Properties

Label 91.2.i.a.34.4
Level $91$
Weight $2$
Character 91.34
Analytic conductor $0.727$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.i (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.726638658394\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 35 x^{8} + 295 x^{4} + 169\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 34.4
Root \(1.52891 - 1.52891i\) of defining polynomial
Character \(\chi\) \(=\) 91.34
Dual form 91.2.i.a.83.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.403032 - 0.403032i) q^{2} +1.23240i q^{3} -1.67513i q^{4} +(1.03221 - 1.03221i) q^{5} +(0.496696 - 0.496696i) q^{6} +(2.60707 + 0.450747i) q^{7} +(-1.48119 + 1.48119i) q^{8} +1.48119 q^{9} +O(q^{10})\) \(q+(-0.403032 - 0.403032i) q^{2} +1.23240i q^{3} -1.67513i q^{4} +(1.03221 - 1.03221i) q^{5} +(0.496696 - 0.496696i) q^{6} +(2.60707 + 0.450747i) q^{7} +(-1.48119 + 1.48119i) q^{8} +1.48119 q^{9} -0.832030 q^{10} +(-0.596968 + 0.596968i) q^{11} +2.06443 q^{12} +(-3.59334 + 0.296512i) q^{13} +(-0.869067 - 1.23240i) q^{14} +(1.27210 + 1.27210i) q^{15} -2.15633 q^{16} -7.34804 q^{17} +(-0.596968 - 0.596968i) q^{18} +(3.59334 - 3.59334i) q^{19} +(-1.72909 - 1.72909i) q^{20} +(-0.555500 + 3.21295i) q^{21} +0.481194 q^{22} +4.44358i q^{23} +(-1.82542 - 1.82542i) q^{24} +2.86907i q^{25} +(1.56773 + 1.32873i) q^{26} +5.52262i q^{27} +(0.755061 - 4.36719i) q^{28} -3.54420 q^{29} -1.02539i q^{30} +(-1.27122 + 1.27122i) q^{31} +(3.83146 + 3.83146i) q^{32} +(-0.735703 - 0.735703i) q^{33} +(2.96149 + 2.96149i) q^{34} +(3.15633 - 2.22579i) q^{35} -2.48119i q^{36} +(2.88423 - 2.88423i) q^{37} -2.89646 q^{38} +(-0.365420 - 4.42842i) q^{39} +3.05782i q^{40} +(1.23240 - 1.23240i) q^{41} +(1.51881 - 1.07104i) q^{42} -8.66291i q^{43} +(1.00000 + 1.00000i) q^{44} +(1.52891 - 1.52891i) q^{45} +(1.79090 - 1.79090i) q^{46} +(2.52230 + 2.52230i) q^{47} -2.65745i q^{48} +(6.59365 + 2.35026i) q^{49} +(1.15633 - 1.15633i) q^{50} -9.05571i q^{51} +(0.496696 + 6.01931i) q^{52} -9.79384 q^{53} +(2.22579 - 2.22579i) q^{54} +1.23240i q^{55} +(-4.52923 + 3.19394i) q^{56} +(4.42842 + 4.42842i) q^{57} +(1.42842 + 1.42842i) q^{58} +(-1.08972 - 1.08972i) q^{59} +(2.13093 - 2.13093i) q^{60} -7.10903i q^{61} +1.02469 q^{62} +(3.86158 + 0.667644i) q^{63} +1.22425i q^{64} +(-3.40303 + 4.01516i) q^{65} +0.593023i q^{66} +(8.76845 + 8.76845i) q^{67} +12.3089i q^{68} -5.47626 q^{69} +(-2.16916 - 0.375035i) q^{70} +(-1.46604 - 1.46604i) q^{71} +(-2.19394 + 2.19394i) q^{72} +(-0.103857 - 0.103857i) q^{73} -2.32487 q^{74} -3.53583 q^{75} +(-6.01931 - 6.01931i) q^{76} +(-1.82542 + 1.28726i) q^{77} +(-1.63752 + 1.93207i) q^{78} -4.79877 q^{79} +(-2.22579 + 2.22579i) q^{80} -2.36248 q^{81} -0.993391 q^{82} +(12.3165 - 12.3165i) q^{83} +(5.38211 + 0.930536i) q^{84} +(-7.58475 + 7.58475i) q^{85} +(-3.49143 + 3.49143i) q^{86} -4.36786i q^{87} -1.76845i q^{88} +(-6.89017 - 6.89017i) q^{89} -1.23240 q^{90} +(-9.50175 - 0.846661i) q^{91} +7.44358 q^{92} +(-1.56665 - 1.56665i) q^{93} -2.03313i q^{94} -7.41819i q^{95} +(-4.72188 + 4.72188i) q^{96} +(-6.05814 + 6.05814i) q^{97} +(-1.71022 - 3.60468i) q^{98} +(-0.884226 + 0.884226i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 4q^{2} - 8q^{7} + 4q^{8} - 4q^{9} + O(q^{10}) \) \( 12q - 4q^{2} - 8q^{7} + 4q^{8} - 4q^{9} - 8q^{11} + 8q^{14} - 4q^{15} + 16q^{16} - 8q^{18} - 16q^{22} - 20q^{28} - 4q^{29} - 16q^{32} - 4q^{35} + 12q^{37} + 40q^{39} + 40q^{42} + 12q^{44} + 24q^{46} - 28q^{50} - 12q^{53} - 8q^{57} - 44q^{58} + 44q^{60} + 20q^{63} - 40q^{65} + 60q^{67} + 4q^{70} - 28q^{72} - 48q^{74} + 44q^{78} - 4q^{79} - 92q^{81} - 4q^{84} + 12q^{85} + 36q^{86} - 32q^{91} + 24q^{92} - 28q^{93} - 28q^{98} + 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.403032 0.403032i −0.284986 0.284986i 0.550107 0.835094i \(-0.314587\pi\)
−0.835094 + 0.550107i \(0.814587\pi\)
\(3\) 1.23240i 0.711526i 0.934576 + 0.355763i \(0.115779\pi\)
−0.934576 + 0.355763i \(0.884221\pi\)
\(4\) 1.67513i 0.837565i
\(5\) 1.03221 1.03221i 0.461620 0.461620i −0.437566 0.899186i \(-0.644159\pi\)
0.899186 + 0.437566i \(0.144159\pi\)
\(6\) 0.496696 0.496696i 0.202775 0.202775i
\(7\) 2.60707 + 0.450747i 0.985381 + 0.170366i
\(8\) −1.48119 + 1.48119i −0.523681 + 0.523681i
\(9\) 1.48119 0.493731
\(10\) −0.832030 −0.263111
\(11\) −0.596968 + 0.596968i −0.179993 + 0.179993i −0.791353 0.611360i \(-0.790623\pi\)
0.611360 + 0.791353i \(0.290623\pi\)
\(12\) 2.06443 0.595949
\(13\) −3.59334 + 0.296512i −0.996613 + 0.0822375i
\(14\) −0.869067 1.23240i −0.232268 0.329372i
\(15\) 1.27210 + 1.27210i 0.328455 + 0.328455i
\(16\) −2.15633 −0.539081
\(17\) −7.34804 −1.78216 −0.891080 0.453845i \(-0.850052\pi\)
−0.891080 + 0.453845i \(0.850052\pi\)
\(18\) −0.596968 0.596968i −0.140707 0.140707i
\(19\) 3.59334 3.59334i 0.824368 0.824368i −0.162363 0.986731i \(-0.551911\pi\)
0.986731 + 0.162363i \(0.0519115\pi\)
\(20\) −1.72909 1.72909i −0.386637 0.386637i
\(21\) −0.555500 + 3.21295i −0.121220 + 0.701124i
\(22\) 0.481194 0.102591
\(23\) 4.44358i 0.926551i 0.886214 + 0.463276i \(0.153326\pi\)
−0.886214 + 0.463276i \(0.846674\pi\)
\(24\) −1.82542 1.82542i −0.372613 0.372613i
\(25\) 2.86907i 0.573813i
\(26\) 1.56773 + 1.32873i 0.307458 + 0.260585i
\(27\) 5.52262i 1.06283i
\(28\) 0.755061 4.36719i 0.142693 0.825321i
\(29\) −3.54420 −0.658141 −0.329071 0.944305i \(-0.606735\pi\)
−0.329071 + 0.944305i \(0.606735\pi\)
\(30\) 1.02539i 0.187210i
\(31\) −1.27122 + 1.27122i −0.228318 + 0.228318i −0.811990 0.583672i \(-0.801616\pi\)
0.583672 + 0.811990i \(0.301616\pi\)
\(32\) 3.83146 + 3.83146i 0.677312 + 0.677312i
\(33\) −0.735703 0.735703i −0.128069 0.128069i
\(34\) 2.96149 + 2.96149i 0.507892 + 0.507892i
\(35\) 3.15633 2.22579i 0.533516 0.376227i
\(36\) 2.48119i 0.413532i
\(37\) 2.88423 2.88423i 0.474164 0.474164i −0.429095 0.903259i \(-0.641168\pi\)
0.903259 + 0.429095i \(0.141168\pi\)
\(38\) −2.89646 −0.469868
\(39\) −0.365420 4.42842i −0.0585141 0.709115i
\(40\) 3.05782i 0.483484i
\(41\) 1.23240 1.23240i 0.192468 0.192468i −0.604294 0.796762i \(-0.706545\pi\)
0.796762 + 0.604294i \(0.206545\pi\)
\(42\) 1.51881 1.07104i 0.234357 0.165265i
\(43\) 8.66291i 1.32108i −0.750790 0.660541i \(-0.770327\pi\)
0.750790 0.660541i \(-0.229673\pi\)
\(44\) 1.00000 + 1.00000i 0.150756 + 0.150756i
\(45\) 1.52891 1.52891i 0.227916 0.227916i
\(46\) 1.79090 1.79090i 0.264055 0.264055i
\(47\) 2.52230 + 2.52230i 0.367915 + 0.367915i 0.866717 0.498801i \(-0.166226\pi\)
−0.498801 + 0.866717i \(0.666226\pi\)
\(48\) 2.65745i 0.383570i
\(49\) 6.59365 + 2.35026i 0.941951 + 0.335752i
\(50\) 1.15633 1.15633i 0.163529 0.163529i
\(51\) 9.05571i 1.26805i
\(52\) 0.496696 + 6.01931i 0.0688793 + 0.834728i
\(53\) −9.79384 −1.34529 −0.672644 0.739966i \(-0.734841\pi\)
−0.672644 + 0.739966i \(0.734841\pi\)
\(54\) 2.22579 2.22579i 0.302892 0.302892i
\(55\) 1.23240i 0.166177i
\(56\) −4.52923 + 3.19394i −0.605243 + 0.426808i
\(57\) 4.42842 + 4.42842i 0.586559 + 0.586559i
\(58\) 1.42842 + 1.42842i 0.187561 + 0.187561i
\(59\) −1.08972 1.08972i −0.141869 0.141869i 0.632605 0.774474i \(-0.281986\pi\)
−0.774474 + 0.632605i \(0.781986\pi\)
\(60\) 2.13093 2.13093i 0.275102 0.275102i
\(61\) 7.10903i 0.910218i −0.890436 0.455109i \(-0.849600\pi\)
0.890436 0.455109i \(-0.150400\pi\)
\(62\) 1.02469 0.130135
\(63\) 3.86158 + 0.667644i 0.486513 + 0.0841153i
\(64\) 1.22425i 0.153032i
\(65\) −3.40303 + 4.01516i −0.422094 + 0.498019i
\(66\) 0.593023i 0.0729961i
\(67\) 8.76845 + 8.76845i 1.07124 + 1.07124i 0.997260 + 0.0739770i \(0.0235691\pi\)
0.0739770 + 0.997260i \(0.476431\pi\)
\(68\) 12.3089i 1.49268i
\(69\) −5.47626 −0.659265
\(70\) −2.16916 0.375035i −0.259265 0.0448253i
\(71\) −1.46604 1.46604i −0.173986 0.173986i 0.614742 0.788728i \(-0.289260\pi\)
−0.788728 + 0.614742i \(0.789260\pi\)
\(72\) −2.19394 + 2.19394i −0.258558 + 0.258558i
\(73\) −0.103857 0.103857i −0.0121555 0.0121555i 0.701003 0.713158i \(-0.252736\pi\)
−0.713158 + 0.701003i \(0.752736\pi\)
\(74\) −2.32487 −0.270261
\(75\) −3.53583 −0.408283
\(76\) −6.01931 6.01931i −0.690462 0.690462i
\(77\) −1.82542 + 1.28726i −0.208026 + 0.146697i
\(78\) −1.63752 + 1.93207i −0.185413 + 0.218764i
\(79\) −4.79877 −0.539904 −0.269952 0.962874i \(-0.587008\pi\)
−0.269952 + 0.962874i \(0.587008\pi\)
\(80\) −2.22579 + 2.22579i −0.248851 + 0.248851i
\(81\) −2.36248 −0.262498
\(82\) −0.993391 −0.109702
\(83\) 12.3165 12.3165i 1.35191 1.35191i 0.468379 0.883528i \(-0.344838\pi\)
0.883528 0.468379i \(-0.155162\pi\)
\(84\) 5.38211 + 0.930536i 0.587237 + 0.101530i
\(85\) −7.58475 + 7.58475i −0.822682 + 0.822682i
\(86\) −3.49143 + 3.49143i −0.376490 + 0.376490i
\(87\) 4.36786i 0.468284i
\(88\) 1.76845i 0.188518i
\(89\) −6.89017 6.89017i −0.730356 0.730356i 0.240334 0.970690i \(-0.422743\pi\)
−0.970690 + 0.240334i \(0.922743\pi\)
\(90\) −1.23240 −0.129906
\(91\) −9.50175 0.846661i −0.996054 0.0887541i
\(92\) 7.44358 0.776047
\(93\) −1.56665 1.56665i −0.162454 0.162454i
\(94\) 2.03313i 0.209702i
\(95\) 7.41819i 0.761090i
\(96\) −4.72188 + 4.72188i −0.481925 + 0.481925i
\(97\) −6.05814 + 6.05814i −0.615110 + 0.615110i −0.944273 0.329163i \(-0.893234\pi\)
0.329163 + 0.944273i \(0.393234\pi\)
\(98\) −1.71022 3.60468i −0.172758 0.364128i
\(99\) −0.884226 + 0.884226i −0.0888681 + 0.0888681i
\(100\) 4.80606 0.480606
\(101\) 12.8707 1.28068 0.640339 0.768092i \(-0.278794\pi\)
0.640339 + 0.768092i \(0.278794\pi\)
\(102\) −3.64974 + 3.64974i −0.361378 + 0.361378i
\(103\) −6.11564 −0.602592 −0.301296 0.953531i \(-0.597419\pi\)
−0.301296 + 0.953531i \(0.597419\pi\)
\(104\) 4.88324 5.76162i 0.478841 0.564974i
\(105\) 2.74306 + 3.88985i 0.267695 + 0.379610i
\(106\) 3.94723 + 3.94723i 0.383389 + 0.383389i
\(107\) 8.86907 0.857405 0.428703 0.903446i \(-0.358971\pi\)
0.428703 + 0.903446i \(0.358971\pi\)
\(108\) 9.25111 0.890188
\(109\) −4.59697 4.59697i −0.440310 0.440310i 0.451806 0.892116i \(-0.350780\pi\)
−0.892116 + 0.451806i \(0.850780\pi\)
\(110\) 0.496696 0.496696i 0.0473581 0.0473581i
\(111\) 3.55452 + 3.55452i 0.337380 + 0.337380i
\(112\) −5.62170 0.971958i −0.531200 0.0918414i
\(113\) 1.60720 0.151193 0.0755964 0.997138i \(-0.475914\pi\)
0.0755964 + 0.997138i \(0.475914\pi\)
\(114\) 3.56959i 0.334323i
\(115\) 4.58673 + 4.58673i 0.427715 + 0.427715i
\(116\) 5.93700i 0.551236i
\(117\) −5.32243 + 0.439191i −0.492059 + 0.0406032i
\(118\) 0.878382i 0.0808617i
\(119\) −19.1569 3.31211i −1.75611 0.303620i
\(120\) −3.76845 −0.344011
\(121\) 10.2873i 0.935205i
\(122\) −2.86516 + 2.86516i −0.259400 + 0.259400i
\(123\) 1.51881 + 1.51881i 0.136946 + 0.136946i
\(124\) 2.12946 + 2.12946i 0.191231 + 0.191231i
\(125\) 8.12256 + 8.12256i 0.726504 + 0.726504i
\(126\) −1.28726 1.82542i −0.114678 0.162621i
\(127\) 1.54912i 0.137462i −0.997635 0.0687312i \(-0.978105\pi\)
0.997635 0.0687312i \(-0.0218951\pi\)
\(128\) 8.15633 8.15633i 0.720924 0.720924i
\(129\) 10.6762 0.939983
\(130\) 2.98977 0.246707i 0.262220 0.0216376i
\(131\) 5.31490i 0.464365i −0.972672 0.232183i \(-0.925413\pi\)
0.972672 0.232183i \(-0.0745867\pi\)
\(132\) −1.23240 + 1.23240i −0.107267 + 0.107267i
\(133\) 10.9878 7.74841i 0.952761 0.671872i
\(134\) 7.06793i 0.610576i
\(135\) 5.70052 + 5.70052i 0.490623 + 0.490623i
\(136\) 10.8839 10.8839i 0.933284 0.933284i
\(137\) 12.7157 12.7157i 1.08637 1.08637i 0.0904753 0.995899i \(-0.471161\pi\)
0.995899 0.0904753i \(-0.0288386\pi\)
\(138\) 2.20711 + 2.20711i 0.187882 + 0.187882i
\(139\) 6.94767i 0.589294i 0.955606 + 0.294647i \(0.0952020\pi\)
−0.955606 + 0.294647i \(0.904798\pi\)
\(140\) −3.72849 5.28726i −0.315115 0.446855i
\(141\) −3.10848 + 3.10848i −0.261781 + 0.261781i
\(142\) 1.18172i 0.0991676i
\(143\) 1.96810 2.32212i 0.164581 0.194185i
\(144\) −3.19394 −0.266161
\(145\) −3.65837 + 3.65837i −0.303811 + 0.303811i
\(146\) 0.0837150i 0.00692831i
\(147\) −2.89646 + 8.12601i −0.238896 + 0.670222i
\(148\) −4.83146 4.83146i −0.397143 0.397143i
\(149\) −10.9653 10.9653i −0.898315 0.898315i 0.0969724 0.995287i \(-0.469084\pi\)
−0.995287 + 0.0969724i \(0.969084\pi\)
\(150\) 1.42505 + 1.42505i 0.116355 + 0.116355i
\(151\) 6.14117 6.14117i 0.499761 0.499761i −0.411602 0.911363i \(-0.635031\pi\)
0.911363 + 0.411602i \(0.135031\pi\)
\(152\) 10.6449i 0.863413i
\(153\) −10.8839 −0.879909
\(154\) 1.25451 + 0.216897i 0.101091 + 0.0174781i
\(155\) 2.62435i 0.210793i
\(156\) −7.41819 + 0.612127i −0.593931 + 0.0490094i
\(157\) 9.69783i 0.773971i −0.922086 0.386985i \(-0.873516\pi\)
0.922086 0.386985i \(-0.126484\pi\)
\(158\) 1.93406 + 1.93406i 0.153865 + 0.153865i
\(159\) 12.0699i 0.957207i
\(160\) 7.90977 0.625322
\(161\) −2.00293 + 11.5847i −0.157853 + 0.913006i
\(162\) 0.952155 + 0.952155i 0.0748083 + 0.0748083i
\(163\) −5.41327 + 5.41327i −0.424000 + 0.424000i −0.886578 0.462579i \(-0.846924\pi\)
0.462579 + 0.886578i \(0.346924\pi\)
\(164\) −2.06443 2.06443i −0.161205 0.161205i
\(165\) −1.51881 −0.118239
\(166\) −9.92784 −0.770550
\(167\) 8.90824 + 8.90824i 0.689340 + 0.689340i 0.962086 0.272746i \(-0.0879318\pi\)
−0.272746 + 0.962086i \(0.587932\pi\)
\(168\) −3.93620 5.58181i −0.303685 0.430646i
\(169\) 12.8242 2.13093i 0.986474 0.163918i
\(170\) 6.11379 0.468906
\(171\) 5.32243 5.32243i 0.407017 0.407017i
\(172\) −14.5115 −1.10649
\(173\) 7.15538 0.544014 0.272007 0.962295i \(-0.412313\pi\)
0.272007 + 0.962295i \(0.412313\pi\)
\(174\) −1.76039 + 1.76039i −0.133455 + 0.133455i
\(175\) −1.29322 + 7.47987i −0.0977586 + 0.565425i
\(176\) 1.28726 1.28726i 0.0970307 0.0970307i
\(177\) 1.34297 1.34297i 0.100944 0.100944i
\(178\) 5.55391i 0.416283i
\(179\) 13.8119i 1.03235i 0.856482 + 0.516177i \(0.172645\pi\)
−0.856482 + 0.516177i \(0.827355\pi\)
\(180\) −2.56112 2.56112i −0.190895 0.190895i
\(181\) −4.56052 −0.338981 −0.169490 0.985532i \(-0.554212\pi\)
−0.169490 + 0.985532i \(0.554212\pi\)
\(182\) 3.48827 + 4.17074i 0.258568 + 0.309156i
\(183\) 8.76116 0.647643
\(184\) −6.58181 6.58181i −0.485217 0.485217i
\(185\) 5.95428i 0.437767i
\(186\) 1.26282i 0.0925945i
\(187\) 4.38655 4.38655i 0.320776 0.320776i
\(188\) 4.22518 4.22518i 0.308153 0.308153i
\(189\) −2.48930 + 14.3979i −0.181070 + 1.04729i
\(190\) −2.98977 + 2.98977i −0.216900 + 0.216900i
\(191\) 3.70545 0.268117 0.134058 0.990973i \(-0.457199\pi\)
0.134058 + 0.990973i \(0.457199\pi\)
\(192\) −1.50877 −0.108886
\(193\) −17.0508 + 17.0508i −1.22734 + 1.22734i −0.262377 + 0.964965i \(0.584506\pi\)
−0.964965 + 0.262377i \(0.915494\pi\)
\(194\) 4.88324 0.350596
\(195\) −4.94827 4.19389i −0.354353 0.300331i
\(196\) 3.93700 11.0452i 0.281214 0.788945i
\(197\) −8.01810 8.01810i −0.571266 0.571266i 0.361216 0.932482i \(-0.382362\pi\)
−0.932482 + 0.361216i \(0.882362\pi\)
\(198\) 0.712742 0.0506524
\(199\) −4.57558 −0.324354 −0.162177 0.986762i \(-0.551852\pi\)
−0.162177 + 0.986762i \(0.551852\pi\)
\(200\) −4.24965 4.24965i −0.300495 0.300495i
\(201\) −10.8062 + 10.8062i −0.762212 + 0.762212i
\(202\) −5.18728 5.18728i −0.364976 0.364976i
\(203\) −9.23998 1.59754i −0.648520 0.112125i
\(204\) −15.1695 −1.06208
\(205\) 2.54420i 0.177695i
\(206\) 2.46480 + 2.46480i 0.171731 + 0.171731i
\(207\) 6.58181i 0.457467i
\(208\) 7.74841 0.639375i 0.537255 0.0443327i
\(209\) 4.29022i 0.296761i
\(210\) 0.462193 2.67327i 0.0318943 0.184473i
\(211\) −0.594028 −0.0408946 −0.0204473 0.999791i \(-0.506509\pi\)
−0.0204473 + 0.999791i \(0.506509\pi\)
\(212\) 16.4060i 1.12677i
\(213\) 1.80674 1.80674i 0.123796 0.123796i
\(214\) −3.57452 3.57452i −0.244349 0.244349i
\(215\) −8.94198 8.94198i −0.609838 0.609838i
\(216\) −8.18007 8.18007i −0.556583 0.556583i
\(217\) −3.88717 + 2.74117i −0.263878 + 0.186083i
\(218\) 3.70545i 0.250965i
\(219\) 0.127993 0.127993i 0.00864895 0.00864895i
\(220\) 2.06443 0.139184
\(221\) 26.4040 2.17878i 1.77612 0.146560i
\(222\) 2.86516i 0.192297i
\(223\) 2.85764 2.85764i 0.191361 0.191361i −0.604923 0.796284i \(-0.706796\pi\)
0.796284 + 0.604923i \(0.206796\pi\)
\(224\) 8.26187 + 11.7159i 0.552019 + 0.782802i
\(225\) 4.24965i 0.283310i
\(226\) −0.647754 0.647754i −0.0430879 0.0430879i
\(227\) −19.6570 + 19.6570i −1.30468 + 1.30468i −0.379477 + 0.925201i \(0.623896\pi\)
−0.925201 + 0.379477i \(0.876104\pi\)
\(228\) 7.41819 7.41819i 0.491282 0.491282i
\(229\) −13.2060 13.2060i −0.872676 0.872676i 0.120087 0.992763i \(-0.461683\pi\)
−0.992763 + 0.120087i \(0.961683\pi\)
\(230\) 3.69720i 0.243786i
\(231\) −1.58641 2.24965i −0.104378 0.148016i
\(232\) 5.24965 5.24965i 0.344656 0.344656i
\(233\) 16.2243i 1.06289i −0.847094 0.531443i \(-0.821650\pi\)
0.847094 0.531443i \(-0.178350\pi\)
\(234\) 2.32212 + 1.96810i 0.151802 + 0.128659i
\(235\) 5.20711 0.339674
\(236\) −1.82542 + 1.82542i −0.118825 + 0.118825i
\(237\) 5.91400i 0.384155i
\(238\) 6.38594 + 9.05571i 0.413939 + 0.586994i
\(239\) −0.843675 0.843675i −0.0545728 0.0545728i 0.679294 0.733867i \(-0.262286\pi\)
−0.733867 + 0.679294i \(0.762286\pi\)
\(240\) −2.74306 2.74306i −0.177064 0.177064i
\(241\) 15.2966 + 15.2966i 0.985342 + 0.985342i 0.999894 0.0145517i \(-0.00463211\pi\)
−0.0145517 + 0.999894i \(0.504632\pi\)
\(242\) 4.14609 4.14609i 0.266521 0.266521i
\(243\) 13.6563i 0.876054i
\(244\) −11.9086 −0.762367
\(245\) 9.23204 4.38009i 0.589813 0.279834i
\(246\) 1.22425i 0.0780556i
\(247\) −11.8466 + 13.9775i −0.753782 + 0.889370i
\(248\) 3.76585i 0.239132i
\(249\) 15.1788 + 15.1788i 0.961916 + 0.961916i
\(250\) 6.54730i 0.414088i
\(251\) 27.4367 1.73179 0.865893 0.500229i \(-0.166751\pi\)
0.865893 + 0.500229i \(0.166751\pi\)
\(252\) 1.11839 6.46865i 0.0704521 0.407487i
\(253\) −2.65268 2.65268i −0.166772 0.166772i
\(254\) −0.624346 + 0.624346i −0.0391749 + 0.0391749i
\(255\) −9.34743 9.34743i −0.585359 0.585359i
\(256\) −4.12601 −0.257876
\(257\) 20.5727 1.28329 0.641645 0.767002i \(-0.278252\pi\)
0.641645 + 0.767002i \(0.278252\pi\)
\(258\) −4.30283 4.30283i −0.267883 0.267883i
\(259\) 8.81944 6.21933i 0.548014 0.386450i
\(260\) 6.72592 + 5.70052i 0.417124 + 0.353531i
\(261\) −5.24965 −0.324945
\(262\) −2.14207 + 2.14207i −0.132338 + 0.132338i
\(263\) −23.8568 −1.47108 −0.735538 0.677483i \(-0.763071\pi\)
−0.735538 + 0.677483i \(0.763071\pi\)
\(264\) 2.17944 0.134135
\(265\) −10.1093 + 10.1093i −0.621012 + 0.621012i
\(266\) −7.55128 1.30557i −0.462999 0.0800497i
\(267\) 8.49143 8.49143i 0.519667 0.519667i
\(268\) 14.6883 14.6883i 0.897231 0.897231i
\(269\) 1.10840i 0.0675803i −0.999429 0.0337902i \(-0.989242\pi\)
0.999429 0.0337902i \(-0.0107578\pi\)
\(270\) 4.59498i 0.279642i
\(271\) 20.8894 + 20.8894i 1.26894 + 1.26894i 0.946637 + 0.322301i \(0.104456\pi\)
0.322301 + 0.946637i \(0.395544\pi\)
\(272\) 15.8448 0.960730
\(273\) 1.04342 11.7099i 0.0631508 0.708718i
\(274\) −10.2496 −0.619204
\(275\) −1.71274 1.71274i −0.103282 0.103282i
\(276\) 9.17346i 0.552177i
\(277\) 25.8265i 1.55177i −0.630877 0.775883i \(-0.717305\pi\)
0.630877 0.775883i \(-0.282695\pi\)
\(278\) 2.80013 2.80013i 0.167941 0.167941i
\(279\) −1.88293 + 1.88293i −0.112728 + 0.112728i
\(280\) −1.37830 + 7.97196i −0.0823694 + 0.476416i
\(281\) 12.0782 12.0782i 0.720523 0.720523i −0.248189 0.968712i \(-0.579835\pi\)
0.968712 + 0.248189i \(0.0798354\pi\)
\(282\) 2.50563 0.149208
\(283\) −15.3667 −0.913458 −0.456729 0.889606i \(-0.650979\pi\)
−0.456729 + 0.889606i \(0.650979\pi\)
\(284\) −2.45580 + 2.45580i −0.145725 + 0.145725i
\(285\) 9.14217 0.541535
\(286\) −1.72909 + 0.142680i −0.102243 + 0.00843683i
\(287\) 3.76845 2.65745i 0.222445 0.156864i
\(288\) 5.67513 + 5.67513i 0.334410 + 0.334410i
\(289\) 36.9937 2.17610
\(290\) 2.94888 0.173164
\(291\) −7.46604 7.46604i −0.437667 0.437667i
\(292\) −0.173973 + 0.173973i −0.0101810 + 0.0101810i
\(293\) −9.78662 9.78662i −0.571741 0.571741i 0.360874 0.932615i \(-0.382478\pi\)
−0.932615 + 0.360874i \(0.882478\pi\)
\(294\) 4.44240 2.10767i 0.259086 0.122922i
\(295\) −2.24965 −0.130979
\(296\) 8.54420i 0.496621i
\(297\) −3.29683 3.29683i −0.191301 0.191301i
\(298\) 8.83875i 0.512015i
\(299\) −1.31757 15.9673i −0.0761972 0.923413i
\(300\) 5.92298i 0.341964i
\(301\) 3.90478 22.5848i 0.225068 1.30177i
\(302\) −4.95017 −0.284850
\(303\) 15.8618i 0.911235i
\(304\) −7.74841 + 7.74841i −0.444402 + 0.444402i
\(305\) −7.33804 7.33804i −0.420175 0.420175i
\(306\) 4.38655 + 4.38655i 0.250762 + 0.250762i
\(307\) −8.14125 8.14125i −0.464645 0.464645i 0.435529 0.900175i \(-0.356561\pi\)
−0.900175 + 0.435529i \(0.856561\pi\)
\(308\) 2.15633 + 3.05782i 0.122868 + 0.174235i
\(309\) 7.53690i 0.428759i
\(310\) 1.05769 1.05769i 0.0600730 0.0600730i
\(311\) −32.4813 −1.84184 −0.920922 0.389747i \(-0.872562\pi\)
−0.920922 + 0.389747i \(0.872562\pi\)
\(312\) 7.10062 + 6.01810i 0.401993 + 0.340708i
\(313\) 19.7346i 1.11547i 0.830020 + 0.557733i \(0.188329\pi\)
−0.830020 + 0.557733i \(0.811671\pi\)
\(314\) −3.90853 + 3.90853i −0.220571 + 0.220571i
\(315\) 4.67513 3.29683i 0.263414 0.185755i
\(316\) 8.03857i 0.452205i
\(317\) −8.11871 8.11871i −0.455992 0.455992i 0.441345 0.897337i \(-0.354501\pi\)
−0.897337 + 0.441345i \(0.854501\pi\)
\(318\) −4.86456 + 4.86456i −0.272791 + 0.272791i
\(319\) 2.11577 2.11577i 0.118461 0.118461i
\(320\) 1.26369 + 1.26369i 0.0706425 + 0.0706425i
\(321\) 10.9302i 0.610066i
\(322\) 5.47626 3.86177i 0.305180 0.215208i
\(323\) −26.4040 + 26.4040i −1.46916 + 1.46916i
\(324\) 3.95746i 0.219859i
\(325\) −0.850712 10.3095i −0.0471890 0.571870i
\(326\) 4.36344 0.241668
\(327\) 5.66530 5.66530i 0.313292 0.313292i
\(328\) 3.65084i 0.201584i
\(329\) 5.43890 + 7.71274i 0.299856 + 0.425217i
\(330\) 0.612127 + 0.612127i 0.0336965 + 0.0336965i
\(331\) −0.806063 0.806063i −0.0443053 0.0443053i 0.684607 0.728912i \(-0.259974\pi\)
−0.728912 + 0.684607i \(0.759974\pi\)
\(332\) −20.6317 20.6317i −1.13231 1.13231i
\(333\) 4.27210 4.27210i 0.234110 0.234110i
\(334\) 7.18061i 0.392905i
\(335\) 18.1018 0.989009
\(336\) 1.19784 6.92817i 0.0653475 0.377963i
\(337\) 26.6058i 1.44931i 0.689112 + 0.724655i \(0.258001\pi\)
−0.689112 + 0.724655i \(0.741999\pi\)
\(338\) −6.02738 4.30971i −0.327846 0.234417i
\(339\) 1.98071i 0.107578i
\(340\) 12.7054 + 12.7054i 0.689050 + 0.689050i
\(341\) 1.51776i 0.0821912i
\(342\) −4.29022 −0.231988
\(343\) 16.1308 + 9.09937i 0.870979 + 0.491320i
\(344\) 12.8315 + 12.8315i 0.691826 + 0.691826i
\(345\) −5.65268 + 5.65268i −0.304330 + 0.304330i
\(346\) −2.88385 2.88385i −0.155037 0.155037i
\(347\) −20.2071 −1.08477 −0.542387 0.840129i \(-0.682479\pi\)
−0.542387 + 0.840129i \(0.682479\pi\)
\(348\) −7.31674 −0.392219
\(349\) −2.31459 2.31459i −0.123897 0.123897i 0.642439 0.766336i \(-0.277922\pi\)
−0.766336 + 0.642439i \(0.777922\pi\)
\(350\) 3.53583 2.49341i 0.188998 0.133279i
\(351\) −1.63752 19.8446i −0.0874043 1.05923i
\(352\) −4.57452 −0.243822
\(353\) −10.7412 + 10.7412i −0.571696 + 0.571696i −0.932602 0.360906i \(-0.882467\pi\)
0.360906 + 0.932602i \(0.382467\pi\)
\(354\) −1.08252 −0.0575351
\(355\) −3.02653 −0.160631
\(356\) −11.5419 + 11.5419i −0.611721 + 0.611721i
\(357\) 4.08184 23.6089i 0.216034 1.24952i
\(358\) 5.56665 5.56665i 0.294207 0.294207i
\(359\) −16.9726 + 16.9726i −0.895781 + 0.895781i −0.995060 0.0992789i \(-0.968346\pi\)
0.0992789 + 0.995060i \(0.468346\pi\)
\(360\) 4.52923i 0.238711i
\(361\) 6.82416i 0.359166i
\(362\) 1.83803 + 1.83803i 0.0966049 + 0.0966049i
\(363\) −12.6780 −0.665422
\(364\) −1.41827 + 15.9167i −0.0743374 + 0.834260i
\(365\) −0.214405 −0.0112225
\(366\) −3.53102 3.53102i −0.184570 0.184570i
\(367\) 9.79778i 0.511440i −0.966751 0.255720i \(-0.917688\pi\)
0.966751 0.255720i \(-0.0823125\pi\)
\(368\) 9.58181i 0.499486i
\(369\) 1.82542 1.82542i 0.0950276 0.0950276i
\(370\) −2.39976 + 2.39976i −0.124758 + 0.124758i
\(371\) −25.5333 4.41455i −1.32562 0.229192i
\(372\) −2.62435 + 2.62435i −0.136066 + 0.136066i
\(373\) −5.96731 −0.308976 −0.154488 0.987995i \(-0.549373\pi\)
−0.154488 + 0.987995i \(0.549373\pi\)
\(374\) −3.53583 −0.182834
\(375\) −10.0102 + 10.0102i −0.516926 + 0.516926i
\(376\) −7.47204 −0.385341
\(377\) 12.7355 1.05090i 0.655912 0.0541239i
\(378\) 6.80606 4.79953i 0.350066 0.246861i
\(379\) 2.14117 + 2.14117i 0.109984 + 0.109984i 0.759957 0.649973i \(-0.225220\pi\)
−0.649973 + 0.759957i \(0.725220\pi\)
\(380\) −12.4264 −0.637463
\(381\) 1.90914 0.0978080
\(382\) −1.49341 1.49341i −0.0764097 0.0764097i
\(383\) 2.91152 2.91152i 0.148772 0.148772i −0.628798 0.777569i \(-0.716453\pi\)
0.777569 + 0.628798i \(0.216453\pi\)
\(384\) 10.0518 + 10.0518i 0.512956 + 0.512956i
\(385\) −0.555500 + 3.21295i −0.0283109 + 0.163747i
\(386\) 13.7440 0.699552
\(387\) 12.8315i 0.652260i
\(388\) 10.1482 + 10.1482i 0.515195 + 0.515195i
\(389\) 17.4436i 0.884425i 0.896910 + 0.442212i \(0.145806\pi\)
−0.896910 + 0.442212i \(0.854194\pi\)
\(390\) 0.304041 + 3.68458i 0.0153957 + 0.186576i
\(391\) 32.6516i 1.65126i
\(392\) −13.2477 + 6.28529i −0.669109 + 0.317455i
\(393\) 6.55008 0.330408
\(394\) 6.46310i 0.325606i
\(395\) −4.95336 + 4.95336i −0.249230 + 0.249230i
\(396\) 1.48119 + 1.48119i 0.0744328 + 0.0744328i
\(397\) 10.1870 + 10.1870i 0.511270 + 0.511270i 0.914916 0.403645i \(-0.132257\pi\)
−0.403645 + 0.914916i \(0.632257\pi\)
\(398\) 1.84410 + 1.84410i 0.0924365 + 0.0924365i
\(399\) 9.54912 + 13.5413i 0.478054 + 0.677914i
\(400\) 6.18664i 0.309332i
\(401\) 15.5950 15.5950i 0.778776 0.778776i −0.200846 0.979623i \(-0.564369\pi\)
0.979623 + 0.200846i \(0.0643692\pi\)
\(402\) 8.71050 0.434440
\(403\) 4.19100 4.94486i 0.208768 0.246321i
\(404\) 21.5600i 1.07265i
\(405\) −2.43859 + 2.43859i −0.121174 + 0.121174i
\(406\) 3.08015 + 4.36786i 0.152865 + 0.216773i
\(407\) 3.44358i 0.170692i
\(408\) 13.4133 + 13.4133i 0.664056 + 0.664056i
\(409\) 1.79921 1.79921i 0.0889652 0.0889652i −0.661224 0.750189i \(-0.729963\pi\)
0.750189 + 0.661224i \(0.229963\pi\)
\(410\) −1.02539 + 1.02539i −0.0506405 + 0.0506405i
\(411\) 15.6708 + 15.6708i 0.772983 + 0.772983i
\(412\) 10.2445i 0.504710i
\(413\) −2.34979 3.33216i −0.115626 0.163965i
\(414\) 2.65268 2.65268i 0.130372 0.130372i
\(415\) 25.4264i 1.24813i
\(416\) −14.9038 12.6316i −0.730718 0.619317i
\(417\) −8.56230 −0.419297
\(418\) 1.72909 1.72909i 0.0845728 0.0845728i
\(419\) 16.5064i 0.806392i 0.915114 + 0.403196i \(0.132101\pi\)
−0.915114 + 0.403196i \(0.867899\pi\)
\(420\) 6.51601 4.59498i 0.317949 0.224212i
\(421\) −8.53492 8.53492i −0.415967 0.415967i 0.467844 0.883811i \(-0.345031\pi\)
−0.883811 + 0.467844i \(0.845031\pi\)
\(422\) 0.239412 + 0.239412i 0.0116544 + 0.0116544i
\(423\) 3.73602 + 3.73602i 0.181651 + 0.181651i
\(424\) 14.5066 14.5066i 0.704502 0.704502i
\(425\) 21.0820i 1.02263i
\(426\) −1.45635 −0.0705602
\(427\) 3.20438 18.5338i 0.155071 0.896911i
\(428\) 14.8568i 0.718133i
\(429\) 2.86177 + 2.42548i 0.138168 + 0.117103i
\(430\) 7.20780i 0.347591i
\(431\) 24.2071 + 24.2071i 1.16602 + 1.16602i 0.983135 + 0.182880i \(0.0585421\pi\)
0.182880 + 0.983135i \(0.441458\pi\)
\(432\) 11.9086i 0.572951i
\(433\) −35.8708 −1.72384 −0.861920 0.507044i \(-0.830738\pi\)
−0.861920 + 0.507044i \(0.830738\pi\)
\(434\) 2.67143 + 0.461874i 0.128233 + 0.0221707i
\(435\) −4.50857 4.50857i −0.216169 0.216169i
\(436\) −7.70052 + 7.70052i −0.368788 + 0.368788i
\(437\) 15.9673 + 15.9673i 0.763819 + 0.763819i
\(438\) −0.103170 −0.00492967
\(439\) 10.5299 0.502563 0.251281 0.967914i \(-0.419148\pi\)
0.251281 + 0.967914i \(0.419148\pi\)
\(440\) −1.82542 1.82542i −0.0870236 0.0870236i
\(441\) 9.76648 + 3.48119i 0.465071 + 0.165771i
\(442\) −11.5198 9.76353i −0.547939 0.464404i
\(443\) 12.8618 0.611081 0.305541 0.952179i \(-0.401163\pi\)
0.305541 + 0.952179i \(0.401163\pi\)
\(444\) 5.95428 5.95428i 0.282578 0.282578i
\(445\) −14.2243 −0.674294
\(446\) −2.30344 −0.109071
\(447\) 13.5137 13.5137i 0.639174 0.639174i
\(448\) −0.551829 + 3.19172i −0.0260715 + 0.150795i
\(449\) 9.65069 9.65069i 0.455444 0.455444i −0.441712 0.897157i \(-0.645629\pi\)
0.897157 + 0.441712i \(0.145629\pi\)
\(450\) 1.71274 1.71274i 0.0807394 0.0807394i
\(451\) 1.47141i 0.0692858i
\(452\) 2.69227i 0.126634i
\(453\) 7.56836 + 7.56836i 0.355593 + 0.355593i
\(454\) 15.8448 0.743631
\(455\) −10.6818 + 8.93390i −0.500769 + 0.418828i
\(456\) −13.1187 −0.614340
\(457\) −22.1217 22.1217i −1.03481 1.03481i −0.999372 0.0354353i \(-0.988718\pi\)
−0.0354353 0.999372i \(-0.511282\pi\)
\(458\) 10.6449i 0.497402i
\(459\) 40.5804i 1.89413i
\(460\) 7.68337 7.68337i 0.358239 0.358239i
\(461\) 0.593023 0.593023i 0.0276198 0.0276198i −0.693162 0.720782i \(-0.743783\pi\)
0.720782 + 0.693162i \(0.243783\pi\)
\(462\) −0.267304 + 1.54605i −0.0124361 + 0.0719289i
\(463\) 2.47096 2.47096i 0.114835 0.114835i −0.647354 0.762189i \(-0.724124\pi\)
0.762189 + 0.647354i \(0.224124\pi\)
\(464\) 7.64244 0.354792
\(465\) −3.23424 −0.149984
\(466\) −6.53889 + 6.53889i −0.302908 + 0.302908i
\(467\) −13.3860 −0.619432 −0.309716 0.950829i \(-0.600234\pi\)
−0.309716 + 0.950829i \(0.600234\pi\)
\(468\) 0.735703 + 8.91577i 0.0340079 + 0.412132i
\(469\) 18.9076 + 26.8123i 0.873073 + 1.23808i
\(470\) −2.09863 2.09863i −0.0968026 0.0968026i
\(471\) 11.9516 0.550700
\(472\) 3.22817 0.148589
\(473\) 5.17148 + 5.17148i 0.237785 + 0.237785i
\(474\) −2.38353 + 2.38353i −0.109479 + 0.109479i
\(475\) 10.3095 + 10.3095i 0.473034 + 0.473034i
\(476\) −5.54821 + 32.0903i −0.254302 + 1.47085i
\(477\) −14.5066 −0.664211
\(478\) 0.680055i 0.0311050i
\(479\) −8.85827 8.85827i −0.404745 0.404745i 0.475157 0.879901i \(-0.342391\pi\)
−0.879901 + 0.475157i \(0.842391\pi\)
\(480\) 9.74798i 0.444933i
\(481\) −9.50879 + 11.2192i −0.433564 + 0.511552i
\(482\) 12.3301i 0.561619i
\(483\) −14.2770 2.46841i −0.649627 0.112317i
\(484\) 17.2325 0.783296
\(485\) 12.5066i 0.567895i
\(486\) 5.50394 5.50394i 0.249664 0.249664i
\(487\) 17.9805 + 17.9805i 0.814774 + 0.814774i 0.985345 0.170572i \(-0.0545614\pi\)
−0.170572 + 0.985345i \(0.554561\pi\)
\(488\) 10.5299 + 10.5299i 0.476664 + 0.476664i
\(489\) −6.67130 6.67130i −0.301687 0.301687i
\(490\) −5.48612 1.95549i −0.247838 0.0883400i
\(491\) 19.4944i 0.879769i 0.898054 + 0.439884i \(0.144981\pi\)
−0.898054 + 0.439884i \(0.855019\pi\)
\(492\) 2.54420 2.54420i 0.114701 0.114701i
\(493\) 26.0429 1.17291
\(494\) 10.4080 0.858833i 0.468276 0.0386407i
\(495\) 1.82542i 0.0820466i
\(496\) 2.74117 2.74117i 0.123082 0.123082i
\(497\) −3.16125 4.48287i −0.141801 0.201084i
\(498\) 12.2351i 0.548266i
\(499\) 10.2150 + 10.2150i 0.457285 + 0.457285i 0.897763 0.440478i \(-0.145191\pi\)
−0.440478 + 0.897763i \(0.645191\pi\)
\(500\) 13.6064 13.6064i 0.608495 0.608495i
\(501\) −10.9785 + 10.9785i −0.490483 + 0.490483i
\(502\) −11.0578 11.0578i −0.493536 0.493536i
\(503\) 31.8196i 1.41877i −0.704824 0.709383i \(-0.748974\pi\)
0.704824 0.709383i \(-0.251026\pi\)
\(504\) −6.70866 + 4.73084i −0.298828 + 0.210728i
\(505\) 13.2853 13.2853i 0.591187 0.591187i
\(506\) 2.13823i 0.0950558i
\(507\) 2.62616 + 15.8045i 0.116632 + 0.701901i
\(508\) −2.59498 −0.115134
\(509\) −13.6139 + 13.6139i −0.603425 + 0.603425i −0.941220 0.337795i \(-0.890319\pi\)
0.337795 + 0.941220i \(0.390319\pi\)
\(510\) 7.53462i 0.333639i
\(511\) −0.223949 0.317575i −0.00990691 0.0140487i
\(512\) −14.6497 14.6497i −0.647433 0.647433i
\(513\) 19.8446 + 19.8446i 0.876162 + 0.876162i
\(514\) −8.29145 8.29145i −0.365720 0.365720i
\(515\) −6.31265 + 6.31265i −0.278169 + 0.278169i
\(516\) 17.8840i 0.787298i
\(517\) −3.01147 −0.132444
\(518\) −6.06110 1.04793i −0.266310 0.0460433i
\(519\) 8.81828i 0.387080i
\(520\) −0.906679 10.9878i −0.0397605 0.481846i
\(521\) 21.6750i 0.949601i 0.880094 + 0.474800i \(0.157480\pi\)
−0.880094 + 0.474800i \(0.842520\pi\)
\(522\) 2.11577 + 2.11577i 0.0926049 + 0.0926049i
\(523\) 8.77309i 0.383620i 0.981432 + 0.191810i \(0.0614358\pi\)
−0.981432 + 0.191810i \(0.938564\pi\)
\(524\) −8.90316 −0.388936
\(525\) −9.21818 1.59377i −0.402314 0.0695577i
\(526\) 9.61507 + 9.61507i 0.419237 + 0.419237i
\(527\) 9.34098 9.34098i 0.406900 0.406900i
\(528\) 1.58641 + 1.58641i 0.0690398 + 0.0690398i
\(529\) 3.25457 0.141503
\(530\) 8.14877 0.353960
\(531\) −1.61409 1.61409i −0.0700453 0.0700453i
\(532\) −12.9796 18.4060i −0.562737 0.798000i
\(533\) −4.06300 + 4.79384i −0.175988 + 0.207644i
\(534\) −6.84463 −0.296196
\(535\) 9.15478 9.15478i 0.395796 0.395796i
\(536\) −25.9756 −1.12197
\(537\) −17.0218 −0.734546
\(538\) −0.446720 + 0.446720i −0.0192595 + 0.0192595i
\(539\) −5.33923 + 2.53317i −0.229977 + 0.109111i
\(540\) 9.54912 9.54912i 0.410929 0.410929i
\(541\) −23.2853 + 23.2853i −1.00111 + 1.00111i −0.00111270 + 0.999999i \(0.500354\pi\)
−0.999999 + 0.00111270i \(0.999646\pi\)
\(542\) 16.8382i 0.723260i
\(543\) 5.62038i 0.241193i
\(544\) −28.1537 28.1537i −1.20708 1.20708i
\(545\) −9.49011 −0.406512
\(546\) −5.14001 + 4.29894i −0.219972 + 0.183978i
\(547\) −15.1744 −0.648812 −0.324406 0.945918i \(-0.605164\pi\)
−0.324406 + 0.945918i \(0.605164\pi\)
\(548\) −21.3004 21.3004i −0.909909 0.909909i
\(549\) 10.5299i 0.449403i
\(550\) 1.38058i 0.0588681i
\(551\) −12.7355 + 12.7355i −0.542551 + 0.542551i
\(552\) 8.11141 8.11141i 0.345245 0.345245i
\(553\) −12.5107 2.16303i −0.532011 0.0919815i
\(554\) −10.4089 + 10.4089i −0.442232 + 0.442232i
\(555\) 7.33804 0.311483
\(556\) 11.6383 0.493572
\(557\) 8.45676 8.45676i 0.358324 0.358324i −0.504871 0.863195i \(-0.668460\pi\)
0.863195 + 0.504871i \(0.168460\pi\)
\(558\) 1.51776 0.0642518
\(559\) 2.56865 + 31.1288i 0.108642 + 1.31661i
\(560\) −6.80606 + 4.79953i −0.287609 + 0.202817i
\(561\) 5.40597 + 5.40597i 0.228240 + 0.228240i
\(562\) −9.73577 −0.410678
\(563\) 6.34858 0.267561 0.133780 0.991011i \(-0.457288\pi\)
0.133780 + 0.991011i \(0.457288\pi\)
\(564\) 5.20711 + 5.20711i 0.219259 + 0.219259i
\(565\) 1.65898 1.65898i 0.0697937 0.0697937i
\(566\) 6.19329 + 6.19329i 0.260323 + 0.260323i
\(567\) −6.15916 1.06488i −0.258660 0.0447208i
\(568\) 4.34297 0.182227
\(569\) 36.6140i 1.53494i 0.641085 + 0.767470i \(0.278485\pi\)
−0.641085 + 0.767470i \(0.721515\pi\)
\(570\) −3.68458 3.68458i −0.154330 0.154330i
\(571\) 18.8070i 0.787049i −0.919314 0.393525i \(-0.871256\pi\)
0.919314 0.393525i \(-0.128744\pi\)
\(572\) −3.88985 3.29683i −0.162643 0.137847i
\(573\) 4.56659i 0.190772i
\(574\) −2.58984 0.447768i −0.108098 0.0186895i
\(575\) −12.7489 −0.531668
\(576\) 1.81336i 0.0755566i
\(577\) 31.3416 31.3416i 1.30477 1.30477i 0.379627 0.925140i \(-0.376052\pi\)
0.925140 0.379627i \(-0.123948\pi\)
\(578\) −14.9096 14.9096i −0.620158 0.620158i
\(579\) −21.0134 21.0134i −0.873285 0.873285i
\(580\) 6.12825 + 6.12825i 0.254462 + 0.254462i
\(581\) 37.6615 26.5583i 1.56246 1.10182i
\(582\) 6.01810i 0.249458i
\(583\) 5.84661 5.84661i 0.242142 0.242142i
\(584\) 0.307664 0.0127312
\(585\) −5.04055 + 5.94723i −0.208401 + 0.245888i
\(586\) 7.88864i 0.325877i
\(587\) 3.36694 3.36694i 0.138969 0.138969i −0.634200 0.773169i \(-0.718671\pi\)
0.773169 + 0.634200i \(0.218671\pi\)
\(588\) 13.6121 + 4.85195i 0.561355 + 0.200091i
\(589\) 9.13586i 0.376436i
\(590\) 0.906679 + 0.906679i 0.0373274 + 0.0373274i
\(591\) 9.88149 9.88149i 0.406470 0.406470i
\(592\) −6.21933 + 6.21933i −0.255613 + 0.255613i
\(593\) 10.6837 + 10.6837i 0.438726 + 0.438726i 0.891583 0.452857i \(-0.149595\pi\)
−0.452857 + 0.891583i \(0.649595\pi\)
\(594\) 2.65745i 0.109037i
\(595\) −23.1928 + 16.3552i −0.950812 + 0.670497i
\(596\) −18.3684 + 18.3684i −0.752397 + 0.752397i
\(597\) 5.63893i 0.230786i
\(598\) −5.90430 + 6.96635i −0.241445 + 0.284875i
\(599\) −12.8437 −0.524778 −0.262389 0.964962i \(-0.584510\pi\)
−0.262389 + 0.964962i \(0.584510\pi\)
\(600\) 5.23726 5.23726i 0.213810 0.213810i
\(601\) 19.5732i 0.798409i −0.916862 0.399205i \(-0.869286\pi\)
0.916862 0.399205i \(-0.130714\pi\)
\(602\) −10.6762 + 7.52865i −0.435128 + 0.306845i
\(603\) 12.9878 + 12.9878i 0.528903 + 0.528903i
\(604\) −10.2873 10.2873i −0.418583 0.418583i
\(605\) 10.6187 + 10.6187i 0.431710 + 0.431710i
\(606\) 6.39280 6.39280i 0.259690 0.259690i
\(607\) 41.9804i 1.70393i 0.523598 + 0.851965i \(0.324589\pi\)
−0.523598 + 0.851965i \(0.675411\pi\)
\(608\) 27.5354 1.11671
\(609\) 1.96880 11.3873i 0.0797799 0.461438i
\(610\) 5.91493i 0.239488i
\(611\) −9.81137 8.31559i −0.396926 0.336413i
\(612\) 18.2319i 0.736981i
\(613\) 20.4993 + 20.4993i 0.827959 + 0.827959i 0.987234 0.159276i \(-0.0509158\pi\)
−0.159276 + 0.987234i \(0.550916\pi\)
\(614\) 6.56236i 0.264835i
\(615\) 3.13547 0.126434
\(616\) 0.797125 4.61048i 0.0321171 0.185762i
\(617\) 8.21440 + 8.21440i 0.330699 + 0.330699i 0.852852 0.522153i \(-0.174871\pi\)
−0.522153 + 0.852852i \(0.674871\pi\)
\(618\) −3.03761 + 3.03761i −0.122191 + 0.122191i
\(619\) 26.6973 + 26.6973i 1.07306 + 1.07306i 0.997112 + 0.0759445i \(0.0241972\pi\)
0.0759445 + 0.997112i \(0.475803\pi\)
\(620\) 4.39612 0.176553
\(621\) −24.5402 −0.984764
\(622\) 13.0910 + 13.0910i 0.524900 + 0.524900i
\(623\) −14.8574 21.0689i −0.595251 0.844107i
\(624\) 0.787965 + 9.54912i 0.0315438 + 0.382271i
\(625\) 2.42311 0.0969246
\(626\) 7.95367 7.95367i 0.317893 0.317893i
\(627\) −5.28726 −0.211153
\(628\) −16.2451 −0.648251
\(629\) −21.1934 + 21.1934i −0.845036 + 0.845036i
\(630\) −3.21295 0.555500i −0.128007 0.0221317i
\(631\) 5.13093 5.13093i 0.204259 0.204259i −0.597563 0.801822i \(-0.703864\pi\)
0.801822 + 0.597563i \(0.203864\pi\)
\(632\) 7.10791 7.10791i 0.282737 0.282737i
\(633\) 0.732080i 0.0290976i
\(634\) 6.54420i 0.259903i
\(635\) −1.59903 1.59903i −0.0634554 0.0634554i
\(636\) −20.2187 −0.801723
\(637\) −24.3901 6.49019i −0.966371 0.257151i
\(638\) −1.70545 −0.0675193
\(639\) −2.17148 2.17148i −0.0859026 0.0859026i
\(640\) 16.8382i 0.665586i
\(641\) 16.3357i 0.645220i −0.946532 0.322610i \(-0.895440\pi\)
0.946532 0.322610i \(-0.104560\pi\)
\(642\) 4.40523 4.40523i 0.173860 0.173860i
\(643\) 28.1910 28.1910i 1.11175 1.11175i 0.118832 0.992914i \(-0.462085\pi\)
0.992914 0.118832i \(-0.0379150\pi\)
\(644\) 19.4060 + 3.35517i 0.764702 + 0.132212i
\(645\) 11.0201 11.0201i 0.433915 0.433915i
\(646\) 21.2833 0.837380
\(647\) 11.1139 0.436932 0.218466 0.975845i \(-0.429895\pi\)
0.218466 + 0.975845i \(0.429895\pi\)
\(648\) 3.49929 3.49929i 0.137465 0.137465i
\(649\) 1.30105 0.0510709
\(650\) −3.81220 + 4.49793i −0.149527 + 0.176423i
\(651\) −3.37821 4.79054i −0.132402 0.187756i
\(652\) 9.06793 + 9.06793i 0.355127 + 0.355127i
\(653\) 4.95651 0.193963 0.0969816 0.995286i \(-0.469081\pi\)
0.0969816 + 0.995286i \(0.469081\pi\)
\(654\) −4.56659 −0.178568
\(655\) −5.48612 5.48612i −0.214360 0.214360i
\(656\) −2.65745 + 2.65745i −0.103756 + 0.103756i
\(657\) −0.153832 0.153832i −0.00600155 0.00600155i
\(658\) 0.916430 5.30053i 0.0357262 0.206636i
\(659\) 26.1514 1.01871 0.509357 0.860555i \(-0.329883\pi\)
0.509357 + 0.860555i \(0.329883\pi\)
\(660\) 2.54420i 0.0990328i
\(661\) −22.2906 22.2906i −0.867006 0.867006i 0.125134 0.992140i \(-0.460064\pi\)
−0.992140 + 0.125134i \(0.960064\pi\)
\(662\) 0.649738i 0.0252528i
\(663\) 2.68512 + 32.5402i 0.104282 + 1.26376i
\(664\) 36.4861i 1.41594i
\(665\) 3.34373 19.3398i 0.129664 0.749964i
\(666\) −3.44358 −0.133436
\(667\) 15.7489i 0.609801i
\(668\) 14.9225 14.9225i 0.577368 0.577368i
\(669\) 3.52175 + 3.52175i 0.136159 + 0.136159i
\(670\) −7.29562 7.29562i −0.281854 0.281854i
\(671\) 4.24387 + 4.24387i 0.163833 + 0.163833i
\(672\) −14.4387 + 10.1819i −0.556983 + 0.392776i
\(673\) 1.38550i 0.0534072i 0.999643 + 0.0267036i \(0.00850104\pi\)
−0.999643 + 0.0267036i \(0.991499\pi\)
\(674\) 10.7230 10.7230i 0.413034 0.413034i
\(675\) −15.8448 −0.609865
\(676\) −3.56959 21.4821i −0.137292 0.826237i
\(677\) 14.1868i 0.545242i 0.962122 + 0.272621i \(0.0878905\pi\)
−0.962122 + 0.272621i \(0.912110\pi\)
\(678\) 0.798290 0.798290i 0.0306582 0.0306582i
\(679\) −18.5247 + 13.0633i −0.710912 + 0.501324i
\(680\) 22.4690i 0.861646i
\(681\) −24.2252 24.2252i −0.928312 0.928312i
\(682\) −0.611704 + 0.611704i −0.0234234 + 0.0234234i
\(683\) 27.2882 27.2882i 1.04415 1.04415i 0.0451754 0.998979i \(-0.485615\pi\)
0.998979 0.0451754i \(-0.0143847\pi\)
\(684\) −8.91577 8.91577i −0.340903 0.340903i
\(685\) 26.2506i 1.00298i
\(686\) −2.83387 10.1685i −0.108198 0.388237i
\(687\) 16.2750 16.2750i 0.620931 0.620931i
\(688\) 18.6801i 0.712170i
\(689\) 35.1926 2.90399i 1.34073 0.110633i
\(690\) 4.55642 0.173460
\(691\) 16.1937 16.1937i 0.616037 0.616037i −0.328475 0.944513i \(-0.606535\pi\)
0.944513 + 0.328475i \(0.106535\pi\)
\(692\) 11.9862i 0.455647i
\(693\) −2.70380 + 1.90668i −0.102709 + 0.0724287i
\(694\) 8.14411 + 8.14411i 0.309146 + 0.309146i
\(695\) 7.17148 + 7.17148i 0.272030 + 0.272030i
\(696\) 6.46966 + 6.46966i 0.245232 + 0.245232i
\(697\) −9.05571 + 9.05571i −0.343009 + 0.343009i
\(698\) 1.86570i 0.0706180i
\(699\) 19.9947 0.756271
\(700\) 12.5298 + 2.16632i 0.473580 + 0.0818792i
\(701\) 15.2981i 0.577800i −0.957359 0.288900i \(-0.906711\pi\)
0.957359 0.288900i \(-0.0932895\pi\)
\(702\) −7.33804 + 8.65799i −0.276957 + 0.326775i
\(703\) 20.7280i 0.781771i
\(704\) −0.730841 0.730841i −0.0275446 0.0275446i
\(705\) 6.41723i 0.241687i
\(706\) 8.65808 0.325851
\(707\) 33.5547 + 5.80141i 1.26196 + 0.218185i
\(708\) −2.24965 2.24965i −0.0845469 0.0845469i
\(709\) −2.74107 + 2.74107i −0.102943 + 0.102943i −0.756703 0.653759i \(-0.773191\pi\)
0.653759 + 0.756703i \(0.273191\pi\)
\(710\) 1.21979 + 1.21979i 0.0457778 + 0.0457778i
\(711\) −7.10791 −0.266567
\(712\) 20.4113 0.764948
\(713\) −5.64878 5.64878i −0.211548 0.211548i
\(714\) −11.1602 + 7.87002i −0.417662 + 0.294528i
\(715\) −0.365420 4.42842i −0.0136659 0.165614i
\(716\) 23.1368 0.864663
\(717\) 1.03974 1.03974i 0.0388299 0.0388299i
\(718\) 13.6810 0.510571
\(719\) −5.99456 −0.223559 −0.111780 0.993733i \(-0.535655\pi\)
−0.111780 + 0.993733i \(0.535655\pi\)
\(720\) −3.29683 + 3.29683i −0.122865 + 0.122865i
\(721\) −15.9439 2.75661i −0.593782 0.102661i
\(722\) −2.75035 + 2.75035i −0.102358 + 0.102358i
\(723\) −18.8515 + 18.8515i −0.701096 + 0.701096i
\(724\) 7.63947i 0.283919i
\(725\) 10.1685i 0.377650i
\(726\) 5.10964 + 5.10964i 0.189636 + 0.189636i
\(727\) 14.6184 0.542168 0.271084 0.962556i \(-0.412618\pi\)
0.271084 + 0.962556i \(0.412618\pi\)
\(728\) 15.3280 12.8199i 0.568093 0.475136i
\(729\) −23.9175 −0.885833
\(730\) 0.0864119 + 0.0864119i 0.00319825 + 0.00319825i
\(731\) 63.6554i 2.35438i
\(732\) 14.6761i 0.542444i
\(733\) −28.0685 + 28.0685i −1.03673 + 1.03673i −0.0374350 + 0.999299i \(0.511919\pi\)
−0.999299 + 0.0374350i \(0.988081\pi\)
\(734\) −3.94881 + 3.94881i −0.145753 + 0.145753i
\(735\) 5.39802 + 11.3775i 0.199109 + 0.419667i
\(736\) −17.0254 + 17.0254i −0.627564 + 0.627564i
\(737\) −10.4690 −0.385630
\(738\) −1.47141 −0.0541632
\(739\) −16.6028 + 16.6028i −0.610746 + 0.610746i −0.943140 0.332395i \(-0.892143\pi\)
0.332395 + 0.943140i \(0.392143\pi\)
\(740\) −9.97420 −0.366659
\(741\) −17.2259 14.5997i −0.632809 0.536335i
\(742\) 8.51151 + 12.0699i 0.312467 + 0.443101i
\(743\) −2.87636 2.87636i −0.105523 0.105523i 0.652374 0.757897i \(-0.273773\pi\)
−0.757897 + 0.652374i \(0.773773\pi\)
\(744\) 4.64103 0.170148
\(745\) −22.6371 −0.829361
\(746\) 2.40502 + 2.40502i 0.0880539 + 0.0880539i
\(747\) 18.2431 18.2431i 0.667479 0.667479i
\(748\) −7.34804 7.34804i −0.268671 0.268671i
\(749\) 23.1223 + 3.99771i 0.844871 + 0.146073i
\(750\) 8.06888 0.294634
\(751\) 45.9438i 1.67651i −0.545275 0.838257i \(-0.683575\pi\)
0.545275 0.838257i \(-0.316425\pi\)
\(752\) −5.43890 5.43890i −0.198336 0.198336i
\(753\) 33.8129i 1.23221i
\(754\) −5.55636 4.70927i −0.202351 0.171501i
\(755\) 12.6780i 0.461400i
\(756\) 24.1183 + 4.16991i 0.877174 + 0.151658i
\(757\) −24.7889 −0.900969 −0.450484 0.892784i \(-0.648749\pi\)
−0.450484 + 0.892784i \(0.648749\pi\)
\(758\) 1.72592i 0.0626881i
\(759\) 3.26916 3.26916i 0.118663 0.118663i
\(760\) 10.9878 + 10.9878i 0.398569 + 0.398569i
\(761\) 10.8450 + 10.8450i 0.393133 + 0.393133i 0.875802 0.482670i \(-0.160333\pi\)
−0.482670 + 0.875802i \(0.660333\pi\)
\(762\) −0.769443 0.769443i −0.0278740 0.0278740i
\(763\) −9.91256 14.0567i −0.358859 0.508887i
\(764\) 6.20711i 0.224565i
\(765\) −11.2345 + 11.2345i −0.406184 + 0.406184i
\(766\) −2.34687 −0.0847958
\(767\) 4.23884 + 3.59261i 0.153056 + 0.129722i
\(768\) 5.08489i 0.183485i
\(769\) −4.63670 + 4.63670i −0.167204 + 0.167204i −0.785749 0.618545i \(-0.787722\pi\)
0.618545 + 0.785749i \(0.287722\pi\)
\(770\) 1.51881 1.07104i 0.0547340 0.0385975i
\(771\) 25.3538i 0.913094i
\(772\) 28.5623 + 28.5623i 1.02798 + 1.02798i
\(773\) −5.68398 + 5.68398i −0.204438 + 0.204438i −0.801899 0.597460i \(-0.796177\pi\)
0.597460 + 0.801899i \(0.296177\pi\)
\(774\) −5.17148 + 5.17148i −0.185885 + 0.185885i
\(775\) −3.64722 3.64722i −0.131012 0.131012i
\(776\) 17.9466i 0.644244i
\(777\) 7.66469 + 10.8691i 0.274969 + 0.389926i
\(778\) 7.03032 7.03032i 0.252049 0.252049i
\(779\)