Properties

Label 950.2.l.b.101.1
Level $950$
Weight $2$
Character 950.101
Analytic conductor $7.586$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [950,2,Mod(101,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.101");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.l (of order \(9\), degree \(6\), 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: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 101.1
Root \(0.939693 + 0.342020i\) of defining polynomial
Character \(\chi\) \(=\) 950.101
Dual form 950.2.l.b.301.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.766044 + 0.642788i) q^{2} +(-1.26604 - 0.460802i) q^{3} +(0.173648 - 0.984808i) q^{4} +(1.26604 - 0.460802i) q^{6} +(-1.43969 + 2.49362i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.907604 - 0.761570i) q^{9} +O(q^{10})\) \(q+(-0.766044 + 0.642788i) q^{2} +(-1.26604 - 0.460802i) q^{3} +(0.173648 - 0.984808i) q^{4} +(1.26604 - 0.460802i) q^{6} +(-1.43969 + 2.49362i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.907604 - 0.761570i) q^{9} +(0.500000 + 0.866025i) q^{11} +(-0.673648 + 1.16679i) q^{12} +(-0.500000 + 0.181985i) q^{13} +(-0.500000 - 2.83564i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(-1.26604 + 1.06234i) q^{17} +1.18479 q^{18} +(3.79086 - 2.15160i) q^{19} +(2.97178 - 2.49362i) q^{21} +(-0.939693 - 0.342020i) q^{22} +(0.194593 - 1.10359i) q^{23} +(-0.233956 - 1.32683i) q^{24} +(0.266044 - 0.460802i) q^{26} +(2.81908 + 4.88279i) q^{27} +(2.20574 + 1.85083i) q^{28} +(-1.81521 - 1.52314i) q^{29} +(0.847296 - 1.46756i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-0.233956 - 1.32683i) q^{33} +(0.286989 - 1.62760i) q^{34} +(-0.907604 + 0.761570i) q^{36} -2.59627 q^{37} +(-1.52094 + 4.08494i) q^{38} +0.716881 q^{39} +(-4.85844 - 1.76833i) q^{41} +(-0.673648 + 3.82045i) q^{42} +(-1.88666 - 10.6998i) q^{43} +(0.939693 - 0.342020i) q^{44} +(0.560307 + 0.970481i) q^{46} +(-1.39053 - 1.16679i) q^{47} +(1.03209 + 0.866025i) q^{48} +(-0.645430 - 1.11792i) q^{49} +(2.09240 - 0.761570i) q^{51} +(0.0923963 + 0.524005i) q^{52} +(2.08512 - 11.8253i) q^{53} +(-5.29813 - 1.92836i) q^{54} -2.87939 q^{56} +(-5.79086 + 0.977185i) q^{57} +2.36959 q^{58} +(6.72668 - 5.64436i) q^{59} +(1.08512 - 6.15403i) q^{61} +(0.294263 + 1.66885i) q^{62} +(3.20574 - 1.16679i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(1.03209 + 0.866025i) q^{66} +(-1.93969 - 1.62760i) q^{67} +(0.826352 + 1.43128i) q^{68} +(-0.754900 + 1.30753i) q^{69} +(-1.02229 - 5.79769i) q^{71} +(0.205737 - 1.16679i) q^{72} +(-4.68479 - 1.70513i) q^{73} +(1.98886 - 1.66885i) q^{74} +(-1.46064 - 4.10689i) q^{76} -2.87939 q^{77} +(-0.549163 + 0.460802i) q^{78} +(8.05690 + 2.93247i) q^{79} +(-0.701867 - 3.98048i) q^{81} +(4.85844 - 1.76833i) q^{82} +(5.32888 - 9.22989i) q^{83} +(-1.93969 - 3.35965i) q^{84} +(8.32295 + 6.98378i) q^{86} +(1.59627 + 2.76481i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(-0.694593 + 0.252811i) q^{89} +(0.266044 - 1.50881i) q^{91} +(-1.05303 - 0.383273i) q^{92} +(-1.74897 + 1.46756i) q^{93} +1.81521 q^{94} -1.34730 q^{96} +(8.88919 - 7.45891i) q^{97} +(1.21301 + 0.441500i) q^{98} +(0.205737 - 1.16679i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{3} + 3 q^{6} - 3 q^{7} + 3 q^{8} - 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 3 q^{3} + 3 q^{6} - 3 q^{7} + 3 q^{8} - 9 q^{9} + 3 q^{11} - 3 q^{12} - 3 q^{13} - 3 q^{14} - 3 q^{17} - 9 q^{19} + 3 q^{21} - 3 q^{23} - 6 q^{24} - 3 q^{26} + 3 q^{28} - 18 q^{29} + 3 q^{31} - 6 q^{33} - 6 q^{34} - 9 q^{36} + 12 q^{37} - 6 q^{38} - 12 q^{39} - 21 q^{41} - 3 q^{42} - 18 q^{43} + 9 q^{46} + 9 q^{47} - 3 q^{48} + 12 q^{49} + 9 q^{51} - 3 q^{52} - 9 q^{53} - 18 q^{54} - 6 q^{56} - 3 q^{57} + 27 q^{59} - 15 q^{61} + 12 q^{62} + 9 q^{63} - 3 q^{64} - 3 q^{66} - 6 q^{67} + 6 q^{68} - 6 q^{69} + 6 q^{71} - 9 q^{72} - 21 q^{73} + 18 q^{74} - 6 q^{77} - 15 q^{78} + 12 q^{79} - 18 q^{81} + 21 q^{82} + 18 q^{83} - 6 q^{84} + 9 q^{86} - 18 q^{87} - 3 q^{88} - 3 q^{91} + 6 q^{92} + 15 q^{93} + 18 q^{94} - 6 q^{96} + 45 q^{97} + 15 q^{98} - 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{7}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.766044 + 0.642788i −0.541675 + 0.454519i
\(3\) −1.26604 0.460802i −0.730951 0.266044i −0.0503837 0.998730i \(-0.516044\pi\)
−0.680567 + 0.732685i \(0.738267\pi\)
\(4\) 0.173648 0.984808i 0.0868241 0.492404i
\(5\) 0 0
\(6\) 1.26604 0.460802i 0.516860 0.188122i
\(7\) −1.43969 + 2.49362i −0.544153 + 0.942500i 0.454507 + 0.890743i \(0.349815\pi\)
−0.998660 + 0.0517569i \(0.983518\pi\)
\(8\) 0.500000 + 0.866025i 0.176777 + 0.306186i
\(9\) −0.907604 0.761570i −0.302535 0.253857i
\(10\) 0 0
\(11\) 0.500000 + 0.866025i 0.150756 + 0.261116i 0.931505 0.363727i \(-0.118496\pi\)
−0.780750 + 0.624844i \(0.785163\pi\)
\(12\) −0.673648 + 1.16679i −0.194465 + 0.336824i
\(13\) −0.500000 + 0.181985i −0.138675 + 0.0504736i −0.410425 0.911894i \(-0.634620\pi\)
0.271750 + 0.962368i \(0.412398\pi\)
\(14\) −0.500000 2.83564i −0.133631 0.757857i
\(15\) 0 0
\(16\) −0.939693 0.342020i −0.234923 0.0855050i
\(17\) −1.26604 + 1.06234i −0.307061 + 0.257655i −0.783276 0.621674i \(-0.786453\pi\)
0.476215 + 0.879329i \(0.342008\pi\)
\(18\) 1.18479 0.279258
\(19\) 3.79086 2.15160i 0.869683 0.493611i
\(20\) 0 0
\(21\) 2.97178 2.49362i 0.648496 0.544153i
\(22\) −0.939693 0.342020i −0.200343 0.0729189i
\(23\) 0.194593 1.10359i 0.0405754 0.230114i −0.957776 0.287516i \(-0.907170\pi\)
0.998351 + 0.0574018i \(0.0182816\pi\)
\(24\) −0.233956 1.32683i −0.0477560 0.270838i
\(25\) 0 0
\(26\) 0.266044 0.460802i 0.0521756 0.0903708i
\(27\) 2.81908 + 4.88279i 0.542532 + 0.939693i
\(28\) 2.20574 + 1.85083i 0.416845 + 0.349775i
\(29\) −1.81521 1.52314i −0.337076 0.282840i 0.458500 0.888694i \(-0.348387\pi\)
−0.795575 + 0.605854i \(0.792831\pi\)
\(30\) 0 0
\(31\) 0.847296 1.46756i 0.152179 0.263582i −0.779849 0.625967i \(-0.784704\pi\)
0.932028 + 0.362386i \(0.118038\pi\)
\(32\) 0.939693 0.342020i 0.166116 0.0604612i
\(33\) −0.233956 1.32683i −0.0407264 0.230971i
\(34\) 0.286989 1.62760i 0.0492182 0.279130i
\(35\) 0 0
\(36\) −0.907604 + 0.761570i −0.151267 + 0.126928i
\(37\) −2.59627 −0.426824 −0.213412 0.976962i \(-0.568458\pi\)
−0.213412 + 0.976962i \(0.568458\pi\)
\(38\) −1.52094 + 4.08494i −0.246730 + 0.662665i
\(39\) 0.716881 0.114793
\(40\) 0 0
\(41\) −4.85844 1.76833i −0.758761 0.276166i −0.0664735 0.997788i \(-0.521175\pi\)
−0.692288 + 0.721622i \(0.743397\pi\)
\(42\) −0.673648 + 3.82045i −0.103946 + 0.589508i
\(43\) −1.88666 10.6998i −0.287713 1.63170i −0.695431 0.718593i \(-0.744787\pi\)
0.407718 0.913108i \(-0.366325\pi\)
\(44\) 0.939693 0.342020i 0.141664 0.0515615i
\(45\) 0 0
\(46\) 0.560307 + 0.970481i 0.0826128 + 0.143090i
\(47\) −1.39053 1.16679i −0.202830 0.170194i 0.535715 0.844399i \(-0.320042\pi\)
−0.738545 + 0.674205i \(0.764487\pi\)
\(48\) 1.03209 + 0.866025i 0.148969 + 0.125000i
\(49\) −0.645430 1.11792i −0.0922042 0.159702i
\(50\) 0 0
\(51\) 2.09240 0.761570i 0.292994 0.106641i
\(52\) 0.0923963 + 0.524005i 0.0128131 + 0.0726665i
\(53\) 2.08512 11.8253i 0.286414 1.62433i −0.413779 0.910378i \(-0.635791\pi\)
0.700192 0.713955i \(-0.253098\pi\)
\(54\) −5.29813 1.92836i −0.720985 0.262417i
\(55\) 0 0
\(56\) −2.87939 −0.384774
\(57\) −5.79086 + 0.977185i −0.767018 + 0.129431i
\(58\) 2.36959 0.311142
\(59\) 6.72668 5.64436i 0.875739 0.734833i −0.0895592 0.995982i \(-0.528546\pi\)
0.965299 + 0.261149i \(0.0841014\pi\)
\(60\) 0 0
\(61\) 1.08512 6.15403i 0.138936 0.787943i −0.833102 0.553119i \(-0.813437\pi\)
0.972038 0.234824i \(-0.0754515\pi\)
\(62\) 0.294263 + 1.66885i 0.0373714 + 0.211944i
\(63\) 3.20574 1.16679i 0.403885 0.147002i
\(64\) −0.500000 + 0.866025i −0.0625000 + 0.108253i
\(65\) 0 0
\(66\) 1.03209 + 0.866025i 0.127041 + 0.106600i
\(67\) −1.93969 1.62760i −0.236971 0.198842i 0.516567 0.856247i \(-0.327210\pi\)
−0.753538 + 0.657405i \(0.771654\pi\)
\(68\) 0.826352 + 1.43128i 0.100210 + 0.173569i
\(69\) −0.754900 + 1.30753i −0.0908793 + 0.157408i
\(70\) 0 0
\(71\) −1.02229 5.79769i −0.121323 0.688059i −0.983424 0.181322i \(-0.941963\pi\)
0.862101 0.506737i \(-0.169149\pi\)
\(72\) 0.205737 1.16679i 0.0242463 0.137508i
\(73\) −4.68479 1.70513i −0.548313 0.199570i 0.0529835 0.998595i \(-0.483127\pi\)
−0.601297 + 0.799026i \(0.705349\pi\)
\(74\) 1.98886 1.66885i 0.231200 0.194000i
\(75\) 0 0
\(76\) −1.46064 4.10689i −0.167547 0.471093i
\(77\) −2.87939 −0.328136
\(78\) −0.549163 + 0.460802i −0.0621805 + 0.0521756i
\(79\) 8.05690 + 2.93247i 0.906472 + 0.329929i 0.752843 0.658200i \(-0.228682\pi\)
0.153629 + 0.988129i \(0.450904\pi\)
\(80\) 0 0
\(81\) −0.701867 3.98048i −0.0779852 0.442276i
\(82\) 4.85844 1.76833i 0.536525 0.195279i
\(83\) 5.32888 9.22989i 0.584920 1.01311i −0.409965 0.912101i \(-0.634459\pi\)
0.994885 0.101011i \(-0.0322076\pi\)
\(84\) −1.93969 3.35965i −0.211638 0.366567i
\(85\) 0 0
\(86\) 8.32295 + 6.98378i 0.897487 + 0.753081i
\(87\) 1.59627 + 2.76481i 0.171138 + 0.296419i
\(88\) −0.500000 + 0.866025i −0.0533002 + 0.0923186i
\(89\) −0.694593 + 0.252811i −0.0736267 + 0.0267979i −0.378571 0.925572i \(-0.623584\pi\)
0.304944 + 0.952370i \(0.401362\pi\)
\(90\) 0 0
\(91\) 0.266044 1.50881i 0.0278890 0.158167i
\(92\) −1.05303 0.383273i −0.109786 0.0399590i
\(93\) −1.74897 + 1.46756i −0.181360 + 0.152179i
\(94\) 1.81521 0.187224
\(95\) 0 0
\(96\) −1.34730 −0.137508
\(97\) 8.88919 7.45891i 0.902560 0.757338i −0.0681291 0.997677i \(-0.521703\pi\)
0.970689 + 0.240339i \(0.0772585\pi\)
\(98\) 1.21301 + 0.441500i 0.122533 + 0.0445982i
\(99\) 0.205737 1.16679i 0.0206774 0.117267i
\(100\) 0 0
\(101\) −13.4226 + 4.88543i −1.33560 + 0.486119i −0.908424 0.418050i \(-0.862714\pi\)
−0.427176 + 0.904168i \(0.640492\pi\)
\(102\) −1.11334 + 1.92836i −0.110237 + 0.190936i
\(103\) −0.794263 1.37570i −0.0782611 0.135552i 0.824239 0.566243i \(-0.191603\pi\)
−0.902500 + 0.430690i \(0.858270\pi\)
\(104\) −0.407604 0.342020i −0.0399688 0.0335378i
\(105\) 0 0
\(106\) 6.00387 + 10.3990i 0.583147 + 1.01004i
\(107\) 2.52481 4.37311i 0.244083 0.422764i −0.717790 0.696259i \(-0.754846\pi\)
0.961873 + 0.273495i \(0.0881797\pi\)
\(108\) 5.29813 1.92836i 0.509813 0.185557i
\(109\) 0.688196 + 3.90295i 0.0659172 + 0.373835i 0.999865 + 0.0164259i \(0.00522876\pi\)
−0.933948 + 0.357409i \(0.883660\pi\)
\(110\) 0 0
\(111\) 3.28699 + 1.19637i 0.311987 + 0.113554i
\(112\) 2.20574 1.85083i 0.208423 0.174887i
\(113\) −6.98545 −0.657136 −0.328568 0.944480i \(-0.606566\pi\)
−0.328568 + 0.944480i \(0.606566\pi\)
\(114\) 3.80793 4.47086i 0.356646 0.418734i
\(115\) 0 0
\(116\) −1.81521 + 1.52314i −0.168538 + 0.141420i
\(117\) 0.592396 + 0.215615i 0.0547671 + 0.0199336i
\(118\) −1.52481 + 8.64766i −0.140371 + 0.796081i
\(119\) −0.826352 4.68647i −0.0757515 0.429608i
\(120\) 0 0
\(121\) 5.00000 8.66025i 0.454545 0.787296i
\(122\) 3.12449 + 5.41177i 0.282878 + 0.489958i
\(123\) 5.33615 + 4.47756i 0.481145 + 0.403728i
\(124\) −1.29813 1.08926i −0.116576 0.0978187i
\(125\) 0 0
\(126\) −1.70574 + 2.95442i −0.151959 + 0.263201i
\(127\) 17.8059 6.48081i 1.58002 0.575079i 0.604808 0.796371i \(-0.293250\pi\)
0.975208 + 0.221292i \(0.0710275\pi\)
\(128\) −0.173648 0.984808i −0.0153485 0.0870455i
\(129\) −2.54189 + 14.4158i −0.223801 + 1.26924i
\(130\) 0 0
\(131\) −12.8118 + 10.7504i −1.11937 + 0.939265i −0.998573 0.0534118i \(-0.982990\pi\)
−0.120800 + 0.992677i \(0.538546\pi\)
\(132\) −1.34730 −0.117267
\(133\) −0.0923963 + 12.5506i −0.00801177 + 1.08828i
\(134\) 2.53209 0.218739
\(135\) 0 0
\(136\) −1.55303 0.565258i −0.133172 0.0484705i
\(137\) 0.524348 2.97373i 0.0447981 0.254063i −0.954181 0.299229i \(-0.903271\pi\)
0.998979 + 0.0451662i \(0.0143817\pi\)
\(138\) −0.262174 1.48686i −0.0223177 0.126570i
\(139\) 11.6309 4.23329i 0.986519 0.359063i 0.202147 0.979355i \(-0.435208\pi\)
0.784371 + 0.620292i \(0.212986\pi\)
\(140\) 0 0
\(141\) 1.22281 + 2.11797i 0.102979 + 0.178365i
\(142\) 4.50980 + 3.78417i 0.378454 + 0.317561i
\(143\) −0.407604 0.342020i −0.0340855 0.0286012i
\(144\) 0.592396 + 1.02606i 0.0493664 + 0.0855050i
\(145\) 0 0
\(146\) 4.68479 1.70513i 0.387716 0.141117i
\(147\) 0.302004 + 1.71275i 0.0249088 + 0.141265i
\(148\) −0.450837 + 2.55682i −0.0370586 + 0.210170i
\(149\) −8.76517 3.19026i −0.718070 0.261356i −0.0429640 0.999077i \(-0.513680\pi\)
−0.675106 + 0.737720i \(0.735902\pi\)
\(150\) 0 0
\(151\) −4.76651 −0.387893 −0.193947 0.981012i \(-0.562129\pi\)
−0.193947 + 0.981012i \(0.562129\pi\)
\(152\) 3.75877 + 2.20718i 0.304877 + 0.179026i
\(153\) 1.95811 0.158304
\(154\) 2.20574 1.85083i 0.177743 0.149144i
\(155\) 0 0
\(156\) 0.124485 0.705990i 0.00996679 0.0565245i
\(157\) −2.66297 15.1025i −0.212528 1.20531i −0.885145 0.465316i \(-0.845941\pi\)
0.672616 0.739991i \(-0.265170\pi\)
\(158\) −8.05690 + 2.93247i −0.640973 + 0.233295i
\(159\) −8.08899 + 14.0105i −0.641499 + 1.11111i
\(160\) 0 0
\(161\) 2.47178 + 2.07407i 0.194804 + 0.163460i
\(162\) 3.09627 + 2.59808i 0.243266 + 0.204124i
\(163\) 4.12701 + 7.14819i 0.323252 + 0.559890i 0.981157 0.193212i \(-0.0618904\pi\)
−0.657905 + 0.753101i \(0.728557\pi\)
\(164\) −2.58512 + 4.47756i −0.201864 + 0.349639i
\(165\) 0 0
\(166\) 1.85070 + 10.4958i 0.143642 + 0.814635i
\(167\) 3.02007 17.1277i 0.233700 1.32538i −0.611635 0.791140i \(-0.709488\pi\)
0.845335 0.534237i \(-0.179401\pi\)
\(168\) 3.64543 + 1.32683i 0.281251 + 0.102367i
\(169\) −9.74170 + 8.17425i −0.749361 + 0.628789i
\(170\) 0 0
\(171\) −5.07919 0.934204i −0.388416 0.0714404i
\(172\) −10.8648 −0.828436
\(173\) −15.0326 + 12.6138i −1.14290 + 0.959010i −0.999530 0.0306582i \(-0.990240\pi\)
−0.143374 + 0.989669i \(0.545795\pi\)
\(174\) −3.00000 1.09191i −0.227429 0.0827775i
\(175\) 0 0
\(176\) −0.173648 0.984808i −0.0130892 0.0742327i
\(177\) −11.1172 + 4.04633i −0.835621 + 0.304141i
\(178\) 0.369585 0.640140i 0.0277016 0.0479805i
\(179\) 9.66297 + 16.7368i 0.722244 + 1.25096i 0.960098 + 0.279663i \(0.0902227\pi\)
−0.237854 + 0.971301i \(0.576444\pi\)
\(180\) 0 0
\(181\) 20.2422 + 16.9852i 1.50459 + 1.26250i 0.873537 + 0.486758i \(0.161821\pi\)
0.631052 + 0.775741i \(0.282624\pi\)
\(182\) 0.766044 + 1.32683i 0.0567830 + 0.0983510i
\(183\) −4.20961 + 7.29125i −0.311183 + 0.538985i
\(184\) 1.05303 0.383273i 0.0776307 0.0282552i
\(185\) 0 0
\(186\) 0.396459 2.24843i 0.0290698 0.164863i
\(187\) −1.55303 0.565258i −0.113569 0.0413358i
\(188\) −1.39053 + 1.16679i −0.101415 + 0.0850971i
\(189\) −16.2344 −1.18088
\(190\) 0 0
\(191\) −25.6955 −1.85926 −0.929632 0.368490i \(-0.879875\pi\)
−0.929632 + 0.368490i \(0.879875\pi\)
\(192\) 1.03209 0.866025i 0.0744846 0.0625000i
\(193\) −4.93882 1.79758i −0.355504 0.129393i 0.158094 0.987424i \(-0.449465\pi\)
−0.513597 + 0.858031i \(0.671687\pi\)
\(194\) −2.01501 + 11.4277i −0.144670 + 0.820462i
\(195\) 0 0
\(196\) −1.21301 + 0.441500i −0.0866436 + 0.0315357i
\(197\) −12.3191 + 21.3373i −0.877698 + 1.52022i −0.0238373 + 0.999716i \(0.507588\pi\)
−0.853861 + 0.520502i \(0.825745\pi\)
\(198\) 0.592396 + 1.02606i 0.0420998 + 0.0729189i
\(199\) −7.50181 6.29477i −0.531789 0.446224i 0.336929 0.941530i \(-0.390612\pi\)
−0.868719 + 0.495306i \(0.835056\pi\)
\(200\) 0 0
\(201\) 1.70574 + 2.95442i 0.120313 + 0.208389i
\(202\) 7.14203 12.3704i 0.502511 0.870375i
\(203\) 6.41147 2.33359i 0.449997 0.163786i
\(204\) −0.386659 2.19285i −0.0270716 0.153530i
\(205\) 0 0
\(206\) 1.49273 + 0.543308i 0.104003 + 0.0378541i
\(207\) −1.01707 + 0.853427i −0.0706915 + 0.0593172i
\(208\) 0.532089 0.0368937
\(209\) 3.75877 + 2.20718i 0.260000 + 0.152674i
\(210\) 0 0
\(211\) 16.5043 13.8488i 1.13621 0.953390i 0.136897 0.990585i \(-0.456287\pi\)
0.999308 + 0.0371957i \(0.0118425\pi\)
\(212\) −11.2836 4.10689i −0.774960 0.282062i
\(213\) −1.37733 + 7.81120i −0.0943728 + 0.535215i
\(214\) 0.876859 + 4.97291i 0.0599408 + 0.339941i
\(215\) 0 0
\(216\) −2.81908 + 4.88279i −0.191814 + 0.332232i
\(217\) 2.43969 + 4.22567i 0.165617 + 0.286857i
\(218\) −3.03596 2.54747i −0.205621 0.172537i
\(219\) 5.14543 + 4.31753i 0.347696 + 0.291752i
\(220\) 0 0
\(221\) 0.439693 0.761570i 0.0295769 0.0512287i
\(222\) −3.28699 + 1.19637i −0.220608 + 0.0802948i
\(223\) 3.54963 + 20.1310i 0.237701 + 1.34807i 0.836851 + 0.547431i \(0.184394\pi\)
−0.599150 + 0.800637i \(0.704495\pi\)
\(224\) −0.500000 + 2.83564i −0.0334077 + 0.189464i
\(225\) 0 0
\(226\) 5.35117 4.49016i 0.355954 0.298681i
\(227\) −7.78787 −0.516899 −0.258449 0.966025i \(-0.583212\pi\)
−0.258449 + 0.966025i \(0.583212\pi\)
\(228\) −0.0432332 + 5.87257i −0.00286319 + 0.388920i
\(229\) −8.02734 −0.530462 −0.265231 0.964185i \(-0.585448\pi\)
−0.265231 + 0.964185i \(0.585448\pi\)
\(230\) 0 0
\(231\) 3.64543 + 1.32683i 0.239852 + 0.0872989i
\(232\) 0.411474 2.33359i 0.0270146 0.153207i
\(233\) −0.656574 3.72362i −0.0430136 0.243942i 0.955719 0.294282i \(-0.0950806\pi\)
−0.998732 + 0.0503401i \(0.983969\pi\)
\(234\) −0.592396 + 0.215615i −0.0387262 + 0.0140952i
\(235\) 0 0
\(236\) −4.39053 7.60462i −0.285799 0.495019i
\(237\) −8.84911 7.42528i −0.574811 0.482324i
\(238\) 3.64543 + 3.05888i 0.236298 + 0.198278i
\(239\) −3.39053 5.87257i −0.219315 0.379865i 0.735284 0.677760i \(-0.237049\pi\)
−0.954599 + 0.297895i \(0.903716\pi\)
\(240\) 0 0
\(241\) 5.67840 2.06677i 0.365778 0.133132i −0.152591 0.988289i \(-0.548762\pi\)
0.518369 + 0.855157i \(0.326540\pi\)
\(242\) 1.73648 + 9.84808i 0.111625 + 0.633058i
\(243\) 1.99154 11.2946i 0.127758 0.724549i
\(244\) −5.87211 2.13727i −0.375923 0.136825i
\(245\) 0 0
\(246\) −6.96585 −0.444126
\(247\) −1.50387 + 1.76568i −0.0956890 + 0.112348i
\(248\) 1.69459 0.107607
\(249\) −10.9998 + 9.22989i −0.697081 + 0.584920i
\(250\) 0 0
\(251\) −0.992259 + 5.62738i −0.0626308 + 0.355197i 0.937346 + 0.348400i \(0.113275\pi\)
−0.999977 + 0.00679744i \(0.997836\pi\)
\(252\) −0.592396 3.35965i −0.0373175 0.211638i
\(253\) 1.05303 0.383273i 0.0662036 0.0240962i
\(254\) −9.47431 + 16.4100i −0.594471 + 1.02965i
\(255\) 0 0
\(256\) 0.766044 + 0.642788i 0.0478778 + 0.0401742i
\(257\) −9.82888 8.24741i −0.613109 0.514459i 0.282520 0.959261i \(-0.408830\pi\)
−0.895629 + 0.444802i \(0.853274\pi\)
\(258\) −7.31908 12.6770i −0.455666 0.789236i
\(259\) 3.73783 6.47410i 0.232257 0.402281i
\(260\) 0 0
\(261\) 0.487511 + 2.76481i 0.0301762 + 0.171138i
\(262\) 2.90420 16.4705i 0.179422 1.01755i
\(263\) −4.59714 1.67322i −0.283472 0.103175i 0.196371 0.980530i \(-0.437084\pi\)
−0.479843 + 0.877354i \(0.659306\pi\)
\(264\) 1.03209 0.866025i 0.0635207 0.0533002i
\(265\) 0 0
\(266\) −7.99660 9.67372i −0.490303 0.593134i
\(267\) 0.995881 0.0609469
\(268\) −1.93969 + 1.62760i −0.118486 + 0.0994212i
\(269\) 14.9290 + 5.43372i 0.910238 + 0.331300i 0.754348 0.656475i \(-0.227953\pi\)
0.155890 + 0.987774i \(0.450175\pi\)
\(270\) 0 0
\(271\) −4.24082 24.0509i −0.257611 1.46099i −0.789279 0.614034i \(-0.789546\pi\)
0.531668 0.846953i \(-0.321565\pi\)
\(272\) 1.55303 0.565258i 0.0941665 0.0342738i
\(273\) −1.03209 + 1.78763i −0.0624649 + 0.108192i
\(274\) 1.50980 + 2.61505i 0.0912104 + 0.157981i
\(275\) 0 0
\(276\) 1.15657 + 0.970481i 0.0696176 + 0.0584161i
\(277\) 5.76991 + 9.99379i 0.346681 + 0.600468i 0.985658 0.168757i \(-0.0539755\pi\)
−0.638977 + 0.769226i \(0.720642\pi\)
\(278\) −6.18866 + 10.7191i −0.371171 + 0.642888i
\(279\) −1.88666 + 0.686688i −0.112951 + 0.0411109i
\(280\) 0 0
\(281\) −1.36912 + 7.76466i −0.0816747 + 0.463201i 0.916350 + 0.400378i \(0.131121\pi\)
−0.998025 + 0.0628223i \(0.979990\pi\)
\(282\) −2.29813 0.836452i −0.136852 0.0498100i
\(283\) 3.63429 3.04953i 0.216036 0.181276i −0.528347 0.849028i \(-0.677188\pi\)
0.744383 + 0.667753i \(0.232744\pi\)
\(284\) −5.88713 −0.349337
\(285\) 0 0
\(286\) 0.532089 0.0314631
\(287\) 11.4042 9.56926i 0.673169 0.564856i
\(288\) −1.11334 0.405223i −0.0656042 0.0238780i
\(289\) −2.47771 + 14.0518i −0.145748 + 0.826576i
\(290\) 0 0
\(291\) −14.6912 + 5.34716i −0.861213 + 0.313456i
\(292\) −2.49273 + 4.31753i −0.145876 + 0.252664i
\(293\) −6.29679 10.9064i −0.367862 0.637156i 0.621369 0.783518i \(-0.286577\pi\)
−0.989231 + 0.146362i \(0.953244\pi\)
\(294\) −1.33228 1.11792i −0.0777002 0.0651982i
\(295\) 0 0
\(296\) −1.29813 2.24843i −0.0754525 0.130688i
\(297\) −2.81908 + 4.88279i −0.163579 + 0.283328i
\(298\) 8.76517 3.19026i 0.507752 0.184807i
\(299\) 0.103541 + 0.587208i 0.00598791 + 0.0339591i
\(300\) 0 0
\(301\) 29.3974 + 10.6998i 1.69444 + 0.616725i
\(302\) 3.65136 3.06385i 0.210112 0.176305i
\(303\) 19.2449 1.10559
\(304\) −4.29813 + 0.725293i −0.246515 + 0.0415984i
\(305\) 0 0
\(306\) −1.50000 + 1.25865i −0.0857493 + 0.0719522i
\(307\) 28.3692 + 10.3255i 1.61911 + 0.589309i 0.983213 0.182461i \(-0.0584063\pi\)
0.635901 + 0.771770i \(0.280629\pi\)
\(308\) −0.500000 + 2.83564i −0.0284901 + 0.161576i
\(309\) 0.371644 + 2.10770i 0.0211421 + 0.119903i
\(310\) 0 0
\(311\) −5.54236 + 9.59964i −0.314278 + 0.544346i −0.979284 0.202493i \(-0.935096\pi\)
0.665006 + 0.746838i \(0.268429\pi\)
\(312\) 0.358441 + 0.620838i 0.0202927 + 0.0351480i
\(313\) 6.26991 + 5.26108i 0.354397 + 0.297374i 0.802553 0.596581i \(-0.203475\pi\)
−0.448156 + 0.893955i \(0.647919\pi\)
\(314\) 11.7476 + 9.85743i 0.662957 + 0.556287i
\(315\) 0 0
\(316\) 4.28699 7.42528i 0.241162 0.417705i
\(317\) 4.50862 1.64100i 0.253229 0.0921679i −0.212287 0.977207i \(-0.568091\pi\)
0.465516 + 0.885040i \(0.345869\pi\)
\(318\) −2.80928 15.9322i −0.157536 0.893434i
\(319\) 0.411474 2.33359i 0.0230381 0.130656i
\(320\) 0 0
\(321\) −5.21167 + 4.37311i −0.290887 + 0.244083i
\(322\) −3.22668 −0.179816
\(323\) −2.51367 + 6.75119i −0.139864 + 0.375646i
\(324\) −4.04189 −0.224549
\(325\) 0 0
\(326\) −7.75624 2.82304i −0.429579 0.156354i
\(327\) 0.927204 5.25844i 0.0512745 0.290792i
\(328\) −0.897804 5.09170i −0.0495729 0.281142i
\(329\) 4.91147 1.78763i 0.270778 0.0985553i
\(330\) 0 0
\(331\) 6.84864 + 11.8622i 0.376435 + 0.652005i 0.990541 0.137219i \(-0.0438164\pi\)
−0.614105 + 0.789224i \(0.710483\pi\)
\(332\) −8.16431 6.85067i −0.448075 0.375980i
\(333\) 2.35638 + 1.97724i 0.129129 + 0.108352i
\(334\) 8.69594 + 15.0618i 0.475820 + 0.824145i
\(335\) 0 0
\(336\) −3.64543 + 1.32683i −0.198874 + 0.0723844i
\(337\) 1.34952 + 7.65350i 0.0735129 + 0.416913i 0.999249 + 0.0387428i \(0.0123353\pi\)
−0.925736 + 0.378170i \(0.876554\pi\)
\(338\) 2.20826 12.5237i 0.120114 0.681199i
\(339\) 8.84389 + 3.21891i 0.480334 + 0.174827i
\(340\) 0 0
\(341\) 1.69459 0.0917673
\(342\) 4.49138 2.54920i 0.242866 0.137845i
\(343\) −16.4388 −0.887613
\(344\) 8.32295 6.98378i 0.448743 0.376540i
\(345\) 0 0
\(346\) 3.40760 19.3255i 0.183194 1.03894i
\(347\) −0.573978 3.25519i −0.0308128 0.174748i 0.965518 0.260337i \(-0.0838338\pi\)
−0.996330 + 0.0855895i \(0.972723\pi\)
\(348\) 3.00000 1.09191i 0.160817 0.0585326i
\(349\) 12.0851 20.9320i 0.646902 1.12047i −0.336957 0.941520i \(-0.609398\pi\)
0.983859 0.178947i \(-0.0572690\pi\)
\(350\) 0 0
\(351\) −2.29813 1.92836i −0.122665 0.102928i
\(352\) 0.766044 + 0.642788i 0.0408303 + 0.0342607i
\(353\) −14.3721 24.8932i −0.764950 1.32493i −0.940273 0.340422i \(-0.889430\pi\)
0.175323 0.984511i \(-0.443903\pi\)
\(354\) 5.91534 10.2457i 0.314397 0.544552i
\(355\) 0 0
\(356\) 0.128356 + 0.727940i 0.00680283 + 0.0385808i
\(357\) −1.11334 + 6.31407i −0.0589242 + 0.334176i
\(358\) −18.1604 6.60986i −0.959809 0.349342i
\(359\) −9.98751 + 8.38052i −0.527121 + 0.442307i −0.867106 0.498124i \(-0.834022\pi\)
0.339985 + 0.940431i \(0.389578\pi\)
\(360\) 0 0
\(361\) 9.74123 16.3128i 0.512696 0.858570i
\(362\) −26.4243 −1.38883
\(363\) −10.3209 + 8.66025i −0.541706 + 0.454545i
\(364\) −1.43969 0.524005i −0.0754604 0.0274653i
\(365\) 0 0
\(366\) −1.46198 8.29131i −0.0764190 0.433394i
\(367\) 15.1236 5.50454i 0.789446 0.287335i 0.0843402 0.996437i \(-0.473122\pi\)
0.705106 + 0.709102i \(0.250900\pi\)
\(368\) −0.560307 + 0.970481i −0.0292080 + 0.0505898i
\(369\) 3.06283 + 5.30498i 0.159445 + 0.276166i
\(370\) 0 0
\(371\) 26.4859 + 22.2243i 1.37508 + 1.15383i
\(372\) 1.14156 + 1.97724i 0.0591871 + 0.102515i
\(373\) −14.0753 + 24.3792i −0.728793 + 1.26231i 0.228601 + 0.973520i \(0.426585\pi\)
−0.957394 + 0.288786i \(0.906749\pi\)
\(374\) 1.55303 0.565258i 0.0803054 0.0292288i
\(375\) 0 0
\(376\) 0.315207 1.78763i 0.0162556 0.0921900i
\(377\) 1.18479 + 0.431229i 0.0610199 + 0.0222094i
\(378\) 12.4363 10.4353i 0.639654 0.536733i
\(379\) −11.7510 −0.603610 −0.301805 0.953370i \(-0.597589\pi\)
−0.301805 + 0.953370i \(0.597589\pi\)
\(380\) 0 0
\(381\) −25.5294 −1.30791
\(382\) 19.6839 16.5168i 1.00712 0.845071i
\(383\) 16.8229 + 6.12305i 0.859613 + 0.312873i 0.733953 0.679200i \(-0.237673\pi\)
0.125659 + 0.992073i \(0.459895\pi\)
\(384\) −0.233956 + 1.32683i −0.0119390 + 0.0677094i
\(385\) 0 0
\(386\) 4.93882 1.79758i 0.251379 0.0914945i
\(387\) −6.43629 + 11.1480i −0.327175 + 0.566684i
\(388\) −5.80200 10.0494i −0.294552 0.510179i
\(389\) −20.1832 16.9357i −1.02333 0.858675i −0.0332867 0.999446i \(-0.510597\pi\)
−0.990042 + 0.140771i \(0.955042\pi\)
\(390\) 0 0
\(391\) 0.926022 + 1.60392i 0.0468309 + 0.0811136i
\(392\) 0.645430 1.11792i 0.0325991 0.0564633i
\(393\) 21.1741 7.70675i 1.06809 0.388754i
\(394\) −4.27837 24.2638i −0.215541 1.22239i
\(395\) 0 0
\(396\) −1.11334 0.405223i −0.0559475 0.0203632i
\(397\) −12.3923 + 10.3984i −0.621954 + 0.521881i −0.898417 0.439143i \(-0.855282\pi\)
0.276463 + 0.961024i \(0.410838\pi\)
\(398\) 9.79292 0.490875
\(399\) 5.90033 15.8471i 0.295386 0.793345i
\(400\) 0 0
\(401\) 22.3705 18.7711i 1.11713 0.937384i 0.118674 0.992933i \(-0.462136\pi\)
0.998456 + 0.0555495i \(0.0176911\pi\)
\(402\) −3.20574 1.16679i −0.159888 0.0581943i
\(403\) −0.156574 + 0.887975i −0.00779951 + 0.0442332i
\(404\) 2.48040 + 14.0670i 0.123404 + 0.699862i
\(405\) 0 0
\(406\) −3.41147 + 5.90885i −0.169309 + 0.293251i
\(407\) −1.29813 2.24843i −0.0643461 0.111451i
\(408\) 1.70574 + 1.43128i 0.0844466 + 0.0708591i
\(409\) −18.7606 15.7420i −0.927651 0.778392i 0.0477432 0.998860i \(-0.484797\pi\)
−0.975394 + 0.220468i \(0.929242\pi\)
\(410\) 0 0
\(411\) −2.03415 + 3.52325i −0.100337 + 0.173789i
\(412\) −1.49273 + 0.543308i −0.0735413 + 0.0267669i
\(413\) 4.39053 + 24.8999i 0.216044 + 1.22525i
\(414\) 0.230552 1.30753i 0.0113310 0.0642614i
\(415\) 0 0
\(416\) −0.407604 + 0.342020i −0.0199844 + 0.0167689i
\(417\) −16.6759 −0.816624
\(418\) −4.29813 + 0.725293i −0.210229 + 0.0354752i
\(419\) 14.5972 0.713120 0.356560 0.934272i \(-0.383950\pi\)
0.356560 + 0.934272i \(0.383950\pi\)
\(420\) 0 0
\(421\) 14.6557 + 5.33424i 0.714275 + 0.259975i 0.673493 0.739193i \(-0.264793\pi\)
0.0407816 + 0.999168i \(0.487015\pi\)
\(422\) −3.74123 + 21.2176i −0.182120 + 1.03285i
\(423\) 0.373455 + 2.11797i 0.0181580 + 0.102979i
\(424\) 11.2836 4.10689i 0.547979 0.199448i
\(425\) 0 0
\(426\) −3.96585 6.86906i −0.192146 0.332807i
\(427\) 13.7836 + 11.5658i 0.667034 + 0.559708i
\(428\) −3.86824 3.24584i −0.186978 0.156894i
\(429\) 0.358441 + 0.620838i 0.0173057 + 0.0299743i
\(430\) 0 0
\(431\) −35.2857 + 12.8429i −1.69965 + 0.618623i −0.995786 0.0917093i \(-0.970767\pi\)
−0.703867 + 0.710332i \(0.748545\pi\)
\(432\) −0.979055 5.55250i −0.0471048 0.267145i
\(433\) 3.43464 19.4788i 0.165058 0.936092i −0.783946 0.620829i \(-0.786796\pi\)
0.949004 0.315263i \(-0.102093\pi\)
\(434\) −4.58512 1.66885i −0.220093 0.0801073i
\(435\) 0 0
\(436\) 3.96316 0.189801
\(437\) −1.63681 4.60224i −0.0782993 0.220155i
\(438\) −6.71688 −0.320945
\(439\) 14.6120 12.2609i 0.697393 0.585182i −0.223638 0.974672i \(-0.571793\pi\)
0.921031 + 0.389490i \(0.127349\pi\)
\(440\) 0 0
\(441\) −0.265578 + 1.50617i −0.0126466 + 0.0717222i
\(442\) 0.152704 + 0.866025i 0.00726337 + 0.0411926i
\(443\) 16.0125 5.82807i 0.760776 0.276900i 0.0676432 0.997710i \(-0.478452\pi\)
0.693133 + 0.720810i \(0.256230\pi\)
\(444\) 1.74897 3.02931i 0.0830025 0.143764i
\(445\) 0 0
\(446\) −15.6591 13.1395i −0.741480 0.622176i
\(447\) 9.62701 + 8.07802i 0.455342 + 0.382077i
\(448\) −1.43969 2.49362i −0.0680191 0.117813i
\(449\) 19.9368 34.5315i 0.940874 1.62964i 0.177064 0.984199i \(-0.443340\pi\)
0.763810 0.645442i \(-0.223327\pi\)
\(450\) 0 0
\(451\) −0.897804 5.09170i −0.0422759 0.239759i
\(452\) −1.21301 + 6.87933i −0.0570552 + 0.323576i
\(453\) 6.03462 + 2.19642i 0.283531 + 0.103197i
\(454\) 5.96585 5.00594i 0.279991 0.234941i
\(455\) 0 0
\(456\) −3.74170 4.52644i −0.175221 0.211970i
\(457\) −15.4216 −0.721391 −0.360696 0.932684i \(-0.617461\pi\)
−0.360696 + 0.932684i \(0.617461\pi\)
\(458\) 6.14930 5.15988i 0.287338 0.241105i
\(459\) −8.75624 3.18701i −0.408706 0.148757i
\(460\) 0 0
\(461\) −1.58125 8.96773i −0.0736462 0.417669i −0.999234 0.0391353i \(-0.987540\pi\)
0.925588 0.378533i \(-0.123571\pi\)
\(462\) −3.64543 + 1.32683i −0.169601 + 0.0617296i
\(463\) −2.06371 + 3.57445i −0.0959088 + 0.166119i −0.909988 0.414636i \(-0.863909\pi\)
0.814079 + 0.580755i \(0.197242\pi\)
\(464\) 1.18479 + 2.05212i 0.0550026 + 0.0952673i
\(465\) 0 0
\(466\) 2.89646 + 2.43042i 0.134176 + 0.112587i
\(467\) 13.1853 + 22.8375i 0.610141 + 1.05680i 0.991216 + 0.132251i \(0.0422206\pi\)
−0.381075 + 0.924544i \(0.624446\pi\)
\(468\) 0.315207 0.545955i 0.0145705 0.0252368i
\(469\) 6.85117 2.49362i 0.316357 0.115145i
\(470\) 0 0
\(471\) −3.58781 + 20.3475i −0.165318 + 0.937563i
\(472\) 8.25150 + 3.00330i 0.379806 + 0.138238i
\(473\) 8.32295 6.98378i 0.382690 0.321115i
\(474\) 11.5517 0.530587
\(475\) 0 0
\(476\) −4.75877 −0.218118
\(477\) −10.8983 + 9.14473i −0.498998 + 0.418709i
\(478\) 6.37211 + 2.31926i 0.291454 + 0.106080i
\(479\) 2.82207 16.0048i 0.128944 0.731276i −0.849943 0.526874i \(-0.823364\pi\)
0.978887 0.204402i \(-0.0655250\pi\)
\(480\) 0 0
\(481\) 1.29813 0.472482i 0.0591898 0.0215433i
\(482\) −3.02141 + 5.23324i −0.137622 + 0.238367i
\(483\) −2.17365 3.76487i −0.0989044 0.171307i
\(484\) −7.66044 6.42788i −0.348202 0.292176i
\(485\) 0 0
\(486\) 5.73442 + 9.93231i 0.260119 + 0.450539i
\(487\) 8.64883 14.9802i 0.391916 0.678819i −0.600786 0.799410i \(-0.705146\pi\)
0.992702 + 0.120591i \(0.0384790\pi\)
\(488\) 5.87211 2.13727i 0.265818 0.0967498i
\(489\) −1.93107 10.9517i −0.0873262 0.495252i
\(490\) 0 0
\(491\) 14.6630 + 5.33688i 0.661731 + 0.240850i 0.650983 0.759092i \(-0.274357\pi\)
0.0107472 + 0.999942i \(0.496579\pi\)
\(492\) 5.33615 4.47756i 0.240572 0.201864i
\(493\) 3.91622 0.176378
\(494\) 0.0170741 2.31926i 0.000768202 0.104348i
\(495\) 0 0
\(496\) −1.29813 + 1.08926i −0.0582879 + 0.0489094i
\(497\) 15.9290 + 5.79769i 0.714514 + 0.260062i
\(498\) 2.49344 14.1410i 0.111734 0.633674i
\(499\) −6.52394 36.9991i −0.292052 1.65631i −0.678950 0.734184i \(-0.737565\pi\)
0.386899 0.922122i \(-0.373546\pi\)
\(500\) 0 0
\(501\) −11.7160 + 20.2927i −0.523432 + 0.906612i
\(502\) −2.85710 4.94864i −0.127518 0.220868i
\(503\) 23.9500 + 20.0964i 1.06788 + 0.896054i 0.994858 0.101276i \(-0.0322926\pi\)
0.0730176 + 0.997331i \(0.476737\pi\)
\(504\) 2.61334 + 2.19285i 0.116407 + 0.0976774i
\(505\) 0 0
\(506\) −0.560307 + 0.970481i −0.0249087 + 0.0431431i
\(507\) 16.1001 5.85997i 0.715032 0.260250i
\(508\) −3.29039 18.6607i −0.145988 0.827937i
\(509\) 4.05438 22.9935i 0.179707 1.01917i −0.752862 0.658178i \(-0.771327\pi\)
0.932569 0.360991i \(-0.117562\pi\)
\(510\) 0 0
\(511\) 10.9966 9.22724i 0.486461 0.408189i
\(512\) −1.00000 −0.0441942
\(513\) 21.1925 + 12.4444i 0.935673 + 0.549435i
\(514\) 12.8307 0.565937
\(515\) 0 0
\(516\) 13.7554 + 5.00654i 0.605546 + 0.220401i
\(517\) 0.315207 1.78763i 0.0138628 0.0786199i
\(518\) 1.29813 + 7.36208i 0.0570367 + 0.323471i
\(519\) 24.8444 9.04261i 1.09055 0.396926i
\(520\) 0 0
\(521\) −4.58647 7.94399i −0.200937 0.348033i 0.747894 0.663818i \(-0.231065\pi\)
−0.948831 + 0.315786i \(0.897732\pi\)
\(522\) −2.15064 1.80460i −0.0941311 0.0789854i
\(523\) −10.9725 9.20702i −0.479794 0.402595i 0.370558 0.928809i \(-0.379166\pi\)
−0.850352 + 0.526215i \(0.823611\pi\)
\(524\) 8.36231 + 14.4839i 0.365309 + 0.632734i
\(525\) 0 0
\(526\) 4.59714 1.67322i 0.200445 0.0729560i
\(527\) 0.486329 + 2.75811i 0.0211848 + 0.120145i
\(528\) −0.233956 + 1.32683i −0.0101816 + 0.0577428i
\(529\) 20.4329 + 7.43696i 0.888386 + 0.323346i
\(530\) 0 0
\(531\) −10.4037 −0.451484
\(532\) 12.3439 + 2.27038i 0.535176 + 0.0984336i
\(533\) 2.75103 0.119160
\(534\) −0.762889 + 0.640140i −0.0330134 + 0.0277016i
\(535\) 0 0
\(536\) 0.439693 2.49362i 0.0189918 0.107708i
\(537\) −4.52141 25.6422i −0.195113 1.10654i
\(538\) −14.9290 + 5.43372i −0.643636 + 0.234264i
\(539\) 0.645430 1.11792i 0.0278006 0.0481521i
\(540\) 0 0
\(541\) −25.1058 21.0663i −1.07938 0.905710i −0.0835140 0.996507i \(-0.526614\pi\)
−0.995869 + 0.0907964i \(0.971059\pi\)
\(542\) 18.7083 + 15.6981i 0.803589 + 0.674291i
\(543\) −17.8007 30.8316i −0.763899 1.32311i
\(544\) −0.826352 + 1.43128i −0.0354295 + 0.0613658i
\(545\) 0 0
\(546\) −0.358441 2.03282i −0.0153398 0.0869966i
\(547\) −5.04205 + 28.5949i −0.215583 + 1.22263i 0.664310 + 0.747457i \(0.268725\pi\)
−0.879893 + 0.475172i \(0.842386\pi\)
\(548\) −2.83750 1.03276i −0.121212 0.0441175i
\(549\) −5.67159 + 4.75903i −0.242058 + 0.203110i
\(550\) 0 0
\(551\) −10.1584 1.86841i −0.432762 0.0795968i
\(552\) −1.50980 −0.0642614
\(553\) −18.9119 + 15.8690i −0.804218 + 0.674819i
\(554\) −10.8439 3.94685i −0.460713 0.167686i
\(555\) 0 0
\(556\) −2.14930 12.1893i −0.0911506 0.516941i
\(557\) −26.4722 + 9.63511i −1.12167 + 0.408253i −0.835260 0.549856i \(-0.814683\pi\)
−0.286406 + 0.958108i \(0.592460\pi\)
\(558\) 1.00387 1.73875i 0.0424972 0.0736073i
\(559\) 2.89053 + 5.00654i 0.122256 + 0.211754i
\(560\) 0 0
\(561\) 1.70574 + 1.43128i 0.0720163 + 0.0604288i
\(562\) −3.94222 6.82812i −0.166292 0.288027i
\(563\) −5.15270 + 8.92474i −0.217161 + 0.376133i −0.953939 0.300001i \(-0.903013\pi\)
0.736778 + 0.676135i \(0.236346\pi\)
\(564\) 2.29813 0.836452i 0.0967689 0.0352210i
\(565\) 0 0
\(566\) −0.823826 + 4.67215i −0.0346280 + 0.196385i
\(567\) 10.9363 + 3.98048i 0.459281 + 0.167165i
\(568\) 4.50980 3.78417i 0.189227 0.158780i
\(569\) −24.3723 −1.02174 −0.510869 0.859658i \(-0.670676\pi\)
−0.510869 + 0.859658i \(0.670676\pi\)
\(570\) 0 0
\(571\) −40.7844 −1.70677 −0.853386 0.521279i \(-0.825455\pi\)
−0.853386 + 0.521279i \(0.825455\pi\)
\(572\) −0.407604 + 0.342020i −0.0170428 + 0.0143006i
\(573\) 32.5317 + 11.8406i 1.35903 + 0.494647i
\(574\) −2.58512 + 14.6610i −0.107901 + 0.611937i
\(575\) 0 0
\(576\) 1.11334 0.405223i 0.0463892 0.0168843i
\(577\) −16.2815 + 28.2004i −0.677809 + 1.17400i 0.297831 + 0.954619i \(0.403737\pi\)
−0.975639 + 0.219381i \(0.929596\pi\)
\(578\) −7.13429 12.3569i −0.296747 0.513981i
\(579\) 5.42443 + 4.55164i 0.225432 + 0.189160i
\(580\) 0 0
\(581\) 15.3439 + 26.5764i 0.636572 + 1.10257i
\(582\) 7.81702 13.5395i 0.324026 0.561229i
\(583\) 11.2836 4.10689i 0.467318 0.170090i
\(584\) −0.865715 4.90971i −0.0358235 0.203165i
\(585\) 0 0
\(586\) 11.8341 + 4.30726i 0.488862 + 0.177931i
\(587\) 20.0724 16.8427i 0.828476 0.695174i −0.126465 0.991971i \(-0.540363\pi\)
0.954941 + 0.296797i \(0.0959185\pi\)
\(588\) 1.73917 0.0717222
\(589\) 0.0543776 7.38636i 0.00224059 0.304350i
\(590\) 0 0
\(591\) 25.4288 21.3373i 1.04600 0.877698i
\(592\) 2.43969 + 0.887975i 0.100271 + 0.0364956i
\(593\) 8.25893 46.8387i 0.339154 1.92344i −0.0424244 0.999100i \(-0.513508\pi\)
0.381578 0.924337i \(-0.375381\pi\)
\(594\) −0.979055 5.55250i −0.0401711 0.227822i
\(595\) 0 0
\(596\) −4.66385 + 8.07802i −0.191039 + 0.330889i
\(597\) 6.59698 + 11.4263i 0.269996 + 0.467648i
\(598\) −0.456767 0.383273i −0.0186786 0.0156732i
\(599\) −11.9474 10.0251i −0.488159 0.409614i 0.365207 0.930926i \(-0.380998\pi\)
−0.853366 + 0.521312i \(0.825443\pi\)
\(600\) 0 0
\(601\) 18.8876 32.7143i 0.770441 1.33444i −0.166881 0.985977i \(-0.553369\pi\)
0.937321 0.348466i \(-0.113297\pi\)
\(602\) −29.3974 + 10.6998i −1.19815 + 0.436090i
\(603\) 0.520945 + 2.95442i 0.0212145 + 0.120313i
\(604\) −0.827696 + 4.69410i −0.0336785 + 0.191000i
\(605\) 0 0
\(606\) −14.7424 + 12.3704i −0.598870 + 0.502511i
\(607\) −32.7520 −1.32936 −0.664681 0.747128i \(-0.731432\pi\)
−0.664681 + 0.747128i \(0.731432\pi\)
\(608\) 2.82635 3.31839i 0.114624 0.134579i
\(609\) −9.19253 −0.372500
\(610\) 0 0
\(611\) 0.907604 + 0.330341i 0.0367177 + 0.0133642i
\(612\) 0.340022 1.92836i 0.0137446 0.0779494i
\(613\) 5.78729 + 32.8214i 0.233747 + 1.32564i 0.845237 + 0.534391i \(0.179459\pi\)
−0.611491 + 0.791252i \(0.709430\pi\)
\(614\) −28.3692 + 10.3255i −1.14489 + 0.416705i
\(615\) 0 0
\(616\) −1.43969 2.49362i −0.0580069 0.100471i
\(617\) −29.1937 24.4964i −1.17529 0.986189i −0.999999 0.00167362i \(-0.999467\pi\)
−0.175296 0.984516i \(-0.556088\pi\)
\(618\) −1.63950 1.37570i −0.0659504 0.0553389i
\(619\) 12.0312 + 20.8387i 0.483575 + 0.837577i 0.999822 0.0188630i \(-0.00600463\pi\)
−0.516247 + 0.856440i \(0.672671\pi\)
\(620\) 0 0
\(621\) 5.93717 2.16095i 0.238250 0.0867160i
\(622\) −1.92484 10.9163i −0.0771791 0.437704i
\(623\) 0.369585 2.09602i 0.0148071 0.0839753i
\(624\) −0.673648 0.245188i −0.0269675 0.00981537i
\(625\) 0 0
\(626\) −8.18479 −0.327130
\(627\) −3.74170 4.52644i −0.149429 0.180769i
\(628\) −15.3354 −0.611951
\(629\) 3.28699 2.75811i 0.131061 0.109973i
\(630\) 0 0
\(631\) 4.68139 26.5495i 0.186363 1.05692i −0.737828 0.674988i \(-0.764149\pi\)
0.924191 0.381930i \(-0.124740\pi\)
\(632\) 1.48886 + 8.44372i 0.0592235 + 0.335873i
\(633\) −27.2768 + 9.92794i −1.08415 + 0.394600i
\(634\) −2.39899 + 4.15516i −0.0952759 + 0.165023i
\(635\) 0 0
\(636\) 12.3931 + 10.3990i 0.491417 + 0.412348i
\(637\) 0.526159 + 0.441500i 0.0208472 + 0.0174929i
\(638\) 1.18479 + 2.05212i 0.0469064 + 0.0812442i
\(639\) −3.48751 + 6.04055i −0.137964 + 0.238960i
\(640\) 0 0
\(641\) 0.733956 + 4.16247i 0.0289895 + 0.164408i 0.995866 0.0908384i \(-0.0289547\pi\)
−0.966876 + 0.255246i \(0.917844\pi\)
\(642\) 1.18139 6.69999i 0.0466257 0.264428i
\(643\) −24.6459 8.97037i −0.971939 0.353757i −0.193238 0.981152i \(-0.561899\pi\)
−0.778701 + 0.627395i \(0.784121\pi\)
\(644\) 2.47178 2.07407i 0.0974018 0.0817298i
\(645\) 0 0
\(646\) −2.41400 6.78747i −0.0949776 0.267049i
\(647\) −6.31221 −0.248159 −0.124079 0.992272i \(-0.539598\pi\)
−0.124079 + 0.992272i \(0.539598\pi\)
\(648\) 3.09627 2.59808i 0.121633 0.102062i
\(649\) 8.25150 + 3.00330i 0.323900 + 0.117890i
\(650\) 0 0
\(651\) −1.14156 6.47410i −0.0447412 0.253740i
\(652\) 7.75624 2.82304i 0.303758 0.110559i
\(653\) 8.22580 14.2475i 0.321901 0.557548i −0.658980 0.752161i \(-0.729012\pi\)
0.980880 + 0.194613i \(0.0623450\pi\)
\(654\) 2.66978 + 4.62419i 0.104397 + 0.180820i
\(655\) 0 0
\(656\) 3.96064 + 3.32337i 0.154637 + 0.129756i
\(657\) 2.95336 + 5.11538i 0.115222 + 0.199570i
\(658\) −2.61334 + 4.52644i −0.101879 + 0.176459i
\(659\) −33.6168 + 12.2355i −1.30952 + 0.476628i −0.900087 0.435710i \(-0.856497\pi\)
−0.409438 + 0.912338i \(0.634275\pi\)
\(660\) 0 0
\(661\) 5.11159 28.9892i 0.198818 1.12755i −0.708059 0.706154i \(-0.750429\pi\)
0.906876 0.421397i \(-0.138460\pi\)
\(662\) −12.8712 4.68475i −0.500255 0.182078i
\(663\) −0.907604 + 0.761570i −0.0352484 + 0.0295769i
\(664\) 10.6578 0.413601
\(665\) 0 0
\(666\) −3.07604 −0.119194
\(667\) −2.03415 + 1.70685i −0.0787625 + 0.0660896i
\(668\) −16.3430 5.94837i −0.632330 0.230149i
\(669\) 4.78240 27.1224i 0.184898 1.04861i
\(670\) 0 0
\(671\) 5.87211 2.13727i 0.226690 0.0825085i
\(672\) 1.93969 3.35965i 0.0748253 0.129601i
\(673\) −16.0692 27.8327i −0.619423 1.07287i −0.989591 0.143908i \(-0.954033\pi\)
0.370168 0.928965i \(-0.379300\pi\)
\(674\) −5.95336 4.99546i −0.229315 0.192418i
\(675\) 0 0
\(676\) 6.35844 + 11.0131i 0.244555 + 0.423582i
\(677\) −9.00980 + 15.6054i −0.346275 + 0.599765i −0.985585 0.169184i \(-0.945887\pi\)
0.639310 + 0.768949i \(0.279220\pi\)
\(678\) −8.84389 + 3.21891i −0.339648 + 0.123622i
\(679\) 5.80200 + 32.9048i 0.222660 + 1.26277i
\(680\) 0 0
\(681\) 9.85978 + 3.58867i 0.377828 + 0.137518i
\(682\) −1.29813 + 1.08926i −0.0497081 + 0.0417100i
\(683\) 27.6195 1.05683 0.528415 0.848986i \(-0.322786\pi\)
0.528415 + 0.848986i \(0.322786\pi\)
\(684\) −1.80200 + 4.83981i −0.0689013 + 0.185055i
\(685\) 0 0
\(686\) 12.5929 10.5667i 0.480798 0.403437i
\(687\) 10.1630 + 3.69902i 0.387742 + 0.141126i
\(688\) −1.88666 + 10.6998i −0.0719282 + 0.407925i
\(689\) 1.10947 + 6.29212i 0.0422675 + 0.239711i
\(690\) 0 0
\(691\) −14.8089 + 25.6497i −0.563356 + 0.975761i 0.433845 + 0.900988i \(0.357157\pi\)
−0.997201 + 0.0747733i \(0.976177\pi\)
\(692\) 9.81180 + 16.9945i 0.372989 + 0.646036i
\(693\) 2.61334 + 2.19285i 0.0992726 + 0.0832996i
\(694\) 2.53209 + 2.12467i 0.0961168 + 0.0806516i
\(695\) 0 0
\(696\) −1.59627 + 2.76481i −0.0605063 + 0.104800i
\(697\) 8.02956 2.92252i 0.304141 0.110698i
\(698\) 4.19712 + 23.8030i 0.158863 + 0.900959i
\(699\) −0.884600 + 5.01681i −0.0334586 + 0.189753i
\(700\) 0 0
\(701\) 19.9277 16.7213i 0.752658 0.631555i −0.183547 0.983011i \(-0.558758\pi\)
0.936204 + 0.351456i \(0.114313\pi\)
\(702\) 3.00000 0.113228
\(703\) −9.84208 + 5.58613i −0.371201 + 0.210685i
\(704\) −1.00000 −0.0376889
\(705\) 0 0
\(706\) 27.0107 + 9.83110i 1.01656 + 0.369998i
\(707\) 7.14203 40.5044i 0.268604 1.52333i
\(708\) 2.05438 + 11.6510i 0.0772082 + 0.437870i
\(709\) −27.9932 + 10.1887i −1.05131 + 0.382644i −0.809156 0.587594i \(-0.800075\pi\)
−0.242151 + 0.970239i \(0.577853\pi\)
\(710\) 0 0
\(711\) −5.07919 8.79742i −0.190485 0.329929i
\(712\) −0.566237 0.475129i −0.0212206 0.0178062i
\(713\) −1.45471 1.22064i −0.0544792 0.0457135i
\(714\) −3.20574 5.55250i −0.119972 0.207797i
\(715\) 0 0
\(716\) 18.1604 6.60986i 0.678688 0.247022i
\(717\) 1.58647 + 8.99730i 0.0592477 + 0.336010i
\(718\) 2.26399 12.8397i 0.0844912 0.479173i
\(719\) 14.2007 + 5.16863i 0.529596 + 0.192757i 0.592958 0.805233i \(-0.297960\pi\)
−0.0633618 + 0.997991i \(0.520182\pi\)
\(720\) 0 0
\(721\) 4.57398 0.170344
\(722\) 3.02347 + 18.7579i 0.112522 + 0.698097i
\(723\) −8.14147 −0.302785
\(724\) 20.2422 16.9852i 0.752294 0.631250i
\(725\) 0 0
\(726\) 2.33956 13.2683i 0.0868291 0.492432i
\(727\) −1.30335 7.39165i −0.0483385 0.274141i 0.951053 0.309029i \(-0.100004\pi\)
−0.999391 + 0.0348873i \(0.988893\pi\)
\(728\) 1.43969 0.524005i 0.0533586 0.0194209i
\(729\) −13.7888 + 23.8829i −0.510696 + 0.884552i
\(730\) 0 0
\(731\) 13.7554 + 11.5421i 0.508761 + 0.426901i
\(732\) 6.44949 + 5.41177i 0.238380 + 0.200025i
\(733\) −7.86706 13.6261i −0.290576 0.503293i 0.683370 0.730072i \(-0.260514\pi\)
−0.973946 + 0.226779i \(0.927180\pi\)
\(734\) −8.04710 + 13.9380i −0.297024 + 0.514461i
\(735\) 0 0
\(736\) −0.194593 1.10359i −0.00717278 0.0406789i
\(737\) 0.439693 2.49362i 0.0161963 0.0918537i
\(738\) −5.75624 2.09510i −0.211890 0.0771218i
\(739\) −16.6570 + 13.9769i −0.612739 + 0.514149i −0.895512 0.445038i \(-0.853190\pi\)
0.282773 + 0.959187i \(0.408746\pi\)
\(740\) 0 0
\(741\) 2.71760 1.54244i 0.0998334 0.0566630i
\(742\) −34.5749 −1.26928
\(743\) −20.7442 + 17.4065i −0.761032 + 0.638581i −0.938395 0.345564i \(-0.887688\pi\)
0.177363 + 0.984145i \(0.443243\pi\)
\(744\) −2.14543 0.780873i −0.0786553 0.0286282i
\(745\) 0 0
\(746\) −4.88831 27.7230i −0.178974 1.01501i
\(747\) −11.8657 + 4.31877i −0.434144 + 0.158015i
\(748\) −0.826352 + 1.43128i −0.0302144 + 0.0523329i
\(749\) 7.26991 + 12.5919i 0.265637 + 0.460097i
\(750\) 0 0
\(751\) 27.8733 + 23.3885i 1.01711 + 0.853457i 0.989262 0.146155i \(-0.0466897\pi\)
0.0278492 + 0.999612i \(0.491134\pi\)
\(752\) 0.907604 + 1.57202i 0.0330969 + 0.0573255i
\(753\) 3.84936 6.66728i 0.140278 0.242969i
\(754\) −1.18479 + 0.431229i −0.0431476 + 0.0157044i
\(755\) 0 0
\(756\) −2.81908 + 15.9878i −0.102529 + 0.581470i
\(757\) 19.3307 + 7.03580i 0.702586 + 0.255720i 0.668515 0.743699i \(-0.266930\pi\)
0.0340713 + 0.999419i \(0.489153\pi\)
\(758\) 9.00181 7.55342i 0.326960 0.274352i
\(759\) −1.50980 −0.0548023
\(760\) 0 0
\(761\) −47.5850 −1.72496 −0.862478 0.506095i \(-0.831089\pi\)
−0.862478 + 0.506095i \(0.831089\pi\)
\(762\) 19.5567 16.4100i 0.708463 0.594471i
\(763\) −10.7233 3.90295i −0.388209 0.141296i
\(764\) −4.46198 + 25.3052i −0.161429 + 0.915508i
\(765\) 0 0
\(766\) −16.8229 + 6.12305i −0.607838 + 0.221235i
\(767\) −2.33615 + 4.04633i −0.0843536 + 0.146105i
\(768\) −0.673648 1.16679i −0.0243082 0.0421030i
\(769\) 12.2215 + 10.2550i 0.440717 + 0.369806i 0.835978 0.548763i \(-0.184901\pi\)
−0.395260 + 0.918569i \(0.629346\pi\)
\(770\) 0 0
\(771\) 8.64337 + 14.9708i 0.311283 + 0.539159i
\(772\) −2.62789 + 4.55164i −0.0945798 + 0.163817i
\(773\) −15.4483 + 5.62273i −0.555637 + 0.202235i −0.604549 0.796568i \(-0.706647\pi\)
0.0489122 + 0.998803i \(0.484425\pi\)
\(774\) −2.23530 12.6770i −0.0803462 0.455666i
\(775\) 0 0
\(776\) 10.9042 + 3.96880i 0.391438 + 0.142472i
\(777\) −7.71554 + 6.47410i −0.276793 + 0.232257i
\(778\) 26.3473 0.944596
\(779\) −22.2224 + 3.74994i −0.796200 + 0.134356i
\(780\) 0 0
\(781\) 4.50980 3.78417i 0.161373 0.135408i
\(782\) −1.74035 0.633436i −0.0622349 0.0226516i
\(783\) 2.31996 13.1571i 0.0829084 0.470197i
\(784\) 0.224155 + 1.27125i 0.00800555 + 0.0454017i
\(785\) 0 0
\(786\) −11.2665 + 19.5142i −0.401863 + 0.696047i
\(787\) −24.9873 43.2792i −0.890700 1.54274i −0.839038 0.544073i \(-0.816882\pi\)
−0.0516616 0.998665i \(-0.516452\pi\)
\(788\) 18.8739 + 15.8371i 0.672356 + 0.564173i
\(789\) 5.04916 + 4.23675i 0.179755 + 0.150832i
\(790\) 0 0
\(791\) 10.0569 17.4191i 0.357582 0.619351i
\(792\) 1.11334 0.405223i 0.0395608 0.0143990i
\(793\) 0.577382 + 3.27449i 0.0205034 + 0.116281i
\(794\) 2.80912 15.9313i 0.0996918 0.565380i
\(795\) 0 0
\(796\) −7.50181 + 6.29477i −0.265895 + 0.223112i
\(797\) 11.9314 0.422631 0.211316 0.977418i \(-0.432225\pi\)
0.211316 + 0.977418i \(0.432225\pi\)
\(798\) 5.66637 + 15.9322i 0.200587 + 0.563994i
\(799\) 3.00000 0.106132
\(800\) 0 0
\(801\) 0.822948 + 0.299529i 0.0290774 + 0.0105833i
\(802\) −5.07098 + 28.7590i −0.179063 + 1.01552i
\(803\) −0.865715 4.90971i −0.0305504 0.173260i
\(804\) 3.20574 1.16679i 0.113058 0.0411496i
\(805\) 0 0
\(806\) −0.450837 0.780873i −0.0158801 0.0275051i
\(807\) −16.3969 13.7587i −0.577199 0.484328i
\(808\) −10.9422 9.18161i −0.384946 0.323008i
\(809\) 25.0744 + 43.4302i 0.881571 + 1.52692i 0.849595 + 0.527436i \(0.176847\pi\)
0.0319760 + 0.999489i \(0.489820\pi\)
\(810\) 0 0
\(811\) −22.8567 + 8.31915i −0.802607 + 0.292125i −0.710566 0.703630i \(-0.751561\pi\)
−0.0920405 + 0.995755i \(0.529339\pi\)
\(812\) −1.18479 6.71929i −0.0415781 0.235801i
\(813\) −5.71364 + 32.4037i −0.200386 + 1.13645i
\(814\) 2.43969 + 0.887975i 0.0855112 + 0.0311235i
\(815\) 0 0
\(816\) −2.22668 −0.0779494
\(817\) −30.1737 36.5020i −1.05564 1.27704i
\(818\) 24.4902 0.856280
\(819\) −1.39053 + 1.16679i −0.0485890 + 0.0407710i
\(820\) 0 0
\(821\) −7.12671 + 40.4176i −0.248724 + 1.41058i 0.562959 + 0.826485i \(0.309663\pi\)
−0.811683 + 0.584098i \(0.801448\pi\)
\(822\) −0.706452 4.00649i −0.0246404 0.139742i
\(823\) 9.89693 3.60219i 0.344985 0.125564i −0.163716 0.986508i \(-0.552348\pi\)
0.508701 + 0.860943i \(0.330126\pi\)
\(824\) 0.794263 1.37570i 0.0276695 0.0479249i
\(825\) 0 0
\(826\) −19.3687 16.2523i −0.673924 0.565489i
\(827\) 37.0565 + 31.0941i 1.28858 + 1.08125i 0.992000 + 0.126240i \(0.0402908\pi\)
0.296581 + 0.955008i \(0.404154\pi\)
\(828\) 0.663848 + 1.14982i 0.0230703 + 0.0399590i
\(829\) 11.1279 19.2741i 0.386488 0.669416i −0.605487 0.795855i \(-0.707022\pi\)
0.991974 + 0.126439i \(0.0403549\pi\)
\(830\) 0 0
\(831\) −2.69981 15.3114i −0.0936553 0.531145i
\(832\) 0.0923963 0.524005i 0.00320326 0.0181666i
\(833\) 2.00475 + 0.729669i 0.0694604 + 0.0252815i
\(834\) 12.7745 10.7191i 0.442345 0.371171i
\(835\) 0 0
\(836\) 2.82635 3.31839i 0.0977514 0.114769i
\(837\) 9.55438 0.330248
\(838\) −11.1821 + 9.38290i −0.386279 + 0.324127i
\(839\) −13.6638 4.97323i −0.471728 0.171695i 0.0952067 0.995458i \(-0.469649\pi\)
−0.566935 + 0.823762i \(0.691871\pi\)
\(840\) 0 0
\(841\) −4.06077 23.0298i −0.140027 0.794131i
\(842\) −14.6557 + 5.33424i −0.505069 + 0.183830i
\(843\) 5.31134 9.19951i 0.182932 0.316848i
\(844\) −10.7724 18.6584i −0.370803 0.642249i
\(845\) 0 0
\(846\) −1.64749 1.38241i −0.0566418 0.0475281i
\(847\) 14.3969 + 24.9362i 0.494684 + 0.856818i
\(848\) −6.00387 + 10.3990i −0.206174 + 0.357103i
\(849\) −6.00640 + 2.18615i −0.206139 + 0.0750285i
\(850\) 0 0
\(851\) −0.505215 + 2.86521i −0.0173185 + 0.0982183i
\(852\) 7.45336 + 2.71280i 0.255348 + 0.0929391i
\(853\) −16.1550 + 13.5556i −0.553136 + 0.464136i −0.876001 0.482309i \(-0.839798\pi\)
0.322865 + 0.946445i \(0.395354\pi\)
\(854\) −17.9932 −0.615714
\(855\) 0 0
\(856\) 5.04963 0.172593
\(857\) 23.6909 19.8791i 0.809267 0.679056i −0.141166 0.989986i \(-0.545085\pi\)
0.950433 + 0.310930i \(0.100641\pi\)
\(858\) −0.673648 0.245188i −0.0229980 0.00837058i
\(859\) −3.27110 + 18.5513i −0.111608 + 0.632963i 0.876765 + 0.480918i \(0.159697\pi\)
−0.988374 + 0.152044i \(0.951414\pi\)
\(860\) 0 0
\(861\) −18.8478 + 6.86002i −0.642330 + 0.233789i
\(862\) 18.7751 32.5195i 0.639483 1.10762i
\(863\) 20.6689 + 35.7996i 0.703578 + 1.21863i 0.967202 + 0.254007i \(0.0817486\pi\)
−0.263625 + 0.964625i \(0.584918\pi\)
\(864\) 4.31908 + 3.62414i 0.146938 + 0.123296i
\(865\) 0 0
\(866\) 9.88965 + 17.1294i 0.336064 + 0.582080i
\(867\) 9.61200 16.6485i 0.326441 0.565412i
\(868\) 4.58512 1.66885i 0.155629 0.0566444i
\(869\) 1.48886 + 8.44372i 0.0505060 + 0.286434i
\(870\) 0 0
\(871\) 1.26604 + 0.460802i 0.0428983 + 0.0156137i
\(872\) −3.03596 + 2.54747i −0.102811 + 0.0862683i
\(873\) −13.7483 −0.465311
\(874\) 4.21213 + 2.47340i 0.142478 + 0.0836640i
\(875\) 0 0
\(876\) 5.14543 4.31753i 0.173848 0.145876i
\(877\) 2.20604 + 0.802934i 0.0744927 + 0.0271131i 0.378998 0.925398i \(-0.376269\pi\)
−0.304505 + 0.952511i \(0.598491\pi\)
\(878\) −3.31227 + 18.7848i −0.111784 + 0.633957i
\(879\) 2.94634 + 16.7095i 0.0993775 + 0.563598i
\(880\) 0 0
\(881\) −13.6792 + 23.6930i −0.460863 + 0.798238i −0.999004 0.0446167i \(-0.985793\pi\)
0.538141 + 0.842855i \(0.319127\pi\)
\(882\) −0.764700 1.32450i −0.0257488 0.0445982i
\(883\) 0.590585 + 0.495560i 0.0198748 + 0.0166769i 0.652671 0.757642i \(-0.273648\pi\)
−0.632796 + 0.774318i \(0.718093\pi\)
\(884\) −0.673648 0.565258i −0.0226572 0.0190117i
\(885\) 0 0
\(886\) −8.52007 + 14.7572i −0.286237 + 0.495777i
\(887\) −4.22106 + 1.53634i −0.141729 + 0.0515852i −0.411911 0.911224i \(-0.635138\pi\)
0.270182 + 0.962809i \(0.412916\pi\)
\(888\) 0.607411 + 3.44480i 0.0203834 + 0.115600i
\(889\) −9.47431 + 53.7315i −0.317758 + 1.80210i
\(890\) 0 0
\(891\) 3.09627 2.59808i 0.103729 0.0870388i
\(892\) 20.4415 0.684432
\(893\) −7.78177 1.43128i −0.260407 0.0478961i
\(894\) −12.5672 −0.420309
\(895\) 0 0
\(896\) 2.70574 + 0.984808i 0.0903923 + 0.0329001i
\(897\) 0.139500 0.791143i 0.00465777 0.0264155i
\(898\) 6.92396 + 39.2677i 0.231056 + 1.31038i
\(899\) −3.77332 + 1.37338i −0.125847 + 0.0458046i
\(900\) 0 0
\(901\) 9.92262 + 17.1865i 0.330570 + 0.572565i
\(902\) 3.96064 + 3.32337i 0.131875 + 0.110656i
\(903\) −32.2879 27.0928i −1.07447 0.901591i
\(904\) −3.49273 6.04958i −0.116166 0.201206i
\(905\) 0 0
\(906\) −6.03462 + 2.19642i −0.200487 + 0.0729712i
\(907\) −3.10653 17.6180i −0.103151 0.584997i −0.991943 0.126686i \(-0.959566\pi\)
0.888792 0.458311i \(-0.151545\pi\)
\(908\) −1.35235 + 7.66955i −0.0448793 + 0.254523i
\(909\) 15.9030 + 5.78823i 0.527470 + 0.191983i
\(910\) 0 0
\(911\) −21.2398 −0.703706 −0.351853 0.936055i \(-0.614448\pi\)
−0.351853 + 0.936055i \(0.614448\pi\)
\(912\) 5.77584 + 1.06234i 0.191257 + 0.0351775i
\(913\) 10.6578 0.352720
\(914\) 11.8136 9.91280i 0.390760 0.327886i
\(915\) 0 0
\(916\) −1.39393 + 7.90539i −0.0460568 + 0.261201i
\(917\) −8.36231 47.4250i −0.276148 1.56611i
\(918\) 8.75624 3.18701i 0.288999 0.105187i
\(919\) −6.68913 + 11.5859i −0.220654 + 0.382184i −0.955007 0.296584i \(-0.904153\pi\)
0.734353 + 0.678768i \(0.237486\pi\)
\(920\) 0 0
\(921\) −31.1586 26.1452i −1.02671 0.861513i
\(922\) 6.97565 + 5.85327i 0.229731 + 0.192767i
\(923\) 1.56624 + 2.71280i 0.0515533 + 0.0892930i
\(924\) 1.93969 3.35965i 0.0638112 0.110524i
\(925\) 0 0
\(926\) −0.716719 4.06472i −0.0235529 0.133575i
\(927\) −0.326819 + 1.85348i −0.0107341 + 0.0608763i
\(928\) −2.22668 0.810446i −0.0730944 0.0266042i
\(929\) −8.74241 + 7.33575i −0.286829 + 0.240678i −0.774837 0.632161i \(-0.782168\pi\)
0.488008 + 0.872839i \(0.337724\pi\)
\(930\) 0 0
\(931\) −4.85204 2.84916i −0.159019 0.0933774i
\(932\) −3.78106 −0.123853
\(933\) 11.4404 9.59964i 0.374542 0.314278i
\(934\) −24.7802 9.01925i −0.810832 0.295119i
\(935\) 0 0
\(936\) 0.109470 + 0.620838i 0.00357815 + 0.0202927i
\(937\) 47.0941 17.1409i 1.53850 0.559967i 0.572813 0.819686i \(-0.305852\pi\)
0.965684 + 0.259719i \(0.0836299\pi\)
\(938\) −3.64543 + 6.31407i −0.119027 + 0.206162i
\(939\) −5.51367 9.54996i −0.179932 0.311651i
\(940\) 0 0
\(941\) 24.0514 + 20.1816i 0.784055 + 0.657900i 0.944266 0.329183i \(-0.106773\pi\)
−0.160212 + 0.987083i \(0.551218\pi\)
\(942\) −10.3307 17.8933i −0.336592 0.582995i
\(943\) −2.89693 + 5.01762i −0.0943369 + 0.163396i
\(944\) −8.25150 + 3.00330i −0.268563 + 0.0977491i
\(945\) 0 0
\(946\) −1.88666 + 10.6998i −0.0613406 + 0.347880i
\(947\) 23.4602 + 8.53882i 0.762355 + 0.277475i 0.693795 0.720173i \(-0.255937\pi\)
0.0685599 + 0.997647i \(0.478160\pi\)
\(948\) −8.84911 + 7.42528i −0.287406 + 0.241162i
\(949\) 2.65270 0.0861104
\(950\) 0 0
\(951\) −6.46429 −0.209619
\(952\) 3.64543 3.05888i 0.118149 0.0991388i
\(953\) −24.0590 8.75677i −0.779348 0.283660i −0.0784473 0.996918i \(-0.524996\pi\)
−0.700901 + 0.713259i \(0.747218\pi\)
\(954\) 2.47044 14.0105i 0.0799834 0.453608i
\(955\) 0 0
\(956\) −6.37211 + 2.31926i −0.206089 + 0.0750102i
\(957\) −1.59627 + 2.76481i −0.0516000 + 0.0893738i
\(958\) 8.12583 + 14.0743i 0.262534 + 0.454722i
\(959\) 6.66044 + 5.58878i 0.215077 + 0.180471i
\(960\) 0 0
\(961\) 14.0642 + 24.3599i 0.453683 + 0.785802i
\(962\) −0.690722 + 1.19637i −0.0222698 + 0.0385724i
\(963\) −5.62196 + 2.04623i −0.181165 + 0.0659387i
\(964\) −1.04933 5.95102i −0.0337965 0.191669i
\(965\) 0 0
\(966\) 4.08512 + 1.48686i 0.131437 + 0.0478390i
\(967\) −39.3155 + 32.9896i −1.26430 + 1.06088i −0.269092 + 0.963115i \(0.586723\pi\)
−0.995210 + 0.0977605i \(0.968832\pi\)
\(968\) 10.0000 0.321412
\(969\) 6.29339 7.38901i 0.202173 0.237369i
\(970\) 0 0
\(971\) 13.2554 11.1226i 0.425385 0.356940i −0.404822 0.914395i \(-0.632667\pi\)
0.830207 + 0.557455i \(0.188222\pi\)
\(972\) −10.7772 3.92258i −0.345678 0.125817i
\(973\) −6.18866 + 35.0977i −0.198399 + 1.12518i
\(974\) 3.00371 + 17.0349i 0.0962450 + 0.545833i
\(975\) 0 0
\(976\) −3.12449 + 5.41177i −0.100012 + 0.173226i
\(977\) −6.90554 11.9608i −0.220928 0.382658i 0.734162 0.678974i \(-0.237575\pi\)
−0.955090 + 0.296316i \(0.904242\pi\)
\(978\) 8.51889 + 7.14819i 0.272404 + 0.228574i
\(979\) −0.566237 0.475129i −0.0180970 0.0151852i
\(980\) 0 0
\(981\) 2.34776 4.06645i 0.0749583 0.129832i
\(982\) −14.6630 + 5.33688i −0.467914 + 0.170307i
\(983\) 1.03028 + 5.84300i 0.0328608 + 0.186363i 0.996820 0.0796878i \(-0.0253923\pi\)
−0.963959 + 0.266050i \(0.914281\pi\)
\(984\) −1.20961 + 6.86002i −0.0385609 + 0.218690i
\(985\) 0 0
\(986\) −3.00000 + 2.51730i −0.0955395 + 0.0801671i
\(987\) −7.04189 −0.224146
\(988\) 1.47771 + 1.78763i 0.0470123 + 0.0568721i
\(989\) −12.1753 −0.387152
\(990\) 0 0
\(991\) −29.8901 10.8791i −0.949491 0.345586i −0.179584 0.983743i \(-0.557475\pi\)
−0.769907 + 0.638156i \(0.779697\pi\)
\(992\) 0.294263 1.66885i 0.00934286 0.0529860i
\(993\) −3.20456 18.1739i −0.101693 0.576732i
\(994\) −15.9290 + 5.79769i −0.505238 + 0.183891i
\(995\) 0 0
\(996\) 7.17958 + 12.4354i 0.227494 + 0.394031i
\(997\) 25.4937 + 21.3917i 0.807392 + 0.677483i 0.949984 0.312299i \(-0.101099\pi\)
−0.142592 + 0.989782i \(0.545544\pi\)
\(998\) 28.7802 + 24.1494i 0.911021 + 0.764437i
\(999\) −7.31908 12.6770i −0.231565 0.401083i
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 950.2.l.b.101.1 6
5.2 odd 4 950.2.u.d.899.1 12
5.3 odd 4 950.2.u.d.899.2 12
5.4 even 2 950.2.l.e.101.1 yes 6
19.16 even 9 inner 950.2.l.b.301.1 yes 6
95.54 even 18 950.2.l.e.301.1 yes 6
95.73 odd 36 950.2.u.d.149.1 12
95.92 odd 36 950.2.u.d.149.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.l.b.101.1 6 1.1 even 1 trivial
950.2.l.b.301.1 yes 6 19.16 even 9 inner
950.2.l.e.101.1 yes 6 5.4 even 2
950.2.l.e.301.1 yes 6 95.54 even 18
950.2.u.d.149.1 12 95.73 odd 36
950.2.u.d.149.2 12 95.92 odd 36
950.2.u.d.899.1 12 5.2 odd 4
950.2.u.d.899.2 12 5.3 odd 4