Properties

Label 495.2.n.e.361.1
Level $495$
Weight $2$
Character 495.361
Analytic conductor $3.953$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [495,2,Mod(91,495)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(495, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("495.91");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 495.n (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.95259490005\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.13140625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 55)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 361.1
Root \(-0.386111 + 0.280526i\) of defining polynomial
Character \(\chi\) \(=\) 495.361
Dual form 495.2.n.e.181.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.147481 + 0.453901i) q^{2} +(1.43376 + 1.04169i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-2.17239 - 1.57833i) q^{7} +(-1.45650 + 1.05821i) q^{8} +O(q^{10})\) \(q+(-0.147481 + 0.453901i) q^{2} +(1.43376 + 1.04169i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-2.17239 - 1.57833i) q^{7} +(-1.45650 + 1.05821i) q^{8} -0.477260 q^{10} +(2.79042 + 1.79264i) q^{11} +(-1.44244 + 4.43939i) q^{13} +(1.03679 - 0.753275i) q^{14} +(0.829779 + 2.55380i) q^{16} +(1.42961 + 4.39990i) q^{17} +(3.51149 - 2.55125i) q^{19} +(-0.547647 + 1.68548i) q^{20} +(-1.22522 + 1.00220i) q^{22} -2.77222 q^{23} +(-0.809017 + 0.587785i) q^{25} +(-1.80231 - 1.30945i) q^{26} +(-1.47055 - 4.52590i) q^{28} +(-2.43790 - 1.77124i) q^{29} +(0.737407 - 2.26951i) q^{31} -4.88221 q^{32} -2.20796 q^{34} +(0.829779 - 2.55380i) q^{35} +(8.61029 + 6.25574i) q^{37} +(0.640135 + 1.97013i) q^{38} +(-1.45650 - 1.05821i) q^{40} +(-1.78826 + 1.29924i) q^{41} -7.06719 q^{43} +(2.13343 + 5.47695i) q^{44} +(0.408851 - 1.25832i) q^{46} +(3.52905 - 2.56401i) q^{47} +(0.0650188 + 0.200107i) q^{49} +(-0.147481 - 0.453901i) q^{50} +(-6.69257 + 4.86243i) q^{52} +(1.95733 - 6.02403i) q^{53} +(-0.842610 + 3.20780i) q^{55} +4.83428 q^{56} +(1.16351 - 0.845342i) q^{58} +(9.50375 + 6.90488i) q^{59} +(-1.23070 - 3.78770i) q^{61} +(0.921378 + 0.669420i) q^{62} +(-0.939522 + 2.89155i) q^{64} -4.66785 q^{65} +7.31984 q^{67} +(-2.53359 + 7.79760i) q^{68} +(1.03679 + 0.753275i) q^{70} +(-0.369495 - 1.13719i) q^{71} +(-0.826577 - 0.600544i) q^{73} +(-4.10935 + 2.98562i) q^{74} +7.69223 q^{76} +(-3.23251 - 8.29852i) q^{77} +(1.08222 - 3.33073i) q^{79} +(-2.17239 + 1.57833i) q^{80} +(-0.325994 - 1.00331i) q^{82} +(-3.43498 - 10.5718i) q^{83} +(-3.74278 + 2.71929i) q^{85} +(1.04228 - 3.20780i) q^{86} +(-5.96123 + 0.341876i) q^{88} -2.76978 q^{89} +(10.1404 - 7.36742i) q^{91} +(-3.97470 - 2.88779i) q^{92} +(0.643336 + 1.97998i) q^{94} +(3.51149 + 2.55125i) q^{95} +(5.72738 - 17.6271i) q^{97} -0.100418 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - q^{7} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - q^{7} - 4 q^{8} + 2 q^{10} - 3 q^{11} - 2 q^{13} + 16 q^{14} + 4 q^{16} + 13 q^{17} + 15 q^{19} + 3 q^{20} - 7 q^{22} - 10 q^{23} - 2 q^{25} - 10 q^{26} - 6 q^{28} + 9 q^{29} - 10 q^{31} - 16 q^{32} + 4 q^{34} + 4 q^{35} + 24 q^{37} - 4 q^{40} - 8 q^{41} - 38 q^{43} + 12 q^{44} + 3 q^{46} + q^{49} + 2 q^{50} - 28 q^{52} - 13 q^{53} + 7 q^{55} - 22 q^{56} + 12 q^{58} + 27 q^{59} + 6 q^{61} + 30 q^{62} - 26 q^{64} - 2 q^{65} - 38 q^{67} - 11 q^{68} + 16 q^{70} + 20 q^{71} + 13 q^{73} - 20 q^{74} - 34 q^{77} + 37 q^{79} - q^{80} + 28 q^{82} - 27 q^{83} - 12 q^{85} + 3 q^{86} - 36 q^{88} + 16 q^{89} + 44 q^{91} - 11 q^{92} + 17 q^{94} + 15 q^{95} + 24 q^{97} - 16 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/495\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(397\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.147481 + 0.453901i −0.104285 + 0.320957i −0.989562 0.144108i \(-0.953969\pi\)
0.885277 + 0.465064i \(0.153969\pi\)
\(3\) 0 0
\(4\) 1.43376 + 1.04169i 0.716879 + 0.520843i
\(5\) 0.309017 + 0.951057i 0.138197 + 0.425325i
\(6\) 0 0
\(7\) −2.17239 1.57833i −0.821086 0.596554i 0.0959376 0.995387i \(-0.469415\pi\)
−0.917023 + 0.398834i \(0.869415\pi\)
\(8\) −1.45650 + 1.05821i −0.514950 + 0.374133i
\(9\) 0 0
\(10\) −0.477260 −0.150923
\(11\) 2.79042 + 1.79264i 0.841344 + 0.540500i
\(12\) 0 0
\(13\) −1.44244 + 4.43939i −0.400062 + 1.23126i 0.524886 + 0.851172i \(0.324108\pi\)
−0.924949 + 0.380092i \(0.875892\pi\)
\(14\) 1.03679 0.753275i 0.277095 0.201321i
\(15\) 0 0
\(16\) 0.829779 + 2.55380i 0.207445 + 0.638449i
\(17\) 1.42961 + 4.39990i 0.346732 + 1.06713i 0.960650 + 0.277762i \(0.0895926\pi\)
−0.613918 + 0.789370i \(0.710407\pi\)
\(18\) 0 0
\(19\) 3.51149 2.55125i 0.805592 0.585297i −0.106958 0.994264i \(-0.534111\pi\)
0.912549 + 0.408967i \(0.134111\pi\)
\(20\) −0.547647 + 1.68548i −0.122458 + 0.376886i
\(21\) 0 0
\(22\) −1.22522 + 1.00220i −0.261217 + 0.213669i
\(23\) −2.77222 −0.578048 −0.289024 0.957322i \(-0.593331\pi\)
−0.289024 + 0.957322i \(0.593331\pi\)
\(24\) 0 0
\(25\) −0.809017 + 0.587785i −0.161803 + 0.117557i
\(26\) −1.80231 1.30945i −0.353462 0.256805i
\(27\) 0 0
\(28\) −1.47055 4.52590i −0.277908 0.855314i
\(29\) −2.43790 1.77124i −0.452707 0.328911i 0.337956 0.941162i \(-0.390264\pi\)
−0.790664 + 0.612251i \(0.790264\pi\)
\(30\) 0 0
\(31\) 0.737407 2.26951i 0.132442 0.407615i −0.862741 0.505646i \(-0.831254\pi\)
0.995183 + 0.0980305i \(0.0312543\pi\)
\(32\) −4.88221 −0.863061
\(33\) 0 0
\(34\) −2.20796 −0.378662
\(35\) 0.829779 2.55380i 0.140258 0.431670i
\(36\) 0 0
\(37\) 8.61029 + 6.25574i 1.41552 + 1.02844i 0.992490 + 0.122324i \(0.0390346\pi\)
0.423033 + 0.906114i \(0.360965\pi\)
\(38\) 0.640135 + 1.97013i 0.103844 + 0.319598i
\(39\) 0 0
\(40\) −1.45650 1.05821i −0.230293 0.167317i
\(41\) −1.78826 + 1.29924i −0.279279 + 0.202908i −0.718603 0.695421i \(-0.755218\pi\)
0.439324 + 0.898329i \(0.355218\pi\)
\(42\) 0 0
\(43\) −7.06719 −1.07774 −0.538868 0.842390i \(-0.681148\pi\)
−0.538868 + 0.842390i \(0.681148\pi\)
\(44\) 2.13343 + 5.47695i 0.321626 + 0.825682i
\(45\) 0 0
\(46\) 0.408851 1.25832i 0.0602819 0.185528i
\(47\) 3.52905 2.56401i 0.514765 0.373999i −0.299863 0.953982i \(-0.596941\pi\)
0.814628 + 0.579983i \(0.196941\pi\)
\(48\) 0 0
\(49\) 0.0650188 + 0.200107i 0.00928840 + 0.0285868i
\(50\) −0.147481 0.453901i −0.0208570 0.0641913i
\(51\) 0 0
\(52\) −6.69257 + 4.86243i −0.928092 + 0.674298i
\(53\) 1.95733 6.02403i 0.268859 0.827464i −0.721920 0.691977i \(-0.756740\pi\)
0.990779 0.135487i \(-0.0432600\pi\)
\(54\) 0 0
\(55\) −0.842610 + 3.20780i −0.113617 + 0.432540i
\(56\) 4.83428 0.646008
\(57\) 0 0
\(58\) 1.16351 0.845342i 0.152777 0.110999i
\(59\) 9.50375 + 6.90488i 1.23728 + 0.898939i 0.997414 0.0718667i \(-0.0228956\pi\)
0.239869 + 0.970805i \(0.422896\pi\)
\(60\) 0 0
\(61\) −1.23070 3.78770i −0.157575 0.484966i 0.840838 0.541287i \(-0.182063\pi\)
−0.998413 + 0.0563214i \(0.982063\pi\)
\(62\) 0.921378 + 0.669420i 0.117015 + 0.0850164i
\(63\) 0 0
\(64\) −0.939522 + 2.89155i −0.117440 + 0.361444i
\(65\) −4.66785 −0.578975
\(66\) 0 0
\(67\) 7.31984 0.894260 0.447130 0.894469i \(-0.352446\pi\)
0.447130 + 0.894469i \(0.352446\pi\)
\(68\) −2.53359 + 7.79760i −0.307243 + 0.945598i
\(69\) 0 0
\(70\) 1.03679 + 0.753275i 0.123921 + 0.0900336i
\(71\) −0.369495 1.13719i −0.0438510 0.134960i 0.926734 0.375718i \(-0.122604\pi\)
−0.970585 + 0.240758i \(0.922604\pi\)
\(72\) 0 0
\(73\) −0.826577 0.600544i −0.0967436 0.0702883i 0.538362 0.842714i \(-0.319043\pi\)
−0.635105 + 0.772425i \(0.719043\pi\)
\(74\) −4.10935 + 2.98562i −0.477702 + 0.347071i
\(75\) 0 0
\(76\) 7.69223 0.882360
\(77\) −3.23251 8.29852i −0.368378 0.945704i
\(78\) 0 0
\(79\) 1.08222 3.33073i 0.121759 0.374736i −0.871538 0.490329i \(-0.836877\pi\)
0.993297 + 0.115593i \(0.0368767\pi\)
\(80\) −2.17239 + 1.57833i −0.242880 + 0.176463i
\(81\) 0 0
\(82\) −0.325994 1.00331i −0.0360000 0.110797i
\(83\) −3.43498 10.5718i −0.377038 1.16040i −0.942093 0.335351i \(-0.891145\pi\)
0.565055 0.825053i \(-0.308855\pi\)
\(84\) 0 0
\(85\) −3.74278 + 2.71929i −0.405961 + 0.294948i
\(86\) 1.04228 3.20780i 0.112392 0.345906i
\(87\) 0 0
\(88\) −5.96123 + 0.341876i −0.635469 + 0.0364442i
\(89\) −2.76978 −0.293596 −0.146798 0.989167i \(-0.546897\pi\)
−0.146798 + 0.989167i \(0.546897\pi\)
\(90\) 0 0
\(91\) 10.1404 7.36742i 1.06300 0.772315i
\(92\) −3.97470 2.88779i −0.414391 0.301073i
\(93\) 0 0
\(94\) 0.643336 + 1.97998i 0.0663550 + 0.204220i
\(95\) 3.51149 + 2.55125i 0.360271 + 0.261753i
\(96\) 0 0
\(97\) 5.72738 17.6271i 0.581528 1.78976i −0.0312615 0.999511i \(-0.509952\pi\)
0.612789 0.790247i \(-0.290048\pi\)
\(98\) −0.100418 −0.0101438
\(99\) 0 0
\(100\) −1.77222 −0.177222
\(101\) 2.19852 6.76634i 0.218761 0.673276i −0.780104 0.625649i \(-0.784834\pi\)
0.998865 0.0476270i \(-0.0151659\pi\)
\(102\) 0 0
\(103\) −6.09056 4.42505i −0.600121 0.436014i 0.245801 0.969320i \(-0.420949\pi\)
−0.845922 + 0.533307i \(0.820949\pi\)
\(104\) −2.59688 7.99237i −0.254645 0.783716i
\(105\) 0 0
\(106\) 2.44565 + 1.77687i 0.237542 + 0.172584i
\(107\) 14.5859 10.5973i 1.41008 1.02448i 0.416764 0.909015i \(-0.363164\pi\)
0.993312 0.115465i \(-0.0368358\pi\)
\(108\) 0 0
\(109\) −16.3653 −1.56751 −0.783756 0.621068i \(-0.786699\pi\)
−0.783756 + 0.621068i \(0.786699\pi\)
\(110\) −1.33176 0.855553i −0.126978 0.0815738i
\(111\) 0 0
\(112\) 2.22814 6.85750i 0.210539 0.647973i
\(113\) −1.66154 + 1.20718i −0.156304 + 0.113562i −0.663188 0.748453i \(-0.730797\pi\)
0.506884 + 0.862014i \(0.330797\pi\)
\(114\) 0 0
\(115\) −0.856664 2.63654i −0.0798843 0.245859i
\(116\) −1.65029 5.07906i −0.153225 0.471579i
\(117\) 0 0
\(118\) −4.53576 + 3.29542i −0.417551 + 0.303368i
\(119\) 3.83883 11.8147i 0.351905 1.08305i
\(120\) 0 0
\(121\) 4.57291 + 10.0044i 0.415720 + 0.909493i
\(122\) 1.90075 0.172086
\(123\) 0 0
\(124\) 3.42138 2.48578i 0.307249 0.223229i
\(125\) −0.809017 0.587785i −0.0723607 0.0525731i
\(126\) 0 0
\(127\) −0.0235677 0.0725340i −0.00209130 0.00643635i 0.950005 0.312233i \(-0.101077\pi\)
−0.952097 + 0.305797i \(0.901077\pi\)
\(128\) −9.07350 6.59228i −0.801992 0.582681i
\(129\) 0 0
\(130\) 0.688421 2.11874i 0.0603785 0.185826i
\(131\) 11.4831 1.00328 0.501642 0.865075i \(-0.332730\pi\)
0.501642 + 0.865075i \(0.332730\pi\)
\(132\) 0 0
\(133\) −11.6550 −1.01062
\(134\) −1.07954 + 3.32248i −0.0932580 + 0.287019i
\(135\) 0 0
\(136\) −6.73823 4.89561i −0.577799 0.419795i
\(137\) 5.66406 + 17.4322i 0.483914 + 1.48933i 0.833548 + 0.552447i \(0.186306\pi\)
−0.349635 + 0.936886i \(0.613694\pi\)
\(138\) 0 0
\(139\) 18.7590 + 13.6292i 1.59111 + 1.15601i 0.902330 + 0.431046i \(0.141855\pi\)
0.688785 + 0.724966i \(0.258145\pi\)
\(140\) 3.84996 2.79716i 0.325381 0.236403i
\(141\) 0 0
\(142\) 0.570666 0.0478892
\(143\) −11.9832 + 9.80199i −1.00209 + 0.819683i
\(144\) 0 0
\(145\) 0.931196 2.86593i 0.0773317 0.238002i
\(146\) 0.394492 0.286615i 0.0326484 0.0237205i
\(147\) 0 0
\(148\) 5.82856 + 17.9385i 0.479104 + 1.47453i
\(149\) −4.53161 13.9469i −0.371244 1.14257i −0.945978 0.324232i \(-0.894894\pi\)
0.574733 0.818341i \(-0.305106\pi\)
\(150\) 0 0
\(151\) 6.08301 4.41957i 0.495028 0.359659i −0.312086 0.950054i \(-0.601028\pi\)
0.807115 + 0.590394i \(0.201028\pi\)
\(152\) −2.41473 + 7.43178i −0.195861 + 0.602797i
\(153\) 0 0
\(154\) 4.24344 0.243361i 0.341946 0.0196106i
\(155\) 2.38630 0.191672
\(156\) 0 0
\(157\) 10.8262 7.86568i 0.864023 0.627750i −0.0649531 0.997888i \(-0.520690\pi\)
0.928977 + 0.370139i \(0.120690\pi\)
\(158\) 1.35221 + 0.982441i 0.107576 + 0.0781588i
\(159\) 0 0
\(160\) −1.50869 4.64326i −0.119272 0.367082i
\(161\) 6.02234 + 4.37549i 0.474627 + 0.344837i
\(162\) 0 0
\(163\) −0.238558 + 0.734206i −0.0186853 + 0.0575075i −0.959964 0.280122i \(-0.909625\pi\)
0.941279 + 0.337629i \(0.109625\pi\)
\(164\) −3.91733 −0.305892
\(165\) 0 0
\(166\) 5.30514 0.411759
\(167\) 2.62118 8.06716i 0.202833 0.624256i −0.796962 0.604029i \(-0.793561\pi\)
0.999795 0.0202268i \(-0.00643884\pi\)
\(168\) 0 0
\(169\) −7.11029 5.16593i −0.546946 0.397379i
\(170\) −0.682297 2.09989i −0.0523298 0.161055i
\(171\) 0 0
\(172\) −10.1326 7.36179i −0.772606 0.561331i
\(173\) 4.10876 2.98519i 0.312384 0.226960i −0.420535 0.907276i \(-0.638158\pi\)
0.732919 + 0.680316i \(0.238158\pi\)
\(174\) 0 0
\(175\) 2.68522 0.202984
\(176\) −2.26259 + 8.61366i −0.170549 + 0.649279i
\(177\) 0 0
\(178\) 0.408491 1.25721i 0.0306177 0.0942315i
\(179\) −9.15568 + 6.65199i −0.684328 + 0.497193i −0.874791 0.484501i \(-0.839001\pi\)
0.190463 + 0.981694i \(0.439001\pi\)
\(180\) 0 0
\(181\) 2.28674 + 7.03787i 0.169972 + 0.523121i 0.999368 0.0355402i \(-0.0113152\pi\)
−0.829396 + 0.558661i \(0.811315\pi\)
\(182\) 1.84856 + 5.68929i 0.137025 + 0.421718i
\(183\) 0 0
\(184\) 4.03774 2.93359i 0.297666 0.216267i
\(185\) −3.28884 + 10.1220i −0.241800 + 0.744185i
\(186\) 0 0
\(187\) −3.89819 + 14.8403i −0.285064 + 1.08523i
\(188\) 7.73070 0.563819
\(189\) 0 0
\(190\) −1.67589 + 1.21761i −0.121582 + 0.0883346i
\(191\) −4.17135 3.03067i −0.301829 0.219291i 0.426554 0.904462i \(-0.359728\pi\)
−0.728382 + 0.685171i \(0.759728\pi\)
\(192\) 0 0
\(193\) −1.24605 3.83494i −0.0896925 0.276045i 0.896142 0.443768i \(-0.146359\pi\)
−0.985834 + 0.167723i \(0.946359\pi\)
\(194\) 7.15627 + 5.19933i 0.513790 + 0.373290i
\(195\) 0 0
\(196\) −0.115228 + 0.354635i −0.00823056 + 0.0253311i
\(197\) −11.4176 −0.813469 −0.406734 0.913547i \(-0.633333\pi\)
−0.406734 + 0.913547i \(0.633333\pi\)
\(198\) 0 0
\(199\) −7.16644 −0.508015 −0.254008 0.967202i \(-0.581749\pi\)
−0.254008 + 0.967202i \(0.581749\pi\)
\(200\) 0.556333 1.71222i 0.0393387 0.121072i
\(201\) 0 0
\(202\) 2.74701 + 1.99582i 0.193279 + 0.140425i
\(203\) 2.50047 + 7.69565i 0.175498 + 0.540128i
\(204\) 0 0
\(205\) −1.78826 1.29924i −0.124897 0.0907431i
\(206\) 2.90678 2.11190i 0.202525 0.147143i
\(207\) 0 0
\(208\) −12.5342 −0.869090
\(209\) 14.3720 0.824235i 0.994132 0.0570135i
\(210\) 0 0
\(211\) 1.07649 3.31309i 0.0741086 0.228083i −0.907140 0.420829i \(-0.861739\pi\)
0.981249 + 0.192746i \(0.0617393\pi\)
\(212\) 9.08148 6.59808i 0.623719 0.453158i
\(213\) 0 0
\(214\) 2.65897 + 8.18348i 0.181764 + 0.559411i
\(215\) −2.18388 6.72129i −0.148939 0.458388i
\(216\) 0 0
\(217\) −5.18397 + 3.76638i −0.351911 + 0.255678i
\(218\) 2.41358 7.42824i 0.163468 0.503104i
\(219\) 0 0
\(220\) −4.54963 + 3.72148i −0.306736 + 0.250902i
\(221\) −21.5950 −1.45264
\(222\) 0 0
\(223\) −8.53103 + 6.19816i −0.571280 + 0.415059i −0.835570 0.549384i \(-0.814862\pi\)
0.264290 + 0.964443i \(0.414862\pi\)
\(224\) 10.6061 + 7.70575i 0.708647 + 0.514862i
\(225\) 0 0
\(226\) −0.302893 0.932209i −0.0201481 0.0620096i
\(227\) 0.174762 + 0.126972i 0.0115994 + 0.00842743i 0.593570 0.804782i \(-0.297718\pi\)
−0.581970 + 0.813210i \(0.697718\pi\)
\(228\) 0 0
\(229\) −0.0233956 + 0.0720042i −0.00154602 + 0.00475817i −0.951827 0.306637i \(-0.900796\pi\)
0.950281 + 0.311395i \(0.100796\pi\)
\(230\) 1.32307 0.0872407
\(231\) 0 0
\(232\) 5.42514 0.356178
\(233\) −4.67235 + 14.3800i −0.306096 + 0.942067i 0.673170 + 0.739488i \(0.264932\pi\)
−0.979266 + 0.202579i \(0.935068\pi\)
\(234\) 0 0
\(235\) 3.52905 + 2.56401i 0.230210 + 0.167257i
\(236\) 6.43336 + 19.7999i 0.418776 + 1.28886i
\(237\) 0 0
\(238\) 4.79655 + 3.48489i 0.310914 + 0.225892i
\(239\) −18.7406 + 13.6158i −1.21223 + 0.880734i −0.995431 0.0954825i \(-0.969561\pi\)
−0.216796 + 0.976217i \(0.569561\pi\)
\(240\) 0 0
\(241\) −21.3349 −1.37430 −0.687151 0.726515i \(-0.741139\pi\)
−0.687151 + 0.726515i \(0.741139\pi\)
\(242\) −5.21544 + 0.600185i −0.335261 + 0.0385814i
\(243\) 0 0
\(244\) 2.18107 6.71266i 0.139629 0.429734i
\(245\) −0.170221 + 0.123673i −0.0108750 + 0.00790119i
\(246\) 0 0
\(247\) 6.26085 + 19.2689i 0.398368 + 1.22605i
\(248\) 1.32758 + 4.08586i 0.0843012 + 0.259453i
\(249\) 0 0
\(250\) 0.386111 0.280526i 0.0244198 0.0177420i
\(251\) 1.92266 5.91734i 0.121357 0.373499i −0.871863 0.489751i \(-0.837088\pi\)
0.993220 + 0.116251i \(0.0370878\pi\)
\(252\) 0 0
\(253\) −7.73567 4.96959i −0.486338 0.312435i
\(254\) 0.0363991 0.00228388
\(255\) 0 0
\(256\) −0.588982 + 0.427920i −0.0368113 + 0.0267450i
\(257\) −11.5611 8.39964i −0.721163 0.523955i 0.165593 0.986194i \(-0.447046\pi\)
−0.886755 + 0.462239i \(0.847046\pi\)
\(258\) 0 0
\(259\) −8.83126 27.1798i −0.548748 1.68887i
\(260\) −6.69257 4.86243i −0.415055 0.301555i
\(261\) 0 0
\(262\) −1.69355 + 5.21220i −0.104628 + 0.322011i
\(263\) −4.13132 −0.254748 −0.127374 0.991855i \(-0.540655\pi\)
−0.127374 + 0.991855i \(0.540655\pi\)
\(264\) 0 0
\(265\) 6.33404 0.389097
\(266\) 1.71890 5.29024i 0.105393 0.324365i
\(267\) 0 0
\(268\) 10.4949 + 7.62497i 0.641077 + 0.465769i
\(269\) 0.520367 + 1.60152i 0.0317273 + 0.0976466i 0.965666 0.259786i \(-0.0836521\pi\)
−0.933939 + 0.357433i \(0.883652\pi\)
\(270\) 0 0
\(271\) 14.9110 + 10.8335i 0.905778 + 0.658086i 0.939943 0.341330i \(-0.110877\pi\)
−0.0341657 + 0.999416i \(0.510877\pi\)
\(272\) −10.0502 + 7.30188i −0.609381 + 0.442741i
\(273\) 0 0
\(274\) −8.74784 −0.528476
\(275\) −3.31118 + 0.189896i −0.199672 + 0.0114512i
\(276\) 0 0
\(277\) −1.05914 + 3.25969i −0.0636375 + 0.195856i −0.977820 0.209446i \(-0.932834\pi\)
0.914183 + 0.405303i \(0.132834\pi\)
\(278\) −8.95290 + 6.50466i −0.536959 + 0.390124i
\(279\) 0 0
\(280\) 1.49388 + 4.59768i 0.0892762 + 0.274764i
\(281\) 7.05230 + 21.7048i 0.420705 + 1.29480i 0.907047 + 0.421029i \(0.138331\pi\)
−0.486342 + 0.873769i \(0.661669\pi\)
\(282\) 0 0
\(283\) 23.5416 17.1040i 1.39941 1.01673i 0.404647 0.914473i \(-0.367394\pi\)
0.994758 0.102255i \(-0.0326057\pi\)
\(284\) 0.654828 2.01535i 0.0388569 0.119589i
\(285\) 0 0
\(286\) −2.68183 6.88482i −0.158580 0.407108i
\(287\) 5.93542 0.350357
\(288\) 0 0
\(289\) −3.56201 + 2.58795i −0.209530 + 0.152232i
\(290\) 1.16351 + 0.845342i 0.0683239 + 0.0496402i
\(291\) 0 0
\(292\) −0.559534 1.72207i −0.0327443 0.100776i
\(293\) 17.1621 + 12.4690i 1.00262 + 0.728448i 0.962649 0.270753i \(-0.0872725\pi\)
0.0399740 + 0.999201i \(0.487273\pi\)
\(294\) 0 0
\(295\) −3.63011 + 11.1723i −0.211353 + 0.650478i
\(296\) −19.1608 −1.11370
\(297\) 0 0
\(298\) 6.99883 0.405432
\(299\) 3.99878 12.3070i 0.231255 0.711731i
\(300\) 0 0
\(301\) 15.3527 + 11.1544i 0.884913 + 0.642927i
\(302\) 1.10892 + 3.41289i 0.0638109 + 0.196390i
\(303\) 0 0
\(304\) 9.42913 + 6.85066i 0.540798 + 0.392912i
\(305\) 3.22201 2.34093i 0.184492 0.134041i
\(306\) 0 0
\(307\) −6.87520 −0.392388 −0.196194 0.980565i \(-0.562858\pi\)
−0.196194 + 0.980565i \(0.562858\pi\)
\(308\) 4.00982 15.2653i 0.228481 0.869823i
\(309\) 0 0
\(310\) −0.351935 + 1.08314i −0.0199886 + 0.0615185i
\(311\) 20.3530 14.7873i 1.15411 0.838511i 0.165089 0.986279i \(-0.447209\pi\)
0.989022 + 0.147768i \(0.0472087\pi\)
\(312\) 0 0
\(313\) −3.57821 11.0126i −0.202252 0.622469i −0.999815 0.0192328i \(-0.993878\pi\)
0.797563 0.603236i \(-0.206122\pi\)
\(314\) 1.97358 + 6.07406i 0.111376 + 0.342779i
\(315\) 0 0
\(316\) 5.02121 3.64812i 0.282465 0.205223i
\(317\) −6.40940 + 19.7261i −0.359988 + 1.10793i 0.593073 + 0.805149i \(0.297915\pi\)
−0.953061 + 0.302780i \(0.902085\pi\)
\(318\) 0 0
\(319\) −3.62759 9.31278i −0.203106 0.521416i
\(320\) −3.04036 −0.169961
\(321\) 0 0
\(322\) −2.87422 + 2.08825i −0.160174 + 0.116373i
\(323\) 16.2453 + 11.8029i 0.903913 + 0.656731i
\(324\) 0 0
\(325\) −1.44244 4.43939i −0.0800124 0.246253i
\(326\) −0.298074 0.216564i −0.0165088 0.0119943i
\(327\) 0 0
\(328\) 1.22972 3.78469i 0.0679000 0.208975i
\(329\) −11.7133 −0.645777
\(330\) 0 0
\(331\) −32.1415 −1.76665 −0.883327 0.468757i \(-0.844702\pi\)
−0.883327 + 0.468757i \(0.844702\pi\)
\(332\) 6.08755 18.7356i 0.334098 1.02825i
\(333\) 0 0
\(334\) 3.27512 + 2.37951i 0.179207 + 0.130201i
\(335\) 2.26195 + 6.96158i 0.123584 + 0.380352i
\(336\) 0 0
\(337\) 14.5594 + 10.5780i 0.793100 + 0.576221i 0.908882 0.417054i \(-0.136937\pi\)
−0.115782 + 0.993275i \(0.536937\pi\)
\(338\) 3.39346 2.46549i 0.184580 0.134105i
\(339\) 0 0
\(340\) −8.19888 −0.444647
\(341\) 6.12608 5.01098i 0.331746 0.271360i
\(342\) 0 0
\(343\) −5.63386 + 17.3392i −0.304200 + 0.936231i
\(344\) 10.2933 7.47855i 0.554980 0.403217i
\(345\) 0 0
\(346\) 0.749016 + 2.30523i 0.0402673 + 0.123930i
\(347\) 2.48753 + 7.65583i 0.133538 + 0.410986i 0.995360 0.0962243i \(-0.0306766\pi\)
−0.861822 + 0.507211i \(0.830677\pi\)
\(348\) 0 0
\(349\) −15.5569 + 11.3027i −0.832741 + 0.605022i −0.920333 0.391135i \(-0.872083\pi\)
0.0875926 + 0.996156i \(0.472083\pi\)
\(350\) −0.396020 + 1.21882i −0.0211682 + 0.0651489i
\(351\) 0 0
\(352\) −13.6234 8.75202i −0.726131 0.466484i
\(353\) −14.8497 −0.790371 −0.395186 0.918601i \(-0.629320\pi\)
−0.395186 + 0.918601i \(0.629320\pi\)
\(354\) 0 0
\(355\) 0.967351 0.702822i 0.0513417 0.0373019i
\(356\) −3.97119 2.88524i −0.210473 0.152917i
\(357\) 0 0
\(358\) −1.66905 5.13682i −0.0882123 0.271489i
\(359\) 8.27079 + 6.00908i 0.436516 + 0.317147i 0.784249 0.620446i \(-0.213048\pi\)
−0.347733 + 0.937594i \(0.613048\pi\)
\(360\) 0 0
\(361\) −0.0496143 + 0.152697i −0.00261128 + 0.00803670i
\(362\) −3.53175 −0.185625
\(363\) 0 0
\(364\) 22.2134 1.16430
\(365\) 0.315724 0.971700i 0.0165258 0.0508611i
\(366\) 0 0
\(367\) −11.4422 8.31327i −0.597280 0.433949i 0.247632 0.968854i \(-0.420347\pi\)
−0.844912 + 0.534905i \(0.820347\pi\)
\(368\) −2.30033 7.07969i −0.119913 0.369054i
\(369\) 0 0
\(370\) −4.10935 2.98562i −0.213635 0.155215i
\(371\) −13.7600 + 9.99722i −0.714383 + 0.519030i
\(372\) 0 0
\(373\) 12.4600 0.645154 0.322577 0.946543i \(-0.395451\pi\)
0.322577 + 0.946543i \(0.395451\pi\)
\(374\) −6.16114 3.95807i −0.318585 0.204667i
\(375\) 0 0
\(376\) −2.42681 + 7.46894i −0.125153 + 0.385181i
\(377\) 11.3798 8.26788i 0.586088 0.425818i
\(378\) 0 0
\(379\) 5.04840 + 15.5374i 0.259319 + 0.798102i 0.992948 + 0.118552i \(0.0378251\pi\)
−0.733629 + 0.679550i \(0.762175\pi\)
\(380\) 2.37703 + 7.31575i 0.121939 + 0.375290i
\(381\) 0 0
\(382\) 1.99082 1.44642i 0.101859 0.0740051i
\(383\) 0.251122 0.772874i 0.0128317 0.0394920i −0.944436 0.328696i \(-0.893391\pi\)
0.957267 + 0.289204i \(0.0933907\pi\)
\(384\) 0 0
\(385\) 6.89346 5.63868i 0.351323 0.287374i
\(386\) 1.92445 0.0979522
\(387\) 0 0
\(388\) 26.5736 19.3068i 1.34907 0.980155i
\(389\) −24.5894 17.8652i −1.24673 0.905802i −0.248702 0.968580i \(-0.580004\pi\)
−0.998028 + 0.0627780i \(0.980004\pi\)
\(390\) 0 0
\(391\) −3.96321 12.1975i −0.200428 0.616854i
\(392\) −0.306455 0.222653i −0.0154783 0.0112457i
\(393\) 0 0
\(394\) 1.68388 5.18245i 0.0848327 0.261088i
\(395\) 3.50213 0.176211
\(396\) 0 0
\(397\) −14.8996 −0.747789 −0.373894 0.927471i \(-0.621978\pi\)
−0.373894 + 0.927471i \(0.621978\pi\)
\(398\) 1.05692 3.25285i 0.0529784 0.163051i
\(399\) 0 0
\(400\) −2.17239 1.57833i −0.108619 0.0789166i
\(401\) −3.76049 11.5736i −0.187790 0.577957i 0.812196 0.583385i \(-0.198272\pi\)
−0.999985 + 0.00542792i \(0.998272\pi\)
\(402\) 0 0
\(403\) 9.01155 + 6.54727i 0.448897 + 0.326143i
\(404\) 10.2006 7.41114i 0.507496 0.368718i
\(405\) 0 0
\(406\) −3.86184 −0.191660
\(407\) 12.8121 + 32.8913i 0.635071 + 1.63036i
\(408\) 0 0
\(409\) −0.0809957 + 0.249279i −0.00400498 + 0.0123261i −0.953039 0.302847i \(-0.902063\pi\)
0.949034 + 0.315174i \(0.102063\pi\)
\(410\) 0.853463 0.620077i 0.0421495 0.0306234i
\(411\) 0 0
\(412\) −4.12288 12.6889i −0.203120 0.625138i
\(413\) −9.74764 30.0002i −0.479650 1.47621i
\(414\) 0 0
\(415\) 8.99290 6.53372i 0.441444 0.320728i
\(416\) 7.04232 21.6740i 0.345278 1.06266i
\(417\) 0 0
\(418\) −1.74548 + 6.64503i −0.0853744 + 0.325019i
\(419\) 1.26916 0.0620023 0.0310012 0.999519i \(-0.490130\pi\)
0.0310012 + 0.999519i \(0.490130\pi\)
\(420\) 0 0
\(421\) 23.9999 17.4369i 1.16968 0.849824i 0.178712 0.983902i \(-0.442807\pi\)
0.990971 + 0.134078i \(0.0428071\pi\)
\(422\) 1.34506 + 0.977240i 0.0654763 + 0.0475713i
\(423\) 0 0
\(424\) 3.52384 + 10.8452i 0.171133 + 0.526692i
\(425\) −3.74278 2.71929i −0.181551 0.131905i
\(426\) 0 0
\(427\) −3.30470 + 10.1708i −0.159926 + 0.492200i
\(428\) 31.9518 1.54445
\(429\) 0 0
\(430\) 3.37289 0.162655
\(431\) −9.68919 + 29.8203i −0.466712 + 1.43639i 0.390105 + 0.920771i \(0.372439\pi\)
−0.856817 + 0.515621i \(0.827561\pi\)
\(432\) 0 0
\(433\) 21.0607 + 15.3015i 1.01212 + 0.735345i 0.964652 0.263528i \(-0.0848863\pi\)
0.0474634 + 0.998873i \(0.484886\pi\)
\(434\) −0.945023 2.90848i −0.0453625 0.139612i
\(435\) 0 0
\(436\) −23.4639 17.0475i −1.12372 0.816429i
\(437\) −9.73464 + 7.07263i −0.465671 + 0.338330i
\(438\) 0 0
\(439\) 14.4191 0.688185 0.344093 0.938936i \(-0.388187\pi\)
0.344093 + 0.938936i \(0.388187\pi\)
\(440\) −2.16726 5.56382i −0.103320 0.265245i
\(441\) 0 0
\(442\) 3.18486 9.80199i 0.151488 0.466233i
\(443\) −0.267467 + 0.194326i −0.0127078 + 0.00923273i −0.594121 0.804376i \(-0.702500\pi\)
0.581413 + 0.813608i \(0.302500\pi\)
\(444\) 0 0
\(445\) −0.855908 2.63421i −0.0405739 0.124874i
\(446\) −1.55518 4.78636i −0.0736400 0.226641i
\(447\) 0 0
\(448\) 6.60483 4.79869i 0.312049 0.226717i
\(449\) −2.62920 + 8.09185i −0.124080 + 0.381878i −0.993732 0.111786i \(-0.964343\pi\)
0.869653 + 0.493664i \(0.164343\pi\)
\(450\) 0 0
\(451\) −7.31906 + 0.419748i −0.344641 + 0.0197652i
\(452\) −3.63974 −0.171199
\(453\) 0 0
\(454\) −0.0834069 + 0.0605986i −0.00391448 + 0.00284404i
\(455\) 10.1404 + 7.36742i 0.475388 + 0.345390i
\(456\) 0 0
\(457\) 0.351807 + 1.08275i 0.0164569 + 0.0506490i 0.958948 0.283583i \(-0.0915231\pi\)
−0.942491 + 0.334232i \(0.891523\pi\)
\(458\) −0.0292324 0.0212386i −0.00136594 0.000992413i
\(459\) 0 0
\(460\) 1.51820 4.67254i 0.0707864 0.217858i
\(461\) −14.5073 −0.675670 −0.337835 0.941205i \(-0.609695\pi\)
−0.337835 + 0.941205i \(0.609695\pi\)
\(462\) 0 0
\(463\) −4.89739 −0.227601 −0.113801 0.993504i \(-0.536302\pi\)
−0.113801 + 0.993504i \(0.536302\pi\)
\(464\) 2.50047 7.69565i 0.116081 0.357261i
\(465\) 0 0
\(466\) −5.83803 4.24157i −0.270441 0.196487i
\(467\) −10.0193 30.8361i −0.463637 1.42693i −0.860689 0.509131i \(-0.829967\pi\)
0.397053 0.917796i \(-0.370033\pi\)
\(468\) 0 0
\(469\) −15.9015 11.5531i −0.734264 0.533474i
\(470\) −1.68428 + 1.22370i −0.0776898 + 0.0564450i
\(471\) 0 0
\(472\) −21.1490 −0.973461
\(473\) −19.7204 12.6689i −0.906747 0.582516i
\(474\) 0 0
\(475\) −1.34127 + 4.12801i −0.0615417 + 0.189406i
\(476\) 17.8111 12.9406i 0.816373 0.593129i
\(477\) 0 0
\(478\) −3.41635 10.5145i −0.156260 0.480920i
\(479\) −5.48054 16.8674i −0.250412 0.770690i −0.994699 0.102830i \(-0.967210\pi\)
0.744287 0.667860i \(-0.232790\pi\)
\(480\) 0 0
\(481\) −40.1915 + 29.2009i −1.83258 + 1.33144i
\(482\) 3.14650 9.68394i 0.143319 0.441091i
\(483\) 0 0
\(484\) −3.86502 + 19.1075i −0.175683 + 0.868521i
\(485\) 18.5342 0.841595
\(486\) 0 0
\(487\) 14.9347 10.8507i 0.676754 0.491691i −0.195525 0.980699i \(-0.562641\pi\)
0.872279 + 0.489008i \(0.162641\pi\)
\(488\) 5.80069 + 4.21445i 0.262585 + 0.190779i
\(489\) 0 0
\(490\) −0.0310309 0.0955032i −0.00140183 0.00431440i
\(491\) −9.25018 6.72065i −0.417455 0.303299i 0.359158 0.933277i \(-0.383064\pi\)
−0.776613 + 0.629978i \(0.783064\pi\)
\(492\) 0 0
\(493\) 4.30802 13.2587i 0.194023 0.597142i
\(494\) −9.66954 −0.435053
\(495\) 0 0
\(496\) 6.40774 0.287716
\(497\) −0.992176 + 3.05360i −0.0445052 + 0.136973i
\(498\) 0 0
\(499\) −8.80335 6.39601i −0.394092 0.286325i 0.373038 0.927816i \(-0.378316\pi\)
−0.767130 + 0.641491i \(0.778316\pi\)
\(500\) −0.547647 1.68548i −0.0244915 0.0753771i
\(501\) 0 0
\(502\) 2.40233 + 1.74540i 0.107221 + 0.0779009i
\(503\) 36.1830 26.2885i 1.61332 1.17215i 0.761831 0.647776i \(-0.224301\pi\)
0.851490 0.524371i \(-0.175699\pi\)
\(504\) 0 0
\(505\) 7.11455 0.316594
\(506\) 3.39657 2.77831i 0.150996 0.123511i
\(507\) 0 0
\(508\) 0.0417673 0.128546i 0.00185312 0.00570332i
\(509\) −11.1720 + 8.11693i −0.495190 + 0.359777i −0.807177 0.590310i \(-0.799006\pi\)
0.311987 + 0.950086i \(0.399006\pi\)
\(510\) 0 0
\(511\) 0.847790 + 2.60923i 0.0375040 + 0.115425i
\(512\) −7.03891 21.6635i −0.311079 0.957402i
\(513\) 0 0
\(514\) 5.51766 4.00881i 0.243374 0.176821i
\(515\) 2.32639 7.15989i 0.102513 0.315502i
\(516\) 0 0
\(517\) 14.4439 0.828356i 0.635241 0.0364311i
\(518\) 13.6394 0.599281
\(519\) 0 0
\(520\) 6.79871 4.93955i 0.298143 0.216614i
\(521\) −2.95269 2.14525i −0.129360 0.0939852i 0.521224 0.853420i \(-0.325476\pi\)
−0.650584 + 0.759435i \(0.725476\pi\)
\(522\) 0 0
\(523\) −1.54109 4.74299i −0.0673872 0.207396i 0.911693 0.410873i \(-0.134776\pi\)
−0.979080 + 0.203476i \(0.934776\pi\)
\(524\) 16.4640 + 11.9618i 0.719233 + 0.522553i
\(525\) 0 0
\(526\) 0.609292 1.87521i 0.0265664 0.0817630i
\(527\) 11.0398 0.480901
\(528\) 0 0
\(529\) −15.3148 −0.665860
\(530\) −0.934153 + 2.87503i −0.0405770 + 0.124883i
\(531\) 0 0
\(532\) −16.7105 12.1409i −0.724493 0.526375i
\(533\) −3.18839 9.81284i −0.138104 0.425041i
\(534\) 0 0
\(535\) 14.5859 + 10.5973i 0.630605 + 0.458161i
\(536\) −10.6613 + 7.74591i −0.460499 + 0.334572i
\(537\) 0 0
\(538\) −0.803678 −0.0346490
\(539\) −0.177290 + 0.674939i −0.00763640 + 0.0290717i
\(540\) 0 0
\(541\) 0.0765109 0.235476i 0.00328946 0.0101239i −0.949398 0.314075i \(-0.898306\pi\)
0.952688 + 0.303951i \(0.0983058\pi\)
\(542\) −7.11642 + 5.17038i −0.305676 + 0.222087i
\(543\) 0 0
\(544\) −6.97967 21.4812i −0.299251 0.921000i
\(545\) −5.05716 15.5643i −0.216625 0.666703i
\(546\) 0 0
\(547\) 20.4779 14.8780i 0.875570 0.636139i −0.0565056 0.998402i \(-0.517996\pi\)
0.932076 + 0.362263i \(0.117996\pi\)
\(548\) −10.0380 + 30.8937i −0.428801 + 1.31971i
\(549\) 0 0
\(550\) 0.402144 1.53096i 0.0171475 0.0652802i
\(551\) −13.0796 −0.557208
\(552\) 0 0
\(553\) −7.60799 + 5.52753i −0.323525 + 0.235054i
\(554\) −1.32338 0.961489i −0.0562249 0.0408498i
\(555\) 0 0
\(556\) 12.6985 + 39.0819i 0.538536 + 1.65744i
\(557\) −31.2824 22.7280i −1.32548 0.963015i −0.999847 0.0175177i \(-0.994424\pi\)
−0.325630 0.945497i \(-0.605576\pi\)
\(558\) 0 0
\(559\) 10.1940 31.3740i 0.431161 1.32698i
\(560\) 7.21041 0.304695
\(561\) 0 0
\(562\) −10.8919 −0.459447
\(563\) −4.30653 + 13.2541i −0.181498 + 0.558595i −0.999870 0.0160940i \(-0.994877\pi\)
0.818372 + 0.574689i \(0.194877\pi\)
\(564\) 0 0
\(565\) −1.66154 1.20718i −0.0699013 0.0507863i
\(566\) 4.29157 + 13.2081i 0.180388 + 0.555178i
\(567\) 0 0
\(568\) 1.74155 + 1.26531i 0.0730739 + 0.0530913i
\(569\) 22.5817 16.4065i 0.946672 0.687798i −0.00334520 0.999994i \(-0.501065\pi\)
0.950017 + 0.312197i \(0.101065\pi\)
\(570\) 0 0
\(571\) −31.4113 −1.31452 −0.657261 0.753663i \(-0.728285\pi\)
−0.657261 + 0.753663i \(0.728285\pi\)
\(572\) −27.3917 + 1.57091i −1.14530 + 0.0656831i
\(573\) 0 0
\(574\) −0.875365 + 2.69410i −0.0365370 + 0.112449i
\(575\) 2.24278 1.62947i 0.0935302 0.0679537i
\(576\) 0 0
\(577\) 6.40744 + 19.7201i 0.266745 + 0.820958i 0.991286 + 0.131726i \(0.0420519\pi\)
−0.724541 + 0.689232i \(0.757948\pi\)
\(578\) −0.649343 1.99847i −0.0270091 0.0831255i
\(579\) 0 0
\(580\) 4.32051 3.13903i 0.179399 0.130341i
\(581\) −9.22368 + 28.3876i −0.382663 + 1.17771i
\(582\) 0 0
\(583\) 16.2607 13.3008i 0.673448 0.550864i
\(584\) 1.83941 0.0761153
\(585\) 0 0
\(586\) −8.19080 + 5.95097i −0.338359 + 0.245832i
\(587\) 12.3267 + 8.95591i 0.508779 + 0.369650i 0.812360 0.583156i \(-0.198182\pi\)
−0.303581 + 0.952806i \(0.598182\pi\)
\(588\) 0 0
\(589\) −3.20067 9.85066i −0.131881 0.405889i
\(590\) −4.53576 3.29542i −0.186734 0.135670i
\(591\) 0 0
\(592\) −8.83126 + 27.1798i −0.362962 + 1.11708i
\(593\) −27.5413 −1.13098 −0.565492 0.824754i \(-0.691314\pi\)
−0.565492 + 0.824754i \(0.691314\pi\)
\(594\) 0 0
\(595\) 12.4227 0.509281
\(596\) 8.03103 24.7170i 0.328964 1.01245i
\(597\) 0 0
\(598\) 4.99640 + 3.63010i 0.204318 + 0.148446i
\(599\) 8.26097 + 25.4247i 0.337534 + 1.03882i 0.965460 + 0.260551i \(0.0839041\pi\)
−0.627926 + 0.778273i \(0.716096\pi\)
\(600\) 0 0
\(601\) −1.94714 1.41468i −0.0794255 0.0577060i 0.547364 0.836895i \(-0.315631\pi\)
−0.626789 + 0.779189i \(0.715631\pi\)
\(602\) −7.32722 + 5.32353i −0.298635 + 0.216971i
\(603\) 0 0
\(604\) 13.3254 0.542202
\(605\) −8.10166 + 7.44064i −0.329379 + 0.302505i
\(606\) 0 0
\(607\) 3.18067 9.78909i 0.129099 0.397327i −0.865526 0.500864i \(-0.833016\pi\)
0.994626 + 0.103536i \(0.0330159\pi\)
\(608\) −17.1438 + 12.4557i −0.695275 + 0.505147i
\(609\) 0 0
\(610\) 0.587364 + 1.80772i 0.0237817 + 0.0731924i
\(611\) 6.29216 + 19.3653i 0.254553 + 0.783435i
\(612\) 0 0
\(613\) −22.5519 + 16.3849i −0.910861 + 0.661779i −0.941232 0.337759i \(-0.890331\pi\)
0.0303715 + 0.999539i \(0.490331\pi\)
\(614\) 1.01396 3.12066i 0.0409203 0.125940i
\(615\) 0 0
\(616\) 13.4897 + 8.66611i 0.543515 + 0.349168i
\(617\) 28.7216 1.15629 0.578143 0.815935i \(-0.303778\pi\)
0.578143 + 0.815935i \(0.303778\pi\)
\(618\) 0 0
\(619\) −18.3621 + 13.3408i −0.738035 + 0.536214i −0.892095 0.451848i \(-0.850765\pi\)
0.154060 + 0.988061i \(0.450765\pi\)
\(620\) 3.42138 + 2.48578i 0.137406 + 0.0998312i
\(621\) 0 0
\(622\) 3.71029 + 11.4191i 0.148769 + 0.457864i
\(623\) 6.01703 + 4.37163i 0.241067 + 0.175146i
\(624\) 0 0
\(625\) 0.309017 0.951057i 0.0123607 0.0380423i
\(626\) 5.52635 0.220877
\(627\) 0 0
\(628\) 23.7157 0.946360
\(629\) −15.2152 + 46.8277i −0.606671 + 1.86714i
\(630\) 0 0
\(631\) −23.0864 16.7733i −0.919056 0.667733i 0.0242327 0.999706i \(-0.492286\pi\)
−0.943289 + 0.331973i \(0.892286\pi\)
\(632\) 1.94835 + 5.99641i 0.0775013 + 0.238524i
\(633\) 0 0
\(634\) −8.00844 5.81847i −0.318056 0.231081i
\(635\) 0.0617011 0.0448285i 0.00244853 0.00177896i
\(636\) 0 0
\(637\) −0.982140 −0.0389138
\(638\) 4.76209 0.273106i 0.188533 0.0108124i
\(639\) 0 0
\(640\) 3.46577 10.6665i 0.136997 0.421632i
\(641\) 1.92040 1.39526i 0.0758514 0.0551093i −0.549213 0.835682i \(-0.685073\pi\)
0.625065 + 0.780573i \(0.285073\pi\)
\(642\) 0 0
\(643\) 3.51053 + 10.8043i 0.138442 + 0.426080i 0.996109 0.0881244i \(-0.0280873\pi\)
−0.857668 + 0.514204i \(0.828087\pi\)
\(644\) 4.07670 + 12.5468i 0.160644 + 0.494413i
\(645\) 0 0
\(646\) −7.75323 + 5.63305i −0.305047 + 0.221630i
\(647\) 14.9632 46.0520i 0.588264 1.81049i 0.00251822 0.999997i \(-0.499198\pi\)
0.585746 0.810495i \(-0.300802\pi\)
\(648\) 0 0
\(649\) 14.1415 + 36.3043i 0.555104 + 1.42507i
\(650\) 2.22778 0.0873806
\(651\) 0 0
\(652\) −1.10685 + 0.804171i −0.0433475 + 0.0314938i
\(653\) 24.0722 + 17.4894i 0.942016 + 0.684415i 0.948905 0.315562i \(-0.102193\pi\)
−0.00688905 + 0.999976i \(0.502193\pi\)
\(654\) 0 0
\(655\) 3.54847 + 10.9211i 0.138650 + 0.426722i
\(656\) −4.80186 3.48875i −0.187481 0.136213i
\(657\) 0 0
\(658\) 1.72750 5.31669i 0.0673449 0.207266i
\(659\) 28.4931 1.10993 0.554966 0.831873i \(-0.312731\pi\)
0.554966 + 0.831873i \(0.312731\pi\)
\(660\) 0 0
\(661\) −1.02875 −0.0400139 −0.0200070 0.999800i \(-0.506369\pi\)
−0.0200070 + 0.999800i \(0.506369\pi\)
\(662\) 4.74027 14.5890i 0.184236 0.567019i
\(663\) 0 0
\(664\) 16.1902 + 11.7629i 0.628301 + 0.456488i
\(665\) −3.60161 11.0846i −0.139664 0.429843i
\(666\) 0 0
\(667\) 6.75841 + 4.91027i 0.261687 + 0.190127i
\(668\) 12.1616 8.83591i 0.470546 0.341872i
\(669\) 0 0
\(670\) −3.49346 −0.134964
\(671\) 3.35580 12.7755i 0.129549 0.493192i
\(672\) 0 0
\(673\) 4.02863 12.3988i 0.155292 0.477940i −0.842898 0.538073i \(-0.819152\pi\)
0.998190 + 0.0601327i \(0.0191524\pi\)
\(674\) −6.94861 + 5.04846i −0.267651 + 0.194459i
\(675\) 0 0
\(676\) −4.81316 14.8134i −0.185122 0.569746i
\(677\) 11.4665 + 35.2903i 0.440694 + 1.35632i 0.887138 + 0.461505i \(0.152690\pi\)
−0.446444 + 0.894812i \(0.647310\pi\)
\(678\) 0 0
\(679\) −40.2635 + 29.2531i −1.54517 + 1.12263i
\(680\) 2.57378 7.92127i 0.0986998 0.303767i
\(681\) 0 0
\(682\) 1.37101 + 3.51966i 0.0524986 + 0.134775i
\(683\) 32.8992 1.25885 0.629426 0.777061i \(-0.283290\pi\)
0.629426 + 0.777061i \(0.283290\pi\)
\(684\) 0 0
\(685\) −14.8287 + 10.7737i −0.566576 + 0.411641i
\(686\) −7.03941 5.11443i −0.268766 0.195270i
\(687\) 0 0
\(688\) −5.86420 18.0481i −0.223570 0.688079i
\(689\) 23.9197 + 17.3787i 0.911267 + 0.662074i
\(690\) 0 0
\(691\) 11.3409 34.9036i 0.431427 1.32780i −0.465277 0.885165i \(-0.654045\pi\)
0.896704 0.442631i \(-0.145955\pi\)
\(692\) 9.00061 0.342152
\(693\) 0 0
\(694\) −3.84185 −0.145835
\(695\) −7.16529 + 22.0525i −0.271795 + 0.836498i
\(696\) 0 0
\(697\) −8.27305 6.01072i −0.313364 0.227672i
\(698\) −2.83597 8.72823i −0.107343 0.330368i
\(699\) 0 0
\(700\) 3.84996 + 2.79716i 0.145515 + 0.105723i
\(701\) −29.3266 + 21.3070i −1.10765 + 0.804755i −0.982292 0.187356i \(-0.940008\pi\)
−0.125359 + 0.992111i \(0.540008\pi\)
\(702\) 0 0
\(703\) 46.1949 1.74227
\(704\) −7.80516 + 6.38443i −0.294168 + 0.240622i
\(705\) 0 0
\(706\) 2.19006 6.74031i 0.0824240 0.253675i
\(707\) −15.4556 + 11.2291i −0.581267 + 0.422315i
\(708\) 0 0
\(709\) −5.74811 17.6909i −0.215875 0.664394i −0.999090 0.0426440i \(-0.986422\pi\)
0.783216 0.621750i \(-0.213578\pi\)
\(710\) 0.176345 + 0.542735i 0.00661812 + 0.0203685i
\(711\) 0 0
\(712\) 4.03418 2.93100i 0.151187 0.109844i
\(713\) −2.04426 + 6.29158i −0.0765580 + 0.235621i
\(714\) 0 0
\(715\) −13.0253 8.36775i −0.487117 0.312936i
\(716\) −20.0563 −0.749540
\(717\) 0 0
\(718\) −3.94732 + 2.86790i −0.147313 + 0.107029i
\(719\) −30.2799 21.9996i −1.12925 0.820447i −0.143664 0.989627i \(-0.545888\pi\)
−0.985585 + 0.169179i \(0.945888\pi\)
\(720\) 0 0
\(721\) 6.24687 + 19.2259i 0.232645 + 0.716009i
\(722\) −0.0619923 0.0450400i −0.00230711 0.00167622i
\(723\) 0 0
\(724\) −4.05262 + 12.4727i −0.150614 + 0.463544i
\(725\) 3.01341 0.111915
\(726\) 0 0
\(727\) 14.6011 0.541526 0.270763 0.962646i \(-0.412724\pi\)
0.270763 + 0.962646i \(0.412724\pi\)
\(728\) −6.97319 + 21.4613i −0.258443 + 0.795407i
\(729\) 0 0
\(730\) 0.394492 + 0.286615i 0.0146008 + 0.0106081i
\(731\) −10.1033 31.0949i −0.373686 1.15009i
\(732\) 0 0
\(733\) −33.8468 24.5911i −1.25016 0.908293i −0.251927 0.967746i \(-0.581064\pi\)
−0.998231 + 0.0594528i \(0.981064\pi\)
\(734\) 5.46092 3.96759i 0.201566 0.146447i
\(735\) 0 0
\(736\) 13.5346 0.498891
\(737\) 20.4254 + 13.1218i 0.752381 + 0.483348i
\(738\) 0 0
\(739\) −3.68654 + 11.3460i −0.135612 + 0.417370i −0.995685 0.0928012i \(-0.970418\pi\)
0.860073 + 0.510171i \(0.170418\pi\)
\(740\) −15.2594 + 11.0866i −0.560945 + 0.407550i
\(741\) 0 0
\(742\) −2.50841 7.72008i −0.0920865 0.283413i
\(743\) −14.4250 44.3956i −0.529202 1.62872i −0.755854 0.654740i \(-0.772778\pi\)
0.226652 0.973976i \(-0.427222\pi\)
\(744\) 0 0
\(745\) 11.8639 8.61964i 0.434660 0.315799i
\(746\) −1.83762 + 5.65561i −0.0672800 + 0.207067i
\(747\) 0 0
\(748\) −21.0480 + 17.2168i −0.769593 + 0.629508i
\(749\) −48.4124 −1.76895
\(750\) 0 0
\(751\) −11.6530 + 8.46642i −0.425225 + 0.308944i −0.779737 0.626108i \(-0.784647\pi\)
0.354512 + 0.935052i \(0.384647\pi\)
\(752\) 9.47628 + 6.88492i 0.345564 + 0.251067i
\(753\) 0 0
\(754\) 2.07450 + 6.38465i 0.0755488 + 0.232515i
\(755\) 6.08301 + 4.41957i 0.221383 + 0.160845i
\(756\) 0 0
\(757\) −4.96330 + 15.2755i −0.180394 + 0.555196i −0.999839 0.0179624i \(-0.994282\pi\)
0.819444 + 0.573159i \(0.194282\pi\)
\(758\) −7.79698 −0.283199
\(759\) 0 0
\(760\) −7.81423 −0.283452
\(761\) 12.0158 36.9809i 0.435573 1.34056i −0.456925 0.889505i \(-0.651049\pi\)
0.892498 0.451051i \(-0.148951\pi\)
\(762\) 0 0
\(763\) 35.5518 + 25.8299i 1.28706 + 0.935106i
\(764\) −2.82371 8.69049i −0.102158 0.314411i
\(765\) 0 0
\(766\) 0.313773 + 0.227969i 0.0113371 + 0.00823686i
\(767\) −44.3621 + 32.2309i −1.60182 + 1.16379i
\(768\) 0 0
\(769\) 43.0017 1.55068 0.775341 0.631543i \(-0.217578\pi\)
0.775341 + 0.631543i \(0.217578\pi\)
\(770\) 1.54275 + 3.96055i 0.0555967 + 0.142728i
\(771\) 0 0
\(772\) 2.20828 6.79637i 0.0794776 0.244607i
\(773\) −6.35452 + 4.61683i −0.228556 + 0.166056i −0.696170 0.717877i \(-0.745114\pi\)
0.467613 + 0.883933i \(0.345114\pi\)
\(774\) 0 0
\(775\) 0.737407 + 2.26951i 0.0264885 + 0.0815231i
\(776\) 10.3112 + 31.7346i 0.370150 + 1.13920i
\(777\) 0 0
\(778\) 11.7355 8.52635i 0.420739 0.305684i
\(779\) −2.96475 + 9.12457i −0.106223 + 0.326922i
\(780\) 0 0
\(781\) 1.00752 3.83561i 0.0360519 0.137249i
\(782\) 6.12096 0.218885
\(783\) 0 0
\(784\) −0.457082 + 0.332090i −0.0163244 + 0.0118603i
\(785\) 10.8262 + 7.86568i 0.386403 + 0.280738i
\(786\) 0 0
\(787\) −3.53048 10.8657i −0.125848 0.387321i 0.868206 0.496203i \(-0.165273\pi\)
−0.994055 + 0.108882i \(0.965273\pi\)
\(788\) −16.3700 11.8935i −0.583159 0.423690i
\(789\) 0 0
\(790\) −0.516500 + 1.58962i −0.0183762 + 0.0565562i
\(791\) 5.51483 0.196085
\(792\) 0 0
\(793\) 18.5903 0.660161
\(794\) 2.19741 6.76294i 0.0779832 0.240008i
\(795\) 0 0
\(796\) −10.2749 7.46518i −0.364186 0.264596i
\(797\) 1.32414 + 4.07529i 0.0469035 + 0.144354i 0.971766 0.235949i \(-0.0758197\pi\)
−0.924862 + 0.380303i \(0.875820\pi\)
\(798\) 0 0
\(799\) 16.3265 + 11.8619i 0.577592 + 0.419645i
\(800\) 3.94979 2.86969i 0.139646 0.101459i
\(801\) 0 0
\(802\) 5.80787 0.205083
\(803\) −1.22994 3.15752i −0.0434038 0.111427i
\(804\) 0 0
\(805\) −2.30033 + 7.07969i −0.0810760 + 0.249526i
\(806\) −4.30085 + 3.12475i −0.151491 + 0.110065i
\(807\) 0 0
\(808\) 3.95806 + 12.1817i 0.139244 + 0.428549i
\(809\) 6.13350 + 18.8770i 0.215642 + 0.663679i 0.999107 + 0.0422430i \(0.0134504\pi\)
−0.783465 + 0.621436i \(0.786550\pi\)
\(810\) 0 0
\(811\) 2.53899 1.84468i 0.0891559 0.0647756i −0.542314 0.840176i \(-0.682452\pi\)
0.631470 + 0.775400i \(0.282452\pi\)
\(812\) −4.43138 + 13.6384i −0.155511 + 0.478614i
\(813\) 0 0
\(814\) −16.8189 + 0.964566i −0.589504 + 0.0338080i
\(815\) −0.771990 −0.0270416
\(816\) 0 0
\(817\) −24.8164 + 18.0301i −0.868215 + 0.630795i
\(818\) −0.101203 0.0735281i −0.00353847 0.00257085i
\(819\) 0 0
\(820\) −1.21052 3.72560i −0.0422733 0.130104i
\(821\) 19.0118 + 13.8129i 0.663516 + 0.482073i 0.867849 0.496829i \(-0.165502\pi\)
−0.204332 + 0.978902i \(0.565502\pi\)
\(822\) 0 0
\(823\) −3.91103 + 12.0369i −0.136330 + 0.419580i −0.995795 0.0916150i \(-0.970797\pi\)
0.859465 + 0.511195i \(0.170797\pi\)
\(824\) 13.5535 0.472159
\(825\) 0 0
\(826\) 15.0547 0.523820
\(827\) −9.33959 + 28.7443i −0.324770 + 0.999538i 0.646775 + 0.762681i \(0.276117\pi\)
−0.971545 + 0.236857i \(0.923883\pi\)
\(828\) 0 0
\(829\) −1.61937 1.17654i −0.0562432 0.0408630i 0.559308 0.828960i \(-0.311067\pi\)
−0.615552 + 0.788097i \(0.711067\pi\)
\(830\) 1.63938 + 5.04549i 0.0569037 + 0.175132i
\(831\) 0 0
\(832\) −11.4815 8.34180i −0.398050 0.289200i
\(833\) −0.787500 + 0.572152i −0.0272852 + 0.0198239i
\(834\) 0 0
\(835\) 8.48232 0.293543
\(836\) 21.4646 + 13.7894i 0.742368 + 0.476915i
\(837\) 0 0
\(838\) −0.187177 + 0.576072i −0.00646592 + 0.0199001i
\(839\) 28.6185 20.7925i 0.988019 0.717838i 0.0285326 0.999593i \(-0.490917\pi\)
0.959486 + 0.281755i \(0.0909166\pi\)
\(840\) 0 0
\(841\) −6.15541 18.9444i −0.212256 0.653255i
\(842\) 4.37511 + 13.4652i 0.150776 + 0.464041i
\(843\) 0 0
\(844\) 4.99463 3.62881i 0.171922 0.124909i
\(845\) 2.71589 8.35865i 0.0934295 0.287546i
\(846\) 0 0
\(847\) 5.85616 28.9511i 0.201220 0.994771i
\(848\) 17.0083 0.584067
\(849\) 0 0
\(850\) 1.78628 1.29781i 0.0612688 0.0445144i
\(851\) −23.8696 17.3423i −0.818241 0.594487i
\(852\) 0 0
\(853\) −5.62515 17.3124i −0.192602 0.592767i −0.999996 0.00275489i \(-0.999123\pi\)
0.807395 0.590012i \(-0.200877\pi\)
\(854\) −4.12917 3.00001i −0.141297 0.102658i
\(855\) 0 0
\(856\) −10.0302 + 30.8699i −0.342827 + 1.05511i
\(857\) 29.2837 1.00031 0.500156 0.865935i \(-0.333276\pi\)
0.500156 + 0.865935i \(0.333276\pi\)
\(858\) 0 0
\(859\) 8.44030 0.287979 0.143990 0.989579i \(-0.454007\pi\)
0.143990 + 0.989579i \(0.454007\pi\)
\(860\) 3.87032 11.9116i 0.131977 0.406183i
\(861\) 0 0
\(862\) −12.1065 8.79587i −0.412348 0.299589i
\(863\) 5.97907 + 18.4017i 0.203530 + 0.626400i 0.999771 + 0.0214204i \(0.00681885\pi\)
−0.796241 + 0.604980i \(0.793181\pi\)
\(864\) 0 0
\(865\) 4.10876 + 2.98519i 0.139702 + 0.101500i
\(866\) −10.0515 + 7.30281i −0.341562 + 0.248160i
\(867\) 0 0
\(868\) −11.3559 −0.385446
\(869\) 8.99063 7.35411i 0.304986 0.249471i
\(870\) 0 0
\(871\) −10.5585 + 32.4956i −0.357760 + 1.10107i
\(872\) 23.8361 17.3179i 0.807191 0.586458i
\(873\) 0 0
\(874\) −1.77460 5.46165i −0.0600266 0.184743i
\(875\) 0.829779 + 2.55380i 0.0280516 + 0.0863341i
\(876\) 0 0
\(877\) −14.1691 + 10.2945i −0.478456 + 0.347619i −0.800728 0.599028i \(-0.795554\pi\)
0.322271 + 0.946647i \(0.395554\pi\)
\(878\) −2.12655 + 6.54484i −0.0717675 + 0.220878i
\(879\) 0 0
\(880\) −8.89126 + 0.509914i −0.299724 + 0.0171892i
\(881\) 20.0575 0.675754 0.337877 0.941190i \(-0.390291\pi\)
0.337877 + 0.941190i \(0.390291\pi\)
\(882\) 0 0
\(883\) −21.7609 + 15.8102i −0.732313 + 0.532057i −0.890294 0.455386i \(-0.849501\pi\)
0.157981 + 0.987442i \(0.449501\pi\)
\(884\) −30.9620 22.4952i −1.04136 0.756595i
\(885\) 0 0
\(886\) −0.0487585 0.150063i −0.00163807 0.00504148i
\(887\) 5.50591 + 4.00028i 0.184870 + 0.134316i 0.676371 0.736561i \(-0.263552\pi\)
−0.491501 + 0.870877i \(0.663552\pi\)
\(888\) 0 0
\(889\) −0.0632845 + 0.194770i −0.00212249 + 0.00653237i
\(890\) 1.32190 0.0443103
\(891\) 0 0
\(892\) −18.6880 −0.625720
\(893\) 5.85082 18.0070i 0.195790 0.602581i
\(894\) 0 0
\(895\) −9.15568 6.65199i −0.306041 0.222352i
\(896\) 9.30635 + 28.6420i 0.310903 + 0.956862i
\(897\) 0 0
\(898\) −3.28514 2.38680i −0.109627 0.0796484i
\(899\) −5.81757 + 4.22671i −0.194027 + 0.140969i
\(900\) 0 0
\(901\) 29.3033 0.976235
\(902\) 0.888901 3.38403i 0.0295972 0.112676i
\(903\) 0 0
\(904\) 1.14258 3.51650i 0.0380017 0.116957i
\(905\) −5.98677 + 4.34965i −0.199007 + 0.144587i
\(906\) 0 0
\(907\) −6.59174 20.2873i −0.218875 0.673629i −0.998856 0.0478248i \(-0.984771\pi\)
0.779981 0.625804i \(-0.215229\pi\)
\(908\) 0.118301 + 0.364094i 0.00392597 + 0.0120829i
\(909\) 0 0
\(910\) −4.83960 + 3.51617i −0.160431 + 0.116560i
\(911\) 8.52542 26.2385i 0.282460 0.869322i −0.704689 0.709516i \(-0.748913\pi\)
0.987149 0.159805i \(-0.0510866\pi\)
\(912\) 0 0
\(913\) 9.36631 35.6574i 0.309980 1.18009i
\(914\) −0.543347 −0.0179723
\(915\) 0 0
\(916\) −0.108549 + 0.0788658i −0.00358657 + 0.00260580i
\(917\) −24.9458 18.1242i −0.823782 0.598512i
\(918\) 0 0
\(919\) −1.85685 5.71479i −0.0612518 0.188514i 0.915748 0.401752i \(-0.131599\pi\)
−0.977000 + 0.213239i \(0.931599\pi\)
\(920\) 4.03774 + 2.93359i 0.133120 + 0.0967176i
\(921\) 0 0
\(922\) 2.13955 6.58486i 0.0704624 0.216861i
\(923\) 5.58140 0.183714
\(924\) 0 0
\(925\) −10.6429 −0.349937
\(926\) 0.722274 2.22293i 0.0237354 0.0730501i
\(927\) 0 0
\(928\) 11.9024 + 8.64757i 0.390714 + 0.283870i
\(929\) −2.96576 9.12766i −0.0973034 0.299469i 0.890544 0.454898i \(-0.150324\pi\)
−0.987847 + 0.155429i \(0.950324\pi\)
\(930\) 0 0
\(931\) 0.738836 + 0.536796i 0.0242144 + 0.0175928i
\(932\) −21.6785 + 15.7504i −0.710103 + 0.515920i
\(933\) 0 0
\(934\) 15.4742 0.506332
\(935\) −15.3186 + 0.878523i −0.500972 + 0.0287308i
\(936\) 0 0
\(937\) −11.9255 + 36.7029i −0.389589 + 1.19903i 0.543507 + 0.839405i \(0.317096\pi\)
−0.933096 + 0.359628i \(0.882904\pi\)
\(938\) 7.58916 5.51385i 0.247795 0.180034i
\(939\) 0 0
\(940\) 2.38892 + 7.35233i 0.0779179 + 0.239807i
\(941\) 9.01854 + 27.7562i 0.293996 + 0.904826i 0.983557 + 0.180599i \(0.0578035\pi\)
−0.689561 + 0.724228i \(0.742196\pi\)
\(942\) 0 0
\(943\) 4.95744 3.60179i 0.161437 0.117291i
\(944\) −9.74764 + 30.0002i −0.317259 + 0.976422i
\(945\) 0 0
\(946\) 8.65882 7.08270i 0.281523 0.230279i
\(947\) −46.7623 −1.51957 −0.759785 0.650174i \(-0.774696\pi\)
−0.759785 + 0.650174i \(0.774696\pi\)
\(948\) 0 0
\(949\) 3.85834 2.80325i 0.125247 0.0909972i
\(950\) −1.67589 1.21761i −0.0543732 0.0395044i
\(951\) 0 0
\(952\) 6.91116 + 21.2704i 0.223992 + 0.689376i
\(953\) −4.97738 3.61628i −0.161233 0.117143i 0.504243 0.863562i \(-0.331772\pi\)
−0.665476 + 0.746419i \(0.731772\pi\)
\(954\) 0 0
\(955\) 1.59332 4.90372i 0.0515585 0.158681i
\(956\) −41.0529 −1.32774
\(957\) 0 0
\(958\) 8.46440 0.273472
\(959\) 15.2093 46.8093i 0.491132 1.51155i
\(960\) 0 0
\(961\) 20.4726 + 14.8742i 0.660408 + 0.479814i
\(962\) −7.32680 22.5496i −0.236226 0.727027i
\(963\) 0 0
\(964\) −30.5891 22.2243i −0.985209 0.715796i
\(965\) 3.26220 2.37013i 0.105014 0.0762970i
\(966\) 0 0
\(967\) 3.39625 0.109216 0.0546080 0.998508i \(-0.482609\pi\)
0.0546080 + 0.998508i \(0.482609\pi\)
\(968\) −17.2472 9.73233i −0.554346 0.312809i
\(969\) 0 0
\(970\) −2.73345 + 8.41270i −0.0877658 + 0.270115i
\(971\) −7.60072 + 5.52224i −0.243919 + 0.177217i −0.703027 0.711163i \(-0.748169\pi\)
0.459109 + 0.888380i \(0.348169\pi\)
\(972\) 0 0
\(973\) −19.2404 59.2158i −0.616818 1.89837i
\(974\) 2.72255 + 8.37914i 0.0872360 + 0.268485i
\(975\) 0 0
\(976\) 8.65182 6.28591i 0.276938 0.201207i
\(977\) 5.11585 15.7450i 0.163671 0.503726i −0.835265 0.549847i \(-0.814686\pi\)
0.998936 + 0.0461210i \(0.0146860\pi\)
\(978\) 0 0
\(979\) −7.72885 4.96520i −0.247015 0.158689i
\(980\) −0.372885 −0.0119114
\(981\) 0 0
\(982\) 4.41474 3.20750i 0.140880 0.102355i
\(983\) 41.1126 + 29.8701i 1.31129 + 0.952707i 0.999997 + 0.00239240i \(0.000761525\pi\)
0.311291 + 0.950315i \(0.399238\pi\)
\(984\) 0 0
\(985\) −3.52822 10.8588i −0.112419 0.345989i
\(986\) 5.38279 + 3.91083i 0.171423 + 0.124546i
\(987\) 0 0
\(988\) −11.0956 + 34.1488i −0.352999 + 1.08642i
\(989\) 19.5918 0.622983
\(990\) 0 0
\(991\) 11.3642 0.360996 0.180498 0.983575i \(-0.442229\pi\)
0.180498 + 0.983575i \(0.442229\pi\)
\(992\) −3.60018 + 11.0802i −0.114306 + 0.351797i
\(993\) 0 0
\(994\) −1.23971 0.900700i −0.0393211 0.0285685i
\(995\) −2.21455 6.81569i −0.0702060 0.216072i
\(996\) 0 0
\(997\) 23.5945 + 17.1424i 0.747246 + 0.542906i 0.894972 0.446122i \(-0.147195\pi\)
−0.147726 + 0.989028i \(0.547195\pi\)
\(998\) 4.20149 3.05256i 0.132996 0.0966271i
\(999\) 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 495.2.n.e.361.1 8
3.2 odd 2 55.2.g.b.31.2 yes 8
11.4 even 5 5445.2.a.bp.1.2 4
11.5 even 5 inner 495.2.n.e.181.1 8
11.7 odd 10 5445.2.a.bi.1.3 4
12.11 even 2 880.2.bo.h.801.1 8
15.2 even 4 275.2.z.a.174.3 16
15.8 even 4 275.2.z.a.174.2 16
15.14 odd 2 275.2.h.a.251.1 8
33.2 even 10 605.2.g.e.366.2 8
33.5 odd 10 55.2.g.b.16.2 8
33.8 even 10 605.2.g.e.81.2 8
33.14 odd 10 605.2.g.m.81.1 8
33.17 even 10 605.2.g.k.511.1 8
33.20 odd 10 605.2.g.m.366.1 8
33.26 odd 10 605.2.a.j.1.3 4
33.29 even 10 605.2.a.k.1.2 4
33.32 even 2 605.2.g.k.251.1 8
132.59 even 10 9680.2.a.cn.1.3 4
132.71 even 10 880.2.bo.h.401.1 8
132.95 odd 10 9680.2.a.cm.1.3 4
165.29 even 10 3025.2.a.w.1.3 4
165.38 even 20 275.2.z.a.49.3 16
165.59 odd 10 3025.2.a.bd.1.2 4
165.104 odd 10 275.2.h.a.126.1 8
165.137 even 20 275.2.z.a.49.2 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.2.g.b.16.2 8 33.5 odd 10
55.2.g.b.31.2 yes 8 3.2 odd 2
275.2.h.a.126.1 8 165.104 odd 10
275.2.h.a.251.1 8 15.14 odd 2
275.2.z.a.49.2 16 165.137 even 20
275.2.z.a.49.3 16 165.38 even 20
275.2.z.a.174.2 16 15.8 even 4
275.2.z.a.174.3 16 15.2 even 4
495.2.n.e.181.1 8 11.5 even 5 inner
495.2.n.e.361.1 8 1.1 even 1 trivial
605.2.a.j.1.3 4 33.26 odd 10
605.2.a.k.1.2 4 33.29 even 10
605.2.g.e.81.2 8 33.8 even 10
605.2.g.e.366.2 8 33.2 even 10
605.2.g.k.251.1 8 33.32 even 2
605.2.g.k.511.1 8 33.17 even 10
605.2.g.m.81.1 8 33.14 odd 10
605.2.g.m.366.1 8 33.20 odd 10
880.2.bo.h.401.1 8 132.71 even 10
880.2.bo.h.801.1 8 12.11 even 2
3025.2.a.w.1.3 4 165.29 even 10
3025.2.a.bd.1.2 4 165.59 odd 10
5445.2.a.bi.1.3 4 11.7 odd 10
5445.2.a.bp.1.2 4 11.4 even 5
9680.2.a.cm.1.3 4 132.95 odd 10
9680.2.a.cn.1.3 4 132.59 even 10