Properties

Label 225.2.e.b.76.2
Level $225$
Weight $2$
Character 225.76
Analytic conductor $1.797$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [225,2,Mod(76,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.76");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.e (of order \(3\), 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: \(1.79663404548\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.954288.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 76.2
Root \(-1.62241 - 0.606458i\) of defining polynomial
Character \(\chi\) \(=\) 225.76
Dual form 225.2.e.b.151.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.285997 + 0.495361i) q^{2} +(-0.285997 - 1.70828i) q^{3} +(0.836412 - 1.44871i) q^{4} +(0.764419 - 0.630233i) q^{6} +(0.714003 + 1.23669i) q^{7} +2.10083 q^{8} +(-2.83641 + 0.977122i) q^{9} +O(q^{10})\) \(q+(0.285997 + 0.495361i) q^{2} +(-0.285997 - 1.70828i) q^{3} +(0.836412 - 1.44871i) q^{4} +(0.764419 - 0.630233i) q^{6} +(0.714003 + 1.23669i) q^{7} +2.10083 q^{8} +(-2.83641 + 0.977122i) q^{9} +(-1.33641 - 2.31473i) q^{11} +(-2.71400 - 1.01450i) q^{12} +(2.33641 - 4.04678i) q^{13} +(-0.408405 + 0.707378i) q^{14} +(-1.07199 - 1.85675i) q^{16} -2.67282 q^{17} +(-1.29523 - 1.12559i) q^{18} +4.67282 q^{19} +(1.90841 - 1.57340i) q^{21} +(0.764419 - 1.32401i) q^{22} +(-2.95882 + 5.12483i) q^{23} +(-0.600830 - 3.58880i) q^{24} +2.67282 q^{26} +(2.48040 + 4.56592i) q^{27} +2.38880 q^{28} +(4.74482 + 8.21826i) q^{29} +(-3.48040 + 6.02823i) q^{31} +(2.71400 - 4.70079i) q^{32} +(-3.57199 + 2.94497i) q^{33} +(-0.764419 - 1.32401i) q^{34} +(-0.956844 + 4.92641i) q^{36} +1.81681 q^{37} +(1.33641 + 2.31473i) q^{38} +(-7.58123 - 2.83387i) q^{39} +(0.735581 - 1.27406i) q^{41} +(1.32520 + 0.495361i) q^{42} +(0.235581 + 0.408039i) q^{43} -4.47116 q^{44} -3.38485 q^{46} +(3.47842 + 6.02480i) q^{47} +(-2.86525 + 2.36228i) q^{48} +(2.48040 - 4.29618i) q^{49} +(0.764419 + 4.56592i) q^{51} +(-3.90841 - 6.76956i) q^{52} +1.14399 q^{53} +(-1.55239 + 2.53453i) q^{54} +(1.50000 + 2.59808i) q^{56} +(-1.33641 - 7.98247i) q^{57} +(-2.71400 + 4.70079i) q^{58} +(0.571993 - 0.990721i) q^{59} +(1.26442 + 2.19004i) q^{61} -3.98153 q^{62} +(-3.23360 - 2.81009i) q^{63} -1.18319 q^{64} +(-2.48040 - 0.927175i) q^{66} +(-3.29523 + 5.70751i) q^{67} +(-2.23558 + 3.87214i) q^{68} +(9.60083 + 3.58880i) q^{69} -12.8745 q^{71} +(-5.95882 + 2.05277i) q^{72} +1.71203 q^{73} +(0.519602 + 0.899976i) q^{74} +(3.90841 - 6.76956i) q^{76} +(1.90841 - 3.30545i) q^{77} +(-0.764419 - 4.56592i) q^{78} +(0.143987 + 0.249392i) q^{79} +(7.09046 - 5.54304i) q^{81} +0.841495 q^{82} +(-2.14201 - 3.71007i) q^{83} +(-0.683190 - 4.08074i) q^{84} +(-0.134751 + 0.233396i) q^{86} +(12.6821 - 10.4559i) q^{87} +(-2.80757 - 4.86286i) q^{88} -3.00000 q^{89} +6.67282 q^{91} +(4.94958 + 8.57293i) q^{92} +(11.2933 + 4.22143i) q^{93} +(-1.98963 + 3.44615i) q^{94} +(-8.80644 - 3.29186i) q^{96} +(3.91764 + 6.78555i) q^{97} +2.83754 q^{98} +(6.05239 + 5.25970i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + q^{2} - q^{3} - 5 q^{4} - 4 q^{6} + 5 q^{7} - 6 q^{8} - 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + q^{2} - q^{3} - 5 q^{4} - 4 q^{6} + 5 q^{7} - 6 q^{8} - 7 q^{9} + 2 q^{11} - 17 q^{12} + 4 q^{13} + 9 q^{14} - 5 q^{16} + 4 q^{17} + 23 q^{18} + 8 q^{19} - 4 q^{22} + 3 q^{23} + 15 q^{24} - 4 q^{26} + 2 q^{27} - 10 q^{28} + 7 q^{29} - 8 q^{31} + 17 q^{32} - 20 q^{33} + 4 q^{34} + 10 q^{36} - 12 q^{37} - 2 q^{38} - 14 q^{39} + 13 q^{41} + 33 q^{42} + 10 q^{43} - 44 q^{44} - 6 q^{46} + 13 q^{47} + 10 q^{48} + 2 q^{49} - 4 q^{51} - 12 q^{52} + 4 q^{53} + 5 q^{54} + 9 q^{56} + 2 q^{57} - 17 q^{58} + 2 q^{59} - q^{61} - 84 q^{62} - 33 q^{63} - 30 q^{64} - 2 q^{66} + 11 q^{67} - 22 q^{68} + 39 q^{69} - 20 q^{71} - 15 q^{72} + 16 q^{73} + 16 q^{74} + 12 q^{76} + 4 q^{78} - 2 q^{79} - 19 q^{81} + 58 q^{82} - 15 q^{83} - 27 q^{84} - 28 q^{86} + 26 q^{87} - 24 q^{88} - 18 q^{89} + 20 q^{91} + 39 q^{92} + 42 q^{93} + 31 q^{94} + 13 q^{96} - 18 q^{97} + 80 q^{98} + 22 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.285997 + 0.495361i 0.202230 + 0.350273i 0.949247 0.314533i \(-0.101848\pi\)
−0.747017 + 0.664805i \(0.768514\pi\)
\(3\) −0.285997 1.70828i −0.165120 0.986273i
\(4\) 0.836412 1.44871i 0.418206 0.724354i
\(5\) 0 0
\(6\) 0.764419 0.630233i 0.312073 0.257291i
\(7\) 0.714003 + 1.23669i 0.269868 + 0.467425i 0.968828 0.247736i \(-0.0796866\pi\)
−0.698960 + 0.715161i \(0.746353\pi\)
\(8\) 2.10083 0.742756
\(9\) −2.83641 + 0.977122i −0.945471 + 0.325707i
\(10\) 0 0
\(11\) −1.33641 2.31473i −0.402943 0.697918i 0.591136 0.806572i \(-0.298679\pi\)
−0.994080 + 0.108653i \(0.965346\pi\)
\(12\) −2.71400 1.01450i −0.783465 0.292860i
\(13\) 2.33641 4.04678i 0.648004 1.12238i −0.335595 0.942006i \(-0.608937\pi\)
0.983599 0.180370i \(-0.0577294\pi\)
\(14\) −0.408405 + 0.707378i −0.109151 + 0.189055i
\(15\) 0 0
\(16\) −1.07199 1.85675i −0.267998 0.464187i
\(17\) −2.67282 −0.648255 −0.324127 0.946013i \(-0.605071\pi\)
−0.324127 + 0.946013i \(0.605071\pi\)
\(18\) −1.29523 1.12559i −0.305289 0.265305i
\(19\) 4.67282 1.07202 0.536010 0.844212i \(-0.319931\pi\)
0.536010 + 0.844212i \(0.319931\pi\)
\(20\) 0 0
\(21\) 1.90841 1.57340i 0.416448 0.343345i
\(22\) 0.764419 1.32401i 0.162975 0.282280i
\(23\) −2.95882 + 5.12483i −0.616957 + 1.06860i 0.373081 + 0.927799i \(0.378301\pi\)
−0.990038 + 0.140802i \(0.955032\pi\)
\(24\) −0.600830 3.58880i −0.122644 0.732560i
\(25\) 0 0
\(26\) 2.67282 0.524184
\(27\) 2.48040 + 4.56592i 0.477353 + 0.878712i
\(28\) 2.38880 0.451441
\(29\) 4.74482 + 8.21826i 0.881090 + 1.52609i 0.850130 + 0.526573i \(0.176523\pi\)
0.0309603 + 0.999521i \(0.490143\pi\)
\(30\) 0 0
\(31\) −3.48040 + 6.02823i −0.625098 + 1.08270i 0.363424 + 0.931624i \(0.381608\pi\)
−0.988522 + 0.151078i \(0.951726\pi\)
\(32\) 2.71400 4.70079i 0.479773 0.830990i
\(33\) −3.57199 + 2.94497i −0.621804 + 0.512653i
\(34\) −0.764419 1.32401i −0.131097 0.227066i
\(35\) 0 0
\(36\) −0.956844 + 4.92641i −0.159474 + 0.821068i
\(37\) 1.81681 0.298682 0.149341 0.988786i \(-0.452285\pi\)
0.149341 + 0.988786i \(0.452285\pi\)
\(38\) 1.33641 + 2.31473i 0.216795 + 0.375499i
\(39\) −7.58123 2.83387i −1.21397 0.453782i
\(40\) 0 0
\(41\) 0.735581 1.27406i 0.114879 0.198975i −0.802853 0.596177i \(-0.796685\pi\)
0.917731 + 0.397202i \(0.130019\pi\)
\(42\) 1.32520 + 0.495361i 0.204483 + 0.0764358i
\(43\) 0.235581 + 0.408039i 0.0359258 + 0.0622254i 0.883429 0.468565i \(-0.155229\pi\)
−0.847503 + 0.530790i \(0.821895\pi\)
\(44\) −4.47116 −0.674053
\(45\) 0 0
\(46\) −3.38485 −0.499069
\(47\) 3.47842 + 6.02480i 0.507380 + 0.878808i 0.999964 + 0.00854274i \(0.00271927\pi\)
−0.492584 + 0.870265i \(0.663947\pi\)
\(48\) −2.86525 + 2.36228i −0.413563 + 0.340966i
\(49\) 2.48040 4.29618i 0.354343 0.613739i
\(50\) 0 0
\(51\) 0.764419 + 4.56592i 0.107040 + 0.639357i
\(52\) −3.90841 6.76956i −0.541998 0.938769i
\(53\) 1.14399 0.157139 0.0785693 0.996909i \(-0.474965\pi\)
0.0785693 + 0.996909i \(0.474965\pi\)
\(54\) −1.55239 + 2.53453i −0.211254 + 0.344906i
\(55\) 0 0
\(56\) 1.50000 + 2.59808i 0.200446 + 0.347183i
\(57\) −1.33641 7.98247i −0.177012 1.05730i
\(58\) −2.71400 + 4.70079i −0.356366 + 0.617244i
\(59\) 0.571993 0.990721i 0.0744672 0.128981i −0.826387 0.563102i \(-0.809608\pi\)
0.900854 + 0.434121i \(0.142941\pi\)
\(60\) 0 0
\(61\) 1.26442 + 2.19004i 0.161892 + 0.280406i 0.935547 0.353201i \(-0.114907\pi\)
−0.773655 + 0.633607i \(0.781574\pi\)
\(62\) −3.98153 −0.505655
\(63\) −3.23360 2.81009i −0.407396 0.354039i
\(64\) −1.18319 −0.147899
\(65\) 0 0
\(66\) −2.48040 0.927175i −0.305316 0.114127i
\(67\) −3.29523 + 5.70751i −0.402577 + 0.697283i −0.994036 0.109051i \(-0.965219\pi\)
0.591459 + 0.806335i \(0.298552\pi\)
\(68\) −2.23558 + 3.87214i −0.271104 + 0.469566i
\(69\) 9.60083 + 3.58880i 1.15580 + 0.432040i
\(70\) 0 0
\(71\) −12.8745 −1.52792 −0.763960 0.645263i \(-0.776748\pi\)
−0.763960 + 0.645263i \(0.776748\pi\)
\(72\) −5.95882 + 2.05277i −0.702254 + 0.241921i
\(73\) 1.71203 0.200378 0.100189 0.994968i \(-0.468055\pi\)
0.100189 + 0.994968i \(0.468055\pi\)
\(74\) 0.519602 + 0.899976i 0.0604025 + 0.104620i
\(75\) 0 0
\(76\) 3.90841 6.76956i 0.448325 0.776521i
\(77\) 1.90841 3.30545i 0.217483 0.376692i
\(78\) −0.764419 4.56592i −0.0865534 0.516989i
\(79\) 0.143987 + 0.249392i 0.0161998 + 0.0280588i 0.874012 0.485905i \(-0.161510\pi\)
−0.857812 + 0.513964i \(0.828177\pi\)
\(80\) 0 0
\(81\) 7.09046 5.54304i 0.787829 0.615894i
\(82\) 0.841495 0.0929276
\(83\) −2.14201 3.71007i −0.235116 0.407233i 0.724190 0.689600i \(-0.242214\pi\)
−0.959306 + 0.282367i \(0.908880\pi\)
\(84\) −0.683190 4.08074i −0.0745421 0.445245i
\(85\) 0 0
\(86\) −0.134751 + 0.233396i −0.0145306 + 0.0251677i
\(87\) 12.6821 10.4559i 1.35966 1.12098i
\(88\) −2.80757 4.86286i −0.299288 0.518383i
\(89\) −3.00000 −0.317999 −0.159000 0.987279i \(-0.550827\pi\)
−0.159000 + 0.987279i \(0.550827\pi\)
\(90\) 0 0
\(91\) 6.67282 0.699502
\(92\) 4.94958 + 8.57293i 0.516030 + 0.893790i
\(93\) 11.2933 + 4.22143i 1.17106 + 0.437742i
\(94\) −1.98963 + 3.44615i −0.205215 + 0.355443i
\(95\) 0 0
\(96\) −8.80644 3.29186i −0.898804 0.335974i
\(97\) 3.91764 + 6.78555i 0.397776 + 0.688968i 0.993451 0.114257i \(-0.0364487\pi\)
−0.595675 + 0.803225i \(0.703115\pi\)
\(98\) 2.83754 0.286635
\(99\) 6.05239 + 5.25970i 0.608288 + 0.528620i
\(100\) 0 0
\(101\) 2.10083 + 3.63875i 0.209040 + 0.362069i 0.951413 0.307919i \(-0.0996326\pi\)
−0.742372 + 0.669988i \(0.766299\pi\)
\(102\) −2.04316 + 1.68450i −0.202303 + 0.166790i
\(103\) −0.908405 + 1.57340i −0.0895078 + 0.155032i −0.907303 0.420477i \(-0.861863\pi\)
0.817795 + 0.575509i \(0.195196\pi\)
\(104\) 4.90841 8.50161i 0.481309 0.833651i
\(105\) 0 0
\(106\) 0.327176 + 0.566686i 0.0317782 + 0.0550414i
\(107\) −11.9176 −1.15212 −0.576061 0.817407i \(-0.695411\pi\)
−0.576061 + 0.817407i \(0.695411\pi\)
\(108\) 8.68932 + 0.225617i 0.836130 + 0.0217100i
\(109\) −16.6521 −1.59498 −0.797491 0.603331i \(-0.793840\pi\)
−0.797491 + 0.603331i \(0.793840\pi\)
\(110\) 0 0
\(111\) −0.519602 3.10361i −0.0493184 0.294582i
\(112\) 1.53081 2.65145i 0.144648 0.250538i
\(113\) 10.0616 17.4272i 0.946518 1.63942i 0.193836 0.981034i \(-0.437907\pi\)
0.752682 0.658384i \(-0.228760\pi\)
\(114\) 3.57199 2.94497i 0.334548 0.275821i
\(115\) 0 0
\(116\) 15.8745 1.47391
\(117\) −2.67282 + 13.7613i −0.247103 + 1.27223i
\(118\) 0.654353 0.0602380
\(119\) −1.90841 3.30545i −0.174943 0.303011i
\(120\) 0 0
\(121\) 1.92801 3.33941i 0.175273 0.303582i
\(122\) −0.723239 + 1.25269i −0.0654790 + 0.113413i
\(123\) −2.38683 0.892198i −0.215213 0.0804468i
\(124\) 5.82209 + 10.0842i 0.522839 + 0.905584i
\(125\) 0 0
\(126\) 0.467210 2.40548i 0.0416224 0.214297i
\(127\) −2.18714 −0.194078 −0.0970388 0.995281i \(-0.530937\pi\)
−0.0970388 + 0.995281i \(0.530937\pi\)
\(128\) −5.76640 9.98769i −0.509682 0.882795i
\(129\) 0.629668 0.519136i 0.0554391 0.0457074i
\(130\) 0 0
\(131\) 3.00000 5.19615i 0.262111 0.453990i −0.704692 0.709514i \(-0.748915\pi\)
0.966803 + 0.255524i \(0.0822479\pi\)
\(132\) 1.27874 + 7.63798i 0.111300 + 0.664801i
\(133\) 3.33641 + 5.77883i 0.289304 + 0.501089i
\(134\) −3.76970 −0.325653
\(135\) 0 0
\(136\) −5.61515 −0.481495
\(137\) −5.10083 8.83490i −0.435793 0.754816i 0.561567 0.827431i \(-0.310199\pi\)
−0.997360 + 0.0726153i \(0.976865\pi\)
\(138\) 0.968056 + 5.78226i 0.0824064 + 0.492218i
\(139\) −4.00000 + 6.92820i −0.339276 + 0.587643i −0.984297 0.176522i \(-0.943515\pi\)
0.645021 + 0.764165i \(0.276849\pi\)
\(140\) 0 0
\(141\) 9.29721 7.66518i 0.782966 0.645524i
\(142\) −3.68206 6.37751i −0.308992 0.535189i
\(143\) −12.4896 −1.04444
\(144\) 4.85488 + 4.21903i 0.404574 + 0.351586i
\(145\) 0 0
\(146\) 0.489634 + 0.848071i 0.0405224 + 0.0701868i
\(147\) −8.04844 3.00851i −0.663824 0.248138i
\(148\) 1.51960 2.63203i 0.124910 0.216351i
\(149\) 10.0381 17.3865i 0.822351 1.42435i −0.0815762 0.996667i \(-0.525995\pi\)
0.903927 0.427687i \(-0.140671\pi\)
\(150\) 0 0
\(151\) −1.51960 2.63203i −0.123663 0.214191i 0.797546 0.603258i \(-0.206131\pi\)
−0.921210 + 0.389066i \(0.872798\pi\)
\(152\) 9.81681 0.796248
\(153\) 7.58123 2.61168i 0.612906 0.211141i
\(154\) 2.18319 0.175926
\(155\) 0 0
\(156\) −10.4465 + 8.61270i −0.836388 + 0.689568i
\(157\) 0.100830 0.174643i 0.00804714 0.0139381i −0.861974 0.506953i \(-0.830772\pi\)
0.870021 + 0.493015i \(0.164105\pi\)
\(158\) −0.0823593 + 0.142651i −0.00655216 + 0.0113487i
\(159\) −0.327176 1.95424i −0.0259468 0.154982i
\(160\) 0 0
\(161\) −8.45043 −0.665987
\(162\) 4.77365 + 1.92705i 0.375054 + 0.151403i
\(163\) −17.8168 −1.39552 −0.697760 0.716331i \(-0.745820\pi\)
−0.697760 + 0.716331i \(0.745820\pi\)
\(164\) −1.23050 2.13129i −0.0960858 0.166425i
\(165\) 0 0
\(166\) 1.22522 2.12214i 0.0950952 0.164710i
\(167\) 7.05042 12.2117i 0.545578 0.944968i −0.452993 0.891514i \(-0.649644\pi\)
0.998570 0.0534538i \(-0.0170230\pi\)
\(168\) 4.00924 3.30545i 0.309319 0.255021i
\(169\) −4.41764 7.65158i −0.339819 0.588583i
\(170\) 0 0
\(171\) −13.2541 + 4.56592i −1.01356 + 0.349165i
\(172\) 0.788172 0.0600976
\(173\) 2.18319 + 3.78140i 0.165985 + 0.287494i 0.937005 0.349317i \(-0.113586\pi\)
−0.771020 + 0.636811i \(0.780253\pi\)
\(174\) 8.80644 + 3.29186i 0.667615 + 0.249555i
\(175\) 0 0
\(176\) −2.86525 + 4.96276i −0.215976 + 0.374082i
\(177\) −1.85601 0.693779i −0.139507 0.0521476i
\(178\) −0.857990 1.48608i −0.0643091 0.111387i
\(179\) −15.1625 −1.13330 −0.566648 0.823960i \(-0.691760\pi\)
−0.566648 + 0.823960i \(0.691760\pi\)
\(180\) 0 0
\(181\) 3.20166 0.237978 0.118989 0.992896i \(-0.462035\pi\)
0.118989 + 0.992896i \(0.462035\pi\)
\(182\) 1.90841 + 3.30545i 0.141460 + 0.245017i
\(183\) 3.37957 2.78632i 0.249825 0.205971i
\(184\) −6.21598 + 10.7664i −0.458248 + 0.793709i
\(185\) 0 0
\(186\) 1.13870 + 6.80155i 0.0834938 + 0.498714i
\(187\) 3.57199 + 6.18687i 0.261210 + 0.452429i
\(188\) 11.6376 0.848757
\(189\) −3.87562 + 6.32757i −0.281910 + 0.460263i
\(190\) 0 0
\(191\) 1.41877 + 2.45738i 0.102659 + 0.177810i 0.912779 0.408453i \(-0.133932\pi\)
−0.810121 + 0.586263i \(0.800598\pi\)
\(192\) 0.338388 + 2.02121i 0.0244211 + 0.145869i
\(193\) −9.39409 + 16.2710i −0.676201 + 1.17121i 0.299915 + 0.953966i \(0.403042\pi\)
−0.976116 + 0.217249i \(0.930292\pi\)
\(194\) −2.24086 + 3.88129i −0.160885 + 0.278660i
\(195\) 0 0
\(196\) −4.14927 7.18675i −0.296376 0.513339i
\(197\) −5.83528 −0.415747 −0.207873 0.978156i \(-0.566654\pi\)
−0.207873 + 0.978156i \(0.566654\pi\)
\(198\) −0.874485 + 4.50237i −0.0621469 + 0.319970i
\(199\) 13.0761 0.926943 0.463472 0.886112i \(-0.346604\pi\)
0.463472 + 0.886112i \(0.346604\pi\)
\(200\) 0 0
\(201\) 10.6924 + 3.99684i 0.754186 + 0.281915i
\(202\) −1.20166 + 2.08134i −0.0845486 + 0.146442i
\(203\) −6.77563 + 11.7357i −0.475556 + 0.823687i
\(204\) 7.25405 + 2.71157i 0.507885 + 0.189848i
\(205\) 0 0
\(206\) −1.03920 −0.0724047
\(207\) 3.38485 17.4272i 0.235263 1.21128i
\(208\) −10.0185 −0.694656
\(209\) −6.24482 10.8163i −0.431963 0.748182i
\(210\) 0 0
\(211\) −4.19243 + 7.26149i −0.288618 + 0.499902i −0.973480 0.228771i \(-0.926529\pi\)
0.684862 + 0.728673i \(0.259863\pi\)
\(212\) 0.956844 1.65730i 0.0657163 0.113824i
\(213\) 3.68206 + 21.9932i 0.252291 + 1.50695i
\(214\) −3.40841 5.90353i −0.232994 0.403557i
\(215\) 0 0
\(216\) 5.21090 + 9.59222i 0.354557 + 0.652668i
\(217\) −9.94006 −0.674776
\(218\) −4.76244 8.24879i −0.322553 0.558679i
\(219\) −0.489634 2.92461i −0.0330864 0.197627i
\(220\) 0 0
\(221\) −6.24482 + 10.8163i −0.420072 + 0.727586i
\(222\) 1.38880 1.14501i 0.0932104 0.0768482i
\(223\) 4.58321 + 7.93834i 0.306914 + 0.531591i 0.977686 0.210073i \(-0.0673702\pi\)
−0.670772 + 0.741664i \(0.734037\pi\)
\(224\) 7.75123 0.517901
\(225\) 0 0
\(226\) 11.5104 0.765658
\(227\) −1.33641 2.31473i −0.0887008 0.153634i 0.818261 0.574846i \(-0.194938\pi\)
−0.906962 + 0.421212i \(0.861605\pi\)
\(228\) −12.6821 4.74056i −0.839890 0.313951i
\(229\) −1.27365 + 2.20603i −0.0841654 + 0.145779i −0.905035 0.425336i \(-0.860156\pi\)
0.820870 + 0.571115i \(0.193489\pi\)
\(230\) 0 0
\(231\) −6.19243 2.31473i −0.407432 0.152298i
\(232\) 9.96806 + 17.2652i 0.654435 + 1.13351i
\(233\) 6.22013 0.407494 0.203747 0.979024i \(-0.434688\pi\)
0.203747 + 0.979024i \(0.434688\pi\)
\(234\) −7.58123 + 2.61168i −0.495600 + 0.170731i
\(235\) 0 0
\(236\) −0.956844 1.65730i −0.0622852 0.107881i
\(237\) 0.384851 0.317294i 0.0249987 0.0206105i
\(238\) 1.09159 1.89070i 0.0707576 0.122556i
\(239\) −4.06163 + 7.03494i −0.262725 + 0.455053i −0.966965 0.254909i \(-0.917954\pi\)
0.704240 + 0.709962i \(0.251288\pi\)
\(240\) 0 0
\(241\) 13.1821 + 22.8320i 0.849131 + 1.47074i 0.881985 + 0.471278i \(0.156207\pi\)
−0.0328536 + 0.999460i \(0.510460\pi\)
\(242\) 2.20561 0.141782
\(243\) −11.4969 10.5272i −0.737526 0.675319i
\(244\) 4.23030 0.270817
\(245\) 0 0
\(246\) −0.240665 1.43751i −0.0153442 0.0916520i
\(247\) 10.9176 18.9099i 0.694673 1.20321i
\(248\) −7.31173 + 12.6643i −0.464295 + 0.804183i
\(249\) −5.72522 + 4.72021i −0.362821 + 0.299131i
\(250\) 0 0
\(251\) −0.549569 −0.0346885 −0.0173443 0.999850i \(-0.505521\pi\)
−0.0173443 + 0.999850i \(0.505521\pi\)
\(252\) −6.77563 + 2.33415i −0.426825 + 0.147038i
\(253\) 15.8168 0.994394
\(254\) −0.625515 1.08342i −0.0392483 0.0679801i
\(255\) 0 0
\(256\) 2.11515 3.66355i 0.132197 0.228972i
\(257\) −9.00000 + 15.5885i −0.561405 + 0.972381i 0.435970 + 0.899961i \(0.356405\pi\)
−0.997374 + 0.0724199i \(0.976928\pi\)
\(258\) 0.437242 + 0.163441i 0.0272215 + 0.0101754i
\(259\) 1.29721 + 2.24683i 0.0806046 + 0.139611i
\(260\) 0 0
\(261\) −21.4885 18.6741i −1.33010 1.15590i
\(262\) 3.43196 0.212027
\(263\) 5.94761 + 10.3016i 0.366745 + 0.635221i 0.989055 0.147550i \(-0.0471387\pi\)
−0.622309 + 0.782771i \(0.713805\pi\)
\(264\) −7.50415 + 6.18687i −0.461849 + 0.380776i
\(265\) 0 0
\(266\) −1.90841 + 3.30545i −0.117012 + 0.202670i
\(267\) 0.857990 + 5.12483i 0.0525081 + 0.313634i
\(268\) 5.51234 + 9.54766i 0.336720 + 0.583216i
\(269\) 28.5737 1.74217 0.871084 0.491134i \(-0.163417\pi\)
0.871084 + 0.491134i \(0.163417\pi\)
\(270\) 0 0
\(271\) −23.3641 −1.41927 −0.709635 0.704570i \(-0.751140\pi\)
−0.709635 + 0.704570i \(0.751140\pi\)
\(272\) 2.86525 + 4.96276i 0.173731 + 0.300911i
\(273\) −1.90841 11.3990i −0.115502 0.689900i
\(274\) 2.91764 5.05350i 0.176261 0.305293i
\(275\) 0 0
\(276\) 13.2294 10.9071i 0.796314 0.656529i
\(277\) −7.53807 13.0563i −0.452919 0.784479i 0.545647 0.838015i \(-0.316284\pi\)
−0.998566 + 0.0535366i \(0.982951\pi\)
\(278\) −4.57595 −0.274447
\(279\) 3.98153 20.4993i 0.238368 1.22726i
\(280\) 0 0
\(281\) −3.32605 5.76088i −0.198415 0.343665i 0.749599 0.661892i \(-0.230246\pi\)
−0.948015 + 0.318226i \(0.896913\pi\)
\(282\) 6.45600 + 2.41326i 0.384449 + 0.143707i
\(283\) 13.4485 23.2934i 0.799428 1.38465i −0.120562 0.992706i \(-0.538470\pi\)
0.919989 0.391943i \(-0.128197\pi\)
\(284\) −10.7684 + 18.6514i −0.638985 + 1.10675i
\(285\) 0 0
\(286\) −3.57199 6.18687i −0.211216 0.365838i
\(287\) 2.10083 0.124008
\(288\) −3.10478 + 15.9853i −0.182951 + 0.941943i
\(289\) −9.85601 −0.579765
\(290\) 0 0
\(291\) 10.4712 8.63306i 0.613830 0.506079i
\(292\) 1.43196 2.48023i 0.0837991 0.145144i
\(293\) 6.19243 10.7256i 0.361765 0.626596i −0.626486 0.779433i \(-0.715507\pi\)
0.988251 + 0.152837i \(0.0488408\pi\)
\(294\) −0.811528 4.84730i −0.0473292 0.282701i
\(295\) 0 0
\(296\) 3.81681 0.221848
\(297\) 7.25405 11.8434i 0.420923 0.687224i
\(298\) 11.4834 0.665217
\(299\) 13.8260 + 23.9474i 0.799581 + 1.38491i
\(300\) 0 0
\(301\) −0.336412 + 0.582682i −0.0193905 + 0.0335853i
\(302\) 0.869202 1.50550i 0.0500169 0.0866319i
\(303\) 5.61515 4.62947i 0.322582 0.265956i
\(304\) −5.00924 8.67625i −0.287299 0.497617i
\(305\) 0 0
\(306\) 3.46193 + 3.00851i 0.197905 + 0.171985i
\(307\) 2.49359 0.142317 0.0711583 0.997465i \(-0.477330\pi\)
0.0711583 + 0.997465i \(0.477330\pi\)
\(308\) −3.19243 5.52944i −0.181905 0.315069i
\(309\) 2.94761 + 1.10182i 0.167684 + 0.0626802i
\(310\) 0 0
\(311\) 12.1101 20.9752i 0.686699 1.18940i −0.286201 0.958170i \(-0.592392\pi\)
0.972900 0.231228i \(-0.0742742\pi\)
\(312\) −15.9269 5.95348i −0.901682 0.337049i
\(313\) −17.5420 30.3837i −0.991534 1.71739i −0.608219 0.793770i \(-0.708116\pi\)
−0.383315 0.923618i \(-0.625218\pi\)
\(314\) 0.115349 0.00650950
\(315\) 0 0
\(316\) 0.481728 0.0270993
\(317\) −5.23558 9.06829i −0.294060 0.509326i 0.680706 0.732557i \(-0.261673\pi\)
−0.974766 + 0.223231i \(0.928340\pi\)
\(318\) 0.874485 0.720978i 0.0490387 0.0404304i
\(319\) 12.6821 21.9660i 0.710059 1.22986i
\(320\) 0 0
\(321\) 3.40841 + 20.3586i 0.190239 + 1.13631i
\(322\) −2.41679 4.18601i −0.134683 0.233277i
\(323\) −12.4896 −0.694942
\(324\) −2.09970 14.9083i −0.116650 0.828238i
\(325\) 0 0
\(326\) −5.09555 8.82575i −0.282216 0.488813i
\(327\) 4.76244 + 28.4464i 0.263364 + 1.57309i
\(328\) 1.54533 2.67659i 0.0853267 0.147790i
\(329\) −4.96721 + 8.60346i −0.273851 + 0.474324i
\(330\) 0 0
\(331\) −8.38880 14.5298i −0.461090 0.798632i 0.537925 0.842993i \(-0.319208\pi\)
−0.999016 + 0.0443606i \(0.985875\pi\)
\(332\) −7.16641 −0.393308
\(333\) −5.15322 + 1.77525i −0.282395 + 0.0972829i
\(334\) 8.06558 0.441329
\(335\) 0 0
\(336\) −4.96721 1.85675i −0.270984 0.101294i
\(337\) −13.5905 + 23.5394i −0.740320 + 1.28227i 0.212030 + 0.977263i \(0.431993\pi\)
−0.952350 + 0.305008i \(0.901341\pi\)
\(338\) 2.52686 4.37665i 0.137443 0.238058i
\(339\) −32.6481 12.2039i −1.77320 0.662825i
\(340\) 0 0
\(341\) 18.6050 1.00752
\(342\) −6.05239 5.25970i −0.327276 0.284412i
\(343\) 17.0801 0.922239
\(344\) 0.494917 + 0.857221i 0.0266841 + 0.0462182i
\(345\) 0 0
\(346\) −1.24877 + 2.16293i −0.0671343 + 0.116280i
\(347\) −11.7829 + 20.4086i −0.632539 + 1.09559i 0.354492 + 0.935059i \(0.384654\pi\)
−0.987031 + 0.160530i \(0.948680\pi\)
\(348\) −4.54005 27.1180i −0.243372 1.45368i
\(349\) 5.35601 + 9.27689i 0.286701 + 0.496580i 0.973020 0.230720i \(-0.0741081\pi\)
−0.686319 + 0.727300i \(0.740775\pi\)
\(350\) 0 0
\(351\) 24.2725 + 0.630233i 1.29557 + 0.0336393i
\(352\) −14.5081 −0.773285
\(353\) 13.6336 + 23.6141i 0.725644 + 1.25685i 0.958708 + 0.284392i \(0.0917916\pi\)
−0.233064 + 0.972461i \(0.574875\pi\)
\(354\) −0.187143 1.11781i −0.00994652 0.0594112i
\(355\) 0 0
\(356\) −2.50924 + 4.34612i −0.132989 + 0.230344i
\(357\) −5.10083 + 4.20543i −0.269965 + 0.222575i
\(358\) −4.33641 7.51089i −0.229186 0.396963i
\(359\) −10.6807 −0.563707 −0.281854 0.959457i \(-0.590949\pi\)
−0.281854 + 0.959457i \(0.590949\pi\)
\(360\) 0 0
\(361\) 2.83528 0.149225
\(362\) 0.915664 + 1.58598i 0.0481262 + 0.0833571i
\(363\) −6.25603 2.33851i −0.328356 0.122740i
\(364\) 5.58123 9.66697i 0.292536 0.506687i
\(365\) 0 0
\(366\) 2.34678 + 0.877227i 0.122668 + 0.0458534i
\(367\) −4.23558 7.33624i −0.221096 0.382949i 0.734045 0.679100i \(-0.237630\pi\)
−0.955141 + 0.296152i \(0.904297\pi\)
\(368\) 12.6873 0.661373
\(369\) −0.841495 + 4.33252i −0.0438065 + 0.225542i
\(370\) 0 0
\(371\) 0.816810 + 1.41476i 0.0424067 + 0.0734505i
\(372\) 15.5614 12.8298i 0.806822 0.665193i
\(373\) 5.06163 8.76700i 0.262081 0.453938i −0.704714 0.709492i \(-0.748925\pi\)
0.966795 + 0.255554i \(0.0822579\pi\)
\(374\) −2.04316 + 3.53885i −0.105649 + 0.182990i
\(375\) 0 0
\(376\) 7.30757 + 12.6571i 0.376859 + 0.652740i
\(377\) 44.3434 2.28380
\(378\) −4.24284 0.110165i −0.218228 0.00566626i
\(379\) 11.9216 0.612371 0.306186 0.951972i \(-0.400947\pi\)
0.306186 + 0.951972i \(0.400947\pi\)
\(380\) 0 0
\(381\) 0.625515 + 3.73624i 0.0320461 + 0.191414i
\(382\) −0.811528 + 1.40561i −0.0415214 + 0.0719171i
\(383\) 4.90841 8.50161i 0.250808 0.434412i −0.712941 0.701224i \(-0.752637\pi\)
0.963748 + 0.266813i \(0.0859705\pi\)
\(384\) −15.4126 + 12.7070i −0.786519 + 0.648453i
\(385\) 0 0
\(386\) −10.7467 −0.546993
\(387\) −1.06691 0.927175i −0.0542341 0.0471309i
\(388\) 13.1070 0.665409
\(389\) −4.61007 7.98487i −0.233740 0.404849i 0.725166 0.688574i \(-0.241763\pi\)
−0.958906 + 0.283725i \(0.908430\pi\)
\(390\) 0 0
\(391\) 7.90841 13.6978i 0.399945 0.692725i
\(392\) 5.21090 9.02554i 0.263190 0.455858i
\(393\) −9.73445 3.63875i −0.491038 0.183550i
\(394\) −1.66887 2.89057i −0.0840765 0.145625i
\(395\) 0 0
\(396\) 12.6821 4.36887i 0.637297 0.219544i
\(397\) 22.9793 1.15330 0.576648 0.816993i \(-0.304360\pi\)
0.576648 + 0.816993i \(0.304360\pi\)
\(398\) 3.73973 + 6.47741i 0.187456 + 0.324683i
\(399\) 8.91764 7.35224i 0.446440 0.368072i
\(400\) 0 0
\(401\) 5.53279 9.58307i 0.276294 0.478556i −0.694167 0.719814i \(-0.744227\pi\)
0.970461 + 0.241259i \(0.0775602\pi\)
\(402\) 1.07812 + 6.43969i 0.0537718 + 0.321183i
\(403\) 16.2633 + 28.1688i 0.810132 + 1.40319i
\(404\) 7.02864 0.349688
\(405\) 0 0
\(406\) −7.75123 −0.384687
\(407\) −2.42801 4.20543i −0.120352 0.208455i
\(408\) 1.60591 + 9.59222i 0.0795046 + 0.474886i
\(409\) 8.81681 15.2712i 0.435963 0.755110i −0.561411 0.827537i \(-0.689741\pi\)
0.997374 + 0.0724270i \(0.0230744\pi\)
\(410\) 0 0
\(411\) −13.6336 + 11.2404i −0.672497 + 0.554447i
\(412\) 1.51960 + 2.63203i 0.0748654 + 0.129671i
\(413\) 1.63362 0.0803852
\(414\) 9.60083 3.30741i 0.471855 0.162550i
\(415\) 0 0
\(416\) −12.6821 21.9660i −0.621789 1.07697i
\(417\) 12.9793 + 4.85166i 0.635597 + 0.237587i
\(418\) 3.57199 6.18687i 0.174712 0.302610i
\(419\) −18.5173 + 32.0730i −0.904631 + 1.56687i −0.0832199 + 0.996531i \(0.526520\pi\)
−0.821411 + 0.570336i \(0.806813\pi\)
\(420\) 0 0
\(421\) −2.52884 4.38007i −0.123248 0.213472i 0.797799 0.602924i \(-0.205998\pi\)
−0.921047 + 0.389452i \(0.872664\pi\)
\(422\) −4.79608 −0.233469
\(423\) −15.7532 13.6900i −0.765947 0.665630i
\(424\) 2.40332 0.116716
\(425\) 0 0
\(426\) −9.84150 + 8.11392i −0.476822 + 0.393121i
\(427\) −1.80560 + 3.12739i −0.0873790 + 0.151345i
\(428\) −9.96806 + 17.2652i −0.481824 + 0.834544i
\(429\) 3.57199 + 21.3357i 0.172457 + 1.03010i
\(430\) 0 0
\(431\) −5.23030 −0.251935 −0.125967 0.992034i \(-0.540203\pi\)
−0.125967 + 0.992034i \(0.540203\pi\)
\(432\) 5.81879 9.50011i 0.279957 0.457074i
\(433\) −34.3434 −1.65044 −0.825219 0.564813i \(-0.808948\pi\)
−0.825219 + 0.564813i \(0.808948\pi\)
\(434\) −2.84283 4.92392i −0.136460 0.236356i
\(435\) 0 0
\(436\) −13.9280 + 24.1240i −0.667031 + 1.15533i
\(437\) −13.8260 + 23.9474i −0.661389 + 1.14556i
\(438\) 1.30871 1.07898i 0.0625324 0.0515554i
\(439\) 9.77365 + 16.9285i 0.466471 + 0.807952i 0.999267 0.0382924i \(-0.0121918\pi\)
−0.532796 + 0.846244i \(0.678859\pi\)
\(440\) 0 0
\(441\) −2.83754 + 14.6094i −0.135121 + 0.695685i
\(442\) −7.14399 −0.339805
\(443\) 5.25208 + 9.09686i 0.249534 + 0.432205i 0.963396 0.268081i \(-0.0863893\pi\)
−0.713863 + 0.700286i \(0.753056\pi\)
\(444\) −4.93083 1.84315i −0.234007 0.0874719i
\(445\) 0 0
\(446\) −2.62156 + 4.54068i −0.124135 + 0.215007i
\(447\) −32.5717 12.1753i −1.54059 0.575873i
\(448\) −0.844801 1.46324i −0.0399131 0.0691315i
\(449\) 22.8560 1.07864 0.539321 0.842100i \(-0.318681\pi\)
0.539321 + 0.842100i \(0.318681\pi\)
\(450\) 0 0
\(451\) −3.93216 −0.185158
\(452\) −16.8313 29.1527i −0.791679 1.37123i
\(453\) −4.06163 + 3.34865i −0.190832 + 0.157333i
\(454\) 0.764419 1.32401i 0.0358759 0.0621390i
\(455\) 0 0
\(456\) −2.80757 16.7698i −0.131477 0.785319i
\(457\) −7.01319 12.1472i −0.328063 0.568222i 0.654064 0.756439i \(-0.273063\pi\)
−0.982127 + 0.188217i \(0.939729\pi\)
\(458\) −1.45704 −0.0680832
\(459\) −6.62967 12.2039i −0.309446 0.569629i
\(460\) 0 0
\(461\) 12.0513 + 20.8734i 0.561283 + 0.972171i 0.997385 + 0.0722736i \(0.0230255\pi\)
−0.436102 + 0.899897i \(0.643641\pi\)
\(462\) −0.624385 3.72949i −0.0290490 0.173512i
\(463\) −16.9700 + 29.3930i −0.788664 + 1.36601i 0.138121 + 0.990415i \(0.455894\pi\)
−0.926785 + 0.375591i \(0.877440\pi\)
\(464\) 10.1728 17.6198i 0.472261 0.817981i
\(465\) 0 0
\(466\) 1.77894 + 3.08121i 0.0824077 + 0.142734i
\(467\) 27.3720 1.26663 0.633313 0.773896i \(-0.281695\pi\)
0.633313 + 0.773896i \(0.281695\pi\)
\(468\) 17.7005 + 15.3823i 0.818207 + 0.711045i
\(469\) −9.41123 −0.434570
\(470\) 0 0
\(471\) −0.327176 0.122299i −0.0150755 0.00563523i
\(472\) 1.20166 2.08134i 0.0553109 0.0958013i
\(473\) 0.629668 1.09062i 0.0289521 0.0501466i
\(474\) 0.267241 + 0.0998949i 0.0122748 + 0.00458832i
\(475\) 0 0
\(476\) −6.38485 −0.292649
\(477\) −3.24482 + 1.11781i −0.148570 + 0.0511812i
\(478\) −4.64645 −0.212524
\(479\) −2.61515 4.52957i −0.119489 0.206961i 0.800076 0.599898i \(-0.204792\pi\)
−0.919565 + 0.392937i \(0.871459\pi\)
\(480\) 0 0
\(481\) 4.24482 7.35224i 0.193547 0.335233i
\(482\) −7.54005 + 13.0597i −0.343440 + 0.594855i
\(483\) 2.41679 + 14.4357i 0.109968 + 0.656846i
\(484\) −3.22522 5.58624i −0.146601 0.253920i
\(485\) 0 0
\(486\) 1.92668 8.70585i 0.0873958 0.394905i
\(487\) 24.0185 1.08838 0.544190 0.838962i \(-0.316837\pi\)
0.544190 + 0.838962i \(0.316837\pi\)
\(488\) 2.65633 + 4.60090i 0.120246 + 0.208273i
\(489\) 5.09555 + 30.4360i 0.230429 + 1.37636i
\(490\) 0 0
\(491\) −7.38880 + 12.7978i −0.333452 + 0.577556i −0.983186 0.182606i \(-0.941547\pi\)
0.649734 + 0.760161i \(0.274880\pi\)
\(492\) −3.28890 + 2.71157i −0.148275 + 0.122247i
\(493\) −12.6821 21.9660i −0.571171 0.989298i
\(494\) 12.4896 0.561935
\(495\) 0 0
\(496\) 14.9239 0.670101
\(497\) −9.19243 15.9217i −0.412337 0.714188i
\(498\) −3.97560 1.48608i −0.178151 0.0665929i
\(499\) −12.4280 + 21.5259i −0.556354 + 0.963633i 0.441443 + 0.897289i \(0.354467\pi\)
−0.997797 + 0.0663440i \(0.978867\pi\)
\(500\) 0 0
\(501\) −22.8773 8.55155i −1.02208 0.382055i
\(502\) −0.157175 0.272235i −0.00701506 0.0121504i
\(503\) −38.9154 −1.73515 −0.867576 0.497305i \(-0.834323\pi\)
−0.867576 + 0.497305i \(0.834323\pi\)
\(504\) −6.79326 5.90353i −0.302596 0.262964i
\(505\) 0 0
\(506\) 4.52355 + 7.83503i 0.201097 + 0.348309i
\(507\) −11.8076 + 9.73487i −0.524393 + 0.432341i
\(508\) −1.82935 + 3.16853i −0.0811644 + 0.140581i
\(509\) −1.01037 + 1.75001i −0.0447837 + 0.0775676i −0.887548 0.460715i \(-0.847593\pi\)
0.842765 + 0.538282i \(0.180927\pi\)
\(510\) 0 0
\(511\) 1.22239 + 2.11725i 0.0540755 + 0.0936615i
\(512\) −20.6459 −0.912428
\(513\) 11.5905 + 21.3357i 0.511732 + 0.941996i
\(514\) −10.2959 −0.454132
\(515\) 0 0
\(516\) −0.225415 1.34642i −0.00992333 0.0592726i
\(517\) 9.29721 16.1032i 0.408891 0.708220i
\(518\) −0.741995 + 1.28517i −0.0326014 + 0.0564672i
\(519\) 5.83528 4.81096i 0.256140 0.211178i
\(520\) 0 0
\(521\) −23.0290 −1.00892 −0.504460 0.863435i \(-0.668308\pi\)
−0.504460 + 0.863435i \(0.668308\pi\)
\(522\) 3.10478 15.9853i 0.135893 0.699657i
\(523\) 41.1170 1.79792 0.898961 0.438028i \(-0.144323\pi\)
0.898961 + 0.438028i \(0.144323\pi\)
\(524\) −5.01847 8.69225i −0.219233 0.379723i
\(525\) 0 0
\(526\) −3.40199 + 5.89242i −0.148334 + 0.256922i
\(527\) 9.30249 16.1124i 0.405223 0.701867i
\(528\) 9.29721 + 3.47530i 0.404609 + 0.151243i
\(529\) −6.00924 10.4083i −0.261271 0.452535i
\(530\) 0 0
\(531\) −0.654353 + 3.36900i −0.0283965 + 0.146202i
\(532\) 11.1625 0.483954
\(533\) −3.43724 5.95348i −0.148883 0.257874i
\(534\) −2.29326 + 1.89070i −0.0992389 + 0.0818185i
\(535\) 0 0
\(536\) −6.92272 + 11.9905i −0.299016 + 0.517911i
\(537\) 4.33641 + 25.9017i 0.187130 + 1.11774i
\(538\) 8.17198 + 14.1543i 0.352319 + 0.610234i
\(539\) −13.2593 −0.571120
\(540\) 0 0
\(541\) 5.20957 0.223977 0.111988 0.993710i \(-0.464278\pi\)
0.111988 + 0.993710i \(0.464278\pi\)
\(542\) −6.68206 11.5737i −0.287019 0.497132i
\(543\) −0.915664 5.46932i −0.0392949 0.234711i
\(544\) −7.25405 + 12.5644i −0.311015 + 0.538694i
\(545\) 0 0
\(546\) 5.10083 4.20543i 0.218295 0.179976i
\(547\) 20.0204 + 34.6764i 0.856013 + 1.48266i 0.875702 + 0.482851i \(0.160399\pi\)
−0.0196900 + 0.999806i \(0.506268\pi\)
\(548\) −17.0656 −0.729005
\(549\) −5.72635 4.97636i −0.244394 0.212386i
\(550\) 0 0
\(551\) 22.1717 + 38.4025i 0.944546 + 1.63600i
\(552\) 20.1697 + 7.53946i 0.858480 + 0.320901i
\(553\) −0.205614 + 0.356133i −0.00874359 + 0.0151443i
\(554\) 4.31173 7.46813i 0.183188 0.317290i
\(555\) 0 0
\(556\) 6.69129 + 11.5897i 0.283774 + 0.491511i
\(557\) 14.4033 0.610288 0.305144 0.952306i \(-0.401295\pi\)
0.305144 + 0.952306i \(0.401295\pi\)
\(558\) 11.2933 3.89044i 0.478082 0.164695i
\(559\) 2.20166 0.0931203
\(560\) 0 0
\(561\) 9.54731 7.87137i 0.403088 0.332330i
\(562\) 1.90248 3.29518i 0.0802511 0.138999i
\(563\) 14.6840 25.4335i 0.618858 1.07189i −0.370836 0.928698i \(-0.620929\pi\)
0.989694 0.143196i \(-0.0457378\pi\)
\(564\) −3.32831 19.8802i −0.140147 0.837107i
\(565\) 0 0
\(566\) 15.3849 0.646674
\(567\) 11.9176 + 4.81096i 0.500494 + 0.202041i
\(568\) −27.0471 −1.13487
\(569\) −23.4033 40.5357i −0.981118 1.69935i −0.658056 0.752969i \(-0.728621\pi\)
−0.323062 0.946378i \(-0.604712\pi\)
\(570\) 0 0
\(571\) −10.0000 + 17.3205i −0.418487 + 0.724841i −0.995788 0.0916910i \(-0.970773\pi\)
0.577301 + 0.816532i \(0.304106\pi\)
\(572\) −10.4465 + 18.0938i −0.436789 + 0.756541i
\(573\) 3.79213 3.12646i 0.158418 0.130610i
\(574\) 0.600830 + 1.04067i 0.0250782 + 0.0434367i
\(575\) 0 0
\(576\) 3.35601 1.15612i 0.139834 0.0481717i
\(577\) −28.2386 −1.17559 −0.587794 0.809010i \(-0.700004\pi\)
−0.587794 + 0.809010i \(0.700004\pi\)
\(578\) −2.81879 4.88228i −0.117246 0.203076i
\(579\) 30.4821 + 11.3942i 1.26679 + 0.473528i
\(580\) 0 0
\(581\) 3.05880 5.29801i 0.126901 0.219798i
\(582\) 7.27119 + 2.71798i 0.301401 + 0.112664i
\(583\) −1.52884 2.64802i −0.0633180 0.109670i
\(584\) 3.59668 0.148832
\(585\) 0 0
\(586\) 7.08405 0.292639
\(587\) 9.04118 + 15.6598i 0.373169 + 0.646348i 0.990051 0.140707i \(-0.0449377\pi\)
−0.616882 + 0.787056i \(0.711604\pi\)
\(588\) −11.0903 + 9.14348i −0.457355 + 0.377071i
\(589\) −16.2633 + 28.1688i −0.670117 + 1.16068i
\(590\) 0 0
\(591\) 1.66887 + 9.96827i 0.0686482 + 0.410040i
\(592\) −1.94761 3.37336i −0.0800462 0.138644i
\(593\) 7.73840 0.317778 0.158889 0.987296i \(-0.449209\pi\)
0.158889 + 0.987296i \(0.449209\pi\)
\(594\) 7.94139 + 0.206197i 0.325839 + 0.00846037i
\(595\) 0 0
\(596\) −16.7919 29.0845i −0.687824 1.19135i
\(597\) −3.73973 22.3377i −0.153057 0.914220i
\(598\) −7.90841 + 13.6978i −0.323399 + 0.560143i
\(599\) 13.9608 24.1808i 0.570423 0.988001i −0.426100 0.904676i \(-0.640113\pi\)
0.996522 0.0833249i \(-0.0265539\pi\)
\(600\) 0 0
\(601\) −19.2201 33.2902i −0.784006 1.35794i −0.929591 0.368592i \(-0.879840\pi\)
0.145586 0.989346i \(-0.453493\pi\)
\(602\) −0.384851 −0.0156853
\(603\) 3.76970 19.4087i 0.153514 0.790383i
\(604\) −5.08405 −0.206867
\(605\) 0 0
\(606\) 3.89917 + 1.45751i 0.158393 + 0.0592074i
\(607\) −0.319917 + 0.554113i −0.0129850 + 0.0224907i −0.872445 0.488712i \(-0.837467\pi\)
0.859460 + 0.511203i \(0.170800\pi\)
\(608\) 12.6821 21.9660i 0.514325 0.890838i
\(609\) 21.9857 + 8.21826i 0.890905 + 0.333021i
\(610\) 0 0
\(611\) 32.5081 1.31514
\(612\) 2.55748 13.1674i 0.103380 0.532261i
\(613\) −42.7467 −1.72652 −0.863262 0.504757i \(-0.831582\pi\)
−0.863262 + 0.504757i \(0.831582\pi\)
\(614\) 0.713157 + 1.23522i 0.0287807 + 0.0498496i
\(615\) 0 0
\(616\) 4.00924 6.94420i 0.161537 0.279790i
\(617\) 10.5513 18.2753i 0.424778 0.735737i −0.571622 0.820517i \(-0.693686\pi\)
0.996400 + 0.0847805i \(0.0270189\pi\)
\(618\) 0.297209 + 1.77525i 0.0119555 + 0.0714109i
\(619\) 6.82605 + 11.8231i 0.274362 + 0.475209i 0.969974 0.243209i \(-0.0782000\pi\)
−0.695612 + 0.718418i \(0.744867\pi\)
\(620\) 0 0
\(621\) −30.7386 0.798123i −1.23350 0.0320276i
\(622\) 13.8538 0.555485
\(623\) −2.14201 3.71007i −0.0858178 0.148641i
\(624\) 2.86525 + 17.1143i 0.114702 + 0.685121i
\(625\) 0 0
\(626\) 10.0339 17.3793i 0.401036 0.694615i
\(627\) −16.6913 + 13.7613i −0.666586 + 0.549574i
\(628\) −0.168672 0.292148i −0.00673073 0.0116580i
\(629\) −4.85601 −0.193622
\(630\) 0 0
\(631\) 33.2593 1.32403 0.662017 0.749489i \(-0.269701\pi\)
0.662017 + 0.749489i \(0.269701\pi\)
\(632\) 0.302491 + 0.523930i 0.0120325 + 0.0208408i
\(633\) 13.6037 + 5.08506i 0.540697 + 0.202113i
\(634\) 2.99472 5.18700i 0.118935 0.206002i
\(635\) 0 0
\(636\) −3.10478 1.16057i −0.123113 0.0460196i
\(637\) −11.5905 20.0753i −0.459231 0.795411i
\(638\) 14.5081 0.574381
\(639\) 36.5173 12.5799i 1.44460 0.497655i
\(640\) 0 0
\(641\) −13.1429 22.7641i −0.519112 0.899128i −0.999753 0.0222106i \(-0.992930\pi\)
0.480642 0.876917i \(-0.340404\pi\)
\(642\) −9.11007 + 7.51089i −0.359546 + 0.296431i
\(643\) 10.2913 17.8250i 0.405848 0.702950i −0.588571 0.808445i \(-0.700309\pi\)
0.994420 + 0.105495i \(0.0336427\pi\)
\(644\) −7.06804 + 12.2422i −0.278520 + 0.482410i
\(645\) 0 0
\(646\) −3.57199 6.18687i −0.140538 0.243419i
\(647\) −23.2527 −0.914159 −0.457079 0.889426i \(-0.651104\pi\)
−0.457079 + 0.889426i \(0.651104\pi\)
\(648\) 14.8959 11.6450i 0.585165 0.457458i
\(649\) −3.05767 −0.120024
\(650\) 0 0
\(651\) 2.84283 + 16.9804i 0.111419 + 0.665513i
\(652\) −14.9022 + 25.8114i −0.583615 + 1.01085i
\(653\) 9.37957 16.2459i 0.367051 0.635751i −0.622052 0.782976i \(-0.713701\pi\)
0.989103 + 0.147225i \(0.0470342\pi\)
\(654\) −12.7292 + 10.4947i −0.497750 + 0.410375i
\(655\) 0 0
\(656\) −3.15415 −0.123149
\(657\) −4.85601 + 1.67286i −0.189451 + 0.0652645i
\(658\) −5.68242 −0.221524
\(659\) 0.140034 + 0.242545i 0.00545494 + 0.00944823i 0.868740 0.495268i \(-0.164930\pi\)
−0.863285 + 0.504717i \(0.831597\pi\)
\(660\) 0 0
\(661\) 19.8930 34.4556i 0.773746 1.34017i −0.161750 0.986832i \(-0.551714\pi\)
0.935496 0.353336i \(-0.114953\pi\)
\(662\) 4.79834 8.31097i 0.186493 0.323015i
\(663\) 20.2633 + 7.57443i 0.786961 + 0.294167i
\(664\) −4.50000 7.79423i −0.174634 0.302475i
\(665\) 0 0
\(666\) −2.35319 2.04499i −0.0911843 0.0792417i
\(667\) −56.1562 −2.17438
\(668\) −11.7941 20.4280i −0.456327 0.790382i
\(669\) 12.2501 10.0997i 0.473616 0.390478i
\(670\) 0 0
\(671\) 3.37957 5.85358i 0.130467 0.225975i
\(672\) −2.21683 13.2412i −0.0855159 0.510792i
\(673\) 16.7644 + 29.0368i 0.646221 + 1.11929i 0.984018 + 0.178068i \(0.0569848\pi\)
−0.337797 + 0.941219i \(0.609682\pi\)
\(674\) −15.5473 −0.598860
\(675\) 0 0
\(676\) −14.7799 −0.568456
\(677\) 13.7437 + 23.8048i 0.528213 + 0.914891i 0.999459 + 0.0328897i \(0.0104710\pi\)
−0.471246 + 0.882002i \(0.656196\pi\)
\(678\) −3.29193 19.6629i −0.126426 0.755148i
\(679\) −5.59442 + 9.68981i −0.214694 + 0.371861i
\(680\) 0 0
\(681\) −3.57199 + 2.94497i −0.136879 + 0.112851i
\(682\) 5.32096 + 9.21618i 0.203750 + 0.352906i
\(683\) 34.5865 1.32342 0.661708 0.749762i \(-0.269832\pi\)
0.661708 + 0.749762i \(0.269832\pi\)
\(684\) −4.47116 + 23.0202i −0.170959 + 0.880201i
\(685\) 0 0
\(686\) 4.88485 + 8.46081i 0.186504 + 0.323035i
\(687\) 4.13277 + 1.54483i 0.157675 + 0.0589391i
\(688\) 0.505083 0.874830i 0.0192561 0.0333526i
\(689\) 2.67282 4.62947i 0.101826 0.176369i
\(690\) 0 0
\(691\) −20.3641 35.2717i −0.774688 1.34180i −0.934970 0.354727i \(-0.884574\pi\)
0.160282 0.987071i \(-0.448760\pi\)
\(692\) 7.30418 0.277663
\(693\) −2.18319 + 11.2404i −0.0829325 + 0.426987i
\(694\) −13.4795 −0.511674
\(695\) 0 0
\(696\) 26.6429 21.9660i 1.00989 0.832618i
\(697\) −1.96608 + 3.40535i −0.0744706 + 0.128987i
\(698\) −3.06360 + 5.30632i −0.115959 + 0.200847i
\(699\) −1.77894 10.6257i −0.0672856 0.401901i
\(700\) 0 0
\(701\) −19.4712 −0.735416 −0.367708 0.929941i \(-0.619857\pi\)
−0.367708 + 0.929941i \(0.619857\pi\)
\(702\) 6.62967 + 12.2039i 0.250221 + 0.460606i
\(703\) 8.48963 0.320193
\(704\) 1.58123 + 2.73877i 0.0595948 + 0.103221i
\(705\) 0 0
\(706\) −7.79834 + 13.5071i −0.293494 + 0.508347i
\(707\) −3.00000 + 5.19615i −0.112827 + 0.195421i
\(708\) −2.55748 + 2.10854i −0.0961158 + 0.0792436i
\(709\) −7.54316 13.0651i −0.283289 0.490671i 0.688904 0.724853i \(-0.258092\pi\)
−0.972193 + 0.234182i \(0.924759\pi\)
\(710\) 0 0
\(711\) −0.652092 0.566686i −0.0244553 0.0212524i
\(712\) −6.30249 −0.236196
\(713\) −20.5957 35.6729i −0.771317 1.33596i
\(714\) −3.54203 1.32401i −0.132557 0.0495499i
\(715\) 0 0
\(716\) −12.6821 + 21.9660i −0.473951 + 0.820907i
\(717\) 13.1792 + 4.92641i 0.492188 + 0.183980i
\(718\) −3.05465 5.29081i −0.113999 0.197451i
\(719\) −3.43196 −0.127990 −0.0639952 0.997950i \(-0.520384\pi\)
−0.0639952 + 0.997950i \(0.520384\pi\)
\(720\) 0 0
\(721\) −2.59442 −0.0966211
\(722\) 0.810881 + 1.40449i 0.0301779 + 0.0522696i
\(723\) 35.2333 29.0485i 1.31034 1.08032i
\(724\) 2.67791 4.63827i 0.0995236 0.172380i
\(725\) 0 0
\(726\) −0.630798 3.76780i −0.0234111 0.139836i
\(727\) −17.8857 30.9789i −0.663344 1.14895i −0.979732 0.200315i \(-0.935803\pi\)
0.316388 0.948630i \(-0.397530\pi\)
\(728\) 14.0185 0.519559
\(729\) −14.6952 + 22.6506i −0.544268 + 0.838911i
\(730\) 0 0
\(731\) −0.629668 1.09062i −0.0232891 0.0403379i
\(732\) −1.20985 7.22652i −0.0447174 0.267100i
\(733\) −11.0000 + 19.0526i −0.406294 + 0.703722i −0.994471 0.105010i \(-0.966513\pi\)
0.588177 + 0.808732i \(0.299846\pi\)
\(734\) 2.42272 4.19628i 0.0894244 0.154888i
\(735\) 0 0
\(736\) 16.0605 + 27.8176i 0.591998 + 1.02537i
\(737\) 17.6151 0.648862
\(738\) −2.38683 + 0.822244i −0.0878603 + 0.0302672i
\(739\) 6.08631 0.223889 0.111944 0.993714i \(-0.464292\pi\)
0.111944 + 0.993714i \(0.464292\pi\)
\(740\) 0 0
\(741\) −35.4257 13.2422i −1.30140 0.486463i
\(742\) −0.467210 + 0.809231i −0.0171518 + 0.0297078i
\(743\) −12.7509 + 22.0853i −0.467787 + 0.810231i −0.999322 0.0368054i \(-0.988282\pi\)
0.531536 + 0.847036i \(0.321615\pi\)
\(744\) 23.7252 + 8.86850i 0.869809 + 0.325135i
\(745\) 0 0
\(746\) 5.79043 0.212003
\(747\) 9.70081 + 8.43028i 0.354934 + 0.308448i
\(748\) 11.9506 0.436958
\(749\) −8.50924 14.7384i −0.310921 0.538530i
\(750\) 0 0
\(751\) 9.19638 15.9286i 0.335581 0.581243i −0.648016 0.761627i \(-0.724401\pi\)
0.983596 + 0.180384i \(0.0577342\pi\)
\(752\) 7.45769 12.9171i 0.271954 0.471038i
\(753\) 0.157175 + 0.938816i 0.00572777 + 0.0342124i
\(754\) 12.6821 + 21.9660i 0.461853 + 0.799953i
\(755\) 0 0
\(756\) 5.92518 + 10.9071i 0.215497 + 0.396687i
\(757\) 41.8986 1.52283 0.761415 0.648264i \(-0.224505\pi\)
0.761415 + 0.648264i \(0.224505\pi\)
\(758\) 3.40954 + 5.90549i 0.123840 + 0.214497i
\(759\) −4.52355 27.0195i −0.164195 0.980745i
\(760\) 0 0
\(761\) 3.98568 6.90340i 0.144481 0.250248i −0.784698 0.619878i \(-0.787182\pi\)
0.929179 + 0.369630i \(0.120515\pi\)
\(762\) −1.67189 + 1.37841i −0.0605663 + 0.0499345i
\(763\) −11.8896 20.5935i −0.430434 0.745534i
\(764\) 4.74671 0.171730
\(765\) 0 0
\(766\) 5.61515 0.202884
\(767\) −2.67282 4.62947i −0.0965101 0.167160i
\(768\) −6.86327 2.56550i −0.247657 0.0925744i
\(769\) −3.01432 + 5.22095i −0.108699 + 0.188272i −0.915244 0.402901i \(-0.868002\pi\)
0.806544 + 0.591174i \(0.201335\pi\)
\(770\) 0 0
\(771\) 29.2034 + 10.9162i 1.05173 + 0.393139i
\(772\) 15.7147 + 27.2186i 0.565583 + 0.979618i
\(773\) −44.4033 −1.59708 −0.798538 0.601944i \(-0.794393\pi\)
−0.798538 + 0.601944i \(0.794393\pi\)
\(774\) 0.154153 0.793674i 0.00554093 0.0285280i
\(775\) 0 0
\(776\) 8.23030 + 14.2553i 0.295451 + 0.511735i
\(777\) 3.46721 2.85858i 0.124385 0.102551i
\(778\) 2.63693 4.56729i 0.0945384 0.163745i
\(779\) 3.43724 5.95348i 0.123152 0.213305i
\(780\) 0 0
\(781\) 17.2056 + 29.8010i 0.615665 + 1.06636i
\(782\) 9.04711 0.323524
\(783\) −25.7549 + 42.0490i −0.920405 + 1.50271i
\(784\) −10.6359 −0.379853
\(785\) 0 0
\(786\) −0.981529 5.86273i −0.0350100 0.209117i
\(787\) 8.41877 14.5817i 0.300097 0.519783i −0.676061 0.736846i \(-0.736314\pi\)
0.976158 + 0.217063i \(0.0696477\pi\)
\(788\) −4.88070 + 8.45362i −0.173868 + 0.301148i
\(789\) 15.8969 13.1064i 0.565945 0.466599i
\(790\) 0 0
\(791\) 28.7361 1.02174
\(792\) 12.7150 + 11.0497i 0.451810 + 0.392635i
\(793\) 11.8168 0.419627
\(794\) 6.57199 + 11.3830i 0.233231 + 0.403968i
\(795\) 0 0
\(796\) 10.9370 18.9435i 0.387653 0.671435i
\(797\) −16.6860 + 28.9010i −0.591049 + 1.02373i 0.403043 + 0.915181i \(0.367953\pi\)
−0.994091 + 0.108545i \(0.965381\pi\)
\(798\) 6.19243 + 2.31473i 0.219209 + 0.0819407i
\(799\) −9.29721 16.1032i −0.328912 0.569692i
\(800\) 0 0
\(801\) 8.50924 2.93137i 0.300659 0.103575i
\(802\) 6.32944 0.223500
\(803\) −2.28797 3.96289i −0.0807408 0.139847i
\(804\) 14.7335 12.1472i 0.519611 0.428399i
\(805\) 0 0
\(806\) −9.30249 + 16.1124i −0.327666 + 0.567535i
\(807\) −8.17198 48.8117i −0.287667 1.71825i
\(808\) 4.41349 + 7.64439i 0.155266 + 0.268929i
\(809\) 29.1809 1.02595 0.512973 0.858404i \(-0.328544\pi\)
0.512973 + 0.858404i \(0.328544\pi\)
\(810\) 0 0
\(811\) −15.5552 −0.546217 −0.273109 0.961983i \(-0.588052\pi\)
−0.273109 + 0.961983i \(0.588052\pi\)
\(812\) 11.3344 + 19.6318i 0.397761 + 0.688942i
\(813\) 6.68206 + 39.9124i 0.234350 + 1.39979i
\(814\) 1.38880 2.40548i 0.0486775 0.0843120i
\(815\) 0 0
\(816\) 7.65831 6.31397i 0.268094 0.221033i
\(817\) 1.10083 + 1.90669i 0.0385132 + 0.0667068i
\(818\) 10.0863 0.352660
\(819\) −18.9269 + 6.52016i −0.661359 + 0.227833i
\(820\) 0 0
\(821\) 11.8588 + 20.5401i 0.413876 + 0.716855i 0.995310 0.0967393i \(-0.0308413\pi\)
−0.581434 + 0.813594i \(0.697508\pi\)
\(822\) −9.46721 3.53885i −0.330207 0.123432i
\(823\) 9.68404 16.7732i 0.337564 0.584678i −0.646410 0.762990i \(-0.723730\pi\)
0.983974 + 0.178312i \(0.0570636\pi\)
\(824\) −1.90841 + 3.30545i −0.0664824 + 0.115151i
\(825\) 0 0
\(826\) 0.467210 + 0.809231i 0.0162563 + 0.0281568i
\(827\) −52.2241 −1.81601 −0.908005 0.418960i \(-0.862395\pi\)
−0.908005 + 0.418960i \(0.862395\pi\)
\(828\) −22.4159 19.4800i −0.779005 0.676977i
\(829\) −26.6442 −0.925391 −0.462695 0.886517i \(-0.653118\pi\)
−0.462695 + 0.886517i \(0.653118\pi\)
\(830\) 0 0
\(831\) −20.1479 + 16.6112i −0.698924 + 0.576235i
\(832\) −2.76442 + 4.78811i −0.0958390 + 0.165998i
\(833\) −6.62967 + 11.4829i −0.229704 + 0.397860i
\(834\) 1.30871 + 7.81698i 0.0453168 + 0.270680i
\(835\) 0 0
\(836\) −20.8930 −0.722598
\(837\) −36.1572 0.938816i −1.24977 0.0324502i
\(838\) −21.1836 −0.731775
\(839\) 12.5196 + 21.6846i 0.432225 + 0.748635i 0.997065 0.0765655i \(-0.0243954\pi\)
−0.564840 + 0.825201i \(0.691062\pi\)
\(840\) 0 0
\(841\) −30.5266 + 52.8736i −1.05264 + 1.82323i
\(842\) 1.44648 2.50537i 0.0498489 0.0863409i
\(843\) −8.88993 + 7.32940i −0.306186 + 0.252438i
\(844\) 7.01319 + 12.1472i 0.241404 + 0.418124i
\(845\) 0 0
\(846\) 2.27611 11.7188i 0.0782544 0.402901i
\(847\) 5.50641 0.189203
\(848\) −1.22635 2.12409i −0.0421129 0.0729417i
\(849\) −43.6378 16.3118i −1.49764 0.559821i
\(850\) 0 0
\(851\) −5.37562 + 9.31084i −0.184274 + 0.319171i
\(852\) 34.9414 + 13.0611i 1.19707 + 0.447467i
\(853\) −5.43724 9.41758i −0.186168 0.322452i 0.757802 0.652485i \(-0.226273\pi\)
−0.943969 + 0.330033i \(0.892940\pi\)
\(854\) −2.06558 −0.0706827
\(855\) 0 0
\(856\) −25.0369 −0.855745
\(857\) −9.29721 16.1032i −0.317587 0.550076i 0.662397 0.749153i \(-0.269539\pi\)
−0.979984 + 0.199077i \(0.936206\pi\)
\(858\) −9.54731 + 7.87137i −0.325940 + 0.268724i
\(859\) 2.33246 4.03994i 0.0795825 0.137841i −0.823487 0.567335i \(-0.807975\pi\)
0.903070 + 0.429494i \(0.141308\pi\)
\(860\) 0 0
\(861\) −0.600830 3.58880i −0.0204762 0.122306i
\(862\) −1.49585 2.59088i −0.0509488 0.0882459i
\(863\) 28.0594 0.955152 0.477576 0.878590i \(-0.341516\pi\)
0.477576 + 0.878590i \(0.341516\pi\)
\(864\) 28.1952 + 0.732086i 0.959222 + 0.0249061i
\(865\) 0 0
\(866\) −9.82209 17.0124i −0.333768 0.578104i
\(867\) 2.81879 + 16.8368i 0.0957310 + 0.571807i
\(868\) −8.31399 + 14.4002i −0.282195 + 0.488776i
\(869\) 0.384851 0.666581i 0.0130552 0.0226122i
\(870\) 0 0
\(871\) 15.3980 + 26.6702i 0.521743 + 0.903685i
\(872\) −34.9832 −1.18468
\(873\) −17.7424 15.4186i −0.600488 0.521841i
\(874\) −15.8168 −0.535012
\(875\) 0 0
\(876\) −4.64645 1.73685i −0.156989 0.0586826i
\(877\) 17.3342 30.0236i 0.585333 1.01383i −0.409501 0.912310i \(-0.634297\pi\)
0.994834 0.101516i \(-0.0323694\pi\)
\(878\) −5.59046 + 9.68297i −0.188669 + 0.326784i
\(879\) −20.0933 7.51089i −0.677730 0.253336i
\(880\) 0 0
\(881\) −5.29854 −0.178512 −0.0892561 0.996009i \(-0.528449\pi\)
−0.0892561 + 0.996009i \(0.528449\pi\)
\(882\) −8.04844 + 2.77263i −0.271005 + 0.0933592i
\(883\) 10.3025 0.346706 0.173353 0.984860i \(-0.444540\pi\)
0.173353 + 0.984860i \(0.444540\pi\)
\(884\) 10.4465 + 18.0938i 0.351353 + 0.608561i
\(885\) 0 0
\(886\) −3.00415 + 5.20334i −0.100926 + 0.174810i
\(887\) 20.7252 35.8971i 0.695885 1.20531i −0.273997 0.961731i \(-0.588346\pi\)
0.969882 0.243577i \(-0.0783208\pi\)
\(888\) −1.09159 6.52016i −0.0366315 0.218802i
\(889\) −1.56163 2.70482i −0.0523753 0.0907167i
\(890\) 0 0
\(891\) −22.3064 9.00475i −0.747294 0.301670i
\(892\) 15.3338 0.513413
\(893\) 16.2541 + 28.1528i 0.543921 + 0.942099i
\(894\) −3.28422 19.6168i −0.109841 0.656086i
\(895\) 0 0
\(896\) 8.23445 14.2625i 0.275094 0.476476i
\(897\) 36.9546 30.4676i 1.23388 1.01728i
\(898\) 6.53674 + 11.3220i 0.218134 + 0.377819i
\(899\) −66.0554 −2.20307
\(900\) 0 0
\(901\) −3.05767 −0.101866
\(902\) −1.12458 1.94784i −0.0374446 0.0648559i
\(903\) 1.09159 + 0.408039i 0.0363260 + 0.0135787i
\(904\) 21.1378 36.6117i 0.703032 1.21769i
\(905\) 0 0
\(906\) −2.82040 1.05427i −0.0937015 0.0350257i
\(907\) −8.39606 14.5424i −0.278787 0.482873i 0.692297 0.721613i \(-0.256599\pi\)
−0.971083 + 0.238740i \(0.923266\pi\)
\(908\) −4.47116 −0.148381
\(909\) −9.51432 8.26821i −0.315570 0.274239i
\(910\) 0 0
\(911\) −18.6768 32.3491i −0.618789 1.07177i −0.989707 0.143109i \(-0.954290\pi\)
0.370918 0.928666i \(-0.379043\pi\)
\(912\) −13.3888 + 11.0385i −0.443348 + 0.365522i
\(913\) −5.72522 + 9.91636i −0.189477 + 0.328184i
\(914\) 4.01150 6.94812i 0.132689 0.229823i
\(915\) 0 0
\(916\) 2.13060 + 3.69031i 0.0703970 + 0.121931i
\(917\) 8.56804 0.282942
\(918\) 4.14927 6.77435i 0.136946 0.223587i
\(919\) 37.1316 1.22486 0.612429 0.790526i \(-0.290193\pi\)
0.612429 + 0.790526i \(0.290193\pi\)
\(920\) 0 0
\(921\) −0.713157 4.25973i −0.0234993 0.140363i
\(922\) −6.89324 + 11.9394i −0.227017 + 0.393205i
\(923\) −30.0801 + 52.1003i −0.990098 + 1.71490i
\(924\) −8.53279 + 7.03494i −0.280708 + 0.231433i
\(925\) 0 0
\(926\) −19.4135 −0.637967
\(927\) 1.03920 5.35044i 0.0341319 0.175732i
\(928\) 51.5098 1.69089
\(929\) 23.9977 + 41.5653i 0.787340 + 1.36371i 0.927591 + 0.373597i \(0.121876\pi\)
−0.140251 + 0.990116i \(0.544791\pi\)
\(930\) 0 0
\(931\) 11.5905 20.0753i 0.379862 0.657941i
\(932\) 5.20259 9.01115i 0.170417 0.295170i
\(933\) −39.2949 14.6885i −1.28646 0.480879i
\(934\) 7.82831 + 13.5590i 0.256150 + 0.443665i
\(935\) 0 0
\(936\) −5.61515 + 28.9102i −0.183537 + 0.944958i
\(937\) −22.0079 −0.718967 −0.359483 0.933151i \(-0.617047\pi\)
−0.359483 + 0.933151i \(0.617047\pi\)
\(938\) −2.69158 4.66195i −0.0878832 0.152218i
\(939\) −46.8867 + 38.6562i −1.53009 + 1.26150i
\(940\) 0 0
\(941\) −20.2921 + 35.1470i −0.661504 + 1.14576i 0.318716 + 0.947850i \(0.396748\pi\)
−0.980220 + 0.197909i \(0.936585\pi\)
\(942\) −0.0329893 0.197047i −0.00107485 0.00642015i
\(943\) 4.35291 + 7.53946i 0.141750 + 0.245518i
\(944\) −2.45269 −0.0798283
\(945\) 0 0
\(946\) 0.720331 0.0234200
\(947\) 15.1160 + 26.1817i 0.491204 + 0.850790i 0.999949 0.0101273i \(-0.00322368\pi\)
−0.508745 + 0.860917i \(0.669890\pi\)
\(948\) −0.137773 0.822925i −0.00447465 0.0267273i
\(949\) 4.00000 6.92820i 0.129845 0.224899i
\(950\) 0 0
\(951\) −13.9938 + 11.5373i −0.453780 + 0.374123i
\(952\) −4.00924 6.94420i −0.129940 0.225063i
\(953\) −2.50811 −0.0812455 −0.0406227 0.999175i \(-0.512934\pi\)
−0.0406227 + 0.999175i \(0.512934\pi\)
\(954\) −1.48173 1.28766i −0.0479727 0.0416896i
\(955\) 0 0
\(956\) 6.79439 + 11.7682i 0.219746 + 0.380612i
\(957\) −41.1510 15.3823i −1.33022 0.497238i
\(958\) 1.49585 2.59088i 0.0483286 0.0837077i
\(959\) 7.28402 12.6163i 0.235213 0.407401i
\(960\) 0 0
\(961\) −8.72635 15.1145i −0.281495 0.487564i
\(962\) 4.85601 0.156564
\(963\) 33.8033 11.6450i 1.08930 0.375255i
\(964\) 44.1025 1.42045
\(965\) 0 0
\(966\) −6.45967 + 5.32574i −0.207836 + 0.171353i
\(967\) −10.8765 + 18.8386i −0.349763 + 0.605808i −0.986207 0.165515i \(-0.947071\pi\)
0.636444 + 0.771323i \(0.280405\pi\)
\(968\) 4.05042 7.01552i 0.130185 0.225488i
\(969\) 3.57199 + 21.3357i 0.114749 + 0.685403i
\(970\) 0 0
\(971\) 22.7512 0.730122 0.365061 0.930984i \(-0.381048\pi\)
0.365061 + 0.930984i \(0.381048\pi\)
\(972\) −24.8669 + 7.85058i −0.797608 + 0.251808i
\(973\) −11.4241 −0.366238
\(974\) 6.86920 + 11.8978i 0.220103 + 0.381230i
\(975\) 0 0
\(976\) 2.71090 4.69541i 0.0867737 0.150296i
\(977\) 19.6389 34.0156i 0.628304 1.08825i −0.359588 0.933111i \(-0.617083\pi\)
0.987892 0.155143i \(-0.0495840\pi\)
\(978\) −13.6195 + 11.2287i −0.435504 + 0.359055i
\(979\) 4.00924 + 6.94420i 0.128136 + 0.221938i
\(980\) 0 0
\(981\) 47.2322 16.2711i 1.50801 0.519497i
\(982\) −8.45269 −0.269736
\(983\) 16.8949 + 29.2629i 0.538865 + 0.933341i 0.998966 + 0.0454743i \(0.0144799\pi\)
−0.460101 + 0.887867i \(0.652187\pi\)
\(984\) −5.01432 1.87436i −0.159851 0.0597523i
\(985\) 0 0
\(986\) 7.25405 12.5644i 0.231016 0.400132i
\(987\) 16.1177 + 6.02480i 0.513032 + 0.191772i
\(988\) −18.2633 31.6329i −0.581033 1.00638i
\(989\) −2.78817 −0.0886587
\(990\) 0 0
\(991\) −23.7983 −0.755979 −0.377990 0.925810i \(-0.623384\pi\)
−0.377990 + 0.925810i \(0.623384\pi\)
\(992\) 18.8916 + 32.7213i 0.599810 + 1.03890i
\(993\) −22.4218 + 18.4859i −0.711534 + 0.586631i
\(994\) 5.25801 9.10713i 0.166774 0.288861i
\(995\) 0 0
\(996\) 2.04957 + 12.2422i 0.0649431 + 0.387909i
\(997\) 25.8392 + 44.7549i 0.818337 + 1.41740i 0.906907 + 0.421331i \(0.138437\pi\)
−0.0885702 + 0.996070i \(0.528230\pi\)
\(998\) −14.2175 −0.450046
\(999\) 4.50641 + 8.29541i 0.142577 + 0.262455i
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 225.2.e.b.76.2 6
3.2 odd 2 675.2.e.b.226.2 6
5.2 odd 4 225.2.k.b.49.3 12
5.3 odd 4 225.2.k.b.49.4 12
5.4 even 2 45.2.e.b.31.2 yes 6
9.2 odd 6 675.2.e.b.451.2 6
9.4 even 3 2025.2.a.n.1.2 3
9.5 odd 6 2025.2.a.o.1.2 3
9.7 even 3 inner 225.2.e.b.151.2 6
15.2 even 4 675.2.k.b.199.4 12
15.8 even 4 675.2.k.b.199.3 12
15.14 odd 2 135.2.e.b.91.2 6
20.19 odd 2 720.2.q.i.481.2 6
45.2 even 12 675.2.k.b.424.3 12
45.4 even 6 405.2.a.j.1.2 3
45.7 odd 12 225.2.k.b.124.4 12
45.13 odd 12 2025.2.b.l.649.4 6
45.14 odd 6 405.2.a.i.1.2 3
45.22 odd 12 2025.2.b.l.649.3 6
45.23 even 12 2025.2.b.m.649.3 6
45.29 odd 6 135.2.e.b.46.2 6
45.32 even 12 2025.2.b.m.649.4 6
45.34 even 6 45.2.e.b.16.2 6
45.38 even 12 675.2.k.b.424.4 12
45.43 odd 12 225.2.k.b.124.3 12
60.59 even 2 2160.2.q.k.1441.2 6
180.59 even 6 6480.2.a.bs.1.2 3
180.79 odd 6 720.2.q.i.241.2 6
180.119 even 6 2160.2.q.k.721.2 6
180.139 odd 6 6480.2.a.bv.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.2.e.b.16.2 6 45.34 even 6
45.2.e.b.31.2 yes 6 5.4 even 2
135.2.e.b.46.2 6 45.29 odd 6
135.2.e.b.91.2 6 15.14 odd 2
225.2.e.b.76.2 6 1.1 even 1 trivial
225.2.e.b.151.2 6 9.7 even 3 inner
225.2.k.b.49.3 12 5.2 odd 4
225.2.k.b.49.4 12 5.3 odd 4
225.2.k.b.124.3 12 45.43 odd 12
225.2.k.b.124.4 12 45.7 odd 12
405.2.a.i.1.2 3 45.14 odd 6
405.2.a.j.1.2 3 45.4 even 6
675.2.e.b.226.2 6 3.2 odd 2
675.2.e.b.451.2 6 9.2 odd 6
675.2.k.b.199.3 12 15.8 even 4
675.2.k.b.199.4 12 15.2 even 4
675.2.k.b.424.3 12 45.2 even 12
675.2.k.b.424.4 12 45.38 even 12
720.2.q.i.241.2 6 180.79 odd 6
720.2.q.i.481.2 6 20.19 odd 2
2025.2.a.n.1.2 3 9.4 even 3
2025.2.a.o.1.2 3 9.5 odd 6
2025.2.b.l.649.3 6 45.22 odd 12
2025.2.b.l.649.4 6 45.13 odd 12
2025.2.b.m.649.3 6 45.23 even 12
2025.2.b.m.649.4 6 45.32 even 12
2160.2.q.k.721.2 6 180.119 even 6
2160.2.q.k.1441.2 6 60.59 even 2
6480.2.a.bs.1.2 3 180.59 even 6
6480.2.a.bv.1.2 3 180.139 odd 6