Properties

Label 6037.2.a.a.1.8
Level $6037$
Weight $2$
Character 6037.1
Self dual yes
Analytic conductor $48.206$
Analytic rank $1$
Dimension $243$
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] = [6037,2,Mod(1,6037)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6037, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6037.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6037 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6037.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: \(48.2056877002\)
Analytic rank: \(1\)
Dimension: \(243\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) \(=\) 6037.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.73652 q^{2} -0.570094 q^{3} +5.48855 q^{4} -2.26504 q^{5} +1.56007 q^{6} +4.66290 q^{7} -9.54649 q^{8} -2.67499 q^{9} +O(q^{10})\) \(q-2.73652 q^{2} -0.570094 q^{3} +5.48855 q^{4} -2.26504 q^{5} +1.56007 q^{6} +4.66290 q^{7} -9.54649 q^{8} -2.67499 q^{9} +6.19832 q^{10} +3.99394 q^{11} -3.12899 q^{12} +1.10898 q^{13} -12.7601 q^{14} +1.29128 q^{15} +15.1471 q^{16} -1.14193 q^{17} +7.32018 q^{18} +4.86859 q^{19} -12.4318 q^{20} -2.65829 q^{21} -10.9295 q^{22} -3.27795 q^{23} +5.44240 q^{24} +0.130390 q^{25} -3.03475 q^{26} +3.23528 q^{27} +25.5926 q^{28} +4.88836 q^{29} -3.53362 q^{30} -7.53269 q^{31} -22.3573 q^{32} -2.27692 q^{33} +3.12491 q^{34} -10.5616 q^{35} -14.6818 q^{36} +5.56677 q^{37} -13.3230 q^{38} -0.632223 q^{39} +21.6232 q^{40} -1.67443 q^{41} +7.27447 q^{42} -8.74394 q^{43} +21.9210 q^{44} +6.05896 q^{45} +8.97017 q^{46} +0.657846 q^{47} -8.63526 q^{48} +14.7427 q^{49} -0.356816 q^{50} +0.651006 q^{51} +6.08670 q^{52} -12.2321 q^{53} -8.85341 q^{54} -9.04643 q^{55} -44.5144 q^{56} -2.77555 q^{57} -13.3771 q^{58} +9.39157 q^{59} +7.08727 q^{60} -14.8702 q^{61} +20.6134 q^{62} -12.4732 q^{63} +30.8872 q^{64} -2.51188 q^{65} +6.23085 q^{66} -1.48566 q^{67} -6.26753 q^{68} +1.86874 q^{69} +28.9022 q^{70} -12.8358 q^{71} +25.5368 q^{72} -5.21937 q^{73} -15.2336 q^{74} -0.0743346 q^{75} +26.7215 q^{76} +18.6234 q^{77} +1.73009 q^{78} +0.371565 q^{79} -34.3087 q^{80} +6.18057 q^{81} +4.58211 q^{82} +6.60968 q^{83} -14.5902 q^{84} +2.58651 q^{85} +23.9280 q^{86} -2.78682 q^{87} -38.1282 q^{88} -0.198728 q^{89} -16.5805 q^{90} +5.17107 q^{91} -17.9912 q^{92} +4.29434 q^{93} -1.80021 q^{94} -11.0275 q^{95} +12.7458 q^{96} +5.89498 q^{97} -40.3436 q^{98} -10.6838 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9} - 14 q^{10} - 112 q^{11} - 54 q^{12} - 45 q^{13} - 35 q^{14} - 56 q^{15} + 213 q^{16} - 71 q^{17} - 135 q^{18} - 69 q^{19} - 107 q^{20} - 36 q^{21} - 24 q^{22} - 162 q^{23} - 57 q^{24} + 203 q^{25} - 55 q^{26} - 115 q^{27} - 87 q^{28} - 76 q^{29} - 64 q^{30} - 35 q^{31} - 302 q^{32} - 77 q^{33} - 9 q^{34} - 264 q^{35} + 173 q^{36} - 61 q^{37} - 71 q^{38} - 123 q^{39} - 16 q^{40} - 74 q^{41} - 70 q^{42} - 178 q^{43} - 209 q^{44} - 107 q^{45} - 11 q^{46} - 191 q^{47} - 65 q^{48} + 211 q^{49} - 188 q^{50} - 175 q^{51} - 95 q^{52} - 122 q^{53} - 36 q^{54} - 47 q^{55} - 69 q^{56} - 103 q^{57} - 37 q^{58} - 212 q^{59} - 79 q^{60} - 14 q^{61} - 152 q^{62} - 203 q^{63} + 217 q^{64} - 159 q^{65} + 5 q^{66} - 202 q^{67} - 176 q^{68} - 34 q^{69} + 45 q^{70} - 170 q^{71} - 347 q^{72} - 57 q^{73} - 68 q^{74} - 124 q^{75} - 74 q^{76} - 166 q^{77} - 63 q^{78} - 48 q^{79} - 222 q^{80} + 159 q^{81} - 27 q^{82} - 434 q^{83} - 52 q^{84} - 57 q^{85} - 77 q^{86} - 184 q^{87} - 15 q^{88} - 62 q^{89} - 24 q^{90} - 81 q^{91} - 330 q^{92} - 164 q^{93} + 40 q^{94} - 182 q^{95} - 66 q^{96} - 21 q^{97} - 254 q^{98} - 306 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.73652 −1.93501 −0.967506 0.252846i \(-0.918633\pi\)
−0.967506 + 0.252846i \(0.918633\pi\)
\(3\) −0.570094 −0.329144 −0.164572 0.986365i \(-0.552624\pi\)
−0.164572 + 0.986365i \(0.552624\pi\)
\(4\) 5.48855 2.74428
\(5\) −2.26504 −1.01296 −0.506478 0.862253i \(-0.669053\pi\)
−0.506478 + 0.862253i \(0.669053\pi\)
\(6\) 1.56007 0.636897
\(7\) 4.66290 1.76241 0.881206 0.472733i \(-0.156732\pi\)
0.881206 + 0.472733i \(0.156732\pi\)
\(8\) −9.54649 −3.37520
\(9\) −2.67499 −0.891664
\(10\) 6.19832 1.96008
\(11\) 3.99394 1.20422 0.602110 0.798413i \(-0.294327\pi\)
0.602110 + 0.798413i \(0.294327\pi\)
\(12\) −3.12899 −0.903261
\(13\) 1.10898 0.307576 0.153788 0.988104i \(-0.450853\pi\)
0.153788 + 0.988104i \(0.450853\pi\)
\(14\) −12.7601 −3.41029
\(15\) 1.29128 0.333408
\(16\) 15.1471 3.78677
\(17\) −1.14193 −0.276958 −0.138479 0.990365i \(-0.544221\pi\)
−0.138479 + 0.990365i \(0.544221\pi\)
\(18\) 7.32018 1.72538
\(19\) 4.86859 1.11693 0.558465 0.829528i \(-0.311390\pi\)
0.558465 + 0.829528i \(0.311390\pi\)
\(20\) −12.4318 −2.77983
\(21\) −2.65829 −0.580087
\(22\) −10.9295 −2.33018
\(23\) −3.27795 −0.683499 −0.341749 0.939791i \(-0.611019\pi\)
−0.341749 + 0.939791i \(0.611019\pi\)
\(24\) 5.44240 1.11092
\(25\) 0.130390 0.0260780
\(26\) −3.03475 −0.595164
\(27\) 3.23528 0.622629
\(28\) 25.5926 4.83654
\(29\) 4.88836 0.907746 0.453873 0.891066i \(-0.350042\pi\)
0.453873 + 0.891066i \(0.350042\pi\)
\(30\) −3.53362 −0.645148
\(31\) −7.53269 −1.35291 −0.676456 0.736483i \(-0.736485\pi\)
−0.676456 + 0.736483i \(0.736485\pi\)
\(32\) −22.3573 −3.95226
\(33\) −2.27692 −0.396361
\(34\) 3.12491 0.535917
\(35\) −10.5616 −1.78524
\(36\) −14.6818 −2.44697
\(37\) 5.56677 0.915171 0.457585 0.889166i \(-0.348714\pi\)
0.457585 + 0.889166i \(0.348714\pi\)
\(38\) −13.3230 −2.16128
\(39\) −0.632223 −0.101237
\(40\) 21.6232 3.41892
\(41\) −1.67443 −0.261502 −0.130751 0.991415i \(-0.541739\pi\)
−0.130751 + 0.991415i \(0.541739\pi\)
\(42\) 7.27447 1.12248
\(43\) −8.74394 −1.33344 −0.666719 0.745309i \(-0.732302\pi\)
−0.666719 + 0.745309i \(0.732302\pi\)
\(44\) 21.9210 3.30471
\(45\) 6.05896 0.903216
\(46\) 8.97017 1.32258
\(47\) 0.657846 0.0959567 0.0479784 0.998848i \(-0.484722\pi\)
0.0479784 + 0.998848i \(0.484722\pi\)
\(48\) −8.63526 −1.24639
\(49\) 14.7427 2.10609
\(50\) −0.356816 −0.0504613
\(51\) 0.651006 0.0911590
\(52\) 6.08670 0.844074
\(53\) −12.2321 −1.68021 −0.840105 0.542424i \(-0.817507\pi\)
−0.840105 + 0.542424i \(0.817507\pi\)
\(54\) −8.85341 −1.20480
\(55\) −9.04643 −1.21982
\(56\) −44.5144 −5.94848
\(57\) −2.77555 −0.367631
\(58\) −13.3771 −1.75650
\(59\) 9.39157 1.22268 0.611339 0.791369i \(-0.290631\pi\)
0.611339 + 0.791369i \(0.290631\pi\)
\(60\) 7.08727 0.914963
\(61\) −14.8702 −1.90394 −0.951970 0.306191i \(-0.900945\pi\)
−0.951970 + 0.306191i \(0.900945\pi\)
\(62\) 20.6134 2.61790
\(63\) −12.4732 −1.57148
\(64\) 30.8872 3.86090
\(65\) −2.51188 −0.311561
\(66\) 6.23085 0.766964
\(67\) −1.48566 −0.181502 −0.0907509 0.995874i \(-0.528927\pi\)
−0.0907509 + 0.995874i \(0.528927\pi\)
\(68\) −6.26753 −0.760049
\(69\) 1.86874 0.224969
\(70\) 28.9022 3.45447
\(71\) −12.8358 −1.52333 −0.761666 0.647970i \(-0.775618\pi\)
−0.761666 + 0.647970i \(0.775618\pi\)
\(72\) 25.5368 3.00954
\(73\) −5.21937 −0.610881 −0.305441 0.952211i \(-0.598804\pi\)
−0.305441 + 0.952211i \(0.598804\pi\)
\(74\) −15.2336 −1.77087
\(75\) −0.0743346 −0.00858342
\(76\) 26.7215 3.06516
\(77\) 18.6234 2.12233
\(78\) 1.73009 0.195894
\(79\) 0.371565 0.0418043 0.0209022 0.999782i \(-0.493346\pi\)
0.0209022 + 0.999782i \(0.493346\pi\)
\(80\) −34.3087 −3.83583
\(81\) 6.18057 0.686730
\(82\) 4.58211 0.506010
\(83\) 6.60968 0.725506 0.362753 0.931885i \(-0.381837\pi\)
0.362753 + 0.931885i \(0.381837\pi\)
\(84\) −14.5902 −1.59192
\(85\) 2.58651 0.280546
\(86\) 23.9280 2.58022
\(87\) −2.78682 −0.298779
\(88\) −38.1282 −4.06448
\(89\) −0.198728 −0.0210651 −0.0105326 0.999945i \(-0.503353\pi\)
−0.0105326 + 0.999945i \(0.503353\pi\)
\(90\) −16.5805 −1.74773
\(91\) 5.17107 0.542076
\(92\) −17.9912 −1.87571
\(93\) 4.29434 0.445302
\(94\) −1.80021 −0.185678
\(95\) −11.0275 −1.13140
\(96\) 12.7458 1.30086
\(97\) 5.89498 0.598544 0.299272 0.954168i \(-0.403256\pi\)
0.299272 + 0.954168i \(0.403256\pi\)
\(98\) −40.3436 −4.07532
\(99\) −10.6838 −1.07376
\(100\) 0.715653 0.0715653
\(101\) 1.51723 0.150970 0.0754848 0.997147i \(-0.475950\pi\)
0.0754848 + 0.997147i \(0.475950\pi\)
\(102\) −1.78149 −0.176394
\(103\) −13.2376 −1.30434 −0.652169 0.758073i \(-0.726141\pi\)
−0.652169 + 0.758073i \(0.726141\pi\)
\(104\) −10.5869 −1.03813
\(105\) 6.02113 0.587602
\(106\) 33.4734 3.25123
\(107\) −7.23165 −0.699110 −0.349555 0.936916i \(-0.613667\pi\)
−0.349555 + 0.936916i \(0.613667\pi\)
\(108\) 17.7570 1.70867
\(109\) 5.16154 0.494386 0.247193 0.968966i \(-0.420492\pi\)
0.247193 + 0.968966i \(0.420492\pi\)
\(110\) 24.7557 2.36037
\(111\) −3.17358 −0.301223
\(112\) 70.6294 6.67385
\(113\) −18.6681 −1.75615 −0.878073 0.478526i \(-0.841171\pi\)
−0.878073 + 0.478526i \(0.841171\pi\)
\(114\) 7.59535 0.711370
\(115\) 7.42467 0.692354
\(116\) 26.8300 2.49110
\(117\) −2.96652 −0.274255
\(118\) −25.7002 −2.36590
\(119\) −5.32470 −0.488114
\(120\) −12.3272 −1.12532
\(121\) 4.95158 0.450144
\(122\) 40.6928 3.68415
\(123\) 0.954582 0.0860717
\(124\) −41.3435 −3.71276
\(125\) 11.0298 0.986539
\(126\) 34.1333 3.04083
\(127\) 16.5464 1.46825 0.734127 0.679012i \(-0.237592\pi\)
0.734127 + 0.679012i \(0.237592\pi\)
\(128\) −39.8087 −3.51863
\(129\) 4.98487 0.438893
\(130\) 6.87383 0.602874
\(131\) −18.3023 −1.59908 −0.799541 0.600612i \(-0.794924\pi\)
−0.799541 + 0.600612i \(0.794924\pi\)
\(132\) −12.4970 −1.08772
\(133\) 22.7017 1.96849
\(134\) 4.06553 0.351208
\(135\) −7.32802 −0.630696
\(136\) 10.9014 0.934788
\(137\) −22.4113 −1.91472 −0.957361 0.288893i \(-0.906713\pi\)
−0.957361 + 0.288893i \(0.906713\pi\)
\(138\) −5.11384 −0.435319
\(139\) 6.85597 0.581516 0.290758 0.956797i \(-0.406093\pi\)
0.290758 + 0.956797i \(0.406093\pi\)
\(140\) −57.9681 −4.89920
\(141\) −0.375034 −0.0315836
\(142\) 35.1255 2.94767
\(143\) 4.42921 0.370389
\(144\) −40.5183 −3.37653
\(145\) −11.0723 −0.919506
\(146\) 14.2829 1.18206
\(147\) −8.40470 −0.693208
\(148\) 30.5535 2.51148
\(149\) −16.3769 −1.34165 −0.670823 0.741617i \(-0.734059\pi\)
−0.670823 + 0.741617i \(0.734059\pi\)
\(150\) 0.203418 0.0166090
\(151\) 9.00679 0.732963 0.366481 0.930425i \(-0.380562\pi\)
0.366481 + 0.930425i \(0.380562\pi\)
\(152\) −46.4779 −3.76986
\(153\) 3.05465 0.246954
\(154\) −50.9632 −4.10674
\(155\) 17.0618 1.37044
\(156\) −3.46999 −0.277822
\(157\) −11.2499 −0.897842 −0.448921 0.893571i \(-0.648192\pi\)
−0.448921 + 0.893571i \(0.648192\pi\)
\(158\) −1.01680 −0.0808919
\(159\) 6.97345 0.553030
\(160\) 50.6402 4.00346
\(161\) −15.2847 −1.20461
\(162\) −16.9133 −1.32883
\(163\) 10.5409 0.825624 0.412812 0.910816i \(-0.364547\pi\)
0.412812 + 0.910816i \(0.364547\pi\)
\(164\) −9.19019 −0.717633
\(165\) 5.15731 0.401496
\(166\) −18.0875 −1.40386
\(167\) 0.470374 0.0363987 0.0181993 0.999834i \(-0.494207\pi\)
0.0181993 + 0.999834i \(0.494207\pi\)
\(168\) 25.3774 1.95791
\(169\) −11.7702 −0.905397
\(170\) −7.07803 −0.542860
\(171\) −13.0234 −0.995927
\(172\) −47.9916 −3.65932
\(173\) −0.558076 −0.0424297 −0.0212149 0.999775i \(-0.506753\pi\)
−0.0212149 + 0.999775i \(0.506753\pi\)
\(174\) 7.62620 0.578141
\(175\) 0.607997 0.0459602
\(176\) 60.4966 4.56010
\(177\) −5.35408 −0.402437
\(178\) 0.543823 0.0407613
\(179\) −5.04141 −0.376812 −0.188406 0.982091i \(-0.560332\pi\)
−0.188406 + 0.982091i \(0.560332\pi\)
\(180\) 33.2549 2.47867
\(181\) −11.8697 −0.882271 −0.441136 0.897441i \(-0.645424\pi\)
−0.441136 + 0.897441i \(0.645424\pi\)
\(182\) −14.1508 −1.04892
\(183\) 8.47743 0.626670
\(184\) 31.2929 2.30694
\(185\) −12.6089 −0.927027
\(186\) −11.7516 −0.861665
\(187\) −4.56079 −0.333518
\(188\) 3.61062 0.263332
\(189\) 15.0858 1.09733
\(190\) 30.1771 2.18927
\(191\) 2.82705 0.204558 0.102279 0.994756i \(-0.467387\pi\)
0.102279 + 0.994756i \(0.467387\pi\)
\(192\) −17.6086 −1.27079
\(193\) −6.08253 −0.437830 −0.218915 0.975744i \(-0.570252\pi\)
−0.218915 + 0.975744i \(0.570252\pi\)
\(194\) −16.1317 −1.15819
\(195\) 1.43201 0.102548
\(196\) 80.9158 5.77970
\(197\) 11.9295 0.849941 0.424970 0.905207i \(-0.360284\pi\)
0.424970 + 0.905207i \(0.360284\pi\)
\(198\) 29.2364 2.07774
\(199\) 1.27930 0.0906874 0.0453437 0.998971i \(-0.485562\pi\)
0.0453437 + 0.998971i \(0.485562\pi\)
\(200\) −1.24477 −0.0880185
\(201\) 0.846963 0.0597402
\(202\) −4.15192 −0.292128
\(203\) 22.7940 1.59982
\(204\) 3.57308 0.250165
\(205\) 3.79264 0.264890
\(206\) 36.2250 2.52391
\(207\) 8.76848 0.609452
\(208\) 16.7978 1.16472
\(209\) 19.4449 1.34503
\(210\) −16.4769 −1.13702
\(211\) 22.6476 1.55913 0.779563 0.626324i \(-0.215441\pi\)
0.779563 + 0.626324i \(0.215441\pi\)
\(212\) −67.1366 −4.61096
\(213\) 7.31762 0.501395
\(214\) 19.7896 1.35279
\(215\) 19.8053 1.35071
\(216\) −30.8856 −2.10150
\(217\) −35.1242 −2.38439
\(218\) −14.1247 −0.956644
\(219\) 2.97553 0.201068
\(220\) −49.6518 −3.34752
\(221\) −1.26638 −0.0851857
\(222\) 8.68456 0.582870
\(223\) 8.00449 0.536020 0.268010 0.963416i \(-0.413634\pi\)
0.268010 + 0.963416i \(0.413634\pi\)
\(224\) −104.250 −6.96550
\(225\) −0.348793 −0.0232529
\(226\) 51.0856 3.39817
\(227\) 11.9382 0.792365 0.396182 0.918172i \(-0.370335\pi\)
0.396182 + 0.918172i \(0.370335\pi\)
\(228\) −15.2337 −1.00888
\(229\) −10.7594 −0.711001 −0.355500 0.934676i \(-0.615690\pi\)
−0.355500 + 0.934676i \(0.615690\pi\)
\(230\) −20.3178 −1.33971
\(231\) −10.6171 −0.698551
\(232\) −46.6667 −3.06382
\(233\) −15.4873 −1.01460 −0.507302 0.861768i \(-0.669357\pi\)
−0.507302 + 0.861768i \(0.669357\pi\)
\(234\) 8.11794 0.530687
\(235\) −1.49005 −0.0971999
\(236\) 51.5461 3.35537
\(237\) −0.211827 −0.0137596
\(238\) 14.5711 0.944507
\(239\) −0.939021 −0.0607402 −0.0303701 0.999539i \(-0.509669\pi\)
−0.0303701 + 0.999539i \(0.509669\pi\)
\(240\) 19.5592 1.26254
\(241\) −3.34297 −0.215340 −0.107670 0.994187i \(-0.534339\pi\)
−0.107670 + 0.994187i \(0.534339\pi\)
\(242\) −13.5501 −0.871035
\(243\) −13.2293 −0.848662
\(244\) −81.6161 −5.22494
\(245\) −33.3927 −2.13338
\(246\) −2.61223 −0.166550
\(247\) 5.39917 0.343541
\(248\) 71.9108 4.56634
\(249\) −3.76813 −0.238796
\(250\) −30.1834 −1.90897
\(251\) 26.2692 1.65810 0.829049 0.559176i \(-0.188882\pi\)
0.829049 + 0.559176i \(0.188882\pi\)
\(252\) −68.4600 −4.31257
\(253\) −13.0919 −0.823082
\(254\) −45.2796 −2.84109
\(255\) −1.47455 −0.0923400
\(256\) 47.1631 2.94769
\(257\) −11.4111 −0.711806 −0.355903 0.934523i \(-0.615827\pi\)
−0.355903 + 0.934523i \(0.615827\pi\)
\(258\) −13.6412 −0.849264
\(259\) 25.9573 1.61291
\(260\) −13.7866 −0.855009
\(261\) −13.0763 −0.809405
\(262\) 50.0847 3.09424
\(263\) 21.1481 1.30405 0.652025 0.758198i \(-0.273920\pi\)
0.652025 + 0.758198i \(0.273920\pi\)
\(264\) 21.7366 1.33780
\(265\) 27.7062 1.70198
\(266\) −62.1238 −3.80906
\(267\) 0.113294 0.00693345
\(268\) −8.15410 −0.498091
\(269\) −6.32645 −0.385731 −0.192865 0.981225i \(-0.561778\pi\)
−0.192865 + 0.981225i \(0.561778\pi\)
\(270\) 20.0533 1.22040
\(271\) 17.9303 1.08919 0.544593 0.838701i \(-0.316684\pi\)
0.544593 + 0.838701i \(0.316684\pi\)
\(272\) −17.2969 −1.04878
\(273\) −2.94800 −0.178421
\(274\) 61.3289 3.70501
\(275\) 0.520771 0.0314037
\(276\) 10.2567 0.617378
\(277\) 20.5334 1.23373 0.616865 0.787069i \(-0.288402\pi\)
0.616865 + 0.787069i \(0.288402\pi\)
\(278\) −18.7615 −1.12524
\(279\) 20.1499 1.20634
\(280\) 100.827 6.02555
\(281\) 18.7804 1.12034 0.560172 0.828377i \(-0.310735\pi\)
0.560172 + 0.828377i \(0.310735\pi\)
\(282\) 1.02629 0.0611146
\(283\) −28.2003 −1.67634 −0.838168 0.545412i \(-0.816373\pi\)
−0.838168 + 0.545412i \(0.816373\pi\)
\(284\) −70.4500 −4.18044
\(285\) 6.28672 0.372393
\(286\) −12.1206 −0.716708
\(287\) −7.80770 −0.460874
\(288\) 59.8057 3.52409
\(289\) −15.6960 −0.923294
\(290\) 30.2996 1.77926
\(291\) −3.36069 −0.197007
\(292\) −28.6468 −1.67643
\(293\) 6.16240 0.360011 0.180006 0.983666i \(-0.442388\pi\)
0.180006 + 0.983666i \(0.442388\pi\)
\(294\) 22.9996 1.34137
\(295\) −21.2723 −1.23852
\(296\) −53.1431 −3.08888
\(297\) 12.9215 0.749782
\(298\) 44.8157 2.59610
\(299\) −3.63518 −0.210228
\(300\) −0.407989 −0.0235553
\(301\) −40.7721 −2.35007
\(302\) −24.6473 −1.41829
\(303\) −0.864961 −0.0496907
\(304\) 73.7449 4.22956
\(305\) 33.6817 1.92861
\(306\) −8.35911 −0.477859
\(307\) 13.3326 0.760930 0.380465 0.924795i \(-0.375764\pi\)
0.380465 + 0.924795i \(0.375764\pi\)
\(308\) 102.215 5.82426
\(309\) 7.54667 0.429315
\(310\) −46.6900 −2.65182
\(311\) 10.3884 0.589075 0.294537 0.955640i \(-0.404834\pi\)
0.294537 + 0.955640i \(0.404834\pi\)
\(312\) 6.03552 0.341694
\(313\) −22.9733 −1.29853 −0.649263 0.760564i \(-0.724923\pi\)
−0.649263 + 0.760564i \(0.724923\pi\)
\(314\) 30.7857 1.73734
\(315\) 28.2523 1.59184
\(316\) 2.03935 0.114723
\(317\) 14.4741 0.812947 0.406473 0.913663i \(-0.366758\pi\)
0.406473 + 0.913663i \(0.366758\pi\)
\(318\) −19.0830 −1.07012
\(319\) 19.5238 1.09313
\(320\) −69.9606 −3.91091
\(321\) 4.12272 0.230108
\(322\) 41.8270 2.33093
\(323\) −5.55957 −0.309343
\(324\) 33.9224 1.88458
\(325\) 0.144600 0.00802098
\(326\) −28.8453 −1.59759
\(327\) −2.94256 −0.162724
\(328\) 15.9849 0.882620
\(329\) 3.06747 0.169115
\(330\) −14.1131 −0.776900
\(331\) −1.97181 −0.108380 −0.0541902 0.998531i \(-0.517258\pi\)
−0.0541902 + 0.998531i \(0.517258\pi\)
\(332\) 36.2775 1.99099
\(333\) −14.8911 −0.816025
\(334\) −1.28719 −0.0704319
\(335\) 3.36507 0.183853
\(336\) −40.2654 −2.19666
\(337\) −8.64558 −0.470955 −0.235477 0.971880i \(-0.575665\pi\)
−0.235477 + 0.971880i \(0.575665\pi\)
\(338\) 32.2093 1.75195
\(339\) 10.6426 0.578024
\(340\) 14.1962 0.769896
\(341\) −30.0851 −1.62920
\(342\) 35.6389 1.92713
\(343\) 36.1033 1.94939
\(344\) 83.4740 4.50062
\(345\) −4.23275 −0.227884
\(346\) 1.52719 0.0821020
\(347\) 30.3428 1.62889 0.814443 0.580244i \(-0.197043\pi\)
0.814443 + 0.580244i \(0.197043\pi\)
\(348\) −15.2956 −0.819931
\(349\) 23.1148 1.23731 0.618653 0.785664i \(-0.287679\pi\)
0.618653 + 0.785664i \(0.287679\pi\)
\(350\) −1.66380 −0.0889336
\(351\) 3.58786 0.191506
\(352\) −89.2939 −4.75938
\(353\) −33.2273 −1.76851 −0.884254 0.467006i \(-0.845333\pi\)
−0.884254 + 0.467006i \(0.845333\pi\)
\(354\) 14.6515 0.778721
\(355\) 29.0736 1.54307
\(356\) −1.09073 −0.0578085
\(357\) 3.03558 0.160660
\(358\) 13.7959 0.729137
\(359\) 23.1646 1.22258 0.611290 0.791407i \(-0.290651\pi\)
0.611290 + 0.791407i \(0.290651\pi\)
\(360\) −57.8418 −3.04853
\(361\) 4.70314 0.247534
\(362\) 32.4818 1.70721
\(363\) −2.82287 −0.148162
\(364\) 28.3817 1.48761
\(365\) 11.8221 0.618795
\(366\) −23.1987 −1.21261
\(367\) −32.9042 −1.71759 −0.858793 0.512323i \(-0.828785\pi\)
−0.858793 + 0.512323i \(0.828785\pi\)
\(368\) −49.6513 −2.58825
\(369\) 4.47909 0.233172
\(370\) 34.5046 1.79381
\(371\) −57.0371 −2.96122
\(372\) 23.5697 1.22203
\(373\) −13.0324 −0.674790 −0.337395 0.941363i \(-0.609546\pi\)
−0.337395 + 0.941363i \(0.609546\pi\)
\(374\) 12.4807 0.645362
\(375\) −6.28804 −0.324713
\(376\) −6.28012 −0.323873
\(377\) 5.42110 0.279201
\(378\) −41.2826 −2.12335
\(379\) 16.4968 0.847385 0.423692 0.905806i \(-0.360734\pi\)
0.423692 + 0.905806i \(0.360734\pi\)
\(380\) −60.5251 −3.10487
\(381\) −9.43299 −0.483267
\(382\) −7.73628 −0.395822
\(383\) −14.9958 −0.766249 −0.383125 0.923697i \(-0.625152\pi\)
−0.383125 + 0.923697i \(0.625152\pi\)
\(384\) 22.6947 1.15813
\(385\) −42.1826 −2.14982
\(386\) 16.6450 0.847207
\(387\) 23.3900 1.18898
\(388\) 32.3549 1.64257
\(389\) 21.4816 1.08916 0.544581 0.838708i \(-0.316689\pi\)
0.544581 + 0.838708i \(0.316689\pi\)
\(390\) −3.91872 −0.198432
\(391\) 3.74318 0.189301
\(392\) −140.741 −7.10848
\(393\) 10.4340 0.526328
\(394\) −32.6453 −1.64465
\(395\) −0.841608 −0.0423459
\(396\) −58.6384 −2.94669
\(397\) 29.9077 1.50103 0.750513 0.660856i \(-0.229806\pi\)
0.750513 + 0.660856i \(0.229806\pi\)
\(398\) −3.50084 −0.175481
\(399\) −12.9421 −0.647916
\(400\) 1.97503 0.0987516
\(401\) −7.91642 −0.395327 −0.197663 0.980270i \(-0.563335\pi\)
−0.197663 + 0.980270i \(0.563335\pi\)
\(402\) −2.31773 −0.115598
\(403\) −8.35362 −0.416123
\(404\) 8.32737 0.414302
\(405\) −13.9992 −0.695627
\(406\) −62.3761 −3.09568
\(407\) 22.2334 1.10207
\(408\) −6.21482 −0.307679
\(409\) −21.3544 −1.05591 −0.527954 0.849273i \(-0.677041\pi\)
−0.527954 + 0.849273i \(0.677041\pi\)
\(410\) −10.3787 −0.512565
\(411\) 12.7765 0.630219
\(412\) −72.6552 −3.57946
\(413\) 43.7920 2.15486
\(414\) −23.9951 −1.17930
\(415\) −14.9712 −0.734905
\(416\) −24.7939 −1.21562
\(417\) −3.90855 −0.191402
\(418\) −53.2113 −2.60265
\(419\) −10.8263 −0.528901 −0.264451 0.964399i \(-0.585191\pi\)
−0.264451 + 0.964399i \(0.585191\pi\)
\(420\) 33.0473 1.61254
\(421\) −29.4021 −1.43297 −0.716486 0.697601i \(-0.754251\pi\)
−0.716486 + 0.697601i \(0.754251\pi\)
\(422\) −61.9757 −3.01693
\(423\) −1.75973 −0.0855612
\(424\) 116.774 5.67104
\(425\) −0.148896 −0.00722252
\(426\) −20.0248 −0.970206
\(427\) −69.3385 −3.35553
\(428\) −39.6913 −1.91855
\(429\) −2.52506 −0.121911
\(430\) −54.1978 −2.61365
\(431\) −21.6035 −1.04060 −0.520302 0.853983i \(-0.674181\pi\)
−0.520302 + 0.853983i \(0.674181\pi\)
\(432\) 49.0050 2.35776
\(433\) −6.67032 −0.320555 −0.160277 0.987072i \(-0.551239\pi\)
−0.160277 + 0.987072i \(0.551239\pi\)
\(434\) 96.1181 4.61382
\(435\) 6.31226 0.302650
\(436\) 28.3294 1.35673
\(437\) −15.9590 −0.763421
\(438\) −8.14261 −0.389069
\(439\) −32.8386 −1.56730 −0.783650 0.621203i \(-0.786644\pi\)
−0.783650 + 0.621203i \(0.786644\pi\)
\(440\) 86.3617 4.11713
\(441\) −39.4365 −1.87793
\(442\) 3.46547 0.164835
\(443\) −0.761013 −0.0361568 −0.0180784 0.999837i \(-0.505755\pi\)
−0.0180784 + 0.999837i \(0.505755\pi\)
\(444\) −17.4183 −0.826638
\(445\) 0.450126 0.0213380
\(446\) −21.9045 −1.03721
\(447\) 9.33635 0.441594
\(448\) 144.024 6.80449
\(449\) 37.9504 1.79099 0.895494 0.445073i \(-0.146822\pi\)
0.895494 + 0.445073i \(0.146822\pi\)
\(450\) 0.954479 0.0449946
\(451\) −6.68758 −0.314906
\(452\) −102.461 −4.81935
\(453\) −5.13472 −0.241250
\(454\) −32.6691 −1.53324
\(455\) −11.7127 −0.549098
\(456\) 26.4968 1.24083
\(457\) −1.85047 −0.0865615 −0.0432807 0.999063i \(-0.513781\pi\)
−0.0432807 + 0.999063i \(0.513781\pi\)
\(458\) 29.4433 1.37580
\(459\) −3.69445 −0.172442
\(460\) 40.7507 1.90001
\(461\) −5.50219 −0.256262 −0.128131 0.991757i \(-0.540898\pi\)
−0.128131 + 0.991757i \(0.540898\pi\)
\(462\) 29.0538 1.35171
\(463\) −8.90663 −0.413926 −0.206963 0.978349i \(-0.566358\pi\)
−0.206963 + 0.978349i \(0.566358\pi\)
\(464\) 74.0444 3.43743
\(465\) −9.72683 −0.451071
\(466\) 42.3812 1.96327
\(467\) −10.9198 −0.505310 −0.252655 0.967556i \(-0.581304\pi\)
−0.252655 + 0.967556i \(0.581304\pi\)
\(468\) −16.2819 −0.752631
\(469\) −6.92747 −0.319881
\(470\) 4.07754 0.188083
\(471\) 6.41351 0.295519
\(472\) −89.6566 −4.12678
\(473\) −34.9228 −1.60575
\(474\) 0.579668 0.0266251
\(475\) 0.634816 0.0291274
\(476\) −29.2249 −1.33952
\(477\) 32.7208 1.49818
\(478\) 2.56965 0.117533
\(479\) 24.6855 1.12791 0.563954 0.825806i \(-0.309280\pi\)
0.563954 + 0.825806i \(0.309280\pi\)
\(480\) −28.8696 −1.31771
\(481\) 6.17344 0.281485
\(482\) 9.14811 0.416685
\(483\) 8.71373 0.396489
\(484\) 27.1770 1.23532
\(485\) −13.3523 −0.606298
\(486\) 36.2024 1.64217
\(487\) 17.4160 0.789195 0.394598 0.918854i \(-0.370884\pi\)
0.394598 + 0.918854i \(0.370884\pi\)
\(488\) 141.959 6.42617
\(489\) −6.00928 −0.271749
\(490\) 91.3797 4.12812
\(491\) 19.7496 0.891287 0.445644 0.895210i \(-0.352975\pi\)
0.445644 + 0.895210i \(0.352975\pi\)
\(492\) 5.23927 0.236205
\(493\) −5.58215 −0.251408
\(494\) −14.7750 −0.664757
\(495\) 24.1991 1.08767
\(496\) −114.098 −5.12316
\(497\) −59.8522 −2.68474
\(498\) 10.3116 0.462073
\(499\) 30.9889 1.38726 0.693628 0.720334i \(-0.256011\pi\)
0.693628 + 0.720334i \(0.256011\pi\)
\(500\) 60.5379 2.70734
\(501\) −0.268157 −0.0119804
\(502\) −71.8863 −3.20844
\(503\) 0.284066 0.0126659 0.00633294 0.999980i \(-0.497984\pi\)
0.00633294 + 0.999980i \(0.497984\pi\)
\(504\) 119.076 5.30405
\(505\) −3.43657 −0.152925
\(506\) 35.8263 1.59268
\(507\) 6.71009 0.298006
\(508\) 90.8157 4.02929
\(509\) 16.1085 0.713997 0.356999 0.934105i \(-0.383800\pi\)
0.356999 + 0.934105i \(0.383800\pi\)
\(510\) 4.03514 0.178679
\(511\) −24.3374 −1.07662
\(512\) −49.4454 −2.18520
\(513\) 15.7512 0.695434
\(514\) 31.2268 1.37735
\(515\) 29.9836 1.32124
\(516\) 27.3597 1.20444
\(517\) 2.62740 0.115553
\(518\) −71.0327 −3.12100
\(519\) 0.318155 0.0139655
\(520\) 23.9797 1.05158
\(521\) 12.9782 0.568587 0.284293 0.958737i \(-0.408241\pi\)
0.284293 + 0.958737i \(0.408241\pi\)
\(522\) 35.7837 1.56621
\(523\) 2.41474 0.105589 0.0527946 0.998605i \(-0.483187\pi\)
0.0527946 + 0.998605i \(0.483187\pi\)
\(524\) −100.453 −4.38832
\(525\) −0.346615 −0.0151275
\(526\) −57.8723 −2.52335
\(527\) 8.60179 0.374700
\(528\) −34.4887 −1.50093
\(529\) −12.2551 −0.532829
\(530\) −75.8185 −3.29335
\(531\) −25.1224 −1.09022
\(532\) 124.600 5.40208
\(533\) −1.85691 −0.0804318
\(534\) −0.310030 −0.0134163
\(535\) 16.3800 0.708167
\(536\) 14.1828 0.612604
\(537\) 2.87407 0.124025
\(538\) 17.3125 0.746394
\(539\) 58.8813 2.53620
\(540\) −40.2202 −1.73080
\(541\) −0.722846 −0.0310776 −0.0155388 0.999879i \(-0.504946\pi\)
−0.0155388 + 0.999879i \(0.504946\pi\)
\(542\) −49.0665 −2.10759
\(543\) 6.76686 0.290394
\(544\) 25.5305 1.09461
\(545\) −11.6911 −0.500791
\(546\) 8.06726 0.345247
\(547\) 7.81021 0.333941 0.166970 0.985962i \(-0.446602\pi\)
0.166970 + 0.985962i \(0.446602\pi\)
\(548\) −123.005 −5.25453
\(549\) 39.7778 1.69768
\(550\) −1.42510 −0.0607665
\(551\) 23.7994 1.01389
\(552\) −17.8399 −0.759315
\(553\) 1.73257 0.0736764
\(554\) −56.1900 −2.38728
\(555\) 7.18827 0.305125
\(556\) 37.6294 1.59584
\(557\) −38.5719 −1.63434 −0.817172 0.576394i \(-0.804459\pi\)
−0.817172 + 0.576394i \(0.804459\pi\)
\(558\) −55.1406 −2.33429
\(559\) −9.69687 −0.410134
\(560\) −159.978 −6.76031
\(561\) 2.60008 0.109775
\(562\) −51.3929 −2.16788
\(563\) −34.0066 −1.43321 −0.716604 0.697480i \(-0.754304\pi\)
−0.716604 + 0.697480i \(0.754304\pi\)
\(564\) −2.05839 −0.0866740
\(565\) 42.2839 1.77890
\(566\) 77.1708 3.24373
\(567\) 28.8194 1.21030
\(568\) 122.537 5.14154
\(569\) 13.7389 0.575966 0.287983 0.957635i \(-0.407015\pi\)
0.287983 + 0.957635i \(0.407015\pi\)
\(570\) −17.2038 −0.720586
\(571\) −17.5097 −0.732758 −0.366379 0.930466i \(-0.619403\pi\)
−0.366379 + 0.930466i \(0.619403\pi\)
\(572\) 24.3099 1.01645
\(573\) −1.61168 −0.0673290
\(574\) 21.3659 0.891797
\(575\) −0.427412 −0.0178243
\(576\) −82.6230 −3.44262
\(577\) 8.73053 0.363457 0.181728 0.983349i \(-0.441831\pi\)
0.181728 + 0.983349i \(0.441831\pi\)
\(578\) 42.9524 1.78659
\(579\) 3.46761 0.144109
\(580\) −60.7710 −2.52338
\(581\) 30.8203 1.27864
\(582\) 9.19660 0.381211
\(583\) −48.8544 −2.02334
\(584\) 49.8267 2.06184
\(585\) 6.71927 0.277808
\(586\) −16.8635 −0.696626
\(587\) −36.6607 −1.51315 −0.756575 0.653907i \(-0.773129\pi\)
−0.756575 + 0.653907i \(0.773129\pi\)
\(588\) −46.1296 −1.90235
\(589\) −36.6736 −1.51111
\(590\) 58.2120 2.39655
\(591\) −6.80093 −0.279753
\(592\) 84.3203 3.46554
\(593\) 36.1801 1.48574 0.742869 0.669437i \(-0.233465\pi\)
0.742869 + 0.669437i \(0.233465\pi\)
\(594\) −35.3600 −1.45084
\(595\) 12.0606 0.494438
\(596\) −89.8853 −3.68185
\(597\) −0.729323 −0.0298492
\(598\) 9.94775 0.406794
\(599\) 12.2345 0.499887 0.249944 0.968260i \(-0.419588\pi\)
0.249944 + 0.968260i \(0.419588\pi\)
\(600\) 0.709635 0.0289707
\(601\) −34.6320 −1.41267 −0.706335 0.707878i \(-0.749653\pi\)
−0.706335 + 0.707878i \(0.749653\pi\)
\(602\) 111.574 4.54741
\(603\) 3.97412 0.161839
\(604\) 49.4342 2.01145
\(605\) −11.2155 −0.455976
\(606\) 2.36698 0.0961521
\(607\) −29.3800 −1.19250 −0.596249 0.802800i \(-0.703343\pi\)
−0.596249 + 0.802800i \(0.703343\pi\)
\(608\) −108.849 −4.41440
\(609\) −12.9947 −0.526571
\(610\) −92.1706 −3.73188
\(611\) 0.729539 0.0295140
\(612\) 16.7656 0.677709
\(613\) −40.4015 −1.63180 −0.815902 0.578191i \(-0.803759\pi\)
−0.815902 + 0.578191i \(0.803759\pi\)
\(614\) −36.4849 −1.47241
\(615\) −2.16216 −0.0871868
\(616\) −177.788 −7.16328
\(617\) −28.6182 −1.15212 −0.576062 0.817406i \(-0.695411\pi\)
−0.576062 + 0.817406i \(0.695411\pi\)
\(618\) −20.6516 −0.830730
\(619\) −25.4238 −1.02187 −0.510934 0.859620i \(-0.670700\pi\)
−0.510934 + 0.859620i \(0.670700\pi\)
\(620\) 93.6446 3.76086
\(621\) −10.6051 −0.425567
\(622\) −28.4282 −1.13987
\(623\) −0.926649 −0.0371254
\(624\) −9.57634 −0.383361
\(625\) −25.6349 −1.02540
\(626\) 62.8669 2.51267
\(627\) −11.0854 −0.442708
\(628\) −61.7458 −2.46393
\(629\) −6.35684 −0.253464
\(630\) −77.3131 −3.08023
\(631\) 37.6747 1.49981 0.749903 0.661548i \(-0.230100\pi\)
0.749903 + 0.661548i \(0.230100\pi\)
\(632\) −3.54714 −0.141098
\(633\) −12.9113 −0.513176
\(634\) −39.6087 −1.57306
\(635\) −37.4782 −1.48728
\(636\) 38.2741 1.51767
\(637\) 16.3493 0.647784
\(638\) −53.4274 −2.11521
\(639\) 34.3357 1.35830
\(640\) 90.1682 3.56421
\(641\) −16.2592 −0.642198 −0.321099 0.947046i \(-0.604052\pi\)
−0.321099 + 0.947046i \(0.604052\pi\)
\(642\) −11.2819 −0.445261
\(643\) −25.4105 −1.00209 −0.501047 0.865420i \(-0.667052\pi\)
−0.501047 + 0.865420i \(0.667052\pi\)
\(644\) −83.8911 −3.30577
\(645\) −11.2909 −0.444579
\(646\) 15.2139 0.598583
\(647\) 26.4320 1.03915 0.519574 0.854426i \(-0.326091\pi\)
0.519574 + 0.854426i \(0.326091\pi\)
\(648\) −59.0028 −2.31785
\(649\) 37.5094 1.47237
\(650\) −0.395702 −0.0155207
\(651\) 20.0241 0.784806
\(652\) 57.8540 2.26574
\(653\) −34.3875 −1.34569 −0.672843 0.739785i \(-0.734927\pi\)
−0.672843 + 0.739785i \(0.734927\pi\)
\(654\) 8.05239 0.314873
\(655\) 41.4554 1.61980
\(656\) −25.3627 −0.990248
\(657\) 13.9618 0.544701
\(658\) −8.39420 −0.327240
\(659\) −26.0143 −1.01337 −0.506687 0.862130i \(-0.669130\pi\)
−0.506687 + 0.862130i \(0.669130\pi\)
\(660\) 28.3062 1.10182
\(661\) −31.3902 −1.22094 −0.610469 0.792041i \(-0.709019\pi\)
−0.610469 + 0.792041i \(0.709019\pi\)
\(662\) 5.39590 0.209718
\(663\) 0.721953 0.0280383
\(664\) −63.0992 −2.44872
\(665\) −51.4203 −1.99399
\(666\) 40.7497 1.57902
\(667\) −16.0238 −0.620443
\(668\) 2.58167 0.0998880
\(669\) −4.56331 −0.176428
\(670\) −9.20857 −0.355758
\(671\) −59.3909 −2.29276
\(672\) 59.4323 2.29265
\(673\) 3.97673 0.153292 0.0766459 0.997058i \(-0.475579\pi\)
0.0766459 + 0.997058i \(0.475579\pi\)
\(674\) 23.6588 0.911304
\(675\) 0.421848 0.0162370
\(676\) −64.6011 −2.48466
\(677\) −18.9777 −0.729372 −0.364686 0.931131i \(-0.618824\pi\)
−0.364686 + 0.931131i \(0.618824\pi\)
\(678\) −29.1236 −1.11848
\(679\) 27.4877 1.05488
\(680\) −24.6921 −0.946898
\(681\) −6.80588 −0.260802
\(682\) 82.3286 3.15253
\(683\) −41.5834 −1.59115 −0.795573 0.605858i \(-0.792830\pi\)
−0.795573 + 0.605858i \(0.792830\pi\)
\(684\) −71.4798 −2.73310
\(685\) 50.7623 1.93953
\(686\) −98.7973 −3.77210
\(687\) 6.13386 0.234021
\(688\) −132.445 −5.04943
\(689\) −13.5652 −0.516793
\(690\) 11.5830 0.440958
\(691\) −15.7627 −0.599643 −0.299821 0.953995i \(-0.596927\pi\)
−0.299821 + 0.953995i \(0.596927\pi\)
\(692\) −3.06303 −0.116439
\(693\) −49.8174 −1.89241
\(694\) −83.0336 −3.15191
\(695\) −15.5290 −0.589050
\(696\) 26.6044 1.00844
\(697\) 1.91208 0.0724251
\(698\) −63.2541 −2.39420
\(699\) 8.82919 0.333951
\(700\) 3.33702 0.126128
\(701\) 33.1418 1.25175 0.625874 0.779924i \(-0.284742\pi\)
0.625874 + 0.779924i \(0.284742\pi\)
\(702\) −9.81827 −0.370567
\(703\) 27.1023 1.02218
\(704\) 123.362 4.64937
\(705\) 0.849466 0.0319927
\(706\) 90.9271 3.42209
\(707\) 7.07468 0.266071
\(708\) −29.3861 −1.10440
\(709\) −45.4726 −1.70776 −0.853880 0.520470i \(-0.825757\pi\)
−0.853880 + 0.520470i \(0.825757\pi\)
\(710\) −79.5605 −2.98585
\(711\) −0.993933 −0.0372754
\(712\) 1.89716 0.0710989
\(713\) 24.6917 0.924713
\(714\) −8.30692 −0.310879
\(715\) −10.0323 −0.375188
\(716\) −27.6700 −1.03408
\(717\) 0.535330 0.0199923
\(718\) −63.3904 −2.36571
\(719\) −41.2700 −1.53911 −0.769555 0.638580i \(-0.779522\pi\)
−0.769555 + 0.638580i \(0.779522\pi\)
\(720\) 91.7755 3.42027
\(721\) −61.7256 −2.29878
\(722\) −12.8703 −0.478981
\(723\) 1.90581 0.0708777
\(724\) −65.1477 −2.42119
\(725\) 0.637394 0.0236722
\(726\) 7.72484 0.286696
\(727\) −48.5167 −1.79938 −0.899692 0.436525i \(-0.856209\pi\)
−0.899692 + 0.436525i \(0.856209\pi\)
\(728\) −49.3656 −1.82961
\(729\) −10.9997 −0.407398
\(730\) −32.3514 −1.19738
\(731\) 9.98495 0.369307
\(732\) 46.5288 1.71975
\(733\) −7.90627 −0.292025 −0.146012 0.989283i \(-0.546644\pi\)
−0.146012 + 0.989283i \(0.546644\pi\)
\(734\) 90.0431 3.32355
\(735\) 19.0369 0.702188
\(736\) 73.2861 2.70136
\(737\) −5.93363 −0.218568
\(738\) −12.2571 −0.451191
\(739\) −2.15503 −0.0792740 −0.0396370 0.999214i \(-0.512620\pi\)
−0.0396370 + 0.999214i \(0.512620\pi\)
\(740\) −69.2047 −2.54402
\(741\) −3.07804 −0.113074
\(742\) 156.083 5.73000
\(743\) 43.2663 1.58729 0.793644 0.608383i \(-0.208181\pi\)
0.793644 + 0.608383i \(0.208181\pi\)
\(744\) −40.9959 −1.50298
\(745\) 37.0942 1.35903
\(746\) 35.6633 1.30573
\(747\) −17.6808 −0.646908
\(748\) −25.0321 −0.915266
\(749\) −33.7205 −1.23212
\(750\) 17.2074 0.628324
\(751\) −34.5166 −1.25953 −0.629764 0.776787i \(-0.716848\pi\)
−0.629764 + 0.776787i \(0.716848\pi\)
\(752\) 9.96445 0.363366
\(753\) −14.9759 −0.545752
\(754\) −14.8350 −0.540258
\(755\) −20.4007 −0.742458
\(756\) 82.7991 3.01137
\(757\) −40.2371 −1.46244 −0.731220 0.682141i \(-0.761049\pi\)
−0.731220 + 0.682141i \(0.761049\pi\)
\(758\) −45.1439 −1.63970
\(759\) 7.46362 0.270912
\(760\) 105.274 3.81870
\(761\) 12.9575 0.469708 0.234854 0.972031i \(-0.424539\pi\)
0.234854 + 0.972031i \(0.424539\pi\)
\(762\) 25.8136 0.935127
\(763\) 24.0678 0.871312
\(764\) 15.5164 0.561363
\(765\) −6.91889 −0.250153
\(766\) 41.0363 1.48270
\(767\) 10.4151 0.376067
\(768\) −26.8874 −0.970215
\(769\) 26.5850 0.958680 0.479340 0.877629i \(-0.340876\pi\)
0.479340 + 0.877629i \(0.340876\pi\)
\(770\) 115.434 4.15994
\(771\) 6.50541 0.234286
\(772\) −33.3843 −1.20153
\(773\) 19.8923 0.715477 0.357739 0.933822i \(-0.383548\pi\)
0.357739 + 0.933822i \(0.383548\pi\)
\(774\) −64.0072 −2.30069
\(775\) −0.982189 −0.0352813
\(776\) −56.2764 −2.02020
\(777\) −14.7981 −0.530878
\(778\) −58.7850 −2.10754
\(779\) −8.15211 −0.292080
\(780\) 7.85965 0.281421
\(781\) −51.2655 −1.83442
\(782\) −10.2433 −0.366299
\(783\) 15.8152 0.565189
\(784\) 223.308 7.97530
\(785\) 25.4815 0.909474
\(786\) −28.5530 −1.01845
\(787\) 29.1242 1.03816 0.519082 0.854724i \(-0.326274\pi\)
0.519082 + 0.854724i \(0.326274\pi\)
\(788\) 65.4756 2.33247
\(789\) −12.0564 −0.429220
\(790\) 2.30308 0.0819398
\(791\) −87.0475 −3.09505
\(792\) 101.993 3.62415
\(793\) −16.4908 −0.585607
\(794\) −81.8432 −2.90451
\(795\) −15.7951 −0.560195
\(796\) 7.02152 0.248871
\(797\) −52.2311 −1.85012 −0.925060 0.379821i \(-0.875985\pi\)
−0.925060 + 0.379821i \(0.875985\pi\)
\(798\) 35.4164 1.25373
\(799\) −0.751213 −0.0265760
\(800\) −2.91518 −0.103067
\(801\) 0.531596 0.0187830
\(802\) 21.6634 0.764963
\(803\) −20.8459 −0.735635
\(804\) 4.64860 0.163943
\(805\) 34.6205 1.22021
\(806\) 22.8599 0.805204
\(807\) 3.60667 0.126961
\(808\) −14.4842 −0.509552
\(809\) −19.1441 −0.673070 −0.336535 0.941671i \(-0.609255\pi\)
−0.336535 + 0.941671i \(0.609255\pi\)
\(810\) 38.3091 1.34605
\(811\) 30.1992 1.06044 0.530218 0.847861i \(-0.322110\pi\)
0.530218 + 0.847861i \(0.322110\pi\)
\(812\) 125.106 4.39035
\(813\) −10.2219 −0.358499
\(814\) −60.8420 −2.13251
\(815\) −23.8754 −0.836320
\(816\) 9.86084 0.345198
\(817\) −42.5706 −1.48936
\(818\) 58.4369 2.04320
\(819\) −13.8326 −0.483350
\(820\) 20.8161 0.726930
\(821\) −6.17622 −0.215551 −0.107776 0.994175i \(-0.534373\pi\)
−0.107776 + 0.994175i \(0.534373\pi\)
\(822\) −34.9632 −1.21948
\(823\) 20.5679 0.716953 0.358476 0.933539i \(-0.383296\pi\)
0.358476 + 0.933539i \(0.383296\pi\)
\(824\) 126.373 4.40240
\(825\) −0.296888 −0.0103363
\(826\) −119.838 −4.16969
\(827\) −42.4866 −1.47740 −0.738702 0.674032i \(-0.764561\pi\)
−0.738702 + 0.674032i \(0.764561\pi\)
\(828\) 48.1263 1.67250
\(829\) −5.82469 −0.202300 −0.101150 0.994871i \(-0.532252\pi\)
−0.101150 + 0.994871i \(0.532252\pi\)
\(830\) 40.9689 1.42205
\(831\) −11.7059 −0.406075
\(832\) 34.2533 1.18752
\(833\) −16.8350 −0.583300
\(834\) 10.6958 0.370366
\(835\) −1.06542 −0.0368702
\(836\) 106.724 3.69113
\(837\) −24.3703 −0.842362
\(838\) 29.6265 1.02343
\(839\) 18.5192 0.639353 0.319677 0.947527i \(-0.396426\pi\)
0.319677 + 0.947527i \(0.396426\pi\)
\(840\) −57.4806 −1.98327
\(841\) −5.10392 −0.175997
\(842\) 80.4596 2.77282
\(843\) −10.7066 −0.368754
\(844\) 124.303 4.27867
\(845\) 26.6598 0.917126
\(846\) 4.81555 0.165562
\(847\) 23.0888 0.793339
\(848\) −185.281 −6.36257
\(849\) 16.0768 0.551755
\(850\) 0.407457 0.0139757
\(851\) −18.2476 −0.625518
\(852\) 40.1631 1.37597
\(853\) −14.8095 −0.507067 −0.253534 0.967327i \(-0.581593\pi\)
−0.253534 + 0.967327i \(0.581593\pi\)
\(854\) 189.746 6.49299
\(855\) 29.4986 1.00883
\(856\) 69.0369 2.35963
\(857\) 4.18096 0.142819 0.0714095 0.997447i \(-0.477250\pi\)
0.0714095 + 0.997447i \(0.477250\pi\)
\(858\) 6.90989 0.235900
\(859\) −55.5340 −1.89479 −0.947397 0.320060i \(-0.896297\pi\)
−0.947397 + 0.320060i \(0.896297\pi\)
\(860\) 108.703 3.70673
\(861\) 4.45112 0.151694
\(862\) 59.1184 2.01358
\(863\) 10.9966 0.374328 0.187164 0.982329i \(-0.440070\pi\)
0.187164 + 0.982329i \(0.440070\pi\)
\(864\) −72.3322 −2.46079
\(865\) 1.26406 0.0429794
\(866\) 18.2535 0.620278
\(867\) 8.94819 0.303896
\(868\) −192.781 −6.54341
\(869\) 1.48401 0.0503416
\(870\) −17.2736 −0.585631
\(871\) −1.64757 −0.0558256
\(872\) −49.2746 −1.66865
\(873\) −15.7690 −0.533701
\(874\) 43.6720 1.47723
\(875\) 51.4311 1.73869
\(876\) 16.3314 0.551785
\(877\) −30.5762 −1.03248 −0.516242 0.856443i \(-0.672670\pi\)
−0.516242 + 0.856443i \(0.672670\pi\)
\(878\) 89.8634 3.03274
\(879\) −3.51314 −0.118495
\(880\) −137.027 −4.61918
\(881\) 11.5721 0.389874 0.194937 0.980816i \(-0.437550\pi\)
0.194937 + 0.980816i \(0.437550\pi\)
\(882\) 107.919 3.63382
\(883\) 7.27647 0.244873 0.122436 0.992476i \(-0.460929\pi\)
0.122436 + 0.992476i \(0.460929\pi\)
\(884\) −6.95057 −0.233773
\(885\) 12.1272 0.407651
\(886\) 2.08253 0.0699639
\(887\) 24.6195 0.826642 0.413321 0.910585i \(-0.364369\pi\)
0.413321 + 0.910585i \(0.364369\pi\)
\(888\) 30.2965 1.01669
\(889\) 77.1542 2.58767
\(890\) −1.23178 −0.0412894
\(891\) 24.6848 0.826973
\(892\) 43.9330 1.47099
\(893\) 3.20278 0.107177
\(894\) −25.5491 −0.854491
\(895\) 11.4190 0.381694
\(896\) −185.624 −6.20127
\(897\) 2.07239 0.0691952
\(898\) −103.852 −3.46559
\(899\) −36.8225 −1.22810
\(900\) −1.91437 −0.0638122
\(901\) 13.9682 0.465348
\(902\) 18.3007 0.609347
\(903\) 23.2439 0.773510
\(904\) 178.215 5.92734
\(905\) 26.8854 0.893701
\(906\) 14.0513 0.466822
\(907\) 9.52432 0.316250 0.158125 0.987419i \(-0.449455\pi\)
0.158125 + 0.987419i \(0.449455\pi\)
\(908\) 65.5233 2.17447
\(909\) −4.05857 −0.134614
\(910\) 32.0520 1.06251
\(911\) 24.4041 0.808542 0.404271 0.914639i \(-0.367525\pi\)
0.404271 + 0.914639i \(0.367525\pi\)
\(912\) −42.0415 −1.39213
\(913\) 26.3987 0.873668
\(914\) 5.06386 0.167498
\(915\) −19.2017 −0.634789
\(916\) −59.0535 −1.95118
\(917\) −85.3419 −2.81824
\(918\) 10.1099 0.333678
\(919\) 37.8082 1.24718 0.623589 0.781753i \(-0.285674\pi\)
0.623589 + 0.781753i \(0.285674\pi\)
\(920\) −70.8795 −2.33683
\(921\) −7.60081 −0.250455
\(922\) 15.0568 0.495871
\(923\) −14.2347 −0.468540
\(924\) −58.2723 −1.91702
\(925\) 0.725852 0.0238659
\(926\) 24.3732 0.800952
\(927\) 35.4105 1.16303
\(928\) −109.291 −3.58764
\(929\) −41.3478 −1.35658 −0.678288 0.734796i \(-0.737278\pi\)
−0.678288 + 0.734796i \(0.737278\pi\)
\(930\) 26.6177 0.872828
\(931\) 71.7759 2.35236
\(932\) −85.0026 −2.78435
\(933\) −5.92238 −0.193890
\(934\) 29.8824 0.977782
\(935\) 10.3304 0.337839
\(936\) 28.3199 0.925663
\(937\) −36.1228 −1.18008 −0.590039 0.807374i \(-0.700888\pi\)
−0.590039 + 0.807374i \(0.700888\pi\)
\(938\) 18.9572 0.618974
\(939\) 13.0969 0.427402
\(940\) −8.17819 −0.266743
\(941\) 19.6689 0.641188 0.320594 0.947217i \(-0.396118\pi\)
0.320594 + 0.947217i \(0.396118\pi\)
\(942\) −17.5507 −0.571833
\(943\) 5.48869 0.178736
\(944\) 142.255 4.63000
\(945\) −34.1698 −1.11155
\(946\) 95.5670 3.10715
\(947\) −44.3838 −1.44228 −0.721140 0.692790i \(-0.756381\pi\)
−0.721140 + 0.692790i \(0.756381\pi\)
\(948\) −1.16262 −0.0377602
\(949\) −5.78819 −0.187893
\(950\) −1.73719 −0.0563618
\(951\) −8.25159 −0.267576
\(952\) 50.8322 1.64748
\(953\) −4.56764 −0.147960 −0.0739802 0.997260i \(-0.523570\pi\)
−0.0739802 + 0.997260i \(0.523570\pi\)
\(954\) −89.5412 −2.89900
\(955\) −6.40337 −0.207208
\(956\) −5.15386 −0.166688
\(957\) −11.1304 −0.359795
\(958\) −67.5523 −2.18252
\(959\) −104.502 −3.37453
\(960\) 39.8841 1.28725
\(961\) 25.7414 0.830368
\(962\) −16.8938 −0.544677
\(963\) 19.3446 0.623371
\(964\) −18.3481 −0.590951
\(965\) 13.7771 0.443502
\(966\) −23.8453 −0.767210
\(967\) −49.8239 −1.60223 −0.801115 0.598511i \(-0.795759\pi\)
−0.801115 + 0.598511i \(0.795759\pi\)
\(968\) −47.2703 −1.51932
\(969\) 3.16948 0.101818
\(970\) 36.5390 1.17320
\(971\) −6.28595 −0.201726 −0.100863 0.994900i \(-0.532160\pi\)
−0.100863 + 0.994900i \(0.532160\pi\)
\(972\) −72.6099 −2.32896
\(973\) 31.9687 1.02487
\(974\) −47.6593 −1.52710
\(975\) −0.0824357 −0.00264006
\(976\) −225.241 −7.20979
\(977\) −30.0439 −0.961188 −0.480594 0.876943i \(-0.659579\pi\)
−0.480594 + 0.876943i \(0.659579\pi\)
\(978\) 16.4445 0.525838
\(979\) −0.793708 −0.0253670
\(980\) −183.277 −5.85458
\(981\) −13.8071 −0.440827
\(982\) −54.0452 −1.72465
\(983\) 17.7807 0.567116 0.283558 0.958955i \(-0.408485\pi\)
0.283558 + 0.958955i \(0.408485\pi\)
\(984\) −9.11291 −0.290509
\(985\) −27.0207 −0.860952
\(986\) 15.2757 0.486477
\(987\) −1.74875 −0.0556632
\(988\) 29.6336 0.942772
\(989\) 28.6622 0.911404
\(990\) −66.2214 −2.10466
\(991\) −12.4615 −0.395854 −0.197927 0.980217i \(-0.563421\pi\)
−0.197927 + 0.980217i \(0.563421\pi\)
\(992\) 168.411 5.34705
\(993\) 1.12412 0.0356727
\(994\) 163.787 5.19500
\(995\) −2.89767 −0.0918623
\(996\) −20.6816 −0.655321
\(997\) −2.10260 −0.0665900 −0.0332950 0.999446i \(-0.510600\pi\)
−0.0332950 + 0.999446i \(0.510600\pi\)
\(998\) −84.8019 −2.68436
\(999\) 18.0100 0.569812
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 6037.2.a.a.1.8 243
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6037.2.a.a.1.8 243 1.1 even 1 trivial