Properties

Label 950.2.h.e.191.8
Level $950$
Weight $2$
Character 950.191
Analytic conductor $7.586$
Analytic rank $0$
Dimension $44$
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(191,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.191");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.h (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(11\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 191.8
Character \(\chi\) \(=\) 950.191
Dual form 950.2.h.e.761.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.809017 + 0.587785i) q^{2} +(0.625820 + 1.92608i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.243465 - 2.22277i) q^{5} +(-0.625820 + 1.92608i) q^{6} +4.25141 q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.891064 + 0.647396i) q^{9} +O(q^{10})\) \(q+(0.809017 + 0.587785i) q^{2} +(0.625820 + 1.92608i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.243465 - 2.22277i) q^{5} +(-0.625820 + 1.92608i) q^{6} +4.25141 q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.891064 + 0.647396i) q^{9} +(1.10955 - 1.94137i) q^{10} +(1.65703 + 1.20390i) q^{11} +(-1.63842 + 1.19038i) q^{12} +(-5.06290 + 3.67841i) q^{13} +(3.43946 + 2.49891i) q^{14} +(4.12886 - 1.85999i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(2.46489 - 7.58616i) q^{17} -1.10142 q^{18} +(0.309017 - 0.951057i) q^{19} +(2.03875 - 0.918424i) q^{20} +(2.66061 + 8.18853i) q^{21} +(0.632927 + 1.94795i) q^{22} +(7.35345 + 5.34259i) q^{23} -2.02520 q^{24} +(-4.88145 + 1.08233i) q^{25} -6.25808 q^{26} +(3.11067 + 2.26004i) q^{27} +(1.31376 + 4.04333i) q^{28} +(-0.163054 - 0.501828i) q^{29} +(4.43359 + 0.922124i) q^{30} +(0.159734 - 0.491612i) q^{31} -1.00000 q^{32} +(-1.28180 + 3.94498i) q^{33} +(6.45317 - 4.68850i) q^{34} +(-1.03507 - 9.44992i) q^{35} +(-0.891064 - 0.647396i) q^{36} +(-5.18795 + 3.76927i) q^{37} +(0.809017 - 0.587785i) q^{38} +(-10.2534 - 7.44950i) q^{39} +(2.18922 + 0.455326i) q^{40} +(-5.45398 + 3.96255i) q^{41} +(-2.66061 + 8.18853i) q^{42} +2.00411 q^{43} +(-0.632927 + 1.94795i) q^{44} +(1.65596 + 1.82302i) q^{45} +(2.80877 + 8.64450i) q^{46} +(-1.04669 - 3.22139i) q^{47} +(-1.63842 - 1.19038i) q^{48} +11.0745 q^{49} +(-4.58536 - 1.99362i) q^{50} +16.1541 q^{51} +(-5.06290 - 3.67841i) q^{52} +(-2.45411 - 7.55298i) q^{53} +(1.18817 + 3.65682i) q^{54} +(2.27257 - 3.97630i) q^{55} +(-1.31376 + 4.04333i) q^{56} +2.02520 q^{57} +(0.163054 - 0.501828i) q^{58} +(-9.19597 + 6.68126i) q^{59} +(3.04484 + 3.35202i) q^{60} +(-5.04018 - 3.66190i) q^{61} +(0.418190 - 0.303833i) q^{62} +(-3.78828 + 2.75234i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(9.40891 + 10.3581i) q^{65} +(-3.35580 + 2.43813i) q^{66} +(0.629014 - 1.93591i) q^{67} +7.97656 q^{68} +(-5.68830 + 17.5068i) q^{69} +(4.71714 - 8.25354i) q^{70} +(-0.362014 - 1.11417i) q^{71} +(-0.340356 - 1.04751i) q^{72} +(-11.3386 - 8.23798i) q^{73} -6.41266 q^{74} +(-5.13957 - 8.72469i) q^{75} +1.00000 q^{76} +(7.04469 + 5.11827i) q^{77} +(-3.91643 - 12.0535i) q^{78} +(0.617760 + 1.90127i) q^{79} +(1.50348 + 1.65516i) q^{80} +(-3.42735 + 10.5483i) q^{81} -6.74149 q^{82} +(-0.965793 + 2.97241i) q^{83} +(-6.96558 + 5.06079i) q^{84} +(-17.4624 - 3.63194i) q^{85} +(1.62136 + 1.17798i) q^{86} +(0.864517 - 0.628108i) q^{87} +(-1.65703 + 1.20390i) q^{88} +(2.20612 + 1.60284i) q^{89} +(0.268156 + 2.44820i) q^{90} +(-21.5244 + 15.6384i) q^{91} +(-2.80877 + 8.64450i) q^{92} +1.04685 q^{93} +(1.04669 - 3.22139i) q^{94} +(-2.18922 - 0.455326i) q^{95} +(-0.625820 - 1.92608i) q^{96} +(-5.31877 - 16.3695i) q^{97} +(8.95943 + 6.50941i) q^{98} -2.25591 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 5 q^{5} + q^{6} + 28 q^{7} + 11 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 5 q^{5} + q^{6} + 28 q^{7} + 11 q^{8} - 8 q^{9} + 5 q^{10} - 6 q^{12} - 10 q^{13} + 12 q^{14} - 11 q^{16} - 20 q^{17} - 42 q^{18} - 11 q^{19} + 5 q^{20} - 3 q^{21} - 10 q^{22} - 6 q^{23} - 14 q^{24} - 15 q^{25} - 40 q^{26} + 5 q^{27} - 2 q^{28} + 6 q^{29} - 5 q^{31} - 44 q^{32} - 36 q^{33} - 10 q^{34} - 8 q^{36} - 10 q^{37} + 11 q^{38} + 39 q^{39} - 22 q^{41} + 3 q^{42} + 68 q^{43} + 10 q^{44} + 20 q^{45} + 6 q^{46} + 19 q^{47} - 6 q^{48} + 40 q^{49} - 30 q^{50} + 86 q^{51} - 10 q^{52} + 30 q^{54} + 2 q^{56} + 14 q^{57} - 6 q^{58} - 4 q^{59} + 15 q^{60} + 26 q^{61} - 15 q^{62} - 41 q^{63} - 11 q^{64} + 30 q^{65} - 4 q^{66} - 59 q^{67} + 20 q^{68} - 59 q^{69} - 25 q^{70} + 30 q^{71} + 13 q^{72} - 38 q^{73} - 50 q^{74} - 15 q^{75} + 44 q^{76} + 29 q^{77} + 16 q^{78} + 3 q^{79} + 5 q^{80} - 54 q^{81} - 8 q^{82} + 9 q^{83} + 7 q^{84} + 12 q^{86} - 43 q^{87} + 33 q^{89} - 6 q^{91} - 6 q^{92} + 84 q^{93} - 19 q^{94} + q^{96} + 30 q^{97} - 15 q^{98} - 54 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(77\) \(401\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.809017 + 0.587785i 0.572061 + 0.415627i
\(3\) 0.625820 + 1.92608i 0.361317 + 1.11202i 0.952255 + 0.305303i \(0.0987578\pi\)
−0.590938 + 0.806717i \(0.701242\pi\)
\(4\) 0.309017 + 0.951057i 0.154508 + 0.475528i
\(5\) −0.243465 2.22277i −0.108881 0.994055i
\(6\) −0.625820 + 1.92608i −0.255490 + 0.786317i
\(7\) 4.25141 1.60688 0.803441 0.595385i \(-0.203000\pi\)
0.803441 + 0.595385i \(0.203000\pi\)
\(8\) −0.309017 + 0.951057i −0.109254 + 0.336249i
\(9\) −0.891064 + 0.647396i −0.297021 + 0.215799i
\(10\) 1.10955 1.94137i 0.350869 0.613914i
\(11\) 1.65703 + 1.20390i 0.499612 + 0.362989i 0.808869 0.587989i \(-0.200080\pi\)
−0.309257 + 0.950979i \(0.600080\pi\)
\(12\) −1.63842 + 1.19038i −0.472970 + 0.343633i
\(13\) −5.06290 + 3.67841i −1.40419 + 1.02021i −0.410060 + 0.912059i \(0.634492\pi\)
−0.994135 + 0.108149i \(0.965508\pi\)
\(14\) 3.43946 + 2.49891i 0.919235 + 0.667863i
\(15\) 4.12886 1.85999i 1.06607 0.480247i
\(16\) −0.809017 + 0.587785i −0.202254 + 0.146946i
\(17\) 2.46489 7.58616i 0.597824 1.83991i 0.0576896 0.998335i \(-0.481627\pi\)
0.540134 0.841579i \(-0.318373\pi\)
\(18\) −1.10142 −0.259606
\(19\) 0.309017 0.951057i 0.0708934 0.218187i
\(20\) 2.03875 0.918424i 0.455878 0.205366i
\(21\) 2.66061 + 8.18853i 0.580594 + 1.78688i
\(22\) 0.632927 + 1.94795i 0.134941 + 0.415304i
\(23\) 7.35345 + 5.34259i 1.53330 + 1.11401i 0.954368 + 0.298632i \(0.0965303\pi\)
0.578932 + 0.815376i \(0.303470\pi\)
\(24\) −2.02520 −0.413391
\(25\) −4.88145 + 1.08233i −0.976290 + 0.216467i
\(26\) −6.25808 −1.22731
\(27\) 3.11067 + 2.26004i 0.598649 + 0.434944i
\(28\) 1.31376 + 4.04333i 0.248277 + 0.764117i
\(29\) −0.163054 0.501828i −0.0302783 0.0931872i 0.934775 0.355240i \(-0.115601\pi\)
−0.965054 + 0.262052i \(0.915601\pi\)
\(30\) 4.43359 + 0.922124i 0.809460 + 0.168356i
\(31\) 0.159734 0.491612i 0.0286891 0.0882961i −0.935687 0.352832i \(-0.885219\pi\)
0.964376 + 0.264536i \(0.0852187\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.28180 + 3.94498i −0.223133 + 0.686733i
\(34\) 6.45317 4.68850i 1.10671 0.804072i
\(35\) −1.03507 9.44992i −0.174958 1.59733i
\(36\) −0.891064 0.647396i −0.148511 0.107899i
\(37\) −5.18795 + 3.76927i −0.852894 + 0.619664i −0.925942 0.377665i \(-0.876727\pi\)
0.0730484 + 0.997328i \(0.476727\pi\)
\(38\) 0.809017 0.587785i 0.131240 0.0953514i
\(39\) −10.2534 7.44950i −1.64185 1.19287i
\(40\) 2.18922 + 0.455326i 0.346146 + 0.0719934i
\(41\) −5.45398 + 3.96255i −0.851769 + 0.618846i −0.925633 0.378422i \(-0.876467\pi\)
0.0738645 + 0.997268i \(0.476467\pi\)
\(42\) −2.66061 + 8.18853i −0.410542 + 1.26352i
\(43\) 2.00411 0.305623 0.152812 0.988255i \(-0.451167\pi\)
0.152812 + 0.988255i \(0.451167\pi\)
\(44\) −0.632927 + 1.94795i −0.0954174 + 0.293665i
\(45\) 1.65596 + 1.82302i 0.246856 + 0.271759i
\(46\) 2.80877 + 8.64450i 0.414130 + 1.27456i
\(47\) −1.04669 3.22139i −0.152676 0.469888i 0.845242 0.534383i \(-0.179456\pi\)
−0.997918 + 0.0644958i \(0.979456\pi\)
\(48\) −1.63842 1.19038i −0.236485 0.171817i
\(49\) 11.0745 1.58207
\(50\) −4.58536 1.99362i −0.648467 0.281940i
\(51\) 16.1541 2.26202
\(52\) −5.06290 3.67841i −0.702097 0.510104i
\(53\) −2.45411 7.55298i −0.337098 1.03748i −0.965679 0.259737i \(-0.916364\pi\)
0.628581 0.777744i \(-0.283636\pi\)
\(54\) 1.18817 + 3.65682i 0.161690 + 0.497630i
\(55\) 2.27257 3.97630i 0.306433 0.536164i
\(56\) −1.31376 + 4.04333i −0.175558 + 0.540313i
\(57\) 2.02520 0.268244
\(58\) 0.163054 0.501828i 0.0214100 0.0658933i
\(59\) −9.19597 + 6.68126i −1.19721 + 0.869826i −0.994008 0.109310i \(-0.965136\pi\)
−0.203205 + 0.979136i \(0.565136\pi\)
\(60\) 3.04484 + 3.35202i 0.393087 + 0.432743i
\(61\) −5.04018 3.66190i −0.645329 0.468859i 0.216348 0.976316i \(-0.430585\pi\)
−0.861677 + 0.507458i \(0.830585\pi\)
\(62\) 0.418190 0.303833i 0.0531102 0.0385868i
\(63\) −3.78828 + 2.75234i −0.477278 + 0.346763i
\(64\) −0.809017 0.587785i −0.101127 0.0734732i
\(65\) 9.40891 + 10.3581i 1.16703 + 1.28477i
\(66\) −3.35580 + 2.43813i −0.413070 + 0.300113i
\(67\) 0.629014 1.93591i 0.0768463 0.236509i −0.905253 0.424873i \(-0.860319\pi\)
0.982099 + 0.188365i \(0.0603186\pi\)
\(68\) 7.97656 0.967300
\(69\) −5.68830 + 17.5068i −0.684791 + 2.10757i
\(70\) 4.71714 8.25354i 0.563805 0.986487i
\(71\) −0.362014 1.11417i −0.0429632 0.132227i 0.927274 0.374383i \(-0.122145\pi\)
−0.970237 + 0.242156i \(0.922145\pi\)
\(72\) −0.340356 1.04751i −0.0401114 0.123450i
\(73\) −11.3386 8.23798i −1.32708 0.964182i −0.999815 0.0192509i \(-0.993872\pi\)
−0.327268 0.944931i \(-0.606128\pi\)
\(74\) −6.41266 −0.745457
\(75\) −5.13957 8.72469i −0.593466 1.00744i
\(76\) 1.00000 0.114708
\(77\) 7.04469 + 5.11827i 0.802817 + 0.583281i
\(78\) −3.91643 12.0535i −0.443449 1.36479i
\(79\) 0.617760 + 1.90127i 0.0695034 + 0.213910i 0.979775 0.200102i \(-0.0641273\pi\)
−0.910272 + 0.414011i \(0.864127\pi\)
\(80\) 1.50348 + 1.65516i 0.168094 + 0.185052i
\(81\) −3.42735 + 10.5483i −0.380816 + 1.17203i
\(82\) −6.74149 −0.744473
\(83\) −0.965793 + 2.97241i −0.106010 + 0.326264i −0.989966 0.141305i \(-0.954870\pi\)
0.883957 + 0.467569i \(0.154870\pi\)
\(84\) −6.96558 + 5.06079i −0.760007 + 0.552177i
\(85\) −17.4624 3.63194i −1.89407 0.393939i
\(86\) 1.62136 + 1.17798i 0.174835 + 0.127025i
\(87\) 0.864517 0.628108i 0.0926859 0.0673402i
\(88\) −1.65703 + 1.20390i −0.176640 + 0.128336i
\(89\) 2.20612 + 1.60284i 0.233848 + 0.169900i 0.698538 0.715573i \(-0.253834\pi\)
−0.464690 + 0.885473i \(0.653834\pi\)
\(90\) 0.268156 + 2.44820i 0.0282661 + 0.258063i
\(91\) −21.5244 + 15.6384i −2.25637 + 1.63935i
\(92\) −2.80877 + 8.64450i −0.292834 + 0.901251i
\(93\) 1.04685 0.108553
\(94\) 1.04669 3.22139i 0.107958 0.332261i
\(95\) −2.18922 0.455326i −0.224609 0.0467155i
\(96\) −0.625820 1.92608i −0.0638725 0.196579i
\(97\) −5.31877 16.3695i −0.540039 1.66207i −0.732502 0.680765i \(-0.761647\pi\)
0.192463 0.981304i \(-0.438353\pi\)
\(98\) 8.95943 + 6.50941i 0.905039 + 0.657549i
\(99\) −2.25591 −0.226728
\(100\) −2.53781 4.30807i −0.253781 0.430807i
\(101\) 13.0600 1.29952 0.649762 0.760138i \(-0.274869\pi\)
0.649762 + 0.760138i \(0.274869\pi\)
\(102\) 13.0689 + 9.49513i 1.29402 + 0.940158i
\(103\) −2.18293 6.71838i −0.215091 0.661981i −0.999147 0.0412916i \(-0.986853\pi\)
0.784056 0.620690i \(-0.213147\pi\)
\(104\) −1.93385 5.95179i −0.189630 0.583621i
\(105\) 17.5535 7.90756i 1.71304 0.771699i
\(106\) 2.45411 7.55298i 0.238364 0.733610i
\(107\) 2.89307 0.279684 0.139842 0.990174i \(-0.455341\pi\)
0.139842 + 0.990174i \(0.455341\pi\)
\(108\) −1.18817 + 3.65682i −0.114332 + 0.351877i
\(109\) 1.72479 1.25313i 0.165205 0.120028i −0.502111 0.864803i \(-0.667443\pi\)
0.667316 + 0.744775i \(0.267443\pi\)
\(110\) 4.17576 1.88111i 0.398143 0.179357i
\(111\) −10.5066 7.63350i −0.997244 0.724540i
\(112\) −3.43946 + 2.49891i −0.324999 + 0.236125i
\(113\) 11.1086 8.07087i 1.04501 0.759243i 0.0737517 0.997277i \(-0.476503\pi\)
0.971257 + 0.238033i \(0.0765028\pi\)
\(114\) 1.63842 + 1.19038i 0.153452 + 0.111489i
\(115\) 10.0851 17.6458i 0.940438 1.64548i
\(116\) 0.426881 0.310147i 0.0396349 0.0287964i
\(117\) 2.12998 6.55539i 0.196916 0.606046i
\(118\) −11.3668 −1.04640
\(119\) 10.4793 32.2518i 0.960632 2.95652i
\(120\) 0.493064 + 4.50155i 0.0450104 + 0.410934i
\(121\) −2.10283 6.47184i −0.191166 0.588349i
\(122\) −1.92518 5.92508i −0.174297 0.536432i
\(123\) −11.0454 8.02493i −0.995928 0.723584i
\(124\) 0.516911 0.0464200
\(125\) 3.59425 + 10.5868i 0.321479 + 0.946917i
\(126\) −4.68257 −0.417156
\(127\) 3.03440 + 2.20462i 0.269259 + 0.195628i 0.714219 0.699922i \(-0.246782\pi\)
−0.444960 + 0.895551i \(0.646782\pi\)
\(128\) −0.309017 0.951057i −0.0273135 0.0840623i
\(129\) 1.25421 + 3.86006i 0.110427 + 0.339859i
\(130\) 1.52362 + 13.9103i 0.133631 + 1.22001i
\(131\) −3.75554 + 11.5584i −0.328123 + 1.00986i 0.641888 + 0.766798i \(0.278151\pi\)
−0.970011 + 0.243060i \(0.921849\pi\)
\(132\) −4.14800 −0.361037
\(133\) 1.31376 4.04333i 0.113917 0.350601i
\(134\) 1.64678 1.19646i 0.142260 0.103358i
\(135\) 4.26621 7.46456i 0.367177 0.642447i
\(136\) 6.45317 + 4.68850i 0.553355 + 0.402036i
\(137\) −12.6851 + 9.21626i −1.08376 + 0.787398i −0.978335 0.207029i \(-0.933621\pi\)
−0.105426 + 0.994427i \(0.533621\pi\)
\(138\) −14.8922 + 10.8198i −1.26771 + 0.921042i
\(139\) −0.582072 0.422900i −0.0493707 0.0358699i 0.562826 0.826575i \(-0.309714\pi\)
−0.612197 + 0.790705i \(0.709714\pi\)
\(140\) 8.66755 3.90459i 0.732542 0.329998i
\(141\) 5.54959 4.03201i 0.467360 0.339557i
\(142\) 0.362014 1.11417i 0.0303796 0.0934987i
\(143\) −12.8178 −1.07188
\(144\) 0.340356 1.04751i 0.0283630 0.0872924i
\(145\) −1.07575 + 0.484609i −0.0893364 + 0.0402446i
\(146\) −4.33096 13.3293i −0.358433 1.10314i
\(147\) 6.93062 + 21.3303i 0.571628 + 1.75929i
\(148\) −5.18795 3.76927i −0.426447 0.309832i
\(149\) −8.37597 −0.686186 −0.343093 0.939301i \(-0.611475\pi\)
−0.343093 + 0.939301i \(0.611475\pi\)
\(150\) 0.970250 10.0794i 0.0792206 0.822978i
\(151\) 10.6004 0.862645 0.431323 0.902198i \(-0.358047\pi\)
0.431323 + 0.902198i \(0.358047\pi\)
\(152\) 0.809017 + 0.587785i 0.0656199 + 0.0476757i
\(153\) 2.71487 + 8.35551i 0.219484 + 0.675503i
\(154\) 2.69083 + 8.28153i 0.216833 + 0.667345i
\(155\) −1.13163 0.235363i −0.0908948 0.0189048i
\(156\) 3.91643 12.0535i 0.313566 0.965055i
\(157\) 0.524726 0.0418777 0.0209388 0.999781i \(-0.493334\pi\)
0.0209388 + 0.999781i \(0.493334\pi\)
\(158\) −0.617760 + 1.90127i −0.0491463 + 0.151257i
\(159\) 13.0118 9.45360i 1.03190 0.749719i
\(160\) 0.243465 + 2.22277i 0.0192476 + 0.175726i
\(161\) 31.2625 + 22.7135i 2.46383 + 1.79008i
\(162\) −8.97291 + 6.51920i −0.704979 + 0.512197i
\(163\) 0.620455 0.450787i 0.0485978 0.0353084i −0.563221 0.826306i \(-0.690438\pi\)
0.611819 + 0.790998i \(0.290438\pi\)
\(164\) −5.45398 3.96255i −0.425884 0.309423i
\(165\) 9.08087 + 1.88869i 0.706945 + 0.147034i
\(166\) −2.52848 + 1.83705i −0.196248 + 0.142583i
\(167\) 0.891847 2.74482i 0.0690132 0.212401i −0.910602 0.413285i \(-0.864381\pi\)
0.979615 + 0.200884i \(0.0643814\pi\)
\(168\) −8.60993 −0.664271
\(169\) 8.08500 24.8831i 0.621923 1.91408i
\(170\) −11.9926 13.2025i −0.919791 1.01258i
\(171\) 0.340356 + 1.04751i 0.0260277 + 0.0801050i
\(172\) 0.619303 + 1.90602i 0.0472214 + 0.145332i
\(173\) −2.02111 1.46842i −0.153662 0.111642i 0.508297 0.861182i \(-0.330275\pi\)
−0.661960 + 0.749539i \(0.730275\pi\)
\(174\) 1.06860 0.0810104
\(175\) −20.7530 + 4.60145i −1.56878 + 0.347837i
\(176\) −2.04820 −0.154389
\(177\) −18.6236 13.5309i −1.39984 1.01704i
\(178\) 0.842662 + 2.59345i 0.0631602 + 0.194387i
\(179\) 0.424524 + 1.30655i 0.0317304 + 0.0976562i 0.965667 0.259781i \(-0.0836505\pi\)
−0.933937 + 0.357438i \(0.883650\pi\)
\(180\) −1.22207 + 2.13825i −0.0910879 + 0.159376i
\(181\) 2.95629 9.09854i 0.219740 0.676289i −0.779043 0.626970i \(-0.784295\pi\)
0.998783 0.0493191i \(-0.0157051\pi\)
\(182\) −26.6057 −1.97214
\(183\) 3.89886 11.9995i 0.288212 0.887025i
\(184\) −7.35345 + 5.34259i −0.542104 + 0.393861i
\(185\) 9.64131 + 10.6140i 0.708844 + 0.780354i
\(186\) 0.846916 + 0.615321i 0.0620989 + 0.0451175i
\(187\) 13.2174 9.60297i 0.966549 0.702239i
\(188\) 2.74028 1.99093i 0.199855 0.145203i
\(189\) 13.2247 + 9.60834i 0.961958 + 0.698904i
\(190\) −1.50348 1.65516i −0.109074 0.120078i
\(191\) 13.6861 9.94354i 0.990292 0.719489i 0.0303070 0.999541i \(-0.490351\pi\)
0.959985 + 0.280051i \(0.0903515\pi\)
\(192\) 0.625820 1.92608i 0.0451646 0.139002i
\(193\) 13.9088 1.00118 0.500588 0.865686i \(-0.333117\pi\)
0.500588 + 0.865686i \(0.333117\pi\)
\(194\) 5.31877 16.3695i 0.381865 1.17526i
\(195\) −14.0622 + 24.6046i −1.00702 + 1.76197i
\(196\) 3.42220 + 10.5324i 0.244443 + 0.752317i
\(197\) 1.93044 + 5.94127i 0.137538 + 0.423298i 0.995976 0.0896189i \(-0.0285649\pi\)
−0.858438 + 0.512917i \(0.828565\pi\)
\(198\) −1.82507 1.32599i −0.129702 0.0942343i
\(199\) 13.5991 0.964015 0.482008 0.876167i \(-0.339908\pi\)
0.482008 + 0.876167i \(0.339908\pi\)
\(200\) 0.479090 4.97699i 0.0338767 0.351927i
\(201\) 4.12235 0.290768
\(202\) 10.5658 + 7.67650i 0.743407 + 0.540117i
\(203\) −0.693209 2.13348i −0.0486537 0.149741i
\(204\) 4.99189 + 15.3634i 0.349502 + 1.07566i
\(205\) 10.1357 + 11.1582i 0.707908 + 0.779324i
\(206\) 2.18293 6.71838i 0.152092 0.468091i
\(207\) −10.0112 −0.695824
\(208\) 1.93385 5.95179i 0.134089 0.412682i
\(209\) 1.65703 1.20390i 0.114619 0.0832755i
\(210\) 18.8490 + 3.92033i 1.30071 + 0.270528i
\(211\) −5.09035 3.69836i −0.350434 0.254605i 0.398617 0.917118i \(-0.369490\pi\)
−0.749051 + 0.662512i \(0.769490\pi\)
\(212\) 6.42495 4.66800i 0.441267 0.320599i
\(213\) 1.91941 1.39453i 0.131516 0.0955518i
\(214\) 2.34055 + 1.70051i 0.159996 + 0.116244i
\(215\) −0.487929 4.45467i −0.0332765 0.303806i
\(216\) −3.11067 + 2.26004i −0.211655 + 0.153776i
\(217\) 0.679096 2.09004i 0.0461000 0.141881i
\(218\) 2.13195 0.144394
\(219\) 8.77104 26.9945i 0.592692 1.82412i
\(220\) 4.48395 + 0.932597i 0.302308 + 0.0628757i
\(221\) 15.4255 + 47.4748i 1.03763 + 3.19350i
\(222\) −4.01317 12.3513i −0.269346 0.828963i
\(223\) −14.8405 10.7822i −0.993793 0.722033i −0.0330445 0.999454i \(-0.510520\pi\)
−0.960748 + 0.277421i \(0.910520\pi\)
\(224\) −4.25141 −0.284059
\(225\) 3.64898 4.12466i 0.243266 0.274977i
\(226\) 13.7310 0.913371
\(227\) −8.17792 5.94161i −0.542788 0.394358i 0.282332 0.959317i \(-0.408892\pi\)
−0.825119 + 0.564959i \(0.808892\pi\)
\(228\) 0.625820 + 1.92608i 0.0414459 + 0.127557i
\(229\) 0.529968 + 1.63107i 0.0350213 + 0.107784i 0.967039 0.254628i \(-0.0819531\pi\)
−0.932018 + 0.362413i \(0.881953\pi\)
\(230\) 18.5309 8.34789i 1.22189 0.550443i
\(231\) −5.44946 + 16.7717i −0.358548 + 1.10350i
\(232\) 0.527653 0.0346421
\(233\) 2.64497 8.14038i 0.173278 0.533294i −0.826273 0.563270i \(-0.809543\pi\)
0.999551 + 0.0299758i \(0.00954303\pi\)
\(234\) 5.57635 4.05146i 0.364538 0.264852i
\(235\) −6.90558 + 3.11085i −0.450471 + 0.202930i
\(236\) −9.19597 6.68126i −0.598606 0.434913i
\(237\) −3.27538 + 2.37970i −0.212759 + 0.154578i
\(238\) 27.4351 19.9327i 1.77835 1.29205i
\(239\) 4.99344 + 3.62794i 0.322999 + 0.234672i 0.737454 0.675397i \(-0.236028\pi\)
−0.414455 + 0.910070i \(0.636028\pi\)
\(240\) −2.24705 + 3.93165i −0.145046 + 0.253787i
\(241\) 2.87918 2.09184i 0.185464 0.134748i −0.491179 0.871059i \(-0.663434\pi\)
0.676643 + 0.736311i \(0.263434\pi\)
\(242\) 2.10283 6.47184i 0.135175 0.416025i
\(243\) −10.9267 −0.700948
\(244\) 1.92518 5.92508i 0.123247 0.379315i
\(245\) −2.69624 24.6160i −0.172257 1.57266i
\(246\) −4.21896 12.9846i −0.268991 0.827869i
\(247\) 1.93385 + 5.95179i 0.123048 + 0.378703i
\(248\) 0.418190 + 0.303833i 0.0265551 + 0.0192934i
\(249\) −6.32949 −0.401115
\(250\) −3.31499 + 10.6776i −0.209658 + 0.675310i
\(251\) −17.4245 −1.09982 −0.549912 0.835222i \(-0.685339\pi\)
−0.549912 + 0.835222i \(0.685339\pi\)
\(252\) −3.78828 2.75234i −0.238639 0.173381i
\(253\) 5.75291 + 17.7056i 0.361682 + 1.11314i
\(254\) 1.15904 + 3.56715i 0.0727245 + 0.223823i
\(255\) −3.93295 35.9069i −0.246291 2.24858i
\(256\) 0.309017 0.951057i 0.0193136 0.0594410i
\(257\) −27.2371 −1.69900 −0.849500 0.527588i \(-0.823096\pi\)
−0.849500 + 0.527588i \(0.823096\pi\)
\(258\) −1.25421 + 3.86006i −0.0780836 + 0.240317i
\(259\) −22.0561 + 16.0247i −1.37050 + 0.995726i
\(260\) −6.94364 + 12.1492i −0.430626 + 0.753464i
\(261\) 0.470173 + 0.341601i 0.0291030 + 0.0211445i
\(262\) −9.83212 + 7.14346i −0.607431 + 0.441324i
\(263\) −19.4428 + 14.1261i −1.19890 + 0.871050i −0.994176 0.107770i \(-0.965629\pi\)
−0.204722 + 0.978820i \(0.565629\pi\)
\(264\) −3.35580 2.43813i −0.206535 0.150057i
\(265\) −16.1911 + 7.29382i −0.994610 + 0.448056i
\(266\) 3.43946 2.49891i 0.210887 0.153218i
\(267\) −1.70655 + 5.25223i −0.104439 + 0.321432i
\(268\) 2.03553 0.124340
\(269\) 8.48802 26.1234i 0.517523 1.59277i −0.261120 0.965306i \(-0.584092\pi\)
0.778643 0.627467i \(-0.215908\pi\)
\(270\) 7.83900 3.53134i 0.477066 0.214911i
\(271\) 2.35945 + 7.26165i 0.143327 + 0.441114i 0.996792 0.0800356i \(-0.0255034\pi\)
−0.853465 + 0.521150i \(0.825503\pi\)
\(272\) 2.46489 + 7.58616i 0.149456 + 0.459978i
\(273\) −43.5912 31.6708i −2.63826 1.91681i
\(274\) −15.6796 −0.947242
\(275\) −9.39171 4.08332i −0.566341 0.246233i
\(276\) −18.4077 −1.10802
\(277\) 9.81599 + 7.13174i 0.589786 + 0.428505i 0.842239 0.539105i \(-0.181237\pi\)
−0.252453 + 0.967609i \(0.581237\pi\)
\(278\) −0.222332 0.684267i −0.0133346 0.0410396i
\(279\) 0.175934 + 0.541469i 0.0105329 + 0.0324169i
\(280\) 9.30726 + 1.93578i 0.556215 + 0.115685i
\(281\) 1.11285 3.42499i 0.0663868 0.204318i −0.912360 0.409388i \(-0.865742\pi\)
0.978747 + 0.205070i \(0.0657423\pi\)
\(282\) 6.85967 0.408488
\(283\) −2.99189 + 9.20809i −0.177849 + 0.547364i −0.999752 0.0222636i \(-0.992913\pi\)
0.821903 + 0.569628i \(0.192913\pi\)
\(284\) 0.947766 0.688592i 0.0562395 0.0408604i
\(285\) −0.493064 4.50155i −0.0292066 0.266649i
\(286\) −10.3698 7.53410i −0.613179 0.445501i
\(287\) −23.1871 + 16.8464i −1.36869 + 0.994412i
\(288\) 0.891064 0.647396i 0.0525064 0.0381482i
\(289\) −37.7208 27.4058i −2.21887 1.61210i
\(290\) −1.15515 0.240254i −0.0678327 0.0141082i
\(291\) 28.2003 20.4887i 1.65313 1.20107i
\(292\) 4.33096 13.3293i 0.253450 0.780040i
\(293\) 19.0672 1.11392 0.556959 0.830540i \(-0.311968\pi\)
0.556959 + 0.830540i \(0.311968\pi\)
\(294\) −6.93062 + 21.3303i −0.404202 + 1.24401i
\(295\) 17.0898 + 18.8139i 0.995008 + 1.09539i
\(296\) −1.98162 6.09880i −0.115179 0.354486i
\(297\) 2.43361 + 7.48988i 0.141212 + 0.434607i
\(298\) −6.77630 4.92327i −0.392540 0.285197i
\(299\) −56.8820 −3.28957
\(300\) 6.70946 7.58410i 0.387371 0.437868i
\(301\) 8.52027 0.491100
\(302\) 8.57587 + 6.23074i 0.493486 + 0.358539i
\(303\) 8.17324 + 25.1546i 0.469540 + 1.44510i
\(304\) 0.309017 + 0.951057i 0.0177233 + 0.0545468i
\(305\) −6.91248 + 12.0947i −0.395807 + 0.692542i
\(306\) −2.71487 + 8.35551i −0.155199 + 0.477653i
\(307\) −26.8892 −1.53465 −0.767324 0.641260i \(-0.778412\pi\)
−0.767324 + 0.641260i \(0.778412\pi\)
\(308\) −2.69083 + 8.28153i −0.153324 + 0.471884i
\(309\) 11.5740 8.40898i 0.658420 0.478370i
\(310\) −0.777166 0.855569i −0.0441401 0.0485931i
\(311\) 25.9908 + 18.8834i 1.47380 + 1.07078i 0.979489 + 0.201496i \(0.0645803\pi\)
0.494313 + 0.869284i \(0.335420\pi\)
\(312\) 10.2534 7.44950i 0.580482 0.421745i
\(313\) 4.19748 3.04965i 0.237256 0.172376i −0.462804 0.886461i \(-0.653157\pi\)
0.700060 + 0.714084i \(0.253157\pi\)
\(314\) 0.424512 + 0.308426i 0.0239566 + 0.0174055i
\(315\) 7.04015 + 7.75038i 0.396667 + 0.436685i
\(316\) −1.61732 + 1.17505i −0.0909812 + 0.0661017i
\(317\) 7.41829 22.8311i 0.416653 1.28232i −0.494112 0.869398i \(-0.664507\pi\)
0.910764 0.412927i \(-0.135493\pi\)
\(318\) 16.0834 0.901914
\(319\) 0.333966 1.02784i 0.0186985 0.0575481i
\(320\) −1.10955 + 1.94137i −0.0620255 + 0.108526i
\(321\) 1.81054 + 5.57228i 0.101055 + 0.311014i
\(322\) 11.9412 + 36.7513i 0.665458 + 2.04807i
\(323\) −6.45317 4.68850i −0.359064 0.260875i
\(324\) −11.0911 −0.616174
\(325\) 20.7330 23.4357i 1.15006 1.29998i
\(326\) 0.766925 0.0424760
\(327\) 3.49303 + 2.53783i 0.193165 + 0.140343i
\(328\) −2.08324 6.41154i −0.115027 0.354018i
\(329\) −4.44991 13.6954i −0.245332 0.755053i
\(330\) 6.23643 + 6.86559i 0.343304 + 0.377938i
\(331\) −9.61543 + 29.5933i −0.528512 + 1.62659i 0.228753 + 0.973484i \(0.426535\pi\)
−0.757265 + 0.653108i \(0.773465\pi\)
\(332\) −3.12537 −0.171527
\(333\) 2.18259 6.71732i 0.119605 0.368107i
\(334\) 2.33489 1.69639i 0.127759 0.0928226i
\(335\) −4.45623 0.926832i −0.243470 0.0506382i
\(336\) −6.96558 5.06079i −0.380004 0.276089i
\(337\) −21.9501 + 15.9477i −1.19570 + 0.868727i −0.993855 0.110691i \(-0.964694\pi\)
−0.201845 + 0.979418i \(0.564694\pi\)
\(338\) 21.1668 15.3786i 1.15132 0.836485i
\(339\) 22.4971 + 16.3451i 1.22187 + 0.887743i
\(340\) −1.94201 17.7301i −0.105320 0.961549i
\(341\) 0.856535 0.622309i 0.0463840 0.0336999i
\(342\) −0.340356 + 1.04751i −0.0184043 + 0.0566428i
\(343\) 17.3222 0.935312
\(344\) −0.619303 + 1.90602i −0.0333906 + 0.102766i
\(345\) 40.2986 + 8.38152i 2.16960 + 0.451246i
\(346\) −0.771996 2.37596i −0.0415028 0.127732i
\(347\) −0.874135 2.69031i −0.0469260 0.144423i 0.924848 0.380337i \(-0.124192\pi\)
−0.971774 + 0.235913i \(0.924192\pi\)
\(348\) 0.864517 + 0.628108i 0.0463430 + 0.0336701i
\(349\) −24.9032 −1.33304 −0.666519 0.745488i \(-0.732217\pi\)
−0.666519 + 0.745488i \(0.732217\pi\)
\(350\) −19.4942 8.47568i −1.04201 0.453044i
\(351\) −24.0624 −1.28435
\(352\) −1.65703 1.20390i −0.0883198 0.0641681i
\(353\) −2.33483 7.18586i −0.124270 0.382465i 0.869497 0.493938i \(-0.164443\pi\)
−0.993767 + 0.111473i \(0.964443\pi\)
\(354\) −7.11359 21.8934i −0.378083 1.16362i
\(355\) −2.38840 + 1.07594i −0.126763 + 0.0571047i
\(356\) −0.842662 + 2.59345i −0.0446610 + 0.137452i
\(357\) 68.6776 3.63480
\(358\) −0.424524 + 1.30655i −0.0224368 + 0.0690534i
\(359\) −18.3358 + 13.3217i −0.967724 + 0.703093i −0.954932 0.296825i \(-0.904072\pi\)
−0.0127926 + 0.999918i \(0.504072\pi\)
\(360\) −2.24551 + 1.01157i −0.118349 + 0.0533142i
\(361\) −0.809017 0.587785i −0.0425798 0.0309361i
\(362\) 7.73968 5.62321i 0.406789 0.295549i
\(363\) 11.1493 8.10041i 0.585184 0.425161i
\(364\) −21.5244 15.6384i −1.12819 0.819676i
\(365\) −15.5506 + 27.2088i −0.813956 + 1.42417i
\(366\) 10.2073 7.41607i 0.533546 0.387644i
\(367\) 4.13604 12.7294i 0.215900 0.664470i −0.783189 0.621784i \(-0.786408\pi\)
0.999089 0.0426867i \(-0.0135917\pi\)
\(368\) −9.08936 −0.473816
\(369\) 2.29451 7.06177i 0.119447 0.367621i
\(370\) 1.56126 + 14.2539i 0.0811659 + 0.741025i
\(371\) −10.4334 32.1108i −0.541676 1.66711i
\(372\) 0.323493 + 0.995610i 0.0167723 + 0.0516200i
\(373\) −3.26207 2.37003i −0.168904 0.122716i 0.500122 0.865955i \(-0.333288\pi\)
−0.669026 + 0.743239i \(0.733288\pi\)
\(374\) 16.3376 0.844795
\(375\) −18.1417 + 13.5482i −0.936834 + 0.699629i
\(376\) 3.38717 0.174680
\(377\) 2.67145 + 1.94093i 0.137587 + 0.0999627i
\(378\) 5.05140 + 15.5466i 0.259816 + 0.799632i
\(379\) −1.30323 4.01093i −0.0669425 0.206028i 0.911990 0.410213i \(-0.134546\pi\)
−0.978932 + 0.204185i \(0.934546\pi\)
\(380\) −0.243465 2.22277i −0.0124895 0.114026i
\(381\) −2.34728 + 7.22418i −0.120255 + 0.370106i
\(382\) 16.9170 0.865547
\(383\) −8.18364 + 25.1866i −0.418164 + 1.28698i 0.491225 + 0.871032i \(0.336549\pi\)
−0.909390 + 0.415945i \(0.863451\pi\)
\(384\) 1.63842 1.19038i 0.0836101 0.0607463i
\(385\) 9.66162 16.9049i 0.492402 0.861552i
\(386\) 11.2524 + 8.17537i 0.572734 + 0.416115i
\(387\) −1.78579 + 1.29745i −0.0907766 + 0.0659531i
\(388\) 13.9247 10.1169i 0.706920 0.513608i
\(389\) −1.36576 0.992286i −0.0692470 0.0503109i 0.552623 0.833431i \(-0.313627\pi\)
−0.621870 + 0.783120i \(0.713627\pi\)
\(390\) −25.8388 + 11.6400i −1.30840 + 0.589412i
\(391\) 58.6552 42.6155i 2.96632 2.15516i
\(392\) −3.42220 + 10.5324i −0.172847 + 0.531969i
\(393\) −24.6125 −1.24154
\(394\) −1.93044 + 5.94127i −0.0972539 + 0.299317i
\(395\) 4.07569 1.83603i 0.205070 0.0923808i
\(396\) −0.697116 2.14550i −0.0350314 0.107816i
\(397\) −5.29503 16.2964i −0.265750 0.817895i −0.991520 0.129957i \(-0.958516\pi\)
0.725770 0.687938i \(-0.241484\pi\)
\(398\) 11.0019 + 7.99336i 0.551476 + 0.400671i
\(399\) 8.60993 0.431036
\(400\) 3.31300 3.74487i 0.165650 0.187244i
\(401\) −18.7274 −0.935203 −0.467601 0.883939i \(-0.654882\pi\)
−0.467601 + 0.883939i \(0.654882\pi\)
\(402\) 3.33505 + 2.42306i 0.166337 + 0.120851i
\(403\) 0.999631 + 3.07655i 0.0497952 + 0.153254i
\(404\) 4.03578 + 12.4208i 0.200787 + 0.617960i
\(405\) 24.2809 + 5.05008i 1.20653 + 0.250941i
\(406\) 0.693209 2.13348i 0.0344034 0.105883i
\(407\) −13.1344 −0.651047
\(408\) −4.99189 + 15.3634i −0.247135 + 0.760604i
\(409\) −11.7482 + 8.53554i −0.580909 + 0.422055i −0.839052 0.544052i \(-0.816890\pi\)
0.258143 + 0.966107i \(0.416890\pi\)
\(410\) 1.64132 + 14.9848i 0.0810588 + 0.740047i
\(411\) −25.6898 18.6647i −1.26718 0.920663i
\(412\) 5.71499 4.15218i 0.281557 0.204563i
\(413\) −39.0958 + 28.4048i −1.92378 + 1.39771i
\(414\) −8.09920 5.88442i −0.398054 0.289203i
\(415\) 6.84212 + 1.42306i 0.335867 + 0.0698555i
\(416\) 5.06290 3.67841i 0.248229 0.180349i
\(417\) 0.450265 1.38577i 0.0220496 0.0678617i
\(418\) 2.04820 0.100181
\(419\) 2.92896 9.01442i 0.143089 0.440383i −0.853671 0.520812i \(-0.825629\pi\)
0.996760 + 0.0804292i \(0.0256291\pi\)
\(420\) 12.9449 + 14.2508i 0.631645 + 0.695367i
\(421\) 5.89159 + 18.1325i 0.287139 + 0.883722i 0.985749 + 0.168220i \(0.0538019\pi\)
−0.698611 + 0.715502i \(0.746198\pi\)
\(422\) −1.94434 5.98407i −0.0946490 0.291300i
\(423\) 3.01818 + 2.19284i 0.146749 + 0.106619i
\(424\) 7.94167 0.385682
\(425\) −3.82149 + 39.6993i −0.185369 + 1.92570i
\(426\) 2.37252 0.114949
\(427\) −21.4278 15.5682i −1.03697 0.753400i
\(428\) 0.894009 + 2.75148i 0.0432136 + 0.132998i
\(429\) −8.02162 24.6880i −0.387288 1.19195i
\(430\) 2.22365 3.89070i 0.107234 0.187626i
\(431\) −7.54663 + 23.2261i −0.363508 + 1.11876i 0.587402 + 0.809295i \(0.300151\pi\)
−0.950910 + 0.309468i \(0.899849\pi\)
\(432\) −3.84500 −0.184993
\(433\) −7.70086 + 23.7008i −0.370080 + 1.13899i 0.576659 + 0.816985i \(0.304356\pi\)
−0.946738 + 0.322003i \(0.895644\pi\)
\(434\) 1.77790 1.29172i 0.0853417 0.0620044i
\(435\) −1.60662 1.76870i −0.0770316 0.0848028i
\(436\) 1.72479 + 1.25313i 0.0826023 + 0.0600141i
\(437\) 7.35345 5.34259i 0.351763 0.255571i
\(438\) 22.9629 16.6835i 1.09721 0.797169i
\(439\) 30.6064 + 22.2369i 1.46076 + 1.06131i 0.983163 + 0.182730i \(0.0584935\pi\)
0.477601 + 0.878577i \(0.341506\pi\)
\(440\) 3.07942 + 3.39009i 0.146806 + 0.161616i
\(441\) −9.86806 + 7.16956i −0.469907 + 0.341408i
\(442\) −15.4255 + 47.4748i −0.733716 + 2.25815i
\(443\) 22.1461 1.05219 0.526096 0.850425i \(-0.323655\pi\)
0.526096 + 0.850425i \(0.323655\pi\)
\(444\) 4.01317 12.3513i 0.190457 0.586165i
\(445\) 3.02563 5.29393i 0.143429 0.250957i
\(446\) −5.66856 17.4460i −0.268414 0.826094i
\(447\) −5.24185 16.1327i −0.247931 0.763052i
\(448\) −3.43946 2.49891i −0.162499 0.118063i
\(449\) 33.1179 1.56293 0.781465 0.623949i \(-0.214473\pi\)
0.781465 + 0.623949i \(0.214473\pi\)
\(450\) 5.37650 1.19210i 0.253451 0.0561961i
\(451\) −13.8079 −0.650188
\(452\) 11.1086 + 8.07087i 0.522504 + 0.379622i
\(453\) 6.63391 + 20.4171i 0.311689 + 0.959279i
\(454\) −3.12369 9.61372i −0.146602 0.451194i
\(455\) 40.0011 + 44.0366i 1.87528 + 2.06447i
\(456\) −0.625820 + 1.92608i −0.0293067 + 0.0901967i
\(457\) −23.1121 −1.08114 −0.540569 0.841300i \(-0.681791\pi\)
−0.540569 + 0.841300i \(0.681791\pi\)
\(458\) −0.529968 + 1.63107i −0.0247638 + 0.0762151i
\(459\) 24.8125 18.0273i 1.15815 0.841443i
\(460\) 19.8986 + 4.13863i 0.927777 + 0.192964i
\(461\) 18.1891 + 13.2152i 0.847152 + 0.615492i 0.924359 0.381523i \(-0.124600\pi\)
−0.0772071 + 0.997015i \(0.524600\pi\)
\(462\) −14.2669 + 10.3655i −0.663755 + 0.482246i
\(463\) −12.6326 + 9.17810i −0.587085 + 0.426542i −0.841271 0.540613i \(-0.818192\pi\)
0.254186 + 0.967155i \(0.418192\pi\)
\(464\) 0.426881 + 0.310147i 0.0198174 + 0.0143982i
\(465\) −0.254870 2.32690i −0.0118193 0.107908i
\(466\) 6.92462 5.03103i 0.320777 0.233058i
\(467\) −8.51591 + 26.2093i −0.394069 + 1.21282i 0.535615 + 0.844462i \(0.320080\pi\)
−0.929684 + 0.368358i \(0.879920\pi\)
\(468\) 6.89275 0.318617
\(469\) 2.67420 8.23033i 0.123483 0.380041i
\(470\) −7.41525 1.54227i −0.342040 0.0711394i
\(471\) 0.328384 + 1.01066i 0.0151311 + 0.0465688i
\(472\) −3.51255 10.8105i −0.161678 0.497594i
\(473\) 3.32085 + 2.41274i 0.152693 + 0.110938i
\(474\) −4.04859 −0.185958
\(475\) −0.479090 + 4.97699i −0.0219821 + 0.228360i
\(476\) 33.9116 1.55434
\(477\) 7.07653 + 5.14140i 0.324012 + 0.235409i
\(478\) 1.90732 + 5.87014i 0.0872389 + 0.268494i
\(479\) 6.62148 + 20.3788i 0.302543 + 0.931132i 0.980583 + 0.196106i \(0.0628298\pi\)
−0.678040 + 0.735025i \(0.737170\pi\)
\(480\) −4.12886 + 1.85999i −0.188456 + 0.0848964i
\(481\) 12.4012 38.1668i 0.565444 1.74026i
\(482\) 3.55886 0.162102
\(483\) −24.1833 + 74.4285i −1.10038 + 3.38662i
\(484\) 5.50527 3.99982i 0.250240 0.181810i
\(485\) −35.0907 + 15.8078i −1.59339 + 0.717796i
\(486\) −8.83988 6.42255i −0.400985 0.291333i
\(487\) −19.7604 + 14.3567i −0.895428 + 0.650566i −0.937288 0.348557i \(-0.886672\pi\)
0.0418598 + 0.999123i \(0.486672\pi\)
\(488\) 5.04018 3.66190i 0.228158 0.165767i
\(489\) 1.25654 + 0.912932i 0.0568228 + 0.0412842i
\(490\) 12.2876 21.4996i 0.555099 0.971253i
\(491\) −4.87061 + 3.53870i −0.219807 + 0.159699i −0.692240 0.721667i \(-0.743376\pi\)
0.472433 + 0.881367i \(0.343376\pi\)
\(492\) 4.21896 12.9846i 0.190205 0.585392i
\(493\) −4.20886 −0.189557
\(494\) −1.93385 + 5.95179i −0.0870082 + 0.267784i
\(495\) 0.549236 + 5.01439i 0.0246863 + 0.225380i
\(496\) 0.159734 + 0.491612i 0.00717228 + 0.0220740i
\(497\) −1.53907 4.73677i −0.0690367 0.212473i
\(498\) −5.12066 3.72038i −0.229462 0.166714i
\(499\) 24.5265 1.09796 0.548980 0.835836i \(-0.315016\pi\)
0.548980 + 0.835836i \(0.315016\pi\)
\(500\) −8.95801 + 6.68985i −0.400614 + 0.299179i
\(501\) 5.84487 0.261130
\(502\) −14.0967 10.2419i −0.629167 0.457117i
\(503\) −10.2958 31.6871i −0.459065 1.41286i −0.866296 0.499532i \(-0.833505\pi\)
0.407230 0.913325i \(-0.366495\pi\)
\(504\) −1.44699 4.45338i −0.0644542 0.198370i
\(505\) −3.17966 29.0295i −0.141493 1.29180i
\(506\) −5.75291 + 17.7056i −0.255748 + 0.787111i
\(507\) 52.9864 2.35321
\(508\) −1.15904 + 3.56715i −0.0514240 + 0.158267i
\(509\) 29.3592 21.3307i 1.30132 0.945468i 0.301357 0.953511i \(-0.402560\pi\)
0.999968 + 0.00804351i \(0.00256036\pi\)
\(510\) 17.9237 31.3610i 0.793675 1.38869i
\(511\) −48.2050 35.0230i −2.13246 1.54933i
\(512\) 0.809017 0.587785i 0.0357538 0.0259767i
\(513\) 3.11067 2.26004i 0.137340 0.0997831i
\(514\) −22.0352 16.0095i −0.971933 0.706150i
\(515\) −14.4020 + 6.48785i −0.634626 + 0.285889i
\(516\) −3.28356 + 2.38565i −0.144551 + 0.105022i
\(517\) 2.14383 6.59803i 0.0942856 0.290181i
\(518\) −27.2628 −1.19786
\(519\) 1.56344 4.81178i 0.0686275 0.211214i
\(520\) −12.7587 + 5.74757i −0.559504 + 0.252048i
\(521\) 4.67375 + 14.3843i 0.204761 + 0.630189i 0.999723 + 0.0235301i \(0.00749057\pi\)
−0.794962 + 0.606659i \(0.792509\pi\)
\(522\) 0.179590 + 0.552721i 0.00786044 + 0.0241920i
\(523\) 8.14440 + 5.91725i 0.356130 + 0.258743i 0.751436 0.659806i \(-0.229362\pi\)
−0.395306 + 0.918549i \(0.629362\pi\)
\(524\) −12.1532 −0.530914
\(525\) −21.8504 37.0922i −0.953629 1.61884i
\(526\) −24.0327 −1.04787
\(527\) −3.33572 2.42354i −0.145306 0.105571i
\(528\) −1.28180 3.94498i −0.0557833 0.171683i
\(529\) 18.4225 + 56.6987i 0.800979 + 2.46516i
\(530\) −17.3861 3.61605i −0.755202 0.157071i
\(531\) 3.86877 11.9069i 0.167890 0.516714i
\(532\) 4.25141 0.184322
\(533\) 13.0371 40.1239i 0.564698 1.73796i
\(534\) −4.46782 + 3.24606i −0.193341 + 0.140471i
\(535\) −0.704362 6.43065i −0.0304522 0.278021i
\(536\) 1.64678 + 1.19646i 0.0711301 + 0.0516791i
\(537\) −2.25084 + 1.63533i −0.0971309 + 0.0705697i
\(538\) 22.2219 16.1452i 0.958055 0.696067i
\(539\) 18.3507 + 13.3325i 0.790419 + 0.574273i
\(540\) 8.41755 + 1.75073i 0.362234 + 0.0753395i
\(541\) 1.17321 0.852384i 0.0504401 0.0366468i −0.562280 0.826947i \(-0.690076\pi\)
0.612720 + 0.790300i \(0.290076\pi\)
\(542\) −2.35945 + 7.26165i −0.101347 + 0.311915i
\(543\) 19.3746 0.831443
\(544\) −2.46489 + 7.58616i −0.105681 + 0.325254i
\(545\) −3.20535 3.52872i −0.137302 0.151154i
\(546\) −16.6503 51.2445i −0.712569 2.19306i
\(547\) −6.05832 18.6456i −0.259035 0.797227i −0.993008 0.118049i \(-0.962336\pi\)
0.733973 0.679179i \(-0.237664\pi\)
\(548\) −12.6851 9.21626i −0.541880 0.393699i
\(549\) 6.86182 0.292855
\(550\) −5.19794 8.82378i −0.221641 0.376247i
\(551\) −0.527653 −0.0224788
\(552\) −14.8922 10.8198i −0.633853 0.460521i
\(553\) 2.62635 + 8.08307i 0.111684 + 0.343727i
\(554\) 3.74938 + 11.5394i 0.159296 + 0.490262i
\(555\) −14.4096 + 25.2123i −0.611652 + 1.07020i
\(556\) 0.222332 0.684267i 0.00942897 0.0290194i
\(557\) 39.1478 1.65875 0.829373 0.558695i \(-0.188698\pi\)
0.829373 + 0.558695i \(0.188698\pi\)
\(558\) −0.175934 + 0.541469i −0.00744788 + 0.0229222i
\(559\) −10.1466 + 7.37192i −0.429154 + 0.311799i
\(560\) 6.39191 + 7.03675i 0.270108 + 0.297357i
\(561\) 26.7677 + 19.4479i 1.13013 + 0.821091i
\(562\) 2.91347 2.11676i 0.122897 0.0892901i
\(563\) −3.73310 + 2.71226i −0.157332 + 0.114308i −0.663666 0.748029i \(-0.731000\pi\)
0.506334 + 0.862337i \(0.331000\pi\)
\(564\) 5.54959 + 4.03201i 0.233680 + 0.169778i
\(565\) −20.6443 22.7269i −0.868511 0.956129i
\(566\) −7.83287 + 5.69091i −0.329240 + 0.239207i
\(567\) −14.5711 + 44.8451i −0.611927 + 1.88332i
\(568\) 1.17150 0.0491552
\(569\) −5.40168 + 16.6247i −0.226450 + 0.696942i 0.771691 + 0.635998i \(0.219411\pi\)
−0.998141 + 0.0609442i \(0.980589\pi\)
\(570\) 2.24705 3.93165i 0.0941185 0.164679i
\(571\) −6.93749 21.3514i −0.290325 0.893528i −0.984752 0.173965i \(-0.944342\pi\)
0.694427 0.719563i \(-0.255658\pi\)
\(572\) −3.96091 12.1904i −0.165614 0.509708i
\(573\) 27.7170 + 20.1376i 1.15790 + 0.841261i
\(574\) −28.6608 −1.19628
\(575\) −41.6780 18.1207i −1.73809 0.755686i
\(576\) 1.10142 0.0458923
\(577\) −22.1122 16.0655i −0.920545 0.668815i 0.0231147 0.999733i \(-0.492642\pi\)
−0.943660 + 0.330918i \(0.892642\pi\)
\(578\) −14.4081 44.3435i −0.599296 1.84444i
\(579\) 8.70438 + 26.7893i 0.361742 + 1.11333i
\(580\) −0.793317 0.873349i −0.0329407 0.0362639i
\(581\) −4.10598 + 12.6369i −0.170345 + 0.524267i
\(582\) 34.8574 1.44489
\(583\) 5.02650 15.4700i 0.208176 0.640701i
\(584\) 11.3386 8.23798i 0.469195 0.340890i
\(585\) −15.0897 3.13845i −0.623884 0.129759i
\(586\) 15.4257 + 11.2074i 0.637230 + 0.462975i
\(587\) 0.595380 0.432569i 0.0245740 0.0178540i −0.575430 0.817851i \(-0.695165\pi\)
0.600004 + 0.799997i \(0.295165\pi\)
\(588\) −18.1446 + 13.1828i −0.748271 + 0.543650i
\(589\) −0.418190 0.303833i −0.0172312 0.0125192i
\(590\) 2.76743 + 25.2659i 0.113933 + 1.04018i
\(591\) −10.2352 + 7.43633i −0.421021 + 0.305890i
\(592\) 1.98162 6.09880i 0.0814441 0.250659i
\(593\) 18.7978 0.771934 0.385967 0.922513i \(-0.373868\pi\)
0.385967 + 0.922513i \(0.373868\pi\)
\(594\) −2.43361 + 7.48988i −0.0998522 + 0.307313i
\(595\) −74.2399 15.4408i −3.04354 0.633013i
\(596\) −2.58832 7.96602i −0.106022 0.326301i
\(597\) 8.51059 + 26.1929i 0.348315 + 1.07200i
\(598\) −46.0185 33.4344i −1.88184 1.36723i
\(599\) 35.3473 1.44425 0.722125 0.691763i \(-0.243166\pi\)
0.722125 + 0.691763i \(0.243166\pi\)
\(600\) 9.88589 2.19194i 0.403590 0.0894855i
\(601\) 21.0604 0.859072 0.429536 0.903050i \(-0.358677\pi\)
0.429536 + 0.903050i \(0.358677\pi\)
\(602\) 6.89304 + 5.00809i 0.280939 + 0.204114i
\(603\) 0.692806 + 2.13224i 0.0282133 + 0.0868315i
\(604\) 3.27569 + 10.0815i 0.133286 + 0.410212i
\(605\) −13.8735 + 6.24978i −0.564037 + 0.254089i
\(606\) −8.17324 + 25.1546i −0.332015 + 1.02184i
\(607\) 22.6110 0.917751 0.458876 0.888500i \(-0.348252\pi\)
0.458876 + 0.888500i \(0.348252\pi\)
\(608\) −0.309017 + 0.951057i −0.0125323 + 0.0385704i
\(609\) 3.67541 2.67034i 0.148935 0.108208i
\(610\) −12.7014 + 5.72178i −0.514265 + 0.231668i
\(611\) 17.1489 + 12.4594i 0.693769 + 0.504053i
\(612\) −7.10762 + 5.16399i −0.287309 + 0.208742i
\(613\) 22.9168 16.6500i 0.925601 0.672489i −0.0193108 0.999814i \(-0.506147\pi\)
0.944912 + 0.327325i \(0.106147\pi\)
\(614\) −21.7538 15.8051i −0.877913 0.637841i
\(615\) −15.1485 + 26.5052i −0.610845 + 1.06879i
\(616\) −7.04469 + 5.11827i −0.283839 + 0.206221i
\(617\) −3.04098 + 9.35917i −0.122425 + 0.376786i −0.993423 0.114501i \(-0.963473\pi\)
0.870998 + 0.491287i \(0.163473\pi\)
\(618\) 14.3062 0.575481
\(619\) −4.03812 + 12.4281i −0.162306 + 0.499526i −0.998828 0.0484076i \(-0.984585\pi\)
0.836522 + 0.547934i \(0.184585\pi\)
\(620\) −0.125850 1.14898i −0.00505425 0.0461440i
\(621\) 10.7997 + 33.2381i 0.433378 + 1.33380i
\(622\) 9.92760 + 30.5540i 0.398060 + 1.22510i
\(623\) 9.37910 + 6.81432i 0.375766 + 0.273010i
\(624\) 12.6738 0.507360
\(625\) 22.6571 10.5667i 0.906284 0.422669i
\(626\) 5.18837 0.207369
\(627\) 3.35580 + 2.43813i 0.134018 + 0.0973696i
\(628\) 0.162149 + 0.499044i 0.00647046 + 0.0199140i
\(629\) 15.8065 + 48.6475i 0.630247 + 1.93970i
\(630\) 1.14004 + 10.4083i 0.0454203 + 0.414676i
\(631\) 4.75318 14.6288i 0.189221 0.582363i −0.810774 0.585359i \(-0.800954\pi\)
0.999996 + 0.00299591i \(0.000953630\pi\)
\(632\) −1.99911 −0.0795204
\(633\) 3.93767 12.1189i 0.156508 0.481683i
\(634\) 19.4213 14.1104i 0.771320 0.560397i
\(635\) 4.16160 7.28153i 0.165148 0.288959i
\(636\) 13.0118 + 9.45360i 0.515950 + 0.374860i
\(637\) −56.0689 + 40.7364i −2.22153 + 1.61404i
\(638\) 0.874335 0.635242i 0.0346153 0.0251495i
\(639\) 1.04388 + 0.758426i 0.0412954 + 0.0300029i
\(640\) −2.03875 + 0.918424i −0.0805886 + 0.0363039i
\(641\) −0.836583 + 0.607813i −0.0330431 + 0.0240072i −0.604184 0.796845i \(-0.706501\pi\)
0.571141 + 0.820852i \(0.306501\pi\)
\(642\) −1.81054 + 5.57228i −0.0714564 + 0.219920i
\(643\) 5.92156 0.233523 0.116762 0.993160i \(-0.462749\pi\)
0.116762 + 0.993160i \(0.462749\pi\)
\(644\) −11.9412 + 36.7513i −0.470550 + 1.44820i
\(645\) 8.27468 3.72761i 0.325815 0.146775i
\(646\) −2.46489 7.58616i −0.0969799 0.298473i
\(647\) 6.89415 + 21.2180i 0.271037 + 0.834166i 0.990241 + 0.139367i \(0.0445068\pi\)
−0.719204 + 0.694799i \(0.755493\pi\)
\(648\) −8.97291 6.51920i −0.352489 0.256098i
\(649\) −23.2815 −0.913880
\(650\) 30.5485 6.77334i 1.19821 0.265672i
\(651\) 4.45057 0.174432
\(652\) 0.620455 + 0.450787i 0.0242989 + 0.0176542i
\(653\) −11.5665 35.5982i −0.452634 1.39306i −0.873891 0.486123i \(-0.838411\pi\)
0.421257 0.906941i \(-0.361589\pi\)
\(654\) 1.33422 + 4.10630i 0.0521721 + 0.160569i
\(655\) 26.6060 + 5.53366i 1.03958 + 0.216218i
\(656\) 2.08324 6.41154i 0.0813367 0.250329i
\(657\) 15.4367 0.602241
\(658\) 4.44991 13.6954i 0.173476 0.533903i
\(659\) −1.89192 + 1.37456i −0.0736986 + 0.0535452i −0.624025 0.781405i \(-0.714503\pi\)
0.550326 + 0.834950i \(0.314503\pi\)
\(660\) 1.00989 + 9.22006i 0.0393100 + 0.358890i
\(661\) 2.54168 + 1.84664i 0.0988597 + 0.0718258i 0.636117 0.771593i \(-0.280540\pi\)
−0.537257 + 0.843418i \(0.680540\pi\)
\(662\) −25.1735 + 18.2896i −0.978397 + 0.710847i
\(663\) −81.7865 + 59.4213i −3.17632 + 2.30773i
\(664\) −2.52848 1.83705i −0.0981240 0.0712913i
\(665\) −9.30726 1.93578i −0.360920 0.0750662i
\(666\) 5.71409 4.15153i 0.221417 0.160869i
\(667\) 1.48206 4.56130i 0.0573854 0.176614i
\(668\) 2.88608 0.111666
\(669\) 11.4799 35.3316i 0.443840 1.36600i
\(670\) −3.06039 3.36913i −0.118233 0.130161i
\(671\) −3.94314 12.1357i −0.152223 0.468495i
\(672\) −2.66061 8.18853i −0.102635 0.315879i
\(673\) −18.0811 13.1367i −0.696976 0.506383i 0.181970 0.983304i \(-0.441753\pi\)
−0.878946 + 0.476921i \(0.841753\pi\)
\(674\) −27.1318 −1.04508
\(675\) −17.6307 7.66547i −0.678606 0.295044i
\(676\) 26.1636 1.00629
\(677\) −19.3170 14.0347i −0.742414 0.539396i 0.151052 0.988526i \(-0.451734\pi\)
−0.893466 + 0.449130i \(0.851734\pi\)
\(678\) 8.59312 + 26.4469i 0.330017 + 1.01569i
\(679\) −22.6123 69.5934i −0.867779 2.67075i
\(680\) 8.85036 15.4854i 0.339396 0.593839i
\(681\) 6.32608 19.4697i 0.242416 0.746079i
\(682\) 1.05874 0.0405411
\(683\) −7.95351 + 24.4784i −0.304333 + 0.936640i 0.675593 + 0.737275i \(0.263888\pi\)
−0.979925 + 0.199365i \(0.936112\pi\)
\(684\) −0.891064 + 0.647396i −0.0340707 + 0.0247538i
\(685\) 23.5740 + 25.9523i 0.900718 + 0.991585i
\(686\) 14.0140 + 10.1817i 0.535056 + 0.388741i
\(687\) −2.80991 + 2.04152i −0.107205 + 0.0778887i
\(688\) −1.62136 + 1.17798i −0.0618136 + 0.0449102i
\(689\) 40.2078 + 29.2127i 1.53180 + 1.11292i
\(690\) 27.6757 + 30.4677i 1.05360 + 1.15989i
\(691\) −18.2696 + 13.2736i −0.695008 + 0.504953i −0.878303 0.478105i \(-0.841324\pi\)
0.183295 + 0.983058i \(0.441324\pi\)
\(692\) 0.771996 2.37596i 0.0293469 0.0903205i
\(693\) −9.59081 −0.364325
\(694\) 0.874135 2.69031i 0.0331817 0.102123i
\(695\) −0.798298 + 1.39678i −0.0302812 + 0.0529828i
\(696\) 0.330216 + 1.01630i 0.0125168 + 0.0385228i
\(697\) 16.6170 + 51.1420i 0.629415 + 1.93714i
\(698\) −20.1471 14.6377i −0.762580 0.554047i
\(699\) 17.3343 0.655642
\(700\) −10.7893 18.3154i −0.407796 0.692256i
\(701\) −32.1051 −1.21259 −0.606297 0.795239i \(-0.707346\pi\)
−0.606297 + 0.795239i \(0.707346\pi\)
\(702\) −19.4669 14.1435i −0.734729 0.533812i
\(703\) 1.98162 + 6.09880i 0.0747383 + 0.230021i
\(704\) −0.632927 1.94795i −0.0238543 0.0734161i
\(705\) −10.3134 11.3538i −0.388425 0.427610i
\(706\) 2.33483 7.18586i 0.0878724 0.270444i
\(707\) 55.5236 2.08818
\(708\) 7.11359 21.8934i 0.267345 0.822804i
\(709\) −21.6702 + 15.7443i −0.813842 + 0.591291i −0.914942 0.403585i \(-0.867764\pi\)
0.101100 + 0.994876i \(0.467764\pi\)
\(710\) −2.56468 0.533416i −0.0962505 0.0200187i
\(711\) −1.78134 1.29422i −0.0668054 0.0485369i
\(712\) −2.20612 + 1.60284i −0.0826777 + 0.0600689i
\(713\) 3.80108 2.76165i 0.142352 0.103424i
\(714\) 55.5613 + 40.3677i 2.07933 + 1.51072i
\(715\) 3.12068 + 28.4910i 0.116707 + 1.06550i
\(716\) −1.11142 + 0.807493i −0.0415357 + 0.0301774i
\(717\) −3.86270 + 11.8882i −0.144255 + 0.443972i
\(718\) −22.6642 −0.845822
\(719\) 9.96146 30.6582i 0.371500 1.14336i −0.574310 0.818638i \(-0.694730\pi\)
0.945810 0.324721i \(-0.105270\pi\)
\(720\) −2.41124 0.501503i −0.0898616 0.0186899i
\(721\) −9.28054 28.5626i −0.345625 1.06373i
\(722\) −0.309017 0.951057i −0.0115004 0.0353947i
\(723\) 5.83090 + 4.23639i 0.216853 + 0.157553i
\(724\) 9.56677 0.355546
\(725\) 1.33909 + 2.27317i 0.0497324 + 0.0844234i
\(726\) 13.7812 0.511470
\(727\) 20.3061 + 14.7533i 0.753113 + 0.547169i 0.896790 0.442456i \(-0.145893\pi\)
−0.143677 + 0.989625i \(0.545893\pi\)
\(728\) −8.22160 25.3035i −0.304713 0.937810i
\(729\) 3.44390 + 10.5992i 0.127552 + 0.392565i
\(730\) −28.5736 + 12.8720i −1.05756 + 0.476413i
\(731\) 4.93990 15.2035i 0.182709 0.562320i
\(732\) 12.6170 0.466337
\(733\) −12.7385 + 39.2051i −0.470508 + 1.44807i 0.381413 + 0.924405i \(0.375437\pi\)
−0.851921 + 0.523670i \(0.824563\pi\)
\(734\) 10.8283 7.86721i 0.399680 0.290384i
\(735\) 45.7250 20.5984i 1.68659 0.759782i
\(736\) −7.35345 5.34259i −0.271052 0.196931i
\(737\) 3.37293 2.45058i 0.124244 0.0902682i
\(738\) 6.00710 4.36441i 0.221124 0.160656i
\(739\) 32.1474 + 23.3565i 1.18256 + 0.859182i 0.992458 0.122582i \(-0.0391173\pi\)
0.190105 + 0.981764i \(0.439117\pi\)
\(740\) −7.11515 + 12.4493i −0.261558 + 0.457646i
\(741\) −10.2534 + 7.44950i −0.376666 + 0.273664i
\(742\) 10.4334 32.1108i 0.383023 1.17882i
\(743\) 0.225801 0.00828385 0.00414193 0.999991i \(-0.498682\pi\)
0.00414193 + 0.999991i \(0.498682\pi\)
\(744\) −0.323493 + 0.995610i −0.0118598 + 0.0365008i
\(745\) 2.03925 + 18.6179i 0.0747125 + 0.682106i
\(746\) −1.24600 3.83479i −0.0456193 0.140402i
\(747\) −1.06374 3.27385i −0.0389202 0.119784i
\(748\) 13.2174 + 9.60297i 0.483275 + 0.351119i
\(749\) 12.2996 0.449419
\(750\) −22.6404 + 0.297329i −0.826711 + 0.0108569i
\(751\) −48.7573 −1.77918 −0.889589 0.456761i \(-0.849009\pi\)
−0.889589 + 0.456761i \(0.849009\pi\)
\(752\) 2.74028 + 1.99093i 0.0999276 + 0.0726016i
\(753\) −10.9046 33.5609i −0.397385 1.22303i
\(754\) 1.02040 + 3.14048i 0.0371610 + 0.114370i
\(755\) −2.58081 23.5622i −0.0939255 0.857517i
\(756\) −5.05140 + 15.5466i −0.183718 + 0.565425i
\(757\) −37.3824 −1.35869 −0.679343 0.733821i \(-0.737735\pi\)
−0.679343 + 0.733821i \(0.737735\pi\)
\(758\) 1.30323 4.01093i 0.0473355 0.145684i
\(759\) −30.5021 + 22.1611i −1.10716 + 0.804396i
\(760\) 1.10955 1.94137i 0.0402475 0.0704208i
\(761\) 21.0643 + 15.3041i 0.763580 + 0.554773i 0.900006 0.435877i \(-0.143562\pi\)
−0.136426 + 0.990650i \(0.543562\pi\)
\(762\) −6.14525 + 4.46479i −0.222619 + 0.161742i
\(763\) 7.33277 5.32757i 0.265464 0.192871i
\(764\) 13.6861 + 9.94354i 0.495146 + 0.359745i
\(765\) 17.9114 8.06882i 0.647589 0.291729i
\(766\) −21.4250 + 15.5662i −0.774118 + 0.562430i
\(767\) 21.9818 67.6531i 0.793717 2.44281i
\(768\) 2.02520 0.0730779
\(769\) 10.5539 32.4816i 0.380584 1.17132i −0.559050 0.829134i \(-0.688834\pi\)
0.939633 0.342183i \(-0.111166\pi\)
\(770\) 17.7528 7.99737i 0.639768 0.288205i
\(771\) −17.0455 52.4606i −0.613878 1.88932i
\(772\) 4.29805 + 13.2280i 0.154690 + 0.476087i
\(773\) 31.9779 + 23.2333i 1.15016 + 0.835643i 0.988503 0.151203i \(-0.0483148\pi\)
0.161661 + 0.986846i \(0.448315\pi\)
\(774\) −2.20735 −0.0793417
\(775\) −0.247647 + 2.57266i −0.00889574 + 0.0924128i
\(776\) 17.2119 0.617871
\(777\) −44.6679 32.4531i −1.60245 1.16425i
\(778\) −0.521676 1.60555i −0.0187030 0.0575618i
\(779\) 2.08324 + 6.41154i 0.0746396 + 0.229717i
\(780\) −27.7458 5.77073i −0.993459 0.206625i
\(781\) 0.741476 2.28203i 0.0265321 0.0816574i
\(782\) 72.5018 2.59266
\(783\) 0.626943 1.92953i 0.0224051 0.0689558i
\(784\) −8.95943 + 6.50941i −0.319980 + 0.232479i
\(785\) −0.127752 1.16635i −0.00455967 0.0416287i
\(786\) −19.9120 14.4669i −0.710236 0.516017i
\(787\) 26.8935 19.5393i 0.958649 0.696499i 0.00581237 0.999983i \(-0.498150\pi\)
0.952837 + 0.303484i \(0.0981499\pi\)
\(788\) −5.05395 + 3.67191i −0.180039 + 0.130806i
\(789\) −39.3756 28.6080i −1.40181 1.01847i
\(790\) 4.37650 + 0.910249i 0.155709 + 0.0323852i
\(791\) 47.2272 34.3125i 1.67920 1.22001i
\(792\) 0.697116 2.14550i 0.0247709 0.0762371i
\(793\) 38.9879 1.38450
\(794\) 5.29503 16.2964i 0.187914 0.578339i
\(795\) −24.1811 26.6206i −0.857616 0.944135i
\(796\) 4.20236 + 12.9335i 0.148949 + 0.458417i
\(797\) −6.81817 20.9842i −0.241512 0.743298i −0.996191 0.0872029i \(-0.972207\pi\)
0.754678 0.656095i \(-0.227793\pi\)
\(798\) 6.96558 + 5.06079i 0.246579 + 0.179150i
\(799\) −27.0179 −0.955826
\(800\) 4.88145 1.08233i 0.172585 0.0382663i
\(801\) −3.00346 −0.106122
\(802\) −15.1508 11.0077i −0.534994 0.388696i
\(803\) −8.87066 27.3011i −0.313039 0.963434i
\(804\) 1.27388 + 3.92059i 0.0449262 + 0.138269i
\(805\) 42.8758 75.0195i 1.51117 2.64409i
\(806\) −0.999631 + 3.07655i −0.0352105 + 0.108367i
\(807\) 55.6276 1.95819
\(808\) −4.03578 + 12.4208i −0.141978 + 0.436964i
\(809\) 8.02341 5.82935i 0.282088 0.204949i −0.437740 0.899102i \(-0.644221\pi\)
0.719828 + 0.694153i \(0.244221\pi\)
\(810\) 16.6753 + 18.3576i 0.585910 + 0.645019i
\(811\) −43.3992 31.5314i −1.52395 1.10722i −0.959485 0.281760i \(-0.909082\pi\)
−0.564467 0.825456i \(-0.690918\pi\)
\(812\) 1.81484 1.31856i 0.0636885 0.0462724i
\(813\) −12.5099 + 9.08897i −0.438741 + 0.318764i
\(814\) −10.6259 7.72020i −0.372439 0.270593i
\(815\) −1.15306 1.26938i −0.0403898 0.0444645i
\(816\) −13.0689 + 9.49513i −0.457504 + 0.332396i
\(817\) 0.619303 1.90602i 0.0216667 0.0666831i
\(818\) −14.5215 −0.507733
\(819\) 9.05540 27.8697i 0.316421 0.973845i
\(820\) −7.48000 + 13.0877i −0.261213 + 0.457043i
\(821\) 15.8069 + 48.6485i 0.551664 + 1.69785i 0.704596 + 0.709609i \(0.251128\pi\)
−0.152932 + 0.988237i \(0.548872\pi\)
\(822\) −9.81263 30.2002i −0.342255 1.05335i
\(823\) 5.31704 + 3.86306i 0.185340 + 0.134658i 0.676587 0.736363i \(-0.263458\pi\)
−0.491246 + 0.871021i \(0.663458\pi\)
\(824\) 7.06412 0.246090
\(825\) 1.98726 20.6446i 0.0691876 0.718751i
\(826\) −48.3251 −1.68144
\(827\) 14.1207 + 10.2593i 0.491024 + 0.356750i 0.805578 0.592490i \(-0.201855\pi\)
−0.314554 + 0.949240i \(0.601855\pi\)
\(828\) −3.09362 9.52118i −0.107511 0.330884i
\(829\) −0.563900 1.73550i −0.0195850 0.0602766i 0.940786 0.339000i \(-0.110089\pi\)
−0.960371 + 0.278724i \(0.910089\pi\)
\(830\) 4.69894 + 5.17298i 0.163103 + 0.179557i
\(831\) −7.59322 + 23.3695i −0.263406 + 0.810680i
\(832\) 6.25808 0.216960
\(833\) 27.2974 84.0126i 0.945797 2.91087i
\(834\) 1.17881 0.856456i 0.0408188 0.0296566i
\(835\) −6.31826 1.31411i −0.218652 0.0454766i
\(836\) 1.65703 + 1.20390i 0.0573094 + 0.0416377i
\(837\) 1.60794 1.16824i 0.0555786 0.0403802i
\(838\) 7.66812 5.57122i 0.264891 0.192455i
\(839\) 1.32103 + 0.959786i 0.0456071 + 0.0331355i 0.610355 0.792128i \(-0.291027\pi\)
−0.564748 + 0.825263i \(0.691027\pi\)
\(840\) 2.09622 + 19.1379i 0.0723263 + 0.660321i
\(841\) 23.2362 16.8821i 0.801250 0.582142i
\(842\) −5.89159 + 18.1325i −0.203038 + 0.624886i
\(843\) 7.29322 0.251192
\(844\) 1.94434 5.98407i 0.0669270 0.205980i
\(845\) −57.2779 11.9130i −1.97042 0.409819i
\(846\) 1.15284 + 3.54809i 0.0396355 + 0.121986i
\(847\) −8.93998 27.5144i −0.307181 0.945407i
\(848\) 6.42495 + 4.66800i 0.220634 + 0.160300i
\(849\) −19.6079 −0.672940
\(850\) −26.4263 + 29.8712i −0.906415 + 1.02457i
\(851\) −58.2870 −1.99805
\(852\) 1.91941 + 1.39453i 0.0657579 + 0.0477759i
\(853\) 13.8220 + 42.5398i 0.473257 + 1.45654i 0.848294 + 0.529526i \(0.177630\pi\)
−0.375036 + 0.927010i \(0.622370\pi\)
\(854\) −8.18471 25.1899i −0.280075 0.861982i
\(855\) 2.24551 1.01157i 0.0767948 0.0345948i
\(856\) −0.894009 + 2.75148i −0.0305566 + 0.0940436i
\(857\) 39.7755 1.35871 0.679353 0.733812i \(-0.262261\pi\)
0.679353 + 0.733812i \(0.262261\pi\)
\(858\) 8.02162 24.6880i 0.273854 0.842835i
\(859\) −4.37594 + 3.17931i −0.149305 + 0.108476i −0.659930 0.751327i \(-0.729414\pi\)
0.510625 + 0.859804i \(0.329414\pi\)
\(860\) 4.08587 1.84062i 0.139327 0.0627646i
\(861\) −46.9584 34.1173i −1.60034 1.16271i
\(862\) −19.7573 + 14.3545i −0.672937 + 0.488917i
\(863\) 47.4499 34.4744i 1.61521 1.17352i 0.772912 0.634513i \(-0.218799\pi\)
0.842301 0.539008i \(-0.181201\pi\)
\(864\) −3.11067 2.26004i −0.105827 0.0768880i
\(865\) −2.77191 + 4.84999i −0.0942476 + 0.164904i
\(866\) −20.1611 + 14.6479i −0.685103 + 0.497756i
\(867\) 29.1791 89.8042i 0.990975 3.04991i
\(868\) 2.19760 0.0745914
\(869\) −1.26529 + 3.89417i −0.0429221 + 0.132101i
\(870\) −0.260167 2.37526i −0.00882048 0.0805288i
\(871\) 3.93643 + 12.1151i 0.133381 + 0.410504i
\(872\) 0.658810 + 2.02761i 0.0223101 + 0.0686635i
\(873\) 15.3369 + 11.1429i 0.519075 + 0.377130i
\(874\) 9.08936 0.307452
\(875\) 15.2806 + 45.0090i 0.516579 + 1.52158i
\(876\) 28.3837 0.958996
\(877\) 3.90835 + 2.83958i 0.131976 + 0.0958859i 0.651815 0.758378i \(-0.274008\pi\)
−0.519839 + 0.854264i \(0.674008\pi\)
\(878\) 11.6906 + 35.9800i 0.394539 + 1.21427i
\(879\) 11.9326 + 36.7249i 0.402478 + 1.23870i
\(880\) 0.498664 + 4.55268i 0.0168099 + 0.153471i
\(881\) −0.626401 + 1.92786i −0.0211040 + 0.0649514i −0.961054 0.276361i \(-0.910871\pi\)
0.939950 + 0.341312i \(0.110871\pi\)
\(882\) −12.1976 −0.410714
\(883\) 7.92440 24.3888i 0.266677 0.820749i −0.724625 0.689144i \(-0.757987\pi\)
0.991302 0.131605i \(-0.0420131\pi\)
\(884\) −40.3845 + 29.3410i −1.35828 + 0.986846i
\(885\) −25.5418 + 44.6904i −0.858580 + 1.50225i
\(886\) 17.9165 + 13.0171i 0.601918 + 0.437319i
\(887\) 43.9199 31.9097i 1.47469 1.07142i 0.495465 0.868628i \(-0.334998\pi\)
0.979221 0.202795i \(-0.0650024\pi\)
\(888\) 10.5066 7.63350i 0.352579 0.256164i
\(889\) 12.9005 + 9.37274i 0.432668 + 0.314352i
\(890\) 5.55949 2.50446i 0.186354 0.0839497i
\(891\) −18.3783 + 13.3526i −0.615696 + 0.447329i
\(892\) 5.66856 17.4460i 0.189798 0.584137i
\(893\) −3.38717 −0.113347
\(894\) 5.24185 16.1327i 0.175314 0.539560i
\(895\) 2.80081 1.26172i 0.0936208 0.0421747i
\(896\) −1.31376 4.04333i −0.0438895 0.135078i
\(897\) −35.5979 109.559i −1.18858 3.65807i
\(898\) 26.7929 + 19.4662i 0.894092 + 0.649596i
\(899\) −0.272750 −0.00909672
\(900\) 5.05038 + 2.19580i 0.168346 + 0.0731934i
\(901\) −63.3472 −2.11040
\(902\) −11.1708 8.11608i −0.371948 0.270236i
\(903\) 5.33215 + 16.4107i 0.177443 + 0.546113i
\(904\) 4.24311 + 13.0589i 0.141124 + 0.434334i
\(905\) −20.9438 4.35600i −0.696194 0.144798i
\(906\) −6.63391 + 20.4171i −0.220397 + 0.678312i
\(907\) −27.2456 −0.904676 −0.452338 0.891847i \(-0.649410\pi\)
−0.452338 + 0.891847i \(0.649410\pi\)
\(908\) 3.12369 9.61372i 0.103663 0.319042i
\(909\) −11.6373 + 8.45502i −0.385986 + 0.280435i
\(910\) 6.47754 + 59.1384i 0.214728 + 1.96042i
\(911\) 16.0608 + 11.6688i 0.532116 + 0.386605i 0.821149 0.570714i \(-0.193334\pi\)
−0.289032 + 0.957319i \(0.593334\pi\)
\(912\) −1.63842 + 1.19038i −0.0542534 + 0.0394174i
\(913\) −5.17882 + 3.76263i −0.171394 + 0.124525i
\(914\) −18.6981 13.5849i −0.618477 0.449350i
\(915\) −27.6213 5.74484i −0.913132 0.189918i
\(916\) −1.38747 + 1.00806i −0.0458434 + 0.0333072i
\(917\) −15.9663 + 49.1393i −0.527254 + 1.62272i
\(918\) 30.6699 1.01226
\(919\) −7.57618 + 23.3171i −0.249915 + 0.769160i 0.744874 + 0.667205i \(0.232510\pi\)
−0.994789 + 0.101955i \(0.967490\pi\)
\(920\) 13.6657 + 15.0443i 0.450544 + 0.495997i
\(921\) −16.8278 51.7906i −0.554495 1.70656i
\(922\) 6.94763 + 21.3826i 0.228808 + 0.704199i
\(923\) 5.93120 + 4.30927i 0.195228 + 0.141841i
\(924\) −17.6348 −0.580143
\(925\) 21.2451 24.0146i 0.698535 0.789595i
\(926\) −15.6147 −0.513131
\(927\) 6.29458 + 4.57328i 0.206741 + 0.150206i
\(928\) 0.163054 + 0.501828i 0.00535251 + 0.0164733i
\(929\) 13.3034 + 40.9438i 0.436472 + 1.34332i 0.891571 + 0.452881i \(0.149604\pi\)
−0.455099 + 0.890441i \(0.650396\pi\)
\(930\) 1.16152 2.03231i 0.0380879 0.0666422i
\(931\) 3.42220 10.5324i 0.112158 0.345187i
\(932\) 8.55931 0.280369
\(933\) −20.1053 + 61.8778i −0.658219 + 2.02579i
\(934\) −22.2949 + 16.1982i −0.729512 + 0.530022i
\(935\) −24.5632 27.0412i −0.803303 0.884342i
\(936\) 5.57635 + 4.05146i 0.182269 + 0.132426i
\(937\) −10.4557 + 7.59650i −0.341572 + 0.248167i −0.745325 0.666701i \(-0.767706\pi\)
0.403753 + 0.914868i \(0.367706\pi\)
\(938\) 7.00114 5.08662i 0.228595 0.166084i
\(939\) 8.50072 + 6.17614i 0.277411 + 0.201551i
\(940\) −5.09254 5.60629i −0.166100 0.182857i
\(941\) −5.24177 + 3.80837i −0.170877 + 0.124149i −0.669937 0.742418i \(-0.733679\pi\)
0.499060 + 0.866567i \(0.333679\pi\)
\(942\) −0.328384 + 1.01066i −0.0106993 + 0.0329291i
\(943\) −61.2759 −1.99542
\(944\) 3.51255 10.8105i 0.114324 0.351852i
\(945\) 18.1374 31.7349i 0.590010 1.03234i
\(946\) 1.26845 + 3.90390i 0.0412410 + 0.126927i
\(947\) 9.34239 + 28.7529i 0.303587 + 0.934344i 0.980201 + 0.198006i \(0.0634466\pi\)
−0.676614 + 0.736338i \(0.736553\pi\)
\(948\) −3.27538 2.37970i −0.106379 0.0772892i
\(949\) 87.7088 2.84715
\(950\) −3.31300 + 3.74487i −0.107488 + 0.121500i
\(951\) 48.6170 1.57651
\(952\) 27.4351 + 19.9327i 0.889175 + 0.646024i
\(953\) −13.1110 40.3516i −0.424708 1.30712i −0.903273 0.429065i \(-0.858843\pi\)
0.478565 0.878052i \(-0.341157\pi\)
\(954\) 2.70300 + 8.31897i 0.0875127 + 0.269336i
\(955\) −25.4343 28.0002i −0.823036 0.906066i
\(956\) −1.90732 + 5.87014i −0.0616872 + 0.189854i
\(957\) 2.18870 0.0707508
\(958\) −6.62148 + 20.3788i −0.213930 + 0.658409i
\(959\) −53.9295 + 39.1821i −1.74147 + 1.26526i
\(960\) −4.43359 0.922124i −0.143094 0.0297614i
\(961\) 24.8634 + 18.0643i 0.802044 + 0.582719i
\(962\) 32.4666 23.5884i 1.04677 0.760520i
\(963\) −2.57791 + 1.87296i −0.0830721 + 0.0603554i
\(964\) 2.87918 + 2.09184i 0.0927320 + 0.0673738i
\(965\) −3.38630 30.9161i −0.109009 0.995223i
\(966\) −63.3127 + 45.9994i −2.03705 + 1.48001i
\(967\) 5.60764 17.2586i 0.180330 0.554998i −0.819507 0.573069i \(-0.805753\pi\)
0.999837 + 0.0180715i \(0.00575264\pi\)
\(968\) 6.80489 0.218718
\(969\) 4.99189 15.3634i 0.160363 0.493545i
\(970\) −37.6806 7.83703i −1.20985 0.251632i
\(971\) −8.27421 25.4654i −0.265532 0.817224i −0.991570 0.129570i \(-0.958640\pi\)
0.726038 0.687654i \(-0.241360\pi\)
\(972\) −3.37653 10.3919i −0.108302 0.333320i
\(973\) −2.47463 1.79792i −0.0793329 0.0576387i
\(974\) −24.4252 −0.782633
\(975\) 58.1141 + 25.2668i 1.86114 + 0.809185i
\(976\) 6.23000 0.199418
\(977\) −28.5804 20.7649i −0.914369 0.664328i 0.0277467 0.999615i \(-0.491167\pi\)
−0.942116 + 0.335287i \(0.891167\pi\)
\(978\) 0.479957 + 1.47716i 0.0153473 + 0.0472342i
\(979\) 1.72594 + 5.31189i 0.0551612 + 0.169769i
\(980\) 22.5781 10.1711i 0.721230 0.324902i
\(981\) −0.725623 + 2.23324i −0.0231674 + 0.0713018i
\(982\) −6.02040 −0.192119
\(983\) 18.8353 57.9690i 0.600752 1.84892i 0.0770404 0.997028i \(-0.475453\pi\)
0.523711 0.851896i \(-0.324547\pi\)
\(984\) 11.0454 8.02493i 0.352114 0.255826i
\(985\) 12.7361 5.73741i 0.405806 0.182809i
\(986\) −3.40504 2.47390i −0.108438 0.0787852i
\(987\) 23.5936 17.1417i 0.750992 0.545628i
\(988\) −5.06290 + 3.67841i −0.161072 + 0.117026i
\(989\) 14.7371 + 10.7071i 0.468612 + 0.340467i
\(990\) −2.50304 + 4.37956i −0.0795519 + 0.139192i
\(991\) 22.2227 16.1458i 0.705928 0.512887i −0.175929 0.984403i \(-0.556293\pi\)
0.881857 + 0.471516i \(0.156293\pi\)
\(992\) −0.159734 + 0.491612i −0.00507157 + 0.0156087i
\(993\) −63.0163 −1.99976
\(994\) 1.53907 4.73677i 0.0488163 0.150241i
\(995\) −3.31091 30.2278i −0.104963 0.958284i
\(996\) −1.95592 6.01970i −0.0619757 0.190742i
\(997\) −3.29139 10.1299i −0.104239 0.320816i 0.885312 0.464998i \(-0.153945\pi\)
−0.989551 + 0.144182i \(0.953945\pi\)
\(998\) 19.8424 + 14.4163i 0.628100 + 0.456341i
\(999\) −24.6567 −0.780104
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.h.e.191.8 44
25.11 even 5 inner 950.2.h.e.761.8 yes 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.h.e.191.8 44 1.1 even 1 trivial
950.2.h.e.761.8 yes 44 25.11 even 5 inner