Properties

Label 4033.2.a.c.1.6
Level $4033$
Weight $2$
Character 4033.1
Self dual yes
Analytic conductor $32.204$
Analytic rank $1$
Dimension $77$
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] = [4033,2,Mod(1,4033)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4033, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4033.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4033 = 37 \cdot 109 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4033.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: \(32.2036671352\)
Analytic rank: \(1\)
Dimension: \(77\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) \(=\) 4033.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.57274 q^{2} -3.14788 q^{3} +4.61898 q^{4} -2.11075 q^{5} +8.09868 q^{6} -0.361357 q^{7} -6.73794 q^{8} +6.90917 q^{9} +O(q^{10})\) \(q-2.57274 q^{2} -3.14788 q^{3} +4.61898 q^{4} -2.11075 q^{5} +8.09868 q^{6} -0.361357 q^{7} -6.73794 q^{8} +6.90917 q^{9} +5.43041 q^{10} +6.02489 q^{11} -14.5400 q^{12} -5.65995 q^{13} +0.929676 q^{14} +6.64440 q^{15} +8.09699 q^{16} -1.42134 q^{17} -17.7755 q^{18} +6.49301 q^{19} -9.74952 q^{20} +1.13751 q^{21} -15.5005 q^{22} +7.36071 q^{23} +21.2102 q^{24} -0.544723 q^{25} +14.5616 q^{26} -12.3056 q^{27} -1.66910 q^{28} -9.80257 q^{29} -17.0943 q^{30} -1.31642 q^{31} -7.35555 q^{32} -18.9657 q^{33} +3.65675 q^{34} +0.762735 q^{35} +31.9133 q^{36} +1.00000 q^{37} -16.7048 q^{38} +17.8169 q^{39} +14.2221 q^{40} -3.12744 q^{41} -2.92651 q^{42} +12.1352 q^{43} +27.8288 q^{44} -14.5835 q^{45} -18.9372 q^{46} -10.1468 q^{47} -25.4884 q^{48} -6.86942 q^{49} +1.40143 q^{50} +4.47423 q^{51} -26.1432 q^{52} -3.72654 q^{53} +31.6591 q^{54} -12.7171 q^{55} +2.43480 q^{56} -20.4392 q^{57} +25.2194 q^{58} -5.13640 q^{59} +30.6903 q^{60} +4.78639 q^{61} +3.38680 q^{62} -2.49667 q^{63} +2.72991 q^{64} +11.9468 q^{65} +48.7937 q^{66} +2.48641 q^{67} -6.56516 q^{68} -23.1706 q^{69} -1.96232 q^{70} -9.23380 q^{71} -46.5535 q^{72} +4.42815 q^{73} -2.57274 q^{74} +1.71472 q^{75} +29.9911 q^{76} -2.17714 q^{77} -45.8381 q^{78} +5.02268 q^{79} -17.0907 q^{80} +18.0091 q^{81} +8.04609 q^{82} -10.4629 q^{83} +5.25413 q^{84} +3.00011 q^{85} -31.2208 q^{86} +30.8574 q^{87} -40.5954 q^{88} +8.14651 q^{89} +37.5196 q^{90} +2.04526 q^{91} +33.9989 q^{92} +4.14393 q^{93} +26.1051 q^{94} -13.7051 q^{95} +23.1544 q^{96} +8.63894 q^{97} +17.6732 q^{98} +41.6270 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 77 q - 9 q^{2} - 27 q^{3} + 73 q^{4} - 16 q^{5} - 2 q^{6} - 23 q^{7} - 24 q^{8} + 66 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 77 q - 9 q^{2} - 27 q^{3} + 73 q^{4} - 16 q^{5} - 2 q^{6} - 23 q^{7} - 24 q^{8} + 66 q^{9} - 11 q^{10} - 33 q^{11} - 52 q^{12} - 10 q^{13} - 18 q^{14} - 33 q^{15} + 53 q^{16} - 44 q^{17} - 27 q^{18} - 9 q^{19} - 45 q^{20} - 7 q^{21} - 3 q^{22} - 74 q^{23} + 21 q^{24} + 59 q^{25} - 47 q^{26} - 99 q^{27} - 49 q^{28} - 9 q^{29} - 39 q^{30} - 27 q^{31} - 47 q^{32} - 28 q^{33} - 23 q^{34} - 48 q^{35} + 77 q^{36} + 77 q^{37} - 66 q^{38} - 11 q^{39} - 2 q^{40} - 37 q^{41} - 24 q^{42} - 44 q^{43} - 54 q^{44} - 36 q^{45} - 41 q^{46} - 150 q^{47} - 135 q^{48} + 64 q^{49} + 4 q^{50} + 3 q^{51} - 57 q^{52} - 72 q^{53} + 21 q^{54} - 65 q^{55} - 92 q^{56} - 13 q^{57} - 12 q^{58} - 70 q^{59} - 22 q^{60} + 15 q^{61} - 86 q^{62} - 108 q^{63} + 10 q^{64} - 53 q^{65} - 55 q^{66} - 48 q^{67} - 70 q^{68} - 2 q^{69} + 11 q^{70} - 127 q^{71} - 12 q^{72} - 33 q^{73} - 9 q^{74} - 115 q^{75} - 24 q^{76} - 40 q^{77} + 81 q^{78} - 7 q^{79} - 62 q^{80} + 53 q^{81} - 68 q^{82} - 164 q^{83} + 7 q^{84} - 9 q^{85} - 50 q^{86} - 75 q^{87} - 82 q^{88} - 26 q^{89} + 23 q^{90} + 16 q^{91} - 117 q^{92} + 19 q^{93} + 23 q^{94} - 92 q^{95} - 35 q^{96} - 19 q^{97} - 10 q^{98} - 19 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.57274 −1.81920 −0.909600 0.415485i \(-0.863612\pi\)
−0.909600 + 0.415485i \(0.863612\pi\)
\(3\) −3.14788 −1.81743 −0.908716 0.417416i \(-0.862936\pi\)
−0.908716 + 0.417416i \(0.862936\pi\)
\(4\) 4.61898 2.30949
\(5\) −2.11075 −0.943957 −0.471979 0.881610i \(-0.656460\pi\)
−0.471979 + 0.881610i \(0.656460\pi\)
\(6\) 8.09868 3.30627
\(7\) −0.361357 −0.136580 −0.0682900 0.997666i \(-0.521754\pi\)
−0.0682900 + 0.997666i \(0.521754\pi\)
\(8\) −6.73794 −2.38222
\(9\) 6.90917 2.30306
\(10\) 5.43041 1.71725
\(11\) 6.02489 1.81657 0.908287 0.418348i \(-0.137391\pi\)
0.908287 + 0.418348i \(0.137391\pi\)
\(12\) −14.5400 −4.19734
\(13\) −5.65995 −1.56979 −0.784894 0.619630i \(-0.787283\pi\)
−0.784894 + 0.619630i \(0.787283\pi\)
\(14\) 0.929676 0.248466
\(15\) 6.64440 1.71558
\(16\) 8.09699 2.02425
\(17\) −1.42134 −0.344727 −0.172363 0.985033i \(-0.555140\pi\)
−0.172363 + 0.985033i \(0.555140\pi\)
\(18\) −17.7755 −4.18972
\(19\) 6.49301 1.48960 0.744800 0.667288i \(-0.232545\pi\)
0.744800 + 0.667288i \(0.232545\pi\)
\(20\) −9.74952 −2.18006
\(21\) 1.13751 0.248225
\(22\) −15.5005 −3.30471
\(23\) 7.36071 1.53481 0.767407 0.641161i \(-0.221547\pi\)
0.767407 + 0.641161i \(0.221547\pi\)
\(24\) 21.2102 4.32952
\(25\) −0.544723 −0.108945
\(26\) 14.5616 2.85576
\(27\) −12.3056 −2.36821
\(28\) −1.66910 −0.315430
\(29\) −9.80257 −1.82029 −0.910146 0.414287i \(-0.864031\pi\)
−0.910146 + 0.414287i \(0.864031\pi\)
\(30\) −17.0943 −3.12098
\(31\) −1.31642 −0.236436 −0.118218 0.992988i \(-0.537718\pi\)
−0.118218 + 0.992988i \(0.537718\pi\)
\(32\) −7.35555 −1.30029
\(33\) −18.9657 −3.30150
\(34\) 3.65675 0.627127
\(35\) 0.762735 0.128926
\(36\) 31.9133 5.31888
\(37\) 1.00000 0.164399
\(38\) −16.7048 −2.70988
\(39\) 17.8169 2.85298
\(40\) 14.2221 2.24871
\(41\) −3.12744 −0.488425 −0.244212 0.969722i \(-0.578529\pi\)
−0.244212 + 0.969722i \(0.578529\pi\)
\(42\) −2.92651 −0.451570
\(43\) 12.1352 1.85061 0.925304 0.379227i \(-0.123810\pi\)
0.925304 + 0.379227i \(0.123810\pi\)
\(44\) 27.8288 4.19536
\(45\) −14.5835 −2.17399
\(46\) −18.9372 −2.79213
\(47\) −10.1468 −1.48007 −0.740034 0.672569i \(-0.765191\pi\)
−0.740034 + 0.672569i \(0.765191\pi\)
\(48\) −25.4884 −3.67893
\(49\) −6.86942 −0.981346
\(50\) 1.40143 0.198192
\(51\) 4.47423 0.626517
\(52\) −26.1432 −3.62541
\(53\) −3.72654 −0.511880 −0.255940 0.966693i \(-0.582385\pi\)
−0.255940 + 0.966693i \(0.582385\pi\)
\(54\) 31.6591 4.30825
\(55\) −12.7171 −1.71477
\(56\) 2.43480 0.325364
\(57\) −20.4392 −2.70724
\(58\) 25.2194 3.31148
\(59\) −5.13640 −0.668702 −0.334351 0.942449i \(-0.608517\pi\)
−0.334351 + 0.942449i \(0.608517\pi\)
\(60\) 30.6903 3.96211
\(61\) 4.78639 0.612834 0.306417 0.951897i \(-0.400870\pi\)
0.306417 + 0.951897i \(0.400870\pi\)
\(62\) 3.38680 0.430124
\(63\) −2.49667 −0.314551
\(64\) 2.72991 0.341239
\(65\) 11.9468 1.48181
\(66\) 48.7937 6.00608
\(67\) 2.48641 0.303763 0.151882 0.988399i \(-0.451467\pi\)
0.151882 + 0.988399i \(0.451467\pi\)
\(68\) −6.56516 −0.796142
\(69\) −23.1706 −2.78942
\(70\) −1.96232 −0.234542
\(71\) −9.23380 −1.09585 −0.547925 0.836527i \(-0.684582\pi\)
−0.547925 + 0.836527i \(0.684582\pi\)
\(72\) −46.5535 −5.48639
\(73\) 4.42815 0.518276 0.259138 0.965840i \(-0.416562\pi\)
0.259138 + 0.965840i \(0.416562\pi\)
\(74\) −2.57274 −0.299075
\(75\) 1.71472 0.197999
\(76\) 29.9911 3.44021
\(77\) −2.17714 −0.248108
\(78\) −45.8381 −5.19014
\(79\) 5.02268 0.565096 0.282548 0.959253i \(-0.408820\pi\)
0.282548 + 0.959253i \(0.408820\pi\)
\(80\) −17.0907 −1.91080
\(81\) 18.0091 2.00101
\(82\) 8.04609 0.888542
\(83\) −10.4629 −1.14846 −0.574228 0.818695i \(-0.694698\pi\)
−0.574228 + 0.818695i \(0.694698\pi\)
\(84\) 5.25413 0.573272
\(85\) 3.00011 0.325407
\(86\) −31.2208 −3.36663
\(87\) 30.8574 3.30826
\(88\) −40.5954 −4.32748
\(89\) 8.14651 0.863528 0.431764 0.901987i \(-0.357891\pi\)
0.431764 + 0.901987i \(0.357891\pi\)
\(90\) 37.5196 3.95492
\(91\) 2.04526 0.214402
\(92\) 33.9989 3.54463
\(93\) 4.14393 0.429706
\(94\) 26.1051 2.69254
\(95\) −13.7051 −1.40612
\(96\) 23.1544 2.36319
\(97\) 8.63894 0.877152 0.438576 0.898694i \(-0.355483\pi\)
0.438576 + 0.898694i \(0.355483\pi\)
\(98\) 17.6732 1.78526
\(99\) 41.6270 4.18367
\(100\) −2.51606 −0.251606
\(101\) −5.51163 −0.548428 −0.274214 0.961669i \(-0.588418\pi\)
−0.274214 + 0.961669i \(0.588418\pi\)
\(102\) −11.5110 −1.13976
\(103\) −2.22124 −0.218866 −0.109433 0.993994i \(-0.534903\pi\)
−0.109433 + 0.993994i \(0.534903\pi\)
\(104\) 38.1364 3.73958
\(105\) −2.40100 −0.234314
\(106\) 9.58741 0.931212
\(107\) 16.7560 1.61987 0.809934 0.586521i \(-0.199503\pi\)
0.809934 + 0.586521i \(0.199503\pi\)
\(108\) −56.8393 −5.46936
\(109\) 1.00000 0.0957826
\(110\) 32.7177 3.11951
\(111\) −3.14788 −0.298784
\(112\) −2.92590 −0.276472
\(113\) −16.5451 −1.55643 −0.778217 0.627996i \(-0.783875\pi\)
−0.778217 + 0.627996i \(0.783875\pi\)
\(114\) 52.5848 4.92502
\(115\) −15.5366 −1.44880
\(116\) −45.2779 −4.20394
\(117\) −39.1056 −3.61531
\(118\) 13.2146 1.21650
\(119\) 0.513612 0.0470828
\(120\) −44.7696 −4.08688
\(121\) 25.2993 2.29994
\(122\) −12.3141 −1.11487
\(123\) 9.84483 0.887678
\(124\) −6.08050 −0.546045
\(125\) 11.7035 1.04680
\(126\) 6.42329 0.572232
\(127\) −6.09011 −0.540410 −0.270205 0.962803i \(-0.587092\pi\)
−0.270205 + 0.962803i \(0.587092\pi\)
\(128\) 7.68775 0.679507
\(129\) −38.2003 −3.36335
\(130\) −30.7359 −2.69571
\(131\) 7.66576 0.669761 0.334880 0.942261i \(-0.391304\pi\)
0.334880 + 0.942261i \(0.391304\pi\)
\(132\) −87.6019 −7.62477
\(133\) −2.34629 −0.203449
\(134\) −6.39688 −0.552606
\(135\) 25.9741 2.23549
\(136\) 9.57693 0.821215
\(137\) 5.38160 0.459781 0.229891 0.973216i \(-0.426163\pi\)
0.229891 + 0.973216i \(0.426163\pi\)
\(138\) 59.6120 5.07451
\(139\) −1.50088 −0.127303 −0.0636515 0.997972i \(-0.520275\pi\)
−0.0636515 + 0.997972i \(0.520275\pi\)
\(140\) 3.52305 0.297752
\(141\) 31.9411 2.68992
\(142\) 23.7561 1.99357
\(143\) −34.1006 −2.85164
\(144\) 55.9434 4.66195
\(145\) 20.6908 1.71828
\(146\) −11.3925 −0.942847
\(147\) 21.6241 1.78353
\(148\) 4.61898 0.379677
\(149\) −2.99909 −0.245695 −0.122847 0.992426i \(-0.539203\pi\)
−0.122847 + 0.992426i \(0.539203\pi\)
\(150\) −4.41153 −0.360200
\(151\) −3.49006 −0.284017 −0.142008 0.989865i \(-0.545356\pi\)
−0.142008 + 0.989865i \(0.545356\pi\)
\(152\) −43.7495 −3.54855
\(153\) −9.82030 −0.793925
\(154\) 5.60120 0.451358
\(155\) 2.77863 0.223185
\(156\) 82.2957 6.58893
\(157\) 14.3183 1.14272 0.571362 0.820698i \(-0.306415\pi\)
0.571362 + 0.820698i \(0.306415\pi\)
\(158\) −12.9220 −1.02802
\(159\) 11.7307 0.930307
\(160\) 15.5257 1.22742
\(161\) −2.65984 −0.209625
\(162\) −46.3326 −3.64024
\(163\) 22.9105 1.79449 0.897246 0.441531i \(-0.145564\pi\)
0.897246 + 0.441531i \(0.145564\pi\)
\(164\) −14.4456 −1.12801
\(165\) 40.0318 3.11647
\(166\) 26.9184 2.08927
\(167\) 7.38929 0.571801 0.285900 0.958259i \(-0.407707\pi\)
0.285900 + 0.958259i \(0.407707\pi\)
\(168\) −7.66446 −0.591326
\(169\) 19.0351 1.46423
\(170\) −7.71848 −0.591981
\(171\) 44.8613 3.43063
\(172\) 56.0524 4.27396
\(173\) −25.0782 −1.90666 −0.953329 0.301934i \(-0.902368\pi\)
−0.953329 + 0.301934i \(0.902368\pi\)
\(174\) −79.3879 −6.01838
\(175\) 0.196839 0.0148797
\(176\) 48.7835 3.67719
\(177\) 16.1688 1.21532
\(178\) −20.9588 −1.57093
\(179\) 24.9587 1.86550 0.932749 0.360526i \(-0.117403\pi\)
0.932749 + 0.360526i \(0.117403\pi\)
\(180\) −67.3610 −5.02080
\(181\) −5.75277 −0.427600 −0.213800 0.976877i \(-0.568584\pi\)
−0.213800 + 0.976877i \(0.568584\pi\)
\(182\) −5.26192 −0.390040
\(183\) −15.0670 −1.11378
\(184\) −49.5960 −3.65626
\(185\) −2.11075 −0.155186
\(186\) −10.6612 −0.781720
\(187\) −8.56345 −0.626221
\(188\) −46.8680 −3.41820
\(189\) 4.44671 0.323451
\(190\) 35.2597 2.55801
\(191\) −5.01845 −0.363123 −0.181561 0.983380i \(-0.558115\pi\)
−0.181561 + 0.983380i \(0.558115\pi\)
\(192\) −8.59345 −0.620179
\(193\) 3.53640 0.254556 0.127278 0.991867i \(-0.459376\pi\)
0.127278 + 0.991867i \(0.459376\pi\)
\(194\) −22.2257 −1.59571
\(195\) −37.6070 −2.69309
\(196\) −31.7297 −2.26641
\(197\) −8.67106 −0.617788 −0.308894 0.951097i \(-0.599959\pi\)
−0.308894 + 0.951097i \(0.599959\pi\)
\(198\) −107.095 −7.61093
\(199\) 7.09379 0.502865 0.251433 0.967875i \(-0.419098\pi\)
0.251433 + 0.967875i \(0.419098\pi\)
\(200\) 3.67031 0.259530
\(201\) −7.82693 −0.552069
\(202\) 14.1800 0.997699
\(203\) 3.54223 0.248616
\(204\) 20.6663 1.44693
\(205\) 6.60126 0.461052
\(206\) 5.71467 0.398160
\(207\) 50.8563 3.53476
\(208\) −45.8286 −3.17764
\(209\) 39.1197 2.70597
\(210\) 6.17714 0.426263
\(211\) 12.6517 0.870979 0.435489 0.900194i \(-0.356575\pi\)
0.435489 + 0.900194i \(0.356575\pi\)
\(212\) −17.2128 −1.18218
\(213\) 29.0669 1.99163
\(214\) −43.1089 −2.94686
\(215\) −25.6145 −1.74689
\(216\) 82.9144 5.64161
\(217\) 0.475697 0.0322924
\(218\) −2.57274 −0.174248
\(219\) −13.9393 −0.941930
\(220\) −58.7398 −3.96024
\(221\) 8.04474 0.541148
\(222\) 8.09868 0.543547
\(223\) 11.1399 0.745981 0.372990 0.927835i \(-0.378332\pi\)
0.372990 + 0.927835i \(0.378332\pi\)
\(224\) 2.65798 0.177594
\(225\) −3.76358 −0.250905
\(226\) 42.5662 2.83146
\(227\) −2.82180 −0.187289 −0.0936447 0.995606i \(-0.529852\pi\)
−0.0936447 + 0.995606i \(0.529852\pi\)
\(228\) −94.4084 −6.25235
\(229\) −21.8370 −1.44303 −0.721516 0.692398i \(-0.756554\pi\)
−0.721516 + 0.692398i \(0.756554\pi\)
\(230\) 39.9717 2.63565
\(231\) 6.85337 0.450919
\(232\) 66.0491 4.33634
\(233\) 9.44507 0.618767 0.309384 0.950937i \(-0.399877\pi\)
0.309384 + 0.950937i \(0.399877\pi\)
\(234\) 100.608 6.57697
\(235\) 21.4175 1.39712
\(236\) −23.7249 −1.54436
\(237\) −15.8108 −1.02702
\(238\) −1.32139 −0.0856530
\(239\) 4.67138 0.302166 0.151083 0.988521i \(-0.451724\pi\)
0.151083 + 0.988521i \(0.451724\pi\)
\(240\) 53.7996 3.47275
\(241\) −30.2526 −1.94874 −0.974371 0.224946i \(-0.927779\pi\)
−0.974371 + 0.224946i \(0.927779\pi\)
\(242\) −65.0886 −4.18405
\(243\) −19.7737 −1.26848
\(244\) 22.1082 1.41533
\(245\) 14.4996 0.926349
\(246\) −25.3282 −1.61486
\(247\) −36.7501 −2.33835
\(248\) 8.86994 0.563242
\(249\) 32.9361 2.08724
\(250\) −30.1101 −1.90433
\(251\) 3.70982 0.234162 0.117081 0.993122i \(-0.462646\pi\)
0.117081 + 0.993122i \(0.462646\pi\)
\(252\) −11.5321 −0.726453
\(253\) 44.3475 2.78810
\(254\) 15.6683 0.983114
\(255\) −9.44398 −0.591405
\(256\) −25.2384 −1.57740
\(257\) 15.5303 0.968751 0.484376 0.874860i \(-0.339047\pi\)
0.484376 + 0.874860i \(0.339047\pi\)
\(258\) 98.2794 6.11861
\(259\) −0.361357 −0.0224536
\(260\) 55.1818 3.42223
\(261\) −67.7276 −4.19223
\(262\) −19.7220 −1.21843
\(263\) −14.3488 −0.884786 −0.442393 0.896821i \(-0.645870\pi\)
−0.442393 + 0.896821i \(0.645870\pi\)
\(264\) 127.789 7.86490
\(265\) 7.86581 0.483193
\(266\) 6.03640 0.370115
\(267\) −25.6443 −1.56940
\(268\) 11.4847 0.701538
\(269\) 10.9408 0.667072 0.333536 0.942737i \(-0.391758\pi\)
0.333536 + 0.942737i \(0.391758\pi\)
\(270\) −66.8245 −4.06681
\(271\) 1.45386 0.0883158 0.0441579 0.999025i \(-0.485940\pi\)
0.0441579 + 0.999025i \(0.485940\pi\)
\(272\) −11.5086 −0.697812
\(273\) −6.43824 −0.389660
\(274\) −13.8455 −0.836434
\(275\) −3.28190 −0.197906
\(276\) −107.025 −6.44213
\(277\) −20.2827 −1.21867 −0.609334 0.792914i \(-0.708563\pi\)
−0.609334 + 0.792914i \(0.708563\pi\)
\(278\) 3.86137 0.231590
\(279\) −9.09535 −0.544525
\(280\) −5.13926 −0.307129
\(281\) −28.9772 −1.72863 −0.864317 0.502947i \(-0.832249\pi\)
−0.864317 + 0.502947i \(0.832249\pi\)
\(282\) −82.1759 −4.89351
\(283\) 19.6897 1.17043 0.585216 0.810878i \(-0.301010\pi\)
0.585216 + 0.810878i \(0.301010\pi\)
\(284\) −42.6507 −2.53085
\(285\) 43.1422 2.55552
\(286\) 87.7319 5.18770
\(287\) 1.13012 0.0667091
\(288\) −50.8207 −2.99464
\(289\) −14.9798 −0.881164
\(290\) −53.2320 −3.12589
\(291\) −27.1944 −1.59416
\(292\) 20.4535 1.19695
\(293\) 1.08123 0.0631663 0.0315832 0.999501i \(-0.489945\pi\)
0.0315832 + 0.999501i \(0.489945\pi\)
\(294\) −55.6332 −3.24459
\(295\) 10.8417 0.631227
\(296\) −6.73794 −0.391635
\(297\) −74.1399 −4.30204
\(298\) 7.71586 0.446968
\(299\) −41.6612 −2.40933
\(300\) 7.92027 0.457277
\(301\) −4.38515 −0.252756
\(302\) 8.97900 0.516684
\(303\) 17.3500 0.996729
\(304\) 52.5738 3.01532
\(305\) −10.1029 −0.578489
\(306\) 25.2651 1.44431
\(307\) 10.3642 0.591518 0.295759 0.955263i \(-0.404427\pi\)
0.295759 + 0.955263i \(0.404427\pi\)
\(308\) −10.0561 −0.573002
\(309\) 6.99221 0.397773
\(310\) −7.14869 −0.406019
\(311\) 9.03585 0.512376 0.256188 0.966627i \(-0.417533\pi\)
0.256188 + 0.966627i \(0.417533\pi\)
\(312\) −120.049 −6.79643
\(313\) −12.9425 −0.731553 −0.365776 0.930703i \(-0.619197\pi\)
−0.365776 + 0.930703i \(0.619197\pi\)
\(314\) −36.8372 −2.07884
\(315\) 5.26986 0.296923
\(316\) 23.1996 1.30508
\(317\) 4.99636 0.280624 0.140312 0.990107i \(-0.455189\pi\)
0.140312 + 0.990107i \(0.455189\pi\)
\(318\) −30.1801 −1.69241
\(319\) −59.0595 −3.30670
\(320\) −5.76217 −0.322115
\(321\) −52.7461 −2.94400
\(322\) 6.84307 0.381349
\(323\) −9.22880 −0.513504
\(324\) 83.1835 4.62131
\(325\) 3.08311 0.171020
\(326\) −58.9428 −3.26454
\(327\) −3.14788 −0.174078
\(328\) 21.0725 1.16354
\(329\) 3.66663 0.202148
\(330\) −102.991 −5.66949
\(331\) 18.5412 1.01912 0.509559 0.860435i \(-0.329808\pi\)
0.509559 + 0.860435i \(0.329808\pi\)
\(332\) −48.3281 −2.65235
\(333\) 6.90917 0.378620
\(334\) −19.0107 −1.04022
\(335\) −5.24820 −0.286740
\(336\) 9.21040 0.502468
\(337\) 12.5914 0.685895 0.342948 0.939355i \(-0.388575\pi\)
0.342948 + 0.939355i \(0.388575\pi\)
\(338\) −48.9722 −2.66374
\(339\) 52.0821 2.82871
\(340\) 13.8574 0.751524
\(341\) −7.93128 −0.429503
\(342\) −115.416 −6.24100
\(343\) 5.01181 0.270612
\(344\) −81.7665 −4.40856
\(345\) 48.9075 2.63309
\(346\) 64.5195 3.46859
\(347\) −28.3632 −1.52262 −0.761308 0.648391i \(-0.775442\pi\)
−0.761308 + 0.648391i \(0.775442\pi\)
\(348\) 142.529 7.64038
\(349\) 25.1264 1.34498 0.672492 0.740105i \(-0.265224\pi\)
0.672492 + 0.740105i \(0.265224\pi\)
\(350\) −0.506416 −0.0270691
\(351\) 69.6491 3.71759
\(352\) −44.3164 −2.36207
\(353\) −6.76895 −0.360275 −0.180137 0.983641i \(-0.557654\pi\)
−0.180137 + 0.983641i \(0.557654\pi\)
\(354\) −41.5980 −2.21091
\(355\) 19.4903 1.03444
\(356\) 37.6285 1.99431
\(357\) −1.61679 −0.0855697
\(358\) −64.2121 −3.39371
\(359\) −19.0913 −1.00760 −0.503800 0.863820i \(-0.668065\pi\)
−0.503800 + 0.863820i \(0.668065\pi\)
\(360\) 98.2630 5.17891
\(361\) 23.1592 1.21891
\(362\) 14.8004 0.777890
\(363\) −79.6394 −4.17998
\(364\) 9.44702 0.495158
\(365\) −9.34673 −0.489230
\(366\) 38.7634 2.02620
\(367\) −23.7962 −1.24215 −0.621075 0.783751i \(-0.713304\pi\)
−0.621075 + 0.783751i \(0.713304\pi\)
\(368\) 59.5995 3.10684
\(369\) −21.6080 −1.12487
\(370\) 5.43041 0.282314
\(371\) 1.34661 0.0699126
\(372\) 19.1407 0.992400
\(373\) 10.0157 0.518592 0.259296 0.965798i \(-0.416509\pi\)
0.259296 + 0.965798i \(0.416509\pi\)
\(374\) 22.0315 1.13922
\(375\) −36.8414 −1.90248
\(376\) 68.3688 3.52585
\(377\) 55.4821 2.85747
\(378\) −11.4402 −0.588421
\(379\) −25.0787 −1.28821 −0.644103 0.764939i \(-0.722769\pi\)
−0.644103 + 0.764939i \(0.722769\pi\)
\(380\) −63.3037 −3.24741
\(381\) 19.1710 0.982158
\(382\) 12.9112 0.660592
\(383\) −5.11922 −0.261580 −0.130790 0.991410i \(-0.541751\pi\)
−0.130790 + 0.991410i \(0.541751\pi\)
\(384\) −24.2001 −1.23496
\(385\) 4.59540 0.234203
\(386\) −9.09823 −0.463088
\(387\) 83.8444 4.26205
\(388\) 39.9031 2.02577
\(389\) 25.7759 1.30689 0.653445 0.756974i \(-0.273323\pi\)
0.653445 + 0.756974i \(0.273323\pi\)
\(390\) 96.7529 4.89927
\(391\) −10.4621 −0.529091
\(392\) 46.2857 2.33778
\(393\) −24.1309 −1.21724
\(394\) 22.3084 1.12388
\(395\) −10.6016 −0.533426
\(396\) 192.274 9.66214
\(397\) −32.9421 −1.65332 −0.826659 0.562703i \(-0.809761\pi\)
−0.826659 + 0.562703i \(0.809761\pi\)
\(398\) −18.2505 −0.914813
\(399\) 7.38586 0.369755
\(400\) −4.41061 −0.220531
\(401\) 24.8764 1.24227 0.621133 0.783705i \(-0.286673\pi\)
0.621133 + 0.783705i \(0.286673\pi\)
\(402\) 20.1366 1.00432
\(403\) 7.45086 0.371154
\(404\) −25.4581 −1.26659
\(405\) −38.0127 −1.88887
\(406\) −9.11322 −0.452281
\(407\) 6.02489 0.298643
\(408\) −30.1470 −1.49250
\(409\) 20.9581 1.03631 0.518155 0.855287i \(-0.326619\pi\)
0.518155 + 0.855287i \(0.326619\pi\)
\(410\) −16.9833 −0.838746
\(411\) −16.9407 −0.835621
\(412\) −10.2599 −0.505467
\(413\) 1.85607 0.0913314
\(414\) −130.840 −6.43044
\(415\) 22.0847 1.08409
\(416\) 41.6320 2.04118
\(417\) 4.72460 0.231365
\(418\) −100.645 −4.92269
\(419\) −28.5675 −1.39561 −0.697806 0.716287i \(-0.745840\pi\)
−0.697806 + 0.716287i \(0.745840\pi\)
\(420\) −11.0902 −0.541144
\(421\) 31.1856 1.51990 0.759948 0.649984i \(-0.225225\pi\)
0.759948 + 0.649984i \(0.225225\pi\)
\(422\) −32.5495 −1.58448
\(423\) −70.1062 −3.40868
\(424\) 25.1092 1.21941
\(425\) 0.774239 0.0375561
\(426\) −74.7815 −3.62318
\(427\) −1.72959 −0.0837009
\(428\) 77.3958 3.74107
\(429\) 107.345 5.18265
\(430\) 65.8994 3.17795
\(431\) −5.79032 −0.278910 −0.139455 0.990228i \(-0.544535\pi\)
−0.139455 + 0.990228i \(0.544535\pi\)
\(432\) −99.6383 −4.79385
\(433\) −14.1746 −0.681187 −0.340593 0.940211i \(-0.610628\pi\)
−0.340593 + 0.940211i \(0.610628\pi\)
\(434\) −1.22384 −0.0587463
\(435\) −65.1322 −3.12285
\(436\) 4.61898 0.221209
\(437\) 47.7931 2.28626
\(438\) 35.8621 1.71356
\(439\) −6.10292 −0.291276 −0.145638 0.989338i \(-0.546524\pi\)
−0.145638 + 0.989338i \(0.546524\pi\)
\(440\) 85.6868 4.08496
\(441\) −47.4620 −2.26009
\(442\) −20.6970 −0.984456
\(443\) −12.8666 −0.611311 −0.305656 0.952142i \(-0.598876\pi\)
−0.305656 + 0.952142i \(0.598876\pi\)
\(444\) −14.5400 −0.690038
\(445\) −17.1953 −0.815134
\(446\) −28.6600 −1.35709
\(447\) 9.44078 0.446533
\(448\) −0.986472 −0.0466064
\(449\) −20.6886 −0.976354 −0.488177 0.872745i \(-0.662338\pi\)
−0.488177 + 0.872745i \(0.662338\pi\)
\(450\) 9.68271 0.456447
\(451\) −18.8425 −0.887260
\(452\) −76.4215 −3.59456
\(453\) 10.9863 0.516181
\(454\) 7.25975 0.340717
\(455\) −4.31704 −0.202386
\(456\) 137.718 6.44925
\(457\) −18.6793 −0.873782 −0.436891 0.899514i \(-0.643921\pi\)
−0.436891 + 0.899514i \(0.643921\pi\)
\(458\) 56.1809 2.62516
\(459\) 17.4905 0.816386
\(460\) −71.7633 −3.34598
\(461\) 3.84650 0.179150 0.0895748 0.995980i \(-0.471449\pi\)
0.0895748 + 0.995980i \(0.471449\pi\)
\(462\) −17.6319 −0.820311
\(463\) −2.09063 −0.0971596 −0.0485798 0.998819i \(-0.515470\pi\)
−0.0485798 + 0.998819i \(0.515470\pi\)
\(464\) −79.3713 −3.68472
\(465\) −8.74681 −0.405624
\(466\) −24.2997 −1.12566
\(467\) −0.664455 −0.0307473 −0.0153737 0.999882i \(-0.504894\pi\)
−0.0153737 + 0.999882i \(0.504894\pi\)
\(468\) −180.628 −8.34951
\(469\) −0.898482 −0.0414880
\(470\) −55.1015 −2.54164
\(471\) −45.0723 −2.07682
\(472\) 34.6087 1.59300
\(473\) 73.1136 3.36177
\(474\) 40.6771 1.86836
\(475\) −3.53689 −0.162284
\(476\) 2.37236 0.108737
\(477\) −25.7473 −1.17889
\(478\) −12.0182 −0.549701
\(479\) −31.2081 −1.42594 −0.712968 0.701196i \(-0.752650\pi\)
−0.712968 + 0.701196i \(0.752650\pi\)
\(480\) −48.8732 −2.23075
\(481\) −5.65995 −0.258072
\(482\) 77.8320 3.54515
\(483\) 8.37287 0.380979
\(484\) 116.857 5.31169
\(485\) −18.2347 −0.827994
\(486\) 50.8725 2.30762
\(487\) −3.80054 −0.172219 −0.0861095 0.996286i \(-0.527443\pi\)
−0.0861095 + 0.996286i \(0.527443\pi\)
\(488\) −32.2504 −1.45991
\(489\) −72.1197 −3.26137
\(490\) −37.3038 −1.68521
\(491\) −26.9962 −1.21832 −0.609160 0.793047i \(-0.708493\pi\)
−0.609160 + 0.793047i \(0.708493\pi\)
\(492\) 45.4730 2.05008
\(493\) 13.9328 0.627503
\(494\) 94.5484 4.25393
\(495\) −87.8643 −3.94921
\(496\) −10.6590 −0.478604
\(497\) 3.33670 0.149671
\(498\) −84.7360 −3.79711
\(499\) −33.4899 −1.49921 −0.749607 0.661883i \(-0.769758\pi\)
−0.749607 + 0.661883i \(0.769758\pi\)
\(500\) 54.0584 2.41756
\(501\) −23.2606 −1.03921
\(502\) −9.54439 −0.425987
\(503\) −29.4808 −1.31448 −0.657242 0.753680i \(-0.728277\pi\)
−0.657242 + 0.753680i \(0.728277\pi\)
\(504\) 16.8224 0.749331
\(505\) 11.6337 0.517692
\(506\) −114.094 −5.07211
\(507\) −59.9201 −2.66115
\(508\) −28.1301 −1.24807
\(509\) −16.7184 −0.741031 −0.370516 0.928826i \(-0.620819\pi\)
−0.370516 + 0.928826i \(0.620819\pi\)
\(510\) 24.2969 1.07588
\(511\) −1.60014 −0.0707861
\(512\) 49.5562 2.19010
\(513\) −79.9004 −3.52769
\(514\) −39.9553 −1.76235
\(515\) 4.68849 0.206600
\(516\) −176.446 −7.76762
\(517\) −61.1336 −2.68865
\(518\) 0.929676 0.0408476
\(519\) 78.9431 3.46522
\(520\) −80.4965 −3.53001
\(521\) −30.9648 −1.35659 −0.678296 0.734789i \(-0.737281\pi\)
−0.678296 + 0.734789i \(0.737281\pi\)
\(522\) 174.245 7.62651
\(523\) 4.10598 0.179542 0.0897710 0.995962i \(-0.471386\pi\)
0.0897710 + 0.995962i \(0.471386\pi\)
\(524\) 35.4080 1.54680
\(525\) −0.619627 −0.0270427
\(526\) 36.9157 1.60960
\(527\) 1.87108 0.0815057
\(528\) −153.565 −6.68305
\(529\) 31.1800 1.35565
\(530\) −20.2367 −0.879024
\(531\) −35.4883 −1.54006
\(532\) −10.8375 −0.469864
\(533\) 17.7012 0.766723
\(534\) 65.9759 2.85506
\(535\) −35.3679 −1.52909
\(536\) −16.7533 −0.723632
\(537\) −78.5670 −3.39041
\(538\) −28.1478 −1.21354
\(539\) −41.3875 −1.78269
\(540\) 119.974 5.16284
\(541\) 19.8016 0.851337 0.425669 0.904879i \(-0.360039\pi\)
0.425669 + 0.904879i \(0.360039\pi\)
\(542\) −3.74040 −0.160664
\(543\) 18.1091 0.777134
\(544\) 10.4548 0.448244
\(545\) −2.11075 −0.0904147
\(546\) 16.5639 0.708870
\(547\) −16.0675 −0.686995 −0.343498 0.939154i \(-0.611612\pi\)
−0.343498 + 0.939154i \(0.611612\pi\)
\(548\) 24.8575 1.06186
\(549\) 33.0700 1.41139
\(550\) 8.44346 0.360030
\(551\) −63.6482 −2.71151
\(552\) 156.122 6.64501
\(553\) −1.81498 −0.0771808
\(554\) 52.1820 2.21700
\(555\) 6.64440 0.282039
\(556\) −6.93253 −0.294005
\(557\) −8.52073 −0.361035 −0.180518 0.983572i \(-0.557777\pi\)
−0.180518 + 0.983572i \(0.557777\pi\)
\(558\) 23.4000 0.990599
\(559\) −68.6849 −2.90506
\(560\) 6.17585 0.260977
\(561\) 26.9567 1.13811
\(562\) 74.5507 3.14473
\(563\) 36.6604 1.54505 0.772525 0.634984i \(-0.218993\pi\)
0.772525 + 0.634984i \(0.218993\pi\)
\(564\) 147.535 6.21234
\(565\) 34.9226 1.46921
\(566\) −50.6564 −2.12925
\(567\) −6.50771 −0.273298
\(568\) 62.2168 2.61056
\(569\) −18.7379 −0.785535 −0.392768 0.919638i \(-0.628482\pi\)
−0.392768 + 0.919638i \(0.628482\pi\)
\(570\) −110.993 −4.64901
\(571\) 7.49718 0.313747 0.156874 0.987619i \(-0.449858\pi\)
0.156874 + 0.987619i \(0.449858\pi\)
\(572\) −157.510 −6.58582
\(573\) 15.7975 0.659950
\(574\) −2.90751 −0.121357
\(575\) −4.00955 −0.167210
\(576\) 18.8614 0.785893
\(577\) 15.7852 0.657145 0.328572 0.944479i \(-0.393433\pi\)
0.328572 + 0.944479i \(0.393433\pi\)
\(578\) 38.5390 1.60301
\(579\) −11.1322 −0.462637
\(580\) 95.5703 3.96834
\(581\) 3.78085 0.156856
\(582\) 69.9640 2.90010
\(583\) −22.4520 −0.929868
\(584\) −29.8366 −1.23465
\(585\) 82.5421 3.41270
\(586\) −2.78173 −0.114912
\(587\) 30.5177 1.25960 0.629801 0.776756i \(-0.283136\pi\)
0.629801 + 0.776756i \(0.283136\pi\)
\(588\) 99.8814 4.11904
\(589\) −8.54752 −0.352194
\(590\) −27.8928 −1.14833
\(591\) 27.2955 1.12279
\(592\) 8.09699 0.332784
\(593\) 45.2409 1.85782 0.928911 0.370303i \(-0.120746\pi\)
0.928911 + 0.370303i \(0.120746\pi\)
\(594\) 190.743 7.82626
\(595\) −1.08411 −0.0444441
\(596\) −13.8527 −0.567429
\(597\) −22.3304 −0.913923
\(598\) 107.183 4.38306
\(599\) −12.1439 −0.496187 −0.248094 0.968736i \(-0.579804\pi\)
−0.248094 + 0.968736i \(0.579804\pi\)
\(600\) −11.5537 −0.471678
\(601\) −27.5013 −1.12180 −0.560900 0.827883i \(-0.689545\pi\)
−0.560900 + 0.827883i \(0.689545\pi\)
\(602\) 11.2818 0.459814
\(603\) 17.1790 0.699584
\(604\) −16.1205 −0.655934
\(605\) −53.4007 −2.17105
\(606\) −44.6369 −1.81325
\(607\) 19.2574 0.781633 0.390817 0.920469i \(-0.372193\pi\)
0.390817 + 0.920469i \(0.372193\pi\)
\(608\) −47.7597 −1.93691
\(609\) −11.1505 −0.451842
\(610\) 25.9921 1.05239
\(611\) 57.4306 2.32339
\(612\) −45.3598 −1.83356
\(613\) 4.69155 0.189490 0.0947450 0.995502i \(-0.469796\pi\)
0.0947450 + 0.995502i \(0.469796\pi\)
\(614\) −26.6645 −1.07609
\(615\) −20.7800 −0.837931
\(616\) 14.6694 0.591047
\(617\) −40.9627 −1.64909 −0.824547 0.565793i \(-0.808570\pi\)
−0.824547 + 0.565793i \(0.808570\pi\)
\(618\) −17.9891 −0.723629
\(619\) 34.9099 1.40315 0.701574 0.712596i \(-0.252481\pi\)
0.701574 + 0.712596i \(0.252481\pi\)
\(620\) 12.8344 0.515444
\(621\) −90.5779 −3.63477
\(622\) −23.2469 −0.932115
\(623\) −2.94380 −0.117941
\(624\) 144.263 5.77514
\(625\) −21.9797 −0.879186
\(626\) 33.2976 1.33084
\(627\) −123.144 −4.91791
\(628\) 66.1359 2.63911
\(629\) −1.42134 −0.0566727
\(630\) −13.5580 −0.540162
\(631\) 8.72381 0.347289 0.173645 0.984808i \(-0.444446\pi\)
0.173645 + 0.984808i \(0.444446\pi\)
\(632\) −33.8425 −1.34618
\(633\) −39.8261 −1.58294
\(634\) −12.8543 −0.510511
\(635\) 12.8547 0.510124
\(636\) 54.1839 2.14853
\(637\) 38.8806 1.54051
\(638\) 151.944 6.01554
\(639\) −63.7979 −2.52380
\(640\) −16.2269 −0.641426
\(641\) 10.9052 0.430728 0.215364 0.976534i \(-0.430906\pi\)
0.215364 + 0.976534i \(0.430906\pi\)
\(642\) 135.702 5.35572
\(643\) −10.9230 −0.430761 −0.215381 0.976530i \(-0.569099\pi\)
−0.215381 + 0.976530i \(0.569099\pi\)
\(644\) −12.2857 −0.484126
\(645\) 80.6315 3.17486
\(646\) 23.7433 0.934167
\(647\) 18.1368 0.713030 0.356515 0.934290i \(-0.383965\pi\)
0.356515 + 0.934290i \(0.383965\pi\)
\(648\) −121.344 −4.76685
\(649\) −30.9463 −1.21475
\(650\) −7.93202 −0.311119
\(651\) −1.49744 −0.0586892
\(652\) 105.823 4.14436
\(653\) 5.34357 0.209110 0.104555 0.994519i \(-0.466658\pi\)
0.104555 + 0.994519i \(0.466658\pi\)
\(654\) 8.09868 0.316683
\(655\) −16.1805 −0.632225
\(656\) −25.3229 −0.988692
\(657\) 30.5948 1.19362
\(658\) −9.43327 −0.367747
\(659\) 12.5265 0.487965 0.243983 0.969780i \(-0.421546\pi\)
0.243983 + 0.969780i \(0.421546\pi\)
\(660\) 184.906 7.19746
\(661\) 0.208838 0.00812288 0.00406144 0.999992i \(-0.498707\pi\)
0.00406144 + 0.999992i \(0.498707\pi\)
\(662\) −47.7017 −1.85398
\(663\) −25.3239 −0.983499
\(664\) 70.4986 2.73588
\(665\) 4.95245 0.192048
\(666\) −17.7755 −0.688785
\(667\) −72.1539 −2.79381
\(668\) 34.1310 1.32057
\(669\) −35.0670 −1.35577
\(670\) 13.5022 0.521637
\(671\) 28.8375 1.11326
\(672\) −8.36700 −0.322764
\(673\) −4.33561 −0.167125 −0.0835627 0.996503i \(-0.526630\pi\)
−0.0835627 + 0.996503i \(0.526630\pi\)
\(674\) −32.3943 −1.24778
\(675\) 6.70314 0.258004
\(676\) 87.9225 3.38163
\(677\) 29.3308 1.12728 0.563638 0.826022i \(-0.309401\pi\)
0.563638 + 0.826022i \(0.309401\pi\)
\(678\) −133.994 −5.14599
\(679\) −3.12174 −0.119801
\(680\) −20.2145 −0.775192
\(681\) 8.88270 0.340386
\(682\) 20.4051 0.781352
\(683\) 9.44450 0.361384 0.180692 0.983540i \(-0.442166\pi\)
0.180692 + 0.983540i \(0.442166\pi\)
\(684\) 207.213 7.92300
\(685\) −11.3592 −0.434014
\(686\) −12.8941 −0.492298
\(687\) 68.7404 2.62261
\(688\) 98.2589 3.74609
\(689\) 21.0921 0.803543
\(690\) −125.826 −4.79012
\(691\) 8.03341 0.305605 0.152803 0.988257i \(-0.451170\pi\)
0.152803 + 0.988257i \(0.451170\pi\)
\(692\) −115.835 −4.40340
\(693\) −15.0422 −0.571406
\(694\) 72.9710 2.76994
\(695\) 3.16799 0.120169
\(696\) −207.915 −7.88099
\(697\) 4.44518 0.168373
\(698\) −64.6435 −2.44679
\(699\) −29.7320 −1.12457
\(700\) 0.909196 0.0343644
\(701\) 30.7632 1.16191 0.580956 0.813935i \(-0.302679\pi\)
0.580956 + 0.813935i \(0.302679\pi\)
\(702\) −179.189 −6.76305
\(703\) 6.49301 0.244889
\(704\) 16.4474 0.619886
\(705\) −67.4197 −2.53917
\(706\) 17.4147 0.655412
\(707\) 1.99166 0.0749042
\(708\) 74.6833 2.80677
\(709\) −20.4700 −0.768768 −0.384384 0.923173i \(-0.625586\pi\)
−0.384384 + 0.923173i \(0.625586\pi\)
\(710\) −50.1433 −1.88185
\(711\) 34.7025 1.30145
\(712\) −54.8907 −2.05711
\(713\) −9.68977 −0.362885
\(714\) 4.15958 0.155668
\(715\) 71.9780 2.69182
\(716\) 115.283 4.30835
\(717\) −14.7049 −0.549166
\(718\) 49.1169 1.83303
\(719\) −1.64073 −0.0611888 −0.0305944 0.999532i \(-0.509740\pi\)
−0.0305944 + 0.999532i \(0.509740\pi\)
\(720\) −118.083 −4.40069
\(721\) 0.802661 0.0298927
\(722\) −59.5825 −2.21743
\(723\) 95.2317 3.54170
\(724\) −26.5719 −0.987537
\(725\) 5.33969 0.198311
\(726\) 204.891 7.60423
\(727\) −19.2673 −0.714583 −0.357292 0.933993i \(-0.616300\pi\)
−0.357292 + 0.933993i \(0.616300\pi\)
\(728\) −13.7808 −0.510752
\(729\) 8.21803 0.304371
\(730\) 24.0467 0.890007
\(731\) −17.2484 −0.637954
\(732\) −69.5941 −2.57227
\(733\) 47.2261 1.74434 0.872168 0.489206i \(-0.162713\pi\)
0.872168 + 0.489206i \(0.162713\pi\)
\(734\) 61.2213 2.25972
\(735\) −45.6432 −1.68357
\(736\) −54.1420 −1.99570
\(737\) 14.9804 0.551809
\(738\) 55.5918 2.04636
\(739\) 3.88514 0.142917 0.0714587 0.997444i \(-0.477235\pi\)
0.0714587 + 0.997444i \(0.477235\pi\)
\(740\) −9.74952 −0.358399
\(741\) 115.685 4.24980
\(742\) −3.46448 −0.127185
\(743\) 52.4388 1.92379 0.961897 0.273413i \(-0.0881524\pi\)
0.961897 + 0.273413i \(0.0881524\pi\)
\(744\) −27.9215 −1.02365
\(745\) 6.33033 0.231925
\(746\) −25.7677 −0.943423
\(747\) −72.2902 −2.64496
\(748\) −39.5544 −1.44625
\(749\) −6.05491 −0.221242
\(750\) 94.7832 3.46099
\(751\) 13.0876 0.477574 0.238787 0.971072i \(-0.423250\pi\)
0.238787 + 0.971072i \(0.423250\pi\)
\(752\) −82.1588 −2.99602
\(753\) −11.6781 −0.425573
\(754\) −142.741 −5.19831
\(755\) 7.36665 0.268100
\(756\) 20.5393 0.747006
\(757\) 12.3486 0.448819 0.224410 0.974495i \(-0.427955\pi\)
0.224410 + 0.974495i \(0.427955\pi\)
\(758\) 64.5209 2.34351
\(759\) −139.601 −5.06718
\(760\) 92.3444 3.34968
\(761\) −14.2912 −0.518055 −0.259028 0.965870i \(-0.583402\pi\)
−0.259028 + 0.965870i \(0.583402\pi\)
\(762\) −49.3219 −1.78674
\(763\) −0.361357 −0.0130820
\(764\) −23.1801 −0.838627
\(765\) 20.7282 0.749431
\(766\) 13.1704 0.475866
\(767\) 29.0718 1.04972
\(768\) 79.4474 2.86681
\(769\) 23.3553 0.842213 0.421106 0.907011i \(-0.361642\pi\)
0.421106 + 0.907011i \(0.361642\pi\)
\(770\) −11.8227 −0.426062
\(771\) −48.8875 −1.76064
\(772\) 16.3345 0.587893
\(773\) −24.4042 −0.877758 −0.438879 0.898546i \(-0.644624\pi\)
−0.438879 + 0.898546i \(0.644624\pi\)
\(774\) −215.710 −7.75353
\(775\) 0.717083 0.0257584
\(776\) −58.2087 −2.08957
\(777\) 1.13751 0.0408079
\(778\) −66.3146 −2.37749
\(779\) −20.3065 −0.727557
\(780\) −173.706 −6.21967
\(781\) −55.6327 −1.99069
\(782\) 26.9162 0.962522
\(783\) 120.627 4.31084
\(784\) −55.6216 −1.98649
\(785\) −30.2224 −1.07868
\(786\) 62.0825 2.21441
\(787\) −21.1116 −0.752549 −0.376274 0.926508i \(-0.622795\pi\)
−0.376274 + 0.926508i \(0.622795\pi\)
\(788\) −40.0514 −1.42677
\(789\) 45.1684 1.60804
\(790\) 27.2752 0.970409
\(791\) 5.97869 0.212578
\(792\) −280.480 −9.96643
\(793\) −27.0907 −0.962020
\(794\) 84.7514 3.00772
\(795\) −24.7607 −0.878170
\(796\) 32.7660 1.16136
\(797\) 17.9877 0.637157 0.318578 0.947897i \(-0.396795\pi\)
0.318578 + 0.947897i \(0.396795\pi\)
\(798\) −19.0019 −0.672659
\(799\) 14.4222 0.510219
\(800\) 4.00673 0.141659
\(801\) 56.2856 1.98875
\(802\) −64.0003 −2.25993
\(803\) 26.6791 0.941486
\(804\) −36.1524 −1.27500
\(805\) 5.61427 0.197877
\(806\) −19.1691 −0.675203
\(807\) −34.4403 −1.21236
\(808\) 37.1370 1.30648
\(809\) −0.322349 −0.0113332 −0.00566659 0.999984i \(-0.501804\pi\)
−0.00566659 + 0.999984i \(0.501804\pi\)
\(810\) 97.7968 3.43623
\(811\) 14.4791 0.508430 0.254215 0.967148i \(-0.418183\pi\)
0.254215 + 0.967148i \(0.418183\pi\)
\(812\) 16.3615 0.574175
\(813\) −4.57659 −0.160508
\(814\) −15.5005 −0.543291
\(815\) −48.3585 −1.69392
\(816\) 36.2277 1.26822
\(817\) 78.7943 2.75666
\(818\) −53.9196 −1.88525
\(819\) 14.1311 0.493779
\(820\) 30.4911 1.06479
\(821\) −11.5570 −0.403342 −0.201671 0.979453i \(-0.564637\pi\)
−0.201671 + 0.979453i \(0.564637\pi\)
\(822\) 43.5839 1.52016
\(823\) 45.2217 1.57633 0.788165 0.615464i \(-0.211031\pi\)
0.788165 + 0.615464i \(0.211031\pi\)
\(824\) 14.9666 0.521386
\(825\) 10.3310 0.359680
\(826\) −4.77519 −0.166150
\(827\) 0.519011 0.0180478 0.00902389 0.999959i \(-0.497128\pi\)
0.00902389 + 0.999959i \(0.497128\pi\)
\(828\) 234.904 8.16349
\(829\) 1.69161 0.0587520 0.0293760 0.999568i \(-0.490648\pi\)
0.0293760 + 0.999568i \(0.490648\pi\)
\(830\) −56.8181 −1.97218
\(831\) 63.8475 2.21485
\(832\) −15.4512 −0.535673
\(833\) 9.76381 0.338296
\(834\) −12.1551 −0.420898
\(835\) −15.5970 −0.539755
\(836\) 180.693 6.24940
\(837\) 16.1993 0.559930
\(838\) 73.4965 2.53890
\(839\) −2.74416 −0.0947388 −0.0473694 0.998877i \(-0.515084\pi\)
−0.0473694 + 0.998877i \(0.515084\pi\)
\(840\) 16.1778 0.558187
\(841\) 67.0904 2.31346
\(842\) −80.2325 −2.76499
\(843\) 91.2168 3.14167
\(844\) 58.4379 2.01152
\(845\) −40.1783 −1.38218
\(846\) 180.365 6.20107
\(847\) −9.14209 −0.314126
\(848\) −30.1738 −1.03617
\(849\) −61.9809 −2.12718
\(850\) −1.99191 −0.0683220
\(851\) 7.36071 0.252322
\(852\) 134.259 4.59965
\(853\) −16.4082 −0.561806 −0.280903 0.959736i \(-0.590634\pi\)
−0.280903 + 0.959736i \(0.590634\pi\)
\(854\) 4.44979 0.152269
\(855\) −94.6911 −3.23837
\(856\) −112.901 −3.85888
\(857\) 20.9390 0.715262 0.357631 0.933863i \(-0.383585\pi\)
0.357631 + 0.933863i \(0.383585\pi\)
\(858\) −276.170 −9.42828
\(859\) −31.0093 −1.05802 −0.529011 0.848615i \(-0.677437\pi\)
−0.529011 + 0.848615i \(0.677437\pi\)
\(860\) −118.313 −4.03443
\(861\) −3.55750 −0.121239
\(862\) 14.8970 0.507393
\(863\) −4.04705 −0.137763 −0.0688817 0.997625i \(-0.521943\pi\)
−0.0688817 + 0.997625i \(0.521943\pi\)
\(864\) 90.5144 3.07936
\(865\) 52.9338 1.79980
\(866\) 36.4675 1.23921
\(867\) 47.1546 1.60145
\(868\) 2.19723 0.0745789
\(869\) 30.2611 1.02654
\(870\) 167.568 5.68109
\(871\) −14.0730 −0.476844
\(872\) −6.73794 −0.228175
\(873\) 59.6879 2.02013
\(874\) −122.959 −4.15916
\(875\) −4.22915 −0.142971
\(876\) −64.3853 −2.17538
\(877\) −34.6771 −1.17096 −0.585481 0.810686i \(-0.699095\pi\)
−0.585481 + 0.810686i \(0.699095\pi\)
\(878\) 15.7012 0.529890
\(879\) −3.40359 −0.114800
\(880\) −102.970 −3.47111
\(881\) −7.55028 −0.254375 −0.127188 0.991879i \(-0.540595\pi\)
−0.127188 + 0.991879i \(0.540595\pi\)
\(882\) 122.107 4.11156
\(883\) −9.27157 −0.312013 −0.156007 0.987756i \(-0.549862\pi\)
−0.156007 + 0.987756i \(0.549862\pi\)
\(884\) 37.1585 1.24977
\(885\) −34.1283 −1.14721
\(886\) 33.1024 1.11210
\(887\) −9.33134 −0.313316 −0.156658 0.987653i \(-0.550072\pi\)
−0.156658 + 0.987653i \(0.550072\pi\)
\(888\) 21.2102 0.711769
\(889\) 2.20070 0.0738092
\(890\) 44.2389 1.48289
\(891\) 108.503 3.63498
\(892\) 51.4548 1.72283
\(893\) −65.8835 −2.20471
\(894\) −24.2886 −0.812334
\(895\) −52.6816 −1.76095
\(896\) −2.77802 −0.0928071
\(897\) 131.145 4.37879
\(898\) 53.2262 1.77618
\(899\) 12.9043 0.430382
\(900\) −17.3839 −0.579463
\(901\) 5.29670 0.176459
\(902\) 48.4769 1.61410
\(903\) 13.8039 0.459367
\(904\) 111.480 3.70777
\(905\) 12.1427 0.403636
\(906\) −28.2649 −0.939037
\(907\) −43.9512 −1.45937 −0.729687 0.683781i \(-0.760334\pi\)
−0.729687 + 0.683781i \(0.760334\pi\)
\(908\) −13.0338 −0.432543
\(909\) −38.0808 −1.26306
\(910\) 11.1066 0.368181
\(911\) 13.7011 0.453937 0.226968 0.973902i \(-0.427119\pi\)
0.226968 + 0.973902i \(0.427119\pi\)
\(912\) −165.496 −5.48013
\(913\) −63.0381 −2.08626
\(914\) 48.0570 1.58958
\(915\) 31.8027 1.05136
\(916\) −100.865 −3.33266
\(917\) −2.77007 −0.0914759
\(918\) −44.9984 −1.48517
\(919\) −53.5232 −1.76557 −0.882783 0.469781i \(-0.844333\pi\)
−0.882783 + 0.469781i \(0.844333\pi\)
\(920\) 104.685 3.45136
\(921\) −32.6254 −1.07504
\(922\) −9.89604 −0.325909
\(923\) 52.2629 1.72025
\(924\) 31.6556 1.04139
\(925\) −0.544723 −0.0179104
\(926\) 5.37863 0.176753
\(927\) −15.3469 −0.504060
\(928\) 72.1033 2.36691
\(929\) −39.7919 −1.30553 −0.652765 0.757560i \(-0.726391\pi\)
−0.652765 + 0.757560i \(0.726391\pi\)
\(930\) 22.5033 0.737911
\(931\) −44.6032 −1.46181
\(932\) 43.6266 1.42904
\(933\) −28.4438 −0.931209
\(934\) 1.70947 0.0559355
\(935\) 18.0753 0.591126
\(936\) 263.491 8.61246
\(937\) −19.8514 −0.648518 −0.324259 0.945968i \(-0.605115\pi\)
−0.324259 + 0.945968i \(0.605115\pi\)
\(938\) 2.31156 0.0754750
\(939\) 40.7414 1.32955
\(940\) 98.9268 3.22664
\(941\) −23.0351 −0.750924 −0.375462 0.926838i \(-0.622516\pi\)
−0.375462 + 0.926838i \(0.622516\pi\)
\(942\) 115.959 3.77816
\(943\) −23.0202 −0.749641
\(944\) −41.5894 −1.35362
\(945\) −9.38591 −0.305324
\(946\) −188.102 −6.11572
\(947\) −39.8512 −1.29499 −0.647495 0.762070i \(-0.724183\pi\)
−0.647495 + 0.762070i \(0.724183\pi\)
\(948\) −73.0298 −2.37190
\(949\) −25.0631 −0.813583
\(950\) 9.09949 0.295227
\(951\) −15.7280 −0.510014
\(952\) −3.46069 −0.112162
\(953\) 25.9279 0.839887 0.419944 0.907550i \(-0.362050\pi\)
0.419944 + 0.907550i \(0.362050\pi\)
\(954\) 66.2411 2.14463
\(955\) 10.5927 0.342772
\(956\) 21.5770 0.697849
\(957\) 185.912 6.00969
\(958\) 80.2904 2.59406
\(959\) −1.94468 −0.0627970
\(960\) 18.1386 0.585422
\(961\) −29.2670 −0.944098
\(962\) 14.5616 0.469484
\(963\) 115.770 3.73065
\(964\) −139.736 −4.50060
\(965\) −7.46446 −0.240290
\(966\) −21.5412 −0.693076
\(967\) 41.1762 1.32414 0.662069 0.749443i \(-0.269679\pi\)
0.662069 + 0.749443i \(0.269679\pi\)
\(968\) −170.465 −5.47897
\(969\) 29.0512 0.933259
\(970\) 46.9130 1.50629
\(971\) 58.8135 1.88742 0.943708 0.330779i \(-0.107312\pi\)
0.943708 + 0.330779i \(0.107312\pi\)
\(972\) −91.3342 −2.92955
\(973\) 0.542354 0.0173871
\(974\) 9.77779 0.313301
\(975\) −9.70525 −0.310817
\(976\) 38.7553 1.24053
\(977\) 33.5927 1.07473 0.537363 0.843351i \(-0.319420\pi\)
0.537363 + 0.843351i \(0.319420\pi\)
\(978\) 185.545 5.93308
\(979\) 49.0819 1.56866
\(980\) 66.9735 2.13939
\(981\) 6.90917 0.220593
\(982\) 69.4541 2.21637
\(983\) 35.3837 1.12856 0.564282 0.825582i \(-0.309153\pi\)
0.564282 + 0.825582i \(0.309153\pi\)
\(984\) −66.3338 −2.11465
\(985\) 18.3025 0.583165
\(986\) −35.8455 −1.14155
\(987\) −11.5421 −0.367390
\(988\) −169.748 −5.40040
\(989\) 89.3240 2.84034
\(990\) 226.052 7.18440
\(991\) 42.0547 1.33591 0.667956 0.744201i \(-0.267170\pi\)
0.667956 + 0.744201i \(0.267170\pi\)
\(992\) 9.68298 0.307435
\(993\) −58.3657 −1.85218
\(994\) −8.58444 −0.272282
\(995\) −14.9732 −0.474683
\(996\) 152.131 4.82046
\(997\) −49.8311 −1.57817 −0.789083 0.614286i \(-0.789444\pi\)
−0.789083 + 0.614286i \(0.789444\pi\)
\(998\) 86.1607 2.72737
\(999\) −12.3056 −0.389332
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 4033.2.a.c.1.6 77
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4033.2.a.c.1.6 77 1.1 even 1 trivial