Properties

Label 819.2.o.d.757.2
Level $819$
Weight $2$
Character 819.757
Analytic conductor $6.540$
Analytic rank $0$
Dimension $6$
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] = [819,2,Mod(568,819)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(819, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("819.568");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.o (of order \(3\), degree \(2\), 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: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.771147.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 5x^{4} + 6x^{3} + 15x^{2} + 4x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 757.2
Root \(1.32555 + 2.29591i\) of defining polynomial
Character \(\chi\) \(=\) 819.757
Dual form 819.2.o.d.568.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.636945 - 1.10322i) q^{2} +(0.188601 - 0.326667i) q^{4} -1.10331 q^{5} +(0.500000 - 0.866025i) q^{7} -3.02830 q^{8} +O(q^{10})\) \(q+(-0.636945 - 1.10322i) q^{2} +(0.188601 - 0.326667i) q^{4} -1.10331 q^{5} +(0.500000 - 0.866025i) q^{7} -3.02830 q^{8} +(0.702750 + 1.21720i) q^{10} +(-0.174453 - 0.302162i) q^{11} +(-3.47664 - 0.955496i) q^{13} -1.27389 q^{14} +(1.55166 + 2.68755i) q^{16} +(0.363055 - 0.628829i) q^{17} +(-1.15109 + 1.99375i) q^{19} +(-0.208086 + 0.360416i) q^{20} +(-0.222234 + 0.384921i) q^{22} +(0.0375080 + 0.0649658i) q^{23} -3.78270 q^{25} +(1.16031 + 4.44410i) q^{26} +(-0.188601 - 0.326667i) q^{28} +(0.240258 + 0.416138i) q^{29} -6.85772 q^{31} +(-1.05166 + 1.82152i) q^{32} -0.924984 q^{34} +(-0.551656 + 0.955496i) q^{35} +(0.551656 + 0.955496i) q^{37} +2.93273 q^{38} +3.34116 q^{40} +(1.54778 + 2.68084i) q^{41} +(2.31140 - 4.00346i) q^{43} -0.131609 q^{44} +(0.0477811 - 0.0827593i) q^{46} -4.70769 q^{47} +(-0.500000 - 0.866025i) q^{49} +(2.40937 + 4.17316i) q^{50} +(-0.967829 + 0.955496i) q^{52} -5.54778 q^{53} +(0.192476 + 0.333379i) q^{55} +(-1.51415 + 2.62258i) q^{56} +(0.306062 - 0.530115i) q^{58} +(-1.96249 + 3.39914i) q^{59} +(-2.77389 + 4.80452i) q^{61} +(4.36799 + 7.56558i) q^{62} +8.88601 q^{64} +(3.83582 + 1.05421i) q^{65} +(-4.06193 - 7.03547i) q^{67} +(-0.136945 - 0.237196i) q^{68} +1.40550 q^{70} +(-4.76468 + 8.25267i) q^{71} -10.4338 q^{73} +(0.702750 - 1.21720i) q^{74} +(0.434196 + 0.752049i) q^{76} -0.348907 q^{77} +17.1054 q^{79} +(-1.71196 - 2.96520i) q^{80} +(1.97170 - 3.41509i) q^{82} +11.9143 q^{83} +(-0.400563 + 0.693795i) q^{85} -5.88894 q^{86} +(0.528296 + 0.915036i) q^{88} +(-5.98052 - 10.3586i) q^{89} +(-2.56580 + 2.53311i) q^{91} +0.0282963 q^{92} +(2.99854 + 5.19362i) q^{94} +(1.27002 - 2.19973i) q^{95} +(-5.05166 + 8.74973i) q^{97} +(-0.636945 + 1.10322i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 2 q^{2} - 4 q^{4} + 3 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 2 q^{2} - 4 q^{4} + 3 q^{7} + 6 q^{8} - 13 q^{10} - 8 q^{11} - 4 q^{14} + 6 q^{16} + 4 q^{17} + 7 q^{19} - 13 q^{20} - q^{22} + 9 q^{23} + 22 q^{25} + 26 q^{26} + 4 q^{28} - 7 q^{29} - 14 q^{31} - 3 q^{32} + 12 q^{34} + 8 q^{38} + 26 q^{40} + 2 q^{41} + 19 q^{43} + 30 q^{44} - 7 q^{46} + 34 q^{47} - 3 q^{49} - 16 q^{50} - 26 q^{52} - 26 q^{53} + 3 q^{56} - 22 q^{58} - 3 q^{59} - 13 q^{61} - 17 q^{62} + 2 q^{64} - 5 q^{67} + q^{68} - 26 q^{70} + 8 q^{71} - 4 q^{73} - 13 q^{74} + 18 q^{76} - 16 q^{77} - 2 q^{79} - 26 q^{80} + 36 q^{82} - 4 q^{83} - 13 q^{85} - 34 q^{86} - 21 q^{88} - 19 q^{89} - 24 q^{92} - 7 q^{94} - 27 q^{97} - 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.636945 1.10322i −0.450388 0.780095i 0.548022 0.836464i \(-0.315381\pi\)
−0.998410 + 0.0563687i \(0.982048\pi\)
\(3\) 0 0
\(4\) 0.188601 0.326667i 0.0943007 0.163334i
\(5\) −1.10331 −0.493416 −0.246708 0.969090i \(-0.579349\pi\)
−0.246708 + 0.969090i \(0.579349\pi\)
\(6\) 0 0
\(7\) 0.500000 0.866025i 0.188982 0.327327i
\(8\) −3.02830 −1.07066
\(9\) 0 0
\(10\) 0.702750 + 1.21720i 0.222229 + 0.384912i
\(11\) −0.174453 0.302162i −0.0525996 0.0911053i 0.838527 0.544860i \(-0.183417\pi\)
−0.891126 + 0.453755i \(0.850084\pi\)
\(12\) 0 0
\(13\) −3.47664 0.955496i −0.964246 0.265007i
\(14\) −1.27389 −0.340462
\(15\) 0 0
\(16\) 1.55166 + 2.68755i 0.387914 + 0.671887i
\(17\) 0.363055 0.628829i 0.0880537 0.152513i −0.818635 0.574315i \(-0.805269\pi\)
0.906688 + 0.421801i \(0.138602\pi\)
\(18\) 0 0
\(19\) −1.15109 + 1.99375i −0.264079 + 0.457398i −0.967322 0.253551i \(-0.918401\pi\)
0.703243 + 0.710950i \(0.251735\pi\)
\(20\) −0.208086 + 0.360416i −0.0465295 + 0.0805915i
\(21\) 0 0
\(22\) −0.222234 + 0.384921i −0.0473805 + 0.0820655i
\(23\) 0.0375080 + 0.0649658i 0.00782096 + 0.0135463i 0.869909 0.493212i \(-0.164177\pi\)
−0.862088 + 0.506758i \(0.830844\pi\)
\(24\) 0 0
\(25\) −3.78270 −0.756540
\(26\) 1.16031 + 4.44410i 0.227555 + 0.871560i
\(27\) 0 0
\(28\) −0.188601 0.326667i −0.0356423 0.0617343i
\(29\) 0.240258 + 0.416138i 0.0446147 + 0.0772749i 0.887470 0.460865i \(-0.152461\pi\)
−0.842856 + 0.538140i \(0.819127\pi\)
\(30\) 0 0
\(31\) −6.85772 −1.23168 −0.615841 0.787870i \(-0.711184\pi\)
−0.615841 + 0.787870i \(0.711184\pi\)
\(32\) −1.05166 + 1.82152i −0.185908 + 0.322003i
\(33\) 0 0
\(34\) −0.924984 −0.158633
\(35\) −0.551656 + 0.955496i −0.0932469 + 0.161508i
\(36\) 0 0
\(37\) 0.551656 + 0.955496i 0.0906917 + 0.157083i 0.907802 0.419398i \(-0.137759\pi\)
−0.817111 + 0.576481i \(0.804426\pi\)
\(38\) 2.93273 0.475752
\(39\) 0 0
\(40\) 3.34116 0.528283
\(41\) 1.54778 + 2.68084i 0.241723 + 0.418676i 0.961205 0.275835i \(-0.0889542\pi\)
−0.719482 + 0.694511i \(0.755621\pi\)
\(42\) 0 0
\(43\) 2.31140 4.00346i 0.352485 0.610522i −0.634199 0.773170i \(-0.718670\pi\)
0.986684 + 0.162648i \(0.0520034\pi\)
\(44\) −0.131609 −0.0198407
\(45\) 0 0
\(46\) 0.0477811 0.0827593i 0.00704494 0.0122022i
\(47\) −4.70769 −0.686687 −0.343343 0.939210i \(-0.611559\pi\)
−0.343343 + 0.939210i \(0.611559\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 2.40937 + 4.17316i 0.340737 + 0.590174i
\(51\) 0 0
\(52\) −0.967829 + 0.955496i −0.134214 + 0.132504i
\(53\) −5.54778 −0.762046 −0.381023 0.924565i \(-0.624428\pi\)
−0.381023 + 0.924565i \(0.624428\pi\)
\(54\) 0 0
\(55\) 0.192476 + 0.333379i 0.0259535 + 0.0449528i
\(56\) −1.51415 + 2.62258i −0.202337 + 0.350457i
\(57\) 0 0
\(58\) 0.306062 0.530115i 0.0401879 0.0696075i
\(59\) −1.96249 + 3.39914i −0.255495 + 0.442530i −0.965030 0.262140i \(-0.915572\pi\)
0.709535 + 0.704670i \(0.248905\pi\)
\(60\) 0 0
\(61\) −2.77389 + 4.80452i −0.355160 + 0.615156i −0.987145 0.159825i \(-0.948907\pi\)
0.631985 + 0.774981i \(0.282240\pi\)
\(62\) 4.36799 + 7.56558i 0.554735 + 0.960830i
\(63\) 0 0
\(64\) 8.88601 1.11075
\(65\) 3.83582 + 1.05421i 0.475775 + 0.130759i
\(66\) 0 0
\(67\) −4.06193 7.03547i −0.496244 0.859519i 0.503747 0.863851i \(-0.331954\pi\)
−0.999991 + 0.00433206i \(0.998621\pi\)
\(68\) −0.136945 0.237196i −0.0166071 0.0287643i
\(69\) 0 0
\(70\) 1.40550 0.167989
\(71\) −4.76468 + 8.25267i −0.565463 + 0.979411i 0.431543 + 0.902092i \(0.357969\pi\)
−0.997006 + 0.0773189i \(0.975364\pi\)
\(72\) 0 0
\(73\) −10.4338 −1.22118 −0.610592 0.791946i \(-0.709068\pi\)
−0.610592 + 0.791946i \(0.709068\pi\)
\(74\) 0.702750 1.21720i 0.0816930 0.141496i
\(75\) 0 0
\(76\) 0.434196 + 0.752049i 0.0498057 + 0.0862659i
\(77\) −0.348907 −0.0397616
\(78\) 0 0
\(79\) 17.1054 1.92451 0.962256 0.272146i \(-0.0877335\pi\)
0.962256 + 0.272146i \(0.0877335\pi\)
\(80\) −1.71196 2.96520i −0.191403 0.331520i
\(81\) 0 0
\(82\) 1.97170 3.41509i 0.217738 0.377134i
\(83\) 11.9143 1.30777 0.653883 0.756596i \(-0.273139\pi\)
0.653883 + 0.756596i \(0.273139\pi\)
\(84\) 0 0
\(85\) −0.400563 + 0.693795i −0.0434471 + 0.0752526i
\(86\) −5.88894 −0.635020
\(87\) 0 0
\(88\) 0.528296 + 0.915036i 0.0563166 + 0.0975432i
\(89\) −5.98052 10.3586i −0.633933 1.09800i −0.986740 0.162309i \(-0.948106\pi\)
0.352807 0.935696i \(-0.385227\pi\)
\(90\) 0 0
\(91\) −2.56580 + 2.53311i −0.268969 + 0.265542i
\(92\) 0.0282963 0.00295009
\(93\) 0 0
\(94\) 2.99854 + 5.19362i 0.309276 + 0.535681i
\(95\) 1.27002 2.19973i 0.130301 0.225688i
\(96\) 0 0
\(97\) −5.05166 + 8.74973i −0.512918 + 0.888400i 0.486970 + 0.873419i \(0.338102\pi\)
−0.999888 + 0.0149812i \(0.995231\pi\)
\(98\) −0.636945 + 1.10322i −0.0643412 + 0.111442i
\(99\) 0 0
\(100\) −0.713423 + 1.23568i −0.0713423 + 0.123568i
\(101\) 2.03751 + 3.52907i 0.202740 + 0.351155i 0.949410 0.314039i \(-0.101682\pi\)
−0.746671 + 0.665194i \(0.768349\pi\)
\(102\) 0 0
\(103\) −4.11106 −0.405075 −0.202538 0.979275i \(-0.564919\pi\)
−0.202538 + 0.979275i \(0.564919\pi\)
\(104\) 10.5283 + 2.89353i 1.03238 + 0.283734i
\(105\) 0 0
\(106\) 3.53363 + 6.12043i 0.343217 + 0.594469i
\(107\) −3.08529 5.34388i −0.298266 0.516612i 0.677473 0.735547i \(-0.263075\pi\)
−0.975739 + 0.218935i \(0.929742\pi\)
\(108\) 0 0
\(109\) −8.82167 −0.844963 −0.422481 0.906372i \(-0.638841\pi\)
−0.422481 + 0.906372i \(0.638841\pi\)
\(110\) 0.245194 0.424688i 0.0233783 0.0404924i
\(111\) 0 0
\(112\) 3.10331 0.293235
\(113\) 6.00494 10.4009i 0.564897 0.978430i −0.432162 0.901796i \(-0.642249\pi\)
0.997059 0.0766343i \(-0.0244174\pi\)
\(114\) 0 0
\(115\) −0.0413831 0.0716776i −0.00385899 0.00668397i
\(116\) 0.181252 0.0168288
\(117\) 0 0
\(118\) 5.00000 0.460287
\(119\) −0.363055 0.628829i −0.0332812 0.0576447i
\(120\) 0 0
\(121\) 5.43913 9.42085i 0.494467 0.856441i
\(122\) 7.06727 0.639840
\(123\) 0 0
\(124\) −1.29338 + 2.24019i −0.116149 + 0.201175i
\(125\) 9.69006 0.866706
\(126\) 0 0
\(127\) 2.92886 + 5.07293i 0.259894 + 0.450150i 0.966213 0.257744i \(-0.0829790\pi\)
−0.706319 + 0.707894i \(0.749646\pi\)
\(128\) −3.55659 6.16020i −0.314361 0.544490i
\(129\) 0 0
\(130\) −1.28018 4.90323i −0.112279 0.430042i
\(131\) −22.4055 −1.95758 −0.978789 0.204872i \(-0.934322\pi\)
−0.978789 + 0.204872i \(0.934322\pi\)
\(132\) 0 0
\(133\) 1.15109 + 1.99375i 0.0998125 + 0.172880i
\(134\) −5.17445 + 8.96242i −0.447005 + 0.774235i
\(135\) 0 0
\(136\) −1.09944 + 1.90428i −0.0942760 + 0.163291i
\(137\) 10.1044 17.5013i 0.863275 1.49524i −0.00547505 0.999985i \(-0.501743\pi\)
0.868750 0.495251i \(-0.164924\pi\)
\(138\) 0 0
\(139\) −2.13695 + 3.70130i −0.181253 + 0.313940i −0.942308 0.334748i \(-0.891349\pi\)
0.761054 + 0.648688i \(0.224682\pi\)
\(140\) 0.208086 + 0.360416i 0.0175865 + 0.0304607i
\(141\) 0 0
\(142\) 12.1394 1.01871
\(143\) 0.317797 + 1.21720i 0.0265755 + 0.101787i
\(144\) 0 0
\(145\) −0.265079 0.459131i −0.0220136 0.0381287i
\(146\) 6.64576 + 11.5108i 0.550007 + 0.952640i
\(147\) 0 0
\(148\) 0.416173 0.0342092
\(149\) −2.44834 + 4.24066i −0.200576 + 0.347408i −0.948714 0.316135i \(-0.897615\pi\)
0.748138 + 0.663543i \(0.230948\pi\)
\(150\) 0 0
\(151\) −8.94553 −0.727977 −0.363988 0.931403i \(-0.618585\pi\)
−0.363988 + 0.931403i \(0.618585\pi\)
\(152\) 3.48585 6.03767i 0.282740 0.489720i
\(153\) 0 0
\(154\) 0.222234 + 0.384921i 0.0179082 + 0.0310178i
\(155\) 7.56620 0.607732
\(156\) 0 0
\(157\) 6.59450 0.526298 0.263149 0.964755i \(-0.415239\pi\)
0.263149 + 0.964755i \(0.415239\pi\)
\(158\) −10.8952 18.8711i −0.866778 1.50130i
\(159\) 0 0
\(160\) 1.16031 2.00971i 0.0917302 0.158881i
\(161\) 0.0750160 0.00591209
\(162\) 0 0
\(163\) 4.95222 8.57749i 0.387888 0.671841i −0.604277 0.796774i \(-0.706538\pi\)
0.992165 + 0.124933i \(0.0398715\pi\)
\(164\) 1.16765 0.0911785
\(165\) 0 0
\(166\) −7.58876 13.1441i −0.589002 1.02018i
\(167\) −8.37826 14.5116i −0.648330 1.12294i −0.983522 0.180790i \(-0.942135\pi\)
0.335192 0.942150i \(-0.391199\pi\)
\(168\) 0 0
\(169\) 11.1741 + 6.64383i 0.859543 + 0.511064i
\(170\) 1.02055 0.0782723
\(171\) 0 0
\(172\) −0.871866 1.51012i −0.0664792 0.115145i
\(173\) 6.85918 11.8804i 0.521494 0.903254i −0.478194 0.878254i \(-0.658708\pi\)
0.999687 0.0249993i \(-0.00795836\pi\)
\(174\) 0 0
\(175\) −1.89135 + 3.27592i −0.142973 + 0.247636i
\(176\) 0.541383 0.937703i 0.0408083 0.0706820i
\(177\) 0 0
\(178\) −7.61852 + 13.1957i −0.571032 + 0.989057i
\(179\) −11.0152 19.0789i −0.823315 1.42602i −0.903200 0.429220i \(-0.858789\pi\)
0.0798846 0.996804i \(-0.474545\pi\)
\(180\) 0 0
\(181\) 9.43380 0.701208 0.350604 0.936524i \(-0.385976\pi\)
0.350604 + 0.936524i \(0.385976\pi\)
\(182\) 4.42886 + 1.21720i 0.328289 + 0.0902247i
\(183\) 0 0
\(184\) −0.113585 0.196736i −0.00837363 0.0145035i
\(185\) −0.608649 1.05421i −0.0447488 0.0775071i
\(186\) 0 0
\(187\) −0.253344 −0.0185264
\(188\) −0.887876 + 1.53785i −0.0647550 + 0.112159i
\(189\) 0 0
\(190\) −3.23572 −0.234744
\(191\) −1.68860 + 2.92474i −0.122183 + 0.211627i −0.920628 0.390440i \(-0.872323\pi\)
0.798445 + 0.602067i \(0.205656\pi\)
\(192\) 0 0
\(193\) −11.1614 19.3321i −0.803413 1.39155i −0.917357 0.398065i \(-0.869682\pi\)
0.113945 0.993487i \(-0.463651\pi\)
\(194\) 12.8705 0.924049
\(195\) 0 0
\(196\) −0.377203 −0.0269431
\(197\) −12.7257 22.0416i −0.906669 1.57040i −0.818661 0.574277i \(-0.805283\pi\)
−0.0880085 0.996120i \(-0.528050\pi\)
\(198\) 0 0
\(199\) 11.1702 19.3473i 0.791833 1.37149i −0.132998 0.991116i \(-0.542460\pi\)
0.924831 0.380379i \(-0.124206\pi\)
\(200\) 11.4551 0.810001
\(201\) 0 0
\(202\) 2.59556 4.49565i 0.182623 0.316313i
\(203\) 0.480515 0.0337256
\(204\) 0 0
\(205\) −1.70769 2.95780i −0.119270 0.206582i
\(206\) 2.61852 + 4.53541i 0.182441 + 0.315997i
\(207\) 0 0
\(208\) −2.82661 10.8262i −0.195990 0.750664i
\(209\) 0.803248 0.0555618
\(210\) 0 0
\(211\) −5.01908 8.69331i −0.345528 0.598472i 0.639922 0.768440i \(-0.278967\pi\)
−0.985450 + 0.169968i \(0.945634\pi\)
\(212\) −1.04632 + 1.81228i −0.0718615 + 0.124468i
\(213\) 0 0
\(214\) −3.93032 + 6.80752i −0.268671 + 0.465352i
\(215\) −2.55019 + 4.41707i −0.173922 + 0.301241i
\(216\) 0 0
\(217\) −3.42886 + 5.93896i −0.232766 + 0.403163i
\(218\) 5.61892 + 9.73226i 0.380561 + 0.659152i
\(219\) 0 0
\(220\) 0.145205 0.00978974
\(221\) −1.86305 + 1.83932i −0.125323 + 0.123726i
\(222\) 0 0
\(223\) 2.56727 + 4.44664i 0.171917 + 0.297769i 0.939090 0.343671i \(-0.111671\pi\)
−0.767173 + 0.641440i \(0.778337\pi\)
\(224\) 1.05166 + 1.82152i 0.0702667 + 0.121706i
\(225\) 0 0
\(226\) −15.2993 −1.01769
\(227\) −14.4855 + 25.0895i −0.961433 + 1.66525i −0.242526 + 0.970145i \(0.577976\pi\)
−0.718907 + 0.695106i \(0.755357\pi\)
\(228\) 0 0
\(229\) 0.679390 0.0448953 0.0224477 0.999748i \(-0.492854\pi\)
0.0224477 + 0.999748i \(0.492854\pi\)
\(230\) −0.0527175 + 0.0913094i −0.00347609 + 0.00602076i
\(231\) 0 0
\(232\) −0.727571 1.26019i −0.0477674 0.0827355i
\(233\) 18.3022 1.19902 0.599508 0.800369i \(-0.295363\pi\)
0.599508 + 0.800369i \(0.295363\pi\)
\(234\) 0 0
\(235\) 5.19405 0.338822
\(236\) 0.740258 + 1.28216i 0.0481867 + 0.0834618i
\(237\) 0 0
\(238\) −0.462492 + 0.801060i −0.0299789 + 0.0519250i
\(239\) 5.45222 0.352675 0.176337 0.984330i \(-0.443575\pi\)
0.176337 + 0.984330i \(0.443575\pi\)
\(240\) 0 0
\(241\) 7.73105 13.3906i 0.498000 0.862562i −0.501997 0.864869i \(-0.667401\pi\)
0.999997 + 0.00230736i \(0.000734455\pi\)
\(242\) −13.8577 −0.890808
\(243\) 0 0
\(244\) 1.04632 + 1.81228i 0.0669837 + 0.116019i
\(245\) 0.551656 + 0.955496i 0.0352440 + 0.0610444i
\(246\) 0 0
\(247\) 5.90696 5.83169i 0.375851 0.371062i
\(248\) 20.7672 1.31872
\(249\) 0 0
\(250\) −6.17204 10.6903i −0.390354 0.676113i
\(251\) −4.14722 + 7.18319i −0.261770 + 0.453399i −0.966712 0.255866i \(-0.917640\pi\)
0.704942 + 0.709265i \(0.250973\pi\)
\(252\) 0 0
\(253\) 0.0130868 0.0226670i 0.000822760 0.00142506i
\(254\) 3.73105 6.46236i 0.234107 0.405485i
\(255\) 0 0
\(256\) 4.35530 7.54361i 0.272207 0.471476i
\(257\) −7.51908 13.0234i −0.469028 0.812380i 0.530346 0.847782i \(-0.322062\pi\)
−0.999373 + 0.0354019i \(0.988729\pi\)
\(258\) 0 0
\(259\) 1.10331 0.0685565
\(260\) 1.06782 1.05421i 0.0662232 0.0653794i
\(261\) 0 0
\(262\) 14.2711 + 24.7182i 0.881670 + 1.52710i
\(263\) −8.62240 14.9344i −0.531680 0.920896i −0.999316 0.0369754i \(-0.988228\pi\)
0.467636 0.883921i \(-0.345106\pi\)
\(264\) 0 0
\(265\) 6.12094 0.376006
\(266\) 1.46637 2.53982i 0.0899087 0.155726i
\(267\) 0 0
\(268\) −3.06434 −0.187185
\(269\) −12.1472 + 21.0396i −0.740629 + 1.28281i 0.211580 + 0.977361i \(0.432139\pi\)
−0.952209 + 0.305446i \(0.901194\pi\)
\(270\) 0 0
\(271\) −9.16630 15.8765i −0.556813 0.964429i −0.997760 0.0668956i \(-0.978691\pi\)
0.440947 0.897533i \(-0.354643\pi\)
\(272\) 2.25334 0.136629
\(273\) 0 0
\(274\) −25.7437 −1.55524
\(275\) 0.659905 + 1.14299i 0.0397938 + 0.0689248i
\(276\) 0 0
\(277\) −4.22717 + 7.32167i −0.253986 + 0.439917i −0.964620 0.263646i \(-0.915075\pi\)
0.710634 + 0.703562i \(0.248408\pi\)
\(278\) 5.44447 0.326538
\(279\) 0 0
\(280\) 1.67058 2.89353i 0.0998361 0.172921i
\(281\) 25.0120 1.49209 0.746045 0.665895i \(-0.231950\pi\)
0.746045 + 0.665895i \(0.231950\pi\)
\(282\) 0 0
\(283\) −13.5707 23.5052i −0.806697 1.39724i −0.915140 0.403137i \(-0.867920\pi\)
0.108443 0.994103i \(-0.465414\pi\)
\(284\) 1.79725 + 3.11293i 0.106647 + 0.184718i
\(285\) 0 0
\(286\) 1.14042 1.12589i 0.0674344 0.0665752i
\(287\) 3.09556 0.182725
\(288\) 0 0
\(289\) 8.23638 + 14.2658i 0.484493 + 0.839167i
\(290\) −0.337682 + 0.584882i −0.0198294 + 0.0343455i
\(291\) 0 0
\(292\) −1.96783 + 3.40838i −0.115158 + 0.199460i
\(293\) −5.27002 + 9.12793i −0.307878 + 0.533260i −0.977898 0.209083i \(-0.932952\pi\)
0.670020 + 0.742343i \(0.266285\pi\)
\(294\) 0 0
\(295\) 2.16524 3.75031i 0.126065 0.218351i
\(296\) −1.67058 2.89353i −0.0971004 0.168183i
\(297\) 0 0
\(298\) 6.23784 0.361349
\(299\) −0.0683273 0.261701i −0.00395147 0.0151346i
\(300\) 0 0
\(301\) −2.31140 4.00346i −0.133227 0.230756i
\(302\) 5.69781 + 9.86890i 0.327872 + 0.567891i
\(303\) 0 0
\(304\) −7.14440 −0.409760
\(305\) 3.06047 5.30089i 0.175242 0.303528i
\(306\) 0 0
\(307\) −4.40842 −0.251602 −0.125801 0.992055i \(-0.540150\pi\)
−0.125801 + 0.992055i \(0.540150\pi\)
\(308\) −0.0658043 + 0.113976i −0.00374955 + 0.00649441i
\(309\) 0 0
\(310\) −4.81926 8.34720i −0.273715 0.474089i
\(311\) 2.32836 0.132029 0.0660146 0.997819i \(-0.478972\pi\)
0.0660146 + 0.997819i \(0.478972\pi\)
\(312\) 0 0
\(313\) 12.6687 0.716078 0.358039 0.933707i \(-0.383445\pi\)
0.358039 + 0.933707i \(0.383445\pi\)
\(314\) −4.20034 7.27520i −0.237039 0.410563i
\(315\) 0 0
\(316\) 3.22611 5.58779i 0.181483 0.314337i
\(317\) 12.2915 0.690360 0.345180 0.938536i \(-0.387818\pi\)
0.345180 + 0.938536i \(0.387818\pi\)
\(318\) 0 0
\(319\) 0.0838275 0.145193i 0.00469344 0.00812927i
\(320\) −9.80405 −0.548063
\(321\) 0 0
\(322\) −0.0477811 0.0827593i −0.00266274 0.00461200i
\(323\) 0.835820 + 1.44768i 0.0465063 + 0.0805512i
\(324\) 0 0
\(325\) 13.1511 + 3.61436i 0.729491 + 0.200489i
\(326\) −12.6172 −0.698800
\(327\) 0 0
\(328\) −4.68714 8.11836i −0.258804 0.448262i
\(329\) −2.35384 + 4.07698i −0.129772 + 0.224771i
\(330\) 0 0
\(331\) −6.64576 + 11.5108i −0.365284 + 0.632690i −0.988822 0.149103i \(-0.952361\pi\)
0.623538 + 0.781793i \(0.285695\pi\)
\(332\) 2.24706 3.89202i 0.123323 0.213602i
\(333\) 0 0
\(334\) −10.6730 + 18.4862i −0.584000 + 1.01152i
\(335\) 4.48158 + 7.76232i 0.244855 + 0.424101i
\(336\) 0 0
\(337\) −3.40550 −0.185509 −0.0927547 0.995689i \(-0.529567\pi\)
−0.0927547 + 0.995689i \(0.529567\pi\)
\(338\) 0.212362 16.5592i 0.0115510 0.900703i
\(339\) 0 0
\(340\) 0.151093 + 0.261701i 0.00819419 + 0.0141928i
\(341\) 1.19635 + 2.07214i 0.0647861 + 0.112213i
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) −6.99960 + 12.1237i −0.377393 + 0.653664i
\(345\) 0 0
\(346\) −17.4757 −0.939499
\(347\) −16.7491 + 29.0102i −0.899137 + 1.55735i −0.0705378 + 0.997509i \(0.522472\pi\)
−0.828599 + 0.559842i \(0.810862\pi\)
\(348\) 0 0
\(349\) 14.0902 + 24.4050i 0.754232 + 1.30637i 0.945755 + 0.324881i \(0.105324\pi\)
−0.191523 + 0.981488i \(0.561342\pi\)
\(350\) 4.81875 0.257573
\(351\) 0 0
\(352\) 0.733860 0.0391148
\(353\) −1.49612 2.59136i −0.0796307 0.137924i 0.823460 0.567374i \(-0.192041\pi\)
−0.903091 + 0.429450i \(0.858707\pi\)
\(354\) 0 0
\(355\) 5.25693 9.10527i 0.279009 0.483257i
\(356\) −4.51173 −0.239121
\(357\) 0 0
\(358\) −14.0322 + 24.3044i −0.741623 + 1.28453i
\(359\) −3.80888 −0.201025 −0.100512 0.994936i \(-0.532048\pi\)
−0.100512 + 0.994936i \(0.532048\pi\)
\(360\) 0 0
\(361\) 6.84997 + 11.8645i 0.360525 + 0.624447i
\(362\) −6.00881 10.4076i −0.315816 0.547010i
\(363\) 0 0
\(364\) 0.343570 + 1.31591i 0.0180080 + 0.0689726i
\(365\) 11.5117 0.602552
\(366\) 0 0
\(367\) 13.2257 + 22.9076i 0.690376 + 1.19577i 0.971715 + 0.236158i \(0.0758884\pi\)
−0.281338 + 0.959609i \(0.590778\pi\)
\(368\) −0.116399 + 0.201609i −0.00606772 + 0.0105096i
\(369\) 0 0
\(370\) −0.775352 + 1.34295i −0.0403086 + 0.0698166i
\(371\) −2.77389 + 4.80452i −0.144013 + 0.249438i
\(372\) 0 0
\(373\) −1.06580 + 1.84603i −0.0551853 + 0.0955837i −0.892298 0.451446i \(-0.850908\pi\)
0.837113 + 0.547030i \(0.184242\pi\)
\(374\) 0.161367 + 0.279495i 0.00834406 + 0.0144523i
\(375\) 0 0
\(376\) 14.2563 0.735211
\(377\) −0.437670 1.67633i −0.0225412 0.0863353i
\(378\) 0 0
\(379\) 6.97170 + 12.0753i 0.358112 + 0.620269i 0.987645 0.156705i \(-0.0500871\pi\)
−0.629533 + 0.776974i \(0.716754\pi\)
\(380\) −0.479053 0.829745i −0.0245749 0.0425650i
\(381\) 0 0
\(382\) 4.30219 0.220119
\(383\) −9.30219 + 16.1119i −0.475320 + 0.823278i −0.999600 0.0282678i \(-0.991001\pi\)
0.524281 + 0.851545i \(0.324334\pi\)
\(384\) 0 0
\(385\) 0.384953 0.0196190
\(386\) −14.2184 + 24.6269i −0.723695 + 1.25348i
\(387\) 0 0
\(388\) 1.90550 + 3.30042i 0.0967371 + 0.167554i
\(389\) 1.23009 0.0623682 0.0311841 0.999514i \(-0.490072\pi\)
0.0311841 + 0.999514i \(0.490072\pi\)
\(390\) 0 0
\(391\) 0.0544699 0.00275466
\(392\) 1.51415 + 2.62258i 0.0764760 + 0.132460i
\(393\) 0 0
\(394\) −16.2112 + 28.0786i −0.816706 + 1.41458i
\(395\) −18.8726 −0.949585
\(396\) 0 0
\(397\) −14.8071 + 25.6467i −0.743148 + 1.28717i 0.207907 + 0.978149i \(0.433335\pi\)
−0.951055 + 0.309022i \(0.899998\pi\)
\(398\) −28.4592 −1.42653
\(399\) 0 0
\(400\) −5.86945 10.1662i −0.293473 0.508310i
\(401\) 4.09023 + 7.08448i 0.204256 + 0.353782i 0.949895 0.312568i \(-0.101189\pi\)
−0.745639 + 0.666350i \(0.767856\pi\)
\(402\) 0 0
\(403\) 23.8418 + 6.55253i 1.18765 + 0.326405i
\(404\) 1.53711 0.0764740
\(405\) 0 0
\(406\) −0.306062 0.530115i −0.0151896 0.0263092i
\(407\) 0.192476 0.333379i 0.00954070 0.0165250i
\(408\) 0 0
\(409\) −5.03363 + 8.71851i −0.248897 + 0.431102i −0.963220 0.268714i \(-0.913401\pi\)
0.714323 + 0.699816i \(0.246735\pi\)
\(410\) −2.17540 + 3.76791i −0.107436 + 0.186084i
\(411\) 0 0
\(412\) −0.775352 + 1.34295i −0.0381989 + 0.0661624i
\(413\) 1.96249 + 3.39914i 0.0965679 + 0.167261i
\(414\) 0 0
\(415\) −13.1452 −0.645273
\(416\) 5.39669 5.32792i 0.264594 0.261223i
\(417\) 0 0
\(418\) −0.511625 0.886161i −0.0250244 0.0433435i
\(419\) 4.72998 + 8.19257i 0.231075 + 0.400233i 0.958125 0.286351i \(-0.0924424\pi\)
−0.727050 + 0.686585i \(0.759109\pi\)
\(420\) 0 0
\(421\) 31.0643 1.51398 0.756992 0.653424i \(-0.226668\pi\)
0.756992 + 0.653424i \(0.226668\pi\)
\(422\) −6.39376 + 11.0743i −0.311244 + 0.539090i
\(423\) 0 0
\(424\) 16.8003 0.815896
\(425\) −1.37333 + 2.37867i −0.0666162 + 0.115383i
\(426\) 0 0
\(427\) 2.77389 + 4.80452i 0.134238 + 0.232507i
\(428\) −2.32756 −0.112507
\(429\) 0 0
\(430\) 6.49734 0.313329
\(431\) −12.6093 21.8400i −0.607369 1.05199i −0.991672 0.128787i \(-0.958892\pi\)
0.384303 0.923207i \(-0.374442\pi\)
\(432\) 0 0
\(433\) −1.88495 + 3.26483i −0.0905851 + 0.156898i −0.907757 0.419495i \(-0.862207\pi\)
0.817172 + 0.576393i \(0.195540\pi\)
\(434\) 8.73598 0.419341
\(435\) 0 0
\(436\) −1.66378 + 2.88175i −0.0796806 + 0.138011i
\(437\) −0.172701 −0.00826141
\(438\) 0 0
\(439\) 11.3174 + 19.6023i 0.540150 + 0.935567i 0.998895 + 0.0469991i \(0.0149658\pi\)
−0.458745 + 0.888568i \(0.651701\pi\)
\(440\) −0.582876 1.00957i −0.0277875 0.0481294i
\(441\) 0 0
\(442\) 3.21584 + 0.883819i 0.152962 + 0.0420390i
\(443\) −4.64334 −0.220612 −0.110306 0.993898i \(-0.535183\pi\)
−0.110306 + 0.993898i \(0.535183\pi\)
\(444\) 0 0
\(445\) 6.59838 + 11.4287i 0.312793 + 0.541773i
\(446\) 3.27042 5.66453i 0.154859 0.268223i
\(447\) 0 0
\(448\) 4.44301 7.69551i 0.209912 0.363579i
\(449\) 4.71156 8.16066i 0.222352 0.385125i −0.733170 0.680046i \(-0.761960\pi\)
0.955522 + 0.294920i \(0.0952931\pi\)
\(450\) 0 0
\(451\) 0.540031 0.935361i 0.0254291 0.0440444i
\(452\) −2.26508 3.92323i −0.106540 0.184533i
\(453\) 0 0
\(454\) 36.9058 1.73207
\(455\) 2.83088 2.79481i 0.132714 0.131023i
\(456\) 0 0
\(457\) −6.35812 11.0126i −0.297420 0.515147i 0.678125 0.734947i \(-0.262793\pi\)
−0.975545 + 0.219800i \(0.929460\pi\)
\(458\) −0.432734 0.749517i −0.0202203 0.0350226i
\(459\) 0 0
\(460\) −0.0312196 −0.00145562
\(461\) −14.8627 + 25.7429i −0.692223 + 1.19897i 0.278885 + 0.960324i \(0.410035\pi\)
−0.971108 + 0.238641i \(0.923298\pi\)
\(462\) 0 0
\(463\) −15.2838 −0.710297 −0.355148 0.934810i \(-0.615570\pi\)
−0.355148 + 0.934810i \(0.615570\pi\)
\(464\) −0.745594 + 1.29141i −0.0346133 + 0.0599521i
\(465\) 0 0
\(466\) −11.6575 20.1914i −0.540023 0.935347i
\(467\) 26.6503 1.23323 0.616614 0.787265i \(-0.288504\pi\)
0.616614 + 0.787265i \(0.288504\pi\)
\(468\) 0 0
\(469\) −8.12386 −0.375125
\(470\) −3.30832 5.73019i −0.152602 0.264314i
\(471\) 0 0
\(472\) 5.94301 10.2936i 0.273549 0.473801i
\(473\) −1.61292 −0.0741623
\(474\) 0 0
\(475\) 4.35424 7.54177i 0.199786 0.346040i
\(476\) −0.273891 −0.0125538
\(477\) 0 0
\(478\) −3.47277 6.01501i −0.158841 0.275120i
\(479\) −11.1058 19.2359i −0.507439 0.878909i −0.999963 0.00861072i \(-0.997259\pi\)
0.492524 0.870299i \(-0.336074\pi\)
\(480\) 0 0
\(481\) −1.00494 3.84902i −0.0458212 0.175500i
\(482\) −19.6970 −0.897174
\(483\) 0 0
\(484\) −2.05166 3.55357i −0.0932571 0.161526i
\(485\) 5.57355 9.65368i 0.253082 0.438351i
\(486\) 0 0
\(487\) 0.485852 0.841520i 0.0220160 0.0381329i −0.854807 0.518945i \(-0.826325\pi\)
0.876824 + 0.480812i \(0.159658\pi\)
\(488\) 8.40016 14.5495i 0.380257 0.658625i
\(489\) 0 0
\(490\) 0.702750 1.21720i 0.0317470 0.0549874i
\(491\) 13.4674 + 23.3263i 0.607777 + 1.05270i 0.991606 + 0.129296i \(0.0412717\pi\)
−0.383830 + 0.923404i \(0.625395\pi\)
\(492\) 0 0
\(493\) 0.348907 0.0157140
\(494\) −10.1961 2.80222i −0.458742 0.126078i
\(495\) 0 0
\(496\) −10.6408 18.4304i −0.477787 0.827551i
\(497\) 4.76468 + 8.25267i 0.213725 + 0.370183i
\(498\) 0 0
\(499\) −21.1239 −0.945634 −0.472817 0.881161i \(-0.656763\pi\)
−0.472817 + 0.881161i \(0.656763\pi\)
\(500\) 1.82756 3.16543i 0.0817310 0.141562i
\(501\) 0 0
\(502\) 10.5662 0.471593
\(503\) 6.28270 10.8820i 0.280132 0.485203i −0.691285 0.722582i \(-0.742955\pi\)
0.971417 + 0.237379i \(0.0762885\pi\)
\(504\) 0 0
\(505\) −2.24801 3.89366i −0.100035 0.173266i
\(506\) −0.0333423 −0.00148225
\(507\) 0 0
\(508\) 2.20955 0.0980328
\(509\) 13.8032 + 23.9079i 0.611818 + 1.05970i 0.990934 + 0.134351i \(0.0428949\pi\)
−0.379116 + 0.925349i \(0.623772\pi\)
\(510\) 0 0
\(511\) −5.21690 + 9.03593i −0.230782 + 0.399726i
\(512\) −25.3227 −1.11912
\(513\) 0 0
\(514\) −9.57849 + 16.5904i −0.422489 + 0.731773i
\(515\) 4.53579 0.199871
\(516\) 0 0
\(517\) 0.821271 + 1.42248i 0.0361195 + 0.0625608i
\(518\) −0.702750 1.21720i −0.0308770 0.0534806i
\(519\) 0 0
\(520\) −11.6160 3.19246i −0.509395 0.139999i
\(521\) 36.8783 1.61567 0.807833 0.589411i \(-0.200640\pi\)
0.807833 + 0.589411i \(0.200640\pi\)
\(522\) 0 0
\(523\) −15.4027 26.6782i −0.673512 1.16656i −0.976901 0.213691i \(-0.931451\pi\)
0.303389 0.952867i \(-0.401882\pi\)
\(524\) −4.22571 + 7.31914i −0.184601 + 0.319738i
\(525\) 0 0
\(526\) −10.9840 + 19.0248i −0.478925 + 0.829522i
\(527\) −2.48973 + 4.31233i −0.108454 + 0.187848i
\(528\) 0 0
\(529\) 11.4972 19.9137i 0.499878 0.865814i
\(530\) −3.89870 6.75275i −0.169349 0.293321i
\(531\) 0 0
\(532\) 0.868391 0.0376495
\(533\) −2.81955 10.7992i −0.122128 0.467765i
\(534\) 0 0
\(535\) 3.40404 + 5.89597i 0.147169 + 0.254905i
\(536\) 12.3007 + 21.3055i 0.531310 + 0.920257i
\(537\) 0 0
\(538\) 30.9485 1.33428
\(539\) −0.174453 + 0.302162i −0.00751424 + 0.0130150i
\(540\) 0 0
\(541\) −41.4981 −1.78414 −0.892072 0.451893i \(-0.850749\pi\)
−0.892072 + 0.451893i \(0.850749\pi\)
\(542\) −11.6769 + 20.2249i −0.501564 + 0.868735i
\(543\) 0 0
\(544\) 0.763617 + 1.32262i 0.0327398 + 0.0567070i
\(545\) 9.73306 0.416918
\(546\) 0 0
\(547\) −41.3716 −1.76892 −0.884460 0.466615i \(-0.845473\pi\)
−0.884460 + 0.466615i \(0.845473\pi\)
\(548\) −3.81140 6.60154i −0.162815 0.282004i
\(549\) 0 0
\(550\) 0.840647 1.45604i 0.0358453 0.0620859i
\(551\) −1.10624 −0.0471272
\(552\) 0 0
\(553\) 8.55272 14.8137i 0.363699 0.629944i
\(554\) 10.7699 0.457569
\(555\) 0 0
\(556\) 0.806062 + 1.39614i 0.0341846 + 0.0592095i
\(557\) 15.0075 + 25.9937i 0.635886 + 1.10139i 0.986327 + 0.164803i \(0.0526987\pi\)
−0.350440 + 0.936585i \(0.613968\pi\)
\(558\) 0 0
\(559\) −11.8612 + 11.7101i −0.501675 + 0.495283i
\(560\) −3.42392 −0.144687
\(561\) 0 0
\(562\) −15.9313 27.5938i −0.672020 1.16397i
\(563\) 12.9674 22.4602i 0.546512 0.946586i −0.451998 0.892019i \(-0.649289\pi\)
0.998510 0.0545676i \(-0.0173780\pi\)
\(564\) 0 0
\(565\) −6.62532 + 11.4754i −0.278729 + 0.482773i
\(566\) −17.2876 + 29.9431i −0.726654 + 1.25860i
\(567\) 0 0
\(568\) 14.4289 24.9915i 0.605421 1.04862i
\(569\) −3.28310 5.68650i −0.137635 0.238390i 0.788966 0.614437i \(-0.210617\pi\)
−0.926601 + 0.376046i \(0.877283\pi\)
\(570\) 0 0
\(571\) −30.0539 −1.25772 −0.628858 0.777520i \(-0.716477\pi\)
−0.628858 + 0.777520i \(0.716477\pi\)
\(572\) 0.457556 + 0.125752i 0.0191314 + 0.00525794i
\(573\) 0 0
\(574\) −1.97170 3.41509i −0.0822973 0.142543i
\(575\) −0.141882 0.245746i −0.00591687 0.0102483i
\(576\) 0 0
\(577\) 21.1706 0.881343 0.440671 0.897669i \(-0.354740\pi\)
0.440671 + 0.897669i \(0.354740\pi\)
\(578\) 10.4922 18.1731i 0.436420 0.755902i
\(579\) 0 0
\(580\) −0.199977 −0.00830360
\(581\) 5.95716 10.3181i 0.247144 0.428067i
\(582\) 0 0
\(583\) 0.967829 + 1.67633i 0.0400834 + 0.0694264i
\(584\) 31.5966 1.30748
\(585\) 0 0
\(586\) 13.4268 0.554658
\(587\) 0.0156098 + 0.0270370i 0.000644286 + 0.00111594i 0.866347 0.499442i \(-0.166462\pi\)
−0.865703 + 0.500558i \(0.833128\pi\)
\(588\) 0 0
\(589\) 7.89387 13.6726i 0.325261 0.563369i
\(590\) −5.51656 −0.227113
\(591\) 0 0
\(592\) −1.71196 + 2.96520i −0.0703612 + 0.121869i
\(593\) 10.3150 0.423586 0.211793 0.977315i \(-0.432070\pi\)
0.211793 + 0.977315i \(0.432070\pi\)
\(594\) 0 0
\(595\) 0.400563 + 0.693795i 0.0164215 + 0.0284428i
\(596\) 0.923522 + 1.59959i 0.0378289 + 0.0655217i
\(597\) 0 0
\(598\) −0.245194 + 0.242070i −0.0100267 + 0.00989896i
\(599\) −44.0176 −1.79851 −0.899256 0.437423i \(-0.855891\pi\)
−0.899256 + 0.437423i \(0.855891\pi\)
\(600\) 0 0
\(601\) −2.52336 4.37059i −0.102930 0.178280i 0.809961 0.586484i \(-0.199488\pi\)
−0.912891 + 0.408204i \(0.866155\pi\)
\(602\) −2.94447 + 5.09997i −0.120008 + 0.207859i
\(603\) 0 0
\(604\) −1.68714 + 2.92221i −0.0686487 + 0.118903i
\(605\) −6.00106 + 10.3941i −0.243978 + 0.422582i
\(606\) 0 0
\(607\) −8.32409 + 14.4177i −0.337864 + 0.585198i −0.984031 0.177998i \(-0.943038\pi\)
0.646167 + 0.763196i \(0.276371\pi\)
\(608\) −2.42111 4.19348i −0.0981889 0.170068i
\(609\) 0 0
\(610\) −7.79740 −0.315708
\(611\) 16.3669 + 4.49818i 0.662135 + 0.181977i
\(612\) 0 0
\(613\) −19.0060 32.9194i −0.767645 1.32960i −0.938837 0.344362i \(-0.888095\pi\)
0.171192 0.985238i \(-0.445238\pi\)
\(614\) 2.80792 + 4.86347i 0.113319 + 0.196274i
\(615\) 0 0
\(616\) 1.05659 0.0425713
\(617\) 7.83330 13.5677i 0.315357 0.546214i −0.664157 0.747593i \(-0.731209\pi\)
0.979513 + 0.201380i \(0.0645425\pi\)
\(618\) 0 0
\(619\) 3.26109 0.131074 0.0655372 0.997850i \(-0.479124\pi\)
0.0655372 + 0.997850i \(0.479124\pi\)
\(620\) 1.42700 2.47163i 0.0573096 0.0992631i
\(621\) 0 0
\(622\) −1.48304 2.56870i −0.0594644 0.102995i
\(623\) −11.9610 −0.479209
\(624\) 0 0
\(625\) 8.22234 0.328894
\(626\) −8.06928 13.9764i −0.322513 0.558609i
\(627\) 0 0
\(628\) 1.24373 2.15421i 0.0496303 0.0859622i
\(629\) 0.801125 0.0319430
\(630\) 0 0
\(631\) −0.799773 + 1.38525i −0.0318385 + 0.0551459i −0.881506 0.472174i \(-0.843470\pi\)
0.849667 + 0.527319i \(0.176803\pi\)
\(632\) −51.8003 −2.06051
\(633\) 0 0
\(634\) −7.82902 13.5603i −0.310930 0.538547i
\(635\) −3.23145 5.59703i −0.128236 0.222111i
\(636\) 0 0
\(637\) 0.910836 + 3.48861i 0.0360886 + 0.138224i
\(638\) −0.213574 −0.00845548
\(639\) 0 0
\(640\) 3.92403 + 6.79662i 0.155111 + 0.268660i
\(641\) 15.6779 27.1550i 0.619241 1.07256i −0.370384 0.928879i \(-0.620774\pi\)
0.989625 0.143678i \(-0.0458929\pi\)
\(642\) 0 0
\(643\) 9.33154 16.1627i 0.368000 0.637395i −0.621253 0.783610i \(-0.713376\pi\)
0.989253 + 0.146215i \(0.0467092\pi\)
\(644\) 0.0141481 0.0245053i 0.000557514 0.000965643i
\(645\) 0 0
\(646\) 1.06474 1.84419i 0.0418918 0.0725586i
\(647\) 3.26855 + 5.66130i 0.128500 + 0.222569i 0.923096 0.384570i \(-0.125650\pi\)
−0.794596 + 0.607139i \(0.792317\pi\)
\(648\) 0 0
\(649\) 1.36945 0.0537557
\(650\) −4.38909 16.8107i −0.172154 0.659371i
\(651\) 0 0
\(652\) −1.86799 3.23546i −0.0731562 0.126710i
\(653\) 7.92605 + 13.7283i 0.310170 + 0.537230i 0.978399 0.206725i \(-0.0662806\pi\)
−0.668229 + 0.743956i \(0.732947\pi\)
\(654\) 0 0
\(655\) 24.7203 0.965901
\(656\) −4.80325 + 8.31947i −0.187535 + 0.324821i
\(657\) 0 0
\(658\) 5.99708 0.233790
\(659\) −24.8987 + 43.1258i −0.969916 + 1.67994i −0.274132 + 0.961692i \(0.588390\pi\)
−0.695784 + 0.718251i \(0.744943\pi\)
\(660\) 0 0
\(661\) −1.78552 3.09260i −0.0694485 0.120288i 0.829210 0.558937i \(-0.188791\pi\)
−0.898659 + 0.438649i \(0.855457\pi\)
\(662\) 16.9319 0.658078
\(663\) 0 0
\(664\) −36.0801 −1.40018
\(665\) −1.27002 2.19973i −0.0492491 0.0853019i
\(666\) 0 0
\(667\) −0.0180232 + 0.0312170i −0.000697860 + 0.00120873i
\(668\) −6.32061 −0.244552
\(669\) 0 0
\(670\) 5.70904 9.88834i 0.220559 0.382020i
\(671\) 1.93566 0.0747252
\(672\) 0 0
\(673\) −5.86693 10.1618i −0.226154 0.391709i 0.730511 0.682901i \(-0.239282\pi\)
−0.956665 + 0.291191i \(0.905948\pi\)
\(674\) 2.16912 + 3.75702i 0.0835512 + 0.144715i
\(675\) 0 0
\(676\) 4.27777 2.39716i 0.164529 0.0921985i
\(677\) −17.3326 −0.666146 −0.333073 0.942901i \(-0.608086\pi\)
−0.333073 + 0.942901i \(0.608086\pi\)
\(678\) 0 0
\(679\) 5.05166 + 8.74973i 0.193865 + 0.335784i
\(680\) 1.21302 2.10102i 0.0465173 0.0805703i
\(681\) 0 0
\(682\) 1.52402 2.63968i 0.0583578 0.101079i
\(683\) 8.48198 14.6912i 0.324554 0.562144i −0.656868 0.754005i \(-0.728119\pi\)
0.981422 + 0.191862i \(0.0614525\pi\)
\(684\) 0 0
\(685\) −11.1483 + 19.3094i −0.425954 + 0.737774i
\(686\) 0.636945 + 1.10322i 0.0243187 + 0.0421212i
\(687\) 0 0
\(688\) 14.3460 0.546935
\(689\) 19.2876 + 5.30089i 0.734801 + 0.201948i
\(690\) 0 0
\(691\) −18.3213 31.7334i −0.696974 1.20719i −0.969511 0.245049i \(-0.921196\pi\)
0.272537 0.962145i \(-0.412137\pi\)
\(692\) −2.58730 4.48134i −0.0983545 0.170355i
\(693\) 0 0
\(694\) 42.6730 1.61984
\(695\) 2.35772 4.08369i 0.0894333 0.154903i
\(696\) 0 0
\(697\) 2.24772 0.0851384
\(698\) 17.9494 31.0893i 0.679395 1.17675i
\(699\) 0 0
\(700\) 0.713423 + 1.23568i 0.0269649 + 0.0467045i
\(701\) 14.6092 0.551782 0.275891 0.961189i \(-0.411027\pi\)
0.275891 + 0.961189i \(0.411027\pi\)
\(702\) 0 0
\(703\) −2.54003 −0.0957991
\(704\) −1.55019 2.68502i −0.0584252 0.101195i
\(705\) 0 0
\(706\) −1.90590 + 3.30111i −0.0717295 + 0.124239i
\(707\) 4.07502 0.153257
\(708\) 0 0
\(709\) 11.7930 20.4260i 0.442894 0.767116i −0.555008 0.831845i \(-0.687285\pi\)
0.997903 + 0.0647290i \(0.0206183\pi\)
\(710\) −13.3935 −0.502649
\(711\) 0 0
\(712\) 18.1108 + 31.3688i 0.678730 + 1.17559i
\(713\) −0.257219 0.445517i −0.00963294 0.0166847i
\(714\) 0 0
\(715\) −0.350629 1.34295i −0.0131128 0.0502235i
\(716\) −8.30994 −0.310557
\(717\) 0 0
\(718\) 2.42605 + 4.20203i 0.0905392 + 0.156819i
\(719\) 17.0669 29.5607i 0.636487 1.10243i −0.349711 0.936857i \(-0.613720\pi\)
0.986198 0.165570i \(-0.0529463\pi\)
\(720\) 0 0
\(721\) −2.05553 + 3.56028i −0.0765520 + 0.132592i
\(722\) 8.72611 15.1141i 0.324752 0.562487i
\(723\) 0 0
\(724\) 1.77923 3.08171i 0.0661245 0.114531i
\(725\) −0.908823 1.57413i −0.0337528 0.0584616i
\(726\) 0 0
\(727\) −15.3481 −0.569230 −0.284615 0.958642i \(-0.591866\pi\)
−0.284615 + 0.958642i \(0.591866\pi\)
\(728\) 7.77002 7.67101i 0.287976 0.284307i
\(729\) 0 0
\(730\) −7.33235 12.7000i −0.271382 0.470048i
\(731\) −1.67833 2.90695i −0.0620752 0.107517i
\(732\) 0 0
\(733\) 23.2894 0.860213 0.430107 0.902778i \(-0.358476\pi\)
0.430107 + 0.902778i \(0.358476\pi\)
\(734\) 16.8481 29.1818i 0.621875 1.07712i
\(735\) 0 0
\(736\) −0.157782 −0.00581593
\(737\) −1.41723 + 2.45472i −0.0522045 + 0.0904208i
\(738\) 0 0
\(739\) 5.13307 + 8.89074i 0.188823 + 0.327051i 0.944858 0.327480i \(-0.106199\pi\)
−0.756035 + 0.654531i \(0.772866\pi\)
\(740\) −0.459168 −0.0168794
\(741\) 0 0
\(742\) 7.06727 0.259447
\(743\) −22.6741 39.2726i −0.831830 1.44077i −0.896585 0.442871i \(-0.853960\pi\)
0.0647549 0.997901i \(-0.479373\pi\)
\(744\) 0 0
\(745\) 2.70129 4.67877i 0.0989675 0.171417i
\(746\) 2.71544 0.0994192
\(747\) 0 0
\(748\) −0.0477811 + 0.0827593i −0.00174705 + 0.00302598i
\(749\) −6.17058 −0.225468
\(750\) 0 0
\(751\) 14.8057 + 25.6442i 0.540266 + 0.935769i 0.998888 + 0.0471372i \(0.0150098\pi\)
−0.458622 + 0.888631i \(0.651657\pi\)
\(752\) −7.30471 12.6521i −0.266375 0.461376i
\(753\) 0 0
\(754\) −1.57059 + 1.55058i −0.0571975 + 0.0564687i
\(755\) 9.86971 0.359196
\(756\) 0 0
\(757\) 12.9908 + 22.5007i 0.472158 + 0.817802i 0.999492 0.0318559i \(-0.0101418\pi\)
−0.527334 + 0.849658i \(0.676808\pi\)
\(758\) 8.88119 15.3827i 0.322579 0.558724i
\(759\) 0 0
\(760\) −3.84598 + 6.66144i −0.139508 + 0.241636i
\(761\) −27.0332 + 46.8229i −0.979954 + 1.69733i −0.317444 + 0.948277i \(0.602824\pi\)
−0.662510 + 0.749053i \(0.730509\pi\)
\(762\) 0 0
\(763\) −4.41084 + 7.63979i −0.159683 + 0.276579i
\(764\) 0.636945 + 1.10322i 0.0230439 + 0.0399132i
\(765\) 0 0
\(766\) 23.6999 0.856313
\(767\) 10.0707 9.94242i 0.363633 0.359000i
\(768\) 0 0
\(769\) −12.8967 22.3377i −0.465066 0.805519i 0.534138 0.845397i \(-0.320636\pi\)
−0.999205 + 0.0398785i \(0.987303\pi\)
\(770\) −0.245194 0.424688i −0.00883618 0.0153047i
\(771\) 0 0
\(772\) −8.42020 −0.303050
\(773\) −0.0608679 + 0.105426i −0.00218927 + 0.00379192i −0.867118 0.498103i \(-0.834030\pi\)
0.864929 + 0.501895i \(0.167364\pi\)
\(774\) 0 0
\(775\) 25.9407 0.931818
\(776\) 15.2979 26.4968i 0.549163 0.951178i
\(777\) 0 0
\(778\) −0.783503 1.35707i −0.0280899 0.0486532i
\(779\) −7.12656 −0.255336
\(780\) 0 0
\(781\) 3.32486 0.118973
\(782\) −0.0346943 0.0600923i −0.00124067 0.00214890i
\(783\) 0 0
\(784\) 1.55166 2.68755i 0.0554163 0.0959838i
\(785\) −7.27579 −0.259684
\(786\) 0 0
\(787\) 10.1108 17.5124i 0.360410 0.624249i −0.627618 0.778521i \(-0.715970\pi\)
0.988028 + 0.154273i \(0.0493034\pi\)
\(788\) −9.60035 −0.341998
\(789\) 0 0
\(790\) 12.0208 + 20.8207i 0.427682 + 0.740767i
\(791\) −6.00494 10.4009i −0.213511 0.369812i
\(792\) 0 0
\(793\) 14.2345 14.0531i 0.505483 0.499042i
\(794\) 37.7253 1.33882
\(795\) 0 0
\(796\) −4.21342 7.29786i −0.149341 0.258666i
\(797\) 16.2062 28.0700i 0.574054 0.994291i −0.422090 0.906554i \(-0.638703\pi\)
0.996144 0.0877365i \(-0.0279634\pi\)
\(798\) 0 0
\(799\) −1.70915 + 2.96033i −0.0604653 + 0.104729i
\(800\) 3.97810 6.89027i 0.140647 0.243608i
\(801\) 0 0
\(802\) 5.21050 9.02485i 0.183989 0.318679i
\(803\) 1.82021 + 3.15270i 0.0642338 + 0.111256i
\(804\) 0 0
\(805\) −0.0827661 −0.00291712
\(806\) −7.95705 30.4764i −0.280275 1.07349i
\(807\) 0 0
\(808\) −6.17018 10.6871i −0.217066 0.375970i
\(809\) 12.2314 + 21.1855i 0.430035 + 0.744842i 0.996876 0.0789852i \(-0.0251680\pi\)
−0.566841 + 0.823827i \(0.691835\pi\)
\(810\) 0 0
\(811\) −45.2448 −1.58876 −0.794380 0.607421i \(-0.792204\pi\)
−0.794380 + 0.607421i \(0.792204\pi\)
\(812\) 0.0906258 0.156969i 0.00318034 0.00550852i
\(813\) 0 0
\(814\) −0.490388 −0.0171881
\(815\) −5.46384 + 9.46366i −0.191390 + 0.331497i
\(816\) 0 0
\(817\) 5.32127 + 9.21671i 0.186168 + 0.322452i
\(818\) 12.8246 0.448401
\(819\) 0 0
\(820\) −1.28829 −0.0449890
\(821\) 18.3665 + 31.8118i 0.640996 + 1.11024i 0.985211 + 0.171347i \(0.0548120\pi\)
−0.344214 + 0.938891i \(0.611855\pi\)
\(822\) 0 0
\(823\) −21.3238 + 36.9339i −0.743301 + 1.28743i 0.207684 + 0.978196i \(0.433408\pi\)
−0.950984 + 0.309239i \(0.899926\pi\)
\(824\) 12.4495 0.433699
\(825\) 0 0
\(826\) 2.50000 4.33013i 0.0869861 0.150664i
\(827\) 50.0635 1.74088 0.870440 0.492275i \(-0.163834\pi\)
0.870440 + 0.492275i \(0.163834\pi\)
\(828\) 0 0
\(829\) −12.9455 22.4223i −0.449617 0.778759i 0.548744 0.835990i \(-0.315106\pi\)
−0.998361 + 0.0572312i \(0.981773\pi\)
\(830\) 8.37278 + 14.5021i 0.290623 + 0.503374i
\(831\) 0 0
\(832\) −30.8935 8.49056i −1.07104 0.294357i
\(833\) −0.726109 −0.0251582
\(834\) 0 0
\(835\) 9.24384 + 16.0108i 0.319896 + 0.554077i
\(836\) 0.151494 0.262395i 0.00523952 0.00907512i
\(837\) 0 0
\(838\) 6.02548 10.4364i 0.208147 0.360521i
\(839\) −14.4674 + 25.0583i −0.499471 + 0.865109i −1.00000 0.000610619i \(-0.999806\pi\)
0.500529 + 0.865720i \(0.333139\pi\)
\(840\) 0 0
\(841\) 14.3846 24.9148i 0.496019 0.859130i
\(842\) −19.7863 34.2709i −0.681880 1.18105i
\(843\) 0 0
\(844\) −3.78643 −0.130334
\(845\) −12.3285 7.33022i −0.424112 0.252167i
\(846\) 0 0
\(847\) −5.43913 9.42085i −0.186891 0.323704i
\(848\) −8.60825 14.9099i −0.295608 0.512009i
\(849\) 0 0
\(850\) 3.49894 0.120013
\(851\) −0.0413831 + 0.0716776i −0.00141859 + 0.00245708i
\(852\) 0 0
\(853\) 40.3094 1.38017 0.690083 0.723730i \(-0.257574\pi\)
0.690083 + 0.723730i \(0.257574\pi\)
\(854\) 3.53363 6.12043i 0.120918 0.209437i
\(855\) 0 0
\(856\) 9.34317 + 16.1828i 0.319343 + 0.553118i
\(857\) −40.0459 −1.36794 −0.683971 0.729509i \(-0.739749\pi\)
−0.683971 + 0.729509i \(0.739749\pi\)
\(858\) 0 0
\(859\) 6.66659 0.227461 0.113731 0.993512i \(-0.463720\pi\)
0.113731 + 0.993512i \(0.463720\pi\)
\(860\) 0.961941 + 1.66613i 0.0328019 + 0.0568146i
\(861\) 0 0
\(862\) −16.0629 + 27.8217i −0.547104 + 0.947612i
\(863\) 5.85289 0.199235 0.0996174 0.995026i \(-0.468238\pi\)
0.0996174 + 0.995026i \(0.468238\pi\)
\(864\) 0 0
\(865\) −7.56782 + 13.1078i −0.257314 + 0.445680i
\(866\) 4.80245 0.163194
\(867\) 0 0
\(868\) 1.29338 + 2.24019i 0.0439000 + 0.0760371i
\(869\) −2.98410 5.16861i −0.101229 0.175333i
\(870\) 0 0
\(871\) 7.39950 + 28.3409i 0.250723 + 0.960296i
\(872\) 26.7146 0.904672
\(873\) 0 0
\(874\) 0.110001 + 0.190527i 0.00372084 + 0.00644469i
\(875\) 4.84503 8.39184i 0.163792 0.283696i
\(876\) 0 0
\(877\) −2.18367 + 3.78222i −0.0737371 + 0.127716i −0.900536 0.434781i \(-0.856826\pi\)
0.826799 + 0.562497i \(0.190159\pi\)
\(878\) 14.4171 24.9712i 0.486554 0.842737i
\(879\) 0 0
\(880\) −0.597315 + 1.03458i −0.0201355 + 0.0348757i
\(881\) 1.57366 + 2.72567i 0.0530181 + 0.0918300i 0.891316 0.453382i \(-0.149783\pi\)
−0.838298 + 0.545212i \(0.816449\pi\)
\(882\) 0 0
\(883\) 14.9554 0.503289 0.251645 0.967820i \(-0.419029\pi\)
0.251645 + 0.967820i \(0.419029\pi\)
\(884\) 0.249469 + 0.955496i 0.00839056 + 0.0321368i
\(885\) 0 0
\(886\) 2.95756 + 5.12264i 0.0993610 + 0.172098i
\(887\) 11.2632 + 19.5085i 0.378182 + 0.655030i 0.990798 0.135351i \(-0.0432161\pi\)
−0.612616 + 0.790381i \(0.709883\pi\)
\(888\) 0 0
\(889\) 5.85772 0.196462
\(890\) 8.40561 14.5589i 0.281757 0.488017i
\(891\) 0 0
\(892\) 1.93676 0.0648475
\(893\) 5.41899 9.38596i 0.181339 0.314089i
\(894\) 0 0
\(895\) 12.1532 + 21.0500i 0.406237 + 0.703623i
\(896\) −7.11319 −0.237635
\(897\) 0 0
\(898\) −12.0040 −0.400580
\(899\) −1.64762 2.85376i −0.0549512 0.0951782i
\(900\) 0 0
\(901\) −2.01415 + 3.48861i −0.0671010 + 0.116222i
\(902\) −1.37588 −0.0458118
\(903\) 0 0
\(904\) −18.1847 + 31.4969i −0.604815 + 1.04757i
\(905\) −10.4084 −0.345988
\(906\) 0 0
\(907\) 9.32661 + 16.1542i 0.309685 + 0.536390i 0.978293 0.207225i \(-0.0664431\pi\)
−0.668608 + 0.743615i \(0.733110\pi\)
\(908\) 5.46395 + 9.46385i 0.181328 + 0.314069i
\(909\) 0 0
\(910\) −4.88641 1.34295i −0.161983 0.0445183i
\(911\) −18.3278 −0.607226 −0.303613 0.952795i \(-0.598193\pi\)
−0.303613 + 0.952795i \(0.598193\pi\)
\(912\) 0 0
\(913\) −2.07849 3.60005i −0.0687880 0.119144i
\(914\) −8.09955 + 14.0288i −0.267909 + 0.464032i
\(915\) 0 0
\(916\) 0.128134 0.221934i 0.00423366 0.00733292i
\(917\) −11.2027 + 19.4037i −0.369947 + 0.640768i
\(918\) 0 0
\(919\) −7.55272 + 13.0817i −0.249141 + 0.431525i −0.963288 0.268471i \(-0.913482\pi\)
0.714147 + 0.699996i \(0.246815\pi\)
\(920\) 0.125320 + 0.217061i 0.00413168 + 0.00715629i
\(921\) 0 0
\(922\) 37.8668 1.24708
\(923\) 24.4505 24.1389i 0.804797 0.794542i
\(924\) 0 0
\(925\) −2.08675 3.61436i −0.0686119 0.118839i
\(926\) 9.73492 + 16.8614i 0.319909 + 0.554099i
\(927\) 0 0
\(928\) −1.01067 −0.0331770
\(929\) −3.12909 + 5.41974i −0.102662 + 0.177816i −0.912781 0.408450i \(-0.866069\pi\)
0.810119 + 0.586266i \(0.199403\pi\)
\(930\) 0 0
\(931\) 2.30219 0.0754511
\(932\) 3.45182 5.97873i 0.113068 0.195840i
\(933\) 0 0
\(934\) −16.9748 29.4012i −0.555432 0.962036i
\(935\) 0.279518 0.00914121
\(936\) 0 0
\(937\) −22.6610 −0.740301 −0.370151 0.928972i \(-0.620694\pi\)
−0.370151 + 0.928972i \(0.620694\pi\)
\(938\) 5.17445 + 8.96242i 0.168952 + 0.292633i
\(939\) 0 0
\(940\) 0.979605 1.69673i 0.0319512 0.0553411i
\(941\) −17.2944 −0.563783 −0.281891 0.959446i \(-0.590962\pi\)
−0.281891 + 0.959446i \(0.590962\pi\)
\(942\) 0 0
\(943\) −0.116108 + 0.201106i −0.00378101 + 0.00654890i
\(944\) −12.1805 −0.396440
\(945\) 0 0
\(946\) 1.02734 + 1.77941i 0.0334019 + 0.0578537i
\(947\) −13.8061 23.9128i −0.448637 0.777062i 0.549661 0.835388i \(-0.314757\pi\)
−0.998298 + 0.0583263i \(0.981424\pi\)
\(948\) 0 0
\(949\) 36.2746 + 9.96945i 1.17752 + 0.323622i
\(950\) −11.0937 −0.359926
\(951\) 0 0
\(952\) 1.09944 + 1.90428i 0.0356330 + 0.0617181i
\(953\) 2.19540 3.80254i 0.0711160 0.123176i −0.828275 0.560322i \(-0.810677\pi\)
0.899391 + 0.437146i \(0.144011\pi\)
\(954\) 0 0
\(955\) 1.86305 3.22691i 0.0602870 0.104420i
\(956\) 1.02830 1.78106i 0.0332575 0.0576036i
\(957\) 0 0
\(958\) −14.1476 + 24.5044i −0.457089 + 0.791701i
\(959\) −10.1044 17.5013i −0.326287 0.565146i
\(960\) 0 0
\(961\) 16.0283 0.517042
\(962\) −3.60624 + 3.56028i −0.116270 + 0.114788i
\(963\) 0 0
\(964\) −2.91617 5.05096i −0.0939236 0.162680i
\(965\) 12.3145 + 21.3293i 0.396417 + 0.686614i
\(966\) 0 0
\(967\) −18.4875 −0.594517 −0.297258 0.954797i \(-0.596072\pi\)
−0.297258 + 0.954797i \(0.596072\pi\)
\(968\) −16.4713 + 28.5291i −0.529408 + 0.916961i
\(969\) 0 0
\(970\) −14.2002 −0.455941
\(971\) −26.1687 + 45.3255i −0.839794 + 1.45457i 0.0502726 + 0.998736i \(0.483991\pi\)
−0.890067 + 0.455830i \(0.849342\pi\)
\(972\) 0 0
\(973\) 2.13695 + 3.70130i 0.0685073 + 0.118658i
\(974\) −1.23784 −0.0396631
\(975\) 0 0
\(976\) −17.2165 −0.551087
\(977\) 25.8223 + 44.7256i 0.826130 + 1.43090i 0.901053 + 0.433709i \(0.142795\pi\)
−0.0749233 + 0.997189i \(0.523871\pi\)
\(978\) 0 0
\(979\) −2.08664 + 3.61417i −0.0666893 + 0.115509i
\(980\) 0.416173 0.0132941
\(981\) 0 0
\(982\) 17.1560 29.7151i 0.547471 0.948247i
\(983\) −37.5419 −1.19740 −0.598701 0.800973i \(-0.704316\pi\)
−0.598701 + 0.800973i \(0.704316\pi\)
\(984\) 0 0
\(985\) 14.0404 + 24.3187i 0.447365 + 0.774860i
\(986\) −0.222234 0.384921i −0.00707739 0.0122584i
\(987\) 0 0
\(988\) −0.790962 3.02948i −0.0251639 0.0963805i
\(989\) 0.346784 0.0110271
\(990\) 0 0
\(991\) 25.2862 + 43.7969i 0.803242 + 1.39126i 0.917472 + 0.397801i \(0.130227\pi\)
−0.114230 + 0.993454i \(0.536440\pi\)
\(992\) 7.21196 12.4915i 0.228980 0.396605i
\(993\) 0 0
\(994\) 6.06968 10.5130i 0.192519 0.333452i
\(995\) −12.3242 + 21.3461i −0.390703 + 0.676718i
\(996\) 0 0
\(997\) 12.9610 22.4492i 0.410480 0.710972i −0.584462 0.811421i \(-0.698695\pi\)
0.994942 + 0.100449i \(0.0320278\pi\)
\(998\) 13.4547 + 23.3043i 0.425902 + 0.737685i
\(999\) 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 819.2.o.d.757.2 6
3.2 odd 2 273.2.k.d.211.2 yes 6
13.9 even 3 inner 819.2.o.d.568.2 6
39.23 odd 6 3549.2.a.s.1.2 3
39.29 odd 6 3549.2.a.h.1.2 3
39.35 odd 6 273.2.k.d.22.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.k.d.22.2 6 39.35 odd 6
273.2.k.d.211.2 yes 6 3.2 odd 2
819.2.o.d.568.2 6 13.9 even 3 inner
819.2.o.d.757.2 6 1.1 even 1 trivial
3549.2.a.h.1.2 3 39.29 odd 6
3549.2.a.s.1.2 3 39.23 odd 6