Properties

Label 525.2.g.d.524.6
Level $525$
Weight $2$
Character 525.524
Analytic conductor $4.192$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [525,2,Mod(524,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.524");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.g (of order \(2\), degree \(1\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.303595776.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 524.6
Root \(1.26217 - 1.18614i\) of defining polynomial
Character \(\chi\) \(=\) 525.524
Dual form 525.2.g.d.524.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.792287 q^{2} +(-1.26217 + 1.18614i) q^{3} -1.37228 q^{4} +(-1.00000 + 0.939764i) q^{6} +(1.73205 - 2.00000i) q^{7} -2.67181 q^{8} +(0.186141 - 2.99422i) q^{9} +O(q^{10})\) \(q+0.792287 q^{2} +(-1.26217 + 1.18614i) q^{3} -1.37228 q^{4} +(-1.00000 + 0.939764i) q^{6} +(1.73205 - 2.00000i) q^{7} -2.67181 q^{8} +(0.186141 - 2.99422i) q^{9} -2.52434i q^{11} +(1.73205 - 1.62772i) q^{12} +4.10891 q^{13} +(1.37228 - 1.58457i) q^{14} +0.627719 q^{16} +4.37228i q^{17} +(0.147477 - 2.37228i) q^{18} -3.46410i q^{19} +(0.186141 + 4.57879i) q^{21} -2.00000i q^{22} +8.51278 q^{23} +(3.37228 - 3.16915i) q^{24} +3.25544 q^{26} +(3.31662 + 4.00000i) q^{27} +(-2.37686 + 2.74456i) q^{28} -0.939764i q^{29} -3.46410i q^{31} +5.84096 q^{32} +(2.99422 + 3.18614i) q^{33} +3.46410i q^{34} +(-0.255437 + 4.10891i) q^{36} -6.74456i q^{37} -2.74456i q^{38} +(-5.18614 + 4.87375i) q^{39} -6.00000 q^{41} +(0.147477 + 3.62772i) q^{42} -4.74456i q^{43} +3.46410i q^{44} +6.74456 q^{46} -1.62772i q^{47} +(-0.792287 + 0.744563i) q^{48} +(-1.00000 - 6.92820i) q^{49} +(-5.18614 - 5.51856i) q^{51} -5.63858 q^{52} -1.87953 q^{53} +(2.62772 + 3.16915i) q^{54} +(-4.62772 + 5.34363i) q^{56} +(4.10891 + 4.37228i) q^{57} -0.744563i q^{58} +8.74456 q^{59} -6.92820i q^{61} -2.74456i q^{62} +(-5.66603 - 5.55842i) q^{63} +3.37228 q^{64} +(2.37228 + 2.52434i) q^{66} +4.74456i q^{67} -6.00000i q^{68} +(-10.7446 + 10.0974i) q^{69} +0.294954i q^{71} +(-0.497333 + 8.00000i) q^{72} -6.92820 q^{73} -5.34363i q^{74} +4.75372i q^{76} +(-5.04868 - 4.37228i) q^{77} +(-4.10891 + 3.86141i) q^{78} +2.37228 q^{79} +(-8.93070 - 1.11469i) q^{81} -4.75372 q^{82} +17.4891i q^{83} +(-0.255437 - 6.28339i) q^{84} -3.75906i q^{86} +(1.11469 + 1.18614i) q^{87} +6.74456i q^{88} -14.7446 q^{89} +(7.11684 - 8.21782i) q^{91} -11.6819 q^{92} +(4.10891 + 4.37228i) q^{93} -1.28962i q^{94} +(-7.37228 + 6.92820i) q^{96} -11.0371 q^{97} +(-0.792287 - 5.48913i) q^{98} +(-7.55842 - 0.469882i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 12 q^{4} - 8 q^{6} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 12 q^{4} - 8 q^{6} - 10 q^{9} - 12 q^{14} + 28 q^{16} - 10 q^{21} + 4 q^{24} + 72 q^{26} - 48 q^{36} - 30 q^{39} - 48 q^{41} + 8 q^{46} - 8 q^{49} - 30 q^{51} + 44 q^{54} - 60 q^{56} + 24 q^{59} + 4 q^{64} - 4 q^{66} - 40 q^{69} - 4 q^{79} - 14 q^{81} - 48 q^{84} - 72 q^{89} - 12 q^{91} - 36 q^{96} - 26 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.792287 0.560232 0.280116 0.959966i \(-0.409627\pi\)
0.280116 + 0.959966i \(0.409627\pi\)
\(3\) −1.26217 + 1.18614i −0.728714 + 0.684819i
\(4\) −1.37228 −0.686141
\(5\) 0 0
\(6\) −1.00000 + 0.939764i −0.408248 + 0.383657i
\(7\) 1.73205 2.00000i 0.654654 0.755929i
\(8\) −2.67181 −0.944629
\(9\) 0.186141 2.99422i 0.0620469 0.998073i
\(10\) 0 0
\(11\) 2.52434i 0.761116i −0.924757 0.380558i \(-0.875732\pi\)
0.924757 0.380558i \(-0.124268\pi\)
\(12\) 1.73205 1.62772i 0.500000 0.469882i
\(13\) 4.10891 1.13961 0.569804 0.821781i \(-0.307019\pi\)
0.569804 + 0.821781i \(0.307019\pi\)
\(14\) 1.37228 1.58457i 0.366758 0.423495i
\(15\) 0 0
\(16\) 0.627719 0.156930
\(17\) 4.37228i 1.06043i 0.847862 + 0.530217i \(0.177890\pi\)
−0.847862 + 0.530217i \(0.822110\pi\)
\(18\) 0.147477 2.37228i 0.0347606 0.559152i
\(19\) 3.46410i 0.794719i −0.917663 0.397360i \(-0.869927\pi\)
0.917663 0.397360i \(-0.130073\pi\)
\(20\) 0 0
\(21\) 0.186141 + 4.57879i 0.0406192 + 0.999175i
\(22\) 2.00000i 0.426401i
\(23\) 8.51278 1.77504 0.887518 0.460772i \(-0.152428\pi\)
0.887518 + 0.460772i \(0.152428\pi\)
\(24\) 3.37228 3.16915i 0.688364 0.646900i
\(25\) 0 0
\(26\) 3.25544 0.638444
\(27\) 3.31662 + 4.00000i 0.638285 + 0.769800i
\(28\) −2.37686 + 2.74456i −0.449185 + 0.518674i
\(29\) 0.939764i 0.174510i −0.996186 0.0872549i \(-0.972191\pi\)
0.996186 0.0872549i \(-0.0278095\pi\)
\(30\) 0 0
\(31\) 3.46410i 0.622171i −0.950382 0.311086i \(-0.899307\pi\)
0.950382 0.311086i \(-0.100693\pi\)
\(32\) 5.84096 1.03255
\(33\) 2.99422 + 3.18614i 0.521227 + 0.554636i
\(34\) 3.46410i 0.594089i
\(35\) 0 0
\(36\) −0.255437 + 4.10891i −0.0425729 + 0.684819i
\(37\) 6.74456i 1.10880i −0.832251 0.554400i \(-0.812948\pi\)
0.832251 0.554400i \(-0.187052\pi\)
\(38\) 2.74456i 0.445227i
\(39\) −5.18614 + 4.87375i −0.830447 + 0.780424i
\(40\) 0 0
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0.147477 + 3.62772i 0.0227562 + 0.559769i
\(43\) 4.74456i 0.723539i −0.932268 0.361770i \(-0.882173\pi\)
0.932268 0.361770i \(-0.117827\pi\)
\(44\) 3.46410i 0.522233i
\(45\) 0 0
\(46\) 6.74456 0.994432
\(47\) 1.62772i 0.237427i −0.992929 0.118714i \(-0.962123\pi\)
0.992929 0.118714i \(-0.0378770\pi\)
\(48\) −0.792287 + 0.744563i −0.114357 + 0.107468i
\(49\) −1.00000 6.92820i −0.142857 0.989743i
\(50\) 0 0
\(51\) −5.18614 5.51856i −0.726205 0.772753i
\(52\) −5.63858 −0.781931
\(53\) −1.87953 −0.258173 −0.129086 0.991633i \(-0.541204\pi\)
−0.129086 + 0.991633i \(0.541204\pi\)
\(54\) 2.62772 + 3.16915i 0.357587 + 0.431266i
\(55\) 0 0
\(56\) −4.62772 + 5.34363i −0.618405 + 0.714072i
\(57\) 4.10891 + 4.37228i 0.544239 + 0.579123i
\(58\) 0.744563i 0.0977659i
\(59\) 8.74456 1.13845 0.569223 0.822183i \(-0.307244\pi\)
0.569223 + 0.822183i \(0.307244\pi\)
\(60\) 0 0
\(61\) 6.92820i 0.887066i −0.896258 0.443533i \(-0.853725\pi\)
0.896258 0.443533i \(-0.146275\pi\)
\(62\) 2.74456i 0.348560i
\(63\) −5.66603 5.55842i −0.713853 0.700295i
\(64\) 3.37228 0.421535
\(65\) 0 0
\(66\) 2.37228 + 2.52434i 0.292008 + 0.310725i
\(67\) 4.74456i 0.579641i 0.957081 + 0.289820i \(0.0935955\pi\)
−0.957081 + 0.289820i \(0.906404\pi\)
\(68\) 6.00000i 0.727607i
\(69\) −10.7446 + 10.0974i −1.29349 + 1.21558i
\(70\) 0 0
\(71\) 0.294954i 0.0350046i 0.999847 + 0.0175023i \(0.00557143\pi\)
−0.999847 + 0.0175023i \(0.994429\pi\)
\(72\) −0.497333 + 8.00000i −0.0586113 + 0.942809i
\(73\) −6.92820 −0.810885 −0.405442 0.914121i \(-0.632883\pi\)
−0.405442 + 0.914121i \(0.632883\pi\)
\(74\) 5.34363i 0.621184i
\(75\) 0 0
\(76\) 4.75372i 0.545289i
\(77\) −5.04868 4.37228i −0.575350 0.498268i
\(78\) −4.10891 + 3.86141i −0.465243 + 0.437218i
\(79\) 2.37228 0.266903 0.133451 0.991055i \(-0.457394\pi\)
0.133451 + 0.991055i \(0.457394\pi\)
\(80\) 0 0
\(81\) −8.93070 1.11469i −0.992300 0.123855i
\(82\) −4.75372 −0.524961
\(83\) 17.4891i 1.91968i 0.280546 + 0.959840i \(0.409484\pi\)
−0.280546 + 0.959840i \(0.590516\pi\)
\(84\) −0.255437 6.28339i −0.0278705 0.685574i
\(85\) 0 0
\(86\) 3.75906i 0.405349i
\(87\) 1.11469 + 1.18614i 0.119508 + 0.127168i
\(88\) 6.74456i 0.718973i
\(89\) −14.7446 −1.56292 −0.781460 0.623955i \(-0.785525\pi\)
−0.781460 + 0.623955i \(0.785525\pi\)
\(90\) 0 0
\(91\) 7.11684 8.21782i 0.746048 0.861462i
\(92\) −11.6819 −1.21792
\(93\) 4.10891 + 4.37228i 0.426074 + 0.453384i
\(94\) 1.28962i 0.133014i
\(95\) 0 0
\(96\) −7.37228 + 6.92820i −0.752430 + 0.707107i
\(97\) −11.0371 −1.12065 −0.560325 0.828273i \(-0.689324\pi\)
−0.560325 + 0.828273i \(0.689324\pi\)
\(98\) −0.792287 5.48913i −0.0800331 0.554485i
\(99\) −7.55842 0.469882i −0.759650 0.0472249i
\(100\) 0 0
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) −4.10891 4.37228i −0.406843 0.432920i
\(103\) 6.28339 0.619121 0.309561 0.950880i \(-0.399818\pi\)
0.309561 + 0.950880i \(0.399818\pi\)
\(104\) −10.9783 −1.07651
\(105\) 0 0
\(106\) −1.48913 −0.144637
\(107\) 6.63325 0.641260 0.320630 0.947204i \(-0.396105\pi\)
0.320630 + 0.947204i \(0.396105\pi\)
\(108\) −4.55134 5.48913i −0.437953 0.528191i
\(109\) 17.1168 1.63950 0.819748 0.572724i \(-0.194113\pi\)
0.819748 + 0.572724i \(0.194113\pi\)
\(110\) 0 0
\(111\) 8.00000 + 8.51278i 0.759326 + 0.807997i
\(112\) 1.08724 1.25544i 0.102735 0.118628i
\(113\) −3.16915 −0.298128 −0.149064 0.988828i \(-0.547626\pi\)
−0.149064 + 0.988828i \(0.547626\pi\)
\(114\) 3.25544 + 3.46410i 0.304900 + 0.324443i
\(115\) 0 0
\(116\) 1.28962i 0.119738i
\(117\) 0.764836 12.3030i 0.0707091 1.13741i
\(118\) 6.92820 0.637793
\(119\) 8.74456 + 7.57301i 0.801613 + 0.694217i
\(120\) 0 0
\(121\) 4.62772 0.420702
\(122\) 5.48913i 0.496962i
\(123\) 7.57301 7.11684i 0.682836 0.641704i
\(124\) 4.75372i 0.426897i
\(125\) 0 0
\(126\) −4.48913 4.40387i −0.399923 0.392328i
\(127\) 0.744563i 0.0660693i −0.999454 0.0330346i \(-0.989483\pi\)
0.999454 0.0330346i \(-0.0105172\pi\)
\(128\) −9.01011 −0.796389
\(129\) 5.62772 + 5.98844i 0.495493 + 0.527253i
\(130\) 0 0
\(131\) 5.48913 0.479587 0.239794 0.970824i \(-0.422920\pi\)
0.239794 + 0.970824i \(0.422920\pi\)
\(132\) −4.10891 4.37228i −0.357635 0.380558i
\(133\) −6.92820 6.00000i −0.600751 0.520266i
\(134\) 3.75906i 0.324733i
\(135\) 0 0
\(136\) 11.6819i 1.00172i
\(137\) −13.2665 −1.13343 −0.566717 0.823913i \(-0.691787\pi\)
−0.566717 + 0.823913i \(0.691787\pi\)
\(138\) −8.51278 + 8.00000i −0.724656 + 0.681005i
\(139\) 18.6101i 1.57849i 0.614078 + 0.789245i \(0.289528\pi\)
−0.614078 + 0.789245i \(0.710472\pi\)
\(140\) 0 0
\(141\) 1.93070 + 2.05446i 0.162595 + 0.173016i
\(142\) 0.233688i 0.0196107i
\(143\) 10.3723i 0.867374i
\(144\) 0.116844 1.87953i 0.00973700 0.156627i
\(145\) 0 0
\(146\) −5.48913 −0.454283
\(147\) 9.47999 + 7.55842i 0.781897 + 0.623408i
\(148\) 9.25544i 0.760792i
\(149\) 3.16915i 0.259627i 0.991538 + 0.129813i \(0.0414378\pi\)
−0.991538 + 0.129813i \(0.958562\pi\)
\(150\) 0 0
\(151\) −2.37228 −0.193054 −0.0965268 0.995330i \(-0.530773\pi\)
−0.0965268 + 0.995330i \(0.530773\pi\)
\(152\) 9.25544i 0.750715i
\(153\) 13.0916 + 0.813859i 1.05839 + 0.0657966i
\(154\) −4.00000 3.46410i −0.322329 0.279145i
\(155\) 0 0
\(156\) 7.11684 6.68815i 0.569804 0.535481i
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 1.87953 0.149527
\(159\) 2.37228 2.22938i 0.188134 0.176802i
\(160\) 0 0
\(161\) 14.7446 17.0256i 1.16203 1.34180i
\(162\) −7.07568 0.883156i −0.555918 0.0693873i
\(163\) 8.00000i 0.626608i −0.949653 0.313304i \(-0.898564\pi\)
0.949653 0.313304i \(-0.101436\pi\)
\(164\) 8.23369 0.642943
\(165\) 0 0
\(166\) 13.8564i 1.07547i
\(167\) 4.88316i 0.377870i −0.981990 0.188935i \(-0.939496\pi\)
0.981990 0.188935i \(-0.0605035\pi\)
\(168\) −0.497333 12.2337i −0.0383701 0.943850i
\(169\) 3.88316 0.298704
\(170\) 0 0
\(171\) −10.3723 0.644810i −0.793188 0.0493099i
\(172\) 6.51087i 0.496450i
\(173\) 1.11684i 0.0849121i 0.999098 + 0.0424560i \(0.0135182\pi\)
−0.999098 + 0.0424560i \(0.986482\pi\)
\(174\) 0.883156 + 0.939764i 0.0669519 + 0.0712433i
\(175\) 0 0
\(176\) 1.58457i 0.119442i
\(177\) −11.0371 + 10.3723i −0.829600 + 0.779628i
\(178\) −11.6819 −0.875597
\(179\) 6.63325i 0.495792i 0.968787 + 0.247896i \(0.0797392\pi\)
−0.968787 + 0.247896i \(0.920261\pi\)
\(180\) 0 0
\(181\) 1.28962i 0.0958567i −0.998851 0.0479284i \(-0.984738\pi\)
0.998851 0.0479284i \(-0.0152619\pi\)
\(182\) 5.63858 6.51087i 0.417960 0.482618i
\(183\) 8.21782 + 8.74456i 0.607479 + 0.646417i
\(184\) −22.7446 −1.67675
\(185\) 0 0
\(186\) 3.25544 + 3.46410i 0.238700 + 0.254000i
\(187\) 11.0371 0.807114
\(188\) 2.23369i 0.162908i
\(189\) 13.7446 + 0.294954i 0.999770 + 0.0214547i
\(190\) 0 0
\(191\) 20.8395i 1.50789i 0.656935 + 0.753947i \(0.271853\pi\)
−0.656935 + 0.753947i \(0.728147\pi\)
\(192\) −4.25639 + 4.00000i −0.307178 + 0.288675i
\(193\) 12.2337i 0.880600i 0.897851 + 0.440300i \(0.145128\pi\)
−0.897851 + 0.440300i \(0.854872\pi\)
\(194\) −8.74456 −0.627823
\(195\) 0 0
\(196\) 1.37228 + 9.50744i 0.0980201 + 0.679103i
\(197\) 15.7359 1.12114 0.560569 0.828107i \(-0.310582\pi\)
0.560569 + 0.828107i \(0.310582\pi\)
\(198\) −5.98844 0.372281i −0.425580 0.0264569i
\(199\) 26.8280i 1.90178i −0.309524 0.950892i \(-0.600170\pi\)
0.309524 0.950892i \(-0.399830\pi\)
\(200\) 0 0
\(201\) −5.62772 5.98844i −0.396949 0.422392i
\(202\) 4.75372 0.334471
\(203\) −1.87953 1.62772i −0.131917 0.114243i
\(204\) 7.11684 + 7.57301i 0.498279 + 0.530217i
\(205\) 0 0
\(206\) 4.97825 0.346851
\(207\) 1.58457 25.4891i 0.110136 1.77162i
\(208\) 2.57924 0.178838
\(209\) −8.74456 −0.604874
\(210\) 0 0
\(211\) −11.1168 −0.765315 −0.382658 0.923890i \(-0.624991\pi\)
−0.382658 + 0.923890i \(0.624991\pi\)
\(212\) 2.57924 0.177143
\(213\) −0.349857 0.372281i −0.0239718 0.0255083i
\(214\) 5.25544 0.359254
\(215\) 0 0
\(216\) −8.86141 10.6873i −0.602942 0.727176i
\(217\) −6.92820 6.00000i −0.470317 0.407307i
\(218\) 13.5615 0.918497
\(219\) 8.74456 8.21782i 0.590903 0.555309i
\(220\) 0 0
\(221\) 17.9653i 1.20848i
\(222\) 6.33830 + 6.74456i 0.425399 + 0.452665i
\(223\) 8.86263 0.593486 0.296743 0.954957i \(-0.404100\pi\)
0.296743 + 0.954957i \(0.404100\pi\)
\(224\) 10.1168 11.6819i 0.675960 0.780531i
\(225\) 0 0
\(226\) −2.51087 −0.167021
\(227\) 24.6060i 1.63316i 0.577235 + 0.816578i \(0.304131\pi\)
−0.577235 + 0.816578i \(0.695869\pi\)
\(228\) −5.63858 6.00000i −0.373424 0.397360i
\(229\) 15.1460i 1.00088i 0.865772 + 0.500439i \(0.166828\pi\)
−0.865772 + 0.500439i \(0.833172\pi\)
\(230\) 0 0
\(231\) 11.5584 0.469882i 0.760488 0.0309160i
\(232\) 2.51087i 0.164847i
\(233\) −17.0256 −1.11538 −0.557691 0.830049i \(-0.688312\pi\)
−0.557691 + 0.830049i \(0.688312\pi\)
\(234\) 0.605969 9.74749i 0.0396134 0.637214i
\(235\) 0 0
\(236\) −12.0000 −0.781133
\(237\) −2.99422 + 2.81386i −0.194495 + 0.182780i
\(238\) 6.92820 + 6.00000i 0.449089 + 0.388922i
\(239\) 20.8395i 1.34800i −0.738733 0.673998i \(-0.764576\pi\)
0.738733 0.673998i \(-0.235424\pi\)
\(240\) 0 0
\(241\) 16.4356i 1.05871i 0.848399 + 0.529357i \(0.177567\pi\)
−0.848399 + 0.529357i \(0.822433\pi\)
\(242\) 3.66648 0.235690
\(243\) 12.5942 9.18614i 0.807921 0.589291i
\(244\) 9.50744i 0.608652i
\(245\) 0 0
\(246\) 6.00000 5.63858i 0.382546 0.359503i
\(247\) 14.2337i 0.905668i
\(248\) 9.25544i 0.587721i
\(249\) −20.7446 22.0742i −1.31463 1.39890i
\(250\) 0 0
\(251\) −5.48913 −0.346471 −0.173235 0.984880i \(-0.555422\pi\)
−0.173235 + 0.984880i \(0.555422\pi\)
\(252\) 7.77539 + 7.62772i 0.489804 + 0.480501i
\(253\) 21.4891i 1.35101i
\(254\) 0.589907i 0.0370141i
\(255\) 0 0
\(256\) −13.8832 −0.867697
\(257\) 0.510875i 0.0318675i 0.999873 + 0.0159337i \(0.00507208\pi\)
−0.999873 + 0.0159337i \(0.994928\pi\)
\(258\) 4.45877 + 4.74456i 0.277591 + 0.295384i
\(259\) −13.4891 11.6819i −0.838173 0.725880i
\(260\) 0 0
\(261\) −2.81386 0.174928i −0.174174 0.0108278i
\(262\) 4.34896 0.268680
\(263\) 0.294954 0.0181876 0.00909381 0.999959i \(-0.497105\pi\)
0.00909381 + 0.999959i \(0.497105\pi\)
\(264\) −8.00000 8.51278i −0.492366 0.523925i
\(265\) 0 0
\(266\) −5.48913 4.75372i −0.336560 0.291469i
\(267\) 18.6101 17.4891i 1.13892 1.07032i
\(268\) 6.51087i 0.397715i
\(269\) −2.74456 −0.167339 −0.0836695 0.996494i \(-0.526664\pi\)
−0.0836695 + 0.996494i \(0.526664\pi\)
\(270\) 0 0
\(271\) 4.75372i 0.288768i 0.989522 + 0.144384i \(0.0461201\pi\)
−0.989522 + 0.144384i \(0.953880\pi\)
\(272\) 2.74456i 0.166414i
\(273\) 0.764836 + 18.8139i 0.0462900 + 1.13867i
\(274\) −10.5109 −0.634985
\(275\) 0 0
\(276\) 14.7446 13.8564i 0.887518 0.834058i
\(277\) 28.2337i 1.69640i 0.529678 + 0.848199i \(0.322313\pi\)
−0.529678 + 0.848199i \(0.677687\pi\)
\(278\) 14.7446i 0.884320i
\(279\) −10.3723 0.644810i −0.620972 0.0386038i
\(280\) 0 0
\(281\) 28.0627i 1.67408i −0.547143 0.837039i \(-0.684285\pi\)
0.547143 0.837039i \(-0.315715\pi\)
\(282\) 1.52967 + 1.62772i 0.0910906 + 0.0969292i
\(283\) −0.644810 −0.0383300 −0.0191650 0.999816i \(-0.506101\pi\)
−0.0191650 + 0.999816i \(0.506101\pi\)
\(284\) 0.404759i 0.0240181i
\(285\) 0 0
\(286\) 8.21782i 0.485930i
\(287\) −10.3923 + 12.0000i −0.613438 + 0.708338i
\(288\) 1.08724 17.4891i 0.0640663 1.03056i
\(289\) −2.11684 −0.124520
\(290\) 0 0
\(291\) 13.9307 13.0916i 0.816632 0.767441i
\(292\) 9.50744 0.556381
\(293\) 10.8832i 0.635801i 0.948124 + 0.317900i \(0.102978\pi\)
−0.948124 + 0.317900i \(0.897022\pi\)
\(294\) 7.51087 + 5.98844i 0.438043 + 0.349253i
\(295\) 0 0
\(296\) 18.0202i 1.04740i
\(297\) 10.0974 8.37228i 0.585908 0.485809i
\(298\) 2.51087i 0.145451i
\(299\) 34.9783 2.02284
\(300\) 0 0
\(301\) −9.48913 8.21782i −0.546944 0.473667i
\(302\) −1.87953 −0.108155
\(303\) −7.57301 + 7.11684i −0.435058 + 0.408852i
\(304\) 2.17448i 0.124715i
\(305\) 0 0
\(306\) 10.3723 + 0.644810i 0.592944 + 0.0368613i
\(307\) 22.7190 1.29664 0.648322 0.761366i \(-0.275471\pi\)
0.648322 + 0.761366i \(0.275471\pi\)
\(308\) 6.92820 + 6.00000i 0.394771 + 0.341882i
\(309\) −7.93070 + 7.45299i −0.451162 + 0.423986i
\(310\) 0 0
\(311\) −14.2337 −0.807118 −0.403559 0.914954i \(-0.632227\pi\)
−0.403559 + 0.914954i \(0.632227\pi\)
\(312\) 13.8564 13.0217i 0.784465 0.737211i
\(313\) −5.39853 −0.305143 −0.152572 0.988292i \(-0.548755\pi\)
−0.152572 + 0.988292i \(0.548755\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −3.25544 −0.183133
\(317\) 1.87953 0.105565 0.0527824 0.998606i \(-0.483191\pi\)
0.0527824 + 0.998606i \(0.483191\pi\)
\(318\) 1.87953 1.76631i 0.105399 0.0990499i
\(319\) −2.37228 −0.132822
\(320\) 0 0
\(321\) −8.37228 + 7.86797i −0.467295 + 0.439147i
\(322\) 11.6819 13.4891i 0.651008 0.751720i
\(323\) 15.1460 0.842747
\(324\) 12.2554 + 1.52967i 0.680858 + 0.0849817i
\(325\) 0 0
\(326\) 6.33830i 0.351046i
\(327\) −21.6043 + 20.3030i −1.19472 + 1.12276i
\(328\) 16.0309 0.885158
\(329\) −3.25544 2.81929i −0.179478 0.155433i
\(330\) 0 0
\(331\) −4.00000 −0.219860 −0.109930 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) 24.0000i 1.31717i
\(333\) −20.1947 1.25544i −1.10666 0.0687975i
\(334\) 3.86886i 0.211695i
\(335\) 0 0
\(336\) 0.116844 + 2.87419i 0.00637436 + 0.156800i
\(337\) 16.2337i 0.884305i 0.896940 + 0.442153i \(0.145785\pi\)
−0.896940 + 0.442153i \(0.854215\pi\)
\(338\) 3.07657 0.167344
\(339\) 4.00000 3.75906i 0.217250 0.204164i
\(340\) 0 0
\(341\) −8.74456 −0.473545
\(342\) −8.21782 0.510875i −0.444369 0.0276249i
\(343\) −15.5885 10.0000i −0.841698 0.539949i
\(344\) 12.6766i 0.683476i
\(345\) 0 0
\(346\) 0.884861i 0.0475704i
\(347\) 14.8511 0.797247 0.398624 0.917115i \(-0.369488\pi\)
0.398624 + 0.917115i \(0.369488\pi\)
\(348\) −1.52967 1.62772i −0.0819990 0.0872549i
\(349\) 15.1460i 0.810748i −0.914151 0.405374i \(-0.867141\pi\)
0.914151 0.405374i \(-0.132859\pi\)
\(350\) 0 0
\(351\) 13.6277 + 16.4356i 0.727394 + 0.877270i
\(352\) 14.7446i 0.785888i
\(353\) 25.1168i 1.33683i −0.743786 0.668417i \(-0.766972\pi\)
0.743786 0.668417i \(-0.233028\pi\)
\(354\) −8.74456 + 8.21782i −0.464768 + 0.436772i
\(355\) 0 0
\(356\) 20.2337 1.07238
\(357\) −20.0198 + 0.813859i −1.05956 + 0.0430740i
\(358\) 5.25544i 0.277758i
\(359\) 16.7306i 0.883007i −0.897259 0.441504i \(-0.854445\pi\)
0.897259 0.441504i \(-0.145555\pi\)
\(360\) 0 0
\(361\) 7.00000 0.368421
\(362\) 1.02175i 0.0537020i
\(363\) −5.84096 + 5.48913i −0.306571 + 0.288104i
\(364\) −9.76631 + 11.2772i −0.511894 + 0.591084i
\(365\) 0 0
\(366\) 6.51087 + 6.92820i 0.340329 + 0.362143i
\(367\) 35.2858 1.84191 0.920953 0.389675i \(-0.127413\pi\)
0.920953 + 0.389675i \(0.127413\pi\)
\(368\) 5.34363 0.278556
\(369\) −1.11684 + 17.9653i −0.0581406 + 0.935237i
\(370\) 0 0
\(371\) −3.25544 + 3.75906i −0.169014 + 0.195160i
\(372\) −5.63858 6.00000i −0.292347 0.311086i
\(373\) 13.2554i 0.686341i 0.939273 + 0.343170i \(0.111501\pi\)
−0.939273 + 0.343170i \(0.888499\pi\)
\(374\) 8.74456 0.452171
\(375\) 0 0
\(376\) 4.34896i 0.224281i
\(377\) 3.86141i 0.198873i
\(378\) 10.8896 + 0.233688i 0.560103 + 0.0120196i
\(379\) 21.4891 1.10382 0.551911 0.833903i \(-0.313899\pi\)
0.551911 + 0.833903i \(0.313899\pi\)
\(380\) 0 0
\(381\) 0.883156 + 0.939764i 0.0452455 + 0.0481456i
\(382\) 16.5109i 0.844770i
\(383\) 5.48913i 0.280481i −0.990117 0.140241i \(-0.955212\pi\)
0.990117 0.140241i \(-0.0447876\pi\)
\(384\) 11.3723 10.6873i 0.580339 0.545382i
\(385\) 0 0
\(386\) 9.69259i 0.493340i
\(387\) −14.2063 0.883156i −0.722145 0.0448933i
\(388\) 15.1460 0.768923
\(389\) 29.3523i 1.48822i 0.668057 + 0.744110i \(0.267126\pi\)
−0.668057 + 0.744110i \(0.732874\pi\)
\(390\) 0 0
\(391\) 37.2203i 1.88231i
\(392\) 2.67181 + 18.5109i 0.134947 + 0.934940i
\(393\) −6.92820 + 6.51087i −0.349482 + 0.328430i
\(394\) 12.4674 0.628097
\(395\) 0 0
\(396\) 10.3723 + 0.644810i 0.521227 + 0.0324029i
\(397\) −26.1831 −1.31409 −0.657047 0.753850i \(-0.728195\pi\)
−0.657047 + 0.753850i \(0.728195\pi\)
\(398\) 21.2554i 1.06544i
\(399\) 15.8614 0.644810i 0.794064 0.0322809i
\(400\) 0 0
\(401\) 5.98844i 0.299048i −0.988758 0.149524i \(-0.952226\pi\)
0.988758 0.149524i \(-0.0477742\pi\)
\(402\) −4.45877 4.74456i −0.222383 0.236637i
\(403\) 14.2337i 0.709030i
\(404\) −8.23369 −0.409641
\(405\) 0 0
\(406\) −1.48913 1.28962i −0.0739040 0.0640028i
\(407\) −17.0256 −0.843925
\(408\) 13.8564 + 14.7446i 0.685994 + 0.729965i
\(409\) 24.6535i 1.21904i 0.792772 + 0.609518i \(0.208637\pi\)
−0.792772 + 0.609518i \(0.791363\pi\)
\(410\) 0 0
\(411\) 16.7446 15.7359i 0.825948 0.776196i
\(412\) −8.62258 −0.424804
\(413\) 15.1460 17.4891i 0.745287 0.860584i
\(414\) 1.25544 20.1947i 0.0617014 0.992515i
\(415\) 0 0
\(416\) 24.0000 1.17670
\(417\) −22.0742 23.4891i −1.08098 1.15027i
\(418\) −6.92820 −0.338869
\(419\) −8.74456 −0.427200 −0.213600 0.976921i \(-0.568519\pi\)
−0.213600 + 0.976921i \(0.568519\pi\)
\(420\) 0 0
\(421\) 14.6060 0.711851 0.355926 0.934514i \(-0.384166\pi\)
0.355926 + 0.934514i \(0.384166\pi\)
\(422\) −8.80773 −0.428754
\(423\) −4.87375 0.302985i −0.236970 0.0147316i
\(424\) 5.02175 0.243878
\(425\) 0 0
\(426\) −0.277187 0.294954i −0.0134297 0.0142906i
\(427\) −13.8564 12.0000i −0.670559 0.580721i
\(428\) −9.10268 −0.439995
\(429\) 12.3030 + 13.0916i 0.593994 + 0.632067i
\(430\) 0 0
\(431\) 15.0911i 0.726914i −0.931611 0.363457i \(-0.881596\pi\)
0.931611 0.363457i \(-0.118404\pi\)
\(432\) 2.08191 + 2.51087i 0.100166 + 0.120805i
\(433\) −37.2203 −1.78869 −0.894346 0.447377i \(-0.852358\pi\)
−0.894346 + 0.447377i \(0.852358\pi\)
\(434\) −5.48913 4.75372i −0.263486 0.228186i
\(435\) 0 0
\(436\) −23.4891 −1.12493
\(437\) 29.4891i 1.41066i
\(438\) 6.92820 6.51087i 0.331042 0.311102i
\(439\) 18.6101i 0.888213i −0.895974 0.444106i \(-0.853521\pi\)
0.895974 0.444106i \(-0.146479\pi\)
\(440\) 0 0
\(441\) −20.9307 + 1.70460i −0.996700 + 0.0811714i
\(442\) 14.2337i 0.677027i
\(443\) −6.63325 −0.315155 −0.157578 0.987507i \(-0.550368\pi\)
−0.157578 + 0.987507i \(0.550368\pi\)
\(444\) −10.9783 11.6819i −0.521005 0.554400i
\(445\) 0 0
\(446\) 7.02175 0.332489
\(447\) −3.75906 4.00000i −0.177797 0.189194i
\(448\) 5.84096 6.74456i 0.275960 0.318651i
\(449\) 11.6270i 0.548713i 0.961628 + 0.274357i \(0.0884648\pi\)
−0.961628 + 0.274357i \(0.911535\pi\)
\(450\) 0 0
\(451\) 15.1460i 0.713199i
\(452\) 4.34896 0.204558
\(453\) 2.99422 2.81386i 0.140681 0.132207i
\(454\) 19.4950i 0.914945i
\(455\) 0 0
\(456\) −10.9783 11.6819i −0.514104 0.547056i
\(457\) 12.9783i 0.607097i 0.952816 + 0.303548i \(0.0981714\pi\)
−0.952816 + 0.303548i \(0.901829\pi\)
\(458\) 12.0000i 0.560723i
\(459\) −17.4891 + 14.5012i −0.816322 + 0.676859i
\(460\) 0 0
\(461\) 2.74456 0.127827 0.0639135 0.997955i \(-0.479642\pi\)
0.0639135 + 0.997955i \(0.479642\pi\)
\(462\) 9.15759 0.372281i 0.426050 0.0173201i
\(463\) 32.4674i 1.50889i 0.656365 + 0.754443i \(0.272093\pi\)
−0.656365 + 0.754443i \(0.727907\pi\)
\(464\) 0.589907i 0.0273858i
\(465\) 0 0
\(466\) −13.4891 −0.624872
\(467\) 31.1168i 1.43992i −0.694018 0.719958i \(-0.744161\pi\)
0.694018 0.719958i \(-0.255839\pi\)
\(468\) −1.04957 + 16.8832i −0.0485164 + 0.780424i
\(469\) 9.48913 + 8.21782i 0.438167 + 0.379464i
\(470\) 0 0
\(471\) 0 0
\(472\) −23.3639 −1.07541
\(473\) −11.9769 −0.550697
\(474\) −2.37228 + 2.22938i −0.108962 + 0.102399i
\(475\) 0 0
\(476\) −12.0000 10.3923i −0.550019 0.476331i
\(477\) −0.349857 + 5.62772i −0.0160188 + 0.257676i
\(478\) 16.5109i 0.755190i
\(479\) −41.4891 −1.89569 −0.947843 0.318737i \(-0.896741\pi\)
−0.947843 + 0.318737i \(0.896741\pi\)
\(480\) 0 0
\(481\) 27.7128i 1.26360i
\(482\) 13.0217i 0.593124i
\(483\) 1.58457 + 38.9783i 0.0721006 + 1.77357i
\(484\) −6.35053 −0.288661
\(485\) 0 0
\(486\) 9.97825 7.27806i 0.452623 0.330139i
\(487\) 37.4891i 1.69879i 0.527754 + 0.849397i \(0.323034\pi\)
−0.527754 + 0.849397i \(0.676966\pi\)
\(488\) 18.5109i 0.837948i
\(489\) 9.48913 + 10.0974i 0.429113 + 0.456618i
\(490\) 0 0
\(491\) 5.69349i 0.256943i 0.991713 + 0.128472i \(0.0410072\pi\)
−0.991713 + 0.128472i \(0.958993\pi\)
\(492\) −10.3923 + 9.76631i −0.468521 + 0.440299i
\(493\) 4.10891 0.185056
\(494\) 11.2772i 0.507384i
\(495\) 0 0
\(496\) 2.17448i 0.0976371i
\(497\) 0.589907 + 0.510875i 0.0264610 + 0.0229159i
\(498\) −16.4356 17.4891i −0.736499 0.783706i
\(499\) −41.3505 −1.85110 −0.925552 0.378620i \(-0.876399\pi\)
−0.925552 + 0.378620i \(0.876399\pi\)
\(500\) 0 0
\(501\) 5.79211 + 6.16337i 0.258772 + 0.275359i
\(502\) −4.34896 −0.194104
\(503\) 12.6060i 0.562072i −0.959697 0.281036i \(-0.909322\pi\)
0.959697 0.281036i \(-0.0906781\pi\)
\(504\) 15.1386 + 14.8511i 0.674327 + 0.661519i
\(505\) 0 0
\(506\) 17.0256i 0.756878i
\(507\) −4.90120 + 4.60597i −0.217670 + 0.204558i
\(508\) 1.02175i 0.0453328i
\(509\) 3.76631 0.166939 0.0834694 0.996510i \(-0.473400\pi\)
0.0834694 + 0.996510i \(0.473400\pi\)
\(510\) 0 0
\(511\) −12.0000 + 13.8564i −0.530849 + 0.612971i
\(512\) 7.02078 0.310277
\(513\) 13.8564 11.4891i 0.611775 0.507257i
\(514\) 0.404759i 0.0178532i
\(515\) 0 0
\(516\) −7.72281 8.21782i −0.339978 0.361770i
\(517\) −4.10891 −0.180710
\(518\) −10.6873 9.25544i −0.469571 0.406661i
\(519\) −1.32473 1.40965i −0.0581494 0.0618766i
\(520\) 0 0
\(521\) −34.4674 −1.51004 −0.755022 0.655700i \(-0.772374\pi\)
−0.755022 + 0.655700i \(0.772374\pi\)
\(522\) −2.22938 0.138593i −0.0975775 0.00606607i
\(523\) −10.3923 −0.454424 −0.227212 0.973845i \(-0.572961\pi\)
−0.227212 + 0.973845i \(0.572961\pi\)
\(524\) −7.53262 −0.329064
\(525\) 0 0
\(526\) 0.233688 0.0101893
\(527\) 15.1460 0.659771
\(528\) 1.87953 + 2.00000i 0.0817959 + 0.0870388i
\(529\) 49.4674 2.15076
\(530\) 0 0
\(531\) 1.62772 26.1831i 0.0706370 1.13625i
\(532\) 9.50744 + 8.23369i 0.412200 + 0.356976i
\(533\) −24.6535 −1.06786
\(534\) 14.7446 13.8564i 0.638060 0.599625i
\(535\) 0 0
\(536\) 12.6766i 0.547545i
\(537\) −7.86797 8.37228i −0.339528 0.361291i
\(538\) −2.17448 −0.0937485
\(539\) −17.4891 + 2.52434i −0.753310 + 0.108731i
\(540\) 0 0
\(541\) 24.3723 1.04785 0.523923 0.851766i \(-0.324468\pi\)
0.523923 + 0.851766i \(0.324468\pi\)
\(542\) 3.76631i 0.161777i
\(543\) 1.52967 + 1.62772i 0.0656445 + 0.0698521i
\(544\) 25.5383i 1.09495i
\(545\) 0 0
\(546\) 0.605969 + 14.9060i 0.0259331 + 0.637917i
\(547\) 2.97825i 0.127341i −0.997971 0.0636704i \(-0.979719\pi\)
0.997971 0.0636704i \(-0.0202806\pi\)
\(548\) 18.2054 0.777695
\(549\) −20.7446 1.28962i −0.885356 0.0550397i
\(550\) 0 0
\(551\) −3.25544 −0.138686
\(552\) 28.7075 26.9783i 1.22187 1.14827i
\(553\) 4.10891 4.74456i 0.174729 0.201759i
\(554\) 22.3692i 0.950376i
\(555\) 0 0
\(556\) 25.5383i 1.08307i
\(557\) −17.6155 −0.746391 −0.373196 0.927753i \(-0.621738\pi\)
−0.373196 + 0.927753i \(0.621738\pi\)
\(558\) −8.21782 0.510875i −0.347888 0.0216271i
\(559\) 19.4950i 0.824550i
\(560\) 0 0
\(561\) −13.9307 + 13.0916i −0.588155 + 0.552727i
\(562\) 22.2337i 0.937872i
\(563\) 17.4891i 0.737079i 0.929612 + 0.368539i \(0.120142\pi\)
−0.929612 + 0.368539i \(0.879858\pi\)
\(564\) −2.64947 2.81929i −0.111563 0.118714i
\(565\) 0 0
\(566\) −0.510875 −0.0214737
\(567\) −17.6978 + 15.9307i −0.743238 + 0.669027i
\(568\) 0.788061i 0.0330663i
\(569\) 23.9538i 1.00419i 0.864811 + 0.502097i \(0.167438\pi\)
−0.864811 + 0.502097i \(0.832562\pi\)
\(570\) 0 0
\(571\) −4.00000 −0.167395 −0.0836974 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) 14.2337i 0.595140i
\(573\) −24.7186 26.3030i −1.03263 1.09882i
\(574\) −8.23369 + 9.50744i −0.343667 + 0.396833i
\(575\) 0 0
\(576\) 0.627719 10.0974i 0.0261549 0.420723i
\(577\) −2.81929 −0.117369 −0.0586843 0.998277i \(-0.518691\pi\)
−0.0586843 + 0.998277i \(0.518691\pi\)
\(578\) −1.67715 −0.0697602
\(579\) −14.5109 15.4410i −0.603051 0.641705i
\(580\) 0 0
\(581\) 34.9783 + 30.2921i 1.45114 + 1.25673i
\(582\) 11.0371 10.3723i 0.457503 0.429945i
\(583\) 4.74456i 0.196500i
\(584\) 18.5109 0.765985
\(585\) 0 0
\(586\) 8.62258i 0.356196i
\(587\) 17.4891i 0.721853i 0.932594 + 0.360927i \(0.117540\pi\)
−0.932594 + 0.360927i \(0.882460\pi\)
\(588\) −13.0092 10.3723i −0.536491 0.427746i
\(589\) −12.0000 −0.494451
\(590\) 0 0
\(591\) −19.8614 + 18.6650i −0.816989 + 0.767777i
\(592\) 4.23369i 0.174004i
\(593\) 4.37228i 0.179548i −0.995962 0.0897740i \(-0.971386\pi\)
0.995962 0.0897740i \(-0.0286145\pi\)
\(594\) 8.00000 6.63325i 0.328244 0.272166i
\(595\) 0 0
\(596\) 4.34896i 0.178140i
\(597\) 31.8217 + 33.8614i 1.30238 + 1.38586i
\(598\) 27.7128 1.13326
\(599\) 34.6959i 1.41764i −0.705391 0.708818i \(-0.749229\pi\)
0.705391 0.708818i \(-0.250771\pi\)
\(600\) 0 0
\(601\) 22.0742i 0.900427i −0.892921 0.450213i \(-0.851348\pi\)
0.892921 0.450213i \(-0.148652\pi\)
\(602\) −7.51811 6.51087i −0.306415 0.265363i
\(603\) 14.2063 + 0.883156i 0.578524 + 0.0359649i
\(604\) 3.25544 0.132462
\(605\) 0 0
\(606\) −6.00000 + 5.63858i −0.243733 + 0.229052i
\(607\) −8.86263 −0.359723 −0.179862 0.983692i \(-0.557565\pi\)
−0.179862 + 0.983692i \(0.557565\pi\)
\(608\) 20.2337i 0.820584i
\(609\) 4.30298 0.174928i 0.174366 0.00708845i
\(610\) 0 0
\(611\) 6.68815i 0.270574i
\(612\) −17.9653 1.11684i −0.726205 0.0451457i
\(613\) 27.4891i 1.11028i 0.831758 + 0.555138i \(0.187334\pi\)
−0.831758 + 0.555138i \(0.812666\pi\)
\(614\) 18.0000 0.726421
\(615\) 0 0
\(616\) 13.4891 + 11.6819i 0.543492 + 0.470678i
\(617\) −24.5437 −0.988091 −0.494045 0.869436i \(-0.664482\pi\)
−0.494045 + 0.869436i \(0.664482\pi\)
\(618\) −6.28339 + 5.90491i −0.252755 + 0.237530i
\(619\) 18.6101i 0.748004i 0.927428 + 0.374002i \(0.122015\pi\)
−0.927428 + 0.374002i \(0.877985\pi\)
\(620\) 0 0
\(621\) 28.2337 + 34.0511i 1.13298 + 1.36642i
\(622\) −11.2772 −0.452173
\(623\) −25.5383 + 29.4891i −1.02317 + 1.18146i
\(624\) −3.25544 + 3.05934i −0.130322 + 0.122472i
\(625\) 0 0
\(626\) −4.27719 −0.170951
\(627\) 11.0371 10.3723i 0.440780 0.414229i
\(628\) 0 0
\(629\) 29.4891 1.17581
\(630\) 0 0
\(631\) −23.1168 −0.920267 −0.460134 0.887850i \(-0.652198\pi\)
−0.460134 + 0.887850i \(0.652198\pi\)
\(632\) −6.33830 −0.252124
\(633\) 14.0313 13.1861i 0.557695 0.524102i
\(634\) 1.48913 0.0591407
\(635\) 0 0
\(636\) −3.25544 + 3.05934i −0.129086 + 0.121311i
\(637\) −4.10891 28.4674i −0.162801 1.12792i
\(638\) −1.87953 −0.0744112
\(639\) 0.883156 + 0.0549029i 0.0349371 + 0.00217192i
\(640\) 0 0
\(641\) 36.6303i 1.44681i 0.690423 + 0.723406i \(0.257424\pi\)
−0.690423 + 0.723406i \(0.742576\pi\)
\(642\) −6.63325 + 6.23369i −0.261793 + 0.246024i
\(643\) 10.1523 0.400366 0.200183 0.979759i \(-0.435846\pi\)
0.200183 + 0.979759i \(0.435846\pi\)
\(644\) −20.2337 + 23.3639i −0.797319 + 0.920665i
\(645\) 0 0
\(646\) 12.0000 0.472134
\(647\) 12.0000i 0.471769i 0.971781 + 0.235884i \(0.0757987\pi\)
−0.971781 + 0.235884i \(0.924201\pi\)
\(648\) 23.8612 + 2.97825i 0.937356 + 0.116997i
\(649\) 22.0742i 0.866489i
\(650\) 0 0
\(651\) 15.8614 0.644810i 0.621658 0.0252721i
\(652\) 10.9783i 0.429941i
\(653\) 39.6897 1.55318 0.776589 0.630008i \(-0.216948\pi\)
0.776589 + 0.630008i \(0.216948\pi\)
\(654\) −17.1168 + 16.0858i −0.669322 + 0.629004i
\(655\) 0 0
\(656\) −3.76631 −0.147050
\(657\) −1.28962 + 20.7446i −0.0503129 + 0.809322i
\(658\) −2.57924 2.23369i −0.100549 0.0870782i
\(659\) 35.9855i 1.40180i −0.713261 0.700899i \(-0.752782\pi\)
0.713261 0.700899i \(-0.247218\pi\)
\(660\) 0 0
\(661\) 6.92820i 0.269476i 0.990881 + 0.134738i \(0.0430193\pi\)
−0.990881 + 0.134738i \(0.956981\pi\)
\(662\) −3.16915 −0.123172
\(663\) −21.3094 22.6753i −0.827588 0.880634i
\(664\) 46.7277i 1.81339i
\(665\) 0 0
\(666\) −16.0000 0.994667i −0.619987 0.0385426i
\(667\) 8.00000i 0.309761i
\(668\) 6.70106i 0.259272i
\(669\) −11.1861 + 10.5123i −0.432481 + 0.406430i
\(670\) 0 0
\(671\) −17.4891 −0.675160
\(672\) 1.08724 + 26.7446i 0.0419412 + 1.03169i
\(673\) 12.2337i 0.471574i 0.971805 + 0.235787i \(0.0757668\pi\)
−0.971805 + 0.235787i \(0.924233\pi\)
\(674\) 12.8617i 0.495416i
\(675\) 0 0
\(676\) −5.32878 −0.204953
\(677\) 18.6060i 0.715085i −0.933897 0.357543i \(-0.883615\pi\)
0.933897 0.357543i \(-0.116385\pi\)
\(678\) 3.16915 2.97825i 0.121710 0.114379i
\(679\) −19.1168 + 22.0742i −0.733637 + 0.847131i
\(680\) 0 0
\(681\) −29.1861 31.0569i −1.11842 1.19010i
\(682\) −6.92820 −0.265295
\(683\) 34.4559 1.31842 0.659209 0.751960i \(-0.270891\pi\)
0.659209 + 0.751960i \(0.270891\pi\)
\(684\) 14.2337 + 0.884861i 0.544239 + 0.0338335i
\(685\) 0 0
\(686\) −12.3505 7.92287i −0.471545 0.302497i
\(687\) −17.9653 19.1168i −0.685420 0.729353i
\(688\) 2.97825i 0.113545i
\(689\) −7.72281 −0.294216
\(690\) 0 0
\(691\) 21.1894i 0.806082i −0.915182 0.403041i \(-0.867953\pi\)
0.915182 0.403041i \(-0.132047\pi\)
\(692\) 1.53262i 0.0582616i
\(693\) −14.0313 + 14.3030i −0.533006 + 0.543325i
\(694\) 11.7663 0.446643
\(695\) 0 0
\(696\) −2.97825 3.16915i −0.112890 0.120126i
\(697\) 26.2337i 0.993672i
\(698\) 12.0000i 0.454207i
\(699\) 21.4891 20.1947i 0.812793 0.763834i
\(700\) 0 0
\(701\) 42.5090i 1.60554i 0.596287 + 0.802771i \(0.296642\pi\)
−0.596287 + 0.802771i \(0.703358\pi\)
\(702\) 10.7971 + 13.0217i 0.407509 + 0.491474i
\(703\) −23.3639 −0.881184
\(704\) 8.51278i 0.320837i
\(705\) 0 0
\(706\) 19.8997i 0.748937i
\(707\) 10.3923 12.0000i 0.390843 0.451306i
\(708\) 15.1460 14.2337i 0.569223 0.534935i
\(709\) −6.88316 −0.258502 −0.129251 0.991612i \(-0.541257\pi\)
−0.129251 + 0.991612i \(0.541257\pi\)
\(710\) 0 0
\(711\) 0.441578 7.10313i 0.0165605 0.266388i
\(712\) 39.3947 1.47638
\(713\) 29.4891i 1.10438i
\(714\) −15.8614 + 0.644810i −0.593598 + 0.0241314i
\(715\) 0 0
\(716\) 9.10268i 0.340183i
\(717\) 24.7186 + 26.3030i 0.923133 + 0.982303i
\(718\) 13.2554i 0.494689i
\(719\) 28.4674 1.06165 0.530827 0.847480i \(-0.321881\pi\)
0.530827 + 0.847480i \(0.321881\pi\)
\(720\) 0 0
\(721\) 10.8832 12.5668i 0.405310 0.468012i
\(722\) 5.54601 0.206401
\(723\) −19.4950 20.7446i −0.725026 0.771499i
\(724\) 1.76972i 0.0657712i
\(725\) 0 0
\(726\) −4.62772 + 4.34896i −0.171751 + 0.161405i
\(727\) 3.46410 0.128476 0.0642382 0.997935i \(-0.479538\pi\)
0.0642382 + 0.997935i \(0.479538\pi\)
\(728\) −19.0149 + 21.9565i −0.704739 + 0.813762i
\(729\) −5.00000 + 26.5330i −0.185185 + 0.982704i
\(730\) 0 0
\(731\) 20.7446 0.767265
\(732\) −11.2772 12.0000i −0.416816 0.443533i
\(733\) 40.0395 1.47889 0.739447 0.673215i \(-0.235087\pi\)
0.739447 + 0.673215i \(0.235087\pi\)
\(734\) 27.9565 1.03189
\(735\) 0 0
\(736\) 49.7228 1.83281
\(737\) 11.9769 0.441174
\(738\) −0.884861 + 14.2337i −0.0325722 + 0.523949i
\(739\) 14.3723 0.528693 0.264346 0.964428i \(-0.414844\pi\)
0.264346 + 0.964428i \(0.414844\pi\)
\(740\) 0 0
\(741\) 16.8832 + 17.9653i 0.620218 + 0.659972i
\(742\) −2.57924 + 2.97825i −0.0946869 + 0.109335i
\(743\) −16.1407 −0.592145 −0.296072 0.955166i \(-0.595677\pi\)
−0.296072 + 0.955166i \(0.595677\pi\)
\(744\) −10.9783 11.6819i −0.402482 0.428280i
\(745\) 0 0
\(746\) 10.5021i 0.384510i
\(747\) 52.3663 + 3.25544i 1.91598 + 0.119110i
\(748\) −15.1460 −0.553794
\(749\) 11.4891 13.2665i 0.419804 0.484747i
\(750\) 0 0
\(751\) 29.3505 1.07102 0.535508 0.844530i \(-0.320120\pi\)
0.535508 + 0.844530i \(0.320120\pi\)
\(752\) 1.02175i 0.0372594i
\(753\) 6.92820 6.51087i 0.252478 0.237269i
\(754\) 3.05934i 0.111415i
\(755\) 0 0
\(756\) −18.8614 0.404759i −0.685983 0.0147210i
\(757\) 19.7663i 0.718419i −0.933257 0.359209i \(-0.883046\pi\)
0.933257 0.359209i \(-0.116954\pi\)
\(758\) 17.0256 0.618396
\(759\) 25.4891 + 27.1229i 0.925197 + 0.984499i
\(760\) 0 0
\(761\) 8.23369 0.298471 0.149235 0.988802i \(-0.452319\pi\)
0.149235 + 0.988802i \(0.452319\pi\)
\(762\) 0.699713 + 0.744563i 0.0253479 + 0.0269727i
\(763\) 29.6472 34.2337i 1.07330 1.23934i
\(764\) 28.5977i 1.03463i
\(765\) 0 0
\(766\) 4.34896i 0.157134i
\(767\) 35.9306 1.29738
\(768\) 17.5229 16.4674i 0.632303 0.594215i
\(769\) 38.5099i 1.38870i −0.719637 0.694351i \(-0.755692\pi\)
0.719637 0.694351i \(-0.244308\pi\)
\(770\) 0 0
\(771\) −0.605969 0.644810i −0.0218234 0.0232223i
\(772\) 16.7881i 0.604216i
\(773\) 52.3723i 1.88370i 0.336034 + 0.941850i \(0.390914\pi\)
−0.336034 + 0.941850i \(0.609086\pi\)
\(774\) −11.2554 0.699713i −0.404568 0.0251507i
\(775\) 0 0
\(776\) 29.4891 1.05860
\(777\) 30.8820 1.25544i 1.10788 0.0450386i
\(778\) 23.2554i 0.833748i
\(779\) 20.7846i 0.744686i
\(780\) 0 0
\(781\) 0.744563 0.0266425
\(782\) 29.4891i 1.05453i
\(783\) 3.75906 3.11684i 0.134338 0.111387i
\(784\) −0.627719 4.34896i −0.0224185 0.155320i
\(785\) 0 0
\(786\) −5.48913 + 5.15848i −0.195791 + 0.183997i
\(787\) 3.22405 0.114925 0.0574625 0.998348i \(-0.481699\pi\)
0.0574625 + 0.998348i \(0.481699\pi\)
\(788\) −21.5941 −0.769259
\(789\) −0.372281 + 0.349857i −0.0132536 + 0.0124552i
\(790\) 0 0
\(791\) −5.48913 + 6.33830i −0.195171 + 0.225364i
\(792\) 20.1947 + 1.25544i 0.717588 + 0.0446100i
\(793\) 28.4674i 1.01091i
\(794\) −20.7446 −0.736197
\(795\) 0 0
\(796\) 36.8155i 1.30489i
\(797\) 14.1386i 0.500815i −0.968141 0.250407i \(-0.919435\pi\)
0.968141 0.250407i \(-0.0805645\pi\)
\(798\) 12.5668 0.510875i 0.444859 0.0180848i
\(799\) 7.11684 0.251776
\(800\) 0 0
\(801\) −2.74456 + 44.1485i −0.0969744 + 1.55991i
\(802\) 4.74456i 0.167536i
\(803\) 17.4891i 0.617178i
\(804\) 7.72281 + 8.21782i 0.272363 + 0.289820i
\(805\) 0 0
\(806\) 11.2772i 0.397221i
\(807\) 3.46410 3.25544i 0.121942 0.114597i
\(808\) −16.0309 −0.563965
\(809\) 13.5065i 0.474865i −0.971404 0.237433i \(-0.923694\pi\)
0.971404 0.237433i \(-0.0763059\pi\)
\(810\) 0 0
\(811\) 18.6101i 0.653490i −0.945113 0.326745i \(-0.894048\pi\)
0.945113 0.326745i \(-0.105952\pi\)
\(812\) 2.57924 + 2.23369i 0.0905136 + 0.0783871i
\(813\) −5.63858 6.00000i −0.197754 0.210429i
\(814\) −13.4891 −0.472794
\(815\) 0 0
\(816\) −3.25544 3.46410i −0.113963 0.121268i
\(817\) −16.4356 −0.575011
\(818\) 19.5326i 0.682942i
\(819\) −23.2812 22.8391i −0.813512 0.798062i
\(820\) 0 0
\(821\) 34.9909i 1.22119i −0.791943 0.610595i \(-0.790930\pi\)
0.791943 0.610595i \(-0.209070\pi\)
\(822\) 13.2665 12.4674i 0.462722 0.434850i
\(823\) 13.7663i 0.479863i 0.970790 + 0.239932i \(0.0771251\pi\)
−0.970790 + 0.239932i \(0.922875\pi\)
\(824\) −16.7881 −0.584840
\(825\) 0 0
\(826\) 12.0000 13.8564i 0.417533 0.482126i
\(827\) 14.8511 0.516422 0.258211 0.966088i \(-0.416867\pi\)
0.258211 + 0.966088i \(0.416867\pi\)
\(828\) −2.17448 + 34.9783i −0.0755684 + 1.21558i
\(829\) 12.5668i 0.436463i 0.975897 + 0.218231i \(0.0700287\pi\)
−0.975897 + 0.218231i \(0.929971\pi\)
\(830\) 0 0
\(831\) −33.4891 35.6357i −1.16172 1.23619i
\(832\) 13.8564 0.480384
\(833\) 30.2921 4.37228i 1.04956 0.151491i
\(834\) −17.4891 18.6101i −0.605599 0.644416i
\(835\) 0 0
\(836\) 12.0000 0.415029
\(837\) 13.8564 11.4891i 0.478947 0.397122i
\(838\) −6.92820 −0.239331
\(839\) 30.5109 1.05335 0.526676 0.850066i \(-0.323438\pi\)
0.526676 + 0.850066i \(0.323438\pi\)
\(840\) 0 0
\(841\) 28.1168 0.969546
\(842\) 11.5721 0.398802
\(843\) 33.2863 + 35.4198i 1.14644 + 1.21992i
\(844\) 15.2554 0.525114
\(845\) 0 0
\(846\) −3.86141 0.240051i −0.132758 0.00825312i
\(847\) 8.01544 9.25544i 0.275414 0.318021i
\(848\) −1.17981 −0.0405150
\(849\) 0.813859 0.764836i 0.0279316 0.0262491i
\(850\) 0 0
\(851\) 57.4150i 1.96816i
\(852\) 0.480102 + 0.510875i 0.0164480 + 0.0175023i
\(853\) −32.8713 −1.12549 −0.562746 0.826630i \(-0.690255\pi\)
−0.562746 + 0.826630i \(0.690255\pi\)
\(854\) −10.9783 9.50744i −0.375668 0.325338i
\(855\) 0 0
\(856\) −17.7228 −0.605753
\(857\) 46.4674i 1.58730i 0.608378 + 0.793648i \(0.291821\pi\)
−0.608378 + 0.793648i \(0.708179\pi\)
\(858\) 9.74749 + 10.3723i 0.332774 + 0.354104i
\(859\) 14.2612i 0.486585i −0.969953 0.243292i \(-0.921773\pi\)
0.969953 0.243292i \(-0.0782274\pi\)
\(860\) 0 0
\(861\) −1.11684 27.4728i −0.0380619 0.936269i
\(862\) 11.9565i 0.407240i
\(863\) −41.2743 −1.40499 −0.702496 0.711688i \(-0.747931\pi\)
−0.702496 + 0.711688i \(0.747931\pi\)
\(864\) 19.3723 + 23.3639i 0.659058 + 0.794854i
\(865\) 0 0
\(866\) −29.4891 −1.00208
\(867\) 2.67181 2.51087i 0.0907396 0.0852738i
\(868\) 9.50744 + 8.23369i 0.322704 + 0.279470i
\(869\) 5.98844i 0.203144i
\(870\) 0 0
\(871\) 19.4950i 0.660563i
\(872\) −45.7330 −1.54872
\(873\) −2.05446 + 33.0475i −0.0695328 + 1.11849i
\(874\) 23.3639i 0.790294i
\(875\) 0 0
\(876\) −12.0000 + 11.2772i −0.405442 + 0.381020i
\(877\) 38.4674i 1.29895i −0.760383 0.649475i \(-0.774989\pi\)
0.760383 0.649475i \(-0.225011\pi\)
\(878\) 14.7446i 0.497605i
\(879\) −12.9090 13.7364i −0.435408 0.463317i
\(880\) 0 0
\(881\) 32.2337 1.08598 0.542990 0.839739i \(-0.317292\pi\)
0.542990 + 0.839739i \(0.317292\pi\)
\(882\) −16.5831 + 1.35053i −0.558383 + 0.0454748i
\(883\) 49.4891i 1.66544i −0.553693 0.832721i \(-0.686782\pi\)
0.553693 0.832721i \(-0.313218\pi\)
\(884\) 24.6535i 0.829186i
\(885\) 0 0
\(886\) −5.25544 −0.176560
\(887\) 18.5109i 0.621534i 0.950486 + 0.310767i \(0.100586\pi\)
−0.950486 + 0.310767i \(0.899414\pi\)
\(888\) −21.3745 22.7446i −0.717282 0.763258i
\(889\) −1.48913 1.28962i −0.0499437 0.0432525i
\(890\) 0 0
\(891\) −2.81386 + 22.5441i −0.0942678 + 0.755256i
\(892\) −12.1620 −0.407215
\(893\) −5.63858 −0.188688
\(894\) −2.97825 3.16915i −0.0996076 0.105992i
\(895\) 0 0
\(896\) −15.6060 + 18.0202i −0.521359 + 0.602013i
\(897\) −44.1485 + 41.4891i −1.47407 + 1.38528i
\(898\) 9.21194i 0.307406i
\(899\) −3.25544 −0.108575
\(900\) 0 0
\(901\) 8.21782i 0.273775i
\(902\) 12.0000i 0.399556i
\(903\) 21.7244 0.883156i 0.722942 0.0293896i
\(904\) 8.46738 0.281621
\(905\) 0 0
\(906\) 2.37228 2.22938i 0.0788138 0.0740663i
\(907\) 8.00000i 0.265636i 0.991140 + 0.132818i \(0.0424025\pi\)
−0.991140 + 0.132818i \(0.957597\pi\)
\(908\) 33.7663i 1.12057i
\(909\) 1.11684 17.9653i 0.0370434 0.595872i
\(910\) 0 0
\(911\) 2.87419i 0.0952263i 0.998866 + 0.0476132i \(0.0151615\pi\)
−0.998866 + 0.0476132i \(0.984839\pi\)
\(912\) 2.57924 + 2.74456i 0.0854072 + 0.0908816i
\(913\) 44.1485 1.46110
\(914\) 10.2825i 0.340115i
\(915\) 0 0
\(916\) 20.7846i 0.686743i
\(917\) 9.50744 10.9783i 0.313963 0.362534i
\(918\) −13.8564 + 11.4891i −0.457330 + 0.379198i
\(919\) 5.62772 0.185641 0.0928207 0.995683i \(-0.470412\pi\)
0.0928207 + 0.995683i \(0.470412\pi\)
\(920\) 0 0
\(921\) −28.6753 + 26.9480i −0.944882 + 0.887966i
\(922\) 2.17448 0.0716127
\(923\) 1.21194i 0.0398914i
\(924\) −15.8614 + 0.644810i −0.521802 + 0.0212127i
\(925\) 0 0
\(926\) 25.7235i 0.845326i
\(927\) 1.16959 18.8139i 0.0384145 0.617928i
\(928\) 5.48913i 0.180189i
\(929\) −52.9783 −1.73816 −0.869080 0.494672i \(-0.835288\pi\)
−0.869080 + 0.494672i \(0.835288\pi\)
\(930\) 0 0
\(931\) −24.0000 + 3.46410i −0.786568 + 0.113531i
\(932\) 23.3639 0.765308
\(933\) 17.9653 16.8832i 0.588158 0.552730i
\(934\) 24.6535i 0.806686i
\(935\) 0 0
\(936\) −2.04350 + 32.8713i −0.0667938 + 1.07443i
\(937\) −0.240051 −0.00784212 −0.00392106 0.999992i \(-0.501248\pi\)
−0.00392106 + 0.999992i \(0.501248\pi\)
\(938\) 7.51811 + 6.51087i 0.245475 + 0.212588i
\(939\) 6.81386 6.40342i 0.222362 0.208968i
\(940\) 0 0
\(941\) −38.7446 −1.26304 −0.631518 0.775361i \(-0.717568\pi\)
−0.631518 + 0.775361i \(0.717568\pi\)
\(942\) 0 0
\(943\) −51.0767 −1.66329
\(944\) 5.48913 0.178656
\(945\) 0 0
\(946\) −9.48913 −0.308518
\(947\) −34.9360 −1.13527 −0.567633 0.823282i \(-0.692141\pi\)
−0.567633 + 0.823282i \(0.692141\pi\)
\(948\) 4.10891 3.86141i 0.133451 0.125413i
\(949\) −28.4674 −0.924090
\(950\) 0 0
\(951\) −2.37228 + 2.22938i −0.0769265 + 0.0722927i
\(952\) −23.3639 20.2337i −0.757227 0.655778i
\(953\) 7.62792 0.247092 0.123546 0.992339i \(-0.460573\pi\)
0.123546 + 0.992339i \(0.460573\pi\)
\(954\) −0.277187 + 4.45877i −0.00897425 + 0.144358i
\(955\) 0 0
\(956\) 28.5977i 0.924915i
\(957\) 2.99422 2.81386i 0.0967894 0.0909592i
\(958\) −32.8713 −1.06202
\(959\) −22.9783 + 26.5330i −0.742006 + 0.856795i
\(960\) 0 0
\(961\) 19.0000 0.612903
\(962\) 21.9565i 0.707906i
\(963\) 1.23472 19.8614i 0.0397882 0.640025i
\(964\) 22.5543i 0.726426i
\(965\) 0 0
\(966\) 1.25544 + 30.8820i 0.0403930 + 0.993611i
\(967\) 10.2337i 0.329093i 0.986369 + 0.164547i \(0.0526161\pi\)
−0.986369 + 0.164547i \(0.947384\pi\)
\(968\) −12.3644 −0.397407
\(969\) −19.1168 + 17.9653i −0.614122 + 0.577129i
\(970\) 0 0
\(971\) 37.2119 1.19419 0.597094 0.802171i \(-0.296322\pi\)
0.597094 + 0.802171i \(0.296322\pi\)
\(972\) −17.2828 + 12.6060i −0.554347 + 0.404337i
\(973\) 37.2203 + 32.2337i 1.19323 + 1.03336i
\(974\) 29.7021i 0.951718i
\(975\) 0 0
\(976\) 4.34896i 0.139207i
\(977\) −7.62792 −0.244039 −0.122019 0.992528i \(-0.538937\pi\)
−0.122019 + 0.992528i \(0.538937\pi\)
\(978\) 7.51811 + 8.00000i 0.240403 + 0.255812i
\(979\) 37.2203i 1.18956i
\(980\) 0 0
\(981\) 3.18614 51.2516i 0.101726 1.63634i
\(982\) 4.51087i 0.143948i
\(983\) 39.8614i 1.27138i −0.771944 0.635691i \(-0.780715\pi\)
0.771944 0.635691i \(-0.219285\pi\)
\(984\) −20.2337 + 19.0149i −0.645026 + 0.606172i
\(985\) 0 0
\(986\) 3.25544 0.103674
\(987\) 7.45299 0.302985i 0.237231 0.00964411i
\(988\) 19.5326i 0.621416i
\(989\) 40.3894i 1.28431i
\(990\) 0 0
\(991\) 25.4891 0.809689 0.404844 0.914386i \(-0.367326\pi\)
0.404844 + 0.914386i \(0.367326\pi\)
\(992\) 20.2337i 0.642420i
\(993\) 5.04868 4.74456i 0.160215 0.150564i
\(994\) 0.467376 + 0.404759i 0.0148243 + 0.0128382i
\(995\) 0 0
\(996\) 28.4674 + 30.2921i 0.902023 + 0.959840i
\(997\) −31.8217 −1.00780 −0.503902 0.863761i \(-0.668103\pi\)
−0.503902 + 0.863761i \(0.668103\pi\)
\(998\) −32.7615 −1.03705
\(999\) 26.9783 22.3692i 0.853554 0.707730i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 525.2.g.d.524.6 8
3.2 odd 2 525.2.g.e.524.3 8
5.2 odd 4 525.2.b.e.251.3 4
5.3 odd 4 105.2.b.d.41.2 yes 4
5.4 even 2 inner 525.2.g.d.524.3 8
7.6 odd 2 525.2.g.e.524.5 8
15.2 even 4 525.2.b.g.251.2 4
15.8 even 4 105.2.b.c.41.3 yes 4
15.14 odd 2 525.2.g.e.524.6 8
20.3 even 4 1680.2.f.g.881.4 4
21.20 even 2 inner 525.2.g.d.524.4 8
35.3 even 12 735.2.s.h.656.2 4
35.13 even 4 105.2.b.c.41.2 4
35.18 odd 12 735.2.s.g.656.2 4
35.23 odd 12 735.2.s.j.521.1 4
35.27 even 4 525.2.b.g.251.3 4
35.33 even 12 735.2.s.i.521.1 4
35.34 odd 2 525.2.g.e.524.4 8
60.23 odd 4 1680.2.f.h.881.2 4
105.23 even 12 735.2.s.h.521.2 4
105.38 odd 12 735.2.s.j.656.1 4
105.53 even 12 735.2.s.i.656.1 4
105.62 odd 4 525.2.b.e.251.2 4
105.68 odd 12 735.2.s.g.521.2 4
105.83 odd 4 105.2.b.d.41.3 yes 4
105.104 even 2 inner 525.2.g.d.524.5 8
140.83 odd 4 1680.2.f.h.881.1 4
420.83 even 4 1680.2.f.g.881.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.b.c.41.2 4 35.13 even 4
105.2.b.c.41.3 yes 4 15.8 even 4
105.2.b.d.41.2 yes 4 5.3 odd 4
105.2.b.d.41.3 yes 4 105.83 odd 4
525.2.b.e.251.2 4 105.62 odd 4
525.2.b.e.251.3 4 5.2 odd 4
525.2.b.g.251.2 4 15.2 even 4
525.2.b.g.251.3 4 35.27 even 4
525.2.g.d.524.3 8 5.4 even 2 inner
525.2.g.d.524.4 8 21.20 even 2 inner
525.2.g.d.524.5 8 105.104 even 2 inner
525.2.g.d.524.6 8 1.1 even 1 trivial
525.2.g.e.524.3 8 3.2 odd 2
525.2.g.e.524.4 8 35.34 odd 2
525.2.g.e.524.5 8 7.6 odd 2
525.2.g.e.524.6 8 15.14 odd 2
735.2.s.g.521.2 4 105.68 odd 12
735.2.s.g.656.2 4 35.18 odd 12
735.2.s.h.521.2 4 105.23 even 12
735.2.s.h.656.2 4 35.3 even 12
735.2.s.i.521.1 4 35.33 even 12
735.2.s.i.656.1 4 105.53 even 12
735.2.s.j.521.1 4 35.23 odd 12
735.2.s.j.656.1 4 105.38 odd 12
1680.2.f.g.881.3 4 420.83 even 4
1680.2.f.g.881.4 4 20.3 even 4
1680.2.f.h.881.1 4 140.83 odd 4
1680.2.f.h.881.2 4 60.23 odd 4