Properties

Label 1183.2.a.q.1.4
Level $1183$
Weight $2$
Character 1183.1
Self dual yes
Analytic conductor $9.446$
Analytic rank $0$
Dimension $12$
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] = [1183,2,Mod(1,1183)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1183, 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("1183.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.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: \(9.44630255912\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 3 x^{11} - 15 x^{10} + 46 x^{9} + 80 x^{8} - 246 x^{7} - 199 x^{6} + 562 x^{5} + 262 x^{4} - 542 x^{3} - 157 x^{2} + 183 x + 29 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(2.06743\) of defining polynomial
Character \(\chi\) \(=\) 1183.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.06743 q^{2} +2.11889 q^{3} +2.27425 q^{4} -2.43928 q^{5} -4.38065 q^{6} -1.00000 q^{7} -0.566992 q^{8} +1.48970 q^{9} +O(q^{10})\) \(q-2.06743 q^{2} +2.11889 q^{3} +2.27425 q^{4} -2.43928 q^{5} -4.38065 q^{6} -1.00000 q^{7} -0.566992 q^{8} +1.48970 q^{9} +5.04303 q^{10} +3.64779 q^{11} +4.81889 q^{12} +2.06743 q^{14} -5.16857 q^{15} -3.37629 q^{16} +7.04993 q^{17} -3.07985 q^{18} +2.76410 q^{19} -5.54753 q^{20} -2.11889 q^{21} -7.54154 q^{22} -7.75601 q^{23} -1.20139 q^{24} +0.950076 q^{25} -3.20015 q^{27} -2.27425 q^{28} +2.31600 q^{29} +10.6856 q^{30} -7.00738 q^{31} +8.11421 q^{32} +7.72927 q^{33} -14.5752 q^{34} +2.43928 q^{35} +3.38796 q^{36} +7.28412 q^{37} -5.71456 q^{38} +1.38305 q^{40} +3.49162 q^{41} +4.38065 q^{42} +3.44630 q^{43} +8.29599 q^{44} -3.63380 q^{45} +16.0350 q^{46} -2.66883 q^{47} -7.15399 q^{48} +1.00000 q^{49} -1.96421 q^{50} +14.9380 q^{51} +13.3378 q^{53} +6.61608 q^{54} -8.89797 q^{55} +0.566992 q^{56} +5.85682 q^{57} -4.78816 q^{58} +8.24978 q^{59} -11.7546 q^{60} +13.9465 q^{61} +14.4872 q^{62} -1.48970 q^{63} -10.0229 q^{64} -15.9797 q^{66} +3.20893 q^{67} +16.0333 q^{68} -16.4341 q^{69} -5.04303 q^{70} +9.74080 q^{71} -0.844650 q^{72} +3.75697 q^{73} -15.0594 q^{74} +2.01311 q^{75} +6.28624 q^{76} -3.64779 q^{77} -12.8682 q^{79} +8.23570 q^{80} -11.2499 q^{81} -7.21867 q^{82} +5.42451 q^{83} -4.81889 q^{84} -17.1967 q^{85} -7.12496 q^{86} +4.90736 q^{87} -2.06827 q^{88} +0.335808 q^{89} +7.51262 q^{90} -17.6391 q^{92} -14.8479 q^{93} +5.51762 q^{94} -6.74240 q^{95} +17.1931 q^{96} -10.9424 q^{97} -2.06743 q^{98} +5.43413 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 3 q^{2} + 8 q^{3} + 15 q^{4} + 4 q^{5} - 2 q^{6} - 12 q^{7} - 12 q^{8} + 26 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 3 q^{2} + 8 q^{3} + 15 q^{4} + 4 q^{5} - 2 q^{6} - 12 q^{7} - 12 q^{8} + 26 q^{9} - 6 q^{10} - 12 q^{11} + 13 q^{12} + 3 q^{14} - 11 q^{15} + 13 q^{16} + 31 q^{17} + 29 q^{18} + 3 q^{19} + 18 q^{20} - 8 q^{21} - 4 q^{22} + 18 q^{23} + 6 q^{24} + 32 q^{25} + 32 q^{27} - 15 q^{28} + 15 q^{29} - 10 q^{30} + 21 q^{31} + 3 q^{32} + 29 q^{33} - 3 q^{34} - 4 q^{35} + 49 q^{36} - 5 q^{37} + 45 q^{38} - 20 q^{40} + 16 q^{41} + 2 q^{42} - 22 q^{43} - 35 q^{44} - 5 q^{45} - 2 q^{46} + 4 q^{47} + 11 q^{48} + 12 q^{49} - 13 q^{50} + 18 q^{51} + 53 q^{53} + 5 q^{54} - 26 q^{55} + 12 q^{56} + 8 q^{57} - 32 q^{58} + 26 q^{59} - 38 q^{60} + 22 q^{61} + 19 q^{62} - 26 q^{63} + 2 q^{64} - 34 q^{66} - 12 q^{67} + 34 q^{68} + 3 q^{69} + 6 q^{70} - 21 q^{71} + 4 q^{72} + 15 q^{73} - 40 q^{74} + 15 q^{75} - 43 q^{76} + 12 q^{77} + 2 q^{79} - 13 q^{80} + 36 q^{81} - 32 q^{82} + 9 q^{83} - 13 q^{84} + 39 q^{85} - 44 q^{86} + 27 q^{87} - 48 q^{88} + 22 q^{89} - 26 q^{90} + 52 q^{92} + 53 q^{93} - 44 q^{94} + 29 q^{95} + 114 q^{96} - 9 q^{97} - 3 q^{98} - 37 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.06743 −1.46189 −0.730945 0.682436i \(-0.760921\pi\)
−0.730945 + 0.682436i \(0.760921\pi\)
\(3\) 2.11889 1.22334 0.611671 0.791112i \(-0.290497\pi\)
0.611671 + 0.791112i \(0.290497\pi\)
\(4\) 2.27425 1.13713
\(5\) −2.43928 −1.09088 −0.545439 0.838150i \(-0.683637\pi\)
−0.545439 + 0.838150i \(0.683637\pi\)
\(6\) −4.38065 −1.78839
\(7\) −1.00000 −0.377964
\(8\) −0.566992 −0.200462
\(9\) 1.48970 0.496568
\(10\) 5.04303 1.59474
\(11\) 3.64779 1.09985 0.549925 0.835214i \(-0.314656\pi\)
0.549925 + 0.835214i \(0.314656\pi\)
\(12\) 4.81889 1.39109
\(13\) 0 0
\(14\) 2.06743 0.552543
\(15\) −5.16857 −1.33452
\(16\) −3.37629 −0.844072
\(17\) 7.04993 1.70986 0.854929 0.518745i \(-0.173600\pi\)
0.854929 + 0.518745i \(0.173600\pi\)
\(18\) −3.07985 −0.725928
\(19\) 2.76410 0.634127 0.317063 0.948404i \(-0.397303\pi\)
0.317063 + 0.948404i \(0.397303\pi\)
\(20\) −5.54753 −1.24046
\(21\) −2.11889 −0.462380
\(22\) −7.54154 −1.60786
\(23\) −7.75601 −1.61724 −0.808620 0.588332i \(-0.799785\pi\)
−0.808620 + 0.588332i \(0.799785\pi\)
\(24\) −1.20139 −0.245234
\(25\) 0.950076 0.190015
\(26\) 0 0
\(27\) −3.20015 −0.615870
\(28\) −2.27425 −0.429793
\(29\) 2.31600 0.430071 0.215035 0.976606i \(-0.431013\pi\)
0.215035 + 0.976606i \(0.431013\pi\)
\(30\) 10.6856 1.95092
\(31\) −7.00738 −1.25856 −0.629281 0.777178i \(-0.716651\pi\)
−0.629281 + 0.777178i \(0.716651\pi\)
\(32\) 8.11421 1.43440
\(33\) 7.72927 1.34549
\(34\) −14.5752 −2.49963
\(35\) 2.43928 0.412313
\(36\) 3.38796 0.564660
\(37\) 7.28412 1.19750 0.598751 0.800935i \(-0.295664\pi\)
0.598751 + 0.800935i \(0.295664\pi\)
\(38\) −5.71456 −0.927024
\(39\) 0 0
\(40\) 1.38305 0.218679
\(41\) 3.49162 0.545300 0.272650 0.962113i \(-0.412100\pi\)
0.272650 + 0.962113i \(0.412100\pi\)
\(42\) 4.38065 0.675949
\(43\) 3.44630 0.525555 0.262778 0.964856i \(-0.415361\pi\)
0.262778 + 0.964856i \(0.415361\pi\)
\(44\) 8.29599 1.25067
\(45\) −3.63380 −0.541695
\(46\) 16.0350 2.36423
\(47\) −2.66883 −0.389289 −0.194645 0.980874i \(-0.562355\pi\)
−0.194645 + 0.980874i \(0.562355\pi\)
\(48\) −7.15399 −1.03259
\(49\) 1.00000 0.142857
\(50\) −1.96421 −0.277782
\(51\) 14.9380 2.09174
\(52\) 0 0
\(53\) 13.3378 1.83208 0.916041 0.401086i \(-0.131367\pi\)
0.916041 + 0.401086i \(0.131367\pi\)
\(54\) 6.61608 0.900335
\(55\) −8.89797 −1.19980
\(56\) 0.566992 0.0757675
\(57\) 5.85682 0.775755
\(58\) −4.78816 −0.628716
\(59\) 8.24978 1.07403 0.537015 0.843573i \(-0.319552\pi\)
0.537015 + 0.843573i \(0.319552\pi\)
\(60\) −11.7546 −1.51751
\(61\) 13.9465 1.78566 0.892831 0.450392i \(-0.148716\pi\)
0.892831 + 0.450392i \(0.148716\pi\)
\(62\) 14.4872 1.83988
\(63\) −1.48970 −0.187685
\(64\) −10.0229 −1.25287
\(65\) 0 0
\(66\) −15.9797 −1.96697
\(67\) 3.20893 0.392033 0.196017 0.980601i \(-0.437199\pi\)
0.196017 + 0.980601i \(0.437199\pi\)
\(68\) 16.0333 1.94432
\(69\) −16.4341 −1.97844
\(70\) −5.04303 −0.602757
\(71\) 9.74080 1.15602 0.578010 0.816029i \(-0.303829\pi\)
0.578010 + 0.816029i \(0.303829\pi\)
\(72\) −0.844650 −0.0995429
\(73\) 3.75697 0.439720 0.219860 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(74\) −15.0594 −1.75062
\(75\) 2.01311 0.232454
\(76\) 6.28624 0.721082
\(77\) −3.64779 −0.415704
\(78\) 0 0
\(79\) −12.8682 −1.44778 −0.723890 0.689915i \(-0.757648\pi\)
−0.723890 + 0.689915i \(0.757648\pi\)
\(80\) 8.23570 0.920779
\(81\) −11.2499 −1.24999
\(82\) −7.21867 −0.797168
\(83\) 5.42451 0.595417 0.297709 0.954657i \(-0.403778\pi\)
0.297709 + 0.954657i \(0.403778\pi\)
\(84\) −4.81889 −0.525784
\(85\) −17.1967 −1.86525
\(86\) −7.12496 −0.768304
\(87\) 4.90736 0.526124
\(88\) −2.06827 −0.220478
\(89\) 0.335808 0.0355955 0.0177978 0.999842i \(-0.494334\pi\)
0.0177978 + 0.999842i \(0.494334\pi\)
\(90\) 7.51262 0.791899
\(91\) 0 0
\(92\) −17.6391 −1.83900
\(93\) −14.8479 −1.53965
\(94\) 5.51762 0.569099
\(95\) −6.74240 −0.691755
\(96\) 17.1931 1.75477
\(97\) −10.9424 −1.11103 −0.555517 0.831505i \(-0.687480\pi\)
−0.555517 + 0.831505i \(0.687480\pi\)
\(98\) −2.06743 −0.208842
\(99\) 5.43413 0.546150
\(100\) 2.16071 0.216071
\(101\) 8.92269 0.887841 0.443920 0.896066i \(-0.353587\pi\)
0.443920 + 0.896066i \(0.353587\pi\)
\(102\) −30.8833 −3.05790
\(103\) −2.66966 −0.263049 −0.131525 0.991313i \(-0.541987\pi\)
−0.131525 + 0.991313i \(0.541987\pi\)
\(104\) 0 0
\(105\) 5.16857 0.504400
\(106\) −27.5748 −2.67830
\(107\) 14.9485 1.44513 0.722563 0.691305i \(-0.242964\pi\)
0.722563 + 0.691305i \(0.242964\pi\)
\(108\) −7.27795 −0.700321
\(109\) 1.45686 0.139542 0.0697710 0.997563i \(-0.477773\pi\)
0.0697710 + 0.997563i \(0.477773\pi\)
\(110\) 18.3959 1.75398
\(111\) 15.4343 1.46496
\(112\) 3.37629 0.319029
\(113\) 14.8440 1.39641 0.698204 0.715899i \(-0.253983\pi\)
0.698204 + 0.715899i \(0.253983\pi\)
\(114\) −12.1085 −1.13407
\(115\) 18.9191 1.76421
\(116\) 5.26716 0.489044
\(117\) 0 0
\(118\) −17.0558 −1.57011
\(119\) −7.04993 −0.646266
\(120\) 2.93053 0.267520
\(121\) 2.30638 0.209670
\(122\) −28.8333 −2.61044
\(123\) 7.39837 0.667088
\(124\) −15.9365 −1.43114
\(125\) 9.87889 0.883595
\(126\) 3.07985 0.274375
\(127\) 5.83060 0.517382 0.258691 0.965960i \(-0.416709\pi\)
0.258691 + 0.965960i \(0.416709\pi\)
\(128\) 4.49329 0.397154
\(129\) 7.30233 0.642934
\(130\) 0 0
\(131\) 15.0558 1.31543 0.657714 0.753268i \(-0.271523\pi\)
0.657714 + 0.753268i \(0.271523\pi\)
\(132\) 17.5783 1.52999
\(133\) −2.76410 −0.239677
\(134\) −6.63423 −0.573110
\(135\) 7.80607 0.671839
\(136\) −3.99725 −0.342761
\(137\) −4.23709 −0.361999 −0.181000 0.983483i \(-0.557933\pi\)
−0.181000 + 0.983483i \(0.557933\pi\)
\(138\) 33.9764 2.89226
\(139\) −2.70802 −0.229691 −0.114846 0.993383i \(-0.536637\pi\)
−0.114846 + 0.993383i \(0.536637\pi\)
\(140\) 5.54753 0.468852
\(141\) −5.65497 −0.476235
\(142\) −20.1384 −1.68998
\(143\) 0 0
\(144\) −5.02967 −0.419139
\(145\) −5.64937 −0.469155
\(146\) −7.76726 −0.642823
\(147\) 2.11889 0.174763
\(148\) 16.5659 1.36171
\(149\) −0.891186 −0.0730088 −0.0365044 0.999333i \(-0.511622\pi\)
−0.0365044 + 0.999333i \(0.511622\pi\)
\(150\) −4.16195 −0.339822
\(151\) −16.2557 −1.32287 −0.661436 0.750001i \(-0.730053\pi\)
−0.661436 + 0.750001i \(0.730053\pi\)
\(152\) −1.56722 −0.127118
\(153\) 10.5023 0.849061
\(154\) 7.54154 0.607714
\(155\) 17.0929 1.37294
\(156\) 0 0
\(157\) −3.94721 −0.315022 −0.157511 0.987517i \(-0.550347\pi\)
−0.157511 + 0.987517i \(0.550347\pi\)
\(158\) 26.6040 2.11650
\(159\) 28.2613 2.24126
\(160\) −19.7928 −1.56476
\(161\) 7.75601 0.611259
\(162\) 23.2583 1.82735
\(163\) 4.48439 0.351245 0.175622 0.984458i \(-0.443806\pi\)
0.175622 + 0.984458i \(0.443806\pi\)
\(164\) 7.94082 0.620074
\(165\) −18.8538 −1.46777
\(166\) −11.2148 −0.870435
\(167\) −8.06225 −0.623875 −0.311938 0.950103i \(-0.600978\pi\)
−0.311938 + 0.950103i \(0.600978\pi\)
\(168\) 1.20139 0.0926896
\(169\) 0 0
\(170\) 35.5530 2.72679
\(171\) 4.11768 0.314887
\(172\) 7.83774 0.597622
\(173\) −7.74395 −0.588761 −0.294381 0.955688i \(-0.595113\pi\)
−0.294381 + 0.955688i \(0.595113\pi\)
\(174\) −10.1456 −0.769136
\(175\) −0.950076 −0.0718190
\(176\) −12.3160 −0.928352
\(177\) 17.4804 1.31391
\(178\) −0.694258 −0.0520368
\(179\) −16.3124 −1.21924 −0.609621 0.792693i \(-0.708679\pi\)
−0.609621 + 0.792693i \(0.708679\pi\)
\(180\) −8.26417 −0.615975
\(181\) 8.28425 0.615763 0.307882 0.951425i \(-0.400380\pi\)
0.307882 + 0.951425i \(0.400380\pi\)
\(182\) 0 0
\(183\) 29.5510 2.18448
\(184\) 4.39759 0.324195
\(185\) −17.7680 −1.30633
\(186\) 30.6969 2.25081
\(187\) 25.7167 1.88059
\(188\) −6.06960 −0.442671
\(189\) 3.20015 0.232777
\(190\) 13.9394 1.01127
\(191\) 10.7356 0.776803 0.388402 0.921490i \(-0.373027\pi\)
0.388402 + 0.921490i \(0.373027\pi\)
\(192\) −21.2375 −1.53269
\(193\) −0.762728 −0.0549024 −0.0274512 0.999623i \(-0.508739\pi\)
−0.0274512 + 0.999623i \(0.508739\pi\)
\(194\) 22.6226 1.62421
\(195\) 0 0
\(196\) 2.27425 0.162446
\(197\) 12.1127 0.862997 0.431498 0.902114i \(-0.357985\pi\)
0.431498 + 0.902114i \(0.357985\pi\)
\(198\) −11.2347 −0.798412
\(199\) −4.27032 −0.302715 −0.151358 0.988479i \(-0.548364\pi\)
−0.151358 + 0.988479i \(0.548364\pi\)
\(200\) −0.538685 −0.0380908
\(201\) 6.79938 0.479591
\(202\) −18.4470 −1.29793
\(203\) −2.31600 −0.162551
\(204\) 33.9728 2.37857
\(205\) −8.51703 −0.594855
\(206\) 5.51932 0.384549
\(207\) −11.5542 −0.803069
\(208\) 0 0
\(209\) 10.0828 0.697445
\(210\) −10.6856 −0.737378
\(211\) −7.26849 −0.500384 −0.250192 0.968196i \(-0.580494\pi\)
−0.250192 + 0.968196i \(0.580494\pi\)
\(212\) 30.3334 2.08331
\(213\) 20.6397 1.41421
\(214\) −30.9049 −2.11262
\(215\) −8.40647 −0.573317
\(216\) 1.81446 0.123458
\(217\) 7.00738 0.475692
\(218\) −3.01195 −0.203995
\(219\) 7.96062 0.537929
\(220\) −20.2362 −1.36433
\(221\) 0 0
\(222\) −31.9092 −2.14161
\(223\) 11.5634 0.774343 0.387172 0.922008i \(-0.373452\pi\)
0.387172 + 0.922008i \(0.373452\pi\)
\(224\) −8.11421 −0.542153
\(225\) 1.41533 0.0943555
\(226\) −30.6889 −2.04140
\(227\) 3.02967 0.201086 0.100543 0.994933i \(-0.467942\pi\)
0.100543 + 0.994933i \(0.467942\pi\)
\(228\) 13.3199 0.882130
\(229\) −3.56377 −0.235500 −0.117750 0.993043i \(-0.537568\pi\)
−0.117750 + 0.993043i \(0.537568\pi\)
\(230\) −39.1137 −2.57908
\(231\) −7.72927 −0.508549
\(232\) −1.31315 −0.0862127
\(233\) −12.8151 −0.839547 −0.419774 0.907629i \(-0.637891\pi\)
−0.419774 + 0.907629i \(0.637891\pi\)
\(234\) 0 0
\(235\) 6.51003 0.424667
\(236\) 18.7621 1.22131
\(237\) −27.2662 −1.77113
\(238\) 14.5752 0.944770
\(239\) −25.3757 −1.64142 −0.820708 0.571347i \(-0.806421\pi\)
−0.820708 + 0.571347i \(0.806421\pi\)
\(240\) 17.4506 1.12643
\(241\) −6.80302 −0.438221 −0.219111 0.975700i \(-0.570316\pi\)
−0.219111 + 0.975700i \(0.570316\pi\)
\(242\) −4.76826 −0.306515
\(243\) −14.2368 −0.913294
\(244\) 31.7177 2.03052
\(245\) −2.43928 −0.155840
\(246\) −15.2956 −0.975210
\(247\) 0 0
\(248\) 3.97313 0.252294
\(249\) 11.4940 0.728400
\(250\) −20.4239 −1.29172
\(251\) −22.8556 −1.44263 −0.721317 0.692605i \(-0.756463\pi\)
−0.721317 + 0.692605i \(0.756463\pi\)
\(252\) −3.38796 −0.213421
\(253\) −28.2923 −1.77872
\(254\) −12.0543 −0.756356
\(255\) −36.4380 −2.28184
\(256\) 10.7564 0.672272
\(257\) −3.85941 −0.240743 −0.120372 0.992729i \(-0.538409\pi\)
−0.120372 + 0.992729i \(0.538409\pi\)
\(258\) −15.0970 −0.939899
\(259\) −7.28412 −0.452613
\(260\) 0 0
\(261\) 3.45016 0.213559
\(262\) −31.1267 −1.92301
\(263\) −16.2197 −1.00015 −0.500075 0.865982i \(-0.666694\pi\)
−0.500075 + 0.865982i \(0.666694\pi\)
\(264\) −4.38243 −0.269720
\(265\) −32.5345 −1.99858
\(266\) 5.71456 0.350382
\(267\) 0.711540 0.0435456
\(268\) 7.29791 0.445791
\(269\) −23.0815 −1.40731 −0.703653 0.710544i \(-0.748449\pi\)
−0.703653 + 0.710544i \(0.748449\pi\)
\(270\) −16.1385 −0.982156
\(271\) 10.7673 0.654067 0.327034 0.945013i \(-0.393951\pi\)
0.327034 + 0.945013i \(0.393951\pi\)
\(272\) −23.8026 −1.44324
\(273\) 0 0
\(274\) 8.75987 0.529203
\(275\) 3.46568 0.208988
\(276\) −37.3753 −2.24973
\(277\) −11.7786 −0.707708 −0.353854 0.935301i \(-0.615129\pi\)
−0.353854 + 0.935301i \(0.615129\pi\)
\(278\) 5.59863 0.335784
\(279\) −10.4389 −0.624962
\(280\) −1.38305 −0.0826531
\(281\) 27.3072 1.62901 0.814507 0.580154i \(-0.197008\pi\)
0.814507 + 0.580154i \(0.197008\pi\)
\(282\) 11.6912 0.696203
\(283\) 22.8247 1.35679 0.678393 0.734699i \(-0.262677\pi\)
0.678393 + 0.734699i \(0.262677\pi\)
\(284\) 22.1530 1.31454
\(285\) −14.2864 −0.846254
\(286\) 0 0
\(287\) −3.49162 −0.206104
\(288\) 12.0878 0.712278
\(289\) 32.7015 1.92362
\(290\) 11.6797 0.685853
\(291\) −23.1858 −1.35918
\(292\) 8.54430 0.500017
\(293\) 19.8388 1.15899 0.579497 0.814974i \(-0.303249\pi\)
0.579497 + 0.814974i \(0.303249\pi\)
\(294\) −4.38065 −0.255485
\(295\) −20.1235 −1.17164
\(296\) −4.13004 −0.240054
\(297\) −11.6735 −0.677365
\(298\) 1.84246 0.106731
\(299\) 0 0
\(300\) 4.57831 0.264329
\(301\) −3.44630 −0.198641
\(302\) 33.6075 1.93390
\(303\) 18.9062 1.08613
\(304\) −9.33238 −0.535249
\(305\) −34.0193 −1.94794
\(306\) −21.7127 −1.24123
\(307\) −10.3240 −0.589219 −0.294610 0.955618i \(-0.595190\pi\)
−0.294610 + 0.955618i \(0.595190\pi\)
\(308\) −8.29599 −0.472708
\(309\) −5.65672 −0.321800
\(310\) −35.3384 −2.00709
\(311\) 22.2930 1.26412 0.632060 0.774919i \(-0.282210\pi\)
0.632060 + 0.774919i \(0.282210\pi\)
\(312\) 0 0
\(313\) −19.4600 −1.09995 −0.549973 0.835182i \(-0.685362\pi\)
−0.549973 + 0.835182i \(0.685362\pi\)
\(314\) 8.16057 0.460528
\(315\) 3.63380 0.204742
\(316\) −29.2654 −1.64631
\(317\) −27.4413 −1.54126 −0.770629 0.637284i \(-0.780058\pi\)
−0.770629 + 0.637284i \(0.780058\pi\)
\(318\) −58.4281 −3.27648
\(319\) 8.44829 0.473013
\(320\) 24.4488 1.36673
\(321\) 31.6743 1.76789
\(322\) −16.0350 −0.893594
\(323\) 19.4867 1.08427
\(324\) −25.5851 −1.42139
\(325\) 0 0
\(326\) −9.27115 −0.513481
\(327\) 3.08693 0.170708
\(328\) −1.97972 −0.109312
\(329\) 2.66883 0.147138
\(330\) 38.9789 2.14572
\(331\) −20.3710 −1.11969 −0.559846 0.828596i \(-0.689140\pi\)
−0.559846 + 0.828596i \(0.689140\pi\)
\(332\) 12.3367 0.677064
\(333\) 10.8512 0.594641
\(334\) 16.6681 0.912038
\(335\) −7.82748 −0.427661
\(336\) 7.15399 0.390282
\(337\) −2.67053 −0.145473 −0.0727366 0.997351i \(-0.523173\pi\)
−0.0727366 + 0.997351i \(0.523173\pi\)
\(338\) 0 0
\(339\) 31.4529 1.70829
\(340\) −39.1097 −2.12102
\(341\) −25.5615 −1.38423
\(342\) −8.51301 −0.460331
\(343\) −1.00000 −0.0539949
\(344\) −1.95402 −0.105354
\(345\) 40.0874 2.15823
\(346\) 16.0100 0.860705
\(347\) −0.317819 −0.0170614 −0.00853071 0.999964i \(-0.502715\pi\)
−0.00853071 + 0.999964i \(0.502715\pi\)
\(348\) 11.1606 0.598268
\(349\) −0.514513 −0.0275413 −0.0137706 0.999905i \(-0.504383\pi\)
−0.0137706 + 0.999905i \(0.504383\pi\)
\(350\) 1.96421 0.104992
\(351\) 0 0
\(352\) 29.5989 1.57763
\(353\) −0.627678 −0.0334080 −0.0167040 0.999860i \(-0.505317\pi\)
−0.0167040 + 0.999860i \(0.505317\pi\)
\(354\) −36.1394 −1.92079
\(355\) −23.7605 −1.26108
\(356\) 0.763711 0.0404766
\(357\) −14.9380 −0.790605
\(358\) 33.7246 1.78240
\(359\) −31.9224 −1.68480 −0.842399 0.538854i \(-0.818857\pi\)
−0.842399 + 0.538854i \(0.818857\pi\)
\(360\) 2.06034 0.108589
\(361\) −11.3598 −0.597883
\(362\) −17.1271 −0.900179
\(363\) 4.88696 0.256499
\(364\) 0 0
\(365\) −9.16430 −0.479681
\(366\) −61.0946 −3.19347
\(367\) 10.6064 0.553651 0.276826 0.960920i \(-0.410718\pi\)
0.276826 + 0.960920i \(0.410718\pi\)
\(368\) 26.1865 1.36507
\(369\) 5.20148 0.270778
\(370\) 36.7340 1.90971
\(371\) −13.3378 −0.692462
\(372\) −33.7678 −1.75078
\(373\) 10.6129 0.549514 0.274757 0.961514i \(-0.411403\pi\)
0.274757 + 0.961514i \(0.411403\pi\)
\(374\) −53.1673 −2.74921
\(375\) 20.9323 1.08094
\(376\) 1.51321 0.0780377
\(377\) 0 0
\(378\) −6.61608 −0.340295
\(379\) 13.5259 0.694779 0.347390 0.937721i \(-0.387068\pi\)
0.347390 + 0.937721i \(0.387068\pi\)
\(380\) −15.3339 −0.786612
\(381\) 12.3544 0.632935
\(382\) −22.1951 −1.13560
\(383\) 14.4264 0.737155 0.368577 0.929597i \(-0.379845\pi\)
0.368577 + 0.929597i \(0.379845\pi\)
\(384\) 9.52079 0.485856
\(385\) 8.89797 0.453483
\(386\) 1.57688 0.0802613
\(387\) 5.13396 0.260974
\(388\) −24.8858 −1.26338
\(389\) 15.1018 0.765692 0.382846 0.923812i \(-0.374944\pi\)
0.382846 + 0.923812i \(0.374944\pi\)
\(390\) 0 0
\(391\) −54.6793 −2.76525
\(392\) −0.566992 −0.0286374
\(393\) 31.9015 1.60922
\(394\) −25.0422 −1.26161
\(395\) 31.3890 1.57935
\(396\) 12.3586 0.621041
\(397\) −15.6944 −0.787679 −0.393840 0.919179i \(-0.628853\pi\)
−0.393840 + 0.919179i \(0.628853\pi\)
\(398\) 8.82858 0.442536
\(399\) −5.85682 −0.293208
\(400\) −3.20773 −0.160386
\(401\) −18.9270 −0.945168 −0.472584 0.881286i \(-0.656679\pi\)
−0.472584 + 0.881286i \(0.656679\pi\)
\(402\) −14.0572 −0.701110
\(403\) 0 0
\(404\) 20.2924 1.00959
\(405\) 27.4416 1.36358
\(406\) 4.78816 0.237632
\(407\) 26.5710 1.31707
\(408\) −8.46974 −0.419315
\(409\) 2.37052 0.117215 0.0586074 0.998281i \(-0.481334\pi\)
0.0586074 + 0.998281i \(0.481334\pi\)
\(410\) 17.6083 0.869614
\(411\) −8.97794 −0.442849
\(412\) −6.07147 −0.299120
\(413\) −8.24978 −0.405945
\(414\) 23.8874 1.17400
\(415\) −13.2319 −0.649528
\(416\) 0 0
\(417\) −5.73800 −0.280991
\(418\) −20.8455 −1.01959
\(419\) 21.4796 1.04935 0.524673 0.851304i \(-0.324188\pi\)
0.524673 + 0.851304i \(0.324188\pi\)
\(420\) 11.7546 0.573566
\(421\) 20.1413 0.981626 0.490813 0.871265i \(-0.336700\pi\)
0.490813 + 0.871265i \(0.336700\pi\)
\(422\) 15.0271 0.731506
\(423\) −3.97577 −0.193309
\(424\) −7.56239 −0.367262
\(425\) 6.69797 0.324899
\(426\) −42.6711 −2.06742
\(427\) −13.9465 −0.674917
\(428\) 33.9966 1.64329
\(429\) 0 0
\(430\) 17.3798 0.838126
\(431\) −18.0221 −0.868092 −0.434046 0.900891i \(-0.642915\pi\)
−0.434046 + 0.900891i \(0.642915\pi\)
\(432\) 10.8046 0.519838
\(433\) 35.8293 1.72184 0.860922 0.508737i \(-0.169887\pi\)
0.860922 + 0.508737i \(0.169887\pi\)
\(434\) −14.4872 −0.695410
\(435\) −11.9704 −0.573937
\(436\) 3.31327 0.158677
\(437\) −21.4383 −1.02553
\(438\) −16.4580 −0.786393
\(439\) −2.24154 −0.106983 −0.0534914 0.998568i \(-0.517035\pi\)
−0.0534914 + 0.998568i \(0.517035\pi\)
\(440\) 5.04508 0.240515
\(441\) 1.48970 0.0709383
\(442\) 0 0
\(443\) −5.70925 −0.271254 −0.135627 0.990760i \(-0.543305\pi\)
−0.135627 + 0.990760i \(0.543305\pi\)
\(444\) 35.1014 1.66584
\(445\) −0.819128 −0.0388304
\(446\) −23.9065 −1.13201
\(447\) −1.88833 −0.0893148
\(448\) 10.0229 0.473540
\(449\) −32.3594 −1.52714 −0.763568 0.645728i \(-0.776554\pi\)
−0.763568 + 0.645728i \(0.776554\pi\)
\(450\) −2.92609 −0.137937
\(451\) 12.7367 0.599748
\(452\) 33.7590 1.58789
\(453\) −34.4441 −1.61833
\(454\) −6.26362 −0.293966
\(455\) 0 0
\(456\) −3.32077 −0.155509
\(457\) 24.8614 1.16297 0.581483 0.813559i \(-0.302473\pi\)
0.581483 + 0.813559i \(0.302473\pi\)
\(458\) 7.36782 0.344276
\(459\) −22.5609 −1.05305
\(460\) 43.0267 2.00613
\(461\) 17.5977 0.819607 0.409804 0.912174i \(-0.365597\pi\)
0.409804 + 0.912174i \(0.365597\pi\)
\(462\) 15.9797 0.743443
\(463\) 31.9863 1.48653 0.743265 0.668997i \(-0.233276\pi\)
0.743265 + 0.668997i \(0.233276\pi\)
\(464\) −7.81948 −0.363010
\(465\) 36.2181 1.67957
\(466\) 26.4943 1.22733
\(467\) 2.98855 0.138294 0.0691468 0.997606i \(-0.477972\pi\)
0.0691468 + 0.997606i \(0.477972\pi\)
\(468\) 0 0
\(469\) −3.20893 −0.148175
\(470\) −13.4590 −0.620817
\(471\) −8.36372 −0.385380
\(472\) −4.67756 −0.215302
\(473\) 12.5714 0.578032
\(474\) 56.3709 2.58920
\(475\) 2.62610 0.120494
\(476\) −16.0333 −0.734885
\(477\) 19.8693 0.909753
\(478\) 52.4624 2.39957
\(479\) −19.2718 −0.880553 −0.440277 0.897862i \(-0.645120\pi\)
−0.440277 + 0.897862i \(0.645120\pi\)
\(480\) −41.9388 −1.91424
\(481\) 0 0
\(482\) 14.0647 0.640632
\(483\) 16.4341 0.747779
\(484\) 5.24527 0.238422
\(485\) 26.6916 1.21200
\(486\) 29.4336 1.33514
\(487\) 18.2603 0.827451 0.413726 0.910402i \(-0.364227\pi\)
0.413726 + 0.910402i \(0.364227\pi\)
\(488\) −7.90753 −0.357957
\(489\) 9.50194 0.429693
\(490\) 5.04303 0.227821
\(491\) −32.6604 −1.47394 −0.736971 0.675924i \(-0.763745\pi\)
−0.736971 + 0.675924i \(0.763745\pi\)
\(492\) 16.8257 0.758563
\(493\) 16.3276 0.735360
\(494\) 0 0
\(495\) −13.2553 −0.595784
\(496\) 23.6589 1.06232
\(497\) −9.74080 −0.436935
\(498\) −23.7629 −1.06484
\(499\) −5.35967 −0.239932 −0.119966 0.992778i \(-0.538279\pi\)
−0.119966 + 0.992778i \(0.538279\pi\)
\(500\) 22.4671 1.00476
\(501\) −17.0830 −0.763214
\(502\) 47.2523 2.10897
\(503\) −20.9055 −0.932129 −0.466065 0.884751i \(-0.654329\pi\)
−0.466065 + 0.884751i \(0.654329\pi\)
\(504\) 0.844650 0.0376237
\(505\) −21.7649 −0.968526
\(506\) 58.4922 2.60030
\(507\) 0 0
\(508\) 13.2602 0.588328
\(509\) −25.0852 −1.11188 −0.555941 0.831222i \(-0.687642\pi\)
−0.555941 + 0.831222i \(0.687642\pi\)
\(510\) 75.3329 3.33580
\(511\) −3.75697 −0.166199
\(512\) −31.2245 −1.37994
\(513\) −8.84553 −0.390540
\(514\) 7.97905 0.351941
\(515\) 6.51204 0.286955
\(516\) 16.6073 0.731096
\(517\) −9.73535 −0.428160
\(518\) 15.0594 0.661671
\(519\) −16.4086 −0.720257
\(520\) 0 0
\(521\) −8.13575 −0.356434 −0.178217 0.983991i \(-0.557033\pi\)
−0.178217 + 0.983991i \(0.557033\pi\)
\(522\) −7.13294 −0.312200
\(523\) 36.6634 1.60318 0.801589 0.597875i \(-0.203988\pi\)
0.801589 + 0.597875i \(0.203988\pi\)
\(524\) 34.2406 1.49581
\(525\) −2.01311 −0.0878593
\(526\) 33.5330 1.46211
\(527\) −49.4015 −2.15196
\(528\) −26.0962 −1.13569
\(529\) 37.1556 1.61546
\(530\) 67.2626 2.92170
\(531\) 12.2897 0.533329
\(532\) −6.28624 −0.272543
\(533\) 0 0
\(534\) −1.47106 −0.0636589
\(535\) −36.4636 −1.57646
\(536\) −1.81944 −0.0785877
\(537\) −34.5641 −1.49155
\(538\) 47.7194 2.05733
\(539\) 3.64779 0.157121
\(540\) 17.7529 0.763965
\(541\) −16.6320 −0.715063 −0.357532 0.933901i \(-0.616382\pi\)
−0.357532 + 0.933901i \(0.616382\pi\)
\(542\) −22.2606 −0.956175
\(543\) 17.5534 0.753290
\(544\) 57.2046 2.45263
\(545\) −3.55369 −0.152223
\(546\) 0 0
\(547\) −36.0139 −1.53984 −0.769921 0.638139i \(-0.779704\pi\)
−0.769921 + 0.638139i \(0.779704\pi\)
\(548\) −9.63620 −0.411638
\(549\) 20.7761 0.886702
\(550\) −7.16503 −0.305518
\(551\) 6.40165 0.272719
\(552\) 9.31802 0.396601
\(553\) 12.8682 0.547210
\(554\) 24.3514 1.03459
\(555\) −37.6485 −1.59809
\(556\) −6.15872 −0.261188
\(557\) 11.2328 0.475948 0.237974 0.971272i \(-0.423517\pi\)
0.237974 + 0.971272i \(0.423517\pi\)
\(558\) 21.5817 0.913626
\(559\) 0 0
\(560\) −8.23570 −0.348022
\(561\) 54.4908 2.30060
\(562\) −56.4557 −2.38144
\(563\) 11.1199 0.468649 0.234324 0.972158i \(-0.424712\pi\)
0.234324 + 0.972158i \(0.424712\pi\)
\(564\) −12.8608 −0.541538
\(565\) −36.2087 −1.52331
\(566\) −47.1883 −1.98347
\(567\) 11.2499 0.472451
\(568\) −5.52296 −0.231738
\(569\) −2.48545 −0.104196 −0.0520978 0.998642i \(-0.516591\pi\)
−0.0520978 + 0.998642i \(0.516591\pi\)
\(570\) 29.5361 1.23713
\(571\) 0.537621 0.0224987 0.0112494 0.999937i \(-0.496419\pi\)
0.0112494 + 0.999937i \(0.496419\pi\)
\(572\) 0 0
\(573\) 22.7476 0.950297
\(574\) 7.21867 0.301301
\(575\) −7.36880 −0.307300
\(576\) −14.9312 −0.622134
\(577\) −27.0563 −1.12637 −0.563184 0.826331i \(-0.690424\pi\)
−0.563184 + 0.826331i \(0.690424\pi\)
\(578\) −67.6079 −2.81212
\(579\) −1.61614 −0.0671644
\(580\) −12.8481 −0.533487
\(581\) −5.42451 −0.225047
\(582\) 47.9349 1.98697
\(583\) 48.6533 2.01501
\(584\) −2.13017 −0.0881472
\(585\) 0 0
\(586\) −41.0152 −1.69432
\(587\) −20.7196 −0.855189 −0.427594 0.903971i \(-0.640639\pi\)
−0.427594 + 0.903971i \(0.640639\pi\)
\(588\) 4.81889 0.198728
\(589\) −19.3691 −0.798089
\(590\) 41.6039 1.71280
\(591\) 25.6656 1.05574
\(592\) −24.5933 −1.01078
\(593\) −23.2747 −0.955776 −0.477888 0.878421i \(-0.658598\pi\)
−0.477888 + 0.878421i \(0.658598\pi\)
\(594\) 24.1341 0.990233
\(595\) 17.1967 0.704997
\(596\) −2.02678 −0.0830202
\(597\) −9.04835 −0.370324
\(598\) 0 0
\(599\) 9.28114 0.379217 0.189609 0.981860i \(-0.439278\pi\)
0.189609 + 0.981860i \(0.439278\pi\)
\(600\) −1.14142 −0.0465981
\(601\) −23.6534 −0.964843 −0.482421 0.875939i \(-0.660243\pi\)
−0.482421 + 0.875939i \(0.660243\pi\)
\(602\) 7.12496 0.290392
\(603\) 4.78036 0.194671
\(604\) −36.9696 −1.50427
\(605\) −5.62589 −0.228725
\(606\) −39.0872 −1.58781
\(607\) −24.1600 −0.980623 −0.490312 0.871547i \(-0.663117\pi\)
−0.490312 + 0.871547i \(0.663117\pi\)
\(608\) 22.4284 0.909593
\(609\) −4.90736 −0.198856
\(610\) 70.3324 2.84767
\(611\) 0 0
\(612\) 23.8849 0.965488
\(613\) 27.6780 1.11790 0.558952 0.829200i \(-0.311204\pi\)
0.558952 + 0.829200i \(0.311204\pi\)
\(614\) 21.3440 0.861374
\(615\) −18.0467 −0.727712
\(616\) 2.06827 0.0833328
\(617\) 10.5982 0.426669 0.213335 0.976979i \(-0.431568\pi\)
0.213335 + 0.976979i \(0.431568\pi\)
\(618\) 11.6948 0.470436
\(619\) −42.9657 −1.72694 −0.863468 0.504403i \(-0.831712\pi\)
−0.863468 + 0.504403i \(0.831712\pi\)
\(620\) 38.8736 1.56120
\(621\) 24.8204 0.996009
\(622\) −46.0891 −1.84801
\(623\) −0.335808 −0.0134539
\(624\) 0 0
\(625\) −28.8477 −1.15391
\(626\) 40.2322 1.60800
\(627\) 21.3645 0.853214
\(628\) −8.97695 −0.358219
\(629\) 51.3525 2.04756
\(630\) −7.51262 −0.299310
\(631\) −15.4963 −0.616899 −0.308449 0.951241i \(-0.599810\pi\)
−0.308449 + 0.951241i \(0.599810\pi\)
\(632\) 7.29614 0.290225
\(633\) −15.4012 −0.612141
\(634\) 56.7329 2.25315
\(635\) −14.2224 −0.564400
\(636\) 64.2732 2.54860
\(637\) 0 0
\(638\) −17.4662 −0.691494
\(639\) 14.5109 0.574043
\(640\) −10.9604 −0.433247
\(641\) 22.2240 0.877796 0.438898 0.898537i \(-0.355369\pi\)
0.438898 + 0.898537i \(0.355369\pi\)
\(642\) −65.4842 −2.58446
\(643\) 26.6384 1.05052 0.525259 0.850943i \(-0.323969\pi\)
0.525259 + 0.850943i \(0.323969\pi\)
\(644\) 17.6391 0.695078
\(645\) −17.8124 −0.701363
\(646\) −40.2872 −1.58508
\(647\) 15.7389 0.618758 0.309379 0.950939i \(-0.399879\pi\)
0.309379 + 0.950939i \(0.399879\pi\)
\(648\) 6.37860 0.250575
\(649\) 30.0935 1.18127
\(650\) 0 0
\(651\) 14.8479 0.581934
\(652\) 10.1986 0.399409
\(653\) −9.13364 −0.357427 −0.178714 0.983901i \(-0.557194\pi\)
−0.178714 + 0.983901i \(0.557194\pi\)
\(654\) −6.38201 −0.249556
\(655\) −36.7252 −1.43497
\(656\) −11.7887 −0.460272
\(657\) 5.59678 0.218351
\(658\) −5.51762 −0.215099
\(659\) 0.447782 0.0174431 0.00872156 0.999962i \(-0.497224\pi\)
0.00872156 + 0.999962i \(0.497224\pi\)
\(660\) −42.8784 −1.66904
\(661\) −46.9277 −1.82528 −0.912638 0.408769i \(-0.865958\pi\)
−0.912638 + 0.408769i \(0.865958\pi\)
\(662\) 42.1156 1.63687
\(663\) 0 0
\(664\) −3.07565 −0.119358
\(665\) 6.74240 0.261459
\(666\) −22.4340 −0.869301
\(667\) −17.9629 −0.695527
\(668\) −18.3356 −0.709424
\(669\) 24.5016 0.947287
\(670\) 16.1827 0.625193
\(671\) 50.8738 1.96396
\(672\) −17.1931 −0.663239
\(673\) −16.5829 −0.639225 −0.319612 0.947548i \(-0.603553\pi\)
−0.319612 + 0.947548i \(0.603553\pi\)
\(674\) 5.52113 0.212666
\(675\) −3.04039 −0.117025
\(676\) 0 0
\(677\) 16.1027 0.618878 0.309439 0.950919i \(-0.399859\pi\)
0.309439 + 0.950919i \(0.399859\pi\)
\(678\) −65.0265 −2.49733
\(679\) 10.9424 0.419931
\(680\) 9.75040 0.373911
\(681\) 6.41954 0.245997
\(682\) 52.8464 2.02359
\(683\) −10.7304 −0.410589 −0.205294 0.978700i \(-0.565815\pi\)
−0.205294 + 0.978700i \(0.565815\pi\)
\(684\) 9.36464 0.358066
\(685\) 10.3354 0.394897
\(686\) 2.06743 0.0789347
\(687\) −7.55123 −0.288098
\(688\) −11.6357 −0.443606
\(689\) 0 0
\(690\) −82.8778 −3.15510
\(691\) 24.1742 0.919631 0.459815 0.888015i \(-0.347916\pi\)
0.459815 + 0.888015i \(0.347916\pi\)
\(692\) −17.6117 −0.669495
\(693\) −5.43413 −0.206425
\(694\) 0.657068 0.0249419
\(695\) 6.60562 0.250565
\(696\) −2.78243 −0.105468
\(697\) 24.6157 0.932385
\(698\) 1.06372 0.0402623
\(699\) −27.1539 −1.02705
\(700\) −2.16071 −0.0816672
\(701\) −14.4328 −0.545120 −0.272560 0.962139i \(-0.587870\pi\)
−0.272560 + 0.962139i \(0.587870\pi\)
\(702\) 0 0
\(703\) 20.1340 0.759369
\(704\) −36.5616 −1.37797
\(705\) 13.7940 0.519514
\(706\) 1.29768 0.0488388
\(707\) −8.92269 −0.335572
\(708\) 39.7548 1.49408
\(709\) 15.1940 0.570623 0.285311 0.958435i \(-0.407903\pi\)
0.285311 + 0.958435i \(0.407903\pi\)
\(710\) 49.1231 1.84356
\(711\) −19.1697 −0.718921
\(712\) −0.190400 −0.00713555
\(713\) 54.3493 2.03540
\(714\) 30.8833 1.15578
\(715\) 0 0
\(716\) −37.0984 −1.38643
\(717\) −53.7683 −2.00802
\(718\) 65.9971 2.46299
\(719\) 4.99848 0.186412 0.0932060 0.995647i \(-0.470288\pi\)
0.0932060 + 0.995647i \(0.470288\pi\)
\(720\) 12.2688 0.457230
\(721\) 2.66966 0.0994233
\(722\) 23.4855 0.874040
\(723\) −14.4149 −0.536095
\(724\) 18.8405 0.700200
\(725\) 2.20038 0.0817199
\(726\) −10.1034 −0.374973
\(727\) −7.22850 −0.268090 −0.134045 0.990975i \(-0.542797\pi\)
−0.134045 + 0.990975i \(0.542797\pi\)
\(728\) 0 0
\(729\) 3.58334 0.132716
\(730\) 18.9465 0.701242
\(731\) 24.2961 0.898625
\(732\) 67.2065 2.48402
\(733\) 34.3382 1.26831 0.634154 0.773206i \(-0.281348\pi\)
0.634154 + 0.773206i \(0.281348\pi\)
\(734\) −21.9280 −0.809377
\(735\) −5.16857 −0.190645
\(736\) −62.9338 −2.31977
\(737\) 11.7055 0.431178
\(738\) −10.7537 −0.395848
\(739\) −40.3619 −1.48474 −0.742369 0.669992i \(-0.766298\pi\)
−0.742369 + 0.669992i \(0.766298\pi\)
\(740\) −40.4089 −1.48546
\(741\) 0 0
\(742\) 27.5748 1.01230
\(743\) −15.9115 −0.583736 −0.291868 0.956459i \(-0.594277\pi\)
−0.291868 + 0.956459i \(0.594277\pi\)
\(744\) 8.41863 0.308642
\(745\) 2.17385 0.0796437
\(746\) −21.9413 −0.803329
\(747\) 8.08091 0.295665
\(748\) 58.4861 2.13846
\(749\) −14.9485 −0.546207
\(750\) −43.2760 −1.58022
\(751\) 1.10100 0.0401760 0.0200880 0.999798i \(-0.493605\pi\)
0.0200880 + 0.999798i \(0.493605\pi\)
\(752\) 9.01075 0.328588
\(753\) −48.4286 −1.76484
\(754\) 0 0
\(755\) 39.6522 1.44309
\(756\) 7.27795 0.264697
\(757\) −28.9466 −1.05208 −0.526041 0.850459i \(-0.676324\pi\)
−0.526041 + 0.850459i \(0.676324\pi\)
\(758\) −27.9638 −1.01569
\(759\) −59.9483 −2.17599
\(760\) 3.82288 0.138671
\(761\) −12.6820 −0.459721 −0.229860 0.973224i \(-0.573827\pi\)
−0.229860 + 0.973224i \(0.573827\pi\)
\(762\) −25.5418 −0.925282
\(763\) −1.45686 −0.0527419
\(764\) 24.4155 0.883322
\(765\) −25.6180 −0.926222
\(766\) −29.8255 −1.07764
\(767\) 0 0
\(768\) 22.7916 0.822419
\(769\) −40.2042 −1.44980 −0.724899 0.688855i \(-0.758114\pi\)
−0.724899 + 0.688855i \(0.758114\pi\)
\(770\) −18.3959 −0.662942
\(771\) −8.17768 −0.294512
\(772\) −1.73463 −0.0624309
\(773\) 42.3905 1.52468 0.762340 0.647177i \(-0.224051\pi\)
0.762340 + 0.647177i \(0.224051\pi\)
\(774\) −10.6141 −0.381515
\(775\) −6.65754 −0.239146
\(776\) 6.20426 0.222720
\(777\) −15.4343 −0.553701
\(778\) −31.2218 −1.11936
\(779\) 9.65117 0.345789
\(780\) 0 0
\(781\) 35.5324 1.27145
\(782\) 113.045 4.04249
\(783\) −7.41156 −0.264868
\(784\) −3.37629 −0.120582
\(785\) 9.62835 0.343650
\(786\) −65.9541 −2.35250
\(787\) 43.9833 1.56784 0.783918 0.620865i \(-0.213218\pi\)
0.783918 + 0.620865i \(0.213218\pi\)
\(788\) 27.5474 0.981335
\(789\) −34.3678 −1.22353
\(790\) −64.8944 −2.30884
\(791\) −14.8440 −0.527793
\(792\) −3.08111 −0.109482
\(793\) 0 0
\(794\) 32.4470 1.15150
\(795\) −68.9371 −2.44495
\(796\) −9.71178 −0.344225
\(797\) 48.0486 1.70197 0.850984 0.525192i \(-0.176007\pi\)
0.850984 + 0.525192i \(0.176007\pi\)
\(798\) 12.1085 0.428638
\(799\) −18.8151 −0.665630
\(800\) 7.70911 0.272558
\(801\) 0.500254 0.0176756
\(802\) 39.1301 1.38173
\(803\) 13.7046 0.483627
\(804\) 15.4635 0.545355
\(805\) −18.9191 −0.666809
\(806\) 0 0
\(807\) −48.9073 −1.72162
\(808\) −5.05909 −0.177978
\(809\) 0.460055 0.0161747 0.00808733 0.999967i \(-0.497426\pi\)
0.00808733 + 0.999967i \(0.497426\pi\)
\(810\) −56.7335 −1.99341
\(811\) 29.7828 1.04582 0.522908 0.852389i \(-0.324847\pi\)
0.522908 + 0.852389i \(0.324847\pi\)
\(812\) −5.26716 −0.184841
\(813\) 22.8148 0.800148
\(814\) −54.9335 −1.92542
\(815\) −10.9387 −0.383165
\(816\) −50.4351 −1.76558
\(817\) 9.52589 0.333269
\(818\) −4.90088 −0.171355
\(819\) 0 0
\(820\) −19.3699 −0.676425
\(821\) −3.59326 −0.125406 −0.0627028 0.998032i \(-0.519972\pi\)
−0.0627028 + 0.998032i \(0.519972\pi\)
\(822\) 18.5612 0.647397
\(823\) 21.8141 0.760391 0.380196 0.924906i \(-0.375857\pi\)
0.380196 + 0.924906i \(0.375857\pi\)
\(824\) 1.51367 0.0527313
\(825\) 7.34340 0.255664
\(826\) 17.0558 0.593447
\(827\) −42.7217 −1.48558 −0.742790 0.669525i \(-0.766498\pi\)
−0.742790 + 0.669525i \(0.766498\pi\)
\(828\) −26.2770 −0.913190
\(829\) −36.5078 −1.26797 −0.633985 0.773345i \(-0.718582\pi\)
−0.633985 + 0.773345i \(0.718582\pi\)
\(830\) 27.3559 0.949539
\(831\) −24.9576 −0.865770
\(832\) 0 0
\(833\) 7.04993 0.244265
\(834\) 11.8629 0.410779
\(835\) 19.6661 0.680572
\(836\) 22.9309 0.793082
\(837\) 22.4247 0.775111
\(838\) −44.4075 −1.53403
\(839\) 6.70588 0.231513 0.115756 0.993278i \(-0.463071\pi\)
0.115756 + 0.993278i \(0.463071\pi\)
\(840\) −2.93053 −0.101113
\(841\) −23.6361 −0.815039
\(842\) −41.6406 −1.43503
\(843\) 57.8611 1.99284
\(844\) −16.5304 −0.568999
\(845\) 0 0
\(846\) 8.21962 0.282596
\(847\) −2.30638 −0.0792480
\(848\) −45.0321 −1.54641
\(849\) 48.3630 1.65981
\(850\) −13.8475 −0.474967
\(851\) −56.4957 −1.93665
\(852\) 46.9399 1.60813
\(853\) 27.2554 0.933207 0.466603 0.884467i \(-0.345478\pi\)
0.466603 + 0.884467i \(0.345478\pi\)
\(854\) 28.8333 0.986654
\(855\) −10.0442 −0.343504
\(856\) −8.47568 −0.289693
\(857\) 46.1474 1.57637 0.788183 0.615441i \(-0.211022\pi\)
0.788183 + 0.615441i \(0.211022\pi\)
\(858\) 0 0
\(859\) −9.45682 −0.322662 −0.161331 0.986900i \(-0.551579\pi\)
−0.161331 + 0.986900i \(0.551579\pi\)
\(860\) −19.1184 −0.651933
\(861\) −7.39837 −0.252136
\(862\) 37.2593 1.26906
\(863\) 28.8550 0.982237 0.491119 0.871093i \(-0.336588\pi\)
0.491119 + 0.871093i \(0.336588\pi\)
\(864\) −25.9667 −0.883406
\(865\) 18.8896 0.642267
\(866\) −74.0743 −2.51715
\(867\) 69.2909 2.35324
\(868\) 15.9365 0.540921
\(869\) −46.9403 −1.59234
\(870\) 24.7479 0.839033
\(871\) 0 0
\(872\) −0.826029 −0.0279729
\(873\) −16.3010 −0.551704
\(874\) 44.3222 1.49922
\(875\) −9.87889 −0.333967
\(876\) 18.1044 0.611692
\(877\) 8.55393 0.288846 0.144423 0.989516i \(-0.453867\pi\)
0.144423 + 0.989516i \(0.453867\pi\)
\(878\) 4.63422 0.156397
\(879\) 42.0363 1.41785
\(880\) 30.0421 1.01272
\(881\) 27.9911 0.943046 0.471523 0.881854i \(-0.343704\pi\)
0.471523 + 0.881854i \(0.343704\pi\)
\(882\) −3.07985 −0.103704
\(883\) −44.7564 −1.50617 −0.753086 0.657922i \(-0.771436\pi\)
−0.753086 + 0.657922i \(0.771436\pi\)
\(884\) 0 0
\(885\) −42.6395 −1.43331
\(886\) 11.8034 0.396544
\(887\) −9.56744 −0.321243 −0.160622 0.987016i \(-0.551350\pi\)
−0.160622 + 0.987016i \(0.551350\pi\)
\(888\) −8.75110 −0.293668
\(889\) −5.83060 −0.195552
\(890\) 1.69349 0.0567658
\(891\) −41.0373 −1.37480
\(892\) 26.2981 0.880525
\(893\) −7.37691 −0.246859
\(894\) 3.90398 0.130569
\(895\) 39.7904 1.33005
\(896\) −4.49329 −0.150110
\(897\) 0 0
\(898\) 66.9007 2.23251
\(899\) −16.2291 −0.541271
\(900\) 3.21882 0.107294
\(901\) 94.0302 3.13260
\(902\) −26.3322 −0.876766
\(903\) −7.30233 −0.243006
\(904\) −8.41644 −0.279926
\(905\) −20.2076 −0.671723
\(906\) 71.2107 2.36582
\(907\) −18.8652 −0.626408 −0.313204 0.949686i \(-0.601402\pi\)
−0.313204 + 0.949686i \(0.601402\pi\)
\(908\) 6.89023 0.228660
\(909\) 13.2922 0.440873
\(910\) 0 0
\(911\) −0.358293 −0.0118708 −0.00593539 0.999982i \(-0.501889\pi\)
−0.00593539 + 0.999982i \(0.501889\pi\)
\(912\) −19.7743 −0.654793
\(913\) 19.7875 0.654870
\(914\) −51.3990 −1.70013
\(915\) −72.0832 −2.38300
\(916\) −8.10489 −0.267793
\(917\) −15.0558 −0.497185
\(918\) 46.6429 1.53944
\(919\) −12.0902 −0.398818 −0.199409 0.979916i \(-0.563902\pi\)
−0.199409 + 0.979916i \(0.563902\pi\)
\(920\) −10.7269 −0.353657
\(921\) −21.8753 −0.720817
\(922\) −36.3820 −1.19818
\(923\) 0 0
\(924\) −17.5783 −0.578284
\(925\) 6.92047 0.227544
\(926\) −66.1294 −2.17315
\(927\) −3.97700 −0.130622
\(928\) 18.7925 0.616894
\(929\) 4.34400 0.142522 0.0712610 0.997458i \(-0.477298\pi\)
0.0712610 + 0.997458i \(0.477298\pi\)
\(930\) −74.8783 −2.45535
\(931\) 2.76410 0.0905896
\(932\) −29.1448 −0.954670
\(933\) 47.2365 1.54645
\(934\) −6.17860 −0.202170
\(935\) −62.7301 −2.05149
\(936\) 0 0
\(937\) 44.7092 1.46059 0.730294 0.683133i \(-0.239383\pi\)
0.730294 + 0.683133i \(0.239383\pi\)
\(938\) 6.63423 0.216615
\(939\) −41.2337 −1.34561
\(940\) 14.8054 0.482900
\(941\) 57.3375 1.86915 0.934574 0.355768i \(-0.115781\pi\)
0.934574 + 0.355768i \(0.115781\pi\)
\(942\) 17.2914 0.563383
\(943\) −27.0810 −0.881880
\(944\) −27.8536 −0.906558
\(945\) −7.80607 −0.253931
\(946\) −25.9904 −0.845020
\(947\) 46.9376 1.52527 0.762634 0.646830i \(-0.223906\pi\)
0.762634 + 0.646830i \(0.223906\pi\)
\(948\) −62.0102 −2.01400
\(949\) 0 0
\(950\) −5.42927 −0.176149
\(951\) −58.1452 −1.88549
\(952\) 3.99725 0.129552
\(953\) −35.5773 −1.15246 −0.576231 0.817287i \(-0.695477\pi\)
−0.576231 + 0.817287i \(0.695477\pi\)
\(954\) −41.0783 −1.32996
\(955\) −26.1872 −0.847398
\(956\) −57.7107 −1.86650
\(957\) 17.9010 0.578657
\(958\) 39.8431 1.28727
\(959\) 4.23709 0.136823
\(960\) 51.8043 1.67198
\(961\) 18.1034 0.583980
\(962\) 0 0
\(963\) 22.2689 0.717604
\(964\) −15.4718 −0.498312
\(965\) 1.86051 0.0598918
\(966\) −33.9764 −1.09317
\(967\) −18.5576 −0.596772 −0.298386 0.954445i \(-0.596448\pi\)
−0.298386 + 0.954445i \(0.596448\pi\)
\(968\) −1.30770 −0.0420309
\(969\) 41.2902 1.32643
\(970\) −55.1829 −1.77182
\(971\) 47.2286 1.51564 0.757819 0.652465i \(-0.226265\pi\)
0.757819 + 0.652465i \(0.226265\pi\)
\(972\) −32.3782 −1.03853
\(973\) 2.70802 0.0868152
\(974\) −37.7517 −1.20964
\(975\) 0 0
\(976\) −47.0873 −1.50723
\(977\) −47.9846 −1.53516 −0.767582 0.640951i \(-0.778540\pi\)
−0.767582 + 0.640951i \(0.778540\pi\)
\(978\) −19.6446 −0.628164
\(979\) 1.22496 0.0391498
\(980\) −5.54753 −0.177209
\(981\) 2.17029 0.0692921
\(982\) 67.5229 2.15474
\(983\) 27.9789 0.892387 0.446193 0.894937i \(-0.352779\pi\)
0.446193 + 0.894937i \(0.352779\pi\)
\(984\) −4.19481 −0.133726
\(985\) −29.5463 −0.941425
\(986\) −33.7562 −1.07502
\(987\) 5.65497 0.180000
\(988\) 0 0
\(989\) −26.7295 −0.849948
\(990\) 27.4044 0.870971
\(991\) −19.4925 −0.619199 −0.309600 0.950867i \(-0.600195\pi\)
−0.309600 + 0.950867i \(0.600195\pi\)
\(992\) −56.8593 −1.80529
\(993\) −43.1640 −1.36977
\(994\) 20.1384 0.638751
\(995\) 10.4165 0.330225
\(996\) 26.1401 0.828281
\(997\) 17.2637 0.546748 0.273374 0.961908i \(-0.411860\pi\)
0.273374 + 0.961908i \(0.411860\pi\)
\(998\) 11.0807 0.350754
\(999\) −23.3103 −0.737506
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 1183.2.a.q.1.4 12
7.6 odd 2 8281.2.a.cn.1.4 12
13.5 odd 4 1183.2.c.j.337.19 24
13.8 odd 4 1183.2.c.j.337.6 24
13.12 even 2 1183.2.a.r.1.9 yes 12
91.90 odd 2 8281.2.a.cq.1.9 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1183.2.a.q.1.4 12 1.1 even 1 trivial
1183.2.a.r.1.9 yes 12 13.12 even 2
1183.2.c.j.337.6 24 13.8 odd 4
1183.2.c.j.337.19 24 13.5 odd 4
8281.2.a.cn.1.4 12 7.6 odd 2
8281.2.a.cq.1.9 12 91.90 odd 2