.974460i \(0.572094\pi\)
\(558\) 11.3775 0.481646
\(559\) −5.04950 −0.213571
\(560\) 0.812592 0.0343383
\(561\) 20.3113 0.857542
\(562\) −4.97958 −0.210051
\(563\) 15.3788 0.648138 0.324069 0.946034i \(-0.394949\pi\)
0.324069 + 0.946034i \(0.394949\pi\)
\(564\) 21.3036 0.897044
\(565\) −4.85680 −0.204327
\(566\) −20.3586 −0.855735
\(567\) −11.0053 −0.462179
\(568\) −16.1273 −0.676687
\(569\) 19.3679 0.811943 0.405972 0.913886i \(-0.366933\pi\)
0.405972 + 0.913886i \(0.366933\pi\)
\(570\) 7.85213 0.328890
\(571\) 20.1297 0.842400 0.421200 0.906968i \(-0.361609\pi\)
0.421200 + 0.906968i \(0.361609\pi\)
\(572\) 9.67527 0.404544
\(573\) 20.7044 0.864939
\(574\) 1.76139 0.0735190
\(575\) 37.4897 1.56343
\(576\) 1.99468 0.0831116
\(577\) 24.7523 1.03045 0.515226 0.857054i \(-0.327708\pi\)
0.515226 + 0.857054i \(0.327708\pi\)
\(578\) −9.25330 −0.384887
\(579\) −52.6555 −2.18829
\(580\) −7.61866 −0.316348
\(581\) 10.2662 0.425914
\(582\) 2.79897 0.116021
\(583\) −38.3681 −1.58904
\(584\) −11.0969 −0.459193
\(585\) 4.80268 0.198566
\(586\) −6.82559 −0.281962
\(587\) 24.9304 1.02899 0.514493 0.857495i \(-0.327980\pi\)
0.514493 + 0.857495i \(0.327980\pi\)
\(588\) −2.23488 −0.0921648
\(589\) −24.6623 −1.01619
\(590\) −7.08160 −0.291545
\(591\) 55.2979 2.27465
\(592\) 7.34378 0.301828
\(593\) −19.1377 −0.785893 −0.392947 0.919561i \(-0.628544\pi\)
−0.392947 + 0.919561i \(0.628544\pi\)
\(594\) 7.33641 0.301017
\(595\) −2.26168 −0.0927198
\(596\) −16.3307 −0.668931
\(597\) 20.1270 0.823742
\(598\) −25.5971 −1.04674
\(599\) 24.8622 1.01584 0.507922 0.861403i \(-0.330414\pi\)
0.507922 + 0.861403i \(0.330414\pi\)
\(600\) 9.69869 0.395947
\(601\) −20.4523 −0.834266 −0.417133 0.908846i \(-0.636965\pi\)
−0.417133 + 0.908846i \(0.636965\pi\)
\(602\) −1.70416 −0.0694563
\(603\) 18.5369 0.754882
\(604\) −4.18363 −0.170230
\(605\) −0.274432 −0.0111572
\(606\) −30.8989 −1.25518
\(607\) −3.54318 −0.143813 −0.0719066 0.997411i \(-0.522908\pi\)
−0.0719066 + 0.997411i \(0.522908\pi\)
\(608\) −4.32376 −0.175351
\(609\) 20.9537 0.849085
\(610\) −3.76980 −0.152635
\(611\) −28.2448 −1.14266
\(612\) −5.55177 −0.224417
\(613\) −32.3409 −1.30624 −0.653118 0.757256i \(-0.726540\pi\)
−0.653118 + 0.757256i \(0.726540\pi\)
\(614\) 20.6120 0.831832
\(615\) −3.19876 −0.128987
\(616\) 3.26531 0.131563
\(617\) 5.03574 0.202731 0.101366 0.994849i \(-0.467679\pi\)
0.101366 + 0.994849i \(0.467679\pi\)
\(618\) −8.03591 −0.323252
\(619\) −1.01794 −0.0409144 −0.0204572 0.999791i \(-0.506512\pi\)
−0.0204572 + 0.999791i \(0.506512\pi\)
\(620\) 4.63495 0.186144
\(621\) −19.4094 −0.778871
\(622\) 1.90679 0.0764553
\(623\) 6.52666 0.261485
\(624\) −6.62204 −0.265094
\(625\) 15.5314 0.621257
\(626\) −23.7618 −0.949711
\(627\) 31.5530 1.26010
\(628\) 22.1358 0.883314
\(629\) −20.4399 −0.814991
\(630\) 1.62086 0.0645766
\(631\) −40.2620 −1.60280 −0.801402 0.598126i \(-0.795912\pi\)
−0.801402 + 0.598126i \(0.795912\pi\)
\(632\) 9.75479 0.388025
\(633\) 22.3299 0.887532
\(634\) −7.97081 −0.316561
\(635\) 5.67715 0.225291
\(636\) 26.2603 1.04129
\(637\) 2.96305 0.117400
\(638\) −30.6148 −1.21205
\(639\) −32.1688 −1.27258
\(640\) 0.812592 0.0321205
\(641\) 40.7674 1.61022 0.805108 0.593128i \(-0.202107\pi\)
0.805108 + 0.593128i \(0.202107\pi\)
\(642\) 1.70078 0.0671246
\(643\) 44.3194 1.74779 0.873893 0.486119i \(-0.161588\pi\)
0.873893 + 0.486119i \(0.161588\pi\)
\(644\) −8.63879 −0.340416
\(645\) 3.09483 0.121859
\(646\) 12.0343 0.473482
\(647\) 36.3016 1.42716 0.713581 0.700573i \(-0.247072\pi\)
0.713581 + 0.700573i \(0.247072\pi\)
\(648\) −11.0053 −0.432329
\(649\) −28.4566 −1.11702
\(650\) −12.8587 −0.504360
\(651\) −12.7475 −0.499615
\(652\) 0.335627 0.0131442
\(653\) −42.3260 −1.65634 −0.828172 0.560474i \(-0.810619\pi\)
−0.828172 + 0.560474i \(0.810619\pi\)
\(654\) −18.1770 −0.710776
\(655\) −0.0736584 −0.00287807
\(656\) 1.76139 0.0687707
\(657\) −22.1348 −0.863559
\(658\) −9.53234 −0.371609
\(659\) 47.6809 1.85738 0.928692 0.370851i \(-0.120934\pi\)
0.928692 + 0.370851i \(0.120934\pi\)
\(660\) −5.92995 −0.230823
\(661\) −16.5427 −0.643435 −0.321718 0.946836i \(-0.604260\pi\)
−0.321718 + 0.946836i \(0.604260\pi\)
\(662\) −20.3369 −0.790415
\(663\) 18.4311 0.715803
\(664\) 10.2662 0.398406
\(665\) −3.51345 −0.136246
\(666\) 14.6485 0.567617
\(667\) 80.9951 3.13614
\(668\) 11.5237 0.445864
\(669\) 42.0207 1.62461
\(670\) 7.55157 0.291743
\(671\) −15.1485 −0.584803
\(672\) −2.23488 −0.0862123
\(673\) 42.0819 1.62214 0.811069 0.584950i \(-0.198886\pi\)
0.811069 + 0.584950i \(0.198886\pi\)
\(674\) 25.4833 0.981581
\(675\) −9.75029 −0.375289
\(676\) −4.22036 −0.162322
\(677\) 7.22910 0.277837 0.138918 0.990304i \(-0.455637\pi\)
0.138918 + 0.990304i \(0.455637\pi\)
\(678\) 13.3577 0.512999
\(679\) −1.25240 −0.0480629
\(680\) −2.26168 −0.0867314
\(681\) −10.0178 −0.383883
\(682\) 18.6250 0.713189
\(683\) −11.6165 −0.444493 −0.222246 0.974991i \(-0.571339\pi\)
−0.222246 + 0.974991i \(0.571339\pi\)
\(684\) −8.62451 −0.329766
\(685\) −10.3796 −0.396584
\(686\) 1.00000 0.0381802
\(687\) −28.6491 −1.09303
\(688\) −1.70416 −0.0649704
\(689\) −34.8164 −1.32640
\(690\) 15.6884 0.597248
\(691\) −17.0283 −0.647787 −0.323894 0.946093i \(-0.604992\pi\)
−0.323894 + 0.946093i \(0.604992\pi\)
\(692\) −9.73755 −0.370166
\(693\) 6.51325 0.247418
\(694\) −25.6592 −0.974008
\(695\) 11.7291 0.444910
\(696\) 20.9537 0.794246
\(697\) −4.90246 −0.185694
\(698\) 20.7876 0.786824
\(699\) 13.2254 0.500231
\(700\) −4.33969 −0.164025
\(701\) −3.01004 −0.113688 −0.0568439 0.998383i \(-0.518104\pi\)
−0.0568439 + 0.998383i \(0.518104\pi\)
\(702\) 6.65728 0.251263
\(703\) −31.7527 −1.19758
\(704\) 3.26531 0.123066
\(705\) 17.3111 0.651975
\(706\) −6.60536 −0.248596
\(707\) 13.8258 0.519972
\(708\) 19.4766 0.731974
\(709\) 27.5541 1.03482 0.517408 0.855739i \(-0.326897\pi\)
0.517408 + 0.855739i \(0.326897\pi\)
\(710\) −13.1049 −0.491819
\(711\) 19.4577 0.729720
\(712\) 6.52666 0.244597
\(713\) −49.2748 −1.84536
\(714\) 6.22031 0.232789
\(715\) 7.86205 0.294024
\(716\) −23.6562 −0.884075
\(717\) −40.3309 −1.50619
\(718\) −5.63025 −0.210119
\(719\) −27.5142 −1.02611 −0.513053 0.858357i \(-0.671486\pi\)
−0.513053 + 0.858357i \(0.671486\pi\)
\(720\) 1.62086 0.0604059
\(721\) 3.59568 0.133910
\(722\) −0.305127 −0.0113557
\(723\) 65.1227 2.42194
\(724\) −14.9888 −0.557053
\(725\) 40.6879 1.51111
\(726\) 0.754771 0.0280122
\(727\) 39.0112 1.44685 0.723423 0.690406i \(-0.242568\pi\)
0.723423 + 0.690406i \(0.242568\pi\)
\(728\) 2.96305 0.109818
\(729\) −6.88826 −0.255121
\(730\) −9.01725 −0.333743
\(731\) 4.74317 0.175432
\(732\) 10.3681 0.383216
\(733\) −49.3662 −1.82338 −0.911690 0.410878i \(-0.865222\pi\)
−0.911690 + 0.410878i \(0.865222\pi\)
\(734\) 6.20611 0.229072
\(735\) −1.81604 −0.0669858
\(736\) −8.63879 −0.318430
\(737\) 30.3452 1.11778
\(738\) 3.51341 0.129330
\(739\) 3.28671 0.120903 0.0604517 0.998171i \(-0.480746\pi\)
0.0604517 + 0.998171i \(0.480746\pi\)
\(740\) 5.96750 0.219370
\(741\) 28.6321 1.05183
\(742\) −11.7502 −0.431364
\(743\) 11.6914 0.428915 0.214458 0.976733i \(-0.431202\pi\)
0.214458 + 0.976733i \(0.431202\pi\)
\(744\) −12.7475 −0.467347
\(745\) −13.2702 −0.486182
\(746\) −11.4320 −0.418556
\(747\) 20.4778 0.749243
\(748\) −9.08831 −0.332302
\(749\) −0.761019 −0.0278070
\(750\) 16.9613 0.619339
\(751\) −6.49083 −0.236854 −0.118427 0.992963i \(-0.537785\pi\)
−0.118427 + 0.992963i \(0.537785\pi\)
\(752\) −9.53234 −0.347609
\(753\) −46.1733 −1.68265
\(754\) −27.7808 −1.01172
\(755\) −3.39959 −0.123724
\(756\) 2.24677 0.0817142
\(757\) 11.4748 0.417059 0.208530 0.978016i \(-0.433132\pi\)
0.208530 + 0.978016i \(0.433132\pi\)
\(758\) 25.5794 0.929086
\(759\) 63.0422 2.28829
\(760\) −3.51345 −0.127446
\(761\) 6.25685 0.226811 0.113405 0.993549i \(-0.463824\pi\)
0.113405 + 0.993549i \(0.463824\pi\)
\(762\) −15.6139 −0.565632
\(763\) 8.13333 0.294446
\(764\) −9.26422 −0.335168
\(765\) −4.51132 −0.163107
\(766\) 22.9519 0.829286
\(767\) −25.8224 −0.932394
\(768\) −2.23488 −0.0806442
\(769\) 38.5889 1.39155 0.695775 0.718259i \(-0.255061\pi\)
0.695775 + 0.718259i \(0.255061\pi\)
\(770\) 2.65337 0.0956207
\(771\) 6.34206 0.228404
\(772\) 23.5608 0.847971
\(773\) −7.19501 −0.258787 −0.129393 0.991593i \(-0.541303\pi\)
−0.129393 + 0.991593i \(0.541303\pi\)
\(774\) −3.39925 −0.122183
\(775\) −24.7532 −0.889161
\(776\) −1.25240 −0.0449587
\(777\) −16.4125 −0.588794
\(778\) −20.9052 −0.749489
\(779\) −7.61582 −0.272865
\(780\) −5.38102 −0.192671
\(781\) −52.6607 −1.88435
\(782\) 24.0442 0.859820
\(783\) −21.0652 −0.752807
\(784\) 1.00000 0.0357143
\(785\) 17.9874 0.641996
\(786\) 0.202583 0.00722590
\(787\) −8.86735 −0.316087 −0.158043 0.987432i \(-0.550519\pi\)
−0.158043 + 0.987432i \(0.550519\pi\)
\(788\) −24.7432 −0.881438
\(789\) −42.3857 −1.50897
\(790\) 7.92667 0.282018
\(791\) −5.97693 −0.212515
\(792\) 6.51325 0.231438
\(793\) −13.7462 −0.488143
\(794\) 14.8338 0.526433
\(795\) 21.3389 0.756812
\(796\) −9.00585 −0.319204
\(797\) 1.87871 0.0665474 0.0332737 0.999446i \(-0.489407\pi\)
0.0332737 + 0.999446i \(0.489407\pi\)
\(798\) 9.66307 0.342069
\(799\) 26.5313 0.938608
\(800\) −4.33969 −0.153431
\(801\) 13.0186 0.459989
\(802\) −1.99975 −0.0706138
\(803\) −36.2349 −1.27870
\(804\) −20.7691 −0.732471
\(805\) −7.01981 −0.247416
\(806\) 16.9009 0.595310
\(807\) −48.0112 −1.69008
\(808\) 13.8258 0.486389
\(809\) −46.3154 −1.62836 −0.814182 0.580610i \(-0.802814\pi\)
−0.814182 + 0.580610i \(0.802814\pi\)
\(810\) −8.94281 −0.314218
\(811\) 15.1610 0.532374 0.266187 0.963921i \(-0.414236\pi\)
0.266187 + 0.963921i \(0.414236\pi\)
\(812\) −9.37575 −0.329024
\(813\) 70.8063 2.48328
\(814\) 23.9798 0.840490
\(815\) 0.272728 0.00955325
\(816\) 6.22031 0.217754
\(817\) 7.36837 0.257787
\(818\) −38.6230 −1.35042
\(819\) 5.91032 0.206523
\(820\) 1.43129 0.0499829
\(821\) −17.2740 −0.602868 −0.301434 0.953487i \(-0.597465\pi\)
−0.301434 + 0.953487i \(0.597465\pi\)
\(822\) 28.5471 0.995695
\(823\) 36.5942 1.27559 0.637796 0.770205i \(-0.279846\pi\)
0.637796 + 0.770205i \(0.279846\pi\)
\(824\) 3.59568 0.125262
\(825\) 31.6693 1.10258
\(826\) −8.71482 −0.303228
\(827\) −6.57553 −0.228654 −0.114327 0.993443i \(-0.536471\pi\)
−0.114327 + 0.993443i \(0.536471\pi\)
\(828\) −17.2316 −0.598840
\(829\) 16.3087 0.566424 0.283212 0.959057i \(-0.408600\pi\)
0.283212 + 0.959057i \(0.408600\pi\)
\(830\) 8.34224 0.289563
\(831\) 30.8637 1.07065
\(832\) 2.96305 0.102725
\(833\) −2.78329 −0.0964353
\(834\) −32.2586 −1.11703
\(835\) 9.36403 0.324056
\(836\) −14.1184 −0.488296
\(837\) 12.8154 0.442964
\(838\) 2.18635 0.0755263
\(839\) −49.1941 −1.69837 −0.849184 0.528097i \(-0.822906\pi\)
−0.849184 + 0.528097i \(0.822906\pi\)
\(840\) −1.81604 −0.0626595
\(841\) 58.9047 2.03120
\(842\) 10.6823 0.368137
\(843\) 11.1288 0.383295
\(844\) −9.99153 −0.343923
\(845\) −3.42943 −0.117976
\(846\) −19.0140 −0.653713
\(847\) −0.337724 −0.0116043
\(848\) −11.7502 −0.403504
\(849\) 45.4989 1.56152
\(850\) 12.0786 0.414293
\(851\) −63.4414 −2.17474
\(852\) 36.0426 1.23480
\(853\) −52.0438 −1.78195 −0.890973 0.454056i \(-0.849977\pi\)
−0.890973 + 0.454056i \(0.849977\pi\)
\(854\) −4.63923 −0.158751
\(855\) −7.00820 −0.239676
\(856\) −0.761019 −0.0260111
\(857\) 7.18768 0.245527 0.122763 0.992436i \(-0.460824\pi\)
0.122763 + 0.992436i \(0.460824\pi\)
\(858\) −21.6231 −0.738199
\(859\) −8.75697 −0.298784 −0.149392 0.988778i \(-0.547732\pi\)
−0.149392 + 0.988778i \(0.547732\pi\)
\(860\) −1.38479 −0.0472208
\(861\) −3.93649 −0.134155
\(862\) −1.00000 −0.0340601
\(863\) −25.7682 −0.877159 −0.438579 0.898693i \(-0.644518\pi\)
−0.438579 + 0.898693i \(0.644518\pi\)
\(864\) 2.24677 0.0764367
\(865\) −7.91266 −0.269038
\(866\) 8.63850 0.293548
\(867\) 20.6800 0.702330
\(868\) 5.70390 0.193603
\(869\) 31.8525 1.08052
\(870\) 17.0268 0.577262
\(871\) 27.5361 0.933026
\(872\) 8.13333 0.275429
\(873\) −2.49815 −0.0845494
\(874\) 37.3520 1.26345
\(875\) −7.58936 −0.256567
\(876\) 24.8002 0.837922
\(877\) 46.4632 1.56895 0.784476 0.620159i \(-0.212932\pi\)
0.784476 + 0.620159i \(0.212932\pi\)
\(878\) 12.0109 0.405347
\(879\) 15.2543 0.514516
\(880\) 2.65337 0.0894450
\(881\) 23.4137 0.788827 0.394414 0.918933i \(-0.370948\pi\)
0.394414 + 0.918933i \(0.370948\pi\)
\(882\) 1.99468 0.0671643
\(883\) −32.3704 −1.08935 −0.544675 0.838647i \(-0.683347\pi\)
−0.544675 + 0.838647i \(0.683347\pi\)
\(884\) −8.24701 −0.277377
\(885\) 15.8265 0.532002
\(886\) 17.0802 0.573821
\(887\) −0.832155 −0.0279410 −0.0139705 0.999902i \(-0.504447\pi\)
−0.0139705 + 0.999902i \(0.504447\pi\)
\(888\) −16.4125 −0.550766
\(889\) 6.98647 0.234319
\(890\) 5.30351 0.177774
\(891\) −35.9357 −1.20389
\(892\) −18.8022 −0.629546
\(893\) 41.2155 1.37922
\(894\) 36.4971 1.22065
\(895\) −19.2229 −0.642549
\(896\) 1.00000 0.0334077
\(897\) 57.2064 1.91007
\(898\) −22.2276 −0.741746
\(899\) −53.4784 −1.78360
\(900\) −8.65630 −0.288543
\(901\) 32.7042 1.08954
\(902\) 5.75149 0.191504
\(903\) 3.80859 0.126742
\(904\) −5.97693 −0.198790
\(905\) −12.1798 −0.404869
\(906\) 9.34991 0.310630
\(907\) 14.3369 0.476049 0.238024 0.971259i \(-0.423500\pi\)
0.238024 + 0.971259i \(0.423500\pi\)
\(908\) 4.48248 0.148756
\(909\) 27.5780 0.914705
\(910\) 2.40775 0.0798160
\(911\) 12.1591 0.402850 0.201425 0.979504i \(-0.435443\pi\)
0.201425 + 0.979504i \(0.435443\pi\)
\(912\) 9.66307 0.319976
\(913\) 33.5224 1.10943
\(914\) −37.6890 −1.24664
\(915\) 8.42504 0.278523
\(916\) 12.8191 0.423555
\(917\) −0.0906462 −0.00299340
\(918\) −6.25341 −0.206393
\(919\) −45.3983 −1.49755 −0.748775 0.662824i \(-0.769358\pi\)
−0.748775 + 0.662824i \(0.769358\pi\)
\(920\) −7.01981 −0.231436
\(921\) −46.0652 −1.51790
\(922\) −4.33600 −0.142799
\(923\) −47.7859 −1.57289
\(924\) −7.29758 −0.240073
\(925\) −31.8698 −1.04787
\(926\) 29.7916 0.979011
\(927\) 7.17223 0.235567
\(928\) −9.37575 −0.307774
\(929\) 0.869939 0.0285418 0.0142709 0.999898i \(-0.495457\pi\)
0.0142709 + 0.999898i \(0.495457\pi\)
\(930\) −10.3585 −0.339670
\(931\) −4.32376 −0.141705
\(932\) −5.91773 −0.193842
\(933\) −4.26144 −0.139513
\(934\) −27.6527 −0.904826
\(935\) −7.38509 −0.241518
\(936\) 5.91032 0.193185
\(937\) −1.89466 −0.0618958 −0.0309479 0.999521i \(-0.509853\pi\)
−0.0309479 + 0.999521i \(0.509853\pi\)
\(938\) 9.29319 0.303433
\(939\) 53.1046 1.73300
\(940\) −7.74590 −0.252643
\(941\) 34.2486 1.11647 0.558236 0.829682i \(-0.311478\pi\)
0.558236 + 0.829682i \(0.311478\pi\)
\(942\) −49.4708 −1.61184
\(943\) −15.2163 −0.495510
\(944\) −8.71482 −0.283643
\(945\) 1.82571 0.0593903
\(946\) −5.56461 −0.180921
\(947\) 58.6802 1.90685 0.953425 0.301631i \(-0.0975312\pi\)
0.953425 + 0.301631i \(0.0975312\pi\)
\(948\) −21.8008 −0.708056
\(949\) −32.8806 −1.06735
\(950\) 18.7638 0.608777
\(951\) 17.8138 0.577652
\(952\) −2.78329 −0.0902069
\(953\) 37.1216 1.20249 0.601244 0.799066i \(-0.294672\pi\)
0.601244 + 0.799066i \(0.294672\pi\)
\(954\) −23.4379 −0.758830
\(955\) −7.52803 −0.243601
\(956\) 18.0461 0.583654
\(957\) 68.4203 2.21171
\(958\) 4.07882 0.131781
\(959\) −12.7735 −0.412476
\(960\) −1.81604 −0.0586126
\(961\) 1.53450 0.0495001
\(962\) 21.7600 0.701569
\(963\) −1.51799 −0.0489165
\(964\) −29.1393 −0.938513
\(965\) 19.1453 0.616309
\(966\) 19.3066 0.621181
\(967\) −4.43537 −0.142632 −0.0713159 0.997454i \(-0.522720\pi\)
−0.0713159 + 0.997454i \(0.522720\pi\)
\(968\) −0.337724 −0.0108549
\(969\) −26.8951 −0.863995
\(970\) −1.01769 −0.0326762
\(971\) −44.7507 −1.43612 −0.718059 0.695982i \(-0.754969\pi\)
−0.718059 + 0.695982i \(0.754969\pi\)
\(972\) 17.8552 0.572705
\(973\) 14.4342 0.462739
\(974\) 27.6331 0.885421
\(975\) 28.7376 0.920341
\(976\) −4.63923 −0.148498
\(977\) −12.5393 −0.401168 −0.200584 0.979677i \(-0.564284\pi\)
−0.200584 + 0.979677i \(0.564284\pi\)
\(978\) −0.750086 −0.0239851
\(979\) 21.3116 0.681122
\(980\) 0.812592 0.0259573
\(981\) 16.2234 0.517972
\(982\) 20.9329 0.667997
\(983\) −4.61837 −0.147303 −0.0736516 0.997284i \(-0.523465\pi\)
−0.0736516 + 0.997284i \(0.523465\pi\)
\(984\) −3.93649 −0.125491
\(985\) −20.1061 −0.640633
\(986\) 26.0954 0.831048
\(987\) 21.3036 0.678102
\(988\) −12.8115 −0.407588
\(989\) 14.7219 0.468128
\(990\) 5.29262 0.168210
\(991\) 37.7918 1.20050 0.600248 0.799814i \(-0.295068\pi\)
0.600248 + 0.799814i \(0.295068\pi\)
\(992\) 5.70390 0.181099
\(993\) 45.4504 1.44233
\(994\) −16.1273 −0.511527
\(995\) −7.31808 −0.231999
\(996\) −22.9437 −0.727000
\(997\) −52.4042 −1.65966 −0.829828 0.558019i \(-0.811562\pi\)
−0.829828 + 0.558019i \(0.811562\pi\)
\(998\) −28.6722 −0.907602
\(999\) 16.4998 0.522030
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 6034.2.a.m.1.5 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6034.2.a.m.1.5 21 1.1 even 1 trivial