Properties

Label 1470.2.m.d.97.6
Level $1470$
Weight $2$
Character 1470.97
Analytic conductor $11.738$
Analytic rank $0$
Dimension $16$
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] = [1470,2,Mod(97,1470)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1470, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1470.97");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.m (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(11.7380090971\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} - 180 x^{7} + 358 x^{6} - 336 x^{5} + 390 x^{4} - 344 x^{3} + 164 x^{2} - 40 x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 97.6
Root \(0.277956 - 0.213283i\) of defining polynomial
Character \(\chi\) \(=\) 1470.97
Dual form 1470.2.m.d.1273.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-1.36519 + 1.77095i) q^{5} -1.00000i q^{6} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-1.36519 + 1.77095i) q^{5} -1.00000i q^{6} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(-2.21758 + 0.286912i) q^{10} +5.48630 q^{11} +(0.707107 - 0.707107i) q^{12} +(2.41668 + 2.41668i) q^{13} +(2.21758 - 0.286912i) q^{15} -1.00000 q^{16} +(1.49783 - 1.49783i) q^{17} +(-0.707107 + 0.707107i) q^{18} -6.99593 q^{19} +(-1.77095 - 1.36519i) q^{20} +(3.87940 + 3.87940i) q^{22} +(-1.24054 + 1.24054i) q^{23} +1.00000 q^{24} +(-1.27250 - 4.83536i) q^{25} +3.41770i q^{26} +(0.707107 - 0.707107i) q^{27} +0.684610i q^{29} +(1.77095 + 1.36519i) q^{30} +5.57642i q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.87940 - 3.87940i) q^{33} +2.11825 q^{34} -1.00000 q^{36} +(6.92974 + 6.92974i) q^{37} +(-4.94687 - 4.94687i) q^{38} -3.41770i q^{39} +(-0.286912 - 2.21758i) q^{40} +2.50597i q^{41} +(-1.95305 + 1.95305i) q^{43} +5.48630i q^{44} +(-1.77095 - 1.36519i) q^{45} -1.75439 q^{46} +(-2.49268 + 2.49268i) q^{47} +(0.707107 + 0.707107i) q^{48} +(2.51932 - 4.31891i) q^{50} -2.11825 q^{51} +(-2.41668 + 2.41668i) q^{52} +(-6.64852 + 6.64852i) q^{53} +1.00000 q^{54} +(-7.48985 + 9.71594i) q^{55} +(4.94687 + 4.94687i) q^{57} +(-0.484092 + 0.484092i) q^{58} -10.1603 q^{59} +(0.286912 + 2.21758i) q^{60} -1.17166i q^{61} +(-3.94312 + 3.94312i) q^{62} -1.00000i q^{64} +(-7.57904 + 0.980578i) q^{65} -5.48630i q^{66} +(7.03792 + 7.03792i) q^{67} +(1.49783 + 1.49783i) q^{68} +1.75439 q^{69} -11.9716 q^{71} +(-0.707107 - 0.707107i) q^{72} +(3.44417 + 3.44417i) q^{73} +9.80013i q^{74} +(-2.51932 + 4.31891i) q^{75} -6.99593i q^{76} +(2.41668 - 2.41668i) q^{78} +8.33087i q^{79} +(1.36519 - 1.77095i) q^{80} -1.00000 q^{81} +(-1.77199 + 1.77199i) q^{82} +(4.05281 + 4.05281i) q^{83} +(0.607749 + 4.69739i) q^{85} -2.76202 q^{86} +(0.484092 - 0.484092i) q^{87} +(-3.87940 + 3.87940i) q^{88} -7.18356 q^{89} +(-0.286912 - 2.21758i) q^{90} +(-1.24054 - 1.24054i) q^{92} +(3.94312 - 3.94312i) q^{93} -3.52518 q^{94} +(9.55079 - 12.3894i) q^{95} +1.00000i q^{96} +(13.1212 - 13.1212i) q^{97} +5.48630i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{10} - 8 q^{11} - 16 q^{13} + 4 q^{15} - 16 q^{16} + 24 q^{17} + 16 q^{19} - 8 q^{20} + 4 q^{22} + 8 q^{23} + 16 q^{24} + 16 q^{25} + 8 q^{30} - 4 q^{33} + 16 q^{34} - 16 q^{36} + 16 q^{37} + 8 q^{38} - 24 q^{43} - 8 q^{45} + 8 q^{46} + 24 q^{47} - 16 q^{51} + 16 q^{52} - 16 q^{53} + 16 q^{54} - 56 q^{55} - 8 q^{57} - 36 q^{58} - 16 q^{59} + 8 q^{62} - 32 q^{65} + 48 q^{67} + 24 q^{68} - 8 q^{69} - 32 q^{71} + 56 q^{73} - 16 q^{78} - 16 q^{81} + 24 q^{82} - 16 q^{83} + 8 q^{85} + 16 q^{86} + 36 q^{87} - 4 q^{88} + 32 q^{89} + 8 q^{92} - 8 q^{93} - 16 q^{94} - 24 q^{95} + 44 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) −0.707107 0.707107i −0.408248 0.408248i
\(4\) 1.00000i 0.500000i
\(5\) −1.36519 + 1.77095i −0.610532 + 0.791991i
\(6\) 1.00000i 0.408248i
\(7\) 0 0
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) −2.21758 + 0.286912i −0.701262 + 0.0907294i
\(11\) 5.48630 1.65418 0.827091 0.562068i \(-0.189994\pi\)
0.827091 + 0.562068i \(0.189994\pi\)
\(12\) 0.707107 0.707107i 0.204124 0.204124i
\(13\) 2.41668 + 2.41668i 0.670266 + 0.670266i 0.957777 0.287511i \(-0.0928279\pi\)
−0.287511 + 0.957777i \(0.592828\pi\)
\(14\) 0 0
\(15\) 2.21758 0.286912i 0.572578 0.0740803i
\(16\) −1.00000 −0.250000
\(17\) 1.49783 1.49783i 0.363276 0.363276i −0.501742 0.865018i \(-0.667307\pi\)
0.865018 + 0.501742i \(0.167307\pi\)
\(18\) −0.707107 + 0.707107i −0.166667 + 0.166667i
\(19\) −6.99593 −1.60498 −0.802489 0.596668i \(-0.796491\pi\)
−0.802489 + 0.596668i \(0.796491\pi\)
\(20\) −1.77095 1.36519i −0.395996 0.305266i
\(21\) 0 0
\(22\) 3.87940 + 3.87940i 0.827091 + 0.827091i
\(23\) −1.24054 + 1.24054i −0.258670 + 0.258670i −0.824513 0.565843i \(-0.808551\pi\)
0.565843 + 0.824513i \(0.308551\pi\)
\(24\) 1.00000 0.204124
\(25\) −1.27250 4.83536i −0.254500 0.967073i
\(26\) 3.41770i 0.670266i
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) 0 0
\(29\) 0.684610i 0.127129i 0.997978 + 0.0635644i \(0.0202468\pi\)
−0.997978 + 0.0635644i \(0.979753\pi\)
\(30\) 1.77095 + 1.36519i 0.323329 + 0.249249i
\(31\) 5.57642i 1.00155i 0.865576 + 0.500777i \(0.166952\pi\)
−0.865576 + 0.500777i \(0.833048\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) −3.87940 3.87940i −0.675317 0.675317i
\(34\) 2.11825 0.363276
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) 6.92974 + 6.92974i 1.13924 + 1.13924i 0.988586 + 0.150656i \(0.0481386\pi\)
0.150656 + 0.988586i \(0.451861\pi\)
\(38\) −4.94687 4.94687i −0.802489 0.802489i
\(39\) 3.41770i 0.547270i
\(40\) −0.286912 2.21758i −0.0453647 0.350631i
\(41\) 2.50597i 0.391366i 0.980667 + 0.195683i \(0.0626924\pi\)
−0.980667 + 0.195683i \(0.937308\pi\)
\(42\) 0 0
\(43\) −1.95305 + 1.95305i −0.297837 + 0.297837i −0.840166 0.542329i \(-0.817543\pi\)
0.542329 + 0.840166i \(0.317543\pi\)
\(44\) 5.48630i 0.827091i
\(45\) −1.77095 1.36519i −0.263997 0.203511i
\(46\) −1.75439 −0.258670
\(47\) −2.49268 + 2.49268i −0.363594 + 0.363594i −0.865134 0.501540i \(-0.832767\pi\)
0.501540 + 0.865134i \(0.332767\pi\)
\(48\) 0.707107 + 0.707107i 0.102062 + 0.102062i
\(49\) 0 0
\(50\) 2.51932 4.31891i 0.356286 0.610787i
\(51\) −2.11825 −0.296614
\(52\) −2.41668 + 2.41668i −0.335133 + 0.335133i
\(53\) −6.64852 + 6.64852i −0.913244 + 0.913244i −0.996526 0.0832822i \(-0.973460\pi\)
0.0832822 + 0.996526i \(0.473460\pi\)
\(54\) 1.00000 0.136083
\(55\) −7.48985 + 9.71594i −1.00993 + 1.31010i
\(56\) 0 0
\(57\) 4.94687 + 4.94687i 0.655229 + 0.655229i
\(58\) −0.484092 + 0.484092i −0.0635644 + 0.0635644i
\(59\) −10.1603 −1.32276 −0.661379 0.750052i \(-0.730028\pi\)
−0.661379 + 0.750052i \(0.730028\pi\)
\(60\) 0.286912 + 2.21758i 0.0370401 + 0.286289i
\(61\) 1.17166i 0.150016i −0.997183 0.0750079i \(-0.976102\pi\)
0.997183 0.0750079i \(-0.0238982\pi\)
\(62\) −3.94312 + 3.94312i −0.500777 + 0.500777i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) −7.57904 + 0.980578i −0.940064 + 0.121626i
\(66\) 5.48630i 0.675317i
\(67\) 7.03792 + 7.03792i 0.859819 + 0.859819i 0.991317 0.131497i \(-0.0419784\pi\)
−0.131497 + 0.991317i \(0.541978\pi\)
\(68\) 1.49783 + 1.49783i 0.181638 + 0.181638i
\(69\) 1.75439 0.211204
\(70\) 0 0
\(71\) −11.9716 −1.42077 −0.710383 0.703816i \(-0.751478\pi\)
−0.710383 + 0.703816i \(0.751478\pi\)
\(72\) −0.707107 0.707107i −0.0833333 0.0833333i
\(73\) 3.44417 + 3.44417i 0.403109 + 0.403109i 0.879327 0.476218i \(-0.157993\pi\)
−0.476218 + 0.879327i \(0.657993\pi\)
\(74\) 9.80013i 1.13924i
\(75\) −2.51932 + 4.31891i −0.290906 + 0.498705i
\(76\) 6.99593i 0.802489i
\(77\) 0 0
\(78\) 2.41668 2.41668i 0.273635 0.273635i
\(79\) 8.33087i 0.937296i 0.883385 + 0.468648i \(0.155259\pi\)
−0.883385 + 0.468648i \(0.844741\pi\)
\(80\) 1.36519 1.77095i 0.152633 0.197998i
\(81\) −1.00000 −0.111111
\(82\) −1.77199 + 1.77199i −0.195683 + 0.195683i
\(83\) 4.05281 + 4.05281i 0.444854 + 0.444854i 0.893639 0.448786i \(-0.148143\pi\)
−0.448786 + 0.893639i \(0.648143\pi\)
\(84\) 0 0
\(85\) 0.607749 + 4.69739i 0.0659197 + 0.509503i
\(86\) −2.76202 −0.297837
\(87\) 0.484092 0.484092i 0.0519001 0.0519001i
\(88\) −3.87940 + 3.87940i −0.413545 + 0.413545i
\(89\) −7.18356 −0.761456 −0.380728 0.924687i \(-0.624327\pi\)
−0.380728 + 0.924687i \(0.624327\pi\)
\(90\) −0.286912 2.21758i −0.0302431 0.233754i
\(91\) 0 0
\(92\) −1.24054 1.24054i −0.129335 0.129335i
\(93\) 3.94312 3.94312i 0.408883 0.408883i
\(94\) −3.52518 −0.363594
\(95\) 9.55079 12.3894i 0.979891 1.27113i
\(96\) 1.00000i 0.102062i
\(97\) 13.1212 13.1212i 1.33226 1.33226i 0.428909 0.903348i \(-0.358898\pi\)
0.903348 0.428909i \(-0.141102\pi\)
\(98\) 0 0
\(99\) 5.48630i 0.551394i
\(100\) 4.83536 1.27250i 0.483536 0.127250i
\(101\) 8.26766i 0.822663i 0.911486 + 0.411332i \(0.134936\pi\)
−0.911486 + 0.411332i \(0.865064\pi\)
\(102\) −1.49783 1.49783i −0.148307 0.148307i
\(103\) 6.58048 + 6.58048i 0.648394 + 0.648394i 0.952605 0.304211i \(-0.0983928\pi\)
−0.304211 + 0.952605i \(0.598393\pi\)
\(104\) −3.41770 −0.335133
\(105\) 0 0
\(106\) −9.40242 −0.913244
\(107\) −8.67454 8.67454i −0.838600 0.838600i 0.150075 0.988675i \(-0.452049\pi\)
−0.988675 + 0.150075i \(0.952049\pi\)
\(108\) 0.707107 + 0.707107i 0.0680414 + 0.0680414i
\(109\) 0.336622i 0.0322425i 0.999870 + 0.0161213i \(0.00513178\pi\)
−0.999870 + 0.0161213i \(0.994868\pi\)
\(110\) −12.1663 + 1.57408i −1.16001 + 0.150083i
\(111\) 9.80013i 0.930188i
\(112\) 0 0
\(113\) 10.1896 10.1896i 0.958555 0.958555i −0.0406198 0.999175i \(-0.512933\pi\)
0.999175 + 0.0406198i \(0.0129332\pi\)
\(114\) 6.99593i 0.655229i
\(115\) −0.503355 3.89051i −0.0469380 0.362792i
\(116\) −0.684610 −0.0635644
\(117\) −2.41668 + 2.41668i −0.223422 + 0.223422i
\(118\) −7.18441 7.18441i −0.661379 0.661379i
\(119\) 0 0
\(120\) −1.36519 + 1.77095i −0.124624 + 0.161665i
\(121\) 19.0995 1.73632
\(122\) 0.828489 0.828489i 0.0750079 0.0750079i
\(123\) 1.77199 1.77199i 0.159775 0.159775i
\(124\) −5.57642 −0.500777
\(125\) 10.3004 + 4.34767i 0.921294 + 0.388867i
\(126\) 0 0
\(127\) −4.77054 4.77054i −0.423317 0.423317i 0.463027 0.886344i \(-0.346763\pi\)
−0.886344 + 0.463027i \(0.846763\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) 2.76202 0.243183
\(130\) −6.05256 4.66582i −0.530845 0.409219i
\(131\) 18.2091i 1.59094i −0.605996 0.795468i \(-0.707225\pi\)
0.605996 0.795468i \(-0.292775\pi\)
\(132\) 3.87940 3.87940i 0.337658 0.337658i
\(133\) 0 0
\(134\) 9.95313i 0.859819i
\(135\) 0.286912 + 2.21758i 0.0246934 + 0.190859i
\(136\) 2.11825i 0.181638i
\(137\) 1.54481 + 1.54481i 0.131982 + 0.131982i 0.770012 0.638030i \(-0.220250\pi\)
−0.638030 + 0.770012i \(0.720250\pi\)
\(138\) 1.24054 + 1.24054i 0.105602 + 0.105602i
\(139\) 18.1446 1.53900 0.769501 0.638645i \(-0.220505\pi\)
0.769501 + 0.638645i \(0.220505\pi\)
\(140\) 0 0
\(141\) 3.52518 0.296873
\(142\) −8.46519 8.46519i −0.710383 0.710383i
\(143\) 13.2586 + 13.2586i 1.10874 + 1.10874i
\(144\) 1.00000i 0.0833333i
\(145\) −1.21241 0.934623i −0.100685 0.0776163i
\(146\) 4.87079i 0.403109i
\(147\) 0 0
\(148\) −6.92974 + 6.92974i −0.569621 + 0.569621i
\(149\) 0.193656i 0.0158649i −0.999969 0.00793245i \(-0.997475\pi\)
0.999969 0.00793245i \(-0.00252500\pi\)
\(150\) −4.83536 + 1.27250i −0.394806 + 0.103899i
\(151\) −21.3227 −1.73522 −0.867610 0.497245i \(-0.834345\pi\)
−0.867610 + 0.497245i \(0.834345\pi\)
\(152\) 4.94687 4.94687i 0.401244 0.401244i
\(153\) 1.49783 + 1.49783i 0.121092 + 0.121092i
\(154\) 0 0
\(155\) −9.87553 7.61288i −0.793222 0.611481i
\(156\) 3.41770 0.273635
\(157\) 2.60217 2.60217i 0.207676 0.207676i −0.595603 0.803279i \(-0.703087\pi\)
0.803279 + 0.595603i \(0.203087\pi\)
\(158\) −5.89081 + 5.89081i −0.468648 + 0.468648i
\(159\) 9.40242 0.745660
\(160\) 2.21758 0.286912i 0.175315 0.0226824i
\(161\) 0 0
\(162\) −0.707107 0.707107i −0.0555556 0.0555556i
\(163\) −9.95676 + 9.95676i −0.779874 + 0.779874i −0.979809 0.199935i \(-0.935927\pi\)
0.199935 + 0.979809i \(0.435927\pi\)
\(164\) −2.50597 −0.195683
\(165\) 12.1663 1.57408i 0.947148 0.122542i
\(166\) 5.73154i 0.444854i
\(167\) −6.07259 + 6.07259i −0.469911 + 0.469911i −0.901886 0.431974i \(-0.857817\pi\)
0.431974 + 0.901886i \(0.357817\pi\)
\(168\) 0 0
\(169\) 1.31933i 0.101487i
\(170\) −2.89181 + 3.75130i −0.221792 + 0.287711i
\(171\) 6.99593i 0.534992i
\(172\) −1.95305 1.95305i −0.148918 0.148918i
\(173\) 2.86311 + 2.86311i 0.217678 + 0.217678i 0.807519 0.589841i \(-0.200810\pi\)
−0.589841 + 0.807519i \(0.700810\pi\)
\(174\) 0.684610 0.0519001
\(175\) 0 0
\(176\) −5.48630 −0.413545
\(177\) 7.18441 + 7.18441i 0.540014 + 0.540014i
\(178\) −5.07954 5.07954i −0.380728 0.380728i
\(179\) 3.66534i 0.273960i −0.990574 0.136980i \(-0.956260\pi\)
0.990574 0.136980i \(-0.0437396\pi\)
\(180\) 1.36519 1.77095i 0.101755 0.131999i
\(181\) 2.39985i 0.178379i −0.996015 0.0891896i \(-0.971572\pi\)
0.996015 0.0891896i \(-0.0284277\pi\)
\(182\) 0 0
\(183\) −0.828489 + 0.828489i −0.0612437 + 0.0612437i
\(184\) 1.75439i 0.129335i
\(185\) −21.7326 + 2.81177i −1.59781 + 0.206726i
\(186\) 5.57642 0.408883
\(187\) 8.21752 8.21752i 0.600925 0.600925i
\(188\) −2.49268 2.49268i −0.181797 0.181797i
\(189\) 0 0
\(190\) 15.5141 2.00721i 1.12551 0.145619i
\(191\) 8.07532 0.584310 0.292155 0.956371i \(-0.405628\pi\)
0.292155 + 0.956371i \(0.405628\pi\)
\(192\) −0.707107 + 0.707107i −0.0510310 + 0.0510310i
\(193\) −1.21801 + 1.21801i −0.0876740 + 0.0876740i −0.749584 0.661910i \(-0.769746\pi\)
0.661910 + 0.749584i \(0.269746\pi\)
\(194\) 18.5562 1.33226
\(195\) 6.05256 + 4.66582i 0.433433 + 0.334126i
\(196\) 0 0
\(197\) 6.01174 + 6.01174i 0.428319 + 0.428319i 0.888055 0.459737i \(-0.152056\pi\)
−0.459737 + 0.888055i \(0.652056\pi\)
\(198\) −3.87940 + 3.87940i −0.275697 + 0.275697i
\(199\) 11.0179 0.781041 0.390520 0.920594i \(-0.372295\pi\)
0.390520 + 0.920594i \(0.372295\pi\)
\(200\) 4.31891 + 2.51932i 0.305393 + 0.178143i
\(201\) 9.95313i 0.702040i
\(202\) −5.84612 + 5.84612i −0.411332 + 0.411332i
\(203\) 0 0
\(204\) 2.11825i 0.148307i
\(205\) −4.43793 3.42113i −0.309959 0.238942i
\(206\) 9.30620i 0.648394i
\(207\) −1.24054 1.24054i −0.0862235 0.0862235i
\(208\) −2.41668 2.41668i −0.167566 0.167566i
\(209\) −38.3818 −2.65492
\(210\) 0 0
\(211\) 10.3323 0.711302 0.355651 0.934619i \(-0.384259\pi\)
0.355651 + 0.934619i \(0.384259\pi\)
\(212\) −6.64852 6.64852i −0.456622 0.456622i
\(213\) 8.46519 + 8.46519i 0.580025 + 0.580025i
\(214\) 12.2677i 0.838600i
\(215\) −0.792457 6.12502i −0.0540451 0.417723i
\(216\) 1.00000i 0.0680414i
\(217\) 0 0
\(218\) −0.238027 + 0.238027i −0.0161213 + 0.0161213i
\(219\) 4.87079i 0.329137i
\(220\) −9.71594 7.48985i −0.655049 0.504966i
\(221\) 7.23953 0.486983
\(222\) 6.92974 6.92974i 0.465094 0.465094i
\(223\) −3.41183 3.41183i −0.228473 0.228473i 0.583582 0.812054i \(-0.301651\pi\)
−0.812054 + 0.583582i \(0.801651\pi\)
\(224\) 0 0
\(225\) 4.83536 1.27250i 0.322358 0.0848334i
\(226\) 14.4102 0.958555
\(227\) 12.7942 12.7942i 0.849182 0.849182i −0.140849 0.990031i \(-0.544983\pi\)
0.990031 + 0.140849i \(0.0449831\pi\)
\(228\) −4.94687 + 4.94687i −0.327615 + 0.327615i
\(229\) 9.64749 0.637524 0.318762 0.947835i \(-0.396733\pi\)
0.318762 + 0.947835i \(0.396733\pi\)
\(230\) 2.39508 3.10693i 0.157927 0.204865i
\(231\) 0 0
\(232\) −0.484092 0.484092i −0.0317822 0.0317822i
\(233\) 10.2342 10.2342i 0.670463 0.670463i −0.287360 0.957823i \(-0.592777\pi\)
0.957823 + 0.287360i \(0.0927775\pi\)
\(234\) −3.41770 −0.223422
\(235\) −1.01141 7.81738i −0.0659774 0.509949i
\(236\) 10.1603i 0.661379i
\(237\) 5.89081 5.89081i 0.382649 0.382649i
\(238\) 0 0
\(239\) 29.9736i 1.93883i −0.245427 0.969415i \(-0.578928\pi\)
0.245427 0.969415i \(-0.421072\pi\)
\(240\) −2.21758 + 0.286912i −0.143144 + 0.0185201i
\(241\) 16.6201i 1.07059i 0.844664 + 0.535296i \(0.179800\pi\)
−0.844664 + 0.535296i \(0.820200\pi\)
\(242\) 13.5054 + 13.5054i 0.868158 + 0.868158i
\(243\) 0.707107 + 0.707107i 0.0453609 + 0.0453609i
\(244\) 1.17166 0.0750079
\(245\) 0 0
\(246\) 2.50597 0.159775
\(247\) −16.9069 16.9069i −1.07576 1.07576i
\(248\) −3.94312 3.94312i −0.250388 0.250388i
\(249\) 5.73154i 0.363222i
\(250\) 4.20920 + 10.3577i 0.266213 + 0.655081i
\(251\) 10.7660i 0.679546i 0.940508 + 0.339773i \(0.110350\pi\)
−0.940508 + 0.339773i \(0.889650\pi\)
\(252\) 0 0
\(253\) −6.80597 + 6.80597i −0.427888 + 0.427888i
\(254\) 6.74657i 0.423317i
\(255\) 2.89181 3.75130i 0.181092 0.234915i
\(256\) 1.00000 0.0625000
\(257\) −10.6366 + 10.6366i −0.663495 + 0.663495i −0.956202 0.292707i \(-0.905444\pi\)
0.292707 + 0.956202i \(0.405444\pi\)
\(258\) 1.95305 + 1.95305i 0.121591 + 0.121591i
\(259\) 0 0
\(260\) −0.980578 7.57904i −0.0608128 0.470032i
\(261\) −0.684610 −0.0423763
\(262\) 12.8758 12.8758i 0.795468 0.795468i
\(263\) 15.9321 15.9321i 0.982418 0.982418i −0.0174300 0.999848i \(-0.505548\pi\)
0.999848 + 0.0174300i \(0.00554843\pi\)
\(264\) 5.48630 0.337658
\(265\) −2.69766 20.8507i −0.165716 1.28085i
\(266\) 0 0
\(267\) 5.07954 + 5.07954i 0.310863 + 0.310863i
\(268\) −7.03792 + 7.03792i −0.429910 + 0.429910i
\(269\) 11.0424 0.673270 0.336635 0.941635i \(-0.390711\pi\)
0.336635 + 0.941635i \(0.390711\pi\)
\(270\) −1.36519 + 1.77095i −0.0830829 + 0.107776i
\(271\) 5.01640i 0.304724i −0.988325 0.152362i \(-0.951312\pi\)
0.988325 0.152362i \(-0.0486880\pi\)
\(272\) −1.49783 + 1.49783i −0.0908190 + 0.0908190i
\(273\) 0 0
\(274\) 2.18468i 0.131982i
\(275\) −6.98132 26.5283i −0.420990 1.59971i
\(276\) 1.75439i 0.105602i
\(277\) 4.47957 + 4.47957i 0.269151 + 0.269151i 0.828758 0.559607i \(-0.189048\pi\)
−0.559607 + 0.828758i \(0.689048\pi\)
\(278\) 12.8302 + 12.8302i 0.769501 + 0.769501i
\(279\) −5.57642 −0.333851
\(280\) 0 0
\(281\) −29.4723 −1.75817 −0.879085 0.476665i \(-0.841846\pi\)
−0.879085 + 0.476665i \(0.841846\pi\)
\(282\) 2.49268 + 2.49268i 0.148437 + 0.148437i
\(283\) −0.0691733 0.0691733i −0.00411193 0.00411193i 0.705048 0.709160i \(-0.250926\pi\)
−0.709160 + 0.705048i \(0.750926\pi\)
\(284\) 11.9716i 0.710383i
\(285\) −15.5141 + 2.00721i −0.918974 + 0.118897i
\(286\) 18.7505i 1.10874i
\(287\) 0 0
\(288\) 0.707107 0.707107i 0.0416667 0.0416667i
\(289\) 12.5130i 0.736061i
\(290\) −0.196422 1.51818i −0.0115343 0.0891506i
\(291\) −18.5562 −1.08778
\(292\) −3.44417 + 3.44417i −0.201555 + 0.201555i
\(293\) 14.0076 + 14.0076i 0.818330 + 0.818330i 0.985866 0.167536i \(-0.0535810\pi\)
−0.167536 + 0.985866i \(0.553581\pi\)
\(294\) 0 0
\(295\) 13.8708 17.9933i 0.807587 1.04761i
\(296\) −9.80013 −0.569621
\(297\) 3.87940 3.87940i 0.225106 0.225106i
\(298\) 0.136935 0.136935i 0.00793245 0.00793245i
\(299\) −5.99597 −0.346756
\(300\) −4.31891 2.51932i −0.249353 0.145453i
\(301\) 0 0
\(302\) −15.0775 15.0775i −0.867610 0.867610i
\(303\) 5.84612 5.84612i 0.335851 0.335851i
\(304\) 6.99593 0.401244
\(305\) 2.07495 + 1.59954i 0.118811 + 0.0915895i
\(306\) 2.11825i 0.121092i
\(307\) 3.05320 3.05320i 0.174255 0.174255i −0.614591 0.788846i \(-0.710679\pi\)
0.788846 + 0.614591i \(0.210679\pi\)
\(308\) 0 0
\(309\) 9.30620i 0.529411i
\(310\) −1.59994 12.3662i −0.0908704 0.702351i
\(311\) 8.44532i 0.478890i −0.970910 0.239445i \(-0.923035\pi\)
0.970910 0.239445i \(-0.0769655\pi\)
\(312\) 2.41668 + 2.41668i 0.136817 + 0.136817i
\(313\) 13.7247 + 13.7247i 0.775764 + 0.775764i 0.979107 0.203343i \(-0.0651808\pi\)
−0.203343 + 0.979107i \(0.565181\pi\)
\(314\) 3.68003 0.207676
\(315\) 0 0
\(316\) −8.33087 −0.468648
\(317\) −10.9957 10.9957i −0.617581 0.617581i 0.327329 0.944910i \(-0.393851\pi\)
−0.944910 + 0.327329i \(0.893851\pi\)
\(318\) 6.64852 + 6.64852i 0.372830 + 0.372830i
\(319\) 3.75597i 0.210294i
\(320\) 1.77095 + 1.36519i 0.0989989 + 0.0763166i
\(321\) 12.2677i 0.684714i
\(322\) 0 0
\(323\) −10.4787 + 10.4787i −0.583050 + 0.583050i
\(324\) 1.00000i 0.0555556i
\(325\) 8.61029 14.7607i 0.477613 0.818779i
\(326\) −14.0810 −0.779874
\(327\) 0.238027 0.238027i 0.0131629 0.0131629i
\(328\) −1.77199 1.77199i −0.0978416 0.0978416i
\(329\) 0 0
\(330\) 9.71594 + 7.48985i 0.534845 + 0.412303i
\(331\) 16.1859 0.889659 0.444830 0.895615i \(-0.353264\pi\)
0.444830 + 0.895615i \(0.353264\pi\)
\(332\) −4.05281 + 4.05281i −0.222427 + 0.222427i
\(333\) −6.92974 + 6.92974i −0.379747 + 0.379747i
\(334\) −8.58794 −0.469911
\(335\) −22.0719 + 2.85567i −1.20592 + 0.156022i
\(336\) 0 0
\(337\) 19.2055 + 19.2055i 1.04619 + 1.04619i 0.998880 + 0.0473073i \(0.0150640\pi\)
0.0473073 + 0.998880i \(0.484936\pi\)
\(338\) 0.932908 0.932908i 0.0507435 0.0507435i
\(339\) −14.4102 −0.782657
\(340\) −4.69739 + 0.607749i −0.254752 + 0.0329598i
\(341\) 30.5939i 1.65675i
\(342\) 4.94687 4.94687i 0.267496 0.267496i
\(343\) 0 0
\(344\) 2.76202i 0.148918i
\(345\) −2.39508 + 3.10693i −0.128947 + 0.167271i
\(346\) 4.04905i 0.217678i
\(347\) 7.25896 + 7.25896i 0.389681 + 0.389681i 0.874574 0.484892i \(-0.161141\pi\)
−0.484892 + 0.874574i \(0.661141\pi\)
\(348\) 0.484092 + 0.484092i 0.0259501 + 0.0259501i
\(349\) −6.61441 −0.354061 −0.177031 0.984205i \(-0.556649\pi\)
−0.177031 + 0.984205i \(0.556649\pi\)
\(350\) 0 0
\(351\) 3.41770 0.182423
\(352\) −3.87940 3.87940i −0.206773 0.206773i
\(353\) 9.63411 + 9.63411i 0.512772 + 0.512772i 0.915375 0.402603i \(-0.131894\pi\)
−0.402603 + 0.915375i \(0.631894\pi\)
\(354\) 10.1603i 0.540014i
\(355\) 16.3435 21.2010i 0.867423 1.12523i
\(356\) 7.18356i 0.380728i
\(357\) 0 0
\(358\) 2.59178 2.59178i 0.136980 0.136980i
\(359\) 17.2964i 0.912871i −0.889757 0.456435i \(-0.849126\pi\)
0.889757 0.456435i \(-0.150874\pi\)
\(360\) 2.21758 0.286912i 0.116877 0.0151216i
\(361\) 29.9431 1.57595
\(362\) 1.69695 1.69695i 0.0891896 0.0891896i
\(363\) −13.5054 13.5054i −0.708848 0.708848i
\(364\) 0 0
\(365\) −10.8014 + 1.39749i −0.565370 + 0.0731477i
\(366\) −1.17166 −0.0612437
\(367\) 18.3007 18.3007i 0.955288 0.955288i −0.0437539 0.999042i \(-0.513932\pi\)
0.999042 + 0.0437539i \(0.0139317\pi\)
\(368\) 1.24054 1.24054i 0.0646676 0.0646676i
\(369\) −2.50597 −0.130455
\(370\) −17.3555 13.3791i −0.902270 0.695544i
\(371\) 0 0
\(372\) 3.94312 + 3.94312i 0.204441 + 0.204441i
\(373\) 6.48161 6.48161i 0.335605 0.335605i −0.519105 0.854710i \(-0.673735\pi\)
0.854710 + 0.519105i \(0.173735\pi\)
\(374\) 11.6213 0.600925
\(375\) −4.20920 10.3577i −0.217362 0.534871i
\(376\) 3.52518i 0.181797i
\(377\) −1.65448 + 1.65448i −0.0852101 + 0.0852101i
\(378\) 0 0
\(379\) 18.6871i 0.959891i −0.877298 0.479946i \(-0.840656\pi\)
0.877298 0.479946i \(-0.159344\pi\)
\(380\) 12.3894 + 9.55079i 0.635564 + 0.489945i
\(381\) 6.74657i 0.345637i
\(382\) 5.71012 + 5.71012i 0.292155 + 0.292155i
\(383\) 14.0300 + 14.0300i 0.716900 + 0.716900i 0.967969 0.251069i \(-0.0807820\pi\)
−0.251069 + 0.967969i \(0.580782\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −1.72252 −0.0876740
\(387\) −1.95305 1.95305i −0.0992789 0.0992789i
\(388\) 13.1212 + 13.1212i 0.666128 + 0.666128i
\(389\) 5.12717i 0.259958i 0.991517 + 0.129979i \(0.0414910\pi\)
−0.991517 + 0.129979i \(0.958509\pi\)
\(390\) 0.980578 + 7.57904i 0.0496535 + 0.383779i
\(391\) 3.71623i 0.187938i
\(392\) 0 0
\(393\) −12.8758 + 12.8758i −0.649497 + 0.649497i
\(394\) 8.50188i 0.428319i
\(395\) −14.7535 11.3732i −0.742330 0.572249i
\(396\) −5.48630 −0.275697
\(397\) 18.6630 18.6630i 0.936668 0.936668i −0.0614422 0.998111i \(-0.519570\pi\)
0.998111 + 0.0614422i \(0.0195700\pi\)
\(398\) 7.79086 + 7.79086i 0.390520 + 0.390520i
\(399\) 0 0
\(400\) 1.27250 + 4.83536i 0.0636251 + 0.241768i
\(401\) −17.2294 −0.860396 −0.430198 0.902735i \(-0.641556\pi\)
−0.430198 + 0.902735i \(0.641556\pi\)
\(402\) 7.03792 7.03792i 0.351020 0.351020i
\(403\) −13.4764 + 13.4764i −0.671307 + 0.671307i
\(404\) −8.26766 −0.411332
\(405\) 1.36519 1.77095i 0.0678369 0.0879990i
\(406\) 0 0
\(407\) 38.0186 + 38.0186i 1.88451 + 1.88451i
\(408\) 1.49783 1.49783i 0.0741534 0.0741534i
\(409\) −35.7138 −1.76593 −0.882967 0.469436i \(-0.844457\pi\)
−0.882967 + 0.469436i \(0.844457\pi\)
\(410\) −0.718991 5.55719i −0.0355084 0.274450i
\(411\) 2.18468i 0.107763i
\(412\) −6.58048 + 6.58048i −0.324197 + 0.324197i
\(413\) 0 0
\(414\) 1.75439i 0.0862235i
\(415\) −12.7102 + 1.64445i −0.623918 + 0.0807227i
\(416\) 3.41770i 0.167566i
\(417\) −12.8302 12.8302i −0.628295 0.628295i
\(418\) −27.1400 27.1400i −1.32746 1.32746i
\(419\) −14.0414 −0.685966 −0.342983 0.939342i \(-0.611437\pi\)
−0.342983 + 0.939342i \(0.611437\pi\)
\(420\) 0 0
\(421\) 24.4332 1.19080 0.595401 0.803429i \(-0.296993\pi\)
0.595401 + 0.803429i \(0.296993\pi\)
\(422\) 7.30601 + 7.30601i 0.355651 + 0.355651i
\(423\) −2.49268 2.49268i −0.121198 0.121198i
\(424\) 9.40242i 0.456622i
\(425\) −9.14852 5.33655i −0.443768 0.258861i
\(426\) 11.9716i 0.580025i
\(427\) 0 0
\(428\) 8.67454 8.67454i 0.419300 0.419300i
\(429\) 18.7505i 0.905284i
\(430\) 3.77069 4.89140i 0.181839 0.235884i
\(431\) −38.7771 −1.86783 −0.933914 0.357498i \(-0.883630\pi\)
−0.933914 + 0.357498i \(0.883630\pi\)
\(432\) −0.707107 + 0.707107i −0.0340207 + 0.0340207i
\(433\) 7.85700 + 7.85700i 0.377583 + 0.377583i 0.870230 0.492646i \(-0.163970\pi\)
−0.492646 + 0.870230i \(0.663970\pi\)
\(434\) 0 0
\(435\) 0.196422 + 1.51818i 0.00941774 + 0.0727911i
\(436\) −0.336622 −0.0161213
\(437\) 8.67874 8.67874i 0.415160 0.415160i
\(438\) 3.44417 3.44417i 0.164569 0.164569i
\(439\) 21.1279 1.00838 0.504190 0.863593i \(-0.331791\pi\)
0.504190 + 0.863593i \(0.331791\pi\)
\(440\) −1.57408 12.1663i −0.0750415 0.580007i
\(441\) 0 0
\(442\) 5.11912 + 5.11912i 0.243492 + 0.243492i
\(443\) 4.74580 4.74580i 0.225480 0.225480i −0.585321 0.810801i \(-0.699032\pi\)
0.810801 + 0.585321i \(0.199032\pi\)
\(444\) 9.80013 0.465094
\(445\) 9.80694 12.7217i 0.464894 0.603066i
\(446\) 4.82505i 0.228473i
\(447\) −0.136935 + 0.136935i −0.00647682 + 0.00647682i
\(448\) 0 0
\(449\) 8.28979i 0.391219i 0.980682 + 0.195610i \(0.0626685\pi\)
−0.980682 + 0.195610i \(0.937331\pi\)
\(450\) 4.31891 + 2.51932i 0.203596 + 0.118762i
\(451\) 13.7485i 0.647391i
\(452\) 10.1896 + 10.1896i 0.479277 + 0.479277i
\(453\) 15.0775 + 15.0775i 0.708401 + 0.708401i
\(454\) 18.0938 0.849182
\(455\) 0 0
\(456\) −6.99593 −0.327615
\(457\) 15.6143 + 15.6143i 0.730407 + 0.730407i 0.970700 0.240293i \(-0.0772436\pi\)
−0.240293 + 0.970700i \(0.577244\pi\)
\(458\) 6.82181 + 6.82181i 0.318762 + 0.318762i
\(459\) 2.11825i 0.0988712i
\(460\) 3.89051 0.503355i 0.181396 0.0234690i
\(461\) 19.0130i 0.885524i −0.896639 0.442762i \(-0.853999\pi\)
0.896639 0.442762i \(-0.146001\pi\)
\(462\) 0 0
\(463\) −16.6091 + 16.6091i −0.771891 + 0.771891i −0.978437 0.206546i \(-0.933778\pi\)
0.206546 + 0.978437i \(0.433778\pi\)
\(464\) 0.684610i 0.0317822i
\(465\) 1.59994 + 12.3662i 0.0741954 + 0.573468i
\(466\) 14.4733 0.670463
\(467\) 11.3062 11.3062i 0.523190 0.523190i −0.395343 0.918533i \(-0.629374\pi\)
0.918533 + 0.395343i \(0.129374\pi\)
\(468\) −2.41668 2.41668i −0.111711 0.111711i
\(469\) 0 0
\(470\) 4.81254 6.24290i 0.221986 0.287963i
\(471\) −3.68003 −0.169567
\(472\) 7.18441 7.18441i 0.330689 0.330689i
\(473\) −10.7150 + 10.7150i −0.492676 + 0.492676i
\(474\) 8.33087 0.382649
\(475\) 8.90234 + 33.8279i 0.408467 + 1.55213i
\(476\) 0 0
\(477\) −6.64852 6.64852i −0.304415 0.304415i
\(478\) 21.1945 21.1945i 0.969415 0.969415i
\(479\) 9.01051 0.411701 0.205850 0.978583i \(-0.434004\pi\)
0.205850 + 0.978583i \(0.434004\pi\)
\(480\) −1.77095 1.36519i −0.0808323 0.0623122i
\(481\) 33.4939i 1.52719i
\(482\) −11.7522 + 11.7522i −0.535296 + 0.535296i
\(483\) 0 0
\(484\) 19.0995i 0.868158i
\(485\) 5.32399 + 41.1499i 0.241750 + 1.86852i
\(486\) 1.00000i 0.0453609i
\(487\) 6.60446 + 6.60446i 0.299277 + 0.299277i 0.840731 0.541454i \(-0.182126\pi\)
−0.541454 + 0.840731i \(0.682126\pi\)
\(488\) 0.828489 + 0.828489i 0.0375039 + 0.0375039i
\(489\) 14.0810 0.636764
\(490\) 0 0
\(491\) 2.08535 0.0941107 0.0470554 0.998892i \(-0.485016\pi\)
0.0470554 + 0.998892i \(0.485016\pi\)
\(492\) 1.77199 + 1.77199i 0.0798873 + 0.0798873i
\(493\) 1.02543 + 1.02543i 0.0461829 + 0.0461829i
\(494\) 23.9100i 1.07576i
\(495\) −9.71594 7.48985i −0.436699 0.336644i
\(496\) 5.57642i 0.250388i
\(497\) 0 0
\(498\) 4.05281 4.05281i 0.181611 0.181611i
\(499\) 13.4246i 0.600966i −0.953787 0.300483i \(-0.902852\pi\)
0.953787 0.300483i \(-0.0971479\pi\)
\(500\) −4.34767 + 10.3004i −0.194434 + 0.460647i
\(501\) 8.58794 0.383681
\(502\) −7.61273 + 7.61273i −0.339773 + 0.339773i
\(503\) 7.19669 + 7.19669i 0.320885 + 0.320885i 0.849106 0.528222i \(-0.177141\pi\)
−0.528222 + 0.849106i \(0.677141\pi\)
\(504\) 0 0
\(505\) −14.6416 11.2869i −0.651542 0.502263i
\(506\) −9.62510 −0.427888
\(507\) −0.932908 + 0.932908i −0.0414319 + 0.0414319i
\(508\) 4.77054 4.77054i 0.211659 0.211659i
\(509\) 4.28156 0.189777 0.0948884 0.995488i \(-0.469751\pi\)
0.0948884 + 0.995488i \(0.469751\pi\)
\(510\) 4.69739 0.607749i 0.208004 0.0269116i
\(511\) 0 0
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) −4.94687 + 4.94687i −0.218410 + 0.218410i
\(514\) −15.0425 −0.663495
\(515\) −20.6373 + 2.67006i −0.909388 + 0.117657i
\(516\) 2.76202i 0.121591i
\(517\) −13.6756 + 13.6756i −0.601451 + 0.601451i
\(518\) 0 0
\(519\) 4.04905i 0.177733i
\(520\) 4.66582 6.05256i 0.204610 0.265422i
\(521\) 14.5754i 0.638558i −0.947661 0.319279i \(-0.896559\pi\)
0.947661 0.319279i \(-0.103441\pi\)
\(522\) −0.484092 0.484092i −0.0211881 0.0211881i
\(523\) −26.9324 26.9324i −1.17767 1.17767i −0.980336 0.197336i \(-0.936771\pi\)
−0.197336 0.980336i \(-0.563229\pi\)
\(524\) 18.2091 0.795468
\(525\) 0 0
\(526\) 22.5315 0.982418
\(527\) 8.35250 + 8.35250i 0.363841 + 0.363841i
\(528\) 3.87940 + 3.87940i 0.168829 + 0.168829i
\(529\) 19.9221i 0.866179i
\(530\) 12.8361 16.6512i 0.557565 0.723281i
\(531\) 10.1603i 0.440919i
\(532\) 0 0
\(533\) −6.05612 + 6.05612i −0.262319 + 0.262319i
\(534\) 7.18356i 0.310863i
\(535\) 27.2046 3.51973i 1.17616 0.152171i
\(536\) −9.95313 −0.429910
\(537\) −2.59178 + 2.59178i −0.111844 + 0.111844i
\(538\) 7.80819 + 7.80819i 0.336635 + 0.336635i
\(539\) 0 0
\(540\) −2.21758 + 0.286912i −0.0954296 + 0.0123467i
\(541\) 16.8603 0.724882 0.362441 0.932007i \(-0.381944\pi\)
0.362441 + 0.932007i \(0.381944\pi\)
\(542\) 3.54713 3.54713i 0.152362 0.152362i
\(543\) −1.69695 + 1.69695i −0.0728230 + 0.0728230i
\(544\) −2.11825 −0.0908190
\(545\) −0.596139 0.459553i −0.0255358 0.0196851i
\(546\) 0 0
\(547\) −2.04444 2.04444i −0.0874141 0.0874141i 0.662048 0.749462i \(-0.269688\pi\)
−0.749462 + 0.662048i \(0.769688\pi\)
\(548\) −1.54481 + 1.54481i −0.0659908 + 0.0659908i
\(549\) 1.17166 0.0500052
\(550\) 13.8218 23.6948i 0.589362 1.01035i
\(551\) 4.78948i 0.204039i
\(552\) −1.24054 + 1.24054i −0.0528009 + 0.0528009i
\(553\) 0 0
\(554\) 6.33506i 0.269151i
\(555\) 17.3555 + 13.3791i 0.736700 + 0.567910i
\(556\) 18.1446i 0.769501i
\(557\) 2.95885 + 2.95885i 0.125371 + 0.125371i 0.767008 0.641637i \(-0.221745\pi\)
−0.641637 + 0.767008i \(0.721745\pi\)
\(558\) −3.94312 3.94312i −0.166926 0.166926i
\(559\) −9.43977 −0.399260
\(560\) 0 0
\(561\) −11.6213 −0.490653
\(562\) −20.8401 20.8401i −0.879085 0.879085i
\(563\) 17.7096 + 17.7096i 0.746372 + 0.746372i 0.973796 0.227424i \(-0.0730304\pi\)
−0.227424 + 0.973796i \(0.573030\pi\)
\(564\) 3.52518i 0.148437i
\(565\) 4.13447 + 31.9559i 0.173938 + 1.34440i
\(566\) 0.0978259i 0.00411193i
\(567\) 0 0
\(568\) 8.46519 8.46519i 0.355191 0.355191i
\(569\) 2.30741i 0.0967316i −0.998830 0.0483658i \(-0.984599\pi\)
0.998830 0.0483658i \(-0.0154013\pi\)
\(570\) −12.3894 9.55079i −0.518936 0.400039i
\(571\) 15.8865 0.664830 0.332415 0.943133i \(-0.392137\pi\)
0.332415 + 0.943133i \(0.392137\pi\)
\(572\) −13.2586 + 13.2586i −0.554371 + 0.554371i
\(573\) −5.71012 5.71012i −0.238544 0.238544i
\(574\) 0 0
\(575\) 7.57705 + 4.41987i 0.315985 + 0.184321i
\(576\) 1.00000 0.0416667
\(577\) −2.82904 + 2.82904i −0.117774 + 0.117774i −0.763538 0.645763i \(-0.776539\pi\)
0.645763 + 0.763538i \(0.276539\pi\)
\(578\) −8.84805 + 8.84805i −0.368030 + 0.368030i
\(579\) 1.72252 0.0715855
\(580\) 0.934623 1.21241i 0.0388081 0.0503425i
\(581\) 0 0
\(582\) −13.1212 13.1212i −0.543891 0.543891i
\(583\) −36.4757 + 36.4757i −1.51067 + 1.51067i
\(584\) −4.87079 −0.201555
\(585\) −0.980578 7.57904i −0.0405419 0.313355i
\(586\) 19.8097i 0.818330i
\(587\) 5.31785 5.31785i 0.219491 0.219491i −0.588793 0.808284i \(-0.700397\pi\)
0.808284 + 0.588793i \(0.200397\pi\)
\(588\) 0 0
\(589\) 39.0122i 1.60747i
\(590\) 22.5313 2.91511i 0.927600 0.120013i
\(591\) 8.50188i 0.349721i
\(592\) −6.92974 6.92974i −0.284811 0.284811i
\(593\) −12.5171 12.5171i −0.514014 0.514014i 0.401740 0.915754i \(-0.368406\pi\)
−0.915754 + 0.401740i \(0.868406\pi\)
\(594\) 5.48630 0.225106
\(595\) 0 0
\(596\) 0.193656 0.00793245
\(597\) −7.79086 7.79086i −0.318858 0.318858i
\(598\) −4.23979 4.23979i −0.173378 0.173378i
\(599\) 31.2892i 1.27844i 0.769024 + 0.639220i \(0.220743\pi\)
−0.769024 + 0.639220i \(0.779257\pi\)
\(600\) −1.27250 4.83536i −0.0519497 0.197403i
\(601\) 47.5637i 1.94016i −0.242776 0.970082i \(-0.578058\pi\)
0.242776 0.970082i \(-0.421942\pi\)
\(602\) 0 0
\(603\) −7.03792 + 7.03792i −0.286606 + 0.286606i
\(604\) 21.3227i 0.867610i
\(605\) −26.0745 + 33.8242i −1.06008 + 1.37515i
\(606\) 8.26766 0.335851
\(607\) 17.3556 17.3556i 0.704443 0.704443i −0.260918 0.965361i \(-0.584025\pi\)
0.965361 + 0.260918i \(0.0840253\pi\)
\(608\) 4.94687 + 4.94687i 0.200622 + 0.200622i
\(609\) 0 0
\(610\) 0.336163 + 2.59826i 0.0136108 + 0.105200i
\(611\) −12.0480 −0.487410
\(612\) −1.49783 + 1.49783i −0.0605460 + 0.0605460i
\(613\) −19.6837 + 19.6837i −0.795016 + 0.795016i −0.982305 0.187289i \(-0.940030\pi\)
0.187289 + 0.982305i \(0.440030\pi\)
\(614\) 4.31788 0.174255
\(615\) 0.718991 + 5.55719i 0.0289925 + 0.224088i
\(616\) 0 0
\(617\) −24.4884 24.4884i −0.985865 0.985865i 0.0140365 0.999901i \(-0.495532\pi\)
−0.999901 + 0.0140365i \(0.995532\pi\)
\(618\) 6.58048 6.58048i 0.264706 0.264706i
\(619\) −31.8275 −1.27925 −0.639627 0.768686i \(-0.720911\pi\)
−0.639627 + 0.768686i \(0.720911\pi\)
\(620\) 7.61288 9.87553i 0.305741 0.396611i
\(621\) 1.75439i 0.0704012i
\(622\) 5.97174 5.97174i 0.239445 0.239445i
\(623\) 0 0
\(624\) 3.41770i 0.136817i
\(625\) −21.7615 + 12.3060i −0.870459 + 0.492241i
\(626\) 19.4096i 0.775764i
\(627\) 27.1400 + 27.1400i 1.08387 + 1.08387i
\(628\) 2.60217 + 2.60217i 0.103838 + 0.103838i
\(629\) 20.7591 0.827719
\(630\) 0 0
\(631\) −34.9471 −1.39122 −0.695610 0.718419i \(-0.744866\pi\)
−0.695610 + 0.718419i \(0.744866\pi\)
\(632\) −5.89081 5.89081i −0.234324 0.234324i
\(633\) −7.30601 7.30601i −0.290388 0.290388i
\(634\) 15.5503i 0.617581i
\(635\) 14.9611 1.93567i 0.593713 0.0768147i
\(636\) 9.40242i 0.372830i
\(637\) 0 0
\(638\) −2.65587 + 2.65587i −0.105147 + 0.105147i
\(639\) 11.9716i 0.473589i
\(640\) 0.286912 + 2.21758i 0.0113412 + 0.0876577i
\(641\) −11.2298 −0.443549 −0.221774 0.975098i \(-0.571185\pi\)
−0.221774 + 0.975098i \(0.571185\pi\)
\(642\) −8.67454 + 8.67454i −0.342357 + 0.342357i
\(643\) −9.89036 9.89036i −0.390038 0.390038i 0.484663 0.874701i \(-0.338942\pi\)
−0.874701 + 0.484663i \(0.838942\pi\)
\(644\) 0 0
\(645\) −3.77069 + 4.89140i −0.148471 + 0.192599i
\(646\) −14.8191 −0.583050
\(647\) −11.0962 + 11.0962i −0.436235 + 0.436235i −0.890743 0.454508i \(-0.849815\pi\)
0.454508 + 0.890743i \(0.349815\pi\)
\(648\) 0.707107 0.707107i 0.0277778 0.0277778i
\(649\) −55.7424 −2.18808
\(650\) 16.5258 4.34903i 0.648196 0.170583i
\(651\) 0 0
\(652\) −9.95676 9.95676i −0.389937 0.389937i
\(653\) 11.2769 11.2769i 0.441297 0.441297i −0.451151 0.892448i \(-0.648986\pi\)
0.892448 + 0.451151i \(0.148986\pi\)
\(654\) 0.336622 0.0131629
\(655\) 32.2473 + 24.8589i 1.26001 + 0.971318i
\(656\) 2.50597i 0.0978416i
\(657\) −3.44417 + 3.44417i −0.134370 + 0.134370i
\(658\) 0 0
\(659\) 10.4778i 0.408157i −0.978955 0.204078i \(-0.934580\pi\)
0.978955 0.204078i \(-0.0654198\pi\)
\(660\) 1.57408 + 12.1663i 0.0612711 + 0.473574i
\(661\) 24.2215i 0.942106i −0.882105 0.471053i \(-0.843874\pi\)
0.882105 0.471053i \(-0.156126\pi\)
\(662\) 11.4452 + 11.4452i 0.444830 + 0.444830i
\(663\) −5.11912 5.11912i −0.198810 0.198810i
\(664\) −5.73154 −0.222427
\(665\) 0 0
\(666\) −9.80013 −0.379747
\(667\) −0.849286 0.849286i −0.0328845 0.0328845i
\(668\) −6.07259 6.07259i −0.234956 0.234956i
\(669\) 4.82505i 0.186547i
\(670\) −17.6265 13.5879i −0.680969 0.524948i
\(671\) 6.42808i 0.248153i
\(672\) 0 0
\(673\) −1.16725 + 1.16725i −0.0449943 + 0.0449943i −0.729246 0.684252i \(-0.760129\pi\)
0.684252 + 0.729246i \(0.260129\pi\)
\(674\) 27.1606i 1.04619i
\(675\) −4.31891 2.51932i −0.166235 0.0969688i
\(676\) 1.31933 0.0507435
\(677\) −9.07752 + 9.07752i −0.348877 + 0.348877i −0.859691 0.510814i \(-0.829344\pi\)
0.510814 + 0.859691i \(0.329344\pi\)
\(678\) −10.1896 10.1896i −0.391328 0.391328i
\(679\) 0 0
\(680\) −3.75130 2.89181i −0.143856 0.110896i
\(681\) −18.0938 −0.693354
\(682\) −21.6331 + 21.6331i −0.828376 + 0.828376i
\(683\) 15.1075 15.1075i 0.578073 0.578073i −0.356299 0.934372i \(-0.615962\pi\)
0.934372 + 0.356299i \(0.115962\pi\)
\(684\) 6.99593 0.267496
\(685\) −4.84472 + 0.626811i −0.185107 + 0.0239492i
\(686\) 0 0
\(687\) −6.82181 6.82181i −0.260268 0.260268i
\(688\) 1.95305 1.95305i 0.0744592 0.0744592i
\(689\) −32.1346 −1.22423
\(690\) −3.89051 + 0.503355i −0.148109 + 0.0191624i
\(691\) 42.7386i 1.62585i 0.582365 + 0.812927i \(0.302127\pi\)
−0.582365 + 0.812927i \(0.697873\pi\)
\(692\) −2.86311 + 2.86311i −0.108839 + 0.108839i
\(693\) 0 0
\(694\) 10.2657i 0.389681i
\(695\) −24.7708 + 32.1331i −0.939611 + 1.21888i
\(696\) 0.684610i 0.0259501i
\(697\) 3.75350 + 3.75350i 0.142174 + 0.142174i
\(698\) −4.67709 4.67709i −0.177031 0.177031i
\(699\) −14.4733 −0.547431
\(700\) 0 0
\(701\) 44.5959 1.68436 0.842182 0.539194i \(-0.181271\pi\)
0.842182 + 0.539194i \(0.181271\pi\)
\(702\) 2.41668 + 2.41668i 0.0912116 + 0.0912116i
\(703\) −48.4800 48.4800i −1.82846 1.82846i
\(704\) 5.48630i 0.206773i
\(705\) −4.81254 + 6.24290i −0.181251 + 0.235121i
\(706\) 13.6247i 0.512772i
\(707\) 0 0
\(708\) −7.18441 + 7.18441i −0.270007 + 0.270007i
\(709\) 41.4249i 1.55575i 0.628422 + 0.777873i \(0.283701\pi\)
−0.628422 + 0.777873i \(0.716299\pi\)
\(710\) 26.5480 3.43479i 0.996329 0.128905i
\(711\) −8.33087 −0.312432
\(712\) 5.07954 5.07954i 0.190364 0.190364i
\(713\) −6.91777 6.91777i −0.259072 0.259072i
\(714\) 0 0
\(715\) −41.5809 + 5.37974i −1.55504 + 0.201191i
\(716\) 3.66534 0.136980
\(717\) −21.1945 + 21.1945i −0.791524 + 0.791524i
\(718\) 12.2304 12.2304i 0.456435 0.456435i
\(719\) −23.5677 −0.878928 −0.439464 0.898260i \(-0.644832\pi\)
−0.439464 + 0.898260i \(0.644832\pi\)
\(720\) 1.77095 + 1.36519i 0.0659993 + 0.0508777i
\(721\) 0 0
\(722\) 21.1730 + 21.1730i 0.787976 + 0.787976i
\(723\) 11.7522 11.7522i 0.437068 0.437068i
\(724\) 2.39985 0.0891896
\(725\) 3.31034 0.871167i 0.122943 0.0323543i
\(726\) 19.0995i 0.708848i
\(727\) −3.38556 + 3.38556i −0.125563 + 0.125563i −0.767096 0.641532i \(-0.778299\pi\)
0.641532 + 0.767096i \(0.278299\pi\)
\(728\) 0 0
\(729\) 1.00000i 0.0370370i
\(730\) −8.62590 6.64956i −0.319259 0.246111i
\(731\) 5.85065i 0.216394i
\(732\) −0.828489 0.828489i −0.0306218 0.0306218i
\(733\) −27.7720 27.7720i −1.02578 1.02578i −0.999659 0.0261249i \(-0.991683\pi\)
−0.0261249 0.999659i \(-0.508317\pi\)
\(734\) 25.8811 0.955288
\(735\) 0 0
\(736\) 1.75439 0.0646676
\(737\) 38.6122 + 38.6122i 1.42230 + 1.42230i
\(738\) −1.77199 1.77199i −0.0652277 0.0652277i
\(739\) 44.5958i 1.64048i −0.572016 0.820242i \(-0.693839\pi\)
0.572016 0.820242i \(-0.306161\pi\)
\(740\) −2.81177 21.7326i −0.103363 0.798907i
\(741\) 23.9100i 0.878356i
\(742\) 0 0
\(743\) 24.7787 24.7787i 0.909041 0.909041i −0.0871537 0.996195i \(-0.527777\pi\)
0.996195 + 0.0871537i \(0.0277771\pi\)
\(744\) 5.57642i 0.204441i
\(745\) 0.342954 + 0.264377i 0.0125649 + 0.00968604i
\(746\) 9.16638 0.335605
\(747\) −4.05281 + 4.05281i −0.148285 + 0.148285i
\(748\) 8.21752 + 8.21752i 0.300462 + 0.300462i
\(749\) 0 0
\(750\) 4.34767 10.3004i 0.158754 0.376117i
\(751\) 5.09462 0.185905 0.0929526 0.995671i \(-0.470369\pi\)
0.0929526 + 0.995671i \(0.470369\pi\)
\(752\) 2.49268 2.49268i 0.0908985 0.0908985i
\(753\) 7.61273 7.61273i 0.277423 0.277423i
\(754\) −2.33979 −0.0852101
\(755\) 29.1096 37.7614i 1.05941 1.37428i
\(756\) 0 0
\(757\) 18.2623 + 18.2623i 0.663754 + 0.663754i 0.956263 0.292509i \(-0.0944900\pi\)
−0.292509 + 0.956263i \(0.594490\pi\)
\(758\) 13.2138 13.2138i 0.479946 0.479946i
\(759\) 9.62510 0.349369
\(760\) 2.00721 + 15.5141i 0.0728093 + 0.562755i
\(761\) 28.1315i 1.01976i −0.860244 0.509882i \(-0.829689\pi\)
0.860244 0.509882i \(-0.170311\pi\)
\(762\) −4.77054 + 4.77054i −0.172819 + 0.172819i
\(763\) 0 0
\(764\) 8.07532i 0.292155i
\(765\) −4.69739 + 0.607749i −0.169834 + 0.0219732i
\(766\) 19.8414i 0.716900i
\(767\) −24.5542 24.5542i −0.886600 0.886600i
\(768\) −0.707107 0.707107i −0.0255155 0.0255155i
\(769\) 3.03517 0.109451 0.0547256 0.998501i \(-0.482572\pi\)
0.0547256 + 0.998501i \(0.482572\pi\)
\(770\) 0 0
\(771\) 15.0425 0.541742
\(772\) −1.21801 1.21801i −0.0438370 0.0438370i
\(773\) −34.3021 34.3021i −1.23376 1.23376i −0.962508 0.271253i \(-0.912562\pi\)
−0.271253 0.962508i \(-0.587438\pi\)
\(774\) 2.76202i 0.0992789i
\(775\) 26.9640 7.09600i 0.968575 0.254896i
\(776\) 18.5562i 0.666128i
\(777\) 0 0
\(778\) −3.62546 + 3.62546i −0.129979 + 0.129979i
\(779\) 17.5316i 0.628134i
\(780\) −4.66582 + 6.05256i −0.167063 + 0.216716i
\(781\) −65.6797 −2.35020
\(782\) −2.62777 + 2.62777i −0.0939688 + 0.0939688i
\(783\) 0.484092 + 0.484092i 0.0173000 + 0.0173000i
\(784\) 0 0
\(785\) 1.05584 + 8.16078i 0.0376847 + 0.291271i
\(786\) −18.2091 −0.649497
\(787\) 26.8578 26.8578i 0.957376 0.957376i −0.0417518 0.999128i \(-0.513294\pi\)
0.999128 + 0.0417518i \(0.0132939\pi\)
\(788\) −6.01174 + 6.01174i −0.214159 + 0.214159i
\(789\) −22.5315 −0.802141
\(790\) −2.39022 18.4744i −0.0850403 0.657290i
\(791\) 0 0
\(792\) −3.87940 3.87940i −0.137848 0.137848i
\(793\) 2.83153 2.83153i 0.100550 0.100550i
\(794\) 26.3934 0.936668
\(795\) −12.8361 + 16.6512i −0.455250 + 0.590557i
\(796\) 11.0179i 0.390520i
\(797\) 34.4058 34.4058i 1.21871 1.21871i 0.250632 0.968082i \(-0.419362\pi\)
0.968082 0.250632i \(-0.0806384\pi\)
\(798\) 0 0
\(799\) 7.46719i 0.264170i
\(800\) −2.51932 + 4.31891i −0.0890715 + 0.152697i
\(801\) 7.18356i 0.253819i
\(802\) −12.1830 12.1830i −0.430198 0.430198i
\(803\) 18.8957 + 18.8957i 0.666816 + 0.666816i
\(804\) 9.95313 0.351020
\(805\) 0 0
\(806\) −19.0585 −0.671307
\(807\) −7.80819 7.80819i −0.274861 0.274861i
\(808\) −5.84612 5.84612i −0.205666 0.205666i
\(809\) 38.8636i 1.36637i −0.730244 0.683186i \(-0.760594\pi\)
0.730244 0.683186i \(-0.239406\pi\)
\(810\) 2.21758 0.286912i 0.0779180 0.0100810i
\(811\) 15.3545i 0.539168i −0.962977 0.269584i \(-0.913114\pi\)
0.962977 0.269584i \(-0.0868862\pi\)
\(812\) 0 0
\(813\) −3.54713 + 3.54713i −0.124403 + 0.124403i
\(814\) 53.7665i 1.88451i
\(815\) −4.04000 31.2258i −0.141515 1.09379i
\(816\) 2.11825 0.0741534
\(817\) 13.6634 13.6634i 0.478021 0.478021i
\(818\) −25.2535 25.2535i −0.882967 0.882967i
\(819\) 0 0
\(820\) 3.42113 4.43793i 0.119471 0.154979i
\(821\) 23.9122 0.834542 0.417271 0.908782i \(-0.362987\pi\)
0.417271 + 0.908782i \(0.362987\pi\)
\(822\) 1.54481 1.54481i 0.0538813 0.0538813i
\(823\) −20.0196 + 20.0196i −0.697840 + 0.697840i −0.963944 0.266105i \(-0.914263\pi\)
0.266105 + 0.963944i \(0.414263\pi\)
\(824\) −9.30620 −0.324197
\(825\) −13.8218 + 23.6948i −0.481212 + 0.824949i
\(826\) 0 0
\(827\) 20.7600 + 20.7600i 0.721898 + 0.721898i 0.968992 0.247094i \(-0.0794757\pi\)
−0.247094 + 0.968992i \(0.579476\pi\)
\(828\) 1.24054 1.24054i 0.0431117 0.0431117i
\(829\) −8.28212 −0.287650 −0.143825 0.989603i \(-0.545940\pi\)
−0.143825 + 0.989603i \(0.545940\pi\)
\(830\) −10.1502 7.82465i −0.352320 0.271598i
\(831\) 6.33506i 0.219761i
\(832\) 2.41668 2.41668i 0.0837832 0.0837832i
\(833\) 0 0
\(834\) 18.1446i 0.628295i
\(835\) −2.46398 19.0445i −0.0852696 0.659062i
\(836\) 38.3818i 1.32746i
\(837\) 3.94312 + 3.94312i 0.136294 + 0.136294i
\(838\) −9.92875 9.92875i −0.342983 0.342983i
\(839\) 8.03334 0.277342 0.138671 0.990339i \(-0.455717\pi\)
0.138671 + 0.990339i \(0.455717\pi\)
\(840\) 0 0
\(841\) 28.5313 0.983838
\(842\) 17.2769 + 17.2769i 0.595401 + 0.595401i
\(843\) 20.8401 + 20.8401i 0.717770 + 0.717770i
\(844\) 10.3323i 0.355651i
\(845\) 2.33647 + 1.80114i 0.0803769 + 0.0619611i
\(846\) 3.52518i 0.121198i
\(847\) 0 0
\(848\) 6.64852 6.64852i 0.228311 0.228311i
\(849\) 0.0978259i 0.00335738i
\(850\) −2.69547 10.2425i −0.0924539 0.351314i
\(851\) −17.1932 −0.589377
\(852\) −8.46519 + 8.46519i −0.290013 + 0.290013i
\(853\) 23.8654 + 23.8654i 0.817136 + 0.817136i 0.985692 0.168556i \(-0.0539105\pi\)
−0.168556 + 0.985692i \(0.553911\pi\)
\(854\) 0 0
\(855\) 12.3894 + 9.55079i 0.423709 + 0.326630i
\(856\) 12.2677 0.419300
\(857\) −16.9824 + 16.9824i −0.580107 + 0.580107i −0.934933 0.354826i \(-0.884540\pi\)
0.354826 + 0.934933i \(0.384540\pi\)
\(858\) 13.2586 13.2586i 0.452642 0.452642i
\(859\) 6.52841 0.222747 0.111373 0.993779i \(-0.464475\pi\)
0.111373 + 0.993779i \(0.464475\pi\)
\(860\) 6.12502 0.792457i 0.208862 0.0270226i
\(861\) 0 0
\(862\) −27.4196 27.4196i −0.933914 0.933914i
\(863\) −11.7091 + 11.7091i −0.398582 + 0.398582i −0.877733 0.479151i \(-0.840945\pi\)
0.479151 + 0.877733i \(0.340945\pi\)
\(864\) −1.00000 −0.0340207
\(865\) −8.97910 + 1.16172i −0.305299 + 0.0394996i
\(866\) 11.1115i 0.377583i
\(867\) 8.84805 8.84805i 0.300496 0.300496i
\(868\) 0 0
\(869\) 45.7056i 1.55046i
\(870\) −0.934623 + 1.21241i −0.0316867 + 0.0411044i
\(871\) 34.0168i 1.15262i
\(872\) −0.238027 0.238027i −0.00806063 0.00806063i
\(873\) 13.1212 + 13.1212i 0.444086 + 0.444086i
\(874\) 12.2736 0.415160
\(875\) 0 0
\(876\) 4.87079 0.164569
\(877\) 26.1379 + 26.1379i 0.882613 + 0.882613i 0.993800 0.111186i \(-0.0354651\pi\)
−0.111186 + 0.993800i \(0.535465\pi\)
\(878\) 14.9397 + 14.9397i 0.504190 + 0.504190i
\(879\) 19.8097i 0.668164i
\(880\) 7.48985 9.71594i 0.252483 0.327524i
\(881\) 17.4940i 0.589386i 0.955592 + 0.294693i \(0.0952174\pi\)
−0.955592 + 0.294693i \(0.904783\pi\)
\(882\) 0 0
\(883\) −14.0857 + 14.0857i −0.474022 + 0.474022i −0.903214 0.429191i \(-0.858799\pi\)
0.429191 + 0.903214i \(0.358799\pi\)
\(884\) 7.23953i 0.243492i
\(885\) −22.5313 + 2.91511i −0.757382 + 0.0979902i
\(886\) 6.71158 0.225480
\(887\) −29.0011 + 29.0011i −0.973763 + 0.973763i −0.999664 0.0259017i \(-0.991754\pi\)
0.0259017 + 0.999664i \(0.491754\pi\)
\(888\) 6.92974 + 6.92974i 0.232547 + 0.232547i
\(889\) 0 0
\(890\) 15.9302 2.06105i 0.533980 0.0690865i
\(891\) −5.48630 −0.183798
\(892\) 3.41183 3.41183i 0.114236 0.114236i
\(893\) 17.4386 17.4386i 0.583560 0.583560i
\(894\) −0.193656 −0.00647682
\(895\) 6.49112 + 5.00389i 0.216974 + 0.167262i
\(896\) 0 0
\(897\) 4.23979 + 4.23979i 0.141563 + 0.141563i
\(898\) −5.86176 + 5.86176i −0.195610 + 0.195610i
\(899\) −3.81767 −0.127326
\(900\) 1.27250 + 4.83536i 0.0424167 + 0.161179i
\(901\) 19.9166i 0.663519i
\(902\) −9.72165 + 9.72165i −0.323695 + 0.323695i
\(903\) 0 0
\(904\) 14.4102i 0.479277i
\(905\) 4.25000 + 3.27625i 0.141275 + 0.108906i
\(906\) 21.3227i 0.708401i
\(907\) 14.1293 + 14.1293i 0.469156 + 0.469156i 0.901641 0.432485i \(-0.142363\pi\)
−0.432485 + 0.901641i \(0.642363\pi\)
\(908\) 12.7942 + 12.7942i 0.424591 + 0.424591i
\(909\) −8.26766 −0.274221
\(910\) 0 0
\(911\) −21.3131 −0.706136 −0.353068 0.935598i \(-0.614862\pi\)
−0.353068 + 0.935598i \(0.614862\pi\)
\(912\) −4.94687 4.94687i −0.163807 0.163807i
\(913\) 22.2349 + 22.2349i 0.735869 + 0.735869i
\(914\) 22.0820i 0.730407i
\(915\) −0.336163 2.59826i −0.0111132 0.0858957i
\(916\) 9.64749i 0.318762i
\(917\) 0 0
\(918\) 1.49783 1.49783i 0.0494356 0.0494356i
\(919\) 13.1648i 0.434266i −0.976142 0.217133i \(-0.930330\pi\)
0.976142 0.217133i \(-0.0696705\pi\)
\(920\) 3.10693 + 2.39508i 0.102432 + 0.0789634i
\(921\) −4.31788 −0.142279
\(922\) 13.4442 13.4442i 0.442762 0.442762i
\(923\) −28.9315 28.9315i −0.952291 0.952291i
\(924\) 0 0
\(925\) 24.6897 42.3259i 0.811793 1.39167i
\(926\) −23.4888 −0.771891
\(927\) −6.58048 + 6.58048i −0.216131 + 0.216131i
\(928\) 0.484092 0.484092i 0.0158911 0.0158911i
\(929\) 5.19844 0.170555 0.0852777 0.996357i \(-0.472822\pi\)
0.0852777 + 0.996357i \(0.472822\pi\)
\(930\) −7.61288 + 9.87553i −0.249636 + 0.323831i
\(931\) 0 0
\(932\) 10.2342 + 10.2342i 0.335232 + 0.335232i
\(933\) −5.97174 + 5.97174i −0.195506 + 0.195506i
\(934\) 15.9894 0.523190
\(935\) 3.33429 + 25.7713i 0.109043 + 0.842811i
\(936\) 3.41770i 0.111711i
\(937\) 3.54515 3.54515i 0.115815 0.115815i −0.646824 0.762639i \(-0.723903\pi\)
0.762639 + 0.646824i \(0.223903\pi\)
\(938\) 0 0
\(939\) 19.4096i 0.633409i
\(940\) 7.81738 1.01141i 0.254975 0.0329887i
\(941\) 10.2591i 0.334437i 0.985920 + 0.167219i \(0.0534786\pi\)
−0.985920 + 0.167219i \(0.946521\pi\)
\(942\) −2.60217 2.60217i −0.0847834 0.0847834i
\(943\) −3.10875 3.10875i −0.101235 0.101235i
\(944\) 10.1603 0.330689
\(945\) 0 0
\(946\) −15.1533 −0.492676
\(947\) 19.8496 + 19.8496i 0.645025 + 0.645025i 0.951786 0.306761i \(-0.0992454\pi\)
−0.306761 + 0.951786i \(0.599245\pi\)
\(948\) 5.89081 + 5.89081i 0.191325 + 0.191325i
\(949\) 16.6469i 0.540381i
\(950\) −17.6250 + 30.2148i −0.571831 + 0.980298i
\(951\) 15.5503i 0.504253i
\(952\) 0 0
\(953\) −29.6648 + 29.6648i −0.960937 + 0.960937i −0.999265 0.0383279i \(-0.987797\pi\)
0.0383279 + 0.999265i \(0.487797\pi\)
\(954\) 9.40242i 0.304415i
\(955\) −11.0244 + 14.3010i −0.356740 + 0.462768i
\(956\) 29.9736 0.969415
\(957\) 2.65587 2.65587i 0.0858522 0.0858522i
\(958\) 6.37140 + 6.37140i 0.205850 + 0.205850i
\(959\) 0 0
\(960\) −0.286912 2.21758i −0.00926003 0.0715722i
\(961\) −0.0964085 −0.00310995
\(962\) −23.6838 + 23.6838i −0.763595 + 0.763595i
\(963\) 8.67454 8.67454i 0.279533 0.279533i
\(964\) −16.6201 −0.535296
\(965\) −0.494211 3.81984i −0.0159092 0.122965i
\(966\) 0 0
\(967\) −3.20889 3.20889i −0.103191 0.103191i 0.653626 0.756817i \(-0.273247\pi\)
−0.756817 + 0.653626i \(0.773247\pi\)
\(968\) −13.5054 + 13.5054i −0.434079 + 0.434079i
\(969\) 14.8191 0.476058
\(970\) −25.3328 + 32.8620i −0.813386 + 1.05514i
\(971\) 59.0859i 1.89616i −0.318036 0.948079i \(-0.603023\pi\)
0.318036 0.948079i \(-0.396977\pi\)
\(972\) −0.707107 + 0.707107i −0.0226805 + 0.0226805i
\(973\) 0 0
\(974\) 9.34012i 0.299277i
\(975\) −16.5258 + 4.34903i −0.529250 + 0.139280i
\(976\) 1.17166i 0.0375039i
\(977\) −8.36251 8.36251i −0.267540 0.267540i 0.560568 0.828108i \(-0.310583\pi\)
−0.828108 + 0.560568i \(0.810583\pi\)
\(978\) 9.95676 + 9.95676i 0.318382 + 0.318382i
\(979\) −39.4112 −1.25959
\(980\) 0 0
\(981\) −0.336622 −0.0107475
\(982\) 1.47457 + 1.47457i 0.0470554 + 0.0470554i
\(983\) −26.8714 26.8714i −0.857064 0.857064i 0.133927 0.990991i \(-0.457241\pi\)
−0.990991 + 0.133927i \(0.957241\pi\)
\(984\) 2.50597i 0.0798873i
\(985\) −18.8536 + 2.43929i −0.600727 + 0.0777222i
\(986\) 1.45017i 0.0461829i
\(987\) 0 0
\(988\) 16.9069 16.9069i 0.537881 0.537881i
\(989\) 4.84566i 0.154083i
\(990\) −1.57408 12.1663i −0.0500276 0.386671i
\(991\) 8.01259 0.254528 0.127264 0.991869i \(-0.459380\pi\)
0.127264 + 0.991869i \(0.459380\pi\)
\(992\) 3.94312 3.94312i 0.125194 0.125194i
\(993\) −11.4452 11.4452i −0.363202 0.363202i
\(994\) 0 0
\(995\) −15.0416 + 19.5122i −0.476851 + 0.618577i
\(996\) 5.73154 0.181611
\(997\) −30.0935 + 30.0935i −0.953072 + 0.953072i −0.998947 0.0458749i \(-0.985392\pi\)
0.0458749 + 0.998947i \(0.485392\pi\)
\(998\) 9.49260 9.49260i 0.300483 0.300483i
\(999\) 9.80013 0.310063
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 1470.2.m.d.97.6 16
5.3 odd 4 1470.2.m.e.1273.7 16
7.4 even 3 210.2.u.a.187.1 yes 16
7.5 odd 6 210.2.u.b.157.3 yes 16
7.6 odd 2 1470.2.m.e.97.7 16
21.5 even 6 630.2.bv.b.577.2 16
21.11 odd 6 630.2.bv.a.397.4 16
35.4 even 6 1050.2.bc.h.607.3 16
35.12 even 12 1050.2.bc.h.493.3 16
35.13 even 4 inner 1470.2.m.d.1273.6 16
35.18 odd 12 210.2.u.b.103.3 yes 16
35.19 odd 6 1050.2.bc.g.157.2 16
35.32 odd 12 1050.2.bc.g.943.2 16
35.33 even 12 210.2.u.a.73.1 16
105.53 even 12 630.2.bv.b.523.2 16
105.68 odd 12 630.2.bv.a.73.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.u.a.73.1 16 35.33 even 12
210.2.u.a.187.1 yes 16 7.4 even 3
210.2.u.b.103.3 yes 16 35.18 odd 12
210.2.u.b.157.3 yes 16 7.5 odd 6
630.2.bv.a.73.4 16 105.68 odd 12
630.2.bv.a.397.4 16 21.11 odd 6
630.2.bv.b.523.2 16 105.53 even 12
630.2.bv.b.577.2 16 21.5 even 6
1050.2.bc.g.157.2 16 35.19 odd 6
1050.2.bc.g.943.2 16 35.32 odd 12
1050.2.bc.h.493.3 16 35.12 even 12
1050.2.bc.h.607.3 16 35.4 even 6
1470.2.m.d.97.6 16 1.1 even 1 trivial
1470.2.m.d.1273.6 16 35.13 even 4 inner
1470.2.m.e.97.7 16 7.6 odd 2
1470.2.m.e.1273.7 16 5.3 odd 4