Properties

Label 671.2.a.d.1.10
Level $671$
Weight $2$
Character 671.1
Self dual yes
Analytic conductor $5.358$
Analytic rank $0$
Dimension $21$
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] = [671,2,Mod(1,671)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(671, 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("671.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 671 = 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 671.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: \(5.35796197563\)
Analytic rank: \(0\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 671.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.404310 q^{2} +1.66838 q^{3} -1.83653 q^{4} +0.0975766 q^{5} -0.674545 q^{6} +1.38056 q^{7} +1.55115 q^{8} -0.216497 q^{9} +O(q^{10})\) \(q-0.404310 q^{2} +1.66838 q^{3} -1.83653 q^{4} +0.0975766 q^{5} -0.674545 q^{6} +1.38056 q^{7} +1.55115 q^{8} -0.216497 q^{9} -0.0394512 q^{10} -1.00000 q^{11} -3.06404 q^{12} +1.91382 q^{13} -0.558177 q^{14} +0.162795 q^{15} +3.04592 q^{16} +6.39070 q^{17} +0.0875320 q^{18} +2.68107 q^{19} -0.179203 q^{20} +2.30331 q^{21} +0.404310 q^{22} +3.27987 q^{23} +2.58791 q^{24} -4.99048 q^{25} -0.773778 q^{26} -5.36635 q^{27} -2.53545 q^{28} +3.68854 q^{29} -0.0658198 q^{30} +8.77643 q^{31} -4.33380 q^{32} -1.66838 q^{33} -2.58383 q^{34} +0.134711 q^{35} +0.397604 q^{36} +8.11523 q^{37} -1.08399 q^{38} +3.19299 q^{39} +0.151356 q^{40} -7.68669 q^{41} -0.931253 q^{42} +0.587590 q^{43} +1.83653 q^{44} -0.0211251 q^{45} -1.32609 q^{46} -3.82618 q^{47} +5.08176 q^{48} -5.09404 q^{49} +2.01770 q^{50} +10.6621 q^{51} -3.51480 q^{52} +12.1754 q^{53} +2.16967 q^{54} -0.0975766 q^{55} +2.14146 q^{56} +4.47306 q^{57} -1.49132 q^{58} +4.38430 q^{59} -0.298979 q^{60} +1.00000 q^{61} -3.54840 q^{62} -0.298888 q^{63} -4.33964 q^{64} +0.186744 q^{65} +0.674545 q^{66} +2.09197 q^{67} -11.7367 q^{68} +5.47209 q^{69} -0.0544650 q^{70} -7.30897 q^{71} -0.335820 q^{72} +7.39795 q^{73} -3.28107 q^{74} -8.32603 q^{75} -4.92388 q^{76} -1.38056 q^{77} -1.29096 q^{78} -15.9826 q^{79} +0.297210 q^{80} -8.30364 q^{81} +3.10781 q^{82} -0.649661 q^{83} -4.23011 q^{84} +0.623582 q^{85} -0.237569 q^{86} +6.15390 q^{87} -1.55115 q^{88} -8.11324 q^{89} +0.00854108 q^{90} +2.64215 q^{91} -6.02360 q^{92} +14.6425 q^{93} +1.54696 q^{94} +0.261610 q^{95} -7.23044 q^{96} +6.04986 q^{97} +2.05957 q^{98} +0.216497 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9} + q^{10} - 21 q^{11} + 6 q^{12} + 20 q^{13} + 17 q^{14} + 18 q^{15} + 50 q^{16} + q^{17} - 5 q^{18} + 15 q^{19} - 2 q^{20} + 16 q^{21} + 11 q^{23} - 16 q^{24} + 48 q^{25} - 5 q^{26} + 12 q^{27} - 16 q^{28} - 9 q^{29} + 16 q^{30} + 22 q^{31} + 3 q^{32} - 3 q^{33} + 33 q^{34} - 39 q^{35} + 57 q^{36} + 21 q^{37} + 11 q^{38} - 28 q^{39} - 16 q^{40} + 7 q^{41} - 55 q^{42} + 16 q^{43} - 32 q^{44} + 44 q^{45} - 3 q^{46} + 5 q^{47} - 71 q^{48} + 80 q^{49} - 33 q^{50} - 19 q^{51} + 60 q^{52} + 9 q^{53} + 13 q^{54} - 7 q^{55} + 44 q^{56} + 39 q^{57} - 27 q^{58} + 13 q^{59} + 70 q^{60} + 21 q^{61} - 23 q^{62} + 24 q^{63} + 66 q^{64} + 25 q^{65} - 5 q^{66} + 38 q^{67} - 74 q^{68} - 17 q^{69} - 33 q^{70} + 12 q^{71} - 75 q^{72} + 20 q^{73} - 12 q^{74} - 10 q^{75} + 59 q^{76} - 5 q^{77} - 14 q^{78} + q^{79} - 38 q^{80} + 89 q^{81} + 7 q^{82} - 19 q^{83} - 14 q^{84} + 38 q^{85} - 3 q^{86} + 4 q^{87} + 6 q^{88} + 37 q^{89} - 174 q^{90} + 24 q^{91} + 31 q^{92} - 15 q^{93} - 64 q^{94} - 43 q^{95} - 38 q^{96} + 68 q^{97} - 2 q^{98} - 40 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.404310 −0.285891 −0.142945 0.989731i \(-0.545657\pi\)
−0.142945 + 0.989731i \(0.545657\pi\)
\(3\) 1.66838 0.963242 0.481621 0.876380i \(-0.340048\pi\)
0.481621 + 0.876380i \(0.340048\pi\)
\(4\) −1.83653 −0.918267
\(5\) 0.0975766 0.0436376 0.0218188 0.999762i \(-0.493054\pi\)
0.0218188 + 0.999762i \(0.493054\pi\)
\(6\) −0.674545 −0.275382
\(7\) 1.38056 0.521804 0.260902 0.965365i \(-0.415980\pi\)
0.260902 + 0.965365i \(0.415980\pi\)
\(8\) 1.55115 0.548414
\(9\) −0.216497 −0.0721657
\(10\) −0.0394512 −0.0124756
\(11\) −1.00000 −0.301511
\(12\) −3.06404 −0.884512
\(13\) 1.91382 0.530799 0.265399 0.964139i \(-0.414496\pi\)
0.265399 + 0.964139i \(0.414496\pi\)
\(14\) −0.558177 −0.149179
\(15\) 0.162795 0.0420335
\(16\) 3.04592 0.761480
\(17\) 6.39070 1.54997 0.774986 0.631979i \(-0.217757\pi\)
0.774986 + 0.631979i \(0.217757\pi\)
\(18\) 0.0875320 0.0206315
\(19\) 2.68107 0.615080 0.307540 0.951535i \(-0.400494\pi\)
0.307540 + 0.951535i \(0.400494\pi\)
\(20\) −0.179203 −0.0400709
\(21\) 2.30331 0.502624
\(22\) 0.404310 0.0861993
\(23\) 3.27987 0.683901 0.341951 0.939718i \(-0.388912\pi\)
0.341951 + 0.939718i \(0.388912\pi\)
\(24\) 2.58791 0.528256
\(25\) −4.99048 −0.998096
\(26\) −0.773778 −0.151750
\(27\) −5.36635 −1.03275
\(28\) −2.53545 −0.479156
\(29\) 3.68854 0.684945 0.342472 0.939528i \(-0.388736\pi\)
0.342472 + 0.939528i \(0.388736\pi\)
\(30\) −0.0658198 −0.0120170
\(31\) 8.77643 1.57629 0.788147 0.615487i \(-0.211041\pi\)
0.788147 + 0.615487i \(0.211041\pi\)
\(32\) −4.33380 −0.766114
\(33\) −1.66838 −0.290428
\(34\) −2.58383 −0.443122
\(35\) 0.134711 0.0227703
\(36\) 0.397604 0.0662674
\(37\) 8.11523 1.33414 0.667068 0.744997i \(-0.267549\pi\)
0.667068 + 0.744997i \(0.267549\pi\)
\(38\) −1.08399 −0.175846
\(39\) 3.19299 0.511287
\(40\) 0.151356 0.0239315
\(41\) −7.68669 −1.20046 −0.600230 0.799827i \(-0.704924\pi\)
−0.600230 + 0.799827i \(0.704924\pi\)
\(42\) −0.931253 −0.143695
\(43\) 0.587590 0.0896067 0.0448033 0.998996i \(-0.485734\pi\)
0.0448033 + 0.998996i \(0.485734\pi\)
\(44\) 1.83653 0.276868
\(45\) −0.0211251 −0.00314914
\(46\) −1.32609 −0.195521
\(47\) −3.82618 −0.558106 −0.279053 0.960276i \(-0.590020\pi\)
−0.279053 + 0.960276i \(0.590020\pi\)
\(48\) 5.08176 0.733489
\(49\) −5.09404 −0.727720
\(50\) 2.01770 0.285346
\(51\) 10.6621 1.49300
\(52\) −3.51480 −0.487415
\(53\) 12.1754 1.67242 0.836210 0.548410i \(-0.184767\pi\)
0.836210 + 0.548410i \(0.184767\pi\)
\(54\) 2.16967 0.295255
\(55\) −0.0975766 −0.0131572
\(56\) 2.14146 0.286165
\(57\) 4.47306 0.592471
\(58\) −1.49132 −0.195819
\(59\) 4.38430 0.570787 0.285394 0.958410i \(-0.407876\pi\)
0.285394 + 0.958410i \(0.407876\pi\)
\(60\) −0.298979 −0.0385980
\(61\) 1.00000 0.128037
\(62\) −3.54840 −0.450648
\(63\) −0.298888 −0.0376564
\(64\) −4.33964 −0.542455
\(65\) 0.186744 0.0231628
\(66\) 0.674545 0.0830307
\(67\) 2.09197 0.255575 0.127787 0.991802i \(-0.459212\pi\)
0.127787 + 0.991802i \(0.459212\pi\)
\(68\) −11.7367 −1.42329
\(69\) 5.47209 0.658762
\(70\) −0.0544650 −0.00650981
\(71\) −7.30897 −0.867416 −0.433708 0.901054i \(-0.642795\pi\)
−0.433708 + 0.901054i \(0.642795\pi\)
\(72\) −0.335820 −0.0395767
\(73\) 7.39795 0.865865 0.432933 0.901426i \(-0.357479\pi\)
0.432933 + 0.901426i \(0.357479\pi\)
\(74\) −3.28107 −0.381417
\(75\) −8.32603 −0.961407
\(76\) −4.92388 −0.564807
\(77\) −1.38056 −0.157330
\(78\) −1.29096 −0.146172
\(79\) −15.9826 −1.79819 −0.899093 0.437757i \(-0.855773\pi\)
−0.899093 + 0.437757i \(0.855773\pi\)
\(80\) 0.297210 0.0332291
\(81\) −8.30364 −0.922626
\(82\) 3.10781 0.343200
\(83\) −0.649661 −0.0713096 −0.0356548 0.999364i \(-0.511352\pi\)
−0.0356548 + 0.999364i \(0.511352\pi\)
\(84\) −4.23011 −0.461543
\(85\) 0.623582 0.0676370
\(86\) −0.237569 −0.0256177
\(87\) 6.15390 0.659767
\(88\) −1.55115 −0.165353
\(89\) −8.11324 −0.860001 −0.430001 0.902829i \(-0.641487\pi\)
−0.430001 + 0.902829i \(0.641487\pi\)
\(90\) 0.00854108 0.000900309 0
\(91\) 2.64215 0.276973
\(92\) −6.02360 −0.628004
\(93\) 14.6425 1.51835
\(94\) 1.54696 0.159557
\(95\) 0.261610 0.0268406
\(96\) −7.23044 −0.737953
\(97\) 6.04986 0.614271 0.307135 0.951666i \(-0.400630\pi\)
0.307135 + 0.951666i \(0.400630\pi\)
\(98\) 2.05957 0.208048
\(99\) 0.216497 0.0217588
\(100\) 9.16518 0.916518
\(101\) −13.4229 −1.33563 −0.667815 0.744327i \(-0.732770\pi\)
−0.667815 + 0.744327i \(0.732770\pi\)
\(102\) −4.31081 −0.426834
\(103\) 13.3184 1.31230 0.656151 0.754630i \(-0.272183\pi\)
0.656151 + 0.754630i \(0.272183\pi\)
\(104\) 2.96863 0.291098
\(105\) 0.224749 0.0219333
\(106\) −4.92264 −0.478129
\(107\) −11.4259 −1.10458 −0.552290 0.833652i \(-0.686246\pi\)
−0.552290 + 0.833652i \(0.686246\pi\)
\(108\) 9.85548 0.948344
\(109\) −19.4090 −1.85904 −0.929521 0.368768i \(-0.879780\pi\)
−0.929521 + 0.368768i \(0.879780\pi\)
\(110\) 0.0394512 0.00376153
\(111\) 13.5393 1.28510
\(112\) 4.20509 0.397344
\(113\) 11.7630 1.10657 0.553286 0.832992i \(-0.313374\pi\)
0.553286 + 0.832992i \(0.313374\pi\)
\(114\) −1.80850 −0.169382
\(115\) 0.320039 0.0298438
\(116\) −6.77413 −0.628962
\(117\) −0.414337 −0.0383055
\(118\) −1.77262 −0.163183
\(119\) 8.82277 0.808782
\(120\) 0.252520 0.0230518
\(121\) 1.00000 0.0909091
\(122\) −0.404310 −0.0366045
\(123\) −12.8244 −1.15633
\(124\) −16.1182 −1.44746
\(125\) −0.974837 −0.0871921
\(126\) 0.120844 0.0107656
\(127\) 12.7715 1.13329 0.566645 0.823962i \(-0.308241\pi\)
0.566645 + 0.823962i \(0.308241\pi\)
\(128\) 10.4222 0.921197
\(129\) 0.980326 0.0863129
\(130\) −0.0755026 −0.00662202
\(131\) 11.1301 0.972440 0.486220 0.873836i \(-0.338375\pi\)
0.486220 + 0.873836i \(0.338375\pi\)
\(132\) 3.06404 0.266691
\(133\) 3.70139 0.320952
\(134\) −0.845806 −0.0730665
\(135\) −0.523630 −0.0450669
\(136\) 9.91293 0.850027
\(137\) −6.41607 −0.548162 −0.274081 0.961707i \(-0.588374\pi\)
−0.274081 + 0.961707i \(0.588374\pi\)
\(138\) −2.21242 −0.188334
\(139\) 10.3340 0.876518 0.438259 0.898849i \(-0.355595\pi\)
0.438259 + 0.898849i \(0.355595\pi\)
\(140\) −0.247401 −0.0209092
\(141\) −6.38354 −0.537591
\(142\) 2.95509 0.247986
\(143\) −1.91382 −0.160042
\(144\) −0.659433 −0.0549527
\(145\) 0.359915 0.0298893
\(146\) −2.99107 −0.247543
\(147\) −8.49881 −0.700970
\(148\) −14.9039 −1.22509
\(149\) −10.9469 −0.896806 −0.448403 0.893832i \(-0.648007\pi\)
−0.448403 + 0.893832i \(0.648007\pi\)
\(150\) 3.36630 0.274857
\(151\) −14.0261 −1.14143 −0.570715 0.821149i \(-0.693334\pi\)
−0.570715 + 0.821149i \(0.693334\pi\)
\(152\) 4.15875 0.337319
\(153\) −1.38357 −0.111855
\(154\) 0.558177 0.0449792
\(155\) 0.856375 0.0687857
\(156\) −5.86403 −0.469498
\(157\) −20.5792 −1.64240 −0.821201 0.570639i \(-0.806695\pi\)
−0.821201 + 0.570639i \(0.806695\pi\)
\(158\) 6.46194 0.514085
\(159\) 20.3132 1.61094
\(160\) −0.422877 −0.0334314
\(161\) 4.52808 0.356863
\(162\) 3.35725 0.263770
\(163\) 1.51365 0.118559 0.0592793 0.998241i \(-0.481120\pi\)
0.0592793 + 0.998241i \(0.481120\pi\)
\(164\) 14.1169 1.10234
\(165\) −0.162795 −0.0126736
\(166\) 0.262665 0.0203867
\(167\) −16.5914 −1.28388 −0.641941 0.766754i \(-0.721870\pi\)
−0.641941 + 0.766754i \(0.721870\pi\)
\(168\) 3.57278 0.275646
\(169\) −9.33729 −0.718253
\(170\) −0.252121 −0.0193368
\(171\) −0.580444 −0.0443877
\(172\) −1.07913 −0.0822828
\(173\) −17.7599 −1.35026 −0.675128 0.737700i \(-0.735912\pi\)
−0.675128 + 0.737700i \(0.735912\pi\)
\(174\) −2.48809 −0.188621
\(175\) −6.88968 −0.520811
\(176\) −3.04592 −0.229595
\(177\) 7.31469 0.549806
\(178\) 3.28027 0.245866
\(179\) −19.8327 −1.48236 −0.741181 0.671305i \(-0.765734\pi\)
−0.741181 + 0.671305i \(0.765734\pi\)
\(180\) 0.0387969 0.00289175
\(181\) 7.18951 0.534392 0.267196 0.963642i \(-0.413903\pi\)
0.267196 + 0.963642i \(0.413903\pi\)
\(182\) −1.06825 −0.0791840
\(183\) 1.66838 0.123330
\(184\) 5.08758 0.375061
\(185\) 0.791857 0.0582185
\(186\) −5.92010 −0.434083
\(187\) −6.39070 −0.467334
\(188\) 7.02691 0.512490
\(189\) −7.40859 −0.538896
\(190\) −0.105772 −0.00767348
\(191\) −10.4136 −0.753503 −0.376751 0.926314i \(-0.622959\pi\)
−0.376751 + 0.926314i \(0.622959\pi\)
\(192\) −7.24018 −0.522515
\(193\) −6.92074 −0.498166 −0.249083 0.968482i \(-0.580129\pi\)
−0.249083 + 0.968482i \(0.580129\pi\)
\(194\) −2.44602 −0.175614
\(195\) 0.311561 0.0223113
\(196\) 9.35537 0.668241
\(197\) 5.12309 0.365005 0.182502 0.983205i \(-0.441580\pi\)
0.182502 + 0.983205i \(0.441580\pi\)
\(198\) −0.0875320 −0.00622063
\(199\) −9.17574 −0.650451 −0.325226 0.945636i \(-0.605440\pi\)
−0.325226 + 0.945636i \(0.605440\pi\)
\(200\) −7.74098 −0.547370
\(201\) 3.49021 0.246180
\(202\) 5.42702 0.381844
\(203\) 5.09227 0.357407
\(204\) −19.5814 −1.37097
\(205\) −0.750041 −0.0523852
\(206\) −5.38477 −0.375175
\(207\) −0.710083 −0.0493542
\(208\) 5.82935 0.404193
\(209\) −2.68107 −0.185454
\(210\) −0.0908685 −0.00627052
\(211\) 10.0749 0.693588 0.346794 0.937941i \(-0.387270\pi\)
0.346794 + 0.937941i \(0.387270\pi\)
\(212\) −22.3605 −1.53573
\(213\) −12.1942 −0.835531
\(214\) 4.61959 0.315789
\(215\) 0.0573350 0.00391022
\(216\) −8.32402 −0.566378
\(217\) 12.1164 0.822517
\(218\) 7.84725 0.531483
\(219\) 12.3426 0.834037
\(220\) 0.179203 0.0120818
\(221\) 12.2307 0.822723
\(222\) −5.47409 −0.367397
\(223\) 25.6563 1.71807 0.859037 0.511913i \(-0.171063\pi\)
0.859037 + 0.511913i \(0.171063\pi\)
\(224\) −5.98309 −0.399762
\(225\) 1.08042 0.0720283
\(226\) −4.75591 −0.316358
\(227\) −22.7936 −1.51286 −0.756431 0.654074i \(-0.773059\pi\)
−0.756431 + 0.654074i \(0.773059\pi\)
\(228\) −8.21491 −0.544046
\(229\) 22.0797 1.45907 0.729535 0.683943i \(-0.239736\pi\)
0.729535 + 0.683943i \(0.239736\pi\)
\(230\) −0.129395 −0.00853206
\(231\) −2.30331 −0.151547
\(232\) 5.72148 0.375634
\(233\) 24.2302 1.58737 0.793686 0.608327i \(-0.208159\pi\)
0.793686 + 0.608327i \(0.208159\pi\)
\(234\) 0.167521 0.0109512
\(235\) −0.373346 −0.0243544
\(236\) −8.05191 −0.524135
\(237\) −26.6652 −1.73209
\(238\) −3.56714 −0.231223
\(239\) −22.4004 −1.44896 −0.724481 0.689295i \(-0.757920\pi\)
−0.724481 + 0.689295i \(0.757920\pi\)
\(240\) 0.495861 0.0320077
\(241\) 17.1080 1.10202 0.551011 0.834498i \(-0.314242\pi\)
0.551011 + 0.834498i \(0.314242\pi\)
\(242\) −0.404310 −0.0259901
\(243\) 2.24540 0.144042
\(244\) −1.83653 −0.117572
\(245\) −0.497059 −0.0317559
\(246\) 5.18502 0.330585
\(247\) 5.13109 0.326484
\(248\) 13.6136 0.864463
\(249\) −1.08388 −0.0686883
\(250\) 0.394137 0.0249274
\(251\) −21.1591 −1.33555 −0.667774 0.744364i \(-0.732753\pi\)
−0.667774 + 0.744364i \(0.732753\pi\)
\(252\) 0.548918 0.0345786
\(253\) −3.27987 −0.206204
\(254\) −5.16366 −0.323997
\(255\) 1.04037 0.0651508
\(256\) 4.46549 0.279093
\(257\) 18.3294 1.14336 0.571680 0.820477i \(-0.306292\pi\)
0.571680 + 0.820477i \(0.306292\pi\)
\(258\) −0.396356 −0.0246760
\(259\) 11.2036 0.696158
\(260\) −0.342962 −0.0212696
\(261\) −0.798558 −0.0494295
\(262\) −4.50001 −0.278012
\(263\) −7.41077 −0.456968 −0.228484 0.973548i \(-0.573377\pi\)
−0.228484 + 0.973548i \(0.573377\pi\)
\(264\) −2.58791 −0.159275
\(265\) 1.18803 0.0729803
\(266\) −1.49651 −0.0917570
\(267\) −13.5360 −0.828389
\(268\) −3.84197 −0.234686
\(269\) −28.5189 −1.73883 −0.869415 0.494082i \(-0.835504\pi\)
−0.869415 + 0.494082i \(0.835504\pi\)
\(270\) 0.211709 0.0128842
\(271\) 23.7868 1.44495 0.722473 0.691399i \(-0.243005\pi\)
0.722473 + 0.691399i \(0.243005\pi\)
\(272\) 19.4655 1.18027
\(273\) 4.40813 0.266792
\(274\) 2.59408 0.156714
\(275\) 4.99048 0.300937
\(276\) −10.0497 −0.604919
\(277\) 10.2932 0.618460 0.309230 0.950987i \(-0.399929\pi\)
0.309230 + 0.950987i \(0.399929\pi\)
\(278\) −4.17814 −0.250588
\(279\) −1.90007 −0.113754
\(280\) 0.208957 0.0124876
\(281\) −20.1829 −1.20401 −0.602004 0.798493i \(-0.705631\pi\)
−0.602004 + 0.798493i \(0.705631\pi\)
\(282\) 2.58093 0.153692
\(283\) 5.16490 0.307021 0.153511 0.988147i \(-0.450942\pi\)
0.153511 + 0.988147i \(0.450942\pi\)
\(284\) 13.4232 0.796519
\(285\) 0.436465 0.0258540
\(286\) 0.773778 0.0457545
\(287\) −10.6120 −0.626405
\(288\) 0.938255 0.0552872
\(289\) 23.8410 1.40241
\(290\) −0.145517 −0.00854508
\(291\) 10.0935 0.591691
\(292\) −13.5866 −0.795095
\(293\) 1.92764 0.112614 0.0563071 0.998413i \(-0.482067\pi\)
0.0563071 + 0.998413i \(0.482067\pi\)
\(294\) 3.43616 0.200401
\(295\) 0.427805 0.0249078
\(296\) 12.5879 0.731660
\(297\) 5.36635 0.311387
\(298\) 4.42595 0.256388
\(299\) 6.27710 0.363014
\(300\) 15.2910 0.882828
\(301\) 0.811206 0.0467572
\(302\) 5.67090 0.326324
\(303\) −22.3946 −1.28653
\(304\) 8.16633 0.468371
\(305\) 0.0975766 0.00558722
\(306\) 0.559391 0.0319782
\(307\) 11.9619 0.682699 0.341350 0.939936i \(-0.389116\pi\)
0.341350 + 0.939936i \(0.389116\pi\)
\(308\) 2.53545 0.144471
\(309\) 22.2202 1.26406
\(310\) −0.346241 −0.0196652
\(311\) 8.08067 0.458213 0.229106 0.973401i \(-0.426420\pi\)
0.229106 + 0.973401i \(0.426420\pi\)
\(312\) 4.95280 0.280397
\(313\) 29.4242 1.66316 0.831578 0.555408i \(-0.187438\pi\)
0.831578 + 0.555408i \(0.187438\pi\)
\(314\) 8.32040 0.469547
\(315\) −0.0291645 −0.00164323
\(316\) 29.3526 1.65121
\(317\) 22.5448 1.26624 0.633120 0.774054i \(-0.281774\pi\)
0.633120 + 0.774054i \(0.281774\pi\)
\(318\) −8.21285 −0.460554
\(319\) −3.68854 −0.206519
\(320\) −0.423447 −0.0236714
\(321\) −19.0627 −1.06398
\(322\) −1.83075 −0.102024
\(323\) 17.1339 0.953357
\(324\) 15.2499 0.847217
\(325\) −9.55089 −0.529788
\(326\) −0.611986 −0.0338948
\(327\) −32.3816 −1.79071
\(328\) −11.9232 −0.658350
\(329\) −5.28229 −0.291222
\(330\) 0.0658198 0.00362326
\(331\) 11.1529 0.613020 0.306510 0.951867i \(-0.400839\pi\)
0.306510 + 0.951867i \(0.400839\pi\)
\(332\) 1.19312 0.0654812
\(333\) −1.75692 −0.0962789
\(334\) 6.70808 0.367050
\(335\) 0.204127 0.0111527
\(336\) 7.01570 0.382738
\(337\) −14.9848 −0.816274 −0.408137 0.912921i \(-0.633821\pi\)
−0.408137 + 0.912921i \(0.633821\pi\)
\(338\) 3.77516 0.205342
\(339\) 19.6252 1.06590
\(340\) −1.14523 −0.0621088
\(341\) −8.77643 −0.475271
\(342\) 0.234680 0.0126900
\(343\) −16.6966 −0.901532
\(344\) 0.911441 0.0491416
\(345\) 0.533948 0.0287468
\(346\) 7.18049 0.386026
\(347\) 14.5439 0.780760 0.390380 0.920654i \(-0.372344\pi\)
0.390380 + 0.920654i \(0.372344\pi\)
\(348\) −11.3018 −0.605842
\(349\) 15.7833 0.844863 0.422431 0.906395i \(-0.361177\pi\)
0.422431 + 0.906395i \(0.361177\pi\)
\(350\) 2.78557 0.148895
\(351\) −10.2702 −0.548185
\(352\) 4.33380 0.230992
\(353\) 11.2517 0.598869 0.299434 0.954117i \(-0.403202\pi\)
0.299434 + 0.954117i \(0.403202\pi\)
\(354\) −2.95741 −0.157184
\(355\) −0.713185 −0.0378519
\(356\) 14.9002 0.789710
\(357\) 14.7198 0.779052
\(358\) 8.01855 0.423793
\(359\) −10.7378 −0.566721 −0.283360 0.959013i \(-0.591449\pi\)
−0.283360 + 0.959013i \(0.591449\pi\)
\(360\) −0.0327681 −0.00172703
\(361\) −11.8119 −0.621677
\(362\) −2.90679 −0.152778
\(363\) 1.66838 0.0875674
\(364\) −4.85240 −0.254335
\(365\) 0.721867 0.0377843
\(366\) −0.674545 −0.0352590
\(367\) −31.2795 −1.63278 −0.816388 0.577503i \(-0.804027\pi\)
−0.816388 + 0.577503i \(0.804027\pi\)
\(368\) 9.99024 0.520777
\(369\) 1.66415 0.0866320
\(370\) −0.320156 −0.0166441
\(371\) 16.8089 0.872676
\(372\) −26.8914 −1.39425
\(373\) −6.69105 −0.346449 −0.173225 0.984882i \(-0.555419\pi\)
−0.173225 + 0.984882i \(0.555419\pi\)
\(374\) 2.58383 0.133606
\(375\) −1.62640 −0.0839870
\(376\) −5.93498 −0.306073
\(377\) 7.05921 0.363568
\(378\) 2.99537 0.154065
\(379\) 17.4406 0.895866 0.447933 0.894067i \(-0.352160\pi\)
0.447933 + 0.894067i \(0.352160\pi\)
\(380\) −0.480455 −0.0246468
\(381\) 21.3078 1.09163
\(382\) 4.21033 0.215419
\(383\) −11.5754 −0.591473 −0.295736 0.955270i \(-0.595565\pi\)
−0.295736 + 0.955270i \(0.595565\pi\)
\(384\) 17.3882 0.887335
\(385\) −0.134711 −0.00686550
\(386\) 2.79813 0.142421
\(387\) −0.127212 −0.00646653
\(388\) −11.1108 −0.564064
\(389\) 14.2848 0.724266 0.362133 0.932126i \(-0.382049\pi\)
0.362133 + 0.932126i \(0.382049\pi\)
\(390\) −0.125967 −0.00637860
\(391\) 20.9607 1.06003
\(392\) −7.90162 −0.399092
\(393\) 18.5692 0.936695
\(394\) −2.07132 −0.104352
\(395\) −1.55953 −0.0784685
\(396\) −0.397604 −0.0199804
\(397\) 27.6351 1.38696 0.693482 0.720474i \(-0.256075\pi\)
0.693482 + 0.720474i \(0.256075\pi\)
\(398\) 3.70985 0.185958
\(399\) 6.17534 0.309154
\(400\) −15.2006 −0.760030
\(401\) 24.1900 1.20799 0.603996 0.796987i \(-0.293574\pi\)
0.603996 + 0.796987i \(0.293574\pi\)
\(402\) −1.41113 −0.0703807
\(403\) 16.7965 0.836695
\(404\) 24.6516 1.22646
\(405\) −0.810241 −0.0402612
\(406\) −2.05886 −0.102179
\(407\) −8.11523 −0.402257
\(408\) 16.5386 0.818781
\(409\) 7.93089 0.392157 0.196079 0.980588i \(-0.437179\pi\)
0.196079 + 0.980588i \(0.437179\pi\)
\(410\) 0.303250 0.0149764
\(411\) −10.7045 −0.528012
\(412\) −24.4597 −1.20504
\(413\) 6.05281 0.297839
\(414\) 0.287094 0.0141099
\(415\) −0.0633917 −0.00311178
\(416\) −8.29412 −0.406653
\(417\) 17.2411 0.844299
\(418\) 1.08399 0.0530195
\(419\) 10.8385 0.529496 0.264748 0.964318i \(-0.414711\pi\)
0.264748 + 0.964318i \(0.414711\pi\)
\(420\) −0.412759 −0.0201406
\(421\) −10.7357 −0.523228 −0.261614 0.965173i \(-0.584255\pi\)
−0.261614 + 0.965173i \(0.584255\pi\)
\(422\) −4.07341 −0.198290
\(423\) 0.828357 0.0402761
\(424\) 18.8859 0.917179
\(425\) −31.8926 −1.54702
\(426\) 4.93023 0.238870
\(427\) 1.38056 0.0668102
\(428\) 20.9840 1.01430
\(429\) −3.19299 −0.154159
\(430\) −0.0231812 −0.00111789
\(431\) −30.2153 −1.45542 −0.727710 0.685885i \(-0.759415\pi\)
−0.727710 + 0.685885i \(0.759415\pi\)
\(432\) −16.3455 −0.786422
\(433\) 17.6507 0.848237 0.424119 0.905607i \(-0.360584\pi\)
0.424119 + 0.905607i \(0.360584\pi\)
\(434\) −4.89880 −0.235150
\(435\) 0.600476 0.0287906
\(436\) 35.6452 1.70710
\(437\) 8.79358 0.420654
\(438\) −4.99025 −0.238443
\(439\) −19.7097 −0.940693 −0.470347 0.882482i \(-0.655871\pi\)
−0.470347 + 0.882482i \(0.655871\pi\)
\(440\) −0.151356 −0.00721561
\(441\) 1.10285 0.0525164
\(442\) −4.94498 −0.235209
\(443\) −36.4139 −1.73008 −0.865038 0.501706i \(-0.832706\pi\)
−0.865038 + 0.501706i \(0.832706\pi\)
\(444\) −24.8654 −1.18006
\(445\) −0.791662 −0.0375284
\(446\) −10.3731 −0.491181
\(447\) −18.2636 −0.863840
\(448\) −5.99115 −0.283055
\(449\) −7.81784 −0.368947 −0.184473 0.982838i \(-0.559058\pi\)
−0.184473 + 0.982838i \(0.559058\pi\)
\(450\) −0.436827 −0.0205922
\(451\) 7.68669 0.361952
\(452\) −21.6032 −1.01613
\(453\) −23.4009 −1.09947
\(454\) 9.21567 0.432513
\(455\) 0.257812 0.0120864
\(456\) 6.93838 0.324919
\(457\) 1.28959 0.0603245 0.0301622 0.999545i \(-0.490398\pi\)
0.0301622 + 0.999545i \(0.490398\pi\)
\(458\) −8.92707 −0.417135
\(459\) −34.2947 −1.60074
\(460\) −0.587762 −0.0274046
\(461\) −12.1738 −0.566991 −0.283495 0.958974i \(-0.591494\pi\)
−0.283495 + 0.958974i \(0.591494\pi\)
\(462\) 0.931253 0.0433258
\(463\) 33.2077 1.54329 0.771647 0.636050i \(-0.219433\pi\)
0.771647 + 0.636050i \(0.219433\pi\)
\(464\) 11.2350 0.521572
\(465\) 1.42876 0.0662572
\(466\) −9.79652 −0.453815
\(467\) −25.1563 −1.16410 −0.582048 0.813154i \(-0.697748\pi\)
−0.582048 + 0.813154i \(0.697748\pi\)
\(468\) 0.760943 0.0351746
\(469\) 2.88810 0.133360
\(470\) 0.150948 0.00696269
\(471\) −34.3340 −1.58203
\(472\) 6.80071 0.313028
\(473\) −0.587590 −0.0270174
\(474\) 10.7810 0.495188
\(475\) −13.3798 −0.613909
\(476\) −16.2033 −0.742677
\(477\) −2.63594 −0.120691
\(478\) 9.05672 0.414245
\(479\) −14.0023 −0.639779 −0.319890 0.947455i \(-0.603646\pi\)
−0.319890 + 0.947455i \(0.603646\pi\)
\(480\) −0.705521 −0.0322025
\(481\) 15.5311 0.708158
\(482\) −6.91694 −0.315058
\(483\) 7.55457 0.343745
\(484\) −1.83653 −0.0834788
\(485\) 0.590325 0.0268053
\(486\) −0.907839 −0.0411804
\(487\) −28.1486 −1.27553 −0.637767 0.770229i \(-0.720142\pi\)
−0.637767 + 0.770229i \(0.720142\pi\)
\(488\) 1.55115 0.0702173
\(489\) 2.52536 0.114201
\(490\) 0.200966 0.00907873
\(491\) 27.6795 1.24916 0.624580 0.780961i \(-0.285270\pi\)
0.624580 + 0.780961i \(0.285270\pi\)
\(492\) 23.5523 1.06182
\(493\) 23.5723 1.06164
\(494\) −2.07455 −0.0933386
\(495\) 0.0211251 0.000949500 0
\(496\) 26.7323 1.20032
\(497\) −10.0905 −0.452621
\(498\) 0.438225 0.0196374
\(499\) −14.1755 −0.634582 −0.317291 0.948328i \(-0.602773\pi\)
−0.317291 + 0.948328i \(0.602773\pi\)
\(500\) 1.79032 0.0800655
\(501\) −27.6808 −1.23669
\(502\) 8.55483 0.381821
\(503\) 26.0229 1.16030 0.580152 0.814508i \(-0.302993\pi\)
0.580152 + 0.814508i \(0.302993\pi\)
\(504\) −0.463621 −0.0206513
\(505\) −1.30976 −0.0582836
\(506\) 1.32609 0.0589518
\(507\) −15.5782 −0.691851
\(508\) −23.4553 −1.04066
\(509\) 7.54307 0.334341 0.167170 0.985928i \(-0.446537\pi\)
0.167170 + 0.985928i \(0.446537\pi\)
\(510\) −0.420634 −0.0186260
\(511\) 10.2134 0.451812
\(512\) −22.6498 −1.00099
\(513\) −14.3876 −0.635227
\(514\) −7.41079 −0.326876
\(515\) 1.29957 0.0572657
\(516\) −1.80040 −0.0792582
\(517\) 3.82618 0.168275
\(518\) −4.52973 −0.199025
\(519\) −29.6302 −1.30062
\(520\) 0.289668 0.0127028
\(521\) 33.3174 1.45966 0.729831 0.683628i \(-0.239599\pi\)
0.729831 + 0.683628i \(0.239599\pi\)
\(522\) 0.322865 0.0141314
\(523\) −39.4616 −1.72554 −0.862768 0.505601i \(-0.831271\pi\)
−0.862768 + 0.505601i \(0.831271\pi\)
\(524\) −20.4408 −0.892959
\(525\) −11.4946 −0.501667
\(526\) 2.99625 0.130643
\(527\) 56.0875 2.44321
\(528\) −5.08176 −0.221155
\(529\) −12.2424 −0.532279
\(530\) −0.480334 −0.0208644
\(531\) −0.949188 −0.0411913
\(532\) −6.79773 −0.294719
\(533\) −14.7110 −0.637202
\(534\) 5.47274 0.236829
\(535\) −1.11490 −0.0482012
\(536\) 3.24496 0.140161
\(537\) −33.0885 −1.42787
\(538\) 11.5305 0.497115
\(539\) 5.09404 0.219416
\(540\) 0.961664 0.0413834
\(541\) −13.8024 −0.593409 −0.296705 0.954969i \(-0.595888\pi\)
−0.296705 + 0.954969i \(0.595888\pi\)
\(542\) −9.61726 −0.413097
\(543\) 11.9949 0.514748
\(544\) −27.6960 −1.18746
\(545\) −1.89386 −0.0811241
\(546\) −1.78225 −0.0762733
\(547\) −24.3353 −1.04050 −0.520250 0.854014i \(-0.674161\pi\)
−0.520250 + 0.854014i \(0.674161\pi\)
\(548\) 11.7833 0.503358
\(549\) −0.216497 −0.00923987
\(550\) −2.01770 −0.0860351
\(551\) 9.88924 0.421296
\(552\) 8.48803 0.361275
\(553\) −22.0651 −0.938302
\(554\) −4.16166 −0.176812
\(555\) 1.32112 0.0560785
\(556\) −18.9787 −0.804877
\(557\) 0.570434 0.0241701 0.0120850 0.999927i \(-0.496153\pi\)
0.0120850 + 0.999927i \(0.496153\pi\)
\(558\) 0.768219 0.0325213
\(559\) 1.12454 0.0475631
\(560\) 0.410318 0.0173391
\(561\) −10.6621 −0.450156
\(562\) 8.16014 0.344215
\(563\) 26.8221 1.13042 0.565209 0.824948i \(-0.308796\pi\)
0.565209 + 0.824948i \(0.308796\pi\)
\(564\) 11.7236 0.493652
\(565\) 1.14779 0.0482881
\(566\) −2.08822 −0.0877745
\(567\) −11.4637 −0.481431
\(568\) −11.3373 −0.475703
\(569\) −1.76168 −0.0738534 −0.0369267 0.999318i \(-0.511757\pi\)
−0.0369267 + 0.999318i \(0.511757\pi\)
\(570\) −0.176468 −0.00739141
\(571\) −26.0955 −1.09206 −0.546031 0.837765i \(-0.683862\pi\)
−0.546031 + 0.837765i \(0.683862\pi\)
\(572\) 3.51480 0.146961
\(573\) −17.3739 −0.725805
\(574\) 4.29053 0.179083
\(575\) −16.3681 −0.682599
\(576\) 0.939520 0.0391467
\(577\) 17.7705 0.739794 0.369897 0.929073i \(-0.379393\pi\)
0.369897 + 0.929073i \(0.379393\pi\)
\(578\) −9.63916 −0.400936
\(579\) −11.5464 −0.479854
\(580\) −0.660996 −0.0274464
\(581\) −0.896899 −0.0372096
\(582\) −4.08090 −0.169159
\(583\) −12.1754 −0.504253
\(584\) 11.4753 0.474853
\(585\) −0.0404296 −0.00167156
\(586\) −0.779367 −0.0321953
\(587\) −13.5033 −0.557339 −0.278669 0.960387i \(-0.589893\pi\)
−0.278669 + 0.960387i \(0.589893\pi\)
\(588\) 15.6084 0.643678
\(589\) 23.5303 0.969547
\(590\) −0.172966 −0.00712090
\(591\) 8.54728 0.351588
\(592\) 24.7184 1.01592
\(593\) 9.48660 0.389568 0.194784 0.980846i \(-0.437599\pi\)
0.194784 + 0.980846i \(0.437599\pi\)
\(594\) −2.16967 −0.0890227
\(595\) 0.860896 0.0352933
\(596\) 20.1044 0.823507
\(597\) −15.3087 −0.626542
\(598\) −2.53790 −0.103782
\(599\) −5.01686 −0.204983 −0.102492 0.994734i \(-0.532681\pi\)
−0.102492 + 0.994734i \(0.532681\pi\)
\(600\) −12.9149 −0.527250
\(601\) 9.73474 0.397088 0.198544 0.980092i \(-0.436379\pi\)
0.198544 + 0.980092i \(0.436379\pi\)
\(602\) −0.327979 −0.0133674
\(603\) −0.452906 −0.0184437
\(604\) 25.7594 1.04814
\(605\) 0.0975766 0.00396705
\(606\) 9.05436 0.367808
\(607\) 20.1566 0.818130 0.409065 0.912505i \(-0.365855\pi\)
0.409065 + 0.912505i \(0.365855\pi\)
\(608\) −11.6192 −0.471222
\(609\) 8.49585 0.344269
\(610\) −0.0394512 −0.00159733
\(611\) −7.32263 −0.296242
\(612\) 2.54097 0.102713
\(613\) 1.56278 0.0631202 0.0315601 0.999502i \(-0.489952\pi\)
0.0315601 + 0.999502i \(0.489952\pi\)
\(614\) −4.83630 −0.195177
\(615\) −1.25136 −0.0504596
\(616\) −2.14146 −0.0862820
\(617\) −28.1019 −1.13134 −0.565670 0.824632i \(-0.691382\pi\)
−0.565670 + 0.824632i \(0.691382\pi\)
\(618\) −8.98387 −0.361384
\(619\) 7.18499 0.288789 0.144394 0.989520i \(-0.453877\pi\)
0.144394 + 0.989520i \(0.453877\pi\)
\(620\) −1.57276 −0.0631636
\(621\) −17.6010 −0.706302
\(622\) −3.26710 −0.130999
\(623\) −11.2008 −0.448753
\(624\) 9.72559 0.389335
\(625\) 24.8573 0.994291
\(626\) −11.8965 −0.475481
\(627\) −4.47306 −0.178637
\(628\) 37.7944 1.50816
\(629\) 51.8620 2.06787
\(630\) 0.0117915 0.000469785 0
\(631\) −41.4917 −1.65176 −0.825879 0.563848i \(-0.809321\pi\)
−0.825879 + 0.563848i \(0.809321\pi\)
\(632\) −24.7915 −0.986152
\(633\) 16.8089 0.668093
\(634\) −9.11508 −0.362006
\(635\) 1.24620 0.0494540
\(636\) −37.3059 −1.47928
\(637\) −9.74909 −0.386273
\(638\) 1.49132 0.0590417
\(639\) 1.58237 0.0625977
\(640\) 1.01696 0.0401988
\(641\) 5.36615 0.211950 0.105975 0.994369i \(-0.466204\pi\)
0.105975 + 0.994369i \(0.466204\pi\)
\(642\) 7.70725 0.304181
\(643\) −16.8713 −0.665341 −0.332670 0.943043i \(-0.607950\pi\)
−0.332670 + 0.943043i \(0.607950\pi\)
\(644\) −8.31597 −0.327695
\(645\) 0.0956568 0.00376648
\(646\) −6.92742 −0.272556
\(647\) 15.1912 0.597229 0.298614 0.954374i \(-0.403476\pi\)
0.298614 + 0.954374i \(0.403476\pi\)
\(648\) −12.8802 −0.505982
\(649\) −4.38430 −0.172099
\(650\) 3.86152 0.151461
\(651\) 20.2149 0.792283
\(652\) −2.77988 −0.108868
\(653\) 10.8434 0.424334 0.212167 0.977233i \(-0.431948\pi\)
0.212167 + 0.977233i \(0.431948\pi\)
\(654\) 13.0922 0.511946
\(655\) 1.08604 0.0424349
\(656\) −23.4131 −0.914126
\(657\) −1.60164 −0.0624858
\(658\) 2.13569 0.0832577
\(659\) −39.8700 −1.55312 −0.776558 0.630046i \(-0.783036\pi\)
−0.776558 + 0.630046i \(0.783036\pi\)
\(660\) 0.298979 0.0116377
\(661\) 2.58629 0.100595 0.0502975 0.998734i \(-0.483983\pi\)
0.0502975 + 0.998734i \(0.483983\pi\)
\(662\) −4.50924 −0.175257
\(663\) 20.4054 0.792481
\(664\) −1.00772 −0.0391072
\(665\) 0.361169 0.0140055
\(666\) 0.710343 0.0275252
\(667\) 12.0979 0.468434
\(668\) 30.4707 1.17895
\(669\) 42.8046 1.65492
\(670\) −0.0825308 −0.00318844
\(671\) −1.00000 −0.0386046
\(672\) −9.98209 −0.385067
\(673\) −40.7325 −1.57012 −0.785060 0.619419i \(-0.787368\pi\)
−0.785060 + 0.619419i \(0.787368\pi\)
\(674\) 6.05851 0.233365
\(675\) 26.7807 1.03079
\(676\) 17.1482 0.659548
\(677\) 42.3469 1.62752 0.813761 0.581199i \(-0.197416\pi\)
0.813761 + 0.581199i \(0.197416\pi\)
\(678\) −7.93468 −0.304730
\(679\) 8.35223 0.320529
\(680\) 0.967270 0.0370931
\(681\) −38.0284 −1.45725
\(682\) 3.54840 0.135875
\(683\) −11.4726 −0.438985 −0.219492 0.975614i \(-0.570440\pi\)
−0.219492 + 0.975614i \(0.570440\pi\)
\(684\) 1.06601 0.0407597
\(685\) −0.626058 −0.0239204
\(686\) 6.75061 0.257740
\(687\) 36.8375 1.40544
\(688\) 1.78975 0.0682337
\(689\) 23.3015 0.887718
\(690\) −0.215881 −0.00821844
\(691\) −4.48114 −0.170471 −0.0852354 0.996361i \(-0.527164\pi\)
−0.0852354 + 0.996361i \(0.527164\pi\)
\(692\) 32.6166 1.23990
\(693\) 0.298888 0.0113538
\(694\) −5.88027 −0.223212
\(695\) 1.00836 0.0382491
\(696\) 9.54562 0.361826
\(697\) −49.1233 −1.86068
\(698\) −6.38137 −0.241538
\(699\) 40.4252 1.52902
\(700\) 12.6531 0.478243
\(701\) −23.8141 −0.899445 −0.449722 0.893168i \(-0.648477\pi\)
−0.449722 + 0.893168i \(0.648477\pi\)
\(702\) 4.15236 0.156721
\(703\) 21.7575 0.820601
\(704\) 4.33964 0.163556
\(705\) −0.622884 −0.0234592
\(706\) −4.54919 −0.171211
\(707\) −18.5312 −0.696937
\(708\) −13.4337 −0.504868
\(709\) 40.1995 1.50972 0.754862 0.655884i \(-0.227704\pi\)
0.754862 + 0.655884i \(0.227704\pi\)
\(710\) 0.288348 0.0108215
\(711\) 3.46019 0.129767
\(712\) −12.5849 −0.471637
\(713\) 28.7856 1.07803
\(714\) −5.95135 −0.222724
\(715\) −0.186744 −0.00698384
\(716\) 36.4233 1.36120
\(717\) −37.3725 −1.39570
\(718\) 4.34142 0.162020
\(719\) −20.7734 −0.774719 −0.387359 0.921929i \(-0.626613\pi\)
−0.387359 + 0.921929i \(0.626613\pi\)
\(720\) −0.0643452 −0.00239800
\(721\) 18.3869 0.684765
\(722\) 4.77566 0.177732
\(723\) 28.5427 1.06151
\(724\) −13.2038 −0.490714
\(725\) −18.4076 −0.683640
\(726\) −0.674545 −0.0250347
\(727\) −22.1783 −0.822549 −0.411275 0.911512i \(-0.634916\pi\)
−0.411275 + 0.911512i \(0.634916\pi\)
\(728\) 4.09838 0.151896
\(729\) 28.6571 1.06137
\(730\) −0.291858 −0.0108022
\(731\) 3.75511 0.138888
\(732\) −3.06404 −0.113250
\(733\) −22.3172 −0.824304 −0.412152 0.911115i \(-0.635223\pi\)
−0.412152 + 0.911115i \(0.635223\pi\)
\(734\) 12.6466 0.466796
\(735\) −0.829285 −0.0305886
\(736\) −14.2143 −0.523947
\(737\) −2.09197 −0.0770587
\(738\) −0.672832 −0.0247673
\(739\) −48.0693 −1.76826 −0.884129 0.467243i \(-0.845247\pi\)
−0.884129 + 0.467243i \(0.845247\pi\)
\(740\) −1.45427 −0.0534601
\(741\) 8.56063 0.314483
\(742\) −6.79602 −0.249490
\(743\) −25.5828 −0.938542 −0.469271 0.883054i \(-0.655483\pi\)
−0.469271 + 0.883054i \(0.655483\pi\)
\(744\) 22.7127 0.832686
\(745\) −1.06816 −0.0391344
\(746\) 2.70526 0.0990467
\(747\) 0.140650 0.00514611
\(748\) 11.7367 0.429137
\(749\) −15.7741 −0.576374
\(750\) 0.657571 0.0240111
\(751\) 45.0859 1.64521 0.822604 0.568615i \(-0.192521\pi\)
0.822604 + 0.568615i \(0.192521\pi\)
\(752\) −11.6542 −0.424986
\(753\) −35.3014 −1.28646
\(754\) −2.85411 −0.103941
\(755\) −1.36862 −0.0498092
\(756\) 13.6061 0.494850
\(757\) −8.81976 −0.320560 −0.160280 0.987072i \(-0.551240\pi\)
−0.160280 + 0.987072i \(0.551240\pi\)
\(758\) −7.05143 −0.256120
\(759\) −5.47209 −0.198624
\(760\) 0.405796 0.0147198
\(761\) 43.9572 1.59345 0.796723 0.604344i \(-0.206565\pi\)
0.796723 + 0.604344i \(0.206565\pi\)
\(762\) −8.61497 −0.312087
\(763\) −26.7953 −0.970057
\(764\) 19.1249 0.691916
\(765\) −0.135004 −0.00488107
\(766\) 4.68004 0.169097
\(767\) 8.39077 0.302973
\(768\) 7.45015 0.268834
\(769\) 3.56562 0.128580 0.0642898 0.997931i \(-0.479522\pi\)
0.0642898 + 0.997931i \(0.479522\pi\)
\(770\) 0.0544650 0.00196278
\(771\) 30.5805 1.10133
\(772\) 12.7102 0.457449
\(773\) −47.7439 −1.71723 −0.858614 0.512622i \(-0.828674\pi\)
−0.858614 + 0.512622i \(0.828674\pi\)
\(774\) 0.0514330 0.00184872
\(775\) −43.7986 −1.57329
\(776\) 9.38425 0.336875
\(777\) 18.6919 0.670569
\(778\) −5.77548 −0.207061
\(779\) −20.6086 −0.738379
\(780\) −0.572192 −0.0204878
\(781\) 7.30897 0.261536
\(782\) −8.47462 −0.303052
\(783\) −19.7940 −0.707380
\(784\) −15.5160 −0.554144
\(785\) −2.00805 −0.0716704
\(786\) −7.50774 −0.267792
\(787\) −14.5262 −0.517803 −0.258902 0.965904i \(-0.583361\pi\)
−0.258902 + 0.965904i \(0.583361\pi\)
\(788\) −9.40872 −0.335172
\(789\) −12.3640 −0.440170
\(790\) 0.630535 0.0224334
\(791\) 16.2396 0.577414
\(792\) 0.335820 0.0119328
\(793\) 1.91382 0.0679618
\(794\) −11.1732 −0.396520
\(795\) 1.98210 0.0702977
\(796\) 16.8516 0.597288
\(797\) −25.7378 −0.911679 −0.455839 0.890062i \(-0.650661\pi\)
−0.455839 + 0.890062i \(0.650661\pi\)
\(798\) −2.49676 −0.0883842
\(799\) −24.4520 −0.865048
\(800\) 21.6277 0.764656
\(801\) 1.75649 0.0620626
\(802\) −9.78028 −0.345354
\(803\) −7.39795 −0.261068
\(804\) −6.40988 −0.226059
\(805\) 0.441835 0.0155726
\(806\) −6.79101 −0.239203
\(807\) −47.5805 −1.67491
\(808\) −20.8210 −0.732479
\(809\) 16.1314 0.567150 0.283575 0.958950i \(-0.408479\pi\)
0.283575 + 0.958950i \(0.408479\pi\)
\(810\) 0.327589 0.0115103
\(811\) −37.2088 −1.30658 −0.653289 0.757108i \(-0.726611\pi\)
−0.653289 + 0.757108i \(0.726611\pi\)
\(812\) −9.35212 −0.328195
\(813\) 39.6855 1.39183
\(814\) 3.28107 0.115002
\(815\) 0.147697 0.00517361
\(816\) 32.4760 1.13689
\(817\) 1.57537 0.0551153
\(818\) −3.20654 −0.112114
\(819\) −0.572019 −0.0199880
\(820\) 1.37748 0.0481035
\(821\) −24.8527 −0.867366 −0.433683 0.901065i \(-0.642786\pi\)
−0.433683 + 0.901065i \(0.642786\pi\)
\(822\) 4.32792 0.150954
\(823\) −27.3472 −0.953262 −0.476631 0.879104i \(-0.658142\pi\)
−0.476631 + 0.879104i \(0.658142\pi\)
\(824\) 20.6589 0.719685
\(825\) 8.32603 0.289875
\(826\) −2.44721 −0.0851495
\(827\) 3.62847 0.126174 0.0630871 0.998008i \(-0.479905\pi\)
0.0630871 + 0.998008i \(0.479905\pi\)
\(828\) 1.30409 0.0453203
\(829\) 26.8941 0.934070 0.467035 0.884239i \(-0.345322\pi\)
0.467035 + 0.884239i \(0.345322\pi\)
\(830\) 0.0256299 0.000889628 0
\(831\) 17.1731 0.595727
\(832\) −8.30530 −0.287934
\(833\) −32.5545 −1.12795
\(834\) −6.97074 −0.241377
\(835\) −1.61893 −0.0560255
\(836\) 4.92388 0.170296
\(837\) −47.0974 −1.62792
\(838\) −4.38212 −0.151378
\(839\) 8.01173 0.276596 0.138298 0.990391i \(-0.455837\pi\)
0.138298 + 0.990391i \(0.455837\pi\)
\(840\) 0.348620 0.0120285
\(841\) −15.3947 −0.530851
\(842\) 4.34057 0.149586
\(843\) −33.6728 −1.15975
\(844\) −18.5030 −0.636899
\(845\) −0.911101 −0.0313428
\(846\) −0.334913 −0.0115146
\(847\) 1.38056 0.0474368
\(848\) 37.0853 1.27351
\(849\) 8.61703 0.295736
\(850\) 12.8945 0.442279
\(851\) 26.6170 0.912417
\(852\) 22.3950 0.767240
\(853\) 27.7986 0.951807 0.475904 0.879497i \(-0.342121\pi\)
0.475904 + 0.879497i \(0.342121\pi\)
\(854\) −0.558177 −0.0191004
\(855\) −0.0566378 −0.00193697
\(856\) −17.7232 −0.605767
\(857\) −36.1854 −1.23607 −0.618035 0.786150i \(-0.712071\pi\)
−0.618035 + 0.786150i \(0.712071\pi\)
\(858\) 1.29096 0.0440726
\(859\) −36.5369 −1.24662 −0.623312 0.781974i \(-0.714213\pi\)
−0.623312 + 0.781974i \(0.714213\pi\)
\(860\) −0.105298 −0.00359062
\(861\) −17.7048 −0.603380
\(862\) 12.2164 0.416091
\(863\) 17.8996 0.609309 0.304655 0.952463i \(-0.401459\pi\)
0.304655 + 0.952463i \(0.401459\pi\)
\(864\) 23.2567 0.791208
\(865\) −1.73295 −0.0589219
\(866\) −7.13635 −0.242503
\(867\) 39.7759 1.35086
\(868\) −22.2522 −0.755290
\(869\) 15.9826 0.542174
\(870\) −0.242779 −0.00823097
\(871\) 4.00366 0.135659
\(872\) −30.1062 −1.01953
\(873\) −1.30978 −0.0443293
\(874\) −3.55534 −0.120261
\(875\) −1.34583 −0.0454972
\(876\) −22.6676 −0.765868
\(877\) −28.7263 −0.970019 −0.485009 0.874509i \(-0.661184\pi\)
−0.485009 + 0.874509i \(0.661184\pi\)
\(878\) 7.96884 0.268935
\(879\) 3.21605 0.108475
\(880\) −0.297210 −0.0100190
\(881\) 18.4462 0.621467 0.310734 0.950497i \(-0.399425\pi\)
0.310734 + 0.950497i \(0.399425\pi\)
\(882\) −0.445892 −0.0150140
\(883\) −8.21016 −0.276294 −0.138147 0.990412i \(-0.544115\pi\)
−0.138147 + 0.990412i \(0.544115\pi\)
\(884\) −22.4620 −0.755479
\(885\) 0.713743 0.0239922
\(886\) 14.7225 0.494613
\(887\) −1.69374 −0.0568703 −0.0284352 0.999596i \(-0.509052\pi\)
−0.0284352 + 0.999596i \(0.509052\pi\)
\(888\) 21.0015 0.704765
\(889\) 17.6319 0.591356
\(890\) 0.320077 0.0107290
\(891\) 8.30364 0.278182
\(892\) −47.1187 −1.57765
\(893\) −10.2583 −0.343280
\(894\) 7.38418 0.246964
\(895\) −1.93520 −0.0646867
\(896\) 14.3885 0.480685
\(897\) 10.4726 0.349670
\(898\) 3.16083 0.105478
\(899\) 32.3722 1.07967
\(900\) −1.98424 −0.0661412
\(901\) 77.8093 2.59220
\(902\) −3.10781 −0.103479
\(903\) 1.35340 0.0450384
\(904\) 18.2462 0.606860
\(905\) 0.701527 0.0233196
\(906\) 9.46124 0.314329
\(907\) 41.0996 1.36469 0.682345 0.731031i \(-0.260960\pi\)
0.682345 + 0.731031i \(0.260960\pi\)
\(908\) 41.8611 1.38921
\(909\) 2.90602 0.0963867
\(910\) −0.104236 −0.00345540
\(911\) −10.5470 −0.349437 −0.174719 0.984618i \(-0.555902\pi\)
−0.174719 + 0.984618i \(0.555902\pi\)
\(912\) 13.6246 0.451155
\(913\) 0.649661 0.0215006
\(914\) −0.521395 −0.0172462
\(915\) 0.162795 0.00538184
\(916\) −40.5502 −1.33982
\(917\) 15.3658 0.507424
\(918\) 13.8657 0.457637
\(919\) −2.90139 −0.0957080 −0.0478540 0.998854i \(-0.515238\pi\)
−0.0478540 + 0.998854i \(0.515238\pi\)
\(920\) 0.496429 0.0163668
\(921\) 19.9570 0.657604
\(922\) 4.92200 0.162097
\(923\) −13.9881 −0.460423
\(924\) 4.23011 0.139160
\(925\) −40.4989 −1.33160
\(926\) −13.4262 −0.441214
\(927\) −2.88340 −0.0947032
\(928\) −15.9854 −0.524746
\(929\) −37.3322 −1.22483 −0.612416 0.790536i \(-0.709802\pi\)
−0.612416 + 0.790536i \(0.709802\pi\)
\(930\) −0.577663 −0.0189423
\(931\) −13.6575 −0.447606
\(932\) −44.4995 −1.45763
\(933\) 13.4817 0.441370
\(934\) 10.1710 0.332804
\(935\) −0.623582 −0.0203933
\(936\) −0.642699 −0.0210073
\(937\) 1.64643 0.0537867 0.0268933 0.999638i \(-0.491439\pi\)
0.0268933 + 0.999638i \(0.491439\pi\)
\(938\) −1.16769 −0.0381264
\(939\) 49.0909 1.60202
\(940\) 0.685662 0.0223638
\(941\) −55.6461 −1.81401 −0.907005 0.421120i \(-0.861637\pi\)
−0.907005 + 0.421120i \(0.861637\pi\)
\(942\) 13.8816 0.452287
\(943\) −25.2114 −0.820996
\(944\) 13.3542 0.434643
\(945\) −0.722905 −0.0235161
\(946\) 0.237569 0.00772403
\(947\) −27.5185 −0.894230 −0.447115 0.894476i \(-0.647549\pi\)
−0.447115 + 0.894476i \(0.647549\pi\)
\(948\) 48.9714 1.59052
\(949\) 14.1584 0.459600
\(950\) 5.40961 0.175511
\(951\) 37.6133 1.21970
\(952\) 13.6854 0.443548
\(953\) 26.8576 0.870003 0.435002 0.900430i \(-0.356748\pi\)
0.435002 + 0.900430i \(0.356748\pi\)
\(954\) 1.06574 0.0345045
\(955\) −1.01612 −0.0328810
\(956\) 41.1391 1.33053
\(957\) −6.15390 −0.198927
\(958\) 5.66126 0.182907
\(959\) −8.85780 −0.286033
\(960\) −0.706472 −0.0228013
\(961\) 46.0258 1.48470
\(962\) −6.27939 −0.202456
\(963\) 2.47367 0.0797128
\(964\) −31.4194 −1.01195
\(965\) −0.675302 −0.0217387
\(966\) −3.05439 −0.0982735
\(967\) −7.13631 −0.229488 −0.114744 0.993395i \(-0.536605\pi\)
−0.114744 + 0.993395i \(0.536605\pi\)
\(968\) 1.55115 0.0498559
\(969\) 28.5859 0.918313
\(970\) −0.238675 −0.00766338
\(971\) 48.6208 1.56032 0.780158 0.625582i \(-0.215138\pi\)
0.780158 + 0.625582i \(0.215138\pi\)
\(972\) −4.12375 −0.132269
\(973\) 14.2668 0.457371
\(974\) 11.3808 0.364663
\(975\) −15.9345 −0.510314
\(976\) 3.04592 0.0974975
\(977\) 37.7471 1.20764 0.603819 0.797122i \(-0.293645\pi\)
0.603819 + 0.797122i \(0.293645\pi\)
\(978\) −1.02103 −0.0326489
\(979\) 8.11324 0.259300
\(980\) 0.912866 0.0291604
\(981\) 4.20199 0.134159
\(982\) −11.1911 −0.357123
\(983\) −31.2734 −0.997467 −0.498734 0.866755i \(-0.666201\pi\)
−0.498734 + 0.866755i \(0.666201\pi\)
\(984\) −19.8925 −0.634150
\(985\) 0.499894 0.0159279
\(986\) −9.53054 −0.303514
\(987\) −8.81289 −0.280517
\(988\) −9.42342 −0.299799
\(989\) 1.92722 0.0612821
\(990\) −0.00854108 −0.000271453 0
\(991\) −34.5374 −1.09712 −0.548558 0.836112i \(-0.684823\pi\)
−0.548558 + 0.836112i \(0.684823\pi\)
\(992\) −38.0353 −1.20762
\(993\) 18.6074 0.590487
\(994\) 4.07970 0.129400
\(995\) −0.895338 −0.0283841
\(996\) 1.99059 0.0630742
\(997\) 1.18905 0.0376577 0.0188288 0.999823i \(-0.494006\pi\)
0.0188288 + 0.999823i \(0.494006\pi\)
\(998\) 5.73130 0.181421
\(999\) −43.5492 −1.37784
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 671.2.a.d.1.10 21
3.2 odd 2 6039.2.a.l.1.12 21
11.10 odd 2 7381.2.a.j.1.12 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
671.2.a.d.1.10 21 1.1 even 1 trivial
6039.2.a.l.1.12 21 3.2 odd 2
7381.2.a.j.1.12 21 11.10 odd 2