Properties

Label 875.2.bb.a.143.5
Level $875$
Weight $2$
Character 875.143
Analytic conductor $6.987$
Analytic rank $0$
Dimension $288$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [875,2,Mod(82,875)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(875, base_ring=CyclotomicField(60))
 
chi = DirichletCharacter(H, H._module([27, 50]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("875.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 875 = 5^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 875.bb (of order \(60\), degree \(16\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.98691017686\)
Analytic rank: \(0\)
Dimension: \(288\)
Relative dimension: \(18\) over \(\Q(\zeta_{60})\)
Twist minimal: no (minimal twist has level 175)
Sato-Tate group: $\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label 143.5
Character \(\chi\) \(=\) 875.143
Dual form 875.2.bb.a.257.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0848016 - 1.61811i) q^{2} +(-2.12290 - 1.71909i) q^{3} +(-0.622046 + 0.0653797i) q^{4} +(-2.60166 + 3.58087i) q^{6} +(2.64114 - 0.156130i) q^{7} +(-0.348409 - 2.19977i) q^{8} +(0.927701 + 4.36449i) q^{9} +(-3.84181 - 0.816603i) q^{11} +(1.43294 + 0.930561i) q^{12} +(0.0441012 + 0.0865535i) q^{13} +(-0.476608 - 4.26042i) q^{14} +(-4.75353 + 1.01039i) q^{16} +(-3.12891 - 1.20108i) q^{17} +(6.98356 - 1.87124i) q^{18} +(-0.637130 + 6.06189i) q^{19} +(-5.87529 - 4.20892i) q^{21} +(-0.995562 + 6.28573i) q^{22} +(-5.23739 + 0.274480i) q^{23} +(-3.04197 + 5.26884i) q^{24} +(0.136313 - 0.0787005i) q^{26} +(1.81310 - 3.55840i) q^{27} +(-1.63270 + 0.269797i) q^{28} +(-2.51245 - 3.45809i) q^{29} +(-0.287036 - 0.644694i) q^{31} +(0.885159 + 3.30346i) q^{32} +(6.75198 + 8.33800i) q^{33} +(-1.67814 + 5.16477i) q^{34} +(-0.862422 - 2.65426i) q^{36} +(-4.20336 + 6.47261i) q^{37} +(9.86284 + 0.516889i) q^{38} +(0.0551709 - 0.259559i) q^{39} +(0.124652 + 0.0405019i) q^{41} +(-6.31226 + 9.86378i) q^{42} +(-8.25770 - 8.25770i) q^{43} +(2.44318 + 0.256788i) q^{44} +(0.888279 + 8.45141i) q^{46} +(0.970816 + 2.52906i) q^{47} +(11.8282 + 6.02679i) q^{48} +(6.95125 - 0.824720i) q^{49} +(4.57761 + 7.92865i) q^{51} +(-0.0330918 - 0.0509570i) q^{52} +(7.40118 - 9.13970i) q^{53} +(-5.91164 - 2.63203i) q^{54} +(-1.26365 - 5.75550i) q^{56} +(11.7735 - 11.7735i) q^{57} +(-5.38252 + 4.35867i) q^{58} +(3.45304 + 3.83499i) q^{59} +(5.30099 + 4.77304i) q^{61} +(-1.01885 + 0.519128i) q^{62} +(3.13162 + 11.3824i) q^{63} +(-3.97346 + 1.29105i) q^{64} +(12.9192 - 11.6325i) q^{66} +(0.200027 - 0.521089i) q^{67} +(2.02485 + 0.542557i) q^{68} +(11.5903 + 8.42087i) q^{69} +(0.818370 - 0.594581i) q^{71} +(9.27765 - 3.56136i) q^{72} +(-1.78952 + 1.16213i) q^{73} +(10.8299 + 6.25262i) q^{74} -3.81243i q^{76} +(-10.2743 - 1.55694i) q^{77} +(-0.424673 - 0.0672616i) q^{78} +(6.28497 - 14.1163i) q^{79} +(2.26247 - 1.00731i) q^{81} +(0.0549659 - 0.205136i) q^{82} +(-10.6837 + 1.69214i) q^{83} +(3.92988 + 2.23402i) q^{84} +(-12.6616 + 14.0621i) q^{86} +(-0.611092 + 11.6603i) q^{87} +(-0.457814 + 8.73562i) q^{88} +(0.671570 - 0.745854i) q^{89} +(0.129991 + 0.221714i) q^{91} +(3.23996 - 0.513159i) q^{92} +(-0.498939 + 1.86207i) q^{93} +(4.00998 - 1.78536i) q^{94} +(3.79985 - 8.53459i) q^{96} +(11.1837 + 1.77133i) q^{97} +(-1.92397 - 11.1779i) q^{98} -17.5251i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/875\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(626\)
\(\chi(n)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0848016 1.61811i −0.0599638 1.14418i −0.848502 0.529192i \(-0.822495\pi\)
0.788539 0.614985i \(-0.210838\pi\)
\(3\) −2.12290 1.71909i −1.22566 0.992519i −0.999832 0.0183512i \(-0.994158\pi\)
−0.225827 0.974167i \(-0.572508\pi\)
\(4\) −0.622046 + 0.0653797i −0.311023 + 0.0326899i
\(5\) 0 0
\(6\) −2.60166 + 3.58087i −1.06212 + 1.46189i
\(7\) 2.64114 0.156130i 0.998257 0.0590114i
\(8\) −0.348409 2.19977i −0.123181 0.777736i
\(9\) 0.927701 + 4.36449i 0.309234 + 1.45483i
\(10\) 0 0
\(11\) −3.84181 0.816603i −1.15835 0.246215i −0.411629 0.911352i \(-0.635040\pi\)
−0.746722 + 0.665137i \(0.768373\pi\)
\(12\) 1.43294 + 0.930561i 0.413653 + 0.268630i
\(13\) 0.0441012 + 0.0865535i 0.0122315 + 0.0240056i 0.897041 0.441946i \(-0.145712\pi\)
−0.884810 + 0.465952i \(0.845712\pi\)
\(14\) −0.476608 4.26042i −0.127379 1.13864i
\(15\) 0 0
\(16\) −4.75353 + 1.01039i −1.18838 + 0.252599i
\(17\) −3.12891 1.20108i −0.758872 0.291304i −0.0520016 0.998647i \(-0.516560\pi\)
−0.706870 + 0.707343i \(0.749893\pi\)
\(18\) 6.98356 1.87124i 1.64604 0.441055i
\(19\) −0.637130 + 6.06189i −0.146168 + 1.39069i 0.637948 + 0.770079i \(0.279783\pi\)
−0.784116 + 0.620614i \(0.786883\pi\)
\(20\) 0 0
\(21\) −5.87529 4.20892i −1.28209 0.918461i
\(22\) −0.995562 + 6.28573i −0.212254 + 1.34012i
\(23\) −5.23739 + 0.274480i −1.09207 + 0.0572331i −0.589856 0.807509i \(-0.700815\pi\)
−0.502217 + 0.864742i \(0.667482\pi\)
\(24\) −3.04197 + 5.26884i −0.620939 + 1.07550i
\(25\) 0 0
\(26\) 0.136313 0.0787005i 0.0267332 0.0154344i
\(27\) 1.81310 3.55840i 0.348930 0.684814i
\(28\) −1.63270 + 0.269797i −0.308552 + 0.0509868i
\(29\) −2.51245 3.45809i −0.466550 0.642152i 0.509301 0.860589i \(-0.329904\pi\)
−0.975851 + 0.218437i \(0.929904\pi\)
\(30\) 0 0
\(31\) −0.287036 0.644694i −0.0515533 0.115791i 0.885932 0.463814i \(-0.153520\pi\)
−0.937486 + 0.348024i \(0.886853\pi\)
\(32\) 0.885159 + 3.30346i 0.156475 + 0.583975i
\(33\) 6.75198 + 8.33800i 1.17537 + 1.45146i
\(34\) −1.67814 + 5.16477i −0.287798 + 0.885751i
\(35\) 0 0
\(36\) −0.862422 2.65426i −0.143737 0.442377i
\(37\) −4.20336 + 6.47261i −0.691029 + 1.06409i 0.302788 + 0.953058i \(0.402083\pi\)
−0.993817 + 0.111033i \(0.964584\pi\)
\(38\) 9.86284 + 0.516889i 1.59996 + 0.0838505i
\(39\) 0.0551709 0.259559i 0.00883442 0.0415627i
\(40\) 0 0
\(41\) 0.124652 + 0.0405019i 0.0194674 + 0.00632534i 0.318735 0.947844i \(-0.396742\pi\)
−0.299267 + 0.954169i \(0.596742\pi\)
\(42\) −6.31226 + 9.86378i −0.974003 + 1.52202i
\(43\) −8.25770 8.25770i −1.25929 1.25929i −0.951434 0.307854i \(-0.900389\pi\)
−0.307854 0.951434i \(-0.599611\pi\)
\(44\) 2.44318 + 0.256788i 0.368323 + 0.0387123i
\(45\) 0 0
\(46\) 0.888279 + 8.45141i 0.130970 + 1.24609i
\(47\) 0.970816 + 2.52906i 0.141608 + 0.368902i 0.985982 0.166853i \(-0.0533605\pi\)
−0.844374 + 0.535755i \(0.820027\pi\)
\(48\) 11.8282 + 6.02679i 1.70726 + 0.869893i
\(49\) 6.95125 0.824720i 0.993035 0.117817i
\(50\) 0 0
\(51\) 4.57761 + 7.92865i 0.640993 + 1.11023i
\(52\) −0.0330918 0.0509570i −0.00458901 0.00706646i
\(53\) 7.40118 9.13970i 1.01663 1.25543i 0.0501369 0.998742i \(-0.484034\pi\)
0.966493 0.256691i \(-0.0826324\pi\)
\(54\) −5.91164 2.63203i −0.804472 0.358174i
\(55\) 0 0
\(56\) −1.26365 5.75550i −0.168862 0.769111i
\(57\) 11.7735 11.7735i 1.55944 1.55944i
\(58\) −5.38252 + 4.35867i −0.706759 + 0.572322i
\(59\) 3.45304 + 3.83499i 0.449548 + 0.499273i 0.924735 0.380611i \(-0.124286\pi\)
−0.475188 + 0.879885i \(0.657620\pi\)
\(60\) 0 0
\(61\) 5.30099 + 4.77304i 0.678723 + 0.611125i 0.934649 0.355572i \(-0.115714\pi\)
−0.255926 + 0.966696i \(0.582380\pi\)
\(62\) −1.01885 + 0.519128i −0.129394 + 0.0659293i
\(63\) 3.13162 + 11.3824i 0.394546 + 1.43405i
\(64\) −3.97346 + 1.29105i −0.496682 + 0.161382i
\(65\) 0 0
\(66\) 12.9192 11.6325i 1.59025 1.43187i
\(67\) 0.200027 0.521089i 0.0244372 0.0636611i −0.920819 0.389990i \(-0.872478\pi\)
0.945256 + 0.326329i \(0.105812\pi\)
\(68\) 2.02485 + 0.542557i 0.245549 + 0.0657947i
\(69\) 11.5903 + 8.42087i 1.39531 + 1.01375i
\(70\) 0 0
\(71\) 0.818370 0.594581i 0.0971227 0.0705637i −0.538164 0.842840i \(-0.680882\pi\)
0.635287 + 0.772276i \(0.280882\pi\)
\(72\) 9.27765 3.56136i 1.09338 0.419710i
\(73\) −1.78952 + 1.16213i −0.209448 + 0.136017i −0.645100 0.764098i \(-0.723184\pi\)
0.435652 + 0.900115i \(0.356518\pi\)
\(74\) 10.8299 + 6.25262i 1.25894 + 0.726852i
\(75\) 0 0
\(76\) 3.81243i 0.437316i
\(77\) −10.2743 1.55694i −1.17086 0.177430i
\(78\) −0.424673 0.0672616i −0.0480848 0.00761588i
\(79\) 6.28497 14.1163i 0.707114 1.58820i −0.0980696 0.995180i \(-0.531267\pi\)
0.805184 0.593025i \(-0.202067\pi\)
\(80\) 0 0
\(81\) 2.26247 1.00731i 0.251385 0.111924i
\(82\) 0.0549659 0.205136i 0.00606997 0.0226534i
\(83\) −10.6837 + 1.69214i −1.17269 + 0.185736i −0.712232 0.701944i \(-0.752316\pi\)
−0.460461 + 0.887680i \(0.652316\pi\)
\(84\) 3.92988 + 2.23402i 0.428785 + 0.243751i
\(85\) 0 0
\(86\) −12.6616 + 14.0621i −1.36534 + 1.51636i
\(87\) −0.611092 + 11.6603i −0.0655159 + 1.25012i
\(88\) −0.457814 + 8.73562i −0.0488032 + 0.931220i
\(89\) 0.671570 0.745854i 0.0711863 0.0790604i −0.706500 0.707713i \(-0.749727\pi\)
0.777686 + 0.628653i \(0.216393\pi\)
\(90\) 0 0
\(91\) 0.129991 + 0.221714i 0.0136268 + 0.0232420i
\(92\) 3.23996 0.513159i 0.337789 0.0535005i
\(93\) −0.498939 + 1.86207i −0.0517376 + 0.193087i
\(94\) 4.00998 1.78536i 0.413597 0.184145i
\(95\) 0 0
\(96\) 3.79985 8.53459i 0.387820 0.871058i
\(97\) 11.1837 + 1.77133i 1.13554 + 0.179851i 0.695773 0.718262i \(-0.255062\pi\)
0.439764 + 0.898113i \(0.355062\pi\)
\(98\) −1.92397 11.1779i −0.194350 1.12914i
\(99\) 17.5251i 1.76134i
\(100\) 0 0
\(101\) −10.1623 5.86718i −1.01118 0.583807i −0.0996449 0.995023i \(-0.531771\pi\)
−0.911538 + 0.411216i \(0.865104\pi\)
\(102\) 12.4412 8.07944i 1.23187 0.799983i
\(103\) −9.40258 + 3.60931i −0.926464 + 0.355636i −0.774372 0.632730i \(-0.781934\pi\)
−0.152092 + 0.988366i \(0.548601\pi\)
\(104\) 0.175032 0.127168i 0.0171633 0.0124699i
\(105\) 0 0
\(106\) −15.4167 11.2009i −1.49740 1.08792i
\(107\) −1.09349 0.292999i −0.105711 0.0283253i 0.205576 0.978641i \(-0.434093\pi\)
−0.311287 + 0.950316i \(0.600760\pi\)
\(108\) −0.895182 + 2.33203i −0.0861389 + 0.224400i
\(109\) 2.17553 1.95886i 0.208378 0.187624i −0.558333 0.829617i \(-0.688559\pi\)
0.766711 + 0.641993i \(0.221892\pi\)
\(110\) 0 0
\(111\) 20.0504 6.51476i 1.90310 0.618353i
\(112\) −12.3970 + 3.41076i −1.17141 + 0.322287i
\(113\) −4.16270 + 2.12100i −0.391594 + 0.199527i −0.638690 0.769464i \(-0.720523\pi\)
0.247097 + 0.968991i \(0.420523\pi\)
\(114\) −20.0493 18.0524i −1.87779 1.69077i
\(115\) 0 0
\(116\) 1.78895 + 1.98683i 0.166100 + 0.184473i
\(117\) −0.336849 + 0.272775i −0.0311417 + 0.0252181i
\(118\) 5.91261 5.91261i 0.544300 0.544300i
\(119\) −8.45141 2.68369i −0.774739 0.246014i
\(120\) 0 0
\(121\) 4.04370 + 1.80037i 0.367609 + 0.163670i
\(122\) 7.27377 8.98236i 0.658536 0.813224i
\(123\) −0.194998 0.300270i −0.0175824 0.0270745i
\(124\) 0.220700 + 0.382263i 0.0198194 + 0.0343283i
\(125\) 0 0
\(126\) 18.1524 6.03254i 1.61714 0.537422i
\(127\) −14.7555 7.51832i −1.30934 0.667143i −0.346713 0.937971i \(-0.612702\pi\)
−0.962628 + 0.270829i \(0.912702\pi\)
\(128\) 4.87725 + 12.7057i 0.431092 + 1.12303i
\(129\) 3.33454 + 31.7260i 0.293590 + 2.79332i
\(130\) 0 0
\(131\) −0.400325 0.0420758i −0.0349765 0.00367618i 0.0870240 0.996206i \(-0.472264\pi\)
−0.122001 + 0.992530i \(0.538931\pi\)
\(132\) −4.74518 4.74518i −0.413015 0.413015i
\(133\) −0.736311 + 16.1098i −0.0638462 + 1.39690i
\(134\) −0.860142 0.279477i −0.0743049 0.0241431i
\(135\) 0 0
\(136\) −1.55195 + 7.30134i −0.133078 + 0.626085i
\(137\) 12.6497 + 0.662940i 1.08073 + 0.0566388i 0.584378 0.811481i \(-0.301338\pi\)
0.496354 + 0.868120i \(0.334672\pi\)
\(138\) 12.6430 19.4685i 1.07625 1.65727i
\(139\) −4.44619 13.6840i −0.377121 1.16066i −0.942036 0.335511i \(-0.891091\pi\)
0.564915 0.825149i \(-0.308909\pi\)
\(140\) 0 0
\(141\) 2.28674 7.03788i 0.192579 0.592696i
\(142\) −1.03150 1.27379i −0.0865612 0.106894i
\(143\) −0.0987488 0.368536i −0.00825779 0.0308185i
\(144\) −8.81972 19.8094i −0.734976 1.65078i
\(145\) 0 0
\(146\) 2.03221 + 2.79710i 0.168187 + 0.231489i
\(147\) −16.1746 10.1990i −1.33406 0.841202i
\(148\) 2.19151 4.30108i 0.180141 0.353547i
\(149\) −9.24670 + 5.33859i −0.757519 + 0.437354i −0.828404 0.560131i \(-0.810751\pi\)
0.0708851 + 0.997484i \(0.477418\pi\)
\(150\) 0 0
\(151\) −10.4396 + 18.0820i −0.849565 + 1.47149i 0.0320315 + 0.999487i \(0.489802\pi\)
−0.881597 + 0.472003i \(0.843531\pi\)
\(152\) 13.5567 0.710479i 1.09960 0.0576274i
\(153\) 2.33939 14.7703i 0.189128 1.19411i
\(154\) −1.64803 + 16.7569i −0.132802 + 1.35031i
\(155\) 0 0
\(156\) −0.0173490 + 0.165065i −0.00138903 + 0.0132157i
\(157\) −11.5468 + 3.09395i −0.921533 + 0.246924i −0.688241 0.725483i \(-0.741617\pi\)
−0.233293 + 0.972407i \(0.574950\pi\)
\(158\) −23.3747 8.97269i −1.85959 0.713829i
\(159\) −31.4240 + 6.67937i −2.49208 + 0.529709i
\(160\) 0 0
\(161\) −13.7898 + 1.54265i −1.08679 + 0.121578i
\(162\) −1.82181 3.57550i −0.143135 0.280918i
\(163\) −12.1623 7.89827i −0.952622 0.618640i −0.0280333 0.999607i \(-0.508924\pi\)
−0.924589 + 0.380967i \(0.875591\pi\)
\(164\) −0.0801874 0.0170444i −0.00626159 0.00133094i
\(165\) 0 0
\(166\) 3.64407 + 17.1440i 0.282834 + 1.33063i
\(167\) 0.261681 + 1.65219i 0.0202495 + 0.127850i 0.995742 0.0921813i \(-0.0293839\pi\)
−0.975493 + 0.220032i \(0.929384\pi\)
\(168\) −7.21164 + 14.3907i −0.556390 + 1.11027i
\(169\) 7.63566 10.5096i 0.587359 0.808430i
\(170\) 0 0
\(171\) −27.0481 + 2.84287i −2.06842 + 0.217400i
\(172\) 5.67656 + 4.59679i 0.432834 + 0.350502i
\(173\) 0.0147195 + 0.280864i 0.00111910 + 0.0213537i 0.999132 0.0416561i \(-0.0132634\pi\)
−0.998013 + 0.0630098i \(0.979930\pi\)
\(174\) 18.9195 1.43429
\(175\) 0 0
\(176\) 19.0873 1.43876
\(177\) −0.737766 14.0774i −0.0554539 1.05812i
\(178\) −1.26383 1.02343i −0.0947277 0.0767090i
\(179\) −13.0417 + 1.37074i −0.974782 + 0.102454i −0.578506 0.815678i \(-0.696364\pi\)
−0.396275 + 0.918132i \(0.629697\pi\)
\(180\) 0 0
\(181\) 13.5383 18.6338i 1.00629 1.38504i 0.0849076 0.996389i \(-0.472940\pi\)
0.921384 0.388653i \(-0.127060\pi\)
\(182\) 0.347735 0.229142i 0.0257758 0.0169851i
\(183\) −3.04820 19.2456i −0.225330 1.42268i
\(184\) 2.42855 + 11.4254i 0.179035 + 0.842294i
\(185\) 0 0
\(186\) 3.05534 + 0.649432i 0.224028 + 0.0476187i
\(187\) 11.0399 + 7.16938i 0.807316 + 0.524277i
\(188\) −0.769242 1.50972i −0.0561027 0.110108i
\(189\) 4.23307 9.68131i 0.307910 0.704212i
\(190\) 0 0
\(191\) −3.95786 + 0.841270i −0.286381 + 0.0608722i −0.348862 0.937174i \(-0.613432\pi\)
0.0624813 + 0.998046i \(0.480099\pi\)
\(192\) 10.6547 + 4.08996i 0.768937 + 0.295167i
\(193\) 2.96976 0.795745i 0.213768 0.0572790i −0.150346 0.988634i \(-0.548039\pi\)
0.364114 + 0.931355i \(0.381372\pi\)
\(194\) 1.91781 18.2467i 0.137691 1.31004i
\(195\) 0 0
\(196\) −4.27008 + 0.967485i −0.305006 + 0.0691061i
\(197\) −1.97286 + 12.4561i −0.140560 + 0.887464i 0.812120 + 0.583490i \(0.198313\pi\)
−0.952681 + 0.303973i \(0.901687\pi\)
\(198\) −28.3576 + 1.48616i −2.01529 + 0.105617i
\(199\) 2.17496 3.76715i 0.154179 0.267046i −0.778581 0.627545i \(-0.784060\pi\)
0.932760 + 0.360498i \(0.117393\pi\)
\(200\) 0 0
\(201\) −1.32044 + 0.762355i −0.0931365 + 0.0537724i
\(202\) −8.63198 + 16.9412i −0.607344 + 1.19198i
\(203\) −7.17565 8.74104i −0.503632 0.613501i
\(204\) −3.36586 4.63270i −0.235657 0.324354i
\(205\) 0 0
\(206\) 6.63762 + 14.9083i 0.462465 + 1.03871i
\(207\) −6.05670 22.6039i −0.420970 1.57108i
\(208\) −0.297090 0.366875i −0.0205995 0.0254382i
\(209\) 7.39789 22.7684i 0.511723 1.57492i
\(210\) 0 0
\(211\) 2.05986 + 6.33961i 0.141807 + 0.436437i 0.996587 0.0825543i \(-0.0263078\pi\)
−0.854780 + 0.518991i \(0.826308\pi\)
\(212\) −4.00633 + 6.16920i −0.275156 + 0.423703i
\(213\) −2.75946 0.144617i −0.189075 0.00990900i
\(214\) −0.381375 + 1.79423i −0.0260703 + 0.122651i
\(215\) 0 0
\(216\) −8.45936 2.74861i −0.575586 0.187019i
\(217\) −0.858760 1.65791i −0.0582964 0.112547i
\(218\) −3.35413 3.35413i −0.227171 0.227171i
\(219\) 5.79680 + 0.609268i 0.391711 + 0.0411705i
\(220\) 0 0
\(221\) −0.0340314 0.323787i −0.00228920 0.0217803i
\(222\) −12.2419 31.8912i −0.821622 2.14040i
\(223\) 13.7309 + 6.99626i 0.919491 + 0.468504i 0.848633 0.528982i \(-0.177426\pi\)
0.0708583 + 0.997486i \(0.477426\pi\)
\(224\) 2.85360 + 8.58670i 0.190664 + 0.573723i
\(225\) 0 0
\(226\) 3.78502 + 6.55584i 0.251776 + 0.436088i
\(227\) −7.21647 11.1124i −0.478974 0.737556i 0.513753 0.857938i \(-0.328255\pi\)
−0.992728 + 0.120382i \(0.961588\pi\)
\(228\) −6.55393 + 8.09342i −0.434044 + 0.536000i
\(229\) 3.78909 + 1.68701i 0.250390 + 0.111481i 0.528094 0.849186i \(-0.322907\pi\)
−0.277704 + 0.960667i \(0.589574\pi\)
\(230\) 0 0
\(231\) 19.1347 + 20.9677i 1.25897 + 1.37957i
\(232\) −6.73164 + 6.73164i −0.441954 + 0.441954i
\(233\) 20.0258 16.2166i 1.31194 1.06238i 0.318508 0.947920i \(-0.396818\pi\)
0.993427 0.114464i \(-0.0365152\pi\)
\(234\) 0.469946 + 0.521927i 0.0307213 + 0.0341195i
\(235\) 0 0
\(236\) −2.39868 2.15978i −0.156141 0.140590i
\(237\) −37.6096 + 19.1630i −2.44300 + 1.24477i
\(238\) −3.62582 + 13.9029i −0.235027 + 0.901191i
\(239\) 0.618920 0.201099i 0.0400346 0.0130080i −0.288931 0.957350i \(-0.593300\pi\)
0.328966 + 0.944342i \(0.393300\pi\)
\(240\) 0 0
\(241\) −0.853202 + 0.768226i −0.0549596 + 0.0494858i −0.696153 0.717894i \(-0.745106\pi\)
0.641193 + 0.767379i \(0.278440\pi\)
\(242\) 2.57029 6.69582i 0.165224 0.430424i
\(243\) −18.1075 4.85188i −1.16159 0.311248i
\(244\) −3.60952 2.62247i −0.231076 0.167887i
\(245\) 0 0
\(246\) −0.469334 + 0.340991i −0.0299237 + 0.0217408i
\(247\) −0.552776 + 0.212191i −0.0351723 + 0.0135014i
\(248\) −1.31817 + 0.856031i −0.0837040 + 0.0543580i
\(249\) 25.5895 + 14.7741i 1.62167 + 0.936270i
\(250\) 0 0
\(251\) 13.8492i 0.874153i −0.899424 0.437076i \(-0.856014\pi\)
0.899424 0.437076i \(-0.143986\pi\)
\(252\) −2.69219 6.87563i −0.169592 0.433124i
\(253\) 20.3452 + 3.22237i 1.27909 + 0.202589i
\(254\) −10.9142 + 24.5136i −0.684816 + 1.53812i
\(255\) 0 0
\(256\) 12.5121 5.57076i 0.782008 0.348172i
\(257\) 0.0943752 0.352213i 0.00588696 0.0219704i −0.962920 0.269788i \(-0.913047\pi\)
0.968807 + 0.247817i \(0.0797132\pi\)
\(258\) 51.0535 8.08608i 3.17845 0.503417i
\(259\) −10.0911 + 17.7513i −0.627031 + 1.10302i
\(260\) 0 0
\(261\) 12.7620 14.1736i 0.789948 0.877327i
\(262\) −0.0341352 + 0.651338i −0.00210888 + 0.0402398i
\(263\) 1.55688 29.7070i 0.0960011 1.83181i −0.349967 0.936762i \(-0.613807\pi\)
0.445968 0.895049i \(-0.352859\pi\)
\(264\) 15.9892 17.7578i 0.984069 1.09292i
\(265\) 0 0
\(266\) 26.1298 0.174703i 1.60212 0.0107117i
\(267\) −2.70787 + 0.428885i −0.165719 + 0.0262473i
\(268\) −0.0903576 + 0.337219i −0.00551947 + 0.0205989i
\(269\) −18.9335 + 8.42973i −1.15439 + 0.513970i −0.892465 0.451117i \(-0.851026\pi\)
−0.261930 + 0.965087i \(0.584359\pi\)
\(270\) 0 0
\(271\) −2.28034 + 5.12174i −0.138521 + 0.311123i −0.969464 0.245235i \(-0.921135\pi\)
0.830943 + 0.556358i \(0.187802\pi\)
\(272\) 16.0869 + 2.54792i 0.975413 + 0.154490i
\(273\) 0.105189 0.694145i 0.00636635 0.0420116i
\(274\) 20.5248i 1.23995i
\(275\) 0 0
\(276\) −7.76028 4.48040i −0.467114 0.269688i
\(277\) 4.95771 3.21957i 0.297880 0.193445i −0.387042 0.922062i \(-0.626503\pi\)
0.684922 + 0.728617i \(0.259836\pi\)
\(278\) −21.7651 + 8.35486i −1.30539 + 0.501091i
\(279\) 2.54748 1.85085i 0.152514 0.110808i
\(280\) 0 0
\(281\) −6.92124 5.02858i −0.412887 0.299980i 0.361883 0.932224i \(-0.382134\pi\)
−0.774769 + 0.632244i \(0.782134\pi\)
\(282\) −11.5820 3.10338i −0.689697 0.184804i
\(283\) 5.40796 14.0882i 0.321470 0.837458i −0.673674 0.739028i \(-0.735285\pi\)
0.995144 0.0984291i \(-0.0313818\pi\)
\(284\) −0.470191 + 0.423361i −0.0279007 + 0.0251219i
\(285\) 0 0
\(286\) −0.587957 + 0.191039i −0.0347666 + 0.0112964i
\(287\) 0.335547 + 0.0875094i 0.0198067 + 0.00516552i
\(288\) −13.5968 + 6.92789i −0.801196 + 0.408230i
\(289\) −4.28598 3.85911i −0.252116 0.227007i
\(290\) 0 0
\(291\) −20.6969 22.9863i −1.21327 1.34748i
\(292\) 1.03719 0.839898i 0.0606968 0.0491513i
\(293\) −7.80680 + 7.80680i −0.456078 + 0.456078i −0.897366 0.441288i \(-0.854522\pi\)
0.441288 + 0.897366i \(0.354522\pi\)
\(294\) −15.1315 + 27.0372i −0.882489 + 1.57684i
\(295\) 0 0
\(296\) 15.7027 + 6.99131i 0.912703 + 0.406362i
\(297\) −9.87137 + 12.1901i −0.572795 + 0.707343i
\(298\) 9.42256 + 14.5095i 0.545834 + 0.840511i
\(299\) −0.254733 0.441210i −0.0147316 0.0255158i
\(300\) 0 0
\(301\) −23.0990 20.5205i −1.33141 1.18278i
\(302\) 30.1439 + 15.3591i 1.73459 + 0.883817i
\(303\) 11.4873 + 29.9253i 0.659926 + 1.71917i
\(304\) −3.09628 29.4592i −0.177584 1.68960i
\(305\) 0 0
\(306\) −24.0984 2.53284i −1.37761 0.144793i
\(307\) −8.14095 8.14095i −0.464628 0.464628i 0.435541 0.900169i \(-0.356557\pi\)
−0.900169 + 0.435541i \(0.856557\pi\)
\(308\) 6.49286 + 0.296762i 0.369965 + 0.0169096i
\(309\) 26.1655 + 8.50169i 1.48850 + 0.483644i
\(310\) 0 0
\(311\) 5.97488 28.1096i 0.338804 1.59395i −0.397700 0.917516i \(-0.630192\pi\)
0.736504 0.676433i \(-0.236475\pi\)
\(312\) −0.590191 0.0309306i −0.0334130 0.00175110i
\(313\) −5.18386 + 7.98245i −0.293009 + 0.451195i −0.954263 0.298967i \(-0.903358\pi\)
0.661254 + 0.750162i \(0.270025\pi\)
\(314\) 5.98554 + 18.4216i 0.337783 + 1.03959i
\(315\) 0 0
\(316\) −2.98662 + 9.19189i −0.168011 + 0.517084i
\(317\) −4.91231 6.06620i −0.275903 0.340712i 0.620293 0.784370i \(-0.287014\pi\)
−0.896196 + 0.443658i \(0.853680\pi\)
\(318\) 13.4728 + 50.2810i 0.755515 + 2.81962i
\(319\) 6.82848 + 15.3370i 0.382322 + 0.858708i
\(320\) 0 0
\(321\) 1.81768 + 2.50182i 0.101453 + 0.139638i
\(322\) 3.66558 + 22.1827i 0.204275 + 1.23619i
\(323\) 9.27431 18.2019i 0.516036 1.01278i
\(324\) −1.34150 + 0.774516i −0.0745278 + 0.0430287i
\(325\) 0 0
\(326\) −11.7489 + 20.3497i −0.650711 + 1.12706i
\(327\) −7.98590 + 0.418523i −0.441621 + 0.0231444i
\(328\) 0.0456650 0.288317i 0.00252143 0.0159197i
\(329\) 2.95892 + 6.52804i 0.163131 + 0.359902i
\(330\) 0 0
\(331\) −0.108165 + 1.02912i −0.00594527 + 0.0565654i −0.997092 0.0762035i \(-0.975720\pi\)
0.991147 + 0.132769i \(0.0423868\pi\)
\(332\) 6.53515 1.75109i 0.358663 0.0961035i
\(333\) −32.1491 12.3409i −1.76176 0.676277i
\(334\) 2.65124 0.563538i 0.145069 0.0308354i
\(335\) 0 0
\(336\) 32.1810 + 14.0709i 1.75562 + 0.767629i
\(337\) −0.849753 1.66773i −0.0462890 0.0908472i 0.866703 0.498824i \(-0.166235\pi\)
−0.912992 + 0.407977i \(0.866235\pi\)
\(338\) −17.6532 11.4641i −0.960207 0.623566i
\(339\) 12.4832 + 2.65339i 0.677994 + 0.144112i
\(340\) 0 0
\(341\) 0.576281 + 2.71119i 0.0312074 + 0.146819i
\(342\) 6.89381 + 43.5258i 0.372774 + 2.35361i
\(343\) 18.2305 3.26350i 0.984352 0.176212i
\(344\) −15.2880 + 21.0421i −0.824272 + 1.13451i
\(345\) 0 0
\(346\) 0.453221 0.0476355i 0.0243653 0.00256090i
\(347\) 1.54512 + 1.25122i 0.0829465 + 0.0671688i 0.669897 0.742454i \(-0.266338\pi\)
−0.586950 + 0.809623i \(0.699672\pi\)
\(348\) −0.382221 7.29322i −0.0204892 0.390958i
\(349\) 4.37015 0.233929 0.116964 0.993136i \(-0.462684\pi\)
0.116964 + 0.993136i \(0.462684\pi\)
\(350\) 0 0
\(351\) 0.387952 0.0207073
\(352\) −0.703003 13.4141i −0.0374702 0.714974i
\(353\) 14.5133 + 11.7526i 0.772464 + 0.625529i 0.932330 0.361610i \(-0.117773\pi\)
−0.159865 + 0.987139i \(0.551106\pi\)
\(354\) −22.7162 + 2.38757i −1.20735 + 0.126898i
\(355\) 0 0
\(356\) −0.368984 + 0.507863i −0.0195561 + 0.0269167i
\(357\) 13.3280 + 20.2260i 0.705393 + 1.07047i
\(358\) 3.32396 + 20.9867i 0.175677 + 1.10918i
\(359\) 3.47497 + 16.3485i 0.183402 + 0.862838i 0.969568 + 0.244823i \(0.0787298\pi\)
−0.786166 + 0.618016i \(0.787937\pi\)
\(360\) 0 0
\(361\) −17.7558 3.77411i −0.934515 0.198637i
\(362\) −31.2997 20.3262i −1.64507 1.06832i
\(363\) −5.48937 10.7735i −0.288117 0.565462i
\(364\) −0.0953561 0.129418i −0.00499802 0.00678334i
\(365\) 0 0
\(366\) −30.8830 + 6.56439i −1.61428 + 0.343126i
\(367\) 9.01861 + 3.46192i 0.470768 + 0.180711i 0.582174 0.813064i \(-0.302202\pi\)
−0.111406 + 0.993775i \(0.535536\pi\)
\(368\) 24.6188 6.59659i 1.28334 0.343871i
\(369\) −0.0611304 + 0.581617i −0.00318232 + 0.0302778i
\(370\) 0 0
\(371\) 18.1206 25.2948i 0.940774 1.31324i
\(372\) 0.188622 1.19091i 0.00977959 0.0617459i
\(373\) −4.91126 + 0.257388i −0.254295 + 0.0133271i −0.179058 0.983839i \(-0.557305\pi\)
−0.0752376 + 0.997166i \(0.523972\pi\)
\(374\) 10.6647 18.4717i 0.551456 0.955150i
\(375\) 0 0
\(376\) 5.22511 3.01672i 0.269465 0.155575i
\(377\) 0.188508 0.369967i 0.00970865 0.0190543i
\(378\) −16.0244 6.02858i −0.824206 0.310077i
\(379\) −7.39900 10.1839i −0.380061 0.523109i 0.575540 0.817774i \(-0.304792\pi\)
−0.955601 + 0.294665i \(0.904792\pi\)
\(380\) 0 0
\(381\) 18.3999 + 41.3268i 0.942654 + 2.11723i
\(382\) 1.69690 + 6.33292i 0.0868210 + 0.324020i
\(383\) 11.2845 + 13.9353i 0.576613 + 0.712058i 0.979103 0.203366i \(-0.0651883\pi\)
−0.402489 + 0.915425i \(0.631855\pi\)
\(384\) 11.4883 35.3574i 0.586260 1.80432i
\(385\) 0 0
\(386\) −1.53944 4.73792i −0.0783556 0.241154i
\(387\) 28.3800 43.7013i 1.44264 2.22146i
\(388\) −7.07262 0.370660i −0.359058 0.0188174i
\(389\) 2.47971 11.6661i 0.125726 0.591495i −0.869503 0.493928i \(-0.835561\pi\)
0.995229 0.0975672i \(-0.0311061\pi\)
\(390\) 0 0
\(391\) 16.7170 + 5.43168i 0.845415 + 0.274692i
\(392\) −4.23607 15.0038i −0.213954 0.757806i
\(393\) 0.777518 + 0.777518i 0.0392206 + 0.0392206i
\(394\) 20.3227 + 2.13600i 1.02384 + 0.107610i
\(395\) 0 0
\(396\) 1.14579 + 10.9014i 0.0575780 + 0.547818i
\(397\) 13.4462 + 35.0286i 0.674846 + 1.75803i 0.651909 + 0.758297i \(0.273968\pi\)
0.0229366 + 0.999737i \(0.492698\pi\)
\(398\) −6.28010 3.19987i −0.314793 0.160395i
\(399\) 29.2573 32.9337i 1.46470 1.64875i
\(400\) 0 0
\(401\) 0.106730 + 0.184861i 0.00532982 + 0.00923152i 0.868678 0.495377i \(-0.164970\pi\)
−0.863348 + 0.504609i \(0.831637\pi\)
\(402\) 1.34555 + 2.07197i 0.0671099 + 0.103340i
\(403\) 0.0431419 0.0532758i 0.00214905 0.00265386i
\(404\) 6.70499 + 2.98525i 0.333586 + 0.148522i
\(405\) 0 0
\(406\) −13.5355 + 12.3522i −0.671754 + 0.613032i
\(407\) 21.4341 21.4341i 1.06245 1.06245i
\(408\) 15.8463 12.8321i 0.784509 0.635283i
\(409\) −21.3736 23.7377i −1.05685 1.17376i −0.984320 0.176390i \(-0.943558\pi\)
−0.0725340 0.997366i \(-0.523109\pi\)
\(410\) 0 0
\(411\) −25.7143 23.1533i −1.26839 1.14207i
\(412\) 5.61287 2.85990i 0.276526 0.140897i
\(413\) 9.71872 + 9.58962i 0.478227 + 0.471875i
\(414\) −36.0620 + 11.7173i −1.77235 + 0.575872i
\(415\) 0 0
\(416\) −0.246889 + 0.222300i −0.0121047 + 0.0108992i
\(417\) −14.0852 + 36.6932i −0.689755 + 1.79687i
\(418\) −37.4691 10.0398i −1.83267 0.491063i
\(419\) −8.57555 6.23050i −0.418943 0.304380i 0.358269 0.933618i \(-0.383367\pi\)
−0.777212 + 0.629238i \(0.783367\pi\)
\(420\) 0 0
\(421\) 7.12732 5.17830i 0.347364 0.252375i −0.400398 0.916341i \(-0.631128\pi\)
0.747762 + 0.663966i \(0.231128\pi\)
\(422\) 10.0835 3.87070i 0.490858 0.188423i
\(423\) −10.1374 + 6.58333i −0.492899 + 0.320093i
\(424\) −22.6839 13.0965i −1.10163 0.636024i
\(425\) 0 0
\(426\) 4.47737i 0.216929i
\(427\) 14.7459 + 11.7786i 0.713603 + 0.570007i
\(428\) 0.699356 + 0.110767i 0.0338047 + 0.00535413i
\(429\) −0.423913 + 0.952124i −0.0204667 + 0.0459690i
\(430\) 0 0
\(431\) 5.59847 2.49260i 0.269669 0.120064i −0.267448 0.963572i \(-0.586180\pi\)
0.537116 + 0.843508i \(0.319514\pi\)
\(432\) −5.02322 + 18.7469i −0.241680 + 0.901961i
\(433\) −35.2854 + 5.58866i −1.69571 + 0.268574i −0.928097 0.372339i \(-0.878556\pi\)
−0.767613 + 0.640913i \(0.778556\pi\)
\(434\) −2.60986 + 1.53016i −0.125277 + 0.0734501i
\(435\) 0 0
\(436\) −1.22521 + 1.36074i −0.0586770 + 0.0651674i
\(437\) 1.67303 31.9234i 0.0800321 1.52710i
\(438\) 0.494285 9.43153i 0.0236179 0.450656i
\(439\) 17.4485 19.3785i 0.832769 0.924884i −0.165347 0.986235i \(-0.552874\pi\)
0.998116 + 0.0613516i \(0.0195411\pi\)
\(440\) 0 0
\(441\) 10.0482 + 29.5736i 0.478484 + 1.40826i
\(442\) −0.521037 + 0.0825241i −0.0247832 + 0.00392527i
\(443\) 8.76626 32.7161i 0.416498 1.55439i −0.365319 0.930882i \(-0.619040\pi\)
0.781817 0.623508i \(-0.214293\pi\)
\(444\) −12.0463 + 5.36337i −0.571693 + 0.254534i
\(445\) 0 0
\(446\) 10.1563 22.8115i 0.480915 1.08015i
\(447\) 28.8074 + 4.56264i 1.36254 + 0.215805i
\(448\) −10.2929 + 4.03023i −0.486293 + 0.190410i
\(449\) 17.8247i 0.841199i −0.907246 0.420600i \(-0.861820\pi\)
0.907246 0.420600i \(-0.138180\pi\)
\(450\) 0 0
\(451\) −0.445816 0.257392i −0.0209927 0.0121201i
\(452\) 2.45072 1.59152i 0.115272 0.0748586i
\(453\) 53.2469 20.4396i 2.50176 0.960335i
\(454\) −17.3691 + 12.6194i −0.815173 + 0.592258i
\(455\) 0 0
\(456\) −30.0010 21.7970i −1.40493 1.02074i
\(457\) −8.24133 2.20826i −0.385513 0.103298i 0.0608568 0.998147i \(-0.480617\pi\)
−0.446370 + 0.894849i \(0.647283\pi\)
\(458\) 2.40845 6.27422i 0.112539 0.293175i
\(459\) −9.94691 + 8.95624i −0.464282 + 0.418042i
\(460\) 0 0
\(461\) −25.2246 + 8.19596i −1.17483 + 0.381724i −0.830442 0.557105i \(-0.811912\pi\)
−0.344384 + 0.938829i \(0.611912\pi\)
\(462\) 32.3053 32.7402i 1.50298 1.52321i
\(463\) −20.3912 + 10.3899i −0.947661 + 0.482857i −0.858304 0.513142i \(-0.828481\pi\)
−0.0893575 + 0.996000i \(0.528481\pi\)
\(464\) 15.4371 + 13.8996i 0.716647 + 0.645272i
\(465\) 0 0
\(466\) −27.9385 31.0288i −1.29422 1.43738i
\(467\) 6.92961 5.61149i 0.320664 0.259669i −0.455450 0.890262i \(-0.650521\pi\)
0.776114 + 0.630593i \(0.217188\pi\)
\(468\) 0.191702 0.191702i 0.00886142 0.00886142i
\(469\) 0.446943 1.40750i 0.0206379 0.0649922i
\(470\) 0 0
\(471\) 29.8315 + 13.2818i 1.37456 + 0.611994i
\(472\) 7.23302 8.93204i 0.332927 0.411130i
\(473\) 24.9813 + 38.4678i 1.14864 + 1.76875i
\(474\) 34.1972 + 59.2314i 1.57073 + 2.72059i
\(475\) 0 0
\(476\) 5.43263 + 1.11683i 0.249004 + 0.0511899i
\(477\) 46.7562 + 23.8235i 2.14082 + 1.09080i
\(478\) −0.377886 0.984427i −0.0172841 0.0450266i
\(479\) 0.250187 + 2.38037i 0.0114314 + 0.108762i 0.998750 0.0499911i \(-0.0159193\pi\)
−0.987318 + 0.158753i \(0.949253\pi\)
\(480\) 0 0
\(481\) −0.745601 0.0783658i −0.0339965 0.00357317i
\(482\) 1.31543 + 1.31543i 0.0599161 + 0.0599161i
\(483\) 31.9265 + 20.4311i 1.45270 + 0.929648i
\(484\) −2.63308 0.855538i −0.119685 0.0388881i
\(485\) 0 0
\(486\) −6.31534 + 29.7113i −0.286470 + 1.34773i
\(487\) −4.83930 0.253617i −0.219290 0.0114925i −0.0576252 0.998338i \(-0.518353\pi\)
−0.161664 + 0.986846i \(0.551686\pi\)
\(488\) 8.65266 13.3239i 0.391688 0.603146i
\(489\) 12.2414 + 37.6753i 0.553577 + 1.70374i
\(490\) 0 0
\(491\) −9.20020 + 28.3153i −0.415199 + 1.27785i 0.496874 + 0.867823i \(0.334481\pi\)
−0.912073 + 0.410029i \(0.865519\pi\)
\(492\) 0.140929 + 0.174033i 0.00635358 + 0.00784602i
\(493\) 3.70780 + 13.8377i 0.166991 + 0.623218i
\(494\) 0.390225 + 0.876459i 0.0175570 + 0.0394337i
\(495\) 0 0
\(496\) 2.01583 + 2.77456i 0.0905136 + 0.124581i
\(497\) 2.06860 1.69814i 0.0927893 0.0761721i
\(498\) 21.7361 42.6595i 0.974018 1.91162i
\(499\) −33.6862 + 19.4488i −1.50800 + 0.870646i −0.508046 + 0.861330i \(0.669632\pi\)
−0.999957 + 0.00931623i \(0.997035\pi\)
\(500\) 0 0
\(501\) 2.28474 3.95729i 0.102075 0.176799i
\(502\) −22.4095 + 1.17443i −1.00019 + 0.0524175i
\(503\) −5.93752 + 37.4880i −0.264741 + 1.67151i 0.393979 + 0.919120i \(0.371098\pi\)
−0.658719 + 0.752389i \(0.728902\pi\)
\(504\) 23.9475 10.8546i 1.06671 0.483501i
\(505\) 0 0
\(506\) 3.48884 33.1941i 0.155098 1.47566i
\(507\) −34.2767 + 9.18442i −1.52228 + 0.407894i
\(508\) 9.67017 + 3.71203i 0.429044 + 0.164695i
\(509\) 10.1538 2.15825i 0.450057 0.0956626i 0.0226937 0.999742i \(-0.492776\pi\)
0.427364 + 0.904080i \(0.359442\pi\)
\(510\) 0 0
\(511\) −4.54494 + 3.34875i −0.201056 + 0.148140i
\(512\) 2.28214 + 4.47894i 0.100857 + 0.197943i
\(513\) 20.4155 + 13.2579i 0.901364 + 0.585353i
\(514\) −0.577923 0.122841i −0.0254911 0.00541830i
\(515\) 0 0
\(516\) −4.14848 19.5171i −0.182627 0.859191i
\(517\) −1.66446 10.5090i −0.0732027 0.462184i
\(518\) 29.5794 + 14.8232i 1.29964 + 0.651293i
\(519\) 0.451584 0.621552i 0.0198223 0.0272831i
\(520\) 0 0
\(521\) −11.9577 + 1.25680i −0.523874 + 0.0550614i −0.362775 0.931877i \(-0.618171\pi\)
−0.161099 + 0.986938i \(0.551504\pi\)
\(522\) −24.0168 19.4484i −1.05119 0.851233i
\(523\) 1.25486 + 23.9442i 0.0548713 + 1.04701i 0.877850 + 0.478935i \(0.158977\pi\)
−0.822979 + 0.568071i \(0.807690\pi\)
\(524\) 0.251771 0.0109987
\(525\) 0 0
\(526\) −48.2012 −2.10167
\(527\) 0.123784 + 2.36194i 0.00539212 + 0.102888i
\(528\) −40.5204 32.8128i −1.76343 1.42799i
\(529\) 4.48096 0.470968i 0.194824 0.0204769i
\(530\) 0 0
\(531\) −13.5344 + 18.6285i −0.587342 + 0.808407i
\(532\) −0.595233 10.0692i −0.0258066 0.436554i
\(533\) 0.00199173 + 0.0125753i 8.62712e−5 + 0.000544695i
\(534\) 0.923615 + 4.34527i 0.0399687 + 0.188038i
\(535\) 0 0
\(536\) −1.21597 0.258462i −0.0525217 0.0111638i
\(537\) 30.0427 + 19.5099i 1.29644 + 0.841916i
\(538\) 15.2458 + 29.9216i 0.657294 + 1.29001i
\(539\) −27.3789 2.50799i −1.17929 0.108027i
\(540\) 0 0
\(541\) 18.7246 3.98003i 0.805031 0.171115i 0.213024 0.977047i \(-0.431669\pi\)
0.592008 + 0.805932i \(0.298336\pi\)
\(542\) 8.48091 + 3.25552i 0.364286 + 0.139836i
\(543\) −60.7737 + 16.2843i −2.60805 + 0.698825i
\(544\) 1.19812 11.3994i 0.0513690 0.488744i
\(545\) 0 0
\(546\) −1.13212 0.111343i −0.0484504 0.00476506i
\(547\) 1.95187 12.3236i 0.0834558 0.526919i −0.910174 0.414226i \(-0.864052\pi\)
0.993630 0.112693i \(-0.0359477\pi\)
\(548\) −7.91201 + 0.414651i −0.337984 + 0.0177130i
\(549\) −15.9141 + 27.5641i −0.679199 + 1.17641i
\(550\) 0 0
\(551\) 22.5633 13.0269i 0.961230 0.554967i
\(552\) 14.4858 28.4300i 0.616556 1.21006i
\(553\) 14.3955 38.2643i 0.612160 1.62716i
\(554\) −5.63005 7.74910i −0.239198 0.329228i
\(555\) 0 0
\(556\) 3.66039 + 8.22138i 0.155235 + 0.348664i
\(557\) 5.89390 + 21.9963i 0.249732 + 0.932014i 0.970946 + 0.239301i \(0.0769182\pi\)
−0.721213 + 0.692713i \(0.756415\pi\)
\(558\) −3.21091 3.96515i −0.135929 0.167858i
\(559\) 0.350558 1.07891i 0.0148270 0.0456329i
\(560\) 0 0
\(561\) −11.1118 34.1985i −0.469139 1.44386i
\(562\) −7.54986 + 11.6258i −0.318472 + 0.490403i
\(563\) −29.1436 1.52735i −1.22826 0.0643701i −0.572858 0.819654i \(-0.694165\pi\)
−0.655397 + 0.755284i \(0.727499\pi\)
\(564\) −0.962327 + 4.52739i −0.0405213 + 0.190638i
\(565\) 0 0
\(566\) −23.2549 7.55597i −0.977476 0.317601i
\(567\) 5.81822 3.01370i 0.244342 0.126563i
\(568\) −1.59307 1.59307i −0.0668436 0.0668436i
\(569\) 1.57943 + 0.166005i 0.0662130 + 0.00695927i 0.137577 0.990491i \(-0.456069\pi\)
−0.0713640 + 0.997450i \(0.522735\pi\)
\(570\) 0 0
\(571\) −0.375690 3.57445i −0.0157221 0.149586i 0.983844 0.179025i \(-0.0572945\pi\)
−0.999567 + 0.0294394i \(0.990628\pi\)
\(572\) 0.0855211 + 0.222790i 0.00357582 + 0.00931532i
\(573\) 9.84838 + 5.01800i 0.411422 + 0.209630i
\(574\) 0.113145 0.550374i 0.00472258 0.0229722i
\(575\) 0 0
\(576\) −9.32098 16.1444i −0.388374 0.672683i
\(577\) 12.1657 + 18.7335i 0.506465 + 0.779887i 0.995736 0.0922444i \(-0.0294041\pi\)
−0.489272 + 0.872131i \(0.662737\pi\)
\(578\) −5.88101 + 7.26245i −0.244618 + 0.302078i
\(579\) −7.67247 3.41601i −0.318857 0.141964i
\(580\) 0 0
\(581\) −27.9531 + 6.13722i −1.15969 + 0.254615i
\(582\) −35.4392 + 35.4392i −1.46900 + 1.46900i
\(583\) −35.8975 + 29.0692i −1.48672 + 1.20392i
\(584\) 3.17991 + 3.53164i 0.131585 + 0.146140i
\(585\) 0 0
\(586\) 13.2943 + 11.9702i 0.549182 + 0.494486i
\(587\) −38.6684 + 19.7026i −1.59602 + 0.813211i −0.596070 + 0.802933i \(0.703272\pi\)
−0.999947 + 0.0102788i \(0.996728\pi\)
\(588\) 10.7282 + 5.28678i 0.442422 + 0.218023i
\(589\) 4.09095 1.32923i 0.168565 0.0547699i
\(590\) 0 0
\(591\) 25.6015 23.0517i 1.05310 0.948218i
\(592\) 13.4409 35.0148i 0.552419 1.43910i
\(593\) 12.4912 + 3.34701i 0.512953 + 0.137445i 0.506005 0.862531i \(-0.331122\pi\)
0.00694789 + 0.999976i \(0.497788\pi\)
\(594\) 20.5621 + 14.9392i 0.843673 + 0.612964i
\(595\) 0 0
\(596\) 5.40284 3.92539i 0.221309 0.160790i
\(597\) −11.0933 + 4.25833i −0.454019 + 0.174282i
\(598\) −0.692325 + 0.449601i −0.0283113 + 0.0183855i
\(599\) 19.9444 + 11.5149i 0.814905 + 0.470485i 0.848656 0.528945i \(-0.177412\pi\)
−0.0337516 + 0.999430i \(0.510745\pi\)
\(600\) 0 0
\(601\) 14.0409i 0.572740i 0.958119 + 0.286370i \(0.0924486\pi\)
−0.958119 + 0.286370i \(0.907551\pi\)
\(602\) −31.2456 + 39.1169i −1.27347 + 1.59429i
\(603\) 2.45985 + 0.389602i 0.100173 + 0.0158658i
\(604\) 5.31174 11.9304i 0.216132 0.485440i
\(605\) 0 0
\(606\) 47.4483 21.1254i 1.92746 0.858159i
\(607\) −10.2468 + 38.2415i −0.415904 + 1.55218i 0.367113 + 0.930176i \(0.380346\pi\)
−0.783017 + 0.622000i \(0.786320\pi\)
\(608\) −20.5892 + 3.26100i −0.835001 + 0.132251i
\(609\) 0.206542 + 30.8920i 0.00836952 + 1.25181i
\(610\) 0 0
\(611\) −0.176085 + 0.195562i −0.00712364 + 0.00791160i
\(612\) −0.489529 + 9.34078i −0.0197881 + 0.377579i
\(613\) −0.203103 + 3.87544i −0.00820325 + 0.156527i 0.991456 + 0.130439i \(0.0416386\pi\)
−0.999660 + 0.0260887i \(0.991695\pi\)
\(614\) −12.4826 + 13.8633i −0.503756 + 0.559478i
\(615\) 0 0
\(616\) 0.154736 + 23.1435i 0.00623450 + 0.932477i
\(617\) 27.5463 4.36290i 1.10897 0.175644i 0.425029 0.905180i \(-0.360264\pi\)
0.683943 + 0.729536i \(0.260264\pi\)
\(618\) 11.5378 43.0597i 0.464118 1.73211i
\(619\) 24.6623 10.9803i 0.991260 0.441337i 0.153958 0.988077i \(-0.450798\pi\)
0.837302 + 0.546740i \(0.184131\pi\)
\(620\) 0 0
\(621\) −8.51918 + 19.1344i −0.341863 + 0.767837i
\(622\) −45.9911 7.28427i −1.84408 0.292073i
\(623\) 1.65726 2.07476i 0.0663968 0.0831234i
\(624\) 1.28957i 0.0516239i
\(625\) 0 0
\(626\) 13.3561 + 7.71114i 0.533816 + 0.308199i
\(627\) −54.8460 + 35.6174i −2.19034 + 1.42242i
\(628\) 6.98035 2.67950i 0.278546 0.106924i
\(629\) 20.9260 15.2037i 0.834376 0.606209i
\(630\) 0 0
\(631\) 8.70119 + 6.32178i 0.346389 + 0.251666i 0.747353 0.664428i \(-0.231325\pi\)
−0.400964 + 0.916094i \(0.631325\pi\)
\(632\) −33.2423 8.90724i −1.32231 0.354311i
\(633\) 6.52549 16.9995i 0.259365 0.675668i
\(634\) −9.39921 + 8.46309i −0.373290 + 0.336112i
\(635\) 0 0
\(636\) 19.1105 6.20937i 0.757780 0.246217i
\(637\) 0.377941 + 0.565284i 0.0149746 + 0.0223974i
\(638\) 24.2379 12.3498i 0.959589 0.488935i
\(639\) 3.35424 + 3.02018i 0.132692 + 0.119476i
\(640\) 0 0
\(641\) 20.1580 + 22.3877i 0.796191 + 0.884260i 0.995411 0.0956947i \(-0.0305073\pi\)
−0.199219 + 0.979955i \(0.563841\pi\)
\(642\) 3.89407 3.15336i 0.153687 0.124453i
\(643\) 20.4056 20.4056i 0.804720 0.804720i −0.179110 0.983829i \(-0.557322\pi\)
0.983829 + 0.179110i \(0.0573217\pi\)
\(644\) 8.47706 1.86118i 0.334043 0.0733407i
\(645\) 0 0
\(646\) −30.2391 13.4633i −1.18974 0.529707i
\(647\) 12.0473 14.8771i 0.473627 0.584880i −0.483211 0.875504i \(-0.660529\pi\)
0.956837 + 0.290624i \(0.0938628\pi\)
\(648\) −3.00412 4.62594i −0.118013 0.181724i
\(649\) −10.1343 17.5531i −0.397805 0.689019i
\(650\) 0 0
\(651\) −1.02704 + 4.99588i −0.0402531 + 0.195804i
\(652\) 8.08188 + 4.11792i 0.316511 + 0.161270i
\(653\) 4.32563 + 11.2686i 0.169275 + 0.440976i 0.991807 0.127742i \(-0.0407729\pi\)
−0.822533 + 0.568718i \(0.807440\pi\)
\(654\) 1.35443 + 12.8866i 0.0529625 + 0.503905i
\(655\) 0 0
\(656\) −0.633461 0.0665794i −0.0247325 0.00259949i
\(657\) −6.73225 6.73225i −0.262650 0.262650i
\(658\) 10.3122 5.34145i 0.402010 0.208232i
\(659\) −15.5052 5.03793i −0.603995 0.196250i −0.00897383 0.999960i \(-0.502856\pi\)
−0.595022 + 0.803710i \(0.702856\pi\)
\(660\) 0 0
\(661\) −2.91594 + 13.7184i −0.113417 + 0.533585i 0.884352 + 0.466821i \(0.154601\pi\)
−0.997769 + 0.0667642i \(0.978732\pi\)
\(662\) 1.67440 + 0.0877515i 0.0650774 + 0.00341056i
\(663\) −0.484374 + 0.745871i −0.0188115 + 0.0289672i
\(664\) 7.44463 + 22.9122i 0.288908 + 0.889166i
\(665\) 0 0
\(666\) −17.2426 + 53.0674i −0.668138 + 2.05632i
\(667\) 14.1079 + 17.4218i 0.546259 + 0.674574i
\(668\) −0.270798 1.01063i −0.0104775 0.0391025i
\(669\) −17.1222 38.4571i −0.661983 1.48684i
\(670\) 0 0
\(671\) −16.4678 22.6659i −0.635731 0.875008i
\(672\) 8.70342 23.1343i 0.335742 0.892426i
\(673\) −0.128682 + 0.252552i −0.00496031 + 0.00973515i −0.893473 0.449116i \(-0.851739\pi\)
0.888513 + 0.458851i \(0.151739\pi\)
\(674\) −2.62652 + 1.51642i −0.101170 + 0.0584103i
\(675\) 0 0
\(676\) −4.06262 + 7.03667i −0.156255 + 0.270641i
\(677\) −33.4491 + 1.75299i −1.28555 + 0.0673729i −0.682829 0.730578i \(-0.739251\pi\)
−0.602723 + 0.797951i \(0.705917\pi\)
\(678\) 3.23488 20.4242i 0.124235 0.784387i
\(679\) 29.8144 + 2.93222i 1.14417 + 0.112528i
\(680\) 0 0
\(681\) −3.78337 + 35.9963i −0.144979 + 1.37938i
\(682\) 4.33814 1.16240i 0.166116 0.0445106i
\(683\) 21.1225 + 8.10815i 0.808228 + 0.310250i 0.727168 0.686460i \(-0.240836\pi\)
0.0810601 + 0.996709i \(0.474169\pi\)
\(684\) 16.6393 3.53680i 0.636221 0.135233i
\(685\) 0 0
\(686\) −6.82667 29.2221i −0.260644 1.11571i
\(687\) −5.14374 10.0951i −0.196246 0.385154i
\(688\) 47.5968 + 30.9097i 1.81461 + 1.17842i
\(689\) 1.11747 + 0.237526i 0.0425724 + 0.00904903i
\(690\) 0 0
\(691\) −5.91700 27.8373i −0.225093 1.05898i −0.934990 0.354674i \(-0.884592\pi\)
0.709897 0.704306i \(-0.248742\pi\)
\(692\) −0.0275190 0.173748i −0.00104612 0.00660492i
\(693\) −2.73619 46.2863i −0.103939 1.75827i
\(694\) 1.89358 2.60628i 0.0718792 0.0989332i
\(695\) 0 0
\(696\) 25.8629 2.71830i 0.980332 0.103037i
\(697\) −0.341379 0.276443i −0.0129307 0.0104710i
\(698\) −0.370596 7.07139i −0.0140273 0.267656i
\(699\) −70.3907 −2.66242
\(700\) 0 0
\(701\) 29.7376 1.12317 0.561587 0.827418i \(-0.310191\pi\)
0.561587 + 0.827418i \(0.310191\pi\)
\(702\) −0.0328989 0.627749i −0.00124169 0.0236928i
\(703\) −36.5582 29.6042i −1.37882 1.11654i
\(704\) 16.3196 1.71525i 0.615067 0.0646461i
\(705\) 0 0
\(706\) 17.7863 24.4807i 0.669396 0.921345i
\(707\) −27.7560 13.9094i −1.04387 0.523118i
\(708\) 1.37930 + 8.70856i 0.0518373 + 0.327288i
\(709\) 1.79995 + 8.46811i 0.0675986 + 0.318026i 0.998935 0.0461328i \(-0.0146897\pi\)
−0.931337 + 0.364159i \(0.881356\pi\)
\(710\) 0 0
\(711\) 67.4409 + 14.3350i 2.52923 + 0.537605i
\(712\) −1.87469 1.21744i −0.0702569 0.0456254i
\(713\) 1.68028 + 3.29773i 0.0629269 + 0.123501i
\(714\) 31.5976 23.2814i 1.18251 0.871283i
\(715\) 0 0
\(716\) 8.02292 1.70532i 0.299830 0.0637309i
\(717\) −1.65961 0.637066i −0.0619794 0.0237917i
\(718\) 26.1589 7.00926i 0.976242 0.261583i
\(719\) 2.82649 26.8922i 0.105410 1.00291i −0.806141 0.591724i \(-0.798448\pi\)
0.911551 0.411187i \(-0.134886\pi\)
\(720\) 0 0
\(721\) −24.2700 + 11.0007i −0.903863 + 0.409689i
\(722\) −4.60121 + 29.0509i −0.171239 + 1.08116i
\(723\) 3.13192 0.164137i 0.116477 0.00610431i
\(724\) −7.20316 + 12.4762i −0.267703 + 0.463676i
\(725\) 0 0
\(726\) −16.9672 + 9.79602i −0.629712 + 0.363565i
\(727\) 7.90873 15.5218i 0.293318 0.575670i −0.696575 0.717484i \(-0.745294\pi\)
0.989893 + 0.141814i \(0.0452936\pi\)
\(728\) 0.442430 0.363198i 0.0163976 0.0134610i
\(729\) 25.7325 + 35.4177i 0.953055 + 1.31177i
\(730\) 0 0
\(731\) 15.9195 + 35.7557i 0.588803 + 1.32247i
\(732\) 3.15439 + 11.7724i 0.116590 + 0.435119i
\(733\) −28.8928 35.6797i −1.06718 1.31786i −0.945619 0.325275i \(-0.894543\pi\)
−0.121562 0.992584i \(-0.538790\pi\)
\(734\) 4.83698 14.8867i 0.178536 0.549477i
\(735\) 0 0
\(736\) −5.54266 17.0586i −0.204305 0.628787i
\(737\) −1.19399 + 1.83858i −0.0439812 + 0.0677251i
\(738\) 0.946304 + 0.0495937i 0.0348339 + 0.00182557i
\(739\) 5.11747 24.0758i 0.188249 0.885642i −0.778046 0.628207i \(-0.783789\pi\)
0.966296 0.257435i \(-0.0828774\pi\)
\(740\) 0 0
\(741\) 1.53827 + 0.499813i 0.0565096 + 0.0183611i
\(742\) −42.4664 27.1761i −1.55899 0.997665i
\(743\) 10.2323 + 10.2323i 0.375388 + 0.375388i 0.869435 0.494047i \(-0.164483\pi\)
−0.494047 + 0.869435i \(0.664483\pi\)
\(744\) 4.26995 + 0.448790i 0.156544 + 0.0164534i
\(745\) 0 0
\(746\) 0.832965 + 7.92513i 0.0304970 + 0.290160i
\(747\) −17.2966 45.0593i −0.632851 1.64863i
\(748\) −7.33605 3.73790i −0.268233 0.136671i
\(749\) −2.93380 0.603126i −0.107199 0.0220377i
\(750\) 0 0
\(751\) 5.60583 + 9.70959i 0.204560 + 0.354308i 0.949992 0.312273i \(-0.101090\pi\)
−0.745433 + 0.666581i \(0.767757\pi\)
\(752\) −7.17016 11.0411i −0.261469 0.402627i
\(753\) −23.8080 + 29.4005i −0.867613 + 1.07141i
\(754\) −0.614634 0.273653i −0.0223836 0.00996584i
\(755\) 0 0
\(756\) −2.00020 + 6.29898i −0.0727467 + 0.229092i
\(757\) 34.2009 34.2009i 1.24305 1.24305i 0.284326 0.958728i \(-0.408230\pi\)
0.958728 0.284326i \(-0.0917697\pi\)
\(758\) −15.8511 + 12.8360i −0.575740 + 0.466225i
\(759\) −37.6514 41.8161i −1.36666 1.51783i
\(760\) 0 0
\(761\) 12.7666 + 11.4951i 0.462789 + 0.416697i 0.867261 0.497853i \(-0.165878\pi\)
−0.404472 + 0.914550i \(0.632545\pi\)
\(762\) 65.3109 33.2776i 2.36597 1.20552i
\(763\) 5.44005 5.51328i 0.196943 0.199594i
\(764\) 2.40697 0.782073i 0.0870812 0.0282944i
\(765\) 0 0
\(766\) 21.5918 19.4414i 0.780145 0.702445i
\(767\) −0.179649 + 0.468000i −0.00648673 + 0.0168985i
\(768\) −36.1387 9.68333i −1.30404 0.349417i
\(769\) 15.2142 + 11.0538i 0.548638 + 0.398609i 0.827283 0.561785i \(-0.189885\pi\)
−0.278645 + 0.960394i \(0.589885\pi\)
\(770\) 0 0
\(771\) −0.805836 + 0.585474i −0.0290215 + 0.0210853i
\(772\) −1.79530 + 0.689152i −0.0646144 + 0.0248031i
\(773\) 27.1011 17.5997i 0.974759 0.633016i 0.0441474 0.999025i \(-0.485943\pi\)
0.930611 + 0.366009i \(0.119276\pi\)
\(774\) −73.1203 42.2160i −2.62825 1.51742i
\(775\) 0 0
\(776\) 25.2188i 0.905302i
\(777\) 51.9387 20.3368i 1.86329 0.729580i
\(778\) −19.0873 3.02314i −0.684314 0.108385i
\(779\) −0.324938 + 0.729823i −0.0116421 + 0.0261486i
\(780\) 0 0
\(781\) −3.62956 + 1.61599i −0.129876 + 0.0578245i
\(782\) 7.37143 27.5106i 0.263602 0.983776i
\(783\) −16.8606 + 2.67045i −0.602548 + 0.0954343i
\(784\) −32.2097 + 10.9438i −1.15035 + 0.390851i
\(785\) 0 0
\(786\) 1.19218 1.32405i 0.0425235 0.0472271i
\(787\) 0.695360 13.2683i 0.0247869 0.472962i −0.957832 0.287328i \(-0.907233\pi\)
0.982619 0.185634i \(-0.0594338\pi\)
\(788\) 0.412831 7.87728i 0.0147065 0.280617i
\(789\) −54.3742 + 60.3886i −1.93577 + 2.14989i
\(790\) 0 0
\(791\) −10.6631 + 6.25178i −0.379137 + 0.222288i
\(792\) −38.5512 + 6.10592i −1.36986 + 0.216964i
\(793\) −0.179343 + 0.669316i −0.00636865 + 0.0237681i
\(794\) 55.5398 24.7279i 1.97104 0.877561i
\(795\) 0 0
\(796\) −1.10663 + 2.48554i −0.0392236 + 0.0880976i
\(797\) −37.9724 6.01424i −1.34505 0.213035i −0.557959 0.829869i \(-0.688415\pi\)
−0.787094 + 0.616833i \(0.788415\pi\)
\(798\) −55.7715 44.5488i −1.97429 1.57701i
\(799\) 9.07923i 0.321200i
\(800\) 0 0
\(801\) 3.87829 + 2.23913i 0.137033 + 0.0791159i
\(802\) 0.290075 0.188377i 0.0102429 0.00665182i
\(803\) 7.82402 3.00336i 0.276104 0.105986i
\(804\) 0.771531 0.560550i 0.0272098 0.0197691i
\(805\) 0 0
\(806\) −0.0898647 0.0652905i −0.00316535 0.00229976i
\(807\) 54.6854 + 14.6529i 1.92502 + 0.515807i
\(808\) −9.36582 + 24.3988i −0.329488 + 0.858347i
\(809\) 0.858767 0.773238i 0.0301927 0.0271856i −0.653896 0.756584i \(-0.726867\pi\)
0.684089 + 0.729399i \(0.260200\pi\)
\(810\) 0 0
\(811\) −11.7589 + 3.82070i −0.412911 + 0.134163i −0.508104 0.861296i \(-0.669653\pi\)
0.0951926 + 0.995459i \(0.469653\pi\)
\(812\) 5.03507 + 4.96819i 0.176696 + 0.174349i
\(813\) 13.6457 6.95282i 0.478575 0.243846i
\(814\) −36.5004 32.8651i −1.27934 1.15192i
\(815\) 0 0
\(816\) −29.7709 33.0639i −1.04219 1.15747i
\(817\) 55.3185 44.7960i 1.93535 1.56722i
\(818\) −36.5978 + 36.5978i −1.27961 + 1.27961i
\(819\) −0.847078 + 0.773030i −0.0295993 + 0.0270118i
\(820\) 0 0
\(821\) −33.8881 15.0880i −1.18270 0.526574i −0.281328 0.959612i \(-0.590775\pi\)
−0.901376 + 0.433038i \(0.857442\pi\)
\(822\) −35.2840 + 43.5721i −1.23067 + 1.51975i
\(823\) −27.3912 42.1788i −0.954799 1.47026i −0.881072 0.472983i \(-0.843177\pi\)
−0.0737269 0.997278i \(-0.523489\pi\)
\(824\) 11.2156 + 19.4260i 0.390714 + 0.676737i
\(825\) 0 0
\(826\) 14.6929 16.5392i 0.511232 0.575472i
\(827\) −17.5564 8.94542i −0.610495 0.311063i 0.121270 0.992620i \(-0.461303\pi\)
−0.731765 + 0.681557i \(0.761303\pi\)
\(828\) 5.24539 + 13.6647i 0.182290 + 0.474881i
\(829\) −2.37030 22.5519i −0.0823239 0.783260i −0.955328 0.295547i \(-0.904498\pi\)
0.873004 0.487713i \(-0.162169\pi\)
\(830\) 0 0
\(831\) −16.0595 1.68792i −0.557097 0.0585533i
\(832\) −0.286979 0.286979i −0.00994922 0.00994922i
\(833\) −22.7404 5.76850i −0.787907 0.199867i
\(834\) 60.5681 + 19.6798i 2.09730 + 0.681454i
\(835\) 0 0
\(836\) −3.11324 + 14.6467i −0.107674 + 0.506565i
\(837\) −2.81450 0.147502i −0.0972835 0.00509841i
\(838\) −9.35442 + 14.4045i −0.323143 + 0.497597i
\(839\) −5.77620 17.7773i −0.199417 0.613742i −0.999897 0.0143819i \(-0.995422\pi\)
0.800480 0.599360i \(-0.204578\pi\)
\(840\) 0 0
\(841\) 3.31550 10.2041i 0.114328 0.351864i
\(842\) −8.98347 11.0937i −0.309591 0.382313i
\(843\) 6.04853 + 22.5734i 0.208323 + 0.777470i
\(844\) −1.69581 3.80886i −0.0583723 0.131106i
\(845\) 0 0
\(846\) 11.5122 + 15.8452i 0.395799 + 0.544770i
\(847\) 10.9611 + 4.12369i 0.376627 + 0.141692i
\(848\) −25.9471 + 50.9240i −0.891025 + 1.74874i
\(849\) −35.6995 + 20.6111i −1.22520 + 0.707372i
\(850\) 0 0
\(851\) 20.2381 35.0534i 0.693752 1.20161i
\(852\) 1.72597 0.0904541i 0.0591306 0.00309891i
\(853\) 5.30806 33.5138i 0.181744 1.14749i −0.713084 0.701079i \(-0.752702\pi\)
0.894828 0.446410i \(-0.147298\pi\)
\(854\) 17.8086 24.8593i 0.609399 0.850668i
\(855\) 0 0
\(856\) −0.263549 + 2.50750i −0.00900793 + 0.0857047i
\(857\) 8.64649 2.31682i 0.295358 0.0791410i −0.108097 0.994140i \(-0.534476\pi\)
0.403455 + 0.914999i \(0.367809\pi\)
\(858\) 1.57659 + 0.605196i 0.0538239 + 0.0206611i
\(859\) 22.5915 4.80196i 0.770810 0.163841i 0.194313 0.980940i \(-0.437752\pi\)
0.576498 + 0.817099i \(0.304419\pi\)
\(860\) 0 0
\(861\) −0.561898 0.762611i −0.0191494 0.0259897i
\(862\) −4.50806 8.84757i −0.153545 0.301349i
\(863\) 3.09204 + 2.00799i 0.105254 + 0.0683529i 0.596193 0.802841i \(-0.296679\pi\)
−0.490939 + 0.871194i \(0.663346\pi\)
\(864\) 13.3599 + 2.83974i 0.454513 + 0.0966098i
\(865\) 0 0
\(866\) 12.0353 + 56.6218i 0.408977 + 1.92409i
\(867\) 2.46454 + 15.5605i 0.0837003 + 0.528463i
\(868\) 0.642582 + 0.975154i 0.0218107 + 0.0330989i
\(869\) −35.6731 + 49.0998i −1.21013 + 1.66560i
\(870\) 0 0
\(871\) 0.0539235 0.00566759i 0.00182713 0.000192039i
\(872\) −5.06701 4.10318i −0.171590 0.138951i
\(873\) 2.64421 + 50.4546i 0.0894931 + 1.70763i
\(874\) −51.7975 −1.75208
\(875\) 0 0
\(876\) −3.64571 −0.123177
\(877\) 1.57330 + 30.0203i 0.0531265 + 1.01371i 0.887003 + 0.461763i \(0.152783\pi\)
−0.833877 + 0.551951i \(0.813884\pi\)
\(878\) −32.8362 26.5902i −1.10817 0.897376i
\(879\) 29.9937 3.15246i 1.01166 0.106330i
\(880\) 0 0
\(881\) 26.3597 36.2810i 0.888079 1.22234i −0.0860376 0.996292i \(-0.527421\pi\)
0.974117 0.226045i \(-0.0725795\pi\)
\(882\) 47.0012 18.7669i 1.58261 0.631915i
\(883\) 4.53057 + 28.6049i 0.152466 + 0.962631i 0.938708 + 0.344713i \(0.112024\pi\)
−0.786242 + 0.617918i \(0.787976\pi\)
\(884\) 0.0423382 + 0.199185i 0.00142399 + 0.00669933i
\(885\) 0 0
\(886\) −53.6817 11.4104i −1.80347 0.383340i
\(887\) 20.2001 + 13.1181i 0.678253 + 0.440463i 0.837253 0.546816i \(-0.184160\pi\)
−0.159000 + 0.987279i \(0.550827\pi\)
\(888\) −21.3167 41.8363i −0.715341 1.40394i
\(889\) −40.1452 17.5532i −1.34643 0.588714i
\(890\) 0 0
\(891\) −9.51455 + 2.02238i −0.318749 + 0.0677523i
\(892\) −8.99869 3.45427i −0.301298 0.115658i
\(893\) −15.9494 + 4.27364i −0.533728 + 0.143012i
\(894\) 4.93994 47.0004i 0.165216 1.57193i
\(895\) 0 0
\(896\) 14.8652 + 32.7960i 0.496613 + 1.09564i
\(897\) −0.217708 + 1.37455i −0.00726906 + 0.0458950i
\(898\) −28.8423 + 1.51156i −0.962481 + 0.0504415i
\(899\) −1.50825 + 2.61236i −0.0503029 + 0.0871271i
\(900\) 0 0
\(901\) −34.1351 + 19.7079i −1.13720 + 0.656565i
\(902\) −0.378683 + 0.743207i −0.0126088 + 0.0247461i
\(903\) 13.7604 + 83.2723i 0.457916 + 2.77113i
\(904\) 6.11603 + 8.41800i 0.203416 + 0.279978i
\(905\) 0 0
\(906\) −37.5889 84.4261i −1.24881 2.80487i
\(907\) −0.937438 3.49857i −0.0311271 0.116168i 0.948614 0.316435i \(-0.102486\pi\)
−0.979741 + 0.200267i \(0.935819\pi\)
\(908\) 5.21551 + 6.44061i 0.173083 + 0.213739i
\(909\) 16.1797 49.7961i 0.536648 1.65163i
\(910\) 0 0
\(911\) 2.97054 + 9.14238i 0.0984183 + 0.302900i 0.988129 0.153623i \(-0.0490943\pi\)
−0.889711 + 0.456524i \(0.849094\pi\)
\(912\) −44.0699 + 67.8617i −1.45930 + 2.24713i
\(913\) 42.4268 + 2.22349i 1.40412 + 0.0735869i
\(914\) −2.87433 + 13.5226i −0.0950743 + 0.447289i
\(915\) 0 0
\(916\) −2.46728 0.801669i −0.0815213 0.0264879i
\(917\) −1.06388 0.0486256i −0.0351325 0.00160576i
\(918\) 15.3357 + 15.3357i 0.506154 + 0.506154i
\(919\) 7.32146 + 0.769517i 0.241513 + 0.0253840i 0.224511 0.974471i \(-0.427921\pi\)
0.0170013 + 0.999855i \(0.494588\pi\)
\(920\) 0 0
\(921\) 3.28740 + 31.2775i 0.108323 + 1.03063i
\(922\) 15.4011 + 40.1211i 0.507207 + 1.32132i
\(923\) 0.0875541 + 0.0446111i 0.00288188 + 0.00146839i
\(924\) −13.2736 11.7918i −0.436668 0.387923i
\(925\) 0 0
\(926\) 18.5411 + 32.1142i 0.609300 + 1.05534i
\(927\) −24.4756 37.6891i −0.803884 1.23787i
\(928\) 9.19975 11.3607i 0.301996 0.372935i
\(929\) −53.5074 23.8230i −1.75552 0.781608i −0.990485 0.137618i \(-0.956055\pi\)
−0.765034 0.643989i \(-0.777278\pi\)
\(930\) 0 0
\(931\) 0.570514 + 42.6632i 0.0186978 + 1.39823i
\(932\) −11.3968 + 11.3968i −0.373313 + 0.373313i
\(933\) −61.0071 + 49.4026i −1.99728 + 1.61737i
\(934\) −9.66765 10.7370i −0.316335 0.351326i
\(935\) 0 0
\(936\) 0.717404 + 0.645953i 0.0234491 + 0.0211136i
\(937\) 4.14402 2.11148i 0.135379 0.0689791i −0.384989 0.922921i \(-0.625795\pi\)
0.520368 + 0.853942i \(0.325795\pi\)
\(938\) −2.31539 0.603844i −0.0756002 0.0197162i
\(939\) 24.7274 8.03442i 0.806948 0.262193i
\(940\) 0 0
\(941\) 21.7072 19.5452i 0.707634 0.637157i −0.234608 0.972090i \(-0.575381\pi\)
0.942242 + 0.334933i \(0.108714\pi\)
\(942\) 18.9617 49.3969i 0.617806 1.60944i
\(943\) −0.663969 0.177910i −0.0216218 0.00579355i
\(944\) −20.2890 14.7408i −0.660350 0.479773i
\(945\) 0 0
\(946\) 60.1267 43.6846i 1.95489 1.42031i
\(947\) −5.68779 + 2.18334i −0.184828 + 0.0709490i −0.449022 0.893521i \(-0.648228\pi\)
0.264194 + 0.964470i \(0.414894\pi\)
\(948\) 22.1420 14.3792i 0.719139 0.467015i
\(949\) −0.179507 0.103638i −0.00582703 0.00336424i
\(950\) 0 0
\(951\) 21.3227i 0.691435i
\(952\) −2.95896 + 19.5262i −0.0959003 + 0.632847i
\(953\) 5.50713 + 0.872243i 0.178393 + 0.0282547i 0.244992 0.969525i \(-0.421215\pi\)
−0.0665986 + 0.997780i \(0.521215\pi\)
\(954\) 34.5840 77.6770i 1.11970 2.51488i
\(955\) 0 0
\(956\) −0.371849 + 0.165558i −0.0120265 + 0.00535452i
\(957\) 11.8696 44.2978i 0.383688 1.43194i
\(958\) 3.83049 0.606690i 0.123758 0.0196013i
\(959\) 33.5130 0.224067i 1.08219 0.00723549i
\(960\) 0 0
\(961\) 20.4098 22.6674i 0.658381 0.731206i
\(962\) −0.0635764 + 1.21311i −0.00204979 + 0.0391122i
\(963\) 0.264362 5.04433i 0.00851895 0.162551i
\(964\) 0.480505 0.533655i 0.0154760 0.0171879i
\(965\) 0 0
\(966\) 30.3524 53.3931i 0.976572 1.71790i
\(967\) −58.4215 + 9.25305i −1.87871 + 0.297558i −0.987692 0.156414i \(-0.950007\pi\)
−0.891016 + 0.453972i \(0.850007\pi\)
\(968\) 2.55154 9.52247i 0.0820095 0.306064i
\(969\) −50.9791 + 22.6974i −1.63769 + 0.729145i
\(970\) 0 0
\(971\) −21.4670 + 48.2157i −0.688909 + 1.54731i 0.141364 + 0.989958i \(0.454851\pi\)
−0.830273 + 0.557357i \(0.811815\pi\)
\(972\) 11.5809 + 1.83423i 0.371458 + 0.0588331i
\(973\) −13.8795 35.4471i −0.444956 1.13638i
\(974\) 7.85203i 0.251595i
\(975\) 0 0
\(976\) −30.0211 17.3327i −0.960952 0.554806i
\(977\) 11.0553 7.17937i 0.353689 0.229688i −0.355549 0.934658i \(-0.615706\pi\)
0.709238 + 0.704969i \(0.249039\pi\)
\(978\) 59.9247 23.0029i 1.91618 0.735553i
\(979\) −3.18912 + 2.31703i −0.101925 + 0.0740525i
\(980\) 0 0
\(981\) 10.5677 + 7.67785i 0.337399 + 0.245135i
\(982\) 46.5975 + 12.4858i 1.48699 + 0.398436i
\(983\) 19.2414 50.1256i 0.613706 1.59876i −0.175398 0.984498i \(-0.556121\pi\)
0.789103 0.614260i \(-0.210546\pi\)
\(984\) −0.592586 + 0.533567i −0.0188910 + 0.0170095i
\(985\) 0 0
\(986\) 22.0765 7.17309i 0.703059 0.228438i
\(987\) 4.94079 18.9451i 0.157267 0.603028i
\(988\) 0.329979 0.168133i 0.0104980 0.00534902i
\(989\) 45.5154 + 40.9823i 1.44731 + 1.30316i
\(990\) 0 0
\(991\) 7.06342 + 7.84472i 0.224377 + 0.249196i 0.844814 0.535061i \(-0.179711\pi\)
−0.620437 + 0.784257i \(0.713045\pi\)
\(992\) 1.87565 1.51887i 0.0595519 0.0482242i
\(993\) 1.99877 1.99877i 0.0634291 0.0634291i
\(994\) −2.92320 3.20322i −0.0927184 0.101600i
\(995\) 0 0
\(996\) −16.8838 7.51714i −0.534983 0.238190i
\(997\) 37.6753 46.5252i 1.19319 1.47347i 0.349249 0.937030i \(-0.386437\pi\)
0.843940 0.536437i \(-0.180230\pi\)
\(998\) 34.3269 + 52.8588i 1.08660 + 1.67321i
\(999\) 15.4110 + 26.6927i 0.487584 + 0.844520i
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 875.2.bb.a.143.5 288
5.2 odd 4 875.2.bb.c.857.14 288
5.3 odd 4 175.2.x.a.17.5 yes 288
5.4 even 2 875.2.bb.b.143.14 288
7.5 odd 6 inner 875.2.bb.a.768.5 288
25.3 odd 20 875.2.bb.b.507.14 288
25.4 even 10 175.2.x.a.3.14 288
25.21 even 5 875.2.bb.c.493.5 288
25.22 odd 20 inner 875.2.bb.a.507.5 288
35.12 even 12 875.2.bb.c.607.5 288
35.19 odd 6 875.2.bb.b.768.14 288
35.33 even 12 175.2.x.a.117.14 yes 288
175.47 even 60 inner 875.2.bb.a.257.5 288
175.54 odd 30 175.2.x.a.103.5 yes 288
175.96 odd 30 875.2.bb.c.243.14 288
175.103 even 60 875.2.bb.b.257.14 288
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
175.2.x.a.3.14 288 25.4 even 10
175.2.x.a.17.5 yes 288 5.3 odd 4
175.2.x.a.103.5 yes 288 175.54 odd 30
175.2.x.a.117.14 yes 288 35.33 even 12
875.2.bb.a.143.5 288 1.1 even 1 trivial
875.2.bb.a.257.5 288 175.47 even 60 inner
875.2.bb.a.507.5 288 25.22 odd 20 inner
875.2.bb.a.768.5 288 7.5 odd 6 inner
875.2.bb.b.143.14 288 5.4 even 2
875.2.bb.b.257.14 288 175.103 even 60
875.2.bb.b.507.14 288 25.3 odd 20
875.2.bb.b.768.14 288 35.19 odd 6
875.2.bb.c.243.14 288 175.96 odd 30
875.2.bb.c.493.5 288 25.21 even 5
875.2.bb.c.607.5 288 35.12 even 12
875.2.bb.c.857.14 288 5.2 odd 4