Properties

Label 231.2.n.a.89.17
Level $231$
Weight $2$
Character 231.89
Analytic conductor $1.845$
Analytic rank $0$
Dimension $52$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [231,2,Mod(89,231)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(231, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("231.89");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 231 = 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 231.n (of order \(6\), degree \(2\), 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: \(1.84454428669\)
Analytic rank: \(0\)
Dimension: \(52\)
Relative dimension: \(26\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 89.17
Character \(\chi\) \(=\) 231.89
Dual form 231.2.n.a.122.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.872412 + 0.503687i) q^{2} +(-0.195057 - 1.72103i) q^{3} +(-0.492598 - 0.853205i) q^{4} +(-0.168910 + 0.292561i) q^{5} +(0.696692 - 1.59970i) q^{6} +(2.63835 + 0.197774i) q^{7} -3.00721i q^{8} +(-2.92391 + 0.671400i) q^{9} +O(q^{10})\) \(q+(0.872412 + 0.503687i) q^{2} +(-0.195057 - 1.72103i) q^{3} +(-0.492598 - 0.853205i) q^{4} +(-0.168910 + 0.292561i) q^{5} +(0.696692 - 1.59970i) q^{6} +(2.63835 + 0.197774i) q^{7} -3.00721i q^{8} +(-2.92391 + 0.671400i) q^{9} +(-0.294718 + 0.170156i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(-1.37231 + 1.01420i) q^{12} -6.18751i q^{13} +(2.20211 + 1.50144i) q^{14} +(0.536454 + 0.233634i) q^{15} +(0.529497 - 0.917116i) q^{16} +(-0.517054 - 0.895564i) q^{17} +(-2.88903 - 0.886996i) q^{18} +(4.76552 + 2.75137i) q^{19} +0.332819 q^{20} +(-0.174254 - 4.57926i) q^{21} -1.00737 q^{22} +(0.780699 + 0.450737i) q^{23} +(-5.17551 + 0.586579i) q^{24} +(2.44294 + 4.23129i) q^{25} +(3.11657 - 5.39806i) q^{26} +(1.72583 + 4.90117i) q^{27} +(-1.13090 - 2.34848i) q^{28} +10.4471i q^{29} +(0.350331 + 0.474030i) q^{30} +(-2.82520 + 1.63113i) q^{31} +(-4.28476 + 2.47381i) q^{32} +(1.02944 + 1.39293i) q^{33} -1.04173i q^{34} +(-0.503505 + 0.738472i) q^{35} +(2.01315 + 2.16396i) q^{36} +(-1.95816 + 3.39162i) q^{37} +(2.77166 + 4.80066i) q^{38} +(-10.6489 + 1.20692i) q^{39} +(0.879793 + 0.507948i) q^{40} +11.2247 q^{41} +(2.15449 - 4.08277i) q^{42} -6.76228 q^{43} +(0.853205 + 0.492598i) q^{44} +(0.297452 - 0.968827i) q^{45} +(0.454061 + 0.786456i) q^{46} +(3.61562 - 6.26243i) q^{47} +(-1.68167 - 0.732392i) q^{48} +(6.92177 + 1.04359i) q^{49} +4.92191i q^{50} +(-1.44044 + 1.06455i) q^{51} +(-5.27922 + 3.04796i) q^{52} +(7.55149 - 4.35985i) q^{53} +(-0.963024 + 5.14512i) q^{54} -0.337820i q^{55} +(0.594748 - 7.93407i) q^{56} +(3.80565 - 8.73829i) q^{57} +(-5.26205 + 9.11414i) q^{58} +(-2.65866 - 4.60494i) q^{59} +(-0.0649189 - 0.572793i) q^{60} +(-2.79724 - 1.61499i) q^{61} -3.28632 q^{62} +(-7.84707 + 1.19312i) q^{63} -7.10209 q^{64} +(1.81023 + 1.04513i) q^{65} +(0.196496 + 1.73372i) q^{66} +(-5.29852 - 9.17731i) q^{67} +(-0.509400 + 0.882306i) q^{68} +(0.623452 - 1.43153i) q^{69} +(-0.811223 + 0.390643i) q^{70} +9.05873i q^{71} +(2.01904 + 8.79280i) q^{72} +(-3.38869 + 1.95646i) q^{73} +(-3.41664 + 1.97260i) q^{74} +(6.80568 - 5.02972i) q^{75} -5.42129i q^{76} +(-2.38376 + 1.14790i) q^{77} +(-9.89815 - 4.31079i) q^{78} +(-2.94659 + 5.10365i) q^{79} +(0.178875 + 0.309821i) q^{80} +(8.09844 - 3.92622i) q^{81} +(9.79259 + 5.65376i) q^{82} -6.94128 q^{83} +(-3.82121 + 2.40441i) q^{84} +0.349343 q^{85} +(-5.89950 - 3.40608i) q^{86} +(17.9797 - 2.03778i) q^{87} +(1.50361 + 2.60432i) q^{88} +(1.82637 - 3.16337i) q^{89} +(0.747486 - 0.695393i) q^{90} +(1.22373 - 16.3248i) q^{91} -0.888129i q^{92} +(3.35830 + 4.54409i) q^{93} +(6.30861 - 3.64228i) q^{94} +(-1.60989 + 0.929470i) q^{95} +(5.09328 + 6.89168i) q^{96} +9.23676i q^{97} +(5.51299 + 4.39685i) q^{98} +(2.19648 - 2.04340i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52 q + 24 q^{4} - 6 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 52 q + 24 q^{4} - 6 q^{7} - 4 q^{9} - 30 q^{12} - 4 q^{15} - 20 q^{16} - 18 q^{18} + 6 q^{19} - 2 q^{21} + 36 q^{24} - 22 q^{25} - 40 q^{28} - 20 q^{30} - 54 q^{31} + 36 q^{36} + 2 q^{37} + 20 q^{39} + 60 q^{40} - 36 q^{42} + 36 q^{43} - 54 q^{45} + 4 q^{46} + 22 q^{49} - 16 q^{51} + 12 q^{52} + 66 q^{54} - 44 q^{57} - 16 q^{58} + 20 q^{60} - 36 q^{61} - 24 q^{63} - 48 q^{64} - 30 q^{66} - 6 q^{67} - 116 q^{70} + 36 q^{72} - 6 q^{73} + 72 q^{75} + 112 q^{78} + 14 q^{79} + 52 q^{81} - 84 q^{82} + 8 q^{84} + 8 q^{85} + 18 q^{87} - 12 q^{88} + 46 q^{91} + 6 q^{93} + 48 q^{94} - 18 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/231\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.872412 + 0.503687i 0.616888 + 0.356161i 0.775657 0.631155i \(-0.217419\pi\)
−0.158768 + 0.987316i \(0.550752\pi\)
\(3\) −0.195057 1.72103i −0.112616 0.993639i
\(4\) −0.492598 0.853205i −0.246299 0.426603i
\(5\) −0.168910 + 0.292561i −0.0755389 + 0.130837i −0.901321 0.433153i \(-0.857401\pi\)
0.825782 + 0.563990i \(0.190734\pi\)
\(6\) 0.696692 1.59970i 0.284423 0.653074i
\(7\) 2.63835 + 0.197774i 0.997202 + 0.0747515i
\(8\) 3.00721i 1.06321i
\(9\) −2.92391 + 0.671400i −0.974635 + 0.223800i
\(10\) −0.294718 + 0.170156i −0.0931982 + 0.0538080i
\(11\) −0.866025 + 0.500000i −0.261116 + 0.150756i
\(12\) −1.37231 + 1.01420i −0.396151 + 0.292775i
\(13\) 6.18751i 1.71611i −0.513560 0.858054i \(-0.671674\pi\)
0.513560 0.858054i \(-0.328326\pi\)
\(14\) 2.20211 + 1.50144i 0.588539 + 0.401278i
\(15\) 0.536454 + 0.233634i 0.138512 + 0.0603240i
\(16\) 0.529497 0.917116i 0.132374 0.229279i
\(17\) −0.517054 0.895564i −0.125404 0.217206i 0.796487 0.604656i \(-0.206689\pi\)
−0.921891 + 0.387450i \(0.873356\pi\)
\(18\) −2.88903 0.886996i −0.680950 0.209067i
\(19\) 4.76552 + 2.75137i 1.09329 + 0.631209i 0.934449 0.356096i \(-0.115893\pi\)
0.158836 + 0.987305i \(0.449226\pi\)
\(20\) 0.332819 0.0744207
\(21\) −0.174254 4.57926i −0.0380254 0.999277i
\(22\) −1.00737 −0.214773
\(23\) 0.780699 + 0.450737i 0.162787 + 0.0939851i 0.579180 0.815199i \(-0.303373\pi\)
−0.416393 + 0.909185i \(0.636706\pi\)
\(24\) −5.17551 + 0.586579i −1.05645 + 0.119735i
\(25\) 2.44294 + 4.23129i 0.488588 + 0.846259i
\(26\) 3.11657 5.39806i 0.611210 1.05865i
\(27\) 1.72583 + 4.90117i 0.332136 + 0.943231i
\(28\) −1.13090 2.34848i −0.213721 0.443820i
\(29\) 10.4471i 1.93997i 0.243163 + 0.969985i \(0.421815\pi\)
−0.243163 + 0.969985i \(0.578185\pi\)
\(30\) 0.350331 + 0.474030i 0.0639613 + 0.0865456i
\(31\) −2.82520 + 1.63113i −0.507421 + 0.292959i −0.731773 0.681549i \(-0.761307\pi\)
0.224352 + 0.974508i \(0.427973\pi\)
\(32\) −4.28476 + 2.47381i −0.757446 + 0.437312i
\(33\) 1.02944 + 1.39293i 0.179203 + 0.242478i
\(34\) 1.04173i 0.178656i
\(35\) −0.503505 + 0.738472i −0.0851079 + 0.124825i
\(36\) 2.01315 + 2.16396i 0.335525 + 0.360660i
\(37\) −1.95816 + 3.39162i −0.321919 + 0.557580i −0.980884 0.194594i \(-0.937661\pi\)
0.658965 + 0.752173i \(0.270994\pi\)
\(38\) 2.77166 + 4.80066i 0.449623 + 0.778770i
\(39\) −10.6489 + 1.20692i −1.70519 + 0.193262i
\(40\) 0.879793 + 0.507948i 0.139107 + 0.0803137i
\(41\) 11.2247 1.75301 0.876504 0.481394i \(-0.159869\pi\)
0.876504 + 0.481394i \(0.159869\pi\)
\(42\) 2.15449 4.08277i 0.332446 0.629985i
\(43\) −6.76228 −1.03124 −0.515619 0.856818i \(-0.672438\pi\)
−0.515619 + 0.856818i \(0.672438\pi\)
\(44\) 0.853205 + 0.492598i 0.128626 + 0.0742620i
\(45\) 0.297452 0.968827i 0.0443415 0.144424i
\(46\) 0.454061 + 0.786456i 0.0669476 + 0.115957i
\(47\) 3.61562 6.26243i 0.527392 0.913469i −0.472098 0.881546i \(-0.656503\pi\)
0.999490 0.0319237i \(-0.0101633\pi\)
\(48\) −1.68167 0.732392i −0.242728 0.105712i
\(49\) 6.92177 + 1.04359i 0.988824 + 0.149085i
\(50\) 4.92191i 0.696063i
\(51\) −1.44044 + 1.06455i −0.201702 + 0.149067i
\(52\) −5.27922 + 3.04796i −0.732096 + 0.422676i
\(53\) 7.55149 4.35985i 1.03728 0.598872i 0.118216 0.992988i \(-0.462282\pi\)
0.919061 + 0.394116i \(0.128949\pi\)
\(54\) −0.963024 + 5.14512i −0.131051 + 0.700162i
\(55\) 0.337820i 0.0455517i
\(56\) 0.594748 7.93407i 0.0794765 1.06023i
\(57\) 3.80565 8.73829i 0.504071 1.15741i
\(58\) −5.26205 + 9.11414i −0.690941 + 1.19675i
\(59\) −2.65866 4.60494i −0.346128 0.599512i 0.639430 0.768849i \(-0.279170\pi\)
−0.985558 + 0.169338i \(0.945837\pi\)
\(60\) −0.0649189 0.572793i −0.00838099 0.0739473i
\(61\) −2.79724 1.61499i −0.358150 0.206778i 0.310119 0.950698i \(-0.399631\pi\)
−0.668269 + 0.743920i \(0.732964\pi\)
\(62\) −3.28632 −0.417362
\(63\) −7.84707 + 1.19312i −0.988638 + 0.150318i
\(64\) −7.10209 −0.887762
\(65\) 1.81023 + 1.04513i 0.224531 + 0.129633i
\(66\) 0.196496 + 1.73372i 0.0241870 + 0.213407i
\(67\) −5.29852 9.17731i −0.647318 1.12119i −0.983761 0.179484i \(-0.942557\pi\)
0.336443 0.941704i \(-0.390776\pi\)
\(68\) −0.509400 + 0.882306i −0.0617738 + 0.106995i
\(69\) 0.623452 1.43153i 0.0750547 0.172336i
\(70\) −0.811223 + 0.390643i −0.0969596 + 0.0466907i
\(71\) 9.05873i 1.07507i 0.843240 + 0.537537i \(0.180645\pi\)
−0.843240 + 0.537537i \(0.819355\pi\)
\(72\) 2.01904 + 8.79280i 0.237946 + 1.03624i
\(73\) −3.38869 + 1.95646i −0.396616 + 0.228987i −0.685023 0.728522i \(-0.740208\pi\)
0.288407 + 0.957508i \(0.406875\pi\)
\(74\) −3.41664 + 1.97260i −0.397176 + 0.229310i
\(75\) 6.80568 5.02972i 0.785852 0.580782i
\(76\) 5.42129i 0.621864i
\(77\) −2.38376 + 1.14790i −0.271655 + 0.130815i
\(78\) −9.89815 4.31079i −1.12074 0.488101i
\(79\) −2.94659 + 5.10365i −0.331518 + 0.574205i −0.982810 0.184622i \(-0.940894\pi\)
0.651292 + 0.758827i \(0.274227\pi\)
\(80\) 0.178875 + 0.309821i 0.0199988 + 0.0346390i
\(81\) 8.09844 3.92622i 0.899827 0.436247i
\(82\) 9.79259 + 5.65376i 1.08141 + 0.624353i
\(83\) −6.94128 −0.761904 −0.380952 0.924595i \(-0.624404\pi\)
−0.380952 + 0.924595i \(0.624404\pi\)
\(84\) −3.82121 + 2.40441i −0.416928 + 0.262343i
\(85\) 0.349343 0.0378915
\(86\) −5.89950 3.40608i −0.636159 0.367287i
\(87\) 17.9797 2.03778i 1.92763 0.218473i
\(88\) 1.50361 + 2.60432i 0.160285 + 0.277622i
\(89\) 1.82637 3.16337i 0.193595 0.335317i −0.752844 0.658199i \(-0.771319\pi\)
0.946439 + 0.322882i \(0.104652\pi\)
\(90\) 0.747486 0.695393i 0.0787920 0.0733009i
\(91\) 1.22373 16.3248i 0.128282 1.71131i
\(92\) 0.888129i 0.0925938i
\(93\) 3.35830 + 4.54409i 0.348240 + 0.471201i
\(94\) 6.30861 3.64228i 0.650684 0.375672i
\(95\) −1.60989 + 0.929470i −0.165171 + 0.0953616i
\(96\) 5.09328 + 6.89168i 0.519831 + 0.703379i
\(97\) 9.23676i 0.937851i 0.883238 + 0.468925i \(0.155359\pi\)
−0.883238 + 0.468925i \(0.844641\pi\)
\(98\) 5.51299 + 4.39685i 0.556896 + 0.444149i
\(99\) 2.19648 2.04340i 0.220754 0.205370i
\(100\) 2.40677 4.16866i 0.240677 0.416866i
\(101\) −0.464343 0.804266i −0.0462039 0.0800275i 0.841999 0.539480i \(-0.181379\pi\)
−0.888202 + 0.459452i \(0.848046\pi\)
\(102\) −1.79286 + 0.203198i −0.177519 + 0.0201196i
\(103\) −2.16678 1.25099i −0.213499 0.123264i 0.389438 0.921053i \(-0.372669\pi\)
−0.602936 + 0.797789i \(0.706003\pi\)
\(104\) −18.6072 −1.82458
\(105\) 1.36915 + 0.722504i 0.133615 + 0.0705091i
\(106\) 8.78401 0.853179
\(107\) −7.12304 4.11249i −0.688611 0.397570i 0.114481 0.993425i \(-0.463480\pi\)
−0.803091 + 0.595856i \(0.796813\pi\)
\(108\) 3.33157 3.88680i 0.320580 0.374007i
\(109\) −2.32520 4.02736i −0.222714 0.385751i 0.732917 0.680318i \(-0.238158\pi\)
−0.955631 + 0.294566i \(0.904825\pi\)
\(110\) 0.170156 0.294718i 0.0162237 0.0281003i
\(111\) 6.21905 + 2.70849i 0.590286 + 0.257078i
\(112\) 1.57838 2.31495i 0.149143 0.218742i
\(113\) 4.52821i 0.425978i 0.977055 + 0.212989i \(0.0683198\pi\)
−0.977055 + 0.212989i \(0.931680\pi\)
\(114\) 7.72146 5.70653i 0.723181 0.534465i
\(115\) −0.263736 + 0.152268i −0.0245935 + 0.0141991i
\(116\) 8.91349 5.14620i 0.827597 0.477813i
\(117\) 4.15430 + 18.0917i 0.384065 + 1.67258i
\(118\) 5.35654i 0.493109i
\(119\) −1.18705 2.46507i −0.108817 0.225973i
\(120\) 0.702586 1.61323i 0.0641370 0.147267i
\(121\) 0.500000 0.866025i 0.0454545 0.0787296i
\(122\) −1.62690 2.81787i −0.147292 0.255118i
\(123\) −2.18947 19.3181i −0.197418 1.74186i
\(124\) 2.78338 + 1.60698i 0.249954 + 0.144311i
\(125\) −3.33965 −0.298707
\(126\) −7.44683 2.91158i −0.663417 0.259384i
\(127\) 10.9941 0.975572 0.487786 0.872963i \(-0.337805\pi\)
0.487786 + 0.872963i \(0.337805\pi\)
\(128\) 2.37357 + 1.37038i 0.209796 + 0.121126i
\(129\) 1.31903 + 11.6381i 0.116134 + 1.02468i
\(130\) 1.05284 + 1.82357i 0.0923403 + 0.159938i
\(131\) −7.13990 + 12.3667i −0.623816 + 1.08048i 0.364952 + 0.931026i \(0.381085\pi\)
−0.988768 + 0.149455i \(0.952248\pi\)
\(132\) 0.681354 1.56448i 0.0593042 0.136170i
\(133\) 12.0290 + 8.20158i 1.04304 + 0.711167i
\(134\) 10.6752i 0.922197i
\(135\) −1.72540 0.322947i −0.148499 0.0277949i
\(136\) −2.69315 + 1.55489i −0.230936 + 0.133331i
\(137\) −4.49906 + 2.59753i −0.384381 + 0.221922i −0.679722 0.733469i \(-0.737900\pi\)
0.295342 + 0.955392i \(0.404566\pi\)
\(138\) 1.26495 0.934857i 0.107680 0.0795803i
\(139\) 0.823165i 0.0698199i 0.999390 + 0.0349100i \(0.0111144\pi\)
−0.999390 + 0.0349100i \(0.988886\pi\)
\(140\) 0.878094 + 0.0658230i 0.0742125 + 0.00556306i
\(141\) −11.4831 5.00106i −0.967051 0.421165i
\(142\) −4.56277 + 7.90295i −0.382899 + 0.663201i
\(143\) 3.09376 + 5.35854i 0.258713 + 0.448104i
\(144\) −0.932448 + 3.03707i −0.0777040 + 0.253089i
\(145\) −3.05640 1.76461i −0.253820 0.146543i
\(146\) −3.94178 −0.326224
\(147\) 0.445914 12.1162i 0.0367784 0.999323i
\(148\) 3.85834 0.317153
\(149\) −0.992777 0.573180i −0.0813314 0.0469567i 0.458783 0.888548i \(-0.348286\pi\)
−0.540114 + 0.841592i \(0.681619\pi\)
\(150\) 8.47076 0.960054i 0.691635 0.0783881i
\(151\) −7.29020 12.6270i −0.593268 1.02757i −0.993789 0.111282i \(-0.964504\pi\)
0.400521 0.916288i \(-0.368829\pi\)
\(152\) 8.27396 14.3309i 0.671107 1.16239i
\(153\) 2.11310 + 2.27139i 0.170834 + 0.183631i
\(154\) −2.65781 0.199232i −0.214172 0.0160546i
\(155\) 1.10206i 0.0885193i
\(156\) 6.27539 + 8.49118i 0.502433 + 0.679839i
\(157\) 10.2799 5.93507i 0.820421 0.473671i −0.0301404 0.999546i \(-0.509595\pi\)
0.850562 + 0.525875i \(0.176262\pi\)
\(158\) −5.14129 + 2.96832i −0.409019 + 0.236147i
\(159\) −8.97642 12.1459i −0.711877 0.963235i
\(160\) 1.67141i 0.132136i
\(161\) 1.97061 + 1.34360i 0.155306 + 0.105891i
\(162\) 9.04277 + 0.653802i 0.710467 + 0.0513675i
\(163\) 7.27542 12.6014i 0.569855 0.987017i −0.426725 0.904381i \(-0.640333\pi\)
0.996580 0.0826359i \(-0.0263339\pi\)
\(164\) −5.52928 9.57700i −0.431765 0.747838i
\(165\) −0.581400 + 0.0658943i −0.0452619 + 0.00512987i
\(166\) −6.05565 3.49623i −0.470010 0.271360i
\(167\) −19.1863 −1.48468 −0.742342 0.670021i \(-0.766285\pi\)
−0.742342 + 0.670021i \(0.766285\pi\)
\(168\) −13.7708 + 0.524019i −1.06244 + 0.0404290i
\(169\) −25.2853 −1.94503
\(170\) 0.304771 + 0.175959i 0.0233748 + 0.0134955i
\(171\) −15.7812 4.84519i −1.20682 0.370521i
\(172\) 3.33109 + 5.76962i 0.253993 + 0.439929i
\(173\) 10.3037 17.8464i 0.783372 1.35684i −0.146595 0.989197i \(-0.546831\pi\)
0.929967 0.367644i \(-0.119835\pi\)
\(174\) 16.7121 + 7.27838i 1.26694 + 0.551773i
\(175\) 5.60849 + 11.6468i 0.423962 + 0.880414i
\(176\) 1.05899i 0.0798247i
\(177\) −7.40665 + 5.47387i −0.556718 + 0.411441i
\(178\) 3.18670 1.83984i 0.238853 0.137902i
\(179\) 0.717382 0.414181i 0.0536197 0.0309573i −0.472951 0.881089i \(-0.656811\pi\)
0.526570 + 0.850132i \(0.323478\pi\)
\(180\) −0.973132 + 0.223455i −0.0725330 + 0.0166554i
\(181\) 8.14952i 0.605749i 0.953030 + 0.302875i \(0.0979463\pi\)
−0.953030 + 0.302875i \(0.902054\pi\)
\(182\) 9.29020 13.6256i 0.688635 1.01000i
\(183\) −2.23383 + 5.12916i −0.165129 + 0.379158i
\(184\) 1.35546 2.34773i 0.0999259 0.173077i
\(185\) −0.661505 1.14576i −0.0486348 0.0842379i
\(186\) 0.641020 + 5.65586i 0.0470019 + 0.414707i
\(187\) 0.895564 + 0.517054i 0.0654901 + 0.0378107i
\(188\) −7.12419 −0.519585
\(189\) 3.58402 + 13.2723i 0.260699 + 0.965420i
\(190\) −1.87265 −0.135856
\(191\) 16.8944 + 9.75398i 1.22244 + 0.705773i 0.965437 0.260638i \(-0.0839330\pi\)
0.256999 + 0.966412i \(0.417266\pi\)
\(192\) 1.38532 + 12.2229i 0.0999765 + 0.882114i
\(193\) 8.67207 + 15.0205i 0.624230 + 1.08120i 0.988689 + 0.149978i \(0.0479204\pi\)
−0.364460 + 0.931219i \(0.618746\pi\)
\(194\) −4.65244 + 8.05826i −0.334026 + 0.578549i
\(195\) 1.44561 3.31932i 0.103522 0.237701i
\(196\) −2.51925 6.41976i −0.179947 0.458555i
\(197\) 5.76409i 0.410675i −0.978691 0.205337i \(-0.934171\pi\)
0.978691 0.205337i \(-0.0658292\pi\)
\(198\) 2.94547 0.676351i 0.209325 0.0480662i
\(199\) −11.2355 + 6.48682i −0.796464 + 0.459839i −0.842233 0.539113i \(-0.818759\pi\)
0.0457694 + 0.998952i \(0.485426\pi\)
\(200\) 12.7244 7.34643i 0.899751 0.519471i
\(201\) −14.7609 + 10.9090i −1.04116 + 0.769464i
\(202\) 0.935535i 0.0658240i
\(203\) −2.06616 + 27.5630i −0.145016 + 1.93454i
\(204\) 1.61784 + 0.704593i 0.113271 + 0.0493314i
\(205\) −1.89597 + 3.28392i −0.132420 + 0.229359i
\(206\) −1.26021 2.18275i −0.0878033 0.152080i
\(207\) −2.58531 0.793750i −0.179692 0.0551695i
\(208\) −5.67467 3.27627i −0.393468 0.227169i
\(209\) −5.50275 −0.380633
\(210\) 0.830544 + 1.31994i 0.0573130 + 0.0910847i
\(211\) −5.58202 −0.384282 −0.192141 0.981367i \(-0.561543\pi\)
−0.192141 + 0.981367i \(0.561543\pi\)
\(212\) −7.43970 4.29531i −0.510961 0.295003i
\(213\) 15.5904 1.76697i 1.06823 0.121071i
\(214\) −4.14282 7.17557i −0.283197 0.490512i
\(215\) 1.14222 1.97838i 0.0778987 0.134924i
\(216\) 14.7389 5.18994i 1.00285 0.353130i
\(217\) −7.77645 + 3.74474i −0.527900 + 0.254209i
\(218\) 4.68469i 0.317287i
\(219\) 4.02812 + 5.45042i 0.272195 + 0.368306i
\(220\) −0.288230 + 0.166410i −0.0194325 + 0.0112193i
\(221\) −5.54131 + 3.19928i −0.372749 + 0.215207i
\(222\) 4.06134 + 5.49537i 0.272579 + 0.368825i
\(223\) 2.32096i 0.155423i −0.996976 0.0777116i \(-0.975239\pi\)
0.996976 0.0777116i \(-0.0247613\pi\)
\(224\) −11.7940 + 5.67936i −0.788017 + 0.379468i
\(225\) −9.98381 10.7317i −0.665587 0.715448i
\(226\) −2.28080 + 3.95046i −0.151717 + 0.262781i
\(227\) −0.207712 0.359767i −0.0137863 0.0238786i 0.859050 0.511892i \(-0.171055\pi\)
−0.872836 + 0.488013i \(0.837722\pi\)
\(228\) −9.33021 + 1.05746i −0.617908 + 0.0700321i
\(229\) 5.54470 + 3.20124i 0.366404 + 0.211544i 0.671886 0.740654i \(-0.265484\pi\)
−0.305482 + 0.952198i \(0.598818\pi\)
\(230\) −0.306782 −0.0202286
\(231\) 2.44054 + 3.87863i 0.160576 + 0.255195i
\(232\) 31.4165 2.06260
\(233\) −0.676221 0.390416i −0.0443007 0.0255770i 0.477686 0.878531i \(-0.341476\pi\)
−0.521987 + 0.852954i \(0.674809\pi\)
\(234\) −5.48830 + 17.8759i −0.358782 + 1.16858i
\(235\) 1.22143 + 2.11558i 0.0796772 + 0.138005i
\(236\) −2.61930 + 4.53677i −0.170502 + 0.295318i
\(237\) 9.35830 + 4.07568i 0.607887 + 0.264744i
\(238\) 0.206028 2.74846i 0.0133548 0.178156i
\(239\) 27.1066i 1.75338i 0.481056 + 0.876690i \(0.340253\pi\)
−0.481056 + 0.876690i \(0.659747\pi\)
\(240\) 0.498320 0.368282i 0.0321664 0.0237725i
\(241\) −10.7835 + 6.22588i −0.694629 + 0.401044i −0.805344 0.592808i \(-0.798019\pi\)
0.110715 + 0.993852i \(0.464686\pi\)
\(242\) 0.872412 0.503687i 0.0560808 0.0323782i
\(243\) −8.33681 13.1718i −0.534807 0.844974i
\(244\) 3.18216i 0.203717i
\(245\) −1.47447 + 1.84877i −0.0942006 + 0.118113i
\(246\) 7.82018 17.9562i 0.498596 1.14484i
\(247\) 17.0242 29.4867i 1.08322 1.87620i
\(248\) 4.90515 + 8.49597i 0.311477 + 0.539494i
\(249\) 1.35395 + 11.9462i 0.0858029 + 0.757057i
\(250\) −2.91355 1.68214i −0.184269 0.106388i
\(251\) −6.22012 −0.392610 −0.196305 0.980543i \(-0.562894\pi\)
−0.196305 + 0.980543i \(0.562894\pi\)
\(252\) 4.88342 + 6.10743i 0.307627 + 0.384732i
\(253\) −0.901474 −0.0566752
\(254\) 9.59142 + 5.53761i 0.601819 + 0.347460i
\(255\) −0.0681419 0.601230i −0.00426721 0.0376505i
\(256\) 8.48258 + 14.6923i 0.530161 + 0.918267i
\(257\) −0.261862 + 0.453557i −0.0163345 + 0.0282921i −0.874077 0.485787i \(-0.838533\pi\)
0.857743 + 0.514079i \(0.171866\pi\)
\(258\) −4.71123 + 10.8176i −0.293308 + 0.673475i
\(259\) −5.83707 + 8.56102i −0.362698 + 0.531956i
\(260\) 2.05932i 0.127714i
\(261\) −7.01416 30.5462i −0.434166 1.89076i
\(262\) −12.4579 + 7.19256i −0.769650 + 0.444358i
\(263\) 0.672889 0.388493i 0.0414921 0.0239555i −0.479110 0.877755i \(-0.659041\pi\)
0.520603 + 0.853799i \(0.325707\pi\)
\(264\) 4.18883 3.09575i 0.257805 0.190530i
\(265\) 2.94569i 0.180953i
\(266\) 6.36317 + 13.2140i 0.390151 + 0.810202i
\(267\) −5.80051 2.52621i −0.354986 0.154601i
\(268\) −5.22009 + 9.04146i −0.318868 + 0.552295i
\(269\) −5.98065 10.3588i −0.364646 0.631586i 0.624073 0.781366i \(-0.285477\pi\)
−0.988719 + 0.149780i \(0.952143\pi\)
\(270\) −1.34260 1.15081i −0.0817079 0.0700359i
\(271\) −9.58028 5.53117i −0.581960 0.335995i 0.179952 0.983675i \(-0.442406\pi\)
−0.761912 + 0.647681i \(0.775739\pi\)
\(272\) −1.09511 −0.0664011
\(273\) −28.3342 + 1.07820i −1.71487 + 0.0652557i
\(274\) −5.23338 −0.316160
\(275\) −4.23129 2.44294i −0.255157 0.147315i
\(276\) −1.52850 + 0.173236i −0.0920048 + 0.0104276i
\(277\) 5.92603 + 10.2642i 0.356061 + 0.616716i 0.987299 0.158874i \(-0.0507862\pi\)
−0.631238 + 0.775589i \(0.717453\pi\)
\(278\) −0.414618 + 0.718139i −0.0248671 + 0.0430711i
\(279\) 7.16547 6.66610i 0.428986 0.399089i
\(280\) 2.22074 + 1.51415i 0.132715 + 0.0904875i
\(281\) 11.8914i 0.709379i 0.934984 + 0.354689i \(0.115413\pi\)
−0.934984 + 0.354689i \(0.884587\pi\)
\(282\) −7.49902 10.1469i −0.446560 0.604238i
\(283\) −23.9902 + 13.8507i −1.42607 + 0.823341i −0.996808 0.0798405i \(-0.974559\pi\)
−0.429260 + 0.903181i \(0.641226\pi\)
\(284\) 7.72896 4.46232i 0.458629 0.264790i
\(285\) 1.91367 + 2.58937i 0.113356 + 0.153381i
\(286\) 6.23314i 0.368574i
\(287\) 29.6148 + 2.21996i 1.74810 + 0.131040i
\(288\) 10.8673 10.1100i 0.640363 0.595736i
\(289\) 7.96531 13.7963i 0.468548 0.811548i
\(290\) −1.77763 3.07894i −0.104386 0.180802i
\(291\) 15.8968 1.80170i 0.931885 0.105617i
\(292\) 3.33853 + 1.92750i 0.195372 + 0.112798i
\(293\) 10.5335 0.615376 0.307688 0.951487i \(-0.400445\pi\)
0.307688 + 0.951487i \(0.400445\pi\)
\(294\) 6.49177 10.3457i 0.378608 0.603372i
\(295\) 1.79630 0.104585
\(296\) 10.1993 + 5.88859i 0.592824 + 0.342267i
\(297\) −3.94520 3.38163i −0.228924 0.196222i
\(298\) −0.577407 1.00010i −0.0334483 0.0579341i
\(299\) 2.78894 4.83059i 0.161289 0.279360i
\(300\) −7.64385 3.32901i −0.441318 0.192201i
\(301\) −17.8413 1.33740i −1.02835 0.0770866i
\(302\) 14.6879i 0.845195i
\(303\) −1.29359 + 0.956028i −0.0743151 + 0.0549224i
\(304\) 5.04666 2.91369i 0.289446 0.167112i
\(305\) 0.944965 0.545576i 0.0541086 0.0312396i
\(306\) 0.699420 + 3.04593i 0.0399832 + 0.174124i
\(307\) 1.47636i 0.0842604i 0.999112 + 0.0421302i \(0.0134144\pi\)
−0.999112 + 0.0421302i \(0.986586\pi\)
\(308\) 2.15363 + 1.46839i 0.122714 + 0.0836692i
\(309\) −1.73035 + 3.97311i −0.0984360 + 0.226022i
\(310\) 0.555092 0.961448i 0.0315271 0.0546066i
\(311\) −11.1828 19.3692i −0.634118 1.09832i −0.986701 0.162544i \(-0.948030\pi\)
0.352584 0.935780i \(-0.385303\pi\)
\(312\) 3.62946 + 32.0235i 0.205478 + 1.81298i
\(313\) 1.53205 + 0.884531i 0.0865967 + 0.0499967i 0.542673 0.839944i \(-0.317412\pi\)
−0.456076 + 0.889941i \(0.650746\pi\)
\(314\) 11.9577 0.674811
\(315\) 0.976390 2.49728i 0.0550134 0.140706i
\(316\) 5.80595 0.326610
\(317\) −9.92682 5.73125i −0.557546 0.321899i 0.194614 0.980880i \(-0.437655\pi\)
−0.752160 + 0.658981i \(0.770988\pi\)
\(318\) −1.71339 15.1176i −0.0960819 0.847751i
\(319\) −5.22353 9.04742i −0.292462 0.506558i
\(320\) 1.19962 2.07780i 0.0670606 0.116152i
\(321\) −5.68833 + 13.0612i −0.317492 + 0.729003i
\(322\) 1.04243 + 2.16475i 0.0580924 + 0.120637i
\(323\) 5.69044i 0.316624i
\(324\) −7.33915 4.97559i −0.407731 0.276421i
\(325\) 26.1812 15.1157i 1.45227 0.838469i
\(326\) 12.6943 7.32907i 0.703074 0.405920i
\(327\) −6.47768 + 4.78731i −0.358216 + 0.264739i
\(328\) 33.7551i 1.86382i
\(329\) 10.7778 15.8074i 0.594199 0.871490i
\(330\) −0.540410 0.235357i −0.0297486 0.0129560i
\(331\) 2.04107 3.53524i 0.112187 0.194314i −0.804465 0.594001i \(-0.797548\pi\)
0.916652 + 0.399686i \(0.130881\pi\)
\(332\) 3.41926 + 5.92233i 0.187656 + 0.325030i
\(333\) 3.44832 11.2315i 0.188967 0.615482i
\(334\) −16.7384 9.66391i −0.915884 0.528786i
\(335\) 3.57990 0.195591
\(336\) −4.29198 2.26490i −0.234147 0.123560i
\(337\) −28.2782 −1.54041 −0.770207 0.637795i \(-0.779847\pi\)
−0.770207 + 0.637795i \(0.779847\pi\)
\(338\) −22.0592 12.7359i −1.19986 0.692742i
\(339\) 7.79319 0.883260i 0.423268 0.0479721i
\(340\) −0.172086 0.298061i −0.00933265 0.0161646i
\(341\) 1.63113 2.82520i 0.0883306 0.152993i
\(342\) −11.3272 12.1758i −0.612508 0.658391i
\(343\) 18.0557 + 4.12231i 0.974914 + 0.222584i
\(344\) 20.3356i 1.09642i
\(345\) 0.313502 + 0.424197i 0.0168784 + 0.0228380i
\(346\) 17.9781 10.3796i 0.966506 0.558013i
\(347\) −16.7024 + 9.64311i −0.896629 + 0.517669i −0.876105 0.482120i \(-0.839867\pi\)
−0.0205242 + 0.999789i \(0.506534\pi\)
\(348\) −10.5954 14.3366i −0.567974 0.768522i
\(349\) 5.54773i 0.296963i −0.988915 0.148482i \(-0.952561\pi\)
0.988915 0.148482i \(-0.0474386\pi\)
\(350\) −0.973425 + 12.9857i −0.0520317 + 0.694116i
\(351\) 30.3261 10.6786i 1.61869 0.569982i
\(352\) 2.47381 4.28476i 0.131854 0.228379i
\(353\) −7.60042 13.1643i −0.404529 0.700665i 0.589737 0.807595i \(-0.299231\pi\)
−0.994267 + 0.106930i \(0.965898\pi\)
\(354\) −9.21877 + 1.04483i −0.489972 + 0.0555322i
\(355\) −2.65023 1.53011i −0.140660 0.0812099i
\(356\) −3.59867 −0.190729
\(357\) −4.01092 + 2.52378i −0.212280 + 0.133573i
\(358\) 0.834471 0.0441031
\(359\) −21.0219 12.1370i −1.10949 0.640567i −0.170796 0.985306i \(-0.554634\pi\)
−0.938698 + 0.344740i \(0.887967\pi\)
\(360\) −2.91347 0.894500i −0.153553 0.0471443i
\(361\) 5.64012 + 9.76897i 0.296848 + 0.514157i
\(362\) −4.10481 + 7.10974i −0.215744 + 0.373680i
\(363\) −1.58799 0.691592i −0.0833477 0.0362991i
\(364\) −14.5312 + 6.99749i −0.761643 + 0.366768i
\(365\) 1.32186i 0.0691896i
\(366\) −4.53231 + 3.34959i −0.236908 + 0.175086i
\(367\) 28.6358 16.5329i 1.49478 0.863010i 0.494794 0.869010i \(-0.335243\pi\)
0.999982 + 0.00600056i \(0.00191005\pi\)
\(368\) 0.826756 0.477328i 0.0430976 0.0248824i
\(369\) −32.8201 + 7.53629i −1.70854 + 0.392323i
\(370\) 1.33277i 0.0692872i
\(371\) 20.7857 10.0093i 1.07914 0.519659i
\(372\) 2.22275 5.10373i 0.115244 0.264616i
\(373\) −3.11212 + 5.39035i −0.161140 + 0.279102i −0.935278 0.353915i \(-0.884850\pi\)
0.774138 + 0.633017i \(0.218184\pi\)
\(374\) 0.520867 + 0.902168i 0.0269334 + 0.0466500i
\(375\) 0.651423 + 5.74765i 0.0336394 + 0.296807i
\(376\) −18.8325 10.8729i −0.971210 0.560728i
\(377\) 64.6413 3.32920
\(378\) −3.55836 + 13.3842i −0.183022 + 0.688407i
\(379\) 4.68995 0.240907 0.120453 0.992719i \(-0.461565\pi\)
0.120453 + 0.992719i \(0.461565\pi\)
\(380\) 1.58606 + 0.915711i 0.0813630 + 0.0469750i
\(381\) −2.14449 18.9213i −0.109865 0.969366i
\(382\) 9.82591 + 17.0190i 0.502737 + 0.870767i
\(383\) −15.1879 + 26.3062i −0.776066 + 1.34419i 0.158127 + 0.987419i \(0.449455\pi\)
−0.934193 + 0.356768i \(0.883879\pi\)
\(384\) 1.89549 4.35230i 0.0967289 0.222102i
\(385\) 0.0668120 0.891288i 0.00340506 0.0454242i
\(386\) 17.4721i 0.889304i
\(387\) 19.7723 4.54020i 1.00508 0.230791i
\(388\) 7.88085 4.55001i 0.400090 0.230992i
\(389\) 13.3267 7.69415i 0.675688 0.390109i −0.122540 0.992464i \(-0.539104\pi\)
0.798228 + 0.602355i \(0.205771\pi\)
\(390\) 2.93307 2.16768i 0.148522 0.109765i
\(391\) 0.932221i 0.0471444i
\(392\) 3.13830 20.8152i 0.158508 1.05133i
\(393\) 22.6761 + 9.87580i 1.14386 + 0.498168i
\(394\) 2.90330 5.02867i 0.146266 0.253340i
\(395\) −0.995419 1.72412i −0.0500850 0.0867497i
\(396\) −2.82542 0.867469i −0.141983 0.0435919i
\(397\) 17.0604 + 9.84982i 0.856236 + 0.494348i 0.862750 0.505631i \(-0.168740\pi\)
−0.00651405 + 0.999979i \(0.502074\pi\)
\(398\) −13.0693 −0.655106
\(399\) 11.7688 22.3020i 0.589179 1.11650i
\(400\) 5.17412 0.258706
\(401\) 30.2790 + 17.4816i 1.51206 + 0.872990i 0.999901 + 0.0141006i \(0.00448851\pi\)
0.512162 + 0.858889i \(0.328845\pi\)
\(402\) −18.3724 + 2.08228i −0.916330 + 0.103854i
\(403\) 10.0926 + 17.4810i 0.502750 + 0.870788i
\(404\) −0.457469 + 0.792360i −0.0227600 + 0.0394214i
\(405\) −0.219251 + 3.03247i −0.0108946 + 0.150685i
\(406\) −15.6857 + 23.0056i −0.778467 + 1.14175i
\(407\) 3.91631i 0.194124i
\(408\) 3.20134 + 4.33170i 0.158490 + 0.214451i
\(409\) 2.18524 1.26165i 0.108053 0.0623844i −0.445000 0.895531i \(-0.646796\pi\)
0.553053 + 0.833146i \(0.313463\pi\)
\(410\) −3.30814 + 1.90995i −0.163377 + 0.0943259i
\(411\) 5.34801 + 7.23636i 0.263798 + 0.356943i
\(412\) 2.46494i 0.121439i
\(413\) −6.10374 12.6752i −0.300345 0.623708i
\(414\) −1.85566 1.99467i −0.0912006 0.0980325i
\(415\) 1.17245 2.03075i 0.0575534 0.0996854i
\(416\) 15.3067 + 26.5120i 0.750474 + 1.29986i
\(417\) 1.41669 0.160564i 0.0693758 0.00786287i
\(418\) −4.80066 2.77166i −0.234808 0.135567i
\(419\) −15.0762 −0.736521 −0.368260 0.929723i \(-0.620046\pi\)
−0.368260 + 0.929723i \(0.620046\pi\)
\(420\) −0.0579952 1.52407i −0.00282988 0.0743669i
\(421\) 16.4642 0.802416 0.401208 0.915987i \(-0.368590\pi\)
0.401208 + 0.915987i \(0.368590\pi\)
\(422\) −4.86982 2.81159i −0.237059 0.136866i
\(423\) −6.36712 + 20.7383i −0.309580 + 1.00833i
\(424\) −13.1110 22.7089i −0.636726 1.10284i
\(425\) 2.52626 4.37561i 0.122542 0.212248i
\(426\) 14.4912 + 6.31114i 0.702102 + 0.305776i
\(427\) −7.06070 4.81413i −0.341691 0.232972i
\(428\) 8.10323i 0.391684i
\(429\) 8.61877 6.36968i 0.416118 0.307531i
\(430\) 1.99297 1.15064i 0.0961096 0.0554889i
\(431\) −15.1701 + 8.75845i −0.730717 + 0.421880i −0.818685 0.574243i \(-0.805296\pi\)
0.0879672 + 0.996123i \(0.471963\pi\)
\(432\) 5.40877 + 1.01237i 0.260230 + 0.0487077i
\(433\) 37.2422i 1.78974i 0.446322 + 0.894872i \(0.352733\pi\)
−0.446322 + 0.894872i \(0.647267\pi\)
\(434\) −8.67045 0.649947i −0.416195 0.0311985i
\(435\) −2.44079 + 5.60437i −0.117027 + 0.268709i
\(436\) −2.29078 + 3.96774i −0.109708 + 0.190020i
\(437\) 2.48029 + 4.29599i 0.118648 + 0.205505i
\(438\) 0.768873 + 6.78393i 0.0367382 + 0.324149i
\(439\) −23.4810 13.5567i −1.12069 0.647028i −0.179110 0.983829i \(-0.557322\pi\)
−0.941576 + 0.336801i \(0.890655\pi\)
\(440\) −1.01590 −0.0484310
\(441\) −20.9393 + 1.59591i −0.997108 + 0.0759958i
\(442\) −6.44574 −0.306593
\(443\) −15.4316 8.90943i −0.733177 0.423300i 0.0864065 0.996260i \(-0.472462\pi\)
−0.819583 + 0.572960i \(0.805795\pi\)
\(444\) −0.752597 6.64032i −0.0357167 0.315136i
\(445\) 0.616986 + 1.06865i 0.0292479 + 0.0506589i
\(446\) 1.16904 2.02484i 0.0553557 0.0958788i
\(447\) −0.792813 + 1.82040i −0.0374988 + 0.0861022i
\(448\) −18.7378 1.40461i −0.885278 0.0663615i
\(449\) 27.7358i 1.30893i 0.756092 + 0.654466i \(0.227106\pi\)
−0.756092 + 0.654466i \(0.772894\pi\)
\(450\) −3.30457 14.3912i −0.155779 0.678407i
\(451\) −9.72090 + 5.61237i −0.457740 + 0.264276i
\(452\) 3.86349 2.23059i 0.181723 0.104918i
\(453\) −20.3095 + 15.0097i −0.954221 + 0.705215i
\(454\) 0.418487i 0.0196406i
\(455\) 4.56931 + 3.11544i 0.214212 + 0.146054i
\(456\) −26.2779 11.4444i −1.23057 0.535933i
\(457\) 1.13233 1.96125i 0.0529682 0.0917436i −0.838326 0.545170i \(-0.816465\pi\)
0.891294 + 0.453426i \(0.149798\pi\)
\(458\) 3.22484 + 5.58559i 0.150687 + 0.260998i
\(459\) 3.49697 4.07976i 0.163224 0.190427i
\(460\) 0.259832 + 0.150014i 0.0121147 + 0.00699444i
\(461\) −20.6585 −0.962161 −0.481081 0.876676i \(-0.659756\pi\)
−0.481081 + 0.876676i \(0.659756\pi\)
\(462\) 0.175539 + 4.61303i 0.00816683 + 0.214618i
\(463\) 29.3828 1.36554 0.682768 0.730635i \(-0.260776\pi\)
0.682768 + 0.730635i \(0.260776\pi\)
\(464\) 9.58117 + 5.53169i 0.444795 + 0.256802i
\(465\) −1.89668 + 0.214964i −0.0879562 + 0.00996873i
\(466\) −0.393295 0.681208i −0.0182191 0.0315563i
\(467\) 20.3668 35.2764i 0.942464 1.63240i 0.181714 0.983351i \(-0.441836\pi\)
0.760750 0.649045i \(-0.224831\pi\)
\(468\) 13.3895 12.4564i 0.618932 0.575798i
\(469\) −12.1643 25.2609i −0.561696 1.16644i
\(470\) 2.46087i 0.113512i
\(471\) −12.2196 16.5343i −0.563050 0.761859i
\(472\) −13.8480 + 7.99516i −0.637407 + 0.368007i
\(473\) 5.85631 3.38114i 0.269273 0.155465i
\(474\) 6.11142 + 8.26933i 0.280707 + 0.379823i
\(475\) 26.8858i 1.23360i
\(476\) −1.51847 + 2.22709i −0.0695990 + 0.102078i
\(477\) −19.1526 + 17.8179i −0.876939 + 0.815824i
\(478\) −13.6532 + 23.6481i −0.624485 + 1.08164i
\(479\) −8.33913 14.4438i −0.381025 0.659954i 0.610184 0.792259i \(-0.291095\pi\)
−0.991209 + 0.132306i \(0.957762\pi\)
\(480\) −2.87654 + 0.326020i −0.131296 + 0.0148807i
\(481\) 20.9857 + 12.1161i 0.956867 + 0.552447i
\(482\) −12.5436 −0.571345
\(483\) 1.92800 3.65357i 0.0877271 0.166243i
\(484\) −0.985197 −0.0447817
\(485\) −2.70232 1.56018i −0.122706 0.0708442i
\(486\) −0.638644 15.6904i −0.0289695 0.711732i
\(487\) 0.404579 + 0.700752i 0.0183332 + 0.0317541i 0.875046 0.484039i \(-0.160831\pi\)
−0.856713 + 0.515793i \(0.827497\pi\)
\(488\) −4.85661 + 8.41190i −0.219848 + 0.380789i
\(489\) −23.1065 10.0632i −1.04491 0.455075i
\(490\) −2.21755 + 0.870213i −0.100179 + 0.0393122i
\(491\) 2.13467i 0.0963365i 0.998839 + 0.0481682i \(0.0153384\pi\)
−0.998839 + 0.0481682i \(0.984662\pi\)
\(492\) −15.4038 + 11.3841i −0.694457 + 0.513237i
\(493\) 9.35601 5.40169i 0.421374 0.243280i
\(494\) 29.7042 17.1497i 1.33645 0.771602i
\(495\) 0.226813 + 0.987755i 0.0101945 + 0.0443963i
\(496\) 3.45471i 0.155121i
\(497\) −1.79158 + 23.9001i −0.0803633 + 1.07207i
\(498\) −4.83593 + 11.1039i −0.216703 + 0.497579i
\(499\) −0.305648 + 0.529398i −0.0136827 + 0.0236991i −0.872786 0.488104i \(-0.837689\pi\)
0.859103 + 0.511803i \(0.171022\pi\)
\(500\) 1.64511 + 2.84941i 0.0735714 + 0.127429i
\(501\) 3.74244 + 33.0203i 0.167200 + 1.47524i
\(502\) −5.42651 3.13299i −0.242197 0.139832i
\(503\) 29.3406 1.30823 0.654116 0.756394i \(-0.273041\pi\)
0.654116 + 0.756394i \(0.273041\pi\)
\(504\) 3.58795 + 23.5978i 0.159820 + 1.05113i
\(505\) 0.313729 0.0139608
\(506\) −0.786456 0.454061i −0.0349622 0.0201855i
\(507\) 4.93209 + 43.5169i 0.219042 + 1.93265i
\(508\) −5.41569 9.38025i −0.240283 0.416182i
\(509\) 2.26128 3.91665i 0.100229 0.173602i −0.811550 0.584283i \(-0.801376\pi\)
0.911779 + 0.410681i \(0.134709\pi\)
\(510\) 0.243384 0.558842i 0.0107772 0.0247460i
\(511\) −9.32749 + 4.49163i −0.412624 + 0.198698i
\(512\) 11.6087i 0.513039i
\(513\) −5.26048 + 28.1050i −0.232256 + 1.24087i
\(514\) −0.456902 + 0.263793i −0.0201531 + 0.0116354i
\(515\) 0.731981 0.422609i 0.0322549 0.0186224i
\(516\) 9.27994 6.85832i 0.408527 0.301921i
\(517\) 7.23123i 0.318029i
\(518\) −9.40441 + 4.52868i −0.413206 + 0.198979i
\(519\) −32.7241 14.2518i −1.43643 0.625586i
\(520\) 3.14294 5.44373i 0.137827 0.238723i
\(521\) 5.56886 + 9.64555i 0.243976 + 0.422579i 0.961843 0.273601i \(-0.0882148\pi\)
−0.717867 + 0.696180i \(0.754881\pi\)
\(522\) 9.26651 30.1818i 0.405584 1.32102i
\(523\) 5.05795 + 2.92021i 0.221169 + 0.127692i 0.606491 0.795090i \(-0.292577\pi\)
−0.385323 + 0.922782i \(0.625910\pi\)
\(524\) 14.0684 0.614582
\(525\) 18.9505 11.9242i 0.827068 0.520414i
\(526\) 0.782716 0.0341280
\(527\) 2.92156 + 1.68676i 0.127265 + 0.0734766i
\(528\) 1.82256 0.206565i 0.0793169 0.00898958i
\(529\) −11.0937 19.2148i −0.482334 0.835426i
\(530\) −1.48371 + 2.56986i −0.0644482 + 0.111628i
\(531\) 10.8654 + 11.6794i 0.471519 + 0.506842i
\(532\) 1.07219 14.3033i 0.0464853 0.620125i
\(533\) 69.4532i 3.00835i
\(534\) −3.78802 5.12554i −0.163923 0.221804i
\(535\) 2.40631 1.38928i 0.104034 0.0600640i
\(536\) −27.5981 + 15.9338i −1.19206 + 0.688235i
\(537\) −0.852750 1.15385i −0.0367989 0.0497923i
\(538\) 12.0495i 0.519491i
\(539\) −6.51623 + 2.55711i −0.280674 + 0.110142i
\(540\) 0.574390 + 1.63121i 0.0247178 + 0.0701959i
\(541\) 15.8159 27.3939i 0.679978 1.17776i −0.295009 0.955494i \(-0.595323\pi\)
0.974987 0.222262i \(-0.0713439\pi\)
\(542\) −5.57196 9.65093i −0.239336 0.414543i
\(543\) 14.0256 1.58962i 0.601896 0.0682173i
\(544\) 4.43091 + 2.55819i 0.189974 + 0.109681i
\(545\) 1.57100 0.0672942
\(546\) −25.2622 13.3310i −1.08112 0.570513i
\(547\) 6.31442 0.269985 0.134993 0.990847i \(-0.456899\pi\)
0.134993 + 0.990847i \(0.456899\pi\)
\(548\) 4.43246 + 2.55908i 0.189345 + 0.109319i
\(549\) 9.26318 + 2.84401i 0.395343 + 0.121379i
\(550\) −2.46095 4.26250i −0.104935 0.181754i
\(551\) −28.7438 + 49.7857i −1.22453 + 2.12094i
\(552\) −4.30491 1.87485i −0.183229 0.0797989i
\(553\) −8.78351 + 12.8824i −0.373513 + 0.547817i
\(554\) 11.9395i 0.507260i
\(555\) −1.84286 + 1.36196i −0.0782250 + 0.0578120i
\(556\) 0.702329 0.405490i 0.0297854 0.0171966i
\(557\) 1.41798 0.818668i 0.0600815 0.0346881i −0.469658 0.882848i \(-0.655623\pi\)
0.529740 + 0.848160i \(0.322290\pi\)
\(558\) 9.60887 2.20643i 0.406776 0.0934057i
\(559\) 41.8417i 1.76972i
\(560\) 0.410660 + 0.852791i 0.0173536 + 0.0360370i
\(561\) 0.715180 1.64215i 0.0301949 0.0693316i
\(562\) −5.98952 + 10.3742i −0.252653 + 0.437608i
\(563\) 10.6341 + 18.4189i 0.448175 + 0.776263i 0.998267 0.0588414i \(-0.0187406\pi\)
−0.550092 + 0.835104i \(0.685407\pi\)
\(564\) 1.38962 + 12.2610i 0.0585138 + 0.516279i
\(565\) −1.32478 0.764860i −0.0557338 0.0321779i
\(566\) −27.9057 −1.17297
\(567\) 22.1430 8.75708i 0.929920 0.367763i
\(568\) 27.2415 1.14303
\(569\) −5.93181 3.42473i −0.248674 0.143572i 0.370483 0.928839i \(-0.379192\pi\)
−0.619157 + 0.785267i \(0.712526\pi\)
\(570\) 0.365274 + 3.22289i 0.0152996 + 0.134992i
\(571\) −10.7464 18.6134i −0.449725 0.778946i 0.548643 0.836057i \(-0.315145\pi\)
−0.998368 + 0.0571108i \(0.981811\pi\)
\(572\) 3.04796 5.27922i 0.127442 0.220735i
\(573\) 13.4915 30.9784i 0.563617 1.29414i
\(574\) 24.7181 + 16.8533i 1.03171 + 0.703443i
\(575\) 4.40449i 0.183680i
\(576\) 20.7658 4.76835i 0.865244 0.198681i
\(577\) 2.43897 1.40814i 0.101536 0.0586216i −0.448372 0.893847i \(-0.647996\pi\)
0.549908 + 0.835225i \(0.314663\pi\)
\(578\) 13.8981 8.02405i 0.578083 0.333757i
\(579\) 24.1592 17.8548i 1.00402 0.742019i
\(580\) 3.47699i 0.144374i
\(581\) −18.3135 1.37280i −0.759772 0.0569534i
\(582\) 14.7760 + 6.43517i 0.612486 + 0.266747i
\(583\) −4.35985 + 7.55149i −0.180567 + 0.312751i
\(584\) 5.88349 + 10.1905i 0.243461 + 0.421686i
\(585\) −5.99463 1.84049i −0.247847 0.0760948i
\(586\) 9.18959 + 5.30561i 0.379619 + 0.219173i
\(587\) −35.6049 −1.46957 −0.734785 0.678300i \(-0.762717\pi\)
−0.734785 + 0.678300i \(0.762717\pi\)
\(588\) −10.5572 + 5.58794i −0.435372 + 0.230443i
\(589\) −17.9514 −0.739674
\(590\) 1.56711 + 0.904773i 0.0645170 + 0.0372489i
\(591\) −9.92019 + 1.12433i −0.408062 + 0.0462487i
\(592\) 2.07368 + 3.59171i 0.0852276 + 0.147618i
\(593\) 11.0826 19.1956i 0.455107 0.788269i −0.543587 0.839353i \(-0.682934\pi\)
0.998694 + 0.0510837i \(0.0162675\pi\)
\(594\) −1.73856 4.93732i −0.0713339 0.202581i
\(595\) 0.921688 + 0.0690908i 0.0377855 + 0.00283245i
\(596\) 1.12939i 0.0462616i
\(597\) 13.3556 + 18.0714i 0.546608 + 0.739612i
\(598\) 4.86621 2.80951i 0.198994 0.114889i
\(599\) 24.1121 13.9211i 0.985193 0.568802i 0.0813594 0.996685i \(-0.474074\pi\)
0.903834 + 0.427883i \(0.140741\pi\)
\(600\) −15.1254 20.4661i −0.617493 0.835526i
\(601\) 28.3202i 1.15521i −0.816318 0.577603i \(-0.803988\pi\)
0.816318 0.577603i \(-0.196012\pi\)
\(602\) −14.8913 10.1532i −0.606924 0.413813i
\(603\) 21.6540 + 23.2762i 0.881820 + 0.947879i
\(604\) −7.18228 + 12.4401i −0.292243 + 0.506179i
\(605\) 0.168910 + 0.292561i 0.00686717 + 0.0118943i
\(606\) −1.61009 + 0.182483i −0.0654053 + 0.00741287i
\(607\) 22.3848 + 12.9239i 0.908573 + 0.524565i 0.879972 0.475026i \(-0.157561\pi\)
0.0286011 + 0.999591i \(0.490895\pi\)
\(608\) −27.2255 −1.10414
\(609\) 47.8398 1.82045i 1.93857 0.0737682i
\(610\) 1.09920 0.0445053
\(611\) −38.7489 22.3717i −1.56761 0.905061i
\(612\) 0.897056 2.92179i 0.0362613 0.118106i
\(613\) −9.15558 15.8579i −0.369790 0.640496i 0.619742 0.784805i \(-0.287237\pi\)
−0.989533 + 0.144310i \(0.953904\pi\)
\(614\) −0.743624 + 1.28799i −0.0300102 + 0.0519792i
\(615\) 6.02155 + 2.62248i 0.242813 + 0.105748i
\(616\) 3.45197 + 7.16848i 0.139084 + 0.288826i
\(617\) 41.3739i 1.66565i −0.553537 0.832825i \(-0.686722\pi\)
0.553537 0.832825i \(-0.313278\pi\)
\(618\) −3.51078 + 2.59463i −0.141224 + 0.104371i
\(619\) −14.6907 + 8.48170i −0.590470 + 0.340908i −0.765284 0.643693i \(-0.777401\pi\)
0.174813 + 0.984602i \(0.444068\pi\)
\(620\) −0.940281 + 0.542871i −0.0377626 + 0.0218022i
\(621\) −0.861785 + 4.60424i −0.0345823 + 0.184762i
\(622\) 22.5305i 0.903391i
\(623\) 5.44424 7.98487i 0.218119 0.319907i
\(624\) −4.53168 + 10.4054i −0.181413 + 0.416547i
\(625\) −11.6506 + 20.1794i −0.466024 + 0.807177i
\(626\) 0.891054 + 1.54335i 0.0356137 + 0.0616847i
\(627\) 1.07335 + 9.47041i 0.0428655 + 0.378212i
\(628\) −10.1277 5.84721i −0.404138 0.233329i
\(629\) 4.04989 0.161480
\(630\) 2.10966 1.68686i 0.0840509 0.0672060i
\(631\) 0.630437 0.0250973 0.0125487 0.999921i \(-0.496006\pi\)
0.0125487 + 0.999921i \(0.496006\pi\)
\(632\) 15.3477 + 8.86103i 0.610501 + 0.352473i
\(633\) 1.08881 + 9.60683i 0.0432765 + 0.381837i
\(634\) −5.77352 10.0000i −0.229296 0.397152i
\(635\) −1.85702 + 3.21646i −0.0736936 + 0.127641i
\(636\) −5.94120 + 13.6418i −0.235584 + 0.540932i
\(637\) 6.45724 42.8286i 0.255845 1.69693i
\(638\) 10.5241i 0.416653i
\(639\) −6.08203 26.4869i −0.240602 1.04780i
\(640\) −0.801841 + 0.462943i −0.0316956 + 0.0182994i
\(641\) −11.7256 + 6.76979i −0.463134 + 0.267391i −0.713361 0.700797i \(-0.752828\pi\)
0.250227 + 0.968187i \(0.419495\pi\)
\(642\) −11.5413 + 8.52958i −0.455499 + 0.336635i
\(643\) 1.36678i 0.0539005i 0.999637 + 0.0269503i \(0.00857958\pi\)
−0.999637 + 0.0269503i \(0.991420\pi\)
\(644\) 0.175649 2.34319i 0.00692152 0.0923347i
\(645\) −3.62766 1.57990i −0.142839 0.0622084i
\(646\) 2.86620 4.96440i 0.112769 0.195322i
\(647\) −7.64192 13.2362i −0.300435 0.520368i 0.675800 0.737085i \(-0.263798\pi\)
−0.976234 + 0.216717i \(0.930465\pi\)
\(648\) −11.8070 24.3537i −0.463822 0.956705i
\(649\) 4.60494 + 2.65866i 0.180760 + 0.104362i
\(650\) 30.4544 1.19452
\(651\) 7.96167 + 12.6531i 0.312042 + 0.495914i
\(652\) −14.3354 −0.561419
\(653\) 7.60587 + 4.39125i 0.297641 + 0.171843i 0.641382 0.767221i \(-0.278361\pi\)
−0.343742 + 0.939064i \(0.611695\pi\)
\(654\) −8.06251 + 0.913784i −0.315269 + 0.0357318i
\(655\) −2.41200 4.17771i −0.0942448 0.163237i
\(656\) 5.94347 10.2944i 0.232053 0.401928i
\(657\) 8.59464 7.99568i 0.335309 0.311941i
\(658\) 17.3647 8.36193i 0.676945 0.325982i
\(659\) 16.6074i 0.646932i −0.946240 0.323466i \(-0.895152\pi\)
0.946240 0.323466i \(-0.104848\pi\)
\(660\) 0.342618 + 0.463594i 0.0133364 + 0.0180454i
\(661\) 30.8566 17.8151i 1.20018 0.692927i 0.239588 0.970875i \(-0.422988\pi\)
0.960596 + 0.277948i \(0.0896542\pi\)
\(662\) 3.56131 2.05612i 0.138414 0.0799135i
\(663\) 6.58694 + 8.91274i 0.255815 + 0.346142i
\(664\) 20.8739i 0.810064i
\(665\) −4.43128 + 2.13387i −0.171837 + 0.0827480i
\(666\) 8.66552 8.06161i 0.335782 0.312381i
\(667\) −4.70888 + 8.15601i −0.182328 + 0.315802i
\(668\) 9.45116 + 16.3699i 0.365676 + 0.633370i
\(669\) −3.99446 + 0.452721i −0.154435 + 0.0175032i
\(670\) 3.12315 + 1.80315i 0.120658 + 0.0696617i
\(671\) 3.22998 0.124692
\(672\) 12.0749 + 19.1900i 0.465798 + 0.740269i
\(673\) −3.23910 −0.124858 −0.0624290 0.998049i \(-0.519885\pi\)
−0.0624290 + 0.998049i \(0.519885\pi\)
\(674\) −24.6703 14.2434i −0.950263 0.548635i
\(675\) −16.5222 + 19.2758i −0.635940 + 0.741925i
\(676\) 12.4555 + 21.5736i 0.479058 + 0.829753i
\(677\) −9.42272 + 16.3206i −0.362145 + 0.627253i −0.988314 0.152435i \(-0.951289\pi\)
0.626169 + 0.779687i \(0.284622\pi\)
\(678\) 7.24376 + 3.15476i 0.278195 + 0.121158i
\(679\) −1.82679 + 24.3698i −0.0701057 + 0.935227i
\(680\) 1.05055i 0.0402866i
\(681\) −0.578655 + 0.427654i −0.0221741 + 0.0163877i
\(682\) 2.84603 1.64316i 0.108980 0.0629198i
\(683\) −25.0963 + 14.4894i −0.960284 + 0.554420i −0.896260 0.443528i \(-0.853727\pi\)
−0.0640233 + 0.997948i \(0.520393\pi\)
\(684\) 3.63985 + 15.8513i 0.139173 + 0.606091i
\(685\) 1.75500i 0.0670551i
\(686\) 13.6756 + 12.6908i 0.522137 + 0.484535i
\(687\) 4.42790 10.1670i 0.168935 0.387897i
\(688\) −3.58061 + 6.20180i −0.136510 + 0.236441i
\(689\) −26.9767 46.7249i −1.02773 1.78008i
\(690\) 0.0598401 + 0.527982i 0.00227807 + 0.0200999i
\(691\) 17.6136 + 10.1692i 0.670052 + 0.386855i 0.796096 0.605170i \(-0.206895\pi\)
−0.126044 + 0.992025i \(0.540228\pi\)
\(692\) −20.3022 −0.771775
\(693\) 6.19920 4.95680i 0.235488 0.188293i
\(694\) −19.4284 −0.737494
\(695\) −0.240826 0.139041i −0.00913505 0.00527412i
\(696\) −6.12802 54.0689i −0.232282 2.04947i
\(697\) −5.80379 10.0525i −0.219834 0.380764i
\(698\) 2.79432 4.83991i 0.105767 0.183193i
\(699\) −0.540017 + 1.23995i −0.0204253 + 0.0468993i
\(700\) 7.17436 10.5224i 0.271165 0.397708i
\(701\) 16.8832i 0.637670i 0.947810 + 0.318835i \(0.103292\pi\)
−0.947810 + 0.318835i \(0.896708\pi\)
\(702\) 31.8355 + 5.95872i 1.20155 + 0.224898i
\(703\) −18.6633 + 10.7752i −0.703898 + 0.406396i
\(704\) 6.15059 3.55105i 0.231809 0.133835i
\(705\) 3.40273 2.51478i 0.128154 0.0947120i
\(706\) 15.3129i 0.576310i
\(707\) −1.06604 2.21377i −0.0400924 0.0832574i
\(708\) 8.31884 + 3.62298i 0.312641 + 0.136160i
\(709\) 20.7229 35.8931i 0.778264 1.34799i −0.154677 0.987965i \(-0.549434\pi\)
0.932941 0.360028i \(-0.117233\pi\)
\(710\) −1.54140 2.66978i −0.0578476 0.100195i
\(711\) 5.18897 16.9009i 0.194602 0.633834i
\(712\) −9.51292 5.49229i −0.356512 0.205832i
\(713\) −2.94084 −0.110135
\(714\) −4.77037 + 0.181527i −0.178527 + 0.00679346i
\(715\) −2.09027 −0.0781716
\(716\) −0.706763 0.408050i −0.0264130 0.0152495i
\(717\) 46.6513 5.28734i 1.74223 0.197459i
\(718\) −12.2265 21.1769i −0.456289 0.790316i
\(719\) 11.4358 19.8073i 0.426482 0.738689i −0.570075 0.821592i \(-0.693086\pi\)
0.996558 + 0.0829037i \(0.0264194\pi\)
\(720\) −0.731027 0.785789i −0.0272438 0.0292846i
\(721\) −5.46930 3.72908i −0.203687 0.138878i
\(722\) 11.3634i 0.422903i
\(723\) 12.8183 + 17.3444i 0.476720 + 0.645046i
\(724\) 6.95321 4.01444i 0.258414 0.149196i
\(725\) −44.2046 + 25.5215i −1.64172 + 0.947846i
\(726\) −1.03703 1.40320i −0.0384879 0.0520777i
\(727\) 6.85223i 0.254135i −0.991894 0.127067i \(-0.959444\pi\)
0.991894 0.127067i \(-0.0405565\pi\)
\(728\) −49.0922 3.68001i −1.81948 0.136390i
\(729\) −21.0430 + 16.9172i −0.779371 + 0.626563i
\(730\) 0.665807 1.15321i 0.0246426 0.0426822i
\(731\) 3.49647 + 6.05606i 0.129321 + 0.223991i
\(732\) 5.47660 0.620704i 0.202421 0.0229419i
\(733\) −8.40368 4.85187i −0.310397 0.179208i 0.336707 0.941609i \(-0.390687\pi\)
−0.647104 + 0.762402i \(0.724020\pi\)
\(734\) 33.3096 1.22948
\(735\) 3.46939 + 2.17700i 0.127971 + 0.0802998i
\(736\) −4.46015 −0.164403
\(737\) 9.17731 + 5.29852i 0.338051 + 0.195174i
\(738\) −32.4285 9.95630i −1.19371 0.366496i
\(739\) −7.19141 12.4559i −0.264540 0.458197i 0.702903 0.711286i \(-0.251887\pi\)
−0.967443 + 0.253089i \(0.918554\pi\)
\(740\) −0.651712 + 1.12880i −0.0239574 + 0.0414955i
\(741\) −54.0683 23.5475i −1.98625 0.865041i
\(742\) 23.1753 + 1.73725i 0.850792 + 0.0637764i
\(743\) 13.4799i 0.494531i 0.968948 + 0.247265i \(0.0795319\pi\)
−0.968948 + 0.247265i \(0.920468\pi\)
\(744\) 13.6650 10.0991i 0.500985 0.370252i
\(745\) 0.335380 0.193632i 0.0122874 0.00709412i
\(746\) −5.43010 + 3.13507i −0.198810 + 0.114783i
\(747\) 20.2956 4.66037i 0.742578 0.170514i
\(748\) 1.01880i 0.0372510i
\(749\) −17.9797 12.2589i −0.656965 0.447932i
\(750\) −2.32671 + 5.34243i −0.0849593 + 0.195078i
\(751\) −8.97435 + 15.5440i −0.327479 + 0.567209i −0.982011 0.188825i \(-0.939532\pi\)
0.654532 + 0.756034i \(0.272866\pi\)
\(752\) −3.82892 6.63188i −0.139626 0.241840i
\(753\) 1.21328 + 10.7050i 0.0442144 + 0.390113i
\(754\) 56.3939 + 32.5590i 2.05374 + 1.18573i
\(755\) 4.92555 0.179259
\(756\) 9.55854 9.59583i 0.347641 0.348997i
\(757\) −6.03729 −0.219429 −0.109714 0.993963i \(-0.534994\pi\)
−0.109714 + 0.993963i \(0.534994\pi\)
\(758\) 4.09157 + 2.36227i 0.148612 + 0.0858015i
\(759\) 0.175839 + 1.55147i 0.00638255 + 0.0563146i
\(760\) 2.79511 + 4.84128i 0.101389 + 0.175612i
\(761\) 18.9559 32.8326i 0.687151 1.19018i −0.285605 0.958348i \(-0.592194\pi\)
0.972756 0.231833i \(-0.0744723\pi\)
\(762\) 7.65952 17.5873i 0.277475 0.637120i
\(763\) −5.33818 11.0855i −0.193255 0.401320i
\(764\) 19.2192i 0.695326i
\(765\) −1.02144 + 0.234549i −0.0369304 + 0.00848013i
\(766\) −26.5002 + 15.2999i −0.957493 + 0.552809i
\(767\) −28.4931 + 16.4505i −1.02883 + 0.593993i
\(768\) 23.6313 17.4646i 0.852720 0.630201i
\(769\) 9.07800i 0.327361i −0.986513 0.163681i \(-0.947663\pi\)
0.986513 0.163681i \(-0.0523366\pi\)
\(770\) 0.507218 0.743918i 0.0182789 0.0268089i
\(771\) 0.831665 + 0.362202i 0.0299517 + 0.0130444i
\(772\) 8.54370 14.7981i 0.307494 0.532596i
\(773\) 24.1552 + 41.8380i 0.868802 + 1.50481i 0.863222 + 0.504824i \(0.168443\pi\)
0.00557968 + 0.999984i \(0.498224\pi\)
\(774\) 19.5364 + 5.99812i 0.702222 + 0.215598i
\(775\) −13.8036 7.96950i −0.495839 0.286273i
\(776\) 27.7769 0.997132
\(777\) 15.8724 + 8.37590i 0.569417 + 0.300484i
\(778\) 15.5018 0.555766
\(779\) 53.4917 + 30.8834i 1.91654 + 1.10651i
\(780\) −3.54416 + 0.401686i −0.126901 + 0.0143827i
\(781\) −4.52937 7.84509i −0.162073 0.280720i
\(782\) 0.469548 0.813281i 0.0167910 0.0290829i
\(783\) −51.2029 + 18.0299i −1.82984 + 0.644335i
\(784\) 4.62216 5.79549i 0.165077 0.206982i
\(785\) 4.00998i 0.143122i
\(786\) 14.8086 + 20.0374i 0.528206 + 0.714712i
\(787\) −1.67827 + 0.968947i −0.0598237 + 0.0345392i −0.529614 0.848239i \(-0.677663\pi\)
0.469790 + 0.882778i \(0.344330\pi\)
\(788\) −4.91796 + 2.83938i −0.175195 + 0.101149i
\(789\) −0.799861 1.08229i −0.0284758 0.0385304i
\(790\) 2.00552i 0.0713532i
\(791\) −0.895560 + 11.9470i −0.0318425 + 0.424786i
\(792\) −6.14494 6.60527i −0.218351 0.234708i
\(793\) −9.99277 + 17.3080i −0.354854 + 0.614624i
\(794\) 9.92245 + 17.1862i 0.352135 + 0.609915i
\(795\) 5.06964 0.574579i 0.179801 0.0203782i
\(796\) 11.0692 + 6.39079i 0.392337 + 0.226516i
\(797\) −21.5831 −0.764512 −0.382256 0.924057i \(-0.624853\pi\)
−0.382256 + 0.924057i \(0.624853\pi\)
\(798\) 21.5005 13.5287i 0.761110 0.478911i
\(799\) −7.47788 −0.264548
\(800\) −20.9348 12.0867i −0.740158 0.427330i
\(801\) −3.21625 + 10.4756i −0.113641 + 0.370138i
\(802\) 17.6105 + 30.5023i 0.621849 + 1.07707i
\(803\) 1.95646 3.38869i 0.0690420 0.119584i
\(804\) 16.5789 + 7.22034i 0.584691 + 0.254642i
\(805\) −0.725942 + 0.349576i −0.0255861 + 0.0123209i
\(806\) 20.3341i 0.716239i
\(807\) −16.6612 + 12.3134i −0.586503 + 0.433454i
\(808\) −2.41860 + 1.39638i −0.0850860 + 0.0491244i
\(809\) −8.50377 + 4.90965i −0.298977 + 0.172614i −0.641983 0.766719i \(-0.721888\pi\)
0.343006 + 0.939333i \(0.388555\pi\)
\(810\) −1.71869 + 2.53513i −0.0603887 + 0.0890753i
\(811\) 32.6254i 1.14563i −0.819684 0.572817i \(-0.805851\pi\)
0.819684 0.572817i \(-0.194149\pi\)
\(812\) 24.5347 11.8146i 0.860998 0.414612i
\(813\) −7.65063 + 17.5669i −0.268319 + 0.616097i
\(814\) 1.97260 3.41664i 0.0691394 0.119753i
\(815\) 2.45778 + 4.25701i 0.0860924 + 0.149116i
\(816\) 0.213610 + 1.88473i 0.00747785 + 0.0659787i
\(817\) −32.2258 18.6056i −1.12744 0.650927i
\(818\) 2.54190 0.0888755
\(819\) 7.38242 + 48.5538i 0.257963 + 1.69661i
\(820\) 3.73581 0.130460
\(821\) −0.270687 0.156281i −0.00944703 0.00545425i 0.495269 0.868740i \(-0.335069\pi\)
−0.504716 + 0.863285i \(0.668403\pi\)
\(822\) 1.02081 + 9.00681i 0.0356048 + 0.314149i
\(823\) 14.3081 + 24.7823i 0.498749 + 0.863858i 0.999999 0.00144440i \(-0.000459768\pi\)
−0.501250 + 0.865302i \(0.667126\pi\)
\(824\) −3.76199 + 6.51595i −0.131055 + 0.226994i
\(825\) −3.37903 + 7.75871i −0.117643 + 0.270124i
\(826\) 1.05938 14.1324i 0.0368606 0.491729i
\(827\) 50.6285i 1.76052i −0.474487 0.880262i \(-0.657366\pi\)
0.474487 0.880262i \(-0.342634\pi\)
\(828\) 0.596290 + 2.59680i 0.0207225 + 0.0902452i
\(829\) 8.10428 4.67901i 0.281473 0.162509i −0.352617 0.935768i \(-0.614708\pi\)
0.634090 + 0.773259i \(0.281375\pi\)
\(830\) 2.04572 1.18110i 0.0710081 0.0409965i
\(831\) 16.5091 12.2010i 0.572694 0.423248i
\(832\) 43.9443i 1.52349i
\(833\) −2.64433 6.73848i −0.0916204 0.233475i
\(834\) 1.31681 + 0.573492i 0.0455976 + 0.0198584i
\(835\) 3.24077 5.61317i 0.112151 0.194252i
\(836\) 2.71064 + 4.69497i 0.0937496 + 0.162379i
\(837\) −12.8703 11.0317i −0.444861 0.381313i
\(838\) −13.1527 7.59369i −0.454351 0.262320i
\(839\) 14.1563 0.488730 0.244365 0.969683i \(-0.421421\pi\)
0.244365 + 0.969683i \(0.421421\pi\)
\(840\) 2.17272 4.11731i 0.0749660 0.142061i
\(841\) −80.1411 −2.76349
\(842\) 14.3636 + 8.29281i 0.495001 + 0.285789i
\(843\) 20.4654 2.31950i 0.704866 0.0798877i
\(844\) 2.74969 + 4.76261i 0.0946483 + 0.163936i
\(845\) 4.27095 7.39750i 0.146925 0.254482i
\(846\) −16.0004 + 14.8853i −0.550104 + 0.511767i
\(847\) 1.49045 2.18599i 0.0512125 0.0751115i
\(848\) 9.23412i 0.317101i
\(849\) 28.5170 + 38.5862i 0.978701 + 1.32427i
\(850\) 4.40788 2.54489i 0.151189 0.0872891i
\(851\) −3.05746 + 1.76523i −0.104808 + 0.0605111i
\(852\) −9.18738 12.4314i −0.314755 0.425892i
\(853\) 8.47986i 0.290345i 0.989406 + 0.145172i \(0.0463737\pi\)
−0.989406 + 0.145172i \(0.953626\pi\)
\(854\) −3.73503 7.75628i −0.127810 0.265415i
\(855\) 4.08312 3.79856i 0.139640 0.129908i
\(856\) −12.3671 + 21.4205i −0.422700 + 0.732138i
\(857\) −12.7652 22.1100i −0.436050 0.755262i 0.561330 0.827592i \(-0.310290\pi\)
−0.997381 + 0.0723303i \(0.976956\pi\)
\(858\) 10.7274 1.21582i 0.366229 0.0415074i
\(859\) 21.5846 + 12.4619i 0.736458 + 0.425195i 0.820780 0.571244i \(-0.193539\pi\)
−0.0843218 + 0.996439i \(0.526872\pi\)
\(860\) −2.25062 −0.0767455
\(861\) −1.95596 51.4010i −0.0666589 1.75174i
\(862\) −17.6461 −0.601028
\(863\) 18.7071 + 10.8006i 0.636799 + 0.367656i 0.783380 0.621543i \(-0.213494\pi\)
−0.146582 + 0.989199i \(0.546827\pi\)
\(864\) −19.5193 16.7310i −0.664062 0.569200i
\(865\) 3.48078 + 6.02889i 0.118350 + 0.204988i
\(866\) −18.7584 + 32.4905i −0.637437 + 1.10407i
\(867\) −25.2976 11.0175i −0.859152 0.374173i
\(868\) 7.02570 + 4.79026i 0.238468 + 0.162592i
\(869\) 5.89319i 0.199913i
\(870\) −4.95222 + 3.65993i −0.167896 + 0.124083i
\(871\) −56.7848 + 32.7847i −1.92408 + 1.11087i
\(872\) −12.1111 + 6.99237i −0.410135 + 0.236791i
\(873\) −6.20156 27.0074i −0.209891 0.914062i
\(874\) 4.99716i 0.169032i
\(875\) −8.81116 0.660495i −0.297872 0.0223288i
\(876\) 2.66608 6.12169i 0.0900786 0.206833i
\(877\) −19.1285 + 33.1315i −0.645924 + 1.11877i 0.338164 + 0.941087i \(0.390194\pi\)
−0.984087 + 0.177685i \(0.943139\pi\)
\(878\) −13.6567 23.6541i −0.460892 0.798288i
\(879\) −2.05465 18.1286i −0.0693015 0.611462i
\(880\) −0.309821 0.178875i −0.0104440 0.00602987i
\(881\) −5.41544 −0.182451 −0.0912255 0.995830i \(-0.529078\pi\)
−0.0912255 + 0.995830i \(0.529078\pi\)
\(882\) −19.0715 9.15455i −0.642171 0.308250i
\(883\) 39.9085 1.34303 0.671514 0.740992i \(-0.265645\pi\)
0.671514 + 0.740992i \(0.265645\pi\)
\(884\) 5.45928 + 3.15192i 0.183616 + 0.106010i
\(885\) −0.350381 3.09149i −0.0117779 0.103919i
\(886\) −8.97513 15.5454i −0.301525 0.522257i
\(887\) 9.36502 16.2207i 0.314447 0.544638i −0.664873 0.746956i \(-0.731514\pi\)
0.979320 + 0.202319i \(0.0648477\pi\)
\(888\) 8.14499 18.7020i 0.273328 0.627598i
\(889\) 29.0064 + 2.17435i 0.972842 + 0.0729254i
\(890\) 1.24307i 0.0416679i
\(891\) −5.05035 + 7.44943i −0.169193 + 0.249565i
\(892\) −1.98026 + 1.14330i −0.0663040 + 0.0382806i
\(893\) 34.4606 19.8958i 1.15318 0.665788i
\(894\) −1.60857 + 1.18881i −0.0537988 + 0.0397598i
\(895\) 0.279837i 0.00935394i
\(896\) 5.99129 + 4.08498i 0.200155 + 0.136470i
\(897\) −8.85760 3.85762i −0.295747 0.128802i
\(898\) −13.9702 + 24.1970i −0.466190 + 0.807465i
\(899\) −17.0405 29.5150i −0.568333 0.984381i
\(900\) −4.23835 + 13.8047i −0.141278 + 0.460155i
\(901\) −7.80905 4.50856i −0.260157 0.150202i
\(902\) −11.3075 −0.376499
\(903\) 1.17836 + 30.9663i 0.0392133 + 1.03049i
\(904\) 13.6173 0.452904
\(905\) −2.38423 1.37654i −0.0792546 0.0457576i
\(906\) −25.2784 + 2.86499i −0.839818 + 0.0951828i
\(907\) −17.1561 29.7152i −0.569658 0.986677i −0.996600 0.0823976i \(-0.973742\pi\)
0.426941 0.904279i \(-0.359591\pi\)
\(908\) −0.204637 + 0.354441i −0.00679111 + 0.0117625i
\(909\) 1.89768 + 2.03984i 0.0629421 + 0.0676572i
\(910\) 2.41711 + 5.01945i 0.0801263 + 0.166393i
\(911\) 40.7756i 1.35095i −0.737381 0.675477i \(-0.763938\pi\)
0.737381 0.675477i \(-0.236062\pi\)
\(912\) −5.99894 8.11713i −0.198645 0.268785i
\(913\) 6.01132 3.47064i 0.198946 0.114861i
\(914\) 1.97572 1.14068i 0.0653509 0.0377304i
\(915\) −1.12328 1.51990i −0.0371344 0.0502463i
\(916\) 6.30769i 0.208412i
\(917\) −21.2834 + 31.2155i −0.702839 + 1.03083i
\(918\) 5.10572 1.79786i 0.168514 0.0593381i
\(919\) −16.9993 + 29.4436i −0.560754 + 0.971254i 0.436677 + 0.899618i \(0.356155\pi\)
−0.997431 + 0.0716354i \(0.977178\pi\)
\(920\) 0.457902 + 0.793110i 0.0150966 + 0.0261481i
\(921\) 2.54086 0.287975i 0.0837243 0.00948910i
\(922\) −18.0227 10.4054i −0.593546 0.342684i
\(923\) 56.0510 1.84494
\(924\) 2.10706 3.99289i 0.0693172 0.131356i
\(925\) −19.1346 −0.629142
\(926\) 25.6339 + 14.7998i 0.842383 + 0.486350i
\(927\) 7.17536 + 2.20300i 0.235670 + 0.0723560i
\(928\) −25.8440 44.7632i −0.848372 1.46942i
\(929\) −26.6421 + 46.1454i −0.874098 + 1.51398i −0.0163773 + 0.999866i \(0.505213\pi\)
−0.857721 + 0.514116i \(0.828120\pi\)
\(930\) −1.76296 0.767794i −0.0578096 0.0251770i
\(931\) 30.1145 + 24.0176i 0.986964 + 0.787146i
\(932\) 0.769273i 0.0251984i
\(933\) −31.1537 + 23.0240i −1.01992 + 0.753773i
\(934\) 35.5365 20.5170i 1.16279 0.671337i
\(935\) −0.302540 + 0.174671i −0.00989410 + 0.00571236i
\(936\) 54.4056 12.4928i 1.77830 0.408342i
\(937\) 45.4029i 1.48325i −0.670816 0.741623i \(-0.734056\pi\)
0.670816 0.741623i \(-0.265944\pi\)
\(938\) 2.11127 28.1649i 0.0689356 0.919617i
\(939\) 1.22347 2.80925i 0.0399264 0.0916763i
\(940\) 1.20335 2.08426i 0.0392489 0.0679810i
\(941\) 18.0339 + 31.2356i 0.587888 + 1.01825i 0.994509 + 0.104655i \(0.0333740\pi\)
−0.406620 + 0.913597i \(0.633293\pi\)
\(942\) −2.33243 20.5796i −0.0759948 0.670518i
\(943\) 8.76314 + 5.05940i 0.285367 + 0.164757i
\(944\) −5.63102 −0.183274
\(945\) −4.48834 1.19329i −0.146006 0.0388176i
\(946\) 6.81215 0.221482
\(947\) 32.9502 + 19.0238i 1.07074 + 0.618191i 0.928383 0.371625i \(-0.121199\pi\)
0.142355 + 0.989816i \(0.454533\pi\)
\(948\) −1.13249 9.99222i −0.0367816 0.324532i
\(949\) 12.1056 + 20.9676i 0.392965 + 0.680636i
\(950\) −13.5420 + 23.4555i −0.439361 + 0.760995i
\(951\) −7.92738 + 18.2023i −0.257063 + 0.590250i
\(952\) −7.41298 + 3.56971i −0.240256 + 0.115695i
\(953\) 48.8499i 1.58241i 0.611554 + 0.791203i \(0.290545\pi\)
−0.611554 + 0.791203i \(0.709455\pi\)
\(954\) −25.6836 + 5.89759i −0.831538 + 0.190941i
\(955\) −5.70727 + 3.29509i −0.184683 + 0.106627i
\(956\) 23.1275 13.3527i 0.747996 0.431856i
\(957\) −14.5520 + 10.7546i −0.470400 + 0.347648i
\(958\) 16.8013i 0.542824i
\(959\) −12.3838 + 5.96340i −0.399894 + 0.192568i
\(960\) −3.80995 1.65929i −0.122966 0.0535533i
\(961\) −10.1788 + 17.6303i −0.328350 + 0.568718i
\(962\) 12.2055 + 21.1405i 0.393520 + 0.681597i
\(963\) 23.5882 + 7.24212i 0.760120 + 0.233374i
\(964\) 10.6239 + 6.13371i 0.342173 + 0.197554i
\(965\) −5.85921 −0.188615
\(966\) 3.52227 2.21631i 0.113327 0.0713085i
\(967\) −39.0059 −1.25435 −0.627173 0.778880i \(-0.715788\pi\)
−0.627173 + 0.778880i \(0.715788\pi\)
\(968\) −2.60432 1.50361i −0.0837061 0.0483277i
\(969\) −9.79342 + 1.10996i −0.314610 + 0.0356571i
\(970\) −1.57169 2.72224i −0.0504639 0.0874060i
\(971\) −6.71773 + 11.6354i −0.215582 + 0.373399i −0.953453 0.301543i \(-0.902498\pi\)
0.737870 + 0.674943i \(0.235832\pi\)
\(972\) −7.13159 + 13.6014i −0.228746 + 0.436266i
\(973\) −0.162800 + 2.17180i −0.00521914 + 0.0696246i
\(974\) 0.815126i 0.0261183i
\(975\) −31.1215 42.1102i −0.996685 1.34861i
\(976\) −2.96227 + 1.71026i −0.0948198 + 0.0547442i
\(977\) −6.62790 + 3.82662i −0.212045 + 0.122424i −0.602262 0.798299i \(-0.705734\pi\)
0.390216 + 0.920723i \(0.372400\pi\)
\(978\) −15.0897 20.4178i −0.482515 0.652888i
\(979\) 3.65275i 0.116742i
\(980\) 2.30370 + 0.347328i 0.0735890 + 0.0110950i
\(981\) 9.50263 + 10.2145i 0.303396 + 0.326124i
\(982\) −1.07521 + 1.86231i −0.0343113 + 0.0594289i
\(983\) −4.30533 7.45706i −0.137319 0.237843i 0.789162 0.614185i \(-0.210515\pi\)
−0.926481 + 0.376342i \(0.877182\pi\)
\(984\) −58.0937 + 6.58419i −1.85196 + 0.209896i
\(985\) 1.68635 + 0.973614i 0.0537316 + 0.0310219i
\(986\) 10.8831 0.346587
\(987\) −29.3073 15.4656i −0.932863 0.492275i
\(988\) −33.5443 −1.06719
\(989\) −5.27931 3.04801i −0.167872 0.0969211i
\(990\) −0.299645 + 0.975972i −0.00952336 + 0.0310184i
\(991\) 9.55178 + 16.5442i 0.303422 + 0.525543i 0.976909 0.213657i \(-0.0685374\pi\)
−0.673486 + 0.739200i \(0.735204\pi\)
\(992\) 8.07020 13.9780i 0.256229 0.443802i
\(993\) −6.48239 2.82317i −0.205712 0.0895907i
\(994\) −13.6012 + 19.9483i −0.431403 + 0.632723i
\(995\) 4.38276i 0.138943i
\(996\) 9.52558 7.03985i 0.301829 0.223066i
\(997\) −14.5101 + 8.37740i −0.459539 + 0.265315i −0.711850 0.702331i \(-0.752143\pi\)
0.252311 + 0.967646i \(0.418809\pi\)
\(998\) −0.533302 + 0.307902i −0.0168814 + 0.00974648i
\(999\) −20.0024 3.74389i −0.632848 0.118451i
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 231.2.n.a.89.17 yes 52
3.2 odd 2 inner 231.2.n.a.89.10 52
7.3 odd 6 inner 231.2.n.a.122.10 yes 52
21.17 even 6 inner 231.2.n.a.122.17 yes 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
231.2.n.a.89.10 52 3.2 odd 2 inner
231.2.n.a.89.17 yes 52 1.1 even 1 trivial
231.2.n.a.122.10 yes 52 7.3 odd 6 inner
231.2.n.a.122.17 yes 52 21.17 even 6 inner