Properties

Label 1170.2.w.h.307.7
Level $1170$
Weight $2$
Character 1170.307
Analytic conductor $9.342$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1170,2,Mod(307,1170)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1170, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 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("1170.307");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.w (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.34249703649\)
Analytic rank: \(0\)
Dimension: \(14\)
Relative dimension: \(7\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{14} - 2 x^{13} + 2 x^{12} + 4 x^{11} + 112 x^{10} - 208 x^{9} + 200 x^{8} + 392 x^{7} + 1708 x^{6} - 1744 x^{5} + 872 x^{4} - 80 x^{3} + 4 x^{2} - 8 x + 8 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 307.7
Root \(2.18338 + 2.18338i\) of defining polynomial
Character \(\chi\) \(=\) 1170.307
Dual form 1170.2.w.h.343.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000 q^{4} +(2.18338 - 0.482541i) q^{5} +2.10714 q^{7} +1.00000i q^{8} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000 q^{4} +(2.18338 - 0.482541i) q^{5} +2.10714 q^{7} +1.00000i q^{8} +(-0.482541 - 2.18338i) q^{10} +(1.24283 - 1.24283i) q^{11} +(-3.37977 - 1.25584i) q^{13} -2.10714i q^{14} +1.00000 q^{16} +(1.54027 - 1.54027i) q^{17} +(1.19612 - 1.19612i) q^{19} +(-2.18338 + 0.482541i) q^{20} +(-1.24283 - 1.24283i) q^{22} +(2.88018 + 2.88018i) q^{23} +(4.53431 - 2.10714i) q^{25} +(-1.25584 + 3.37977i) q^{26} -2.10714 q^{28} +0.655858i q^{29} +(-5.01590 - 5.01590i) q^{31} -1.00000i q^{32} +(-1.54027 - 1.54027i) q^{34} +(4.60070 - 1.01678i) q^{35} +6.16468 q^{37} +(-1.19612 - 1.19612i) q^{38} +(0.482541 + 2.18338i) q^{40} +(5.07630 + 5.07630i) q^{41} +(-3.01007 - 3.01007i) q^{43} +(-1.24283 + 1.24283i) q^{44} +(2.88018 - 2.88018i) q^{46} +9.52254 q^{47} -2.55995 q^{49} +(-2.10714 - 4.53431i) q^{50} +(3.37977 + 1.25584i) q^{52} +(-3.88517 + 3.88517i) q^{53} +(2.11386 - 3.31330i) q^{55} +2.10714i q^{56} +0.655858 q^{58} +(1.87321 + 1.87321i) q^{59} +4.35868 q^{61} +(-5.01590 + 5.01590i) q^{62} -1.00000 q^{64} +(-7.98533 - 1.11111i) q^{65} -7.11822i q^{67} +(-1.54027 + 1.54027i) q^{68} +(-1.01678 - 4.60070i) q^{70} +(-1.46384 - 1.46384i) q^{71} -14.7472i q^{73} -6.16468i q^{74} +(-1.19612 + 1.19612i) q^{76} +(2.61883 - 2.61883i) q^{77} +1.75410i q^{79} +(2.18338 - 0.482541i) q^{80} +(5.07630 - 5.07630i) q^{82} -13.9129 q^{83} +(2.61975 - 4.10623i) q^{85} +(-3.01007 + 3.01007i) q^{86} +(1.24283 + 1.24283i) q^{88} +(1.31506 + 1.31506i) q^{89} +(-7.12166 - 2.64624i) q^{91} +(-2.88018 - 2.88018i) q^{92} -9.52254i q^{94} +(2.03441 - 3.18877i) q^{95} -6.58936i q^{97} +2.55995i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q - 14 q^{4} + 2 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 14 q - 14 q^{4} + 2 q^{5} + 4 q^{13} + 14 q^{16} - 14 q^{17} - 12 q^{19} - 2 q^{20} - 10 q^{25} - 6 q^{26} + 12 q^{31} + 14 q^{34} - 12 q^{35} + 20 q^{37} + 12 q^{38} + 2 q^{41} + 8 q^{47} + 14 q^{49} - 4 q^{52} - 6 q^{53} + 32 q^{55} + 16 q^{58} + 16 q^{59} + 24 q^{61} + 12 q^{62} - 14 q^{64} + 4 q^{65} + 14 q^{68} - 4 q^{70} + 24 q^{71} + 12 q^{76} - 16 q^{77} + 2 q^{80} + 2 q^{82} - 8 q^{83} + 2 q^{85} - 42 q^{89} - 8 q^{91} - 24 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) 2.18338 0.482541i 0.976438 0.215799i
\(6\) 0 0
\(7\) 2.10714 0.796425 0.398213 0.917293i \(-0.369631\pi\)
0.398213 + 0.917293i \(0.369631\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −0.482541 2.18338i −0.152593 0.690446i
\(11\) 1.24283 1.24283i 0.374729 0.374729i −0.494467 0.869196i \(-0.664637\pi\)
0.869196 + 0.494467i \(0.164637\pi\)
\(12\) 0 0
\(13\) −3.37977 1.25584i −0.937380 0.348308i
\(14\) 2.10714i 0.563158i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 1.54027 1.54027i 0.373569 0.373569i −0.495206 0.868775i \(-0.664907\pi\)
0.868775 + 0.495206i \(0.164907\pi\)
\(18\) 0 0
\(19\) 1.19612 1.19612i 0.274410 0.274410i −0.556463 0.830872i \(-0.687842\pi\)
0.830872 + 0.556463i \(0.187842\pi\)
\(20\) −2.18338 + 0.482541i −0.488219 + 0.107900i
\(21\) 0 0
\(22\) −1.24283 1.24283i −0.264973 0.264973i
\(23\) 2.88018 + 2.88018i 0.600559 + 0.600559i 0.940461 0.339902i \(-0.110394\pi\)
−0.339902 + 0.940461i \(0.610394\pi\)
\(24\) 0 0
\(25\) 4.53431 2.10714i 0.906862 0.421429i
\(26\) −1.25584 + 3.37977i −0.246291 + 0.662828i
\(27\) 0 0
\(28\) −2.10714 −0.398213
\(29\) 0.655858i 0.121790i 0.998144 + 0.0608948i \(0.0193954\pi\)
−0.998144 + 0.0608948i \(0.980605\pi\)
\(30\) 0 0
\(31\) −5.01590 5.01590i −0.900882 0.900882i 0.0946301 0.995513i \(-0.469833\pi\)
−0.995513 + 0.0946301i \(0.969833\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) −1.54027 1.54027i −0.264153 0.264153i
\(35\) 4.60070 1.01678i 0.777660 0.171868i
\(36\) 0 0
\(37\) 6.16468 1.01347 0.506734 0.862103i \(-0.330853\pi\)
0.506734 + 0.862103i \(0.330853\pi\)
\(38\) −1.19612 1.19612i −0.194037 0.194037i
\(39\) 0 0
\(40\) 0.482541 + 2.18338i 0.0762965 + 0.345223i
\(41\) 5.07630 + 5.07630i 0.792785 + 0.792785i 0.981946 0.189161i \(-0.0605768\pi\)
−0.189161 + 0.981946i \(0.560577\pi\)
\(42\) 0 0
\(43\) −3.01007 3.01007i −0.459031 0.459031i 0.439307 0.898337i \(-0.355224\pi\)
−0.898337 + 0.439307i \(0.855224\pi\)
\(44\) −1.24283 + 1.24283i −0.187364 + 0.187364i
\(45\) 0 0
\(46\) 2.88018 2.88018i 0.424659 0.424659i
\(47\) 9.52254 1.38901 0.694503 0.719490i \(-0.255624\pi\)
0.694503 + 0.719490i \(0.255624\pi\)
\(48\) 0 0
\(49\) −2.55995 −0.365706
\(50\) −2.10714 4.53431i −0.297995 0.641248i
\(51\) 0 0
\(52\) 3.37977 + 1.25584i 0.468690 + 0.174154i
\(53\) −3.88517 + 3.88517i −0.533669 + 0.533669i −0.921662 0.387993i \(-0.873168\pi\)
0.387993 + 0.921662i \(0.373168\pi\)
\(54\) 0 0
\(55\) 2.11386 3.31330i 0.285033 0.446765i
\(56\) 2.10714i 0.281579i
\(57\) 0 0
\(58\) 0.655858 0.0861183
\(59\) 1.87321 + 1.87321i 0.243871 + 0.243871i 0.818449 0.574579i \(-0.194834\pi\)
−0.574579 + 0.818449i \(0.694834\pi\)
\(60\) 0 0
\(61\) 4.35868 0.558072 0.279036 0.960281i \(-0.409985\pi\)
0.279036 + 0.960281i \(0.409985\pi\)
\(62\) −5.01590 + 5.01590i −0.637020 + 0.637020i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −7.98533 1.11111i −0.990458 0.137816i
\(66\) 0 0
\(67\) 7.11822i 0.869629i −0.900520 0.434815i \(-0.856814\pi\)
0.900520 0.434815i \(-0.143186\pi\)
\(68\) −1.54027 + 1.54027i −0.186785 + 0.186785i
\(69\) 0 0
\(70\) −1.01678 4.60070i −0.121529 0.549889i
\(71\) −1.46384 1.46384i −0.173726 0.173726i 0.614888 0.788614i \(-0.289201\pi\)
−0.788614 + 0.614888i \(0.789201\pi\)
\(72\) 0 0
\(73\) 14.7472i 1.72603i −0.505174 0.863017i \(-0.668572\pi\)
0.505174 0.863017i \(-0.331428\pi\)
\(74\) 6.16468i 0.716630i
\(75\) 0 0
\(76\) −1.19612 + 1.19612i −0.137205 + 0.137205i
\(77\) 2.61883 2.61883i 0.298444 0.298444i
\(78\) 0 0
\(79\) 1.75410i 0.197352i 0.995120 + 0.0986760i \(0.0314607\pi\)
−0.995120 + 0.0986760i \(0.968539\pi\)
\(80\) 2.18338 0.482541i 0.244109 0.0539498i
\(81\) 0 0
\(82\) 5.07630 5.07630i 0.560584 0.560584i
\(83\) −13.9129 −1.52714 −0.763569 0.645726i \(-0.776555\pi\)
−0.763569 + 0.645726i \(0.776555\pi\)
\(84\) 0 0
\(85\) 2.61975 4.10623i 0.284151 0.445383i
\(86\) −3.01007 + 3.01007i −0.324584 + 0.324584i
\(87\) 0 0
\(88\) 1.24283 + 1.24283i 0.132487 + 0.132487i
\(89\) 1.31506 + 1.31506i 0.139396 + 0.139396i 0.773362 0.633965i \(-0.218574\pi\)
−0.633965 + 0.773362i \(0.718574\pi\)
\(90\) 0 0
\(91\) −7.12166 2.64624i −0.746553 0.277402i
\(92\) −2.88018 2.88018i −0.300279 0.300279i
\(93\) 0 0
\(94\) 9.52254i 0.982175i
\(95\) 2.03441 3.18877i 0.208726 0.327161i
\(96\) 0 0
\(97\) 6.58936i 0.669048i −0.942387 0.334524i \(-0.891425\pi\)
0.942387 0.334524i \(-0.108575\pi\)
\(98\) 2.55995i 0.258594i
\(99\) 0 0
\(100\) −4.53431 + 2.10714i −0.453431 + 0.210714i
\(101\) 1.61904i 0.161101i −0.996751 0.0805505i \(-0.974332\pi\)
0.996751 0.0805505i \(-0.0256678\pi\)
\(102\) 0 0
\(103\) −5.42044 5.42044i −0.534092 0.534092i 0.387695 0.921788i \(-0.373271\pi\)
−0.921788 + 0.387695i \(0.873271\pi\)
\(104\) 1.25584 3.37977i 0.123146 0.331414i
\(105\) 0 0
\(106\) 3.88517 + 3.88517i 0.377361 + 0.377361i
\(107\) 5.59200 + 5.59200i 0.540599 + 0.540599i 0.923705 0.383106i \(-0.125145\pi\)
−0.383106 + 0.923705i \(0.625145\pi\)
\(108\) 0 0
\(109\) −8.50709 + 8.50709i −0.814832 + 0.814832i −0.985354 0.170522i \(-0.945455\pi\)
0.170522 + 0.985354i \(0.445455\pi\)
\(110\) −3.31330 2.11386i −0.315911 0.201549i
\(111\) 0 0
\(112\) 2.10714 0.199106
\(113\) 3.53973 3.53973i 0.332990 0.332990i −0.520731 0.853721i \(-0.674341\pi\)
0.853721 + 0.520731i \(0.174341\pi\)
\(114\) 0 0
\(115\) 7.67833 + 4.89872i 0.716008 + 0.456808i
\(116\) 0.655858i 0.0608948i
\(117\) 0 0
\(118\) 1.87321 1.87321i 0.172443 0.172443i
\(119\) 3.24556 3.24556i 0.297520 0.297520i
\(120\) 0 0
\(121\) 7.91072i 0.719157i
\(122\) 4.35868i 0.394616i
\(123\) 0 0
\(124\) 5.01590 + 5.01590i 0.450441 + 0.450441i
\(125\) 8.88334 6.78869i 0.794550 0.607199i
\(126\) 0 0
\(127\) −9.45775 + 9.45775i −0.839240 + 0.839240i −0.988759 0.149519i \(-0.952228\pi\)
0.149519 + 0.988759i \(0.452228\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) −1.11111 + 7.98533i −0.0974504 + 0.700359i
\(131\) −21.7528 −1.90055 −0.950276 0.311408i \(-0.899199\pi\)
−0.950276 + 0.311408i \(0.899199\pi\)
\(132\) 0 0
\(133\) 2.52040 2.52040i 0.218547 0.218547i
\(134\) −7.11822 −0.614921
\(135\) 0 0
\(136\) 1.54027 + 1.54027i 0.132077 + 0.132077i
\(137\) 18.4668 1.57773 0.788864 0.614568i \(-0.210669\pi\)
0.788864 + 0.614568i \(0.210669\pi\)
\(138\) 0 0
\(139\) 1.02338i 0.0868015i 0.999058 + 0.0434008i \(0.0138192\pi\)
−0.999058 + 0.0434008i \(0.986181\pi\)
\(140\) −4.60070 + 1.01678i −0.388830 + 0.0859339i
\(141\) 0 0
\(142\) −1.46384 + 1.46384i −0.122843 + 0.122843i
\(143\) −5.76130 + 2.63969i −0.481784 + 0.220742i
\(144\) 0 0
\(145\) 0.316478 + 1.43199i 0.0262821 + 0.118920i
\(146\) −14.7472 −1.22049
\(147\) 0 0
\(148\) −6.16468 −0.506734
\(149\) 6.88021 6.88021i 0.563649 0.563649i −0.366693 0.930342i \(-0.619510\pi\)
0.930342 + 0.366693i \(0.119510\pi\)
\(150\) 0 0
\(151\) −1.76761 + 1.76761i −0.143846 + 0.143846i −0.775363 0.631516i \(-0.782433\pi\)
0.631516 + 0.775363i \(0.282433\pi\)
\(152\) 1.19612 + 1.19612i 0.0970184 + 0.0970184i
\(153\) 0 0
\(154\) −2.61883 2.61883i −0.211031 0.211031i
\(155\) −13.3720 8.53124i −1.07407 0.685246i
\(156\) 0 0
\(157\) 1.73178 + 1.73178i 0.138211 + 0.138211i 0.772827 0.634616i \(-0.218842\pi\)
−0.634616 + 0.772827i \(0.718842\pi\)
\(158\) 1.75410 0.139549
\(159\) 0 0
\(160\) −0.482541 2.18338i −0.0381482 0.172611i
\(161\) 6.06895 + 6.06895i 0.478300 + 0.478300i
\(162\) 0 0
\(163\) 15.9324i 1.24792i 0.781455 + 0.623962i \(0.214478\pi\)
−0.781455 + 0.623962i \(0.785522\pi\)
\(164\) −5.07630 5.07630i −0.396393 0.396393i
\(165\) 0 0
\(166\) 13.9129i 1.07985i
\(167\) 22.6158 1.75006 0.875032 0.484065i \(-0.160840\pi\)
0.875032 + 0.484065i \(0.160840\pi\)
\(168\) 0 0
\(169\) 9.84571 + 8.48893i 0.757363 + 0.652995i
\(170\) −4.10623 2.61975i −0.314933 0.200925i
\(171\) 0 0
\(172\) 3.01007 + 3.01007i 0.229515 + 0.229515i
\(173\) 12.8009 + 12.8009i 0.973237 + 0.973237i 0.999651 0.0264145i \(-0.00840898\pi\)
−0.0264145 + 0.999651i \(0.508409\pi\)
\(174\) 0 0
\(175\) 9.55444 4.44005i 0.722248 0.335637i
\(176\) 1.24283 1.24283i 0.0936822 0.0936822i
\(177\) 0 0
\(178\) 1.31506 1.31506i 0.0985680 0.0985680i
\(179\) −18.7205 −1.39923 −0.699617 0.714518i \(-0.746646\pi\)
−0.699617 + 0.714518i \(0.746646\pi\)
\(180\) 0 0
\(181\) 16.6965i 1.24104i 0.784190 + 0.620520i \(0.213079\pi\)
−0.784190 + 0.620520i \(0.786921\pi\)
\(182\) −2.64624 + 7.12166i −0.196153 + 0.527893i
\(183\) 0 0
\(184\) −2.88018 + 2.88018i −0.212330 + 0.212330i
\(185\) 13.4598 2.97471i 0.989588 0.218705i
\(186\) 0 0
\(187\) 3.82859i 0.279974i
\(188\) −9.52254 −0.694503
\(189\) 0 0
\(190\) −3.18877 2.03441i −0.231338 0.147592i
\(191\) −6.58561 −0.476518 −0.238259 0.971202i \(-0.576577\pi\)
−0.238259 + 0.971202i \(0.576577\pi\)
\(192\) 0 0
\(193\) 10.4497i 0.752185i 0.926582 + 0.376092i \(0.122732\pi\)
−0.926582 + 0.376092i \(0.877268\pi\)
\(194\) −6.58936 −0.473088
\(195\) 0 0
\(196\) 2.55995 0.182853
\(197\) 11.5736i 0.824583i 0.911052 + 0.412292i \(0.135271\pi\)
−0.911052 + 0.412292i \(0.864729\pi\)
\(198\) 0 0
\(199\) −23.7883 −1.68631 −0.843155 0.537671i \(-0.819304\pi\)
−0.843155 + 0.537671i \(0.819304\pi\)
\(200\) 2.10714 + 4.53431i 0.148998 + 0.320624i
\(201\) 0 0
\(202\) −1.61904 −0.113916
\(203\) 1.38199i 0.0969964i
\(204\) 0 0
\(205\) 13.5330 + 8.63398i 0.945188 + 0.603023i
\(206\) −5.42044 + 5.42044i −0.377660 + 0.377660i
\(207\) 0 0
\(208\) −3.37977 1.25584i −0.234345 0.0870771i
\(209\) 2.97317i 0.205658i
\(210\) 0 0
\(211\) 3.22265 0.221857 0.110928 0.993828i \(-0.464618\pi\)
0.110928 + 0.993828i \(0.464618\pi\)
\(212\) 3.88517 3.88517i 0.266835 0.266835i
\(213\) 0 0
\(214\) 5.59200 5.59200i 0.382261 0.382261i
\(215\) −8.02460 5.11964i −0.547273 0.349156i
\(216\) 0 0
\(217\) −10.5692 10.5692i −0.717486 0.717486i
\(218\) 8.50709 + 8.50709i 0.576173 + 0.576173i
\(219\) 0 0
\(220\) −2.11386 + 3.31330i −0.142517 + 0.223383i
\(221\) −7.14008 + 3.27141i −0.480294 + 0.220059i
\(222\) 0 0
\(223\) 6.20878 0.415771 0.207885 0.978153i \(-0.433342\pi\)
0.207885 + 0.978153i \(0.433342\pi\)
\(224\) 2.10714i 0.140789i
\(225\) 0 0
\(226\) −3.53973 3.53973i −0.235459 0.235459i
\(227\) 1.01019i 0.0670489i 0.999438 + 0.0335244i \(0.0106732\pi\)
−0.999438 + 0.0335244i \(0.989327\pi\)
\(228\) 0 0
\(229\) −8.16009 8.16009i −0.539234 0.539234i 0.384070 0.923304i \(-0.374522\pi\)
−0.923304 + 0.384070i \(0.874522\pi\)
\(230\) 4.89872 7.67833i 0.323012 0.506294i
\(231\) 0 0
\(232\) −0.655858 −0.0430592
\(233\) 8.81549 + 8.81549i 0.577522 + 0.577522i 0.934220 0.356698i \(-0.116097\pi\)
−0.356698 + 0.934220i \(0.616097\pi\)
\(234\) 0 0
\(235\) 20.7913 4.59502i 1.35628 0.299746i
\(236\) −1.87321 1.87321i −0.121935 0.121935i
\(237\) 0 0
\(238\) −3.24556 3.24556i −0.210379 0.210379i
\(239\) −14.8422 + 14.8422i −0.960061 + 0.960061i −0.999233 0.0391714i \(-0.987528\pi\)
0.0391714 + 0.999233i \(0.487528\pi\)
\(240\) 0 0
\(241\) −16.7506 + 16.7506i −1.07900 + 1.07900i −0.0823985 + 0.996599i \(0.526258\pi\)
−0.996599 + 0.0823985i \(0.973742\pi\)
\(242\) 7.91072 0.508521
\(243\) 0 0
\(244\) −4.35868 −0.279036
\(245\) −5.58934 + 1.23528i −0.357090 + 0.0789191i
\(246\) 0 0
\(247\) −5.54477 + 2.54048i −0.352805 + 0.161647i
\(248\) 5.01590 5.01590i 0.318510 0.318510i
\(249\) 0 0
\(250\) −6.78869 8.88334i −0.429354 0.561832i
\(251\) 12.6899i 0.800981i 0.916301 + 0.400491i \(0.131160\pi\)
−0.916301 + 0.400491i \(0.868840\pi\)
\(252\) 0 0
\(253\) 7.15917 0.450093
\(254\) 9.45775 + 9.45775i 0.593432 + 0.593432i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 6.27952 6.27952i 0.391706 0.391706i −0.483589 0.875295i \(-0.660667\pi\)
0.875295 + 0.483589i \(0.160667\pi\)
\(258\) 0 0
\(259\) 12.9899 0.807151
\(260\) 7.98533 + 1.11111i 0.495229 + 0.0689079i
\(261\) 0 0
\(262\) 21.7528i 1.34389i
\(263\) 1.75042 1.75042i 0.107935 0.107935i −0.651077 0.759012i \(-0.725682\pi\)
0.759012 + 0.651077i \(0.225682\pi\)
\(264\) 0 0
\(265\) −6.60805 + 10.3576i −0.405929 + 0.636260i
\(266\) −2.52040 2.52040i −0.154536 0.154536i
\(267\) 0 0
\(268\) 7.11822i 0.434815i
\(269\) 22.0044i 1.34163i −0.741623 0.670817i \(-0.765944\pi\)
0.741623 0.670817i \(-0.234056\pi\)
\(270\) 0 0
\(271\) −6.44668 + 6.44668i −0.391608 + 0.391608i −0.875260 0.483652i \(-0.839310\pi\)
0.483652 + 0.875260i \(0.339310\pi\)
\(272\) 1.54027 1.54027i 0.0933923 0.0933923i
\(273\) 0 0
\(274\) 18.4668i 1.11562i
\(275\) 3.01656 8.25423i 0.181906 0.497749i
\(276\) 0 0
\(277\) −0.610861 + 0.610861i −0.0367031 + 0.0367031i −0.725220 0.688517i \(-0.758262\pi\)
0.688517 + 0.725220i \(0.258262\pi\)
\(278\) 1.02338 0.0613780
\(279\) 0 0
\(280\) 1.01678 + 4.60070i 0.0607645 + 0.274944i
\(281\) 2.98812 2.98812i 0.178256 0.178256i −0.612339 0.790595i \(-0.709771\pi\)
0.790595 + 0.612339i \(0.209771\pi\)
\(282\) 0 0
\(283\) 19.2284 + 19.2284i 1.14301 + 1.14301i 0.987896 + 0.155116i \(0.0495752\pi\)
0.155116 + 0.987896i \(0.450425\pi\)
\(284\) 1.46384 + 1.46384i 0.0868630 + 0.0868630i
\(285\) 0 0
\(286\) 2.63969 + 5.76130i 0.156088 + 0.340673i
\(287\) 10.6965 + 10.6965i 0.631394 + 0.631394i
\(288\) 0 0
\(289\) 12.2552i 0.720892i
\(290\) 1.43199 0.316478i 0.0840892 0.0185843i
\(291\) 0 0
\(292\) 14.7472i 0.863017i
\(293\) 22.2931i 1.30238i 0.758916 + 0.651188i \(0.225729\pi\)
−0.758916 + 0.651188i \(0.774271\pi\)
\(294\) 0 0
\(295\) 4.99383 + 3.18603i 0.290752 + 0.185498i
\(296\) 6.16468i 0.358315i
\(297\) 0 0
\(298\) −6.88021 6.88021i −0.398560 0.398560i
\(299\) −6.11729 13.3514i −0.353772 0.772132i
\(300\) 0 0
\(301\) −6.34264 6.34264i −0.365584 0.365584i
\(302\) 1.76761 + 1.76761i 0.101715 + 0.101715i
\(303\) 0 0
\(304\) 1.19612 1.19612i 0.0686024 0.0686024i
\(305\) 9.51666 2.10324i 0.544922 0.120431i
\(306\) 0 0
\(307\) −19.0008 −1.08444 −0.542218 0.840238i \(-0.682415\pi\)
−0.542218 + 0.840238i \(0.682415\pi\)
\(308\) −2.61883 + 2.61883i −0.149222 + 0.149222i
\(309\) 0 0
\(310\) −8.53124 + 13.3720i −0.484542 + 0.759479i
\(311\) 7.95375i 0.451016i −0.974241 0.225508i \(-0.927596\pi\)
0.974241 0.225508i \(-0.0724042\pi\)
\(312\) 0 0
\(313\) 21.4521 21.4521i 1.21254 1.21254i 0.242358 0.970187i \(-0.422079\pi\)
0.970187 0.242358i \(-0.0779209\pi\)
\(314\) 1.73178 1.73178i 0.0977300 0.0977300i
\(315\) 0 0
\(316\) 1.75410i 0.0986760i
\(317\) 9.21536i 0.517586i 0.965933 + 0.258793i \(0.0833248\pi\)
−0.965933 + 0.258793i \(0.916675\pi\)
\(318\) 0 0
\(319\) 0.815122 + 0.815122i 0.0456381 + 0.0456381i
\(320\) −2.18338 + 0.482541i −0.122055 + 0.0269749i
\(321\) 0 0
\(322\) 6.06895 6.06895i 0.338209 0.338209i
\(323\) 3.68470i 0.205022i
\(324\) 0 0
\(325\) −17.9712 + 1.42728i −0.996861 + 0.0791714i
\(326\) 15.9324 0.882416
\(327\) 0 0
\(328\) −5.07630 + 5.07630i −0.280292 + 0.280292i
\(329\) 20.0654 1.10624
\(330\) 0 0
\(331\) 6.58330 + 6.58330i 0.361851 + 0.361851i 0.864494 0.502643i \(-0.167639\pi\)
−0.502643 + 0.864494i \(0.667639\pi\)
\(332\) 13.9129 0.763569
\(333\) 0 0
\(334\) 22.6158i 1.23748i
\(335\) −3.43484 15.5418i −0.187665 0.849139i
\(336\) 0 0
\(337\) 10.4607 10.4607i 0.569832 0.569832i −0.362249 0.932081i \(-0.617991\pi\)
0.932081 + 0.362249i \(0.117991\pi\)
\(338\) 8.48893 9.84571i 0.461737 0.535536i
\(339\) 0 0
\(340\) −2.61975 + 4.10623i −0.142076 + 0.222692i
\(341\) −12.4679 −0.675173
\(342\) 0 0
\(343\) −20.1442 −1.08768
\(344\) 3.01007 3.01007i 0.162292 0.162292i
\(345\) 0 0
\(346\) 12.8009 12.8009i 0.688182 0.688182i
\(347\) −12.9575 12.9575i −0.695596 0.695596i 0.267861 0.963458i \(-0.413683\pi\)
−0.963458 + 0.267861i \(0.913683\pi\)
\(348\) 0 0
\(349\) 14.4575 + 14.4575i 0.773892 + 0.773892i 0.978784 0.204893i \(-0.0656846\pi\)
−0.204893 + 0.978784i \(0.565685\pi\)
\(350\) −4.44005 9.55444i −0.237331 0.510706i
\(351\) 0 0
\(352\) −1.24283 1.24283i −0.0662433 0.0662433i
\(353\) 28.3107 1.50683 0.753413 0.657547i \(-0.228406\pi\)
0.753413 + 0.657547i \(0.228406\pi\)
\(354\) 0 0
\(355\) −3.90249 2.48976i −0.207123 0.132143i
\(356\) −1.31506 1.31506i −0.0696981 0.0696981i
\(357\) 0 0
\(358\) 18.7205i 0.989407i
\(359\) −3.64287 3.64287i −0.192263 0.192263i 0.604410 0.796673i \(-0.293409\pi\)
−0.796673 + 0.604410i \(0.793409\pi\)
\(360\) 0 0
\(361\) 16.1386i 0.849399i
\(362\) 16.6965 0.877548
\(363\) 0 0
\(364\) 7.12166 + 2.64624i 0.373277 + 0.138701i
\(365\) −7.11616 32.1989i −0.372477 1.68537i
\(366\) 0 0
\(367\) 6.99757 + 6.99757i 0.365270 + 0.365270i 0.865749 0.500479i \(-0.166843\pi\)
−0.500479 + 0.865749i \(0.666843\pi\)
\(368\) 2.88018 + 2.88018i 0.150140 + 0.150140i
\(369\) 0 0
\(370\) −2.97471 13.4598i −0.154648 0.699744i
\(371\) −8.18661 + 8.18661i −0.425028 + 0.425028i
\(372\) 0 0
\(373\) 2.34687 2.34687i 0.121516 0.121516i −0.643733 0.765250i \(-0.722615\pi\)
0.765250 + 0.643733i \(0.222615\pi\)
\(374\) −3.82859 −0.197972
\(375\) 0 0
\(376\) 9.52254i 0.491088i
\(377\) 0.823655 2.21665i 0.0424204 0.114163i
\(378\) 0 0
\(379\) −3.34919 + 3.34919i −0.172037 + 0.172037i −0.787874 0.615837i \(-0.788818\pi\)
0.615837 + 0.787874i \(0.288818\pi\)
\(380\) −2.03441 + 3.18877i −0.104363 + 0.163581i
\(381\) 0 0
\(382\) 6.58561i 0.336949i
\(383\) −24.7318 −1.26373 −0.631867 0.775077i \(-0.717711\pi\)
−0.631867 + 0.775077i \(0.717711\pi\)
\(384\) 0 0
\(385\) 4.45421 6.98160i 0.227008 0.355815i
\(386\) 10.4497 0.531875
\(387\) 0 0
\(388\) 6.58936i 0.334524i
\(389\) 3.36767 0.170748 0.0853738 0.996349i \(-0.472792\pi\)
0.0853738 + 0.996349i \(0.472792\pi\)
\(390\) 0 0
\(391\) 8.87248 0.448701
\(392\) 2.55995i 0.129297i
\(393\) 0 0
\(394\) 11.5736 0.583068
\(395\) 0.846427 + 3.82987i 0.0425884 + 0.192702i
\(396\) 0 0
\(397\) −15.6097 −0.783427 −0.391714 0.920087i \(-0.628118\pi\)
−0.391714 + 0.920087i \(0.628118\pi\)
\(398\) 23.7883i 1.19240i
\(399\) 0 0
\(400\) 4.53431 2.10714i 0.226715 0.105357i
\(401\) −26.3476 + 26.3476i −1.31574 + 1.31574i −0.398620 + 0.917116i \(0.630511\pi\)
−0.917116 + 0.398620i \(0.869489\pi\)
\(402\) 0 0
\(403\) 10.6534 + 23.2518i 0.530684 + 1.15825i
\(404\) 1.61904i 0.0805505i
\(405\) 0 0
\(406\) 1.38199 0.0685868
\(407\) 7.66168 7.66168i 0.379775 0.379775i
\(408\) 0 0
\(409\) −21.1408 + 21.1408i −1.04535 + 1.04535i −0.0464256 + 0.998922i \(0.514783\pi\)
−0.998922 + 0.0464256i \(0.985217\pi\)
\(410\) 8.63398 13.5330i 0.426402 0.668349i
\(411\) 0 0
\(412\) 5.42044 + 5.42044i 0.267046 + 0.267046i
\(413\) 3.94712 + 3.94712i 0.194225 + 0.194225i
\(414\) 0 0
\(415\) −30.3772 + 6.71355i −1.49116 + 0.329555i
\(416\) −1.25584 + 3.37977i −0.0615728 + 0.165707i
\(417\) 0 0
\(418\) −2.97317 −0.145422
\(419\) 14.7707i 0.721595i 0.932644 + 0.360797i \(0.117495\pi\)
−0.932644 + 0.360797i \(0.882505\pi\)
\(420\) 0 0
\(421\) −21.9707 21.9707i −1.07079 1.07079i −0.997296 0.0734913i \(-0.976586\pi\)
−0.0734913 0.997296i \(-0.523414\pi\)
\(422\) 3.22265i 0.156876i
\(423\) 0 0
\(424\) −3.88517 3.88517i −0.188680 0.188680i
\(425\) 3.73848 10.2296i 0.181343 0.496209i
\(426\) 0 0
\(427\) 9.18436 0.444462
\(428\) −5.59200 5.59200i −0.270299 0.270299i
\(429\) 0 0
\(430\) −5.11964 + 8.02460i −0.246891 + 0.386981i
\(431\) −1.95159 1.95159i −0.0940049 0.0940049i 0.658540 0.752545i \(-0.271174\pi\)
−0.752545 + 0.658540i \(0.771174\pi\)
\(432\) 0 0
\(433\) −23.1334 23.1334i −1.11172 1.11172i −0.992918 0.118804i \(-0.962094\pi\)
−0.118804 0.992918i \(-0.537906\pi\)
\(434\) −10.5692 + 10.5692i −0.507339 + 0.507339i
\(435\) 0 0
\(436\) 8.50709 8.50709i 0.407416 0.407416i
\(437\) 6.89010 0.329598
\(438\) 0 0
\(439\) 35.1398 1.67713 0.838566 0.544800i \(-0.183395\pi\)
0.838566 + 0.544800i \(0.183395\pi\)
\(440\) 3.31330 + 2.11386i 0.157955 + 0.100774i
\(441\) 0 0
\(442\) 3.27141 + 7.14008i 0.155605 + 0.339619i
\(443\) −3.49624 + 3.49624i −0.166111 + 0.166111i −0.785268 0.619156i \(-0.787475\pi\)
0.619156 + 0.785268i \(0.287475\pi\)
\(444\) 0 0
\(445\) 3.50585 + 2.23671i 0.166193 + 0.106030i
\(446\) 6.20878i 0.293994i
\(447\) 0 0
\(448\) −2.10714 −0.0995532
\(449\) −7.86444 7.86444i −0.371146 0.371146i 0.496749 0.867894i \(-0.334527\pi\)
−0.867894 + 0.496749i \(0.834527\pi\)
\(450\) 0 0
\(451\) 12.6180 0.594159
\(452\) −3.53973 + 3.53973i −0.166495 + 0.166495i
\(453\) 0 0
\(454\) 1.01019 0.0474107
\(455\) −16.8262 2.34126i −0.788826 0.109760i
\(456\) 0 0
\(457\) 6.00799i 0.281042i −0.990078 0.140521i \(-0.955122\pi\)
0.990078 0.140521i \(-0.0448778\pi\)
\(458\) −8.16009 + 8.16009i −0.381296 + 0.381296i
\(459\) 0 0
\(460\) −7.67833 4.89872i −0.358004 0.228404i
\(461\) 26.1391 + 26.1391i 1.21742 + 1.21742i 0.968532 + 0.248889i \(0.0800656\pi\)
0.248889 + 0.968532i \(0.419934\pi\)
\(462\) 0 0
\(463\) 30.7752i 1.43024i −0.698999 0.715122i \(-0.746371\pi\)
0.698999 0.715122i \(-0.253629\pi\)
\(464\) 0.655858i 0.0304474i
\(465\) 0 0
\(466\) 8.81549 8.81549i 0.408370 0.408370i
\(467\) −27.6301 + 27.6301i −1.27857 + 1.27857i −0.337096 + 0.941470i \(0.609445\pi\)
−0.941470 + 0.337096i \(0.890555\pi\)
\(468\) 0 0
\(469\) 14.9991i 0.692595i
\(470\) −4.59502 20.7913i −0.211953 0.959033i
\(471\) 0 0
\(472\) −1.87321 + 1.87321i −0.0862214 + 0.0862214i
\(473\) −7.48203 −0.344024
\(474\) 0 0
\(475\) 2.90319 7.94399i 0.133207 0.364495i
\(476\) −3.24556 + 3.24556i −0.148760 + 0.148760i
\(477\) 0 0
\(478\) 14.8422 + 14.8422i 0.678866 + 0.678866i
\(479\) −11.7482 11.7482i −0.536787 0.536787i 0.385797 0.922584i \(-0.373927\pi\)
−0.922584 + 0.385797i \(0.873927\pi\)
\(480\) 0 0
\(481\) −20.8352 7.74188i −0.950004 0.352999i
\(482\) 16.7506 + 16.7506i 0.762967 + 0.762967i
\(483\) 0 0
\(484\) 7.91072i 0.359578i
\(485\) −3.17964 14.3871i −0.144380 0.653283i
\(486\) 0 0
\(487\) 10.8941i 0.493657i −0.969059 0.246829i \(-0.920612\pi\)
0.969059 0.246829i \(-0.0793884\pi\)
\(488\) 4.35868i 0.197308i
\(489\) 0 0
\(490\) 1.23528 + 5.58934i 0.0558042 + 0.252500i
\(491\) 19.7178i 0.889854i −0.895567 0.444927i \(-0.853230\pi\)
0.895567 0.444927i \(-0.146770\pi\)
\(492\) 0 0
\(493\) 1.01019 + 1.01019i 0.0454969 + 0.0454969i
\(494\) 2.54048 + 5.54477i 0.114302 + 0.249471i
\(495\) 0 0
\(496\) −5.01590 5.01590i −0.225221 0.225221i
\(497\) −3.08452 3.08452i −0.138360 0.138360i
\(498\) 0 0
\(499\) −25.8969 + 25.8969i −1.15930 + 1.15930i −0.174678 + 0.984626i \(0.555888\pi\)
−0.984626 + 0.174678i \(0.944112\pi\)
\(500\) −8.88334 + 6.78869i −0.397275 + 0.303599i
\(501\) 0 0
\(502\) 12.6899 0.566379
\(503\) −18.7885 + 18.7885i −0.837737 + 0.837737i −0.988561 0.150824i \(-0.951807\pi\)
0.150824 + 0.988561i \(0.451807\pi\)
\(504\) 0 0
\(505\) −0.781256 3.53499i −0.0347654 0.157305i
\(506\) 7.15917i 0.318264i
\(507\) 0 0
\(508\) 9.45775 9.45775i 0.419620 0.419620i
\(509\) −9.87855 + 9.87855i −0.437859 + 0.437859i −0.891291 0.453432i \(-0.850200\pi\)
0.453432 + 0.891291i \(0.350200\pi\)
\(510\) 0 0
\(511\) 31.0746i 1.37466i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −6.27952 6.27952i −0.276978 0.276978i
\(515\) −14.4505 9.21931i −0.636765 0.406251i
\(516\) 0 0
\(517\) 11.8349 11.8349i 0.520500 0.520500i
\(518\) 12.9899i 0.570742i
\(519\) 0 0
\(520\) 1.11111 7.98533i 0.0487252 0.350180i
\(521\) 23.5852 1.03329 0.516643 0.856201i \(-0.327182\pi\)
0.516643 + 0.856201i \(0.327182\pi\)
\(522\) 0 0
\(523\) 13.1997 13.1997i 0.577184 0.577184i −0.356943 0.934126i \(-0.616181\pi\)
0.934126 + 0.356943i \(0.116181\pi\)
\(524\) 21.7528 0.950276
\(525\) 0 0
\(526\) −1.75042 1.75042i −0.0763217 0.0763217i
\(527\) −15.4516 −0.673084
\(528\) 0 0
\(529\) 6.40914i 0.278658i
\(530\) 10.3576 + 6.60805i 0.449904 + 0.287035i
\(531\) 0 0
\(532\) −2.52040 + 2.52040i −0.109273 + 0.109273i
\(533\) −10.7817 23.5318i −0.467007 1.01927i
\(534\) 0 0
\(535\) 14.9078 + 9.51109i 0.644522 + 0.411200i
\(536\) 7.11822 0.307460
\(537\) 0 0
\(538\) −22.0044 −0.948679
\(539\) −3.18159 + 3.18159i −0.137041 + 0.137041i
\(540\) 0 0
\(541\) 24.0817 24.0817i 1.03535 1.03535i 0.0360013 0.999352i \(-0.488538\pi\)
0.999352 0.0360013i \(-0.0114620\pi\)
\(542\) 6.44668 + 6.44668i 0.276908 + 0.276908i
\(543\) 0 0
\(544\) −1.54027 1.54027i −0.0660384 0.0660384i
\(545\) −14.4692 + 22.6793i −0.619793 + 0.971473i
\(546\) 0 0
\(547\) −13.5594 13.5594i −0.579760 0.579760i 0.355077 0.934837i \(-0.384455\pi\)
−0.934837 + 0.355077i \(0.884455\pi\)
\(548\) −18.4668 −0.788864
\(549\) 0 0
\(550\) −8.25423 3.01656i −0.351961 0.128627i
\(551\) 0.784486 + 0.784486i 0.0334202 + 0.0334202i
\(552\) 0 0
\(553\) 3.69615i 0.157176i
\(554\) 0.610861 + 0.610861i 0.0259530 + 0.0259530i
\(555\) 0 0
\(556\) 1.02338i 0.0434008i
\(557\) 10.4636 0.443359 0.221679 0.975120i \(-0.428846\pi\)
0.221679 + 0.975120i \(0.428846\pi\)
\(558\) 0 0
\(559\) 6.39316 + 13.9535i 0.270402 + 0.590170i
\(560\) 4.60070 1.01678i 0.194415 0.0429670i
\(561\) 0 0
\(562\) −2.98812 2.98812i −0.126046 0.126046i
\(563\) −11.8657 11.8657i −0.500078 0.500078i 0.411384 0.911462i \(-0.365045\pi\)
−0.911462 + 0.411384i \(0.865045\pi\)
\(564\) 0 0
\(565\) 6.02052 9.43665i 0.253285 0.397003i
\(566\) 19.2284 19.2284i 0.808232 0.808232i
\(567\) 0 0
\(568\) 1.46384 1.46384i 0.0614214 0.0614214i
\(569\) −31.9702 −1.34026 −0.670129 0.742244i \(-0.733761\pi\)
−0.670129 + 0.742244i \(0.733761\pi\)
\(570\) 0 0
\(571\) 40.3412i 1.68823i −0.536165 0.844113i \(-0.680127\pi\)
0.536165 0.844113i \(-0.319873\pi\)
\(572\) 5.76130 2.63969i 0.240892 0.110371i
\(573\) 0 0
\(574\) 10.6965 10.6965i 0.446463 0.446463i
\(575\) 19.1286 + 6.99067i 0.797716 + 0.291531i
\(576\) 0 0
\(577\) 6.68207i 0.278178i −0.990280 0.139089i \(-0.955583\pi\)
0.990280 0.139089i \(-0.0444175\pi\)
\(578\) 12.2552 0.509748
\(579\) 0 0
\(580\) −0.316478 1.43199i −0.0131411 0.0594600i
\(581\) −29.3165 −1.21625
\(582\) 0 0
\(583\) 9.65725i 0.399962i
\(584\) 14.7472 0.610245
\(585\) 0 0
\(586\) 22.2931 0.920919
\(587\) 27.0614i 1.11694i −0.829524 0.558472i \(-0.811388\pi\)
0.829524 0.558472i \(-0.188612\pi\)
\(588\) 0 0
\(589\) −11.9993 −0.494421
\(590\) 3.18603 4.99383i 0.131167 0.205593i
\(591\) 0 0
\(592\) 6.16468 0.253367
\(593\) 24.5808i 1.00941i 0.863292 + 0.504705i \(0.168399\pi\)
−0.863292 + 0.504705i \(0.831601\pi\)
\(594\) 0 0
\(595\) 5.52018 8.65242i 0.226305 0.354714i
\(596\) −6.88021 + 6.88021i −0.281824 + 0.281824i
\(597\) 0 0
\(598\) −13.3514 + 6.11729i −0.545979 + 0.250155i
\(599\) 27.0675i 1.10595i 0.833199 + 0.552974i \(0.186507\pi\)
−0.833199 + 0.552974i \(0.813493\pi\)
\(600\) 0 0
\(601\) 6.64287 0.270968 0.135484 0.990780i \(-0.456741\pi\)
0.135484 + 0.990780i \(0.456741\pi\)
\(602\) −6.34264 + 6.34264i −0.258507 + 0.258507i
\(603\) 0 0
\(604\) 1.76761 1.76761i 0.0719231 0.0719231i
\(605\) 3.81725 + 17.2721i 0.155193 + 0.702212i
\(606\) 0 0
\(607\) −12.3366 12.3366i −0.500728 0.500728i 0.410936 0.911664i \(-0.365202\pi\)
−0.911664 + 0.410936i \(0.865202\pi\)
\(608\) −1.19612 1.19612i −0.0485092 0.0485092i
\(609\) 0 0
\(610\) −2.10324 9.51666i −0.0851578 0.385318i
\(611\) −32.1840 11.9588i −1.30203 0.483802i
\(612\) 0 0
\(613\) −43.4995 −1.75693 −0.878464 0.477808i \(-0.841432\pi\)
−0.878464 + 0.477808i \(0.841432\pi\)
\(614\) 19.0008i 0.766812i
\(615\) 0 0
\(616\) 2.61883 + 2.61883i 0.105516 + 0.105516i
\(617\) 6.19626i 0.249452i 0.992191 + 0.124726i \(0.0398052\pi\)
−0.992191 + 0.124726i \(0.960195\pi\)
\(618\) 0 0
\(619\) 23.3512 + 23.3512i 0.938565 + 0.938565i 0.998219 0.0596543i \(-0.0189998\pi\)
−0.0596543 + 0.998219i \(0.519000\pi\)
\(620\) 13.3720 + 8.53124i 0.537033 + 0.342623i
\(621\) 0 0
\(622\) −7.95375 −0.318916
\(623\) 2.77102 + 2.77102i 0.111019 + 0.111019i
\(624\) 0 0
\(625\) 16.1199 19.1089i 0.644796 0.764355i
\(626\) −21.4521 21.4521i −0.857399 0.857399i
\(627\) 0 0
\(628\) −1.73178 1.73178i −0.0691055 0.0691055i
\(629\) 9.49525 9.49525i 0.378600 0.378600i
\(630\) 0 0
\(631\) 17.4170 17.4170i 0.693360 0.693360i −0.269610 0.962970i \(-0.586895\pi\)
0.962970 + 0.269610i \(0.0868948\pi\)
\(632\) −1.75410 −0.0697744
\(633\) 0 0
\(634\) 9.21536 0.365989
\(635\) −16.0861 + 25.2136i −0.638358 + 1.00057i
\(636\) 0 0
\(637\) 8.65203 + 3.21489i 0.342806 + 0.127379i
\(638\) 0.815122 0.815122i 0.0322710 0.0322710i
\(639\) 0 0
\(640\) 0.482541 + 2.18338i 0.0190741 + 0.0863057i
\(641\) 5.10269i 0.201544i −0.994910 0.100772i \(-0.967869\pi\)
0.994910 0.100772i \(-0.0321313\pi\)
\(642\) 0 0
\(643\) 46.9867 1.85297 0.926487 0.376327i \(-0.122813\pi\)
0.926487 + 0.376327i \(0.122813\pi\)
\(644\) −6.06895 6.06895i −0.239150 0.239150i
\(645\) 0 0
\(646\) −3.68470 −0.144972
\(647\) 19.2898 19.2898i 0.758358 0.758358i −0.217665 0.976024i \(-0.569844\pi\)
0.976024 + 0.217665i \(0.0698441\pi\)
\(648\) 0 0
\(649\) 4.65618 0.182771
\(650\) 1.42728 + 17.9712i 0.0559826 + 0.704887i
\(651\) 0 0
\(652\) 15.9324i 0.623962i
\(653\) 22.6253 22.6253i 0.885395 0.885395i −0.108682 0.994077i \(-0.534663\pi\)
0.994077 + 0.108682i \(0.0346629\pi\)
\(654\) 0 0
\(655\) −47.4947 + 10.4966i −1.85577 + 0.410137i
\(656\) 5.07630 + 5.07630i 0.198196 + 0.198196i
\(657\) 0 0
\(658\) 20.0654i 0.782230i
\(659\) 45.2569i 1.76296i −0.472222 0.881480i \(-0.656548\pi\)
0.472222 0.881480i \(-0.343452\pi\)
\(660\) 0 0
\(661\) −23.2218 + 23.2218i −0.903222 + 0.903222i −0.995713 0.0924919i \(-0.970517\pi\)
0.0924919 + 0.995713i \(0.470517\pi\)
\(662\) 6.58330 6.58330i 0.255867 0.255867i
\(663\) 0 0
\(664\) 13.9129i 0.539925i
\(665\) 4.28680 6.71920i 0.166235 0.260559i
\(666\) 0 0
\(667\) −1.88899 + 1.88899i −0.0731419 + 0.0731419i
\(668\) −22.6158 −0.875032
\(669\) 0 0
\(670\) −15.5418 + 3.43484i −0.600432 + 0.132699i
\(671\) 5.41712 5.41712i 0.209125 0.209125i
\(672\) 0 0
\(673\) 26.3770 + 26.3770i 1.01676 + 1.01676i 0.999857 + 0.0169012i \(0.00538009\pi\)
0.0169012 + 0.999857i \(0.494620\pi\)
\(674\) −10.4607 10.4607i −0.402932 0.402932i
\(675\) 0 0
\(676\) −9.84571 8.48893i −0.378681 0.326497i
\(677\) −10.0002 10.0002i −0.384340 0.384340i 0.488323 0.872663i \(-0.337609\pi\)
−0.872663 + 0.488323i \(0.837609\pi\)
\(678\) 0 0
\(679\) 13.8847i 0.532847i
\(680\) 4.10623 + 2.61975i 0.157467 + 0.100463i
\(681\) 0 0
\(682\) 12.4679i 0.477419i
\(683\) 28.2136i 1.07956i 0.841805 + 0.539782i \(0.181493\pi\)
−0.841805 + 0.539782i \(0.818507\pi\)
\(684\) 0 0
\(685\) 40.3201 8.91101i 1.54055 0.340472i
\(686\) 20.1442i 0.769108i
\(687\) 0 0
\(688\) −3.01007 3.01007i −0.114758 0.114758i
\(689\) 18.0101 8.25182i 0.686132 0.314369i
\(690\) 0 0
\(691\) −18.2102 18.2102i −0.692747 0.692747i 0.270089 0.962835i \(-0.412947\pi\)
−0.962835 + 0.270089i \(0.912947\pi\)
\(692\) −12.8009 12.8009i −0.486618 0.486618i
\(693\) 0 0
\(694\) −12.9575 + 12.9575i −0.491861 + 0.491861i
\(695\) 0.493821 + 2.23442i 0.0187317 + 0.0847563i
\(696\) 0 0
\(697\) 15.6377 0.592321
\(698\) 14.4575 14.4575i 0.547224 0.547224i
\(699\) 0 0
\(700\) −9.55444 + 4.44005i −0.361124 + 0.167818i
\(701\) 5.82154i 0.219876i −0.993938 0.109938i \(-0.964935\pi\)
0.993938 0.109938i \(-0.0350653\pi\)
\(702\) 0 0
\(703\) 7.37372 7.37372i 0.278105 0.278105i
\(704\) −1.24283 + 1.24283i −0.0468411 + 0.0468411i
\(705\) 0 0
\(706\) 28.3107i 1.06549i
\(707\) 3.41156i 0.128305i
\(708\) 0 0
\(709\) 9.34798 + 9.34798i 0.351071 + 0.351071i 0.860508 0.509437i \(-0.170146\pi\)
−0.509437 + 0.860508i \(0.670146\pi\)
\(710\) −2.48976 + 3.90249i −0.0934390 + 0.146458i
\(711\) 0 0
\(712\) −1.31506 + 1.31506i −0.0492840 + 0.0492840i
\(713\) 28.8934i 1.08207i
\(714\) 0 0
\(715\) −11.3054 + 8.54352i −0.422797 + 0.319510i
\(716\) 18.7205 0.699617
\(717\) 0 0
\(718\) −3.64287 + 3.64287i −0.135951 + 0.135951i
\(719\) −19.9476 −0.743920 −0.371960 0.928249i \(-0.621314\pi\)
−0.371960 + 0.928249i \(0.621314\pi\)
\(720\) 0 0
\(721\) −11.4217 11.4217i −0.425365 0.425365i
\(722\) 16.1386 0.600616
\(723\) 0 0
\(724\) 16.6965i 0.620520i
\(725\) 1.38199 + 2.97386i 0.0513257 + 0.110446i
\(726\) 0 0
\(727\) 6.61314 6.61314i 0.245268 0.245268i −0.573757 0.819025i \(-0.694515\pi\)
0.819025 + 0.573757i \(0.194515\pi\)
\(728\) 2.64624 7.12166i 0.0980763 0.263946i
\(729\) 0 0
\(730\) −32.1989 + 7.11616i −1.19173 + 0.263381i
\(731\) −9.27260 −0.342960
\(732\) 0 0
\(733\) 0.105862 0.00391011 0.00195506 0.999998i \(-0.499378\pi\)
0.00195506 + 0.999998i \(0.499378\pi\)
\(734\) 6.99757 6.99757i 0.258285 0.258285i
\(735\) 0 0
\(736\) 2.88018 2.88018i 0.106165 0.106165i
\(737\) −8.84677 8.84677i −0.325875 0.325875i
\(738\) 0 0
\(739\) 13.2967 + 13.2967i 0.489128 + 0.489128i 0.908031 0.418903i \(-0.137585\pi\)
−0.418903 + 0.908031i \(0.637585\pi\)
\(740\) −13.4598 + 2.97471i −0.494794 + 0.109353i
\(741\) 0 0
\(742\) 8.18661 + 8.18661i 0.300540 + 0.300540i
\(743\) 10.0152 0.367421 0.183710 0.982980i \(-0.441189\pi\)
0.183710 + 0.982980i \(0.441189\pi\)
\(744\) 0 0
\(745\) 11.7021 18.3421i 0.428733 0.672003i
\(746\) −2.34687 2.34687i −0.0859250 0.0859250i
\(747\) 0 0
\(748\) 3.82859i 0.139987i
\(749\) 11.7831 + 11.7831i 0.430547 + 0.430547i
\(750\) 0 0
\(751\) 17.0923i 0.623708i −0.950130 0.311854i \(-0.899050\pi\)
0.950130 0.311854i \(-0.100950\pi\)
\(752\) 9.52254 0.347251
\(753\) 0 0
\(754\) −2.21665 0.823655i −0.0807256 0.0299957i
\(755\) −3.00642 + 4.71231i −0.109415 + 0.171499i
\(756\) 0 0
\(757\) −8.13441 8.13441i −0.295650 0.295650i 0.543657 0.839307i \(-0.317039\pi\)
−0.839307 + 0.543657i \(0.817039\pi\)
\(758\) 3.34919 + 3.34919i 0.121648 + 0.121648i
\(759\) 0 0
\(760\) 3.18877 + 2.03441i 0.115669 + 0.0737960i
\(761\) −12.7947 + 12.7947i −0.463806 + 0.463806i −0.899901 0.436095i \(-0.856361\pi\)
0.436095 + 0.899901i \(0.356361\pi\)
\(762\) 0 0
\(763\) −17.9257 + 17.9257i −0.648953 + 0.648953i
\(764\) 6.58561 0.238259
\(765\) 0 0
\(766\) 24.7318i 0.893595i
\(767\) −3.97856 8.68347i −0.143657 0.313542i
\(768\) 0 0
\(769\) 0.446059 0.446059i 0.0160853 0.0160853i −0.699018 0.715104i \(-0.746379\pi\)
0.715104 + 0.699018i \(0.246379\pi\)
\(770\) −6.98160 4.45421i −0.251599 0.160519i
\(771\) 0 0
\(772\) 10.4497i 0.376092i
\(773\) 12.4535 0.447920 0.223960 0.974598i \(-0.428102\pi\)
0.223960 + 0.974598i \(0.428102\pi\)
\(774\) 0 0
\(775\) −33.3129 12.1744i −1.19663 0.437318i
\(776\) 6.58936 0.236544
\(777\) 0 0
\(778\) 3.36767i 0.120737i
\(779\) 12.1438 0.435096
\(780\) 0 0
\(781\) −3.63862 −0.130200
\(782\) 8.87248i 0.317279i
\(783\) 0 0
\(784\) −2.55995 −0.0914266
\(785\) 4.61679 + 2.94548i 0.164780 + 0.105129i
\(786\) 0 0
\(787\) −22.6968 −0.809053 −0.404527 0.914526i \(-0.632564\pi\)
−0.404527 + 0.914526i \(0.632564\pi\)
\(788\) 11.5736i 0.412292i
\(789\) 0 0
\(790\) 3.82987 0.846427i 0.136261 0.0301145i
\(791\) 7.45872 7.45872i 0.265202 0.265202i
\(792\) 0 0
\(793\) −14.7313 5.47382i −0.523125 0.194381i
\(794\) 15.6097i 0.553967i
\(795\) 0 0
\(796\) 23.7883 0.843155
\(797\) 4.98891 4.98891i 0.176716 0.176716i −0.613206 0.789923i \(-0.710121\pi\)
0.789923 + 0.613206i \(0.210121\pi\)
\(798\) 0 0
\(799\) 14.6672 14.6672i 0.518890 0.518890i
\(800\) −2.10714 4.53431i −0.0744988 0.160312i
\(801\) 0 0
\(802\) 26.3476 + 26.3476i 0.930366 + 0.930366i
\(803\) −18.3284 18.3284i −0.646795 0.646795i
\(804\) 0 0
\(805\) 16.1794 + 10.3223i 0.570247 + 0.363814i
\(806\) 23.2518 10.6534i 0.819009 0.375250i
\(807\) 0 0
\(808\) 1.61904 0.0569578
\(809\) 19.9396i 0.701040i −0.936555 0.350520i \(-0.886005\pi\)
0.936555 0.350520i \(-0.113995\pi\)
\(810\) 0 0
\(811\) −31.3132 31.3132i −1.09955 1.09955i −0.994462 0.105092i \(-0.966486\pi\)
−0.105092 0.994462i \(-0.533514\pi\)
\(812\) 1.38199i 0.0484982i
\(813\) 0 0
\(814\) −7.66168 7.66168i −0.268542 0.268542i
\(815\) 7.68806 + 34.7866i 0.269301 + 1.21852i
\(816\) 0 0
\(817\) −7.20082 −0.251925
\(818\) 21.1408 + 21.1408i 0.739172 + 0.739172i
\(819\) 0 0
\(820\) −13.5330 8.63398i −0.472594 0.301512i
\(821\) 16.2309 + 16.2309i 0.566463 + 0.566463i 0.931136 0.364673i \(-0.118819\pi\)
−0.364673 + 0.931136i \(0.618819\pi\)
\(822\) 0 0
\(823\) 6.00377 + 6.00377i 0.209278 + 0.209278i 0.803961 0.594683i \(-0.202722\pi\)
−0.594683 + 0.803961i \(0.702722\pi\)
\(824\) 5.42044 5.42044i 0.188830 0.188830i
\(825\) 0 0
\(826\) 3.94712 3.94712i 0.137338 0.137338i
\(827\) −45.4835 −1.58162 −0.790808 0.612064i \(-0.790339\pi\)
−0.790808 + 0.612064i \(0.790339\pi\)
\(828\) 0 0
\(829\) 12.9896 0.451148 0.225574 0.974226i \(-0.427574\pi\)
0.225574 + 0.974226i \(0.427574\pi\)
\(830\) 6.71355 + 30.3772i 0.233031 + 1.05441i
\(831\) 0 0
\(832\) 3.37977 + 1.25584i 0.117173 + 0.0435385i
\(833\) −3.94300 + 3.94300i −0.136617 + 0.136617i
\(834\) 0 0
\(835\) 49.3789 10.9131i 1.70883 0.377662i
\(836\) 2.97317i 0.102829i
\(837\) 0 0
\(838\) 14.7707 0.510244
\(839\) 29.4940 + 29.4940i 1.01824 + 1.01824i 0.999830 + 0.0184141i \(0.00586173\pi\)
0.0184141 + 0.999830i \(0.494138\pi\)
\(840\) 0 0
\(841\) 28.5699 0.985167
\(842\) −21.9707 + 21.9707i −0.757161 + 0.757161i
\(843\) 0 0
\(844\) −3.22265 −0.110928
\(845\) 25.5932 + 13.7836i 0.880433 + 0.474171i
\(846\) 0 0
\(847\) 16.6690i 0.572755i
\(848\) −3.88517 + 3.88517i −0.133417 + 0.133417i
\(849\) 0 0
\(850\) −10.2296 3.73848i −0.350872 0.128229i
\(851\) 17.7554 + 17.7554i 0.608647 + 0.608647i
\(852\) 0 0
\(853\) 46.2016i 1.58191i −0.611873 0.790956i \(-0.709584\pi\)
0.611873 0.790956i \(-0.290416\pi\)
\(854\) 9.18436i 0.314282i
\(855\) 0 0
\(856\) −5.59200 + 5.59200i −0.191131 + 0.191131i
\(857\) −28.5928 + 28.5928i −0.976711 + 0.976711i −0.999735 0.0230243i \(-0.992670\pi\)
0.0230243 + 0.999735i \(0.492670\pi\)
\(858\) 0 0
\(859\) 31.1464i 1.06270i −0.847152 0.531351i \(-0.821685\pi\)
0.847152 0.531351i \(-0.178315\pi\)
\(860\) 8.02460 + 5.11964i 0.273637 + 0.174578i
\(861\) 0 0
\(862\) −1.95159 + 1.95159i −0.0664715 + 0.0664715i
\(863\) 13.1379 0.447221 0.223610 0.974679i \(-0.428216\pi\)
0.223610 + 0.974679i \(0.428216\pi\)
\(864\) 0 0
\(865\) 34.1263 + 21.7723i 1.16033 + 0.740281i
\(866\) −23.1334 + 23.1334i −0.786106 + 0.786106i
\(867\) 0 0
\(868\) 10.5692 + 10.5692i 0.358743 + 0.358743i
\(869\) 2.18006 + 2.18006i 0.0739534 + 0.0739534i
\(870\) 0 0
\(871\) −8.93937 + 24.0580i −0.302899 + 0.815173i
\(872\) −8.50709 8.50709i −0.288087 0.288087i
\(873\) 0 0
\(874\) 6.89010i 0.233061i
\(875\) 18.7185 14.3047i 0.632800 0.483589i
\(876\) 0 0
\(877\) 50.9786i 1.72143i 0.509091 + 0.860713i \(0.329982\pi\)
−0.509091 + 0.860713i \(0.670018\pi\)
\(878\) 35.1398i 1.18591i
\(879\) 0 0
\(880\) 2.11386 3.31330i 0.0712583 0.111691i
\(881\) 55.2917i 1.86282i −0.363968 0.931412i \(-0.618578\pi\)
0.363968 0.931412i \(-0.381422\pi\)
\(882\) 0 0
\(883\) −5.18223 5.18223i −0.174396 0.174396i 0.614512 0.788908i \(-0.289353\pi\)
−0.788908 + 0.614512i \(0.789353\pi\)
\(884\) 7.14008 3.27141i 0.240147 0.110030i
\(885\) 0 0
\(886\) 3.49624 + 3.49624i 0.117458 + 0.117458i
\(887\) 33.3749 + 33.3749i 1.12062 + 1.12062i 0.991649 + 0.128969i \(0.0411669\pi\)
0.128969 + 0.991649i \(0.458833\pi\)
\(888\) 0 0
\(889\) −19.9288 + 19.9288i −0.668392 + 0.668392i
\(890\) 2.23671 3.50585i 0.0749746 0.117516i
\(891\) 0 0
\(892\) −6.20878 −0.207885
\(893\) 11.3901 11.3901i 0.381156 0.381156i
\(894\) 0 0
\(895\) −40.8739 + 9.03340i −1.36626 + 0.301953i
\(896\) 2.10714i 0.0703947i
\(897\) 0 0
\(898\) −7.86444 + 7.86444i −0.262440 + 0.262440i
\(899\) 3.28972 3.28972i 0.109718 0.109718i
\(900\) 0 0
\(901\) 11.9684i 0.398725i
\(902\) 12.6180i 0.420134i
\(903\) 0 0
\(904\) 3.53973 + 3.53973i 0.117730 + 0.117730i
\(905\) 8.05675 + 36.4548i 0.267816 + 1.21180i
\(906\) 0 0
\(907\) −20.9601 + 20.9601i −0.695969 + 0.695969i −0.963539 0.267569i \(-0.913780\pi\)
0.267569 + 0.963539i \(0.413780\pi\)
\(908\) 1.01019i 0.0335244i
\(909\) 0 0
\(910\) −2.34126 + 16.8262i −0.0776120 + 0.557784i
\(911\) 41.4685 1.37391 0.686956 0.726699i \(-0.258947\pi\)
0.686956 + 0.726699i \(0.258947\pi\)
\(912\) 0 0
\(913\) −17.2914 + 17.2914i −0.572263 + 0.572263i
\(914\) −6.00799 −0.198727
\(915\) 0 0
\(916\) 8.16009 + 8.16009i 0.269617 + 0.269617i
\(917\) −45.8363 −1.51365
\(918\) 0 0
\(919\) 34.0132i 1.12199i 0.827818 + 0.560996i \(0.189582\pi\)
−0.827818 + 0.560996i \(0.810418\pi\)
\(920\) −4.89872 + 7.67833i −0.161506 + 0.253147i
\(921\) 0 0
\(922\) 26.1391 26.1391i 0.860847 0.860847i
\(923\) 3.10909 + 6.78580i 0.102337 + 0.223357i
\(924\) 0 0
\(925\) 27.9526 12.9899i 0.919075 0.427104i
\(926\) −30.7752 −1.01134
\(927\) 0 0
\(928\) 0.655858 0.0215296
\(929\) 15.6158 15.6158i 0.512338 0.512338i −0.402904 0.915242i \(-0.631999\pi\)
0.915242 + 0.402904i \(0.131999\pi\)
\(930\) 0 0
\(931\) −3.06201 + 3.06201i −0.100353 + 0.100353i
\(932\) −8.81549 8.81549i −0.288761 0.288761i
\(933\) 0 0
\(934\) 27.6301 + 27.6301i 0.904083 + 0.904083i
\(935\) −1.84745 8.35927i −0.0604182 0.273378i
\(936\) 0 0
\(937\) 5.35972 + 5.35972i 0.175094 + 0.175094i 0.789213 0.614119i \(-0.210489\pi\)
−0.614119 + 0.789213i \(0.710489\pi\)
\(938\) −14.9991 −0.489739
\(939\) 0 0
\(940\) −20.7913 + 4.59502i −0.678139 + 0.149873i
\(941\) 34.8653 + 34.8653i 1.13658 + 1.13658i 0.989059 + 0.147518i \(0.0471286\pi\)
0.147518 + 0.989059i \(0.452871\pi\)
\(942\) 0 0
\(943\) 29.2413i 0.952228i
\(944\) 1.87321 + 1.87321i 0.0609677 + 0.0609677i
\(945\) 0 0
\(946\) 7.48203i 0.243262i
\(947\) 12.1066 0.393411 0.196706 0.980463i \(-0.436976\pi\)
0.196706 + 0.980463i \(0.436976\pi\)
\(948\) 0 0
\(949\) −18.5202 + 49.8423i −0.601192 + 1.61795i
\(950\) −7.94399 2.90319i −0.257737 0.0941918i
\(951\) 0 0
\(952\) 3.24556 + 3.24556i 0.105189 + 0.105189i
\(953\) −25.0126 25.0126i −0.810237 0.810237i 0.174432 0.984669i \(-0.444191\pi\)
−0.984669 + 0.174432i \(0.944191\pi\)
\(954\) 0 0
\(955\) −14.3789 + 3.17783i −0.465290 + 0.102832i
\(956\) 14.8422 14.8422i 0.480031 0.480031i
\(957\) 0 0
\(958\) −11.7482 + 11.7482i −0.379566 + 0.379566i
\(959\) 38.9123 1.25654
\(960\) 0 0
\(961\) 19.3185i 0.623178i
\(962\) −7.74188 + 20.8352i −0.249608 + 0.671754i
\(963\) 0 0
\(964\) 16.7506 16.7506i 0.539499 0.539499i
\(965\) 5.04241 + 22.8156i 0.162321 + 0.734462i
\(966\) 0 0
\(967\) 1.24404i 0.0400056i −0.999800 0.0200028i \(-0.993632\pi\)
0.999800 0.0200028i \(-0.00636751\pi\)
\(968\) −7.91072 −0.254260
\(969\) 0 0
\(970\) −14.3871 + 3.17964i −0.461941 + 0.102092i
\(971\) −5.03837 −0.161689 −0.0808445 0.996727i \(-0.525762\pi\)
−0.0808445 + 0.996727i \(0.525762\pi\)
\(972\) 0 0
\(973\) 2.15640i 0.0691310i
\(974\) −10.8941 −0.349068
\(975\) 0 0
\(976\) 4.35868 0.139518
\(977\) 28.7753i 0.920604i 0.887762 + 0.460302i \(0.152259\pi\)
−0.887762 + 0.460302i \(0.847741\pi\)
\(978\) 0 0
\(979\) 3.26881 0.104472
\(980\) 5.58934 1.23528i 0.178545 0.0394596i
\(981\) 0 0
\(982\) −19.7178 −0.629222
\(983\) 47.1354i 1.50338i −0.659514 0.751692i \(-0.729238\pi\)
0.659514 0.751692i \(-0.270762\pi\)
\(984\) 0 0
\(985\) 5.58473 + 25.2695i 0.177944 + 0.805154i
\(986\) 1.01019 1.01019i 0.0321712 0.0321712i
\(987\) 0 0
\(988\) 5.54477 2.54048i 0.176403 0.0808234i
\(989\) 17.3391i 0.551350i
\(990\) 0 0
\(991\) −8.72707 −0.277225 −0.138612 0.990347i \(-0.544264\pi\)
−0.138612 + 0.990347i \(0.544264\pi\)
\(992\) −5.01590 + 5.01590i −0.159255 + 0.159255i
\(993\) 0 0
\(994\) −3.08452 + 3.08452i −0.0978352 + 0.0978352i
\(995\) −51.9390 + 11.4789i −1.64658 + 0.363904i
\(996\) 0 0
\(997\) −18.6404 18.6404i −0.590347 0.590347i 0.347378 0.937725i \(-0.387072\pi\)
−0.937725 + 0.347378i \(0.887072\pi\)
\(998\) 25.8969 + 25.8969i 0.819751 + 0.819751i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1170.2.w.h.307.7 yes 14
3.2 odd 2 1170.2.w.g.307.1 yes 14
5.3 odd 4 1170.2.m.g.73.3 14
13.5 odd 4 1170.2.m.g.577.3 yes 14
15.8 even 4 1170.2.m.h.73.5 yes 14
39.5 even 4 1170.2.m.h.577.5 yes 14
65.18 even 4 inner 1170.2.w.h.343.7 yes 14
195.83 odd 4 1170.2.w.g.343.1 yes 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1170.2.m.g.73.3 14 5.3 odd 4
1170.2.m.g.577.3 yes 14 13.5 odd 4
1170.2.m.h.73.5 yes 14 15.8 even 4
1170.2.m.h.577.5 yes 14 39.5 even 4
1170.2.w.g.307.1 yes 14 3.2 odd 2
1170.2.w.g.343.1 yes 14 195.83 odd 4
1170.2.w.h.307.7 yes 14 1.1 even 1 trivial
1170.2.w.h.343.7 yes 14 65.18 even 4 inner