Properties

Label 1710.2.p.c.37.6
Level $1710$
Weight $2$
Character 1710.37
Analytic conductor $13.654$
Analytic rank $0$
Dimension $20$
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] = [1710,2,Mod(37,1710)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1710, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1710.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1710.p (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(13.6544187456\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 108x^{16} + 1318x^{12} + 4652x^{8} + 5057x^{4} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{9} \)
Twist minimal: no (minimal twist has level 570)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 37.6
Root \(-0.850665 + 0.850665i\) of defining polynomial
Character \(\chi\) \(=\) 1710.37
Dual form 1710.2.p.c.1063.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-2.23583 + 0.0328054i) q^{5} +(-3.17648 - 3.17648i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-2.23583 + 0.0328054i) q^{5} +(-3.17648 - 3.17648i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.55777 + 1.60417i) q^{10} -1.49820 q^{11} +(2.38967 + 2.38967i) q^{13} -4.49222 q^{14} -1.00000 q^{16} +(-0.853306 - 0.853306i) q^{17} +(4.34485 + 0.349716i) q^{19} +(0.0328054 + 2.23583i) q^{20} +(-1.05939 + 1.05939i) q^{22} +(-4.67468 + 4.67468i) q^{23} +(4.99785 - 0.146694i) q^{25} +3.37950 q^{26} +(-3.17648 + 3.17648i) q^{28} -5.40423 q^{29} -0.364245i q^{31} +(-0.707107 + 0.707107i) q^{32} -1.20676 q^{34} +(7.20626 + 6.99785i) q^{35} +(-4.29845 + 4.29845i) q^{37} +(3.31956 - 2.82498i) q^{38} +(1.60417 + 1.55777i) q^{40} +1.79412i q^{41} +(0.623738 - 0.623738i) q^{43} +1.49820i q^{44} +6.61099i q^{46} +(5.24209 + 5.24209i) q^{47} +13.1800i q^{49} +(3.43028 - 3.63774i) q^{50} +(2.38967 - 2.38967i) q^{52} +(5.27391 + 5.27391i) q^{53} +(3.34972 - 0.0491491i) q^{55} +4.49222i q^{56} +(-3.82137 + 3.82137i) q^{58} -1.49134 q^{59} +15.2432 q^{61} +(-0.257560 - 0.257560i) q^{62} +1.00000i q^{64} +(-5.42128 - 5.26449i) q^{65} +(-0.989147 + 0.989147i) q^{67} +(-0.853306 + 0.853306i) q^{68} +(10.0438 - 0.147369i) q^{70} -8.98443i q^{71} +(-11.2572 + 11.2572i) q^{73} +6.07893i q^{74} +(0.349716 - 4.34485i) q^{76} +(4.75900 + 4.75900i) q^{77} -7.95317 q^{79} +(2.23583 - 0.0328054i) q^{80} +(1.26863 + 1.26863i) q^{82} +(-3.94546 + 3.94546i) q^{83} +(1.93584 + 1.87985i) q^{85} -0.882099i q^{86} +(1.05939 + 1.05939i) q^{88} +9.30909 q^{89} -15.1814i q^{91} +(4.67468 + 4.67468i) q^{92} +7.41343 q^{94} +(-9.72580 - 0.639371i) q^{95} +(-8.79952 + 8.79952i) q^{97} +(9.31967 + 9.31967i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 12 q^{5} - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 12 q^{5} - 4 q^{7} + 8 q^{11} - 20 q^{16} + 12 q^{17} + 4 q^{23} - 28 q^{25} - 24 q^{26} - 4 q^{28} - 4 q^{35} + 12 q^{38} - 12 q^{43} + 44 q^{47} + 64 q^{55} - 8 q^{58} + 24 q^{62} + 12 q^{68} - 4 q^{73} + 4 q^{76} - 88 q^{77} + 12 q^{80} - 8 q^{82} - 76 q^{83} - 12 q^{85} - 4 q^{92} + 24 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(1027\) \(1351\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) 0 0
\(4\) 1.00000i 0.500000i
\(5\) −2.23583 + 0.0328054i −0.999892 + 0.0146710i
\(6\) 0 0
\(7\) −3.17648 3.17648i −1.20060 1.20060i −0.973986 0.226610i \(-0.927236\pi\)
−0.226610 0.973986i \(-0.572764\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 0 0
\(10\) −1.55777 + 1.60417i −0.492611 + 0.507282i
\(11\) −1.49820 −0.451724 −0.225862 0.974159i \(-0.572520\pi\)
−0.225862 + 0.974159i \(0.572520\pi\)
\(12\) 0 0
\(13\) 2.38967 + 2.38967i 0.662774 + 0.662774i 0.956033 0.293259i \(-0.0947398\pi\)
−0.293259 + 0.956033i \(0.594740\pi\)
\(14\) −4.49222 −1.20060
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) −0.853306 0.853306i −0.206957 0.206957i 0.596016 0.802973i \(-0.296750\pi\)
−0.802973 + 0.596016i \(0.796750\pi\)
\(18\) 0 0
\(19\) 4.34485 + 0.349716i 0.996776 + 0.0802304i
\(20\) 0.0328054 + 2.23583i 0.00733551 + 0.499946i
\(21\) 0 0
\(22\) −1.05939 + 1.05939i −0.225862 + 0.225862i
\(23\) −4.67468 + 4.67468i −0.974737 + 0.974737i −0.999689 0.0249512i \(-0.992057\pi\)
0.0249512 + 0.999689i \(0.492057\pi\)
\(24\) 0 0
\(25\) 4.99785 0.146694i 0.999570 0.0293389i
\(26\) 3.37950 0.662774
\(27\) 0 0
\(28\) −3.17648 + 3.17648i −0.600298 + 0.600298i
\(29\) −5.40423 −1.00354 −0.501771 0.865001i \(-0.667318\pi\)
−0.501771 + 0.865001i \(0.667318\pi\)
\(30\) 0 0
\(31\) 0.364245i 0.0654204i −0.999465 0.0327102i \(-0.989586\pi\)
0.999465 0.0327102i \(-0.0104138\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) 0 0
\(34\) −1.20676 −0.206957
\(35\) 7.20626 + 6.99785i 1.21808 + 1.18285i
\(36\) 0 0
\(37\) −4.29845 + 4.29845i −0.706661 + 0.706661i −0.965832 0.259170i \(-0.916551\pi\)
0.259170 + 0.965832i \(0.416551\pi\)
\(38\) 3.31956 2.82498i 0.538503 0.458273i
\(39\) 0 0
\(40\) 1.60417 + 1.55777i 0.253641 + 0.246305i
\(41\) 1.79412i 0.280194i 0.990138 + 0.140097i \(0.0447415\pi\)
−0.990138 + 0.140097i \(0.955259\pi\)
\(42\) 0 0
\(43\) 0.623738 0.623738i 0.0951192 0.0951192i −0.657946 0.753065i \(-0.728574\pi\)
0.753065 + 0.657946i \(0.228574\pi\)
\(44\) 1.49820i 0.225862i
\(45\) 0 0
\(46\) 6.61099i 0.974737i
\(47\) 5.24209 + 5.24209i 0.764637 + 0.764637i 0.977157 0.212520i \(-0.0681670\pi\)
−0.212520 + 0.977157i \(0.568167\pi\)
\(48\) 0 0
\(49\) 13.1800i 1.88286i
\(50\) 3.43028 3.63774i 0.485115 0.514454i
\(51\) 0 0
\(52\) 2.38967 2.38967i 0.331387 0.331387i
\(53\) 5.27391 + 5.27391i 0.724427 + 0.724427i 0.969504 0.245077i \(-0.0788132\pi\)
−0.245077 + 0.969504i \(0.578813\pi\)
\(54\) 0 0
\(55\) 3.34972 0.0491491i 0.451676 0.00662726i
\(56\) 4.49222i 0.600298i
\(57\) 0 0
\(58\) −3.82137 + 3.82137i −0.501771 + 0.501771i
\(59\) −1.49134 −0.194156 −0.0970781 0.995277i \(-0.530950\pi\)
−0.0970781 + 0.995277i \(0.530950\pi\)
\(60\) 0 0
\(61\) 15.2432 1.95169 0.975844 0.218468i \(-0.0701060\pi\)
0.975844 + 0.218468i \(0.0701060\pi\)
\(62\) −0.257560 0.257560i −0.0327102 0.0327102i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) −5.42128 5.26449i −0.672426 0.652979i
\(66\) 0 0
\(67\) −0.989147 + 0.989147i −0.120844 + 0.120844i −0.764942 0.644099i \(-0.777233\pi\)
0.644099 + 0.764942i \(0.277233\pi\)
\(68\) −0.853306 + 0.853306i −0.103478 + 0.103478i
\(69\) 0 0
\(70\) 10.0438 0.147369i 1.20047 0.0176140i
\(71\) 8.98443i 1.06626i −0.846035 0.533128i \(-0.821016\pi\)
0.846035 0.533128i \(-0.178984\pi\)
\(72\) 0 0
\(73\) −11.2572 + 11.2572i −1.31756 + 1.31756i −0.401850 + 0.915706i \(0.631633\pi\)
−0.915706 + 0.401850i \(0.868367\pi\)
\(74\) 6.07893i 0.706661i
\(75\) 0 0
\(76\) 0.349716 4.34485i 0.0401152 0.498388i
\(77\) 4.75900 + 4.75900i 0.542338 + 0.542338i
\(78\) 0 0
\(79\) −7.95317 −0.894801 −0.447401 0.894334i \(-0.647650\pi\)
−0.447401 + 0.894334i \(0.647650\pi\)
\(80\) 2.23583 0.0328054i 0.249973 0.00366776i
\(81\) 0 0
\(82\) 1.26863 + 1.26863i 0.140097 + 0.140097i
\(83\) −3.94546 + 3.94546i −0.433071 + 0.433071i −0.889672 0.456601i \(-0.849067\pi\)
0.456601 + 0.889672i \(0.349067\pi\)
\(84\) 0 0
\(85\) 1.93584 + 1.87985i 0.209971 + 0.203898i
\(86\) 0.882099i 0.0951192i
\(87\) 0 0
\(88\) 1.05939 + 1.05939i 0.112931 + 0.112931i
\(89\) 9.30909 0.986762 0.493381 0.869813i \(-0.335761\pi\)
0.493381 + 0.869813i \(0.335761\pi\)
\(90\) 0 0
\(91\) 15.1814i 1.59145i
\(92\) 4.67468 + 4.67468i 0.487369 + 0.487369i
\(93\) 0 0
\(94\) 7.41343 0.764637
\(95\) −9.72580 0.639371i −0.997846 0.0655981i
\(96\) 0 0
\(97\) −8.79952 + 8.79952i −0.893456 + 0.893456i −0.994847 0.101391i \(-0.967671\pi\)
0.101391 + 0.994847i \(0.467671\pi\)
\(98\) 9.31967 + 9.31967i 0.941429 + 0.941429i
\(99\) 0 0
\(100\) −0.146694 4.99785i −0.0146694 0.499785i
\(101\) −2.17827 −0.216746 −0.108373 0.994110i \(-0.534564\pi\)
−0.108373 + 0.994110i \(0.534564\pi\)
\(102\) 0 0
\(103\) −9.44827 9.44827i −0.930966 0.930966i 0.0668005 0.997766i \(-0.478721\pi\)
−0.997766 + 0.0668005i \(0.978721\pi\)
\(104\) 3.37950i 0.331387i
\(105\) 0 0
\(106\) 7.45843 0.724427
\(107\) 0.300245 0.300245i 0.0290258 0.0290258i −0.692445 0.721471i \(-0.743466\pi\)
0.721471 + 0.692445i \(0.243466\pi\)
\(108\) 0 0
\(109\) −7.83545 −0.750500 −0.375250 0.926924i \(-0.622443\pi\)
−0.375250 + 0.926924i \(0.622443\pi\)
\(110\) 2.33385 2.40336i 0.222524 0.229151i
\(111\) 0 0
\(112\) 3.17648 + 3.17648i 0.300149 + 0.300149i
\(113\) 12.3606 + 12.3606i 1.16279 + 1.16279i 0.983862 + 0.178928i \(0.0572631\pi\)
0.178928 + 0.983862i \(0.442737\pi\)
\(114\) 0 0
\(115\) 10.2984 10.6051i 0.960332 0.988933i
\(116\) 5.40423i 0.501771i
\(117\) 0 0
\(118\) −1.05454 + 1.05454i −0.0970781 + 0.0970781i
\(119\) 5.42101i 0.496943i
\(120\) 0 0
\(121\) −8.75540 −0.795945
\(122\) 10.7786 10.7786i 0.975844 0.975844i
\(123\) 0 0
\(124\) −0.364245 −0.0327102
\(125\) −11.1695 + 0.491940i −0.999032 + 0.0440004i
\(126\) 0 0
\(127\) −8.31864 + 8.31864i −0.738160 + 0.738160i −0.972222 0.234062i \(-0.924798\pi\)
0.234062 + 0.972222i \(0.424798\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) 0 0
\(130\) −7.55598 + 0.110866i −0.662703 + 0.00972358i
\(131\) −8.07719 −0.705707 −0.352854 0.935679i \(-0.614789\pi\)
−0.352854 + 0.935679i \(0.614789\pi\)
\(132\) 0 0
\(133\) −12.6904 14.9122i −1.10040 1.29305i
\(134\) 1.39887i 0.120844i
\(135\) 0 0
\(136\) 1.20676i 0.103478i
\(137\) −6.99785 6.99785i −0.597866 0.597866i 0.341878 0.939744i \(-0.388937\pi\)
−0.939744 + 0.341878i \(0.888937\pi\)
\(138\) 0 0
\(139\) 10.8866i 0.923393i 0.887038 + 0.461696i \(0.152759\pi\)
−0.887038 + 0.461696i \(0.847241\pi\)
\(140\) 6.99785 7.20626i 0.591426 0.609040i
\(141\) 0 0
\(142\) −6.35295 6.35295i −0.533128 0.533128i
\(143\) −3.58020 3.58020i −0.299391 0.299391i
\(144\) 0 0
\(145\) 12.0829 0.177288i 1.00343 0.0147230i
\(146\) 15.9201i 1.31756i
\(147\) 0 0
\(148\) 4.29845 + 4.29845i 0.353331 + 0.353331i
\(149\) 12.6624i 1.03735i 0.854972 + 0.518674i \(0.173574\pi\)
−0.854972 + 0.518674i \(0.826426\pi\)
\(150\) 0 0
\(151\) 15.4280i 1.25551i −0.778411 0.627755i \(-0.783974\pi\)
0.778411 0.627755i \(-0.216026\pi\)
\(152\) −2.82498 3.31956i −0.229136 0.269252i
\(153\) 0 0
\(154\) 6.73024 0.542338
\(155\) 0.0119492 + 0.814389i 0.000959784 + 0.0654133i
\(156\) 0 0
\(157\) −13.2948 13.2948i −1.06104 1.06104i −0.998012 0.0630301i \(-0.979924\pi\)
−0.0630301 0.998012i \(-0.520076\pi\)
\(158\) −5.62374 + 5.62374i −0.447401 + 0.447401i
\(159\) 0 0
\(160\) 1.55777 1.60417i 0.123153 0.126820i
\(161\) 29.6980 2.34053
\(162\) 0 0
\(163\) 0.0438073 0.0438073i 0.00343125 0.00343125i −0.705389 0.708820i \(-0.749228\pi\)
0.708820 + 0.705389i \(0.249228\pi\)
\(164\) 1.79412 0.140097
\(165\) 0 0
\(166\) 5.57973i 0.433071i
\(167\) −6.61861 + 6.61861i −0.512164 + 0.512164i −0.915189 0.403025i \(-0.867959\pi\)
0.403025 + 0.915189i \(0.367959\pi\)
\(168\) 0 0
\(169\) 1.57899i 0.121461i
\(170\) 2.69810 0.0395881i 0.206935 0.00303627i
\(171\) 0 0
\(172\) −0.623738 0.623738i −0.0475596 0.0475596i
\(173\) −17.7594 17.7594i −1.35022 1.35022i −0.885412 0.464807i \(-0.846124\pi\)
−0.464807 0.885412i \(-0.653876\pi\)
\(174\) 0 0
\(175\) −16.3415 15.4096i −1.23530 1.16485i
\(176\) 1.49820 0.112931
\(177\) 0 0
\(178\) 6.58252 6.58252i 0.493381 0.493381i
\(179\) −9.00631 −0.673164 −0.336582 0.941654i \(-0.609271\pi\)
−0.336582 + 0.941654i \(0.609271\pi\)
\(180\) 0 0
\(181\) 18.7616i 1.39454i −0.716808 0.697271i \(-0.754398\pi\)
0.716808 0.697271i \(-0.245602\pi\)
\(182\) −10.7349 10.7349i −0.795724 0.795724i
\(183\) 0 0
\(184\) 6.61099 0.487369
\(185\) 9.46959 9.75161i 0.696218 0.716953i
\(186\) 0 0
\(187\) 1.27842 + 1.27842i 0.0934875 + 0.0934875i
\(188\) 5.24209 5.24209i 0.382319 0.382319i
\(189\) 0 0
\(190\) −7.32928 + 6.42508i −0.531722 + 0.466124i
\(191\) 6.38310 0.461865 0.230932 0.972970i \(-0.425822\pi\)
0.230932 + 0.972970i \(0.425822\pi\)
\(192\) 0 0
\(193\) 15.6976 + 15.6976i 1.12994 + 1.12994i 0.990186 + 0.139754i \(0.0446311\pi\)
0.139754 + 0.990186i \(0.455369\pi\)
\(194\) 12.4444i 0.893456i
\(195\) 0 0
\(196\) 13.1800 0.941429
\(197\) −2.62159 2.62159i −0.186780 0.186780i 0.607522 0.794303i \(-0.292164\pi\)
−0.794303 + 0.607522i \(0.792164\pi\)
\(198\) 0 0
\(199\) 6.73685i 0.477563i 0.971073 + 0.238781i \(0.0767479\pi\)
−0.971073 + 0.238781i \(0.923252\pi\)
\(200\) −3.63774 3.43028i −0.257227 0.242558i
\(201\) 0 0
\(202\) −1.54027 + 1.54027i −0.108373 + 0.108373i
\(203\) 17.1664 + 17.1664i 1.20485 + 1.20485i
\(204\) 0 0
\(205\) −0.0588568 4.01134i −0.00411073 0.280164i
\(206\) −13.3619 −0.930966
\(207\) 0 0
\(208\) −2.38967 2.38967i −0.165694 0.165694i
\(209\) −6.50945 0.523945i −0.450268 0.0362420i
\(210\) 0 0
\(211\) 15.1654i 1.04403i −0.852937 0.522013i \(-0.825181\pi\)
0.852937 0.522013i \(-0.174819\pi\)
\(212\) 5.27391 5.27391i 0.362213 0.362213i
\(213\) 0 0
\(214\) 0.424610i 0.0290258i
\(215\) −1.37411 + 1.41503i −0.0937135 + 0.0965045i
\(216\) 0 0
\(217\) −1.15702 + 1.15702i −0.0785434 + 0.0785434i
\(218\) −5.54050 + 5.54050i −0.375250 + 0.375250i
\(219\) 0 0
\(220\) −0.0491491 3.34972i −0.00331363 0.225838i
\(221\) 4.07823i 0.274332i
\(222\) 0 0
\(223\) 1.90756 + 1.90756i 0.127739 + 0.127739i 0.768086 0.640347i \(-0.221209\pi\)
−0.640347 + 0.768086i \(0.721209\pi\)
\(224\) 4.49222 0.300149
\(225\) 0 0
\(226\) 17.4806 1.16279
\(227\) 19.8625 19.8625i 1.31832 1.31832i 0.403212 0.915106i \(-0.367894\pi\)
0.915106 0.403212i \(-0.132106\pi\)
\(228\) 0 0
\(229\) 19.0279i 1.25740i 0.777648 + 0.628700i \(0.216413\pi\)
−0.777648 + 0.628700i \(0.783587\pi\)
\(230\) −0.216876 14.7810i −0.0143004 0.974633i
\(231\) 0 0
\(232\) 3.82137 + 3.82137i 0.250885 + 0.250885i
\(233\) 8.22028 8.22028i 0.538529 0.538529i −0.384568 0.923097i \(-0.625650\pi\)
0.923097 + 0.384568i \(0.125650\pi\)
\(234\) 0 0
\(235\) −11.8924 11.5484i −0.775773 0.753337i
\(236\) 1.49134i 0.0970781i
\(237\) 0 0
\(238\) 3.83323 + 3.83323i 0.248472 + 0.248472i
\(239\) 5.40164i 0.349403i −0.984621 0.174702i \(-0.944104\pi\)
0.984621 0.174702i \(-0.0558961\pi\)
\(240\) 0 0
\(241\) 24.3252i 1.56692i 0.621440 + 0.783462i \(0.286548\pi\)
−0.621440 + 0.783462i \(0.713452\pi\)
\(242\) −6.19100 + 6.19100i −0.397973 + 0.397973i
\(243\) 0 0
\(244\) 15.2432i 0.975844i
\(245\) −0.432375 29.4682i −0.0276235 1.88266i
\(246\) 0 0
\(247\) 9.54703 + 11.2184i 0.607463 + 0.713812i
\(248\) −0.257560 + 0.257560i −0.0163551 + 0.0163551i
\(249\) 0 0
\(250\) −7.55018 + 8.24589i −0.477516 + 0.521516i
\(251\) 28.4372 1.79494 0.897470 0.441075i \(-0.145403\pi\)
0.897470 + 0.441075i \(0.145403\pi\)
\(252\) 0 0
\(253\) 7.00360 7.00360i 0.440313 0.440313i
\(254\) 11.7643i 0.738160i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −14.1711 + 14.1711i −0.883966 + 0.883966i −0.993935 0.109969i \(-0.964925\pi\)
0.109969 + 0.993935i \(0.464925\pi\)
\(258\) 0 0
\(259\) 27.3079 1.69683
\(260\) −5.26449 + 5.42128i −0.326490 + 0.336213i
\(261\) 0 0
\(262\) −5.71144 + 5.71144i −0.352854 + 0.352854i
\(263\) 3.16396 3.16396i 0.195098 0.195098i −0.602797 0.797895i \(-0.705947\pi\)
0.797895 + 0.602797i \(0.205947\pi\)
\(264\) 0 0
\(265\) −11.9646 11.6185i −0.734977 0.713721i
\(266\) −19.5180 1.57100i −1.19673 0.0963243i
\(267\) 0 0
\(268\) 0.989147 + 0.989147i 0.0604218 + 0.0604218i
\(269\) 5.14967 0.313981 0.156990 0.987600i \(-0.449821\pi\)
0.156990 + 0.987600i \(0.449821\pi\)
\(270\) 0 0
\(271\) −9.33799 −0.567242 −0.283621 0.958936i \(-0.591536\pi\)
−0.283621 + 0.958936i \(0.591536\pi\)
\(272\) 0.853306 + 0.853306i 0.0517392 + 0.0517392i
\(273\) 0 0
\(274\) −9.89645 −0.597866
\(275\) −7.48777 + 0.219778i −0.451530 + 0.0132531i
\(276\) 0 0
\(277\) 6.94186 + 6.94186i 0.417096 + 0.417096i 0.884202 0.467106i \(-0.154703\pi\)
−0.467106 + 0.884202i \(0.654703\pi\)
\(278\) 7.69802 + 7.69802i 0.461696 + 0.461696i
\(279\) 0 0
\(280\) −0.147369 10.0438i −0.00880698 0.600233i
\(281\) 13.9366i 0.831390i −0.909504 0.415695i \(-0.863538\pi\)
0.909504 0.415695i \(-0.136462\pi\)
\(282\) 0 0
\(283\) −13.0086 + 13.0086i −0.773280 + 0.773280i −0.978678 0.205399i \(-0.934151\pi\)
0.205399 + 0.978678i \(0.434151\pi\)
\(284\) −8.98443 −0.533128
\(285\) 0 0
\(286\) −5.06316 −0.299391
\(287\) 5.69897 5.69897i 0.336400 0.336400i
\(288\) 0 0
\(289\) 15.5437i 0.914338i
\(290\) 8.41856 8.66929i 0.494355 0.509078i
\(291\) 0 0
\(292\) 11.2572 + 11.2572i 0.658778 + 0.658778i
\(293\) −11.5186 11.5186i −0.672924 0.672924i 0.285465 0.958389i \(-0.407852\pi\)
−0.958389 + 0.285465i \(0.907852\pi\)
\(294\) 0 0
\(295\) 3.33438 0.0489241i 0.194135 0.00284847i
\(296\) 6.07893 0.353331
\(297\) 0 0
\(298\) 8.95370 + 8.95370i 0.518674 + 0.518674i
\(299\) −22.3418 −1.29206
\(300\) 0 0
\(301\) −3.96258 −0.228399
\(302\) −10.9092 10.9092i −0.627755 0.627755i
\(303\) 0 0
\(304\) −4.34485 0.349716i −0.249194 0.0200576i
\(305\) −34.0811 + 0.500058i −1.95148 + 0.0286333i
\(306\) 0 0
\(307\) 19.8832 19.8832i 1.13480 1.13480i 0.145427 0.989369i \(-0.453545\pi\)
0.989369 0.145427i \(-0.0464555\pi\)
\(308\) 4.75900 4.75900i 0.271169 0.271169i
\(309\) 0 0
\(310\) 0.584310 + 0.567411i 0.0331866 + 0.0322268i
\(311\) −25.6191 −1.45272 −0.726362 0.687312i \(-0.758790\pi\)
−0.726362 + 0.687312i \(0.758790\pi\)
\(312\) 0 0
\(313\) −1.42367 + 1.42367i −0.0804705 + 0.0804705i −0.746196 0.665726i \(-0.768122\pi\)
0.665726 + 0.746196i \(0.268122\pi\)
\(314\) −18.8017 −1.06104
\(315\) 0 0
\(316\) 7.95317i 0.447401i
\(317\) −22.0096 + 22.0096i −1.23618 + 1.23618i −0.274630 + 0.961550i \(0.588555\pi\)
−0.961550 + 0.274630i \(0.911445\pi\)
\(318\) 0 0
\(319\) 8.09662 0.453324
\(320\) −0.0328054 2.23583i −0.00183388 0.124987i
\(321\) 0 0
\(322\) 20.9997 20.9997i 1.17027 1.17027i
\(323\) −3.40907 4.00590i −0.189686 0.222894i
\(324\) 0 0
\(325\) 12.2937 + 11.5926i 0.681934 + 0.643044i
\(326\) 0.0619528i 0.00343125i
\(327\) 0 0
\(328\) 1.26863 1.26863i 0.0700485 0.0700485i
\(329\) 33.3027i 1.83604i
\(330\) 0 0
\(331\) 19.0483i 1.04699i 0.852028 + 0.523496i \(0.175372\pi\)
−0.852028 + 0.523496i \(0.824628\pi\)
\(332\) 3.94546 + 3.94546i 0.216535 + 0.216535i
\(333\) 0 0
\(334\) 9.36013i 0.512164i
\(335\) 2.17911 2.24401i 0.119058 0.122603i
\(336\) 0 0
\(337\) −10.2649 + 10.2649i −0.559164 + 0.559164i −0.929069 0.369905i \(-0.879390\pi\)
0.369905 + 0.929069i \(0.379390\pi\)
\(338\) −1.11651 1.11651i −0.0607304 0.0607304i
\(339\) 0 0
\(340\) 1.87985 1.93584i 0.101949 0.104985i
\(341\) 0.545712i 0.0295520i
\(342\) 0 0
\(343\) 19.6306 19.6306i 1.05996 1.05996i
\(344\) −0.882099 −0.0475596
\(345\) 0 0
\(346\) −25.1155 −1.35022
\(347\) 21.2020 + 21.2020i 1.13818 + 1.13818i 0.988776 + 0.149404i \(0.0477356\pi\)
0.149404 + 0.988776i \(0.452264\pi\)
\(348\) 0 0
\(349\) 19.7333i 1.05630i 0.849152 + 0.528148i \(0.177114\pi\)
−0.849152 + 0.528148i \(0.822886\pi\)
\(350\) −22.4514 + 0.658983i −1.20008 + 0.0352241i
\(351\) 0 0
\(352\) 1.05939 1.05939i 0.0564655 0.0564655i
\(353\) −18.4563 + 18.4563i −0.982329 + 0.982329i −0.999847 0.0175180i \(-0.994424\pi\)
0.0175180 + 0.999847i \(0.494424\pi\)
\(354\) 0 0
\(355\) 0.294738 + 20.0876i 0.0156431 + 1.06614i
\(356\) 9.30909i 0.493381i
\(357\) 0 0
\(358\) −6.36843 + 6.36843i −0.336582 + 0.336582i
\(359\) 1.52209i 0.0803327i −0.999193 0.0401663i \(-0.987211\pi\)
0.999193 0.0401663i \(-0.0127888\pi\)
\(360\) 0 0
\(361\) 18.7554 + 3.03893i 0.987126 + 0.159944i
\(362\) −13.2665 13.2665i −0.697271 0.697271i
\(363\) 0 0
\(364\) −15.1814 −0.795724
\(365\) 24.7999 25.5384i 1.29808 1.33674i
\(366\) 0 0
\(367\) −15.6342 15.6342i −0.816099 0.816099i 0.169442 0.985540i \(-0.445804\pi\)
−0.985540 + 0.169442i \(0.945804\pi\)
\(368\) 4.67468 4.67468i 0.243684 0.243684i
\(369\) 0 0
\(370\) −0.199422 13.5914i −0.0103674 0.706585i
\(371\) 33.5049i 1.73949i
\(372\) 0 0
\(373\) −10.2074 10.2074i −0.528520 0.528520i 0.391611 0.920131i \(-0.371918\pi\)
−0.920131 + 0.391611i \(0.871918\pi\)
\(374\) 1.80796 0.0934875
\(375\) 0 0
\(376\) 7.41343i 0.382319i
\(377\) −12.9143 12.9143i −0.665121 0.665121i
\(378\) 0 0
\(379\) −17.3997 −0.893762 −0.446881 0.894593i \(-0.647465\pi\)
−0.446881 + 0.894593i \(0.647465\pi\)
\(380\) −0.639371 + 9.72580i −0.0327990 + 0.498923i
\(381\) 0 0
\(382\) 4.51353 4.51353i 0.230932 0.230932i
\(383\) 14.2959 + 14.2959i 0.730485 + 0.730485i 0.970716 0.240231i \(-0.0772230\pi\)
−0.240231 + 0.970716i \(0.577223\pi\)
\(384\) 0 0
\(385\) −10.7964 10.4842i −0.550236 0.534323i
\(386\) 22.1998 1.12994
\(387\) 0 0
\(388\) 8.79952 + 8.79952i 0.446728 + 0.446728i
\(389\) 11.0275i 0.559116i 0.960129 + 0.279558i \(0.0901879\pi\)
−0.960129 + 0.279558i \(0.909812\pi\)
\(390\) 0 0
\(391\) 7.97786 0.403457
\(392\) 9.31967 9.31967i 0.470715 0.470715i
\(393\) 0 0
\(394\) −3.70748 −0.186780
\(395\) 17.7819 0.260907i 0.894705 0.0131276i
\(396\) 0 0
\(397\) −1.09266 1.09266i −0.0548392 0.0548392i 0.679155 0.733995i \(-0.262346\pi\)
−0.733995 + 0.679155i \(0.762346\pi\)
\(398\) 4.76367 + 4.76367i 0.238781 + 0.238781i
\(399\) 0 0
\(400\) −4.99785 + 0.146694i −0.249892 + 0.00733472i
\(401\) 13.6821i 0.683249i 0.939836 + 0.341625i \(0.110977\pi\)
−0.939836 + 0.341625i \(0.889023\pi\)
\(402\) 0 0
\(403\) 0.870424 0.870424i 0.0433589 0.0433589i
\(404\) 2.17827i 0.108373i
\(405\) 0 0
\(406\) 24.2770 1.20485
\(407\) 6.43994 6.43994i 0.319216 0.319216i
\(408\) 0 0
\(409\) −13.9275 −0.688673 −0.344336 0.938846i \(-0.611896\pi\)
−0.344336 + 0.938846i \(0.611896\pi\)
\(410\) −2.87806 2.79483i −0.142137 0.138027i
\(411\) 0 0
\(412\) −9.44827 + 9.44827i −0.465483 + 0.465483i
\(413\) 4.73721 + 4.73721i 0.233103 + 0.233103i
\(414\) 0 0
\(415\) 8.69194 8.95080i 0.426670 0.439378i
\(416\) −3.37950 −0.165694
\(417\) 0 0
\(418\) −4.97336 + 4.23239i −0.243255 + 0.207013i
\(419\) 31.7859i 1.55284i −0.630215 0.776421i \(-0.717033\pi\)
0.630215 0.776421i \(-0.282967\pi\)
\(420\) 0 0
\(421\) 29.9617i 1.46025i 0.683316 + 0.730123i \(0.260537\pi\)
−0.683316 + 0.730123i \(0.739463\pi\)
\(422\) −10.7235 10.7235i −0.522013 0.522013i
\(423\) 0 0
\(424\) 7.45843i 0.362213i
\(425\) −4.38987 4.13952i −0.212940 0.200796i
\(426\) 0 0
\(427\) −48.4196 48.4196i −2.34319 2.34319i
\(428\) −0.300245 0.300245i −0.0145129 0.0145129i
\(429\) 0 0
\(430\) 0.0289376 + 1.97222i 0.00139550 + 0.0951090i
\(431\) 19.4154i 0.935207i 0.883938 + 0.467603i \(0.154882\pi\)
−0.883938 + 0.467603i \(0.845118\pi\)
\(432\) 0 0
\(433\) −5.53848 5.53848i −0.266162 0.266162i 0.561390 0.827552i \(-0.310267\pi\)
−0.827552 + 0.561390i \(0.810267\pi\)
\(434\) 1.63627i 0.0785434i
\(435\) 0 0
\(436\) 7.83545i 0.375250i
\(437\) −21.9456 + 18.6759i −1.04980 + 0.893392i
\(438\) 0 0
\(439\) −19.2533 −0.918908 −0.459454 0.888202i \(-0.651955\pi\)
−0.459454 + 0.888202i \(0.651955\pi\)
\(440\) −2.40336 2.33385i −0.114576 0.111262i
\(441\) 0 0
\(442\) −2.88374 2.88374i −0.137166 0.137166i
\(443\) 0.822360 0.822360i 0.0390715 0.0390715i −0.687301 0.726373i \(-0.741205\pi\)
0.726373 + 0.687301i \(0.241205\pi\)
\(444\) 0 0
\(445\) −20.8135 + 0.305388i −0.986655 + 0.0144768i
\(446\) 2.69769 0.127739
\(447\) 0 0
\(448\) 3.17648 3.17648i 0.150074 0.150074i
\(449\) 34.0243 1.60570 0.802852 0.596178i \(-0.203315\pi\)
0.802852 + 0.596178i \(0.203315\pi\)
\(450\) 0 0
\(451\) 2.68795i 0.126570i
\(452\) 12.3606 12.3606i 0.581395 0.581395i
\(453\) 0 0
\(454\) 28.0898i 1.31832i
\(455\) 0.498033 + 33.9431i 0.0233482 + 1.59128i
\(456\) 0 0
\(457\) 26.2360 + 26.2360i 1.22727 + 1.22727i 0.964994 + 0.262273i \(0.0844722\pi\)
0.262273 + 0.964994i \(0.415528\pi\)
\(458\) 13.4548 + 13.4548i 0.628700 + 0.628700i
\(459\) 0 0
\(460\) −10.6051 10.2984i −0.494466 0.480166i
\(461\) 26.7535 1.24604 0.623018 0.782207i \(-0.285906\pi\)
0.623018 + 0.782207i \(0.285906\pi\)
\(462\) 0 0
\(463\) −16.5215 + 16.5215i −0.767820 + 0.767820i −0.977722 0.209902i \(-0.932685\pi\)
0.209902 + 0.977722i \(0.432685\pi\)
\(464\) 5.40423 0.250885
\(465\) 0 0
\(466\) 11.6252i 0.538529i
\(467\) −6.89955 6.89955i −0.319273 0.319273i 0.529215 0.848488i \(-0.322487\pi\)
−0.848488 + 0.529215i \(0.822487\pi\)
\(468\) 0 0
\(469\) 6.28401 0.290168
\(470\) −16.5752 + 0.243201i −0.764555 + 0.0112180i
\(471\) 0 0
\(472\) 1.05454 + 1.05454i 0.0485391 + 0.0485391i
\(473\) −0.934485 + 0.934485i −0.0429677 + 0.0429677i
\(474\) 0 0
\(475\) 21.7662 + 1.11046i 0.998701 + 0.0509516i
\(476\) 5.42101 0.248472
\(477\) 0 0
\(478\) −3.81954 3.81954i −0.174702 0.174702i
\(479\) 10.1104i 0.461958i 0.972959 + 0.230979i \(0.0741929\pi\)
−0.972959 + 0.230979i \(0.925807\pi\)
\(480\) 0 0
\(481\) −20.5437 −0.936714
\(482\) 17.2005 + 17.2005i 0.783462 + 0.783462i
\(483\) 0 0
\(484\) 8.75540i 0.397973i
\(485\) 19.3855 19.9629i 0.880252 0.906468i
\(486\) 0 0
\(487\) −19.5066 + 19.5066i −0.883928 + 0.883928i −0.993931 0.110003i \(-0.964914\pi\)
0.110003 + 0.993931i \(0.464914\pi\)
\(488\) −10.7786 10.7786i −0.487922 0.487922i
\(489\) 0 0
\(490\) −21.1429 20.5314i −0.955140 0.927516i
\(491\) 14.0700 0.634970 0.317485 0.948263i \(-0.397162\pi\)
0.317485 + 0.948263i \(0.397162\pi\)
\(492\) 0 0
\(493\) 4.61146 + 4.61146i 0.207690 + 0.207690i
\(494\) 14.6834 + 1.18187i 0.660638 + 0.0531747i
\(495\) 0 0
\(496\) 0.364245i 0.0163551i
\(497\) −28.5388 + 28.5388i −1.28014 + 1.28014i
\(498\) 0 0
\(499\) 4.43607i 0.198586i −0.995058 0.0992929i \(-0.968342\pi\)
0.995058 0.0992929i \(-0.0316581\pi\)
\(500\) 0.491940 + 11.1695i 0.0220002 + 0.499516i
\(501\) 0 0
\(502\) 20.1081 20.1081i 0.897470 0.897470i
\(503\) 3.35985 3.35985i 0.149808 0.149808i −0.628224 0.778032i \(-0.716218\pi\)
0.778032 + 0.628224i \(0.216218\pi\)
\(504\) 0 0
\(505\) 4.87023 0.0714589i 0.216722 0.00317988i
\(506\) 9.90459i 0.440313i
\(507\) 0 0
\(508\) 8.31864 + 8.31864i 0.369080 + 0.369080i
\(509\) −37.6552 −1.66904 −0.834519 0.550979i \(-0.814254\pi\)
−0.834519 + 0.550979i \(0.814254\pi\)
\(510\) 0 0
\(511\) 71.5164 3.16370
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 0 0
\(514\) 20.0409i 0.883966i
\(515\) 21.4347 + 20.8147i 0.944524 + 0.917207i
\(516\) 0 0
\(517\) −7.85370 7.85370i −0.345405 0.345405i
\(518\) 19.3096 19.3096i 0.848414 0.848414i
\(519\) 0 0
\(520\) 0.110866 + 7.55598i 0.00486179 + 0.331351i
\(521\) 27.2139i 1.19226i −0.802887 0.596131i \(-0.796704\pi\)
0.802887 0.596131i \(-0.203296\pi\)
\(522\) 0 0
\(523\) −11.9984 11.9984i −0.524655 0.524655i 0.394319 0.918974i \(-0.370981\pi\)
−0.918974 + 0.394319i \(0.870981\pi\)
\(524\) 8.07719i 0.352854i
\(525\) 0 0
\(526\) 4.47451i 0.195098i
\(527\) −0.310812 + 0.310812i −0.0135392 + 0.0135392i
\(528\) 0 0
\(529\) 20.7052i 0.900226i
\(530\) −16.6758 + 0.244677i −0.724349 + 0.0106281i
\(531\) 0 0
\(532\) −14.9122 + 12.6904i −0.646525 + 0.550200i
\(533\) −4.28734 + 4.28734i −0.185705 + 0.185705i
\(534\) 0 0
\(535\) −0.661446 + 0.681146i −0.0285968 + 0.0294485i
\(536\) 1.39887 0.0604218
\(537\) 0 0
\(538\) 3.64136 3.64136i 0.156990 0.156990i
\(539\) 19.7463i 0.850533i
\(540\) 0 0
\(541\) −2.33439 −0.100363 −0.0501816 0.998740i \(-0.515980\pi\)
−0.0501816 + 0.998740i \(0.515980\pi\)
\(542\) −6.60295 + 6.60295i −0.283621 + 0.283621i
\(543\) 0 0
\(544\) 1.20676 0.0517392
\(545\) 17.5187 0.257045i 0.750420 0.0110106i
\(546\) 0 0
\(547\) 8.46036 8.46036i 0.361739 0.361739i −0.502714 0.864453i \(-0.667665\pi\)
0.864453 + 0.502714i \(0.167665\pi\)
\(548\) −6.99785 + 6.99785i −0.298933 + 0.298933i
\(549\) 0 0
\(550\) −5.13925 + 5.45006i −0.219138 + 0.232391i
\(551\) −23.4806 1.88995i −1.00031 0.0805145i
\(552\) 0 0
\(553\) 25.2630 + 25.2630i 1.07429 + 1.07429i
\(554\) 9.81727 0.417096
\(555\) 0 0
\(556\) 10.8866 0.461696
\(557\) −14.2030 14.2030i −0.601801 0.601801i 0.338989 0.940790i \(-0.389915\pi\)
−0.940790 + 0.338989i \(0.889915\pi\)
\(558\) 0 0
\(559\) 2.98105 0.126085
\(560\) −7.20626 6.99785i −0.304520 0.295713i
\(561\) 0 0
\(562\) −9.85468 9.85468i −0.415695 0.415695i
\(563\) −30.8429 30.8429i −1.29987 1.29987i −0.928472 0.371401i \(-0.878877\pi\)
−0.371401 0.928472i \(-0.621123\pi\)
\(564\) 0 0
\(565\) −28.0417 27.2307i −1.17972 1.14561i
\(566\) 18.3969i 0.773280i
\(567\) 0 0
\(568\) −6.35295 + 6.35295i −0.266564 + 0.266564i
\(569\) 13.5457 0.567864 0.283932 0.958844i \(-0.408361\pi\)
0.283932 + 0.958844i \(0.408361\pi\)
\(570\) 0 0
\(571\) 10.5825 0.442863 0.221431 0.975176i \(-0.428927\pi\)
0.221431 + 0.975176i \(0.428927\pi\)
\(572\) −3.58020 + 3.58020i −0.149696 + 0.149696i
\(573\) 0 0
\(574\) 8.05956i 0.336400i
\(575\) −22.6776 + 24.0491i −0.945720 + 1.00292i
\(576\) 0 0
\(577\) −4.85640 4.85640i −0.202175 0.202175i 0.598757 0.800931i \(-0.295662\pi\)
−0.800931 + 0.598757i \(0.795662\pi\)
\(578\) −10.9911 10.9911i −0.457169 0.457169i
\(579\) 0 0
\(580\) −0.177288 12.0829i −0.00736149 0.501717i
\(581\) 25.0653 1.03989
\(582\) 0 0
\(583\) −7.90137 7.90137i −0.327241 0.327241i
\(584\) 15.9201 0.658778
\(585\) 0 0
\(586\) −16.2898 −0.672924
\(587\) −7.59468 7.59468i −0.313466 0.313466i 0.532785 0.846251i \(-0.321146\pi\)
−0.846251 + 0.532785i \(0.821146\pi\)
\(588\) 0 0
\(589\) 0.127383 1.58259i 0.00524870 0.0652095i
\(590\) 2.32317 2.39236i 0.0956434 0.0984919i
\(591\) 0 0
\(592\) 4.29845 4.29845i 0.176665 0.176665i
\(593\) −16.8852 + 16.8852i −0.693392 + 0.693392i −0.962977 0.269585i \(-0.913114\pi\)
0.269585 + 0.962977i \(0.413114\pi\)
\(594\) 0 0
\(595\) −0.177838 12.1204i −0.00729066 0.496890i
\(596\) 12.6624 0.518674
\(597\) 0 0
\(598\) −15.7981 + 15.7981i −0.646031 + 0.646031i
\(599\) 40.3029 1.64673 0.823365 0.567512i \(-0.192094\pi\)
0.823365 + 0.567512i \(0.192094\pi\)
\(600\) 0 0
\(601\) 37.1125i 1.51385i −0.653503 0.756924i \(-0.726701\pi\)
0.653503 0.756924i \(-0.273299\pi\)
\(602\) −2.80197 + 2.80197i −0.114200 + 0.114200i
\(603\) 0 0
\(604\) −15.4280 −0.627755
\(605\) 19.5756 0.287224i 0.795860 0.0116773i
\(606\) 0 0
\(607\) 21.9049 21.9049i 0.889091 0.889091i −0.105345 0.994436i \(-0.533595\pi\)
0.994436 + 0.105345i \(0.0335945\pi\)
\(608\) −3.31956 + 2.82498i −0.134626 + 0.114568i
\(609\) 0 0
\(610\) −23.7454 + 24.4526i −0.961422 + 0.990056i
\(611\) 25.0537i 1.01356i
\(612\) 0 0
\(613\) 3.66633 3.66633i 0.148082 0.148082i −0.629179 0.777261i \(-0.716609\pi\)
0.777261 + 0.629179i \(0.216609\pi\)
\(614\) 28.1191i 1.13480i
\(615\) 0 0
\(616\) 6.73024i 0.271169i
\(617\) 21.5484 + 21.5484i 0.867507 + 0.867507i 0.992196 0.124689i \(-0.0397932\pi\)
−0.124689 + 0.992196i \(0.539793\pi\)
\(618\) 0 0
\(619\) 23.0888i 0.928017i 0.885831 + 0.464008i \(0.153589\pi\)
−0.885831 + 0.464008i \(0.846411\pi\)
\(620\) 0.814389 0.0119492i 0.0327067 0.000479892i
\(621\) 0 0
\(622\) −18.1154 + 18.1154i −0.726362 + 0.726362i
\(623\) −29.5701 29.5701i −1.18470 1.18470i
\(624\) 0 0
\(625\) 24.9570 1.46631i 0.998278 0.0586525i
\(626\) 2.01337i 0.0804705i
\(627\) 0 0
\(628\) −13.2948 + 13.2948i −0.530521 + 0.530521i
\(629\) 7.33579 0.292497
\(630\) 0 0
\(631\) 37.3658 1.48751 0.743754 0.668453i \(-0.233043\pi\)
0.743754 + 0.668453i \(0.233043\pi\)
\(632\) 5.62374 + 5.62374i 0.223700 + 0.223700i
\(633\) 0 0
\(634\) 31.1262i 1.23618i
\(635\) 18.3262 18.8719i 0.727251 0.748910i
\(636\) 0 0
\(637\) −31.4958 + 31.4958i −1.24791 + 1.24791i
\(638\) 5.72518 5.72518i 0.226662 0.226662i
\(639\) 0 0
\(640\) −1.60417 1.55777i −0.0634102 0.0615763i
\(641\) 35.6140i 1.40667i 0.710859 + 0.703335i \(0.248307\pi\)
−0.710859 + 0.703335i \(0.751693\pi\)
\(642\) 0 0
\(643\) −35.3543 + 35.3543i −1.39424 + 1.39424i −0.578694 + 0.815545i \(0.696437\pi\)
−0.815545 + 0.578694i \(0.803563\pi\)
\(644\) 29.6980i 1.17027i
\(645\) 0 0
\(646\) −5.24317 0.422022i −0.206290 0.0166042i
\(647\) −20.9716 20.9716i −0.824480 0.824480i 0.162267 0.986747i \(-0.448120\pi\)
−0.986747 + 0.162267i \(0.948120\pi\)
\(648\) 0 0
\(649\) 2.23433 0.0877051
\(650\) 16.8902 0.495754i 0.662489 0.0194451i
\(651\) 0 0
\(652\) −0.0438073 0.0438073i −0.00171563 0.00171563i
\(653\) −31.2511 + 31.2511i −1.22295 + 1.22295i −0.256372 + 0.966578i \(0.582527\pi\)
−0.966578 + 0.256372i \(0.917473\pi\)
\(654\) 0 0
\(655\) 18.0592 0.264975i 0.705631 0.0103534i
\(656\) 1.79412i 0.0700485i
\(657\) 0 0
\(658\) −23.5486 23.5486i −0.918020 0.918020i
\(659\) 32.1135 1.25097 0.625483 0.780238i \(-0.284902\pi\)
0.625483 + 0.780238i \(0.284902\pi\)
\(660\) 0 0
\(661\) 1.31818i 0.0512712i 0.999671 + 0.0256356i \(0.00816097\pi\)
−0.999671 + 0.0256356i \(0.991839\pi\)
\(662\) 13.4692 + 13.4692i 0.523496 + 0.523496i
\(663\) 0 0
\(664\) 5.57973 0.216535
\(665\) 28.8628 + 32.9247i 1.11925 + 1.27677i
\(666\) 0 0
\(667\) 25.2630 25.2630i 0.978189 0.978189i
\(668\) 6.61861 + 6.61861i 0.256082 + 0.256082i
\(669\) 0 0
\(670\) −0.0458903 3.12762i −0.00177290 0.120831i
\(671\) −22.8373 −0.881625
\(672\) 0 0
\(673\) −2.51419 2.51419i −0.0969147 0.0969147i 0.656987 0.753902i \(-0.271831\pi\)
−0.753902 + 0.656987i \(0.771831\pi\)
\(674\) 14.5167i 0.559164i
\(675\) 0 0
\(676\) −1.57899 −0.0607304
\(677\) −18.7510 + 18.7510i −0.720658 + 0.720658i −0.968739 0.248081i \(-0.920200\pi\)
0.248081 + 0.968739i \(0.420200\pi\)
\(678\) 0 0
\(679\) 55.9030 2.14536
\(680\) −0.0395881 2.69810i −0.00151814 0.103467i
\(681\) 0 0
\(682\) 0.385877 + 0.385877i 0.0147760 + 0.0147760i
\(683\) −17.3262 17.3262i −0.662968 0.662968i 0.293110 0.956079i \(-0.405310\pi\)
−0.956079 + 0.293110i \(0.905310\pi\)
\(684\) 0 0
\(685\) 15.8755 + 15.4164i 0.606573 + 0.589031i
\(686\) 27.7619i 1.05996i
\(687\) 0 0
\(688\) −0.623738 + 0.623738i −0.0237798 + 0.0237798i
\(689\) 25.2058i 0.960263i
\(690\) 0 0
\(691\) −10.3859 −0.395097 −0.197549 0.980293i \(-0.563298\pi\)
−0.197549 + 0.980293i \(0.563298\pi\)
\(692\) −17.7594 + 17.7594i −0.675110 + 0.675110i
\(693\) 0 0
\(694\) 29.9841 1.13818
\(695\) −0.357141 24.3406i −0.0135471 0.923293i
\(696\) 0 0
\(697\) 1.53093 1.53093i 0.0579881 0.0579881i
\(698\) 13.9535 + 13.9535i 0.528148 + 0.528148i
\(699\) 0 0
\(700\) −15.4096 + 16.3415i −0.582427 + 0.617651i
\(701\) −31.8741 −1.20387 −0.601934 0.798546i \(-0.705603\pi\)
−0.601934 + 0.798546i \(0.705603\pi\)
\(702\) 0 0
\(703\) −20.1794 + 17.1729i −0.761079 + 0.647688i
\(704\) 1.49820i 0.0564655i
\(705\) 0 0
\(706\) 26.1011i 0.982329i
\(707\) 6.91921 + 6.91921i 0.260224 + 0.260224i
\(708\) 0 0
\(709\) 13.1134i 0.492483i 0.969209 + 0.246241i \(0.0791956\pi\)
−0.969209 + 0.246241i \(0.920804\pi\)
\(710\) 14.4125 + 13.9957i 0.540892 + 0.525249i
\(711\) 0 0
\(712\) −6.58252 6.58252i −0.246690 0.246690i
\(713\) 1.70273 + 1.70273i 0.0637677 + 0.0637677i
\(714\) 0 0
\(715\) 8.12215 + 7.88725i 0.303751 + 0.294967i
\(716\) 9.00631i 0.336582i
\(717\) 0 0
\(718\) −1.07628 1.07628i −0.0401663 0.0401663i
\(719\) 16.8894i 0.629869i 0.949113 + 0.314935i \(0.101983\pi\)
−0.949113 + 0.314935i \(0.898017\pi\)
\(720\) 0 0
\(721\) 60.0244i 2.23543i
\(722\) 15.4109 11.1132i 0.573535 0.413591i
\(723\) 0 0
\(724\) −18.7616 −0.697271
\(725\) −27.0095 + 0.792771i −1.00311 + 0.0294428i
\(726\) 0 0
\(727\) 10.7209 + 10.7209i 0.397617 + 0.397617i 0.877392 0.479775i \(-0.159282\pi\)
−0.479775 + 0.877392i \(0.659282\pi\)
\(728\) −10.7349 + 10.7349i −0.397862 + 0.397862i
\(729\) 0 0
\(730\) −0.522265 35.5946i −0.0193299 1.31741i
\(731\) −1.06448 −0.0393712
\(732\) 0 0
\(733\) −24.7783 + 24.7783i −0.915207 + 0.915207i −0.996676 0.0814690i \(-0.974039\pi\)
0.0814690 + 0.996676i \(0.474039\pi\)
\(734\) −22.1101 −0.816099
\(735\) 0 0
\(736\) 6.61099i 0.243684i
\(737\) 1.48194 1.48194i 0.0545880 0.0545880i
\(738\) 0 0
\(739\) 0.497280i 0.0182928i −0.999958 0.00914638i \(-0.997089\pi\)
0.999958 0.00914638i \(-0.00291142\pi\)
\(740\) −9.75161 9.46959i −0.358476 0.348109i
\(741\) 0 0
\(742\) −23.6915 23.6915i −0.869743 0.869743i
\(743\) −15.6060 15.6060i −0.572529 0.572529i 0.360305 0.932835i \(-0.382673\pi\)
−0.932835 + 0.360305i \(0.882673\pi\)
\(744\) 0 0
\(745\) −0.415396 28.3110i −0.0152189 1.03724i
\(746\) −14.4355 −0.528520
\(747\) 0 0
\(748\) 1.27842 1.27842i 0.0467438 0.0467438i
\(749\) −1.90744 −0.0696964
\(750\) 0 0
\(751\) 5.39804i 0.196977i −0.995138 0.0984887i \(-0.968599\pi\)
0.995138 0.0984887i \(-0.0314008\pi\)
\(752\) −5.24209 5.24209i −0.191159 0.191159i
\(753\) 0 0
\(754\) −18.2636 −0.665121
\(755\) 0.506121 + 34.4943i 0.0184196 + 1.25538i
\(756\) 0 0
\(757\) −3.00432 3.00432i −0.109194 0.109194i 0.650399 0.759593i \(-0.274602\pi\)
−0.759593 + 0.650399i \(0.774602\pi\)
\(758\) −12.3034 + 12.3034i −0.446881 + 0.446881i
\(759\) 0 0
\(760\) 6.42508 + 7.32928i 0.233062 + 0.265861i
\(761\) 9.42821 0.341772 0.170886 0.985291i \(-0.445337\pi\)
0.170886 + 0.985291i \(0.445337\pi\)
\(762\) 0 0
\(763\) 24.8891 + 24.8891i 0.901047 + 0.901047i
\(764\) 6.38310i 0.230932i
\(765\) 0 0
\(766\) 20.2174 0.730485
\(767\) −3.56381 3.56381i −0.128682 0.128682i
\(768\) 0 0
\(769\) 25.1986i 0.908683i −0.890828 0.454342i \(-0.849875\pi\)
0.890828 0.454342i \(-0.150125\pi\)
\(770\) −15.0477 + 0.220788i −0.542280 + 0.00795665i
\(771\) 0 0
\(772\) 15.6976 15.6976i 0.564970 0.564970i
\(773\) −8.32250 8.32250i −0.299340 0.299340i 0.541416 0.840755i \(-0.317889\pi\)
−0.840755 + 0.541416i \(0.817889\pi\)
\(774\) 0 0
\(775\) −0.0534327 1.82044i −0.00191936 0.0653922i
\(776\) 12.4444 0.446728
\(777\) 0 0
\(778\) 7.79761 + 7.79761i 0.279558 + 0.279558i
\(779\) −0.627432 + 7.79517i −0.0224801 + 0.279291i
\(780\) 0 0
\(781\) 13.4605i 0.481654i
\(782\) 5.64120 5.64120i 0.201729 0.201729i
\(783\) 0 0
\(784\) 13.1800i 0.470715i
\(785\) 30.1611 + 29.2888i 1.07649 + 1.04536i
\(786\) 0 0
\(787\) 33.1356 33.1356i 1.18116 1.18116i 0.201710 0.979445i \(-0.435350\pi\)
0.979445 0.201710i \(-0.0646498\pi\)
\(788\) −2.62159 + 2.62159i −0.0933901 + 0.0933901i
\(789\) 0 0
\(790\) 12.3892 12.7582i 0.440789 0.453916i
\(791\) 78.5265i 2.79208i
\(792\) 0 0
\(793\) 36.4261 + 36.4261i 1.29353 + 1.29353i
\(794\) −1.54526 −0.0548392
\(795\) 0 0
\(796\) 6.73685 0.238781
\(797\) 10.3195 10.3195i 0.365534 0.365534i −0.500311 0.865846i \(-0.666781\pi\)
0.865846 + 0.500311i \(0.166781\pi\)
\(798\) 0 0
\(799\) 8.94620i 0.316494i
\(800\) −3.43028 + 3.63774i −0.121279 + 0.128614i
\(801\) 0 0
\(802\) 9.67468 + 9.67468i 0.341625 + 0.341625i
\(803\) 16.8655 16.8655i 0.595172 0.595172i
\(804\) 0 0
\(805\) −66.3996 + 0.974255i −2.34028 + 0.0343380i
\(806\) 1.23097i 0.0433589i
\(807\) 0 0
\(808\) 1.54027 + 1.54027i 0.0541864 + 0.0541864i
\(809\) 27.5401i 0.968260i 0.874996 + 0.484130i \(0.160864\pi\)
−0.874996 + 0.484130i \(0.839136\pi\)
\(810\) 0 0
\(811\) 39.9597i 1.40318i −0.712583 0.701588i \(-0.752475\pi\)
0.712583 0.701588i \(-0.247525\pi\)
\(812\) 17.1664 17.1664i 0.602423 0.602423i
\(813\) 0 0
\(814\) 9.10745i 0.319216i
\(815\) −0.0965084 + 0.0993826i −0.00338054 + 0.00348122i
\(816\) 0 0
\(817\) 2.92818 2.49192i 0.102444 0.0871811i
\(818\) −9.84826 + 9.84826i −0.344336 + 0.344336i
\(819\) 0 0
\(820\) −4.01134 + 0.0588568i −0.140082 + 0.00205537i
\(821\) −23.0062 −0.802922 −0.401461 0.915876i \(-0.631498\pi\)
−0.401461 + 0.915876i \(0.631498\pi\)
\(822\) 0 0
\(823\) 15.1426 15.1426i 0.527839 0.527839i −0.392088 0.919928i \(-0.628247\pi\)
0.919928 + 0.392088i \(0.128247\pi\)
\(824\) 13.3619i 0.465483i
\(825\) 0 0
\(826\) 6.69943 0.233103
\(827\) 30.6119 30.6119i 1.06448 1.06448i 0.0667089 0.997772i \(-0.478750\pi\)
0.997772 0.0667089i \(-0.0212499\pi\)
\(828\) 0 0
\(829\) −20.6550 −0.717377 −0.358688 0.933457i \(-0.616776\pi\)
−0.358688 + 0.933457i \(0.616776\pi\)
\(830\) −0.183045 12.4753i −0.00635359 0.433024i
\(831\) 0 0
\(832\) −2.38967 + 2.38967i −0.0828468 + 0.0828468i
\(833\) 11.2466 11.2466i 0.389671 0.389671i
\(834\) 0 0
\(835\) 14.5809 15.0152i 0.504595 0.519622i
\(836\) −0.523945 + 6.50945i −0.0181210 + 0.225134i
\(837\) 0 0
\(838\) −22.4760 22.4760i −0.776421 0.776421i
\(839\) 14.8706 0.513391 0.256696 0.966492i \(-0.417366\pi\)
0.256696 + 0.966492i \(0.417366\pi\)
\(840\) 0 0
\(841\) 0.205753 0.00709491
\(842\) 21.1861 + 21.1861i 0.730123 + 0.730123i
\(843\) 0 0
\(844\) −15.1654 −0.522013
\(845\) 0.0517994 + 3.53035i 0.00178195 + 0.121448i
\(846\) 0 0
\(847\) 27.8113 + 27.8113i 0.955608 + 0.955608i
\(848\) −5.27391 5.27391i −0.181107 0.181107i
\(849\) 0 0
\(850\) −6.03118 + 0.177024i −0.206868 + 0.00607189i
\(851\) 40.1878i 1.37762i
\(852\) 0 0
\(853\) 18.8845 18.8845i 0.646592 0.646592i −0.305576 0.952168i \(-0.598849\pi\)
0.952168 + 0.305576i \(0.0988490\pi\)
\(854\) −68.4756 −2.34319
\(855\) 0 0
\(856\) −0.424610 −0.0145129
\(857\) −3.38649 + 3.38649i −0.115680 + 0.115680i −0.762577 0.646897i \(-0.776066\pi\)
0.646897 + 0.762577i \(0.276066\pi\)
\(858\) 0 0
\(859\) 20.3135i 0.693089i 0.938034 + 0.346544i \(0.112645\pi\)
−0.938034 + 0.346544i \(0.887355\pi\)
\(860\) 1.41503 + 1.37411i 0.0482522 + 0.0468567i
\(861\) 0 0
\(862\) 13.7288 + 13.7288i 0.467603 + 0.467603i
\(863\) −20.2596 20.2596i −0.689645 0.689645i 0.272508 0.962153i \(-0.412147\pi\)
−0.962153 + 0.272508i \(0.912147\pi\)
\(864\) 0 0
\(865\) 40.2895 + 39.1243i 1.36988 + 1.33026i
\(866\) −7.83259 −0.266162
\(867\) 0 0
\(868\) 1.15702 + 1.15702i 0.0392717 + 0.0392717i
\(869\) 11.9154 0.404203
\(870\) 0 0
\(871\) −4.72746 −0.160184
\(872\) 5.54050 + 5.54050i 0.187625 + 0.187625i
\(873\) 0 0
\(874\) −2.31197 + 28.7237i −0.0782036 + 0.971595i
\(875\) 37.0423 + 33.9171i 1.25226 + 1.14661i
\(876\) 0 0
\(877\) 22.8421 22.8421i 0.771322 0.771322i −0.207016 0.978338i \(-0.566375\pi\)
0.978338 + 0.207016i \(0.0663752\pi\)
\(878\) −13.6141 + 13.6141i −0.459454 + 0.459454i
\(879\) 0 0
\(880\) −3.34972 + 0.0491491i −0.112919 + 0.00165681i
\(881\) 43.2232 1.45623 0.728113 0.685457i \(-0.240397\pi\)
0.728113 + 0.685457i \(0.240397\pi\)
\(882\) 0 0
\(883\) −33.6956 + 33.6956i −1.13395 + 1.13395i −0.144431 + 0.989515i \(0.546135\pi\)
−0.989515 + 0.144431i \(0.953865\pi\)
\(884\) −4.07823 −0.137166
\(885\) 0 0
\(886\) 1.16299i 0.0390715i
\(887\) −22.5354 + 22.5354i −0.756666 + 0.756666i −0.975714 0.219048i \(-0.929705\pi\)
0.219048 + 0.975714i \(0.429705\pi\)
\(888\) 0 0
\(889\) 52.8480 1.77246
\(890\) −14.5014 + 14.9333i −0.486089 + 0.500566i
\(891\) 0 0
\(892\) 1.90756 1.90756i 0.0638697 0.0638697i
\(893\) 20.9428 + 24.6093i 0.700825 + 0.823519i
\(894\) 0 0
\(895\) 20.1366 0.295456i 0.673091 0.00987600i
\(896\) 4.49222i 0.150074i
\(897\) 0 0
\(898\) 24.0588 24.0588i 0.802852 0.802852i
\(899\) 1.96847i 0.0656520i
\(900\) 0 0
\(901\) 9.00051i 0.299850i
\(902\) −1.90067 1.90067i −0.0632852 0.0632852i
\(903\) 0 0
\(904\) 17.4806i 0.581395i
\(905\) 0.615483 + 41.9478i 0.0204593 + 1.39439i
\(906\) 0 0
\(907\) 16.4318 16.4318i 0.545611 0.545611i −0.379558 0.925168i \(-0.623924\pi\)
0.925168 + 0.379558i \(0.123924\pi\)
\(908\) −19.8625 19.8625i −0.659159 0.659159i
\(909\) 0 0
\(910\) 24.3535 + 23.6492i 0.807312 + 0.783964i
\(911\) 12.8284i 0.425024i −0.977158 0.212512i \(-0.931836\pi\)
0.977158 0.212512i \(-0.0681644\pi\)
\(912\) 0 0
\(913\) 5.91109 5.91109i 0.195629 0.195629i
\(914\) 37.1033 1.22727
\(915\) 0 0
\(916\) 19.0279 0.628700
\(917\) 25.6570 + 25.6570i 0.847269 + 0.847269i
\(918\) 0 0
\(919\) 15.1134i 0.498544i 0.968434 + 0.249272i \(0.0801913\pi\)
−0.968434 + 0.249272i \(0.919809\pi\)
\(920\) −14.7810 + 0.216876i −0.487316 + 0.00715020i
\(921\) 0 0
\(922\) 18.9176 18.9176i 0.623018 0.623018i
\(923\) 21.4698 21.4698i 0.706687 0.706687i
\(924\) 0 0
\(925\) −20.8525 + 22.1136i −0.685625 + 0.727090i
\(926\) 23.3650i 0.767820i
\(927\) 0 0
\(928\) 3.82137 3.82137i 0.125443 0.125443i
\(929\) 54.6979i 1.79458i 0.441442 + 0.897290i \(0.354467\pi\)
−0.441442 + 0.897290i \(0.645533\pi\)
\(930\) 0 0
\(931\) −4.60926 + 57.2651i −0.151063 + 1.87679i
\(932\) −8.22028 8.22028i −0.269264 0.269264i
\(933\) 0 0
\(934\) −9.75744 −0.319273
\(935\) −2.90027 2.81639i −0.0948490 0.0921059i
\(936\) 0 0
\(937\) 19.3024 + 19.3024i 0.630582 + 0.630582i 0.948214 0.317632i \(-0.102888\pi\)
−0.317632 + 0.948214i \(0.602888\pi\)
\(938\) 4.44346 4.44346i 0.145084 0.145084i
\(939\) 0 0
\(940\) −11.5484 + 11.8924i −0.376668 + 0.387886i
\(941\) 3.83170i 0.124910i −0.998048 0.0624549i \(-0.980107\pi\)
0.998048 0.0624549i \(-0.0198930\pi\)
\(942\) 0 0
\(943\) −8.38692 8.38692i −0.273116 0.273116i
\(944\) 1.49134 0.0485391
\(945\) 0 0
\(946\) 1.32156i 0.0429677i
\(947\) 22.3934 + 22.3934i 0.727689 + 0.727689i 0.970159 0.242470i \(-0.0779575\pi\)
−0.242470 + 0.970159i \(0.577958\pi\)
\(948\) 0 0
\(949\) −53.8019 −1.74648
\(950\) 16.1762 14.6058i 0.524826 0.473875i
\(951\) 0 0
\(952\) 3.83323 3.83323i 0.124236 0.124236i
\(953\) −0.832761 0.832761i −0.0269758 0.0269758i 0.693490 0.720466i \(-0.256072\pi\)
−0.720466 + 0.693490i \(0.756072\pi\)
\(954\) 0 0
\(955\) −14.2715 + 0.209400i −0.461815 + 0.00677603i
\(956\) −5.40164 −0.174702
\(957\) 0 0
\(958\) 7.14916 + 7.14916i 0.230979 + 0.230979i
\(959\) 44.4570i 1.43559i
\(960\) 0 0
\(961\) 30.8673 0.995720
\(962\) −14.5266 + 14.5266i −0.468357 + 0.468357i
\(963\) 0 0
\(964\) 24.3252 0.783462
\(965\) −35.6122 34.5822i −1.14640 1.11324i
\(966\) 0 0
\(967\) −8.69878 8.69878i −0.279734 0.279734i 0.553269 0.833003i \(-0.313380\pi\)
−0.833003 + 0.553269i \(0.813380\pi\)
\(968\) 6.19100 + 6.19100i 0.198986 + 0.198986i
\(969\) 0 0
\(970\) −0.408244 27.8235i −0.0131079 0.893360i
\(971\) 27.6771i 0.888202i 0.895977 + 0.444101i \(0.146477\pi\)
−0.895977 + 0.444101i \(0.853523\pi\)
\(972\) 0 0
\(973\) 34.5812 34.5812i 1.10862 1.10862i
\(974\) 27.5865i 0.883928i
\(975\) 0 0
\(976\) −15.2432 −0.487922
\(977\) 14.3182 14.3182i 0.458079 0.458079i −0.439946 0.898024i \(-0.645002\pi\)
0.898024 + 0.439946i \(0.145002\pi\)
\(978\) 0 0
\(979\) −13.9469 −0.445744
\(980\) −29.4682 + 0.432375i −0.941328 + 0.0138117i
\(981\) 0 0
\(982\) 9.94898 9.94898i 0.317485 0.317485i
\(983\) 32.4108 + 32.4108i 1.03374 + 1.03374i 0.999410 + 0.0343335i \(0.0109308\pi\)
0.0343335 + 0.999410i \(0.489069\pi\)
\(984\) 0 0
\(985\) 5.94742 + 5.77541i 0.189500 + 0.184020i
\(986\) 6.52159 0.207690
\(987\) 0 0
\(988\) 11.2184 9.54703i 0.356906 0.303731i
\(989\) 5.83155i 0.185433i
\(990\) 0 0
\(991\) 26.7718i 0.850435i −0.905091 0.425218i \(-0.860198\pi\)
0.905091 0.425218i \(-0.139802\pi\)
\(992\) 0.257560 + 0.257560i 0.00817755 + 0.00817755i
\(993\) 0 0
\(994\) 40.3600i 1.28014i
\(995\) −0.221005 15.0624i −0.00700633 0.477511i
\(996\) 0 0
\(997\) −3.08169 3.08169i −0.0975982 0.0975982i 0.656622 0.754220i \(-0.271985\pi\)
−0.754220 + 0.656622i \(0.771985\pi\)
\(998\) −3.13678 3.13678i −0.0992929 0.0992929i
\(999\) 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 1710.2.p.c.37.6 20
3.2 odd 2 570.2.m.b.37.5 20
5.3 odd 4 inner 1710.2.p.c.1063.1 20
15.8 even 4 570.2.m.b.493.10 yes 20
19.18 odd 2 inner 1710.2.p.c.37.1 20
57.56 even 2 570.2.m.b.37.10 yes 20
95.18 even 4 inner 1710.2.p.c.1063.6 20
285.113 odd 4 570.2.m.b.493.5 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.2.m.b.37.5 20 3.2 odd 2
570.2.m.b.37.10 yes 20 57.56 even 2
570.2.m.b.493.5 yes 20 285.113 odd 4
570.2.m.b.493.10 yes 20 15.8 even 4
1710.2.p.c.37.1 20 19.18 odd 2 inner
1710.2.p.c.37.6 20 1.1 even 1 trivial
1710.2.p.c.1063.1 20 5.3 odd 4 inner
1710.2.p.c.1063.6 20 95.18 even 4 inner