Properties

Label 605.2.j.d.9.1
Level $605$
Weight $2$
Character 605.9
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: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 55)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 9.1
Root \(-0.972539 - 1.33858i\) of defining polynomial
Character \(\chi\) \(=\) 605.9
Dual form 605.2.j.d.269.1

$q$-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} -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} +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} +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} +(-1.97371 - 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} +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} +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} -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} -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} +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 \( 16 q - 4 q^{4} - 2 q^{5} + 18 q^{6} + 2 q^{9} - 12 q^{14} - 16 q^{15} + 16 q^{16} - 6 q^{19} - 8 q^{20} - 8 q^{21} - 6 q^{24} - 16 q^{25} + 40 q^{26} - 2 q^{29} - 26 q^{30} + 8 q^{31} - 16 q^{34} - 22 q^{35} + 10 q^{36} - 30 q^{39} - 12 q^{40} + 52 q^{41} + 12 q^{45} + 62 q^{46} - 10 q^{49} - 28 q^{50} + 42 q^{51} + 40 q^{54} - 20 q^{56} + 2 q^{59} - 32 q^{60} + 40 q^{61} - 8 q^{64} + 40 q^{65} + 26 q^{69} - 34 q^{70} + 36 q^{71} - 48 q^{74} - 20 q^{75} - 56 q^{76} - 38 q^{79} + 34 q^{80} + 68 q^{81} - 12 q^{84} - 58 q^{85} + 22 q^{86} + 24 q^{89} - 78 q^{90} - 20 q^{91} - 14 q^{94} - 48 q^{95} + 86 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(122\) \(486\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{5}\right)\)

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 \(-0.598899\pi\)
−0.806979 + 0.590581i \(0.798899\pi\)
\(3\) −1.16075 1.59764i −0.670160 0.922396i 0.329604 0.944119i \(-0.393085\pi\)
−0.999764 + 0.0217231i \(0.993085\pi\)
\(4\) 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 \(-0.660660\pi\)
0.981896 + 0.189419i \(0.0606604\pi\)
\(8\) 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
\(11\) 0 0
\(12\) 1.45668i 0.420508i
\(13\) −3.51868 1.14329i −0.975906 0.317091i −0.222708 0.974885i \(-0.571490\pi\)
−0.753198 + 0.657794i \(0.771490\pi\)
\(14\) −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 \(-0.686949\pi\)
0.0409903 + 0.999160i \(0.486949\pi\)
\(18\) 0.875078 1.20444i 0.206258 0.283890i
\(19\) −4.27714 + 3.10753i −0.981244 + 0.712916i −0.957986 0.286814i \(-0.907404\pi\)
−0.0232580 + 0.999729i \(0.507404\pi\)
\(20\) −0.804534 + 1.43989i −0.179899 + 0.321970i
\(21\) −4.42960 −0.966617
\(22\) 0 0
\(23\) 3.85415i 0.803647i 0.915717 + 0.401823i \(0.131623\pi\)
−0.915717 + 0.401823i \(0.868377\pi\)
\(24\) 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 \(-0.305569\pi\)
−0.601850 + 0.798609i \(0.705569\pi\)
\(30\) −6.63212 + 3.06530i −1.21085 + 0.559644i
\(31\) 0.212253 0.653249i 0.0381218 0.117327i −0.930185 0.367092i \(-0.880353\pi\)
0.968306 + 0.249765i \(0.0803534\pi\)
\(32\) 3.98166i 0.703866i
\(33\) 0 0
\(34\) 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 −0.665134 0.746724i \(-0.731626\pi\)
0.915714 + 0.401830i \(0.131626\pi\)
\(38\) 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 \(-0.487887\pi\)
0.962124 + 0.272611i \(0.0878870\pi\)
\(42\) 6.97041 + 2.26482i 1.07556 + 0.349470i
\(43\) 8.41368i 1.28307i 0.767092 + 0.641537i \(0.221703\pi\)
−0.767092 + 0.641537i \(0.778297\pi\)
\(44\) 0 0
\(45\) −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 0.904965 + 0.425486i \(0.139897\pi\)
0.125012 + 0.992155i \(0.460103\pi\)
\(48\) −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 −0.673947 0.738779i \(-0.735403\pi\)
−0.979479 + 0.201549i \(0.935403\pi\)
\(54\) 6.86233 0.933845
\(55\) 0 0
\(56\) 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 0.569539 0.821965i \(-0.307122\pi\)
−0.605738 + 0.795664i \(0.707122\pi\)
\(60\) 3.23429 0.386003i 0.417545 0.0498328i
\(61\) −0.535643 1.64854i −0.0685821 0.211074i 0.910892 0.412645i \(-0.135395\pi\)
−0.979474 + 0.201572i \(0.935395\pi\)
\(62\) −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
\(66\) 0 0
\(67\) 0.650461i 0.0794664i 0.999210 + 0.0397332i \(0.0126508\pi\)
−0.999210 + 0.0397332i \(0.987349\pi\)
\(68\) −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 0.999396 0.0347464i \(-0.0110624\pi\)
−0.828952 + 0.559320i \(0.811062\pi\)
\(72\) −1.78738 + 0.580756i −0.210645 + 0.0684427i
\(73\) −5.20684 + 7.16660i −0.609415 + 0.838787i −0.996529 0.0832444i \(-0.973472\pi\)
0.387115 + 0.922032i \(0.373472\pi\)
\(74\) −3.47116 + 2.52195i −0.403515 + 0.293171i
\(75\) 7.52070 + 6.39795i 0.868416 + 0.738772i
\(76\) −3.89979 −0.447336
\(77\) 0 0
\(78\) 12.0888i 1.36878i
\(79\) −2.23551 + 6.88019i −0.251514 + 0.774082i 0.742982 + 0.669311i \(0.233411\pi\)
−0.994496 + 0.104770i \(0.966589\pi\)
\(80\) 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 \(-0.655868\pi\)
0.138200 + 0.990404i \(0.455868\pi\)
\(84\) −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
\(88\) 0 0
\(89\) −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 0.416472 0.909149i \(-0.363266\pi\)
−0.197451 + 0.980313i \(0.563266\pi\)
\(98\) 3.25724i 0.329031i
\(99\) 0 0
\(100\) −3.41020 1.40476i −0.341020 0.140476i
\(101\) −3.05830 + 9.41247i −0.304312 + 0.936576i 0.675621 + 0.737249i \(0.263876\pi\)
−0.979933 + 0.199327i \(0.936124\pi\)
\(102\) −4.27249 5.88057i −0.423039 0.582263i
\(103\) −6.01958 + 8.28525i −0.593127 + 0.816370i −0.995057 0.0993007i \(-0.968339\pi\)
0.401930 + 0.915670i \(0.368339\pi\)
\(104\) −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 \(-0.0385900\pi\)
−0.421767 + 0.906704i \(0.638590\pi\)
\(108\) −2.90961 0.945389i −0.279977 0.0909701i
\(109\) −8.80173 −0.843053 −0.421527 0.906816i \(-0.638506\pi\)
−0.421527 + 0.906816i \(0.638506\pi\)
\(110\) 0 0
\(111\) −5.12094 −0.486058
\(112\) −10.5196 3.41803i −0.994010 0.322973i
\(113\) 0.135985 + 0.187168i 0.0127924 + 0.0176073i 0.815365 0.578947i \(-0.196536\pi\)
−0.802573 + 0.596554i \(0.796536\pi\)
\(114\) −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
\(121\) 0 0
\(122\) 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 \(-0.634390\pi\)
0.204664 + 0.978832i \(0.434390\pi\)
\(128\) 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 \(-0.522106\pi\)
−0.0693924 + 0.997589i \(0.522106\pi\)
\(132\) 0 0
\(133\) 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 0.573943 0.818895i \(-0.305413\pi\)
0.945664 + 0.325145i \(0.105413\pi\)
\(138\) −11.9769 + 3.89153i −1.01954 + 0.331269i
\(139\) −9.40675 6.83441i −0.797870 0.579687i 0.112418 0.993661i \(-0.464140\pi\)
−0.910289 + 0.413974i \(0.864140\pi\)
\(140\) 1.55222 + 3.35840i 0.131186 + 0.283836i
\(141\) 7.33095 22.5624i 0.617378 1.90009i
\(142\) 7.68984i 0.645317i
\(143\) 0 0
\(144\) 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 \(-0.0220951\pi\)
−0.847836 + 0.530258i \(0.822095\pi\)
\(150\) −8.56335 13.9131i −0.699194 1.13600i
\(151\) 10.3375 7.51064i 0.841254 0.611207i −0.0814664 0.996676i \(-0.525960\pi\)
0.922721 + 0.385469i \(0.125960\pi\)
\(152\) −10.5020 3.41232i −0.851828 0.276776i
\(153\) 2.00167i 0.161826i
\(154\) 0 0
\(155\) 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 0.326724 0.945120i \(-0.394055\pi\)
−0.999826 + 0.0186749i \(0.994055\pi\)
\(158\) 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 0.440982 0.897516i \(-0.354630\pi\)
−0.170785 + 0.985308i \(0.554630\pi\)
\(164\) 5.83919 0.455964
\(165\) 0 0
\(166\) 5.26430 0.408589
\(167\) 3.63370 + 1.18066i 0.281184 + 0.0913623i 0.446214 0.894926i \(-0.352772\pi\)
−0.165030 + 0.986289i \(0.552772\pi\)
\(168\) −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 \(-0.225524\pi\)
−0.853500 + 0.521093i \(0.825524\pi\)
\(174\) 0.190266 0.585579i 0.0144240 0.0443926i
\(175\) −4.27171 + 10.3700i −0.322911 + 0.783899i
\(176\) 0 0
\(177\) 0.678711i 0.0510151i
\(178\) 15.6132 + 5.07303i 1.17026 + 0.380240i
\(179\) 4.06448 2.95302i 0.303793 0.220719i −0.425435 0.904989i \(-0.639879\pi\)
0.729229 + 0.684270i \(0.239879\pi\)
\(180\) −1.00849 1.08884i −0.0751681 0.0811574i
\(181\) −4.83538 14.8818i −0.359411 1.10615i −0.953408 0.301685i \(-0.902451\pi\)
0.593997 0.804467i \(-0.297549\pi\)
\(182\) 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
\(187\) 0 0
\(188\) 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 0.492840 0.870120i \(-0.335959\pi\)
−0.675237 + 0.737601i \(0.735959\pi\)
\(192\) 6.14966 1.99815i 0.443814 0.144204i
\(193\) 9.16474 2.97780i 0.659692 0.214347i 0.0400095 0.999199i \(-0.487261\pi\)
0.619683 + 0.784852i \(0.287261\pi\)
\(194\) −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 \(-0.171423\pi\)
\(198\) 0 0
\(199\) −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
\(209\) 0 0
\(210\) −3.18154 + 16.0766i −0.219547 + 1.10939i
\(211\) 2.09250 6.44005i 0.144054 0.443352i −0.852834 0.522181i \(-0.825118\pi\)
0.996888 + 0.0788298i \(0.0251184\pi\)
\(212\) −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
\(220\) 0 0
\(221\) 8.23051 0.553644
\(222\) 8.05832 + 2.61831i 0.540839 + 0.175729i
\(223\) 5.12388 + 7.05242i 0.343121 + 0.472265i 0.945350 0.326058i \(-0.105721\pi\)
−0.602229 + 0.798323i \(0.705721\pi\)
\(224\) 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 \(-0.759672\pi\)
0.876802 + 0.480852i \(0.159672\pi\)
\(228\) 4.52668 + 6.23044i 0.299787 + 0.412621i
\(229\) 0.838570 2.58085i 0.0554142 0.170547i −0.919519 0.393046i \(-0.871421\pi\)
0.974933 + 0.222499i \(0.0714213\pi\)
\(230\) 13.9881 + 2.76823i 0.922351 + 0.182532i
\(231\) 0 0
\(232\) 0.393588i 0.0258403i
\(233\) 9.99634 + 3.24801i 0.654882 + 0.212784i 0.617566 0.786519i \(-0.288119\pi\)
0.0373166 + 0.999303i \(0.488119\pi\)
\(234\) −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 \(-0.924448\pi\)
−0.0767288 + 0.997052i \(0.524448\pi\)
\(240\) −19.0088 10.6211i −1.22702 0.685590i
\(241\) −28.4450 −1.83230 −0.916152 0.400832i \(-0.868721\pi\)
−0.916152 + 0.400832i \(0.868721\pi\)
\(242\) 0 0
\(243\) 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 0.394117 + 0.919060i \(0.371050\pi\)
−0.859058 + 0.511879i \(0.828950\pi\)
\(252\) 1.48877i 0.0937838i
\(253\) 0 0
\(254\) 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 0.0641671 + 0.997939i \(0.479561\pi\)
−0.968925 + 0.247354i \(0.920439\pi\)
\(258\) −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 \(-0.0536510\pi\)
\(264\) 0 0
\(265\) 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 0.994143 0.108074i \(-0.0344682\pi\)
−0.867803 + 0.496909i \(0.834468\pi\)
\(270\) 1.81843 + 15.2365i 0.110666 + 0.927265i
\(271\) −4.09349 2.97409i −0.248662 0.180663i 0.456472 0.889738i \(-0.349113\pi\)
−0.705134 + 0.709075i \(0.749113\pi\)
\(272\) 6.44795 + 8.87484i 0.390964 + 0.538116i
\(273\) 15.5863 + 5.06430i 0.943327 + 0.306505i
\(274\) −30.9438 −1.86938
\(275\) 0 0
\(276\) 5.61428 0.337940
\(277\) −10.1703 3.30453i −0.611074 0.198550i −0.0129009 0.999917i \(-0.504107\pi\)
−0.598173 + 0.801367i \(0.704107\pi\)
\(278\) 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 0.994233 + 0.107238i \(0.0342008\pi\)
−0.741319 + 0.671153i \(0.765799\pi\)
\(282\) −23.0720 + 31.7559i −1.37392 + 1.89103i
\(283\) −12.9132 17.7735i −0.767611 1.05653i −0.996543 0.0830832i \(-0.973523\pi\)
0.228932 0.973442i \(-0.426477\pi\)
\(284\) −1.05939 + 3.26047i −0.0628633 + 0.193473i
\(285\) −4.53213 + 22.9013i −0.268460 + 1.35655i
\(286\) 0 0
\(287\) 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 \(-0.934491\pi\)
0.496848 + 0.867837i \(0.334491\pi\)
\(294\) −5.20389 + 3.78085i −0.303497 + 0.220504i
\(295\) 0.374856 0.670888i 0.0218250 0.0390606i
\(296\) 5.41627 0.314815
\(297\) 0 0
\(298\) 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 \(-0.0628056\pi\)
\(308\) 0 0
\(309\) 20.2241 1.15051
\(310\) −2.21843 1.23954i −0.125998 0.0704011i
\(311\) 4.45087 3.23374i 0.252385 0.183369i −0.454398 0.890799i \(-0.650146\pi\)
0.706783 + 0.707430i \(0.250146\pi\)
\(312\) −8.96982 + 12.3459i −0.507816 + 0.698949i
\(313\) −13.5354 + 4.39793i −0.765068 + 0.248586i −0.665452 0.746440i \(-0.731761\pi\)
−0.0996156 + 0.995026i \(0.531761\pi\)
\(314\) 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 −0.236033 0.971745i \(-0.575847\pi\)
−0.762132 + 0.647421i \(0.775847\pi\)
\(318\) 41.3547i 2.31906i
\(319\) 0 0
\(320\) −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
\(330\) 0 0
\(331\) 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 0.245146 0.969486i \(-0.421164\pi\)
0.846282 0.532735i \(-0.178836\pi\)
\(338\) −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
\(341\) 0 0
\(342\) 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 \(-0.630745\pi\)
0.215858 + 0.976425i \(0.430745\pi\)
\(348\) −0.161345 + 0.222072i −0.00864898 + 0.0119043i
\(349\) 5.15433 3.74484i 0.275905 0.200457i −0.441224 0.897397i \(-0.645456\pi\)
0.717129 + 0.696940i \(0.245456\pi\)
\(350\) 12.0241 14.1341i 0.642714 0.755502i
\(351\) 15.3446 0.819037
\(352\) 0 0
\(353\) 12.1971i 0.649186i −0.945854 0.324593i \(-0.894773\pi\)
0.945854 0.324593i \(-0.105227\pi\)
\(354\) 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 \(-0.519564\pi\)
−0.968241 + 0.250018i \(0.919564\pi\)
\(360\) −1.76309 3.81465i −0.0929232 0.201050i
\(361\) 2.76592 8.51262i 0.145575 0.448032i
\(362\) 25.8902i 1.36076i
\(363\) 0 0
\(364\) −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 −0.372140 0.928177i \(-0.621376\pi\)
0.997746 + 0.0671034i \(0.0213757\pi\)
\(368\) 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 \(-0.0623684\pi\)
\(374\) 0 0
\(375\) −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 −0.948006 0.318254i \(-0.896904\pi\)
0.579888 0.814696i \(-0.303096\pi\)
\(380\) −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 0.367713 0.929939i \(-0.380141\pi\)
−0.249118 + 0.968473i \(0.580141\pi\)
\(384\) −26.4246 −1.34848
\(385\) 0 0
\(386\) −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 0.995467 + 0.0951096i \(0.0303201\pi\)
0.398071 + 0.917355i \(0.369680\pi\)
\(390\) 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
\(396\) 0 0
\(397\) 27.4961i 1.37999i 0.723814 + 0.689995i \(0.242387\pi\)
−0.723814 + 0.689995i \(0.757613\pi\)
\(398\) 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 0.935437 0.353494i \(-0.115006\pi\)
−0.964563 + 0.263853i \(0.915006\pi\)
\(402\) −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
\(407\) 0 0
\(408\) 9.17582i 0.454271i
\(409\) 4.18949 12.8939i 0.207157 0.637563i −0.792461 0.609923i \(-0.791201\pi\)
0.999618 0.0276408i \(-0.00879945\pi\)
\(410\) −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
\(418\) 0 0
\(419\) 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 −0.881842 0.471544i \(-0.843697\pi\)
0.175961 + 0.984397i \(0.443697\pi\)
\(422\) −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
\(429\) 0 0
\(430\) 30.5364 + 6.04310i 1.47259 + 0.291424i
\(431\) −10.3353 + 31.8087i −0.497833 + 1.53217i 0.314662 + 0.949204i \(0.398109\pi\)
−0.812495 + 0.582968i \(0.801891\pi\)
\(432\) 12.0213 + 16.5459i 0.578376 + 0.796066i
\(433\) 18.5102 25.4771i 0.889543 1.22435i −0.0841428 0.996454i \(-0.526815\pi\)
0.973685 0.227897i \(-0.0731848\pi\)
\(434\) 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 \(-0.176575\pi\)
0.850045 + 0.526710i \(0.176575\pi\)
\(440\) 0 0
\(441\) −1.77134 −0.0843495
\(442\) −12.9515 4.20821i −0.616041 0.200164i
\(443\) −13.8056 19.0018i −0.655926 0.902805i 0.343412 0.939185i \(-0.388417\pi\)
−0.999338 + 0.0363802i \(0.988417\pi\)
\(444\) −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 −0.410011 0.912080i \(-0.634475\pi\)
0.867814 0.496890i \(-0.165525\pi\)
\(450\) −2.83522 + 6.88277i −0.133653 + 0.324457i
\(451\) 0 0
\(452\) 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 \(-0.967620\pi\)
−0.745145 + 0.666903i \(0.767620\pi\)
\(458\) −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 \(-0.433668\pi\)
0.206884 + 0.978365i \(0.433668\pi\)
\(462\) 0 0
\(463\) 4.21081i 0.195693i 0.995202 + 0.0978464i \(0.0311954\pi\)
−0.995202 + 0.0978464i \(0.968805\pi\)
\(464\) −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 −0.453307 0.891354i \(-0.649756\pi\)
0.157191 + 0.987568i \(0.449756\pi\)
\(468\) 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
\(473\) 0 0
\(474\) −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 0.983617 + 0.180272i \(0.0576977\pi\)
−0.689802 + 0.723998i \(0.742302\pi\)
\(480\) 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
\(484\) 0 0
\(485\) −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 0.545404 0.838173i \(-0.316376\pi\)
−0.965689 + 0.259700i \(0.916376\pi\)
\(488\) 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 \(-0.156330\pi\)
−0.176044 + 0.984382i \(0.556330\pi\)
\(492\) −6.77784 9.32890i −0.305569 0.420579i
\(493\) 0.398685 + 0.129541i 0.0179559 + 0.00583422i
\(494\) −32.3637 −1.45611
\(495\) 0 0
\(496\) −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 −0.969769 0.244026i \(-0.921532\pi\)
−0.531758 0.846896i \(-0.678468\pi\)
\(500\) 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 −0.982511 0.186205i \(-0.940381\pi\)
0.126521 0.991964i \(-0.459619\pi\)
\(504\) −1.30268 + 4.00923i −0.0580259 + 0.178585i
\(505\) −21.7090 4.29618i −0.966039 0.191178i
\(506\) 0 0
\(507\) 1.35905i 0.0603576i
\(508\) −1.70498 0.553981i −0.0756462 0.0245789i
\(509\) 13.4662 9.78379i 0.596881 0.433659i −0.247890 0.968788i \(-0.579737\pi\)
0.844770 + 0.535129i \(0.179737\pi\)
\(510\) 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
\(517\) 0 0
\(518\) 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 0.310126 0.950696i \(-0.399629\pi\)
−0.808331 + 0.588728i \(0.799629\pi\)
\(522\) −0.266812 + 0.0866924i −0.0116780 + 0.00379442i
\(523\) −14.9009 + 4.84159i −0.651570 + 0.211708i −0.616106 0.787663i \(-0.711291\pi\)
−0.0354635 + 0.999371i \(0.511291\pi\)
\(524\) −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
\(528\) 0 0
\(529\) 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 0
\(540\) 1.32805 6.71075i 0.0571501 0.288785i
\(541\) 12.2489 37.6983i 0.526623 1.62078i −0.234461 0.972125i \(-0.575333\pi\)
0.761084 0.648653i \(-0.224667\pi\)
\(542\) 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 0.901445 + 0.432895i \(0.142508\pi\)
0.133145 + 0.991097i \(0.457492\pi\)
\(548\) 13.1201 + 4.26297i 0.560462 + 0.182105i
\(549\) 1.55967 0.0665651
\(550\) 0 0
\(551\) 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 0.254306 + 0.967124i \(0.418153\pi\)
−0.998374 + 0.0569987i \(0.981847\pi\)
\(558\) −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
\(561\) 0 0
\(562\) 22.7004i 0.957558i
\(563\) 2.05218 + 0.666795i 0.0864892 + 0.0281021i 0.351942 0.936022i \(-0.385521\pi\)
−0.265453 + 0.964124i \(0.585521\pi\)
\(564\) 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 \(-0.704786\pi\)
0.575555 + 0.817763i \(0.304786\pi\)
\(570\) 18.8410 33.7202i 0.789164 1.41238i
\(571\) 21.6311 0.905235 0.452617 0.891705i \(-0.350490\pi\)
0.452617 + 0.891705i \(0.350490\pi\)
\(572\) 0 0
\(573\) 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 −0.733568 0.679616i \(-0.762146\pi\)
−0.194000 + 0.981001i \(0.562146\pi\)
\(578\) 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
\(583\) 0 0
\(584\) −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 −0.835407 0.549632i \(-0.814768\pi\)
0.780886 + 0.624674i \(0.214768\pi\)
\(588\) 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 \(0.825337\pi\)
\(594\) 0 0
\(595\) −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 0.997732 + 0.0673118i \(0.0214422\pi\)
−0.767617 + 0.640909i \(0.778558\pi\)
\(600\) −1.57798 + 20.5630i −0.0644208 + 0.839482i
\(601\) −28.0242 20.3608i −1.14313 0.830533i −0.155579 0.987824i \(-0.549724\pi\)
−0.987552 + 0.157290i \(0.949724\pi\)
\(602\) −18.3542 25.2625i −0.748063 1.02962i
\(603\) −0.556631 0.180860i −0.0226678 0.00736520i
\(604\) 9.42547 0.383517
\(605\) 0 0
\(606\) −32.3375 −1.31362
\(607\) −24.2027 7.86394i −0.982358 0.319187i −0.226564 0.973996i \(-0.572749\pi\)
−0.755794 + 0.654809i \(0.772749\pi\)
\(608\) −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 0.976460 + 0.215698i \(0.0692027\pi\)
−0.0966016 + 0.995323i \(0.530797\pi\)
\(614\) −3.51234 + 10.8099i −0.141746 + 0.436251i
\(615\) 6.78600 34.2903i 0.273638 1.38272i
\(616\) 0 0
\(617\) 27.5937i 1.11088i −0.831557 0.555439i \(-0.812550\pi\)
0.831557 0.555439i \(-0.187450\pi\)
\(618\) −31.8246 10.3404i −1.28017 0.415953i
\(619\) 16.5391 12.0164i 0.664764 0.482979i −0.203504 0.979074i \(-0.565233\pi\)
0.868268 + 0.496095i \(0.165233\pi\)
\(620\) 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
\(627\) 0 0
\(628\) 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 0.575494 0.817806i \(-0.304810\pi\)
−0.599943 + 0.800043i \(0.704810\pi\)
\(632\) −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 0
\(639\) −4.18186 −0.165432
\(640\) 26.1201 + 14.5945i 1.03249 + 0.576897i
\(641\) 12.0584 8.76094i 0.476278 0.346037i −0.323605 0.946192i \(-0.604895\pi\)
0.799883 + 0.600156i \(0.204895\pi\)
\(642\) −19.2955 + 26.5579i −0.761531 + 1.04816i
\(643\) 26.2820 8.53955i 1.03646 0.336767i 0.259120 0.965845i \(-0.416568\pi\)
0.777342 + 0.629078i \(0.216568\pi\)
\(644\) 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 0.736175 0.676791i \(-0.236630\pi\)
0.197770 + 0.980248i \(0.436630\pi\)
\(648\) 22.7452i 0.893514i
\(649\) 0 0
\(650\) −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 −0.998540 0.0540191i \(-0.982797\pi\)
0.359941 + 0.932975i \(0.382797\pi\)
\(654\) −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 \(-0.638125\pi\)
−0.420442 + 0.907320i \(0.638125\pi\)
\(660\) 0 0
\(661\) −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 0
\(672\) 17.6372i 0.680368i
\(673\) 29.8127 + 9.68673i 1.14920 + 0.373396i 0.820840 0.571158i \(-0.193506\pi\)
0.328355 + 0.944554i \(0.393506\pi\)
\(674\) −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 \(-0.800597\pi\)
−0.310801 + 0.950475i \(0.600597\pi\)
\(678\) −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
\(682\) 0 0
\(683\) 3.27236i 0.125213i 0.998038 + 0.0626066i \(0.0199414\pi\)
−0.998038 + 0.0626066i \(0.980059\pi\)
\(684\) 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 0.470083 + 0.882622i \(0.344224\pi\)
−0.899098 + 0.437748i \(0.855776\pi\)
\(692\) 1.55431i 0.0590862i
\(693\) 0 0
\(694\) 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 0.431399 0.902161i \(-0.358020\pi\)
0.991316 0.131502i \(-0.0419800\pi\)
\(702\) −24.1463 7.84562i −0.911345 0.296114i
\(703\) 13.7096i 0.517068i
\(704\) 0 0
\(705\) 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 0.913929 + 0.405874i \(0.133033\pi\)
−0.500817 + 0.865553i \(0.666967\pi\)
\(710\) 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
\(715\) 0 0
\(716\) 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 0.868859 0.495060i \(-0.164854\pi\)
−0.202337 + 0.979316i \(0.564854\pi\)
\(720\) 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 0
\(727\) 45.5415i 1.68904i 0.535522 + 0.844521i \(0.320115\pi\)
−0.535522 + 0.844521i \(0.679885\pi\)
\(728\) −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 \(-0.732607\pi\)
0.914472 + 0.404650i \(0.132607\pi\)
\(734\) −27.2936 + 19.8300i −1.00743 + 0.731938i
\(735\) 7.58871 + 4.24016i 0.279914 + 0.156401i
\(736\) −15.3459 −0.565659
\(737\) 0 0
\(738\) 11.7852i 0.433818i
\(739\) −1.34045 + 4.12547i −0.0493091 + 0.151758i −0.972679 0.232153i \(-0.925423\pi\)
0.923370 + 0.383911i \(0.125423\pi\)
\(740\) 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 \(-0.702755\pi\)
−0.00865478 + 0.999963i \(0.502755\pi\)
\(744\) −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
\(748\) 0 0
\(749\) 22.5357 0.823437
\(750\) 28.6222 22.7001i 1.04514 0.828890i
\(751\) 25.4946 18.5229i 0.930310 0.675910i −0.0157586 0.999876i \(-0.505016\pi\)
0.946069 + 0.323966i \(0.105016\pi\)
\(752\) 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 0.464938 0.885343i \(-0.346077\pi\)
−0.144249 + 0.989541i \(0.546077\pi\)
\(758\) 38.3718i 1.39373i
\(759\) 0 0
\(760\) 4.79350 24.2220i 0.173879 0.878626i
\(761\) 1.28492 3.95459i 0.0465784 0.143354i −0.925062 0.379815i \(-0.875988\pi\)
0.971641 + 0.236461i \(0.0759876\pi\)
\(762\) −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 \(-0.401559\pi\)
0.304355 + 0.952559i \(0.401559\pi\)
\(770\) 0 0
\(771\) 48.7305 1.75499
\(772\) 6.76028 + 2.19655i 0.243308 + 0.0790555i
\(773\) −4.98301 6.85852i −0.179226 0.246684i 0.709946 0.704256i \(-0.248719\pi\)
−0.889173 + 0.457572i \(0.848719\pi\)
\(774\) 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
\(781\) 0 0
\(782\) 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 0.817796 0.575508i \(-0.195196\pi\)
0.999886 0.0150924i \(-0.00480424\pi\)
\(788\) 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
\(792\) 0 0
\(793\) 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 −0.747429 0.664342i \(-0.768712\pi\)
−0.214192 + 0.976792i \(0.568712\pi\)
\(798\) −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
\(803\) 0 0
\(804\) 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 0.923865 + 0.382718i \(0.125012\pi\)
−0.522466 + 0.852660i \(0.674988\pi\)
\(810\) 29.5587 27.3773i 1.03859 0.961941i
\(811\) −31.0475 + 22.5573i −1.09022 + 0.792094i −0.979437 0.201750i \(-0.935337\pi\)
−0.110787 + 0.993844i \(0.535337\pi\)
\(812\) −0.296528 0.0963477i −0.0104061 0.00338114i
\(813\) 9.99209i 0.350438i
\(814\) 0 0
\(815\) −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 \(-0.357240\pi\)
−0.723006 + 0.690842i \(0.757240\pi\)
\(822\) 35.9181 + 49.4370i 1.25279 + 1.72431i
\(823\) −23.9948 7.79637i −0.836405 0.271764i −0.140664 0.990057i \(-0.544924\pi\)
−0.695741 + 0.718293i \(0.744924\pi\)
\(824\) −21.3904 −0.745170
\(825\) 0 0
\(826\) 1.27555 0.0443820
\(827\) 17.4505 + 5.67001i 0.606813 + 0.197165i 0.596277 0.802779i \(-0.296646\pi\)
0.0105362 + 0.999944i \(0.496646\pi\)
\(828\) −1.50360 2.06953i −0.0522537 0.0719211i
\(829\) 19.7259 + 14.3317i 0.685110 + 0.497761i 0.875049 0.484035i \(-0.160829\pi\)
−0.189939 + 0.981796i \(0.560829\pi\)
\(830\) 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
\(836\) 0 0
\(837\) 2.84876i 0.0984676i
\(838\) −34.8345 11.3184i −1.20334 0.390988i
\(839\) −34.2059 + 24.8520i −1.18092 + 0.857988i −0.992275 0.124058i \(-0.960409\pi\)
−0.188644 + 0.982046i \(0.560409\pi\)
\(840\) 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
\(847\) 0 0
\(848\) 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 \(-0.684859\pi\)
0.0475493 + 0.998869i \(0.484859\pi\)
\(854\) 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 \(-0.211507\pi\)
\(858\) 0 0
\(859\) −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 0.362743 0.931889i \(-0.381840\pi\)
0.841216 + 0.540699i \(0.181840\pi\)
\(864\) −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
\(869\) 0 0
\(870\) 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 \(-0.343424\pi\)
−0.984246 + 0.176804i \(0.943424\pi\)
\(878\) −56.0530 18.2127i −1.89170 0.614649i
\(879\) 27.7221 0.935044
\(880\) 0 0
\(881\) −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 0.757069 0.653335i \(-0.226631\pi\)
−0.855306 + 0.518124i \(0.826631\pi\)
\(884\) 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 \(-0.961389\pi\)
0.421827 + 0.906677i \(0.361389\pi\)
\(888\) −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
\(891\) 0 0
\(892\) 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
\(902\) 0 0
\(903\) 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 −0.0921887 0.995742i \(-0.529386\pi\)
0.510700 + 0.859759i \(0.329386\pi\)
\(908\) 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 −0.855822 0.517271i \(-0.826948\pi\)
0.996419 + 0.0845580i \(0.0269478\pi\)
\(912\) 51.4833i 1.70478i
\(913\) 0 0
\(914\) 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 0.494774 + 0.869022i \(0.335251\pi\)
0.110517 + 0.993874i \(0.464749\pi\)
\(920\) −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
\(924\) 0 0
\(925\) −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 −0.999916 0.0129763i \(-0.995869\pi\)
0.801322 0.598234i \(-0.204131\pi\)
\(930\) 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
\(935\) 0 0
\(936\) 6.95320 0.227272
\(937\) −38.5608 12.5292i −1.25973 0.409310i −0.398329 0.917242i \(-0.630410\pi\)
−0.861397 + 0.507933i \(0.830410\pi\)
\(938\) −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 \(-0.0978744\pi\)
−0.948972 + 0.315361i \(0.897874\pi\)
\(942\) 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
\(946\) 0 0
\(947\) 2.45729i 0.0798511i 0.999203 + 0.0399256i \(0.0127121\pi\)
−0.999203 + 0.0399256i \(0.987288\pi\)
\(948\) 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 0.458215 0.888841i \(-0.348489\pi\)
0.703742 0.710456i \(-0.251511\pi\)
\(954\) −15.2441 + 11.0755i −0.493546 + 0.358582i
\(955\) 3.39842 6.08222i 0.109970 0.196816i
\(956\) −14.7820 −0.478085
\(957\) 0 0
\(958\) 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 \(-0.0891921\pi\)
\(968\) 0 0
\(969\) −23.2258 −0.746119
\(970\) 4.09310 7.32550i 0.131421 0.235208i
\(971\) −22.0125 + 15.9930i −0.706415 + 0.513241i −0.882015 0.471221i \(-0.843813\pi\)
0.175600 + 0.984462i \(0.443813\pi\)
\(972\) 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 0.00244904 0.999997i \(-0.499220\pi\)
−0.585802 + 0.810454i \(0.699220\pi\)
\(978\) 11.8516i 0.378971i
\(979\) 0 0
\(980\) −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 −0.520524 0.853847i \(-0.674263\pi\)
0.972908 + 0.231194i \(0.0742632\pi\)
\(984\) −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
\(990\) 0 0
\(991\) 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 \(-0.977935\pi\)
0.374148 + 0.927369i \(0.377935\pi\)
\(998\) 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 605.2.j.d.9.1 16
5.4 even 2 inner 605.2.j.d.9.4 16
11.2 odd 10 605.2.j.h.124.1 16
11.3 even 5 605.2.j.g.444.1 16
11.4 even 5 605.2.b.f.364.2 8
11.5 even 5 inner 605.2.j.d.269.4 16
11.6 odd 10 55.2.j.a.49.1 yes 16
11.7 odd 10 605.2.b.g.364.7 8
11.8 odd 10 605.2.j.h.444.4 16
11.9 even 5 605.2.j.g.124.4 16
11.10 odd 2 55.2.j.a.9.4 yes 16
33.17 even 10 495.2.ba.a.379.4 16
33.32 even 2 495.2.ba.a.64.1 16
44.39 even 10 880.2.cd.c.49.1 16
44.43 even 2 880.2.cd.c.449.4 16
55.4 even 10 605.2.b.f.364.7 8
55.7 even 20 3025.2.a.bl.1.2 8
55.9 even 10 605.2.j.g.124.1 16
55.14 even 10 605.2.j.g.444.4 16
55.17 even 20 275.2.h.d.126.1 16
55.18 even 20 3025.2.a.bl.1.7 8
55.19 odd 10 605.2.j.h.444.1 16
55.24 odd 10 605.2.j.h.124.4 16
55.28 even 20 275.2.h.d.126.4 16
55.29 odd 10 605.2.b.g.364.2 8
55.32 even 4 275.2.h.d.251.1 16
55.37 odd 20 3025.2.a.bk.1.7 8
55.39 odd 10 55.2.j.a.49.4 yes 16
55.43 even 4 275.2.h.d.251.4 16
55.48 odd 20 3025.2.a.bk.1.2 8
55.49 even 10 inner 605.2.j.d.269.1 16
55.54 odd 2 55.2.j.a.9.1 16
165.149 even 10 495.2.ba.a.379.1 16
165.164 even 2 495.2.ba.a.64.4 16
220.39 even 10 880.2.cd.c.49.4 16
220.219 even 2 880.2.cd.c.449.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.2.j.a.9.1 16 55.54 odd 2
55.2.j.a.9.4 yes 16 11.10 odd 2
55.2.j.a.49.1 yes 16 11.6 odd 10
55.2.j.a.49.4 yes 16 55.39 odd 10
275.2.h.d.126.1 16 55.17 even 20
275.2.h.d.126.4 16 55.28 even 20
275.2.h.d.251.1 16 55.32 even 4
275.2.h.d.251.4 16 55.43 even 4
495.2.ba.a.64.1 16 33.32 even 2
495.2.ba.a.64.4 16 165.164 even 2
495.2.ba.a.379.1 16 165.149 even 10
495.2.ba.a.379.4 16 33.17 even 10
605.2.b.f.364.2 8 11.4 even 5
605.2.b.f.364.7 8 55.4 even 10
605.2.b.g.364.2 8 55.29 odd 10
605.2.b.g.364.7 8 11.7 odd 10
605.2.j.d.9.1 16 1.1 even 1 trivial
605.2.j.d.9.4 16 5.4 even 2 inner
605.2.j.d.269.1 16 55.49 even 10 inner
605.2.j.d.269.4 16 11.5 even 5 inner
605.2.j.g.124.1 16 55.9 even 10
605.2.j.g.124.4 16 11.9 even 5
605.2.j.g.444.1 16 11.3 even 5
605.2.j.g.444.4 16 55.14 even 10
605.2.j.h.124.1 16 11.2 odd 10
605.2.j.h.124.4 16 55.24 odd 10
605.2.j.h.444.1 16 55.19 odd 10
605.2.j.h.444.4 16 11.8 odd 10
880.2.cd.c.49.1 16 44.39 even 10
880.2.cd.c.49.4 16 220.39 even 10
880.2.cd.c.449.1 16 220.219 even 2
880.2.cd.c.449.4 16 44.43 even 2
3025.2.a.bk.1.2 8 55.48 odd 20
3025.2.a.bk.1.7 8 55.37 odd 20
3025.2.a.bl.1.2 8 55.7 even 20
3025.2.a.bl.1.7 8 55.18 even 20