Properties

Label 280.2.l.a.29.1
Level $280$
Weight $2$
Character 280.29
Analytic conductor $2.236$
Analytic rank $0$
Dimension $36$
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] = [280,2,Mod(29,280)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(280, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("280.29");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.l (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: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(36\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 29.1
Character \(\chi\) \(=\) 280.29
Dual form 280.2.l.a.29.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.38397 - 0.290898i) q^{2} -1.83171 q^{3} +(1.83076 + 0.805189i) q^{4} +(1.41945 - 1.72776i) q^{5} +(2.53504 + 0.532841i) q^{6} +1.00000i q^{7} +(-2.29949 - 1.64692i) q^{8} +0.355171 q^{9} +O(q^{10})\) \(q+(-1.38397 - 0.290898i) q^{2} -1.83171 q^{3} +(1.83076 + 0.805189i) q^{4} +(1.41945 - 1.72776i) q^{5} +(2.53504 + 0.532841i) q^{6} +1.00000i q^{7} +(-2.29949 - 1.64692i) q^{8} +0.355171 q^{9} +(-2.46708 + 1.97826i) q^{10} +1.36479i q^{11} +(-3.35342 - 1.47487i) q^{12} +3.84009 q^{13} +(0.290898 - 1.38397i) q^{14} +(-2.60002 + 3.16476i) q^{15} +(2.70334 + 2.94821i) q^{16} -4.27642i q^{17} +(-0.491547 - 0.103318i) q^{18} -3.72521i q^{19} +(3.98984 - 2.02019i) q^{20} -1.83171i q^{21} +(0.397014 - 1.88883i) q^{22} -5.92347i q^{23} +(4.21200 + 3.01669i) q^{24} +(-0.970325 - 4.90494i) q^{25} +(-5.31458 - 1.11707i) q^{26} +4.84457 q^{27} +(-0.805189 + 1.83076i) q^{28} -7.35246i q^{29} +(4.51898 - 3.62360i) q^{30} -2.11284 q^{31} +(-2.88372 - 4.86664i) q^{32} -2.49990i q^{33} +(-1.24400 + 5.91844i) q^{34} +(1.72776 + 1.41945i) q^{35} +(0.650232 + 0.285980i) q^{36} +2.33445 q^{37} +(-1.08365 + 5.15558i) q^{38} -7.03395 q^{39} +(-6.10950 + 1.63525i) q^{40} +10.1468 q^{41} +(-0.532841 + 2.53504i) q^{42} +0.234620 q^{43} +(-1.09891 + 2.49860i) q^{44} +(0.504147 - 0.613651i) q^{45} +(-1.72312 + 8.19792i) q^{46} +9.73129i q^{47} +(-4.95175 - 5.40027i) q^{48} -1.00000 q^{49} +(-0.0839346 + 7.07057i) q^{50} +7.83317i q^{51} +(7.03028 + 3.09200i) q^{52} -11.3946 q^{53} +(-6.70474 - 1.40927i) q^{54} +(2.35803 + 1.93725i) q^{55} +(1.64692 - 2.29949i) q^{56} +6.82351i q^{57} +(-2.13881 + 10.1756i) q^{58} -13.1591i q^{59} +(-7.30824 + 3.70040i) q^{60} +6.91090i q^{61} +(2.92411 + 0.614621i) q^{62} +0.355171i q^{63} +(2.57530 + 7.57416i) q^{64} +(5.45082 - 6.63477i) q^{65} +(-0.727215 + 3.45979i) q^{66} +5.95033 q^{67} +(3.44332 - 7.82908i) q^{68} +10.8501i q^{69} +(-1.97826 - 2.46708i) q^{70} +3.49386 q^{71} +(-0.816712 - 0.584939i) q^{72} +2.20420i q^{73} +(-3.23081 - 0.679085i) q^{74} +(1.77736 + 8.98445i) q^{75} +(2.99949 - 6.81995i) q^{76} -1.36479 q^{77} +(9.73479 + 2.04616i) q^{78} -13.1691 q^{79} +(8.93106 - 0.485898i) q^{80} -9.93937 q^{81} +(-14.0429 - 2.95167i) q^{82} +6.90211 q^{83} +(1.47487 - 3.35342i) q^{84} +(-7.38863 - 6.07016i) q^{85} +(-0.324707 - 0.0682503i) q^{86} +13.4676i q^{87} +(2.24770 - 3.13832i) q^{88} +8.59946 q^{89} +(-0.876236 + 0.702621i) q^{90} +3.84009i q^{91} +(4.76951 - 10.8444i) q^{92} +3.87012 q^{93} +(2.83081 - 13.4678i) q^{94} +(-6.43627 - 5.28774i) q^{95} +(5.28215 + 8.91428i) q^{96} +9.01176i q^{97} +(1.38397 + 0.290898i) q^{98} +0.484733i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9} - 8 q^{10} + 20 q^{16} - 24 q^{20} - 48 q^{24} + 4 q^{25} - 4 q^{26} + 4 q^{30} - 16 q^{31} + 12 q^{34} - 20 q^{36} - 32 q^{39} + 16 q^{40} - 8 q^{41} + 56 q^{44} - 36 q^{49} - 12 q^{50} - 52 q^{54} - 32 q^{55} + 12 q^{56} - 20 q^{60} - 20 q^{64} - 24 q^{65} - 28 q^{66} - 12 q^{70} + 56 q^{71} - 24 q^{74} + 48 q^{76} + 24 q^{79} + 64 q^{80} + 36 q^{81} + 24 q^{86} - 40 q^{89} - 52 q^{90} - 92 q^{94} + 40 q^{95} + 48 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.38397 0.290898i −0.978616 0.205696i
\(3\) −1.83171 −1.05754 −0.528770 0.848765i \(-0.677347\pi\)
−0.528770 + 0.848765i \(0.677347\pi\)
\(4\) 1.83076 + 0.805189i 0.915379 + 0.402594i
\(5\) 1.41945 1.72776i 0.634797 0.772679i
\(6\) 2.53504 + 0.532841i 1.03493 + 0.217531i
\(7\) 1.00000i 0.377964i
\(8\) −2.29949 1.64692i −0.812992 0.582275i
\(9\) 0.355171 0.118390
\(10\) −2.46708 + 1.97826i −0.780159 + 0.625581i
\(11\) 1.36479i 0.411499i 0.978605 + 0.205750i \(0.0659632\pi\)
−0.978605 + 0.205750i \(0.934037\pi\)
\(12\) −3.35342 1.47487i −0.968049 0.425760i
\(13\) 3.84009 1.06505 0.532525 0.846414i \(-0.321243\pi\)
0.532525 + 0.846414i \(0.321243\pi\)
\(14\) 0.290898 1.38397i 0.0777457 0.369882i
\(15\) −2.60002 + 3.16476i −0.671323 + 0.817139i
\(16\) 2.70334 + 2.94821i 0.675836 + 0.737052i
\(17\) 4.27642i 1.03718i −0.855022 0.518592i \(-0.826456\pi\)
0.855022 0.518592i \(-0.173544\pi\)
\(18\) −0.491547 0.103318i −0.115859 0.0243524i
\(19\) 3.72521i 0.854621i −0.904105 0.427311i \(-0.859461\pi\)
0.904105 0.427311i \(-0.140539\pi\)
\(20\) 3.98984 2.02019i 0.892156 0.451728i
\(21\) 1.83171i 0.399712i
\(22\) 0.397014 1.88883i 0.0846436 0.402700i
\(23\) 5.92347i 1.23513i −0.786520 0.617564i \(-0.788119\pi\)
0.786520 0.617564i \(-0.211881\pi\)
\(24\) 4.21200 + 3.01669i 0.859771 + 0.615779i
\(25\) −0.970325 4.90494i −0.194065 0.980989i
\(26\) −5.31458 1.11707i −1.04228 0.219076i
\(27\) 4.84457 0.932337
\(28\) −0.805189 + 1.83076i −0.152166 + 0.345981i
\(29\) 7.35246i 1.36532i −0.730737 0.682659i \(-0.760824\pi\)
0.730737 0.682659i \(-0.239176\pi\)
\(30\) 4.51898 3.62360i 0.825050 0.661576i
\(31\) −2.11284 −0.379478 −0.189739 0.981835i \(-0.560764\pi\)
−0.189739 + 0.981835i \(0.560764\pi\)
\(32\) −2.88372 4.86664i −0.509775 0.860308i
\(33\) 2.49990i 0.435177i
\(34\) −1.24400 + 5.91844i −0.213344 + 1.01500i
\(35\) 1.72776 + 1.41945i 0.292045 + 0.239931i
\(36\) 0.650232 + 0.285980i 0.108372 + 0.0476633i
\(37\) 2.33445 0.383781 0.191890 0.981416i \(-0.438538\pi\)
0.191890 + 0.981416i \(0.438538\pi\)
\(38\) −1.08365 + 5.15558i −0.175792 + 0.836346i
\(39\) −7.03395 −1.12633
\(40\) −6.10950 + 1.63525i −0.965996 + 0.258555i
\(41\) 10.1468 1.58466 0.792330 0.610093i \(-0.208868\pi\)
0.792330 + 0.610093i \(0.208868\pi\)
\(42\) −0.532841 + 2.53504i −0.0822192 + 0.391165i
\(43\) 0.234620 0.0357791 0.0178896 0.999840i \(-0.494305\pi\)
0.0178896 + 0.999840i \(0.494305\pi\)
\(44\) −1.09891 + 2.49860i −0.165667 + 0.376678i
\(45\) 0.504147 0.613651i 0.0751539 0.0914777i
\(46\) −1.72312 + 8.19792i −0.254061 + 1.20872i
\(47\) 9.73129i 1.41946i 0.704476 + 0.709728i \(0.251182\pi\)
−0.704476 + 0.709728i \(0.748818\pi\)
\(48\) −4.95175 5.40027i −0.714723 0.779462i
\(49\) −1.00000 −0.142857
\(50\) −0.0839346 + 7.07057i −0.0118702 + 0.999930i
\(51\) 7.83317i 1.09686i
\(52\) 7.03028 + 3.09200i 0.974924 + 0.428783i
\(53\) −11.3946 −1.56517 −0.782587 0.622541i \(-0.786100\pi\)
−0.782587 + 0.622541i \(0.786100\pi\)
\(54\) −6.70474 1.40927i −0.912400 0.191778i
\(55\) 2.35803 + 1.93725i 0.317957 + 0.261219i
\(56\) 1.64692 2.29949i 0.220079 0.307282i
\(57\) 6.82351i 0.903796i
\(58\) −2.13881 + 10.1756i −0.280840 + 1.33612i
\(59\) 13.1591i 1.71317i −0.516003 0.856587i \(-0.672581\pi\)
0.516003 0.856587i \(-0.327419\pi\)
\(60\) −7.30824 + 3.70040i −0.943490 + 0.477720i
\(61\) 6.91090i 0.884850i 0.896806 + 0.442425i \(0.145882\pi\)
−0.896806 + 0.442425i \(0.854118\pi\)
\(62\) 2.92411 + 0.614621i 0.371363 + 0.0780569i
\(63\) 0.355171i 0.0447473i
\(64\) 2.57530 + 7.57416i 0.321912 + 0.946770i
\(65\) 5.45082 6.63477i 0.676091 0.822942i
\(66\) −0.727215 + 3.45979i −0.0895140 + 0.425871i
\(67\) 5.95033 0.726949 0.363474 0.931604i \(-0.381590\pi\)
0.363474 + 0.931604i \(0.381590\pi\)
\(68\) 3.44332 7.82908i 0.417564 0.949415i
\(69\) 10.8501i 1.30620i
\(70\) −1.97826 2.46708i −0.236447 0.294873i
\(71\) 3.49386 0.414645 0.207322 0.978273i \(-0.433525\pi\)
0.207322 + 0.978273i \(0.433525\pi\)
\(72\) −0.816712 0.584939i −0.0962504 0.0689357i
\(73\) 2.20420i 0.257982i 0.991646 + 0.128991i \(0.0411739\pi\)
−0.991646 + 0.128991i \(0.958826\pi\)
\(74\) −3.23081 0.679085i −0.375574 0.0789421i
\(75\) 1.77736 + 8.98445i 0.205231 + 1.03743i
\(76\) 2.99949 6.81995i 0.344066 0.782302i
\(77\) −1.36479 −0.155532
\(78\) 9.73479 + 2.04616i 1.10225 + 0.231682i
\(79\) −13.1691 −1.48164 −0.740819 0.671704i \(-0.765563\pi\)
−0.740819 + 0.671704i \(0.765563\pi\)
\(80\) 8.93106 0.485898i 0.998523 0.0543250i
\(81\) −9.93937 −1.10437
\(82\) −14.0429 2.95167i −1.55077 0.325958i
\(83\) 6.90211 0.757605 0.378803 0.925478i \(-0.376336\pi\)
0.378803 + 0.925478i \(0.376336\pi\)
\(84\) 1.47487 3.35342i 0.160922 0.365888i
\(85\) −7.38863 6.07016i −0.801410 0.658401i
\(86\) −0.324707 0.0682503i −0.0350140 0.00735962i
\(87\) 13.4676i 1.44388i
\(88\) 2.24770 3.13832i 0.239606 0.334546i
\(89\) 8.59946 0.911541 0.455770 0.890097i \(-0.349364\pi\)
0.455770 + 0.890097i \(0.349364\pi\)
\(90\) −0.876236 + 0.702621i −0.0923633 + 0.0740627i
\(91\) 3.84009i 0.402551i
\(92\) 4.76951 10.8444i 0.497256 1.13061i
\(93\) 3.87012 0.401313
\(94\) 2.83081 13.4678i 0.291976 1.38910i
\(95\) −6.43627 5.28774i −0.660348 0.542511i
\(96\) 5.28215 + 8.91428i 0.539107 + 0.909810i
\(97\) 9.01176i 0.915005i 0.889208 + 0.457503i \(0.151256\pi\)
−0.889208 + 0.457503i \(0.848744\pi\)
\(98\) 1.38397 + 0.290898i 0.139802 + 0.0293851i
\(99\) 0.484733i 0.0487175i
\(100\) 2.17298 9.76105i 0.217298 0.976105i
\(101\) 9.39707i 0.935043i 0.883982 + 0.467522i \(0.154853\pi\)
−0.883982 + 0.467522i \(0.845147\pi\)
\(102\) 2.27865 10.8409i 0.225620 1.07341i
\(103\) 7.44864i 0.733936i −0.930234 0.366968i \(-0.880396\pi\)
0.930234 0.366968i \(-0.119604\pi\)
\(104\) −8.83026 6.32434i −0.865878 0.620152i
\(105\) −3.16476 2.60002i −0.308849 0.253736i
\(106\) 15.7699 + 3.31468i 1.53170 + 0.321950i
\(107\) −7.42534 −0.717835 −0.358917 0.933369i \(-0.616854\pi\)
−0.358917 + 0.933369i \(0.616854\pi\)
\(108\) 8.86922 + 3.90079i 0.853441 + 0.375354i
\(109\) 5.06625i 0.485259i 0.970119 + 0.242629i \(0.0780099\pi\)
−0.970119 + 0.242629i \(0.921990\pi\)
\(110\) −2.69991 3.36704i −0.257426 0.321035i
\(111\) −4.27604 −0.405863
\(112\) −2.94821 + 2.70334i −0.278580 + 0.255442i
\(113\) 4.60255i 0.432971i 0.976286 + 0.216486i \(0.0694594\pi\)
−0.976286 + 0.216486i \(0.930541\pi\)
\(114\) 1.98494 9.44354i 0.185907 0.884469i
\(115\) −10.2343 8.40807i −0.954358 0.784056i
\(116\) 5.92012 13.4606i 0.549669 1.24978i
\(117\) 1.36389 0.126092
\(118\) −3.82796 + 18.2119i −0.352393 + 1.67654i
\(119\) 4.27642 0.392019
\(120\) 11.1908 2.99530i 1.02158 0.273433i
\(121\) 9.13735 0.830668
\(122\) 2.01036 9.56449i 0.182010 0.865928i
\(123\) −18.5860 −1.67584
\(124\) −3.86810 1.70124i −0.347366 0.152776i
\(125\) −9.85190 5.28583i −0.881181 0.472779i
\(126\) 0.103318 0.491547i 0.00920434 0.0437905i
\(127\) 7.68741i 0.682147i 0.940037 + 0.341074i \(0.110791\pi\)
−0.940037 + 0.341074i \(0.889209\pi\)
\(128\) −1.36084 11.2316i −0.120282 0.992740i
\(129\) −0.429756 −0.0378379
\(130\) −9.47382 + 7.59671i −0.830909 + 0.666275i
\(131\) 9.17717i 0.801813i 0.916119 + 0.400907i \(0.131305\pi\)
−0.916119 + 0.400907i \(0.868695\pi\)
\(132\) 2.01289 4.57671i 0.175200 0.398351i
\(133\) 3.72521 0.323016
\(134\) −8.23509 1.73094i −0.711404 0.149530i
\(135\) 6.87662 8.37026i 0.591845 0.720397i
\(136\) −7.04292 + 9.83357i −0.603926 + 0.843222i
\(137\) 9.98734i 0.853276i −0.904422 0.426638i \(-0.859698\pi\)
0.904422 0.426638i \(-0.140302\pi\)
\(138\) 3.15627 15.0162i 0.268679 1.27827i
\(139\) 5.23949i 0.444407i −0.975000 0.222204i \(-0.928675\pi\)
0.975000 0.222204i \(-0.0713250\pi\)
\(140\) 2.02019 + 3.98984i 0.170737 + 0.337203i
\(141\) 17.8249i 1.50113i
\(142\) −4.83540 1.01636i −0.405778 0.0852907i
\(143\) 5.24092i 0.438268i
\(144\) 0.960149 + 1.04712i 0.0800124 + 0.0872599i
\(145\) −12.7033 10.4364i −1.05495 0.866700i
\(146\) 0.641197 3.05055i 0.0530659 0.252466i
\(147\) 1.83171 0.151077
\(148\) 4.27381 + 1.87967i 0.351305 + 0.154508i
\(149\) 21.1821i 1.73531i 0.497168 + 0.867654i \(0.334373\pi\)
−0.497168 + 0.867654i \(0.665627\pi\)
\(150\) 0.153744 12.9513i 0.0125532 1.05747i
\(151\) 20.1991 1.64378 0.821892 0.569644i \(-0.192919\pi\)
0.821892 + 0.569644i \(0.192919\pi\)
\(152\) −6.13512 + 8.56607i −0.497624 + 0.694800i
\(153\) 1.51886i 0.122792i
\(154\) 1.88883 + 0.397014i 0.152206 + 0.0319923i
\(155\) −2.99907 + 3.65049i −0.240891 + 0.293214i
\(156\) −12.8775 5.66366i −1.03102 0.453455i
\(157\) 10.6974 0.853748 0.426874 0.904311i \(-0.359615\pi\)
0.426874 + 0.904311i \(0.359615\pi\)
\(158\) 18.2257 + 3.83086i 1.44996 + 0.304767i
\(159\) 20.8717 1.65523
\(160\) −12.5017 1.92556i −0.988345 0.152229i
\(161\) 5.92347 0.466835
\(162\) 13.7558 + 2.89134i 1.08076 + 0.227165i
\(163\) −1.78960 −0.140173 −0.0700863 0.997541i \(-0.522327\pi\)
−0.0700863 + 0.997541i \(0.522327\pi\)
\(164\) 18.5763 + 8.17007i 1.45056 + 0.637975i
\(165\) −4.31923 3.54848i −0.336252 0.276249i
\(166\) −9.55233 2.00781i −0.741404 0.155836i
\(167\) 8.12242i 0.628531i −0.949335 0.314266i \(-0.898242\pi\)
0.949335 0.314266i \(-0.101758\pi\)
\(168\) −3.01669 + 4.21200i −0.232742 + 0.324963i
\(169\) 1.74633 0.134333
\(170\) 8.45986 + 10.5503i 0.648842 + 0.809169i
\(171\) 1.32309i 0.101179i
\(172\) 0.429531 + 0.188913i 0.0327515 + 0.0144045i
\(173\) 4.00480 0.304479 0.152240 0.988344i \(-0.451351\pi\)
0.152240 + 0.988344i \(0.451351\pi\)
\(174\) 3.91769 18.6388i 0.297000 1.41300i
\(175\) 4.90494 0.970325i 0.370779 0.0733497i
\(176\) −4.02368 + 3.68949i −0.303296 + 0.278106i
\(177\) 24.1038i 1.81175i
\(178\) −11.9014 2.50156i −0.892049 0.187500i
\(179\) 0.524171i 0.0391784i −0.999808 0.0195892i \(-0.993764\pi\)
0.999808 0.0195892i \(-0.00623583\pi\)
\(180\) 1.41708 0.717512i 0.105623 0.0534802i
\(181\) 8.89156i 0.660905i −0.943823 0.330452i \(-0.892799\pi\)
0.943823 0.330452i \(-0.107201\pi\)
\(182\) 1.11707 5.31458i 0.0828031 0.393943i
\(183\) 12.6588i 0.935764i
\(184\) −9.75549 + 13.6210i −0.719184 + 1.00415i
\(185\) 3.31363 4.03337i 0.243623 0.296539i
\(186\) −5.35614 1.12581i −0.392731 0.0825483i
\(187\) 5.83640 0.426800
\(188\) −7.83553 + 17.8156i −0.571465 + 1.29934i
\(189\) 4.84457i 0.352390i
\(190\) 7.36943 + 9.19039i 0.534634 + 0.666741i
\(191\) −12.8169 −0.927399 −0.463700 0.885992i \(-0.653478\pi\)
−0.463700 + 0.885992i \(0.653478\pi\)
\(192\) −4.71721 13.8737i −0.340435 1.00125i
\(193\) 2.52960i 0.182085i 0.995847 + 0.0910424i \(0.0290199\pi\)
−0.995847 + 0.0910424i \(0.970980\pi\)
\(194\) 2.62150 12.4720i 0.188213 0.895439i
\(195\) −9.98434 + 12.1530i −0.714993 + 0.870294i
\(196\) −1.83076 0.805189i −0.130768 0.0575135i
\(197\) −23.6070 −1.68193 −0.840963 0.541092i \(-0.818011\pi\)
−0.840963 + 0.541092i \(0.818011\pi\)
\(198\) 0.141008 0.670857i 0.0100210 0.0476758i
\(199\) 10.2257 0.724877 0.362439 0.932008i \(-0.381944\pi\)
0.362439 + 0.932008i \(0.381944\pi\)
\(200\) −5.84681 + 12.8769i −0.413432 + 0.910535i
\(201\) −10.8993 −0.768777
\(202\) 2.73359 13.0053i 0.192334 0.915048i
\(203\) 7.35246 0.516042
\(204\) −6.30718 + 14.3406i −0.441591 + 1.00404i
\(205\) 14.4028 17.5312i 1.00594 1.22443i
\(206\) −2.16679 + 10.3087i −0.150968 + 0.718242i
\(207\) 2.10384i 0.146227i
\(208\) 10.3811 + 11.3214i 0.719799 + 0.784998i
\(209\) 5.08412 0.351676
\(210\) 3.62360 + 4.51898i 0.250052 + 0.311839i
\(211\) 19.2218i 1.32329i −0.749819 0.661643i \(-0.769860\pi\)
0.749819 0.661643i \(-0.230140\pi\)
\(212\) −20.8608 9.17484i −1.43273 0.630130i
\(213\) −6.39975 −0.438503
\(214\) 10.2765 + 2.16001i 0.702485 + 0.147656i
\(215\) 0.333031 0.405367i 0.0227125 0.0276458i
\(216\) −11.1400 7.97862i −0.757983 0.542876i
\(217\) 2.11284i 0.143429i
\(218\) 1.47376 7.01155i 0.0998156 0.474882i
\(219\) 4.03746i 0.272827i
\(220\) 2.75713 + 5.44529i 0.185886 + 0.367121i
\(221\) 16.4218i 1.10465i
\(222\) 5.91791 + 1.24389i 0.397184 + 0.0834844i
\(223\) 14.4606i 0.968353i −0.874970 0.484177i \(-0.839119\pi\)
0.874970 0.484177i \(-0.160881\pi\)
\(224\) 4.86664 2.88372i 0.325166 0.192677i
\(225\) −0.344631 1.74209i −0.0229754 0.116140i
\(226\) 1.33887 6.36980i 0.0890604 0.423713i
\(227\) −10.3997 −0.690255 −0.345128 0.938556i \(-0.612164\pi\)
−0.345128 + 0.938556i \(0.612164\pi\)
\(228\) −5.49421 + 12.4922i −0.363863 + 0.827315i
\(229\) 19.3490i 1.27862i 0.768951 + 0.639308i \(0.220779\pi\)
−0.768951 + 0.639308i \(0.779221\pi\)
\(230\) 11.7182 + 14.6137i 0.772673 + 0.963597i
\(231\) 2.49990 0.164481
\(232\) −12.1089 + 16.9069i −0.794990 + 1.10999i
\(233\) 27.8455i 1.82422i 0.409949 + 0.912108i \(0.365546\pi\)
−0.409949 + 0.912108i \(0.634454\pi\)
\(234\) −1.88759 0.396753i −0.123395 0.0259365i
\(235\) 16.8134 + 13.8131i 1.09678 + 0.901066i
\(236\) 10.5956 24.0912i 0.689714 1.56820i
\(237\) 24.1220 1.56689
\(238\) −5.91844 1.24400i −0.383636 0.0806365i
\(239\) −13.7910 −0.892065 −0.446032 0.895017i \(-0.647163\pi\)
−0.446032 + 0.895017i \(0.647163\pi\)
\(240\) −16.3591 + 0.890025i −1.05598 + 0.0574509i
\(241\) −30.8170 −1.98510 −0.992550 0.121835i \(-0.961122\pi\)
−0.992550 + 0.121835i \(0.961122\pi\)
\(242\) −12.6458 2.65804i −0.812905 0.170865i
\(243\) 3.67236 0.235582
\(244\) −5.56458 + 12.6522i −0.356236 + 0.809973i
\(245\) −1.41945 + 1.72776i −0.0906853 + 0.110383i
\(246\) 25.7225 + 5.40662i 1.64000 + 0.344713i
\(247\) 14.3051i 0.910215i
\(248\) 4.85846 + 3.47968i 0.308512 + 0.220960i
\(249\) −12.6427 −0.801198
\(250\) 12.0971 + 10.1813i 0.765089 + 0.643924i
\(251\) 16.9921i 1.07253i 0.844048 + 0.536267i \(0.180166\pi\)
−0.844048 + 0.536267i \(0.819834\pi\)
\(252\) −0.285980 + 0.650232i −0.0180150 + 0.0409608i
\(253\) 8.08428 0.508255
\(254\) 2.23625 10.6392i 0.140315 0.667560i
\(255\) 13.5339 + 11.1188i 0.847523 + 0.696285i
\(256\) −1.38388 + 15.9400i −0.0864925 + 0.996253i
\(257\) 8.91195i 0.555912i −0.960594 0.277956i \(-0.910343\pi\)
0.960594 0.277956i \(-0.0896570\pi\)
\(258\) 0.594770 + 0.125015i 0.0370287 + 0.00778309i
\(259\) 2.33445i 0.145056i
\(260\) 15.3214 7.75771i 0.950191 0.481113i
\(261\) 2.61138i 0.161640i
\(262\) 2.66962 12.7010i 0.164930 0.784667i
\(263\) 24.5263i 1.51235i 0.654367 + 0.756177i \(0.272935\pi\)
−0.654367 + 0.756177i \(0.727065\pi\)
\(264\) −4.11714 + 5.74849i −0.253392 + 0.353795i
\(265\) −16.1741 + 19.6872i −0.993568 + 1.20938i
\(266\) −5.15558 1.08365i −0.316109 0.0664431i
\(267\) −15.7517 −0.963991
\(268\) 10.8936 + 4.79114i 0.665433 + 0.292665i
\(269\) 8.90520i 0.542959i 0.962444 + 0.271480i \(0.0875130\pi\)
−0.962444 + 0.271480i \(0.912487\pi\)
\(270\) −11.9519 + 9.58381i −0.727372 + 0.583252i
\(271\) −10.0308 −0.609325 −0.304663 0.952460i \(-0.598544\pi\)
−0.304663 + 0.952460i \(0.598544\pi\)
\(272\) 12.6078 11.5606i 0.764459 0.700966i
\(273\) 7.03395i 0.425714i
\(274\) −2.90529 + 13.8222i −0.175515 + 0.835029i
\(275\) 6.69421 1.32429i 0.403676 0.0798576i
\(276\) −8.73637 + 19.8639i −0.525868 + 1.19567i
\(277\) 10.5093 0.631443 0.315721 0.948852i \(-0.397754\pi\)
0.315721 + 0.948852i \(0.397754\pi\)
\(278\) −1.52415 + 7.25130i −0.0914127 + 0.434904i
\(279\) −0.750420 −0.0449265
\(280\) −1.63525 6.10950i −0.0977247 0.365112i
\(281\) −29.9327 −1.78564 −0.892818 0.450417i \(-0.851275\pi\)
−0.892818 + 0.450417i \(0.851275\pi\)
\(282\) −5.18523 + 24.6692i −0.308776 + 1.46903i
\(283\) 28.9911 1.72334 0.861670 0.507470i \(-0.169419\pi\)
0.861670 + 0.507470i \(0.169419\pi\)
\(284\) 6.39641 + 2.81322i 0.379557 + 0.166934i
\(285\) 11.7894 + 9.68563i 0.698344 + 0.573727i
\(286\) 1.52457 7.25328i 0.0901498 0.428896i
\(287\) 10.1468i 0.598945i
\(288\) −1.02421 1.72849i −0.0603524 0.101852i
\(289\) −1.28774 −0.0757496
\(290\) 14.5451 + 18.1391i 0.854116 + 1.06517i
\(291\) 16.5070i 0.967655i
\(292\) −1.77480 + 4.03536i −0.103862 + 0.236151i
\(293\) 5.38493 0.314591 0.157295 0.987552i \(-0.449723\pi\)
0.157295 + 0.987552i \(0.449723\pi\)
\(294\) −2.53504 0.532841i −0.147846 0.0310759i
\(295\) −22.7359 18.6787i −1.32373 1.08752i
\(296\) −5.36804 3.84465i −0.312011 0.223466i
\(297\) 6.61181i 0.383656i
\(298\) 6.16184 29.3155i 0.356946 1.69820i
\(299\) 22.7467i 1.31547i
\(300\) −3.98027 + 17.8794i −0.229801 + 1.03227i
\(301\) 0.234620i 0.0135232i
\(302\) −27.9551 5.87589i −1.60863 0.338119i
\(303\) 17.2127i 0.988845i
\(304\) 10.9827 10.0705i 0.629900 0.577583i
\(305\) 11.9404 + 9.80967i 0.683705 + 0.561700i
\(306\) −0.441833 + 2.10206i −0.0252579 + 0.120167i
\(307\) 18.8807 1.07758 0.538789 0.842441i \(-0.318882\pi\)
0.538789 + 0.842441i \(0.318882\pi\)
\(308\) −2.49860 1.09891i −0.142371 0.0626163i
\(309\) 13.6438i 0.776167i
\(310\) 5.21255 4.17975i 0.296053 0.237394i
\(311\) 9.76621 0.553791 0.276896 0.960900i \(-0.410694\pi\)
0.276896 + 0.960900i \(0.410694\pi\)
\(312\) 16.1745 + 11.5844i 0.915700 + 0.655835i
\(313\) 19.2542i 1.08831i −0.838983 0.544157i \(-0.816850\pi\)
0.838983 0.544157i \(-0.183150\pi\)
\(314\) −14.8049 3.11186i −0.835491 0.175612i
\(315\) 0.613651 + 0.504147i 0.0345753 + 0.0284055i
\(316\) −24.1094 10.6036i −1.35626 0.596499i
\(317\) 4.71367 0.264746 0.132373 0.991200i \(-0.457740\pi\)
0.132373 + 0.991200i \(0.457740\pi\)
\(318\) −28.8859 6.07153i −1.61984 0.340475i
\(319\) 10.0346 0.561827
\(320\) 16.7418 + 6.30163i 0.935898 + 0.352272i
\(321\) 13.6011 0.759139
\(322\) −8.19792 1.72312i −0.456852 0.0960259i
\(323\) −15.9305 −0.886399
\(324\) −18.1966 8.00307i −1.01092 0.444615i
\(325\) −3.72614 18.8354i −0.206689 1.04480i
\(326\) 2.47676 + 0.520592i 0.137175 + 0.0288329i
\(327\) 9.27991i 0.513180i
\(328\) −23.3324 16.7109i −1.28832 0.922708i
\(329\) −9.73129 −0.536504
\(330\) 4.94545 + 6.16746i 0.272238 + 0.339507i
\(331\) 12.3760i 0.680244i −0.940381 0.340122i \(-0.889532\pi\)
0.940381 0.340122i \(-0.110468\pi\)
\(332\) 12.6361 + 5.55750i 0.693495 + 0.305008i
\(333\) 0.829128 0.0454359
\(334\) −2.36279 + 11.2412i −0.129286 + 0.615091i
\(335\) 8.44620 10.2808i 0.461465 0.561698i
\(336\) 5.40027 4.95175i 0.294609 0.270140i
\(337\) 23.4702i 1.27850i 0.768997 + 0.639252i \(0.220756\pi\)
−0.768997 + 0.639252i \(0.779244\pi\)
\(338\) −2.41687 0.508003i −0.131460 0.0276317i
\(339\) 8.43054i 0.457884i
\(340\) −8.63917 17.0622i −0.468525 0.925329i
\(341\) 2.88358i 0.156155i
\(342\) −0.384883 + 1.83111i −0.0208121 + 0.0990153i
\(343\) 1.00000i 0.0539949i
\(344\) −0.539505 0.386400i −0.0290882 0.0208333i
\(345\) 18.7464 + 15.4012i 1.00927 + 0.829171i
\(346\) −5.54253 1.16499i −0.297968 0.0626301i
\(347\) 21.3424 1.14572 0.572861 0.819653i \(-0.305834\pi\)
0.572861 + 0.819653i \(0.305834\pi\)
\(348\) −10.8440 + 24.6559i −0.581297 + 1.32169i
\(349\) 3.50818i 0.187789i −0.995582 0.0938943i \(-0.970068\pi\)
0.995582 0.0938943i \(-0.0299316\pi\)
\(350\) −7.07057 0.0839346i −0.377938 0.00448650i
\(351\) 18.6036 0.992986
\(352\) 6.64193 3.93567i 0.354016 0.209772i
\(353\) 35.4482i 1.88672i −0.331773 0.943359i \(-0.607647\pi\)
0.331773 0.943359i \(-0.392353\pi\)
\(354\) 7.01173 33.3589i 0.372669 1.77301i
\(355\) 4.95936 6.03656i 0.263215 0.320387i
\(356\) 15.7435 + 6.92419i 0.834405 + 0.366981i
\(357\) −7.83317 −0.414575
\(358\) −0.152480 + 0.725438i −0.00805883 + 0.0383406i
\(359\) −17.0959 −0.902285 −0.451143 0.892452i \(-0.648983\pi\)
−0.451143 + 0.892452i \(0.648983\pi\)
\(360\) −2.16992 + 0.580792i −0.114365 + 0.0306105i
\(361\) 5.12283 0.269623
\(362\) −2.58654 + 12.3057i −0.135945 + 0.646772i
\(363\) −16.7370 −0.878465
\(364\) −3.09200 + 7.03028i −0.162065 + 0.368487i
\(365\) 3.80834 + 3.12875i 0.199337 + 0.163766i
\(366\) −3.68241 + 17.5194i −0.192483 + 0.915754i
\(367\) 13.1849i 0.688247i −0.938924 0.344123i \(-0.888176\pi\)
0.938924 0.344123i \(-0.111824\pi\)
\(368\) 17.4636 16.0132i 0.910355 0.834744i
\(369\) 3.60384 0.187608
\(370\) −5.75927 + 4.61814i −0.299410 + 0.240086i
\(371\) 11.3946i 0.591580i
\(372\) 7.08525 + 3.11618i 0.367353 + 0.161566i
\(373\) −20.7850 −1.07621 −0.538104 0.842879i \(-0.680859\pi\)
−0.538104 + 0.842879i \(0.680859\pi\)
\(374\) −8.07742 1.69780i −0.417673 0.0877910i
\(375\) 18.0459 + 9.68212i 0.931884 + 0.499983i
\(376\) 16.0267 22.3770i 0.826513 1.15401i
\(377\) 28.2341i 1.45413i
\(378\) 1.40927 6.70474i 0.0724852 0.344855i
\(379\) 36.4225i 1.87090i −0.353460 0.935450i \(-0.614995\pi\)
0.353460 0.935450i \(-0.385005\pi\)
\(380\) −7.52562 14.8630i −0.386056 0.762455i
\(381\) 14.0811i 0.721398i
\(382\) 17.7382 + 3.72841i 0.907568 + 0.190762i
\(383\) 29.9092i 1.52829i 0.645044 + 0.764145i \(0.276839\pi\)
−0.645044 + 0.764145i \(0.723161\pi\)
\(384\) 2.49266 + 20.5730i 0.127203 + 1.04986i
\(385\) −1.93725 + 2.35803i −0.0987313 + 0.120176i
\(386\) 0.735856 3.50090i 0.0374541 0.178191i
\(387\) 0.0833301 0.00423590
\(388\) −7.25617 + 16.4983i −0.368376 + 0.837576i
\(389\) 7.71507i 0.391170i 0.980687 + 0.195585i \(0.0626605\pi\)
−0.980687 + 0.195585i \(0.937340\pi\)
\(390\) 17.3533 13.9150i 0.878720 0.704612i
\(391\) −25.3312 −1.28106
\(392\) 2.29949 + 1.64692i 0.116142 + 0.0831821i
\(393\) 16.8099i 0.847950i
\(394\) 32.6714 + 6.86721i 1.64596 + 0.345965i
\(395\) −18.6929 + 22.7531i −0.940540 + 1.14483i
\(396\) −0.390302 + 0.887429i −0.0196134 + 0.0445950i
\(397\) −2.95881 −0.148498 −0.0742491 0.997240i \(-0.523656\pi\)
−0.0742491 + 0.997240i \(0.523656\pi\)
\(398\) −14.1520 2.97462i −0.709376 0.149104i
\(399\) −6.82351 −0.341603
\(400\) 11.8377 16.1205i 0.591884 0.806023i
\(401\) 30.7112 1.53364 0.766822 0.641859i \(-0.221837\pi\)
0.766822 + 0.641859i \(0.221837\pi\)
\(402\) 15.0843 + 3.17058i 0.752338 + 0.158134i
\(403\) −8.11351 −0.404163
\(404\) −7.56641 + 17.2037i −0.376443 + 0.855919i
\(405\) −14.1084 + 17.1729i −0.701054 + 0.853326i
\(406\) −10.1756 2.13881i −0.505007 0.106148i
\(407\) 3.18603i 0.157925i
\(408\) 12.9006 18.0123i 0.638675 0.891741i
\(409\) −4.88808 −0.241700 −0.120850 0.992671i \(-0.538562\pi\)
−0.120850 + 0.992671i \(0.538562\pi\)
\(410\) −25.0329 + 20.0730i −1.23629 + 0.991333i
\(411\) 18.2939i 0.902373i
\(412\) 5.99756 13.6366i 0.295478 0.671829i
\(413\) 13.1591 0.647519
\(414\) −0.612004 + 2.91166i −0.0300783 + 0.143100i
\(415\) 9.79720 11.9252i 0.480926 0.585385i
\(416\) −11.0738 18.6883i −0.542936 0.916271i
\(417\) 9.59723i 0.469979i
\(418\) −7.03628 1.47896i −0.344156 0.0723382i
\(419\) 15.6141i 0.762799i 0.924410 + 0.381400i \(0.124558\pi\)
−0.924410 + 0.381400i \(0.875442\pi\)
\(420\) −3.70040 7.30824i −0.180561 0.356606i
\(421\) 10.6841i 0.520709i 0.965513 + 0.260355i \(0.0838394\pi\)
−0.965513 + 0.260355i \(0.916161\pi\)
\(422\) −5.59159 + 26.6025i −0.272194 + 1.29499i
\(423\) 3.45627i 0.168050i
\(424\) 26.2019 + 18.7661i 1.27247 + 0.911361i
\(425\) −20.9756 + 4.14951i −1.01747 + 0.201281i
\(426\) 8.85707 + 1.86167i 0.429126 + 0.0901983i
\(427\) −6.91090 −0.334442
\(428\) −13.5940 5.97880i −0.657091 0.288996i
\(429\) 9.59985i 0.463485i
\(430\) −0.578825 + 0.464138i −0.0279134 + 0.0223827i
\(431\) 5.98746 0.288406 0.144203 0.989548i \(-0.453938\pi\)
0.144203 + 0.989548i \(0.453938\pi\)
\(432\) 13.0965 + 14.2828i 0.630107 + 0.687181i
\(433\) 7.68624i 0.369377i 0.982797 + 0.184688i \(0.0591276\pi\)
−0.982797 + 0.184688i \(0.940872\pi\)
\(434\) −0.614621 + 2.92411i −0.0295027 + 0.140362i
\(435\) 23.2688 + 19.1166i 1.11565 + 0.916570i
\(436\) −4.07929 + 9.27507i −0.195362 + 0.444195i
\(437\) −22.0661 −1.05557
\(438\) −1.17449 + 5.58774i −0.0561193 + 0.266992i
\(439\) 34.5363 1.64833 0.824165 0.566350i \(-0.191645\pi\)
0.824165 + 0.566350i \(0.191645\pi\)
\(440\) −2.23177 8.33817i −0.106395 0.397507i
\(441\) −0.355171 −0.0169129
\(442\) −4.77708 + 22.7274i −0.227222 + 1.08103i
\(443\) 10.3440 0.491458 0.245729 0.969339i \(-0.420973\pi\)
0.245729 + 0.969339i \(0.420973\pi\)
\(444\) −7.82838 3.44302i −0.371519 0.163398i
\(445\) 12.2065 14.8578i 0.578644 0.704328i
\(446\) −4.20655 + 20.0131i −0.199186 + 0.947646i
\(447\) 38.7996i 1.83516i
\(448\) −7.57416 + 2.57530i −0.357845 + 0.121671i
\(449\) 41.6726 1.96665 0.983326 0.181853i \(-0.0582096\pi\)
0.983326 + 0.181853i \(0.0582096\pi\)
\(450\) −0.0298112 + 2.51126i −0.00140531 + 0.118382i
\(451\) 13.8482i 0.652086i
\(452\) −3.70592 + 8.42615i −0.174312 + 0.396333i
\(453\) −36.9990 −1.73837
\(454\) 14.3930 + 3.02526i 0.675495 + 0.141983i
\(455\) 6.63477 + 5.45082i 0.311043 + 0.255538i
\(456\) 11.2378 15.6906i 0.526257 0.734779i
\(457\) 1.30299i 0.0609513i −0.999536 0.0304757i \(-0.990298\pi\)
0.999536 0.0304757i \(-0.00970220\pi\)
\(458\) 5.62857 26.7784i 0.263006 1.25127i
\(459\) 20.7174i 0.967005i
\(460\) −11.9665 23.6337i −0.557942 1.10193i
\(461\) 6.67282i 0.310784i −0.987853 0.155392i \(-0.950336\pi\)
0.987853 0.155392i \(-0.0496641\pi\)
\(462\) −3.45979 0.727215i −0.160964 0.0338331i
\(463\) 15.6427i 0.726977i 0.931599 + 0.363488i \(0.118414\pi\)
−0.931599 + 0.363488i \(0.881586\pi\)
\(464\) 21.6766 19.8762i 1.00631 0.922730i
\(465\) 5.49344 6.68664i 0.254752 0.310086i
\(466\) 8.10018 38.5373i 0.375234 1.78521i
\(467\) −12.4919 −0.578058 −0.289029 0.957320i \(-0.593332\pi\)
−0.289029 + 0.957320i \(0.593332\pi\)
\(468\) 2.49695 + 1.09819i 0.115422 + 0.0507638i
\(469\) 5.95033i 0.274761i
\(470\) −19.2510 24.0079i −0.887984 1.10740i
\(471\) −19.5946 −0.902872
\(472\) −21.6721 + 30.2593i −0.997538 + 1.39280i
\(473\) 0.320206i 0.0147231i
\(474\) −33.3842 7.01703i −1.53339 0.322303i
\(475\) −18.2719 + 3.61466i −0.838374 + 0.165852i
\(476\) 7.82908 + 3.44332i 0.358845 + 0.157824i
\(477\) −4.04705 −0.185302
\(478\) 19.0863 + 4.01177i 0.872989 + 0.183494i
\(479\) −29.8270 −1.36283 −0.681415 0.731897i \(-0.738635\pi\)
−0.681415 + 0.731897i \(0.738635\pi\)
\(480\) 22.8995 + 3.52707i 1.04521 + 0.160988i
\(481\) 8.96450 0.408746
\(482\) 42.6499 + 8.96461i 1.94265 + 0.408327i
\(483\) −10.8501 −0.493696
\(484\) 16.7283 + 7.35729i 0.760376 + 0.334422i
\(485\) 15.5702 + 12.7917i 0.707005 + 0.580843i
\(486\) −5.08245 1.06828i −0.230545 0.0484583i
\(487\) 14.7112i 0.666628i 0.942816 + 0.333314i \(0.108167\pi\)
−0.942816 + 0.333314i \(0.891833\pi\)
\(488\) 11.3817 15.8915i 0.515226 0.719376i
\(489\) 3.27804 0.148238
\(490\) 2.46708 1.97826i 0.111451 0.0893687i
\(491\) 19.8675i 0.896606i 0.893882 + 0.448303i \(0.147971\pi\)
−0.893882 + 0.448303i \(0.852029\pi\)
\(492\) −34.0264 14.9652i −1.53403 0.674684i
\(493\) −31.4422 −1.41609
\(494\) −4.16134 + 19.7979i −0.187227 + 0.890751i
\(495\) 0.837504 + 0.688055i 0.0376430 + 0.0309258i
\(496\) −5.71173 6.22910i −0.256464 0.279695i
\(497\) 3.49386i 0.156721i
\(498\) 17.4971 + 3.67773i 0.784065 + 0.164803i
\(499\) 22.5504i 1.00949i 0.863268 + 0.504747i \(0.168414\pi\)
−0.863268 + 0.504747i \(0.831586\pi\)
\(500\) −13.7804 17.6097i −0.616276 0.787530i
\(501\) 14.8779i 0.664697i
\(502\) 4.94297 23.5166i 0.220616 1.04960i
\(503\) 31.9427i 1.42425i 0.702050 + 0.712127i \(0.252268\pi\)
−0.702050 + 0.712127i \(0.747732\pi\)
\(504\) 0.584939 0.816712i 0.0260552 0.0363792i
\(505\) 16.2359 + 13.3387i 0.722488 + 0.593563i
\(506\) −11.1884 2.35170i −0.497386 0.104546i
\(507\) −3.19877 −0.142062
\(508\) −6.18981 + 14.0738i −0.274629 + 0.624423i
\(509\) 29.9980i 1.32964i −0.747004 0.664820i \(-0.768508\pi\)
0.747004 0.664820i \(-0.231492\pi\)
\(510\) −15.4960 19.3251i −0.686176 0.855728i
\(511\) −2.20420 −0.0975082
\(512\) 6.55217 21.6580i 0.289568 0.957157i
\(513\) 18.0470i 0.796795i
\(514\) −2.59247 + 12.3339i −0.114349 + 0.544025i
\(515\) −12.8695 10.5730i −0.567097 0.465901i
\(516\) −0.786778 0.346034i −0.0346360 0.0152333i
\(517\) −13.2812 −0.584105
\(518\) 0.679085 3.23081i 0.0298373 0.141954i
\(519\) −7.33565 −0.321999
\(520\) −23.4611 + 6.27951i −1.02884 + 0.275375i
\(521\) −9.14935 −0.400840 −0.200420 0.979710i \(-0.564231\pi\)
−0.200420 + 0.979710i \(0.564231\pi\)
\(522\) −0.759645 + 3.61408i −0.0332488 + 0.158184i
\(523\) 9.24800 0.404387 0.202193 0.979346i \(-0.435193\pi\)
0.202193 + 0.979346i \(0.435193\pi\)
\(524\) −7.38936 + 16.8012i −0.322806 + 0.733963i
\(525\) −8.98445 + 1.77736i −0.392113 + 0.0775702i
\(526\) 7.13464 33.9437i 0.311085 1.48001i
\(527\) 9.03539i 0.393588i
\(528\) 7.37023 6.75809i 0.320748 0.294108i
\(529\) −12.0875 −0.525543
\(530\) 28.1115 22.5416i 1.22109 0.979143i
\(531\) 4.67374i 0.202823i
\(532\) 6.81995 + 2.99949i 0.295682 + 0.130045i
\(533\) 38.9646 1.68774
\(534\) 21.8000 + 4.58215i 0.943377 + 0.198289i
\(535\) −10.5399 + 12.8292i −0.455680 + 0.554656i
\(536\) −13.6827 9.79973i −0.591004 0.423284i
\(537\) 0.960131i 0.0414327i
\(538\) 2.59050 12.3245i 0.111684 0.531349i
\(539\) 1.36479i 0.0587856i
\(540\) 19.3291 9.78694i 0.831790 0.421163i
\(541\) 1.52266i 0.0654642i 0.999464 + 0.0327321i \(0.0104208\pi\)
−0.999464 + 0.0327321i \(0.989579\pi\)
\(542\) 13.8823 + 2.91792i 0.596295 + 0.125336i
\(543\) 16.2868i 0.698933i
\(544\) −20.8118 + 12.3320i −0.892297 + 0.528730i
\(545\) 8.75327 + 7.19129i 0.374949 + 0.308041i
\(546\) −2.04616 + 9.73479i −0.0875676 + 0.416611i
\(547\) −8.09720 −0.346211 −0.173106 0.984903i \(-0.555380\pi\)
−0.173106 + 0.984903i \(0.555380\pi\)
\(548\) 8.04169 18.2844i 0.343524 0.781070i
\(549\) 2.45455i 0.104758i
\(550\) −9.64983 0.114553i −0.411470 0.00488456i
\(551\) −27.3894 −1.16683
\(552\) 17.8693 24.9497i 0.760566 1.06193i
\(553\) 13.1691i 0.560007i
\(554\) −14.5446 3.05713i −0.617940 0.129885i
\(555\) −6.06962 + 7.38797i −0.257641 + 0.313602i
\(556\) 4.21878 9.59223i 0.178916 0.406801i
\(557\) 8.56805 0.363040 0.181520 0.983387i \(-0.441898\pi\)
0.181520 + 0.983387i \(0.441898\pi\)
\(558\) 1.03856 + 0.218295i 0.0439658 + 0.00924119i
\(559\) 0.900961 0.0381066
\(560\) 0.485898 + 8.93106i 0.0205329 + 0.377406i
\(561\) −10.6906 −0.451358
\(562\) 41.4261 + 8.70736i 1.74745 + 0.367298i
\(563\) 34.2736 1.44446 0.722229 0.691654i \(-0.243118\pi\)
0.722229 + 0.691654i \(0.243118\pi\)
\(564\) 14.3524 32.6331i 0.604347 1.37410i
\(565\) 7.95211 + 6.53308i 0.334548 + 0.274849i
\(566\) −40.1228 8.43343i −1.68649 0.354484i
\(567\) 9.93937i 0.417414i
\(568\) −8.03409 5.75411i −0.337103 0.241437i
\(569\) 19.5357 0.818979 0.409490 0.912315i \(-0.365707\pi\)
0.409490 + 0.912315i \(0.365707\pi\)
\(570\) −13.4987 16.8341i −0.565397 0.705105i
\(571\) 9.14907i 0.382877i 0.981505 + 0.191438i \(0.0613152\pi\)
−0.981505 + 0.191438i \(0.938685\pi\)
\(572\) −4.21993 + 9.59485i −0.176444 + 0.401181i
\(573\) 23.4769 0.980762
\(574\) 2.95167 14.0429i 0.123201 0.586137i
\(575\) −29.0543 + 5.74769i −1.21165 + 0.239695i
\(576\) 0.914671 + 2.69012i 0.0381113 + 0.112088i
\(577\) 38.9999i 1.62359i −0.583946 0.811793i \(-0.698492\pi\)
0.583946 0.811793i \(-0.301508\pi\)
\(578\) 1.78220 + 0.374602i 0.0741298 + 0.0155814i
\(579\) 4.63350i 0.192562i
\(580\) −14.8534 29.3352i −0.616752 1.21808i
\(581\) 6.90211i 0.286348i
\(582\) −4.80183 + 22.8452i −0.199042 + 0.946962i
\(583\) 15.5513i 0.644068i
\(584\) 3.63015 5.06854i 0.150217 0.209738i
\(585\) 1.93597 2.35648i 0.0800427 0.0974284i
\(586\) −7.45259 1.56646i −0.307864 0.0647100i
\(587\) −1.63836 −0.0676222 −0.0338111 0.999428i \(-0.510764\pi\)
−0.0338111 + 0.999428i \(0.510764\pi\)
\(588\) 3.35342 + 1.47487i 0.138293 + 0.0608228i
\(589\) 7.87077i 0.324310i
\(590\) 26.0322 + 32.4647i 1.07173 + 1.33655i
\(591\) 43.2412 1.77870
\(592\) 6.31081 + 6.88244i 0.259373 + 0.282867i
\(593\) 34.5547i 1.41899i 0.704711 + 0.709495i \(0.251077\pi\)
−0.704711 + 0.709495i \(0.748923\pi\)
\(594\) 1.92336 9.15056i 0.0789164 0.375452i
\(595\) 6.07016 7.38863i 0.248852 0.302904i
\(596\) −17.0556 + 38.7794i −0.698625 + 1.58846i
\(597\) −18.7305 −0.766587
\(598\) −6.61696 + 31.4808i −0.270588 + 1.28734i
\(599\) −47.9265 −1.95823 −0.979113 0.203318i \(-0.934828\pi\)
−0.979113 + 0.203318i \(0.934828\pi\)
\(600\) 10.7097 23.5868i 0.437220 0.962927i
\(601\) −0.470617 −0.0191969 −0.00959843 0.999954i \(-0.503055\pi\)
−0.00959843 + 0.999954i \(0.503055\pi\)
\(602\) 0.0682503 0.324707i 0.00278167 0.0132341i
\(603\) 2.11339 0.0860637
\(604\) 36.9797 + 16.2641i 1.50468 + 0.661778i
\(605\) 12.9700 15.7872i 0.527306 0.641840i
\(606\) −5.00714 + 23.8219i −0.203401 + 0.967700i
\(607\) 23.0958i 0.937430i 0.883349 + 0.468715i \(0.155283\pi\)
−0.883349 + 0.468715i \(0.844717\pi\)
\(608\) −18.1292 + 10.7425i −0.735237 + 0.435664i
\(609\) −13.4676 −0.545735
\(610\) −13.6716 17.0497i −0.553545 0.690324i
\(611\) 37.3691i 1.51179i
\(612\) 1.22297 2.78066i 0.0494356 0.112402i
\(613\) 14.7889 0.597320 0.298660 0.954360i \(-0.403460\pi\)
0.298660 + 0.954360i \(0.403460\pi\)
\(614\) −26.1303 5.49235i −1.05453 0.221653i
\(615\) −26.3819 + 32.1122i −1.06382 + 1.29489i
\(616\) 3.13832 + 2.24770i 0.126446 + 0.0905624i
\(617\) 45.0729i 1.81456i −0.420522 0.907282i \(-0.638153\pi\)
0.420522 0.907282i \(-0.361847\pi\)
\(618\) 3.96894 18.8826i 0.159654 0.759569i
\(619\) 46.1211i 1.85377i 0.375351 + 0.926883i \(0.377522\pi\)
−0.375351 + 0.926883i \(0.622478\pi\)
\(620\) −8.42990 + 4.26834i −0.338553 + 0.171421i
\(621\) 28.6966i 1.15156i
\(622\) −13.5162 2.84097i −0.541949 0.113913i
\(623\) 8.59946i 0.344530i
\(624\) −19.0152 20.7376i −0.761216 0.830167i
\(625\) −23.1169 + 9.51878i −0.924678 + 0.380751i
\(626\) −5.60101 + 26.6473i −0.223862 + 1.06504i
\(627\) −9.31265 −0.371911
\(628\) 19.5844 + 8.61345i 0.781502 + 0.343714i
\(629\) 9.98307i 0.398051i
\(630\) −0.702621 0.876236i −0.0279931 0.0349101i
\(631\) 26.8644 1.06946 0.534728 0.845024i \(-0.320414\pi\)
0.534728 + 0.845024i \(0.320414\pi\)
\(632\) 30.2822 + 21.6885i 1.20456 + 0.862721i
\(633\) 35.2089i 1.39943i
\(634\) −6.52359 1.37120i −0.259085 0.0544571i
\(635\) 13.2820 + 10.9119i 0.527081 + 0.433025i
\(636\) 38.2110 + 16.8057i 1.51517 + 0.666388i
\(637\) −3.84009 −0.152150
\(638\) −13.8875 2.91903i −0.549813 0.115565i
\(639\) 1.24092 0.0490899
\(640\) −21.3371 13.5914i −0.843424 0.537249i
\(641\) 30.3005 1.19680 0.598398 0.801199i \(-0.295804\pi\)
0.598398 + 0.801199i \(0.295804\pi\)
\(642\) −18.8235 3.95653i −0.742905 0.156152i
\(643\) −29.5531 −1.16546 −0.582730 0.812665i \(-0.698016\pi\)
−0.582730 + 0.812665i \(0.698016\pi\)
\(644\) 10.8444 + 4.76951i 0.427331 + 0.187945i
\(645\) −0.610016 + 0.742515i −0.0240194 + 0.0292365i
\(646\) 22.0474 + 4.63416i 0.867444 + 0.182328i
\(647\) 12.6646i 0.497896i 0.968517 + 0.248948i \(0.0800848\pi\)
−0.968517 + 0.248948i \(0.919915\pi\)
\(648\) 22.8555 + 16.3694i 0.897847 + 0.643049i
\(649\) 17.9594 0.704970
\(650\) −0.322317 + 27.1517i −0.0126423 + 1.06498i
\(651\) 3.87012i 0.151682i
\(652\) −3.27633 1.44097i −0.128311 0.0564327i
\(653\) 11.7561 0.460050 0.230025 0.973185i \(-0.426119\pi\)
0.230025 + 0.973185i \(0.426119\pi\)
\(654\) −2.69951 + 12.8431i −0.105559 + 0.502206i
\(655\) 15.8560 + 13.0265i 0.619544 + 0.508989i
\(656\) 27.4302 + 29.9148i 1.07097 + 1.16798i
\(657\) 0.782869i 0.0305426i
\(658\) 13.4678 + 2.83081i 0.525031 + 0.110357i
\(659\) 12.1150i 0.471933i 0.971761 + 0.235967i \(0.0758256\pi\)
−0.971761 + 0.235967i \(0.924174\pi\)
\(660\) −5.05027 9.97421i −0.196581 0.388246i
\(661\) 14.7784i 0.574812i 0.957809 + 0.287406i \(0.0927929\pi\)
−0.957809 + 0.287406i \(0.907207\pi\)
\(662\) −3.60014 + 17.1280i −0.139923 + 0.665698i
\(663\) 30.0801i 1.16821i
\(664\) −15.8713 11.3672i −0.615927 0.441134i
\(665\) 5.28774 6.43627i 0.205050 0.249588i
\(666\) −1.14749 0.241191i −0.0444643 0.00934598i
\(667\) −43.5521 −1.68634
\(668\) 6.54008 14.8702i 0.253043 0.575344i
\(669\) 26.4877i 1.02407i
\(670\) −14.6799 + 11.7713i −0.567136 + 0.454765i
\(671\) −9.43192 −0.364115
\(672\) −8.91428 + 5.28215i −0.343876 + 0.203763i
\(673\) 9.85860i 0.380021i 0.981782 + 0.190011i \(0.0608522\pi\)
−0.981782 + 0.190011i \(0.939148\pi\)
\(674\) 6.82744 32.4821i 0.262983 1.25117i
\(675\) −4.70080 23.7623i −0.180934 0.914612i
\(676\) 3.19710 + 1.40612i 0.122965 + 0.0540817i
\(677\) −5.15066 −0.197956 −0.0989779 0.995090i \(-0.531557\pi\)
−0.0989779 + 0.995090i \(0.531557\pi\)
\(678\) −2.45243 + 11.6676i −0.0941849 + 0.448093i
\(679\) −9.01176 −0.345840
\(680\) 6.99300 + 26.1268i 0.268169 + 1.00192i
\(681\) 19.0493 0.729972
\(682\) −0.838827 + 3.99080i −0.0321204 + 0.152815i
\(683\) −31.3990 −1.20145 −0.600725 0.799455i \(-0.705122\pi\)
−0.600725 + 0.799455i \(0.705122\pi\)
\(684\) 1.06533 2.42225i 0.0407340 0.0926170i
\(685\) −17.2557 14.1765i −0.659308 0.541657i
\(686\) −0.290898 + 1.38397i −0.0111065 + 0.0528403i
\(687\) 35.4418i 1.35219i
\(688\) 0.634257 + 0.691708i 0.0241808 + 0.0263711i
\(689\) −43.7565 −1.66699
\(690\) −21.4643 26.7681i −0.817132 1.01904i
\(691\) 29.1794i 1.11004i −0.831838 0.555018i \(-0.812711\pi\)
0.831838 0.555018i \(-0.187289\pi\)
\(692\) 7.33182 + 3.22462i 0.278714 + 0.122582i
\(693\) −0.484733 −0.0184135
\(694\) −29.5373 6.20846i −1.12122 0.235670i
\(695\) −9.05259 7.43719i −0.343384 0.282109i
\(696\) 22.1801 30.9686i 0.840734 1.17386i
\(697\) 43.3918i 1.64358i
\(698\) −1.02052 + 4.85522i −0.0386273 + 0.183773i
\(699\) 51.0049i 1.92918i
\(700\) 9.76105 + 2.17298i 0.368933 + 0.0821308i
\(701\) 49.3433i 1.86367i 0.362883 + 0.931835i \(0.381793\pi\)
−0.362883 + 0.931835i \(0.618207\pi\)
\(702\) −25.7469 5.41174i −0.971752 0.204253i
\(703\) 8.69630i 0.327987i
\(704\) −10.3371 + 3.51474i −0.389595 + 0.132467i
\(705\) −30.7972 25.3016i −1.15989 0.952913i
\(706\) −10.3118 + 49.0594i −0.388090 + 1.84637i
\(707\) −9.39707 −0.353413
\(708\) −19.4081 + 44.1281i −0.729400 + 1.65844i
\(709\) 27.4478i 1.03082i −0.856943 0.515411i \(-0.827639\pi\)
0.856943 0.515411i \(-0.172361\pi\)
\(710\) −8.61963 + 6.91176i −0.323489 + 0.259394i
\(711\) −4.67728 −0.175412
\(712\) −19.7744 14.1626i −0.741076 0.530767i
\(713\) 12.5154i 0.468704i
\(714\) 10.8409 + 2.27865i 0.405710 + 0.0852764i
\(715\) 9.05506 + 7.43922i 0.338640 + 0.278211i
\(716\) 0.422057 0.959630i 0.0157730 0.0358630i
\(717\) 25.2611 0.943394
\(718\) 23.6602 + 4.97315i 0.882991 + 0.185596i
\(719\) 27.7325 1.03425 0.517125 0.855910i \(-0.327002\pi\)
0.517125 + 0.855910i \(0.327002\pi\)
\(720\) 3.17205 0.172577i 0.118216 0.00643156i
\(721\) 7.44864 0.277402
\(722\) −7.08986 1.49022i −0.263857 0.0554603i
\(723\) 56.4480 2.09932
\(724\) 7.15939 16.2783i 0.266077 0.604978i
\(725\) −36.0634 + 7.13428i −1.33936 + 0.264960i
\(726\) 23.1635 + 4.86876i 0.859680 + 0.180697i
\(727\) 2.97264i 0.110249i 0.998479 + 0.0551246i \(0.0175556\pi\)
−0.998479 + 0.0551246i \(0.982444\pi\)
\(728\) 6.32434 8.83026i 0.234395 0.327271i
\(729\) 23.0914 0.855237
\(730\) −4.36048 5.43794i −0.161389 0.201267i
\(731\) 1.00333i 0.0371095i
\(732\) 10.1927 23.1752i 0.376733 0.856578i
\(733\) 12.7789 0.472000 0.236000 0.971753i \(-0.424164\pi\)
0.236000 + 0.971753i \(0.424164\pi\)
\(734\) −3.83546 + 18.2475i −0.141569 + 0.673529i
\(735\) 2.60002 3.16476i 0.0959033 0.116734i
\(736\) −28.8274 + 17.0816i −1.06259 + 0.629638i
\(737\) 8.12094i 0.299139i
\(738\) −4.98761 1.04835i −0.183597 0.0385903i
\(739\) 36.8126i 1.35417i 0.735903 + 0.677087i \(0.236758\pi\)
−0.735903 + 0.677087i \(0.763242\pi\)
\(740\) 9.31408 4.71602i 0.342392 0.173364i
\(741\) 26.2029i 0.962588i
\(742\) −3.31468 + 15.7699i −0.121686 + 0.578930i
\(743\) 1.08547i 0.0398220i 0.999802 + 0.0199110i \(0.00633828\pi\)
−0.999802 + 0.0199110i \(0.993662\pi\)
\(744\) −8.89929 6.37378i −0.326264 0.233674i
\(745\) 36.5977 + 30.0670i 1.34084 + 1.10157i
\(746\) 28.7659 + 6.04631i 1.05319 + 0.221371i
\(747\) 2.45143 0.0896931
\(748\) 10.6850 + 4.69941i 0.390684 + 0.171827i
\(749\) 7.42534i 0.271316i
\(750\) −22.1585 18.6493i −0.809112 0.680976i
\(751\) −14.2742 −0.520873 −0.260436 0.965491i \(-0.583866\pi\)
−0.260436 + 0.965491i \(0.583866\pi\)
\(752\) −28.6899 + 26.3070i −1.04621 + 0.959318i
\(753\) 31.1247i 1.13425i
\(754\) −8.21325 + 39.0753i −0.299109 + 1.42304i
\(755\) 28.6717 34.8993i 1.04347 1.27012i
\(756\) −3.90079 + 8.86922i −0.141870 + 0.322571i
\(757\) 9.95779 0.361922 0.180961 0.983490i \(-0.442079\pi\)
0.180961 + 0.983490i \(0.442079\pi\)
\(758\) −10.5952 + 50.4077i −0.384836 + 1.83089i
\(759\) −14.8081 −0.537499
\(760\) 6.09164 + 22.7591i 0.220967 + 0.825561i
\(761\) 35.2392 1.27742 0.638710 0.769447i \(-0.279468\pi\)
0.638710 + 0.769447i \(0.279468\pi\)
\(762\) −4.09617 + 19.4879i −0.148388 + 0.705971i
\(763\) −5.06625 −0.183411
\(764\) −23.4647 10.3200i −0.848921 0.373366i
\(765\) −2.62423 2.15594i −0.0948792 0.0779483i
\(766\) 8.70053 41.3935i 0.314363 1.49561i
\(767\) 50.5323i 1.82462i
\(768\) 2.53487 29.1976i 0.0914692 1.05358i
\(769\) 27.1046 0.977415 0.488708 0.872448i \(-0.337468\pi\)
0.488708 + 0.872448i \(0.337468\pi\)
\(770\) 3.36704 2.69991i 0.121340 0.0972979i
\(771\) 16.3241i 0.587899i
\(772\) −2.03681 + 4.63109i −0.0733063 + 0.166676i
\(773\) −38.6612 −1.39055 −0.695273 0.718746i \(-0.744717\pi\)
−0.695273 + 0.718746i \(0.744717\pi\)
\(774\) −0.115326 0.0242405i −0.00414532 0.000871308i
\(775\) 2.05014 + 10.3634i 0.0736433 + 0.372263i
\(776\) 14.8417 20.7224i 0.532785 0.743892i
\(777\) 4.27604i 0.153402i
\(778\) 2.24430 10.6774i 0.0804619 0.382805i
\(779\) 37.7988i 1.35428i
\(780\) −28.0643 + 14.2099i −1.00486 + 0.508796i
\(781\) 4.76838i 0.170626i
\(782\) 35.0577 + 7.36880i 1.25366 + 0.263508i
\(783\) 35.6195i 1.27294i
\(784\) −2.70334 2.94821i −0.0965479 0.105293i
\(785\) 15.1845 18.4826i 0.541957 0.659673i
\(786\) −4.88998 + 23.2645i −0.174420 + 0.829817i
\(787\) 21.0967 0.752015 0.376007 0.926617i \(-0.377297\pi\)
0.376007 + 0.926617i \(0.377297\pi\)
\(788\) −43.2186 19.0081i −1.53960 0.677134i
\(789\) 44.9251i 1.59938i
\(790\) 32.4892 26.0519i 1.15591 0.926885i
\(791\) −4.60255 −0.163648
\(792\) 0.798318 1.11464i 0.0283670 0.0396070i
\(793\) 26.5385i 0.942410i
\(794\) 4.09491 + 0.860710i 0.145323 + 0.0305455i
\(795\) 29.6263 36.0613i 1.05074 1.27896i
\(796\) 18.7207 + 8.23358i 0.663537 + 0.291831i
\(797\) −1.60768 −0.0569471 −0.0284736 0.999595i \(-0.509065\pi\)
−0.0284736 + 0.999595i \(0.509065\pi\)
\(798\) 9.44354 + 1.98494i 0.334298 + 0.0702662i
\(799\) 41.6151 1.47224
\(800\) −21.0724 + 18.8667i −0.745023 + 0.667039i
\(801\) 3.05428 0.107918
\(802\) −42.5035 8.93382i −1.50085 0.315464i
\(803\) −3.00827 −0.106160
\(804\) −19.9540 8.77599i −0.703722 0.309505i
\(805\) 8.40807 10.2343i 0.296345 0.360713i
\(806\) 11.2289 + 2.36020i 0.395520 + 0.0831346i
\(807\) 16.3118i 0.574201i
\(808\) 15.4762 21.6085i 0.544452 0.760183i
\(809\) −27.5712 −0.969353 −0.484676 0.874694i \(-0.661063\pi\)
−0.484676 + 0.874694i \(0.661063\pi\)
\(810\) 24.5212 19.6626i 0.861588 0.690875i
\(811\) 33.1906i 1.16548i −0.812659 0.582740i \(-0.801981\pi\)
0.812659 0.582740i \(-0.198019\pi\)
\(812\) 13.4606 + 5.92012i 0.472373 + 0.207755i
\(813\) 18.3735 0.644385
\(814\) 0.926808 4.40937i 0.0324846 0.154548i
\(815\) −2.54025 + 3.09201i −0.0889812 + 0.108308i
\(816\) −23.0938 + 21.1757i −0.808445 + 0.741299i
\(817\) 0.874006i 0.0305776i
\(818\) 6.76497 + 1.42193i 0.236531 + 0.0497167i
\(819\) 1.36389i 0.0476582i
\(820\) 40.4840 20.4984i 1.41376 0.715835i
\(821\) 50.2595i 1.75407i −0.480426 0.877035i \(-0.659518\pi\)
0.480426 0.877035i \(-0.340482\pi\)
\(822\) 5.32166 25.3183i 0.185614 0.883077i
\(823\) 27.9633i 0.974739i −0.873196 0.487370i \(-0.837956\pi\)
0.873196 0.487370i \(-0.162044\pi\)
\(824\) −12.2673 + 17.1281i −0.427352 + 0.596684i
\(825\) −12.2619 + 2.42572i −0.426903 + 0.0844526i
\(826\) −18.2119 3.82796i −0.633672 0.133192i
\(827\) 25.9992 0.904082 0.452041 0.891997i \(-0.350696\pi\)
0.452041 + 0.891997i \(0.350696\pi\)
\(828\) 1.69399 3.85163i 0.0588703 0.133853i
\(829\) 5.13607i 0.178383i 0.996014 + 0.0891915i \(0.0284283\pi\)
−0.996014 + 0.0891915i \(0.971572\pi\)
\(830\) −17.0281 + 13.6542i −0.591053 + 0.473943i
\(831\) −19.2500 −0.667776
\(832\) 9.88939 + 29.0855i 0.342853 + 1.00836i
\(833\) 4.27642i 0.148169i
\(834\) 2.79181 13.2823i 0.0966726 0.459929i
\(835\) −14.0336 11.5294i −0.485653 0.398990i
\(836\) 9.30779 + 4.09368i 0.321917 + 0.141583i
\(837\) −10.2358 −0.353801
\(838\) 4.54211 21.6095i 0.156905 0.746488i
\(839\) 23.2811 0.803752 0.401876 0.915694i \(-0.368358\pi\)
0.401876 + 0.915694i \(0.368358\pi\)
\(840\) 2.99530 + 11.1908i 0.103348 + 0.386121i
\(841\) −25.0587 −0.864093
\(842\) 3.10797 14.7864i 0.107108 0.509574i
\(843\) 54.8282 1.88838
\(844\) 15.4772 35.1905i 0.532747 1.21131i
\(845\) 2.47882 3.01724i 0.0852742 0.103796i
\(846\) 1.00542 4.78339i 0.0345671 0.164456i
\(847\) 9.13735i 0.313963i
\(848\) −30.8036 33.5938i −1.05780 1.15362i
\(849\) −53.1033 −1.82250
\(850\) 30.2367 + 0.358940i 1.03711 + 0.0123115i
\(851\) 13.8280i 0.474019i
\(852\) −11.7164 5.15300i −0.401397 0.176539i
\(853\) −22.7793 −0.779948 −0.389974 0.920826i \(-0.627516\pi\)
−0.389974 + 0.920826i \(0.627516\pi\)
\(854\) 9.56449 + 2.01036i 0.327290 + 0.0687933i
\(855\) −2.28598 1.87805i −0.0781788 0.0642281i
\(856\) 17.0745 + 12.2290i 0.583594 + 0.417977i
\(857\) 29.7120i 1.01494i −0.861669 0.507471i \(-0.830581\pi\)
0.861669 0.507471i \(-0.169419\pi\)
\(858\) −2.79258 + 13.2859i −0.0953370 + 0.453574i
\(859\) 15.1272i 0.516133i 0.966127 + 0.258067i \(0.0830854\pi\)
−0.966127 + 0.258067i \(0.916915\pi\)
\(860\) 0.936095 0.473976i 0.0319206 0.0161624i
\(861\) 18.5860i 0.633408i
\(862\) −8.28648 1.74174i −0.282239 0.0593239i
\(863\) 7.86992i 0.267895i 0.990988 + 0.133948i \(0.0427654\pi\)
−0.990988 + 0.133948i \(0.957235\pi\)
\(864\) −13.9704 23.5767i −0.475282 0.802097i
\(865\) 5.68462 6.91935i 0.193283 0.235265i
\(866\) 2.23591 10.6375i 0.0759793 0.361478i
\(867\) 2.35878 0.0801082
\(868\) 1.70124 3.86810i 0.0577437 0.131292i
\(869\) 17.9730i 0.609693i
\(870\) −26.6424 33.2256i −0.903262 1.12645i
\(871\) 22.8498 0.774237
\(872\) 8.34371 11.6498i 0.282554 0.394511i
\(873\) 3.20072i 0.108328i
\(874\) 30.5389 + 6.41899i 1.03299 + 0.217126i
\(875\) 5.28583 9.85190i 0.178694 0.333055i
\(876\) 3.25092 7.39162i 0.109838 0.249740i
\(877\) −24.0347 −0.811595 −0.405798 0.913963i \(-0.633006\pi\)
−0.405798 + 0.913963i \(0.633006\pi\)
\(878\) −47.7973 10.0465i −1.61308 0.339054i
\(879\) −9.86364 −0.332692
\(880\) 0.663147 + 12.1890i 0.0223547 + 0.410892i
\(881\) −2.99314 −0.100841 −0.0504207 0.998728i \(-0.516056\pi\)
−0.0504207 + 0.998728i \(0.516056\pi\)
\(882\) 0.491547 + 0.103318i 0.0165512 + 0.00347891i
\(883\) −10.6397 −0.358055 −0.179028 0.983844i \(-0.557295\pi\)
−0.179028 + 0.983844i \(0.557295\pi\)
\(884\) 13.2227 30.0644i 0.444727 1.01118i
\(885\) 41.6456 + 34.2141i 1.39990 + 1.15009i
\(886\) −14.3158 3.00905i −0.480949 0.101091i
\(887\) 1.68812i 0.0566816i 0.999598 + 0.0283408i \(0.00902236\pi\)
−0.999598 + 0.0283408i \(0.990978\pi\)
\(888\) 9.83270 + 7.04230i 0.329964 + 0.236324i
\(889\) −7.68741 −0.257827
\(890\) −21.2156 + 17.0120i −0.711147 + 0.570242i
\(891\) 13.5651i 0.454449i
\(892\) 11.6435 26.4738i 0.389853 0.886410i
\(893\) 36.2511 1.21310
\(894\) −11.2867 + 53.6976i −0.377484 + 1.79591i
\(895\) −0.905643 0.744034i −0.0302723 0.0248703i
\(896\) 11.2316 1.36084i 0.375220 0.0454623i
\(897\) 41.6654i 1.39117i
\(898\) −57.6737 12.1225i −1.92460 0.404532i
\(899\) 15.5346i 0.518107i
\(900\) 0.771778 3.46684i 0.0257259 0.115561i
\(901\) 48.7282i 1.62337i
\(902\) 4.02841 19.1655i 0.134131 0.638142i
\(903\) 0.429756i 0.0143014i
\(904\) 7.58004 10.5835i 0.252108 0.352002i
\(905\) −15.3625 12.6211i −0.510667 0.419541i
\(906\) 51.2056 + 10.7629i 1.70119 + 0.357575i
\(907\) 28.3463 0.941223 0.470612 0.882340i \(-0.344033\pi\)
0.470612 + 0.882340i \(0.344033\pi\)
\(908\) −19.0394 8.37376i −0.631845 0.277893i
\(909\) 3.33757i 0.110700i
\(910\) −7.59671 9.47382i −0.251828 0.314054i
\(911\) 3.10079 0.102734 0.0513669 0.998680i \(-0.483642\pi\)
0.0513669 + 0.998680i \(0.483642\pi\)
\(912\) −20.1171 + 18.4463i −0.666145 + 0.610817i
\(913\) 9.41992i 0.311754i
\(914\) −0.379037 + 1.80330i −0.0125374 + 0.0596479i
\(915\) −21.8714 17.9685i −0.723045 0.594020i
\(916\) −15.5796 + 35.4233i −0.514764 + 1.17042i
\(917\) −9.17717 −0.303057
\(918\) −6.02664 + 28.6723i −0.198909 + 0.946326i
\(919\) −11.4846 −0.378843 −0.189421 0.981896i \(-0.560661\pi\)
−0.189421 + 0.981896i \(0.560661\pi\)
\(920\) 9.68634 + 36.1894i 0.319349 + 1.19313i
\(921\) −34.5840 −1.13958
\(922\) −1.94111 + 9.23500i −0.0639270 + 0.304139i
\(923\) 13.4168 0.441618
\(924\) 4.57671 + 2.01289i 0.150563 + 0.0662193i
\(925\) −2.26517 11.4503i −0.0744784 0.376485i
\(926\) 4.55042 21.6490i 0.149536 0.711431i
\(927\) 2.64554i 0.0868909i
\(928\) −35.7818 + 21.2025i −1.17459 + 0.696005i
\(929\) 3.40928 0.111855 0.0559274 0.998435i \(-0.482188\pi\)
0.0559274 + 0.998435i \(0.482188\pi\)
\(930\) −9.54790 + 7.65610i −0.313088 + 0.251053i
\(931\) 3.72521i 0.122089i
\(932\) −22.4208 + 50.9783i −0.734419 + 1.66985i
\(933\) −17.8889 −0.585656
\(934\) 17.2885 + 3.63388i 0.565697 + 0.118904i
\(935\) 8.28448 10.0839i 0.270932 0.329779i
\(936\) −3.13625 2.24622i −0.102512 0.0734200i
\(937\) 8.41945i 0.275052i 0.990498 + 0.137526i \(0.0439150\pi\)
−0.990498 + 0.137526i \(0.956085\pi\)
\(938\) 1.73094 8.23509i 0.0565171 0.268885i
\(939\) 35.2682i 1.15094i
\(940\) 19.6590 + 38.8263i 0.641207 + 1.26638i
\(941\) 23.1299i 0.754014i −0.926210 0.377007i \(-0.876953\pi\)
0.926210 0.377007i \(-0.123047\pi\)
\(942\) 27.1184 + 5.70003i 0.883565 + 0.185717i
\(943\) 60.1041i 1.95726i
\(944\) 38.7959 35.5737i 1.26270 1.15782i
\(945\) 8.37026 + 6.87662i 0.272285 + 0.223696i
\(946\) 0.0931472 0.443156i 0.00302848 0.0144083i
\(947\) 2.30010 0.0747431 0.0373716 0.999301i \(-0.488101\pi\)
0.0373716 + 0.999301i \(0.488101\pi\)
\(948\) 44.1615 + 19.4228i 1.43430 + 0.630822i
\(949\) 8.46434i 0.274764i
\(950\) 26.3393 + 0.312674i 0.854561 + 0.0101445i
\(951\) −8.63409 −0.279979
\(952\) −9.83357 7.04292i −0.318708 0.228262i
\(953\) 9.82067i 0.318123i −0.987269 0.159061i \(-0.949153\pi\)
0.987269 0.159061i \(-0.0508468\pi\)
\(954\) 5.60100 + 1.17728i 0.181339 + 0.0381157i
\(955\) −18.1930 + 22.1446i −0.588710 + 0.716582i
\(956\) −25.2479 11.1043i −0.816577 0.359140i
\(957\) −18.3804 −0.594155
\(958\) 41.2797 + 8.67661i 1.33369 + 0.280328i
\(959\) 9.98734 0.322508
\(960\) −30.6663 11.5428i −0.989749 0.372542i
\(961\) −26.5359 −0.855997
\(962\) −12.4066 2.60775i −0.400005 0.0840773i
\(963\) −2.63727 −0.0849847
\(964\) −56.4185 24.8135i −1.81712 0.799190i
\(965\) 4.37055 + 3.59064i 0.140693 + 0.115587i
\(966\) 15.0162 + 3.15627i 0.483139 + 0.101551i
\(967\) 15.1978i 0.488728i 0.969684 + 0.244364i \(0.0785791\pi\)
−0.969684 + 0.244364i \(0.921421\pi\)
\(968\) −21.0112 15.0485i −0.675327 0.483677i
\(969\) 29.1802 0.937402
\(970\) −17.8276 22.2327i −0.572410 0.713850i
\(971\) 3.72008i 0.119383i 0.998217 + 0.0596915i \(0.0190117\pi\)
−0.998217 + 0.0596915i \(0.980988\pi\)
\(972\) 6.72320 + 2.95695i 0.215647 + 0.0948441i
\(973\) 5.23949 0.167970
\(974\) 4.27946 20.3599i 0.137123 0.652373i
\(975\) 6.82522 + 34.5011i 0.218582 + 1.10492i
\(976\) −20.3748 + 18.6825i −0.652181 + 0.598013i
\(977\) 29.4900i 0.943467i 0.881741 + 0.471734i \(0.156372\pi\)
−0.881741 + 0.471734i \(0.843628\pi\)
\(978\) −4.53672 0.953575i −0.145068 0.0304920i
\(979\) 11.7364i 0.375098i
\(980\) −3.98984 + 2.02019i −0.127451 + 0.0645325i
\(981\) 1.79938i 0.0574499i
\(982\) 5.77940 27.4960i 0.184428 0.877433i
\(983\) 22.6176i 0.721389i −0.932684 0.360695i \(-0.882540\pi\)
0.932684 0.360695i \(-0.117460\pi\)
\(984\) 42.7382 + 30.6096i 1.36245 + 0.975800i
\(985\) −33.5089 + 40.7872i −1.06768 + 1.29959i
\(986\) 43.5151 + 9.14646i 1.38580 + 0.291283i
\(987\) 17.8249 0.567374
\(988\) 11.5183 26.1892i 0.366447 0.833191i
\(989\) 1.38976i 0.0441918i
\(990\) −0.958928 1.19588i −0.0304767 0.0380074i
\(991\) 5.62557 0.178702 0.0893510 0.996000i \(-0.471521\pi\)
0.0893510 + 0.996000i \(0.471521\pi\)
\(992\) 6.09285 + 10.2824i 0.193448 + 0.326467i
\(993\) 22.6692i 0.719385i
\(994\) 1.01636 4.83540i 0.0322369 0.153370i
\(995\) 14.5148 17.6675i 0.460150 0.560097i
\(996\) −23.1457 10.1797i −0.733399 0.322558i
\(997\) 52.3481 1.65788 0.828940 0.559337i \(-0.188944\pi\)
0.828940 + 0.559337i \(0.188944\pi\)
\(998\) 6.55985 31.2091i 0.207648 0.987906i
\(999\) 11.3094 0.357813
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 280.2.l.a.29.1 36
4.3 odd 2 1120.2.l.a.1009.28 36
5.4 even 2 inner 280.2.l.a.29.36 yes 36
8.3 odd 2 1120.2.l.a.1009.9 36
8.5 even 2 inner 280.2.l.a.29.35 yes 36
20.19 odd 2 1120.2.l.a.1009.10 36
40.19 odd 2 1120.2.l.a.1009.27 36
40.29 even 2 inner 280.2.l.a.29.2 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.2.l.a.29.1 36 1.1 even 1 trivial
280.2.l.a.29.2 yes 36 40.29 even 2 inner
280.2.l.a.29.35 yes 36 8.5 even 2 inner
280.2.l.a.29.36 yes 36 5.4 even 2 inner
1120.2.l.a.1009.9 36 8.3 odd 2
1120.2.l.a.1009.10 36 20.19 odd 2
1120.2.l.a.1009.27 36 40.19 odd 2
1120.2.l.a.1009.28 36 4.3 odd 2