Properties

Label 690.3.g.a.461.2
Level $690$
Weight $3$
Character 690.461
Analytic conductor $18.801$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [690,3,Mod(461,690)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(690, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("690.461");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.g (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(56\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 461.2
Character \(\chi\) \(=\) 690.461
Dual form 690.3.g.a.461.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.41421i q^{2} +(2.78199 + 1.12272i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(-1.58777 + 3.93433i) q^{6} +9.71289 q^{7} -2.82843i q^{8} +(6.47899 + 6.24682i) q^{9} +O(q^{10})\) \(q+1.41421i q^{2} +(2.78199 + 1.12272i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(-1.58777 + 3.93433i) q^{6} +9.71289 q^{7} -2.82843i q^{8} +(6.47899 + 6.24682i) q^{9} -3.16228 q^{10} -16.7924i q^{11} +(-5.56399 - 2.24544i) q^{12} +14.2200 q^{13} +13.7361i q^{14} +(-2.51048 + 6.22073i) q^{15} +4.00000 q^{16} -8.32060i q^{17} +(-8.83433 + 9.16267i) q^{18} +18.7748 q^{19} -4.47214i q^{20} +(27.0212 + 10.9049i) q^{21} +23.7480 q^{22} -4.79583i q^{23} +(3.17554 - 7.86867i) q^{24} -5.00000 q^{25} +20.1101i q^{26} +(11.0111 + 24.6527i) q^{27} -19.4258 q^{28} -8.35888i q^{29} +(-8.79744 - 3.55036i) q^{30} +12.7798 q^{31} +5.65685i q^{32} +(18.8532 - 46.7163i) q^{33} +11.7671 q^{34} +21.7187i q^{35} +(-12.9580 - 12.4936i) q^{36} -48.4043 q^{37} +26.5516i q^{38} +(39.5598 + 15.9651i) q^{39} +6.32456 q^{40} -33.7058i q^{41} +(-15.4218 + 38.2138i) q^{42} -41.8569 q^{43} +33.5848i q^{44} +(-13.9683 + 14.4875i) q^{45} +6.78233 q^{46} +25.4461i q^{47} +(11.1280 + 4.49089i) q^{48} +45.3403 q^{49} -7.07107i q^{50} +(9.34172 - 23.1479i) q^{51} -28.4399 q^{52} +64.6839i q^{53} +(-34.8642 + 15.5720i) q^{54} +37.5489 q^{55} -27.4722i q^{56} +(52.2314 + 21.0789i) q^{57} +11.8212 q^{58} +35.0667i q^{59} +(5.02097 - 12.4415i) q^{60} -57.1839 q^{61} +18.0734i q^{62} +(62.9297 + 60.6746i) q^{63} -8.00000 q^{64} +31.7968i q^{65} +(66.0668 + 26.6624i) q^{66} -61.2135 q^{67} +16.6412i q^{68} +(5.38439 - 13.3420i) q^{69} -30.7149 q^{70} +99.0489i q^{71} +(17.6687 - 18.3253i) q^{72} +1.71337 q^{73} -68.4541i q^{74} +(-13.9100 - 5.61361i) q^{75} -37.5496 q^{76} -163.103i q^{77} +(-22.5780 + 55.9461i) q^{78} +118.909 q^{79} +8.94427i q^{80} +(2.95460 + 80.9461i) q^{81} +47.6672 q^{82} +13.2505i q^{83} +(-54.0424 - 21.8098i) q^{84} +18.6054 q^{85} -59.1947i q^{86} +(9.38470 - 23.2544i) q^{87} -47.4960 q^{88} -145.864i q^{89} +(-20.4884 - 19.7542i) q^{90} +138.117 q^{91} +9.59166i q^{92} +(35.5533 + 14.3482i) q^{93} -35.9862 q^{94} +41.9818i q^{95} +(-6.35108 + 15.7373i) q^{96} -166.157 q^{97} +64.1208i q^{98} +(104.899 - 108.798i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q - 8 q^{3} - 112 q^{4} + 16 q^{6} - 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 56 q - 8 q^{3} - 112 q^{4} + 16 q^{6} - 16 q^{7} + 16 q^{12} + 80 q^{13} - 40 q^{15} + 224 q^{16} - 32 q^{18} - 64 q^{19} + 56 q^{21} - 96 q^{22} - 32 q^{24} - 280 q^{25} + 40 q^{27} + 32 q^{28} - 80 q^{31} + 32 q^{33} + 192 q^{34} + 240 q^{37} - 56 q^{39} - 144 q^{43} - 32 q^{48} + 72 q^{49} - 24 q^{51} - 160 q^{52} + 16 q^{54} - 16 q^{57} + 80 q^{60} + 112 q^{61} - 64 q^{63} - 448 q^{64} + 160 q^{66} + 832 q^{67} + 64 q^{72} - 608 q^{73} + 40 q^{75} + 128 q^{76} - 320 q^{78} + 48 q^{79} - 32 q^{81} - 448 q^{82} - 112 q^{84} + 240 q^{85} + 200 q^{87} + 192 q^{88} + 80 q^{91} - 232 q^{93} + 160 q^{94} + 64 q^{96} - 448 q^{97} + 464 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 0.707107i
\(3\) 2.78199 + 1.12272i 0.927332 + 0.374241i
\(4\) −2.00000 −0.500000
\(5\) 2.23607i 0.447214i
\(6\) −1.58777 + 3.93433i −0.264628 + 0.655722i
\(7\) 9.71289 1.38756 0.693778 0.720189i \(-0.255945\pi\)
0.693778 + 0.720189i \(0.255945\pi\)
\(8\) 2.82843i 0.353553i
\(9\) 6.47899 + 6.24682i 0.719888 + 0.694091i
\(10\) −3.16228 −0.316228
\(11\) 16.7924i 1.52658i −0.646056 0.763290i \(-0.723583\pi\)
0.646056 0.763290i \(-0.276417\pi\)
\(12\) −5.56399 2.24544i −0.463666 0.187120i
\(13\) 14.2200 1.09384 0.546921 0.837184i \(-0.315800\pi\)
0.546921 + 0.837184i \(0.315800\pi\)
\(14\) 13.7361i 0.981150i
\(15\) −2.51048 + 6.22073i −0.167366 + 0.414715i
\(16\) 4.00000 0.250000
\(17\) 8.32060i 0.489447i −0.969593 0.244724i \(-0.921303\pi\)
0.969593 0.244724i \(-0.0786972\pi\)
\(18\) −8.83433 + 9.16267i −0.490796 + 0.509037i
\(19\) 18.7748 0.988148 0.494074 0.869420i \(-0.335507\pi\)
0.494074 + 0.869420i \(0.335507\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 27.0212 + 10.9049i 1.28672 + 0.519280i
\(22\) 23.7480 1.07946
\(23\) 4.79583i 0.208514i
\(24\) 3.17554 7.86867i 0.132314 0.327861i
\(25\) −5.00000 −0.200000
\(26\) 20.1101i 0.773464i
\(27\) 11.0111 + 24.6527i 0.407818 + 0.913063i
\(28\) −19.4258 −0.693778
\(29\) 8.35888i 0.288237i −0.989560 0.144119i \(-0.953965\pi\)
0.989560 0.144119i \(-0.0460347\pi\)
\(30\) −8.79744 3.55036i −0.293248 0.118345i
\(31\) 12.7798 0.412252 0.206126 0.978526i \(-0.433914\pi\)
0.206126 + 0.978526i \(0.433914\pi\)
\(32\) 5.65685i 0.176777i
\(33\) 18.8532 46.7163i 0.571309 1.41565i
\(34\) 11.7671 0.346091
\(35\) 21.7187i 0.620534i
\(36\) −12.9580 12.4936i −0.359944 0.347045i
\(37\) −48.4043 −1.30823 −0.654113 0.756397i \(-0.726958\pi\)
−0.654113 + 0.756397i \(0.726958\pi\)
\(38\) 26.5516i 0.698726i
\(39\) 39.5598 + 15.9651i 1.01435 + 0.409361i
\(40\) 6.32456 0.158114
\(41\) 33.7058i 0.822093i −0.911614 0.411046i \(-0.865163\pi\)
0.911614 0.411046i \(-0.134837\pi\)
\(42\) −15.4218 + 38.2138i −0.367186 + 0.909852i
\(43\) −41.8569 −0.973417 −0.486709 0.873564i \(-0.661803\pi\)
−0.486709 + 0.873564i \(0.661803\pi\)
\(44\) 33.5848i 0.763290i
\(45\) −13.9683 + 14.4875i −0.310407 + 0.321944i
\(46\) 6.78233 0.147442
\(47\) 25.4461i 0.541406i 0.962663 + 0.270703i \(0.0872561\pi\)
−0.962663 + 0.270703i \(0.912744\pi\)
\(48\) 11.1280 + 4.49089i 0.231833 + 0.0935602i
\(49\) 45.3403 0.925312
\(50\) 7.07107i 0.141421i
\(51\) 9.34172 23.1479i 0.183171 0.453880i
\(52\) −28.4399 −0.546921
\(53\) 64.6839i 1.22045i 0.792228 + 0.610225i \(0.208921\pi\)
−0.792228 + 0.610225i \(0.791079\pi\)
\(54\) −34.8642 + 15.5720i −0.645633 + 0.288371i
\(55\) 37.5489 0.682707
\(56\) 27.4722i 0.490575i
\(57\) 52.2314 + 21.0789i 0.916341 + 0.369805i
\(58\) 11.8212 0.203815
\(59\) 35.0667i 0.594351i 0.954823 + 0.297175i \(0.0960446\pi\)
−0.954823 + 0.297175i \(0.903955\pi\)
\(60\) 5.02097 12.4415i 0.0836828 0.207358i
\(61\) −57.1839 −0.937441 −0.468721 0.883347i \(-0.655285\pi\)
−0.468721 + 0.883347i \(0.655285\pi\)
\(62\) 18.0734i 0.291506i
\(63\) 62.9297 + 60.6746i 0.998884 + 0.963090i
\(64\) −8.00000 −0.125000
\(65\) 31.7968i 0.489181i
\(66\) 66.0668 + 26.6624i 1.00101 + 0.403976i
\(67\) −61.2135 −0.913634 −0.456817 0.889561i \(-0.651011\pi\)
−0.456817 + 0.889561i \(0.651011\pi\)
\(68\) 16.6412i 0.244724i
\(69\) 5.38439 13.3420i 0.0780346 0.193362i
\(70\) −30.7149 −0.438784
\(71\) 99.0489i 1.39505i 0.716558 + 0.697527i \(0.245716\pi\)
−0.716558 + 0.697527i \(0.754284\pi\)
\(72\) 17.6687 18.3253i 0.245398 0.254519i
\(73\) 1.71337 0.0234709 0.0117354 0.999931i \(-0.496264\pi\)
0.0117354 + 0.999931i \(0.496264\pi\)
\(74\) 68.4541i 0.925055i
\(75\) −13.9100 5.61361i −0.185466 0.0748482i
\(76\) −37.5496 −0.494074
\(77\) 163.103i 2.11822i
\(78\) −22.5780 + 55.9461i −0.289462 + 0.717257i
\(79\) 118.909 1.50517 0.752586 0.658493i \(-0.228806\pi\)
0.752586 + 0.658493i \(0.228806\pi\)
\(80\) 8.94427i 0.111803i
\(81\) 2.95460 + 80.9461i 0.0364765 + 0.999335i
\(82\) 47.6672 0.581307
\(83\) 13.2505i 0.159645i 0.996809 + 0.0798226i \(0.0254354\pi\)
−0.996809 + 0.0798226i \(0.974565\pi\)
\(84\) −54.0424 21.8098i −0.643362 0.259640i
\(85\) 18.6054 0.218887
\(86\) 59.1947i 0.688310i
\(87\) 9.38470 23.2544i 0.107870 0.267292i
\(88\) −47.4960 −0.539728
\(89\) 145.864i 1.63892i −0.573133 0.819462i \(-0.694272\pi\)
0.573133 0.819462i \(-0.305728\pi\)
\(90\) −20.4884 19.7542i −0.227648 0.219491i
\(91\) 138.117 1.51777
\(92\) 9.59166i 0.104257i
\(93\) 35.5533 + 14.3482i 0.382294 + 0.154281i
\(94\) −35.9862 −0.382832
\(95\) 41.9818i 0.441913i
\(96\) −6.35108 + 15.7373i −0.0661570 + 0.163931i
\(97\) −166.157 −1.71296 −0.856478 0.516183i \(-0.827352\pi\)
−0.856478 + 0.516183i \(0.827352\pi\)
\(98\) 64.1208i 0.654294i
\(99\) 104.899 108.798i 1.05958 1.09897i
\(100\) 10.0000 0.100000
\(101\) 101.312i 1.00309i 0.865131 + 0.501546i \(0.167235\pi\)
−0.865131 + 0.501546i \(0.832765\pi\)
\(102\) 32.7360 + 13.2112i 0.320941 + 0.129521i
\(103\) −156.509 −1.51951 −0.759754 0.650210i \(-0.774681\pi\)
−0.759754 + 0.650210i \(0.774681\pi\)
\(104\) 40.2201i 0.386732i
\(105\) −24.3841 + 60.4213i −0.232229 + 0.575441i
\(106\) −91.4768 −0.862989
\(107\) 49.5970i 0.463523i −0.972773 0.231762i \(-0.925551\pi\)
0.972773 0.231762i \(-0.0744489\pi\)
\(108\) −22.0221 49.3054i −0.203909 0.456532i
\(109\) −9.54244 −0.0875453 −0.0437727 0.999042i \(-0.513938\pi\)
−0.0437727 + 0.999042i \(0.513938\pi\)
\(110\) 53.1022i 0.482747i
\(111\) −134.661 54.3446i −1.21316 0.489591i
\(112\) 38.8516 0.346889
\(113\) 194.702i 1.72303i 0.507736 + 0.861513i \(0.330483\pi\)
−0.507736 + 0.861513i \(0.669517\pi\)
\(114\) −29.8101 + 73.8664i −0.261492 + 0.647951i
\(115\) 10.7238 0.0932505
\(116\) 16.7178i 0.144119i
\(117\) 92.1309 + 88.8294i 0.787444 + 0.759226i
\(118\) −49.5918 −0.420269
\(119\) 80.8171i 0.679135i
\(120\) 17.5949 + 7.10072i 0.146624 + 0.0591727i
\(121\) −160.984 −1.33045
\(122\) 80.8703i 0.662871i
\(123\) 37.8423 93.7694i 0.307661 0.762353i
\(124\) −25.5596 −0.206126
\(125\) 11.1803i 0.0894427i
\(126\) −85.8069 + 88.9961i −0.681007 + 0.706318i
\(127\) 91.5991 0.721253 0.360626 0.932710i \(-0.382563\pi\)
0.360626 + 0.932710i \(0.382563\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) −116.446 46.9937i −0.902681 0.364292i
\(130\) −44.9675 −0.345903
\(131\) 137.955i 1.05309i −0.850148 0.526544i \(-0.823488\pi\)
0.850148 0.526544i \(-0.176512\pi\)
\(132\) −37.7064 + 93.4326i −0.285654 + 0.707823i
\(133\) 182.358 1.37111
\(134\) 86.5689i 0.646037i
\(135\) −55.1251 + 24.6215i −0.408334 + 0.182382i
\(136\) −23.5342 −0.173046
\(137\) 60.6857i 0.442961i 0.975165 + 0.221481i \(0.0710889\pi\)
−0.975165 + 0.221481i \(0.928911\pi\)
\(138\) 18.8684 + 7.61467i 0.136728 + 0.0551788i
\(139\) 107.481 0.773243 0.386622 0.922238i \(-0.373642\pi\)
0.386622 + 0.922238i \(0.373642\pi\)
\(140\) 43.4374i 0.310267i
\(141\) −28.5689 + 70.7908i −0.202616 + 0.502063i
\(142\) −140.076 −0.986453
\(143\) 238.787i 1.66984i
\(144\) 25.9160 + 24.9873i 0.179972 + 0.173523i
\(145\) 18.6910 0.128904
\(146\) 2.42308i 0.0165964i
\(147\) 126.136 + 50.9045i 0.858071 + 0.346289i
\(148\) 96.8087 0.654113
\(149\) 34.1446i 0.229158i −0.993414 0.114579i \(-0.963448\pi\)
0.993414 0.114579i \(-0.0365520\pi\)
\(150\) 7.93885 19.6717i 0.0529256 0.131144i
\(151\) −153.941 −1.01947 −0.509737 0.860330i \(-0.670257\pi\)
−0.509737 + 0.860330i \(0.670257\pi\)
\(152\) 53.1032i 0.349363i
\(153\) 51.9773 53.9091i 0.339721 0.352347i
\(154\) 230.662 1.49780
\(155\) 28.5765i 0.184364i
\(156\) −79.1197 31.9301i −0.507177 0.204680i
\(157\) 68.3351 0.435255 0.217628 0.976032i \(-0.430168\pi\)
0.217628 + 0.976032i \(0.430168\pi\)
\(158\) 168.162i 1.06432i
\(159\) −72.6220 + 179.950i −0.456742 + 1.13176i
\(160\) −12.6491 −0.0790569
\(161\) 46.5814i 0.289325i
\(162\) −114.475 + 4.17844i −0.706636 + 0.0257928i
\(163\) 160.804 0.986527 0.493264 0.869880i \(-0.335804\pi\)
0.493264 + 0.869880i \(0.335804\pi\)
\(164\) 67.4116i 0.411046i
\(165\) 104.461 + 42.1570i 0.633096 + 0.255497i
\(166\) −18.7391 −0.112886
\(167\) 203.880i 1.22084i 0.792078 + 0.610420i \(0.208999\pi\)
−0.792078 + 0.610420i \(0.791001\pi\)
\(168\) 30.8437 76.4275i 0.183593 0.454926i
\(169\) 33.2072 0.196492
\(170\) 26.3120i 0.154777i
\(171\) 121.642 + 117.283i 0.711356 + 0.685864i
\(172\) 83.7139 0.486709
\(173\) 38.3584i 0.221725i −0.993836 0.110863i \(-0.964639\pi\)
0.993836 0.110863i \(-0.0353613\pi\)
\(174\) 32.8866 + 13.2720i 0.189004 + 0.0762757i
\(175\) −48.5645 −0.277511
\(176\) 67.1695i 0.381645i
\(177\) −39.3702 + 97.5553i −0.222430 + 0.551160i
\(178\) 206.283 1.15889
\(179\) 36.4722i 0.203755i 0.994797 + 0.101878i \(0.0324850\pi\)
−0.994797 + 0.101878i \(0.967515\pi\)
\(180\) 27.9366 28.9749i 0.155203 0.160972i
\(181\) −340.697 −1.88231 −0.941153 0.337981i \(-0.890256\pi\)
−0.941153 + 0.337981i \(0.890256\pi\)
\(182\) 195.327i 1.07322i
\(183\) −159.085 64.2016i −0.869319 0.350829i
\(184\) −13.5647 −0.0737210
\(185\) 108.235i 0.585056i
\(186\) −20.2914 + 50.2800i −0.109093 + 0.270323i
\(187\) −139.723 −0.747180
\(188\) 50.8921i 0.270703i
\(189\) 106.949 + 239.449i 0.565870 + 1.26693i
\(190\) −59.3712 −0.312480
\(191\) 187.221i 0.980216i −0.871662 0.490108i \(-0.836957\pi\)
0.871662 0.490108i \(-0.163043\pi\)
\(192\) −22.2560 8.98178i −0.115916 0.0467801i
\(193\) 375.100 1.94352 0.971760 0.235970i \(-0.0758266\pi\)
0.971760 + 0.235970i \(0.0758266\pi\)
\(194\) 234.981i 1.21124i
\(195\) −35.6990 + 88.4585i −0.183072 + 0.453633i
\(196\) −90.6806 −0.462656
\(197\) 199.478i 1.01258i −0.862363 0.506290i \(-0.831016\pi\)
0.862363 0.506290i \(-0.168984\pi\)
\(198\) 153.863 + 148.349i 0.777086 + 0.749240i
\(199\) 331.088 1.66376 0.831880 0.554955i \(-0.187265\pi\)
0.831880 + 0.554955i \(0.187265\pi\)
\(200\) 14.1421i 0.0707107i
\(201\) −170.296 68.7257i −0.847242 0.341919i
\(202\) −143.277 −0.709293
\(203\) 81.1889i 0.399945i
\(204\) −18.6834 + 46.2957i −0.0915855 + 0.226940i
\(205\) 75.3685 0.367651
\(206\) 221.338i 1.07445i
\(207\) 29.9587 31.0721i 0.144728 0.150107i
\(208\) 56.8798 0.273461
\(209\) 315.274i 1.50849i
\(210\) −85.4486 34.4843i −0.406898 0.164211i
\(211\) −327.623 −1.55272 −0.776358 0.630293i \(-0.782935\pi\)
−0.776358 + 0.630293i \(0.782935\pi\)
\(212\) 129.368i 0.610225i
\(213\) −111.204 + 275.553i −0.522086 + 1.29368i
\(214\) 70.1407 0.327760
\(215\) 93.5950i 0.435325i
\(216\) 69.7284 31.1440i 0.322817 0.144185i
\(217\) 124.129 0.572022
\(218\) 13.4950i 0.0619039i
\(219\) 4.76660 + 1.92364i 0.0217653 + 0.00878376i
\(220\) −75.0978 −0.341354
\(221\) 118.319i 0.535378i
\(222\) 76.8549 190.439i 0.346193 0.857833i
\(223\) −397.757 −1.78366 −0.891832 0.452367i \(-0.850580\pi\)
−0.891832 + 0.452367i \(0.850580\pi\)
\(224\) 54.9444i 0.245288i
\(225\) −32.3949 31.2341i −0.143978 0.138818i
\(226\) −275.350 −1.21836
\(227\) 76.3503i 0.336345i −0.985758 0.168172i \(-0.946213\pi\)
0.985758 0.168172i \(-0.0537865\pi\)
\(228\) −104.463 42.1578i −0.458171 0.184903i
\(229\) −95.0705 −0.415155 −0.207578 0.978219i \(-0.566558\pi\)
−0.207578 + 0.978219i \(0.566558\pi\)
\(230\) 15.1658i 0.0659380i
\(231\) 183.119 453.751i 0.792723 1.96429i
\(232\) −23.6425 −0.101907
\(233\) 372.400i 1.59828i −0.601144 0.799141i \(-0.705288\pi\)
0.601144 0.799141i \(-0.294712\pi\)
\(234\) −125.624 + 130.293i −0.536854 + 0.556807i
\(235\) −56.8991 −0.242124
\(236\) 70.1334i 0.297175i
\(237\) 330.803 + 133.501i 1.39579 + 0.563297i
\(238\) 114.293 0.480221
\(239\) 337.680i 1.41289i −0.707770 0.706443i \(-0.750299\pi\)
0.707770 0.706443i \(-0.249701\pi\)
\(240\) −10.0419 + 24.8829i −0.0418414 + 0.103679i
\(241\) 127.860 0.530539 0.265270 0.964174i \(-0.414539\pi\)
0.265270 + 0.964174i \(0.414539\pi\)
\(242\) 227.666i 0.940768i
\(243\) −82.6603 + 228.509i −0.340166 + 0.940365i
\(244\) 114.368 0.468721
\(245\) 101.384i 0.413812i
\(246\) 132.610 + 53.5170i 0.539065 + 0.217549i
\(247\) 266.977 1.08088
\(248\) 36.1467i 0.145753i
\(249\) −14.8767 + 36.8630i −0.0597457 + 0.148044i
\(250\) 15.8114 0.0632456
\(251\) 117.132i 0.466662i 0.972397 + 0.233331i \(0.0749625\pi\)
−0.972397 + 0.233331i \(0.925037\pi\)
\(252\) −125.859 121.349i −0.499442 0.481545i
\(253\) −80.5334 −0.318314
\(254\) 129.541i 0.510003i
\(255\) 51.7602 + 20.8887i 0.202981 + 0.0819166i
\(256\) 16.0000 0.0625000
\(257\) 95.1801i 0.370351i −0.982706 0.185175i \(-0.940715\pi\)
0.982706 0.185175i \(-0.0592853\pi\)
\(258\) 66.4592 164.679i 0.257594 0.638292i
\(259\) −470.146 −1.81524
\(260\) 63.5936i 0.244591i
\(261\) 52.2164 54.1571i 0.200063 0.207498i
\(262\) 195.097 0.744646
\(263\) 189.537i 0.720673i −0.932822 0.360336i \(-0.882662\pi\)
0.932822 0.360336i \(-0.117338\pi\)
\(264\) −132.134 53.3248i −0.500506 0.201988i
\(265\) −144.638 −0.545802
\(266\) 257.893i 0.969522i
\(267\) 163.765 405.794i 0.613352 1.51983i
\(268\) 122.427 0.456817
\(269\) 44.1590i 0.164160i 0.996626 + 0.0820799i \(0.0261563\pi\)
−0.996626 + 0.0820799i \(0.973844\pi\)
\(270\) −34.8201 77.9587i −0.128963 0.288736i
\(271\) −198.521 −0.732548 −0.366274 0.930507i \(-0.619367\pi\)
−0.366274 + 0.930507i \(0.619367\pi\)
\(272\) 33.2824i 0.122362i
\(273\) 384.240 + 155.067i 1.40747 + 0.568011i
\(274\) −85.8225 −0.313221
\(275\) 83.9619i 0.305316i
\(276\) −10.7688 + 26.6840i −0.0390173 + 0.0966810i
\(277\) 516.578 1.86490 0.932452 0.361295i \(-0.117665\pi\)
0.932452 + 0.361295i \(0.117665\pi\)
\(278\) 152.001i 0.546766i
\(279\) 82.8002 + 79.8330i 0.296775 + 0.286140i
\(280\) 61.4297 0.219392
\(281\) 263.794i 0.938769i −0.882994 0.469385i \(-0.844476\pi\)
0.882994 0.469385i \(-0.155524\pi\)
\(282\) −100.113 40.4025i −0.355012 0.143271i
\(283\) 100.543 0.355277 0.177639 0.984096i \(-0.443154\pi\)
0.177639 + 0.984096i \(0.443154\pi\)
\(284\) 198.098i 0.697527i
\(285\) −47.1339 + 116.793i −0.165382 + 0.409800i
\(286\) 337.696 1.18075
\(287\) 327.381i 1.14070i
\(288\) −35.3373 + 36.6507i −0.122699 + 0.127259i
\(289\) 219.768 0.760442
\(290\) 26.4331i 0.0911486i
\(291\) −462.247 186.548i −1.58848 0.641058i
\(292\) −3.42675 −0.0117354
\(293\) 334.768i 1.14255i −0.820758 0.571276i \(-0.806449\pi\)
0.820758 0.571276i \(-0.193551\pi\)
\(294\) −71.9899 + 178.384i −0.244864 + 0.606748i
\(295\) −78.4115 −0.265802
\(296\) 136.908i 0.462527i
\(297\) 413.978 184.902i 1.39386 0.622566i
\(298\) 48.2878 0.162039
\(299\) 68.1965i 0.228082i
\(300\) 27.8199 + 11.2272i 0.0927332 + 0.0374241i
\(301\) −406.552 −1.35067
\(302\) 217.705i 0.720878i
\(303\) −113.746 + 281.850i −0.375398 + 0.930199i
\(304\) 75.0993 0.247037
\(305\) 127.867i 0.419236i
\(306\) 76.2389 + 73.5069i 0.249147 + 0.240219i
\(307\) −273.175 −0.889819 −0.444910 0.895575i \(-0.646764\pi\)
−0.444910 + 0.895575i \(0.646764\pi\)
\(308\) 326.205i 1.05911i
\(309\) −435.408 175.717i −1.40909 0.568662i
\(310\) −40.4133 −0.130365
\(311\) 364.172i 1.17097i 0.810683 + 0.585485i \(0.199096\pi\)
−0.810683 + 0.585485i \(0.800904\pi\)
\(312\) 45.1560 111.892i 0.144731 0.358629i
\(313\) −499.143 −1.59471 −0.797354 0.603512i \(-0.793767\pi\)
−0.797354 + 0.603512i \(0.793767\pi\)
\(314\) 96.6404i 0.307772i
\(315\) −135.673 + 140.715i −0.430707 + 0.446715i
\(316\) −237.817 −0.752586
\(317\) 609.173i 1.92168i 0.277099 + 0.960841i \(0.410627\pi\)
−0.277099 + 0.960841i \(0.589373\pi\)
\(318\) −254.488 102.703i −0.800277 0.322966i
\(319\) −140.366 −0.440017
\(320\) 17.8885i 0.0559017i
\(321\) 55.6836 137.979i 0.173469 0.429840i
\(322\) 65.8760 0.204584
\(323\) 156.218i 0.483646i
\(324\) −5.90920 161.892i −0.0182383 0.499667i
\(325\) −71.0998 −0.218769
\(326\) 227.411i 0.697580i
\(327\) −26.5470 10.7135i −0.0811835 0.0327630i
\(328\) −95.3344 −0.290654
\(329\) 247.155i 0.751231i
\(330\) −59.6190 + 147.730i −0.180664 + 0.447667i
\(331\) 212.610 0.642326 0.321163 0.947024i \(-0.395926\pi\)
0.321163 + 0.947024i \(0.395926\pi\)
\(332\) 26.5011i 0.0798226i
\(333\) −313.611 302.373i −0.941775 0.908027i
\(334\) −288.330 −0.863265
\(335\) 136.877i 0.408589i
\(336\) 108.085 + 43.6195i 0.321681 + 0.129820i
\(337\) 186.428 0.553199 0.276600 0.960985i \(-0.410792\pi\)
0.276600 + 0.960985i \(0.410792\pi\)
\(338\) 46.9620i 0.138941i
\(339\) −218.596 + 541.660i −0.644826 + 1.59782i
\(340\) −37.2109 −0.109444
\(341\) 214.603i 0.629335i
\(342\) −165.863 + 172.028i −0.484979 + 0.503005i
\(343\) −35.5465 −0.103634
\(344\) 118.389i 0.344155i
\(345\) 29.8336 + 12.0399i 0.0864741 + 0.0348981i
\(346\) 54.2470 0.156783
\(347\) 144.932i 0.417672i −0.977951 0.208836i \(-0.933033\pi\)
0.977951 0.208836i \(-0.0669674\pi\)
\(348\) −18.7694 + 46.5087i −0.0539351 + 0.133646i
\(349\) 217.428 0.623003 0.311502 0.950246i \(-0.399168\pi\)
0.311502 + 0.950246i \(0.399168\pi\)
\(350\) 68.6805i 0.196230i
\(351\) 156.577 + 350.560i 0.446088 + 0.998748i
\(352\) 94.9921 0.269864
\(353\) 252.766i 0.716052i 0.933712 + 0.358026i \(0.116550\pi\)
−0.933712 + 0.358026i \(0.883450\pi\)
\(354\) −137.964 55.6778i −0.389729 0.157282i
\(355\) −221.480 −0.623887
\(356\) 291.729i 0.819462i
\(357\) 90.7352 224.833i 0.254160 0.629784i
\(358\) −51.5795 −0.144077
\(359\) 310.853i 0.865887i 0.901421 + 0.432943i \(0.142525\pi\)
−0.901421 + 0.432943i \(0.857475\pi\)
\(360\) 40.9767 + 39.5083i 0.113824 + 0.109745i
\(361\) −8.50620 −0.0235629
\(362\) 481.819i 1.33099i
\(363\) −447.857 180.740i −1.23377 0.497907i
\(364\) −276.234 −0.758884
\(365\) 3.83122i 0.0104965i
\(366\) 90.7948 224.981i 0.248073 0.614701i
\(367\) 578.070 1.57512 0.787561 0.616237i \(-0.211344\pi\)
0.787561 + 0.616237i \(0.211344\pi\)
\(368\) 19.1833i 0.0521286i
\(369\) 210.554 218.380i 0.570607 0.591814i
\(370\) 153.068 0.413697
\(371\) 628.267i 1.69344i
\(372\) −71.1067 28.6963i −0.191147 0.0771407i
\(373\) 547.166 1.46693 0.733466 0.679726i \(-0.237901\pi\)
0.733466 + 0.679726i \(0.237901\pi\)
\(374\) 197.598i 0.528336i
\(375\) 12.5524 31.1036i 0.0334731 0.0829431i
\(376\) 71.9723 0.191416
\(377\) 118.863i 0.315286i
\(378\) −338.632 + 151.249i −0.895852 + 0.400130i
\(379\) −176.439 −0.465539 −0.232769 0.972532i \(-0.574779\pi\)
−0.232769 + 0.972532i \(0.574779\pi\)
\(380\) 83.9635i 0.220957i
\(381\) 254.828 + 102.840i 0.668841 + 0.269922i
\(382\) 264.771 0.693118
\(383\) 102.841i 0.268513i 0.990947 + 0.134257i \(0.0428646\pi\)
−0.990947 + 0.134257i \(0.957135\pi\)
\(384\) 12.7022 31.4747i 0.0330785 0.0819653i
\(385\) 364.708 0.947295
\(386\) 530.471i 1.37428i
\(387\) −271.191 261.473i −0.700751 0.675640i
\(388\) 332.314 0.856478
\(389\) 225.716i 0.580248i −0.956989 0.290124i \(-0.906304\pi\)
0.956989 0.290124i \(-0.0936965\pi\)
\(390\) −125.099 50.4860i −0.320767 0.129451i
\(391\) −39.9042 −0.102057
\(392\) 128.242i 0.327147i
\(393\) 154.885 383.789i 0.394108 0.976562i
\(394\) 282.105 0.716002
\(395\) 265.888i 0.673134i
\(396\) −209.798 + 217.595i −0.529792 + 0.549483i
\(397\) 267.452 0.673682 0.336841 0.941562i \(-0.390642\pi\)
0.336841 + 0.941562i \(0.390642\pi\)
\(398\) 468.230i 1.17646i
\(399\) 507.318 + 204.737i 1.27147 + 0.513126i
\(400\) −20.0000 −0.0500000
\(401\) 440.820i 1.09930i 0.835395 + 0.549651i \(0.185239\pi\)
−0.835395 + 0.549651i \(0.814761\pi\)
\(402\) 97.1929 240.834i 0.241773 0.599090i
\(403\) 181.728 0.450938
\(404\) 202.625i 0.501546i
\(405\) −181.001 + 6.60669i −0.446916 + 0.0163128i
\(406\) 114.818 0.282804
\(407\) 812.824i 1.99711i
\(408\) −65.4720 26.4224i −0.160471 0.0647607i
\(409\) 62.7728 0.153479 0.0767393 0.997051i \(-0.475549\pi\)
0.0767393 + 0.997051i \(0.475549\pi\)
\(410\) 106.587i 0.259969i
\(411\) −68.1332 + 168.827i −0.165774 + 0.410772i
\(412\) 313.019 0.759754
\(413\) 340.599i 0.824695i
\(414\) 43.9426 + 42.3680i 0.106142 + 0.102338i
\(415\) −29.6291 −0.0713955
\(416\) 80.4402i 0.193366i
\(417\) 299.011 + 120.671i 0.717053 + 0.289379i
\(418\) 445.865 1.06666
\(419\) 678.217i 1.61866i 0.587357 + 0.809328i \(0.300168\pi\)
−0.587357 + 0.809328i \(0.699832\pi\)
\(420\) 48.7681 120.843i 0.116115 0.287720i
\(421\) 104.952 0.249293 0.124646 0.992201i \(-0.460220\pi\)
0.124646 + 0.992201i \(0.460220\pi\)
\(422\) 463.329i 1.09794i
\(423\) −158.957 + 164.865i −0.375785 + 0.389751i
\(424\) 182.954 0.431494
\(425\) 41.6030i 0.0978894i
\(426\) −389.691 157.267i −0.914769 0.369171i
\(427\) −555.421 −1.30075
\(428\) 99.1940i 0.231762i
\(429\) 268.091 664.304i 0.624922 1.54849i
\(430\) 132.363 0.307822
\(431\) 155.310i 0.360349i −0.983635 0.180174i \(-0.942334\pi\)
0.983635 0.180174i \(-0.0576662\pi\)
\(432\) 44.0443 + 98.6109i 0.101954 + 0.228266i
\(433\) −618.290 −1.42792 −0.713961 0.700185i \(-0.753101\pi\)
−0.713961 + 0.700185i \(0.753101\pi\)
\(434\) 175.545i 0.404481i
\(435\) 51.9983 + 20.9848i 0.119536 + 0.0482410i
\(436\) 19.0849 0.0437727
\(437\) 90.0409i 0.206043i
\(438\) −2.72044 + 6.74099i −0.00621106 + 0.0153904i
\(439\) −103.321 −0.235356 −0.117678 0.993052i \(-0.537545\pi\)
−0.117678 + 0.993052i \(0.537545\pi\)
\(440\) 106.204i 0.241374i
\(441\) 293.759 + 283.232i 0.666121 + 0.642250i
\(442\) 167.328 0.378570
\(443\) 190.496i 0.430013i 0.976613 + 0.215006i \(0.0689772\pi\)
−0.976613 + 0.215006i \(0.931023\pi\)
\(444\) 269.321 + 108.689i 0.606579 + 0.244796i
\(445\) 326.162 0.732949
\(446\) 562.513i 1.26124i
\(447\) 38.3349 94.9901i 0.0857604 0.212506i
\(448\) −77.7031 −0.173445
\(449\) 2.15568i 0.00480107i −0.999997 0.00240053i \(-0.999236\pi\)
0.999997 0.00240053i \(-0.000764114\pi\)
\(450\) 44.1717 45.8134i 0.0981592 0.101807i
\(451\) −566.001 −1.25499
\(452\) 389.404i 0.861513i
\(453\) −428.262 172.833i −0.945391 0.381529i
\(454\) 107.976 0.237832
\(455\) 308.839i 0.678767i
\(456\) 59.6202 147.733i 0.130746 0.323976i
\(457\) −400.938 −0.877326 −0.438663 0.898652i \(-0.644548\pi\)
−0.438663 + 0.898652i \(0.644548\pi\)
\(458\) 134.450i 0.293559i
\(459\) 205.125 91.6187i 0.446896 0.199605i
\(460\) −21.4476 −0.0466252
\(461\) 416.867i 0.904266i 0.891951 + 0.452133i \(0.149337\pi\)
−0.891951 + 0.452133i \(0.850663\pi\)
\(462\) 641.700 + 258.969i 1.38896 + 0.560540i
\(463\) −211.974 −0.457827 −0.228913 0.973447i \(-0.573517\pi\)
−0.228913 + 0.973447i \(0.573517\pi\)
\(464\) 33.4355i 0.0720593i
\(465\) −32.0835 + 79.4997i −0.0689967 + 0.170967i
\(466\) 526.652 1.13016
\(467\) 536.033i 1.14782i 0.818918 + 0.573911i \(0.194574\pi\)
−0.818918 + 0.573911i \(0.805426\pi\)
\(468\) −184.262 177.659i −0.393722 0.379613i
\(469\) −594.560 −1.26772
\(470\) 80.4675i 0.171208i
\(471\) 190.108 + 76.7214i 0.403626 + 0.162890i
\(472\) 99.1836 0.210135
\(473\) 702.878i 1.48600i
\(474\) −188.800 + 467.826i −0.398311 + 0.986976i
\(475\) −93.8741 −0.197630
\(476\) 161.634i 0.339568i
\(477\) −404.068 + 419.086i −0.847103 + 0.878587i
\(478\) 477.551 0.999061
\(479\) 143.758i 0.300120i 0.988677 + 0.150060i \(0.0479467\pi\)
−0.988677 + 0.150060i \(0.952053\pi\)
\(480\) −35.1898 14.2014i −0.0733120 0.0295863i
\(481\) −688.307 −1.43099
\(482\) 180.821i 0.375148i
\(483\) 52.2980 129.589i 0.108277 0.268301i
\(484\) 321.968 0.665223
\(485\) 371.538i 0.766058i
\(486\) −323.160 116.899i −0.664939 0.240534i
\(487\) −454.474 −0.933211 −0.466605 0.884466i \(-0.654523\pi\)
−0.466605 + 0.884466i \(0.654523\pi\)
\(488\) 161.741i 0.331435i
\(489\) 447.356 + 180.538i 0.914838 + 0.369199i
\(490\) −143.379 −0.292609
\(491\) 414.443i 0.844079i 0.906577 + 0.422039i \(0.138686\pi\)
−0.906577 + 0.422039i \(0.861314\pi\)
\(492\) −75.6845 + 187.539i −0.153830 + 0.381176i
\(493\) −69.5509 −0.141077
\(494\) 377.563i 0.764297i
\(495\) 243.279 + 234.561i 0.491473 + 0.473861i
\(496\) 51.1192 0.103063
\(497\) 962.051i 1.93572i
\(498\) −52.1321 21.0388i −0.104683 0.0422466i
\(499\) −408.192 −0.818021 −0.409010 0.912530i \(-0.634126\pi\)
−0.409010 + 0.912530i \(0.634126\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) −228.901 + 567.194i −0.456888 + 1.13212i
\(502\) −165.650 −0.329980
\(503\) 541.009i 1.07556i −0.843084 0.537782i \(-0.819262\pi\)
0.843084 0.537782i \(-0.180738\pi\)
\(504\) 171.614 177.992i 0.340504 0.353159i
\(505\) −226.541 −0.448596
\(506\) 113.891i 0.225082i
\(507\) 92.3821 + 37.2824i 0.182213 + 0.0735353i
\(508\) −183.198 −0.360626
\(509\) 508.935i 0.999872i −0.866062 0.499936i \(-0.833357\pi\)
0.866062 0.499936i \(-0.166643\pi\)
\(510\) −29.5411 + 73.2000i −0.0579238 + 0.143529i
\(511\) 16.6418 0.0325672
\(512\) 22.6274i 0.0441942i
\(513\) 206.731 + 462.850i 0.402984 + 0.902242i
\(514\) 134.605 0.261877
\(515\) 349.966i 0.679545i
\(516\) 232.892 + 93.9874i 0.451340 + 0.182146i
\(517\) 427.300 0.826499
\(518\) 664.887i 1.28357i
\(519\) 43.0659 106.713i 0.0829786 0.205613i
\(520\) 89.9349 0.172952
\(521\) 326.505i 0.626689i −0.949640 0.313344i \(-0.898551\pi\)
0.949640 0.313344i \(-0.101449\pi\)
\(522\) 76.5897 + 73.8451i 0.146724 + 0.141466i
\(523\) 651.561 1.24581 0.622907 0.782296i \(-0.285951\pi\)
0.622907 + 0.782296i \(0.285951\pi\)
\(524\) 275.909i 0.526544i
\(525\) −135.106 54.5244i −0.257345 0.103856i
\(526\) 268.046 0.509592
\(527\) 106.336i 0.201775i
\(528\) 75.4127 186.865i 0.142827 0.353911i
\(529\) −23.0000 −0.0434783
\(530\) 204.548i 0.385940i
\(531\) −219.055 + 227.197i −0.412533 + 0.427866i
\(532\) −364.716 −0.685556
\(533\) 479.295i 0.899240i
\(534\) 573.879 + 231.599i 1.07468 + 0.433706i
\(535\) 110.902 0.207294
\(536\) 173.138i 0.323018i
\(537\) −40.9482 + 101.465i −0.0762535 + 0.188949i
\(538\) −62.4502 −0.116078
\(539\) 761.371i 1.41256i
\(540\) 110.250 49.2430i 0.204167 0.0911908i
\(541\) −561.296 −1.03752 −0.518758 0.854921i \(-0.673605\pi\)
−0.518758 + 0.854921i \(0.673605\pi\)
\(542\) 280.751i 0.517990i
\(543\) −947.818 382.509i −1.74552 0.704436i
\(544\) 47.0684 0.0865228
\(545\) 21.3375i 0.0391514i
\(546\) −219.298 + 543.398i −0.401644 + 0.995235i
\(547\) −539.069 −0.985500 −0.492750 0.870171i \(-0.664008\pi\)
−0.492750 + 0.870171i \(0.664008\pi\)
\(548\) 121.371i 0.221481i
\(549\) −370.494 357.217i −0.674852 0.650669i
\(550\) −118.740 −0.215891
\(551\) 156.936i 0.284821i
\(552\) −37.7368 15.2293i −0.0683638 0.0275894i
\(553\) 1154.95 2.08851
\(554\) 730.552i 1.31869i
\(555\) 121.518 301.110i 0.218952 0.542541i
\(556\) −214.962 −0.386622
\(557\) 613.984i 1.10231i −0.834404 0.551153i \(-0.814188\pi\)
0.834404 0.551153i \(-0.185812\pi\)
\(558\) −112.901 + 117.097i −0.202331 + 0.209851i
\(559\) −595.204 −1.06477
\(560\) 86.8747i 0.155133i
\(561\) −388.708 156.870i −0.692884 0.279625i
\(562\) 373.061 0.663810
\(563\) 522.289i 0.927689i 0.885917 + 0.463844i \(0.153530\pi\)
−0.885917 + 0.463844i \(0.846470\pi\)
\(564\) 57.1377 141.582i 0.101308 0.251031i
\(565\) −435.367 −0.770560
\(566\) 142.190i 0.251219i
\(567\) 28.6977 + 786.221i 0.0506132 + 1.38663i
\(568\) 280.153 0.493226
\(569\) 835.117i 1.46769i −0.679316 0.733846i \(-0.737723\pi\)
0.679316 0.733846i \(-0.262277\pi\)
\(570\) −165.170 66.6574i −0.289773 0.116943i
\(571\) −973.842 −1.70550 −0.852752 0.522316i \(-0.825068\pi\)
−0.852752 + 0.522316i \(0.825068\pi\)
\(572\) 477.574i 0.834919i
\(573\) 210.198 520.849i 0.366837 0.908986i
\(574\) 462.986 0.806596
\(575\) 23.9792i 0.0417029i
\(576\) −51.8319 49.9745i −0.0899860 0.0867613i
\(577\) 556.066 0.963719 0.481859 0.876249i \(-0.339962\pi\)
0.481859 + 0.876249i \(0.339962\pi\)
\(578\) 310.798i 0.537713i
\(579\) 1043.52 + 421.133i 1.80229 + 0.727345i
\(580\) −37.3821 −0.0644518
\(581\) 128.701i 0.221517i
\(582\) 263.819 653.716i 0.453297 1.12322i
\(583\) 1086.20 1.86312
\(584\) 4.84616i 0.00829821i
\(585\) −198.629 + 206.011i −0.339536 + 0.352156i
\(586\) 473.433 0.807906
\(587\) 455.905i 0.776669i 0.921519 + 0.388334i \(0.126949\pi\)
−0.921519 + 0.388334i \(0.873051\pi\)
\(588\) −252.273 101.809i −0.429035 0.173145i
\(589\) 239.938 0.407366
\(590\) 110.891i 0.187950i
\(591\) 223.959 554.948i 0.378949 0.938998i
\(592\) −193.617 −0.327056
\(593\) 1016.74i 1.71457i 0.514842 + 0.857285i \(0.327851\pi\)
−0.514842 + 0.857285i \(0.672149\pi\)
\(594\) 261.491 + 585.453i 0.440221 + 0.985611i
\(595\) 180.713 0.303719
\(596\) 68.2892i 0.114579i
\(597\) 921.086 + 371.720i 1.54286 + 0.622647i
\(598\) 96.4444 0.161278
\(599\) 6.66161i 0.0111212i −0.999985 0.00556061i \(-0.998230\pi\)
0.999985 0.00556061i \(-0.00177001\pi\)
\(600\) −15.8777 + 39.3433i −0.0264628 + 0.0655722i
\(601\) 451.786 0.751724 0.375862 0.926676i \(-0.377347\pi\)
0.375862 + 0.926676i \(0.377347\pi\)
\(602\) 574.951i 0.955069i
\(603\) −396.601 382.389i −0.657714 0.634145i
\(604\) 307.881 0.509737
\(605\) 359.971i 0.594994i
\(606\) −398.596 160.861i −0.657750 0.265446i
\(607\) −263.050 −0.433361 −0.216680 0.976243i \(-0.569523\pi\)
−0.216680 + 0.976243i \(0.569523\pi\)
\(608\) 106.206i 0.174682i
\(609\) 91.1526 225.867i 0.149676 0.370882i
\(610\) 180.831 0.296445
\(611\) 361.842i 0.592213i
\(612\) −103.955 + 107.818i −0.169860 + 0.176173i
\(613\) 613.976 1.00159 0.500796 0.865565i \(-0.333041\pi\)
0.500796 + 0.865565i \(0.333041\pi\)
\(614\) 386.327i 0.629197i
\(615\) 209.675 + 84.6179i 0.340934 + 0.137590i
\(616\) −461.324 −0.748902
\(617\) 1142.79i 1.85217i 0.377316 + 0.926084i \(0.376847\pi\)
−0.377316 + 0.926084i \(0.623153\pi\)
\(618\) 248.501 615.760i 0.402105 0.996376i
\(619\) −590.671 −0.954234 −0.477117 0.878840i \(-0.658318\pi\)
−0.477117 + 0.878840i \(0.658318\pi\)
\(620\) 57.1530i 0.0921822i
\(621\) 118.230 52.8073i 0.190387 0.0850358i
\(622\) −515.017 −0.828001
\(623\) 1416.76i 2.27410i
\(624\) 158.239 + 63.8603i 0.253589 + 0.102340i
\(625\) 25.0000 0.0400000
\(626\) 705.895i 1.12763i
\(627\) 353.965 877.090i 0.564538 1.39887i
\(628\) −136.670 −0.217628
\(629\) 402.753i 0.640307i
\(630\) −199.001 191.870i −0.315875 0.304556i
\(631\) 316.818 0.502089 0.251044 0.967976i \(-0.419226\pi\)
0.251044 + 0.967976i \(0.419226\pi\)
\(632\) 336.324i 0.532159i
\(633\) −911.445 367.830i −1.43988 0.581089i
\(634\) −861.501 −1.35883
\(635\) 204.822i 0.322554i
\(636\) 145.244 359.900i 0.228371 0.565881i
\(637\) 644.737 1.01215
\(638\) 198.507i 0.311139i
\(639\) −618.740 + 641.737i −0.968294 + 1.00428i
\(640\) 25.2982 0.0395285
\(641\) 617.453i 0.963265i −0.876373 0.481633i \(-0.840044\pi\)
0.876373 0.481633i \(-0.159956\pi\)
\(642\) 195.131 + 78.7486i 0.303943 + 0.122661i
\(643\) −465.627 −0.724148 −0.362074 0.932149i \(-0.617931\pi\)
−0.362074 + 0.932149i \(0.617931\pi\)
\(644\) 93.1628i 0.144663i
\(645\) 105.081 260.381i 0.162917 0.403691i
\(646\) 220.925 0.341990
\(647\) 439.316i 0.679005i −0.940605 0.339503i \(-0.889741\pi\)
0.940605 0.339503i \(-0.110259\pi\)
\(648\) 228.950 8.35687i 0.353318 0.0128964i
\(649\) 588.853 0.907324
\(650\) 100.550i 0.154693i
\(651\) 345.326 + 139.362i 0.530454 + 0.214074i
\(652\) −321.608 −0.493264
\(653\) 1275.64i 1.95350i 0.214377 + 0.976751i \(0.431228\pi\)
−0.214377 + 0.976751i \(0.568772\pi\)
\(654\) 15.1512 37.5431i 0.0231670 0.0574054i
\(655\) 308.476 0.470955
\(656\) 134.823i 0.205523i
\(657\) 11.1009 + 10.7031i 0.0168964 + 0.0162909i
\(658\) −349.530 −0.531200
\(659\) 1058.48i 1.60619i −0.595851 0.803095i \(-0.703185\pi\)
0.595851 0.803095i \(-0.296815\pi\)
\(660\) −208.922 84.3140i −0.316548 0.127748i
\(661\) 74.3586 0.112494 0.0562470 0.998417i \(-0.482087\pi\)
0.0562470 + 0.998417i \(0.482087\pi\)
\(662\) 300.676i 0.454193i
\(663\) 132.839 329.162i 0.200360 0.496473i
\(664\) 37.4782 0.0564431
\(665\) 407.764i 0.613180i
\(666\) 427.620 443.513i 0.642072 0.665936i
\(667\) −40.0878 −0.0601016
\(668\) 407.761i 0.610420i
\(669\) −1106.56 446.571i −1.65405 0.667520i
\(670\) 193.574 0.288916
\(671\) 960.254i 1.43108i
\(672\) −61.6873 + 152.855i −0.0917966 + 0.227463i
\(673\) 495.673 0.736513 0.368256 0.929724i \(-0.379955\pi\)
0.368256 + 0.929724i \(0.379955\pi\)
\(674\) 263.649i 0.391171i
\(675\) −55.0554 123.264i −0.0815635 0.182613i
\(676\) −66.4143 −0.0982460
\(677\) 179.621i 0.265319i −0.991162 0.132660i \(-0.957648\pi\)
0.991162 0.132660i \(-0.0423517\pi\)
\(678\) −766.022 309.142i −1.12983 0.455961i
\(679\) −1613.86 −2.37682
\(680\) 52.6241i 0.0773884i
\(681\) 85.7201 212.406i 0.125874 0.311903i
\(682\) 303.495 0.445007
\(683\) 144.842i 0.212067i 0.994363 + 0.106034i \(0.0338151\pi\)
−0.994363 + 0.106034i \(0.966185\pi\)
\(684\) −243.284 234.566i −0.355678 0.342932i
\(685\) −135.697 −0.198098
\(686\) 50.2704i 0.0732804i
\(687\) −264.486 106.738i −0.384986 0.155368i
\(688\) −167.428 −0.243354
\(689\) 919.802i 1.33498i
\(690\) −17.0269 + 42.1910i −0.0246767 + 0.0611464i
\(691\) −877.963 −1.27057 −0.635284 0.772278i \(-0.719117\pi\)
−0.635284 + 0.772278i \(0.719117\pi\)
\(692\) 76.7169i 0.110863i
\(693\) 1018.87 1056.74i 1.47023 1.52488i
\(694\) 204.965 0.295338
\(695\) 240.334i 0.345805i
\(696\) −65.7733 26.5439i −0.0945018 0.0381379i
\(697\) −280.452 −0.402371
\(698\) 307.490i 0.440530i
\(699\) 418.101 1036.01i 0.598142 1.48214i
\(700\) 97.1289 0.138756
\(701\) 1173.42i 1.67393i −0.547259 0.836964i \(-0.684329\pi\)
0.547259 0.836964i \(-0.315671\pi\)
\(702\) −495.767 + 221.433i −0.706221 + 0.315432i
\(703\) −908.783 −1.29272
\(704\) 134.339i 0.190823i
\(705\) −158.293 63.8819i −0.224529 0.0906127i
\(706\) −357.466 −0.506325
\(707\) 984.035i 1.39185i
\(708\) 78.7403 195.111i 0.111215 0.275580i
\(709\) 1123.63 1.58481 0.792407 0.609993i \(-0.208828\pi\)
0.792407 + 0.609993i \(0.208828\pi\)
\(710\) 313.220i 0.441155i
\(711\) 770.408 + 742.800i 1.08356 + 1.04473i
\(712\) −412.566 −0.579447
\(713\) 61.2898i 0.0859604i
\(714\) 317.961 + 128.319i 0.445324 + 0.179718i
\(715\) 533.944 0.746775
\(716\) 72.9444i 0.101878i
\(717\) 379.120 939.423i 0.528759 1.31021i
\(718\) −439.613 −0.612274
\(719\) 1040.78i 1.44753i −0.690044 0.723767i \(-0.742409\pi\)
0.690044 0.723767i \(-0.257591\pi\)
\(720\) −55.8732 + 57.9498i −0.0776017 + 0.0804859i
\(721\) −1520.16 −2.10840
\(722\) 12.0296i 0.0166615i
\(723\) 355.706 + 143.551i 0.491986 + 0.198549i
\(724\) 681.395 0.941153
\(725\) 41.7944i 0.0576475i
\(726\) 255.606 633.365i 0.352074 0.872404i
\(727\) 501.507 0.689831 0.344916 0.938634i \(-0.387908\pi\)
0.344916 + 0.938634i \(0.387908\pi\)
\(728\) 390.654i 0.536612i
\(729\) −486.512 + 542.906i −0.667370 + 0.744727i
\(730\) −5.41817 −0.00742215
\(731\) 348.275i 0.476436i
\(732\) 318.171 + 128.403i 0.434659 + 0.175414i
\(733\) −110.721 −0.151052 −0.0755261 0.997144i \(-0.524064\pi\)
−0.0755261 + 0.997144i \(0.524064\pi\)
\(734\) 817.514i 1.11378i
\(735\) −113.826 + 282.050i −0.154865 + 0.383741i
\(736\) 27.1293 0.0368605
\(737\) 1027.92i 1.39474i
\(738\) 308.835 + 297.768i 0.418476 + 0.403480i
\(739\) −637.166 −0.862200 −0.431100 0.902304i \(-0.641874\pi\)
−0.431100 + 0.902304i \(0.641874\pi\)
\(740\) 216.471i 0.292528i
\(741\) 742.729 + 299.741i 1.00233 + 0.404509i
\(742\) −888.504 −1.19745
\(743\) 174.168i 0.234412i 0.993108 + 0.117206i \(0.0373937\pi\)
−0.993108 + 0.117206i \(0.962606\pi\)
\(744\) 40.5827 100.560i 0.0545467 0.135161i
\(745\) 76.3497 0.102483
\(746\) 773.809i 1.03728i
\(747\) −82.7737 + 85.8502i −0.110808 + 0.114927i
\(748\) 279.445 0.373590
\(749\) 481.730i 0.643164i
\(750\) 43.9872 + 17.7518i 0.0586496 + 0.0236691i
\(751\) 1041.90 1.38735 0.693676 0.720287i \(-0.255990\pi\)
0.693676 + 0.720287i \(0.255990\pi\)
\(752\) 101.784i 0.135351i
\(753\) −131.507 + 325.861i −0.174644 + 0.432750i
\(754\) 168.098 0.222941
\(755\) 344.222i 0.455923i
\(756\) −213.899 478.898i −0.282935 0.633463i
\(757\) 1352.49 1.78664 0.893321 0.449419i \(-0.148369\pi\)
0.893321 + 0.449419i \(0.148369\pi\)
\(758\) 249.523i 0.329186i
\(759\) −224.044 90.4167i −0.295183 0.119126i
\(760\) 118.742 0.156240
\(761\) 786.105i 1.03299i −0.856290 0.516495i \(-0.827237\pi\)
0.856290 0.516495i \(-0.172763\pi\)
\(762\) −145.438 + 360.382i −0.190864 + 0.472942i
\(763\) −92.6847 −0.121474
\(764\) 374.443i 0.490108i
\(765\) 120.544 + 116.225i 0.157574 + 0.151928i
\(766\) −145.438 −0.189867
\(767\) 498.647i 0.650126i
\(768\) 44.5119 + 17.9636i 0.0579582 + 0.0233900i
\(769\) 273.919 0.356202 0.178101 0.984012i \(-0.443005\pi\)
0.178101 + 0.984012i \(0.443005\pi\)
\(770\) 515.776i 0.669839i
\(771\) 106.861 264.790i 0.138600 0.343438i
\(772\) −750.199 −0.971760
\(773\) 396.276i 0.512647i −0.966591 0.256324i \(-0.917489\pi\)
0.966591 0.256324i \(-0.0825113\pi\)
\(774\) 369.778 383.522i 0.477749 0.495506i
\(775\) −63.8990 −0.0824503
\(776\) 469.962i 0.605622i
\(777\) −1307.94 527.843i −1.68333 0.679335i
\(778\) 319.211 0.410297
\(779\) 632.820i 0.812350i
\(780\) 71.3979 176.917i 0.0915358 0.226817i
\(781\) 1663.27 2.12966
\(782\) 56.4331i 0.0721650i
\(783\) 206.069 92.0403i 0.263179 0.117548i
\(784\) 181.361 0.231328
\(785\) 152.802i 0.194652i
\(786\) 542.759 + 219.040i 0.690533 + 0.278677i
\(787\) −755.682 −0.960206 −0.480103 0.877212i \(-0.659401\pi\)
−0.480103 + 0.877212i \(0.659401\pi\)
\(788\) 398.957i 0.506290i
\(789\) 212.797 527.291i 0.269705 0.668302i
\(790\) −376.022 −0.475977
\(791\) 1891.12i 2.39079i
\(792\) −307.726 296.699i −0.388543 0.374620i
\(793\) −813.153 −1.02541
\(794\) 378.234i 0.476365i
\(795\) −402.381 162.388i −0.506139 0.204261i
\(796\) −662.177 −0.831880
\(797\) 396.840i 0.497917i −0.968514 0.248958i \(-0.919912\pi\)
0.968514 0.248958i \(-0.0800883\pi\)
\(798\) −289.542 + 717.457i −0.362835 + 0.899068i
\(799\) 211.727 0.264989
\(800\) 28.2843i 0.0353553i
\(801\) 911.187 945.053i 1.13756 1.17984i
\(802\) −623.413 −0.777323
\(803\) 28.7716i 0.0358302i
\(804\) 340.591 + 137.451i 0.423621 + 0.170960i
\(805\) 104.159 0.129390
\(806\) 257.002i 0.318862i
\(807\) −49.5783 + 122.850i −0.0614353 + 0.152230i
\(808\) 286.554 0.354647
\(809\) 902.391i 1.11544i 0.830029 + 0.557720i \(0.188324\pi\)
−0.830029 + 0.557720i \(0.811676\pi\)
\(810\) −9.34327 255.974i −0.0115349 0.316017i
\(811\) 137.716 0.169810 0.0849049 0.996389i \(-0.472941\pi\)
0.0849049 + 0.996389i \(0.472941\pi\)
\(812\) 162.378i 0.199973i
\(813\) −552.283 222.884i −0.679315 0.274149i
\(814\) −1149.51 −1.41217
\(815\) 359.569i 0.441188i
\(816\) 37.3669 92.5915i 0.0457928 0.113470i
\(817\) −785.856 −0.961881
\(818\) 88.7741i 0.108526i
\(819\) 894.858 + 862.791i 1.09262 + 1.05347i
\(820\) −150.737 −0.183826
\(821\) 69.2262i 0.0843194i −0.999111 0.0421597i \(-0.986576\pi\)
0.999111 0.0421597i \(-0.0134238\pi\)
\(822\) −238.758 96.3548i −0.290460 0.117220i
\(823\) 850.393 1.03328 0.516642 0.856201i \(-0.327182\pi\)
0.516642 + 0.856201i \(0.327182\pi\)
\(824\) 442.675i 0.537227i
\(825\) −94.2659 + 233.582i −0.114262 + 0.283129i
\(826\) −481.680 −0.583147
\(827\) 1439.96i 1.74118i −0.492006 0.870592i \(-0.663736\pi\)
0.492006 0.870592i \(-0.336264\pi\)
\(828\) −59.9173 + 62.1443i −0.0723639 + 0.0750535i
\(829\) 782.251 0.943608 0.471804 0.881704i \(-0.343603\pi\)
0.471804 + 0.881704i \(0.343603\pi\)
\(830\) 41.9019i 0.0504842i
\(831\) 1437.12 + 579.974i 1.72938 + 0.697923i
\(832\) −113.760 −0.136730
\(833\) 377.258i 0.452891i
\(834\) −170.655 + 422.866i −0.204622 + 0.507033i
\(835\) −455.890 −0.545976
\(836\) 630.548i 0.754244i
\(837\) 140.719 + 315.057i 0.168123 + 0.376412i
\(838\) −959.143 −1.14456
\(839\) 249.787i 0.297720i 0.988858 + 0.148860i \(0.0475604\pi\)
−0.988858 + 0.148860i \(0.952440\pi\)
\(840\) 170.897 + 68.9685i 0.203449 + 0.0821054i
\(841\) 771.129 0.916919
\(842\) 148.425i 0.176277i
\(843\) 296.168 733.874i 0.351326 0.870550i
\(844\) 655.246 0.776358
\(845\) 74.2535i 0.0878739i
\(846\) −233.154 224.799i −0.275596 0.265720i
\(847\) −1563.62 −1.84607
\(848\) 258.735i 0.305113i
\(849\) 279.711 + 112.882i 0.329460 + 0.132959i
\(850\) −58.8355 −0.0692183
\(851\) 232.139i 0.272784i
\(852\) 222.409 551.107i 0.261043 0.646839i
\(853\) 213.094 0.249817 0.124909 0.992168i \(-0.460136\pi\)
0.124909 + 0.992168i \(0.460136\pi\)
\(854\) 785.484i 0.919771i
\(855\) −262.252 + 271.999i −0.306728 + 0.318128i
\(856\) −140.281 −0.163880
\(857\) 347.089i 0.405005i 0.979282 + 0.202503i \(0.0649075\pi\)
−0.979282 + 0.202503i \(0.935093\pi\)
\(858\) 939.468 + 379.139i 1.09495 + 0.441886i
\(859\) −629.153 −0.732425 −0.366212 0.930531i \(-0.619346\pi\)
−0.366212 + 0.930531i \(0.619346\pi\)
\(860\) 187.190i 0.217663i
\(861\) 367.558 910.772i 0.426896 1.05781i
\(862\) 219.642 0.254805
\(863\) 434.058i 0.502964i 0.967862 + 0.251482i \(0.0809179\pi\)
−0.967862 + 0.251482i \(0.919082\pi\)
\(864\) −139.457 + 62.2880i −0.161408 + 0.0720926i
\(865\) 85.7721 0.0991585
\(866\) 874.395i 1.00969i
\(867\) 611.392 + 246.738i 0.705181 + 0.284588i
\(868\) −248.258 −0.286011
\(869\) 1996.76i 2.29777i
\(870\) −29.6770 + 73.5368i −0.0341115 + 0.0845250i
\(871\) −870.453 −0.999372
\(872\) 26.9901i 0.0309519i
\(873\) −1076.53 1037.95i −1.23314 1.18895i
\(874\) 127.337 0.145695
\(875\) 108.593i 0.124107i
\(876\) −9.53320 3.84729i −0.0108826 0.00439188i
\(877\) −1239.84 −1.41373 −0.706864 0.707350i \(-0.749891\pi\)
−0.706864 + 0.707350i \(0.749891\pi\)
\(878\) 146.118i 0.166422i
\(879\) 375.851 931.322i 0.427589 1.05952i
\(880\) 150.196 0.170677
\(881\) 1441.46i 1.63617i −0.575100 0.818083i \(-0.695037\pi\)
0.575100 0.818083i \(-0.304963\pi\)
\(882\) −400.551 + 415.438i −0.454139 + 0.471018i
\(883\) −1682.05 −1.90493 −0.952464 0.304652i \(-0.901460\pi\)
−0.952464 + 0.304652i \(0.901460\pi\)
\(884\) 236.637i 0.267689i
\(885\) −218.140 88.0343i −0.246486 0.0994738i
\(886\) −269.401 −0.304065
\(887\) 65.3052i 0.0736249i −0.999322 0.0368124i \(-0.988280\pi\)
0.999322 0.0368124i \(-0.0117204\pi\)
\(888\) −153.710 + 380.878i −0.173097 + 0.428916i
\(889\) 889.692 1.00078
\(890\) 461.263i 0.518273i
\(891\) 1359.28 49.6148i 1.52556 0.0556844i
\(892\) 795.514 0.891832
\(893\) 477.745i 0.534989i
\(894\) 134.336 + 54.2137i 0.150264 + 0.0606418i
\(895\) −81.5543 −0.0911221
\(896\) 109.889i 0.122644i
\(897\) 76.5658 189.722i 0.0853576 0.211508i
\(898\) 3.04859 0.00339487
\(899\) 106.825i 0.118826i
\(900\) 64.7899 + 62.4682i 0.0719888 + 0.0694091i
\(901\) 538.209 0.597346
\(902\) 800.446i 0.887412i
\(903\) −1131.03 456.445i −1.25252 0.505476i
\(904\) 550.700 0.609181
\(905\) 761.823i 0.841793i
\(906\) 244.422 605.654i 0.269782 0.668493i
\(907\) −951.333 −1.04888 −0.524439 0.851448i \(-0.675725\pi\)
−0.524439 + 0.851448i \(0.675725\pi\)
\(908\) 152.701i 0.168172i
\(909\) −632.879 + 656.401i −0.696237 + 0.722113i
\(910\) −436.764 −0.479960
\(911\) 381.220i 0.418463i −0.977866 0.209231i \(-0.932904\pi\)
0.977866 0.209231i \(-0.0670962\pi\)
\(912\) 208.926 + 84.3156i 0.229085 + 0.0924513i
\(913\) 222.508 0.243711
\(914\) 567.012i 0.620363i
\(915\) 143.559 355.726i 0.156895 0.388771i
\(916\) 190.141 0.207578
\(917\) 1339.94i 1.46122i
\(918\) 129.568 + 290.091i 0.141142 + 0.316003i
\(919\) 1499.36 1.63151 0.815757 0.578395i \(-0.196321\pi\)
0.815757 + 0.578395i \(0.196321\pi\)
\(920\) 30.3315i 0.0329690i
\(921\) −759.970 306.699i −0.825158 0.333007i
\(922\) −589.538 −0.639413
\(923\) 1408.47i 1.52597i
\(924\) −366.238 + 907.501i −0.396361 + 0.982144i
\(925\) 242.022 0.261645
\(926\) 299.776i 0.323732i
\(927\) −1014.02 977.685i −1.09388 1.05468i
\(928\) 47.2850 0.0509536
\(929\) 925.130i 0.995834i −0.867225 0.497917i \(-0.834098\pi\)
0.867225 0.497917i \(-0.165902\pi\)
\(930\) −112.429 45.3729i −0.120892 0.0487880i
\(931\) 851.255 0.914345
\(932\) 744.799i 0.799141i
\(933\) −408.864 + 1013.12i −0.438225 + 1.08588i
\(934\) −758.064 −0.811632
\(935\) 312.429i 0.334149i
\(936\) 251.248 260.586i 0.268427 0.278403i
\(937\) 1474.31 1.57344 0.786718 0.617313i \(-0.211779\pi\)
0.786718 + 0.617313i \(0.211779\pi\)
\(938\) 840.835i 0.896412i
\(939\) −1388.61 560.399i −1.47882 0.596805i
\(940\) 113.798 0.121062
\(941\) 1018.88i 1.08276i −0.840777 0.541381i \(-0.817902\pi\)
0.840777 0.541381i \(-0.182098\pi\)
\(942\) −108.500 + 268.853i −0.115181 + 0.285407i
\(943\) −161.647 −0.171418
\(944\) 140.267i 0.148588i
\(945\) −535.425 + 239.146i −0.566587 + 0.253065i
\(946\) −994.019 −1.05076
\(947\) 741.719i 0.783230i 0.920129 + 0.391615i \(0.128084\pi\)
−0.920129 + 0.391615i \(0.871916\pi\)
\(948\) −661.607 267.003i −0.697897 0.281649i
\(949\) 24.3641 0.0256735
\(950\) 132.758i 0.139745i
\(951\) −683.933 + 1694.72i −0.719172 + 1.78204i
\(952\) −228.585 −0.240111
\(953\) 184.758i 0.193870i −0.995291 0.0969352i \(-0.969096\pi\)
0.995291 0.0969352i \(-0.0309039\pi\)
\(954\) −592.677 571.439i −0.621255 0.598992i
\(955\) 418.640 0.438366
\(956\) 675.359i 0.706443i
\(957\) −390.496 157.592i −0.408042 0.164672i
\(958\) −203.304 −0.212217
\(959\) 589.433i 0.614633i
\(960\) 20.0839 49.7658i 0.0209207 0.0518394i
\(961\) −797.677 −0.830049
\(962\) 973.414i 1.01186i
\(963\) 309.823 321.338i 0.321727 0.333685i
\(964\) −255.720 −0.265270
\(965\) 838.748i 0.869169i
\(966\) 183.267 + 73.9605i 0.189717 + 0.0765637i
\(967\) 615.373 0.636373 0.318187 0.948028i \(-0.396926\pi\)
0.318187 + 0.948028i \(0.396926\pi\)
\(968\) 455.332i 0.470384i
\(969\) 175.389 434.597i 0.181000 0.448500i
\(970\) 525.434 0.541684
\(971\) 22.2504i 0.0229149i −0.999934 0.0114574i \(-0.996353\pi\)
0.999934 0.0114574i \(-0.00364710\pi\)
\(972\) 165.321 457.018i 0.170083 0.470183i
\(973\) 1043.95 1.07292
\(974\) 642.723i 0.659880i
\(975\) −197.799 79.8253i −0.202871 0.0818721i
\(976\) −228.736 −0.234360
\(977\) 981.189i 1.00429i 0.864784 + 0.502144i \(0.167455\pi\)
−0.864784 + 0.502144i \(0.832545\pi\)
\(978\) −255.320 + 632.657i −0.261063 + 0.646888i
\(979\) −2449.41 −2.50195
\(980\) 202.768i 0.206906i
\(981\) −61.8254 59.6098i −0.0630228 0.0607644i
\(982\) −586.111 −0.596854
\(983\) 1186.61i 1.20713i −0.797312 0.603567i \(-0.793746\pi\)
0.797312 0.603567i \(-0.206254\pi\)
\(984\) −265.220 107.034i −0.269532 0.108774i
\(985\) 446.047 0.452840
\(986\) 98.3598i 0.0997564i
\(987\) −277.486 + 687.584i −0.281141 + 0.696640i
\(988\) −533.954 −0.540439
\(989\) 200.739i 0.202972i
\(990\) −331.719 + 344.048i −0.335070 + 0.347524i
\(991\) −579.495 −0.584758 −0.292379 0.956303i \(-0.594447\pi\)
−0.292379 + 0.956303i \(0.594447\pi\)
\(992\) 72.2935i 0.0728765i
\(993\) 591.480 + 238.702i 0.595649 + 0.240385i
\(994\) −1360.55 −1.36876
\(995\) 740.336i 0.744056i
\(996\) 29.7534 73.7259i 0.0298729 0.0740220i
\(997\) −1032.17 −1.03528 −0.517640 0.855599i \(-0.673189\pi\)
−0.517640 + 0.855599i \(0.673189\pi\)
\(998\) 577.271i 0.578428i
\(999\) −532.984 1193.30i −0.533517 1.19449i
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 690.3.g.a.461.2 yes 56
3.2 odd 2 inner 690.3.g.a.461.1 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
690.3.g.a.461.1 56 3.2 odd 2 inner
690.3.g.a.461.2 yes 56 1.1 even 1 trivial