Properties

Label 1805.2.b.i.1084.5
Level $1805$
Weight $2$
Character 1805.1084
Analytic conductor $14.413$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1805,2,Mod(1084,1805)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1805.1084");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1805.b (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: \(14.4129975648\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 22x^{14} + 190x^{12} + 820x^{10} + 1862x^{8} + 2154x^{6} + 1163x^{4} + 256x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1084.5
Root \(-1.24938i\) of defining polynomial
Character \(\chi\) \(=\) 1805.1084
Dual form 1805.2.b.i.1084.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.24938i q^{2} -1.51315i q^{3} +0.439042 q^{4} +(-1.95031 + 1.09375i) q^{5} -1.89050 q^{6} +0.568589i q^{7} -3.04730i q^{8} +0.710386 q^{9} +O(q^{10})\) \(q-1.24938i q^{2} -1.51315i q^{3} +0.439042 q^{4} +(-1.95031 + 1.09375i) q^{5} -1.89050 q^{6} +0.568589i q^{7} -3.04730i q^{8} +0.710386 q^{9} +(1.36651 + 2.43669i) q^{10} +3.18990 q^{11} -0.664336i q^{12} -2.28031i q^{13} +0.710386 q^{14} +(1.65500 + 2.95111i) q^{15} -2.92916 q^{16} +2.21494i q^{17} -0.887544i q^{18} +(-0.856270 + 0.480201i) q^{20} +0.860359 q^{21} -3.98541i q^{22} -0.0101715i q^{23} -4.61101 q^{24} +(2.60744 - 4.26630i) q^{25} -2.84898 q^{26} -5.61436i q^{27} +0.249635i q^{28} +1.14455 q^{29} +(3.68707 - 2.06773i) q^{30} +9.12067 q^{31} -2.43496i q^{32} -4.82679i q^{33} +2.76731 q^{34} +(-0.621893 - 1.10893i) q^{35} +0.311889 q^{36} -8.97487i q^{37} -3.45044 q^{39} +(3.33297 + 5.94318i) q^{40} -10.5778 q^{41} -1.07492i q^{42} +7.91273i q^{43} +1.40050 q^{44} +(-1.38547 + 0.776982i) q^{45} -0.0127081 q^{46} -12.5442i q^{47} +4.43225i q^{48} +6.67671 q^{49} +(-5.33024 - 3.25769i) q^{50} +3.35154 q^{51} -1.00115i q^{52} +7.43944i q^{53} -7.01448 q^{54} +(-6.22130 + 3.48894i) q^{55} +1.73266 q^{56} -1.42998i q^{58} +8.46844 q^{59} +(0.726615 + 1.29566i) q^{60} -7.36372 q^{61} -11.3952i q^{62} +0.403918i q^{63} -8.90051 q^{64} +(2.49408 + 4.44731i) q^{65} -6.03051 q^{66} -3.51270i q^{67} +0.972455i q^{68} -0.0153909 q^{69} +(-1.38547 + 0.776982i) q^{70} -4.56784 q^{71} -2.16476i q^{72} -9.66012i q^{73} -11.2130 q^{74} +(-6.45553 - 3.94543i) q^{75} +1.81374i q^{77} +4.31092i q^{78} -7.97511 q^{79} +(5.71277 - 3.20376i) q^{80} -6.36420 q^{81} +13.2157i q^{82} -13.7395i q^{83} +0.377734 q^{84} +(-2.42259 - 4.31983i) q^{85} +9.88603 q^{86} -1.73187i q^{87} -9.72058i q^{88} -3.41038 q^{89} +(0.970748 + 1.73099i) q^{90} +1.29656 q^{91} -0.00446571i q^{92} -13.8009i q^{93} -15.6725 q^{94} -3.68445 q^{96} -3.01777i q^{97} -8.34176i q^{98} +2.26606 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 12 q^{4} + 4 q^{5} - 10 q^{6} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 12 q^{4} + 4 q^{5} - 10 q^{6} - 6 q^{9} - 16 q^{10} - 22 q^{11} - 6 q^{14} + 10 q^{15} + 8 q^{16} - 14 q^{20} - 20 q^{21} + 14 q^{24} + 4 q^{25} - 16 q^{26} - 2 q^{29} - 12 q^{30} + 16 q^{31} + 8 q^{34} - 10 q^{35} + 18 q^{36} + 36 q^{39} + 38 q^{40} + 26 q^{41} + 64 q^{44} - 2 q^{45} + 2 q^{46} + 20 q^{49} - 48 q^{50} - 38 q^{51} + 12 q^{54} - 10 q^{55} + 6 q^{56} - 10 q^{59} - 10 q^{60} - 30 q^{61} + 16 q^{64} - 36 q^{65} + 4 q^{66} - 68 q^{69} - 2 q^{70} - 20 q^{71} + 40 q^{74} - 32 q^{75} - 12 q^{79} + 40 q^{80} - 48 q^{81} + 2 q^{84} - 2 q^{85} - 20 q^{86} + 30 q^{90} - 86 q^{91} + 38 q^{94} + 22 q^{96} + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times\).

\(n\) \(362\) \(1446\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.24938i 0.883447i −0.897151 0.441724i \(-0.854367\pi\)
0.897151 0.441724i \(-0.145633\pi\)
\(3\) 1.51315i 0.873616i −0.899555 0.436808i \(-0.856109\pi\)
0.899555 0.436808i \(-0.143891\pi\)
\(4\) 0.439042 0.219521
\(5\) −1.95031 + 1.09375i −0.872206 + 0.489138i
\(6\) −1.89050 −0.771793
\(7\) 0.568589i 0.214907i 0.994210 + 0.107453i \(0.0342696\pi\)
−0.994210 + 0.107453i \(0.965730\pi\)
\(8\) 3.04730i 1.07738i
\(9\) 0.710386 0.236795
\(10\) 1.36651 + 2.43669i 0.432128 + 0.770548i
\(11\) 3.18990 0.961792 0.480896 0.876778i \(-0.340312\pi\)
0.480896 + 0.876778i \(0.340312\pi\)
\(12\) 0.664336i 0.191777i
\(13\) 2.28031i 0.632443i −0.948685 0.316222i \(-0.897586\pi\)
0.948685 0.316222i \(-0.102414\pi\)
\(14\) 0.710386 0.189859
\(15\) 1.65500 + 2.95111i 0.427319 + 0.761973i
\(16\) −2.92916 −0.732289
\(17\) 2.21494i 0.537203i 0.963251 + 0.268601i \(0.0865615\pi\)
−0.963251 + 0.268601i \(0.913439\pi\)
\(18\) 0.887544i 0.209196i
\(19\) 0 0
\(20\) −0.856270 + 0.480201i −0.191468 + 0.107376i
\(21\) 0.860359 0.187746
\(22\) 3.98541i 0.849692i
\(23\) 0.0101715i 0.00212090i −0.999999 0.00106045i \(-0.999662\pi\)
0.999999 0.00106045i \(-0.000337552\pi\)
\(24\) −4.61101 −0.941219
\(25\) 2.60744 4.26630i 0.521487 0.853259i
\(26\) −2.84898 −0.558730
\(27\) 5.61436i 1.08048i
\(28\) 0.249635i 0.0471765i
\(29\) 1.14455 0.212537 0.106268 0.994337i \(-0.466110\pi\)
0.106268 + 0.994337i \(0.466110\pi\)
\(30\) 3.68707 2.06773i 0.673163 0.377514i
\(31\) 9.12067 1.63812 0.819060 0.573708i \(-0.194495\pi\)
0.819060 + 0.573708i \(0.194495\pi\)
\(32\) 2.43496i 0.430444i
\(33\) 4.82679i 0.840236i
\(34\) 2.76731 0.474590
\(35\) −0.621893 1.10893i −0.105119 0.187443i
\(36\) 0.311889 0.0519816
\(37\) 8.97487i 1.47546i −0.675096 0.737730i \(-0.735898\pi\)
0.675096 0.737730i \(-0.264102\pi\)
\(38\) 0 0
\(39\) −3.45044 −0.552512
\(40\) 3.33297 + 5.94318i 0.526989 + 0.939700i
\(41\) −10.5778 −1.65197 −0.825985 0.563692i \(-0.809381\pi\)
−0.825985 + 0.563692i \(0.809381\pi\)
\(42\) 1.07492i 0.165863i
\(43\) 7.91273i 1.20668i 0.797484 + 0.603340i \(0.206164\pi\)
−0.797484 + 0.603340i \(0.793836\pi\)
\(44\) 1.40050 0.211134
\(45\) −1.38547 + 0.776982i −0.206534 + 0.115826i
\(46\) −0.0127081 −0.00187370
\(47\) 12.5442i 1.82976i −0.403731 0.914878i \(-0.632287\pi\)
0.403731 0.914878i \(-0.367713\pi\)
\(48\) 4.43225i 0.639740i
\(49\) 6.67671 0.953815
\(50\) −5.33024 3.25769i −0.753809 0.460706i
\(51\) 3.35154 0.469309
\(52\) 1.00115i 0.138835i
\(53\) 7.43944i 1.02189i 0.859615 + 0.510943i \(0.170704\pi\)
−0.859615 + 0.510943i \(0.829296\pi\)
\(54\) −7.01448 −0.954550
\(55\) −6.22130 + 3.48894i −0.838881 + 0.470449i
\(56\) 1.73266 0.231537
\(57\) 0 0
\(58\) 1.42998i 0.187765i
\(59\) 8.46844 1.10250 0.551249 0.834341i \(-0.314152\pi\)
0.551249 + 0.834341i \(0.314152\pi\)
\(60\) 0.726615 + 1.29566i 0.0938056 + 0.167269i
\(61\) −7.36372 −0.942828 −0.471414 0.881912i \(-0.656256\pi\)
−0.471414 + 0.881912i \(0.656256\pi\)
\(62\) 11.3952i 1.44719i
\(63\) 0.403918i 0.0508888i
\(64\) −8.90051 −1.11256
\(65\) 2.49408 + 4.44731i 0.309352 + 0.551621i
\(66\) −6.03051 −0.742304
\(67\) 3.51270i 0.429144i −0.976708 0.214572i \(-0.931164\pi\)
0.976708 0.214572i \(-0.0688357\pi\)
\(68\) 0.972455i 0.117927i
\(69\) −0.0153909 −0.00185285
\(70\) −1.38547 + 0.776982i −0.165596 + 0.0928671i
\(71\) −4.56784 −0.542103 −0.271052 0.962565i \(-0.587371\pi\)
−0.271052 + 0.962565i \(0.587371\pi\)
\(72\) 2.16476i 0.255119i
\(73\) 9.66012i 1.13063i −0.824875 0.565316i \(-0.808754\pi\)
0.824875 0.565316i \(-0.191246\pi\)
\(74\) −11.2130 −1.30349
\(75\) −6.45553 3.94543i −0.745421 0.455579i
\(76\) 0 0
\(77\) 1.81374i 0.206695i
\(78\) 4.31092i 0.488115i
\(79\) −7.97511 −0.897270 −0.448635 0.893715i \(-0.648090\pi\)
−0.448635 + 0.893715i \(0.648090\pi\)
\(80\) 5.71277 3.20376i 0.638707 0.358191i
\(81\) −6.36420 −0.707133
\(82\) 13.2157i 1.45943i
\(83\) 13.7395i 1.50811i −0.656810 0.754056i \(-0.728095\pi\)
0.656810 0.754056i \(-0.271905\pi\)
\(84\) 0.377734 0.0412142
\(85\) −2.42259 4.31983i −0.262767 0.468552i
\(86\) 9.88603 1.06604
\(87\) 1.73187i 0.185676i
\(88\) 9.72058i 1.03622i
\(89\) −3.41038 −0.361500 −0.180750 0.983529i \(-0.557852\pi\)
−0.180750 + 0.983529i \(0.557852\pi\)
\(90\) 0.970748 + 1.73099i 0.102326 + 0.182462i
\(91\) 1.29656 0.135916
\(92\) 0.00446571i 0.000465582i
\(93\) 13.8009i 1.43109i
\(94\) −15.6725 −1.61649
\(95\) 0 0
\(96\) −3.68445 −0.376042
\(97\) 3.01777i 0.306408i −0.988195 0.153204i \(-0.951041\pi\)
0.988195 0.153204i \(-0.0489592\pi\)
\(98\) 8.34176i 0.842645i
\(99\) 2.26606 0.227748
\(100\) 1.14478 1.87308i 0.114478 0.187308i
\(101\) −14.4164 −1.43449 −0.717243 0.696823i \(-0.754596\pi\)
−0.717243 + 0.696823i \(0.754596\pi\)
\(102\) 4.18735i 0.414610i
\(103\) 4.41406i 0.434931i −0.976068 0.217465i \(-0.930221\pi\)
0.976068 0.217465i \(-0.0697789\pi\)
\(104\) −6.94877 −0.681383
\(105\) −1.67797 + 0.941015i −0.163753 + 0.0918337i
\(106\) 9.29471 0.902782
\(107\) 13.8931i 1.34309i 0.740962 + 0.671547i \(0.234370\pi\)
−0.740962 + 0.671547i \(0.765630\pi\)
\(108\) 2.46494i 0.237189i
\(109\) 3.59943 0.344762 0.172381 0.985030i \(-0.444854\pi\)
0.172381 + 0.985030i \(0.444854\pi\)
\(110\) 4.35903 + 7.77279i 0.415617 + 0.741107i
\(111\) −13.5803 −1.28898
\(112\) 1.66549i 0.157374i
\(113\) 15.7601i 1.48258i 0.671183 + 0.741291i \(0.265786\pi\)
−0.671183 + 0.741291i \(0.734214\pi\)
\(114\) 0 0
\(115\) 0.0111250 + 0.0198375i 0.00103741 + 0.00184986i
\(116\) 0.502505 0.0466564
\(117\) 1.61990i 0.149759i
\(118\) 10.5803i 0.973998i
\(119\) −1.25939 −0.115448
\(120\) 8.99291 5.04328i 0.820937 0.460386i
\(121\) −0.824527 −0.0749570
\(122\) 9.20011i 0.832939i
\(123\) 16.0057i 1.44319i
\(124\) 4.00436 0.359602
\(125\) −0.419067 + 11.1725i −0.0374825 + 0.999297i
\(126\) 0.504648 0.0449576
\(127\) 1.35801i 0.120504i −0.998183 0.0602518i \(-0.980810\pi\)
0.998183 0.0602518i \(-0.0191904\pi\)
\(128\) 6.25023i 0.552447i
\(129\) 11.9731 1.05417
\(130\) 5.55639 3.11606i 0.487328 0.273296i
\(131\) 13.9257 1.21669 0.608346 0.793672i \(-0.291833\pi\)
0.608346 + 0.793672i \(0.291833\pi\)
\(132\) 2.11917i 0.184450i
\(133\) 0 0
\(134\) −4.38870 −0.379126
\(135\) 6.14069 + 10.9498i 0.528506 + 0.942405i
\(136\) 6.74960 0.578773
\(137\) 16.6294i 1.42074i 0.703826 + 0.710372i \(0.251473\pi\)
−0.703826 + 0.710372i \(0.748527\pi\)
\(138\) 0.0192292i 0.00163690i
\(139\) 4.26670 0.361897 0.180948 0.983493i \(-0.442083\pi\)
0.180948 + 0.983493i \(0.442083\pi\)
\(140\) −0.273037 0.486866i −0.0230759 0.0411477i
\(141\) −18.9812 −1.59850
\(142\) 5.70698i 0.478919i
\(143\) 7.27395i 0.608278i
\(144\) −2.08083 −0.173403
\(145\) −2.23222 + 1.25184i −0.185376 + 0.103960i
\(146\) −12.0692 −0.998853
\(147\) 10.1028i 0.833268i
\(148\) 3.94035i 0.323895i
\(149\) 9.16824 0.751092 0.375546 0.926804i \(-0.377455\pi\)
0.375546 + 0.926804i \(0.377455\pi\)
\(150\) −4.92936 + 8.06543i −0.402480 + 0.658540i
\(151\) 5.58655 0.454627 0.227314 0.973822i \(-0.427006\pi\)
0.227314 + 0.973822i \(0.427006\pi\)
\(152\) 0 0
\(153\) 1.57346i 0.127207i
\(154\) 2.26606 0.182604
\(155\) −17.7881 + 9.97570i −1.42878 + 0.801268i
\(156\) −1.51489 −0.121288
\(157\) 16.7284i 1.33507i −0.744578 0.667535i \(-0.767349\pi\)
0.744578 0.667535i \(-0.232651\pi\)
\(158\) 9.96397i 0.792691i
\(159\) 11.2570 0.892736
\(160\) 2.66323 + 4.74893i 0.210547 + 0.375436i
\(161\) 0.00578339 0.000455795
\(162\) 7.95132i 0.624714i
\(163\) 24.3332i 1.90592i 0.303090 + 0.952962i \(0.401982\pi\)
−0.303090 + 0.952962i \(0.598018\pi\)
\(164\) −4.64409 −0.362643
\(165\) 5.27929 + 9.41375i 0.410992 + 0.732859i
\(166\) −17.1660 −1.33234
\(167\) 3.96229i 0.306611i 0.988179 + 0.153305i \(0.0489918\pi\)
−0.988179 + 0.153305i \(0.951008\pi\)
\(168\) 2.62177i 0.202274i
\(169\) 7.80021 0.600016
\(170\) −5.39713 + 3.02674i −0.413941 + 0.232140i
\(171\) 0 0
\(172\) 3.47402i 0.264892i
\(173\) 22.4611i 1.70769i −0.520528 0.853844i \(-0.674265\pi\)
0.520528 0.853844i \(-0.325735\pi\)
\(174\) −2.16377 −0.164035
\(175\) 2.42577 + 1.48256i 0.183371 + 0.112071i
\(176\) −9.34372 −0.704310
\(177\) 12.8140i 0.963159i
\(178\) 4.26087i 0.319366i
\(179\) −8.56842 −0.640434 −0.320217 0.947344i \(-0.603756\pi\)
−0.320217 + 0.947344i \(0.603756\pi\)
\(180\) −0.608282 + 0.341128i −0.0453387 + 0.0254262i
\(181\) 21.5945 1.60511 0.802554 0.596580i \(-0.203474\pi\)
0.802554 + 0.596580i \(0.203474\pi\)
\(182\) 1.61990i 0.120075i
\(183\) 11.1424i 0.823670i
\(184\) −0.0309955 −0.00228502
\(185\) 9.81623 + 17.5038i 0.721704 + 1.28690i
\(186\) −17.2426 −1.26429
\(187\) 7.06545i 0.516677i
\(188\) 5.50742i 0.401670i
\(189\) 3.19226 0.232203
\(190\) 0 0
\(191\) 5.25980 0.380586 0.190293 0.981727i \(-0.439056\pi\)
0.190293 + 0.981727i \(0.439056\pi\)
\(192\) 13.4678i 0.971953i
\(193\) 6.86172i 0.493918i −0.969026 0.246959i \(-0.920569\pi\)
0.969026 0.246959i \(-0.0794312\pi\)
\(194\) −3.77035 −0.270696
\(195\) 6.72943 3.77391i 0.481905 0.270255i
\(196\) 2.93136 0.209383
\(197\) 3.97259i 0.283035i 0.989936 + 0.141518i \(0.0451982\pi\)
−0.989936 + 0.141518i \(0.954802\pi\)
\(198\) 2.83118i 0.201203i
\(199\) 13.8356 0.980780 0.490390 0.871503i \(-0.336854\pi\)
0.490390 + 0.871503i \(0.336854\pi\)
\(200\) −13.0007 7.94563i −0.919286 0.561841i
\(201\) −5.31523 −0.374907
\(202\) 18.0116i 1.26729i
\(203\) 0.650777i 0.0456756i
\(204\) 1.47147 0.103023
\(205\) 20.6300 11.5694i 1.44086 0.808042i
\(206\) −5.51486 −0.384238
\(207\) 0.00722567i 0.000502219i
\(208\) 6.67937i 0.463131i
\(209\) 0 0
\(210\) 1.17569 + 2.09643i 0.0811302 + 0.144667i
\(211\) −11.5957 −0.798282 −0.399141 0.916890i \(-0.630692\pi\)
−0.399141 + 0.916890i \(0.630692\pi\)
\(212\) 3.26623i 0.224326i
\(213\) 6.91182i 0.473590i
\(214\) 17.3578 1.18655
\(215\) −8.65452 15.4323i −0.590233 1.05247i
\(216\) −17.1086 −1.16409
\(217\) 5.18591i 0.352043i
\(218\) 4.49706i 0.304579i
\(219\) −14.6172 −0.987737
\(220\) −2.73142 + 1.53179i −0.184152 + 0.103274i
\(221\) 5.05075 0.339750
\(222\) 16.9670i 1.13875i
\(223\) 1.95798i 0.131116i 0.997849 + 0.0655580i \(0.0208827\pi\)
−0.997849 + 0.0655580i \(0.979117\pi\)
\(224\) 1.38449 0.0925052
\(225\) 1.85228 3.03072i 0.123486 0.202048i
\(226\) 19.6904 1.30978
\(227\) 7.20506i 0.478217i −0.970993 0.239108i \(-0.923145\pi\)
0.970993 0.239108i \(-0.0768551\pi\)
\(228\) 0 0
\(229\) 17.4984 1.15632 0.578162 0.815922i \(-0.303770\pi\)
0.578162 + 0.815922i \(0.303770\pi\)
\(230\) 0.0247847 0.0138994i 0.00163425 0.000916499i
\(231\) 2.74446 0.180572
\(232\) 3.48777i 0.228984i
\(233\) 3.79613i 0.248693i 0.992239 + 0.124346i \(0.0396834\pi\)
−0.992239 + 0.124346i \(0.960317\pi\)
\(234\) −2.02387 −0.132305
\(235\) 13.7201 + 24.4651i 0.895004 + 1.59592i
\(236\) 3.71801 0.242022
\(237\) 12.0675i 0.783870i
\(238\) 1.57346i 0.101993i
\(239\) −10.4757 −0.677614 −0.338807 0.940856i \(-0.610023\pi\)
−0.338807 + 0.940856i \(0.610023\pi\)
\(240\) −4.84775 8.64426i −0.312921 0.557985i
\(241\) −2.86967 −0.184851 −0.0924257 0.995720i \(-0.529462\pi\)
−0.0924257 + 0.995720i \(0.529462\pi\)
\(242\) 1.03015i 0.0662205i
\(243\) 7.21311i 0.462721i
\(244\) −3.23299 −0.206971
\(245\) −13.0217 + 7.30263i −0.831923 + 0.466548i
\(246\) 19.9973 1.27498
\(247\) 0 0
\(248\) 27.7934i 1.76488i
\(249\) −20.7900 −1.31751
\(250\) 13.9587 + 0.523575i 0.882826 + 0.0331138i
\(251\) −19.1428 −1.20828 −0.604141 0.796877i \(-0.706484\pi\)
−0.604141 + 0.796877i \(0.706484\pi\)
\(252\) 0.177337i 0.0111712i
\(253\) 0.0324460i 0.00203986i
\(254\) −1.69667 −0.106459
\(255\) −6.53654 + 3.66573i −0.409334 + 0.229557i
\(256\) −9.99209 −0.624506
\(257\) 10.2306i 0.638169i 0.947726 + 0.319085i \(0.103375\pi\)
−0.947726 + 0.319085i \(0.896625\pi\)
\(258\) 14.9590i 0.931308i
\(259\) 5.10301 0.317086
\(260\) 1.09501 + 1.95256i 0.0679094 + 0.121092i
\(261\) 0.813069 0.0503277
\(262\) 17.3985i 1.07488i
\(263\) 6.62838i 0.408723i 0.978895 + 0.204362i \(0.0655119\pi\)
−0.978895 + 0.204362i \(0.934488\pi\)
\(264\) −14.7087 −0.905256
\(265\) −8.13686 14.5092i −0.499844 0.891295i
\(266\) 0 0
\(267\) 5.16041i 0.315812i
\(268\) 1.54222i 0.0942062i
\(269\) 12.8640 0.784333 0.392167 0.919894i \(-0.371726\pi\)
0.392167 + 0.919894i \(0.371726\pi\)
\(270\) 13.6804 7.67207i 0.832565 0.466907i
\(271\) 9.26123 0.562579 0.281290 0.959623i \(-0.409238\pi\)
0.281290 + 0.959623i \(0.409238\pi\)
\(272\) 6.48792i 0.393388i
\(273\) 1.96188i 0.118739i
\(274\) 20.7765 1.25515
\(275\) 8.31746 13.6091i 0.501562 0.820657i
\(276\) −0.00675727 −0.000406740
\(277\) 12.6774i 0.761712i −0.924634 0.380856i \(-0.875629\pi\)
0.924634 0.380856i \(-0.124371\pi\)
\(278\) 5.33074i 0.319717i
\(279\) 6.47919 0.387899
\(280\) −3.37923 + 1.89509i −0.201948 + 0.113253i
\(281\) −28.6975 −1.71195 −0.855976 0.517016i \(-0.827043\pi\)
−0.855976 + 0.517016i \(0.827043\pi\)
\(282\) 23.7148i 1.41219i
\(283\) 13.9723i 0.830565i −0.909692 0.415283i \(-0.863683\pi\)
0.909692 0.415283i \(-0.136317\pi\)
\(284\) −2.00548 −0.119003
\(285\) 0 0
\(286\) −9.08795 −0.537382
\(287\) 6.01441i 0.355019i
\(288\) 1.72976i 0.101927i
\(289\) 12.0940 0.711413
\(290\) 1.56403 + 2.78890i 0.0918432 + 0.163770i
\(291\) −4.56634 −0.267683
\(292\) 4.24120i 0.248198i
\(293\) 5.77232i 0.337223i −0.985683 0.168611i \(-0.946072\pi\)
0.985683 0.168611i \(-0.0539283\pi\)
\(294\) −12.6223 −0.736148
\(295\) −16.5161 + 9.26233i −0.961605 + 0.539274i
\(296\) −27.3491 −1.58963
\(297\) 17.9093i 1.03920i
\(298\) 11.4546i 0.663550i
\(299\) −0.0231941 −0.00134135
\(300\) −2.83425 1.73221i −0.163636 0.100009i
\(301\) −4.49909 −0.259323
\(302\) 6.97975i 0.401639i
\(303\) 21.8141i 1.25319i
\(304\) 0 0
\(305\) 14.3616 8.05405i 0.822340 0.461173i
\(306\) 1.96586 0.112381
\(307\) 10.3450i 0.590419i 0.955433 + 0.295209i \(0.0953894\pi\)
−0.955433 + 0.295209i \(0.904611\pi\)
\(308\) 0.796311i 0.0453740i
\(309\) −6.67913 −0.379962
\(310\) 12.4635 + 22.2242i 0.707878 + 1.26225i
\(311\) −14.8195 −0.840339 −0.420169 0.907446i \(-0.638029\pi\)
−0.420169 + 0.907446i \(0.638029\pi\)
\(312\) 10.5145i 0.595267i
\(313\) 18.3966i 1.03984i 0.854216 + 0.519919i \(0.174038\pi\)
−0.854216 + 0.519919i \(0.825962\pi\)
\(314\) −20.9002 −1.17946
\(315\) −0.441784 0.787765i −0.0248917 0.0443856i
\(316\) −3.50141 −0.196970
\(317\) 0.484179i 0.0271942i −0.999908 0.0135971i \(-0.995672\pi\)
0.999908 0.0135971i \(-0.00432823\pi\)
\(318\) 14.0643i 0.788685i
\(319\) 3.65099 0.204416
\(320\) 17.3588 9.73490i 0.970385 0.544198i
\(321\) 21.0223 1.17335
\(322\) 0.00722567i 0.000402671i
\(323\) 0 0
\(324\) −2.79415 −0.155231
\(325\) −9.72846 5.94575i −0.539638 0.329811i
\(326\) 30.4015 1.68378
\(327\) 5.44646i 0.301190i
\(328\) 32.2336i 1.77980i
\(329\) 7.13248 0.393226
\(330\) 11.7614 6.59585i 0.647443 0.363090i
\(331\) 27.6808 1.52147 0.760737 0.649060i \(-0.224838\pi\)
0.760737 + 0.649060i \(0.224838\pi\)
\(332\) 6.03225i 0.331062i
\(333\) 6.37562i 0.349382i
\(334\) 4.95041 0.270875
\(335\) 3.84200 + 6.85085i 0.209911 + 0.374302i
\(336\) −2.52013 −0.137484
\(337\) 9.97412i 0.543325i −0.962393 0.271663i \(-0.912427\pi\)
0.962393 0.271663i \(-0.0875734\pi\)
\(338\) 9.74544i 0.530082i
\(339\) 23.8473 1.29521
\(340\) −1.06362 1.89659i −0.0576828 0.102857i
\(341\) 29.0940 1.57553
\(342\) 0 0
\(343\) 7.77643i 0.419888i
\(344\) 24.1124 1.30006
\(345\) 0.0300171 0.0168338i 0.00161607 0.000906300i
\(346\) −28.0626 −1.50865
\(347\) 29.0836i 1.56129i 0.624975 + 0.780645i \(0.285109\pi\)
−0.624975 + 0.780645i \(0.714891\pi\)
\(348\) 0.760363i 0.0407598i
\(349\) 28.5033 1.52575 0.762874 0.646547i \(-0.223788\pi\)
0.762874 + 0.646547i \(0.223788\pi\)
\(350\) 1.85228 3.03072i 0.0990088 0.161999i
\(351\) −12.8025 −0.683345
\(352\) 7.76727i 0.413997i
\(353\) 6.01136i 0.319952i −0.987121 0.159976i \(-0.948858\pi\)
0.987121 0.159976i \(-0.0511417\pi\)
\(354\) −16.0096 −0.850900
\(355\) 8.90872 4.99606i 0.472826 0.265163i
\(356\) −1.49730 −0.0793569
\(357\) 1.90565i 0.100858i
\(358\) 10.7052i 0.565789i
\(359\) 10.5528 0.556953 0.278477 0.960443i \(-0.410170\pi\)
0.278477 + 0.960443i \(0.410170\pi\)
\(360\) 2.36770 + 4.22195i 0.124789 + 0.222516i
\(361\) 0 0
\(362\) 26.9798i 1.41803i
\(363\) 1.24763i 0.0654836i
\(364\) 0.569244 0.0298365
\(365\) 10.5657 + 18.8402i 0.553035 + 0.986144i
\(366\) 13.9211 0.727668
\(367\) 4.20063i 0.219271i 0.993972 + 0.109636i \(0.0349684\pi\)
−0.993972 + 0.109636i \(0.965032\pi\)
\(368\) 0.0297938i 0.00155311i
\(369\) −7.51430 −0.391179
\(370\) 21.8689 12.2642i 1.13691 0.637587i
\(371\) −4.22998 −0.219610
\(372\) 6.05919i 0.314154i
\(373\) 20.6921i 1.07140i −0.844410 0.535698i \(-0.820049\pi\)
0.844410 0.535698i \(-0.179951\pi\)
\(374\) 8.82746 0.456457
\(375\) 16.9056 + 0.634110i 0.873002 + 0.0327453i
\(376\) −38.2258 −1.97135
\(377\) 2.60992i 0.134418i
\(378\) 3.98836i 0.205139i
\(379\) 4.75485 0.244240 0.122120 0.992515i \(-0.461031\pi\)
0.122120 + 0.992515i \(0.461031\pi\)
\(380\) 0 0
\(381\) −2.05487 −0.105274
\(382\) 6.57150i 0.336227i
\(383\) 8.35408i 0.426874i 0.976957 + 0.213437i \(0.0684658\pi\)
−0.976957 + 0.213437i \(0.931534\pi\)
\(384\) 9.45751 0.482627
\(385\) −1.98378 3.53737i −0.101103 0.180281i
\(386\) −8.57292 −0.436350
\(387\) 5.62109i 0.285736i
\(388\) 1.32493i 0.0672632i
\(389\) 38.3140 1.94260 0.971298 0.237867i \(-0.0764483\pi\)
0.971298 + 0.237867i \(0.0764483\pi\)
\(390\) −4.71505 8.40764i −0.238756 0.425737i
\(391\) 0.0225292 0.00113935
\(392\) 20.3459i 1.02762i
\(393\) 21.0716i 1.06292i
\(394\) 4.96328 0.250047
\(395\) 15.5540 8.72276i 0.782605 0.438889i
\(396\) 0.994897 0.0499954
\(397\) 30.6407i 1.53781i 0.639362 + 0.768906i \(0.279198\pi\)
−0.639362 + 0.768906i \(0.720802\pi\)
\(398\) 17.2860i 0.866467i
\(399\) 0 0
\(400\) −7.63759 + 12.4966i −0.381879 + 0.624832i
\(401\) −9.79094 −0.488936 −0.244468 0.969657i \(-0.578613\pi\)
−0.244468 + 0.969657i \(0.578613\pi\)
\(402\) 6.64075i 0.331211i
\(403\) 20.7979i 1.03602i
\(404\) −6.32941 −0.314900
\(405\) 12.4122 6.96082i 0.616766 0.345886i
\(406\) 0.813069 0.0403520
\(407\) 28.6289i 1.41908i
\(408\) 10.2131i 0.505625i
\(409\) 11.1987 0.553742 0.276871 0.960907i \(-0.410703\pi\)
0.276871 + 0.960907i \(0.410703\pi\)
\(410\) −14.4546 25.7747i −0.713863 1.27292i
\(411\) 25.1627 1.24119
\(412\) 1.93796i 0.0954765i
\(413\) 4.81507i 0.236934i
\(414\) −0.00902762 −0.000443684
\(415\) 15.0276 + 26.7964i 0.737675 + 1.31538i
\(416\) −5.55245 −0.272231
\(417\) 6.45615i 0.316159i
\(418\) 0 0
\(419\) −4.38783 −0.214359 −0.107180 0.994240i \(-0.534182\pi\)
−0.107180 + 0.994240i \(0.534182\pi\)
\(420\) −0.736700 + 0.413146i −0.0359473 + 0.0201594i
\(421\) 18.3686 0.895231 0.447615 0.894226i \(-0.352273\pi\)
0.447615 + 0.894226i \(0.352273\pi\)
\(422\) 14.4875i 0.705240i
\(423\) 8.91120i 0.433277i
\(424\) 22.6702 1.10096
\(425\) 9.44961 + 5.77533i 0.458373 + 0.280144i
\(426\) 8.63551 0.418392
\(427\) 4.18693i 0.202620i
\(428\) 6.09965i 0.294838i
\(429\) −11.0066 −0.531402
\(430\) −19.2808 + 10.8128i −0.929805 + 0.521440i
\(431\) 6.90083 0.332401 0.166201 0.986092i \(-0.446850\pi\)
0.166201 + 0.986092i \(0.446850\pi\)
\(432\) 16.4453i 0.791227i
\(433\) 7.72000i 0.371000i 0.982644 + 0.185500i \(0.0593904\pi\)
−0.982644 + 0.185500i \(0.940610\pi\)
\(434\) 6.47919 0.311011
\(435\) 1.89422 + 3.37768i 0.0908211 + 0.161947i
\(436\) 1.58030 0.0756827
\(437\) 0 0
\(438\) 18.2625i 0.872614i
\(439\) −34.7457 −1.65832 −0.829161 0.559010i \(-0.811181\pi\)
−0.829161 + 0.559010i \(0.811181\pi\)
\(440\) 10.6319 + 18.9582i 0.506854 + 0.903795i
\(441\) 4.74304 0.225859
\(442\) 6.31032i 0.300151i
\(443\) 12.7539i 0.605956i 0.952998 + 0.302978i \(0.0979809\pi\)
−0.952998 + 0.302978i \(0.902019\pi\)
\(444\) −5.96233 −0.282960
\(445\) 6.65131 3.73009i 0.315302 0.176823i
\(446\) 2.44627 0.115834
\(447\) 13.8729i 0.656166i
\(448\) 5.06073i 0.239097i
\(449\) −10.3766 −0.489703 −0.244851 0.969561i \(-0.578739\pi\)
−0.244851 + 0.969561i \(0.578739\pi\)
\(450\) −3.78652 2.31421i −0.178498 0.109093i
\(451\) −33.7421 −1.58885
\(452\) 6.91934i 0.325458i
\(453\) 8.45328i 0.397170i
\(454\) −9.00188 −0.422479
\(455\) −2.52869 + 1.41811i −0.118547 + 0.0664818i
\(456\) 0 0
\(457\) 38.0961i 1.78206i 0.453945 + 0.891030i \(0.350016\pi\)
−0.453945 + 0.891030i \(0.649984\pi\)
\(458\) 21.8621i 1.02155i
\(459\) 12.4355 0.580439
\(460\) 0.00488435 + 0.00870952i 0.000227734 + 0.000406084i
\(461\) −11.7738 −0.548359 −0.274179 0.961679i \(-0.588406\pi\)
−0.274179 + 0.961679i \(0.588406\pi\)
\(462\) 3.42888i 0.159526i
\(463\) 10.4282i 0.484639i 0.970197 + 0.242319i \(0.0779082\pi\)
−0.970197 + 0.242319i \(0.922092\pi\)
\(464\) −3.35256 −0.155639
\(465\) 15.0947 + 26.9161i 0.700000 + 1.24820i
\(466\) 4.74282 0.219707
\(467\) 5.69440i 0.263505i −0.991283 0.131753i \(-0.957940\pi\)
0.991283 0.131753i \(-0.0420605\pi\)
\(468\) 0.711203i 0.0328754i
\(469\) 1.99728 0.0922259
\(470\) 30.5662 17.1417i 1.40991 0.790689i
\(471\) −25.3125 −1.16634
\(472\) 25.8059i 1.18781i
\(473\) 25.2408i 1.16057i
\(474\) 15.0770 0.692507
\(475\) 0 0
\(476\) −0.552927 −0.0253434
\(477\) 5.28487i 0.241978i
\(478\) 13.0881i 0.598637i
\(479\) 24.3790 1.11391 0.556954 0.830544i \(-0.311970\pi\)
0.556954 + 0.830544i \(0.311970\pi\)
\(480\) 7.18583 4.02985i 0.327987 0.183937i
\(481\) −20.4654 −0.933144
\(482\) 3.58531i 0.163306i
\(483\) 0.00875112i 0.000398190i
\(484\) −0.362002 −0.0164546
\(485\) 3.30068 + 5.88560i 0.149876 + 0.267251i
\(486\) −9.01194 −0.408790
\(487\) 5.30022i 0.240176i −0.992763 0.120088i \(-0.961682\pi\)
0.992763 0.120088i \(-0.0383176\pi\)
\(488\) 22.4395i 1.01579i
\(489\) 36.8197 1.66505
\(490\) 9.12378 + 16.2690i 0.412170 + 0.734960i
\(491\) −11.7908 −0.532109 −0.266055 0.963958i \(-0.585720\pi\)
−0.266055 + 0.963958i \(0.585720\pi\)
\(492\) 7.02719i 0.316810i
\(493\) 2.53511i 0.114175i
\(494\) 0 0
\(495\) −4.41953 + 2.47850i −0.198643 + 0.111400i
\(496\) −26.7159 −1.19958
\(497\) 2.59723i 0.116501i
\(498\) 25.9746i 1.16395i
\(499\) 33.7253 1.50975 0.754877 0.655867i \(-0.227697\pi\)
0.754877 + 0.655867i \(0.227697\pi\)
\(500\) −0.183988 + 4.90519i −0.00822820 + 0.219367i
\(501\) 5.99552 0.267860
\(502\) 23.9167i 1.06745i
\(503\) 4.11086i 0.183294i −0.995792 0.0916471i \(-0.970787\pi\)
0.995792 0.0916471i \(-0.0292132\pi\)
\(504\) 1.23086 0.0548267
\(505\) 28.1165 15.7679i 1.25117 0.701662i
\(506\) −0.0405375 −0.00180211
\(507\) 11.8029i 0.524183i
\(508\) 0.596223i 0.0264531i
\(509\) −16.7776 −0.743656 −0.371828 0.928302i \(-0.621269\pi\)
−0.371828 + 0.928302i \(0.621269\pi\)
\(510\) 4.57990 + 8.16665i 0.202802 + 0.361625i
\(511\) 5.49264 0.242980
\(512\) 24.9844i 1.10416i
\(513\) 0 0
\(514\) 12.7820 0.563789
\(515\) 4.82787 + 8.60880i 0.212741 + 0.379349i
\(516\) 5.25671 0.231414
\(517\) 40.0147i 1.75984i
\(518\) 6.37562i 0.280129i
\(519\) −33.9870 −1.49186
\(520\) 13.5523 7.60020i 0.594307 0.333291i
\(521\) −35.3846 −1.55023 −0.775114 0.631822i \(-0.782307\pi\)
−0.775114 + 0.631822i \(0.782307\pi\)
\(522\) 1.01583i 0.0444619i
\(523\) 19.9927i 0.874221i −0.899408 0.437110i \(-0.856002\pi\)
0.899408 0.437110i \(-0.143998\pi\)
\(524\) 6.11396 0.267090
\(525\) 2.24333 3.67055i 0.0979070 0.160196i
\(526\) 8.28139 0.361086
\(527\) 20.2018i 0.880003i
\(528\) 14.1384i 0.615296i
\(529\) 22.9999 0.999996
\(530\) −18.1276 + 10.1661i −0.787412 + 0.441585i
\(531\) 6.01586 0.261066
\(532\) 0 0
\(533\) 24.1206i 1.04478i
\(534\) 6.44733 0.279003
\(535\) −15.1955 27.0958i −0.656959 1.17145i
\(536\) −10.7042 −0.462352
\(537\) 12.9653i 0.559493i
\(538\) 16.0721i 0.692917i
\(539\) 21.2980 0.917371
\(540\) 2.69602 + 4.80741i 0.116018 + 0.206878i
\(541\) 4.66775 0.200682 0.100341 0.994953i \(-0.468007\pi\)
0.100341 + 0.994953i \(0.468007\pi\)
\(542\) 11.5708i 0.497009i
\(543\) 32.6757i 1.40225i
\(544\) 5.39330 0.231236
\(545\) −7.02000 + 3.93686i −0.300704 + 0.168637i
\(546\) −2.45114 −0.104899
\(547\) 35.9629i 1.53766i 0.639451 + 0.768832i \(0.279162\pi\)
−0.639451 + 0.768832i \(0.720838\pi\)
\(548\) 7.30101i 0.311884i
\(549\) −5.23108 −0.223257
\(550\) −17.0029 10.3917i −0.725007 0.443103i
\(551\) 0 0
\(552\) 0.0469008i 0.00199623i
\(553\) 4.53456i 0.192829i
\(554\) −15.8389 −0.672932
\(555\) 26.4858 14.8534i 1.12426 0.630492i
\(556\) 1.87326 0.0794441
\(557\) 2.43899i 0.103343i −0.998664 0.0516716i \(-0.983545\pi\)
0.998664 0.0516716i \(-0.0164549\pi\)
\(558\) 8.09499i 0.342688i
\(559\) 18.0434 0.763156
\(560\) 1.82162 + 3.24822i 0.0769775 + 0.137262i
\(561\) 10.6911 0.451377
\(562\) 35.8542i 1.51242i
\(563\) 37.5088i 1.58081i 0.612586 + 0.790404i \(0.290129\pi\)
−0.612586 + 0.790404i \(0.709871\pi\)
\(564\) −8.33354 −0.350905
\(565\) −17.2375 30.7371i −0.725188 1.29312i
\(566\) −17.4567 −0.733760
\(567\) 3.61861i 0.151967i
\(568\) 13.9196i 0.584052i
\(569\) 8.58058 0.359717 0.179858 0.983693i \(-0.442436\pi\)
0.179858 + 0.983693i \(0.442436\pi\)
\(570\) 0 0
\(571\) −14.8947 −0.623324 −0.311662 0.950193i \(-0.600886\pi\)
−0.311662 + 0.950193i \(0.600886\pi\)
\(572\) 3.19357i 0.133530i
\(573\) 7.95885i 0.332486i
\(574\) −7.51430 −0.313641
\(575\) −0.0433945 0.0265215i −0.00180968 0.00110602i
\(576\) −6.32279 −0.263450
\(577\) 31.7203i 1.32054i 0.751030 + 0.660268i \(0.229557\pi\)
−0.751030 + 0.660268i \(0.770443\pi\)
\(578\) 15.1101i 0.628496i
\(579\) −10.3828 −0.431494
\(580\) −0.980041 + 0.549613i −0.0406940 + 0.0228214i
\(581\) 7.81216 0.324103
\(582\) 5.70510i 0.236484i
\(583\) 23.7311i 0.982841i
\(584\) −29.4373 −1.21812
\(585\) 1.77176 + 3.15930i 0.0732531 + 0.130621i
\(586\) −7.21184 −0.297918
\(587\) 6.36781i 0.262828i 0.991328 + 0.131414i \(0.0419516\pi\)
−0.991328 + 0.131414i \(0.958048\pi\)
\(588\) 4.43558i 0.182920i
\(589\) 0 0
\(590\) 11.5722 + 20.6349i 0.476420 + 0.849527i
\(591\) 6.01111 0.247264
\(592\) 26.2888i 1.08046i
\(593\) 15.9159i 0.653590i 0.945095 + 0.326795i \(0.105969\pi\)
−0.945095 + 0.326795i \(0.894031\pi\)
\(594\) −22.3755 −0.918079
\(595\) 2.45621 1.37746i 0.100695 0.0564703i
\(596\) 4.02525 0.164881
\(597\) 20.9353i 0.856825i
\(598\) 0.0289783i 0.00118501i
\(599\) −43.2212 −1.76597 −0.882985 0.469401i \(-0.844470\pi\)
−0.882985 + 0.469401i \(0.844470\pi\)
\(600\) −12.0229 + 19.6719i −0.490833 + 0.803103i
\(601\) 31.4293 1.28203 0.641015 0.767528i \(-0.278514\pi\)
0.641015 + 0.767528i \(0.278514\pi\)
\(602\) 5.62109i 0.229098i
\(603\) 2.49537i 0.101619i
\(604\) 2.45273 0.0998004
\(605\) 1.60808 0.901823i 0.0653779 0.0366643i
\(606\) 27.2542 1.10713
\(607\) 29.2401i 1.18682i 0.804900 + 0.593410i \(0.202219\pi\)
−0.804900 + 0.593410i \(0.797781\pi\)
\(608\) 0 0
\(609\) 0.984721 0.0399029
\(610\) −10.0626 17.9431i −0.407422 0.726494i
\(611\) −28.6046 −1.15722
\(612\) 0.690818i 0.0279247i
\(613\) 29.0513i 1.17337i −0.809815 0.586685i \(-0.800433\pi\)
0.809815 0.586685i \(-0.199567\pi\)
\(614\) 12.9248 0.521604
\(615\) −17.5062 31.2162i −0.705919 1.25876i
\(616\) 5.52702 0.222690
\(617\) 11.6592i 0.469383i −0.972070 0.234691i \(-0.924592\pi\)
0.972070 0.234691i \(-0.0754080\pi\)
\(618\) 8.34479i 0.335677i
\(619\) −6.40765 −0.257545 −0.128773 0.991674i \(-0.541104\pi\)
−0.128773 + 0.991674i \(0.541104\pi\)
\(620\) −7.80975 + 4.37976i −0.313647 + 0.175895i
\(621\) −0.0571063 −0.00229160
\(622\) 18.5153i 0.742395i
\(623\) 1.93911i 0.0776886i
\(624\) 10.1069 0.404599
\(625\) −11.4026 22.2482i −0.456102 0.889927i
\(626\) 22.9844 0.918641
\(627\) 0 0
\(628\) 7.34447i 0.293076i
\(629\) 19.8788 0.792621
\(630\) −0.984221 + 0.551957i −0.0392123 + 0.0219905i
\(631\) −36.4184 −1.44979 −0.724896 0.688858i \(-0.758112\pi\)
−0.724896 + 0.688858i \(0.758112\pi\)
\(632\) 24.3025i 0.966703i
\(633\) 17.5460i 0.697392i
\(634\) −0.604925 −0.0240246
\(635\) 1.48532 + 2.64854i 0.0589430 + 0.105104i
\(636\) 4.94229 0.195974
\(637\) 15.2249i 0.603234i
\(638\) 4.56149i 0.180591i
\(639\) −3.24493 −0.128367
\(640\) −6.83617 12.1899i −0.270223 0.481848i
\(641\) 8.52575 0.336747 0.168373 0.985723i \(-0.446149\pi\)
0.168373 + 0.985723i \(0.446149\pi\)
\(642\) 26.2648i 1.03659i
\(643\) 2.82522i 0.111416i 0.998447 + 0.0557079i \(0.0177416\pi\)
−0.998447 + 0.0557079i \(0.982258\pi\)
\(644\) 0.00253915 0.000100057
\(645\) −23.3513 + 13.0956i −0.919458 + 0.515637i
\(646\) 0 0
\(647\) 20.7093i 0.814168i −0.913391 0.407084i \(-0.866546\pi\)
0.913391 0.407084i \(-0.133454\pi\)
\(648\) 19.3936i 0.761853i
\(649\) 27.0135 1.06037
\(650\) −7.42852 + 12.1546i −0.291371 + 0.476741i
\(651\) 7.84705 0.307550
\(652\) 10.6833i 0.418391i
\(653\) 18.4680i 0.722709i −0.932428 0.361355i \(-0.882314\pi\)
0.932428 0.361355i \(-0.117686\pi\)
\(654\) −6.80471 −0.266085
\(655\) −27.1594 + 15.2312i −1.06121 + 0.595131i
\(656\) 30.9840 1.20972
\(657\) 6.86241i 0.267728i
\(658\) 8.91120i 0.347395i
\(659\) 19.0672 0.742754 0.371377 0.928482i \(-0.378886\pi\)
0.371377 + 0.928482i \(0.378886\pi\)
\(660\) 2.31783 + 4.13304i 0.0902215 + 0.160878i
\(661\) 34.5435 1.34359 0.671793 0.740739i \(-0.265524\pi\)
0.671793 + 0.740739i \(0.265524\pi\)
\(662\) 34.5839i 1.34414i
\(663\) 7.64253i 0.296811i
\(664\) −41.8685 −1.62481
\(665\) 0 0
\(666\) −7.96559 −0.308660
\(667\) 0.0116417i 0.000450769i
\(668\) 1.73961i 0.0673076i
\(669\) 2.96271 0.114545
\(670\) 8.55934 4.80013i 0.330676 0.185445i
\(671\) −23.4896 −0.906804
\(672\) 2.09494i 0.0808140i
\(673\) 35.7304i 1.37731i 0.725091 + 0.688653i \(0.241798\pi\)
−0.725091 + 0.688653i \(0.758202\pi\)
\(674\) −12.4615 −0.479999
\(675\) −23.9525 14.6391i −0.921933 0.563459i
\(676\) 3.42462 0.131716
\(677\) 22.3529i 0.859090i −0.903045 0.429545i \(-0.858674\pi\)
0.903045 0.429545i \(-0.141326\pi\)
\(678\) 29.7944i 1.14425i
\(679\) 1.71587 0.0658492
\(680\) −13.1638 + 7.38235i −0.504809 + 0.283100i
\(681\) −10.9023 −0.417778
\(682\) 36.3496i 1.39190i
\(683\) 16.4252i 0.628492i −0.949342 0.314246i \(-0.898248\pi\)
0.949342 0.314246i \(-0.101752\pi\)
\(684\) 0 0
\(685\) −18.1883 32.4325i −0.694941 1.23918i
\(686\) 9.71574 0.370949
\(687\) 26.4776i 1.01018i
\(688\) 23.1776i 0.883639i
\(689\) 16.9642 0.646284
\(690\) −0.0210318 0.0375029i −0.000800669 0.00142771i
\(691\) 4.36093 0.165898 0.0829489 0.996554i \(-0.473566\pi\)
0.0829489 + 0.996554i \(0.473566\pi\)
\(692\) 9.86139i 0.374874i
\(693\) 1.28846i 0.0489445i
\(694\) 36.3365 1.37932
\(695\) −8.32140 + 4.66669i −0.315649 + 0.177018i
\(696\) −5.27752 −0.200044
\(697\) 23.4292i 0.887443i
\(698\) 35.6116i 1.34792i
\(699\) 5.74411 0.217262
\(700\) 1.06502 + 0.650907i 0.0402538 + 0.0246020i
\(701\) 27.8728 1.05274 0.526371 0.850255i \(-0.323552\pi\)
0.526371 + 0.850255i \(0.323552\pi\)
\(702\) 15.9952i 0.603699i
\(703\) 0 0
\(704\) −28.3917 −1.07005
\(705\) 37.0192 20.7606i 1.39422 0.781890i
\(706\) −7.51049 −0.282661
\(707\) 8.19701i 0.308280i
\(708\) 5.62589i 0.211434i
\(709\) 19.8448 0.745288 0.372644 0.927974i \(-0.378451\pi\)
0.372644 + 0.927974i \(0.378451\pi\)
\(710\) −6.24199 11.1304i −0.234258 0.417716i
\(711\) −5.66541 −0.212469
\(712\) 10.3924i 0.389473i
\(713\) 0.0927706i 0.00347429i
\(714\) 2.38088 0.0891023
\(715\) 7.95586 + 14.1865i 0.297532 + 0.530544i
\(716\) −3.76190 −0.140589
\(717\) 15.8512i 0.591975i
\(718\) 13.1844i 0.492039i
\(719\) −25.9216 −0.966713 −0.483357 0.875424i \(-0.660583\pi\)
−0.483357 + 0.875424i \(0.660583\pi\)
\(720\) 4.05827 2.27590i 0.151243 0.0848179i
\(721\) 2.50979 0.0934694
\(722\) 0 0
\(723\) 4.34223i 0.161489i
\(724\) 9.48091 0.352355
\(725\) 2.98433 4.88297i 0.110835 0.181349i
\(726\) 1.55877 0.0578513
\(727\) 15.0074i 0.556595i 0.960495 + 0.278297i \(0.0897701\pi\)
−0.960495 + 0.278297i \(0.910230\pi\)
\(728\) 3.95100i 0.146434i
\(729\) −30.0071 −1.11137
\(730\) 23.5387 13.2006i 0.871206 0.488577i
\(731\) −17.5263 −0.648232
\(732\) 4.89198i 0.180813i
\(733\) 35.9465i 1.32771i 0.747859 + 0.663857i \(0.231082\pi\)
−0.747859 + 0.663857i \(0.768918\pi\)
\(734\) 5.24820 0.193715
\(735\) 11.0499 + 19.7037i 0.407583 + 0.726782i
\(736\) −0.0247671 −0.000912927
\(737\) 11.2052i 0.412747i
\(738\) 9.38823i 0.345586i
\(739\) −25.5211 −0.938811 −0.469405 0.882983i \(-0.655532\pi\)
−0.469405 + 0.882983i \(0.655532\pi\)
\(740\) 4.30974 + 7.68491i 0.158429 + 0.282503i
\(741\) 0 0
\(742\) 5.28487i 0.194014i
\(743\) 46.9698i 1.72315i 0.507627 + 0.861577i \(0.330523\pi\)
−0.507627 + 0.861577i \(0.669477\pi\)
\(744\) −42.0555 −1.54183
\(745\) −17.8809 + 10.0277i −0.655107 + 0.367388i
\(746\) −25.8523 −0.946521
\(747\) 9.76038i 0.357114i
\(748\) 3.10203i 0.113422i
\(749\) −7.89945 −0.288640
\(750\) 0.792246 21.1216i 0.0289287 0.771251i
\(751\) 15.4684 0.564450 0.282225 0.959348i \(-0.408927\pi\)
0.282225 + 0.959348i \(0.408927\pi\)
\(752\) 36.7438i 1.33991i
\(753\) 28.9659i 1.05558i
\(754\) −3.26078 −0.118751
\(755\) −10.8955 + 6.11028i −0.396529 + 0.222376i
\(756\) 1.40154 0.0509735
\(757\) 21.7345i 0.789953i −0.918691 0.394976i \(-0.870753\pi\)
0.918691 0.394976i \(-0.129247\pi\)
\(758\) 5.94063i 0.215773i
\(759\) −0.0490956 −0.00178206
\(760\) 0 0
\(761\) 21.2697 0.771026 0.385513 0.922703i \(-0.374025\pi\)
0.385513 + 0.922703i \(0.374025\pi\)
\(762\) 2.56731i 0.0930039i
\(763\) 2.04659i 0.0740917i
\(764\) 2.30927 0.0835466
\(765\) −1.72097 3.06875i −0.0622219 0.110951i
\(766\) 10.4374 0.377120
\(767\) 19.3106i 0.697267i
\(768\) 15.1195i 0.545578i
\(769\) −12.9195 −0.465888 −0.232944 0.972490i \(-0.574836\pi\)
−0.232944 + 0.972490i \(0.574836\pi\)
\(770\) −4.41953 + 2.47850i −0.159269 + 0.0893188i
\(771\) 15.4805 0.557515
\(772\) 3.01259i 0.108425i
\(773\) 47.4575i 1.70693i 0.521151 + 0.853464i \(0.325503\pi\)
−0.521151 + 0.853464i \(0.674497\pi\)
\(774\) 7.02289 0.252433
\(775\) 23.7816 38.9115i 0.854259 1.39774i
\(776\) −9.19605 −0.330119
\(777\) 7.72161i 0.277011i
\(778\) 47.8688i 1.71618i
\(779\) 0 0
\(780\) 2.95451 1.65690i 0.105788 0.0593267i
\(781\) −14.5710 −0.521390
\(782\) 0.0281476i 0.00100656i
\(783\) 6.42590i 0.229643i
\(784\) −19.5571 −0.698469
\(785\) 18.2966 + 32.6256i 0.653034 + 1.16446i
\(786\) −26.3265 −0.939035
\(787\) 41.7297i 1.48750i 0.668456 + 0.743752i \(0.266955\pi\)
−0.668456 + 0.743752i \(0.733045\pi\)
\(788\) 1.74414i 0.0621322i
\(789\) 10.0297 0.357067
\(790\) −10.8981 19.4329i −0.387736 0.691390i
\(791\) −8.96101 −0.318617
\(792\) 6.90536i 0.245371i
\(793\) 16.7915i 0.596285i
\(794\) 38.2819 1.35857
\(795\) −21.9546 + 12.3123i −0.778649 + 0.436671i
\(796\) 6.07442 0.215302
\(797\) 19.5110i 0.691117i −0.938397 0.345558i \(-0.887690\pi\)
0.938397 0.345558i \(-0.112310\pi\)
\(798\) 0 0
\(799\) 27.7846 0.982950
\(800\) −10.3882 6.34900i −0.367280 0.224471i
\(801\) −2.42269 −0.0856014
\(802\) 12.2326i 0.431949i
\(803\) 30.8148i 1.08743i
\(804\) −2.33361 −0.0823001
\(805\) −0.0112794 + 0.00632556i −0.000397547 + 0.000222947i
\(806\) −25.9846 −0.915267
\(807\) 19.4652i 0.685206i
\(808\) 43.9311i 1.54549i
\(809\) 6.34419 0.223050 0.111525 0.993762i \(-0.464427\pi\)
0.111525 + 0.993762i \(0.464427\pi\)
\(810\) −8.69673 15.5076i −0.305572 0.544880i
\(811\) −44.8038 −1.57327 −0.786637 0.617416i \(-0.788179\pi\)
−0.786637 + 0.617416i \(0.788179\pi\)
\(812\) 0.285719i 0.0100268i
\(813\) 14.0136i 0.491478i
\(814\) −35.7685 −1.25369
\(815\) −26.6144 47.4574i −0.932261 1.66236i
\(816\) −9.81718 −0.343670
\(817\) 0 0
\(818\) 13.9915i 0.489201i
\(819\) 0.921056 0.0321843
\(820\) 9.05743 5.07946i 0.316299 0.177382i
\(821\) 44.2814 1.54543 0.772716 0.634752i \(-0.218898\pi\)
0.772716 + 0.634752i \(0.218898\pi\)
\(822\) 31.4379i 1.09652i
\(823\) 20.6550i 0.719988i −0.932955 0.359994i \(-0.882779\pi\)
0.932955 0.359994i \(-0.117221\pi\)
\(824\) −13.4510 −0.468587
\(825\) −20.5925 12.5855i −0.716939 0.438173i
\(826\) 6.01586 0.209319
\(827\) 44.6161i 1.55145i 0.631068 + 0.775727i \(0.282617\pi\)
−0.631068 + 0.775727i \(0.717383\pi\)
\(828\) 0.00317237i 0.000110248i
\(829\) −28.3748 −0.985496 −0.492748 0.870172i \(-0.664008\pi\)
−0.492748 + 0.870172i \(0.664008\pi\)
\(830\) 33.4790 18.7752i 1.16207 0.651697i
\(831\) −19.1828 −0.665443
\(832\) 20.2959i 0.703633i
\(833\) 14.7885i 0.512392i
\(834\) −8.06620 −0.279310
\(835\) −4.33374 7.72770i −0.149975 0.267428i
\(836\) 0 0
\(837\) 51.2067i 1.76996i
\(838\) 5.48208i 0.189375i
\(839\) −13.5641 −0.468283 −0.234142 0.972203i \(-0.575228\pi\)
−0.234142 + 0.972203i \(0.575228\pi\)
\(840\) 2.86755 + 5.11327i 0.0989400 + 0.176425i
\(841\) −27.6900 −0.954828
\(842\) 22.9494i 0.790889i
\(843\) 43.4236i 1.49559i
\(844\) −5.09101 −0.175240
\(845\) −15.2128 + 8.53145i −0.523337 + 0.293491i
\(846\) −11.1335 −0.382778
\(847\) 0.468817i 0.0161087i
\(848\) 21.7913i 0.748316i
\(849\) −21.1421 −0.725595
\(850\) 7.21559 11.8062i 0.247493 0.404949i
\(851\) −0.0912876 −0.00312930
\(852\) 3.03458i 0.103963i
\(853\) 39.4266i 1.34994i 0.737844 + 0.674971i \(0.235844\pi\)
−0.737844 + 0.674971i \(0.764156\pi\)
\(854\) −5.23108 −0.179004
\(855\) 0 0
\(856\) 42.3363 1.44703
\(857\) 39.4383i 1.34719i 0.739102 + 0.673594i \(0.235250\pi\)
−0.739102 + 0.673594i \(0.764750\pi\)
\(858\) 13.7514i 0.469465i
\(859\) −42.4044 −1.44682 −0.723410 0.690419i \(-0.757426\pi\)
−0.723410 + 0.690419i \(0.757426\pi\)
\(860\) −3.79970 6.77543i −0.129569 0.231040i
\(861\) −9.10068 −0.310150
\(862\) 8.62178i 0.293659i
\(863\) 17.5670i 0.597986i 0.954255 + 0.298993i \(0.0966508\pi\)
−0.954255 + 0.298993i \(0.903349\pi\)
\(864\) −13.6707 −0.465088
\(865\) 24.5668 + 43.8062i 0.835296 + 1.48946i
\(866\) 9.64524 0.327759
\(867\) 18.3000i 0.621502i
\(868\) 2.27684i 0.0772809i
\(869\) −25.4398 −0.862987
\(870\) 4.22002 2.36661i 0.143072 0.0802356i
\(871\) −8.01002 −0.271409
\(872\) 10.9685i 0.371441i
\(873\) 2.14378i 0.0725561i
\(874\) 0 0
\(875\) −6.35255 0.238277i −0.214756 0.00805523i
\(876\) −6.41756 −0.216829
\(877\) 23.3460i 0.788339i −0.919038 0.394170i \(-0.871032\pi\)
0.919038 0.394170i \(-0.128968\pi\)
\(878\) 43.4107i 1.46504i
\(879\) −8.73437 −0.294603
\(880\) 18.2232 10.2197i 0.614303 0.344505i
\(881\) −32.9857 −1.11132 −0.555659 0.831410i \(-0.687534\pi\)
−0.555659 + 0.831410i \(0.687534\pi\)
\(882\) 5.92587i 0.199534i
\(883\) 39.9863i 1.34565i −0.739803 0.672823i \(-0.765081\pi\)
0.739803 0.672823i \(-0.234919\pi\)
\(884\) 2.21749 0.0745824
\(885\) 14.0153 + 24.9913i 0.471118 + 0.840074i
\(886\) 15.9345 0.535330
\(887\) 32.2412i 1.08255i 0.840844 + 0.541277i \(0.182059\pi\)
−0.840844 + 0.541277i \(0.817941\pi\)
\(888\) 41.3832i 1.38873i
\(889\) 0.772148 0.0258970
\(890\) −4.66032 8.31003i −0.156214 0.278553i
\(891\) −20.3012 −0.680114
\(892\) 0.859636i 0.0287827i
\(893\) 0 0
\(894\) −17.3326 −0.579688
\(895\) 16.7111 9.37168i 0.558590 0.313261i
\(896\) −3.55381 −0.118725
\(897\) 0.0350960i 0.00117182i
\(898\) 12.9644i 0.432626i
\(899\) 10.4390 0.348161
\(900\) 0.813232 1.33061i 0.0271077 0.0443538i
\(901\) −16.4779 −0.548960
\(902\) 42.1567i 1.40367i
\(903\) 6.80779i 0.226549i
\(904\) 48.0256 1.59731
\(905\) −42.1160 + 23.6189i −1.39998 + 0.785120i
\(906\) −10.5614 −0.350878
\(907\) 23.6201i 0.784294i −0.919903 0.392147i \(-0.871732\pi\)
0.919903 0.392147i \(-0.128268\pi\)
\(908\) 3.16333i 0.104979i
\(909\) −10.2412 −0.339679
\(910\) 1.77176 + 3.15930i 0.0587332 + 0.104730i
\(911\) −31.5189 −1.04427 −0.522135 0.852863i \(-0.674864\pi\)
−0.522135 + 0.852863i \(0.674864\pi\)
\(912\) 0 0
\(913\) 43.8278i 1.45049i
\(914\) 47.5966 1.57436
\(915\) −12.1870 21.7312i −0.402888 0.718410i
\(916\) 7.68252 0.253838
\(917\) 7.91799i 0.261475i
\(918\) 15.5367i 0.512787i
\(919\) −9.34643 −0.308310 −0.154155 0.988047i \(-0.549266\pi\)
−0.154155 + 0.988047i \(0.549266\pi\)
\(920\) 0.0604509 0.0339012i 0.00199301 0.00111769i
\(921\) 15.6535 0.515799
\(922\) 14.7099i 0.484446i
\(923\) 10.4161i 0.342849i
\(924\) 1.20494 0.0396395
\(925\) −38.2894 23.4014i −1.25895 0.769433i
\(926\) 13.0288 0.428153
\(927\) 3.13569i 0.102989i
\(928\) 2.78692i 0.0914852i
\(929\) 19.7560 0.648172 0.324086 0.946028i \(-0.394943\pi\)
0.324086 + 0.946028i \(0.394943\pi\)
\(930\) 33.6285 18.8591i 1.10272 0.618413i
\(931\) 0 0
\(932\) 1.66666i 0.0545934i
\(933\) 22.4241i 0.734133i
\(934\) −7.11448 −0.232793
\(935\) −7.72782 13.7798i −0.252727 0.450649i
\(936\) −4.93631 −0.161348
\(937\) 10.9310i 0.357099i 0.983931 + 0.178550i \(0.0571405\pi\)
−0.983931 + 0.178550i \(0.942859\pi\)
\(938\) 2.49537i 0.0814767i
\(939\) 27.8368 0.908418
\(940\) 6.02373 + 10.7412i 0.196472 + 0.350339i
\(941\) 4.48898 0.146337 0.0731683 0.997320i \(-0.476689\pi\)
0.0731683 + 0.997320i \(0.476689\pi\)
\(942\) 31.6250i 1.03040i
\(943\) 0.107592i 0.00350366i
\(944\) −24.8054 −0.807347
\(945\) −6.22591 + 3.49153i −0.202529 + 0.113579i
\(946\) 31.5355 1.02531
\(947\) 21.4661i 0.697554i 0.937206 + 0.348777i \(0.113403\pi\)
−0.937206 + 0.348777i \(0.886597\pi\)
\(948\) 5.29815i 0.172076i
\(949\) −22.0280 −0.715060
\(950\) 0 0
\(951\) −0.732634 −0.0237573
\(952\) 3.83775i 0.124382i
\(953\) 17.6118i 0.570502i 0.958453 + 0.285251i \(0.0920770\pi\)
−0.958453 + 0.285251i \(0.907923\pi\)
\(954\) 6.60283 0.213774
\(955\) −10.2582 + 5.75289i −0.331949 + 0.186159i
\(956\) −4.59926 −0.148751
\(957\) 5.52449i 0.178581i
\(958\) 30.4588i 0.984078i
\(959\) −9.45529 −0.305327
\(960\) −14.7303 26.2664i −0.475420 0.847744i
\(961\) 52.1866 1.68344
\(962\) 25.5692i 0.824383i
\(963\) 9.86944i 0.318038i
\(964\) −1.25991 −0.0405788
\(965\) 7.50499 + 13.3825i 0.241594 + 0.430798i
\(966\) −0.0109335 −0.000351780
\(967\) 18.1535i 0.583777i −0.956452 0.291888i \(-0.905716\pi\)
0.956452 0.291888i \(-0.0942836\pi\)
\(968\) 2.51258i 0.0807573i
\(969\) 0 0
\(970\) 7.35337 4.12381i 0.236102 0.132408i
\(971\) 26.8785 0.862571 0.431286 0.902215i \(-0.358060\pi\)
0.431286 + 0.902215i \(0.358060\pi\)
\(972\) 3.16686i 0.101577i
\(973\) 2.42600i 0.0777740i
\(974\) −6.62200 −0.212183
\(975\) −8.99680 + 14.7206i −0.288128 + 0.471436i
\(976\) 21.5695 0.690423
\(977\) 25.0326i 0.800863i −0.916327 0.400431i \(-0.868860\pi\)
0.916327 0.400431i \(-0.131140\pi\)
\(978\) 46.0019i 1.47098i
\(979\) −10.8788 −0.347687
\(980\) −5.71706 + 3.20616i −0.182625 + 0.102417i
\(981\) 2.55698 0.0816381
\(982\) 14.7312i 0.470090i
\(983\) 34.3362i 1.09516i 0.836755 + 0.547578i \(0.184450\pi\)
−0.836755 + 0.547578i \(0.815550\pi\)
\(984\) 48.7742 1.55487
\(985\) −4.34501 7.74779i −0.138443 0.246865i
\(986\) 3.16732 0.100868
\(987\) 10.7925i 0.343529i
\(988\) 0 0
\(989\) 0.0804841 0.00255925
\(990\) 3.09659 + 5.52168i 0.0984161 + 0.175490i
\(991\) −24.3932 −0.774875 −0.387438 0.921896i \(-0.626640\pi\)
−0.387438 + 0.921896i \(0.626640\pi\)
\(992\) 22.2084i 0.705119i
\(993\) 41.8851i 1.32918i
\(994\) −3.24493 −0.102923
\(995\) −26.9837 + 15.1326i −0.855442 + 0.479737i
\(996\) −9.12768 −0.289221
\(997\) 39.4701i 1.25003i 0.780613 + 0.625015i \(0.214907\pi\)
−0.780613 + 0.625015i \(0.785093\pi\)
\(998\) 42.1359i 1.33379i
\(999\) −50.3881 −1.59421
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 1805.2.b.i.1084.5 16
5.2 odd 4 9025.2.a.cl.1.12 16
5.3 odd 4 9025.2.a.cl.1.5 16
5.4 even 2 inner 1805.2.b.i.1084.12 yes 16
19.18 odd 2 1805.2.b.j.1084.12 yes 16
95.18 even 4 9025.2.a.ck.1.12 16
95.37 even 4 9025.2.a.ck.1.5 16
95.94 odd 2 1805.2.b.j.1084.5 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1805.2.b.i.1084.5 16 1.1 even 1 trivial
1805.2.b.i.1084.12 yes 16 5.4 even 2 inner
1805.2.b.j.1084.5 yes 16 95.94 odd 2
1805.2.b.j.1084.12 yes 16 19.18 odd 2
9025.2.a.ck.1.5 16 95.37 even 4
9025.2.a.ck.1.12 16 95.18 even 4
9025.2.a.cl.1.5 16 5.3 odd 4
9025.2.a.cl.1.12 16 5.2 odd 4