Properties

Label 525.2.t.h.101.3
Level $525$
Weight $2$
Character 525.101
Analytic conductor $4.192$
Analytic rank $0$
Dimension $20$
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] = [525,2,Mod(26,525)]
 
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, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.26");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.t (of order \(6\), degree \(2\), 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: \(20\)
Relative dimension: \(10\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 3 x^{19} + 8 x^{18} - 15 x^{17} + 18 x^{16} - 45 x^{15} + 59 x^{14} - 147 x^{13} + 271 x^{12} - 330 x^{11} + 879 x^{10} - 990 x^{9} + 2439 x^{8} - 3969 x^{7} + 4779 x^{6} + \cdots + 59049 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 101.3
Root \(0.803015 + 1.53466i\) of defining polynomial
Character \(\chi\) \(=\) 525.101
Dual form 525.2.t.h.26.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.46613 + 0.846473i) q^{2} +(-0.803015 - 1.53466i) q^{3} +(0.433034 - 0.750036i) q^{4} +(2.47637 + 1.57028i) q^{6} +(1.71236 - 2.01688i) q^{7} -1.91969i q^{8} +(-1.71033 + 2.46470i) q^{9} +O(q^{10})\) \(q+(-1.46613 + 0.846473i) q^{2} +(-0.803015 - 1.53466i) q^{3} +(0.433034 - 0.750036i) q^{4} +(2.47637 + 1.57028i) q^{6} +(1.71236 - 2.01688i) q^{7} -1.91969i q^{8} +(-1.71033 + 2.46470i) q^{9} +(-0.399511 - 0.230658i) q^{11} +(-1.49878 - 0.0622670i) q^{12} -3.38501i q^{13} +(-0.803314 + 4.40649i) q^{14} +(2.49103 + 4.31459i) q^{16} +(-2.75166 + 4.76601i) q^{17} +(0.421275 - 5.06134i) q^{18} +(3.49334 - 2.01688i) q^{19} +(-4.47027 - 1.00830i) q^{21} +0.780983 q^{22} +(-3.90097 + 2.25223i) q^{23} +(-2.94606 + 1.54154i) q^{24} +(2.86532 + 4.96289i) q^{26} +(5.15589 + 0.645580i) q^{27} +(-0.771225 - 2.15771i) q^{28} -7.71756i q^{29} +(-3.01611 - 1.74135i) q^{31} +(-3.97938 - 2.29749i) q^{32} +(-0.0331669 + 0.798334i) q^{33} -9.31681i q^{34} +(1.10798 + 2.35011i) q^{36} +(-2.89964 - 5.02232i) q^{37} +(-3.41448 + 5.91404i) q^{38} +(-5.19483 + 2.71822i) q^{39} -6.25727 q^{41} +(7.40752 - 2.30567i) q^{42} -8.35453 q^{43} +(-0.346004 + 0.199765i) q^{44} +(3.81290 - 6.60414i) q^{46} +(-1.57980 - 2.73630i) q^{47} +(4.62108 - 7.28756i) q^{48} +(-1.13564 - 6.90727i) q^{49} +(9.52380 + 0.395668i) q^{51} +(-2.53888 - 1.46582i) q^{52} +(-10.0154 - 5.78238i) q^{53} +(-8.10570 + 3.41782i) q^{54} +(-3.87179 - 3.28720i) q^{56} +(-5.90043 - 3.74149i) q^{57} +(6.53271 + 11.3150i) q^{58} +(4.88061 - 8.45346i) q^{59} +(-6.90647 + 3.98746i) q^{61} +5.89604 q^{62} +(2.04231 + 7.67001i) q^{63} -2.18506 q^{64} +(-0.627141 - 1.19854i) q^{66} +(0.458116 - 0.793481i) q^{67} +(2.38312 + 4.12768i) q^{68} +(6.58893 + 4.17808i) q^{69} +1.52593i q^{71} +(4.73146 + 3.28331i) q^{72} +(6.75338 + 3.89906i) q^{73} +(8.50252 + 4.90893i) q^{74} -3.49351i q^{76} +(-1.14932 + 0.410798i) q^{77} +(5.31542 - 8.38256i) q^{78} +(3.58521 + 6.20977i) q^{79} +(-3.14952 - 8.43093i) q^{81} +(9.17399 - 5.29661i) q^{82} +17.5632 q^{83} +(-2.69204 + 2.91624i) q^{84} +(12.2489 - 7.07188i) q^{86} +(-11.8438 + 6.19732i) q^{87} +(-0.442791 + 0.766937i) q^{88} +(-1.35247 - 2.34254i) q^{89} +(-6.82718 - 5.79637i) q^{91} +3.90116i q^{92} +(-0.250394 + 6.02703i) q^{93} +(4.63241 + 2.67452i) q^{94} +(-0.330363 + 7.95189i) q^{96} +4.44253i q^{97} +(7.51181 + 9.16569i) q^{98} +(1.25180 - 0.590174i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 3 q^{3} + 14 q^{4} - 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 3 q^{3} + 14 q^{4} - 7 q^{9} + 21 q^{12} - 18 q^{16} - 14 q^{18} - 9 q^{21} - 20 q^{22} + 18 q^{24} + 10 q^{28} + 42 q^{31} - 12 q^{33} - 36 q^{36} - 24 q^{37} - 33 q^{42} - 36 q^{43} - 8 q^{46} - 4 q^{49} + 21 q^{51} + 84 q^{52} - 75 q^{54} - 6 q^{57} + 4 q^{58} - 90 q^{61} + 5 q^{63} - 120 q^{64} + 6 q^{66} - 20 q^{67} + 35 q^{72} + 48 q^{73} + 108 q^{78} + 46 q^{79} + 29 q^{81} - 36 q^{82} + 75 q^{84} - 69 q^{87} - 4 q^{88} - 30 q^{91} + 30 q^{93} + 6 q^{94} + 135 q^{96} + 94 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.46613 + 0.846473i −1.03671 + 0.598547i −0.918901 0.394489i \(-0.870922\pi\)
−0.117813 + 0.993036i \(0.537588\pi\)
\(3\) −0.803015 1.53466i −0.463621 0.886034i
\(4\) 0.433034 0.750036i 0.216517 0.375018i
\(5\) 0 0
\(6\) 2.47637 + 1.57028i 1.01097 + 0.641064i
\(7\) 1.71236 2.01688i 0.647212 0.762310i
\(8\) 1.91969i 0.678712i
\(9\) −1.71033 + 2.46470i −0.570111 + 0.821567i
\(10\) 0 0
\(11\) −0.399511 0.230658i −0.120457 0.0695460i 0.438561 0.898702i \(-0.355488\pi\)
−0.559018 + 0.829156i \(0.688822\pi\)
\(12\) −1.49878 0.0622670i −0.432660 0.0179749i
\(13\) 3.38501i 0.938834i −0.882977 0.469417i \(-0.844464\pi\)
0.882977 0.469417i \(-0.155536\pi\)
\(14\) −0.803314 + 4.40649i −0.214695 + 1.17768i
\(15\) 0 0
\(16\) 2.49103 + 4.31459i 0.622758 + 1.07865i
\(17\) −2.75166 + 4.76601i −0.667374 + 1.15593i 0.311261 + 0.950324i \(0.399249\pi\)
−0.978636 + 0.205602i \(0.934085\pi\)
\(18\) 0.421275 5.06134i 0.0992955 1.19297i
\(19\) 3.49334 2.01688i 0.801428 0.462705i −0.0425421 0.999095i \(-0.513546\pi\)
0.843970 + 0.536390i \(0.180212\pi\)
\(20\) 0 0
\(21\) −4.47027 1.00830i −0.975493 0.220028i
\(22\) 0.780983 0.166506
\(23\) −3.90097 + 2.25223i −0.813409 + 0.469622i −0.848138 0.529775i \(-0.822276\pi\)
0.0347292 + 0.999397i \(0.488943\pi\)
\(24\) −2.94606 + 1.54154i −0.601362 + 0.314665i
\(25\) 0 0
\(26\) 2.86532 + 4.96289i 0.561936 + 0.973302i
\(27\) 5.15589 + 0.645580i 0.992252 + 0.124242i
\(28\) −0.771225 2.15771i −0.145748 0.407769i
\(29\) 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 0.204062 0.978958i \(-0.434586\pi\)
−0.745772 + 0.666202i \(0.767919\pi\)
\(32\) −3.97938 2.29749i −0.703461 0.406143i
\(33\) −0.0331669 + 0.798334i −0.00577362 + 0.138972i
\(34\) 9.31681i 1.59782i
\(35\) 0 0
\(36\) 1.10798 + 2.35011i 0.184664 + 0.391685i
\(37\) −2.89964 5.02232i −0.476698 0.825665i 0.522946 0.852366i \(-0.324833\pi\)
−0.999643 + 0.0267011i \(0.991500\pi\)
\(38\) −3.41448 + 5.91404i −0.553901 + 0.959385i
\(39\) −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 \(0.662496\pi\)
\(42\) 7.40752 2.30567i 1.14300 0.355772i
\(43\) −8.35453 −1.27405 −0.637027 0.770842i \(-0.719836\pi\)
−0.637027 + 0.770842i \(0.719836\pi\)
\(44\) −0.346004 + 0.199765i −0.0521620 + 0.0301157i
\(45\) 0 0
\(46\) 3.81290 6.60414i 0.562182 0.973727i
\(47\) −1.57980 2.73630i −0.230438 0.399130i 0.727499 0.686109i \(-0.240683\pi\)
−0.957937 + 0.286978i \(0.907349\pi\)
\(48\) 4.62108 7.28756i 0.666995 1.05187i
\(49\) −1.13564 6.90727i −0.162234 0.986752i
\(50\) 0 0
\(51\) 9.52380 + 0.395668i 1.33360 + 0.0554046i
\(52\) −2.53888 1.46582i −0.352080 0.203273i
\(53\) −10.0154 5.78238i −1.37572 0.794271i −0.384078 0.923301i \(-0.625481\pi\)
−0.991641 + 0.129029i \(0.958814\pi\)
\(54\) −8.10570 + 3.41782i −1.10305 + 0.465106i
\(55\) 0 0
\(56\) −3.87179 3.28720i −0.517389 0.439270i
\(57\) −5.90043 3.74149i −0.781531 0.495573i
\(58\) 6.53271 + 11.3150i 0.857786 + 1.48573i
\(59\) 4.88061 8.45346i 0.635401 1.10055i −0.351029 0.936365i \(-0.614168\pi\)
0.986430 0.164183i \(-0.0524986\pi\)
\(60\) 0 0
\(61\) −6.90647 + 3.98746i −0.884283 + 0.510541i −0.872068 0.489384i \(-0.837222\pi\)
−0.0122151 + 0.999925i \(0.503888\pi\)
\(62\) 5.89604 0.748798
\(63\) 2.04231 + 7.67001i 0.257307 + 0.966330i
\(64\) −2.18506 −0.273132
\(65\) 0 0
\(66\) −0.627141 1.19854i −0.0771957 0.147530i
\(67\) 0.458116 0.793481i 0.0559678 0.0969391i −0.836684 0.547686i \(-0.815509\pi\)
0.892652 + 0.450747i \(0.148842\pi\)
\(68\) 2.38312 + 4.12768i 0.288995 + 0.500555i
\(69\) 6.58893 + 4.17808i 0.793214 + 0.502981i
\(70\) 0 0
\(71\) 1.52593i 0.181094i 0.995892 + 0.0905471i \(0.0288616\pi\)
−0.995892 + 0.0905471i \(0.971138\pi\)
\(72\) 4.73146 + 3.28331i 0.557608 + 0.386941i
\(73\) 6.75338 + 3.89906i 0.790423 + 0.456351i 0.840112 0.542414i \(-0.182489\pi\)
−0.0496883 + 0.998765i \(0.515823\pi\)
\(74\) 8.50252 + 4.90893i 0.988398 + 0.570652i
\(75\) 0 0
\(76\) 3.49351i 0.400733i
\(77\) −1.14932 + 0.410798i −0.130977 + 0.0468148i
\(78\) 5.31542 8.38256i 0.601853 0.949138i
\(79\) 3.58521 + 6.20977i 0.403368 + 0.698654i 0.994130 0.108192i \(-0.0345061\pi\)
−0.590762 + 0.806846i \(0.701173\pi\)
\(80\) 0 0
\(81\) −3.14952 8.43093i −0.349946 0.936770i
\(82\) 9.17399 5.29661i 1.01310 0.584912i
\(83\) 17.5632 1.92781 0.963904 0.266250i \(-0.0857848\pi\)
0.963904 + 0.266250i \(0.0857848\pi\)
\(84\) −2.69204 + 2.91624i −0.293725 + 0.318188i
\(85\) 0 0
\(86\) 12.2489 7.07188i 1.32083 0.762581i
\(87\) −11.8438 + 6.19732i −1.26979 + 0.664422i
\(88\) −0.442791 + 0.766937i −0.0472017 + 0.0817558i
\(89\) −1.35247 2.34254i −0.143361 0.248309i 0.785399 0.618990i \(-0.212458\pi\)
−0.928760 + 0.370681i \(0.879124\pi\)
\(90\) 0 0
\(91\) −6.82718 5.79637i −0.715683 0.607625i
\(92\) 3.90116i 0.406724i
\(93\) −0.250394 + 6.02703i −0.0259646 + 0.624974i
\(94\) 4.63241 + 2.67452i 0.477796 + 0.275856i
\(95\) 0 0
\(96\) −0.330363 + 7.95189i −0.0337175 + 0.811587i
\(97\) 4.44253i 0.451070i 0.974235 + 0.225535i \(0.0724130\pi\)
−0.974235 + 0.225535i \(0.927587\pi\)
\(98\) 7.51181 + 9.16569i 0.758808 + 0.925875i
\(99\) 1.25180 0.590174i 0.125811 0.0593148i
\(100\) 0 0
\(101\) −1.36822 + 2.36982i −0.136143 + 0.235806i −0.926033 0.377442i \(-0.876804\pi\)
0.789891 + 0.613248i \(0.210137\pi\)
\(102\) −14.2981 + 7.48154i −1.41572 + 0.740782i
\(103\) −15.9618 + 9.21552i −1.57276 + 0.908033i −0.576930 + 0.816794i \(0.695749\pi\)
−0.995829 + 0.0912387i \(0.970917\pi\)
\(104\) −6.49817 −0.637198
\(105\) 0 0
\(106\) 19.5785 1.90163
\(107\) −5.76162 + 3.32647i −0.556997 + 0.321582i −0.751939 0.659232i \(-0.770881\pi\)
0.194942 + 0.980815i \(0.437548\pi\)
\(108\) 2.71688 3.58755i 0.261432 0.345212i
\(109\) 3.91662 6.78379i 0.375144 0.649769i −0.615204 0.788368i \(-0.710927\pi\)
0.990349 + 0.138599i \(0.0442599\pi\)
\(110\) 0 0
\(111\) −5.37908 + 8.48295i −0.510560 + 0.805166i
\(112\) 12.9676 + 2.36402i 1.22532 + 0.223379i
\(113\) 17.3914i 1.63604i −0.575187 0.818022i \(-0.695071\pi\)
0.575187 0.818022i \(-0.304929\pi\)
\(114\) 11.8179 + 0.490976i 1.10685 + 0.0459842i
\(115\) 0 0
\(116\) −5.78845 3.34196i −0.537444 0.310293i
\(117\) 8.34305 + 5.78951i 0.771316 + 0.535240i
\(118\) 16.5252i 1.52127i
\(119\) 4.90065 + 13.7109i 0.449242 + 1.25688i
\(120\) 0 0
\(121\) −5.39359 9.34198i −0.490327 0.849271i
\(122\) 6.75055 11.6923i 0.611166 1.05857i
\(123\) 5.02468 + 9.60275i 0.453060 + 0.865850i
\(124\) −2.61216 + 1.50813i −0.234579 + 0.135434i
\(125\) 0 0
\(126\) −9.48675 9.51650i −0.845147 0.847797i
\(127\) −12.5556 −1.11413 −0.557065 0.830469i \(-0.688073\pi\)
−0.557065 + 0.830469i \(0.688073\pi\)
\(128\) 11.1623 6.44458i 0.986621 0.569626i
\(129\) 6.70881 + 12.8213i 0.590678 + 1.12885i
\(130\) 0 0
\(131\) 3.36275 + 5.82446i 0.293805 + 0.508886i 0.974706 0.223490i \(-0.0717450\pi\)
−0.680901 + 0.732375i \(0.738412\pi\)
\(132\) 0.584417 + 0.370582i 0.0508670 + 0.0322550i
\(133\) 1.91405 10.4993i 0.165969 0.910405i
\(134\) 1.55113i 0.133997i
\(135\) 0 0
\(136\) 9.14924 + 5.28232i 0.784541 + 0.452955i
\(137\) 17.6208 + 10.1734i 1.50545 + 0.869171i 0.999980 + 0.00632592i \(0.00201362\pi\)
0.505468 + 0.862845i \(0.331320\pi\)
\(138\) −13.1969 0.548267i −1.12339 0.0466716i
\(139\) 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
\(142\) −1.29166 2.23721i −0.108393 0.187743i
\(143\) −0.780781 + 1.35235i −0.0652922 + 0.113089i
\(144\) −14.8947 1.23974i −1.24122 0.103312i
\(145\) 0 0
\(146\) −13.2018 −1.09259
\(147\) −9.68834 + 7.28945i −0.799081 + 0.601224i
\(148\) −5.02257 −0.412852
\(149\) −14.1195 + 8.15190i −1.15671 + 0.667830i −0.950514 0.310680i \(-0.899443\pi\)
−0.206200 + 0.978510i \(0.566110\pi\)
\(150\) 0 0
\(151\) 7.54351 13.0657i 0.613882 1.06328i −0.376697 0.926336i \(-0.622940\pi\)
0.990580 0.136939i \(-0.0437263\pi\)
\(152\) −3.87179 6.70613i −0.314043 0.543939i
\(153\) −7.04054 14.9335i −0.569194 1.20730i
\(154\) 1.33733 1.57515i 0.107765 0.126929i
\(155\) 0 0
\(156\) −0.210775 + 5.07339i −0.0168755 + 0.406196i
\(157\) 10.7831 + 6.22562i 0.860584 + 0.496858i 0.864208 0.503135i \(-0.167820\pi\)
−0.00362372 + 0.999993i \(0.501153\pi\)
\(158\) −10.5128 6.06958i −0.836354 0.482869i
\(159\) −0.831464 + 20.0135i −0.0659394 + 1.58717i
\(160\) 0 0
\(161\) −2.13739 + 11.7244i −0.168450 + 0.924015i
\(162\) 11.7542 + 9.69489i 0.923495 + 0.761703i
\(163\) 2.75193 + 4.76649i 0.215548 + 0.373340i 0.953442 0.301577i \(-0.0975129\pi\)
−0.737894 + 0.674917i \(0.764180\pi\)
\(164\) −2.70961 + 4.69317i −0.211585 + 0.366475i
\(165\) 0 0
\(166\) −25.7500 + 14.8667i −1.99858 + 1.15388i
\(167\) 0.799023 0.0618302 0.0309151 0.999522i \(-0.490158\pi\)
0.0309151 + 0.999522i \(0.490158\pi\)
\(168\) −1.93562 + 8.58153i −0.149336 + 0.662079i
\(169\) 1.54168 0.118590
\(170\) 0 0
\(171\) −1.00377 + 12.0596i −0.0767601 + 0.922221i
\(172\) −3.61779 + 6.26620i −0.275854 + 0.477793i
\(173\) 7.25944 + 12.5737i 0.551925 + 0.955962i 0.998136 + 0.0610338i \(0.0194397\pi\)
−0.446211 + 0.894928i \(0.647227\pi\)
\(174\) 12.1187 19.1116i 0.918719 1.44884i
\(175\) 0 0
\(176\) 2.29830i 0.173241i
\(177\) −16.8924 0.701796i −1.26971 0.0527502i
\(178\) 3.96579 + 2.28965i 0.297249 + 0.171617i
\(179\) −2.04442 1.18035i −0.152807 0.0882234i 0.421647 0.906760i \(-0.361452\pi\)
−0.574454 + 0.818537i \(0.694786\pi\)
\(180\) 0 0
\(181\) 9.70696i 0.721513i −0.932660 0.360756i \(-0.882519\pi\)
0.932660 0.360756i \(-0.117481\pi\)
\(182\) 14.9160 + 2.71923i 1.10565 + 0.201563i
\(183\) 11.6654 + 7.39707i 0.862329 + 0.546807i
\(184\) 4.32357 + 7.48865i 0.318738 + 0.552071i
\(185\) 0 0
\(186\) −4.73461 9.04839i −0.347158 0.663460i
\(187\) 2.19863 1.26938i 0.160780 0.0928264i
\(188\) −2.73643 −0.199575
\(189\) 10.1308 9.29337i 0.736908 0.675993i
\(190\) 0 0
\(191\) 4.37389 2.52527i 0.316484 0.182722i −0.333341 0.942807i \(-0.608176\pi\)
0.649824 + 0.760085i \(0.274843\pi\)
\(192\) 1.75463 + 3.35331i 0.126630 + 0.242004i
\(193\) 6.55182 11.3481i 0.471610 0.816853i −0.527862 0.849330i \(-0.677006\pi\)
0.999472 + 0.0324769i \(0.0103396\pi\)
\(194\) −3.76048 6.51334i −0.269987 0.467631i
\(195\) 0 0
\(196\) −5.67247 2.13931i −0.405176 0.152808i
\(197\) 21.2925i 1.51703i −0.651655 0.758516i \(-0.725925\pi\)
0.651655 0.758516i \(-0.274075\pi\)
\(198\) −1.33574 + 1.92489i −0.0949270 + 0.136796i
\(199\) −5.78974 3.34271i −0.410424 0.236958i 0.280548 0.959840i \(-0.409484\pi\)
−0.690972 + 0.722882i \(0.742817\pi\)
\(200\) 0 0
\(201\) −1.58559 0.0658738i −0.111839 0.00464638i
\(202\) 4.63263i 0.325951i
\(203\) −15.5654 13.2153i −1.09248 0.927529i
\(204\) 4.42089 6.97185i 0.309524 0.488127i
\(205\) 0 0
\(206\) 15.6014 27.0224i 1.08700 1.88274i
\(207\) 1.12090 13.4668i 0.0779076 0.936007i
\(208\) 14.6050 8.43218i 1.01267 0.584666i
\(209\) −1.86084 −0.128717
\(210\) 0 0
\(211\) 5.72156 0.393889 0.196944 0.980415i \(-0.436898\pi\)
0.196944 + 0.980415i \(0.436898\pi\)
\(212\) −8.67399 + 5.00793i −0.595732 + 0.343946i
\(213\) 2.34177 1.22534i 0.160456 0.0839591i
\(214\) 5.63154 9.75412i 0.384964 0.666778i
\(215\) 0 0
\(216\) 1.23931 9.89770i 0.0843245 0.673453i
\(217\) −8.67678 + 3.10132i −0.589019 + 0.210531i
\(218\) 13.2613i 0.898166i
\(219\) 0.560657 13.4951i 0.0378857 0.911915i
\(220\) 0 0
\(221\) 16.1330 + 9.31439i 1.08522 + 0.626554i
\(222\) 0.705869 16.9904i 0.0473748 1.14032i
\(223\) 5.83493i 0.390736i −0.980730 0.195368i \(-0.937410\pi\)
0.980730 0.195368i \(-0.0625901\pi\)
\(224\) −11.4479 + 4.09180i −0.764896 + 0.273395i
\(225\) 0 0
\(226\) 14.7213 + 25.4981i 0.979249 + 1.69611i
\(227\) 5.70646 9.88387i 0.378751 0.656016i −0.612130 0.790757i \(-0.709687\pi\)
0.990881 + 0.134741i \(0.0430204\pi\)
\(228\) −5.36134 + 2.80534i −0.355063 + 0.185788i
\(229\) 0.910719 0.525804i 0.0601820 0.0347461i −0.469607 0.882876i \(-0.655604\pi\)
0.529789 + 0.848129i \(0.322271\pi\)
\(230\) 0 0
\(231\) 1.55335 + 1.43393i 0.102203 + 0.0943457i
\(232\) −14.8153 −0.972672
\(233\) 3.36441 1.94244i 0.220410 0.127254i −0.385730 0.922612i \(-0.626050\pi\)
0.606140 + 0.795358i \(0.292717\pi\)
\(234\) −17.1327 1.42602i −1.12000 0.0932220i
\(235\) 0 0
\(236\) −4.22694 7.32127i −0.275150 0.476574i
\(237\) 6.65088 10.4886i 0.432021 0.681308i
\(238\) −18.7909 15.9537i −1.21803 1.03413i
\(239\) 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 0.561826 0.827255i \(-0.310099\pi\)
−0.435511 + 0.900183i \(0.643432\pi\)
\(242\) 15.8155 + 9.13106i 1.01666 + 0.586967i
\(243\) −10.4095 + 11.6036i −0.667767 + 0.744370i
\(244\) 6.90681i 0.442163i
\(245\) 0 0
\(246\) −15.4953 9.82566i −0.987945 0.626461i
\(247\) −6.82718 11.8250i −0.434403 0.752408i
\(248\) −3.34286 + 5.79000i −0.212272 + 0.367665i
\(249\) −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 \(0.361875\pi\)
\(252\) 6.63717 + 1.78957i 0.418102 + 0.112732i
\(253\) 2.07798 0.130641
\(254\) 18.4082 10.6280i 1.15503 0.666859i
\(255\) 0 0
\(256\) −8.72527 + 15.1126i −0.545329 + 0.944538i
\(257\) −9.79648 16.9680i −0.611088 1.05844i −0.991057 0.133436i \(-0.957399\pi\)
0.379969 0.924999i \(-0.375934\pi\)
\(258\) −20.6889 13.1190i −1.28804 0.816750i
\(259\) −15.0947 2.75180i −0.937937 0.170988i
\(260\) 0 0
\(261\) 19.0215 + 13.1996i 1.17740 + 0.817035i
\(262\) −9.86050 5.69296i −0.609184 0.351712i
\(263\) 14.5263 + 8.38678i 0.895732 + 0.517151i 0.875813 0.482651i \(-0.160326\pi\)
0.0199186 + 0.999802i \(0.493659\pi\)
\(264\) 1.53255 + 0.0636701i 0.0943220 + 0.00391863i
\(265\) 0 0
\(266\) 6.08112 + 17.0136i 0.372858 + 1.04317i
\(267\) −2.50894 + 3.95666i −0.153545 + 0.242144i
\(268\) −0.396759 0.687207i −0.0242359 0.0419779i
\(269\) 14.6703 25.4097i 0.894465 1.54926i 0.0599988 0.998198i \(-0.480890\pi\)
0.834466 0.551060i \(-0.185776\pi\)
\(270\) 0 0
\(271\) 2.57129 1.48454i 0.156195 0.0901792i −0.419865 0.907586i \(-0.637923\pi\)
0.576060 + 0.817407i \(0.304589\pi\)
\(272\) −27.4178 −1.66245
\(273\) −3.41310 + 15.1319i −0.206570 + 0.915827i
\(274\) −34.4460 −2.08096
\(275\) 0 0
\(276\) 5.98694 3.13269i 0.360371 0.188566i
\(277\) −6.51269 + 11.2803i −0.391309 + 0.677768i −0.992623 0.121246i \(-0.961311\pi\)
0.601313 + 0.799014i \(0.294644\pi\)
\(278\) −8.28830 14.3558i −0.497099 0.861001i
\(279\) 9.45048 4.45553i 0.565786 0.266745i
\(280\) 0 0
\(281\) 19.4404i 1.15972i −0.814717 0.579859i \(-0.803108\pi\)
0.814717 0.579859i \(-0.196892\pi\)
\(282\) 0.384577 9.25683i 0.0229012 0.551236i
\(283\) −4.88399 2.81977i −0.290323 0.167618i 0.347764 0.937582i \(-0.386941\pi\)
−0.638088 + 0.769964i \(0.720274\pi\)
\(284\) 1.14450 + 0.660778i 0.0679136 + 0.0392099i
\(285\) 0 0
\(286\) 2.64364i 0.156322i
\(287\) −10.7147 + 12.6202i −0.632469 + 0.744945i
\(288\) 12.4687 5.87850i 0.734725 0.346394i
\(289\) −6.64321 11.5064i −0.390777 0.676846i
\(290\) 0 0
\(291\) 6.81775 3.56741i 0.399663 0.209126i
\(292\) 5.84888 3.37685i 0.342280 0.197615i
\(293\) −21.5754 −1.26045 −0.630226 0.776412i \(-0.717038\pi\)
−0.630226 + 0.776412i \(0.717038\pi\)
\(294\) 8.03409 18.8882i 0.468557 1.10158i
\(295\) 0 0
\(296\) −9.64129 + 5.56640i −0.560389 + 0.323541i
\(297\) −1.91093 1.44716i −0.110883 0.0839730i
\(298\) 13.8007 23.9036i 0.799455 1.38470i
\(299\) 7.62382 + 13.2049i 0.440897 + 0.763656i
\(300\) 0 0
\(301\) −14.3060 + 16.8501i −0.824582 + 0.971224i
\(302\) 25.5415i 1.46975i
\(303\) 4.73555 + 0.196739i 0.272050 + 0.0113024i
\(304\) 17.4041 + 10.0482i 0.998191 + 0.576306i
\(305\) 0 0
\(306\) 22.9632 + 15.9349i 1.31272 + 0.910935i
\(307\) 22.9288i 1.30861i 0.756229 + 0.654307i \(0.227040\pi\)
−0.756229 + 0.654307i \(0.772960\pi\)
\(308\) −0.189580 + 1.03992i −0.0108023 + 0.0592549i
\(309\) 26.9602 + 17.0956i 1.53371 + 0.972534i
\(310\) 0 0
\(311\) −0.799023 + 1.38395i −0.0453084 + 0.0784765i −0.887790 0.460248i \(-0.847760\pi\)
0.842482 + 0.538725i \(0.181094\pi\)
\(312\) 5.21813 + 9.97245i 0.295418 + 0.564579i
\(313\) 25.0145 14.4421i 1.41390 0.816318i 0.418151 0.908378i \(-0.362678\pi\)
0.995754 + 0.0920593i \(0.0293449\pi\)
\(314\) −21.0793 −1.18957
\(315\) 0 0
\(316\) 6.21007 0.349344
\(317\) 5.68143 3.28018i 0.319101 0.184233i −0.331891 0.943318i \(-0.607687\pi\)
0.650992 + 0.759085i \(0.274353\pi\)
\(318\) −15.7219 30.0463i −0.881638 1.68491i
\(319\) −1.78012 + 3.08325i −0.0996674 + 0.172629i
\(320\) 0 0
\(321\) 9.73166 + 6.17090i 0.543168 + 0.344426i
\(322\) −6.79071 18.9988i −0.378432 1.05876i
\(323\) 22.1991i 1.23519i
\(324\) −7.68735 1.28862i −0.427075 0.0715903i
\(325\) 0 0
\(326\) −8.06940 4.65887i −0.446923 0.258031i
\(327\) −13.5559 0.563181i −0.749642 0.0311440i
\(328\) 12.0120i 0.663251i
\(329\) −8.22399 1.49925i −0.453403 0.0826566i
\(330\) 0 0
\(331\) 6.76497 + 11.7173i 0.371836 + 0.644040i 0.989848 0.142129i \(-0.0453949\pi\)
−0.618012 + 0.786169i \(0.712062\pi\)
\(332\) 7.60544 13.1730i 0.417403 0.722963i
\(333\) 17.3379 + 1.44310i 0.950110 + 0.0790815i
\(334\) −1.17147 + 0.676351i −0.0641002 + 0.0370083i
\(335\) 0 0
\(336\) −6.78520 21.7991i −0.370163 1.18924i
\(337\) 30.7122 1.67300 0.836501 0.547966i \(-0.184598\pi\)
0.836501 + 0.547966i \(0.184598\pi\)
\(338\) −2.26030 + 1.30499i −0.122944 + 0.0709819i
\(339\) −26.6898 + 13.9655i −1.44959 + 0.758504i
\(340\) 0 0
\(341\) 0.803314 + 1.39138i 0.0435019 + 0.0753475i
\(342\) −8.73647 18.5307i −0.472414 1.00202i
\(343\) −15.8758 9.53729i −0.857211 0.514965i
\(344\) 16.0381i 0.864715i
\(345\) 0 0
\(346\) −21.2866 12.2898i −1.14438 0.660706i
\(347\) 6.77295 + 3.91036i 0.363591 + 0.209919i 0.670655 0.741770i \(-0.266013\pi\)
−0.307064 + 0.951689i \(0.599347\pi\)
\(348\) −0.480550 + 11.5669i −0.0257602 + 0.620052i
\(349\) 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
\(352\) 1.05987 + 1.83575i 0.0564913 + 0.0978458i
\(353\) 6.13445 10.6252i 0.326504 0.565521i −0.655312 0.755359i \(-0.727463\pi\)
0.981816 + 0.189837i \(0.0607960\pi\)
\(354\) 25.3605 13.2700i 1.34790 0.705292i
\(355\) 0 0
\(356\) −2.34265 −0.124160
\(357\) 17.1062 18.5309i 0.905356 0.980757i
\(358\) 3.99653 0.211223
\(359\) −7.11574 + 4.10828i −0.375555 + 0.216827i −0.675882 0.737010i \(-0.736237\pi\)
0.300328 + 0.953836i \(0.402904\pi\)
\(360\) 0 0
\(361\) −1.36436 + 2.36315i −0.0718086 + 0.124376i
\(362\) 8.21668 + 14.2317i 0.431859 + 0.748002i
\(363\) −10.0056 + 15.7791i −0.525157 + 0.828186i
\(364\) −7.30388 + 2.61061i −0.382827 + 0.136833i
\(365\) 0 0
\(366\) −23.3644 0.970679i −1.22128 0.0507382i
\(367\) 24.1666 + 13.9526i 1.26149 + 0.728320i 0.973362 0.229273i \(-0.0736349\pi\)
0.288125 + 0.957593i \(0.406968\pi\)
\(368\) −19.4349 11.2207i −1.01311 0.584921i
\(369\) 10.7020 15.4223i 0.557125 0.802853i
\(370\) 0 0
\(371\) −28.8123 + 10.2983i −1.49586 + 0.534663i
\(372\) 4.41206 + 2.79771i 0.228755 + 0.145054i
\(373\) −9.04199 15.6612i −0.468176 0.810905i 0.531162 0.847270i \(-0.321755\pi\)
−0.999339 + 0.0363650i \(0.988422\pi\)
\(374\) −2.14900 + 3.72217i −0.111122 + 0.192469i
\(375\) 0 0
\(376\) −5.25284 + 3.03273i −0.270895 + 0.156401i
\(377\) −26.1241 −1.34546
\(378\) −6.98655 + 22.2008i −0.359349 + 1.14189i
\(379\) 24.7450 1.27107 0.635534 0.772073i \(-0.280780\pi\)
0.635534 + 0.772073i \(0.280780\pi\)
\(380\) 0 0
\(381\) 10.0823 + 19.2685i 0.516534 + 0.987157i
\(382\) −4.27514 + 7.40476i −0.218735 + 0.378861i
\(383\) 6.46470 + 11.1972i 0.330331 + 0.572150i 0.982577 0.185858i \(-0.0595063\pi\)
−0.652246 + 0.758008i \(0.726173\pi\)
\(384\) −18.8537 11.9552i −0.962126 0.610089i
\(385\) 0 0
\(386\) 22.1838i 1.12912i
\(387\) 14.2890 20.5914i 0.726352 1.04672i
\(388\) 3.33205 + 1.92376i 0.169159 + 0.0976642i
\(389\) 16.4024 + 9.46992i 0.831634 + 0.480144i 0.854412 0.519596i \(-0.173918\pi\)
−0.0227777 + 0.999741i \(0.507251\pi\)
\(390\) 0 0
\(391\) 24.7894i 1.25365i
\(392\) −13.2598 + 2.18007i −0.669721 + 0.110110i
\(393\) 6.23820 9.83780i 0.314675 0.496251i
\(394\) 18.0236 + 31.2177i 0.908014 + 1.57273i
\(395\) 0 0
\(396\) 0.0994198 1.19446i 0.00499603 0.0600239i
\(397\) 6.31044 3.64333i 0.316712 0.182854i −0.333214 0.942851i \(-0.608133\pi\)
0.649926 + 0.759998i \(0.274800\pi\)
\(398\) 11.3181 0.567323
\(399\) −17.6498 + 5.49369i −0.883596 + 0.275028i
\(400\) 0 0
\(401\) −13.7394 + 7.93243i −0.686111 + 0.396126i −0.802154 0.597118i \(-0.796312\pi\)
0.116042 + 0.993244i \(0.462979\pi\)
\(402\) 2.38045 1.24558i 0.118726 0.0621240i
\(403\) −5.89451 + 10.2096i −0.293626 + 0.508576i
\(404\) 1.18497 + 2.05242i 0.0589543 + 0.102112i
\(405\) 0 0
\(406\) 34.0073 + 6.19963i 1.68776 + 0.307682i
\(407\) 2.67530i 0.132610i
\(408\) 0.759558 18.2827i 0.0376037 0.905129i
\(409\) −22.8109 13.1699i −1.12793 0.651209i −0.184515 0.982830i \(-0.559071\pi\)
−0.943413 + 0.331620i \(0.892405\pi\)
\(410\) 0 0
\(411\) 1.46286 35.2113i 0.0721575 1.73684i
\(412\) 15.9625i 0.786417i
\(413\) −8.69228 24.3190i −0.427719 1.19666i
\(414\) 9.75590 + 20.6929i 0.479476 + 1.01700i
\(415\) 0 0
\(416\) −7.77705 + 13.4702i −0.381301 + 0.660433i
\(417\) 15.0267 7.86278i 0.735860 0.385042i
\(418\) 2.72824 1.57515i 0.133443 0.0770432i
\(419\) −14.3499 −0.701039 −0.350519 0.936555i \(-0.613995\pi\)
−0.350519 + 0.936555i \(0.613995\pi\)
\(420\) 0 0
\(421\) −10.0679 −0.490682 −0.245341 0.969437i \(-0.578900\pi\)
−0.245341 + 0.969437i \(0.578900\pi\)
\(422\) −8.38858 + 4.84315i −0.408350 + 0.235761i
\(423\) 9.44616 + 0.786241i 0.459288 + 0.0382284i
\(424\) −11.1004 + 19.2264i −0.539082 + 0.933717i
\(425\) 0 0
\(426\) −2.39613 + 3.77876i −0.116093 + 0.183082i
\(427\) −3.78415 + 20.7575i −0.183128 + 1.00453i
\(428\) 5.76190i 0.278512i
\(429\) 2.70237 + 0.112271i 0.130472 + 0.00542047i
\(430\) 0 0
\(431\) −7.13983 4.12218i −0.343914 0.198559i 0.318088 0.948061i \(-0.396959\pi\)
−0.662001 + 0.749503i \(0.730293\pi\)
\(432\) 10.0581 + 23.8537i 0.483919 + 1.14766i
\(433\) 10.7241i 0.515367i 0.966229 + 0.257683i \(0.0829591\pi\)
−0.966229 + 0.257683i \(0.917041\pi\)
\(434\) 10.0961 11.8916i 0.484631 0.570816i
\(435\) 0 0
\(436\) −3.39206 5.87521i −0.162450 0.281372i
\(437\) −9.08496 + 15.7356i −0.434593 + 0.752737i
\(438\) 10.6013 + 20.2602i 0.506548 + 0.968071i
\(439\) −2.74233 + 1.58329i −0.130884 + 0.0755661i −0.564013 0.825766i \(-0.690743\pi\)
0.433128 + 0.901332i \(0.357410\pi\)
\(440\) 0 0
\(441\) 18.9667 + 9.01472i 0.903175 + 0.429273i
\(442\) −31.5375 −1.50009
\(443\) 15.1150 8.72667i 0.718137 0.414617i −0.0959297 0.995388i \(-0.530582\pi\)
0.814067 + 0.580772i \(0.197249\pi\)
\(444\) 4.03319 + 7.70791i 0.191407 + 0.365801i
\(445\) 0 0
\(446\) 4.93911 + 8.55480i 0.233874 + 0.405081i
\(447\) 23.8485 + 15.1225i 1.12800 + 0.715268i
\(448\) −3.74161 + 4.40700i −0.176774 + 0.208211i
\(449\) 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
\(452\) −13.0442 7.53105i −0.613546 0.354231i
\(453\) −26.1090 1.08470i −1.22671 0.0509637i
\(454\) 19.3215i 0.906801i
\(455\) 0 0
\(456\) −7.18250 + 11.3270i −0.336351 + 0.530434i
\(457\) 2.44467 + 4.23430i 0.114357 + 0.198072i 0.917523 0.397684i \(-0.130186\pi\)
−0.803165 + 0.595756i \(0.796853\pi\)
\(458\) −0.890158 + 1.54180i −0.0415943 + 0.0720435i
\(459\) −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 \(0.461901\pi\)
\(462\) −3.49121 0.787463i −0.162426 0.0366361i
\(463\) −39.9073 −1.85465 −0.927325 0.374257i \(-0.877898\pi\)
−0.927325 + 0.374257i \(0.877898\pi\)
\(464\) 33.2981 19.2247i 1.54583 0.892483i
\(465\) 0 0
\(466\) −3.28845 + 5.69577i −0.152335 + 0.263851i
\(467\) 4.56309 + 7.90350i 0.211155 + 0.365730i 0.952076 0.305861i \(-0.0989443\pi\)
−0.740922 + 0.671592i \(0.765611\pi\)
\(468\) 7.95516 3.75054i 0.367727 0.173369i
\(469\) −0.815897 2.28269i −0.0376746 0.105405i
\(470\) 0 0
\(471\) 0.895198 21.5476i 0.0412486 0.992860i
\(472\) −16.2280 9.36925i −0.746955 0.431254i
\(473\) 3.33773 + 1.92704i 0.153469 + 0.0886053i
\(474\) −0.872760 + 21.0075i −0.0400872 + 0.964907i
\(475\) 0 0
\(476\) 12.4058 + 2.26161i 0.568619 + 0.103661i
\(477\) 31.3815 14.7951i 1.43686 0.677422i
\(478\) 5.42002 + 9.38775i 0.247906 + 0.429386i
\(479\) 6.20210 10.7424i 0.283381 0.490831i −0.688834 0.724919i \(-0.741877\pi\)
0.972215 + 0.234088i \(0.0752105\pi\)
\(480\) 0 0
\(481\) −17.0006 + 9.81532i −0.775162 + 0.447540i
\(482\) −3.83332 −0.174603
\(483\) 19.7093 6.13473i 0.896805 0.279140i
\(484\) −9.34243 −0.424656
\(485\) 0 0
\(486\) 5.43955 25.8237i 0.246743 1.17139i
\(487\) 7.08208 12.2665i 0.320920 0.555849i −0.659758 0.751478i \(-0.729341\pi\)
0.980678 + 0.195628i \(0.0626747\pi\)
\(488\) 7.65467 + 13.2583i 0.346511 + 0.600174i
\(489\) 5.10507 8.05083i 0.230859 0.364071i
\(490\) 0 0
\(491\) 32.1216i 1.44963i −0.688946 0.724813i \(-0.741926\pi\)
0.688946 0.724813i \(-0.258074\pi\)
\(492\) 9.37826 + 0.389621i 0.422805 + 0.0175655i
\(493\) 36.7819 + 21.2361i 1.65658 + 0.956424i
\(494\) 20.0191 + 11.5580i 0.900703 + 0.520021i
\(495\) 0 0
\(496\) 17.3511i 0.779086i
\(497\) 3.07762 + 2.61294i 0.138050 + 0.117206i
\(498\) 43.4929 + 27.5791i 1.94897 + 1.23585i
\(499\) −13.3589 23.1383i −0.598027 1.03581i −0.993112 0.117168i \(-0.962618\pi\)
0.395085 0.918644i \(-0.370715\pi\)
\(500\) 0 0
\(501\) −0.641627 1.22622i −0.0286658 0.0547837i
\(502\) −19.5320 + 11.2768i −0.871758 + 0.503310i
\(503\) −9.55539 −0.426054 −0.213027 0.977046i \(-0.568332\pi\)
−0.213027 + 0.977046i \(0.568332\pi\)
\(504\) 14.7240 3.92059i 0.655860 0.174637i
\(505\) 0 0
\(506\) −3.04659 + 1.75895i −0.135438 + 0.0781950i
\(507\) −1.23799 2.36594i −0.0549810 0.105075i
\(508\) −5.43700 + 9.41716i −0.241228 + 0.417819i
\(509\) −9.10071 15.7629i −0.403382 0.698678i 0.590750 0.806855i \(-0.298832\pi\)
−0.994132 + 0.108177i \(0.965499\pi\)
\(510\) 0 0
\(511\) 19.4282 6.94417i 0.859452 0.307192i
\(512\) 3.76451i 0.166369i
\(513\) 19.3134 8.14360i 0.852706 0.359549i
\(514\) 28.7259 + 16.5849i 1.26705 + 0.731530i
\(515\) 0 0
\(516\) 12.5216 + 0.520212i 0.551232 + 0.0229010i
\(517\) 1.45758i 0.0641042i
\(518\) 24.4601 8.74273i 1.07472 0.384133i
\(519\) 13.4669 21.2376i 0.591130 0.932228i
\(520\) 0 0
\(521\) −1.93741 + 3.35569i −0.0848794 + 0.147015i −0.905340 0.424688i \(-0.860384\pi\)
0.820460 + 0.571703i \(0.193717\pi\)
\(522\) −39.0612 3.25122i −1.70966 0.142302i
\(523\) 16.3176 9.42099i 0.713520 0.411951i −0.0988429 0.995103i \(-0.531514\pi\)
0.812363 + 0.583152i \(0.198181\pi\)
\(524\) 5.82474 0.254455
\(525\) 0 0
\(526\) −28.3967 −1.23816
\(527\) 16.5986 9.58321i 0.723047 0.417451i
\(528\) −3.52711 + 1.84557i −0.153498 + 0.0803183i
\(529\) −1.35494 + 2.34682i −0.0589104 + 0.102036i
\(530\) 0 0
\(531\) 12.4878 + 26.4875i 0.541924 + 1.14946i
\(532\) −7.04601 5.98216i −0.305483 0.259359i
\(533\) 21.1809i 0.917448i
\(534\) 0.329235 7.92475i 0.0142474 0.342937i
\(535\) 0 0
\(536\) −1.52324 0.879440i −0.0657937 0.0379860i
\(537\) −0.169725 + 4.08532i −0.00732419 + 0.176295i
\(538\) 49.6721i 2.14152i
\(539\) −1.13952 + 3.02147i −0.0490824 + 0.130144i
\(540\) 0 0
\(541\) −11.0977 19.2218i −0.477128 0.826410i 0.522528 0.852622i \(-0.324989\pi\)
−0.999656 + 0.0262117i \(0.991656\pi\)
\(542\) −2.51324 + 4.35306i −0.107953 + 0.186980i
\(543\) −14.8968 + 7.79483i −0.639285 + 0.334508i
\(544\) 21.8997 12.6438i 0.938944 0.542099i
\(545\) 0 0
\(546\) −7.80472 25.0746i −0.334011 1.07309i
\(547\) 1.23468 0.0527911 0.0263956 0.999652i \(-0.491597\pi\)
0.0263956 + 0.999652i \(0.491597\pi\)
\(548\) 15.2608 8.81083i 0.651910 0.376380i
\(549\) 1.98449 23.8423i 0.0846959 1.01756i
\(550\) 0 0
\(551\) −15.5654 26.9601i −0.663109 1.14854i
\(552\) 8.02060 12.6487i 0.341379 0.538364i
\(553\) 18.6636 + 3.40242i 0.793656 + 0.144685i
\(554\) 22.0513i 0.936868i
\(555\) 0 0
\(556\) 7.34403 + 4.24008i 0.311456 + 0.179819i
\(557\) 2.00365 + 1.15681i 0.0848973 + 0.0490155i 0.541848 0.840477i \(-0.317725\pi\)
−0.456950 + 0.889492i \(0.651058\pi\)
\(558\) −10.0842 + 14.5320i −0.426898 + 0.615188i
\(559\) 28.2802i 1.19612i
\(560\) 0 0
\(561\) −3.71360 2.35481i −0.156788 0.0994203i
\(562\) 16.4558 + 28.5023i 0.694146 + 1.20230i
\(563\) −9.07818 + 15.7239i −0.382600 + 0.662682i −0.991433 0.130616i \(-0.958304\pi\)
0.608833 + 0.793298i \(0.291638\pi\)
\(564\) 2.19740 + 4.19948i 0.0925270 + 0.176830i
\(565\) 0 0
\(566\) 9.54745 0.401309
\(567\) −22.3973 8.08459i −0.940599 0.339521i
\(568\) 2.92930 0.122911
\(569\) −12.9811 + 7.49465i −0.544197 + 0.314192i −0.746778 0.665073i \(-0.768400\pi\)
0.202581 + 0.979265i \(0.435067\pi\)
\(570\) 0 0
\(571\) −11.6375 + 20.1568i −0.487015 + 0.843535i −0.999889 0.0149293i \(-0.995248\pi\)
0.512873 + 0.858464i \(0.328581\pi\)
\(572\) 0.676208 + 1.17123i 0.0282737 + 0.0489715i
\(573\) −7.38771 4.68459i −0.308626 0.195701i
\(574\) 5.02655 27.5726i 0.209804 1.15086i
\(575\) 0 0
\(576\) 3.73718 5.38551i 0.155716 0.224396i
\(577\) −23.0953 13.3341i −0.961471 0.555105i −0.0648455 0.997895i \(-0.520655\pi\)
−0.896625 + 0.442790i \(0.853989\pi\)
\(578\) 19.4797 + 11.2466i 0.810248 + 0.467797i
\(579\) −22.6766 0.942104i −0.942408 0.0391525i
\(580\) 0 0
\(581\) 30.0745 35.4229i 1.24770 1.46959i
\(582\) −6.97601 + 11.0013i −0.289165 + 0.456021i
\(583\) 2.66751 + 4.62026i 0.110477 + 0.191351i
\(584\) 7.48499 12.9644i 0.309731 0.536470i
\(585\) 0 0
\(586\) 31.6325 18.2630i 1.30673 0.754439i
\(587\) 45.9722 1.89748 0.948738 0.316065i \(-0.102362\pi\)
0.948738 + 0.316065i \(0.102362\pi\)
\(588\) 1.27197 + 10.4232i 0.0524553 + 0.429845i
\(589\) −14.0484 −0.578856
\(590\) 0 0
\(591\) −32.6767 + 17.0982i −1.34414 + 0.703327i
\(592\) 14.4462 25.0215i 0.593735 1.02838i
\(593\) −1.55298 2.68984i −0.0637732 0.110458i 0.832376 0.554211i \(-0.186980\pi\)
−0.896149 + 0.443753i \(0.853647\pi\)
\(594\) 4.02666 + 0.504187i 0.165216 + 0.0206871i
\(595\) 0 0
\(596\) 14.1202i 0.578385i
\(597\) −0.480657 + 11.5695i −0.0196720 + 0.473508i
\(598\) −22.3551 12.9067i −0.914168 0.527795i
\(599\) 7.34708 + 4.24184i 0.300193 + 0.173317i 0.642530 0.766261i \(-0.277885\pi\)
−0.342336 + 0.939577i \(0.611218\pi\)
\(600\) 0 0
\(601\) 2.63388i 0.107438i 0.998556 + 0.0537191i \(0.0171076\pi\)
−0.998556 + 0.0537191i \(0.982892\pi\)
\(602\) 6.71131 36.8141i 0.273533 1.50043i
\(603\) 1.17216 + 2.48624i 0.0477341 + 0.101247i
\(604\) −6.53319 11.3158i −0.265832 0.460434i
\(605\) 0 0
\(606\) −7.10949 + 3.72007i −0.288803 + 0.151118i
\(607\) 26.2154 15.1355i 1.06405 0.614330i 0.137501 0.990502i \(-0.456093\pi\)
0.926550 + 0.376171i \(0.122760\pi\)
\(608\) −18.5351 −0.751698
\(609\) −7.78159 + 34.4996i −0.315326 + 1.39799i
\(610\) 0 0
\(611\) −9.26241 + 5.34766i −0.374717 + 0.216343i
\(612\) −14.2494 1.18604i −0.575999 0.0479427i
\(613\) 9.01861 15.6207i 0.364258 0.630914i −0.624399 0.781106i \(-0.714656\pi\)
0.988657 + 0.150192i \(0.0479893\pi\)
\(614\) −19.4086 33.6167i −0.783267 1.35666i
\(615\) 0 0
\(616\) 0.788604 + 2.20633i 0.0317738 + 0.0888956i
\(617\) 11.2586i 0.453254i −0.973982 0.226627i \(-0.927230\pi\)
0.973982 0.226627i \(-0.0727699\pi\)
\(618\) −53.9982 2.24336i −2.17213 0.0902414i
\(619\) −5.23950 3.02503i −0.210593 0.121586i 0.390994 0.920393i \(-0.372131\pi\)
−0.601587 + 0.798807i \(0.705465\pi\)
\(620\) 0 0
\(621\) −21.5670 + 9.09385i −0.865454 + 0.364924i
\(622\) 2.70540i 0.108477i
\(623\) −7.04054 1.28351i −0.282073 0.0514227i
\(624\) −24.6685 15.6424i −0.987530 0.626198i
\(625\) 0 0
\(626\) −24.4498 + 42.3482i −0.977209 + 1.69258i
\(627\) 1.49428 + 2.85575i 0.0596759 + 0.114048i
\(628\) 9.33888 5.39180i 0.372662 0.215156i
\(629\) 31.9152 1.27254
\(630\) 0 0
\(631\) 47.3970 1.88684 0.943422 0.331594i \(-0.107586\pi\)
0.943422 + 0.331594i \(0.107586\pi\)
\(632\) 11.9208 6.88249i 0.474185 0.273771i
\(633\) −4.59450 8.78063i −0.182615 0.348999i
\(634\) −5.55316 + 9.61836i −0.220544 + 0.381994i
\(635\) 0 0
\(636\) 14.6508 + 9.29014i 0.580942 + 0.368378i
\(637\) −23.3812 + 3.84415i −0.926397 + 0.152311i
\(638\) 6.02728i 0.238622i
\(639\) −3.76096 2.60984i −0.148781 0.103244i
\(640\) 0 0
\(641\) 2.08690 + 1.20488i 0.0824278 + 0.0475897i 0.540647 0.841249i \(-0.318179\pi\)
−0.458220 + 0.888839i \(0.651513\pi\)
\(642\) −19.4914 0.809774i −0.769265 0.0319592i
\(643\) 30.1631i 1.18952i 0.803904 + 0.594759i \(0.202753\pi\)
−0.803904 + 0.594759i \(0.797247\pi\)
\(644\) 7.86819 + 6.68020i 0.310050 + 0.263237i
\(645\) 0 0
\(646\) −18.7909 32.5468i −0.739319 1.28054i
\(647\) −6.98967 + 12.1065i −0.274792 + 0.475954i −0.970083 0.242775i \(-0.921942\pi\)
0.695291 + 0.718729i \(0.255276\pi\)
\(648\) −16.1847 + 6.04609i −0.635797 + 0.237513i
\(649\) −3.89972 + 2.25150i −0.153077 + 0.0883792i
\(650\) 0 0
\(651\) 11.7270 + 10.8255i 0.459619 + 0.424283i
\(652\) 4.76671 0.186679
\(653\) −5.92653 + 3.42169i −0.231923 + 0.133901i −0.611459 0.791276i \(-0.709417\pi\)
0.379536 + 0.925177i \(0.376084\pi\)
\(654\) 20.3515 10.6490i 0.795805 0.416408i
\(655\) 0 0
\(656\) −15.5870 26.9975i −0.608572 1.05408i
\(657\) −21.1606 + 9.97636i −0.825552 + 0.389215i
\(658\) 13.3266 4.76328i 0.519523 0.185692i
\(659\) 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 0.318022 0.948083i \(-0.396981\pi\)
−0.662053 + 0.749457i \(0.730315\pi\)
\(662\) −19.8367 11.4527i −0.770976 0.445123i
\(663\) 1.33934 32.2382i 0.0520157 1.25203i
\(664\) 33.7158i 1.30843i
\(665\) 0 0
\(666\) −26.6412 + 12.5603i −1.03233 + 0.486701i
\(667\) 17.3817 + 30.1060i 0.673022 + 1.16571i
\(668\) 0.346004 0.599296i 0.0133873 0.0231875i
\(669\) −8.95461 + 4.68554i −0.346205 + 0.181153i
\(670\) 0 0
\(671\) 3.67895 0.142024
\(672\) 15.4723 + 14.2828i 0.596858 + 0.550972i
\(673\) −19.1004 −0.736266 −0.368133 0.929773i \(-0.620003\pi\)
−0.368133 + 0.929773i \(0.620003\pi\)
\(674\) −45.0282 + 25.9971i −1.73442 + 1.00137i
\(675\) 0 0
\(676\) 0.667597 1.15631i 0.0256768 0.0444735i
\(677\) −1.98790 3.44314i −0.0764011 0.132331i 0.825294 0.564704i \(-0.191010\pi\)
−0.901695 + 0.432373i \(0.857676\pi\)
\(678\) 27.3094 43.0675i 1.04881 1.65400i
\(679\) 8.96006 + 7.60721i 0.343855 + 0.291938i
\(680\) 0 0
\(681\) −19.7507 0.820547i −0.756849 0.0314434i
\(682\) −2.35553 1.35997i −0.0901981 0.0520759i
\(683\) 9.21993 + 5.32313i 0.352791 + 0.203684i 0.665914 0.746029i \(-0.268042\pi\)
−0.313123 + 0.949713i \(0.601375\pi\)
\(684\) 8.61047 + 5.97507i 0.329229 + 0.228463i
\(685\) 0 0
\(686\) 31.3491 + 0.544533i 1.19691 + 0.0207904i
\(687\) −1.53825 0.975412i −0.0586879 0.0372143i
\(688\) −20.8114 36.0464i −0.793427 1.37426i
\(689\) −19.5735 + 33.9022i −0.745689 + 1.29157i
\(690\) 0 0
\(691\) 14.3020 8.25729i 0.544076 0.314122i −0.202653 0.979251i \(-0.564956\pi\)
0.746729 + 0.665128i \(0.231623\pi\)
\(692\) 12.5743 0.478004
\(693\) 0.953223 3.53533i 0.0362099 0.134296i
\(694\) −13.2401 −0.502586
\(695\) 0 0
\(696\) 11.8969 + 22.7364i 0.450951 + 0.861820i
\(697\) 17.2178 29.8222i 0.652172 1.12960i
\(698\) −21.2889 36.8735i −0.805797 1.39568i
\(699\) −5.68265 3.60340i −0.214938 0.136293i
\(700\) 0 0
\(701\) 19.5702i 0.739158i 0.929199 + 0.369579i \(0.120498\pi\)
−0.929199 + 0.369579i \(0.879502\pi\)
\(702\) 11.5694 + 27.4379i 0.436657 + 1.03558i
\(703\) −20.2589 11.6965i −0.764078 0.441141i
\(704\) 0.872955 + 0.504001i 0.0329007 + 0.0189952i
\(705\) 0 0
\(706\) 20.7706i 0.781712i
\(707\) 2.43677 + 6.81752i 0.0916441 + 0.256399i
\(708\) −7.84133 + 12.3660i −0.294695 + 0.464742i
\(709\) −14.1418 24.4943i −0.531106 0.919903i −0.999341 0.0362991i \(-0.988443\pi\)
0.468235 0.883604i \(-0.344890\pi\)
\(710\) 0 0
\(711\) −21.4372 1.78430i −0.803956 0.0669165i
\(712\) −4.49694 + 2.59631i −0.168530 + 0.0973009i
\(713\) 15.6877 0.587509
\(714\) −9.39411 + 41.6487i −0.351566 + 1.55866i
\(715\) 0 0
\(716\) −1.77061 + 1.02226i −0.0661707 + 0.0382037i
\(717\) −9.82650 + 5.14176i −0.366977 + 0.192022i
\(718\) 6.95509 12.0466i 0.259562 0.449574i
\(719\) 9.75873 + 16.9026i 0.363939 + 0.630361i 0.988605 0.150531i \(-0.0480983\pi\)
−0.624666 + 0.780892i \(0.714765\pi\)
\(720\) 0 0
\(721\) −8.74566 + 47.9733i −0.325705 + 1.78662i
\(722\) 4.61959i 0.171923i
\(723\) 0.162794 3.91849i 0.00605438 0.145730i
\(724\) −7.28057 4.20344i −0.270580 0.156220i
\(725\) 0 0
\(726\) 1.31298 31.6037i 0.0487293 1.17292i
\(727\) 26.5060i 0.983052i −0.870863 0.491526i \(-0.836439\pi\)
0.870863 0.491526i \(-0.163561\pi\)
\(728\) −11.1272 + 13.1061i −0.412402 + 0.485743i
\(729\) 26.1665 + 6.65709i 0.969128 + 0.246559i
\(730\) 0 0
\(731\) 22.9888 39.8177i 0.850271 1.47271i
\(732\) 10.5996 5.54627i 0.391771 0.204996i
\(733\) 0.184602 0.106580i 0.00681844 0.00393663i −0.496587 0.867987i \(-0.665414\pi\)
0.503405 + 0.864050i \(0.332080\pi\)
\(734\) −47.2420 −1.74373
\(735\) 0 0
\(736\) 20.6979 0.762935
\(737\) −0.366045 + 0.211336i −0.0134835 + 0.00778467i
\(738\) −2.63603 + 31.6701i −0.0970337 + 1.16579i
\(739\) 23.2265 40.2296i 0.854402 1.47987i −0.0227959 0.999740i \(-0.507257\pi\)
0.877198 0.480128i \(-0.159410\pi\)
\(740\) 0 0
\(741\) −12.6650 + 19.9730i −0.465261 + 0.733728i
\(742\) 33.5255 39.4876i 1.23076 1.44964i
\(743\) 28.0937i 1.03066i −0.856992 0.515330i \(-0.827670\pi\)
0.856992 0.515330i \(-0.172330\pi\)
\(744\) 11.5700 + 0.480678i 0.424177 + 0.0176225i
\(745\) 0 0
\(746\) 26.5135 + 15.3076i 0.970729 + 0.560451i
\(747\) −30.0389 + 43.2880i −1.09907 + 1.58382i
\(748\) 2.19874i 0.0803939i
\(749\) −3.15687 + 17.3166i −0.115349 + 0.632736i
\(750\) 0 0
\(751\) −12.4832 21.6215i −0.455518 0.788981i 0.543199 0.839604i \(-0.317213\pi\)
−0.998718 + 0.0506227i \(0.983879\pi\)
\(752\) 7.87068 13.6324i 0.287014 0.497123i
\(753\) −10.6979 20.4449i −0.389852 0.745053i
\(754\) 38.3014 22.1133i 1.39485 0.805319i
\(755\) 0 0
\(756\) −2.58338 11.6228i −0.0939566 0.422718i
\(757\) −6.25577 −0.227370 −0.113685 0.993517i \(-0.536265\pi\)
−0.113685 + 0.993517i \(0.536265\pi\)
\(758\) −36.2796 + 20.9460i −1.31773 + 0.760794i
\(759\) −1.66865 3.18898i −0.0605680 0.115753i
\(760\) 0 0
\(761\) 26.3374 + 45.6178i 0.954731 + 1.65364i 0.734982 + 0.678087i \(0.237191\pi\)
0.219750 + 0.975556i \(0.429476\pi\)
\(762\) −31.0924 19.7158i −1.12636 0.714229i
\(763\) −6.97543 19.5157i −0.252528 0.706514i
\(764\) 4.37410i 0.158249i
\(765\) 0 0
\(766\) −18.9563 10.9444i −0.684917 0.395437i
\(767\) −28.6151 16.5209i −1.03323 0.596536i
\(768\) 30.1992 + 1.25463i 1.08972 + 0.0452725i
\(769\) 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
\(772\) −5.67432 9.82820i −0.204223 0.353725i
\(773\) 1.22649 2.12434i 0.0441138 0.0764073i −0.843125 0.537717i \(-0.819287\pi\)
0.887239 + 0.461310i \(0.152620\pi\)
\(774\) −3.51956 + 42.2851i −0.126508 + 1.51991i
\(775\) 0 0
\(776\) 8.52826 0.306147
\(777\) 7.89819 + 25.3749i 0.283346 + 0.910318i
\(778\) −32.0641 −1.14956
\(779\) −21.8588 + 12.6202i −0.783172 + 0.452165i
\(780\) 0 0
\(781\) 0.351967 0.609625i 0.0125944 0.0218141i
\(782\) 20.9836 + 36.3446i 0.750371 + 1.29968i
\(783\) 4.98230 39.7909i 0.178053 1.42201i
\(784\) 26.9731 22.1060i 0.963326 0.789501i
\(785\) 0 0
\(786\) −0.818606 + 19.7040i −0.0291987 + 0.702818i
\(787\) 35.6885 + 20.6048i 1.27216 + 0.734481i 0.975394 0.220470i \(-0.0707590\pi\)
0.296764 + 0.954951i \(0.404092\pi\)
\(788\) −15.9702 9.22039i −0.568914 0.328463i
\(789\) 1.20596 29.0276i 0.0429332 1.03341i
\(790\) 0 0
\(791\) −35.0764 29.7803i −1.24717 1.05887i
\(792\) −1.13295 2.40307i −0.0402576 0.0853893i
\(793\) 13.4976 + 23.3785i 0.479314 + 0.830196i
\(794\) −6.16797 + 10.6832i −0.218893 + 0.379134i
\(795\) 0 0
\(796\) −5.01431 + 2.89501i −0.177727 + 0.102611i
\(797\) 36.9407 1.30851 0.654253 0.756276i \(-0.272983\pi\)
0.654253 + 0.756276i \(0.272983\pi\)
\(798\) 21.2267 22.9946i 0.751419 0.814000i
\(799\) 17.3883 0.615154
\(800\) 0 0
\(801\) 8.08683 + 0.673099i 0.285734 + 0.0237828i
\(802\) 13.4292 23.2600i 0.474200 0.821339i
\(803\) −1.79870 3.11544i −0.0634748 0.109942i
\(804\) −0.736023 + 1.16073i −0.0259575 + 0.0409357i
\(805\) 0 0
\(806\) 19.9582i 0.702997i
\(807\) −50.7756 2.10948i −1.78739 0.0742573i
\(808\) 4.54931 + 2.62655i 0.160044 + 0.0924016i
\(809\) −45.9461 26.5270i −1.61538 0.932640i −0.988094 0.153850i \(-0.950833\pi\)
−0.627285 0.778790i \(-0.715834\pi\)
\(810\) 0 0
\(811\) 19.0686i 0.669590i 0.942291 + 0.334795i \(0.108667\pi\)
−0.942291 + 0.334795i \(0.891333\pi\)
\(812\) −16.6523 + 5.95198i −0.584380 + 0.208873i
\(813\) −4.34304 2.75394i −0.152317 0.0965850i
\(814\) −2.26457 3.92235i −0.0793731 0.137478i
\(815\) 0 0
\(816\) 22.0169 + 42.0769i 0.770747 + 1.47299i
\(817\) −29.1852 + 16.8501i −1.02106 + 0.589511i
\(818\) 44.5918 1.55912
\(819\) 25.9631 6.91324i 0.907223 0.241568i
\(820\) 0 0
\(821\) −9.46302 + 5.46348i −0.330262 + 0.190677i −0.655957 0.754798i \(-0.727735\pi\)
0.325696 + 0.945475i \(0.394402\pi\)
\(822\) 27.6606 + 52.8627i 0.964776 + 1.84380i
\(823\) −20.9937 + 36.3622i −0.731794 + 1.26750i 0.224321 + 0.974515i \(0.427984\pi\)
−0.956116 + 0.292990i \(0.905350\pi\)
\(824\) 17.6909 + 30.6416i 0.616293 + 1.06745i
\(825\) 0 0
\(826\) 33.3294 + 28.2971i 1.15968 + 0.984584i
\(827\) 22.1128i 0.768937i 0.923138 + 0.384468i \(0.125615\pi\)
−0.923138 + 0.384468i \(0.874385\pi\)
\(828\) −9.61520 6.67229i −0.334151 0.231878i
\(829\) 27.1141 + 15.6543i 0.941711 + 0.543697i 0.890496 0.454990i \(-0.150357\pi\)
0.0512148 + 0.998688i \(0.483691\pi\)
\(830\) 0 0
\(831\) 22.5412 + 0.936477i 0.781944 + 0.0324860i
\(832\) 7.39645i 0.256426i
\(833\) 36.0450 + 13.5940i 1.24888 + 0.471003i
\(834\) −15.3755 + 24.2476i −0.532410 + 0.839625i
\(835\) 0 0
\(836\) −0.805806 + 1.39570i −0.0278694 + 0.0482712i
\(837\) −14.4266 10.9254i −0.498655 0.377636i
\(838\) 21.0389 12.1468i 0.726777 0.419605i
\(839\) 8.65688 0.298869 0.149434 0.988772i \(-0.452255\pi\)
0.149434 + 0.988772i \(0.452255\pi\)
\(840\) 0 0
\(841\) −30.5607 −1.05382
\(842\) 14.7610 8.52225i 0.508696 0.293696i
\(843\) −29.8343 + 15.6109i −1.02755 + 0.537669i
\(844\) 2.47763 4.29138i 0.0852835 0.147715i
\(845\) 0 0
\(846\) −14.5149 + 6.84318i −0.499031 + 0.235273i
\(847\) −28.0775 5.11859i −0.964753 0.175877i
\(848\) 57.6164i 1.97855i
\(849\) −0.405463 + 9.75956i −0.0139154 + 0.334947i
\(850\) 0 0
\(851\) 22.6228 + 13.0613i 0.775501 + 0.447736i
\(852\) 0.0950150 2.28703i 0.00325516 0.0783523i
\(853\) 48.3400i 1.65513i −0.561370 0.827565i \(-0.689726\pi\)
0.561370 0.827565i \(-0.310274\pi\)
\(854\) −12.0226 33.6365i −0.411405 1.15102i
\(855\) 0 0
\(856\) 6.38579 + 11.0605i 0.218262 + 0.378041i
\(857\) −16.8218 + 29.1362i −0.574622 + 0.995274i 0.421461 + 0.906847i \(0.361517\pi\)
−0.996083 + 0.0884274i \(0.971816\pi\)
\(858\) −4.05708 + 2.12288i −0.138506 + 0.0724740i
\(859\) 22.6082 13.0528i 0.771382 0.445357i −0.0619856 0.998077i \(-0.519743\pi\)
0.833367 + 0.552720i \(0.186410\pi\)
\(860\) 0 0
\(861\) 27.9717 + 6.30918i 0.953272 + 0.215016i
\(862\) 13.9573 0.475387
\(863\) −34.0767 + 19.6742i −1.15998 + 0.669718i −0.951300 0.308265i \(-0.900252\pi\)
−0.208685 + 0.977983i \(0.566918\pi\)
\(864\) −19.0340 14.4146i −0.647550 0.490396i
\(865\) 0 0
\(866\) −9.07765 15.7230i −0.308471 0.534288i
\(867\) −12.3237 + 19.4348i −0.418536 + 0.660042i
\(868\) −1.43124 + 7.85088i −0.0485793 + 0.266476i
\(869\) 3.30783i 0.112211i
\(870\) 0 0
\(871\) −2.68594 1.55073i −0.0910097 0.0525445i
\(872\) −13.0227 7.51869i −0.441006 0.254615i
\(873\) −10.9495 7.59820i −0.370585 0.257160i
\(874\) 30.7607i 1.04050i
\(875\) 0 0
\(876\) −9.87904 6.26435i −0.333782 0.211653i
\(877\) −13.2655 22.9766i −0.447945 0.775864i 0.550307 0.834963i \(-0.314511\pi\)
−0.998252 + 0.0590984i \(0.981177\pi\)
\(878\) 2.68042 4.64262i 0.0904597 0.156681i
\(879\) 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 \(0.428594\pi\)
\(882\) −35.4384 + 2.83798i −1.19327 + 0.0955598i
\(883\) −27.3728 −0.921169 −0.460584 0.887616i \(-0.652360\pi\)
−0.460584 + 0.887616i \(0.652360\pi\)
\(884\) 13.9723 8.06689i 0.469938 0.271319i
\(885\) 0 0
\(886\) −14.7738 + 25.5889i −0.496335 + 0.859677i
\(887\) −16.4606 28.5105i −0.552692 0.957290i −0.998079 0.0619524i \(-0.980267\pi\)
0.445387 0.895338i \(-0.353066\pi\)
\(888\) 16.2846 + 10.3262i 0.546476 + 0.346523i
\(889\) −21.4997 + 25.3232i −0.721078 + 0.849313i
\(890\) 0 0
\(891\) −0.686394 + 4.09471i −0.0229951 + 0.137178i
\(892\) −4.37641 2.52672i −0.146533 0.0846009i
\(893\) −11.0376 6.37256i −0.369359 0.213250i
\(894\) −47.7659 1.98444i −1.59753 0.0663697i
\(895\) 0 0
\(896\) 6.11599 33.5486i 0.204321 1.12078i
\(897\) 14.1429 22.3036i 0.472216 0.744697i
\(898\) −10.4009 18.0149i −0.347083 0.601165i
\(899\) −13.4390 + 23.2770i −0.448216 + 0.776333i
\(900\) 0 0
\(901\) 55.1178 31.8223i 1.83624 1.06015i
\(902\) −4.88682 −0.162713
\(903\) 37.3470 + 8.42384i 1.24283 + 0.280328i
\(904\) −33.3860 −1.11040
\(905\) 0 0
\(906\) 39.1974 20.5102i 1.30225 0.681406i
\(907\) −10.4117 + 18.0335i −0.345714 + 0.598793i −0.985483 0.169773i \(-0.945696\pi\)
0.639770 + 0.768567i \(0.279030\pi\)
\(908\) −4.94217 8.56010i −0.164012 0.284077i
\(909\) −3.50079 7.42543i −0.116114 0.246286i
\(910\) 0 0
\(911\) 50.2293i 1.66417i 0.554648 + 0.832085i \(0.312853\pi\)
−0.554648 + 0.832085i \(0.687147\pi\)
\(912\) 1.44486 34.7781i 0.0478442 1.15162i
\(913\) −7.01668 4.05108i −0.232218 0.134071i
\(914\) −7.16844 4.13870i −0.237111 0.136896i
\(915\) 0 0
\(916\) 0.910763i 0.0300925i
\(917\) 17.5055 + 3.19130i 0.578083 + 0.105386i
\(918\) 6.01475 48.0365i 0.198516 1.58544i
\(919\) 9.88707 + 17.1249i 0.326144 + 0.564899i 0.981743 0.190211i \(-0.0609171\pi\)
−0.655599 + 0.755109i \(0.727584\pi\)
\(920\) 0 0
\(921\) 35.1878 18.4121i 1.15948 0.606701i
\(922\) −7.51755 + 4.34026i −0.247577 + 0.142939i
\(923\) 5.16529 0.170017
\(924\) 1.74815 0.544131i 0.0575100 0.0179006i
\(925\) 0 0
\(926\) 58.5095 33.7805i 1.92274 1.11009i
\(927\) 4.58641 55.1026i 0.150637 1.80981i
\(928\) −17.7310 + 30.7111i −0.582050 + 1.00814i
\(929\) −1.84133 3.18927i −0.0604119 0.104637i 0.834238 0.551405i \(-0.185908\pi\)
−0.894650 + 0.446769i \(0.852575\pi\)
\(930\) 0 0
\(931\) −17.8983 21.8390i −0.586594 0.715745i
\(932\) 3.36457i 0.110210i
\(933\) 2.76551 + 0.114894i 0.0905387 + 0.00376145i
\(934\) −13.3802 7.72506i −0.437814 0.252772i
\(935\) 0 0
\(936\) 11.1140 16.0161i 0.363274 0.523501i
\(937\) 36.7871i 1.20178i −0.799331 0.600891i \(-0.794813\pi\)
0.799331 0.600891i \(-0.205187\pi\)
\(938\) 3.12845 + 2.65610i 0.102148 + 0.0867247i
\(939\) −42.2507 26.7914i −1.37880 0.874305i
\(940\) 0 0
\(941\) 10.1072 17.5061i 0.329484 0.570684i −0.652925 0.757422i \(-0.726458\pi\)
0.982410 + 0.186739i \(0.0597917\pi\)
\(942\) 16.9270 + 32.3494i 0.551511 + 1.05400i
\(943\) 24.4094 14.0928i 0.794880 0.458924i
\(944\) 48.6310 1.58280
\(945\) 0 0
\(946\) −6.52474 −0.212138
\(947\) 8.50752 4.91182i 0.276457 0.159613i −0.355361 0.934729i \(-0.615642\pi\)
0.631819 + 0.775116i \(0.282309\pi\)
\(948\) −4.98678 9.53032i −0.161963 0.309530i
\(949\) 13.1984 22.8603i 0.428438 0.742076i
\(950\) 0 0
\(951\) −9.59621 6.08501i −0.311179 0.197320i
\(952\) 26.3206 9.40772i 0.853057 0.304906i
\(953\) 24.7365i 0.801294i 0.916232 + 0.400647i \(0.131215\pi\)
−0.916232 + 0.400647i \(0.868785\pi\)
\(954\) −33.4858 + 48.2552i −1.08414 + 1.56232i
\(955\) 0 0
\(956\) −4.80253 2.77274i −0.155325 0.0896769i
\(957\) 6.16119 + 0.255968i 0.199163 + 0.00827426i
\(958\) 20.9996i 0.678468i
\(959\) 50.6917 18.1186i 1.63692 0.585081i
\(960\) 0 0
\(961\) −9.43537 16.3425i −0.304367 0.527179i
\(962\) 16.6168 28.7812i 0.535748 0.927942i
\(963\) 1.65553 19.8901i 0.0533487 0.640948i
\(964\) 1.69830 0.980514i 0.0546986 0.0315802i
\(965\) 0 0
\(966\) −23.7036 + 25.6778i −0.762652 + 0.826168i
\(967\) −14.0157 −0.450713 −0.225357 0.974276i \(-0.572355\pi\)
−0.225357 + 0.974276i \(0.572355\pi\)
\(968\) −17.9337 + 10.3540i −0.576410 + 0.332791i
\(969\) 34.0679 17.8262i 1.09442 0.572660i
\(970\) 0 0
\(971\) −0.0308306 0.0534003i −0.000989403 0.00171370i 0.865530 0.500857i \(-0.166982\pi\)
−0.866520 + 0.499143i \(0.833648\pi\)
\(972\) 4.19546 + 12.8322i 0.134569 + 0.411593i
\(973\) 19.7485 + 16.7667i 0.633106 + 0.537516i
\(974\) 23.9792i 0.768342i
\(975\) 0 0
\(976\) −34.4085 19.8657i −1.10139 0.635887i
\(977\) −16.5237 9.53996i −0.528640 0.305210i 0.211822 0.977308i \(-0.432060\pi\)
−0.740462 + 0.672098i \(0.765393\pi\)
\(978\) −0.669912 + 16.1249i −0.0214214 + 0.515617i
\(979\) 1.24783i 0.0398808i
\(980\) 0 0
\(981\) 10.0213 + 21.2558i 0.319955 + 0.678647i
\(982\) 27.1900 + 47.0945i 0.867669 + 1.50285i
\(983\) 4.07300 7.05465i 0.129909 0.225008i −0.793732 0.608267i \(-0.791865\pi\)
0.923641 + 0.383259i \(0.125198\pi\)
\(984\) 18.4343 9.64581i 0.587663 0.307497i
\(985\) 0 0
\(986\) −71.9030 −2.28986
\(987\) 4.30315 + 13.8249i 0.136971 + 0.440052i
\(988\) −11.8256 −0.376222
\(989\) 32.5908 18.8163i 1.03633 0.598324i
\(990\) 0 0
\(991\) −5.21862 + 9.03891i −0.165775 + 0.287130i −0.936930 0.349517i \(-0.886346\pi\)
0.771155 + 0.636647i \(0.219679\pi\)
\(992\) 8.00150 + 13.8590i 0.254048 + 0.440024i
\(993\) 12.5496 19.7910i 0.398250 0.628050i
\(994\) −6.72398 1.22580i −0.213272 0.0388800i
\(995\) 0 0
\(996\) −26.3233 1.09361i −0.834086 0.0346522i
\(997\) −11.6811 6.74411i −0.369945 0.213588i 0.303489 0.952835i \(-0.401848\pi\)
−0.673435 + 0.739247i \(0.735182\pi\)
\(998\) 39.1719 + 22.6159i 1.23996 + 0.715894i
\(999\) −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.t.h.101.3 yes 20
3.2 odd 2 inner 525.2.t.h.101.8 yes 20
5.2 odd 4 525.2.q.g.374.5 40
5.3 odd 4 525.2.q.g.374.16 40
5.4 even 2 525.2.t.i.101.8 yes 20
7.5 odd 6 inner 525.2.t.h.26.8 yes 20
15.2 even 4 525.2.q.g.374.15 40
15.8 even 4 525.2.q.g.374.6 40
15.14 odd 2 525.2.t.i.101.3 yes 20
21.5 even 6 inner 525.2.t.h.26.3 20
35.12 even 12 525.2.q.g.299.6 40
35.19 odd 6 525.2.t.i.26.3 yes 20
35.33 even 12 525.2.q.g.299.15 40
105.47 odd 12 525.2.q.g.299.16 40
105.68 odd 12 525.2.q.g.299.5 40
105.89 even 6 525.2.t.i.26.8 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
525.2.q.g.299.5 40 105.68 odd 12
525.2.q.g.299.6 40 35.12 even 12
525.2.q.g.299.15 40 35.33 even 12
525.2.q.g.299.16 40 105.47 odd 12
525.2.q.g.374.5 40 5.2 odd 4
525.2.q.g.374.6 40 15.8 even 4
525.2.q.g.374.15 40 15.2 even 4
525.2.q.g.374.16 40 5.3 odd 4
525.2.t.h.26.3 20 21.5 even 6 inner
525.2.t.h.26.8 yes 20 7.5 odd 6 inner
525.2.t.h.101.3 yes 20 1.1 even 1 trivial
525.2.t.h.101.8 yes 20 3.2 odd 2 inner
525.2.t.i.26.3 yes 20 35.19 odd 6
525.2.t.i.26.8 yes 20 105.89 even 6
525.2.t.i.101.3 yes 20 15.14 odd 2
525.2.t.i.101.8 yes 20 5.4 even 2