Properties

Label 525.2.q.g.299.5
Level $525$
Weight $2$
Character 525.299
Analytic conductor $4.192$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [525,2,Mod(299,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.299");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.q (of order \(6\), degree \(2\), 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: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 299.5
Character \(\chi\) \(=\) 525.299
Dual form 525.2.q.g.374.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.846473 + 1.46613i) q^{2} +(-1.53466 - 0.803015i) q^{3} +(-0.433034 - 0.750036i) q^{4} +(2.47637 - 1.57028i) q^{6} +(2.01688 - 1.71236i) q^{7} -1.91969 q^{8} +(1.71033 + 2.46470i) q^{9} +O(q^{10})\) \(q+(-0.846473 + 1.46613i) q^{2} +(-1.53466 - 0.803015i) q^{3} +(-0.433034 - 0.750036i) q^{4} +(2.47637 - 1.57028i) q^{6} +(2.01688 - 1.71236i) q^{7} -1.91969 q^{8} +(1.71033 + 2.46470i) q^{9} +(-0.399511 + 0.230658i) q^{11} +(0.0622670 + 1.49878i) q^{12} -3.38501 q^{13} +(0.803314 + 4.40649i) q^{14} +(2.49103 - 4.31459i) q^{16} +(-4.76601 + 2.75166i) q^{17} +(-5.06134 + 0.421275i) q^{18} +(-3.49334 - 2.01688i) q^{19} +(-4.47027 + 1.00830i) q^{21} -0.780983i q^{22} +(2.25223 - 3.90097i) q^{23} +(2.94606 + 1.54154i) q^{24} +(2.86532 - 4.96289i) q^{26} +(-0.645580 - 5.15589i) q^{27} +(-2.15771 - 0.771225i) q^{28} -7.71756i q^{29} +(-3.01611 + 1.74135i) q^{31} +(2.29749 + 3.97938i) q^{32} +(0.798334 - 0.0331669i) q^{33} -9.31681i q^{34} +(1.10798 - 2.35011i) q^{36} +(5.02232 + 2.89964i) q^{37} +(5.91404 - 3.41448i) q^{38} +(5.19483 + 2.71822i) q^{39} -6.25727 q^{41} +(2.30567 - 7.40752i) q^{42} -8.35453i q^{43} +(0.346004 + 0.199765i) q^{44} +(3.81290 + 6.60414i) q^{46} +(2.73630 + 1.57980i) q^{47} +(-7.28756 + 4.62108i) q^{48} +(1.13564 - 6.90727i) q^{49} +(9.52380 - 0.395668i) q^{51} +(1.46582 + 2.53888i) q^{52} +(-5.78238 - 10.0154i) q^{53} +(8.10570 + 3.41782i) q^{54} +(-3.87179 + 3.28720i) q^{56} +(3.74149 + 5.90043i) q^{57} +(11.3150 + 6.53271i) q^{58} +(-4.88061 - 8.45346i) q^{59} +(-6.90647 - 3.98746i) q^{61} -5.89604i q^{62} +(7.67001 + 2.04231i) q^{63} +2.18506 q^{64} +(-0.627141 + 1.19854i) q^{66} +(0.793481 - 0.458116i) q^{67} +(4.12768 + 2.38312i) q^{68} +(-6.58893 + 4.17808i) q^{69} -1.52593i q^{71} +(-3.28331 - 4.73146i) q^{72} +(3.89906 + 6.75338i) q^{73} +(-8.50252 + 4.90893i) q^{74} +3.49351i q^{76} +(-0.410798 + 1.14932i) q^{77} +(-8.38256 + 5.31542i) q^{78} +(-3.58521 + 6.20977i) q^{79} +(-3.14952 + 8.43093i) q^{81} +(5.29661 - 9.17399i) q^{82} +17.5632i q^{83} +(2.69204 + 2.91624i) q^{84} +(12.2489 + 7.07188i) q^{86} +(-6.19732 + 11.8438i) q^{87} +(0.766937 - 0.442791i) q^{88} +(1.35247 - 2.34254i) q^{89} +(-6.82718 + 5.79637i) q^{91} -3.90116 q^{92} +(6.02703 - 0.250394i) q^{93} +(-4.63241 + 2.67452i) q^{94} +(-0.330363 - 7.95189i) q^{96} -4.44253 q^{97} +(9.16569 + 7.51181i) q^{98} +(-1.25180 - 0.590174i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 28 q^{4} + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 28 q^{4} + 14 q^{9} - 36 q^{16} - 18 q^{21} - 36 q^{24} + 84 q^{31} - 72 q^{36} - 16 q^{46} + 8 q^{49} + 42 q^{51} + 150 q^{54} - 180 q^{61} + 240 q^{64} + 12 q^{66} - 92 q^{79} + 58 q^{81} - 150 q^{84} - 60 q^{91} - 12 q^{94} + 270 q^{96} - 188 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.846473 + 1.46613i −0.598547 + 1.03671i 0.394489 + 0.918901i \(0.370922\pi\)
−0.993036 + 0.117813i \(0.962412\pi\)
\(3\) −1.53466 0.803015i −0.886034 0.463621i
\(4\) −0.433034 0.750036i −0.216517 0.375018i
\(5\) 0 0
\(6\) 2.47637 1.57028i 1.01097 0.641064i
\(7\) 2.01688 1.71236i 0.762310 0.647212i
\(8\) −1.91969 −0.678712
\(9\) 1.71033 + 2.46470i 0.570111 + 0.821567i
\(10\) 0 0
\(11\) −0.399511 + 0.230658i −0.120457 + 0.0695460i −0.559018 0.829156i \(-0.688822\pi\)
0.438561 + 0.898702i \(0.355488\pi\)
\(12\) 0.0622670 + 1.49878i 0.0179749 + 0.432660i
\(13\) −3.38501 −0.938834 −0.469417 0.882977i \(-0.655536\pi\)
−0.469417 + 0.882977i \(0.655536\pi\)
\(14\) 0.803314 + 4.40649i 0.214695 + 1.17768i
\(15\) 0 0
\(16\) 2.49103 4.31459i 0.622758 1.07865i
\(17\) −4.76601 + 2.75166i −1.15593 + 0.667374i −0.950324 0.311261i \(-0.899249\pi\)
−0.205602 + 0.978636i \(0.565915\pi\)
\(18\) −5.06134 + 0.421275i −1.19297 + 0.0992955i
\(19\) −3.49334 2.01688i −0.801428 0.462705i 0.0425421 0.999095i \(-0.486454\pi\)
−0.843970 + 0.536390i \(0.819788\pi\)
\(20\) 0 0
\(21\) −4.47027 + 1.00830i −0.975493 + 0.220028i
\(22\) 0.780983i 0.166506i
\(23\) 2.25223 3.90097i 0.469622 0.813409i −0.529775 0.848138i \(-0.677724\pi\)
0.999397 + 0.0347292i \(0.0110569\pi\)
\(24\) 2.94606 + 1.54154i 0.601362 + 0.314665i
\(25\) 0 0
\(26\) 2.86532 4.96289i 0.561936 0.973302i
\(27\) −0.645580 5.15589i −0.124242 0.992252i
\(28\) −2.15771 0.771225i −0.407769 0.145748i
\(29\) 7.71756i 1.43311i −0.697528 0.716557i \(-0.745717\pi\)
0.697528 0.716557i \(-0.254283\pi\)
\(30\) 0 0
\(31\) −3.01611 + 1.74135i −0.541710 + 0.312756i −0.745772 0.666202i \(-0.767919\pi\)
0.204062 + 0.978958i \(0.434586\pi\)
\(32\) 2.29749 + 3.97938i 0.406143 + 0.703461i
\(33\) 0.798334 0.0331669i 0.138972 0.00577362i
\(34\) 9.31681i 1.59782i
\(35\) 0 0
\(36\) 1.10798 2.35011i 0.184664 0.391685i
\(37\) 5.02232 + 2.89964i 0.825665 + 0.476698i 0.852366 0.522946i \(-0.175167\pi\)
−0.0267011 + 0.999643i \(0.508500\pi\)
\(38\) 5.91404 3.41448i 0.959385 0.553901i
\(39\) 5.19483 + 2.71822i 0.831839 + 0.435263i
\(40\) 0 0
\(41\) −6.25727 −0.977221 −0.488610 0.872502i \(-0.662496\pi\)
−0.488610 + 0.872502i \(0.662496\pi\)
\(42\) 2.30567 7.40752i 0.355772 1.14300i
\(43\) 8.35453i 1.27405i −0.770842 0.637027i \(-0.780164\pi\)
0.770842 0.637027i \(-0.219836\pi\)
\(44\) 0.346004 + 0.199765i 0.0521620 + 0.0301157i
\(45\) 0 0
\(46\) 3.81290 + 6.60414i 0.562182 + 0.973727i
\(47\) 2.73630 + 1.57980i 0.399130 + 0.230438i 0.686109 0.727499i \(-0.259317\pi\)
−0.286978 + 0.957937i \(0.592651\pi\)
\(48\) −7.28756 + 4.62108i −1.05187 + 0.666995i
\(49\) 1.13564 6.90727i 0.162234 0.986752i
\(50\) 0 0
\(51\) 9.52380 0.395668i 1.33360 0.0554046i
\(52\) 1.46582 + 2.53888i 0.203273 + 0.352080i
\(53\) −5.78238 10.0154i −0.794271 1.37572i −0.923301 0.384078i \(-0.874519\pi\)
0.129029 0.991641i \(-0.458814\pi\)
\(54\) 8.10570 + 3.41782i 1.10305 + 0.465106i
\(55\) 0 0
\(56\) −3.87179 + 3.28720i −0.517389 + 0.439270i
\(57\) 3.74149 + 5.90043i 0.495573 + 0.781531i
\(58\) 11.3150 + 6.53271i 1.48573 + 0.857786i
\(59\) −4.88061 8.45346i −0.635401 1.10055i −0.986430 0.164183i \(-0.947501\pi\)
0.351029 0.936365i \(-0.385832\pi\)
\(60\) 0 0
\(61\) −6.90647 3.98746i −0.884283 0.510541i −0.0122151 0.999925i \(-0.503888\pi\)
−0.872068 + 0.489384i \(0.837222\pi\)
\(62\) 5.89604i 0.748798i
\(63\) 7.67001 + 2.04231i 0.966330 + 0.257307i
\(64\) 2.18506 0.273132
\(65\) 0 0
\(66\) −0.627141 + 1.19854i −0.0771957 + 0.147530i
\(67\) 0.793481 0.458116i 0.0969391 0.0559678i −0.450747 0.892652i \(-0.648842\pi\)
0.547686 + 0.836684i \(0.315509\pi\)
\(68\) 4.12768 + 2.38312i 0.500555 + 0.288995i
\(69\) −6.58893 + 4.17808i −0.793214 + 0.502981i
\(70\) 0 0
\(71\) 1.52593i 0.181094i −0.995892 0.0905471i \(-0.971138\pi\)
0.995892 0.0905471i \(-0.0288616\pi\)
\(72\) −3.28331 4.73146i −0.386941 0.557608i
\(73\) 3.89906 + 6.75338i 0.456351 + 0.790423i 0.998765 0.0496883i \(-0.0158228\pi\)
−0.542414 + 0.840112i \(0.682489\pi\)
\(74\) −8.50252 + 4.90893i −0.988398 + 0.570652i
\(75\) 0 0
\(76\) 3.49351i 0.400733i
\(77\) −0.410798 + 1.14932i −0.0468148 + 0.130977i
\(78\) −8.38256 + 5.31542i −0.949138 + 0.601853i
\(79\) −3.58521 + 6.20977i −0.403368 + 0.698654i −0.994130 0.108192i \(-0.965494\pi\)
0.590762 + 0.806846i \(0.298827\pi\)
\(80\) 0 0
\(81\) −3.14952 + 8.43093i −0.349946 + 0.936770i
\(82\) 5.29661 9.17399i 0.584912 1.01310i
\(83\) 17.5632i 1.92781i 0.266250 + 0.963904i \(0.414215\pi\)
−0.266250 + 0.963904i \(0.585785\pi\)
\(84\) 2.69204 + 2.91624i 0.293725 + 0.318188i
\(85\) 0 0
\(86\) 12.2489 + 7.07188i 1.32083 + 0.762581i
\(87\) −6.19732 + 11.8438i −0.664422 + 1.26979i
\(88\) 0.766937 0.442791i 0.0817558 0.0472017i
\(89\) 1.35247 2.34254i 0.143361 0.248309i −0.785399 0.618990i \(-0.787542\pi\)
0.928760 + 0.370681i \(0.120876\pi\)
\(90\) 0 0
\(91\) −6.82718 + 5.79637i −0.715683 + 0.607625i
\(92\) −3.90116 −0.406724
\(93\) 6.02703 0.250394i 0.624974 0.0259646i
\(94\) −4.63241 + 2.67452i −0.477796 + 0.275856i
\(95\) 0 0
\(96\) −0.330363 7.95189i −0.0337175 0.811587i
\(97\) −4.44253 −0.451070 −0.225535 0.974235i \(-0.572413\pi\)
−0.225535 + 0.974235i \(0.572413\pi\)
\(98\) 9.16569 + 7.51181i 0.925875 + 0.758808i
\(99\) −1.25180 0.590174i −0.125811 0.0593148i
\(100\) 0 0
\(101\) −1.36822 2.36982i −0.136143 0.235806i 0.789891 0.613248i \(-0.210137\pi\)
−0.926033 + 0.377442i \(0.876804\pi\)
\(102\) −7.48154 + 14.2981i −0.740782 + 1.41572i
\(103\) 9.21552 15.9618i 0.908033 1.57276i 0.0912387 0.995829i \(-0.470917\pi\)
0.816794 0.576930i \(-0.195749\pi\)
\(104\) 6.49817 0.637198
\(105\) 0 0
\(106\) 19.5785 1.90163
\(107\) −3.32647 + 5.76162i −0.321582 + 0.556997i −0.980815 0.194942i \(-0.937548\pi\)
0.659232 + 0.751939i \(0.270881\pi\)
\(108\) −3.58755 + 2.71688i −0.345212 + 0.261432i
\(109\) −3.91662 6.78379i −0.375144 0.649769i 0.615204 0.788368i \(-0.289073\pi\)
−0.990349 + 0.138599i \(0.955740\pi\)
\(110\) 0 0
\(111\) −5.37908 8.48295i −0.510560 0.805166i
\(112\) −2.36402 12.9676i −0.223379 1.22532i
\(113\) −17.3914 −1.63604 −0.818022 0.575187i \(-0.804929\pi\)
−0.818022 + 0.575187i \(0.804929\pi\)
\(114\) −11.8179 + 0.490976i −1.10685 + 0.0459842i
\(115\) 0 0
\(116\) −5.78845 + 3.34196i −0.537444 + 0.310293i
\(117\) −5.78951 8.34305i −0.535240 0.771316i
\(118\) 16.5252 1.52127
\(119\) −4.90065 + 13.7109i −0.449242 + 1.25688i
\(120\) 0 0
\(121\) −5.39359 + 9.34198i −0.490327 + 0.849271i
\(122\) 11.6923 6.75055i 1.05857 0.611166i
\(123\) 9.60275 + 5.02468i 0.865850 + 0.453060i
\(124\) 2.61216 + 1.50813i 0.234579 + 0.135434i
\(125\) 0 0
\(126\) −9.48675 + 9.51650i −0.845147 + 0.847797i
\(127\) 12.5556i 1.11413i 0.830469 + 0.557065i \(0.188073\pi\)
−0.830469 + 0.557065i \(0.811927\pi\)
\(128\) −6.44458 + 11.1623i −0.569626 + 0.986621i
\(129\) −6.70881 + 12.8213i −0.590678 + 1.12885i
\(130\) 0 0
\(131\) 3.36275 5.82446i 0.293805 0.508886i −0.680901 0.732375i \(-0.738412\pi\)
0.974706 + 0.223490i \(0.0717450\pi\)
\(132\) −0.370582 0.584417i −0.0322550 0.0508670i
\(133\) −10.4993 + 1.91405i −0.910405 + 0.165969i
\(134\) 1.55113i 0.133997i
\(135\) 0 0
\(136\) 9.14924 5.28232i 0.784541 0.452955i
\(137\) −10.1734 17.6208i −0.869171 1.50545i −0.862845 0.505468i \(-0.831320\pi\)
−0.00632592 0.999980i \(-0.502014\pi\)
\(138\) −0.548267 13.1969i −0.0466716 1.12339i
\(139\) 9.79157i 0.830510i 0.909705 + 0.415255i \(0.136308\pi\)
−0.909705 + 0.415255i \(0.863692\pi\)
\(140\) 0 0
\(141\) −2.93067 4.62174i −0.246807 0.389221i
\(142\) 2.23721 + 1.29166i 0.187743 + 0.108393i
\(143\) 1.35235 0.780781i 0.113089 0.0652922i
\(144\) 14.8947 1.23974i 1.24122 0.103312i
\(145\) 0 0
\(146\) −13.2018 −1.09259
\(147\) −7.28945 + 9.68834i −0.601224 + 0.799081i
\(148\) 5.02257i 0.412852i
\(149\) 14.1195 + 8.15190i 1.15671 + 0.667830i 0.950514 0.310680i \(-0.100557\pi\)
0.206200 + 0.978510i \(0.433890\pi\)
\(150\) 0 0
\(151\) 7.54351 + 13.0657i 0.613882 + 1.06328i 0.990580 + 0.136939i \(0.0437263\pi\)
−0.376697 + 0.926336i \(0.622940\pi\)
\(152\) 6.70613 + 3.87179i 0.543939 + 0.314043i
\(153\) −14.9335 7.04054i −1.20730 0.569194i
\(154\) −1.33733 1.57515i −0.107765 0.126929i
\(155\) 0 0
\(156\) −0.210775 5.07339i −0.0168755 0.406196i
\(157\) −6.22562 10.7831i −0.496858 0.860584i 0.503135 0.864208i \(-0.332180\pi\)
−0.999993 + 0.00362372i \(0.998847\pi\)
\(158\) −6.06958 10.5128i −0.482869 0.836354i
\(159\) 0.831464 + 20.0135i 0.0659394 + 1.58717i
\(160\) 0 0
\(161\) −2.13739 11.7244i −0.168450 0.924015i
\(162\) −9.69489 11.7542i −0.761703 0.923495i
\(163\) 4.76649 + 2.75193i 0.373340 + 0.215548i 0.674917 0.737894i \(-0.264180\pi\)
−0.301577 + 0.953442i \(0.597513\pi\)
\(164\) 2.70961 + 4.69317i 0.211585 + 0.366475i
\(165\) 0 0
\(166\) −25.7500 14.8667i −1.99858 1.15388i
\(167\) 0.799023i 0.0618302i −0.999522 0.0309151i \(-0.990158\pi\)
0.999522 0.0309151i \(-0.00984216\pi\)
\(168\) 8.58153 1.93562i 0.662079 0.149336i
\(169\) −1.54168 −0.118590
\(170\) 0 0
\(171\) −1.00377 12.0596i −0.0767601 0.922221i
\(172\) −6.26620 + 3.61779i −0.477793 + 0.275854i
\(173\) 12.5737 + 7.25944i 0.955962 + 0.551925i 0.894928 0.446211i \(-0.147227\pi\)
0.0610338 + 0.998136i \(0.480560\pi\)
\(174\) −12.1187 19.1116i −0.918719 1.44884i
\(175\) 0 0
\(176\) 2.29830i 0.173241i
\(177\) 0.701796 + 16.8924i 0.0527502 + 1.26971i
\(178\) 2.28965 + 3.96579i 0.171617 + 0.297249i
\(179\) 2.04442 1.18035i 0.152807 0.0882234i −0.421647 0.906760i \(-0.638548\pi\)
0.574454 + 0.818537i \(0.305214\pi\)
\(180\) 0 0
\(181\) 9.70696i 0.721513i 0.932660 + 0.360756i \(0.117481\pi\)
−0.932660 + 0.360756i \(0.882519\pi\)
\(182\) −2.71923 14.9160i −0.201563 1.10565i
\(183\) 7.39707 + 11.6654i 0.546807 + 0.862329i
\(184\) −4.32357 + 7.48865i −0.318738 + 0.552071i
\(185\) 0 0
\(186\) −4.73461 + 9.04839i −0.347158 + 0.663460i
\(187\) 1.26938 2.19863i 0.0928264 0.160780i
\(188\) 2.73643i 0.199575i
\(189\) −10.1308 9.29337i −0.736908 0.675993i
\(190\) 0 0
\(191\) 4.37389 + 2.52527i 0.316484 + 0.182722i 0.649824 0.760085i \(-0.274843\pi\)
−0.333341 + 0.942807i \(0.608176\pi\)
\(192\) −3.35331 1.75463i −0.242004 0.126630i
\(193\) −11.3481 + 6.55182i −0.816853 + 0.471610i −0.849330 0.527862i \(-0.822994\pi\)
0.0324769 + 0.999472i \(0.489660\pi\)
\(194\) 3.76048 6.51334i 0.269987 0.467631i
\(195\) 0 0
\(196\) −5.67247 + 2.13931i −0.405176 + 0.152808i
\(197\) 21.2925 1.51703 0.758516 0.651655i \(-0.225925\pi\)
0.758516 + 0.651655i \(0.225925\pi\)
\(198\) 1.92489 1.33574i 0.136796 0.0949270i
\(199\) 5.78974 3.34271i 0.410424 0.236958i −0.280548 0.959840i \(-0.590516\pi\)
0.690972 + 0.722882i \(0.257183\pi\)
\(200\) 0 0
\(201\) −1.58559 + 0.0658738i −0.111839 + 0.00464638i
\(202\) 4.63263 0.325951
\(203\) −13.2153 15.5654i −0.927529 1.09248i
\(204\) −4.42089 6.97185i −0.309524 0.488127i
\(205\) 0 0
\(206\) 15.6014 + 27.0224i 1.08700 + 1.88274i
\(207\) 13.4668 1.12090i 0.936007 0.0779076i
\(208\) −8.43218 + 14.6050i −0.584666 + 1.01267i
\(209\) 1.86084 0.128717
\(210\) 0 0
\(211\) 5.72156 0.393889 0.196944 0.980415i \(-0.436898\pi\)
0.196944 + 0.980415i \(0.436898\pi\)
\(212\) −5.00793 + 8.67399i −0.343946 + 0.595732i
\(213\) −1.22534 + 2.34177i −0.0839591 + 0.160456i
\(214\) −5.63154 9.75412i −0.384964 0.666778i
\(215\) 0 0
\(216\) 1.23931 + 9.89770i 0.0843245 + 0.673453i
\(217\) −3.10132 + 8.67678i −0.210531 + 0.589019i
\(218\) 13.2613 0.898166
\(219\) −0.560657 13.4951i −0.0378857 0.911915i
\(220\) 0 0
\(221\) 16.1330 9.31439i 1.08522 0.626554i
\(222\) 16.9904 0.705869i 1.14032 0.0473748i
\(223\) −5.83493 −0.390736 −0.195368 0.980730i \(-0.562590\pi\)
−0.195368 + 0.980730i \(0.562590\pi\)
\(224\) 11.4479 + 4.09180i 0.764896 + 0.273395i
\(225\) 0 0
\(226\) 14.7213 25.4981i 0.979249 1.69611i
\(227\) 9.88387 5.70646i 0.656016 0.378751i −0.134741 0.990881i \(-0.543020\pi\)
0.790757 + 0.612130i \(0.209687\pi\)
\(228\) 2.80534 5.36134i 0.185788 0.355063i
\(229\) −0.910719 0.525804i −0.0601820 0.0347461i 0.469607 0.882876i \(-0.344396\pi\)
−0.529789 + 0.848129i \(0.677729\pi\)
\(230\) 0 0
\(231\) 1.55335 1.43393i 0.102203 0.0943457i
\(232\) 14.8153i 0.972672i
\(233\) −1.94244 + 3.36441i −0.127254 + 0.220410i −0.922612 0.385730i \(-0.873950\pi\)
0.795358 + 0.606140i \(0.207283\pi\)
\(234\) 17.1327 1.42602i 1.12000 0.0932220i
\(235\) 0 0
\(236\) −4.22694 + 7.32127i −0.275150 + 0.476574i
\(237\) 10.4886 6.65088i 0.681308 0.432021i
\(238\) −15.9537 18.7909i −1.03413 1.21803i
\(239\) 6.40306i 0.414180i −0.978322 0.207090i \(-0.933601\pi\)
0.978322 0.207090i \(-0.0663993\pi\)
\(240\) 0 0
\(241\) 1.96093 1.13215i 0.126315 0.0729279i −0.435511 0.900183i \(-0.643432\pi\)
0.561826 + 0.827255i \(0.310099\pi\)
\(242\) −9.13106 15.8155i −0.586967 1.01666i
\(243\) 11.6036 10.4095i 0.744370 0.667767i
\(244\) 6.90681i 0.442163i
\(245\) 0 0
\(246\) −15.4953 + 9.82566i −0.987945 + 0.626461i
\(247\) 11.8250 + 6.82718i 0.752408 + 0.434403i
\(248\) 5.79000 3.34286i 0.367665 0.212272i
\(249\) 14.1035 26.9534i 0.893772 1.70810i
\(250\) 0 0
\(251\) 13.3221 0.840886 0.420443 0.907319i \(-0.361875\pi\)
0.420443 + 0.907319i \(0.361875\pi\)
\(252\) −1.78957 6.63717i −0.112732 0.418102i
\(253\) 2.07798i 0.130641i
\(254\) −18.4082 10.6280i −1.15503 0.666859i
\(255\) 0 0
\(256\) −8.72527 15.1126i −0.545329 0.944538i
\(257\) 16.9680 + 9.79648i 1.05844 + 0.611088i 0.924999 0.379969i \(-0.124066\pi\)
0.133436 + 0.991057i \(0.457399\pi\)
\(258\) −13.1190 20.6889i −0.816750 1.28804i
\(259\) 15.0947 2.75180i 0.937937 0.170988i
\(260\) 0 0
\(261\) 19.0215 13.1996i 1.17740 0.817035i
\(262\) 5.69296 + 9.86050i 0.351712 + 0.609184i
\(263\) 8.38678 + 14.5263i 0.517151 + 0.895732i 0.999802 + 0.0199186i \(0.00634072\pi\)
−0.482651 + 0.875813i \(0.660326\pi\)
\(264\) −1.53255 + 0.0636701i −0.0943220 + 0.00391863i
\(265\) 0 0
\(266\) 6.08112 17.0136i 0.372858 1.04317i
\(267\) −3.95666 + 2.50894i −0.242144 + 0.153545i
\(268\) −0.687207 0.396759i −0.0419779 0.0242359i
\(269\) −14.6703 25.4097i −0.894465 1.54926i −0.834466 0.551060i \(-0.814224\pi\)
−0.0599988 0.998198i \(-0.519110\pi\)
\(270\) 0 0
\(271\) 2.57129 + 1.48454i 0.156195 + 0.0901792i 0.576060 0.817407i \(-0.304589\pi\)
−0.419865 + 0.907586i \(0.637923\pi\)
\(272\) 27.4178i 1.66245i
\(273\) 15.1319 3.41310i 0.915827 0.206570i
\(274\) 34.4460 2.08096
\(275\) 0 0
\(276\) 5.98694 + 3.13269i 0.360371 + 0.188566i
\(277\) −11.2803 + 6.51269i −0.677768 + 0.391309i −0.799014 0.601313i \(-0.794644\pi\)
0.121246 + 0.992623i \(0.461311\pi\)
\(278\) −14.3558 8.28830i −0.861001 0.497099i
\(279\) −9.45048 4.45553i −0.565786 0.266745i
\(280\) 0 0
\(281\) 19.4404i 1.15972i 0.814717 + 0.579859i \(0.196892\pi\)
−0.814717 + 0.579859i \(0.803108\pi\)
\(282\) 9.25683 0.384577i 0.551236 0.0229012i
\(283\) −2.81977 4.88399i −0.167618 0.290323i 0.769964 0.638088i \(-0.220274\pi\)
−0.937582 + 0.347764i \(0.886941\pi\)
\(284\) −1.14450 + 0.660778i −0.0679136 + 0.0392099i
\(285\) 0 0
\(286\) 2.64364i 0.156322i
\(287\) −12.6202 + 10.7147i −0.744945 + 0.632469i
\(288\) −5.87850 + 12.4687i −0.346394 + 0.734725i
\(289\) 6.64321 11.5064i 0.390777 0.676846i
\(290\) 0 0
\(291\) 6.81775 + 3.56741i 0.399663 + 0.209126i
\(292\) 3.37685 5.84888i 0.197615 0.342280i
\(293\) 21.5754i 1.26045i −0.776412 0.630226i \(-0.782962\pi\)
0.776412 0.630226i \(-0.217038\pi\)
\(294\) −8.03409 18.8882i −0.468557 1.10158i
\(295\) 0 0
\(296\) −9.64129 5.56640i −0.560389 0.323541i
\(297\) 1.44716 + 1.91093i 0.0839730 + 0.110883i
\(298\) −23.9036 + 13.8007i −1.38470 + 0.799455i
\(299\) −7.62382 + 13.2049i −0.440897 + 0.763656i
\(300\) 0 0
\(301\) −14.3060 16.8501i −0.824582 0.971224i
\(302\) −25.5415 −1.46975
\(303\) 0.196739 + 4.73555i 0.0113024 + 0.272050i
\(304\) −17.4041 + 10.0482i −0.998191 + 0.576306i
\(305\) 0 0
\(306\) 22.9632 15.9349i 1.31272 0.910935i
\(307\) −22.9288 −1.30861 −0.654307 0.756229i \(-0.727040\pi\)
−0.654307 + 0.756229i \(0.727040\pi\)
\(308\) 1.03992 0.189580i 0.0592549 0.0108023i
\(309\) −26.9602 + 17.0956i −1.53371 + 0.972534i
\(310\) 0 0
\(311\) −0.799023 1.38395i −0.0453084 0.0784765i 0.842482 0.538725i \(-0.181094\pi\)
−0.887790 + 0.460248i \(0.847760\pi\)
\(312\) −9.97245 5.21813i −0.564579 0.295418i
\(313\) −14.4421 + 25.0145i −0.816318 + 1.41390i 0.0920593 + 0.995754i \(0.470655\pi\)
−0.908378 + 0.418151i \(0.862678\pi\)
\(314\) 21.0793 1.18957
\(315\) 0 0
\(316\) 6.21007 0.349344
\(317\) 3.28018 5.68143i 0.184233 0.319101i −0.759085 0.650992i \(-0.774353\pi\)
0.943318 + 0.331891i \(0.107687\pi\)
\(318\) −30.0463 15.7219i −1.68491 0.881638i
\(319\) 1.78012 + 3.08325i 0.0996674 + 0.172629i
\(320\) 0 0
\(321\) 9.73166 6.17090i 0.543168 0.344426i
\(322\) 18.9988 + 6.79071i 1.05876 + 0.378432i
\(323\) 22.1991 1.23519
\(324\) 7.68735 1.28862i 0.427075 0.0715903i
\(325\) 0 0
\(326\) −8.06940 + 4.65887i −0.446923 + 0.258031i
\(327\) 0.563181 + 13.5559i 0.0311440 + 0.749642i
\(328\) 12.0120 0.663251
\(329\) 8.22399 1.49925i 0.453403 0.0826566i
\(330\) 0 0
\(331\) 6.76497 11.7173i 0.371836 0.644040i −0.618012 0.786169i \(-0.712062\pi\)
0.989848 + 0.142129i \(0.0453949\pi\)
\(332\) 13.1730 7.60544i 0.722963 0.417403i
\(333\) 1.44310 + 17.3379i 0.0790815 + 0.950110i
\(334\) 1.17147 + 0.676351i 0.0641002 + 0.0370083i
\(335\) 0 0
\(336\) −6.78520 + 21.7991i −0.370163 + 1.18924i
\(337\) 30.7122i 1.67300i −0.547966 0.836501i \(-0.684598\pi\)
0.547966 0.836501i \(-0.315402\pi\)
\(338\) 1.30499 2.26030i 0.0709819 0.122944i
\(339\) 26.6898 + 13.9655i 1.44959 + 0.758504i
\(340\) 0 0
\(341\) 0.803314 1.39138i 0.0435019 0.0753475i
\(342\) 18.5307 + 8.73647i 1.00202 + 0.472414i
\(343\) −9.53729 15.8758i −0.514965 0.857211i
\(344\) 16.0381i 0.864715i
\(345\) 0 0
\(346\) −21.2866 + 12.2898i −1.14438 + 0.660706i
\(347\) −3.91036 6.77295i −0.209919 0.363591i 0.741770 0.670655i \(-0.233987\pi\)
−0.951689 + 0.307064i \(0.900653\pi\)
\(348\) 11.5669 0.480550i 0.620052 0.0257602i
\(349\) 25.1501i 1.34625i 0.739526 + 0.673127i \(0.235049\pi\)
−0.739526 + 0.673127i \(0.764951\pi\)
\(350\) 0 0
\(351\) 2.18530 + 17.4528i 0.116643 + 0.931560i
\(352\) −1.83575 1.05987i −0.0978458 0.0564913i
\(353\) −10.6252 + 6.13445i −0.565521 + 0.326504i −0.755359 0.655312i \(-0.772537\pi\)
0.189837 + 0.981816i \(0.439204\pi\)
\(354\) −25.3605 13.2700i −1.34790 0.705292i
\(355\) 0 0
\(356\) −2.34265 −0.124160
\(357\) 18.5309 17.1062i 0.980757 0.905356i
\(358\) 3.99653i 0.211223i
\(359\) 7.11574 + 4.10828i 0.375555 + 0.216827i 0.675882 0.737010i \(-0.263763\pi\)
−0.300328 + 0.953836i \(0.597096\pi\)
\(360\) 0 0
\(361\) −1.36436 2.36315i −0.0718086 0.124376i
\(362\) −14.2317 8.21668i −0.748002 0.431859i
\(363\) 15.7791 10.0056i 0.828186 0.525157i
\(364\) 7.30388 + 2.61061i 0.382827 + 0.136833i
\(365\) 0 0
\(366\) −23.3644 + 0.970679i −1.22128 + 0.0507382i
\(367\) −13.9526 24.1666i −0.728320 1.26149i −0.957593 0.288125i \(-0.906968\pi\)
0.229273 0.973362i \(-0.426365\pi\)
\(368\) −11.2207 19.4349i −0.584921 1.01311i
\(369\) −10.7020 15.4223i −0.557125 0.802853i
\(370\) 0 0
\(371\) −28.8123 10.2983i −1.49586 0.534663i
\(372\) −2.79771 4.41206i −0.145054 0.228755i
\(373\) −15.6612 9.04199i −0.810905 0.468176i 0.0363650 0.999339i \(-0.488422\pi\)
−0.847270 + 0.531162i \(0.821755\pi\)
\(374\) 2.14900 + 3.72217i 0.111122 + 0.192469i
\(375\) 0 0
\(376\) −5.25284 3.03273i −0.270895 0.156401i
\(377\) 26.1241i 1.34546i
\(378\) 22.2008 6.98655i 1.14189 0.359349i
\(379\) −24.7450 −1.27107 −0.635534 0.772073i \(-0.719220\pi\)
−0.635534 + 0.772073i \(0.719220\pi\)
\(380\) 0 0
\(381\) 10.0823 19.2685i 0.516534 0.987157i
\(382\) −7.40476 + 4.27514i −0.378861 + 0.218735i
\(383\) 11.1972 + 6.46470i 0.572150 + 0.330331i 0.758008 0.652246i \(-0.226173\pi\)
−0.185858 + 0.982577i \(0.559506\pi\)
\(384\) 18.8537 11.9552i 0.962126 0.610089i
\(385\) 0 0
\(386\) 22.1838i 1.12912i
\(387\) 20.5914 14.2890i 1.04672 0.726352i
\(388\) 1.92376 + 3.33205i 0.0976642 + 0.169159i
\(389\) −16.4024 + 9.46992i −0.831634 + 0.480144i −0.854412 0.519596i \(-0.826082\pi\)
0.0227777 + 0.999741i \(0.492749\pi\)
\(390\) 0 0
\(391\) 24.7894i 1.25365i
\(392\) −2.18007 + 13.2598i −0.110110 + 0.669721i
\(393\) −9.83780 + 6.23820i −0.496251 + 0.314675i
\(394\) −18.0236 + 31.2177i −0.908014 + 1.57273i
\(395\) 0 0
\(396\) 0.0994198 + 1.19446i 0.00499603 + 0.0600239i
\(397\) 3.64333 6.31044i 0.182854 0.316712i −0.759998 0.649926i \(-0.774800\pi\)
0.942851 + 0.333214i \(0.108133\pi\)
\(398\) 11.3181i 0.567323i
\(399\) 17.6498 + 5.49369i 0.883596 + 0.275028i
\(400\) 0 0
\(401\) −13.7394 7.93243i −0.686111 0.396126i 0.116042 0.993244i \(-0.462979\pi\)
−0.802154 + 0.597118i \(0.796312\pi\)
\(402\) 1.24558 2.38045i 0.0621240 0.118726i
\(403\) 10.2096 5.89451i 0.508576 0.293626i
\(404\) −1.18497 + 2.05242i −0.0589543 + 0.102112i
\(405\) 0 0
\(406\) 34.0073 6.19963i 1.68776 0.307682i
\(407\) −2.67530 −0.132610
\(408\) −18.2827 + 0.759558i −0.905129 + 0.0376037i
\(409\) 22.8109 13.1699i 1.12793 0.651209i 0.184515 0.982830i \(-0.440929\pi\)
0.943413 + 0.331620i \(0.107595\pi\)
\(410\) 0 0
\(411\) 1.46286 + 35.2113i 0.0721575 + 1.73684i
\(412\) −15.9625 −0.786417
\(413\) −24.3190 8.69228i −1.19666 0.427719i
\(414\) −9.75590 + 20.6929i −0.479476 + 1.01700i
\(415\) 0 0
\(416\) −7.77705 13.4702i −0.381301 0.660433i
\(417\) 7.86278 15.0267i 0.385042 0.735860i
\(418\) −1.57515 + 2.72824i −0.0770432 + 0.133443i
\(419\) 14.3499 0.701039 0.350519 0.936555i \(-0.386005\pi\)
0.350519 + 0.936555i \(0.386005\pi\)
\(420\) 0 0
\(421\) −10.0679 −0.490682 −0.245341 0.969437i \(-0.578900\pi\)
−0.245341 + 0.969437i \(0.578900\pi\)
\(422\) −4.84315 + 8.38858i −0.235761 + 0.408350i
\(423\) 0.786241 + 9.44616i 0.0382284 + 0.459288i
\(424\) 11.1004 + 19.2264i 0.539082 + 0.933717i
\(425\) 0 0
\(426\) −2.39613 3.77876i −0.116093 0.183082i
\(427\) −20.7575 + 3.78415i −1.00453 + 0.183128i
\(428\) 5.76190 0.278512
\(429\) −2.70237 + 0.112271i −0.130472 + 0.00542047i
\(430\) 0 0
\(431\) −7.13983 + 4.12218i −0.343914 + 0.198559i −0.662001 0.749503i \(-0.730293\pi\)
0.318088 + 0.948061i \(0.396959\pi\)
\(432\) −23.8537 10.0581i −1.14766 0.483919i
\(433\) 10.7241 0.515367 0.257683 0.966229i \(-0.417041\pi\)
0.257683 + 0.966229i \(0.417041\pi\)
\(434\) −10.0961 11.8916i −0.484631 0.570816i
\(435\) 0 0
\(436\) −3.39206 + 5.87521i −0.162450 + 0.281372i
\(437\) −15.7356 + 9.08496i −0.752737 + 0.434593i
\(438\) 20.2602 + 10.6013i 0.968071 + 0.506548i
\(439\) 2.74233 + 1.58329i 0.130884 + 0.0755661i 0.564013 0.825766i \(-0.309257\pi\)
−0.433128 + 0.901332i \(0.642590\pi\)
\(440\) 0 0
\(441\) 18.9667 9.01472i 0.903175 0.429273i
\(442\) 31.5375i 1.50009i
\(443\) −8.72667 + 15.1150i −0.414617 + 0.718137i −0.995388 0.0959297i \(-0.969418\pi\)
0.580772 + 0.814067i \(0.302751\pi\)
\(444\) −4.03319 + 7.70791i −0.191407 + 0.365801i
\(445\) 0 0
\(446\) 4.93911 8.55480i 0.233874 0.405081i
\(447\) −15.1225 23.8485i −0.715268 1.12800i
\(448\) 4.40700 3.74161i 0.208211 0.176774i
\(449\) 12.2873i 0.579876i 0.957046 + 0.289938i \(0.0936346\pi\)
−0.957046 + 0.289938i \(0.906365\pi\)
\(450\) 0 0
\(451\) 2.49985 1.44329i 0.117713 0.0679618i
\(452\) 7.53105 + 13.0442i 0.354231 + 0.613546i
\(453\) −1.08470 26.1090i −0.0509637 1.22671i
\(454\) 19.3215i 0.906801i
\(455\) 0 0
\(456\) −7.18250 11.3270i −0.336351 0.530434i
\(457\) −4.23430 2.44467i −0.198072 0.114357i 0.397684 0.917523i \(-0.369814\pi\)
−0.595756 + 0.803165i \(0.703147\pi\)
\(458\) 1.54180 0.890158i 0.0720435 0.0415943i
\(459\) 17.2641 + 22.7966i 0.805818 + 1.06405i
\(460\) 0 0
\(461\) 5.12746 0.238810 0.119405 0.992846i \(-0.461901\pi\)
0.119405 + 0.992846i \(0.461901\pi\)
\(462\) 0.787463 + 3.49121i 0.0366361 + 0.162426i
\(463\) 39.9073i 1.85465i −0.374257 0.927325i \(-0.622102\pi\)
0.374257 0.927325i \(-0.377898\pi\)
\(464\) −33.2981 19.2247i −1.54583 0.892483i
\(465\) 0 0
\(466\) −3.28845 5.69577i −0.152335 0.263851i
\(467\) −7.90350 4.56309i −0.365730 0.211155i 0.305861 0.952076i \(-0.401056\pi\)
−0.671592 + 0.740922i \(0.734389\pi\)
\(468\) −3.75054 + 7.95516i −0.173369 + 0.367727i
\(469\) 0.815897 2.28269i 0.0376746 0.105405i
\(470\) 0 0
\(471\) 0.895198 + 21.5476i 0.0412486 + 0.992860i
\(472\) 9.36925 + 16.2280i 0.431254 + 0.746955i
\(473\) 1.92704 + 3.33773i 0.0886053 + 0.153469i
\(474\) 0.872760 + 21.0075i 0.0400872 + 0.964907i
\(475\) 0 0
\(476\) 12.4058 2.26161i 0.568619 0.103661i
\(477\) 14.7951 31.3815i 0.677422 1.43686i
\(478\) 9.38775 + 5.42002i 0.429386 + 0.247906i
\(479\) −6.20210 10.7424i −0.283381 0.490831i 0.688834 0.724919i \(-0.258123\pi\)
−0.972215 + 0.234088i \(0.924790\pi\)
\(480\) 0 0
\(481\) −17.0006 9.81532i −0.775162 0.447540i
\(482\) 3.83332i 0.174603i
\(483\) −6.13473 + 19.7093i −0.279140 + 0.896805i
\(484\) 9.34243 0.424656
\(485\) 0 0
\(486\) 5.43955 + 25.8237i 0.246743 + 1.17139i
\(487\) 12.2665 7.08208i 0.555849 0.320920i −0.195628 0.980678i \(-0.562675\pi\)
0.751478 + 0.659758i \(0.229341\pi\)
\(488\) 13.2583 + 7.65467i 0.600174 + 0.346511i
\(489\) −5.10507 8.05083i −0.230859 0.364071i
\(490\) 0 0
\(491\) 32.1216i 1.44963i 0.688946 + 0.724813i \(0.258074\pi\)
−0.688946 + 0.724813i \(0.741926\pi\)
\(492\) −0.389621 9.37826i −0.0175655 0.422805i
\(493\) 21.2361 + 36.7819i 0.956424 + 1.65658i
\(494\) −20.0191 + 11.5580i −0.900703 + 0.520021i
\(495\) 0 0
\(496\) 17.3511i 0.779086i
\(497\) −2.61294 3.07762i −0.117206 0.138050i
\(498\) 27.5791 + 43.4929i 1.23585 + 1.94897i
\(499\) 13.3589 23.1383i 0.598027 1.03581i −0.395085 0.918644i \(-0.629285\pi\)
0.993112 0.117168i \(-0.0373817\pi\)
\(500\) 0 0
\(501\) −0.641627 + 1.22622i −0.0286658 + 0.0547837i
\(502\) −11.2768 + 19.5320i −0.503310 + 0.871758i
\(503\) 9.55539i 0.426054i −0.977046 0.213027i \(-0.931668\pi\)
0.977046 0.213027i \(-0.0683322\pi\)
\(504\) −14.7240 3.92059i −0.655860 0.174637i
\(505\) 0 0
\(506\) −3.04659 1.75895i −0.135438 0.0781950i
\(507\) 2.36594 + 1.23799i 0.105075 + 0.0549810i
\(508\) 9.41716 5.43700i 0.417819 0.241228i
\(509\) 9.10071 15.7629i 0.403382 0.698678i −0.590750 0.806855i \(-0.701168\pi\)
0.994132 + 0.108177i \(0.0345013\pi\)
\(510\) 0 0
\(511\) 19.4282 + 6.94417i 0.859452 + 0.307192i
\(512\) 3.76451 0.166369
\(513\) −8.14360 + 19.3134i −0.359549 + 0.852706i
\(514\) −28.7259 + 16.5849i −1.26705 + 0.731530i
\(515\) 0 0
\(516\) 12.5216 0.520212i 0.551232 0.0229010i
\(517\) −1.45758 −0.0641042
\(518\) −8.74273 + 24.4601i −0.384133 + 1.07472i
\(519\) −13.4669 21.2376i −0.591130 0.932228i
\(520\) 0 0
\(521\) −1.93741 3.35569i −0.0848794 0.147015i 0.820460 0.571703i \(-0.193717\pi\)
−0.905340 + 0.424688i \(0.860384\pi\)
\(522\) 3.25122 + 39.0612i 0.142302 + 1.70966i
\(523\) −9.42099 + 16.3176i −0.411951 + 0.713520i −0.995103 0.0988429i \(-0.968486\pi\)
0.583152 + 0.812363i \(0.301819\pi\)
\(524\) −5.82474 −0.254455
\(525\) 0 0
\(526\) −28.3967 −1.23816
\(527\) 9.58321 16.5986i 0.417451 0.723047i
\(528\) 1.84557 3.52711i 0.0803183 0.153498i
\(529\) 1.35494 + 2.34682i 0.0589104 + 0.102036i
\(530\) 0 0
\(531\) 12.4878 26.4875i 0.541924 1.14946i
\(532\) 5.98216 + 7.04601i 0.259359 + 0.305483i
\(533\) 21.1809 0.917448
\(534\) −0.329235 7.92475i −0.0142474 0.342937i
\(535\) 0 0
\(536\) −1.52324 + 0.879440i −0.0657937 + 0.0379860i
\(537\) −4.08532 + 0.169725i −0.176295 + 0.00732419i
\(538\) 49.6721 2.14152
\(539\) 1.13952 + 3.02147i 0.0490824 + 0.130144i
\(540\) 0 0
\(541\) −11.0977 + 19.2218i −0.477128 + 0.826410i −0.999656 0.0262117i \(-0.991656\pi\)
0.522528 + 0.852622i \(0.324989\pi\)
\(542\) −4.35306 + 2.51324i −0.186980 + 0.107953i
\(543\) 7.79483 14.8968i 0.334508 0.639285i
\(544\) −21.8997 12.6438i −0.938944 0.542099i
\(545\) 0 0
\(546\) −7.80472 + 25.0746i −0.334011 + 1.07309i
\(547\) 1.23468i 0.0527911i −0.999652 0.0263956i \(-0.991597\pi\)
0.999652 0.0263956i \(-0.00840295\pi\)
\(548\) −8.81083 + 15.2608i −0.376380 + 0.651910i
\(549\) −1.98449 23.8423i −0.0846959 1.01756i
\(550\) 0 0
\(551\) −15.5654 + 26.9601i −0.663109 + 1.14854i
\(552\) 12.6487 8.02060i 0.538364 0.341379i
\(553\) 3.40242 + 18.6636i 0.144685 + 0.793656i
\(554\) 22.0513i 0.936868i
\(555\) 0 0
\(556\) 7.34403 4.24008i 0.311456 0.179819i
\(557\) −1.15681 2.00365i −0.0490155 0.0848973i 0.840477 0.541848i \(-0.182275\pi\)
−0.889492 + 0.456950i \(0.848942\pi\)
\(558\) 14.5320 10.0842i 0.615188 0.426898i
\(559\) 28.2802i 1.19612i
\(560\) 0 0
\(561\) −3.71360 + 2.35481i −0.156788 + 0.0994203i
\(562\) −28.5023 16.4558i −1.20230 0.694146i
\(563\) 15.7239 9.07818i 0.662682 0.382600i −0.130616 0.991433i \(-0.541696\pi\)
0.793298 + 0.608833i \(0.208362\pi\)
\(564\) −2.19740 + 4.19948i −0.0925270 + 0.176830i
\(565\) 0 0
\(566\) 9.54745 0.401309
\(567\) 8.08459 + 22.3973i 0.339521 + 0.940599i
\(568\) 2.92930i 0.122911i
\(569\) 12.9811 + 7.49465i 0.544197 + 0.314192i 0.746778 0.665073i \(-0.231600\pi\)
−0.202581 + 0.979265i \(0.564933\pi\)
\(570\) 0 0
\(571\) −11.6375 20.1568i −0.487015 0.843535i 0.512873 0.858464i \(-0.328581\pi\)
−0.999889 + 0.0149293i \(0.995248\pi\)
\(572\) −1.17123 0.676208i −0.0489715 0.0282737i
\(573\) −4.68459 7.38771i −0.195701 0.308626i
\(574\) −5.02655 27.5726i −0.209804 1.15086i
\(575\) 0 0
\(576\) 3.73718 + 5.38551i 0.155716 + 0.224396i
\(577\) 13.3341 + 23.0953i 0.555105 + 0.961471i 0.997895 + 0.0648455i \(0.0206554\pi\)
−0.442790 + 0.896625i \(0.646011\pi\)
\(578\) 11.2466 + 19.4797i 0.467797 + 0.810248i
\(579\) 22.6766 0.942104i 0.942408 0.0391525i
\(580\) 0 0
\(581\) 30.0745 + 35.4229i 1.24770 + 1.46959i
\(582\) −11.0013 + 6.97601i −0.456021 + 0.289165i
\(583\) 4.62026 + 2.66751i 0.191351 + 0.110477i
\(584\) −7.48499 12.9644i −0.309731 0.536470i
\(585\) 0 0
\(586\) 31.6325 + 18.2630i 1.30673 + 0.754439i
\(587\) 45.9722i 1.89748i −0.316065 0.948738i \(-0.602362\pi\)
0.316065 0.948738i \(-0.397638\pi\)
\(588\) 10.4232 + 1.27197i 0.429845 + 0.0524553i
\(589\) 14.0484 0.578856
\(590\) 0 0
\(591\) −32.6767 17.0982i −1.34414 0.703327i
\(592\) 25.0215 14.4462i 1.02838 0.593735i
\(593\) −2.68984 1.55298i −0.110458 0.0637732i 0.443753 0.896149i \(-0.353647\pi\)
−0.554211 + 0.832376i \(0.686980\pi\)
\(594\) −4.02666 + 0.504187i −0.165216 + 0.0206871i
\(595\) 0 0
\(596\) 14.1202i 0.578385i
\(597\) −11.5695 + 0.480657i −0.473508 + 0.0196720i
\(598\) −12.9067 22.3551i −0.527795 0.914168i
\(599\) −7.34708 + 4.24184i −0.300193 + 0.173317i −0.642530 0.766261i \(-0.722115\pi\)
0.342336 + 0.939577i \(0.388782\pi\)
\(600\) 0 0
\(601\) 2.63388i 0.107438i −0.998556 0.0537191i \(-0.982892\pi\)
0.998556 0.0537191i \(-0.0171076\pi\)
\(602\) 36.8141 6.71131i 1.50043 0.273533i
\(603\) 2.48624 + 1.17216i 0.101247 + 0.0477341i
\(604\) 6.53319 11.3158i 0.265832 0.460434i
\(605\) 0 0
\(606\) −7.10949 3.72007i −0.288803 0.151118i
\(607\) 15.1355 26.2154i 0.614330 1.06405i −0.376171 0.926550i \(-0.622760\pi\)
0.990502 0.137501i \(-0.0439070\pi\)
\(608\) 18.5351i 0.751698i
\(609\) 7.78159 + 34.4996i 0.315326 + 1.39799i
\(610\) 0 0
\(611\) −9.26241 5.34766i −0.374717 0.216343i
\(612\) 1.18604 + 14.2494i 0.0479427 + 0.575999i
\(613\) −15.6207 + 9.01861i −0.630914 + 0.364258i −0.781106 0.624399i \(-0.785344\pi\)
0.150192 + 0.988657i \(0.452011\pi\)
\(614\) 19.4086 33.6167i 0.783267 1.35666i
\(615\) 0 0
\(616\) 0.788604 2.20633i 0.0317738 0.0888956i
\(617\) 11.2586 0.453254 0.226627 0.973982i \(-0.427230\pi\)
0.226627 + 0.973982i \(0.427230\pi\)
\(618\) −2.24336 53.9982i −0.0902414 2.17213i
\(619\) 5.23950 3.02503i 0.210593 0.121586i −0.390994 0.920393i \(-0.627869\pi\)
0.601587 + 0.798807i \(0.294535\pi\)
\(620\) 0 0
\(621\) −21.5670 9.09385i −0.865454 0.364924i
\(622\) 2.70540 0.108477
\(623\) −1.28351 7.04054i −0.0514227 0.282073i
\(624\) 24.6685 15.6424i 0.987530 0.626198i
\(625\) 0 0
\(626\) −24.4498 42.3482i −0.977209 1.69258i
\(627\) −2.85575 1.49428i −0.114048 0.0596759i
\(628\) −5.39180 + 9.33888i −0.215156 + 0.372662i
\(629\) −31.9152 −1.27254
\(630\) 0 0
\(631\) 47.3970 1.88684 0.943422 0.331594i \(-0.107586\pi\)
0.943422 + 0.331594i \(0.107586\pi\)
\(632\) 6.88249 11.9208i 0.273771 0.474185i
\(633\) −8.78063 4.59450i −0.348999 0.182615i
\(634\) 5.55316 + 9.61836i 0.220544 + 0.381994i
\(635\) 0 0
\(636\) 14.6508 9.29014i 0.580942 0.368378i
\(637\) −3.84415 + 23.3812i −0.152311 + 0.926397i
\(638\) −6.02728 −0.238622
\(639\) 3.76096 2.60984i 0.148781 0.103244i
\(640\) 0 0
\(641\) 2.08690 1.20488i 0.0824278 0.0475897i −0.458220 0.888839i \(-0.651513\pi\)
0.540647 + 0.841249i \(0.318179\pi\)
\(642\) 0.809774 + 19.4914i 0.0319592 + 0.769265i
\(643\) 30.1631 1.18952 0.594759 0.803904i \(-0.297247\pi\)
0.594759 + 0.803904i \(0.297247\pi\)
\(644\) −7.86819 + 6.68020i −0.310050 + 0.263237i
\(645\) 0 0
\(646\) −18.7909 + 32.5468i −0.739319 + 1.28054i
\(647\) −12.1065 + 6.98967i −0.475954 + 0.274792i −0.718729 0.695291i \(-0.755276\pi\)
0.242775 + 0.970083i \(0.421942\pi\)
\(648\) 6.04609 16.1847i 0.237513 0.635797i
\(649\) 3.89972 + 2.25150i 0.153077 + 0.0883792i
\(650\) 0 0
\(651\) 11.7270 10.8255i 0.459619 0.424283i
\(652\) 4.76671i 0.186679i
\(653\) 3.42169 5.92653i 0.133901 0.231923i −0.791276 0.611459i \(-0.790583\pi\)
0.925177 + 0.379536i \(0.123916\pi\)
\(654\) −20.3515 10.6490i −0.795805 0.416408i
\(655\) 0 0
\(656\) −15.5870 + 26.9975i −0.608572 + 1.05408i
\(657\) −9.97636 + 21.1606i −0.389215 + 0.825552i
\(658\) −4.76328 + 13.3266i −0.185692 + 0.519523i
\(659\) 10.0735i 0.392409i 0.980563 + 0.196204i \(0.0628616\pi\)
−0.980563 + 0.196204i \(0.937138\pi\)
\(660\) 0 0
\(661\) −8.84503 + 5.10668i −0.344032 + 0.198627i −0.662053 0.749457i \(-0.730315\pi\)
0.318022 + 0.948083i \(0.396981\pi\)
\(662\) 11.4527 + 19.8367i 0.445123 + 0.770976i
\(663\) −32.2382 + 1.33934i −1.25203 + 0.0520157i
\(664\) 33.7158i 1.30843i
\(665\) 0 0
\(666\) −26.6412 12.5603i −1.03233 0.486701i
\(667\) −30.1060 17.3817i −1.16571 0.673022i
\(668\) −0.599296 + 0.346004i −0.0231875 + 0.0133873i
\(669\) 8.95461 + 4.68554i 0.346205 + 0.181153i
\(670\) 0 0
\(671\) 3.67895 0.142024
\(672\) −14.2828 15.4723i −0.550972 0.596858i
\(673\) 19.1004i 0.736266i −0.929773 0.368133i \(-0.879997\pi\)
0.929773 0.368133i \(-0.120003\pi\)
\(674\) 45.0282 + 25.9971i 1.73442 + 1.00137i
\(675\) 0 0
\(676\) 0.667597 + 1.15631i 0.0256768 + 0.0444735i
\(677\) 3.44314 + 1.98790i 0.132331 + 0.0764011i 0.564704 0.825294i \(-0.308990\pi\)
−0.432373 + 0.901695i \(0.642324\pi\)
\(678\) −43.0675 + 27.3094i −1.65400 + 1.04881i
\(679\) −8.96006 + 7.60721i −0.343855 + 0.291938i
\(680\) 0 0
\(681\) −19.7507 + 0.820547i −0.756849 + 0.0314434i
\(682\) 1.35997 + 2.35553i 0.0520759 + 0.0901981i
\(683\) 5.32313 + 9.21993i 0.203684 + 0.352791i 0.949713 0.313123i \(-0.101375\pi\)
−0.746029 + 0.665914i \(0.768042\pi\)
\(684\) −8.61047 + 5.97507i −0.329229 + 0.228463i
\(685\) 0 0
\(686\) 31.3491 0.544533i 1.19691 0.0207904i
\(687\) 0.975412 + 1.53825i 0.0372143 + 0.0586879i
\(688\) −36.0464 20.8114i −1.37426 0.793427i
\(689\) 19.5735 + 33.9022i 0.745689 + 1.29157i
\(690\) 0 0
\(691\) 14.3020 + 8.25729i 0.544076 + 0.314122i 0.746729 0.665128i \(-0.231623\pi\)
−0.202653 + 0.979251i \(0.564956\pi\)
\(692\) 12.5743i 0.478004i
\(693\) −3.53533 + 0.953223i −0.134296 + 0.0362099i
\(694\) 13.2401 0.502586
\(695\) 0 0
\(696\) 11.8969 22.7364i 0.450951 0.861820i
\(697\) 29.8222 17.2178i 1.12960 0.652172i
\(698\) −36.8735 21.2889i −1.39568 0.805797i
\(699\) 5.68265 3.60340i 0.214938 0.136293i
\(700\) 0 0
\(701\) 19.5702i 0.739158i −0.929199 0.369579i \(-0.879502\pi\)
0.929199 0.369579i \(-0.120498\pi\)
\(702\) −27.4379 11.5694i −1.03558 0.436657i
\(703\) −11.6965 20.2589i −0.441141 0.764078i
\(704\) −0.872955 + 0.504001i −0.0329007 + 0.0189952i
\(705\) 0 0
\(706\) 20.7706i 0.781712i
\(707\) −6.81752 2.43677i −0.256399 0.0916441i
\(708\) 12.3660 7.84133i 0.464742 0.294695i
\(709\) 14.1418 24.4943i 0.531106 0.919903i −0.468235 0.883604i \(-0.655110\pi\)
0.999341 0.0362991i \(-0.0115569\pi\)
\(710\) 0 0
\(711\) −21.4372 + 1.78430i −0.803956 + 0.0669165i
\(712\) −2.59631 + 4.49694i −0.0973009 + 0.168530i
\(713\) 15.6877i 0.587509i
\(714\) 9.39411 + 41.6487i 0.351566 + 1.55866i
\(715\) 0 0
\(716\) −1.77061 1.02226i −0.0661707 0.0382037i
\(717\) −5.14176 + 9.82650i −0.192022 + 0.366977i
\(718\) −12.0466 + 6.95509i −0.449574 + 0.259562i
\(719\) −9.75873 + 16.9026i −0.363939 + 0.630361i −0.988605 0.150531i \(-0.951902\pi\)
0.624666 + 0.780892i \(0.285235\pi\)
\(720\) 0 0
\(721\) −8.74566 47.9733i −0.325705 1.78662i
\(722\) 4.61959 0.171923
\(723\) −3.91849 + 0.162794i −0.145730 + 0.00605438i
\(724\) 7.28057 4.20344i 0.270580 0.156220i
\(725\) 0 0
\(726\) 1.31298 + 31.6037i 0.0487293 + 1.17292i
\(727\) 26.5060 0.983052 0.491526 0.870863i \(-0.336439\pi\)
0.491526 + 0.870863i \(0.336439\pi\)
\(728\) 13.1061 11.1272i 0.485743 0.412402i
\(729\) −26.1665 + 6.65709i −0.969128 + 0.246559i
\(730\) 0 0
\(731\) 22.9888 + 39.8177i 0.850271 + 1.47271i
\(732\) 5.54627 10.5996i 0.204996 0.391771i
\(733\) −0.106580 + 0.184602i −0.00393663 + 0.00681844i −0.867987 0.496587i \(-0.834586\pi\)
0.864050 + 0.503405i \(0.167920\pi\)
\(734\) 47.2420 1.74373
\(735\) 0 0
\(736\) 20.6979 0.762935
\(737\) −0.211336 + 0.366045i −0.00778467 + 0.0134835i
\(738\) 31.6701 2.63603i 1.16579 0.0970337i
\(739\) −23.2265 40.2296i −0.854402 1.47987i −0.877198 0.480128i \(-0.840590\pi\)
0.0227959 0.999740i \(-0.492743\pi\)
\(740\) 0 0
\(741\) −12.6650 19.9730i −0.465261 0.733728i
\(742\) 39.4876 33.5255i 1.44964 1.23076i
\(743\) −28.0937 −1.03066 −0.515330 0.856992i \(-0.672330\pi\)
−0.515330 + 0.856992i \(0.672330\pi\)
\(744\) −11.5700 + 0.480678i −0.424177 + 0.0176225i
\(745\) 0 0
\(746\) 26.5135 15.3076i 0.970729 0.560451i
\(747\) −43.2880 + 30.0389i −1.58382 + 1.09907i
\(748\) −2.19874 −0.0803939
\(749\) 3.15687 + 17.3166i 0.115349 + 0.632736i
\(750\) 0 0
\(751\) −12.4832 + 21.6215i −0.455518 + 0.788981i −0.998718 0.0506227i \(-0.983879\pi\)
0.543199 + 0.839604i \(0.317213\pi\)
\(752\) 13.6324 7.87068i 0.497123 0.287014i
\(753\) −20.4449 10.6979i −0.745053 0.389852i
\(754\) −38.3014 22.1133i −1.39485 0.805319i
\(755\) 0 0
\(756\) −2.58338 + 11.6228i −0.0939566 + 0.422718i
\(757\) 6.25577i 0.227370i 0.993517 + 0.113685i \(0.0362655\pi\)
−0.993517 + 0.113685i \(0.963735\pi\)
\(758\) 20.9460 36.2796i 0.760794 1.31773i
\(759\) 1.66865 3.18898i 0.0605680 0.115753i
\(760\) 0 0
\(761\) 26.3374 45.6178i 0.954731 1.65364i 0.219750 0.975556i \(-0.429476\pi\)
0.734982 0.678087i \(-0.237191\pi\)
\(762\) 19.7158 + 31.0924i 0.714229 + 1.12636i
\(763\) −19.5157 6.97543i −0.706514 0.252528i
\(764\) 4.37410i 0.158249i
\(765\) 0 0
\(766\) −18.9563 + 10.9444i −0.684917 + 0.395437i
\(767\) 16.5209 + 28.6151i 0.596536 + 1.03323i
\(768\) 1.25463 + 30.1992i 0.0452725 + 1.08972i
\(769\) 5.37059i 0.193669i −0.995301 0.0968343i \(-0.969128\pi\)
0.995301 0.0968343i \(-0.0308717\pi\)
\(770\) 0 0
\(771\) −18.1733 28.6598i −0.654496 1.03216i
\(772\) 9.82820 + 5.67432i 0.353725 + 0.204223i
\(773\) −2.12434 + 1.22649i −0.0764073 + 0.0441138i −0.537717 0.843125i \(-0.680713\pi\)
0.461310 + 0.887239i \(0.347380\pi\)
\(774\) 3.51956 + 42.2851i 0.126508 + 1.51991i
\(775\) 0 0
\(776\) 8.52826 0.306147
\(777\) −25.3749 7.89819i −0.910318 0.283346i
\(778\) 32.0641i 1.14956i
\(779\) 21.8588 + 12.6202i 0.783172 + 0.452165i
\(780\) 0 0
\(781\) 0.351967 + 0.609625i 0.0125944 + 0.0218141i
\(782\) −36.3446 20.9836i −1.29968 0.750371i
\(783\) −39.7909 + 4.98230i −1.42201 + 0.178053i
\(784\) −26.9731 22.1060i −0.963326 0.789501i
\(785\) 0 0
\(786\) −0.818606 19.7040i −0.0291987 0.702818i
\(787\) −20.6048 35.6885i −0.734481 1.27216i −0.954951 0.296764i \(-0.904092\pi\)
0.220470 0.975394i \(-0.429241\pi\)
\(788\) −9.22039 15.9702i −0.328463 0.568914i
\(789\) −1.20596 29.0276i −0.0429332 1.03341i
\(790\) 0 0
\(791\) −35.0764 + 29.7803i −1.24717 + 1.05887i
\(792\) 2.40307 + 1.13295i 0.0853893 + 0.0402576i
\(793\) 23.3785 + 13.4976i 0.830196 + 0.479314i
\(794\) 6.16797 + 10.6832i 0.218893 + 0.379134i
\(795\) 0 0
\(796\) −5.01431 2.89501i −0.177727 0.102611i
\(797\) 36.9407i 1.30851i −0.756276 0.654253i \(-0.772983\pi\)
0.756276 0.654253i \(-0.227017\pi\)
\(798\) −22.9946 + 21.2267i −0.814000 + 0.751419i
\(799\) −17.3883 −0.615154
\(800\) 0 0
\(801\) 8.08683 0.673099i 0.285734 0.0237828i
\(802\) 23.2600 13.4292i 0.821339 0.474200i
\(803\) −3.11544 1.79870i −0.109942 0.0634748i
\(804\) 0.736023 + 1.16073i 0.0259575 + 0.0409357i
\(805\) 0 0
\(806\) 19.9582i 0.702997i
\(807\) 2.10948 + 50.7756i 0.0742573 + 1.78739i
\(808\) 2.62655 + 4.54931i 0.0924016 + 0.160044i
\(809\) 45.9461 26.5270i 1.61538 0.932640i 0.627285 0.778790i \(-0.284166\pi\)
0.988094 0.153850i \(-0.0491672\pi\)
\(810\) 0 0
\(811\) 19.0686i 0.669590i −0.942291 0.334795i \(-0.891333\pi\)
0.942291 0.334795i \(-0.108667\pi\)
\(812\) −5.95198 + 16.6523i −0.208873 + 0.584380i
\(813\) −2.75394 4.34304i −0.0965850 0.152317i
\(814\) 2.26457 3.92235i 0.0793731 0.137478i
\(815\) 0 0
\(816\) 22.0169 42.0769i 0.770747 1.47299i
\(817\) −16.8501 + 29.1852i −0.589511 + 1.02106i
\(818\) 44.5918i 1.55912i
\(819\) −25.9631 6.91324i −0.907223 0.241568i
\(820\) 0 0
\(821\) −9.46302 5.46348i −0.330262 0.190677i 0.325696 0.945475i \(-0.394402\pi\)
−0.655957 + 0.754798i \(0.727735\pi\)
\(822\) −52.8627 27.6606i −1.84380 0.964776i
\(823\) 36.3622 20.9937i 1.26750 0.731794i 0.292990 0.956116i \(-0.405350\pi\)
0.974515 + 0.224321i \(0.0720165\pi\)
\(824\) −17.6909 + 30.6416i −0.616293 + 1.06745i
\(825\) 0 0
\(826\) 33.3294 28.2971i 1.15968 0.984584i
\(827\) −22.1128 −0.768937 −0.384468 0.923138i \(-0.625615\pi\)
−0.384468 + 0.923138i \(0.625615\pi\)
\(828\) −6.67229 9.61520i −0.231878 0.334151i
\(829\) −27.1141 + 15.6543i −0.941711 + 0.543697i −0.890496 0.454990i \(-0.849643\pi\)
−0.0512148 + 0.998688i \(0.516309\pi\)
\(830\) 0 0
\(831\) 22.5412 0.936477i 0.781944 0.0324860i
\(832\) −7.39645 −0.256426
\(833\) 13.5940 + 36.0450i 0.471003 + 1.24888i
\(834\) 15.3755 + 24.2476i 0.532410 + 0.839625i
\(835\) 0 0
\(836\) −0.805806 1.39570i −0.0278694 0.0482712i
\(837\) 10.9254 + 14.4266i 0.377636 + 0.498655i
\(838\) −12.1468 + 21.0389i −0.419605 + 0.726777i
\(839\) −8.65688 −0.298869 −0.149434 0.988772i \(-0.547745\pi\)
−0.149434 + 0.988772i \(0.547745\pi\)
\(840\) 0 0
\(841\) −30.5607 −1.05382
\(842\) 8.52225 14.7610i 0.293696 0.508696i
\(843\) 15.6109 29.8343i 0.537669 1.02755i
\(844\) −2.47763 4.29138i −0.0852835 0.147715i
\(845\) 0 0
\(846\) −14.5149 6.84318i −0.499031 0.235273i
\(847\) 5.11859 + 28.0775i 0.175877 + 0.964753i
\(848\) −57.6164 −1.97855
\(849\) 0.405463 + 9.75956i 0.0139154 + 0.334947i
\(850\) 0 0
\(851\) 22.6228 13.0613i 0.775501 0.447736i
\(852\) 2.28703 0.0950150i 0.0783523 0.00325516i
\(853\) −48.3400 −1.65513 −0.827565 0.561370i \(-0.810274\pi\)
−0.827565 + 0.561370i \(0.810274\pi\)
\(854\) 12.0226 33.6365i 0.411405 1.15102i
\(855\) 0 0
\(856\) 6.38579 11.0605i 0.218262 0.378041i
\(857\) −29.1362 + 16.8218i −0.995274 + 0.574622i −0.906847 0.421461i \(-0.861517\pi\)
−0.0884274 + 0.996083i \(0.528184\pi\)
\(858\) 2.12288 4.05708i 0.0724740 0.138506i
\(859\) −22.6082 13.0528i −0.771382 0.445357i 0.0619856 0.998077i \(-0.480257\pi\)
−0.833367 + 0.552720i \(0.813590\pi\)
\(860\) 0 0
\(861\) 27.9717 6.30918i 0.953272 0.215016i
\(862\) 13.9573i 0.475387i
\(863\) 19.6742 34.0767i 0.669718 1.15998i −0.308265 0.951300i \(-0.599748\pi\)
0.977983 0.208685i \(-0.0669182\pi\)
\(864\) 19.0340 14.4146i 0.647550 0.490396i
\(865\) 0 0
\(866\) −9.07765 + 15.7230i −0.308471 + 0.534288i
\(867\) −19.4348 + 12.3237i −0.660042 + 0.418536i
\(868\) 7.85088 1.43124i 0.266476 0.0485793i
\(869\) 3.30783i 0.112211i
\(870\) 0 0
\(871\) −2.68594 + 1.55073i −0.0910097 + 0.0525445i
\(872\) 7.51869 + 13.0227i 0.254615 + 0.441006i
\(873\) −7.59820 10.9495i −0.257160 0.370585i
\(874\) 30.7607i 1.04050i
\(875\) 0 0
\(876\) −9.87904 + 6.26435i −0.333782 + 0.211653i
\(877\) 22.9766 + 13.2655i 0.775864 + 0.447945i 0.834963 0.550307i \(-0.185489\pi\)
−0.0590984 + 0.998252i \(0.518823\pi\)
\(878\) −4.64262 + 2.68042i −0.156681 + 0.0904597i
\(879\) −17.3254 + 33.1109i −0.584371 + 1.11680i
\(880\) 0 0
\(881\) 13.2055 0.444904 0.222452 0.974944i \(-0.428594\pi\)
0.222452 + 0.974944i \(0.428594\pi\)
\(882\) −2.83798 + 35.4384i −0.0955598 + 1.19327i
\(883\) 27.3728i 0.921169i −0.887616 0.460584i \(-0.847640\pi\)
0.887616 0.460584i \(-0.152360\pi\)
\(884\) −13.9723 8.06689i −0.469938 0.271319i
\(885\) 0 0
\(886\) −14.7738 25.5889i −0.496335 0.859677i
\(887\) 28.5105 + 16.4606i 0.957290 + 0.552692i 0.895338 0.445387i \(-0.146934\pi\)
0.0619524 + 0.998079i \(0.480267\pi\)
\(888\) 10.3262 + 16.2846i 0.346523 + 0.546476i
\(889\) 21.4997 + 25.3232i 0.721078 + 0.849313i
\(890\) 0 0
\(891\) −0.686394 4.09471i −0.0229951 0.137178i
\(892\) 2.52672 + 4.37641i 0.0846009 + 0.146533i
\(893\) −6.37256 11.0376i −0.213250 0.369359i
\(894\) 47.7659 1.98444i 1.59753 0.0663697i
\(895\) 0 0
\(896\) 6.11599 + 33.5486i 0.204321 + 1.12078i
\(897\) 22.3036 14.1429i 0.744697 0.472216i
\(898\) −18.0149 10.4009i −0.601165 0.347083i
\(899\) 13.4390 + 23.2770i 0.448216 + 0.776333i
\(900\) 0 0
\(901\) 55.1178 + 31.8223i 1.83624 + 1.06015i
\(902\) 4.88682i 0.162713i
\(903\) 8.42384 + 37.3470i 0.280328 + 1.24283i
\(904\) 33.3860 1.11040
\(905\) 0 0
\(906\) 39.1974 + 20.5102i 1.30225 + 0.681406i
\(907\) −18.0335 + 10.4117i −0.598793 + 0.345714i −0.768567 0.639770i \(-0.779030\pi\)
0.169773 + 0.985483i \(0.445696\pi\)
\(908\) −8.56010 4.94217i −0.284077 0.164012i
\(909\) 3.50079 7.42543i 0.116114 0.246286i
\(910\) 0 0
\(911\) 50.2293i 1.66417i −0.554648 0.832085i \(-0.687147\pi\)
0.554648 0.832085i \(-0.312853\pi\)
\(912\) 34.7781 1.44486i 1.15162 0.0478442i
\(913\) −4.05108 7.01668i −0.134071 0.232218i
\(914\) 7.16844 4.13870i 0.237111 0.136896i
\(915\) 0 0
\(916\) 0.910763i 0.0300925i
\(917\) −3.19130 17.5055i −0.105386 0.578083i
\(918\) −48.0365 + 6.01475i −1.58544 + 0.198516i
\(919\) −9.88707 + 17.1249i −0.326144 + 0.564899i −0.981743 0.190211i \(-0.939083\pi\)
0.655599 + 0.755109i \(0.272416\pi\)
\(920\) 0 0
\(921\) 35.1878 + 18.4121i 1.15948 + 0.606701i
\(922\) −4.34026 + 7.51755i −0.142939 + 0.247577i
\(923\) 5.16529i 0.170017i
\(924\) −1.74815 0.544131i −0.0575100 0.0179006i
\(925\) 0 0
\(926\) 58.5095 + 33.7805i 1.92274 + 1.11009i
\(927\) 55.1026 4.58641i 1.80981 0.150637i
\(928\) 30.7111 17.7310i 1.00814 0.582050i
\(929\) 1.84133 3.18927i 0.0604119 0.104637i −0.834238 0.551405i \(-0.814092\pi\)
0.894650 + 0.446769i \(0.147425\pi\)
\(930\) 0 0
\(931\) −17.8983 + 21.8390i −0.586594 + 0.715745i
\(932\) 3.36457 0.110210
\(933\) 0.114894 + 2.76551i 0.00376145 + 0.0905387i
\(934\) 13.3802 7.72506i 0.437814 0.252772i
\(935\) 0 0
\(936\) 11.1140 + 16.0161i 0.363274 + 0.523501i
\(937\) 36.7871 1.20178 0.600891 0.799331i \(-0.294813\pi\)
0.600891 + 0.799331i \(0.294813\pi\)
\(938\) 2.65610 + 3.12845i 0.0867247 + 0.102148i
\(939\) 42.2507 26.7914i 1.37880 0.874305i
\(940\) 0 0
\(941\) 10.1072 + 17.5061i 0.329484 + 0.570684i 0.982410 0.186739i \(-0.0597917\pi\)
−0.652925 + 0.757422i \(0.726458\pi\)
\(942\) −32.3494 16.9270i −1.05400 0.551511i
\(943\) −14.0928 + 24.4094i −0.458924 + 0.794880i
\(944\) −48.6310 −1.58280
\(945\) 0 0
\(946\) −6.52474 −0.212138
\(947\) 4.91182 8.50752i 0.159613 0.276457i −0.775116 0.631819i \(-0.782309\pi\)
0.934729 + 0.355361i \(0.115642\pi\)
\(948\) −9.53032 4.98678i −0.309530 0.161963i
\(949\) −13.1984 22.8603i −0.428438 0.742076i
\(950\) 0 0
\(951\) −9.59621 + 6.08501i −0.311179 + 0.197320i
\(952\) 9.40772 26.3206i 0.304906 0.853057i
\(953\) 24.7365 0.801294 0.400647 0.916232i \(-0.368785\pi\)
0.400647 + 0.916232i \(0.368785\pi\)
\(954\) 33.4858 + 48.2552i 1.08414 + 1.56232i
\(955\) 0 0
\(956\) −4.80253 + 2.77274i −0.155325 + 0.0896769i
\(957\) −0.255968 6.16119i −0.00827426 0.199163i
\(958\) 20.9996 0.678468
\(959\) −50.6917 18.1186i −1.63692 0.585081i
\(960\) 0 0
\(961\) −9.43537 + 16.3425i −0.304367 + 0.527179i
\(962\) 28.7812 16.6168i 0.927942 0.535748i
\(963\) −19.8901 + 1.65553i −0.640948 + 0.0533487i
\(964\) −1.69830 0.980514i −0.0546986 0.0315802i
\(965\) 0 0
\(966\) −23.7036 25.6778i −0.762652 0.826168i
\(967\) 14.0157i 0.450713i 0.974276 + 0.225357i \(0.0723547\pi\)
−0.974276 + 0.225357i \(0.927645\pi\)
\(968\) 10.3540 17.9337i 0.332791 0.576410i
\(969\) −34.0679 17.8262i −1.09442 0.572660i
\(970\) 0 0
\(971\) −0.0308306 + 0.0534003i −0.000989403 + 0.00171370i −0.866520 0.499143i \(-0.833648\pi\)
0.865530 + 0.500857i \(0.166982\pi\)
\(972\) −12.8322 4.19546i −0.411593 0.134569i
\(973\) 16.7667 + 19.7485i 0.537516 + 0.633106i
\(974\) 23.9792i 0.768342i
\(975\) 0 0
\(976\) −34.4085 + 19.8657i −1.10139 + 0.635887i
\(977\) 9.53996 + 16.5237i 0.305210 + 0.528640i 0.977308 0.211822i \(-0.0679399\pi\)
−0.672098 + 0.740462i \(0.734607\pi\)
\(978\) 16.1249 0.669912i 0.515617 0.0214214i
\(979\) 1.24783i 0.0398808i
\(980\) 0 0
\(981\) 10.0213 21.2558i 0.319955 0.678647i
\(982\) −47.0945 27.1900i −1.50285 0.867669i
\(983\) −7.05465 + 4.07300i −0.225008 + 0.129909i −0.608267 0.793732i \(-0.708135\pi\)
0.383259 + 0.923641i \(0.374802\pi\)
\(984\) −18.4343 9.64581i −0.587663 0.307497i
\(985\) 0 0
\(986\) −71.9030 −2.28986
\(987\) −13.8249 4.30315i −0.440052 0.136971i
\(988\) 11.8256i 0.376222i
\(989\) −32.5908 18.8163i −1.03633 0.598324i
\(990\) 0 0
\(991\) −5.21862 9.03891i −0.165775 0.287130i 0.771155 0.636647i \(-0.219679\pi\)
−0.936930 + 0.349517i \(0.886346\pi\)
\(992\) −13.8590 8.00150i −0.440024 0.254048i
\(993\) −19.7910 + 12.5496i −0.628050 + 0.398250i
\(994\) 6.72398 1.22580i 0.213272 0.0388800i
\(995\) 0 0
\(996\) −26.3233 + 1.09361i −0.834086 + 0.0346522i
\(997\) 6.74411 + 11.6811i 0.213588 + 0.369945i 0.952835 0.303489i \(-0.0981517\pi\)
−0.739247 + 0.673435i \(0.764818\pi\)
\(998\) 22.6159 + 39.1719i 0.715894 + 1.23996i
\(999\) 11.7079 27.7665i 0.370422 0.878494i
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 525.2.q.g.299.5 40
3.2 odd 2 inner 525.2.q.g.299.15 40
5.2 odd 4 525.2.t.h.26.3 20
5.3 odd 4 525.2.t.i.26.8 yes 20
5.4 even 2 inner 525.2.q.g.299.16 40
7.3 odd 6 inner 525.2.q.g.374.6 40
15.2 even 4 525.2.t.h.26.8 yes 20
15.8 even 4 525.2.t.i.26.3 yes 20
15.14 odd 2 inner 525.2.q.g.299.6 40
21.17 even 6 inner 525.2.q.g.374.16 40
35.3 even 12 525.2.t.i.101.3 yes 20
35.17 even 12 525.2.t.h.101.8 yes 20
35.24 odd 6 inner 525.2.q.g.374.15 40
105.17 odd 12 525.2.t.h.101.3 yes 20
105.38 odd 12 525.2.t.i.101.8 yes 20
105.59 even 6 inner 525.2.q.g.374.5 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
525.2.q.g.299.5 40 1.1 even 1 trivial
525.2.q.g.299.6 40 15.14 odd 2 inner
525.2.q.g.299.15 40 3.2 odd 2 inner
525.2.q.g.299.16 40 5.4 even 2 inner
525.2.q.g.374.5 40 105.59 even 6 inner
525.2.q.g.374.6 40 7.3 odd 6 inner
525.2.q.g.374.15 40 35.24 odd 6 inner
525.2.q.g.374.16 40 21.17 even 6 inner
525.2.t.h.26.3 20 5.2 odd 4
525.2.t.h.26.8 yes 20 15.2 even 4
525.2.t.h.101.3 yes 20 105.17 odd 12
525.2.t.h.101.8 yes 20 35.17 even 12
525.2.t.i.26.3 yes 20 15.8 even 4
525.2.t.i.26.8 yes 20 5.3 odd 4
525.2.t.i.101.3 yes 20 35.3 even 12
525.2.t.i.101.8 yes 20 105.38 odd 12