Properties

Label 165.2.s.a.49.7
Level $165$
Weight $2$
Character 165.49
Analytic conductor $1.318$
Analytic rank $0$
Dimension $48$
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] = [165,2,Mod(4,165)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(165, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 5, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("165.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 165.s (of order \(10\), 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: \(1.31753163335\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 49.7
Character \(\chi\) \(=\) 165.49
Dual form 165.2.s.a.64.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.283476 - 0.0921069i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(-1.54616 + 1.12335i) q^{4} +(-1.92187 + 1.14299i) q^{5} +(-0.0921069 + 0.283476i) q^{6} +(-1.36429 - 1.87778i) q^{7} +(-0.685226 + 0.943133i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})\) \(q+(0.283476 - 0.0921069i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(-1.54616 + 1.12335i) q^{4} +(-1.92187 + 1.14299i) q^{5} +(-0.0921069 + 0.283476i) q^{6} +(-1.36429 - 1.87778i) q^{7} +(-0.685226 + 0.943133i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(-0.439527 + 0.501026i) q^{10} +(-0.521566 + 3.27536i) q^{11} -1.91116i q^{12} +(-4.36612 + 1.41864i) q^{13} +(-0.559700 - 0.406646i) q^{14} +(0.204952 - 2.22666i) q^{15} +(1.07378 - 3.30477i) q^{16} +(4.88887 + 1.58849i) q^{17} +(-0.175198 - 0.241139i) q^{18} +(4.60482 + 3.34560i) q^{19} +(1.68754 - 3.92617i) q^{20} +2.32107 q^{21} +(0.153832 + 0.976525i) q^{22} +6.02600i q^{23} +(-0.360245 - 1.10872i) q^{24} +(2.38717 - 4.39334i) q^{25} +(-1.10702 + 0.804299i) q^{26} +(0.951057 + 0.309017i) q^{27} +(4.21882 + 1.37078i) q^{28} +(-4.93288 + 3.58395i) q^{29} +(-0.146991 - 0.650081i) q^{30} +(-2.60554 - 8.01903i) q^{31} -3.36728i q^{32} +(-2.34325 - 2.34716i) q^{33} +1.53219 q^{34} +(4.76826 + 2.04949i) q^{35} +(1.54616 + 1.12335i) q^{36} +(-1.86492 - 2.56684i) q^{37} +(1.61351 + 0.524260i) q^{38} +(1.41864 - 4.36612i) q^{39} +(0.238928 - 2.59578i) q^{40} +(-0.379099 - 0.275431i) q^{41} +(0.657967 - 0.213786i) q^{42} +8.08805i q^{43} +(-2.87295 - 5.65013i) q^{44} +(1.68093 + 1.47460i) q^{45} +(0.555036 + 1.70823i) q^{46} +(-5.40020 + 7.43273i) q^{47} +(2.04246 + 2.81120i) q^{48} +(0.498336 - 1.53372i) q^{49} +(0.272047 - 1.46528i) q^{50} +(-4.15872 + 3.02149i) q^{51} +(5.15709 - 7.09812i) q^{52} +(4.05047 - 1.31608i) q^{53} +0.298064 q^{54} +(-2.74131 - 6.89095i) q^{55} +2.70584 q^{56} +(-5.41329 + 1.75888i) q^{57} +(-1.06825 + 1.47031i) q^{58} +(5.38782 - 3.91448i) q^{59} +(2.18443 + 3.67300i) q^{60} +(-0.562537 + 1.73131i) q^{61} +(-1.47722 - 2.03321i) q^{62} +(-1.36429 + 1.87778i) q^{63} +(1.83742 + 5.65499i) q^{64} +(6.76963 - 7.71685i) q^{65} +(-0.880445 - 0.449534i) q^{66} +8.86541i q^{67} +(-9.34341 + 3.03586i) q^{68} +(-4.87514 - 3.54199i) q^{69} +(1.54046 + 0.141791i) q^{70} +(-0.756682 + 2.32883i) q^{71} +(1.10872 + 0.360245i) q^{72} +(-5.33885 - 7.34830i) q^{73} +(-0.765084 - 0.555866i) q^{74} +(2.15114 + 4.51360i) q^{75} -10.8781 q^{76} +(6.86198 - 3.48915i) q^{77} -1.36836i q^{78} +(3.99441 + 12.2935i) q^{79} +(1.71363 + 7.57866i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-0.132834 - 0.0431605i) q^{82} +(-7.93896 - 2.57952i) q^{83} +(-3.58874 + 2.60737i) q^{84} +(-11.2114 + 2.53504i) q^{85} +(0.744965 + 2.29277i) q^{86} -6.09737i q^{87} +(-2.73171 - 2.73627i) q^{88} +3.73882 q^{89} +(0.612326 + 0.263189i) q^{90} +(8.62054 + 6.26319i) q^{91} +(-6.76931 - 9.31716i) q^{92} +(8.01903 + 2.60554i) q^{93} +(-0.846220 + 2.60440i) q^{94} +(-12.6738 - 1.16656i) q^{95} +(2.72418 + 1.97924i) q^{96} +(5.31638 - 1.72740i) q^{97} -0.480673i q^{98} +(3.27622 - 0.516103i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 12 q^{4} - 4 q^{5} + 4 q^{6} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 12 q^{4} - 4 q^{5} + 4 q^{6} + 12 q^{9} - 12 q^{10} - 4 q^{14} + 10 q^{15} - 44 q^{16} - 16 q^{19} + 46 q^{20} - 32 q^{21} - 12 q^{24} + 14 q^{25} - 76 q^{26} + 4 q^{30} - 20 q^{31} - 24 q^{34} - 40 q^{35} - 12 q^{36} - 8 q^{39} - 72 q^{40} + 60 q^{41} - 48 q^{44} + 4 q^{45} + 108 q^{46} - 28 q^{49} - 38 q^{50} + 28 q^{51} + 16 q^{54} - 20 q^{55} + 24 q^{56} + 60 q^{59} + 48 q^{60} + 40 q^{61} + 64 q^{64} + 20 q^{65} + 12 q^{66} + 20 q^{69} + 86 q^{70} - 32 q^{71} - 32 q^{74} - 40 q^{75} - 136 q^{76} - 52 q^{79} + 42 q^{80} - 12 q^{81} - 70 q^{85} - 104 q^{86} + 40 q^{89} - 8 q^{90} - 40 q^{91} + 72 q^{94} - 2 q^{95} + 28 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(67\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.283476 0.0921069i 0.200448 0.0651294i −0.207072 0.978326i \(-0.566394\pi\)
0.407520 + 0.913196i \(0.366394\pi\)
\(3\) −0.587785 + 0.809017i −0.339358 + 0.467086i
\(4\) −1.54616 + 1.12335i −0.773080 + 0.561675i
\(5\) −1.92187 + 1.14299i −0.859486 + 0.511159i
\(6\) −0.0921069 + 0.283476i −0.0376025 + 0.115729i
\(7\) −1.36429 1.87778i −0.515653 0.709735i 0.469207 0.883088i \(-0.344540\pi\)
−0.984860 + 0.173353i \(0.944540\pi\)
\(8\) −0.685226 + 0.943133i −0.242264 + 0.333448i
\(9\) −0.309017 0.951057i −0.103006 0.317019i
\(10\) −0.439527 + 0.501026i −0.138991 + 0.158438i
\(11\) −0.521566 + 3.27536i −0.157258 + 0.987558i
\(12\) 1.91116i 0.551704i
\(13\) −4.36612 + 1.41864i −1.21094 + 0.393459i −0.843776 0.536695i \(-0.819672\pi\)
−0.367168 + 0.930155i \(0.619672\pi\)
\(14\) −0.559700 0.406646i −0.149586 0.108681i
\(15\) 0.204952 2.22666i 0.0529183 0.574920i
\(16\) 1.07378 3.30477i 0.268446 0.826192i
\(17\) 4.88887 + 1.58849i 1.18573 + 0.385266i 0.834491 0.551022i \(-0.185762\pi\)
0.351235 + 0.936287i \(0.385762\pi\)
\(18\) −0.175198 0.241139i −0.0412945 0.0568370i
\(19\) 4.60482 + 3.34560i 1.05642 + 0.767532i 0.973422 0.229018i \(-0.0735514\pi\)
0.0829952 + 0.996550i \(0.473551\pi\)
\(20\) 1.68754 3.92617i 0.377346 0.877918i
\(21\) 2.32107 0.506498
\(22\) 0.153832 + 0.976525i 0.0327970 + 0.208196i
\(23\) 6.02600i 1.25651i 0.778008 + 0.628254i \(0.216230\pi\)
−0.778008 + 0.628254i \(0.783770\pi\)
\(24\) −0.360245 1.10872i −0.0735346 0.226316i
\(25\) 2.38717 4.39334i 0.477433 0.878668i
\(26\) −1.10702 + 0.804299i −0.217105 + 0.157736i
\(27\) 0.951057 + 0.309017i 0.183031 + 0.0594703i
\(28\) 4.21882 + 1.37078i 0.797281 + 0.259052i
\(29\) −4.93288 + 3.58395i −0.916013 + 0.665522i −0.942528 0.334126i \(-0.891559\pi\)
0.0265157 + 0.999648i \(0.491559\pi\)
\(30\) −0.146991 0.650081i −0.0268368 0.118688i
\(31\) −2.60554 8.01903i −0.467969 1.44026i −0.855210 0.518282i \(-0.826572\pi\)
0.387241 0.921978i \(-0.373428\pi\)
\(32\) 3.36728i 0.595256i
\(33\) −2.34325 2.34716i −0.407908 0.408589i
\(34\) 1.53219 0.262768
\(35\) 4.76826 + 2.04949i 0.805984 + 0.346427i
\(36\) 1.54616 + 1.12335i 0.257693 + 0.187225i
\(37\) −1.86492 2.56684i −0.306591 0.421986i 0.627723 0.778436i \(-0.283987\pi\)
−0.934314 + 0.356450i \(0.883987\pi\)
\(38\) 1.61351 + 0.524260i 0.261745 + 0.0850462i
\(39\) 1.41864 4.36612i 0.227164 0.699139i
\(40\) 0.238928 2.59578i 0.0377778 0.410429i
\(41\) −0.379099 0.275431i −0.0592053 0.0430151i 0.557789 0.829983i \(-0.311650\pi\)
−0.616994 + 0.786968i \(0.711650\pi\)
\(42\) 0.657967 0.213786i 0.101526 0.0329879i
\(43\) 8.08805i 1.23342i 0.787192 + 0.616708i \(0.211534\pi\)
−0.787192 + 0.616708i \(0.788466\pi\)
\(44\) −2.87295 5.65013i −0.433114 0.851788i
\(45\) 1.68093 + 1.47460i 0.250579 + 0.219821i
\(46\) 0.555036 + 1.70823i 0.0818357 + 0.251864i
\(47\) −5.40020 + 7.43273i −0.787700 + 1.08418i 0.206691 + 0.978406i \(0.433730\pi\)
−0.994391 + 0.105769i \(0.966270\pi\)
\(48\) 2.04246 + 2.81120i 0.294804 + 0.405762i
\(49\) 0.498336 1.53372i 0.0711908 0.219103i
\(50\) 0.272047 1.46528i 0.0384733 0.207222i
\(51\) −4.15872 + 3.02149i −0.582338 + 0.423093i
\(52\) 5.15709 7.09812i 0.715159 0.984332i
\(53\) 4.05047 1.31608i 0.556375 0.180777i −0.0173146 0.999850i \(-0.505512\pi\)
0.573689 + 0.819073i \(0.305512\pi\)
\(54\) 0.298064 0.0405614
\(55\) −2.74131 6.89095i −0.369638 0.929176i
\(56\) 2.70584 0.361584
\(57\) −5.41329 + 1.75888i −0.717007 + 0.232970i
\(58\) −1.06825 + 1.47031i −0.140268 + 0.193062i
\(59\) 5.38782 3.91448i 0.701434 0.509622i −0.178965 0.983855i \(-0.557275\pi\)
0.880399 + 0.474234i \(0.157275\pi\)
\(60\) 2.18443 + 3.67300i 0.282008 + 0.474182i
\(61\) −0.562537 + 1.73131i −0.0720255 + 0.221672i −0.980589 0.196076i \(-0.937180\pi\)
0.908563 + 0.417747i \(0.137180\pi\)
\(62\) −1.47722 2.03321i −0.187607 0.258218i
\(63\) −1.36429 + 1.87778i −0.171884 + 0.236578i
\(64\) 1.83742 + 5.65499i 0.229677 + 0.706874i
\(65\) 6.76963 7.71685i 0.839669 0.957157i
\(66\) −0.880445 0.449534i −0.108375 0.0553339i
\(67\) 8.86541i 1.08308i 0.840674 + 0.541541i \(0.182159\pi\)
−0.840674 + 0.541541i \(0.817841\pi\)
\(68\) −9.34341 + 3.03586i −1.13305 + 0.368152i
\(69\) −4.87514 3.54199i −0.586898 0.426406i
\(70\) 1.54046 + 0.141791i 0.184120 + 0.0169473i
\(71\) −0.756682 + 2.32883i −0.0898017 + 0.276381i −0.985864 0.167547i \(-0.946415\pi\)
0.896062 + 0.443928i \(0.146415\pi\)
\(72\) 1.10872 + 0.360245i 0.130664 + 0.0424552i
\(73\) −5.33885 7.34830i −0.624865 0.860053i 0.372831 0.927899i \(-0.378387\pi\)
−0.997696 + 0.0678465i \(0.978387\pi\)
\(74\) −0.765084 0.555866i −0.0889392 0.0646181i
\(75\) 2.15114 + 4.51360i 0.248393 + 0.521186i
\(76\) −10.8781 −1.24780
\(77\) 6.86198 3.48915i 0.781995 0.397625i
\(78\) 1.36836i 0.154936i
\(79\) 3.99441 + 12.2935i 0.449406 + 1.38313i 0.877579 + 0.479433i \(0.159157\pi\)
−0.428173 + 0.903697i \(0.640843\pi\)
\(80\) 1.71363 + 7.57866i 0.191590 + 0.847319i
\(81\) −0.809017 + 0.587785i −0.0898908 + 0.0653095i
\(82\) −0.132834 0.0431605i −0.0146691 0.00476628i
\(83\) −7.93896 2.57952i −0.871414 0.283139i −0.161026 0.986950i \(-0.551480\pi\)
−0.710388 + 0.703811i \(0.751480\pi\)
\(84\) −3.58874 + 2.60737i −0.391563 + 0.284488i
\(85\) −11.2114 + 2.53504i −1.21605 + 0.274964i
\(86\) 0.744965 + 2.29277i 0.0803317 + 0.247235i
\(87\) 6.09737i 0.653707i
\(88\) −2.73171 2.73627i −0.291201 0.291687i
\(89\) 3.73882 0.396314 0.198157 0.980170i \(-0.436504\pi\)
0.198157 + 0.980170i \(0.436504\pi\)
\(90\) 0.612326 + 0.263189i 0.0645448 + 0.0277426i
\(91\) 8.62054 + 6.26319i 0.903678 + 0.656561i
\(92\) −6.76931 9.31716i −0.705749 0.971381i
\(93\) 8.01903 + 2.60554i 0.831535 + 0.270182i
\(94\) −0.846220 + 2.60440i −0.0872809 + 0.268623i
\(95\) −12.6738 1.16656i −1.30031 0.119686i
\(96\) 2.72418 + 1.97924i 0.278036 + 0.202005i
\(97\) 5.31638 1.72740i 0.539797 0.175391i −0.0264138 0.999651i \(-0.508409\pi\)
0.566211 + 0.824260i \(0.308409\pi\)
\(98\) 0.480673i 0.0485553i
\(99\) 3.27622 0.516103i 0.329273 0.0518703i
\(100\) 1.24432 + 9.47443i 0.124432 + 0.947443i
\(101\) −0.498799 1.53515i −0.0496324 0.152753i 0.923169 0.384395i \(-0.125590\pi\)
−0.972801 + 0.231643i \(0.925590\pi\)
\(102\) −0.900598 + 1.23957i −0.0891725 + 0.122735i
\(103\) 5.00700 + 6.89154i 0.493354 + 0.679043i 0.981002 0.193997i \(-0.0621451\pi\)
−0.487648 + 0.873040i \(0.662145\pi\)
\(104\) 1.65381 5.08992i 0.162170 0.499107i
\(105\) −4.46079 + 2.65295i −0.435328 + 0.258901i
\(106\) 1.02699 0.746152i 0.0997502 0.0724727i
\(107\) −3.59375 + 4.94637i −0.347421 + 0.478183i −0.946590 0.322439i \(-0.895497\pi\)
0.599170 + 0.800622i \(0.295497\pi\)
\(108\) −1.81762 + 0.590580i −0.174900 + 0.0568286i
\(109\) −5.73259 −0.549082 −0.274541 0.961575i \(-0.588526\pi\)
−0.274541 + 0.961575i \(0.588526\pi\)
\(110\) −1.41180 1.70093i −0.134610 0.162177i
\(111\) 3.17279 0.301148
\(112\) −7.67059 + 2.49233i −0.724802 + 0.235503i
\(113\) 4.84353 6.66655i 0.455641 0.627136i −0.517956 0.855407i \(-0.673307\pi\)
0.973598 + 0.228271i \(0.0733071\pi\)
\(114\) −1.37253 + 0.997202i −0.128549 + 0.0933966i
\(115\) −6.88763 11.5812i −0.642275 1.07995i
\(116\) 3.60099 11.0827i 0.334343 1.02900i
\(117\) 2.69841 + 3.71404i 0.249468 + 0.343363i
\(118\) 1.16677 1.60592i 0.107410 0.147837i
\(119\) −3.68699 11.3474i −0.337986 1.04021i
\(120\) 1.95959 + 1.71906i 0.178886 + 0.156928i
\(121\) −10.4559 3.41663i −0.950540 0.310603i
\(122\) 0.542598i 0.0491245i
\(123\) 0.445657 0.144803i 0.0401836 0.0130564i
\(124\) 13.0368 + 9.47176i 1.17074 + 0.850589i
\(125\) 0.433700 + 11.1719i 0.0387913 + 0.999247i
\(126\) −0.213786 + 0.657967i −0.0190456 + 0.0586163i
\(127\) 11.4871 + 3.73239i 1.01932 + 0.331196i 0.770559 0.637369i \(-0.219977\pi\)
0.248759 + 0.968565i \(0.419977\pi\)
\(128\) 5.00020 + 6.88219i 0.441959 + 0.608305i
\(129\) −6.54337 4.75404i −0.576112 0.418570i
\(130\) 1.20825 2.81107i 0.105971 0.246547i
\(131\) 3.28131 0.286689 0.143345 0.989673i \(-0.454214\pi\)
0.143345 + 0.989673i \(0.454214\pi\)
\(132\) 6.25973 + 0.996794i 0.544839 + 0.0867598i
\(133\) 13.2112i 1.14556i
\(134\) 0.816565 + 2.51313i 0.0705405 + 0.217101i
\(135\) −2.18101 + 0.493154i −0.187711 + 0.0424439i
\(136\) −4.84814 + 3.52238i −0.415725 + 0.302042i
\(137\) 3.82077 + 1.24144i 0.326431 + 0.106064i 0.467648 0.883915i \(-0.345102\pi\)
−0.141217 + 0.989979i \(0.545102\pi\)
\(138\) −1.70823 0.555036i −0.145414 0.0472478i
\(139\) −1.43963 + 1.04595i −0.122108 + 0.0887167i −0.647163 0.762352i \(-0.724045\pi\)
0.525055 + 0.851068i \(0.324045\pi\)
\(140\) −9.67479 + 2.18759i −0.817669 + 0.184885i
\(141\) −2.83905 8.73770i −0.239091 0.735847i
\(142\) 0.729862i 0.0612487i
\(143\) −2.36933 15.0405i −0.198133 1.25775i
\(144\) −3.47484 −0.289570
\(145\) 5.38395 12.5261i 0.447113 1.04024i
\(146\) −2.19026 1.59132i −0.181268 0.131699i
\(147\) 0.947891 + 1.30466i 0.0781808 + 0.107607i
\(148\) 5.76692 + 1.87379i 0.474038 + 0.154024i
\(149\) 0.682251 2.09975i 0.0558922 0.172018i −0.919213 0.393760i \(-0.871174\pi\)
0.975105 + 0.221742i \(0.0711741\pi\)
\(150\) 1.02553 + 1.08136i 0.0837343 + 0.0882928i
\(151\) 10.3988 + 7.55517i 0.846242 + 0.614831i 0.924107 0.382133i \(-0.124810\pi\)
−0.0778651 + 0.996964i \(0.524810\pi\)
\(152\) −6.31068 + 2.05046i −0.511864 + 0.166315i
\(153\) 5.14046i 0.415582i
\(154\) 1.62383 1.62112i 0.130852 0.130634i
\(155\) 14.1731 + 12.4334i 1.13841 + 0.998677i
\(156\) 2.71124 + 8.34434i 0.217073 + 0.668082i
\(157\) −0.493533 + 0.679290i −0.0393882 + 0.0542132i −0.828257 0.560349i \(-0.810667\pi\)
0.788869 + 0.614562i \(0.210667\pi\)
\(158\) 2.26464 + 3.11701i 0.180165 + 0.247976i
\(159\) −1.31608 + 4.05047i −0.104372 + 0.321223i
\(160\) 3.84875 + 6.47147i 0.304270 + 0.511615i
\(161\) 11.3155 8.22121i 0.891788 0.647922i
\(162\) −0.175198 + 0.241139i −0.0137648 + 0.0189457i
\(163\) 10.5452 3.42634i 0.825963 0.268372i 0.134619 0.990897i \(-0.457019\pi\)
0.691344 + 0.722526i \(0.257019\pi\)
\(164\) 0.895553 0.0699309
\(165\) 7.18620 + 1.83264i 0.559445 + 0.142671i
\(166\) −2.48810 −0.193114
\(167\) 4.24625 1.37969i 0.328585 0.106764i −0.140079 0.990140i \(-0.544736\pi\)
0.468664 + 0.883377i \(0.344736\pi\)
\(168\) −1.59046 + 2.18907i −0.122706 + 0.168891i
\(169\) 6.53324 4.74668i 0.502557 0.365129i
\(170\) −2.94467 + 1.75127i −0.225846 + 0.134316i
\(171\) 1.75888 5.41329i 0.134505 0.413964i
\(172\) −9.08571 12.5054i −0.692779 0.953529i
\(173\) 10.6195 14.6165i 0.807386 1.11127i −0.184336 0.982863i \(-0.559013\pi\)
0.991721 0.128408i \(-0.0409867\pi\)
\(174\) −0.561610 1.72846i −0.0425756 0.131034i
\(175\) −11.5065 + 1.51120i −0.869811 + 0.114236i
\(176\) 10.2643 + 5.24068i 0.773697 + 0.395031i
\(177\) 6.65971i 0.500575i
\(178\) 1.05987 0.344371i 0.0794403 0.0258117i
\(179\) −9.68751 7.03839i −0.724079 0.526074i 0.163606 0.986526i \(-0.447687\pi\)
−0.887685 + 0.460452i \(0.847687\pi\)
\(180\) −4.25549 0.391695i −0.317185 0.0291952i
\(181\) 4.88818 15.0443i 0.363336 1.11823i −0.587681 0.809093i \(-0.699959\pi\)
0.951017 0.309140i \(-0.100041\pi\)
\(182\) 3.02060 + 0.981452i 0.223902 + 0.0727501i
\(183\) −1.07001 1.47274i −0.0790973 0.108868i
\(184\) −5.68332 4.12917i −0.418980 0.304407i
\(185\) 6.51800 + 2.80156i 0.479213 + 0.205975i
\(186\) 2.51319 0.184276
\(187\) −7.75275 + 15.1843i −0.566937 + 1.11039i
\(188\) 17.5585i 1.28059i
\(189\) −0.717249 2.20747i −0.0521722 0.160570i
\(190\) −3.70017 + 0.836656i −0.268439 + 0.0606974i
\(191\) −7.28719 + 5.29446i −0.527283 + 0.383093i −0.819340 0.573307i \(-0.805660\pi\)
0.292058 + 0.956401i \(0.405660\pi\)
\(192\) −5.65499 1.83742i −0.408114 0.132604i
\(193\) −3.65139 1.18641i −0.262833 0.0853995i 0.174636 0.984633i \(-0.444125\pi\)
−0.437469 + 0.899234i \(0.644125\pi\)
\(194\) 1.34796 0.979352i 0.0967780 0.0703133i
\(195\) 2.26397 + 10.0126i 0.162127 + 0.717017i
\(196\) 0.952399 + 2.93118i 0.0680285 + 0.209370i
\(197\) 8.33739i 0.594015i 0.954875 + 0.297007i \(0.0959886\pi\)
−0.954875 + 0.297007i \(0.904011\pi\)
\(198\) 0.881194 0.448065i 0.0626237 0.0318426i
\(199\) −2.22397 −0.157653 −0.0788266 0.996888i \(-0.525117\pi\)
−0.0788266 + 0.996888i \(0.525117\pi\)
\(200\) 2.50775 + 5.26185i 0.177325 + 0.372069i
\(201\) −7.17227 5.21096i −0.505893 0.367553i
\(202\) −0.282795 0.389234i −0.0198974 0.0273864i
\(203\) 13.4597 + 4.37334i 0.944689 + 0.306948i
\(204\) 3.03586 9.34341i 0.212552 0.654169i
\(205\) 1.04339 + 0.0960387i 0.0728737 + 0.00670764i
\(206\) 2.05412 + 1.49241i 0.143117 + 0.103981i
\(207\) 5.73107 1.86214i 0.398337 0.129427i
\(208\) 15.9523i 1.10609i
\(209\) −13.3597 + 13.3375i −0.924112 + 0.922572i
\(210\) −1.02017 + 1.16292i −0.0703985 + 0.0802488i
\(211\) 1.55209 + 4.77683i 0.106850 + 0.328850i 0.990160 0.139939i \(-0.0446905\pi\)
−0.883310 + 0.468789i \(0.844690\pi\)
\(212\) −4.78425 + 6.58496i −0.328584 + 0.452257i
\(213\) −1.43930 1.98102i −0.0986189 0.135737i
\(214\) −0.563146 + 1.73318i −0.0384959 + 0.118478i
\(215\) −9.24453 15.5442i −0.630471 1.06010i
\(216\) −0.943133 + 0.685226i −0.0641721 + 0.0466237i
\(217\) −11.5033 + 15.8329i −0.780894 + 1.07481i
\(218\) −1.62505 + 0.528011i −0.110062 + 0.0357614i
\(219\) 9.08299 0.613772
\(220\) 11.9794 + 7.57506i 0.807654 + 0.510711i
\(221\) −23.5989 −1.58743
\(222\) 0.899410 0.292236i 0.0603644 0.0196136i
\(223\) 16.6769 22.9538i 1.11677 1.53710i 0.305720 0.952122i \(-0.401103\pi\)
0.811049 0.584979i \(-0.198897\pi\)
\(224\) −6.32302 + 4.59394i −0.422474 + 0.306945i
\(225\) −4.91599 0.912714i −0.327733 0.0608476i
\(226\) 0.758989 2.33593i 0.0504872 0.155384i
\(227\) 3.86901 + 5.32524i 0.256795 + 0.353448i 0.917877 0.396866i \(-0.129902\pi\)
−0.661081 + 0.750314i \(0.729902\pi\)
\(228\) 6.39396 8.80053i 0.423450 0.582829i
\(229\) 5.10750 + 15.7193i 0.337513 + 1.03876i 0.965471 + 0.260511i \(0.0838909\pi\)
−0.627958 + 0.778247i \(0.716109\pi\)
\(230\) −3.01919 2.64859i −0.199079 0.174643i
\(231\) −1.21059 + 7.60232i −0.0796509 + 0.500196i
\(232\) 7.10817i 0.466674i
\(233\) −22.2218 + 7.22032i −1.45580 + 0.473019i −0.926785 0.375593i \(-0.877439\pi\)
−0.529017 + 0.848611i \(0.677439\pi\)
\(234\) 1.10702 + 0.804299i 0.0723684 + 0.0525787i
\(235\) 1.88297 20.4571i 0.122831 1.33447i
\(236\) −3.93309 + 12.1048i −0.256023 + 0.787957i
\(237\) −12.2935 3.99441i −0.798550 0.259465i
\(238\) −2.09035 2.87712i −0.135497 0.186496i
\(239\) 14.3890 + 10.4542i 0.930746 + 0.676227i 0.946175 0.323654i \(-0.104911\pi\)
−0.0154293 + 0.999881i \(0.504911\pi\)
\(240\) −7.13851 3.06827i −0.460789 0.198056i
\(241\) −6.95713 −0.448148 −0.224074 0.974572i \(-0.571936\pi\)
−0.224074 + 0.974572i \(0.571936\pi\)
\(242\) −3.27870 0.00546796i −0.210763 0.000351494i
\(243\) 1.00000i 0.0641500i
\(244\) −1.07510 3.30881i −0.0688260 0.211825i
\(245\) 0.795284 + 3.51720i 0.0508088 + 0.224706i
\(246\) 0.112996 0.0820962i 0.00720435 0.00523426i
\(247\) −24.8514 8.07470i −1.58125 0.513781i
\(248\) 9.34839 + 3.03748i 0.593624 + 0.192880i
\(249\) 6.75328 4.90655i 0.427972 0.310940i
\(250\) 1.15195 + 3.12702i 0.0728560 + 0.197770i
\(251\) −0.196752 0.605539i −0.0124188 0.0382213i 0.944655 0.328065i \(-0.106397\pi\)
−0.957074 + 0.289844i \(0.906397\pi\)
\(252\) 4.43592i 0.279437i
\(253\) −19.7373 3.14296i −1.24087 0.197596i
\(254\) 3.60010 0.225891
\(255\) 4.53901 10.5603i 0.284244 0.661310i
\(256\) −7.56952 5.49958i −0.473095 0.343724i
\(257\) −0.283345 0.389991i −0.0176746 0.0243270i 0.800088 0.599882i \(-0.204786\pi\)
−0.817763 + 0.575555i \(0.804786\pi\)
\(258\) −2.29277 0.744965i −0.142741 0.0463795i
\(259\) −2.27568 + 7.00383i −0.141404 + 0.435197i
\(260\) −1.79820 + 19.5361i −0.111520 + 1.21158i
\(261\) 4.93288 + 3.58395i 0.305338 + 0.221841i
\(262\) 0.930172 0.302231i 0.0574662 0.0186719i
\(263\) 18.2072i 1.12270i 0.827578 + 0.561351i \(0.189718\pi\)
−0.827578 + 0.561351i \(0.810282\pi\)
\(264\) 3.81934 0.601660i 0.235064 0.0370296i
\(265\) −6.28022 + 7.15896i −0.385791 + 0.439771i
\(266\) −1.21684 3.74506i −0.0746094 0.229624i
\(267\) −2.19762 + 3.02477i −0.134492 + 0.185113i
\(268\) −9.95896 13.7073i −0.608340 0.837309i
\(269\) −8.05132 + 24.7794i −0.490898 + 1.51083i 0.332356 + 0.943154i \(0.392156\pi\)
−0.823254 + 0.567673i \(0.807844\pi\)
\(270\) −0.572841 + 0.340683i −0.0348620 + 0.0207333i
\(271\) −0.238170 + 0.173040i −0.0144678 + 0.0105115i −0.594996 0.803729i \(-0.702846\pi\)
0.580528 + 0.814240i \(0.302846\pi\)
\(272\) 10.4992 14.4509i 0.636607 0.876214i
\(273\) −10.1341 + 3.29275i −0.613341 + 0.199287i
\(274\) 1.19744 0.0723402
\(275\) 13.1447 + 10.1102i 0.792655 + 0.609671i
\(276\) 11.5166 0.693220
\(277\) 28.8068 9.35990i 1.73083 0.562382i 0.737263 0.675605i \(-0.236118\pi\)
0.993570 + 0.113224i \(0.0361176\pi\)
\(278\) −0.311762 + 0.429103i −0.0186982 + 0.0257359i
\(279\) −6.82139 + 4.95603i −0.408386 + 0.296710i
\(280\) −5.20028 + 3.09274i −0.310776 + 0.184827i
\(281\) −9.18352 + 28.2640i −0.547843 + 1.68609i 0.166290 + 0.986077i \(0.446821\pi\)
−0.714133 + 0.700010i \(0.753179\pi\)
\(282\) −1.60961 2.21543i −0.0958506 0.131927i
\(283\) 0.934506 1.28624i 0.0555506 0.0764589i −0.780338 0.625358i \(-0.784953\pi\)
0.835889 + 0.548899i \(0.184953\pi\)
\(284\) −1.44614 4.45076i −0.0858126 0.264104i
\(285\) 8.39325 9.56766i 0.497173 0.566739i
\(286\) −2.05698 4.04539i −0.121632 0.239209i
\(287\) 1.08763i 0.0642009i
\(288\) −3.20247 + 1.04055i −0.188707 + 0.0613148i
\(289\) 7.62448 + 5.53951i 0.448499 + 0.325854i
\(290\) 0.372481 4.04674i 0.0218729 0.237633i
\(291\) −1.72740 + 5.31638i −0.101262 + 0.311652i
\(292\) 16.5094 + 5.36424i 0.966141 + 0.313918i
\(293\) 0.247489 + 0.340640i 0.0144585 + 0.0199004i 0.816185 0.577791i \(-0.196085\pi\)
−0.801727 + 0.597691i \(0.796085\pi\)
\(294\) 0.388873 + 0.282532i 0.0226795 + 0.0164776i
\(295\) −5.88049 + 13.6813i −0.342376 + 0.796557i
\(296\) 3.69876 0.214986
\(297\) −1.50818 + 2.95388i −0.0875135 + 0.171401i
\(298\) 0.658069i 0.0381209i
\(299\) −8.54872 26.3102i −0.494385 1.52156i
\(300\) −8.39636 4.56225i −0.484764 0.263402i
\(301\) 15.1876 11.0344i 0.875399 0.636014i
\(302\) 3.64369 + 1.18391i 0.209671 + 0.0681262i
\(303\) 1.53515 + 0.498799i 0.0881918 + 0.0286553i
\(304\) 16.0010 11.6254i 0.917720 0.666763i
\(305\) −0.897741 3.97033i −0.0514045 0.227340i
\(306\) −0.473472 1.45720i −0.0270666 0.0833025i
\(307\) 9.29536i 0.530514i −0.964178 0.265257i \(-0.914543\pi\)
0.964178 0.265257i \(-0.0854569\pi\)
\(308\) −6.69017 + 13.1032i −0.381208 + 0.746623i
\(309\) −8.51841 −0.484595
\(310\) 5.16295 + 2.21913i 0.293236 + 0.126038i
\(311\) −9.78478 7.10906i −0.554844 0.403118i 0.274724 0.961523i \(-0.411413\pi\)
−0.829568 + 0.558405i \(0.811413\pi\)
\(312\) 3.14574 + 4.32974i 0.178093 + 0.245123i
\(313\) 6.63461 + 2.15572i 0.375010 + 0.121848i 0.490457 0.871465i \(-0.336830\pi\)
−0.115447 + 0.993314i \(0.536830\pi\)
\(314\) −0.0773374 + 0.238020i −0.00436440 + 0.0134322i
\(315\) 0.475707 5.16822i 0.0268030 0.291196i
\(316\) −19.9859 14.5206i −1.12430 0.816849i
\(317\) −6.88514 + 2.23712i −0.386708 + 0.125649i −0.495917 0.868370i \(-0.665168\pi\)
0.109209 + 0.994019i \(0.465168\pi\)
\(318\) 1.26943i 0.0711861i
\(319\) −9.16589 18.0262i −0.513191 1.00927i
\(320\) −9.99486 8.76802i −0.558730 0.490147i
\(321\) −1.88934 5.81480i −0.105453 0.324551i
\(322\) 2.45045 3.37275i 0.136558 0.187956i
\(323\) 17.1979 + 23.6709i 0.956918 + 1.31708i
\(324\) 0.590580 1.81762i 0.0328100 0.100979i
\(325\) −4.19010 + 22.5684i −0.232425 + 1.25187i
\(326\) 2.67372 1.94257i 0.148083 0.107589i
\(327\) 3.36953 4.63776i 0.186335 0.256469i
\(328\) 0.519537 0.168808i 0.0286866 0.00932084i
\(329\) 21.3245 1.17566
\(330\) 2.20591 0.142390i 0.121431 0.00783830i
\(331\) 27.6629 1.52049 0.760244 0.649637i \(-0.225079\pi\)
0.760244 + 0.649637i \(0.225079\pi\)
\(332\) 15.1726 4.92988i 0.832705 0.270562i
\(333\) −1.86492 + 2.56684i −0.102197 + 0.140662i
\(334\) 1.07663 0.782218i 0.0589106 0.0428011i
\(335\) −10.1330 17.0382i −0.553627 0.930894i
\(336\) 2.49233 7.67059i 0.135967 0.418465i
\(337\) 12.9418 + 17.8128i 0.704983 + 0.970325i 0.999890 + 0.0147997i \(0.00471105\pi\)
−0.294908 + 0.955526i \(0.595289\pi\)
\(338\) 1.41481 1.94733i 0.0769558 0.105921i
\(339\) 2.54640 + 7.83700i 0.138301 + 0.425647i
\(340\) 14.4869 16.5139i 0.785661 0.895592i
\(341\) 27.6241 4.35163i 1.49593 0.235654i
\(342\) 1.69654i 0.0917385i
\(343\) −19.0121 + 6.17741i −1.02656 + 0.333549i
\(344\) −7.62811 5.54214i −0.411280 0.298812i
\(345\) 13.4178 + 1.23504i 0.722392 + 0.0664923i
\(346\) 1.66409 5.12155i 0.0894622 0.275336i
\(347\) −25.4571 8.27152i −1.36661 0.444038i −0.468365 0.883535i \(-0.655157\pi\)
−0.898244 + 0.439496i \(0.855157\pi\)
\(348\) 6.84949 + 9.42751i 0.367171 + 0.505368i
\(349\) −17.5081 12.7204i −0.937189 0.680908i 0.0105533 0.999944i \(-0.496641\pi\)
−0.947742 + 0.319037i \(0.896641\pi\)
\(350\) −3.12263 + 1.48822i −0.166912 + 0.0795487i
\(351\) −4.59081 −0.245039
\(352\) 11.0290 + 1.75626i 0.587850 + 0.0936088i
\(353\) 31.5144i 1.67734i −0.544636 0.838672i \(-0.683332\pi\)
0.544636 0.838672i \(-0.316668\pi\)
\(354\) 0.613405 + 1.88787i 0.0326021 + 0.100339i
\(355\) −1.20757 5.34058i −0.0640913 0.283449i
\(356\) −5.78081 + 4.20001i −0.306383 + 0.222600i
\(357\) 11.3474 + 3.68699i 0.600568 + 0.195136i
\(358\) −3.39446 1.10293i −0.179403 0.0582915i
\(359\) −3.60899 + 2.62208i −0.190475 + 0.138388i −0.678936 0.734198i \(-0.737559\pi\)
0.488461 + 0.872586i \(0.337559\pi\)
\(360\) −2.54257 + 0.574907i −0.134005 + 0.0303002i
\(361\) 4.14001 + 12.7416i 0.217895 + 0.670612i
\(362\) 4.71493i 0.247811i
\(363\) 8.90996 6.45079i 0.467651 0.338579i
\(364\) −20.3645 −1.06739
\(365\) 18.6596 + 8.02024i 0.976686 + 0.419798i
\(366\) −0.438971 0.318931i −0.0229454 0.0166708i
\(367\) 0.607183 + 0.835716i 0.0316947 + 0.0436240i 0.824570 0.565760i \(-0.191417\pi\)
−0.792876 + 0.609384i \(0.791417\pi\)
\(368\) 19.9145 + 6.47063i 1.03812 + 0.337305i
\(369\) −0.144803 + 0.445657i −0.00753813 + 0.0232000i
\(370\) 2.10574 + 0.193822i 0.109472 + 0.0100763i
\(371\) −7.99732 5.81039i −0.415200 0.301660i
\(372\) −15.3256 + 4.97960i −0.794597 + 0.258180i
\(373\) 32.6921i 1.69273i 0.532600 + 0.846367i \(0.321215\pi\)
−0.532600 + 0.846367i \(0.678785\pi\)
\(374\) −0.799137 + 5.01847i −0.0413224 + 0.259499i
\(375\) −9.29320 6.21582i −0.479899 0.320984i
\(376\) −3.30970 10.1862i −0.170685 0.525313i
\(377\) 16.4532 22.6459i 0.847384 1.16632i
\(378\) −0.406646 0.559700i −0.0209156 0.0287879i
\(379\) 1.32345 4.07318i 0.0679813 0.209225i −0.911295 0.411754i \(-0.864916\pi\)
0.979276 + 0.202529i \(0.0649162\pi\)
\(380\) 20.9062 12.4335i 1.07247 0.637823i
\(381\) −9.77153 + 7.09944i −0.500611 + 0.363715i
\(382\) −1.57809 + 2.17205i −0.0807420 + 0.111132i
\(383\) −25.6198 + 8.32438i −1.30911 + 0.425356i −0.878742 0.477297i \(-0.841617\pi\)
−0.430369 + 0.902653i \(0.641617\pi\)
\(384\) −8.50685 −0.434113
\(385\) −9.19978 + 14.5488i −0.468864 + 0.741477i
\(386\) −1.14436 −0.0582462
\(387\) 7.69219 2.49935i 0.391016 0.127049i
\(388\) −6.27950 + 8.64299i −0.318793 + 0.438782i
\(389\) 29.6936 21.5736i 1.50552 1.09383i 0.537408 0.843322i \(-0.319403\pi\)
0.968115 0.250505i \(-0.0805965\pi\)
\(390\) 1.56401 + 2.62980i 0.0791968 + 0.133165i
\(391\) −9.57225 + 29.4604i −0.484089 + 1.48987i
\(392\) 1.10503 + 1.52094i 0.0558124 + 0.0768192i
\(393\) −1.92871 + 2.65464i −0.0972903 + 0.133909i
\(394\) 0.767931 + 2.36345i 0.0386878 + 0.119069i
\(395\) −21.7281 19.0610i −1.09326 0.959063i
\(396\) −4.48580 + 4.47832i −0.225420 + 0.225044i
\(397\) 7.52289i 0.377563i −0.982019 0.188782i \(-0.939546\pi\)
0.982019 0.188782i \(-0.0604538\pi\)
\(398\) −0.630443 + 0.204843i −0.0316012 + 0.0102679i
\(399\) 10.6881 + 7.76535i 0.535074 + 0.388754i
\(400\) −11.9557 12.6065i −0.597783 0.630327i
\(401\) 4.75870 14.6458i 0.237638 0.731375i −0.759122 0.650948i \(-0.774372\pi\)
0.996761 0.0804269i \(-0.0256284\pi\)
\(402\) −2.51313 0.816565i −0.125344 0.0407266i
\(403\) 22.7522 + 31.3157i 1.13337 + 1.55995i
\(404\) 2.49573 + 1.81325i 0.124167 + 0.0902127i
\(405\) 0.882995 2.05434i 0.0438764 0.102081i
\(406\) 4.21833 0.209352
\(407\) 9.38000 4.76950i 0.464949 0.236415i
\(408\) 5.99263i 0.296679i
\(409\) −5.03340 15.4912i −0.248886 0.765992i −0.994973 0.100143i \(-0.968070\pi\)
0.746087 0.665848i \(-0.231930\pi\)
\(410\) 0.304622 0.0688790i 0.0150442 0.00340169i
\(411\) −3.25014 + 2.36137i −0.160318 + 0.116478i
\(412\) −15.4832 5.03080i −0.762804 0.247850i
\(413\) −14.7011 4.77667i −0.723393 0.235045i
\(414\) 1.45310 1.05574i 0.0714162 0.0518869i
\(415\) 18.2060 4.11661i 0.893697 0.202076i
\(416\) 4.77695 + 14.7019i 0.234209 + 0.720822i
\(417\) 1.77948i 0.0871417i
\(418\) −2.55869 + 5.01138i −0.125150 + 0.245114i
\(419\) 11.3868 0.556281 0.278140 0.960540i \(-0.410282\pi\)
0.278140 + 0.960540i \(0.410282\pi\)
\(420\) 3.91690 9.11290i 0.191125 0.444664i
\(421\) 8.96175 + 6.51109i 0.436769 + 0.317331i 0.784350 0.620319i \(-0.212997\pi\)
−0.347581 + 0.937650i \(0.612997\pi\)
\(422\) 0.879958 + 1.21116i 0.0428357 + 0.0589582i
\(423\) 8.73770 + 2.83905i 0.424842 + 0.138039i
\(424\) −1.53425 + 4.72194i −0.0745098 + 0.229318i
\(425\) 18.6493 17.6865i 0.904626 0.857921i
\(426\) −0.590471 0.429002i −0.0286084 0.0207852i
\(427\) 4.01849 1.30569i 0.194468 0.0631866i
\(428\) 11.6849i 0.564811i
\(429\) 13.5607 + 6.92377i 0.654716 + 0.334283i
\(430\) −4.05233 3.55492i −0.195421 0.171433i
\(431\) −9.40890 28.9576i −0.453211 1.39484i −0.873223 0.487321i \(-0.837974\pi\)
0.420012 0.907519i \(-0.362026\pi\)
\(432\) 2.04246 2.81120i 0.0982679 0.135254i
\(433\) 8.87831 + 12.2200i 0.426665 + 0.587253i 0.967184 0.254078i \(-0.0817721\pi\)
−0.540519 + 0.841332i \(0.681772\pi\)
\(434\) −1.80258 + 5.54778i −0.0865268 + 0.266302i
\(435\) 6.96921 + 11.7184i 0.334148 + 0.561852i
\(436\) 8.86349 6.43970i 0.424484 0.308406i
\(437\) −20.1606 + 27.7486i −0.964411 + 1.32740i
\(438\) 2.57481 0.836606i 0.123029 0.0399746i
\(439\) −23.6799 −1.13018 −0.565090 0.825030i \(-0.691158\pi\)
−0.565090 + 0.825030i \(0.691158\pi\)
\(440\) 8.37750 + 2.13645i 0.399382 + 0.101851i
\(441\) −1.61265 −0.0767928
\(442\) −6.68972 + 2.17362i −0.318197 + 0.103389i
\(443\) −18.0930 + 24.9029i −0.859626 + 1.18317i 0.122033 + 0.992526i \(0.461059\pi\)
−0.981659 + 0.190648i \(0.938941\pi\)
\(444\) −4.90564 + 3.56416i −0.232811 + 0.169147i
\(445\) −7.18553 + 4.27342i −0.340627 + 0.202580i
\(446\) 2.61330 8.04291i 0.123743 0.380843i
\(447\) 1.29772 + 1.78616i 0.0613800 + 0.0844823i
\(448\) 8.11208 11.1653i 0.383260 0.527512i
\(449\) 1.42411 + 4.38295i 0.0672078 + 0.206844i 0.979020 0.203762i \(-0.0653170\pi\)
−0.911813 + 0.410607i \(0.865317\pi\)
\(450\) −1.47763 + 0.194064i −0.0696562 + 0.00914827i
\(451\) 1.09986 1.09803i 0.0517904 0.0517041i
\(452\) 15.7485i 0.740749i
\(453\) −12.2245 + 3.97199i −0.574358 + 0.186620i
\(454\) 1.58726 + 1.15321i 0.0744939 + 0.0541230i
\(455\) −23.7263 2.18388i −1.11231 0.102382i
\(456\) 2.05046 6.31068i 0.0960218 0.295525i
\(457\) −27.7976 9.03198i −1.30032 0.422498i −0.424624 0.905370i \(-0.639594\pi\)
−0.875691 + 0.482872i \(0.839594\pi\)
\(458\) 2.89570 + 3.98560i 0.135307 + 0.186235i
\(459\) 4.15872 + 3.02149i 0.194113 + 0.141031i
\(460\) 23.6591 + 10.1691i 1.10311 + 0.474138i
\(461\) 5.76367 0.268441 0.134220 0.990951i \(-0.457147\pi\)
0.134220 + 0.990951i \(0.457147\pi\)
\(462\) 0.357054 + 2.26658i 0.0166116 + 0.105451i
\(463\) 21.9028i 1.01791i −0.860794 0.508954i \(-0.830032\pi\)
0.860794 0.508954i \(-0.169968\pi\)
\(464\) 6.54726 + 20.1504i 0.303949 + 0.935459i
\(465\) −18.3896 + 4.15813i −0.852798 + 0.192828i
\(466\) −5.63432 + 4.09357i −0.261005 + 0.189631i
\(467\) −13.9193 4.52264i −0.644106 0.209283i −0.0312926 0.999510i \(-0.509962\pi\)
−0.612814 + 0.790227i \(0.709962\pi\)
\(468\) −8.34434 2.71124i −0.385717 0.125327i
\(469\) 16.6473 12.0950i 0.768701 0.558494i
\(470\) −1.35046 5.97253i −0.0622922 0.275492i
\(471\) −0.259466 0.798553i −0.0119555 0.0367954i
\(472\) 7.76373i 0.357355i
\(473\) −26.4913 4.21845i −1.21807 0.193965i
\(474\) −3.85283 −0.176966
\(475\) 25.6908 12.2440i 1.17877 0.561795i
\(476\) 18.4478 + 13.4031i 0.845553 + 0.614330i
\(477\) −2.50333 3.44553i −0.114619 0.157760i
\(478\) 5.04184 + 1.63819i 0.230608 + 0.0749292i
\(479\) −8.91924 + 27.4506i −0.407530 + 1.25425i 0.511234 + 0.859442i \(0.329189\pi\)
−0.918764 + 0.394807i \(0.870811\pi\)
\(480\) −7.49777 0.690130i −0.342225 0.0315000i
\(481\) 11.7839 + 8.56149i 0.537299 + 0.390370i
\(482\) −1.97218 + 0.640800i −0.0898303 + 0.0291876i
\(483\) 13.9868i 0.636419i
\(484\) 20.0046 6.46303i 0.909301 0.293774i
\(485\) −8.24301 + 9.39639i −0.374296 + 0.426668i
\(486\) −0.0921069 0.283476i −0.00417805 0.0128587i
\(487\) 13.0246 17.9268i 0.590200 0.812341i −0.404567 0.914508i \(-0.632578\pi\)
0.994767 + 0.102167i \(0.0325777\pi\)
\(488\) −1.24739 1.71689i −0.0564667 0.0777198i
\(489\) −3.42634 + 10.5452i −0.154944 + 0.476870i
\(490\) 0.549402 + 0.923791i 0.0248195 + 0.0417326i
\(491\) 13.0437 9.47680i 0.588654 0.427682i −0.253180 0.967419i \(-0.581476\pi\)
0.841833 + 0.539737i \(0.181476\pi\)
\(492\) −0.526393 + 0.724517i −0.0237316 + 0.0326638i
\(493\) −29.8093 + 9.68562i −1.34254 + 0.436219i
\(494\) −7.78850 −0.350421
\(495\) −5.70658 + 4.73656i −0.256492 + 0.212892i
\(496\) −29.2988 −1.31556
\(497\) 5.40537 1.75631i 0.242464 0.0787813i
\(498\) 1.46247 2.01291i 0.0655347 0.0902007i
\(499\) −24.9683 + 18.1406i −1.11774 + 0.812083i −0.983864 0.178916i \(-0.942741\pi\)
−0.133872 + 0.990999i \(0.542741\pi\)
\(500\) −13.2206 16.7864i −0.591241 0.750710i
\(501\) −1.37969 + 4.24625i −0.0616400 + 0.189709i
\(502\) −0.111549 0.153534i −0.00497866 0.00685254i
\(503\) 4.95604 6.82141i 0.220979 0.304152i −0.684106 0.729383i \(-0.739807\pi\)
0.905085 + 0.425231i \(0.139807\pi\)
\(504\) −0.836152 2.57341i −0.0372452 0.114629i
\(505\) 2.71328 + 2.38023i 0.120739 + 0.105919i
\(506\) −5.88454 + 0.926990i −0.261600 + 0.0412097i
\(507\) 8.07553i 0.358647i
\(508\) −21.9537 + 7.13319i −0.974039 + 0.316484i
\(509\) −23.8592 17.3347i −1.05754 0.768349i −0.0839094 0.996473i \(-0.526741\pi\)
−0.973632 + 0.228125i \(0.926741\pi\)
\(510\) 0.314025 3.41166i 0.0139053 0.151071i
\(511\) −6.51477 + 20.0504i −0.288196 + 0.886977i
\(512\) −18.8333 6.11931i −0.832323 0.270438i
\(513\) 3.34560 + 4.60482i 0.147712 + 0.203308i
\(514\) −0.116242 0.0844550i −0.00512723 0.00372515i
\(515\) −17.4997 7.52171i −0.771130 0.331446i
\(516\) 15.4575 0.680480
\(517\) −21.5283 21.5642i −0.946814 0.948394i
\(518\) 2.19502i 0.0964437i
\(519\) 5.58300 + 17.1827i 0.245067 + 0.754238i
\(520\) 2.63929 + 11.6724i 0.115740 + 0.511871i
\(521\) 7.77559 5.64930i 0.340655 0.247500i −0.404283 0.914634i \(-0.632479\pi\)
0.744938 + 0.667134i \(0.232479\pi\)
\(522\) 1.72846 + 0.561610i 0.0756526 + 0.0245810i
\(523\) 3.94423 + 1.28156i 0.172469 + 0.0560387i 0.393979 0.919120i \(-0.371098\pi\)
−0.221509 + 0.975158i \(0.571098\pi\)
\(524\) −5.07343 + 3.68606i −0.221634 + 0.161026i
\(525\) 5.54077 10.1972i 0.241819 0.445044i
\(526\) 1.67701 + 5.16129i 0.0731209 + 0.225043i
\(527\) 43.3429i 1.88805i
\(528\) −10.2730 + 5.22356i −0.447074 + 0.227326i
\(529\) −13.3127 −0.578813
\(530\) −1.12090 + 2.60784i −0.0486888 + 0.113277i
\(531\) −5.38782 3.91448i −0.233811 0.169874i
\(532\) 14.8408 + 20.4266i 0.643431 + 0.885606i
\(533\) 2.04593 + 0.664762i 0.0886189 + 0.0287940i
\(534\) −0.344371 + 1.05987i −0.0149024 + 0.0458649i
\(535\) 1.25309 13.6139i 0.0541756 0.588579i
\(536\) −8.36126 6.07481i −0.361151 0.262392i
\(537\) 11.3884 3.70030i 0.491444 0.159680i
\(538\) 7.76595i 0.334814i
\(539\) 4.76357 + 2.43216i 0.205181 + 0.104761i
\(540\) 2.81820 3.21253i 0.121276 0.138245i
\(541\) 9.65751 + 29.7228i 0.415209 + 1.27788i 0.912064 + 0.410048i \(0.134488\pi\)
−0.496855 + 0.867833i \(0.665512\pi\)
\(542\) −0.0515772 + 0.0709899i −0.00221543 + 0.00304928i
\(543\) 9.29788 + 12.7974i 0.399010 + 0.549190i
\(544\) 5.34889 16.4622i 0.229332 0.705811i
\(545\) 11.0173 6.55226i 0.471929 0.280668i
\(546\) −2.56947 + 1.86683i −0.109963 + 0.0798931i
\(547\) −5.30558 + 7.30250i −0.226850 + 0.312232i −0.907236 0.420621i \(-0.861812\pi\)
0.680386 + 0.732854i \(0.261812\pi\)
\(548\) −7.30210 + 2.37260i −0.311930 + 0.101352i
\(549\) 1.82041 0.0776931
\(550\) 4.65743 + 1.65529i 0.198593 + 0.0705819i
\(551\) −34.7054 −1.47850
\(552\) 6.68114 2.17083i 0.284368 0.0923969i
\(553\) 17.6350 24.2725i 0.749918 1.03217i
\(554\) 7.30392 5.30661i 0.310314 0.225456i
\(555\) −6.09769 + 3.62645i −0.258833 + 0.153934i
\(556\) 1.05093 3.23442i 0.0445693 0.137170i
\(557\) 4.23520 + 5.82925i 0.179451 + 0.246993i 0.889261 0.457400i \(-0.151219\pi\)
−0.709810 + 0.704393i \(0.751219\pi\)
\(558\) −1.47722 + 2.03321i −0.0625355 + 0.0860728i
\(559\) −11.4740 35.3134i −0.485299 1.49360i
\(560\) 11.8932 13.5573i 0.502579 0.572900i
\(561\) −7.72741 15.1972i −0.326252 0.641627i
\(562\) 8.85802i 0.373653i
\(563\) 25.1185 8.16149i 1.05862 0.343966i 0.272573 0.962135i \(-0.412125\pi\)
0.786045 + 0.618169i \(0.212125\pi\)
\(564\) 14.2051 + 10.3206i 0.598144 + 0.434577i
\(565\) −1.68887 + 18.3483i −0.0710512 + 0.771920i
\(566\) 0.146439 0.450692i 0.00615528 0.0189440i
\(567\) 2.20747 + 0.717249i 0.0927048 + 0.0301216i
\(568\) −1.67790 2.30943i −0.0704030 0.0969014i
\(569\) 35.0343 + 25.4539i 1.46871 + 1.06708i 0.980984 + 0.194088i \(0.0621748\pi\)
0.487730 + 0.872995i \(0.337825\pi\)
\(570\) 1.49804 3.48528i 0.0627459 0.145982i
\(571\) −1.82495 −0.0763718 −0.0381859 0.999271i \(-0.512158\pi\)
−0.0381859 + 0.999271i \(0.512158\pi\)
\(572\) 20.5591 + 20.5934i 0.859620 + 0.861055i
\(573\) 9.00747i 0.376292i
\(574\) 0.100178 + 0.308318i 0.00418137 + 0.0128689i
\(575\) 26.4743 + 14.3851i 1.10405 + 0.599899i
\(576\) 4.81043 3.49498i 0.200434 0.145624i
\(577\) 24.7392 + 8.03825i 1.02991 + 0.334637i 0.774753 0.632264i \(-0.217874\pi\)
0.255153 + 0.966901i \(0.417874\pi\)
\(578\) 2.67158 + 0.868050i 0.111123 + 0.0361061i
\(579\) 3.10606 2.25668i 0.129083 0.0937845i
\(580\) 5.74674 + 25.4154i 0.238620 + 1.05532i
\(581\) 5.98725 + 18.4269i 0.248393 + 0.764475i
\(582\) 1.66617i 0.0690651i
\(583\) 2.19804 + 13.9532i 0.0910334 + 0.577881i
\(584\) 10.5887 0.438165
\(585\) −9.43109 4.05366i −0.389928 0.167598i
\(586\) 0.101532 + 0.0737677i 0.00419427 + 0.00304731i
\(587\) −2.35319 3.23889i −0.0971267 0.133683i 0.757688 0.652617i \(-0.226329\pi\)
−0.854814 + 0.518934i \(0.826329\pi\)
\(588\) −2.93118 0.952399i −0.120880 0.0392763i
\(589\) 14.8304 45.6432i 0.611076 1.88070i
\(590\) −0.406834 + 4.41996i −0.0167491 + 0.181967i
\(591\) −6.74509 4.90060i −0.277456 0.201584i
\(592\) −10.4853 + 3.40689i −0.430945 + 0.140022i
\(593\) 32.2116i 1.32277i 0.750045 + 0.661386i \(0.230032\pi\)
−0.750045 + 0.661386i \(0.769968\pi\)
\(594\) −0.155460 + 0.976267i −0.00637861 + 0.0400567i
\(595\) 20.0558 + 17.5940i 0.822209 + 0.721285i
\(596\) 1.30389 + 4.01296i 0.0534094 + 0.164377i
\(597\) 1.30722 1.79923i 0.0535009 0.0736377i
\(598\) −4.84671 6.67092i −0.198197 0.272794i
\(599\) 4.17691 12.8552i 0.170664 0.525250i −0.828745 0.559627i \(-0.810945\pi\)
0.999409 + 0.0343766i \(0.0109446\pi\)
\(600\) −5.73094 1.06402i −0.233965 0.0434385i
\(601\) −22.2420 + 16.1598i −0.907270 + 0.659170i −0.940323 0.340284i \(-0.889477\pi\)
0.0330532 + 0.999454i \(0.489477\pi\)
\(602\) 3.28897 4.52688i 0.134048 0.184502i
\(603\) 8.43150 2.73956i 0.343357 0.111564i
\(604\) −24.5653 −0.999548
\(605\) 24.0001 5.38467i 0.975743 0.218918i
\(606\) 0.481120 0.0195442
\(607\) 35.7706 11.6226i 1.45188 0.471745i 0.526303 0.850297i \(-0.323578\pi\)
0.925580 + 0.378552i \(0.123578\pi\)
\(608\) 11.2655 15.5057i 0.456878 0.628839i
\(609\) −11.4495 + 8.31858i −0.463959 + 0.337086i
\(610\) −0.620182 1.04280i −0.0251104 0.0422219i
\(611\) 13.0335 40.1131i 0.527281 1.62280i
\(612\) 5.77454 + 7.94798i 0.233422 + 0.321278i
\(613\) 17.0946 23.5287i 0.690445 0.950316i −0.309555 0.950882i \(-0.600180\pi\)
1.00000 0.000565226i \(0.000179917\pi\)
\(614\) −0.856167 2.63501i −0.0345521 0.106340i
\(615\) −0.690988 + 0.787672i −0.0278633 + 0.0317620i
\(616\) −1.41128 + 8.86261i −0.0568619 + 0.357085i
\(617\) 9.61911i 0.387251i 0.981076 + 0.193625i \(0.0620246\pi\)
−0.981076 + 0.193625i \(0.937975\pi\)
\(618\) −2.41476 + 0.784604i −0.0971361 + 0.0315614i
\(619\) −18.9370 13.7585i −0.761143 0.553003i 0.138118 0.990416i \(-0.455895\pi\)
−0.899261 + 0.437413i \(0.855895\pi\)
\(620\) −35.8810 3.30266i −1.44102 0.132638i
\(621\) −1.86214 + 5.73107i −0.0747250 + 0.229980i
\(622\) −3.42854 1.11400i −0.137472 0.0446674i
\(623\) −5.10083 7.02069i −0.204361 0.281278i
\(624\) −12.9057 9.37654i −0.516642 0.375362i
\(625\) −13.6029 20.9753i −0.544115 0.839011i
\(626\) 2.07931 0.0831059
\(627\) −2.93759 18.6478i −0.117316 0.744722i
\(628\) 1.60470i 0.0640345i
\(629\) −5.03995 15.5114i −0.200956 0.618479i
\(630\) −0.341177 1.50888i −0.0135928 0.0601152i
\(631\) 18.3295 13.3172i 0.729686 0.530148i −0.159778 0.987153i \(-0.551078\pi\)
0.889464 + 0.457005i \(0.151078\pi\)
\(632\) −14.3315 4.65659i −0.570076 0.185229i
\(633\) −4.77683 1.55209i −0.189862 0.0616899i
\(634\) −1.74572 + 1.26834i −0.0693313 + 0.0503721i
\(635\) −26.3428 + 5.95645i −1.04538 + 0.236374i
\(636\) −2.51523 7.74109i −0.0997354 0.306954i
\(637\) 7.40336i 0.293332i
\(638\) −4.25865 4.26575i −0.168601 0.168883i
\(639\) 2.44868 0.0968681
\(640\) −17.4760 7.51151i −0.690799 0.296918i
\(641\) −18.6047 13.5171i −0.734841 0.533893i 0.156250 0.987717i \(-0.450059\pi\)
−0.891091 + 0.453825i \(0.850059\pi\)
\(642\) −1.07117 1.47434i −0.0422756 0.0581874i
\(643\) 11.0446 + 3.58860i 0.435555 + 0.141520i 0.518584 0.855027i \(-0.326459\pi\)
−0.0830288 + 0.996547i \(0.526459\pi\)
\(644\) −8.26030 + 25.4226i −0.325501 + 1.00179i
\(645\) 18.0093 + 1.65766i 0.709116 + 0.0652703i
\(646\) 7.05545 + 5.12608i 0.277593 + 0.201683i
\(647\) 34.4009 11.1775i 1.35244 0.439434i 0.458928 0.888473i \(-0.348234\pi\)
0.893512 + 0.449039i \(0.148234\pi\)
\(648\) 1.16578i 0.0457960i
\(649\) 10.0112 + 19.6887i 0.392975 + 0.772849i
\(650\) 0.890911 + 6.78353i 0.0349444 + 0.266072i
\(651\) −6.04763 18.6127i −0.237025 0.729489i
\(652\) −12.4556 + 17.1436i −0.487797 + 0.671395i
\(653\) −5.08606 7.00036i −0.199033 0.273945i 0.697821 0.716272i \(-0.254153\pi\)
−0.896854 + 0.442327i \(0.854153\pi\)
\(654\) 0.528011 1.62505i 0.0206469 0.0635445i
\(655\) −6.30625 + 3.75049i −0.246406 + 0.146544i
\(656\) −1.31731 + 0.957079i −0.0514322 + 0.0373677i
\(657\) −5.33885 + 7.34830i −0.208288 + 0.286684i
\(658\) 6.04498 1.96413i 0.235658 0.0765698i
\(659\) 17.4599 0.680143 0.340071 0.940400i \(-0.389549\pi\)
0.340071 + 0.940400i \(0.389549\pi\)
\(660\) −13.1697 + 5.23907i −0.512630 + 0.203930i
\(661\) 16.2393 0.631636 0.315818 0.948820i \(-0.397721\pi\)
0.315818 + 0.948820i \(0.397721\pi\)
\(662\) 7.84176 2.54794i 0.304779 0.0990286i
\(663\) 13.8711 19.0919i 0.538708 0.741468i
\(664\) 7.87281 5.71993i 0.305524 0.221976i
\(665\) 15.1002 + 25.3902i 0.585561 + 0.984590i
\(666\) −0.292236 + 0.899410i −0.0113239 + 0.0348514i
\(667\) −21.5969 29.7255i −0.836234 1.15098i
\(668\) −5.01550 + 6.90325i −0.194056 + 0.267095i
\(669\) 8.76757 + 26.9838i 0.338974 + 1.04325i
\(670\) −4.44180 3.89659i −0.171602 0.150538i
\(671\) −5.37726 2.74550i −0.207587 0.105989i
\(672\) 7.81568i 0.301496i
\(673\) −25.1453 + 8.17022i −0.969282 + 0.314939i −0.750526 0.660841i \(-0.770200\pi\)
−0.218756 + 0.975780i \(0.570200\pi\)
\(674\) 5.30936 + 3.85748i 0.204509 + 0.148584i
\(675\) 3.62795 3.44064i 0.139640 0.132430i
\(676\) −4.76925 + 14.6782i −0.183433 + 0.564548i
\(677\) 29.8203 + 9.68921i 1.14609 + 0.372387i 0.819668 0.572838i \(-0.194158\pi\)
0.326420 + 0.945225i \(0.394158\pi\)
\(678\) 1.44368 + 1.98706i 0.0554443 + 0.0763126i
\(679\) −10.4968 7.62634i −0.402829 0.292672i
\(680\) 5.29146 12.3109i 0.202918 0.472102i
\(681\) −6.58235 −0.252236
\(682\) 7.42997 3.77796i 0.284508 0.144665i
\(683\) 3.85934i 0.147674i −0.997270 0.0738368i \(-0.976476\pi\)
0.997270 0.0738368i \(-0.0235244\pi\)
\(684\) 3.36150 + 10.3456i 0.128530 + 0.395576i
\(685\) −8.76198 + 1.98119i −0.334778 + 0.0756976i
\(686\) −4.82050 + 3.50230i −0.184047 + 0.133718i
\(687\) −15.7193 5.10750i −0.599727 0.194863i
\(688\) 26.7291 + 8.68482i 1.01904 + 0.331106i
\(689\) −15.8178 + 11.4923i −0.602610 + 0.437822i
\(690\) 3.91739 0.885771i 0.149132 0.0337207i
\(691\) −6.82056 20.9915i −0.259466 0.798555i −0.992917 0.118812i \(-0.962091\pi\)
0.733450 0.679743i \(-0.237909\pi\)
\(692\) 34.5288i 1.31259i
\(693\) −5.43884 5.44792i −0.206605 0.206949i
\(694\) −7.97835 −0.302854
\(695\) 1.57128 3.65567i 0.0596019 0.138667i
\(696\) 5.75063 + 4.17808i 0.217977 + 0.158370i
\(697\) −1.41584 1.94874i −0.0536289 0.0738139i
\(698\) −6.13477 1.99331i −0.232205 0.0754478i
\(699\) 7.22032 22.2218i 0.273097 0.840507i
\(700\) 16.0933 15.2624i 0.608270 0.576865i
\(701\) −27.8329 20.2218i −1.05123 0.763767i −0.0787880 0.996891i \(-0.525105\pi\)
−0.972447 + 0.233125i \(0.925105\pi\)
\(702\) −1.30138 + 0.422845i −0.0491176 + 0.0159593i
\(703\) 18.0591i 0.681112i
\(704\) −19.4805 + 3.06875i −0.734198 + 0.115658i
\(705\) 15.4434 + 13.5477i 0.581630 + 0.510237i
\(706\) −2.90270 8.93359i −0.109244 0.336220i
\(707\) −2.20216 + 3.03102i −0.0828209 + 0.113993i
\(708\) −7.48119 10.2970i −0.281160 0.386984i
\(709\) 7.78530 23.9607i 0.292383 0.899863i −0.691705 0.722180i \(-0.743140\pi\)
0.984088 0.177682i \(-0.0568600\pi\)
\(710\) −0.834222 1.40270i −0.0313078 0.0526424i
\(711\) 10.4575 7.59782i 0.392187 0.284940i
\(712\) −2.56194 + 3.52621i −0.0960127 + 0.132150i
\(713\) 48.3227 15.7010i 1.80970 0.588007i
\(714\) 3.55631 0.133092
\(715\) 21.7446 + 26.1978i 0.813203 + 0.979742i
\(716\) 22.8850 0.855253
\(717\) −16.9153 + 5.49610i −0.631712 + 0.205256i
\(718\) −0.781549 + 1.07571i −0.0291671 + 0.0401451i
\(719\) −14.1392 + 10.2727i −0.527304 + 0.383109i −0.819348 0.573296i \(-0.805665\pi\)
0.292044 + 0.956405i \(0.405665\pi\)
\(720\) 6.67819 3.97169i 0.248881 0.148016i
\(721\) 6.10982 18.8041i 0.227542 0.700301i
\(722\) 2.34719 + 3.23062i 0.0873532 + 0.120231i
\(723\) 4.08930 5.62843i 0.152083 0.209324i
\(724\) 9.34209 + 28.7520i 0.347196 + 1.06856i
\(725\) 3.96989 + 30.2273i 0.147438 + 1.12261i
\(726\) 1.93160 2.64931i 0.0716883 0.0983252i
\(727\) 3.60045i 0.133533i −0.997769 0.0667666i \(-0.978732\pi\)
0.997769 0.0667666i \(-0.0212683\pi\)
\(728\) −11.8140 + 3.83861i −0.437857 + 0.142268i
\(729\) 0.809017 + 0.587785i 0.0299636 + 0.0217698i
\(730\) 6.02826 + 0.554869i 0.223116 + 0.0205366i
\(731\) −12.8478 + 39.5415i −0.475193 + 1.46249i
\(732\) 3.30881 + 1.07510i 0.122297 + 0.0397367i
\(733\) −12.8631 17.7046i −0.475110 0.653932i 0.502446 0.864608i \(-0.332434\pi\)
−0.977556 + 0.210676i \(0.932434\pi\)
\(734\) 0.249097 + 0.180980i 0.00919434 + 0.00668008i
\(735\) −3.31293 1.42396i −0.122199 0.0525236i
\(736\) 20.2912 0.747944
\(737\) −29.0374 4.62389i −1.06961 0.170323i
\(738\) 0.139670i 0.00514134i
\(739\) 1.77627 + 5.46681i 0.0653413 + 0.201100i 0.978397 0.206735i \(-0.0662838\pi\)
−0.913056 + 0.407835i \(0.866284\pi\)
\(740\) −13.2250 + 2.99034i −0.486160 + 0.109927i
\(741\) 21.1398 15.3590i 0.776591 0.564227i
\(742\) −2.80222 0.910498i −0.102873 0.0334254i
\(743\) 17.1203 + 5.56273i 0.628084 + 0.204077i 0.605726 0.795673i \(-0.292883\pi\)
0.0223576 + 0.999750i \(0.492883\pi\)
\(744\) −7.95222 + 5.77762i −0.291542 + 0.211818i
\(745\) 1.08879 + 4.81525i 0.0398902 + 0.176417i
\(746\) 3.01117 + 9.26743i 0.110247 + 0.339305i
\(747\) 8.34751i 0.305420i
\(748\) −5.07032 32.1864i −0.185389 1.17685i
\(749\) 14.1911 0.518532
\(750\) −3.20692 0.906068i −0.117100 0.0330849i
\(751\) 15.3848 + 11.1777i 0.561400 + 0.407881i 0.831971 0.554819i \(-0.187213\pi\)
−0.270571 + 0.962700i \(0.587213\pi\)
\(752\) 18.7648 + 25.8275i 0.684282 + 0.941834i
\(753\) 0.605539 + 0.196752i 0.0220671 + 0.00717002i
\(754\) 2.57825 7.93502i 0.0938942 0.288977i
\(755\) −28.6206 2.63437i −1.04161 0.0958747i
\(756\) 3.58874 + 2.60737i 0.130521 + 0.0948292i
\(757\) 2.27835 0.740280i 0.0828079 0.0269059i −0.267320 0.963608i \(-0.586138\pi\)
0.350128 + 0.936702i \(0.386138\pi\)
\(758\) 1.27655i 0.0463663i
\(759\) 14.1440 14.1204i 0.513395 0.512539i
\(760\) 9.78466 11.1537i 0.354927 0.404589i
\(761\) 14.0321 + 43.1864i 0.508664 + 1.56551i 0.794523 + 0.607234i \(0.207721\pi\)
−0.285860 + 0.958272i \(0.592279\pi\)
\(762\) −2.11609 + 2.91254i −0.0766578 + 0.105510i
\(763\) 7.82090 + 10.7646i 0.283136 + 0.389703i
\(764\) 5.31963 16.3721i 0.192458 0.592323i
\(765\) 5.87548 + 9.87930i 0.212428 + 0.357187i
\(766\) −6.49587 + 4.71953i −0.234705 + 0.170523i
\(767\) −17.9706 + 24.7345i −0.648882 + 0.893109i
\(768\) 8.89850 2.89130i 0.321097 0.104331i
\(769\) 49.1931 1.77395 0.886975 0.461818i \(-0.152803\pi\)
0.886975 + 0.461818i \(0.152803\pi\)
\(770\) −1.26787 + 4.97161i −0.0456908 + 0.179164i
\(771\) 0.482055 0.0173608
\(772\) 6.97838 2.26741i 0.251157 0.0816059i
\(773\) 12.4780 17.1745i 0.448803 0.617724i −0.523337 0.852126i \(-0.675313\pi\)
0.972140 + 0.234402i \(0.0753132\pi\)
\(774\) 1.95034 1.41701i 0.0701037 0.0509333i
\(775\) −41.4502 7.69574i −1.48893 0.276439i
\(776\) −2.01376 + 6.19771i −0.0722898 + 0.222485i
\(777\) −4.32860 5.95781i −0.155288 0.213735i
\(778\) 6.43033 8.85059i 0.230538 0.317309i
\(779\) −0.824198 2.53662i −0.0295300 0.0908839i
\(780\) −14.7481 12.9378i −0.528067 0.463249i
\(781\) −7.23309 3.69304i −0.258820 0.132147i
\(782\) 9.23297i 0.330170i
\(783\) −5.79895 + 1.88419i −0.207237 + 0.0673355i
\(784\) −4.53349 3.29377i −0.161910 0.117635i
\(785\) 0.172087 1.86961i 0.00614206 0.0667291i
\(786\) −0.302231 + 0.930172i −0.0107802 + 0.0331781i
\(787\) −7.84951 2.55046i −0.279805 0.0909141i 0.165753 0.986167i \(-0.446995\pi\)
−0.445558 + 0.895253i \(0.646995\pi\)
\(788\) −9.36581 12.8909i −0.333643 0.459221i
\(789\) −14.7299 10.7019i −0.524398 0.380998i
\(790\) −7.91503 3.40203i −0.281604 0.121039i
\(791\) −19.1263 −0.680053
\(792\) −1.75820 + 3.44356i −0.0624749 + 0.122362i
\(793\) 8.35714i 0.296771i
\(794\) −0.692910 2.13256i −0.0245905 0.0756817i
\(795\) −2.10030 9.28873i −0.0744899 0.329437i
\(796\) 3.43862 2.49830i 0.121879 0.0885499i
\(797\) −5.99002 1.94627i −0.212177 0.0689406i 0.201000 0.979591i \(-0.435581\pi\)
−0.413177 + 0.910651i \(0.635581\pi\)
\(798\) 3.74506 + 1.21684i 0.132574 + 0.0430758i
\(799\) −38.2077 + 27.7595i −1.35169 + 0.982061i
\(800\) −14.7936 8.03825i −0.523033 0.284195i
\(801\) −1.15536 3.55583i −0.0408226 0.125639i
\(802\) 4.59003i 0.162080i
\(803\) 26.8529 13.6540i 0.947617 0.481840i
\(804\) 16.9432 0.597540
\(805\) −12.3502 + 28.7336i −0.435289 + 1.01273i
\(806\) 9.33409 + 6.78162i 0.328779 + 0.238872i
\(807\) −15.3145 21.0786i −0.539097 0.742003i
\(808\) 1.78964 + 0.581488i 0.0629592 + 0.0204567i
\(809\) −16.8675 + 51.9127i −0.593029 + 1.82515i −0.0287239 + 0.999587i \(0.509144\pi\)
−0.564305 + 0.825567i \(0.690856\pi\)
\(810\) 0.0610888 0.663686i 0.00214644 0.0233196i
\(811\) 8.91273 + 6.47547i 0.312968 + 0.227385i 0.733169 0.680046i \(-0.238040\pi\)
−0.420201 + 0.907431i \(0.638040\pi\)
\(812\) −25.7237 + 8.35813i −0.902725 + 0.293313i
\(813\) 0.294394i 0.0103248i
\(814\) 2.21970 2.21600i 0.0778005 0.0776708i
\(815\) −16.3502 + 18.6380i −0.572723 + 0.652860i
\(816\) 5.51975 + 16.9880i 0.193230 + 0.594701i
\(817\) −27.0593 + 37.2440i −0.946687 + 1.30300i
\(818\) −2.85370 3.92778i −0.0997772 0.137332i
\(819\) 3.29275 10.1341i 0.115058 0.354113i
\(820\) −1.72114 + 1.02360i −0.0601047 + 0.0357458i
\(821\) −33.7463 + 24.5181i −1.17775 + 0.855689i −0.991917 0.126892i \(-0.959500\pi\)
−0.185838 + 0.982580i \(0.559500\pi\)
\(822\) −0.703839 + 0.968752i −0.0245492 + 0.0337891i
\(823\) −2.85953 + 0.929117i −0.0996769 + 0.0323870i −0.358431 0.933556i \(-0.616688\pi\)
0.258754 + 0.965943i \(0.416688\pi\)
\(824\) −9.93056 −0.345947
\(825\) −15.9056 + 4.69163i −0.553762 + 0.163342i
\(826\) −4.60737 −0.160311
\(827\) −42.6193 + 13.8478i −1.48202 + 0.481537i −0.934715 0.355398i \(-0.884345\pi\)
−0.547303 + 0.836935i \(0.684345\pi\)
\(828\) −6.76931 + 9.31716i −0.235250 + 0.323794i
\(829\) −31.3024 + 22.7425i −1.08718 + 0.789879i −0.978920 0.204244i \(-0.934526\pi\)
−0.108256 + 0.994123i \(0.534526\pi\)
\(830\) 4.78180 2.84386i 0.165979 0.0987117i
\(831\) −9.35990 + 28.8068i −0.324691 + 0.999297i
\(832\) −16.0448 22.0837i −0.556253 0.765616i
\(833\) 4.87260 6.70656i 0.168826 0.232369i
\(834\) −0.163903 0.504441i −0.00567549 0.0174674i
\(835\) −6.58378 + 7.50499i −0.227841 + 0.259721i
\(836\) 5.67362 35.6295i 0.196226 1.23227i
\(837\) 8.43171i 0.291442i
\(838\) 3.22788 1.04880i 0.111505 0.0362303i
\(839\) −17.2208 12.5117i −0.594530 0.431951i 0.249403 0.968400i \(-0.419766\pi\)
−0.843933 + 0.536449i \(0.819766\pi\)
\(840\) 0.554568 6.02498i 0.0191344 0.207882i
\(841\) 2.52713 7.77771i 0.0871424 0.268197i
\(842\) 3.14016 + 1.02030i 0.108217 + 0.0351618i
\(843\) −17.4681 24.0428i −0.601633 0.828077i
\(844\) −7.76582 5.64220i −0.267311 0.194213i
\(845\) −7.13065 + 16.5899i −0.245302 + 0.570710i
\(846\) 2.73842 0.0941490
\(847\) 7.84923 + 24.2952i 0.269703 + 0.834795i
\(848\) 14.7990i 0.508201i
\(849\) 0.491299 + 1.51206i 0.0168613 + 0.0518939i
\(850\) 3.65759 6.73143i 0.125454 0.230886i
\(851\) 15.4678 11.2380i 0.530229 0.385234i
\(852\) 4.45076 + 1.44614i 0.152480 + 0.0495439i
\(853\) −22.7440 7.38997i −0.778740 0.253028i −0.107438 0.994212i \(-0.534265\pi\)
−0.671302 + 0.741184i \(0.734265\pi\)
\(854\) 1.01888 0.740261i 0.0348654 0.0253312i
\(855\) 2.80696 + 12.4140i 0.0959962 + 0.424550i
\(856\) −2.20255 6.77876i −0.0752817 0.231693i
\(857\) 23.7057i 0.809773i −0.914367 0.404886i \(-0.867311\pi\)
0.914367 0.404886i \(-0.132689\pi\)
\(858\) 4.48186 + 0.713688i 0.153008 + 0.0243649i
\(859\) 29.2131 0.996739 0.498369 0.866965i \(-0.333932\pi\)
0.498369 + 0.866965i \(0.333932\pi\)
\(860\) 31.7551 + 13.6489i 1.08284 + 0.465425i
\(861\) −0.879913 0.639294i −0.0299874 0.0217871i
\(862\) −5.33439 7.34216i −0.181690 0.250075i
\(863\) 35.4580 + 11.5210i 1.20700 + 0.392180i 0.842333 0.538957i \(-0.181181\pi\)
0.364671 + 0.931136i \(0.381181\pi\)
\(864\) 1.04055 3.20247i 0.0354001 0.108950i
\(865\) −3.70286 + 40.2289i −0.125901 + 1.36782i
\(866\) 3.64233 + 2.64631i 0.123771 + 0.0899252i
\(867\) −8.96312 + 2.91229i −0.304403 + 0.0989067i
\(868\) 37.4024i 1.26952i
\(869\) −42.3490 + 6.67123i −1.43659 + 0.226306i
\(870\) 3.05495 + 2.67996i 0.103572 + 0.0908592i
\(871\) −12.5768 38.7074i −0.426149 1.31155i
\(872\) 3.92812 5.40659i 0.133023 0.183090i
\(873\) −3.28571 4.52239i −0.111204 0.153060i
\(874\) −3.15919 + 9.72300i −0.106861 + 0.328885i
\(875\) 20.3868 16.0561i 0.689198 0.542796i
\(876\) −14.0438 + 10.2034i −0.474494 + 0.344740i
\(877\) 15.6986 21.6072i 0.530103 0.729624i −0.457043 0.889444i \(-0.651092\pi\)
0.987146 + 0.159821i \(0.0510915\pi\)
\(878\) −6.71268 + 2.18108i −0.226542 + 0.0736079i
\(879\) −0.421054 −0.0142018
\(880\) −25.7166 + 1.65998i −0.866906 + 0.0559580i
\(881\) 51.3146 1.72883 0.864417 0.502775i \(-0.167688\pi\)
0.864417 + 0.502775i \(0.167688\pi\)
\(882\) −0.457147 + 0.148536i −0.0153929 + 0.00500147i
\(883\) −32.2812 + 44.4312i −1.08635 + 1.49523i −0.234012 + 0.972234i \(0.575185\pi\)
−0.852336 + 0.522995i \(0.824815\pi\)
\(884\) 36.4876 26.5098i 1.22721 0.891622i
\(885\) −7.61196 12.7991i −0.255873 0.430237i
\(886\) −2.83521 + 8.72587i −0.0952507 + 0.293151i
\(887\) −2.98155 4.10375i −0.100111 0.137790i 0.756023 0.654545i \(-0.227140\pi\)
−0.856133 + 0.516755i \(0.827140\pi\)
\(888\) −2.17408 + 2.99236i −0.0729573 + 0.100417i
\(889\) −8.66314 26.6624i −0.290552 0.894228i
\(890\) −1.64331 + 1.87325i −0.0550840 + 0.0627914i
\(891\) −1.50325 2.95639i −0.0503608 0.0990428i
\(892\) 54.2242i 1.81556i
\(893\) −49.7338 + 16.1595i −1.66428 + 0.540757i
\(894\) 0.532389 + 0.386803i 0.0178058 + 0.0129366i
\(895\) 26.6629 + 2.45418i 0.891243 + 0.0820342i
\(896\) 6.10153 18.7786i 0.203838 0.627348i
\(897\) 26.3102 + 8.54872i 0.878473 + 0.285433i
\(898\) 0.807400 + 1.11129i 0.0269433 + 0.0370843i
\(899\) 41.5926 + 30.2188i 1.38719 + 1.00785i
\(900\) 8.62620 4.11118i 0.287540 0.137039i
\(901\) 21.8928 0.729355
\(902\) 0.210648 0.412569i 0.00701381 0.0137371i
\(903\) 18.7729i 0.624723i
\(904\) 2.96853 + 9.13619i 0.0987318 + 0.303865i
\(905\) 7.80095 + 34.5003i 0.259312 + 1.14683i
\(906\) −3.09951 + 2.25193i −0.102974 + 0.0748152i
\(907\) 22.6661 + 7.36465i 0.752615 + 0.244539i 0.660106 0.751173i \(-0.270511\pi\)
0.0925087 + 0.995712i \(0.470511\pi\)
\(908\) −11.9642 3.88741i −0.397046 0.129008i
\(909\) −1.30587 + 0.948772i −0.0433131 + 0.0314688i
\(910\) −6.92698 + 1.56628i −0.229627 + 0.0519216i
\(911\) 4.92602 + 15.1607i 0.163206 + 0.502298i 0.998900 0.0468988i \(-0.0149338\pi\)
−0.835693 + 0.549197i \(0.814934\pi\)
\(912\) 19.7783i 0.654926i
\(913\) 12.5896 24.6575i 0.416653 0.816045i
\(914\) −8.71185 −0.288162
\(915\) 3.73974 + 1.60741i 0.123632 + 0.0531394i
\(916\) −25.5552 18.5670i −0.844369 0.613470i
\(917\) −4.47665 6.16159i −0.147832 0.203473i
\(918\) 1.45720 + 0.473472i 0.0480947 + 0.0156269i
\(919\) 10.8050 33.2543i 0.356423 1.09696i −0.598756 0.800931i \(-0.704338\pi\)
0.955180 0.296027i \(-0.0956618\pi\)
\(920\) 15.6422 + 1.43978i 0.515708 + 0.0474682i
\(921\) 7.52011 + 5.46368i 0.247796 + 0.180034i
\(922\) 1.63386 0.530874i 0.0538084 0.0174834i
\(923\) 11.2414i 0.370015i
\(924\) −6.66831 13.1143i −0.219371 0.431429i
\(925\) −15.7289 + 2.06574i −0.517162 + 0.0679213i
\(926\) −2.01740 6.20891i −0.0662958 0.204037i
\(927\) 5.00700 6.89154i 0.164451 0.226348i
\(928\) 12.0681 + 16.6104i 0.396156 + 0.545262i
\(929\) 10.6033 32.6335i 0.347882 1.07067i −0.612141 0.790749i \(-0.709692\pi\)
0.960023 0.279922i \(-0.0903085\pi\)
\(930\) −4.83002 + 2.87254i −0.158383 + 0.0941943i
\(931\) 7.42595 5.39527i 0.243376 0.176823i
\(932\) 26.2476 36.1267i 0.859768 1.18337i
\(933\) 11.5027 3.73745i 0.376581 0.122359i
\(934\) −4.36234 −0.142740
\(935\) −2.45568 38.0435i −0.0803092 1.24416i
\(936\) −5.35186 −0.174931
\(937\) −27.5787 + 8.96086i −0.900957 + 0.292739i −0.722632 0.691233i \(-0.757068\pi\)
−0.178325 + 0.983972i \(0.557068\pi\)
\(938\) 3.60508 4.96197i 0.117710 0.162014i
\(939\) −5.64374 + 4.10041i −0.184176 + 0.133812i
\(940\) 20.0691 + 33.7451i 0.654582 + 1.10065i
\(941\) 5.18921 15.9707i 0.169163 0.520631i −0.830156 0.557532i \(-0.811749\pi\)
0.999319 + 0.0369007i \(0.0117485\pi\)
\(942\) −0.147104 0.202472i −0.00479292 0.00659689i
\(943\) 1.65975 2.28445i 0.0540489 0.0743919i
\(944\) −7.15109 22.0088i −0.232748 0.716326i
\(945\) 3.90156 + 3.42266i 0.126918 + 0.111339i
\(946\) −7.89818 + 1.24420i −0.256792 + 0.0404524i
\(947\) 17.4385i 0.566677i −0.959020 0.283338i \(-0.908558\pi\)
0.959020 0.283338i \(-0.0914419\pi\)
\(948\) 23.4949 7.63394i 0.763078 0.247939i
\(949\) 33.7346 + 24.5096i 1.09507 + 0.795616i
\(950\) 6.15496 5.83719i 0.199693 0.189383i
\(951\) 2.23712 6.88514i 0.0725435 0.223266i
\(952\) 13.2285 + 4.29821i 0.428739 + 0.139306i
\(953\) −0.868687 1.19565i −0.0281395 0.0387308i 0.794715 0.606982i \(-0.207620\pi\)
−0.822855 + 0.568251i \(0.807620\pi\)
\(954\) −1.02699 0.746152i −0.0332501 0.0241576i
\(955\) 7.95355 18.5044i 0.257371 0.598789i
\(956\) −33.9914 −1.09936
\(957\) 19.9711 + 3.18018i 0.645573 + 0.102801i
\(958\) 8.60310i 0.277954i
\(959\) −2.88148 8.86827i −0.0930477 0.286371i
\(960\) 12.9683 2.93230i 0.418550 0.0946395i
\(961\) −32.4365 + 23.5665i −1.04634 + 0.760208i
\(962\) 4.12902 + 1.34160i 0.133125 + 0.0432549i
\(963\) 5.81480 + 1.88934i 0.187379 + 0.0608833i
\(964\) 10.7568 7.81529i 0.346454 0.251714i
\(965\) 8.37354 1.89336i 0.269554 0.0609495i
\(966\) 1.28828 + 3.96491i 0.0414496 + 0.127569i
\(967\) 26.6515i 0.857054i −0.903529 0.428527i \(-0.859033\pi\)
0.903529 0.428527i \(-0.140967\pi\)
\(968\) 10.3870 7.52017i 0.333851 0.241708i
\(969\) −29.2588 −0.939929
\(970\) −1.47122 + 3.42289i −0.0472381 + 0.109902i
\(971\) 31.3110 + 22.7487i 1.00482 + 0.730042i 0.963116 0.269088i \(-0.0867222\pi\)
0.0417012 + 0.999130i \(0.486722\pi\)
\(972\) 1.12335 + 1.54616i 0.0360315 + 0.0495931i
\(973\) 3.92815 + 1.27633i 0.125931 + 0.0409174i
\(974\) 2.04097 6.28147i 0.0653970 0.201271i
\(975\) −15.7953 16.6552i −0.505855 0.533394i
\(976\) 5.11754 + 3.71811i 0.163808 + 0.119014i
\(977\) 47.3070 15.3710i 1.51349 0.491761i 0.569568 0.821944i \(-0.307110\pi\)
0.943917 + 0.330183i \(0.107110\pi\)
\(978\) 3.30490i 0.105679i
\(979\) −1.95004 + 12.2460i −0.0623236 + 0.391383i
\(980\) −5.18068 4.54477i −0.165491 0.145177i
\(981\) 1.77147 + 5.45201i 0.0565586 + 0.174069i
\(982\) 2.82469 3.88786i 0.0901396 0.124067i
\(983\) −14.4260 19.8557i −0.460119 0.633300i 0.514414 0.857542i \(-0.328009\pi\)
−0.974534 + 0.224242i \(0.928009\pi\)
\(984\) −0.168808 + 0.519537i −0.00538139 + 0.0165622i
\(985\) −9.52952 16.0234i −0.303636 0.510547i
\(986\) −7.55810 + 5.49128i −0.240699 + 0.174878i
\(987\) −12.5342 + 17.2519i −0.398968 + 0.549133i
\(988\) 47.4949 15.4320i 1.51101 0.490958i
\(989\) −48.7386 −1.54980
\(990\) −1.18141 + 1.86832i −0.0375476 + 0.0593790i
\(991\) 32.4673 1.03136 0.515679 0.856782i \(-0.327540\pi\)
0.515679 + 0.856782i \(0.327540\pi\)
\(992\) −27.0023 + 8.77358i −0.857324 + 0.278561i
\(993\) −16.2598 + 22.3797i −0.515990 + 0.710199i
\(994\) 1.37052 0.995743i 0.0434703 0.0315831i
\(995\) 4.27419 2.54197i 0.135501 0.0805859i
\(996\) −4.92988 + 15.1726i −0.156209 + 0.480762i
\(997\) 23.3319 + 32.1136i 0.738929 + 1.01705i 0.998680 + 0.0513732i \(0.0163598\pi\)
−0.259750 + 0.965676i \(0.583640\pi\)
\(998\) −5.40705 + 7.44217i −0.171157 + 0.235578i
\(999\) −0.980446 3.01750i −0.0310199 0.0954696i
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 165.2.s.a.49.7 yes 48
3.2 odd 2 495.2.ba.c.379.6 48
5.2 odd 4 825.2.n.o.676.3 24
5.3 odd 4 825.2.n.p.676.4 24
5.4 even 2 inner 165.2.s.a.49.6 48
11.3 even 5 1815.2.c.j.364.11 24
11.8 odd 10 1815.2.c.k.364.14 24
11.9 even 5 inner 165.2.s.a.64.6 yes 48
15.14 odd 2 495.2.ba.c.379.7 48
33.20 odd 10 495.2.ba.c.64.7 48
55.3 odd 20 9075.2.a.dy.1.7 12
55.8 even 20 9075.2.a.ea.1.6 12
55.9 even 10 inner 165.2.s.a.64.7 yes 48
55.14 even 10 1815.2.c.j.364.14 24
55.19 odd 10 1815.2.c.k.364.11 24
55.42 odd 20 825.2.n.o.526.3 24
55.47 odd 20 9075.2.a.dz.1.6 12
55.52 even 20 9075.2.a.dx.1.7 12
55.53 odd 20 825.2.n.p.526.4 24
165.119 odd 10 495.2.ba.c.64.6 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.s.a.49.6 48 5.4 even 2 inner
165.2.s.a.49.7 yes 48 1.1 even 1 trivial
165.2.s.a.64.6 yes 48 11.9 even 5 inner
165.2.s.a.64.7 yes 48 55.9 even 10 inner
495.2.ba.c.64.6 48 165.119 odd 10
495.2.ba.c.64.7 48 33.20 odd 10
495.2.ba.c.379.6 48 3.2 odd 2
495.2.ba.c.379.7 48 15.14 odd 2
825.2.n.o.526.3 24 55.42 odd 20
825.2.n.o.676.3 24 5.2 odd 4
825.2.n.p.526.4 24 55.53 odd 20
825.2.n.p.676.4 24 5.3 odd 4
1815.2.c.j.364.11 24 11.3 even 5
1815.2.c.j.364.14 24 55.14 even 10
1815.2.c.k.364.11 24 55.19 odd 10
1815.2.c.k.364.14 24 11.8 odd 10
9075.2.a.dx.1.7 12 55.52 even 20
9075.2.a.dy.1.7 12 55.3 odd 20
9075.2.a.dz.1.6 12 55.47 odd 20
9075.2.a.ea.1.6 12 55.8 even 20