Properties

Label 297.2.n.a.262.1
Level $297$
Weight $2$
Character 297.262
Analytic conductor $2.372$
Analytic rank $0$
Dimension $8$
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] = [297,2,Mod(37,297)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(297, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([10, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("297.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 297 = 3^{3} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 297.n (of order \(15\), degree \(8\), not 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: \(2.37155694003\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\Q(\zeta_{15})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 99)
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 262.1
Root \(-0.978148 + 0.207912i\) of defining polynomial
Character \(\chi\) \(=\) 297.262
Dual form 297.2.n.a.280.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.255585 + 0.283856i) q^{2} +(0.193806 - 1.84395i) q^{4} +(0.827091 - 0.918578i) q^{5} +(-0.913545 + 0.406737i) q^{7} +(1.19098 - 0.865300i) q^{8} +O(q^{10})\) \(q+(0.255585 + 0.283856i) q^{2} +(0.193806 - 1.84395i) q^{4} +(0.827091 - 0.918578i) q^{5} +(-0.913545 + 0.406737i) q^{7} +(1.19098 - 0.865300i) q^{8} +0.472136 q^{10} +(-2.70528 - 1.91872i) q^{11} +(6.33070 - 1.34563i) q^{13} +(-0.348943 - 0.155360i) q^{14} +(-3.07715 - 0.654069i) q^{16} +(-1.50000 - 4.61653i) q^{17} +(-0.809017 + 0.587785i) q^{19} +(-1.53351 - 1.70314i) q^{20} +(-0.146790 - 1.25830i) q^{22} +(2.30902 + 3.99933i) q^{23} +(0.362937 + 3.45312i) q^{25} +(2.00000 + 1.45309i) q^{26} +(0.572949 + 1.76336i) q^{28} +(4.43444 - 1.97434i) q^{29} +(-0.604528 + 0.128496i) q^{31} +(-2.07295 - 3.59045i) q^{32} +(0.927051 - 1.60570i) q^{34} +(-0.381966 + 1.17557i) q^{35} +(4.11803 + 2.99193i) q^{37} +(-0.373619 - 0.0794152i) q^{38} +(0.190206 - 1.80969i) q^{40} +(2.30932 + 1.02817i) q^{41} +(-0.927051 + 1.60570i) q^{43} +(-4.06231 + 4.61653i) q^{44} +(-0.545085 + 1.67760i) q^{46} +(1.24852 + 11.8788i) q^{47} +(-4.01478 + 4.45887i) q^{49} +(-0.887426 + 0.985587i) q^{50} +(-1.25434 - 11.9343i) q^{52} +(-1.26393 + 3.88998i) q^{53} +(-4.00000 + 0.898056i) q^{55} +(-0.736068 + 1.27491i) q^{56} +(1.69381 + 0.754131i) q^{58} +(0.169131 - 1.60917i) q^{59} +(-10.6169 - 2.25669i) q^{61} +(-0.190983 - 0.138757i) q^{62} +(-1.45492 + 4.47777i) q^{64} +(4.00000 - 6.92820i) q^{65} +(-3.00000 - 5.19615i) q^{67} +(-8.80333 + 1.87121i) q^{68} +(-0.431318 + 0.192035i) q^{70} +(0.899187 + 2.76741i) q^{71} +(0.118034 + 0.0857567i) q^{73} +(0.203232 + 1.93362i) q^{74} +(0.927051 + 1.60570i) q^{76} +(3.25181 + 0.652498i) q^{77} +(7.06756 + 7.84932i) q^{79} +(-3.14590 + 2.28563i) q^{80} +(0.298374 + 0.918300i) q^{82} +(-9.55057 - 2.03004i) q^{83} +(-5.48127 - 2.44042i) q^{85} +(-0.692728 + 0.147244i) q^{86} +(-4.88220 + 0.0557196i) q^{88} +6.76393 q^{89} +(-5.23607 + 3.80423i) q^{91} +(7.82206 - 3.48260i) q^{92} +(-3.05278 + 3.39045i) q^{94} +(-0.129204 + 1.22930i) q^{95} +(4.01478 + 4.45887i) q^{97} -2.29180 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} - 6 q^{4} - 6 q^{5} - q^{7} + 14 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{2} - 6 q^{4} - 6 q^{5} - q^{7} + 14 q^{8} - 32 q^{10} - q^{11} + 8 q^{13} + q^{14} + 14 q^{16} - 12 q^{17} - 2 q^{19} - 24 q^{20} + 11 q^{22} + 14 q^{23} - 9 q^{25} + 16 q^{26} + 18 q^{28} + 9 q^{29} - 3 q^{31} - 30 q^{32} - 6 q^{34} - 12 q^{35} + 24 q^{37} + 4 q^{38} + 12 q^{40} - 3 q^{41} + 6 q^{43} + 48 q^{44} + 18 q^{46} - 23 q^{47} - 6 q^{49} + 24 q^{50} + 12 q^{52} - 28 q^{53} - 32 q^{55} + 12 q^{56} + 6 q^{58} - 3 q^{59} - 6 q^{62} - 34 q^{64} + 32 q^{65} - 24 q^{67} + 9 q^{68} - 6 q^{70} - 42 q^{71} - 8 q^{73} - 13 q^{74} - 6 q^{76} + 11 q^{77} - 22 q^{79} - 52 q^{80} - 96 q^{82} + 17 q^{83} - 6 q^{85} - 21 q^{86} + 37 q^{88} + 72 q^{89} - 24 q^{91} + 21 q^{92} + 28 q^{94} + 4 q^{95} + 6 q^{97} - 72 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/297\mathbb{Z}\right)^\times\).

\(n\) \(56\) \(244\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.255585 + 0.283856i 0.180726 + 0.200717i 0.826700 0.562643i \(-0.190215\pi\)
−0.645974 + 0.763359i \(0.723549\pi\)
\(3\) 0 0
\(4\) 0.193806 1.84395i 0.0969032 0.921973i
\(5\) 0.827091 0.918578i 0.369886 0.410800i −0.529252 0.848465i \(-0.677527\pi\)
0.899139 + 0.437664i \(0.144194\pi\)
\(6\) 0 0
\(7\) −0.913545 + 0.406737i −0.345288 + 0.153732i −0.572051 0.820218i \(-0.693852\pi\)
0.226764 + 0.973950i \(0.427186\pi\)
\(8\) 1.19098 0.865300i 0.421076 0.305930i
\(9\) 0 0
\(10\) 0.472136 0.149302
\(11\) −2.70528 1.91872i −0.815672 0.578514i
\(12\) 0 0
\(13\) 6.33070 1.34563i 1.75582 0.373211i 0.786229 0.617936i \(-0.212031\pi\)
0.969593 + 0.244724i \(0.0786974\pi\)
\(14\) −0.348943 0.155360i −0.0932590 0.0415216i
\(15\) 0 0
\(16\) −3.07715 0.654069i −0.769288 0.163517i
\(17\) −1.50000 4.61653i −0.363803 1.11967i −0.950727 0.310029i \(-0.899661\pi\)
0.586924 0.809642i \(-0.300339\pi\)
\(18\) 0 0
\(19\) −0.809017 + 0.587785i −0.185601 + 0.134847i −0.676706 0.736253i \(-0.736593\pi\)
0.491105 + 0.871100i \(0.336593\pi\)
\(20\) −1.53351 1.70314i −0.342903 0.380833i
\(21\) 0 0
\(22\) −0.146790 1.25830i −0.0312957 0.268271i
\(23\) 2.30902 + 3.99933i 0.481463 + 0.833919i 0.999774 0.0212736i \(-0.00677212\pi\)
−0.518310 + 0.855193i \(0.673439\pi\)
\(24\) 0 0
\(25\) 0.362937 + 3.45312i 0.0725874 + 0.690623i
\(26\) 2.00000 + 1.45309i 0.392232 + 0.284973i
\(27\) 0 0
\(28\) 0.572949 + 1.76336i 0.108277 + 0.333243i
\(29\) 4.43444 1.97434i 0.823455 0.366626i 0.0486422 0.998816i \(-0.484511\pi\)
0.774813 + 0.632190i \(0.217844\pi\)
\(30\) 0 0
\(31\) −0.604528 + 0.128496i −0.108577 + 0.0230787i −0.261879 0.965101i \(-0.584342\pi\)
0.153303 + 0.988179i \(0.451009\pi\)
\(32\) −2.07295 3.59045i −0.366449 0.634708i
\(33\) 0 0
\(34\) 0.927051 1.60570i 0.158988 0.275375i
\(35\) −0.381966 + 1.17557i −0.0645640 + 0.198708i
\(36\) 0 0
\(37\) 4.11803 + 2.99193i 0.677001 + 0.491870i 0.872361 0.488862i \(-0.162588\pi\)
−0.195361 + 0.980731i \(0.562588\pi\)
\(38\) −0.373619 0.0794152i −0.0606090 0.0128828i
\(39\) 0 0
\(40\) 0.190206 1.80969i 0.0300743 0.286137i
\(41\) 2.30932 + 1.02817i 0.360655 + 0.160574i 0.579061 0.815284i \(-0.303419\pi\)
−0.218406 + 0.975858i \(0.570086\pi\)
\(42\) 0 0
\(43\) −0.927051 + 1.60570i −0.141374 + 0.244867i −0.928014 0.372545i \(-0.878485\pi\)
0.786640 + 0.617412i \(0.211819\pi\)
\(44\) −4.06231 + 4.61653i −0.612416 + 0.695967i
\(45\) 0 0
\(46\) −0.545085 + 1.67760i −0.0803684 + 0.247348i
\(47\) 1.24852 + 11.8788i 0.182115 + 1.73271i 0.579428 + 0.815024i \(0.303276\pi\)
−0.397313 + 0.917683i \(0.630057\pi\)
\(48\) 0 0
\(49\) −4.01478 + 4.45887i −0.573541 + 0.636981i
\(50\) −0.887426 + 0.985587i −0.125501 + 0.139383i
\(51\) 0 0
\(52\) −1.25434 11.9343i −0.173946 1.65498i
\(53\) −1.26393 + 3.88998i −0.173614 + 0.534330i −0.999567 0.0294087i \(-0.990638\pi\)
0.825953 + 0.563739i \(0.190638\pi\)
\(54\) 0 0
\(55\) −4.00000 + 0.898056i −0.539360 + 0.121094i
\(56\) −0.736068 + 1.27491i −0.0983612 + 0.170367i
\(57\) 0 0
\(58\) 1.69381 + 0.754131i 0.222408 + 0.0990223i
\(59\) 0.169131 1.60917i 0.0220189 0.209496i −0.977981 0.208695i \(-0.933078\pi\)
1.00000 0.000801000i \(-0.000254966\pi\)
\(60\) 0 0
\(61\) −10.6169 2.25669i −1.35936 0.288940i −0.530160 0.847898i \(-0.677868\pi\)
−0.829196 + 0.558957i \(0.811202\pi\)
\(62\) −0.190983 0.138757i −0.0242549 0.0176222i
\(63\) 0 0
\(64\) −1.45492 + 4.47777i −0.181864 + 0.559721i
\(65\) 4.00000 6.92820i 0.496139 0.859338i
\(66\) 0 0
\(67\) −3.00000 5.19615i −0.366508 0.634811i 0.622509 0.782613i \(-0.286114\pi\)
−0.989017 + 0.147802i \(0.952780\pi\)
\(68\) −8.80333 + 1.87121i −1.06756 + 0.226917i
\(69\) 0 0
\(70\) −0.431318 + 0.192035i −0.0515523 + 0.0229526i
\(71\) 0.899187 + 2.76741i 0.106714 + 0.328431i 0.990129 0.140160i \(-0.0447617\pi\)
−0.883415 + 0.468591i \(0.844762\pi\)
\(72\) 0 0
\(73\) 0.118034 + 0.0857567i 0.0138148 + 0.0100371i 0.594671 0.803969i \(-0.297282\pi\)
−0.580856 + 0.814006i \(0.697282\pi\)
\(74\) 0.203232 + 1.93362i 0.0236252 + 0.224779i
\(75\) 0 0
\(76\) 0.927051 + 1.60570i 0.106340 + 0.184186i
\(77\) 3.25181 + 0.652498i 0.370578 + 0.0743590i
\(78\) 0 0
\(79\) 7.06756 + 7.84932i 0.795163 + 0.883118i 0.995319 0.0966462i \(-0.0308115\pi\)
−0.200156 + 0.979764i \(0.564145\pi\)
\(80\) −3.14590 + 2.28563i −0.351722 + 0.255541i
\(81\) 0 0
\(82\) 0.298374 + 0.918300i 0.0329499 + 0.101409i
\(83\) −9.55057 2.03004i −1.04831 0.222825i −0.348615 0.937266i \(-0.613348\pi\)
−0.699696 + 0.714441i \(0.746681\pi\)
\(84\) 0 0
\(85\) −5.48127 2.44042i −0.594528 0.264701i
\(86\) −0.692728 + 0.147244i −0.0746988 + 0.0158777i
\(87\) 0 0
\(88\) −4.88220 + 0.0557196i −0.520445 + 0.00593972i
\(89\) 6.76393 0.716975 0.358488 0.933534i \(-0.383293\pi\)
0.358488 + 0.933534i \(0.383293\pi\)
\(90\) 0 0
\(91\) −5.23607 + 3.80423i −0.548889 + 0.398791i
\(92\) 7.82206 3.48260i 0.815506 0.363087i
\(93\) 0 0
\(94\) −3.05278 + 3.39045i −0.314870 + 0.349699i
\(95\) −0.129204 + 1.22930i −0.0132561 + 0.126123i
\(96\) 0 0
\(97\) 4.01478 + 4.45887i 0.407640 + 0.452730i 0.911650 0.410968i \(-0.134809\pi\)
−0.504010 + 0.863698i \(0.668143\pi\)
\(98\) −2.29180 −0.231506
\(99\) 0 0
\(100\) 6.43769 0.643769
\(101\) 5.66897 + 6.29602i 0.564083 + 0.626478i 0.955945 0.293546i \(-0.0948355\pi\)
−0.391862 + 0.920024i \(0.628169\pi\)
\(102\) 0 0
\(103\) 1.06996 10.1800i 0.105426 1.00306i −0.806088 0.591796i \(-0.798419\pi\)
0.911514 0.411269i \(-0.134914\pi\)
\(104\) 6.37539 7.08058i 0.625158 0.694308i
\(105\) 0 0
\(106\) −1.42724 + 0.635447i −0.138626 + 0.0617201i
\(107\) 11.3541 8.24924i 1.09764 0.797484i 0.116969 0.993136i \(-0.462682\pi\)
0.980673 + 0.195652i \(0.0626822\pi\)
\(108\) 0 0
\(109\) 7.14590 0.684453 0.342226 0.939618i \(-0.388819\pi\)
0.342226 + 0.939618i \(0.388819\pi\)
\(110\) −1.27726 0.905894i −0.121782 0.0863737i
\(111\) 0 0
\(112\) 3.07715 0.654069i 0.290764 0.0618037i
\(113\) −15.7459 7.01054i −1.48125 0.659496i −0.502507 0.864573i \(-0.667589\pi\)
−0.978746 + 0.205077i \(0.934255\pi\)
\(114\) 0 0
\(115\) 5.58347 + 1.18680i 0.520661 + 0.110670i
\(116\) −2.78115 8.55951i −0.258224 0.794730i
\(117\) 0 0
\(118\) 0.500000 0.363271i 0.0460287 0.0334418i
\(119\) 3.24803 + 3.60730i 0.297746 + 0.330681i
\(120\) 0 0
\(121\) 3.63706 + 10.3813i 0.330642 + 0.943756i
\(122\) −2.07295 3.59045i −0.187676 0.325064i
\(123\) 0 0
\(124\) 0.119779 + 1.13962i 0.0107565 + 0.102341i
\(125\) 8.47214 + 6.15537i 0.757771 + 0.550553i
\(126\) 0 0
\(127\) −3.26393 10.0453i −0.289627 0.891381i −0.984973 0.172706i \(-0.944749\pi\)
0.695346 0.718675i \(-0.255251\pi\)
\(128\) −9.21783 + 4.10404i −0.814749 + 0.362749i
\(129\) 0 0
\(130\) 2.98895 0.635322i 0.262149 0.0557214i
\(131\) 10.6180 + 18.3910i 0.927702 + 1.60683i 0.787157 + 0.616753i \(0.211552\pi\)
0.140545 + 0.990074i \(0.455115\pi\)
\(132\) 0 0
\(133\) 0.500000 0.866025i 0.0433555 0.0750939i
\(134\) 0.708204 2.17963i 0.0611795 0.188291i
\(135\) 0 0
\(136\) −5.78115 4.20025i −0.495730 0.360169i
\(137\) −8.42971 1.79179i −0.720199 0.153083i −0.166790 0.985993i \(-0.553340\pi\)
−0.553409 + 0.832910i \(0.686673\pi\)
\(138\) 0 0
\(139\) −1.01478 + 9.65502i −0.0860728 + 0.818928i 0.863282 + 0.504722i \(0.168405\pi\)
−0.949355 + 0.314206i \(0.898262\pi\)
\(140\) 2.09366 + 0.932157i 0.176947 + 0.0787817i
\(141\) 0 0
\(142\) −0.555728 + 0.962549i −0.0466357 + 0.0807753i
\(143\) −19.7082 8.50651i −1.64808 0.711350i
\(144\) 0 0
\(145\) 1.85410 5.70634i 0.153975 0.473886i
\(146\) 0.00582517 + 0.0554228i 0.000482095 + 0.00458682i
\(147\) 0 0
\(148\) 6.31505 7.01357i 0.519094 0.576512i
\(149\) 10.1576 11.2812i 0.832145 0.924191i −0.165934 0.986137i \(-0.553064\pi\)
0.998080 + 0.0619457i \(0.0197306\pi\)
\(150\) 0 0
\(151\) −0.452215 4.30254i −0.0368007 0.350136i −0.997392 0.0721716i \(-0.977007\pi\)
0.960591 0.277964i \(-0.0896596\pi\)
\(152\) −0.454915 + 1.40008i −0.0368985 + 0.113562i
\(153\) 0 0
\(154\) 0.645898 + 1.08981i 0.0520479 + 0.0878197i
\(155\) −0.381966 + 0.661585i −0.0306802 + 0.0531397i
\(156\) 0 0
\(157\) 6.52810 + 2.90650i 0.520999 + 0.231964i 0.650349 0.759635i \(-0.274622\pi\)
−0.129350 + 0.991599i \(0.541289\pi\)
\(158\) −0.421714 + 4.01234i −0.0335498 + 0.319205i
\(159\) 0 0
\(160\) −5.01263 1.06547i −0.396283 0.0842325i
\(161\) −3.73607 2.71441i −0.294443 0.213926i
\(162\) 0 0
\(163\) 6.39919 19.6947i 0.501223 1.54261i −0.305806 0.952094i \(-0.598926\pi\)
0.807029 0.590512i \(-0.201074\pi\)
\(164\) 2.34346 4.05899i 0.182993 0.316954i
\(165\) 0 0
\(166\) −1.86475 3.22983i −0.144732 0.250684i
\(167\) −5.63798 + 1.19839i −0.436280 + 0.0927341i −0.420815 0.907146i \(-0.638256\pi\)
−0.0154643 + 0.999880i \(0.504923\pi\)
\(168\) 0 0
\(169\) 26.3910 11.7500i 2.03008 0.903848i
\(170\) −0.708204 2.17963i −0.0543168 0.167170i
\(171\) 0 0
\(172\) 2.78115 + 2.02063i 0.212061 + 0.154071i
\(173\) −2.41358 22.9637i −0.183501 1.74590i −0.568233 0.822868i \(-0.692373\pi\)
0.384732 0.923028i \(-0.374294\pi\)
\(174\) 0 0
\(175\) −1.73607 3.00696i −0.131234 0.227305i
\(176\) 7.06958 + 7.67362i 0.532890 + 0.578421i
\(177\) 0 0
\(178\) 1.72876 + 1.91998i 0.129576 + 0.143909i
\(179\) −4.09017 + 2.97168i −0.305714 + 0.222114i −0.730055 0.683388i \(-0.760506\pi\)
0.424341 + 0.905502i \(0.360506\pi\)
\(180\) 0 0
\(181\) −3.06231 9.42481i −0.227619 0.700540i −0.998015 0.0629745i \(-0.979941\pi\)
0.770396 0.637566i \(-0.220059\pi\)
\(182\) −2.41811 0.513986i −0.179243 0.0380992i
\(183\) 0 0
\(184\) 6.21062 + 2.76515i 0.457853 + 0.203849i
\(185\) 6.15431 1.30814i 0.452474 0.0961762i
\(186\) 0 0
\(187\) −4.79988 + 15.3671i −0.351002 + 1.12375i
\(188\) 22.1459 1.61516
\(189\) 0 0
\(190\) −0.381966 + 0.277515i −0.0277107 + 0.0201330i
\(191\) −5.43036 + 2.41775i −0.392927 + 0.174942i −0.593683 0.804699i \(-0.702327\pi\)
0.200756 + 0.979641i \(0.435660\pi\)
\(192\) 0 0
\(193\) −7.36044 + 8.17459i −0.529816 + 0.588420i −0.947333 0.320249i \(-0.896234\pi\)
0.417518 + 0.908669i \(0.362900\pi\)
\(194\) −0.239558 + 2.27924i −0.0171993 + 0.163640i
\(195\) 0 0
\(196\) 7.44382 + 8.26720i 0.531701 + 0.590514i
\(197\) −8.23607 −0.586796 −0.293398 0.955990i \(-0.594786\pi\)
−0.293398 + 0.955990i \(0.594786\pi\)
\(198\) 0 0
\(199\) −7.14590 −0.506559 −0.253280 0.967393i \(-0.581509\pi\)
−0.253280 + 0.967393i \(0.581509\pi\)
\(200\) 3.42023 + 3.79855i 0.241847 + 0.268598i
\(201\) 0 0
\(202\) −0.338261 + 3.21834i −0.0238000 + 0.226442i
\(203\) −3.24803 + 3.60730i −0.227967 + 0.253183i
\(204\) 0 0
\(205\) 2.85447 1.27089i 0.199365 0.0887631i
\(206\) 3.16312 2.29814i 0.220385 0.160119i
\(207\) 0 0
\(208\) −20.3607 −1.41176
\(209\) 3.31641 0.0378495i 0.229401 0.00261810i
\(210\) 0 0
\(211\) −20.0248 + 4.25640i −1.37856 + 0.293022i −0.836800 0.547509i \(-0.815576\pi\)
−0.541762 + 0.840532i \(0.682243\pi\)
\(212\) 6.92796 + 3.08452i 0.475814 + 0.211846i
\(213\) 0 0
\(214\) 5.24354 + 1.11455i 0.358441 + 0.0761889i
\(215\) 0.708204 + 2.17963i 0.0482991 + 0.148649i
\(216\) 0 0
\(217\) 0.500000 0.363271i 0.0339422 0.0246605i
\(218\) 1.82639 + 2.02841i 0.123698 + 0.137381i
\(219\) 0 0
\(220\) 0.880740 + 7.54983i 0.0593795 + 0.509009i
\(221\) −15.7082 27.2074i −1.05665 1.83017i
\(222\) 0 0
\(223\) 1.62088 + 15.4216i 0.108542 + 1.03271i 0.904243 + 0.427019i \(0.140436\pi\)
−0.795701 + 0.605690i \(0.792897\pi\)
\(224\) 3.35410 + 2.43690i 0.224105 + 0.162822i
\(225\) 0 0
\(226\) −2.03444 6.26137i −0.135329 0.416500i
\(227\) 15.1813 6.75916i 1.00762 0.448621i 0.164518 0.986374i \(-0.447393\pi\)
0.843103 + 0.537753i \(0.180727\pi\)
\(228\) 0 0
\(229\) −9.95788 + 2.11661i −0.658035 + 0.139870i −0.524814 0.851217i \(-0.675865\pi\)
−0.133221 + 0.991086i \(0.542532\pi\)
\(230\) 1.09017 + 1.88823i 0.0718837 + 0.124506i
\(231\) 0 0
\(232\) 3.57295 6.18853i 0.234576 0.406297i
\(233\) 3.43769 10.5801i 0.225211 0.693128i −0.773059 0.634334i \(-0.781275\pi\)
0.998270 0.0587939i \(-0.0187255\pi\)
\(234\) 0 0
\(235\) 11.9443 + 8.67802i 0.779158 + 0.566092i
\(236\) −2.93444 0.623735i −0.191016 0.0406017i
\(237\) 0 0
\(238\) −0.193806 + 1.84395i −0.0125626 + 0.119525i
\(239\) −9.56677 4.25940i −0.618823 0.275518i 0.0732857 0.997311i \(-0.476651\pi\)
−0.692109 + 0.721793i \(0.743318\pi\)
\(240\) 0 0
\(241\) 13.4164 23.2379i 0.864227 1.49688i −0.00358606 0.999994i \(-0.501141\pi\)
0.867813 0.496891i \(-0.165525\pi\)
\(242\) −2.01722 + 3.68571i −0.129672 + 0.236927i
\(243\) 0 0
\(244\) −6.21885 + 19.1396i −0.398121 + 1.22529i
\(245\) 0.775226 + 7.37578i 0.0495274 + 0.471221i
\(246\) 0 0
\(247\) −4.33070 + 4.80973i −0.275556 + 0.306036i
\(248\) −0.608795 + 0.676135i −0.0386585 + 0.0429346i
\(249\) 0 0
\(250\) 0.418114 + 3.97809i 0.0264438 + 0.251596i
\(251\) −6.35410 + 19.5559i −0.401067 + 1.23436i 0.523067 + 0.852291i \(0.324788\pi\)
−0.924135 + 0.382067i \(0.875212\pi\)
\(252\) 0 0
\(253\) 1.42705 15.2497i 0.0897179 0.958738i
\(254\) 2.01722 3.49393i 0.126572 0.219229i
\(255\) 0 0
\(256\) 5.08142 + 2.26239i 0.317589 + 0.141400i
\(257\) −1.55850 + 14.8282i −0.0972167 + 0.924955i 0.831840 + 0.555016i \(0.187288\pi\)
−0.929056 + 0.369939i \(0.879379\pi\)
\(258\) 0 0
\(259\) −4.97894 1.05831i −0.309376 0.0657599i
\(260\) −12.0000 8.71851i −0.744208 0.540699i
\(261\) 0 0
\(262\) −2.50658 + 7.71445i −0.154857 + 0.476601i
\(263\) −6.35410 + 11.0056i −0.391811 + 0.678636i −0.992688 0.120705i \(-0.961485\pi\)
0.600878 + 0.799341i \(0.294818\pi\)
\(264\) 0 0
\(265\) 2.52786 + 4.37839i 0.155285 + 0.268962i
\(266\) 0.373619 0.0794152i 0.0229081 0.00486926i
\(267\) 0 0
\(268\) −10.1628 + 4.52479i −0.620794 + 0.276395i
\(269\) 6.57295 + 20.2295i 0.400760 + 1.23341i 0.924384 + 0.381463i \(0.124579\pi\)
−0.523625 + 0.851949i \(0.675421\pi\)
\(270\) 0 0
\(271\) −8.70820 6.32688i −0.528986 0.384331i 0.290993 0.956725i \(-0.406015\pi\)
−0.819978 + 0.572395i \(0.806015\pi\)
\(272\) 1.59620 + 15.1869i 0.0967840 + 0.920838i
\(273\) 0 0
\(274\) −1.64590 2.85078i −0.0994323 0.172222i
\(275\) 5.64370 10.0380i 0.340328 0.605315i
\(276\) 0 0
\(277\) −12.8714 14.2952i −0.773370 0.858914i 0.219806 0.975544i \(-0.429458\pi\)
−0.993176 + 0.116629i \(0.962791\pi\)
\(278\) −3.00000 + 2.17963i −0.179928 + 0.130725i
\(279\) 0 0
\(280\) 0.562306 + 1.73060i 0.0336042 + 0.103423i
\(281\) −9.12244 1.93903i −0.544199 0.115673i −0.0723942 0.997376i \(-0.523064\pi\)
−0.471805 + 0.881703i \(0.656397\pi\)
\(282\) 0 0
\(283\) −15.5303 6.91452i −0.923179 0.411026i −0.110592 0.993866i \(-0.535275\pi\)
−0.812587 + 0.582840i \(0.801941\pi\)
\(284\) 5.27723 1.12171i 0.313146 0.0665612i
\(285\) 0 0
\(286\) −2.62250 7.76843i −0.155072 0.459357i
\(287\) −2.52786 −0.149215
\(288\) 0 0
\(289\) −5.30902 + 3.85723i −0.312295 + 0.226896i
\(290\) 2.09366 0.932157i 0.122944 0.0547382i
\(291\) 0 0
\(292\) 0.181006 0.201028i 0.0105926 0.0117643i
\(293\) −3.05018 + 29.0205i −0.178193 + 1.69539i 0.430983 + 0.902360i \(0.358167\pi\)
−0.609176 + 0.793035i \(0.708500\pi\)
\(294\) 0 0
\(295\) −1.33826 1.48629i −0.0779166 0.0865351i
\(296\) 7.49342 0.435546
\(297\) 0 0
\(298\) 5.79837 0.335891
\(299\) 19.9993 + 22.2115i 1.15659 + 1.28453i
\(300\) 0 0
\(301\) 0.193806 1.84395i 0.0111708 0.106283i
\(302\) 1.10572 1.22803i 0.0636272 0.0706651i
\(303\) 0 0
\(304\) 2.87392 1.27955i 0.164831 0.0733873i
\(305\) −10.8541 + 7.88597i −0.621504 + 0.451549i
\(306\) 0 0
\(307\) 7.85410 0.448257 0.224129 0.974560i \(-0.428046\pi\)
0.224129 + 0.974560i \(0.428046\pi\)
\(308\) 1.83339 5.86969i 0.104467 0.334457i
\(309\) 0 0
\(310\) −0.285420 + 0.0606678i −0.0162107 + 0.00344570i
\(311\) −13.8679 6.17440i −0.786378 0.350118i −0.0260529 0.999661i \(-0.508294\pi\)
−0.760325 + 0.649542i \(0.774960\pi\)
\(312\) 0 0
\(313\) −3.39626 0.721898i −0.191968 0.0408041i 0.110924 0.993829i \(-0.464619\pi\)
−0.302892 + 0.953025i \(0.597952\pi\)
\(314\) 0.843459 + 2.59590i 0.0475991 + 0.146495i
\(315\) 0 0
\(316\) 15.8435 11.5109i 0.891264 0.647541i
\(317\) −14.0145 15.5646i −0.787130 0.874197i 0.207442 0.978247i \(-0.433486\pi\)
−0.994572 + 0.104051i \(0.966820\pi\)
\(318\) 0 0
\(319\) −15.7846 3.16729i −0.883768 0.177334i
\(320\) 2.90983 + 5.03997i 0.162664 + 0.281743i
\(321\) 0 0
\(322\) −0.184381 1.75427i −0.0102752 0.0977616i
\(323\) 3.92705 + 2.85317i 0.218507 + 0.158755i
\(324\) 0 0
\(325\) 6.94427 + 21.3723i 0.385199 + 1.18552i
\(326\) 7.22599 3.21722i 0.400211 0.178185i
\(327\) 0 0
\(328\) 3.64004 0.773714i 0.200988 0.0427212i
\(329\) −5.97214 10.3440i −0.329255 0.570286i
\(330\) 0 0
\(331\) −7.20820 + 12.4850i −0.396199 + 0.686236i −0.993253 0.115964i \(-0.963004\pi\)
0.597055 + 0.802201i \(0.296338\pi\)
\(332\) −5.59424 + 17.2173i −0.307024 + 0.944921i
\(333\) 0 0
\(334\) −1.78115 1.29408i −0.0974604 0.0708091i
\(335\) −7.25434 1.54196i −0.396347 0.0842462i
\(336\) 0 0
\(337\) 1.19916 11.4093i 0.0653227 0.621504i −0.912065 0.410047i \(-0.865512\pi\)
0.977387 0.211457i \(-0.0678209\pi\)
\(338\) 10.0805 + 4.48811i 0.548305 + 0.244121i
\(339\) 0 0
\(340\) −5.56231 + 9.63420i −0.301658 + 0.522488i
\(341\) 1.88197 + 0.812299i 0.101914 + 0.0439885i
\(342\) 0 0
\(343\) 4.01722 12.3637i 0.216910 0.667579i
\(344\) 0.285309 + 2.71454i 0.0153829 + 0.146358i
\(345\) 0 0
\(346\) 5.90150 6.55428i 0.317267 0.352361i
\(347\) 5.94760 6.60548i 0.319284 0.354600i −0.562043 0.827108i \(-0.689984\pi\)
0.881327 + 0.472508i \(0.156651\pi\)
\(348\) 0 0
\(349\) 0.433364 + 4.12319i 0.0231975 + 0.220709i 0.999979 + 0.00647159i \(0.00205999\pi\)
−0.976782 + 0.214238i \(0.931273\pi\)
\(350\) 0.409830 1.26133i 0.0219063 0.0674208i
\(351\) 0 0
\(352\) −1.28115 + 13.6906i −0.0682857 + 0.729710i
\(353\) −8.20820 + 14.2170i −0.436879 + 0.756696i −0.997447 0.0714123i \(-0.977249\pi\)
0.560568 + 0.828108i \(0.310583\pi\)
\(354\) 0 0
\(355\) 3.28579 + 1.46293i 0.174392 + 0.0776442i
\(356\) 1.31089 12.4723i 0.0694772 0.661032i
\(357\) 0 0
\(358\) −1.88892 0.401502i −0.0998324 0.0212200i
\(359\) −18.4894 13.4333i −0.975831 0.708983i −0.0190579 0.999818i \(-0.506067\pi\)
−0.956773 + 0.290836i \(0.906067\pi\)
\(360\) 0 0
\(361\) −5.56231 + 17.1190i −0.292753 + 0.901001i
\(362\) 1.89261 3.27810i 0.0994733 0.172293i
\(363\) 0 0
\(364\) 6.00000 + 10.3923i 0.314485 + 0.544705i
\(365\) 0.176399 0.0374948i 0.00923315 0.00196257i
\(366\) 0 0
\(367\) −11.6095 + 5.16889i −0.606012 + 0.269814i −0.686718 0.726924i \(-0.740949\pi\)
0.0807058 + 0.996738i \(0.474283\pi\)
\(368\) −4.48936 13.8168i −0.234024 0.720252i
\(369\) 0 0
\(370\) 1.94427 + 1.41260i 0.101078 + 0.0734374i
\(371\) −0.427539 4.06776i −0.0221967 0.211188i
\(372\) 0 0
\(373\) 2.82624 + 4.89519i 0.146337 + 0.253463i 0.929871 0.367886i \(-0.119918\pi\)
−0.783534 + 0.621349i \(0.786585\pi\)
\(374\) −5.58881 + 2.56512i −0.288991 + 0.132639i
\(375\) 0 0
\(376\) 11.7657 + 13.0672i 0.606771 + 0.673887i
\(377\) 25.4164 18.4661i 1.30901 0.951053i
\(378\) 0 0
\(379\) 4.88197 + 15.0251i 0.250770 + 0.771790i 0.994634 + 0.103459i \(0.0329910\pi\)
−0.743864 + 0.668331i \(0.767009\pi\)
\(380\) 2.24171 + 0.476491i 0.114998 + 0.0244435i
\(381\) 0 0
\(382\) −2.07421 0.923500i −0.106126 0.0472503i
\(383\) 19.4202 4.12790i 0.992328 0.210926i 0.316986 0.948430i \(-0.397329\pi\)
0.675342 + 0.737504i \(0.263996\pi\)
\(384\) 0 0
\(385\) 3.28891 2.44736i 0.167618 0.124729i
\(386\) −4.20163 −0.213857
\(387\) 0 0
\(388\) 9.00000 6.53888i 0.456906 0.331961i
\(389\) 20.6941 9.21359i 1.04923 0.467148i 0.191632 0.981467i \(-0.438622\pi\)
0.857599 + 0.514319i \(0.171955\pi\)
\(390\) 0 0
\(391\) 14.9995 16.6586i 0.758558 0.842464i
\(392\) −0.923281 + 8.78443i −0.0466327 + 0.443681i
\(393\) 0 0
\(394\) −2.10502 2.33786i −0.106049 0.117780i
\(395\) 13.0557 0.656905
\(396\) 0 0
\(397\) −2.12461 −0.106631 −0.0533156 0.998578i \(-0.516979\pi\)
−0.0533156 + 0.998578i \(0.516979\pi\)
\(398\) −1.82639 2.02841i −0.0915484 0.101675i
\(399\) 0 0
\(400\) 1.14176 10.8631i 0.0570881 0.543157i
\(401\) −9.74408 + 10.8219i −0.486596 + 0.540420i −0.935578 0.353121i \(-0.885120\pi\)
0.448981 + 0.893541i \(0.351787\pi\)
\(402\) 0 0
\(403\) −3.65418 + 1.62695i −0.182028 + 0.0810440i
\(404\) 12.7082 9.23305i 0.632257 0.459361i
\(405\) 0 0
\(406\) −1.85410 −0.0920175
\(407\) −5.39977 15.9953i −0.267657 0.792859i
\(408\) 0 0
\(409\) 33.0053 7.01549i 1.63201 0.346894i 0.701358 0.712809i \(-0.252577\pi\)
0.930648 + 0.365915i \(0.119244\pi\)
\(410\) 1.09031 + 0.485438i 0.0538467 + 0.0239741i
\(411\) 0 0
\(412\) −18.5640 3.94590i −0.914582 0.194400i
\(413\) 0.500000 + 1.53884i 0.0246034 + 0.0757215i
\(414\) 0 0
\(415\) −9.76393 + 7.09391i −0.479293 + 0.348226i
\(416\) −17.9547 19.9407i −0.880300 0.977672i
\(417\) 0 0
\(418\) 0.858369 + 0.931709i 0.0419842 + 0.0455714i
\(419\) 4.04508 + 7.00629i 0.197615 + 0.342280i 0.947755 0.319000i \(-0.103347\pi\)
−0.750139 + 0.661280i \(0.770014\pi\)
\(420\) 0 0
\(421\) −1.06996 10.1800i −0.0521467 0.496143i −0.989159 0.146847i \(-0.953088\pi\)
0.937013 0.349296i \(-0.113579\pi\)
\(422\) −6.32624 4.59628i −0.307956 0.223743i
\(423\) 0 0
\(424\) 1.86068 + 5.72658i 0.0903626 + 0.278107i
\(425\) 15.3970 6.85518i 0.746864 0.332525i
\(426\) 0 0
\(427\) 10.6169 2.25669i 0.513788 0.109209i
\(428\) −13.0106 22.5351i −0.628893 1.08927i
\(429\) 0 0
\(430\) −0.437694 + 0.758108i −0.0211075 + 0.0365592i
\(431\) 10.5279 32.4014i 0.507109 1.56072i −0.290086 0.957001i \(-0.593684\pi\)
0.797195 0.603722i \(-0.206316\pi\)
\(432\) 0 0
\(433\) −11.9271 8.66551i −0.573177 0.416438i 0.263081 0.964774i \(-0.415261\pi\)
−0.836258 + 0.548336i \(0.815261\pi\)
\(434\) 0.230909 + 0.0490813i 0.0110840 + 0.00235598i
\(435\) 0 0
\(436\) 1.38492 13.1766i 0.0663257 0.631047i
\(437\) −4.21878 1.87832i −0.201812 0.0898524i
\(438\) 0 0
\(439\) 0.354102 0.613323i 0.0169004 0.0292723i −0.857452 0.514565i \(-0.827954\pi\)
0.874352 + 0.485292i \(0.161287\pi\)
\(440\) −3.98684 + 4.53077i −0.190065 + 0.215996i
\(441\) 0 0
\(442\) 3.70820 11.4127i 0.176381 0.542846i
\(443\) −0.129204 1.22930i −0.00613868 0.0584056i 0.991024 0.133686i \(-0.0426814\pi\)
−0.997162 + 0.0752806i \(0.976015\pi\)
\(444\) 0 0
\(445\) 5.59439 6.21320i 0.265199 0.294534i
\(446\) −3.96325 + 4.40164i −0.187665 + 0.208424i
\(447\) 0 0
\(448\) −0.492141 4.68241i −0.0232515 0.221223i
\(449\) −2.30902 + 7.10642i −0.108969 + 0.335373i −0.990642 0.136489i \(-0.956418\pi\)
0.881672 + 0.471862i \(0.156418\pi\)
\(450\) 0 0
\(451\) −4.27458 7.21242i −0.201282 0.339620i
\(452\) −15.9787 + 27.6759i −0.751575 + 1.30177i
\(453\) 0 0
\(454\) 5.79875 + 2.58177i 0.272149 + 0.121169i
\(455\) −0.836228 + 7.95618i −0.0392030 + 0.372991i
\(456\) 0 0
\(457\) 0.978148 + 0.207912i 0.0457558 + 0.00972570i 0.230733 0.973017i \(-0.425888\pi\)
−0.184977 + 0.982743i \(0.559221\pi\)
\(458\) −3.14590 2.28563i −0.146998 0.106800i
\(459\) 0 0
\(460\) 3.27051 10.0656i 0.152488 0.469311i
\(461\) −8.07295 + 13.9828i −0.375995 + 0.651242i −0.990475 0.137690i \(-0.956032\pi\)
0.614481 + 0.788932i \(0.289366\pi\)
\(462\) 0 0
\(463\) −8.50000 14.7224i −0.395029 0.684209i 0.598076 0.801439i \(-0.295932\pi\)
−0.993105 + 0.117230i \(0.962599\pi\)
\(464\) −14.9368 + 3.17492i −0.693424 + 0.147392i
\(465\) 0 0
\(466\) 3.88186 1.72831i 0.179824 0.0800626i
\(467\) 0.236068 + 0.726543i 0.0109239 + 0.0336204i 0.956370 0.292159i \(-0.0943735\pi\)
−0.945446 + 0.325779i \(0.894373\pi\)
\(468\) 0 0
\(469\) 4.85410 + 3.52671i 0.224142 + 0.162848i
\(470\) 0.589469 + 5.60843i 0.0271902 + 0.258697i
\(471\) 0 0
\(472\) −1.19098 2.06284i −0.0548194 0.0949500i
\(473\) 5.58881 2.56512i 0.256974 0.117944i
\(474\) 0 0
\(475\) −2.32331 2.58030i −0.106601 0.118392i
\(476\) 7.28115 5.29007i 0.333731 0.242470i
\(477\) 0 0
\(478\) −1.23607 3.80423i −0.0565364 0.174001i
\(479\) −11.5069 2.44586i −0.525762 0.111754i −0.0626186 0.998038i \(-0.519945\pi\)
−0.463143 + 0.886283i \(0.653278\pi\)
\(480\) 0 0
\(481\) 30.0961 + 13.3996i 1.37226 + 0.610971i
\(482\) 10.0253 2.13093i 0.456638 0.0970614i
\(483\) 0 0
\(484\) 19.8475 4.69458i 0.902158 0.213390i
\(485\) 7.41641 0.336762
\(486\) 0 0
\(487\) 10.5000 7.62870i 0.475800 0.345689i −0.323897 0.946092i \(-0.604993\pi\)
0.799698 + 0.600403i \(0.204993\pi\)
\(488\) −14.5973 + 6.49913i −0.660788 + 0.294202i
\(489\) 0 0
\(490\) −1.89552 + 2.10519i −0.0856310 + 0.0951029i
\(491\) 0.765800 7.28610i 0.0345601 0.328817i −0.963558 0.267499i \(-0.913803\pi\)
0.998118 0.0613184i \(-0.0195305\pi\)
\(492\) 0 0
\(493\) −15.7663 17.5102i −0.710077 0.788620i
\(494\) −2.47214 −0.111227
\(495\) 0 0
\(496\) 1.94427 0.0873004
\(497\) −1.94706 2.16243i −0.0873374 0.0969980i
\(498\) 0 0
\(499\) −4.01561 + 38.2060i −0.179763 + 1.71033i 0.417823 + 0.908529i \(0.362793\pi\)
−0.597586 + 0.801805i \(0.703873\pi\)
\(500\) 12.9921 14.4292i 0.581025 0.645294i
\(501\) 0 0
\(502\) −7.17508 + 3.19455i −0.320239 + 0.142580i
\(503\) −7.70820 + 5.60034i −0.343692 + 0.249707i −0.746218 0.665702i \(-0.768132\pi\)
0.402526 + 0.915409i \(0.368132\pi\)
\(504\) 0 0
\(505\) 10.4721 0.466004
\(506\) 4.69344 3.49251i 0.208649 0.155261i
\(507\) 0 0
\(508\) −19.1556 + 4.07166i −0.849894 + 0.180651i
\(509\) 24.8305 + 11.0552i 1.10059 + 0.490015i 0.874959 0.484198i \(-0.160888\pi\)
0.225633 + 0.974212i \(0.427555\pi\)
\(510\) 0 0
\(511\) −0.142710 0.0303339i −0.00631311 0.00134189i
\(512\) 6.89261 + 21.2133i 0.304613 + 0.937503i
\(513\) 0 0
\(514\) −4.60739 + 3.34747i −0.203223 + 0.147650i
\(515\) −8.46616 9.40262i −0.373064 0.414329i
\(516\) 0 0
\(517\) 19.4145 34.5311i 0.853850 1.51868i
\(518\) −0.972136 1.68379i −0.0427132 0.0739814i
\(519\) 0 0
\(520\) −1.23104 11.7126i −0.0539847 0.513630i
\(521\) −32.6525 23.7234i −1.43053 1.03934i −0.989918 0.141645i \(-0.954761\pi\)
−0.440613 0.897697i \(-0.645239\pi\)
\(522\) 0 0
\(523\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(524\) 35.9698 16.0148i 1.57135 0.699609i
\(525\) 0 0
\(526\) −4.74803 + 1.00922i −0.207024 + 0.0440043i
\(527\) 1.50000 + 2.59808i 0.0653410 + 0.113174i
\(528\) 0 0
\(529\) 0.836881 1.44952i 0.0363861 0.0630226i
\(530\) −0.596748 + 1.83660i −0.0259211 + 0.0797768i
\(531\) 0 0
\(532\) −1.50000 1.08981i −0.0650332 0.0472494i
\(533\) 16.0032 + 3.40158i 0.693174 + 0.147339i
\(534\) 0 0
\(535\) 1.81331 17.2525i 0.0783962 0.745890i
\(536\) −8.06918 3.59263i −0.348535 0.155178i
\(537\) 0 0
\(538\) −4.06231 + 7.03612i −0.175138 + 0.303349i
\(539\) 19.4164 4.35926i 0.836324 0.187766i
\(540\) 0 0
\(541\) −3.68034 + 11.3269i −0.158230 + 0.486982i −0.998474 0.0552266i \(-0.982412\pi\)
0.840244 + 0.542209i \(0.182412\pi\)
\(542\) −0.429764 4.08893i −0.0184600 0.175635i
\(543\) 0 0
\(544\) −13.4660 + 14.9555i −0.577350 + 0.641212i
\(545\) 5.91031 6.56406i 0.253170 0.281173i
\(546\) 0 0
\(547\) 3.37901 + 32.1492i 0.144476 + 1.37460i 0.791052 + 0.611749i \(0.209534\pi\)
−0.646576 + 0.762850i \(0.723800\pi\)
\(548\) −4.93769 + 15.1967i −0.210928 + 0.649169i
\(549\) 0 0
\(550\) 4.29180 0.963568i 0.183003 0.0410867i
\(551\) −2.42705 + 4.20378i −0.103396 + 0.179087i
\(552\) 0 0
\(553\) −9.64915 4.29608i −0.410323 0.182688i
\(554\) 0.768025 7.30727i 0.0326303 0.310456i
\(555\) 0 0
\(556\) 17.6067 + 3.74241i 0.746689 + 0.158714i
\(557\) −0.527864 0.383516i −0.0223663 0.0162501i 0.576546 0.817065i \(-0.304400\pi\)
−0.598912 + 0.800815i \(0.704400\pi\)
\(558\) 0 0
\(559\) −3.70820 + 11.4127i −0.156840 + 0.482705i
\(560\) 1.94427 3.36758i 0.0821605 0.142306i
\(561\) 0 0
\(562\) −1.78115 3.08505i −0.0751334 0.130135i
\(563\) −19.8612 + 4.22164i −0.837051 + 0.177921i −0.606444 0.795126i \(-0.707405\pi\)
−0.230607 + 0.973047i \(0.574071\pi\)
\(564\) 0 0
\(565\) −19.4630 + 8.66550i −0.818816 + 0.364561i
\(566\) −2.00658 6.17561i −0.0843428 0.259580i
\(567\) 0 0
\(568\) 3.46556 + 2.51788i 0.145412 + 0.105648i
\(569\) 4.05553 + 38.5858i 0.170017 + 1.61760i 0.663726 + 0.747975i \(0.268974\pi\)
−0.493710 + 0.869627i \(0.664359\pi\)
\(570\) 0 0
\(571\) 9.26393 + 16.0456i 0.387683 + 0.671488i 0.992138 0.125153i \(-0.0399420\pi\)
−0.604454 + 0.796640i \(0.706609\pi\)
\(572\) −19.5051 + 34.6922i −0.815550 + 1.45055i
\(573\) 0 0
\(574\) −0.646085 0.717550i −0.0269670 0.0299499i
\(575\) −12.9721 + 9.42481i −0.540975 + 0.393042i
\(576\) 0 0
\(577\) 10.9443 + 33.6830i 0.455616 + 1.40224i 0.870410 + 0.492327i \(0.163853\pi\)
−0.414794 + 0.909915i \(0.636147\pi\)
\(578\) −2.45180 0.521147i −0.101982 0.0216769i
\(579\) 0 0
\(580\) −10.1628 4.52479i −0.421989 0.187882i
\(581\) 9.55057 2.03004i 0.396224 0.0842201i
\(582\) 0 0
\(583\) 10.8831 8.09836i 0.450730 0.335400i
\(584\) 0.214782 0.00888773
\(585\) 0 0
\(586\) −9.01722 + 6.55139i −0.372498 + 0.270636i
\(587\) −12.2565 + 5.45694i −0.505880 + 0.225232i −0.643775 0.765215i \(-0.722633\pi\)
0.137895 + 0.990447i \(0.455966\pi\)
\(588\) 0 0
\(589\) 0.413545 0.459289i 0.0170398 0.0189247i
\(590\) 0.0798526 0.759747i 0.00328748 0.0312783i
\(591\) 0 0
\(592\) −10.7149 11.9001i −0.440379 0.489091i
\(593\) 10.9443 0.449427 0.224714 0.974425i \(-0.427855\pi\)
0.224714 + 0.974425i \(0.427855\pi\)
\(594\) 0 0
\(595\) 6.00000 0.245976
\(596\) −18.8333 20.9165i −0.771441 0.856772i
\(597\) 0 0
\(598\) −1.19334 + 11.3539i −0.0487993 + 0.464294i
\(599\) 8.94004 9.92892i 0.365280 0.405685i −0.532286 0.846565i \(-0.678667\pi\)
0.897566 + 0.440880i \(0.145334\pi\)
\(600\) 0 0
\(601\) −15.9616 + 7.10656i −0.651087 + 0.289883i −0.705579 0.708632i \(-0.749313\pi\)
0.0544917 + 0.998514i \(0.482646\pi\)
\(602\) 0.572949 0.416272i 0.0233517 0.0169660i
\(603\) 0 0
\(604\) −8.02129 −0.326382
\(605\) 12.5442 + 5.24537i 0.509995 + 0.213255i
\(606\) 0 0
\(607\) 3.50528 0.745071i 0.142275 0.0302415i −0.136224 0.990678i \(-0.543497\pi\)
0.278499 + 0.960437i \(0.410163\pi\)
\(608\) 3.78747 + 1.68629i 0.153602 + 0.0683880i
\(609\) 0 0
\(610\) −5.01263 1.06547i −0.202955 0.0431395i
\(611\) 23.8885 + 73.5214i 0.966427 + 2.97436i
\(612\) 0 0
\(613\) −16.0623 + 11.6699i −0.648750 + 0.471345i −0.862845 0.505468i \(-0.831320\pi\)
0.214095 + 0.976813i \(0.431320\pi\)
\(614\) 2.00739 + 2.22943i 0.0810117 + 0.0899727i
\(615\) 0 0
\(616\) 4.43745 2.03667i 0.178790 0.0820599i
\(617\) −13.5795 23.5204i −0.546691 0.946897i −0.998498 0.0547813i \(-0.982554\pi\)
0.451807 0.892116i \(-0.350779\pi\)
\(618\) 0 0
\(619\) −2.88105 27.4113i −0.115799 1.10175i −0.885914 0.463849i \(-0.846468\pi\)
0.770115 0.637905i \(-0.220199\pi\)
\(620\) 1.14590 + 0.832544i 0.0460204 + 0.0334358i
\(621\) 0 0
\(622\) −1.79180 5.51458i −0.0718445 0.221115i
\(623\) −6.17916 + 2.75114i −0.247563 + 0.110222i
\(624\) 0 0
\(625\) −4.31990 + 0.918223i −0.172796 + 0.0367289i
\(626\) −0.663119 1.14856i −0.0265036 0.0459055i
\(627\) 0 0
\(628\) 6.62461 11.4742i 0.264351 0.457869i
\(629\) 7.63525 23.4989i 0.304438 0.936962i
\(630\) 0 0
\(631\) 8.80902 + 6.40013i 0.350681 + 0.254785i 0.749155 0.662395i \(-0.230460\pi\)
−0.398473 + 0.917180i \(0.630460\pi\)
\(632\) 15.2094 + 3.23285i 0.604996 + 0.128596i
\(633\) 0 0
\(634\) 0.836228 7.95618i 0.0332108 0.315980i
\(635\) −11.9270 5.31024i −0.473309 0.210731i
\(636\) 0 0
\(637\) −19.4164 + 33.6302i −0.769306 + 1.33248i
\(638\) −3.13525 5.29007i −0.124126 0.209436i
\(639\) 0 0
\(640\) −3.85410 + 11.8617i −0.152347 + 0.468875i
\(641\) −2.13770 20.3388i −0.0844339 0.803335i −0.952017 0.306044i \(-0.900995\pi\)
0.867584 0.497291i \(-0.165672\pi\)
\(642\) 0 0
\(643\) −4.58629 + 5.09359i −0.180866 + 0.200872i −0.826759 0.562556i \(-0.809818\pi\)
0.645894 + 0.763427i \(0.276485\pi\)
\(644\) −5.72930 + 6.36303i −0.225766 + 0.250739i
\(645\) 0 0
\(646\) 0.193806 + 1.84395i 0.00762521 + 0.0725490i
\(647\) 1.29180 3.97574i 0.0507857 0.156302i −0.922447 0.386123i \(-0.873814\pi\)
0.973233 + 0.229821i \(0.0738140\pi\)
\(648\) 0 0
\(649\) −3.54508 + 4.02874i −0.139157 + 0.158142i
\(650\) −4.29180 + 7.43361i −0.168338 + 0.291570i
\(651\) 0 0
\(652\) −35.0757 15.6167i −1.37367 0.611597i
\(653\) −0.142230 + 1.35323i −0.00556588 + 0.0529558i −0.996952 0.0780135i \(-0.975142\pi\)
0.991386 + 0.130969i \(0.0418089\pi\)
\(654\) 0 0
\(655\) 25.6756 + 5.45752i 1.00323 + 0.213243i
\(656\) −6.43363 4.67430i −0.251191 0.182501i
\(657\) 0 0
\(658\) 1.40983 4.33901i 0.0549609 0.169152i
\(659\) 4.98936 8.64182i 0.194358 0.336637i −0.752332 0.658784i \(-0.771071\pi\)
0.946690 + 0.322147i \(0.104404\pi\)
\(660\) 0 0
\(661\) 2.14590 + 3.71680i 0.0834658 + 0.144567i 0.904736 0.425972i \(-0.140068\pi\)
−0.821271 + 0.570539i \(0.806734\pi\)
\(662\) −5.38625 + 1.14488i −0.209342 + 0.0444971i
\(663\) 0 0
\(664\) −13.1312 + 5.84637i −0.509588 + 0.226883i
\(665\) −0.381966 1.17557i −0.0148120 0.0455867i
\(666\) 0 0
\(667\) 18.1353 + 13.1760i 0.702200 + 0.510178i
\(668\) 1.11709 + 10.6284i 0.0432214 + 0.411224i
\(669\) 0 0
\(670\) −1.41641 2.45329i −0.0547206 0.0947789i
\(671\) 24.3918 + 26.4758i 0.941633 + 1.02209i
\(672\) 0 0
\(673\) −19.7810 21.9691i −0.762503 0.846846i 0.229467 0.973316i \(-0.426302\pi\)
−0.991970 + 0.126471i \(0.959635\pi\)
\(674\) 3.54508 2.57565i 0.136552 0.0992105i
\(675\) 0 0
\(676\) −16.5517 50.9408i −0.636602 1.95926i
\(677\) 5.92340 + 1.25906i 0.227655 + 0.0483895i 0.320326 0.947307i \(-0.396207\pi\)
−0.0926718 + 0.995697i \(0.529541\pi\)
\(678\) 0 0
\(679\) −5.48127 2.44042i −0.210352 0.0936547i
\(680\) −8.63980 + 1.83645i −0.331321 + 0.0704245i
\(681\) 0 0
\(682\) 0.250426 + 0.741819i 0.00958933 + 0.0284057i
\(683\) 5.52786 0.211518 0.105759 0.994392i \(-0.466273\pi\)
0.105759 + 0.994392i \(0.466273\pi\)
\(684\) 0 0
\(685\) −8.61803 + 6.26137i −0.329278 + 0.239235i
\(686\) 4.53626 2.01967i 0.173195 0.0771115i
\(687\) 0 0
\(688\) 3.90292 4.33463i 0.148797 0.165256i
\(689\) −2.76709 + 26.3271i −0.105418 + 1.00298i
\(690\) 0 0
\(691\) 9.76713 + 10.8475i 0.371559 + 0.412658i 0.899707 0.436494i \(-0.143780\pi\)
−0.528148 + 0.849152i \(0.677113\pi\)
\(692\) −42.8115 −1.62745
\(693\) 0 0
\(694\) 3.39512 0.128877
\(695\) 8.02957 + 8.91774i 0.304579 + 0.338269i
\(696\) 0 0
\(697\) 1.28262 12.2033i 0.0485826 0.462233i
\(698\) −1.05963 + 1.17684i −0.0401076 + 0.0445440i
\(699\) 0 0
\(700\) −5.88113 + 2.61845i −0.222286 + 0.0989680i
\(701\) −38.6074 + 28.0499i −1.45818 + 1.05943i −0.474349 + 0.880337i \(0.657317\pi\)
−0.983832 + 0.179094i \(0.942683\pi\)
\(702\) 0 0
\(703\) −5.09017 −0.191979
\(704\) 12.5275 9.32204i 0.472148 0.351338i
\(705\) 0 0
\(706\) −6.13348 + 1.30371i −0.230837 + 0.0490659i
\(707\) −7.73968 3.44593i −0.291081 0.129597i
\(708\) 0 0
\(709\) 25.2009 + 5.35662i 0.946441 + 0.201172i 0.655181 0.755472i \(-0.272592\pi\)
0.291260 + 0.956644i \(0.405926\pi\)
\(710\) 0.424538 + 1.30660i 0.0159326 + 0.0490356i
\(711\) 0 0
\(712\) 8.05573 5.85283i 0.301901 0.219344i
\(713\) −1.90977 2.12101i −0.0715213 0.0794325i
\(714\) 0 0
\(715\) −24.1144 + 11.0679i −0.901826 + 0.413914i
\(716\) 4.68692 + 8.11798i 0.175158 + 0.303383i
\(717\) 0 0
\(718\) −0.912480 8.68167i −0.0340535 0.323997i
\(719\) −15.8541 11.5187i −0.591258 0.429574i 0.251507 0.967855i \(-0.419074\pi\)
−0.842765 + 0.538281i \(0.819074\pi\)
\(720\) 0 0
\(721\) 3.16312 + 9.73508i 0.117801 + 0.362553i
\(722\) −6.28098 + 2.79647i −0.233754 + 0.104074i
\(723\) 0 0
\(724\) −17.9723 + 3.82014i −0.667936 + 0.141974i
\(725\) 8.42705 + 14.5961i 0.312973 + 0.542085i
\(726\) 0 0
\(727\) −9.41641 + 16.3097i −0.349235 + 0.604893i −0.986114 0.166071i \(-0.946892\pi\)
0.636879 + 0.770964i \(0.280225\pi\)
\(728\) −2.94427 + 9.06154i −0.109122 + 0.335843i
\(729\) 0 0
\(730\) 0.0557281 + 0.0404888i 0.00206259 + 0.00149856i
\(731\) 8.80333 + 1.87121i 0.325603 + 0.0692090i
\(732\) 0 0
\(733\) −5.06672 + 48.2066i −0.187143 + 1.78055i 0.349692 + 0.936865i \(0.386286\pi\)
−0.536836 + 0.843687i \(0.680381\pi\)
\(734\) −4.43444 1.97434i −0.163678 0.0728743i
\(735\) 0 0
\(736\) 9.57295 16.5808i 0.352864 0.611178i
\(737\) −1.85410 + 19.8132i −0.0682967 + 0.729828i
\(738\) 0 0
\(739\) 13.1459 40.4589i 0.483580 1.48831i −0.350448 0.936582i \(-0.613971\pi\)
0.834027 0.551723i \(-0.186029\pi\)
\(740\) −1.21939 11.6017i −0.0448257 0.426488i
\(741\) 0 0
\(742\) 1.04539 1.16102i 0.0383774 0.0426224i
\(743\) 28.3448 31.4801i 1.03987 1.15489i 0.0521540 0.998639i \(-0.483391\pi\)
0.987717 0.156255i \(-0.0499420\pi\)
\(744\) 0 0
\(745\) −1.96136 18.6611i −0.0718589 0.683691i
\(746\) −0.667184 + 2.05338i −0.0244274 + 0.0751797i
\(747\) 0 0
\(748\) 27.4058 + 11.8290i 1.00205 + 0.432509i
\(749\) −7.01722 + 12.1542i −0.256404 + 0.444104i
\(750\) 0 0
\(751\) −28.5476 12.7102i −1.04172 0.463802i −0.186707 0.982416i \(-0.559782\pi\)
−0.855009 + 0.518614i \(0.826448\pi\)
\(752\) 3.92771 37.3696i 0.143229 1.36273i
\(753\) 0 0
\(754\) 11.7378 + 2.49494i 0.427464 + 0.0908604i
\(755\) −4.32624 3.14320i −0.157448 0.114393i
\(756\) 0 0
\(757\) 3.39919 10.4616i 0.123546 0.380234i −0.870088 0.492897i \(-0.835938\pi\)
0.993633 + 0.112663i \(0.0359380\pi\)
\(758\) −3.01722 + 5.22598i −0.109590 + 0.189816i
\(759\) 0 0
\(760\) 0.909830 + 1.57587i 0.0330030 + 0.0571629i
\(761\) 6.82621 1.45096i 0.247450 0.0525971i −0.0825167 0.996590i \(-0.526296\pi\)
0.329967 + 0.943993i \(0.392962\pi\)
\(762\) 0 0
\(763\) −6.52810 + 2.90650i −0.236333 + 0.105222i
\(764\) 3.40576 + 10.4819i 0.123216 + 0.379221i
\(765\) 0 0
\(766\) 6.13525 + 4.45752i 0.221676 + 0.161057i
\(767\) −1.09464 10.4148i −0.0395250 0.376055i
\(768\) 0 0
\(769\) 7.89919 + 13.6818i 0.284852 + 0.493378i 0.972573 0.232597i \(-0.0747222\pi\)
−0.687721 + 0.725975i \(0.741389\pi\)
\(770\) 1.53529 + 0.308068i 0.0553282 + 0.0111020i
\(771\) 0 0
\(772\) 13.6470 + 15.1565i 0.491166 + 0.545495i
\(773\) 19.1353 13.9026i 0.688247 0.500041i −0.187836 0.982200i \(-0.560147\pi\)
0.876083 + 0.482159i \(0.160147\pi\)
\(774\) 0 0
\(775\) −0.663119 2.04087i −0.0238199 0.0733102i
\(776\) 8.63980 + 1.83645i 0.310151 + 0.0659246i
\(777\) 0 0
\(778\) 7.90443 + 3.51928i 0.283388 + 0.126172i
\(779\) −2.47262 + 0.525572i −0.0885910 + 0.0188306i
\(780\) 0 0
\(781\) 2.87733 9.21191i 0.102959 0.329628i
\(782\) 8.56231 0.306187
\(783\) 0 0
\(784\) 15.2705 11.0947i 0.545375 0.396238i
\(785\) 8.06918 3.59263i 0.288001 0.128226i
\(786\) 0 0
\(787\) 24.0887 26.7532i 0.858669 0.953649i −0.140668 0.990057i \(-0.544925\pi\)
0.999337 + 0.0364078i \(0.0115915\pi\)
\(788\) −1.59620 + 15.1869i −0.0568624 + 0.541009i
\(789\) 0 0
\(790\) 3.33685 + 3.70595i 0.118720 + 0.131852i
\(791\) 17.2361 0.612844
\(792\) 0 0
\(793\) −70.2492 −2.49462
\(794\) −0.543019 0.603084i −0.0192710 0.0214026i
\(795\) 0 0
\(796\) −1.38492 + 13.1766i −0.0490872 + 0.467034i
\(797\) −16.2401 + 18.0365i −0.575255 + 0.638886i −0.958612 0.284714i \(-0.908101\pi\)
0.383357 + 0.923600i \(0.374768\pi\)
\(798\) 0 0
\(799\) 52.9662 23.5821i 1.87381 0.834274i
\(800\) 11.6459 8.46124i 0.411745 0.299150i
\(801\) 0 0
\(802\) −5.56231 −0.196412
\(803\) −0.154772 0.458469i −0.00546179 0.0161790i
\(804\) 0 0
\(805\) −5.58347 + 1.18680i −0.196791 + 0.0418293i
\(806\) −1.39577 0.621438i −0.0491640 0.0218892i
\(807\) 0 0
\(808\) 12.1996 + 2.59310i 0.429180 + 0.0912250i
\(809\) 5.59017 + 17.2048i 0.196540 + 0.604888i 0.999955 + 0.00946853i \(0.00301397\pi\)
−0.803415 + 0.595419i \(0.796986\pi\)
\(810\) 0 0
\(811\) −7.02786 + 5.10604i −0.246782 + 0.179297i −0.704299 0.709903i \(-0.748739\pi\)
0.457518 + 0.889201i \(0.348739\pi\)
\(812\) 6.02218 + 6.68830i 0.211337 + 0.234713i
\(813\) 0 0
\(814\) 3.16027 5.62093i 0.110767 0.197013i
\(815\) −12.7984 22.1674i −0.448307 0.776491i
\(816\) 0 0
\(817\) −0.193806 1.84395i −0.00678043 0.0645115i
\(818\) 10.4271 + 7.57570i 0.364573 + 0.264878i
\(819\) 0 0
\(820\) −1.79024 5.50980i −0.0625180 0.192411i
\(821\) −34.9109 + 15.5434i −1.21840 + 0.542467i −0.912296 0.409531i \(-0.865692\pi\)
−0.306104 + 0.951998i \(0.599026\pi\)
\(822\) 0 0
\(823\) 41.3676 8.79296i 1.44198 0.306503i 0.580489 0.814268i \(-0.302861\pi\)
0.861496 + 0.507765i \(0.169528\pi\)
\(824\) −7.53444 13.0500i −0.262475 0.454620i
\(825\) 0 0
\(826\) −0.309017 + 0.535233i −0.0107521 + 0.0186231i
\(827\) 17.6246 54.2430i 0.612868 1.88621i 0.183721 0.982978i \(-0.441186\pi\)
0.429147 0.903235i \(-0.358814\pi\)
\(828\) 0 0
\(829\) −35.2254 25.5928i −1.22343 0.888874i −0.227049 0.973883i \(-0.572908\pi\)
−0.996380 + 0.0850096i \(0.972908\pi\)
\(830\) −4.50917 0.958453i −0.156515 0.0332684i
\(831\) 0 0
\(832\) −3.18521 + 30.3052i −0.110427 + 1.05064i
\(833\) 26.6067 + 11.8460i 0.921866 + 0.410441i
\(834\) 0 0
\(835\) −3.56231 + 6.17009i −0.123279 + 0.213525i
\(836\) 0.572949 6.12261i 0.0198159 0.211755i
\(837\) 0 0
\(838\) −0.954915 + 2.93893i −0.0329870 + 0.101524i
\(839\) −1.80748 17.1971i −0.0624013 0.593709i −0.980385 0.197091i \(-0.936851\pi\)
0.917984 0.396618i \(-0.129816\pi\)
\(840\) 0 0
\(841\) −3.63853 + 4.04099i −0.125466 + 0.139345i
\(842\) 2.61619 2.90557i 0.0901598 0.100133i
\(843\) 0 0
\(844\) 3.96763 + 37.7495i 0.136572 + 1.29939i
\(845\) 11.0344 33.9605i 0.379596 1.16828i
\(846\) 0 0
\(847\) −7.54508 8.00448i −0.259252 0.275037i
\(848\) 6.43363 11.1434i 0.220932 0.382665i
\(849\) 0 0
\(850\) 5.88113 + 2.61845i 0.201721 + 0.0898120i
\(851\) −2.45711 + 23.3778i −0.0842285 + 0.801381i
\(852\) 0 0
\(853\) 34.6633 + 7.36791i 1.18685 + 0.252272i 0.758703 0.651437i \(-0.225834\pi\)
0.428146 + 0.903710i \(0.359167\pi\)
\(854\) 3.35410 + 2.43690i 0.114775 + 0.0833889i
\(855\) 0 0
\(856\) 6.38448 19.6494i 0.218217 0.671603i
\(857\) 12.6803 21.9630i 0.433152 0.750242i −0.563991 0.825781i \(-0.690735\pi\)
0.997143 + 0.0755396i \(0.0240679\pi\)
\(858\) 0 0
\(859\) 16.2812 + 28.1998i 0.555506 + 0.962164i 0.997864 + 0.0653258i \(0.0208087\pi\)
−0.442358 + 0.896838i \(0.645858\pi\)
\(860\) 4.15637 0.883463i 0.141731 0.0301258i
\(861\) 0 0
\(862\) 11.8881 5.29293i 0.404911 0.180278i
\(863\) −4.46556 13.7436i −0.152009 0.467837i 0.845836 0.533443i \(-0.179102\pi\)
−0.997846 + 0.0656059i \(0.979102\pi\)
\(864\) 0 0
\(865\) −23.0902 16.7760i −0.785089 0.570401i
\(866\) −0.588620 5.60034i −0.0200021 0.190307i
\(867\) 0 0
\(868\) −0.572949 0.992377i −0.0194472 0.0336835i
\(869\) −4.05911 34.7952i −0.137696 1.18035i
\(870\) 0 0
\(871\) −25.9842 28.8584i −0.880442 0.977830i
\(872\) 8.51064 6.18334i 0.288207 0.209394i
\(873\) 0 0
\(874\) −0.545085 1.67760i −0.0184378 0.0567456i
\(875\) −10.2433 2.17728i −0.346287 0.0736055i
\(876\) 0 0
\(877\) 10.5942 + 4.71682i 0.357739 + 0.159276i 0.577734 0.816225i \(-0.303937\pi\)
−0.219994 + 0.975501i \(0.570604\pi\)
\(878\) 0.264599 0.0562422i 0.00892977 0.00189808i
\(879\) 0 0
\(880\) 12.8960 0.147179i 0.434724 0.00496141i
\(881\) −1.81966 −0.0613059 −0.0306530 0.999530i \(-0.509759\pi\)
−0.0306530 + 0.999530i \(0.509759\pi\)
\(882\) 0 0
\(883\) 28.8435 20.9560i 0.970660 0.705226i 0.0150579 0.999887i \(-0.495207\pi\)
0.955602 + 0.294661i \(0.0952068\pi\)
\(884\) −53.2133 + 23.6921i −1.78976 + 0.796851i
\(885\) 0 0
\(886\) 0.315921 0.350865i 0.0106136 0.0117876i
\(887\) −0.421714 + 4.01234i −0.0141598 + 0.134721i −0.999318 0.0369278i \(-0.988243\pi\)
0.985158 + 0.171649i \(0.0549095\pi\)
\(888\) 0 0
\(889\) 7.06756 + 7.84932i 0.237038 + 0.263258i
\(890\) 3.19350 0.107046
\(891\) 0 0
\(892\) 28.7508 0.962647
\(893\) −7.99228 8.87632i −0.267451 0.297035i
\(894\) 0 0
\(895\) −0.653222 + 6.21499i −0.0218348 + 0.207744i
\(896\) 6.75164 7.49846i 0.225557 0.250506i
\(897\) 0 0
\(898\) −2.60735 + 1.16087i −0.0870085 + 0.0387387i
\(899\) −2.42705 + 1.76336i −0.0809467 + 0.0588112i
\(900\) 0 0
\(901\) 19.8541 0.661436
\(902\) 0.954773 3.05675i 0.0317904 0.101779i
\(903\) 0 0
\(904\) −24.8194 + 5.27552i −0.825480 + 0.175461i
\(905\) −11.1902 4.98221i −0.371976 0.165614i
\(906\) 0 0
\(907\) 14.2649 + 3.03210i 0.473658 + 0.100679i 0.438555 0.898704i \(-0.355491\pi\)
0.0351037 + 0.999384i \(0.488824\pi\)
\(908\) −9.52129 29.3035i −0.315975 0.972471i
\(909\) 0 0
\(910\) −2.47214 + 1.79611i −0.0819505 + 0.0595405i
\(911\) 12.8342 + 14.2538i 0.425214 + 0.472248i 0.917242 0.398331i \(-0.130411\pi\)
−0.492027 + 0.870580i \(0.663744\pi\)
\(912\) 0 0
\(913\) 21.9419 + 23.8166i 0.726170 + 0.788215i
\(914\) 0.190983 + 0.330792i 0.00631716 + 0.0109416i
\(915\) 0 0
\(916\) 1.97302 + 18.7720i 0.0651903 + 0.620244i
\(917\) −17.1803 12.4822i −0.567345 0.412200i
\(918\) 0 0
\(919\) −8.30244 25.5523i −0.273872 0.842892i −0.989516 0.144426i \(-0.953866\pi\)
0.715643 0.698466i \(-0.246134\pi\)
\(920\) 7.67675 3.41791i 0.253095 0.112685i
\(921\) 0 0
\(922\) −6.03242 + 1.28223i −0.198667 + 0.0422280i
\(923\) 9.41641 + 16.3097i 0.309945 + 0.536840i
\(924\) 0 0
\(925\) −8.83688 + 15.3059i −0.290555 + 0.503256i
\(926\) 2.00658 6.17561i 0.0659402 0.202943i
\(927\) 0 0
\(928\) −16.2812 11.8290i −0.534455 0.388304i
\(929\) −47.2157 10.0360i −1.54910 0.329271i −0.647574 0.762003i \(-0.724216\pi\)
−0.901523 + 0.432732i \(0.857550\pi\)
\(930\) 0 0
\(931\) 0.627171 5.96713i 0.0205547 0.195565i
\(932\) −18.8429 8.38942i −0.617221 0.274804i
\(933\) 0 0
\(934\) −0.145898 + 0.252703i −0.00477393 + 0.00826869i
\(935\) 10.1459 + 17.1190i 0.331806 + 0.559852i
\(936\) 0 0
\(937\) −7.11803 + 21.9071i −0.232536 + 0.715672i 0.764903 + 0.644146i \(0.222787\pi\)
−0.997439 + 0.0715265i \(0.977213\pi\)
\(938\) 0.239558 + 2.27924i 0.00782184 + 0.0744199i
\(939\) 0 0
\(940\) 18.3167 20.3427i 0.597424 0.663507i
\(941\) −18.1730 + 20.1831i −0.592421 + 0.657951i −0.962574 0.271021i \(-0.912639\pi\)
0.370152 + 0.928971i \(0.379306\pi\)
\(942\) 0 0
\(943\) 1.22024 + 11.6098i 0.0397365 + 0.378067i
\(944\) −1.57295 + 4.84104i −0.0511951 + 0.157562i
\(945\) 0 0
\(946\) 2.15654 + 0.930812i 0.0701152 + 0.0302633i
\(947\) 18.3541 31.7902i 0.596428 1.03304i −0.396915 0.917855i \(-0.629919\pi\)
0.993344 0.115189i \(-0.0367473\pi\)
\(948\) 0 0
\(949\) 0.862635 + 0.384070i 0.0280023 + 0.0124674i
\(950\) 0.138630 1.31897i 0.00449774 0.0427931i
\(951\) 0 0
\(952\) 6.98974 + 1.48572i 0.226539 + 0.0481523i
\(953\) −7.68034 5.58009i −0.248791 0.180757i 0.456400 0.889775i \(-0.349139\pi\)
−0.705191 + 0.709018i \(0.749139\pi\)
\(954\) 0 0
\(955\) −2.27051 + 6.98791i −0.0734720 + 0.226123i
\(956\) −9.70820 + 16.8151i −0.313986 + 0.543839i
\(957\) 0 0
\(958\) −2.24671 3.89142i −0.0725879 0.125726i
\(959\) 8.42971 1.79179i 0.272210 0.0578599i
\(960\) 0 0
\(961\) −27.9710 + 12.4535i −0.902289 + 0.401725i
\(962\) 3.88854 + 11.9677i 0.125372 + 0.385854i
\(963\) 0 0
\(964\) −40.2492 29.2428i −1.29634 0.941846i
\(965\) 1.42125 + 13.5223i 0.0457516 + 0.435297i
\(966\) 0 0
\(967\) −26.2426 45.4536i −0.843907 1.46169i −0.886567 0.462599i \(-0.846917\pi\)
0.0426608 0.999090i \(-0.486417\pi\)
\(968\) 13.3146 + 9.21682i 0.427949 + 0.296240i
\(969\) 0 0
\(970\) 1.89552 + 2.10519i 0.0608616 + 0.0675937i
\(971\) 7.50000 5.44907i 0.240686 0.174869i −0.460903 0.887451i \(-0.652474\pi\)
0.701589 + 0.712582i \(0.252474\pi\)
\(972\) 0 0
\(973\) −3.00000 9.23305i −0.0961756 0.295998i
\(974\) 4.84910 + 1.03071i 0.155375 + 0.0330260i
\(975\) 0 0
\(976\) 31.1938 + 13.8884i 0.998490 + 0.444556i
\(977\) 15.4195 3.27751i 0.493312 0.104857i 0.0454632 0.998966i \(-0.485524\pi\)
0.447849 + 0.894109i \(0.352190\pi\)
\(978\) 0 0
\(979\) −18.2983 12.9781i −0.584817 0.414781i
\(980\) 13.7508 0.439252
\(981\) 0 0
\(982\) 2.26393 1.64484i 0.0722450 0.0524890i
\(983\) −8.45701 + 3.76531i −0.269737 + 0.120095i −0.537148 0.843488i \(-0.680498\pi\)
0.267411 + 0.963582i \(0.413832\pi\)
\(984\) 0 0
\(985\) −6.81198 + 7.56547i −0.217048 + 0.241056i
\(986\) 0.940756 8.95070i 0.0299598 0.285048i
\(987\) 0 0
\(988\) 8.02957 + 8.91774i 0.255455 + 0.283711i
\(989\) −8.56231 −0.272265
\(990\) 0 0
\(991\) 20.5967 0.654277 0.327139 0.944976i \(-0.393916\pi\)
0.327139 + 0.944976i \(0.393916\pi\)
\(992\) 1.71452 + 1.90416i 0.0544360 + 0.0604573i
\(993\) 0 0
\(994\) 0.116179 1.10537i 0.00368497 0.0350601i
\(995\) −5.91031 + 6.56406i −0.187369 + 0.208095i
\(996\) 0 0
\(997\) 6.74376 3.00252i 0.213577 0.0950906i −0.297160 0.954828i \(-0.596039\pi\)
0.510737 + 0.859737i \(0.329373\pi\)
\(998\) −11.8713 + 8.62502i −0.375780 + 0.273020i
\(999\) 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 297.2.n.a.262.1 8
3.2 odd 2 99.2.m.a.97.1 yes 8
9.2 odd 6 891.2.f.b.163.1 4
9.4 even 3 inner 297.2.n.a.64.1 8
9.5 odd 6 99.2.m.a.31.1 yes 8
9.7 even 3 891.2.f.a.163.1 4
11.5 even 5 inner 297.2.n.a.181.1 8
33.5 odd 10 99.2.m.a.16.1 8
33.26 odd 10 1089.2.e.g.727.1 4
33.29 even 10 1089.2.e.d.727.2 4
99.5 odd 30 99.2.m.a.49.1 yes 8
99.7 odd 30 9801.2.a.m.1.2 2
99.16 even 15 891.2.f.a.82.1 4
99.29 even 30 9801.2.a.bc.1.1 2
99.38 odd 30 891.2.f.b.82.1 4
99.49 even 15 inner 297.2.n.a.280.1 8
99.59 odd 30 1089.2.e.g.364.1 4
99.70 even 15 9801.2.a.bb.1.1 2
99.92 odd 30 9801.2.a.n.1.2 2
99.95 even 30 1089.2.e.d.364.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.m.a.16.1 8 33.5 odd 10
99.2.m.a.31.1 yes 8 9.5 odd 6
99.2.m.a.49.1 yes 8 99.5 odd 30
99.2.m.a.97.1 yes 8 3.2 odd 2
297.2.n.a.64.1 8 9.4 even 3 inner
297.2.n.a.181.1 8 11.5 even 5 inner
297.2.n.a.262.1 8 1.1 even 1 trivial
297.2.n.a.280.1 8 99.49 even 15 inner
891.2.f.a.82.1 4 99.16 even 15
891.2.f.a.163.1 4 9.7 even 3
891.2.f.b.82.1 4 99.38 odd 30
891.2.f.b.163.1 4 9.2 odd 6
1089.2.e.d.364.2 4 99.95 even 30
1089.2.e.d.727.2 4 33.29 even 10
1089.2.e.g.364.1 4 99.59 odd 30
1089.2.e.g.727.1 4 33.26 odd 10
9801.2.a.m.1.2 2 99.7 odd 30
9801.2.a.n.1.2 2 99.92 odd 30
9801.2.a.bb.1.1 2 99.70 even 15
9801.2.a.bc.1.1 2 99.29 even 30