Properties

Label 1155.2.i.d.76.17
Level $1155$
Weight $2$
Character 1155.76
Analytic conductor $9.223$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1155,2,Mod(76,1155)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1155.76");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1155.i (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(9.22272143346\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 76.17
Character \(\chi\) \(=\) 1155.76
Dual form 1155.2.i.d.76.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.23885i q^{2} +1.00000i q^{3} -3.01246 q^{4} +1.00000i q^{5} +2.23885 q^{6} +(0.322004 + 2.62608i) q^{7} +2.26674i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-2.23885i q^{2} +1.00000i q^{3} -3.01246 q^{4} +1.00000i q^{5} +2.23885 q^{6} +(0.322004 + 2.62608i) q^{7} +2.26674i q^{8} -1.00000 q^{9} +2.23885 q^{10} +(-2.55226 - 2.11802i) q^{11} -3.01246i q^{12} +0.842387 q^{13} +(5.87941 - 0.720920i) q^{14} -1.00000 q^{15} -0.950014 q^{16} -3.42003 q^{17} +2.23885i q^{18} +6.30984 q^{19} -3.01246i q^{20} +(-2.62608 + 0.322004i) q^{21} +(-4.74192 + 5.71412i) q^{22} -5.97493 q^{23} -2.26674 q^{24} -1.00000 q^{25} -1.88598i q^{26} -1.00000i q^{27} +(-0.970024 - 7.91096i) q^{28} +9.40952i q^{29} +2.23885i q^{30} +0.997372i q^{31} +6.66043i q^{32} +(2.11802 - 2.55226i) q^{33} +7.65694i q^{34} +(-2.62608 + 0.322004i) q^{35} +3.01246 q^{36} +1.41004 q^{37} -14.1268i q^{38} +0.842387i q^{39} -2.26674 q^{40} -10.3306 q^{41} +(0.720920 + 5.87941i) q^{42} +10.0756i q^{43} +(7.68856 + 6.38043i) q^{44} -1.00000i q^{45} +13.3770i q^{46} +8.10188i q^{47} -0.950014i q^{48} +(-6.79263 + 1.69122i) q^{49} +2.23885i q^{50} -3.42003i q^{51} -2.53766 q^{52} -3.80872 q^{53} -2.23885 q^{54} +(2.11802 - 2.55226i) q^{55} +(-5.95266 + 0.729901i) q^{56} +6.30984i q^{57} +21.0665 q^{58} +10.7490i q^{59} +3.01246 q^{60} -3.15296 q^{61} +2.23297 q^{62} +(-0.322004 - 2.62608i) q^{63} +13.0117 q^{64} +0.842387i q^{65} +(-5.71412 - 4.74192i) q^{66} -11.4139 q^{67} +10.3027 q^{68} -5.97493i q^{69} +(0.720920 + 5.87941i) q^{70} -4.24318 q^{71} -2.26674i q^{72} +15.6260 q^{73} -3.15688i q^{74} -1.00000i q^{75} -19.0081 q^{76} +(4.74025 - 7.38445i) q^{77} +1.88598 q^{78} -14.3009i q^{79} -0.950014i q^{80} +1.00000 q^{81} +23.1286i q^{82} -0.946456 q^{83} +(7.91096 - 0.970024i) q^{84} -3.42003i q^{85} +22.5578 q^{86} -9.40952 q^{87} +(4.80100 - 5.78531i) q^{88} -17.4593i q^{89} -2.23885 q^{90} +(0.271252 + 2.21218i) q^{91} +17.9992 q^{92} -0.997372 q^{93} +18.1389 q^{94} +6.30984i q^{95} -6.66043 q^{96} +17.6891i q^{97} +(3.78639 + 15.2077i) q^{98} +(2.55226 + 2.11802i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 36 q^{4} - 32 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 36 q^{4} - 32 q^{9} - 8 q^{11} - 28 q^{14} - 32 q^{15} + 44 q^{16} - 12 q^{22} + 4 q^{23} - 32 q^{25} + 36 q^{36} - 16 q^{37} + 8 q^{42} + 56 q^{44} + 16 q^{49} - 20 q^{53} + 52 q^{56} - 48 q^{58} + 36 q^{60} - 156 q^{64} - 72 q^{67} + 8 q^{70} + 48 q^{71} - 20 q^{77} - 8 q^{78} + 32 q^{81} + 56 q^{86} + 4 q^{88} - 80 q^{91} + 64 q^{92} + 32 q^{93} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(232\) \(386\) \(661\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.23885i 1.58311i −0.611100 0.791554i \(-0.709273\pi\)
0.611100 0.791554i \(-0.290727\pi\)
\(3\) 1.00000i 0.577350i
\(4\) −3.01246 −1.50623
\(5\) 1.00000i 0.447214i
\(6\) 2.23885 0.914007
\(7\) 0.322004 + 2.62608i 0.121706 + 0.992566i
\(8\) 2.26674i 0.801415i
\(9\) −1.00000 −0.333333
\(10\) 2.23885 0.707987
\(11\) −2.55226 2.11802i −0.769534 0.638606i
\(12\) 3.01246i 0.869622i
\(13\) 0.842387 0.233636 0.116818 0.993153i \(-0.462731\pi\)
0.116818 + 0.993153i \(0.462731\pi\)
\(14\) 5.87941 0.720920i 1.57134 0.192674i
\(15\) −1.00000 −0.258199
\(16\) −0.950014 −0.237504
\(17\) −3.42003 −0.829479 −0.414739 0.909940i \(-0.636127\pi\)
−0.414739 + 0.909940i \(0.636127\pi\)
\(18\) 2.23885i 0.527702i
\(19\) 6.30984 1.44758 0.723788 0.690022i \(-0.242399\pi\)
0.723788 + 0.690022i \(0.242399\pi\)
\(20\) 3.01246i 0.673606i
\(21\) −2.62608 + 0.322004i −0.573058 + 0.0702671i
\(22\) −4.74192 + 5.71412i −1.01098 + 1.21826i
\(23\) −5.97493 −1.24586 −0.622929 0.782278i \(-0.714058\pi\)
−0.622929 + 0.782278i \(0.714058\pi\)
\(24\) −2.26674 −0.462697
\(25\) −1.00000 −0.200000
\(26\) 1.88598i 0.369871i
\(27\) 1.00000i 0.192450i
\(28\) −0.970024 7.91096i −0.183317 1.49503i
\(29\) 9.40952i 1.74730i 0.486550 + 0.873652i \(0.338255\pi\)
−0.486550 + 0.873652i \(0.661745\pi\)
\(30\) 2.23885i 0.408757i
\(31\) 0.997372i 0.179133i 0.995981 + 0.0895666i \(0.0285482\pi\)
−0.995981 + 0.0895666i \(0.971452\pi\)
\(32\) 6.66043i 1.17741i
\(33\) 2.11802 2.55226i 0.368699 0.444291i
\(34\) 7.65694i 1.31315i
\(35\) −2.62608 + 0.322004i −0.443889 + 0.0544286i
\(36\) 3.01246 0.502076
\(37\) 1.41004 0.231810 0.115905 0.993260i \(-0.463023\pi\)
0.115905 + 0.993260i \(0.463023\pi\)
\(38\) 14.1268i 2.29167i
\(39\) 0.842387i 0.134890i
\(40\) −2.26674 −0.358403
\(41\) −10.3306 −1.61337 −0.806683 0.590984i \(-0.798740\pi\)
−0.806683 + 0.590984i \(0.798740\pi\)
\(42\) 0.720920 + 5.87941i 0.111240 + 0.907213i
\(43\) 10.0756i 1.53652i 0.640140 + 0.768258i \(0.278876\pi\)
−0.640140 + 0.768258i \(0.721124\pi\)
\(44\) 7.68856 + 6.38043i 1.15909 + 0.961886i
\(45\) 1.00000i 0.149071i
\(46\) 13.3770i 1.97233i
\(47\) 8.10188i 1.18178i 0.806752 + 0.590891i \(0.201224\pi\)
−0.806752 + 0.590891i \(0.798776\pi\)
\(48\) 0.950014i 0.137123i
\(49\) −6.79263 + 1.69122i −0.970375 + 0.241603i
\(50\) 2.23885i 0.316621i
\(51\) 3.42003i 0.478900i
\(52\) −2.53766 −0.351910
\(53\) −3.80872 −0.523167 −0.261584 0.965181i \(-0.584245\pi\)
−0.261584 + 0.965181i \(0.584245\pi\)
\(54\) −2.23885 −0.304669
\(55\) 2.11802 2.55226i 0.285593 0.344146i
\(56\) −5.95266 + 0.729901i −0.795457 + 0.0975371i
\(57\) 6.30984i 0.835759i
\(58\) 21.0665 2.76617
\(59\) 10.7490i 1.39940i 0.714437 + 0.699700i \(0.246683\pi\)
−0.714437 + 0.699700i \(0.753317\pi\)
\(60\) 3.01246 0.388907
\(61\) −3.15296 −0.403695 −0.201848 0.979417i \(-0.564695\pi\)
−0.201848 + 0.979417i \(0.564695\pi\)
\(62\) 2.23297 0.283587
\(63\) −0.322004 2.62608i −0.0405687 0.330855i
\(64\) 13.0117 1.62646
\(65\) 0.842387i 0.104485i
\(66\) −5.71412 4.74192i −0.703360 0.583690i
\(67\) −11.4139 −1.39442 −0.697212 0.716865i \(-0.745576\pi\)
−0.697212 + 0.716865i \(0.745576\pi\)
\(68\) 10.3027 1.24939
\(69\) 5.97493i 0.719297i
\(70\) 0.720920 + 5.87941i 0.0861664 + 0.702724i
\(71\) −4.24318 −0.503573 −0.251786 0.967783i \(-0.581018\pi\)
−0.251786 + 0.967783i \(0.581018\pi\)
\(72\) 2.26674i 0.267138i
\(73\) 15.6260 1.82889 0.914445 0.404710i \(-0.132628\pi\)
0.914445 + 0.404710i \(0.132628\pi\)
\(74\) 3.15688i 0.366980i
\(75\) 1.00000i 0.115470i
\(76\) −19.0081 −2.18038
\(77\) 4.74025 7.38445i 0.540201 0.841536i
\(78\) 1.88598 0.213545
\(79\) 14.3009i 1.60898i −0.593969 0.804488i \(-0.702440\pi\)
0.593969 0.804488i \(-0.297560\pi\)
\(80\) 0.950014i 0.106215i
\(81\) 1.00000 0.111111
\(82\) 23.1286i 2.55413i
\(83\) −0.946456 −0.103887 −0.0519435 0.998650i \(-0.516542\pi\)
−0.0519435 + 0.998650i \(0.516542\pi\)
\(84\) 7.91096 0.970024i 0.863157 0.105838i
\(85\) 3.42003i 0.370954i
\(86\) 22.5578 2.43247
\(87\) −9.40952 −1.00881
\(88\) 4.80100 5.78531i 0.511788 0.616716i
\(89\) 17.4593i 1.85068i −0.379142 0.925339i \(-0.623781\pi\)
0.379142 0.925339i \(-0.376219\pi\)
\(90\) −2.23885 −0.235996
\(91\) 0.271252 + 2.21218i 0.0284350 + 0.231899i
\(92\) 17.9992 1.87655
\(93\) −0.997372 −0.103423
\(94\) 18.1389 1.87089
\(95\) 6.30984i 0.647376i
\(96\) −6.66043 −0.679777
\(97\) 17.6891i 1.79605i 0.439943 + 0.898026i \(0.354999\pi\)
−0.439943 + 0.898026i \(0.645001\pi\)
\(98\) 3.78639 + 15.2077i 0.382483 + 1.53621i
\(99\) 2.55226 + 2.11802i 0.256511 + 0.212869i
\(100\) 3.01246 0.301246
\(101\) 0.702211 0.0698727 0.0349363 0.999390i \(-0.488877\pi\)
0.0349363 + 0.999390i \(0.488877\pi\)
\(102\) −7.65694 −0.758150
\(103\) 7.05904i 0.695548i −0.937578 0.347774i \(-0.886938\pi\)
0.937578 0.347774i \(-0.113062\pi\)
\(104\) 1.90948i 0.187239i
\(105\) −0.322004 2.62608i −0.0314244 0.256279i
\(106\) 8.52715i 0.828230i
\(107\) 10.5977i 1.02451i −0.858832 0.512257i \(-0.828810\pi\)
0.858832 0.512257i \(-0.171190\pi\)
\(108\) 3.01246i 0.289874i
\(109\) 8.56633i 0.820505i 0.911972 + 0.410253i \(0.134559\pi\)
−0.911972 + 0.410253i \(0.865441\pi\)
\(110\) −5.71412 4.74192i −0.544820 0.452125i
\(111\) 1.41004i 0.133835i
\(112\) −0.305909 2.49482i −0.0289056 0.235738i
\(113\) −1.51910 −0.142905 −0.0714526 0.997444i \(-0.522763\pi\)
−0.0714526 + 0.997444i \(0.522763\pi\)
\(114\) 14.1268 1.32310
\(115\) 5.97493i 0.557165i
\(116\) 28.3458i 2.63184i
\(117\) −0.842387 −0.0778787
\(118\) 24.0654 2.21540
\(119\) −1.10126 8.98128i −0.100953 0.823313i
\(120\) 2.26674i 0.206924i
\(121\) 2.02802 + 10.8114i 0.184365 + 0.982858i
\(122\) 7.05901i 0.639093i
\(123\) 10.3306i 0.931477i
\(124\) 3.00454i 0.269816i
\(125\) 1.00000i 0.0894427i
\(126\) −5.87941 + 0.720920i −0.523780 + 0.0642246i
\(127\) 4.72234i 0.419040i −0.977804 0.209520i \(-0.932810\pi\)
0.977804 0.209520i \(-0.0671901\pi\)
\(128\) 15.8104i 1.39745i
\(129\) −10.0756 −0.887108
\(130\) 1.88598 0.165411
\(131\) 9.88715 0.863844 0.431922 0.901911i \(-0.357836\pi\)
0.431922 + 0.901911i \(0.357836\pi\)
\(132\) −6.38043 + 7.68856i −0.555345 + 0.669203i
\(133\) 2.03180 + 16.5702i 0.176179 + 1.43682i
\(134\) 25.5539i 2.20752i
\(135\) 1.00000 0.0860663
\(136\) 7.75233i 0.664757i
\(137\) −5.77144 −0.493087 −0.246544 0.969132i \(-0.579295\pi\)
−0.246544 + 0.969132i \(0.579295\pi\)
\(138\) −13.3770 −1.13872
\(139\) −9.94116 −0.843198 −0.421599 0.906782i \(-0.638531\pi\)
−0.421599 + 0.906782i \(0.638531\pi\)
\(140\) 7.91096 0.970024i 0.668599 0.0819820i
\(141\) −8.10188 −0.682302
\(142\) 9.49985i 0.797210i
\(143\) −2.14999 1.78419i −0.179791 0.149201i
\(144\) 0.950014 0.0791678
\(145\) −9.40952 −0.781419
\(146\) 34.9844i 2.89533i
\(147\) −1.69122 6.79263i −0.139489 0.560246i
\(148\) −4.24770 −0.349159
\(149\) 12.3780i 1.01405i −0.861933 0.507023i \(-0.830746\pi\)
0.861933 0.507023i \(-0.169254\pi\)
\(150\) −2.23885 −0.182801
\(151\) 13.3219i 1.08412i −0.840340 0.542060i \(-0.817644\pi\)
0.840340 0.542060i \(-0.182356\pi\)
\(152\) 14.3028i 1.16011i
\(153\) 3.42003 0.276493
\(154\) −16.5327 10.6127i −1.33224 0.855197i
\(155\) −0.997372 −0.0801108
\(156\) 2.53766i 0.203175i
\(157\) 8.99722i 0.718056i 0.933327 + 0.359028i \(0.116892\pi\)
−0.933327 + 0.359028i \(0.883108\pi\)
\(158\) −32.0176 −2.54718
\(159\) 3.80872i 0.302051i
\(160\) −6.66043 −0.526553
\(161\) −1.92395 15.6907i −0.151629 1.23660i
\(162\) 2.23885i 0.175901i
\(163\) −1.25085 −0.0979742 −0.0489871 0.998799i \(-0.515599\pi\)
−0.0489871 + 0.998799i \(0.515599\pi\)
\(164\) 31.1204 2.43010
\(165\) 2.55226 + 2.11802i 0.198693 + 0.164887i
\(166\) 2.11897i 0.164464i
\(167\) 16.5043 1.27714 0.638572 0.769562i \(-0.279525\pi\)
0.638572 + 0.769562i \(0.279525\pi\)
\(168\) −0.729901 5.95266i −0.0563131 0.459257i
\(169\) −12.2904 −0.945414
\(170\) −7.65694 −0.587260
\(171\) −6.30984 −0.482526
\(172\) 30.3524i 2.31435i
\(173\) 19.4351 1.47762 0.738811 0.673912i \(-0.235387\pi\)
0.738811 + 0.673912i \(0.235387\pi\)
\(174\) 21.0665i 1.59705i
\(175\) −0.322004 2.62608i −0.0243412 0.198513i
\(176\) 2.42468 + 2.01214i 0.182767 + 0.151671i
\(177\) −10.7490 −0.807944
\(178\) −39.0887 −2.92982
\(179\) 15.1145 1.12971 0.564856 0.825189i \(-0.308932\pi\)
0.564856 + 0.825189i \(0.308932\pi\)
\(180\) 3.01246i 0.224535i
\(181\) 10.4440i 0.776298i −0.921597 0.388149i \(-0.873115\pi\)
0.921597 0.388149i \(-0.126885\pi\)
\(182\) 4.95274 0.607294i 0.367122 0.0450156i
\(183\) 3.15296i 0.233074i
\(184\) 13.5436i 0.998449i
\(185\) 1.41004i 0.103669i
\(186\) 2.23297i 0.163729i
\(187\) 8.72879 + 7.24368i 0.638312 + 0.529710i
\(188\) 24.4066i 1.78003i
\(189\) 2.62608 0.322004i 0.191019 0.0234224i
\(190\) 14.1268 1.02487
\(191\) 12.2395 0.885622 0.442811 0.896615i \(-0.353981\pi\)
0.442811 + 0.896615i \(0.353981\pi\)
\(192\) 13.0117i 0.939037i
\(193\) 6.70826i 0.482871i 0.970417 + 0.241435i \(0.0776182\pi\)
−0.970417 + 0.241435i \(0.922382\pi\)
\(194\) 39.6032 2.84334
\(195\) −0.842387 −0.0603246
\(196\) 20.4625 5.09473i 1.46161 0.363909i
\(197\) 7.20052i 0.513015i 0.966542 + 0.256508i \(0.0825719\pi\)
−0.966542 + 0.256508i \(0.917428\pi\)
\(198\) 4.74192 5.71412i 0.336994 0.406085i
\(199\) 24.0485i 1.70475i −0.522927 0.852377i \(-0.675160\pi\)
0.522927 0.852377i \(-0.324840\pi\)
\(200\) 2.26674i 0.160283i
\(201\) 11.4139i 0.805071i
\(202\) 1.57215i 0.110616i
\(203\) −24.7102 + 3.02991i −1.73432 + 0.212658i
\(204\) 10.3027i 0.721333i
\(205\) 10.3306i 0.721519i
\(206\) −15.8042 −1.10113
\(207\) 5.97493 0.415286
\(208\) −0.800280 −0.0554894
\(209\) −16.1043 13.3643i −1.11396 0.924431i
\(210\) −5.87941 + 0.720920i −0.405718 + 0.0497482i
\(211\) 6.53762i 0.450068i 0.974351 + 0.225034i \(0.0722493\pi\)
−0.974351 + 0.225034i \(0.927751\pi\)
\(212\) 11.4736 0.788010
\(213\) 4.24318i 0.290738i
\(214\) −23.7266 −1.62192
\(215\) −10.0756 −0.687151
\(216\) 2.26674 0.154232
\(217\) −2.61918 + 0.321158i −0.177802 + 0.0218016i
\(218\) 19.1787 1.29895
\(219\) 15.6260i 1.05591i
\(220\) −6.38043 + 7.68856i −0.430169 + 0.518363i
\(221\) −2.88099 −0.193796
\(222\) 3.15688 0.211876
\(223\) 25.7539i 1.72461i 0.506388 + 0.862305i \(0.330980\pi\)
−0.506388 + 0.862305i \(0.669020\pi\)
\(224\) −17.4908 + 2.14469i −1.16866 + 0.143298i
\(225\) 1.00000 0.0666667
\(226\) 3.40105i 0.226234i
\(227\) −7.83215 −0.519838 −0.259919 0.965630i \(-0.583696\pi\)
−0.259919 + 0.965630i \(0.583696\pi\)
\(228\) 19.0081i 1.25884i
\(229\) 12.8659i 0.850205i 0.905145 + 0.425102i \(0.139762\pi\)
−0.905145 + 0.425102i \(0.860238\pi\)
\(230\) −13.3770 −0.882052
\(231\) 7.38445 + 4.74025i 0.485861 + 0.311885i
\(232\) −21.3290 −1.40032
\(233\) 17.1634i 1.12441i 0.826997 + 0.562206i \(0.190047\pi\)
−0.826997 + 0.562206i \(0.809953\pi\)
\(234\) 1.88598i 0.123290i
\(235\) −8.10188 −0.528509
\(236\) 32.3809i 2.10782i
\(237\) 14.3009 0.928943
\(238\) −20.1078 + 2.46557i −1.30339 + 0.159819i
\(239\) 10.3445i 0.669129i −0.942373 0.334564i \(-0.891411\pi\)
0.942373 0.334564i \(-0.108589\pi\)
\(240\) 0.950014 0.0613231
\(241\) 8.03134 0.517344 0.258672 0.965965i \(-0.416715\pi\)
0.258672 + 0.965965i \(0.416715\pi\)
\(242\) 24.2052 4.54044i 1.55597 0.291870i
\(243\) 1.00000i 0.0641500i
\(244\) 9.49816 0.608057
\(245\) −1.69122 6.79263i −0.108048 0.433965i
\(246\) −23.1286 −1.47463
\(247\) 5.31533 0.338206
\(248\) −2.26079 −0.143560
\(249\) 0.946456i 0.0599792i
\(250\) −2.23885 −0.141597
\(251\) 27.1281i 1.71231i −0.516717 0.856156i \(-0.672846\pi\)
0.516717 0.856156i \(-0.327154\pi\)
\(252\) 0.970024 + 7.91096i 0.0611058 + 0.498344i
\(253\) 15.2495 + 12.6550i 0.958731 + 0.795613i
\(254\) −10.5726 −0.663385
\(255\) 3.42003 0.214171
\(256\) −9.37372 −0.585857
\(257\) 23.0643i 1.43871i 0.694641 + 0.719356i \(0.255563\pi\)
−0.694641 + 0.719356i \(0.744437\pi\)
\(258\) 22.5578i 1.40439i
\(259\) 0.454040 + 3.70289i 0.0282127 + 0.230087i
\(260\) 2.53766i 0.157379i
\(261\) 9.40952i 0.582435i
\(262\) 22.1359i 1.36756i
\(263\) 2.49039i 0.153564i 0.997048 + 0.0767820i \(0.0244645\pi\)
−0.997048 + 0.0767820i \(0.975535\pi\)
\(264\) 5.78531 + 4.80100i 0.356061 + 0.295481i
\(265\) 3.80872i 0.233968i
\(266\) 37.0981 4.54889i 2.27463 0.278910i
\(267\) 17.4593 1.06849
\(268\) 34.3837 2.10032
\(269\) 4.78537i 0.291769i 0.989302 + 0.145885i \(0.0466029\pi\)
−0.989302 + 0.145885i \(0.953397\pi\)
\(270\) 2.23885i 0.136252i
\(271\) −12.9173 −0.784671 −0.392336 0.919822i \(-0.628333\pi\)
−0.392336 + 0.919822i \(0.628333\pi\)
\(272\) 3.24908 0.197004
\(273\) −2.21218 + 0.271252i −0.133887 + 0.0164169i
\(274\) 12.9214i 0.780610i
\(275\) 2.55226 + 2.11802i 0.153907 + 0.127721i
\(276\) 17.9992i 1.08343i
\(277\) 5.81500i 0.349389i 0.984623 + 0.174695i \(0.0558938\pi\)
−0.984623 + 0.174695i \(0.944106\pi\)
\(278\) 22.2568i 1.33487i
\(279\) 0.997372i 0.0597111i
\(280\) −0.729901 5.95266i −0.0436199 0.355739i
\(281\) 2.47572i 0.147689i −0.997270 0.0738446i \(-0.976473\pi\)
0.997270 0.0738446i \(-0.0235269\pi\)
\(282\) 18.1389i 1.08016i
\(283\) 26.9187 1.60015 0.800075 0.599901i \(-0.204793\pi\)
0.800075 + 0.599901i \(0.204793\pi\)
\(284\) 12.7824 0.758496
\(285\) −6.30984 −0.373763
\(286\) −3.99454 + 4.81350i −0.236202 + 0.284628i
\(287\) −3.32649 27.1290i −0.196357 1.60137i
\(288\) 6.66043i 0.392469i
\(289\) −5.30340 −0.311965
\(290\) 21.0665i 1.23707i
\(291\) −17.6891 −1.03695
\(292\) −47.0728 −2.75473
\(293\) 5.92944 0.346402 0.173201 0.984887i \(-0.444589\pi\)
0.173201 + 0.984887i \(0.444589\pi\)
\(294\) −15.2077 + 3.78639i −0.886930 + 0.220827i
\(295\) −10.7490 −0.625831
\(296\) 3.19621i 0.185776i
\(297\) −2.11802 + 2.55226i −0.122900 + 0.148097i
\(298\) −27.7125 −1.60534
\(299\) −5.03320 −0.291078
\(300\) 3.01246i 0.173924i
\(301\) −26.4594 + 3.24439i −1.52509 + 0.187003i
\(302\) −29.8257 −1.71628
\(303\) 0.702211i 0.0403410i
\(304\) −5.99444 −0.343805
\(305\) 3.15296i 0.180538i
\(306\) 7.65694i 0.437718i
\(307\) 7.12996 0.406928 0.203464 0.979082i \(-0.434780\pi\)
0.203464 + 0.979082i \(0.434780\pi\)
\(308\) −14.2798 + 22.2453i −0.813667 + 1.26755i
\(309\) 7.05904 0.401575
\(310\) 2.23297i 0.126824i
\(311\) 34.4437i 1.95312i 0.215238 + 0.976562i \(0.430947\pi\)
−0.215238 + 0.976562i \(0.569053\pi\)
\(312\) −1.90948 −0.108103
\(313\) 6.36649i 0.359855i 0.983680 + 0.179928i \(0.0575864\pi\)
−0.983680 + 0.179928i \(0.942414\pi\)
\(314\) 20.1434 1.13676
\(315\) 2.62608 0.322004i 0.147963 0.0181429i
\(316\) 43.0808i 2.42349i
\(317\) −16.9314 −0.950961 −0.475480 0.879726i \(-0.657726\pi\)
−0.475480 + 0.879726i \(0.657726\pi\)
\(318\) −8.52715 −0.478179
\(319\) 19.9295 24.0155i 1.11584 1.34461i
\(320\) 13.0117i 0.727375i
\(321\) 10.5977 0.591503
\(322\) −35.1291 + 4.30744i −1.95767 + 0.240044i
\(323\) −21.5798 −1.20073
\(324\) −3.01246 −0.167359
\(325\) −0.842387 −0.0467272
\(326\) 2.80047i 0.155104i
\(327\) −8.56633 −0.473719
\(328\) 23.4168i 1.29298i
\(329\) −21.2762 + 2.60884i −1.17300 + 0.143830i
\(330\) 4.74192 5.71412i 0.261034 0.314552i
\(331\) −22.2475 −1.22284 −0.611418 0.791308i \(-0.709400\pi\)
−0.611418 + 0.791308i \(0.709400\pi\)
\(332\) 2.85116 0.156478
\(333\) −1.41004 −0.0772699
\(334\) 36.9508i 2.02186i
\(335\) 11.4139i 0.623605i
\(336\) 2.49482 0.305909i 0.136103 0.0166887i
\(337\) 15.7574i 0.858361i 0.903219 + 0.429180i \(0.141198\pi\)
−0.903219 + 0.429180i \(0.858802\pi\)
\(338\) 27.5163i 1.49669i
\(339\) 1.51910i 0.0825064i
\(340\) 10.3027i 0.558742i
\(341\) 2.11245 2.54555i 0.114396 0.137849i
\(342\) 14.1268i 0.763890i
\(343\) −6.62854 17.2934i −0.357907 0.933757i
\(344\) −22.8388 −1.23139
\(345\) 5.97493 0.321679
\(346\) 43.5123i 2.33924i
\(347\) 12.6941i 0.681454i 0.940162 + 0.340727i \(0.110673\pi\)
−0.940162 + 0.340727i \(0.889327\pi\)
\(348\) 28.3458 1.51949
\(349\) 21.6081 1.15665 0.578326 0.815805i \(-0.303706\pi\)
0.578326 + 0.815805i \(0.303706\pi\)
\(350\) −5.87941 + 0.720920i −0.314268 + 0.0385348i
\(351\) 0.842387i 0.0449633i
\(352\) 14.1069 16.9991i 0.751900 0.906056i
\(353\) 8.18411i 0.435596i 0.975994 + 0.217798i \(0.0698874\pi\)
−0.975994 + 0.217798i \(0.930113\pi\)
\(354\) 24.0654i 1.27906i
\(355\) 4.24318i 0.225205i
\(356\) 52.5953i 2.78754i
\(357\) 8.98128 1.10126i 0.475340 0.0582851i
\(358\) 33.8392i 1.78846i
\(359\) 13.4331i 0.708970i −0.935062 0.354485i \(-0.884656\pi\)
0.935062 0.354485i \(-0.115344\pi\)
\(360\) 2.26674 0.119468
\(361\) 20.8141 1.09548
\(362\) −23.3826 −1.22896
\(363\) −10.8114 + 2.02802i −0.567453 + 0.106443i
\(364\) −0.817136 6.66410i −0.0428296 0.349294i
\(365\) 15.6260i 0.817905i
\(366\) −7.05901 −0.368980
\(367\) 19.2541i 1.00506i −0.864561 0.502529i \(-0.832403\pi\)
0.864561 0.502529i \(-0.167597\pi\)
\(368\) 5.67627 0.295896
\(369\) 10.3306 0.537789
\(370\) 3.15688 0.164118
\(371\) −1.22642 10.0020i −0.0636727 0.519278i
\(372\) 3.00454 0.155778
\(373\) 29.4605i 1.52541i −0.646748 0.762704i \(-0.723872\pi\)
0.646748 0.762704i \(-0.276128\pi\)
\(374\) 16.2175 19.5425i 0.838588 1.01052i
\(375\) 1.00000 0.0516398
\(376\) −18.3649 −0.947097
\(377\) 7.92646i 0.408234i
\(378\) −0.720920 5.87941i −0.0370801 0.302404i
\(379\) −32.0801 −1.64785 −0.823923 0.566701i \(-0.808219\pi\)
−0.823923 + 0.566701i \(0.808219\pi\)
\(380\) 19.0081i 0.975096i
\(381\) 4.72234 0.241933
\(382\) 27.4025i 1.40203i
\(383\) 1.37119i 0.0700644i −0.999386 0.0350322i \(-0.988847\pi\)
0.999386 0.0350322i \(-0.0111534\pi\)
\(384\) 15.8104 0.806820
\(385\) 7.38445 + 4.74025i 0.376346 + 0.241585i
\(386\) 15.0188 0.764436
\(387\) 10.0756i 0.512172i
\(388\) 53.2875i 2.70526i
\(389\) 4.19889 0.212892 0.106446 0.994318i \(-0.466053\pi\)
0.106446 + 0.994318i \(0.466053\pi\)
\(390\) 1.88598i 0.0955003i
\(391\) 20.4344 1.03341
\(392\) −3.83356 15.3971i −0.193624 0.777673i
\(393\) 9.88715i 0.498741i
\(394\) 16.1209 0.812159
\(395\) 14.3009 0.719556
\(396\) −7.68856 6.38043i −0.386365 0.320629i
\(397\) 4.12458i 0.207007i −0.994629 0.103503i \(-0.966995\pi\)
0.994629 0.103503i \(-0.0330052\pi\)
\(398\) −53.8411 −2.69881
\(399\) −16.5702 + 2.03180i −0.829546 + 0.101717i
\(400\) 0.950014 0.0475007
\(401\) 12.2122 0.609847 0.304923 0.952377i \(-0.401369\pi\)
0.304923 + 0.952377i \(0.401369\pi\)
\(402\) −25.5539 −1.27451
\(403\) 0.840173i 0.0418520i
\(404\) −2.11538 −0.105244
\(405\) 1.00000i 0.0496904i
\(406\) 6.78351 + 55.3225i 0.336660 + 2.74561i
\(407\) −3.59879 2.98650i −0.178386 0.148035i
\(408\) 7.75233 0.383797
\(409\) 1.39729 0.0690914 0.0345457 0.999403i \(-0.489002\pi\)
0.0345457 + 0.999403i \(0.489002\pi\)
\(410\) −23.1286 −1.14224
\(411\) 5.77144i 0.284684i
\(412\) 21.2651i 1.04765i
\(413\) −28.2278 + 3.46122i −1.38900 + 0.170316i
\(414\) 13.3770i 0.657443i
\(415\) 0.946456i 0.0464597i
\(416\) 5.61066i 0.275085i
\(417\) 9.94116i 0.486821i
\(418\) −29.9208 + 36.0552i −1.46347 + 1.76352i
\(419\) 13.6032i 0.664558i 0.943181 + 0.332279i \(0.107817\pi\)
−0.943181 + 0.332279i \(0.892183\pi\)
\(420\) 0.970024 + 7.91096i 0.0473323 + 0.386016i
\(421\) 19.9582 0.972703 0.486352 0.873763i \(-0.338327\pi\)
0.486352 + 0.873763i \(0.338327\pi\)
\(422\) 14.6368 0.712506
\(423\) 8.10188i 0.393927i
\(424\) 8.63338i 0.419274i
\(425\) 3.42003 0.165896
\(426\) −9.49985 −0.460269
\(427\) −1.01527 8.27994i −0.0491322 0.400694i
\(428\) 31.9250i 1.54315i
\(429\) 1.78419 2.14999i 0.0861415 0.103802i
\(430\) 22.5578i 1.08783i
\(431\) 11.6976i 0.563454i −0.959495 0.281727i \(-0.909093\pi\)
0.959495 0.281727i \(-0.0909072\pi\)
\(432\) 0.950014i 0.0457076i
\(433\) 22.6313i 1.08759i −0.839218 0.543796i \(-0.816987\pi\)
0.839218 0.543796i \(-0.183013\pi\)
\(434\) 0.719025 + 5.86396i 0.0345143 + 0.281479i
\(435\) 9.40952i 0.451152i
\(436\) 25.8057i 1.23587i
\(437\) −37.7009 −1.80348
\(438\) 34.9844 1.67162
\(439\) −8.05202 −0.384302 −0.192151 0.981365i \(-0.561546\pi\)
−0.192151 + 0.981365i \(0.561546\pi\)
\(440\) 5.78531 + 4.80100i 0.275804 + 0.228879i
\(441\) 6.79263 1.69122i 0.323458 0.0805343i
\(442\) 6.45011i 0.306800i
\(443\) −18.0248 −0.856384 −0.428192 0.903688i \(-0.640849\pi\)
−0.428192 + 0.903688i \(0.640849\pi\)
\(444\) 4.24770i 0.201587i
\(445\) 17.4593 0.827648
\(446\) 57.6592 2.73024
\(447\) 12.3780 0.585460
\(448\) 4.18982 + 34.1698i 0.197950 + 1.61437i
\(449\) 32.9988 1.55731 0.778655 0.627452i \(-0.215902\pi\)
0.778655 + 0.627452i \(0.215902\pi\)
\(450\) 2.23885i 0.105540i
\(451\) 26.3663 + 21.8803i 1.24154 + 1.03030i
\(452\) 4.57623 0.215248
\(453\) 13.3219 0.625917
\(454\) 17.5350i 0.822959i
\(455\) −2.21218 + 0.271252i −0.103709 + 0.0127165i
\(456\) −14.3028 −0.669789
\(457\) 1.75226i 0.0819673i 0.999160 + 0.0409836i \(0.0130492\pi\)
−0.999160 + 0.0409836i \(0.986951\pi\)
\(458\) 28.8049 1.34597
\(459\) 3.42003i 0.159633i
\(460\) 17.9992i 0.839218i
\(461\) −29.6847 −1.38255 −0.691277 0.722589i \(-0.742952\pi\)
−0.691277 + 0.722589i \(0.742952\pi\)
\(462\) 10.6127 16.5327i 0.493748 0.769170i
\(463\) 19.0858 0.886994 0.443497 0.896276i \(-0.353738\pi\)
0.443497 + 0.896276i \(0.353738\pi\)
\(464\) 8.93918i 0.414991i
\(465\) 0.997372i 0.0462520i
\(466\) 38.4263 1.78007
\(467\) 7.19573i 0.332979i 0.986043 + 0.166489i \(0.0532431\pi\)
−0.986043 + 0.166489i \(0.946757\pi\)
\(468\) 2.53766 0.117303
\(469\) −3.67531 29.9737i −0.169710 1.38406i
\(470\) 18.1389i 0.836686i
\(471\) −8.99722 −0.414570
\(472\) −24.3652 −1.12150
\(473\) 21.3403 25.7155i 0.981228 1.18240i
\(474\) 32.0176i 1.47062i
\(475\) −6.30984 −0.289515
\(476\) 3.31751 + 27.0557i 0.152058 + 1.24010i
\(477\) 3.80872 0.174389
\(478\) −23.1598 −1.05930
\(479\) −19.1149 −0.873382 −0.436691 0.899611i \(-0.643850\pi\)
−0.436691 + 0.899611i \(0.643850\pi\)
\(480\) 6.66043i 0.304005i
\(481\) 1.18780 0.0541592
\(482\) 17.9810i 0.819011i
\(483\) 15.6907 1.92395i 0.713950 0.0875429i
\(484\) −6.10932 32.5690i −0.277697 1.48041i
\(485\) −17.6891 −0.803219
\(486\) 2.23885 0.101556
\(487\) 14.7143 0.666768 0.333384 0.942791i \(-0.391810\pi\)
0.333384 + 0.942791i \(0.391810\pi\)
\(488\) 7.14695i 0.323527i
\(489\) 1.25085i 0.0565655i
\(490\) −15.2077 + 3.78639i −0.687013 + 0.171052i
\(491\) 19.2562i 0.869022i −0.900667 0.434511i \(-0.856921\pi\)
0.900667 0.434511i \(-0.143079\pi\)
\(492\) 31.1204i 1.40302i
\(493\) 32.1809i 1.44935i
\(494\) 11.9002i 0.535417i
\(495\) −2.11802 + 2.55226i −0.0951977 + 0.114715i
\(496\) 0.947517i 0.0425448i
\(497\) −1.36632 11.1429i −0.0612879 0.499830i
\(498\) −2.11897 −0.0949535
\(499\) −10.7689 −0.482081 −0.241040 0.970515i \(-0.577489\pi\)
−0.241040 + 0.970515i \(0.577489\pi\)
\(500\) 3.01246i 0.134721i
\(501\) 16.5043i 0.737360i
\(502\) −60.7359 −2.71077
\(503\) −8.00112 −0.356752 −0.178376 0.983962i \(-0.557084\pi\)
−0.178376 + 0.983962i \(0.557084\pi\)
\(504\) 5.95266 0.729901i 0.265152 0.0325124i
\(505\) 0.702211i 0.0312480i
\(506\) 28.3327 34.1415i 1.25954 1.51777i
\(507\) 12.2904i 0.545835i
\(508\) 14.2258i 0.631169i
\(509\) 7.68605i 0.340678i −0.985385 0.170339i \(-0.945514\pi\)
0.985385 0.170339i \(-0.0544863\pi\)
\(510\) 7.65694i 0.339055i
\(511\) 5.03165 + 41.0353i 0.222587 + 1.81529i
\(512\) 10.6344i 0.469977i
\(513\) 6.30984i 0.278586i
\(514\) 51.6376 2.27764
\(515\) 7.05904 0.311059
\(516\) 30.3524 1.33619
\(517\) 17.1599 20.6781i 0.754692 0.909421i
\(518\) 8.29023 1.01653i 0.364252 0.0446637i
\(519\) 19.4351i 0.853106i
\(520\) −1.90948 −0.0837360
\(521\) 41.8300i 1.83261i 0.400486 + 0.916303i \(0.368841\pi\)
−0.400486 + 0.916303i \(0.631159\pi\)
\(522\) −21.0665 −0.922057
\(523\) 8.26292 0.361312 0.180656 0.983546i \(-0.442178\pi\)
0.180656 + 0.983546i \(0.442178\pi\)
\(524\) −29.7846 −1.30115
\(525\) 2.62608 0.322004i 0.114612 0.0140534i
\(526\) 5.57561 0.243108
\(527\) 3.41104i 0.148587i
\(528\) −2.01214 + 2.42468i −0.0875674 + 0.105521i
\(529\) 12.6998 0.552164
\(530\) −8.52715 −0.370396
\(531\) 10.7490i 0.466467i
\(532\) −6.12070 49.9169i −0.265366 2.16417i
\(533\) −8.70235 −0.376941
\(534\) 39.0887i 1.69153i
\(535\) 10.5977 0.458177
\(536\) 25.8723i 1.11751i
\(537\) 15.1145i 0.652240i
\(538\) 10.7137 0.461902
\(539\) 20.9186 + 10.0705i 0.901026 + 0.433766i
\(540\) −3.01246 −0.129636
\(541\) 22.0864i 0.949569i 0.880102 + 0.474784i \(0.157474\pi\)
−0.880102 + 0.474784i \(0.842526\pi\)
\(542\) 28.9200i 1.24222i
\(543\) 10.4440 0.448196
\(544\) 22.7789i 0.976635i
\(545\) −8.56633 −0.366941
\(546\) 0.607294 + 4.95274i 0.0259898 + 0.211958i
\(547\) 5.38070i 0.230062i −0.993362 0.115031i \(-0.963303\pi\)
0.993362 0.115031i \(-0.0366967\pi\)
\(548\) 17.3862 0.742702
\(549\) 3.15296 0.134565
\(550\) 4.74192 5.71412i 0.202196 0.243651i
\(551\) 59.3726i 2.52936i
\(552\) 13.5436 0.576455
\(553\) 37.5553 4.60495i 1.59702 0.195822i
\(554\) 13.0189 0.553121
\(555\) −1.41004 −0.0598530
\(556\) 29.9473 1.27005
\(557\) 8.75524i 0.370971i 0.982647 + 0.185486i \(0.0593858\pi\)
−0.982647 + 0.185486i \(0.940614\pi\)
\(558\) −2.23297 −0.0945291
\(559\) 8.48757i 0.358986i
\(560\) 2.49482 0.305909i 0.105425 0.0129270i
\(561\) −7.24368 + 8.72879i −0.305828 + 0.368530i
\(562\) −5.54277 −0.233808
\(563\) 16.7749 0.706977 0.353488 0.935439i \(-0.384995\pi\)
0.353488 + 0.935439i \(0.384995\pi\)
\(564\) 24.4066 1.02770
\(565\) 1.51910i 0.0639092i
\(566\) 60.2669i 2.53321i
\(567\) 0.322004 + 2.62608i 0.0135229 + 0.110285i
\(568\) 9.61820i 0.403571i
\(569\) 11.1514i 0.467491i 0.972298 + 0.233745i \(0.0750982\pi\)
−0.972298 + 0.233745i \(0.924902\pi\)
\(570\) 14.1268i 0.591706i
\(571\) 11.1466i 0.466469i −0.972420 0.233235i \(-0.925069\pi\)
0.972420 0.233235i \(-0.0749310\pi\)
\(572\) 6.47675 + 5.37479i 0.270806 + 0.224731i
\(573\) 12.2395i 0.511314i
\(574\) −60.7378 + 7.44752i −2.53515 + 0.310854i
\(575\) 5.97493 0.249172
\(576\) −13.0117 −0.542153
\(577\) 18.4249i 0.767038i 0.923533 + 0.383519i \(0.125288\pi\)
−0.923533 + 0.383519i \(0.874712\pi\)
\(578\) 11.8735i 0.493873i
\(579\) −6.70826 −0.278786
\(580\) 28.3458 1.17700
\(581\) −0.304763 2.48547i −0.0126437 0.103115i
\(582\) 39.6032i 1.64160i
\(583\) 9.72082 + 8.06692i 0.402595 + 0.334098i
\(584\) 35.4202i 1.46570i
\(585\) 0.842387i 0.0348284i
\(586\) 13.2751i 0.548391i
\(587\) 14.8917i 0.614645i −0.951605 0.307323i \(-0.900567\pi\)
0.951605 0.307323i \(-0.0994331\pi\)
\(588\) 5.09473 + 20.4625i 0.210103 + 0.843859i
\(589\) 6.29326i 0.259309i
\(590\) 24.0654i 0.990757i
\(591\) −7.20052 −0.296190
\(592\) −1.33956 −0.0550557
\(593\) 15.1514 0.622195 0.311098 0.950378i \(-0.399303\pi\)
0.311098 + 0.950378i \(0.399303\pi\)
\(594\) 5.71412 + 4.74192i 0.234453 + 0.194563i
\(595\) 8.98128 1.10126i 0.368197 0.0451474i
\(596\) 37.2882i 1.52739i
\(597\) 24.0485 0.984241
\(598\) 11.2686i 0.460807i
\(599\) 38.6892 1.58080 0.790398 0.612593i \(-0.209874\pi\)
0.790398 + 0.612593i \(0.209874\pi\)
\(600\) 2.26674 0.0925394
\(601\) −40.7993 −1.66424 −0.832118 0.554598i \(-0.812872\pi\)
−0.832118 + 0.554598i \(0.812872\pi\)
\(602\) 7.26371 + 59.2387i 0.296047 + 2.41439i
\(603\) 11.4139 0.464808
\(604\) 40.1316i 1.63293i
\(605\) −10.8114 + 2.02802i −0.439547 + 0.0824507i
\(606\) 1.57215 0.0638641
\(607\) −8.74411 −0.354912 −0.177456 0.984129i \(-0.556787\pi\)
−0.177456 + 0.984129i \(0.556787\pi\)
\(608\) 42.0262i 1.70439i
\(609\) −3.02991 24.7102i −0.122778 1.00131i
\(610\) −7.05901 −0.285811
\(611\) 6.82492i 0.276107i
\(612\) −10.3027 −0.416462
\(613\) 20.0772i 0.810911i 0.914115 + 0.405455i \(0.132887\pi\)
−0.914115 + 0.405455i \(0.867113\pi\)
\(614\) 15.9629i 0.644211i
\(615\) 10.3306 0.416569
\(616\) 16.7386 + 10.7449i 0.674419 + 0.432925i
\(617\) −2.92259 −0.117659 −0.0588296 0.998268i \(-0.518737\pi\)
−0.0588296 + 0.998268i \(0.518737\pi\)
\(618\) 15.8042i 0.635736i
\(619\) 33.9078i 1.36287i −0.731880 0.681434i \(-0.761357\pi\)
0.731880 0.681434i \(-0.238643\pi\)
\(620\) 3.00454 0.120665
\(621\) 5.97493i 0.239766i
\(622\) 77.1144 3.09200
\(623\) 45.8494 5.62195i 1.83692 0.225239i
\(624\) 0.800280i 0.0320368i
\(625\) 1.00000 0.0400000
\(626\) 14.2536 0.569690
\(627\) 13.3643 16.1043i 0.533720 0.643145i
\(628\) 27.1037i 1.08156i
\(629\) −4.82239 −0.192281
\(630\) −0.720920 5.87941i −0.0287221 0.234241i
\(631\) 3.05134 0.121472 0.0607360 0.998154i \(-0.480655\pi\)
0.0607360 + 0.998154i \(0.480655\pi\)
\(632\) 32.4164 1.28946
\(633\) −6.53762 −0.259847
\(634\) 37.9068i 1.50547i
\(635\) 4.72234 0.187400
\(636\) 11.4736i 0.454958i
\(637\) −5.72202 + 1.42466i −0.226715 + 0.0564472i
\(638\) −53.7672 44.6192i −2.12866 1.76649i
\(639\) 4.24318 0.167858
\(640\) 15.8104 0.624960
\(641\) 42.3257 1.67176 0.835882 0.548910i \(-0.184957\pi\)
0.835882 + 0.548910i \(0.184957\pi\)
\(642\) 23.7266i 0.936413i
\(643\) 22.3867i 0.882847i 0.897299 + 0.441423i \(0.145526\pi\)
−0.897299 + 0.441423i \(0.854474\pi\)
\(644\) 5.79582 + 47.2675i 0.228387 + 1.86260i
\(645\) 10.0756i 0.396727i
\(646\) 48.3141i 1.90089i
\(647\) 7.10723i 0.279414i 0.990193 + 0.139707i \(0.0446161\pi\)
−0.990193 + 0.139707i \(0.955384\pi\)
\(648\) 2.26674i 0.0890461i
\(649\) 22.7665 27.4342i 0.893665 1.07689i
\(650\) 1.88598i 0.0739742i
\(651\) −0.321158 2.61918i −0.0125872 0.102654i
\(652\) 3.76814 0.147572
\(653\) 22.3253 0.873655 0.436827 0.899545i \(-0.356102\pi\)
0.436827 + 0.899545i \(0.356102\pi\)
\(654\) 19.1787i 0.749948i
\(655\) 9.88715i 0.386323i
\(656\) 9.81420 0.383180
\(657\) −15.6260 −0.609630
\(658\) 5.84081 + 47.6343i 0.227698 + 1.85698i
\(659\) 39.4137i 1.53534i −0.640846 0.767670i \(-0.721416\pi\)
0.640846 0.767670i \(-0.278584\pi\)
\(660\) −7.68856 6.38043i −0.299277 0.248358i
\(661\) 35.0721i 1.36414i 0.731285 + 0.682072i \(0.238921\pi\)
−0.731285 + 0.682072i \(0.761079\pi\)
\(662\) 49.8090i 1.93588i
\(663\) 2.88099i 0.111888i
\(664\) 2.14537i 0.0832566i
\(665\) −16.5702 + 2.03180i −0.642564 + 0.0787896i
\(666\) 3.15688i 0.122327i
\(667\) 56.2212i 2.17690i
\(668\) −49.7186 −1.92367
\(669\) −25.7539 −0.995705
\(670\) −25.5539 −0.987234
\(671\) 8.04716 + 6.67802i 0.310657 + 0.257802i
\(672\) −2.14469 17.4908i −0.0827330 0.674724i
\(673\) 19.1635i 0.738697i 0.929291 + 0.369349i \(0.120419\pi\)
−0.929291 + 0.369349i \(0.879581\pi\)
\(674\) 35.2785 1.35888
\(675\) 1.00000i 0.0384900i
\(676\) 37.0243 1.42401
\(677\) −36.5750 −1.40569 −0.702846 0.711342i \(-0.748088\pi\)
−0.702846 + 0.711342i \(0.748088\pi\)
\(678\) −3.40105 −0.130616
\(679\) −46.4529 + 5.69595i −1.78270 + 0.218590i
\(680\) 7.75233 0.297288
\(681\) 7.83215i 0.300129i
\(682\) −5.69910 4.72946i −0.218230 0.181100i
\(683\) 20.6810 0.791337 0.395668 0.918393i \(-0.370513\pi\)
0.395668 + 0.918393i \(0.370513\pi\)
\(684\) 19.0081 0.726794
\(685\) 5.77144i 0.220515i
\(686\) −38.7174 + 14.8403i −1.47824 + 0.566606i
\(687\) −12.8659 −0.490866
\(688\) 9.57197i 0.364928i
\(689\) −3.20841 −0.122231
\(690\) 13.3770i 0.509253i
\(691\) 11.4257i 0.434655i −0.976099 0.217327i \(-0.930266\pi\)
0.976099 0.217327i \(-0.0697339\pi\)
\(692\) −58.5474 −2.22564
\(693\) −4.74025 + 7.38445i −0.180067 + 0.280512i
\(694\) 28.4202 1.07881
\(695\) 9.94116i 0.377090i
\(696\) 21.3290i 0.808473i
\(697\) 35.3309 1.33825
\(698\) 48.3772i 1.83111i
\(699\) −17.1634 −0.649180
\(700\) 0.970024 + 7.91096i 0.0366635 + 0.299006i
\(701\) 7.53673i 0.284658i 0.989819 + 0.142329i \(0.0454592\pi\)
−0.989819 + 0.142329i \(0.954541\pi\)
\(702\) −1.88598 −0.0711817
\(703\) 8.89715 0.335563
\(704\) −33.2091 27.5589i −1.25162 1.03867i
\(705\) 8.10188i 0.305135i
\(706\) 18.3230 0.689595
\(707\) 0.226115 + 1.84407i 0.00850393 + 0.0693532i
\(708\) 32.3809 1.21695
\(709\) 10.9203 0.410121 0.205061 0.978749i \(-0.434261\pi\)
0.205061 + 0.978749i \(0.434261\pi\)
\(710\) −9.49985 −0.356523
\(711\) 14.3009i 0.536325i
\(712\) 39.5756 1.48316
\(713\) 5.95923i 0.223175i
\(714\) −2.46557 20.1078i −0.0922715 0.752514i
\(715\) 1.78419 2.14999i 0.0667249 0.0804050i
\(716\) −45.5319 −1.70161
\(717\) 10.3445 0.386322
\(718\) −30.0746 −1.12238
\(719\) 13.1791i 0.491496i −0.969334 0.245748i \(-0.920966\pi\)
0.969334 0.245748i \(-0.0790336\pi\)
\(720\) 0.950014i 0.0354049i
\(721\) 18.5376 2.27304i 0.690378 0.0846525i
\(722\) 46.5997i 1.73426i
\(723\) 8.03134i 0.298689i
\(724\) 31.4622i 1.16928i
\(725\) 9.40952i 0.349461i
\(726\) 4.54044 + 24.2052i 0.168511 + 0.898339i
\(727\) 32.0278i 1.18784i −0.804522 0.593922i \(-0.797579\pi\)
0.804522 0.593922i \(-0.202421\pi\)
\(728\) −5.01444 + 0.614859i −0.185848 + 0.0227882i
\(729\) −1.00000 −0.0370370
\(730\) 34.9844 1.29483
\(731\) 34.4589i 1.27451i
\(732\) 9.49816i 0.351062i
\(733\) 48.4494 1.78952 0.894759 0.446549i \(-0.147347\pi\)
0.894759 + 0.446549i \(0.147347\pi\)
\(734\) −43.1071 −1.59111
\(735\) 6.79263 1.69122i 0.250550 0.0623816i
\(736\) 39.7956i 1.46688i
\(737\) 29.1311 + 24.1747i 1.07306 + 0.890487i
\(738\) 23.1286i 0.851377i
\(739\) 29.2845i 1.07725i 0.842546 + 0.538624i \(0.181056\pi\)
−0.842546 + 0.538624i \(0.818944\pi\)
\(740\) 4.24770i 0.156149i
\(741\) 5.31533i 0.195263i
\(742\) −22.3930 + 2.74578i −0.822073 + 0.100801i
\(743\) 18.2116i 0.668118i −0.942552 0.334059i \(-0.891581\pi\)
0.942552 0.334059i \(-0.108419\pi\)
\(744\) 2.26079i 0.0828844i
\(745\) 12.3780 0.453495
\(746\) −65.9577 −2.41488
\(747\) 0.946456 0.0346290
\(748\) −26.2951 21.8213i −0.961444 0.797865i
\(749\) 27.8303 3.41249i 1.01690 0.124690i
\(750\) 2.23885i 0.0817513i
\(751\) −31.6089 −1.15343 −0.576713 0.816947i \(-0.695665\pi\)
−0.576713 + 0.816947i \(0.695665\pi\)
\(752\) 7.69690i 0.280677i
\(753\) 27.1281 0.988604
\(754\) 17.7462 0.646278
\(755\) 13.3219 0.484833
\(756\) −7.91096 + 0.970024i −0.287719 + 0.0352794i
\(757\) −31.2329 −1.13518 −0.567589 0.823312i \(-0.692124\pi\)
−0.567589 + 0.823312i \(0.692124\pi\)
\(758\) 71.8227i 2.60872i
\(759\) −12.6550 + 15.2495i −0.459347 + 0.553524i
\(760\) −14.3028 −0.518817
\(761\) −47.1414 −1.70887 −0.854437 0.519556i \(-0.826097\pi\)
−0.854437 + 0.519556i \(0.826097\pi\)
\(762\) 10.5726i 0.383005i
\(763\) −22.4959 + 2.75839i −0.814406 + 0.0998605i
\(764\) −36.8711 −1.33395
\(765\) 3.42003i 0.123651i
\(766\) −3.06989 −0.110920
\(767\) 9.05481i 0.326950i
\(768\) 9.37372i 0.338245i
\(769\) −3.27088 −0.117951 −0.0589756 0.998259i \(-0.518783\pi\)
−0.0589756 + 0.998259i \(0.518783\pi\)
\(770\) 10.6127 16.5327i 0.382456 0.595796i
\(771\) −23.0643 −0.830641
\(772\) 20.2083i 0.727314i
\(773\) 0.757839i 0.0272576i −0.999907 0.0136288i \(-0.995662\pi\)
0.999907 0.0136288i \(-0.00433831\pi\)
\(774\) −22.5578 −0.810823
\(775\) 0.997372i 0.0358266i
\(776\) −40.0965 −1.43938
\(777\) −3.70289 + 0.454040i −0.132841 + 0.0162886i
\(778\) 9.40068i 0.337031i
\(779\) −65.1843 −2.33547
\(780\) 2.53766 0.0908627
\(781\) 10.8297 + 8.98712i 0.387517 + 0.321585i
\(782\) 45.7497i 1.63600i
\(783\) 9.40952 0.336269
\(784\) 6.45309 1.60668i 0.230468 0.0573815i
\(785\) −8.99722 −0.321124
\(786\) 22.1359 0.789560
\(787\) −31.1745 −1.11125 −0.555626 0.831433i \(-0.687521\pi\)
−0.555626 + 0.831433i \(0.687521\pi\)
\(788\) 21.6912i 0.772719i
\(789\) −2.49039 −0.0886602
\(790\) 32.0176i 1.13913i
\(791\) −0.489158 3.98929i −0.0173924 0.141843i
\(792\) −4.80100 + 5.78531i −0.170596 + 0.205572i
\(793\) −2.65601 −0.0943178
\(794\) −9.23431 −0.327714
\(795\) 3.80872 0.135081
\(796\) 72.4452i 2.56775i
\(797\) 15.7552i 0.558079i 0.960280 + 0.279040i \(0.0900161\pi\)
−0.960280 + 0.279040i \(0.909984\pi\)
\(798\) 4.54889 + 37.0981i 0.161029 + 1.31326i
\(799\) 27.7087i 0.980263i
\(800\) 6.66043i 0.235482i
\(801\) 17.4593i 0.616892i
\(802\) 27.3412i 0.965453i
\(803\) −39.8817 33.0962i −1.40739 1.16794i
\(804\) 34.3837i 1.21262i
\(805\) 15.6907 1.92395i 0.553023 0.0678104i
\(806\) 1.88102 0.0662562
\(807\) −4.78537 −0.168453
\(808\) 1.59173i 0.0559970i
\(809\) 30.3467i 1.06693i 0.845821 + 0.533467i \(0.179111\pi\)
−0.845821 + 0.533467i \(0.820889\pi\)
\(810\) 2.23885 0.0786652
\(811\) 18.4970 0.649516 0.324758 0.945797i \(-0.394717\pi\)
0.324758 + 0.945797i \(0.394717\pi\)
\(812\) 74.4384 9.12746i 2.61228 0.320311i
\(813\) 12.9173i 0.453030i
\(814\) −6.68632 + 8.05717i −0.234355 + 0.282404i
\(815\) 1.25085i 0.0438154i
\(816\) 3.24908i 0.113740i
\(817\) 63.5755i 2.22423i
\(818\) 3.12832i 0.109379i
\(819\) −0.271252 2.21218i −0.00947832 0.0772998i
\(820\) 31.1204i 1.08677i
\(821\) 43.9533i 1.53398i −0.641659 0.766990i \(-0.721754\pi\)
0.641659 0.766990i \(-0.278246\pi\)
\(822\) −12.9214 −0.450685
\(823\) −37.6212 −1.31139 −0.655697 0.755024i \(-0.727625\pi\)
−0.655697 + 0.755024i \(0.727625\pi\)
\(824\) 16.0010 0.557422
\(825\) −2.11802 + 2.55226i −0.0737398 + 0.0888581i
\(826\) 7.74916 + 63.1978i 0.269628 + 2.19893i
\(827\) 43.1499i 1.50047i 0.661171 + 0.750235i \(0.270060\pi\)
−0.661171 + 0.750235i \(0.729940\pi\)
\(828\) −17.9992 −0.625516
\(829\) 5.19313i 0.180365i 0.995925 + 0.0901825i \(0.0287450\pi\)
−0.995925 + 0.0901825i \(0.971255\pi\)
\(830\) −2.11897 −0.0735507
\(831\) −5.81500 −0.201720
\(832\) 10.9609 0.380000
\(833\) 23.2310 5.78402i 0.804906 0.200404i
\(834\) −22.2568 −0.770689
\(835\) 16.5043i 0.571156i
\(836\) 48.5136 + 40.2595i 1.67788 + 1.39240i
\(837\) 0.997372 0.0344742
\(838\) 30.4554 1.05207
\(839\) 13.4423i 0.464080i 0.972706 + 0.232040i \(0.0745401\pi\)
−0.972706 + 0.232040i \(0.925460\pi\)
\(840\) 5.95266 0.729901i 0.205386 0.0251840i
\(841\) −59.5392 −2.05307
\(842\) 44.6835i 1.53989i
\(843\) 2.47572 0.0852683
\(844\) 19.6943i 0.677905i
\(845\) 12.2904i 0.422802i
\(846\) −18.1389 −0.623629
\(847\) −27.7387 + 8.80708i −0.953113 + 0.302615i
\(848\) 3.61833 0.124254
\(849\) 26.9187i 0.923847i
\(850\) 7.65694i 0.262631i
\(851\) −8.42491 −0.288802
\(852\) 12.7824i 0.437918i
\(853\) −4.82906 −0.165344 −0.0826719 0.996577i \(-0.526345\pi\)
−0.0826719 + 0.996577i \(0.526345\pi\)
\(854\) −18.5376 + 2.27303i −0.634342 + 0.0777815i
\(855\) 6.30984i 0.215792i
\(856\) 24.0222 0.821060
\(857\) 5.94945 0.203229 0.101615 0.994824i \(-0.467599\pi\)
0.101615 + 0.994824i \(0.467599\pi\)
\(858\) −4.81350 3.99454i −0.164330 0.136371i
\(859\) 19.8001i 0.675570i −0.941223 0.337785i \(-0.890322\pi\)
0.941223 0.337785i \(-0.109678\pi\)
\(860\) 30.3524 1.03501
\(861\) 27.1290 3.32649i 0.924553 0.113367i
\(862\) −26.1892 −0.892007
\(863\) 9.47598 0.322566 0.161283 0.986908i \(-0.448437\pi\)
0.161283 + 0.986908i \(0.448437\pi\)
\(864\) 6.66043 0.226592
\(865\) 19.4351i 0.660813i
\(866\) −50.6681 −1.72177
\(867\) 5.30340i 0.180113i
\(868\) 7.89017 0.967474i 0.267810 0.0328382i
\(869\) −30.2895 + 36.4995i −1.02750 + 1.23816i
\(870\) −21.0665 −0.714222
\(871\) −9.61488 −0.325788
\(872\) −19.4177 −0.657565
\(873\) 17.6891i 0.598684i
\(874\) 84.4066i 2.85510i
\(875\) 2.62608 0.322004i 0.0887778 0.0108857i
\(876\) 47.0728i 1.59044i
\(877\) 35.3287i 1.19297i 0.802626 + 0.596483i \(0.203436\pi\)
−0.802626 + 0.596483i \(0.796564\pi\)
\(878\) 18.0273i 0.608391i
\(879\) 5.92944i 0.199995i
\(880\) −2.01214 + 2.42468i −0.0678294 + 0.0817359i
\(881\) 26.0042i 0.876105i 0.898949 + 0.438052i \(0.144332\pi\)
−0.898949 + 0.438052i \(0.855668\pi\)
\(882\) −3.78639 15.2077i −0.127494 0.512069i
\(883\) −9.50807 −0.319972 −0.159986 0.987119i \(-0.551145\pi\)
−0.159986 + 0.987119i \(0.551145\pi\)
\(884\) 8.67886 0.291902
\(885\) 10.7490i 0.361323i
\(886\) 40.3548i 1.35575i
\(887\) −15.5638 −0.522582 −0.261291 0.965260i \(-0.584148\pi\)
−0.261291 + 0.965260i \(0.584148\pi\)
\(888\) −3.19621 −0.107258
\(889\) 12.4012 1.52061i 0.415925 0.0509997i
\(890\) 39.0887i 1.31026i
\(891\) −2.55226 2.11802i −0.0855038 0.0709562i
\(892\) 77.5826i 2.59766i
\(893\) 51.1216i 1.71072i
\(894\) 27.7125i 0.926846i
\(895\) 15.1145i 0.505223i
\(896\) 41.5193 5.09101i 1.38706 0.170079i
\(897\) 5.03320i 0.168054i
\(898\) 73.8795i 2.46539i
\(899\) −9.38479 −0.313000
\(900\) −3.01246 −0.100415
\(901\) 13.0259 0.433956
\(902\) 48.9868 59.0302i 1.63108 1.96549i
\(903\) −3.24439 26.4594i −0.107967 0.880514i
\(904\) 3.44342i 0.114526i
\(905\) 10.4440 0.347171
\(906\) 29.8257i 0.990894i
\(907\) 4.27141 0.141830 0.0709149 0.997482i \(-0.477408\pi\)
0.0709149 + 0.997482i \(0.477408\pi\)
\(908\) 23.5940 0.782995
\(909\) −0.702211 −0.0232909
\(910\) 0.607294 + 4.95274i 0.0201316 + 0.164182i
\(911\) −41.7023 −1.38166 −0.690829 0.723018i \(-0.742754\pi\)
−0.690829 + 0.723018i \(0.742754\pi\)
\(912\) 5.99444i 0.198496i
\(913\) 2.41560 + 2.00461i 0.0799446 + 0.0663429i
\(914\) 3.92305 0.129763
\(915\) 3.15296 0.104234
\(916\) 38.7581i 1.28060i
\(917\) 3.18370 + 25.9645i 0.105135 + 0.857423i
\(918\) 7.65694 0.252717
\(919\) 28.0644i 0.925758i 0.886421 + 0.462879i \(0.153184\pi\)
−0.886421 + 0.462879i \(0.846816\pi\)
\(920\) 13.5436 0.446520
\(921\) 7.12996i 0.234940i
\(922\) 66.4597i 2.18873i
\(923\) −3.57440 −0.117653
\(924\) −22.2453 14.2798i −0.731818 0.469771i
\(925\) −1.41004 −0.0463620
\(926\) 42.7304i 1.40421i
\(927\) 7.05904i 0.231849i
\(928\) −62.6714 −2.05729
\(929\) 2.91014i 0.0954785i −0.998860 0.0477392i \(-0.984798\pi\)
0.998860 0.0477392i \(-0.0152017\pi\)
\(930\) −2.23297 −0.0732219
\(931\) −42.8604 + 10.6713i −1.40469 + 0.349739i
\(932\) 51.7040i 1.69362i
\(933\) −34.4437 −1.12764
\(934\) 16.1102 0.527141
\(935\) −7.24368 + 8.72879i −0.236894 + 0.285462i
\(936\) 1.90948i 0.0624131i
\(937\) −25.5190 −0.833669 −0.416835 0.908982i \(-0.636861\pi\)
−0.416835 + 0.908982i \(0.636861\pi\)
\(938\) −67.1067 + 8.22847i −2.19111 + 0.268669i
\(939\) −6.36649 −0.207763
\(940\) 24.4066 0.796055
\(941\) 28.3781 0.925099 0.462550 0.886593i \(-0.346935\pi\)
0.462550 + 0.886593i \(0.346935\pi\)
\(942\) 20.1434i 0.656309i
\(943\) 61.7245 2.01003
\(944\) 10.2117i 0.332362i
\(945\) 0.322004 + 2.62608i 0.0104748 + 0.0854265i
\(946\) −57.5733 47.7778i −1.87187 1.55339i
\(947\) −37.1288 −1.20652 −0.603262 0.797543i \(-0.706133\pi\)
−0.603262 + 0.797543i \(0.706133\pi\)
\(948\) −43.0808 −1.39920
\(949\) 13.1632 0.427295
\(950\) 14.1268i 0.458334i
\(951\) 16.9314i 0.549038i
\(952\) 20.3583 2.49628i 0.659815 0.0809050i
\(953\) 4.50804i 0.146030i 0.997331 + 0.0730148i \(0.0232620\pi\)
−0.997331 + 0.0730148i \(0.976738\pi\)
\(954\) 8.52715i 0.276077i
\(955\) 12.2395i 0.396062i
\(956\) 31.1623i 1.00786i
\(957\) 24.0155 + 19.9295i 0.776311 + 0.644230i
\(958\) 42.7954i 1.38266i
\(959\) −1.85843 15.1563i −0.0600117 0.489422i
\(960\) −13.0117 −0.419950
\(961\) 30.0052 0.967911
\(962\) 2.65932i 0.0857398i
\(963\) 10.5977i 0.341505i
\(964\) −24.1941 −0.779239
\(965\) −6.70826 −0.215946
\(966\) −4.30744 35.1291i −0.138590 1.13026i
\(967\) 2.23412i 0.0718443i 0.999355 + 0.0359222i \(0.0114368\pi\)
−0.999355 + 0.0359222i \(0.988563\pi\)
\(968\) −24.5067 + 4.59700i −0.787677 + 0.147753i
\(969\) 21.5798i 0.693244i
\(970\) 39.6032i 1.27158i
\(971\) 38.0083i 1.21974i −0.792500 0.609872i \(-0.791221\pi\)
0.792500 0.609872i \(-0.208779\pi\)
\(972\) 3.01246i 0.0966246i
\(973\) −3.20109 26.1063i −0.102622 0.836930i
\(974\) 32.9431i 1.05556i
\(975\) 0.842387i 0.0269780i
\(976\) 2.99536 0.0958790
\(977\) −6.02399 −0.192725 −0.0963623 0.995346i \(-0.530721\pi\)
−0.0963623 + 0.995346i \(0.530721\pi\)
\(978\) −2.80047 −0.0895492
\(979\) −36.9790 + 44.5605i −1.18185 + 1.42416i
\(980\) 5.09473 + 20.4625i 0.162745 + 0.653651i
\(981\) 8.56633i 0.273502i
\(982\) −43.1119 −1.37576
\(983\) 11.4819i 0.366214i 0.983093 + 0.183107i \(0.0586155\pi\)
−0.983093 + 0.183107i \(0.941384\pi\)
\(984\) 23.4168 0.746500
\(985\) −7.20052 −0.229427
\(986\) −72.0482 −2.29448
\(987\) −2.60884 21.2762i −0.0830403 0.677230i
\(988\) −16.0122 −0.509416
\(989\) 60.2011i 1.91428i
\(990\) 5.71412 + 4.74192i 0.181607 + 0.150708i
\(991\) 42.8247 1.36037 0.680185 0.733040i \(-0.261899\pi\)
0.680185 + 0.733040i \(0.261899\pi\)
\(992\) −6.64292 −0.210913
\(993\) 22.2475i 0.706004i
\(994\) −24.9474 + 3.05899i −0.791284 + 0.0970254i
\(995\) 24.0485 0.762390
\(996\) 2.85116i 0.0903424i
\(997\) −19.3516 −0.612873 −0.306436 0.951891i \(-0.599137\pi\)
−0.306436 + 0.951891i \(0.599137\pi\)
\(998\) 24.1099i 0.763185i
\(999\) 1.41004i 0.0446118i
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 1155.2.i.d.76.17 yes 32
7.6 odd 2 inner 1155.2.i.d.76.15 32
11.10 odd 2 inner 1155.2.i.d.76.16 yes 32
77.76 even 2 inner 1155.2.i.d.76.18 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1155.2.i.d.76.15 32 7.6 odd 2 inner
1155.2.i.d.76.16 yes 32 11.10 odd 2 inner
1155.2.i.d.76.17 yes 32 1.1 even 1 trivial
1155.2.i.d.76.18 yes 32 77.76 even 2 inner