Properties

Label 1170.2.cu.a.1151.2
Level $1170$
Weight $2$
Character 1170.1151
Analytic conductor $9.342$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [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: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 1151.2
Root \(0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 1170.1151
Dual form 1170.2.cu.a.431.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-2.36603 - 0.633975i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\) \(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-2.36603 - 0.633975i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{10} +(0.965926 - 0.258819i) q^{11} +(1.00000 + 3.46410i) q^{13} -2.44949i q^{14} +(0.500000 - 0.866025i) q^{16} +(-2.63896 - 4.57081i) q^{17} +(-1.00000 + 3.73205i) q^{19} +(0.258819 - 0.965926i) q^{20} +(0.500000 + 0.866025i) q^{22} +(-0.258819 + 0.448288i) q^{23} -1.00000i q^{25} +(-3.08725 + 1.86250i) q^{26} +(2.36603 - 0.633975i) q^{28} +(-8.03699 - 4.64016i) q^{29} +(-7.09808 - 7.09808i) q^{31} +(0.965926 + 0.258819i) q^{32} +(3.73205 - 3.73205i) q^{34} +(2.12132 - 1.22474i) q^{35} +(-0.133975 - 0.500000i) q^{37} -3.86370 q^{38} +1.00000 q^{40} +(-2.82843 - 10.5558i) q^{41} +(10.7942 - 6.23205i) q^{43} +(-0.707107 + 0.707107i) q^{44} +(-0.500000 - 0.133975i) q^{46} +(-3.53553 - 3.53553i) q^{47} +(-0.866025 - 0.500000i) q^{49} +(0.965926 - 0.258819i) q^{50} +(-2.59808 - 2.50000i) q^{52} +10.1769i q^{53} +(-0.500000 + 0.866025i) q^{55} +(1.22474 + 2.12132i) q^{56} +(2.40192 - 8.96410i) q^{58} +(3.55412 - 13.2641i) q^{59} +(5.83013 + 10.0981i) q^{61} +(5.01910 - 8.69333i) q^{62} +1.00000i q^{64} +(-3.15660 - 1.74238i) q^{65} +(-4.09808 + 1.09808i) q^{67} +(4.57081 + 2.63896i) q^{68} +(1.73205 + 1.73205i) q^{70} +(-14.0914 - 3.77577i) q^{71} +(-7.92820 + 7.92820i) q^{73} +(0.448288 - 0.258819i) q^{74} +(-1.00000 - 3.73205i) q^{76} -2.44949 q^{77} +5.92820 q^{79} +(0.258819 + 0.965926i) q^{80} +(9.46410 - 5.46410i) q^{82} +(-7.72741 + 7.72741i) q^{83} +(5.09808 + 1.36603i) q^{85} +(8.81345 + 8.81345i) q^{86} +(-0.866025 - 0.500000i) q^{88} +(9.84873 - 2.63896i) q^{89} +(-0.169873 - 8.83013i) q^{91} -0.517638i q^{92} +(2.50000 - 4.33013i) q^{94} +(-1.93185 - 3.34607i) q^{95} +(0.464102 - 1.73205i) q^{97} +(0.258819 - 0.965926i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 12 q^{7} + 8 q^{13} + 4 q^{16} - 8 q^{19} + 4 q^{22} + 12 q^{28} - 36 q^{31} + 16 q^{34} - 8 q^{37} + 8 q^{40} + 24 q^{43} - 4 q^{46} - 4 q^{55} + 40 q^{58} + 12 q^{61} - 12 q^{67} - 8 q^{73} - 8 q^{76} - 8 q^{79} + 48 q^{82} + 20 q^{85} - 36 q^{91} + 20 q^{94} - 24 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\)

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
\(7\) −2.36603 0.633975i −0.894274 0.239620i −0.217718 0.976012i \(-0.569861\pi\)
−0.676555 + 0.736392i \(0.736528\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 0 0
\(10\) −0.866025 0.500000i −0.273861 0.158114i
\(11\) 0.965926 0.258819i 0.291238 0.0780369i −0.110242 0.993905i \(-0.535163\pi\)
0.401480 + 0.915868i \(0.368496\pi\)
\(12\) 0 0
\(13\) 1.00000 + 3.46410i 0.277350 + 0.960769i
\(14\) 2.44949i 0.654654i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) −2.63896 4.57081i −0.640041 1.10858i −0.985423 0.170122i \(-0.945584\pi\)
0.345382 0.938462i \(-0.387749\pi\)
\(18\) 0 0
\(19\) −1.00000 + 3.73205i −0.229416 + 0.856191i 0.751171 + 0.660107i \(0.229489\pi\)
−0.980587 + 0.196084i \(0.937177\pi\)
\(20\) 0.258819 0.965926i 0.0578737 0.215988i
\(21\) 0 0
\(22\) 0.500000 + 0.866025i 0.106600 + 0.184637i
\(23\) −0.258819 + 0.448288i −0.0539675 + 0.0934745i −0.891747 0.452534i \(-0.850520\pi\)
0.837780 + 0.546009i \(0.183853\pi\)
\(24\) 0 0
\(25\) 1.00000i 0.200000i
\(26\) −3.08725 + 1.86250i −0.605459 + 0.365267i
\(27\) 0 0
\(28\) 2.36603 0.633975i 0.447137 0.119810i
\(29\) −8.03699 4.64016i −1.49243 0.861656i −0.492470 0.870329i \(-0.663906\pi\)
−0.999962 + 0.00867333i \(0.997239\pi\)
\(30\) 0 0
\(31\) −7.09808 7.09808i −1.27485 1.27485i −0.943511 0.331341i \(-0.892499\pi\)
−0.331341 0.943511i \(-0.607501\pi\)
\(32\) 0.965926 + 0.258819i 0.170753 + 0.0457532i
\(33\) 0 0
\(34\) 3.73205 3.73205i 0.640041 0.640041i
\(35\) 2.12132 1.22474i 0.358569 0.207020i
\(36\) 0 0
\(37\) −0.133975 0.500000i −0.0220253 0.0821995i 0.954038 0.299684i \(-0.0968814\pi\)
−0.976064 + 0.217485i \(0.930215\pi\)
\(38\) −3.86370 −0.626775
\(39\) 0 0
\(40\) 1.00000 0.158114
\(41\) −2.82843 10.5558i −0.441726 1.64854i −0.724438 0.689340i \(-0.757901\pi\)
0.282712 0.959205i \(-0.408766\pi\)
\(42\) 0 0
\(43\) 10.7942 6.23205i 1.64610 0.950379i 0.667505 0.744606i \(-0.267362\pi\)
0.978600 0.205773i \(-0.0659709\pi\)
\(44\) −0.707107 + 0.707107i −0.106600 + 0.106600i
\(45\) 0 0
\(46\) −0.500000 0.133975i −0.0737210 0.0197535i
\(47\) −3.53553 3.53553i −0.515711 0.515711i 0.400560 0.916271i \(-0.368816\pi\)
−0.916271 + 0.400560i \(0.868816\pi\)
\(48\) 0 0
\(49\) −0.866025 0.500000i −0.123718 0.0714286i
\(50\) 0.965926 0.258819i 0.136603 0.0366025i
\(51\) 0 0
\(52\) −2.59808 2.50000i −0.360288 0.346688i
\(53\) 10.1769i 1.39790i 0.715168 + 0.698952i \(0.246350\pi\)
−0.715168 + 0.698952i \(0.753650\pi\)
\(54\) 0 0
\(55\) −0.500000 + 0.866025i −0.0674200 + 0.116775i
\(56\) 1.22474 + 2.12132i 0.163663 + 0.283473i
\(57\) 0 0
\(58\) 2.40192 8.96410i 0.315388 1.17704i
\(59\) 3.55412 13.2641i 0.462707 1.72684i −0.201677 0.979452i \(-0.564639\pi\)
0.664383 0.747392i \(-0.268694\pi\)
\(60\) 0 0
\(61\) 5.83013 + 10.0981i 0.746471 + 1.29293i 0.949504 + 0.313754i \(0.101587\pi\)
−0.203033 + 0.979172i \(0.565080\pi\)
\(62\) 5.01910 8.69333i 0.637426 1.10405i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) −3.15660 1.74238i −0.391528 0.216116i
\(66\) 0 0
\(67\) −4.09808 + 1.09808i −0.500660 + 0.134151i −0.500306 0.865849i \(-0.666779\pi\)
−0.000353546 1.00000i \(0.500113\pi\)
\(68\) 4.57081 + 2.63896i 0.554292 + 0.320021i
\(69\) 0 0
\(70\) 1.73205 + 1.73205i 0.207020 + 0.207020i
\(71\) −14.0914 3.77577i −1.67234 0.448102i −0.706598 0.707615i \(-0.749771\pi\)
−0.965739 + 0.259513i \(0.916438\pi\)
\(72\) 0 0
\(73\) −7.92820 + 7.92820i −0.927926 + 0.927926i −0.997572 0.0696458i \(-0.977813\pi\)
0.0696458 + 0.997572i \(0.477813\pi\)
\(74\) 0.448288 0.258819i 0.0521124 0.0300871i
\(75\) 0 0
\(76\) −1.00000 3.73205i −0.114708 0.428096i
\(77\) −2.44949 −0.279145
\(78\) 0 0
\(79\) 5.92820 0.666975 0.333487 0.942755i \(-0.391775\pi\)
0.333487 + 0.942755i \(0.391775\pi\)
\(80\) 0.258819 + 0.965926i 0.0289368 + 0.107994i
\(81\) 0 0
\(82\) 9.46410 5.46410i 1.04514 0.603409i
\(83\) −7.72741 + 7.72741i −0.848193 + 0.848193i −0.989908 0.141715i \(-0.954739\pi\)
0.141715 + 0.989908i \(0.454739\pi\)
\(84\) 0 0
\(85\) 5.09808 + 1.36603i 0.552964 + 0.148166i
\(86\) 8.81345 + 8.81345i 0.950379 + 0.950379i
\(87\) 0 0
\(88\) −0.866025 0.500000i −0.0923186 0.0533002i
\(89\) 9.84873 2.63896i 1.04396 0.279729i 0.304208 0.952606i \(-0.401608\pi\)
0.739755 + 0.672877i \(0.234941\pi\)
\(90\) 0 0
\(91\) −0.169873 8.83013i −0.0178075 0.925649i
\(92\) 0.517638i 0.0539675i
\(93\) 0 0
\(94\) 2.50000 4.33013i 0.257855 0.446619i
\(95\) −1.93185 3.34607i −0.198204 0.343299i
\(96\) 0 0
\(97\) 0.464102 1.73205i 0.0471224 0.175863i −0.938354 0.345676i \(-0.887650\pi\)
0.985476 + 0.169813i \(0.0543163\pi\)
\(98\) 0.258819 0.965926i 0.0261447 0.0975732i
\(99\) 0 0
\(100\) 0.500000 + 0.866025i 0.0500000 + 0.0866025i
\(101\) 0.328169 0.568406i 0.0326541 0.0565585i −0.849237 0.528013i \(-0.822937\pi\)
0.881891 + 0.471454i \(0.156271\pi\)
\(102\) 0 0
\(103\) 2.00000i 0.197066i 0.995134 + 0.0985329i \(0.0314150\pi\)
−0.995134 + 0.0985329i \(0.968585\pi\)
\(104\) 1.74238 3.15660i 0.170855 0.309530i
\(105\) 0 0
\(106\) −9.83013 + 2.63397i −0.954786 + 0.255834i
\(107\) 3.67423 + 2.12132i 0.355202 + 0.205076i 0.666974 0.745081i \(-0.267589\pi\)
−0.311772 + 0.950157i \(0.600923\pi\)
\(108\) 0 0
\(109\) 9.92820 + 9.92820i 0.950949 + 0.950949i 0.998852 0.0479026i \(-0.0152537\pi\)
−0.0479026 + 0.998852i \(0.515254\pi\)
\(110\) −0.965926 0.258819i −0.0920974 0.0246774i
\(111\) 0 0
\(112\) −1.73205 + 1.73205i −0.163663 + 0.163663i
\(113\) −9.91808 + 5.72620i −0.933014 + 0.538676i −0.887764 0.460300i \(-0.847742\pi\)
−0.0452506 + 0.998976i \(0.514409\pi\)
\(114\) 0 0
\(115\) −0.133975 0.500000i −0.0124932 0.0466252i
\(116\) 9.28032 0.861656
\(117\) 0 0
\(118\) 13.7321 1.26414
\(119\) 3.34607 + 12.4877i 0.306733 + 1.14474i
\(120\) 0 0
\(121\) −8.66025 + 5.00000i −0.787296 + 0.454545i
\(122\) −8.24504 + 8.24504i −0.746471 + 0.746471i
\(123\) 0 0
\(124\) 9.69615 + 2.59808i 0.870740 + 0.233314i
\(125\) 0.707107 + 0.707107i 0.0632456 + 0.0632456i
\(126\) 0 0
\(127\) −2.53590 1.46410i −0.225025 0.129918i 0.383250 0.923645i \(-0.374805\pi\)
−0.608275 + 0.793727i \(0.708138\pi\)
\(128\) −0.965926 + 0.258819i −0.0853766 + 0.0228766i
\(129\) 0 0
\(130\) 0.866025 3.50000i 0.0759555 0.306970i
\(131\) 6.55343i 0.572576i −0.958144 0.286288i \(-0.907579\pi\)
0.958144 0.286288i \(-0.0924214\pi\)
\(132\) 0 0
\(133\) 4.73205 8.19615i 0.410321 0.710697i
\(134\) −2.12132 3.67423i −0.183254 0.317406i
\(135\) 0 0
\(136\) −1.36603 + 5.09808i −0.117136 + 0.437156i
\(137\) −0.360355 + 1.34486i −0.0307872 + 0.114899i −0.979609 0.200911i \(-0.935610\pi\)
0.948822 + 0.315811i \(0.102276\pi\)
\(138\) 0 0
\(139\) −5.00000 8.66025i −0.424094 0.734553i 0.572241 0.820086i \(-0.306074\pi\)
−0.996335 + 0.0855324i \(0.972741\pi\)
\(140\) −1.22474 + 2.12132i −0.103510 + 0.179284i
\(141\) 0 0
\(142\) 14.5885i 1.22424i
\(143\) 1.86250 + 3.08725i 0.155750 + 0.258168i
\(144\) 0 0
\(145\) 8.96410 2.40192i 0.744428 0.199469i
\(146\) −9.71003 5.60609i −0.803607 0.463963i
\(147\) 0 0
\(148\) 0.366025 + 0.366025i 0.0300871 + 0.0300871i
\(149\) −14.1607 3.79435i −1.16009 0.310846i −0.373089 0.927796i \(-0.621701\pi\)
−0.787002 + 0.616950i \(0.788368\pi\)
\(150\) 0 0
\(151\) −9.00000 + 9.00000i −0.732410 + 0.732410i −0.971097 0.238687i \(-0.923283\pi\)
0.238687 + 0.971097i \(0.423283\pi\)
\(152\) 3.34607 1.93185i 0.271402 0.156694i
\(153\) 0 0
\(154\) −0.633975 2.36603i −0.0510871 0.190660i
\(155\) 10.0382 0.806287
\(156\) 0 0
\(157\) −21.3923 −1.70729 −0.853646 0.520854i \(-0.825614\pi\)
−0.853646 + 0.520854i \(0.825614\pi\)
\(158\) 1.53433 + 5.72620i 0.122065 + 0.455552i
\(159\) 0 0
\(160\) −0.866025 + 0.500000i −0.0684653 + 0.0395285i
\(161\) 0.896575 0.896575i 0.0706600 0.0706600i
\(162\) 0 0
\(163\) 6.69615 + 1.79423i 0.524483 + 0.140535i 0.511340 0.859379i \(-0.329149\pi\)
0.0131436 + 0.999914i \(0.495816\pi\)
\(164\) 7.72741 + 7.72741i 0.603409 + 0.603409i
\(165\) 0 0
\(166\) −9.46410 5.46410i −0.734557 0.424097i
\(167\) 8.36516 2.24144i 0.647316 0.173448i 0.0798008 0.996811i \(-0.474572\pi\)
0.567515 + 0.823363i \(0.307905\pi\)
\(168\) 0 0
\(169\) −11.0000 + 6.92820i −0.846154 + 0.532939i
\(170\) 5.27792i 0.404798i
\(171\) 0 0
\(172\) −6.23205 + 10.7942i −0.475189 + 0.823052i
\(173\) 2.82843 + 4.89898i 0.215041 + 0.372463i 0.953285 0.302071i \(-0.0976780\pi\)
−0.738244 + 0.674534i \(0.764345\pi\)
\(174\) 0 0
\(175\) −0.633975 + 2.36603i −0.0479240 + 0.178855i
\(176\) 0.258819 0.965926i 0.0195092 0.0728094i
\(177\) 0 0
\(178\) 5.09808 + 8.83013i 0.382117 + 0.661846i
\(179\) −6.19307 + 10.7267i −0.462892 + 0.801753i −0.999104 0.0423310i \(-0.986522\pi\)
0.536212 + 0.844084i \(0.319855\pi\)
\(180\) 0 0
\(181\) 2.39230i 0.177819i −0.996040 0.0889093i \(-0.971662\pi\)
0.996040 0.0889093i \(-0.0283381\pi\)
\(182\) 8.48528 2.44949i 0.628971 0.181568i
\(183\) 0 0
\(184\) 0.500000 0.133975i 0.0368605 0.00987674i
\(185\) 0.448288 + 0.258819i 0.0329588 + 0.0190288i
\(186\) 0 0
\(187\) −3.73205 3.73205i −0.272915 0.272915i
\(188\) 4.82963 + 1.29410i 0.352237 + 0.0943816i
\(189\) 0 0
\(190\) 2.73205 2.73205i 0.198204 0.198204i
\(191\) 10.3664 5.98502i 0.750084 0.433061i −0.0756404 0.997135i \(-0.524100\pi\)
0.825724 + 0.564074i \(0.190767\pi\)
\(192\) 0 0
\(193\) 0.509619 + 1.90192i 0.0366832 + 0.136903i 0.981839 0.189717i \(-0.0607569\pi\)
−0.945156 + 0.326620i \(0.894090\pi\)
\(194\) 1.79315 0.128741
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 1.98262 + 7.39924i 0.141256 + 0.527174i 0.999894 + 0.0145909i \(0.00464460\pi\)
−0.858638 + 0.512583i \(0.828689\pi\)
\(198\) 0 0
\(199\) 22.0526 12.7321i 1.56326 0.902551i 0.566341 0.824171i \(-0.308359\pi\)
0.996924 0.0783801i \(-0.0249748\pi\)
\(200\) −0.707107 + 0.707107i −0.0500000 + 0.0500000i
\(201\) 0 0
\(202\) 0.633975 + 0.169873i 0.0446063 + 0.0119522i
\(203\) 16.0740 + 16.0740i 1.12817 + 1.12817i
\(204\) 0 0
\(205\) 9.46410 + 5.46410i 0.661002 + 0.381629i
\(206\) −1.93185 + 0.517638i −0.134598 + 0.0360656i
\(207\) 0 0
\(208\) 3.50000 + 0.866025i 0.242681 + 0.0600481i
\(209\) 3.86370i 0.267258i
\(210\) 0 0
\(211\) 0.901924 1.56218i 0.0620910 0.107545i −0.833309 0.552808i \(-0.813556\pi\)
0.895400 + 0.445263i \(0.146890\pi\)
\(212\) −5.08845 8.81345i −0.349476 0.605310i
\(213\) 0 0
\(214\) −1.09808 + 4.09808i −0.0750629 + 0.280139i
\(215\) −3.22595 + 12.0394i −0.220008 + 0.821080i
\(216\) 0 0
\(217\) 12.2942 + 21.2942i 0.834587 + 1.44555i
\(218\) −7.02030 + 12.1595i −0.475475 + 0.823546i
\(219\) 0 0
\(220\) 1.00000i 0.0674200i
\(221\) 13.1948 13.7124i 0.887578 0.922398i
\(222\) 0 0
\(223\) −9.92820 + 2.66025i −0.664842 + 0.178144i −0.575430 0.817851i \(-0.695165\pi\)
−0.0894116 + 0.995995i \(0.528499\pi\)
\(224\) −2.12132 1.22474i −0.141737 0.0818317i
\(225\) 0 0
\(226\) −8.09808 8.09808i −0.538676 0.538676i
\(227\) 6.12372 + 1.64085i 0.406446 + 0.108907i 0.456249 0.889852i \(-0.349193\pi\)
−0.0498030 + 0.998759i \(0.515859\pi\)
\(228\) 0 0
\(229\) −13.1962 + 13.1962i −0.872026 + 0.872026i −0.992693 0.120667i \(-0.961497\pi\)
0.120667 + 0.992693i \(0.461497\pi\)
\(230\) 0.448288 0.258819i 0.0295592 0.0170660i
\(231\) 0 0
\(232\) 2.40192 + 8.96410i 0.157694 + 0.588522i
\(233\) 0.998111 0.0653885 0.0326942 0.999465i \(-0.489591\pi\)
0.0326942 + 0.999465i \(0.489591\pi\)
\(234\) 0 0
\(235\) 5.00000 0.326164
\(236\) 3.55412 + 13.2641i 0.231353 + 0.863422i
\(237\) 0 0
\(238\) −11.1962 + 6.46410i −0.725739 + 0.419005i
\(239\) 10.7961 10.7961i 0.698340 0.698340i −0.265713 0.964052i \(-0.585607\pi\)
0.964052 + 0.265713i \(0.0856072\pi\)
\(240\) 0 0
\(241\) −17.8923 4.79423i −1.15254 0.308823i −0.368560 0.929604i \(-0.620149\pi\)
−0.783984 + 0.620780i \(0.786816\pi\)
\(242\) −7.07107 7.07107i −0.454545 0.454545i
\(243\) 0 0
\(244\) −10.0981 5.83013i −0.646463 0.373236i
\(245\) 0.965926 0.258819i 0.0617107 0.0165353i
\(246\) 0 0
\(247\) −13.9282 + 0.267949i −0.886230 + 0.0170492i
\(248\) 10.0382i 0.637426i
\(249\) 0 0
\(250\) −0.500000 + 0.866025i −0.0316228 + 0.0547723i
\(251\) −1.81173 3.13801i −0.114356 0.198070i 0.803166 0.595755i \(-0.203147\pi\)
−0.917522 + 0.397685i \(0.869814\pi\)
\(252\) 0 0
\(253\) −0.133975 + 0.500000i −0.00842291 + 0.0314347i
\(254\) 0.757875 2.82843i 0.0475533 0.177471i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −4.12252 + 7.14042i −0.257156 + 0.445407i −0.965479 0.260481i \(-0.916119\pi\)
0.708323 + 0.705888i \(0.249452\pi\)
\(258\) 0 0
\(259\) 1.26795i 0.0787865i
\(260\) 3.60488 0.0693504i 0.223565 0.00430093i
\(261\) 0 0
\(262\) 6.33013 1.69615i 0.391077 0.104789i
\(263\) −11.4710 6.62278i −0.707332 0.408378i 0.102741 0.994708i \(-0.467239\pi\)
−0.810072 + 0.586330i \(0.800572\pi\)
\(264\) 0 0
\(265\) −7.19615 7.19615i −0.442056 0.442056i
\(266\) 9.14162 + 2.44949i 0.560509 + 0.150188i
\(267\) 0 0
\(268\) 3.00000 3.00000i 0.183254 0.183254i
\(269\) 20.4046 11.7806i 1.24409 0.718275i 0.274164 0.961683i \(-0.411599\pi\)
0.969924 + 0.243408i \(0.0782655\pi\)
\(270\) 0 0
\(271\) −0.624356 2.33013i −0.0379269 0.141545i 0.944366 0.328896i \(-0.106677\pi\)
−0.982293 + 0.187351i \(0.940010\pi\)
\(272\) −5.27792 −0.320021
\(273\) 0 0
\(274\) −1.39230 −0.0841122
\(275\) −0.258819 0.965926i −0.0156074 0.0582475i
\(276\) 0 0
\(277\) −9.23205 + 5.33013i −0.554700 + 0.320256i −0.751016 0.660285i \(-0.770436\pi\)
0.196315 + 0.980541i \(0.437102\pi\)
\(278\) 7.07107 7.07107i 0.424094 0.424094i
\(279\) 0 0
\(280\) −2.36603 0.633975i −0.141397 0.0378872i
\(281\) −4.52004 4.52004i −0.269643 0.269643i 0.559313 0.828956i \(-0.311065\pi\)
−0.828956 + 0.559313i \(0.811065\pi\)
\(282\) 0 0
\(283\) 8.76795 + 5.06218i 0.521200 + 0.300915i 0.737426 0.675428i \(-0.236041\pi\)
−0.216225 + 0.976344i \(0.569375\pi\)
\(284\) 14.0914 3.77577i 0.836169 0.224051i
\(285\) 0 0
\(286\) −2.50000 + 2.59808i −0.147828 + 0.153627i
\(287\) 26.7685i 1.58010i
\(288\) 0 0
\(289\) −5.42820 + 9.40192i −0.319306 + 0.553054i
\(290\) 4.64016 + 8.03699i 0.272480 + 0.471949i
\(291\) 0 0
\(292\) 2.90192 10.8301i 0.169822 0.633785i
\(293\) −2.82843 + 10.5558i −0.165238 + 0.616678i 0.832771 + 0.553617i \(0.186753\pi\)
−0.998010 + 0.0630611i \(0.979914\pi\)
\(294\) 0 0
\(295\) 6.86603 + 11.8923i 0.399755 + 0.692397i
\(296\) −0.258819 + 0.448288i −0.0150436 + 0.0260562i
\(297\) 0 0
\(298\) 14.6603i 0.849246i
\(299\) −1.81173 0.448288i −0.104775 0.0259251i
\(300\) 0 0
\(301\) −29.4904 + 7.90192i −1.69980 + 0.455459i
\(302\) −11.0227 6.36396i −0.634285 0.366205i
\(303\) 0 0
\(304\) 2.73205 + 2.73205i 0.156694 + 0.156694i
\(305\) −11.2629 3.01790i −0.644914 0.172804i
\(306\) 0 0
\(307\) −24.1244 + 24.1244i −1.37685 + 1.37685i −0.526959 + 0.849891i \(0.676668\pi\)
−0.849891 + 0.526959i \(0.823332\pi\)
\(308\) 2.12132 1.22474i 0.120873 0.0697863i
\(309\) 0 0
\(310\) 2.59808 + 9.69615i 0.147561 + 0.550704i
\(311\) −6.59059 −0.373718 −0.186859 0.982387i \(-0.559831\pi\)
−0.186859 + 0.982387i \(0.559831\pi\)
\(312\) 0 0
\(313\) 18.5359 1.04771 0.523855 0.851807i \(-0.324493\pi\)
0.523855 + 0.851807i \(0.324493\pi\)
\(314\) −5.53674 20.6634i −0.312456 1.16610i
\(315\) 0 0
\(316\) −5.13397 + 2.96410i −0.288809 + 0.166744i
\(317\) −21.7308 + 21.7308i −1.22053 + 1.22053i −0.253080 + 0.967445i \(0.581444\pi\)
−0.967445 + 0.253080i \(0.918556\pi\)
\(318\) 0 0
\(319\) −8.96410 2.40192i −0.501893 0.134482i
\(320\) −0.707107 0.707107i −0.0395285 0.0395285i
\(321\) 0 0
\(322\) 1.09808 + 0.633975i 0.0611934 + 0.0353300i
\(323\) 19.6975 5.27792i 1.09600 0.293671i
\(324\) 0 0
\(325\) 3.46410 1.00000i 0.192154 0.0554700i
\(326\) 6.93237i 0.383948i
\(327\) 0 0
\(328\) −5.46410 + 9.46410i −0.301705 + 0.522568i
\(329\) 6.12372 + 10.6066i 0.337612 + 0.584761i
\(330\) 0 0
\(331\) 2.66025 9.92820i 0.146221 0.545703i −0.853477 0.521130i \(-0.825511\pi\)
0.999698 0.0245733i \(-0.00782271\pi\)
\(332\) 2.82843 10.5558i 0.155230 0.579327i
\(333\) 0 0
\(334\) 4.33013 + 7.50000i 0.236934 + 0.410382i
\(335\) 2.12132 3.67423i 0.115900 0.200745i
\(336\) 0 0
\(337\) 17.5167i 0.954193i −0.878851 0.477097i \(-0.841689\pi\)
0.878851 0.477097i \(-0.158311\pi\)
\(338\) −9.53914 8.83203i −0.518861 0.480399i
\(339\) 0 0
\(340\) −5.09808 + 1.36603i −0.276482 + 0.0740831i
\(341\) −8.69333 5.01910i −0.470770 0.271799i
\(342\) 0 0
\(343\) 13.8564 + 13.8564i 0.748176 + 0.748176i
\(344\) −12.0394 3.22595i −0.649121 0.173931i
\(345\) 0 0
\(346\) −4.00000 + 4.00000i −0.215041 + 0.215041i
\(347\) 27.4249 15.8338i 1.47224 0.850000i 0.472731 0.881207i \(-0.343268\pi\)
0.999513 + 0.0312067i \(0.00993501\pi\)
\(348\) 0 0
\(349\) −4.49038 16.7583i −0.240365 0.897053i −0.975657 0.219303i \(-0.929622\pi\)
0.735292 0.677750i \(-0.237045\pi\)
\(350\) −2.44949 −0.130931
\(351\) 0 0
\(352\) 1.00000 0.0533002
\(353\) 5.55532 + 20.7327i 0.295680 + 1.10349i 0.940676 + 0.339306i \(0.110192\pi\)
−0.644996 + 0.764186i \(0.723141\pi\)
\(354\) 0 0
\(355\) 12.6340 7.29423i 0.670542 0.387137i
\(356\) −7.20977 + 7.20977i −0.382117 + 0.382117i
\(357\) 0 0
\(358\) −11.9641 3.20577i −0.632322 0.169430i
\(359\) 7.45001 + 7.45001i 0.393196 + 0.393196i 0.875825 0.482629i \(-0.160318\pi\)
−0.482629 + 0.875825i \(0.660318\pi\)
\(360\) 0 0
\(361\) 3.52628 + 2.03590i 0.185594 + 0.107153i
\(362\) 2.31079 0.619174i 0.121452 0.0325431i
\(363\) 0 0
\(364\) 4.56218 + 7.56218i 0.239123 + 0.396366i
\(365\) 11.2122i 0.586872i
\(366\) 0 0
\(367\) −1.16987 + 2.02628i −0.0610669 + 0.105771i −0.894943 0.446181i \(-0.852784\pi\)
0.833876 + 0.551952i \(0.186117\pi\)
\(368\) 0.258819 + 0.448288i 0.0134919 + 0.0233686i
\(369\) 0 0
\(370\) −0.133975 + 0.500000i −0.00696501 + 0.0259938i
\(371\) 6.45189 24.0788i 0.334966 1.25011i
\(372\) 0 0
\(373\) 5.40192 + 9.35641i 0.279701 + 0.484456i 0.971310 0.237815i \(-0.0764313\pi\)
−0.691609 + 0.722272i \(0.743098\pi\)
\(374\) 2.63896 4.57081i 0.136457 0.236351i
\(375\) 0 0
\(376\) 5.00000i 0.257855i
\(377\) 8.03699 32.4811i 0.413926 1.67286i
\(378\) 0 0
\(379\) −34.6865 + 9.29423i −1.78173 + 0.477412i −0.990897 0.134623i \(-0.957018\pi\)
−0.790831 + 0.612035i \(0.790351\pi\)
\(380\) 3.34607 + 1.93185i 0.171650 + 0.0991019i
\(381\) 0 0
\(382\) 8.46410 + 8.46410i 0.433061 + 0.433061i
\(383\) −16.6102 4.45069i −0.848742 0.227420i −0.191869 0.981421i \(-0.561455\pi\)
−0.656873 + 0.754001i \(0.728121\pi\)
\(384\) 0 0
\(385\) 1.73205 1.73205i 0.0882735 0.0882735i
\(386\) −1.70522 + 0.984508i −0.0867933 + 0.0501101i
\(387\) 0 0
\(388\) 0.464102 + 1.73205i 0.0235612 + 0.0879316i
\(389\) −19.9377 −1.01088 −0.505441 0.862861i \(-0.668670\pi\)
−0.505441 + 0.862861i \(0.668670\pi\)
\(390\) 0 0
\(391\) 2.73205 0.138166
\(392\) 0.258819 + 0.965926i 0.0130723 + 0.0487866i
\(393\) 0 0
\(394\) −6.63397 + 3.83013i −0.334215 + 0.192959i
\(395\) −4.19187 + 4.19187i −0.210916 + 0.210916i
\(396\) 0 0
\(397\) 23.7942 + 6.37564i 1.19420 + 0.319984i 0.800544 0.599274i \(-0.204544\pi\)
0.393654 + 0.919259i \(0.371211\pi\)
\(398\) 18.0058 + 18.0058i 0.902551 + 0.902551i
\(399\) 0 0
\(400\) −0.866025 0.500000i −0.0433013 0.0250000i
\(401\) 7.58871 2.03339i 0.378962 0.101543i −0.0643095 0.997930i \(-0.520484\pi\)
0.443271 + 0.896387i \(0.353818\pi\)
\(402\) 0 0
\(403\) 17.4904 31.6865i 0.871258 1.57842i
\(404\) 0.656339i 0.0326541i
\(405\) 0 0
\(406\) −11.3660 + 19.6865i −0.564086 + 0.977026i
\(407\) −0.258819 0.448288i −0.0128292 0.0222208i
\(408\) 0 0
\(409\) 1.50962 5.63397i 0.0746459 0.278582i −0.918507 0.395405i \(-0.870604\pi\)
0.993153 + 0.116823i \(0.0372710\pi\)
\(410\) −2.82843 + 10.5558i −0.139686 + 0.521315i
\(411\) 0 0
\(412\) −1.00000 1.73205i −0.0492665 0.0853320i
\(413\) −16.8183 + 29.1301i −0.827572 + 1.43340i
\(414\) 0 0
\(415\) 10.9282i 0.536444i
\(416\) 0.0693504 + 3.60488i 0.00340018 + 0.176744i
\(417\) 0 0
\(418\) −3.73205 + 1.00000i −0.182541 + 0.0489116i
\(419\) 9.88589 + 5.70762i 0.482957 + 0.278836i 0.721648 0.692260i \(-0.243385\pi\)
−0.238691 + 0.971096i \(0.576718\pi\)
\(420\) 0 0
\(421\) 13.9282 + 13.9282i 0.678819 + 0.678819i 0.959733 0.280914i \(-0.0906375\pi\)
−0.280914 + 0.959733i \(0.590638\pi\)
\(422\) 1.74238 + 0.466870i 0.0848179 + 0.0227269i
\(423\) 0 0
\(424\) 7.19615 7.19615i 0.349476 0.349476i
\(425\) −4.57081 + 2.63896i −0.221717 + 0.128008i
\(426\) 0 0
\(427\) −7.39230 27.5885i −0.357739 1.33510i
\(428\) −4.24264 −0.205076
\(429\) 0 0
\(430\) −12.4641 −0.601072
\(431\) 1.88108 + 7.02030i 0.0906086 + 0.338156i 0.996317 0.0857451i \(-0.0273271\pi\)
−0.905708 + 0.423901i \(0.860660\pi\)
\(432\) 0 0
\(433\) 24.8827 14.3660i 1.19579 0.690387i 0.236173 0.971711i \(-0.424107\pi\)
0.959613 + 0.281324i \(0.0907736\pi\)
\(434\) −17.3867 + 17.3867i −0.834587 + 0.834587i
\(435\) 0 0
\(436\) −13.5622 3.63397i −0.649511 0.174036i
\(437\) −1.41421 1.41421i −0.0676510 0.0676510i
\(438\) 0 0
\(439\) −25.5167 14.7321i −1.21784 0.703122i −0.253387 0.967365i \(-0.581545\pi\)
−0.964456 + 0.264242i \(0.914878\pi\)
\(440\) 0.965926 0.258819i 0.0460487 0.0123387i
\(441\) 0 0
\(442\) 16.6603 + 9.19615i 0.792447 + 0.437416i
\(443\) 17.9043i 0.850659i 0.905039 + 0.425330i \(0.139842\pi\)
−0.905039 + 0.425330i \(0.860158\pi\)
\(444\) 0 0
\(445\) −5.09808 + 8.83013i −0.241672 + 0.418588i
\(446\) −5.13922 8.90138i −0.243349 0.421493i
\(447\) 0 0
\(448\) 0.633975 2.36603i 0.0299525 0.111784i
\(449\) −0.998111 + 3.72500i −0.0471038 + 0.175794i −0.985470 0.169848i \(-0.945672\pi\)
0.938366 + 0.345642i \(0.112339\pi\)
\(450\) 0 0
\(451\) −5.46410 9.46410i −0.257294 0.445647i
\(452\) 5.72620 9.91808i 0.269338 0.466507i
\(453\) 0 0
\(454\) 6.33975i 0.297539i
\(455\) 6.36396 + 6.12372i 0.298347 + 0.287085i
\(456\) 0 0
\(457\) −3.92820 + 1.05256i −0.183754 + 0.0492366i −0.349522 0.936928i \(-0.613656\pi\)
0.165769 + 0.986165i \(0.446989\pi\)
\(458\) −16.1619 9.33109i −0.755197 0.436013i
\(459\) 0 0
\(460\) 0.366025 + 0.366025i 0.0170660 + 0.0170660i
\(461\) −28.2521 7.57012i −1.31583 0.352576i −0.468416 0.883508i \(-0.655175\pi\)
−0.847414 + 0.530932i \(0.821842\pi\)
\(462\) 0 0
\(463\) 21.0000 21.0000i 0.975953 0.975953i −0.0237648 0.999718i \(-0.507565\pi\)
0.999718 + 0.0237648i \(0.00756529\pi\)
\(464\) −8.03699 + 4.64016i −0.373108 + 0.215414i
\(465\) 0 0
\(466\) 0.258330 + 0.964102i 0.0119669 + 0.0446611i
\(467\) 8.10634 0.375117 0.187558 0.982253i \(-0.439943\pi\)
0.187558 + 0.982253i \(0.439943\pi\)
\(468\) 0 0
\(469\) 10.3923 0.479872
\(470\) 1.29410 + 4.82963i 0.0596922 + 0.222774i
\(471\) 0 0
\(472\) −11.8923 + 6.86603i −0.547388 + 0.316034i
\(473\) 8.81345 8.81345i 0.405243 0.405243i
\(474\) 0 0
\(475\) 3.73205 + 1.00000i 0.171238 + 0.0458831i
\(476\) −9.14162 9.14162i −0.419005 0.419005i
\(477\) 0 0
\(478\) 13.2224 + 7.63397i 0.604780 + 0.349170i
\(479\) −5.22715 + 1.40061i −0.238835 + 0.0639955i −0.376251 0.926518i \(-0.622787\pi\)
0.137416 + 0.990513i \(0.456120\pi\)
\(480\) 0 0
\(481\) 1.59808 0.964102i 0.0728660 0.0439592i
\(482\) 18.5235i 0.843721i
\(483\) 0 0
\(484\) 5.00000 8.66025i 0.227273 0.393648i
\(485\) 0.896575 + 1.55291i 0.0407114 + 0.0705142i
\(486\) 0 0
\(487\) 5.78461 21.5885i 0.262126 0.978266i −0.701861 0.712314i \(-0.747647\pi\)
0.963986 0.265952i \(-0.0856863\pi\)
\(488\) 3.01790 11.2629i 0.136614 0.509849i
\(489\) 0 0
\(490\) 0.500000 + 0.866025i 0.0225877 + 0.0391230i
\(491\) 3.53553 6.12372i 0.159556 0.276360i −0.775152 0.631774i \(-0.782327\pi\)
0.934709 + 0.355415i \(0.115660\pi\)
\(492\) 0 0
\(493\) 48.9808i 2.20598i
\(494\) −3.86370 13.3843i −0.173836 0.602186i
\(495\) 0 0
\(496\) −9.69615 + 2.59808i −0.435370 + 0.116657i
\(497\) 30.9468 + 17.8671i 1.38815 + 0.801451i
\(498\) 0 0
\(499\) −30.3205 30.3205i −1.35733 1.35733i −0.877191 0.480141i \(-0.840585\pi\)
−0.480141 0.877191i \(-0.659415\pi\)
\(500\) −0.965926 0.258819i −0.0431975 0.0115747i
\(501\) 0 0
\(502\) 2.56218 2.56218i 0.114356 0.114356i
\(503\) 28.4094 16.4022i 1.26671 0.731336i 0.292347 0.956312i \(-0.405564\pi\)
0.974364 + 0.224976i \(0.0722305\pi\)
\(504\) 0 0
\(505\) 0.169873 + 0.633975i 0.00755925 + 0.0282115i
\(506\) −0.517638 −0.0230118
\(507\) 0 0
\(508\) 2.92820 0.129918
\(509\) 4.77886 + 17.8350i 0.211819 + 0.790520i 0.987262 + 0.159103i \(0.0508600\pi\)
−0.775443 + 0.631418i \(0.782473\pi\)
\(510\) 0 0
\(511\) 23.7846 13.7321i 1.05217 0.607470i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 0 0
\(514\) −7.96410 2.13397i −0.351281 0.0941256i
\(515\) −1.41421 1.41421i −0.0623177 0.0623177i
\(516\) 0 0
\(517\) −4.33013 2.50000i −0.190439 0.109950i
\(518\) −1.22474 + 0.328169i −0.0538122 + 0.0144189i
\(519\) 0 0
\(520\) 1.00000 + 3.46410i 0.0438529 + 0.151911i
\(521\) 9.24316i 0.404950i 0.979287 + 0.202475i \(0.0648985\pi\)
−0.979287 + 0.202475i \(0.935102\pi\)
\(522\) 0 0
\(523\) 18.8205 32.5981i 0.822963 1.42541i −0.0805026 0.996754i \(-0.525653\pi\)
0.903466 0.428660i \(-0.141014\pi\)
\(524\) 3.27671 + 5.67544i 0.143144 + 0.247933i
\(525\) 0 0
\(526\) 3.42820 12.7942i 0.149477 0.557855i
\(527\) −13.7124 + 51.1755i −0.597323 + 2.22924i
\(528\) 0 0
\(529\) 11.3660 + 19.6865i 0.494175 + 0.855936i
\(530\) 5.08845 8.81345i 0.221028 0.382832i
\(531\) 0 0
\(532\) 9.46410i 0.410321i
\(533\) 33.7381 20.3538i 1.46136 0.881621i
\(534\) 0 0
\(535\) −4.09808 + 1.09808i −0.177175 + 0.0474740i
\(536\) 3.67423 + 2.12132i 0.158703 + 0.0916271i
\(537\) 0 0
\(538\) 16.6603 + 16.6603i 0.718275 + 0.718275i
\(539\) −0.965926 0.258819i −0.0416054 0.0111481i
\(540\) 0 0
\(541\) 18.0000 18.0000i 0.773880 0.773880i −0.204902 0.978782i \(-0.565688\pi\)
0.978782 + 0.204902i \(0.0656876\pi\)
\(542\) 2.08913 1.20616i 0.0897360 0.0518091i
\(543\) 0 0
\(544\) −1.36603 5.09808i −0.0585679 0.218578i
\(545\) −14.0406 −0.601433
\(546\) 0 0
\(547\) 38.7846 1.65831 0.829155 0.559019i \(-0.188822\pi\)
0.829155 + 0.559019i \(0.188822\pi\)
\(548\) −0.360355 1.34486i −0.0153936 0.0574497i
\(549\) 0 0
\(550\) 0.866025 0.500000i 0.0369274 0.0213201i
\(551\) 25.3543 25.3543i 1.08013 1.08013i
\(552\) 0 0
\(553\) −14.0263 3.75833i −0.596458 0.159820i
\(554\) −7.53794 7.53794i −0.320256 0.320256i
\(555\) 0 0
\(556\) 8.66025 + 5.00000i 0.367277 + 0.212047i
\(557\) −24.9754 + 6.69213i −1.05824 + 0.283555i −0.745653 0.666334i \(-0.767862\pi\)
−0.312587 + 0.949889i \(0.601196\pi\)
\(558\) 0 0
\(559\) 32.3827 + 31.1603i 1.36964 + 1.31794i
\(560\) 2.44949i 0.103510i
\(561\) 0 0
\(562\) 3.19615 5.53590i 0.134822 0.233518i
\(563\) −19.2306 33.3083i −0.810472 1.40378i −0.912534 0.409001i \(-0.865877\pi\)
0.102061 0.994778i \(-0.467456\pi\)
\(564\) 0 0
\(565\) 2.96410 11.0622i 0.124701 0.465389i
\(566\) −2.62038 + 9.77938i −0.110143 + 0.411058i
\(567\) 0 0
\(568\) 7.29423 + 12.6340i 0.306059 + 0.530110i
\(569\) −4.38134 + 7.58871i −0.183675 + 0.318135i −0.943129 0.332426i \(-0.892133\pi\)
0.759454 + 0.650561i \(0.225466\pi\)
\(570\) 0 0
\(571\) 9.12436i 0.381842i −0.981605 0.190921i \(-0.938853\pi\)
0.981605 0.190921i \(-0.0611475\pi\)
\(572\) −3.15660 1.74238i −0.131984 0.0728527i
\(573\) 0 0
\(574\) −25.8564 + 6.92820i −1.07923 + 0.289178i
\(575\) 0.448288 + 0.258819i 0.0186949 + 0.0107935i
\(576\) 0 0
\(577\) −23.9282 23.9282i −0.996144 0.996144i 0.00384846 0.999993i \(-0.498775\pi\)
−0.999993 + 0.00384846i \(0.998775\pi\)
\(578\) −10.4865 2.80984i −0.436180 0.116874i
\(579\) 0 0
\(580\) −6.56218 + 6.56218i −0.272480 + 0.272480i
\(581\) 23.1822 13.3843i 0.961761 0.555273i
\(582\) 0 0
\(583\) 2.63397 + 9.83013i 0.109088 + 0.407122i
\(584\) 11.2122 0.463963
\(585\) 0 0
\(586\) −10.9282 −0.451440
\(587\) −6.32680 23.6119i −0.261135 0.974568i −0.964574 0.263813i \(-0.915020\pi\)
0.703439 0.710756i \(-0.251647\pi\)
\(588\) 0 0
\(589\) 33.5885 19.3923i 1.38399 0.799046i
\(590\) −9.71003 + 9.71003i −0.399755 + 0.399755i
\(591\) 0 0
\(592\) −0.500000 0.133975i −0.0205499 0.00550632i
\(593\) −19.9241 19.9241i −0.818184 0.818184i 0.167661 0.985845i \(-0.446379\pi\)
−0.985845 + 0.167661i \(0.946379\pi\)
\(594\) 0 0
\(595\) −11.1962 6.46410i −0.458997 0.265002i
\(596\) 14.1607 3.79435i 0.580046 0.155423i
\(597\) 0 0
\(598\) −0.0358984 1.86603i −0.00146799 0.0763075i
\(599\) 9.04008i 0.369368i 0.982798 + 0.184684i \(0.0591261\pi\)
−0.982798 + 0.184684i \(0.940874\pi\)
\(600\) 0 0
\(601\) 13.2321 22.9186i 0.539747 0.934869i −0.459171 0.888348i \(-0.651853\pi\)
0.998917 0.0465205i \(-0.0148133\pi\)
\(602\) −15.2653 26.4404i −0.622169 1.07763i
\(603\) 0 0
\(604\) 3.29423 12.2942i 0.134040 0.500245i
\(605\) 2.58819 9.65926i 0.105225 0.392705i
\(606\) 0 0
\(607\) 1.70577 + 2.95448i 0.0692351 + 0.119919i 0.898565 0.438841i \(-0.144611\pi\)
−0.829330 + 0.558760i \(0.811277\pi\)
\(608\) −1.93185 + 3.34607i −0.0783469 + 0.135701i
\(609\) 0 0
\(610\) 11.6603i 0.472110i
\(611\) 8.71191 15.7830i 0.352446 0.638511i
\(612\) 0 0
\(613\) −9.96410 + 2.66987i −0.402446 + 0.107835i −0.454364 0.890816i \(-0.650133\pi\)
0.0519175 + 0.998651i \(0.483467\pi\)
\(614\) −29.5462 17.0585i −1.19239 0.688425i
\(615\) 0 0
\(616\) 1.73205 + 1.73205i 0.0697863 + 0.0697863i
\(617\) −29.4768 7.89829i −1.18669 0.317973i −0.389115 0.921189i \(-0.627219\pi\)
−0.797578 + 0.603216i \(0.793886\pi\)
\(618\) 0 0
\(619\) 6.05256 6.05256i 0.243273 0.243273i −0.574930 0.818203i \(-0.694971\pi\)
0.818203 + 0.574930i \(0.194971\pi\)
\(620\) −8.69333 + 5.01910i −0.349133 + 0.201572i
\(621\) 0 0
\(622\) −1.70577 6.36603i −0.0683952 0.255254i
\(623\) −24.9754 −1.00062
\(624\) 0 0
\(625\) −1.00000 −0.0400000
\(626\) 4.79744 + 17.9043i 0.191744 + 0.715600i
\(627\) 0 0
\(628\) 18.5263 10.6962i 0.739279 0.426823i
\(629\) −1.93185 + 1.93185i −0.0770280 + 0.0770280i
\(630\) 0 0
\(631\) 34.1506 + 9.15064i 1.35952 + 0.364281i 0.863638 0.504112i \(-0.168180\pi\)
0.495877 + 0.868393i \(0.334847\pi\)
\(632\) −4.19187 4.19187i −0.166744 0.166744i
\(633\) 0 0
\(634\) −26.6147 15.3660i −1.05701 0.610263i
\(635\) 2.82843 0.757875i 0.112243 0.0300753i
\(636\) 0 0
\(637\) 0.866025 3.50000i 0.0343132 0.138675i
\(638\) 9.28032i 0.367411i
\(639\) 0 0
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) 1.36345 + 2.36156i 0.0538529 + 0.0932759i 0.891695 0.452636i \(-0.149516\pi\)
−0.837842 + 0.545912i \(0.816183\pi\)
\(642\) 0 0
\(643\) 7.29423 27.2224i 0.287656 1.07355i −0.659220 0.751950i \(-0.729113\pi\)
0.946876 0.321598i \(-0.104220\pi\)
\(644\) −0.328169 + 1.22474i −0.0129317 + 0.0482617i
\(645\) 0 0
\(646\) 10.1962 + 17.6603i 0.401162 + 0.694833i
\(647\) −11.5403 + 19.9885i −0.453698 + 0.785827i −0.998612 0.0526641i \(-0.983229\pi\)
0.544915 + 0.838492i \(0.316562\pi\)
\(648\) 0 0
\(649\) 13.7321i 0.539030i
\(650\) 1.86250 + 3.08725i 0.0730533 + 0.121092i
\(651\) 0 0
\(652\) −6.69615 + 1.79423i −0.262242 + 0.0702674i
\(653\) −2.27362 1.31268i −0.0889738 0.0513690i 0.454853 0.890567i \(-0.349692\pi\)
−0.543827 + 0.839198i \(0.683025\pi\)
\(654\) 0 0
\(655\) 4.63397 + 4.63397i 0.181064 + 0.181064i
\(656\) −10.5558 2.82843i −0.412136 0.110432i
\(657\) 0 0
\(658\) −8.66025 + 8.66025i −0.337612 + 0.337612i
\(659\) 0.120118 0.0693504i 0.00467915 0.00270151i −0.497659 0.867373i \(-0.665807\pi\)
0.502338 + 0.864671i \(0.332473\pi\)
\(660\) 0 0
\(661\) 2.11731 + 7.90192i 0.0823540 + 0.307349i 0.994800 0.101848i \(-0.0324755\pi\)
−0.912446 + 0.409197i \(0.865809\pi\)
\(662\) 10.2784 0.399483
\(663\) 0 0
\(664\) 10.9282 0.424097
\(665\) 2.44949 + 9.14162i 0.0949871 + 0.354497i
\(666\) 0 0
\(667\) 4.16025 2.40192i 0.161086 0.0930029i
\(668\) −6.12372 + 6.12372i −0.236934 + 0.236934i
\(669\) 0 0
\(670\) 4.09808 + 1.09808i 0.158322 + 0.0424224i
\(671\) 8.24504 + 8.24504i 0.318296 + 0.318296i
\(672\) 0 0
\(673\) 6.12436 + 3.53590i 0.236077 + 0.136299i 0.613372 0.789794i \(-0.289813\pi\)
−0.377296 + 0.926093i \(0.623146\pi\)
\(674\) 16.9198 4.53365i 0.651726 0.174629i
\(675\) 0 0
\(676\) 6.06218 11.5000i 0.233161 0.442308i
\(677\) 42.8797i 1.64800i −0.566590 0.824000i \(-0.691738\pi\)
0.566590 0.824000i \(-0.308262\pi\)
\(678\) 0 0
\(679\) −2.19615 + 3.80385i −0.0842806 + 0.145978i
\(680\) −2.63896 4.57081i −0.101199 0.175283i
\(681\) 0 0
\(682\) 2.59808 9.69615i 0.0994855 0.371285i
\(683\) 0.175865 0.656339i 0.00672930 0.0251141i −0.962480 0.271354i \(-0.912529\pi\)
0.969209 + 0.246240i \(0.0791952\pi\)
\(684\) 0 0
\(685\) −0.696152 1.20577i −0.0265986 0.0460702i
\(686\) −9.79796 + 16.9706i −0.374088 + 0.647939i
\(687\) 0 0
\(688\) 12.4641i 0.475189i
\(689\) −35.2538 + 10.1769i −1.34306 + 0.387709i
\(690\) 0 0
\(691\) 11.6603 3.12436i 0.443577 0.118856i −0.0301155 0.999546i \(-0.509588\pi\)
0.473692 + 0.880690i \(0.342921\pi\)
\(692\) −4.89898 2.82843i −0.186231 0.107521i
\(693\) 0 0
\(694\) 22.3923 + 22.3923i 0.850000 + 0.850000i
\(695\) 9.65926 + 2.58819i 0.366397 + 0.0981757i
\(696\) 0 0
\(697\) −40.7846 + 40.7846i −1.54483 + 1.54483i
\(698\) 15.0251 8.67475i 0.568709 0.328344i
\(699\) 0 0
\(700\) −0.633975 2.36603i −0.0239620 0.0894274i
\(701\) −45.3663 −1.71346 −0.856731 0.515763i \(-0.827508\pi\)
−0.856731 + 0.515763i \(0.827508\pi\)
\(702\) 0 0
\(703\) 2.00000 0.0754314
\(704\) 0.258819 + 0.965926i 0.00975461 + 0.0364047i
\(705\) 0 0
\(706\) −18.5885 + 10.7321i −0.699586 + 0.403906i
\(707\) −1.13681 + 1.13681i −0.0427542 + 0.0427542i
\(708\) 0 0
\(709\) 18.1244 + 4.85641i 0.680674 + 0.182386i 0.582558 0.812789i \(-0.302052\pi\)
0.0981160 + 0.995175i \(0.468718\pi\)
\(710\) 10.3156 + 10.3156i 0.387137 + 0.387137i
\(711\) 0 0
\(712\) −8.83013 5.09808i −0.330923 0.191058i
\(713\) 5.01910 1.34486i 0.187967 0.0503655i
\(714\) 0 0
\(715\) −3.50000 0.866025i −0.130893 0.0323875i
\(716\) 12.3861i 0.462892i
\(717\) 0 0
\(718\) −5.26795 + 9.12436i −0.196598 + 0.340518i
\(719\) 6.55343 + 11.3509i 0.244402 + 0.423316i 0.961963 0.273179i \(-0.0880751\pi\)
−0.717562 + 0.696495i \(0.754742\pi\)
\(720\) 0 0
\(721\) 1.26795 4.73205i 0.0472209 0.176231i
\(722\) −1.05386 + 3.93305i −0.0392206 + 0.146373i
\(723\) 0 0
\(724\) 1.19615 + 2.07180i 0.0444547 + 0.0769977i
\(725\) −4.64016 + 8.03699i −0.172331 + 0.298486i
\(726\) 0 0
\(727\) 14.3923i 0.533781i −0.963727 0.266891i \(-0.914004\pi\)
0.963727 0.266891i \(-0.0859962\pi\)
\(728\) −6.12372 + 6.36396i −0.226960 + 0.235864i
\(729\) 0 0
\(730\) 10.8301 2.90192i 0.400841 0.107405i
\(731\) −56.9710 32.8922i −2.10715 1.21656i
\(732\) 0 0
\(733\) −8.66025 8.66025i −0.319874 0.319874i 0.528845 0.848719i \(-0.322625\pi\)
−0.848719 + 0.528845i \(0.822625\pi\)
\(734\) −2.26002 0.605571i −0.0834189 0.0223520i
\(735\) 0 0
\(736\) −0.366025 + 0.366025i −0.0134919 + 0.0134919i
\(737\) −3.67423 + 2.12132i −0.135342 + 0.0781398i
\(738\) 0 0
\(739\) −2.29423 8.56218i −0.0843946 0.314965i 0.910804 0.412838i \(-0.135463\pi\)
−0.995199 + 0.0978736i \(0.968796\pi\)
\(740\) −0.517638 −0.0190288
\(741\) 0 0
\(742\) 24.9282 0.915143
\(743\) −4.08536 15.2468i −0.149877 0.559349i −0.999490 0.0319420i \(-0.989831\pi\)
0.849612 0.527407i \(-0.176836\pi\)
\(744\) 0 0
\(745\) 12.6962 7.33013i 0.465151 0.268555i
\(746\) −7.63947 + 7.63947i −0.279701 + 0.279701i
\(747\) 0 0
\(748\) 5.09808 + 1.36603i 0.186404 + 0.0499468i
\(749\) −7.34847 7.34847i −0.268507 0.268507i
\(750\) 0 0
\(751\) 36.3564 + 20.9904i 1.32666 + 0.765950i 0.984782 0.173793i \(-0.0556024\pi\)
0.341882 + 0.939743i \(0.388936\pi\)
\(752\) −4.82963 + 1.29410i −0.176118 + 0.0471908i
\(753\) 0 0
\(754\) 33.4545 0.643594i 1.21834 0.0234383i
\(755\) 12.7279i 0.463217i
\(756\) 0 0
\(757\) −7.80385 + 13.5167i −0.283636 + 0.491271i −0.972277 0.233830i \(-0.924874\pi\)
0.688642 + 0.725102i \(0.258207\pi\)
\(758\) −17.9551 31.0991i −0.652158 1.12957i
\(759\) 0 0
\(760\) −1.00000 + 3.73205i −0.0362738 + 0.135376i
\(761\) 8.24504 30.7709i 0.298883 1.11545i −0.639202 0.769039i \(-0.720735\pi\)
0.938085 0.346406i \(-0.112598\pi\)
\(762\) 0 0
\(763\) −17.1962 29.7846i −0.622543 1.07828i
\(764\) −5.98502 + 10.3664i −0.216531 + 0.375042i
\(765\) 0 0
\(766\) 17.1962i 0.621322i
\(767\) 49.5025 0.952323i 1.78743 0.0343864i
\(768\) 0 0
\(769\) 6.50000 1.74167i 0.234396 0.0628062i −0.139709 0.990193i \(-0.544617\pi\)
0.374105 + 0.927386i \(0.377950\pi\)
\(770\) 2.12132 + 1.22474i 0.0764471 + 0.0441367i
\(771\) 0 0
\(772\) −1.39230 1.39230i −0.0501101 0.0501101i
\(773\) 35.9101 + 9.62209i 1.29160 + 0.346083i 0.838267 0.545260i \(-0.183569\pi\)
0.453331 + 0.891342i \(0.350236\pi\)
\(774\) 0 0
\(775\) −7.09808 + 7.09808i −0.254970 + 0.254970i
\(776\) −1.55291 + 0.896575i −0.0557464 + 0.0321852i
\(777\) 0 0
\(778\) −5.16025 19.2583i −0.185004 0.690445i
\(779\) 42.2233 1.51281
\(780\) 0 0
\(781\) −14.5885 −0.522016
\(782\) 0.707107 + 2.63896i 0.0252861 + 0.0943690i
\(783\) 0 0
\(784\) −0.866025 + 0.500000i −0.0309295 + 0.0178571i
\(785\) 15.1266 15.1266i 0.539893 0.539893i
\(786\) 0 0
\(787\) −7.33013 1.96410i −0.261291 0.0700127i 0.125795 0.992056i \(-0.459852\pi\)
−0.387086 + 0.922044i \(0.626518\pi\)
\(788\) −5.41662 5.41662i −0.192959 0.192959i
\(789\) 0 0
\(790\) −5.13397 2.96410i −0.182659 0.105458i
\(791\) 27.0967 7.26054i 0.963447 0.258155i
\(792\) 0 0
\(793\) −29.1506 + 30.2942i −1.03517 + 1.07578i
\(794\) 24.6336i 0.874214i
\(795\) 0 0
\(796\) −12.7321 + 22.0526i −0.451276 + 0.781632i
\(797\) 3.06866 + 5.31508i 0.108698 + 0.188270i 0.915243 0.402903i \(-0.131999\pi\)
−0.806545 + 0.591172i \(0.798665\pi\)
\(798\) 0 0
\(799\) −6.83013 + 25.4904i −0.241633 + 0.901785i
\(800\) 0.258819 0.965926i 0.00915064 0.0341506i
\(801\) 0 0
\(802\) 3.92820 + 6.80385i 0.138710 + 0.240252i
\(803\) −5.60609 + 9.71003i −0.197834 + 0.342659i
\(804\) 0 0
\(805\) 1.26795i 0.0446893i
\(806\) 35.1337 + 8.69333i 1.23753 + 0.306210i
\(807\) 0 0
\(808\) −0.633975 + 0.169873i −0.0223031 + 0.00597611i
\(809\) −41.2017 23.7878i −1.44857 0.836334i −0.450177 0.892940i \(-0.648639\pi\)
−0.998397 + 0.0566053i \(0.981972\pi\)
\(810\) 0 0
\(811\) −36.0526 36.0526i −1.26598 1.26598i −0.948148 0.317828i \(-0.897046\pi\)
−0.317828 0.948148i \(-0.602954\pi\)
\(812\) −21.9575 5.88349i −0.770556 0.206470i
\(813\) 0 0
\(814\) 0.366025 0.366025i 0.0128292 0.0128292i
\(815\) −6.00361 + 3.46618i −0.210297 + 0.121415i
\(816\) 0 0
\(817\) 12.4641 + 46.5167i 0.436064 + 1.62741i
\(818\) 5.83272 0.203936
\(819\) 0 0
\(820\) −10.9282 −0.381629
\(821\) 6.24384 + 23.3023i 0.217912 + 0.813257i 0.985121 + 0.171861i \(0.0549779\pi\)
−0.767210 + 0.641396i \(0.778355\pi\)
\(822\) 0 0
\(823\) −47.0263 + 27.1506i −1.63923 + 0.946412i −0.658135 + 0.752900i \(0.728654\pi\)
−0.981098 + 0.193512i \(0.938012\pi\)
\(824\) 1.41421 1.41421i 0.0492665 0.0492665i
\(825\) 0 0
\(826\) −32.4904 8.70577i −1.13048 0.302913i
\(827\) 18.0430 + 18.0430i 0.627417 + 0.627417i 0.947417 0.320001i \(-0.103683\pi\)
−0.320001 + 0.947417i \(0.603683\pi\)
\(828\) 0 0
\(829\) −29.0263 16.7583i −1.00812 0.582041i −0.0974824 0.995237i \(-0.531079\pi\)
−0.910642 + 0.413196i \(0.864412\pi\)
\(830\) 10.5558 2.82843i 0.366398 0.0981761i
\(831\) 0 0
\(832\) −3.46410 + 1.00000i −0.120096 + 0.0346688i
\(833\) 5.27792i 0.182869i
\(834\) 0 0
\(835\) −4.33013 + 7.50000i −0.149850 + 0.259548i
\(836\) −1.93185 3.34607i −0.0668145 0.115726i
\(837\) 0 0
\(838\) −2.95448 + 11.0263i −0.102061 + 0.380897i
\(839\) −10.5930 + 39.5336i −0.365711 + 1.36485i 0.500744 + 0.865596i \(0.333060\pi\)
−0.866454 + 0.499256i \(0.833607\pi\)
\(840\) 0 0
\(841\) 28.5622 + 49.4711i 0.984903 + 1.70590i
\(842\) −9.84873 + 17.0585i −0.339410 + 0.587875i
\(843\) 0 0
\(844\) 1.80385i 0.0620910i
\(845\) 2.87920 12.6772i 0.0990473 0.436107i
\(846\) 0 0
\(847\) 23.6603 6.33975i 0.812976 0.217836i
\(848\) 8.81345 + 5.08845i 0.302655 + 0.174738i
\(849\) 0 0
\(850\) −3.73205 3.73205i −0.128008 0.128008i
\(851\) 0.258819 + 0.0693504i 0.00887220 + 0.00237730i
\(852\) 0 0
\(853\) −23.1699 + 23.1699i −0.793321 + 0.793321i −0.982033 0.188711i \(-0.939569\pi\)
0.188711 + 0.982033i \(0.439569\pi\)
\(854\) 24.7351 14.2808i 0.846419 0.488680i
\(855\) 0 0
\(856\) −1.09808 4.09808i −0.0375315 0.140069i
\(857\) 26.7314 0.913126 0.456563 0.889691i \(-0.349080\pi\)
0.456563 + 0.889691i \(0.349080\pi\)
\(858\) 0 0
\(859\) −26.5885 −0.907186 −0.453593 0.891209i \(-0.649858\pi\)
−0.453593 + 0.891209i \(0.649858\pi\)
\(860\) −3.22595 12.0394i −0.110004 0.410540i
\(861\) 0 0
\(862\) −6.29423 + 3.63397i −0.214382 + 0.123774i
\(863\) −16.6796 + 16.6796i −0.567779 + 0.567779i −0.931506 0.363727i \(-0.881504\pi\)
0.363727 + 0.931506i \(0.381504\pi\)
\(864\) 0 0
\(865\) −5.46410 1.46410i −0.185785 0.0497809i
\(866\) 20.3166 + 20.3166i 0.690387 + 0.690387i
\(867\) 0 0
\(868\) −21.2942 12.2942i −0.722773 0.417293i
\(869\) 5.72620 1.53433i 0.194248 0.0520486i
\(870\) 0 0
\(871\) −7.90192 13.0981i −0.267746 0.443811i
\(872\) 14.0406i 0.475475i
\(873\) 0 0
\(874\) 1.00000 1.73205i 0.0338255 0.0585875i
\(875\) −1.22474 2.12132i −0.0414039 0.0717137i
\(876\) 0 0
\(877\) 6.37564 23.7942i 0.215290 0.803474i −0.770774 0.637109i \(-0.780130\pi\)
0.986064 0.166365i \(-0.0532031\pi\)
\(878\) 7.62587 28.4601i 0.257361 0.960483i
\(879\) 0 0
\(880\) 0.500000 + 0.866025i 0.0168550 + 0.0291937i
\(881\) −5.46739 + 9.46979i −0.184201 + 0.319045i −0.943307 0.331922i \(-0.892303\pi\)
0.759106 + 0.650967i \(0.225636\pi\)
\(882\) 0 0
\(883\) 20.6077i 0.693504i 0.937957 + 0.346752i \(0.112715\pi\)
−0.937957 + 0.346752i \(0.887285\pi\)
\(884\) −4.57081 + 18.4727i −0.153733 + 0.621304i
\(885\) 0 0
\(886\) −17.2942 + 4.63397i −0.581011 + 0.155681i
\(887\) −31.3951 18.1260i −1.05414 0.608610i −0.130337 0.991470i \(-0.541606\pi\)
−0.923807 + 0.382860i \(0.874939\pi\)
\(888\) 0 0
\(889\) 5.07180 + 5.07180i 0.170103 + 0.170103i
\(890\) −9.84873 2.63896i −0.330130 0.0884581i
\(891\) 0 0
\(892\) 7.26795 7.26795i 0.243349 0.243349i
\(893\) 16.7303 9.65926i 0.559859 0.323235i
\(894\) 0 0
\(895\) −3.20577 11.9641i −0.107157 0.399916i
\(896\) 2.44949 0.0818317
\(897\) 0 0
\(898\) −3.85641 −0.128690
\(899\) 24.1110 + 89.9834i 0.804146 + 3.00111i
\(900\) 0 0
\(901\) 46.5167 26.8564i 1.54969 0.894717i
\(902\) 7.72741 7.72741i 0.257294 0.257294i
\(903\) 0 0
\(904\) 11.0622 + 2.96410i 0.367923 + 0.0985846i
\(905\) 1.69161 + 1.69161i 0.0562312 + 0.0562312i
\(906\) 0 0
\(907\) −4.16025 2.40192i −0.138139 0.0797546i 0.429338 0.903144i \(-0.358747\pi\)
−0.567477 + 0.823389i \(0.692080\pi\)
\(908\) −6.12372 + 1.64085i −0.203223 + 0.0544534i
\(909\) 0 0
\(910\) −4.26795 + 7.73205i −0.141481 + 0.256315i
\(911\) 10.2784i 0.340540i −0.985397 0.170270i \(-0.945536\pi\)
0.985397 0.170270i \(-0.0544639\pi\)
\(912\) 0 0
\(913\) −5.46410 + 9.46410i −0.180835 + 0.313216i
\(914\) −2.03339 3.52193i −0.0672585 0.116495i
\(915\) 0 0
\(916\) 4.83013 18.0263i 0.159592 0.595605i
\(917\) −4.15471 + 15.5056i −0.137201 + 0.512039i
\(918\) 0 0
\(919\) −0.392305 0.679492i −0.0129409 0.0224144i 0.859482 0.511165i \(-0.170786\pi\)
−0.872423 + 0.488751i \(0.837453\pi\)
\(920\) −0.258819 + 0.448288i −0.00853301 + 0.0147796i
\(921\) 0 0
\(922\) 29.2487i 0.963255i
\(923\) −1.01171 52.5897i −0.0333010 1.73101i
\(924\) 0 0
\(925\) −0.500000 + 0.133975i −0.0164399 + 0.00440506i
\(926\) 25.7196 + 14.8492i 0.845200 + 0.487976i
\(927\) 0 0
\(928\) −6.56218 6.56218i −0.215414 0.215414i
\(929\) −35.3925 9.48339i −1.16119 0.311140i −0.373749 0.927530i \(-0.621928\pi\)
−0.787441 + 0.616390i \(0.788595\pi\)
\(930\) 0 0
\(931\) 2.73205 2.73205i 0.0895393 0.0895393i
\(932\) −0.864390 + 0.499056i −0.0283140 + 0.0163471i
\(933\) 0 0
\(934\) 2.09808 + 7.83013i 0.0686512 + 0.256210i
\(935\) 5.27792 0.172606
\(936\) 0 0
\(937\) −5.07180 −0.165688 −0.0828442 0.996563i \(-0.526400\pi\)
−0.0828442 + 0.996563i \(0.526400\pi\)
\(938\) 2.68973 + 10.0382i 0.0878227 + 0.327759i
\(939\) 0 0
\(940\) −4.33013 + 2.50000i −0.141233 + 0.0815410i
\(941\) −31.1870 + 31.1870i −1.01667 + 1.01667i −0.0168093 + 0.999859i \(0.505351\pi\)
−0.999859 + 0.0168093i \(0.994649\pi\)
\(942\) 0 0
\(943\) 5.46410 + 1.46410i 0.177936 + 0.0476777i
\(944\) −9.71003 9.71003i −0.316034 0.316034i
\(945\) 0 0
\(946\) 10.7942 + 6.23205i 0.350951 + 0.202621i
\(947\) 34.0662 9.12802i 1.10700 0.296621i 0.341390 0.939922i \(-0.389102\pi\)
0.765613 + 0.643301i \(0.222436\pi\)
\(948\) 0 0
\(949\) −35.3923 19.5359i −1.14888 0.634162i
\(950\) 3.86370i 0.125355i
\(951\) 0 0
\(952\) 6.46410 11.1962i 0.209503 0.362869i
\(953\) 2.34297 + 4.05815i 0.0758964 + 0.131456i 0.901476 0.432830i \(-0.142485\pi\)
−0.825579 + 0.564286i \(0.809152\pi\)
\(954\) 0 0
\(955\) −3.09808 + 11.5622i −0.100251 + 0.374143i
\(956\) −3.95164 + 14.7477i −0.127805 + 0.476975i
\(957\) 0 0
\(958\) −2.70577 4.68653i −0.0874195 0.151415i
\(959\) 1.70522 2.95352i 0.0550644 0.0953743i
\(960\) 0 0
\(961\) 69.7654i 2.25050i
\(962\) 1.34486 + 1.29410i 0.0433601 + 0.0417233i
\(963\) 0 0
\(964\) 17.8923 4.79423i 0.576272 0.154412i
\(965\) −1.70522 0.984508i −0.0548929 0.0316924i
\(966\) 0 0
\(967\) −17.7321 17.7321i −0.570224 0.570224i 0.361967 0.932191i \(-0.382105\pi\)
−0.932191 + 0.361967i \(0.882105\pi\)
\(968\) 9.65926 + 2.58819i 0.310460 + 0.0831876i
\(969\) 0 0
\(970\) −1.26795 + 1.26795i −0.0407114 + 0.0407114i
\(971\) −20.3402 + 11.7434i −0.652748 + 0.376864i −0.789508 0.613740i \(-0.789664\pi\)
0.136760 + 0.990604i \(0.456331\pi\)
\(972\) 0 0
\(973\) 6.33975 + 23.6603i 0.203243 + 0.758513i
\(974\) 22.3500 0.716141
\(975\) 0 0
\(976\) 11.6603 0.373236
\(977\) 12.8852 + 48.0882i 0.412234 + 1.53848i 0.790312 + 0.612705i \(0.209919\pi\)
−0.378077 + 0.925774i \(0.623415\pi\)
\(978\) 0 0
\(979\) 8.83013 5.09808i 0.282212 0.162935i
\(980\) −0.707107 + 0.707107i −0.0225877 + 0.0225877i
\(981\) 0 0
\(982\) 6.83013 + 1.83013i 0.217958 + 0.0584017i
\(983\) −28.7883 28.7883i −0.918204 0.918204i 0.0786944 0.996899i \(-0.474925\pi\)
−0.996899 + 0.0786944i \(0.974925\pi\)
\(984\) 0 0
\(985\) −6.63397 3.83013i −0.211376 0.122038i
\(986\) −47.3118 + 12.6772i −1.50671 + 0.403723i
\(987\) 0 0
\(988\) 11.9282 7.19615i 0.379487 0.228940i
\(989\) 6.45189i 0.205158i
\(990\) 0 0
\(991\) 4.25833 7.37564i 0.135270 0.234295i −0.790430 0.612552i \(-0.790143\pi\)
0.925701 + 0.378257i \(0.123476\pi\)
\(992\) −5.01910 8.69333i −0.159357 0.276014i
\(993\) 0 0
\(994\) −9.24871 + 34.5167i −0.293351 + 1.09480i
\(995\) −6.59059 + 24.5964i −0.208936 + 0.779759i
\(996\) 0 0
\(997\) −24.0526 41.6603i −0.761752 1.31939i −0.941947 0.335762i \(-0.891006\pi\)
0.180195 0.983631i \(-0.442327\pi\)
\(998\) 21.4398 37.1349i 0.678666 1.17548i
\(999\) 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.a.1151.2 yes 8
3.2 odd 2 inner 1170.2.cu.a.1151.1 yes 8
13.2 odd 12 inner 1170.2.cu.a.431.1 8
39.2 even 12 inner 1170.2.cu.a.431.2 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1170.2.cu.a.431.1 8 13.2 odd 12 inner
1170.2.cu.a.431.2 yes 8 39.2 even 12 inner
1170.2.cu.a.1151.1 yes 8 3.2 odd 2 inner
1170.2.cu.a.1151.2 yes 8 1.1 even 1 trivial