Properties

Label 55.2.j.a.49.4
Level $55$
Weight $2$
Character 55.49
Analytic conductor $0.439$
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] = [55,2,Mod(4,55)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(55, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([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("55.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 55 = 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 55.j (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: \(0.439177211117\)
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: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 49.4
Root \(0.972539 - 1.33858i\) of defining polynomial
Character \(\chi\) \(=\) 55.49
Dual form 55.2.j.a.9.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.57360 - 0.511294i) q^{2} +(-1.16075 + 1.59764i) q^{3} +(0.596764 - 0.433574i) q^{4} +(0.264988 - 2.22031i) q^{5} +(-1.00970 + 3.10753i) q^{6} +(-1.31845 - 1.81468i) q^{7} +(-1.22769 + 1.68978i) q^{8} +(-0.278050 - 0.855749i) q^{9} +O(q^{10})\) \(q+(1.57360 - 0.511294i) q^{2} +(-1.16075 + 1.59764i) q^{3} +(0.596764 - 0.433574i) q^{4} +(0.264988 - 2.22031i) q^{5} +(-1.00970 + 3.10753i) q^{6} +(-1.31845 - 1.81468i) q^{7} +(-1.22769 + 1.68978i) q^{8} +(-0.278050 - 0.855749i) q^{9} +(-0.718246 - 3.62937i) q^{10} +(-3.27115 + 0.547326i) q^{11} +1.45668i q^{12} +(3.51868 - 1.14329i) q^{13} +(-3.00254 - 2.18148i) q^{14} +(3.23967 + 3.00058i) q^{15} +(-1.52381 + 4.68982i) q^{16} +(2.11573 + 0.687441i) q^{17} +(-0.875078 - 1.20444i) q^{18} +(4.27714 + 3.10753i) q^{19} +(-0.804534 - 1.43989i) q^{20} +4.42960 q^{21} +(-4.86764 + 2.53379i) q^{22} -3.85415i q^{23} +(-1.27460 - 3.92282i) q^{24} +(-4.85956 - 1.17671i) q^{25} +(4.95244 - 3.59816i) q^{26} +(-3.94448 - 1.28164i) q^{27} +(-1.57360 - 0.511294i) q^{28} +(0.152450 - 0.110762i) q^{29} +(6.63212 + 3.06530i) q^{30} +(0.212253 + 0.653249i) q^{31} +3.98166i q^{32} +(2.92256 - 5.86142i) q^{33} +3.68079 q^{34} +(-4.37854 + 2.44649i) q^{35} +(-0.536960 - 0.390125i) q^{36} +(1.52422 + 2.09791i) q^{37} +(8.31938 + 2.70313i) q^{38} +(-2.25775 + 6.94864i) q^{39} +(3.42650 + 3.17363i) q^{40} +(-6.40421 - 4.65293i) q^{41} +(6.97041 - 2.26482i) q^{42} +8.41368i q^{43} +(-1.71480 + 1.74491i) q^{44} +(-1.97371 + 0.390594i) q^{45} +(-1.97060 - 6.06490i) q^{46} +(7.06117 - 9.71886i) q^{47} +(-5.72386 - 7.87822i) q^{48} +(0.608337 - 1.87227i) q^{49} +(-8.24866 + 0.632992i) q^{50} +(-3.55411 + 2.58222i) q^{51} +(1.60412 - 2.20788i) q^{52} +(-12.0371 + 3.91110i) q^{53} -6.86233 q^{54} +(0.348420 + 7.40801i) q^{55} +4.68506 q^{56} +(-9.92940 + 3.22626i) q^{57} +(0.183264 - 0.252241i) q^{58} +(-0.278050 + 0.202015i) q^{59} +(3.23429 + 0.386003i) q^{60} +(0.535643 - 1.64854i) q^{61} +(0.668004 + 0.919429i) q^{62} +(-1.18632 + 1.63283i) q^{63} +(-1.01183 - 3.11409i) q^{64} +(-1.60605 - 8.11552i) q^{65} +(1.60204 - 10.7178i) q^{66} -0.650461i q^{67} +(1.56065 - 0.507084i) q^{68} +(6.15754 + 4.47371i) q^{69} +(-5.63919 + 6.08852i) q^{70} +(1.43619 - 4.42013i) q^{71} +(1.78738 + 0.580756i) q^{72} +(5.20684 + 7.16660i) q^{73} +(3.47116 + 2.52195i) q^{74} +(7.52070 - 6.39795i) q^{75} +3.89979 q^{76} +(5.30606 + 5.21449i) q^{77} +12.0888i q^{78} +(2.23551 + 6.88019i) q^{79} +(10.0091 + 4.62609i) q^{80} +(8.80999 - 6.40083i) q^{81} +(-12.4567 - 4.04742i) q^{82} +(3.02593 + 0.983185i) q^{83} +(2.64342 - 1.92056i) q^{84} +(2.08698 - 4.51541i) q^{85} +(4.30186 + 13.2398i) q^{86} +0.372127i q^{87} +(3.09111 - 6.19946i) q^{88} -9.92195 q^{89} +(-2.90612 + 1.62378i) q^{90} +(-6.71389 - 4.87793i) q^{91} +(-1.67106 - 2.30002i) q^{92} +(-1.29003 - 0.419156i) q^{93} +(6.14226 - 18.9039i) q^{94} +(8.03307 - 8.67314i) q^{95} +(-6.36125 - 4.62172i) q^{96} +(2.15710 - 0.700884i) q^{97} -3.25724i q^{98} +(1.37792 + 2.64710i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{9} - 6 q^{11} - 12 q^{14} - 16 q^{15} + 16 q^{16} + 6 q^{19} - 8 q^{20} + 8 q^{21} + 6 q^{24} - 16 q^{25} + 40 q^{26} + 2 q^{29} + 26 q^{30} + 8 q^{31} - 16 q^{34} + 22 q^{35} + 10 q^{36} + 30 q^{39} + 12 q^{40} - 52 q^{41} + 4 q^{44} + 12 q^{45} - 62 q^{46} - 10 q^{49} + 28 q^{50} - 42 q^{51} - 40 q^{54} - 8 q^{55} - 20 q^{56} + 2 q^{59} - 32 q^{60} - 40 q^{61} - 8 q^{64} - 40 q^{65} + 58 q^{66} + 26 q^{69} - 34 q^{70} + 36 q^{71} + 48 q^{74} - 20 q^{75} + 56 q^{76} + 38 q^{79} + 34 q^{80} + 68 q^{81} + 12 q^{84} + 58 q^{85} + 22 q^{86} + 24 q^{89} + 78 q^{90} - 20 q^{91} + 14 q^{94} + 48 q^{95} - 86 q^{96} - 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/55\mathbb{Z}\right)^\times\).

\(n\) \(12\) \(46\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.57360 0.511294i 1.11270 0.361539i 0.305725 0.952120i \(-0.401101\pi\)
0.806979 + 0.590581i \(0.201101\pi\)
\(3\) −1.16075 + 1.59764i −0.670160 + 0.922396i −0.999764 0.0217231i \(-0.993085\pi\)
0.329604 + 0.944119i \(0.393085\pi\)
\(4\) 0.596764 0.433574i 0.298382 0.216787i
\(5\) 0.264988 2.22031i 0.118506 0.992953i
\(6\) −1.00970 + 3.10753i −0.412207 + 1.26864i
\(7\) −1.31845 1.81468i −0.498326 0.685886i 0.483571 0.875305i \(-0.339340\pi\)
−0.981896 + 0.189419i \(0.939340\pi\)
\(8\) −1.22769 + 1.68978i −0.434055 + 0.597426i
\(9\) −0.278050 0.855749i −0.0926832 0.285250i
\(10\) −0.718246 3.62937i −0.227129 1.14771i
\(11\) −3.27115 + 0.547326i −0.986289 + 0.165025i
\(12\) 1.45668i 0.420508i
\(13\) 3.51868 1.14329i 0.975906 0.317091i 0.222708 0.974885i \(-0.428510\pi\)
0.753198 + 0.657794i \(0.228510\pi\)
\(14\) −3.00254 2.18148i −0.802464 0.583024i
\(15\) 3.23967 + 3.00058i 0.836478 + 0.774747i
\(16\) −1.52381 + 4.68982i −0.380954 + 1.17245i
\(17\) 2.11573 + 0.687441i 0.513139 + 0.166729i 0.554129 0.832431i \(-0.313051\pi\)
−0.0409903 + 0.999160i \(0.513051\pi\)
\(18\) −0.875078 1.20444i −0.206258 0.283890i
\(19\) 4.27714 + 3.10753i 0.981244 + 0.712916i 0.957986 0.286814i \(-0.0925961\pi\)
0.0232580 + 0.999729i \(0.492596\pi\)
\(20\) −0.804534 1.43989i −0.179899 0.321970i
\(21\) 4.42960 0.966617
\(22\) −4.86764 + 2.53379i −1.03778 + 0.540206i
\(23\) 3.85415i 0.803647i −0.915717 0.401823i \(-0.868377\pi\)
0.915717 0.401823i \(-0.131623\pi\)
\(24\) −1.27460 3.92282i −0.260177 0.800742i
\(25\) −4.85956 1.17671i −0.971913 0.235342i
\(26\) 4.95244 3.59816i 0.971253 0.705657i
\(27\) −3.94448 1.28164i −0.759116 0.246652i
\(28\) −1.57360 0.511294i −0.297383 0.0966255i
\(29\) 0.152450 0.110762i 0.0283093 0.0205679i −0.573541 0.819177i \(-0.694431\pi\)
0.601850 + 0.798609i \(0.294431\pi\)
\(30\) 6.63212 + 3.06530i 1.21085 + 0.559644i
\(31\) 0.212253 + 0.653249i 0.0381218 + 0.117327i 0.968306 0.249765i \(-0.0803534\pi\)
−0.930185 + 0.367092i \(0.880353\pi\)
\(32\) 3.98166i 0.703866i
\(33\) 2.92256 5.86142i 0.508753 1.02034i
\(34\) 3.68079 0.631251
\(35\) −4.37854 + 2.44649i −0.740108 + 0.413532i
\(36\) −0.536960 0.390125i −0.0894934 0.0650208i
\(37\) 1.52422 + 2.09791i 0.250580 + 0.344894i 0.915714 0.401830i \(-0.131626\pi\)
−0.665134 + 0.746724i \(0.731626\pi\)
\(38\) 8.31938 + 2.70313i 1.34958 + 0.438506i
\(39\) −2.25775 + 6.94864i −0.361529 + 1.11267i
\(40\) 3.42650 + 3.17363i 0.541778 + 0.501795i
\(41\) −6.40421 4.65293i −1.00017 0.726666i −0.0380448 0.999276i \(-0.512113\pi\)
−0.962124 + 0.272611i \(0.912113\pi\)
\(42\) 6.97041 2.26482i 1.07556 0.349470i
\(43\) 8.41368i 1.28307i 0.767092 + 0.641537i \(0.221703\pi\)
−0.767092 + 0.641537i \(0.778297\pi\)
\(44\) −1.71480 + 1.74491i −0.258515 + 0.263055i
\(45\) −1.97371 + 0.390594i −0.294223 + 0.0582263i
\(46\) −1.97060 6.06490i −0.290550 0.894220i
\(47\) 7.06117 9.71886i 1.02998 1.41764i 0.125012 0.992155i \(-0.460103\pi\)
0.904965 0.425486i \(-0.139897\pi\)
\(48\) −5.72386 7.87822i −0.826168 1.13712i
\(49\) 0.608337 1.87227i 0.0869053 0.267467i
\(50\) −8.24866 + 0.632992i −1.16654 + 0.0895186i
\(51\) −3.55411 + 2.58222i −0.497676 + 0.361582i
\(52\) 1.60412 2.20788i 0.222451 0.306178i
\(53\) −12.0371 + 3.91110i −1.65343 + 0.537231i −0.979479 0.201549i \(-0.935403\pi\)
−0.673947 + 0.738779i \(0.735403\pi\)
\(54\) −6.86233 −0.933845
\(55\) 0.348420 + 7.40801i 0.0469809 + 0.998896i
\(56\) 4.68506 0.626067
\(57\) −9.92940 + 3.22626i −1.31518 + 0.427328i
\(58\) 0.183264 0.252241i 0.0240638 0.0331209i
\(59\) −0.278050 + 0.202015i −0.0361990 + 0.0263001i −0.605738 0.795664i \(-0.707122\pi\)
0.569539 + 0.821965i \(0.307122\pi\)
\(60\) 3.23429 + 0.386003i 0.417545 + 0.0498328i
\(61\) 0.535643 1.64854i 0.0685821 0.211074i −0.910892 0.412645i \(-0.864605\pi\)
0.979474 + 0.201572i \(0.0646049\pi\)
\(62\) 0.668004 + 0.919429i 0.0848366 + 0.116768i
\(63\) −1.18632 + 1.63283i −0.149462 + 0.205717i
\(64\) −1.01183 3.11409i −0.126479 0.389261i
\(65\) −1.60605 8.11552i −0.199206 1.00661i
\(66\) 1.60204 10.7178i 0.197197 1.31927i
\(67\) 0.650461i 0.0794664i −0.999210 0.0397332i \(-0.987349\pi\)
0.999210 0.0397332i \(-0.0126508\pi\)
\(68\) 1.56065 0.507084i 0.189256 0.0614930i
\(69\) 6.15754 + 4.47371i 0.741281 + 0.538572i
\(70\) −5.63919 + 6.08852i −0.674012 + 0.727717i
\(71\) 1.43619 4.42013i 0.170444 0.524573i −0.828952 0.559320i \(-0.811062\pi\)
0.999396 + 0.0347464i \(0.0110624\pi\)
\(72\) 1.78738 + 0.580756i 0.210645 + 0.0684427i
\(73\) 5.20684 + 7.16660i 0.609415 + 0.838787i 0.996529 0.0832444i \(-0.0265282\pi\)
−0.387115 + 0.922032i \(0.626528\pi\)
\(74\) 3.47116 + 2.52195i 0.403515 + 0.293171i
\(75\) 7.52070 6.39795i 0.868416 0.738772i
\(76\) 3.89979 0.447336
\(77\) 5.30606 + 5.21449i 0.604682 + 0.594246i
\(78\) 12.0888i 1.36878i
\(79\) 2.23551 + 6.88019i 0.251514 + 0.774082i 0.994496 + 0.104770i \(0.0334108\pi\)
−0.742982 + 0.669311i \(0.766589\pi\)
\(80\) 10.0091 + 4.62609i 1.11905 + 0.517212i
\(81\) 8.80999 6.40083i 0.978888 0.711203i
\(82\) −12.4567 4.04742i −1.37561 0.446963i
\(83\) 3.02593 + 0.983185i 0.332139 + 0.107919i 0.470339 0.882486i \(-0.344132\pi\)
−0.138200 + 0.990404i \(0.544132\pi\)
\(84\) 2.64342 1.92056i 0.288421 0.209550i
\(85\) 2.08698 4.51541i 0.226364 0.489765i
\(86\) 4.30186 + 13.2398i 0.463882 + 1.42768i
\(87\) 0.372127i 0.0398962i
\(88\) 3.09111 6.19946i 0.329514 0.660865i
\(89\) −9.92195 −1.05172 −0.525862 0.850570i \(-0.676257\pi\)
−0.525862 + 0.850570i \(0.676257\pi\)
\(90\) −2.90612 + 1.62378i −0.306332 + 0.171162i
\(91\) −6.71389 4.87793i −0.703807 0.511346i
\(92\) −1.67106 2.30002i −0.174220 0.239793i
\(93\) −1.29003 0.419156i −0.133770 0.0434644i
\(94\) 6.14226 18.9039i 0.633526 1.94979i
\(95\) 8.03307 8.67314i 0.824175 0.889845i
\(96\) −6.36125 4.62172i −0.649243 0.471703i
\(97\) 2.15710 0.700884i 0.219020 0.0711640i −0.197451 0.980313i \(-0.563266\pi\)
0.416472 + 0.909149i \(0.363266\pi\)
\(98\) 3.25724i 0.329031i
\(99\) 1.37792 + 2.64710i 0.138486 + 0.266044i
\(100\) −3.41020 + 1.40476i −0.341020 + 0.140476i
\(101\) 3.05830 + 9.41247i 0.304312 + 0.936576i 0.979933 + 0.199327i \(0.0638756\pi\)
−0.675621 + 0.737249i \(0.736124\pi\)
\(102\) −4.27249 + 5.88057i −0.423039 + 0.582263i
\(103\) −6.01958 8.28525i −0.593127 0.816370i 0.401930 0.915670i \(-0.368339\pi\)
−0.995057 + 0.0993007i \(0.968339\pi\)
\(104\) −2.38796 + 7.34938i −0.234159 + 0.720666i
\(105\) 1.17379 9.83508i 0.114550 0.959805i
\(106\) −16.9419 + 12.3090i −1.64554 + 1.19556i
\(107\) −5.90536 + 8.12803i −0.570893 + 0.785767i −0.992660 0.120937i \(-0.961410\pi\)
0.421767 + 0.906704i \(0.361410\pi\)
\(108\) −2.90961 + 0.945389i −0.279977 + 0.0909701i
\(109\) 8.80173 0.843053 0.421527 0.906816i \(-0.361494\pi\)
0.421527 + 0.906816i \(0.361494\pi\)
\(110\) 4.33594 + 11.4791i 0.413416 + 1.09449i
\(111\) −5.12094 −0.486058
\(112\) 10.5196 3.41803i 0.994010 0.322973i
\(113\) 0.135985 0.187168i 0.0127924 0.0176073i −0.802573 0.596554i \(-0.796536\pi\)
0.815365 + 0.578947i \(0.196536\pi\)
\(114\) −13.9753 + 10.1537i −1.30891 + 0.950980i
\(115\) −8.55742 1.02130i −0.797984 0.0952370i
\(116\) 0.0429534 0.132197i 0.00398812 0.0122742i
\(117\) −1.95673 2.69321i −0.180900 0.248988i
\(118\) −0.334250 + 0.460056i −0.0307702 + 0.0423516i
\(119\) −1.54198 4.74573i −0.141353 0.435040i
\(120\) −9.04763 + 1.79051i −0.825932 + 0.163451i
\(121\) 10.4009 3.58078i 0.945533 0.325525i
\(122\) 2.86801i 0.259658i
\(123\) 14.8674 4.83071i 1.34055 0.435570i
\(124\) 0.409897 + 0.297808i 0.0368098 + 0.0267439i
\(125\) −3.90039 + 10.4779i −0.348861 + 0.937174i
\(126\) −1.03194 + 3.17598i −0.0919324 + 0.282939i
\(127\) 2.31140 + 0.751018i 0.205103 + 0.0666421i 0.409767 0.912190i \(-0.365610\pi\)
−0.204664 + 0.978832i \(0.565610\pi\)
\(128\) −7.86516 10.8255i −0.695188 0.956844i
\(129\) −13.4420 9.76619i −1.18350 0.859865i
\(130\) −6.67669 11.9494i −0.585585 1.04803i
\(131\) 1.58846 0.138785 0.0693924 0.997589i \(-0.477894\pi\)
0.0693924 + 0.997589i \(0.477894\pi\)
\(132\) −0.797281 4.76503i −0.0693944 0.414743i
\(133\) 11.8588i 1.02829i
\(134\) −0.332577 1.02357i −0.0287302 0.0884226i
\(135\) −3.89088 + 8.41836i −0.334874 + 0.724537i
\(136\) −3.75909 + 2.73114i −0.322339 + 0.234193i
\(137\) 17.7866 + 5.77920i 1.51961 + 0.493750i 0.945664 0.325145i \(-0.105413\pi\)
0.573943 + 0.818895i \(0.305413\pi\)
\(138\) 11.9769 + 3.89153i 1.01954 + 0.331269i
\(139\) 9.40675 6.83441i 0.797870 0.579687i −0.112418 0.993661i \(-0.535860\pi\)
0.910289 + 0.413974i \(0.135860\pi\)
\(140\) −1.55222 + 3.35840i −0.131186 + 0.283836i
\(141\) 7.33095 + 22.5624i 0.617378 + 1.90009i
\(142\) 7.68984i 0.645317i
\(143\) −10.8844 + 5.66573i −0.910197 + 0.473792i
\(144\) 4.43700 0.369750
\(145\) −0.205528 0.367838i −0.0170682 0.0305472i
\(146\) 11.8577 + 8.61514i 0.981352 + 0.712994i
\(147\) 2.28508 + 3.14514i 0.188470 + 0.259407i
\(148\) 1.81920 + 0.591094i 0.149537 + 0.0485876i
\(149\) −1.82800 + 5.62600i −0.149755 + 0.460900i −0.997592 0.0693580i \(-0.977905\pi\)
0.847836 + 0.530258i \(0.177905\pi\)
\(150\) 8.56335 13.9131i 0.699194 1.13600i
\(151\) −10.3375 7.51064i −0.841254 0.611207i 0.0814664 0.996676i \(-0.474040\pi\)
−0.922721 + 0.385469i \(0.874040\pi\)
\(152\) −10.5020 + 3.41232i −0.851828 + 0.276776i
\(153\) 2.00167i 0.161826i
\(154\) 11.0158 + 5.49257i 0.887675 + 0.442604i
\(155\) 1.50666 0.298166i 0.121018 0.0239492i
\(156\) 1.66541 + 5.12560i 0.133339 + 0.410376i
\(157\) −8.43394 + 11.6083i −0.673102 + 0.926445i −0.999826 0.0186749i \(-0.994055\pi\)
0.326724 + 0.945120i \(0.394055\pi\)
\(158\) 7.03560 + 9.68367i 0.559722 + 0.770391i
\(159\) 7.72359 23.7708i 0.612520 1.88514i
\(160\) 8.84053 + 1.05509i 0.698906 + 0.0834124i
\(161\) −6.99407 + 5.08149i −0.551210 + 0.400478i
\(162\) 10.5907 14.5768i 0.832084 1.14527i
\(163\) 3.44963 1.12085i 0.270196 0.0877921i −0.170785 0.985308i \(-0.554630\pi\)
0.440982 + 0.897516i \(0.354630\pi\)
\(164\) −5.83919 −0.455964
\(165\) −12.2397 8.04221i −0.952862 0.626085i
\(166\) 5.26430 0.408589
\(167\) −3.63370 + 1.18066i −0.281184 + 0.0913623i −0.446214 0.894926i \(-0.647228\pi\)
0.165030 + 0.986289i \(0.447228\pi\)
\(168\) −5.43819 + 7.48502i −0.419565 + 0.577482i
\(169\) 0.556767 0.404515i 0.0428282 0.0311165i
\(170\) 0.975365 8.17251i 0.0748071 0.626803i
\(171\) 1.47000 4.52421i 0.112414 0.345975i
\(172\) 3.64795 + 5.02098i 0.278154 + 0.382846i
\(173\) 1.23855 1.70472i 0.0941651 0.129607i −0.759335 0.650700i \(-0.774476\pi\)
0.853500 + 0.521093i \(0.174476\pi\)
\(174\) 0.190266 + 0.585579i 0.0144240 + 0.0443926i
\(175\) 4.27171 + 10.3700i 0.322911 + 0.783899i
\(176\) 2.41777 16.1751i 0.182246 1.21925i
\(177\) 0.678711i 0.0510151i
\(178\) −15.6132 + 5.07303i −1.17026 + 0.380240i
\(179\) 4.06448 + 2.95302i 0.303793 + 0.220719i 0.729229 0.684270i \(-0.239879\pi\)
−0.425435 + 0.904989i \(0.639879\pi\)
\(180\) −1.00849 + 1.08884i −0.0751681 + 0.0811574i
\(181\) −4.83538 + 14.8818i −0.359411 + 1.10615i 0.593997 + 0.804467i \(0.297549\pi\)
−0.953408 + 0.301685i \(0.902451\pi\)
\(182\) −13.0590 4.24314i −0.968000 0.314522i
\(183\) 2.01202 + 2.76931i 0.148733 + 0.204713i
\(184\) 6.51265 + 4.73172i 0.480119 + 0.348827i
\(185\) 5.06191 2.82832i 0.372159 0.207943i
\(186\) −2.24430 −0.164560
\(187\) −7.29712 1.09073i −0.533618 0.0797622i
\(188\) 8.86140i 0.646284i
\(189\) 2.87481 + 8.84777i 0.209112 + 0.643580i
\(190\) 8.20632 17.7553i 0.595349 1.28811i
\(191\) −2.52078 + 1.83145i −0.182397 + 0.132519i −0.675237 0.737601i \(-0.735959\pi\)
0.492840 + 0.870120i \(0.335959\pi\)
\(192\) 6.14966 + 1.99815i 0.443814 + 0.144204i
\(193\) −9.16474 2.97780i −0.659692 0.214347i −0.0400095 0.999199i \(-0.512739\pi\)
−0.619683 + 0.784852i \(0.712739\pi\)
\(194\) 3.03606 2.20582i 0.217976 0.158369i
\(195\) 14.8299 + 6.85421i 1.06199 + 0.490841i
\(196\) −0.448734 1.38106i −0.0320524 0.0986472i
\(197\) 14.3974i 1.02577i −0.858457 0.512885i \(-0.828577\pi\)
0.858457 0.512885i \(-0.171423\pi\)
\(198\) 3.52174 + 3.46096i 0.250279 + 0.245960i
\(199\) −14.7978 −1.04899 −0.524493 0.851415i \(-0.675745\pi\)
−0.524493 + 0.851415i \(0.675745\pi\)
\(200\) 7.95443 6.76693i 0.562463 0.478494i
\(201\) 1.03920 + 0.755023i 0.0732995 + 0.0532552i
\(202\) 9.62508 + 13.2478i 0.677218 + 0.932111i
\(203\) −0.401995 0.130616i −0.0282145 0.00916745i
\(204\) −1.00138 + 3.08194i −0.0701109 + 0.215779i
\(205\) −12.0280 + 12.9864i −0.840071 + 0.907007i
\(206\) −13.7086 9.95989i −0.955125 0.693939i
\(207\) −3.29819 + 1.07165i −0.229240 + 0.0744845i
\(208\) 18.2441i 1.26500i
\(209\) −15.6920 7.82420i −1.08544 0.541211i
\(210\) −3.18154 16.0766i −0.219547 1.10939i
\(211\) −2.09250 6.44005i −0.144054 0.443352i 0.852834 0.522181i \(-0.174882\pi\)
−0.996888 + 0.0788298i \(0.974882\pi\)
\(212\) −5.48756 + 7.55299i −0.376888 + 0.518741i
\(213\) 5.39471 + 7.42518i 0.369640 + 0.508765i
\(214\) −5.13687 + 15.8097i −0.351149 + 1.08073i
\(215\) 18.6810 + 2.22952i 1.27403 + 0.152052i
\(216\) 7.00830 5.09183i 0.476854 0.346455i
\(217\) 0.905596 1.24645i 0.0614759 0.0846143i
\(218\) 13.8504 4.50027i 0.938069 0.304797i
\(219\) −17.4935 −1.18210
\(220\) 3.41985 + 4.26976i 0.230566 + 0.287867i
\(221\) 8.23051 0.553644
\(222\) −8.05832 + 2.61831i −0.540839 + 0.175729i
\(223\) 5.12388 7.05242i 0.343121 0.472265i −0.602229 0.798323i \(-0.705721\pi\)
0.945350 + 0.326058i \(0.105721\pi\)
\(224\) 7.22547 5.24961i 0.482772 0.350754i
\(225\) 0.344231 + 4.48575i 0.0229487 + 0.299050i
\(226\) 0.118289 0.364056i 0.00786846 0.0242166i
\(227\) −2.23795 3.08028i −0.148538 0.204445i 0.728264 0.685297i \(-0.240328\pi\)
−0.876802 + 0.480852i \(0.840328\pi\)
\(228\) −4.52668 + 6.23044i −0.299787 + 0.412621i
\(229\) 0.838570 + 2.58085i 0.0554142 + 0.170547i 0.974933 0.222499i \(-0.0714213\pi\)
−0.919519 + 0.393046i \(0.871421\pi\)
\(230\) −13.9881 + 2.76823i −0.922351 + 0.182532i
\(231\) −14.4899 + 2.42443i −0.953364 + 0.159516i
\(232\) 0.393588i 0.0258403i
\(233\) −9.99634 + 3.24801i −0.654882 + 0.212784i −0.617566 0.786519i \(-0.711881\pi\)
−0.0373166 + 0.999303i \(0.511881\pi\)
\(234\) −4.45614 3.23758i −0.291307 0.211647i
\(235\) −19.7078 18.2534i −1.28559 1.19072i
\(236\) −0.0783415 + 0.241110i −0.00509959 + 0.0156949i
\(237\) −13.5869 4.41466i −0.882565 0.286763i
\(238\) −4.85293 6.67948i −0.314569 0.432966i
\(239\) 16.2124 + 11.7790i 1.04869 + 0.761919i 0.971963 0.235133i \(-0.0755524\pi\)
0.0767288 + 0.997052i \(0.475552\pi\)
\(240\) −19.0088 + 10.6211i −1.22702 + 0.685590i
\(241\) 28.4450 1.83230 0.916152 0.400832i \(-0.131279\pi\)
0.916152 + 0.400832i \(0.131279\pi\)
\(242\) 14.5360 10.9526i 0.934408 0.704060i
\(243\) 9.06251i 0.581361i
\(244\) −0.395112 1.21603i −0.0252944 0.0778483i
\(245\) −3.99582 1.84683i −0.255283 0.117989i
\(246\) 20.9254 15.2032i 1.33416 0.969321i
\(247\) 18.6027 + 6.04438i 1.18366 + 0.384595i
\(248\) −1.36443 0.443329i −0.0866411 0.0281514i
\(249\) −5.08313 + 3.69311i −0.322130 + 0.234041i
\(250\) −0.780354 + 18.4823i −0.0493539 + 1.16892i
\(251\) −7.36604 22.6703i −0.464940 1.43094i −0.859058 0.511879i \(-0.828950\pi\)
0.394117 0.919060i \(-0.371050\pi\)
\(252\) 1.48877i 0.0937838i
\(253\) 2.10948 + 12.6075i 0.132622 + 0.792628i
\(254\) 4.02120 0.252313
\(255\) 4.79152 + 8.57550i 0.300057 + 0.537018i
\(256\) −12.6136 9.16432i −0.788350 0.572770i
\(257\) −14.5044 19.9636i −0.904758 1.24529i −0.968925 0.247354i \(-0.920439\pi\)
0.0641671 0.997939i \(-0.479561\pi\)
\(258\) −26.1458 8.49527i −1.62776 0.528892i
\(259\) 1.79744 5.53196i 0.111688 0.343739i
\(260\) −4.47711 4.14670i −0.277659 0.257168i
\(261\) −0.137173 0.0996619i −0.00849079 0.00616892i
\(262\) 2.49961 0.812172i 0.154426 0.0501761i
\(263\) 5.44098i 0.335505i −0.985829 0.167753i \(-0.946349\pi\)
0.985829 0.167753i \(-0.0536510\pi\)
\(264\) 6.31647 + 12.1345i 0.388752 + 0.746827i
\(265\) 5.49416 + 27.7625i 0.337504 + 1.70544i
\(266\) −6.06332 18.6610i −0.371766 1.14418i
\(267\) 11.5169 15.8517i 0.704824 0.970107i
\(268\) −0.282023 0.388171i −0.0172273 0.0237113i
\(269\) 2.07213 6.37738i 0.126340 0.388835i −0.867803 0.496909i \(-0.834468\pi\)
0.994143 + 0.108074i \(0.0344682\pi\)
\(270\) −1.81843 + 15.2365i −0.110666 + 0.927265i
\(271\) 4.09349 2.97409i 0.248662 0.180663i −0.456472 0.889738i \(-0.650887\pi\)
0.705134 + 0.709075i \(0.250887\pi\)
\(272\) −6.44795 + 8.87484i −0.390964 + 0.538116i
\(273\) 15.5863 5.06430i 0.943327 0.306505i
\(274\) 30.9438 1.86938
\(275\) 16.5404 + 1.18943i 0.997424 + 0.0717254i
\(276\) 5.61428 0.337940
\(277\) 10.1703 3.30453i 0.611074 0.198550i 0.0129009 0.999917i \(-0.495893\pi\)
0.598173 + 0.801367i \(0.295893\pi\)
\(278\) 11.3081 15.5642i 0.678214 0.933481i
\(279\) 0.500000 0.363271i 0.0299342 0.0217485i
\(280\) 1.24148 10.4023i 0.0741928 0.621655i
\(281\) −4.23963 + 13.0482i −0.252915 + 0.778392i 0.741319 + 0.671153i \(0.234201\pi\)
−0.994233 + 0.107238i \(0.965799\pi\)
\(282\) 23.0720 + 31.7559i 1.37392 + 1.89103i
\(283\) 12.9132 17.7735i 0.767611 1.05653i −0.228932 0.973442i \(-0.573523\pi\)
0.996543 0.0830832i \(-0.0264767\pi\)
\(284\) −1.05939 3.26047i −0.0628633 0.193473i
\(285\) 4.53213 + 22.9013i 0.268460 + 1.35655i
\(286\) −14.2308 + 14.4807i −0.841485 + 0.856263i
\(287\) 17.7563i 1.04812i
\(288\) 3.40730 1.10710i 0.200777 0.0652365i
\(289\) −9.74956 7.08347i −0.573504 0.416675i
\(290\) −0.511492 0.473744i −0.0300358 0.0278192i
\(291\) −1.38410 + 4.25981i −0.0811372 + 0.249715i
\(292\) 6.21450 + 2.01922i 0.363676 + 0.118166i
\(293\) 8.25135 + 11.3570i 0.482049 + 0.663483i 0.978897 0.204354i \(-0.0655094\pi\)
−0.496848 + 0.867837i \(0.665509\pi\)
\(294\) 5.20389 + 3.78085i 0.303497 + 0.220504i
\(295\) 0.374856 + 0.670888i 0.0218250 + 0.0390606i
\(296\) −5.41627 −0.314815
\(297\) 13.6045 + 2.03352i 0.789412 + 0.117997i
\(298\) 9.78772i 0.566988i
\(299\) −4.40641 13.5615i −0.254829 0.784283i
\(300\) 1.71409 7.07884i 0.0989633 0.408697i
\(301\) 15.2682 11.0930i 0.880043 0.639389i
\(302\) −20.1073 6.53324i −1.15704 0.375946i
\(303\) −18.5876 6.03949i −1.06783 0.346960i
\(304\) −21.0913 + 15.3237i −1.20967 + 0.878877i
\(305\) −3.51833 1.62614i −0.201459 0.0931123i
\(306\) −1.02344 3.14983i −0.0585064 0.180064i
\(307\) 6.86951i 0.392064i −0.980598 0.196032i \(-0.937194\pi\)
0.980598 0.196032i \(-0.0628056\pi\)
\(308\) 5.42733 + 0.811246i 0.309251 + 0.0462251i
\(309\) 20.2241 1.15051
\(310\) 2.21843 1.23954i 0.125998 0.0704011i
\(311\) 4.45087 + 3.23374i 0.252385 + 0.183369i 0.706783 0.707430i \(-0.250146\pi\)
−0.454398 + 0.890799i \(0.650146\pi\)
\(312\) −8.96982 12.3459i −0.507816 0.698949i
\(313\) −13.5354 4.39793i −0.765068 0.248586i −0.0996156 0.995026i \(-0.531761\pi\)
−0.665452 + 0.746440i \(0.731761\pi\)
\(314\) −7.33639 + 22.5791i −0.414016 + 1.27421i
\(315\) 3.31103 + 3.06668i 0.186555 + 0.172788i
\(316\) 4.31714 + 3.13659i 0.242858 + 0.176447i
\(317\) −17.7718 + 5.77442i −0.998166 + 0.324324i −0.762132 0.647421i \(-0.775847\pi\)
−0.236033 + 0.971745i \(0.575847\pi\)
\(318\) 41.3547i 2.31906i
\(319\) −0.438065 + 0.445758i −0.0245269 + 0.0249577i
\(320\) −7.18237 + 1.42138i −0.401506 + 0.0794575i
\(321\) −6.13099 18.8693i −0.342199 1.05318i
\(322\) −8.40774 + 11.5723i −0.468545 + 0.644897i
\(323\) 6.91303 + 9.51497i 0.384651 + 0.529427i
\(324\) 2.48225 7.63957i 0.137903 0.424420i
\(325\) −18.4446 + 1.41541i −1.02312 + 0.0785130i
\(326\) 4.85526 3.52755i 0.268908 0.195373i
\(327\) −10.2166 + 14.0620i −0.564981 + 0.777629i
\(328\) 15.7248 5.10930i 0.868257 0.282114i
\(329\) −26.9464 −1.48560
\(330\) −23.3724 6.39712i −1.28661 0.352150i
\(331\) 0.468249 0.0257373 0.0128686 0.999917i \(-0.495904\pi\)
0.0128686 + 0.999917i \(0.495904\pi\)
\(332\) 2.23205 0.725237i 0.122500 0.0398025i
\(333\) 1.37148 1.88767i 0.0751564 0.103444i
\(334\) −5.11433 + 3.71578i −0.279844 + 0.203318i
\(335\) −1.44423 0.172364i −0.0789065 0.00941726i
\(336\) −6.74988 + 20.7740i −0.368236 + 1.13331i
\(337\) −20.0360 27.5771i −1.09143 1.50222i −0.846282 0.532735i \(-0.821164\pi\)
−0.245146 0.969486i \(-0.578836\pi\)
\(338\) 0.669303 0.921216i 0.0364053 0.0501075i
\(339\) 0.141181 + 0.434511i 0.00766790 + 0.0235994i
\(340\) −0.712333 3.59949i −0.0386317 0.195210i
\(341\) −1.05185 2.02070i −0.0569611 0.109427i
\(342\) 7.87090i 0.425610i
\(343\) −19.1327 + 6.21658i −1.03307 + 0.335664i
\(344\) −14.2172 10.3294i −0.766542 0.556925i
\(345\) 11.5647 12.4862i 0.622623 0.672233i
\(346\) 1.07737 3.31580i 0.0579198 0.178259i
\(347\) 3.41707 + 1.11027i 0.183438 + 0.0596026i 0.399296 0.916822i \(-0.369255\pi\)
−0.215858 + 0.976425i \(0.569255\pi\)
\(348\) 0.161345 + 0.222072i 0.00864898 + 0.0119043i
\(349\) −5.15433 3.74484i −0.275905 0.200457i 0.441224 0.897397i \(-0.354544\pi\)
−0.717129 + 0.696940i \(0.754544\pi\)
\(350\) 12.0241 + 14.1341i 0.642714 + 0.755502i
\(351\) −15.3446 −0.819037
\(352\) −2.17927 13.0246i −0.116156 0.694215i
\(353\) 12.1971i 0.649186i 0.945854 + 0.324593i \(0.105227\pi\)
−0.945854 + 0.324593i \(0.894773\pi\)
\(354\) −0.347021 1.06802i −0.0184440 0.0567647i
\(355\) −9.43350 4.36007i −0.500678 0.231408i
\(356\) −5.92106 + 4.30190i −0.313815 + 0.228000i
\(357\) 9.37181 + 3.04509i 0.496009 + 0.161163i
\(358\) 7.90573 + 2.56873i 0.417831 + 0.135761i
\(359\) 19.5093 14.1744i 1.02966 0.748094i 0.0614222 0.998112i \(-0.480436\pi\)
0.968241 + 0.250018i \(0.0804364\pi\)
\(360\) 1.76309 3.81465i 0.0929232 0.201050i
\(361\) 2.76592 + 8.51262i 0.145575 + 0.448032i
\(362\) 25.8902i 1.36076i
\(363\) −6.35204 + 20.7732i −0.333396 + 1.09031i
\(364\) −6.12155 −0.320856
\(365\) 17.2918 9.66174i 0.905096 0.505719i
\(366\) 4.58205 + 3.32905i 0.239507 + 0.174012i
\(367\) 11.9849 + 16.4958i 0.625606 + 0.861073i 0.997746 0.0671034i \(-0.0213757\pi\)
−0.372140 + 0.928177i \(0.621376\pi\)
\(368\) 18.0753 + 5.87302i 0.942239 + 0.306152i
\(369\) −2.20105 + 6.77414i −0.114582 + 0.352648i
\(370\) 6.51933 7.03878i 0.338924 0.365929i
\(371\) 22.9677 + 16.6870i 1.19242 + 0.866347i
\(372\) −0.951577 + 0.309186i −0.0493370 + 0.0160305i
\(373\) 7.51997i 0.389369i −0.980866 0.194685i \(-0.937632\pi\)
0.980866 0.194685i \(-0.0623684\pi\)
\(374\) −12.0404 + 2.01460i −0.622596 + 0.104172i
\(375\) −12.2125 18.3937i −0.630653 0.949845i
\(376\) 7.75374 + 23.8636i 0.399869 + 1.23067i
\(377\) 0.409791 0.564029i 0.0211053 0.0290490i
\(378\) 9.04762 + 12.4530i 0.465359 + 0.640512i
\(379\) −7.16649 + 22.0562i −0.368118 + 1.13295i 0.579888 + 0.814696i \(0.303096\pi\)
−0.948006 + 0.318254i \(0.896904\pi\)
\(380\) 1.03340 8.65874i 0.0530121 0.444184i
\(381\) −3.88281 + 2.82103i −0.198922 + 0.144526i
\(382\) −3.03029 + 4.17083i −0.155043 + 0.213398i
\(383\) 2.32095 0.754123i 0.118595 0.0385339i −0.249118 0.968473i \(-0.580141\pi\)
0.367713 + 0.929939i \(0.380141\pi\)
\(384\) 26.4246 1.34848
\(385\) 12.9838 10.3993i 0.661717 0.529999i
\(386\) −15.9442 −0.811537
\(387\) 7.20000 2.33942i 0.365997 0.118919i
\(388\) 0.983393 1.35352i 0.0499242 0.0687148i
\(389\) 27.4849 19.9689i 1.39354 1.01246i 0.398071 0.917355i \(-0.369680\pi\)
0.995467 0.0951096i \(-0.0303201\pi\)
\(390\) 26.8408 + 3.20337i 1.35914 + 0.162209i
\(391\) 2.64950 8.15434i 0.133991 0.412383i
\(392\) 2.41686 + 3.32653i 0.122070 + 0.168015i
\(393\) −1.84381 + 2.53779i −0.0930080 + 0.128015i
\(394\) −7.36129 22.6557i −0.370856 1.14138i
\(395\) 15.8685 3.14036i 0.798433 0.158009i
\(396\) 1.97000 + 0.982264i 0.0989964 + 0.0493606i
\(397\) 27.4961i 1.37999i −0.723814 0.689995i \(-0.757613\pi\)
0.723814 0.689995i \(-0.242387\pi\)
\(398\) −23.2858 + 7.56601i −1.16721 + 0.379250i
\(399\) 18.9460 + 13.7651i 0.948487 + 0.689116i
\(400\) 12.9236 20.9974i 0.646182 1.04987i
\(401\) −0.583247 + 1.79505i −0.0291259 + 0.0896404i −0.964563 0.263853i \(-0.915006\pi\)
0.935437 + 0.353494i \(0.115006\pi\)
\(402\) 2.02132 + 0.656768i 0.100815 + 0.0327566i
\(403\) 1.49370 + 2.05591i 0.0744067 + 0.102412i
\(404\) 5.90608 + 4.29102i 0.293839 + 0.213486i
\(405\) −11.8773 21.2571i −0.590188 1.05627i
\(406\) −0.699363 −0.0347088
\(407\) −6.13420 6.02834i −0.304061 0.298814i
\(408\) 9.17582i 0.454271i
\(409\) −4.18949 12.8939i −0.207157 0.637563i −0.999618 0.0276408i \(-0.991201\pi\)
0.792461 0.609923i \(-0.208799\pi\)
\(410\) −12.2874 + 26.5852i −0.606831 + 1.31295i
\(411\) −29.8788 + 21.7082i −1.47381 + 1.07079i
\(412\) −7.18454 2.33440i −0.353957 0.115008i
\(413\) 0.733187 + 0.238227i 0.0360778 + 0.0117224i
\(414\) −4.64210 + 3.37269i −0.228147 + 0.165758i
\(415\) 2.98481 6.45798i 0.146519 0.317010i
\(416\) 4.55219 + 14.0102i 0.223189 + 0.686906i
\(417\) 22.9616i 1.12444i
\(418\) −28.6934 4.28893i −1.40344 0.209779i
\(419\) 22.1368 1.08145 0.540727 0.841198i \(-0.318149\pi\)
0.540727 + 0.841198i \(0.318149\pi\)
\(420\) −3.56376 6.37814i −0.173894 0.311221i
\(421\) −14.4835 10.5229i −0.705881 0.512853i 0.175961 0.984397i \(-0.443697\pi\)
−0.881842 + 0.471544i \(0.843697\pi\)
\(422\) −6.58552 9.06419i −0.320578 0.441238i
\(423\) −10.2803 3.34026i −0.499843 0.162409i
\(424\) 8.16902 25.1417i 0.396723 1.22099i
\(425\) −9.47259 5.83026i −0.459488 0.282809i
\(426\) 12.2856 + 8.92599i 0.595238 + 0.432466i
\(427\) −3.69780 + 1.20149i −0.178949 + 0.0581440i
\(428\) 7.41093i 0.358221i
\(429\) 3.58227 23.9658i 0.172954 1.15708i
\(430\) 30.5364 6.04310i 1.47259 0.291424i
\(431\) 10.3353 + 31.8087i 0.497833 + 1.53217i 0.812495 + 0.582968i \(0.198109\pi\)
−0.314662 + 0.949204i \(0.601891\pi\)
\(432\) 12.0213 16.5459i 0.578376 0.796066i
\(433\) 18.5102 + 25.4771i 0.889543 + 1.22435i 0.973685 + 0.227897i \(0.0731848\pi\)
−0.0841428 + 0.996454i \(0.526815\pi\)
\(434\) 0.787747 2.42443i 0.0378130 0.116377i
\(435\) 0.826238 + 0.0986091i 0.0396151 + 0.00472794i
\(436\) 5.25255 3.81620i 0.251552 0.182763i
\(437\) 11.9769 16.4848i 0.572932 0.788574i
\(438\) −27.5277 + 8.94431i −1.31533 + 0.427375i
\(439\) −35.6208 −1.70009 −0.850045 0.526710i \(-0.823425\pi\)
−0.850045 + 0.526710i \(0.823425\pi\)
\(440\) −12.9456 8.50601i −0.617158 0.405508i
\(441\) −1.77134 −0.0843495
\(442\) 12.9515 4.20821i 0.616041 0.200164i
\(443\) −13.8056 + 19.0018i −0.655926 + 0.902805i −0.999338 0.0363802i \(-0.988417\pi\)
0.343412 + 0.939185i \(0.388417\pi\)
\(444\) −3.05599 + 2.22031i −0.145031 + 0.105371i
\(445\) −2.62920 + 22.0298i −0.124636 + 1.04431i
\(446\) 4.45709 13.7175i 0.211049 0.649543i
\(447\) −6.86646 9.45086i −0.324772 0.447011i
\(448\) −4.31705 + 5.94191i −0.203961 + 0.280729i
\(449\) 9.70066 + 29.8555i 0.457802 + 1.40897i 0.867814 + 0.496890i \(0.165525\pi\)
−0.410011 + 0.912080i \(0.634475\pi\)
\(450\) 2.83522 + 6.88277i 0.133653 + 0.324457i
\(451\) 23.4958 + 11.7152i 1.10637 + 0.551649i
\(452\) 0.170655i 0.00802692i
\(453\) 23.9985 7.79760i 1.12755 0.366363i
\(454\) −5.09658 3.70288i −0.239194 0.173785i
\(455\) −12.6096 + 13.6143i −0.591148 + 0.638250i
\(456\) 6.73861 20.7393i 0.315564 0.971207i
\(457\) 37.1964 + 12.0859i 1.73998 + 0.565352i 0.994830 0.101550i \(-0.0323803\pi\)
0.745145 + 0.666903i \(0.232380\pi\)
\(458\) 2.63915 + 3.63247i 0.123319 + 0.169734i
\(459\) −7.46440 5.42320i −0.348408 0.253133i
\(460\) −5.54957 + 3.10080i −0.258750 + 0.144575i
\(461\) −8.88399 −0.413769 −0.206884 0.978365i \(-0.566332\pi\)
−0.206884 + 0.978365i \(0.566332\pi\)
\(462\) −21.5617 + 11.2237i −1.00314 + 0.522173i
\(463\) 4.21081i 0.195693i −0.995202 0.0978464i \(-0.968805\pi\)
0.995202 0.0978464i \(-0.0311954\pi\)
\(464\) 0.287146 + 0.883744i 0.0133304 + 0.0410268i
\(465\) −1.27250 + 2.75319i −0.0590107 + 0.127676i
\(466\) −14.0696 + 10.2221i −0.651760 + 0.473531i
\(467\) −6.39912 2.07920i −0.296116 0.0962139i 0.157191 0.987568i \(-0.449756\pi\)
−0.453307 + 0.891354i \(0.649756\pi\)
\(468\) −2.33542 0.758822i −0.107955 0.0350766i
\(469\) −1.18038 + 0.857597i −0.0545049 + 0.0396002i
\(470\) −40.3450 18.6470i −1.86098 0.860124i
\(471\) −8.75618 26.9487i −0.403463 1.24173i
\(472\) 0.717854i 0.0330419i
\(473\) −4.60503 27.5224i −0.211740 1.26548i
\(474\) −23.6376 −1.08571
\(475\) −17.1284 20.1342i −0.785905 0.923820i
\(476\) −2.97782 2.16352i −0.136488 0.0991646i
\(477\) 6.69383 + 9.21327i 0.306490 + 0.421847i
\(478\) 31.5343 + 10.2461i 1.44235 + 0.468647i
\(479\) −6.43046 + 19.7909i −0.293815 + 0.904270i 0.689802 + 0.723998i \(0.257698\pi\)
−0.983617 + 0.180272i \(0.942302\pi\)
\(480\) −11.9473 + 12.8993i −0.545318 + 0.588768i
\(481\) 7.76176 + 5.63925i 0.353906 + 0.257128i
\(482\) 44.7611 14.5437i 2.03881 0.662450i
\(483\) 17.0723i 0.776818i
\(484\) 4.65433 6.64642i 0.211560 0.302110i
\(485\) −0.984576 4.97516i −0.0447073 0.225910i
\(486\) 4.63361 + 14.2608i 0.210185 + 0.646882i
\(487\) −9.27489 + 12.7658i −0.420285 + 0.578473i −0.965689 0.259700i \(-0.916376\pi\)
0.545404 + 0.838173i \(0.316376\pi\)
\(488\) 2.12806 + 2.92902i 0.0963326 + 0.132590i
\(489\) −2.21345 + 6.81230i −0.100096 + 0.308063i
\(490\) −7.23209 0.863129i −0.326713 0.0389922i
\(491\) −15.6386 + 11.3621i −0.705759 + 0.512764i −0.881803 0.471618i \(-0.843670\pi\)
0.176044 + 0.984382i \(0.443670\pi\)
\(492\) 6.77784 9.32890i 0.305569 0.420579i
\(493\) 0.398685 0.129541i 0.0179559 0.00583422i
\(494\) 32.3637 1.45611
\(495\) 6.24252 2.35795i 0.280580 0.105982i
\(496\) −3.38705 −0.152083
\(497\) −9.91469 + 3.22148i −0.444734 + 0.144503i
\(498\) −6.11055 + 8.41045i −0.273820 + 0.376881i
\(499\) −33.5416 + 24.3694i −1.50153 + 1.09092i −0.531758 + 0.846896i \(0.678468\pi\)
−0.969769 + 0.244026i \(0.921532\pi\)
\(500\) 2.21535 + 7.94395i 0.0990734 + 0.355264i
\(501\) 2.33156 7.17579i 0.104166 0.320591i
\(502\) −23.1824 31.9078i −1.03468 1.42412i
\(503\) 19.1978 26.4236i 0.855990 1.17817i −0.126521 0.991964i \(-0.540381\pi\)
0.982511 0.186205i \(-0.0596188\pi\)
\(504\) −1.30268 4.00923i −0.0580259 0.178585i
\(505\) 21.7090 4.29618i 0.966039 0.191178i
\(506\) 9.76563 + 18.7606i 0.434135 + 0.834012i
\(507\) 1.35905i 0.0603576i
\(508\) 1.70498 0.553981i 0.0756462 0.0245789i
\(509\) 13.4662 + 9.78379i 0.596881 + 0.433659i 0.844770 0.535129i \(-0.179737\pi\)
−0.247890 + 0.968788i \(0.579737\pi\)
\(510\) 11.9245 + 11.0445i 0.528028 + 0.489060i
\(511\) 6.14019 18.8975i 0.271626 0.835978i
\(512\) 0.917749 + 0.298195i 0.0405592 + 0.0131785i
\(513\) −12.8884 17.7393i −0.569036 0.783211i
\(514\) −33.0313 23.9987i −1.45695 1.05854i
\(515\) −19.9909 + 11.1699i −0.880906 + 0.492203i
\(516\) −12.2561 −0.539543
\(517\) −17.7788 + 35.6566i −0.781909 + 1.56818i
\(518\) 9.62412i 0.422860i
\(519\) 1.28587 + 3.95750i 0.0564434 + 0.173715i
\(520\) 15.6851 + 7.24951i 0.687839 + 0.317912i
\(521\) −11.3717 + 8.26206i −0.498205 + 0.361967i −0.808331 0.588728i \(-0.799629\pi\)
0.310126 + 0.950696i \(0.399629\pi\)
\(522\) −0.266812 0.0866924i −0.0116780 0.00379442i
\(523\) 14.9009 + 4.84159i 0.651570 + 0.211708i 0.616106 0.787663i \(-0.288709\pi\)
0.0354635 + 0.999371i \(0.488709\pi\)
\(524\) 0.947937 0.688717i 0.0414108 0.0300867i
\(525\) −21.5259 5.21235i −0.939467 0.227486i
\(526\) −2.78194 8.56194i −0.121298 0.373318i
\(527\) 1.52801i 0.0665611i
\(528\) 23.0356 + 22.6380i 1.00249 + 0.985193i
\(529\) 8.14550 0.354152
\(530\) 22.8404 + 40.8780i 0.992125 + 1.77563i
\(531\) 0.250186 + 0.181770i 0.0108571 + 0.00788817i
\(532\) −5.14166 7.07689i −0.222919 0.306822i
\(533\) −27.8540 9.05031i −1.20649 0.392012i
\(534\) 10.0182 30.8327i 0.433528 1.33426i
\(535\) 16.4819 + 15.2656i 0.712575 + 0.659988i
\(536\) 1.09913 + 0.798567i 0.0474753 + 0.0344928i
\(537\) −9.43570 + 3.06584i −0.407180 + 0.132301i
\(538\) 11.0949i 0.478336i
\(539\) −0.965221 + 6.45743i −0.0415750 + 0.278141i
\(540\) 1.32805 + 6.71075i 0.0571501 + 0.288785i
\(541\) −12.2489 37.6983i −0.526623 1.62078i −0.761084 0.648653i \(-0.775333\pi\)
0.234461 0.972125i \(-0.424667\pi\)
\(542\) 4.92088 6.77301i 0.211370 0.290926i
\(543\) −18.1630 24.9992i −0.779448 1.07282i
\(544\) −2.73716 + 8.42412i −0.117355 + 0.361181i
\(545\) 2.33235 19.5426i 0.0999070 0.837113i
\(546\) 21.9373 15.9384i 0.938830 0.682100i
\(547\) −24.1970 + 33.3043i −1.03459 + 1.42399i −0.133145 + 0.991097i \(0.542508\pi\)
−0.901445 + 0.432895i \(0.857492\pi\)
\(548\) 13.1201 4.26297i 0.560462 0.182105i
\(549\) −1.55967 −0.0665651
\(550\) 26.6362 6.58532i 1.13577 0.280799i
\(551\) 0.996247 0.0424415
\(552\) −15.1191 + 4.91251i −0.643513 + 0.209090i
\(553\) 9.53798 13.1279i 0.405596 0.558255i
\(554\) 14.3144 10.4000i 0.608161 0.441855i
\(555\) −1.35699 + 11.3701i −0.0576009 + 0.482633i
\(556\) 2.65039 8.15705i 0.112401 0.345936i
\(557\) 17.5606 + 24.1702i 0.744069 + 1.02412i 0.998374 + 0.0569987i \(0.0181531\pi\)
−0.254306 + 0.967124i \(0.581847\pi\)
\(558\) 0.601062 0.827291i 0.0254450 0.0350220i
\(559\) 9.61926 + 29.6050i 0.406851 + 1.25216i
\(560\) −4.80152 24.2625i −0.202901 1.02528i
\(561\) 10.2127 10.3921i 0.431182 0.438754i
\(562\) 22.7004i 0.957558i
\(563\) −2.05218 + 0.666795i −0.0864892 + 0.0281021i −0.351942 0.936022i \(-0.614479\pi\)
0.265453 + 0.964124i \(0.414479\pi\)
\(564\) 14.1573 + 10.2859i 0.596130 + 0.433114i
\(565\) −0.379536 0.351527i −0.0159672 0.0147889i
\(566\) 11.2328 34.5709i 0.472148 1.45312i
\(567\) −23.2310 7.54820i −0.975610 0.316995i
\(568\) 5.70583 + 7.85341i 0.239411 + 0.329522i
\(569\) 0.580298 + 0.421611i 0.0243274 + 0.0176749i 0.599882 0.800088i \(-0.295214\pi\)
−0.575555 + 0.817763i \(0.695214\pi\)
\(570\) 18.8410 + 33.7202i 0.789164 + 1.41238i
\(571\) −21.6311 −0.905235 −0.452617 0.891705i \(-0.649510\pi\)
−0.452617 + 0.891705i \(0.649510\pi\)
\(572\) −4.03888 + 8.10029i −0.168874 + 0.338690i
\(573\) 6.15315i 0.257051i
\(574\) 9.07866 + 27.9413i 0.378936 + 1.16625i
\(575\) −4.53522 + 18.7295i −0.189132 + 0.781074i
\(576\) −2.38354 + 1.73174i −0.0993141 + 0.0721559i
\(577\) −22.2810 7.23952i −0.927568 0.301385i −0.194000 0.981001i \(-0.562146\pi\)
−0.733568 + 0.679616i \(0.762146\pi\)
\(578\) −18.9637 6.16167i −0.788784 0.256291i
\(579\) 15.3954 11.1854i 0.639812 0.464851i
\(580\) −0.282136 0.130401i −0.0117151 0.00541459i
\(581\) −2.20536 6.78739i −0.0914936 0.281588i
\(582\) 7.41093i 0.307193i
\(583\) 37.2346 19.3820i 1.54210 0.802722i
\(584\) −18.5023 −0.765633
\(585\) −6.49828 + 3.63089i −0.268671 + 0.150119i
\(586\) 18.7911 + 13.6525i 0.776253 + 0.563981i
\(587\) −1.32095 1.81814i −0.0545216 0.0750425i 0.780886 0.624674i \(-0.214768\pi\)
−0.835407 + 0.549632i \(0.814768\pi\)
\(588\) 2.72730 + 0.886154i 0.112472 + 0.0365444i
\(589\) −1.12215 + 3.45362i −0.0462374 + 0.142304i
\(590\) 0.932895 + 0.864048i 0.0384067 + 0.0355723i
\(591\) 23.0018 + 16.7118i 0.946167 + 0.687431i
\(592\) −12.1615 + 3.95149i −0.499833 + 0.162405i
\(593\) 25.4034i 1.04319i 0.853193 + 0.521596i \(0.174663\pi\)
−0.853193 + 0.521596i \(0.825337\pi\)
\(594\) 22.4477 3.75594i 0.921042 0.154108i
\(595\) −10.9456 + 2.16612i −0.448726 + 0.0888022i
\(596\) 1.34841 + 4.14996i 0.0552328 + 0.169989i
\(597\) 17.1765 23.6415i 0.702988 0.967580i
\(598\) −13.8678 19.0875i −0.567098 0.780544i
\(599\) 5.63194 17.3333i 0.230115 0.708220i −0.767617 0.640909i \(-0.778558\pi\)
0.997732 0.0673118i \(-0.0214422\pi\)
\(600\) 1.57798 + 20.5630i 0.0644208 + 0.839482i
\(601\) 28.0242 20.3608i 1.14313 0.830533i 0.155579 0.987824i \(-0.450276\pi\)
0.987552 + 0.157290i \(0.0502758\pi\)
\(602\) 18.3542 25.2625i 0.748063 1.02962i
\(603\) −0.556631 + 0.180860i −0.0226678 + 0.00736520i
\(604\) −9.42547 −0.383517
\(605\) −5.19433 24.0420i −0.211180 0.977447i
\(606\) −32.3375 −1.31362
\(607\) 24.2027 7.86394i 0.982358 0.319187i 0.226564 0.973996i \(-0.427251\pi\)
0.755794 + 0.654809i \(0.227251\pi\)
\(608\) −12.3731 + 17.0302i −0.501797 + 0.690664i
\(609\) 0.675293 0.490629i 0.0273643 0.0198813i
\(610\) −6.36788 0.759989i −0.257828 0.0307710i
\(611\) 13.7345 42.2705i 0.555639 1.71008i
\(612\) −0.867874 1.19453i −0.0350817 0.0482858i
\(613\) −21.7843 + 29.9835i −0.879859 + 1.21102i 0.0966016 + 0.995323i \(0.469203\pi\)
−0.976460 + 0.215698i \(0.930797\pi\)
\(614\) −3.51234 10.8099i −0.141746 0.436251i
\(615\) −6.78600 34.2903i −0.273638 1.38272i
\(616\) −15.3255 + 2.56426i −0.617483 + 0.103317i
\(617\) 27.5937i 1.11088i 0.831557 + 0.555439i \(0.187450\pi\)
−0.831557 + 0.555439i \(0.812550\pi\)
\(618\) 31.8246 10.3404i 1.28017 0.415953i
\(619\) 16.5391 + 12.0164i 0.664764 + 0.482979i 0.868268 0.496095i \(-0.165233\pi\)
−0.203504 + 0.979074i \(0.565233\pi\)
\(620\) 0.769843 0.831183i 0.0309176 0.0333811i
\(621\) −4.93964 + 15.2026i −0.198221 + 0.610061i
\(622\) 8.65728 + 2.81292i 0.347125 + 0.112788i
\(623\) 13.0816 + 18.0052i 0.524101 + 0.721364i
\(624\) −29.1475 21.1769i −1.16683 0.847754i
\(625\) 22.2307 + 11.4366i 0.889228 + 0.457464i
\(626\) −23.5480 −0.941167
\(627\) 30.7148 15.9882i 1.22663 0.638507i
\(628\) 10.5842i 0.422354i
\(629\) 1.78265 + 5.48642i 0.0710787 + 0.218758i
\(630\) 6.77822 + 3.13282i 0.270051 + 0.124815i
\(631\) −0.614155 + 0.446210i −0.0244491 + 0.0177633i −0.599943 0.800043i \(-0.704810\pi\)
0.575494 + 0.817806i \(0.304810\pi\)
\(632\) −14.3705 4.66926i −0.571627 0.185733i
\(633\) 12.7177 + 4.13224i 0.505485 + 0.164242i
\(634\) −25.0133 + 18.1733i −0.993407 + 0.721752i
\(635\) 2.27998 4.93301i 0.0904784 0.195760i
\(636\) −5.69723 17.5343i −0.225910 0.695279i
\(637\) 7.28342i 0.288579i
\(638\) −0.461426 + 0.925425i −0.0182680 + 0.0366379i
\(639\) −4.18186 −0.165432
\(640\) −26.1201 + 14.5945i −1.03249 + 0.576897i
\(641\) 12.0584 + 8.76094i 0.476278 + 0.346037i 0.799883 0.600156i \(-0.204895\pi\)
−0.323605 + 0.946192i \(0.604895\pi\)
\(642\) −19.2955 26.5579i −0.761531 1.04816i
\(643\) 26.2820 + 8.53955i 1.03646 + 0.336767i 0.777342 0.629078i \(-0.216568\pi\)
0.259120 + 0.965845i \(0.416568\pi\)
\(644\) −1.97060 + 6.06490i −0.0776527 + 0.238990i
\(645\) −25.2460 + 27.2575i −0.994059 + 1.07326i
\(646\) 15.7433 + 11.4382i 0.619411 + 0.450029i
\(647\) 23.7560 7.71879i 0.933945 0.303457i 0.197770 0.980248i \(-0.436630\pi\)
0.736175 + 0.676791i \(0.236630\pi\)
\(648\) 22.7452i 0.893514i
\(649\) 0.798974 0.813005i 0.0313625 0.0319132i
\(650\) −28.3007 + 11.6579i −1.11004 + 0.457260i
\(651\) 0.940197 + 2.89363i 0.0368492 + 0.113410i
\(652\) 1.57264 2.16456i 0.0615895 0.0847706i
\(653\) −16.3187 22.4607i −0.638599 0.878956i 0.359941 0.932975i \(-0.382797\pi\)
−0.998540 + 0.0540191i \(0.982797\pi\)
\(654\) −8.88708 + 27.3516i −0.347513 + 1.06953i
\(655\) 0.420923 3.52688i 0.0164468 0.137807i
\(656\) 31.5802 22.9444i 1.23300 0.895827i
\(657\) 4.68505 6.44842i 0.182781 0.251577i
\(658\) −42.4029 + 13.7775i −1.65304 + 0.537105i
\(659\) 21.5863 0.840883 0.420442 0.907320i \(-0.361875\pi\)
0.420442 + 0.907320i \(0.361875\pi\)
\(660\) −10.7911 + 0.507537i −0.420044 + 0.0197559i
\(661\) −16.0174 −0.623003 −0.311502 0.950246i \(-0.600832\pi\)
−0.311502 + 0.950246i \(0.600832\pi\)
\(662\) 0.736837 0.239413i 0.0286380 0.00930504i
\(663\) −9.55357 + 13.1494i −0.371030 + 0.510679i
\(664\) −5.37628 + 3.90609i −0.208640 + 0.151586i
\(665\) −26.3302 3.14243i −1.02104 0.121858i
\(666\) 1.19300 3.67167i 0.0462277 0.142274i
\(667\) −0.426892 0.587567i −0.0165293 0.0227507i
\(668\) −1.65656 + 2.28005i −0.0640941 + 0.0882180i
\(669\) 5.31966 + 16.3722i 0.205670 + 0.632986i
\(670\) −2.36076 + 0.467191i −0.0912042 + 0.0180492i
\(671\) −0.849880 + 5.68579i −0.0328093 + 0.219498i
\(672\) 17.6372i 0.680368i
\(673\) −29.8127 + 9.68673i −1.14920 + 0.373396i −0.820840 0.571158i \(-0.806494\pi\)
−0.328355 + 0.944554i \(0.606494\pi\)
\(674\) −45.6286 33.1511i −1.75755 1.27693i
\(675\) 17.6603 + 10.8697i 0.679747 + 0.418376i
\(676\) 0.156871 0.482799i 0.00603350 0.0185692i
\(677\) 29.1654 + 9.47642i 1.12092 + 0.364209i 0.810118 0.586267i \(-0.199403\pi\)
0.310801 + 0.950475i \(0.399403\pi\)
\(678\) 0.444325 + 0.611561i 0.0170642 + 0.0234869i
\(679\) −4.11590 2.99038i −0.157954 0.114760i
\(680\) 5.06786 + 9.07006i 0.194344 + 0.347821i
\(681\) 7.51888 0.288124
\(682\) −2.68837 2.64198i −0.102943 0.101166i
\(683\) 3.27236i 0.125213i −0.998038 0.0626066i \(-0.980059\pi\)
0.998038 0.0626066i \(-0.0199414\pi\)
\(684\) −1.08433 3.33724i −0.0414606 0.127602i
\(685\) 17.5448 37.9603i 0.670354 1.45039i
\(686\) −26.9287 + 19.5648i −1.02814 + 0.746989i
\(687\) −5.09664 1.65600i −0.194449 0.0631802i
\(688\) −39.4586 12.8209i −1.50435 0.488792i
\(689\) −37.8832 + 27.5238i −1.44324 + 1.04857i
\(690\) 11.8141 25.5612i 0.449756 0.973099i
\(691\) −11.2774 34.7084i −0.429014 1.32037i −0.899098 0.437748i \(-0.855776\pi\)
0.470083 0.882622i \(-0.344224\pi\)
\(692\) 1.55431i 0.0590862i
\(693\) 2.98694 5.99054i 0.113465 0.227562i
\(694\) 5.94478 0.225661
\(695\) −12.6818 22.6970i −0.481049 0.860944i
\(696\) −0.628811 0.456858i −0.0238350 0.0173172i
\(697\) −10.3509 14.2468i −0.392070 0.539638i
\(698\) −10.0256 3.25750i −0.379473 0.123298i
\(699\) 6.41413 19.7407i 0.242605 0.746660i
\(700\) 7.04537 + 4.33634i 0.266290 + 0.163898i
\(701\) −37.6684 27.3677i −1.42272 1.03366i −0.991316 0.131502i \(-0.958020\pi\)
−0.431399 0.902161i \(-0.641980\pi\)
\(702\) −24.1463 + 7.84562i −0.911345 + 0.296114i
\(703\) 13.7096i 0.517068i
\(704\) 5.01427 + 9.63285i 0.188982 + 0.363052i
\(705\) 52.0381 10.2983i 1.95987 0.387855i
\(706\) 6.23630 + 19.1933i 0.234706 + 0.722351i
\(707\) 13.0485 17.9597i 0.490738 0.675443i
\(708\) −0.294272 0.405030i −0.0110594 0.0152220i
\(709\) 11.0000 33.8544i 0.413112 1.27143i −0.500817 0.865553i \(-0.666967\pi\)
0.913929 0.405874i \(-0.133033\pi\)
\(710\) −17.0738 2.03771i −0.640770 0.0764740i
\(711\) 5.26613 3.82607i 0.197495 0.143489i
\(712\) 12.1811 16.7659i 0.456507 0.628327i
\(713\) 2.51772 0.818057i 0.0942894 0.0306365i
\(714\) 16.3044 0.610178
\(715\) 9.69546 + 25.6681i 0.362590 + 0.959931i
\(716\) 3.70588 0.138495
\(717\) −37.6371 + 12.2290i −1.40558 + 0.456702i
\(718\) 23.4526 32.2798i 0.875245 1.20467i
\(719\) 17.8722 12.9849i 0.666522 0.484256i −0.202337 0.979316i \(-0.564854\pi\)
0.868859 + 0.495060i \(0.164854\pi\)
\(720\) 1.17575 9.85153i 0.0438177 0.367145i
\(721\) −7.09862 + 21.8473i −0.264366 + 0.813636i
\(722\) 8.70490 + 11.9813i 0.323963 + 0.445896i
\(723\) −33.0176 + 45.4448i −1.22794 + 1.69011i
\(724\) 3.56677 + 10.9774i 0.132558 + 0.407971i
\(725\) −0.871176 + 0.358863i −0.0323547 + 0.0133278i
\(726\) 0.625636 + 35.9365i 0.0232195 + 1.33373i
\(727\) 45.5415i 1.68904i −0.535522 0.844521i \(-0.679885\pi\)
0.535522 0.844521i \(-0.320115\pi\)
\(728\) 16.4852 5.35637i 0.610982 0.198520i
\(729\) 11.9514 + 8.68317i 0.442643 + 0.321599i
\(730\) 22.2704 24.0449i 0.824266 0.889943i
\(731\) −5.78391 + 17.8011i −0.213926 + 0.658396i
\(732\) 2.40140 + 0.780262i 0.0887583 + 0.0288393i
\(733\) −6.68835 9.20572i −0.247040 0.340021i 0.667432 0.744671i \(-0.267393\pi\)
−0.914472 + 0.404650i \(0.867393\pi\)
\(734\) 27.2936 + 19.8300i 1.00743 + 0.731938i
\(735\) 7.58871 4.24016i 0.279914 0.156401i
\(736\) 15.3459 0.565659
\(737\) 0.356014 + 2.12776i 0.0131140 + 0.0783769i
\(738\) 11.7852i 0.433818i
\(739\) 1.34045 + 4.12547i 0.0493091 + 0.151758i 0.972679 0.232153i \(-0.0745770\pi\)
−0.923370 + 0.383911i \(0.874577\pi\)
\(740\) 1.79448 3.88256i 0.0659663 0.142726i
\(741\) −31.2498 + 22.7043i −1.14799 + 0.834064i
\(742\) 44.6740 + 14.5154i 1.64003 + 0.532879i
\(743\) 16.4480 + 5.34429i 0.603420 + 0.196063i 0.594765 0.803900i \(-0.297245\pi\)
0.00865478 + 0.999963i \(0.497245\pi\)
\(744\) 2.29204 1.66526i 0.0840302 0.0610515i
\(745\) 12.0071 + 5.54955i 0.439905 + 0.203320i
\(746\) −3.84491 11.8334i −0.140772 0.433253i
\(747\) 2.86281i 0.104745i
\(748\) −4.82757 + 2.51293i −0.176513 + 0.0918819i
\(749\) 22.5357 0.823437
\(750\) −28.6222 22.7001i −1.04514 0.828890i
\(751\) 25.4946 + 18.5229i 0.930310 + 0.675910i 0.946069 0.323966i \(-0.105016\pi\)
−0.0157586 + 0.999876i \(0.505016\pi\)
\(752\) 34.8198 + 47.9253i 1.26975 + 1.74766i
\(753\) 44.7691 + 14.5464i 1.63148 + 0.530099i
\(754\) 0.356463 1.09708i 0.0129816 0.0399533i
\(755\) −19.4153 + 20.9623i −0.706594 + 0.762895i
\(756\) 5.55175 + 4.03358i 0.201915 + 0.146700i
\(757\) 8.82332 2.86687i 0.320689 0.104198i −0.144249 0.989541i \(-0.546077\pi\)
0.464938 + 0.885343i \(0.346077\pi\)
\(758\) 38.3718i 1.39373i
\(759\) −22.5908 11.2640i −0.819995 0.408858i
\(760\) 4.79350 + 24.2220i 0.173879 + 0.878626i
\(761\) −1.28492 3.95459i −0.0465784 0.143354i 0.925062 0.379815i \(-0.124012\pi\)
−0.971641 + 0.236461i \(0.924012\pi\)
\(762\) −4.66762 + 6.42442i −0.169090 + 0.232732i
\(763\) −11.6046 15.9724i −0.420115 0.578239i
\(764\) −0.710238 + 2.18589i −0.0256955 + 0.0790827i
\(765\) −4.44434 0.530419i −0.160685 0.0191773i
\(766\) 3.26667 2.37338i 0.118030 0.0857536i
\(767\) −0.747406 + 1.02872i −0.0269873 + 0.0371448i
\(768\) 29.2825 9.51446i 1.05664 0.343324i
\(769\) −16.8800 −0.608709 −0.304355 0.952559i \(-0.598441\pi\)
−0.304355 + 0.952559i \(0.598441\pi\)
\(770\) 15.1142 23.0029i 0.544680 0.828969i
\(771\) 48.7305 1.75499
\(772\) −6.76028 + 2.19655i −0.243308 + 0.0790555i
\(773\) −4.98301 + 6.85852i −0.179226 + 0.246684i −0.889173 0.457572i \(-0.848719\pi\)
0.709946 + 0.704256i \(0.248719\pi\)
\(774\) 10.1338 7.36263i 0.364252 0.264644i
\(775\) −0.262774 3.42427i −0.00943912 0.123003i
\(776\) −1.46392 + 4.50548i −0.0525517 + 0.161737i
\(777\) 6.75168 + 9.29289i 0.242215 + 0.333381i
\(778\) 33.0402 45.4759i 1.18455 1.63039i
\(779\) −12.9326 39.8025i −0.463359 1.42607i
\(780\) 11.8217 2.33950i 0.423286 0.0837676i
\(781\) −2.27873 + 15.2450i −0.0815395 + 0.545509i
\(782\) 14.1863i 0.507303i
\(783\) −0.743294 + 0.241511i −0.0265632 + 0.00863089i
\(784\) 7.85361 + 5.70598i 0.280486 + 0.203785i
\(785\) 23.5392 + 21.8020i 0.840150 + 0.778148i
\(786\) −1.60387 + 4.93620i −0.0572080 + 0.176068i
\(787\) −50.9924 16.5684i −1.81768 0.590601i −0.999886 0.0150924i \(-0.995196\pi\)
−0.817796 0.575508i \(-0.804804\pi\)
\(788\) −6.24233 8.59183i −0.222374 0.306071i
\(789\) 8.69272 + 6.31563i 0.309469 + 0.224842i
\(790\) 23.3651 13.0552i 0.831293 0.464482i
\(791\) −0.518940 −0.0184514
\(792\) −6.16466 0.921459i −0.219052 0.0327426i
\(793\) 6.41307i 0.227735i
\(794\) −14.0586 43.2679i −0.498921 1.53552i
\(795\) −50.7318 23.4477i −1.79927 0.831605i
\(796\) −8.83077 + 6.41593i −0.312998 + 0.227407i
\(797\) −27.1477 8.82082i −0.961621 0.312450i −0.214192 0.976792i \(-0.568712\pi\)
−0.747429 + 0.664342i \(0.768712\pi\)
\(798\) 36.8515 + 11.9738i 1.30453 + 0.423867i
\(799\) 21.6206 15.7083i 0.764883 0.555720i
\(800\) 4.68527 19.3491i 0.165649 0.684096i
\(801\) 2.75879 + 8.49070i 0.0974772 + 0.300004i
\(802\) 3.12290i 0.110273i
\(803\) −20.9548 20.5932i −0.739480 0.726718i
\(804\) 0.947515 0.0334163
\(805\) 9.42915 + 16.8756i 0.332334 + 0.594785i
\(806\) 3.40166 + 2.47145i 0.119819 + 0.0870532i
\(807\) 7.78350 + 10.7131i 0.273992 + 0.377118i
\(808\) −19.6596 6.38780i −0.691623 0.224722i
\(809\) −11.4170 + 35.1378i −0.401399 + 1.23538i 0.522466 + 0.852660i \(0.325012\pi\)
−0.923865 + 0.382718i \(0.874988\pi\)
\(810\) −29.5587 27.3773i −1.03859 0.961941i
\(811\) 31.0475 + 22.5573i 1.09022 + 0.792094i 0.979437 0.201750i \(-0.0646629\pi\)
0.110787 + 0.993844i \(0.464663\pi\)
\(812\) −0.296528 + 0.0963477i −0.0104061 + 0.00338114i
\(813\) 9.99209i 0.350438i
\(814\) −12.7350 6.34982i −0.446363 0.222561i
\(815\) −1.57453 7.95628i −0.0551535 0.278696i
\(816\) −6.69431 20.6030i −0.234348 0.721248i
\(817\) −26.1458 + 35.9865i −0.914724 + 1.25901i
\(818\) −13.1852 18.1478i −0.461008 0.634524i
\(819\) −2.30749 + 7.10171i −0.0806301 + 0.248154i
\(820\) −1.54731 + 12.9648i −0.0540345 + 0.452751i
\(821\) 8.29214 6.02459i 0.289398 0.210260i −0.433608 0.901101i \(-0.642760\pi\)
0.723006 + 0.690842i \(0.242760\pi\)
\(822\) −35.9181 + 49.4370i −1.25279 + 1.72431i
\(823\) −23.9948 + 7.79637i −0.836405 + 0.271764i −0.695741 0.718293i \(-0.744924\pi\)
−0.140664 + 0.990057i \(0.544924\pi\)
\(824\) 21.3904 0.745170
\(825\) −21.0996 + 25.0449i −0.734593 + 0.871953i
\(826\) 1.27555 0.0443820
\(827\) −17.4505 + 5.67001i −0.606813 + 0.197165i −0.596277 0.802779i \(-0.703354\pi\)
−0.0105362 + 0.999944i \(0.503354\pi\)
\(828\) −1.50360 + 2.06953i −0.0522537 + 0.0719211i
\(829\) 19.7259 14.3317i 0.685110 0.497761i −0.189939 0.981796i \(-0.560829\pi\)
0.875049 + 0.484035i \(0.160829\pi\)
\(830\) 1.39498 11.6884i 0.0484203 0.405710i
\(831\) −6.52575 + 20.0842i −0.226376 + 0.696713i
\(832\) −7.12060 9.80066i −0.246862 0.339777i
\(833\) 2.57415 3.54301i 0.0891890 0.122758i
\(834\) 11.7401 + 36.1324i 0.406528 + 1.25116i
\(835\) 1.65855 + 8.38081i 0.0573964 + 0.290030i
\(836\) −12.7568 + 2.13446i −0.441203 + 0.0738217i
\(837\) 2.84876i 0.0984676i
\(838\) 34.8345 11.3184i 1.20334 0.390988i
\(839\) −34.2059 24.8520i −1.18092 0.857988i −0.188644 0.982046i \(-0.560409\pi\)
−0.992275 + 0.124058i \(0.960409\pi\)
\(840\) 15.1780 + 14.0579i 0.523691 + 0.485044i
\(841\) −8.95052 + 27.5469i −0.308639 + 0.949892i
\(842\) −28.1715 9.15347i −0.970853 0.315449i
\(843\) −15.9252 21.9191i −0.548492 0.754935i
\(844\) −4.04097 2.93594i −0.139096 0.101059i
\(845\) −0.750612 1.34339i −0.0258218 0.0462139i
\(846\) −17.8849 −0.614895
\(847\) −20.2110 14.1532i −0.694457 0.486311i
\(848\) 62.4117i 2.14323i
\(849\) 13.4066 + 41.2613i 0.460113 + 1.41608i
\(850\) −17.8870 4.33123i −0.613521 0.148560i
\(851\) 8.08567 5.87458i 0.277173 0.201378i
\(852\) 6.43874 + 2.09207i 0.220587 + 0.0716732i
\(853\) 14.6353 + 4.75529i 0.501103 + 0.162818i 0.548652 0.836051i \(-0.315141\pi\)
−0.0475493 + 0.998869i \(0.515141\pi\)
\(854\) −5.20454 + 3.78132i −0.178096 + 0.129394i
\(855\) −9.65562 4.46273i −0.330215 0.152622i
\(856\) −6.48458 19.9575i −0.221638 0.682132i
\(857\) 36.1038i 1.23328i −0.787245 0.616641i \(-0.788493\pi\)
0.787245 0.616641i \(-0.211507\pi\)
\(858\) −6.61650 39.5442i −0.225884 1.35002i
\(859\) −48.3509 −1.64971 −0.824855 0.565344i \(-0.808743\pi\)
−0.824855 + 0.565344i \(0.808743\pi\)
\(860\) 12.1148 6.76910i 0.413111 0.230824i
\(861\) −28.3680 20.6106i −0.966781 0.702407i
\(862\) 32.5272 + 44.7699i 1.10788 + 1.52487i
\(863\) 35.3685 + 11.4919i 1.20396 + 0.391190i 0.841216 0.540699i \(-0.181840\pi\)
0.362743 + 0.931889i \(0.381840\pi\)
\(864\) 5.10306 15.7056i 0.173610 0.534316i
\(865\) −3.45680 3.20169i −0.117535 0.108861i
\(866\) 42.1539 + 30.6266i 1.43245 + 1.04073i
\(867\) 22.6336 7.35411i 0.768679 0.249759i
\(868\) 1.13648i 0.0385745i
\(869\) −11.0784 21.2826i −0.375809 0.721962i
\(870\) 1.35059 0.267279i 0.0457892 0.00906160i
\(871\) −0.743664 2.28876i −0.0251981 0.0775517i
\(872\) −10.8058 + 14.8730i −0.365932 + 0.503662i
\(873\) −1.19956 1.65105i −0.0405990 0.0558797i
\(874\) 10.4183 32.0642i 0.352403 1.08459i
\(875\) 24.1566 6.73660i 0.816642 0.227739i
\(876\) −10.4395 + 7.58472i −0.352717 + 0.256264i
\(877\) 15.1609 20.8672i 0.511947 0.704634i −0.472299 0.881438i \(-0.656576\pi\)
0.984246 + 0.176804i \(0.0565758\pi\)
\(878\) −56.0530 + 18.2127i −1.89170 + 0.614649i
\(879\) −27.7221 −0.935044
\(880\) −35.2731 9.65441i −1.18906 0.325450i
\(881\) −45.6820 −1.53906 −0.769532 0.638608i \(-0.779511\pi\)
−0.769532 + 0.638608i \(0.779511\pi\)
\(882\) −2.78738 + 0.905675i −0.0938560 + 0.0304957i
\(883\) −2.91912 + 4.01783i −0.0982364 + 0.135211i −0.855306 0.518124i \(-0.826631\pi\)
0.757069 + 0.653335i \(0.226631\pi\)
\(884\) 4.91167 3.56853i 0.165197 0.120023i
\(885\) −1.50695 0.179850i −0.0506556 0.00604560i
\(886\) −12.0090 + 36.9600i −0.403452 + 1.24170i
\(887\) 17.0006 + 23.3994i 0.570826 + 0.785674i 0.992652 0.121002i \(-0.0386109\pi\)
−0.421827 + 0.906677i \(0.638611\pi\)
\(888\) 6.28695 8.65324i 0.210976 0.290384i
\(889\) −1.68459 5.18463i −0.0564993 0.173887i
\(890\) 7.12641 + 36.0104i 0.238878 + 1.20707i
\(891\) −25.3155 + 25.7600i −0.848100 + 0.862994i
\(892\) 6.43021i 0.215299i
\(893\) 60.4033 19.6262i 2.02132 0.656766i
\(894\) −15.6372 11.3611i −0.522987 0.379972i
\(895\) 7.63365 8.24189i 0.255165 0.275496i
\(896\) −9.27501 + 28.5456i −0.309856 + 0.953640i
\(897\) 26.7811 + 8.70172i 0.894196 + 0.290542i
\(898\) 30.5299 + 42.0208i 1.01880 + 1.40225i
\(899\) 0.104713 + 0.0760785i 0.00349237 + 0.00253736i
\(900\) 2.15033 + 2.52768i 0.0716776 + 0.0842561i
\(901\) −28.1559 −0.938010
\(902\) 42.9630 + 6.42186i 1.43051 + 0.213824i
\(903\) 37.2692i 1.24024i
\(904\) 0.149323 + 0.459570i 0.00496642 + 0.0152851i
\(905\) 31.7608 + 14.6795i 1.05577 + 0.487964i
\(906\) 33.7773 24.5406i 1.12217 0.815307i
\(907\) 12.6041 + 4.09531i 0.418511 + 0.135983i 0.510700 0.859759i \(-0.329386\pi\)
−0.0921887 + 0.995742i \(0.529386\pi\)
\(908\) −2.67106 0.867880i −0.0886422 0.0288016i
\(909\) 7.20435 5.23427i 0.238953 0.173610i
\(910\) −12.8816 + 27.8708i −0.427020 + 0.923906i
\(911\) 4.24361 + 13.0605i 0.140597 + 0.432713i 0.996419 0.0845580i \(-0.0269478\pi\)
−0.855822 + 0.517271i \(0.826948\pi\)
\(912\) 51.4833i 1.70478i
\(913\) −10.4364 1.55997i −0.345395 0.0516276i
\(914\) 64.7117 2.14047
\(915\) 6.68188 3.73348i 0.220896 0.123425i
\(916\) 1.61942 + 1.17658i 0.0535071 + 0.0388752i
\(917\) −2.09430 2.88256i −0.0691600 0.0951906i
\(918\) −14.5188 4.71745i −0.479193 0.155699i
\(919\) −18.3494 + 56.4737i −0.605292 + 1.86290i −0.110517 + 0.993874i \(0.535251\pi\)
−0.494774 + 0.869022i \(0.664749\pi\)
\(920\) 12.2317 13.2063i 0.403266 0.435398i
\(921\) 10.9750 + 7.97379i 0.361638 + 0.262745i
\(922\) −13.9798 + 4.54233i −0.460402 + 0.149594i
\(923\) 17.1950i 0.565981i
\(924\) −7.59586 + 7.72925i −0.249885 + 0.254274i
\(925\) −4.93842 11.9885i −0.162374 0.394179i
\(926\) −2.15296 6.62613i −0.0707507 0.217748i
\(927\) −5.41635 + 7.45496i −0.177896 + 0.244853i
\(928\) 0.441016 + 0.607006i 0.0144770 + 0.0199259i
\(929\) −6.05305 + 18.6294i −0.198594 + 0.611210i 0.801322 + 0.598234i \(0.204131\pi\)
−0.999916 + 0.0129763i \(0.995869\pi\)
\(930\) −0.594712 + 4.98305i −0.0195014 + 0.163401i
\(931\) 8.42007 6.11754i 0.275957 0.200494i
\(932\) −4.55720 + 6.27245i −0.149276 + 0.205461i
\(933\) −10.3327 + 3.35730i −0.338277 + 0.109913i
\(934\) −11.1327 −0.364275
\(935\) −4.35541 + 15.9128i −0.142437 + 0.520406i
\(936\) 6.95320 0.227272
\(937\) 38.5608 12.5292i 1.25973 0.409310i 0.398329 0.917242i \(-0.369590\pi\)
0.861397 + 0.507933i \(0.169590\pi\)
\(938\) −1.41896 + 1.95304i −0.0463308 + 0.0637689i
\(939\) 22.7376 16.5198i 0.742012 0.539104i
\(940\) −19.6751 2.34816i −0.641730 0.0765886i
\(941\) −0.126602 + 0.389640i −0.00412709 + 0.0127019i −0.953099 0.302659i \(-0.902126\pi\)
0.948972 + 0.315361i \(0.102126\pi\)
\(942\) −27.5575 37.9296i −0.897870 1.23581i
\(943\) −17.9331 + 24.6828i −0.583982 + 0.803783i
\(944\) −0.523717 1.61184i −0.0170455 0.0524608i
\(945\) 20.4066 4.03843i 0.663826 0.131370i
\(946\) −21.3185 40.9548i −0.693125 1.33156i
\(947\) 2.45729i 0.0798511i −0.999203 0.0399256i \(-0.987288\pi\)
0.999203 0.0399256i \(-0.0127121\pi\)
\(948\) −10.0223 + 3.25643i −0.325508 + 0.105764i
\(949\) 26.5147 + 19.2640i 0.860703 + 0.625337i
\(950\) −37.2477 22.9255i −1.20848 0.743802i
\(951\) 11.4033 35.0956i 0.369776 1.13805i
\(952\) 9.91230 + 3.22070i 0.321260 + 0.104384i
\(953\) −35.8704 49.3714i −1.16196 1.59930i −0.703742 0.710456i \(-0.748489\pi\)
−0.458215 0.888841i \(-0.651511\pi\)
\(954\) 15.2441 + 11.0755i 0.493546 + 0.358582i
\(955\) 3.39842 + 6.08222i 0.109970 + 0.196816i
\(956\) 14.7820 0.478085
\(957\) −0.203675 1.21728i −0.00658387 0.0393492i
\(958\) 34.4309i 1.11241i
\(959\) −12.9632 39.8965i −0.418603 1.28833i
\(960\) 6.06609 13.1247i 0.195782 0.423597i
\(961\) 24.6978 17.9440i 0.796705 0.578840i
\(962\) 15.0972 + 4.90538i 0.486754 + 0.158156i
\(963\) 8.59754 + 2.79351i 0.277052 + 0.0900196i
\(964\) 16.9749 12.3330i 0.546726 0.397220i
\(965\) −9.04020 + 19.5595i −0.291014 + 0.629642i
\(966\) −8.72898 26.8650i −0.280850 0.864369i
\(967\) 17.1997i 0.553106i −0.960999 0.276553i \(-0.910808\pi\)
0.960999 0.276553i \(-0.0891921\pi\)
\(968\) −6.71837 + 21.9712i −0.215937 + 0.706182i
\(969\) −23.2258 −0.746119
\(970\) −4.09310 7.32550i −0.131421 0.235208i
\(971\) −22.0125 15.9930i −0.706415 0.513241i 0.175600 0.984462i \(-0.443813\pi\)
−0.882015 + 0.471221i \(0.843813\pi\)
\(972\) 3.92927 + 5.40818i 0.126031 + 0.173467i
\(973\) −24.8046 8.05950i −0.795198 0.258376i
\(974\) −8.06790 + 24.8304i −0.258512 + 0.795619i
\(975\) 19.1482 31.1106i 0.613234 0.996338i
\(976\) 6.91513 + 5.02414i 0.221348 + 0.160819i
\(977\) −18.2339 + 5.92454i −0.583353 + 0.189543i −0.585802 0.810454i \(-0.699220\pi\)
0.00244904 + 0.999997i \(0.499220\pi\)
\(978\) 11.8516i 0.378971i
\(979\) 32.4562 5.43055i 1.03730 0.173561i
\(980\) −3.18529 + 0.630365i −0.101750 + 0.0201363i
\(981\) −2.44732 7.53207i −0.0781369 0.240481i
\(982\) −18.7995 + 25.8753i −0.599916 + 0.825714i
\(983\) 14.1835 + 19.5219i 0.452384 + 0.622653i 0.972908 0.231194i \(-0.0742632\pi\)
−0.520524 + 0.853847i \(0.674263\pi\)
\(984\) −10.0898 + 31.0532i −0.321651 + 0.989939i
\(985\) −31.9667 3.81513i −1.01854 0.121560i
\(986\) 0.561138 0.407691i 0.0178703 0.0129835i
\(987\) 31.2781 43.0506i 0.995593 1.37032i
\(988\) 13.7221 4.45858i 0.436558 0.141846i
\(989\) 32.4276 1.03114
\(990\) 8.61762 6.90224i 0.273886 0.219368i
\(991\) 27.7081 0.880177 0.440089 0.897954i \(-0.354947\pi\)
0.440089 + 0.897954i \(0.354947\pi\)
\(992\) −2.60102 + 0.845122i −0.0825824 + 0.0268327i
\(993\) −0.543521 + 0.748092i −0.0172481 + 0.0237400i
\(994\) −13.9546 + 10.1386i −0.442614 + 0.321578i
\(995\) −3.92123 + 32.8556i −0.124311 + 1.04159i
\(996\) −1.43219 + 4.40782i −0.0453806 + 0.139667i
\(997\) 19.6856 + 27.0950i 0.623451 + 0.858106i 0.997598 0.0692628i \(-0.0220647\pi\)
−0.374148 + 0.927369i \(0.622065\pi\)
\(998\) −40.3211 + 55.4972i −1.27634 + 1.75673i
\(999\) −3.32350 10.2287i −0.105151 0.323621i
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 55.2.j.a.49.4 yes 16
3.2 odd 2 495.2.ba.a.379.1 16
4.3 odd 2 880.2.cd.c.49.4 16
5.2 odd 4 275.2.h.d.126.4 16
5.3 odd 4 275.2.h.d.126.1 16
5.4 even 2 inner 55.2.j.a.49.1 yes 16
11.2 odd 10 605.2.j.d.9.4 16
11.3 even 5 605.2.b.g.364.2 8
11.4 even 5 605.2.j.h.124.4 16
11.5 even 5 605.2.j.h.444.1 16
11.6 odd 10 605.2.j.g.444.4 16
11.7 odd 10 605.2.j.g.124.1 16
11.8 odd 10 605.2.b.f.364.7 8
11.9 even 5 inner 55.2.j.a.9.1 16
11.10 odd 2 605.2.j.d.269.1 16
15.14 odd 2 495.2.ba.a.379.4 16
20.19 odd 2 880.2.cd.c.49.1 16
33.20 odd 10 495.2.ba.a.64.4 16
44.31 odd 10 880.2.cd.c.449.1 16
55.3 odd 20 3025.2.a.bl.1.2 8
55.4 even 10 605.2.j.h.124.1 16
55.8 even 20 3025.2.a.bk.1.7 8
55.9 even 10 inner 55.2.j.a.9.4 yes 16
55.14 even 10 605.2.b.g.364.7 8
55.19 odd 10 605.2.b.f.364.2 8
55.24 odd 10 605.2.j.d.9.1 16
55.29 odd 10 605.2.j.g.124.4 16
55.39 odd 10 605.2.j.g.444.1 16
55.42 odd 20 275.2.h.d.251.4 16
55.47 odd 20 3025.2.a.bl.1.7 8
55.49 even 10 605.2.j.h.444.4 16
55.52 even 20 3025.2.a.bk.1.2 8
55.53 odd 20 275.2.h.d.251.1 16
55.54 odd 2 605.2.j.d.269.4 16
165.119 odd 10 495.2.ba.a.64.1 16
220.119 odd 10 880.2.cd.c.449.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.2.j.a.9.1 16 11.9 even 5 inner
55.2.j.a.9.4 yes 16 55.9 even 10 inner
55.2.j.a.49.1 yes 16 5.4 even 2 inner
55.2.j.a.49.4 yes 16 1.1 even 1 trivial
275.2.h.d.126.1 16 5.3 odd 4
275.2.h.d.126.4 16 5.2 odd 4
275.2.h.d.251.1 16 55.53 odd 20
275.2.h.d.251.4 16 55.42 odd 20
495.2.ba.a.64.1 16 165.119 odd 10
495.2.ba.a.64.4 16 33.20 odd 10
495.2.ba.a.379.1 16 3.2 odd 2
495.2.ba.a.379.4 16 15.14 odd 2
605.2.b.f.364.2 8 55.19 odd 10
605.2.b.f.364.7 8 11.8 odd 10
605.2.b.g.364.2 8 11.3 even 5
605.2.b.g.364.7 8 55.14 even 10
605.2.j.d.9.1 16 55.24 odd 10
605.2.j.d.9.4 16 11.2 odd 10
605.2.j.d.269.1 16 11.10 odd 2
605.2.j.d.269.4 16 55.54 odd 2
605.2.j.g.124.1 16 11.7 odd 10
605.2.j.g.124.4 16 55.29 odd 10
605.2.j.g.444.1 16 55.39 odd 10
605.2.j.g.444.4 16 11.6 odd 10
605.2.j.h.124.1 16 55.4 even 10
605.2.j.h.124.4 16 11.4 even 5
605.2.j.h.444.1 16 11.5 even 5
605.2.j.h.444.4 16 55.49 even 10
880.2.cd.c.49.1 16 20.19 odd 2
880.2.cd.c.49.4 16 4.3 odd 2
880.2.cd.c.449.1 16 44.31 odd 10
880.2.cd.c.449.4 16 220.119 odd 10
3025.2.a.bk.1.2 8 55.52 even 20
3025.2.a.bk.1.7 8 55.8 even 20
3025.2.a.bl.1.2 8 55.3 odd 20
3025.2.a.bl.1.7 8 55.47 odd 20