Properties

Label 605.2.j.g.124.3
Level $605$
Weight $2$
Character 605.124
Analytic conductor $4.831$
Analytic rank $0$
Dimension $16$
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] = [605,2,Mod(9,605)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(605, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("605.9");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.j (of order \(10\), degree \(4\), not 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: \(4.83094932229\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 7x^{14} + 25x^{12} - 57x^{10} + 194x^{8} - 303x^{6} + 235x^{4} - 33x^{2} + 121 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 55)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 124.3
Root \(0.471815 - 0.649397i\) of defining polynomial
Character \(\chi\) \(=\) 605.124
Dual form 605.2.j.g.444.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.471815 + 0.649397i) q^{2} +(1.67457 - 0.544099i) q^{3} +(0.418926 - 1.28932i) q^{4} +(2.07703 - 0.828231i) q^{5} +(1.14342 + 0.830744i) q^{6} +(-0.563124 - 0.182970i) q^{7} +(2.56176 - 0.832367i) q^{8} +(0.0810736 - 0.0589034i) q^{9} +O(q^{10})\) \(q+(0.471815 + 0.649397i) q^{2} +(1.67457 - 0.544099i) q^{3} +(0.418926 - 1.28932i) q^{4} +(2.07703 - 0.828231i) q^{5} +(1.14342 + 0.830744i) q^{6} +(-0.563124 - 0.182970i) q^{7} +(2.56176 - 0.832367i) q^{8} +(0.0810736 - 0.0589034i) q^{9} +(1.51782 + 0.958043i) q^{10} -2.38699i q^{12} +(1.05501 + 1.45210i) q^{13} +(-0.146870 - 0.452019i) q^{14} +(3.02747 - 2.51703i) q^{15} +(-0.444313 - 0.322812i) q^{16} +(-4.15982 + 5.72551i) q^{17} +(0.0765034 + 0.0248575i) q^{18} +(-0.706673 - 2.17492i) q^{19} +(-0.197736 - 3.02492i) q^{20} -1.04254 q^{21} -1.49081i q^{23} +(3.83695 - 2.78771i) q^{24} +(3.62807 - 3.44051i) q^{25} +(-0.445218 + 1.37024i) q^{26} +(-3.00110 + 4.13066i) q^{27} +(-0.471815 + 0.649397i) q^{28} +(1.10489 - 3.40050i) q^{29} +(3.06296 + 0.778460i) q^{30} +(-4.98940 + 3.62501i) q^{31} -5.82804i q^{32} -5.68079 q^{34} +(-1.32116 + 0.0863629i) q^{35} +(-0.0419817 - 0.129206i) q^{36} +(6.97831 + 2.26739i) q^{37} +(1.07897 - 1.48507i) q^{38} +(2.55677 + 1.85760i) q^{39} +(4.63145 - 3.85058i) q^{40} +(-2.59890 - 7.99858i) q^{41} +(-0.491886 - 0.677023i) q^{42} +9.51936i q^{43} +(0.119606 - 0.189492i) q^{45} +(0.968128 - 0.703386i) q^{46} +(-1.83711 + 0.596914i) q^{47} +(-0.919674 - 0.298820i) q^{48} +(-5.37949 - 3.90843i) q^{49} +(3.94603 + 0.732773i) q^{50} +(-3.85065 + 11.8511i) q^{51} +(2.31419 - 0.751927i) q^{52} +(1.40064 + 1.92781i) q^{53} -4.09840 q^{54} -1.59489 q^{56} +(-2.36674 - 3.25754i) q^{57} +(2.72957 - 0.886893i) q^{58} +(0.0118285 - 0.0364043i) q^{59} +(-1.97698 - 4.95784i) q^{60} +(-2.78430 - 2.02291i) q^{61} +(-4.70814 - 1.52977i) q^{62} +(-0.0564320 + 0.0183359i) q^{63} +(2.89608 - 2.10413i) q^{64} +(3.39395 + 2.14225i) q^{65} +6.79162i q^{67} +(5.63937 + 7.76192i) q^{68} +(-0.811149 - 2.49646i) q^{69} +(-0.679428 - 0.817212i) q^{70} +(9.54114 + 6.93205i) q^{71} +(0.158662 - 0.218380i) q^{72} +(6.48882 + 2.10835i) q^{73} +(1.82003 + 5.60148i) q^{74} +(4.20346 - 7.73539i) q^{75} -3.10021 q^{76} +2.53680i q^{78} +(-3.66165 + 2.66035i) q^{79} +(-1.19021 - 0.302496i) q^{80} +(-2.87095 + 8.83588i) q^{81} +(3.96806 - 5.46156i) q^{82} +(3.49299 - 4.80768i) q^{83} +(-0.436748 + 1.34417i) q^{84} +(-3.89802 + 15.3373i) q^{85} +(-6.18185 + 4.49137i) q^{86} -6.29552i q^{87} +6.21375 q^{89} +(0.179487 - 0.0117329i) q^{90} +(-0.328411 - 1.01074i) q^{91} +(-1.92214 - 0.624540i) q^{92} +(-6.38271 + 8.78504i) q^{93} +(-1.25441 - 0.911382i) q^{94} +(-3.26911 - 3.93207i) q^{95} +(-3.17103 - 9.75943i) q^{96} +(3.15976 + 4.34904i) q^{97} -5.33748i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 6 q^{4} - 2 q^{5} - 12 q^{6} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 6 q^{4} - 2 q^{5} - 12 q^{6} + 2 q^{9} + 8 q^{14} + 24 q^{15} + 6 q^{16} - 6 q^{19} + 12 q^{20} - 8 q^{21} + 4 q^{24} + 24 q^{25} - 50 q^{26} - 22 q^{29} + 4 q^{30} - 22 q^{31} - 16 q^{34} + 8 q^{35} - 30 q^{36} - 12 q^{40} - 18 q^{41} + 12 q^{45} - 38 q^{46} - 20 q^{49} + 12 q^{50} + 12 q^{51} + 40 q^{54} - 20 q^{56} - 8 q^{59} - 2 q^{60} - 20 q^{61} + 22 q^{64} + 40 q^{65} + 6 q^{69} + 26 q^{70} + 6 q^{71} + 52 q^{74} + 40 q^{75} - 56 q^{76} + 22 q^{79} - 6 q^{80} - 32 q^{81} + 18 q^{84} + 62 q^{85} - 68 q^{86} + 24 q^{89} + 32 q^{90} + 56 q^{94} + 22 q^{95} - 94 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(-1\) \(e\left(\frac{4}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.471815 + 0.649397i 0.333623 + 0.459193i 0.942565 0.334022i \(-0.108406\pi\)
−0.608942 + 0.793215i \(0.708406\pi\)
\(3\) 1.67457 0.544099i 0.966811 0.314136i 0.217283 0.976109i \(-0.430281\pi\)
0.749528 + 0.661973i \(0.230281\pi\)
\(4\) 0.418926 1.28932i 0.209463 0.644661i
\(5\) 2.07703 0.828231i 0.928874 0.370396i
\(6\) 1.14342 + 0.830744i 0.466800 + 0.339150i
\(7\) −0.563124 0.182970i −0.212841 0.0691561i 0.200656 0.979662i \(-0.435693\pi\)
−0.413497 + 0.910506i \(0.635693\pi\)
\(8\) 2.56176 0.832367i 0.905720 0.294286i
\(9\) 0.0810736 0.0589034i 0.0270245 0.0196345i
\(10\) 1.51782 + 0.958043i 0.479977 + 0.302960i
\(11\) 0 0
\(12\) 2.38699i 0.689065i
\(13\) 1.05501 + 1.45210i 0.292607 + 0.402739i 0.929859 0.367917i \(-0.119929\pi\)
−0.637252 + 0.770656i \(0.719929\pi\)
\(14\) −0.146870 0.452019i −0.0392526 0.120807i
\(15\) 3.02747 2.51703i 0.781691 0.649895i
\(16\) −0.444313 0.322812i −0.111078 0.0807031i
\(17\) −4.15982 + 5.72551i −1.00891 + 1.38864i −0.0892075 + 0.996013i \(0.528433\pi\)
−0.919698 + 0.392626i \(0.871567\pi\)
\(18\) 0.0765034 + 0.0248575i 0.0180320 + 0.00585896i
\(19\) −0.706673 2.17492i −0.162122 0.498960i 0.836691 0.547676i \(-0.184487\pi\)
−0.998813 + 0.0487157i \(0.984487\pi\)
\(20\) −0.197736 3.02492i −0.0442151 0.676394i
\(21\) −1.04254 −0.227501
\(22\) 0 0
\(23\) 1.49081i 0.310855i −0.987847 0.155428i \(-0.950324\pi\)
0.987847 0.155428i \(-0.0496756\pi\)
\(24\) 3.83695 2.78771i 0.783214 0.569038i
\(25\) 3.62807 3.44051i 0.725614 0.688102i
\(26\) −0.445218 + 1.37024i −0.0873145 + 0.268726i
\(27\) −3.00110 + 4.13066i −0.577562 + 0.794946i
\(28\) −0.471815 + 0.649397i −0.0891646 + 0.122725i
\(29\) 1.10489 3.40050i 0.205173 0.631456i −0.794534 0.607220i \(-0.792285\pi\)
0.999706 0.0242362i \(-0.00771537\pi\)
\(30\) 3.06296 + 0.778460i 0.559218 + 0.142127i
\(31\) −4.98940 + 3.62501i −0.896122 + 0.651071i −0.937467 0.348074i \(-0.886836\pi\)
0.0413447 + 0.999145i \(0.486836\pi\)
\(32\) 5.82804i 1.03026i
\(33\) 0 0
\(34\) −5.68079 −0.974248
\(35\) −1.32116 + 0.0863629i −0.223317 + 0.0145980i
\(36\) −0.0419817 0.129206i −0.00699694 0.0215344i
\(37\) 6.97831 + 2.26739i 1.14723 + 0.372757i 0.820098 0.572223i \(-0.193919\pi\)
0.327129 + 0.944980i \(0.393919\pi\)
\(38\) 1.07897 1.48507i 0.175031 0.240910i
\(39\) 2.55677 + 1.85760i 0.409410 + 0.297454i
\(40\) 4.63145 3.85058i 0.732297 0.608830i
\(41\) −2.59890 7.99858i −0.405879 1.24917i −0.920159 0.391545i \(-0.871941\pi\)
0.514280 0.857623i \(-0.328059\pi\)
\(42\) −0.491886 0.677023i −0.0758997 0.104467i
\(43\) 9.51936i 1.45169i 0.687859 + 0.725844i \(0.258551\pi\)
−0.687859 + 0.725844i \(0.741449\pi\)
\(44\) 0 0
\(45\) 0.119606 0.189492i 0.0178299 0.0282477i
\(46\) 0.968128 0.703386i 0.142743 0.103709i
\(47\) −1.83711 + 0.596914i −0.267970 + 0.0870688i −0.439920 0.898037i \(-0.644993\pi\)
0.171950 + 0.985106i \(0.444993\pi\)
\(48\) −0.919674 0.298820i −0.132743 0.0431310i
\(49\) −5.37949 3.90843i −0.768498 0.558347i
\(50\) 3.94603 + 0.732773i 0.558054 + 0.103630i
\(51\) −3.85065 + 11.8511i −0.539199 + 1.65948i
\(52\) 2.31419 0.751927i 0.320921 0.104273i
\(53\) 1.40064 + 1.92781i 0.192392 + 0.264806i 0.894305 0.447457i \(-0.147670\pi\)
−0.701913 + 0.712263i \(0.747670\pi\)
\(54\) −4.09840 −0.557722
\(55\) 0 0
\(56\) −1.59489 −0.213126
\(57\) −2.36674 3.25754i −0.313482 0.431471i
\(58\) 2.72957 0.886893i 0.358411 0.116455i
\(59\) 0.0118285 0.0364043i 0.00153994 0.00473944i −0.950284 0.311386i \(-0.899207\pi\)
0.951824 + 0.306646i \(0.0992069\pi\)
\(60\) −1.97698 4.95784i −0.255227 0.640055i
\(61\) −2.78430 2.02291i −0.356493 0.259007i 0.395095 0.918640i \(-0.370712\pi\)
−0.751588 + 0.659633i \(0.770712\pi\)
\(62\) −4.70814 1.52977i −0.597935 0.194281i
\(63\) −0.0564320 + 0.0183359i −0.00710977 + 0.00231010i
\(64\) 2.89608 2.10413i 0.362010 0.263016i
\(65\) 3.39395 + 2.14225i 0.420968 + 0.265713i
\(66\) 0 0
\(67\) 6.79162i 0.829728i 0.909883 + 0.414864i \(0.136171\pi\)
−0.909883 + 0.414864i \(0.863829\pi\)
\(68\) 5.63937 + 7.76192i 0.683874 + 0.941271i
\(69\) −0.811149 2.49646i −0.0976508 0.300538i
\(70\) −0.679428 0.817212i −0.0812072 0.0976756i
\(71\) 9.54114 + 6.93205i 1.13233 + 0.822683i 0.986032 0.166559i \(-0.0532655\pi\)
0.146294 + 0.989241i \(0.453265\pi\)
\(72\) 0.158662 0.218380i 0.0186985 0.0257363i
\(73\) 6.48882 + 2.10835i 0.759459 + 0.246763i 0.663046 0.748578i \(-0.269263\pi\)
0.0964127 + 0.995341i \(0.469263\pi\)
\(74\) 1.82003 + 5.60148i 0.211574 + 0.651159i
\(75\) 4.20346 7.73539i 0.485373 0.893206i
\(76\) −3.10021 −0.355619
\(77\) 0 0
\(78\) 2.53680i 0.287236i
\(79\) −3.66165 + 2.66035i −0.411968 + 0.299313i −0.774398 0.632699i \(-0.781947\pi\)
0.362430 + 0.932011i \(0.381947\pi\)
\(80\) −1.19021 0.302496i −0.133070 0.0338201i
\(81\) −2.87095 + 8.83588i −0.318995 + 0.981765i
\(82\) 3.96806 5.46156i 0.438198 0.603128i
\(83\) 3.49299 4.80768i 0.383405 0.527712i −0.573077 0.819501i \(-0.694251\pi\)
0.956483 + 0.291789i \(0.0942506\pi\)
\(84\) −0.436748 + 1.34417i −0.0476531 + 0.146661i
\(85\) −3.89802 + 15.3373i −0.422800 + 1.66357i
\(86\) −6.18185 + 4.49137i −0.666606 + 0.484317i
\(87\) 6.29552i 0.674951i
\(88\) 0 0
\(89\) 6.21375 0.658656 0.329328 0.944216i \(-0.393178\pi\)
0.329328 + 0.944216i \(0.393178\pi\)
\(90\) 0.179487 0.0117329i 0.0189196 0.00123675i
\(91\) −0.328411 1.01074i −0.0344268 0.105955i
\(92\) −1.92214 0.624540i −0.200396 0.0651128i
\(93\) −6.38271 + 8.78504i −0.661856 + 0.910967i
\(94\) −1.25441 0.911382i −0.129383 0.0940019i
\(95\) −3.26911 3.93207i −0.335404 0.403422i
\(96\) −3.17103 9.75943i −0.323642 0.996067i
\(97\) 3.15976 + 4.34904i 0.320825 + 0.441578i 0.938719 0.344684i \(-0.112014\pi\)
−0.617894 + 0.786262i \(0.712014\pi\)
\(98\) 5.33748i 0.539167i
\(99\) 0 0
\(100\) −2.91604 6.11907i −0.291604 0.611907i
\(101\) −8.03459 + 5.83747i −0.799472 + 0.580850i −0.910759 0.412938i \(-0.864503\pi\)
0.111287 + 0.993788i \(0.464503\pi\)
\(102\) −9.51286 + 3.09092i −0.941913 + 0.306046i
\(103\) −12.8596 4.17833i −1.26709 0.411703i −0.403076 0.915166i \(-0.632059\pi\)
−0.864017 + 0.503463i \(0.832059\pi\)
\(104\) 3.91136 + 2.84177i 0.383541 + 0.278658i
\(105\) −2.16538 + 0.863464i −0.211320 + 0.0842655i
\(106\) −0.591075 + 1.81914i −0.0574103 + 0.176691i
\(107\) −5.33010 + 1.73185i −0.515280 + 0.167425i −0.555102 0.831782i \(-0.687321\pi\)
0.0398221 + 0.999207i \(0.487321\pi\)
\(108\) 4.06852 + 5.59983i 0.391493 + 0.538844i
\(109\) 18.6001 1.78157 0.890784 0.454428i \(-0.150156\pi\)
0.890784 + 0.454428i \(0.150156\pi\)
\(110\) 0 0
\(111\) 12.9193 1.22625
\(112\) 0.191138 + 0.263079i 0.0180609 + 0.0248587i
\(113\) −11.2238 + 3.64683i −1.05584 + 0.343065i −0.784960 0.619547i \(-0.787316\pi\)
−0.270885 + 0.962612i \(0.587316\pi\)
\(114\) 0.998773 3.07391i 0.0935437 0.287898i
\(115\) −1.23473 3.09645i −0.115140 0.288745i
\(116\) −3.92147 2.84912i −0.364099 0.264534i
\(117\) 0.171067 + 0.0555830i 0.0158151 + 0.00513865i
\(118\) 0.0292217 0.00949471i 0.00269008 0.000874059i
\(119\) 3.39009 2.46304i 0.310769 0.225787i
\(120\) 5.66057 8.96801i 0.516737 0.818664i
\(121\) 0 0
\(122\) 2.76255i 0.250110i
\(123\) −8.70404 11.9801i −0.784817 1.08021i
\(124\) 2.58362 + 7.95156i 0.232016 + 0.714071i
\(125\) 4.68605 10.1509i 0.419133 0.907925i
\(126\) −0.0385327 0.0279957i −0.00343277 0.00249405i
\(127\) 9.43784 12.9901i 0.837473 1.15268i −0.149013 0.988835i \(-0.547610\pi\)
0.986486 0.163847i \(-0.0523904\pi\)
\(128\) −8.35275 2.71397i −0.738286 0.239884i
\(129\) 5.17948 + 15.9408i 0.456027 + 1.40351i
\(130\) 0.210146 + 3.21477i 0.0184310 + 0.281954i
\(131\) −18.0296 −1.57525 −0.787625 0.616154i \(-0.788690\pi\)
−0.787625 + 0.616154i \(0.788690\pi\)
\(132\) 0 0
\(133\) 1.35405i 0.117411i
\(134\) −4.41046 + 3.20438i −0.381005 + 0.276817i
\(135\) −2.81222 + 11.0651i −0.242038 + 0.952331i
\(136\) −5.89076 + 18.1299i −0.505128 + 1.55463i
\(137\) −2.36999 + 3.26202i −0.202482 + 0.278693i −0.898167 0.439654i \(-0.855101\pi\)
0.695685 + 0.718347i \(0.255101\pi\)
\(138\) 1.23848 1.70462i 0.105427 0.145107i
\(139\) 2.45203 7.54656i 0.207978 0.640091i −0.791600 0.611040i \(-0.790752\pi\)
0.999578 0.0290509i \(-0.00924848\pi\)
\(140\) −0.442120 + 1.73959i −0.0373660 + 0.147022i
\(141\) −2.75158 + 1.99914i −0.231725 + 0.168358i
\(142\) 9.46663i 0.794422i
\(143\) 0 0
\(144\) −0.0550368 −0.00458640
\(145\) −0.521514 7.97802i −0.0433094 0.662538i
\(146\) 1.69237 + 5.20857i 0.140061 + 0.431064i
\(147\) −11.1349 3.61794i −0.918389 0.298403i
\(148\) 5.84679 8.04742i 0.480604 0.661494i
\(149\) −10.1134 7.34783i −0.828524 0.601958i 0.0906173 0.995886i \(-0.471116\pi\)
−0.919141 + 0.393928i \(0.871116\pi\)
\(150\) 7.00659 0.919957i 0.572086 0.0751142i
\(151\) −2.59651 7.99123i −0.211301 0.650317i −0.999396 0.0347632i \(-0.988932\pi\)
0.788095 0.615554i \(-0.211068\pi\)
\(152\) −3.62066 4.98341i −0.293674 0.404208i
\(153\) 0.709215i 0.0573367i
\(154\) 0 0
\(155\) −7.36076 + 11.6616i −0.591231 + 0.936683i
\(156\) 3.46614 2.51830i 0.277514 0.201625i
\(157\) 13.3109 4.32496i 1.06232 0.345170i 0.274830 0.961493i \(-0.411379\pi\)
0.787493 + 0.616323i \(0.211379\pi\)
\(158\) −3.45524 1.12268i −0.274885 0.0893154i
\(159\) 3.39438 + 2.46616i 0.269192 + 0.195579i
\(160\) −4.82696 12.1050i −0.381605 0.956983i
\(161\) −0.272773 + 0.839510i −0.0214976 + 0.0661627i
\(162\) −7.09255 + 2.30451i −0.557244 + 0.181059i
\(163\) −6.96025 9.57996i −0.545169 0.750360i 0.444178 0.895939i \(-0.353496\pi\)
−0.989347 + 0.145578i \(0.953496\pi\)
\(164\) −11.4015 −0.890307
\(165\) 0 0
\(166\) 4.77014 0.370235
\(167\) −5.12918 7.05971i −0.396908 0.546297i 0.563057 0.826418i \(-0.309625\pi\)
−0.959965 + 0.280121i \(0.909625\pi\)
\(168\) −2.67074 + 0.867777i −0.206052 + 0.0669504i
\(169\) 3.02168 9.29978i 0.232437 0.715368i
\(170\) −11.7992 + 4.70501i −0.904954 + 0.360858i
\(171\) −0.185402 0.134703i −0.0141781 0.0103010i
\(172\) 12.2735 + 3.98791i 0.935848 + 0.304075i
\(173\) −8.72938 + 2.83635i −0.663682 + 0.215643i −0.621437 0.783464i \(-0.713451\pi\)
−0.0422448 + 0.999107i \(0.513451\pi\)
\(174\) 4.08829 2.97032i 0.309933 0.225179i
\(175\) −2.67256 + 1.27361i −0.202027 + 0.0962755i
\(176\) 0 0
\(177\) 0.0673973i 0.00506589i
\(178\) 2.93174 + 4.03519i 0.219743 + 0.302450i
\(179\) −0.447507 1.37729i −0.0334483 0.102943i 0.932939 0.360036i \(-0.117235\pi\)
−0.966387 + 0.257093i \(0.917235\pi\)
\(180\) −0.194210 0.233594i −0.0144755 0.0174111i
\(181\) −0.641957 0.466409i −0.0477163 0.0346679i 0.563671 0.825999i \(-0.309388\pi\)
−0.611388 + 0.791331i \(0.709388\pi\)
\(182\) 0.501426 0.690153i 0.0371681 0.0511576i
\(183\) −5.76315 1.87256i −0.426024 0.138424i
\(184\) −1.24090 3.81910i −0.0914804 0.281548i
\(185\) 16.3720 1.07022i 1.20370 0.0786843i
\(186\) −8.71644 −0.639120
\(187\) 0 0
\(188\) 2.61869i 0.190988i
\(189\) 2.44578 1.77696i 0.177904 0.129255i
\(190\) 1.01106 3.97816i 0.0733500 0.288606i
\(191\) −2.51858 + 7.75139i −0.182238 + 0.560871i −0.999890 0.0148421i \(-0.995275\pi\)
0.817652 + 0.575713i \(0.195275\pi\)
\(192\) 3.70483 5.09926i 0.267373 0.368007i
\(193\) 2.56766 3.53408i 0.184824 0.254389i −0.706544 0.707670i \(-0.749747\pi\)
0.891368 + 0.453281i \(0.149747\pi\)
\(194\) −1.33343 + 4.10388i −0.0957348 + 0.294642i
\(195\) 6.84899 + 1.74069i 0.490466 + 0.124653i
\(196\) −7.29283 + 5.29855i −0.520917 + 0.378468i
\(197\) 15.6525i 1.11520i 0.830111 + 0.557599i \(0.188277\pi\)
−0.830111 + 0.557599i \(0.811723\pi\)
\(198\) 0 0
\(199\) −1.43830 −0.101959 −0.0509793 0.998700i \(-0.516234\pi\)
−0.0509793 + 0.998700i \(0.516234\pi\)
\(200\) 6.43048 11.8337i 0.454704 0.836766i
\(201\) 3.69531 + 11.3730i 0.260647 + 0.802190i
\(202\) −7.58168 2.46344i −0.533445 0.173327i
\(203\) −1.24438 + 1.71274i −0.0873381 + 0.120211i
\(204\) 13.6667 + 9.92947i 0.956863 + 0.695202i
\(205\) −12.0226 14.4608i −0.839697 1.00998i
\(206\) −3.35394 10.3224i −0.233680 0.719194i
\(207\) −0.0878138 0.120865i −0.00610348 0.00840072i
\(208\) 0.985756i 0.0683499i
\(209\) 0 0
\(210\) −1.58239 0.998799i −0.109195 0.0689237i
\(211\) 7.02332 5.10274i 0.483505 0.351287i −0.319176 0.947696i \(-0.603406\pi\)
0.802681 + 0.596408i \(0.203406\pi\)
\(212\) 3.07234 0.998263i 0.211009 0.0685610i
\(213\) 19.7490 + 6.41684i 1.35318 + 0.439674i
\(214\) −3.63948 2.64424i −0.248790 0.180756i
\(215\) 7.88422 + 19.7720i 0.537700 + 1.34844i
\(216\) −4.24988 + 13.0798i −0.289168 + 0.889967i
\(217\) 3.47292 1.12842i 0.235757 0.0766020i
\(218\) 8.77580 + 12.0789i 0.594372 + 0.818083i
\(219\) 12.0131 0.811770
\(220\) 0 0
\(221\) −12.7026 −0.854472
\(222\) 6.09552 + 8.38977i 0.409105 + 0.563084i
\(223\) 5.99740 1.94867i 0.401616 0.130493i −0.101243 0.994862i \(-0.532282\pi\)
0.502858 + 0.864369i \(0.332282\pi\)
\(224\) −1.06636 + 3.28190i −0.0712489 + 0.219281i
\(225\) 0.0914827 0.492640i 0.00609884 0.0328427i
\(226\) −7.66379 5.56807i −0.509787 0.370382i
\(227\) −1.06215 0.345113i −0.0704973 0.0229060i 0.273556 0.961856i \(-0.411800\pi\)
−0.344053 + 0.938950i \(0.611800\pi\)
\(228\) −5.19151 + 1.68682i −0.343816 + 0.111713i
\(229\) −3.39477 + 2.46644i −0.224332 + 0.162987i −0.694275 0.719710i \(-0.744275\pi\)
0.469942 + 0.882697i \(0.344275\pi\)
\(230\) 1.42826 2.26278i 0.0941767 0.149204i
\(231\) 0 0
\(232\) 9.63094i 0.632302i
\(233\) −3.98487 5.48471i −0.261058 0.359315i 0.658288 0.752766i \(-0.271281\pi\)
−0.919345 + 0.393451i \(0.871281\pi\)
\(234\) 0.0446164 + 0.137315i 0.00291667 + 0.00897658i
\(235\) −3.32135 + 2.76136i −0.216661 + 0.180131i
\(236\) −0.0419817 0.0305015i −0.00273277 0.00198548i
\(237\) −4.68419 + 6.44723i −0.304271 + 0.418793i
\(238\) 3.19899 + 1.03941i 0.207360 + 0.0673752i
\(239\) 1.35908 + 4.18282i 0.0879117 + 0.270564i 0.985342 0.170593i \(-0.0545682\pi\)
−0.897430 + 0.441157i \(0.854568\pi\)
\(240\) −2.15768 + 0.141045i −0.139277 + 0.00910441i
\(241\) 9.61218 0.619175 0.309587 0.950871i \(-0.399809\pi\)
0.309587 + 0.950871i \(0.399809\pi\)
\(242\) 0 0
\(243\) 1.04101i 0.0667807i
\(244\) −3.77460 + 2.74241i −0.241644 + 0.175565i
\(245\) −14.4104 3.66245i −0.920648 0.233985i
\(246\) 3.67314 11.3048i 0.234191 0.720765i
\(247\) 2.41264 3.32071i 0.153513 0.211292i
\(248\) −9.76431 + 13.4394i −0.620035 + 0.853404i
\(249\) 3.23338 9.95131i 0.204907 0.630639i
\(250\) 8.80292 1.74624i 0.556745 0.110442i
\(251\) −10.8575 + 7.88843i −0.685319 + 0.497913i −0.875118 0.483910i \(-0.839216\pi\)
0.189799 + 0.981823i \(0.439216\pi\)
\(252\) 0.0804405i 0.00506727i
\(253\) 0 0
\(254\) 12.8886 0.808704
\(255\) 1.81753 + 27.8042i 0.113818 + 1.74117i
\(256\) −4.39092 13.5138i −0.274432 0.844616i
\(257\) 10.2879 + 3.34275i 0.641743 + 0.208515i 0.611770 0.791036i \(-0.290458\pi\)
0.0299732 + 0.999551i \(0.490458\pi\)
\(258\) −7.90815 + 10.8846i −0.492340 + 0.677648i
\(259\) −3.51479 2.55364i −0.218398 0.158676i
\(260\) 4.18387 3.47846i 0.259472 0.215725i
\(261\) −0.110724 0.340772i −0.00685362 0.0210933i
\(262\) −8.50662 11.7084i −0.525540 0.723344i
\(263\) 24.6351i 1.51906i −0.650471 0.759531i \(-0.725428\pi\)
0.650471 0.759531i \(-0.274572\pi\)
\(264\) 0 0
\(265\) 4.50584 + 2.84407i 0.276791 + 0.174710i
\(266\) −0.879314 + 0.638859i −0.0539142 + 0.0391709i
\(267\) 10.4053 3.38089i 0.636795 0.206907i
\(268\) 8.75659 + 2.84519i 0.534894 + 0.173797i
\(269\) −3.88410 2.82196i −0.236818 0.172058i 0.463047 0.886334i \(-0.346756\pi\)
−0.699864 + 0.714276i \(0.746756\pi\)
\(270\) −8.51249 + 3.39442i −0.518053 + 0.206578i
\(271\) −7.20947 + 22.1885i −0.437944 + 1.34785i 0.452095 + 0.891970i \(0.350677\pi\)
−0.890039 + 0.455884i \(0.849323\pi\)
\(272\) 3.69653 1.20108i 0.224135 0.0728259i
\(273\) −1.09989 1.51387i −0.0665684 0.0916236i
\(274\) −3.23654 −0.195527
\(275\) 0 0
\(276\) −3.55855 −0.214200
\(277\) 12.8709 + 17.7153i 0.773337 + 1.06441i 0.995986 + 0.0895089i \(0.0285297\pi\)
−0.222649 + 0.974899i \(0.571470\pi\)
\(278\) 6.05761 1.96824i 0.363312 0.118047i
\(279\) −0.190983 + 0.587785i −0.0114339 + 0.0351898i
\(280\) −3.31262 + 1.32093i −0.197967 + 0.0789409i
\(281\) 12.7626 + 9.27257i 0.761353 + 0.553155i 0.899325 0.437281i \(-0.144058\pi\)
−0.137972 + 0.990436i \(0.544058\pi\)
\(282\) −2.59647 0.843646i −0.154618 0.0502384i
\(283\) 21.5026 6.98661i 1.27819 0.415311i 0.410251 0.911973i \(-0.365441\pi\)
0.867944 + 0.496662i \(0.165441\pi\)
\(284\) 12.9347 9.39760i 0.767532 0.557645i
\(285\) −7.61377 4.80578i −0.451001 0.284670i
\(286\) 0 0
\(287\) 4.97971i 0.293943i
\(288\) −0.343291 0.472500i −0.0202286 0.0278423i
\(289\) −10.2240 31.4662i −0.601412 1.85096i
\(290\) 4.93484 4.10282i 0.289784 0.240926i
\(291\) 7.65754 + 5.56353i 0.448893 + 0.326140i
\(292\) 5.43668 7.48294i 0.318157 0.437906i
\(293\) 12.6106 + 4.09744i 0.736721 + 0.239375i 0.653258 0.757136i \(-0.273402\pi\)
0.0834635 + 0.996511i \(0.473402\pi\)
\(294\) −2.90412 8.93795i −0.169372 0.521272i
\(295\) −0.00558312 0.0854094i −0.000325062 0.00497273i
\(296\) 19.7641 1.14876
\(297\) 0 0
\(298\) 10.0344i 0.581280i
\(299\) 2.16480 1.57282i 0.125194 0.0909585i
\(300\) −8.21248 8.66017i −0.474148 0.499995i
\(301\) 1.74176 5.36058i 0.100393 0.308978i
\(302\) 3.96441 5.45655i 0.228126 0.313989i
\(303\) −10.2783 + 14.1468i −0.590472 + 0.812715i
\(304\) −0.388106 + 1.19447i −0.0222594 + 0.0685074i
\(305\) −7.45849 1.89560i −0.427072 0.108542i
\(306\) −0.460562 + 0.334618i −0.0263286 + 0.0191288i
\(307\) 10.0161i 0.571650i 0.958282 + 0.285825i \(0.0922676\pi\)
−0.958282 + 0.285825i \(0.907732\pi\)
\(308\) 0 0
\(309\) −23.8076 −1.35437
\(310\) −11.0459 + 0.722060i −0.627367 + 0.0410103i
\(311\) −1.05321 3.24145i −0.0597220 0.183806i 0.916745 0.399474i \(-0.130807\pi\)
−0.976467 + 0.215668i \(0.930807\pi\)
\(312\) 8.09603 + 2.63056i 0.458348 + 0.148926i
\(313\) 14.4012 19.8216i 0.814005 1.12038i −0.176688 0.984267i \(-0.556538\pi\)
0.990693 0.136115i \(-0.0434616\pi\)
\(314\) 9.08888 + 6.60346i 0.512915 + 0.372655i
\(315\) −0.102024 + 0.0848228i −0.00574842 + 0.00477922i
\(316\) 1.89608 + 5.83555i 0.106663 + 0.328275i
\(317\) 4.10774 + 5.65382i 0.230714 + 0.317550i 0.908641 0.417579i \(-0.137121\pi\)
−0.677927 + 0.735129i \(0.737121\pi\)
\(318\) 3.36787i 0.188861i
\(319\) 0 0
\(320\) 4.27254 6.76895i 0.238842 0.378396i
\(321\) −7.98330 + 5.80020i −0.445584 + 0.323736i
\(322\) −0.673874 + 0.218955i −0.0375535 + 0.0122019i
\(323\) 15.3921 + 5.00121i 0.856441 + 0.278275i
\(324\) 10.1896 + 7.40317i 0.566088 + 0.411287i
\(325\) 8.82360 + 1.63853i 0.489445 + 0.0908894i
\(326\) 2.93725 9.03993i 0.162679 0.500675i
\(327\) 31.1471 10.1203i 1.72244 0.559654i
\(328\) −13.3155 18.3272i −0.735226 1.01195i
\(329\) 1.14374 0.0630563
\(330\) 0 0
\(331\) 5.64321 0.310179 0.155089 0.987900i \(-0.450433\pi\)
0.155089 + 0.987900i \(0.450433\pi\)
\(332\) −4.73535 6.51765i −0.259886 0.357703i
\(333\) 0.699314 0.227221i 0.0383221 0.0124516i
\(334\) 2.16453 6.66175i 0.118438 0.364515i
\(335\) 5.62502 + 14.1064i 0.307328 + 0.770713i
\(336\) 0.463215 + 0.336545i 0.0252704 + 0.0183600i
\(337\) 21.5094 + 6.98884i 1.17169 + 0.380706i 0.829275 0.558841i \(-0.188754\pi\)
0.342419 + 0.939547i \(0.388754\pi\)
\(338\) 7.46493 2.42550i 0.406039 0.131930i
\(339\) −16.8107 + 12.2137i −0.913033 + 0.663357i
\(340\) 18.1418 + 11.4510i 0.983876 + 0.621018i
\(341\) 0 0
\(342\) 0.183955i 0.00994713i
\(343\) 4.75040 + 6.53836i 0.256497 + 0.353038i
\(344\) 7.92360 + 24.3863i 0.427212 + 1.31482i
\(345\) −3.75242 4.51339i −0.202023 0.242993i
\(346\) −5.96056 4.33060i −0.320442 0.232815i
\(347\) −0.107209 + 0.147560i −0.00575527 + 0.00792145i −0.811885 0.583817i \(-0.801558\pi\)
0.806130 + 0.591739i \(0.201558\pi\)
\(348\) −8.11696 2.63736i −0.435115 0.141377i
\(349\) −4.76729 14.6722i −0.255187 0.785385i −0.993793 0.111248i \(-0.964515\pi\)
0.738606 0.674138i \(-0.235485\pi\)
\(350\) −2.08803 1.13465i −0.111610 0.0606495i
\(351\) −9.16431 −0.489155
\(352\) 0 0
\(353\) 23.9103i 1.27262i −0.771435 0.636308i \(-0.780461\pi\)
0.771435 0.636308i \(-0.219539\pi\)
\(354\) 0.0437676 0.0317990i 0.00232622 0.00169010i
\(355\) 25.5585 + 6.49577i 1.35651 + 0.344760i
\(356\) 2.60310 8.01152i 0.137964 0.424610i
\(357\) 4.33679 5.96907i 0.229527 0.315917i
\(358\) 0.683265 0.940433i 0.0361117 0.0497035i
\(359\) −2.70926 + 8.33824i −0.142989 + 0.440075i −0.996747 0.0805950i \(-0.974318\pi\)
0.853758 + 0.520670i \(0.174318\pi\)
\(360\) 0.148676 0.584989i 0.00783594 0.0308316i
\(361\) 11.1405 8.09401i 0.586340 0.426001i
\(362\) 0.636943i 0.0334770i
\(363\) 0 0
\(364\) −1.44076 −0.0755161
\(365\) 15.2236 0.995152i 0.796842 0.0520887i
\(366\) −1.50310 4.62608i −0.0785685 0.241809i
\(367\) −5.11889 1.66323i −0.267204 0.0868198i 0.172351 0.985036i \(-0.444864\pi\)
−0.439555 + 0.898216i \(0.644864\pi\)
\(368\) −0.481252 + 0.662387i −0.0250870 + 0.0345293i
\(369\) −0.681845 0.495390i −0.0354954 0.0257890i
\(370\) 8.41957 + 10.1270i 0.437713 + 0.526478i
\(371\) −0.436001 1.34187i −0.0226360 0.0696665i
\(372\) 8.65287 + 11.9097i 0.448631 + 0.617487i
\(373\) 3.22450i 0.166958i 0.996510 + 0.0834792i \(0.0266032\pi\)
−0.996510 + 0.0834792i \(0.973397\pi\)
\(374\) 0 0
\(375\) 2.32400 19.5480i 0.120011 1.00946i
\(376\) −4.20939 + 3.05830i −0.217083 + 0.157720i
\(377\) 6.10351 1.98315i 0.314347 0.102138i
\(378\) 2.30791 + 0.749884i 0.118706 + 0.0385699i
\(379\) −15.9080 11.5578i −0.817139 0.593687i 0.0987522 0.995112i \(-0.468515\pi\)
−0.915892 + 0.401425i \(0.868515\pi\)
\(380\) −6.43922 + 2.56769i −0.330325 + 0.131720i
\(381\) 8.73639 26.8878i 0.447579 1.37751i
\(382\) −6.22203 + 2.02166i −0.318347 + 0.103437i
\(383\) −16.4434 22.6323i −0.840216 1.15646i −0.985934 0.167132i \(-0.946549\pi\)
0.145718 0.989326i \(-0.453451\pi\)
\(384\) −15.4639 −0.789139
\(385\) 0 0
\(386\) 3.50648 0.178475
\(387\) 0.560723 + 0.771769i 0.0285031 + 0.0392312i
\(388\) 6.93103 2.25203i 0.351870 0.114329i
\(389\) −4.02958 + 12.4018i −0.204308 + 0.628795i 0.795433 + 0.606041i \(0.207243\pi\)
−0.999741 + 0.0227539i \(0.992757\pi\)
\(390\) 2.10106 + 5.26900i 0.106391 + 0.266806i
\(391\) 8.53564 + 6.20151i 0.431666 + 0.313624i
\(392\) −17.0342 5.53475i −0.860358 0.279547i
\(393\) −30.1917 + 9.80987i −1.52297 + 0.494843i
\(394\) −10.1647 + 7.38510i −0.512091 + 0.372056i
\(395\) −5.40197 + 8.55830i −0.271803 + 0.430615i
\(396\) 0 0
\(397\) 1.82243i 0.0914651i 0.998954 + 0.0457325i \(0.0145622\pi\)
−0.998954 + 0.0457325i \(0.985438\pi\)
\(398\) −0.678612 0.934030i −0.0340158 0.0468187i
\(399\) 0.736735 + 2.26744i 0.0368829 + 0.113514i
\(400\) −2.72264 + 0.357479i −0.136132 + 0.0178740i
\(401\) −4.35320 3.16278i −0.217388 0.157942i 0.473762 0.880653i \(-0.342896\pi\)
−0.691150 + 0.722711i \(0.742896\pi\)
\(402\) −5.64209 + 7.76568i −0.281402 + 0.387317i
\(403\) −10.5277 3.42067i −0.524423 0.170395i
\(404\) 4.16048 + 12.8047i 0.206992 + 0.637055i
\(405\) 1.35511 + 20.7302i 0.0673358 + 1.03009i
\(406\) −1.69936 −0.0843379
\(407\) 0 0
\(408\) 33.5648i 1.66171i
\(409\) 29.6764 21.5612i 1.46740 1.06613i 0.486049 0.873931i \(-0.338438\pi\)
0.981356 0.192201i \(-0.0615624\pi\)
\(410\) 3.71832 14.6303i 0.183635 0.722537i
\(411\) −2.19385 + 6.75197i −0.108215 + 0.333050i
\(412\) −10.7744 + 14.8297i −0.530819 + 0.730609i
\(413\) −0.0133218 + 0.0183359i −0.000655522 + 0.000902249i
\(414\) 0.0370578 0.114052i 0.00182129 0.00560535i
\(415\) 3.27315 12.8787i 0.160673 0.632190i
\(416\) 8.46287 6.14863i 0.414926 0.301462i
\(417\) 13.9713i 0.684180i
\(418\) 0 0
\(419\) −2.86630 −0.140028 −0.0700141 0.997546i \(-0.522304\pi\)
−0.0700141 + 0.997546i \(0.522304\pi\)
\(420\) 0.206148 + 3.15361i 0.0100590 + 0.153880i
\(421\) 1.43994 + 4.43169i 0.0701785 + 0.215987i 0.979994 0.199025i \(-0.0637774\pi\)
−0.909816 + 0.415012i \(0.863777\pi\)
\(422\) 6.62741 + 2.15338i 0.322617 + 0.104825i
\(423\) −0.113781 + 0.156606i −0.00553222 + 0.00761445i
\(424\) 5.19275 + 3.77275i 0.252182 + 0.183221i
\(425\) 4.60655 + 35.0845i 0.223450 + 1.70185i
\(426\) 5.15079 + 15.8525i 0.249556 + 0.768056i
\(427\) 1.19777 + 1.64859i 0.0579642 + 0.0797809i
\(428\) 7.59774i 0.367250i
\(429\) 0 0
\(430\) −9.11996 + 14.4487i −0.439803 + 0.696778i
\(431\) 16.8026 12.2078i 0.809351 0.588028i −0.104291 0.994547i \(-0.533257\pi\)
0.913642 + 0.406519i \(0.133257\pi\)
\(432\) 2.66686 0.866515i 0.128309 0.0416902i
\(433\) −12.1708 3.95454i −0.584893 0.190043i 0.00159840 0.999999i \(-0.499491\pi\)
−0.586491 + 0.809955i \(0.699491\pi\)
\(434\) 2.37136 + 1.72290i 0.113829 + 0.0827017i
\(435\) −5.21414 13.0760i −0.249999 0.626944i
\(436\) 7.79208 23.9815i 0.373173 1.14851i
\(437\) −3.24239 + 1.05352i −0.155104 + 0.0503965i
\(438\) 5.66796 + 7.80128i 0.270826 + 0.372759i
\(439\) −10.6208 −0.506905 −0.253452 0.967348i \(-0.581566\pi\)
−0.253452 + 0.967348i \(0.581566\pi\)
\(440\) 0 0
\(441\) −0.666354 −0.0317312
\(442\) −5.99329 8.24906i −0.285072 0.392368i
\(443\) −6.27596 + 2.03918i −0.298180 + 0.0968846i −0.454286 0.890856i \(-0.650106\pi\)
0.156106 + 0.987740i \(0.450106\pi\)
\(444\) 5.41224 16.6572i 0.256854 0.790514i
\(445\) 12.9061 5.14641i 0.611808 0.243963i
\(446\) 4.09512 + 2.97528i 0.193910 + 0.140884i
\(447\) −20.9335 6.80172i −0.990122 0.321710i
\(448\) −2.01585 + 0.654988i −0.0952397 + 0.0309453i
\(449\) 11.0253 8.01037i 0.520317 0.378033i −0.296406 0.955062i \(-0.595788\pi\)
0.816723 + 0.577029i \(0.195788\pi\)
\(450\) 0.363082 0.173026i 0.0171159 0.00815654i
\(451\) 0 0
\(452\) 15.9988i 0.752522i
\(453\) −8.69605 11.9691i −0.408576 0.562356i
\(454\) −0.277022 0.852586i −0.0130013 0.0400138i
\(455\) −1.51925 1.82734i −0.0712234 0.0856671i
\(456\) −8.77449 6.37504i −0.410903 0.298539i
\(457\) −7.93503 + 10.9216i −0.371185 + 0.510893i −0.953223 0.302269i \(-0.902256\pi\)
0.582037 + 0.813162i \(0.302256\pi\)
\(458\) −3.20340 1.04085i −0.149685 0.0486356i
\(459\) −11.1661 34.3656i −0.521188 1.60405i
\(460\) −4.50959 + 0.294787i −0.210261 + 0.0137445i
\(461\) −11.3217 −0.527303 −0.263652 0.964618i \(-0.584927\pi\)
−0.263652 + 0.964618i \(0.584927\pi\)
\(462\) 0 0
\(463\) 4.82990i 0.224464i −0.993682 0.112232i \(-0.964200\pi\)
0.993682 0.112232i \(-0.0358001\pi\)
\(464\) −1.58864 + 1.15421i −0.0737507 + 0.0535830i
\(465\) −5.98100 + 23.5331i −0.277362 + 1.09132i
\(466\) 1.68163 5.17553i 0.0779001 0.239752i
\(467\) −14.1170 + 19.4304i −0.653257 + 0.899131i −0.999235 0.0391117i \(-0.987547\pi\)
0.345978 + 0.938243i \(0.387547\pi\)
\(468\) 0.143329 0.197275i 0.00662538 0.00911905i
\(469\) 1.24266 3.82452i 0.0573808 0.176600i
\(470\) −3.36028 0.854023i −0.154998 0.0393932i
\(471\) 19.9367 14.4849i 0.918635 0.667427i
\(472\) 0.103105i 0.00474579i
\(473\) 0 0
\(474\) −6.39688 −0.293818
\(475\) −10.0467 5.45943i −0.460973 0.250496i
\(476\) −1.75546 5.40276i −0.0804615 0.247635i
\(477\) 0.227110 + 0.0737924i 0.0103986 + 0.00337872i
\(478\) −2.07508 + 2.85610i −0.0949119 + 0.130635i
\(479\) −34.9698 25.4070i −1.59781 1.16088i −0.891547 0.452929i \(-0.850379\pi\)
−0.706264 0.707949i \(-0.749621\pi\)
\(480\) −14.6694 17.6442i −0.669562 0.805345i
\(481\) 4.06971 + 12.5253i 0.185563 + 0.571104i
\(482\) 4.53517 + 6.24212i 0.206571 + 0.284321i
\(483\) 1.55423i 0.0707199i
\(484\) 0 0
\(485\) 10.1649 + 6.41606i 0.461565 + 0.291338i
\(486\) −0.676027 + 0.491163i −0.0306652 + 0.0222796i
\(487\) −39.9072 + 12.9666i −1.80837 + 0.587574i −0.999999 0.00110438i \(-0.999648\pi\)
−0.808367 + 0.588678i \(0.799648\pi\)
\(488\) −8.81651 2.86466i −0.399105 0.129677i
\(489\) −16.8678 12.2552i −0.762790 0.554199i
\(490\) −4.42066 11.0861i −0.199705 0.500818i
\(491\) 2.79964 8.61641i 0.126346 0.388853i −0.867798 0.496917i \(-0.834465\pi\)
0.994144 + 0.108064i \(0.0344652\pi\)
\(492\) −19.0925 + 6.20354i −0.860758 + 0.279677i
\(493\) 14.8734 + 20.4715i 0.669865 + 0.921990i
\(494\) 3.29478 0.148239
\(495\) 0 0
\(496\) 3.38705 0.152083
\(497\) −4.10449 5.64934i −0.184111 0.253408i
\(498\) 7.98791 2.59543i 0.357947 0.116304i
\(499\) −9.35682 + 28.7973i −0.418869 + 1.28915i 0.489875 + 0.871792i \(0.337042\pi\)
−0.908744 + 0.417353i \(0.862958\pi\)
\(500\) −11.1247 10.2943i −0.497511 0.460376i
\(501\) −12.4303 9.03116i −0.555346 0.403483i
\(502\) −10.2454 3.32895i −0.457277 0.148578i
\(503\) 17.1797 5.58203i 0.766006 0.248890i 0.100152 0.994972i \(-0.468067\pi\)
0.665854 + 0.746082i \(0.268067\pi\)
\(504\) −0.129303 + 0.0939443i −0.00575962 + 0.00418461i
\(505\) −11.8533 + 18.7791i −0.527464 + 0.835658i
\(506\) 0 0
\(507\) 17.2172i 0.764642i
\(508\) −12.7946 17.6103i −0.567670 0.781331i
\(509\) 7.69937 + 23.6962i 0.341269 + 1.05032i 0.963551 + 0.267524i \(0.0862056\pi\)
−0.622282 + 0.782793i \(0.713794\pi\)
\(510\) −17.1985 + 14.2988i −0.761561 + 0.633159i
\(511\) −3.26824 2.37452i −0.144579 0.105043i
\(512\) −3.62042 + 4.98307i −0.160001 + 0.220223i
\(513\) 11.1046 + 3.60811i 0.490282 + 0.159302i
\(514\) 2.68322 + 8.25811i 0.118352 + 0.364249i
\(515\) −30.1703 + 1.97220i −1.32946 + 0.0869055i
\(516\) 22.7226 1.00031
\(517\) 0 0
\(518\) 3.48734i 0.153225i
\(519\) −13.0747 + 9.49929i −0.573914 + 0.416973i
\(520\) 10.4776 + 2.66292i 0.459475 + 0.116777i
\(521\) 11.2121 34.5073i 0.491211 1.51179i −0.331568 0.943431i \(-0.607578\pi\)
0.822779 0.568362i \(-0.192422\pi\)
\(522\) 0.169055 0.232685i 0.00739936 0.0101843i
\(523\) 14.5224 19.9884i 0.635021 0.874032i −0.363316 0.931666i \(-0.618356\pi\)
0.998338 + 0.0576339i \(0.0183556\pi\)
\(524\) −7.55306 + 23.2459i −0.329957 + 1.01550i
\(525\) −3.78241 + 3.58687i −0.165078 + 0.156544i
\(526\) 15.9979 11.6232i 0.697543 0.506795i
\(527\) 43.6462i 1.90126i
\(528\) 0 0
\(529\) 20.7775 0.903369
\(530\) 0.278991 + 4.26795i 0.0121186 + 0.185388i
\(531\) −0.00118536 0.00364817i −5.14403e−5 0.000158317i
\(532\) 1.74580 + 0.567246i 0.0756901 + 0.0245932i
\(533\) 8.87284 12.2124i 0.384325 0.528979i
\(534\) 7.10493 + 5.16203i 0.307460 + 0.223383i
\(535\) −9.63638 + 8.01165i −0.416617 + 0.346374i
\(536\) 5.65312 + 17.3985i 0.244177 + 0.751501i
\(537\) −1.49876 2.06287i −0.0646763 0.0890193i
\(538\) 3.85376i 0.166148i
\(539\) 0 0
\(540\) 13.0884 + 8.26132i 0.563233 + 0.355511i
\(541\) −10.1467 + 7.37198i −0.436239 + 0.316946i −0.784139 0.620586i \(-0.786895\pi\)
0.347900 + 0.937532i \(0.386895\pi\)
\(542\) −17.8107 + 5.78704i −0.765034 + 0.248574i
\(543\) −1.32877 0.431744i −0.0570230 0.0185279i
\(544\) 33.3685 + 24.2436i 1.43066 + 1.03944i
\(545\) 38.6329 15.4052i 1.65485 0.659885i
\(546\) 0.464158 1.42853i 0.0198641 0.0611355i
\(547\) −29.2361 + 9.49940i −1.25005 + 0.406165i −0.857938 0.513754i \(-0.828255\pi\)
−0.392110 + 0.919919i \(0.628255\pi\)
\(548\) 3.21294 + 4.42223i 0.137250 + 0.188908i
\(549\) −0.344889 −0.0147195
\(550\) 0 0
\(551\) −8.17659 −0.348334
\(552\) −4.15594 5.72016i −0.176889 0.243466i
\(553\) 2.54873 0.828132i 0.108383 0.0352157i
\(554\) −5.43157 + 16.7167i −0.230765 + 0.710222i
\(555\) 26.8337 10.7002i 1.13903 0.454197i
\(556\) −8.70273 6.32290i −0.369078 0.268151i
\(557\) 12.7721 + 4.14990i 0.541171 + 0.175837i 0.566832 0.823834i \(-0.308169\pi\)
−0.0256608 + 0.999671i \(0.508169\pi\)
\(558\) −0.471815 + 0.153302i −0.0199735 + 0.00648979i
\(559\) −13.8230 + 10.0430i −0.584652 + 0.424774i
\(560\) 0.614889 + 0.388116i 0.0259838 + 0.0164009i
\(561\) 0 0
\(562\) 12.6629i 0.534154i
\(563\) 17.9510 + 24.7075i 0.756546 + 1.04130i 0.997494 + 0.0707576i \(0.0225417\pi\)
−0.240948 + 0.970538i \(0.577458\pi\)
\(564\) 1.42483 + 4.38517i 0.0599961 + 0.184649i
\(565\) −20.2917 + 16.8704i −0.853677 + 0.709745i
\(566\) 14.6823 + 10.6673i 0.617143 + 0.448381i
\(567\) 3.23340 4.45039i 0.135790 0.186899i
\(568\) 30.2122 + 9.81652i 1.26767 + 0.411892i
\(569\) 7.94804 + 24.4616i 0.333199 + 1.02548i 0.967602 + 0.252479i \(0.0812460\pi\)
−0.634403 + 0.773003i \(0.718754\pi\)
\(570\) −0.471427 7.21180i −0.0197459 0.302069i
\(571\) 27.1115 1.13458 0.567291 0.823518i \(-0.307992\pi\)
0.567291 + 0.823518i \(0.307992\pi\)
\(572\) 0 0
\(573\) 14.3506i 0.599504i
\(574\) −3.23381 + 2.34950i −0.134977 + 0.0980662i
\(575\) −5.12915 5.40876i −0.213900 0.225561i
\(576\) 0.110856 0.341178i 0.00461898 0.0142158i
\(577\) −1.68703 + 2.32200i −0.0702321 + 0.0966662i −0.842688 0.538402i \(-0.819028\pi\)
0.772456 + 0.635068i \(0.219028\pi\)
\(578\) 15.6103 21.4857i 0.649301 0.893686i
\(579\) 2.37682 7.31511i 0.0987773 0.304005i
\(580\) −10.5047 2.66980i −0.436185 0.110858i
\(581\) −2.84664 + 2.06821i −0.118099 + 0.0858037i
\(582\) 7.59774i 0.314936i
\(583\) 0 0
\(584\) 18.3777 0.760476
\(585\) 0.401346 0.0262355i 0.0165936 0.00108471i
\(586\) 3.28901 + 10.1225i 0.135868 + 0.418159i
\(587\) −42.6416 13.8551i −1.76001 0.571860i −0.762804 0.646629i \(-0.776178\pi\)
−0.997201 + 0.0747690i \(0.976178\pi\)
\(588\) −9.32939 + 12.8408i −0.384737 + 0.529546i
\(589\) 11.4100 + 8.28982i 0.470139 + 0.341576i
\(590\) 0.0528304 0.0439231i 0.00217499 0.00180828i
\(591\) 8.51654 + 26.2112i 0.350324 + 1.07819i
\(592\) −2.36861 3.26012i −0.0973494 0.133990i
\(593\) 6.09322i 0.250219i 0.992143 + 0.125109i \(0.0399282\pi\)
−0.992143 + 0.125109i \(0.960072\pi\)
\(594\) 0 0
\(595\) 5.00133 7.92358i 0.205035 0.324835i
\(596\) −13.7105 + 9.96127i −0.561604 + 0.408029i
\(597\) −2.40853 + 0.782579i −0.0985746 + 0.0320288i
\(598\) 2.04277 + 0.663736i 0.0835350 + 0.0271422i
\(599\) −10.4636 7.60225i −0.427531 0.310619i 0.353130 0.935574i \(-0.385117\pi\)
−0.780661 + 0.624955i \(0.785117\pi\)
\(600\) 4.32958 23.3151i 0.176754 0.951833i
\(601\) 3.41374 10.5064i 0.139249 0.428566i −0.856977 0.515354i \(-0.827660\pi\)
0.996227 + 0.0867885i \(0.0276604\pi\)
\(602\) 4.30293 1.39811i 0.175374 0.0569826i
\(603\) 0.400049 + 0.550621i 0.0162913 + 0.0224230i
\(604\) −11.3910 −0.463494
\(605\) 0 0
\(606\) −14.0364 −0.570188
\(607\) −0.0681317 0.0937752i −0.00276538 0.00380622i 0.807632 0.589687i \(-0.200749\pi\)
−0.810397 + 0.585881i \(0.800749\pi\)
\(608\) −12.6755 + 4.11852i −0.514059 + 0.167028i
\(609\) −1.15189 + 3.54516i −0.0466770 + 0.143657i
\(610\) −2.28803 5.73789i −0.0926397 0.232321i
\(611\) −2.80495 2.03791i −0.113476 0.0824451i
\(612\) 0.914408 + 0.297109i 0.0369627 + 0.0120099i
\(613\) −18.1124 + 5.88509i −0.731554 + 0.237696i −0.651025 0.759056i \(-0.725661\pi\)
−0.0805288 + 0.996752i \(0.525661\pi\)
\(614\) −6.50444 + 4.72575i −0.262498 + 0.190716i
\(615\) −28.0008 17.6740i −1.12910 0.712684i
\(616\) 0 0
\(617\) 30.8894i 1.24356i −0.783192 0.621780i \(-0.786410\pi\)
0.783192 0.621780i \(-0.213590\pi\)
\(618\) −11.2328 15.4606i −0.451849 0.621917i
\(619\) −10.3736 31.9266i −0.416950 1.28324i −0.910495 0.413520i \(-0.864299\pi\)
0.493545 0.869720i \(-0.335701\pi\)
\(620\) 11.9520 + 14.3758i 0.480002 + 0.577344i
\(621\) 6.15803 + 4.47407i 0.247113 + 0.179538i
\(622\) 1.60807 2.21331i 0.0644776 0.0887458i
\(623\) −3.49911 1.13693i −0.140189 0.0455501i
\(624\) −0.536349 1.65071i −0.0214711 0.0660814i
\(625\) 1.32576 24.9648i 0.0530304 0.998593i
\(626\) 19.6668 0.786043
\(627\) 0 0
\(628\) 18.9738i 0.757139i
\(629\) −42.0105 + 30.5224i −1.67507 + 1.21701i
\(630\) −0.103220 0.0262337i −0.00411239 0.00104518i
\(631\) 7.61952 23.4505i 0.303328 0.933548i −0.676968 0.736013i \(-0.736706\pi\)
0.980296 0.197535i \(-0.0632937\pi\)
\(632\) −7.16590 + 9.86302i −0.285044 + 0.392330i
\(633\) 8.98461 12.3663i 0.357106 0.491515i
\(634\) −1.73348 + 5.33511i −0.0688454 + 0.211884i
\(635\) 8.84386 34.7974i 0.350958 1.38089i
\(636\) 4.60168 3.34331i 0.182468 0.132571i
\(637\) 11.9350i 0.472880i
\(638\) 0 0
\(639\) 1.18186 0.0467535
\(640\) −19.5967 + 1.28101i −0.774627 + 0.0506365i
\(641\) 2.16821 + 6.67306i 0.0856390 + 0.263570i 0.984701 0.174251i \(-0.0557504\pi\)
−0.899062 + 0.437821i \(0.855750\pi\)
\(642\) −7.53327 2.44771i −0.297315 0.0966034i
\(643\) 7.20185 9.91249i 0.284013 0.390910i −0.643045 0.765828i \(-0.722329\pi\)
0.927058 + 0.374918i \(0.122329\pi\)
\(644\) 0.968128 + 0.703386i 0.0381496 + 0.0277173i
\(645\) 23.9606 + 28.8196i 0.943446 + 1.13477i
\(646\) 4.01446 + 12.3552i 0.157947 + 0.486111i
\(647\) 3.59733 + 4.95130i 0.141426 + 0.194656i 0.873854 0.486188i \(-0.161613\pi\)
−0.732428 + 0.680844i \(0.761613\pi\)
\(648\) 25.0251i 0.983079i
\(649\) 0 0
\(650\) 3.09905 + 6.50310i 0.121555 + 0.255073i
\(651\) 5.20165 3.77922i 0.203869 0.148119i
\(652\) −15.2675 + 4.96071i −0.597921 + 0.194276i
\(653\) −36.1702 11.7524i −1.41545 0.459907i −0.501295 0.865277i \(-0.667143\pi\)
−0.914153 + 0.405370i \(0.867143\pi\)
\(654\) 21.2678 + 15.4519i 0.831635 + 0.604218i
\(655\) −37.4479 + 14.9326i −1.46321 + 0.583467i
\(656\) −1.42732 + 4.39283i −0.0557274 + 0.171511i
\(657\) 0.650261 0.211283i 0.0253691 0.00824292i
\(658\) 0.539632 + 0.742740i 0.0210371 + 0.0289550i
\(659\) 15.7879 0.615011 0.307505 0.951546i \(-0.400506\pi\)
0.307505 + 0.951546i \(0.400506\pi\)
\(660\) 0 0
\(661\) −24.5794 −0.956027 −0.478014 0.878352i \(-0.658643\pi\)
−0.478014 + 0.878352i \(0.658643\pi\)
\(662\) 2.66255 + 3.66468i 0.103483 + 0.142432i
\(663\) −21.2714 + 6.91150i −0.826113 + 0.268420i
\(664\) 4.94644 15.2236i 0.191959 0.590790i
\(665\) 1.12146 + 2.81239i 0.0434884 + 0.109060i
\(666\) 0.477503 + 0.346926i 0.0185029 + 0.0134431i
\(667\) −5.06949 1.64718i −0.196292 0.0637790i
\(668\) −11.2510 + 3.65567i −0.435314 + 0.141442i
\(669\) 8.98277 6.52636i 0.347294 0.252324i
\(670\) −6.50666 + 10.3085i −0.251374 + 0.398251i
\(671\) 0 0
\(672\) 6.07597i 0.234385i
\(673\) 17.6179 + 24.2489i 0.679119 + 0.934727i 0.999923 0.0124187i \(-0.00395310\pi\)
−0.320804 + 0.947146i \(0.603953\pi\)
\(674\) 5.60993 + 17.2656i 0.216087 + 0.665046i
\(675\) 3.32339 + 25.3116i 0.127917 + 0.974246i
\(676\) −10.7246 7.79185i −0.412483 0.299687i
\(677\) 2.20836 3.03955i 0.0848744 0.116820i −0.764469 0.644661i \(-0.776999\pi\)
0.849343 + 0.527842i \(0.176999\pi\)
\(678\) −15.8631 5.15423i −0.609218 0.197947i
\(679\) −0.983593 3.02719i −0.0377468 0.116173i
\(680\) 2.78047 + 42.5351i 0.106626 + 1.63115i
\(681\) −1.96641 −0.0753531
\(682\) 0 0
\(683\) 21.0157i 0.804144i 0.915608 + 0.402072i \(0.131710\pi\)
−0.915608 + 0.402072i \(0.868290\pi\)
\(684\) −0.251345 + 0.182613i −0.00961043 + 0.00698239i
\(685\) −2.22084 + 8.73819i −0.0848538 + 0.333869i
\(686\) −2.00469 + 6.16979i −0.0765393 + 0.235564i
\(687\) −4.34277 + 5.97731i −0.165687 + 0.228049i
\(688\) 3.07297 4.22958i 0.117156 0.161251i
\(689\) −1.32168 + 4.06772i −0.0503521 + 0.154968i
\(690\) 1.16054 4.56629i 0.0441808 0.173836i
\(691\) 30.9712 22.5019i 1.17820 0.856012i 0.186232 0.982506i \(-0.440372\pi\)
0.991967 + 0.126494i \(0.0403723\pi\)
\(692\) 12.4432i 0.473020i
\(693\) 0 0
\(694\) −0.146408 −0.00555757
\(695\) −1.15737 17.7052i −0.0439016 0.671598i
\(696\) −5.24018 16.1276i −0.198629 0.611316i
\(697\) 56.6069 + 18.3927i 2.14414 + 0.696672i
\(698\) 7.27881 10.0184i 0.275507 0.379203i
\(699\) −9.65715 7.01633i −0.365267 0.265382i
\(700\) 0.522483 + 3.97934i 0.0197480 + 0.150405i
\(701\) 10.5790 + 32.5589i 0.399564 + 1.22973i 0.925350 + 0.379115i \(0.123772\pi\)
−0.525785 + 0.850617i \(0.676228\pi\)
\(702\) −4.32385 5.95127i −0.163193 0.224616i
\(703\) 16.7795i 0.632852i
\(704\) 0 0
\(705\) −4.05936 + 6.43121i −0.152884 + 0.242214i
\(706\) 15.5273 11.2812i 0.584376 0.424574i
\(707\) 5.59255 1.81713i 0.210329 0.0683402i
\(708\) −0.0868968 0.0282345i −0.00326578 0.00106112i
\(709\) −3.33701 2.42448i −0.125324 0.0910533i 0.523357 0.852113i \(-0.324679\pi\)
−0.648682 + 0.761060i \(0.724679\pi\)
\(710\) 7.84055 + 19.6624i 0.294251 + 0.737918i
\(711\) −0.140160 + 0.431368i −0.00525641 + 0.0161776i
\(712\) 15.9181 5.17212i 0.596558 0.193833i
\(713\) 5.40420 + 7.43824i 0.202389 + 0.278564i
\(714\) 5.92246 0.221642
\(715\) 0 0
\(716\) −1.96324 −0.0733697
\(717\) 4.55174 + 6.26494i 0.169988 + 0.233968i
\(718\) −6.69310 + 2.17472i −0.249784 + 0.0811598i
\(719\) −9.07260 + 27.9226i −0.338351 + 1.04134i 0.626697 + 0.779263i \(0.284406\pi\)
−0.965048 + 0.262074i \(0.915594\pi\)
\(720\) −0.114313 + 0.0455832i −0.00426019 + 0.00169879i
\(721\) 6.47703 + 4.70584i 0.241217 + 0.175255i
\(722\) 10.5125 + 3.41570i 0.391233 + 0.127119i
\(723\) 16.0962 5.22998i 0.598625 0.194505i
\(724\) −0.870284 + 0.632299i −0.0323439 + 0.0234992i
\(725\) −7.69084 16.1386i −0.285630 0.599373i
\(726\) 0 0
\(727\) 44.0893i 1.63518i 0.575799 + 0.817591i \(0.304691\pi\)
−0.575799 + 0.817591i \(0.695309\pi\)
\(728\) −1.68262 2.31593i −0.0623621 0.0858340i
\(729\) −8.04644 24.7644i −0.298016 0.917200i
\(730\) 7.82899 + 9.41666i 0.289764 + 0.348526i
\(731\) −54.5032 39.5989i −2.01587 1.46462i
\(732\) −4.82867 + 6.64610i −0.178473 + 0.245647i
\(733\) −46.5533 15.1261i −1.71948 0.558694i −0.727619 0.685982i \(-0.759373\pi\)
−0.991866 + 0.127287i \(0.959373\pi\)
\(734\) −1.33507 4.10893i −0.0492784 0.151663i
\(735\) −26.1239 + 1.70769i −0.963595 + 0.0629891i
\(736\) −8.68849 −0.320262
\(737\) 0 0
\(738\) 0.676520i 0.0249031i
\(739\) 16.7161 12.1450i 0.614911 0.446759i −0.236229 0.971697i \(-0.575912\pi\)
0.851140 + 0.524938i \(0.175912\pi\)
\(740\) 5.47882 21.5572i 0.201405 0.792458i
\(741\) 2.23332 6.87347i 0.0820432 0.252503i
\(742\) 0.665696 0.916252i 0.0244385 0.0336367i
\(743\) −17.7294 + 24.4025i −0.650429 + 0.895239i −0.999118 0.0419994i \(-0.986627\pi\)
0.348688 + 0.937239i \(0.386627\pi\)
\(744\) −9.03860 + 27.8179i −0.331371 + 1.01986i
\(745\) −27.0915 6.88539i −0.992557 0.252261i
\(746\) −2.09398 + 1.52137i −0.0766661 + 0.0557012i
\(747\) 0.595525i 0.0217891i
\(748\) 0 0
\(749\) 3.31838 0.121251
\(750\) 13.7909 7.71385i 0.503574 0.281670i
\(751\) 3.73806 + 11.5046i 0.136404 + 0.419808i 0.995806 0.0914930i \(-0.0291639\pi\)
−0.859402 + 0.511301i \(0.829164\pi\)
\(752\) 1.00894 + 0.327826i 0.0367924 + 0.0119546i
\(753\) −13.8895 + 19.1172i −0.506161 + 0.696671i
\(754\) 4.16758 + 3.02792i 0.151774 + 0.110271i
\(755\) −12.0116 14.4475i −0.437147 0.525798i
\(756\) −1.26648 3.89781i −0.0460613 0.141762i
\(757\) 12.1143 + 16.6739i 0.440302 + 0.606023i 0.970279 0.241988i \(-0.0777996\pi\)
−0.529977 + 0.848012i \(0.677800\pi\)
\(758\) 15.7838i 0.573293i
\(759\) 0 0
\(760\) −11.6476 7.35192i −0.422503 0.266682i
\(761\) 16.8640 12.2524i 0.611319 0.444149i −0.238560 0.971128i \(-0.576675\pi\)
0.849878 + 0.526979i \(0.176675\pi\)
\(762\) 21.5828 7.01269i 0.781864 0.254043i
\(763\) −10.4742 3.40326i −0.379190 0.123206i
\(764\) 8.93895 + 6.49452i 0.323400 + 0.234964i
\(765\) 0.587394 + 1.47306i 0.0212373 + 0.0532585i
\(766\) 6.93916 21.3565i 0.250722 0.771643i
\(767\) 0.0653417 0.0212308i 0.00235935 0.000766600i
\(768\) −14.7057 20.2407i −0.530648 0.730374i
\(769\) 10.7167 0.386455 0.193228 0.981154i \(-0.438104\pi\)
0.193228 + 0.981154i \(0.438104\pi\)
\(770\) 0 0
\(771\) 19.0466 0.685946
\(772\) −3.48091 4.79106i −0.125281 0.172434i
\(773\) 19.3600 6.29043i 0.696329 0.226251i 0.0605989 0.998162i \(-0.480699\pi\)
0.635731 + 0.771911i \(0.280699\pi\)
\(774\) −0.236627 + 0.728264i −0.00850539 + 0.0261769i
\(775\) −5.62999 + 30.3179i −0.202235 + 1.08905i
\(776\) 11.7146 + 8.51113i 0.420528 + 0.305532i
\(777\) −7.27517 2.36385i −0.260995 0.0848025i
\(778\) −9.95490 + 3.23454i −0.356900 + 0.115964i
\(779\) −15.5597 + 11.3048i −0.557483 + 0.405035i
\(780\) 5.11353 8.10134i 0.183094 0.290074i
\(781\) 0 0
\(782\) 8.46898i 0.302850i
\(783\) 10.7304 + 14.7691i 0.383474 + 0.527806i
\(784\) 1.12849 + 3.47313i 0.0403032 + 0.124040i
\(785\) 24.0649 20.0075i 0.858915 0.714099i
\(786\) −20.6154 14.9780i −0.735326 0.534246i
\(787\) 8.35961 11.5060i 0.297988 0.410145i −0.633600 0.773661i \(-0.718424\pi\)
0.931588 + 0.363516i \(0.118424\pi\)
\(788\) 20.1812 + 6.55727i 0.718925 + 0.233593i
\(789\) −13.4039 41.2530i −0.477192 1.46865i
\(790\) −8.10647 + 0.529911i −0.288415 + 0.0188534i
\(791\) 6.98764 0.248452
\(792\) 0 0
\(793\) 6.17726i 0.219361i
\(794\) −1.18348 + 0.859849i −0.0420001 + 0.0305149i
\(795\) 9.09277 + 2.31095i 0.322487 + 0.0819610i
\(796\) −0.602543 + 1.85444i −0.0213566 + 0.0657288i
\(797\) 26.4729 36.4368i 0.937719 1.29066i −0.0190529 0.999818i \(-0.506065\pi\)
0.956772 0.290841i \(-0.0939349\pi\)
\(798\) −1.12487 + 1.54824i −0.0398198 + 0.0548073i
\(799\) 4.22443 13.0015i 0.149450 0.459958i
\(800\) −20.0514 21.1445i −0.708925 0.747571i
\(801\) 0.503771 0.366011i 0.0177999 0.0129324i
\(802\) 4.31920i 0.152516i
\(803\) 0 0
\(804\) 16.2115 0.571737
\(805\) 0.128751 + 1.96960i 0.00453787 + 0.0694194i
\(806\) −2.74576 8.45060i −0.0967154 0.297660i
\(807\) −8.03960 2.61223i −0.283007 0.0919547i
\(808\) −15.7238 + 21.6419i −0.553161 + 0.761361i
\(809\) −19.2346 13.9748i −0.676254 0.491327i 0.195859 0.980632i \(-0.437251\pi\)
−0.872113 + 0.489305i \(0.837251\pi\)
\(810\) −12.8227 + 10.6608i −0.450545 + 0.374582i
\(811\) 2.53354 + 7.79742i 0.0889645 + 0.273804i 0.985634 0.168896i \(-0.0540204\pi\)
−0.896669 + 0.442701i \(0.854020\pi\)
\(812\) 1.68697 + 2.32192i 0.0592010 + 0.0814832i
\(813\) 41.0787i 1.44069i
\(814\) 0 0
\(815\) −22.3910 14.1331i −0.784323 0.495062i
\(816\) 5.53658 4.02256i 0.193819 0.140818i
\(817\) 20.7038 6.72707i 0.724334 0.235351i
\(818\) 28.0035 + 9.09890i 0.979121 + 0.318136i
\(819\) −0.0861618 0.0626002i −0.00301074 0.00218743i
\(820\) −23.6812 + 9.44307i −0.826983 + 0.329766i
\(821\) 13.4229 41.3113i 0.468461 1.44177i −0.386116 0.922450i \(-0.626184\pi\)
0.854577 0.519324i \(-0.173816\pi\)
\(822\) −5.41980 + 1.76100i −0.189037 + 0.0614219i
\(823\) 30.3768 + 41.8101i 1.05887 + 1.45741i 0.880859 + 0.473378i \(0.156966\pi\)
0.178009 + 0.984029i \(0.443034\pi\)
\(824\) −36.4211 −1.26879
\(825\) 0 0
\(826\) −0.0181927 −0.000633004
\(827\) −14.8756 20.4745i −0.517276 0.711969i 0.467849 0.883808i \(-0.345029\pi\)
−0.985125 + 0.171839i \(0.945029\pi\)
\(828\) −0.192622 + 0.0625867i −0.00669408 + 0.00217504i
\(829\) 12.9404 39.8264i 0.449439 1.38323i −0.428103 0.903730i \(-0.640818\pi\)
0.877542 0.479500i \(-0.159182\pi\)
\(830\) 9.90770 3.95077i 0.343901 0.137133i
\(831\) 31.1920 + 22.6623i 1.08204 + 0.786148i
\(832\) 6.11079 + 1.98552i 0.211854 + 0.0688354i
\(833\) 44.7555 14.5419i 1.55068 0.503848i
\(834\) 9.07295 6.59189i 0.314171 0.228258i
\(835\) −16.5005 10.4151i −0.571024 0.360428i
\(836\) 0 0
\(837\) 31.4885i 1.08840i
\(838\) −1.35236 1.86137i −0.0467167 0.0643000i
\(839\) 4.44515 + 13.6808i 0.153464 + 0.472313i 0.998002 0.0631825i \(-0.0201250\pi\)
−0.844538 + 0.535495i \(0.820125\pi\)
\(840\) −4.82848 + 4.01438i −0.166598 + 0.138509i
\(841\) 13.1189 + 9.53144i 0.452376 + 0.328670i
\(842\) −2.19854 + 3.02603i −0.0757666 + 0.104284i
\(843\) 26.4170 + 8.58341i 0.909850 + 0.295628i
\(844\) −3.63683 11.1930i −0.125185 0.385279i
\(845\) −1.42625 21.8185i −0.0490646 0.750580i
\(846\) −0.155383 −0.00534218
\(847\) 0 0
\(848\) 1.30870i 0.0449408i
\(849\) 32.2060 23.3991i 1.10531 0.803053i
\(850\) −20.6103 + 19.5448i −0.706928 + 0.670382i
\(851\) 3.38025 10.4033i 0.115873 0.356622i
\(852\) 16.5467 22.7746i 0.566882 0.780246i
\(853\) −25.2756 + 34.7889i −0.865420 + 1.19115i 0.114830 + 0.993385i \(0.463368\pi\)
−0.980250 + 0.197763i \(0.936632\pi\)
\(854\) −0.505464 + 1.55566i −0.0172966 + 0.0532336i
\(855\) −0.496651 0.126225i −0.0169851 0.00431681i
\(856\) −12.2129 + 8.87320i −0.417429 + 0.303280i
\(857\) 54.3052i 1.85503i 0.373784 + 0.927516i \(0.378060\pi\)
−0.373784 + 0.927516i \(0.621940\pi\)
\(858\) 0 0
\(859\) −24.3361 −0.830336 −0.415168 0.909745i \(-0.636277\pi\)
−0.415168 + 0.909745i \(0.636277\pi\)
\(860\) 28.7953 1.88232i 0.981913 0.0641865i
\(861\) 2.70945 + 8.33884i 0.0923380 + 0.284187i
\(862\) 15.8554 + 5.15173i 0.540037 + 0.175469i
\(863\) −23.0118 + 31.6731i −0.783332 + 1.07816i 0.211575 + 0.977362i \(0.432141\pi\)
−0.994906 + 0.100802i \(0.967859\pi\)
\(864\) 24.0736 + 17.4905i 0.819002 + 0.595040i
\(865\) −15.7820 + 13.1211i −0.536604 + 0.446131i
\(866\) −3.17431 9.76952i −0.107867 0.331982i
\(867\) −34.2415 47.1294i −1.16290 1.60060i
\(868\) 4.95043i 0.168029i
\(869\) 0 0
\(870\) 6.03138 9.55548i 0.204483 0.323961i
\(871\) −9.86208 + 7.16522i −0.334164 + 0.242784i
\(872\) 47.6491 15.4821i 1.61360 0.524291i
\(873\) 0.512347 + 0.166472i 0.0173403 + 0.00563421i
\(874\) −2.21395 1.60853i −0.0748881 0.0544094i
\(875\) −4.49614 + 4.85881i −0.151997 + 0.164258i
\(876\) 5.03261 15.4888i 0.170036 0.523317i
\(877\) 40.9793 13.3150i 1.38377 0.449615i 0.479865 0.877342i \(-0.340686\pi\)
0.903908 + 0.427727i \(0.140686\pi\)
\(878\) −5.01107 6.89714i −0.169115 0.232767i
\(879\) 23.3468 0.787466
\(880\) 0 0
\(881\) −38.1083 −1.28390 −0.641950 0.766746i \(-0.721874\pi\)
−0.641950 + 0.766746i \(0.721874\pi\)
\(882\) −0.314396 0.432729i −0.0105863 0.0145707i
\(883\) 27.6054 8.96955i 0.928997 0.301849i 0.194845 0.980834i \(-0.437580\pi\)
0.734152 + 0.678985i \(0.237580\pi\)
\(884\) −5.32147 + 16.3778i −0.178980 + 0.550845i
\(885\) −0.0558205 0.139986i −0.00187638 0.00470557i
\(886\) −4.28533 3.11348i −0.143969 0.104599i
\(887\) −2.10349 0.683467i −0.0706284 0.0229486i 0.273490 0.961875i \(-0.411822\pi\)
−0.344118 + 0.938926i \(0.611822\pi\)
\(888\) 33.0962 10.7536i 1.11064 0.360868i
\(889\) −7.69146 + 5.58817i −0.257963 + 0.187421i
\(890\) 9.43136 + 5.95304i 0.316140 + 0.199546i
\(891\) 0 0
\(892\) 8.54894i 0.286240i
\(893\) 2.59647 + 3.57374i 0.0868877 + 0.119591i
\(894\) −5.45973 16.8033i −0.182601 0.561987i
\(895\) −2.07019 2.49002i −0.0691990 0.0832321i
\(896\) 4.20706 + 3.05661i 0.140548 + 0.102114i
\(897\) 2.76933 3.81165i 0.0924652 0.127267i
\(898\) 10.4038 + 3.38041i 0.347180 + 0.112806i
\(899\) 6.81411 + 20.9717i 0.227263 + 0.699444i
\(900\) −0.596848 0.324331i −0.0198949 0.0108110i
\(901\) −16.8641 −0.561825
\(902\) 0 0
\(903\) 9.92432i 0.330261i
\(904\) −25.7172 + 18.6846i −0.855340 + 0.621441i
\(905\) −1.71965 0.437055i −0.0571632 0.0145282i
\(906\) 3.66976 11.2944i 0.121920 0.375230i
\(907\) 15.6858 21.5897i 0.520840 0.716874i −0.464860 0.885384i \(-0.653895\pi\)
0.985700 + 0.168510i \(0.0538954\pi\)
\(908\) −0.889924 + 1.22488i −0.0295332 + 0.0406489i
\(909\) −0.307546 + 0.946530i −0.0102007 + 0.0313944i
\(910\) 0.469868 1.84876i 0.0155760 0.0612858i
\(911\) 29.3460 21.3211i 0.972276 0.706400i 0.0163067 0.999867i \(-0.494809\pi\)
0.955969 + 0.293467i \(0.0948092\pi\)
\(912\) 2.21138i 0.0732261i
\(913\) 0 0
\(914\) −10.8363 −0.358434
\(915\) −13.5211 + 0.883861i −0.446995 + 0.0292195i
\(916\) 1.75788 + 5.41021i 0.0580821 + 0.178758i
\(917\) 10.1529 + 3.29887i 0.335277 + 0.108938i
\(918\) 17.0486 23.4654i 0.562689 0.774475i
\(919\) 24.0050 + 17.4406i 0.791851 + 0.575313i 0.908512 0.417859i \(-0.137219\pi\)
−0.116661 + 0.993172i \(0.537219\pi\)
\(920\) −5.74048 6.90462i −0.189258 0.227638i
\(921\) 5.44976 + 16.7726i 0.179576 + 0.552677i
\(922\) −5.34174 7.35227i −0.175921 0.242134i
\(923\) 21.1680i 0.696754i
\(924\) 0 0
\(925\) 33.1188 15.7827i 1.08894 0.518932i
\(926\) 3.13652 2.27882i 0.103073 0.0748866i
\(927\) −1.28869 + 0.418721i −0.0423262 + 0.0137526i
\(928\) −19.8182 6.43933i −0.650565 0.211381i
\(929\) 22.4685 + 16.3243i 0.737168 + 0.535584i 0.891823 0.452385i \(-0.149427\pi\)
−0.154655 + 0.987968i \(0.549427\pi\)
\(930\) −18.1043 + 7.21922i −0.593662 + 0.236728i
\(931\) −4.69896 + 14.4619i −0.154002 + 0.473970i
\(932\) −8.74093 + 2.84010i −0.286319 + 0.0930305i
\(933\) −3.52734 4.85496i −0.115480 0.158944i
\(934\) −19.2786 −0.630817
\(935\) 0 0
\(936\) 0.484498 0.0158363
\(937\) 17.7759 + 24.4664i 0.580712 + 0.799282i 0.993773 0.111422i \(-0.0355404\pi\)
−0.413061 + 0.910703i \(0.635540\pi\)
\(938\) 3.06994 0.997483i 0.100237 0.0325690i
\(939\) 13.3309 41.0282i 0.435037 1.33891i
\(940\) 2.16888 + 5.43909i 0.0707411 + 0.177404i
\(941\) −4.85954 3.53066i −0.158416 0.115096i 0.505753 0.862678i \(-0.331215\pi\)
−0.664169 + 0.747582i \(0.731215\pi\)
\(942\) 18.8129 + 6.11267i 0.612956 + 0.199162i
\(943\) −11.9244 + 3.87446i −0.388311 + 0.126170i
\(944\) −0.0170073 + 0.0123565i −0.000553541 + 0.000402171i
\(945\) 3.60821 5.71646i 0.117375 0.185956i
\(946\) 0 0
\(947\) 10.0218i 0.325665i −0.986654 0.162833i \(-0.947937\pi\)
0.986654 0.162833i \(-0.0520630\pi\)
\(948\) 6.35023 + 8.74034i 0.206246 + 0.283873i
\(949\) 3.78425 + 11.6467i 0.122842 + 0.378068i
\(950\) −1.19484 9.10012i −0.0387656 0.295247i
\(951\) 9.95492 + 7.23267i 0.322810 + 0.234535i
\(952\) 6.63445 9.13154i 0.215024 0.295955i
\(953\) 9.30263 + 3.02261i 0.301342 + 0.0979118i 0.455785 0.890090i \(-0.349359\pi\)
−0.154444 + 0.988002i \(0.549359\pi\)
\(954\) 0.0592331 + 0.182301i 0.00191774 + 0.00590220i
\(955\) 1.18879 + 18.1858i 0.0384682 + 0.588479i
\(956\) 5.96237 0.192837
\(957\) 0 0
\(958\) 34.6967i 1.12100i
\(959\) 1.93145 1.40328i 0.0623698 0.0453143i
\(960\) 3.47166 13.6597i 0.112047 0.440866i
\(961\) 2.17387 6.69048i 0.0701248 0.215822i
\(962\) −6.21374 + 8.55248i −0.200339 + 0.275743i
\(963\) −0.330118 + 0.454369i −0.0106379 + 0.0146418i
\(964\) 4.02679 12.3932i 0.129694 0.399158i
\(965\) 2.40606 9.46698i 0.0774538 0.304753i
\(966\) −1.00931 + 0.733309i −0.0324741 + 0.0235938i
\(967\) 1.22635i 0.0394367i −0.999806 0.0197184i \(-0.993723\pi\)
0.999806 0.0197184i \(-0.00627695\pi\)
\(968\) 0 0
\(969\) 28.4963 0.915432
\(970\) 0.629388 + 9.62826i 0.0202084 + 0.309145i
\(971\) −13.7966 42.4615i −0.442753 1.36265i −0.884929 0.465726i \(-0.845793\pi\)
0.442176 0.896928i \(-0.354207\pi\)
\(972\) 1.34220 + 0.436106i 0.0430509 + 0.0139881i
\(973\) −2.76159 + 3.80100i −0.0885324 + 0.121854i
\(974\) −27.2493 19.7978i −0.873123 0.634361i
\(975\) 15.6672 2.05709i 0.501753 0.0658795i
\(976\) 0.584080 + 1.79761i 0.0186959 + 0.0575402i
\(977\) −27.7700 38.2221i −0.888441 1.22283i −0.974011 0.226502i \(-0.927271\pi\)
0.0855696 0.996332i \(-0.472729\pi\)
\(978\) 16.7361i 0.535162i
\(979\) 0 0
\(980\) −10.7590 + 17.0454i −0.343683 + 0.544495i
\(981\) 1.50798 1.09561i 0.0481460 0.0349801i
\(982\) 6.91639 2.24727i 0.220711 0.0717133i
\(983\) 13.2530 + 4.30617i 0.422706 + 0.137345i 0.512643 0.858602i \(-0.328667\pi\)
−0.0899369 + 0.995947i \(0.528667\pi\)
\(984\) −32.2695 23.4452i −1.02871 0.747405i
\(985\) 12.9639 + 32.5107i 0.413065 + 1.03588i
\(986\) −6.27664 + 19.3175i −0.199889 + 0.615195i
\(987\) 1.91526 0.622307i 0.0609635 0.0198082i
\(988\) −3.27075 4.50181i −0.104057 0.143222i
\(989\) 14.1916 0.451265
\(990\) 0 0
\(991\) 36.5755 1.16186 0.580930 0.813953i \(-0.302689\pi\)
0.580930 + 0.813953i \(0.302689\pi\)
\(992\) 21.1267 + 29.0784i 0.670773 + 0.923240i
\(993\) 9.44992 3.07046i 0.299884 0.0974382i
\(994\) 1.73211 5.33088i 0.0549392 0.169085i
\(995\) −2.98739 + 1.19125i −0.0947067 + 0.0377650i
\(996\) −11.4759 8.33773i −0.363628 0.264191i
\(997\) 18.3949 + 5.97686i 0.582572 + 0.189289i 0.585452 0.810707i \(-0.300917\pi\)
−0.00288064 + 0.999996i \(0.500917\pi\)
\(998\) −23.1156 + 7.51071i −0.731711 + 0.237747i
\(999\) −30.3084 + 22.0204i −0.958916 + 0.696693i
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 605.2.j.g.124.3 16
5.4 even 2 inner 605.2.j.g.124.2 16
11.2 odd 10 605.2.b.g.364.5 8
11.3 even 5 605.2.j.d.269.3 16
11.4 even 5 inner 605.2.j.g.444.2 16
11.5 even 5 605.2.j.d.9.2 16
11.6 odd 10 55.2.j.a.9.3 yes 16
11.7 odd 10 605.2.j.h.444.3 16
11.8 odd 10 55.2.j.a.49.2 yes 16
11.9 even 5 605.2.b.f.364.4 8
11.10 odd 2 605.2.j.h.124.2 16
33.8 even 10 495.2.ba.a.379.3 16
33.17 even 10 495.2.ba.a.64.2 16
44.19 even 10 880.2.cd.c.49.3 16
44.39 even 10 880.2.cd.c.449.2 16
55.2 even 20 3025.2.a.bl.1.4 8
55.4 even 10 inner 605.2.j.g.444.3 16
55.8 even 20 275.2.h.d.126.3 16
55.9 even 10 605.2.b.f.364.5 8
55.13 even 20 3025.2.a.bl.1.5 8
55.14 even 10 605.2.j.d.269.2 16
55.17 even 20 275.2.h.d.251.2 16
55.19 odd 10 55.2.j.a.49.3 yes 16
55.24 odd 10 605.2.b.g.364.4 8
55.28 even 20 275.2.h.d.251.3 16
55.29 odd 10 605.2.j.h.444.2 16
55.39 odd 10 55.2.j.a.9.2 16
55.42 odd 20 3025.2.a.bk.1.5 8
55.49 even 10 605.2.j.d.9.3 16
55.52 even 20 275.2.h.d.126.2 16
55.53 odd 20 3025.2.a.bk.1.4 8
55.54 odd 2 605.2.j.h.124.3 16
165.74 even 10 495.2.ba.a.379.2 16
165.149 even 10 495.2.ba.a.64.3 16
220.19 even 10 880.2.cd.c.49.2 16
220.39 even 10 880.2.cd.c.449.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.2.j.a.9.2 16 55.39 odd 10
55.2.j.a.9.3 yes 16 11.6 odd 10
55.2.j.a.49.2 yes 16 11.8 odd 10
55.2.j.a.49.3 yes 16 55.19 odd 10
275.2.h.d.126.2 16 55.52 even 20
275.2.h.d.126.3 16 55.8 even 20
275.2.h.d.251.2 16 55.17 even 20
275.2.h.d.251.3 16 55.28 even 20
495.2.ba.a.64.2 16 33.17 even 10
495.2.ba.a.64.3 16 165.149 even 10
495.2.ba.a.379.2 16 165.74 even 10
495.2.ba.a.379.3 16 33.8 even 10
605.2.b.f.364.4 8 11.9 even 5
605.2.b.f.364.5 8 55.9 even 10
605.2.b.g.364.4 8 55.24 odd 10
605.2.b.g.364.5 8 11.2 odd 10
605.2.j.d.9.2 16 11.5 even 5
605.2.j.d.9.3 16 55.49 even 10
605.2.j.d.269.2 16 55.14 even 10
605.2.j.d.269.3 16 11.3 even 5
605.2.j.g.124.2 16 5.4 even 2 inner
605.2.j.g.124.3 16 1.1 even 1 trivial
605.2.j.g.444.2 16 11.4 even 5 inner
605.2.j.g.444.3 16 55.4 even 10 inner
605.2.j.h.124.2 16 11.10 odd 2
605.2.j.h.124.3 16 55.54 odd 2
605.2.j.h.444.2 16 55.29 odd 10
605.2.j.h.444.3 16 11.7 odd 10
880.2.cd.c.49.2 16 220.19 even 10
880.2.cd.c.49.3 16 44.19 even 10
880.2.cd.c.449.2 16 44.39 even 10
880.2.cd.c.449.3 16 220.39 even 10
3025.2.a.bk.1.4 8 55.53 odd 20
3025.2.a.bk.1.5 8 55.42 odd 20
3025.2.a.bl.1.4 8 55.2 even 20
3025.2.a.bl.1.5 8 55.13 even 20