Properties

Label 552.2.n.b.91.1
Level $552$
Weight $2$
Character 552.91
Analytic conductor $4.408$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [552,2,Mod(91,552)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(552, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("552.91");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 552.n (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: \(4.40774219157\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 91.1
Character \(\chi\) \(=\) 552.91
Dual form 552.2.n.b.91.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.38507 - 0.285614i) q^{2} -1.00000 q^{3} +(1.83685 + 0.791193i) q^{4} -2.03317 q^{5} +(1.38507 + 0.285614i) q^{6} +1.21988 q^{7} +(-2.31819 - 1.62049i) q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(-1.38507 - 0.285614i) q^{2} -1.00000 q^{3} +(1.83685 + 0.791193i) q^{4} -2.03317 q^{5} +(1.38507 + 0.285614i) q^{6} +1.21988 q^{7} +(-2.31819 - 1.62049i) q^{8} +1.00000 q^{9} +(2.81608 + 0.580701i) q^{10} +1.88814i q^{11} +(-1.83685 - 0.791193i) q^{12} -3.19024i q^{13} +(-1.68962 - 0.348415i) q^{14} +2.03317 q^{15} +(2.74803 + 2.90660i) q^{16} +5.91574i q^{17} +(-1.38507 - 0.285614i) q^{18} -6.08344i q^{19} +(-3.73462 - 1.60863i) q^{20} -1.21988 q^{21} +(0.539280 - 2.61521i) q^{22} +(-3.96642 + 2.69583i) q^{23} +(2.31819 + 1.62049i) q^{24} -0.866240 q^{25} +(-0.911179 + 4.41871i) q^{26} -1.00000 q^{27} +(2.24073 + 0.965159i) q^{28} -9.30575i q^{29} +(-2.81608 - 0.580701i) q^{30} +3.55669i q^{31} +(-2.97605 - 4.81073i) q^{32} -1.88814i q^{33} +(1.68962 - 8.19372i) q^{34} -2.48021 q^{35} +(1.83685 + 0.791193i) q^{36} -11.1137 q^{37} +(-1.73752 + 8.42601i) q^{38} +3.19024i q^{39} +(4.71327 + 3.29472i) q^{40} -2.52410 q^{41} +(1.68962 + 0.348415i) q^{42} +11.6630i q^{43} +(-1.49388 + 3.46823i) q^{44} -2.03317 q^{45} +(6.26374 - 2.60106i) q^{46} -11.2078i q^{47} +(-2.74803 - 2.90660i) q^{48} -5.51190 q^{49} +(1.19980 + 0.247411i) q^{50} -5.91574i q^{51} +(2.52410 - 5.85999i) q^{52} -11.0682 q^{53} +(1.38507 + 0.285614i) q^{54} -3.83890i q^{55} +(-2.82791 - 1.97680i) q^{56} +6.08344i q^{57} +(-2.65786 + 12.8891i) q^{58} +0.657857 q^{59} +(3.73462 + 1.60863i) q^{60} -10.3789 q^{61} +(1.01584 - 4.92627i) q^{62} +1.21988 q^{63} +(2.74803 + 7.51321i) q^{64} +6.48629i q^{65} +(-0.539280 + 2.61521i) q^{66} +2.45869i q^{67} +(-4.68049 + 10.8663i) q^{68} +(3.96642 - 2.69583i) q^{69} +(3.43528 + 0.708385i) q^{70} -4.84611i q^{71} +(-2.31819 - 1.62049i) q^{72} -7.87149 q^{73} +(15.3933 + 3.17425i) q^{74} +0.866240 q^{75} +(4.81318 - 11.1744i) q^{76} +2.30330i q^{77} +(0.911179 - 4.41871i) q^{78} +4.23131 q^{79} +(-5.58719 - 5.90960i) q^{80} +1.00000 q^{81} +(3.49606 + 0.720918i) q^{82} +7.58314i q^{83} +(-2.24073 - 0.965159i) q^{84} -12.0277i q^{85} +(3.33113 - 16.1541i) q^{86} +9.30575i q^{87} +(3.05971 - 4.37708i) q^{88} -3.85989i q^{89} +(2.81608 + 0.580701i) q^{90} -3.89171i q^{91} +(-9.41864 + 1.81364i) q^{92} -3.55669i q^{93} +(-3.20111 + 15.5236i) q^{94} +12.3686i q^{95} +(2.97605 + 4.81073i) q^{96} -3.03678i q^{97} +(7.63437 + 1.57428i) q^{98} +1.88814i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 24 q^{3} + 4 q^{4} + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 24 q^{3} + 4 q^{4} + 24 q^{9} - 4 q^{12} + 4 q^{16} + 24 q^{25} - 24 q^{27} + 4 q^{36} - 44 q^{46} - 4 q^{48} + 56 q^{49} - 40 q^{50} - 48 q^{58} - 40 q^{62} + 4 q^{64} + 32 q^{73} - 24 q^{75} + 24 q^{81} - 40 q^{82} + 40 q^{92} - 48 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(185\) \(277\) \(415\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.38507 0.285614i −0.979394 0.201960i
\(3\) −1.00000 −0.577350
\(4\) 1.83685 + 0.791193i 0.918424 + 0.395596i
\(5\) −2.03317 −0.909259 −0.454630 0.890681i \(-0.650228\pi\)
−0.454630 + 0.890681i \(0.650228\pi\)
\(6\) 1.38507 + 0.285614i 0.565453 + 0.116602i
\(7\) 1.21988 0.461071 0.230535 0.973064i \(-0.425952\pi\)
0.230535 + 0.973064i \(0.425952\pi\)
\(8\) −2.31819 1.62049i −0.819605 0.572930i
\(9\) 1.00000 0.333333
\(10\) 2.81608 + 0.580701i 0.890523 + 0.183634i
\(11\) 1.88814i 0.569296i 0.958632 + 0.284648i \(0.0918768\pi\)
−0.958632 + 0.284648i \(0.908123\pi\)
\(12\) −1.83685 0.791193i −0.530253 0.228398i
\(13\) 3.19024i 0.884814i −0.896814 0.442407i \(-0.854125\pi\)
0.896814 0.442407i \(-0.145875\pi\)
\(14\) −1.68962 0.348415i −0.451570 0.0931178i
\(15\) 2.03317 0.524961
\(16\) 2.74803 + 2.90660i 0.687007 + 0.726651i
\(17\) 5.91574i 1.43478i 0.696673 + 0.717389i \(0.254663\pi\)
−0.696673 + 0.717389i \(0.745337\pi\)
\(18\) −1.38507 0.285614i −0.326465 0.0673199i
\(19\) 6.08344i 1.39564i −0.716274 0.697819i \(-0.754154\pi\)
0.716274 0.697819i \(-0.245846\pi\)
\(20\) −3.73462 1.60863i −0.835086 0.359700i
\(21\) −1.21988 −0.266199
\(22\) 0.539280 2.61521i 0.114975 0.557565i
\(23\) −3.96642 + 2.69583i −0.827056 + 0.562120i
\(24\) 2.31819 + 1.62049i 0.473199 + 0.330781i
\(25\) −0.866240 −0.173248
\(26\) −0.911179 + 4.41871i −0.178697 + 0.866581i
\(27\) −1.00000 −0.192450
\(28\) 2.24073 + 0.965159i 0.423459 + 0.182398i
\(29\) 9.30575i 1.72804i −0.503462 0.864018i \(-0.667941\pi\)
0.503462 0.864018i \(-0.332059\pi\)
\(30\) −2.81608 0.580701i −0.514144 0.106021i
\(31\) 3.55669i 0.638800i 0.947620 + 0.319400i \(0.103481\pi\)
−0.947620 + 0.319400i \(0.896519\pi\)
\(32\) −2.97605 4.81073i −0.526096 0.850425i
\(33\) 1.88814i 0.328683i
\(34\) 1.68962 8.19372i 0.289767 1.40521i
\(35\) −2.48021 −0.419233
\(36\) 1.83685 + 0.791193i 0.306141 + 0.131865i
\(37\) −11.1137 −1.82709 −0.913544 0.406739i \(-0.866666\pi\)
−0.913544 + 0.406739i \(0.866666\pi\)
\(38\) −1.73752 + 8.42601i −0.281863 + 1.36688i
\(39\) 3.19024i 0.510848i
\(40\) 4.71327 + 3.29472i 0.745233 + 0.520941i
\(41\) −2.52410 −0.394198 −0.197099 0.980384i \(-0.563152\pi\)
−0.197099 + 0.980384i \(0.563152\pi\)
\(42\) 1.68962 + 0.348415i 0.260714 + 0.0537616i
\(43\) 11.6630i 1.77859i 0.457330 + 0.889297i \(0.348806\pi\)
−0.457330 + 0.889297i \(0.651194\pi\)
\(44\) −1.49388 + 3.46823i −0.225212 + 0.522856i
\(45\) −2.03317 −0.303086
\(46\) 6.26374 2.60106i 0.923539 0.383505i
\(47\) 11.2078i 1.63483i −0.576052 0.817413i \(-0.695408\pi\)
0.576052 0.817413i \(-0.304592\pi\)
\(48\) −2.74803 2.90660i −0.396644 0.419532i
\(49\) −5.51190 −0.787414
\(50\) 1.19980 + 0.247411i 0.169678 + 0.0349891i
\(51\) 5.91574i 0.828369i
\(52\) 2.52410 5.85999i 0.350029 0.812635i
\(53\) −11.0682 −1.52034 −0.760169 0.649725i \(-0.774884\pi\)
−0.760169 + 0.649725i \(0.774884\pi\)
\(54\) 1.38507 + 0.285614i 0.188484 + 0.0388672i
\(55\) 3.83890i 0.517638i
\(56\) −2.82791 1.97680i −0.377896 0.264161i
\(57\) 6.08344i 0.805772i
\(58\) −2.65786 + 12.8891i −0.348994 + 1.69243i
\(59\) 0.657857 0.0856456 0.0428228 0.999083i \(-0.486365\pi\)
0.0428228 + 0.999083i \(0.486365\pi\)
\(60\) 3.73462 + 1.60863i 0.482137 + 0.207673i
\(61\) −10.3789 −1.32888 −0.664441 0.747341i \(-0.731330\pi\)
−0.664441 + 0.747341i \(0.731330\pi\)
\(62\) 1.01584 4.92627i 0.129012 0.625637i
\(63\) 1.21988 0.153690
\(64\) 2.74803 + 7.51321i 0.343503 + 0.939151i
\(65\) 6.48629i 0.804525i
\(66\) −0.539280 + 2.61521i −0.0663808 + 0.321910i
\(67\) 2.45869i 0.300377i 0.988657 + 0.150189i \(0.0479881\pi\)
−0.988657 + 0.150189i \(0.952012\pi\)
\(68\) −4.68049 + 10.8663i −0.567593 + 1.31773i
\(69\) 3.96642 2.69583i 0.477501 0.324540i
\(70\) 3.43528 + 0.708385i 0.410594 + 0.0846682i
\(71\) 4.84611i 0.575127i −0.957762 0.287564i \(-0.907155\pi\)
0.957762 0.287564i \(-0.0928453\pi\)
\(72\) −2.31819 1.62049i −0.273202 0.190977i
\(73\) −7.87149 −0.921288 −0.460644 0.887585i \(-0.652382\pi\)
−0.460644 + 0.887585i \(0.652382\pi\)
\(74\) 15.3933 + 3.17425i 1.78944 + 0.368999i
\(75\) 0.866240 0.100025
\(76\) 4.81318 11.1744i 0.552109 1.28179i
\(77\) 2.30330i 0.262486i
\(78\) 0.911179 4.41871i 0.103171 0.500321i
\(79\) 4.23131 0.476060 0.238030 0.971258i \(-0.423498\pi\)
0.238030 + 0.971258i \(0.423498\pi\)
\(80\) −5.58719 5.90960i −0.624667 0.660714i
\(81\) 1.00000 0.111111
\(82\) 3.49606 + 0.720918i 0.386075 + 0.0796121i
\(83\) 7.58314i 0.832358i 0.909283 + 0.416179i \(0.136631\pi\)
−0.909283 + 0.416179i \(0.863369\pi\)
\(84\) −2.24073 0.965159i −0.244484 0.105307i
\(85\) 12.0277i 1.30458i
\(86\) 3.33113 16.1541i 0.359205 1.74194i
\(87\) 9.30575i 0.997681i
\(88\) 3.05971 4.37708i 0.326167 0.466598i
\(89\) 3.85989i 0.409147i −0.978851 0.204574i \(-0.934419\pi\)
0.978851 0.204574i \(-0.0655808\pi\)
\(90\) 2.81608 + 0.580701i 0.296841 + 0.0612113i
\(91\) 3.89171i 0.407962i
\(92\) −9.41864 + 1.81364i −0.981961 + 0.189085i
\(93\) 3.55669i 0.368811i
\(94\) −3.20111 + 15.5236i −0.330169 + 1.60114i
\(95\) 12.3686i 1.26900i
\(96\) 2.97605 + 4.81073i 0.303742 + 0.490993i
\(97\) 3.03678i 0.308338i −0.988044 0.154169i \(-0.950730\pi\)
0.988044 0.154169i \(-0.0492701\pi\)
\(98\) 7.63437 + 1.57428i 0.771188 + 0.159026i
\(99\) 1.88814i 0.189765i
\(100\) −1.59115 0.685363i −0.159115 0.0685363i
\(101\) 7.00245i 0.696770i 0.937352 + 0.348385i \(0.113270\pi\)
−0.937352 + 0.348385i \(0.886730\pi\)
\(102\) −1.68962 + 8.19372i −0.167297 + 0.811299i
\(103\) 3.05695 0.301210 0.150605 0.988594i \(-0.451878\pi\)
0.150605 + 0.988594i \(0.451878\pi\)
\(104\) −5.16975 + 7.39559i −0.506936 + 0.725198i
\(105\) 2.48021 0.242044
\(106\) 15.3303 + 3.16124i 1.48901 + 0.307047i
\(107\) 4.21095i 0.407088i −0.979066 0.203544i \(-0.934754\pi\)
0.979066 0.203544i \(-0.0652459\pi\)
\(108\) −1.83685 0.791193i −0.176751 0.0761326i
\(109\) −3.18091 −0.304676 −0.152338 0.988328i \(-0.548680\pi\)
−0.152338 + 0.988328i \(0.548680\pi\)
\(110\) −1.09645 + 5.31716i −0.104542 + 0.506971i
\(111\) 11.1137 1.05487
\(112\) 3.35226 + 3.54570i 0.316759 + 0.335037i
\(113\) 18.9194i 1.77979i −0.456169 0.889893i \(-0.650779\pi\)
0.456169 0.889893i \(-0.349221\pi\)
\(114\) 1.73752 8.42601i 0.162734 0.789168i
\(115\) 8.06438 5.48108i 0.752008 0.511113i
\(116\) 7.36265 17.0933i 0.683604 1.58707i
\(117\) 3.19024i 0.294938i
\(118\) −0.911179 0.187893i −0.0838808 0.0172970i
\(119\) 7.21648i 0.661534i
\(120\) −4.71327 3.29472i −0.430260 0.300766i
\(121\) 7.43492 0.675902
\(122\) 14.3755 + 2.96436i 1.30150 + 0.268381i
\(123\) 2.52410 0.227590
\(124\) −2.81403 + 6.53310i −0.252707 + 0.586690i
\(125\) 11.9270 1.06679
\(126\) −1.68962 0.348415i −0.150523 0.0310393i
\(127\) 7.44653i 0.660773i 0.943846 + 0.330386i \(0.107179\pi\)
−0.943846 + 0.330386i \(0.892821\pi\)
\(128\) −1.66034 11.1912i −0.146754 0.989173i
\(129\) 11.6630i 1.02687i
\(130\) 1.85258 8.98398i 0.162482 0.787947i
\(131\) 1.82236 0.159220 0.0796101 0.996826i \(-0.474632\pi\)
0.0796101 + 0.996826i \(0.474632\pi\)
\(132\) 1.49388 3.46823i 0.130026 0.301871i
\(133\) 7.42106i 0.643488i
\(134\) 0.702238 3.40547i 0.0606641 0.294187i
\(135\) 2.03317 0.174987
\(136\) 9.58639 13.7138i 0.822026 1.17595i
\(137\) 0.220739i 0.0188590i −0.999956 0.00942952i \(-0.996998\pi\)
0.999956 0.00942952i \(-0.00300155\pi\)
\(138\) −6.26374 + 2.60106i −0.533205 + 0.221417i
\(139\) 21.9828 1.86456 0.932279 0.361741i \(-0.117817\pi\)
0.932279 + 0.361741i \(0.117817\pi\)
\(140\) −4.55578 1.96233i −0.385034 0.165847i
\(141\) 11.2078i 0.943867i
\(142\) −1.38412 + 6.71221i −0.116153 + 0.563276i
\(143\) 6.02363 0.503721
\(144\) 2.74803 + 2.90660i 0.229002 + 0.242217i
\(145\) 18.9201i 1.57123i
\(146\) 10.9026 + 2.24821i 0.902304 + 0.186063i
\(147\) 5.51190 0.454614
\(148\) −20.4143 8.79312i −1.67804 0.722790i
\(149\) 14.3997 1.17967 0.589835 0.807524i \(-0.299193\pi\)
0.589835 + 0.807524i \(0.299193\pi\)
\(150\) −1.19980 0.247411i −0.0979636 0.0202010i
\(151\) 4.90495i 0.399160i −0.979882 0.199580i \(-0.936042\pi\)
0.979882 0.199580i \(-0.0639577\pi\)
\(152\) −9.85816 + 14.1026i −0.799602 + 1.14387i
\(153\) 5.91574i 0.478259i
\(154\) 0.657857 3.19024i 0.0530116 0.257077i
\(155\) 7.23133i 0.580835i
\(156\) −2.52410 + 5.85999i −0.202089 + 0.469175i
\(157\) 5.78202 0.461455 0.230728 0.973018i \(-0.425889\pi\)
0.230728 + 0.973018i \(0.425889\pi\)
\(158\) −5.86067 1.20852i −0.466250 0.0961450i
\(159\) 11.0682 0.877768
\(160\) 6.05080 + 9.78101i 0.478358 + 0.773257i
\(161\) −4.83855 + 3.28859i −0.381331 + 0.259177i
\(162\) −1.38507 0.285614i −0.108822 0.0224400i
\(163\) −11.2880 −0.884146 −0.442073 0.896979i \(-0.645757\pi\)
−0.442073 + 0.896979i \(0.645757\pi\)
\(164\) −4.63638 1.99705i −0.362041 0.155943i
\(165\) 3.83890i 0.298858i
\(166\) 2.16585 10.5032i 0.168103 0.815206i
\(167\) 0.358139i 0.0277136i −0.999904 0.0138568i \(-0.995589\pi\)
0.999904 0.0138568i \(-0.00441090\pi\)
\(168\) 2.82791 + 1.97680i 0.218178 + 0.152513i
\(169\) 2.82236 0.217104
\(170\) −3.43528 + 16.6592i −0.263474 + 1.27770i
\(171\) 6.08344i 0.465213i
\(172\) −9.22770 + 21.4232i −0.703605 + 1.63350i
\(173\) 10.1430i 0.771157i 0.922675 + 0.385578i \(0.125998\pi\)
−0.922675 + 0.385578i \(0.874002\pi\)
\(174\) 2.65786 12.8891i 0.201492 0.977123i
\(175\) −1.05671 −0.0798796
\(176\) −5.48808 + 5.18867i −0.413680 + 0.391110i
\(177\) −0.657857 −0.0494475
\(178\) −1.10244 + 5.34622i −0.0826313 + 0.400716i
\(179\) −11.8262 −0.883931 −0.441966 0.897032i \(-0.645719\pi\)
−0.441966 + 0.897032i \(0.645719\pi\)
\(180\) −3.73462 1.60863i −0.278362 0.119900i
\(181\) −20.2209 −1.50301 −0.751506 0.659727i \(-0.770672\pi\)
−0.751506 + 0.659727i \(0.770672\pi\)
\(182\) −1.11153 + 5.39029i −0.0823919 + 0.399555i
\(183\) 10.3789 0.767230
\(184\) 13.5635 + 0.178080i 0.999914 + 0.0131282i
\(185\) 22.5961 1.66130
\(186\) −1.01584 + 4.92627i −0.0744851 + 0.361212i
\(187\) −11.1698 −0.816813
\(188\) 8.86753 20.5870i 0.646731 1.50146i
\(189\) −1.21988 −0.0887331
\(190\) 3.53266 17.1315i 0.256286 1.24285i
\(191\) −4.20470 −0.304241 −0.152121 0.988362i \(-0.548610\pi\)
−0.152121 + 0.988362i \(0.548610\pi\)
\(192\) −2.74803 7.51321i −0.198322 0.542219i
\(193\) −6.30116 −0.453567 −0.226784 0.973945i \(-0.572821\pi\)
−0.226784 + 0.973945i \(0.572821\pi\)
\(194\) −0.867348 + 4.20616i −0.0622719 + 0.301985i
\(195\) 6.48629i 0.464493i
\(196\) −10.1245 4.36097i −0.723180 0.311498i
\(197\) 11.6091i 0.827111i 0.910479 + 0.413556i \(0.135713\pi\)
−0.910479 + 0.413556i \(0.864287\pi\)
\(198\) 0.539280 2.61521i 0.0383250 0.185855i
\(199\) 8.61769 0.610892 0.305446 0.952209i \(-0.401194\pi\)
0.305446 + 0.952209i \(0.401194\pi\)
\(200\) 2.00811 + 1.40373i 0.141995 + 0.0992589i
\(201\) 2.45869i 0.173423i
\(202\) 2.00000 9.69890i 0.140720 0.682412i
\(203\) 11.3519i 0.796746i
\(204\) 4.68049 10.8663i 0.327700 0.760794i
\(205\) 5.13190 0.358428
\(206\) −4.23410 0.873109i −0.295004 0.0608324i
\(207\) −3.96642 + 2.69583i −0.275685 + 0.187373i
\(208\) 9.27277 8.76687i 0.642951 0.607873i
\(209\) 11.4864 0.794531
\(210\) −3.43528 0.708385i −0.237057 0.0488832i
\(211\) −19.6552 −1.35312 −0.676561 0.736387i \(-0.736530\pi\)
−0.676561 + 0.736387i \(0.736530\pi\)
\(212\) −20.3307 8.75710i −1.39632 0.601440i
\(213\) 4.84611i 0.332050i
\(214\) −1.20271 + 5.83246i −0.0822153 + 0.398699i
\(215\) 23.7128i 1.61720i
\(216\) 2.31819 + 1.62049i 0.157733 + 0.110260i
\(217\) 4.33873i 0.294532i
\(218\) 4.40579 + 0.908513i 0.298398 + 0.0615323i
\(219\) 7.87149 0.531906
\(220\) 3.03731 7.05149i 0.204776 0.475411i
\(221\) 18.8726 1.26951
\(222\) −15.3933 3.17425i −1.03313 0.213041i
\(223\) 14.8511i 0.994501i 0.867607 + 0.497250i \(0.165657\pi\)
−0.867607 + 0.497250i \(0.834343\pi\)
\(224\) −3.63042 5.86851i −0.242567 0.392106i
\(225\) −0.866240 −0.0577493
\(226\) −5.40365 + 26.2047i −0.359445 + 1.74311i
\(227\) 17.2433i 1.14448i −0.820086 0.572240i \(-0.806074\pi\)
0.820086 0.572240i \(-0.193926\pi\)
\(228\) −4.81318 + 11.1744i −0.318760 + 0.740041i
\(229\) −2.59033 −0.171174 −0.0855869 0.996331i \(-0.527277\pi\)
−0.0855869 + 0.996331i \(0.527277\pi\)
\(230\) −12.7352 + 5.28838i −0.839736 + 0.348705i
\(231\) 2.30330i 0.151546i
\(232\) −15.0799 + 21.5725i −0.990042 + 1.41631i
\(233\) −22.1288 −1.44970 −0.724852 0.688905i \(-0.758092\pi\)
−0.724852 + 0.688905i \(0.758092\pi\)
\(234\) −0.911179 + 4.41871i −0.0595656 + 0.288860i
\(235\) 22.7873i 1.48648i
\(236\) 1.20838 + 0.520491i 0.0786590 + 0.0338811i
\(237\) −4.23131 −0.274853
\(238\) 2.06113 9.99535i 0.133603 0.647902i
\(239\) 20.5586i 1.32983i 0.746920 + 0.664914i \(0.231532\pi\)
−0.746920 + 0.664914i \(0.768468\pi\)
\(240\) 5.58719 + 5.90960i 0.360652 + 0.381463i
\(241\) 13.5001i 0.869619i −0.900522 0.434810i \(-0.856816\pi\)
0.900522 0.434810i \(-0.143184\pi\)
\(242\) −10.2979 2.12352i −0.661974 0.136505i
\(243\) −1.00000 −0.0641500
\(244\) −19.0645 8.21171i −1.22048 0.525701i
\(245\) 11.2066 0.715963
\(246\) −3.49606 0.720918i −0.222900 0.0459641i
\(247\) −19.4077 −1.23488
\(248\) 5.76358 8.24509i 0.365987 0.523563i
\(249\) 7.58314i 0.480562i
\(250\) −16.5198 3.40653i −1.04480 0.215448i
\(251\) 25.0872i 1.58349i 0.610853 + 0.791744i \(0.290827\pi\)
−0.610853 + 0.791744i \(0.709173\pi\)
\(252\) 2.24073 + 0.965159i 0.141153 + 0.0607993i
\(253\) −5.09012 7.48916i −0.320013 0.470840i
\(254\) 2.12684 10.3140i 0.133450 0.647157i
\(255\) 12.0277i 0.753202i
\(256\) −0.896688 + 15.9749i −0.0560430 + 0.998428i
\(257\) −12.4382 −0.775875 −0.387937 0.921686i \(-0.626812\pi\)
−0.387937 + 0.921686i \(0.626812\pi\)
\(258\) −3.33113 + 16.1541i −0.207387 + 1.00571i
\(259\) −13.5574 −0.842417
\(260\) −5.13190 + 11.9143i −0.318267 + 0.738895i
\(261\) 9.30575i 0.576012i
\(262\) −2.52410 0.520491i −0.155939 0.0321561i
\(263\) −10.3726 −0.639602 −0.319801 0.947485i \(-0.603616\pi\)
−0.319801 + 0.947485i \(0.603616\pi\)
\(264\) −3.05971 + 4.37708i −0.188312 + 0.269390i
\(265\) 22.5035 1.38238
\(266\) −2.11956 + 10.2787i −0.129959 + 0.630228i
\(267\) 3.85989i 0.236221i
\(268\) −1.94530 + 4.51625i −0.118828 + 0.275874i
\(269\) 17.9895i 1.09684i 0.836202 + 0.548421i \(0.184771\pi\)
−0.836202 + 0.548421i \(0.815229\pi\)
\(270\) −2.81608 0.580701i −0.171381 0.0353403i
\(271\) 7.39559i 0.449250i −0.974445 0.224625i \(-0.927884\pi\)
0.974445 0.224625i \(-0.0721158\pi\)
\(272\) −17.1947 + 16.2566i −1.04258 + 0.985702i
\(273\) 3.89171i 0.235537i
\(274\) −0.0630463 + 0.305740i −0.00380877 + 0.0184704i
\(275\) 1.63558i 0.0986294i
\(276\) 9.41864 1.81364i 0.566935 0.109168i
\(277\) 30.0768i 1.80714i −0.428441 0.903570i \(-0.640937\pi\)
0.428441 0.903570i \(-0.359063\pi\)
\(278\) −30.4478 6.27861i −1.82614 0.376566i
\(279\) 3.55669i 0.212933i
\(280\) 5.74961 + 4.01916i 0.343605 + 0.240191i
\(281\) 6.06727i 0.361943i 0.983488 + 0.180971i \(0.0579242\pi\)
−0.983488 + 0.180971i \(0.942076\pi\)
\(282\) 3.20111 15.5236i 0.190623 0.924418i
\(283\) 25.5734i 1.52018i −0.649818 0.760090i \(-0.725155\pi\)
0.649818 0.760090i \(-0.274845\pi\)
\(284\) 3.83421 8.90157i 0.227518 0.528211i
\(285\) 12.3686i 0.732655i
\(286\) −8.34316 1.72044i −0.493341 0.101731i
\(287\) −3.07909 −0.181753
\(288\) −2.97605 4.81073i −0.175365 0.283475i
\(289\) −17.9960 −1.05859
\(290\) 5.40386 26.2057i 0.317326 1.53885i
\(291\) 3.03678i 0.178019i
\(292\) −14.4587 6.22787i −0.846134 0.364458i
\(293\) 19.4122 1.13407 0.567035 0.823694i \(-0.308090\pi\)
0.567035 + 0.823694i \(0.308090\pi\)
\(294\) −7.63437 1.57428i −0.445246 0.0918137i
\(295\) −1.33753 −0.0778741
\(296\) 25.7638 + 18.0097i 1.49749 + 1.04679i
\(297\) 1.88814i 0.109561i
\(298\) −19.9446 4.11276i −1.15536 0.238246i
\(299\) 8.60036 + 12.6538i 0.497372 + 0.731790i
\(300\) 1.59115 + 0.685363i 0.0918652 + 0.0395694i
\(301\) 14.2275i 0.820058i
\(302\) −1.40093 + 6.79371i −0.0806142 + 0.390934i
\(303\) 7.00245i 0.402280i
\(304\) 17.6822 16.7175i 1.01414 0.958813i
\(305\) 21.1020 1.20830
\(306\) 1.68962 8.19372i 0.0965891 0.468404i
\(307\) 2.20932 0.126093 0.0630464 0.998011i \(-0.479918\pi\)
0.0630464 + 0.998011i \(0.479918\pi\)
\(308\) −1.82236 + 4.23082i −0.103838 + 0.241073i
\(309\) −3.05695 −0.173904
\(310\) −2.06537 + 10.0159i −0.117305 + 0.568866i
\(311\) 18.3744i 1.04192i −0.853583 0.520958i \(-0.825575\pi\)
0.853583 0.520958i \(-0.174425\pi\)
\(312\) 5.16975 7.39559i 0.292680 0.418693i
\(313\) 14.6786i 0.829684i 0.909893 + 0.414842i \(0.136163\pi\)
−0.909893 + 0.414842i \(0.863837\pi\)
\(314\) −8.00851 1.65143i −0.451947 0.0931955i
\(315\) −2.48021 −0.139744
\(316\) 7.77228 + 3.34778i 0.437225 + 0.188328i
\(317\) 1.06596i 0.0598705i 0.999552 + 0.0299353i \(0.00953011\pi\)
−0.999552 + 0.0299353i \(0.990470\pi\)
\(318\) −15.3303 3.16124i −0.859680 0.177274i
\(319\) 17.5706 0.983764
\(320\) −5.58719 15.2756i −0.312334 0.853932i
\(321\) 4.21095i 0.235032i
\(322\) 7.64101 3.17297i 0.425817 0.176823i
\(323\) 35.9881 2.00243
\(324\) 1.83685 + 0.791193i 0.102047 + 0.0439552i
\(325\) 2.76351i 0.153292i
\(326\) 15.6347 + 3.22402i 0.865927 + 0.178562i
\(327\) 3.18091 0.175905
\(328\) 5.85134 + 4.09027i 0.323086 + 0.225847i
\(329\) 13.6722i 0.753770i
\(330\) 1.09645 5.31716i 0.0603574 0.292700i
\(331\) 11.3481 0.623748 0.311874 0.950124i \(-0.399043\pi\)
0.311874 + 0.950124i \(0.399043\pi\)
\(332\) −5.99973 + 13.9291i −0.329278 + 0.764458i
\(333\) −11.1137 −0.609030
\(334\) −0.102290 + 0.496048i −0.00559703 + 0.0271425i
\(335\) 4.99893i 0.273121i
\(336\) −3.35226 3.54570i −0.182881 0.193434i
\(337\) 9.38843i 0.511420i 0.966754 + 0.255710i \(0.0823093\pi\)
−0.966754 + 0.255710i \(0.917691\pi\)
\(338\) −3.90917 0.806106i −0.212631 0.0438464i
\(339\) 18.9194i 1.02756i
\(340\) 9.51621 22.0930i 0.516089 1.19816i
\(341\) −6.71553 −0.363666
\(342\) −1.73752 + 8.42601i −0.0939543 + 0.455626i
\(343\) −15.2630 −0.824124
\(344\) 18.8998 27.0371i 1.01901 1.45774i
\(345\) −8.06438 + 5.48108i −0.434172 + 0.295091i
\(346\) 2.89698 14.0488i 0.155743 0.755266i
\(347\) 4.53959 0.243698 0.121849 0.992549i \(-0.461118\pi\)
0.121849 + 0.992549i \(0.461118\pi\)
\(348\) −7.36265 + 17.0933i −0.394679 + 0.916295i
\(349\) 35.2981i 1.88946i 0.327847 + 0.944731i \(0.393677\pi\)
−0.327847 + 0.944731i \(0.606323\pi\)
\(350\) 1.46362 + 0.301811i 0.0782336 + 0.0161325i
\(351\) 3.19024i 0.170283i
\(352\) 9.08334 5.61920i 0.484144 0.299505i
\(353\) 31.1526 1.65808 0.829042 0.559187i \(-0.188886\pi\)
0.829042 + 0.559187i \(0.188886\pi\)
\(354\) 0.911179 + 0.187893i 0.0484286 + 0.00998642i
\(355\) 9.85294i 0.522940i
\(356\) 3.05392 7.09003i 0.161857 0.375771i
\(357\) 7.21648i 0.381937i
\(358\) 16.3801 + 3.37773i 0.865717 + 0.178519i
\(359\) −24.9684 −1.31778 −0.658891 0.752239i \(-0.728974\pi\)
−0.658891 + 0.752239i \(0.728974\pi\)
\(360\) 4.71327 + 3.29472i 0.248411 + 0.173647i
\(361\) −18.0083 −0.947805
\(362\) 28.0075 + 5.77539i 1.47204 + 0.303548i
\(363\) −7.43492 −0.390232
\(364\) 3.07909 7.14848i 0.161388 0.374682i
\(365\) 16.0040 0.837690
\(366\) −14.3755 2.96436i −0.751421 0.154950i
\(367\) 25.0550 1.30786 0.653931 0.756554i \(-0.273119\pi\)
0.653931 + 0.756554i \(0.273119\pi\)
\(368\) −18.7355 4.12058i −0.976658 0.214800i
\(369\) −2.52410 −0.131399
\(370\) −31.2972 6.45377i −1.62706 0.335515i
\(371\) −13.5019 −0.700983
\(372\) 2.81403 6.53310i 0.145900 0.338725i
\(373\) −17.3417 −0.897918 −0.448959 0.893552i \(-0.648205\pi\)
−0.448959 + 0.893552i \(0.648205\pi\)
\(374\) 15.4709 + 3.19024i 0.799982 + 0.164963i
\(375\) −11.9270 −0.615909
\(376\) −18.1621 + 25.9818i −0.936640 + 1.33991i
\(377\) −29.6876 −1.52899
\(378\) 1.68962 + 0.348415i 0.0869046 + 0.0179205i
\(379\) 16.9340i 0.869841i −0.900469 0.434920i \(-0.856777\pi\)
0.900469 0.434920i \(-0.143223\pi\)
\(380\) −9.78599 + 22.7193i −0.502010 + 1.16548i
\(381\) 7.44653i 0.381497i
\(382\) 5.82381 + 1.20092i 0.297972 + 0.0614445i
\(383\) 29.5868 1.51182 0.755908 0.654677i \(-0.227196\pi\)
0.755908 + 0.654677i \(0.227196\pi\)
\(384\) 1.66034 + 11.1912i 0.0847286 + 0.571099i
\(385\) 4.68300i 0.238668i
\(386\) 8.72756 + 1.79970i 0.444221 + 0.0916024i
\(387\) 11.6630i 0.592865i
\(388\) 2.40268 5.57811i 0.121978 0.283185i
\(389\) 9.18306 0.465600 0.232800 0.972525i \(-0.425211\pi\)
0.232800 + 0.972525i \(0.425211\pi\)
\(390\) −1.85258 + 8.98398i −0.0938089 + 0.454921i
\(391\) −15.9478 23.4643i −0.806517 1.18664i
\(392\) 12.7776 + 8.93197i 0.645368 + 0.451133i
\(393\) −1.82236 −0.0919258
\(394\) 3.31571 16.0794i 0.167043 0.810067i
\(395\) −8.60296 −0.432862
\(396\) −1.49388 + 3.46823i −0.0750705 + 0.174285i
\(397\) 12.2452i 0.614568i −0.951618 0.307284i \(-0.900580\pi\)
0.951618 0.307284i \(-0.0994202\pi\)
\(398\) −11.9361 2.46134i −0.598304 0.123376i
\(399\) 7.42106i 0.371518i
\(400\) −2.38045 2.51782i −0.119023 0.125891i
\(401\) 8.99372i 0.449125i −0.974460 0.224563i \(-0.927905\pi\)
0.974460 0.224563i \(-0.0720953\pi\)
\(402\) −0.702238 + 3.40547i −0.0350244 + 0.169849i
\(403\) 11.3467 0.565219
\(404\) −5.54029 + 12.8624i −0.275640 + 0.639930i
\(405\) −2.03317 −0.101029
\(406\) −3.24226 + 15.7232i −0.160911 + 0.780328i
\(407\) 20.9843i 1.04015i
\(408\) −9.58639 + 13.7138i −0.474597 + 0.678935i
\(409\) 29.6011 1.46368 0.731840 0.681477i \(-0.238662\pi\)
0.731840 + 0.681477i \(0.238662\pi\)
\(410\) −7.10806 1.46575i −0.351042 0.0723880i
\(411\) 0.220739i 0.0108883i
\(412\) 5.61516 + 2.41864i 0.276639 + 0.119158i
\(413\) 0.802505 0.0394887
\(414\) 6.26374 2.60106i 0.307846 0.127835i
\(415\) 15.4178i 0.756829i
\(416\) −15.3474 + 9.49431i −0.752468 + 0.465497i
\(417\) −21.9828 −1.07650
\(418\) −15.9095 3.28068i −0.778159 0.160463i
\(419\) 13.6353i 0.666126i −0.942905 0.333063i \(-0.891918\pi\)
0.942905 0.333063i \(-0.108082\pi\)
\(420\) 4.55578 + 1.96233i 0.222299 + 0.0957518i
\(421\) −4.56033 −0.222257 −0.111128 0.993806i \(-0.535447\pi\)
−0.111128 + 0.993806i \(0.535447\pi\)
\(422\) 27.2239 + 5.61381i 1.32524 + 0.273276i
\(423\) 11.2078i 0.544942i
\(424\) 25.6583 + 17.9359i 1.24608 + 0.871047i
\(425\) 5.12445i 0.248572i
\(426\) 1.38412 6.71221i 0.0670608 0.325208i
\(427\) −12.6610 −0.612709
\(428\) 3.33167 7.73487i 0.161042 0.373879i
\(429\) −6.02363 −0.290824
\(430\) −6.77273 + 32.8440i −0.326610 + 1.58388i
\(431\) −30.0775 −1.44878 −0.724392 0.689389i \(-0.757879\pi\)
−0.724392 + 0.689389i \(0.757879\pi\)
\(432\) −2.74803 2.90660i −0.132215 0.139844i
\(433\) 17.0843i 0.821018i −0.911857 0.410509i \(-0.865351\pi\)
0.911857 0.410509i \(-0.134649\pi\)
\(434\) 1.23920 6.00945i 0.0594836 0.288463i
\(435\) 18.9201i 0.907151i
\(436\) −5.84285 2.51671i −0.279822 0.120529i
\(437\) 16.4000 + 24.1295i 0.784516 + 1.15427i
\(438\) −10.9026 2.24821i −0.520946 0.107424i
\(439\) 17.2515i 0.823371i 0.911326 + 0.411685i \(0.135060\pi\)
−0.911326 + 0.411685i \(0.864940\pi\)
\(440\) −6.22090 + 8.89932i −0.296570 + 0.424258i
\(441\) −5.51190 −0.262471
\(442\) −26.1400 5.39029i −1.24335 0.256390i
\(443\) −19.0033 −0.902875 −0.451437 0.892303i \(-0.649089\pi\)
−0.451437 + 0.892303i \(0.649089\pi\)
\(444\) 20.4143 + 8.79312i 0.968819 + 0.417303i
\(445\) 7.84779i 0.372021i
\(446\) 4.24168 20.5698i 0.200849 0.974008i
\(447\) −14.3997 −0.681083
\(448\) 3.35226 + 9.16520i 0.158379 + 0.433015i
\(449\) 9.95996 0.470039 0.235020 0.971991i \(-0.424485\pi\)
0.235020 + 0.971991i \(0.424485\pi\)
\(450\) 1.19980 + 0.247411i 0.0565593 + 0.0116630i
\(451\) 4.76585i 0.224415i
\(452\) 14.9689 34.7520i 0.704077 1.63460i
\(453\) 4.90495i 0.230455i
\(454\) −4.92495 + 23.8833i −0.231139 + 1.12090i
\(455\) 7.91248i 0.370943i
\(456\) 9.85816 14.1026i 0.461651 0.660414i
\(457\) 11.2976i 0.528478i −0.964457 0.264239i \(-0.914879\pi\)
0.964457 0.264239i \(-0.0851207\pi\)
\(458\) 3.58779 + 0.739835i 0.167647 + 0.0345702i
\(459\) 5.91574i 0.276123i
\(460\) 19.1496 3.68742i 0.892857 0.171927i
\(461\) 7.73780i 0.360385i −0.983631 0.180193i \(-0.942328\pi\)
0.983631 0.180193i \(-0.0576721\pi\)
\(462\) −0.657857 + 3.19024i −0.0306063 + 0.148423i
\(463\) 15.8063i 0.734581i 0.930106 + 0.367290i \(0.119714\pi\)
−0.930106 + 0.367290i \(0.880286\pi\)
\(464\) 27.0481 25.5725i 1.25568 1.18717i
\(465\) 7.23133i 0.335345i
\(466\) 30.6499 + 6.32029i 1.41983 + 0.292782i
\(467\) 32.5241i 1.50504i 0.658572 + 0.752518i \(0.271161\pi\)
−0.658572 + 0.752518i \(0.728839\pi\)
\(468\) 2.52410 5.85999i 0.116676 0.270878i
\(469\) 2.99931i 0.138495i
\(470\) 6.50838 31.5621i 0.300209 1.45585i
\(471\) −5.78202 −0.266421
\(472\) −1.52504 1.06605i −0.0701956 0.0490689i
\(473\) −22.0214 −1.01255
\(474\) 5.86067 + 1.20852i 0.269190 + 0.0555093i
\(475\) 5.26972i 0.241791i
\(476\) −5.70963 + 13.2556i −0.261700 + 0.607569i
\(477\) −11.0682 −0.506779
\(478\) 5.87184 28.4752i 0.268572 1.30243i
\(479\) 16.2098 0.740643 0.370322 0.928904i \(-0.379247\pi\)
0.370322 + 0.928904i \(0.379247\pi\)
\(480\) −6.05080 9.78101i −0.276180 0.446440i
\(481\) 35.4555i 1.61663i
\(482\) −3.85583 + 18.6986i −0.175628 + 0.851700i
\(483\) 4.83855 3.28859i 0.220162 0.149636i
\(484\) 13.6568 + 5.88246i 0.620765 + 0.267384i
\(485\) 6.17427i 0.280359i
\(486\) 1.38507 + 0.285614i 0.0628281 + 0.0129557i
\(487\) 15.4990i 0.702327i 0.936314 + 0.351164i \(0.114214\pi\)
−0.936314 + 0.351164i \(0.885786\pi\)
\(488\) 24.0603 + 16.8189i 1.08916 + 0.761356i
\(489\) 11.2880 0.510462
\(490\) −15.5219 3.20076i −0.701210 0.144596i
\(491\) 25.3264 1.14296 0.571481 0.820615i \(-0.306369\pi\)
0.571481 + 0.820615i \(0.306369\pi\)
\(492\) 4.63638 + 1.99705i 0.209024 + 0.0900338i
\(493\) 55.0504 2.47935
\(494\) 26.8810 + 5.54311i 1.20943 + 0.249396i
\(495\) 3.83890i 0.172546i
\(496\) −10.3379 + 9.77388i −0.464185 + 0.438860i
\(497\) 5.91166i 0.265174i
\(498\) −2.16585 + 10.5032i −0.0970542 + 0.470659i
\(499\) 1.02051 0.0456842 0.0228421 0.999739i \(-0.492729\pi\)
0.0228421 + 0.999739i \(0.492729\pi\)
\(500\) 21.9082 + 9.43658i 0.979763 + 0.422017i
\(501\) 0.358139i 0.0160005i
\(502\) 7.16526 34.7476i 0.319801 1.55086i
\(503\) −14.2820 −0.636805 −0.318403 0.947956i \(-0.603146\pi\)
−0.318403 + 0.947956i \(0.603146\pi\)
\(504\) −2.82791 1.97680i −0.125965 0.0880537i
\(505\) 14.2371i 0.633544i
\(506\) 4.91117 + 11.8268i 0.218328 + 0.525767i
\(507\) −2.82236 −0.125345
\(508\) −5.89164 + 13.6782i −0.261399 + 0.606870i
\(509\) 16.0929i 0.713307i 0.934237 + 0.356654i \(0.116082\pi\)
−0.934237 + 0.356654i \(0.883918\pi\)
\(510\) 3.43528 16.6592i 0.152117 0.737681i
\(511\) −9.60226 −0.424779
\(512\) 5.80462 21.8702i 0.256531 0.966536i
\(513\) 6.08344i 0.268591i
\(514\) 17.2278 + 3.55253i 0.759887 + 0.156695i
\(515\) −6.21529 −0.273878
\(516\) 9.22770 21.4232i 0.406227 0.943104i
\(517\) 21.1619 0.930700
\(518\) 18.7780 + 3.87219i 0.825058 + 0.170134i
\(519\) 10.1430i 0.445227i
\(520\) 10.5110 15.0365i 0.460936 0.659392i
\(521\) 40.0850i 1.75615i −0.478519 0.878077i \(-0.658826\pi\)
0.478519 0.878077i \(-0.341174\pi\)
\(522\) −2.65786 + 12.8891i −0.116331 + 0.564142i
\(523\) 3.67778i 0.160818i −0.996762 0.0804091i \(-0.974377\pi\)
0.996762 0.0804091i \(-0.0256227\pi\)
\(524\) 3.34740 + 1.44184i 0.146232 + 0.0629869i
\(525\) 1.05671 0.0461185
\(526\) 14.3668 + 2.96256i 0.626422 + 0.129174i
\(527\) −21.0404 −0.916536
\(528\) 5.48808 5.18867i 0.238838 0.225808i
\(529\) 8.46496 21.3856i 0.368042 0.929809i
\(530\) −31.1690 6.42733i −1.35390 0.279185i
\(531\) 0.657857 0.0285485
\(532\) 5.87149 13.6314i 0.254561 0.590995i
\(533\) 8.05248i 0.348792i
\(534\) 1.10244 5.34622i 0.0477072 0.231354i
\(535\) 8.56155i 0.370148i
\(536\) 3.98429 5.69972i 0.172095 0.246190i
\(537\) 11.8262 0.510338
\(538\) 5.13807 24.9168i 0.221518 1.07424i
\(539\) 10.4072i 0.448272i
\(540\) 3.73462 + 1.60863i 0.160712 + 0.0692242i
\(541\) 39.3379i 1.69127i −0.533761 0.845635i \(-0.679222\pi\)
0.533761 0.845635i \(-0.320778\pi\)
\(542\) −2.11229 + 10.2434i −0.0907305 + 0.439993i
\(543\) 20.2209 0.867764
\(544\) 28.4590 17.6055i 1.22017 0.754831i
\(545\) 6.46731 0.277029
\(546\) 1.11153 5.39029i 0.0475690 0.230683i
\(547\) 14.0964 0.602718 0.301359 0.953511i \(-0.402560\pi\)
0.301359 + 0.953511i \(0.402560\pi\)
\(548\) 0.174647 0.405465i 0.00746057 0.0173206i
\(549\) −10.3789 −0.442961
\(550\) −0.467146 + 2.26540i −0.0199192 + 0.0965970i
\(551\) −56.6110 −2.41171
\(552\) −13.5635 0.178080i −0.577301 0.00757959i
\(553\) 5.16169 0.219497
\(554\) −8.59036 + 41.6585i −0.364970 + 1.76990i
\(555\) −22.5961 −0.959150
\(556\) 40.3791 + 17.3926i 1.71246 + 0.737612i
\(557\) 10.4485 0.442715 0.221358 0.975193i \(-0.428951\pi\)
0.221358 + 0.975193i \(0.428951\pi\)
\(558\) 1.01584 4.92627i 0.0430040 0.208546i
\(559\) 37.2079 1.57372
\(560\) −6.81570 7.20900i −0.288016 0.304636i
\(561\) 11.1698 0.471587
\(562\) 1.73290 8.40361i 0.0730979 0.354485i
\(563\) 19.6672i 0.828873i 0.910078 + 0.414436i \(0.136021\pi\)
−0.910078 + 0.414436i \(0.863979\pi\)
\(564\) −8.86753 + 20.5870i −0.373390 + 0.866871i
\(565\) 38.4662i 1.61829i
\(566\) −7.30412 + 35.4210i −0.307015 + 1.48885i
\(567\) 1.21988 0.0512301
\(568\) −7.85307 + 11.2342i −0.329507 + 0.471377i
\(569\) 1.07567i 0.0450943i −0.999746 0.0225471i \(-0.992822\pi\)
0.999746 0.0225471i \(-0.00717759\pi\)
\(570\) −3.53266 + 17.1315i −0.147967 + 0.717558i
\(571\) 28.5359i 1.19419i 0.802170 + 0.597096i \(0.203679\pi\)
−0.802170 + 0.597096i \(0.796321\pi\)
\(572\) 11.0645 + 4.76585i 0.462630 + 0.199270i
\(573\) 4.20470 0.175654
\(574\) 4.26476 + 0.879433i 0.178008 + 0.0367068i
\(575\) 3.43587 2.33524i 0.143286 0.0973862i
\(576\) 2.74803 + 7.51321i 0.114501 + 0.313050i
\(577\) 4.04788 0.168515 0.0842577 0.996444i \(-0.473148\pi\)
0.0842577 + 0.996444i \(0.473148\pi\)
\(578\) 24.9257 + 5.13990i 1.03677 + 0.213792i
\(579\) 6.30116 0.261867
\(580\) −14.9695 + 34.7534i −0.621574 + 1.44306i
\(581\) 9.25051i 0.383776i
\(582\) 0.867348 4.20616i 0.0359527 0.174351i
\(583\) 20.8984i 0.865523i
\(584\) 18.2476 + 12.7557i 0.755092 + 0.527833i
\(585\) 6.48629i 0.268175i
\(586\) −26.8872 5.54439i −1.11070 0.229037i
\(587\) −15.3197 −0.632312 −0.316156 0.948707i \(-0.602392\pi\)
−0.316156 + 0.948707i \(0.602392\pi\)
\(588\) 10.1245 + 4.36097i 0.417528 + 0.179844i
\(589\) 21.6369 0.891534
\(590\) 1.85258 + 0.382018i 0.0762694 + 0.0157274i
\(591\) 11.6091i 0.477533i
\(592\) −30.5409 32.3033i −1.25522 1.32766i
\(593\) 2.25798 0.0927240 0.0463620 0.998925i \(-0.485237\pi\)
0.0463620 + 0.998925i \(0.485237\pi\)
\(594\) −0.539280 + 2.61521i −0.0221269 + 0.107303i
\(595\) 14.6723i 0.601506i
\(596\) 26.4501 + 11.3929i 1.08344 + 0.466673i
\(597\) −8.61769 −0.352699
\(598\) −8.29800 19.9829i −0.339331 0.817160i
\(599\) 22.8436i 0.933362i −0.884426 0.466681i \(-0.845450\pi\)
0.884426 0.466681i \(-0.154550\pi\)
\(600\) −2.00811 1.40373i −0.0819808 0.0573071i
\(601\) −9.74798 −0.397628 −0.198814 0.980037i \(-0.563709\pi\)
−0.198814 + 0.980037i \(0.563709\pi\)
\(602\) 4.06357 19.7061i 0.165619 0.803159i
\(603\) 2.45869i 0.100126i
\(604\) 3.88076 9.00966i 0.157906 0.366598i
\(605\) −15.1164 −0.614570
\(606\) −2.00000 + 9.69890i −0.0812444 + 0.393991i
\(607\) 27.7790i 1.12752i −0.825940 0.563758i \(-0.809355\pi\)
0.825940 0.563758i \(-0.190645\pi\)
\(608\) −29.2658 + 18.1046i −1.18689 + 0.734240i
\(609\) 11.3519i 0.460002i
\(610\) −29.2278 6.02704i −1.18340 0.244028i
\(611\) −35.7556 −1.44652
\(612\) −4.68049 + 10.8663i −0.189198 + 0.439245i
\(613\) −13.1317 −0.530386 −0.265193 0.964195i \(-0.585436\pi\)
−0.265193 + 0.964195i \(0.585436\pi\)
\(614\) −3.06007 0.631015i −0.123495 0.0254657i
\(615\) −5.13190 −0.206938
\(616\) 3.73248 5.33950i 0.150386 0.215135i
\(617\) 26.8543i 1.08111i 0.841307 + 0.540557i \(0.181787\pi\)
−0.841307 + 0.540557i \(0.818213\pi\)
\(618\) 4.23410 + 0.873109i 0.170320 + 0.0351216i
\(619\) 37.7150i 1.51589i −0.652317 0.757946i \(-0.726203\pi\)
0.652317 0.757946i \(-0.273797\pi\)
\(620\) 5.72138 13.2829i 0.229776 0.533453i
\(621\) 3.96642 2.69583i 0.159167 0.108180i
\(622\) −5.24799 + 25.4498i −0.210425 + 1.02045i
\(623\) 4.70859i 0.188646i
\(624\) −9.27277 + 8.76687i −0.371208 + 0.350956i
\(625\) −19.9184 −0.796737
\(626\) 4.19242 20.3309i 0.167563 0.812588i
\(627\) −11.4864 −0.458723
\(628\) 10.6207 + 4.57469i 0.423812 + 0.182550i
\(629\) 65.7460i 2.62147i
\(630\) 3.43528 + 0.708385i 0.136865 + 0.0282227i
\(631\) −38.4398 −1.53027 −0.765133 0.643872i \(-0.777327\pi\)
−0.765133 + 0.643872i \(0.777327\pi\)
\(632\) −9.80899 6.85680i −0.390181 0.272749i
\(633\) 19.6552 0.781225
\(634\) 0.304455 1.47644i 0.0120914 0.0586368i
\(635\) 15.1400i 0.600814i
\(636\) 20.3307 + 8.75710i 0.806163 + 0.347242i
\(637\) 17.5843i 0.696715i
\(638\) −24.3365 5.01841i −0.963492 0.198681i
\(639\) 4.84611i 0.191709i
\(640\) 3.37574 + 22.7536i 0.133438 + 0.899414i
\(641\) 45.0011i 1.77744i 0.458455 + 0.888718i \(0.348403\pi\)
−0.458455 + 0.888718i \(0.651597\pi\)
\(642\) 1.20271 5.83246i 0.0474670 0.230189i
\(643\) 25.2162i 0.994430i 0.867627 + 0.497215i \(0.165644\pi\)
−0.867627 + 0.497215i \(0.834356\pi\)
\(644\) −11.4896 + 2.21242i −0.452753 + 0.0871814i
\(645\) 23.7128i 0.933692i
\(646\) −49.8461 10.2787i −1.96117 0.404410i
\(647\) 18.2382i 0.717017i −0.933527 0.358508i \(-0.883285\pi\)
0.933527 0.358508i \(-0.116715\pi\)
\(648\) −2.31819 1.62049i −0.0910672 0.0636588i
\(649\) 1.24213i 0.0487577i
\(650\) 0.789299 3.82767i 0.0309589 0.150133i
\(651\) 4.33873i 0.170048i
\(652\) −20.7344 8.93100i −0.812021 0.349765i
\(653\) 12.8376i 0.502373i 0.967939 + 0.251186i \(0.0808207\pi\)
−0.967939 + 0.251186i \(0.919179\pi\)
\(654\) −4.40579 0.908513i −0.172280 0.0355257i
\(655\) −3.70515 −0.144772
\(656\) −6.93629 7.33655i −0.270817 0.286444i
\(657\) −7.87149 −0.307096
\(658\) −3.90496 + 18.9369i −0.152231 + 0.738238i
\(659\) 6.88484i 0.268195i −0.990968 0.134098i \(-0.957186\pi\)
0.990968 0.134098i \(-0.0428136\pi\)
\(660\) −3.03731 + 7.05149i −0.118227 + 0.274479i
\(661\) 11.3609 0.441888 0.220944 0.975287i \(-0.429086\pi\)
0.220944 + 0.975287i \(0.429086\pi\)
\(662\) −15.7179 3.24118i −0.610895 0.125972i
\(663\) −18.8726 −0.732952
\(664\) 12.2884 17.5792i 0.476882 0.682204i
\(665\) 15.0882i 0.585097i
\(666\) 15.3933 + 3.17425i 0.596480 + 0.123000i
\(667\) 25.0868 + 36.9105i 0.971363 + 1.42918i
\(668\) 0.283357 0.657846i 0.0109634 0.0254528i
\(669\) 14.8511i 0.574175i
\(670\) −1.42777 + 6.92388i −0.0551594 + 0.267493i
\(671\) 19.5968i 0.756527i
\(672\) 3.63042 + 5.86851i 0.140046 + 0.226383i
\(673\) 1.24484 0.0479849 0.0239925 0.999712i \(-0.492362\pi\)
0.0239925 + 0.999712i \(0.492362\pi\)
\(674\) 2.68147 13.0036i 0.103286 0.500882i
\(675\) 0.866240 0.0333416
\(676\) 5.18424 + 2.23303i 0.199394 + 0.0858857i
\(677\) −18.1961 −0.699333 −0.349667 0.936874i \(-0.613705\pi\)
−0.349667 + 0.936874i \(0.613705\pi\)
\(678\) 5.40365 26.2047i 0.207526 1.00639i
\(679\) 3.70450i 0.142166i
\(680\) −19.4907 + 27.8824i −0.747435 + 1.06924i
\(681\) 17.2433i 0.660766i
\(682\) 9.30150 + 1.91805i 0.356173 + 0.0734460i
\(683\) 22.9048 0.876428 0.438214 0.898871i \(-0.355611\pi\)
0.438214 + 0.898871i \(0.355611\pi\)
\(684\) 4.81318 11.1744i 0.184036 0.427263i
\(685\) 0.448799i 0.0171477i
\(686\) 21.1403 + 4.35933i 0.807142 + 0.166440i
\(687\) 2.59033 0.0988272
\(688\) −33.8998 + 32.0503i −1.29242 + 1.22191i
\(689\) 35.3103i 1.34522i
\(690\) 12.7352 5.28838i 0.484822 0.201325i
\(691\) 39.6585 1.50868 0.754340 0.656484i \(-0.227957\pi\)
0.754340 + 0.656484i \(0.227957\pi\)
\(692\) −8.02505 + 18.6311i −0.305067 + 0.708249i
\(693\) 2.30330i 0.0874953i
\(694\) −6.28766 1.29657i −0.238676 0.0492172i
\(695\) −44.6947 −1.69537
\(696\) 15.0799 21.5725i 0.571601 0.817704i
\(697\) 14.9319i 0.565586i
\(698\) 10.0816 48.8904i 0.381595 1.85053i
\(699\) 22.1288 0.836987
\(700\) −1.94101 0.836059i −0.0733633 0.0316001i
\(701\) −22.9169 −0.865560 −0.432780 0.901499i \(-0.642467\pi\)
−0.432780 + 0.901499i \(0.642467\pi\)
\(702\) 0.911179 4.41871i 0.0343902 0.166774i
\(703\) 67.6099i 2.54995i
\(704\) −14.1860 + 5.18867i −0.534655 + 0.195555i
\(705\) 22.7873i 0.858220i
\(706\) −43.1485 8.89762i −1.62392 0.334866i
\(707\) 8.54214i 0.321260i
\(708\) −1.20838 0.520491i −0.0454138 0.0195613i
\(709\) 5.57334 0.209311 0.104656 0.994509i \(-0.466626\pi\)
0.104656 + 0.994509i \(0.466626\pi\)
\(710\) 2.81414 13.6470i 0.105613 0.512164i
\(711\) 4.23131 0.158687
\(712\) −6.25491 + 8.94796i −0.234413 + 0.335339i
\(713\) −9.58824 14.1073i −0.359082 0.528323i
\(714\) −2.06113 + 9.99535i −0.0771359 + 0.374066i
\(715\) −12.2470 −0.458013
\(716\) −21.7229 9.35680i −0.811824 0.349680i
\(717\) 20.5586i 0.767776i
\(718\) 34.5830 + 7.13133i 1.29063 + 0.266139i
\(719\) 3.83953i 0.143190i −0.997434 0.0715952i \(-0.977191\pi\)
0.997434 0.0715952i \(-0.0228090\pi\)
\(720\) −5.58719 5.90960i −0.208222 0.220238i
\(721\) 3.72911 0.138879
\(722\) 24.9428 + 5.14343i 0.928274 + 0.191419i
\(723\) 13.5001i 0.502075i
\(724\) −37.1428 15.9987i −1.38040 0.594586i
\(725\) 8.06101i 0.299379i
\(726\) 10.2979 + 2.12352i 0.382191 + 0.0788112i
\(727\) −12.5993 −0.467281 −0.233641 0.972323i \(-0.575064\pi\)
−0.233641 + 0.972323i \(0.575064\pi\)
\(728\) −6.30647 + 9.02172i −0.233733 + 0.334367i
\(729\) 1.00000 0.0370370
\(730\) −22.1668 4.57098i −0.820428 0.169180i
\(731\) −68.9954 −2.55189
\(732\) 19.0645 + 8.21171i 0.704643 + 0.303514i
\(733\) −5.84348 −0.215834 −0.107917 0.994160i \(-0.534418\pi\)
−0.107917 + 0.994160i \(0.534418\pi\)
\(734\) −34.7030 7.15608i −1.28091 0.264136i
\(735\) −11.2066 −0.413361
\(736\) 24.7732 + 11.0584i 0.913152 + 0.407620i
\(737\) −4.64236 −0.171004
\(738\) 3.49606 + 0.720918i 0.128692 + 0.0265374i
\(739\) −22.0429 −0.810861 −0.405430 0.914126i \(-0.632878\pi\)
−0.405430 + 0.914126i \(0.632878\pi\)
\(740\) 41.5056 + 17.8779i 1.52578 + 0.657203i
\(741\) 19.4077 0.712958
\(742\) 18.7011 + 3.85633i 0.686539 + 0.141570i
\(743\) 27.7944 1.01968 0.509839 0.860270i \(-0.329705\pi\)
0.509839 + 0.860270i \(0.329705\pi\)
\(744\) −5.76358 + 8.24509i −0.211303 + 0.302280i
\(745\) −29.2770 −1.07263
\(746\) 24.0195 + 4.95303i 0.879415 + 0.181343i
\(747\) 7.58314i 0.277453i
\(748\) −20.5171 8.83743i −0.750181 0.323128i
\(749\) 5.13684i 0.187696i
\(750\) 16.5198 + 3.40653i 0.603218 + 0.124389i
\(751\) −38.5857 −1.40801 −0.704005 0.710195i \(-0.748607\pi\)
−0.704005 + 0.710195i \(0.748607\pi\)
\(752\) 32.5766 30.7993i 1.18795 1.12314i
\(753\) 25.0872i 0.914228i
\(754\) 41.1195 + 8.47921i 1.49748 + 0.308794i
\(755\) 9.97258i 0.362939i
\(756\) −2.24073 0.965159i −0.0814946 0.0351025i
\(757\) −38.4124 −1.39612 −0.698060 0.716039i \(-0.745953\pi\)
−0.698060 + 0.716039i \(0.745953\pi\)
\(758\) −4.83659 + 23.4548i −0.175673 + 0.851916i
\(759\) 5.09012 + 7.48916i 0.184760 + 0.271839i
\(760\) 20.0433 28.6729i 0.727046 1.04008i
\(761\) 26.4292 0.958056 0.479028 0.877800i \(-0.340989\pi\)
0.479028 + 0.877800i \(0.340989\pi\)
\(762\) −2.12684 + 10.3140i −0.0770472 + 0.373636i
\(763\) −3.88032 −0.140477
\(764\) −7.72339 3.32673i −0.279423 0.120357i
\(765\) 12.0277i 0.434861i
\(766\) −40.9799 8.45043i −1.48066 0.305326i
\(767\) 2.09872i 0.0757804i
\(768\) 0.896688 15.9749i 0.0323564 0.576443i
\(769\) 31.7255i 1.14405i −0.820236 0.572025i \(-0.806158\pi\)
0.820236 0.572025i \(-0.193842\pi\)
\(770\) −1.33753 + 6.48629i −0.0482013 + 0.233750i
\(771\) 12.4382 0.447951
\(772\) −11.5743 4.98543i −0.416567 0.179430i
\(773\) 21.0369 0.756645 0.378322 0.925674i \(-0.376501\pi\)
0.378322 + 0.925674i \(0.376501\pi\)
\(774\) 3.33113 16.1541i 0.119735 0.580648i
\(775\) 3.08095i 0.110671i
\(776\) −4.92107 + 7.03984i −0.176656 + 0.252715i
\(777\) 13.5574 0.486370
\(778\) −12.7192 2.62281i −0.456006 0.0940325i
\(779\) 15.3552i 0.550157i
\(780\) 5.13190 11.9143i 0.183752 0.426601i
\(781\) 9.15014 0.327418
\(782\) 15.3872 + 37.0547i 0.550244 + 1.32507i
\(783\) 9.30575i 0.332560i
\(784\) −15.1468 16.0209i −0.540959 0.572175i
\(785\) −11.7558 −0.419583
\(786\) 2.52410 + 0.520491i 0.0900315 + 0.0185653i
\(787\) 26.6770i 0.950934i −0.879734 0.475467i \(-0.842279\pi\)
0.879734 0.475467i \(-0.157721\pi\)
\(788\) −9.18500 + 21.3241i −0.327202 + 0.759639i
\(789\) 10.3726 0.369274
\(790\) 11.9157 + 2.45713i 0.423942 + 0.0874207i
\(791\) 23.0793i 0.820607i
\(792\) 3.05971 4.37708i 0.108722 0.155533i
\(793\) 33.1112i 1.17581i
\(794\) −3.49740 + 16.9605i −0.124118 + 0.601904i
\(795\) −22.5035 −0.798118
\(796\) 15.8294 + 6.81826i 0.561058 + 0.241667i
\(797\) −25.5900 −0.906443 −0.453222 0.891398i \(-0.649725\pi\)
−0.453222 + 0.891398i \(0.649725\pi\)
\(798\) 2.11956 10.2787i 0.0750317 0.363862i
\(799\) 66.3024 2.34561
\(800\) 2.57797 + 4.16725i 0.0911451 + 0.147334i
\(801\) 3.85989i 0.136382i
\(802\) −2.56874 + 12.4570i −0.0907052 + 0.439870i
\(803\) 14.8625i 0.524486i
\(804\) 1.94530 4.51625i 0.0686054 0.159276i
\(805\) 9.83757 6.68625i 0.346729 0.235659i
\(806\) −15.7160 3.24078i −0.553572 0.114152i
\(807\) 17.9895i 0.633262i
\(808\) 11.3474 16.2330i 0.399200 0.571076i
\(809\) −34.2026 −1.20250 −0.601250 0.799061i \(-0.705331\pi\)
−0.601250 + 0.799061i \(0.705331\pi\)
\(810\) 2.81608 + 0.580701i 0.0989470 + 0.0204038i
\(811\) −52.9847 −1.86054 −0.930272 0.366869i \(-0.880430\pi\)
−0.930272 + 0.366869i \(0.880430\pi\)
\(812\) 8.98153 20.8517i 0.315190 0.731751i
\(813\) 7.39559i 0.259375i
\(814\) −5.99343 + 29.0648i −0.210070 + 1.01872i
\(815\) 22.9504 0.803918
\(816\) 17.1947 16.2566i 0.601935 0.569095i
\(817\) 70.9513 2.48227
\(818\) −40.9996 8.45450i −1.43352 0.295605i
\(819\) 3.89171i 0.135987i
\(820\) 9.42653 + 4.06033i 0.329189 + 0.141793i
\(821\) 31.4859i 1.09886i −0.835538 0.549432i \(-0.814844\pi\)
0.835538 0.549432i \(-0.185156\pi\)
\(822\) 0.0630463 0.305740i 0.00219899 0.0106639i
\(823\) 48.2371i 1.68144i −0.541469 0.840720i \(-0.682132\pi\)
0.541469 0.840720i \(-0.317868\pi\)
\(824\) −7.08660 4.95376i −0.246873 0.172572i
\(825\) 1.63558i 0.0569437i
\(826\) −1.11153 0.229207i −0.0386750 0.00797513i
\(827\) 1.17993i 0.0410300i 0.999790 + 0.0205150i \(0.00653059\pi\)
−0.999790 + 0.0205150i \(0.993469\pi\)
\(828\) −9.41864 + 1.81364i −0.327320 + 0.0630282i
\(829\) 26.1335i 0.907654i 0.891090 + 0.453827i \(0.149942\pi\)
−0.891090 + 0.453827i \(0.850058\pi\)
\(830\) −4.40354 + 21.3547i −0.152849 + 0.741233i
\(831\) 30.0768i 1.04335i
\(832\) 23.9690 8.76687i 0.830974 0.303937i
\(833\) 32.6069i 1.12976i
\(834\) 30.4478 + 6.27861i 1.05432 + 0.217410i
\(835\) 0.728155i 0.0251988i
\(836\) 21.0988 + 9.08796i 0.729717 + 0.314314i
\(837\) 3.55669i 0.122937i
\(838\) −3.89443 + 18.8858i −0.134531 + 0.652400i
\(839\) −20.5929 −0.710946 −0.355473 0.934687i \(-0.615680\pi\)
−0.355473 + 0.934687i \(0.615680\pi\)
\(840\) −5.74961 4.01916i −0.198380 0.138674i
\(841\) −57.5970 −1.98610
\(842\) 6.31639 + 1.30250i 0.217677 + 0.0448870i
\(843\) 6.06727i 0.208968i
\(844\) −36.1037 15.5511i −1.24274 0.535290i
\(845\) −5.73832 −0.197404
\(846\) −3.20111 + 15.5236i −0.110056 + 0.533713i
\(847\) 9.06970 0.311639
\(848\) −30.4158 32.1710i −1.04448 1.10476i
\(849\) 25.5734i 0.877676i
\(850\) −1.46362 + 7.09773i −0.0502016 + 0.243450i
\(851\) 44.0818 29.9608i 1.51110 1.02704i
\(852\) −3.83421 + 8.90157i −0.131358 + 0.304963i
\(853\) 13.1368i 0.449794i 0.974383 + 0.224897i \(0.0722045\pi\)
−0.974383 + 0.224897i \(0.927795\pi\)
\(854\) 17.5364 + 3.61616i 0.600083 + 0.123743i
\(855\) 12.3686i 0.422999i
\(856\) −6.82379 + 9.76178i −0.233232 + 0.333651i
\(857\) 31.3190 1.06984 0.534918 0.844904i \(-0.320342\pi\)
0.534918 + 0.844904i \(0.320342\pi\)
\(858\) 8.34316 + 1.72044i 0.284831 + 0.0587347i
\(859\) 10.4517 0.356606 0.178303 0.983976i \(-0.442939\pi\)
0.178303 + 0.983976i \(0.442939\pi\)
\(860\) 18.7614 43.5569i 0.639760 1.48528i
\(861\) 3.07909 0.104935
\(862\) 41.6595 + 8.59057i 1.41893 + 0.292596i
\(863\) 31.2021i 1.06213i 0.847331 + 0.531066i \(0.178208\pi\)
−0.847331 + 0.531066i \(0.821792\pi\)
\(864\) 2.97605 + 4.81073i 0.101247 + 0.163664i
\(865\) 20.6224i 0.701181i
\(866\) −4.87951 + 23.6630i −0.165813 + 0.804100i
\(867\) 17.9960 0.611175
\(868\) −3.43277 + 7.96959i −0.116516 + 0.270505i
\(869\) 7.98932i 0.271019i
\(870\) −5.40386 + 26.2057i −0.183208 + 0.888458i
\(871\) 7.84382 0.265778
\(872\) 7.37396 + 5.15463i 0.249714 + 0.174558i
\(873\) 3.03678i 0.102779i
\(874\) −15.8234 38.1051i −0.535234 1.28893i
\(875\) 14.5495 0.491864
\(876\) 14.4587 + 6.22787i 0.488516 + 0.210420i
\(877\) 33.3576i 1.12641i 0.826318 + 0.563203i \(0.190431\pi\)
−0.826318 + 0.563203i \(0.809569\pi\)
\(878\) 4.92728 23.8946i 0.166288 0.806404i
\(879\) −19.4122 −0.654756
\(880\) 11.1582 10.5494i 0.376142 0.355621i
\(881\) 3.93660i 0.132627i 0.997799 + 0.0663137i \(0.0211238\pi\)
−0.997799 + 0.0663137i \(0.978876\pi\)
\(882\) 7.63437 + 1.57428i 0.257063 + 0.0530087i
\(883\) 25.8164 0.868790 0.434395 0.900722i \(-0.356962\pi\)
0.434395 + 0.900722i \(0.356962\pi\)
\(884\) 34.6662 + 14.9319i 1.16595 + 0.502214i
\(885\) 1.33753 0.0449606
\(886\) 26.3210 + 5.42762i 0.884270 + 0.182344i
\(887\) 50.2556i 1.68742i 0.536800 + 0.843709i \(0.319633\pi\)
−0.536800 + 0.843709i \(0.680367\pi\)
\(888\) −25.7638 18.0097i −0.864576 0.604366i
\(889\) 9.08387i 0.304663i
\(890\) 2.24144 10.8698i 0.0751333 0.364355i
\(891\) 1.88814i 0.0632551i
\(892\) −11.7501 + 27.2792i −0.393421 + 0.913374i
\(893\) −68.1820 −2.28162
\(894\) 19.9446 + 4.11276i 0.667048 + 0.137551i
\(895\) 24.0446 0.803723
\(896\) −2.02541 13.6519i −0.0676641 0.456079i
\(897\) −8.60036 12.6538i −0.287158 0.422499i
\(898\) −13.7953 2.84471i −0.460354 0.0949291i
\(899\) 33.0977 1.10387
\(900\) −1.59115 0.685363i −0.0530384 0.0228454i
\(901\) 65.4767i 2.18135i
\(902\) −1.36120 + 6.60105i −0.0453229 + 0.219791i
\(903\) 14.2275i 0.473460i
\(904\) −30.6587 + 43.8588i −1.01969 + 1.45872i
\(905\) 41.1125 1.36663
\(906\) 1.40093 6.79371i 0.0465426 0.225706i
\(907\) 18.7971i 0.624147i −0.950058 0.312074i \(-0.898976\pi\)
0.950058 0.312074i \(-0.101024\pi\)
\(908\) 13.6428 31.6734i 0.452753 1.05112i
\(909\) 7.00245i 0.232257i
\(910\) 2.25992 10.9594i 0.0749156 0.363299i
\(911\) −5.60263 −0.185623 −0.0928117 0.995684i \(-0.529585\pi\)
−0.0928117 + 0.995684i \(0.529585\pi\)
\(912\) −17.6822 + 16.7175i −0.585515 + 0.553571i
\(913\) −14.3180 −0.473858
\(914\) −3.22675 + 15.6479i −0.106731 + 0.517588i
\(915\) −21.1020 −0.697611
\(916\) −4.75804 2.04945i −0.157210 0.0677157i
\(917\) 2.22305 0.0734117
\(918\) −1.68962 + 8.19372i −0.0557658 + 0.270433i
\(919\) 29.5139 0.973572 0.486786 0.873521i \(-0.338169\pi\)
0.486786 + 0.873521i \(0.338169\pi\)
\(920\) −27.5768 0.362066i −0.909181 0.0119370i
\(921\) −2.20932 −0.0727997
\(922\) −2.21003 + 10.7174i −0.0727833 + 0.352959i
\(923\) −15.4603 −0.508881
\(924\) 1.82236 4.23082i 0.0599512 0.139184i
\(925\) 9.62717 0.316539
\(926\) 4.51450 21.8929i 0.148356 0.719444i
\(927\) 3.05695 0.100403
\(928\) −44.7675 + 27.6944i −1.46956 + 0.909112i
\(929\) −59.0986 −1.93896 −0.969481 0.245165i \(-0.921158\pi\)
−0.969481 + 0.245165i \(0.921158\pi\)
\(930\) 2.06537 10.0159i 0.0677262 0.328435i
\(931\) 33.5313i 1.09894i
\(932\) −40.6472 17.5081i −1.33144 0.573498i
\(933\) 18.3744i 0.601550i
\(934\) 9.28935 45.0482i 0.303957 1.47402i
\(935\) 22.7100 0.742695
\(936\) −5.16975 + 7.39559i −0.168979 + 0.241733i
\(937\) 13.5151i 0.441518i 0.975328 + 0.220759i \(0.0708535\pi\)
−0.975328 + 0.220759i \(0.929147\pi\)
\(938\) 0.856645 4.15426i 0.0279704 0.135641i
\(939\) 14.6786i 0.479018i
\(940\) −18.0292 + 41.8568i −0.588046 + 1.36522i
\(941\) 13.6282 0.444267 0.222133 0.975016i \(-0.428698\pi\)
0.222133 + 0.975016i \(0.428698\pi\)
\(942\) 8.00851 + 1.65143i 0.260931 + 0.0538064i
\(943\) 10.0116 6.80454i 0.326023 0.221586i
\(944\) 1.80781 + 1.91213i 0.0588391 + 0.0622345i
\(945\) 2.48021 0.0806814
\(946\) 30.5013 + 6.28964i 0.991682 + 0.204494i
\(947\) 5.13751 0.166947 0.0834733 0.996510i \(-0.473399\pi\)
0.0834733 + 0.996510i \(0.473399\pi\)
\(948\) −7.77228 3.34778i −0.252432 0.108731i
\(949\) 25.1120i 0.815169i
\(950\) 1.50511 7.29894i 0.0488322 0.236809i
\(951\) 1.06596i 0.0345663i
\(952\) 11.6942 16.7292i 0.379012 0.542196i
\(953\) 20.0968i 0.651000i 0.945542 + 0.325500i \(0.105533\pi\)
−0.945542 + 0.325500i \(0.894467\pi\)
\(954\) 15.3303 + 3.16124i 0.496337 + 0.102349i
\(955\) 8.54884 0.276634
\(956\) −16.2658 + 37.7631i −0.526075 + 1.22135i
\(957\) −17.5706 −0.567976
\(958\) −22.4517 4.62974i −0.725381 0.149580i
\(959\) 0.269275i 0.00869535i
\(960\) 5.58719 + 15.2756i 0.180326 + 0.493018i
\(961\) 18.3500 0.591935
\(962\) 10.1266 49.1085i 0.326495 1.58332i
\(963\) 4.21095i 0.135696i
\(964\) 10.6812 24.7977i 0.344018 0.798680i
\(965\) 12.8113 0.412410
\(966\) −7.64101 + 3.17297i −0.245845 + 0.102089i
\(967\) 4.12341i 0.132600i 0.997800 + 0.0663000i \(0.0211194\pi\)
−0.997800 + 0.0663000i \(0.978881\pi\)
\(968\) −17.2356 12.0482i −0.553972 0.387244i
\(969\) −35.9881 −1.15610
\(970\) 1.76346 8.55181i 0.0566213 0.274582i
\(971\) 29.8517i 0.957987i 0.877818 + 0.478993i \(0.158998\pi\)
−0.877818 + 0.478993i \(0.841002\pi\)
\(972\) −1.83685 0.791193i −0.0589170 0.0253775i
\(973\) 26.8164 0.859693
\(974\) 4.42674 21.4672i 0.141842 0.687855i
\(975\) 2.76351i 0.0885033i
\(976\) −28.5215 30.1673i −0.912951 0.965633i
\(977\) 27.9916i 0.895531i −0.894151 0.447766i \(-0.852220\pi\)
0.894151 0.447766i \(-0.147780\pi\)
\(978\) −15.6347 3.22402i −0.499943 0.103093i
\(979\) 7.28802 0.232926
\(980\) 20.5848 + 8.86658i 0.657558 + 0.283232i
\(981\) −3.18091 −0.101559
\(982\) −35.0788 7.23357i −1.11941 0.230833i
\(983\) 23.2880 0.742773 0.371386 0.928478i \(-0.378882\pi\)
0.371386 + 0.928478i \(0.378882\pi\)
\(984\) −5.85134 4.09027i −0.186534 0.130393i
\(985\) 23.6031i 0.752058i
\(986\) −76.2488 15.7232i −2.42826 0.500728i
\(987\) 13.6722i 0.435189i
\(988\) −35.6489 15.3552i −1.13414 0.488514i
\(989\) −31.4416 46.2604i −0.999784 1.47100i
\(990\) −1.09645 + 5.31716i −0.0348473 + 0.168990i
\(991\) 20.0895i 0.638164i −0.947727 0.319082i \(-0.896626\pi\)
0.947727 0.319082i \(-0.103374\pi\)
\(992\) 17.1103 10.5849i 0.543252 0.336070i
\(993\) −11.3481 −0.360121
\(994\) −1.68846 + 8.18808i −0.0535546 + 0.259710i
\(995\) −17.5212 −0.555459
\(996\) 5.99973 13.9291i 0.190109 0.441360i
\(997\) 28.4733i 0.901758i 0.892585 + 0.450879i \(0.148889\pi\)
−0.892585 + 0.450879i \(0.851111\pi\)
\(998\) −1.41348 0.291471i −0.0447428 0.00922637i
\(999\) 11.1137 0.351623
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 552.2.n.b.91.1 24
4.3 odd 2 2208.2.n.b.367.7 24
8.3 odd 2 inner 552.2.n.b.91.4 yes 24
8.5 even 2 2208.2.n.b.367.17 24
23.22 odd 2 inner 552.2.n.b.91.2 yes 24
92.91 even 2 2208.2.n.b.367.18 24
184.45 odd 2 2208.2.n.b.367.8 24
184.91 even 2 inner 552.2.n.b.91.3 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
552.2.n.b.91.1 24 1.1 even 1 trivial
552.2.n.b.91.2 yes 24 23.22 odd 2 inner
552.2.n.b.91.3 yes 24 184.91 even 2 inner
552.2.n.b.91.4 yes 24 8.3 odd 2 inner
2208.2.n.b.367.7 24 4.3 odd 2
2208.2.n.b.367.8 24 184.45 odd 2
2208.2.n.b.367.17 24 8.5 even 2
2208.2.n.b.367.18 24 92.91 even 2