Properties

Label 325.2.x.b.7.3
Level $325$
Weight $2$
Character 325.7
Analytic conductor $2.595$
Analytic rank $0$
Dimension $20$
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] = [325,2,Mod(7,325)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(325, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([3, 11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("325.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 325.x (of order \(12\), 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: \(2.59513806569\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(5\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + 1263 x^{4} + 78 x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 7.3
Root \(0.493902i\) of defining polynomial
Character \(\chi\) \(=\) 325.7
Dual form 325.2.x.b.93.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.427732 + 0.246951i) q^{2} +(0.243392 + 0.908353i) q^{3} +(-0.878030 - 1.52079i) q^{4} +(-0.120212 + 0.448637i) q^{6} +(-1.83775 - 3.18307i) q^{7} -1.85513i q^{8} +(1.83221 - 1.05783i) q^{9} +O(q^{10})\) \(q+(0.427732 + 0.246951i) q^{2} +(0.243392 + 0.908353i) q^{3} +(-0.878030 - 1.52079i) q^{4} +(-0.120212 + 0.448637i) q^{6} +(-1.83775 - 3.18307i) q^{7} -1.85513i q^{8} +(1.83221 - 1.05783i) q^{9} +(-0.177987 - 0.664257i) q^{11} +(1.16771 - 1.16771i) q^{12} +(2.92331 - 2.11051i) q^{13} -1.81533i q^{14} +(-1.29794 + 2.24809i) q^{16} +(-2.29359 - 0.614565i) q^{17} +1.04493 q^{18} +(5.29067 + 1.41763i) q^{19} +(2.44406 - 2.44406i) q^{21} +(0.0879082 - 0.328078i) q^{22} +(-1.30811 + 0.350507i) q^{23} +(1.68511 - 0.451523i) q^{24} +(1.77158 - 0.180816i) q^{26} +(3.40171 + 3.40171i) q^{27} +(-3.22719 + 5.58966i) q^{28} +(-8.24134 - 4.75814i) q^{29} +(4.81595 + 4.81595i) q^{31} +(-4.32351 + 2.49618i) q^{32} +(0.560059 - 0.323350i) q^{33} +(-0.829273 - 0.829273i) q^{34} +(-3.21748 - 1.85761i) q^{36} +(0.917615 - 1.58936i) q^{37} +(1.91290 + 1.91290i) q^{38} +(2.62860 + 2.14172i) q^{39} +(-0.534988 + 0.143350i) q^{41} +(1.64896 - 0.441838i) q^{42} +(0.560778 - 2.09285i) q^{43} +(-0.853919 + 0.853919i) q^{44} +(-0.646078 - 0.173116i) q^{46} +3.80918 q^{47} +(-2.35797 - 0.631815i) q^{48} +(-3.25462 + 5.63717i) q^{49} -2.23297i q^{51} +(-5.77640 - 2.59266i) q^{52} +(2.47293 - 2.47293i) q^{53} +(0.614963 + 2.29507i) q^{54} +(-5.90499 + 3.40925i) q^{56} +5.15084i q^{57} +(-2.35005 - 4.07041i) q^{58} +(-2.69310 + 10.0508i) q^{59} +(-3.09904 - 5.36770i) q^{61} +(0.870630 + 3.24924i) q^{62} +(-6.73428 - 3.88804i) q^{63} +2.72601 q^{64} +0.319406 q^{66} +(10.6066 + 6.12371i) q^{67} +(1.07921 + 4.02768i) q^{68} +(-0.636768 - 1.10291i) q^{69} +(-1.73500 + 6.47512i) q^{71} +(-1.96240 - 3.39898i) q^{72} +3.37642i q^{73} +(0.784986 - 0.453212i) q^{74} +(-2.48945 - 9.29074i) q^{76} +(-1.78728 + 1.78728i) q^{77} +(0.595435 + 1.56521i) q^{78} +3.12149i q^{79} +(0.911483 - 1.57873i) q^{81} +(-0.264231 - 0.0708006i) q^{82} -2.13918 q^{83} +(-5.86286 - 1.57095i) q^{84} +(0.756694 - 0.756694i) q^{86} +(2.31619 - 8.64414i) q^{87} +(-1.23228 + 0.330188i) q^{88} +(3.26255 - 0.874198i) q^{89} +(-12.0902 - 5.42653i) q^{91} +(1.68161 + 1.68161i) q^{92} +(-3.20242 + 5.54675i) q^{93} +(1.62931 + 0.940681i) q^{94} +(-3.31972 - 3.31972i) q^{96} +(-6.12606 + 3.53688i) q^{97} +(-2.78421 + 1.60746i) q^{98} +(-1.02878 - 1.02878i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 8 q^{6} + 2 q^{7} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 8 q^{6} + 2 q^{7} + 12 q^{9} - 16 q^{11} + 24 q^{12} + 4 q^{13} - 2 q^{16} - 4 q^{17} - 20 q^{19} + 4 q^{21} - 16 q^{22} + 10 q^{23} + 32 q^{24} - 24 q^{26} - 4 q^{27} - 18 q^{28} - 48 q^{32} - 18 q^{33} + 2 q^{34} + 36 q^{36} + 4 q^{37} + 8 q^{38} + 4 q^{39} + 10 q^{41} - 40 q^{42} - 10 q^{43} - 36 q^{44} + 4 q^{46} + 40 q^{47} + 56 q^{48} + 18 q^{49} + 30 q^{52} + 10 q^{53} - 48 q^{54} - 16 q^{59} - 16 q^{61} + 44 q^{62} + 36 q^{63} + 20 q^{64} - 32 q^{66} - 18 q^{67} - 22 q^{68} - 16 q^{69} - 16 q^{71} - 4 q^{72} + 18 q^{74} - 64 q^{76} + 28 q^{77} - 68 q^{78} - 14 q^{81} - 56 q^{82} - 48 q^{83} - 40 q^{84} + 60 q^{86} + 34 q^{87} - 82 q^{88} - 6 q^{89} + 8 q^{91} + 8 q^{92} - 32 q^{93} - 48 q^{94} + 56 q^{96} - 66 q^{97} + 30 q^{98} + 60 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(301\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{11}{12}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.427732 + 0.246951i 0.302452 + 0.174621i 0.643544 0.765409i \(-0.277463\pi\)
−0.341092 + 0.940030i \(0.610797\pi\)
\(3\) 0.243392 + 0.908353i 0.140523 + 0.524438i 0.999914 + 0.0131191i \(0.00417607\pi\)
−0.859391 + 0.511318i \(0.829157\pi\)
\(4\) −0.878030 1.52079i −0.439015 0.760397i
\(5\) 0 0
\(6\) −0.120212 + 0.448637i −0.0490763 + 0.183155i
\(7\) −1.83775 3.18307i −0.694603 1.20309i −0.970314 0.241847i \(-0.922247\pi\)
0.275712 0.961240i \(-0.411086\pi\)
\(8\) 1.85513i 0.655886i
\(9\) 1.83221 1.05783i 0.610737 0.352609i
\(10\) 0 0
\(11\) −0.177987 0.664257i −0.0536651 0.200281i 0.933888 0.357565i \(-0.116393\pi\)
−0.987553 + 0.157284i \(0.949726\pi\)
\(12\) 1.16771 1.16771i 0.337089 0.337089i
\(13\) 2.92331 2.11051i 0.810781 0.585350i
\(14\) 1.81533i 0.485168i
\(15\) 0 0
\(16\) −1.29794 + 2.24809i −0.324484 + 0.562023i
\(17\) −2.29359 0.614565i −0.556277 0.149054i −0.0302815 0.999541i \(-0.509640\pi\)
−0.525995 + 0.850487i \(0.676307\pi\)
\(18\) 1.04493 0.246291
\(19\) 5.29067 + 1.41763i 1.21376 + 0.325227i 0.808238 0.588857i \(-0.200422\pi\)
0.405526 + 0.914084i \(0.367088\pi\)
\(20\) 0 0
\(21\) 2.44406 2.44406i 0.533337 0.533337i
\(22\) 0.0879082 0.328078i 0.0187421 0.0699464i
\(23\) −1.30811 + 0.350507i −0.272760 + 0.0730858i −0.392606 0.919707i \(-0.628426\pi\)
0.119846 + 0.992792i \(0.461760\pi\)
\(24\) 1.68511 0.451523i 0.343971 0.0921668i
\(25\) 0 0
\(26\) 1.77158 0.180816i 0.347436 0.0354610i
\(27\) 3.40171 + 3.40171i 0.654659 + 0.654659i
\(28\) −3.22719 + 5.58966i −0.609882 + 1.05635i
\(29\) −8.24134 4.75814i −1.53038 0.883564i −0.999344 0.0362142i \(-0.988470\pi\)
−0.531034 0.847350i \(-0.678197\pi\)
\(30\) 0 0
\(31\) 4.81595 + 4.81595i 0.864970 + 0.864970i 0.991910 0.126940i \(-0.0405157\pi\)
−0.126940 + 0.991910i \(0.540516\pi\)
\(32\) −4.32351 + 2.49618i −0.764295 + 0.441266i
\(33\) 0.560059 0.323350i 0.0974937 0.0562880i
\(34\) −0.829273 0.829273i −0.142219 0.142219i
\(35\) 0 0
\(36\) −3.21748 1.85761i −0.536246 0.309602i
\(37\) 0.917615 1.58936i 0.150855 0.261289i −0.780687 0.624922i \(-0.785131\pi\)
0.931542 + 0.363634i \(0.118464\pi\)
\(38\) 1.91290 + 1.91290i 0.310314 + 0.310314i
\(39\) 2.62860 + 2.14172i 0.420912 + 0.342949i
\(40\) 0 0
\(41\) −0.534988 + 0.143350i −0.0835510 + 0.0223874i −0.300352 0.953828i \(-0.597104\pi\)
0.216801 + 0.976216i \(0.430438\pi\)
\(42\) 1.64896 0.441838i 0.254440 0.0681771i
\(43\) 0.560778 2.09285i 0.0855178 0.319157i −0.909894 0.414841i \(-0.863837\pi\)
0.995412 + 0.0956841i \(0.0305039\pi\)
\(44\) −0.853919 + 0.853919i −0.128733 + 0.128733i
\(45\) 0 0
\(46\) −0.646078 0.173116i −0.0952590 0.0255246i
\(47\) 3.80918 0.555626 0.277813 0.960635i \(-0.410390\pi\)
0.277813 + 0.960635i \(0.410390\pi\)
\(48\) −2.35797 0.631815i −0.340343 0.0911947i
\(49\) −3.25462 + 5.63717i −0.464946 + 0.805310i
\(50\) 0 0
\(51\) 2.23297i 0.312678i
\(52\) −5.77640 2.59266i −0.801043 0.359538i
\(53\) 2.47293 2.47293i 0.339683 0.339683i −0.516565 0.856248i \(-0.672789\pi\)
0.856248 + 0.516565i \(0.172789\pi\)
\(54\) 0.614963 + 2.29507i 0.0836858 + 0.312320i
\(55\) 0 0
\(56\) −5.90499 + 3.40925i −0.789088 + 0.455580i
\(57\) 5.15084i 0.682245i
\(58\) −2.35005 4.07041i −0.308577 0.534471i
\(59\) −2.69310 + 10.0508i −0.350612 + 1.30850i 0.535305 + 0.844659i \(0.320197\pi\)
−0.885917 + 0.463844i \(0.846470\pi\)
\(60\) 0 0
\(61\) −3.09904 5.36770i −0.396792 0.687263i 0.596536 0.802586i \(-0.296543\pi\)
−0.993328 + 0.115323i \(0.963210\pi\)
\(62\) 0.870630 + 3.24924i 0.110570 + 0.412653i
\(63\) −6.73428 3.88804i −0.848439 0.489847i
\(64\) 2.72601 0.340751
\(65\) 0 0
\(66\) 0.319406 0.0393162
\(67\) 10.6066 + 6.12371i 1.29580 + 0.748130i 0.979676 0.200588i \(-0.0642852\pi\)
0.316124 + 0.948718i \(0.397619\pi\)
\(68\) 1.07921 + 4.02768i 0.130874 + 0.488428i
\(69\) −0.636768 1.10291i −0.0766579 0.132775i
\(70\) 0 0
\(71\) −1.73500 + 6.47512i −0.205907 + 0.768456i 0.783264 + 0.621689i \(0.213553\pi\)
−0.989171 + 0.146767i \(0.953113\pi\)
\(72\) −1.96240 3.39898i −0.231271 0.400574i
\(73\) 3.37642i 0.395180i 0.980285 + 0.197590i \(0.0633115\pi\)
−0.980285 + 0.197590i \(0.936688\pi\)
\(74\) 0.784986 0.453212i 0.0912528 0.0526848i
\(75\) 0 0
\(76\) −2.48945 9.29074i −0.285559 1.06572i
\(77\) −1.78728 + 1.78728i −0.203680 + 0.203680i
\(78\) 0.595435 + 1.56521i 0.0674198 + 0.177226i
\(79\) 3.12149i 0.351195i 0.984462 + 0.175598i \(0.0561857\pi\)
−0.984462 + 0.175598i \(0.943814\pi\)
\(80\) 0 0
\(81\) 0.911483 1.57873i 0.101276 0.175415i
\(82\) −0.264231 0.0708006i −0.0291795 0.00781862i
\(83\) −2.13918 −0.234805 −0.117403 0.993084i \(-0.537457\pi\)
−0.117403 + 0.993084i \(0.537457\pi\)
\(84\) −5.86286 1.57095i −0.639691 0.171405i
\(85\) 0 0
\(86\) 0.756694 0.756694i 0.0815964 0.0815964i
\(87\) 2.31619 8.64414i 0.248322 0.926749i
\(88\) −1.23228 + 0.330188i −0.131361 + 0.0351982i
\(89\) 3.26255 0.874198i 0.345830 0.0926648i −0.0817233 0.996655i \(-0.526042\pi\)
0.427553 + 0.903990i \(0.359376\pi\)
\(90\) 0 0
\(91\) −12.0902 5.42653i −1.26740 0.568855i
\(92\) 1.68161 + 1.68161i 0.175320 + 0.175320i
\(93\) −3.20242 + 5.54675i −0.332075 + 0.575171i
\(94\) 1.62931 + 0.940681i 0.168050 + 0.0970238i
\(95\) 0 0
\(96\) −3.31972 3.31972i −0.338817 0.338817i
\(97\) −6.12606 + 3.53688i −0.622007 + 0.359116i −0.777650 0.628697i \(-0.783588\pi\)
0.155643 + 0.987813i \(0.450255\pi\)
\(98\) −2.78421 + 1.60746i −0.281248 + 0.162378i
\(99\) −1.02878 1.02878i −0.103396 0.103396i
\(100\) 0 0
\(101\) 12.9641 + 7.48483i 1.28998 + 0.744769i 0.978650 0.205534i \(-0.0658932\pi\)
0.311327 + 0.950303i \(0.399226\pi\)
\(102\) 0.551433 0.955111i 0.0546000 0.0945700i
\(103\) 3.17851 + 3.17851i 0.313188 + 0.313188i 0.846143 0.532956i \(-0.178919\pi\)
−0.532956 + 0.846143i \(0.678919\pi\)
\(104\) −3.91526 5.42311i −0.383923 0.531780i
\(105\) 0 0
\(106\) 1.66844 0.447058i 0.162054 0.0434221i
\(107\) −14.7329 + 3.94767i −1.42428 + 0.381635i −0.887001 0.461767i \(-0.847216\pi\)
−0.537282 + 0.843403i \(0.680549\pi\)
\(108\) 2.18649 8.16010i 0.210395 0.785206i
\(109\) 2.25902 2.25902i 0.216375 0.216375i −0.590594 0.806969i \(-0.701107\pi\)
0.806969 + 0.590594i \(0.201107\pi\)
\(110\) 0 0
\(111\) 1.66704 + 0.446681i 0.158228 + 0.0423971i
\(112\) 9.54111 0.901550
\(113\) 16.0061 + 4.28882i 1.50573 + 0.403458i 0.915014 0.403423i \(-0.132180\pi\)
0.590713 + 0.806881i \(0.298846\pi\)
\(114\) −1.27200 + 2.20318i −0.119134 + 0.206346i
\(115\) 0 0
\(116\) 16.7112i 1.55159i
\(117\) 3.12357 6.95926i 0.288774 0.643384i
\(118\) −3.63398 + 3.63398i −0.334535 + 0.334535i
\(119\) 2.25883 + 8.43007i 0.207067 + 0.772783i
\(120\) 0 0
\(121\) 9.11672 5.26354i 0.828793 0.478504i
\(122\) 3.06124i 0.277152i
\(123\) −0.260424 0.451067i −0.0234816 0.0406714i
\(124\) 3.09551 11.5526i 0.277985 1.03746i
\(125\) 0 0
\(126\) −1.92031 3.32607i −0.171075 0.296310i
\(127\) 2.14812 + 8.01688i 0.190614 + 0.711383i 0.993359 + 0.115059i \(0.0367058\pi\)
−0.802744 + 0.596324i \(0.796628\pi\)
\(128\) 9.81302 + 5.66555i 0.867356 + 0.500768i
\(129\) 2.03754 0.179395
\(130\) 0 0
\(131\) 1.37409 0.120054 0.0600272 0.998197i \(-0.480881\pi\)
0.0600272 + 0.998197i \(0.480881\pi\)
\(132\) −0.983497 0.567822i −0.0856025 0.0494226i
\(133\) −5.21049 19.4458i −0.451807 1.68617i
\(134\) 3.02451 + 5.23861i 0.261278 + 0.452547i
\(135\) 0 0
\(136\) −1.14010 + 4.25489i −0.0977624 + 0.364854i
\(137\) 6.16380 + 10.6760i 0.526609 + 0.912114i 0.999519 + 0.0310029i \(0.00987013\pi\)
−0.472910 + 0.881111i \(0.656797\pi\)
\(138\) 0.629002i 0.0535442i
\(139\) 5.54392 3.20078i 0.470229 0.271487i −0.246107 0.969243i \(-0.579151\pi\)
0.716336 + 0.697756i \(0.245818\pi\)
\(140\) 0 0
\(141\) 0.927126 + 3.46008i 0.0780781 + 0.291391i
\(142\) −2.34115 + 2.34115i −0.196465 + 0.196465i
\(143\) −1.92223 1.56619i −0.160745 0.130971i
\(144\) 5.49197i 0.457664i
\(145\) 0 0
\(146\) −0.833811 + 1.44420i −0.0690067 + 0.119523i
\(147\) −5.91269 1.58430i −0.487670 0.130671i
\(148\) −3.22278 −0.264911
\(149\) −16.2300 4.34882i −1.32961 0.356269i −0.477043 0.878880i \(-0.658291\pi\)
−0.852571 + 0.522611i \(0.824958\pi\)
\(150\) 0 0
\(151\) −3.31542 + 3.31542i −0.269805 + 0.269805i −0.829022 0.559217i \(-0.811102\pi\)
0.559217 + 0.829022i \(0.311102\pi\)
\(152\) 2.62988 9.81486i 0.213312 0.796090i
\(153\) −4.85244 + 1.30021i −0.392297 + 0.105116i
\(154\) −1.20585 + 0.323106i −0.0971699 + 0.0260366i
\(155\) 0 0
\(156\) 0.949120 5.87805i 0.0759904 0.470620i
\(157\) −9.87941 9.87941i −0.788463 0.788463i 0.192779 0.981242i \(-0.438250\pi\)
−0.981242 + 0.192779i \(0.938250\pi\)
\(158\) −0.770855 + 1.33516i −0.0613259 + 0.106220i
\(159\) 2.84819 + 1.64440i 0.225876 + 0.130410i
\(160\) 0 0
\(161\) 3.51966 + 3.51966i 0.277388 + 0.277388i
\(162\) 0.779740 0.450183i 0.0612622 0.0353697i
\(163\) 0.114289 0.0659848i 0.00895180 0.00516833i −0.495517 0.868598i \(-0.665022\pi\)
0.504469 + 0.863430i \(0.331688\pi\)
\(164\) 0.687741 + 0.687741i 0.0537035 + 0.0537035i
\(165\) 0 0
\(166\) −0.914995 0.528272i −0.0710174 0.0410019i
\(167\) 10.8184 18.7380i 0.837152 1.44999i −0.0551149 0.998480i \(-0.517553\pi\)
0.892267 0.451509i \(-0.149114\pi\)
\(168\) −4.53403 4.53403i −0.349808 0.349808i
\(169\) 4.09151 12.3393i 0.314731 0.949181i
\(170\) 0 0
\(171\) 11.1932 2.99922i 0.855969 0.229356i
\(172\) −3.67518 + 0.984760i −0.280230 + 0.0750873i
\(173\) 2.00162 7.47013i 0.152180 0.567943i −0.847150 0.531353i \(-0.821684\pi\)
0.999330 0.0365902i \(-0.0116496\pi\)
\(174\) 3.12539 3.12539i 0.236935 0.236935i
\(175\) 0 0
\(176\) 1.72433 + 0.462032i 0.129976 + 0.0348270i
\(177\) −9.78515 −0.735497
\(178\) 1.61138 + 0.431768i 0.120778 + 0.0323624i
\(179\) 8.17681 14.1627i 0.611164 1.05857i −0.379881 0.925035i \(-0.624035\pi\)
0.991045 0.133531i \(-0.0426317\pi\)
\(180\) 0 0
\(181\) 18.0387i 1.34081i −0.741997 0.670403i \(-0.766121\pi\)
0.741997 0.670403i \(-0.233879\pi\)
\(182\) −3.83127 5.30678i −0.283993 0.393365i
\(183\) 4.12148 4.12148i 0.304668 0.304668i
\(184\) 0.650235 + 2.42671i 0.0479359 + 0.178899i
\(185\) 0 0
\(186\) −2.73955 + 1.58168i −0.200873 + 0.115974i
\(187\) 1.63292i 0.119411i
\(188\) −3.34458 5.79298i −0.243928 0.422496i
\(189\) 4.57640 17.0793i 0.332884 1.24234i
\(190\) 0 0
\(191\) −2.59552 4.49557i −0.187805 0.325288i 0.756713 0.653747i \(-0.226804\pi\)
−0.944518 + 0.328459i \(0.893471\pi\)
\(192\) 0.663490 + 2.47618i 0.0478833 + 0.178703i
\(193\) 8.74813 + 5.05073i 0.629704 + 0.363560i 0.780637 0.624984i \(-0.214895\pi\)
−0.150934 + 0.988544i \(0.548228\pi\)
\(194\) −3.49375 −0.250836
\(195\) 0 0
\(196\) 11.4306 0.816473
\(197\) 11.3137 + 6.53197i 0.806068 + 0.465384i 0.845589 0.533835i \(-0.179250\pi\)
−0.0395205 + 0.999219i \(0.512583\pi\)
\(198\) −0.185983 0.694099i −0.0132173 0.0493275i
\(199\) −3.92506 6.79840i −0.278240 0.481926i 0.692707 0.721219i \(-0.256418\pi\)
−0.970947 + 0.239293i \(0.923084\pi\)
\(200\) 0 0
\(201\) −2.98093 + 11.1250i −0.210258 + 0.784695i
\(202\) 3.69677 + 6.40300i 0.260104 + 0.450513i
\(203\) 34.9770i 2.45491i
\(204\) −3.39588 + 1.96061i −0.237759 + 0.137270i
\(205\) 0 0
\(206\) 0.574613 + 2.14448i 0.0400352 + 0.149413i
\(207\) −2.02596 + 2.02596i −0.140814 + 0.140814i
\(208\) 0.950343 + 9.31118i 0.0658944 + 0.645614i
\(209\) 3.76669i 0.260547i
\(210\) 0 0
\(211\) −6.21205 + 10.7596i −0.427655 + 0.740720i −0.996664 0.0816108i \(-0.973994\pi\)
0.569009 + 0.822331i \(0.307327\pi\)
\(212\) −5.93213 1.58951i −0.407420 0.109168i
\(213\) −6.30398 −0.431942
\(214\) −7.27661 1.94976i −0.497419 0.133283i
\(215\) 0 0
\(216\) 6.31059 6.31059i 0.429382 0.429382i
\(217\) 6.47901 24.1800i 0.439824 1.64145i
\(218\) 1.52412 0.408387i 0.103226 0.0276594i
\(219\) −3.06698 + 0.821796i −0.207248 + 0.0555318i
\(220\) 0 0
\(221\) −8.00192 + 3.04407i −0.538267 + 0.204766i
\(222\) 0.602736 + 0.602736i 0.0404530 + 0.0404530i
\(223\) 4.97247 8.61258i 0.332981 0.576741i −0.650114 0.759837i \(-0.725279\pi\)
0.983095 + 0.183096i \(0.0586120\pi\)
\(224\) 15.8910 + 9.17468i 1.06176 + 0.613009i
\(225\) 0 0
\(226\) 5.78718 + 5.78718i 0.384958 + 0.384958i
\(227\) −12.6490 + 7.30290i −0.839543 + 0.484710i −0.857109 0.515135i \(-0.827742\pi\)
0.0175659 + 0.999846i \(0.494408\pi\)
\(228\) 7.83336 4.52259i 0.518777 0.299516i
\(229\) 15.6183 + 15.6183i 1.03209 + 1.03209i 0.999468 + 0.0326207i \(0.0103853\pi\)
0.0326207 + 0.999468i \(0.489615\pi\)
\(230\) 0 0
\(231\) −2.05849 1.18847i −0.135439 0.0781956i
\(232\) −8.82695 + 15.2887i −0.579517 + 1.00375i
\(233\) −16.5625 16.5625i −1.08505 1.08505i −0.996030 0.0890148i \(-0.971628\pi\)
−0.0890148 0.996030i \(-0.528372\pi\)
\(234\) 3.05465 2.20533i 0.199688 0.144167i
\(235\) 0 0
\(236\) 17.6498 4.72926i 1.14891 0.307848i
\(237\) −2.83541 + 0.759747i −0.184180 + 0.0493509i
\(238\) −1.11564 + 4.16362i −0.0723162 + 0.269888i
\(239\) −14.6022 + 14.6022i −0.944535 + 0.944535i −0.998541 0.0540053i \(-0.982801\pi\)
0.0540053 + 0.998541i \(0.482801\pi\)
\(240\) 0 0
\(241\) 2.99335 + 0.802065i 0.192818 + 0.0516656i 0.353936 0.935270i \(-0.384843\pi\)
−0.161117 + 0.986935i \(0.551510\pi\)
\(242\) 5.19935 0.334227
\(243\) 15.5964 + 4.17903i 1.00051 + 0.268085i
\(244\) −5.44211 + 9.42600i −0.348395 + 0.603438i
\(245\) 0 0
\(246\) 0.257248i 0.0164015i
\(247\) 18.4582 7.02183i 1.17447 0.446788i
\(248\) 8.93419 8.93419i 0.567322 0.567322i
\(249\) −0.520660 1.94313i −0.0329955 0.123141i
\(250\) 0 0
\(251\) −25.5728 + 14.7645i −1.61414 + 0.931925i −0.625745 + 0.780028i \(0.715205\pi\)
−0.988396 + 0.151897i \(0.951462\pi\)
\(252\) 13.6553i 0.860201i
\(253\) 0.465654 + 0.806536i 0.0292754 + 0.0507065i
\(254\) −1.06096 + 3.95955i −0.0665704 + 0.248444i
\(255\) 0 0
\(256\) 0.0722145 + 0.125079i 0.00451341 + 0.00781745i
\(257\) 1.85447 + 6.92097i 0.115679 + 0.431718i 0.999337 0.0364143i \(-0.0115936\pi\)
−0.883658 + 0.468133i \(0.844927\pi\)
\(258\) 0.871519 + 0.503172i 0.0542584 + 0.0313261i
\(259\) −6.74538 −0.419137
\(260\) 0 0
\(261\) −20.1332 −1.24621
\(262\) 0.587740 + 0.339332i 0.0363107 + 0.0209640i
\(263\) 3.48511 + 13.0066i 0.214901 + 0.802023i 0.986201 + 0.165551i \(0.0529402\pi\)
−0.771300 + 0.636472i \(0.780393\pi\)
\(264\) −0.599855 1.03898i −0.0369185 0.0639448i
\(265\) 0 0
\(266\) 2.57347 9.60433i 0.157790 0.588879i
\(267\) 1.58816 + 2.75077i 0.0971938 + 0.168345i
\(268\) 21.5072i 1.31376i
\(269\) −7.01806 + 4.05188i −0.427899 + 0.247047i −0.698451 0.715658i \(-0.746127\pi\)
0.270552 + 0.962705i \(0.412794\pi\)
\(270\) 0 0
\(271\) −2.38026 8.88325i −0.144590 0.539619i −0.999773 0.0212923i \(-0.993222\pi\)
0.855183 0.518326i \(-0.173445\pi\)
\(272\) 4.35853 4.35853i 0.264275 0.264275i
\(273\) 1.98654 12.3029i 0.120231 0.744608i
\(274\) 6.08862i 0.367827i
\(275\) 0 0
\(276\) −1.11820 + 1.93679i −0.0673080 + 0.116581i
\(277\) −24.9641 6.68911i −1.49995 0.401910i −0.586865 0.809685i \(-0.699638\pi\)
−0.913082 + 0.407775i \(0.866305\pi\)
\(278\) 3.16174 0.189629
\(279\) 13.9183 + 3.72939i 0.833266 + 0.223273i
\(280\) 0 0
\(281\) 5.41928 5.41928i 0.323287 0.323287i −0.526740 0.850027i \(-0.676586\pi\)
0.850027 + 0.526740i \(0.176586\pi\)
\(282\) −0.457909 + 1.70894i −0.0272681 + 0.101766i
\(283\) −8.48623 + 2.27388i −0.504454 + 0.135168i −0.502066 0.864829i \(-0.667427\pi\)
−0.00238762 + 0.999997i \(0.500760\pi\)
\(284\) 11.3707 3.04677i 0.674728 0.180793i
\(285\) 0 0
\(286\) −0.435428 1.14460i −0.0257474 0.0676819i
\(287\) 1.43946 + 1.43946i 0.0849688 + 0.0849688i
\(288\) −5.28105 + 9.14705i −0.311189 + 0.538995i
\(289\) −9.83958 5.68088i −0.578799 0.334170i
\(290\) 0 0
\(291\) −4.70377 4.70377i −0.275740 0.275740i
\(292\) 5.13484 2.96460i 0.300494 0.173490i
\(293\) −11.4627 + 6.61798i −0.669657 + 0.386626i −0.795947 0.605367i \(-0.793026\pi\)
0.126290 + 0.991993i \(0.459693\pi\)
\(294\) −2.13780 2.13780i −0.124679 0.124679i
\(295\) 0 0
\(296\) −2.94846 1.70229i −0.171375 0.0989437i
\(297\) 1.65415 2.86507i 0.0959834 0.166248i
\(298\) −5.86814 5.86814i −0.339932 0.339932i
\(299\) −3.08427 + 3.78542i −0.178368 + 0.218916i
\(300\) 0 0
\(301\) −7.69226 + 2.06114i −0.443375 + 0.118802i
\(302\) −2.23685 + 0.599363i −0.128716 + 0.0344895i
\(303\) −3.64350 + 13.5977i −0.209314 + 0.781169i
\(304\) −10.0539 + 10.0539i −0.576632 + 0.576632i
\(305\) 0 0
\(306\) −2.39663 0.642175i −0.137006 0.0367107i
\(307\) 15.4782 0.883389 0.441695 0.897165i \(-0.354377\pi\)
0.441695 + 0.897165i \(0.354377\pi\)
\(308\) 4.28737 + 1.14880i 0.244296 + 0.0654588i
\(309\) −2.11358 + 3.66083i −0.120237 + 0.208257i
\(310\) 0 0
\(311\) 5.34922i 0.303326i −0.988432 0.151663i \(-0.951537\pi\)
0.988432 0.151663i \(-0.0484629\pi\)
\(312\) 3.97315 4.87638i 0.224936 0.276071i
\(313\) −24.3923 + 24.3923i −1.37873 + 1.37873i −0.531967 + 0.846765i \(0.678547\pi\)
−0.846765 + 0.531967i \(0.821453\pi\)
\(314\) −1.78601 6.66547i −0.100790 0.376154i
\(315\) 0 0
\(316\) 4.74714 2.74076i 0.267048 0.154180i
\(317\) 18.9851i 1.06631i 0.846017 + 0.533156i \(0.178994\pi\)
−0.846017 + 0.533156i \(0.821006\pi\)
\(318\) 0.812173 + 1.40673i 0.0455444 + 0.0788852i
\(319\) −1.69378 + 6.32125i −0.0948332 + 0.353922i
\(320\) 0 0
\(321\) −7.17175 12.4218i −0.400288 0.693319i
\(322\) 0.636287 + 2.37466i 0.0354589 + 0.132334i
\(323\) −11.2634 6.50293i −0.626712 0.361832i
\(324\) −3.20124 −0.177847
\(325\) 0 0
\(326\) 0.0651800 0.00360999
\(327\) 2.60181 + 1.50216i 0.143881 + 0.0830695i
\(328\) 0.265931 + 0.992469i 0.0146836 + 0.0548000i
\(329\) −7.00031 12.1249i −0.385940 0.668467i
\(330\) 0 0
\(331\) −1.81607 + 6.77766i −0.0998202 + 0.372534i −0.997706 0.0676941i \(-0.978436\pi\)
0.897886 + 0.440228i \(0.145102\pi\)
\(332\) 1.87826 + 3.25325i 0.103083 + 0.178545i
\(333\) 3.88272i 0.212772i
\(334\) 9.25473 5.34322i 0.506396 0.292368i
\(335\) 0 0
\(336\) 2.32223 + 8.66669i 0.126688 + 0.472807i
\(337\) 1.10195 1.10195i 0.0600271 0.0600271i −0.676456 0.736483i \(-0.736485\pi\)
0.736483 + 0.676456i \(0.236485\pi\)
\(338\) 4.79728 4.26753i 0.260938 0.232123i
\(339\) 15.5830i 0.846355i
\(340\) 0 0
\(341\) 2.34185 4.05620i 0.126818 0.219656i
\(342\) 5.52836 + 1.48132i 0.298940 + 0.0801006i
\(343\) −1.80378 −0.0973947
\(344\) −3.88250 1.04031i −0.209331 0.0560899i
\(345\) 0 0
\(346\) 2.70091 2.70091i 0.145202 0.145202i
\(347\) −6.68561 + 24.9510i −0.358902 + 1.33944i 0.516600 + 0.856227i \(0.327197\pi\)
−0.875502 + 0.483214i \(0.839469\pi\)
\(348\) −15.1796 + 4.06737i −0.813714 + 0.218034i
\(349\) −9.07958 + 2.43287i −0.486019 + 0.130228i −0.493504 0.869744i \(-0.664284\pi\)
0.00748510 + 0.999972i \(0.497617\pi\)
\(350\) 0 0
\(351\) 17.1236 + 2.76492i 0.913989 + 0.147581i
\(352\) 2.42763 + 2.42763i 0.129393 + 0.129393i
\(353\) −1.63274 + 2.82798i −0.0869017 + 0.150518i −0.906200 0.422849i \(-0.861030\pi\)
0.819298 + 0.573368i \(0.194363\pi\)
\(354\) −4.18542 2.41645i −0.222452 0.128433i
\(355\) 0 0
\(356\) −4.19410 4.19410i −0.222287 0.222287i
\(357\) −7.10769 + 4.10363i −0.376179 + 0.217187i
\(358\) 6.99496 4.03854i 0.369695 0.213444i
\(359\) 3.12090 + 3.12090i 0.164715 + 0.164715i 0.784652 0.619937i \(-0.212842\pi\)
−0.619937 + 0.784652i \(0.712842\pi\)
\(360\) 0 0
\(361\) 9.52706 + 5.50045i 0.501424 + 0.289497i
\(362\) 4.45468 7.71573i 0.234133 0.405530i
\(363\) 7.00009 + 7.00009i 0.367410 + 0.367410i
\(364\) 2.36294 + 23.1514i 0.123852 + 1.21346i
\(365\) 0 0
\(366\) 2.78069 0.745084i 0.145349 0.0389461i
\(367\) 24.2349 6.49371i 1.26505 0.338969i 0.436917 0.899502i \(-0.356070\pi\)
0.828132 + 0.560533i \(0.189404\pi\)
\(368\) 0.909872 3.39569i 0.0474303 0.177012i
\(369\) −0.828572 + 0.828572i −0.0431337 + 0.0431337i
\(370\) 0 0
\(371\) −12.4161 3.32690i −0.644614 0.172724i
\(372\) 11.2473 0.583144
\(373\) −11.0372 2.95740i −0.571483 0.153128i −0.0385061 0.999258i \(-0.512260\pi\)
−0.532976 + 0.846130i \(0.678927\pi\)
\(374\) −0.403250 + 0.698450i −0.0208516 + 0.0361160i
\(375\) 0 0
\(376\) 7.06651i 0.364427i
\(377\) −34.1341 + 3.48389i −1.75800 + 0.179429i
\(378\) 6.17523 6.17523i 0.317620 0.317620i
\(379\) 0.520109 + 1.94107i 0.0267162 + 0.0997062i 0.977997 0.208621i \(-0.0668975\pi\)
−0.951280 + 0.308327i \(0.900231\pi\)
\(380\) 0 0
\(381\) −6.75932 + 3.90249i −0.346290 + 0.199931i
\(382\) 2.56386i 0.131179i
\(383\) −13.2258 22.9077i −0.675806 1.17053i −0.976233 0.216725i \(-0.930462\pi\)
0.300427 0.953805i \(-0.402871\pi\)
\(384\) −2.75790 + 10.2926i −0.140739 + 0.525244i
\(385\) 0 0
\(386\) 2.49457 + 4.32072i 0.126970 + 0.219919i
\(387\) −1.18641 4.42775i −0.0603088 0.225075i
\(388\) 10.7577 + 6.21098i 0.546141 + 0.315315i
\(389\) −0.650094 −0.0329611 −0.0164805 0.999864i \(-0.505246\pi\)
−0.0164805 + 0.999864i \(0.505246\pi\)
\(390\) 0 0
\(391\) 3.21568 0.162624
\(392\) 10.4577 + 6.03773i 0.528191 + 0.304951i
\(393\) 0.334442 + 1.24815i 0.0168704 + 0.0629610i
\(394\) 3.22615 + 5.58786i 0.162531 + 0.281512i
\(395\) 0 0
\(396\) −0.661261 + 2.46786i −0.0332296 + 0.124015i
\(397\) −13.5041 23.3897i −0.677750 1.17390i −0.975657 0.219303i \(-0.929622\pi\)
0.297907 0.954595i \(-0.403712\pi\)
\(398\) 3.87719i 0.194346i
\(399\) 16.3955 9.46593i 0.820800 0.473889i
\(400\) 0 0
\(401\) −1.28339 4.78969i −0.0640896 0.239186i 0.926449 0.376421i \(-0.122845\pi\)
−0.990539 + 0.137235i \(0.956179\pi\)
\(402\) −4.02236 + 4.02236i −0.200617 + 0.200617i
\(403\) 24.2426 + 3.91442i 1.20761 + 0.194991i
\(404\) 26.2876i 1.30786i
\(405\) 0 0
\(406\) −8.63761 + 14.9608i −0.428677 + 0.742491i
\(407\) −1.21906 0.326647i −0.0604268 0.0161913i
\(408\) −4.14243 −0.205081
\(409\) 5.83965 + 1.56473i 0.288752 + 0.0773708i 0.400288 0.916390i \(-0.368910\pi\)
−0.111536 + 0.993760i \(0.535577\pi\)
\(410\) 0 0
\(411\) −8.19736 + 8.19736i −0.404346 + 0.404346i
\(412\) 2.04303 7.62468i 0.100653 0.375641i
\(413\) 36.9416 9.89848i 1.81778 0.487073i
\(414\) −1.36688 + 0.366254i −0.0671784 + 0.0180004i
\(415\) 0 0
\(416\) −7.37076 + 16.4219i −0.361381 + 0.805150i
\(417\) 4.25679 + 4.25679i 0.208456 + 0.208456i
\(418\) 0.930187 1.61113i 0.0454969 0.0788030i
\(419\) 4.65114 + 2.68534i 0.227223 + 0.131187i 0.609290 0.792947i \(-0.291454\pi\)
−0.382067 + 0.924135i \(0.624788\pi\)
\(420\) 0 0
\(421\) 14.1377 + 14.1377i 0.689029 + 0.689029i 0.962017 0.272988i \(-0.0880119\pi\)
−0.272988 + 0.962017i \(0.588012\pi\)
\(422\) −5.31418 + 3.06814i −0.258690 + 0.149355i
\(423\) 6.97923 4.02946i 0.339342 0.195919i
\(424\) −4.58760 4.58760i −0.222794 0.222794i
\(425\) 0 0
\(426\) −2.69641 1.55677i −0.130642 0.0754260i
\(427\) −11.3905 + 19.7289i −0.551225 + 0.954750i
\(428\) 18.9395 + 18.9395i 0.915476 + 0.915476i
\(429\) 0.954794 2.12726i 0.0460979 0.102705i
\(430\) 0 0
\(431\) 16.1219 4.31985i 0.776564 0.208080i 0.151295 0.988489i \(-0.451656\pi\)
0.625269 + 0.780409i \(0.284989\pi\)
\(432\) −12.0625 + 3.23215i −0.580360 + 0.155507i
\(433\) 1.96538 7.33490i 0.0944502 0.352493i −0.902485 0.430721i \(-0.858259\pi\)
0.996936 + 0.0782277i \(0.0249261\pi\)
\(434\) 8.74255 8.74255i 0.419656 0.419656i
\(435\) 0 0
\(436\) −5.41899 1.45201i −0.259522 0.0695388i
\(437\) −7.41767 −0.354835
\(438\) −1.51479 0.405886i −0.0723794 0.0193940i
\(439\) 6.84536 11.8565i 0.326711 0.565880i −0.655146 0.755502i \(-0.727393\pi\)
0.981857 + 0.189622i \(0.0607262\pi\)
\(440\) 0 0
\(441\) 13.7713i 0.655777i
\(442\) −4.17441 0.674036i −0.198556 0.0320606i
\(443\) −6.46290 + 6.46290i −0.307062 + 0.307062i −0.843769 0.536707i \(-0.819668\pi\)
0.536707 + 0.843769i \(0.319668\pi\)
\(444\) −0.784399 2.92742i −0.0372259 0.138929i
\(445\) 0 0
\(446\) 4.25377 2.45591i 0.201422 0.116291i
\(447\) 15.8010i 0.747364i
\(448\) −5.00971 8.67708i −0.236687 0.409953i
\(449\) −6.65458 + 24.8352i −0.314049 + 1.17205i 0.610822 + 0.791768i \(0.290839\pi\)
−0.924872 + 0.380280i \(0.875828\pi\)
\(450\) 0 0
\(451\) 0.190442 + 0.329855i 0.00896755 + 0.0155323i
\(452\) −7.53143 28.1077i −0.354249 1.32207i
\(453\) −3.81852 2.20462i −0.179409 0.103582i
\(454\) −7.21383 −0.338562
\(455\) 0 0
\(456\) 9.55545 0.447475
\(457\) 0.716665 + 0.413767i 0.0335242 + 0.0193552i 0.516668 0.856186i \(-0.327172\pi\)
−0.483144 + 0.875541i \(0.660505\pi\)
\(458\) 2.82349 + 10.5374i 0.131933 + 0.492381i
\(459\) −5.71155 9.89269i −0.266592 0.461751i
\(460\) 0 0
\(461\) 6.23219 23.2589i 0.290262 1.08327i −0.654646 0.755936i \(-0.727182\pi\)
0.944908 0.327337i \(-0.106151\pi\)
\(462\) −0.586988 1.01669i −0.0273091 0.0473008i
\(463\) 6.35566i 0.295373i 0.989034 + 0.147686i \(0.0471826\pi\)
−0.989034 + 0.147686i \(0.952817\pi\)
\(464\) 21.3935 12.3515i 0.993167 0.573405i
\(465\) 0 0
\(466\) −2.99418 11.1744i −0.138703 0.517645i
\(467\) 15.6194 15.6194i 0.722781 0.722781i −0.246390 0.969171i \(-0.579244\pi\)
0.969171 + 0.246390i \(0.0792443\pi\)
\(468\) −13.3262 + 1.36013i −0.616003 + 0.0628722i
\(469\) 45.0153i 2.07861i
\(470\) 0 0
\(471\) 6.56942 11.3786i 0.302703 0.524297i
\(472\) 18.6455 + 4.99605i 0.858229 + 0.229962i
\(473\) −1.49000 −0.0685104
\(474\) −1.40042 0.375240i −0.0643232 0.0172354i
\(475\) 0 0
\(476\) 10.8371 10.8371i 0.496716 0.496716i
\(477\) 1.91500 7.14687i 0.0876818 0.327233i
\(478\) −9.85182 + 2.63979i −0.450612 + 0.120741i
\(479\) 9.14111 2.44935i 0.417668 0.111914i −0.0438638 0.999038i \(-0.513967\pi\)
0.461532 + 0.887124i \(0.347300\pi\)
\(480\) 0 0
\(481\) −0.671874 6.58282i −0.0306348 0.300151i
\(482\) 1.08228 + 1.08228i 0.0492964 + 0.0492964i
\(483\) −2.34044 + 4.05375i −0.106494 + 0.184452i
\(484\) −16.0095 9.24310i −0.727705 0.420141i
\(485\) 0 0
\(486\) 5.63904 + 5.63904i 0.255792 + 0.255792i
\(487\) −5.33382 + 3.07948i −0.241698 + 0.139545i −0.615957 0.787780i \(-0.711231\pi\)
0.374259 + 0.927324i \(0.377897\pi\)
\(488\) −9.95775 + 5.74911i −0.450766 + 0.260250i
\(489\) 0.0877545 + 0.0877545i 0.00396840 + 0.00396840i
\(490\) 0 0
\(491\) 12.8290 + 7.40681i 0.578964 + 0.334265i 0.760721 0.649078i \(-0.224845\pi\)
−0.181758 + 0.983343i \(0.558179\pi\)
\(492\) −0.457320 + 0.792102i −0.0206176 + 0.0357107i
\(493\) 15.9781 + 15.9781i 0.719615 + 0.719615i
\(494\) 9.62921 + 1.55481i 0.433238 + 0.0699544i
\(495\) 0 0
\(496\) −17.0775 + 4.57590i −0.766802 + 0.205464i
\(497\) 23.7993 6.37699i 1.06754 0.286047i
\(498\) 0.257155 0.959715i 0.0115234 0.0430059i
\(499\) 21.0529 21.0529i 0.942459 0.942459i −0.0559733 0.998432i \(-0.517826\pi\)
0.998432 + 0.0559733i \(0.0178262\pi\)
\(500\) 0 0
\(501\) 19.6538 + 5.26622i 0.878068 + 0.235278i
\(502\) −14.5844 −0.650933
\(503\) −37.4393 10.0318i −1.66934 0.447297i −0.704404 0.709799i \(-0.748786\pi\)
−0.964932 + 0.262502i \(0.915452\pi\)
\(504\) −7.21280 + 12.4929i −0.321284 + 0.556479i
\(505\) 0 0
\(506\) 0.459974i 0.0204484i
\(507\) 12.2043 + 0.713230i 0.542013 + 0.0316756i
\(508\) 10.3059 10.3059i 0.457250 0.457250i
\(509\) −1.43699 5.36291i −0.0636933 0.237707i 0.926739 0.375706i \(-0.122600\pi\)
−0.990432 + 0.137999i \(0.955933\pi\)
\(510\) 0 0
\(511\) 10.7474 6.20501i 0.475437 0.274493i
\(512\) 22.5909i 0.998384i
\(513\) 13.1750 + 22.8197i 0.581688 + 1.00751i
\(514\) −0.915926 + 3.41828i −0.0403997 + 0.150774i
\(515\) 0 0
\(516\) −1.78902 3.09867i −0.0787572 0.136411i
\(517\) −0.677985 2.53028i −0.0298178 0.111281i
\(518\) −2.88521 1.66578i −0.126769 0.0731900i
\(519\) 7.27269 0.319236
\(520\) 0 0
\(521\) −13.8692 −0.607619 −0.303809 0.952733i \(-0.598259\pi\)
−0.303809 + 0.952733i \(0.598259\pi\)
\(522\) −8.61159 4.97191i −0.376919 0.217614i
\(523\) −8.10818 30.2601i −0.354546 1.32318i −0.881055 0.473014i \(-0.843166\pi\)
0.526509 0.850170i \(-0.323501\pi\)
\(524\) −1.20649 2.08970i −0.0527057 0.0912890i
\(525\) 0 0
\(526\) −1.72130 + 6.42400i −0.0750524 + 0.280100i
\(527\) −8.08609 14.0055i −0.352236 0.610090i
\(528\) 1.67875i 0.0730583i
\(529\) −18.3303 + 10.5830i −0.796969 + 0.460130i
\(530\) 0 0
\(531\) 5.69768 + 21.2640i 0.247258 + 0.922781i
\(532\) −24.9981 + 24.9981i −1.08381 + 1.08381i
\(533\) −1.26140 + 1.54815i −0.0546371 + 0.0670579i
\(534\) 1.56879i 0.0678882i
\(535\) 0 0
\(536\) 11.3602 19.6765i 0.490688 0.849897i
\(537\) 14.8549 + 3.98035i 0.641035 + 0.171765i
\(538\) −4.00246 −0.172558
\(539\) 4.32381 + 1.15856i 0.186240 + 0.0499028i
\(540\) 0 0
\(541\) −10.7732 + 10.7732i −0.463175 + 0.463175i −0.899695 0.436520i \(-0.856211\pi\)
0.436520 + 0.899695i \(0.356211\pi\)
\(542\) 1.17561 4.38745i 0.0504969 0.188457i
\(543\) 16.3855 4.39048i 0.703170 0.188414i
\(544\) 11.4504 3.06813i 0.490932 0.131545i
\(545\) 0 0
\(546\) 3.88793 4.77178i 0.166388 0.204213i
\(547\) −14.2704 14.2704i −0.610159 0.610159i 0.332828 0.942987i \(-0.391997\pi\)
−0.942987 + 0.332828i \(0.891997\pi\)
\(548\) 10.8240 18.7477i 0.462379 0.800863i
\(549\) −11.3562 6.55650i −0.484671 0.279825i
\(550\) 0 0
\(551\) −36.8569 36.8569i −1.57016 1.57016i
\(552\) −2.04605 + 1.18128i −0.0870855 + 0.0502788i
\(553\) 9.93592 5.73651i 0.422518 0.243941i
\(554\) −9.02605 9.02605i −0.383480 0.383480i
\(555\) 0 0
\(556\) −9.73546 5.62077i −0.412875 0.238374i
\(557\) 8.35584 14.4727i 0.354048 0.613229i −0.632906 0.774228i \(-0.718138\pi\)
0.986955 + 0.160999i \(0.0514716\pi\)
\(558\) 5.03231 + 5.03231i 0.213035 + 0.213035i
\(559\) −2.77765 7.30159i −0.117482 0.308824i
\(560\) 0 0
\(561\) −1.48326 + 0.397439i −0.0626234 + 0.0167799i
\(562\) 3.65629 0.979701i 0.154231 0.0413262i
\(563\) 5.84179 21.8019i 0.246202 0.918839i −0.726573 0.687089i \(-0.758888\pi\)
0.972775 0.231750i \(-0.0744452\pi\)
\(564\) 4.44802 4.44802i 0.187296 0.187296i
\(565\) 0 0
\(566\) −4.19136 1.12307i −0.176176 0.0472063i
\(567\) −6.70030 −0.281386
\(568\) 12.0122 + 3.21865i 0.504019 + 0.135052i
\(569\) 2.86843 4.96826i 0.120251 0.208280i −0.799616 0.600512i \(-0.794963\pi\)
0.919866 + 0.392232i \(0.128297\pi\)
\(570\) 0 0
\(571\) 46.5634i 1.94862i 0.225214 + 0.974309i \(0.427692\pi\)
−0.225214 + 0.974309i \(0.572308\pi\)
\(572\) −0.694069 + 4.29848i −0.0290205 + 0.179728i
\(573\) 3.45183 3.45183i 0.144202 0.144202i
\(574\) 0.260227 + 0.971181i 0.0108617 + 0.0405363i
\(575\) 0 0
\(576\) 4.99463 2.88365i 0.208109 0.120152i
\(577\) 28.9429i 1.20491i 0.798153 + 0.602455i \(0.205811\pi\)
−0.798153 + 0.602455i \(0.794189\pi\)
\(578\) −2.80580 4.85978i −0.116706 0.202140i
\(579\) −2.45862 + 9.17569i −0.102177 + 0.381329i
\(580\) 0 0
\(581\) 3.93127 + 6.80916i 0.163097 + 0.282491i
\(582\) −0.850351 3.17355i −0.0352482 0.131548i
\(583\) −2.08281 1.20251i −0.0862613 0.0498030i
\(584\) 6.26369 0.259193
\(585\) 0 0
\(586\) −6.53726 −0.270052
\(587\) −17.0534 9.84577i −0.703868 0.406379i 0.104918 0.994481i \(-0.466542\pi\)
−0.808787 + 0.588102i \(0.799875\pi\)
\(588\) 2.78213 + 10.3830i 0.114733 + 0.428189i
\(589\) 18.6524 + 32.3069i 0.768558 + 1.33118i
\(590\) 0 0
\(591\) −3.17966 + 11.8667i −0.130794 + 0.488129i
\(592\) 2.38201 + 4.12577i 0.0979001 + 0.169568i
\(593\) 21.8216i 0.896106i −0.894007 0.448053i \(-0.852118\pi\)
0.894007 0.448053i \(-0.147882\pi\)
\(594\) 1.41506 0.816987i 0.0580607 0.0335214i
\(595\) 0 0
\(596\) 7.63679 + 28.5009i 0.312815 + 1.16744i
\(597\) 5.22002 5.22002i 0.213641 0.213641i
\(598\) −2.25405 + 0.857481i −0.0921750 + 0.0350650i
\(599\) 37.6041i 1.53646i 0.640172 + 0.768232i \(0.278863\pi\)
−0.640172 + 0.768232i \(0.721137\pi\)
\(600\) 0 0
\(601\) 10.1487 17.5781i 0.413976 0.717027i −0.581344 0.813658i \(-0.697473\pi\)
0.995320 + 0.0966302i \(0.0308064\pi\)
\(602\) −3.79922 1.01800i −0.154845 0.0414905i
\(603\) 25.9113 1.05519
\(604\) 7.95310 + 2.13103i 0.323607 + 0.0867103i
\(605\) 0 0
\(606\) −4.91641 + 4.91641i −0.199716 + 0.199716i
\(607\) −8.91757 + 33.2808i −0.361953 + 1.35083i 0.509552 + 0.860440i \(0.329811\pi\)
−0.871505 + 0.490387i \(0.836856\pi\)
\(608\) −26.4129 + 7.07732i −1.07119 + 0.287023i
\(609\) −31.7715 + 8.51314i −1.28744 + 0.344970i
\(610\) 0 0
\(611\) 11.1354 8.03931i 0.450491 0.325236i
\(612\) 6.23794 + 6.23794i 0.252154 + 0.252154i
\(613\) −12.4332 + 21.5350i −0.502173 + 0.869790i 0.497824 + 0.867278i \(0.334133\pi\)
−0.999997 + 0.00251133i \(0.999201\pi\)
\(614\) 6.62053 + 3.82236i 0.267183 + 0.154258i
\(615\) 0 0
\(616\) 3.31563 + 3.31563i 0.133591 + 0.133591i
\(617\) 24.0895 13.9081i 0.969805 0.559917i 0.0706286 0.997503i \(-0.477499\pi\)
0.899177 + 0.437585i \(0.144166\pi\)
\(618\) −1.80809 + 1.04390i −0.0727321 + 0.0419919i
\(619\) −19.5593 19.5593i −0.786156 0.786156i 0.194705 0.980862i \(-0.437625\pi\)
−0.980862 + 0.194705i \(0.937625\pi\)
\(620\) 0 0
\(621\) −5.64213 3.25749i −0.226411 0.130718i
\(622\) 1.32099 2.28803i 0.0529671 0.0917416i
\(623\) −8.77838 8.77838i −0.351698 0.351698i
\(624\) −8.22653 + 3.12952i −0.329325 + 0.125281i
\(625\) 0 0
\(626\) −16.4570 + 4.40965i −0.657755 + 0.176245i
\(627\) 3.42148 0.916783i 0.136641 0.0366128i
\(628\) −6.35012 + 23.6990i −0.253397 + 0.945692i
\(629\) −3.08139 + 3.08139i −0.122863 + 0.122863i
\(630\) 0 0
\(631\) 12.6187 + 3.38116i 0.502341 + 0.134602i 0.501086 0.865397i \(-0.332934\pi\)
0.00125496 + 0.999999i \(0.499601\pi\)
\(632\) 5.79076 0.230344
\(633\) −11.2855 3.02393i −0.448557 0.120190i
\(634\) −4.68840 + 8.12054i −0.186200 + 0.322508i
\(635\) 0 0
\(636\) 5.77534i 0.229007i
\(637\) 2.38302 + 23.3481i 0.0944186 + 0.925086i
\(638\) −2.28552 + 2.28552i −0.0904846 + 0.0904846i
\(639\) 3.67067 + 13.6991i 0.145210 + 0.541929i
\(640\) 0 0
\(641\) 23.7092 13.6885i 0.936456 0.540663i 0.0476083 0.998866i \(-0.484840\pi\)
0.888848 + 0.458203i \(0.151507\pi\)
\(642\) 7.08428i 0.279594i
\(643\) 15.7510 + 27.2816i 0.621161 + 1.07588i 0.989270 + 0.146099i \(0.0466719\pi\)
−0.368109 + 0.929783i \(0.619995\pi\)
\(644\) 2.26231 8.44305i 0.0891475 0.332703i
\(645\) 0 0
\(646\) −3.21181 5.56301i −0.126367 0.218874i
\(647\) 10.8106 + 40.3457i 0.425008 + 1.58615i 0.763905 + 0.645329i \(0.223280\pi\)
−0.338896 + 0.940824i \(0.610054\pi\)
\(648\) −2.92875 1.69092i −0.115052 0.0664254i
\(649\) 7.15565 0.280884
\(650\) 0 0
\(651\) 23.5409 0.922641
\(652\) −0.200698 0.115873i −0.00785996 0.00453795i
\(653\) 3.93069 + 14.6695i 0.153820 + 0.574064i 0.999204 + 0.0399041i \(0.0127052\pi\)
−0.845384 + 0.534160i \(0.820628\pi\)
\(654\) 0.741918 + 1.28504i 0.0290113 + 0.0502490i
\(655\) 0 0
\(656\) 0.372117 1.38876i 0.0145287 0.0542220i
\(657\) 3.57167 + 6.18632i 0.139344 + 0.241351i
\(658\) 6.91493i 0.269572i
\(659\) −24.6914 + 14.2556i −0.961840 + 0.555319i −0.896739 0.442560i \(-0.854070\pi\)
−0.0651015 + 0.997879i \(0.520737\pi\)
\(660\) 0 0
\(661\) −1.63091 6.08664i −0.0634351 0.236743i 0.926928 0.375240i \(-0.122440\pi\)
−0.990363 + 0.138497i \(0.955773\pi\)
\(662\) −2.45054 + 2.45054i −0.0952430 + 0.0952430i
\(663\) −4.71270 6.52766i −0.183026 0.253513i
\(664\) 3.96845i 0.154006i
\(665\) 0 0
\(666\) 0.958840 1.66076i 0.0371543 0.0643531i
\(667\) 12.4483 + 3.33552i 0.482002 + 0.129152i
\(668\) −37.9955 −1.47009
\(669\) 9.03352 + 2.42052i 0.349256 + 0.0935829i
\(670\) 0 0
\(671\) −3.01394 + 3.01394i −0.116352 + 0.116352i
\(672\) −4.46610 + 16.6677i −0.172283 + 0.642970i
\(673\) 22.1285 5.92931i 0.852991 0.228558i 0.194272 0.980948i \(-0.437765\pi\)
0.658719 + 0.752389i \(0.271099\pi\)
\(674\) 0.743468 0.199212i 0.0286373 0.00767334i
\(675\) 0 0
\(676\) −22.3581 + 4.61199i −0.859926 + 0.177384i
\(677\) 16.1247 + 16.1247i 0.619724 + 0.619724i 0.945461 0.325736i \(-0.105612\pi\)
−0.325736 + 0.945461i \(0.605612\pi\)
\(678\) −3.84825 + 6.66536i −0.147791 + 0.255982i
\(679\) 22.5163 + 12.9998i 0.864096 + 0.498886i
\(680\) 0 0
\(681\) −9.71227 9.71227i −0.372175 0.372175i
\(682\) 2.00337 1.15664i 0.0767129 0.0442902i
\(683\) −27.7544 + 16.0240i −1.06199 + 0.613142i −0.925983 0.377565i \(-0.876761\pi\)
−0.136010 + 0.990707i \(0.543428\pi\)
\(684\) −14.3892 14.3892i −0.550185 0.550185i
\(685\) 0 0
\(686\) −0.771532 0.445444i −0.0294572 0.0170071i
\(687\) −10.3856 + 17.9883i −0.396234 + 0.686298i
\(688\) 3.97707 + 3.97707i 0.151624 + 0.151624i
\(689\) 2.01001 12.4483i 0.0765753 0.474243i
\(690\) 0 0
\(691\) −0.532264 + 0.142620i −0.0202483 + 0.00542551i −0.268929 0.963160i \(-0.586670\pi\)
0.248681 + 0.968586i \(0.420003\pi\)
\(692\) −13.1180 + 3.51496i −0.498672 + 0.133619i
\(693\) −1.38404 + 5.16531i −0.0525754 + 0.196214i
\(694\) −9.02132 + 9.02132i −0.342445 + 0.342445i
\(695\) 0 0
\(696\) −16.0360 4.29682i −0.607842 0.162871i
\(697\) 1.31514 0.0498144
\(698\) −4.48442 1.20160i −0.169738 0.0454811i
\(699\) 11.0134 19.0758i 0.416565 0.721512i
\(700\) 0 0
\(701\) 9.52279i 0.359671i −0.983697 0.179835i \(-0.942443\pi\)
0.983697 0.179835i \(-0.0575565\pi\)
\(702\) 6.64150 + 5.41133i 0.250667 + 0.204237i
\(703\) 7.10792 7.10792i 0.268080 0.268080i
\(704\) −0.485195 1.81077i −0.0182865 0.0682460i
\(705\) 0 0
\(706\) −1.39674 + 0.806411i −0.0525672 + 0.0303497i
\(707\) 55.0209i 2.06927i
\(708\) 8.59166 + 14.8812i 0.322894 + 0.559270i
\(709\) 8.39944 31.3471i 0.315448 1.17727i −0.608124 0.793842i \(-0.708078\pi\)
0.923572 0.383425i \(-0.125255\pi\)
\(710\) 0 0
\(711\) 3.30200 + 5.71923i 0.123835 + 0.214488i
\(712\) −1.62175 6.05244i −0.0607776 0.226825i
\(713\) −7.98782 4.61177i −0.299146 0.172712i
\(714\) −4.05358 −0.151701
\(715\) 0 0
\(716\) −28.7180 −1.07324
\(717\) −16.8180 9.70986i −0.628079 0.362621i
\(718\) 0.564197 + 2.10561i 0.0210557 + 0.0785808i
\(719\) 4.21240 + 7.29608i 0.157096 + 0.272098i 0.933820 0.357743i \(-0.116454\pi\)
−0.776724 + 0.629841i \(0.783120\pi\)
\(720\) 0 0
\(721\) 4.27612 15.9587i 0.159251 0.594333i
\(722\) 2.71668 + 4.70543i 0.101104 + 0.175118i
\(723\) 2.91423i 0.108381i
\(724\) −27.4332 + 15.8385i −1.01955 + 0.588635i
\(725\) 0 0
\(726\) 1.26548 + 4.72284i 0.0469664 + 0.175281i
\(727\) 8.33682 8.33682i 0.309195 0.309195i −0.535402 0.844597i \(-0.679840\pi\)
0.844597 + 0.535402i \(0.179840\pi\)
\(728\) −10.0669 + 22.4288i −0.373104 + 0.831268i
\(729\) 9.71523i 0.359824i
\(730\) 0 0
\(731\) −2.57239 + 4.45551i −0.0951432 + 0.164793i
\(732\) −9.88670 2.64913i −0.365423 0.0979148i
\(733\) 18.6238 0.687887 0.343944 0.938990i \(-0.388237\pi\)
0.343944 + 0.938990i \(0.388237\pi\)
\(734\) 11.9696 + 3.20725i 0.441807 + 0.118382i
\(735\) 0 0
\(736\) 4.78070 4.78070i 0.176219 0.176219i
\(737\) 2.17988 8.13543i 0.0802970 0.299672i
\(738\) −0.559023 + 0.149790i −0.0205779 + 0.00551383i
\(739\) −31.8740 + 8.54061i −1.17250 + 0.314171i −0.791949 0.610587i \(-0.790934\pi\)
−0.380555 + 0.924758i \(0.624267\pi\)
\(740\) 0 0
\(741\) 10.8709 + 15.0575i 0.399352 + 0.553151i
\(742\) −4.48920 4.48920i −0.164804 0.164804i
\(743\) 18.7850 32.5366i 0.689155 1.19365i −0.282957 0.959133i \(-0.591315\pi\)
0.972112 0.234518i \(-0.0753512\pi\)
\(744\) 10.2899 + 5.94088i 0.377246 + 0.217803i
\(745\) 0 0
\(746\) −3.99061 3.99061i −0.146107 0.146107i
\(747\) −3.91943 + 2.26288i −0.143404 + 0.0827946i
\(748\) 2.48333 1.43375i 0.0907995 0.0524231i
\(749\) 39.6410 + 39.6410i 1.44845 + 1.44845i
\(750\) 0 0
\(751\) −29.1051 16.8038i −1.06206 0.613181i −0.136059 0.990701i \(-0.543444\pi\)
−0.926001 + 0.377520i \(0.876777\pi\)
\(752\) −4.94407 + 8.56339i −0.180292 + 0.312275i
\(753\) −19.6356 19.6356i −0.715560 0.715560i
\(754\) −15.4606 6.93928i −0.563041 0.252714i
\(755\) 0 0
\(756\) −29.9924 + 8.03643i −1.09081 + 0.292282i
\(757\) −15.5871 + 4.17654i −0.566521 + 0.151799i −0.530701 0.847559i \(-0.678071\pi\)
−0.0358205 + 0.999358i \(0.511404\pi\)
\(758\) −0.256883 + 0.958699i −0.00933040 + 0.0348215i
\(759\) −0.619282 + 0.619282i −0.0224785 + 0.0224785i
\(760\) 0 0
\(761\) −15.1340 4.05514i −0.548606 0.146999i −0.0261397 0.999658i \(-0.508321\pi\)
−0.522467 + 0.852660i \(0.674988\pi\)
\(762\) −3.85490 −0.139648
\(763\) −11.3421 3.03911i −0.410612 0.110023i
\(764\) −4.55789 + 7.89449i −0.164899 + 0.285613i
\(765\) 0 0
\(766\) 13.0645i 0.472039i
\(767\) 13.3395 + 35.0655i 0.481662 + 1.26614i
\(768\) −0.0960396 + 0.0960396i −0.00346553 + 0.00346553i
\(769\) 8.43930 + 31.4959i 0.304329 + 1.13577i 0.933522 + 0.358521i \(0.116719\pi\)
−0.629193 + 0.777249i \(0.716614\pi\)
\(770\) 0 0
\(771\) −5.83532 + 3.36902i −0.210154 + 0.121332i
\(772\) 17.7388i 0.638433i
\(773\) 11.9531 + 20.7033i 0.429921 + 0.744646i 0.996866 0.0791103i \(-0.0252079\pi\)
−0.566944 + 0.823756i \(0.691875\pi\)
\(774\) 0.585972 2.18688i 0.0210623 0.0786056i
\(775\) 0 0
\(776\) 6.56136 + 11.3646i 0.235539 + 0.407966i
\(777\) −1.64177 6.12718i −0.0588983 0.219811i
\(778\) −0.278066 0.160541i −0.00996914 0.00575569i
\(779\) −3.03366 −0.108692
\(780\) 0 0
\(781\) 4.60995 0.164957
\(782\) 1.37545 + 0.794114i 0.0491858 + 0.0283975i
\(783\) −11.8488 44.2204i −0.423443 1.58031i
\(784\) −8.44858 14.6334i −0.301735 0.522620i
\(785\) 0 0
\(786\) −0.165181 + 0.616466i −0.00589183 + 0.0219886i
\(787\) 7.85572 + 13.6065i 0.280026 + 0.485020i 0.971391 0.237486i \(-0.0763235\pi\)
−0.691365 + 0.722506i \(0.742990\pi\)
\(788\) 22.9411i 0.817242i
\(789\) −10.9664 + 6.33143i −0.390412 + 0.225405i
\(790\) 0 0
\(791\) −15.7635 58.8303i −0.560487 2.09176i
\(792\) −1.90851 + 1.90851i −0.0678161 + 0.0678161i
\(793\) −20.3880 9.15090i −0.724000 0.324958i
\(794\) 13.3394i 0.473397i
\(795\) 0 0
\(796\) −6.89264 + 11.9384i −0.244303 + 0.423146i
\(797\) 30.1666 + 8.08312i 1.06856 + 0.286319i 0.749900 0.661552i \(-0.230102\pi\)
0.318656 + 0.947870i \(0.396768\pi\)
\(798\) 9.35048 0.331003
\(799\) −8.73669 2.34099i −0.309082 0.0828183i
\(800\) 0 0
\(801\) 5.05293 5.05293i 0.178537 0.178537i
\(802\) 0.633871 2.36564i 0.0223827 0.0835336i
\(803\) 2.24281 0.600960i 0.0791471 0.0212074i
\(804\) 19.5361 5.23469i 0.688986 0.184613i
\(805\) 0 0
\(806\) 9.40267 + 7.66106i 0.331195 + 0.269849i
\(807\) −5.38868 5.38868i −0.189690 0.189690i
\(808\) 13.8853 24.0500i 0.488483 0.846078i
\(809\) 11.4546 + 6.61331i 0.402722 + 0.232512i 0.687658 0.726035i \(-0.258639\pi\)
−0.284936 + 0.958547i \(0.591972\pi\)
\(810\) 0 0
\(811\) 22.0736 + 22.0736i 0.775109 + 0.775109i 0.978995 0.203886i \(-0.0653572\pi\)
−0.203886 + 0.978995i \(0.565357\pi\)
\(812\) 53.1928 30.7109i 1.86670 1.07774i
\(813\) 7.48978 4.32423i 0.262678 0.151657i
\(814\) −0.440767 0.440767i −0.0154489 0.0154489i
\(815\) 0 0
\(816\) 5.01991 + 2.89825i 0.175732 + 0.101459i
\(817\) 5.93379 10.2776i 0.207597 0.359568i
\(818\) 2.11139 + 2.11139i 0.0738230 + 0.0738230i
\(819\) −27.8921 + 2.84680i −0.974630 + 0.0994754i
\(820\) 0 0
\(821\) −8.74860 + 2.34418i −0.305328 + 0.0818124i −0.408230 0.912879i \(-0.633854\pi\)
0.102902 + 0.994692i \(0.467187\pi\)
\(822\) −5.53062 + 1.48192i −0.192902 + 0.0516881i
\(823\) −10.8551 + 40.5117i −0.378384 + 1.41215i 0.469953 + 0.882691i \(0.344271\pi\)
−0.848337 + 0.529457i \(0.822396\pi\)
\(824\) 5.89653 5.89653i 0.205415 0.205415i
\(825\) 0 0
\(826\) 18.2455 + 4.88888i 0.634844 + 0.170106i
\(827\) −38.2009 −1.32838 −0.664188 0.747566i \(-0.731222\pi\)
−0.664188 + 0.747566i \(0.731222\pi\)
\(828\) 4.85992 + 1.30221i 0.168894 + 0.0452550i
\(829\) −14.6750 + 25.4178i −0.509682 + 0.882796i 0.490255 + 0.871579i \(0.336904\pi\)
−0.999937 + 0.0112165i \(0.996430\pi\)
\(830\) 0 0
\(831\) 24.3043i 0.843106i
\(832\) 7.96898 5.75327i 0.276275 0.199459i
\(833\) 10.9292 10.9292i 0.378673 0.378673i
\(834\) 0.769545 + 2.87198i 0.0266471 + 0.0994485i
\(835\) 0 0
\(836\) −5.72835 + 3.30726i −0.198119 + 0.114384i
\(837\) 32.7649i 1.13252i
\(838\) 1.32629 + 2.29721i 0.0458161 + 0.0793557i
\(839\) 9.11914 34.0331i 0.314828 1.17495i −0.609322 0.792923i \(-0.708558\pi\)
0.924150 0.382030i \(-0.124775\pi\)
\(840\) 0 0
\(841\) 30.7798 + 53.3122i 1.06137 + 1.83835i
\(842\) 2.55582 + 9.53846i 0.0880795 + 0.328717i
\(843\) 6.24163 + 3.60361i 0.214973 + 0.124115i
\(844\) 21.8175 0.750988
\(845\) 0 0
\(846\) 3.98031 0.136846
\(847\) −33.5084 19.3461i −1.15136 0.664740i
\(848\) 2.34967 + 8.76909i 0.0806880 + 0.301132i
\(849\) −4.13097 7.15504i −0.141774 0.245560i
\(850\) 0 0
\(851\) −0.643261 + 2.40068i −0.0220507 + 0.0822944i
\(852\) 5.53509 + 9.58705i 0.189629 + 0.328447i
\(853\) 17.6392i 0.603954i 0.953315 + 0.301977i \(0.0976465\pi\)
−0.953315 + 0.301977i \(0.902353\pi\)
\(854\) −9.74415 + 5.62579i −0.333438 + 0.192511i
\(855\) 0 0
\(856\) 7.32342 + 27.3314i 0.250309 + 0.934167i
\(857\) −6.30427 + 6.30427i −0.215350 + 0.215350i −0.806535 0.591186i \(-0.798660\pi\)
0.591186 + 0.806535i \(0.298660\pi\)
\(858\) 0.933725 0.674110i 0.0318768 0.0230137i
\(859\) 29.2307i 0.997338i 0.866793 + 0.498669i \(0.166178\pi\)
−0.866793 + 0.498669i \(0.833822\pi\)
\(860\) 0 0
\(861\) −0.957186 + 1.65789i −0.0326208 + 0.0565009i
\(862\) 7.96263 + 2.13358i 0.271208 + 0.0726701i
\(863\) 15.7688 0.536775 0.268387 0.963311i \(-0.413509\pi\)
0.268387 + 0.963311i \(0.413509\pi\)
\(864\) −23.1986 6.21604i −0.789232 0.211474i
\(865\) 0 0
\(866\) 2.65202 2.65202i 0.0901192 0.0901192i
\(867\) 2.76537 10.3205i 0.0939168 0.350502i
\(868\) −42.4615 + 11.3775i −1.44124 + 0.386179i
\(869\) 2.07347 0.555585i 0.0703377 0.0188469i
\(870\) 0 0
\(871\) 43.9305 4.48375i 1.48853 0.151926i
\(872\) −4.19076 4.19076i −0.141917 0.141917i
\(873\) −7.48283 + 12.9606i −0.253255 + 0.438651i
\(874\) −3.17277 1.83180i −0.107321 0.0619616i
\(875\) 0 0
\(876\) 3.94269 + 3.94269i 0.133211 + 0.133211i
\(877\) 38.7309 22.3613i 1.30785 0.755088i 0.326114 0.945331i \(-0.394261\pi\)
0.981737 + 0.190242i \(0.0609274\pi\)
\(878\) 5.85595 3.38094i 0.197629 0.114101i
\(879\) −8.80139 8.80139i −0.296863 0.296863i
\(880\) 0 0
\(881\) −18.0323 10.4110i −0.607525 0.350755i 0.164471 0.986382i \(-0.447408\pi\)
−0.771996 + 0.635627i \(0.780742\pi\)
\(882\) −3.40084 + 5.89043i −0.114512 + 0.198341i
\(883\) −5.33747 5.33747i −0.179620 0.179620i 0.611570 0.791190i \(-0.290538\pi\)
−0.791190 + 0.611570i \(0.790538\pi\)
\(884\) 11.6553 + 9.49648i 0.392011 + 0.319401i
\(885\) 0 0
\(886\) −4.36041 + 1.16837i −0.146491 + 0.0392521i
\(887\) −25.8911 + 6.93749i −0.869337 + 0.232938i −0.665801 0.746129i \(-0.731910\pi\)
−0.203536 + 0.979067i \(0.565243\pi\)
\(888\) 0.828649 3.09256i 0.0278077 0.103780i
\(889\) 21.5706 21.5706i 0.723454 0.723454i
\(890\) 0 0
\(891\) −1.21092 0.324464i −0.0405673 0.0108700i
\(892\) −17.4639 −0.584736
\(893\) 20.1531 + 5.40002i 0.674399 + 0.180705i
\(894\) 3.90208 6.75861i 0.130505 0.226042i
\(895\) 0 0
\(896\) 41.6474i 1.39134i
\(897\) −4.18918 1.88026i −0.139873 0.0627800i
\(898\) −8.97946 + 8.97946i −0.299648 + 0.299648i
\(899\) −16.7749 62.6048i −0.559475 2.08799i
\(900\) 0 0
\(901\) −7.19167 + 4.15211i −0.239589 + 0.138327i
\(902\) 0.188119i 0.00626368i
\(903\) −3.74447 6.48562i −0.124608 0.215828i
\(904\) 7.95630 29.6933i 0.264623 0.987585i
\(905\) 0 0
\(906\) −1.08887 1.88597i −0.0361752 0.0626572i
\(907\) −10.4931 39.1608i −0.348418 1.30031i −0.888568 0.458744i \(-0.848299\pi\)
0.540151 0.841568i \(-0.318367\pi\)
\(908\) 22.2124 + 12.8243i 0.737144 + 0.425590i
\(909\) 31.6707 1.05045
\(910\) 0 0
\(911\) 8.00072 0.265076 0.132538 0.991178i \(-0.457687\pi\)
0.132538 + 0.991178i \(0.457687\pi\)
\(912\) −11.5796 6.68546i −0.383437 0.221378i
\(913\) 0.380746 + 1.42096i 0.0126009 + 0.0470271i
\(914\) 0.204360 + 0.353962i 0.00675963 + 0.0117080i
\(915\) 0 0
\(916\) 10.0389 37.4656i 0.331694 1.23790i
\(917\) −2.52522 4.37381i −0.0833901 0.144436i
\(918\) 5.64189i 0.186210i
\(919\) −1.84237 + 1.06369i −0.0607741 + 0.0350879i −0.530079 0.847948i \(-0.677838\pi\)
0.469305 + 0.883036i \(0.344504\pi\)
\(920\) 0 0
\(921\) 3.76728 + 14.0597i 0.124136 + 0.463283i
\(922\) 8.40950 8.40950i 0.276952 0.276952i
\(923\) 8.59384 + 22.5905i 0.282870 + 0.743577i
\(924\) 4.17405i 0.137316i
\(925\) 0 0
\(926\) −1.56954 + 2.71852i −0.0515782 + 0.0893360i
\(927\) 9.18601 + 2.46138i 0.301708 + 0.0808425i
\(928\) 47.5087 1.55955
\(929\) 19.2515 + 5.15841i 0.631620 + 0.169242i 0.560405 0.828219i \(-0.310646\pi\)
0.0712153 + 0.997461i \(0.477312\pi\)
\(930\) 0 0
\(931\) −25.2106 + 25.2106i −0.826243 + 0.826243i
\(932\) −10.6458 + 39.7305i −0.348713 + 1.30142i
\(933\) 4.85898 1.30196i 0.159076 0.0426242i
\(934\) 10.5382 2.82369i 0.344819 0.0923940i
\(935\) 0 0
\(936\) −12.9103 5.79462i −0.421986 0.189403i
\(937\) −17.2774 17.2774i −0.564427 0.564427i 0.366135 0.930562i \(-0.380681\pi\)
−0.930562 + 0.366135i \(0.880681\pi\)
\(938\) 11.1166 19.2545i 0.362969 0.628680i
\(939\) −28.0937 16.2199i −0.916802 0.529316i
\(940\) 0 0
\(941\) 24.2129 + 24.2129i 0.789319 + 0.789319i 0.981383 0.192063i \(-0.0615179\pi\)
−0.192063 + 0.981383i \(0.561518\pi\)
\(942\) 5.61989 3.24465i 0.183106 0.105716i
\(943\) 0.649578 0.375034i 0.0211532 0.0122128i
\(944\) −19.0996 19.0996i −0.621640 0.621640i
\(945\) 0 0
\(946\) −0.637321 0.367957i −0.0207211 0.0119633i
\(947\) −4.15045 + 7.18880i −0.134872 + 0.233605i −0.925548 0.378629i \(-0.876396\pi\)
0.790677 + 0.612234i \(0.209729\pi\)
\(948\) 3.64500 + 3.64500i 0.118384 + 0.118384i
\(949\) 7.12597 + 9.87034i 0.231319 + 0.320405i
\(950\) 0 0
\(951\) −17.2452 + 4.62084i −0.559214 + 0.149841i
\(952\) 15.6388 4.19041i 0.506857 0.135812i
\(953\) −1.23858 + 4.62244i −0.0401215 + 0.149736i −0.983081 0.183173i \(-0.941363\pi\)
0.942959 + 0.332908i \(0.108030\pi\)
\(954\) 2.58403 2.58403i 0.0836611 0.0836611i
\(955\) 0 0
\(956\) 35.0280 + 9.38573i 1.13289 + 0.303556i
\(957\) −6.15418 −0.198936
\(958\) 4.51481 + 1.20974i 0.145867 + 0.0390849i
\(959\) 22.6550 39.2396i 0.731568 1.26711i
\(960\) 0 0
\(961\) 15.3867i 0.496346i
\(962\) 1.33825 2.98160i 0.0431470 0.0961306i
\(963\) −22.8178 + 22.8178i −0.735294 + 0.735294i
\(964\) −1.40848 5.25650i −0.0453639 0.169301i
\(965\) 0 0
\(966\) −2.00216 + 1.15595i −0.0644183 + 0.0371919i
\(967\) 8.78782i 0.282597i −0.989967 0.141299i \(-0.954872\pi\)
0.989967 0.141299i \(-0.0451278\pi\)
\(968\) −9.76453 16.9127i −0.313844 0.543594i
\(969\) 3.16552 11.8139i 0.101691 0.379517i
\(970\) 0 0
\(971\) 2.71693 + 4.70586i 0.0871905 + 0.151018i 0.906323 0.422587i \(-0.138878\pi\)
−0.819132 + 0.573605i \(0.805544\pi\)
\(972\) −7.33863 27.3881i −0.235387 0.878475i
\(973\) −20.3766 11.7645i −0.653245 0.377151i
\(974\) −3.04192 −0.0974695
\(975\) 0 0
\(976\) 16.0894 0.515010
\(977\) −16.1709 9.33626i −0.517352 0.298693i 0.218499 0.975837i \(-0.429884\pi\)
−0.735851 + 0.677144i \(0.763217\pi\)
\(978\) 0.0158643 + 0.0592064i 0.000507285 + 0.00189321i
\(979\) −1.16138 2.01158i −0.0371180 0.0642903i
\(980\) 0 0
\(981\) 1.74935 6.52865i 0.0558524 0.208444i
\(982\) 3.65824 + 6.33626i 0.116739 + 0.202198i
\(983\) 6.62470i 0.211295i 0.994404 + 0.105648i \(0.0336915\pi\)
−0.994404 + 0.105648i \(0.966308\pi\)
\(984\) −0.836786 + 0.483119i −0.0266758 + 0.0154013i
\(985\) 0 0
\(986\) 2.88852 + 10.7801i 0.0919893 + 0.343309i
\(987\) 9.30986 9.30986i 0.296336 0.296336i
\(988\) −26.8856 21.9057i −0.855346 0.696915i
\(989\) 2.93424i 0.0933033i
\(990\) 0 0
\(991\) 21.6135 37.4357i 0.686576 1.18919i −0.286362 0.958121i \(-0.592446\pi\)
0.972939 0.231064i \(-0.0742206\pi\)
\(992\) −32.8433 8.80033i −1.04277 0.279411i
\(993\) −6.59853 −0.209398
\(994\) 11.7545 + 3.14961i 0.372830 + 0.0998995i
\(995\) 0 0
\(996\) −2.49794 + 2.49794i −0.0791504 + 0.0791504i
\(997\) −11.7001 + 43.6654i −0.370547 + 1.38290i 0.489197 + 0.872173i \(0.337290\pi\)
−0.859744 + 0.510725i \(0.829377\pi\)
\(998\) 14.2040 3.80596i 0.449621 0.120476i
\(999\) 8.52799 2.28507i 0.269814 0.0722963i
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 325.2.x.b.7.3 20
5.2 odd 4 65.2.o.a.33.3 yes 20
5.3 odd 4 325.2.s.b.293.3 20
5.4 even 2 65.2.t.a.7.3 yes 20
13.2 odd 12 325.2.s.b.132.3 20
15.2 even 4 585.2.cf.a.163.3 20
15.14 odd 2 585.2.dp.a.397.3 20
65.2 even 12 65.2.t.a.28.3 yes 20
65.4 even 6 845.2.f.d.437.5 20
65.7 even 12 845.2.f.d.408.6 20
65.9 even 6 845.2.f.e.437.6 20
65.12 odd 4 845.2.o.g.488.3 20
65.17 odd 12 845.2.k.d.268.5 20
65.19 odd 12 845.2.k.e.577.6 20
65.22 odd 12 845.2.k.e.268.6 20
65.24 odd 12 845.2.o.g.587.3 20
65.28 even 12 inner 325.2.x.b.93.3 20
65.29 even 6 845.2.t.f.427.3 20
65.32 even 12 845.2.f.e.408.5 20
65.34 odd 4 845.2.o.f.357.3 20
65.37 even 12 845.2.t.g.418.3 20
65.42 odd 12 845.2.o.e.258.3 20
65.44 odd 4 845.2.o.e.357.3 20
65.47 even 4 845.2.t.e.188.3 20
65.49 even 6 845.2.t.e.427.3 20
65.54 odd 12 65.2.o.a.2.3 20
65.57 even 4 845.2.t.f.188.3 20
65.59 odd 12 845.2.k.d.577.5 20
65.62 odd 12 845.2.o.f.258.3 20
65.64 even 2 845.2.t.g.657.3 20
195.2 odd 12 585.2.dp.a.28.3 20
195.119 even 12 585.2.cf.a.262.3 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.o.a.2.3 20 65.54 odd 12
65.2.o.a.33.3 yes 20 5.2 odd 4
65.2.t.a.7.3 yes 20 5.4 even 2
65.2.t.a.28.3 yes 20 65.2 even 12
325.2.s.b.132.3 20 13.2 odd 12
325.2.s.b.293.3 20 5.3 odd 4
325.2.x.b.7.3 20 1.1 even 1 trivial
325.2.x.b.93.3 20 65.28 even 12 inner
585.2.cf.a.163.3 20 15.2 even 4
585.2.cf.a.262.3 20 195.119 even 12
585.2.dp.a.28.3 20 195.2 odd 12
585.2.dp.a.397.3 20 15.14 odd 2
845.2.f.d.408.6 20 65.7 even 12
845.2.f.d.437.5 20 65.4 even 6
845.2.f.e.408.5 20 65.32 even 12
845.2.f.e.437.6 20 65.9 even 6
845.2.k.d.268.5 20 65.17 odd 12
845.2.k.d.577.5 20 65.59 odd 12
845.2.k.e.268.6 20 65.22 odd 12
845.2.k.e.577.6 20 65.19 odd 12
845.2.o.e.258.3 20 65.42 odd 12
845.2.o.e.357.3 20 65.44 odd 4
845.2.o.f.258.3 20 65.62 odd 12
845.2.o.f.357.3 20 65.34 odd 4
845.2.o.g.488.3 20 65.12 odd 4
845.2.o.g.587.3 20 65.24 odd 12
845.2.t.e.188.3 20 65.47 even 4
845.2.t.e.427.3 20 65.49 even 6
845.2.t.f.188.3 20 65.57 even 4
845.2.t.f.427.3 20 65.29 even 6
845.2.t.g.418.3 20 65.37 even 12
845.2.t.g.657.3 20 65.64 even 2