Properties

Label 495.2.n.e.361.2
Level $495$
Weight $2$
Character 495.361
Analytic conductor $3.953$
Analytic rank $0$
Dimension $8$
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] = [495,2,Mod(91,495)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(495, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("495.91");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 495.n (of order \(5\), degree \(4\), 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: \(3.95259490005\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.13140625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 55)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 361.2
Root \(1.69513 - 1.23158i\) of defining polynomial
Character \(\chi\) \(=\) 495.361
Dual form 495.2.n.e.181.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.647481 - 1.99274i) q^{2} +(-1.93376 - 1.40496i) q^{4} +(0.309017 + 0.951057i) q^{5} +(2.48141 + 1.80285i) q^{7} +(-0.661536 + 0.480634i) q^{8} +O(q^{10})\) \(q+(0.647481 - 1.99274i) q^{2} +(-1.93376 - 1.40496i) q^{4} +(0.309017 + 0.951057i) q^{5} +(2.48141 + 1.80285i) q^{7} +(-0.661536 + 0.480634i) q^{8} +2.09529 q^{10} +(-1.86337 - 2.74369i) q^{11} +(0.942444 - 2.90055i) q^{13} +(5.19927 - 3.77749i) q^{14} +(-0.947813 - 2.91707i) q^{16} +(0.143336 + 0.441143i) q^{17} +(6.38769 - 4.64093i) q^{19} +(0.738630 - 2.27327i) q^{20} +(-6.67397 + 1.93673i) q^{22} +1.39026 q^{23} +(-0.809017 + 0.587785i) q^{25} +(-5.16983 - 3.75610i) q^{26} +(-2.26552 - 6.97254i) q^{28} +(3.01085 + 2.18751i) q^{29} +(-3.23741 + 9.96371i) q^{31} -8.06206 q^{32} +0.971892 q^{34} +(-0.947813 + 2.91707i) q^{35} +(-1.49226 - 1.08419i) q^{37} +(-5.11227 - 15.7340i) q^{38} +(-0.661536 - 0.480634i) q^{40} +(-3.56585 + 2.59074i) q^{41} -1.31478 q^{43} +(-0.251461 + 7.92360i) q^{44} +(0.900166 - 2.77042i) q^{46} +(-2.41102 + 1.75171i) q^{47} +(0.743998 + 2.28979i) q^{49} +(0.647481 + 1.99274i) q^{50} +(-5.89760 + 4.28486i) q^{52} +(-1.29421 + 3.98316i) q^{53} +(2.03359 - 2.62002i) q^{55} -2.50805 q^{56} +(6.30862 - 4.58348i) q^{58} +(2.27740 + 1.65463i) q^{59} +(-0.623402 - 1.91863i) q^{61} +(17.7590 + 12.9026i) q^{62} +(-3.32441 + 10.2315i) q^{64} +3.04981 q^{65} -6.75753 q^{67} +(0.342610 - 1.05444i) q^{68} +(5.19927 + 3.77749i) q^{70} +(2.01539 + 6.20274i) q^{71} +(7.98970 + 5.80485i) q^{73} +(-3.12672 + 2.27169i) q^{74} -18.8726 q^{76} +(0.322676 - 10.1676i) q^{77} +(-3.57158 + 10.9922i) q^{79} +(2.48141 - 1.80285i) q^{80} +(2.85386 + 8.78327i) q^{82} +(-2.75600 - 8.48210i) q^{83} +(-0.375259 + 0.272641i) q^{85} +(-0.851296 + 2.62002i) q^{86} +(2.55140 + 0.919451i) q^{88} +6.76978 q^{89} +(7.56782 - 5.49835i) q^{91} +(-2.68842 - 1.95325i) q^{92} +(1.92961 + 5.93874i) q^{94} +(6.38769 + 4.64093i) q^{95} +(4.74475 - 14.6029i) q^{97} +5.04469 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - q^{7} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - q^{7} - 4 q^{8} + 2 q^{10} - 3 q^{11} - 2 q^{13} + 16 q^{14} + 4 q^{16} + 13 q^{17} + 15 q^{19} + 3 q^{20} - 7 q^{22} - 10 q^{23} - 2 q^{25} - 10 q^{26} - 6 q^{28} + 9 q^{29} - 10 q^{31} - 16 q^{32} + 4 q^{34} + 4 q^{35} + 24 q^{37} - 4 q^{40} - 8 q^{41} - 38 q^{43} + 12 q^{44} + 3 q^{46} + q^{49} + 2 q^{50} - 28 q^{52} - 13 q^{53} + 7 q^{55} - 22 q^{56} + 12 q^{58} + 27 q^{59} + 6 q^{61} + 30 q^{62} - 26 q^{64} - 2 q^{65} - 38 q^{67} - 11 q^{68} + 16 q^{70} + 20 q^{71} + 13 q^{73} - 20 q^{74} - 34 q^{77} + 37 q^{79} - q^{80} + 28 q^{82} - 27 q^{83} - 12 q^{85} + 3 q^{86} - 36 q^{88} + 16 q^{89} + 44 q^{91} - 11 q^{92} + 17 q^{94} + 15 q^{95} + 24 q^{97} - 16 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/495\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(397\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.647481 1.99274i 0.457839 1.40908i −0.409932 0.912116i \(-0.634447\pi\)
0.867770 0.496966i \(-0.165553\pi\)
\(3\) 0 0
\(4\) −1.93376 1.40496i −0.966879 0.702479i
\(5\) 0.309017 + 0.951057i 0.138197 + 0.425325i
\(6\) 0 0
\(7\) 2.48141 + 1.80285i 0.937883 + 0.681412i 0.947910 0.318538i \(-0.103192\pi\)
−0.0100271 + 0.999950i \(0.503192\pi\)
\(8\) −0.661536 + 0.480634i −0.233888 + 0.169930i
\(9\) 0 0
\(10\) 2.09529 0.662590
\(11\) −1.86337 2.74369i −0.561828 0.827254i
\(12\) 0 0
\(13\) 0.942444 2.90055i 0.261387 0.804467i −0.731117 0.682252i \(-0.761001\pi\)
0.992504 0.122214i \(-0.0389995\pi\)
\(14\) 5.19927 3.77749i 1.38956 1.00958i
\(15\) 0 0
\(16\) −0.947813 2.91707i −0.236953 0.729267i
\(17\) 0.143336 + 0.441143i 0.0347641 + 0.106993i 0.966933 0.255031i \(-0.0820858\pi\)
−0.932169 + 0.362024i \(0.882086\pi\)
\(18\) 0 0
\(19\) 6.38769 4.64093i 1.46544 1.06470i 0.483533 0.875326i \(-0.339353\pi\)
0.981904 0.189377i \(-0.0606468\pi\)
\(20\) 0.738630 2.27327i 0.165163 0.508318i
\(21\) 0 0
\(22\) −6.67397 + 1.93673i −1.42290 + 0.412912i
\(23\) 1.39026 0.289889 0.144944 0.989440i \(-0.453700\pi\)
0.144944 + 0.989440i \(0.453700\pi\)
\(24\) 0 0
\(25\) −0.809017 + 0.587785i −0.161803 + 0.117557i
\(26\) −5.16983 3.75610i −1.01389 0.736632i
\(27\) 0 0
\(28\) −2.26552 6.97254i −0.428142 1.31769i
\(29\) 3.01085 + 2.18751i 0.559101 + 0.406211i 0.831130 0.556078i \(-0.187695\pi\)
−0.272029 + 0.962289i \(0.587695\pi\)
\(30\) 0 0
\(31\) −3.23741 + 9.96371i −0.581456 + 1.78954i 0.0316054 + 0.999500i \(0.489938\pi\)
−0.613061 + 0.790036i \(0.710062\pi\)
\(32\) −8.06206 −1.42518
\(33\) 0 0
\(34\) 0.971892 0.166678
\(35\) −0.947813 + 2.91707i −0.160210 + 0.493074i
\(36\) 0 0
\(37\) −1.49226 1.08419i −0.245326 0.178240i 0.458327 0.888784i \(-0.348449\pi\)
−0.703653 + 0.710544i \(0.748449\pi\)
\(38\) −5.11227 15.7340i −0.829320 2.55238i
\(39\) 0 0
\(40\) −0.661536 0.480634i −0.104598 0.0759949i
\(41\) −3.56585 + 2.59074i −0.556892 + 0.404605i −0.830320 0.557287i \(-0.811842\pi\)
0.273428 + 0.961892i \(0.411842\pi\)
\(42\) 0 0
\(43\) −1.31478 −0.200502 −0.100251 0.994962i \(-0.531965\pi\)
−0.100251 + 0.994962i \(0.531965\pi\)
\(44\) −0.251461 + 7.92360i −0.0379092 + 1.19453i
\(45\) 0 0
\(46\) 0.900166 2.77042i 0.132722 0.408477i
\(47\) −2.41102 + 1.75171i −0.351683 + 0.255513i −0.749575 0.661920i \(-0.769742\pi\)
0.397892 + 0.917432i \(0.369742\pi\)
\(48\) 0 0
\(49\) 0.743998 + 2.28979i 0.106285 + 0.327113i
\(50\) 0.647481 + 1.99274i 0.0915677 + 0.281816i
\(51\) 0 0
\(52\) −5.89760 + 4.28486i −0.817850 + 0.594203i
\(53\) −1.29421 + 3.98316i −0.177773 + 0.547129i −0.999749 0.0223927i \(-0.992872\pi\)
0.821976 + 0.569522i \(0.192872\pi\)
\(54\) 0 0
\(55\) 2.03359 2.62002i 0.274210 0.353283i
\(56\) −2.50805 −0.335152
\(57\) 0 0
\(58\) 6.30862 4.58348i 0.828363 0.601841i
\(59\) 2.27740 + 1.65463i 0.296493 + 0.215414i 0.726079 0.687611i \(-0.241341\pi\)
−0.429586 + 0.903026i \(0.641341\pi\)
\(60\) 0 0
\(61\) −0.623402 1.91863i −0.0798185 0.245656i 0.903182 0.429257i \(-0.141225\pi\)
−0.983001 + 0.183601i \(0.941225\pi\)
\(62\) 17.7590 + 12.9026i 2.25539 + 1.63864i
\(63\) 0 0
\(64\) −3.32441 + 10.2315i −0.415551 + 1.27894i
\(65\) 3.04981 0.378283
\(66\) 0 0
\(67\) −6.75753 −0.825564 −0.412782 0.910830i \(-0.635443\pi\)
−0.412782 + 0.910830i \(0.635443\pi\)
\(68\) 0.342610 1.05444i 0.0415476 0.127870i
\(69\) 0 0
\(70\) 5.19927 + 3.77749i 0.621432 + 0.451497i
\(71\) 2.01539 + 6.20274i 0.239183 + 0.736130i 0.996539 + 0.0831276i \(0.0264909\pi\)
−0.757356 + 0.653003i \(0.773509\pi\)
\(72\) 0 0
\(73\) 7.98970 + 5.80485i 0.935123 + 0.679407i 0.947242 0.320520i \(-0.103858\pi\)
−0.0121186 + 0.999927i \(0.503858\pi\)
\(74\) −3.12672 + 2.27169i −0.363474 + 0.264079i
\(75\) 0 0
\(76\) −18.8726 −2.16483
\(77\) 0.322676 10.1676i 0.0367723 1.15870i
\(78\) 0 0
\(79\) −3.57158 + 10.9922i −0.401834 + 1.23672i 0.521677 + 0.853143i \(0.325307\pi\)
−0.923510 + 0.383573i \(0.874693\pi\)
\(80\) 2.48141 1.80285i 0.277430 0.201564i
\(81\) 0 0
\(82\) 2.85386 + 8.78327i 0.315156 + 0.969950i
\(83\) −2.75600 8.48210i −0.302510 0.931032i −0.980594 0.196047i \(-0.937189\pi\)
0.678084 0.734984i \(-0.262811\pi\)
\(84\) 0 0
\(85\) −0.375259 + 0.272641i −0.0407025 + 0.0295721i
\(86\) −0.851296 + 2.62002i −0.0917976 + 0.282524i
\(87\) 0 0
\(88\) 2.55140 + 0.919451i 0.271980 + 0.0980138i
\(89\) 6.76978 0.717595 0.358797 0.933415i \(-0.383187\pi\)
0.358797 + 0.933415i \(0.383187\pi\)
\(90\) 0 0
\(91\) 7.56782 5.49835i 0.793324 0.576383i
\(92\) −2.68842 1.95325i −0.280287 0.203641i
\(93\) 0 0
\(94\) 1.92961 + 5.93874i 0.199024 + 0.612534i
\(95\) 6.38769 + 4.64093i 0.655364 + 0.476150i
\(96\) 0 0
\(97\) 4.74475 14.6029i 0.481757 1.48269i −0.354867 0.934917i \(-0.615474\pi\)
0.836624 0.547778i \(-0.184526\pi\)
\(98\) 5.04469 0.509591
\(99\) 0 0
\(100\) 2.39026 0.239026
\(101\) −3.62557 + 11.1584i −0.360758 + 1.11030i 0.591838 + 0.806057i \(0.298403\pi\)
−0.952595 + 0.304241i \(0.901597\pi\)
\(102\) 0 0
\(103\) −11.2357 8.16319i −1.10708 0.804343i −0.124882 0.992172i \(-0.539855\pi\)
−0.982202 + 0.187828i \(0.939855\pi\)
\(104\) 0.770639 + 2.37178i 0.0755674 + 0.232573i
\(105\) 0 0
\(106\) 7.09944 + 5.15804i 0.689559 + 0.500994i
\(107\) −5.92282 + 4.30318i −0.572580 + 0.416004i −0.836042 0.548666i \(-0.815136\pi\)
0.263461 + 0.964670i \(0.415136\pi\)
\(108\) 0 0
\(109\) −7.43306 −0.711958 −0.355979 0.934494i \(-0.615853\pi\)
−0.355979 + 0.934494i \(0.615853\pi\)
\(110\) −3.90431 5.74884i −0.372261 0.548131i
\(111\) 0 0
\(112\) 2.90712 8.94719i 0.274697 0.845430i
\(113\) −2.45650 + 1.78475i −0.231088 + 0.167895i −0.697304 0.716776i \(-0.745617\pi\)
0.466216 + 0.884671i \(0.345617\pi\)
\(114\) 0 0
\(115\) 0.429613 + 1.32221i 0.0400616 + 0.123297i
\(116\) −2.74890 8.46024i −0.255229 0.785514i
\(117\) 0 0
\(118\) 4.77183 3.46694i 0.439282 0.319157i
\(119\) −0.439638 + 1.35307i −0.0403016 + 0.124035i
\(120\) 0 0
\(121\) −4.05569 + 10.2250i −0.368699 + 0.929549i
\(122\) −4.22699 −0.382693
\(123\) 0 0
\(124\) 20.2590 14.7190i 1.81931 1.32181i
\(125\) −0.809017 0.587785i −0.0723607 0.0525731i
\(126\) 0 0
\(127\) −0.139551 0.429495i −0.0123832 0.0381115i 0.944674 0.328011i \(-0.106378\pi\)
−0.957057 + 0.289899i \(0.906378\pi\)
\(128\) 5.19153 + 3.77187i 0.458871 + 0.333389i
\(129\) 0 0
\(130\) 1.97470 6.07750i 0.173192 0.533032i
\(131\) −0.629003 −0.0549563 −0.0274781 0.999622i \(-0.508748\pi\)
−0.0274781 + 0.999622i \(0.508748\pi\)
\(132\) 0 0
\(133\) 24.2173 2.09991
\(134\) −4.37538 + 13.4660i −0.377975 + 1.16329i
\(135\) 0 0
\(136\) −0.306850 0.222940i −0.0263122 0.0191169i
\(137\) −3.45586 10.6360i −0.295254 0.908698i −0.983136 0.182876i \(-0.941459\pi\)
0.687882 0.725823i \(-0.258541\pi\)
\(138\) 0 0
\(139\) 1.92138 + 1.39596i 0.162969 + 0.118404i 0.666281 0.745701i \(-0.267885\pi\)
−0.503312 + 0.864105i \(0.667885\pi\)
\(140\) 5.93120 4.30927i 0.501278 0.364199i
\(141\) 0 0
\(142\) 13.6654 1.14678
\(143\) −9.71433 + 2.81902i −0.812353 + 0.235738i
\(144\) 0 0
\(145\) −1.15004 + 3.53947i −0.0955059 + 0.293937i
\(146\) 16.7408 12.1629i 1.38548 1.00661i
\(147\) 0 0
\(148\) 1.36243 + 4.19312i 0.111991 + 0.344672i
\(149\) 2.69473 + 8.29354i 0.220761 + 0.679433i 0.998694 + 0.0510859i \(0.0162682\pi\)
−0.777933 + 0.628347i \(0.783732\pi\)
\(150\) 0 0
\(151\) −9.65596 + 7.01547i −0.785791 + 0.570911i −0.906711 0.421752i \(-0.861415\pi\)
0.120920 + 0.992662i \(0.461415\pi\)
\(152\) −1.99510 + 6.14028i −0.161824 + 0.498043i
\(153\) 0 0
\(154\) −20.0525 7.22633i −1.61587 0.582315i
\(155\) −10.4765 −0.841490
\(156\) 0 0
\(157\) −3.13520 + 2.27786i −0.250216 + 0.181793i −0.705823 0.708389i \(-0.749422\pi\)
0.455606 + 0.890181i \(0.349422\pi\)
\(158\) 19.5921 + 14.2345i 1.55866 + 1.13243i
\(159\) 0 0
\(160\) −2.49131 7.66748i −0.196956 0.606167i
\(161\) 3.44979 + 2.50642i 0.271882 + 0.197534i
\(162\) 0 0
\(163\) −3.07046 + 9.44990i −0.240497 + 0.740173i 0.755848 + 0.654748i \(0.227225\pi\)
−0.996345 + 0.0854258i \(0.972775\pi\)
\(164\) 10.5354 0.822674
\(165\) 0 0
\(166\) −18.6871 −1.45040
\(167\) −4.30152 + 13.2387i −0.332862 + 1.02444i 0.634904 + 0.772591i \(0.281040\pi\)
−0.967766 + 0.251852i \(0.918960\pi\)
\(168\) 0 0
\(169\) 2.99226 + 2.17400i 0.230174 + 0.167231i
\(170\) 0.300331 + 0.924324i 0.0230343 + 0.0708924i
\(171\) 0 0
\(172\) 2.54247 + 1.84721i 0.193861 + 0.140848i
\(173\) 8.76256 6.36637i 0.666205 0.484026i −0.202548 0.979272i \(-0.564922\pi\)
0.868753 + 0.495246i \(0.164922\pi\)
\(174\) 0 0
\(175\) −3.06719 −0.231857
\(176\) −6.23741 + 8.03609i −0.470162 + 0.605743i
\(177\) 0 0
\(178\) 4.38331 13.4904i 0.328543 1.01115i
\(179\) 18.3918 13.3624i 1.37466 0.998752i 0.377307 0.926088i \(-0.376850\pi\)
0.997356 0.0726638i \(-0.0231500\pi\)
\(180\) 0 0
\(181\) 0.741120 + 2.28093i 0.0550870 + 0.169540i 0.974815 0.223017i \(-0.0715905\pi\)
−0.919728 + 0.392557i \(0.871590\pi\)
\(182\) −6.05677 18.6408i −0.448957 1.38175i
\(183\) 0 0
\(184\) −0.919704 + 0.668204i −0.0678015 + 0.0492607i
\(185\) 0.569992 1.75425i 0.0419066 0.128975i
\(186\) 0 0
\(187\) 0.943272 1.21528i 0.0689789 0.0888703i
\(188\) 7.12340 0.519527
\(189\) 0 0
\(190\) 13.3841 9.72412i 0.970985 0.705462i
\(191\) 13.9525 + 10.1371i 1.00957 + 0.733494i 0.964118 0.265473i \(-0.0855280\pi\)
0.0454496 + 0.998967i \(0.485528\pi\)
\(192\) 0 0
\(193\) −0.799036 2.45918i −0.0575159 0.177016i 0.918171 0.396184i \(-0.129666\pi\)
−0.975687 + 0.219168i \(0.929666\pi\)
\(194\) −26.0276 18.9102i −1.86867 1.35767i
\(195\) 0 0
\(196\) 1.77835 5.47319i 0.127025 0.390942i
\(197\) −0.144731 −0.0103116 −0.00515582 0.999987i \(-0.501641\pi\)
−0.00515582 + 0.999987i \(0.501641\pi\)
\(198\) 0 0
\(199\) −7.54177 −0.534622 −0.267311 0.963610i \(-0.586135\pi\)
−0.267311 + 0.963610i \(0.586135\pi\)
\(200\) 0.252684 0.777682i 0.0178675 0.0549904i
\(201\) 0 0
\(202\) 19.8882 + 14.4497i 1.39933 + 1.01667i
\(203\) 3.52740 + 10.8562i 0.247575 + 0.761957i
\(204\) 0 0
\(205\) −3.56585 2.59074i −0.249050 0.180945i
\(206\) −23.5420 + 17.1043i −1.64025 + 1.19171i
\(207\) 0 0
\(208\) −9.35435 −0.648607
\(209\) −24.6359 8.87809i −1.70410 0.614110i
\(210\) 0 0
\(211\) −0.701101 + 2.15777i −0.0482658 + 0.148547i −0.972285 0.233800i \(-0.924884\pi\)
0.924019 + 0.382347i \(0.124884\pi\)
\(212\) 8.09886 5.88416i 0.556232 0.404126i
\(213\) 0 0
\(214\) 4.74021 + 14.5889i 0.324034 + 0.997275i
\(215\) −0.406289 1.25043i −0.0277087 0.0852786i
\(216\) 0 0
\(217\) −25.9964 + 18.8875i −1.76475 + 1.28216i
\(218\) −4.81277 + 14.8122i −0.325962 + 1.00321i
\(219\) 0 0
\(220\) −7.61349 + 2.20937i −0.513302 + 0.148956i
\(221\) 1.41464 0.0951591
\(222\) 0 0
\(223\) −6.94111 + 5.04301i −0.464811 + 0.337705i −0.795415 0.606065i \(-0.792747\pi\)
0.330605 + 0.943769i \(0.392747\pi\)
\(224\) −20.0052 14.5347i −1.33666 0.971138i
\(225\) 0 0
\(226\) 1.96601 + 6.05076i 0.130777 + 0.402491i
\(227\) 5.01622 + 3.64450i 0.332938 + 0.241894i 0.741676 0.670758i \(-0.234031\pi\)
−0.408738 + 0.912652i \(0.634031\pi\)
\(228\) 0 0
\(229\) 7.15865 22.0321i 0.473057 1.45592i −0.375503 0.926821i \(-0.622530\pi\)
0.848560 0.529099i \(-0.177470\pi\)
\(230\) 2.91300 0.192077
\(231\) 0 0
\(232\) −3.04318 −0.199794
\(233\) 8.61005 26.4990i 0.564063 1.73601i −0.106656 0.994296i \(-0.534014\pi\)
0.670719 0.741711i \(-0.265986\pi\)
\(234\) 0 0
\(235\) −2.41102 1.75171i −0.157278 0.114269i
\(236\) −2.07926 6.39931i −0.135348 0.416560i
\(237\) 0 0
\(238\) 2.41166 + 1.75217i 0.156325 + 0.113576i
\(239\) −13.1758 + 9.57280i −0.852274 + 0.619213i −0.925772 0.378082i \(-0.876584\pi\)
0.0734982 + 0.997295i \(0.476584\pi\)
\(240\) 0 0
\(241\) 4.39063 0.282826 0.141413 0.989951i \(-0.454836\pi\)
0.141413 + 0.989951i \(0.454836\pi\)
\(242\) 17.7499 + 14.7025i 1.14101 + 0.945111i
\(243\) 0 0
\(244\) −1.49009 + 4.58603i −0.0953933 + 0.293590i
\(245\) −1.94781 + 1.41517i −0.124441 + 0.0904118i
\(246\) 0 0
\(247\) −7.44119 22.9016i −0.473471 1.45720i
\(248\) −2.64724 8.14736i −0.168100 0.517358i
\(249\) 0 0
\(250\) −1.69513 + 1.23158i −0.107209 + 0.0778921i
\(251\) 0.824050 2.53616i 0.0520136 0.160081i −0.921676 0.387961i \(-0.873179\pi\)
0.973689 + 0.227880i \(0.0731794\pi\)
\(252\) 0 0
\(253\) −2.59056 3.81444i −0.162867 0.239812i
\(254\) −0.946229 −0.0593717
\(255\) 0 0
\(256\) −6.52905 + 4.74363i −0.408066 + 0.296477i
\(257\) −17.5012 12.7154i −1.09169 0.793162i −0.112010 0.993707i \(-0.535729\pi\)
−0.979685 + 0.200545i \(0.935729\pi\)
\(258\) 0 0
\(259\) −1.74827 5.38063i −0.108632 0.334336i
\(260\) −5.89760 4.28486i −0.365754 0.265736i
\(261\) 0 0
\(262\) −0.407268 + 1.25344i −0.0251611 + 0.0774379i
\(263\) −22.1392 −1.36516 −0.682581 0.730810i \(-0.739142\pi\)
−0.682581 + 0.730810i \(0.739142\pi\)
\(264\) 0 0
\(265\) −4.18814 −0.257276
\(266\) 15.6803 48.2590i 0.961420 2.95895i
\(267\) 0 0
\(268\) 13.0674 + 9.49404i 0.798220 + 0.579941i
\(269\) −6.40233 19.7044i −0.390357 1.20140i −0.932519 0.361121i \(-0.882394\pi\)
0.542162 0.840274i \(-0.317606\pi\)
\(270\) 0 0
\(271\) 0.342305 + 0.248699i 0.0207935 + 0.0151074i 0.598133 0.801396i \(-0.295909\pi\)
−0.577340 + 0.816504i \(0.695909\pi\)
\(272\) 1.15099 0.836242i 0.0697889 0.0507046i
\(273\) 0 0
\(274\) −23.4325 −1.41561
\(275\) 3.12020 + 1.12443i 0.188155 + 0.0678058i
\(276\) 0 0
\(277\) −2.64906 + 8.15298i −0.159167 + 0.489865i −0.998559 0.0536607i \(-0.982911\pi\)
0.839392 + 0.543526i \(0.182911\pi\)
\(278\) 4.02585 2.92495i 0.241455 0.175427i
\(279\) 0 0
\(280\) −0.775029 2.38529i −0.0463168 0.142549i
\(281\) 2.16654 + 6.66793i 0.129245 + 0.397776i 0.994651 0.103297i \(-0.0329391\pi\)
−0.865405 + 0.501072i \(0.832939\pi\)
\(282\) 0 0
\(283\) −8.05229 + 5.85033i −0.478659 + 0.347766i −0.800806 0.598924i \(-0.795595\pi\)
0.322147 + 0.946690i \(0.395595\pi\)
\(284\) 4.81731 14.8261i 0.285855 0.879770i
\(285\) 0 0
\(286\) −0.672272 + 21.1834i −0.0397523 + 1.25260i
\(287\) −13.5190 −0.798002
\(288\) 0 0
\(289\) 13.5792 9.86589i 0.798778 0.580346i
\(290\) 6.30862 + 4.58348i 0.370455 + 0.269151i
\(291\) 0 0
\(292\) −7.29457 22.4504i −0.426882 1.31381i
\(293\) 17.6535 + 12.8260i 1.03133 + 0.749302i 0.968574 0.248727i \(-0.0800122\pi\)
0.0627522 + 0.998029i \(0.480012\pi\)
\(294\) 0 0
\(295\) −0.869890 + 2.67725i −0.0506470 + 0.155875i
\(296\) 1.50828 0.0876670
\(297\) 0 0
\(298\) 18.2717 1.05845
\(299\) 1.31024 4.03250i 0.0757731 0.233206i
\(300\) 0 0
\(301\) −3.26250 2.37035i −0.188048 0.136625i
\(302\) 7.72797 + 23.7842i 0.444694 + 1.36863i
\(303\) 0 0
\(304\) −19.5922 14.2346i −1.12369 0.816410i
\(305\) 1.63209 1.18578i 0.0934531 0.0678976i
\(306\) 0 0
\(307\) −30.8674 −1.76170 −0.880849 0.473397i \(-0.843028\pi\)
−0.880849 + 0.473397i \(0.843028\pi\)
\(308\) −14.9090 + 19.2083i −0.849519 + 1.09449i
\(309\) 0 0
\(310\) −6.78332 + 20.8769i −0.385267 + 1.18573i
\(311\) −15.7071 + 11.4119i −0.890667 + 0.647107i −0.936052 0.351862i \(-0.885549\pi\)
0.0453850 + 0.998970i \(0.485549\pi\)
\(312\) 0 0
\(313\) 0.324922 + 1.00001i 0.0183657 + 0.0565237i 0.959819 0.280619i \(-0.0905396\pi\)
−0.941454 + 0.337142i \(0.890540\pi\)
\(314\) 2.50920 + 7.72252i 0.141602 + 0.435807i
\(315\) 0 0
\(316\) 22.3501 16.2383i 1.25729 0.913476i
\(317\) 7.36432 22.6650i 0.413621 1.27300i −0.499857 0.866108i \(-0.666614\pi\)
0.913478 0.406887i \(-0.133386\pi\)
\(318\) 0 0
\(319\) 0.391524 12.3370i 0.0219211 0.690740i
\(320\) −10.7580 −0.601391
\(321\) 0 0
\(322\) 7.22833 5.25169i 0.402819 0.292665i
\(323\) 2.96290 + 2.15267i 0.164860 + 0.119778i
\(324\) 0 0
\(325\) 0.942444 + 2.90055i 0.0522774 + 0.160893i
\(326\) 16.8432 + 12.2373i 0.932856 + 0.677760i
\(327\) 0 0
\(328\) 1.11374 3.42773i 0.0614959 0.189265i
\(329\) −9.14077 −0.503947
\(330\) 0 0
\(331\) 25.6693 1.41091 0.705457 0.708753i \(-0.250742\pi\)
0.705457 + 0.708753i \(0.250742\pi\)
\(332\) −6.58755 + 20.2744i −0.361539 + 1.11270i
\(333\) 0 0
\(334\) 23.5962 + 17.1436i 1.29113 + 0.938059i
\(335\) −2.08819 6.42679i −0.114090 0.351133i
\(336\) 0 0
\(337\) 19.3292 + 14.0435i 1.05293 + 0.764996i 0.972767 0.231786i \(-0.0744570\pi\)
0.0801597 + 0.996782i \(0.474457\pi\)
\(338\) 6.26966 4.55518i 0.341025 0.247769i
\(339\) 0 0
\(340\) 1.10871 0.0601282
\(341\) 33.3699 9.68365i 1.80708 0.524399i
\(342\) 0 0
\(343\) 4.35271 13.3963i 0.235024 0.723330i
\(344\) 0.869774 0.631928i 0.0468951 0.0340713i
\(345\) 0 0
\(346\) −7.01295 21.5836i −0.377018 1.16034i
\(347\) 0.102641 + 0.315895i 0.00551004 + 0.0169582i 0.953774 0.300526i \(-0.0971621\pi\)
−0.948264 + 0.317484i \(0.897162\pi\)
\(348\) 0 0
\(349\) −0.988203 + 0.717971i −0.0528973 + 0.0384321i −0.613920 0.789368i \(-0.710408\pi\)
0.561022 + 0.827801i \(0.310408\pi\)
\(350\) −1.98595 + 6.11211i −0.106153 + 0.326706i
\(351\) 0 0
\(352\) 15.0226 + 22.1198i 0.800708 + 1.17899i
\(353\) 25.7038 1.36808 0.684039 0.729446i \(-0.260222\pi\)
0.684039 + 0.729446i \(0.260222\pi\)
\(354\) 0 0
\(355\) −5.27637 + 3.83351i −0.280041 + 0.203461i
\(356\) −13.0911 9.51125i −0.693828 0.504095i
\(357\) 0 0
\(358\) −14.7195 45.3019i −0.777949 2.39428i
\(359\) −14.5069 10.5399i −0.765643 0.556272i 0.134993 0.990847i \(-0.456899\pi\)
−0.900636 + 0.434574i \(0.856899\pi\)
\(360\) 0 0
\(361\) 13.3931 41.2196i 0.704899 2.16945i
\(362\) 5.02517 0.264117
\(363\) 0 0
\(364\) −22.3593 −1.17195
\(365\) −3.05179 + 9.39245i −0.159738 + 0.491623i
\(366\) 0 0
\(367\) 6.86929 + 4.99083i 0.358574 + 0.260519i 0.752457 0.658641i \(-0.228869\pi\)
−0.393883 + 0.919161i \(0.628869\pi\)
\(368\) −1.31770 4.05547i −0.0686900 0.211406i
\(369\) 0 0
\(370\) −3.12672 2.27169i −0.162550 0.118100i
\(371\) −10.3925 + 7.55058i −0.539551 + 0.392006i
\(372\) 0 0
\(373\) 35.8450 1.85598 0.927991 0.372604i \(-0.121535\pi\)
0.927991 + 0.372604i \(0.121535\pi\)
\(374\) −1.81100 2.66657i −0.0936443 0.137885i
\(375\) 0 0
\(376\) 0.753045 2.31763i 0.0388353 0.119523i
\(377\) 9.18254 6.67151i 0.472925 0.343600i
\(378\) 0 0
\(379\) 5.42373 + 16.6925i 0.278598 + 0.857438i 0.988245 + 0.152880i \(0.0488547\pi\)
−0.709646 + 0.704558i \(0.751145\pi\)
\(380\) −5.83195 17.9489i −0.299172 0.920758i
\(381\) 0 0
\(382\) 29.2346 21.2402i 1.49577 1.08674i
\(383\) 6.68251 20.5666i 0.341460 1.05091i −0.621991 0.783024i \(-0.713676\pi\)
0.963452 0.267882i \(-0.0863238\pi\)
\(384\) 0 0
\(385\) 9.76966 2.83507i 0.497908 0.144489i
\(386\) −5.41788 −0.275763
\(387\) 0 0
\(388\) −29.6916 + 21.5722i −1.50736 + 1.09516i
\(389\) 28.9156 + 21.0084i 1.46608 + 1.06517i 0.981727 + 0.190295i \(0.0609444\pi\)
0.484352 + 0.874873i \(0.339056\pi\)
\(390\) 0 0
\(391\) 0.199274 + 0.613302i 0.0100777 + 0.0310160i
\(392\) −1.59273 1.15719i −0.0804451 0.0584468i
\(393\) 0 0
\(394\) −0.0937106 + 0.288411i −0.00472107 + 0.0145300i
\(395\) −11.5579 −0.581539
\(396\) 0 0
\(397\) −20.0447 −1.00601 −0.503007 0.864282i \(-0.667773\pi\)
−0.503007 + 0.864282i \(0.667773\pi\)
\(398\) −4.88315 + 15.0288i −0.244770 + 0.753326i
\(399\) 0 0
\(400\) 2.48141 + 1.80285i 0.124070 + 0.0901423i
\(401\) 6.45805 + 19.8758i 0.322500 + 0.992551i 0.972557 + 0.232666i \(0.0747449\pi\)
−0.650057 + 0.759885i \(0.725255\pi\)
\(402\) 0 0
\(403\) 25.8491 + 18.7805i 1.28764 + 0.935523i
\(404\) 22.6880 16.4838i 1.12877 0.820099i
\(405\) 0 0
\(406\) 23.9176 1.18701
\(407\) −0.194050 + 6.11454i −0.00961869 + 0.303087i
\(408\) 0 0
\(409\) 7.26134 22.3481i 0.359050 1.10504i −0.594574 0.804041i \(-0.702679\pi\)
0.953624 0.301001i \(-0.0973208\pi\)
\(410\) −7.47150 + 5.42836i −0.368991 + 0.268088i
\(411\) 0 0
\(412\) 10.2581 + 31.5713i 0.505382 + 1.55541i
\(413\) 2.66812 + 8.21161i 0.131289 + 0.404067i
\(414\) 0 0
\(415\) 7.21531 5.24223i 0.354185 0.257331i
\(416\) −7.59804 + 23.3844i −0.372525 + 1.14651i
\(417\) 0 0
\(418\) −33.6431 + 43.3447i −1.64554 + 2.12006i
\(419\) 10.1128 0.494043 0.247022 0.969010i \(-0.420548\pi\)
0.247022 + 0.969010i \(0.420548\pi\)
\(420\) 0 0
\(421\) −7.21872 + 5.24471i −0.351819 + 0.255611i −0.749632 0.661855i \(-0.769769\pi\)
0.397813 + 0.917467i \(0.369769\pi\)
\(422\) 3.84593 + 2.79423i 0.187217 + 0.136021i
\(423\) 0 0
\(424\) −1.05828 3.25704i −0.0513945 0.158176i
\(425\) −0.375259 0.272641i −0.0182027 0.0132250i
\(426\) 0 0
\(427\) 1.91209 5.88481i 0.0925325 0.284786i
\(428\) 17.4991 0.845850
\(429\) 0 0
\(430\) −2.75485 −0.132851
\(431\) 5.44248 16.7502i 0.262155 0.806831i −0.730180 0.683255i \(-0.760564\pi\)
0.992335 0.123576i \(-0.0394362\pi\)
\(432\) 0 0
\(433\) −7.39763 5.37469i −0.355507 0.258291i 0.395668 0.918393i \(-0.370513\pi\)
−0.751176 + 0.660102i \(0.770513\pi\)
\(434\) 20.8057 + 64.0334i 0.998706 + 3.07370i
\(435\) 0 0
\(436\) 14.3737 + 10.4431i 0.688377 + 0.500135i
\(437\) 8.88054 6.45209i 0.424814 0.308645i
\(438\) 0 0
\(439\) 6.46946 0.308770 0.154385 0.988011i \(-0.450660\pi\)
0.154385 + 0.988011i \(0.450660\pi\)
\(440\) −0.0860245 + 2.71065i −0.00410106 + 0.129225i
\(441\) 0 0
\(442\) 0.915954 2.81902i 0.0435675 0.134087i
\(443\) −33.0760 + 24.0311i −1.57149 + 1.14175i −0.645774 + 0.763529i \(0.723465\pi\)
−0.925714 + 0.378224i \(0.876535\pi\)
\(444\) 0 0
\(445\) 2.09198 + 6.43844i 0.0991692 + 0.305211i
\(446\) 5.55518 + 17.0971i 0.263045 + 0.809571i
\(447\) 0 0
\(448\) −26.6950 + 19.3951i −1.26122 + 0.916330i
\(449\) 3.75788 11.5656i 0.177345 0.545813i −0.822387 0.568928i \(-0.807358\pi\)
0.999733 + 0.0231150i \(0.00735838\pi\)
\(450\) 0 0
\(451\) 13.7527 + 4.95608i 0.647589 + 0.233373i
\(452\) 7.25777 0.341377
\(453\) 0 0
\(454\) 10.5105 7.63629i 0.493280 0.358389i
\(455\) 7.56782 + 5.49835i 0.354785 + 0.257766i
\(456\) 0 0
\(457\) −3.06001 9.41775i −0.143141 0.440544i 0.853626 0.520886i \(-0.174398\pi\)
−0.996767 + 0.0803428i \(0.974398\pi\)
\(458\) −39.2691 28.5307i −1.83493 1.33315i
\(459\) 0 0
\(460\) 1.02689 3.16043i 0.0478788 0.147356i
\(461\) 3.12529 0.145559 0.0727796 0.997348i \(-0.476813\pi\)
0.0727796 + 0.997348i \(0.476813\pi\)
\(462\) 0 0
\(463\) −24.3518 −1.13173 −0.565863 0.824499i \(-0.691457\pi\)
−0.565863 + 0.824499i \(0.691457\pi\)
\(464\) 3.52740 10.8562i 0.163755 0.503987i
\(465\) 0 0
\(466\) −47.2309 34.3152i −2.18793 1.58962i
\(467\) −10.2512 31.5501i −0.474371 1.45996i −0.846805 0.531904i \(-0.821477\pi\)
0.372434 0.928059i \(-0.378523\pi\)
\(468\) 0 0
\(469\) −16.7682 12.1828i −0.774282 0.562549i
\(470\) −5.05179 + 3.67034i −0.233022 + 0.169300i
\(471\) 0 0
\(472\) −2.30185 −0.105951
\(473\) 2.44992 + 3.60735i 0.112648 + 0.165866i
\(474\) 0 0
\(475\) −2.43988 + 7.50919i −0.111949 + 0.344545i
\(476\) 2.75116 1.99883i 0.126099 0.0916163i
\(477\) 0 0
\(478\) 10.5450 + 32.4543i 0.482318 + 1.48442i
\(479\) 5.34529 + 16.4511i 0.244232 + 0.751670i 0.995762 + 0.0919705i \(0.0293165\pi\)
−0.751529 + 0.659700i \(0.770683\pi\)
\(480\) 0 0
\(481\) −4.55111 + 3.30658i −0.207513 + 0.150767i
\(482\) 2.84285 8.74941i 0.129488 0.398524i
\(483\) 0 0
\(484\) 22.2085 14.0747i 1.00948 0.639758i
\(485\) 15.3543 0.697205
\(486\) 0 0
\(487\) −6.18138 + 4.49104i −0.280105 + 0.203508i −0.718963 0.695048i \(-0.755383\pi\)
0.438858 + 0.898556i \(0.355383\pi\)
\(488\) 1.33456 + 0.969617i 0.0604128 + 0.0438925i
\(489\) 0 0
\(490\) 1.55889 + 4.79779i 0.0704237 + 0.216742i
\(491\) −24.8015 18.0193i −1.11928 0.813201i −0.135176 0.990822i \(-0.543160\pi\)
−0.984099 + 0.177620i \(0.943160\pi\)
\(492\) 0 0
\(493\) −0.533442 + 1.64177i −0.0240250 + 0.0739414i
\(494\) −50.4551 −2.27008
\(495\) 0 0
\(496\) 32.1333 1.44283
\(497\) −6.18159 + 19.0250i −0.277282 + 0.853386i
\(498\) 0 0
\(499\) 30.3206 + 22.0292i 1.35734 + 0.986162i 0.998609 + 0.0527188i \(0.0167887\pi\)
0.358726 + 0.933443i \(0.383211\pi\)
\(500\) 0.738630 + 2.27327i 0.0330325 + 0.101664i
\(501\) 0 0
\(502\) −4.52037 3.28424i −0.201754 0.146583i
\(503\) 6.85800 4.98263i 0.305783 0.222164i −0.424302 0.905521i \(-0.639480\pi\)
0.730085 + 0.683356i \(0.239480\pi\)
\(504\) 0 0
\(505\) −11.7326 −0.522093
\(506\) −9.27854 + 2.69255i −0.412481 + 0.119699i
\(507\) 0 0
\(508\) −0.333563 + 1.02660i −0.0147995 + 0.0455481i
\(509\) −1.37309 + 0.997609i −0.0608612 + 0.0442183i −0.617800 0.786335i \(-0.711976\pi\)
0.556939 + 0.830554i \(0.311976\pi\)
\(510\) 0 0
\(511\) 9.36041 + 28.8084i 0.414080 + 1.27441i
\(512\) 9.19138 + 28.2882i 0.406206 + 1.25017i
\(513\) 0 0
\(514\) −36.6701 + 26.6424i −1.61745 + 1.17515i
\(515\) 4.29165 13.2083i 0.189112 0.582028i
\(516\) 0 0
\(517\) 9.29877 + 3.35101i 0.408959 + 0.147377i
\(518\) −11.8542 −0.520843
\(519\) 0 0
\(520\) −2.01756 + 1.46584i −0.0884759 + 0.0642815i
\(521\) −30.0088 21.8027i −1.31471 0.955192i −0.999982 0.00601047i \(-0.998087\pi\)
−0.314728 0.949182i \(-0.601913\pi\)
\(522\) 0 0
\(523\) −5.58759 17.1968i −0.244328 0.751965i −0.995746 0.0921382i \(-0.970630\pi\)
0.751418 0.659826i \(-0.229370\pi\)
\(524\) 1.21634 + 0.883723i 0.0531361 + 0.0386056i
\(525\) 0 0
\(526\) −14.3347 + 44.1177i −0.625023 + 1.92362i
\(527\) −4.85946 −0.211681
\(528\) 0 0
\(529\) −21.0672 −0.915965
\(530\) −2.71174 + 8.34589i −0.117791 + 0.362522i
\(531\) 0 0
\(532\) −46.8305 34.0244i −2.03036 1.47514i
\(533\) 4.15394 + 12.7845i 0.179927 + 0.553759i
\(534\) 0 0
\(535\) −5.92282 4.30318i −0.256066 0.186043i
\(536\) 4.47035 3.24790i 0.193090 0.140288i
\(537\) 0 0
\(538\) −43.4111 −1.87159
\(539\) 4.89614 6.30803i 0.210892 0.271706i
\(540\) 0 0
\(541\) 3.63169 11.1772i 0.156139 0.480545i −0.842136 0.539265i \(-0.818702\pi\)
0.998274 + 0.0587201i \(0.0187019\pi\)
\(542\) 0.717229 0.521098i 0.0308076 0.0223831i
\(543\) 0 0
\(544\) −1.15558 3.55652i −0.0495452 0.152485i
\(545\) −2.29694 7.06926i −0.0983902 0.302814i
\(546\) 0 0
\(547\) 17.6017 12.7884i 0.752593 0.546791i −0.144037 0.989572i \(-0.546008\pi\)
0.896629 + 0.442782i \(0.146008\pi\)
\(548\) −8.26039 + 25.4229i −0.352866 + 1.08601i
\(549\) 0 0
\(550\) 4.26097 5.48971i 0.181689 0.234082i
\(551\) 29.3845 1.25182
\(552\) 0 0
\(553\) −28.6797 + 20.8370i −1.21959 + 0.886081i
\(554\) 14.5316 + 10.5578i 0.617388 + 0.448558i
\(555\) 0 0
\(556\) −1.75421 5.39891i −0.0743952 0.228965i
\(557\) 3.91104 + 2.84154i 0.165716 + 0.120400i 0.667552 0.744563i \(-0.267342\pi\)
−0.501836 + 0.864963i \(0.667342\pi\)
\(558\) 0 0
\(559\) −1.23911 + 3.81358i −0.0524086 + 0.161297i
\(560\) 9.40763 0.397545
\(561\) 0 0
\(562\) 14.6903 0.619672
\(563\) −1.47463 + 4.53843i −0.0621481 + 0.191272i −0.977310 0.211815i \(-0.932063\pi\)
0.915162 + 0.403087i \(0.132063\pi\)
\(564\) 0 0
\(565\) −2.45650 1.78475i −0.103346 0.0750850i
\(566\) 6.44449 + 19.8341i 0.270882 + 0.833690i
\(567\) 0 0
\(568\) −4.31450 3.13467i −0.181032 0.131528i
\(569\) 28.8971 20.9949i 1.21143 0.880154i 0.216068 0.976378i \(-0.430677\pi\)
0.995360 + 0.0962246i \(0.0306767\pi\)
\(570\) 0 0
\(571\) −33.9838 −1.42218 −0.711090 0.703101i \(-0.751798\pi\)
−0.711090 + 0.703101i \(0.751798\pi\)
\(572\) 22.7458 + 8.19692i 0.951048 + 0.342731i
\(573\) 0 0
\(574\) −8.75331 + 26.9399i −0.365356 + 1.12445i
\(575\) −1.12474 + 0.817172i −0.0469050 + 0.0340784i
\(576\) 0 0
\(577\) −6.38364 19.6468i −0.265755 0.817909i −0.991519 0.129965i \(-0.958514\pi\)
0.725764 0.687944i \(-0.241486\pi\)
\(578\) −10.8679 33.4479i −0.452044 1.39125i
\(579\) 0 0
\(580\) 7.19671 5.22872i 0.298827 0.217111i
\(581\) 8.45317 26.0162i 0.350697 1.07933i
\(582\) 0 0
\(583\) 13.3402 3.87120i 0.552493 0.160329i
\(584\) −8.07548 −0.334166
\(585\) 0 0
\(586\) 36.9892 26.8742i 1.52801 1.11016i
\(587\) 10.8085 + 7.85284i 0.446115 + 0.324121i 0.788060 0.615599i \(-0.211086\pi\)
−0.341945 + 0.939720i \(0.611086\pi\)
\(588\) 0 0
\(589\) 25.5614 + 78.6698i 1.05324 + 3.24153i
\(590\) 4.77183 + 3.46694i 0.196453 + 0.142731i
\(591\) 0 0
\(592\) −1.74827 + 5.38063i −0.0718535 + 0.221142i
\(593\) −20.8062 −0.854410 −0.427205 0.904155i \(-0.640502\pi\)
−0.427205 + 0.904155i \(0.640502\pi\)
\(594\) 0 0
\(595\) −1.42270 −0.0583250
\(596\) 6.44111 19.8237i 0.263838 0.812010i
\(597\) 0 0
\(598\) −7.18739 5.22194i −0.293914 0.213541i
\(599\) 4.40214 + 13.5484i 0.179867 + 0.553573i 0.999822 0.0188544i \(-0.00600189\pi\)
−0.819956 + 0.572427i \(0.806002\pi\)
\(600\) 0 0
\(601\) 16.7840 + 12.1943i 0.684634 + 0.497416i 0.874892 0.484318i \(-0.160932\pi\)
−0.190257 + 0.981734i \(0.560932\pi\)
\(602\) −6.83590 + 4.96657i −0.278611 + 0.202422i
\(603\) 0 0
\(604\) 28.5287 1.16082
\(605\) −10.9779 0.697484i −0.446314 0.0283568i
\(606\) 0 0
\(607\) 5.53818 17.0448i 0.224788 0.691825i −0.773525 0.633765i \(-0.781508\pi\)
0.998313 0.0580601i \(-0.0184915\pi\)
\(608\) −51.4980 + 37.4155i −2.08852 + 1.51740i
\(609\) 0 0
\(610\) −1.30621 4.02010i −0.0528869 0.162769i
\(611\) 2.80866 + 8.64416i 0.113626 + 0.349705i
\(612\) 0 0
\(613\) 22.8158 16.5766i 0.921521 0.669524i −0.0223811 0.999750i \(-0.507125\pi\)
0.943902 + 0.330225i \(0.107125\pi\)
\(614\) −19.9861 + 61.5109i −0.806573 + 2.48238i
\(615\) 0 0
\(616\) 4.67342 + 6.88131i 0.188298 + 0.277256i
\(617\) 4.72930 0.190394 0.0951972 0.995458i \(-0.469652\pi\)
0.0951972 + 0.995458i \(0.469652\pi\)
\(618\) 0 0
\(619\) 24.3170 17.6673i 0.977383 0.710110i 0.0202609 0.999795i \(-0.493550\pi\)
0.957122 + 0.289684i \(0.0935503\pi\)
\(620\) 20.2590 + 14.7190i 0.813619 + 0.591129i
\(621\) 0 0
\(622\) 12.5709 + 38.6891i 0.504046 + 1.55129i
\(623\) 16.7986 + 12.2049i 0.673020 + 0.488978i
\(624\) 0 0
\(625\) 0.309017 0.951057i 0.0123607 0.0380423i
\(626\) 2.20314 0.0880551
\(627\) 0 0
\(628\) 9.26301 0.369634
\(629\) 0.264388 0.813702i 0.0105418 0.0324444i
\(630\) 0 0
\(631\) 25.6487 + 18.6349i 1.02106 + 0.741843i 0.966500 0.256667i \(-0.0826244\pi\)
0.0545601 + 0.998510i \(0.482624\pi\)
\(632\) −2.92049 8.98834i −0.116171 0.357537i
\(633\) 0 0
\(634\) −40.3973 29.3504i −1.60438 1.16565i
\(635\) 0.365350 0.265442i 0.0144985 0.0105338i
\(636\) 0 0
\(637\) 7.34282 0.290933
\(638\) −24.3310 8.76819i −0.963272 0.347136i
\(639\) 0 0
\(640\) −1.98299 + 6.10301i −0.0783845 + 0.241243i
\(641\) −15.3368 + 11.1428i −0.605768 + 0.440116i −0.847921 0.530122i \(-0.822146\pi\)
0.242154 + 0.970238i \(0.422146\pi\)
\(642\) 0 0
\(643\) −11.2015 34.4747i −0.441745 1.35955i −0.886015 0.463657i \(-0.846537\pi\)
0.444270 0.895893i \(-0.353463\pi\)
\(644\) −3.14965 9.69362i −0.124114 0.381982i
\(645\) 0 0
\(646\) 6.20815 4.51048i 0.244256 0.177463i
\(647\) 10.8007 33.2412i 0.424620 1.30685i −0.478737 0.877958i \(-0.658905\pi\)
0.903357 0.428889i \(-0.141095\pi\)
\(648\) 0 0
\(649\) 0.296148 9.33168i 0.0116248 0.366301i
\(650\) 6.39026 0.250646
\(651\) 0 0
\(652\) 19.2142 13.9600i 0.752488 0.546714i
\(653\) −24.1000 17.5097i −0.943106 0.685207i 0.00605995 0.999982i \(-0.498071\pi\)
−0.949166 + 0.314775i \(0.898071\pi\)
\(654\) 0 0
\(655\) −0.194373 0.598218i −0.00759477 0.0233743i
\(656\) 10.9371 + 7.94628i 0.427023 + 0.310250i
\(657\) 0 0
\(658\) −5.91848 + 18.2152i −0.230726 + 0.710103i
\(659\) 7.30532 0.284575 0.142287 0.989825i \(-0.454554\pi\)
0.142287 + 0.989825i \(0.454554\pi\)
\(660\) 0 0
\(661\) −22.7352 −0.884296 −0.442148 0.896942i \(-0.645783\pi\)
−0.442148 + 0.896942i \(0.645783\pi\)
\(662\) 16.6204 51.1524i 0.645971 1.98809i
\(663\) 0 0
\(664\) 5.89998 + 4.28658i 0.228964 + 0.166352i
\(665\) 7.48357 + 23.0321i 0.290200 + 0.893145i
\(666\) 0 0
\(667\) 4.18586 + 3.04120i 0.162077 + 0.117756i
\(668\) 26.9179 19.5570i 1.04149 0.756684i
\(669\) 0 0
\(670\) −14.1590 −0.547010
\(671\) −4.10251 + 5.28555i −0.158376 + 0.204046i
\(672\) 0 0
\(673\) −5.48354 + 16.8766i −0.211375 + 0.650546i 0.788016 + 0.615655i \(0.211108\pi\)
−0.999391 + 0.0348910i \(0.988892\pi\)
\(674\) 40.5003 29.4252i 1.56001 1.13342i
\(675\) 0 0
\(676\) −2.73192 8.40799i −0.105074 0.323384i
\(677\) −2.52224 7.76267i −0.0969377 0.298344i 0.890816 0.454364i \(-0.150133\pi\)
−0.987754 + 0.156020i \(0.950133\pi\)
\(678\) 0 0
\(679\) 38.1004 27.6815i 1.46216 1.06232i
\(680\) 0.117206 0.360724i 0.00449466 0.0138331i
\(681\) 0 0
\(682\) 2.30933 72.7675i 0.0884289 2.78641i
\(683\) 6.19100 0.236892 0.118446 0.992960i \(-0.462209\pi\)
0.118446 + 0.992960i \(0.462209\pi\)
\(684\) 0 0
\(685\) 9.04756 6.57343i 0.345689 0.251158i
\(686\) −23.8770 17.3477i −0.911628 0.662336i
\(687\) 0 0
\(688\) 1.24617 + 3.83530i 0.0475096 + 0.146220i
\(689\) 10.3336 + 7.50781i 0.393680 + 0.286025i
\(690\) 0 0
\(691\) 7.29438 22.4498i 0.277491 0.854030i −0.711058 0.703133i \(-0.751784\pi\)
0.988549 0.150897i \(-0.0482162\pi\)
\(692\) −25.8892 −0.984158
\(693\) 0 0
\(694\) 0.695956 0.0264181
\(695\) −0.733901 + 2.25872i −0.0278385 + 0.0856779i
\(696\) 0 0
\(697\) −1.65400 1.20170i −0.0626497 0.0455177i
\(698\) 0.790889 + 2.43411i 0.0299356 + 0.0921323i
\(699\) 0 0
\(700\) 5.93120 + 4.30927i 0.224178 + 0.162875i
\(701\) 30.1184 21.8823i 1.13756 0.826483i 0.150779 0.988567i \(-0.451822\pi\)
0.986777 + 0.162084i \(0.0518217\pi\)
\(702\) 0 0
\(703\) −14.5637 −0.549282
\(704\) 34.2667 9.94389i 1.29147 0.374775i
\(705\) 0 0
\(706\) 16.6428 51.2211i 0.626358 1.92773i
\(707\) −29.1133 + 21.1521i −1.09492 + 0.795505i
\(708\) 0 0
\(709\) 5.64072 + 17.3603i 0.211842 + 0.651981i 0.999363 + 0.0356939i \(0.0113641\pi\)
−0.787521 + 0.616288i \(0.788636\pi\)
\(710\) 4.22284 + 12.9966i 0.158480 + 0.487753i
\(711\) 0 0
\(712\) −4.47845 + 3.25378i −0.167837 + 0.121941i
\(713\) −4.50083 + 13.8521i −0.168557 + 0.518766i
\(714\) 0 0
\(715\) −5.68294 8.36775i −0.212530 0.312936i
\(716\) −54.3388 −2.03074
\(717\) 0 0
\(718\) −30.3961 + 22.0841i −1.13437 + 0.824171i
\(719\) 7.74544 + 5.62739i 0.288856 + 0.209866i 0.722771 0.691088i \(-0.242868\pi\)
−0.433915 + 0.900954i \(0.642868\pi\)
\(720\) 0 0
\(721\) −13.1633 40.5124i −0.490226 1.50876i
\(722\) −73.4684 53.3779i −2.73421 1.98652i
\(723\) 0 0
\(724\) 1.77147 5.45202i 0.0658361 0.202623i
\(725\) −3.72162 −0.138217
\(726\) 0 0
\(727\) −14.0175 −0.519882 −0.259941 0.965625i \(-0.583703\pi\)
−0.259941 + 0.965625i \(0.583703\pi\)
\(728\) −2.36369 + 7.27470i −0.0876043 + 0.269618i
\(729\) 0 0
\(730\) 16.7408 + 12.1629i 0.619603 + 0.450168i
\(731\) −0.188455 0.580006i −0.00697027 0.0214523i
\(732\) 0 0
\(733\) −7.51392 5.45918i −0.277533 0.201640i 0.440308 0.897847i \(-0.354869\pi\)
−0.717841 + 0.696207i \(0.754869\pi\)
\(734\) 14.3932 10.4573i 0.531262 0.385984i
\(735\) 0 0
\(736\) −11.2083 −0.413145
\(737\) 12.5918 + 18.5406i 0.463824 + 0.682951i
\(738\) 0 0
\(739\) −12.0389 + 37.0519i −0.442857 + 1.36298i 0.441959 + 0.897035i \(0.354284\pi\)
−0.884816 + 0.465940i \(0.845716\pi\)
\(740\) −3.56688 + 2.59149i −0.131121 + 0.0952651i
\(741\) 0 0
\(742\) 8.31742 + 25.5984i 0.305342 + 0.939747i
\(743\) −14.1930 43.6817i −0.520692 1.60252i −0.772681 0.634795i \(-0.781085\pi\)
0.251989 0.967730i \(-0.418915\pi\)
\(744\) 0 0
\(745\) −7.05490 + 5.12569i −0.258472 + 0.187791i
\(746\) 23.2089 71.4298i 0.849740 2.61523i
\(747\) 0 0
\(748\) −3.53148 + 1.02481i −0.129124 + 0.0374706i
\(749\) −22.4549 −0.820483
\(750\) 0 0
\(751\) −18.7634 + 13.6324i −0.684686 + 0.497453i −0.874909 0.484288i \(-0.839079\pi\)
0.190223 + 0.981741i \(0.439079\pi\)
\(752\) 7.39504 + 5.37281i 0.269669 + 0.195926i
\(753\) 0 0
\(754\) −7.34907 22.6181i −0.267637 0.823703i
\(755\) −9.65596 7.01547i −0.351416 0.255319i
\(756\) 0 0
\(757\) −2.01541 + 6.20281i −0.0732515 + 0.225445i −0.980979 0.194116i \(-0.937816\pi\)
0.907727 + 0.419561i \(0.137816\pi\)
\(758\) 36.7757 1.33575
\(759\) 0 0
\(760\) −6.45628 −0.234194
\(761\) 2.02926 6.24542i 0.0735606 0.226396i −0.907516 0.420018i \(-0.862024\pi\)
0.981076 + 0.193622i \(0.0620236\pi\)
\(762\) 0 0
\(763\) −18.4444 13.4007i −0.667733 0.485137i
\(764\) −12.7386 39.2054i −0.460866 1.41840i
\(765\) 0 0
\(766\) −36.6572 26.6330i −1.32448 0.962291i
\(767\) 6.94565 5.04631i 0.250793 0.182212i
\(768\) 0 0
\(769\) 12.5950 0.454188 0.227094 0.973873i \(-0.427078\pi\)
0.227094 + 0.973873i \(0.427078\pi\)
\(770\) 0.676101 21.3041i 0.0243650 0.767746i
\(771\) 0 0
\(772\) −1.90990 + 5.87807i −0.0687389 + 0.211557i
\(773\) 17.7537 12.8988i 0.638557 0.463939i −0.220797 0.975320i \(-0.570866\pi\)
0.859354 + 0.511381i \(0.170866\pi\)
\(774\) 0 0
\(775\) −3.23741 9.96371i −0.116291 0.357907i
\(776\) 3.87980 + 11.9408i 0.139277 + 0.428650i
\(777\) 0 0
\(778\) 60.5867 44.0188i 2.17214 1.57815i
\(779\) −10.7541 + 33.0977i −0.385305 + 1.18585i
\(780\) 0 0
\(781\) 13.2630 17.0876i 0.474587 0.611444i
\(782\) 1.35118 0.0483181
\(783\) 0 0
\(784\) 5.97430 4.34059i 0.213368 0.155021i
\(785\) −3.13520 2.27786i −0.111900 0.0813002i
\(786\) 0 0
\(787\) 5.16981 + 15.9110i 0.184284 + 0.567167i 0.999935 0.0113766i \(-0.00362136\pi\)
−0.815652 + 0.578543i \(0.803621\pi\)
\(788\) 0.279875 + 0.203341i 0.00997012 + 0.00724372i
\(789\) 0 0
\(790\) −7.48350 + 23.0318i −0.266251 + 0.819436i
\(791\) −9.31320 −0.331139
\(792\) 0 0
\(793\) −6.15261 −0.218486
\(794\) −12.9786 + 39.9439i −0.460592 + 1.41756i
\(795\) 0 0
\(796\) 14.5840 + 10.5959i 0.516915 + 0.375560i
\(797\) 3.63735 + 11.1946i 0.128842 + 0.396533i 0.994581 0.103961i \(-0.0331516\pi\)
−0.865740 + 0.500494i \(0.833152\pi\)
\(798\) 0 0
\(799\) −1.11834 0.812521i −0.0395640 0.0287449i
\(800\) 6.52234 4.73876i 0.230600 0.167541i
\(801\) 0 0
\(802\) 43.7889 1.54624
\(803\) 1.03896 32.7379i 0.0366641 1.15529i
\(804\) 0 0
\(805\) −1.31770 + 4.05547i −0.0464429 + 0.142937i
\(806\) 54.1615 39.3507i 1.90776 1.38607i
\(807\) 0 0
\(808\) −2.96464 9.12422i −0.104296 0.320989i
\(809\) −0.369567 1.13741i −0.0129933 0.0399893i 0.944350 0.328943i \(-0.106693\pi\)
−0.957343 + 0.288954i \(0.906693\pi\)
\(810\) 0 0
\(811\) −28.9833 + 21.0576i −1.01774 + 0.739431i −0.965818 0.259220i \(-0.916535\pi\)
−0.0519216 + 0.998651i \(0.516535\pi\)
\(812\) 8.43138 25.9491i 0.295884 0.910636i
\(813\) 0 0
\(814\) 12.0591 + 4.34575i 0.422670 + 0.152318i
\(815\) −9.93621 −0.348050
\(816\) 0 0
\(817\) −8.39841 + 6.10181i −0.293823 + 0.213475i
\(818\) −39.8324 28.9400i −1.39271 1.01186i
\(819\) 0 0
\(820\) 3.25561 + 10.0197i 0.113691 + 0.349904i
\(821\) 4.44312 + 3.22811i 0.155066 + 0.112662i 0.662613 0.748962i \(-0.269448\pi\)
−0.507547 + 0.861624i \(0.669448\pi\)
\(822\) 0 0
\(823\) 13.2028 40.6341i 0.460222 1.41642i −0.404672 0.914462i \(-0.632614\pi\)
0.864894 0.501955i \(-0.167386\pi\)
\(824\) 11.3563 0.395616
\(825\) 0 0
\(826\) 18.0912 0.629473
\(827\) −10.0186 + 30.8340i −0.348380 + 1.07220i 0.611369 + 0.791345i \(0.290619\pi\)
−0.959749 + 0.280858i \(0.909381\pi\)
\(828\) 0 0
\(829\) 2.35544 + 1.71133i 0.0818079 + 0.0594369i 0.627937 0.778264i \(-0.283899\pi\)
−0.546130 + 0.837701i \(0.683899\pi\)
\(830\) −5.77463 17.7725i −0.200440 0.616892i
\(831\) 0 0
\(832\) 26.5438 + 19.2852i 0.920241 + 0.668594i
\(833\) −0.903483 + 0.656419i −0.0313038 + 0.0227436i
\(834\) 0 0
\(835\) −13.9200 −0.481722
\(836\) 35.1666 + 51.7805i 1.21626 + 1.79087i
\(837\) 0 0
\(838\) 6.54786 20.1522i 0.226192 0.696147i
\(839\) −16.8652 + 12.2533i −0.582250 + 0.423030i −0.839535 0.543306i \(-0.817172\pi\)
0.257284 + 0.966336i \(0.417172\pi\)
\(840\) 0 0
\(841\) −4.68147 14.4081i −0.161430 0.496830i
\(842\) 5.77737 + 17.7809i 0.199101 + 0.612771i
\(843\) 0 0
\(844\) 4.38733 3.18758i 0.151018 0.109721i
\(845\) −1.14294 + 3.51761i −0.0393184 + 0.121009i
\(846\) 0 0
\(847\) −28.4980 + 18.0607i −0.979203 + 0.620572i
\(848\) 12.8458 0.441127
\(849\) 0 0
\(850\) −0.786277 + 0.571264i −0.0269691 + 0.0195942i
\(851\) −2.07462 1.50730i −0.0711171 0.0516696i
\(852\) 0 0
\(853\) 10.6768 + 32.8599i 0.365567 + 1.12510i 0.949625 + 0.313388i \(0.101464\pi\)
−0.584058 + 0.811712i \(0.698536\pi\)
\(854\) −10.4889 7.62061i −0.358922 0.260772i
\(855\) 0 0
\(856\) 1.84990 5.69341i 0.0632283 0.194597i
\(857\) −33.2969 −1.13740 −0.568699 0.822545i \(-0.692553\pi\)
−0.568699 + 0.822545i \(0.692553\pi\)
\(858\) 0 0
\(859\) −16.7665 −0.572067 −0.286034 0.958220i \(-0.592337\pi\)
−0.286034 + 0.958220i \(0.592337\pi\)
\(860\) −0.971136 + 2.98885i −0.0331155 + 0.101919i
\(861\) 0 0
\(862\) −29.8550 21.6909i −1.01687 0.738796i
\(863\) 0.458628 + 1.41151i 0.0156119 + 0.0480484i 0.958559 0.284894i \(-0.0919585\pi\)
−0.942947 + 0.332943i \(0.891958\pi\)
\(864\) 0 0
\(865\) 8.76256 + 6.36637i 0.297936 + 0.216463i
\(866\) −15.5002 + 11.2616i −0.526719 + 0.382683i
\(867\) 0 0
\(868\) 76.8068 2.60699
\(869\) 36.8143 10.6832i 1.24884 0.362403i
\(870\) 0 0
\(871\) −6.36860 + 19.6005i −0.215792 + 0.664138i
\(872\) 4.91723 3.57258i 0.166518 0.120983i
\(873\) 0 0
\(874\) −7.10737 21.8742i −0.240410 0.739907i
\(875\) −0.947813 2.91707i −0.0320419 0.0986149i
\(876\) 0 0
\(877\) 20.1134 14.6132i 0.679180 0.493453i −0.193905 0.981020i \(-0.562115\pi\)
0.873086 + 0.487567i \(0.162115\pi\)
\(878\) 4.18885 12.8920i 0.141367 0.435083i
\(879\) 0 0
\(880\) −9.57024 3.44884i −0.322613 0.116260i
\(881\) −32.6968 −1.10158 −0.550792 0.834643i \(-0.685674\pi\)
−0.550792 + 0.834643i \(0.685674\pi\)
\(882\) 0 0
\(883\) −38.5268 + 27.9914i −1.29653 + 0.941985i −0.999915 0.0130124i \(-0.995858\pi\)
−0.296615 + 0.954997i \(0.595858\pi\)
\(884\) −2.73557 1.98751i −0.0920073 0.0668472i
\(885\) 0 0
\(886\) 26.4717 + 81.4717i 0.889336 + 2.73709i
\(887\) 47.8097 + 34.7358i 1.60529 + 1.16631i 0.876267 + 0.481826i \(0.160026\pi\)
0.729025 + 0.684487i \(0.239974\pi\)
\(888\) 0 0
\(889\) 0.428030 1.31734i 0.0143557 0.0441822i
\(890\) 14.1847 0.475471
\(891\) 0 0
\(892\) 20.5076 0.686646
\(893\) −7.27130 + 22.3787i −0.243325 + 0.748876i
\(894\) 0 0
\(895\) 18.3918 + 13.3624i 0.614768 + 0.446655i
\(896\) 6.08220 + 18.7191i 0.203192 + 0.625360i
\(897\) 0 0
\(898\) −20.6140 14.9770i −0.687900 0.499788i
\(899\) −31.5431 + 22.9174i −1.05202 + 0.764338i
\(900\) 0 0
\(901\) −1.94265 −0.0647190
\(902\) 18.7808 24.1966i 0.625332 0.805659i
\(903\) 0 0
\(904\) 0.767250 2.36135i 0.0255183 0.0785374i
\(905\) −1.94028 + 1.40969i −0.0644970 + 0.0468598i
\(906\) 0 0
\(907\) 10.7098 + 32.9613i 0.355612 + 1.09446i 0.955654 + 0.294493i \(0.0951508\pi\)
−0.600041 + 0.799969i \(0.704849\pi\)
\(908\) −4.57979 14.0952i −0.151986 0.467764i
\(909\) 0 0
\(910\) 15.8568 11.5207i 0.525648 0.381906i
\(911\) 3.14834 9.68961i 0.104309 0.321031i −0.885258 0.465099i \(-0.846019\pi\)
0.989568 + 0.144069i \(0.0460186\pi\)
\(912\) 0 0
\(913\) −18.1368 + 23.3669i −0.600241 + 0.773332i
\(914\) −20.7484 −0.686298
\(915\) 0 0
\(916\) −44.7972 + 32.5471i −1.48014 + 1.07539i
\(917\) −1.56081 1.13400i −0.0515426 0.0374479i
\(918\) 0 0
\(919\) −11.1644 34.3606i −0.368281 1.13345i −0.947901 0.318565i \(-0.896799\pi\)
0.579620 0.814887i \(-0.303201\pi\)
\(920\) −0.919704 0.668204i −0.0303218 0.0220300i
\(921\) 0 0
\(922\) 2.02357 6.22790i 0.0666427 0.205105i
\(923\) 19.8907 0.654711
\(924\) 0 0
\(925\) 1.84453 0.0606479
\(926\) −15.7674 + 48.5269i −0.518148 + 1.59469i
\(927\) 0 0
\(928\) −24.2737 17.6359i −0.796823 0.578926i
\(929\) −8.69078 26.7475i −0.285135 0.877556i −0.986358 0.164614i \(-0.947362\pi\)
0.701223 0.712942i \(-0.252638\pi\)
\(930\) 0 0
\(931\) 15.3792 + 11.1736i 0.504033 + 0.366201i
\(932\) −53.8797 + 39.1459i −1.76489 + 1.28227i
\(933\) 0 0
\(934\) −69.5087 −2.27439
\(935\) 1.44729 + 0.521562i 0.0473314 + 0.0170569i
\(936\) 0 0
\(937\) 0.0263183 0.0809993i 0.000859781 0.00264613i −0.950626 0.310340i \(-0.899557\pi\)
0.951485 + 0.307694i \(0.0995572\pi\)
\(938\) −35.1342 + 25.5265i −1.14717 + 0.833471i
\(939\) 0 0
\(940\) 2.20125 + 6.77476i 0.0717969 + 0.220968i
\(941\) 12.9217 + 39.7688i 0.421234 + 1.29643i 0.906554 + 0.422089i \(0.138703\pi\)
−0.485320 + 0.874337i \(0.661297\pi\)
\(942\) 0 0
\(943\) −4.95744 + 3.60179i −0.161437 + 0.117291i
\(944\) 2.66812 8.21161i 0.0868398 0.267265i
\(945\) 0 0
\(946\) 8.77481 2.54638i 0.285294 0.0827898i
\(947\) −8.92463 −0.290012 −0.145006 0.989431i \(-0.546320\pi\)
−0.145006 + 0.989431i \(0.546320\pi\)
\(948\) 0 0
\(949\) 24.3671 17.7037i 0.790989 0.574687i
\(950\) 13.3841 + 9.72412i 0.434237 + 0.315492i
\(951\) 0 0
\(952\) −0.359493 1.10641i −0.0116512 0.0358589i
\(953\) 4.25853 + 3.09400i 0.137947 + 0.100225i 0.654619 0.755959i \(-0.272829\pi\)
−0.516672 + 0.856184i \(0.672829\pi\)
\(954\) 0 0
\(955\) −5.32938 + 16.4022i −0.172455 + 0.530761i
\(956\) 38.9283 1.25903
\(957\) 0 0
\(958\) 36.2438 1.17098
\(959\) 10.5998 32.6227i 0.342284 1.05344i
\(960\) 0 0
\(961\) −63.7153 46.2919i −2.05533 1.49329i
\(962\) 3.64240 + 11.2101i 0.117436 + 0.361429i
\(963\) 0 0
\(964\) −8.49043 6.16866i −0.273458 0.198679i
\(965\) 2.09190 1.51986i 0.0673408 0.0489259i
\(966\) 0 0
\(967\) −18.5421 −0.596275 −0.298138 0.954523i \(-0.596365\pi\)
−0.298138 + 0.954523i \(0.596365\pi\)
\(968\) −2.23151 8.71353i −0.0717235 0.280063i
\(969\) 0 0
\(970\) 9.94165 30.5973i 0.319207 0.982419i
\(971\) −19.5968 + 14.2379i −0.628893 + 0.456917i −0.856016 0.516949i \(-0.827068\pi\)
0.227124 + 0.973866i \(0.427068\pi\)
\(972\) 0 0
\(973\) 2.25101 + 6.92790i 0.0721641 + 0.222098i
\(974\) 4.94715 + 15.2258i 0.158517 + 0.487865i
\(975\) 0 0
\(976\) −5.00592 + 3.63701i −0.160236 + 0.116418i
\(977\) −15.1609 + 46.6606i −0.485041 + 1.49280i 0.346880 + 0.937910i \(0.387241\pi\)
−0.831921 + 0.554894i \(0.812759\pi\)
\(978\) 0 0
\(979\) −12.6146 18.5742i −0.403165 0.593634i
\(980\) 5.75485 0.183832
\(981\) 0 0
\(982\) −51.9664 + 37.7558i −1.65831 + 1.20484i
\(983\) 39.7546 + 28.8834i 1.26798 + 0.921239i 0.999120 0.0419415i \(-0.0133543\pi\)
0.268856 + 0.963180i \(0.413354\pi\)
\(984\) 0 0
\(985\) −0.0447243 0.137647i −0.00142503 0.00438581i
\(986\) 2.92622 + 2.12603i 0.0931899 + 0.0677064i
\(987\) 0 0
\(988\) −17.7863 + 54.7408i −0.565859 + 1.74154i
\(989\) −1.82788 −0.0581233
\(990\) 0 0
\(991\) 30.9620 0.983541 0.491771 0.870725i \(-0.336350\pi\)
0.491771 + 0.870725i \(0.336350\pi\)
\(992\) 26.1002 80.3281i 0.828681 2.55042i
\(993\) 0 0
\(994\) 33.9094 + 24.6366i 1.07554 + 0.781426i
\(995\) −2.33053 7.17265i −0.0738829 0.227388i
\(996\) 0 0
\(997\) −18.5216 13.4567i −0.586584 0.426178i 0.254507 0.967071i \(-0.418087\pi\)
−0.841092 + 0.540892i \(0.818087\pi\)
\(998\) 63.5305 46.1576i 2.01102 1.46109i
\(999\) 0 0
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 495.2.n.e.361.2 8
3.2 odd 2 55.2.g.b.31.1 yes 8
11.4 even 5 5445.2.a.bp.1.4 4
11.5 even 5 inner 495.2.n.e.181.2 8
11.7 odd 10 5445.2.a.bi.1.1 4
12.11 even 2 880.2.bo.h.801.2 8
15.2 even 4 275.2.z.a.174.1 16
15.8 even 4 275.2.z.a.174.4 16
15.14 odd 2 275.2.h.a.251.2 8
33.2 even 10 605.2.g.e.366.1 8
33.5 odd 10 55.2.g.b.16.1 8
33.8 even 10 605.2.g.e.81.1 8
33.14 odd 10 605.2.g.m.81.2 8
33.17 even 10 605.2.g.k.511.2 8
33.20 odd 10 605.2.g.m.366.2 8
33.26 odd 10 605.2.a.j.1.1 4
33.29 even 10 605.2.a.k.1.4 4
33.32 even 2 605.2.g.k.251.2 8
132.59 even 10 9680.2.a.cn.1.1 4
132.71 even 10 880.2.bo.h.401.2 8
132.95 odd 10 9680.2.a.cm.1.1 4
165.29 even 10 3025.2.a.w.1.1 4
165.38 even 20 275.2.z.a.49.1 16
165.59 odd 10 3025.2.a.bd.1.4 4
165.104 odd 10 275.2.h.a.126.2 8
165.137 even 20 275.2.z.a.49.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.2.g.b.16.1 8 33.5 odd 10
55.2.g.b.31.1 yes 8 3.2 odd 2
275.2.h.a.126.2 8 165.104 odd 10
275.2.h.a.251.2 8 15.14 odd 2
275.2.z.a.49.1 16 165.38 even 20
275.2.z.a.49.4 16 165.137 even 20
275.2.z.a.174.1 16 15.2 even 4
275.2.z.a.174.4 16 15.8 even 4
495.2.n.e.181.2 8 11.5 even 5 inner
495.2.n.e.361.2 8 1.1 even 1 trivial
605.2.a.j.1.1 4 33.26 odd 10
605.2.a.k.1.4 4 33.29 even 10
605.2.g.e.81.1 8 33.8 even 10
605.2.g.e.366.1 8 33.2 even 10
605.2.g.k.251.2 8 33.32 even 2
605.2.g.k.511.2 8 33.17 even 10
605.2.g.m.81.2 8 33.14 odd 10
605.2.g.m.366.2 8 33.20 odd 10
880.2.bo.h.401.2 8 132.71 even 10
880.2.bo.h.801.2 8 12.11 even 2
3025.2.a.w.1.1 4 165.29 even 10
3025.2.a.bd.1.4 4 165.59 odd 10
5445.2.a.bi.1.1 4 11.7 odd 10
5445.2.a.bp.1.4 4 11.4 even 5
9680.2.a.cm.1.1 4 132.95 odd 10
9680.2.a.cn.1.1 4 132.59 even 10