Properties

Label 6037.2.a.a.1.19
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 1.19
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)
 
\(f(q)\) \(=\) \(q-2.62641 q^{2} -3.35140 q^{3} +4.89803 q^{4} -4.35294 q^{5} +8.80215 q^{6} +2.67168 q^{7} -7.61143 q^{8} +8.23188 q^{9} +O(q^{10})\) \(q-2.62641 q^{2} -3.35140 q^{3} +4.89803 q^{4} -4.35294 q^{5} +8.80215 q^{6} +2.67168 q^{7} -7.61143 q^{8} +8.23188 q^{9} +11.4326 q^{10} -0.768445 q^{11} -16.4153 q^{12} +6.00805 q^{13} -7.01694 q^{14} +14.5884 q^{15} +10.1947 q^{16} +4.35173 q^{17} -21.6203 q^{18} -3.91306 q^{19} -21.3208 q^{20} -8.95388 q^{21} +2.01825 q^{22} +2.20940 q^{23} +25.5089 q^{24} +13.9481 q^{25} -15.7796 q^{26} -17.5341 q^{27} +13.0860 q^{28} +6.03569 q^{29} -38.3152 q^{30} +5.87842 q^{31} -11.5525 q^{32} +2.57537 q^{33} -11.4294 q^{34} -11.6297 q^{35} +40.3200 q^{36} +3.95604 q^{37} +10.2773 q^{38} -20.1354 q^{39} +33.1321 q^{40} +8.23293 q^{41} +23.5166 q^{42} -7.07844 q^{43} -3.76387 q^{44} -35.8328 q^{45} -5.80279 q^{46} -6.17473 q^{47} -34.1664 q^{48} +0.137897 q^{49} -36.6333 q^{50} -14.5844 q^{51} +29.4276 q^{52} -6.77161 q^{53} +46.0518 q^{54} +3.34499 q^{55} -20.3353 q^{56} +13.1142 q^{57} -15.8522 q^{58} +1.70484 q^{59} +71.4546 q^{60} +0.753420 q^{61} -15.4392 q^{62} +21.9930 q^{63} +9.95238 q^{64} -26.1527 q^{65} -6.76397 q^{66} -12.2660 q^{67} +21.3149 q^{68} -7.40458 q^{69} +30.5443 q^{70} -14.3058 q^{71} -62.6563 q^{72} -0.962519 q^{73} -10.3902 q^{74} -46.7455 q^{75} -19.1663 q^{76} -2.05304 q^{77} +52.8838 q^{78} -4.69274 q^{79} -44.3768 q^{80} +34.0681 q^{81} -21.6231 q^{82} -10.6501 q^{83} -43.8564 q^{84} -18.9428 q^{85} +18.5909 q^{86} -20.2280 q^{87} +5.84896 q^{88} +4.47991 q^{89} +94.1117 q^{90} +16.0516 q^{91} +10.8217 q^{92} -19.7009 q^{93} +16.2174 q^{94} +17.0333 q^{95} +38.7172 q^{96} -7.80956 q^{97} -0.362173 q^{98} -6.32574 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.62641 −1.85715 −0.928577 0.371141i \(-0.878967\pi\)
−0.928577 + 0.371141i \(0.878967\pi\)
\(3\) −3.35140 −1.93493 −0.967466 0.253003i \(-0.918582\pi\)
−0.967466 + 0.253003i \(0.918582\pi\)
\(4\) 4.89803 2.44902
\(5\) −4.35294 −1.94669 −0.973346 0.229341i \(-0.926343\pi\)
−0.973346 + 0.229341i \(0.926343\pi\)
\(6\) 8.80215 3.59346
\(7\) 2.67168 1.00980 0.504901 0.863177i \(-0.331529\pi\)
0.504901 + 0.863177i \(0.331529\pi\)
\(8\) −7.61143 −2.69105
\(9\) 8.23188 2.74396
\(10\) 11.4326 3.61531
\(11\) −0.768445 −0.231695 −0.115847 0.993267i \(-0.536958\pi\)
−0.115847 + 0.993267i \(0.536958\pi\)
\(12\) −16.4153 −4.73868
\(13\) 6.00805 1.66633 0.833167 0.553022i \(-0.186525\pi\)
0.833167 + 0.553022i \(0.186525\pi\)
\(14\) −7.01694 −1.87536
\(15\) 14.5884 3.76672
\(16\) 10.1947 2.54867
\(17\) 4.35173 1.05545 0.527725 0.849415i \(-0.323045\pi\)
0.527725 + 0.849415i \(0.323045\pi\)
\(18\) −21.6203 −5.09595
\(19\) −3.91306 −0.897718 −0.448859 0.893603i \(-0.648169\pi\)
−0.448859 + 0.893603i \(0.648169\pi\)
\(20\) −21.3208 −4.76748
\(21\) −8.95388 −1.95390
\(22\) 2.01825 0.430293
\(23\) 2.20940 0.460692 0.230346 0.973109i \(-0.426014\pi\)
0.230346 + 0.973109i \(0.426014\pi\)
\(24\) 25.5089 5.20699
\(25\) 13.9481 2.78961
\(26\) −15.7796 −3.09464
\(27\) −17.5341 −3.37444
\(28\) 13.0860 2.47302
\(29\) 6.03569 1.12080 0.560400 0.828222i \(-0.310647\pi\)
0.560400 + 0.828222i \(0.310647\pi\)
\(30\) −38.3152 −6.99537
\(31\) 5.87842 1.05580 0.527898 0.849308i \(-0.322980\pi\)
0.527898 + 0.849308i \(0.322980\pi\)
\(32\) −11.5525 −2.04222
\(33\) 2.57537 0.448314
\(34\) −11.4294 −1.96013
\(35\) −11.6297 −1.96577
\(36\) 40.3200 6.72000
\(37\) 3.95604 0.650368 0.325184 0.945651i \(-0.394574\pi\)
0.325184 + 0.945651i \(0.394574\pi\)
\(38\) 10.2773 1.66720
\(39\) −20.1354 −3.22424
\(40\) 33.1321 5.23864
\(41\) 8.23293 1.28577 0.642884 0.765964i \(-0.277738\pi\)
0.642884 + 0.765964i \(0.277738\pi\)
\(42\) 23.5166 3.62869
\(43\) −7.07844 −1.07945 −0.539726 0.841841i \(-0.681472\pi\)
−0.539726 + 0.841841i \(0.681472\pi\)
\(44\) −3.76387 −0.567425
\(45\) −35.8328 −5.34164
\(46\) −5.80279 −0.855575
\(47\) −6.17473 −0.900677 −0.450338 0.892858i \(-0.648697\pi\)
−0.450338 + 0.892858i \(0.648697\pi\)
\(48\) −34.1664 −4.93150
\(49\) 0.137897 0.0196995
\(50\) −36.6333 −5.18073
\(51\) −14.5844 −2.04222
\(52\) 29.4276 4.08088
\(53\) −6.77161 −0.930152 −0.465076 0.885271i \(-0.653973\pi\)
−0.465076 + 0.885271i \(0.653973\pi\)
\(54\) 46.0518 6.26685
\(55\) 3.34499 0.451039
\(56\) −20.3353 −2.71742
\(57\) 13.1142 1.73702
\(58\) −15.8522 −2.08150
\(59\) 1.70484 0.221952 0.110976 0.993823i \(-0.464602\pi\)
0.110976 + 0.993823i \(0.464602\pi\)
\(60\) 71.4546 9.22475
\(61\) 0.753420 0.0964655 0.0482328 0.998836i \(-0.484641\pi\)
0.0482328 + 0.998836i \(0.484641\pi\)
\(62\) −15.4392 −1.96077
\(63\) 21.9930 2.77085
\(64\) 9.95238 1.24405
\(65\) −26.1527 −3.24384
\(66\) −6.76397 −0.832587
\(67\) −12.2660 −1.49853 −0.749264 0.662271i \(-0.769593\pi\)
−0.749264 + 0.662271i \(0.769593\pi\)
\(68\) 21.3149 2.58482
\(69\) −7.40458 −0.891406
\(70\) 30.5443 3.65074
\(71\) −14.3058 −1.69779 −0.848895 0.528562i \(-0.822731\pi\)
−0.848895 + 0.528562i \(0.822731\pi\)
\(72\) −62.6563 −7.38412
\(73\) −0.962519 −0.112654 −0.0563271 0.998412i \(-0.517939\pi\)
−0.0563271 + 0.998412i \(0.517939\pi\)
\(74\) −10.3902 −1.20783
\(75\) −46.7455 −5.39770
\(76\) −19.1663 −2.19853
\(77\) −2.05304 −0.233966
\(78\) 52.8838 5.98791
\(79\) −4.69274 −0.527975 −0.263987 0.964526i \(-0.585038\pi\)
−0.263987 + 0.964526i \(0.585038\pi\)
\(80\) −44.3768 −4.96147
\(81\) 34.0681 3.78535
\(82\) −21.6231 −2.38787
\(83\) −10.6501 −1.16900 −0.584499 0.811394i \(-0.698709\pi\)
−0.584499 + 0.811394i \(0.698709\pi\)
\(84\) −43.8564 −4.78513
\(85\) −18.9428 −2.05464
\(86\) 18.5909 2.00471
\(87\) −20.2280 −2.16867
\(88\) 5.84896 0.623502
\(89\) 4.47991 0.474870 0.237435 0.971403i \(-0.423693\pi\)
0.237435 + 0.971403i \(0.423693\pi\)
\(90\) 94.1117 9.92025
\(91\) 16.0516 1.68267
\(92\) 10.8217 1.12824
\(93\) −19.7009 −2.04289
\(94\) 16.2174 1.67269
\(95\) 17.0333 1.74758
\(96\) 38.7172 3.95156
\(97\) −7.80956 −0.792941 −0.396470 0.918048i \(-0.629765\pi\)
−0.396470 + 0.918048i \(0.629765\pi\)
\(98\) −0.362173 −0.0365850
\(99\) −6.32574 −0.635761
\(100\) 68.3180 6.83180
\(101\) 9.68037 0.963233 0.481616 0.876382i \(-0.340050\pi\)
0.481616 + 0.876382i \(0.340050\pi\)
\(102\) 38.3046 3.79272
\(103\) 17.5659 1.73082 0.865412 0.501061i \(-0.167057\pi\)
0.865412 + 0.501061i \(0.167057\pi\)
\(104\) −45.7299 −4.48418
\(105\) 38.9757 3.80364
\(106\) 17.7850 1.72744
\(107\) −16.6215 −1.60686 −0.803430 0.595399i \(-0.796994\pi\)
−0.803430 + 0.595399i \(0.796994\pi\)
\(108\) −85.8826 −8.26406
\(109\) 4.94978 0.474103 0.237051 0.971497i \(-0.423819\pi\)
0.237051 + 0.971497i \(0.423819\pi\)
\(110\) −8.78532 −0.837648
\(111\) −13.2583 −1.25842
\(112\) 27.2369 2.57365
\(113\) 5.04932 0.475000 0.237500 0.971388i \(-0.423672\pi\)
0.237500 + 0.971388i \(0.423672\pi\)
\(114\) −34.4434 −3.22592
\(115\) −9.61737 −0.896825
\(116\) 29.5630 2.74486
\(117\) 49.4575 4.57235
\(118\) −4.47762 −0.412198
\(119\) 11.6265 1.06580
\(120\) −111.039 −10.1364
\(121\) −10.4095 −0.946317
\(122\) −1.97879 −0.179151
\(123\) −27.5918 −2.48787
\(124\) 28.7927 2.58566
\(125\) −38.9503 −3.48382
\(126\) −57.7626 −5.14590
\(127\) −5.62832 −0.499432 −0.249716 0.968319i \(-0.580337\pi\)
−0.249716 + 0.968319i \(0.580337\pi\)
\(128\) −3.03395 −0.268166
\(129\) 23.7227 2.08867
\(130\) 68.6876 6.02431
\(131\) 8.28231 0.723628 0.361814 0.932250i \(-0.382157\pi\)
0.361814 + 0.932250i \(0.382157\pi\)
\(132\) 12.6142 1.09793
\(133\) −10.4545 −0.906517
\(134\) 32.2155 2.78300
\(135\) 76.3248 6.56899
\(136\) −33.1229 −2.84027
\(137\) −4.25629 −0.363639 −0.181820 0.983332i \(-0.558199\pi\)
−0.181820 + 0.983332i \(0.558199\pi\)
\(138\) 19.4475 1.65548
\(139\) 2.95510 0.250648 0.125324 0.992116i \(-0.460003\pi\)
0.125324 + 0.992116i \(0.460003\pi\)
\(140\) −56.9625 −4.81421
\(141\) 20.6940 1.74275
\(142\) 37.5730 3.15305
\(143\) −4.61686 −0.386081
\(144\) 83.9213 6.99344
\(145\) −26.2730 −2.18185
\(146\) 2.52797 0.209216
\(147\) −0.462147 −0.0381172
\(148\) 19.3768 1.59276
\(149\) 6.12290 0.501608 0.250804 0.968038i \(-0.419305\pi\)
0.250804 + 0.968038i \(0.419305\pi\)
\(150\) 122.773 10.0244
\(151\) −14.4111 −1.17276 −0.586379 0.810036i \(-0.699447\pi\)
−0.586379 + 0.810036i \(0.699447\pi\)
\(152\) 29.7840 2.41580
\(153\) 35.8229 2.89611
\(154\) 5.39213 0.434510
\(155\) −25.5884 −2.05531
\(156\) −98.6238 −7.89622
\(157\) 7.51763 0.599972 0.299986 0.953944i \(-0.403018\pi\)
0.299986 + 0.953944i \(0.403018\pi\)
\(158\) 12.3251 0.980530
\(159\) 22.6944 1.79978
\(160\) 50.2875 3.97557
\(161\) 5.90282 0.465207
\(162\) −89.4770 −7.02997
\(163\) −18.1477 −1.42143 −0.710717 0.703478i \(-0.751629\pi\)
−0.710717 + 0.703478i \(0.751629\pi\)
\(164\) 40.3252 3.14887
\(165\) −11.2104 −0.872729
\(166\) 27.9715 2.17101
\(167\) −14.5543 −1.12625 −0.563123 0.826373i \(-0.690400\pi\)
−0.563123 + 0.826373i \(0.690400\pi\)
\(168\) 68.1518 5.25803
\(169\) 23.0967 1.77667
\(170\) 49.7516 3.81577
\(171\) −32.2118 −2.46330
\(172\) −34.6705 −2.64360
\(173\) −10.9106 −0.829516 −0.414758 0.909932i \(-0.636134\pi\)
−0.414758 + 0.909932i \(0.636134\pi\)
\(174\) 53.1271 4.02755
\(175\) 37.2648 2.81695
\(176\) −7.83405 −0.590513
\(177\) −5.71361 −0.429461
\(178\) −11.7661 −0.881905
\(179\) 20.2568 1.51407 0.757033 0.653377i \(-0.226648\pi\)
0.757033 + 0.653377i \(0.226648\pi\)
\(180\) −175.510 −13.0818
\(181\) 2.23232 0.165927 0.0829635 0.996553i \(-0.473562\pi\)
0.0829635 + 0.996553i \(0.473562\pi\)
\(182\) −42.1581 −3.12497
\(183\) −2.52501 −0.186654
\(184\) −16.8167 −1.23974
\(185\) −17.2204 −1.26607
\(186\) 51.7428 3.79396
\(187\) −3.34407 −0.244542
\(188\) −30.2440 −2.20577
\(189\) −46.8456 −3.40751
\(190\) −44.7365 −3.24552
\(191\) 2.74977 0.198966 0.0994831 0.995039i \(-0.468281\pi\)
0.0994831 + 0.995039i \(0.468281\pi\)
\(192\) −33.3544 −2.40715
\(193\) 15.0977 1.08676 0.543379 0.839488i \(-0.317145\pi\)
0.543379 + 0.839488i \(0.317145\pi\)
\(194\) 20.5111 1.47261
\(195\) 87.6480 6.27661
\(196\) 0.675423 0.0482445
\(197\) −0.182597 −0.0130095 −0.00650475 0.999979i \(-0.502071\pi\)
−0.00650475 + 0.999979i \(0.502071\pi\)
\(198\) 16.6140 1.18071
\(199\) −13.4157 −0.951015 −0.475508 0.879712i \(-0.657736\pi\)
−0.475508 + 0.879712i \(0.657736\pi\)
\(200\) −106.165 −7.50697
\(201\) 41.1082 2.89955
\(202\) −25.4246 −1.78887
\(203\) 16.1255 1.13179
\(204\) −71.4348 −5.00144
\(205\) −35.8374 −2.50299
\(206\) −46.1354 −3.21440
\(207\) 18.1875 1.26412
\(208\) 61.2501 4.24693
\(209\) 3.00697 0.207997
\(210\) −102.366 −7.06393
\(211\) 6.99188 0.481341 0.240670 0.970607i \(-0.422633\pi\)
0.240670 + 0.970607i \(0.422633\pi\)
\(212\) −33.1676 −2.27796
\(213\) 47.9445 3.28511
\(214\) 43.6549 2.98419
\(215\) 30.8120 2.10136
\(216\) 133.460 9.08077
\(217\) 15.7053 1.06614
\(218\) −13.0001 −0.880481
\(219\) 3.22578 0.217978
\(220\) 16.3839 1.10460
\(221\) 26.1454 1.75873
\(222\) 34.8216 2.33707
\(223\) −27.1657 −1.81915 −0.909575 0.415540i \(-0.863593\pi\)
−0.909575 + 0.415540i \(0.863593\pi\)
\(224\) −30.8647 −2.06224
\(225\) 114.819 7.65457
\(226\) −13.2616 −0.882148
\(227\) −10.4799 −0.695573 −0.347787 0.937574i \(-0.613067\pi\)
−0.347787 + 0.937574i \(0.613067\pi\)
\(228\) 64.2340 4.25400
\(229\) −22.9583 −1.51713 −0.758565 0.651597i \(-0.774099\pi\)
−0.758565 + 0.651597i \(0.774099\pi\)
\(230\) 25.2592 1.66554
\(231\) 6.88056 0.452708
\(232\) −45.9403 −3.01613
\(233\) −4.61222 −0.302157 −0.151078 0.988522i \(-0.548275\pi\)
−0.151078 + 0.988522i \(0.548275\pi\)
\(234\) −129.896 −8.49156
\(235\) 26.8782 1.75334
\(236\) 8.35038 0.543563
\(237\) 15.7273 1.02160
\(238\) −30.5358 −1.97934
\(239\) 1.38394 0.0895198 0.0447599 0.998998i \(-0.485748\pi\)
0.0447599 + 0.998998i \(0.485748\pi\)
\(240\) 148.724 9.60011
\(241\) 20.1105 1.29543 0.647715 0.761883i \(-0.275725\pi\)
0.647715 + 0.761883i \(0.275725\pi\)
\(242\) 27.3396 1.75746
\(243\) −61.5736 −3.94995
\(244\) 3.69028 0.236246
\(245\) −0.600255 −0.0383489
\(246\) 72.4675 4.62036
\(247\) −23.5099 −1.49590
\(248\) −44.7432 −2.84120
\(249\) 35.6927 2.26193
\(250\) 102.299 6.46999
\(251\) 11.3916 0.719031 0.359516 0.933139i \(-0.382942\pi\)
0.359516 + 0.933139i \(0.382942\pi\)
\(252\) 107.722 6.78587
\(253\) −1.69780 −0.106740
\(254\) 14.7823 0.927523
\(255\) 63.4849 3.97558
\(256\) −11.9364 −0.746022
\(257\) −24.4972 −1.52809 −0.764046 0.645162i \(-0.776790\pi\)
−0.764046 + 0.645162i \(0.776790\pi\)
\(258\) −62.3055 −3.87897
\(259\) 10.5693 0.656743
\(260\) −128.097 −7.94422
\(261\) 49.6851 3.07543
\(262\) −21.7527 −1.34389
\(263\) 3.30243 0.203637 0.101818 0.994803i \(-0.467534\pi\)
0.101818 + 0.994803i \(0.467534\pi\)
\(264\) −19.6022 −1.20643
\(265\) 29.4764 1.81072
\(266\) 27.4577 1.68354
\(267\) −15.0140 −0.918840
\(268\) −60.0792 −3.66992
\(269\) −11.1185 −0.677906 −0.338953 0.940803i \(-0.610073\pi\)
−0.338953 + 0.940803i \(0.610073\pi\)
\(270\) −200.460 −12.1996
\(271\) 27.5718 1.67487 0.837433 0.546541i \(-0.184056\pi\)
0.837433 + 0.546541i \(0.184056\pi\)
\(272\) 44.3645 2.68999
\(273\) −53.7954 −3.25584
\(274\) 11.1788 0.675333
\(275\) −10.7183 −0.646338
\(276\) −36.2679 −2.18307
\(277\) −20.0060 −1.20204 −0.601022 0.799233i \(-0.705240\pi\)
−0.601022 + 0.799233i \(0.705240\pi\)
\(278\) −7.76131 −0.465493
\(279\) 48.3904 2.89706
\(280\) 88.5184 5.28999
\(281\) −24.8991 −1.48536 −0.742678 0.669649i \(-0.766445\pi\)
−0.742678 + 0.669649i \(0.766445\pi\)
\(282\) −54.3509 −3.23655
\(283\) 13.3152 0.791505 0.395753 0.918357i \(-0.370484\pi\)
0.395753 + 0.918357i \(0.370484\pi\)
\(284\) −70.0704 −4.15792
\(285\) −57.0854 −3.38145
\(286\) 12.1258 0.717011
\(287\) 21.9958 1.29837
\(288\) −95.0991 −5.60377
\(289\) 1.93757 0.113975
\(290\) 69.0037 4.05203
\(291\) 26.1730 1.53429
\(292\) −4.71445 −0.275892
\(293\) −10.0223 −0.585510 −0.292755 0.956188i \(-0.594572\pi\)
−0.292755 + 0.956188i \(0.594572\pi\)
\(294\) 1.21379 0.0707895
\(295\) −7.42107 −0.432071
\(296\) −30.1111 −1.75017
\(297\) 13.4740 0.781840
\(298\) −16.0813 −0.931562
\(299\) 13.2742 0.767666
\(300\) −228.961 −13.2191
\(301\) −18.9114 −1.09003
\(302\) 37.8495 2.17799
\(303\) −32.4428 −1.86379
\(304\) −39.8924 −2.28799
\(305\) −3.27959 −0.187789
\(306\) −94.0857 −5.37852
\(307\) 14.3416 0.818519 0.409259 0.912418i \(-0.365787\pi\)
0.409259 + 0.912418i \(0.365787\pi\)
\(308\) −10.0559 −0.572986
\(309\) −58.8705 −3.34902
\(310\) 67.2057 3.81702
\(311\) −2.70719 −0.153511 −0.0767555 0.997050i \(-0.524456\pi\)
−0.0767555 + 0.997050i \(0.524456\pi\)
\(312\) 153.259 8.67658
\(313\) −17.3533 −0.980868 −0.490434 0.871478i \(-0.663162\pi\)
−0.490434 + 0.871478i \(0.663162\pi\)
\(314\) −19.7444 −1.11424
\(315\) −95.7340 −5.39400
\(316\) −22.9852 −1.29302
\(317\) 5.28477 0.296822 0.148411 0.988926i \(-0.452584\pi\)
0.148411 + 0.988926i \(0.452584\pi\)
\(318\) −59.6047 −3.34247
\(319\) −4.63810 −0.259684
\(320\) −43.3221 −2.42178
\(321\) 55.7053 3.10916
\(322\) −15.5032 −0.863961
\(323\) −17.0286 −0.947497
\(324\) 166.867 9.27039
\(325\) 83.8006 4.64842
\(326\) 47.6632 2.63982
\(327\) −16.5887 −0.917356
\(328\) −62.6644 −3.46006
\(329\) −16.4969 −0.909505
\(330\) 29.4431 1.62079
\(331\) 17.8100 0.978923 0.489462 0.872025i \(-0.337193\pi\)
0.489462 + 0.872025i \(0.337193\pi\)
\(332\) −52.1645 −2.86290
\(333\) 32.5656 1.78458
\(334\) 38.2256 2.09161
\(335\) 53.3930 2.91717
\(336\) −91.2819 −4.97984
\(337\) −19.6449 −1.07013 −0.535063 0.844812i \(-0.679712\pi\)
−0.535063 + 0.844812i \(0.679712\pi\)
\(338\) −60.6614 −3.29955
\(339\) −16.9223 −0.919092
\(340\) −92.7825 −5.03184
\(341\) −4.51724 −0.244623
\(342\) 84.6015 4.57473
\(343\) −18.3334 −0.989909
\(344\) 53.8771 2.90486
\(345\) 32.2317 1.73529
\(346\) 28.6557 1.54054
\(347\) −21.4519 −1.15160 −0.575799 0.817591i \(-0.695309\pi\)
−0.575799 + 0.817591i \(0.695309\pi\)
\(348\) −99.0775 −5.31111
\(349\) −25.3586 −1.35742 −0.678708 0.734408i \(-0.737460\pi\)
−0.678708 + 0.734408i \(0.737460\pi\)
\(350\) −97.8727 −5.23151
\(351\) −105.346 −5.62294
\(352\) 8.87749 0.473172
\(353\) 8.62680 0.459158 0.229579 0.973290i \(-0.426265\pi\)
0.229579 + 0.973290i \(0.426265\pi\)
\(354\) 15.0063 0.797575
\(355\) 62.2723 3.30507
\(356\) 21.9428 1.16296
\(357\) −38.9649 −2.06224
\(358\) −53.2027 −2.81185
\(359\) 3.48837 0.184109 0.0920545 0.995754i \(-0.470657\pi\)
0.0920545 + 0.995754i \(0.470657\pi\)
\(360\) 272.739 14.3746
\(361\) −3.68794 −0.194102
\(362\) −5.86299 −0.308152
\(363\) 34.8864 1.83106
\(364\) 78.6214 4.12088
\(365\) 4.18978 0.219303
\(366\) 6.63172 0.346645
\(367\) 16.2841 0.850024 0.425012 0.905188i \(-0.360270\pi\)
0.425012 + 0.905188i \(0.360270\pi\)
\(368\) 22.5241 1.17415
\(369\) 67.7725 3.52809
\(370\) 45.2278 2.35128
\(371\) −18.0916 −0.939269
\(372\) −96.4959 −5.00308
\(373\) 19.4325 1.00617 0.503087 0.864235i \(-0.332197\pi\)
0.503087 + 0.864235i \(0.332197\pi\)
\(374\) 8.78289 0.454153
\(375\) 130.538 6.74095
\(376\) 46.9985 2.42376
\(377\) 36.2628 1.86763
\(378\) 123.036 6.32828
\(379\) −4.56565 −0.234522 −0.117261 0.993101i \(-0.537411\pi\)
−0.117261 + 0.993101i \(0.537411\pi\)
\(380\) 83.4297 4.27986
\(381\) 18.8627 0.966367
\(382\) −7.22202 −0.369511
\(383\) −9.37637 −0.479110 −0.239555 0.970883i \(-0.577002\pi\)
−0.239555 + 0.970883i \(0.577002\pi\)
\(384\) 10.1680 0.518883
\(385\) 8.93676 0.455460
\(386\) −39.6528 −2.01827
\(387\) −58.2689 −2.96197
\(388\) −38.2515 −1.94193
\(389\) 29.9200 1.51700 0.758502 0.651671i \(-0.225932\pi\)
0.758502 + 0.651671i \(0.225932\pi\)
\(390\) −230.200 −11.6566
\(391\) 9.61471 0.486237
\(392\) −1.04959 −0.0530123
\(393\) −27.7573 −1.40017
\(394\) 0.479575 0.0241606
\(395\) 20.4272 1.02780
\(396\) −30.9837 −1.55699
\(397\) 12.7544 0.640126 0.320063 0.947396i \(-0.396296\pi\)
0.320063 + 0.947396i \(0.396296\pi\)
\(398\) 35.2352 1.76618
\(399\) 35.0371 1.75405
\(400\) 142.196 7.10979
\(401\) 22.9930 1.14821 0.574107 0.818780i \(-0.305349\pi\)
0.574107 + 0.818780i \(0.305349\pi\)
\(402\) −107.967 −5.38490
\(403\) 35.3179 1.75931
\(404\) 47.4148 2.35897
\(405\) −148.296 −7.36891
\(406\) −42.3521 −2.10190
\(407\) −3.04000 −0.150687
\(408\) 111.008 5.49572
\(409\) 19.3603 0.957303 0.478652 0.878005i \(-0.341126\pi\)
0.478652 + 0.878005i \(0.341126\pi\)
\(410\) 94.1238 4.64844
\(411\) 14.2645 0.703616
\(412\) 86.0386 4.23882
\(413\) 4.55480 0.224127
\(414\) −47.7678 −2.34766
\(415\) 46.3591 2.27568
\(416\) −69.4083 −3.40302
\(417\) −9.90372 −0.484987
\(418\) −7.89755 −0.386282
\(419\) 13.9730 0.682626 0.341313 0.939950i \(-0.389128\pi\)
0.341313 + 0.939950i \(0.389128\pi\)
\(420\) 190.904 9.31517
\(421\) −32.9556 −1.60616 −0.803079 0.595873i \(-0.796806\pi\)
−0.803079 + 0.595873i \(0.796806\pi\)
\(422\) −18.3635 −0.893923
\(423\) −50.8296 −2.47142
\(424\) 51.5416 2.50308
\(425\) 60.6982 2.94429
\(426\) −125.922 −6.10094
\(427\) 2.01290 0.0974111
\(428\) −81.4127 −3.93523
\(429\) 15.4729 0.747040
\(430\) −80.9250 −3.90255
\(431\) −25.4184 −1.22436 −0.612182 0.790717i \(-0.709708\pi\)
−0.612182 + 0.790717i \(0.709708\pi\)
\(432\) −178.754 −8.60033
\(433\) −21.6478 −1.04033 −0.520163 0.854067i \(-0.674129\pi\)
−0.520163 + 0.854067i \(0.674129\pi\)
\(434\) −41.2485 −1.97999
\(435\) 88.0513 4.22174
\(436\) 24.2442 1.16109
\(437\) −8.64552 −0.413571
\(438\) −8.47223 −0.404819
\(439\) −26.8861 −1.28320 −0.641602 0.767038i \(-0.721730\pi\)
−0.641602 + 0.767038i \(0.721730\pi\)
\(440\) −25.4602 −1.21377
\(441\) 1.13515 0.0540547
\(442\) −68.6686 −3.26623
\(443\) −2.33514 −0.110946 −0.0554730 0.998460i \(-0.517667\pi\)
−0.0554730 + 0.998460i \(0.517667\pi\)
\(444\) −64.9394 −3.08189
\(445\) −19.5008 −0.924425
\(446\) 71.3483 3.37844
\(447\) −20.5203 −0.970576
\(448\) 26.5896 1.25624
\(449\) −37.8827 −1.78780 −0.893898 0.448271i \(-0.852040\pi\)
−0.893898 + 0.448271i \(0.852040\pi\)
\(450\) −301.561 −14.2157
\(451\) −6.32655 −0.297906
\(452\) 24.7317 1.16328
\(453\) 48.2974 2.26921
\(454\) 27.5244 1.29179
\(455\) −69.8717 −3.27563
\(456\) −99.8181 −4.67441
\(457\) −32.6601 −1.52777 −0.763887 0.645350i \(-0.776711\pi\)
−0.763887 + 0.645350i \(0.776711\pi\)
\(458\) 60.2980 2.81754
\(459\) −76.3037 −3.56155
\(460\) −47.1062 −2.19634
\(461\) −32.1309 −1.49648 −0.748242 0.663426i \(-0.769102\pi\)
−0.748242 + 0.663426i \(0.769102\pi\)
\(462\) −18.0712 −0.840748
\(463\) −17.1377 −0.796455 −0.398227 0.917287i \(-0.630375\pi\)
−0.398227 + 0.917287i \(0.630375\pi\)
\(464\) 61.5319 2.85655
\(465\) 85.7569 3.97688
\(466\) 12.1136 0.561151
\(467\) 17.9473 0.830503 0.415251 0.909707i \(-0.363694\pi\)
0.415251 + 0.909707i \(0.363694\pi\)
\(468\) 242.245 11.1978
\(469\) −32.7708 −1.51322
\(470\) −70.5932 −3.25622
\(471\) −25.1946 −1.16090
\(472\) −12.9763 −0.597282
\(473\) 5.43939 0.250104
\(474\) −41.3062 −1.89726
\(475\) −54.5796 −2.50428
\(476\) 56.9468 2.61015
\(477\) −55.7431 −2.55230
\(478\) −3.63480 −0.166252
\(479\) 9.25808 0.423013 0.211506 0.977377i \(-0.432163\pi\)
0.211506 + 0.977377i \(0.432163\pi\)
\(480\) −168.533 −7.69246
\(481\) 23.7681 1.08373
\(482\) −52.8184 −2.40581
\(483\) −19.7827 −0.900144
\(484\) −50.9861 −2.31755
\(485\) 33.9945 1.54361
\(486\) 161.718 7.33566
\(487\) 1.99111 0.0902260 0.0451130 0.998982i \(-0.485635\pi\)
0.0451130 + 0.998982i \(0.485635\pi\)
\(488\) −5.73460 −0.259593
\(489\) 60.8200 2.75038
\(490\) 1.57652 0.0712198
\(491\) −20.9652 −0.946145 −0.473073 0.881023i \(-0.656855\pi\)
−0.473073 + 0.881023i \(0.656855\pi\)
\(492\) −135.146 −6.09284
\(493\) 26.2657 1.18295
\(494\) 61.7466 2.77811
\(495\) 27.5356 1.23763
\(496\) 59.9286 2.69087
\(497\) −38.2206 −1.71443
\(498\) −93.7436 −4.20075
\(499\) −26.5168 −1.18705 −0.593527 0.804814i \(-0.702265\pi\)
−0.593527 + 0.804814i \(0.702265\pi\)
\(500\) −190.780 −8.53194
\(501\) 48.7773 2.17921
\(502\) −29.9190 −1.33535
\(503\) 21.2881 0.949190 0.474595 0.880204i \(-0.342594\pi\)
0.474595 + 0.880204i \(0.342594\pi\)
\(504\) −167.398 −7.45650
\(505\) −42.1380 −1.87512
\(506\) 4.45912 0.198232
\(507\) −77.4062 −3.43773
\(508\) −27.5677 −1.22312
\(509\) 6.45756 0.286226 0.143113 0.989706i \(-0.454289\pi\)
0.143113 + 0.989706i \(0.454289\pi\)
\(510\) −166.737 −7.38326
\(511\) −2.57155 −0.113758
\(512\) 37.4177 1.65364
\(513\) 68.6120 3.02930
\(514\) 64.3396 2.83790
\(515\) −76.4634 −3.36938
\(516\) 116.195 5.11518
\(517\) 4.74494 0.208682
\(518\) −27.7593 −1.21967
\(519\) 36.5657 1.60506
\(520\) 199.059 8.72932
\(521\) −22.7340 −0.995994 −0.497997 0.867179i \(-0.665931\pi\)
−0.497997 + 0.867179i \(0.665931\pi\)
\(522\) −130.493 −5.71154
\(523\) −16.8033 −0.734756 −0.367378 0.930072i \(-0.619744\pi\)
−0.367378 + 0.930072i \(0.619744\pi\)
\(524\) 40.5670 1.77218
\(525\) −124.889 −5.45061
\(526\) −8.67354 −0.378184
\(527\) 25.5813 1.11434
\(528\) 26.2550 1.14260
\(529\) −18.1186 −0.787763
\(530\) −77.4171 −3.36278
\(531\) 14.0340 0.609026
\(532\) −51.2063 −2.22008
\(533\) 49.4639 2.14252
\(534\) 39.4329 1.70643
\(535\) 72.3523 3.12806
\(536\) 93.3616 4.03261
\(537\) −67.8887 −2.92961
\(538\) 29.2017 1.25898
\(539\) −0.105966 −0.00456428
\(540\) 373.842 16.0876
\(541\) −17.9150 −0.770227 −0.385114 0.922869i \(-0.625838\pi\)
−0.385114 + 0.922869i \(0.625838\pi\)
\(542\) −72.4148 −3.11048
\(543\) −7.48139 −0.321057
\(544\) −50.2736 −2.15546
\(545\) −21.5461 −0.922932
\(546\) 141.289 6.04660
\(547\) 37.1556 1.58866 0.794330 0.607487i \(-0.207822\pi\)
0.794330 + 0.607487i \(0.207822\pi\)
\(548\) −20.8474 −0.890558
\(549\) 6.20206 0.264697
\(550\) 28.1507 1.20035
\(551\) −23.6180 −1.00616
\(552\) 56.3594 2.39882
\(553\) −12.5375 −0.533150
\(554\) 52.5440 2.23238
\(555\) 57.7123 2.44975
\(556\) 14.4742 0.613842
\(557\) −7.10504 −0.301050 −0.150525 0.988606i \(-0.548096\pi\)
−0.150525 + 0.988606i \(0.548096\pi\)
\(558\) −127.093 −5.38028
\(559\) −42.5277 −1.79873
\(560\) −118.561 −5.01010
\(561\) 11.2073 0.473173
\(562\) 65.3953 2.75853
\(563\) 40.6571 1.71349 0.856746 0.515739i \(-0.172483\pi\)
0.856746 + 0.515739i \(0.172483\pi\)
\(564\) 101.360 4.26802
\(565\) −21.9794 −0.924679
\(566\) −34.9711 −1.46995
\(567\) 91.0193 3.82245
\(568\) 108.888 4.56883
\(569\) 24.3221 1.01964 0.509819 0.860282i \(-0.329713\pi\)
0.509819 + 0.860282i \(0.329713\pi\)
\(570\) 149.930 6.27987
\(571\) −3.25266 −0.136120 −0.0680599 0.997681i \(-0.521681\pi\)
−0.0680599 + 0.997681i \(0.521681\pi\)
\(572\) −22.6135 −0.945519
\(573\) −9.21557 −0.384986
\(574\) −57.7700 −2.41127
\(575\) 30.8168 1.28515
\(576\) 81.9267 3.41361
\(577\) 7.35010 0.305989 0.152994 0.988227i \(-0.451108\pi\)
0.152994 + 0.988227i \(0.451108\pi\)
\(578\) −5.08885 −0.211668
\(579\) −50.5985 −2.10280
\(580\) −128.686 −5.34340
\(581\) −28.4537 −1.18046
\(582\) −68.7409 −2.84940
\(583\) 5.20361 0.215512
\(584\) 7.32614 0.303158
\(585\) −215.285 −8.90096
\(586\) 26.3227 1.08738
\(587\) 40.7603 1.68236 0.841178 0.540759i \(-0.181863\pi\)
0.841178 + 0.540759i \(0.181863\pi\)
\(588\) −2.26361 −0.0933497
\(589\) −23.0026 −0.947807
\(590\) 19.4908 0.802423
\(591\) 0.611955 0.0251725
\(592\) 40.3305 1.65757
\(593\) −26.3182 −1.08076 −0.540379 0.841422i \(-0.681719\pi\)
−0.540379 + 0.841422i \(0.681719\pi\)
\(594\) −35.3882 −1.45200
\(595\) −50.6092 −2.07478
\(596\) 29.9902 1.22845
\(597\) 44.9614 1.84015
\(598\) −34.8635 −1.42567
\(599\) −25.3650 −1.03639 −0.518194 0.855263i \(-0.673395\pi\)
−0.518194 + 0.855263i \(0.673395\pi\)
\(600\) 355.800 14.5255
\(601\) −13.9348 −0.568413 −0.284206 0.958763i \(-0.591730\pi\)
−0.284206 + 0.958763i \(0.591730\pi\)
\(602\) 49.6690 2.02436
\(603\) −100.972 −4.11190
\(604\) −70.5861 −2.87211
\(605\) 45.3119 1.84219
\(606\) 85.2081 3.46134
\(607\) −17.7557 −0.720682 −0.360341 0.932821i \(-0.617340\pi\)
−0.360341 + 0.932821i \(0.617340\pi\)
\(608\) 45.2058 1.83334
\(609\) −54.0429 −2.18993
\(610\) 8.61355 0.348752
\(611\) −37.0981 −1.50083
\(612\) 175.462 7.09263
\(613\) −12.4015 −0.500890 −0.250445 0.968131i \(-0.580577\pi\)
−0.250445 + 0.968131i \(0.580577\pi\)
\(614\) −37.6669 −1.52011
\(615\) 120.106 4.84312
\(616\) 15.6266 0.629613
\(617\) −21.6689 −0.872355 −0.436178 0.899861i \(-0.643668\pi\)
−0.436178 + 0.899861i \(0.643668\pi\)
\(618\) 154.618 6.21965
\(619\) −20.1804 −0.811117 −0.405559 0.914069i \(-0.632923\pi\)
−0.405559 + 0.914069i \(0.632923\pi\)
\(620\) −125.333 −5.03349
\(621\) −38.7398 −1.55458
\(622\) 7.11021 0.285093
\(623\) 11.9689 0.479524
\(624\) −205.274 −8.21752
\(625\) 99.8079 3.99232
\(626\) 45.5770 1.82162
\(627\) −10.0776 −0.402459
\(628\) 36.8216 1.46934
\(629\) 17.2156 0.686431
\(630\) 251.437 10.0175
\(631\) 0.668608 0.0266169 0.0133084 0.999911i \(-0.495764\pi\)
0.0133084 + 0.999911i \(0.495764\pi\)
\(632\) 35.7185 1.42081
\(633\) −23.4326 −0.931361
\(634\) −13.8800 −0.551244
\(635\) 24.4997 0.972241
\(636\) 111.158 4.40769
\(637\) 0.828490 0.0328260
\(638\) 12.1816 0.482272
\(639\) −117.764 −4.65866
\(640\) 13.2066 0.522036
\(641\) −24.3927 −0.963453 −0.481727 0.876322i \(-0.659990\pi\)
−0.481727 + 0.876322i \(0.659990\pi\)
\(642\) −146.305 −5.77419
\(643\) −9.64985 −0.380553 −0.190277 0.981731i \(-0.560938\pi\)
−0.190277 + 0.981731i \(0.560938\pi\)
\(644\) 28.9122 1.13930
\(645\) −103.263 −4.06599
\(646\) 44.7241 1.75965
\(647\) −2.54788 −0.100167 −0.0500837 0.998745i \(-0.515949\pi\)
−0.0500837 + 0.998745i \(0.515949\pi\)
\(648\) −259.307 −10.1866
\(649\) −1.31008 −0.0514250
\(650\) −220.095 −8.63283
\(651\) −52.6347 −2.06292
\(652\) −88.8878 −3.48112
\(653\) −27.5261 −1.07718 −0.538590 0.842568i \(-0.681043\pi\)
−0.538590 + 0.842568i \(0.681043\pi\)
\(654\) 43.5687 1.70367
\(655\) −36.0523 −1.40868
\(656\) 83.9321 3.27700
\(657\) −7.92333 −0.309119
\(658\) 43.3277 1.68909
\(659\) 23.5063 0.915676 0.457838 0.889036i \(-0.348624\pi\)
0.457838 + 0.889036i \(0.348624\pi\)
\(660\) −54.9089 −2.13733
\(661\) 3.89497 0.151497 0.0757484 0.997127i \(-0.475865\pi\)
0.0757484 + 0.997127i \(0.475865\pi\)
\(662\) −46.7763 −1.81801
\(663\) −87.6238 −3.40303
\(664\) 81.0623 3.14583
\(665\) 45.5076 1.76471
\(666\) −85.5306 −3.31424
\(667\) 13.3353 0.516343
\(668\) −71.2875 −2.75820
\(669\) 91.0431 3.51993
\(670\) −140.232 −5.41764
\(671\) −0.578962 −0.0223506
\(672\) 103.440 3.99029
\(673\) 4.02640 0.155206 0.0776031 0.996984i \(-0.475273\pi\)
0.0776031 + 0.996984i \(0.475273\pi\)
\(674\) 51.5956 1.98739
\(675\) −244.567 −9.41337
\(676\) 113.128 4.35109
\(677\) 24.1497 0.928148 0.464074 0.885796i \(-0.346387\pi\)
0.464074 + 0.885796i \(0.346387\pi\)
\(678\) 44.4449 1.70690
\(679\) −20.8647 −0.800713
\(680\) 144.182 5.52912
\(681\) 35.1222 1.34589
\(682\) 11.8641 0.454301
\(683\) −14.8389 −0.567793 −0.283897 0.958855i \(-0.591627\pi\)
−0.283897 + 0.958855i \(0.591627\pi\)
\(684\) −157.775 −6.03267
\(685\) 18.5273 0.707893
\(686\) 48.1510 1.83841
\(687\) 76.9426 2.93554
\(688\) −72.1624 −2.75117
\(689\) −40.6842 −1.54994
\(690\) −84.6536 −3.22271
\(691\) 4.14764 0.157784 0.0788918 0.996883i \(-0.474862\pi\)
0.0788918 + 0.996883i \(0.474862\pi\)
\(692\) −53.4404 −2.03150
\(693\) −16.9004 −0.641993
\(694\) 56.3415 2.13869
\(695\) −12.8634 −0.487935
\(696\) 153.964 5.83600
\(697\) 35.8275 1.35706
\(698\) 66.6022 2.52093
\(699\) 15.4574 0.584652
\(700\) 182.524 6.89877
\(701\) −45.3272 −1.71199 −0.855993 0.516987i \(-0.827053\pi\)
−0.855993 + 0.516987i \(0.827053\pi\)
\(702\) 276.681 10.4427
\(703\) −15.4802 −0.583847
\(704\) −7.64786 −0.288239
\(705\) −90.0796 −3.39259
\(706\) −22.6575 −0.852727
\(707\) 25.8629 0.972674
\(708\) −27.9854 −1.05176
\(709\) 15.5043 0.582277 0.291139 0.956681i \(-0.405966\pi\)
0.291139 + 0.956681i \(0.405966\pi\)
\(710\) −163.553 −6.13803
\(711\) −38.6301 −1.44874
\(712\) −34.0985 −1.27790
\(713\) 12.9878 0.486396
\(714\) 102.338 3.82990
\(715\) 20.0969 0.751581
\(716\) 99.2186 3.70797
\(717\) −4.63814 −0.173215
\(718\) −9.16189 −0.341919
\(719\) −1.49333 −0.0556917 −0.0278458 0.999612i \(-0.508865\pi\)
−0.0278458 + 0.999612i \(0.508865\pi\)
\(720\) −365.304 −13.6141
\(721\) 46.9307 1.74779
\(722\) 9.68605 0.360478
\(723\) −67.3982 −2.50657
\(724\) 10.9340 0.406358
\(725\) 84.1862 3.12660
\(726\) −91.6259 −3.40056
\(727\) 44.2205 1.64005 0.820024 0.572329i \(-0.193960\pi\)
0.820024 + 0.572329i \(0.193960\pi\)
\(728\) −122.176 −4.52814
\(729\) 104.153 3.85753
\(730\) −11.0041 −0.407280
\(731\) −30.8035 −1.13931
\(732\) −12.3676 −0.457119
\(733\) −12.2263 −0.451587 −0.225794 0.974175i \(-0.572497\pi\)
−0.225794 + 0.974175i \(0.572497\pi\)
\(734\) −42.7688 −1.57862
\(735\) 2.01170 0.0742025
\(736\) −25.5242 −0.940834
\(737\) 9.42573 0.347201
\(738\) −177.998 −6.55221
\(739\) 31.2875 1.15093 0.575464 0.817827i \(-0.304821\pi\)
0.575464 + 0.817827i \(0.304821\pi\)
\(740\) −84.3460 −3.10062
\(741\) 78.7910 2.89446
\(742\) 47.5160 1.74437
\(743\) −0.0431752 −0.00158394 −0.000791972 1.00000i \(-0.500252\pi\)
−0.000791972 1.00000i \(0.500252\pi\)
\(744\) 149.952 5.49752
\(745\) −26.6526 −0.976476
\(746\) −51.0376 −1.86862
\(747\) −87.6701 −3.20768
\(748\) −16.3794 −0.598888
\(749\) −44.4074 −1.62261
\(750\) −342.846 −12.5190
\(751\) 4.81612 0.175743 0.0878714 0.996132i \(-0.471994\pi\)
0.0878714 + 0.996132i \(0.471994\pi\)
\(752\) −62.9493 −2.29553
\(753\) −38.1778 −1.39128
\(754\) −95.2409 −3.46847
\(755\) 62.7306 2.28300
\(756\) −229.451 −8.34506
\(757\) −34.8383 −1.26622 −0.633110 0.774062i \(-0.718222\pi\)
−0.633110 + 0.774062i \(0.718222\pi\)
\(758\) 11.9913 0.435542
\(759\) 5.69001 0.206534
\(760\) −129.648 −4.70282
\(761\) 2.21871 0.0804280 0.0402140 0.999191i \(-0.487196\pi\)
0.0402140 + 0.999191i \(0.487196\pi\)
\(762\) −49.5413 −1.79469
\(763\) 13.2242 0.478750
\(764\) 13.4685 0.487272
\(765\) −155.935 −5.63784
\(766\) 24.6262 0.889780
\(767\) 10.2428 0.369845
\(768\) 40.0035 1.44350
\(769\) −27.7572 −1.00095 −0.500474 0.865751i \(-0.666841\pi\)
−0.500474 + 0.865751i \(0.666841\pi\)
\(770\) −23.4716 −0.845858
\(771\) 82.0998 2.95675
\(772\) 73.9491 2.66149
\(773\) 35.4441 1.27484 0.637418 0.770518i \(-0.280002\pi\)
0.637418 + 0.770518i \(0.280002\pi\)
\(774\) 153.038 5.50084
\(775\) 81.9926 2.94526
\(776\) 59.4419 2.13384
\(777\) −35.4219 −1.27075
\(778\) −78.5822 −2.81731
\(779\) −32.2160 −1.15426
\(780\) 429.303 15.3715
\(781\) 10.9932 0.393369
\(782\) −25.2522 −0.903016
\(783\) −105.830 −3.78207
\(784\) 1.40581 0.0502076
\(785\) −32.7238 −1.16796
\(786\) 72.9021 2.60033
\(787\) 38.5862 1.37545 0.687724 0.725972i \(-0.258610\pi\)
0.687724 + 0.725972i \(0.258610\pi\)
\(788\) −0.894367 −0.0318605
\(789\) −11.0678 −0.394023
\(790\) −53.6503 −1.90879
\(791\) 13.4902 0.479656
\(792\) 48.1479 1.71086
\(793\) 4.52659 0.160744
\(794\) −33.4983 −1.18881
\(795\) −98.7871 −3.50362
\(796\) −65.7107 −2.32905
\(797\) 30.9733 1.09713 0.548565 0.836108i \(-0.315174\pi\)
0.548565 + 0.836108i \(0.315174\pi\)
\(798\) −92.0218 −3.25754
\(799\) −26.8708 −0.950619
\(800\) −161.135 −5.69700
\(801\) 36.8781 1.30302
\(802\) −60.3890 −2.13241
\(803\) 0.739643 0.0261014
\(804\) 201.349 7.10104
\(805\) −25.6946 −0.905615
\(806\) −92.7593 −3.26731
\(807\) 37.2625 1.31170
\(808\) −73.6815 −2.59210
\(809\) 18.4802 0.649729 0.324865 0.945761i \(-0.394681\pi\)
0.324865 + 0.945761i \(0.394681\pi\)
\(810\) 389.487 13.6852
\(811\) 17.0647 0.599223 0.299611 0.954061i \(-0.403143\pi\)
0.299611 + 0.954061i \(0.403143\pi\)
\(812\) 78.9831 2.77176
\(813\) −92.4040 −3.24075
\(814\) 7.98428 0.279849
\(815\) 78.9956 2.76709
\(816\) −148.683 −5.20495
\(817\) 27.6984 0.969044
\(818\) −50.8480 −1.77786
\(819\) 132.135 4.61717
\(820\) −175.533 −6.12988
\(821\) 0.0310372 0.00108321 0.000541603 1.00000i \(-0.499828\pi\)
0.000541603 1.00000i \(0.499828\pi\)
\(822\) −37.4645 −1.30672
\(823\) −25.9165 −0.903391 −0.451696 0.892172i \(-0.649181\pi\)
−0.451696 + 0.892172i \(0.649181\pi\)
\(824\) −133.702 −4.65773
\(825\) 35.9213 1.25062
\(826\) −11.9628 −0.416238
\(827\) 48.3252 1.68043 0.840216 0.542251i \(-0.182428\pi\)
0.840216 + 0.542251i \(0.182428\pi\)
\(828\) 89.0830 3.09585
\(829\) −30.1488 −1.04711 −0.523555 0.851992i \(-0.675394\pi\)
−0.523555 + 0.851992i \(0.675394\pi\)
\(830\) −121.758 −4.22629
\(831\) 67.0481 2.32587
\(832\) 59.7944 2.07300
\(833\) 0.600089 0.0207919
\(834\) 26.0113 0.900696
\(835\) 63.3540 2.19246
\(836\) 14.7283 0.509387
\(837\) −103.073 −3.56272
\(838\) −36.6989 −1.26774
\(839\) −14.1237 −0.487603 −0.243802 0.969825i \(-0.578395\pi\)
−0.243802 + 0.969825i \(0.578395\pi\)
\(840\) −296.661 −10.2358
\(841\) 7.42960 0.256193
\(842\) 86.5550 2.98288
\(843\) 83.4468 2.87406
\(844\) 34.2464 1.17881
\(845\) −100.538 −3.45863
\(846\) 133.499 4.58980
\(847\) −27.8109 −0.955593
\(848\) −69.0344 −2.37065
\(849\) −44.6245 −1.53151
\(850\) −159.418 −5.46800
\(851\) 8.74046 0.299619
\(852\) 234.834 8.04528
\(853\) 8.82232 0.302071 0.151035 0.988528i \(-0.451739\pi\)
0.151035 + 0.988528i \(0.451739\pi\)
\(854\) −5.28670 −0.180907
\(855\) 140.216 4.79529
\(856\) 126.513 4.32414
\(857\) −6.95385 −0.237539 −0.118769 0.992922i \(-0.537895\pi\)
−0.118769 + 0.992922i \(0.537895\pi\)
\(858\) −40.6383 −1.38737
\(859\) 6.33425 0.216122 0.108061 0.994144i \(-0.465536\pi\)
0.108061 + 0.994144i \(0.465536\pi\)
\(860\) 150.918 5.14627
\(861\) −73.7167 −2.51226
\(862\) 66.7593 2.27383
\(863\) −11.8354 −0.402883 −0.201441 0.979501i \(-0.564563\pi\)
−0.201441 + 0.979501i \(0.564563\pi\)
\(864\) 202.563 6.89135
\(865\) 47.4930 1.61481
\(866\) 56.8560 1.93204
\(867\) −6.49357 −0.220533
\(868\) 76.9251 2.61101
\(869\) 3.60612 0.122329
\(870\) −231.259 −7.84041
\(871\) −73.6946 −2.49705
\(872\) −37.6749 −1.27583
\(873\) −64.2873 −2.17580
\(874\) 22.7067 0.768065
\(875\) −104.063 −3.51797
\(876\) 15.8000 0.533833
\(877\) 0.952410 0.0321606 0.0160803 0.999871i \(-0.494881\pi\)
0.0160803 + 0.999871i \(0.494881\pi\)
\(878\) 70.6140 2.38311
\(879\) 33.5888 1.13292
\(880\) 34.1011 1.14955
\(881\) −16.1826 −0.545204 −0.272602 0.962127i \(-0.587884\pi\)
−0.272602 + 0.962127i \(0.587884\pi\)
\(882\) −2.98137 −0.100388
\(883\) −3.21186 −0.108088 −0.0540438 0.998539i \(-0.517211\pi\)
−0.0540438 + 0.998539i \(0.517211\pi\)
\(884\) 128.061 4.30717
\(885\) 24.8710 0.836028
\(886\) 6.13304 0.206044
\(887\) 44.4044 1.49095 0.745477 0.666531i \(-0.232222\pi\)
0.745477 + 0.666531i \(0.232222\pi\)
\(888\) 100.914 3.38646
\(889\) −15.0371 −0.504328
\(890\) 51.2170 1.71680
\(891\) −26.1795 −0.877046
\(892\) −133.059 −4.45513
\(893\) 24.1621 0.808554
\(894\) 53.8947 1.80251
\(895\) −88.1766 −2.94742
\(896\) −8.10576 −0.270794
\(897\) −44.4871 −1.48538
\(898\) 99.4956 3.32021
\(899\) 35.4804 1.18334
\(900\) 562.386 18.7462
\(901\) −29.4682 −0.981729
\(902\) 16.6161 0.553257
\(903\) 63.3795 2.10914
\(904\) −38.4325 −1.27825
\(905\) −9.71714 −0.323009
\(906\) −126.849 −4.21427
\(907\) 32.5162 1.07968 0.539842 0.841767i \(-0.318484\pi\)
0.539842 + 0.841767i \(0.318484\pi\)
\(908\) −51.3308 −1.70347
\(909\) 79.6876 2.64307
\(910\) 183.512 6.08335
\(911\) 0.200172 0.00663199 0.00331599 0.999995i \(-0.498944\pi\)
0.00331599 + 0.999995i \(0.498944\pi\)
\(912\) 133.695 4.42709
\(913\) 8.18400 0.270851
\(914\) 85.7788 2.83731
\(915\) 10.9912 0.363358
\(916\) −112.451 −3.71548
\(917\) 22.1277 0.730721
\(918\) 200.405 6.61435
\(919\) −16.0897 −0.530750 −0.265375 0.964145i \(-0.585496\pi\)
−0.265375 + 0.964145i \(0.585496\pi\)
\(920\) 73.2020 2.41340
\(921\) −48.0644 −1.58378
\(922\) 84.3889 2.77920
\(923\) −85.9501 −2.82908
\(924\) 33.7012 1.10869
\(925\) 55.1790 1.81427
\(926\) 45.0105 1.47914
\(927\) 144.601 4.74931
\(928\) −69.7276 −2.28892
\(929\) −2.71569 −0.0890988 −0.0445494 0.999007i \(-0.514185\pi\)
−0.0445494 + 0.999007i \(0.514185\pi\)
\(930\) −225.233 −7.38568
\(931\) −0.539598 −0.0176846
\(932\) −22.5908 −0.739987
\(933\) 9.07289 0.297033
\(934\) −47.1370 −1.54237
\(935\) 14.5565 0.476049
\(936\) −376.443 −12.3044
\(937\) −47.6535 −1.55677 −0.778386 0.627787i \(-0.783961\pi\)
−0.778386 + 0.627787i \(0.783961\pi\)
\(938\) 86.0697 2.81027
\(939\) 58.1579 1.89791
\(940\) 131.650 4.29396
\(941\) −18.6270 −0.607222 −0.303611 0.952796i \(-0.598192\pi\)
−0.303611 + 0.952796i \(0.598192\pi\)
\(942\) 66.1713 2.15598
\(943\) 18.1898 0.592342
\(944\) 17.3803 0.565681
\(945\) 203.916 6.63338
\(946\) −14.2861 −0.464481
\(947\) 19.5673 0.635853 0.317926 0.948115i \(-0.397013\pi\)
0.317926 + 0.948115i \(0.397013\pi\)
\(948\) 77.0326 2.50190
\(949\) −5.78286 −0.187720
\(950\) 143.348 4.65084
\(951\) −17.7114 −0.574331
\(952\) −88.4939 −2.86810
\(953\) 35.7342 1.15754 0.578772 0.815490i \(-0.303532\pi\)
0.578772 + 0.815490i \(0.303532\pi\)
\(954\) 146.404 4.74001
\(955\) −11.9696 −0.387326
\(956\) 6.77860 0.219235
\(957\) 15.5441 0.502470
\(958\) −24.3155 −0.785599
\(959\) −11.3715 −0.367203
\(960\) 145.190 4.68597
\(961\) 3.55586 0.114705
\(962\) −62.4247 −2.01265
\(963\) −136.826 −4.40916
\(964\) 98.5018 3.17253
\(965\) −65.7194 −2.11558
\(966\) 51.9575 1.67170
\(967\) −56.2320 −1.80830 −0.904149 0.427217i \(-0.859494\pi\)
−0.904149 + 0.427217i \(0.859494\pi\)
\(968\) 79.2311 2.54658
\(969\) 57.0696 1.83334
\(970\) −89.2836 −2.86672
\(971\) −19.9665 −0.640756 −0.320378 0.947290i \(-0.603810\pi\)
−0.320378 + 0.947290i \(0.603810\pi\)
\(972\) −301.590 −9.67350
\(973\) 7.89510 0.253105
\(974\) −5.22949 −0.167564
\(975\) −280.849 −8.99438
\(976\) 7.68087 0.245859
\(977\) 40.3805 1.29189 0.645943 0.763386i \(-0.276465\pi\)
0.645943 + 0.763386i \(0.276465\pi\)
\(978\) −159.738 −5.10787
\(979\) −3.44256 −0.110025
\(980\) −2.94007 −0.0939171
\(981\) 40.7460 1.30092
\(982\) 55.0632 1.75714
\(983\) 59.0630 1.88382 0.941909 0.335868i \(-0.109030\pi\)
0.941909 + 0.335868i \(0.109030\pi\)
\(984\) 210.013 6.69498
\(985\) 0.794833 0.0253255
\(986\) −68.9846 −2.19692
\(987\) 55.2878 1.75983
\(988\) −115.152 −3.66348
\(989\) −15.6391 −0.497295
\(990\) −72.3197 −2.29847
\(991\) 34.6694 1.10131 0.550655 0.834733i \(-0.314378\pi\)
0.550655 + 0.834733i \(0.314378\pi\)
\(992\) −67.9107 −2.15617
\(993\) −59.6883 −1.89415
\(994\) 100.383 3.18396
\(995\) 58.3978 1.85133
\(996\) 174.824 5.53951
\(997\) −46.2891 −1.46599 −0.732996 0.680233i \(-0.761879\pi\)
−0.732996 + 0.680233i \(0.761879\pi\)
\(998\) 69.6439 2.20454
\(999\) −69.3655 −2.19463
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.1.19 243
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6037.2.a.a.1.19 243 1.1 even 1 trivial