Properties

Label 6037.2.a.a.1.13
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 1.13
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)
 
\(f(q)\) \(=\) \(q-2.70152 q^{2} -2.60067 q^{3} +5.29822 q^{4} -1.66030 q^{5} +7.02577 q^{6} +3.17610 q^{7} -8.91022 q^{8} +3.76349 q^{9} +O(q^{10})\) \(q-2.70152 q^{2} -2.60067 q^{3} +5.29822 q^{4} -1.66030 q^{5} +7.02577 q^{6} +3.17610 q^{7} -8.91022 q^{8} +3.76349 q^{9} +4.48535 q^{10} -4.43606 q^{11} -13.7789 q^{12} -5.94265 q^{13} -8.58030 q^{14} +4.31790 q^{15} +13.4747 q^{16} -5.95717 q^{17} -10.1672 q^{18} +0.924395 q^{19} -8.79665 q^{20} -8.25999 q^{21} +11.9841 q^{22} +2.09388 q^{23} +23.1726 q^{24} -2.24339 q^{25} +16.0542 q^{26} -1.98560 q^{27} +16.8277 q^{28} -8.93551 q^{29} -11.6649 q^{30} +0.505697 q^{31} -18.5818 q^{32} +11.5367 q^{33} +16.0934 q^{34} -5.27329 q^{35} +19.9398 q^{36} +11.4476 q^{37} -2.49727 q^{38} +15.4549 q^{39} +14.7937 q^{40} +9.67385 q^{41} +22.3146 q^{42} -2.55979 q^{43} -23.5032 q^{44} -6.24854 q^{45} -5.65667 q^{46} +7.56164 q^{47} -35.0433 q^{48} +3.08761 q^{49} +6.06058 q^{50} +15.4926 q^{51} -31.4855 q^{52} -4.54872 q^{53} +5.36413 q^{54} +7.36520 q^{55} -28.2998 q^{56} -2.40405 q^{57} +24.1395 q^{58} -7.06044 q^{59} +22.8772 q^{60} +1.09734 q^{61} -1.36615 q^{62} +11.9532 q^{63} +23.2497 q^{64} +9.86660 q^{65} -31.1667 q^{66} +4.19378 q^{67} -31.5624 q^{68} -5.44550 q^{69} +14.2459 q^{70} +14.7479 q^{71} -33.5336 q^{72} +2.30631 q^{73} -30.9260 q^{74} +5.83433 q^{75} +4.89765 q^{76} -14.0894 q^{77} -41.7517 q^{78} +15.6561 q^{79} -22.3721 q^{80} -6.12660 q^{81} -26.1341 q^{82} +3.16284 q^{83} -43.7633 q^{84} +9.89071 q^{85} +6.91534 q^{86} +23.2383 q^{87} +39.5263 q^{88} +12.8782 q^{89} +16.8806 q^{90} -18.8745 q^{91} +11.0939 q^{92} -1.31515 q^{93} -20.4279 q^{94} -1.53478 q^{95} +48.3252 q^{96} -18.7598 q^{97} -8.34124 q^{98} -16.6951 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.70152 −1.91026 −0.955132 0.296179i \(-0.904287\pi\)
−0.955132 + 0.296179i \(0.904287\pi\)
\(3\) −2.60067 −1.50150 −0.750749 0.660587i \(-0.770307\pi\)
−0.750749 + 0.660587i \(0.770307\pi\)
\(4\) 5.29822 2.64911
\(5\) −1.66030 −0.742510 −0.371255 0.928531i \(-0.621072\pi\)
−0.371255 + 0.928531i \(0.621072\pi\)
\(6\) 7.02577 2.86826
\(7\) 3.17610 1.20045 0.600226 0.799830i \(-0.295077\pi\)
0.600226 + 0.799830i \(0.295077\pi\)
\(8\) −8.91022 −3.15024
\(9\) 3.76349 1.25450
\(10\) 4.48535 1.41839
\(11\) −4.43606 −1.33752 −0.668761 0.743477i \(-0.733175\pi\)
−0.668761 + 0.743477i \(0.733175\pi\)
\(12\) −13.7789 −3.97764
\(13\) −5.94265 −1.64820 −0.824098 0.566448i \(-0.808317\pi\)
−0.824098 + 0.566448i \(0.808317\pi\)
\(14\) −8.58030 −2.29318
\(15\) 4.31790 1.11488
\(16\) 13.4747 3.36868
\(17\) −5.95717 −1.44483 −0.722413 0.691462i \(-0.756967\pi\)
−0.722413 + 0.691462i \(0.756967\pi\)
\(18\) −10.1672 −2.39642
\(19\) 0.924395 0.212071 0.106035 0.994362i \(-0.466184\pi\)
0.106035 + 0.994362i \(0.466184\pi\)
\(20\) −8.79665 −1.96699
\(21\) −8.25999 −1.80248
\(22\) 11.9841 2.55502
\(23\) 2.09388 0.436605 0.218302 0.975881i \(-0.429948\pi\)
0.218302 + 0.975881i \(0.429948\pi\)
\(24\) 23.1726 4.73008
\(25\) −2.24339 −0.448679
\(26\) 16.0542 3.14849
\(27\) −1.98560 −0.382128
\(28\) 16.8277 3.18013
\(29\) −8.93551 −1.65928 −0.829642 0.558296i \(-0.811455\pi\)
−0.829642 + 0.558296i \(0.811455\pi\)
\(30\) −11.6649 −2.12971
\(31\) 0.505697 0.0908259 0.0454129 0.998968i \(-0.485540\pi\)
0.0454129 + 0.998968i \(0.485540\pi\)
\(32\) −18.5818 −3.28483
\(33\) 11.5367 2.00829
\(34\) 16.0934 2.76000
\(35\) −5.27329 −0.891348
\(36\) 19.9398 3.32330
\(37\) 11.4476 1.88198 0.940989 0.338437i \(-0.109898\pi\)
0.940989 + 0.338437i \(0.109898\pi\)
\(38\) −2.49727 −0.405111
\(39\) 15.4549 2.47476
\(40\) 14.7937 2.33908
\(41\) 9.67385 1.51080 0.755400 0.655263i \(-0.227442\pi\)
0.755400 + 0.655263i \(0.227442\pi\)
\(42\) 22.3146 3.44321
\(43\) −2.55979 −0.390365 −0.195182 0.980767i \(-0.562530\pi\)
−0.195182 + 0.980767i \(0.562530\pi\)
\(44\) −23.5032 −3.54325
\(45\) −6.24854 −0.931477
\(46\) −5.65667 −0.834030
\(47\) 7.56164 1.10298 0.551489 0.834182i \(-0.314060\pi\)
0.551489 + 0.834182i \(0.314060\pi\)
\(48\) −35.0433 −5.05807
\(49\) 3.08761 0.441087
\(50\) 6.06058 0.857095
\(51\) 15.4926 2.16940
\(52\) −31.4855 −4.36625
\(53\) −4.54872 −0.624814 −0.312407 0.949948i \(-0.601135\pi\)
−0.312407 + 0.949948i \(0.601135\pi\)
\(54\) 5.36413 0.729966
\(55\) 7.36520 0.993124
\(56\) −28.2998 −3.78171
\(57\) −2.40405 −0.318424
\(58\) 24.1395 3.16967
\(59\) −7.06044 −0.919191 −0.459596 0.888128i \(-0.652006\pi\)
−0.459596 + 0.888128i \(0.652006\pi\)
\(60\) 22.8772 2.95344
\(61\) 1.09734 0.140500 0.0702498 0.997529i \(-0.477620\pi\)
0.0702498 + 0.997529i \(0.477620\pi\)
\(62\) −1.36615 −0.173502
\(63\) 11.9532 1.50597
\(64\) 23.2497 2.90622
\(65\) 9.86660 1.22380
\(66\) −31.1667 −3.83636
\(67\) 4.19378 0.512352 0.256176 0.966630i \(-0.417537\pi\)
0.256176 + 0.966630i \(0.417537\pi\)
\(68\) −31.5624 −3.82751
\(69\) −5.44550 −0.655561
\(70\) 14.2459 1.70271
\(71\) 14.7479 1.75025 0.875126 0.483896i \(-0.160779\pi\)
0.875126 + 0.483896i \(0.160779\pi\)
\(72\) −33.5336 −3.95197
\(73\) 2.30631 0.269933 0.134967 0.990850i \(-0.456907\pi\)
0.134967 + 0.990850i \(0.456907\pi\)
\(74\) −30.9260 −3.59508
\(75\) 5.83433 0.673691
\(76\) 4.89765 0.561799
\(77\) −14.0894 −1.60563
\(78\) −41.7517 −4.72745
\(79\) 15.6561 1.76145 0.880726 0.473626i \(-0.157055\pi\)
0.880726 + 0.473626i \(0.157055\pi\)
\(80\) −22.3721 −2.50128
\(81\) −6.12660 −0.680733
\(82\) −26.1341 −2.88603
\(83\) 3.16284 0.347167 0.173583 0.984819i \(-0.444465\pi\)
0.173583 + 0.984819i \(0.444465\pi\)
\(84\) −43.7633 −4.77496
\(85\) 9.89071 1.07280
\(86\) 6.91534 0.745700
\(87\) 23.2383 2.49141
\(88\) 39.5263 4.21352
\(89\) 12.8782 1.36508 0.682541 0.730847i \(-0.260875\pi\)
0.682541 + 0.730847i \(0.260875\pi\)
\(90\) 16.8806 1.77937
\(91\) −18.8745 −1.97858
\(92\) 11.0939 1.15661
\(93\) −1.31515 −0.136375
\(94\) −20.4279 −2.10698
\(95\) −1.53478 −0.157465
\(96\) 48.3252 4.93217
\(97\) −18.7598 −1.90477 −0.952385 0.304899i \(-0.901377\pi\)
−0.952385 + 0.304899i \(0.901377\pi\)
\(98\) −8.34124 −0.842592
\(99\) −16.6951 −1.67792
\(100\) −11.8860 −1.18860
\(101\) −8.16592 −0.812540 −0.406270 0.913753i \(-0.633171\pi\)
−0.406270 + 0.913753i \(0.633171\pi\)
\(102\) −41.8537 −4.14414
\(103\) −3.64978 −0.359623 −0.179812 0.983701i \(-0.557549\pi\)
−0.179812 + 0.983701i \(0.557549\pi\)
\(104\) 52.9504 5.19221
\(105\) 13.7141 1.33836
\(106\) 12.2885 1.19356
\(107\) −16.0858 −1.55507 −0.777536 0.628838i \(-0.783531\pi\)
−0.777536 + 0.628838i \(0.783531\pi\)
\(108\) −10.5201 −1.01230
\(109\) 2.55439 0.244666 0.122333 0.992489i \(-0.460962\pi\)
0.122333 + 0.992489i \(0.460962\pi\)
\(110\) −19.8973 −1.89713
\(111\) −29.7715 −2.82579
\(112\) 42.7970 4.04394
\(113\) −5.15003 −0.484474 −0.242237 0.970217i \(-0.577881\pi\)
−0.242237 + 0.970217i \(0.577881\pi\)
\(114\) 6.49459 0.608274
\(115\) −3.47648 −0.324183
\(116\) −47.3423 −4.39563
\(117\) −22.3651 −2.06766
\(118\) 19.0739 1.75590
\(119\) −18.9206 −1.73445
\(120\) −38.4735 −3.51213
\(121\) 8.67863 0.788966
\(122\) −2.96448 −0.268391
\(123\) −25.1585 −2.26847
\(124\) 2.67930 0.240608
\(125\) 12.0262 1.07566
\(126\) −32.2919 −2.87679
\(127\) −13.8140 −1.22579 −0.612897 0.790163i \(-0.709996\pi\)
−0.612897 + 0.790163i \(0.709996\pi\)
\(128\) −25.6461 −2.26681
\(129\) 6.65718 0.586132
\(130\) −26.6549 −2.33779
\(131\) 13.8494 1.21003 0.605014 0.796214i \(-0.293167\pi\)
0.605014 + 0.796214i \(0.293167\pi\)
\(132\) 61.1242 5.32018
\(133\) 2.93597 0.254581
\(134\) −11.3296 −0.978728
\(135\) 3.29669 0.283734
\(136\) 53.0797 4.55155
\(137\) 1.91325 0.163460 0.0817300 0.996655i \(-0.473955\pi\)
0.0817300 + 0.996655i \(0.473955\pi\)
\(138\) 14.7111 1.25230
\(139\) 14.9315 1.26647 0.633236 0.773959i \(-0.281726\pi\)
0.633236 + 0.773959i \(0.281726\pi\)
\(140\) −27.9390 −2.36128
\(141\) −19.6653 −1.65612
\(142\) −39.8417 −3.34344
\(143\) 26.3620 2.20450
\(144\) 50.7120 4.22600
\(145\) 14.8357 1.23203
\(146\) −6.23055 −0.515644
\(147\) −8.02985 −0.662291
\(148\) 60.6521 4.98557
\(149\) 8.74809 0.716671 0.358336 0.933593i \(-0.383344\pi\)
0.358336 + 0.933593i \(0.383344\pi\)
\(150\) −15.7616 −1.28693
\(151\) 22.0545 1.79477 0.897387 0.441245i \(-0.145463\pi\)
0.897387 + 0.441245i \(0.145463\pi\)
\(152\) −8.23657 −0.668074
\(153\) −22.4198 −1.81253
\(154\) 38.0627 3.06718
\(155\) −0.839611 −0.0674391
\(156\) 81.8835 6.55592
\(157\) −1.51570 −0.120966 −0.0604828 0.998169i \(-0.519264\pi\)
−0.0604828 + 0.998169i \(0.519264\pi\)
\(158\) −42.2954 −3.36484
\(159\) 11.8297 0.938158
\(160\) 30.8514 2.43902
\(161\) 6.65038 0.524123
\(162\) 16.5511 1.30038
\(163\) −19.3959 −1.51920 −0.759601 0.650389i \(-0.774606\pi\)
−0.759601 + 0.650389i \(0.774606\pi\)
\(164\) 51.2542 4.00228
\(165\) −19.1545 −1.49117
\(166\) −8.54448 −0.663181
\(167\) 8.50159 0.657873 0.328937 0.944352i \(-0.393310\pi\)
0.328937 + 0.944352i \(0.393310\pi\)
\(168\) 73.5984 5.67824
\(169\) 22.3151 1.71655
\(170\) −26.7200 −2.04933
\(171\) 3.47896 0.266042
\(172\) −13.5624 −1.03412
\(173\) 9.42552 0.716609 0.358304 0.933605i \(-0.383355\pi\)
0.358304 + 0.933605i \(0.383355\pi\)
\(174\) −62.7789 −4.75926
\(175\) −7.12524 −0.538618
\(176\) −59.7747 −4.50568
\(177\) 18.3619 1.38016
\(178\) −34.7906 −2.60767
\(179\) 20.1117 1.50322 0.751608 0.659610i \(-0.229278\pi\)
0.751608 + 0.659610i \(0.229278\pi\)
\(180\) −33.1062 −2.46759
\(181\) −11.3487 −0.843544 −0.421772 0.906702i \(-0.638592\pi\)
−0.421772 + 0.906702i \(0.638592\pi\)
\(182\) 50.9898 3.77961
\(183\) −2.85381 −0.210960
\(184\) −18.6570 −1.37541
\(185\) −19.0065 −1.39739
\(186\) 3.55291 0.260512
\(187\) 26.4264 1.93249
\(188\) 40.0633 2.92191
\(189\) −6.30645 −0.458727
\(190\) 4.14623 0.300799
\(191\) 18.6515 1.34958 0.674788 0.738012i \(-0.264235\pi\)
0.674788 + 0.738012i \(0.264235\pi\)
\(192\) −60.4649 −4.36368
\(193\) −21.0126 −1.51252 −0.756259 0.654272i \(-0.772975\pi\)
−0.756259 + 0.654272i \(0.772975\pi\)
\(194\) 50.6800 3.63861
\(195\) −25.6598 −1.83754
\(196\) 16.3588 1.16849
\(197\) −17.7277 −1.26305 −0.631524 0.775356i \(-0.717570\pi\)
−0.631524 + 0.775356i \(0.717570\pi\)
\(198\) 45.1021 3.20527
\(199\) −20.0982 −1.42472 −0.712362 0.701812i \(-0.752375\pi\)
−0.712362 + 0.701812i \(0.752375\pi\)
\(200\) 19.9891 1.41345
\(201\) −10.9067 −0.769296
\(202\) 22.0604 1.55217
\(203\) −28.3801 −1.99189
\(204\) 82.0835 5.74699
\(205\) −16.0615 −1.12178
\(206\) 9.85996 0.686976
\(207\) 7.88031 0.547719
\(208\) −80.0756 −5.55224
\(209\) −4.10067 −0.283650
\(210\) −37.0489 −2.55662
\(211\) 9.08607 0.625511 0.312755 0.949834i \(-0.398748\pi\)
0.312755 + 0.949834i \(0.398748\pi\)
\(212\) −24.1001 −1.65520
\(213\) −38.3544 −2.62800
\(214\) 43.4561 2.97060
\(215\) 4.25003 0.289850
\(216\) 17.6921 1.20379
\(217\) 1.60614 0.109032
\(218\) −6.90074 −0.467377
\(219\) −5.99796 −0.405305
\(220\) 39.0225 2.63090
\(221\) 35.4014 2.38136
\(222\) 80.4284 5.39800
\(223\) 19.8949 1.33226 0.666130 0.745836i \(-0.267950\pi\)
0.666130 + 0.745836i \(0.267950\pi\)
\(224\) −59.0177 −3.94328
\(225\) −8.44300 −0.562867
\(226\) 13.9129 0.925474
\(227\) 21.2188 1.40834 0.704171 0.710030i \(-0.251319\pi\)
0.704171 + 0.710030i \(0.251319\pi\)
\(228\) −12.7372 −0.843541
\(229\) −0.117781 −0.00778319 −0.00389160 0.999992i \(-0.501239\pi\)
−0.00389160 + 0.999992i \(0.501239\pi\)
\(230\) 9.39178 0.619276
\(231\) 36.6418 2.41085
\(232\) 79.6174 5.22714
\(233\) 1.68147 0.110157 0.0550785 0.998482i \(-0.482459\pi\)
0.0550785 + 0.998482i \(0.482459\pi\)
\(234\) 60.4199 3.94977
\(235\) −12.5546 −0.818973
\(236\) −37.4078 −2.43504
\(237\) −40.7165 −2.64482
\(238\) 51.1143 3.31325
\(239\) −20.4982 −1.32592 −0.662961 0.748654i \(-0.730700\pi\)
−0.662961 + 0.748654i \(0.730700\pi\)
\(240\) 58.1825 3.75567
\(241\) 12.1357 0.781731 0.390866 0.920448i \(-0.372176\pi\)
0.390866 + 0.920448i \(0.372176\pi\)
\(242\) −23.4455 −1.50713
\(243\) 21.8901 1.40425
\(244\) 5.81393 0.372199
\(245\) −5.12636 −0.327511
\(246\) 67.9662 4.33337
\(247\) −5.49336 −0.349534
\(248\) −4.50587 −0.286123
\(249\) −8.22551 −0.521271
\(250\) −32.4891 −2.05479
\(251\) 26.9484 1.70097 0.850484 0.526001i \(-0.176309\pi\)
0.850484 + 0.526001i \(0.176309\pi\)
\(252\) 63.3309 3.98947
\(253\) −9.28859 −0.583968
\(254\) 37.3188 2.34159
\(255\) −25.7225 −1.61080
\(256\) 22.7839 1.42400
\(257\) −1.79856 −0.112191 −0.0560955 0.998425i \(-0.517865\pi\)
−0.0560955 + 0.998425i \(0.517865\pi\)
\(258\) −17.9845 −1.11967
\(259\) 36.3588 2.25923
\(260\) 52.2755 3.24199
\(261\) −33.6288 −2.08157
\(262\) −37.4145 −2.31148
\(263\) −16.3387 −1.00749 −0.503745 0.863853i \(-0.668045\pi\)
−0.503745 + 0.863853i \(0.668045\pi\)
\(264\) −102.795 −6.32659
\(265\) 7.55225 0.463931
\(266\) −7.93159 −0.486317
\(267\) −33.4919 −2.04967
\(268\) 22.2196 1.35728
\(269\) −15.8975 −0.969288 −0.484644 0.874712i \(-0.661051\pi\)
−0.484644 + 0.874712i \(0.661051\pi\)
\(270\) −8.90608 −0.542007
\(271\) 16.4572 0.999703 0.499851 0.866111i \(-0.333388\pi\)
0.499851 + 0.866111i \(0.333388\pi\)
\(272\) −80.2712 −4.86716
\(273\) 49.0863 2.97084
\(274\) −5.16869 −0.312252
\(275\) 9.95183 0.600118
\(276\) −28.8515 −1.73665
\(277\) −8.71238 −0.523476 −0.261738 0.965139i \(-0.584296\pi\)
−0.261738 + 0.965139i \(0.584296\pi\)
\(278\) −40.3378 −2.41930
\(279\) 1.90319 0.113941
\(280\) 46.9862 2.80796
\(281\) −4.47201 −0.266778 −0.133389 0.991064i \(-0.542586\pi\)
−0.133389 + 0.991064i \(0.542586\pi\)
\(282\) 53.1264 3.16363
\(283\) −9.70786 −0.577073 −0.288536 0.957469i \(-0.593169\pi\)
−0.288536 + 0.957469i \(0.593169\pi\)
\(284\) 78.1375 4.63661
\(285\) 3.99145 0.236433
\(286\) −71.2174 −4.21118
\(287\) 30.7251 1.81364
\(288\) −69.9325 −4.12081
\(289\) 18.4879 1.08752
\(290\) −40.0789 −2.35351
\(291\) 48.7881 2.86001
\(292\) 12.2194 0.715084
\(293\) −0.113041 −0.00660391 −0.00330196 0.999995i \(-0.501051\pi\)
−0.00330196 + 0.999995i \(0.501051\pi\)
\(294\) 21.6928 1.26515
\(295\) 11.7225 0.682509
\(296\) −102.001 −5.92868
\(297\) 8.80822 0.511105
\(298\) −23.6332 −1.36903
\(299\) −12.4432 −0.719610
\(300\) 30.9116 1.78468
\(301\) −8.13016 −0.468615
\(302\) −59.5808 −3.42849
\(303\) 21.2369 1.22003
\(304\) 12.4560 0.714399
\(305\) −1.82191 −0.104322
\(306\) 60.5675 3.46241
\(307\) −14.3035 −0.816343 −0.408171 0.912905i \(-0.633833\pi\)
−0.408171 + 0.912905i \(0.633833\pi\)
\(308\) −74.6486 −4.25350
\(309\) 9.49187 0.539974
\(310\) 2.26823 0.128827
\(311\) −33.1534 −1.87995 −0.939977 0.341237i \(-0.889154\pi\)
−0.939977 + 0.341237i \(0.889154\pi\)
\(312\) −137.707 −7.79610
\(313\) 7.95116 0.449426 0.224713 0.974425i \(-0.427856\pi\)
0.224713 + 0.974425i \(0.427856\pi\)
\(314\) 4.09469 0.231076
\(315\) −19.8460 −1.11819
\(316\) 82.9497 4.66628
\(317\) 0.186958 0.0105006 0.00525031 0.999986i \(-0.498329\pi\)
0.00525031 + 0.999986i \(0.498329\pi\)
\(318\) −31.9582 −1.79213
\(319\) 39.6385 2.21933
\(320\) −38.6016 −2.15790
\(321\) 41.8339 2.33494
\(322\) −17.9661 −1.00121
\(323\) −5.50678 −0.306405
\(324\) −32.4601 −1.80334
\(325\) 13.3317 0.739510
\(326\) 52.3984 2.90208
\(327\) −6.64313 −0.367366
\(328\) −86.1961 −4.75938
\(329\) 24.0165 1.32407
\(330\) 51.7462 2.84854
\(331\) 3.00795 0.165332 0.0826659 0.996577i \(-0.473657\pi\)
0.0826659 + 0.996577i \(0.473657\pi\)
\(332\) 16.7574 0.919684
\(333\) 43.0831 2.36094
\(334\) −22.9672 −1.25671
\(335\) −6.96295 −0.380427
\(336\) −111.301 −6.07197
\(337\) 31.6413 1.72361 0.861805 0.507240i \(-0.169334\pi\)
0.861805 + 0.507240i \(0.169334\pi\)
\(338\) −60.2848 −3.27906
\(339\) 13.3935 0.727437
\(340\) 52.4032 2.84196
\(341\) −2.24330 −0.121482
\(342\) −9.39848 −0.508211
\(343\) −12.4262 −0.670949
\(344\) 22.8083 1.22974
\(345\) 9.04118 0.486761
\(346\) −25.4633 −1.36891
\(347\) −3.93576 −0.211283 −0.105641 0.994404i \(-0.533690\pi\)
−0.105641 + 0.994404i \(0.533690\pi\)
\(348\) 123.122 6.60003
\(349\) 9.95432 0.532843 0.266421 0.963857i \(-0.414159\pi\)
0.266421 + 0.963857i \(0.414159\pi\)
\(350\) 19.2490 1.02890
\(351\) 11.7997 0.629822
\(352\) 82.4300 4.39354
\(353\) −24.0736 −1.28131 −0.640653 0.767830i \(-0.721336\pi\)
−0.640653 + 0.767830i \(0.721336\pi\)
\(354\) −49.6050 −2.63648
\(355\) −24.4859 −1.29958
\(356\) 68.2314 3.61626
\(357\) 49.2062 2.60427
\(358\) −54.3321 −2.87154
\(359\) 3.40516 0.179717 0.0898586 0.995955i \(-0.471358\pi\)
0.0898586 + 0.995955i \(0.471358\pi\)
\(360\) 55.6759 2.93438
\(361\) −18.1455 −0.955026
\(362\) 30.6588 1.61139
\(363\) −22.5703 −1.18463
\(364\) −100.001 −5.24148
\(365\) −3.82918 −0.200428
\(366\) 7.70964 0.402989
\(367\) 27.3963 1.43008 0.715038 0.699086i \(-0.246409\pi\)
0.715038 + 0.699086i \(0.246409\pi\)
\(368\) 28.2145 1.47078
\(369\) 36.4075 1.89530
\(370\) 51.3466 2.66938
\(371\) −14.4472 −0.750060
\(372\) −6.96797 −0.361272
\(373\) −6.49382 −0.336237 −0.168119 0.985767i \(-0.553769\pi\)
−0.168119 + 0.985767i \(0.553769\pi\)
\(374\) −71.3914 −3.69156
\(375\) −31.2763 −1.61510
\(376\) −67.3759 −3.47465
\(377\) 53.1007 2.73482
\(378\) 17.0370 0.876289
\(379\) 21.4906 1.10390 0.551950 0.833877i \(-0.313884\pi\)
0.551950 + 0.833877i \(0.313884\pi\)
\(380\) −8.13159 −0.417142
\(381\) 35.9257 1.84053
\(382\) −50.3875 −2.57805
\(383\) 17.2400 0.880920 0.440460 0.897772i \(-0.354815\pi\)
0.440460 + 0.897772i \(0.354815\pi\)
\(384\) 66.6970 3.40362
\(385\) 23.3926 1.19220
\(386\) 56.7659 2.88931
\(387\) −9.63377 −0.489712
\(388\) −99.3936 −5.04595
\(389\) 0.378277 0.0191794 0.00958970 0.999954i \(-0.496947\pi\)
0.00958970 + 0.999954i \(0.496947\pi\)
\(390\) 69.3205 3.51018
\(391\) −12.4736 −0.630818
\(392\) −27.5113 −1.38953
\(393\) −36.0178 −1.81686
\(394\) 47.8918 2.41276
\(395\) −25.9939 −1.30790
\(396\) −88.4543 −4.44499
\(397\) −18.6402 −0.935523 −0.467762 0.883855i \(-0.654939\pi\)
−0.467762 + 0.883855i \(0.654939\pi\)
\(398\) 54.2958 2.72160
\(399\) −7.63550 −0.382253
\(400\) −30.2291 −1.51146
\(401\) 19.9607 0.996791 0.498395 0.866950i \(-0.333923\pi\)
0.498395 + 0.866950i \(0.333923\pi\)
\(402\) 29.4646 1.46956
\(403\) −3.00518 −0.149699
\(404\) −43.2649 −2.15251
\(405\) 10.1720 0.505451
\(406\) 76.6694 3.80504
\(407\) −50.7824 −2.51719
\(408\) −138.043 −6.83414
\(409\) 2.48272 0.122762 0.0613812 0.998114i \(-0.480449\pi\)
0.0613812 + 0.998114i \(0.480449\pi\)
\(410\) 43.3905 2.14291
\(411\) −4.97574 −0.245435
\(412\) −19.3373 −0.952682
\(413\) −22.4247 −1.10345
\(414\) −21.2888 −1.04629
\(415\) −5.25127 −0.257775
\(416\) 110.425 5.41404
\(417\) −38.8319 −1.90161
\(418\) 11.0781 0.541846
\(419\) 0.0187896 0.000917933 0 0.000458967 1.00000i \(-0.499854\pi\)
0.000458967 1.00000i \(0.499854\pi\)
\(420\) 72.6603 3.54546
\(421\) −8.09367 −0.394462 −0.197231 0.980357i \(-0.563195\pi\)
−0.197231 + 0.980357i \(0.563195\pi\)
\(422\) −24.5462 −1.19489
\(423\) 28.4582 1.38368
\(424\) 40.5301 1.96831
\(425\) 13.3643 0.648263
\(426\) 103.615 5.02017
\(427\) 3.48525 0.168663
\(428\) −85.2261 −4.11956
\(429\) −68.5588 −3.31005
\(430\) −11.4816 −0.553690
\(431\) −13.0687 −0.629498 −0.314749 0.949175i \(-0.601920\pi\)
−0.314749 + 0.949175i \(0.601920\pi\)
\(432\) −26.7553 −1.28727
\(433\) 13.8960 0.667801 0.333901 0.942608i \(-0.391635\pi\)
0.333901 + 0.942608i \(0.391635\pi\)
\(434\) −4.33904 −0.208280
\(435\) −38.5827 −1.84990
\(436\) 13.5337 0.648148
\(437\) 1.93558 0.0925911
\(438\) 16.2036 0.774239
\(439\) −39.6689 −1.89329 −0.946646 0.322274i \(-0.895553\pi\)
−0.946646 + 0.322274i \(0.895553\pi\)
\(440\) −65.6256 −3.12858
\(441\) 11.6202 0.553342
\(442\) −95.6377 −4.54902
\(443\) −0.687120 −0.0326460 −0.0163230 0.999867i \(-0.505196\pi\)
−0.0163230 + 0.999867i \(0.505196\pi\)
\(444\) −157.736 −7.48583
\(445\) −21.3817 −1.01359
\(446\) −53.7465 −2.54497
\(447\) −22.7509 −1.07608
\(448\) 73.8435 3.48878
\(449\) −5.97951 −0.282190 −0.141095 0.989996i \(-0.545062\pi\)
−0.141095 + 0.989996i \(0.545062\pi\)
\(450\) 22.8090 1.07522
\(451\) −42.9138 −2.02073
\(452\) −27.2860 −1.28343
\(453\) −57.3566 −2.69485
\(454\) −57.3231 −2.69031
\(455\) 31.3373 1.46912
\(456\) 21.4206 1.00311
\(457\) 10.6755 0.499378 0.249689 0.968326i \(-0.419672\pi\)
0.249689 + 0.968326i \(0.419672\pi\)
\(458\) 0.318188 0.0148680
\(459\) 11.8285 0.552109
\(460\) −18.4192 −0.858798
\(461\) 28.8028 1.34148 0.670741 0.741692i \(-0.265976\pi\)
0.670741 + 0.741692i \(0.265976\pi\)
\(462\) −98.9887 −4.60537
\(463\) 8.17095 0.379736 0.189868 0.981810i \(-0.439194\pi\)
0.189868 + 0.981810i \(0.439194\pi\)
\(464\) −120.404 −5.58960
\(465\) 2.18355 0.101260
\(466\) −4.54254 −0.210429
\(467\) −10.8314 −0.501216 −0.250608 0.968089i \(-0.580631\pi\)
−0.250608 + 0.968089i \(0.580631\pi\)
\(468\) −118.495 −5.47746
\(469\) 13.3199 0.615054
\(470\) 33.9166 1.56446
\(471\) 3.94183 0.181630
\(472\) 62.9101 2.89567
\(473\) 11.3554 0.522122
\(474\) 109.996 5.05230
\(475\) −2.07378 −0.0951517
\(476\) −100.245 −4.59474
\(477\) −17.1191 −0.783828
\(478\) 55.3765 2.53286
\(479\) −17.2868 −0.789852 −0.394926 0.918713i \(-0.629230\pi\)
−0.394926 + 0.918713i \(0.629230\pi\)
\(480\) −80.2345 −3.66219
\(481\) −68.0293 −3.10187
\(482\) −32.7850 −1.49331
\(483\) −17.2954 −0.786970
\(484\) 45.9813 2.09006
\(485\) 31.1470 1.41431
\(486\) −59.1365 −2.68249
\(487\) 8.06575 0.365494 0.182747 0.983160i \(-0.441501\pi\)
0.182747 + 0.983160i \(0.441501\pi\)
\(488\) −9.77751 −0.442607
\(489\) 50.4423 2.28108
\(490\) 13.8490 0.625633
\(491\) −32.8835 −1.48401 −0.742005 0.670394i \(-0.766125\pi\)
−0.742005 + 0.670394i \(0.766125\pi\)
\(492\) −133.295 −6.00942
\(493\) 53.2304 2.39738
\(494\) 14.8404 0.667703
\(495\) 27.7189 1.24587
\(496\) 6.81413 0.305963
\(497\) 46.8407 2.10109
\(498\) 22.2214 0.995765
\(499\) 2.07468 0.0928752 0.0464376 0.998921i \(-0.485213\pi\)
0.0464376 + 0.998921i \(0.485213\pi\)
\(500\) 63.7176 2.84954
\(501\) −22.1099 −0.987796
\(502\) −72.8017 −3.24930
\(503\) 7.56513 0.337313 0.168656 0.985675i \(-0.446057\pi\)
0.168656 + 0.985675i \(0.446057\pi\)
\(504\) −106.506 −4.74415
\(505\) 13.5579 0.603319
\(506\) 25.0933 1.11553
\(507\) −58.0343 −2.57739
\(508\) −73.1896 −3.24726
\(509\) 25.4583 1.12842 0.564210 0.825631i \(-0.309181\pi\)
0.564210 + 0.825631i \(0.309181\pi\)
\(510\) 69.4899 3.07706
\(511\) 7.32508 0.324042
\(512\) −10.2592 −0.453397
\(513\) −1.83548 −0.0810382
\(514\) 4.85884 0.214314
\(515\) 6.05974 0.267024
\(516\) 35.2712 1.55273
\(517\) −33.5439 −1.47526
\(518\) −98.2241 −4.31572
\(519\) −24.5127 −1.07599
\(520\) −87.9136 −3.85527
\(521\) 14.1063 0.618009 0.309005 0.951061i \(-0.400004\pi\)
0.309005 + 0.951061i \(0.400004\pi\)
\(522\) 90.8488 3.97634
\(523\) −22.9041 −1.00153 −0.500763 0.865585i \(-0.666947\pi\)
−0.500763 + 0.865585i \(0.666947\pi\)
\(524\) 73.3773 3.20550
\(525\) 18.5304 0.808734
\(526\) 44.1395 1.92457
\(527\) −3.01252 −0.131228
\(528\) 155.454 6.76528
\(529\) −18.6157 −0.809376
\(530\) −20.4026 −0.886231
\(531\) −26.5719 −1.15312
\(532\) 15.5554 0.674414
\(533\) −57.4883 −2.49009
\(534\) 90.4790 3.91541
\(535\) 26.7073 1.15466
\(536\) −37.3675 −1.61403
\(537\) −52.3038 −2.25708
\(538\) 42.9475 1.85160
\(539\) −13.6968 −0.589963
\(540\) 17.4666 0.751643
\(541\) −40.2549 −1.73069 −0.865346 0.501175i \(-0.832901\pi\)
−0.865346 + 0.501175i \(0.832901\pi\)
\(542\) −44.4594 −1.90970
\(543\) 29.5143 1.26658
\(544\) 110.695 4.74601
\(545\) −4.24106 −0.181667
\(546\) −132.608 −5.67508
\(547\) −9.24781 −0.395408 −0.197704 0.980262i \(-0.563348\pi\)
−0.197704 + 0.980262i \(0.563348\pi\)
\(548\) 10.1368 0.433024
\(549\) 4.12982 0.176256
\(550\) −26.8851 −1.14638
\(551\) −8.25995 −0.351886
\(552\) 48.5206 2.06517
\(553\) 49.7254 2.11454
\(554\) 23.5367 0.999979
\(555\) 49.4297 2.09818
\(556\) 79.1104 3.35503
\(557\) 7.66751 0.324883 0.162441 0.986718i \(-0.448063\pi\)
0.162441 + 0.986718i \(0.448063\pi\)
\(558\) −5.14151 −0.217657
\(559\) 15.2120 0.643398
\(560\) −71.0561 −3.00267
\(561\) −68.7263 −2.90163
\(562\) 12.0812 0.509616
\(563\) 16.4276 0.692341 0.346171 0.938172i \(-0.387482\pi\)
0.346171 + 0.938172i \(0.387482\pi\)
\(564\) −104.191 −4.38725
\(565\) 8.55061 0.359727
\(566\) 26.2260 1.10236
\(567\) −19.4587 −0.817188
\(568\) −131.407 −5.51371
\(569\) −29.1778 −1.22320 −0.611598 0.791169i \(-0.709473\pi\)
−0.611598 + 0.791169i \(0.709473\pi\)
\(570\) −10.7830 −0.451650
\(571\) −24.9364 −1.04356 −0.521779 0.853081i \(-0.674731\pi\)
−0.521779 + 0.853081i \(0.674731\pi\)
\(572\) 139.672 5.83996
\(573\) −48.5065 −2.02639
\(574\) −83.0045 −3.46454
\(575\) −4.69740 −0.195895
\(576\) 87.5002 3.64584
\(577\) 41.1748 1.71413 0.857065 0.515208i \(-0.172285\pi\)
0.857065 + 0.515208i \(0.172285\pi\)
\(578\) −49.9454 −2.07746
\(579\) 54.6468 2.27104
\(580\) 78.6026 3.26380
\(581\) 10.0455 0.416757
\(582\) −131.802 −5.46337
\(583\) 20.1784 0.835703
\(584\) −20.5498 −0.850355
\(585\) 37.1329 1.53526
\(586\) 0.305382 0.0126152
\(587\) 10.2758 0.424128 0.212064 0.977256i \(-0.431981\pi\)
0.212064 + 0.977256i \(0.431981\pi\)
\(588\) −42.5439 −1.75448
\(589\) 0.467464 0.0192615
\(590\) −31.6685 −1.30377
\(591\) 46.1040 1.89646
\(592\) 154.254 6.33978
\(593\) −14.6340 −0.600946 −0.300473 0.953790i \(-0.597144\pi\)
−0.300473 + 0.953790i \(0.597144\pi\)
\(594\) −23.7956 −0.976346
\(595\) 31.4139 1.28784
\(596\) 46.3493 1.89854
\(597\) 52.2689 2.13922
\(598\) 33.6156 1.37465
\(599\) 28.5035 1.16462 0.582311 0.812966i \(-0.302148\pi\)
0.582311 + 0.812966i \(0.302148\pi\)
\(600\) −51.9852 −2.12229
\(601\) −3.87714 −0.158152 −0.0790759 0.996869i \(-0.525197\pi\)
−0.0790759 + 0.996869i \(0.525197\pi\)
\(602\) 21.9638 0.895178
\(603\) 15.7833 0.642745
\(604\) 116.850 4.75455
\(605\) −14.4091 −0.585815
\(606\) −57.3719 −2.33058
\(607\) 12.0428 0.488803 0.244401 0.969674i \(-0.421409\pi\)
0.244401 + 0.969674i \(0.421409\pi\)
\(608\) −17.1769 −0.696617
\(609\) 73.8073 2.99082
\(610\) 4.92193 0.199283
\(611\) −44.9362 −1.81792
\(612\) −118.785 −4.80160
\(613\) −14.6608 −0.592145 −0.296072 0.955166i \(-0.595677\pi\)
−0.296072 + 0.955166i \(0.595677\pi\)
\(614\) 38.6412 1.55943
\(615\) 41.7707 1.68436
\(616\) 125.539 5.05813
\(617\) 35.0503 1.41107 0.705536 0.708674i \(-0.250706\pi\)
0.705536 + 0.708674i \(0.250706\pi\)
\(618\) −25.6425 −1.03149
\(619\) 41.5716 1.67090 0.835451 0.549565i \(-0.185207\pi\)
0.835451 + 0.549565i \(0.185207\pi\)
\(620\) −4.44844 −0.178654
\(621\) −4.15760 −0.166839
\(622\) 89.5645 3.59121
\(623\) 40.9023 1.63872
\(624\) 208.250 8.33668
\(625\) −8.75021 −0.350008
\(626\) −21.4802 −0.858523
\(627\) 10.6645 0.425899
\(628\) −8.03049 −0.320452
\(629\) −68.1955 −2.71913
\(630\) 53.6144 2.13605
\(631\) −33.2538 −1.32381 −0.661906 0.749587i \(-0.730252\pi\)
−0.661906 + 0.749587i \(0.730252\pi\)
\(632\) −139.500 −5.54900
\(633\) −23.6299 −0.939203
\(634\) −0.505071 −0.0200589
\(635\) 22.9354 0.910164
\(636\) 62.6765 2.48528
\(637\) −18.3486 −0.726997
\(638\) −107.084 −4.23951
\(639\) 55.5035 2.19569
\(640\) 42.5802 1.68313
\(641\) −13.6559 −0.539375 −0.269687 0.962948i \(-0.586920\pi\)
−0.269687 + 0.962948i \(0.586920\pi\)
\(642\) −113.015 −4.46035
\(643\) 17.6223 0.694955 0.347478 0.937688i \(-0.387038\pi\)
0.347478 + 0.937688i \(0.387038\pi\)
\(644\) 35.2352 1.38846
\(645\) −11.0529 −0.435209
\(646\) 14.8767 0.585316
\(647\) 9.30266 0.365725 0.182863 0.983138i \(-0.441464\pi\)
0.182863 + 0.983138i \(0.441464\pi\)
\(648\) 54.5894 2.14447
\(649\) 31.3205 1.22944
\(650\) −36.0159 −1.41266
\(651\) −4.17705 −0.163712
\(652\) −102.764 −4.02454
\(653\) 23.9780 0.938331 0.469166 0.883110i \(-0.344555\pi\)
0.469166 + 0.883110i \(0.344555\pi\)
\(654\) 17.9466 0.701766
\(655\) −22.9942 −0.898459
\(656\) 130.352 5.08940
\(657\) 8.67979 0.338631
\(658\) −64.8812 −2.52933
\(659\) −22.5794 −0.879569 −0.439784 0.898103i \(-0.644945\pi\)
−0.439784 + 0.898103i \(0.644945\pi\)
\(660\) −101.485 −3.95029
\(661\) −4.18815 −0.162900 −0.0814501 0.996677i \(-0.525955\pi\)
−0.0814501 + 0.996677i \(0.525955\pi\)
\(662\) −8.12604 −0.315827
\(663\) −92.0674 −3.57560
\(664\) −28.1816 −1.09366
\(665\) −4.87460 −0.189029
\(666\) −116.390 −4.51002
\(667\) −18.7099 −0.724451
\(668\) 45.0433 1.74278
\(669\) −51.7400 −2.00039
\(670\) 18.8106 0.726715
\(671\) −4.86785 −0.187921
\(672\) 153.486 5.92084
\(673\) −2.58697 −0.0997205 −0.0498602 0.998756i \(-0.515878\pi\)
−0.0498602 + 0.998756i \(0.515878\pi\)
\(674\) −85.4796 −3.29255
\(675\) 4.45447 0.171453
\(676\) 118.231 4.54733
\(677\) 32.4759 1.24815 0.624075 0.781364i \(-0.285476\pi\)
0.624075 + 0.781364i \(0.285476\pi\)
\(678\) −36.1830 −1.38960
\(679\) −59.5830 −2.28659
\(680\) −88.1284 −3.37957
\(681\) −55.1832 −2.11462
\(682\) 6.06033 0.232062
\(683\) −36.9000 −1.41194 −0.705969 0.708243i \(-0.749488\pi\)
−0.705969 + 0.708243i \(0.749488\pi\)
\(684\) 18.4323 0.704776
\(685\) −3.17657 −0.121371
\(686\) 33.5695 1.28169
\(687\) 0.306310 0.0116864
\(688\) −34.4925 −1.31501
\(689\) 27.0314 1.02982
\(690\) −24.4249 −0.929842
\(691\) −12.7391 −0.484616 −0.242308 0.970199i \(-0.577905\pi\)
−0.242308 + 0.970199i \(0.577905\pi\)
\(692\) 49.9385 1.89838
\(693\) −53.0252 −2.01426
\(694\) 10.6325 0.403606
\(695\) −24.7908 −0.940368
\(696\) −207.059 −7.84854
\(697\) −57.6287 −2.18284
\(698\) −26.8918 −1.01787
\(699\) −4.37296 −0.165401
\(700\) −37.7511 −1.42686
\(701\) −6.55587 −0.247612 −0.123806 0.992306i \(-0.539510\pi\)
−0.123806 + 0.992306i \(0.539510\pi\)
\(702\) −31.8772 −1.20313
\(703\) 10.5821 0.399113
\(704\) −103.137 −3.88713
\(705\) 32.6504 1.22969
\(706\) 65.0353 2.44763
\(707\) −25.9358 −0.975415
\(708\) 97.2854 3.65621
\(709\) −15.6961 −0.589481 −0.294740 0.955577i \(-0.595233\pi\)
−0.294740 + 0.955577i \(0.595233\pi\)
\(710\) 66.1493 2.48254
\(711\) 58.9217 2.20974
\(712\) −114.747 −4.30034
\(713\) 1.05887 0.0396550
\(714\) −132.932 −4.97484
\(715\) −43.7688 −1.63686
\(716\) 106.556 3.98219
\(717\) 53.3092 1.99087
\(718\) −9.19911 −0.343308
\(719\) −32.9918 −1.23039 −0.615194 0.788376i \(-0.710922\pi\)
−0.615194 + 0.788376i \(0.710922\pi\)
\(720\) −84.1973 −3.13785
\(721\) −11.5921 −0.431711
\(722\) 49.0205 1.82435
\(723\) −31.5611 −1.17377
\(724\) −60.1281 −2.23464
\(725\) 20.0459 0.744485
\(726\) 60.9741 2.26296
\(727\) −42.2598 −1.56733 −0.783665 0.621184i \(-0.786652\pi\)
−0.783665 + 0.621184i \(0.786652\pi\)
\(728\) 168.176 6.23300
\(729\) −38.5491 −1.42774
\(730\) 10.3446 0.382871
\(731\) 15.2491 0.564009
\(732\) −15.1201 −0.558856
\(733\) 12.6849 0.468528 0.234264 0.972173i \(-0.424732\pi\)
0.234264 + 0.972173i \(0.424732\pi\)
\(734\) −74.0118 −2.73182
\(735\) 13.3320 0.491758
\(736\) −38.9081 −1.43417
\(737\) −18.6039 −0.685282
\(738\) −98.3555 −3.62052
\(739\) 31.5631 1.16107 0.580534 0.814236i \(-0.302844\pi\)
0.580534 + 0.814236i \(0.302844\pi\)
\(740\) −100.701 −3.70184
\(741\) 14.2864 0.524825
\(742\) 39.0294 1.43281
\(743\) −36.3023 −1.33180 −0.665901 0.746040i \(-0.731953\pi\)
−0.665901 + 0.746040i \(0.731953\pi\)
\(744\) 11.7183 0.429614
\(745\) −14.5245 −0.532136
\(746\) 17.5432 0.642302
\(747\) 11.9033 0.435520
\(748\) 140.013 5.11937
\(749\) −51.0901 −1.86679
\(750\) 84.4935 3.08527
\(751\) −29.7824 −1.08678 −0.543388 0.839482i \(-0.682859\pi\)
−0.543388 + 0.839482i \(0.682859\pi\)
\(752\) 101.891 3.71558
\(753\) −70.0839 −2.55400
\(754\) −143.453 −5.22424
\(755\) −36.6172 −1.33264
\(756\) −33.4130 −1.21522
\(757\) 52.6604 1.91398 0.956988 0.290127i \(-0.0936976\pi\)
0.956988 + 0.290127i \(0.0936976\pi\)
\(758\) −58.0574 −2.10874
\(759\) 24.1566 0.876828
\(760\) 13.6752 0.496052
\(761\) −52.0252 −1.88591 −0.942955 0.332920i \(-0.891966\pi\)
−0.942955 + 0.332920i \(0.891966\pi\)
\(762\) −97.0540 −3.51589
\(763\) 8.11300 0.293710
\(764\) 98.8199 3.57518
\(765\) 37.2236 1.34582
\(766\) −46.5741 −1.68279
\(767\) 41.9577 1.51501
\(768\) −59.2536 −2.13813
\(769\) −11.7357 −0.423199 −0.211599 0.977356i \(-0.567867\pi\)
−0.211599 + 0.977356i \(0.567867\pi\)
\(770\) −63.1957 −2.27741
\(771\) 4.67746 0.168455
\(772\) −111.329 −4.00683
\(773\) 12.8279 0.461386 0.230693 0.973027i \(-0.425901\pi\)
0.230693 + 0.973027i \(0.425901\pi\)
\(774\) 26.0258 0.935480
\(775\) −1.13448 −0.0407517
\(776\) 167.154 6.00048
\(777\) −94.5573 −3.39222
\(778\) −1.02192 −0.0366377
\(779\) 8.94246 0.320397
\(780\) −135.951 −4.86784
\(781\) −65.4225 −2.34100
\(782\) 33.6977 1.20503
\(783\) 17.7423 0.634059
\(784\) 41.6046 1.48588
\(785\) 2.51651 0.0898182
\(786\) 97.3028 3.47068
\(787\) −18.1850 −0.648226 −0.324113 0.946018i \(-0.605066\pi\)
−0.324113 + 0.946018i \(0.605066\pi\)
\(788\) −93.9254 −3.34595
\(789\) 42.4917 1.51274
\(790\) 70.2231 2.49843
\(791\) −16.3570 −0.581588
\(792\) 148.757 5.28585
\(793\) −6.52109 −0.231571
\(794\) 50.3568 1.78710
\(795\) −19.6409 −0.696591
\(796\) −106.485 −3.77425
\(797\) 17.6620 0.625620 0.312810 0.949816i \(-0.398730\pi\)
0.312810 + 0.949816i \(0.398730\pi\)
\(798\) 20.6275 0.730204
\(799\) −45.0460 −1.59361
\(800\) 41.6863 1.47383
\(801\) 48.4669 1.71249
\(802\) −53.9243 −1.90413
\(803\) −10.2309 −0.361042
\(804\) −57.7859 −2.03795
\(805\) −11.0416 −0.389167
\(806\) 8.11857 0.285964
\(807\) 41.3442 1.45538
\(808\) 72.7602 2.55969
\(809\) 39.3413 1.38317 0.691584 0.722296i \(-0.256913\pi\)
0.691584 + 0.722296i \(0.256913\pi\)
\(810\) −27.4799 −0.965545
\(811\) −19.1942 −0.674000 −0.337000 0.941505i \(-0.609412\pi\)
−0.337000 + 0.941505i \(0.609412\pi\)
\(812\) −150.364 −5.27674
\(813\) −42.7997 −1.50105
\(814\) 137.190 4.80849
\(815\) 32.2030 1.12802
\(816\) 208.759 7.30803
\(817\) −2.36626 −0.0827850
\(818\) −6.70712 −0.234509
\(819\) −71.0339 −2.48212
\(820\) −85.0975 −2.97173
\(821\) 21.0144 0.733407 0.366703 0.930338i \(-0.380486\pi\)
0.366703 + 0.930338i \(0.380486\pi\)
\(822\) 13.4421 0.468846
\(823\) 4.32938 0.150913 0.0754563 0.997149i \(-0.475959\pi\)
0.0754563 + 0.997149i \(0.475959\pi\)
\(824\) 32.5203 1.13290
\(825\) −25.8814 −0.901076
\(826\) 60.5807 2.10787
\(827\) 41.2305 1.43372 0.716862 0.697215i \(-0.245578\pi\)
0.716862 + 0.697215i \(0.245578\pi\)
\(828\) 41.7516 1.45097
\(829\) 12.8129 0.445009 0.222505 0.974932i \(-0.428577\pi\)
0.222505 + 0.974932i \(0.428577\pi\)
\(830\) 14.1864 0.492418
\(831\) 22.6581 0.785999
\(832\) −138.165 −4.79001
\(833\) −18.3934 −0.637293
\(834\) 104.905 3.63257
\(835\) −14.1152 −0.488477
\(836\) −21.7263 −0.751419
\(837\) −1.00411 −0.0347071
\(838\) −0.0507606 −0.00175350
\(839\) 20.1927 0.697128 0.348564 0.937285i \(-0.386669\pi\)
0.348564 + 0.937285i \(0.386669\pi\)
\(840\) −122.196 −4.21615
\(841\) 50.8434 1.75322
\(842\) 21.8652 0.753526
\(843\) 11.6302 0.400566
\(844\) 48.1400 1.65705
\(845\) −37.0499 −1.27455
\(846\) −76.8804 −2.64320
\(847\) 27.5642 0.947116
\(848\) −61.2927 −2.10480
\(849\) 25.2470 0.866474
\(850\) −36.1039 −1.23835
\(851\) 23.9700 0.821680
\(852\) −203.210 −6.96186
\(853\) −37.4814 −1.28334 −0.641669 0.766982i \(-0.721758\pi\)
−0.641669 + 0.766982i \(0.721758\pi\)
\(854\) −9.41548 −0.322191
\(855\) −5.77612 −0.197539
\(856\) 143.328 4.89885
\(857\) 14.3079 0.488748 0.244374 0.969681i \(-0.421418\pi\)
0.244374 + 0.969681i \(0.421418\pi\)
\(858\) 185.213 6.32307
\(859\) 5.20329 0.177534 0.0887669 0.996052i \(-0.471707\pi\)
0.0887669 + 0.996052i \(0.471707\pi\)
\(860\) 22.5176 0.767845
\(861\) −79.9059 −2.72318
\(862\) 35.3054 1.20251
\(863\) −15.0824 −0.513409 −0.256705 0.966490i \(-0.582637\pi\)
−0.256705 + 0.966490i \(0.582637\pi\)
\(864\) 36.8960 1.25523
\(865\) −15.6492 −0.532089
\(866\) −37.5405 −1.27568
\(867\) −48.0809 −1.63291
\(868\) 8.50971 0.288838
\(869\) −69.4515 −2.35598
\(870\) 104.232 3.53380
\(871\) −24.9222 −0.844456
\(872\) −22.7602 −0.770757
\(873\) −70.6024 −2.38953
\(874\) −5.22900 −0.176874
\(875\) 38.1965 1.29128
\(876\) −31.7785 −1.07370
\(877\) 56.3955 1.90434 0.952170 0.305569i \(-0.0988467\pi\)
0.952170 + 0.305569i \(0.0988467\pi\)
\(878\) 107.166 3.61669
\(879\) 0.293982 0.00991576
\(880\) 99.2440 3.34552
\(881\) 0.612393 0.0206321 0.0103160 0.999947i \(-0.496716\pi\)
0.0103160 + 0.999947i \(0.496716\pi\)
\(882\) −31.3922 −1.05703
\(883\) −49.2186 −1.65634 −0.828169 0.560478i \(-0.810617\pi\)
−0.828169 + 0.560478i \(0.810617\pi\)
\(884\) 187.564 6.30848
\(885\) −30.4863 −1.02479
\(886\) 1.85627 0.0623626
\(887\) −30.9230 −1.03829 −0.519147 0.854685i \(-0.673750\pi\)
−0.519147 + 0.854685i \(0.673750\pi\)
\(888\) 265.271 8.90191
\(889\) −43.8746 −1.47151
\(890\) 57.7630 1.93622
\(891\) 27.1780 0.910496
\(892\) 105.407 3.52930
\(893\) 6.98995 0.233910
\(894\) 61.4621 2.05560
\(895\) −33.3915 −1.11615
\(896\) −81.4545 −2.72120
\(897\) 32.3607 1.08049
\(898\) 16.1538 0.539058
\(899\) −4.51866 −0.150706
\(900\) −44.7329 −1.49110
\(901\) 27.0975 0.902748
\(902\) 115.932 3.86013
\(903\) 21.1439 0.703624
\(904\) 45.8879 1.52621
\(905\) 18.8423 0.626340
\(906\) 154.950 5.14788
\(907\) 32.6265 1.08335 0.541673 0.840589i \(-0.317791\pi\)
0.541673 + 0.840589i \(0.317791\pi\)
\(908\) 112.422 3.73086
\(909\) −30.7324 −1.01933
\(910\) −84.6584 −2.80640
\(911\) −38.4489 −1.27387 −0.636935 0.770918i \(-0.719798\pi\)
−0.636935 + 0.770918i \(0.719798\pi\)
\(912\) −32.3939 −1.07267
\(913\) −14.0306 −0.464343
\(914\) −28.8401 −0.953944
\(915\) 4.73819 0.156640
\(916\) −0.624030 −0.0206185
\(917\) 43.9871 1.45258
\(918\) −31.9550 −1.05467
\(919\) −26.4208 −0.871543 −0.435771 0.900057i \(-0.643524\pi\)
−0.435771 + 0.900057i \(0.643524\pi\)
\(920\) 30.9762 1.02125
\(921\) 37.1987 1.22574
\(922\) −77.8115 −2.56259
\(923\) −87.6415 −2.88476
\(924\) 194.137 6.38662
\(925\) −25.6815 −0.844404
\(926\) −22.0740 −0.725396
\(927\) −13.7359 −0.451147
\(928\) 166.038 5.45047
\(929\) 16.4854 0.540869 0.270434 0.962738i \(-0.412833\pi\)
0.270434 + 0.962738i \(0.412833\pi\)
\(930\) −5.89891 −0.193433
\(931\) 2.85417 0.0935416
\(932\) 8.90883 0.291818
\(933\) 86.2210 2.82275
\(934\) 29.2612 0.957455
\(935\) −43.8758 −1.43489
\(936\) 199.278 6.51362
\(937\) 4.93821 0.161324 0.0806621 0.996742i \(-0.474297\pi\)
0.0806621 + 0.996742i \(0.474297\pi\)
\(938\) −35.9839 −1.17492
\(939\) −20.6784 −0.674812
\(940\) −66.5172 −2.16955
\(941\) −37.5893 −1.22537 −0.612687 0.790325i \(-0.709911\pi\)
−0.612687 + 0.790325i \(0.709911\pi\)
\(942\) −10.6489 −0.346961
\(943\) 20.2559 0.659623
\(944\) −95.1375 −3.09646
\(945\) 10.4706 0.340609
\(946\) −30.6769 −0.997391
\(947\) −32.4830 −1.05556 −0.527779 0.849382i \(-0.676975\pi\)
−0.527779 + 0.849382i \(0.676975\pi\)
\(948\) −215.725 −7.00642
\(949\) −13.7056 −0.444903
\(950\) 5.60237 0.181765
\(951\) −0.486217 −0.0157667
\(952\) 168.586 5.46392
\(953\) −25.6327 −0.830324 −0.415162 0.909747i \(-0.636275\pi\)
−0.415162 + 0.909747i \(0.636275\pi\)
\(954\) 46.2475 1.49732
\(955\) −30.9672 −1.00207
\(956\) −108.604 −3.51251
\(957\) −103.087 −3.33232
\(958\) 46.7006 1.50883
\(959\) 6.07667 0.196226
\(960\) 100.390 3.24008
\(961\) −30.7443 −0.991751
\(962\) 183.783 5.92539
\(963\) −60.5388 −1.95083
\(964\) 64.2978 2.07089
\(965\) 34.8872 1.12306
\(966\) 46.7240 1.50332
\(967\) 40.1317 1.29055 0.645275 0.763950i \(-0.276743\pi\)
0.645275 + 0.763950i \(0.276743\pi\)
\(968\) −77.3285 −2.48543
\(969\) 14.3213 0.460067
\(970\) −84.1442 −2.70171
\(971\) −7.35583 −0.236060 −0.118030 0.993010i \(-0.537658\pi\)
−0.118030 + 0.993010i \(0.537658\pi\)
\(972\) 115.978 3.72001
\(973\) 47.4239 1.52034
\(974\) −21.7898 −0.698190
\(975\) −34.6714 −1.11037
\(976\) 14.7863 0.473298
\(977\) −33.1256 −1.05978 −0.529891 0.848066i \(-0.677767\pi\)
−0.529891 + 0.848066i \(0.677767\pi\)
\(978\) −136.271 −4.35747
\(979\) −57.1283 −1.82583
\(980\) −27.1606 −0.867614
\(981\) 9.61343 0.306933
\(982\) 88.8354 2.83485
\(983\) 24.7113 0.788167 0.394083 0.919075i \(-0.371062\pi\)
0.394083 + 0.919075i \(0.371062\pi\)
\(984\) 224.168 7.14621
\(985\) 29.4334 0.937826
\(986\) −143.803 −4.57962
\(987\) −62.4591 −1.98810
\(988\) −29.1051 −0.925955
\(989\) −5.35991 −0.170435
\(990\) −74.8832 −2.37994
\(991\) 7.84221 0.249116 0.124558 0.992212i \(-0.460249\pi\)
0.124558 + 0.992212i \(0.460249\pi\)
\(992\) −9.39677 −0.298348
\(993\) −7.82268 −0.248245
\(994\) −126.541 −4.01364
\(995\) 33.3691 1.05787
\(996\) −43.5806 −1.38090
\(997\) 49.9961 1.58339 0.791696 0.610915i \(-0.209198\pi\)
0.791696 + 0.610915i \(0.209198\pi\)
\(998\) −5.60478 −0.177416
\(999\) −22.7304 −0.719157
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.1.13 243
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6037.2.a.a.1.13 243 1.1 even 1 trivial