Properties

Label 1170.2.cu.f.431.1
Level $1170$
Weight $2$
Character 1170.431
Analytic conductor $9.342$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1170,2,Mod(71,1170)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1170, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1170.71");
 
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.cu (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.34249703649\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 12x^{14} + 49x^{12} - 12x^{10} - 600x^{8} + 108x^{6} + 4057x^{4} + 18252x^{2} + 28561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 431.1
Root \(-0.115299 - 1.50155i\) of defining polynomial
Character \(\chi\) \(=\) 1170.431
Dual form 1170.2.cu.f.1151.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.03475 + 0.277260i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\) \(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.03475 + 0.277260i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{10} +(-0.105325 - 0.0282216i) q^{11} +(1.19781 + 3.40077i) q^{13} -1.07125i q^{14} +(0.500000 + 0.866025i) q^{16} +(1.09921 - 1.90389i) q^{17} +(0.578305 + 2.15826i) q^{19} +(0.258819 + 0.965926i) q^{20} +(0.0545200 - 0.0944314i) q^{22} +(-1.34004 - 2.32102i) q^{23} +1.00000i q^{25} +(-3.59491 + 0.276806i) q^{26} +(1.03475 + 0.277260i) q^{28} +(-0.745303 + 0.430301i) q^{29} +(-0.123514 + 0.123514i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(1.55452 + 1.55452i) q^{34} +(0.927730 + 0.535625i) q^{35} +(-2.82648 + 10.5486i) q^{37} -2.23440 q^{38} -1.00000 q^{40} +(-1.03528 + 3.86370i) q^{41} +(10.5279 + 6.07830i) q^{43} +(0.0771029 + 0.0771029i) q^{44} +(2.58877 - 0.693658i) q^{46} +(-8.91173 + 8.91173i) q^{47} +(-5.06835 + 2.92621i) q^{49} +(-0.965926 - 0.258819i) q^{50} +(0.663057 - 3.54406i) q^{52} +3.57666i q^{53} +(0.0545200 + 0.0944314i) q^{55} +(-0.535625 + 0.927730i) q^{56} +(-0.222740 - 0.831277i) q^{58} +(-2.10359 - 7.85072i) q^{59} +(-4.30104 + 7.44963i) q^{61} +(-0.0873374 - 0.151273i) q^{62} -1.00000i q^{64} +(1.55773 - 3.25169i) q^{65} +(-3.67803 - 0.985526i) q^{67} +(-1.90389 + 1.09921i) q^{68} +(-0.757488 + 0.757488i) q^{70} +(-3.12935 + 0.838506i) q^{71} +(9.26565 + 9.26565i) q^{73} +(-9.45759 - 5.46034i) q^{74} +(0.578305 - 2.15826i) q^{76} +0.116809 q^{77} +3.58347 q^{79} +(0.258819 - 0.965926i) q^{80} +(-3.46410 - 2.00000i) q^{82} +(6.23094 + 6.23094i) q^{83} +(-2.12351 + 0.568994i) q^{85} +(-8.59602 + 8.59602i) q^{86} +(-0.0944314 + 0.0545200i) q^{88} +(-0.486484 - 0.130353i) q^{89} +(-2.18233 - 3.18684i) q^{91} +2.68009i q^{92} +(-6.30155 - 10.9146i) q^{94} +(1.11720 - 1.93504i) q^{95} +(-1.35837 - 5.06950i) q^{97} +(-1.51472 - 5.65301i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 12 q^{7} - 8 q^{13} + 8 q^{16} - 52 q^{19} - 8 q^{22} - 12 q^{28} + 36 q^{31} + 16 q^{34} + 8 q^{37} - 16 q^{40} + 72 q^{43} + 32 q^{46} + 60 q^{49} + 12 q^{52} - 8 q^{55} - 8 q^{58} - 12 q^{61} - 12 q^{67} + 12 q^{70} + 8 q^{73} - 52 q^{76} + 8 q^{79} + 4 q^{85} + 24 q^{88} - 84 q^{91} - 16 q^{94} - 96 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.258819 + 0.965926i −0.183013 + 0.683013i
\(3\) 0 0
\(4\) −0.866025 0.500000i −0.433013 0.250000i
\(5\) −0.707107 0.707107i −0.316228 0.316228i
\(6\) 0 0
\(7\) −1.03475 + 0.277260i −0.391098 + 0.104794i −0.449009 0.893527i \(-0.648223\pi\)
0.0579107 + 0.998322i \(0.481556\pi\)
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 0 0
\(10\) 0.866025 0.500000i 0.273861 0.158114i
\(11\) −0.105325 0.0282216i −0.0317565 0.00850914i 0.242906 0.970050i \(-0.421899\pi\)
−0.274662 + 0.961541i \(0.588566\pi\)
\(12\) 0 0
\(13\) 1.19781 + 3.40077i 0.332211 + 0.943205i
\(14\) 1.07125i 0.286304i
\(15\) 0 0
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) 1.09921 1.90389i 0.266598 0.461761i −0.701383 0.712785i \(-0.747434\pi\)
0.967981 + 0.251023i \(0.0807671\pi\)
\(18\) 0 0
\(19\) 0.578305 + 2.15826i 0.132672 + 0.495139i 0.999997 0.00260393i \(-0.000828859\pi\)
−0.867324 + 0.497743i \(0.834162\pi\)
\(20\) 0.258819 + 0.965926i 0.0578737 + 0.215988i
\(21\) 0 0
\(22\) 0.0545200 0.0944314i 0.0116237 0.0201328i
\(23\) −1.34004 2.32102i −0.279418 0.483967i 0.691822 0.722068i \(-0.256808\pi\)
−0.971240 + 0.238101i \(0.923475\pi\)
\(24\) 0 0
\(25\) 1.00000i 0.200000i
\(26\) −3.59491 + 0.276806i −0.705020 + 0.0542861i
\(27\) 0 0
\(28\) 1.03475 + 0.277260i 0.195549 + 0.0523972i
\(29\) −0.745303 + 0.430301i −0.138399 + 0.0799048i −0.567601 0.823304i \(-0.692128\pi\)
0.429202 + 0.903209i \(0.358795\pi\)
\(30\) 0 0
\(31\) −0.123514 + 0.123514i −0.0221837 + 0.0221837i −0.718112 0.695928i \(-0.754993\pi\)
0.695928 + 0.718112i \(0.254993\pi\)
\(32\) −0.965926 + 0.258819i −0.170753 + 0.0457532i
\(33\) 0 0
\(34\) 1.55452 + 1.55452i 0.266598 + 0.266598i
\(35\) 0.927730 + 0.535625i 0.156815 + 0.0905372i
\(36\) 0 0
\(37\) −2.82648 + 10.5486i −0.464671 + 1.73418i 0.193308 + 0.981138i \(0.438078\pi\)
−0.657978 + 0.753037i \(0.728588\pi\)
\(38\) −2.23440 −0.362467
\(39\) 0 0
\(40\) −1.00000 −0.158114
\(41\) −1.03528 + 3.86370i −0.161683 + 0.603409i 0.836757 + 0.547574i \(0.184449\pi\)
−0.998440 + 0.0558348i \(0.982218\pi\)
\(42\) 0 0
\(43\) 10.5279 + 6.07830i 1.60549 + 0.926933i 0.990361 + 0.138510i \(0.0442313\pi\)
0.615134 + 0.788423i \(0.289102\pi\)
\(44\) 0.0771029 + 0.0771029i 0.0116237 + 0.0116237i
\(45\) 0 0
\(46\) 2.58877 0.693658i 0.381693 0.102274i
\(47\) −8.91173 + 8.91173i −1.29991 + 1.29991i −0.371462 + 0.928448i \(0.621143\pi\)
−0.928448 + 0.371462i \(0.878857\pi\)
\(48\) 0 0
\(49\) −5.06835 + 2.92621i −0.724050 + 0.418030i
\(50\) −0.965926 0.258819i −0.136603 0.0366025i
\(51\) 0 0
\(52\) 0.663057 3.54406i 0.0919495 0.491473i
\(53\) 3.57666i 0.491292i 0.969360 + 0.245646i \(0.0790001\pi\)
−0.969360 + 0.245646i \(0.921000\pi\)
\(54\) 0 0
\(55\) 0.0545200 + 0.0944314i 0.00735147 + 0.0127331i
\(56\) −0.535625 + 0.927730i −0.0715759 + 0.123973i
\(57\) 0 0
\(58\) −0.222740 0.831277i −0.0292472 0.109152i
\(59\) −2.10359 7.85072i −0.273865 1.02208i −0.956598 0.291409i \(-0.905876\pi\)
0.682734 0.730667i \(-0.260791\pi\)
\(60\) 0 0
\(61\) −4.30104 + 7.44963i −0.550692 + 0.953827i 0.447532 + 0.894268i \(0.352303\pi\)
−0.998225 + 0.0595594i \(0.981030\pi\)
\(62\) −0.0873374 0.151273i −0.0110919 0.0192117i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) 1.55773 3.25169i 0.193213 0.403322i
\(66\) 0 0
\(67\) −3.67803 0.985526i −0.449343 0.120401i 0.0270488 0.999634i \(-0.491389\pi\)
−0.476392 + 0.879233i \(0.658056\pi\)
\(68\) −1.90389 + 1.09921i −0.230881 + 0.133299i
\(69\) 0 0
\(70\) −0.757488 + 0.757488i −0.0905372 + 0.0905372i
\(71\) −3.12935 + 0.838506i −0.371385 + 0.0995123i −0.439684 0.898153i \(-0.644910\pi\)
0.0682988 + 0.997665i \(0.478243\pi\)
\(72\) 0 0
\(73\) 9.26565 + 9.26565i 1.08446 + 1.08446i 0.996087 + 0.0883749i \(0.0281674\pi\)
0.0883749 + 0.996087i \(0.471833\pi\)
\(74\) −9.45759 5.46034i −1.09942 0.634752i
\(75\) 0 0
\(76\) 0.578305 2.15826i 0.0663361 0.247570i
\(77\) 0.116809 0.0133116
\(78\) 0 0
\(79\) 3.58347 0.403172 0.201586 0.979471i \(-0.435391\pi\)
0.201586 + 0.979471i \(0.435391\pi\)
\(80\) 0.258819 0.965926i 0.0289368 0.107994i
\(81\) 0 0
\(82\) −3.46410 2.00000i −0.382546 0.220863i
\(83\) 6.23094 + 6.23094i 0.683934 + 0.683934i 0.960884 0.276950i \(-0.0893237\pi\)
−0.276950 + 0.960884i \(0.589324\pi\)
\(84\) 0 0
\(85\) −2.12351 + 0.568994i −0.230327 + 0.0617160i
\(86\) −8.59602 + 8.59602i −0.926933 + 0.926933i
\(87\) 0 0
\(88\) −0.0944314 + 0.0545200i −0.0100664 + 0.00581185i
\(89\) −0.486484 0.130353i −0.0515672 0.0138174i 0.232943 0.972490i \(-0.425164\pi\)
−0.284510 + 0.958673i \(0.591831\pi\)
\(90\) 0 0
\(91\) −2.18233 3.18684i −0.228770 0.334072i
\(92\) 2.68009i 0.279418i
\(93\) 0 0
\(94\) −6.30155 10.9146i −0.649955 1.12576i
\(95\) 1.11720 1.93504i 0.114622 0.198531i
\(96\) 0 0
\(97\) −1.35837 5.06950i −0.137921 0.514729i −0.999969 0.00790183i \(-0.997485\pi\)
0.862047 0.506828i \(-0.169182\pi\)
\(98\) −1.51472 5.65301i −0.153010 0.571040i
\(99\) 0 0
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) 4.35338 + 7.54028i 0.433178 + 0.750285i 0.997145 0.0755116i \(-0.0240590\pi\)
−0.563967 + 0.825797i \(0.690726\pi\)
\(102\) 0 0
\(103\) 3.66430i 0.361054i 0.983570 + 0.180527i \(0.0577803\pi\)
−0.983570 + 0.180527i \(0.942220\pi\)
\(104\) 3.25169 + 1.55773i 0.318854 + 0.152748i
\(105\) 0 0
\(106\) −3.45479 0.925708i −0.335559 0.0899127i
\(107\) −1.44217 + 0.832640i −0.139420 + 0.0804944i −0.568088 0.822968i \(-0.692317\pi\)
0.428667 + 0.903462i \(0.358983\pi\)
\(108\) 0 0
\(109\) 3.39561 3.39561i 0.325241 0.325241i −0.525533 0.850773i \(-0.676134\pi\)
0.850773 + 0.525533i \(0.176134\pi\)
\(110\) −0.105325 + 0.0282216i −0.0100423 + 0.00269083i
\(111\) 0 0
\(112\) −0.757488 0.757488i −0.0715759 0.0715759i
\(113\) −8.54251 4.93202i −0.803612 0.463965i 0.0411207 0.999154i \(-0.486907\pi\)
−0.844733 + 0.535189i \(0.820241\pi\)
\(114\) 0 0
\(115\) −0.693658 + 2.58877i −0.0646839 + 0.241404i
\(116\) 0.860601 0.0799048
\(117\) 0 0
\(118\) 8.12766 0.748212
\(119\) −0.609535 + 2.27481i −0.0558760 + 0.208532i
\(120\) 0 0
\(121\) −9.51598 5.49406i −0.865089 0.499460i
\(122\) −6.08260 6.08260i −0.550692 0.550692i
\(123\) 0 0
\(124\) 0.168723 0.0452092i 0.0151518 0.00405990i
\(125\) 0.707107 0.707107i 0.0632456 0.0632456i
\(126\) 0 0
\(127\) 9.27412 5.35441i 0.822945 0.475127i −0.0284860 0.999594i \(-0.509069\pi\)
0.851431 + 0.524467i \(0.175735\pi\)
\(128\) 0.965926 + 0.258819i 0.0853766 + 0.0228766i
\(129\) 0 0
\(130\) 2.73772 + 2.34625i 0.240114 + 0.205780i
\(131\) 2.94079i 0.256938i −0.991714 0.128469i \(-0.958994\pi\)
0.991714 0.128469i \(-0.0410063\pi\)
\(132\) 0 0
\(133\) −1.19680 2.07292i −0.103776 0.179745i
\(134\) 1.90389 3.29763i 0.164471 0.284872i
\(135\) 0 0
\(136\) −0.568994 2.12351i −0.0487908 0.182090i
\(137\) 1.11178 + 4.14923i 0.0949861 + 0.354493i 0.997017 0.0771778i \(-0.0245909\pi\)
−0.902031 + 0.431671i \(0.857924\pi\)
\(138\) 0 0
\(139\) −1.45442 + 2.51913i −0.123363 + 0.213670i −0.921092 0.389346i \(-0.872701\pi\)
0.797729 + 0.603016i \(0.206034\pi\)
\(140\) −0.535625 0.927730i −0.0452686 0.0784075i
\(141\) 0 0
\(142\) 3.23974i 0.271873i
\(143\) −0.0301829 0.391989i −0.00252402 0.0327798i
\(144\) 0 0
\(145\) 0.831277 + 0.222740i 0.0690338 + 0.0184976i
\(146\) −11.3481 + 6.55180i −0.939172 + 0.542231i
\(147\) 0 0
\(148\) 7.72209 7.72209i 0.634752 0.634752i
\(149\) 14.4305 3.86664i 1.18219 0.316767i 0.386396 0.922333i \(-0.373720\pi\)
0.795795 + 0.605566i \(0.207053\pi\)
\(150\) 0 0
\(151\) −8.78063 8.78063i −0.714557 0.714557i 0.252928 0.967485i \(-0.418606\pi\)
−0.967485 + 0.252928i \(0.918606\pi\)
\(152\) 1.93504 + 1.11720i 0.156953 + 0.0906168i
\(153\) 0 0
\(154\) −0.0302324 + 0.112829i −0.00243620 + 0.00909201i
\(155\) 0.174675 0.0140302
\(156\) 0 0
\(157\) −6.19716 −0.494587 −0.247294 0.968941i \(-0.579541\pi\)
−0.247294 + 0.968941i \(0.579541\pi\)
\(158\) −0.927470 + 3.46136i −0.0737855 + 0.275371i
\(159\) 0 0
\(160\) 0.866025 + 0.500000i 0.0684653 + 0.0395285i
\(161\) 2.03013 + 2.03013i 0.159997 + 0.159997i
\(162\) 0 0
\(163\) 13.6514 3.65789i 1.06926 0.286508i 0.319073 0.947730i \(-0.396628\pi\)
0.750191 + 0.661222i \(0.229962\pi\)
\(164\) 2.82843 2.82843i 0.220863 0.220863i
\(165\) 0 0
\(166\) −7.63131 + 4.40594i −0.592304 + 0.341967i
\(167\) 1.84771 + 0.495092i 0.142980 + 0.0383113i 0.329599 0.944121i \(-0.393086\pi\)
−0.186619 + 0.982432i \(0.559753\pi\)
\(168\) 0 0
\(169\) −10.1305 + 8.14693i −0.779271 + 0.626687i
\(170\) 2.19842i 0.168611i
\(171\) 0 0
\(172\) −6.07830 10.5279i −0.463466 0.802747i
\(173\) 5.66735 9.81614i 0.430881 0.746307i −0.566069 0.824358i \(-0.691536\pi\)
0.996949 + 0.0780510i \(0.0248697\pi\)
\(174\) 0 0
\(175\) −0.277260 1.03475i −0.0209589 0.0782196i
\(176\) −0.0282216 0.105325i −0.00212728 0.00793913i
\(177\) 0 0
\(178\) 0.251822 0.436169i 0.0188749 0.0326923i
\(179\) −4.03616 6.99083i −0.301677 0.522519i 0.674839 0.737965i \(-0.264213\pi\)
−0.976516 + 0.215446i \(0.930880\pi\)
\(180\) 0 0
\(181\) 5.34777i 0.397497i −0.980051 0.198748i \(-0.936312\pi\)
0.980051 0.198748i \(-0.0636877\pi\)
\(182\) 3.64308 1.28315i 0.270043 0.0951134i
\(183\) 0 0
\(184\) −2.58877 0.693658i −0.190846 0.0511371i
\(185\) 9.45759 5.46034i 0.695336 0.401452i
\(186\) 0 0
\(187\) −0.169505 + 0.169505i −0.0123954 + 0.0123954i
\(188\) 12.1737 3.26192i 0.887855 0.237900i
\(189\) 0 0
\(190\) 1.57996 + 1.57996i 0.114622 + 0.114622i
\(191\) −0.740223 0.427368i −0.0535606 0.0309232i 0.472981 0.881073i \(-0.343178\pi\)
−0.526541 + 0.850150i \(0.676511\pi\)
\(192\) 0 0
\(193\) −4.33330 + 16.1721i −0.311918 + 1.16409i 0.614908 + 0.788599i \(0.289193\pi\)
−0.926825 + 0.375493i \(0.877473\pi\)
\(194\) 5.24833 0.376808
\(195\) 0 0
\(196\) 5.85242 0.418030
\(197\) −5.60341 + 20.9122i −0.399227 + 1.48993i 0.415233 + 0.909715i \(0.363700\pi\)
−0.814460 + 0.580219i \(0.802967\pi\)
\(198\) 0 0
\(199\) −6.12037 3.53360i −0.433862 0.250490i 0.267129 0.963661i \(-0.413925\pi\)
−0.700990 + 0.713171i \(0.747258\pi\)
\(200\) 0.707107 + 0.707107i 0.0500000 + 0.0500000i
\(201\) 0 0
\(202\) −8.41008 + 2.25348i −0.591731 + 0.158554i
\(203\) 0.651895 0.651895i 0.0457541 0.0457541i
\(204\) 0 0
\(205\) 3.46410 2.00000i 0.241943 0.139686i
\(206\) −3.53944 0.948390i −0.246604 0.0660774i
\(207\) 0 0
\(208\) −2.34625 + 2.73772i −0.162683 + 0.189827i
\(209\) 0.243639i 0.0168528i
\(210\) 0 0
\(211\) −11.3840 19.7177i −0.783707 1.35742i −0.929769 0.368145i \(-0.879993\pi\)
0.146062 0.989275i \(-0.453340\pi\)
\(212\) 1.78833 3.09748i 0.122823 0.212736i
\(213\) 0 0
\(214\) −0.431006 1.60854i −0.0294630 0.109957i
\(215\) −3.14636 11.7424i −0.214580 0.800824i
\(216\) 0 0
\(217\) 0.0935603 0.162051i 0.00635128 0.0110007i
\(218\) 2.40106 + 4.15876i 0.162620 + 0.281667i
\(219\) 0 0
\(220\) 0.109040i 0.00735147i
\(221\) 7.79134 + 1.45768i 0.524102 + 0.0980542i
\(222\) 0 0
\(223\) 14.5443 + 3.89713i 0.973957 + 0.260971i 0.710498 0.703699i \(-0.248470\pi\)
0.263459 + 0.964670i \(0.415136\pi\)
\(224\) 0.927730 0.535625i 0.0619866 0.0357880i
\(225\) 0 0
\(226\) 6.97493 6.97493i 0.463965 0.463965i
\(227\) 4.96291 1.32981i 0.329400 0.0882625i −0.0903288 0.995912i \(-0.528792\pi\)
0.419729 + 0.907649i \(0.362125\pi\)
\(228\) 0 0
\(229\) −9.10674 9.10674i −0.601790 0.601790i 0.338997 0.940787i \(-0.389912\pi\)
−0.940787 + 0.338997i \(0.889912\pi\)
\(230\) −2.32102 1.34004i −0.153044 0.0883599i
\(231\) 0 0
\(232\) −0.222740 + 0.831277i −0.0146236 + 0.0545760i
\(233\) 24.0147 1.57325 0.786626 0.617430i \(-0.211826\pi\)
0.786626 + 0.617430i \(0.211826\pi\)
\(234\) 0 0
\(235\) 12.6031 0.822135
\(236\) −2.10359 + 7.85072i −0.136932 + 0.511038i
\(237\) 0 0
\(238\) −2.03954 1.17753i −0.132204 0.0763280i
\(239\) 9.02287 + 9.02287i 0.583641 + 0.583641i 0.935902 0.352261i \(-0.114587\pi\)
−0.352261 + 0.935902i \(0.614587\pi\)
\(240\) 0 0
\(241\) −5.76565 + 1.54490i −0.371398 + 0.0995158i −0.439690 0.898150i \(-0.644912\pi\)
0.0682920 + 0.997665i \(0.478245\pi\)
\(242\) 7.76977 7.76977i 0.499460 0.499460i
\(243\) 0 0
\(244\) 7.44963 4.30104i 0.476914 0.275346i
\(245\) 5.65301 + 1.51472i 0.361157 + 0.0967718i
\(246\) 0 0
\(247\) −6.64706 + 4.55186i −0.422943 + 0.289628i
\(248\) 0.174675i 0.0110919i
\(249\) 0 0
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) 8.89831 15.4123i 0.561656 0.972817i −0.435696 0.900094i \(-0.643498\pi\)
0.997352 0.0727231i \(-0.0231689\pi\)
\(252\) 0 0
\(253\) 0.0756364 + 0.282279i 0.00475522 + 0.0177467i
\(254\) 2.77165 + 10.3439i 0.173909 + 0.649036i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 5.30881 + 9.19513i 0.331155 + 0.573576i 0.982739 0.185000i \(-0.0592285\pi\)
−0.651584 + 0.758577i \(0.725895\pi\)
\(258\) 0 0
\(259\) 11.6988i 0.726928i
\(260\) −2.97488 + 2.03718i −0.184494 + 0.126340i
\(261\) 0 0
\(262\) 2.84059 + 0.761133i 0.175492 + 0.0470230i
\(263\) 7.65056 4.41706i 0.471754 0.272367i −0.245220 0.969468i \(-0.578860\pi\)
0.716974 + 0.697100i \(0.245527\pi\)
\(264\) 0 0
\(265\) 2.52908 2.52908i 0.155360 0.155360i
\(266\) 2.31204 0.619509i 0.141760 0.0379845i
\(267\) 0 0
\(268\) 2.69251 + 2.69251i 0.164471 + 0.164471i
\(269\) −5.68391 3.28161i −0.346554 0.200083i 0.316612 0.948555i \(-0.397455\pi\)
−0.663167 + 0.748472i \(0.730788\pi\)
\(270\) 0 0
\(271\) −2.18661 + 8.16053i −0.132827 + 0.495717i −0.999997 0.00229451i \(-0.999270\pi\)
0.867170 + 0.498012i \(0.165936\pi\)
\(272\) 2.19842 0.133299
\(273\) 0 0
\(274\) −4.29560 −0.259507
\(275\) 0.0282216 0.105325i 0.00170183 0.00635131i
\(276\) 0 0
\(277\) 14.3496 + 8.28477i 0.862187 + 0.497784i 0.864744 0.502213i \(-0.167481\pi\)
−0.00255715 + 0.999997i \(0.500814\pi\)
\(278\) −2.05686 2.05686i −0.123363 0.123363i
\(279\) 0 0
\(280\) 1.03475 0.277260i 0.0618380 0.0165695i
\(281\) −13.5794 + 13.5794i −0.810079 + 0.810079i −0.984645 0.174566i \(-0.944148\pi\)
0.174566 + 0.984645i \(0.444148\pi\)
\(282\) 0 0
\(283\) 9.69503 5.59743i 0.576310 0.332733i −0.183356 0.983047i \(-0.558696\pi\)
0.759666 + 0.650314i \(0.225363\pi\)
\(284\) 3.12935 + 0.838506i 0.185693 + 0.0497562i
\(285\) 0 0
\(286\) 0.386444 + 0.0722997i 0.0228509 + 0.00427517i
\(287\) 4.28500i 0.252936i
\(288\) 0 0
\(289\) 6.08347 + 10.5369i 0.357851 + 0.619816i
\(290\) −0.430301 + 0.745303i −0.0252681 + 0.0437657i
\(291\) 0 0
\(292\) −3.39146 12.6571i −0.198470 0.740701i
\(293\) −3.44063 12.8406i −0.201004 0.750157i −0.990631 0.136569i \(-0.956392\pi\)
0.789626 0.613588i \(-0.210274\pi\)
\(294\) 0 0
\(295\) −4.06383 + 7.03876i −0.236605 + 0.409813i
\(296\) 5.46034 + 9.45759i 0.317376 + 0.549711i
\(297\) 0 0
\(298\) 14.9395i 0.865424i
\(299\) 6.28816 7.33732i 0.363654 0.424328i
\(300\) 0 0
\(301\) −12.5790 3.37054i −0.725043 0.194275i
\(302\) 10.7540 6.20884i 0.618825 0.357279i
\(303\) 0 0
\(304\) −1.57996 + 1.57996i −0.0906168 + 0.0906168i
\(305\) 8.30898 2.22638i 0.475771 0.127482i
\(306\) 0 0
\(307\) 10.6353 + 10.6353i 0.606991 + 0.606991i 0.942159 0.335167i \(-0.108793\pi\)
−0.335167 + 0.942159i \(0.608793\pi\)
\(308\) −0.101160 0.0584045i −0.00576411 0.00332791i
\(309\) 0 0
\(310\) −0.0452092 + 0.168723i −0.00256771 + 0.00958282i
\(311\) 14.2635 0.808809 0.404404 0.914580i \(-0.367479\pi\)
0.404404 + 0.914580i \(0.367479\pi\)
\(312\) 0 0
\(313\) 15.1236 0.854838 0.427419 0.904054i \(-0.359423\pi\)
0.427419 + 0.904054i \(0.359423\pi\)
\(314\) 1.60394 5.98600i 0.0905157 0.337809i
\(315\) 0 0
\(316\) −3.10337 1.79173i −0.174578 0.100793i
\(317\) 5.54215 + 5.54215i 0.311278 + 0.311278i 0.845405 0.534126i \(-0.179359\pi\)
−0.534126 + 0.845405i \(0.679359\pi\)
\(318\) 0 0
\(319\) 0.0906424 0.0242876i 0.00507500 0.00135984i
\(320\) −0.707107 + 0.707107i −0.0395285 + 0.0395285i
\(321\) 0 0
\(322\) −2.48640 + 1.43552i −0.138562 + 0.0799985i
\(323\) 4.74477 + 1.27136i 0.264006 + 0.0707403i
\(324\) 0 0
\(325\) −3.40077 + 1.19781i −0.188641 + 0.0664423i
\(326\) 14.1330i 0.782755i
\(327\) 0 0
\(328\) 2.00000 + 3.46410i 0.110432 + 0.191273i
\(329\) 6.75053 11.6923i 0.372169 0.644616i
\(330\) 0 0
\(331\) −8.27247 30.8733i −0.454696 1.69695i −0.688981 0.724780i \(-0.741941\pi\)
0.234285 0.972168i \(-0.424725\pi\)
\(332\) −2.28068 8.51162i −0.125169 0.467136i
\(333\) 0 0
\(334\) −0.956444 + 1.65661i −0.0523343 + 0.0906456i
\(335\) 1.90389 + 3.29763i 0.104021 + 0.180169i
\(336\) 0 0
\(337\) 10.3442i 0.563483i −0.959490 0.281742i \(-0.909088\pi\)
0.959490 0.281742i \(-0.0909121\pi\)
\(338\) −5.24736 11.8939i −0.285419 0.646944i
\(339\) 0 0
\(340\) 2.12351 + 0.568994i 0.115164 + 0.0308580i
\(341\) 0.0164948 0.00952327i 0.000893243 0.000515714i
\(342\) 0 0
\(343\) 9.73556 9.73556i 0.525671 0.525671i
\(344\) 11.7424 3.14636i 0.633107 0.169640i
\(345\) 0 0
\(346\) 8.01484 + 8.01484i 0.430881 + 0.430881i
\(347\) −27.4249 15.8338i −1.47224 0.850000i −0.472731 0.881207i \(-0.656732\pi\)
−0.999513 + 0.0312067i \(0.990065\pi\)
\(348\) 0 0
\(349\) −4.22925 + 15.7838i −0.226386 + 0.844886i 0.755458 + 0.655197i \(0.227414\pi\)
−0.981844 + 0.189689i \(0.939252\pi\)
\(350\) 1.07125 0.0572607
\(351\) 0 0
\(352\) 0.109040 0.00581185
\(353\) 0.337999 1.26143i 0.0179899 0.0671392i −0.956347 0.292232i \(-0.905602\pi\)
0.974337 + 0.225093i \(0.0722686\pi\)
\(354\) 0 0
\(355\) 2.80570 + 1.61987i 0.148911 + 0.0859737i
\(356\) 0.356131 + 0.356131i 0.0188749 + 0.0188749i
\(357\) 0 0
\(358\) 7.79726 2.08927i 0.412098 0.110421i
\(359\) −23.5889 + 23.5889i −1.24498 + 1.24498i −0.287064 + 0.957911i \(0.592679\pi\)
−0.957911 + 0.287064i \(0.907321\pi\)
\(360\) 0 0
\(361\) 12.1308 7.00373i 0.638464 0.368618i
\(362\) 5.16555 + 1.38411i 0.271495 + 0.0727470i
\(363\) 0 0
\(364\) 0.296529 + 3.85105i 0.0155423 + 0.201850i
\(365\) 13.1036i 0.685874i
\(366\) 0 0
\(367\) −12.3778 21.4390i −0.646118 1.11911i −0.984042 0.177935i \(-0.943058\pi\)
0.337925 0.941173i \(-0.390275\pi\)
\(368\) 1.34004 2.32102i 0.0698546 0.120992i
\(369\) 0 0
\(370\) 2.82648 + 10.5486i 0.146942 + 0.548394i
\(371\) −0.991665 3.70095i −0.0514847 0.192144i
\(372\) 0 0
\(373\) −11.4375 + 19.8104i −0.592212 + 1.02574i 0.401722 + 0.915762i \(0.368412\pi\)
−0.993934 + 0.109980i \(0.964921\pi\)
\(374\) −0.119858 0.207600i −0.00619771 0.0107347i
\(375\) 0 0
\(376\) 12.6031i 0.649955i
\(377\) −2.35608 2.01919i −0.121344 0.103994i
\(378\) 0 0
\(379\) −7.83077 2.09825i −0.402240 0.107780i 0.0520266 0.998646i \(-0.483432\pi\)
−0.454266 + 0.890866i \(0.650099\pi\)
\(380\) −1.93504 + 1.11720i −0.0992657 + 0.0573111i
\(381\) 0 0
\(382\) 0.604389 0.604389i 0.0309232 0.0309232i
\(383\) 9.70618 2.60076i 0.495963 0.132893i −0.00216304 0.999998i \(-0.500689\pi\)
0.498126 + 0.867105i \(0.334022\pi\)
\(384\) 0 0
\(385\) −0.0825965 0.0825965i −0.00420951 0.00420951i
\(386\) −14.4995 8.37129i −0.738005 0.426087i
\(387\) 0 0
\(388\) −1.35837 + 5.06950i −0.0689607 + 0.257365i
\(389\) 0.817452 0.0414465 0.0207232 0.999785i \(-0.493403\pi\)
0.0207232 + 0.999785i \(0.493403\pi\)
\(390\) 0 0
\(391\) −5.89197 −0.297970
\(392\) −1.51472 + 5.65301i −0.0765048 + 0.285520i
\(393\) 0 0
\(394\) −18.7494 10.8250i −0.944581 0.545354i
\(395\) −2.53389 2.53389i −0.127494 0.127494i
\(396\) 0 0
\(397\) −10.8506 + 2.90742i −0.544577 + 0.145919i −0.520611 0.853794i \(-0.674296\pi\)
−0.0239659 + 0.999713i \(0.507629\pi\)
\(398\) 4.99726 4.99726i 0.250490 0.250490i
\(399\) 0 0
\(400\) −0.866025 + 0.500000i −0.0433013 + 0.0250000i
\(401\) 2.69200 + 0.721320i 0.134432 + 0.0360210i 0.325408 0.945574i \(-0.394498\pi\)
−0.190975 + 0.981595i \(0.561165\pi\)
\(402\) 0 0
\(403\) −0.567988 0.272097i −0.0282935 0.0135541i
\(404\) 8.70676i 0.433178i
\(405\) 0 0
\(406\) 0.460960 + 0.798406i 0.0228770 + 0.0396242i
\(407\) 0.595396 1.03126i 0.0295127 0.0511174i
\(408\) 0 0
\(409\) −4.03354 15.0534i −0.199446 0.744341i −0.991071 0.133335i \(-0.957432\pi\)
0.791625 0.611007i \(-0.209235\pi\)
\(410\) 1.03528 + 3.86370i 0.0511286 + 0.190815i
\(411\) 0 0
\(412\) 1.83215 3.17337i 0.0902635 0.156341i
\(413\) 4.35338 + 7.54028i 0.214216 + 0.371033i
\(414\) 0 0
\(415\) 8.81187i 0.432558i
\(416\) −2.03718 2.97488i −0.0998808 0.145856i
\(417\) 0 0
\(418\) 0.235337 + 0.0630583i 0.0115107 + 0.00308428i
\(419\) −16.5157 + 9.53535i −0.806845 + 0.465832i −0.845859 0.533406i \(-0.820912\pi\)
0.0390138 + 0.999239i \(0.487578\pi\)
\(420\) 0 0
\(421\) −1.84339 + 1.84339i −0.0898414 + 0.0898414i −0.750599 0.660758i \(-0.770235\pi\)
0.660758 + 0.750599i \(0.270235\pi\)
\(422\) 21.9922 5.89279i 1.07056 0.286857i
\(423\) 0 0
\(424\) 2.52908 + 2.52908i 0.122823 + 0.122823i
\(425\) 1.90389 + 1.09921i 0.0923522 + 0.0533196i
\(426\) 0 0
\(427\) 2.38502 8.90100i 0.115419 0.430749i
\(428\) 1.66528 0.0804944
\(429\) 0 0
\(430\) 12.1566 0.586244
\(431\) −5.92299 + 22.1049i −0.285300 + 1.06476i 0.663319 + 0.748337i \(0.269147\pi\)
−0.948620 + 0.316419i \(0.897519\pi\)
\(432\) 0 0
\(433\) 18.0124 + 10.3995i 0.865623 + 0.499768i 0.865891 0.500232i \(-0.166752\pi\)
−0.000268392 1.00000i \(0.500085\pi\)
\(434\) 0.132314 + 0.132314i 0.00635128 + 0.00635128i
\(435\) 0 0
\(436\) −4.63849 + 1.24288i −0.222143 + 0.0595231i
\(437\) 4.23442 4.23442i 0.202560 0.202560i
\(438\) 0 0
\(439\) 26.8169 15.4827i 1.27990 0.738950i 0.303069 0.952968i \(-0.401989\pi\)
0.976830 + 0.214018i \(0.0686553\pi\)
\(440\) 0.105325 + 0.0282216i 0.00502115 + 0.00134541i
\(441\) 0 0
\(442\) −3.42456 + 7.14858i −0.162890 + 0.340023i
\(443\) 24.8913i 1.18262i −0.806444 0.591310i \(-0.798611\pi\)
0.806444 0.591310i \(-0.201389\pi\)
\(444\) 0 0
\(445\) 0.251822 + 0.436169i 0.0119375 + 0.0206764i
\(446\) −7.52867 + 13.0400i −0.356493 + 0.617464i
\(447\) 0 0
\(448\) 0.277260 + 1.03475i 0.0130993 + 0.0488873i
\(449\) 10.3261 + 38.5375i 0.487318 + 1.81870i 0.569386 + 0.822070i \(0.307181\pi\)
−0.0820676 + 0.996627i \(0.526152\pi\)
\(450\) 0 0
\(451\) 0.218080 0.377726i 0.0102690 0.0177864i
\(452\) 4.93202 + 8.54251i 0.231983 + 0.401806i
\(453\) 0 0
\(454\) 5.13799i 0.241138i
\(455\) −0.710300 + 3.79657i −0.0332994 + 0.177986i
\(456\) 0 0
\(457\) 17.8773 + 4.79022i 0.836266 + 0.224077i 0.651445 0.758695i \(-0.274163\pi\)
0.184821 + 0.982772i \(0.440830\pi\)
\(458\) 11.1534 6.43944i 0.521166 0.300895i
\(459\) 0 0
\(460\) 1.89511 1.89511i 0.0883599 0.0883599i
\(461\) 12.6049 3.37748i 0.587070 0.157305i 0.0469562 0.998897i \(-0.485048\pi\)
0.540114 + 0.841592i \(0.318381\pi\)
\(462\) 0 0
\(463\) −17.8003 17.8003i −0.827248 0.827248i 0.159887 0.987135i \(-0.448887\pi\)
−0.987135 + 0.159887i \(0.948887\pi\)
\(464\) −0.745303 0.430301i −0.0345998 0.0199762i
\(465\) 0 0
\(466\) −6.21545 + 23.1964i −0.287925 + 1.07455i
\(467\) −42.5798 −1.97036 −0.985180 0.171526i \(-0.945130\pi\)
−0.985180 + 0.171526i \(0.945130\pi\)
\(468\) 0 0
\(469\) 4.07909 0.188355
\(470\) −3.26192 + 12.1737i −0.150461 + 0.561529i
\(471\) 0 0
\(472\) −7.03876 4.06383i −0.323985 0.187053i
\(473\) −0.937310 0.937310i −0.0430976 0.0430976i
\(474\) 0 0
\(475\) −2.15826 + 0.578305i −0.0990279 + 0.0265344i
\(476\) 1.66528 1.66528i 0.0763280 0.0763280i
\(477\) 0 0
\(478\) −11.0507 + 6.38013i −0.505448 + 0.291820i
\(479\) −28.3109 7.58589i −1.29356 0.346608i −0.454548 0.890722i \(-0.650199\pi\)
−0.839011 + 0.544114i \(0.816866\pi\)
\(480\) 0 0
\(481\) −39.2589 + 3.02291i −1.79005 + 0.137833i
\(482\) 5.96904i 0.271882i
\(483\) 0 0
\(484\) 5.49406 + 9.51598i 0.249730 + 0.432545i
\(485\) −2.62416 + 4.54519i −0.119157 + 0.206386i
\(486\) 0 0
\(487\) −1.16056 4.33128i −0.0525901 0.196269i 0.934633 0.355614i \(-0.115728\pi\)
−0.987223 + 0.159345i \(0.949062\pi\)
\(488\) 2.22638 + 8.30898i 0.100784 + 0.376130i
\(489\) 0 0
\(490\) −2.92621 + 5.06835i −0.132193 + 0.228965i
\(491\) 0.676664 + 1.17202i 0.0305374 + 0.0528923i 0.880890 0.473321i \(-0.156945\pi\)
−0.850353 + 0.526213i \(0.823611\pi\)
\(492\) 0 0
\(493\) 1.89197i 0.0852099i
\(494\) −2.67637 7.59868i −0.120416 0.341881i
\(495\) 0 0
\(496\) −0.168723 0.0452092i −0.00757588 0.00202995i
\(497\) 3.00560 1.73529i 0.134820 0.0778382i
\(498\) 0 0
\(499\) 13.0655 13.0655i 0.584890 0.584890i −0.351353 0.936243i \(-0.614278\pi\)
0.936243 + 0.351353i \(0.114278\pi\)
\(500\) −0.965926 + 0.258819i −0.0431975 + 0.0115747i
\(501\) 0 0
\(502\) 12.5841 + 12.5841i 0.561656 + 0.561656i
\(503\) −21.6756 12.5144i −0.966466 0.557989i −0.0683089 0.997664i \(-0.521760\pi\)
−0.898157 + 0.439675i \(0.855094\pi\)
\(504\) 0 0
\(505\) 2.25348 8.41008i 0.100278 0.374244i
\(506\) −0.292237 −0.0129915
\(507\) 0 0
\(508\) −10.7088 −0.475127
\(509\) −9.53269 + 35.5765i −0.422529 + 1.57690i 0.346731 + 0.937965i \(0.387292\pi\)
−0.769260 + 0.638936i \(0.779375\pi\)
\(510\) 0 0
\(511\) −12.1566 7.01862i −0.537777 0.310486i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 0 0
\(514\) −10.2558 + 2.74804i −0.452366 + 0.121211i
\(515\) 2.59105 2.59105i 0.114175 0.114175i
\(516\) 0 0
\(517\) 1.19013 0.687121i 0.0523418 0.0302195i
\(518\) 11.3002 + 3.02787i 0.496501 + 0.133037i
\(519\) 0 0
\(520\) −1.19781 3.40077i −0.0525272 0.149134i
\(521\) 20.3941i 0.893480i −0.894664 0.446740i \(-0.852585\pi\)
0.894664 0.446740i \(-0.147415\pi\)
\(522\) 0 0
\(523\) 2.63613 + 4.56591i 0.115270 + 0.199653i 0.917888 0.396840i \(-0.129893\pi\)
−0.802618 + 0.596494i \(0.796560\pi\)
\(524\) −1.47040 + 2.54680i −0.0642346 + 0.111258i
\(525\) 0 0
\(526\) 2.28644 + 8.53310i 0.0996933 + 0.372061i
\(527\) 0.0993889 + 0.370924i 0.00432945 + 0.0161577i
\(528\) 0 0
\(529\) 7.90857 13.6980i 0.343851 0.595567i
\(530\) 1.78833 + 3.09748i 0.0776801 + 0.134546i
\(531\) 0 0
\(532\) 2.39360i 0.103776i
\(533\) −14.3796 + 1.10722i −0.622851 + 0.0479592i
\(534\) 0 0
\(535\) 1.60854 + 0.431006i 0.0695431 + 0.0186340i
\(536\) −3.29763 + 1.90389i −0.142436 + 0.0822355i
\(537\) 0 0
\(538\) 4.64090 4.64090i 0.200083 0.200083i
\(539\) 0.616404 0.165165i 0.0265504 0.00711415i
\(540\) 0 0
\(541\) −17.3568 17.3568i −0.746227 0.746227i 0.227541 0.973768i \(-0.426931\pi\)
−0.973768 + 0.227541i \(0.926931\pi\)
\(542\) −7.31653 4.22420i −0.314272 0.181445i
\(543\) 0 0
\(544\) −0.568994 + 2.12351i −0.0243954 + 0.0910449i
\(545\) −4.80212 −0.205700
\(546\) 0 0
\(547\) 23.4243 1.00155 0.500775 0.865578i \(-0.333049\pi\)
0.500775 + 0.865578i \(0.333049\pi\)
\(548\) 1.11178 4.14923i 0.0474930 0.177246i
\(549\) 0 0
\(550\) 0.0944314 + 0.0545200i 0.00402657 + 0.00232474i
\(551\) −1.35971 1.35971i −0.0579257 0.0579257i
\(552\) 0 0
\(553\) −3.70799 + 0.993552i −0.157680 + 0.0422501i
\(554\) −11.7164 + 11.7164i −0.497784 + 0.497784i
\(555\) 0 0
\(556\) 2.51913 1.45442i 0.106835 0.0616813i
\(557\) −21.2427 5.69197i −0.900083 0.241177i −0.221031 0.975267i \(-0.570942\pi\)
−0.679052 + 0.734090i \(0.737609\pi\)
\(558\) 0 0
\(559\) −8.06052 + 43.0837i −0.340924 + 1.82225i
\(560\) 1.07125i 0.0452686i
\(561\) 0 0
\(562\) −9.60209 16.6313i −0.405040 0.701549i
\(563\) 18.3176 31.7270i 0.771994 1.33713i −0.164474 0.986381i \(-0.552593\pi\)
0.936468 0.350752i \(-0.114074\pi\)
\(564\) 0 0
\(565\) 2.55300 + 9.52793i 0.107406 + 0.400843i
\(566\) 2.89744 + 10.8134i 0.121789 + 0.454521i
\(567\) 0 0
\(568\) −1.61987 + 2.80570i −0.0679682 + 0.117724i
\(569\) −8.76469 15.1809i −0.367435 0.636416i 0.621729 0.783232i \(-0.286431\pi\)
−0.989164 + 0.146817i \(0.953097\pi\)
\(570\) 0 0
\(571\) 16.1460i 0.675689i −0.941202 0.337844i \(-0.890302\pi\)
0.941202 0.337844i \(-0.109698\pi\)
\(572\) −0.169855 + 0.354564i −0.00710200 + 0.0148251i
\(573\) 0 0
\(574\) 4.13899 + 1.10904i 0.172758 + 0.0462904i
\(575\) 2.32102 1.34004i 0.0967934 0.0558837i
\(576\) 0 0
\(577\) −25.0194 + 25.0194i −1.04157 + 1.04157i −0.0424718 + 0.999098i \(0.513523\pi\)
−0.999098 + 0.0424718i \(0.986477\pi\)
\(578\) −11.7524 + 3.14903i −0.488834 + 0.130983i
\(579\) 0 0
\(580\) −0.608537 0.608537i −0.0252681 0.0252681i
\(581\) −8.17504 4.71986i −0.339158 0.195813i
\(582\) 0 0
\(583\) 0.100939 0.376710i 0.00418047 0.0156017i
\(584\) 13.1036 0.542231
\(585\) 0 0
\(586\) 13.2936 0.549153
\(587\) −11.5222 + 43.0015i −0.475573 + 1.77486i 0.143632 + 0.989631i \(0.454122\pi\)
−0.619205 + 0.785230i \(0.712545\pi\)
\(588\) 0 0
\(589\) −0.338004 0.195147i −0.0139272 0.00804087i
\(590\) −5.74712 5.74712i −0.236605 0.236605i
\(591\) 0 0
\(592\) −10.5486 + 2.82648i −0.433544 + 0.116168i
\(593\) −31.2099 + 31.2099i −1.28164 + 1.28164i −0.341899 + 0.939737i \(0.611070\pi\)
−0.939737 + 0.341899i \(0.888930\pi\)
\(594\) 0 0
\(595\) 2.03954 1.17753i 0.0836131 0.0482741i
\(596\) −14.4305 3.86664i −0.591096 0.158384i
\(597\) 0 0
\(598\) 5.45981 + 7.97294i 0.223268 + 0.326038i
\(599\) 6.90043i 0.281944i 0.990014 + 0.140972i \(0.0450227\pi\)
−0.990014 + 0.140972i \(0.954977\pi\)
\(600\) 0 0
\(601\) 6.69946 + 11.6038i 0.273277 + 0.473329i 0.969699 0.244303i \(-0.0785592\pi\)
−0.696422 + 0.717632i \(0.745226\pi\)
\(602\) 6.51139 11.2781i 0.265384 0.459659i
\(603\) 0 0
\(604\) 3.21393 + 11.9946i 0.130773 + 0.488052i
\(605\) 2.84393 + 10.6137i 0.115622 + 0.431508i
\(606\) 0 0
\(607\) −5.48852 + 9.50640i −0.222772 + 0.385853i −0.955649 0.294509i \(-0.904844\pi\)
0.732876 + 0.680362i \(0.238177\pi\)
\(608\) −1.11720 1.93504i −0.0453084 0.0784764i
\(609\) 0 0
\(610\) 8.60209i 0.348288i
\(611\) −40.9813 19.6323i −1.65793 0.794237i
\(612\) 0 0
\(613\) 23.5858 + 6.31980i 0.952622 + 0.255254i 0.701475 0.712694i \(-0.252525\pi\)
0.251148 + 0.967949i \(0.419192\pi\)
\(614\) −13.0256 + 7.52033i −0.525670 + 0.303496i
\(615\) 0 0
\(616\) 0.0825965 0.0825965i 0.00332791 0.00332791i
\(617\) −36.8960 + 9.88625i −1.48538 + 0.398006i −0.908173 0.418595i \(-0.862523\pi\)
−0.577204 + 0.816600i \(0.695856\pi\)
\(618\) 0 0
\(619\) 19.6963 + 19.6963i 0.791661 + 0.791661i 0.981764 0.190103i \(-0.0608823\pi\)
−0.190103 + 0.981764i \(0.560882\pi\)
\(620\) −0.151273 0.0873374i −0.00607526 0.00350756i
\(621\) 0 0
\(622\) −3.69167 + 13.7775i −0.148022 + 0.552427i
\(623\) 0.539530 0.0216158
\(624\) 0 0
\(625\) −1.00000 −0.0400000
\(626\) −3.91428 + 14.6083i −0.156446 + 0.583865i
\(627\) 0 0
\(628\) 5.36690 + 3.09858i 0.214162 + 0.123647i
\(629\) 16.9764 + 16.9764i 0.676895 + 0.676895i
\(630\) 0 0
\(631\) 37.5943 10.0734i 1.49661 0.401015i 0.584645 0.811289i \(-0.301234\pi\)
0.911962 + 0.410274i \(0.134567\pi\)
\(632\) 2.53389 2.53389i 0.100793 0.100793i
\(633\) 0 0
\(634\) −6.78772 + 3.91889i −0.269575 + 0.155639i
\(635\) −10.3439 2.77165i −0.410487 0.109990i
\(636\) 0 0
\(637\) −16.0223 13.7313i −0.634826 0.544053i
\(638\) 0.0938399i 0.00371516i
\(639\) 0 0
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) 16.5081 28.5928i 0.652030 1.12935i −0.330600 0.943771i \(-0.607251\pi\)
0.982630 0.185578i \(-0.0594156\pi\)
\(642\) 0 0
\(643\) −12.6305 47.1375i −0.498097 1.85892i −0.511944 0.859019i \(-0.671074\pi\)
0.0138471 0.999904i \(-0.495592\pi\)
\(644\) −0.743081 2.77322i −0.0292815 0.109280i
\(645\) 0 0
\(646\) −2.45608 + 4.25405i −0.0966330 + 0.167373i
\(647\) 12.2654 + 21.2444i 0.482204 + 0.835202i 0.999791 0.0204285i \(-0.00650305\pi\)
−0.517587 + 0.855630i \(0.673170\pi\)
\(648\) 0 0
\(649\) 0.886240i 0.0347880i
\(650\) −0.276806 3.59491i −0.0108572 0.141004i
\(651\) 0 0
\(652\) −13.6514 3.65789i −0.534632 0.143254i
\(653\) −18.8702 + 10.8947i −0.738446 + 0.426342i −0.821504 0.570203i \(-0.806865\pi\)
0.0830579 + 0.996545i \(0.473531\pi\)
\(654\) 0 0
\(655\) −2.07945 + 2.07945i −0.0812510 + 0.0812510i
\(656\) −3.86370 + 1.03528i −0.150852 + 0.0404207i
\(657\) 0 0
\(658\) 9.54670 + 9.54670i 0.372169 + 0.372169i
\(659\) −41.2109 23.7931i −1.60535 0.926848i −0.990392 0.138285i \(-0.955841\pi\)
−0.614955 0.788562i \(-0.710826\pi\)
\(660\) 0 0
\(661\) −0.133840 + 0.499497i −0.00520577 + 0.0194282i −0.968480 0.249092i \(-0.919868\pi\)
0.963274 + 0.268520i \(0.0865346\pi\)
\(662\) 31.9624 1.24225
\(663\) 0 0
\(664\) 8.81187 0.341967
\(665\) −0.619509 + 2.31204i −0.0240235 + 0.0896570i
\(666\) 0 0
\(667\) 1.99748 + 1.15324i 0.0773426 + 0.0446538i
\(668\) −1.35262 1.35262i −0.0523343 0.0523343i
\(669\) 0 0
\(670\) −3.67803 + 0.985526i −0.142095 + 0.0380742i
\(671\) 0.663246 0.663246i 0.0256043 0.0256043i
\(672\) 0 0
\(673\) −17.7680 + 10.2584i −0.684906 + 0.395431i −0.801701 0.597725i \(-0.796071\pi\)
0.116795 + 0.993156i \(0.462738\pi\)
\(674\) 9.99171 + 2.67727i 0.384866 + 0.103125i
\(675\) 0 0
\(676\) 12.8468 1.99019i 0.494106 0.0765456i
\(677\) 32.3765i 1.24433i 0.782886 + 0.622165i \(0.213747\pi\)
−0.782886 + 0.622165i \(0.786253\pi\)
\(678\) 0 0
\(679\) 2.81114 + 4.86903i 0.107882 + 0.186856i
\(680\) −1.09921 + 1.90389i −0.0421528 + 0.0730109i
\(681\) 0 0
\(682\) 0.00492961 + 0.0183975i 0.000188764 + 0.000704478i
\(683\) −6.54431 24.4237i −0.250411 0.934547i −0.970586 0.240754i \(-0.922605\pi\)
0.720175 0.693793i \(-0.244062\pi\)
\(684\) 0 0
\(685\) 2.14780 3.72010i 0.0820633 0.142138i
\(686\) 6.88408 + 11.9236i 0.262835 + 0.455244i
\(687\) 0 0
\(688\) 12.1566i 0.463466i
\(689\) −12.1634 + 4.28415i −0.463389 + 0.163213i
\(690\) 0 0
\(691\) 30.8925 + 8.27763i 1.17521 + 0.314896i 0.793024 0.609191i \(-0.208506\pi\)
0.382183 + 0.924086i \(0.375172\pi\)
\(692\) −9.81614 + 5.66735i −0.373154 + 0.215440i
\(693\) 0 0
\(694\) 22.3923 22.3923i 0.850000 0.850000i
\(695\) 2.80973 0.752865i 0.106579 0.0285578i
\(696\) 0 0
\(697\) 6.21808 + 6.21808i 0.235527 + 0.235527i
\(698\) −14.1513 8.17028i −0.535636 0.309250i
\(699\) 0 0
\(700\) −0.277260 + 1.03475i −0.0104794 + 0.0391098i
\(701\) −18.5210 −0.699528 −0.349764 0.936838i \(-0.613738\pi\)
−0.349764 + 0.936838i \(0.613738\pi\)
\(702\) 0 0
\(703\) −24.4012 −0.920307
\(704\) −0.0282216 + 0.105325i −0.00106364 + 0.00396957i
\(705\) 0 0
\(706\) 1.13097 + 0.652964i 0.0425645 + 0.0245746i
\(707\) −6.59527 6.59527i −0.248041 0.248041i
\(708\) 0 0
\(709\) 8.77434 2.35108i 0.329527 0.0882966i −0.0902623 0.995918i \(-0.528771\pi\)
0.419790 + 0.907621i \(0.362104\pi\)
\(710\) −2.29084 + 2.29084i −0.0859737 + 0.0859737i
\(711\) 0 0
\(712\) −0.436169 + 0.251822i −0.0163461 + 0.00943744i
\(713\) 0.452192 + 0.121165i 0.0169347 + 0.00453765i
\(714\) 0 0
\(715\) −0.255835 + 0.298521i −0.00956770 + 0.0111640i
\(716\) 8.07231i 0.301677i
\(717\) 0 0
\(718\) −16.6799 28.8904i −0.622488 1.07818i
\(719\) −17.0038 + 29.4515i −0.634135 + 1.09835i 0.352563 + 0.935788i \(0.385310\pi\)
−0.986698 + 0.162566i \(0.948023\pi\)
\(720\) 0 0
\(721\) −1.01596 3.79162i −0.0378364 0.141207i
\(722\) 3.62540 + 13.5302i 0.134923 + 0.503541i
\(723\) 0 0
\(724\) −2.67389 + 4.63131i −0.0993742 + 0.172121i
\(725\) −0.430301 0.745303i −0.0159810 0.0276798i
\(726\) 0 0
\(727\) 21.7524i 0.806752i 0.915034 + 0.403376i \(0.132163\pi\)
−0.915034 + 0.403376i \(0.867837\pi\)
\(728\) −3.79657 0.710300i −0.140710 0.0263255i
\(729\) 0 0
\(730\) 12.6571 + 3.39146i 0.468461 + 0.125524i
\(731\) 23.1449 13.3627i 0.856043 0.494237i
\(732\) 0 0
\(733\) −11.3306 + 11.3306i −0.418506 + 0.418506i −0.884689 0.466182i \(-0.845629\pi\)
0.466182 + 0.884689i \(0.345629\pi\)
\(734\) 23.9121 6.40724i 0.882613 0.236495i
\(735\) 0 0
\(736\) 1.89511 + 1.89511i 0.0698546 + 0.0698546i
\(737\) 0.359574 + 0.207600i 0.0132451 + 0.00764705i
\(738\) 0 0
\(739\) 4.06627 15.1755i 0.149580 0.558240i −0.849929 0.526898i \(-0.823355\pi\)
0.999509 0.0313424i \(-0.00997824\pi\)
\(740\) −10.9207 −0.401452
\(741\) 0 0
\(742\) 3.83150 0.140659
\(743\) −5.97479 + 22.2982i −0.219194 + 0.818042i 0.765454 + 0.643490i \(0.222514\pi\)
−0.984648 + 0.174552i \(0.944152\pi\)
\(744\) 0 0
\(745\) −12.9380 7.46977i −0.474012 0.273671i
\(746\) −16.1751 16.1751i −0.592212 0.592212i
\(747\) 0 0
\(748\) 0.231548 0.0620431i 0.00846623 0.00226852i
\(749\) 1.26143 1.26143i 0.0460917 0.0460917i
\(750\) 0 0
\(751\) −40.5841 + 23.4312i −1.48093 + 0.855018i −0.999766 0.0216108i \(-0.993121\pi\)
−0.481168 + 0.876629i \(0.659787\pi\)
\(752\) −12.1737 3.26192i −0.443928 0.118950i
\(753\) 0 0
\(754\) 2.56019 1.75320i 0.0932365 0.0638476i
\(755\) 12.4177i 0.451926i
\(756\) 0 0
\(757\) 2.79868 + 4.84746i 0.101720 + 0.176184i 0.912393 0.409315i \(-0.134232\pi\)
−0.810673 + 0.585499i \(0.800899\pi\)
\(758\) 4.05351 7.02088i 0.147230 0.255010i
\(759\) 0 0
\(760\) −0.578305 2.15826i −0.0209773 0.0782884i
\(761\) −0.436236 1.62806i −0.0158136 0.0590170i 0.957568 0.288207i \(-0.0930590\pi\)
−0.973382 + 0.229190i \(0.926392\pi\)
\(762\) 0 0
\(763\) −2.57214 + 4.45507i −0.0931176 + 0.161284i
\(764\) 0.427368 + 0.740223i 0.0154616 + 0.0267803i
\(765\) 0 0
\(766\) 10.0486i 0.363070i
\(767\) 24.1788 16.5575i 0.873047 0.597856i
\(768\) 0 0
\(769\) 8.70684 + 2.33299i 0.313977 + 0.0841298i 0.412366 0.911018i \(-0.364702\pi\)
−0.0983896 + 0.995148i \(0.531369\pi\)
\(770\) 0.101160 0.0584045i 0.00364554 0.00210475i
\(771\) 0 0
\(772\) 11.8388 11.8388i 0.426087 0.426087i
\(773\) 11.2273 3.00836i 0.403819 0.108203i −0.0511917 0.998689i \(-0.516302\pi\)
0.455011 + 0.890486i \(0.349635\pi\)
\(774\) 0 0
\(775\) −0.123514 0.123514i −0.00443675 0.00443675i
\(776\) −4.54519 2.62416i −0.163163 0.0942020i
\(777\) 0 0
\(778\) −0.211572 + 0.789598i −0.00758523 + 0.0283085i
\(779\) −8.93759 −0.320222
\(780\) 0 0
\(781\) 0.353261 0.0126407
\(782\) 1.52495 5.69120i 0.0545322 0.203517i
\(783\) 0 0
\(784\) −5.06835 2.92621i −0.181012 0.104508i
\(785\) 4.38205 + 4.38205i 0.156402 + 0.156402i
\(786\) 0 0
\(787\) 8.36173 2.24052i 0.298064 0.0798659i −0.106688 0.994293i \(-0.534025\pi\)
0.404752 + 0.914427i \(0.367358\pi\)
\(788\) 15.3088 15.3088i 0.545354 0.545354i
\(789\) 0 0
\(790\) 3.10337 1.79173i 0.110413 0.0637470i
\(791\) 10.2068 + 2.73490i 0.362912 + 0.0972420i
\(792\) 0 0
\(793\) −30.4863 5.70368i −1.08260 0.202543i
\(794\) 11.2334i 0.398658i
\(795\) 0 0
\(796\) 3.53360 + 6.12037i 0.125245 + 0.216931i
\(797\) 20.2024 34.9917i 0.715607 1.23947i −0.247118 0.968986i \(-0.579483\pi\)
0.962725 0.270483i \(-0.0871833\pi\)
\(798\) 0 0
\(799\) 7.17108 + 26.7628i 0.253695 + 0.946801i
\(800\) −0.258819 0.965926i −0.00915064 0.0341506i
\(801\) 0 0
\(802\) −1.39348 + 2.41359i −0.0492056 + 0.0852267i
\(803\) −0.714408 1.23739i −0.0252109 0.0436666i
\(804\) 0 0
\(805\) 2.87104i 0.101191i
\(806\) 0.409832 0.478210i 0.0144357 0.0168442i
\(807\) 0 0
\(808\) 8.41008 + 2.25348i 0.295866 + 0.0792770i
\(809\) 40.9883 23.6646i 1.44107 0.832003i 0.443150 0.896448i \(-0.353861\pi\)
0.997921 + 0.0644447i \(0.0205276\pi\)
\(810\) 0 0
\(811\) 21.7947 21.7947i 0.765317 0.765317i −0.211961 0.977278i \(-0.567985\pi\)
0.977278 + 0.211961i \(0.0679851\pi\)
\(812\) −0.890506 + 0.238610i −0.0312506 + 0.00837358i
\(813\) 0 0
\(814\) 0.842017 + 0.842017i 0.0295127 + 0.0295127i
\(815\) −12.2396 7.06651i −0.428733 0.247529i
\(816\) 0 0
\(817\) −7.03022 + 26.2371i −0.245956 + 0.917922i
\(818\) 15.5844 0.544896
\(819\) 0 0
\(820\) −4.00000 −0.139686
\(821\) 11.6235 43.3794i 0.405662 1.51395i −0.397169 0.917746i \(-0.630007\pi\)
0.802831 0.596207i \(-0.203326\pi\)
\(822\) 0 0
\(823\) −3.74668 2.16315i −0.130601 0.0754025i 0.433276 0.901261i \(-0.357358\pi\)
−0.563877 + 0.825859i \(0.690691\pi\)
\(824\) 2.59105 + 2.59105i 0.0902635 + 0.0902635i
\(825\) 0 0
\(826\) −8.41008 + 2.25348i −0.292624 + 0.0784084i
\(827\) −6.56307 + 6.56307i −0.228220 + 0.228220i −0.811949 0.583729i \(-0.801593\pi\)
0.583729 + 0.811949i \(0.301593\pi\)
\(828\) 0 0
\(829\) 30.4626 17.5876i 1.05801 0.610843i 0.133130 0.991099i \(-0.457497\pi\)
0.924881 + 0.380255i \(0.124164\pi\)
\(830\) 8.51162 + 2.28068i 0.295443 + 0.0791636i
\(831\) 0 0
\(832\) 3.40077 1.19781i 0.117901 0.0415264i
\(833\) 12.8661i 0.445784i
\(834\) 0 0
\(835\) −0.956444 1.65661i −0.0330991 0.0573293i
\(836\) −0.121819 + 0.210997i −0.00421321 + 0.00729749i
\(837\) 0 0
\(838\) −4.93586 18.4209i −0.170506 0.636339i
\(839\) −2.40907 8.99078i −0.0831704 0.310396i 0.911791 0.410654i \(-0.134700\pi\)
−0.994961 + 0.100258i \(0.968033\pi\)
\(840\) 0 0
\(841\) −14.1297 + 24.4733i −0.487230 + 0.843908i
\(842\) −1.30347 2.25768i −0.0449207 0.0778049i
\(843\) 0 0
\(844\) 22.7680i 0.783707i
\(845\) 12.9241 + 1.40261i 0.444603 + 0.0482514i
\(846\) 0 0
\(847\) 11.3699 + 3.04656i 0.390675 + 0.104681i
\(848\) −3.09748 + 1.78833i −0.106368 + 0.0614115i
\(849\) 0 0
\(850\) −1.55452 + 1.55452i −0.0533196 + 0.0533196i
\(851\) 28.2711 7.57522i 0.969121 0.259675i
\(852\) 0 0
\(853\) 23.6039 + 23.6039i 0.808183 + 0.808183i 0.984359 0.176175i \(-0.0563726\pi\)
−0.176175 + 0.984359i \(0.556373\pi\)
\(854\) 7.98042 + 4.60750i 0.273084 + 0.157665i
\(855\) 0 0
\(856\) −0.431006 + 1.60854i −0.0147315 + 0.0549787i
\(857\) −4.43651 −0.151548 −0.0757742 0.997125i \(-0.524143\pi\)
−0.0757742 + 0.997125i \(0.524143\pi\)
\(858\) 0 0
\(859\) 16.6789 0.569078 0.284539 0.958664i \(-0.408159\pi\)
0.284539 + 0.958664i \(0.408159\pi\)
\(860\) −3.14636 + 11.7424i −0.107290 + 0.400412i
\(861\) 0 0
\(862\) −19.8187 11.4423i −0.675028 0.389728i
\(863\) 35.0616 + 35.0616i 1.19351 + 1.19351i 0.976075 + 0.217436i \(0.0697693\pi\)
0.217436 + 0.976075i \(0.430231\pi\)
\(864\) 0 0
\(865\) −10.9485 + 2.93364i −0.372259 + 0.0997466i
\(866\) −14.7071 + 14.7071i −0.499768 + 0.499768i
\(867\) 0 0
\(868\) −0.162051 + 0.0935603i −0.00550037 + 0.00317564i
\(869\) −0.377427 0.101131i −0.0128033 0.00343064i
\(870\) 0 0
\(871\) −1.05402 13.6886i −0.0357140 0.463822i
\(872\) 4.80212i 0.162620i
\(873\) 0 0
\(874\) 2.99419 + 5.18609i 0.101280 + 0.175422i
\(875\) −0.535625 + 0.927730i −0.0181074 + 0.0313630i
\(876\) 0 0
\(877\) −6.14801 22.9447i −0.207603 0.774786i −0.988640 0.150301i \(-0.951976\pi\)
0.781037 0.624485i \(-0.214691\pi\)
\(878\) 8.01445 + 29.9103i 0.270474 + 1.00942i
\(879\) 0 0
\(880\) −0.0545200 + 0.0944314i −0.00183787 + 0.00318328i
\(881\) 8.12877 + 14.0795i 0.273865 + 0.474349i 0.969848 0.243710i \(-0.0783644\pi\)
−0.695983 + 0.718058i \(0.745031\pi\)
\(882\) 0 0
\(883\) 23.3980i 0.787406i −0.919238 0.393703i \(-0.871194\pi\)
0.919238 0.393703i \(-0.128806\pi\)
\(884\) −6.01866 5.15806i −0.202429 0.173484i
\(885\) 0 0
\(886\) 24.0431 + 6.44234i 0.807745 + 0.216435i
\(887\) 35.3067 20.3844i 1.18548 0.684440i 0.228207 0.973613i \(-0.426714\pi\)
0.957277 + 0.289173i \(0.0933803\pi\)
\(888\) 0 0
\(889\) −8.11181 + 8.11181i −0.272061 + 0.272061i
\(890\) −0.486484 + 0.130353i −0.0163070 + 0.00436944i
\(891\) 0 0
\(892\) −10.6472 10.6472i −0.356493 0.356493i
\(893\) −24.3876 14.0802i −0.816098 0.471175i
\(894\) 0 0
\(895\) −2.08927 + 7.79726i −0.0698365 + 0.260634i
\(896\) −1.07125 −0.0357880
\(897\) 0 0
\(898\) −39.8970 −1.33138
\(899\) 0.0389071 0.145203i 0.00129762 0.00484280i
\(900\) 0 0
\(901\) 6.80957 + 3.93151i 0.226860 + 0.130978i
\(902\) 0.308412 + 0.308412i 0.0102690 + 0.0102690i
\(903\) 0 0
\(904\) −9.52793 + 2.55300i −0.316894 + 0.0849116i
\(905\) −3.78145 + 3.78145i −0.125700 + 0.125700i
\(906\) 0 0
\(907\) 47.3499 27.3375i 1.57223 0.907727i 0.576334 0.817214i \(-0.304483\pi\)
0.995895 0.0905127i \(-0.0288506\pi\)
\(908\) −4.96291 1.32981i −0.164700 0.0441313i
\(909\) 0 0
\(910\) −3.48337 1.66872i −0.115473 0.0553176i
\(911\) 19.4958i 0.645925i −0.946412 0.322962i \(-0.895321\pi\)
0.946412 0.322962i \(-0.104679\pi\)
\(912\) 0 0
\(913\) −0.480423 0.832117i −0.0158997 0.0275391i
\(914\) −9.25399 + 16.0284i −0.306095 + 0.530171i
\(915\) 0 0
\(916\) 3.33330 + 12.4400i 0.110135 + 0.411030i
\(917\) 0.815364 + 3.04298i 0.0269257 + 0.100488i
\(918\) 0 0
\(919\) −15.0266 + 26.0269i −0.495683 + 0.858549i −0.999988 0.00497727i \(-0.998416\pi\)
0.504304 + 0.863526i \(0.331749\pi\)
\(920\) 1.34004 + 2.32102i 0.0441799 + 0.0765219i
\(921\) 0 0
\(922\) 13.0496i 0.429765i
\(923\) −6.59992 9.63783i −0.217239 0.317233i
\(924\) 0 0
\(925\) −10.5486 2.82648i −0.346835 0.0929342i
\(926\) 21.8008 12.5867i 0.716418 0.413624i
\(927\) 0 0
\(928\) 0.608537 0.608537i 0.0199762 0.0199762i
\(929\) 34.5256 9.25111i 1.13275 0.303519i 0.356717 0.934213i \(-0.383896\pi\)
0.776032 + 0.630693i \(0.217229\pi\)
\(930\) 0 0
\(931\) −9.24658 9.24658i −0.303044 0.303044i
\(932\) −20.7973 12.0073i −0.681238 0.393313i
\(933\) 0 0
\(934\) 11.0205 41.1290i 0.360601 1.34578i
\(935\) 0.239716 0.00783955
\(936\) 0 0
\(937\) 9.51941 0.310986 0.155493 0.987837i \(-0.450303\pi\)
0.155493 + 0.987837i \(0.450303\pi\)
\(938\) −1.05575 + 3.94009i −0.0344713 + 0.128649i
\(939\) 0 0
\(940\) −10.9146 6.30155i −0.355995 0.205534i
\(941\) 23.7474 + 23.7474i 0.774144 + 0.774144i 0.978828 0.204684i \(-0.0656168\pi\)
−0.204684 + 0.978828i \(0.565617\pi\)
\(942\) 0 0
\(943\) 10.3551 2.77463i 0.337207 0.0903544i
\(944\) 5.74712 5.74712i 0.187053 0.187053i
\(945\) 0 0
\(946\) 1.14797 0.662778i 0.0373236 0.0215488i
\(947\) 15.7557 + 4.22174i 0.511993 + 0.137188i 0.505560 0.862791i \(-0.331286\pi\)
0.00643231 + 0.999979i \(0.497953\pi\)
\(948\) 0 0
\(949\) −20.4119 + 42.6088i −0.662599 + 1.38314i
\(950\) 2.23440i 0.0724934i
\(951\) 0 0
\(952\) 1.17753 + 2.03954i 0.0381640 + 0.0661020i
\(953\) −0.0598968 + 0.103744i −0.00194025 + 0.00336061i −0.866994 0.498319i \(-0.833951\pi\)
0.865054 + 0.501679i \(0.167284\pi\)
\(954\) 0 0
\(955\) 0.221222 + 0.825611i 0.00715857 + 0.0267161i
\(956\) −3.30260 12.3255i −0.106814 0.398634i
\(957\) 0 0
\(958\) 14.6548 25.3829i 0.473475 0.820084i
\(959\) −2.30083 3.98516i −0.0742978 0.128688i
\(960\) 0 0
\(961\) 30.9695i 0.999016i
\(962\) 7.24104 38.7036i 0.233460 1.24785i
\(963\) 0 0
\(964\) 5.76565 + 1.54490i 0.185699 + 0.0497579i
\(965\) 14.4995 8.37129i 0.466755 0.269481i
\(966\) 0 0
\(967\) −12.1095 + 12.1095i −0.389416 + 0.389416i −0.874479 0.485063i \(-0.838797\pi\)
0.485063 + 0.874479i \(0.338797\pi\)
\(968\) −10.6137 + 2.84393i −0.341137 + 0.0914074i
\(969\) 0 0
\(970\) −3.71113 3.71113i −0.119157 0.119157i
\(971\) 46.2626 + 26.7097i 1.48464 + 0.857156i 0.999847 0.0174747i \(-0.00556267\pi\)
0.484790 + 0.874631i \(0.338896\pi\)
\(972\) 0 0
\(973\) 0.806506 3.00992i 0.0258554 0.0964937i
\(974\) 4.48407 0.143679
\(975\) 0 0
\(976\) −8.60209 −0.275346
\(977\) −4.45733 + 16.6350i −0.142603 + 0.532200i 0.857248 + 0.514904i \(0.172172\pi\)
−0.999850 + 0.0172960i \(0.994494\pi\)
\(978\) 0 0
\(979\) 0.0475599 + 0.0274587i 0.00152002 + 0.000877584i
\(980\) −4.13829 4.13829i −0.132193 0.132193i
\(981\) 0 0
\(982\) −1.30721 + 0.350267i −0.0417149 + 0.0111775i
\(983\) 7.63036 7.63036i 0.243371 0.243371i −0.574872 0.818243i \(-0.694948\pi\)
0.818243 + 0.574872i \(0.194948\pi\)
\(984\) 0 0
\(985\) 18.7494 10.8250i 0.597405 0.344912i
\(986\) −1.82750 0.489677i −0.0581994 0.0155945i
\(987\) 0 0
\(988\) 8.03246 0.618495i 0.255547 0.0196769i
\(989\) 32.5808i 1.03601i
\(990\) 0 0
\(991\) 5.66822 + 9.81765i 0.180057 + 0.311868i 0.941900 0.335894i \(-0.109038\pi\)
−0.761843 + 0.647762i \(0.775705\pi\)
\(992\) 0.0873374 0.151273i 0.00277297 0.00480292i
\(993\) 0 0
\(994\) 0.898250 + 3.35231i 0.0284908 + 0.106329i
\(995\) 1.82913 + 6.82639i 0.0579872 + 0.216411i
\(996\) 0 0
\(997\) −3.23856 + 5.60935i −0.102566 + 0.177650i −0.912741 0.408538i \(-0.866039\pi\)
0.810175 + 0.586188i \(0.199372\pi\)
\(998\) 9.23867 + 16.0018i 0.292445 + 0.506530i
\(999\) 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.cu.f.431.1 16
3.2 odd 2 inner 1170.2.cu.f.431.3 yes 16
13.7 odd 12 inner 1170.2.cu.f.1151.3 yes 16
39.20 even 12 inner 1170.2.cu.f.1151.1 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1170.2.cu.f.431.1 16 1.1 even 1 trivial
1170.2.cu.f.431.3 yes 16 3.2 odd 2 inner
1170.2.cu.f.1151.1 yes 16 39.20 even 12 inner
1170.2.cu.f.1151.3 yes 16 13.7 odd 12 inner