Properties

Label 525.2.b.g.251.2
Level $525$
Weight $2$
Character 525.251
Analytic conductor $4.192$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [525,2,Mod(251,525)]
 
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, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.251");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.b (of order \(2\), degree \(1\), 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: \(4\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 251.2
Root \(1.68614 + 0.396143i\) of defining polynomial
Character \(\chi\) \(=\) 525.251
Dual form 525.2.b.g.251.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.792287i q^{2} +(-1.18614 + 1.26217i) q^{3} +1.37228 q^{4} +(1.00000 + 0.939764i) q^{6} +(2.00000 + 1.73205i) q^{7} -2.67181i q^{8} +(-0.186141 - 2.99422i) q^{9} +O(q^{10})\) \(q-0.792287i q^{2} +(-1.18614 + 1.26217i) q^{3} +1.37228 q^{4} +(1.00000 + 0.939764i) q^{6} +(2.00000 + 1.73205i) q^{7} -2.67181i q^{8} +(-0.186141 - 2.99422i) q^{9} +2.52434i q^{11} +(-1.62772 + 1.73205i) q^{12} -4.10891i q^{13} +(1.37228 - 1.58457i) q^{14} +0.627719 q^{16} +4.37228 q^{17} +(-2.37228 + 0.147477i) q^{18} +3.46410i q^{19} +(-4.55842 + 0.469882i) q^{21} +2.00000 q^{22} +8.51278i q^{23} +(3.37228 + 3.16915i) q^{24} -3.25544 q^{26} +(4.00000 + 3.31662i) q^{27} +(2.74456 + 2.37686i) q^{28} -0.939764i q^{29} -3.46410i q^{31} -5.84096i q^{32} +(-3.18614 - 2.99422i) q^{33} -3.46410i q^{34} +(-0.255437 - 4.10891i) q^{36} +6.74456 q^{37} +2.74456 q^{38} +(5.18614 + 4.87375i) q^{39} +6.00000 q^{41} +(0.372281 + 3.61158i) q^{42} -4.74456 q^{43} +3.46410i q^{44} +6.74456 q^{46} -1.62772 q^{47} +(-0.744563 + 0.792287i) q^{48} +(1.00000 + 6.92820i) q^{49} +(-5.18614 + 5.51856i) q^{51} -5.63858i q^{52} -1.87953i q^{53} +(2.62772 - 3.16915i) q^{54} +(4.62772 - 5.34363i) q^{56} +(-4.37228 - 4.10891i) q^{57} -0.744563 q^{58} +8.74456 q^{59} -6.92820i q^{61} -2.74456 q^{62} +(4.81386 - 6.31084i) q^{63} -3.37228 q^{64} +(-2.37228 + 2.52434i) q^{66} -4.74456 q^{67} +6.00000 q^{68} +(-10.7446 - 10.0974i) q^{69} -0.294954i q^{71} +(-8.00000 + 0.497333i) q^{72} +6.92820i q^{73} -5.34363i q^{74} +4.75372i q^{76} +(-4.37228 + 5.04868i) q^{77} +(3.86141 - 4.10891i) q^{78} -2.37228 q^{79} +(-8.93070 + 1.11469i) q^{81} -4.75372i q^{82} -17.4891 q^{83} +(-6.25544 + 0.644810i) q^{84} +3.75906i q^{86} +(1.18614 + 1.11469i) q^{87} +6.74456 q^{88} -14.7446 q^{89} +(7.11684 - 8.21782i) q^{91} +11.6819i q^{92} +(4.37228 + 4.10891i) q^{93} +1.28962i q^{94} +(7.37228 + 6.92820i) q^{96} -11.0371i q^{97} +(5.48913 - 0.792287i) q^{98} +(7.55842 - 0.469882i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{3} - 6 q^{4} + 4 q^{6} + 8 q^{7} + 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + q^{3} - 6 q^{4} + 4 q^{6} + 8 q^{7} + 5 q^{9} - 18 q^{12} - 6 q^{14} + 14 q^{16} + 6 q^{17} + 2 q^{18} - q^{21} + 8 q^{22} + 2 q^{24} - 36 q^{26} + 16 q^{27} - 12 q^{28} - 7 q^{33} - 24 q^{36} + 4 q^{37} - 12 q^{38} + 15 q^{39} + 24 q^{41} - 10 q^{42} + 4 q^{43} + 4 q^{46} - 18 q^{47} + 20 q^{48} + 4 q^{49} - 15 q^{51} + 22 q^{54} + 30 q^{56} - 6 q^{57} + 20 q^{58} + 12 q^{59} + 12 q^{62} + 25 q^{63} - 2 q^{64} + 2 q^{66} + 4 q^{67} + 24 q^{68} - 20 q^{69} - 32 q^{72} - 6 q^{77} - 42 q^{78} + 2 q^{79} - 7 q^{81} - 24 q^{83} - 48 q^{84} - q^{87} + 4 q^{88} - 36 q^{89} - 6 q^{91} + 6 q^{93} + 18 q^{96} - 24 q^{98} + 13 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.792287i 0.560232i −0.959966 0.280116i \(-0.909627\pi\)
0.959966 0.280116i \(-0.0903729\pi\)
\(3\) −1.18614 + 1.26217i −0.684819 + 0.728714i
\(4\) 1.37228 0.686141
\(5\) 0 0
\(6\) 1.00000 + 0.939764i 0.408248 + 0.383657i
\(7\) 2.00000 + 1.73205i 0.755929 + 0.654654i
\(8\) 2.67181i 0.944629i
\(9\) −0.186141 2.99422i −0.0620469 0.998073i
\(10\) 0 0
\(11\) 2.52434i 0.761116i 0.924757 + 0.380558i \(0.124268\pi\)
−0.924757 + 0.380558i \(0.875732\pi\)
\(12\) −1.62772 + 1.73205i −0.469882 + 0.500000i
\(13\) 4.10891i 1.13961i −0.821781 0.569804i \(-0.807019\pi\)
0.821781 0.569804i \(-0.192981\pi\)
\(14\) 1.37228 1.58457i 0.366758 0.423495i
\(15\) 0 0
\(16\) 0.627719 0.156930
\(17\) 4.37228 1.06043 0.530217 0.847862i \(-0.322110\pi\)
0.530217 + 0.847862i \(0.322110\pi\)
\(18\) −2.37228 + 0.147477i −0.559152 + 0.0347606i
\(19\) 3.46410i 0.794719i 0.917663 + 0.397360i \(0.130073\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) 0 0
\(21\) −4.55842 + 0.469882i −0.994729 + 0.102537i
\(22\) 2.00000 0.426401
\(23\) 8.51278i 1.77504i 0.460772 + 0.887518i \(0.347572\pi\)
−0.460772 + 0.887518i \(0.652428\pi\)
\(24\) 3.37228 + 3.16915i 0.688364 + 0.646900i
\(25\) 0 0
\(26\) −3.25544 −0.638444
\(27\) 4.00000 + 3.31662i 0.769800 + 0.638285i
\(28\) 2.74456 + 2.37686i 0.518674 + 0.449185i
\(29\) 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 \(-0.100693\pi\)
\(32\) 5.84096i 1.03255i
\(33\) −3.18614 2.99422i −0.554636 0.521227i
\(34\) 3.46410i 0.594089i
\(35\) 0 0
\(36\) −0.255437 4.10891i −0.0425729 0.684819i
\(37\) 6.74456 1.10880 0.554400 0.832251i \(-0.312948\pi\)
0.554400 + 0.832251i \(0.312948\pi\)
\(38\) 2.74456 0.445227
\(39\) 5.18614 + 4.87375i 0.830447 + 0.780424i
\(40\) 0 0
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0.372281 + 3.61158i 0.0574443 + 0.557279i
\(43\) −4.74456 −0.723539 −0.361770 0.932268i \(-0.617827\pi\)
−0.361770 + 0.932268i \(0.617827\pi\)
\(44\) 3.46410i 0.522233i
\(45\) 0 0
\(46\) 6.74456 0.994432
\(47\) −1.62772 −0.237427 −0.118714 0.992929i \(-0.537877\pi\)
−0.118714 + 0.992929i \(0.537877\pi\)
\(48\) −0.744563 + 0.792287i −0.107468 + 0.114357i
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 0 0
\(51\) −5.18614 + 5.51856i −0.726205 + 0.772753i
\(52\) 5.63858i 0.781931i
\(53\) 1.87953i 0.258173i −0.991633 0.129086i \(-0.958796\pi\)
0.991633 0.129086i \(-0.0412045\pi\)
\(54\) 2.62772 3.16915i 0.357587 0.431266i
\(55\) 0 0
\(56\) 4.62772 5.34363i 0.618405 0.714072i
\(57\) −4.37228 4.10891i −0.579123 0.544239i
\(58\) −0.744563 −0.0977659
\(59\) 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 \(-0.146275\pi\)
\(62\) −2.74456 −0.348560
\(63\) 4.81386 6.31084i 0.606489 0.795092i
\(64\) −3.37228 −0.421535
\(65\) 0 0
\(66\) −2.37228 + 2.52434i −0.292008 + 0.310725i
\(67\) −4.74456 −0.579641 −0.289820 0.957081i \(-0.593596\pi\)
−0.289820 + 0.957081i \(0.593596\pi\)
\(68\) 6.00000 0.727607
\(69\) −10.7446 10.0974i −1.29349 1.21558i
\(70\) 0 0
\(71\) 0.294954i 0.0350046i −0.999847 0.0175023i \(-0.994429\pi\)
0.999847 0.0175023i \(-0.00557143\pi\)
\(72\) −8.00000 + 0.497333i −0.942809 + 0.0586113i
\(73\) 6.92820i 0.810885i 0.914121 + 0.405442i \(0.132883\pi\)
−0.914121 + 0.405442i \(0.867117\pi\)
\(74\) 5.34363i 0.621184i
\(75\) 0 0
\(76\) 4.75372i 0.545289i
\(77\) −4.37228 + 5.04868i −0.498268 + 0.575350i
\(78\) 3.86141 4.10891i 0.437218 0.465243i
\(79\) −2.37228 −0.266903 −0.133451 0.991055i \(-0.542606\pi\)
−0.133451 + 0.991055i \(0.542606\pi\)
\(80\) 0 0
\(81\) −8.93070 + 1.11469i −0.992300 + 0.123855i
\(82\) 4.75372i 0.524961i
\(83\) −17.4891 −1.91968 −0.959840 0.280546i \(-0.909484\pi\)
−0.959840 + 0.280546i \(0.909484\pi\)
\(84\) −6.25544 + 0.644810i −0.682524 + 0.0703546i
\(85\) 0 0
\(86\) 3.75906i 0.405349i
\(87\) 1.18614 + 1.11469i 0.127168 + 0.119508i
\(88\) 6.74456 0.718973
\(89\) −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
\(92\) 11.6819i 1.21792i
\(93\) 4.37228 + 4.10891i 0.453384 + 0.426074i
\(94\) 1.28962i 0.133014i
\(95\) 0 0
\(96\) 7.37228 + 6.92820i 0.752430 + 0.707107i
\(97\) 11.0371i 1.12065i −0.828273 0.560325i \(-0.810676\pi\)
0.828273 0.560325i \(-0.189324\pi\)
\(98\) 5.48913 0.792287i 0.554485 0.0800331i
\(99\) 7.55842 0.469882i 0.759650 0.0472249i
\(100\) 0 0
\(101\) −6.00000 −0.597022 −0.298511 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) 4.37228 + 4.10891i 0.432920 + 0.406843i
\(103\) 6.28339i 0.619121i −0.950880 0.309561i \(-0.899818\pi\)
0.950880 0.309561i \(-0.100182\pi\)
\(104\) −10.9783 −1.07651
\(105\) 0 0
\(106\) −1.48913 −0.144637
\(107\) 6.63325i 0.641260i −0.947204 0.320630i \(-0.896105\pi\)
0.947204 0.320630i \(-0.103895\pi\)
\(108\) 5.48913 + 4.55134i 0.528191 + 0.437953i
\(109\) −17.1168 −1.63950 −0.819748 0.572724i \(-0.805887\pi\)
−0.819748 + 0.572724i \(0.805887\pi\)
\(110\) 0 0
\(111\) −8.00000 + 8.51278i −0.759326 + 0.807997i
\(112\) 1.25544 + 1.08724i 0.118628 + 0.102735i
\(113\) 3.16915i 0.298128i −0.988828 0.149064i \(-0.952374\pi\)
0.988828 0.149064i \(-0.0476261\pi\)
\(114\) −3.25544 + 3.46410i −0.304900 + 0.324443i
\(115\) 0 0
\(116\) 1.28962i 0.119738i
\(117\) −12.3030 + 0.764836i −1.13741 + 0.0707091i
\(118\) 6.92820i 0.637793i
\(119\) 8.74456 + 7.57301i 0.801613 + 0.694217i
\(120\) 0 0
\(121\) 4.62772 0.420702
\(122\) −5.48913 −0.496962
\(123\) −7.11684 + 7.57301i −0.641704 + 0.682836i
\(124\) 4.75372i 0.426897i
\(125\) 0 0
\(126\) −5.00000 3.81396i −0.445435 0.339774i
\(127\) 0.744563 0.0660693 0.0330346 0.999454i \(-0.489483\pi\)
0.0330346 + 0.999454i \(0.489483\pi\)
\(128\) 9.01011i 0.796389i
\(129\) 5.62772 5.98844i 0.495493 0.527253i
\(130\) 0 0
\(131\) −5.48913 −0.479587 −0.239794 0.970824i \(-0.577080\pi\)
−0.239794 + 0.970824i \(0.577080\pi\)
\(132\) −4.37228 4.10891i −0.380558 0.357635i
\(133\) −6.00000 + 6.92820i −0.520266 + 0.600751i
\(134\) 3.75906i 0.324733i
\(135\) 0 0
\(136\) 11.6819i 1.00172i
\(137\) 13.2665i 1.13343i 0.823913 + 0.566717i \(0.191787\pi\)
−0.823913 + 0.566717i \(0.808213\pi\)
\(138\) −8.00000 + 8.51278i −0.681005 + 0.724656i
\(139\) 18.6101i 1.57849i −0.614078 0.789245i \(-0.710472\pi\)
0.614078 0.789245i \(-0.289528\pi\)
\(140\) 0 0
\(141\) 1.93070 2.05446i 0.162595 0.173016i
\(142\) −0.233688 −0.0196107
\(143\) 10.3723 0.867374
\(144\) −0.116844 1.87953i −0.00973700 0.156627i
\(145\) 0 0
\(146\) 5.48913 0.454283
\(147\) −9.93070 6.95565i −0.819071 0.573693i
\(148\) 9.25544 0.760792
\(149\) 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 \(0.530773\pi\)
\(152\) 9.25544 0.750715
\(153\) −0.813859 13.0916i −0.0657966 1.05839i
\(154\) 4.00000 + 3.46410i 0.322329 + 0.279145i
\(155\) 0 0
\(156\) 7.11684 + 6.68815i 0.569804 + 0.535481i
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 1.87953i 0.149527i
\(159\) 2.37228 + 2.22938i 0.188134 + 0.176802i
\(160\) 0 0
\(161\) −14.7446 + 17.0256i −1.16203 + 1.34180i
\(162\) 0.883156 + 7.07568i 0.0693873 + 0.555918i
\(163\) −8.00000 −0.626608 −0.313304 0.949653i \(-0.601436\pi\)
−0.313304 + 0.949653i \(0.601436\pi\)
\(164\) 8.23369 0.642943
\(165\) 0 0
\(166\) 13.8564i 1.07547i
\(167\) −4.88316 −0.377870 −0.188935 0.981990i \(-0.560504\pi\)
−0.188935 + 0.981990i \(0.560504\pi\)
\(168\) 1.25544 + 12.1793i 0.0968591 + 0.939650i
\(169\) −3.88316 −0.298704
\(170\) 0 0
\(171\) 10.3723 0.644810i 0.793188 0.0493099i
\(172\) −6.51087 −0.496450
\(173\) −1.11684 −0.0849121 −0.0424560 0.999098i \(-0.513518\pi\)
−0.0424560 + 0.999098i \(0.513518\pi\)
\(174\) 0.883156 0.939764i 0.0669519 0.0712433i
\(175\) 0 0
\(176\) 1.58457i 0.119442i
\(177\) −10.3723 + 11.0371i −0.779628 + 0.829600i
\(178\) 11.6819i 0.875597i
\(179\) 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 \(-0.0152619\pi\)
\(182\) −6.51087 5.63858i −0.482618 0.417960i
\(183\) 8.74456 + 8.21782i 0.646417 + 0.607479i
\(184\) 22.7446 1.67675
\(185\) 0 0
\(186\) 3.25544 3.46410i 0.238700 0.254000i
\(187\) 11.0371i 0.807114i
\(188\) −2.23369 −0.162908
\(189\) 2.25544 + 13.5615i 0.164059 + 0.986451i
\(190\) 0 0
\(191\) 20.8395i 1.50789i −0.656935 0.753947i \(-0.728147\pi\)
0.656935 0.753947i \(-0.271853\pi\)
\(192\) 4.00000 4.25639i 0.288675 0.307178i
\(193\) 12.2337 0.880600 0.440300 0.897851i \(-0.354872\pi\)
0.440300 + 0.897851i \(0.354872\pi\)
\(194\) −8.74456 −0.627823
\(195\) 0 0
\(196\) 1.37228 + 9.50744i 0.0980201 + 0.679103i
\(197\) 15.7359i 1.12114i −0.828107 0.560569i \(-0.810582\pi\)
0.828107 0.560569i \(-0.189418\pi\)
\(198\) −0.372281 5.98844i −0.0264569 0.425580i
\(199\) 26.8280i 1.90178i 0.309524 + 0.950892i \(0.399830\pi\)
−0.309524 + 0.950892i \(0.600170\pi\)
\(200\) 0 0
\(201\) 5.62772 5.98844i 0.396949 0.422392i
\(202\) 4.75372i 0.334471i
\(203\) 1.62772 1.87953i 0.114243 0.131917i
\(204\) −7.11684 + 7.57301i −0.498279 + 0.530217i
\(205\) 0 0
\(206\) −4.97825 −0.346851
\(207\) 25.4891 1.58457i 1.77162 0.110136i
\(208\) 2.57924i 0.178838i
\(209\) −8.74456 −0.604874
\(210\) 0 0
\(211\) −11.1168 −0.765315 −0.382658 0.923890i \(-0.624991\pi\)
−0.382658 + 0.923890i \(0.624991\pi\)
\(212\) 2.57924i 0.177143i
\(213\) 0.372281 + 0.349857i 0.0255083 + 0.0239718i
\(214\) −5.25544 −0.359254
\(215\) 0 0
\(216\) 8.86141 10.6873i 0.602942 0.727176i
\(217\) 6.00000 6.92820i 0.407307 0.470317i
\(218\) 13.5615i 0.918497i
\(219\) −8.74456 8.21782i −0.590903 0.555309i
\(220\) 0 0
\(221\) 17.9653i 1.20848i
\(222\) 6.74456 + 6.33830i 0.452665 + 0.425399i
\(223\) 8.86263i 0.593486i −0.954957 0.296743i \(-0.904100\pi\)
0.954957 0.296743i \(-0.0959004\pi\)
\(224\) 10.1168 11.6819i 0.675960 0.780531i
\(225\) 0 0
\(226\) −2.51087 −0.167021
\(227\) 24.6060 1.63316 0.816578 0.577235i \(-0.195869\pi\)
0.816578 + 0.577235i \(0.195869\pi\)
\(228\) −6.00000 5.63858i −0.397360 0.373424i
\(229\) 15.1460i 1.00088i −0.865772 0.500439i \(-0.833172\pi\)
0.865772 0.500439i \(-0.166828\pi\)
\(230\) 0 0
\(231\) −1.18614 11.5070i −0.0780423 0.757105i
\(232\) −2.51087 −0.164847
\(233\) 17.0256i 1.11538i −0.830049 0.557691i \(-0.811688\pi\)
0.830049 0.557691i \(-0.188312\pi\)
\(234\) 0.605969 + 9.74749i 0.0396134 + 0.637214i
\(235\) 0 0
\(236\) 12.0000 0.781133
\(237\) 2.81386 2.99422i 0.182780 0.194495i
\(238\) 6.00000 6.92820i 0.388922 0.449089i
\(239\) 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 \(0.822433\pi\)
\(242\) 3.66648i 0.235690i
\(243\) 9.18614 12.5942i 0.589291 0.807921i
\(244\) 9.50744i 0.608652i
\(245\) 0 0
\(246\) 6.00000 + 5.63858i 0.382546 + 0.359503i
\(247\) 14.2337 0.905668
\(248\) −9.25544 −0.587721
\(249\) 20.7446 22.0742i 1.31463 1.39890i
\(250\) 0 0
\(251\) 5.48913 0.346471 0.173235 0.984880i \(-0.444578\pi\)
0.173235 + 0.984880i \(0.444578\pi\)
\(252\) 6.60597 8.66025i 0.416137 0.545545i
\(253\) −21.4891 −1.35101
\(254\) 0.589907i 0.0370141i
\(255\) 0 0
\(256\) −13.8832 −0.867697
\(257\) 0.510875 0.0318675 0.0159337 0.999873i \(-0.494928\pi\)
0.0159337 + 0.999873i \(0.494928\pi\)
\(258\) −4.74456 4.45877i −0.295384 0.277591i
\(259\) 13.4891 + 11.6819i 0.838173 + 0.725880i
\(260\) 0 0
\(261\) −2.81386 + 0.174928i −0.174174 + 0.0108278i
\(262\) 4.34896i 0.268680i
\(263\) 0.294954i 0.0181876i 0.999959 + 0.00909381i \(0.00289469\pi\)
−0.999959 + 0.00909381i \(0.997105\pi\)
\(264\) −8.00000 + 8.51278i −0.492366 + 0.523925i
\(265\) 0 0
\(266\) 5.48913 + 4.75372i 0.336560 + 0.291469i
\(267\) 17.4891 18.6101i 1.07032 1.13892i
\(268\) −6.51087 −0.397715
\(269\) −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 \(0.953880\pi\)
\(272\) 2.74456 0.166414
\(273\) 1.93070 + 18.7302i 0.116851 + 1.13360i
\(274\) 10.5109 0.634985
\(275\) 0 0
\(276\) −14.7446 13.8564i −0.887518 0.834058i
\(277\) −28.2337 −1.69640 −0.848199 0.529678i \(-0.822313\pi\)
−0.848199 + 0.529678i \(0.822313\pi\)
\(278\) −14.7446 −0.884320
\(279\) −10.3723 + 0.644810i −0.620972 + 0.0386038i
\(280\) 0 0
\(281\) 28.0627i 1.67408i 0.547143 + 0.837039i \(0.315715\pi\)
−0.547143 + 0.837039i \(0.684285\pi\)
\(282\) −1.62772 1.52967i −0.0969292 0.0910906i
\(283\) 0.644810i 0.0383300i 0.999816 + 0.0191650i \(0.00610078\pi\)
−0.999816 + 0.0191650i \(0.993899\pi\)
\(284\) 0.404759i 0.0240181i
\(285\) 0 0
\(286\) 8.21782i 0.485930i
\(287\) 12.0000 + 10.3923i 0.708338 + 0.613438i
\(288\) −17.4891 + 1.08724i −1.03056 + 0.0640663i
\(289\) 2.11684 0.124520
\(290\) 0 0
\(291\) 13.9307 + 13.0916i 0.816632 + 0.767441i
\(292\) 9.50744i 0.556381i
\(293\) −10.8832 −0.635801 −0.317900 0.948124i \(-0.602978\pi\)
−0.317900 + 0.948124i \(0.602978\pi\)
\(294\) −5.51087 + 7.86797i −0.321401 + 0.458869i
\(295\) 0 0
\(296\) 18.0202i 1.04740i
\(297\) −8.37228 + 10.0974i −0.485809 + 0.585908i
\(298\) 2.51087 0.145451
\(299\) 34.9783 2.02284
\(300\) 0 0
\(301\) −9.48913 8.21782i −0.546944 0.473667i
\(302\) 1.87953i 0.108155i
\(303\) 7.11684 7.57301i 0.408852 0.435058i
\(304\) 2.17448i 0.124715i
\(305\) 0 0
\(306\) −10.3723 + 0.644810i −0.592944 + 0.0368613i
\(307\) 22.7190i 1.29664i 0.761366 + 0.648322i \(0.224529\pi\)
−0.761366 + 0.648322i \(0.775471\pi\)
\(308\) −6.00000 + 6.92820i −0.341882 + 0.394771i
\(309\) 7.93070 + 7.45299i 0.451162 + 0.423986i
\(310\) 0 0
\(311\) 14.2337 0.807118 0.403559 0.914954i \(-0.367773\pi\)
0.403559 + 0.914954i \(0.367773\pi\)
\(312\) 13.0217 13.8564i 0.737211 0.784465i
\(313\) 5.39853i 0.305143i 0.988292 + 0.152572i \(0.0487554\pi\)
−0.988292 + 0.152572i \(0.951245\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −3.25544 −0.183133
\(317\) 1.87953i 0.105565i −0.998606 0.0527824i \(-0.983191\pi\)
0.998606 0.0527824i \(-0.0168090\pi\)
\(318\) 1.76631 1.87953i 0.0990499 0.105399i
\(319\) 2.37228 0.132822
\(320\) 0 0
\(321\) 8.37228 + 7.86797i 0.467295 + 0.439147i
\(322\) 13.4891 + 11.6819i 0.751720 + 0.651008i
\(323\) 15.1460i 0.842747i
\(324\) −12.2554 + 1.52967i −0.680858 + 0.0849817i
\(325\) 0 0
\(326\) 6.33830i 0.351046i
\(327\) 20.3030 21.6043i 1.12276 1.19472i
\(328\) 16.0309i 0.885158i
\(329\) −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 \(0.535063\pi\)
\(332\) −24.0000 −1.31717
\(333\) −1.25544 20.1947i −0.0687975 1.10666i
\(334\) 3.86886i 0.211695i
\(335\) 0 0
\(336\) −2.86141 + 0.294954i −0.156103 + 0.0160910i
\(337\) −16.2337 −0.884305 −0.442153 0.896940i \(-0.645785\pi\)
−0.442153 + 0.896940i \(0.645785\pi\)
\(338\) 3.07657i 0.167344i
\(339\) 4.00000 + 3.75906i 0.217250 + 0.204164i
\(340\) 0 0
\(341\) 8.74456 0.473545
\(342\) −0.510875 8.21782i −0.0276249 0.444369i
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 12.6766i 0.683476i
\(345\) 0 0
\(346\) 0.884861i 0.0475704i
\(347\) 14.8511i 0.797247i −0.917115 0.398624i \(-0.869488\pi\)
0.917115 0.398624i \(-0.130512\pi\)
\(348\) 1.62772 + 1.52967i 0.0872549 + 0.0819990i
\(349\) 15.1460i 0.810748i 0.914151 + 0.405374i \(0.132859\pi\)
−0.914151 + 0.405374i \(0.867141\pi\)
\(350\) 0 0
\(351\) 13.6277 16.4356i 0.727394 0.877270i
\(352\) 14.7446 0.785888
\(353\) 25.1168 1.33683 0.668417 0.743786i \(-0.266972\pi\)
0.668417 + 0.743786i \(0.266972\pi\)
\(354\) 8.74456 + 8.21782i 0.464768 + 0.436772i
\(355\) 0 0
\(356\) −20.2337 −1.07238
\(357\) −19.9307 + 2.05446i −1.05484 + 0.108733i
\(358\) 5.25544 0.277758
\(359\) 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
\(362\) −1.02175 −0.0537020
\(363\) −5.48913 + 5.84096i −0.288104 + 0.306571i
\(364\) 9.76631 11.2772i 0.511894 0.591084i
\(365\) 0 0
\(366\) 6.51087 6.92820i 0.340329 0.362143i
\(367\) 35.2858i 1.84191i 0.389675 + 0.920953i \(0.372587\pi\)
−0.389675 + 0.920953i \(0.627413\pi\)
\(368\) 5.34363i 0.278556i
\(369\) −1.11684 17.9653i −0.0581406 0.935237i
\(370\) 0 0
\(371\) 3.25544 3.75906i 0.169014 0.195160i
\(372\) 6.00000 + 5.63858i 0.311086 + 0.292347i
\(373\) 13.2554 0.686341 0.343170 0.939273i \(-0.388499\pi\)
0.343170 + 0.939273i \(0.388499\pi\)
\(374\) 8.74456 0.452171
\(375\) 0 0
\(376\) 4.34896i 0.224281i
\(377\) −3.86141 −0.198873
\(378\) 10.7446 1.78695i 0.552641 0.0919110i
\(379\) −21.4891 −1.10382 −0.551911 0.833903i \(-0.686101\pi\)
−0.551911 + 0.833903i \(0.686101\pi\)
\(380\) 0 0
\(381\) −0.883156 + 0.939764i −0.0452455 + 0.0481456i
\(382\) −16.5109 −0.844770
\(383\) 5.48913 0.280481 0.140241 0.990117i \(-0.455212\pi\)
0.140241 + 0.990117i \(0.455212\pi\)
\(384\) 11.3723 + 10.6873i 0.580339 + 0.545382i
\(385\) 0 0
\(386\) 9.69259i 0.493340i
\(387\) 0.883156 + 14.2063i 0.0448933 + 0.722145i
\(388\) 15.1460i 0.768923i
\(389\) 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
\(392\) 18.5109 2.67181i 0.934940 0.134947i
\(393\) 6.51087 6.92820i 0.328430 0.349482i
\(394\) −12.4674 −0.628097
\(395\) 0 0
\(396\) 10.3723 0.644810i 0.521227 0.0324029i
\(397\) 26.1831i 1.31409i −0.753850 0.657047i \(-0.771805\pi\)
0.753850 0.657047i \(-0.228195\pi\)
\(398\) 21.2554 1.06544
\(399\) −1.62772 15.7908i −0.0814879 0.790531i
\(400\) 0 0
\(401\) 5.98844i 0.299048i 0.988758 + 0.149524i \(0.0477742\pi\)
−0.988758 + 0.149524i \(0.952226\pi\)
\(402\) −4.74456 4.45877i −0.236637 0.222383i
\(403\) −14.2337 −0.709030
\(404\) −8.23369 −0.409641
\(405\) 0 0
\(406\) −1.48913 1.28962i −0.0739040 0.0640028i
\(407\) 17.0256i 0.843925i
\(408\) 14.7446 + 13.8564i 0.729965 + 0.685994i
\(409\) 24.6535i 1.21904i −0.792772 0.609518i \(-0.791363\pi\)
0.792772 0.609518i \(-0.208637\pi\)
\(410\) 0 0
\(411\) −16.7446 15.7359i −0.825948 0.776196i
\(412\) 8.62258i 0.424804i
\(413\) 17.4891 + 15.1460i 0.860584 + 0.745287i
\(414\) −1.25544 20.1947i −0.0617014 0.992515i
\(415\) 0 0
\(416\) −24.0000 −1.17670
\(417\) 23.4891 + 22.0742i 1.15027 + 1.08098i
\(418\) 6.92820i 0.338869i
\(419\) −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 \(0.384166\pi\)
\(422\) 8.80773i 0.428754i
\(423\) 0.302985 + 4.87375i 0.0147316 + 0.236970i
\(424\) −5.02175 −0.243878
\(425\) 0 0
\(426\) 0.277187 0.294954i 0.0134297 0.0142906i
\(427\) 12.0000 13.8564i 0.580721 0.670559i
\(428\) 9.10268i 0.439995i
\(429\) −12.3030 + 13.0916i −0.593994 + 0.632067i
\(430\) 0 0
\(431\) 15.0911i 0.726914i 0.931611 + 0.363457i \(0.118404\pi\)
−0.931611 + 0.363457i \(0.881596\pi\)
\(432\) 2.51087 + 2.08191i 0.120805 + 0.100166i
\(433\) 37.2203i 1.78869i 0.447377 + 0.894346i \(0.352358\pi\)
−0.447377 + 0.894346i \(0.647642\pi\)
\(434\) −5.48913 4.75372i −0.263486 0.228186i
\(435\) 0 0
\(436\) −23.4891 −1.12493
\(437\) −29.4891 −1.41066
\(438\) −6.51087 + 6.92820i −0.311102 + 0.331042i
\(439\) 18.6101i 0.888213i 0.895974 + 0.444106i \(0.146479\pi\)
−0.895974 + 0.444106i \(0.853521\pi\)
\(440\) 0 0
\(441\) 20.5584 4.28384i 0.978972 0.203992i
\(442\) −14.2337 −0.677027
\(443\) 6.63325i 0.315155i −0.987507 0.157578i \(-0.949632\pi\)
0.987507 0.157578i \(-0.0503684\pi\)
\(444\) −10.9783 + 11.6819i −0.521005 + 0.554400i
\(445\) 0 0
\(446\) −7.02175 −0.332489
\(447\) −4.00000 3.75906i −0.189194 0.177797i
\(448\) −6.74456 5.84096i −0.318651 0.275960i
\(449\) 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
\(452\) 4.34896i 0.204558i
\(453\) 2.81386 2.99422i 0.132207 0.140681i
\(454\) 19.4950i 0.914945i
\(455\) 0 0
\(456\) −10.9783 + 11.6819i −0.514104 + 0.547056i
\(457\) −12.9783 −0.607097 −0.303548 0.952816i \(-0.598171\pi\)
−0.303548 + 0.952816i \(0.598171\pi\)
\(458\) −12.0000 −0.560723
\(459\) 17.4891 + 14.5012i 0.816322 + 0.676859i
\(460\) 0 0
\(461\) −2.74456 −0.127827 −0.0639135 0.997955i \(-0.520358\pi\)
−0.0639135 + 0.997955i \(0.520358\pi\)
\(462\) −9.11684 + 0.939764i −0.424154 + 0.0437218i
\(463\) 32.4674 1.50889 0.754443 0.656365i \(-0.227907\pi\)
0.754443 + 0.656365i \(0.227907\pi\)
\(464\) 0.589907i 0.0273858i
\(465\) 0 0
\(466\) −13.4891 −0.624872
\(467\) −31.1168 −1.43992 −0.719958 0.694018i \(-0.755839\pi\)
−0.719958 + 0.694018i \(0.755839\pi\)
\(468\) −16.8832 + 1.04957i −0.780424 + 0.0485164i
\(469\) −9.48913 8.21782i −0.438167 0.379464i
\(470\) 0 0
\(471\) 0 0
\(472\) 23.3639i 1.07541i
\(473\) 11.9769i 0.550697i
\(474\) −2.37228 2.22938i −0.108962 0.102399i
\(475\) 0 0
\(476\) 12.0000 + 10.3923i 0.550019 + 0.476331i
\(477\) −5.62772 + 0.349857i −0.257676 + 0.0160188i
\(478\) −16.5109 −0.755190
\(479\) −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
\(482\) 13.0217 0.593124
\(483\) −4.00000 38.8048i −0.182006 1.76568i
\(484\) 6.35053 0.288661
\(485\) 0 0
\(486\) −9.97825 7.27806i −0.452623 0.330139i
\(487\) −37.4891 −1.69879 −0.849397 0.527754i \(-0.823034\pi\)
−0.849397 + 0.527754i \(0.823034\pi\)
\(488\) −18.5109 −0.837948
\(489\) 9.48913 10.0974i 0.429113 0.456618i
\(490\) 0 0
\(491\) 5.69349i 0.256943i −0.991713 0.128472i \(-0.958993\pi\)
0.991713 0.128472i \(-0.0410072\pi\)
\(492\) −9.76631 + 10.3923i −0.440299 + 0.468521i
\(493\) 4.10891i 0.185056i
\(494\) 11.2772i 0.507384i
\(495\) 0 0
\(496\) 2.17448i 0.0976371i
\(497\) 0.510875 0.589907i 0.0229159 0.0264610i
\(498\) −17.4891 16.4356i −0.783706 0.736499i
\(499\) 41.3505 1.85110 0.925552 0.378620i \(-0.123601\pi\)
0.925552 + 0.378620i \(0.123601\pi\)
\(500\) 0 0
\(501\) 5.79211 6.16337i 0.258772 0.275359i
\(502\) 4.34896i 0.194104i
\(503\) 12.6060 0.562072 0.281036 0.959697i \(-0.409322\pi\)
0.281036 + 0.959697i \(0.409322\pi\)
\(504\) −16.8614 12.8617i −0.751067 0.572907i
\(505\) 0 0
\(506\) 17.0256i 0.756878i
\(507\) 4.60597 4.90120i 0.204558 0.217670i
\(508\) 1.02175 0.0453328
\(509\) 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
\(512\) 7.02078i 0.310277i
\(513\) −11.4891 + 13.8564i −0.507257 + 0.611775i
\(514\) 0.404759i 0.0178532i
\(515\) 0 0
\(516\) 7.72281 8.21782i 0.339978 0.361770i
\(517\) 4.10891i 0.180710i
\(518\) 9.25544 10.6873i 0.406661 0.469571i
\(519\) 1.32473 1.40965i 0.0581494 0.0618766i
\(520\) 0 0
\(521\) 34.4674 1.51004 0.755022 0.655700i \(-0.227626\pi\)
0.755022 + 0.655700i \(0.227626\pi\)
\(522\) 0.138593 + 2.22938i 0.00606607 + 0.0975775i
\(523\) 10.3923i 0.454424i 0.973845 + 0.227212i \(0.0729610\pi\)
−0.973845 + 0.227212i \(0.927039\pi\)
\(524\) −7.53262 −0.329064
\(525\) 0 0
\(526\) 0.233688 0.0101893
\(527\) 15.1460i 0.659771i
\(528\) −2.00000 1.87953i −0.0870388 0.0817959i
\(529\) −49.4674 −2.15076
\(530\) 0 0
\(531\) −1.62772 26.1831i −0.0706370 1.13625i
\(532\) −8.23369 + 9.50744i −0.356976 + 0.412200i
\(533\) 24.6535i 1.06786i
\(534\) −14.7446 13.8564i −0.638060 0.599625i
\(535\) 0 0
\(536\) 12.6766i 0.547545i
\(537\) −8.37228 7.86797i −0.361291 0.339528i
\(538\) 2.17448i 0.0937485i
\(539\) −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 \(0.324468\pi\)
\(542\) 3.76631 0.161777
\(543\) 1.62772 + 1.52967i 0.0698521 + 0.0656445i
\(544\) 25.5383i 1.09495i
\(545\) 0 0
\(546\) 14.8397 1.52967i 0.635079 0.0654639i
\(547\) 2.97825 0.127341 0.0636704 0.997971i \(-0.479719\pi\)
0.0636704 + 0.997971i \(0.479719\pi\)
\(548\) 18.2054i 0.777695i
\(549\) −20.7446 + 1.28962i −0.885356 + 0.0550397i
\(550\) 0 0
\(551\) 3.25544 0.138686
\(552\) −26.9783 + 28.7075i −1.14827 + 1.22187i
\(553\) −4.74456 4.10891i −0.201759 0.174729i
\(554\) 22.3692i 0.950376i
\(555\) 0 0
\(556\) 25.5383i 1.08307i
\(557\) 17.6155i 0.746391i 0.927753 + 0.373196i \(0.121738\pi\)
−0.927753 + 0.373196i \(0.878262\pi\)
\(558\) 0.510875 + 8.21782i 0.0216271 + 0.347888i
\(559\) 19.4950i 0.824550i
\(560\) 0 0
\(561\) −13.9307 13.0916i −0.588155 0.552727i
\(562\) 22.2337 0.937872
\(563\) −17.4891 −0.737079 −0.368539 0.929612i \(-0.620142\pi\)
−0.368539 + 0.929612i \(0.620142\pi\)
\(564\) 2.64947 2.81929i 0.111563 0.118714i
\(565\) 0 0
\(566\) 0.510875 0.0214737
\(567\) −19.7921 13.2390i −0.831190 0.555988i
\(568\) −0.788061 −0.0330663
\(569\) 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 \(0.526673\pi\)
\(572\) 14.2337 0.595140
\(573\) 26.3030 + 24.7186i 1.09882 + 1.03263i
\(574\) 8.23369 9.50744i 0.343667 0.396833i
\(575\) 0 0
\(576\) 0.627719 + 10.0974i 0.0261549 + 0.420723i
\(577\) 2.81929i 0.117369i −0.998277 0.0586843i \(-0.981309\pi\)
0.998277 0.0586843i \(-0.0186905\pi\)
\(578\) 1.67715i 0.0697602i
\(579\) −14.5109 + 15.4410i −0.603051 + 0.641705i
\(580\) 0 0
\(581\) −34.9783 30.2921i −1.45114 1.25673i
\(582\) 10.3723 11.0371i 0.429945 0.457503i
\(583\) 4.74456 0.196500
\(584\) 18.5109 0.765985
\(585\) 0 0
\(586\) 8.62258i 0.356196i
\(587\) 17.4891 0.721853 0.360927 0.932594i \(-0.382460\pi\)
0.360927 + 0.932594i \(0.382460\pi\)
\(588\) −13.6277 9.54511i −0.561998 0.393634i
\(589\) 12.0000 0.494451
\(590\) 0 0
\(591\) 19.8614 + 18.6650i 0.816989 + 0.767777i
\(592\) 4.23369 0.174004
\(593\) 4.37228 0.179548 0.0897740 0.995962i \(-0.471386\pi\)
0.0897740 + 0.995962i \(0.471386\pi\)
\(594\) 8.00000 + 6.63325i 0.328244 + 0.272166i
\(595\) 0 0
\(596\) 4.34896i 0.178140i
\(597\) −33.8614 31.8217i −1.38586 1.30238i
\(598\) 27.7128i 1.13326i
\(599\) 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 \(-0.148652\pi\)
\(602\) −6.51087 + 7.51811i −0.265363 + 0.306415i
\(603\) 0.883156 + 14.2063i 0.0359649 + 0.578524i
\(604\) −3.25544 −0.132462
\(605\) 0 0
\(606\) −6.00000 5.63858i −0.243733 0.229052i
\(607\) 8.86263i 0.359723i −0.983692 0.179862i \(-0.942435\pi\)
0.983692 0.179862i \(-0.0575650\pi\)
\(608\) 20.2337 0.820584
\(609\) 0.441578 + 4.28384i 0.0178936 + 0.173590i
\(610\) 0 0
\(611\) 6.68815i 0.270574i
\(612\) −1.11684 17.9653i −0.0451457 0.726205i
\(613\) 27.4891 1.11028 0.555138 0.831758i \(-0.312666\pi\)
0.555138 + 0.831758i \(0.312666\pi\)
\(614\) 18.0000 0.726421
\(615\) 0 0
\(616\) 13.4891 + 11.6819i 0.543492 + 0.470678i
\(617\) 24.5437i 0.988091i 0.869436 + 0.494045i \(0.164482\pi\)
−0.869436 + 0.494045i \(0.835518\pi\)
\(618\) 5.90491 6.28339i 0.237530 0.252755i
\(619\) 18.6101i 0.748004i −0.927428 0.374002i \(-0.877985\pi\)
0.927428 0.374002i \(-0.122015\pi\)
\(620\) 0 0
\(621\) −28.2337 + 34.0511i −1.13298 + 1.36642i
\(622\) 11.2772i 0.452173i
\(623\) −29.4891 25.5383i −1.18146 1.02317i
\(624\) 3.25544 + 3.05934i 0.130322 + 0.122472i
\(625\) 0 0
\(626\) 4.27719 0.170951
\(627\) 10.3723 11.0371i 0.414229 0.440780i
\(628\) 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 \(0.652198\pi\)
\(632\) 6.33830i 0.252124i
\(633\) 13.1861 14.0313i 0.524102 0.557695i
\(634\) −1.48913 −0.0591407
\(635\) 0 0
\(636\) 3.25544 + 3.05934i 0.129086 + 0.121311i
\(637\) 28.4674 4.10891i 1.12792 0.162801i
\(638\) 1.87953i 0.0744112i
\(639\) −0.883156 + 0.0549029i −0.0349371 + 0.00217192i
\(640\) 0 0
\(641\) 36.6303i 1.44681i −0.690423 0.723406i \(-0.742576\pi\)
0.690423 0.723406i \(-0.257424\pi\)
\(642\) 6.23369 6.63325i 0.246024 0.261793i
\(643\) 10.1523i 0.400366i −0.979759 0.200183i \(-0.935846\pi\)
0.979759 0.200183i \(-0.0641536\pi\)
\(644\) −20.2337 + 23.3639i −0.797319 + 0.920665i
\(645\) 0 0
\(646\) 12.0000 0.472134
\(647\) 12.0000 0.471769 0.235884 0.971781i \(-0.424201\pi\)
0.235884 + 0.971781i \(0.424201\pi\)
\(648\) 2.97825 + 23.8612i 0.116997 + 0.937356i
\(649\) 22.0742i 0.866489i
\(650\) 0 0
\(651\) 1.62772 + 15.7908i 0.0637953 + 0.618892i
\(652\) −10.9783 −0.429941
\(653\) 39.6897i 1.55318i 0.630008 + 0.776589i \(0.283052\pi\)
−0.630008 + 0.776589i \(0.716948\pi\)
\(654\) −17.1168 16.0858i −0.669322 0.629004i
\(655\) 0 0
\(656\) 3.76631 0.147050
\(657\) 20.7446 1.28962i 0.809322 0.0503129i
\(658\) −2.23369 + 2.57924i −0.0870782 + 0.100549i
\(659\) 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 \(0.956981\pi\)
\(662\) 3.16915i 0.123172i
\(663\) 22.6753 + 21.3094i 0.880634 + 0.827588i
\(664\) 46.7277i 1.81339i
\(665\) 0 0
\(666\) −16.0000 + 0.994667i −0.619987 + 0.0385426i
\(667\) 8.00000 0.309761
\(668\) −6.70106 −0.259272
\(669\) 11.1861 + 10.5123i 0.432481 + 0.406430i
\(670\) 0 0
\(671\) 17.4891 0.675160
\(672\) 2.74456 + 26.6256i 0.105874 + 1.02710i
\(673\) 12.2337 0.471574 0.235787 0.971805i \(-0.424233\pi\)
0.235787 + 0.971805i \(0.424233\pi\)
\(674\) 12.8617i 0.495416i
\(675\) 0 0
\(676\) −5.32878 −0.204953
\(677\) −18.6060 −0.715085 −0.357543 0.933897i \(-0.616385\pi\)
−0.357543 + 0.933897i \(0.616385\pi\)
\(678\) 2.97825 3.16915i 0.114379 0.121710i
\(679\) 19.1168 22.0742i 0.733637 0.847131i
\(680\) 0 0
\(681\) −29.1861 + 31.0569i −1.11842 + 1.19010i
\(682\) 6.92820i 0.265295i
\(683\) 34.4559i 1.31842i 0.751960 + 0.659209i \(0.229109\pi\)
−0.751960 + 0.659209i \(0.770891\pi\)
\(684\) 14.2337 0.884861i 0.544239 0.0338335i
\(685\) 0 0
\(686\) 12.3505 + 7.92287i 0.471545 + 0.302497i
\(687\) 19.1168 + 17.9653i 0.729353 + 0.685420i
\(688\) −2.97825 −0.113545
\(689\) −7.72281 −0.294216
\(690\) 0 0
\(691\) 21.1894i 0.806082i −0.915182 0.403041i \(-0.867953\pi\)
0.915182 0.403041i \(-0.132047\pi\)
\(692\) −1.53262 −0.0582616
\(693\) 15.9307 + 12.1518i 0.605157 + 0.461609i
\(694\) −11.7663 −0.446643
\(695\) 0 0
\(696\) 2.97825 3.16915i 0.112890 0.120126i
\(697\) 26.2337 0.993672
\(698\) 12.0000 0.454207
\(699\) 21.4891 + 20.1947i 0.812793 + 0.763834i
\(700\) 0 0
\(701\) 42.5090i 1.60554i −0.596287 0.802771i \(-0.703358\pi\)
0.596287 0.802771i \(-0.296642\pi\)
\(702\) −13.0217 10.7971i −0.491474 0.407509i
\(703\) 23.3639i 0.881184i
\(704\) 8.51278i 0.320837i
\(705\) 0 0
\(706\) 19.8997i 0.748937i
\(707\) −12.0000 10.3923i −0.451306 0.390843i
\(708\) −14.2337 + 15.1460i −0.534935 + 0.569223i
\(709\) 6.88316 0.258502 0.129251 0.991612i \(-0.458743\pi\)
0.129251 + 0.991612i \(0.458743\pi\)
\(710\) 0 0
\(711\) 0.441578 + 7.10313i 0.0165605 + 0.266388i
\(712\) 39.3947i 1.47638i
\(713\) 29.4891 1.10438
\(714\) 1.62772 + 15.7908i 0.0609158 + 0.590957i
\(715\) 0 0
\(716\) 9.10268i 0.340183i
\(717\) 26.3030 + 24.7186i 0.982303 + 0.923133i
\(718\) −13.2554 −0.494689
\(719\) 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
\(722\) 5.54601i 0.206401i
\(723\) −20.7446 19.4950i −0.771499 0.725026i
\(724\) 1.76972i 0.0657712i
\(725\) 0 0
\(726\) 4.62772 + 4.34896i 0.171751 + 0.161405i
\(727\) 3.46410i 0.128476i 0.997935 + 0.0642382i \(0.0204617\pi\)
−0.997935 + 0.0642382i \(0.979538\pi\)
\(728\) −21.9565 19.0149i −0.813762 0.704739i
\(729\) 5.00000 + 26.5330i 0.185185 + 0.982704i
\(730\) 0 0
\(731\) −20.7446 −0.767265
\(732\) 12.0000 + 11.2772i 0.443533 + 0.416816i
\(733\) 40.0395i 1.47889i −0.673215 0.739447i \(-0.735087\pi\)
0.673215 0.739447i \(-0.264913\pi\)
\(734\) 27.9565 1.03189
\(735\) 0 0
\(736\) 49.7228 1.83281
\(737\) 11.9769i 0.441174i
\(738\) −14.2337 + 0.884861i −0.523949 + 0.0325722i
\(739\) −14.3723 −0.528693 −0.264346 0.964428i \(-0.585156\pi\)
−0.264346 + 0.964428i \(0.585156\pi\)
\(740\) 0 0
\(741\) −16.8832 + 17.9653i −0.620218 + 0.659972i
\(742\) −2.97825 2.57924i −0.109335 0.0946869i
\(743\) 16.1407i 0.592145i −0.955166 0.296072i \(-0.904323\pi\)
0.955166 0.296072i \(-0.0956769\pi\)
\(744\) 10.9783 11.6819i 0.402482 0.428280i
\(745\) 0 0
\(746\) 10.5021i 0.384510i
\(747\) 3.25544 + 52.3663i 0.119110 + 1.91598i
\(748\) 15.1460i 0.553794i
\(749\) 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 \(0.320120\pi\)
\(752\) −1.02175 −0.0372594
\(753\) −6.51087 + 6.92820i −0.237269 + 0.252478i
\(754\) 3.05934i 0.111415i
\(755\) 0 0
\(756\) 3.09509 + 18.6101i 0.112568 + 0.676844i
\(757\) 19.7663 0.718419 0.359209 0.933257i \(-0.383046\pi\)
0.359209 + 0.933257i \(0.383046\pi\)
\(758\) 17.0256i 0.618396i
\(759\) 25.4891 27.1229i 0.925197 0.984499i
\(760\) 0 0
\(761\) −8.23369 −0.298471 −0.149235 0.988802i \(-0.547681\pi\)
−0.149235 + 0.988802i \(0.547681\pi\)
\(762\) 0.744563 + 0.699713i 0.0269727 + 0.0253479i
\(763\) −34.2337 29.6472i −1.23934 1.07330i
\(764\) 28.5977i 1.03463i
\(765\) 0 0
\(766\) 4.34896i 0.157134i
\(767\) 35.9306i 1.29738i
\(768\) 16.4674 17.5229i 0.594215 0.632303i
\(769\) 38.5099i 1.38870i 0.719637 + 0.694351i \(0.244308\pi\)
−0.719637 + 0.694351i \(0.755692\pi\)
\(770\) 0 0
\(771\) −0.605969 + 0.644810i −0.0218234 + 0.0232223i
\(772\) 16.7881 0.604216
\(773\) −52.3723 −1.88370 −0.941850 0.336034i \(-0.890914\pi\)
−0.941850 + 0.336034i \(0.890914\pi\)
\(774\) 11.2554 0.699713i 0.404568 0.0251507i
\(775\) 0 0
\(776\) −29.4891 −1.05860
\(777\) −30.7446 + 3.16915i −1.10296 + 0.113693i
\(778\) 23.2554 0.833748
\(779\) 20.7846i 0.744686i
\(780\) 0 0
\(781\) 0.744563 0.0266425
\(782\) 29.4891 1.05453
\(783\) 3.11684 3.75906i 0.111387 0.134338i
\(784\) 0.627719 + 4.34896i 0.0224185 + 0.155320i
\(785\) 0 0
\(786\) −5.48913 5.15848i −0.195791 0.183997i
\(787\) 3.22405i 0.114925i 0.998348 + 0.0574625i \(0.0183010\pi\)
−0.998348 + 0.0574625i \(0.981699\pi\)
\(788\) 21.5941i 0.769259i
\(789\) −0.372281 0.349857i −0.0132536 0.0124552i
\(790\) 0 0
\(791\) 5.48913 6.33830i 0.195171 0.225364i
\(792\) −1.25544 20.1947i −0.0446100 0.717588i
\(793\) −28.4674 −1.01091
\(794\) −20.7446 −0.736197
\(795\) 0 0
\(796\) 36.8155i 1.30489i
\(797\) −14.1386 −0.500815 −0.250407 0.968141i \(-0.580565\pi\)
−0.250407 + 0.968141i \(0.580565\pi\)
\(798\) −12.5109 + 1.28962i −0.442880 + 0.0456521i
\(799\) −7.11684 −0.251776
\(800\) 0 0
\(801\) 2.74456 + 44.1485i 0.0969744 + 1.55991i
\(802\) 4.74456 0.167536
\(803\) −17.4891 −0.617178
\(804\) 7.72281 8.21782i 0.272363 0.289820i
\(805\) 0 0
\(806\) 11.2772i 0.397221i
\(807\) 3.25544 3.46410i 0.114597 0.121942i
\(808\) 16.0309i 0.563965i
\(809\) 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 \(-0.105952\pi\)
\(812\) 2.23369 2.57924i 0.0783871 0.0905136i
\(813\) −6.00000 5.63858i −0.210429 0.197754i
\(814\) 13.4891 0.472794
\(815\) 0 0
\(816\) −3.25544 + 3.46410i −0.113963 + 0.121268i
\(817\) 16.4356i 0.575011i
\(818\) −19.5326 −0.682942
\(819\) −25.9307 19.7797i −0.906092 0.691159i
\(820\) 0 0
\(821\) 34.9909i 1.22119i 0.791943 + 0.610595i \(0.209070\pi\)
−0.791943 + 0.610595i \(0.790930\pi\)
\(822\) −12.4674 + 13.2665i −0.434850 + 0.462722i
\(823\) 13.7663 0.479863 0.239932 0.970790i \(-0.422875\pi\)
0.239932 + 0.970790i \(0.422875\pi\)
\(824\) −16.7881 −0.584840
\(825\) 0 0
\(826\) 12.0000 13.8564i 0.417533 0.482126i
\(827\) 14.8511i 0.516422i −0.966088 0.258211i \(-0.916867\pi\)
0.966088 0.258211i \(-0.0831330\pi\)
\(828\) 34.9783 2.17448i 1.21558 0.0755684i
\(829\) 12.5668i 0.436463i −0.975897 0.218231i \(-0.929971\pi\)
0.975897 0.218231i \(-0.0700287\pi\)
\(830\) 0 0
\(831\) 33.4891 35.6357i 1.16172 1.23619i
\(832\) 13.8564i 0.480384i
\(833\) 4.37228 + 30.2921i 0.151491 + 1.04956i
\(834\) 17.4891 18.6101i 0.605599 0.644416i
\(835\) 0 0
\(836\) −12.0000 −0.415029
\(837\) 11.4891 13.8564i 0.397122 0.478947i
\(838\) 6.92820i 0.239331i
\(839\) 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
\(842\) 11.5721i 0.398802i
\(843\) −35.4198 33.2863i −1.21992 1.14644i
\(844\) −15.2554 −0.525114
\(845\) 0 0
\(846\) 3.86141 0.240051i 0.132758 0.00825312i
\(847\) 9.25544 + 8.01544i 0.318021 + 0.275414i
\(848\) 1.17981i 0.0405150i
\(849\) −0.813859 0.764836i −0.0279316 0.0262491i
\(850\) 0 0
\(851\) 57.4150i 1.96816i
\(852\) 0.510875 + 0.480102i 0.0175023 + 0.0164480i
\(853\) 32.8713i 1.12549i 0.826630 + 0.562746i \(0.190255\pi\)
−0.826630 + 0.562746i \(0.809745\pi\)
\(854\) −10.9783 9.50744i −0.375668 0.325338i
\(855\) 0 0
\(856\) −17.7228 −0.605753
\(857\) 46.4674 1.58730 0.793648 0.608378i \(-0.208179\pi\)
0.793648 + 0.608378i \(0.208179\pi\)
\(858\) 10.3723 + 9.74749i 0.354104 + 0.332774i
\(859\) 14.2612i 0.486585i 0.969953 + 0.243292i \(0.0782274\pi\)
−0.969953 + 0.243292i \(0.921773\pi\)
\(860\) 0 0
\(861\) −27.3505 + 2.81929i −0.932104 + 0.0960812i
\(862\) 11.9565 0.407240
\(863\) 41.2743i 1.40499i −0.711688 0.702496i \(-0.752069\pi\)
0.711688 0.702496i \(-0.247931\pi\)
\(864\) 19.3723 23.3639i 0.659058 0.794854i
\(865\) 0 0
\(866\) 29.4891 1.00208
\(867\) −2.51087 + 2.67181i −0.0852738 + 0.0907396i
\(868\) 8.23369 9.50744i 0.279470 0.322704i
\(869\) 5.98844i 0.203144i
\(870\) 0 0
\(871\) 19.4950i 0.660563i
\(872\) 45.7330i 1.54872i
\(873\) −33.0475 + 2.05446i −1.11849 + 0.0695328i
\(874\) 23.3639i 0.790294i
\(875\) 0 0
\(876\) −12.0000 11.2772i −0.405442 0.381020i
\(877\) 38.4674 1.29895 0.649475 0.760383i \(-0.274989\pi\)
0.649475 + 0.760383i \(0.274989\pi\)
\(878\) 14.7446 0.497605
\(879\) 12.9090 13.7364i 0.435408 0.463317i
\(880\) 0 0
\(881\) −32.2337 −1.08598 −0.542990 0.839739i \(-0.682708\pi\)
−0.542990 + 0.839739i \(0.682708\pi\)
\(882\) −3.39403 16.2882i −0.114283 0.548451i
\(883\) −49.4891 −1.66544 −0.832721 0.553693i \(-0.813218\pi\)
−0.832721 + 0.553693i \(0.813218\pi\)
\(884\) 24.6535i 0.829186i
\(885\) 0 0
\(886\) −5.25544 −0.176560
\(887\) 18.5109 0.621534 0.310767 0.950486i \(-0.399414\pi\)
0.310767 + 0.950486i \(0.399414\pi\)
\(888\) 22.7446 + 21.3745i 0.763258 + 0.717282i
\(889\) 1.48913 + 1.28962i 0.0499437 + 0.0432525i
\(890\) 0 0
\(891\) −2.81386 22.5441i −0.0942678 0.755256i
\(892\) 12.1620i 0.407215i
\(893\) 5.63858i 0.188688i
\(894\) −2.97825 + 3.16915i −0.0996076 + 0.105992i
\(895\) 0 0
\(896\) 15.6060 18.0202i 0.521359 0.602013i
\(897\) −41.4891 + 44.1485i −1.38528 + 1.47407i
\(898\) 9.21194 0.307406
\(899\) −3.25544 −0.108575
\(900\) 0 0
\(901\) 8.21782i 0.273775i
\(902\) 12.0000 0.399556
\(903\) 21.6277 2.22938i 0.719725 0.0741893i
\(904\) −8.46738 −0.281621
\(905\) 0 0
\(906\) −2.37228 2.22938i −0.0788138 0.0740663i
\(907\) −8.00000 −0.265636 −0.132818 0.991140i \(-0.542403\pi\)
−0.132818 + 0.991140i \(0.542403\pi\)
\(908\) 33.7663 1.12057
\(909\) 1.11684 + 17.9653i 0.0370434 + 0.595872i
\(910\) 0 0
\(911\) 2.87419i 0.0952263i −0.998866 0.0476132i \(-0.984839\pi\)
0.998866 0.0476132i \(-0.0151615\pi\)
\(912\) −2.74456 2.57924i −0.0908816 0.0854072i
\(913\) 44.1485i 1.46110i
\(914\) 10.2825i 0.340115i
\(915\) 0 0
\(916\) 20.7846i 0.686743i
\(917\) −10.9783 9.50744i −0.362534 0.313963i
\(918\) 11.4891 13.8564i 0.379198 0.457330i
\(919\) −5.62772 −0.185641 −0.0928207 0.995683i \(-0.529588\pi\)
−0.0928207 + 0.995683i \(0.529588\pi\)
\(920\) 0 0
\(921\) −28.6753 26.9480i −0.944882 0.887966i
\(922\) 2.17448i 0.0716127i
\(923\) −1.21194 −0.0398914
\(924\) −1.62772 15.7908i −0.0535480 0.519480i
\(925\) 0 0
\(926\) 25.7235i 0.845326i
\(927\) −18.8139 + 1.16959i −0.617928 + 0.0384145i
\(928\) −5.48913 −0.180189
\(929\) −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
\(932\) 23.3639i 0.765308i
\(933\) −16.8832 + 17.9653i −0.552730 + 0.588158i
\(934\) 24.6535i 0.806686i
\(935\) 0 0
\(936\) 2.04350 + 32.8713i 0.0667938 + 1.07443i
\(937\) 0.240051i 0.00784212i −0.999992 0.00392106i \(-0.998752\pi\)
0.999992 0.00392106i \(-0.00124811\pi\)
\(938\) −6.51087 + 7.51811i −0.212588 + 0.245475i
\(939\) −6.81386 6.40342i −0.222362 0.208968i
\(940\) 0 0
\(941\) 38.7446 1.26304 0.631518 0.775361i \(-0.282432\pi\)
0.631518 + 0.775361i \(0.282432\pi\)
\(942\) 0 0
\(943\) 51.0767i 1.66329i
\(944\) 5.48913 0.178656
\(945\) 0 0
\(946\) −9.48913 −0.308518
\(947\) 34.9360i 1.13527i 0.823282 + 0.567633i \(0.192141\pi\)
−0.823282 + 0.567633i \(0.807859\pi\)
\(948\) 3.86141 4.10891i 0.125413 0.133451i
\(949\) 28.4674 0.924090
\(950\) 0 0
\(951\) 2.37228 + 2.22938i 0.0769265 + 0.0722927i
\(952\) 20.2337 23.3639i 0.655778 0.757227i
\(953\) 7.62792i 0.247092i 0.992339 + 0.123546i \(0.0394267\pi\)
−0.992339 + 0.123546i \(0.960573\pi\)
\(954\) 0.277187 + 4.45877i 0.00897425 + 0.144358i
\(955\) 0 0
\(956\) 28.5977i 0.924915i
\(957\) −2.81386 + 2.99422i −0.0909592 + 0.0967894i
\(958\) 32.8713i 1.06202i
\(959\) −22.9783 + 26.5330i −0.742006 + 0.856795i
\(960\) 0 0
\(961\) 19.0000 0.612903
\(962\) −21.9565 −0.707906
\(963\) −19.8614 + 1.23472i −0.640025 + 0.0397882i
\(964\) 22.5543i 0.726426i
\(965\) 0 0
\(966\) −30.7446 + 3.16915i −0.989190 + 0.101966i
\(967\) −10.2337 −0.329093 −0.164547 0.986369i \(-0.552616\pi\)
−0.164547 + 0.986369i \(0.552616\pi\)
\(968\) 12.3644i 0.397407i
\(969\) −19.1168 17.9653i −0.614122 0.577129i
\(970\) 0 0
\(971\) −37.2119 −1.19419 −0.597094 0.802171i \(-0.703678\pi\)
−0.597094 + 0.802171i \(0.703678\pi\)
\(972\) 12.6060 17.2828i 0.404337 0.554347i
\(973\) 32.2337 37.2203i 1.03336 1.19323i
\(974\) 29.7021i 0.951718i
\(975\) 0 0
\(976\) 4.34896i 0.139207i
\(977\) 7.62792i 0.244039i 0.992528 + 0.122019i \(0.0389370\pi\)
−0.992528 + 0.122019i \(0.961063\pi\)
\(978\) −8.00000 7.51811i −0.255812 0.240403i
\(979\) 37.2203i 1.18956i
\(980\) 0 0
\(981\) 3.18614 + 51.2516i 0.101726 + 1.63634i
\(982\) −4.51087 −0.143948
\(983\) 39.8614 1.27138 0.635691 0.771944i \(-0.280715\pi\)
0.635691 + 0.771944i \(0.280715\pi\)
\(984\) 20.2337 + 19.0149i 0.645026 + 0.606172i
\(985\) 0 0
\(986\) −3.25544 −0.103674
\(987\) 7.41983 0.764836i 0.236176 0.0243450i
\(988\) 19.5326 0.621416
\(989\) 40.3894i 1.28431i
\(990\) 0 0
\(991\) 25.4891 0.809689 0.404844 0.914386i \(-0.367326\pi\)
0.404844 + 0.914386i \(0.367326\pi\)
\(992\) −20.2337 −0.642420
\(993\) 4.74456 5.04868i 0.150564 0.160215i
\(994\) −0.467376 0.404759i −0.0148243 0.0128382i
\(995\) 0 0
\(996\) 28.4674 30.2921i 0.902023 0.959840i
\(997\) 31.8217i 1.00780i −0.863761 0.503902i \(-0.831897\pi\)
0.863761 0.503902i \(-0.168103\pi\)
\(998\) 32.7615i 1.03705i
\(999\) 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.b.g.251.2 4
3.2 odd 2 525.2.b.e.251.3 4
5.2 odd 4 525.2.g.e.524.6 8
5.3 odd 4 525.2.g.e.524.3 8
5.4 even 2 105.2.b.c.41.3 yes 4
7.6 odd 2 525.2.b.e.251.2 4
15.2 even 4 525.2.g.d.524.3 8
15.8 even 4 525.2.g.d.524.6 8
15.14 odd 2 105.2.b.d.41.2 yes 4
20.19 odd 2 1680.2.f.h.881.2 4
21.20 even 2 inner 525.2.b.g.251.3 4
35.4 even 6 735.2.s.i.656.1 4
35.9 even 6 735.2.s.h.521.2 4
35.13 even 4 525.2.g.d.524.4 8
35.19 odd 6 735.2.s.g.521.2 4
35.24 odd 6 735.2.s.j.656.1 4
35.27 even 4 525.2.g.d.524.5 8
35.34 odd 2 105.2.b.d.41.3 yes 4
60.59 even 2 1680.2.f.g.881.4 4
105.44 odd 6 735.2.s.j.521.1 4
105.59 even 6 735.2.s.h.656.2 4
105.62 odd 4 525.2.g.e.524.4 8
105.74 odd 6 735.2.s.g.656.2 4
105.83 odd 4 525.2.g.e.524.5 8
105.89 even 6 735.2.s.i.521.1 4
105.104 even 2 105.2.b.c.41.2 4
140.139 even 2 1680.2.f.g.881.3 4
420.419 odd 2 1680.2.f.h.881.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.b.c.41.2 4 105.104 even 2
105.2.b.c.41.3 yes 4 5.4 even 2
105.2.b.d.41.2 yes 4 15.14 odd 2
105.2.b.d.41.3 yes 4 35.34 odd 2
525.2.b.e.251.2 4 7.6 odd 2
525.2.b.e.251.3 4 3.2 odd 2
525.2.b.g.251.2 4 1.1 even 1 trivial
525.2.b.g.251.3 4 21.20 even 2 inner
525.2.g.d.524.3 8 15.2 even 4
525.2.g.d.524.4 8 35.13 even 4
525.2.g.d.524.5 8 35.27 even 4
525.2.g.d.524.6 8 15.8 even 4
525.2.g.e.524.3 8 5.3 odd 4
525.2.g.e.524.4 8 105.62 odd 4
525.2.g.e.524.5 8 105.83 odd 4
525.2.g.e.524.6 8 5.2 odd 4
735.2.s.g.521.2 4 35.19 odd 6
735.2.s.g.656.2 4 105.74 odd 6
735.2.s.h.521.2 4 35.9 even 6
735.2.s.h.656.2 4 105.59 even 6
735.2.s.i.521.1 4 105.89 even 6
735.2.s.i.656.1 4 35.4 even 6
735.2.s.j.521.1 4 105.44 odd 6
735.2.s.j.656.1 4 35.24 odd 6
1680.2.f.g.881.3 4 140.139 even 2
1680.2.f.g.881.4 4 60.59 even 2
1680.2.f.h.881.1 4 420.419 odd 2
1680.2.f.h.881.2 4 20.19 odd 2