Properties

Label 648.2.v.b.35.30
Level $648$
Weight $2$
Character 648.35
Analytic conductor $5.174$
Analytic rank $0$
Dimension $192$
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] = [648,2,Mod(35,648)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(648, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 9, 13]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("648.35");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 648.v (of order \(18\), degree \(6\), not 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: \(5.17430605098\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(32\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 216)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 35.30
Character \(\chi\) \(=\) 648.35
Dual form 648.2.v.b.611.30

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.38842 + 0.268854i) q^{2} +(1.85543 + 0.746566i) q^{4} +(3.21396 + 1.16979i) q^{5} +(0.199218 + 0.0351275i) q^{7} +(2.37541 + 1.53539i) q^{8} +O(q^{10})\) \(q+(1.38842 + 0.268854i) q^{2} +(1.85543 + 0.746566i) q^{4} +(3.21396 + 1.16979i) q^{5} +(0.199218 + 0.0351275i) q^{7} +(2.37541 + 1.53539i) q^{8} +(4.14784 + 2.48825i) q^{10} +(-1.37658 - 3.78212i) q^{11} +(-1.09713 - 1.30751i) q^{13} +(0.267155 + 0.102332i) q^{14} +(2.88528 + 2.77041i) q^{16} +(-1.57350 + 0.908459i) q^{17} +(-3.24004 + 5.61192i) q^{19} +(5.08997 + 4.56990i) q^{20} +(-0.894435 - 5.62128i) q^{22} +(-1.37566 - 7.80173i) q^{23} +(5.13093 + 4.30536i) q^{25} +(-1.17176 - 2.11035i) q^{26} +(0.343411 + 0.213906i) q^{28} +(-3.08543 - 2.58898i) q^{29} +(-7.51214 + 1.32459i) q^{31} +(3.26115 + 4.62222i) q^{32} +(-2.42892 + 0.838284i) q^{34} +(0.599188 + 0.345941i) q^{35} +(-1.53384 + 0.885560i) q^{37} +(-6.00733 + 6.92061i) q^{38} +(5.83840 + 7.71341i) q^{40} +(6.61260 + 7.88059i) q^{41} +(3.47909 - 1.26628i) q^{43} +(0.269450 - 8.04518i) q^{44} +(0.187536 - 11.2020i) q^{46} +(0.523875 - 2.97105i) q^{47} +(-6.53939 - 2.38014i) q^{49} +(5.96638 + 7.35713i) q^{50} +(-1.05952 - 3.24509i) q^{52} +9.46508 q^{53} -13.7659i q^{55} +(0.419290 + 0.389320i) q^{56} +(-3.58782 - 4.42413i) q^{58} +(-1.23077 + 3.38152i) q^{59} +(8.13039 + 1.43361i) q^{61} +(-10.7861 - 0.180575i) q^{62} +(3.28515 + 7.29437i) q^{64} +(-1.99664 - 5.48571i) q^{65} +(-1.26475 + 1.06125i) q^{67} +(-3.59775 + 0.510867i) q^{68} +(0.738918 + 0.641406i) q^{70} +(-2.24594 - 3.89008i) q^{71} +(-4.05026 + 7.01525i) q^{73} +(-2.36770 + 0.817154i) q^{74} +(-10.2014 + 7.99364i) q^{76} +(-0.141383 - 0.801822i) q^{77} +(0.380899 - 0.453938i) q^{79} +(6.03238 + 12.2792i) q^{80} +(7.06236 + 12.7194i) q^{82} +(8.02454 - 9.56328i) q^{83} +(-6.11986 + 1.07910i) q^{85} +(5.17089 - 0.822771i) q^{86} +(2.53709 - 11.0977i) q^{88} +(-10.7122 - 6.18471i) q^{89} +(-0.172639 - 0.299020i) q^{91} +(3.27207 - 15.5026i) q^{92} +(1.52614 - 3.98422i) q^{94} +(-16.9781 + 14.2463i) q^{95} +(-8.24324 + 3.00029i) q^{97} +(-8.43953 - 5.06279i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8} - 3 q^{10} + 30 q^{11} - 9 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} + 27 q^{20} - 18 q^{22} - 12 q^{25} - 12 q^{28} + 36 q^{32} + 12 q^{34} + 18 q^{35} + 102 q^{38} + 9 q^{40} - 18 q^{41} - 42 q^{43} + 81 q^{44} - 3 q^{46} - 12 q^{49} - 57 q^{50} + 21 q^{52} + 69 q^{56} - 33 q^{58} + 84 q^{59} - 90 q^{62} - 51 q^{64} + 12 q^{65} + 30 q^{67} - 63 q^{68} - 33 q^{70} - 6 q^{73} - 51 q^{74} + 30 q^{76} - 12 q^{82} + 72 q^{83} - 42 q^{86} - 78 q^{88} - 144 q^{89} - 6 q^{91} + 3 q^{92} - 33 q^{94} - 42 q^{97} - 162 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(487\) \(569\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{13}{18}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.38842 + 0.268854i 0.981763 + 0.190109i
\(3\) 0 0
\(4\) 1.85543 + 0.746566i 0.927717 + 0.373283i
\(5\) 3.21396 + 1.16979i 1.43733 + 0.523144i 0.939022 0.343857i \(-0.111734\pi\)
0.498306 + 0.867001i \(0.333956\pi\)
\(6\) 0 0
\(7\) 0.199218 + 0.0351275i 0.0752973 + 0.0132770i 0.211170 0.977449i \(-0.432273\pi\)
−0.135873 + 0.990726i \(0.543384\pi\)
\(8\) 2.37541 + 1.53539i 0.839834 + 0.542843i
\(9\) 0 0
\(10\) 4.14784 + 2.48825i 1.31166 + 0.786852i
\(11\) −1.37658 3.78212i −0.415054 1.14035i −0.954469 0.298311i \(-0.903577\pi\)
0.539414 0.842040i \(-0.318646\pi\)
\(12\) 0 0
\(13\) −1.09713 1.30751i −0.304290 0.362639i 0.592131 0.805842i \(-0.298287\pi\)
−0.896422 + 0.443202i \(0.853842\pi\)
\(14\) 0.267155 + 0.102332i 0.0714001 + 0.0273495i
\(15\) 0 0
\(16\) 2.88528 + 2.77041i 0.721319 + 0.692603i
\(17\) −1.57350 + 0.908459i −0.381629 + 0.220334i −0.678527 0.734576i \(-0.737381\pi\)
0.296898 + 0.954909i \(0.404048\pi\)
\(18\) 0 0
\(19\) −3.24004 + 5.61192i −0.743317 + 1.28746i 0.207661 + 0.978201i \(0.433415\pi\)
−0.950977 + 0.309261i \(0.899918\pi\)
\(20\) 5.08997 + 4.56990i 1.13815 + 1.02186i
\(21\) 0 0
\(22\) −0.894435 5.62128i −0.190694 1.19846i
\(23\) −1.37566 7.80173i −0.286844 1.62677i −0.698623 0.715490i \(-0.746204\pi\)
0.411779 0.911284i \(-0.364908\pi\)
\(24\) 0 0
\(25\) 5.13093 + 4.30536i 1.02619 + 0.861072i
\(26\) −1.17176 2.11035i −0.229800 0.413874i
\(27\) 0 0
\(28\) 0.343411 + 0.213906i 0.0648986 + 0.0404245i
\(29\) −3.08543 2.58898i −0.572949 0.480761i 0.309674 0.950843i \(-0.399780\pi\)
−0.882623 + 0.470081i \(0.844225\pi\)
\(30\) 0 0
\(31\) −7.51214 + 1.32459i −1.34922 + 0.237904i −0.801117 0.598507i \(-0.795761\pi\)
−0.548103 + 0.836411i \(0.684650\pi\)
\(32\) 3.26115 + 4.62222i 0.576495 + 0.817101i
\(33\) 0 0
\(34\) −2.42892 + 0.838284i −0.416557 + 0.143764i
\(35\) 0.599188 + 0.345941i 0.101281 + 0.0584747i
\(36\) 0 0
\(37\) −1.53384 + 0.885560i −0.252161 + 0.145585i −0.620753 0.784006i \(-0.713173\pi\)
0.368592 + 0.929591i \(0.379840\pi\)
\(38\) −6.00733 + 6.92061i −0.974518 + 1.12267i
\(39\) 0 0
\(40\) 5.83840 + 7.71341i 0.923132 + 1.21960i
\(41\) 6.61260 + 7.88059i 1.03271 + 1.23074i 0.972584 + 0.232551i \(0.0747072\pi\)
0.0601305 + 0.998191i \(0.480848\pi\)
\(42\) 0 0
\(43\) 3.47909 1.26628i 0.530556 0.193107i −0.0628305 0.998024i \(-0.520013\pi\)
0.593387 + 0.804918i \(0.297791\pi\)
\(44\) 0.269450 8.04518i 0.0406211 1.21286i
\(45\) 0 0
\(46\) 0.187536 11.2020i 0.0276507 1.65164i
\(47\) 0.523875 2.97105i 0.0764151 0.433371i −0.922466 0.386078i \(-0.873829\pi\)
0.998881 0.0472931i \(-0.0150595\pi\)
\(48\) 0 0
\(49\) −6.53939 2.38014i −0.934199 0.340021i
\(50\) 5.96638 + 7.35713i 0.843774 + 1.04046i
\(51\) 0 0
\(52\) −1.05952 3.24509i −0.146928 0.450013i
\(53\) 9.46508 1.30013 0.650064 0.759879i \(-0.274742\pi\)
0.650064 + 0.759879i \(0.274742\pi\)
\(54\) 0 0
\(55\) 13.7659i 1.85619i
\(56\) 0.419290 + 0.389320i 0.0560300 + 0.0520250i
\(57\) 0 0
\(58\) −3.58782 4.42413i −0.471103 0.580916i
\(59\) −1.23077 + 3.38152i −0.160233 + 0.440237i −0.993665 0.112386i \(-0.964151\pi\)
0.833432 + 0.552623i \(0.186373\pi\)
\(60\) 0 0
\(61\) 8.13039 + 1.43361i 1.04099 + 0.183555i 0.667908 0.744244i \(-0.267190\pi\)
0.373082 + 0.927798i \(0.378301\pi\)
\(62\) −10.7861 0.180575i −1.36984 0.0229330i
\(63\) 0 0
\(64\) 3.28515 + 7.29437i 0.410644 + 0.911796i
\(65\) −1.99664 5.48571i −0.247652 0.680419i
\(66\) 0 0
\(67\) −1.26475 + 1.06125i −0.154514 + 0.129653i −0.716767 0.697312i \(-0.754379\pi\)
0.562253 + 0.826965i \(0.309935\pi\)
\(68\) −3.59775 + 0.510867i −0.436291 + 0.0619517i
\(69\) 0 0
\(70\) 0.738918 + 0.641406i 0.0883176 + 0.0766627i
\(71\) −2.24594 3.89008i −0.266544 0.461668i 0.701423 0.712745i \(-0.252548\pi\)
−0.967967 + 0.251078i \(0.919215\pi\)
\(72\) 0 0
\(73\) −4.05026 + 7.01525i −0.474047 + 0.821073i −0.999558 0.0297132i \(-0.990541\pi\)
0.525512 + 0.850786i \(0.323874\pi\)
\(74\) −2.36770 + 0.817154i −0.275239 + 0.0949922i
\(75\) 0 0
\(76\) −10.2014 + 7.99364i −1.17018 + 0.916934i
\(77\) −0.141383 0.801822i −0.0161121 0.0913761i
\(78\) 0 0
\(79\) 0.380899 0.453938i 0.0428545 0.0510720i −0.744191 0.667966i \(-0.767165\pi\)
0.787046 + 0.616894i \(0.211609\pi\)
\(80\) 6.03238 + 12.2792i 0.674441 + 1.37285i
\(81\) 0 0
\(82\) 7.06236 + 12.7194i 0.779907 + 1.40462i
\(83\) 8.02454 9.56328i 0.880808 1.04971i −0.117586 0.993063i \(-0.537516\pi\)
0.998394 0.0566436i \(-0.0180399\pi\)
\(84\) 0 0
\(85\) −6.11986 + 1.07910i −0.663792 + 0.117044i
\(86\) 5.17089 0.822771i 0.557592 0.0887217i
\(87\) 0 0
\(88\) 2.53709 11.0977i 0.270455 1.18302i
\(89\) −10.7122 6.18471i −1.13549 0.655578i −0.190183 0.981749i \(-0.560908\pi\)
−0.945311 + 0.326171i \(0.894241\pi\)
\(90\) 0 0
\(91\) −0.172639 0.299020i −0.0180975 0.0313458i
\(92\) 3.27207 15.5026i 0.341137 1.61626i
\(93\) 0 0
\(94\) 1.52614 3.98422i 0.157409 0.410941i
\(95\) −16.9781 + 14.2463i −1.74192 + 1.46164i
\(96\) 0 0
\(97\) −8.24324 + 3.00029i −0.836974 + 0.304634i −0.724718 0.689046i \(-0.758030\pi\)
−0.112256 + 0.993679i \(0.535808\pi\)
\(98\) −8.43953 5.06279i −0.852521 0.511419i
\(99\) 0 0
\(100\) 6.30587 + 11.8189i 0.630587 + 1.18189i
\(101\) 1.79803 10.1971i 0.178910 1.01465i −0.754623 0.656159i \(-0.772180\pi\)
0.933533 0.358491i \(-0.116709\pi\)
\(102\) 0 0
\(103\) −2.22000 + 6.09941i −0.218744 + 0.600993i −0.999722 0.0235646i \(-0.992498\pi\)
0.780979 + 0.624558i \(0.214721\pi\)
\(104\) −0.598600 4.79041i −0.0586975 0.469739i
\(105\) 0 0
\(106\) 13.1415 + 2.54473i 1.27642 + 0.247166i
\(107\) 2.26037i 0.218518i 0.994013 + 0.109259i \(0.0348478\pi\)
−0.994013 + 0.109259i \(0.965152\pi\)
\(108\) 0 0
\(109\) 3.00655i 0.287975i −0.989580 0.143987i \(-0.954008\pi\)
0.989580 0.143987i \(-0.0459925\pi\)
\(110\) 3.70102 19.1129i 0.352878 1.82234i
\(111\) 0 0
\(112\) 0.477482 + 0.653268i 0.0451178 + 0.0617281i
\(113\) −1.92611 + 5.29194i −0.181193 + 0.497824i −0.996723 0.0808910i \(-0.974223\pi\)
0.815530 + 0.578715i \(0.196446\pi\)
\(114\) 0 0
\(115\) 4.70506 26.6837i 0.438749 2.48827i
\(116\) −3.79196 7.10716i −0.352075 0.659883i
\(117\) 0 0
\(118\) −2.61797 + 4.36408i −0.241004 + 0.401746i
\(119\) −0.345381 + 0.125708i −0.0316610 + 0.0115237i
\(120\) 0 0
\(121\) −3.98297 + 3.34211i −0.362088 + 0.303828i
\(122\) 10.9030 + 4.17634i 0.987110 + 0.378108i
\(123\) 0 0
\(124\) −14.9272 3.15061i −1.34050 0.282933i
\(125\) 2.90369 + 5.02934i 0.259714 + 0.449838i
\(126\) 0 0
\(127\) −9.60934 5.54795i −0.852691 0.492301i 0.00886716 0.999961i \(-0.497177\pi\)
−0.861558 + 0.507660i \(0.830511\pi\)
\(128\) 2.60006 + 11.0109i 0.229815 + 0.973234i
\(129\) 0 0
\(130\) −1.29732 8.15329i −0.113782 0.715091i
\(131\) −7.26270 + 1.28061i −0.634545 + 0.111887i −0.481662 0.876357i \(-0.659967\pi\)
−0.152883 + 0.988244i \(0.548856\pi\)
\(132\) 0 0
\(133\) −0.842608 + 1.00418i −0.0730633 + 0.0870735i
\(134\) −2.04134 + 1.13344i −0.176345 + 0.0979139i
\(135\) 0 0
\(136\) −5.13254 0.257970i −0.440112 0.0221207i
\(137\) −7.46073 + 8.89135i −0.637413 + 0.759640i −0.983959 0.178393i \(-0.942910\pi\)
0.346546 + 0.938033i \(0.387354\pi\)
\(138\) 0 0
\(139\) 1.37040 + 7.77191i 0.116236 + 0.659205i 0.986131 + 0.165969i \(0.0530751\pi\)
−0.869895 + 0.493236i \(0.835814\pi\)
\(140\) 0.853486 + 1.08920i 0.0721327 + 0.0920546i
\(141\) 0 0
\(142\) −2.07245 6.00490i −0.173916 0.503920i
\(143\) −3.43488 + 5.94939i −0.287239 + 0.497513i
\(144\) 0 0
\(145\) −6.88789 11.9302i −0.572008 0.990747i
\(146\) −7.50955 + 8.65121i −0.621495 + 0.715979i
\(147\) 0 0
\(148\) −3.50706 + 0.497990i −0.288279 + 0.0409345i
\(149\) 5.38903 4.52193i 0.441486 0.370451i −0.394779 0.918776i \(-0.629179\pi\)
0.836265 + 0.548325i \(0.184734\pi\)
\(150\) 0 0
\(151\) −2.14375 5.88990i −0.174456 0.479313i 0.821390 0.570367i \(-0.193199\pi\)
−0.995846 + 0.0910533i \(0.970977\pi\)
\(152\) −16.3129 + 8.35588i −1.32315 + 0.677751i
\(153\) 0 0
\(154\) 0.0192740 1.15128i 0.00155314 0.0927727i
\(155\) −25.6932 4.53041i −2.06373 0.363891i
\(156\) 0 0
\(157\) 1.70377 4.68108i 0.135976 0.373591i −0.852952 0.521990i \(-0.825190\pi\)
0.988928 + 0.148399i \(0.0474120\pi\)
\(158\) 0.650892 0.527851i 0.0517822 0.0419936i
\(159\) 0 0
\(160\) 5.07420 + 18.6705i 0.401151 + 1.47603i
\(161\) 1.60257i 0.126300i
\(162\) 0 0
\(163\) 6.53033 0.511495 0.255747 0.966744i \(-0.417679\pi\)
0.255747 + 0.966744i \(0.417679\pi\)
\(164\) 6.38587 + 19.5587i 0.498652 + 1.52728i
\(165\) 0 0
\(166\) 13.7126 11.1204i 1.06430 0.863114i
\(167\) −11.5164 4.19163i −0.891167 0.324358i −0.144460 0.989511i \(-0.546144\pi\)
−0.746708 + 0.665152i \(0.768367\pi\)
\(168\) 0 0
\(169\) 1.75154 9.93346i 0.134734 0.764113i
\(170\) −8.78707 0.147108i −0.673938 0.0112826i
\(171\) 0 0
\(172\) 7.40059 + 0.247861i 0.564290 + 0.0188992i
\(173\) 22.9308 8.34612i 1.74339 0.634543i 0.743961 0.668223i \(-0.232945\pi\)
0.999433 + 0.0336797i \(0.0107226\pi\)
\(174\) 0 0
\(175\) 0.870937 + 1.03794i 0.0658367 + 0.0784611i
\(176\) 6.50621 14.7262i 0.490424 1.11003i
\(177\) 0 0
\(178\) −13.2103 11.4670i −0.990155 0.859489i
\(179\) 12.4964 7.21481i 0.934026 0.539260i 0.0459437 0.998944i \(-0.485371\pi\)
0.888083 + 0.459684i \(0.152037\pi\)
\(180\) 0 0
\(181\) 17.7079 + 10.2237i 1.31622 + 0.759919i 0.983118 0.182973i \(-0.0585721\pi\)
0.333100 + 0.942892i \(0.391905\pi\)
\(182\) −0.159303 0.461581i −0.0118084 0.0342146i
\(183\) 0 0
\(184\) 8.71096 20.6445i 0.642181 1.52193i
\(185\) −5.96560 + 1.05190i −0.438600 + 0.0773370i
\(186\) 0 0
\(187\) 5.60194 + 4.70059i 0.409655 + 0.343741i
\(188\) 3.19010 5.12147i 0.232662 0.373522i
\(189\) 0 0
\(190\) −27.4030 + 15.2153i −1.98802 + 1.10383i
\(191\) 15.9522 + 13.3855i 1.15426 + 0.968538i 0.999811 0.0194633i \(-0.00619574\pi\)
0.154448 + 0.988001i \(0.450640\pi\)
\(192\) 0 0
\(193\) 0.989078 + 5.60934i 0.0711954 + 0.403769i 0.999490 + 0.0319244i \(0.0101636\pi\)
−0.928295 + 0.371845i \(0.878725\pi\)
\(194\) −12.2517 + 1.94945i −0.879623 + 0.139962i
\(195\) 0 0
\(196\) −10.3565 9.29830i −0.739749 0.664164i
\(197\) −13.4024 + 23.2137i −0.954885 + 1.65391i −0.220254 + 0.975443i \(0.570688\pi\)
−0.734631 + 0.678467i \(0.762645\pi\)
\(198\) 0 0
\(199\) 22.2890 12.8685i 1.58002 0.912226i 0.585168 0.810912i \(-0.301029\pi\)
0.994854 0.101314i \(-0.0323048\pi\)
\(200\) 5.57765 + 18.1050i 0.394400 + 1.28022i
\(201\) 0 0
\(202\) 5.23795 13.6745i 0.368541 0.962134i
\(203\) −0.523728 0.624155i −0.0367585 0.0438071i
\(204\) 0 0
\(205\) 12.0340 + 33.0633i 0.840494 + 2.30924i
\(206\) −4.72216 + 7.87171i −0.329008 + 0.548448i
\(207\) 0 0
\(208\) 0.456812 6.81205i 0.0316742 0.472331i
\(209\) 25.6851 + 4.52898i 1.77668 + 0.313276i
\(210\) 0 0
\(211\) −2.22400 0.809471i −0.153107 0.0557263i 0.264330 0.964432i \(-0.414849\pi\)
−0.417437 + 0.908706i \(0.637071\pi\)
\(212\) 17.5618 + 7.06631i 1.20615 + 0.485316i
\(213\) 0 0
\(214\) −0.607709 + 3.13835i −0.0415421 + 0.214533i
\(215\) 12.6629 0.863606
\(216\) 0 0
\(217\) −1.54308 −0.104751
\(218\) 0.808322 4.17436i 0.0547465 0.282723i
\(219\) 0 0
\(220\) 10.2771 25.5417i 0.692885 1.72202i
\(221\) 2.91416 + 1.06067i 0.196028 + 0.0713482i
\(222\) 0 0
\(223\) −19.7258 3.47820i −1.32094 0.232917i −0.531664 0.846955i \(-0.678433\pi\)
−0.789277 + 0.614038i \(0.789544\pi\)
\(224\) 0.487313 + 1.03539i 0.0325599 + 0.0691796i
\(225\) 0 0
\(226\) −4.09701 + 6.82961i −0.272529 + 0.454299i
\(227\) 8.81116 + 24.2085i 0.584817 + 1.60677i 0.779843 + 0.625975i \(0.215299\pi\)
−0.195026 + 0.980798i \(0.562479\pi\)
\(228\) 0 0
\(229\) −1.43440 1.70946i −0.0947880 0.112964i 0.716565 0.697520i \(-0.245713\pi\)
−0.811353 + 0.584556i \(0.801269\pi\)
\(230\) 13.7066 35.7833i 0.903788 2.35948i
\(231\) 0 0
\(232\) −3.35406 10.8872i −0.220205 0.714781i
\(233\) 7.43882 4.29480i 0.487333 0.281362i −0.236134 0.971720i \(-0.575881\pi\)
0.723467 + 0.690358i \(0.242547\pi\)
\(234\) 0 0
\(235\) 5.15920 8.93600i 0.336549 0.582921i
\(236\) −4.80815 + 5.35534i −0.312984 + 0.348603i
\(237\) 0 0
\(238\) −0.513332 + 0.0816793i −0.0332744 + 0.00529448i
\(239\) −0.254336 1.44241i −0.0164516 0.0933018i 0.975476 0.220104i \(-0.0706397\pi\)
−0.991928 + 0.126802i \(0.959529\pi\)
\(240\) 0 0
\(241\) 1.54665 + 1.29779i 0.0996285 + 0.0835982i 0.691241 0.722624i \(-0.257064\pi\)
−0.591613 + 0.806222i \(0.701509\pi\)
\(242\) −6.42858 + 3.56942i −0.413245 + 0.229451i
\(243\) 0 0
\(244\) 14.0151 + 8.72984i 0.897227 + 0.558871i
\(245\) −18.2331 15.2994i −1.16487 0.977442i
\(246\) 0 0
\(247\) 10.8924 1.92063i 0.693068 0.122207i
\(248\) −19.8782 8.38762i −1.26227 0.532614i
\(249\) 0 0
\(250\) 2.67939 + 7.76352i 0.169460 + 0.491008i
\(251\) 0.0195920 + 0.0113115i 0.00123664 + 0.000713973i 0.500618 0.865668i \(-0.333106\pi\)
−0.499382 + 0.866382i \(0.666439\pi\)
\(252\) 0 0
\(253\) −27.6134 + 15.9426i −1.73604 + 1.00230i
\(254\) −11.8502 10.2864i −0.743550 0.645427i
\(255\) 0 0
\(256\) 0.649655 + 15.9868i 0.0406034 + 0.999175i
\(257\) 10.5865 + 12.6165i 0.660369 + 0.786997i 0.987439 0.158003i \(-0.0505056\pi\)
−0.327070 + 0.945000i \(0.606061\pi\)
\(258\) 0 0
\(259\) −0.336675 + 0.122540i −0.0209200 + 0.00761425i
\(260\) 0.390819 11.6690i 0.0242376 0.723681i
\(261\) 0 0
\(262\) −10.4280 0.174579i −0.644243 0.0107855i
\(263\) 1.02766 5.82816i 0.0633684 0.359380i −0.936592 0.350423i \(-0.886038\pi\)
0.999960 0.00895677i \(-0.00285107\pi\)
\(264\) 0 0
\(265\) 30.4204 + 11.0721i 1.86871 + 0.680155i
\(266\) −1.43987 + 1.16769i −0.0882843 + 0.0715956i
\(267\) 0 0
\(268\) −3.13897 + 1.02487i −0.191743 + 0.0626037i
\(269\) −4.98736 −0.304085 −0.152042 0.988374i \(-0.548585\pi\)
−0.152042 + 0.988374i \(0.548585\pi\)
\(270\) 0 0
\(271\) 7.03519i 0.427358i 0.976904 + 0.213679i \(0.0685446\pi\)
−0.976904 + 0.213679i \(0.931455\pi\)
\(272\) −7.05678 1.73808i −0.427880 0.105386i
\(273\) 0 0
\(274\) −12.7491 + 10.3391i −0.770203 + 0.624608i
\(275\) 9.22026 25.3325i 0.556003 1.52760i
\(276\) 0 0
\(277\) 22.4822 + 3.96421i 1.35082 + 0.238187i 0.801786 0.597611i \(-0.203883\pi\)
0.549037 + 0.835798i \(0.314994\pi\)
\(278\) −0.186819 + 11.1591i −0.0112047 + 0.669281i
\(279\) 0 0
\(280\) 0.892162 + 1.74174i 0.0533169 + 0.104089i
\(281\) −8.38379 23.0343i −0.500135 1.37411i −0.891143 0.453722i \(-0.850096\pi\)
0.391008 0.920387i \(-0.372126\pi\)
\(282\) 0 0
\(283\) −8.31451 + 6.97670i −0.494246 + 0.414722i −0.855545 0.517728i \(-0.826778\pi\)
0.361299 + 0.932450i \(0.382333\pi\)
\(284\) −1.26299 8.89453i −0.0749447 0.527793i
\(285\) 0 0
\(286\) −6.36858 + 7.33678i −0.376582 + 0.433833i
\(287\) 1.04052 + 1.80224i 0.0614202 + 0.106383i
\(288\) 0 0
\(289\) −6.84941 + 11.8635i −0.402906 + 0.697854i
\(290\) −6.35582 18.4160i −0.373227 1.08142i
\(291\) 0 0
\(292\) −12.7523 + 9.99256i −0.746274 + 0.584770i
\(293\) −2.84714 16.1469i −0.166332 0.943313i −0.947681 0.319219i \(-0.896579\pi\)
0.781349 0.624094i \(-0.214532\pi\)
\(294\) 0 0
\(295\) −7.91132 + 9.42834i −0.460615 + 0.548939i
\(296\) −5.00317 0.251467i −0.290803 0.0146162i
\(297\) 0 0
\(298\) 8.69799 4.82949i 0.503861 0.279765i
\(299\) −8.69159 + 10.3582i −0.502648 + 0.599032i
\(300\) 0 0
\(301\) 0.737579 0.130055i 0.0425133 0.00749625i
\(302\) −1.39291 8.75403i −0.0801527 0.503738i
\(303\) 0 0
\(304\) −24.8957 + 7.21569i −1.42787 + 0.413848i
\(305\) 24.4538 + 14.1184i 1.40022 + 0.808416i
\(306\) 0 0
\(307\) 7.29100 + 12.6284i 0.416119 + 0.720740i 0.995545 0.0942851i \(-0.0300565\pi\)
−0.579426 + 0.815025i \(0.696723\pi\)
\(308\) 0.336287 1.59328i 0.0191617 0.0907856i
\(309\) 0 0
\(310\) −34.4550 13.1978i −1.95691 0.749587i
\(311\) −18.0464 + 15.1428i −1.02332 + 0.858667i −0.990041 0.140779i \(-0.955039\pi\)
−0.0332788 + 0.999446i \(0.510595\pi\)
\(312\) 0 0
\(313\) 4.27277 1.55516i 0.241511 0.0879028i −0.218429 0.975853i \(-0.570093\pi\)
0.459940 + 0.887950i \(0.347871\pi\)
\(314\) 3.62409 6.04125i 0.204519 0.340928i
\(315\) 0 0
\(316\) 1.04563 0.557886i 0.0588212 0.0313835i
\(317\) −1.85951 + 10.5458i −0.104440 + 0.592310i 0.887002 + 0.461765i \(0.152784\pi\)
−0.991442 + 0.130545i \(0.958327\pi\)
\(318\) 0 0
\(319\) −5.54450 + 15.2334i −0.310432 + 0.852906i
\(320\) 2.02550 + 27.2867i 0.113229 + 1.52538i
\(321\) 0 0
\(322\) 0.430857 2.22504i 0.0240107 0.123997i
\(323\) 11.7738i 0.655111i
\(324\) 0 0
\(325\) 11.4323i 0.634151i
\(326\) 9.06685 + 1.75570i 0.502166 + 0.0972395i
\(327\) 0 0
\(328\) 3.60786 + 28.8726i 0.199210 + 1.59422i
\(329\) 0.208731 0.573483i 0.0115077 0.0316172i
\(330\) 0 0
\(331\) −2.53127 + 14.3556i −0.139131 + 0.789053i 0.832762 + 0.553631i \(0.186758\pi\)
−0.971893 + 0.235422i \(0.924353\pi\)
\(332\) 22.0286 11.7532i 1.20898 0.645040i
\(333\) 0 0
\(334\) −14.8627 8.91600i −0.813252 0.487862i
\(335\) −5.30631 + 1.93134i −0.289915 + 0.105520i
\(336\) 0 0
\(337\) 19.2969 16.1920i 1.05117 0.882035i 0.0579523 0.998319i \(-0.481543\pi\)
0.993216 + 0.116285i \(0.0370984\pi\)
\(338\) 5.10253 13.3209i 0.277541 0.724564i
\(339\) 0 0
\(340\) −12.1606 2.56669i −0.659502 0.139198i
\(341\) 15.3508 + 26.5884i 0.831293 + 1.43984i
\(342\) 0 0
\(343\) −2.44548 1.41190i −0.132044 0.0762354i
\(344\) 10.2085 + 2.33381i 0.550406 + 0.125831i
\(345\) 0 0
\(346\) 34.0815 5.42291i 1.83223 0.291537i
\(347\) 8.71967 1.53751i 0.468097 0.0825380i 0.0653753 0.997861i \(-0.479176\pi\)
0.402721 + 0.915323i \(0.368064\pi\)
\(348\) 0 0
\(349\) 19.6221 23.3847i 1.05035 1.25175i 0.0834696 0.996510i \(-0.473400\pi\)
0.966877 0.255244i \(-0.0821557\pi\)
\(350\) 0.930174 + 1.67526i 0.0497199 + 0.0895463i
\(351\) 0 0
\(352\) 12.9926 18.6969i 0.692506 0.996548i
\(353\) 8.90806 10.6162i 0.474128 0.565044i −0.474979 0.879997i \(-0.657544\pi\)
0.949107 + 0.314953i \(0.101989\pi\)
\(354\) 0 0
\(355\) −2.66780 15.1298i −0.141592 0.803008i
\(356\) −15.2585 19.4727i −0.808701 1.03205i
\(357\) 0 0
\(358\) 19.2900 6.65750i 1.01951 0.351860i
\(359\) 9.49643 16.4483i 0.501202 0.868108i −0.498797 0.866719i \(-0.666225\pi\)
0.999999 0.00138897i \(-0.000442121\pi\)
\(360\) 0 0
\(361\) −11.4957 19.9112i −0.605039 1.04796i
\(362\) 21.8374 + 18.9556i 1.14775 + 0.996284i
\(363\) 0 0
\(364\) −0.0970827 0.683699i −0.00508852 0.0358355i
\(365\) −21.2237 + 17.8088i −1.11090 + 0.932156i
\(366\) 0 0
\(367\) 6.89218 + 18.9361i 0.359769 + 0.988456i 0.979109 + 0.203334i \(0.0651777\pi\)
−0.619341 + 0.785122i \(0.712600\pi\)
\(368\) 17.6449 26.3213i 0.919801 1.37209i
\(369\) 0 0
\(370\) −8.56559 0.143400i −0.445304 0.00745499i
\(371\) 1.88561 + 0.332485i 0.0978962 + 0.0172617i
\(372\) 0 0
\(373\) −4.70270 + 12.9206i −0.243496 + 0.669001i 0.756393 + 0.654118i \(0.226960\pi\)
−0.999889 + 0.0148833i \(0.995262\pi\)
\(374\) 6.51409 + 8.03251i 0.336836 + 0.415351i
\(375\) 0 0
\(376\) 5.80613 6.25310i 0.299429 0.322479i
\(377\) 6.87469i 0.354065i
\(378\) 0 0
\(379\) −23.0899 −1.18605 −0.593026 0.805184i \(-0.702067\pi\)
−0.593026 + 0.805184i \(0.702067\pi\)
\(380\) −42.1376 + 13.7579i −2.16161 + 0.705763i
\(381\) 0 0
\(382\) 18.5496 + 22.8735i 0.949081 + 1.17031i
\(383\) −1.72830 0.629049i −0.0883119 0.0321429i 0.297486 0.954726i \(-0.403852\pi\)
−0.385798 + 0.922583i \(0.626074\pi\)
\(384\) 0 0
\(385\) 0.483562 2.74241i 0.0246446 0.139766i
\(386\) −0.134836 + 8.05406i −0.00686296 + 0.409941i
\(387\) 0 0
\(388\) −17.5347 0.587274i −0.890190 0.0298143i
\(389\) −27.9217 + 10.1627i −1.41569 + 0.515268i −0.932794 0.360411i \(-0.882636\pi\)
−0.482894 + 0.875679i \(0.660414\pi\)
\(390\) 0 0
\(391\) 9.25214 + 11.0263i 0.467901 + 0.557623i
\(392\) −11.8793 15.6943i −0.599995 0.792684i
\(393\) 0 0
\(394\) −24.8494 + 28.6272i −1.25189 + 1.44222i
\(395\) 1.75521 1.01337i 0.0883140 0.0509881i
\(396\) 0 0
\(397\) −13.2935 7.67501i −0.667182 0.385198i 0.127826 0.991797i \(-0.459200\pi\)
−0.795008 + 0.606599i \(0.792533\pi\)
\(398\) 34.4063 11.8745i 1.72463 0.595214i
\(399\) 0 0
\(400\) 2.87654 + 26.6369i 0.143827 + 1.33185i
\(401\) −16.6682 + 2.93905i −0.832368 + 0.146769i −0.573564 0.819161i \(-0.694440\pi\)
−0.258804 + 0.965930i \(0.583328\pi\)
\(402\) 0 0
\(403\) 9.97375 + 8.36897i 0.496828 + 0.416888i
\(404\) 10.9489 17.5777i 0.544730 0.874525i
\(405\) 0 0
\(406\) −0.559349 1.00740i −0.0277600 0.0499963i
\(407\) 5.46074 + 4.58210i 0.270679 + 0.227126i
\(408\) 0 0
\(409\) 0.249722 + 1.41624i 0.0123480 + 0.0700287i 0.990359 0.138524i \(-0.0442358\pi\)
−0.978011 + 0.208553i \(0.933125\pi\)
\(410\) 7.81914 + 49.1412i 0.386160 + 2.42691i
\(411\) 0 0
\(412\) −8.67269 + 9.65968i −0.427273 + 0.475898i
\(413\) −0.363977 + 0.630426i −0.0179101 + 0.0310212i
\(414\) 0 0
\(415\) 36.9776 21.3490i 1.81516 1.04798i
\(416\) 2.46570 9.33519i 0.120891 0.457695i
\(417\) 0 0
\(418\) 34.4442 + 13.1937i 1.68472 + 0.645324i
\(419\) 17.2769 + 20.5898i 0.844029 + 1.00588i 0.999836 + 0.0180876i \(0.00575778\pi\)
−0.155807 + 0.987788i \(0.549798\pi\)
\(420\) 0 0
\(421\) −13.1300 36.0744i −0.639917 1.75816i −0.651986 0.758231i \(-0.726064\pi\)
0.0120688 0.999927i \(-0.496158\pi\)
\(422\) −2.87023 1.72182i −0.139720 0.0838169i
\(423\) 0 0
\(424\) 22.4835 + 14.5326i 1.09189 + 0.705765i
\(425\) −11.9847 2.11323i −0.581345 0.102507i
\(426\) 0 0
\(427\) 1.56936 + 0.571201i 0.0759467 + 0.0276424i
\(428\) −1.68751 + 4.19396i −0.0815691 + 0.202723i
\(429\) 0 0
\(430\) 17.5815 + 3.40448i 0.847856 + 0.164179i
\(431\) 7.70543 0.371157 0.185579 0.982629i \(-0.440584\pi\)
0.185579 + 0.982629i \(0.440584\pi\)
\(432\) 0 0
\(433\) −18.8564 −0.906183 −0.453091 0.891464i \(-0.649679\pi\)
−0.453091 + 0.891464i \(0.649679\pi\)
\(434\) −2.14245 0.414864i −0.102841 0.0199141i
\(435\) 0 0
\(436\) 2.24459 5.57845i 0.107496 0.267159i
\(437\) 48.2399 + 17.5579i 2.30763 + 0.839907i
\(438\) 0 0
\(439\) 16.3164 + 2.87702i 0.778738 + 0.137313i 0.548868 0.835909i \(-0.315059\pi\)
0.229870 + 0.973221i \(0.426170\pi\)
\(440\) 21.1360 32.6996i 1.00762 1.55889i
\(441\) 0 0
\(442\) 3.76092 + 2.25614i 0.178889 + 0.107314i
\(443\) 2.23622 + 6.14396i 0.106246 + 0.291908i 0.981411 0.191915i \(-0.0614699\pi\)
−0.875166 + 0.483824i \(0.839248\pi\)
\(444\) 0 0
\(445\) −27.1939 32.4084i −1.28911 1.53631i
\(446\) −26.4527 10.1326i −1.25257 0.479792i
\(447\) 0 0
\(448\) 0.398228 + 1.56857i 0.0188145 + 0.0741079i
\(449\) −9.04053 + 5.21955i −0.426649 + 0.246326i −0.697918 0.716178i \(-0.745890\pi\)
0.271269 + 0.962504i \(0.412557\pi\)
\(450\) 0 0
\(451\) 20.7026 35.8579i 0.974846 1.68848i
\(452\) −7.52456 + 8.38089i −0.353925 + 0.394204i
\(453\) 0 0
\(454\) 5.72507 + 35.9805i 0.268691 + 1.68865i
\(455\) −0.205066 1.16299i −0.00961366 0.0545218i
\(456\) 0 0
\(457\) 20.6728 + 17.3466i 0.967034 + 0.811438i 0.982083 0.188449i \(-0.0603460\pi\)
−0.0150490 + 0.999887i \(0.504790\pi\)
\(458\) −1.53196 2.75909i −0.0715840 0.128924i
\(459\) 0 0
\(460\) 28.6511 45.9972i 1.33586 2.14463i
\(461\) 3.79701 + 3.18607i 0.176844 + 0.148390i 0.726913 0.686729i \(-0.240954\pi\)
−0.550069 + 0.835119i \(0.685399\pi\)
\(462\) 0 0
\(463\) −2.96473 + 0.522762i −0.137783 + 0.0242948i −0.242114 0.970248i \(-0.577841\pi\)
0.104331 + 0.994543i \(0.466730\pi\)
\(464\) −1.72977 16.0178i −0.0803028 0.743608i
\(465\) 0 0
\(466\) 11.4829 3.96305i 0.531935 0.183585i
\(467\) 29.0602 + 16.7779i 1.34475 + 0.776390i 0.987500 0.157620i \(-0.0503822\pi\)
0.357247 + 0.934010i \(0.383716\pi\)
\(468\) 0 0
\(469\) −0.289241 + 0.166993i −0.0133559 + 0.00771104i
\(470\) 9.56564 11.0199i 0.441230 0.508309i
\(471\) 0 0
\(472\) −8.11555 + 6.14279i −0.373548 + 0.282745i
\(473\) −9.57848 11.4152i −0.440419 0.524871i
\(474\) 0 0
\(475\) −40.7858 + 14.8448i −1.87138 + 0.681126i
\(476\) −0.734681 0.0246060i −0.0336741 0.00112782i
\(477\) 0 0
\(478\) 0.0346723 2.07106i 0.00158587 0.0947279i
\(479\) −2.69060 + 15.2592i −0.122937 + 0.697208i 0.859575 + 0.511009i \(0.170728\pi\)
−0.982512 + 0.186199i \(0.940383\pi\)
\(480\) 0 0
\(481\) 2.84070 + 1.03393i 0.129525 + 0.0471432i
\(482\) 1.79849 + 2.21771i 0.0819188 + 0.101014i
\(483\) 0 0
\(484\) −9.88524 + 3.22751i −0.449329 + 0.146705i
\(485\) −30.0031 −1.36237
\(486\) 0 0
\(487\) 42.9742i 1.94735i 0.227945 + 0.973674i \(0.426799\pi\)
−0.227945 + 0.973674i \(0.573201\pi\)
\(488\) 17.1119 + 15.8887i 0.774618 + 0.719249i
\(489\) 0 0
\(490\) −21.2020 26.1441i −0.957807 1.18107i
\(491\) 4.27635 11.7492i 0.192989 0.530233i −0.805024 0.593243i \(-0.797848\pi\)
0.998013 + 0.0630092i \(0.0200697\pi\)
\(492\) 0 0
\(493\) 7.20689 + 1.27077i 0.324582 + 0.0572325i
\(494\) 15.6397 + 0.261829i 0.703661 + 0.0117802i
\(495\) 0 0
\(496\) −25.3443 16.9899i −1.13799 0.762869i
\(497\) −0.310783 0.853868i −0.0139405 0.0383012i
\(498\) 0 0
\(499\) 0.451535 0.378883i 0.0202135 0.0169611i −0.632625 0.774458i \(-0.718023\pi\)
0.652838 + 0.757497i \(0.273578\pi\)
\(500\) 1.63287 + 11.4994i 0.0730244 + 0.514270i
\(501\) 0 0
\(502\) 0.0241609 + 0.0209725i 0.00107835 + 0.000936047i
\(503\) −5.40120 9.35516i −0.240828 0.417126i 0.720123 0.693847i \(-0.244086\pi\)
−0.960950 + 0.276721i \(0.910752\pi\)
\(504\) 0 0
\(505\) 17.7072 30.6698i 0.787961 1.36479i
\(506\) −42.6253 + 14.7111i −1.89492 + 0.653988i
\(507\) 0 0
\(508\) −13.6876 17.4679i −0.607288 0.775011i
\(509\) −4.10539 23.2828i −0.181968 1.03199i −0.929789 0.368093i \(-0.880011\pi\)
0.747821 0.663901i \(-0.231100\pi\)
\(510\) 0 0
\(511\) −1.05331 + 1.25529i −0.0465958 + 0.0555307i
\(512\) −3.39612 + 22.3711i −0.150089 + 0.988673i
\(513\) 0 0
\(514\) 11.3066 + 20.3633i 0.498711 + 0.898187i
\(515\) −14.2700 + 17.0064i −0.628812 + 0.749389i
\(516\) 0 0
\(517\) −11.9580 + 2.10852i −0.525912 + 0.0927325i
\(518\) −0.500393 + 0.0796204i −0.0219860 + 0.00349832i
\(519\) 0 0
\(520\) 3.67988 16.0964i 0.161374 0.705875i
\(521\) −29.7943 17.2017i −1.30531 0.753622i −0.324002 0.946056i \(-0.605028\pi\)
−0.981310 + 0.192434i \(0.938362\pi\)
\(522\) 0 0
\(523\) 15.1865 + 26.3038i 0.664059 + 1.15018i 0.979539 + 0.201252i \(0.0645011\pi\)
−0.315480 + 0.948932i \(0.602166\pi\)
\(524\) −14.4315 3.04600i −0.630444 0.133065i
\(525\) 0 0
\(526\) 2.99375 7.81566i 0.130534 0.340779i
\(527\) 10.6170 8.90871i 0.462483 0.388070i
\(528\) 0 0
\(529\) −37.3617 + 13.5985i −1.62442 + 0.591241i
\(530\) 39.2596 + 23.5514i 1.70533 + 1.02301i
\(531\) 0 0
\(532\) −2.31309 + 1.23413i −0.100285 + 0.0535063i
\(533\) 3.04907 17.2921i 0.132070 0.749005i
\(534\) 0 0
\(535\) −2.64415 + 7.26473i −0.114316 + 0.314082i
\(536\) −4.63375 + 0.579024i −0.200148 + 0.0250100i
\(537\) 0 0
\(538\) −6.92456 1.34087i −0.298539 0.0578091i
\(539\) 28.0092i 1.20644i
\(540\) 0 0
\(541\) 4.15389i 0.178590i −0.996005 0.0892948i \(-0.971539\pi\)
0.996005 0.0892948i \(-0.0284613\pi\)
\(542\) −1.89144 + 9.76782i −0.0812443 + 0.419564i
\(543\) 0 0
\(544\) −9.33050 4.31043i −0.400042 0.184808i
\(545\) 3.51702 9.66293i 0.150652 0.413914i
\(546\) 0 0
\(547\) 2.83365 16.0704i 0.121158 0.687122i −0.862358 0.506300i \(-0.831013\pi\)
0.983516 0.180823i \(-0.0578760\pi\)
\(548\) −20.4809 + 10.9274i −0.874900 + 0.466795i
\(549\) 0 0
\(550\) 19.6124 32.6933i 0.836274 1.39404i
\(551\) 24.5260 8.92675i 1.04484 0.380292i
\(552\) 0 0
\(553\) 0.0918277 0.0770526i 0.00390491 0.00327661i
\(554\) 30.1490 + 11.5484i 1.28091 + 0.490646i
\(555\) 0 0
\(556\) −3.25956 + 15.4434i −0.138236 + 0.654945i
\(557\) −14.8098 25.6513i −0.627511 1.08688i −0.988049 0.154137i \(-0.950740\pi\)
0.360538 0.932745i \(-0.382593\pi\)
\(558\) 0 0
\(559\) −5.47271 3.15967i −0.231471 0.133640i
\(560\) 0.770424 + 2.65813i 0.0325563 + 0.112327i
\(561\) 0 0
\(562\) −5.44738 34.2353i −0.229784 1.44413i
\(563\) −22.0013 + 3.87943i −0.927246 + 0.163498i −0.616824 0.787101i \(-0.711581\pi\)
−0.310421 + 0.950599i \(0.600470\pi\)
\(564\) 0 0
\(565\) −12.3809 + 14.7550i −0.520868 + 0.620746i
\(566\) −13.4198 + 7.45122i −0.564075 + 0.313198i
\(567\) 0 0
\(568\) 0.637766 12.6889i 0.0267601 0.532416i
\(569\) 1.10991 1.32274i 0.0465299 0.0554522i −0.742278 0.670093i \(-0.766254\pi\)
0.788807 + 0.614640i \(0.210699\pi\)
\(570\) 0 0
\(571\) 2.73361 + 15.5031i 0.114398 + 0.648783i 0.987047 + 0.160434i \(0.0512894\pi\)
−0.872649 + 0.488349i \(0.837599\pi\)
\(572\) −10.8148 + 8.47434i −0.452190 + 0.354330i
\(573\) 0 0
\(574\) 0.960147 + 2.78202i 0.0400758 + 0.116119i
\(575\) 26.5309 45.9528i 1.10641 1.91637i
\(576\) 0 0
\(577\) 9.83883 + 17.0414i 0.409596 + 0.709441i 0.994844 0.101413i \(-0.0323364\pi\)
−0.585248 + 0.810854i \(0.699003\pi\)
\(578\) −12.6994 + 14.6301i −0.528226 + 0.608531i
\(579\) 0 0
\(580\) −3.87336 27.2779i −0.160833 1.13265i
\(581\) 1.93457 1.62330i 0.0802594 0.0673456i
\(582\) 0 0
\(583\) −13.0294 35.7981i −0.539624 1.48260i
\(584\) −20.3922 + 10.4454i −0.843834 + 0.432233i
\(585\) 0 0
\(586\) 0.388135 23.1842i 0.0160337 0.957731i
\(587\) 1.96505 + 0.346492i 0.0811063 + 0.0143012i 0.214054 0.976822i \(-0.431333\pi\)
−0.132948 + 0.991123i \(0.542444\pi\)
\(588\) 0 0
\(589\) 16.9061 46.4492i 0.696605 1.91391i
\(590\) −13.5191 + 10.9635i −0.556573 + 0.451362i
\(591\) 0 0
\(592\) −6.87890 1.69427i −0.282721 0.0696339i
\(593\) 21.4365i 0.880291i −0.897927 0.440145i \(-0.854927\pi\)
0.897927 0.440145i \(-0.145073\pi\)
\(594\) 0 0
\(595\) −1.25709 −0.0515358
\(596\) 13.3749 4.36688i 0.547858 0.178875i
\(597\) 0 0
\(598\) −14.8525 + 12.0448i −0.607362 + 0.492550i
\(599\) 39.6839 + 14.4438i 1.62144 + 0.590156i 0.983656 0.180059i \(-0.0576288\pi\)
0.637785 + 0.770215i \(0.279851\pi\)
\(600\) 0 0
\(601\) −3.07096 + 17.4163i −0.125267 + 0.710424i 0.855882 + 0.517171i \(0.173015\pi\)
−0.981149 + 0.193253i \(0.938096\pi\)
\(602\) 1.05904 + 0.0177297i 0.0431631 + 0.000722609i
\(603\) 0 0
\(604\) 0.419615 12.5288i 0.0170739 0.509789i
\(605\) −16.7107 + 6.08218i −0.679385 + 0.247276i
\(606\) 0 0
\(607\) 25.0286 + 29.8279i 1.01588 + 1.21068i 0.977395 + 0.211420i \(0.0678087\pi\)
0.0384848 + 0.999259i \(0.487747\pi\)
\(608\) −36.5058 + 3.32511i −1.48050 + 0.134851i
\(609\) 0 0
\(610\) 30.1564 + 26.1768i 1.22100 + 1.05987i
\(611\) −4.45944 + 2.57466i −0.180410 + 0.104160i
\(612\) 0 0
\(613\) −2.98975 1.72613i −0.120755 0.0697178i 0.438406 0.898777i \(-0.355543\pi\)
−0.559161 + 0.829059i \(0.688877\pi\)
\(614\) 6.72780 + 19.4937i 0.271512 + 0.786704i
\(615\) 0 0
\(616\) 0.895268 2.12173i 0.0360714 0.0854871i
\(617\) −3.45250 + 0.608769i −0.138992 + 0.0245081i −0.242711 0.970099i \(-0.578037\pi\)
0.103719 + 0.994607i \(0.466926\pi\)
\(618\) 0 0
\(619\) −5.42408 4.55134i −0.218012 0.182934i 0.527241 0.849716i \(-0.323227\pi\)
−0.745253 + 0.666782i \(0.767671\pi\)
\(620\) −44.2898 27.5876i −1.77872 1.10794i
\(621\) 0 0
\(622\) −29.1273 + 16.1727i −1.16790 + 0.648466i
\(623\) −1.91682 1.60840i −0.0767956 0.0644391i
\(624\) 0 0
\(625\) −2.36634 13.4202i −0.0946535 0.536807i
\(626\) 6.35052 1.01047i 0.253818 0.0403864i
\(627\) 0 0
\(628\) 6.65598 7.41346i 0.265602 0.295829i
\(629\) 1.60899 2.78685i 0.0641546 0.111119i
\(630\) 0 0
\(631\) −6.49028 + 3.74717i −0.258374 + 0.149172i −0.623593 0.781749i \(-0.714328\pi\)
0.365219 + 0.930922i \(0.380994\pi\)
\(632\) 1.60176 0.493460i 0.0637147 0.0196288i
\(633\) 0 0
\(634\) −5.41706 + 14.1421i −0.215139 + 0.561653i
\(635\) −24.3941 29.0718i −0.968051 1.15368i
\(636\) 0 0
\(637\) 4.06252 + 11.1617i 0.160963 + 0.442242i
\(638\) −11.7937 + 19.6597i −0.466916 + 0.778335i
\(639\) 0 0
\(640\) −4.52391 + 38.4301i −0.178823 + 1.51908i
\(641\) −21.3252 3.76021i −0.842295 0.148519i −0.264178 0.964474i \(-0.585101\pi\)
−0.578116 + 0.815955i \(0.696212\pi\)
\(642\) 0 0
\(643\) −22.2522 8.09915i −0.877543 0.319399i −0.136325 0.990664i \(-0.543529\pi\)
−0.741218 + 0.671265i \(0.765751\pi\)
\(644\) 1.19642 2.97346i 0.0471457 0.117171i
\(645\) 0 0
\(646\) 3.16543 16.3470i 0.124542 0.643163i
\(647\) −18.8024 −0.739198 −0.369599 0.929191i \(-0.620505\pi\)
−0.369599 + 0.929191i \(0.620505\pi\)
\(648\) 0 0
\(649\) 14.4836 0.568530
\(650\) 3.07363 15.8729i 0.120558 0.622586i
\(651\) 0 0
\(652\) 12.1166 + 4.87532i 0.474522 + 0.190932i
\(653\) 10.1057 + 3.67818i 0.395467 + 0.143938i 0.532096 0.846684i \(-0.321405\pi\)
−0.136629 + 0.990622i \(0.543627\pi\)
\(654\) 0 0
\(655\) −24.8401 4.37998i −0.970582 0.171140i
\(656\) −2.75328 + 41.0573i −0.107497 + 1.60302i
\(657\) 0 0
\(658\) 0.443990 0.740119i 0.0173085 0.0288528i
\(659\) −8.25777 22.6880i −0.321677 0.883800i −0.990143 0.140058i \(-0.955271\pi\)
0.668466 0.743742i \(-0.266951\pi\)
\(660\) 0 0
\(661\) 1.20921 + 1.44108i 0.0470329 + 0.0560516i 0.789048 0.614331i \(-0.210574\pi\)
−0.742015 + 0.670383i \(0.766130\pi\)
\(662\) −7.37403 + 19.2511i −0.286600 + 0.748213i
\(663\) 0 0
\(664\) 33.7450 10.3959i 1.30956 0.403439i
\(665\) −3.88279 + 2.24173i −0.150568 + 0.0869305i
\(666\) 0 0
\(667\) −15.9540 + 27.6332i −0.617743 + 1.06996i
\(668\) −18.2386 16.3751i −0.705674 0.633571i
\(669\) 0 0
\(670\) −7.88665 + 1.25489i −0.304688 + 0.0484807i
\(671\) −5.77005 32.7236i −0.222750 1.26328i
\(672\) 0 0
\(673\) −20.7393 17.4023i −0.799439 0.670809i 0.148623 0.988894i \(-0.452516\pi\)
−0.948062 + 0.318085i \(0.896960\pi\)
\(674\) 31.1455 17.2933i 1.19968 0.666113i
\(675\) 0 0
\(676\) 10.6659 17.1233i 0.410225 0.658587i
\(677\) −18.1567 15.2353i −0.697820 0.585540i 0.223333 0.974742i \(-0.428306\pi\)
−0.921153 + 0.389202i \(0.872751\pi\)
\(678\) 0 0
\(679\) −1.74759 + 0.308148i −0.0670665 + 0.0118256i
\(680\) −16.1940 6.83308i −0.621012 0.262037i
\(681\) 0 0
\(682\) 14.1650 + 41.0431i 0.542407 + 1.57162i
\(683\) −18.0209 10.4044i −0.689551 0.398113i 0.113893 0.993493i \(-0.463668\pi\)
−0.803444 + 0.595380i \(0.797001\pi\)
\(684\) 0 0
\(685\) −34.3795 + 19.8490i −1.31357 + 0.758392i
\(686\) −3.01577 2.61779i −0.115143 0.0999478i
\(687\) 0 0
\(688\) 13.5463 + 5.98492i 0.516447 + 0.228173i
\(689\) −10.3845 12.3757i −0.395617 0.471478i
\(690\) 0 0
\(691\) 17.7551 6.46235i 0.675438 0.245839i 0.0185503 0.999828i \(-0.494095\pi\)
0.656887 + 0.753989i \(0.271873\pi\)
\(692\) 48.7775 + 1.63366i 1.85424 + 0.0621024i
\(693\) 0 0
\(694\) 12.5200 + 0.209601i 0.475251 + 0.00795635i
\(695\) −4.68707 + 26.5817i −0.177791 + 1.00830i
\(696\) 0 0
\(697\) −17.5641 6.39281i −0.665288 0.242145i
\(698\) 33.5308 27.1924i 1.26916 1.02925i
\(699\) 0 0
\(700\) 0.841074 + 2.57605i 0.0317896 + 0.0973654i
\(701\) −7.59328 −0.286794 −0.143397 0.989665i \(-0.545803\pi\)
−0.143397 + 0.989665i \(0.545803\pi\)
\(702\) 0 0
\(703\) 11.4770i 0.432864i
\(704\) 23.0659 22.4661i 0.869329 0.846723i
\(705\) 0 0
\(706\) 15.2224 12.3448i 0.572901 0.464603i
\(707\) 0.716398 1.96829i 0.0269429 0.0740251i
\(708\) 0 0
\(709\) −47.1054 8.30595i −1.76908 0.311937i −0.808202 0.588906i \(-0.799559\pi\)
−0.960879 + 0.276969i \(0.910670\pi\)
\(710\) 0.363687 21.7239i 0.0136489 0.815282i
\(711\) 0 0
\(712\) −15.9500 31.1387i −0.597751 1.16697i
\(713\) 20.6682 + 56.7855i 0.774032 + 2.12663i
\(714\) 0 0
\(715\) −17.9991 + 15.1030i −0.673128 + 0.564821i
\(716\) 28.5726 4.05721i 1.06781 0.151625i
\(717\) 0 0
\(718\) 17.6073 20.2840i 0.657097 0.756994i
\(719\) −3.52716 6.10922i −0.131541 0.227835i 0.792730 0.609573i \(-0.208659\pi\)
−0.924271 + 0.381738i \(0.875326\pi\)
\(720\) 0 0
\(721\) −0.656522 + 1.13713i −0.0244502 + 0.0423489i
\(722\) −10.6077 30.7359i −0.394779 1.14387i
\(723\) 0 0
\(724\) 25.2232 + 32.1894i 0.937413 + 1.19631i
\(725\) −4.68461 26.5677i −0.173982 0.986701i
\(726\) 0 0
\(727\) −18.2911 + 21.7985i −0.678380 + 0.808462i −0.989898 0.141778i \(-0.954718\pi\)
0.311518 + 0.950240i \(0.399163\pi\)
\(728\) 0.0490234 0.975364i 0.00181693 0.0361494i
\(729\) 0 0
\(730\) −34.2555 + 19.0201i −1.26785 + 0.703965i
\(731\) −4.32397 + 5.15310i −0.159928 + 0.190594i
\(732\) 0 0
\(733\) 14.2179 2.50701i 0.525152 0.0925984i 0.0952137 0.995457i \(-0.469647\pi\)
0.429938 + 0.902858i \(0.358535\pi\)
\(734\) 4.47821 + 28.1443i 0.165294 + 1.03883i
\(735\) 0 0
\(736\) 31.5751 31.8012i 1.16387 1.17221i
\(737\) 5.75483 + 3.32255i 0.211982 + 0.122388i
\(738\) 0 0
\(739\) −7.63499 13.2242i −0.280858 0.486460i 0.690738 0.723105i \(-0.257286\pi\)
−0.971596 + 0.236645i \(0.923952\pi\)
\(740\) −11.8541 2.50199i −0.435765 0.0919751i
\(741\) 0 0
\(742\) 2.52864 + 0.968585i 0.0928293 + 0.0355579i
\(743\) −9.41012 + 7.89602i −0.345224 + 0.289677i −0.798869 0.601505i \(-0.794568\pi\)
0.453645 + 0.891182i \(0.350123\pi\)
\(744\) 0 0
\(745\) 22.6098 8.22931i 0.828360 0.301498i
\(746\) −10.0031 + 16.6749i −0.366239 + 0.610510i
\(747\) 0 0
\(748\) 6.88474 + 12.9039i 0.251731 + 0.471812i
\(749\) −0.0794011 + 0.450306i −0.00290125 + 0.0164538i
\(750\) 0 0
\(751\) 8.22636 22.6017i 0.300184 0.824749i −0.694283 0.719702i \(-0.744278\pi\)
0.994467 0.105047i \(-0.0334993\pi\)
\(752\) 9.74254 7.12094i 0.355274 0.259674i
\(753\) 0 0
\(754\) −1.84829 + 9.54498i −0.0673107 + 0.347608i
\(755\) 21.4376i 0.780196i
\(756\) 0 0
\(757\) 2.57077i 0.0934361i −0.998908 0.0467180i \(-0.985124\pi\)
0.998908 0.0467180i \(-0.0148762\pi\)
\(758\) −32.0586 6.20783i −1.16442 0.225478i
\(759\) 0 0
\(760\) −62.2037 + 7.77284i −2.25636 + 0.281951i
\(761\) 8.41063 23.1080i 0.304885 0.837665i −0.688748 0.725001i \(-0.741839\pi\)
0.993633 0.112664i \(-0.0359384\pi\)
\(762\) 0 0
\(763\) 0.105613 0.598958i 0.00382343 0.0216837i
\(764\) 19.6051 + 36.7452i 0.709287 + 1.32939i
\(765\) 0 0
\(766\) −2.23049 1.33805i −0.0805908 0.0483456i
\(767\) 5.77171 2.10073i 0.208404 0.0758530i
\(768\) 0 0
\(769\) 17.5940 14.7631i 0.634455 0.532371i −0.267855 0.963459i \(-0.586315\pi\)
0.902310 + 0.431088i \(0.141870\pi\)
\(770\) 1.40870 3.67762i 0.0507659 0.132532i
\(771\) 0 0
\(772\) −2.35257 + 11.1462i −0.0846710 + 0.401160i
\(773\) 1.98617 + 3.44015i 0.0714375 + 0.123733i 0.899532 0.436856i \(-0.143908\pi\)
−0.828094 + 0.560589i \(0.810575\pi\)
\(774\) 0 0
\(775\) −44.2471 25.5461i −1.58940 0.917642i
\(776\) −24.1877 5.52966i −0.868287 0.198503i
\(777\) 0 0
\(778\) −41.4994 + 6.60322i −1.48783 + 0.236737i
\(779\) −65.6503 + 11.5759i −2.35217 + 0.414751i
\(780\) 0 0
\(781\) −11.6210 + 13.8494i −0.415833 + 0.495571i
\(782\) 9.88143 + 17.7966i 0.353359 + 0.636405i
\(783\) 0 0
\(784\) −12.2740 24.9842i −0.438357 0.892292i
\(785\) 10.9517 13.0518i 0.390884 0.465837i
\(786\) 0 0
\(787\) 2.43923 + 13.8335i 0.0869490 + 0.493112i 0.996919 + 0.0784382i \(0.0249933\pi\)
−0.909970 + 0.414674i \(0.863896\pi\)
\(788\) −42.1980 + 33.0657i −1.50324 + 1.17792i
\(789\) 0 0
\(790\) 2.70942 0.935090i 0.0963967 0.0332690i
\(791\) −0.569609 + 0.986591i −0.0202529 + 0.0350791i
\(792\) 0 0
\(793\) −7.04567 12.2035i −0.250199 0.433358i
\(794\) −16.3936 14.2302i −0.581785 0.505010i
\(795\) 0 0
\(796\) 50.9629 7.23655i 1.80633 0.256493i
\(797\) −18.0786 + 15.1698i −0.640378 + 0.537341i −0.904134 0.427248i \(-0.859483\pi\)
0.263756 + 0.964589i \(0.415039\pi\)
\(798\) 0 0
\(799\) 1.87476 + 5.15085i 0.0663241 + 0.182224i
\(800\) −3.16760 + 37.7567i −0.111991 + 1.33490i
\(801\) 0 0
\(802\) −23.9326 0.400665i −0.845090 0.0141480i
\(803\) 32.1080 + 5.66151i 1.13307 + 0.199790i
\(804\) 0 0
\(805\) 1.87466 5.15060i 0.0660732 0.181535i
\(806\) 11.5977 + 14.3011i 0.408513 + 0.503736i
\(807\) 0 0
\(808\) 19.9276 21.4617i 0.701050 0.755018i
\(809\) 30.1592i 1.06034i −0.847891 0.530170i \(-0.822128\pi\)
0.847891 0.530170i \(-0.177872\pi\)
\(810\) 0 0
\(811\) −19.2303 −0.675266 −0.337633 0.941278i \(-0.609626\pi\)
−0.337633 + 0.941278i \(0.609626\pi\)
\(812\) −0.505770 1.54908i −0.0177491 0.0543619i
\(813\) 0 0
\(814\) 6.34990 + 7.83004i 0.222564 + 0.274443i
\(815\) 20.9882 + 7.63909i 0.735185 + 0.267586i
\(816\) 0 0
\(817\) −4.16611 + 23.6272i −0.145754 + 0.826610i
\(818\) −0.0340433 + 2.03348i −0.00119029 + 0.0710991i
\(819\) 0 0
\(820\) −2.35553 + 70.3309i −0.0822587 + 2.45606i
\(821\) −4.28889 + 1.56103i −0.149683 + 0.0544802i −0.415775 0.909467i \(-0.636490\pi\)
0.266092 + 0.963948i \(0.414267\pi\)
\(822\) 0 0
\(823\) −9.86833 11.7606i −0.343988 0.409949i 0.566118 0.824324i \(-0.308445\pi\)
−0.910106 + 0.414375i \(0.864000\pi\)
\(824\) −14.6384 + 11.0800i −0.509953 + 0.385991i
\(825\) 0 0
\(826\) −0.674846 + 0.777441i −0.0234809 + 0.0270506i
\(827\) −30.5131 + 17.6168i −1.06104 + 0.612594i −0.925721 0.378207i \(-0.876541\pi\)
−0.135324 + 0.990801i \(0.543207\pi\)
\(828\) 0 0
\(829\) 32.1764 + 18.5771i 1.11753 + 0.645208i 0.940770 0.339045i \(-0.110104\pi\)
0.176763 + 0.984253i \(0.443437\pi\)
\(830\) 57.0803 19.6999i 1.98129 0.683793i
\(831\) 0 0
\(832\) 5.93323 12.2983i 0.205698 0.426366i
\(833\) 12.4520 2.19562i 0.431435 0.0760737i
\(834\) 0 0
\(835\) −32.1100 26.9435i −1.11121 0.932418i
\(836\) 44.2759 + 27.5789i 1.53131 + 0.953835i
\(837\) 0 0
\(838\) 18.4519 + 33.2322i 0.637411 + 1.14799i
\(839\) 12.7067 + 10.6622i 0.438683 + 0.368099i 0.835216 0.549921i \(-0.185342\pi\)
−0.396533 + 0.918020i \(0.629787\pi\)
\(840\) 0 0
\(841\) −2.21876 12.5832i −0.0765090 0.433904i
\(842\) −8.53125 53.6166i −0.294006 1.84775i
\(843\) 0 0
\(844\) −3.52217 3.16229i −0.121238 0.108850i
\(845\) 17.2494 29.8769i 0.593398 1.02779i
\(846\) 0 0
\(847\) −0.910879 + 0.525896i −0.0312982 + 0.0180700i
\(848\) 27.3094 + 26.2222i 0.937808 + 0.900473i
\(849\) 0 0
\(850\) −16.0717 6.15621i −0.551256 0.211156i
\(851\) 9.01893 + 10.7483i 0.309165 + 0.368449i
\(852\) 0 0
\(853\) −6.77920 18.6257i −0.232115 0.637732i 0.767880 0.640593i \(-0.221311\pi\)
−0.999996 + 0.00286126i \(0.999089\pi\)
\(854\) 2.02537 + 1.21500i 0.0693067 + 0.0415764i
\(855\) 0 0
\(856\) −3.47055 + 5.36930i −0.118621 + 0.183519i
\(857\) 17.6147 + 3.10595i 0.601708 + 0.106097i 0.466201 0.884679i \(-0.345623\pi\)
0.135507 + 0.990776i \(0.456734\pi\)
\(858\) 0 0
\(859\) 7.25730 + 2.64144i 0.247616 + 0.0901249i 0.462847 0.886438i \(-0.346828\pi\)
−0.215231 + 0.976563i \(0.569050\pi\)
\(860\) 23.4953 + 9.45373i 0.801182 + 0.322369i
\(861\) 0 0
\(862\) 10.6984 + 2.07164i 0.364389 + 0.0705602i
\(863\) −8.69446 −0.295963 −0.147981 0.988990i \(-0.547278\pi\)
−0.147981 + 0.988990i \(0.547278\pi\)
\(864\) 0 0
\(865\) 83.4618 2.83779
\(866\) −26.1807 5.06963i −0.889657 0.172273i
\(867\) 0 0
\(868\) −2.86309 1.15201i −0.0971796 0.0391019i
\(869\) −2.24118 0.815725i −0.0760270 0.0276716i
\(870\) 0 0
\(871\) 2.77521 + 0.489344i 0.0940344 + 0.0165808i
\(872\) 4.61622 7.14178i 0.156325 0.241851i
\(873\) 0 0
\(874\) 62.2568 + 37.3472i 2.10587 + 1.26329i
\(875\) 0.401800 + 1.10394i 0.0135833 + 0.0373198i
\(876\) 0 0
\(877\) 27.2022 + 32.4183i 0.918553 + 1.09469i 0.995223 + 0.0976318i \(0.0311268\pi\)
−0.0766700 + 0.997057i \(0.524429\pi\)
\(878\) 21.8805 + 8.38124i 0.738432 + 0.282853i
\(879\) 0 0
\(880\) 38.1372 39.7184i 1.28560 1.33891i
\(881\) −23.5185 + 13.5784i −0.792359 + 0.457468i −0.840792 0.541358i \(-0.817910\pi\)
0.0484336 + 0.998826i \(0.484577\pi\)
\(882\) 0 0
\(883\) 4.48989 7.77672i 0.151097 0.261707i −0.780534 0.625113i \(-0.785053\pi\)
0.931631 + 0.363406i \(0.118386\pi\)
\(884\) 4.61517 + 4.14361i 0.155225 + 0.139365i
\(885\) 0 0
\(886\) 1.45299 + 9.13163i 0.0488141 + 0.306783i
\(887\) −1.66173 9.42413i −0.0557954 0.316431i 0.944118 0.329608i \(-0.106917\pi\)
−0.999913 + 0.0131769i \(0.995806\pi\)
\(888\) 0 0
\(889\) −1.71947 1.44280i −0.0576691 0.0483901i
\(890\) −29.0435 52.3078i −0.973540 1.75336i
\(891\) 0 0
\(892\) −34.0033 21.1802i −1.13852 0.709166i
\(893\) 14.9759 + 12.5663i 0.501149 + 0.420514i
\(894\) 0 0
\(895\) 48.6028 8.56999i 1.62461 0.286463i
\(896\) 0.131193 + 2.28490i 0.00438285 + 0.0763332i
\(897\) 0 0
\(898\) −13.9554 + 4.81636i −0.465697 + 0.160724i
\(899\) 26.6075 + 15.3618i 0.887409 + 0.512346i
\(900\) 0 0
\(901\) −14.8933 + 8.59864i −0.496167 + 0.286462i
\(902\) 38.3845 44.2199i 1.27806 1.47236i
\(903\) 0 0
\(904\) −12.7005 + 9.61320i −0.422412 + 0.319730i
\(905\) 44.9530 + 53.5729i 1.49429 + 1.78082i
\(906\) 0 0
\(907\) 22.4084 8.15601i 0.744060 0.270816i 0.0579560 0.998319i \(-0.481542\pi\)
0.686104 + 0.727503i \(0.259319\pi\)
\(908\) −1.72469 + 51.4954i −0.0572358 + 1.70893i
\(909\) 0 0
\(910\) 0.0279556 1.66985i 0.000926720 0.0553551i
\(911\) 4.55164 25.8136i 0.150802 0.855243i −0.811721 0.584045i \(-0.801469\pi\)
0.962524 0.271198i \(-0.0874198\pi\)
\(912\) 0 0
\(913\) −47.2159 17.1852i −1.56262 0.568746i
\(914\) 24.0389 + 29.6423i 0.795137 + 0.980481i
\(915\) 0 0
\(916\) −1.38522 4.24266i −0.0457690 0.140181i
\(917\) −1.49185 −0.0492651
\(918\) 0 0
\(919\) 28.4248i 0.937649i 0.883291 + 0.468824i \(0.155322\pi\)
−0.883291 + 0.468824i \(0.844678\pi\)
\(920\) 52.1463 56.1606i 1.71921 1.85156i
\(921\) 0 0
\(922\) 4.41527 + 5.44446i 0.145409 + 0.179304i
\(923\) −2.62224 + 7.20454i −0.0863120 + 0.237140i
\(924\) 0 0
\(925\) −11.6827 2.05997i −0.384123 0.0677313i
\(926\) −4.25685 0.0712654i −0.139889 0.00234193i
\(927\) 0 0
\(928\) 1.90480 22.7046i 0.0625281 0.745314i
\(929\) −0.817461 2.24596i −0.0268200 0.0736874i 0.925560 0.378601i \(-0.123595\pi\)
−0.952380 + 0.304913i \(0.901372\pi\)
\(930\) 0 0
\(931\) 34.5451 28.9868i 1.13217 0.950003i
\(932\) 17.0086 2.41516i 0.557135 0.0791112i
\(933\) 0 0
\(934\) 35.8370 + 31.1078i 1.17262 + 1.01788i
\(935\) 12.5057 + 21.6606i 0.408982 + 0.708377i
\(936\) 0 0
\(937\) −25.1607 + 43.5796i −0.821965 + 1.42368i 0.0822523 + 0.996612i \(0.473789\pi\)
−0.904217 + 0.427073i \(0.859545\pi\)
\(938\) −0.446486 + 0.154094i −0.0145783 + 0.00503134i
\(939\) 0 0
\(940\) 16.2439 12.7285i 0.529817 0.415157i
\(941\) 7.57703 + 42.9715i 0.247004 + 1.40083i 0.815792 + 0.578346i \(0.196302\pi\)
−0.568787 + 0.822485i \(0.692587\pi\)
\(942\) 0 0
\(943\) 52.3856 62.4307i 1.70591 2.03302i
\(944\) −12.9193 + 6.34688i −0.420488 + 0.206573i
\(945\) 0 0
\(946\) −10.2300 18.4243i −0.332605 0.599026i
\(947\) 19.4528 23.1830i 0.632132 0.753345i −0.350974 0.936385i \(-0.614149\pi\)
0.983105 + 0.183040i \(0.0585938\pi\)
\(948\) 0 0
\(949\) 13.6162 2.40091i 0.442001 0.0779367i
\(950\) −60.6190 + 9.64544i −1.96674 + 0.312939i
\(951\) 0 0
\(952\) −1.01343 0.231686i −0.0328455 0.00750897i
\(953\) −27.2578 15.7373i −0.882965 0.509780i −0.0113304 0.999936i \(-0.503607\pi\)
−0.871635 + 0.490156i \(0.836940\pi\)
\(954\) 0 0
\(955\) 35.6115 + 61.6810i 1.15236 + 1.99595i
\(956\) 0.604952 2.86618i 0.0195655 0.0926989i
\(957\) 0 0
\(958\) −7.83818 + 20.4628i −0.253240 + 0.661122i
\(959\) −1.79864 + 1.50924i −0.0580812 + 0.0487359i
\(960\) 0 0
\(961\) 25.5472 9.29843i 0.824104 0.299949i
\(962\) 3.66612 + 2.19927i 0.118201 + 0.0709073i
\(963\) 0 0
\(964\) 1.90082 + 3.56265i 0.0612213 + 0.114745i
\(965\) −3.38287 + 19.1852i −0.108899 + 0.617594i
\(966\) 0 0
\(967\) 2.57740 7.08136i 0.0828837 0.227721i −0.891327 0.453361i \(-0.850225\pi\)
0.974211 + 0.225640i \(0.0724472\pi\)
\(968\) −14.5926 + 1.82346i −0.469025 + 0.0586084i
\(969\) 0 0
\(970\) −41.6570 8.06647i −1.33753 0.258999i
\(971\) 15.5087i 0.497696i 0.968543 + 0.248848i \(0.0800520\pi\)
−0.968543 + 0.248848i \(0.919948\pi\)
\(972\) 0 0
\(973\) 1.59644i 0.0511796i
\(974\) −11.5538 + 59.6664i −0.370207 + 1.91183i
\(975\) 0 0
\(976\) 19.4868 + 26.6609i 0.623756 + 0.853394i
\(977\) 7.54941 20.7418i 0.241527 0.663590i −0.758403 0.651786i \(-0.774020\pi\)
0.999930 0.0118046i \(-0.00375761\pi\)
\(978\) 0 0
\(979\) −8.64507 + 49.0287i −0.276298 + 1.56696i
\(980\) −22.4083 41.9992i −0.715808 1.34162i
\(981\) 0 0
\(982\) 9.09620 15.1631i 0.290272 0.483875i
\(983\) −13.7881 + 5.01845i −0.439771 + 0.160064i −0.552410 0.833572i \(-0.686292\pi\)
0.112639 + 0.993636i \(0.464070\pi\)
\(984\) 0 0
\(985\) −70.2301 + 58.9300i −2.23772 + 1.87767i
\(986\) 9.66455 + 3.70196i 0.307782 + 0.117895i
\(987\) 0 0
\(988\) 21.6441 + 4.56831i 0.688589 + 0.145337i
\(989\) −14.6652 25.4010i −0.466328 0.807703i
\(990\) 0 0
\(991\) 10.0032 + 5.77533i 0.317761 + 0.183460i 0.650394 0.759597i \(-0.274604\pi\)
−0.332633 + 0.943056i \(0.607937\pi\)
\(992\) −30.6208 30.4031i −0.972210 0.965298i
\(993\) 0 0
\(994\) −0.201932 1.26909i −0.00640488 0.0402529i
\(995\) 86.6893 15.2857i 2.74824 0.484588i
\(996\) 0 0
\(997\) 27.6917 33.0016i 0.877004 1.04517i −0.121612 0.992578i \(-0.538806\pi\)
0.998616 0.0525950i \(-0.0167492\pi\)
\(998\) 0.728786 0.404653i 0.0230693 0.0128091i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 648.2.v.b.35.30 192
3.2 odd 2 216.2.v.b.11.3 192
8.3 odd 2 inner 648.2.v.b.35.13 192
12.11 even 2 864.2.bh.b.335.25 192
24.5 odd 2 864.2.bh.b.335.26 192
24.11 even 2 216.2.v.b.11.20 yes 192
27.5 odd 18 inner 648.2.v.b.611.13 192
27.22 even 9 216.2.v.b.59.20 yes 192
108.103 odd 18 864.2.bh.b.815.26 192
216.59 even 18 inner 648.2.v.b.611.30 192
216.157 even 18 864.2.bh.b.815.25 192
216.211 odd 18 216.2.v.b.59.3 yes 192
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
216.2.v.b.11.3 192 3.2 odd 2
216.2.v.b.11.20 yes 192 24.11 even 2
216.2.v.b.59.3 yes 192 216.211 odd 18
216.2.v.b.59.20 yes 192 27.22 even 9
648.2.v.b.35.13 192 8.3 odd 2 inner
648.2.v.b.35.30 192 1.1 even 1 trivial
648.2.v.b.611.13 192 27.5 odd 18 inner
648.2.v.b.611.30 192 216.59 even 18 inner
864.2.bh.b.335.25 192 12.11 even 2
864.2.bh.b.335.26 192 24.5 odd 2
864.2.bh.b.815.25 192 216.157 even 18
864.2.bh.b.815.26 192 108.103 odd 18