Properties

Label 297.2.n.a.64.1
Level $297$
Weight $2$
Character 297.64
Analytic conductor $2.372$
Analytic rank $0$
Dimension $8$
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 64.1
Root \(0.669131 + 0.743145i\) of defining polynomial
Character \(\chi\) \(=\) 297.64
Dual form 297.2.n.a.181.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.373619 + 0.0794152i) q^{2} +(-1.69381 + 0.754131i) q^{4} +(-1.20906 - 0.256993i) q^{5} +(0.104528 - 0.994522i) q^{7} +(1.19098 - 0.865300i) q^{8} +0.472136 q^{10} +(3.01430 - 1.38348i) q^{11} +(-4.33070 - 4.80973i) q^{13} +(0.0399263 + 0.379874i) q^{14} +(2.10502 - 2.33786i) q^{16} +(-1.50000 - 4.61653i) q^{17} +(-0.809017 + 0.587785i) q^{19} +(2.24171 - 0.476491i) q^{20} +(-1.01633 + 0.756276i) q^{22} +(2.30902 - 3.99933i) q^{23} +(-3.17195 - 1.41224i) q^{25} +(2.00000 + 1.45309i) q^{26} +(0.572949 + 1.76336i) q^{28} +(-0.507392 + 4.82751i) q^{29} +(0.413545 + 0.459289i) q^{31} +(-2.07295 + 3.59045i) q^{32} +(0.927051 + 1.60570i) q^{34} +(-0.381966 + 1.17557i) q^{35} +(4.11803 + 2.99193i) q^{37} +(0.255585 - 0.283856i) q^{38} +(-1.66234 + 0.740122i) q^{40} +(-0.264234 - 2.51402i) q^{41} +(-0.927051 - 1.60570i) q^{43} +(-4.06231 + 4.61653i) q^{44} +(-0.545085 + 1.67760i) q^{46} +(-10.9116 - 4.85817i) q^{47} +(5.86889 + 1.24747i) q^{49} +(1.29726 + 0.275740i) q^{50} +(10.9625 + 4.88084i) q^{52} +(-1.26393 + 3.88998i) q^{53} +(-4.00000 + 0.898056i) q^{55} +(-0.736068 - 1.27491i) q^{56} +(-0.193806 - 1.84395i) q^{58} +(-1.47815 + 0.658114i) q^{59} +(7.26281 - 8.06617i) q^{61} +(-0.190983 - 0.138757i) q^{62} +(-1.45492 + 4.47777i) q^{64} +(4.00000 + 6.92820i) q^{65} +(-3.00000 + 5.19615i) q^{67} +(6.02218 + 6.68830i) q^{68} +(0.0493516 - 0.469550i) q^{70} +(0.899187 + 2.76741i) q^{71} +(0.118034 + 0.0857567i) q^{73} +(-1.77618 - 0.790807i) q^{74} +(0.927051 - 1.60570i) q^{76} +(-1.06082 - 3.14240i) q^{77} +(-10.3315 + 2.19603i) q^{79} +(-3.14590 + 2.28563i) q^{80} +(0.298374 + 0.918300i) q^{82} +(6.53335 - 7.25602i) q^{83} +(0.627171 + 5.96713i) q^{85} +(0.473881 + 0.526298i) q^{86} +(2.39285 - 4.25597i) q^{88} +6.76393 q^{89} +(-5.23607 + 3.80423i) q^{91} +(-0.895005 + 8.51540i) q^{92} +(4.46261 + 0.948557i) q^{94} +(1.12920 - 0.502754i) q^{95} +(-5.86889 + 1.24747i) q^{97} -2.29180 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} - 6 q^{4} - 6 q^{5} - q^{7} + 14 q^{8} - 32 q^{10} - q^{11} + 8 q^{13} + q^{14} + 14 q^{16} - 12 q^{17} - 2 q^{19} - 24 q^{20} + 11 q^{22} + 14 q^{23} - 9 q^{25} + 16 q^{26} + 18 q^{28}+ \cdots - 72 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(56\) \(244\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.373619 + 0.0794152i −0.264189 + 0.0561550i −0.338101 0.941110i \(-0.609785\pi\)
0.0739128 + 0.997265i \(0.476451\pi\)
\(3\) 0 0
\(4\) −1.69381 + 0.754131i −0.846903 + 0.377066i
\(5\) −1.20906 0.256993i −0.540707 0.114931i −0.0705409 0.997509i \(-0.522473\pi\)
−0.470166 + 0.882578i \(0.655806\pi\)
\(6\) 0 0
\(7\) 0.104528 0.994522i 0.0395080 0.375894i −0.956847 0.290592i \(-0.906148\pi\)
0.996355 0.0853021i \(-0.0271855\pi\)
\(8\) 1.19098 0.865300i 0.421076 0.305930i
\(9\) 0 0
\(10\) 0.472136 0.149302
\(11\) 3.01430 1.38348i 0.908844 0.417136i
\(12\) 0 0
\(13\) −4.33070 4.80973i −1.20112 1.33398i −0.928262 0.371926i \(-0.878697\pi\)
−0.272859 0.962054i \(-0.587969\pi\)
\(14\) 0.0399263 + 0.379874i 0.0106708 + 0.101525i
\(15\) 0 0
\(16\) 2.10502 2.33786i 0.526254 0.584464i
\(17\) −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 \(0.336593\pi\)
\(20\) 2.24171 0.476491i 0.501263 0.106547i
\(21\) 0 0
\(22\) −1.01633 + 0.756276i −0.216682 + 0.161239i
\(23\) 2.30902 3.99933i 0.481463 0.833919i −0.518310 0.855193i \(-0.673439\pi\)
0.999774 + 0.0212736i \(0.00677212\pi\)
\(24\) 0 0
\(25\) −3.17195 1.41224i −0.634391 0.282449i
\(26\) 2.00000 + 1.45309i 0.392232 + 0.284973i
\(27\) 0 0
\(28\) 0.572949 + 1.76336i 0.108277 + 0.333243i
\(29\) −0.507392 + 4.82751i −0.0942203 + 0.896446i 0.840679 + 0.541534i \(0.182156\pi\)
−0.934899 + 0.354913i \(0.884511\pi\)
\(30\) 0 0
\(31\) 0.413545 + 0.459289i 0.0742750 + 0.0824907i 0.779137 0.626854i \(-0.215658\pi\)
−0.704862 + 0.709345i \(0.748991\pi\)
\(32\) −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 \(0.562588\pi\)
\(38\) 0.255585 0.283856i 0.0414614 0.0460475i
\(39\) 0 0
\(40\) −1.66234 + 0.740122i −0.262839 + 0.117024i
\(41\) −0.264234 2.51402i −0.0412664 0.392623i −0.995587 0.0938399i \(-0.970086\pi\)
0.954321 0.298783i \(-0.0965808\pi\)
\(42\) 0 0
\(43\) −0.927051 1.60570i −0.141374 0.244867i 0.786640 0.617412i \(-0.211819\pi\)
−0.928014 + 0.372545i \(0.878485\pi\)
\(44\) −4.06231 + 4.61653i −0.612416 + 0.695967i
\(45\) 0 0
\(46\) −0.545085 + 1.67760i −0.0803684 + 0.247348i
\(47\) −10.9116 4.85817i −1.59163 0.708637i −0.596081 0.802925i \(-0.703276\pi\)
−0.995545 + 0.0942873i \(0.969943\pi\)
\(48\) 0 0
\(49\) 5.86889 + 1.24747i 0.838412 + 0.178210i
\(50\) 1.29726 + 0.275740i 0.183460 + 0.0389956i
\(51\) 0 0
\(52\) 10.9625 + 4.88084i 1.52023 + 0.676851i
\(53\) −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
\(58\) −0.193806 1.84395i −0.0254480 0.242122i
\(59\) −1.47815 + 0.658114i −0.192438 + 0.0856791i −0.500694 0.865625i \(-0.666922\pi\)
0.308255 + 0.951304i \(0.400255\pi\)
\(60\) 0 0
\(61\) 7.26281 8.06617i 0.929908 1.03277i −0.0694731 0.997584i \(-0.522132\pi\)
0.999381 0.0351834i \(-0.0112015\pi\)
\(62\) −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 −0.989017 0.147802i \(-0.952780\pi\)
0.622509 + 0.782613i \(0.286114\pi\)
\(68\) 6.02218 + 6.68830i 0.730296 + 0.811076i
\(69\) 0 0
\(70\) 0.0493516 0.469550i 0.00589865 0.0561219i
\(71\) 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 \(0.697282\pi\)
\(74\) −1.77618 0.790807i −0.206477 0.0919294i
\(75\) 0 0
\(76\) 0.927051 1.60570i 0.106340 0.184186i
\(77\) −1.06082 3.14240i −0.120892 0.358109i
\(78\) 0 0
\(79\) −10.3315 + 2.19603i −1.16238 + 0.247072i −0.748423 0.663222i \(-0.769188\pi\)
−0.413961 + 0.910294i \(0.635855\pi\)
\(80\) −3.14590 + 2.28563i −0.351722 + 0.255541i
\(81\) 0 0
\(82\) 0.298374 + 0.918300i 0.0329499 + 0.101409i
\(83\) 6.53335 7.25602i 0.717128 0.796451i −0.268876 0.963175i \(-0.586652\pi\)
0.986004 + 0.166724i \(0.0533188\pi\)
\(84\) 0 0
\(85\) 0.627171 + 5.96713i 0.0680262 + 0.647226i
\(86\) 0.473881 + 0.526298i 0.0510999 + 0.0567522i
\(87\) 0 0
\(88\) 2.39285 4.25597i 0.255078 0.453688i
\(89\) 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
\(92\) −0.895005 + 8.51540i −0.0933107 + 0.887792i
\(93\) 0 0
\(94\) 4.46261 + 0.948557i 0.460283 + 0.0978362i
\(95\) 1.12920 0.502754i 0.115854 0.0515815i
\(96\) 0 0
\(97\) −5.86889 + 1.24747i −0.595895 + 0.126661i −0.495979 0.868334i \(-0.665191\pi\)
−0.0999160 + 0.994996i \(0.531857\pi\)
\(98\) −2.29180 −0.231506
\(99\) 0 0
\(100\) 6.43769 0.643769
\(101\) −8.28700 + 1.76146i −0.824587 + 0.175271i −0.600833 0.799374i \(-0.705165\pi\)
−0.223754 + 0.974646i \(0.571831\pi\)
\(102\) 0 0
\(103\) −9.35111 + 4.16338i −0.921393 + 0.410230i −0.811926 0.583760i \(-0.801581\pi\)
−0.109466 + 0.993990i \(0.534914\pi\)
\(104\) −9.31966 1.98095i −0.913868 0.194249i
\(105\) 0 0
\(106\) 0.163305 1.55375i 0.0158616 0.150913i
\(107\) 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 \(0.388819\pi\)
\(110\) 1.42316 0.653192i 0.135693 0.0622794i
\(111\) 0 0
\(112\) −2.10502 2.33786i −0.198905 0.220907i
\(113\) 1.80166 + 17.1416i 0.169486 + 1.61255i 0.666975 + 0.745080i \(0.267589\pi\)
−0.497489 + 0.867470i \(0.665745\pi\)
\(114\) 0 0
\(115\) −3.81953 + 4.24202i −0.356173 + 0.395571i
\(116\) −2.78115 8.55951i −0.258224 0.794730i
\(117\) 0 0
\(118\) 0.500000 0.363271i 0.0460287 0.0334418i
\(119\) −4.74803 + 1.00922i −0.435251 + 0.0925155i
\(120\) 0 0
\(121\) 7.17195 8.34045i 0.651996 0.758223i
\(122\) −2.07295 + 3.59045i −0.187676 + 0.325064i
\(123\) 0 0
\(124\) −1.04683 0.466079i −0.0940081 0.0418551i
\(125\) 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 \(-0.255251\pi\)
\(128\) 1.05471 10.0349i 0.0932241 0.886968i
\(129\) 0 0
\(130\) −2.04468 2.27085i −0.179330 0.199167i
\(131\) 10.6180 18.3910i 0.927702 1.60683i 0.140545 0.990074i \(-0.455115\pi\)
0.787157 0.616753i \(-0.211552\pi\)
\(132\) 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
\(137\) 5.76659 6.40445i 0.492673 0.547169i −0.444616 0.895721i \(-0.646660\pi\)
0.937289 + 0.348552i \(0.113327\pi\)
\(138\) 0 0
\(139\) 8.86889 3.94868i 0.752249 0.334923i 0.00546112 0.999985i \(-0.498262\pi\)
0.746788 + 0.665062i \(0.231595\pi\)
\(140\) −0.239558 2.27924i −0.0202463 0.192631i
\(141\) 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
\(146\) −0.0509101 0.0226667i −0.00421335 0.00187591i
\(147\) 0 0
\(148\) −9.23146 1.96221i −0.758821 0.161292i
\(149\) −14.8486 3.15617i −1.21645 0.258564i −0.445393 0.895335i \(-0.646936\pi\)
−0.771053 + 0.636772i \(0.780269\pi\)
\(150\) 0 0
\(151\) 3.95222 + 1.75964i 0.321627 + 0.143197i 0.561199 0.827681i \(-0.310340\pi\)
−0.239572 + 0.970879i \(0.577007\pi\)
\(152\) −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
\(157\) −0.746950 7.10675i −0.0596131 0.567181i −0.983038 0.183402i \(-0.941289\pi\)
0.923425 0.383779i \(-0.125378\pi\)
\(158\) 3.68565 1.64096i 0.293214 0.130547i
\(159\) 0 0
\(160\) 3.42903 3.80833i 0.271089 0.301075i
\(161\) −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
\(167\) 3.85682 + 4.28344i 0.298450 + 0.331462i 0.873654 0.486548i \(-0.161744\pi\)
−0.575204 + 0.818010i \(0.695077\pi\)
\(168\) 0 0
\(169\) −3.01968 + 28.7303i −0.232283 + 2.21002i
\(170\) −0.708204 2.17963i −0.0543168 0.167170i
\(171\) 0 0
\(172\) 2.78115 + 2.02063i 0.212061 + 0.154071i
\(173\) 21.0939 + 9.39162i 1.60374 + 0.714032i 0.996741 0.0806702i \(-0.0257060\pi\)
0.607000 + 0.794702i \(0.292373\pi\)
\(174\) 0 0
\(175\) −1.73607 + 3.00696i −0.131234 + 0.227305i
\(176\) 3.11076 9.95925i 0.234482 0.750707i
\(177\) 0 0
\(178\) −2.52713 + 0.537159i −0.189417 + 0.0402618i
\(179\) −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 \(-0.220059\pi\)
\(182\) 1.65418 1.83716i 0.122616 0.136179i
\(183\) 0 0
\(184\) −0.710624 6.76113i −0.0523879 0.498437i
\(185\) −4.21003 4.67572i −0.309528 0.343765i
\(186\) 0 0
\(187\) −10.9083 11.8403i −0.797696 0.865852i
\(188\) 22.1459 1.61516
\(189\) 0 0
\(190\) −0.381966 + 0.277515i −0.0277107 + 0.0201330i
\(191\) 0.621346 5.91171i 0.0449590 0.427756i −0.948772 0.315961i \(-0.897673\pi\)
0.993731 0.111795i \(-0.0356601\pi\)
\(192\) 0 0
\(193\) 10.7596 + 2.28703i 0.774495 + 0.164624i 0.578171 0.815915i \(-0.303766\pi\)
0.196323 + 0.980539i \(0.437100\pi\)
\(194\) 2.09366 0.932157i 0.150316 0.0669250i
\(195\) 0 0
\(196\) −10.8815 + 2.31294i −0.777251 + 0.165210i
\(197\) −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 \(0.581509\pi\)
\(200\) −4.99976 + 1.06273i −0.353536 + 0.0751465i
\(201\) 0 0
\(202\) 2.95630 1.31623i 0.208004 0.0926094i
\(203\) 4.74803 + 1.00922i 0.333246 + 0.0708337i
\(204\) 0 0
\(205\) −0.326611 + 3.10749i −0.0228115 + 0.217037i
\(206\) 3.16312 2.29814i 0.220385 0.160119i
\(207\) 0 0
\(208\) −20.3607 −1.41176
\(209\) −1.62543 + 2.89102i −0.112433 + 0.199976i
\(210\) 0 0
\(211\) 13.6985 + 15.2138i 0.943046 + 1.04736i 0.998803 + 0.0489142i \(0.0155761\pi\)
−0.0557571 + 0.998444i \(0.517757\pi\)
\(212\) −0.792701 7.54205i −0.0544429 0.517990i
\(213\) 0 0
\(214\) −3.58699 + 3.98376i −0.245202 + 0.272324i
\(215\) 0.708204 + 2.17963i 0.0482991 + 0.148649i
\(216\) 0 0
\(217\) 0.500000 0.363271i 0.0339422 0.0246605i
\(218\) −2.66984 + 0.567493i −0.180825 + 0.0384355i
\(219\) 0 0
\(220\) 6.09797 4.53766i 0.411125 0.305929i
\(221\) −15.7082 + 27.2074i −1.05665 + 1.83017i
\(222\) 0 0
\(223\) −14.1660 6.30709i −0.948623 0.422354i −0.126693 0.991942i \(-0.540436\pi\)
−0.821930 + 0.569588i \(0.807103\pi\)
\(224\) 3.35410 + 2.43690i 0.224105 + 0.162822i
\(225\) 0 0
\(226\) −2.03444 6.26137i −0.135329 0.416500i
\(227\) −1.73706 + 16.5270i −0.115293 + 1.09694i 0.771966 + 0.635664i \(0.219273\pi\)
−0.887259 + 0.461272i \(0.847393\pi\)
\(228\) 0 0
\(229\) 6.81198 + 7.56547i 0.450148 + 0.499940i 0.924916 0.380171i \(-0.124135\pi\)
−0.474768 + 0.880111i \(0.657468\pi\)
\(230\) 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
\(236\) 2.00739 2.22943i 0.130670 0.145124i
\(237\) 0 0
\(238\) 1.69381 0.754131i 0.109793 0.0488831i
\(239\) 1.09464 + 10.4148i 0.0708061 + 0.673675i 0.971146 + 0.238487i \(0.0766515\pi\)
−0.900340 + 0.435188i \(0.856682\pi\)
\(240\) 0 0
\(241\) 13.4164 + 23.2379i 0.864227 + 1.49688i 0.867813 + 0.496891i \(0.165525\pi\)
−0.00358606 + 0.999994i \(0.501141\pi\)
\(242\) −2.01722 + 3.68571i −0.129672 + 0.236927i
\(243\) 0 0
\(244\) −6.21885 + 19.1396i −0.398121 + 1.22529i
\(245\) −6.77523 3.01652i −0.432853 0.192719i
\(246\) 0 0
\(247\) 6.33070 + 1.34563i 0.402813 + 0.0856206i
\(248\) 0.889948 + 0.189164i 0.0565118 + 0.0120119i
\(249\) 0 0
\(250\) −3.65418 1.62695i −0.231111 0.102897i
\(251\) −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
\(256\) −0.581419 5.53184i −0.0363387 0.345740i
\(257\) 13.6208 6.06437i 0.849643 0.378285i 0.0647383 0.997902i \(-0.479379\pi\)
0.784904 + 0.619617i \(0.212712\pi\)
\(258\) 0 0
\(259\) 3.40599 3.78273i 0.211638 0.235048i
\(260\) −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 0.600878 0.799341i \(-0.294818\pi\)
−0.992688 + 0.120705i \(0.961485\pi\)
\(264\) 0 0
\(265\) 2.52786 4.37839i 0.155285 0.268962i
\(266\) −0.255585 0.283856i −0.0156709 0.0174043i
\(267\) 0 0
\(268\) 1.16284 11.0637i 0.0710317 0.675821i
\(269\) 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 \(0.806015\pi\)
\(272\) −13.9503 6.21108i −0.845861 0.376602i
\(273\) 0 0
\(274\) −1.64590 + 2.85078i −0.0994323 + 0.172222i
\(275\) −11.5150 + 0.131418i −0.694382 + 0.00792483i
\(276\) 0 0
\(277\) 18.8157 3.99940i 1.13053 0.240301i 0.395584 0.918430i \(-0.370542\pi\)
0.734943 + 0.678129i \(0.237209\pi\)
\(278\) −3.00000 + 2.17963i −0.179928 + 0.130725i
\(279\) 0 0
\(280\) 0.562306 + 1.73060i 0.0336042 + 0.103423i
\(281\) 6.24047 6.93075i 0.372275 0.413454i −0.527675 0.849446i \(-0.676936\pi\)
0.899950 + 0.435993i \(0.143603\pi\)
\(282\) 0 0
\(283\) 1.77698 + 16.9069i 0.105631 + 1.00501i 0.911048 + 0.412301i \(0.135275\pi\)
−0.805417 + 0.592708i \(0.798059\pi\)
\(284\) −3.61004 4.00936i −0.214217 0.237912i
\(285\) 0 0
\(286\) 8.03891 + 1.61306i 0.475351 + 0.0953824i
\(287\) −2.52786 −0.149215
\(288\) 0 0
\(289\) −5.30902 + 3.85723i −0.312295 + 0.226896i
\(290\) −0.239558 + 2.27924i −0.0140673 + 0.133842i
\(291\) 0 0
\(292\) −0.264599 0.0562422i −0.0154845 0.00329132i
\(293\) 26.6576 11.8687i 1.55735 0.693378i 0.565975 0.824422i \(-0.308500\pi\)
0.991376 + 0.131045i \(0.0418331\pi\)
\(294\) 0 0
\(295\) 1.95630 0.415823i 0.113900 0.0242102i
\(296\) 7.49342 0.435546
\(297\) 0 0
\(298\) 5.79837 0.335891
\(299\) −29.2354 + 6.21418i −1.69073 + 0.359375i
\(300\) 0 0
\(301\) −1.69381 + 0.754131i −0.0976294 + 0.0434674i
\(302\) −1.61637 0.343569i −0.0930114 0.0197702i
\(303\) 0 0
\(304\) −0.328836 + 3.12866i −0.0188600 + 0.179441i
\(305\) −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 \(0.428046\pi\)
\(308\) 4.16661 + 4.52261i 0.237415 + 0.257700i
\(309\) 0 0
\(310\) 0.195250 + 0.216847i 0.0110894 + 0.0123161i
\(311\) 1.58678 + 15.0972i 0.0899779 + 0.856083i 0.942683 + 0.333690i \(0.108294\pi\)
−0.852705 + 0.522393i \(0.825040\pi\)
\(312\) 0 0
\(313\) 2.32331 2.58030i 0.131321 0.145847i −0.673898 0.738825i \(-0.735381\pi\)
0.805219 + 0.592978i \(0.202048\pi\)
\(314\) 0.843459 + 2.59590i 0.0475991 + 0.146495i
\(315\) 0 0
\(316\) 15.8435 11.5109i 0.891264 0.647541i
\(317\) 20.4866 4.35456i 1.15064 0.244576i 0.407175 0.913350i \(-0.366514\pi\)
0.743466 + 0.668774i \(0.233180\pi\)
\(318\) 0 0
\(319\) 5.14935 + 15.2535i 0.288308 + 0.854033i
\(320\) 2.90983 5.03997i 0.162664 0.281743i
\(321\) 0 0
\(322\) 1.61143 + 0.717456i 0.0898016 + 0.0399822i
\(323\) 3.92705 + 2.85317i 0.218507 + 0.158755i
\(324\) 0 0
\(325\) 6.94427 + 21.3723i 0.385199 + 1.18552i
\(326\) −0.826802 + 7.86650i −0.0457923 + 0.435685i
\(327\) 0 0
\(328\) −2.49008 2.76551i −0.137491 0.152700i
\(329\) −5.97214 + 10.3440i −0.329255 + 0.570286i
\(330\) 0 0
\(331\) −7.20820 12.4850i −0.396199 0.686236i 0.597055 0.802201i \(-0.296338\pi\)
−0.993253 + 0.115964i \(0.963004\pi\)
\(332\) −5.59424 + 17.2173i −0.307024 + 0.944921i
\(333\) 0 0
\(334\) −1.78115 1.29408i −0.0974604 0.0708091i
\(335\) 4.96255 5.51147i 0.271133 0.301124i
\(336\) 0 0
\(337\) −10.4803 + 4.66614i −0.570899 + 0.254181i −0.671821 0.740714i \(-0.734488\pi\)
0.100922 + 0.994894i \(0.467821\pi\)
\(338\) −1.15341 10.9740i −0.0627374 0.596907i
\(339\) 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
\(344\) −2.49351 1.11018i −0.134441 0.0598571i
\(345\) 0 0
\(346\) −8.62693 1.83371i −0.463787 0.0985809i
\(347\) −8.69431 1.84803i −0.466735 0.0992076i −0.0314597 0.999505i \(-0.510016\pi\)
−0.435275 + 0.900297i \(0.643349\pi\)
\(348\) 0 0
\(349\) −3.78747 1.68629i −0.202738 0.0902650i 0.302856 0.953036i \(-0.402060\pi\)
−0.505594 + 0.862771i \(0.668727\pi\)
\(350\) 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 0.560568 0.828108i \(-0.310583\pi\)
−0.997447 + 0.0714123i \(0.977249\pi\)
\(354\) 0 0
\(355\) −0.375963 3.57704i −0.0199540 0.189850i
\(356\) −11.4568 + 5.10089i −0.607209 + 0.270347i
\(357\) 0 0
\(358\) 1.29217 1.43510i 0.0682933 0.0758473i
\(359\) −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
\(365\) −0.120671 0.134019i −0.00631621 0.00701486i
\(366\) 0 0
\(367\) 1.32837 12.6386i 0.0693403 0.659729i −0.903553 0.428476i \(-0.859051\pi\)
0.972894 0.231253i \(-0.0742826\pi\)
\(368\) −4.48936 13.8168i −0.234024 0.720252i
\(369\) 0 0
\(370\) 1.94427 + 1.41260i 0.101078 + 0.0734374i
\(371\) 3.73656 + 1.66362i 0.193992 + 0.0863710i
\(372\) 0 0
\(373\) 2.82624 4.89519i 0.146337 0.253463i −0.783534 0.621349i \(-0.786585\pi\)
0.929871 + 0.367886i \(0.119918\pi\)
\(374\) 5.01586 + 3.55749i 0.259364 + 0.183954i
\(375\) 0 0
\(376\) −17.1993 + 3.65583i −0.886989 + 0.188535i
\(377\) 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 \(0.767009\pi\)
\(380\) −1.53351 + 1.70314i −0.0786674 + 0.0873691i
\(381\) 0 0
\(382\) 0.237333 + 2.25807i 0.0121430 + 0.115533i
\(383\) −13.2850 14.7545i −0.678831 0.753918i 0.301026 0.953616i \(-0.402671\pi\)
−0.979858 + 0.199697i \(0.936004\pi\)
\(384\) 0 0
\(385\) 0.475022 + 4.07196i 0.0242094 + 0.207526i
\(386\) −4.20163 −0.213857
\(387\) 0 0
\(388\) 9.00000 6.53888i 0.456906 0.331961i
\(389\) −2.36783 + 22.5284i −0.120054 + 1.14223i 0.754159 + 0.656692i \(0.228045\pi\)
−0.874213 + 0.485543i \(0.838622\pi\)
\(390\) 0 0
\(391\) −21.9266 4.66063i −1.10887 0.235698i
\(392\) 8.06918 3.59263i 0.407555 0.181455i
\(393\) 0 0
\(394\) 3.07715 0.654069i 0.155025 0.0329515i
\(395\) 13.0557 0.656905
\(396\) 0 0
\(397\) −2.12461 −0.106631 −0.0533156 0.998578i \(-0.516979\pi\)
−0.0533156 + 0.998578i \(0.516979\pi\)
\(398\) 2.66984 0.567493i 0.133827 0.0284458i
\(399\) 0 0
\(400\) −9.97864 + 4.44278i −0.498932 + 0.222139i
\(401\) 14.2441 + 3.02767i 0.711316 + 0.151195i 0.549339 0.835600i \(-0.314880\pi\)
0.161977 + 0.986795i \(0.448213\pi\)
\(402\) 0 0
\(403\) 0.418114 3.97809i 0.0208277 0.198163i
\(404\) 12.7082 9.23305i 0.632257 0.459361i
\(405\) 0 0
\(406\) −1.85410 −0.0920175
\(407\) 16.5522 + 3.32132i 0.820465 + 0.164632i
\(408\) 0 0
\(409\) −22.5782 25.0757i −1.11642 1.23991i −0.967990 0.250990i \(-0.919244\pi\)
−0.148432 0.988923i \(-0.547423\pi\)
\(410\) −0.124754 1.18696i −0.00616117 0.0586196i
\(411\) 0 0
\(412\) 12.6992 14.1039i 0.625647 0.694851i
\(413\) 0.500000 + 1.53884i 0.0246034 + 0.0757215i
\(414\) 0 0
\(415\) −9.76393 + 7.09391i −0.479293 + 0.348226i
\(416\) 26.2465 5.57886i 1.28684 0.273526i
\(417\) 0 0
\(418\) 0.377699 1.20922i 0.0184739 0.0591451i
\(419\) 4.04508 7.00629i 0.197615 0.342280i −0.750139 0.661280i \(-0.770014\pi\)
0.947755 + 0.319000i \(0.103347\pi\)
\(420\) 0 0
\(421\) 9.35111 + 4.16338i 0.455745 + 0.202911i 0.621753 0.783214i \(-0.286421\pi\)
−0.166007 + 0.986125i \(0.553088\pi\)
\(422\) −6.32624 4.59628i −0.307956 0.223743i
\(423\) 0 0
\(424\) 1.86068 + 5.72658i 0.0903626 + 0.278107i
\(425\) −1.76173 + 16.7618i −0.0854566 + 0.813065i
\(426\) 0 0
\(427\) −7.26281 8.06617i −0.351472 0.390349i
\(428\) −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 \(0.815261\pi\)
\(434\) −0.157960 + 0.175433i −0.00758234 + 0.00842104i
\(435\) 0 0
\(436\) −12.1038 + 5.38894i −0.579665 + 0.258084i
\(437\) 0.482716 + 4.59274i 0.0230914 + 0.219700i
\(438\) 0 0
\(439\) 0.354102 + 0.613323i 0.0169004 + 0.0292723i 0.874352 0.485292i \(-0.161287\pi\)
−0.857452 + 0.514565i \(0.827954\pi\)
\(440\) −3.98684 + 4.53077i −0.190065 + 0.215996i
\(441\) 0 0
\(442\) 3.70820 11.4127i 0.176381 0.542846i
\(443\) 1.12920 + 0.502754i 0.0536501 + 0.0238866i 0.433386 0.901208i \(-0.357319\pi\)
−0.379736 + 0.925095i \(0.623985\pi\)
\(444\) 0 0
\(445\) −8.17798 1.73828i −0.387673 0.0824025i
\(446\) 5.79355 + 1.23146i 0.274333 + 0.0583112i
\(447\) 0 0
\(448\) 4.30116 + 1.91500i 0.203211 + 0.0904752i
\(449\) −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
\(454\) −0.663497 6.31275i −0.0311395 0.296272i
\(455\) 7.30836 3.25389i 0.342621 0.152545i
\(456\) 0 0
\(457\) −0.669131 + 0.743145i −0.0313006 + 0.0347628i −0.758592 0.651566i \(-0.774112\pi\)
0.727291 + 0.686329i \(0.240779\pi\)
\(458\) −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 0.614481 0.788932i \(-0.289366\pi\)
−0.990475 + 0.137690i \(0.956032\pi\)
\(462\) 0 0
\(463\) −8.50000 + 14.7224i −0.395029 + 0.684209i −0.993105 0.117230i \(-0.962599\pi\)
0.598076 + 0.801439i \(0.295932\pi\)
\(464\) 10.2180 + 11.3482i 0.474357 + 0.526827i
\(465\) 0 0
\(466\) −0.444165 + 4.22595i −0.0205755 + 0.195763i
\(467\) 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
\(470\) −5.15178 2.29372i −0.237634 0.105801i
\(471\) 0 0
\(472\) −1.19098 + 2.06284i −0.0548194 + 0.0949500i
\(473\) −5.01586 3.55749i −0.230630 0.163574i
\(474\) 0 0
\(475\) 3.39626 0.721898i 0.155831 0.0331229i
\(476\) 7.28115 5.29007i 0.333731 0.242470i
\(477\) 0 0
\(478\) −1.23607 3.80423i −0.0565364 0.174001i
\(479\) 7.87161 8.74231i 0.359663 0.399446i −0.535972 0.844236i \(-0.680055\pi\)
0.895635 + 0.444789i \(0.146722\pi\)
\(480\) 0 0
\(481\) −3.44361 32.7638i −0.157015 1.49390i
\(482\) −6.85807 7.61666i −0.312376 0.346929i
\(483\) 0 0
\(484\) −5.85811 + 19.5357i −0.266278 + 0.887986i
\(485\) 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 \(0.204993\pi\)
\(488\) 1.67023 15.8912i 0.0756078 0.719360i
\(489\) 0 0
\(490\) 2.77091 + 0.588976i 0.125177 + 0.0266072i
\(491\) −6.69285 + 2.97985i −0.302044 + 0.134479i −0.552162 0.833737i \(-0.686197\pi\)
0.250118 + 0.968215i \(0.419531\pi\)
\(492\) 0 0
\(493\) 23.0474 4.89888i 1.03800 0.220634i
\(494\) −2.47214 −0.111227
\(495\) 0 0
\(496\) 1.94427 0.0873004
\(497\) 2.84624 0.604988i 0.127671 0.0271374i
\(498\) 0 0
\(499\) 35.0951 15.6254i 1.57107 0.699487i 0.577898 0.816109i \(-0.303873\pi\)
0.993176 + 0.116622i \(0.0372066\pi\)
\(500\) −18.9921 4.03690i −0.849353 0.180536i
\(501\) 0 0
\(502\) 0.820977 7.81108i 0.0366420 0.348625i
\(503\) −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
\(506\) 0.677881 + 5.81089i 0.0301355 + 0.258326i
\(507\) 0 0
\(508\) 13.1040 + 14.5534i 0.581395 + 0.645705i
\(509\) −2.84112 27.0314i −0.125930 1.19815i −0.856807 0.515638i \(-0.827555\pi\)
0.730876 0.682510i \(-0.239112\pi\)
\(510\) 0 0
\(511\) 0.0976248 0.108423i 0.00431867 0.00479637i
\(512\) 6.89261 + 21.2133i 0.304613 + 0.937503i
\(513\) 0 0
\(514\) −4.60739 + 3.34747i −0.203223 + 0.147650i
\(515\) 12.3760 2.63060i 0.545351 0.115918i
\(516\) 0 0
\(517\) −39.6121 + 0.452084i −1.74214 + 0.0198826i
\(518\) −0.972136 + 1.68379i −0.0427132 + 0.0739814i
\(519\) 0 0
\(520\) 10.7589 + 4.79017i 0.471809 + 0.210063i
\(521\) −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 \(0.900000\pi\)
\(524\) −4.11569 + 39.1581i −0.179795 + 1.71063i
\(525\) 0 0
\(526\) 3.24803 + 3.60730i 0.141621 + 0.157286i
\(527\) 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
\(533\) −10.9474 + 12.1584i −0.474186 + 0.526637i
\(534\) 0 0
\(535\) −15.8478 + 7.05587i −0.685158 + 0.305052i
\(536\) 0.923281 + 8.78443i 0.0398797 + 0.379430i
\(537\) 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 \(0.182412\pi\)
\(542\) 3.75600 + 1.67228i 0.161334 + 0.0718306i
\(543\) 0 0
\(544\) 19.6848 + 4.18414i 0.843981 + 0.179394i
\(545\) −8.63980 1.83645i −0.370088 0.0786647i
\(546\) 0 0
\(547\) −29.5315 13.1483i −1.26268 0.562179i −0.337359 0.941376i \(-0.609534\pi\)
−0.925316 + 0.379197i \(0.876200\pi\)
\(548\) −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
\(553\) 1.10406 + 10.5044i 0.0469495 + 0.446694i
\(554\) −6.71230 + 2.98851i −0.285178 + 0.126970i
\(555\) 0 0
\(556\) −12.0444 + 13.3766i −0.510794 + 0.567294i
\(557\) −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
\(563\) 13.5867 + 15.0895i 0.572610 + 0.635947i 0.957987 0.286812i \(-0.0925954\pi\)
−0.385377 + 0.922759i \(0.625929\pi\)
\(564\) 0 0
\(565\) 2.22697 21.1882i 0.0936895 0.891396i
\(566\) −2.00658 6.17561i −0.0843428 0.259580i
\(567\) 0 0
\(568\) 3.46556 + 2.51788i 0.145412 + 0.105648i
\(569\) −35.4441 15.7807i −1.48589 0.661562i −0.506264 0.862378i \(-0.668974\pi\)
−0.979629 + 0.200816i \(0.935641\pi\)
\(570\) 0 0
\(571\) 9.26393 16.0456i 0.387683 0.671488i −0.604454 0.796640i \(-0.706609\pi\)
0.992138 + 0.125153i \(0.0399420\pi\)
\(572\) 39.7969 0.454194i 1.66399 0.0189908i
\(573\) 0 0
\(574\) 0.944458 0.200751i 0.0394209 0.00837918i
\(575\) −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 \(0.636147\pi\)
\(578\) 1.67723 1.86275i 0.0697635 0.0774802i
\(579\) 0 0
\(580\) 1.16284 + 11.0637i 0.0482842 + 0.459394i
\(581\) −6.53335 7.25602i −0.271049 0.301030i
\(582\) 0 0
\(583\) 1.57186 + 13.4742i 0.0650997 + 0.558044i
\(584\) 0.214782 0.00888773
\(585\) 0 0
\(586\) −9.01722 + 6.55139i −0.372498 + 0.270636i
\(587\) 1.40240 13.3429i 0.0578831 0.550721i −0.926700 0.375802i \(-0.877367\pi\)
0.984583 0.174918i \(-0.0559662\pi\)
\(588\) 0 0
\(589\) −0.604528 0.128496i −0.0249092 0.00529461i
\(590\) −0.697887 + 0.310719i −0.0287315 + 0.0127921i
\(591\) 0 0
\(592\) 15.6632 3.32932i 0.643755 0.136834i
\(593\) 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
\(596\) 27.5308 5.85186i 1.12771 0.239702i
\(597\) 0 0
\(598\) 10.4294 4.64347i 0.426490 0.189886i
\(599\) −13.0687 2.77784i −0.533973 0.113500i −0.0669698 0.997755i \(-0.521333\pi\)
−0.467003 + 0.884255i \(0.654666\pi\)
\(600\) 0 0
\(601\) 1.82634 17.3764i 0.0744978 0.708799i −0.891985 0.452066i \(-0.850687\pi\)
0.966482 0.256733i \(-0.0826461\pi\)
\(602\) 0.572949 0.416272i 0.0233517 0.0169660i
\(603\) 0 0
\(604\) −8.02129 −0.326382
\(605\) −10.8147 + 8.24093i −0.439682 + 0.335042i
\(606\) 0 0
\(607\) −2.39789 2.66313i −0.0973274 0.108093i 0.692513 0.721405i \(-0.256503\pi\)
−0.789841 + 0.613312i \(0.789837\pi\)
\(608\) −0.433364 4.12319i −0.0175752 0.167217i
\(609\) 0 0
\(610\) 3.42903 3.80833i 0.138838 0.154195i
\(611\) 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 \(0.431320\pi\)
\(614\) −2.93444 + 0.623735i −0.118424 + 0.0251719i
\(615\) 0 0
\(616\) −3.98254 2.82461i −0.160461 0.113807i
\(617\) −13.5795 + 23.5204i −0.546691 + 0.946897i 0.451807 + 0.892116i \(0.350779\pi\)
−0.998498 + 0.0547813i \(0.982554\pi\)
\(618\) 0 0
\(619\) 25.1794 + 11.2106i 1.01205 + 0.450592i 0.844662 0.535300i \(-0.179801\pi\)
0.167384 + 0.985892i \(0.446468\pi\)
\(620\) 1.14590 + 0.832544i 0.0460204 + 0.0334358i
\(621\) 0 0
\(622\) −1.79180 5.51458i −0.0718445 0.221115i
\(623\) 0.707023 6.72688i 0.0283263 0.269507i
\(624\) 0 0
\(625\) 2.95515 + 3.28203i 0.118206 + 0.131281i
\(626\) −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 \(0.630460\pi\)
\(632\) −10.4044 + 11.5553i −0.413865 + 0.459644i
\(633\) 0 0
\(634\) −7.30836 + 3.25389i −0.290252 + 0.129229i
\(635\) 1.36470 + 12.9842i 0.0541563 + 0.515263i
\(636\) 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
\(641\) 18.6828 + 8.31811i 0.737925 + 0.328546i 0.741050 0.671450i \(-0.234328\pi\)
−0.00312481 + 0.999995i \(0.500995\pi\)
\(642\) 0 0
\(643\) 6.70432 + 1.42505i 0.264393 + 0.0561984i 0.338200 0.941074i \(-0.390182\pi\)
−0.0738078 + 0.997272i \(0.523515\pi\)
\(644\) 8.37520 + 1.78020i 0.330029 + 0.0701498i
\(645\) 0 0
\(646\) −1.69381 0.754131i −0.0666419 0.0296709i
\(647\) 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
\(652\) 4.01338 + 38.1848i 0.157176 + 1.49543i
\(653\) 1.24304 0.553438i 0.0486440 0.0216577i −0.382270 0.924050i \(-0.624858\pi\)
0.430914 + 0.902393i \(0.358191\pi\)
\(654\) 0 0
\(655\) −17.5642 + 19.5070i −0.686288 + 0.762201i
\(656\) −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 0.946690 0.322147i \(-0.104404\pi\)
−0.752332 + 0.658784i \(0.771071\pi\)
\(660\) 0 0
\(661\) 2.14590 3.71680i 0.0834658 0.144567i −0.821271 0.570539i \(-0.806734\pi\)
0.904736 + 0.425972i \(0.140068\pi\)
\(662\) 3.68462 + 4.09218i 0.143207 + 0.159047i
\(663\) 0 0
\(664\) 1.50247 14.2951i 0.0583073 0.554757i
\(665\) −0.381966 1.17557i −0.0148120 0.0455867i
\(666\) 0 0
\(667\) 18.1353 + 13.1760i 0.702200 + 0.510178i
\(668\) −9.76299 4.34676i −0.377741 0.168181i
\(669\) 0 0
\(670\) −1.41641 + 2.45329i −0.0547206 + 0.0947789i
\(671\) 10.7329 34.3618i 0.414337 1.32652i
\(672\) 0 0
\(673\) 28.9163 6.14635i 1.11464 0.236924i 0.386458 0.922307i \(-0.373698\pi\)
0.728183 + 0.685383i \(0.240365\pi\)
\(674\) 3.54508 2.57565i 0.136552 0.0992105i
\(675\) 0 0
\(676\) −16.5517 50.9408i −0.636602 1.95926i
\(677\) −4.05207 + 4.50028i −0.155734 + 0.172960i −0.815963 0.578105i \(-0.803793\pi\)
0.660229 + 0.751064i \(0.270459\pi\)
\(678\) 0 0
\(679\) 0.627171 + 5.96713i 0.0240686 + 0.228997i
\(680\) 5.91031 + 6.56406i 0.226650 + 0.251720i
\(681\) 0 0
\(682\) −0.767647 0.154034i −0.0293947 0.00589826i
\(683\) 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
\(686\) −0.519042 + 4.93836i −0.0198171 + 0.188547i
\(687\) 0 0
\(688\) −5.70535 1.21271i −0.217515 0.0462342i
\(689\) 24.1835 10.7672i 0.921318 0.410197i
\(690\) 0 0
\(691\) −14.2778 + 3.03483i −0.543152 + 0.115451i −0.471314 0.881966i \(-0.656220\pi\)
−0.0718386 + 0.997416i \(0.522887\pi\)
\(692\) −42.8115 −1.62745
\(693\) 0 0
\(694\) 3.39512 0.128877
\(695\) −11.7378 + 2.49494i −0.445239 + 0.0946385i
\(696\) 0 0
\(697\) −11.2097 + 4.99087i −0.424596 + 0.189043i
\(698\) 1.54899 + 0.329247i 0.0586300 + 0.0124622i
\(699\) 0 0
\(700\) 0.672922 6.40243i 0.0254341 0.241989i
\(701\) −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
\(704\) 1.80937 + 15.5102i 0.0681931 + 0.584561i
\(705\) 0 0
\(706\) 4.19579 + 4.65990i 0.157911 + 0.175378i
\(707\) 0.885579 + 8.42572i 0.0333056 + 0.316882i
\(708\) 0 0
\(709\) −17.2394 + 19.1463i −0.647441 + 0.719056i −0.974108 0.226084i \(-0.927408\pi\)
0.326667 + 0.945139i \(0.394074\pi\)
\(710\) 0.424538 + 1.30660i 0.0159326 + 0.0490356i
\(711\) 0 0
\(712\) 8.05573 5.85283i 0.301901 0.219344i
\(713\) 2.79173 0.593401i 0.104551 0.0222230i
\(714\) 0 0
\(715\) 21.6422 + 15.3497i 0.809373 + 0.574047i
\(716\) 4.68692 8.11798i 0.175158 0.303383i
\(717\) 0 0
\(718\) 7.97479 + 3.55060i 0.297616 + 0.132507i
\(719\) −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
\(722\) 0.718674 6.83772i 0.0267463 0.254474i
\(723\) 0 0
\(724\) 12.2945 + 13.6544i 0.456921 + 0.507463i
\(725\) 8.42705 14.5961i 0.312973 0.542085i
\(726\) 0 0
\(727\) −9.41641 16.3097i −0.349235 0.604893i 0.636879 0.770964i \(-0.280225\pi\)
−0.986114 + 0.166071i \(0.946892\pi\)
\(728\) −2.94427 + 9.06154i −0.109122 + 0.335843i
\(729\) 0 0
\(730\) 0.0557281 + 0.0404888i 0.00206259 + 0.00149856i
\(731\) −6.02218 + 6.68830i −0.222738 + 0.247376i
\(732\) 0 0
\(733\) 44.2815 19.7154i 1.63557 0.728205i 0.636502 0.771275i \(-0.280381\pi\)
0.999072 + 0.0430700i \(0.0137138\pi\)
\(734\) 0.507392 + 4.82751i 0.0187282 + 0.178187i
\(735\) 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 \(-0.186029\pi\)
\(740\) 10.6571 + 4.74484i 0.391762 + 0.174424i
\(741\) 0 0
\(742\) −1.52817 0.324822i −0.0561007 0.0119246i
\(743\) −41.4350 8.80728i −1.52010 0.323108i −0.629179 0.777261i \(-0.716609\pi\)
−0.890924 + 0.454153i \(0.849942\pi\)
\(744\) 0 0
\(745\) 17.1417 + 7.63198i 0.628023 + 0.279614i
\(746\) −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
\(751\) 3.26643 + 31.0780i 0.119194 + 1.13405i 0.876637 + 0.481152i \(0.159782\pi\)
−0.757443 + 0.652901i \(0.773552\pi\)
\(752\) −34.3269 + 15.2833i −1.25177 + 0.557325i
\(753\) 0 0
\(754\) −8.02957 + 8.91774i −0.292420 + 0.324765i
\(755\) −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
\(761\) −4.66967 5.18620i −0.169275 0.187999i 0.652538 0.757756i \(-0.273704\pi\)
−0.821814 + 0.569756i \(0.807038\pi\)
\(762\) 0 0
\(763\) 0.746950 7.10675i 0.0270414 0.257282i
\(764\) 3.40576 + 10.4819i 0.123216 + 0.379221i
\(765\) 0 0
\(766\) 6.13525 + 4.45752i 0.221676 + 0.161057i
\(767\) 9.56677 + 4.25940i 0.345436 + 0.153798i
\(768\) 0 0
\(769\) 7.89919 13.6818i 0.284852 0.493378i −0.687721 0.725975i \(-0.741389\pi\)
0.972573 + 0.232597i \(0.0747222\pi\)
\(770\) −0.500853 1.48364i −0.0180495 0.0534666i
\(771\) 0 0
\(772\) −19.9494 + 4.24038i −0.717996 + 0.152615i
\(773\) 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
\(776\) −5.91031 + 6.56406i −0.212168 + 0.235636i
\(777\) 0 0
\(778\) −0.904430 8.60508i −0.0324254 0.308507i
\(779\) 1.69147 + 1.87857i 0.0606032 + 0.0673067i
\(780\) 0 0
\(781\) 6.53908 + 7.09779i 0.233987 + 0.253979i
\(782\) 8.56231 0.306187
\(783\) 0 0
\(784\) 15.2705 11.0947i 0.545375 0.396238i
\(785\) −0.923281 + 8.78443i −0.0329533 + 0.313530i
\(786\) 0 0
\(787\) −35.2133 7.48482i −1.25522 0.266805i −0.468138 0.883655i \(-0.655075\pi\)
−0.787081 + 0.616850i \(0.788408\pi\)
\(788\) 13.9503 6.21108i 0.496959 0.221260i
\(789\) 0 0
\(790\) −4.87787 + 1.03682i −0.173547 + 0.0368885i
\(791\) 17.2361 0.612844
\(792\) 0 0
\(793\) −70.2492 −2.49462
\(794\) 0.793796 0.168726i 0.0281708 0.00598788i
\(795\) 0 0
\(796\) 12.1038 5.38894i 0.429007 0.191006i
\(797\) 23.7401 + 5.04612i 0.840919 + 0.178743i 0.608183 0.793797i \(-0.291899\pi\)
0.232736 + 0.972540i \(0.425232\pi\)
\(798\) 0 0
\(799\) −6.06043 + 57.6611i −0.214402 + 2.03990i
\(800\) 11.6459 8.46124i 0.411745 0.299150i
\(801\) 0 0
\(802\) −5.56231 −0.196412
\(803\) 0.474432 + 0.0951981i 0.0167423 + 0.00335947i
\(804\) 0 0
\(805\) 3.81953 + 4.24202i 0.134621 + 0.149512i
\(806\) 0.159705 + 1.51949i 0.00562538 + 0.0535219i
\(807\) 0 0
\(808\) −8.34549 + 9.26860i −0.293593 + 0.326068i
\(809\) 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 \(0.348739\pi\)
\(812\) −8.80333 + 1.87121i −0.308936 + 0.0656664i
\(813\) 0 0
\(814\) −6.44800 + 0.0735897i −0.226002 + 0.00257932i
\(815\) −12.7984 + 22.1674i −0.448307 + 0.776491i
\(816\) 0 0
\(817\) 1.69381 + 0.754131i 0.0592588 + 0.0263837i
\(818\) 10.4271 + 7.57570i 0.364573 + 0.264878i
\(819\) 0 0
\(820\) −1.79024 5.50980i −0.0625180 0.192411i
\(821\) 3.99453 38.0054i 0.139410 1.32640i −0.671402 0.741093i \(-0.734308\pi\)
0.810813 0.585306i \(-0.199026\pi\)
\(822\) 0 0
\(823\) −28.2987 31.4289i −0.986432 1.09554i −0.995421 0.0955840i \(-0.969528\pi\)
0.00898947 0.999960i \(-0.497139\pi\)
\(824\) −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 \(0.972908\pi\)
\(830\) 3.08463 3.42583i 0.107069 0.118912i
\(831\) 0 0
\(832\) 27.8377 12.3941i 0.965098 0.429689i
\(833\) −3.04435 28.9651i −0.105481 1.00358i
\(834\) 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
\(839\) 15.7968 + 7.03321i 0.545368 + 0.242813i 0.660878 0.750493i \(-0.270184\pi\)
−0.115511 + 0.993306i \(0.536851\pi\)
\(840\) 0 0
\(841\) 5.31887 + 1.13056i 0.183409 + 0.0389848i
\(842\) −3.82439 0.812899i −0.131797 0.0280144i
\(843\) 0 0
\(844\) −34.6758 15.4387i −1.19359 0.531421i
\(845\) 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
\(850\) −0.672922 6.40243i −0.0230810 0.219601i
\(851\) 21.4743 9.56099i 0.736130 0.327746i
\(852\) 0 0
\(853\) −23.7124 + 26.3353i −0.811899 + 0.901705i −0.996708 0.0810695i \(-0.974166\pi\)
0.184810 + 0.982774i \(0.440833\pi\)
\(854\) 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 0.997143 0.0755396i \(-0.0240679\pi\)
−0.563991 + 0.825781i \(0.690735\pi\)
\(858\) 0 0
\(859\) 16.2812 28.1998i 0.555506 0.962164i −0.442358 0.896838i \(-0.645858\pi\)
0.997864 0.0653258i \(-0.0208087\pi\)
\(860\) −2.84329 3.15779i −0.0969552 0.107680i
\(861\) 0 0
\(862\) −1.36025 + 12.9419i −0.0463301 + 0.440802i
\(863\) −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
\(866\) 5.14435 + 2.29041i 0.174812 + 0.0778313i
\(867\) 0 0
\(868\) −0.572949 + 0.992377i −0.0194472 + 0.0336835i
\(869\) −28.1040 + 20.9129i −0.953363 + 0.709422i
\(870\) 0 0
\(871\) 37.9842 8.07380i 1.28705 0.273570i
\(872\) 8.51064 6.18334i 0.288207 0.209394i
\(873\) 0 0
\(874\) −0.545085 1.67760i −0.0184378 0.0567456i
\(875\) 7.00723 7.78231i 0.236887 0.263090i
\(876\) 0 0
\(877\) −1.21219 11.5332i −0.0409328 0.389449i −0.995739 0.0922193i \(-0.970604\pi\)
0.954806 0.297230i \(-0.0960628\pi\)
\(878\) −0.181006 0.201028i −0.00610867 0.00678437i
\(879\) 0 0
\(880\) −6.32054 + 11.2419i −0.213065 + 0.378963i
\(881\) −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 \(0.0952068\pi\)
\(884\) 6.08870 57.9301i 0.204785 1.94840i
\(885\) 0 0
\(886\) −0.461819 0.0981626i −0.0155151 0.00329784i
\(887\) 3.68565 1.64096i 0.123752 0.0550979i −0.343927 0.938997i \(-0.611757\pi\)
0.467679 + 0.883899i \(0.345090\pi\)
\(888\) 0 0
\(889\) −10.3315 + 2.19603i −0.346507 + 0.0736524i
\(890\) 3.19350 0.107046
\(891\) 0 0
\(892\) 28.7508 0.962647
\(893\) 11.6833 2.48335i 0.390965 0.0831023i
\(894\) 0 0
\(895\) 5.70895 2.54179i 0.190829 0.0849626i
\(896\) −9.86968 2.09786i −0.329723 0.0700847i
\(897\) 0 0
\(898\) 0.298335 2.83847i 0.00995556 0.0947209i
\(899\) −2.42705 + 1.76336i −0.0809467 + 0.0588112i
\(900\) 0 0
\(901\) 19.8541 0.661436
\(902\) 2.16984 + 2.35523i 0.0722477 + 0.0784207i
\(903\) 0 0
\(904\) 16.9784 + 18.8564i 0.564694 + 0.627156i
\(905\) 1.28039 + 12.1821i 0.0425617 + 0.404947i
\(906\) 0 0
\(907\) −9.75833 + 10.8377i −0.324020 + 0.359861i −0.883043 0.469291i \(-0.844509\pi\)
0.559024 + 0.829152i \(0.311176\pi\)
\(908\) −9.52129 29.3035i −0.315975 0.972471i
\(909\) 0 0
\(910\) −2.47214 + 1.79611i −0.0819505 + 0.0595405i
\(911\) −18.7612 + 3.98782i −0.621586 + 0.132122i −0.507931 0.861398i \(-0.669589\pi\)
−0.113656 + 0.993520i \(0.536256\pi\)
\(912\) 0 0
\(913\) 9.65487 30.9105i 0.319529 1.02299i
\(914\) 0.190983 0.330792i 0.00631716 0.0109416i
\(915\) 0 0
\(916\) −17.2435 7.67731i −0.569742 0.253666i
\(917\) −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 \(-0.246134\pi\)
\(920\) −0.878379 + 8.35722i −0.0289593 + 0.275529i
\(921\) 0 0
\(922\) 4.12665 + 4.58311i 0.135904 + 0.150937i
\(923\) 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
\(929\) 32.2993 35.8720i 1.05970 1.17692i 0.0760042 0.997107i \(-0.475784\pi\)
0.983701 0.179814i \(-0.0575496\pi\)
\(930\) 0 0
\(931\) −5.48127 + 2.44042i −0.179641 + 0.0799815i
\(932\) 2.15602 + 20.5132i 0.0706228 + 0.671931i
\(933\) 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 \(0.977213\pi\)
\(938\) −2.09366 0.932157i −0.0683604 0.0304360i
\(939\) 0 0
\(940\) −26.7757 5.69134i −0.873325 0.185631i
\(941\) 26.5656 + 5.64668i 0.866013 + 0.184077i 0.619436 0.785047i \(-0.287361\pi\)
0.246576 + 0.969123i \(0.420694\pi\)
\(942\) 0 0
\(943\) −10.6645 4.74815i −0.347284 0.154621i
\(944\) −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 0.993344 + 0.115189i \(0.0367473\pi\)
−0.396915 + 0.917855i \(0.629919\pi\)
\(948\) 0 0
\(949\) −0.0987033 0.939099i −0.00320404 0.0304844i
\(950\) −1.21158 + 0.539430i −0.0393088 + 0.0175014i
\(951\) 0 0
\(952\) −4.78154 + 5.31044i −0.154971 + 0.172112i
\(953\) −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
\(959\) −5.76659 6.40445i −0.186213 0.206810i
\(960\) 0 0
\(961\) 3.20046 30.4503i 0.103241 0.982268i
\(962\) 3.88854 + 11.9677i 0.125372 + 0.385854i
\(963\) 0 0
\(964\) −40.2492 29.2428i −1.29634 0.941846i
\(965\) −12.4212 5.53030i −0.399854 0.178027i
\(966\) 0 0
\(967\) −26.2426 + 45.4536i −0.843907 + 1.46169i 0.0426608 + 0.999090i \(0.486417\pi\)
−0.886567 + 0.462599i \(0.846917\pi\)
\(968\) 1.32469 16.1392i 0.0425771 0.518734i
\(969\) 0 0
\(970\) −2.77091 + 0.588976i −0.0889686 + 0.0189109i
\(971\) 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
\(974\) −3.31717 + 3.68409i −0.106289 + 0.118046i
\(975\) 0 0
\(976\) −3.56922 33.9588i −0.114248 1.08700i
\(977\) −10.5481 11.7149i −0.337465 0.374792i 0.550397 0.834903i \(-0.314476\pi\)
−0.887862 + 0.460111i \(0.847810\pi\)
\(978\) 0 0
\(979\) 20.3885 9.35778i 0.651619 0.299076i
\(980\) 13.7508 0.439252
\(981\) 0 0
\(982\) 2.26393 1.64484i 0.0722450 0.0524890i
\(983\) 0.967657 9.20664i 0.0308635 0.293646i −0.968193 0.250206i \(-0.919502\pi\)
0.999056 0.0434400i \(-0.0138317\pi\)
\(984\) 0 0
\(985\) 9.95788 + 2.11661i 0.317284 + 0.0674409i
\(986\) −8.22191 + 3.66063i −0.261839 + 0.116578i
\(987\) 0 0
\(988\) −11.7378 + 2.49494i −0.373428 + 0.0793746i
\(989\) −8.56231 −0.272265
\(990\) 0 0
\(991\) 20.5967 0.654277 0.327139 0.944976i \(-0.393916\pi\)
0.327139 + 0.944976i \(0.393916\pi\)
\(992\) −2.50631 + 0.532733i −0.0795755 + 0.0169143i
\(993\) 0 0
\(994\) −1.01537 + 0.452070i −0.0322054 + 0.0143388i
\(995\) 8.63980 + 1.83645i 0.273900 + 0.0582192i
\(996\) 0 0
\(997\) −0.771626 + 7.34153i −0.0244376 + 0.232508i 0.975485 + 0.220066i \(0.0706273\pi\)
−0.999923 + 0.0124424i \(0.996039\pi\)
\(998\) −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.64.1 8
3.2 odd 2 99.2.m.a.31.1 yes 8
9.2 odd 6 99.2.m.a.97.1 yes 8
9.4 even 3 891.2.f.a.163.1 4
9.5 odd 6 891.2.f.b.163.1 4
9.7 even 3 inner 297.2.n.a.262.1 8
11.5 even 5 inner 297.2.n.a.280.1 8
33.5 odd 10 99.2.m.a.49.1 yes 8
33.26 odd 10 1089.2.e.g.364.1 4
33.29 even 10 1089.2.e.d.364.2 4
99.4 even 15 9801.2.a.bb.1.1 2
99.5 odd 30 891.2.f.b.82.1 4
99.16 even 15 inner 297.2.n.a.181.1 8
99.29 even 30 1089.2.e.d.727.2 4
99.38 odd 30 99.2.m.a.16.1 8
99.40 odd 30 9801.2.a.m.1.2 2
99.49 even 15 891.2.f.a.82.1 4
99.59 odd 30 9801.2.a.n.1.2 2
99.92 odd 30 1089.2.e.g.727.1 4
99.95 even 30 9801.2.a.bc.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.m.a.16.1 8 99.38 odd 30
99.2.m.a.31.1 yes 8 3.2 odd 2
99.2.m.a.49.1 yes 8 33.5 odd 10
99.2.m.a.97.1 yes 8 9.2 odd 6
297.2.n.a.64.1 8 1.1 even 1 trivial
297.2.n.a.181.1 8 99.16 even 15 inner
297.2.n.a.262.1 8 9.7 even 3 inner
297.2.n.a.280.1 8 11.5 even 5 inner
891.2.f.a.82.1 4 99.49 even 15
891.2.f.a.163.1 4 9.4 even 3
891.2.f.b.82.1 4 99.5 odd 30
891.2.f.b.163.1 4 9.5 odd 6
1089.2.e.d.364.2 4 33.29 even 10
1089.2.e.d.727.2 4 99.29 even 30
1089.2.e.g.364.1 4 33.26 odd 10
1089.2.e.g.727.1 4 99.92 odd 30
9801.2.a.m.1.2 2 99.40 odd 30
9801.2.a.n.1.2 2 99.59 odd 30
9801.2.a.bb.1.1 2 99.4 even 15
9801.2.a.bc.1.1 2 99.95 even 30