Properties

Label 1045.2.b.d.419.18
Level $1045$
Weight $2$
Character 1045.419
Analytic conductor $8.344$
Analytic rank $0$
Dimension $22$
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] = [1045,2,Mod(419,1045)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1045.419");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1045.b (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: \(8.34436701122\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 419.18
Character \(\chi\) \(=\) 1045.419
Dual form 1045.2.b.d.419.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.84475i q^{2} -3.33093i q^{3} -1.40312 q^{4} +(-2.19819 - 0.409812i) q^{5} +6.14475 q^{6} -3.04962i q^{7} +1.10110i q^{8} -8.09513 q^{9} +O(q^{10})\) \(q+1.84475i q^{2} -3.33093i q^{3} -1.40312 q^{4} +(-2.19819 - 0.409812i) q^{5} +6.14475 q^{6} -3.04962i q^{7} +1.10110i q^{8} -8.09513 q^{9} +(0.756002 - 4.05513i) q^{10} -1.00000 q^{11} +4.67369i q^{12} -2.03040i q^{13} +5.62579 q^{14} +(-1.36506 + 7.32204i) q^{15} -4.83750 q^{16} +6.84485i q^{17} -14.9335i q^{18} +1.00000 q^{19} +(3.08432 + 0.575014i) q^{20} -10.1581 q^{21} -1.84475i q^{22} -5.01139i q^{23} +3.66770 q^{24} +(4.66411 + 1.80169i) q^{25} +3.74558 q^{26} +16.9715i q^{27} +4.27897i q^{28} -7.08382 q^{29} +(-13.5074 - 2.51819i) q^{30} +5.61832 q^{31} -6.72178i q^{32} +3.33093i q^{33} -12.6271 q^{34} +(-1.24977 + 6.70365i) q^{35} +11.3584 q^{36} +6.54847i q^{37} +1.84475i q^{38} -6.76312 q^{39} +(0.451245 - 2.42044i) q^{40} -8.63500 q^{41} -18.7391i q^{42} -2.80385i q^{43} +1.40312 q^{44} +(17.7947 + 3.31748i) q^{45} +9.24479 q^{46} +6.56671i q^{47} +16.1134i q^{48} -2.30016 q^{49} +(-3.32368 + 8.60413i) q^{50} +22.7998 q^{51} +2.84888i q^{52} +11.3475i q^{53} -31.3083 q^{54} +(2.19819 + 0.409812i) q^{55} +3.35794 q^{56} -3.33093i q^{57} -13.0679i q^{58} +5.84803 q^{59} +(1.91533 - 10.2737i) q^{60} -9.59640 q^{61} +10.3644i q^{62} +24.6870i q^{63} +2.72504 q^{64} +(-0.832080 + 4.46320i) q^{65} -6.14475 q^{66} -9.59976i q^{67} -9.60413i q^{68} -16.6926 q^{69} +(-12.3666 - 2.30552i) q^{70} -3.93583 q^{71} -8.91357i q^{72} +0.181013i q^{73} -12.0803 q^{74} +(6.00132 - 15.5358i) q^{75} -1.40312 q^{76} +3.04962i q^{77} -12.4763i q^{78} -14.8138 q^{79} +(10.6338 + 1.98246i) q^{80} +32.2457 q^{81} -15.9294i q^{82} -3.70100i q^{83} +14.2530 q^{84} +(2.80510 - 15.0463i) q^{85} +5.17242 q^{86} +23.5957i q^{87} -1.10110i q^{88} -10.3263 q^{89} +(-6.11993 + 32.8268i) q^{90} -6.19193 q^{91} +7.03157i q^{92} -18.7143i q^{93} -12.1140 q^{94} +(-2.19819 - 0.409812i) q^{95} -22.3898 q^{96} -5.12653i q^{97} -4.24323i q^{98} +8.09513 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q - 32 q^{4} + 7 q^{5} - 12 q^{6} - 34 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 22 q - 32 q^{4} + 7 q^{5} - 12 q^{6} - 34 q^{9} + 2 q^{10} - 22 q^{11} + 8 q^{14} - 23 q^{15} + 40 q^{16} + 22 q^{19} - 22 q^{20} - 22 q^{21} + 22 q^{24} + 13 q^{25} + 16 q^{26} + 10 q^{29} - 22 q^{30} + 76 q^{31} - 56 q^{34} - 2 q^{35} + 104 q^{36} + 8 q^{39} - 20 q^{40} + 6 q^{41} + 32 q^{44} - 12 q^{45} + 88 q^{46} - 28 q^{49} - 20 q^{50} + 8 q^{51} - 38 q^{54} - 7 q^{55} + 44 q^{56} - 40 q^{59} + 78 q^{60} - 6 q^{61} - 140 q^{64} - 22 q^{65} + 12 q^{66} - 74 q^{69} - 24 q^{70} + 62 q^{71} + 26 q^{74} + 13 q^{75} - 32 q^{76} - 102 q^{79} + 142 q^{80} + 94 q^{81} + 38 q^{84} + 26 q^{85} + 28 q^{86} - 54 q^{89} + 118 q^{90} + 88 q^{91} - 36 q^{94} + 7 q^{95} + 2 q^{96} + 34 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times\).

\(n\) \(496\) \(761\) \(837\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.84475i 1.30444i 0.758031 + 0.652219i \(0.226162\pi\)
−0.758031 + 0.652219i \(0.773838\pi\)
\(3\) 3.33093i 1.92312i −0.274602 0.961558i \(-0.588546\pi\)
0.274602 0.961558i \(-0.411454\pi\)
\(4\) −1.40312 −0.701558
\(5\) −2.19819 0.409812i −0.983062 0.183273i
\(6\) 6.14475 2.50859
\(7\) 3.04962i 1.15265i −0.817222 0.576323i \(-0.804487\pi\)
0.817222 0.576323i \(-0.195513\pi\)
\(8\) 1.10110i 0.389299i
\(9\) −8.09513 −2.69838
\(10\) 0.756002 4.05513i 0.239069 1.28234i
\(11\) −1.00000 −0.301511
\(12\) 4.67369i 1.34918i
\(13\) 2.03040i 0.563130i −0.959542 0.281565i \(-0.909146\pi\)
0.959542 0.281565i \(-0.0908536\pi\)
\(14\) 5.62579 1.50356
\(15\) −1.36506 + 7.32204i −0.352456 + 1.89054i
\(16\) −4.83750 −1.20937
\(17\) 6.84485i 1.66012i 0.557674 + 0.830060i \(0.311694\pi\)
−0.557674 + 0.830060i \(0.688306\pi\)
\(18\) 14.9335i 3.51986i
\(19\) 1.00000 0.229416
\(20\) 3.08432 + 0.575014i 0.689675 + 0.128577i
\(21\) −10.1581 −2.21667
\(22\) 1.84475i 0.393303i
\(23\) 5.01139i 1.04495i −0.852655 0.522474i \(-0.825009\pi\)
0.852655 0.522474i \(-0.174991\pi\)
\(24\) 3.66770 0.748667
\(25\) 4.66411 + 1.80169i 0.932822 + 0.360338i
\(26\) 3.74558 0.734569
\(27\) 16.9715i 3.26617i
\(28\) 4.27897i 0.808649i
\(29\) −7.08382 −1.31543 −0.657716 0.753266i \(-0.728477\pi\)
−0.657716 + 0.753266i \(0.728477\pi\)
\(30\) −13.5074 2.51819i −2.46609 0.459757i
\(31\) 5.61832 1.00908 0.504540 0.863388i \(-0.331662\pi\)
0.504540 + 0.863388i \(0.331662\pi\)
\(32\) 6.72178i 1.18825i
\(33\) 3.33093i 0.579841i
\(34\) −12.6271 −2.16552
\(35\) −1.24977 + 6.70365i −0.211249 + 1.13312i
\(36\) 11.3584 1.89307
\(37\) 6.54847i 1.07656i 0.842766 + 0.538281i \(0.180926\pi\)
−0.842766 + 0.538281i \(0.819074\pi\)
\(38\) 1.84475i 0.299259i
\(39\) −6.76312 −1.08297
\(40\) 0.451245 2.42044i 0.0713481 0.382705i
\(41\) −8.63500 −1.34856 −0.674280 0.738476i \(-0.735546\pi\)
−0.674280 + 0.738476i \(0.735546\pi\)
\(42\) 18.7391i 2.89151i
\(43\) 2.80385i 0.427584i −0.976879 0.213792i \(-0.931419\pi\)
0.976879 0.213792i \(-0.0685814\pi\)
\(44\) 1.40312 0.211528
\(45\) 17.7947 + 3.31748i 2.65267 + 0.494541i
\(46\) 9.24479 1.36307
\(47\) 6.56671i 0.957853i 0.877855 + 0.478927i \(0.158974\pi\)
−0.877855 + 0.478927i \(0.841026\pi\)
\(48\) 16.1134i 2.32577i
\(49\) −2.30016 −0.328594
\(50\) −3.32368 + 8.60413i −0.470039 + 1.21681i
\(51\) 22.7998 3.19260
\(52\) 2.84888i 0.395069i
\(53\) 11.3475i 1.55870i 0.626587 + 0.779352i \(0.284451\pi\)
−0.626587 + 0.779352i \(0.715549\pi\)
\(54\) −31.3083 −4.26052
\(55\) 2.19819 + 0.409812i 0.296404 + 0.0552590i
\(56\) 3.35794 0.448724
\(57\) 3.33093i 0.441193i
\(58\) 13.0679i 1.71590i
\(59\) 5.84803 0.761349 0.380674 0.924709i \(-0.375692\pi\)
0.380674 + 0.924709i \(0.375692\pi\)
\(60\) 1.91533 10.2737i 0.247268 1.32633i
\(61\) −9.59640 −1.22869 −0.614346 0.789036i \(-0.710580\pi\)
−0.614346 + 0.789036i \(0.710580\pi\)
\(62\) 10.3644i 1.31628i
\(63\) 24.6870i 3.11027i
\(64\) 2.72504 0.340630
\(65\) −0.832080 + 4.46320i −0.103207 + 0.553592i
\(66\) −6.14475 −0.756367
\(67\) 9.59976i 1.17280i −0.810023 0.586398i \(-0.800545\pi\)
0.810023 0.586398i \(-0.199455\pi\)
\(68\) 9.60413i 1.16467i
\(69\) −16.6926 −2.00956
\(70\) −12.3666 2.30552i −1.47809 0.275562i
\(71\) −3.93583 −0.467098 −0.233549 0.972345i \(-0.575034\pi\)
−0.233549 + 0.972345i \(0.575034\pi\)
\(72\) 8.91357i 1.05047i
\(73\) 0.181013i 0.0211860i 0.999944 + 0.0105930i \(0.00337192\pi\)
−0.999944 + 0.0105930i \(0.996628\pi\)
\(74\) −12.0803 −1.40431
\(75\) 6.00132 15.5358i 0.692972 1.79392i
\(76\) −1.40312 −0.160948
\(77\) 3.04962i 0.347536i
\(78\) 12.4763i 1.41266i
\(79\) −14.8138 −1.66668 −0.833339 0.552762i \(-0.813574\pi\)
−0.833339 + 0.552762i \(0.813574\pi\)
\(80\) 10.6338 + 1.98246i 1.18889 + 0.221646i
\(81\) 32.2457 3.58285
\(82\) 15.9294i 1.75911i
\(83\) 3.70100i 0.406237i −0.979154 0.203119i \(-0.934892\pi\)
0.979154 0.203119i \(-0.0651077\pi\)
\(84\) 14.2530 1.55513
\(85\) 2.80510 15.0463i 0.304256 1.63200i
\(86\) 5.17242 0.557756
\(87\) 23.5957i 2.52973i
\(88\) 1.10110i 0.117378i
\(89\) −10.3263 −1.09458 −0.547292 0.836942i \(-0.684341\pi\)
−0.547292 + 0.836942i \(0.684341\pi\)
\(90\) −6.11993 + 32.8268i −0.645097 + 3.46024i
\(91\) −6.19193 −0.649090
\(92\) 7.03157i 0.733092i
\(93\) 18.7143i 1.94058i
\(94\) −12.1140 −1.24946
\(95\) −2.19819 0.409812i −0.225530 0.0420458i
\(96\) −22.3898 −2.28515
\(97\) 5.12653i 0.520520i −0.965539 0.260260i \(-0.916192\pi\)
0.965539 0.260260i \(-0.0838084\pi\)
\(98\) 4.24323i 0.428631i
\(99\) 8.09513 0.813591
\(100\) −6.54429 2.52798i −0.654429 0.252798i
\(101\) −11.6087 −1.15511 −0.577556 0.816351i \(-0.695993\pi\)
−0.577556 + 0.816351i \(0.695993\pi\)
\(102\) 42.0599i 4.16455i
\(103\) 1.06418i 0.104857i −0.998625 0.0524284i \(-0.983304\pi\)
0.998625 0.0524284i \(-0.0166961\pi\)
\(104\) 2.23568 0.219226
\(105\) 22.3294 + 4.16290i 2.17913 + 0.406257i
\(106\) −20.9334 −2.03323
\(107\) 8.72445i 0.843425i −0.906730 0.421712i \(-0.861429\pi\)
0.906730 0.421712i \(-0.138571\pi\)
\(108\) 23.8130i 2.29141i
\(109\) −0.307944 −0.0294956 −0.0147478 0.999891i \(-0.504695\pi\)
−0.0147478 + 0.999891i \(0.504695\pi\)
\(110\) −0.756002 + 4.05513i −0.0720820 + 0.386641i
\(111\) 21.8125 2.07035
\(112\) 14.7525i 1.39398i
\(113\) 6.74368i 0.634392i −0.948360 0.317196i \(-0.897259\pi\)
0.948360 0.317196i \(-0.102741\pi\)
\(114\) 6.14475 0.575509
\(115\) −2.05373 + 11.0160i −0.191511 + 1.02725i
\(116\) 9.93943 0.922853
\(117\) 16.4363i 1.51954i
\(118\) 10.7882i 0.993132i
\(119\) 20.8742 1.91353
\(120\) −8.06232 1.50307i −0.735986 0.137211i
\(121\) 1.00000 0.0909091
\(122\) 17.7030i 1.60275i
\(123\) 28.7626i 2.59344i
\(124\) −7.88316 −0.707928
\(125\) −9.51426 5.87187i −0.850981 0.525196i
\(126\) −45.5415 −4.05716
\(127\) 5.71138i 0.506803i −0.967361 0.253401i \(-0.918451\pi\)
0.967361 0.253401i \(-0.0815493\pi\)
\(128\) 8.41654i 0.743924i
\(129\) −9.33945 −0.822293
\(130\) −8.23351 1.53498i −0.722127 0.134627i
\(131\) −13.1950 −1.15285 −0.576425 0.817150i \(-0.695553\pi\)
−0.576425 + 0.817150i \(0.695553\pi\)
\(132\) 4.67369i 0.406792i
\(133\) 3.04962i 0.264435i
\(134\) 17.7092 1.52984
\(135\) 6.95514 37.3067i 0.598603 3.21085i
\(136\) −7.53689 −0.646283
\(137\) 5.25354i 0.448841i 0.974492 + 0.224420i \(0.0720488\pi\)
−0.974492 + 0.224420i \(0.927951\pi\)
\(138\) 30.7938i 2.62134i
\(139\) 10.2849 0.872350 0.436175 0.899862i \(-0.356333\pi\)
0.436175 + 0.899862i \(0.356333\pi\)
\(140\) 1.75357 9.40600i 0.148204 0.794952i
\(141\) 21.8733 1.84206
\(142\) 7.26064i 0.609300i
\(143\) 2.03040i 0.169790i
\(144\) 39.1601 3.26335
\(145\) 15.5716 + 2.90303i 1.29315 + 0.241084i
\(146\) −0.333925 −0.0276358
\(147\) 7.66168i 0.631924i
\(148\) 9.18826i 0.755270i
\(149\) 6.30197 0.516278 0.258139 0.966108i \(-0.416891\pi\)
0.258139 + 0.966108i \(0.416891\pi\)
\(150\) 28.6598 + 11.0710i 2.34006 + 0.903939i
\(151\) 3.24012 0.263677 0.131838 0.991271i \(-0.457912\pi\)
0.131838 + 0.991271i \(0.457912\pi\)
\(152\) 1.10110i 0.0893113i
\(153\) 55.4099i 4.47963i
\(154\) −5.62579 −0.453339
\(155\) −12.3502 2.30245i −0.991988 0.184938i
\(156\) 9.48944 0.759763
\(157\) 1.72729i 0.137853i −0.997622 0.0689263i \(-0.978043\pi\)
0.997622 0.0689263i \(-0.0219573\pi\)
\(158\) 27.3277i 2.17408i
\(159\) 37.7979 2.99757
\(160\) −2.75467 + 14.7758i −0.217776 + 1.16813i
\(161\) −15.2828 −1.20446
\(162\) 59.4853i 4.67361i
\(163\) 9.06614i 0.710115i −0.934845 0.355057i \(-0.884461\pi\)
0.934845 0.355057i \(-0.115539\pi\)
\(164\) 12.1159 0.946093
\(165\) 1.36506 7.32204i 0.106270 0.570020i
\(166\) 6.82743 0.529912
\(167\) 9.85267i 0.762423i −0.924488 0.381211i \(-0.875507\pi\)
0.924488 0.381211i \(-0.124493\pi\)
\(168\) 11.1851i 0.862948i
\(169\) 8.87749 0.682884
\(170\) 27.7567 + 5.17472i 2.12884 + 0.396883i
\(171\) −8.09513 −0.619050
\(172\) 3.93413i 0.299975i
\(173\) 13.6308i 1.03633i −0.855281 0.518165i \(-0.826615\pi\)
0.855281 0.518165i \(-0.173385\pi\)
\(174\) −43.5283 −3.29988
\(175\) 5.49447 14.2237i 0.415343 1.07521i
\(176\) 4.83750 0.364640
\(177\) 19.4794i 1.46416i
\(178\) 19.0495i 1.42782i
\(179\) 1.25492 0.0937970 0.0468985 0.998900i \(-0.485066\pi\)
0.0468985 + 0.998900i \(0.485066\pi\)
\(180\) −24.9680 4.65481i −1.86100 0.346949i
\(181\) −20.8319 −1.54842 −0.774210 0.632929i \(-0.781852\pi\)
−0.774210 + 0.632929i \(0.781852\pi\)
\(182\) 11.4226i 0.846698i
\(183\) 31.9650i 2.36292i
\(184\) 5.51806 0.406797
\(185\) 2.68364 14.3948i 0.197305 1.05833i
\(186\) 34.5232 2.53136
\(187\) 6.84485i 0.500545i
\(188\) 9.21386i 0.671990i
\(189\) 51.7567 3.76474
\(190\) 0.756002 4.05513i 0.0548461 0.294190i
\(191\) 20.6801 1.49636 0.748181 0.663494i \(-0.230927\pi\)
0.748181 + 0.663494i \(0.230927\pi\)
\(192\) 9.07694i 0.655072i
\(193\) 16.6325i 1.19723i 0.801037 + 0.598615i \(0.204282\pi\)
−0.801037 + 0.598615i \(0.795718\pi\)
\(194\) 9.45719 0.678987
\(195\) 14.8666 + 2.77161i 1.06462 + 0.198479i
\(196\) 3.22739 0.230528
\(197\) 18.4260i 1.31280i −0.754414 0.656399i \(-0.772079\pi\)
0.754414 0.656399i \(-0.227921\pi\)
\(198\) 14.9335i 1.06128i
\(199\) −16.4923 −1.16911 −0.584555 0.811354i \(-0.698731\pi\)
−0.584555 + 0.811354i \(0.698731\pi\)
\(200\) −1.98385 + 5.13566i −0.140279 + 0.363146i
\(201\) −31.9762 −2.25542
\(202\) 21.4152i 1.50677i
\(203\) 21.6029i 1.51623i
\(204\) −31.9907 −2.23980
\(205\) 18.9814 + 3.53872i 1.32572 + 0.247155i
\(206\) 1.96315 0.136779
\(207\) 40.5679i 2.81966i
\(208\) 9.82203i 0.681035i
\(209\) −1.00000 −0.0691714
\(210\) −7.67952 + 41.1923i −0.529937 + 2.84254i
\(211\) −6.01612 −0.414167 −0.207083 0.978323i \(-0.566397\pi\)
−0.207083 + 0.978323i \(0.566397\pi\)
\(212\) 15.9219i 1.09352i
\(213\) 13.1100i 0.898283i
\(214\) 16.0945 1.10019
\(215\) −1.14905 + 6.16341i −0.0783647 + 0.420341i
\(216\) −18.6874 −1.27152
\(217\) 17.1337i 1.16311i
\(218\) 0.568080i 0.0384752i
\(219\) 0.602944 0.0407432
\(220\) −3.08432 0.575014i −0.207945 0.0387674i
\(221\) 13.8978 0.934865
\(222\) 40.2387i 2.70065i
\(223\) 20.7672i 1.39068i 0.718683 + 0.695338i \(0.244745\pi\)
−0.718683 + 0.695338i \(0.755255\pi\)
\(224\) −20.4989 −1.36964
\(225\) −37.7565 14.5849i −2.51710 0.972328i
\(226\) 12.4404 0.827525
\(227\) 8.74910i 0.580698i 0.956921 + 0.290349i \(0.0937714\pi\)
−0.956921 + 0.290349i \(0.906229\pi\)
\(228\) 4.67369i 0.309523i
\(229\) −19.4394 −1.28459 −0.642297 0.766456i \(-0.722018\pi\)
−0.642297 + 0.766456i \(0.722018\pi\)
\(230\) −20.3218 3.78862i −1.33998 0.249814i
\(231\) 10.1581 0.668352
\(232\) 7.80002i 0.512096i
\(233\) 3.01048i 0.197223i 0.995126 + 0.0986114i \(0.0314401\pi\)
−0.995126 + 0.0986114i \(0.968560\pi\)
\(234\) −30.3209 −1.98214
\(235\) 2.69112 14.4349i 0.175549 0.941629i
\(236\) −8.20547 −0.534130
\(237\) 49.3437i 3.20522i
\(238\) 38.5077i 2.49608i
\(239\) −9.72562 −0.629098 −0.314549 0.949241i \(-0.601853\pi\)
−0.314549 + 0.949241i \(0.601853\pi\)
\(240\) 6.60346 35.4203i 0.426251 2.28637i
\(241\) 6.21619 0.400420 0.200210 0.979753i \(-0.435838\pi\)
0.200210 + 0.979753i \(0.435838\pi\)
\(242\) 1.84475i 0.118585i
\(243\) 56.4937i 3.62407i
\(244\) 13.4649 0.861999
\(245\) 5.05619 + 0.942632i 0.323028 + 0.0602226i
\(246\) −53.0599 −3.38298
\(247\) 2.03040i 0.129191i
\(248\) 6.18635i 0.392834i
\(249\) −12.3278 −0.781242
\(250\) 10.8322 17.5515i 0.685086 1.11005i
\(251\) −2.92900 −0.184877 −0.0924385 0.995718i \(-0.529466\pi\)
−0.0924385 + 0.995718i \(0.529466\pi\)
\(252\) 34.6388i 2.18204i
\(253\) 5.01139i 0.315064i
\(254\) 10.5361 0.661093
\(255\) −50.1183 9.34361i −3.13853 0.585120i
\(256\) 20.9765 1.31103
\(257\) 13.7445i 0.857361i 0.903456 + 0.428681i \(0.141021\pi\)
−0.903456 + 0.428681i \(0.858979\pi\)
\(258\) 17.2290i 1.07263i
\(259\) 19.9703 1.24089
\(260\) 1.16751 6.26239i 0.0724056 0.388377i
\(261\) 57.3444 3.54953
\(262\) 24.3415i 1.50382i
\(263\) 10.7626i 0.663653i −0.943340 0.331826i \(-0.892335\pi\)
0.943340 0.331826i \(-0.107665\pi\)
\(264\) −3.66770 −0.225732
\(265\) 4.65035 24.9441i 0.285669 1.53230i
\(266\) 5.62579 0.344939
\(267\) 34.3962i 2.10501i
\(268\) 13.4696i 0.822785i
\(269\) 19.0096 1.15903 0.579517 0.814960i \(-0.303241\pi\)
0.579517 + 0.814960i \(0.303241\pi\)
\(270\) 68.8217 + 12.8305i 4.18835 + 0.780840i
\(271\) −16.9828 −1.03163 −0.515816 0.856699i \(-0.672511\pi\)
−0.515816 + 0.856699i \(0.672511\pi\)
\(272\) 33.1120i 2.00771i
\(273\) 20.6249i 1.24828i
\(274\) −9.69149 −0.585485
\(275\) −4.66411 1.80169i −0.281256 0.108646i
\(276\) 23.4217 1.40982
\(277\) 13.0510i 0.784158i −0.919932 0.392079i \(-0.871756\pi\)
0.919932 0.392079i \(-0.128244\pi\)
\(278\) 18.9730i 1.13793i
\(279\) −45.4810 −2.72288
\(280\) −7.38141 1.37612i −0.441123 0.0822392i
\(281\) −4.68913 −0.279730 −0.139865 0.990171i \(-0.544667\pi\)
−0.139865 + 0.990171i \(0.544667\pi\)
\(282\) 40.3508i 2.40286i
\(283\) 31.8679i 1.89435i 0.320715 + 0.947176i \(0.396077\pi\)
−0.320715 + 0.947176i \(0.603923\pi\)
\(284\) 5.52243 0.327696
\(285\) −1.36506 + 7.32204i −0.0808590 + 0.433720i
\(286\) −3.74558 −0.221481
\(287\) 26.3334i 1.55441i
\(288\) 54.4137i 3.20636i
\(289\) −29.8520 −1.75600
\(290\) −5.35538 + 28.7258i −0.314479 + 1.68684i
\(291\) −17.0761 −1.00102
\(292\) 0.253983i 0.0148632i
\(293\) 4.17199i 0.243730i 0.992547 + 0.121865i \(0.0388875\pi\)
−0.992547 + 0.121865i \(0.961112\pi\)
\(294\) −14.1339 −0.824306
\(295\) −12.8551 2.39659i −0.748453 0.139535i
\(296\) −7.21054 −0.419104
\(297\) 16.9715i 0.984788i
\(298\) 11.6256i 0.673452i
\(299\) −10.1751 −0.588442
\(300\) −8.42055 + 21.7986i −0.486160 + 1.25854i
\(301\) −8.55068 −0.492853
\(302\) 5.97722i 0.343950i
\(303\) 38.6679i 2.22141i
\(304\) −4.83750 −0.277449
\(305\) 21.0947 + 3.93272i 1.20788 + 0.225187i
\(306\) 102.218 5.84340
\(307\) 16.6706i 0.951441i −0.879596 0.475721i \(-0.842187\pi\)
0.879596 0.475721i \(-0.157813\pi\)
\(308\) 4.27897i 0.243817i
\(309\) −3.54472 −0.201652
\(310\) 4.24746 22.7830i 0.241240 1.29399i
\(311\) 14.0897 0.798955 0.399478 0.916743i \(-0.369192\pi\)
0.399478 + 0.916743i \(0.369192\pi\)
\(312\) 7.44689i 0.421597i
\(313\) 11.3840i 0.643462i 0.946831 + 0.321731i \(0.104265\pi\)
−0.946831 + 0.321731i \(0.895735\pi\)
\(314\) 3.18642 0.179820
\(315\) 10.1170 54.2669i 0.570030 3.05759i
\(316\) 20.7854 1.16927
\(317\) 21.4233i 1.20325i 0.798777 + 0.601627i \(0.205481\pi\)
−0.798777 + 0.601627i \(0.794519\pi\)
\(318\) 69.7278i 3.91014i
\(319\) 7.08382 0.396618
\(320\) −5.99017 1.11676i −0.334861 0.0624285i
\(321\) −29.0606 −1.62200
\(322\) 28.1931i 1.57114i
\(323\) 6.84485i 0.380858i
\(324\) −45.2445 −2.51358
\(325\) 3.65815 9.46999i 0.202917 0.525300i
\(326\) 16.7248 0.926300
\(327\) 1.02574i 0.0567236i
\(328\) 9.50802i 0.524993i
\(329\) 20.0259 1.10407
\(330\) 13.5074 + 2.51819i 0.743556 + 0.138622i
\(331\) −24.0940 −1.32433 −0.662164 0.749359i \(-0.730362\pi\)
−0.662164 + 0.749359i \(0.730362\pi\)
\(332\) 5.19293i 0.284999i
\(333\) 53.0107i 2.90497i
\(334\) 18.1758 0.994533
\(335\) −3.93409 + 21.1021i −0.214942 + 1.15293i
\(336\) 49.1396 2.68079
\(337\) 3.10795i 0.169301i −0.996411 0.0846505i \(-0.973023\pi\)
0.996411 0.0846505i \(-0.0269774\pi\)
\(338\) 16.3768i 0.890780i
\(339\) −22.4628 −1.22001
\(340\) −3.93588 + 21.1117i −0.213453 + 1.14494i
\(341\) −5.61832 −0.304249
\(342\) 14.9335i 0.807512i
\(343\) 14.3327i 0.773894i
\(344\) 3.08733 0.166458
\(345\) 36.6936 + 6.84084i 1.97552 + 0.368298i
\(346\) 25.1455 1.35183
\(347\) 24.4357i 1.31178i −0.754858 0.655889i \(-0.772294\pi\)
0.754858 0.655889i \(-0.227706\pi\)
\(348\) 33.1076i 1.77475i
\(349\) 17.6089 0.942582 0.471291 0.881978i \(-0.343788\pi\)
0.471291 + 0.881978i \(0.343788\pi\)
\(350\) 26.2393 + 10.1359i 1.40255 + 0.541789i
\(351\) 34.4589 1.83928
\(352\) 6.72178i 0.358272i
\(353\) 1.98528i 0.105666i −0.998603 0.0528329i \(-0.983175\pi\)
0.998603 0.0528329i \(-0.0168251\pi\)
\(354\) 35.9347 1.90991
\(355\) 8.65172 + 1.61295i 0.459186 + 0.0856066i
\(356\) 14.4890 0.767915
\(357\) 69.5305i 3.67994i
\(358\) 2.31501i 0.122352i
\(359\) −20.2134 −1.06682 −0.533410 0.845857i \(-0.679090\pi\)
−0.533410 + 0.845857i \(0.679090\pi\)
\(360\) −3.65289 + 19.5937i −0.192524 + 1.03268i
\(361\) 1.00000 0.0526316
\(362\) 38.4296i 2.01982i
\(363\) 3.33093i 0.174829i
\(364\) 8.68800 0.455375
\(365\) 0.0741814 0.397902i 0.00388283 0.0208272i
\(366\) −58.9675 −3.08228
\(367\) 11.7258i 0.612081i 0.952018 + 0.306041i \(0.0990044\pi\)
−0.952018 + 0.306041i \(0.900996\pi\)
\(368\) 24.2426i 1.26373i
\(369\) 69.9014 3.63892
\(370\) 26.5548 + 4.95065i 1.38052 + 0.257372i
\(371\) 34.6056 1.79663
\(372\) 26.2583i 1.36143i
\(373\) 5.98352i 0.309815i −0.987929 0.154908i \(-0.950492\pi\)
0.987929 0.154908i \(-0.0495080\pi\)
\(374\) 12.6271 0.652930
\(375\) −19.5588 + 31.6914i −1.01001 + 1.63654i
\(376\) −7.23063 −0.372891
\(377\) 14.3830i 0.740760i
\(378\) 95.4783i 4.91087i
\(379\) 24.5366 1.26036 0.630181 0.776448i \(-0.282981\pi\)
0.630181 + 0.776448i \(0.282981\pi\)
\(380\) 3.08432 + 0.575014i 0.158222 + 0.0294976i
\(381\) −19.0242 −0.974641
\(382\) 38.1498i 1.95191i
\(383\) 31.5965i 1.61450i −0.590207 0.807252i \(-0.700954\pi\)
0.590207 0.807252i \(-0.299046\pi\)
\(384\) −28.0349 −1.43065
\(385\) 1.24977 6.70365i 0.0636941 0.341649i
\(386\) −30.6828 −1.56171
\(387\) 22.6975i 1.15378i
\(388\) 7.19312i 0.365175i
\(389\) −3.90790 −0.198139 −0.0990693 0.995081i \(-0.531587\pi\)
−0.0990693 + 0.995081i \(0.531587\pi\)
\(390\) −5.11293 + 27.4253i −0.258903 + 1.38873i
\(391\) 34.3023 1.73474
\(392\) 2.53271i 0.127921i
\(393\) 43.9516i 2.21706i
\(394\) 33.9914 1.71246
\(395\) 32.5635 + 6.07085i 1.63845 + 0.305458i
\(396\) −11.3584 −0.570781
\(397\) 29.3623i 1.47365i −0.676082 0.736826i \(-0.736324\pi\)
0.676082 0.736826i \(-0.263676\pi\)
\(398\) 30.4243i 1.52503i
\(399\) −10.1581 −0.508540
\(400\) −22.5626 8.71568i −1.12813 0.435784i
\(401\) −14.6124 −0.729711 −0.364855 0.931064i \(-0.618882\pi\)
−0.364855 + 0.931064i \(0.618882\pi\)
\(402\) 58.9881i 2.94206i
\(403\) 11.4074i 0.568244i
\(404\) 16.2884 0.810378
\(405\) −70.8823 13.2147i −3.52217 0.656642i
\(406\) −39.8521 −1.97783
\(407\) 6.54847i 0.324595i
\(408\) 25.1049i 1.24288i
\(409\) 2.46414 0.121844 0.0609219 0.998143i \(-0.480596\pi\)
0.0609219 + 0.998143i \(0.480596\pi\)
\(410\) −6.52807 + 35.0160i −0.322399 + 1.72932i
\(411\) 17.4992 0.863172
\(412\) 1.49317i 0.0735632i
\(413\) 17.8342i 0.877566i
\(414\) −74.8377 −3.67807
\(415\) −1.51671 + 8.13551i −0.0744525 + 0.399357i
\(416\) −13.6479 −0.669143
\(417\) 34.2582i 1.67763i
\(418\) 1.84475i 0.0902299i
\(419\) −14.9423 −0.729980 −0.364990 0.931011i \(-0.618928\pi\)
−0.364990 + 0.931011i \(0.618928\pi\)
\(420\) −31.3308 5.84103i −1.52878 0.285013i
\(421\) −4.00737 −0.195307 −0.0976536 0.995220i \(-0.531134\pi\)
−0.0976536 + 0.995220i \(0.531134\pi\)
\(422\) 11.0983i 0.540255i
\(423\) 53.1584i 2.58465i
\(424\) −12.4948 −0.606801
\(425\) −12.3323 + 31.9251i −0.598205 + 1.54860i
\(426\) −24.1847 −1.17175
\(427\) 29.2653i 1.41625i
\(428\) 12.2414i 0.591711i
\(429\) 6.76312 0.326526
\(430\) −11.3700 2.11972i −0.548309 0.102222i
\(431\) 14.0623 0.677358 0.338679 0.940902i \(-0.390020\pi\)
0.338679 + 0.940902i \(0.390020\pi\)
\(432\) 82.0997i 3.95003i
\(433\) 17.6798i 0.849636i 0.905279 + 0.424818i \(0.139662\pi\)
−0.905279 + 0.424818i \(0.860338\pi\)
\(434\) 31.6075 1.51721
\(435\) 9.66982 51.8680i 0.463632 2.48688i
\(436\) 0.432081 0.0206929
\(437\) 5.01139i 0.239727i
\(438\) 1.11228i 0.0531469i
\(439\) −21.4590 −1.02418 −0.512090 0.858932i \(-0.671129\pi\)
−0.512090 + 0.858932i \(0.671129\pi\)
\(440\) −0.451245 + 2.42044i −0.0215123 + 0.115390i
\(441\) 18.6201 0.886670
\(442\) 25.6379i 1.21947i
\(443\) 0.0673464i 0.00319972i 0.999999 + 0.00159986i \(0.000509252\pi\)
−0.999999 + 0.00159986i \(0.999491\pi\)
\(444\) −30.6055 −1.45247
\(445\) 22.6992 + 4.23184i 1.07604 + 0.200608i
\(446\) −38.3104 −1.81405
\(447\) 20.9915i 0.992862i
\(448\) 8.31034i 0.392626i
\(449\) 33.4714 1.57961 0.789806 0.613357i \(-0.210181\pi\)
0.789806 + 0.613357i \(0.210181\pi\)
\(450\) 26.9056 69.6515i 1.26834 3.28340i
\(451\) 8.63500 0.406606
\(452\) 9.46217i 0.445063i
\(453\) 10.7926i 0.507081i
\(454\) −16.1399 −0.757484
\(455\) 13.6111 + 2.53753i 0.638096 + 0.118961i
\(456\) 3.66770 0.171756
\(457\) 19.1342i 0.895059i 0.894269 + 0.447529i \(0.147696\pi\)
−0.894269 + 0.447529i \(0.852304\pi\)
\(458\) 35.8610i 1.67567i
\(459\) −116.168 −5.42224
\(460\) 2.88162 15.4567i 0.134356 0.720675i
\(461\) −32.2664 −1.50280 −0.751398 0.659849i \(-0.770620\pi\)
−0.751398 + 0.659849i \(0.770620\pi\)
\(462\) 18.7391i 0.871824i
\(463\) 15.8834i 0.738163i 0.929397 + 0.369082i \(0.120328\pi\)
−0.929397 + 0.369082i \(0.879672\pi\)
\(464\) 34.2680 1.59085
\(465\) −7.66932 + 41.1375i −0.355656 + 1.90771i
\(466\) −5.55359 −0.257265
\(467\) 20.0295i 0.926853i −0.886135 0.463427i \(-0.846620\pi\)
0.886135 0.463427i \(-0.153380\pi\)
\(468\) 23.0621i 1.06604i
\(469\) −29.2756 −1.35182
\(470\) 26.6288 + 4.96445i 1.22830 + 0.228993i
\(471\) −5.75348 −0.265106
\(472\) 6.43928i 0.296392i
\(473\) 2.80385i 0.128921i
\(474\) −91.0269 −4.18100
\(475\) 4.66411 + 1.80169i 0.214004 + 0.0826673i
\(476\) −29.2889 −1.34245
\(477\) 91.8597i 4.20597i
\(478\) 17.9414i 0.820619i
\(479\) −7.84252 −0.358334 −0.179167 0.983819i \(-0.557340\pi\)
−0.179167 + 0.983819i \(0.557340\pi\)
\(480\) 49.2172 + 9.17562i 2.24645 + 0.418808i
\(481\) 13.2960 0.606244
\(482\) 11.4673i 0.522323i
\(483\) 50.9061i 2.31631i
\(484\) −1.40312 −0.0637780
\(485\) −2.10091 + 11.2691i −0.0953976 + 0.511704i
\(486\) 104.217 4.72738
\(487\) 11.8634i 0.537584i −0.963198 0.268792i \(-0.913376\pi\)
0.963198 0.268792i \(-0.0866244\pi\)
\(488\) 10.5666i 0.478329i
\(489\) −30.1987 −1.36563
\(490\) −1.73892 + 9.32743i −0.0785566 + 0.421370i
\(491\) −0.188713 −0.00851649 −0.00425825 0.999991i \(-0.501355\pi\)
−0.00425825 + 0.999991i \(0.501355\pi\)
\(492\) 40.3573i 1.81945i
\(493\) 48.4877i 2.18378i
\(494\) 3.74558 0.168522
\(495\) −17.7947 3.31748i −0.799810 0.149110i
\(496\) −27.1786 −1.22036
\(497\) 12.0028i 0.538398i
\(498\) 22.7417i 1.01908i
\(499\) −38.9424 −1.74330 −0.871650 0.490130i \(-0.836949\pi\)
−0.871650 + 0.490130i \(0.836949\pi\)
\(500\) 13.3496 + 8.23892i 0.597013 + 0.368456i
\(501\) −32.8186 −1.46623
\(502\) 5.40329i 0.241161i
\(503\) 2.24218i 0.0999739i 0.998750 + 0.0499869i \(0.0159180\pi\)
−0.998750 + 0.0499869i \(0.984082\pi\)
\(504\) −27.1830 −1.21083
\(505\) 25.5182 + 4.75739i 1.13555 + 0.211701i
\(506\) −9.24479 −0.410981
\(507\) 29.5703i 1.31327i
\(508\) 8.01373i 0.355552i
\(509\) 17.6190 0.780948 0.390474 0.920614i \(-0.372311\pi\)
0.390474 + 0.920614i \(0.372311\pi\)
\(510\) 17.2367 92.4559i 0.763252 4.09402i
\(511\) 0.552021 0.0244200
\(512\) 21.8634i 0.966237i
\(513\) 16.9715i 0.749311i
\(514\) −25.3553 −1.11837
\(515\) −0.436114 + 2.33928i −0.0192175 + 0.103081i
\(516\) 13.1043 0.576886
\(517\) 6.56671i 0.288804i
\(518\) 36.8403i 1.61867i
\(519\) −45.4033 −1.99298
\(520\) −4.91445 0.916206i −0.215513 0.0401783i
\(521\) 27.3830 1.19967 0.599836 0.800123i \(-0.295233\pi\)
0.599836 + 0.800123i \(0.295233\pi\)
\(522\) 105.786i 4.63014i
\(523\) 29.1248i 1.27354i −0.771054 0.636770i \(-0.780270\pi\)
0.771054 0.636770i \(-0.219730\pi\)
\(524\) 18.5141 0.808791
\(525\) −47.3783 18.3017i −2.06776 0.798752i
\(526\) 19.8544 0.865694
\(527\) 38.4566i 1.67519i
\(528\) 16.1134i 0.701245i
\(529\) −2.11407 −0.0919159
\(530\) 46.0157 + 8.57876i 1.99879 + 0.372637i
\(531\) −47.3405 −2.05440
\(532\) 4.27897i 0.185517i
\(533\) 17.5325i 0.759415i
\(534\) −63.4525 −2.74586
\(535\) −3.57538 + 19.1780i −0.154577 + 0.829139i
\(536\) 10.5703 0.456568
\(537\) 4.18005i 0.180382i
\(538\) 35.0680i 1.51189i
\(539\) 2.30016 0.0990748
\(540\) −9.75886 + 52.3457i −0.419955 + 2.25260i
\(541\) −24.2865 −1.04416 −0.522079 0.852897i \(-0.674843\pi\)
−0.522079 + 0.852897i \(0.674843\pi\)
\(542\) 31.3291i 1.34570i
\(543\) 69.3896i 2.97779i
\(544\) 46.0096 1.97265
\(545\) 0.676920 + 0.126199i 0.0289960 + 0.00540577i
\(546\) −38.0479 −1.62830
\(547\) 0.567397i 0.0242601i 0.999926 + 0.0121301i \(0.00386122\pi\)
−0.999926 + 0.0121301i \(0.996139\pi\)
\(548\) 7.37133i 0.314888i
\(549\) 77.6840 3.31547
\(550\) 3.32368 8.60413i 0.141722 0.366881i
\(551\) −7.08382 −0.301781
\(552\) 18.3803i 0.782318i
\(553\) 45.1763i 1.92109i
\(554\) 24.0759 1.02289
\(555\) −47.9481 8.93903i −2.03528 0.379440i
\(556\) −14.4308 −0.612004
\(557\) 26.4054i 1.11883i −0.828887 0.559415i \(-0.811026\pi\)
0.828887 0.559415i \(-0.188974\pi\)
\(558\) 83.9012i 3.55182i
\(559\) −5.69293 −0.240785
\(560\) 6.04575 32.4289i 0.255480 1.37037i
\(561\) −22.7998 −0.962607
\(562\) 8.65029i 0.364891i
\(563\) 30.1196i 1.26939i 0.772762 + 0.634695i \(0.218874\pi\)
−0.772762 + 0.634695i \(0.781126\pi\)
\(564\) −30.6908 −1.29231
\(565\) −2.76364 + 14.8239i −0.116267 + 0.623647i
\(566\) −58.7885 −2.47106
\(567\) 98.3370i 4.12976i
\(568\) 4.33376i 0.181840i
\(569\) 28.0302 1.17509 0.587543 0.809193i \(-0.300095\pi\)
0.587543 + 0.809193i \(0.300095\pi\)
\(570\) −13.5074 2.51819i −0.565761 0.105476i
\(571\) 15.1718 0.634918 0.317459 0.948272i \(-0.397170\pi\)
0.317459 + 0.948272i \(0.397170\pi\)
\(572\) 2.84888i 0.119118i
\(573\) 68.8842i 2.87768i
\(574\) −48.5787 −2.02764
\(575\) 9.02899 23.3737i 0.376535 0.974750i
\(576\) −22.0596 −0.919149
\(577\) 29.2142i 1.21620i 0.793859 + 0.608102i \(0.208069\pi\)
−0.793859 + 0.608102i \(0.791931\pi\)
\(578\) 55.0696i 2.29059i
\(579\) 55.4016 2.30241
\(580\) −21.8488 4.07330i −0.907221 0.169134i
\(581\) −11.2866 −0.468248
\(582\) 31.5013i 1.30577i
\(583\) 11.3475i 0.469967i
\(584\) −0.199314 −0.00824769
\(585\) 6.73579 36.1302i 0.278491 1.49380i
\(586\) −7.69629 −0.317931
\(587\) 3.60875i 0.148949i 0.997223 + 0.0744746i \(0.0237280\pi\)
−0.997223 + 0.0744746i \(0.976272\pi\)
\(588\) 10.7502i 0.443332i
\(589\) 5.61832 0.231499
\(590\) 4.42112 23.7145i 0.182015 0.976310i
\(591\) −61.3757 −2.52466
\(592\) 31.6782i 1.30197i
\(593\) 32.6741i 1.34177i 0.741564 + 0.670883i \(0.234085\pi\)
−0.741564 + 0.670883i \(0.765915\pi\)
\(594\) 31.3083 1.28459
\(595\) −45.8855 8.55448i −1.88112 0.350700i
\(596\) −8.84240 −0.362199
\(597\) 54.9349i 2.24833i
\(598\) 18.7706i 0.767586i
\(599\) −10.1407 −0.414336 −0.207168 0.978305i \(-0.566425\pi\)
−0.207168 + 0.978305i \(0.566425\pi\)
\(600\) 17.1066 + 6.60807i 0.698373 + 0.269773i
\(601\) 41.2285 1.68174 0.840872 0.541234i \(-0.182043\pi\)
0.840872 + 0.541234i \(0.182043\pi\)
\(602\) 15.7739i 0.642896i
\(603\) 77.7112i 3.16465i
\(604\) −4.54626 −0.184985
\(605\) −2.19819 0.409812i −0.0893693 0.0166612i
\(606\) −71.3328 −2.89770
\(607\) 2.27253i 0.0922392i −0.998936 0.0461196i \(-0.985314\pi\)
0.998936 0.0461196i \(-0.0146855\pi\)
\(608\) 6.72178i 0.272604i
\(609\) 71.9580 2.91588
\(610\) −7.25489 + 38.9146i −0.293742 + 1.57561i
\(611\) 13.3330 0.539396
\(612\) 77.7466i 3.14272i
\(613\) 19.8710i 0.802584i −0.915950 0.401292i \(-0.868561\pi\)
0.915950 0.401292i \(-0.131439\pi\)
\(614\) 30.7532 1.24110
\(615\) 11.7873 63.2258i 0.475308 2.54951i
\(616\) −3.35794 −0.135295
\(617\) 1.86490i 0.0750781i −0.999295 0.0375390i \(-0.988048\pi\)
0.999295 0.0375390i \(-0.0119519\pi\)
\(618\) 6.53913i 0.263042i
\(619\) −7.82377 −0.314464 −0.157232 0.987562i \(-0.550257\pi\)
−0.157232 + 0.987562i \(0.550257\pi\)
\(620\) 17.3287 + 3.23061i 0.695937 + 0.129744i
\(621\) 85.0510 3.41298
\(622\) 25.9921i 1.04219i
\(623\) 31.4912i 1.26167i
\(624\) 32.7166 1.30971
\(625\) 18.5078 + 16.8066i 0.740313 + 0.672263i
\(626\) −21.0007 −0.839356
\(627\) 3.33093i 0.133025i
\(628\) 2.42358i 0.0967116i
\(629\) −44.8233 −1.78722
\(630\) 100.109 + 18.6634i 3.98844 + 0.743569i
\(631\) −38.8465 −1.54645 −0.773227 0.634130i \(-0.781358\pi\)
−0.773227 + 0.634130i \(0.781358\pi\)
\(632\) 16.3115i 0.648836i
\(633\) 20.0393i 0.796491i
\(634\) −39.5208 −1.56957
\(635\) −2.34059 + 12.5547i −0.0928835 + 0.498219i
\(636\) −53.0348 −2.10297
\(637\) 4.67023i 0.185041i
\(638\) 13.0679i 0.517363i
\(639\) 31.8611 1.26040
\(640\) −3.44920 + 18.5012i −0.136341 + 0.731323i
\(641\) 19.4192 0.767013 0.383507 0.923538i \(-0.374716\pi\)
0.383507 + 0.923538i \(0.374716\pi\)
\(642\) 53.6096i 2.11580i
\(643\) 42.2251i 1.66520i −0.553877 0.832598i \(-0.686852\pi\)
0.553877 0.832598i \(-0.313148\pi\)
\(644\) 21.4436 0.844996
\(645\) 20.5299 + 3.82742i 0.808365 + 0.150704i
\(646\) −12.6271 −0.496805
\(647\) 1.82103i 0.0715920i −0.999359 0.0357960i \(-0.988603\pi\)
0.999359 0.0357960i \(-0.0113967\pi\)
\(648\) 35.5058i 1.39480i
\(649\) −5.84803 −0.229555
\(650\) 17.4698 + 6.74838i 0.685222 + 0.264693i
\(651\) −57.0713 −2.23680
\(652\) 12.7208i 0.498187i
\(653\) 23.1753i 0.906920i −0.891277 0.453460i \(-0.850190\pi\)
0.891277 0.453460i \(-0.149810\pi\)
\(654\) −1.89224 −0.0739924
\(655\) 29.0051 + 5.40745i 1.13332 + 0.211287i
\(656\) 41.7718 1.63091
\(657\) 1.46533i 0.0571678i
\(658\) 36.9429i 1.44019i
\(659\) −19.7606 −0.769762 −0.384881 0.922966i \(-0.625758\pi\)
−0.384881 + 0.922966i \(0.625758\pi\)
\(660\) −1.91533 + 10.2737i −0.0745542 + 0.399902i
\(661\) 48.4365 1.88396 0.941980 0.335669i \(-0.108962\pi\)
0.941980 + 0.335669i \(0.108962\pi\)
\(662\) 44.4475i 1.72750i
\(663\) 46.2925i 1.79785i
\(664\) 4.07518 0.158148
\(665\) −1.24977 + 6.70365i −0.0484640 + 0.259956i
\(666\) 97.7916 3.78935
\(667\) 35.4998i 1.37456i
\(668\) 13.8244i 0.534884i
\(669\) 69.1743 2.67443
\(670\) −38.9282 7.25743i −1.50393 0.280379i
\(671\) 9.59640 0.370465
\(672\) 68.2804i 2.63397i
\(673\) 29.8527i 1.15074i 0.817895 + 0.575368i \(0.195141\pi\)
−0.817895 + 0.575368i \(0.804859\pi\)
\(674\) 5.73341 0.220843
\(675\) −30.5775 + 79.1571i −1.17693 + 3.04676i
\(676\) −12.4562 −0.479083
\(677\) 20.9974i 0.806997i 0.914980 + 0.403498i \(0.132206\pi\)
−0.914980 + 0.403498i \(0.867794\pi\)
\(678\) 41.4383i 1.59143i
\(679\) −15.6340 −0.599976
\(680\) 16.5675 + 3.08871i 0.635336 + 0.118446i
\(681\) 29.1427 1.11675
\(682\) 10.3644i 0.396874i
\(683\) 10.2432i 0.391944i −0.980609 0.195972i \(-0.937214\pi\)
0.980609 0.195972i \(-0.0627863\pi\)
\(684\) 11.3584 0.434299
\(685\) 2.15296 11.5483i 0.0822605 0.441238i
\(686\) 26.4403 1.00950
\(687\) 64.7515i 2.47042i
\(688\) 13.5636i 0.517109i
\(689\) 23.0400 0.877753
\(690\) −12.6197 + 67.6907i −0.480422 + 2.57694i
\(691\) −11.0857 −0.421720 −0.210860 0.977516i \(-0.567626\pi\)
−0.210860 + 0.977516i \(0.567626\pi\)
\(692\) 19.1256i 0.727046i
\(693\) 24.6870i 0.937783i
\(694\) 45.0779 1.71113
\(695\) −22.6081 4.21485i −0.857574 0.159879i
\(696\) −25.9814 −0.984821
\(697\) 59.1053i 2.23877i
\(698\) 32.4841i 1.22954i
\(699\) 10.0277 0.379282
\(700\) −7.70938 + 19.9576i −0.291387 + 0.754325i
\(701\) −8.41247 −0.317735 −0.158867 0.987300i \(-0.550784\pi\)
−0.158867 + 0.987300i \(0.550784\pi\)
\(702\) 63.5682i 2.39923i
\(703\) 6.54847i 0.246980i
\(704\) −2.72504 −0.102704
\(705\) −48.0817 8.96393i −1.81086 0.337601i
\(706\) 3.66235 0.137834
\(707\) 35.4022i 1.33144i
\(708\) 27.3319i 1.02719i
\(709\) 26.1580 0.982383 0.491191 0.871052i \(-0.336562\pi\)
0.491191 + 0.871052i \(0.336562\pi\)
\(710\) −2.97550 + 15.9603i −0.111668 + 0.598979i
\(711\) 119.919 4.49732
\(712\) 11.3703i 0.426120i
\(713\) 28.1556i 1.05444i
\(714\) 128.267 4.80026
\(715\) 0.832080 4.46320i 0.0311180 0.166914i
\(716\) −1.76080 −0.0658040
\(717\) 32.3954i 1.20983i
\(718\) 37.2887i 1.39160i
\(719\) 2.98827 0.111444 0.0557218 0.998446i \(-0.482254\pi\)
0.0557218 + 0.998446i \(0.482254\pi\)
\(720\) −86.0816 16.0483i −3.20807 0.598085i
\(721\) −3.24534 −0.120863
\(722\) 1.84475i 0.0686546i
\(723\) 20.7057i 0.770054i
\(724\) 29.2295 1.08631
\(725\) −33.0397 12.7629i −1.22706 0.474001i
\(726\) 6.14475 0.228053
\(727\) 28.0389i 1.03990i −0.854196 0.519952i \(-0.825950\pi\)
0.854196 0.519952i \(-0.174050\pi\)
\(728\) 6.81795i 0.252690i
\(729\) −91.4397 −3.38666
\(730\) 0.734032 + 0.136847i 0.0271677 + 0.00506492i
\(731\) 19.1920 0.709840
\(732\) 44.8506i 1.65772i
\(733\) 15.1597i 0.559935i 0.960009 + 0.279968i \(0.0903237\pi\)
−0.960009 + 0.279968i \(0.909676\pi\)
\(734\) −21.6312 −0.798422
\(735\) 3.13985 16.8418i 0.115815 0.621221i
\(736\) −33.6855 −1.24166
\(737\) 9.59976i 0.353612i
\(738\) 128.951i 4.74675i
\(739\) −37.6776 −1.38599 −0.692996 0.720942i \(-0.743709\pi\)
−0.692996 + 0.720942i \(0.743709\pi\)
\(740\) −3.76546 + 20.1976i −0.138421 + 0.742477i
\(741\) −6.76312 −0.248449
\(742\) 63.8388i 2.34360i
\(743\) 19.3117i 0.708476i −0.935155 0.354238i \(-0.884740\pi\)
0.935155 0.354238i \(-0.115260\pi\)
\(744\) 20.6063 0.755464
\(745\) −13.8530 2.58262i −0.507533 0.0946200i
\(746\) 11.0381 0.404134
\(747\) 29.9601i 1.09618i
\(748\) 9.60413i 0.351162i
\(749\) −26.6062 −0.972170
\(750\) −58.4628 36.0812i −2.13476 1.31750i
\(751\) 39.8039 1.45246 0.726232 0.687450i \(-0.241270\pi\)
0.726232 + 0.687450i \(0.241270\pi\)
\(752\) 31.7664i 1.15840i
\(753\) 9.75632i 0.355540i
\(754\) −26.5330 −0.966276
\(755\) −7.12240 1.32784i −0.259211 0.0483250i
\(756\) −72.6206 −2.64119
\(757\) 3.30928i 0.120278i 0.998190 + 0.0601389i \(0.0191543\pi\)
−0.998190 + 0.0601389i \(0.980846\pi\)
\(758\) 45.2641i 1.64406i
\(759\) 16.6926 0.605904
\(760\) 0.451245 2.42044i 0.0163684 0.0877985i
\(761\) −35.0055 −1.26895 −0.634475 0.772944i \(-0.718783\pi\)
−0.634475 + 0.772944i \(0.718783\pi\)
\(762\) 35.0950i 1.27136i
\(763\) 0.939110i 0.0339981i
\(764\) −29.0166 −1.04979
\(765\) −22.7077 + 121.802i −0.820997 + 4.40375i
\(766\) 58.2877 2.10602
\(767\) 11.8738i 0.428739i
\(768\) 69.8714i 2.52127i
\(769\) −36.8582 −1.32914 −0.664570 0.747226i \(-0.731385\pi\)
−0.664570 + 0.747226i \(0.731385\pi\)
\(770\) 12.3666 + 2.30552i 0.445660 + 0.0830850i
\(771\) 45.7822 1.64880
\(772\) 23.3373i 0.839927i
\(773\) 11.3631i 0.408704i −0.978898 0.204352i \(-0.934491\pi\)
0.978898 0.204352i \(-0.0655087\pi\)
\(774\) −41.8714 −1.50504
\(775\) 26.2044 + 10.1225i 0.941292 + 0.363610i
\(776\) 5.64484 0.202638
\(777\) 66.5198i 2.38638i
\(778\) 7.20912i 0.258460i
\(779\) −8.63500 −0.309381
\(780\) −20.8596 3.88888i −0.746894 0.139244i
\(781\) 3.93583 0.140835
\(782\) 63.2792i 2.26286i
\(783\) 120.223i 4.29643i
\(784\) 11.1270 0.397393
\(785\) −0.707863 + 3.79691i −0.0252647 + 0.135518i
\(786\) −81.0798 −2.89202
\(787\) 31.4505i 1.12109i −0.828124 0.560545i \(-0.810592\pi\)
0.828124 0.560545i \(-0.189408\pi\)
\(788\) 25.8538i 0.921004i
\(789\) −35.8497 −1.27628
\(790\) −11.1992 + 60.0716i −0.398451 + 2.13725i
\(791\) −20.5656 −0.731230
\(792\) 8.91357i 0.316730i
\(793\) 19.4845i 0.691914i
\(794\) 54.1662 1.92229
\(795\) −83.0871 15.4900i −2.94679 0.549375i
\(796\) 23.1407 0.820199
\(797\) 24.2997i 0.860739i 0.902653 + 0.430370i \(0.141617\pi\)
−0.902653 + 0.430370i \(0.858383\pi\)
\(798\) 18.7391i 0.663358i
\(799\) −44.9482 −1.59015
\(800\) 12.1106 31.3511i 0.428174 1.10843i
\(801\) 83.5926 2.95360
\(802\) 26.9564i 0.951862i
\(803\) 0.181013i 0.00638782i
\(804\) 44.8663 1.58231
\(805\) 33.5946 + 6.26308i 1.18405 + 0.220745i
\(806\) 21.0439 0.741238
\(807\) 63.3197i 2.22896i
\(808\) 12.7824i 0.449684i
\(809\) −7.43324 −0.261339 −0.130669 0.991426i \(-0.541713\pi\)
−0.130669 + 0.991426i \(0.541713\pi\)
\(810\) 24.3778 130.760i 0.856549 4.59445i
\(811\) 37.0856 1.30225 0.651126 0.758969i \(-0.274297\pi\)
0.651126 + 0.758969i \(0.274297\pi\)
\(812\) 30.3114i 1.06372i
\(813\) 56.5686i 1.98395i
\(814\) 12.0803 0.423415
\(815\) −3.71541 + 19.9291i −0.130145 + 0.698087i
\(816\) −110.294 −3.86105
\(817\) 2.80385i 0.0980944i
\(818\) 4.54573i 0.158938i
\(819\) 50.1244 1.75149
\(820\) −26.6331 4.96524i −0.930068 0.173394i
\(821\) −33.4666 −1.16799 −0.583997 0.811756i \(-0.698512\pi\)
−0.583997 + 0.811756i \(0.698512\pi\)
\(822\) 32.2817i 1.12595i
\(823\) 15.7212i 0.548005i −0.961729 0.274002i \(-0.911652\pi\)
0.961729 0.274002i \(-0.0883476\pi\)
\(824\) 1.17177 0.0408207
\(825\) −6.00132 + 15.5358i −0.208939 + 0.540889i
\(826\) 32.8998 1.14473
\(827\) 1.26766i 0.0440808i −0.999757 0.0220404i \(-0.992984\pi\)
0.999757 0.0220404i \(-0.00701624\pi\)
\(828\) 56.9214i 1.97816i
\(829\) −36.9425 −1.28307 −0.641534 0.767095i \(-0.721702\pi\)
−0.641534 + 0.767095i \(0.721702\pi\)
\(830\) −15.0080 2.79796i −0.520936 0.0971187i
\(831\) −43.4720 −1.50803
\(832\) 5.53292i 0.191819i
\(833\) 15.7442i 0.545506i
\(834\) 63.1979 2.18836
\(835\) −4.03774 + 21.6581i −0.139732 + 0.749509i
\(836\) 1.40312 0.0485278
\(837\) 95.3515i 3.29583i
\(838\) 27.5649i 0.952214i
\(839\) −36.7122 −1.26745 −0.633723 0.773560i \(-0.718474\pi\)
−0.633723 + 0.773560i \(0.718474\pi\)
\(840\) −4.58378 + 24.5870i −0.158155 + 0.848331i
\(841\) 21.1805 0.730363
\(842\) 7.39261i 0.254766i
\(843\) 15.6192i 0.537953i
\(844\) 8.44132 0.290562
\(845\) −19.5144 3.63810i −0.671317 0.125155i
\(846\) 98.0641 3.37151
\(847\) 3.04962i 0.104786i
\(848\) 54.8937i 1.88506i
\(849\) 106.150 3.64306
\(850\) −58.8940 22.7501i −2.02005 0.780321i
\(851\) 32.8169 1.12495
\(852\) 18.3949i 0.630198i
\(853\) 49.3564i 1.68993i 0.534820 + 0.844966i \(0.320379\pi\)
−0.534820 + 0.844966i \(0.679621\pi\)
\(854\) −53.9873 −1.84741
\(855\) 17.7947 + 3.31748i 0.608564 + 0.113455i
\(856\) 9.60652 0.328344
\(857\) 20.5776i 0.702916i 0.936204 + 0.351458i \(0.114314\pi\)
−0.936204 + 0.351458i \(0.885686\pi\)
\(858\) 12.4763i 0.425933i
\(859\) 38.0186 1.29718 0.648589 0.761138i \(-0.275359\pi\)
0.648589 + 0.761138i \(0.275359\pi\)
\(860\) 1.61225 8.64798i 0.0549774 0.294894i
\(861\) 87.7149 2.98932
\(862\) 25.9415i 0.883571i
\(863\) 5.66508i 0.192841i 0.995341 + 0.0964207i \(0.0307394\pi\)
−0.995341 + 0.0964207i \(0.969261\pi\)
\(864\) 114.079 3.88105
\(865\) −5.58606 + 29.9631i −0.189932 + 1.01878i
\(866\) −32.6148 −1.10830
\(867\) 99.4351i 3.37699i
\(868\) 24.0406i 0.815991i
\(869\) 14.8138 0.502522
\(870\) 95.6837 + 17.8384i 3.24398 + 0.604779i
\(871\) −19.4913 −0.660438
\(872\) 0.339078i 0.0114826i
\(873\) 41.4999i 1.40456i
\(874\) 9.24479 0.312710
\(875\) −17.9070 + 29.0148i −0.605366 + 0.980880i
\(876\) −0.846000 −0.0285837
\(877\) 34.0684i 1.15041i 0.818010 + 0.575204i \(0.195077\pi\)
−0.818010 + 0.575204i \(0.804923\pi\)
\(878\) 39.5865i 1.33598i
\(879\) 13.8966 0.468721
\(880\) −10.6338 1.98246i −0.358464 0.0668288i
\(881\) −2.23009 −0.0751338 −0.0375669 0.999294i \(-0.511961\pi\)
−0.0375669 + 0.999294i \(0.511961\pi\)
\(882\) 34.3494i 1.15661i
\(883\) 15.3195i 0.515541i 0.966206 + 0.257770i \(0.0829878\pi\)
−0.966206 + 0.257770i \(0.917012\pi\)
\(884\) −19.5002 −0.655862
\(885\) −7.98289 + 42.8195i −0.268342 + 1.43936i
\(886\) −0.124238 −0.00417384
\(887\) 26.1458i 0.877891i 0.898514 + 0.438946i \(0.144648\pi\)
−0.898514 + 0.438946i \(0.855352\pi\)
\(888\) 24.0178i 0.805985i
\(889\) −17.4175 −0.584164
\(890\) −7.80669 + 41.8744i −0.261681 + 1.40363i
\(891\) −32.2457 −1.08027
\(892\) 29.1388i 0.975640i
\(893\) 6.56671i 0.219747i
\(894\) 38.7241 1.29513
\(895\) −2.75855 0.514280i −0.0922082 0.0171905i
\(896\) −25.6672 −0.857481
\(897\) 33.8926i 1.13164i
\(898\) 61.7464i 2.06050i
\(899\) −39.7992 −1.32738
\(900\) 52.9768 + 20.4643i 1.76589 + 0.682145i
\(901\) −77.6722 −2.58764
\(902\) 15.9294i 0.530392i
\(903\) 28.4817i 0.947813i
\(904\) 7.42549 0.246968
\(905\) 45.7924 + 8.53714i 1.52219 + 0.283784i
\(906\) 19.9097 0.661456
\(907\) 22.8895i 0.760033i −0.924980 0.380016i \(-0.875918\pi\)
0.924980 0.380016i \(-0.124082\pi\)
\(908\) 12.2760i 0.407393i
\(909\) 93.9741 3.11692
\(910\) −4.68111 + 25.1090i −0.155177 + 0.832357i
\(911\) 27.2999 0.904486 0.452243 0.891895i \(-0.350624\pi\)
0.452243 + 0.891895i \(0.350624\pi\)
\(912\) 16.1134i 0.533568i
\(913\) 3.70100i 0.122485i
\(914\) −35.2978 −1.16755
\(915\) 13.0996 70.2652i 0.433060 2.32290i
\(916\) 27.2758 0.901217
\(917\) 40.2396i 1.32883i
\(918\) 214.301i 7.07298i
\(919\) −15.2724 −0.503791 −0.251895 0.967754i \(-0.581054\pi\)
−0.251895 + 0.967754i \(0.581054\pi\)
\(920\) −12.1298 2.26137i −0.399907 0.0745551i
\(921\) −55.5287 −1.82973
\(922\) 59.5236i 1.96030i
\(923\) 7.99130i 0.263037i
\(924\) −14.2530 −0.468888
\(925\) −11.7983 + 30.5428i −0.387926 + 1.00424i
\(926\) −29.3009 −0.962888
\(927\) 8.61468i 0.282943i
\(928\) 47.6159i 1.56307i
\(929\) −33.8533 −1.11069 −0.555346 0.831619i \(-0.687414\pi\)
−0.555346 + 0.831619i \(0.687414\pi\)
\(930\) −75.8886 14.1480i −2.48849 0.463932i
\(931\) −2.30016 −0.0753846
\(932\) 4.22405i 0.138363i
\(933\) 46.9320i 1.53648i
\(934\) 36.9494 1.20902
\(935\) −2.80510 + 15.0463i −0.0917366 + 0.492067i
\(936\) −18.0981 −0.591554
\(937\) 18.7055i 0.611082i −0.952179 0.305541i \(-0.901163\pi\)
0.952179 0.305541i \(-0.0988373\pi\)
\(938\) 54.0062i 1.76337i
\(939\) 37.9194 1.23745
\(940\) −3.77595 + 20.2538i −0.123158 + 0.660608i
\(941\) −2.89106 −0.0942457 −0.0471229 0.998889i \(-0.515005\pi\)
−0.0471229 + 0.998889i \(0.515005\pi\)
\(942\) 10.6138i 0.345815i
\(943\) 43.2734i 1.40917i
\(944\) −28.2898 −0.920755
\(945\) −113.771 21.2105i −3.70098 0.689977i
\(946\) −5.17242 −0.168170
\(947\) 47.2698i 1.53606i −0.640412 0.768031i \(-0.721236\pi\)
0.640412 0.768031i \(-0.278764\pi\)
\(948\) 69.2349i 2.24865i
\(949\) 0.367529 0.0119305
\(950\) −3.32368 + 8.60413i −0.107834 + 0.279155i
\(951\) 71.3597 2.31400
\(952\) 22.9846i 0.744936i
\(953\) 26.8871i 0.870958i 0.900199 + 0.435479i \(0.143421\pi\)
−0.900199 + 0.435479i \(0.856579\pi\)
\(954\) 169.459 5.48642
\(955\) −45.4590 8.47497i −1.47102 0.274244i
\(956\) 13.6462 0.441349
\(957\) 23.5957i 0.762742i
\(958\) 14.4675i 0.467424i
\(959\) 16.0213 0.517354
\(960\) −3.71984 + 19.9529i −0.120057 + 0.643976i
\(961\) 0.565505 0.0182421
\(962\) 24.5278i 0.790808i
\(963\) 70.6255i 2.27588i
\(964\) −8.72204 −0.280918
\(965\) 6.81618 36.5614i 0.219421 1.17695i
\(966\) −93.9092 −3.02148
\(967\) 37.8313i 1.21657i 0.793718 + 0.608286i \(0.208143\pi\)
−0.793718 + 0.608286i \(0.791857\pi\)
\(968\) 1.10110i 0.0353908i
\(969\) 22.7998 0.732434
\(970\) −20.7887 3.87567i −0.667486 0.124440i
\(971\) 24.5393 0.787504 0.393752 0.919217i \(-0.371177\pi\)
0.393752 + 0.919217i \(0.371177\pi\)
\(972\) 79.2672i 2.54250i
\(973\) 31.3648i 1.00551i
\(974\) 21.8851 0.701244
\(975\) −31.5439 12.1850i −1.01021 0.390234i
\(976\) 46.4225 1.48595
\(977\) 5.57772i 0.178447i 0.996012 + 0.0892236i \(0.0284386\pi\)
−0.996012 + 0.0892236i \(0.971561\pi\)
\(978\) 55.7092i 1.78138i
\(979\) 10.3263 0.330030
\(980\) −7.09443 1.32262i −0.226623 0.0422496i
\(981\) 2.49284 0.0795903
\(982\) 0.348129i 0.0111092i
\(983\) 38.4618i 1.22674i 0.789795 + 0.613371i \(0.210187\pi\)
−0.789795 + 0.613371i \(0.789813\pi\)
\(984\) −31.6706 −1.00962
\(985\) −7.55119 + 40.5039i −0.240601 + 1.29056i
\(986\) 89.4479 2.84860
\(987\) 66.7051i 2.12325i
\(988\) 2.84888i 0.0906350i
\(989\) −14.0512 −0.446803
\(990\) 6.11993 32.8268i 0.194504 1.04330i
\(991\) 35.2554 1.11992 0.559962 0.828518i \(-0.310816\pi\)
0.559962 + 0.828518i \(0.310816\pi\)
\(992\) 37.7651i 1.19904i
\(993\) 80.2556i 2.54683i
\(994\) −22.1422 −0.702307
\(995\) 36.2533 + 6.75875i 1.14931 + 0.214267i
\(996\) 17.2973 0.548087
\(997\) 50.5160i 1.59986i −0.600094 0.799930i \(-0.704870\pi\)
0.600094 0.799930i \(-0.295130\pi\)
\(998\) 71.8391i 2.27403i
\(999\) −111.137 −3.51623
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 1045.2.b.d.419.18 yes 22
5.2 odd 4 5225.2.a.bb.1.5 22
5.3 odd 4 5225.2.a.bb.1.18 22
5.4 even 2 inner 1045.2.b.d.419.5 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.2.b.d.419.5 22 5.4 even 2 inner
1045.2.b.d.419.18 yes 22 1.1 even 1 trivial
5225.2.a.bb.1.5 22 5.2 odd 4
5225.2.a.bb.1.18 22 5.3 odd 4