Properties

Label 414.2.j.a.89.4
Level $414$
Weight $2$
Character 414.89
Analytic conductor $3.306$
Analytic rank $0$
Dimension $80$
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] = [414,2,Mod(17,414)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(414, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("414.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 414.j (of order \(22\), degree \(10\), 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: \(3.30580664368\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(8\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 89.4
Character \(\chi\) \(=\) 414.89
Dual form 414.2.j.a.107.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.989821 + 0.142315i) q^{2} +(0.959493 - 0.281733i) q^{4} +(2.09328 - 2.41578i) q^{5} +(0.761188 + 1.18443i) q^{7} +(-0.909632 + 0.415415i) q^{8} +O(q^{10})\) \(q+(-0.989821 + 0.142315i) q^{2} +(0.959493 - 0.281733i) q^{4} +(2.09328 - 2.41578i) q^{5} +(0.761188 + 1.18443i) q^{7} +(-0.909632 + 0.415415i) q^{8} +(-1.72817 + 2.68909i) q^{10} +(0.611710 - 4.25454i) q^{11} +(1.51536 + 0.973861i) q^{13} +(-0.922002 - 1.06405i) q^{14} +(0.841254 - 0.540641i) q^{16} +(-1.94380 - 0.570751i) q^{17} +(-0.0167231 - 0.0569538i) q^{19} +(1.32789 - 2.90767i) q^{20} +4.29829i q^{22} +(-2.58260 + 4.04106i) q^{23} +(-0.742571 - 5.16469i) q^{25} +(-1.63853 - 0.748291i) q^{26} +(1.06405 + 0.922002i) q^{28} +(2.29954 - 7.83150i) q^{29} +(-1.82540 - 3.99706i) q^{31} +(-0.755750 + 0.654861i) q^{32} +(2.00524 + 0.288310i) q^{34} +(4.45470 + 0.640489i) q^{35} +(4.96044 - 4.29825i) q^{37} +(0.0246583 + 0.0539941i) q^{38} +(-0.900567 + 3.06705i) q^{40} +(8.47079 + 7.33998i) q^{41} +(6.53347 + 2.98374i) q^{43} +(-0.611710 - 4.25454i) q^{44} +(1.98121 - 4.36747i) q^{46} +0.223550i q^{47} +(2.08443 - 4.56427i) q^{49} +(1.47002 + 5.00645i) q^{50} +(1.72834 + 0.507487i) q^{52} +(1.93957 - 1.24649i) q^{53} +(-8.99753 - 10.3837i) q^{55} +(-1.18443 - 0.761188i) q^{56} +(-1.16159 + 8.07905i) q^{58} +(-6.13821 + 9.55124i) q^{59} +(1.45253 - 0.663348i) q^{61} +(2.37566 + 3.69659i) q^{62} +(0.654861 - 0.755750i) q^{64} +(5.52470 - 1.62220i) q^{65} +(0.815293 - 0.117221i) q^{67} -2.02586 q^{68} -4.50051 q^{70} +(-10.6755 + 1.53490i) q^{71} +(-11.1441 + 3.27221i) q^{73} +(-4.29825 + 4.96044i) q^{74} +(-0.0320915 - 0.0499353i) q^{76} +(5.50483 - 2.51397i) q^{77} +(-8.97046 + 13.9583i) q^{79} +(0.454914 - 3.16399i) q^{80} +(-9.42916 - 6.05975i) q^{82} +(-1.33209 - 1.53731i) q^{83} +(-5.44772 + 3.50104i) q^{85} +(-6.89160 - 2.02356i) q^{86} +(1.21097 + 4.12418i) q^{88} +(2.08277 - 4.56064i) q^{89} +2.53613i q^{91} +(-1.33949 + 4.60497i) q^{92} +(-0.0318145 - 0.221275i) q^{94} +(-0.172594 - 0.0788209i) q^{95} +(-7.36577 - 6.38247i) q^{97} +(-1.41365 + 4.81446i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q + 8 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 80 q + 8 q^{4} - 16 q^{13} - 8 q^{16} + 24 q^{25} - 16 q^{31} + 88 q^{37} + 88 q^{43} + 8 q^{46} + 8 q^{49} + 16 q^{52} - 32 q^{55} - 72 q^{58} - 176 q^{61} + 8 q^{64} - 88 q^{67} - 176 q^{70} - 56 q^{73} - 176 q^{79} - 88 q^{82} - 88 q^{85} + 16 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/414\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(235\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{22}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.989821 + 0.142315i −0.699909 + 0.100632i
\(3\) 0 0
\(4\) 0.959493 0.281733i 0.479746 0.140866i
\(5\) 2.09328 2.41578i 0.936144 1.08037i −0.0604719 0.998170i \(-0.519261\pi\)
0.996616 0.0821980i \(-0.0261940\pi\)
\(6\) 0 0
\(7\) 0.761188 + 1.18443i 0.287702 + 0.447673i 0.954779 0.297315i \(-0.0960913\pi\)
−0.667077 + 0.744988i \(0.732455\pi\)
\(8\) −0.909632 + 0.415415i −0.321603 + 0.146871i
\(9\) 0 0
\(10\) −1.72817 + 2.68909i −0.546497 + 0.850366i
\(11\) 0.611710 4.25454i 0.184438 1.28279i −0.661677 0.749789i \(-0.730155\pi\)
0.846114 0.533002i \(-0.178936\pi\)
\(12\) 0 0
\(13\) 1.51536 + 0.973861i 0.420285 + 0.270101i 0.733644 0.679534i \(-0.237818\pi\)
−0.313359 + 0.949635i \(0.601454\pi\)
\(14\) −0.922002 1.06405i −0.246415 0.284379i
\(15\) 0 0
\(16\) 0.841254 0.540641i 0.210313 0.135160i
\(17\) −1.94380 0.570751i −0.471440 0.138427i 0.0373782 0.999301i \(-0.488099\pi\)
−0.508818 + 0.860874i \(0.669918\pi\)
\(18\) 0 0
\(19\) −0.0167231 0.0569538i −0.00383655 0.0130661i 0.957552 0.288259i \(-0.0930764\pi\)
−0.961389 + 0.275193i \(0.911258\pi\)
\(20\) 1.32789 2.90767i 0.296924 0.650174i
\(21\) 0 0
\(22\) 4.29829i 0.916398i
\(23\) −2.58260 + 4.04106i −0.538510 + 0.842619i
\(24\) 0 0
\(25\) −0.742571 5.16469i −0.148514 1.03294i
\(26\) −1.63853 0.748291i −0.321342 0.146752i
\(27\) 0 0
\(28\) 1.06405 + 0.922002i 0.201086 + 0.174242i
\(29\) 2.29954 7.83150i 0.427013 1.45427i −0.412512 0.910952i \(-0.635348\pi\)
0.839525 0.543321i \(-0.182833\pi\)
\(30\) 0 0
\(31\) −1.82540 3.99706i −0.327851 0.717893i 0.671890 0.740651i \(-0.265483\pi\)
−0.999741 + 0.0227578i \(0.992755\pi\)
\(32\) −0.755750 + 0.654861i −0.133599 + 0.115764i
\(33\) 0 0
\(34\) 2.00524 + 0.288310i 0.343896 + 0.0494447i
\(35\) 4.45470 + 0.640489i 0.752982 + 0.108262i
\(36\) 0 0
\(37\) 4.96044 4.29825i 0.815491 0.706627i −0.143627 0.989632i \(-0.545877\pi\)
0.959119 + 0.283005i \(0.0913312\pi\)
\(38\) 0.0246583 + 0.0539941i 0.00400010 + 0.00875900i
\(39\) 0 0
\(40\) −0.900567 + 3.06705i −0.142392 + 0.484943i
\(41\) 8.47079 + 7.33998i 1.32292 + 1.14631i 0.978214 + 0.207600i \(0.0665653\pi\)
0.344701 + 0.938712i \(0.387980\pi\)
\(42\) 0 0
\(43\) 6.53347 + 2.98374i 0.996345 + 0.455016i 0.845750 0.533580i \(-0.179154\pi\)
0.150596 + 0.988595i \(0.451881\pi\)
\(44\) −0.611710 4.25454i −0.0922188 0.641396i
\(45\) 0 0
\(46\) 1.98121 4.36747i 0.292114 0.643948i
\(47\) 0.223550i 0.0326082i 0.999867 + 0.0163041i \(0.00518998\pi\)
−0.999867 + 0.0163041i \(0.994810\pi\)
\(48\) 0 0
\(49\) 2.08443 4.56427i 0.297776 0.652039i
\(50\) 1.47002 + 5.00645i 0.207893 + 0.708018i
\(51\) 0 0
\(52\) 1.72834 + 0.507487i 0.239678 + 0.0703759i
\(53\) 1.93957 1.24649i 0.266421 0.171218i −0.400609 0.916249i \(-0.631202\pi\)
0.667030 + 0.745031i \(0.267565\pi\)
\(54\) 0 0
\(55\) −8.99753 10.3837i −1.21323 1.40014i
\(56\) −1.18443 0.761188i −0.158276 0.101718i
\(57\) 0 0
\(58\) −1.16159 + 8.07905i −0.152524 + 1.06083i
\(59\) −6.13821 + 9.55124i −0.799127 + 1.24347i 0.167143 + 0.985933i \(0.446546\pi\)
−0.966269 + 0.257533i \(0.917090\pi\)
\(60\) 0 0
\(61\) 1.45253 0.663348i 0.185977 0.0849330i −0.320250 0.947333i \(-0.603767\pi\)
0.506227 + 0.862400i \(0.331040\pi\)
\(62\) 2.37566 + 3.69659i 0.301709 + 0.469468i
\(63\) 0 0
\(64\) 0.654861 0.755750i 0.0818576 0.0944687i
\(65\) 5.52470 1.62220i 0.685255 0.201209i
\(66\) 0 0
\(67\) 0.815293 0.117221i 0.0996039 0.0143209i −0.0923326 0.995728i \(-0.529432\pi\)
0.191937 + 0.981407i \(0.438523\pi\)
\(68\) −2.02586 −0.245672
\(69\) 0 0
\(70\) −4.50051 −0.537914
\(71\) −10.6755 + 1.53490i −1.26694 + 0.182159i −0.742825 0.669486i \(-0.766514\pi\)
−0.524119 + 0.851645i \(0.675605\pi\)
\(72\) 0 0
\(73\) −11.1441 + 3.27221i −1.30432 + 0.382984i −0.858811 0.512293i \(-0.828796\pi\)
−0.445512 + 0.895276i \(0.646978\pi\)
\(74\) −4.29825 + 4.96044i −0.499661 + 0.576639i
\(75\) 0 0
\(76\) −0.0320915 0.0499353i −0.00368114 0.00572797i
\(77\) 5.50483 2.51397i 0.627334 0.286494i
\(78\) 0 0
\(79\) −8.97046 + 13.9583i −1.00926 + 1.57043i −0.202729 + 0.979235i \(0.564981\pi\)
−0.806527 + 0.591198i \(0.798655\pi\)
\(80\) 0.454914 3.16399i 0.0508609 0.353745i
\(81\) 0 0
\(82\) −9.42916 6.05975i −1.04128 0.669188i
\(83\) −1.33209 1.53731i −0.146216 0.168742i 0.677917 0.735138i \(-0.262883\pi\)
−0.824133 + 0.566396i \(0.808337\pi\)
\(84\) 0 0
\(85\) −5.44772 + 3.50104i −0.590889 + 0.379741i
\(86\) −6.89160 2.02356i −0.743141 0.218206i
\(87\) 0 0
\(88\) 1.21097 + 4.12418i 0.129090 + 0.439639i
\(89\) 2.08277 4.56064i 0.220774 0.483427i −0.766543 0.642194i \(-0.778025\pi\)
0.987316 + 0.158767i \(0.0507518\pi\)
\(90\) 0 0
\(91\) 2.53613i 0.265859i
\(92\) −1.33949 + 4.60497i −0.139652 + 0.480101i
\(93\) 0 0
\(94\) −0.0318145 0.221275i −0.00328142 0.0228228i
\(95\) −0.172594 0.0788209i −0.0177077 0.00808686i
\(96\) 0 0
\(97\) −7.36577 6.38247i −0.747880 0.648042i 0.195141 0.980775i \(-0.437484\pi\)
−0.943021 + 0.332733i \(0.892029\pi\)
\(98\) −1.41365 + 4.81446i −0.142801 + 0.486334i
\(99\) 0 0
\(100\) −2.16755 4.74628i −0.216755 0.474628i
\(101\) −13.8249 + 11.9793i −1.37563 + 1.19199i −0.416458 + 0.909155i \(0.636729\pi\)
−0.959169 + 0.282833i \(0.908726\pi\)
\(102\) 0 0
\(103\) 15.8993 + 2.28598i 1.56661 + 0.225244i 0.870308 0.492508i \(-0.163920\pi\)
0.696299 + 0.717752i \(0.254829\pi\)
\(104\) −1.78297 0.256353i −0.174835 0.0251375i
\(105\) 0 0
\(106\) −1.74244 + 1.50983i −0.169240 + 0.146648i
\(107\) 2.43155 + 5.32435i 0.235067 + 0.514724i 0.989998 0.141079i \(-0.0450573\pi\)
−0.754932 + 0.655803i \(0.772330\pi\)
\(108\) 0 0
\(109\) 2.59644 8.84268i 0.248694 0.846975i −0.736632 0.676294i \(-0.763585\pi\)
0.985326 0.170681i \(-0.0545968\pi\)
\(110\) 10.3837 + 8.99753i 0.990047 + 0.857880i
\(111\) 0 0
\(112\) 1.28070 + 0.584878i 0.121015 + 0.0552658i
\(113\) 2.65406 + 18.4594i 0.249673 + 1.73652i 0.600100 + 0.799925i \(0.295128\pi\)
−0.350427 + 0.936590i \(0.613963\pi\)
\(114\) 0 0
\(115\) 4.35617 + 14.6981i 0.406215 + 1.37060i
\(116\) 8.16213i 0.757834i
\(117\) 0 0
\(118\) 4.71645 10.3276i 0.434184 0.950731i
\(119\) −0.803580 2.73674i −0.0736641 0.250877i
\(120\) 0 0
\(121\) −7.17247 2.10603i −0.652043 0.191457i
\(122\) −1.34334 + 0.863313i −0.121620 + 0.0781607i
\(123\) 0 0
\(124\) −2.87756 3.32088i −0.258412 0.298223i
\(125\) −0.585692 0.376402i −0.0523859 0.0336664i
\(126\) 0 0
\(127\) −1.95141 + 13.5723i −0.173160 + 1.20435i 0.698997 + 0.715124i \(0.253630\pi\)
−0.872157 + 0.489227i \(0.837279\pi\)
\(128\) −0.540641 + 0.841254i −0.0477863 + 0.0743570i
\(129\) 0 0
\(130\) −5.23761 + 2.39193i −0.459368 + 0.209787i
\(131\) 2.16064 + 3.36202i 0.188776 + 0.293741i 0.922722 0.385467i \(-0.125960\pi\)
−0.733946 + 0.679208i \(0.762323\pi\)
\(132\) 0 0
\(133\) 0.0547284 0.0631599i 0.00474555 0.00547666i
\(134\) −0.790312 + 0.232057i −0.0682726 + 0.0200466i
\(135\) 0 0
\(136\) 2.00524 0.288310i 0.171948 0.0247224i
\(137\) −12.1475 −1.03783 −0.518914 0.854826i \(-0.673664\pi\)
−0.518914 + 0.854826i \(0.673664\pi\)
\(138\) 0 0
\(139\) −2.48973 −0.211176 −0.105588 0.994410i \(-0.533672\pi\)
−0.105588 + 0.994410i \(0.533672\pi\)
\(140\) 4.45470 0.640489i 0.376491 0.0541312i
\(141\) 0 0
\(142\) 10.3484 3.03855i 0.868415 0.254990i
\(143\) 5.07029 5.85142i 0.423999 0.489321i
\(144\) 0 0
\(145\) −14.1056 21.9487i −1.17140 1.82274i
\(146\) 10.5650 4.82488i 0.874367 0.399310i
\(147\) 0 0
\(148\) 3.54855 5.52165i 0.291689 0.453877i
\(149\) 1.13993 7.92840i 0.0933869 0.649520i −0.888335 0.459197i \(-0.848137\pi\)
0.981721 0.190323i \(-0.0609536\pi\)
\(150\) 0 0
\(151\) 19.1288 + 12.2933i 1.55668 + 1.00042i 0.983483 + 0.181000i \(0.0579333\pi\)
0.573197 + 0.819418i \(0.305703\pi\)
\(152\) 0.0388713 + 0.0448599i 0.00315288 + 0.00363862i
\(153\) 0 0
\(154\) −5.09103 + 3.27180i −0.410247 + 0.263649i
\(155\) −13.4771 3.95722i −1.08250 0.317852i
\(156\) 0 0
\(157\) 5.11443 + 17.4182i 0.408176 + 1.39012i 0.865540 + 0.500840i \(0.166976\pi\)
−0.457364 + 0.889280i \(0.651206\pi\)
\(158\) 6.89268 15.0929i 0.548352 1.20072i
\(159\) 0 0
\(160\) 3.19653i 0.252708i
\(161\) −6.75220 + 0.0170872i −0.532148 + 0.00134666i
\(162\) 0 0
\(163\) 0.147917 + 1.02879i 0.0115858 + 0.0805809i 0.994794 0.101906i \(-0.0324942\pi\)
−0.983208 + 0.182487i \(0.941585\pi\)
\(164\) 10.1956 + 4.65616i 0.796141 + 0.363585i
\(165\) 0 0
\(166\) 1.53731 + 1.33209i 0.119319 + 0.103390i
\(167\) 2.09591 7.13801i 0.162186 0.552356i −0.837793 0.545987i \(-0.816155\pi\)
0.999980 0.00636857i \(-0.00202719\pi\)
\(168\) 0 0
\(169\) −4.05249 8.87372i −0.311730 0.682594i
\(170\) 4.89402 4.24070i 0.375354 0.325246i
\(171\) 0 0
\(172\) 7.10944 + 1.02218i 0.542090 + 0.0779407i
\(173\) 15.1180 + 2.17365i 1.14940 + 0.165259i 0.690572 0.723264i \(-0.257359\pi\)
0.458832 + 0.888523i \(0.348268\pi\)
\(174\) 0 0
\(175\) 5.55199 4.81083i 0.419691 0.363664i
\(176\) −1.78557 3.90986i −0.134593 0.294717i
\(177\) 0 0
\(178\) −1.41253 + 4.81063i −0.105873 + 0.360572i
\(179\) −13.2117 11.4480i −0.987489 0.855665i 0.00203963 0.999998i \(-0.499351\pi\)
−0.989529 + 0.144333i \(0.953896\pi\)
\(180\) 0 0
\(181\) −9.74629 4.45098i −0.724436 0.330839i 0.0188413 0.999822i \(-0.494002\pi\)
−0.743277 + 0.668984i \(0.766730\pi\)
\(182\) −0.360929 2.51031i −0.0267538 0.186077i
\(183\) 0 0
\(184\) 0.670503 4.74873i 0.0494301 0.350081i
\(185\) 20.9808i 1.54254i
\(186\) 0 0
\(187\) −3.61732 + 7.92083i −0.264525 + 0.579228i
\(188\) 0.0629814 + 0.214495i 0.00459339 + 0.0156437i
\(189\) 0 0
\(190\) 0.182054 + 0.0534560i 0.0132076 + 0.00387811i
\(191\) −13.4931 + 8.67148i −0.976325 + 0.627446i −0.928470 0.371408i \(-0.878875\pi\)
−0.0478555 + 0.998854i \(0.515239\pi\)
\(192\) 0 0
\(193\) 0.166139 + 0.191734i 0.0119589 + 0.0138014i 0.761698 0.647933i \(-0.224366\pi\)
−0.749739 + 0.661734i \(0.769821\pi\)
\(194\) 8.19911 + 5.26925i 0.588662 + 0.378310i
\(195\) 0 0
\(196\) 0.714095 4.96664i 0.0510068 0.354760i
\(197\) −3.12738 + 4.86629i −0.222816 + 0.346709i −0.934607 0.355683i \(-0.884248\pi\)
0.711790 + 0.702392i \(0.247885\pi\)
\(198\) 0 0
\(199\) −5.88139 + 2.68594i −0.416920 + 0.190401i −0.612820 0.790223i \(-0.709965\pi\)
0.195899 + 0.980624i \(0.437237\pi\)
\(200\) 2.82096 + 4.38950i 0.199472 + 0.310384i
\(201\) 0 0
\(202\) 11.9793 13.8249i 0.842863 0.972716i
\(203\) 11.0263 3.23760i 0.773891 0.227235i
\(204\) 0 0
\(205\) 35.4635 5.09888i 2.47688 0.356121i
\(206\) −16.0628 −1.11915
\(207\) 0 0
\(208\) 1.80131 0.124898
\(209\) −0.252542 + 0.0363100i −0.0174687 + 0.00251162i
\(210\) 0 0
\(211\) 7.31641 2.14829i 0.503682 0.147894i −0.0200138 0.999800i \(-0.506371\pi\)
0.523696 + 0.851905i \(0.324553\pi\)
\(212\) 1.50983 1.74244i 0.103695 0.119671i
\(213\) 0 0
\(214\) −3.16453 4.92411i −0.216323 0.336605i
\(215\) 20.8844 9.53761i 1.42431 0.650459i
\(216\) 0 0
\(217\) 3.34477 5.20457i 0.227058 0.353309i
\(218\) −1.31157 + 9.12218i −0.0888308 + 0.617832i
\(219\) 0 0
\(220\) −11.5585 7.42819i −0.779273 0.500808i
\(221\) −2.38972 2.75788i −0.160750 0.185515i
\(222\) 0 0
\(223\) −13.1618 + 8.45854i −0.881376 + 0.566426i −0.901213 0.433377i \(-0.857322\pi\)
0.0198366 + 0.999803i \(0.493685\pi\)
\(224\) −1.35090 0.396661i −0.0902611 0.0265031i
\(225\) 0 0
\(226\) −5.25410 17.8938i −0.349497 1.19028i
\(227\) 3.24522 7.10604i 0.215393 0.471644i −0.770835 0.637034i \(-0.780161\pi\)
0.986228 + 0.165390i \(0.0528882\pi\)
\(228\) 0 0
\(229\) 16.8692i 1.11475i 0.830261 + 0.557375i \(0.188191\pi\)
−0.830261 + 0.557375i \(0.811809\pi\)
\(230\) −6.40359 13.9285i −0.422240 0.918419i
\(231\) 0 0
\(232\) 1.16159 + 8.07905i 0.0762622 + 0.530415i
\(233\) 18.7234 + 8.55067i 1.22661 + 0.560173i 0.920096 0.391694i \(-0.128111\pi\)
0.306512 + 0.951867i \(0.400838\pi\)
\(234\) 0 0
\(235\) 0.540048 + 0.467954i 0.0352288 + 0.0305260i
\(236\) −3.19867 + 10.8937i −0.208216 + 0.709118i
\(237\) 0 0
\(238\) 1.18488 + 2.59453i 0.0768044 + 0.168178i
\(239\) 3.92058 3.39720i 0.253601 0.219747i −0.518777 0.854910i \(-0.673612\pi\)
0.772378 + 0.635163i \(0.219067\pi\)
\(240\) 0 0
\(241\) 12.3414 + 1.77442i 0.794978 + 0.114301i 0.527824 0.849353i \(-0.323008\pi\)
0.267153 + 0.963654i \(0.413917\pi\)
\(242\) 7.39918 + 1.06384i 0.475637 + 0.0683863i
\(243\) 0 0
\(244\) 1.20681 1.04570i 0.0772578 0.0669443i
\(245\) −6.66296 14.5898i −0.425681 0.932111i
\(246\) 0 0
\(247\) 0.0301235 0.102591i 0.00191671 0.00652773i
\(248\) 3.32088 + 2.87756i 0.210876 + 0.182725i
\(249\) 0 0
\(250\) 0.633298 + 0.289218i 0.0400533 + 0.0182917i
\(251\) 1.82978 + 12.7264i 0.115495 + 0.803284i 0.962419 + 0.271570i \(0.0875427\pi\)
−0.846924 + 0.531714i \(0.821548\pi\)
\(252\) 0 0
\(253\) 15.6130 + 13.4597i 0.981583 + 0.846207i
\(254\) 13.7119i 0.860362i
\(255\) 0 0
\(256\) 0.415415 0.909632i 0.0259634 0.0568520i
\(257\) 3.30430 + 11.2534i 0.206117 + 0.701969i 0.996051 + 0.0887779i \(0.0282961\pi\)
−0.789935 + 0.613191i \(0.789886\pi\)
\(258\) 0 0
\(259\) 8.86680 + 2.60353i 0.550956 + 0.161775i
\(260\) 4.84389 3.11298i 0.300405 0.193059i
\(261\) 0 0
\(262\) −2.61711 3.02031i −0.161686 0.186595i
\(263\) −12.6567 8.13394i −0.780443 0.501560i 0.0887378 0.996055i \(-0.471717\pi\)
−0.869180 + 0.494495i \(0.835353\pi\)
\(264\) 0 0
\(265\) 1.04884 7.29482i 0.0644295 0.448117i
\(266\) −0.0451827 + 0.0703057i −0.00277033 + 0.00431072i
\(267\) 0 0
\(268\) 0.749243 0.342168i 0.0457673 0.0209012i
\(269\) −6.94788 10.8111i −0.423619 0.659165i 0.562195 0.827005i \(-0.309957\pi\)
−0.985814 + 0.167840i \(0.946321\pi\)
\(270\) 0 0
\(271\) 11.5309 13.3073i 0.700450 0.808362i −0.288363 0.957521i \(-0.593111\pi\)
0.988813 + 0.149159i \(0.0476566\pi\)
\(272\) −1.94380 + 0.570751i −0.117860 + 0.0346068i
\(273\) 0 0
\(274\) 12.0238 1.72877i 0.726386 0.104439i
\(275\) −22.4276 −1.35244
\(276\) 0 0
\(277\) −11.3655 −0.682885 −0.341442 0.939903i \(-0.610915\pi\)
−0.341442 + 0.939903i \(0.610915\pi\)
\(278\) 2.46439 0.354325i 0.147804 0.0212510i
\(279\) 0 0
\(280\) −4.31821 + 1.26794i −0.258062 + 0.0757739i
\(281\) 13.5937 15.6880i 0.810933 0.935866i −0.187995 0.982170i \(-0.560199\pi\)
0.998927 + 0.0463039i \(0.0147443\pi\)
\(282\) 0 0
\(283\) 2.62562 + 4.08554i 0.156077 + 0.242860i 0.910482 0.413549i \(-0.135711\pi\)
−0.754405 + 0.656409i \(0.772075\pi\)
\(284\) −9.81060 + 4.48035i −0.582152 + 0.265860i
\(285\) 0 0
\(286\) −4.18594 + 6.51344i −0.247520 + 0.385148i
\(287\) −2.24584 + 15.6202i −0.132568 + 0.922030i
\(288\) 0 0
\(289\) −10.8487 6.97205i −0.638160 0.410120i
\(290\) 17.0856 + 19.7179i 1.00330 + 1.15787i
\(291\) 0 0
\(292\) −9.77083 + 6.27933i −0.571795 + 0.367470i
\(293\) 22.1230 + 6.49589i 1.29244 + 0.379494i 0.854472 0.519497i \(-0.173881\pi\)
0.437966 + 0.898991i \(0.355699\pi\)
\(294\) 0 0
\(295\) 10.2247 + 34.8220i 0.595303 + 2.02741i
\(296\) −2.72662 + 5.97046i −0.158482 + 0.347026i
\(297\) 0 0
\(298\) 8.00993i 0.464003i
\(299\) −7.84900 + 3.60855i −0.453919 + 0.208688i
\(300\) 0 0
\(301\) 1.43917 + 10.0096i 0.0829523 + 0.576946i
\(302\) −20.6836 9.44589i −1.19021 0.543550i
\(303\) 0 0
\(304\) −0.0448599 0.0388713i −0.00257289 0.00222942i
\(305\) 1.43805 4.89756i 0.0823427 0.280434i
\(306\) 0 0
\(307\) −11.8942 26.0448i −0.678841 1.48645i −0.863867 0.503720i \(-0.831964\pi\)
0.185026 0.982734i \(-0.440763\pi\)
\(308\) 4.57358 3.96303i 0.260604 0.225815i
\(309\) 0 0
\(310\) 13.9031 + 1.99896i 0.789641 + 0.113533i
\(311\) −22.8758 3.28905i −1.29717 0.186505i −0.541079 0.840972i \(-0.681984\pi\)
−0.756090 + 0.654467i \(0.772893\pi\)
\(312\) 0 0
\(313\) −9.41020 + 8.15399i −0.531896 + 0.460891i −0.878922 0.476965i \(-0.841737\pi\)
0.347026 + 0.937855i \(0.387191\pi\)
\(314\) −7.54124 16.5130i −0.425577 0.931883i
\(315\) 0 0
\(316\) −4.67458 + 15.9202i −0.262966 + 0.895580i
\(317\) −12.0880 10.4743i −0.678928 0.588295i 0.245617 0.969367i \(-0.421009\pi\)
−0.924545 + 0.381072i \(0.875555\pi\)
\(318\) 0 0
\(319\) −31.9128 14.5741i −1.78677 0.815991i
\(320\) −0.454914 3.16399i −0.0254304 0.176873i
\(321\) 0 0
\(322\) 6.68104 0.977852i 0.372320 0.0544936i
\(323\) 0.120251i 0.00669096i
\(324\) 0 0
\(325\) 3.90443 8.54952i 0.216579 0.474242i
\(326\) −0.292824 0.997266i −0.0162180 0.0552334i
\(327\) 0 0
\(328\) −10.7544 3.15779i −0.593815 0.174360i
\(329\) −0.264780 + 0.170164i −0.0145978 + 0.00938144i
\(330\) 0 0
\(331\) −11.3271 13.0722i −0.622595 0.718513i 0.353602 0.935396i \(-0.384957\pi\)
−0.976198 + 0.216883i \(0.930411\pi\)
\(332\) −1.71124 1.09975i −0.0939166 0.0603565i
\(333\) 0 0
\(334\) −1.05873 + 7.36364i −0.0579312 + 0.402920i
\(335\) 1.42346 2.21494i 0.0777718 0.121015i
\(336\) 0 0
\(337\) −22.9693 + 10.4897i −1.25122 + 0.571412i −0.927174 0.374631i \(-0.877770\pi\)
−0.324043 + 0.946042i \(0.605042\pi\)
\(338\) 5.27410 + 8.20667i 0.286873 + 0.446384i
\(339\) 0 0
\(340\) −4.24070 + 4.89402i −0.229984 + 0.265416i
\(341\) −18.1222 + 5.32117i −0.981375 + 0.288158i
\(342\) 0 0
\(343\) 16.7480 2.40799i 0.904305 0.130019i
\(344\) −7.18255 −0.387257
\(345\) 0 0
\(346\) −15.2735 −0.821109
\(347\) −14.1623 + 2.03623i −0.760270 + 0.109310i −0.511536 0.859262i \(-0.670923\pi\)
−0.248734 + 0.968572i \(0.580014\pi\)
\(348\) 0 0
\(349\) −21.2707 + 6.24564i −1.13859 + 0.334322i −0.796080 0.605191i \(-0.793097\pi\)
−0.342514 + 0.939513i \(0.611279\pi\)
\(350\) −4.81083 + 5.55199i −0.257149 + 0.296766i
\(351\) 0 0
\(352\) 2.32383 + 3.61595i 0.123861 + 0.192731i
\(353\) 31.5609 14.4134i 1.67982 0.767148i 0.680409 0.732833i \(-0.261802\pi\)
0.999411 0.0343149i \(-0.0109249\pi\)
\(354\) 0 0
\(355\) −18.6388 + 29.0025i −0.989243 + 1.53929i
\(356\) 0.713527 4.96269i 0.0378168 0.263022i
\(357\) 0 0
\(358\) 14.7065 + 9.45126i 0.777260 + 0.499515i
\(359\) 24.7144 + 28.5219i 1.30438 + 1.50533i 0.720401 + 0.693558i \(0.243958\pi\)
0.583974 + 0.811772i \(0.301497\pi\)
\(360\) 0 0
\(361\) 15.9809 10.2703i 0.841098 0.540541i
\(362\) 10.2805 + 3.01863i 0.540332 + 0.158656i
\(363\) 0 0
\(364\) 0.714510 + 2.43340i 0.0374505 + 0.127545i
\(365\) −15.4229 + 33.7714i −0.807271 + 1.76768i
\(366\) 0 0
\(367\) 35.0108i 1.82755i −0.406220 0.913775i \(-0.633153\pi\)
0.406220 0.913775i \(-0.366847\pi\)
\(368\) 0.0121363 + 4.79582i 0.000632649 + 0.249999i
\(369\) 0 0
\(370\) 2.98587 + 20.7672i 0.155228 + 1.07964i
\(371\) 2.95276 + 1.34848i 0.153299 + 0.0700095i
\(372\) 0 0
\(373\) 21.4255 + 18.5653i 1.10937 + 0.961273i 0.999466 0.0326696i \(-0.0104009\pi\)
0.109902 + 0.993942i \(0.464946\pi\)
\(374\) 2.45325 8.35500i 0.126855 0.432027i
\(375\) 0 0
\(376\) −0.0928662 0.203349i −0.00478921 0.0104869i
\(377\) 11.1114 9.62810i 0.572267 0.495872i
\(378\) 0 0
\(379\) −32.4797 4.66987i −1.66837 0.239875i −0.757578 0.652745i \(-0.773618\pi\)
−0.910790 + 0.412869i \(0.864527\pi\)
\(380\) −0.187809 0.0270028i −0.00963440 0.00138522i
\(381\) 0 0
\(382\) 12.1217 10.5035i 0.620198 0.537405i
\(383\) 13.7459 + 30.0992i 0.702381 + 1.53800i 0.837061 + 0.547110i \(0.184272\pi\)
−0.134680 + 0.990889i \(0.543001\pi\)
\(384\) 0 0
\(385\) 5.44997 18.5609i 0.277756 0.945951i
\(386\) −0.191734 0.166139i −0.00975903 0.00845625i
\(387\) 0 0
\(388\) −8.86555 4.04876i −0.450080 0.205545i
\(389\) 3.24429 + 22.5645i 0.164492 + 1.14407i 0.890036 + 0.455891i \(0.150679\pi\)
−0.725544 + 0.688176i \(0.758412\pi\)
\(390\) 0 0
\(391\) 7.32650 6.38098i 0.370517 0.322700i
\(392\) 5.01772i 0.253433i
\(393\) 0 0
\(394\) 2.40300 5.26183i 0.121061 0.265087i
\(395\) 14.9424 + 50.8893i 0.751836 + 2.56052i
\(396\) 0 0
\(397\) −8.48991 2.49286i −0.426096 0.125113i 0.0616515 0.998098i \(-0.480363\pi\)
−0.487748 + 0.872985i \(0.662181\pi\)
\(398\) 5.43927 3.49561i 0.272646 0.175219i
\(399\) 0 0
\(400\) −3.41693 3.94335i −0.170847 0.197168i
\(401\) −3.83342 2.46359i −0.191432 0.123026i 0.441414 0.897304i \(-0.354477\pi\)
−0.632846 + 0.774278i \(0.718113\pi\)
\(402\) 0 0
\(403\) 1.12645 7.83466i 0.0561126 0.390272i
\(404\) −9.88991 + 15.3890i −0.492042 + 0.765632i
\(405\) 0 0
\(406\) −10.4533 + 4.77385i −0.518787 + 0.236922i
\(407\) −15.2527 23.7337i −0.756048 1.17643i
\(408\) 0 0
\(409\) 24.2597 27.9972i 1.19957 1.38437i 0.296411 0.955061i \(-0.404210\pi\)
0.903156 0.429313i \(-0.141244\pi\)
\(410\) −34.3769 + 10.0940i −1.69775 + 0.498505i
\(411\) 0 0
\(412\) 15.8993 2.28598i 0.783304 0.112622i
\(413\) −15.9851 −0.786576
\(414\) 0 0
\(415\) −6.50224 −0.319183
\(416\) −1.78297 + 0.256353i −0.0874175 + 0.0125687i
\(417\) 0 0
\(418\) 0.244804 0.0718808i 0.0119737 0.00351581i
\(419\) 13.7628 15.8831i 0.672356 0.775940i −0.312387 0.949955i \(-0.601129\pi\)
0.984743 + 0.174015i \(0.0556741\pi\)
\(420\) 0 0
\(421\) −7.17175 11.1595i −0.349530 0.543879i 0.621323 0.783554i \(-0.286595\pi\)
−0.970853 + 0.239675i \(0.922959\pi\)
\(422\) −6.93620 + 3.16766i −0.337649 + 0.154199i
\(423\) 0 0
\(424\) −1.24649 + 1.93957i −0.0605348 + 0.0941939i
\(425\) −1.50434 + 10.4629i −0.0729714 + 0.507527i
\(426\) 0 0
\(427\) 1.89134 + 1.21549i 0.0915283 + 0.0588217i
\(428\) 3.83310 + 4.42363i 0.185280 + 0.213824i
\(429\) 0 0
\(430\) −19.3145 + 12.4127i −0.931429 + 0.598593i
\(431\) −4.14925 1.21833i −0.199862 0.0586849i 0.180269 0.983617i \(-0.442303\pi\)
−0.380132 + 0.924932i \(0.624121\pi\)
\(432\) 0 0
\(433\) −1.92680 6.56206i −0.0925959 0.315353i 0.900151 0.435579i \(-0.143456\pi\)
−0.992747 + 0.120226i \(0.961638\pi\)
\(434\) −2.57004 + 5.62760i −0.123366 + 0.270134i
\(435\) 0 0
\(436\) 9.21599i 0.441366i
\(437\) 0.273343 + 0.0795099i 0.0130758 + 0.00380347i
\(438\) 0 0
\(439\) 0.650721 + 4.52587i 0.0310572 + 0.216008i 0.999440 0.0334612i \(-0.0106530\pi\)
−0.968383 + 0.249469i \(0.919744\pi\)
\(440\) 12.4980 + 5.70764i 0.595818 + 0.272101i
\(441\) 0 0
\(442\) 2.75788 + 2.38972i 0.131179 + 0.113667i
\(443\) −2.05792 + 7.00865i −0.0977749 + 0.332991i −0.993825 0.110963i \(-0.964606\pi\)
0.896050 + 0.443954i \(0.146425\pi\)
\(444\) 0 0
\(445\) −6.65765 14.5782i −0.315603 0.691074i
\(446\) 11.8240 10.2456i 0.559883 0.485141i
\(447\) 0 0
\(448\) 1.39361 + 0.200370i 0.0658417 + 0.00946660i
\(449\) 12.2372 + 1.75944i 0.577507 + 0.0830330i 0.424878 0.905251i \(-0.360317\pi\)
0.152629 + 0.988284i \(0.451226\pi\)
\(450\) 0 0
\(451\) 36.4099 31.5493i 1.71447 1.48560i
\(452\) 7.74717 + 16.9639i 0.364396 + 0.797917i
\(453\) 0 0
\(454\) −2.20089 + 7.49555i −0.103293 + 0.351784i
\(455\) 6.12672 + 5.30883i 0.287225 + 0.248882i
\(456\) 0 0
\(457\) −24.2784 11.0876i −1.13570 0.518655i −0.243319 0.969946i \(-0.578236\pi\)
−0.892377 + 0.451292i \(0.850963\pi\)
\(458\) −2.40074 16.6975i −0.112179 0.780224i
\(459\) 0 0
\(460\) 8.32064 + 12.8754i 0.387952 + 0.600319i
\(461\) 14.4388i 0.672482i 0.941776 + 0.336241i \(0.109156\pi\)
−0.941776 + 0.336241i \(0.890844\pi\)
\(462\) 0 0
\(463\) −2.27802 + 4.98817i −0.105869 + 0.231820i −0.955151 0.296119i \(-0.904308\pi\)
0.849283 + 0.527939i \(0.177035\pi\)
\(464\) −2.29954 7.83150i −0.106753 0.363568i
\(465\) 0 0
\(466\) −19.7497 5.79902i −0.914885 0.268635i
\(467\) 20.0609 12.8923i 0.928306 0.596586i 0.0132500 0.999912i \(-0.495782\pi\)
0.915056 + 0.403326i \(0.132146\pi\)
\(468\) 0 0
\(469\) 0.759432 + 0.876431i 0.0350673 + 0.0404698i
\(470\) −0.601148 0.386334i −0.0277289 0.0178203i
\(471\) 0 0
\(472\) 1.61578 11.2380i 0.0743725 0.517272i
\(473\) 16.6910 25.9717i 0.767454 1.19418i
\(474\) 0 0
\(475\) −0.281731 + 0.128662i −0.0129267 + 0.00590342i
\(476\) −1.54206 2.39949i −0.0706802 0.109981i
\(477\) 0 0
\(478\) −3.39720 + 3.92058i −0.155384 + 0.179323i
\(479\) 2.69705 0.791926i 0.123231 0.0361840i −0.219535 0.975605i \(-0.570454\pi\)
0.342767 + 0.939421i \(0.388636\pi\)
\(480\) 0 0
\(481\) 11.7027 1.68260i 0.533599 0.0767199i
\(482\) −12.4683 −0.567915
\(483\) 0 0
\(484\) −7.47527 −0.339785
\(485\) −30.8373 + 4.43373i −1.40025 + 0.201325i
\(486\) 0 0
\(487\) 2.89310 0.849491i 0.131099 0.0384941i −0.215525 0.976498i \(-0.569146\pi\)
0.346624 + 0.938004i \(0.387328\pi\)
\(488\) −1.04570 + 1.20681i −0.0473368 + 0.0546295i
\(489\) 0 0
\(490\) 8.67149 + 13.4931i 0.391738 + 0.609556i
\(491\) 11.2077 5.11839i 0.505797 0.230990i −0.146139 0.989264i \(-0.546685\pi\)
0.651935 + 0.758274i \(0.273957\pi\)
\(492\) 0 0
\(493\) −8.93967 + 13.9104i −0.402622 + 0.626493i
\(494\) −0.0152167 + 0.105834i −0.000684630 + 0.00476170i
\(495\) 0 0
\(496\) −3.69659 2.37566i −0.165982 0.106670i
\(497\) −9.94401 11.4760i −0.446050 0.514769i
\(498\) 0 0
\(499\) 5.68259 3.65198i 0.254388 0.163485i −0.407232 0.913325i \(-0.633506\pi\)
0.661619 + 0.749840i \(0.269869\pi\)
\(500\) −0.668012 0.196146i −0.0298744 0.00877192i
\(501\) 0 0
\(502\) −3.62231 12.3365i −0.161672 0.550603i
\(503\) 7.64114 16.7318i 0.340702 0.746032i −0.659281 0.751896i \(-0.729139\pi\)
0.999983 + 0.00586407i \(0.00186660\pi\)
\(504\) 0 0
\(505\) 58.4739i 2.60206i
\(506\) −17.3696 11.1008i −0.772174 0.493490i
\(507\) 0 0
\(508\) 1.95141 + 13.5723i 0.0865798 + 0.602176i
\(509\) 21.4168 + 9.78073i 0.949283 + 0.433523i 0.829020 0.559219i \(-0.188899\pi\)
0.120263 + 0.992742i \(0.461626\pi\)
\(510\) 0 0
\(511\) −12.3585 10.7087i −0.546708 0.473725i
\(512\) −0.281733 + 0.959493i −0.0124509 + 0.0424040i
\(513\) 0 0
\(514\) −4.87220 10.6686i −0.214903 0.470573i
\(515\) 38.8042 33.6240i 1.70992 1.48165i
\(516\) 0 0
\(517\) 0.951103 + 0.136748i 0.0418295 + 0.00601417i
\(518\) −9.14707 1.31515i −0.401899 0.0577844i
\(519\) 0 0
\(520\) −4.35156 + 3.77065i −0.190829 + 0.165354i
\(521\) −2.64240 5.78605i −0.115766 0.253492i 0.842876 0.538108i \(-0.180861\pi\)
−0.958641 + 0.284617i \(0.908134\pi\)
\(522\) 0 0
\(523\) −8.71575 + 29.6831i −0.381113 + 1.29795i 0.516166 + 0.856489i \(0.327359\pi\)
−0.897279 + 0.441464i \(0.854459\pi\)
\(524\) 3.02031 + 2.61711i 0.131943 + 0.114329i
\(525\) 0 0
\(526\) 13.6854 + 6.24992i 0.596712 + 0.272509i
\(527\) 1.26688 + 8.81132i 0.0551860 + 0.383827i
\(528\) 0 0
\(529\) −9.66031 20.8729i −0.420013 0.907518i
\(530\) 7.36983i 0.320125i
\(531\) 0 0
\(532\) 0.0347173 0.0760203i 0.00150519 0.00329590i
\(533\) 5.68815 + 19.3721i 0.246381 + 0.839098i
\(534\) 0 0
\(535\) 17.9523 + 5.27128i 0.776148 + 0.227898i
\(536\) −0.692921 + 0.445313i −0.0299296 + 0.0192346i
\(537\) 0 0
\(538\) 8.41574 + 9.71228i 0.362828 + 0.418726i
\(539\) −18.1438 11.6603i −0.781509 0.502245i
\(540\) 0 0
\(541\) −0.426802 + 2.96847i −0.0183496 + 0.127624i −0.996937 0.0782065i \(-0.975081\pi\)
0.978588 + 0.205831i \(0.0659897\pi\)
\(542\) −9.51966 + 14.8129i −0.408905 + 0.636268i
\(543\) 0 0
\(544\) 1.84279 0.841572i 0.0790088 0.0360821i
\(545\) −15.9268 24.7826i −0.682231 1.06157i
\(546\) 0 0
\(547\) 26.5853 30.6811i 1.13671 1.31183i 0.192942 0.981210i \(-0.438197\pi\)
0.943764 0.330619i \(-0.107258\pi\)
\(548\) −11.6554 + 3.42234i −0.497895 + 0.146195i
\(549\) 0 0
\(550\) 22.1993 3.19178i 0.946583 0.136098i
\(551\) −0.484489 −0.0206399
\(552\) 0 0
\(553\) −23.3609 −0.993405
\(554\) 11.2498 1.61747i 0.477957 0.0687199i
\(555\) 0 0
\(556\) −2.38888 + 0.701437i −0.101311 + 0.0297476i
\(557\) −1.97378 + 2.27786i −0.0836317 + 0.0965161i −0.796023 0.605266i \(-0.793067\pi\)
0.712391 + 0.701782i \(0.247612\pi\)
\(558\) 0 0
\(559\) 6.99480 + 10.8841i 0.295849 + 0.460350i
\(560\) 4.09381 1.86958i 0.172995 0.0790042i
\(561\) 0 0
\(562\) −11.2227 + 17.4629i −0.473402 + 0.736627i
\(563\) 3.67659 25.5712i 0.154950 1.07770i −0.752819 0.658228i \(-0.771306\pi\)
0.907769 0.419471i \(-0.137784\pi\)
\(564\) 0 0
\(565\) 50.1495 + 32.2291i 2.10981 + 1.35589i
\(566\) −3.18032 3.67029i −0.133679 0.154274i
\(567\) 0 0
\(568\) 9.07312 5.83094i 0.380700 0.244661i
\(569\) −19.6468 5.76881i −0.823635 0.241841i −0.157355 0.987542i \(-0.550297\pi\)
−0.666281 + 0.745701i \(0.732115\pi\)
\(570\) 0 0
\(571\) −1.81675 6.18727i −0.0760285 0.258929i 0.912704 0.408621i \(-0.133990\pi\)
−0.988733 + 0.149691i \(0.952172\pi\)
\(572\) 3.21637 7.04287i 0.134483 0.294477i
\(573\) 0 0
\(574\) 15.7808i 0.658678i
\(575\) 22.7886 + 10.3376i 0.950350 + 0.431107i
\(576\) 0 0
\(577\) 4.97047 + 34.5704i 0.206923 + 1.43918i 0.783119 + 0.621872i \(0.213628\pi\)
−0.576195 + 0.817312i \(0.695463\pi\)
\(578\) 11.7305 + 5.35715i 0.487925 + 0.222828i
\(579\) 0 0
\(580\) −19.7179 17.0856i −0.818740 0.709442i
\(581\) 0.806872 2.74795i 0.0334747 0.114004i
\(582\) 0 0
\(583\) −4.11677 9.01447i −0.170499 0.373341i
\(584\) 8.77774 7.60595i 0.363225 0.314737i
\(585\) 0 0
\(586\) −22.8223 3.28135i −0.942779 0.135551i
\(587\) −22.7888 3.27654i −0.940596 0.135237i −0.345073 0.938576i \(-0.612146\pi\)
−0.595523 + 0.803339i \(0.703055\pi\)
\(588\) 0 0
\(589\) −0.197121 + 0.170806i −0.00812224 + 0.00703796i
\(590\) −15.0763 33.0124i −0.620680 1.35910i
\(591\) 0 0
\(592\) 1.84918 6.29773i 0.0760009 0.258835i
\(593\) −2.05705 1.78245i −0.0844730 0.0731963i 0.611601 0.791167i \(-0.290526\pi\)
−0.696074 + 0.717970i \(0.745071\pi\)
\(594\) 0 0
\(595\) −8.29348 3.78751i −0.340000 0.155273i
\(596\) −1.13993 7.92840i −0.0466934 0.324760i
\(597\) 0 0
\(598\) 7.25556 4.68885i 0.296702 0.191741i
\(599\) 36.6970i 1.49940i −0.661777 0.749700i \(-0.730198\pi\)
0.661777 0.749700i \(-0.269802\pi\)
\(600\) 0 0
\(601\) 14.5841 31.9347i 0.594898 1.30264i −0.337539 0.941311i \(-0.609595\pi\)
0.932437 0.361333i \(-0.117678\pi\)
\(602\) −2.84904 9.70294i −0.116118 0.395462i
\(603\) 0 0
\(604\) 21.8174 + 6.40616i 0.887737 + 0.260663i
\(605\) −20.1017 + 12.9186i −0.817250 + 0.525215i
\(606\) 0 0
\(607\) −19.8048 22.8559i −0.803850 0.927693i 0.194736 0.980856i \(-0.437615\pi\)
−0.998586 + 0.0531631i \(0.983070\pi\)
\(608\) 0.0499353 + 0.0320915i 0.00202514 + 0.00130148i
\(609\) 0 0
\(610\) −0.726421 + 5.05237i −0.0294119 + 0.204564i
\(611\) −0.217707 + 0.338759i −0.00880749 + 0.0137047i
\(612\) 0 0
\(613\) −29.5388 + 13.4899i −1.19306 + 0.544852i −0.910144 0.414293i \(-0.864029\pi\)
−0.282916 + 0.959145i \(0.591302\pi\)
\(614\) 15.4797 + 24.0869i 0.624711 + 0.972070i
\(615\) 0 0
\(616\) −3.96303 + 4.57358i −0.159675 + 0.184275i
\(617\) −2.66921 + 0.783751i −0.107458 + 0.0315526i −0.335020 0.942211i \(-0.608743\pi\)
0.227561 + 0.973764i \(0.426925\pi\)
\(618\) 0 0
\(619\) −5.77427 + 0.830215i −0.232088 + 0.0333692i −0.257377 0.966311i \(-0.582858\pi\)
0.0252896 + 0.999680i \(0.491949\pi\)
\(620\) −14.0460 −0.564102
\(621\) 0 0
\(622\) 23.1111 0.926669
\(623\) 6.98715 1.00460i 0.279934 0.0402484i
\(624\) 0 0
\(625\) 22.8969 6.72314i 0.915876 0.268926i
\(626\) 8.15399 9.41020i 0.325899 0.376107i
\(627\) 0 0
\(628\) 9.81452 + 15.2717i 0.391642 + 0.609407i
\(629\) −12.0953 + 5.52375i −0.482272 + 0.220246i
\(630\) 0 0
\(631\) 13.8896 21.6126i 0.552936 0.860386i −0.446471 0.894798i \(-0.647320\pi\)
0.999408 + 0.0344123i \(0.0109559\pi\)
\(632\) 2.36133 16.4234i 0.0939285 0.653287i
\(633\) 0 0
\(634\) 13.4556 + 8.64738i 0.534390 + 0.343431i
\(635\) 28.7029 + 33.1249i 1.13904 + 1.31452i
\(636\) 0 0
\(637\) 7.60363 4.88656i 0.301267 0.193613i
\(638\) 33.6620 + 9.88407i 1.33269 + 0.391314i
\(639\) 0 0
\(640\) 0.900567 + 3.06705i 0.0355980 + 0.121236i
\(641\) −0.377769 + 0.827199i −0.0149210 + 0.0326724i −0.916946 0.399012i \(-0.869353\pi\)
0.902025 + 0.431684i \(0.142081\pi\)
\(642\) 0 0
\(643\) 22.8166i 0.899800i 0.893079 + 0.449900i \(0.148540\pi\)
−0.893079 + 0.449900i \(0.851460\pi\)
\(644\) −6.47388 + 1.91871i −0.255107 + 0.0756078i
\(645\) 0 0
\(646\) −0.0171136 0.119027i −0.000673324 0.00468307i
\(647\) −18.2807 8.34851i −0.718688 0.328214i 0.0222821 0.999752i \(-0.492907\pi\)
−0.740970 + 0.671538i \(0.765634\pi\)
\(648\) 0 0
\(649\) 36.8813 + 31.9578i 1.44772 + 1.25445i
\(650\) −2.64797 + 9.01816i −0.103862 + 0.353721i
\(651\) 0 0
\(652\) 0.431769 + 0.945442i 0.0169094 + 0.0370264i
\(653\) −16.8177 + 14.5726i −0.658127 + 0.570270i −0.918589 0.395214i \(-0.870670\pi\)
0.260462 + 0.965484i \(0.416125\pi\)
\(654\) 0 0
\(655\) 12.6447 + 1.81803i 0.494069 + 0.0710365i
\(656\) 11.0944 + 1.59513i 0.433163 + 0.0622794i
\(657\) 0 0
\(658\) 0.237868 0.206114i 0.00927307 0.00803516i
\(659\) −13.8092 30.2379i −0.537930 1.17790i −0.962194 0.272363i \(-0.912195\pi\)
0.424265 0.905538i \(-0.360533\pi\)
\(660\) 0 0
\(661\) 2.64227 8.99874i 0.102772 0.350010i −0.892012 0.452012i \(-0.850706\pi\)
0.994784 + 0.102002i \(0.0325247\pi\)
\(662\) 13.0722 + 11.3271i 0.508066 + 0.440241i
\(663\) 0 0
\(664\) 1.85033 + 0.845019i 0.0718069 + 0.0327931i
\(665\) −0.0380183 0.264423i −0.00147429 0.0102539i
\(666\) 0 0
\(667\) 25.7088 + 29.5182i 0.995447 + 1.14295i
\(668\) 7.43936i 0.287837i
\(669\) 0 0
\(670\) −1.09375 + 2.39498i −0.0422552 + 0.0925260i
\(671\) −1.93371 6.58562i −0.0746501 0.254235i
\(672\) 0 0
\(673\) −15.6942 4.60824i −0.604968 0.177635i −0.0351176 0.999383i \(-0.511181\pi\)
−0.569850 + 0.821749i \(0.692999\pi\)
\(674\) 21.2427 13.6518i 0.818237 0.525849i
\(675\) 0 0
\(676\) −6.38835 7.37255i −0.245706 0.283560i
\(677\) −6.76875 4.35001i −0.260144 0.167185i 0.404067 0.914729i \(-0.367596\pi\)
−0.664211 + 0.747545i \(0.731233\pi\)
\(678\) 0 0
\(679\) 1.95287 13.5825i 0.0749443 0.521249i
\(680\) 3.50104 5.44772i 0.134259 0.208911i
\(681\) 0 0
\(682\) 17.1805 7.84607i 0.657876 0.300442i
\(683\) −7.15286 11.1301i −0.273696 0.425880i 0.677009 0.735974i \(-0.263276\pi\)
−0.950706 + 0.310094i \(0.899639\pi\)
\(684\) 0 0
\(685\) −25.4281 + 29.3456i −0.971557 + 1.12124i
\(686\) −16.2348 + 4.76696i −0.619847 + 0.182004i
\(687\) 0 0
\(688\) 7.10944 1.02218i 0.271045 0.0389704i
\(689\) 4.15305 0.158219
\(690\) 0 0
\(691\) −43.2933 −1.64695 −0.823477 0.567350i \(-0.807969\pi\)
−0.823477 + 0.567350i \(0.807969\pi\)
\(692\) 15.1180 2.17365i 0.574702 0.0826297i
\(693\) 0 0
\(694\) 13.7283 4.03100i 0.521120 0.153015i
\(695\) −5.21170 + 6.01463i −0.197691 + 0.228148i
\(696\) 0 0
\(697\) −12.2762 19.1021i −0.464994 0.723546i
\(698\) 20.1653 9.20921i 0.763270 0.348574i
\(699\) 0 0
\(700\) 3.97173 6.18013i 0.150117 0.233587i
\(701\) −3.42315 + 23.8086i −0.129291 + 0.899237i 0.817165 + 0.576404i \(0.195544\pi\)
−0.946456 + 0.322833i \(0.895365\pi\)
\(702\) 0 0
\(703\) −0.327755 0.210636i −0.0123615 0.00794427i
\(704\) −2.81478 3.24843i −0.106086 0.122430i
\(705\) 0 0
\(706\) −29.1885 + 18.7583i −1.09852 + 0.705977i
\(707\) −24.7120 7.25611i −0.929392 0.272894i
\(708\) 0 0
\(709\) 12.7576 + 43.4485i 0.479123 + 1.63174i 0.744517 + 0.667604i \(0.232680\pi\)
−0.265393 + 0.964140i \(0.585502\pi\)
\(710\) 14.3216 31.3599i 0.537479 1.17691i
\(711\) 0 0
\(712\) 5.01372i 0.187897i
\(713\) 20.8666 + 2.94629i 0.781461 + 0.110339i
\(714\) 0 0
\(715\) −3.52219 24.4974i −0.131722 0.916149i
\(716\) −15.9018 7.26212i −0.594279 0.271398i
\(717\) 0 0
\(718\) −28.5219 24.7144i −1.06443 0.922333i
\(719\) 3.28461 11.1864i 0.122495 0.417181i −0.875297 0.483585i \(-0.839334\pi\)
0.997793 + 0.0664040i \(0.0211526\pi\)
\(720\) 0 0
\(721\) 9.39479 + 20.5717i 0.349880 + 0.766131i
\(722\) −14.3566 + 12.4400i −0.534297 + 0.462971i
\(723\) 0 0
\(724\) −10.6055 1.52484i −0.394150 0.0566701i
\(725\) −42.1549 6.06096i −1.56559 0.225098i
\(726\) 0 0
\(727\) −18.2994 + 15.8565i −0.678687 + 0.588086i −0.924477 0.381238i \(-0.875498\pi\)
0.245790 + 0.969323i \(0.420953\pi\)
\(728\) −1.05355 2.30694i −0.0390470 0.0855010i
\(729\) 0 0
\(730\) 10.4597 35.6226i 0.387132 1.31845i
\(731\) −10.9968 9.52877i −0.406731 0.352434i
\(732\) 0 0
\(733\) 18.2074 + 8.31506i 0.672507 + 0.307124i 0.722244 0.691639i \(-0.243111\pi\)
−0.0497364 + 0.998762i \(0.515838\pi\)
\(734\) 4.98256 + 34.6545i 0.183910 + 1.27912i
\(735\) 0 0
\(736\) −0.694529 4.74527i −0.0256007 0.174913i
\(737\) 3.54040i 0.130412i
\(738\) 0 0
\(739\) −0.965761 + 2.11472i −0.0355261 + 0.0777913i −0.926563 0.376139i \(-0.877251\pi\)
0.891037 + 0.453931i \(0.149979\pi\)
\(740\) −5.91096 20.1309i −0.217291 0.740026i
\(741\) 0 0
\(742\) −3.11461 0.914532i −0.114341 0.0335735i
\(743\) 15.3104 9.83940i 0.561684 0.360973i −0.228782 0.973478i \(-0.573474\pi\)
0.790467 + 0.612505i \(0.209838\pi\)
\(744\) 0 0
\(745\) −16.7670 19.3502i −0.614297 0.708936i
\(746\) −23.8495 15.3271i −0.873192 0.561166i
\(747\) 0 0
\(748\) −1.23924 + 8.61909i −0.0453111 + 0.315145i
\(749\) −4.45546 + 6.93283i −0.162799 + 0.253320i
\(750\) 0 0
\(751\) 5.26722 2.40546i 0.192203 0.0877764i −0.316988 0.948429i \(-0.602672\pi\)
0.509192 + 0.860653i \(0.329944\pi\)
\(752\) 0.120860 + 0.188063i 0.00440733 + 0.00685794i
\(753\) 0 0
\(754\) −9.62810 + 11.1114i −0.350635 + 0.404654i
\(755\) 69.7399 20.4775i 2.53810 0.745252i
\(756\) 0 0
\(757\) 1.87780 0.269987i 0.0682499 0.00981286i −0.108105 0.994139i \(-0.534478\pi\)
0.176355 + 0.984327i \(0.443569\pi\)
\(758\) 32.8137 1.19185
\(759\) 0 0
\(760\) 0.189740 0.00688260
\(761\) −0.928675 + 0.133523i −0.0336644 + 0.00484022i −0.159126 0.987258i \(-0.550868\pi\)
0.125462 + 0.992098i \(0.459959\pi\)
\(762\) 0 0
\(763\) 12.4499 3.65563i 0.450717 0.132343i
\(764\) −10.5035 + 12.1217i −0.380003 + 0.438546i
\(765\) 0 0
\(766\) −17.8895 27.8366i −0.646375 1.00578i
\(767\) −18.6032 + 8.49578i −0.671722 + 0.306765i
\(768\) 0 0
\(769\) −0.500315 + 0.778505i −0.0180418 + 0.0280736i −0.850157 0.526529i \(-0.823493\pi\)
0.832116 + 0.554602i \(0.187130\pi\)
\(770\) −2.75301 + 19.1476i −0.0992115 + 0.690031i
\(771\) 0 0
\(772\) 0.213427 + 0.137161i 0.00768140 + 0.00493654i
\(773\) −23.5336 27.1592i −0.846444 0.976849i 0.153492 0.988150i \(-0.450948\pi\)
−0.999936 + 0.0113013i \(0.996403\pi\)
\(774\) 0 0
\(775\) −19.2881 + 12.3957i −0.692849 + 0.445267i
\(776\) 9.35151 + 2.74585i 0.335700 + 0.0985703i
\(777\) 0 0
\(778\) −6.42253 21.8731i −0.230259 0.784190i
\(779\) 0.276381 0.605191i 0.00990239 0.0216832i
\(780\) 0 0
\(781\) 46.3580i 1.65882i
\(782\) −6.34382 + 7.35870i −0.226854 + 0.263147i
\(783\) 0 0
\(784\) −0.714095 4.96664i −0.0255034 0.177380i
\(785\) 52.7843 + 24.1058i 1.88395 + 0.860372i
\(786\) 0 0
\(787\) −9.58029 8.30137i −0.341500 0.295912i 0.467177 0.884164i \(-0.345271\pi\)
−0.808678 + 0.588252i \(0.799816\pi\)
\(788\) −1.62970 + 5.55026i −0.0580557 + 0.197720i
\(789\) 0 0
\(790\) −22.0327 48.2448i −0.783887 1.71647i
\(791\) −19.8437 + 17.1946i −0.705560 + 0.611371i
\(792\) 0 0
\(793\) 2.84711 + 0.409353i 0.101104 + 0.0145365i
\(794\) 8.75826 + 1.25925i 0.310819 + 0.0446891i
\(795\) 0 0
\(796\) −4.88643 + 4.23412i −0.173195 + 0.150074i
\(797\) 1.30941 + 2.86721i 0.0463817 + 0.101562i 0.931404 0.363986i \(-0.118585\pi\)
−0.885023 + 0.465548i \(0.845857\pi\)
\(798\) 0 0
\(799\) 0.127592 0.434537i 0.00451386 0.0153728i
\(800\) 3.94335 + 3.41693i 0.139419 + 0.120807i
\(801\) 0 0
\(802\) 4.14501 + 1.89296i 0.146365 + 0.0668428i
\(803\) 7.10477 + 49.4148i 0.250722 + 1.74381i
\(804\) 0 0
\(805\) −14.0930 + 16.3476i −0.496713 + 0.576176i
\(806\) 7.91522i 0.278802i
\(807\) 0 0
\(808\) 7.59916 16.6398i 0.267338 0.585388i
\(809\) −14.1074 48.0456i −0.495991 1.68919i −0.703281 0.710912i \(-0.748282\pi\)
0.207289 0.978280i \(-0.433536\pi\)
\(810\) 0 0
\(811\) 39.9506 + 11.7306i 1.40286 + 0.411915i 0.893663 0.448738i \(-0.148126\pi\)
0.509192 + 0.860653i \(0.329944\pi\)
\(812\) 9.66748 6.21291i 0.339262 0.218030i
\(813\) 0 0
\(814\) 18.4751 + 21.3214i 0.647552 + 0.747314i
\(815\) 2.79495 + 1.79621i 0.0979030 + 0.0629184i
\(816\) 0 0
\(817\) 0.0606749 0.422003i 0.00212275 0.0147640i
\(818\) −20.0284 + 31.1648i −0.700276 + 1.08965i
\(819\) 0 0
\(820\) 32.5905 14.8836i 1.13811 0.519757i
\(821\) −11.7498 18.2830i −0.410071 0.638083i 0.573373 0.819294i \(-0.305634\pi\)
−0.983444 + 0.181212i \(0.941998\pi\)
\(822\) 0 0
\(823\) 23.9420 27.6306i 0.834566 0.963141i −0.165166 0.986266i \(-0.552816\pi\)
0.999733 + 0.0231248i \(0.00736150\pi\)
\(824\) −15.4122 + 4.52542i −0.536908 + 0.157650i
\(825\) 0 0
\(826\) 15.8224 2.27492i 0.550532 0.0791546i
\(827\) 52.6442 1.83062 0.915309 0.402752i \(-0.131946\pi\)
0.915309 + 0.402752i \(0.131946\pi\)
\(828\) 0 0
\(829\) 29.7388 1.03287 0.516436 0.856326i \(-0.327258\pi\)
0.516436 + 0.856326i \(0.327258\pi\)
\(830\) 6.43606 0.925366i 0.223399 0.0321199i
\(831\) 0 0
\(832\) 1.72834 0.507487i 0.0599195 0.0175940i
\(833\) −6.65678 + 7.68234i −0.230644 + 0.266177i
\(834\) 0 0
\(835\) −12.8565 20.0051i −0.444918 0.692306i
\(836\) −0.232082 + 0.105988i −0.00802673 + 0.00366568i
\(837\) 0 0
\(838\) −11.3623 + 17.6801i −0.392504 + 0.610748i
\(839\) −6.76805 + 47.0728i −0.233659 + 1.62513i 0.448398 + 0.893834i \(0.351995\pi\)
−0.682057 + 0.731299i \(0.738914\pi\)
\(840\) 0 0
\(841\) −31.6482 20.3391i −1.09132 0.701347i
\(842\) 8.68691 + 10.0252i 0.299371 + 0.345492i
\(843\) 0 0
\(844\) 6.41480 4.12254i 0.220806 0.141904i
\(845\) −29.9199 8.78528i −1.02928 0.302223i
\(846\) 0 0
\(847\) −2.96515 10.0984i −0.101884 0.346984i
\(848\) 0.957770 2.09722i 0.0328899 0.0720189i
\(849\) 0 0
\(850\) 10.5705i 0.362566i
\(851\) 4.55861 + 31.1461i 0.156267 + 1.06767i
\(852\) 0 0
\(853\) 2.03530 + 14.1559i 0.0696875 + 0.484687i 0.994540 + 0.104360i \(0.0332795\pi\)
−0.924852 + 0.380327i \(0.875811\pi\)
\(854\) −2.04507 0.933952i −0.0699808 0.0319592i
\(855\) 0 0
\(856\) −4.42363 3.83310i −0.151196 0.131013i
\(857\) −3.86923 + 13.1774i −0.132170 + 0.450131i −0.998808 0.0488067i \(-0.984458\pi\)
0.866638 + 0.498938i \(0.166276\pi\)
\(858\) 0 0
\(859\) 0.767765 + 1.68117i 0.0261958 + 0.0573608i 0.922278 0.386528i \(-0.126326\pi\)
−0.896082 + 0.443889i \(0.853598\pi\)
\(860\) 17.3514 15.0351i 0.591679 0.512692i
\(861\) 0 0
\(862\) 4.28041 + 0.615429i 0.145791 + 0.0209616i
\(863\) 33.1533 + 4.76673i 1.12855 + 0.162261i 0.681200 0.732097i \(-0.261458\pi\)
0.447351 + 0.894358i \(0.352367\pi\)
\(864\) 0 0
\(865\) 36.8974 31.9718i 1.25455 1.08707i
\(866\) 2.84106 + 6.22106i 0.0965432 + 0.211400i
\(867\) 0 0
\(868\) 1.74299 5.93608i 0.0591609 0.201484i
\(869\) 53.8988 + 46.7036i 1.82839 + 1.58431i
\(870\) 0 0
\(871\) 1.34962 + 0.616350i 0.0457301 + 0.0208842i
\(872\) 1.31157 + 9.12218i 0.0444154 + 0.308916i
\(873\) 0 0
\(874\) −0.281876 0.0397998i −0.00953460 0.00134625i
\(875\) 0.980225i 0.0331376i
\(876\) 0 0
\(877\) 2.60842 5.71164i 0.0880800 0.192868i −0.860466 0.509508i \(-0.829827\pi\)
0.948546 + 0.316640i \(0.102555\pi\)
\(878\) −1.28820 4.38719i −0.0434745 0.148061i
\(879\) 0 0
\(880\) −13.1831 3.87089i −0.444401 0.130488i
\(881\) −27.6270 + 17.7548i −0.930776 + 0.598174i −0.915765 0.401714i \(-0.868415\pi\)
−0.0150110 + 0.999887i \(0.504778\pi\)
\(882\) 0 0
\(883\) −5.04941 5.82733i −0.169926 0.196105i 0.664399 0.747378i \(-0.268688\pi\)
−0.834325 + 0.551273i \(0.814142\pi\)
\(884\) −3.06990 1.97291i −0.103252 0.0663560i
\(885\) 0 0
\(886\) 1.03954 7.23018i 0.0349241 0.242903i
\(887\) 5.59634 8.70807i 0.187907 0.292388i −0.734500 0.678609i \(-0.762583\pi\)
0.922407 + 0.386220i \(0.126220\pi\)
\(888\) 0 0
\(889\) −17.5609 + 8.01980i −0.588974 + 0.268975i
\(890\) 8.66458 + 13.4824i 0.290437 + 0.451929i
\(891\) 0 0
\(892\) −10.2456 + 11.8240i −0.343047 + 0.395897i
\(893\) 0.0127320 0.00373846i 0.000426061 0.000125103i
\(894\) 0 0
\(895\) −55.3117 + 7.95262i −1.84886 + 0.265827i
\(896\) −1.40794 −0.0470358
\(897\) 0 0
\(898\) −12.3630 −0.412558
\(899\) −35.5005 + 5.10421i −1.18401 + 0.170235i
\(900\) 0 0
\(901\) −4.48157 + 1.31591i −0.149303 + 0.0438392i
\(902\) −31.5493 + 36.4099i −1.05048 + 1.21232i
\(903\) 0 0
\(904\) −10.0825 15.6887i −0.335340 0.521800i
\(905\) −31.1543 + 14.2277i −1.03560 + 0.472944i
\(906\) 0 0
\(907\) 17.5520 27.3114i 0.582805 0.906862i −0.417194 0.908818i \(-0.636986\pi\)
0.999998 + 0.00195613i \(0.000622656\pi\)
\(908\) 1.11176 7.73248i 0.0368951 0.256611i
\(909\) 0 0
\(910\) −6.81988 4.38287i −0.226077 0.145291i
\(911\) −18.0337 20.8121i −0.597485 0.689534i 0.373785 0.927515i \(-0.378060\pi\)
−0.971270 + 0.237981i \(0.923514\pi\)
\(912\) 0 0
\(913\) −7.35541 + 4.72703i −0.243428 + 0.156442i
\(914\) 25.6092 + 7.51954i 0.847077 + 0.248724i
\(915\) 0 0
\(916\) 4.75261 + 16.1859i 0.157031 + 0.534797i
\(917\) −2.33743 + 5.11825i −0.0771887 + 0.169020i
\(918\) 0 0
\(919\) 12.7876i 0.421826i 0.977505 + 0.210913i \(0.0676436\pi\)
−0.977505 + 0.210913i \(0.932356\pi\)
\(920\) −10.0683 11.5602i −0.331942 0.381129i
\(921\) 0 0
\(922\) −2.05486 14.2918i −0.0676731 0.470676i
\(923\) −17.6719 8.07049i −0.581678 0.265644i
\(924\) 0 0
\(925\) −25.8826 22.4274i −0.851015 0.737408i
\(926\) 1.54494 5.26159i 0.0507700 0.172907i
\(927\) 0 0
\(928\) 3.39067 + 7.42453i 0.111304 + 0.243722i
\(929\) −7.63753 + 6.61796i −0.250579 + 0.217128i −0.771089 0.636728i \(-0.780288\pi\)
0.520509 + 0.853856i \(0.325742\pi\)
\(930\) 0 0
\(931\) −0.294811 0.0423874i −0.00966204 0.00138919i
\(932\) 20.3739 + 2.92933i 0.667370 + 0.0959533i
\(933\) 0 0
\(934\) −18.0219 + 15.6161i −0.589695 + 0.510974i
\(935\) 11.5629 + 25.3192i 0.378146 + 0.828025i
\(936\) 0 0
\(937\) −6.85425 + 23.3434i −0.223918 + 0.762596i 0.768517 + 0.639829i \(0.220995\pi\)
−0.992436 + 0.122767i \(0.960823\pi\)
\(938\) −0.876431 0.759432i −0.0286165 0.0247963i
\(939\) 0 0
\(940\) 0.650010 + 0.296850i 0.0212010 + 0.00968217i
\(941\) 6.14561 + 42.7436i 0.200341 + 1.39340i 0.803274 + 0.595610i \(0.203090\pi\)
−0.602933 + 0.797792i \(0.706001\pi\)
\(942\) 0 0
\(943\) −51.5380 + 15.2747i −1.67831 + 0.497412i
\(944\) 11.3536i 0.369528i
\(945\) 0 0
\(946\) −12.8250 + 28.0827i −0.416975 + 0.913049i
\(947\) −10.0096 34.0897i −0.325270 1.10777i −0.946114 0.323833i \(-0.895028\pi\)
0.620845 0.783934i \(-0.286790\pi\)
\(948\) 0 0
\(949\) −20.0740 5.89427i −0.651631 0.191336i
\(950\) 0.260552 0.167447i 0.00845344 0.00543270i
\(951\) 0 0
\(952\) 1.86785 + 2.15561i 0.0605373 + 0.0698637i
\(953\) 2.88855 + 1.85636i 0.0935694 + 0.0601334i 0.586589 0.809885i \(-0.300470\pi\)
−0.493019 + 0.870018i \(0.664107\pi\)
\(954\) 0 0
\(955\) −7.29648 + 50.7481i −0.236108 + 1.64217i
\(956\) 2.80467 4.36415i 0.0907094 0.141147i
\(957\) 0 0
\(958\) −2.55690 + 1.16770i −0.0826096 + 0.0377265i
\(959\) −9.24651 14.3878i −0.298585 0.464608i
\(960\) 0 0
\(961\) 7.65627 8.83581i 0.246977 0.285026i
\(962\) −11.3442 + 3.33095i −0.365750 + 0.107394i
\(963\) 0 0
\(964\) 12.3414 1.77442i 0.397489 0.0571503i
\(965\) 0.810963 0.0261058
\(966\) 0 0
\(967\) −48.3925 −1.55620 −0.778099 0.628141i \(-0.783816\pi\)
−0.778099 + 0.628141i \(0.783816\pi\)
\(968\) 7.39918 1.06384i 0.237819 0.0341932i
\(969\) 0 0
\(970\) 29.8924 8.77720i 0.959787 0.281819i
\(971\) −37.5348 + 43.3174i −1.20455 + 1.39012i −0.305547 + 0.952177i \(0.598839\pi\)
−0.899001 + 0.437946i \(0.855706\pi\)
\(972\) 0 0
\(973\) −1.89515 2.94891i −0.0607557 0.0945378i
\(974\) −2.74276 + 1.25258i −0.0878836 + 0.0401351i
\(975\) 0 0
\(976\) 0.863313 1.34334i 0.0276340 0.0429993i
\(977\) 4.26489 29.6630i 0.136446 0.949003i −0.800451 0.599398i \(-0.795407\pi\)
0.936897 0.349605i \(-0.113684\pi\)
\(978\) 0 0
\(979\) −18.1294 11.6510i −0.579417 0.372368i
\(980\) −10.5035 12.1217i −0.335522 0.387213i
\(981\) 0 0
\(982\) −10.3652 + 6.66131i −0.330767 + 0.212571i
\(983\) −11.2540 3.30447i −0.358947 0.105396i 0.0972867 0.995256i \(-0.468984\pi\)
−0.456233 + 0.889860i \(0.650802\pi\)
\(984\) 0 0
\(985\) 5.20939 + 17.7416i 0.165985 + 0.565293i
\(986\) 6.86902 15.0411i 0.218754 0.479005i
\(987\) 0 0
\(988\) 0.106922i 0.00340166i
\(989\) −28.9308 + 18.6963i −0.919947 + 0.594509i
\(990\) 0 0
\(991\) −2.08049 14.4701i −0.0660890 0.459659i −0.995814 0.0914042i \(-0.970864\pi\)
0.929725 0.368255i \(-0.120045\pi\)
\(992\) 3.99706 + 1.82540i 0.126907 + 0.0579564i
\(993\) 0 0
\(994\) 11.4760 + 9.94401i 0.363997 + 0.315405i
\(995\) −5.82277 + 19.8305i −0.184594 + 0.628670i
\(996\) 0 0
\(997\) 14.5982 + 31.9656i 0.462330 + 1.01236i 0.986950 + 0.161025i \(0.0514800\pi\)
−0.524620 + 0.851336i \(0.675793\pi\)
\(998\) −5.10502 + 4.42353i −0.161597 + 0.140024i
\(999\) 0 0
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 414.2.j.a.89.4 80
3.2 odd 2 inner 414.2.j.a.89.5 yes 80
23.15 odd 22 inner 414.2.j.a.107.5 yes 80
69.38 even 22 inner 414.2.j.a.107.4 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
414.2.j.a.89.4 80 1.1 even 1 trivial
414.2.j.a.89.5 yes 80 3.2 odd 2 inner
414.2.j.a.107.4 yes 80 69.38 even 22 inner
414.2.j.a.107.5 yes 80 23.15 odd 22 inner