Properties

Label 825.2.n.k.751.1
Level $825$
Weight $2$
Character 825.751
Analytic conductor $6.588$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [825,2,Mod(301,825)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(825, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("825.301");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.n (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.58765816676\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.13140625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 165)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 751.1
Root \(-0.386111 + 0.280526i\) of defining polynomial
Character \(\chi\) \(=\) 825.751
Dual form 825.2.n.k.301.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.12474 + 0.817172i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.0207616 + 0.0638975i) q^{4} +(1.12474 + 0.817172i) q^{6} +(-0.394797 + 1.21506i) q^{7} +(-0.888090 - 2.73326i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(-1.12474 + 0.817172i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.0207616 + 0.0638975i) q^{4} +(1.12474 + 0.817172i) q^{6} +(-0.394797 + 1.21506i) q^{7} +(-0.888090 - 2.73326i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-1.20381 - 3.09044i) q^{11} +0.0671858 q^{12} +(-1.14748 + 0.833694i) q^{13} +(-0.548870 - 1.68925i) q^{14} +(3.12371 + 2.26951i) q^{16} +(4.04508 + 2.93893i) q^{17} +(0.429613 - 1.32221i) q^{18} +(0.0488697 + 0.150406i) q^{19} +1.27759 q^{21} +(3.87940 + 2.49222i) q^{22} +5.00829 q^{23} +(-2.32505 + 1.68925i) q^{24} +(0.609348 - 1.87538i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-0.0694428 - 0.0504531i) q^{28} +(1.93913 - 5.96802i) q^{29} +(-2.46735 + 1.79264i) q^{31} +0.379898 q^{32} +(-2.56719 + 2.09989i) q^{33} -6.95128 q^{34} +(-0.0207616 - 0.0638975i) q^{36} +(1.45235 - 4.46988i) q^{37} +(-0.177873 - 0.129232i) q^{38} +(1.14748 + 0.833694i) q^{39} +(2.34419 + 7.21469i) q^{41} +(-1.43696 + 1.04401i) q^{42} -5.41324 q^{43} +(0.222465 - 0.0127583i) q^{44} +(-5.63303 + 4.09264i) q^{46} +(2.54386 + 7.82920i) q^{47} +(1.19315 - 3.67214i) q^{48} +(4.34261 + 3.15509i) q^{49} +(1.54508 - 4.75528i) q^{51} +(-0.0294475 - 0.0906300i) q^{52} +(7.57764 - 5.50548i) q^{53} -1.39026 q^{54} +3.67169 q^{56} +(0.127943 - 0.0929558i) q^{57} +(2.69588 + 8.29708i) q^{58} +(2.50256 - 7.70209i) q^{59} +(11.5623 + 8.40047i) q^{61} +(1.31024 - 4.03250i) q^{62} +(-0.394797 - 1.21506i) q^{63} +(-6.67470 + 4.84945i) q^{64} +(1.17144 - 4.45967i) q^{66} +7.38362 q^{67} +(-0.271772 + 0.197454i) q^{68} +(-1.54765 - 4.76317i) q^{69} +(5.48204 + 3.98294i) q^{71} +(2.32505 + 1.68925i) q^{72} +(-2.67642 + 8.23717i) q^{73} +(2.01914 + 6.21429i) q^{74} -0.0106252 q^{76} +(4.23034 - 0.242610i) q^{77} -1.97189 q^{78} +(2.05953 - 1.49634i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-8.53225 - 6.19905i) q^{82} +(8.18897 + 5.94964i) q^{83} +(-0.0265248 + 0.0816349i) q^{84} +(6.08850 - 4.42355i) q^{86} -6.27515 q^{87} +(-7.37788 + 6.03493i) q^{88} +11.0447 q^{89} +(-0.559967 - 1.72340i) q^{91} +(-0.103980 + 0.320017i) q^{92} +(2.46735 + 1.79264i) q^{93} +(-9.25900 - 6.72705i) q^{94} +(-0.117395 - 0.361304i) q^{96} +(5.18739 - 3.76886i) q^{97} -7.46257 q^{98} +(2.79042 + 1.79264i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{3} - 2 q^{4} - q^{7} - 5 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{3} - 2 q^{4} - q^{7} - 5 q^{8} - 2 q^{9} - 3 q^{11} - 18 q^{12} - 6 q^{13} - 10 q^{14} - 20 q^{16} + 10 q^{17} + 5 q^{18} + 6 q^{19} - 4 q^{21} + 25 q^{22} + 10 q^{23} - 20 q^{24} - 8 q^{26} + 2 q^{27} - 31 q^{28} + 3 q^{31} - 60 q^{32} - 2 q^{33} + 50 q^{34} - 2 q^{36} + 19 q^{37} + 28 q^{38} + 6 q^{39} - 25 q^{41} - 15 q^{42} + 4 q^{43} + 7 q^{44} - 6 q^{46} - 15 q^{47} - 5 q^{48} + 21 q^{49} - 10 q^{51} - 6 q^{52} - 7 q^{53} + 10 q^{54} + 20 q^{56} + 9 q^{57} + 2 q^{58} + 35 q^{59} + 21 q^{61} + 19 q^{62} - q^{63} - 77 q^{64} + 25 q^{66} + 26 q^{67} + 35 q^{68} - 5 q^{69} + 25 q^{71} + 20 q^{72} - q^{73} - 29 q^{74} - 14 q^{76} + 61 q^{77} - 12 q^{78} + 30 q^{79} - 2 q^{81} - 57 q^{82} - 11 q^{83} - 34 q^{84} - 34 q^{86} - 10 q^{87} + 85 q^{88} + 32 q^{89} + 37 q^{91} + 10 q^{92} - 3 q^{93} - 39 q^{94} + 10 q^{96} - 5 q^{97} - 50 q^{98} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).

\(n\) \(376\) \(551\) \(727\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.12474 + 0.817172i −0.795312 + 0.577828i −0.909535 0.415627i \(-0.863562\pi\)
0.114223 + 0.993455i \(0.463562\pi\)
\(3\) −0.309017 0.951057i −0.178411 0.549093i
\(4\) −0.0207616 + 0.0638975i −0.0103808 + 0.0319487i
\(5\) 0 0
\(6\) 1.12474 + 0.817172i 0.459174 + 0.333609i
\(7\) −0.394797 + 1.21506i −0.149219 + 0.459250i −0.997529 0.0702498i \(-0.977620\pi\)
0.848310 + 0.529500i \(0.177620\pi\)
\(8\) −0.888090 2.73326i −0.313987 0.966353i
\(9\) −0.809017 + 0.587785i −0.269672 + 0.195928i
\(10\) 0 0
\(11\) −1.20381 3.09044i −0.362964 0.931803i
\(12\) 0.0671858 0.0193949
\(13\) −1.14748 + 0.833694i −0.318254 + 0.231225i −0.735430 0.677601i \(-0.763020\pi\)
0.417176 + 0.908826i \(0.363020\pi\)
\(14\) −0.548870 1.68925i −0.146692 0.451470i
\(15\) 0 0
\(16\) 3.12371 + 2.26951i 0.780927 + 0.567377i
\(17\) 4.04508 + 2.93893i 0.981077 + 0.712794i 0.957949 0.286938i \(-0.0926374\pi\)
0.0231281 + 0.999733i \(0.492637\pi\)
\(18\) 0.429613 1.32221i 0.101261 0.311649i
\(19\) 0.0488697 + 0.150406i 0.0112115 + 0.0345054i 0.956506 0.291713i \(-0.0942254\pi\)
−0.945294 + 0.326219i \(0.894225\pi\)
\(20\) 0 0
\(21\) 1.27759 0.278793
\(22\) 3.87940 + 2.49222i 0.827092 + 0.531344i
\(23\) 5.00829 1.04430 0.522150 0.852853i \(-0.325130\pi\)
0.522150 + 0.852853i \(0.325130\pi\)
\(24\) −2.32505 + 1.68925i −0.474599 + 0.344816i
\(25\) 0 0
\(26\) 0.609348 1.87538i 0.119503 0.367792i
\(27\) 0.809017 + 0.587785i 0.155695 + 0.113119i
\(28\) −0.0694428 0.0504531i −0.0131234 0.00953474i
\(29\) 1.93913 5.96802i 0.360087 1.10823i −0.592914 0.805266i \(-0.702023\pi\)
0.953001 0.302967i \(-0.0979773\pi\)
\(30\) 0 0
\(31\) −2.46735 + 1.79264i −0.443149 + 0.321967i −0.786885 0.617100i \(-0.788308\pi\)
0.343736 + 0.939066i \(0.388308\pi\)
\(32\) 0.379898 0.0671570
\(33\) −2.56719 + 2.09989i −0.446890 + 0.365545i
\(34\) −6.95128 −1.19214
\(35\) 0 0
\(36\) −0.0207616 0.0638975i −0.00346026 0.0106496i
\(37\) 1.45235 4.46988i 0.238765 0.734844i −0.757834 0.652447i \(-0.773742\pi\)
0.996600 0.0823971i \(-0.0262576\pi\)
\(38\) −0.177873 0.129232i −0.0288548 0.0209643i
\(39\) 1.14748 + 0.833694i 0.183744 + 0.133498i
\(40\) 0 0
\(41\) 2.34419 + 7.21469i 0.366101 + 1.12674i 0.949288 + 0.314407i \(0.101806\pi\)
−0.583187 + 0.812338i \(0.698194\pi\)
\(42\) −1.43696 + 1.04401i −0.221728 + 0.161095i
\(43\) −5.41324 −0.825512 −0.412756 0.910842i \(-0.635434\pi\)
−0.412756 + 0.910842i \(0.635434\pi\)
\(44\) 0.222465 0.0127583i 0.0335378 0.00192339i
\(45\) 0 0
\(46\) −5.63303 + 4.09264i −0.830545 + 0.603426i
\(47\) 2.54386 + 7.82920i 0.371060 + 1.14201i 0.946098 + 0.323880i \(0.104987\pi\)
−0.575038 + 0.818127i \(0.695013\pi\)
\(48\) 1.19315 3.67214i 0.172216 0.530027i
\(49\) 4.34261 + 3.15509i 0.620373 + 0.450727i
\(50\) 0 0
\(51\) 1.54508 4.75528i 0.216355 0.665873i
\(52\) −0.0294475 0.0906300i −0.00408363 0.0125681i
\(53\) 7.57764 5.50548i 1.04087 0.756236i 0.0704143 0.997518i \(-0.477568\pi\)
0.970455 + 0.241282i \(0.0775679\pi\)
\(54\) −1.39026 −0.189190
\(55\) 0 0
\(56\) 3.67169 0.490651
\(57\) 0.127943 0.0929558i 0.0169464 0.0123123i
\(58\) 2.69588 + 8.29708i 0.353987 + 1.08946i
\(59\) 2.50256 7.70209i 0.325806 1.00273i −0.645270 0.763955i \(-0.723255\pi\)
0.971076 0.238772i \(-0.0767450\pi\)
\(60\) 0 0
\(61\) 11.5623 + 8.40047i 1.48039 + 1.07557i 0.977429 + 0.211263i \(0.0677576\pi\)
0.502965 + 0.864307i \(0.332242\pi\)
\(62\) 1.31024 4.03250i 0.166401 0.512128i
\(63\) −0.394797 1.21506i −0.0497398 0.153083i
\(64\) −6.67470 + 4.84945i −0.834338 + 0.606182i
\(65\) 0 0
\(66\) 1.17144 4.45967i 0.144195 0.548948i
\(67\) 7.38362 0.902053 0.451026 0.892511i \(-0.351058\pi\)
0.451026 + 0.892511i \(0.351058\pi\)
\(68\) −0.271772 + 0.197454i −0.0329572 + 0.0239448i
\(69\) −1.54765 4.76317i −0.186315 0.573418i
\(70\) 0 0
\(71\) 5.48204 + 3.98294i 0.650599 + 0.472688i 0.863475 0.504391i \(-0.168283\pi\)
−0.212876 + 0.977079i \(0.568283\pi\)
\(72\) 2.32505 + 1.68925i 0.274010 + 0.199080i
\(73\) −2.67642 + 8.23717i −0.313251 + 0.964087i 0.663217 + 0.748427i \(0.269190\pi\)
−0.976468 + 0.215661i \(0.930810\pi\)
\(74\) 2.01914 + 6.21429i 0.234721 + 0.722396i
\(75\) 0 0
\(76\) −0.0106252 −0.00121879
\(77\) 4.23034 0.242610i 0.482092 0.0276480i
\(78\) −1.97189 −0.223273
\(79\) 2.05953 1.49634i 0.231716 0.168351i −0.465869 0.884854i \(-0.654258\pi\)
0.697585 + 0.716502i \(0.254258\pi\)
\(80\) 0 0
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) −8.53225 6.19905i −0.942230 0.684570i
\(83\) 8.18897 + 5.94964i 0.898856 + 0.653057i 0.938172 0.346170i \(-0.112518\pi\)
−0.0393157 + 0.999227i \(0.512518\pi\)
\(84\) −0.0265248 + 0.0816349i −0.00289409 + 0.00890709i
\(85\) 0 0
\(86\) 6.08850 4.42355i 0.656539 0.477004i
\(87\) −6.27515 −0.672766
\(88\) −7.37788 + 6.03493i −0.786485 + 0.643325i
\(89\) 11.0447 1.17073 0.585367 0.810768i \(-0.300950\pi\)
0.585367 + 0.810768i \(0.300950\pi\)
\(90\) 0 0
\(91\) −0.559967 1.72340i −0.0587005 0.180661i
\(92\) −0.103980 + 0.320017i −0.0108407 + 0.0333641i
\(93\) 2.46735 + 1.79264i 0.255852 + 0.185888i
\(94\) −9.25900 6.72705i −0.954993 0.693843i
\(95\) 0 0
\(96\) −0.117395 0.361304i −0.0119816 0.0368754i
\(97\) 5.18739 3.76886i 0.526699 0.382669i −0.292422 0.956289i \(-0.594461\pi\)
0.819122 + 0.573620i \(0.194461\pi\)
\(98\) −7.46257 −0.753833
\(99\) 2.79042 + 1.79264i 0.280448 + 0.180167i
\(100\) 0 0
\(101\) −7.09624 + 5.15572i −0.706102 + 0.513013i −0.881914 0.471411i \(-0.843745\pi\)
0.175812 + 0.984424i \(0.443745\pi\)
\(102\) 2.14807 + 6.61106i 0.212690 + 0.654593i
\(103\) −3.57429 + 11.0005i −0.352185 + 1.08391i 0.605439 + 0.795892i \(0.292998\pi\)
−0.957624 + 0.288022i \(0.907002\pi\)
\(104\) 3.29777 + 2.39597i 0.323373 + 0.234944i
\(105\) 0 0
\(106\) −4.02396 + 12.3845i −0.390842 + 1.20289i
\(107\) −4.74238 14.5955i −0.458463 1.41100i −0.867021 0.498272i \(-0.833968\pi\)
0.408557 0.912733i \(-0.366032\pi\)
\(108\) −0.0543544 + 0.0394908i −0.00523026 + 0.00380001i
\(109\) 14.4004 1.37931 0.689656 0.724137i \(-0.257762\pi\)
0.689656 + 0.724137i \(0.257762\pi\)
\(110\) 0 0
\(111\) −4.69991 −0.446096
\(112\) −3.99082 + 2.89950i −0.377097 + 0.273977i
\(113\) −5.98397 18.4168i −0.562924 1.73250i −0.674039 0.738695i \(-0.735442\pi\)
0.111115 0.993808i \(-0.464558\pi\)
\(114\) −0.0679415 + 0.209102i −0.00636330 + 0.0195842i
\(115\) 0 0
\(116\) 0.341082 + 0.247811i 0.0316687 + 0.0230086i
\(117\) 0.438299 1.34895i 0.0405207 0.124710i
\(118\) 3.47920 + 10.7079i 0.320287 + 0.985741i
\(119\) −5.16796 + 3.75475i −0.473747 + 0.344197i
\(120\) 0 0
\(121\) −8.10166 + 7.44064i −0.736515 + 0.676422i
\(122\) −19.8692 −1.79887
\(123\) 6.13718 4.45892i 0.553371 0.402047i
\(124\) −0.0633189 0.194875i −0.00568620 0.0175003i
\(125\) 0 0
\(126\) 1.43696 + 1.04401i 0.128015 + 0.0930080i
\(127\) −4.87364 3.54091i −0.432466 0.314205i 0.350168 0.936687i \(-0.386124\pi\)
−0.782634 + 0.622482i \(0.786124\pi\)
\(128\) 3.30968 10.1862i 0.292537 0.900337i
\(129\) 1.67278 + 5.14830i 0.147280 + 0.453282i
\(130\) 0 0
\(131\) −18.7278 −1.63626 −0.818130 0.575034i \(-0.804989\pi\)
−0.818130 + 0.575034i \(0.804989\pi\)
\(132\) −0.0808792 0.207634i −0.00703963 0.0180722i
\(133\) −0.202046 −0.0175196
\(134\) −8.30467 + 6.03369i −0.717414 + 0.521232i
\(135\) 0 0
\(136\) 4.44045 13.6663i 0.380765 1.17188i
\(137\) 2.45714 + 1.78521i 0.209927 + 0.152521i 0.687781 0.725918i \(-0.258585\pi\)
−0.477853 + 0.878440i \(0.658585\pi\)
\(138\) 5.63303 + 4.09264i 0.479516 + 0.348388i
\(139\) −0.683520 + 2.10366i −0.0579754 + 0.178430i −0.975851 0.218439i \(-0.929903\pi\)
0.917875 + 0.396869i \(0.129903\pi\)
\(140\) 0 0
\(141\) 6.65992 4.83871i 0.560866 0.407493i
\(142\) −9.42063 −0.790562
\(143\) 3.95784 + 2.54261i 0.330971 + 0.212624i
\(144\) −3.86111 −0.321760
\(145\) 0 0
\(146\) −3.72091 11.4518i −0.307945 0.947756i
\(147\) 1.65873 5.10504i 0.136810 0.421057i
\(148\) 0.255461 + 0.185603i 0.0209988 + 0.0152565i
\(149\) −1.19833 0.870637i −0.0981710 0.0713254i 0.537617 0.843189i \(-0.319325\pi\)
−0.635788 + 0.771864i \(0.719325\pi\)
\(150\) 0 0
\(151\) −2.79165 8.59180i −0.227181 0.699191i −0.998063 0.0622129i \(-0.980184\pi\)
0.770882 0.636978i \(-0.219816\pi\)
\(152\) 0.367697 0.267147i 0.0298242 0.0216685i
\(153\) −5.00000 −0.404226
\(154\) −4.55978 + 3.72979i −0.367438 + 0.300555i
\(155\) 0 0
\(156\) −0.0770945 + 0.0560124i −0.00617250 + 0.00448458i
\(157\) 5.45034 + 16.7744i 0.434985 + 1.33874i 0.893102 + 0.449853i \(0.148524\pi\)
−0.458118 + 0.888891i \(0.651476\pi\)
\(158\) −1.09368 + 3.36599i −0.0870082 + 0.267784i
\(159\) −7.57764 5.50548i −0.600946 0.436613i
\(160\) 0 0
\(161\) −1.97726 + 6.08538i −0.155830 + 0.479595i
\(162\) 0.429613 + 1.32221i 0.0337536 + 0.103883i
\(163\) 19.0152 13.8153i 1.48938 1.08210i 0.515002 0.857189i \(-0.327791\pi\)
0.974379 0.224910i \(-0.0722089\pi\)
\(164\) −0.509669 −0.0397985
\(165\) 0 0
\(166\) −14.0724 −1.09223
\(167\) 0.487619 0.354276i 0.0377331 0.0274147i −0.568759 0.822504i \(-0.692576\pi\)
0.606492 + 0.795090i \(0.292576\pi\)
\(168\) −1.13462 3.49199i −0.0875375 0.269413i
\(169\) −3.39555 + 10.4504i −0.261196 + 0.803880i
\(170\) 0 0
\(171\) −0.127943 0.0929558i −0.00978402 0.00710851i
\(172\) 0.112387 0.345893i 0.00856945 0.0263741i
\(173\) −2.98631 9.19091i −0.227045 0.698772i −0.998078 0.0619764i \(-0.980260\pi\)
0.771033 0.636795i \(-0.219740\pi\)
\(174\) 7.05792 5.12788i 0.535059 0.388743i
\(175\) 0 0
\(176\) 3.25341 12.3857i 0.245235 0.933607i
\(177\) −8.09846 −0.608718
\(178\) −12.4224 + 9.02542i −0.931100 + 0.676484i
\(179\) −0.369495 1.13719i −0.0276174 0.0849975i 0.936298 0.351207i \(-0.114229\pi\)
−0.963915 + 0.266210i \(0.914229\pi\)
\(180\) 0 0
\(181\) −12.5997 9.15421i −0.936527 0.680427i 0.0110551 0.999939i \(-0.496481\pi\)
−0.947582 + 0.319512i \(0.896481\pi\)
\(182\) 2.03813 + 1.48079i 0.151076 + 0.109763i
\(183\) 4.41639 13.5922i 0.326469 1.00477i
\(184\) −4.44781 13.6890i −0.327897 1.00916i
\(185\) 0 0
\(186\) −4.24002 −0.310894
\(187\) 4.21305 16.0390i 0.308089 1.17289i
\(188\) −0.553081 −0.0403376
\(189\) −1.03359 + 0.750949i −0.0751828 + 0.0546235i
\(190\) 0 0
\(191\) 5.68641 17.5010i 0.411454 1.26633i −0.503930 0.863744i \(-0.668113\pi\)
0.915384 0.402581i \(-0.131887\pi\)
\(192\) 6.67470 + 4.84945i 0.481705 + 0.349979i
\(193\) 1.26853 + 0.921640i 0.0913107 + 0.0663411i 0.632504 0.774557i \(-0.282027\pi\)
−0.541193 + 0.840898i \(0.682027\pi\)
\(194\) −2.75466 + 8.47798i −0.197773 + 0.608683i
\(195\) 0 0
\(196\) −0.291762 + 0.211977i −0.0208401 + 0.0151412i
\(197\) −7.97000 −0.567839 −0.283920 0.958848i \(-0.591635\pi\)
−0.283920 + 0.958848i \(0.591635\pi\)
\(198\) −4.60340 + 0.264005i −0.327149 + 0.0187620i
\(199\) 3.53141 0.250335 0.125167 0.992136i \(-0.460053\pi\)
0.125167 + 0.992136i \(0.460053\pi\)
\(200\) 0 0
\(201\) −2.28166 7.02224i −0.160936 0.495311i
\(202\) 3.76832 11.5977i 0.265138 0.816011i
\(203\) 6.48595 + 4.71232i 0.455224 + 0.330740i
\(204\) 0.271772 + 0.197454i 0.0190279 + 0.0138246i
\(205\) 0 0
\(206\) −4.96918 15.2936i −0.346219 1.06555i
\(207\) −4.05179 + 2.94380i −0.281619 + 0.204608i
\(208\) −5.47647 −0.379725
\(209\) 0.405990 0.332090i 0.0280829 0.0229711i
\(210\) 0 0
\(211\) −16.3867 + 11.9056i −1.12810 + 0.819616i −0.985418 0.170152i \(-0.945574\pi\)
−0.142686 + 0.989768i \(0.545574\pi\)
\(212\) 0.194463 + 0.598495i 0.0133558 + 0.0411048i
\(213\) 2.09395 6.44453i 0.143475 0.441572i
\(214\) 17.2610 + 12.5409i 1.17994 + 0.857276i
\(215\) 0 0
\(216\) 0.888090 2.73326i 0.0604269 0.185975i
\(217\) −1.20406 3.70571i −0.0817368 0.251560i
\(218\) −16.1968 + 11.7676i −1.09698 + 0.797005i
\(219\) 8.66107 0.585261
\(220\) 0 0
\(221\) −7.09183 −0.477048
\(222\) 5.28619 3.84064i 0.354786 0.257767i
\(223\) −6.96833 21.4463i −0.466634 1.43615i −0.856916 0.515456i \(-0.827623\pi\)
0.390282 0.920695i \(-0.372377\pi\)
\(224\) −0.149983 + 0.461599i −0.0100211 + 0.0308419i
\(225\) 0 0
\(226\) 21.7801 + 15.8242i 1.44879 + 1.05261i
\(227\) −5.81143 + 17.8857i −0.385718 + 1.18712i 0.550240 + 0.835007i \(0.314536\pi\)
−0.935958 + 0.352112i \(0.885464\pi\)
\(228\) 0.00328335 + 0.0101051i 0.000217445 + 0.000669228i
\(229\) 19.2805 14.0081i 1.27409 0.925681i 0.274732 0.961521i \(-0.411411\pi\)
0.999358 + 0.0358402i \(0.0114107\pi\)
\(230\) 0 0
\(231\) −1.53798 3.94832i −0.101192 0.259780i
\(232\) −18.0343 −1.18401
\(233\) −8.16446 + 5.93183i −0.534871 + 0.388607i −0.822177 0.569232i \(-0.807241\pi\)
0.287305 + 0.957839i \(0.407241\pi\)
\(234\) 0.609348 + 1.87538i 0.0398343 + 0.122597i
\(235\) 0 0
\(236\) 0.440187 + 0.319815i 0.0286538 + 0.0208182i
\(237\) −2.05953 1.49634i −0.133781 0.0971977i
\(238\) 2.74435 8.44624i 0.177890 0.547488i
\(239\) 0.0516759 + 0.159042i 0.00334264 + 0.0102876i 0.952714 0.303869i \(-0.0982784\pi\)
−0.949371 + 0.314156i \(0.898278\pi\)
\(240\) 0 0
\(241\) 0.965256 0.0621776 0.0310888 0.999517i \(-0.490103\pi\)
0.0310888 + 0.999517i \(0.490103\pi\)
\(242\) 3.03199 14.9892i 0.194904 0.963545i
\(243\) −1.00000 −0.0641500
\(244\) −0.776819 + 0.564392i −0.0497307 + 0.0361315i
\(245\) 0 0
\(246\) −3.25903 + 10.0303i −0.207788 + 0.639506i
\(247\) −0.181469 0.131845i −0.0115466 0.00838911i
\(248\) 7.09097 + 5.15189i 0.450277 + 0.327145i
\(249\) 3.12791 9.62671i 0.198223 0.610068i
\(250\) 0 0
\(251\) 19.0201 13.8189i 1.20054 0.872244i 0.206203 0.978509i \(-0.433889\pi\)
0.994338 + 0.106265i \(0.0338893\pi\)
\(252\) 0.0858360 0.00540716
\(253\) −6.02905 15.4778i −0.379043 0.973083i
\(254\) 8.37512 0.525502
\(255\) 0 0
\(256\) −0.497709 1.53179i −0.0311068 0.0957369i
\(257\) 2.03418 6.26055i 0.126888 0.390522i −0.867352 0.497695i \(-0.834180\pi\)
0.994240 + 0.107173i \(0.0341798\pi\)
\(258\) −6.08850 4.42355i −0.379053 0.275398i
\(259\) 4.85780 + 3.52940i 0.301849 + 0.219306i
\(260\) 0 0
\(261\) 1.93913 + 5.96802i 0.120029 + 0.369411i
\(262\) 21.0640 15.3039i 1.30134 0.945477i
\(263\) −12.4538 −0.767936 −0.383968 0.923346i \(-0.625443\pi\)
−0.383968 + 0.923346i \(0.625443\pi\)
\(264\) 8.01945 + 5.15189i 0.493563 + 0.317077i
\(265\) 0 0
\(266\) 0.227249 0.165106i 0.0139335 0.0101233i
\(267\) −3.41300 10.5041i −0.208872 0.642842i
\(268\) −0.153295 + 0.471795i −0.00936401 + 0.0288195i
\(269\) −16.8057 12.2100i −1.02466 0.744459i −0.0574266 0.998350i \(-0.518290\pi\)
−0.967233 + 0.253891i \(0.918290\pi\)
\(270\) 0 0
\(271\) 4.44683 13.6859i 0.270126 0.831362i −0.720342 0.693619i \(-0.756015\pi\)
0.990468 0.137743i \(-0.0439848\pi\)
\(272\) 5.96575 + 18.3607i 0.361727 + 1.11328i
\(273\) −1.46601 + 1.06512i −0.0887271 + 0.0644640i
\(274\) −4.22247 −0.255089
\(275\) 0 0
\(276\) 0.336486 0.0202541
\(277\) −14.1474 + 10.2787i −0.850038 + 0.617589i −0.925156 0.379586i \(-0.876066\pi\)
0.0751187 + 0.997175i \(0.476066\pi\)
\(278\) −0.950268 2.92462i −0.0569933 0.175407i
\(279\) 0.942444 2.90055i 0.0564227 0.173651i
\(280\) 0 0
\(281\) 15.2791 + 11.1009i 0.911474 + 0.662224i 0.941387 0.337328i \(-0.109523\pi\)
−0.0299134 + 0.999552i \(0.509523\pi\)
\(282\) −3.53662 + 10.8846i −0.210603 + 0.648169i
\(283\) 4.19686 + 12.9166i 0.249478 + 0.767813i 0.994868 + 0.101185i \(0.0322633\pi\)
−0.745390 + 0.666629i \(0.767737\pi\)
\(284\) −0.368316 + 0.267597i −0.0218555 + 0.0158790i
\(285\) 0 0
\(286\) −6.52930 + 0.374455i −0.386085 + 0.0221420i
\(287\) −9.69177 −0.572087
\(288\) −0.307344 + 0.223298i −0.0181104 + 0.0131580i
\(289\) 2.47214 + 7.60845i 0.145420 + 0.447556i
\(290\) 0 0
\(291\) −5.18739 3.76886i −0.304090 0.220934i
\(292\) −0.470768 0.342033i −0.0275496 0.0200159i
\(293\) −6.15016 + 18.9282i −0.359296 + 1.10580i 0.594180 + 0.804332i \(0.297477\pi\)
−0.953476 + 0.301468i \(0.902523\pi\)
\(294\) 2.30606 + 7.09732i 0.134492 + 0.413924i
\(295\) 0 0
\(296\) −13.5072 −0.785088
\(297\) 0.842610 3.20780i 0.0488932 0.186136i
\(298\) 2.05927 0.119290
\(299\) −5.74692 + 4.17538i −0.332353 + 0.241469i
\(300\) 0 0
\(301\) 2.13713 6.57742i 0.123182 0.379116i
\(302\) 10.1609 + 7.38230i 0.584692 + 0.424804i
\(303\) 7.09624 + 5.15572i 0.407668 + 0.296188i
\(304\) −0.188692 + 0.580733i −0.0108222 + 0.0333073i
\(305\) 0 0
\(306\) 5.62371 4.08586i 0.321486 0.233573i
\(307\) 14.9354 0.852410 0.426205 0.904627i \(-0.359850\pi\)
0.426205 + 0.904627i \(0.359850\pi\)
\(308\) −0.0723262 + 0.275345i −0.00412117 + 0.0156892i
\(309\) 11.5666 0.658003
\(310\) 0 0
\(311\) −1.54416 4.75243i −0.0875611 0.269485i 0.897683 0.440643i \(-0.145249\pi\)
−0.985244 + 0.171157i \(0.945249\pi\)
\(312\) 1.25964 3.87676i 0.0713128 0.219478i
\(313\) 7.60191 + 5.52311i 0.429685 + 0.312185i 0.781523 0.623876i \(-0.214443\pi\)
−0.351838 + 0.936061i \(0.614443\pi\)
\(314\) −19.8378 14.4130i −1.11951 0.813374i
\(315\) 0 0
\(316\) 0.0528532 + 0.162665i 0.00297322 + 0.00915064i
\(317\) 1.74144 1.26523i 0.0978088 0.0710623i −0.537806 0.843069i \(-0.680747\pi\)
0.635615 + 0.772006i \(0.280747\pi\)
\(318\) 13.0218 0.730227
\(319\) −20.7782 + 1.19163i −1.16335 + 0.0667183i
\(320\) 0 0
\(321\) −12.4157 + 9.02054i −0.692978 + 0.503478i
\(322\) −2.74890 8.46024i −0.153190 0.471471i
\(323\) −0.244349 + 0.752028i −0.0135959 + 0.0418440i
\(324\) 0.0543544 + 0.0394908i 0.00301969 + 0.00219393i
\(325\) 0 0
\(326\) −10.0976 + 31.0773i −0.559256 + 1.72121i
\(327\) −4.44998 13.6956i −0.246084 0.757370i
\(328\) 17.6378 12.8146i 0.973882 0.707567i
\(329\) −10.5173 −0.579836
\(330\) 0 0
\(331\) −19.5116 −1.07245 −0.536227 0.844074i \(-0.680151\pi\)
−0.536227 + 0.844074i \(0.680151\pi\)
\(332\) −0.550182 + 0.399731i −0.0301952 + 0.0219381i
\(333\) 1.45235 + 4.46988i 0.0795885 + 0.244948i
\(334\) −0.258941 + 0.796938i −0.0141686 + 0.0436065i
\(335\) 0 0
\(336\) 3.99082 + 2.89950i 0.217717 + 0.158181i
\(337\) −9.76639 + 30.0579i −0.532009 + 1.63736i 0.218015 + 0.975945i \(0.430042\pi\)
−0.750024 + 0.661410i \(0.769958\pi\)
\(338\) −4.72069 14.5288i −0.256772 0.790262i
\(339\) −15.6662 + 11.3822i −0.850873 + 0.618195i
\(340\) 0 0
\(341\) 8.51027 + 5.46721i 0.460857 + 0.296066i
\(342\) 0.219863 0.0118888
\(343\) −12.7832 + 9.28756i −0.690230 + 0.501481i
\(344\) 4.80744 + 14.7958i 0.259200 + 0.797736i
\(345\) 0 0
\(346\) 10.8694 + 7.89707i 0.584341 + 0.424549i
\(347\) 7.59111 + 5.51527i 0.407512 + 0.296075i 0.772594 0.634900i \(-0.218959\pi\)
−0.365082 + 0.930976i \(0.618959\pi\)
\(348\) 0.130282 0.400966i 0.00698384 0.0214940i
\(349\) −7.66768 23.5987i −0.410441 1.26321i −0.916265 0.400572i \(-0.868812\pi\)
0.505824 0.862637i \(-0.331188\pi\)
\(350\) 0 0
\(351\) −1.41837 −0.0757067
\(352\) −0.457326 1.17405i −0.0243756 0.0625771i
\(353\) 19.4788 1.03675 0.518375 0.855153i \(-0.326537\pi\)
0.518375 + 0.855153i \(0.326537\pi\)
\(354\) 9.10867 6.61784i 0.484121 0.351734i
\(355\) 0 0
\(356\) −0.229305 + 0.705728i −0.0121531 + 0.0374035i
\(357\) 5.16796 + 3.75475i 0.273518 + 0.198722i
\(358\) 1.34487 + 0.977103i 0.0710784 + 0.0516415i
\(359\) 9.19946 28.3130i 0.485529 1.49430i −0.345684 0.938351i \(-0.612353\pi\)
0.831213 0.555954i \(-0.187647\pi\)
\(360\) 0 0
\(361\) 15.3511 11.1532i 0.807952 0.587012i
\(362\) 21.6520 1.13800
\(363\) 9.58002 + 5.40586i 0.502820 + 0.283734i
\(364\) 0.121747 0.00638126
\(365\) 0 0
\(366\) 6.13991 + 18.8967i 0.320938 + 0.987747i
\(367\) 1.98882 6.12097i 0.103816 0.319512i −0.885635 0.464382i \(-0.846276\pi\)
0.989451 + 0.144870i \(0.0462764\pi\)
\(368\) 15.6444 + 11.3663i 0.815523 + 0.592512i
\(369\) −6.13718 4.45892i −0.319489 0.232122i
\(370\) 0 0
\(371\) 3.69786 + 11.3809i 0.191983 + 0.590864i
\(372\) −0.165771 + 0.120440i −0.00859482 + 0.00624451i
\(373\) 20.8924 1.08177 0.540883 0.841098i \(-0.318090\pi\)
0.540883 + 0.841098i \(0.318090\pi\)
\(374\) 8.36806 + 21.4825i 0.432702 + 1.11084i
\(375\) 0 0
\(376\) 19.1401 13.9061i 0.987074 0.717151i
\(377\) 2.75039 + 8.46483i 0.141652 + 0.435961i
\(378\) 0.548870 1.68925i 0.0282308 0.0868855i
\(379\) 11.4873 + 8.34603i 0.590064 + 0.428707i 0.842338 0.538949i \(-0.181178\pi\)
−0.252274 + 0.967656i \(0.581178\pi\)
\(380\) 0 0
\(381\) −1.86157 + 5.72931i −0.0953709 + 0.293521i
\(382\) 7.90557 + 24.3308i 0.404484 + 1.24487i
\(383\) −21.4214 + 15.5635i −1.09458 + 0.795260i −0.980167 0.198173i \(-0.936499\pi\)
−0.114415 + 0.993433i \(0.536499\pi\)
\(384\) −10.7104 −0.546561
\(385\) 0 0
\(386\) −2.17990 −0.110954
\(387\) 4.37940 3.18182i 0.222618 0.161741i
\(388\) 0.133122 + 0.409708i 0.00675826 + 0.0207998i
\(389\) −11.2780 + 34.7102i −0.571819 + 1.75988i 0.0749470 + 0.997188i \(0.476121\pi\)
−0.646766 + 0.762689i \(0.723879\pi\)
\(390\) 0 0
\(391\) 20.2590 + 14.7190i 1.02454 + 0.744372i
\(392\) 4.76705 14.6715i 0.240773 0.741022i
\(393\) 5.78722 + 17.8112i 0.291927 + 0.898458i
\(394\) 8.96419 6.51287i 0.451610 0.328114i
\(395\) 0 0
\(396\) −0.172478 + 0.141083i −0.00866737 + 0.00708969i
\(397\) 8.03969 0.403500 0.201750 0.979437i \(-0.435337\pi\)
0.201750 + 0.979437i \(0.435337\pi\)
\(398\) −3.97192 + 2.88577i −0.199094 + 0.144651i
\(399\) 0.0624355 + 0.192157i 0.00312569 + 0.00961988i
\(400\) 0 0
\(401\) 22.7255 + 16.5110i 1.13486 + 0.824521i 0.986394 0.164397i \(-0.0525679\pi\)
0.148461 + 0.988918i \(0.452568\pi\)
\(402\) 8.30467 + 6.03369i 0.414199 + 0.300933i
\(403\) 1.33673 4.11403i 0.0665873 0.204935i
\(404\) −0.182109 0.560473i −0.00906024 0.0278846i
\(405\) 0 0
\(406\) −11.1458 −0.553156
\(407\) −15.5623 + 0.892497i −0.771393 + 0.0442394i
\(408\) −14.3696 −0.711401
\(409\) 4.83752 3.51466i 0.239200 0.173789i −0.461727 0.887022i \(-0.652770\pi\)
0.700927 + 0.713233i \(0.252770\pi\)
\(410\) 0 0
\(411\) 0.938543 2.88854i 0.0462949 0.142481i
\(412\) −0.628698 0.456776i −0.0309737 0.0225037i
\(413\) 8.37051 + 6.08153i 0.411886 + 0.299253i
\(414\) 2.15163 6.62203i 0.105747 0.325455i
\(415\) 0 0
\(416\) −0.435925 + 0.316718i −0.0213730 + 0.0155284i
\(417\) 2.21192 0.108318
\(418\) −0.185259 + 0.705278i −0.00906131 + 0.0344963i
\(419\) −15.4707 −0.755795 −0.377897 0.925847i \(-0.623353\pi\)
−0.377897 + 0.925847i \(0.623353\pi\)
\(420\) 0 0
\(421\) 10.6841 + 32.8824i 0.520713 + 1.60259i 0.772640 + 0.634844i \(0.218936\pi\)
−0.251927 + 0.967746i \(0.581064\pi\)
\(422\) 8.70182 26.7815i 0.423598 1.30370i
\(423\) −6.65992 4.83871i −0.323816 0.235266i
\(424\) −21.7775 15.8223i −1.05761 0.768399i
\(425\) 0 0
\(426\) 2.91113 + 8.95955i 0.141045 + 0.434092i
\(427\) −14.7718 + 10.7324i −0.714859 + 0.519375i
\(428\) 1.03108 0.0498390
\(429\) 1.19513 4.54984i 0.0577013 0.219668i
\(430\) 0 0
\(431\) −2.71871 + 1.97526i −0.130956 + 0.0951450i −0.651335 0.758790i \(-0.725791\pi\)
0.520379 + 0.853935i \(0.325791\pi\)
\(432\) 1.19315 + 3.67214i 0.0574055 + 0.176676i
\(433\) −1.13650 + 3.49779i −0.0546167 + 0.168093i −0.974644 0.223761i \(-0.928166\pi\)
0.920027 + 0.391855i \(0.128166\pi\)
\(434\) 4.38246 + 3.18404i 0.210365 + 0.152839i
\(435\) 0 0
\(436\) −0.298975 + 0.920152i −0.0143183 + 0.0440673i
\(437\) 0.244754 + 0.753275i 0.0117082 + 0.0360340i
\(438\) −9.74146 + 7.07759i −0.465465 + 0.338180i
\(439\) −1.55432 −0.0741835 −0.0370917 0.999312i \(-0.511809\pi\)
−0.0370917 + 0.999312i \(0.511809\pi\)
\(440\) 0 0
\(441\) −5.36776 −0.255608
\(442\) 7.97647 5.79524i 0.379402 0.275652i
\(443\) −6.55298 20.1680i −0.311342 0.958211i −0.977234 0.212163i \(-0.931949\pi\)
0.665893 0.746047i \(-0.268051\pi\)
\(444\) 0.0975775 0.300313i 0.00463082 0.0142522i
\(445\) 0 0
\(446\) 25.3629 + 18.4272i 1.20097 + 0.872555i
\(447\) −0.457721 + 1.40872i −0.0216495 + 0.0666302i
\(448\) −3.25723 10.0247i −0.153890 0.473624i
\(449\) −12.2247 + 8.88179i −0.576921 + 0.419157i −0.837613 0.546265i \(-0.816049\pi\)
0.260692 + 0.965422i \(0.416049\pi\)
\(450\) 0 0
\(451\) 19.4746 15.9297i 0.917023 0.750102i
\(452\) 1.30102 0.0611949
\(453\) −7.30862 + 5.31002i −0.343389 + 0.249487i
\(454\) −8.07938 24.8658i −0.379184 1.16701i
\(455\) 0 0
\(456\) −0.367697 0.267147i −0.0172190 0.0125103i
\(457\) 33.4158 + 24.2780i 1.56312 + 1.13568i 0.933389 + 0.358866i \(0.116837\pi\)
0.629735 + 0.776810i \(0.283163\pi\)
\(458\) −10.2385 + 31.5110i −0.478415 + 1.47241i
\(459\) 1.54508 + 4.75528i 0.0721184 + 0.221958i
\(460\) 0 0
\(461\) −16.3158 −0.759901 −0.379951 0.925007i \(-0.624059\pi\)
−0.379951 + 0.925007i \(0.624059\pi\)
\(462\) 4.95629 + 3.18404i 0.230588 + 0.148135i
\(463\) −8.47904 −0.394054 −0.197027 0.980398i \(-0.563129\pi\)
−0.197027 + 0.980398i \(0.563129\pi\)
\(464\) 19.6017 14.2415i 0.909987 0.661144i
\(465\) 0 0
\(466\) 4.33558 13.3435i 0.200842 0.618128i
\(467\) −29.5833 21.4935i −1.36895 0.994601i −0.997818 0.0660214i \(-0.978969\pi\)
−0.371133 0.928580i \(-0.621031\pi\)
\(468\) 0.0770945 + 0.0560124i 0.00356369 + 0.00258917i
\(469\) −2.91503 + 8.97155i −0.134604 + 0.414268i
\(470\) 0 0
\(471\) 14.2692 10.3672i 0.657489 0.477694i
\(472\) −23.2743 −1.07129
\(473\) 6.51654 + 16.7293i 0.299631 + 0.769214i
\(474\) 3.53921 0.162561
\(475\) 0 0
\(476\) −0.132624 0.408174i −0.00607881 0.0187086i
\(477\) −2.89440 + 8.90805i −0.132526 + 0.407872i
\(478\) −0.188087 0.136653i −0.00860289 0.00625037i
\(479\) 31.5123 + 22.8950i 1.43983 + 1.04610i 0.988077 + 0.153958i \(0.0492021\pi\)
0.451756 + 0.892142i \(0.350798\pi\)
\(480\) 0 0
\(481\) 2.05997 + 6.33993i 0.0939264 + 0.289076i
\(482\) −1.08566 + 0.788781i −0.0494506 + 0.0359280i
\(483\) 6.39855 0.291144
\(484\) −0.307235 0.672155i −0.0139652 0.0305525i
\(485\) 0 0
\(486\) 1.12474 0.817172i 0.0510193 0.0370677i
\(487\) −2.55622 7.86723i −0.115833 0.356498i 0.876287 0.481790i \(-0.160013\pi\)
−0.992120 + 0.125292i \(0.960013\pi\)
\(488\) 12.6923 39.0630i 0.574555 1.76830i
\(489\) −19.0152 13.8153i −0.859895 0.624750i
\(490\) 0 0
\(491\) −3.74905 + 11.5384i −0.169192 + 0.520720i −0.999321 0.0368519i \(-0.988267\pi\)
0.830128 + 0.557572i \(0.188267\pi\)
\(492\) 0.157496 + 0.484724i 0.00710049 + 0.0218531i
\(493\) 25.3835 18.4422i 1.14322 0.830594i
\(494\) 0.311846 0.0140306
\(495\) 0 0
\(496\) −11.7757 −0.528744
\(497\) −7.00381 + 5.08857i −0.314164 + 0.228253i
\(498\) 4.34860 + 13.3836i 0.194865 + 0.599734i
\(499\) −8.76312 + 26.9701i −0.392291 + 1.20735i 0.538760 + 0.842459i \(0.318893\pi\)
−0.931051 + 0.364889i \(0.881107\pi\)
\(500\) 0 0
\(501\) −0.487619 0.354276i −0.0217852 0.0158279i
\(502\) −10.1003 + 31.0855i −0.450798 + 1.38741i
\(503\) 4.72177 + 14.5321i 0.210533 + 0.647955i 0.999441 + 0.0334427i \(0.0106471\pi\)
−0.788907 + 0.614512i \(0.789353\pi\)
\(504\) −2.97046 + 2.15817i −0.132315 + 0.0961324i
\(505\) 0 0
\(506\) 19.4292 + 12.4818i 0.863733 + 0.554883i
\(507\) 10.9882 0.488005
\(508\) 0.327439 0.237899i 0.0145278 0.0105550i
\(509\) −6.81363 20.9702i −0.302009 0.929488i −0.980776 0.195134i \(-0.937486\pi\)
0.678768 0.734353i \(-0.262514\pi\)
\(510\) 0 0
\(511\) −8.95202 6.50402i −0.396014 0.287721i
\(512\) 19.1413 + 13.9069i 0.845932 + 0.614605i
\(513\) −0.0488697 + 0.150406i −0.00215765 + 0.00664057i
\(514\) 2.82803 + 8.70377i 0.124739 + 0.383907i
\(515\) 0 0
\(516\) −0.363693 −0.0160107
\(517\) 21.1334 17.2866i 0.929444 0.760262i
\(518\) −8.34789 −0.366785
\(519\) −7.81825 + 5.68029i −0.343183 + 0.249337i
\(520\) 0 0
\(521\) −7.39725 + 22.7664i −0.324079 + 0.997413i 0.647775 + 0.761831i \(0.275700\pi\)
−0.971855 + 0.235582i \(0.924300\pi\)
\(522\) −7.05792 5.12788i −0.308917 0.224441i
\(523\) −20.5022 14.8957i −0.896498 0.651344i 0.0410660 0.999156i \(-0.486925\pi\)
−0.937564 + 0.347812i \(0.886925\pi\)
\(524\) 0.388819 1.19666i 0.0169856 0.0522764i
\(525\) 0 0
\(526\) 14.0073 10.1769i 0.610749 0.443735i
\(527\) −15.2491 −0.664260
\(528\) −12.7849 + 0.733212i −0.556390 + 0.0319089i
\(529\) 2.08298 0.0905642
\(530\) 0 0
\(531\) 2.50256 + 7.70209i 0.108602 + 0.334242i
\(532\) 0.00419478 0.0129102i 0.000181867 0.000559729i
\(533\) −8.70476 6.32438i −0.377045 0.273939i
\(534\) 12.4224 + 9.02542i 0.537571 + 0.390568i
\(535\) 0 0
\(536\) −6.55732 20.1814i −0.283233 0.871702i
\(537\) −0.967351 + 0.702822i −0.0417443 + 0.0303290i
\(538\) 28.8797 1.24509
\(539\) 4.52293 17.2187i 0.194816 0.741663i
\(540\) 0 0
\(541\) 28.3669 20.6097i 1.21959 0.886082i 0.223522 0.974699i \(-0.428245\pi\)
0.996066 + 0.0886168i \(0.0282447\pi\)
\(542\) 6.18224 + 19.0270i 0.265550 + 0.817279i
\(543\) −4.81265 + 14.8118i −0.206531 + 0.635636i
\(544\) 1.53672 + 1.11649i 0.0658862 + 0.0478692i
\(545\) 0 0
\(546\) 0.778498 2.39597i 0.0333166 0.102538i
\(547\) 0.342349 + 1.05364i 0.0146378 + 0.0450505i 0.958109 0.286405i \(-0.0924603\pi\)
−0.943471 + 0.331456i \(0.892460\pi\)
\(548\) −0.165085 + 0.119941i −0.00705207 + 0.00512363i
\(549\) −14.2917 −0.609956
\(550\) 0 0
\(551\) 0.992388 0.0422771
\(552\) −11.6445 + 8.46024i −0.495624 + 0.360092i
\(553\) 1.00505 + 3.09321i 0.0427389 + 0.131537i
\(554\) 7.51273 23.1218i 0.319185 0.982352i
\(555\) 0 0
\(556\) −0.120228 0.0873504i −0.00509878 0.00370448i
\(557\) 1.67483 5.15461i 0.0709650 0.218408i −0.909284 0.416177i \(-0.863370\pi\)
0.980249 + 0.197769i \(0.0633697\pi\)
\(558\) 1.31024 + 4.03250i 0.0554669 + 0.170709i
\(559\) 6.21159 4.51299i 0.262722 0.190879i
\(560\) 0 0
\(561\) −16.5559 + 0.949482i −0.698991 + 0.0400872i
\(562\) −26.2564 −1.10756
\(563\) 26.4911 19.2469i 1.11647 0.811161i 0.132798 0.991143i \(-0.457604\pi\)
0.983670 + 0.179982i \(0.0576038\pi\)
\(564\) 0.170911 + 0.526011i 0.00719667 + 0.0221491i
\(565\) 0 0
\(566\) −15.2755 11.0983i −0.642077 0.466496i
\(567\) 1.03359 + 0.750949i 0.0434068 + 0.0315369i
\(568\) 6.01786 18.5211i 0.252504 0.777126i
\(569\) −1.08692 3.34521i −0.0455662 0.140238i 0.925685 0.378295i \(-0.123490\pi\)
−0.971251 + 0.238057i \(0.923490\pi\)
\(570\) 0 0
\(571\) −36.0252 −1.50761 −0.753804 0.657099i \(-0.771783\pi\)
−0.753804 + 0.657099i \(0.771783\pi\)
\(572\) −0.244637 + 0.200107i −0.0102288 + 0.00836691i
\(573\) −18.4016 −0.768738
\(574\) 10.9007 7.91984i 0.454988 0.330568i
\(575\) 0 0
\(576\) 2.54951 7.84658i 0.106230 0.326941i
\(577\) 12.5803 + 9.14009i 0.523723 + 0.380507i 0.818005 0.575212i \(-0.195080\pi\)
−0.294281 + 0.955719i \(0.595080\pi\)
\(578\) −8.99793 6.53738i −0.374265 0.271919i
\(579\) 0.484535 1.49124i 0.0201366 0.0619740i
\(580\) 0 0
\(581\) −10.4622 + 7.60120i −0.434043 + 0.315351i
\(582\) 8.91428 0.369509
\(583\) −26.1364 16.7907i −1.08246 0.695399i
\(584\) 24.8912 1.03001
\(585\) 0 0
\(586\) −8.55030 26.3151i −0.353210 1.08707i
\(587\) 7.49687 23.0730i 0.309429 0.952324i −0.668558 0.743660i \(-0.733088\pi\)
0.977987 0.208665i \(-0.0669117\pi\)
\(588\) 0.291762 + 0.211977i 0.0120320 + 0.00874180i
\(589\) −0.390201 0.283498i −0.0160780 0.0116813i
\(590\) 0 0
\(591\) 2.46287 + 7.57992i 0.101309 + 0.311796i
\(592\) 14.6812 10.6665i 0.603392 0.438390i
\(593\) −27.4019 −1.12526 −0.562630 0.826709i \(-0.690210\pi\)
−0.562630 + 0.826709i \(0.690210\pi\)
\(594\) 1.67361 + 4.29651i 0.0686691 + 0.176288i
\(595\) 0 0
\(596\) 0.0805107 0.0584945i 0.00329785 0.00239603i
\(597\) −1.09127 3.35857i −0.0446625 0.137457i
\(598\) 3.05179 9.39245i 0.124797 0.384086i
\(599\) −8.63810 6.27594i −0.352943 0.256428i 0.397160 0.917750i \(-0.369996\pi\)
−0.750103 + 0.661321i \(0.769996\pi\)
\(600\) 0 0
\(601\) 3.41967 10.5247i 0.139491 0.429310i −0.856770 0.515698i \(-0.827533\pi\)
0.996262 + 0.0863885i \(0.0275326\pi\)
\(602\) 2.97116 + 9.14430i 0.121096 + 0.372694i
\(603\) −5.97348 + 4.33998i −0.243259 + 0.176738i
\(604\) 0.606953 0.0246966
\(605\) 0 0
\(606\) −12.1945 −0.495370
\(607\) −0.416254 + 0.302426i −0.0168952 + 0.0122751i −0.596201 0.802835i \(-0.703324\pi\)
0.579306 + 0.815110i \(0.303324\pi\)
\(608\) 0.0185655 + 0.0571387i 0.000752930 + 0.00231728i
\(609\) 2.47741 7.62469i 0.100390 0.308968i
\(610\) 0 0
\(611\) −9.44619 6.86306i −0.382152 0.277650i
\(612\) 0.103808 0.319487i 0.00419618 0.0129145i
\(613\) −5.90150 18.1630i −0.238360 0.733595i −0.996658 0.0816877i \(-0.973969\pi\)
0.758298 0.651908i \(-0.226031\pi\)
\(614\) −16.7985 + 12.2048i −0.677932 + 0.492546i
\(615\) 0 0
\(616\) −4.42004 11.3472i −0.178088 0.457190i
\(617\) 4.70745 0.189515 0.0947573 0.995500i \(-0.469792\pi\)
0.0947573 + 0.995500i \(0.469792\pi\)
\(618\) −13.0095 + 9.45194i −0.523318 + 0.380213i
\(619\) 11.5477 + 35.5402i 0.464141 + 1.42848i 0.860060 + 0.510194i \(0.170426\pi\)
−0.395919 + 0.918286i \(0.629574\pi\)
\(620\) 0 0
\(621\) 4.05179 + 2.94380i 0.162593 + 0.118131i
\(622\) 5.62033 + 4.08341i 0.225355 + 0.163730i
\(623\) −4.36041 + 13.4200i −0.174696 + 0.537660i
\(624\) 1.69232 + 5.20843i 0.0677471 + 0.208504i
\(625\) 0 0
\(626\) −13.0635 −0.522123
\(627\) −0.441294 0.283498i −0.0176236 0.0113218i
\(628\) −1.18500 −0.0472867
\(629\) 19.0115 13.8127i 0.758040 0.550748i
\(630\) 0 0
\(631\) 10.9908 33.8262i 0.437536 1.34660i −0.452928 0.891547i \(-0.649621\pi\)
0.890465 0.455052i \(-0.150379\pi\)
\(632\) −5.91893 4.30036i −0.235443 0.171059i
\(633\) 16.3867 + 11.9056i 0.651311 + 0.473205i
\(634\) −0.924756 + 2.84611i −0.0367268 + 0.113033i
\(635\) 0 0
\(636\) 0.509110 0.369890i 0.0201875 0.0146671i
\(637\) −7.61344 −0.301656
\(638\) 22.3963 18.3196i 0.886678 0.725281i
\(639\) −6.77618 −0.268062
\(640\) 0 0
\(641\) 3.77305 + 11.6123i 0.149027 + 0.458657i 0.997507 0.0705705i \(-0.0224820\pi\)
−0.848480 + 0.529227i \(0.822482\pi\)
\(642\) 6.59313 20.2916i 0.260210 0.800844i
\(643\) −16.9567 12.3197i −0.668705 0.485843i 0.200886 0.979615i \(-0.435618\pi\)
−0.869591 + 0.493772i \(0.835618\pi\)
\(644\) −0.347790 0.252684i −0.0137048 0.00995714i
\(645\) 0 0
\(646\) −0.339707 1.04551i −0.0133656 0.0411351i
\(647\) 12.0354 8.74424i 0.473161 0.343772i −0.325511 0.945538i \(-0.605536\pi\)
0.798672 + 0.601767i \(0.205536\pi\)
\(648\) −2.87392 −0.112898
\(649\) −26.8155 + 1.53787i −1.05260 + 0.0603666i
\(650\) 0 0
\(651\) −3.15227 + 2.29026i −0.123547 + 0.0897622i
\(652\) 0.487980 + 1.50185i 0.0191108 + 0.0588169i
\(653\) 3.74861 11.5370i 0.146694 0.451479i −0.850531 0.525926i \(-0.823719\pi\)
0.997225 + 0.0744465i \(0.0237190\pi\)
\(654\) 16.1968 + 11.7676i 0.633344 + 0.460151i
\(655\) 0 0
\(656\) −9.05120 + 27.8567i −0.353390 + 1.08762i
\(657\) −2.67642 8.23717i −0.104417 0.321362i
\(658\) 11.8292 8.59443i 0.461151 0.335046i
\(659\) 7.49994 0.292156 0.146078 0.989273i \(-0.453335\pi\)
0.146078 + 0.989273i \(0.453335\pi\)
\(660\) 0 0
\(661\) 9.65248 0.375438 0.187719 0.982223i \(-0.439891\pi\)
0.187719 + 0.982223i \(0.439891\pi\)
\(662\) 21.9455 15.9443i 0.852936 0.619694i
\(663\) 2.19149 + 6.74473i 0.0851106 + 0.261943i
\(664\) 8.98936 27.6664i 0.348855 1.07366i
\(665\) 0 0
\(666\) −5.28619 3.84064i −0.204836 0.148822i
\(667\) 9.71171 29.8896i 0.376039 1.15733i
\(668\) 0.0125136 + 0.0385130i 0.000484167 + 0.00149011i
\(669\) −18.2433 + 13.2546i −0.705328 + 0.512451i
\(670\) 0 0
\(671\) 12.0424 45.8451i 0.464890 1.76983i
\(672\) 0.485354 0.0187229
\(673\) 19.7801 14.3711i 0.762469 0.553966i −0.137198 0.990544i \(-0.543810\pi\)
0.899667 + 0.436578i \(0.143810\pi\)
\(674\) −13.5778 41.7881i −0.522997 1.60962i
\(675\) 0 0
\(676\) −0.597260 0.433935i −0.0229715 0.0166898i
\(677\) 37.8130 + 27.4728i 1.45327 + 1.05586i 0.985053 + 0.172251i \(0.0551041\pi\)
0.468219 + 0.883613i \(0.344896\pi\)
\(678\) 8.31925 25.6040i 0.319499 0.983317i
\(679\) 2.53143 + 7.79093i 0.0971472 + 0.298988i
\(680\) 0 0
\(681\) 18.8062 0.720654
\(682\) −14.0395 + 0.805166i −0.537600 + 0.0308314i
\(683\) 28.1941 1.07882 0.539408 0.842045i \(-0.318648\pi\)
0.539408 + 0.842045i \(0.318648\pi\)
\(684\) 0.00859593 0.00624531i 0.000328674 0.000238795i
\(685\) 0 0
\(686\) 6.78829 20.8922i 0.259178 0.797668i
\(687\) −19.2805 14.0081i −0.735596 0.534442i
\(688\) −16.9094 12.2854i −0.644664 0.468376i
\(689\) −4.10532 + 12.6349i −0.156400 + 0.481350i
\(690\) 0 0
\(691\) −9.38225 + 6.81661i −0.356918 + 0.259316i −0.751765 0.659431i \(-0.770797\pi\)
0.394848 + 0.918747i \(0.370797\pi\)
\(692\) 0.649276 0.0246818
\(693\) −3.27981 + 2.68281i −0.124590 + 0.101911i
\(694\) −13.0450 −0.495180
\(695\) 0 0
\(696\) 5.57289 + 17.1516i 0.211240 + 0.650130i
\(697\) −11.7210 + 36.0734i −0.443963 + 1.36638i
\(698\) 27.9083 + 20.2766i 1.05635 + 0.767481i
\(699\) 8.16446 + 5.93183i 0.308808 + 0.224362i
\(700\) 0 0
\(701\) −11.3415 34.9056i −0.428363 1.31837i −0.899737 0.436433i \(-0.856241\pi\)
0.471373 0.881934i \(-0.343759\pi\)
\(702\) 1.59529 1.15905i 0.0602105 0.0437455i
\(703\) 0.743272 0.0280330
\(704\) 23.0221 + 14.7899i 0.867676 + 0.557417i
\(705\) 0 0
\(706\) −21.9086 + 15.9175i −0.824540 + 0.599064i
\(707\) −3.46294 10.6578i −0.130237 0.400829i
\(708\) 0.168137 0.517471i 0.00631896 0.0194478i
\(709\) −29.5214 21.4486i −1.10870 0.805518i −0.126242 0.991999i \(-0.540292\pi\)
−0.982458 + 0.186482i \(0.940292\pi\)
\(710\) 0 0
\(711\) −0.786672 + 2.42113i −0.0295025 + 0.0907994i
\(712\) −9.80868 30.1880i −0.367596 1.13134i
\(713\) −12.3572 + 8.97804i −0.462781 + 0.336230i
\(714\) −8.88090 −0.332359
\(715\) 0 0
\(716\) 0.0803349 0.00300225
\(717\) 0.135289 0.0982934i 0.00505247 0.00367084i
\(718\) 12.7896 + 39.3624i 0.477304 + 1.46899i
\(719\) −2.88278 + 8.87229i −0.107510 + 0.330881i −0.990311 0.138865i \(-0.955654\pi\)
0.882802 + 0.469746i \(0.155654\pi\)
\(720\) 0 0
\(721\) −11.9552 8.68596i −0.445235 0.323482i
\(722\) −8.15190 + 25.0890i −0.303382 + 0.933715i
\(723\) −0.298281 0.918013i −0.0110932 0.0341413i
\(724\) 0.846520 0.615033i 0.0314607 0.0228575i
\(725\) 0 0
\(726\) −15.1926 + 1.74834i −0.563849 + 0.0648869i
\(727\) 8.46883 0.314091 0.157046 0.987591i \(-0.449803\pi\)
0.157046 + 0.987591i \(0.449803\pi\)
\(728\) −4.21320 + 3.06107i −0.156152 + 0.113451i
\(729\) 0.309017 + 0.951057i 0.0114451 + 0.0352243i
\(730\) 0 0
\(731\) −21.8970 15.9091i −0.809891 0.588420i
\(732\) 0.776819 + 0.564392i 0.0287121 + 0.0208605i
\(733\) −8.97601 + 27.6253i −0.331537 + 1.02036i 0.636866 + 0.770974i \(0.280230\pi\)
−0.968403 + 0.249391i \(0.919770\pi\)
\(734\) 2.76498 + 8.50972i 0.102057 + 0.314100i
\(735\) 0 0
\(736\) 1.90264 0.0701322
\(737\) −8.88851 22.8187i −0.327412 0.840536i
\(738\) 10.5464 0.388220
\(739\) 11.1281 8.08505i 0.409354 0.297413i −0.363986 0.931404i \(-0.618584\pi\)
0.773340 + 0.633991i \(0.218584\pi\)
\(740\) 0 0
\(741\) −0.0693151 + 0.213330i −0.00254636 + 0.00783688i
\(742\) −13.4593 9.77872i −0.494105 0.358988i
\(743\) −28.2456 20.5217i −1.03623 0.752867i −0.0666857 0.997774i \(-0.521242\pi\)
−0.969547 + 0.244907i \(0.921242\pi\)
\(744\) 2.70851 8.33593i 0.0992988 0.305610i
\(745\) 0 0
\(746\) −23.4985 + 17.0727i −0.860343 + 0.625075i
\(747\) −10.1221 −0.370349
\(748\) 0.937384 + 0.602198i 0.0342741 + 0.0220185i
\(749\) 19.6068 0.716416
\(750\) 0 0
\(751\) 6.82903 + 21.0176i 0.249195 + 0.766943i 0.994918 + 0.100687i \(0.0321042\pi\)
−0.745723 + 0.666256i \(0.767896\pi\)
\(752\) −9.82214 + 30.2294i −0.358177 + 1.10235i
\(753\) −19.0201 13.8189i −0.693133 0.503590i
\(754\) −10.0107 7.27320i −0.364568 0.264874i
\(755\) 0 0
\(756\) −0.0265248 0.0816349i −0.000964697 0.00296903i
\(757\) −36.4300 + 26.4680i −1.32407 + 0.961994i −0.324200 + 0.945989i \(0.605095\pi\)
−0.999872 + 0.0160057i \(0.994905\pi\)
\(758\) −19.7404 −0.717004
\(759\) −12.8572 + 10.5169i −0.466687 + 0.381739i
\(760\) 0 0
\(761\) −27.1831 + 19.7496i −0.985385 + 0.715924i −0.958906 0.283725i \(-0.908430\pi\)
−0.0264794 + 0.999649i \(0.508430\pi\)
\(762\) −2.58805 7.96521i −0.0937553 0.288549i
\(763\) −5.68525 + 17.4974i −0.205820 + 0.633449i
\(764\) 1.00021 + 0.726694i 0.0361863 + 0.0262909i
\(765\) 0 0
\(766\) 11.3754 35.0099i 0.411011 1.26496i
\(767\) 3.54955 + 10.9244i 0.128167 + 0.394457i
\(768\) −1.30302 + 0.946698i −0.0470186 + 0.0341610i
\(769\) 24.6086 0.887408 0.443704 0.896173i \(-0.353664\pi\)
0.443704 + 0.896173i \(0.353664\pi\)
\(770\) 0 0
\(771\) −6.58273 −0.237071
\(772\) −0.0852271 + 0.0619211i −0.00306739 + 0.00222859i
\(773\) 7.31802 + 22.5225i 0.263211 + 0.810080i 0.992100 + 0.125448i \(0.0400369\pi\)
−0.728889 + 0.684632i \(0.759963\pi\)
\(774\) −2.32560 + 7.15746i −0.0835919 + 0.257269i
\(775\) 0 0
\(776\) −14.9081 10.8314i −0.535171 0.388824i
\(777\) 1.85551 5.71068i 0.0665662 0.204870i
\(778\) −15.6794 48.2561i −0.562132 1.73006i
\(779\) −0.970569 + 0.705160i −0.0347742 + 0.0252650i
\(780\) 0 0
\(781\) 5.70968 21.7367i 0.204308 0.777799i
\(782\) −34.8141 −1.24495
\(783\) 5.07670 3.68844i 0.181426 0.131814i
\(784\) 6.40454 + 19.7112i 0.228734 + 0.703970i
\(785\) 0 0
\(786\) −21.0640 15.3039i −0.751327 0.545871i
\(787\) −14.9029 10.8276i −0.531232 0.385963i 0.289586 0.957152i \(-0.406482\pi\)
−0.820819 + 0.571189i \(0.806482\pi\)
\(788\) 0.165470 0.509263i 0.00589461 0.0181418i
\(789\) 3.84845 + 11.8443i 0.137008 + 0.421668i
\(790\) 0 0
\(791\) 24.7399 0.879651
\(792\) 2.42159 9.21897i 0.0860476 0.327582i
\(793\) −20.2709 −0.719840
\(794\) −9.04257 + 6.56981i −0.320909 + 0.233154i
\(795\) 0 0
\(796\) −0.0733175 + 0.225648i −0.00259867 + 0.00799788i
\(797\) −5.26399 3.82451i −0.186460 0.135471i 0.490639 0.871363i \(-0.336763\pi\)
−0.677099 + 0.735892i \(0.736763\pi\)
\(798\) −0.227249 0.165106i −0.00804453 0.00584470i
\(799\) −12.7193 + 39.1460i −0.449977 + 1.38489i
\(800\) 0 0
\(801\) −8.93534 + 6.49191i −0.315715 + 0.229380i
\(802\) −39.0526 −1.37900
\(803\) 28.6784 1.64471i 1.01204 0.0580404i
\(804\) 0.496074 0.0174952
\(805\) 0 0
\(806\) 1.85840 + 5.71956i 0.0654593 + 0.201463i
\(807\) −6.41919 + 19.7562i −0.225966 + 0.695453i
\(808\) 20.3940 + 14.8171i 0.717459 + 0.521264i
\(809\) −9.58727 6.96556i −0.337071 0.244896i 0.406354 0.913716i \(-0.366800\pi\)
−0.743425 + 0.668819i \(0.766800\pi\)
\(810\) 0 0
\(811\) 2.32193 + 7.14616i 0.0815339 + 0.250936i 0.983511 0.180848i \(-0.0578843\pi\)
−0.901977 + 0.431784i \(0.857884\pi\)
\(812\) −0.435763 + 0.316601i −0.0152923 + 0.0111105i
\(813\) −14.3903 −0.504688
\(814\) 16.7742 13.7209i 0.587936 0.480917i
\(815\) 0 0
\(816\) 15.6185 11.3475i 0.546758 0.397243i
\(817\) −0.264544 0.814182i −0.00925521 0.0284846i
\(818\) −2.56887 + 7.90618i −0.0898185 + 0.276433i
\(819\) 1.46601 + 1.06512i 0.0512266 + 0.0372183i
\(820\) 0 0
\(821\) −11.5376 + 35.5092i −0.402666 + 1.23928i 0.520163 + 0.854067i \(0.325871\pi\)
−0.922829 + 0.385211i \(0.874129\pi\)
\(822\) 1.30482 + 4.01581i 0.0455107 + 0.140067i
\(823\) −34.8280 + 25.3040i −1.21403 + 0.882043i −0.995590 0.0938075i \(-0.970096\pi\)
−0.218438 + 0.975851i \(0.570096\pi\)
\(824\) 33.2416 1.15803
\(825\) 0 0
\(826\) −14.3843 −0.500495
\(827\) −16.2049 + 11.7736i −0.563500 + 0.409407i −0.832738 0.553667i \(-0.813228\pi\)
0.269238 + 0.963074i \(0.413228\pi\)
\(828\) −0.103980 0.320017i −0.00361355 0.0111214i
\(829\) −14.8083 + 45.5753i −0.514314 + 1.58289i 0.270213 + 0.962800i \(0.412906\pi\)
−0.784527 + 0.620094i \(0.787094\pi\)
\(830\) 0 0
\(831\) 14.1474 + 10.2787i 0.490770 + 0.356565i
\(832\) 3.61613 11.1293i 0.125367 0.385840i
\(833\) 8.29365 + 25.5252i 0.287358 + 0.884396i
\(834\) −2.48783 + 1.80752i −0.0861467 + 0.0625892i
\(835\) 0 0
\(836\) 0.0127907 + 0.0328364i 0.000442376 + 0.00113567i
\(837\) −3.04981 −0.105417
\(838\) 17.4006 12.6423i 0.601093 0.436720i
\(839\) 0.686305 + 2.11223i 0.0236939 + 0.0729222i 0.962204 0.272329i \(-0.0877938\pi\)
−0.938510 + 0.345251i \(0.887794\pi\)
\(840\) 0 0
\(841\) −8.39554 6.09971i −0.289501 0.210335i
\(842\) −38.8875 28.2534i −1.34015 0.973677i
\(843\) 5.83609 17.9616i 0.201006 0.618632i
\(844\) −0.420526 1.29425i −0.0144751 0.0445498i
\(845\) 0 0
\(846\) 11.4447 0.393479
\(847\) −5.84231 12.7816i −0.200744 0.439180i
\(848\) 36.1651 1.24191
\(849\) 10.9875 7.98291i 0.377091 0.273973i
\(850\) 0 0
\(851\) 7.27381 22.3865i 0.249343 0.767398i
\(852\) 0.368316 + 0.267597i 0.0126183 + 0.00916772i
\(853\) −5.15474 3.74514i −0.176495 0.128231i 0.496030 0.868305i \(-0.334790\pi\)
−0.672525 + 0.740074i \(0.734790\pi\)
\(854\) 7.84430 24.1423i 0.268426 0.826131i
\(855\) 0 0
\(856\) −35.6818 + 25.9243i −1.21958 + 0.886075i
\(857\) −35.9060 −1.22653 −0.613263 0.789878i \(-0.710144\pi\)
−0.613263 + 0.789878i \(0.710144\pi\)
\(858\) 2.37379 + 6.09402i 0.0810399 + 0.208046i
\(859\) 56.4697 1.92672 0.963360 0.268212i \(-0.0864328\pi\)
0.963360 + 0.268212i \(0.0864328\pi\)
\(860\) 0 0
\(861\) 2.99492 + 9.21742i 0.102067 + 0.314129i
\(862\) 1.44372 4.44332i 0.0491733 0.151340i
\(863\) −25.1395 18.2649i −0.855759 0.621745i 0.0709688 0.997479i \(-0.477391\pi\)
−0.926728 + 0.375733i \(0.877391\pi\)
\(864\) 0.307344 + 0.223298i 0.0104560 + 0.00759676i
\(865\) 0 0
\(866\) −1.58003 4.86283i −0.0536915 0.165246i
\(867\) 6.47214 4.70228i 0.219805 0.159698i
\(868\) 0.261784 0.00888552
\(869\) −7.10365 4.56356i −0.240975 0.154808i
\(870\) 0 0
\(871\) −8.47257 + 6.15568i −0.287082 + 0.208577i
\(872\) −12.7889 39.3601i −0.433086 1.33290i
\(873\) −1.98141 + 6.09814i −0.0670604 + 0.206391i
\(874\) −0.890840 0.647233i −0.0301331 0.0218930i
\(875\) 0 0
\(876\) −0.179817 + 0.553421i −0.00607546 + 0.0186983i
\(877\) −5.19841 15.9991i −0.175538 0.540250i 0.824120 0.566416i \(-0.191670\pi\)
−0.999658 + 0.0261655i \(0.991670\pi\)
\(878\) 1.74820 1.27014i 0.0589990 0.0428653i
\(879\) 19.9023 0.671289
\(880\) 0 0
\(881\) 26.5633 0.894940 0.447470 0.894299i \(-0.352325\pi\)
0.447470 + 0.894299i \(0.352325\pi\)
\(882\) 6.03734 4.38639i 0.203288 0.147697i
\(883\) 16.8026 + 51.7129i 0.565451 + 1.74028i 0.666608 + 0.745409i \(0.267746\pi\)
−0.101157 + 0.994870i \(0.532254\pi\)
\(884\) 0.147237 0.453150i 0.00495213 0.0152411i
\(885\) 0 0
\(886\) 23.8511 + 17.3289i 0.801295 + 0.582175i
\(887\) 12.7396 39.2084i 0.427753 1.31649i −0.472580 0.881288i \(-0.656677\pi\)
0.900333 0.435202i \(-0.143323\pi\)
\(888\) 4.17395 + 12.8461i 0.140068 + 0.431086i
\(889\) 6.22652 4.52383i 0.208831 0.151724i
\(890\) 0 0
\(891\) −3.31118 + 0.189896i −0.110929 + 0.00636177i
\(892\) 1.51504 0.0507273
\(893\) −1.05324 + 0.765222i −0.0352453 + 0.0256072i
\(894\) −0.636350 1.95848i −0.0212827 0.0655015i
\(895\) 0 0
\(896\) 11.0702 + 8.04293i 0.369828 + 0.268696i
\(897\) 5.74692 + 4.17538i 0.191884 + 0.139412i
\(898\) 6.49171 19.9794i 0.216631 0.666722i
\(899\) 5.91398 + 18.2013i 0.197242 + 0.607049i
\(900\) 0 0
\(901\) 46.8324 1.56021
\(902\) −8.88654 + 33.8309i −0.295889 + 1.12645i
\(903\) −6.91591 −0.230147
\(904\) −45.0235 + 32.7115i −1.49746 + 1.08797i
\(905\) 0 0
\(906\) 3.88110 11.9448i 0.128941 0.396840i
\(907\) 34.3060 + 24.9248i 1.13911 + 0.827614i 0.986995 0.160748i \(-0.0513908\pi\)
0.152117 + 0.988362i \(0.451391\pi\)
\(908\) −1.02220 0.742671i −0.0339229 0.0246464i
\(909\) 2.71052 8.34213i 0.0899023 0.276691i
\(910\) 0 0
\(911\) 6.48184 4.70933i 0.214753 0.156027i −0.475209 0.879873i \(-0.657627\pi\)
0.689962 + 0.723846i \(0.257627\pi\)
\(912\) 0.610619 0.0202196
\(913\) 8.52900 32.4698i 0.282269 1.07459i
\(914\) −57.4234 −1.89940
\(915\) 0 0
\(916\) 0.494789 + 1.52280i 0.0163483 + 0.0503149i
\(917\) 7.39370 22.7555i 0.244162 0.751452i
\(918\) −5.62371 4.08586i −0.185610 0.134854i
\(919\) −33.3587 24.2365i −1.10040 0.799489i −0.119277 0.992861i \(-0.538058\pi\)
−0.981125 + 0.193372i \(0.938058\pi\)
\(920\) 0 0
\(921\) −4.61530 14.2044i −0.152079 0.468052i
\(922\) 18.3510 13.3328i 0.604359 0.439092i
\(923\) −9.61110 −0.316353
\(924\) 0.284219 0.0162999i 0.00935011 0.000536229i
\(925\) 0 0
\(926\) 9.53672 6.92884i 0.313396 0.227696i
\(927\) −3.57429 11.0005i −0.117395 0.361305i
\(928\) 0.736670 2.26724i 0.0241824 0.0744257i
\(929\) 12.2921 + 8.93073i 0.403291 + 0.293008i 0.770880 0.636980i \(-0.219817\pi\)
−0.367589 + 0.929988i \(0.619817\pi\)
\(930\) 0 0
\(931\) −0.262321 + 0.807341i −0.00859723 + 0.0264595i
\(932\) −0.209522 0.644842i −0.00686312 0.0211225i
\(933\) −4.04266 + 2.93716i −0.132351 + 0.0961583i
\(934\) 50.8375 1.66345
\(935\) 0 0
\(936\) −4.07627 −0.133237
\(937\) 20.6472 15.0011i 0.674515 0.490064i −0.197019 0.980400i \(-0.563126\pi\)
0.871533 + 0.490336i \(0.163126\pi\)
\(938\) −4.05265 12.4728i −0.132324 0.407250i
\(939\) 2.90367 8.93658i 0.0947577 0.291634i
\(940\) 0 0
\(941\) −26.1857 19.0250i −0.853629 0.620198i 0.0725154 0.997367i \(-0.476897\pi\)
−0.926144 + 0.377170i \(0.876897\pi\)
\(942\) −7.57737 + 23.3208i −0.246884 + 0.759831i
\(943\) 11.7404 + 36.1332i 0.382320 + 1.17666i
\(944\) 25.2972 18.3795i 0.823354 0.598202i
\(945\) 0 0
\(946\) −21.0001 13.4910i −0.682774 0.438631i
\(947\) 40.1516 1.30475 0.652375 0.757896i \(-0.273773\pi\)
0.652375 + 0.757896i \(0.273773\pi\)
\(948\) 0.138371 0.100533i 0.00449410 0.00326515i
\(949\) −3.79614 11.6833i −0.123228 0.379256i
\(950\) 0 0
\(951\) −1.74144 1.26523i −0.0564699 0.0410278i
\(952\) 14.8523 + 10.7908i 0.481366 + 0.349733i
\(953\) −11.0168 + 33.9064i −0.356871 + 1.09833i 0.598046 + 0.801461i \(0.295944\pi\)
−0.954917 + 0.296873i \(0.904056\pi\)
\(954\) −4.02396 12.3845i −0.130281 0.400962i
\(955\) 0 0
\(956\) −0.0112353 −0.000363374
\(957\) 7.55411 + 19.3930i 0.244190 + 0.626886i
\(958\) −54.1524 −1.74958
\(959\) −3.13922 + 2.28077i −0.101371 + 0.0736501i
\(960\) 0 0
\(961\) −6.70525 + 20.6366i −0.216298 + 0.665698i
\(962\) −7.49774 5.44743i −0.241737 0.175632i
\(963\) 12.4157 + 9.02054i 0.400091 + 0.290683i
\(964\) −0.0200402 + 0.0616775i −0.000645452 + 0.00198650i
\(965\) 0 0
\(966\) −7.19671 + 5.22872i −0.231550 + 0.168231i
\(967\) 20.0622 0.645156 0.322578 0.946543i \(-0.395451\pi\)
0.322578 + 0.946543i \(0.395451\pi\)
\(968\) 27.5322 + 15.5360i 0.884918 + 0.499346i
\(969\) 0.790729 0.0254019
\(970\) 0 0
\(971\) −12.8646 39.5931i −0.412844 1.27060i −0.914165 0.405342i \(-0.867152\pi\)
0.501321 0.865261i \(-0.332848\pi\)
\(972\) 0.0207616 0.0638975i 0.000665927 0.00204951i
\(973\) −2.28622 1.66104i −0.0732929 0.0532504i
\(974\) 9.30396 + 6.75972i 0.298118 + 0.216596i
\(975\) 0 0
\(976\) 17.0522 + 52.4812i 0.545827 + 1.67988i
\(977\) 15.4297 11.2104i 0.493641 0.358651i −0.312942 0.949772i \(-0.601315\pi\)
0.806583 + 0.591121i \(0.201315\pi\)
\(978\) 32.6766 1.04488
\(979\) −13.2958 34.1330i −0.424934 1.09089i
\(980\) 0 0
\(981\) −11.6502 + 8.46436i −0.371962 + 0.270246i
\(982\) −5.21214 16.0413i −0.166326 0.511899i
\(983\) −8.20635 + 25.2566i −0.261742 + 0.805559i 0.730684 + 0.682716i \(0.239201\pi\)
−0.992426 + 0.122843i \(0.960799\pi\)
\(984\) −17.6378 12.8146i −0.562271 0.408514i
\(985\) 0 0
\(986\) −13.4794 + 41.4854i −0.429272 + 1.32116i
\(987\) 3.25002 + 10.0025i 0.103449 + 0.318384i
\(988\) 0.0121922 0.00885813i 0.000387884 0.000281815i
\(989\) −27.1111 −0.862082
\(990\) 0 0
\(991\) −24.2494 −0.770307 −0.385153 0.922853i \(-0.625851\pi\)
−0.385153 + 0.922853i \(0.625851\pi\)
\(992\) −0.937341 + 0.681018i −0.0297606 + 0.0216223i
\(993\) 6.02941 + 18.5566i 0.191338 + 0.588877i
\(994\) 3.71924 11.4466i 0.117967 0.363065i
\(995\) 0 0
\(996\) 0.550182 + 0.399731i 0.0174332 + 0.0126660i
\(997\) −4.96330 + 15.2755i −0.157189 + 0.483779i −0.998376 0.0569657i \(-0.981857\pi\)
0.841187 + 0.540745i \(0.181857\pi\)
\(998\) −12.1830 37.4954i −0.385646 1.18690i
\(999\) 3.80231 2.76254i 0.120300 0.0874029i
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 825.2.n.k.751.1 8
5.2 odd 4 825.2.bx.h.124.2 16
5.3 odd 4 825.2.bx.h.124.3 16
5.4 even 2 165.2.m.a.91.2 8
11.2 odd 10 9075.2.a.dj.1.1 4
11.4 even 5 inner 825.2.n.k.301.1 8
11.9 even 5 9075.2.a.cl.1.4 4
15.14 odd 2 495.2.n.d.91.1 8
55.4 even 10 165.2.m.a.136.2 yes 8
55.9 even 10 1815.2.a.x.1.1 4
55.24 odd 10 1815.2.a.o.1.4 4
55.37 odd 20 825.2.bx.h.499.3 16
55.48 odd 20 825.2.bx.h.499.2 16
165.59 odd 10 495.2.n.d.136.1 8
165.119 odd 10 5445.2.a.be.1.4 4
165.134 even 10 5445.2.a.bv.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.m.a.91.2 8 5.4 even 2
165.2.m.a.136.2 yes 8 55.4 even 10
495.2.n.d.91.1 8 15.14 odd 2
495.2.n.d.136.1 8 165.59 odd 10
825.2.n.k.301.1 8 11.4 even 5 inner
825.2.n.k.751.1 8 1.1 even 1 trivial
825.2.bx.h.124.2 16 5.2 odd 4
825.2.bx.h.124.3 16 5.3 odd 4
825.2.bx.h.499.2 16 55.48 odd 20
825.2.bx.h.499.3 16 55.37 odd 20
1815.2.a.o.1.4 4 55.24 odd 10
1815.2.a.x.1.1 4 55.9 even 10
5445.2.a.be.1.4 4 165.119 odd 10
5445.2.a.bv.1.1 4 165.134 even 10
9075.2.a.cl.1.4 4 11.9 even 5
9075.2.a.dj.1.1 4 11.2 odd 10