Properties

Label 950.2.bb.b.257.4
Level $950$
Weight $2$
Character 950.257
Analytic conductor $7.586$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [950,2,Mod(143,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([27, 34]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.143");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.bb (of order \(36\), degree \(12\), 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: \(48\)
Relative dimension: \(4\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 257.4
Character \(\chi\) \(=\) 950.257
Dual form 950.2.bb.b.743.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.819152 + 0.573576i) q^{2} +(-1.52626 - 0.133530i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-1.17365 - 0.984808i) q^{6} +(0.848367 - 0.227319i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-0.642788 - 0.113341i) q^{9} +O(q^{10})\) \(q+(0.819152 + 0.573576i) q^{2} +(-1.52626 - 0.133530i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-1.17365 - 0.984808i) q^{6} +(0.848367 - 0.227319i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-0.642788 - 0.113341i) q^{9} +(-1.39091 - 2.40912i) q^{11} +(-0.396534 - 1.47988i) q^{12} +(0.512546 + 5.85843i) q^{13} +(0.825326 + 0.300394i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(0.306331 - 0.437486i) q^{17} +(-0.461531 - 0.461531i) q^{18} +(-3.66898 + 2.35343i) q^{19} +(-1.32518 + 0.233665i) q^{21} +(0.242451 - 2.77123i) q^{22} +(-2.73357 + 5.86216i) q^{23} +(0.524005 - 1.43969i) q^{24} +(-2.94040 + 5.09293i) q^{26} +(5.40558 + 1.44842i) q^{27} +(0.503769 + 0.719456i) q^{28} +(0.259389 - 1.47107i) q^{29} +(-3.95249 - 2.28197i) q^{31} +(-0.996195 + 0.0871557i) q^{32} +(1.80119 + 3.86268i) q^{33} +(0.501863 - 0.182663i) q^{34} +(-0.113341 - 0.642788i) q^{36} +(-4.22669 + 4.22669i) q^{37} +(-4.35532 - 0.176623i) q^{38} -9.00992i q^{39} +(2.19278 + 2.61325i) q^{41} +(-1.21955 - 0.568685i) q^{42} +(-6.64921 + 3.10058i) q^{43} +(1.78812 - 2.13100i) q^{44} +(-5.60161 + 3.23409i) q^{46} +(-1.49147 + 1.04434i) q^{47} +(1.25501 - 0.878770i) q^{48} +(-5.39413 + 3.11430i) q^{49} +(-0.525958 + 0.626812i) q^{51} +(-5.32982 + 2.48534i) q^{52} +(-3.01279 - 1.40489i) q^{53} +(3.59721 + 4.28699i) q^{54} +0.878294i q^{56} +(5.91406 - 3.10202i) q^{57} +(1.05625 - 1.05625i) q^{58} +(-1.12845 - 6.39974i) q^{59} +(-0.643282 + 0.234136i) q^{61} +(-1.92881 - 4.13634i) q^{62} +(-0.571084 + 0.0499634i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(-0.740087 + 4.19724i) q^{66} +(0.550366 + 0.786005i) q^{67} +(0.515873 + 0.138228i) q^{68} +(4.95491 - 8.58216i) q^{69} +(-1.03247 + 2.83668i) q^{71} +(0.275844 - 0.591550i) q^{72} +(-0.840172 + 9.60321i) q^{73} +(-5.88664 + 1.03797i) q^{74} +(-3.46636 - 2.64279i) q^{76} +(-1.72764 - 1.72764i) q^{77} +(5.16788 - 7.38050i) q^{78} +(1.70192 - 1.42808i) q^{79} +(-6.21688 - 2.26276i) q^{81} +(0.297319 + 3.39838i) q^{82} +(-3.41342 - 12.7391i) q^{83} +(-0.672812 - 1.16535i) q^{84} +(-7.22513 - 1.27399i) q^{86} +(-0.592328 + 2.21060i) q^{87} +(2.68703 - 0.719987i) q^{88} +(10.4737 + 8.78846i) q^{89} +(1.76656 + 4.85359i) q^{91} +(-6.44356 - 0.563739i) q^{92} +(5.72781 + 4.01066i) q^{93} -1.82075 q^{94} +1.53209 q^{96} +(5.53235 + 3.87379i) q^{97} +(-6.20490 - 0.542858i) q^{98} +(0.621007 + 1.70620i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 48 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 48 q^{6} - 12 q^{11} + 36 q^{21} - 72 q^{31} + 48 q^{36} + 96 q^{41} + 72 q^{46} - 48 q^{51} - 108 q^{61} + 24 q^{66} - 60 q^{71} - 48 q^{76} - 168 q^{81} - 48 q^{86} + 252 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(77\) \(401\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{17}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.819152 + 0.573576i 0.579228 + 0.405580i
\(3\) −1.52626 0.133530i −0.881186 0.0770938i −0.362425 0.932013i \(-0.618051\pi\)
−0.518761 + 0.854919i \(0.673607\pi\)
\(4\) 0.342020 + 0.939693i 0.171010 + 0.469846i
\(5\) 0 0
\(6\) −1.17365 0.984808i −0.479140 0.402046i
\(7\) 0.848367 0.227319i 0.320653 0.0859186i −0.0949026 0.995487i \(-0.530254\pi\)
0.415555 + 0.909568i \(0.363587\pi\)
\(8\) −0.258819 + 0.965926i −0.0915064 + 0.341506i
\(9\) −0.642788 0.113341i −0.214263 0.0377803i
\(10\) 0 0
\(11\) −1.39091 2.40912i −0.419375 0.726378i 0.576502 0.817096i \(-0.304417\pi\)
−0.995877 + 0.0907175i \(0.971084\pi\)
\(12\) −0.396534 1.47988i −0.114469 0.427206i
\(13\) 0.512546 + 5.85843i 0.142155 + 1.62484i 0.647602 + 0.761979i \(0.275772\pi\)
−0.505447 + 0.862858i \(0.668672\pi\)
\(14\) 0.825326 + 0.300394i 0.220578 + 0.0802837i
\(15\) 0 0
\(16\) −0.766044 + 0.642788i −0.191511 + 0.160697i
\(17\) 0.306331 0.437486i 0.0742961 0.106106i −0.780284 0.625425i \(-0.784926\pi\)
0.854580 + 0.519319i \(0.173814\pi\)
\(18\) −0.461531 0.461531i −0.108784 0.108784i
\(19\) −3.66898 + 2.35343i −0.841721 + 0.539913i
\(20\) 0 0
\(21\) −1.32518 + 0.233665i −0.289178 + 0.0509899i
\(22\) 0.242451 2.77123i 0.0516908 0.590828i
\(23\) −2.73357 + 5.86216i −0.569989 + 1.22234i 0.384231 + 0.923237i \(0.374467\pi\)
−0.954219 + 0.299108i \(0.903311\pi\)
\(24\) 0.524005 1.43969i 0.106962 0.293876i
\(25\) 0 0
\(26\) −2.94040 + 5.09293i −0.576661 + 0.998806i
\(27\) 5.40558 + 1.44842i 1.04030 + 0.278749i
\(28\) 0.503769 + 0.719456i 0.0952033 + 0.135964i
\(29\) 0.259389 1.47107i 0.0481674 0.273171i −0.951206 0.308555i \(-0.900154\pi\)
0.999374 + 0.0353846i \(0.0112656\pi\)
\(30\) 0 0
\(31\) −3.95249 2.28197i −0.709889 0.409854i 0.101131 0.994873i \(-0.467754\pi\)
−0.811020 + 0.585019i \(0.801087\pi\)
\(32\) −0.996195 + 0.0871557i −0.176104 + 0.0154071i
\(33\) 1.80119 + 3.86268i 0.313548 + 0.672405i
\(34\) 0.501863 0.182663i 0.0860688 0.0313265i
\(35\) 0 0
\(36\) −0.113341 0.642788i −0.0188901 0.107131i
\(37\) −4.22669 + 4.22669i −0.694864 + 0.694864i −0.963298 0.268434i \(-0.913494\pi\)
0.268434 + 0.963298i \(0.413494\pi\)
\(38\) −4.35532 0.176623i −0.706526 0.0286520i
\(39\) 9.00992i 1.44274i
\(40\) 0 0
\(41\) 2.19278 + 2.61325i 0.342454 + 0.408121i 0.909593 0.415501i \(-0.136394\pi\)
−0.567138 + 0.823623i \(0.691949\pi\)
\(42\) −1.21955 0.568685i −0.188181 0.0877501i
\(43\) −6.64921 + 3.10058i −1.01400 + 0.472834i −0.857302 0.514814i \(-0.827861\pi\)
−0.156693 + 0.987647i \(0.550083\pi\)
\(44\) 1.78812 2.13100i 0.269569 0.321260i
\(45\) 0 0
\(46\) −5.60161 + 3.23409i −0.825912 + 0.476840i
\(47\) −1.49147 + 1.04434i −0.217554 + 0.152333i −0.677274 0.735731i \(-0.736839\pi\)
0.459720 + 0.888064i \(0.347950\pi\)
\(48\) 1.25501 0.878770i 0.181146 0.126840i
\(49\) −5.39413 + 3.11430i −0.770589 + 0.444900i
\(50\) 0 0
\(51\) −0.525958 + 0.626812i −0.0736488 + 0.0877712i
\(52\) −5.32982 + 2.48534i −0.739113 + 0.344654i
\(53\) −3.01279 1.40489i −0.413839 0.192976i 0.204537 0.978859i \(-0.434431\pi\)
−0.618376 + 0.785883i \(0.712209\pi\)
\(54\) 3.59721 + 4.28699i 0.489518 + 0.583385i
\(55\) 0 0
\(56\) 0.878294i 0.117367i
\(57\) 5.91406 3.10202i 0.783336 0.410873i
\(58\) 1.05625 1.05625i 0.138692 0.138692i
\(59\) −1.12845 6.39974i −0.146911 0.833175i −0.965813 0.259241i \(-0.916528\pi\)
0.818901 0.573934i \(-0.194583\pi\)
\(60\) 0 0
\(61\) −0.643282 + 0.234136i −0.0823638 + 0.0299780i −0.382873 0.923801i \(-0.625065\pi\)
0.300510 + 0.953779i \(0.402843\pi\)
\(62\) −1.92881 4.13634i −0.244959 0.525316i
\(63\) −0.571084 + 0.0499634i −0.0719499 + 0.00629480i
\(64\) −0.866025 0.500000i −0.108253 0.0625000i
\(65\) 0 0
\(66\) −0.740087 + 4.19724i −0.0910984 + 0.516645i
\(67\) 0.550366 + 0.786005i 0.0672380 + 0.0960258i 0.851363 0.524577i \(-0.175777\pi\)
−0.784125 + 0.620603i \(0.786888\pi\)
\(68\) 0.515873 + 0.138228i 0.0625588 + 0.0167626i
\(69\) 4.95491 8.58216i 0.596501 1.03317i
\(70\) 0 0
\(71\) −1.03247 + 2.83668i −0.122531 + 0.336652i −0.985759 0.168162i \(-0.946217\pi\)
0.863228 + 0.504814i \(0.168439\pi\)
\(72\) 0.275844 0.591550i 0.0325086 0.0697149i
\(73\) −0.840172 + 9.60321i −0.0983347 + 1.12397i 0.773375 + 0.633948i \(0.218567\pi\)
−0.871710 + 0.490022i \(0.836989\pi\)
\(74\) −5.88664 + 1.03797i −0.684308 + 0.120662i
\(75\) 0 0
\(76\) −3.46636 2.64279i −0.397619 0.303149i
\(77\) −1.72764 1.72764i −0.196883 0.196883i
\(78\) 5.16788 7.38050i 0.585147 0.835677i
\(79\) 1.70192 1.42808i 0.191481 0.160672i −0.542007 0.840374i \(-0.682335\pi\)
0.733488 + 0.679702i \(0.237891\pi\)
\(80\) 0 0
\(81\) −6.21688 2.26276i −0.690765 0.251418i
\(82\) 0.297319 + 3.39838i 0.0328334 + 0.375288i
\(83\) −3.41342 12.7391i −0.374672 1.39829i −0.853824 0.520562i \(-0.825723\pi\)
0.479152 0.877732i \(-0.340944\pi\)
\(84\) −0.672812 1.16535i −0.0734098 0.127150i
\(85\) 0 0
\(86\) −7.22513 1.27399i −0.779106 0.137377i
\(87\) −0.592328 + 2.21060i −0.0635042 + 0.237001i
\(88\) 2.68703 0.719987i 0.286438 0.0767509i
\(89\) 10.4737 + 8.78846i 1.11021 + 0.931575i 0.998069 0.0621176i \(-0.0197854\pi\)
0.112139 + 0.993693i \(0.464230\pi\)
\(90\) 0 0
\(91\) 1.76656 + 4.85359i 0.185186 + 0.508794i
\(92\) −6.44356 0.563739i −0.671788 0.0587738i
\(93\) 5.72781 + 4.01066i 0.593947 + 0.415886i
\(94\) −1.82075 −0.187796
\(95\) 0 0
\(96\) 1.53209 0.156368
\(97\) 5.53235 + 3.87379i 0.561725 + 0.393324i 0.819670 0.572835i \(-0.194157\pi\)
−0.257945 + 0.966160i \(0.583045\pi\)
\(98\) −6.20490 0.542858i −0.626789 0.0548370i
\(99\) 0.621007 + 1.70620i 0.0624135 + 0.171480i
\(100\) 0 0
\(101\) 8.59393 + 7.21116i 0.855128 + 0.717537i 0.960913 0.276852i \(-0.0892911\pi\)
−0.105785 + 0.994389i \(0.533736\pi\)
\(102\) −0.790364 + 0.211777i −0.0782577 + 0.0209691i
\(103\) 2.90781 10.8521i 0.286515 1.06929i −0.661210 0.750201i \(-0.729957\pi\)
0.947725 0.319088i \(-0.103377\pi\)
\(104\) −5.79147 1.02119i −0.567900 0.100136i
\(105\) 0 0
\(106\) −1.66213 2.87889i −0.161440 0.279622i
\(107\) 3.71653 + 13.8703i 0.359290 + 1.34089i 0.874999 + 0.484125i \(0.160862\pi\)
−0.515708 + 0.856764i \(0.672471\pi\)
\(108\) 0.487747 + 5.57497i 0.0469335 + 0.536452i
\(109\) −17.9852 6.54609i −1.72267 0.627002i −0.724607 0.689162i \(-0.757979\pi\)
−0.998066 + 0.0621599i \(0.980201\pi\)
\(110\) 0 0
\(111\) 7.01542 5.88664i 0.665874 0.558735i
\(112\) −0.503769 + 0.719456i −0.0476017 + 0.0679822i
\(113\) 4.18532 + 4.18532i 0.393722 + 0.393722i 0.876012 0.482290i \(-0.160195\pi\)
−0.482290 + 0.876012i \(0.660195\pi\)
\(114\) 6.62376 + 0.851139i 0.620372 + 0.0797165i
\(115\) 0 0
\(116\) 1.47107 0.259389i 0.136585 0.0240837i
\(117\) 0.334541 3.82382i 0.0309283 0.353512i
\(118\) 2.74637 5.88961i 0.252824 0.542183i
\(119\) 0.160432 0.440783i 0.0147068 0.0404065i
\(120\) 0 0
\(121\) 1.63075 2.82454i 0.148250 0.256776i
\(122\) −0.661241 0.177179i −0.0598659 0.0160410i
\(123\) −2.99780 4.28130i −0.270302 0.386032i
\(124\) 0.792521 4.49461i 0.0711705 0.403628i
\(125\) 0 0
\(126\) −0.496463 0.286633i −0.0442284 0.0255353i
\(127\) 12.8382 1.12320i 1.13921 0.0996677i 0.498100 0.867119i \(-0.334031\pi\)
0.641107 + 0.767452i \(0.278476\pi\)
\(128\) −0.422618 0.906308i −0.0373545 0.0801070i
\(129\) 10.5624 3.84441i 0.929971 0.338482i
\(130\) 0 0
\(131\) −1.61408 9.15390i −0.141023 0.799780i −0.970475 0.241202i \(-0.922458\pi\)
0.829452 0.558578i \(-0.188653\pi\)
\(132\) −3.01368 + 3.01368i −0.262307 + 0.262307i
\(133\) −2.57766 + 2.83060i −0.223511 + 0.245444i
\(134\) 0.959535i 0.0828912i
\(135\) 0 0
\(136\) 0.343294 + 0.409122i 0.0294373 + 0.0350820i
\(137\) 10.4566 + 4.87598i 0.893364 + 0.416583i 0.814406 0.580295i \(-0.197063\pi\)
0.0789582 + 0.996878i \(0.474841\pi\)
\(138\) 8.98135 4.18807i 0.764543 0.356512i
\(139\) −2.63037 + 3.13475i −0.223105 + 0.265886i −0.865973 0.500091i \(-0.833300\pi\)
0.642868 + 0.765977i \(0.277744\pi\)
\(140\) 0 0
\(141\) 2.41583 1.39478i 0.203449 0.117462i
\(142\) −2.47280 + 1.73147i −0.207513 + 0.145302i
\(143\) 13.4008 9.38333i 1.12063 0.784673i
\(144\) 0.565258 0.326352i 0.0471048 0.0271960i
\(145\) 0 0
\(146\) −6.19640 + 7.38458i −0.512818 + 0.611152i
\(147\) 8.64869 4.03295i 0.713332 0.332632i
\(148\) −5.41741 2.52618i −0.445308 0.207651i
\(149\) 12.3942 + 14.7709i 1.01537 + 1.21008i 0.977531 + 0.210793i \(0.0676045\pi\)
0.0378438 + 0.999284i \(0.487951\pi\)
\(150\) 0 0
\(151\) 9.94008i 0.808912i −0.914557 0.404456i \(-0.867461\pi\)
0.914557 0.404456i \(-0.132539\pi\)
\(152\) −1.32364 4.15307i −0.107361 0.336858i
\(153\) −0.246491 + 0.246491i −0.0199276 + 0.0199276i
\(154\) −0.424266 2.40613i −0.0341884 0.193892i
\(155\) 0 0
\(156\) 8.46656 3.08157i 0.677867 0.246723i
\(157\) −6.39461 13.7133i −0.510346 1.09444i −0.977630 0.210333i \(-0.932545\pi\)
0.467284 0.884107i \(-0.345233\pi\)
\(158\) 2.21325 0.193634i 0.176077 0.0154047i
\(159\) 4.41071 + 2.54652i 0.349792 + 0.201952i
\(160\) 0 0
\(161\) −0.986489 + 5.59466i −0.0777462 + 0.440921i
\(162\) −3.79471 5.41940i −0.298140 0.425788i
\(163\) 11.1934 + 2.99926i 0.876735 + 0.234920i 0.668998 0.743264i \(-0.266723\pi\)
0.207737 + 0.978185i \(0.433390\pi\)
\(164\) −1.70568 + 2.95432i −0.133191 + 0.230694i
\(165\) 0 0
\(166\) 4.51071 12.3931i 0.350099 0.961890i
\(167\) 8.41488 18.0458i 0.651163 1.39642i −0.252254 0.967661i \(-0.581172\pi\)
0.903417 0.428763i \(-0.141050\pi\)
\(168\) 0.117279 1.34050i 0.00904826 0.103422i
\(169\) −21.2560 + 3.74801i −1.63508 + 0.288308i
\(170\) 0 0
\(171\) 2.62511 1.09691i 0.200747 0.0838828i
\(172\) −5.18775 5.18775i −0.395563 0.395563i
\(173\) −5.79482 + 8.27587i −0.440572 + 0.629203i −0.976617 0.214987i \(-0.931029\pi\)
0.536045 + 0.844190i \(0.319918\pi\)
\(174\) −1.75315 + 1.47107i −0.132906 + 0.111522i
\(175\) 0 0
\(176\) 2.61405 + 0.951437i 0.197042 + 0.0717173i
\(177\) 0.867742 + 9.91834i 0.0652235 + 0.745508i
\(178\) 3.53868 + 13.2065i 0.265235 + 0.989872i
\(179\) 3.46095 + 5.99454i 0.258683 + 0.448053i 0.965889 0.258955i \(-0.0833780\pi\)
−0.707206 + 0.707007i \(0.750045\pi\)
\(180\) 0 0
\(181\) 7.96618 + 1.40465i 0.592121 + 0.104407i 0.461676 0.887049i \(-0.347248\pi\)
0.130445 + 0.991456i \(0.458359\pi\)
\(182\) −1.33682 + 4.98908i −0.0990918 + 0.369815i
\(183\) 1.01308 0.271454i 0.0748890 0.0200664i
\(184\) −4.95491 4.15766i −0.365281 0.306507i
\(185\) 0 0
\(186\) 2.39153 + 6.57068i 0.175356 + 0.481785i
\(187\) −1.48004 0.129486i −0.108231 0.00946897i
\(188\) −1.49147 1.04434i −0.108777 0.0761664i
\(189\) 4.91517 0.357526
\(190\) 0 0
\(191\) 23.3900 1.69244 0.846219 0.532835i \(-0.178873\pi\)
0.846219 + 0.532835i \(0.178873\pi\)
\(192\) 1.25501 + 0.878770i 0.0905728 + 0.0634198i
\(193\) 5.53617 + 0.484352i 0.398502 + 0.0348644i 0.284646 0.958633i \(-0.408124\pi\)
0.113856 + 0.993497i \(0.463680\pi\)
\(194\) 2.30992 + 6.34645i 0.165843 + 0.455649i
\(195\) 0 0
\(196\) −4.77138 4.00367i −0.340813 0.285976i
\(197\) −10.1622 + 2.72294i −0.724024 + 0.194002i −0.601967 0.798521i \(-0.705616\pi\)
−0.122058 + 0.992523i \(0.538949\pi\)
\(198\) −0.469938 + 1.75383i −0.0333971 + 0.124640i
\(199\) −4.22841 0.745583i −0.299744 0.0528529i 0.0217536 0.999763i \(-0.493075\pi\)
−0.321498 + 0.946910i \(0.604186\pi\)
\(200\) 0 0
\(201\) −0.735046 1.27314i −0.0518462 0.0898002i
\(202\) 2.90358 + 10.8363i 0.204295 + 0.762440i
\(203\) −0.114345 1.30697i −0.00802546 0.0917314i
\(204\) −0.768899 0.279856i −0.0538337 0.0195939i
\(205\) 0 0
\(206\) 8.60645 7.22167i 0.599639 0.503157i
\(207\) 2.42153 3.45830i 0.168308 0.240368i
\(208\) −4.15836 4.15836i −0.288330 0.288330i
\(209\) 10.7729 + 5.56561i 0.745178 + 0.384982i
\(210\) 0 0
\(211\) 22.3494 3.94081i 1.53860 0.271296i 0.660886 0.750486i \(-0.270180\pi\)
0.877711 + 0.479190i \(0.159069\pi\)
\(212\) 0.289727 3.31160i 0.0198986 0.227442i
\(213\) 1.95460 4.19164i 0.133927 0.287207i
\(214\) −4.91126 + 13.4936i −0.335727 + 0.922402i
\(215\) 0 0
\(216\) −2.79813 + 4.84651i −0.190389 + 0.329763i
\(217\) −3.87190 1.03747i −0.262842 0.0704282i
\(218\) −10.9780 15.6782i −0.743521 1.06186i
\(219\) 2.56464 14.5448i 0.173302 0.982846i
\(220\) 0 0
\(221\) 2.71999 + 1.57039i 0.182966 + 0.105636i
\(222\) 9.12313 0.798171i 0.612305 0.0535697i
\(223\) −10.3926 22.2869i −0.695937 1.49244i −0.862311 0.506379i \(-0.830984\pi\)
0.166374 0.986063i \(-0.446794\pi\)
\(224\) −0.825326 + 0.300394i −0.0551444 + 0.0200709i
\(225\) 0 0
\(226\) 1.02781 + 5.82901i 0.0683690 + 0.387740i
\(227\) −14.2308 + 14.2308i −0.944533 + 0.944533i −0.998541 0.0540074i \(-0.982801\pi\)
0.0540074 + 0.998541i \(0.482801\pi\)
\(228\) 4.93767 + 4.49644i 0.327005 + 0.297784i
\(229\) 13.0081i 0.859598i 0.902925 + 0.429799i \(0.141416\pi\)
−0.902925 + 0.429799i \(0.858584\pi\)
\(230\) 0 0
\(231\) 2.40613 + 2.86752i 0.158312 + 0.188669i
\(232\) 1.35381 + 0.631292i 0.0888819 + 0.0414463i
\(233\) −15.7329 + 7.33635i −1.03069 + 0.480621i −0.862992 0.505217i \(-0.831412\pi\)
−0.167702 + 0.985838i \(0.553635\pi\)
\(234\) 2.46729 2.94040i 0.161292 0.192220i
\(235\) 0 0
\(236\) 5.62784 3.24923i 0.366341 0.211507i
\(237\) −2.78827 + 1.95237i −0.181118 + 0.126820i
\(238\) 0.384241 0.269048i 0.0249066 0.0174398i
\(239\) 4.96526 2.86669i 0.321176 0.185431i −0.330741 0.943722i \(-0.607299\pi\)
0.651917 + 0.758291i \(0.273965\pi\)
\(240\) 0 0
\(241\) 17.4849 20.8377i 1.12630 1.34228i 0.193830 0.981035i \(-0.437909\pi\)
0.932473 0.361240i \(-0.117647\pi\)
\(242\) 2.95592 1.37837i 0.190014 0.0886048i
\(243\) −6.02940 2.81155i −0.386786 0.180361i
\(244\) −0.440031 0.524408i −0.0281701 0.0335718i
\(245\) 0 0
\(246\) 5.22650i 0.333230i
\(247\) −15.6679 20.2882i −0.996925 1.29091i
\(248\) 3.22720 3.22720i 0.204927 0.204927i
\(249\) 3.50871 + 19.8989i 0.222356 + 1.26104i
\(250\) 0 0
\(251\) −22.3073 + 8.11919i −1.40802 + 0.512479i −0.930549 0.366167i \(-0.880670\pi\)
−0.477475 + 0.878645i \(0.658448\pi\)
\(252\) −0.242273 0.519555i −0.0152617 0.0327289i
\(253\) 17.9248 1.56822i 1.12692 0.0985930i
\(254\) 11.1607 + 6.44362i 0.700284 + 0.404309i
\(255\) 0 0
\(256\) 0.173648 0.984808i 0.0108530 0.0615505i
\(257\) −13.0717 18.6683i −0.815389 1.16450i −0.983887 0.178794i \(-0.942781\pi\)
0.168498 0.985702i \(-0.446108\pi\)
\(258\) 10.8573 + 2.90921i 0.675946 + 0.181119i
\(259\) −2.62498 + 4.54660i −0.163108 + 0.282512i
\(260\) 0 0
\(261\) −0.333464 + 0.916186i −0.0206409 + 0.0567105i
\(262\) 3.92829 8.42424i 0.242690 0.520451i
\(263\) 0.548803 6.27285i 0.0338407 0.386801i −0.960321 0.278898i \(-0.910031\pi\)
0.994161 0.107903i \(-0.0344135\pi\)
\(264\) −4.19724 + 0.740087i −0.258322 + 0.0455492i
\(265\) 0 0
\(266\) −3.73506 + 0.840207i −0.229011 + 0.0515164i
\(267\) −14.8120 14.8120i −0.906481 0.906481i
\(268\) −0.550366 + 0.786005i −0.0336190 + 0.0480129i
\(269\) 12.5253 10.5100i 0.763681 0.640804i −0.175401 0.984497i \(-0.556122\pi\)
0.939082 + 0.343693i \(0.111678\pi\)
\(270\) 0 0
\(271\) −19.5905 7.13036i −1.19004 0.433139i −0.330301 0.943876i \(-0.607150\pi\)
−0.859737 + 0.510737i \(0.829373\pi\)
\(272\) 0.0465474 + 0.532039i 0.00282235 + 0.0322596i
\(273\) −2.04813 7.64372i −0.123958 0.462619i
\(274\) 5.76877 + 9.99180i 0.348504 + 0.603627i
\(275\) 0 0
\(276\) 9.75927 + 1.72082i 0.587439 + 0.103581i
\(277\) −6.77687 + 25.2916i −0.407183 + 1.51963i 0.392811 + 0.919619i \(0.371503\pi\)
−0.799994 + 0.600008i \(0.795164\pi\)
\(278\) −3.95269 + 1.05912i −0.237067 + 0.0635219i
\(279\) 2.28197 + 1.91480i 0.136618 + 0.114636i
\(280\) 0 0
\(281\) 8.57330 + 23.5550i 0.511440 + 1.40517i 0.879736 + 0.475462i \(0.157719\pi\)
−0.368296 + 0.929709i \(0.620059\pi\)
\(282\) 2.77894 + 0.243126i 0.165484 + 0.0144779i
\(283\) 1.07390 + 0.751953i 0.0638368 + 0.0446990i 0.605059 0.796180i \(-0.293149\pi\)
−0.541222 + 0.840879i \(0.682038\pi\)
\(284\) −3.01873 −0.179129
\(285\) 0 0
\(286\) 16.3593 0.967348
\(287\) 2.45432 + 1.71854i 0.144874 + 0.101442i
\(288\) 0.650220 + 0.0568869i 0.0383146 + 0.00335209i
\(289\) 5.71679 + 15.7067i 0.336282 + 0.923926i
\(290\) 0 0
\(291\) −7.92653 6.65115i −0.464661 0.389897i
\(292\) −9.31142 + 2.49499i −0.544910 + 0.146008i
\(293\) 3.39841 12.6830i 0.198537 0.740951i −0.792786 0.609501i \(-0.791370\pi\)
0.991323 0.131450i \(-0.0419634\pi\)
\(294\) 9.39779 + 1.65708i 0.548090 + 0.0966431i
\(295\) 0 0
\(296\) −2.98872 5.17662i −0.173716 0.300885i
\(297\) −4.02924 15.0373i −0.233800 0.872554i
\(298\) 1.68054 + 19.2086i 0.0973509 + 1.11273i
\(299\) −35.7441 13.0098i −2.06714 0.752376i
\(300\) 0 0
\(301\) −4.93615 + 4.14192i −0.284515 + 0.238736i
\(302\) 5.70139 8.14244i 0.328078 0.468545i
\(303\) −12.1536 12.1536i −0.698209 0.698209i
\(304\) 1.29784 4.16120i 0.0744364 0.238661i
\(305\) 0 0
\(306\) −0.343294 + 0.0605321i −0.0196248 + 0.00346039i
\(307\) −2.82746 + 32.3180i −0.161371 + 1.84448i 0.295976 + 0.955195i \(0.404355\pi\)
−0.457347 + 0.889288i \(0.651200\pi\)
\(308\) 1.03256 2.21434i 0.0588358 0.126174i
\(309\) −5.88716 + 16.1748i −0.334909 + 0.920154i
\(310\) 0 0
\(311\) −8.27642 + 14.3352i −0.469313 + 0.812874i −0.999385 0.0350792i \(-0.988832\pi\)
0.530072 + 0.847953i \(0.322165\pi\)
\(312\) 8.70292 + 2.33194i 0.492706 + 0.132020i
\(313\) 11.2116 + 16.0118i 0.633718 + 0.905043i 0.999673 0.0255895i \(-0.00814629\pi\)
−0.365954 + 0.930633i \(0.619257\pi\)
\(314\) 2.62746 14.9011i 0.148276 0.840916i
\(315\) 0 0
\(316\) 1.92405 + 1.11085i 0.108236 + 0.0624903i
\(317\) −18.6277 + 1.62971i −1.04624 + 0.0915338i −0.597290 0.802025i \(-0.703756\pi\)
−0.448946 + 0.893559i \(0.648200\pi\)
\(318\) 2.15241 + 4.61587i 0.120701 + 0.258845i
\(319\) −3.90478 + 1.42122i −0.218625 + 0.0795732i
\(320\) 0 0
\(321\) −3.82028 21.6659i −0.213227 1.20927i
\(322\) −4.01705 + 4.01705i −0.223861 + 0.223861i
\(323\) −0.0943291 + 2.32605i −0.00524861 + 0.129425i
\(324\) 6.61587i 0.367548i
\(325\) 0 0
\(326\) 7.44879 + 8.87713i 0.412551 + 0.491659i
\(327\) 26.5760 + 12.3926i 1.46966 + 0.685313i
\(328\) −3.09174 + 1.44170i −0.170713 + 0.0796047i
\(329\) −1.02792 + 1.22503i −0.0566710 + 0.0675378i
\(330\) 0 0
\(331\) −13.6541 + 7.88321i −0.750498 + 0.433300i −0.825874 0.563855i \(-0.809318\pi\)
0.0753756 + 0.997155i \(0.475984\pi\)
\(332\) 10.8033 7.56458i 0.592910 0.415160i
\(333\) 3.19592 2.23781i 0.175136 0.122631i
\(334\) 17.2437 9.95566i 0.943533 0.544749i
\(335\) 0 0
\(336\) 0.864951 1.03081i 0.0471869 0.0562352i
\(337\) −15.5001 + 7.22780i −0.844342 + 0.393723i −0.796139 0.605114i \(-0.793127\pi\)
−0.0482037 + 0.998838i \(0.515350\pi\)
\(338\) −19.5617 9.12176i −1.06401 0.496158i
\(339\) −5.82901 6.94675i −0.316588 0.377295i
\(340\) 0 0
\(341\) 12.6961i 0.687530i
\(342\) 2.77953 + 0.607166i 0.150300 + 0.0328318i
\(343\) −8.21559 + 8.21559i −0.443600 + 0.443600i
\(344\) −1.27399 7.22513i −0.0686887 0.389553i
\(345\) 0 0
\(346\) −9.49369 + 3.45542i −0.510384 + 0.185764i
\(347\) −0.788474 1.69089i −0.0423275 0.0907716i 0.884007 0.467474i \(-0.154836\pi\)
−0.926334 + 0.376702i \(0.877058\pi\)
\(348\) −2.27987 + 0.199463i −0.122214 + 0.0106923i
\(349\) 13.2384 + 7.64317i 0.708633 + 0.409129i 0.810555 0.585663i \(-0.199166\pi\)
−0.101922 + 0.994792i \(0.532499\pi\)
\(350\) 0 0
\(351\) −5.71486 + 32.4106i −0.305037 + 1.72995i
\(352\) 1.59558 + 2.27873i 0.0850449 + 0.121457i
\(353\) 26.9521 + 7.22179i 1.43452 + 0.384377i 0.890609 0.454769i \(-0.150278\pi\)
0.543906 + 0.839146i \(0.316945\pi\)
\(354\) −4.97811 + 8.62235i −0.264584 + 0.458273i
\(355\) 0 0
\(356\) −4.67624 + 12.8479i −0.247840 + 0.680936i
\(357\) −0.303719 + 0.651327i −0.0160745 + 0.0344719i
\(358\) −0.603283 + 6.89556i −0.0318845 + 0.364441i
\(359\) 2.65246 0.467701i 0.139992 0.0246843i −0.103213 0.994659i \(-0.532912\pi\)
0.243205 + 0.969975i \(0.421801\pi\)
\(360\) 0 0
\(361\) 7.92276 17.2693i 0.416987 0.908912i
\(362\) 5.71984 + 5.71984i 0.300628 + 0.300628i
\(363\) −2.86611 + 4.09322i −0.150432 + 0.214838i
\(364\) −3.95668 + 3.32005i −0.207386 + 0.174018i
\(365\) 0 0
\(366\) 0.985566 + 0.358717i 0.0515163 + 0.0187504i
\(367\) −1.25880 14.3881i −0.0657087 0.751054i −0.955559 0.294801i \(-0.904747\pi\)
0.889850 0.456253i \(-0.150809\pi\)
\(368\) −1.67409 6.24778i −0.0872678 0.325688i
\(369\) −1.11330 1.92830i −0.0579562 0.100383i
\(370\) 0 0
\(371\) −2.87531 0.506995i −0.149279 0.0263219i
\(372\) −1.80976 + 6.75411i −0.0938316 + 0.350184i
\(373\) −21.4638 + 5.75121i −1.11135 + 0.297786i −0.767380 0.641193i \(-0.778440\pi\)
−0.343974 + 0.938979i \(0.611773\pi\)
\(374\) −1.13810 0.954982i −0.0588499 0.0493810i
\(375\) 0 0
\(376\) −0.622735 1.71095i −0.0321151 0.0882355i
\(377\) 8.75111 + 0.765623i 0.450705 + 0.0394316i
\(378\) 4.02627 + 2.81922i 0.207089 + 0.145005i
\(379\) −33.1948 −1.70510 −0.852552 0.522643i \(-0.824946\pi\)
−0.852552 + 0.522643i \(0.824946\pi\)
\(380\) 0 0
\(381\) −19.7444 −1.01154
\(382\) 19.1599 + 13.4159i 0.980307 + 0.686419i
\(383\) 0.320302 + 0.0280228i 0.0163667 + 0.00143190i 0.0953361 0.995445i \(-0.469607\pi\)
−0.0789695 + 0.996877i \(0.525163\pi\)
\(384\) 0.524005 + 1.43969i 0.0267405 + 0.0734690i
\(385\) 0 0
\(386\) 4.25715 + 3.57217i 0.216683 + 0.181819i
\(387\) 4.62545 1.23939i 0.235125 0.0630015i
\(388\) −1.74800 + 6.52363i −0.0887413 + 0.331187i
\(389\) 19.0135 + 3.35259i 0.964023 + 0.169983i 0.633438 0.773793i \(-0.281643\pi\)
0.330585 + 0.943776i \(0.392754\pi\)
\(390\) 0 0
\(391\) 1.72723 + 2.99166i 0.0873500 + 0.151295i
\(392\) −1.61208 6.01637i −0.0814223 0.303872i
\(393\) 1.24118 + 14.1868i 0.0626093 + 0.715627i
\(394\) −9.88618 3.59827i −0.498058 0.181278i
\(395\) 0 0
\(396\) −1.39091 + 1.16711i −0.0698958 + 0.0586495i
\(397\) −10.9858 + 15.6894i −0.551363 + 0.787429i −0.994013 0.109266i \(-0.965150\pi\)
0.442649 + 0.896695i \(0.354039\pi\)
\(398\) −3.03606 3.03606i −0.152184 0.152184i
\(399\) 4.31214 3.97603i 0.215877 0.199051i
\(400\) 0 0
\(401\) −3.01390 + 0.531432i −0.150507 + 0.0265385i −0.248394 0.968659i \(-0.579903\pi\)
0.0978869 + 0.995198i \(0.468792\pi\)
\(402\) 0.128127 1.46450i 0.00639039 0.0730425i
\(403\) 11.3429 24.3250i 0.565032 1.21172i
\(404\) −3.83698 + 10.5420i −0.190897 + 0.524485i
\(405\) 0 0
\(406\) 0.655982 1.13619i 0.0325558 0.0563883i
\(407\) 16.0616 + 4.30369i 0.796143 + 0.213326i
\(408\) −0.469326 0.670267i −0.0232351 0.0331832i
\(409\) 6.18153 35.0572i 0.305657 1.73347i −0.314738 0.949178i \(-0.601917\pi\)
0.620395 0.784289i \(-0.286972\pi\)
\(410\) 0 0
\(411\) −15.3083 8.83827i −0.755104 0.435960i
\(412\) 11.1922 0.979188i 0.551398 0.0482411i
\(413\) −2.41212 5.17281i −0.118693 0.254537i
\(414\) 3.96720 1.44394i 0.194977 0.0709659i
\(415\) 0 0
\(416\) −1.02119 5.79147i −0.0500680 0.283950i
\(417\) 4.43321 4.43321i 0.217095 0.217095i
\(418\) 5.63234 + 10.7382i 0.275487 + 0.525221i
\(419\) 29.0702i 1.42017i −0.704115 0.710086i \(-0.748656\pi\)
0.704115 0.710086i \(-0.251344\pi\)
\(420\) 0 0
\(421\) −13.0281 15.5263i −0.634952 0.756706i 0.348612 0.937267i \(-0.386653\pi\)
−0.983564 + 0.180561i \(0.942209\pi\)
\(422\) 20.5679 + 9.59098i 1.00123 + 0.466882i
\(423\) 1.07707 0.502245i 0.0523688 0.0244200i
\(424\) 2.13679 2.54652i 0.103772 0.123670i
\(425\) 0 0
\(426\) 4.00534 2.31248i 0.194059 0.112040i
\(427\) −0.492516 + 0.344863i −0.0238345 + 0.0166891i
\(428\) −11.7627 + 8.23630i −0.568570 + 0.398117i
\(429\) −21.7060 + 12.5320i −1.04798 + 0.605049i
\(430\) 0 0
\(431\) −2.51329 + 2.99522i −0.121061 + 0.144275i −0.823171 0.567794i \(-0.807797\pi\)
0.702110 + 0.712069i \(0.252242\pi\)
\(432\) −5.07194 + 2.36508i −0.244024 + 0.113790i
\(433\) −19.5464 9.11461i −0.939338 0.438020i −0.108226 0.994126i \(-0.534517\pi\)
−0.831111 + 0.556106i \(0.812295\pi\)
\(434\) −2.57660 3.07068i −0.123681 0.147397i
\(435\) 0 0
\(436\) 19.1395i 0.916616i
\(437\) −3.76677 27.9414i −0.180189 1.33662i
\(438\) 10.4434 10.4434i 0.499004 0.499004i
\(439\) −3.23570 18.3506i −0.154432 0.875826i −0.959304 0.282377i \(-0.908877\pi\)
0.804872 0.593449i \(-0.202234\pi\)
\(440\) 0 0
\(441\) 3.82025 1.39046i 0.181917 0.0662123i
\(442\) 1.32735 + 2.84651i 0.0631355 + 0.135394i
\(443\) 15.7425 1.37729i 0.747947 0.0654369i 0.293192 0.956053i \(-0.405282\pi\)
0.454755 + 0.890617i \(0.349727\pi\)
\(444\) 7.93105 + 4.57899i 0.376391 + 0.217309i
\(445\) 0 0
\(446\) 4.27016 24.2173i 0.202198 1.14672i
\(447\) −16.9444 24.1992i −0.801444 1.14458i
\(448\) −0.848367 0.227319i −0.0400816 0.0107398i
\(449\) 15.1991 26.3257i 0.717292 1.24239i −0.244777 0.969579i \(-0.578715\pi\)
0.962069 0.272807i \(-0.0879520\pi\)
\(450\) 0 0
\(451\) 3.24569 8.91747i 0.152834 0.419907i
\(452\) −2.50145 + 5.36438i −0.117658 + 0.252319i
\(453\) −1.32730 + 15.1711i −0.0623621 + 0.712802i
\(454\) −19.8197 + 3.49474i −0.930184 + 0.164016i
\(455\) 0 0
\(456\) 1.46565 + 6.51540i 0.0686354 + 0.305112i
\(457\) −9.66093 9.66093i −0.451919 0.451919i 0.444072 0.895991i \(-0.353533\pi\)
−0.895991 + 0.444072i \(0.853533\pi\)
\(458\) −7.46113 + 10.6556i −0.348636 + 0.497903i
\(459\) 2.28956 1.92117i 0.106867 0.0896724i
\(460\) 0 0
\(461\) −21.5297 7.83617i −1.00274 0.364967i −0.212098 0.977248i \(-0.568030\pi\)
−0.790640 + 0.612282i \(0.790252\pi\)
\(462\) 0.326248 + 3.72904i 0.0151784 + 0.173490i
\(463\) −0.948918 3.54141i −0.0441000 0.164583i 0.940364 0.340170i \(-0.110485\pi\)
−0.984464 + 0.175586i \(0.943818\pi\)
\(464\) 0.746882 + 1.29364i 0.0346731 + 0.0600556i
\(465\) 0 0
\(466\) −17.0956 3.01441i −0.791937 0.139640i
\(467\) 1.27846 4.77127i 0.0591600 0.220788i −0.930017 0.367517i \(-0.880208\pi\)
0.989177 + 0.146729i \(0.0468745\pi\)
\(468\) 3.70763 0.993458i 0.171385 0.0459226i
\(469\) 0.645587 + 0.541711i 0.0298104 + 0.0250139i
\(470\) 0 0
\(471\) 7.92870 + 21.7839i 0.365335 + 1.00375i
\(472\) 6.47374 + 0.566379i 0.297978 + 0.0260697i
\(473\) 16.7181 + 11.7062i 0.768700 + 0.538249i
\(474\) −3.40385 −0.156344
\(475\) 0 0
\(476\) 0.469072 0.0214999
\(477\) 1.77736 + 1.24452i 0.0813795 + 0.0569825i
\(478\) 5.71157 + 0.499698i 0.261241 + 0.0228556i
\(479\) 6.63649 + 18.2336i 0.303229 + 0.833115i 0.993934 + 0.109978i \(0.0350780\pi\)
−0.690705 + 0.723137i \(0.742700\pi\)
\(480\) 0 0
\(481\) −26.9282 22.5954i −1.22782 1.03026i
\(482\) 26.2748 7.04032i 1.19679 0.320678i
\(483\) 2.25269 8.40717i 0.102501 0.382539i
\(484\) 3.21195 + 0.566353i 0.145998 + 0.0257433i
\(485\) 0 0
\(486\) −3.32635 5.76141i −0.150886 0.261343i
\(487\) 7.24146 + 27.0255i 0.328142 + 1.22464i 0.911115 + 0.412151i \(0.135222\pi\)
−0.582974 + 0.812491i \(0.698111\pi\)
\(488\) −0.0596639 0.681962i −0.00270086 0.0308710i
\(489\) −16.6835 6.07231i −0.754456 0.274599i
\(490\) 0 0
\(491\) −0.622060 + 0.521970i −0.0280732 + 0.0235562i −0.656716 0.754138i \(-0.728055\pi\)
0.628643 + 0.777694i \(0.283611\pi\)
\(492\) 2.99780 4.28130i 0.135151 0.193016i
\(493\) −0.564113 0.564113i −0.0254064 0.0254064i
\(494\) −1.19757 25.6059i −0.0538813 1.15206i
\(495\) 0 0
\(496\) 4.49461 0.792521i 0.201814 0.0355852i
\(497\) −0.231079 + 2.64125i −0.0103653 + 0.118476i
\(498\) −8.53937 + 18.3127i −0.382658 + 0.820613i
\(499\) −10.7326 + 29.4875i −0.480457 + 1.32004i 0.428646 + 0.903472i \(0.358991\pi\)
−0.909103 + 0.416571i \(0.863232\pi\)
\(500\) 0 0
\(501\) −15.2530 + 26.4189i −0.681452 + 1.18031i
\(502\) −22.9300 6.14409i −1.02342 0.274224i
\(503\) 10.4941 + 14.9871i 0.467908 + 0.668242i 0.981867 0.189573i \(-0.0607104\pi\)
−0.513959 + 0.857815i \(0.671822\pi\)
\(504\) 0.0995465 0.564557i 0.00443416 0.0251473i
\(505\) 0 0
\(506\) 15.5826 + 8.99664i 0.692733 + 0.399950i
\(507\) 32.9426 2.88211i 1.46303 0.127999i
\(508\) 5.44639 + 11.6798i 0.241644 + 0.518208i
\(509\) 28.4513 10.3554i 1.26108 0.458996i 0.376949 0.926234i \(-0.376973\pi\)
0.884131 + 0.467238i \(0.154751\pi\)
\(510\) 0 0
\(511\) 1.47022 + 8.33803i 0.0650387 + 0.368853i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −23.2417 + 7.40742i −1.02615 + 0.327046i
\(514\) 22.7898i 1.00521i
\(515\) 0 0
\(516\) 7.22513 + 8.61058i 0.318069 + 0.379060i
\(517\) 4.59045 + 2.14056i 0.201888 + 0.0941419i
\(518\) −4.75808 + 2.21873i −0.209058 + 0.0974853i
\(519\) 9.94948 11.8573i 0.436734 0.520479i
\(520\) 0 0
\(521\) −7.72795 + 4.46173i −0.338567 + 0.195472i −0.659638 0.751583i \(-0.729291\pi\)
0.321071 + 0.947055i \(0.395957\pi\)
\(522\) −0.798661 + 0.559228i −0.0349564 + 0.0244768i
\(523\) 3.95304 2.76795i 0.172854 0.121034i −0.483948 0.875097i \(-0.660798\pi\)
0.656802 + 0.754063i \(0.271909\pi\)
\(524\) 8.04981 4.64756i 0.351658 0.203030i
\(525\) 0 0
\(526\) 4.04751 4.82364i 0.176480 0.210321i
\(527\) −2.20910 + 1.03012i −0.0962299 + 0.0448727i
\(528\) −3.86268 1.80119i −0.168101 0.0783869i
\(529\) −12.1084 14.4302i −0.526452 0.627401i
\(530\) 0 0
\(531\) 4.24157i 0.184069i
\(532\) −3.54150 1.45408i −0.153544 0.0630425i
\(533\) −14.1857 + 14.1857i −0.614449 + 0.614449i
\(534\) −3.63747 20.6291i −0.157409 0.892709i
\(535\) 0 0
\(536\) −0.901668 + 0.328180i −0.0389461 + 0.0141752i
\(537\) −4.48185 9.61136i −0.193406 0.414761i
\(538\) 16.2884 1.42505i 0.702243 0.0614383i
\(539\) 15.0055 + 8.66341i 0.646331 + 0.373160i
\(540\) 0 0
\(541\) −2.90646 + 16.4833i −0.124958 + 0.708674i 0.856374 + 0.516355i \(0.172712\pi\)
−0.981333 + 0.192318i \(0.938399\pi\)
\(542\) −11.9578 17.0775i −0.513631 0.733541i
\(543\) −11.9709 3.20759i −0.513720 0.137651i
\(544\) −0.267036 + 0.462519i −0.0114491 + 0.0198304i
\(545\) 0 0
\(546\) 2.70653 7.43613i 0.115829 0.318237i
\(547\) 1.46540 3.14256i 0.0626561 0.134366i −0.872486 0.488639i \(-0.837494\pi\)
0.935142 + 0.354272i \(0.115271\pi\)
\(548\) −1.00556 + 11.4936i −0.0429555 + 0.490984i
\(549\) 0.440031 0.0775893i 0.0187801 0.00331143i
\(550\) 0 0
\(551\) 2.51036 + 6.00777i 0.106945 + 0.255940i
\(552\) 7.00730 + 7.00730i 0.298251 + 0.298251i
\(553\) 1.11922 1.59842i 0.0475943 0.0679717i
\(554\) −20.0580 + 16.8306i −0.852182 + 0.715065i
\(555\) 0 0
\(556\) −3.84534 1.39959i −0.163079 0.0593559i
\(557\) 3.89921 + 44.5681i 0.165215 + 1.88841i 0.400222 + 0.916418i \(0.368933\pi\)
−0.235007 + 0.971994i \(0.575511\pi\)
\(558\) 0.770997 + 2.87740i 0.0326389 + 0.121810i
\(559\) −21.5725 37.3647i −0.912422 1.58036i
\(560\) 0 0
\(561\) 2.24163 + 0.395259i 0.0946415 + 0.0166879i
\(562\) −6.48773 + 24.2125i −0.273668 + 1.02134i
\(563\) 24.9981 6.69821i 1.05354 0.282296i 0.309828 0.950793i \(-0.399729\pi\)
0.743715 + 0.668497i \(0.233062\pi\)
\(564\) 2.13692 + 1.79309i 0.0899808 + 0.0755028i
\(565\) 0 0
\(566\) 0.448385 + 1.23193i 0.0188470 + 0.0517818i
\(567\) −5.78857 0.506434i −0.243097 0.0212682i
\(568\) −2.47280 1.73147i −0.103756 0.0726510i
\(569\) 13.5612 0.568515 0.284258 0.958748i \(-0.408253\pi\)
0.284258 + 0.958748i \(0.408253\pi\)
\(570\) 0 0
\(571\) −10.4116 −0.435712 −0.217856 0.975981i \(-0.569906\pi\)
−0.217856 + 0.975981i \(0.569906\pi\)
\(572\) 13.4008 + 9.38333i 0.560315 + 0.392337i
\(573\) −35.6991 3.12327i −1.49135 0.130476i
\(574\) 1.02475 + 2.81548i 0.0427723 + 0.117516i
\(575\) 0 0
\(576\) 0.500000 + 0.419550i 0.0208333 + 0.0174812i
\(577\) 25.4735 6.82559i 1.06047 0.284153i 0.313901 0.949456i \(-0.398364\pi\)
0.746574 + 0.665303i \(0.231697\pi\)
\(578\) −4.32610 + 16.1452i −0.179942 + 0.671553i
\(579\) −8.38495 1.47849i −0.348467 0.0614441i
\(580\) 0 0
\(581\) −5.79167 10.0315i −0.240279 0.416175i
\(582\) −2.67809 9.99477i −0.111010 0.414297i
\(583\) 0.805969 + 9.21227i 0.0333798 + 0.381533i
\(584\) −9.05853 3.29704i −0.374845 0.136432i
\(585\) 0 0
\(586\) 10.0585 8.44009i 0.415513 0.348657i
\(587\) 5.99906 8.56754i 0.247608 0.353620i −0.676039 0.736866i \(-0.736305\pi\)
0.923646 + 0.383246i \(0.125194\pi\)
\(588\) 6.74776 + 6.74776i 0.278273 + 0.278273i
\(589\) 19.8721 0.929404i 0.818814 0.0382954i
\(590\) 0 0
\(591\) 15.8737 2.79896i 0.652956 0.115134i
\(592\) 0.520969 5.95470i 0.0214117 0.244737i
\(593\) −16.0645 + 34.4504i −0.659690 + 1.41471i 0.236762 + 0.971568i \(0.423914\pi\)
−0.896452 + 0.443141i \(0.853864\pi\)
\(594\) 5.32450 14.6289i 0.218467 0.600232i
\(595\) 0 0
\(596\) −9.64100 + 16.6987i −0.394911 + 0.684005i
\(597\) 6.35409 + 1.70257i 0.260056 + 0.0696817i
\(598\) −21.8178 31.1590i −0.892195 1.27419i
\(599\) 0.114812 0.651133i 0.00469111 0.0266046i −0.982372 0.186935i \(-0.940145\pi\)
0.987063 + 0.160330i \(0.0512559\pi\)
\(600\) 0 0
\(601\) 6.92584 + 3.99864i 0.282511 + 0.163108i 0.634560 0.772874i \(-0.281182\pi\)
−0.352049 + 0.935982i \(0.614515\pi\)
\(602\) −6.41916 + 0.561604i −0.261626 + 0.0228893i
\(603\) −0.264682 0.567613i −0.0107787 0.0231150i
\(604\) 9.34062 3.39971i 0.380064 0.138332i
\(605\) 0 0
\(606\) −2.98464 16.9267i −0.121243 0.687601i
\(607\) −13.1910 + 13.1910i −0.535405 + 0.535405i −0.922176 0.386771i \(-0.873590\pi\)
0.386771 + 0.922176i \(0.373590\pi\)
\(608\) 3.44990 2.66424i 0.139912 0.108049i
\(609\) 2.01004i 0.0814511i
\(610\) 0 0
\(611\) −6.88265 8.20243i −0.278442 0.331835i
\(612\) −0.315930 0.147321i −0.0127707 0.00595508i
\(613\) 30.2884 14.1237i 1.22334 0.570452i 0.299816 0.953997i \(-0.403075\pi\)
0.923522 + 0.383545i \(0.125297\pi\)
\(614\) −20.8529 + 24.8516i −0.841556 + 1.00293i
\(615\) 0 0
\(616\) 2.11592 1.22163i 0.0852528 0.0492207i
\(617\) −8.79520 + 6.15847i −0.354081 + 0.247931i −0.737061 0.675826i \(-0.763787\pi\)
0.382979 + 0.923757i \(0.374898\pi\)
\(618\) −14.1000 + 9.87291i −0.567184 + 0.397147i
\(619\) −34.1055 + 19.6908i −1.37081 + 0.791440i −0.991031 0.133635i \(-0.957335\pi\)
−0.379784 + 0.925075i \(0.624002\pi\)
\(620\) 0 0
\(621\) −23.2674 + 27.7290i −0.933689 + 1.11273i
\(622\) −15.0020 + 6.99553i −0.601524 + 0.280495i
\(623\) 10.8833 + 5.07497i 0.436031 + 0.203324i
\(624\) 5.79147 + 6.90200i 0.231844 + 0.276301i
\(625\) 0 0
\(626\) 19.5469i 0.781250i
\(627\) −15.6991 9.93308i −0.626960 0.396689i
\(628\) 10.6992 10.6992i 0.426944 0.426944i
\(629\) 0.554352 + 3.14388i 0.0221034 + 0.125355i
\(630\) 0 0
\(631\) −45.7950 + 16.6680i −1.82307 + 0.663544i −0.828438 + 0.560081i \(0.810770\pi\)
−0.994633 + 0.103462i \(0.967008\pi\)
\(632\) 0.938933 + 2.01355i 0.0373487 + 0.0800946i
\(633\) −34.6372 + 3.03036i −1.37671 + 0.120446i
\(634\) −16.1937 9.34943i −0.643133 0.371313i
\(635\) 0 0
\(636\) −0.884398 + 5.01567i −0.0350687 + 0.198884i
\(637\) −21.0096 30.0049i −0.832433 1.18884i
\(638\) −4.01378 1.07549i −0.158907 0.0425791i
\(639\) 0.985169 1.70636i 0.0389727 0.0675027i
\(640\) 0 0
\(641\) 8.70399 23.9140i 0.343787 0.944547i −0.640498 0.767960i \(-0.721272\pi\)
0.984285 0.176587i \(-0.0565057\pi\)
\(642\) 9.29765 19.9389i 0.366949 0.786925i
\(643\) −0.874517 + 9.99578i −0.0344876 + 0.394195i 0.959258 + 0.282530i \(0.0911738\pi\)
−0.993746 + 0.111665i \(0.964382\pi\)
\(644\) −5.59466 + 0.986489i −0.220460 + 0.0388731i
\(645\) 0 0
\(646\) −1.41144 + 1.85128i −0.0555323 + 0.0728378i
\(647\) −23.1183 23.1183i −0.908874 0.908874i 0.0873074 0.996181i \(-0.472174\pi\)
−0.996181 + 0.0873074i \(0.972174\pi\)
\(648\) 3.79471 5.41940i 0.149070 0.212894i
\(649\) −13.8482 + 11.6200i −0.543589 + 0.456126i
\(650\) 0 0
\(651\) 5.77099 + 2.10047i 0.226183 + 0.0823238i
\(652\) 1.00998 + 11.5442i 0.0395540 + 0.452105i
\(653\) −6.33914 23.6580i −0.248070 0.925808i −0.971816 0.235742i \(-0.924248\pi\)
0.723746 0.690066i \(-0.242419\pi\)
\(654\) 14.6617 + 25.3948i 0.573318 + 0.993016i
\(655\) 0 0
\(656\) −3.35953 0.592376i −0.131168 0.0231284i
\(657\) 1.62849 6.07760i 0.0635333 0.237110i
\(658\) −1.54467 + 0.413892i −0.0602174 + 0.0161352i
\(659\) 38.7486 + 32.5139i 1.50943 + 1.26656i 0.864854 + 0.502024i \(0.167411\pi\)
0.644577 + 0.764539i \(0.277034\pi\)
\(660\) 0 0
\(661\) 9.14741 + 25.1323i 0.355793 + 0.977533i 0.980473 + 0.196652i \(0.0630070\pi\)
−0.624680 + 0.780881i \(0.714771\pi\)
\(662\) −15.7064 1.37413i −0.610447 0.0534072i
\(663\) −3.94171 2.76002i −0.153083 0.107190i
\(664\) 13.1884 0.511811
\(665\) 0 0
\(666\) 3.90150 0.151180
\(667\) 7.91459 + 5.54185i 0.306454 + 0.214581i
\(668\) 19.8355 + 1.73539i 0.767460 + 0.0671441i
\(669\) 12.8858 + 35.4033i 0.498192 + 1.36877i
\(670\) 0 0
\(671\) 1.45881 + 1.22409i 0.0563167 + 0.0472553i
\(672\) 1.29977 0.348273i 0.0501398 0.0134349i
\(673\) −1.42596 + 5.32176i −0.0549667 + 0.205139i −0.987948 0.154786i \(-0.950531\pi\)
0.932981 + 0.359925i \(0.117198\pi\)
\(674\) −16.8426 2.96981i −0.648753 0.114393i
\(675\) 0 0
\(676\) −10.7920 18.6922i −0.415075 0.718931i
\(677\) 1.81174 + 6.76150i 0.0696308 + 0.259866i 0.991962 0.126534i \(-0.0403853\pi\)
−0.922331 + 0.386400i \(0.873719\pi\)
\(678\) −0.790357 9.03382i −0.0303535 0.346942i
\(679\) 5.57405 + 2.02879i 0.213912 + 0.0778578i
\(680\) 0 0
\(681\) 23.6202 19.8197i 0.905127 0.759492i
\(682\) −7.28216 + 10.4000i −0.278848 + 0.398237i
\(683\) 14.0680 + 14.0680i 0.538298 + 0.538298i 0.923029 0.384731i \(-0.125706\pi\)
−0.384731 + 0.923029i \(0.625706\pi\)
\(684\) 1.92860 + 2.09163i 0.0737418 + 0.0799756i
\(685\) 0 0
\(686\) −11.4421 + 2.01755i −0.436861 + 0.0770304i
\(687\) 1.73697 19.8537i 0.0662696 0.757466i
\(688\) 3.10058 6.64921i 0.118208 0.253499i
\(689\) 6.68625 18.3703i 0.254726 0.699853i
\(690\) 0 0
\(691\) −6.31837 + 10.9437i −0.240362 + 0.416319i −0.960817 0.277182i \(-0.910599\pi\)
0.720455 + 0.693501i \(0.243933\pi\)
\(692\) −9.75872 2.61484i −0.370971 0.0994013i
\(693\) 0.914694 + 1.30632i 0.0347463 + 0.0496229i
\(694\) 0.323973 1.83734i 0.0122979 0.0697446i
\(695\) 0 0
\(696\) −1.98197 1.14429i −0.0751263 0.0433742i
\(697\) 1.81498 0.158790i 0.0687471 0.00601459i
\(698\) 6.46029 + 13.8541i 0.244525 + 0.524386i
\(699\) 24.9920 9.09636i 0.945286 0.344056i
\(700\) 0 0
\(701\) −7.50392 42.5569i −0.283419 1.60735i −0.710878 0.703315i \(-0.751702\pi\)
0.427459 0.904035i \(-0.359409\pi\)
\(702\) −23.2713 + 23.2713i −0.878318 + 0.878318i
\(703\) 5.56042 25.4549i 0.209715 0.960048i
\(704\) 2.78182i 0.104844i
\(705\) 0 0
\(706\) 17.9356 + 21.3748i 0.675016 + 0.804453i
\(707\) 8.93004 + 4.16414i 0.335849 + 0.156609i
\(708\) −9.02341 + 4.20768i −0.339120 + 0.158134i
\(709\) −25.5927 + 30.5002i −0.961153 + 1.14546i 0.0281531 + 0.999604i \(0.491037\pi\)
−0.989306 + 0.145854i \(0.953407\pi\)
\(710\) 0 0
\(711\) −1.25584 + 0.725057i −0.0470975 + 0.0271918i
\(712\) −11.1998 + 7.84218i −0.419730 + 0.293898i
\(713\) 24.1817 16.9322i 0.905612 0.634116i
\(714\) −0.622377 + 0.359330i −0.0232919 + 0.0134476i
\(715\) 0 0
\(716\) −4.44931 + 5.30248i −0.166278 + 0.198163i
\(717\) −7.96106 + 3.71231i −0.297311 + 0.138639i
\(718\) 2.44103 + 1.13827i 0.0910986 + 0.0424800i
\(719\) −9.70751 11.5690i −0.362029 0.431449i 0.554028 0.832498i \(-0.313090\pi\)
−0.916057 + 0.401049i \(0.868646\pi\)
\(720\) 0 0
\(721\) 9.86756i 0.367487i
\(722\) 16.3952 9.60190i 0.610167 0.357346i
\(723\) −29.4690 + 29.4690i −1.09596 + 1.09596i
\(724\) 1.40465 + 7.96618i 0.0522035 + 0.296061i
\(725\) 0 0
\(726\) −4.69555 + 1.70904i −0.174268 + 0.0634285i
\(727\) 15.5205 + 33.2838i 0.575623 + 1.23443i 0.951469 + 0.307745i \(0.0995744\pi\)
−0.375846 + 0.926682i \(0.622648\pi\)
\(728\) −5.14542 + 0.450166i −0.190702 + 0.0166843i
\(729\) 26.0155 + 15.0201i 0.963538 + 0.556299i
\(730\) 0 0
\(731\) −0.680399 + 3.85874i −0.0251655 + 0.142721i
\(732\) 0.601577 + 0.859141i 0.0222349 + 0.0317547i
\(733\) −39.5394 10.5946i −1.46042 0.391319i −0.560787 0.827960i \(-0.689501\pi\)
−0.899636 + 0.436641i \(0.856168\pi\)
\(734\) 7.22154 12.5081i 0.266552 0.461681i
\(735\) 0 0
\(736\) 2.21225 6.07810i 0.0815445 0.224042i
\(737\) 1.12807 2.41916i 0.0415531 0.0891110i
\(738\) 0.194061 2.21813i 0.00714350 0.0816506i
\(739\) −1.95742 + 0.345146i −0.0720049 + 0.0126964i −0.209535 0.977801i \(-0.567195\pi\)
0.137530 + 0.990498i \(0.456084\pi\)
\(740\) 0 0
\(741\) 21.2042 + 33.0572i 0.778956 + 1.21439i
\(742\) −2.06452 2.06452i −0.0757908 0.0757908i
\(743\) −20.1921 + 28.8373i −0.740776 + 1.05794i 0.255073 + 0.966922i \(0.417900\pi\)
−0.995849 + 0.0910163i \(0.970988\pi\)
\(744\) −5.35647 + 4.49461i −0.196378 + 0.164780i
\(745\) 0 0
\(746\) −20.8809 7.60002i −0.764503 0.278256i
\(747\) 0.750249 + 8.57539i 0.0274502 + 0.313757i
\(748\) −0.384524 1.43506i −0.0140596 0.0524712i
\(749\) 6.30596 + 10.9222i 0.230415 + 0.399090i
\(750\) 0 0
\(751\) 32.5691 + 5.74281i 1.18846 + 0.209558i 0.732706 0.680546i \(-0.238257\pi\)
0.455758 + 0.890104i \(0.349368\pi\)
\(752\) 0.471246 1.75871i 0.0171846 0.0641337i
\(753\) 35.1309 9.41329i 1.28024 0.343039i
\(754\) 6.72935 + 5.64659i 0.245068 + 0.205637i
\(755\) 0 0
\(756\) 1.68109 + 4.61875i 0.0611405 + 0.167982i
\(757\) −26.4923 2.31777i −0.962878 0.0842409i −0.405137 0.914256i \(-0.632776\pi\)
−0.557741 + 0.830015i \(0.688332\pi\)
\(758\) −27.1916 19.0398i −0.987643 0.691555i
\(759\) −27.5673 −1.00063
\(760\) 0 0
\(761\) 30.7492 1.11466 0.557329 0.830292i \(-0.311826\pi\)
0.557329 + 0.830292i \(0.311826\pi\)
\(762\) −16.1737 11.3249i −0.585910 0.410259i
\(763\) −16.7461 1.46510i −0.606251 0.0530401i
\(764\) 7.99984 + 21.9794i 0.289424 + 0.795186i
\(765\) 0 0
\(766\) 0.246303 + 0.206673i 0.00889929 + 0.00746739i
\(767\) 36.9140 9.89109i 1.33289 0.357147i
\(768\) −0.396534 + 1.47988i −0.0143087 + 0.0534007i
\(769\) 13.2676 + 2.33944i 0.478443 + 0.0843624i 0.407669 0.913130i \(-0.366342\pi\)
0.0707745 + 0.997492i \(0.477453\pi\)
\(770\) 0 0
\(771\) 17.4580 + 30.2381i 0.628734 + 1.08900i
\(772\) 1.43834 + 5.36796i 0.0517670 + 0.193197i
\(773\) −3.31120 37.8472i −0.119095 1.36127i −0.786969 0.616993i \(-0.788351\pi\)
0.667873 0.744275i \(-0.267205\pi\)
\(774\) 4.49983 + 1.63780i 0.161743 + 0.0588697i
\(775\) 0 0
\(776\) −5.17368 + 4.34123i −0.185724 + 0.155841i
\(777\) 4.61351 6.58877i 0.165509 0.236371i
\(778\) 13.6520 + 13.6520i 0.489447 + 0.489447i
\(779\) −14.1953 4.42741i −0.508601 0.158628i
\(780\) 0 0
\(781\) 8.26999 1.45822i 0.295923 0.0521793i
\(782\) −0.301077 + 3.44132i −0.0107665 + 0.123061i
\(783\) 3.53288 7.57628i 0.126255 0.270754i
\(784\) 2.13031 5.85297i 0.0760824 0.209035i
\(785\) 0 0
\(786\) −7.12047 + 12.3330i −0.253979 + 0.439904i
\(787\) −1.10331 0.295631i −0.0393288 0.0105381i 0.239101 0.970995i \(-0.423147\pi\)
−0.278430 + 0.960457i \(0.589814\pi\)
\(788\) −6.03440 8.61801i −0.214966 0.307004i
\(789\) −1.67523 + 9.50071i −0.0596398 + 0.338234i
\(790\) 0 0
\(791\) 4.50209 + 2.59928i 0.160076 + 0.0924198i
\(792\) −1.80879 + 0.158249i −0.0642726 + 0.00562313i
\(793\) −1.70138 3.64862i −0.0604177 0.129566i
\(794\) −17.9981 + 6.55079i −0.638730 + 0.232479i
\(795\) 0 0
\(796\) −0.745583 4.22841i −0.0264265 0.149872i
\(797\) −29.4427 + 29.4427i −1.04291 + 1.04291i −0.0438768 + 0.999037i \(0.513971\pi\)
−0.999037 + 0.0438768i \(0.986029\pi\)
\(798\) 5.81286 0.783630i 0.205773 0.0277402i
\(799\) 0.972412i 0.0344015i
\(800\) 0 0
\(801\) −5.73626 6.83621i −0.202681 0.241546i
\(802\) −2.77366 1.29338i −0.0979414 0.0456708i
\(803\) 24.3039 11.3331i 0.857667 0.399937i
\(804\) 0.944957 1.12616i 0.0333261 0.0397165i
\(805\) 0 0
\(806\) 23.2439 13.4198i 0.818730 0.472694i
\(807\) −20.5202 + 14.3684i −0.722347 + 0.505793i
\(808\) −9.18972 + 6.43471i −0.323293 + 0.226372i
\(809\) −44.8609 + 25.9004i −1.57722 + 0.910611i −0.581980 + 0.813203i \(0.697722\pi\)
−0.995245 + 0.0974079i \(0.968945\pi\)
\(810\) 0 0
\(811\) 21.6803 25.8375i 0.761297 0.907279i −0.236632 0.971599i \(-0.576044\pi\)
0.997929 + 0.0643204i \(0.0204880\pi\)
\(812\) 1.18904 0.554460i 0.0417272 0.0194577i
\(813\) 28.9481 + 13.4987i 1.01525 + 0.473420i
\(814\) 10.6884 + 12.7379i 0.374627 + 0.446464i
\(815\) 0 0
\(816\) 0.818245i 0.0286443i
\(817\) 17.0988 27.0244i 0.598211 0.945463i
\(818\) 25.1716 25.1716i 0.880105 0.880105i
\(819\) −0.585414 3.32005i −0.0204560 0.116012i
\(820\) 0 0
\(821\) 32.1555 11.7036i 1.12223 0.408460i 0.286767 0.958000i \(-0.407419\pi\)
0.835467 + 0.549540i \(0.185197\pi\)
\(822\) −7.47043 16.0204i −0.260561 0.558775i
\(823\) 21.7414 1.90213i 0.757858 0.0663040i 0.298325 0.954464i \(-0.403572\pi\)
0.459534 + 0.888160i \(0.348017\pi\)
\(824\) 9.72972 + 5.61746i 0.338951 + 0.195693i
\(825\) 0 0
\(826\) 0.991108 5.62085i 0.0344851 0.195574i
\(827\) 3.22377 + 4.60402i 0.112102 + 0.160098i 0.871282 0.490782i \(-0.163289\pi\)
−0.759181 + 0.650880i \(0.774400\pi\)
\(828\) 4.07795 + 1.09268i 0.141719 + 0.0379734i
\(829\) 24.0684 41.6878i 0.835931 1.44788i −0.0573385 0.998355i \(-0.518261\pi\)
0.893270 0.449521i \(-0.148405\pi\)
\(830\) 0 0
\(831\) 13.7205 37.6967i 0.475958 1.30768i
\(832\) 2.48534 5.32982i 0.0861636 0.184778i
\(833\) −0.289925 + 3.31386i −0.0100453 + 0.114818i
\(834\) 6.17426 1.08869i 0.213797 0.0376982i
\(835\) 0 0
\(836\) −1.54541 + 12.0268i −0.0534493 + 0.415955i
\(837\) −18.0603 18.0603i −0.624254 0.624254i
\(838\) 16.6740 23.8129i 0.575993 0.822603i
\(839\) 29.4006 24.6700i 1.01502 0.851704i 0.0260278 0.999661i \(-0.491714\pi\)
0.988994 + 0.147957i \(0.0472697\pi\)
\(840\) 0 0
\(841\) 25.1543 + 9.15542i 0.867390 + 0.315704i
\(842\) −1.76649 20.1910i −0.0608771 0.695829i
\(843\) −9.93978 37.0958i −0.342344 1.27765i
\(844\) 11.3471 + 19.6538i 0.390583 + 0.676510i
\(845\) 0 0
\(846\) 1.17036 + 0.206366i 0.0402377 + 0.00709500i
\(847\) 0.741401 2.76695i 0.0254748 0.0950734i
\(848\) 3.21098 0.860379i 0.110265 0.0295455i
\(849\) −1.53864 1.29107i −0.0528061 0.0443095i
\(850\) 0 0
\(851\) −13.2236 36.3315i −0.453299 1.24543i
\(852\) 4.60737 + 0.403093i 0.157846 + 0.0138097i
\(853\) 24.8075 + 17.3704i 0.849392 + 0.594751i 0.915163 0.403084i \(-0.132062\pi\)
−0.0657710 + 0.997835i \(0.520951\pi\)
\(854\) −0.601251 −0.0205744
\(855\) 0 0
\(856\) −14.3596 −0.490800
\(857\) 18.8455 + 13.1958i 0.643751 + 0.450759i 0.849316 0.527884i \(-0.177015\pi\)
−0.205566 + 0.978643i \(0.565903\pi\)
\(858\) −24.9686 2.18447i −0.852413 0.0745765i
\(859\) 15.3095 + 42.0626i 0.522354 + 1.43516i 0.867893 + 0.496752i \(0.165474\pi\)
−0.345538 + 0.938405i \(0.612304\pi\)
\(860\) 0 0
\(861\) −3.51646 2.95066i −0.119840 0.100558i
\(862\) −3.77676 + 1.01198i −0.128637 + 0.0344681i
\(863\) −0.916555 + 3.42063i −0.0311999 + 0.116440i −0.979770 0.200129i \(-0.935864\pi\)
0.948570 + 0.316568i \(0.102531\pi\)
\(864\) −5.51125 0.971782i −0.187496 0.0330607i
\(865\) 0 0
\(866\) −10.7835 18.6776i −0.366438 0.634690i
\(867\) −6.62797 24.7359i −0.225098 0.840076i
\(868\) −0.349363 3.99323i −0.0118581 0.135539i
\(869\) −5.80765 2.11381i −0.197011 0.0717062i
\(870\) 0 0
\(871\) −4.32267 + 3.62715i −0.146468 + 0.122901i
\(872\) 10.9780 15.6782i 0.371761 0.530929i
\(873\) −3.11707 3.11707i −0.105497 0.105497i
\(874\) 12.9410 25.0488i 0.437734 0.847287i
\(875\) 0 0
\(876\) 14.5448 2.56464i 0.491423 0.0866511i
\(877\) −0.806017 + 9.21282i −0.0272173 + 0.311095i 0.970367 + 0.241634i \(0.0776834\pi\)
−0.997585 + 0.0694606i \(0.977872\pi\)
\(878\) 7.87493 16.8878i 0.265766 0.569937i
\(879\) −6.88042 + 18.9038i −0.232071 + 0.637610i
\(880\) 0 0
\(881\) 5.50606 9.53677i 0.185504 0.321302i −0.758242 0.651973i \(-0.773942\pi\)
0.943746 + 0.330671i \(0.107275\pi\)
\(882\) 3.92690 + 1.05221i 0.132226 + 0.0354298i
\(883\) 9.31326 + 13.3007i 0.313416 + 0.447605i 0.944695 0.327952i \(-0.106358\pi\)
−0.631278 + 0.775556i \(0.717469\pi\)
\(884\) −0.545389 + 3.09306i −0.0183434 + 0.104031i
\(885\) 0 0
\(886\) 13.6855 + 7.90130i 0.459772 + 0.265449i
\(887\) 26.6168 2.32867i 0.893705 0.0781891i 0.368957 0.929447i \(-0.379715\pi\)
0.524748 + 0.851257i \(0.324159\pi\)
\(888\) 3.87033 + 8.29995i 0.129880 + 0.278528i
\(889\) 10.6362 3.87126i 0.356726 0.129838i
\(890\) 0 0
\(891\) 3.19584 + 18.1245i 0.107065 + 0.607195i
\(892\) 17.3884 17.3884i 0.582206 0.582206i
\(893\) 3.01440 7.34174i 0.100873 0.245682i
\(894\) 29.5417i 0.988023i
\(895\) 0 0
\(896\) −0.564557 0.672812i −0.0188605 0.0224771i
\(897\) 52.8176 + 24.6293i 1.76353 + 0.822347i
\(898\) 27.5502 12.8469i 0.919362 0.428706i
\(899\) −4.38217 + 5.22247i −0.146154 + 0.174179i
\(900\) 0 0
\(901\) −1.53753 + 0.887693i −0.0512225 + 0.0295734i
\(902\) 7.77357 5.44311i 0.258831 0.181236i
\(903\) 8.08691 5.66252i 0.269116 0.188437i
\(904\) −5.12595 + 2.95947i −0.170486 + 0.0984304i
\(905\) 0 0
\(906\) −9.78907 + 11.6662i −0.325220 + 0.387582i
\(907\) −43.9809 + 20.5086i −1.46036 + 0.680977i −0.980527 0.196382i \(-0.937081\pi\)
−0.479833 + 0.877360i \(0.659303\pi\)
\(908\) −18.2398 8.50537i −0.605310 0.282261i
\(909\) −4.70675 5.60929i −0.156113 0.186048i
\(910\) 0 0
\(911\) 22.6469i 0.750326i −0.926959 0.375163i \(-0.877587\pi\)
0.926959 0.375163i \(-0.122413\pi\)
\(912\) −2.53649 + 6.17777i −0.0839917 + 0.204566i
\(913\) −25.9422 + 25.9422i −0.858562 + 0.858562i
\(914\) −2.37249 13.4551i −0.0784750 0.445054i
\(915\) 0 0
\(916\) −12.2236 + 4.44902i −0.403879 + 0.147000i
\(917\) −3.45019 7.39896i −0.113935 0.244335i
\(918\) 2.97743 0.260492i 0.0982699 0.00859750i
\(919\) 24.7135 + 14.2683i 0.815222 + 0.470668i 0.848766 0.528769i \(-0.177346\pi\)
−0.0335443 + 0.999437i \(0.510679\pi\)
\(920\) 0 0
\(921\) 8.63086 48.9480i 0.284396 1.61289i
\(922\) −13.1415 18.7679i −0.432791 0.618089i
\(923\) −17.1477 4.59471i −0.564423 0.151237i
\(924\) −1.87164 + 3.24178i −0.0615724 + 0.106647i
\(925\) 0 0
\(926\) 1.25396 3.44523i 0.0412077 0.113217i
\(927\) −3.09909 + 6.64602i −0.101787 + 0.218284i
\(928\) −0.130190 + 1.48808i −0.00427370 + 0.0488486i
\(929\) −21.8075 + 3.84525i −0.715480 + 0.126159i −0.519526 0.854455i \(-0.673892\pi\)
−0.195954 + 0.980613i \(0.562780\pi\)
\(930\) 0 0
\(931\) 12.4616 24.1210i 0.408414 0.790533i
\(932\) −12.2749 12.2749i −0.402077 0.402077i
\(933\) 14.5461 20.7740i 0.476219 0.680112i
\(934\) 3.78394 3.17511i 0.123814 0.103893i
\(935\) 0 0
\(936\) 3.60694 + 1.31282i 0.117897 + 0.0429108i
\(937\) 0.257291 + 2.94085i 0.00840532 + 0.0960733i 0.999239 0.0390177i \(-0.0124229\pi\)
−0.990833 + 0.135091i \(0.956867\pi\)
\(938\) 0.218121 + 0.814037i 0.00712189 + 0.0265793i
\(939\) −14.9738 25.9353i −0.488650 0.846367i
\(940\) 0 0
\(941\) 41.6228 + 7.33922i 1.35686 + 0.239252i 0.804303 0.594220i \(-0.202539\pi\)
0.552562 + 0.833472i \(0.313650\pi\)
\(942\) −5.99993 + 22.3921i −0.195488 + 0.729572i
\(943\) −21.3134 + 5.71091i −0.694060 + 0.185973i
\(944\) 4.97811 + 4.17713i 0.162024 + 0.135954i
\(945\) 0 0
\(946\) 6.98031 + 19.1782i 0.226949 + 0.623538i
\(947\) 6.27934 + 0.549371i 0.204051 + 0.0178522i 0.188723 0.982030i \(-0.439565\pi\)
0.0153281 + 0.999883i \(0.495121\pi\)
\(948\) −2.78827 1.95237i −0.0905588 0.0634099i
\(949\) −56.6903 −1.84025
\(950\) 0 0
\(951\) 28.6483 0.928985
\(952\) 0.384241 + 0.269048i 0.0124533 + 0.00871991i
\(953\) 58.8446 + 5.14824i 1.90616 + 0.166768i 0.978444 0.206510i \(-0.0662106\pi\)
0.927720 + 0.373278i \(0.121766\pi\)
\(954\) 0.742098 + 2.03890i 0.0240263 + 0.0660118i
\(955\) 0 0
\(956\) 4.39203 + 3.68535i 0.142048 + 0.119193i
\(957\) 6.14947 1.64775i 0.198784 0.0532641i
\(958\) −5.02207 + 18.7426i −0.162256 + 0.605547i
\(959\) 9.97940 + 1.75964i 0.322252 + 0.0568217i
\(960\) 0 0
\(961\) −5.08520 8.80783i −0.164039 0.284124i
\(962\) −9.09807 33.9544i −0.293333 1.09474i
\(963\) −0.816870 9.33687i −0.0263233 0.300876i
\(964\) 25.5612 + 9.30353i 0.823272 + 0.299647i
\(965\) 0 0
\(966\) 6.66745 5.59466i 0.214522 0.180005i
\(967\) −8.24159 + 11.7702i −0.265032 + 0.378504i −0.929506 0.368807i \(-0.879766\pi\)
0.664475 + 0.747311i \(0.268655\pi\)
\(968\) 2.30623 + 2.30623i 0.0741249 + 0.0741249i
\(969\) 0.454569 3.53756i 0.0146029 0.113643i
\(970\) 0 0
\(971\) 6.61950 1.16720i 0.212430 0.0374571i −0.0664203 0.997792i \(-0.521158\pi\)
0.278850 + 0.960335i \(0.410047\pi\)
\(972\) 0.579821 6.62739i 0.0185978 0.212574i
\(973\) −1.51893 + 3.25735i −0.0486946 + 0.104426i
\(974\) −9.56933 + 26.2915i −0.306621 + 0.842435i
\(975\) 0 0
\(976\) 0.342283 0.592852i 0.0109562 0.0189767i
\(977\) 55.3159 + 14.8218i 1.76971 + 0.474193i 0.988647 0.150258i \(-0.0480104\pi\)
0.781064 + 0.624451i \(0.214677\pi\)
\(978\) −10.1834 14.5434i −0.325630 0.465048i
\(979\) 6.60456 37.4563i 0.211083 1.19711i
\(980\) 0 0
\(981\) 10.8188 + 6.24621i 0.345416 + 0.199426i
\(982\) −0.808952 + 0.0707741i −0.0258147 + 0.00225849i
\(983\) 10.0174 + 21.4825i 0.319507 + 0.685185i 0.998815 0.0486683i \(-0.0154977\pi\)
−0.679308 + 0.733853i \(0.737720\pi\)
\(984\) 4.91131 1.78757i 0.156567 0.0569856i
\(985\) 0 0
\(986\) −0.138532 0.785656i −0.00441177 0.0250204i
\(987\) 1.73245 1.73245i 0.0551444 0.0551444i
\(988\) 13.7059 21.6620i 0.436044 0.689160i
\(989\) 47.4544i 1.50896i
\(990\) 0 0
\(991\) 8.66294 + 10.3241i 0.275187 + 0.327956i 0.885882 0.463911i \(-0.153554\pi\)
−0.610695 + 0.791866i \(0.709110\pi\)
\(992\) 4.13634 + 1.92881i 0.131329 + 0.0612397i
\(993\) 21.8924 10.2086i 0.694733 0.323959i
\(994\) −1.70425 + 2.03104i −0.0540554 + 0.0644207i
\(995\) 0 0
\(996\) −17.4988 + 10.1029i −0.554471 + 0.320124i
\(997\) 22.2435 15.5750i 0.704458 0.493267i −0.165615 0.986191i \(-0.552961\pi\)
0.870072 + 0.492924i \(0.164072\pi\)
\(998\) −25.7050 + 17.9988i −0.813677 + 0.569743i
\(999\) −28.9698 + 16.7257i −0.916563 + 0.529178i
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.bb.b.257.4 yes 48
5.2 odd 4 inner 950.2.bb.b.143.2 48
5.3 odd 4 inner 950.2.bb.b.143.3 yes 48
5.4 even 2 inner 950.2.bb.b.257.1 yes 48
19.2 odd 18 inner 950.2.bb.b.857.3 yes 48
95.2 even 36 inner 950.2.bb.b.743.1 yes 48
95.59 odd 18 inner 950.2.bb.b.857.2 yes 48
95.78 even 36 inner 950.2.bb.b.743.4 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.bb.b.143.2 48 5.2 odd 4 inner
950.2.bb.b.143.3 yes 48 5.3 odd 4 inner
950.2.bb.b.257.1 yes 48 5.4 even 2 inner
950.2.bb.b.257.4 yes 48 1.1 even 1 trivial
950.2.bb.b.743.1 yes 48 95.2 even 36 inner
950.2.bb.b.743.4 yes 48 95.78 even 36 inner
950.2.bb.b.857.2 yes 48 95.59 odd 18 inner
950.2.bb.b.857.3 yes 48 19.2 odd 18 inner