Properties

Label 4033.2.a.c.1.15
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 1.15
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)
 
\(f(q)\) \(=\) \(q-1.98064 q^{2} -1.34264 q^{3} +1.92294 q^{4} -0.618382 q^{5} +2.65929 q^{6} -3.38656 q^{7} +0.152622 q^{8} -1.19732 q^{9} +O(q^{10})\) \(q-1.98064 q^{2} -1.34264 q^{3} +1.92294 q^{4} -0.618382 q^{5} +2.65929 q^{6} -3.38656 q^{7} +0.152622 q^{8} -1.19732 q^{9} +1.22479 q^{10} +5.41950 q^{11} -2.58182 q^{12} -5.35721 q^{13} +6.70756 q^{14} +0.830265 q^{15} -4.14818 q^{16} -2.80946 q^{17} +2.37145 q^{18} -0.931205 q^{19} -1.18911 q^{20} +4.54693 q^{21} -10.7341 q^{22} +5.12484 q^{23} -0.204916 q^{24} -4.61760 q^{25} +10.6107 q^{26} +5.63549 q^{27} -6.51216 q^{28} +8.79269 q^{29} -1.64446 q^{30} -0.504047 q^{31} +7.91081 q^{32} -7.27644 q^{33} +5.56454 q^{34} +2.09419 q^{35} -2.30237 q^{36} +1.00000 q^{37} +1.84438 q^{38} +7.19281 q^{39} -0.0943784 q^{40} -9.25133 q^{41} -9.00584 q^{42} -8.43110 q^{43} +10.4214 q^{44} +0.740399 q^{45} -10.1505 q^{46} +8.00506 q^{47} +5.56951 q^{48} +4.46878 q^{49} +9.14582 q^{50} +3.77210 q^{51} -10.3016 q^{52} +4.86095 q^{53} -11.1619 q^{54} -3.35132 q^{55} -0.516862 q^{56} +1.25027 q^{57} -17.4152 q^{58} +0.278142 q^{59} +1.59655 q^{60} -0.247985 q^{61} +0.998337 q^{62} +4.05478 q^{63} -7.37213 q^{64} +3.31280 q^{65} +14.4120 q^{66} +3.46510 q^{67} -5.40243 q^{68} -6.88082 q^{69} -4.14783 q^{70} +11.6172 q^{71} -0.182736 q^{72} -2.16574 q^{73} -1.98064 q^{74} +6.19978 q^{75} -1.79066 q^{76} -18.3535 q^{77} -14.2464 q^{78} +12.5551 q^{79} +2.56516 q^{80} -3.97449 q^{81} +18.3236 q^{82} -4.43096 q^{83} +8.74349 q^{84} +1.73732 q^{85} +16.6990 q^{86} -11.8054 q^{87} +0.827133 q^{88} +0.673703 q^{89} -1.46646 q^{90} +18.1425 q^{91} +9.85478 q^{92} +0.676754 q^{93} -15.8552 q^{94} +0.575841 q^{95} -10.6214 q^{96} -8.48462 q^{97} -8.85105 q^{98} -6.48885 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 77 q - 9 q^{2} - 27 q^{3} + 73 q^{4} - 16 q^{5} - 2 q^{6} - 23 q^{7} - 24 q^{8} + 66 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.98064 −1.40053 −0.700263 0.713885i \(-0.746934\pi\)
−0.700263 + 0.713885i \(0.746934\pi\)
\(3\) −1.34264 −0.775174 −0.387587 0.921833i \(-0.626691\pi\)
−0.387587 + 0.921833i \(0.626691\pi\)
\(4\) 1.92294 0.961472
\(5\) −0.618382 −0.276549 −0.138274 0.990394i \(-0.544156\pi\)
−0.138274 + 0.990394i \(0.544156\pi\)
\(6\) 2.65929 1.08565
\(7\) −3.38656 −1.28000 −0.639999 0.768375i \(-0.721065\pi\)
−0.639999 + 0.768375i \(0.721065\pi\)
\(8\) 0.152622 0.0539599
\(9\) −1.19732 −0.399105
\(10\) 1.22479 0.387314
\(11\) 5.41950 1.63404 0.817020 0.576609i \(-0.195624\pi\)
0.817020 + 0.576609i \(0.195624\pi\)
\(12\) −2.58182 −0.745308
\(13\) −5.35721 −1.48582 −0.742911 0.669390i \(-0.766556\pi\)
−0.742911 + 0.669390i \(0.766556\pi\)
\(14\) 6.70756 1.79267
\(15\) 0.830265 0.214373
\(16\) −4.14818 −1.03704
\(17\) −2.80946 −0.681394 −0.340697 0.940173i \(-0.610663\pi\)
−0.340697 + 0.940173i \(0.610663\pi\)
\(18\) 2.37145 0.558957
\(19\) −0.931205 −0.213633 −0.106817 0.994279i \(-0.534066\pi\)
−0.106817 + 0.994279i \(0.534066\pi\)
\(20\) −1.18911 −0.265894
\(21\) 4.54693 0.992222
\(22\) −10.7341 −2.28852
\(23\) 5.12484 1.06860 0.534302 0.845294i \(-0.320575\pi\)
0.534302 + 0.845294i \(0.320575\pi\)
\(24\) −0.204916 −0.0418283
\(25\) −4.61760 −0.923521
\(26\) 10.6107 2.08093
\(27\) 5.63549 1.08455
\(28\) −6.51216 −1.23068
\(29\) 8.79269 1.63276 0.816381 0.577514i \(-0.195977\pi\)
0.816381 + 0.577514i \(0.195977\pi\)
\(30\) −1.64446 −0.300236
\(31\) −0.504047 −0.0905295 −0.0452648 0.998975i \(-0.514413\pi\)
−0.0452648 + 0.998975i \(0.514413\pi\)
\(32\) 7.91081 1.39845
\(33\) −7.27644 −1.26667
\(34\) 5.56454 0.954310
\(35\) 2.09419 0.353982
\(36\) −2.30237 −0.383728
\(37\) 1.00000 0.164399
\(38\) 1.84438 0.299199
\(39\) 7.19281 1.15177
\(40\) −0.0943784 −0.0149225
\(41\) −9.25133 −1.44481 −0.722407 0.691468i \(-0.756964\pi\)
−0.722407 + 0.691468i \(0.756964\pi\)
\(42\) −9.00584 −1.38963
\(43\) −8.43110 −1.28573 −0.642865 0.765979i \(-0.722254\pi\)
−0.642865 + 0.765979i \(0.722254\pi\)
\(44\) 10.4214 1.57108
\(45\) 0.740399 0.110372
\(46\) −10.1505 −1.49661
\(47\) 8.00506 1.16766 0.583829 0.811877i \(-0.301554\pi\)
0.583829 + 0.811877i \(0.301554\pi\)
\(48\) 5.56951 0.803889
\(49\) 4.46878 0.638397
\(50\) 9.14582 1.29341
\(51\) 3.77210 0.528199
\(52\) −10.3016 −1.42858
\(53\) 4.86095 0.667703 0.333852 0.942626i \(-0.391652\pi\)
0.333852 + 0.942626i \(0.391652\pi\)
\(54\) −11.1619 −1.51894
\(55\) −3.35132 −0.451892
\(56\) −0.516862 −0.0690686
\(57\) 1.25027 0.165603
\(58\) −17.4152 −2.28672
\(59\) 0.278142 0.0362110 0.0181055 0.999836i \(-0.494237\pi\)
0.0181055 + 0.999836i \(0.494237\pi\)
\(60\) 1.59655 0.206114
\(61\) −0.247985 −0.0317512 −0.0158756 0.999874i \(-0.505054\pi\)
−0.0158756 + 0.999874i \(0.505054\pi\)
\(62\) 0.998337 0.126789
\(63\) 4.05478 0.510854
\(64\) −7.37213 −0.921516
\(65\) 3.31280 0.410903
\(66\) 14.4120 1.77400
\(67\) 3.46510 0.423329 0.211665 0.977342i \(-0.432112\pi\)
0.211665 + 0.977342i \(0.432112\pi\)
\(68\) −5.40243 −0.655141
\(69\) −6.88082 −0.828354
\(70\) −4.14783 −0.495761
\(71\) 11.6172 1.37870 0.689352 0.724426i \(-0.257895\pi\)
0.689352 + 0.724426i \(0.257895\pi\)
\(72\) −0.182736 −0.0215357
\(73\) −2.16574 −0.253481 −0.126740 0.991936i \(-0.540452\pi\)
−0.126740 + 0.991936i \(0.540452\pi\)
\(74\) −1.98064 −0.230245
\(75\) 6.19978 0.715889
\(76\) −1.79066 −0.205402
\(77\) −18.3535 −2.09157
\(78\) −14.2464 −1.61308
\(79\) 12.5551 1.41256 0.706280 0.707933i \(-0.250372\pi\)
0.706280 + 0.707933i \(0.250372\pi\)
\(80\) 2.56516 0.286793
\(81\) −3.97449 −0.441610
\(82\) 18.3236 2.02350
\(83\) −4.43096 −0.486361 −0.243180 0.969981i \(-0.578191\pi\)
−0.243180 + 0.969981i \(0.578191\pi\)
\(84\) 8.74349 0.953993
\(85\) 1.73732 0.188439
\(86\) 16.6990 1.80070
\(87\) −11.8054 −1.26567
\(88\) 0.827133 0.0881726
\(89\) 0.673703 0.0714124 0.0357062 0.999362i \(-0.488632\pi\)
0.0357062 + 0.999362i \(0.488632\pi\)
\(90\) −1.46646 −0.154579
\(91\) 18.1425 1.90185
\(92\) 9.85478 1.02743
\(93\) 0.676754 0.0701761
\(94\) −15.8552 −1.63534
\(95\) 0.575841 0.0590800
\(96\) −10.6214 −1.08404
\(97\) −8.48462 −0.861482 −0.430741 0.902475i \(-0.641748\pi\)
−0.430741 + 0.902475i \(0.641748\pi\)
\(98\) −8.85105 −0.894091
\(99\) −6.48885 −0.652154
\(100\) −8.87939 −0.887939
\(101\) −2.73137 −0.271782 −0.135891 0.990724i \(-0.543390\pi\)
−0.135891 + 0.990724i \(0.543390\pi\)
\(102\) −7.47117 −0.739757
\(103\) −3.58391 −0.353133 −0.176566 0.984289i \(-0.556499\pi\)
−0.176566 + 0.984289i \(0.556499\pi\)
\(104\) −0.817626 −0.0801748
\(105\) −2.81174 −0.274398
\(106\) −9.62781 −0.935136
\(107\) 3.24554 0.313758 0.156879 0.987618i \(-0.449857\pi\)
0.156879 + 0.987618i \(0.449857\pi\)
\(108\) 10.8367 1.04276
\(109\) 1.00000 0.0957826
\(110\) 6.63777 0.632886
\(111\) −1.34264 −0.127438
\(112\) 14.0480 1.32741
\(113\) 18.0249 1.69564 0.847820 0.530284i \(-0.177915\pi\)
0.847820 + 0.530284i \(0.177915\pi\)
\(114\) −2.47635 −0.231931
\(115\) −3.16911 −0.295521
\(116\) 16.9078 1.56985
\(117\) 6.41427 0.593000
\(118\) −0.550900 −0.0507145
\(119\) 9.51440 0.872184
\(120\) 0.126716 0.0115676
\(121\) 18.3710 1.67009
\(122\) 0.491170 0.0444684
\(123\) 12.4212 1.11998
\(124\) −0.969254 −0.0870416
\(125\) 5.94735 0.531947
\(126\) −8.03107 −0.715464
\(127\) 8.21022 0.728539 0.364270 0.931294i \(-0.381319\pi\)
0.364270 + 0.931294i \(0.381319\pi\)
\(128\) −1.22007 −0.107840
\(129\) 11.3199 0.996664
\(130\) −6.56148 −0.575479
\(131\) 0.781469 0.0682773 0.0341387 0.999417i \(-0.489131\pi\)
0.0341387 + 0.999417i \(0.489131\pi\)
\(132\) −13.9922 −1.21786
\(133\) 3.15358 0.273450
\(134\) −6.86312 −0.592884
\(135\) −3.48488 −0.299931
\(136\) −0.428784 −0.0367680
\(137\) −13.8217 −1.18087 −0.590433 0.807086i \(-0.701043\pi\)
−0.590433 + 0.807086i \(0.701043\pi\)
\(138\) 13.6284 1.16013
\(139\) 17.2952 1.46696 0.733479 0.679712i \(-0.237895\pi\)
0.733479 + 0.679712i \(0.237895\pi\)
\(140\) 4.02700 0.340344
\(141\) −10.7479 −0.905138
\(142\) −23.0095 −1.93091
\(143\) −29.0334 −2.42789
\(144\) 4.96668 0.413890
\(145\) −5.43724 −0.451538
\(146\) 4.28956 0.355007
\(147\) −5.99996 −0.494868
\(148\) 1.92294 0.158065
\(149\) 15.9216 1.30435 0.652174 0.758069i \(-0.273857\pi\)
0.652174 + 0.758069i \(0.273857\pi\)
\(150\) −12.2796 −1.00262
\(151\) 10.0783 0.820163 0.410081 0.912049i \(-0.365500\pi\)
0.410081 + 0.912049i \(0.365500\pi\)
\(152\) −0.142122 −0.0115276
\(153\) 3.36381 0.271948
\(154\) 36.3516 2.92930
\(155\) 0.311694 0.0250358
\(156\) 13.8314 1.10740
\(157\) −17.5447 −1.40022 −0.700110 0.714035i \(-0.746866\pi\)
−0.700110 + 0.714035i \(0.746866\pi\)
\(158\) −24.8672 −1.97833
\(159\) −6.52651 −0.517586
\(160\) −4.89190 −0.386739
\(161\) −17.3556 −1.36781
\(162\) 7.87204 0.618486
\(163\) −13.5562 −1.06180 −0.530901 0.847434i \(-0.678147\pi\)
−0.530901 + 0.847434i \(0.678147\pi\)
\(164\) −17.7898 −1.38915
\(165\) 4.49962 0.350295
\(166\) 8.77614 0.681161
\(167\) −0.267605 −0.0207079 −0.0103539 0.999946i \(-0.503296\pi\)
−0.0103539 + 0.999946i \(0.503296\pi\)
\(168\) 0.693960 0.0535402
\(169\) 15.6997 1.20767
\(170\) −3.44101 −0.263913
\(171\) 1.11495 0.0852621
\(172\) −16.2125 −1.23619
\(173\) −0.882301 −0.0670801 −0.0335400 0.999437i \(-0.510678\pi\)
−0.0335400 + 0.999437i \(0.510678\pi\)
\(174\) 23.3823 1.77261
\(175\) 15.6378 1.18211
\(176\) −22.4810 −1.69457
\(177\) −0.373445 −0.0280698
\(178\) −1.33436 −0.100015
\(179\) 9.22784 0.689721 0.344860 0.938654i \(-0.387926\pi\)
0.344860 + 0.938654i \(0.387926\pi\)
\(180\) 1.42374 0.106120
\(181\) −12.0295 −0.894148 −0.447074 0.894497i \(-0.647534\pi\)
−0.447074 + 0.894497i \(0.647534\pi\)
\(182\) −35.9338 −2.66359
\(183\) 0.332955 0.0246127
\(184\) 0.782162 0.0576617
\(185\) −0.618382 −0.0454644
\(186\) −1.34041 −0.0982835
\(187\) −15.2259 −1.11343
\(188\) 15.3933 1.12267
\(189\) −19.0849 −1.38822
\(190\) −1.14053 −0.0827431
\(191\) −11.7806 −0.852417 −0.426208 0.904625i \(-0.640151\pi\)
−0.426208 + 0.904625i \(0.640151\pi\)
\(192\) 9.89812 0.714335
\(193\) 9.60828 0.691619 0.345810 0.938305i \(-0.387604\pi\)
0.345810 + 0.938305i \(0.387604\pi\)
\(194\) 16.8050 1.20653
\(195\) −4.44790 −0.318521
\(196\) 8.59320 0.613800
\(197\) 11.7998 0.840702 0.420351 0.907362i \(-0.361907\pi\)
0.420351 + 0.907362i \(0.361907\pi\)
\(198\) 12.8521 0.913359
\(199\) −16.0583 −1.13835 −0.569173 0.822218i \(-0.692737\pi\)
−0.569173 + 0.822218i \(0.692737\pi\)
\(200\) −0.704746 −0.0498331
\(201\) −4.65238 −0.328154
\(202\) 5.40987 0.380637
\(203\) −29.7770 −2.08993
\(204\) 7.25353 0.507849
\(205\) 5.72085 0.399562
\(206\) 7.09844 0.494572
\(207\) −6.13606 −0.426485
\(208\) 22.2226 1.54086
\(209\) −5.04667 −0.349085
\(210\) 5.56905 0.384301
\(211\) 8.27089 0.569392 0.284696 0.958618i \(-0.408107\pi\)
0.284696 + 0.958618i \(0.408107\pi\)
\(212\) 9.34734 0.641978
\(213\) −15.5977 −1.06874
\(214\) −6.42824 −0.439426
\(215\) 5.21364 0.355567
\(216\) 0.860097 0.0585222
\(217\) 1.70699 0.115878
\(218\) −1.98064 −0.134146
\(219\) 2.90781 0.196492
\(220\) −6.44440 −0.434481
\(221\) 15.0509 1.01243
\(222\) 2.65929 0.178480
\(223\) −4.66570 −0.312438 −0.156219 0.987722i \(-0.549931\pi\)
−0.156219 + 0.987722i \(0.549931\pi\)
\(224\) −26.7904 −1.79001
\(225\) 5.52873 0.368582
\(226\) −35.7009 −2.37479
\(227\) 5.48397 0.363984 0.181992 0.983300i \(-0.441746\pi\)
0.181992 + 0.983300i \(0.441746\pi\)
\(228\) 2.40421 0.159222
\(229\) −2.48999 −0.164543 −0.0822716 0.996610i \(-0.526217\pi\)
−0.0822716 + 0.996610i \(0.526217\pi\)
\(230\) 6.27687 0.413885
\(231\) 24.6421 1.62133
\(232\) 1.34195 0.0881036
\(233\) −8.34522 −0.546713 −0.273357 0.961913i \(-0.588134\pi\)
−0.273357 + 0.961913i \(0.588134\pi\)
\(234\) −12.7044 −0.830511
\(235\) −4.95019 −0.322915
\(236\) 0.534852 0.0348159
\(237\) −16.8570 −1.09498
\(238\) −18.8446 −1.22152
\(239\) 15.8759 1.02692 0.513462 0.858112i \(-0.328363\pi\)
0.513462 + 0.858112i \(0.328363\pi\)
\(240\) −3.44408 −0.222315
\(241\) 20.0036 1.28855 0.644274 0.764795i \(-0.277160\pi\)
0.644274 + 0.764795i \(0.277160\pi\)
\(242\) −36.3863 −2.33900
\(243\) −11.5702 −0.742226
\(244\) −0.476861 −0.0305279
\(245\) −2.76341 −0.176548
\(246\) −24.6020 −1.56856
\(247\) 4.98866 0.317421
\(248\) −0.0769285 −0.00488496
\(249\) 5.94918 0.377014
\(250\) −11.7796 −0.745006
\(251\) −11.4032 −0.719766 −0.359883 0.932997i \(-0.617183\pi\)
−0.359883 + 0.932997i \(0.617183\pi\)
\(252\) 7.79711 0.491172
\(253\) 27.7741 1.74614
\(254\) −16.2615 −1.02034
\(255\) −2.33260 −0.146073
\(256\) 17.1608 1.07255
\(257\) 6.27447 0.391391 0.195695 0.980665i \(-0.437304\pi\)
0.195695 + 0.980665i \(0.437304\pi\)
\(258\) −22.4207 −1.39585
\(259\) −3.38656 −0.210430
\(260\) 6.37033 0.395071
\(261\) −10.5276 −0.651644
\(262\) −1.54781 −0.0956241
\(263\) −20.1199 −1.24065 −0.620325 0.784345i \(-0.712999\pi\)
−0.620325 + 0.784345i \(0.712999\pi\)
\(264\) −1.11054 −0.0683491
\(265\) −3.00593 −0.184653
\(266\) −6.24612 −0.382974
\(267\) −0.904541 −0.0553570
\(268\) 6.66319 0.407019
\(269\) −13.0264 −0.794234 −0.397117 0.917768i \(-0.629989\pi\)
−0.397117 + 0.917768i \(0.629989\pi\)
\(270\) 6.90231 0.420061
\(271\) 9.26068 0.562546 0.281273 0.959628i \(-0.409243\pi\)
0.281273 + 0.959628i \(0.409243\pi\)
\(272\) 11.6541 0.706636
\(273\) −24.3589 −1.47427
\(274\) 27.3758 1.65383
\(275\) −25.0251 −1.50907
\(276\) −13.2314 −0.796439
\(277\) −6.69465 −0.402242 −0.201121 0.979566i \(-0.564459\pi\)
−0.201121 + 0.979566i \(0.564459\pi\)
\(278\) −34.2556 −2.05451
\(279\) 0.603504 0.0361308
\(280\) 0.319618 0.0191008
\(281\) 26.4566 1.57827 0.789135 0.614220i \(-0.210529\pi\)
0.789135 + 0.614220i \(0.210529\pi\)
\(282\) 21.2878 1.26767
\(283\) −13.4905 −0.801926 −0.400963 0.916094i \(-0.631324\pi\)
−0.400963 + 0.916094i \(0.631324\pi\)
\(284\) 22.3392 1.32559
\(285\) −0.773147 −0.0457973
\(286\) 57.5048 3.40033
\(287\) 31.3302 1.84936
\(288\) −9.47174 −0.558127
\(289\) −9.10693 −0.535702
\(290\) 10.7692 0.632391
\(291\) 11.3918 0.667799
\(292\) −4.16460 −0.243715
\(293\) −2.63011 −0.153652 −0.0768262 0.997044i \(-0.524479\pi\)
−0.0768262 + 0.997044i \(0.524479\pi\)
\(294\) 11.8838 0.693076
\(295\) −0.171998 −0.0100141
\(296\) 0.152622 0.00887095
\(297\) 30.5415 1.77220
\(298\) −31.5350 −1.82677
\(299\) −27.4549 −1.58776
\(300\) 11.9218 0.688307
\(301\) 28.5524 1.64573
\(302\) −19.9616 −1.14866
\(303\) 3.66725 0.210678
\(304\) 3.86280 0.221547
\(305\) 0.153350 0.00878077
\(306\) −6.66251 −0.380870
\(307\) 10.2071 0.582552 0.291276 0.956639i \(-0.405920\pi\)
0.291276 + 0.956639i \(0.405920\pi\)
\(308\) −35.2927 −2.01099
\(309\) 4.81190 0.273739
\(310\) −0.617354 −0.0350633
\(311\) 24.6510 1.39783 0.698915 0.715205i \(-0.253667\pi\)
0.698915 + 0.715205i \(0.253667\pi\)
\(312\) 1.09778 0.0621494
\(313\) −34.2154 −1.93397 −0.966983 0.254839i \(-0.917977\pi\)
−0.966983 + 0.254839i \(0.917977\pi\)
\(314\) 34.7498 1.96104
\(315\) −2.50740 −0.141276
\(316\) 24.1428 1.35814
\(317\) −31.0060 −1.74147 −0.870735 0.491753i \(-0.836356\pi\)
−0.870735 + 0.491753i \(0.836356\pi\)
\(318\) 12.9267 0.724893
\(319\) 47.6520 2.66800
\(320\) 4.55879 0.254844
\(321\) −4.35759 −0.243217
\(322\) 34.3752 1.91565
\(323\) 2.61619 0.145568
\(324\) −7.64271 −0.424595
\(325\) 24.7375 1.37219
\(326\) 26.8500 1.48708
\(327\) −1.34264 −0.0742482
\(328\) −1.41195 −0.0779620
\(329\) −27.1096 −1.49460
\(330\) −8.91214 −0.490597
\(331\) −26.3847 −1.45024 −0.725118 0.688624i \(-0.758215\pi\)
−0.725118 + 0.688624i \(0.758215\pi\)
\(332\) −8.52048 −0.467622
\(333\) −1.19732 −0.0656125
\(334\) 0.530029 0.0290019
\(335\) −2.14276 −0.117071
\(336\) −18.8615 −1.02898
\(337\) −16.2883 −0.887278 −0.443639 0.896206i \(-0.646313\pi\)
−0.443639 + 0.896206i \(0.646313\pi\)
\(338\) −31.0955 −1.69137
\(339\) −24.2010 −1.31442
\(340\) 3.34077 0.181179
\(341\) −2.73168 −0.147929
\(342\) −2.20831 −0.119412
\(343\) 8.57214 0.462852
\(344\) −1.28677 −0.0693778
\(345\) 4.25498 0.229080
\(346\) 1.74752 0.0939474
\(347\) −15.6952 −0.842565 −0.421283 0.906929i \(-0.638420\pi\)
−0.421283 + 0.906929i \(0.638420\pi\)
\(348\) −22.7012 −1.21691
\(349\) −15.8380 −0.847790 −0.423895 0.905711i \(-0.639338\pi\)
−0.423895 + 0.905711i \(0.639338\pi\)
\(350\) −30.9729 −1.65557
\(351\) −30.1905 −1.61145
\(352\) 42.8726 2.28512
\(353\) 16.1608 0.860155 0.430077 0.902792i \(-0.358486\pi\)
0.430077 + 0.902792i \(0.358486\pi\)
\(354\) 0.739661 0.0393125
\(355\) −7.18385 −0.381279
\(356\) 1.29549 0.0686610
\(357\) −12.7744 −0.676094
\(358\) −18.2770 −0.965972
\(359\) −33.8353 −1.78576 −0.892880 0.450294i \(-0.851319\pi\)
−0.892880 + 0.450294i \(0.851319\pi\)
\(360\) 0.113001 0.00595567
\(361\) −18.1329 −0.954361
\(362\) 23.8262 1.25228
\(363\) −24.6656 −1.29461
\(364\) 34.8870 1.82858
\(365\) 1.33926 0.0700999
\(366\) −0.659465 −0.0344708
\(367\) 14.1881 0.740613 0.370306 0.928910i \(-0.379253\pi\)
0.370306 + 0.928910i \(0.379253\pi\)
\(368\) −21.2587 −1.10819
\(369\) 11.0768 0.576633
\(370\) 1.22479 0.0636740
\(371\) −16.4619 −0.854659
\(372\) 1.30136 0.0674724
\(373\) −5.19861 −0.269174 −0.134587 0.990902i \(-0.542971\pi\)
−0.134587 + 0.990902i \(0.542971\pi\)
\(374\) 30.1570 1.55938
\(375\) −7.98516 −0.412352
\(376\) 1.22175 0.0630067
\(377\) −47.1043 −2.42599
\(378\) 37.8004 1.94424
\(379\) −7.54158 −0.387385 −0.193692 0.981062i \(-0.562046\pi\)
−0.193692 + 0.981062i \(0.562046\pi\)
\(380\) 1.10731 0.0568038
\(381\) −11.0234 −0.564745
\(382\) 23.3332 1.19383
\(383\) −34.1790 −1.74646 −0.873232 0.487304i \(-0.837980\pi\)
−0.873232 + 0.487304i \(0.837980\pi\)
\(384\) 1.63811 0.0835945
\(385\) 11.3494 0.578421
\(386\) −19.0306 −0.968630
\(387\) 10.0947 0.513142
\(388\) −16.3154 −0.828291
\(389\) 0.377920 0.0191613 0.00958065 0.999954i \(-0.496950\pi\)
0.00958065 + 0.999954i \(0.496950\pi\)
\(390\) 8.80970 0.446097
\(391\) −14.3980 −0.728141
\(392\) 0.682032 0.0344478
\(393\) −1.04923 −0.0529268
\(394\) −23.3712 −1.17742
\(395\) −7.76385 −0.390642
\(396\) −12.4777 −0.627028
\(397\) −11.2555 −0.564897 −0.282449 0.959282i \(-0.591147\pi\)
−0.282449 + 0.959282i \(0.591147\pi\)
\(398\) 31.8058 1.59428
\(399\) −4.23413 −0.211971
\(400\) 19.1546 0.957732
\(401\) 14.9145 0.744796 0.372398 0.928073i \(-0.378536\pi\)
0.372398 + 0.928073i \(0.378536\pi\)
\(402\) 9.21471 0.459588
\(403\) 2.70029 0.134511
\(404\) −5.25227 −0.261310
\(405\) 2.45775 0.122127
\(406\) 58.9775 2.92700
\(407\) 5.41950 0.268635
\(408\) 0.575703 0.0285016
\(409\) −29.3022 −1.44890 −0.724450 0.689327i \(-0.757906\pi\)
−0.724450 + 0.689327i \(0.757906\pi\)
\(410\) −11.3310 −0.559596
\(411\) 18.5576 0.915377
\(412\) −6.89165 −0.339527
\(413\) −0.941945 −0.0463501
\(414\) 12.1533 0.597304
\(415\) 2.74002 0.134503
\(416\) −42.3799 −2.07784
\(417\) −23.2212 −1.13715
\(418\) 9.99564 0.488903
\(419\) 18.5845 0.907915 0.453957 0.891023i \(-0.350012\pi\)
0.453957 + 0.891023i \(0.350012\pi\)
\(420\) −5.40682 −0.263826
\(421\) −18.9421 −0.923179 −0.461590 0.887094i \(-0.652721\pi\)
−0.461590 + 0.887094i \(0.652721\pi\)
\(422\) −16.3817 −0.797448
\(423\) −9.58459 −0.466019
\(424\) 0.741886 0.0360292
\(425\) 12.9730 0.629282
\(426\) 30.8934 1.49679
\(427\) 0.839816 0.0406415
\(428\) 6.24098 0.301669
\(429\) 38.9814 1.88204
\(430\) −10.3264 −0.497981
\(431\) 21.5017 1.03570 0.517851 0.855471i \(-0.326732\pi\)
0.517851 + 0.855471i \(0.326732\pi\)
\(432\) −23.3770 −1.12473
\(433\) −32.5442 −1.56398 −0.781988 0.623293i \(-0.785794\pi\)
−0.781988 + 0.623293i \(0.785794\pi\)
\(434\) −3.38093 −0.162290
\(435\) 7.30026 0.350021
\(436\) 1.92294 0.0920923
\(437\) −4.77228 −0.228289
\(438\) −5.75934 −0.275192
\(439\) −20.3993 −0.973607 −0.486804 0.873511i \(-0.661837\pi\)
−0.486804 + 0.873511i \(0.661837\pi\)
\(440\) −0.511484 −0.0243840
\(441\) −5.35054 −0.254787
\(442\) −29.8104 −1.41794
\(443\) −2.83110 −0.134510 −0.0672548 0.997736i \(-0.521424\pi\)
−0.0672548 + 0.997736i \(0.521424\pi\)
\(444\) −2.58182 −0.122528
\(445\) −0.416606 −0.0197490
\(446\) 9.24108 0.437578
\(447\) −21.3770 −1.01110
\(448\) 24.9661 1.17954
\(449\) −7.53564 −0.355629 −0.177814 0.984064i \(-0.556903\pi\)
−0.177814 + 0.984064i \(0.556903\pi\)
\(450\) −10.9504 −0.516208
\(451\) −50.1376 −2.36089
\(452\) 34.6609 1.63031
\(453\) −13.5316 −0.635769
\(454\) −10.8618 −0.509768
\(455\) −11.2190 −0.525955
\(456\) 0.190819 0.00893591
\(457\) 6.71365 0.314051 0.157026 0.987595i \(-0.449809\pi\)
0.157026 + 0.987595i \(0.449809\pi\)
\(458\) 4.93178 0.230447
\(459\) −15.8327 −0.739006
\(460\) −6.09402 −0.284135
\(461\) 22.8486 1.06417 0.532083 0.846692i \(-0.321409\pi\)
0.532083 + 0.846692i \(0.321409\pi\)
\(462\) −48.8072 −2.27072
\(463\) −19.7218 −0.916552 −0.458276 0.888810i \(-0.651533\pi\)
−0.458276 + 0.888810i \(0.651533\pi\)
\(464\) −36.4736 −1.69325
\(465\) −0.418493 −0.0194071
\(466\) 16.5289 0.765686
\(467\) −11.3800 −0.526605 −0.263302 0.964713i \(-0.584812\pi\)
−0.263302 + 0.964713i \(0.584812\pi\)
\(468\) 12.3343 0.570152
\(469\) −11.7348 −0.541861
\(470\) 9.80455 0.452250
\(471\) 23.5562 1.08541
\(472\) 0.0424505 0.00195394
\(473\) −45.6923 −2.10094
\(474\) 33.3877 1.53355
\(475\) 4.29994 0.197295
\(476\) 18.2957 0.838580
\(477\) −5.82010 −0.266484
\(478\) −31.4444 −1.43823
\(479\) −38.7162 −1.76899 −0.884495 0.466550i \(-0.845497\pi\)
−0.884495 + 0.466550i \(0.845497\pi\)
\(480\) 6.56807 0.299790
\(481\) −5.35721 −0.244268
\(482\) −39.6200 −1.80464
\(483\) 23.3023 1.06029
\(484\) 35.3264 1.60574
\(485\) 5.24674 0.238242
\(486\) 22.9163 1.03951
\(487\) 4.30432 0.195048 0.0975238 0.995233i \(-0.468908\pi\)
0.0975238 + 0.995233i \(0.468908\pi\)
\(488\) −0.0378479 −0.00171329
\(489\) 18.2011 0.823082
\(490\) 5.47333 0.247260
\(491\) 4.44326 0.200522 0.100261 0.994961i \(-0.468032\pi\)
0.100261 + 0.994961i \(0.468032\pi\)
\(492\) 23.8853 1.07683
\(493\) −24.7027 −1.11255
\(494\) −9.88075 −0.444556
\(495\) 4.01259 0.180353
\(496\) 2.09088 0.0938831
\(497\) −39.3422 −1.76474
\(498\) −11.7832 −0.528018
\(499\) −40.1351 −1.79669 −0.898347 0.439287i \(-0.855231\pi\)
−0.898347 + 0.439287i \(0.855231\pi\)
\(500\) 11.4364 0.511452
\(501\) 0.359297 0.0160522
\(502\) 22.5857 1.00805
\(503\) −18.2884 −0.815440 −0.407720 0.913107i \(-0.633676\pi\)
−0.407720 + 0.913107i \(0.633676\pi\)
\(504\) 0.618847 0.0275656
\(505\) 1.68903 0.0751609
\(506\) −55.0105 −2.44552
\(507\) −21.0790 −0.936153
\(508\) 15.7878 0.700470
\(509\) −22.5704 −1.00041 −0.500207 0.865906i \(-0.666743\pi\)
−0.500207 + 0.865906i \(0.666743\pi\)
\(510\) 4.62004 0.204579
\(511\) 7.33441 0.324455
\(512\) −31.5492 −1.39429
\(513\) −5.24780 −0.231696
\(514\) −12.4275 −0.548153
\(515\) 2.21622 0.0976585
\(516\) 21.7676 0.958265
\(517\) 43.3834 1.90800
\(518\) 6.70756 0.294713
\(519\) 1.18461 0.0519987
\(520\) 0.505605 0.0221722
\(521\) 35.6566 1.56214 0.781072 0.624441i \(-0.214673\pi\)
0.781072 + 0.624441i \(0.214673\pi\)
\(522\) 20.8515 0.912644
\(523\) 18.7053 0.817924 0.408962 0.912552i \(-0.365891\pi\)
0.408962 + 0.912552i \(0.365891\pi\)
\(524\) 1.50272 0.0656467
\(525\) −20.9959 −0.916337
\(526\) 39.8504 1.73756
\(527\) 1.41610 0.0616863
\(528\) 30.1840 1.31359
\(529\) 3.26402 0.141914
\(530\) 5.95366 0.258611
\(531\) −0.333024 −0.0144520
\(532\) 6.06416 0.262915
\(533\) 49.5613 2.14674
\(534\) 1.79157 0.0775289
\(535\) −2.00698 −0.0867693
\(536\) 0.528849 0.0228428
\(537\) −12.3897 −0.534654
\(538\) 25.8006 1.11234
\(539\) 24.2185 1.04317
\(540\) −6.70124 −0.288375
\(541\) −16.8553 −0.724666 −0.362333 0.932049i \(-0.618020\pi\)
−0.362333 + 0.932049i \(0.618020\pi\)
\(542\) −18.3421 −0.787860
\(543\) 16.1513 0.693120
\(544\) −22.2251 −0.952894
\(545\) −0.618382 −0.0264886
\(546\) 48.2462 2.06475
\(547\) −15.5802 −0.666162 −0.333081 0.942898i \(-0.608088\pi\)
−0.333081 + 0.942898i \(0.608088\pi\)
\(548\) −26.5783 −1.13537
\(549\) 0.296917 0.0126721
\(550\) 49.5658 2.11349
\(551\) −8.18780 −0.348812
\(552\) −1.05016 −0.0446979
\(553\) −42.5186 −1.80808
\(554\) 13.2597 0.563351
\(555\) 0.830265 0.0352428
\(556\) 33.2576 1.41044
\(557\) 30.3804 1.28726 0.643630 0.765337i \(-0.277428\pi\)
0.643630 + 0.765337i \(0.277428\pi\)
\(558\) −1.19532 −0.0506021
\(559\) 45.1671 1.91037
\(560\) −8.68705 −0.367095
\(561\) 20.4429 0.863099
\(562\) −52.4011 −2.21041
\(563\) −16.9390 −0.713893 −0.356947 0.934125i \(-0.616182\pi\)
−0.356947 + 0.934125i \(0.616182\pi\)
\(564\) −20.6676 −0.870265
\(565\) −11.1463 −0.468927
\(566\) 26.7198 1.12312
\(567\) 13.4598 0.565260
\(568\) 1.77303 0.0743947
\(569\) 1.18080 0.0495017 0.0247508 0.999694i \(-0.492121\pi\)
0.0247508 + 0.999694i \(0.492121\pi\)
\(570\) 1.53133 0.0641403
\(571\) 27.1901 1.13787 0.568935 0.822382i \(-0.307355\pi\)
0.568935 + 0.822382i \(0.307355\pi\)
\(572\) −55.8296 −2.33435
\(573\) 15.8172 0.660771
\(574\) −62.0538 −2.59008
\(575\) −23.6645 −0.986878
\(576\) 8.82677 0.367782
\(577\) 6.24617 0.260032 0.130016 0.991512i \(-0.458497\pi\)
0.130016 + 0.991512i \(0.458497\pi\)
\(578\) 18.0376 0.750264
\(579\) −12.9005 −0.536125
\(580\) −10.4555 −0.434141
\(581\) 15.0057 0.622541
\(582\) −22.5631 −0.935269
\(583\) 26.3439 1.09105
\(584\) −0.330539 −0.0136778
\(585\) −3.96647 −0.163993
\(586\) 5.20930 0.215194
\(587\) 5.95229 0.245677 0.122839 0.992427i \(-0.460800\pi\)
0.122839 + 0.992427i \(0.460800\pi\)
\(588\) −11.5376 −0.475802
\(589\) 0.469371 0.0193401
\(590\) 0.340667 0.0140250
\(591\) −15.8429 −0.651690
\(592\) −4.14818 −0.170489
\(593\) 36.1326 1.48379 0.741893 0.670518i \(-0.233928\pi\)
0.741893 + 0.670518i \(0.233928\pi\)
\(594\) −60.4918 −2.48201
\(595\) −5.88354 −0.241201
\(596\) 30.6163 1.25409
\(597\) 21.5606 0.882416
\(598\) 54.3782 2.22369
\(599\) −8.09365 −0.330698 −0.165349 0.986235i \(-0.552875\pi\)
−0.165349 + 0.986235i \(0.552875\pi\)
\(600\) 0.946221 0.0386293
\(601\) 43.2733 1.76515 0.882577 0.470168i \(-0.155807\pi\)
0.882577 + 0.470168i \(0.155807\pi\)
\(602\) −56.5521 −2.30489
\(603\) −4.14882 −0.168953
\(604\) 19.3801 0.788563
\(605\) −11.3603 −0.461861
\(606\) −7.26351 −0.295060
\(607\) 13.3527 0.541970 0.270985 0.962584i \(-0.412651\pi\)
0.270985 + 0.962584i \(0.412651\pi\)
\(608\) −7.36659 −0.298755
\(609\) 39.9798 1.62006
\(610\) −0.303731 −0.0122977
\(611\) −42.8848 −1.73493
\(612\) 6.46842 0.261470
\(613\) 2.16839 0.0875804 0.0437902 0.999041i \(-0.486057\pi\)
0.0437902 + 0.999041i \(0.486057\pi\)
\(614\) −20.2167 −0.815879
\(615\) −7.68105 −0.309730
\(616\) −2.80113 −0.112861
\(617\) −37.9751 −1.52882 −0.764410 0.644731i \(-0.776970\pi\)
−0.764410 + 0.644731i \(0.776970\pi\)
\(618\) −9.53065 −0.383379
\(619\) −27.9924 −1.12511 −0.562555 0.826760i \(-0.690181\pi\)
−0.562555 + 0.826760i \(0.690181\pi\)
\(620\) 0.599369 0.0240713
\(621\) 28.8810 1.15895
\(622\) −48.8248 −1.95770
\(623\) −2.28153 −0.0914077
\(624\) −29.8370 −1.19444
\(625\) 19.4103 0.776411
\(626\) 67.7684 2.70857
\(627\) 6.77586 0.270602
\(628\) −33.7375 −1.34627
\(629\) −2.80946 −0.112021
\(630\) 4.96627 0.197861
\(631\) −9.66675 −0.384827 −0.192414 0.981314i \(-0.561632\pi\)
−0.192414 + 0.981314i \(0.561632\pi\)
\(632\) 1.91618 0.0762216
\(633\) −11.1048 −0.441378
\(634\) 61.4118 2.43897
\(635\) −5.07705 −0.201477
\(636\) −12.5501 −0.497645
\(637\) −23.9402 −0.948544
\(638\) −94.3815 −3.73660
\(639\) −13.9094 −0.550248
\(640\) 0.754467 0.0298229
\(641\) −5.72871 −0.226271 −0.113135 0.993580i \(-0.536089\pi\)
−0.113135 + 0.993580i \(0.536089\pi\)
\(642\) 8.63082 0.340631
\(643\) 11.4965 0.453377 0.226689 0.973967i \(-0.427210\pi\)
0.226689 + 0.973967i \(0.427210\pi\)
\(644\) −33.3738 −1.31511
\(645\) −7.00004 −0.275626
\(646\) −5.18173 −0.203872
\(647\) −1.59477 −0.0626968 −0.0313484 0.999509i \(-0.509980\pi\)
−0.0313484 + 0.999509i \(0.509980\pi\)
\(648\) −0.606592 −0.0238292
\(649\) 1.50739 0.0591703
\(650\) −48.9961 −1.92178
\(651\) −2.29187 −0.0898254
\(652\) −26.0678 −1.02089
\(653\) −49.5836 −1.94036 −0.970179 0.242389i \(-0.922069\pi\)
−0.970179 + 0.242389i \(0.922069\pi\)
\(654\) 2.65929 0.103987
\(655\) −0.483247 −0.0188820
\(656\) 38.3761 1.49834
\(657\) 2.59308 0.101166
\(658\) 53.6944 2.09323
\(659\) −42.8682 −1.66991 −0.834954 0.550319i \(-0.814506\pi\)
−0.834954 + 0.550319i \(0.814506\pi\)
\(660\) 8.65252 0.336799
\(661\) −13.2723 −0.516234 −0.258117 0.966114i \(-0.583102\pi\)
−0.258117 + 0.966114i \(0.583102\pi\)
\(662\) 52.2587 2.03109
\(663\) −20.2079 −0.784810
\(664\) −0.676260 −0.0262440
\(665\) −1.95012 −0.0756223
\(666\) 2.37145 0.0918920
\(667\) 45.0612 1.74478
\(668\) −0.514588 −0.0199100
\(669\) 6.26436 0.242194
\(670\) 4.24403 0.163961
\(671\) −1.34396 −0.0518828
\(672\) 35.9699 1.38757
\(673\) 26.9109 1.03734 0.518670 0.854974i \(-0.326427\pi\)
0.518670 + 0.854974i \(0.326427\pi\)
\(674\) 32.2612 1.24266
\(675\) −26.0224 −1.00160
\(676\) 30.1896 1.16114
\(677\) −0.906737 −0.0348487 −0.0174244 0.999848i \(-0.505547\pi\)
−0.0174244 + 0.999848i \(0.505547\pi\)
\(678\) 47.9335 1.84087
\(679\) 28.7337 1.10270
\(680\) 0.265153 0.0101681
\(681\) −7.36300 −0.282151
\(682\) 5.41049 0.207178
\(683\) 24.5925 0.941007 0.470503 0.882398i \(-0.344072\pi\)
0.470503 + 0.882398i \(0.344072\pi\)
\(684\) 2.14398 0.0819771
\(685\) 8.54709 0.326567
\(686\) −16.9783 −0.648236
\(687\) 3.34316 0.127550
\(688\) 34.9737 1.33336
\(689\) −26.0411 −0.992089
\(690\) −8.42759 −0.320833
\(691\) −36.5197 −1.38928 −0.694638 0.719360i \(-0.744435\pi\)
−0.694638 + 0.719360i \(0.744435\pi\)
\(692\) −1.69661 −0.0644956
\(693\) 21.9749 0.834757
\(694\) 31.0867 1.18003
\(695\) −10.6950 −0.405685
\(696\) −1.80176 −0.0682956
\(697\) 25.9912 0.984488
\(698\) 31.3695 1.18735
\(699\) 11.2046 0.423798
\(700\) 30.0706 1.13656
\(701\) 19.8679 0.750400 0.375200 0.926944i \(-0.377574\pi\)
0.375200 + 0.926944i \(0.377574\pi\)
\(702\) 59.7965 2.25688
\(703\) −0.931205 −0.0351211
\(704\) −39.9533 −1.50579
\(705\) 6.64632 0.250315
\(706\) −32.0088 −1.20467
\(707\) 9.24995 0.347880
\(708\) −0.718114 −0.0269884
\(709\) −2.15409 −0.0808985 −0.0404493 0.999182i \(-0.512879\pi\)
−0.0404493 + 0.999182i \(0.512879\pi\)
\(710\) 14.2286 0.533991
\(711\) −15.0324 −0.563760
\(712\) 0.102822 0.00385340
\(713\) −2.58316 −0.0967402
\(714\) 25.3016 0.946887
\(715\) 17.9537 0.671431
\(716\) 17.7446 0.663147
\(717\) −21.3156 −0.796045
\(718\) 67.0157 2.50100
\(719\) 42.5468 1.58673 0.793363 0.608749i \(-0.208328\pi\)
0.793363 + 0.608749i \(0.208328\pi\)
\(720\) −3.07130 −0.114461
\(721\) 12.1371 0.452010
\(722\) 35.9147 1.33661
\(723\) −26.8577 −0.998848
\(724\) −23.1321 −0.859698
\(725\) −40.6012 −1.50789
\(726\) 48.8538 1.81313
\(727\) 12.2622 0.454779 0.227390 0.973804i \(-0.426981\pi\)
0.227390 + 0.973804i \(0.426981\pi\)
\(728\) 2.76894 0.102624
\(729\) 27.4580 1.01696
\(730\) −2.65259 −0.0981767
\(731\) 23.6868 0.876089
\(732\) 0.640253 0.0236644
\(733\) 24.0175 0.887106 0.443553 0.896248i \(-0.353718\pi\)
0.443553 + 0.896248i \(0.353718\pi\)
\(734\) −28.1016 −1.03725
\(735\) 3.71027 0.136855
\(736\) 40.5416 1.49439
\(737\) 18.7791 0.691738
\(738\) −21.9391 −0.807589
\(739\) −25.9424 −0.954305 −0.477152 0.878821i \(-0.658331\pi\)
−0.477152 + 0.878821i \(0.658331\pi\)
\(740\) −1.18911 −0.0437127
\(741\) −6.69798 −0.246056
\(742\) 32.6051 1.19697
\(743\) −44.7577 −1.64200 −0.821000 0.570928i \(-0.806584\pi\)
−0.821000 + 0.570928i \(0.806584\pi\)
\(744\) 0.103287 0.00378670
\(745\) −9.84563 −0.360716
\(746\) 10.2966 0.376985
\(747\) 5.30526 0.194109
\(748\) −29.2785 −1.07053
\(749\) −10.9912 −0.401609
\(750\) 15.8157 0.577509
\(751\) 20.9474 0.764382 0.382191 0.924083i \(-0.375170\pi\)
0.382191 + 0.924083i \(0.375170\pi\)
\(752\) −33.2064 −1.21091
\(753\) 15.3104 0.557944
\(754\) 93.2967 3.39767
\(755\) −6.23226 −0.226815
\(756\) −36.6992 −1.33474
\(757\) −9.25237 −0.336283 −0.168142 0.985763i \(-0.553777\pi\)
−0.168142 + 0.985763i \(0.553777\pi\)
\(758\) 14.9372 0.542542
\(759\) −37.2906 −1.35356
\(760\) 0.0878857 0.00318795
\(761\) 32.8736 1.19167 0.595834 0.803108i \(-0.296822\pi\)
0.595834 + 0.803108i \(0.296822\pi\)
\(762\) 21.8334 0.790939
\(763\) −3.38656 −0.122602
\(764\) −22.6535 −0.819574
\(765\) −2.08012 −0.0752069
\(766\) 67.6963 2.44597
\(767\) −1.49007 −0.0538032
\(768\) −23.0408 −0.831412
\(769\) −8.03230 −0.289652 −0.144826 0.989457i \(-0.546262\pi\)
−0.144826 + 0.989457i \(0.546262\pi\)
\(770\) −22.4792 −0.810094
\(771\) −8.42436 −0.303396
\(772\) 18.4762 0.664972
\(773\) 33.0334 1.18813 0.594064 0.804418i \(-0.297523\pi\)
0.594064 + 0.804418i \(0.297523\pi\)
\(774\) −19.9940 −0.718668
\(775\) 2.32749 0.0836059
\(776\) −1.29494 −0.0464855
\(777\) 4.54693 0.163120
\(778\) −0.748524 −0.0268359
\(779\) 8.61488 0.308660
\(780\) −8.55307 −0.306249
\(781\) 62.9593 2.25286
\(782\) 28.5174 1.01978
\(783\) 49.5511 1.77081
\(784\) −18.5373 −0.662045
\(785\) 10.8493 0.387229
\(786\) 2.07815 0.0741253
\(787\) −1.62205 −0.0578198 −0.0289099 0.999582i \(-0.509204\pi\)
−0.0289099 + 0.999582i \(0.509204\pi\)
\(788\) 22.6904 0.808311
\(789\) 27.0139 0.961719
\(790\) 15.3774 0.547104
\(791\) −61.0424 −2.17042
\(792\) −0.990339 −0.0351902
\(793\) 1.32851 0.0471767
\(794\) 22.2931 0.791153
\(795\) 4.03588 0.143138
\(796\) −30.8793 −1.09449
\(797\) 22.4418 0.794930 0.397465 0.917617i \(-0.369890\pi\)
0.397465 + 0.917617i \(0.369890\pi\)
\(798\) 8.38629 0.296871
\(799\) −22.4899 −0.795636
\(800\) −36.5290 −1.29149
\(801\) −0.806635 −0.0285011
\(802\) −29.5404 −1.04311
\(803\) −11.7372 −0.414198
\(804\) −8.94627 −0.315511
\(805\) 10.7324 0.378267
\(806\) −5.34830 −0.188386
\(807\) 17.4898 0.615670
\(808\) −0.416866 −0.0146653
\(809\) 55.8477 1.96350 0.981750 0.190177i \(-0.0609060\pi\)
0.981750 + 0.190177i \(0.0609060\pi\)
\(810\) −4.86793 −0.171041
\(811\) −1.34389 −0.0471904 −0.0235952 0.999722i \(-0.507511\pi\)
−0.0235952 + 0.999722i \(0.507511\pi\)
\(812\) −57.2594 −2.00941
\(813\) −12.4338 −0.436071
\(814\) −10.7341 −0.376230
\(815\) 8.38291 0.293640
\(816\) −15.6473 −0.547766
\(817\) 7.85108 0.274675
\(818\) 58.0372 2.02922
\(819\) −21.7223 −0.759039
\(820\) 11.0009 0.384167
\(821\) −22.2906 −0.777947 −0.388974 0.921249i \(-0.627170\pi\)
−0.388974 + 0.921249i \(0.627170\pi\)
\(822\) −36.7559 −1.28201
\(823\) −19.0993 −0.665761 −0.332881 0.942969i \(-0.608021\pi\)
−0.332881 + 0.942969i \(0.608021\pi\)
\(824\) −0.546981 −0.0190550
\(825\) 33.5997 1.16979
\(826\) 1.86566 0.0649144
\(827\) 34.2701 1.19169 0.595844 0.803100i \(-0.296818\pi\)
0.595844 + 0.803100i \(0.296818\pi\)
\(828\) −11.7993 −0.410054
\(829\) 43.4107 1.50772 0.753858 0.657038i \(-0.228191\pi\)
0.753858 + 0.657038i \(0.228191\pi\)
\(830\) −5.42701 −0.188374
\(831\) 8.98851 0.311808
\(832\) 39.4940 1.36921
\(833\) −12.5549 −0.435000
\(834\) 45.9929 1.59260
\(835\) 0.165482 0.00572674
\(836\) −9.70446 −0.335636
\(837\) −2.84055 −0.0981838
\(838\) −36.8093 −1.27156
\(839\) −48.7389 −1.68265 −0.841327 0.540527i \(-0.818225\pi\)
−0.841327 + 0.540527i \(0.818225\pi\)
\(840\) −0.429132 −0.0148065
\(841\) 48.3114 1.66591
\(842\) 37.5174 1.29294
\(843\) −35.5218 −1.22343
\(844\) 15.9045 0.547454
\(845\) −9.70841 −0.333979
\(846\) 18.9836 0.652671
\(847\) −62.2144 −2.13771
\(848\) −20.1641 −0.692438
\(849\) 18.1129 0.621632
\(850\) −25.6948 −0.881325
\(851\) 5.12484 0.175677
\(852\) −29.9935 −1.02756
\(853\) −32.3940 −1.10915 −0.554575 0.832134i \(-0.687119\pi\)
−0.554575 + 0.832134i \(0.687119\pi\)
\(854\) −1.66338 −0.0569195
\(855\) −0.689463 −0.0235791
\(856\) 0.495339 0.0169303
\(857\) −10.4501 −0.356969 −0.178485 0.983943i \(-0.557119\pi\)
−0.178485 + 0.983943i \(0.557119\pi\)
\(858\) −77.2082 −2.63585
\(859\) −23.4961 −0.801677 −0.400838 0.916149i \(-0.631281\pi\)
−0.400838 + 0.916149i \(0.631281\pi\)
\(860\) 10.0255 0.341868
\(861\) −42.0651 −1.43358
\(862\) −42.5872 −1.45053
\(863\) −0.346409 −0.0117919 −0.00589595 0.999983i \(-0.501877\pi\)
−0.00589595 + 0.999983i \(0.501877\pi\)
\(864\) 44.5813 1.51669
\(865\) 0.545599 0.0185509
\(866\) 64.4585 2.19039
\(867\) 12.2273 0.415262
\(868\) 3.28244 0.111413
\(869\) 68.0424 2.30818
\(870\) −14.4592 −0.490213
\(871\) −18.5633 −0.628992
\(872\) 0.152622 0.00516842
\(873\) 10.1588 0.343822
\(874\) 9.45218 0.319725
\(875\) −20.1411 −0.680892
\(876\) 5.59156 0.188921
\(877\) −25.9020 −0.874647 −0.437323 0.899304i \(-0.644073\pi\)
−0.437323 + 0.899304i \(0.644073\pi\)
\(878\) 40.4038 1.36356
\(879\) 3.53129 0.119107
\(880\) 13.9019 0.468632
\(881\) 42.8707 1.44435 0.722175 0.691711i \(-0.243143\pi\)
0.722175 + 0.691711i \(0.243143\pi\)
\(882\) 10.5975 0.356836
\(883\) 34.5821 1.16378 0.581891 0.813267i \(-0.302313\pi\)
0.581891 + 0.813267i \(0.302313\pi\)
\(884\) 28.9420 0.973424
\(885\) 0.230932 0.00776268
\(886\) 5.60740 0.188384
\(887\) 23.3777 0.784945 0.392473 0.919764i \(-0.371620\pi\)
0.392473 + 0.919764i \(0.371620\pi\)
\(888\) −0.204916 −0.00687653
\(889\) −27.8044 −0.932529
\(890\) 0.825147 0.0276590
\(891\) −21.5397 −0.721608
\(892\) −8.97188 −0.300401
\(893\) −7.45436 −0.249451
\(894\) 42.3401 1.41607
\(895\) −5.70633 −0.190742
\(896\) 4.13183 0.138035
\(897\) 36.8620 1.23079
\(898\) 14.9254 0.498067
\(899\) −4.43193 −0.147813
\(900\) 10.6314 0.354381
\(901\) −13.6567 −0.454969
\(902\) 99.3046 3.30648
\(903\) −38.3356 −1.27573
\(904\) 2.75099 0.0914965
\(905\) 7.43885 0.247276
\(906\) 26.8012 0.890410
\(907\) 10.5157 0.349167 0.174584 0.984642i \(-0.444142\pi\)
0.174584 + 0.984642i \(0.444142\pi\)
\(908\) 10.5454 0.349960
\(909\) 3.27032 0.108470
\(910\) 22.2208 0.736613
\(911\) 15.8768 0.526022 0.263011 0.964793i \(-0.415284\pi\)
0.263011 + 0.964793i \(0.415284\pi\)
\(912\) −5.18636 −0.171737
\(913\) −24.0136 −0.794733
\(914\) −13.2973 −0.439837
\(915\) −0.205893 −0.00680662
\(916\) −4.78811 −0.158204
\(917\) −2.64649 −0.0873949
\(918\) 31.3589 1.03500
\(919\) −3.98228 −0.131363 −0.0656816 0.997841i \(-0.520922\pi\)
−0.0656816 + 0.997841i \(0.520922\pi\)
\(920\) −0.483675 −0.0159463
\(921\) −13.7045 −0.451579
\(922\) −45.2549 −1.49039
\(923\) −62.2356 −2.04851
\(924\) 47.3854 1.55886
\(925\) −4.61760 −0.151826
\(926\) 39.0619 1.28365
\(927\) 4.29107 0.140937
\(928\) 69.5573 2.28333
\(929\) 7.27481 0.238679 0.119339 0.992854i \(-0.461922\pi\)
0.119339 + 0.992854i \(0.461922\pi\)
\(930\) 0.828884 0.0271802
\(931\) −4.16135 −0.136383
\(932\) −16.0474 −0.525649
\(933\) −33.0974 −1.08356
\(934\) 22.5398 0.737523
\(935\) 9.41541 0.307917
\(936\) 0.978956 0.0319982
\(937\) 20.1417 0.658001 0.329001 0.944330i \(-0.393288\pi\)
0.329001 + 0.944330i \(0.393288\pi\)
\(938\) 23.2424 0.758890
\(939\) 45.9389 1.49916
\(940\) −9.51893 −0.310473
\(941\) −22.4087 −0.730503 −0.365251 0.930909i \(-0.619017\pi\)
−0.365251 + 0.930909i \(0.619017\pi\)
\(942\) −46.6565 −1.52015
\(943\) −47.4116 −1.54393
\(944\) −1.15378 −0.0375524
\(945\) 11.8018 0.383911
\(946\) 90.5001 2.94241
\(947\) 53.4987 1.73847 0.869237 0.494396i \(-0.164611\pi\)
0.869237 + 0.494396i \(0.164611\pi\)
\(948\) −32.4151 −1.05279
\(949\) 11.6023 0.376628
\(950\) −8.51664 −0.276316
\(951\) 41.6299 1.34994
\(952\) 1.45210 0.0470629
\(953\) 58.1206 1.88271 0.941355 0.337418i \(-0.109554\pi\)
0.941355 + 0.337418i \(0.109554\pi\)
\(954\) 11.5275 0.373218
\(955\) 7.28493 0.235735
\(956\) 30.5284 0.987359
\(957\) −63.9795 −2.06816
\(958\) 76.6830 2.47752
\(959\) 46.8080 1.51151
\(960\) −6.12082 −0.197549
\(961\) −30.7459 −0.991804
\(962\) 10.6107 0.342103
\(963\) −3.88593 −0.125222
\(964\) 38.4658 1.23890
\(965\) −5.94159 −0.191267
\(966\) −46.1535 −1.48497
\(967\) 28.9234 0.930113 0.465056 0.885281i \(-0.346034\pi\)
0.465056 + 0.885281i \(0.346034\pi\)
\(968\) 2.80381 0.0901178
\(969\) −3.51260 −0.112841
\(970\) −10.3919 −0.333664
\(971\) −33.5902 −1.07796 −0.538980 0.842319i \(-0.681190\pi\)
−0.538980 + 0.842319i \(0.681190\pi\)
\(972\) −22.2487 −0.713629
\(973\) −58.5711 −1.87770
\(974\) −8.52533 −0.273169
\(975\) −33.2135 −1.06368
\(976\) 1.02869 0.0329274
\(977\) 25.7667 0.824348 0.412174 0.911105i \(-0.364770\pi\)
0.412174 + 0.911105i \(0.364770\pi\)
\(978\) −36.0499 −1.15275
\(979\) 3.65113 0.116691
\(980\) −5.31388 −0.169746
\(981\) −1.19732 −0.0382274
\(982\) −8.80052 −0.280836
\(983\) −31.6310 −1.00887 −0.504436 0.863449i \(-0.668299\pi\)
−0.504436 + 0.863449i \(0.668299\pi\)
\(984\) 1.89574 0.0604341
\(985\) −7.29679 −0.232495
\(986\) 48.9273 1.55816
\(987\) 36.3985 1.15858
\(988\) 9.59291 0.305191
\(989\) −43.2080 −1.37394
\(990\) −7.94751 −0.252588
\(991\) 1.60296 0.0509196 0.0254598 0.999676i \(-0.491895\pi\)
0.0254598 + 0.999676i \(0.491895\pi\)
\(992\) −3.98742 −0.126601
\(993\) 35.4252 1.12419
\(994\) 77.9229 2.47156
\(995\) 9.93019 0.314808
\(996\) 11.4399 0.362488
\(997\) 31.0893 0.984609 0.492304 0.870423i \(-0.336155\pi\)
0.492304 + 0.870423i \(0.336155\pi\)
\(998\) 79.4933 2.51632
\(999\) 5.63549 0.178299
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.1.15 77
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4033.2.a.c.1.15 77 1.1 even 1 trivial