Properties

Label 441.2.h.h.214.1
Level $441$
Weight $2$
Character 441.214
Analytic conductor $3.521$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 214.1
Character \(\chi\) \(=\) 441.214
Dual form 441.2.h.h.373.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.71513 q^{2} +(-1.16958 - 1.27753i) q^{3} +5.37195 q^{4} +(-0.793197 + 1.37386i) q^{5} +(3.17555 + 3.46867i) q^{6} -9.15528 q^{8} +(-0.264183 + 2.98835i) q^{9} +O(q^{10})\) \(q-2.71513 q^{2} +(-1.16958 - 1.27753i) q^{3} +5.37195 q^{4} +(-0.793197 + 1.37386i) q^{5} +(3.17555 + 3.46867i) q^{6} -9.15528 q^{8} +(-0.264183 + 2.98835i) q^{9} +(2.15363 - 3.73020i) q^{10} +(0.674376 + 1.16805i) q^{11} +(-6.28290 - 6.86284i) q^{12} +(-1.58916 - 2.75251i) q^{13} +(2.68285 - 0.593495i) q^{15} +14.1139 q^{16} +(1.40027 - 2.42534i) q^{17} +(0.717292 - 8.11375i) q^{18} +(0.312846 + 0.541866i) q^{19} +(-4.26101 + 7.38028i) q^{20} +(-1.83102 - 3.17142i) q^{22} +(0.142434 - 0.246702i) q^{23} +(10.7078 + 11.6962i) q^{24} +(1.24168 + 2.15065i) q^{25} +(4.31479 + 7.47343i) q^{26} +(4.12669 - 3.15760i) q^{27} +(2.27396 - 3.93861i) q^{29} +(-7.28430 + 1.61142i) q^{30} -7.43005 q^{31} -20.0106 q^{32} +(0.703493 - 2.22767i) q^{33} +(-3.80191 + 6.58511i) q^{34} +(-1.41918 + 16.0532i) q^{36} +(-4.01126 - 6.94770i) q^{37} +(-0.849420 - 1.47124i) q^{38} +(-1.65778 + 5.24948i) q^{39} +(7.26194 - 12.5780i) q^{40} +(-5.01329 - 8.68327i) q^{41} +(-3.12937 + 5.42022i) q^{43} +(3.62271 + 6.27472i) q^{44} +(-3.89601 - 2.73329i) q^{45} +(-0.386726 + 0.669829i) q^{46} -11.1477 q^{47} +(-16.5073 - 18.0310i) q^{48} +(-3.37132 - 5.83930i) q^{50} +(-4.73617 + 1.04773i) q^{51} +(-8.53689 - 14.7863i) q^{52} +(-1.39349 + 2.41359i) q^{53} +(-11.2045 + 8.57329i) q^{54} -2.13965 q^{55} +(0.326354 - 1.03343i) q^{57} +(-6.17410 + 10.6939i) q^{58} -4.57469 q^{59} +(14.4121 - 3.18822i) q^{60} +0.385014 q^{61} +20.1736 q^{62} +26.1036 q^{64} +5.04207 q^{65} +(-1.91008 + 6.04841i) q^{66} -2.53916 q^{67} +(7.52217 - 13.0288i) q^{68} +(-0.481757 + 0.106573i) q^{69} -1.45208 q^{71} +(2.41867 - 27.3591i) q^{72} +(-0.234067 + 0.405416i) q^{73} +(10.8911 + 18.8639i) q^{74} +(1.29529 - 4.10164i) q^{75} +(1.68059 + 2.91087i) q^{76} +(4.50108 - 14.2530i) q^{78} -15.7124 q^{79} +(-11.1951 + 19.3905i) q^{80} +(-8.86041 - 1.57894i) q^{81} +(13.6117 + 23.5762i) q^{82} +(6.99338 - 12.1129i) q^{83} +(2.22138 + 3.84754i) q^{85} +(8.49665 - 14.7166i) q^{86} +(-7.69128 + 1.70145i) q^{87} +(-6.17410 - 10.6939i) q^{88} +(-1.29353 - 2.24046i) q^{89} +(10.5782 + 7.42126i) q^{90} +(0.765146 - 1.32527i) q^{92} +(8.69001 + 9.49213i) q^{93} +30.2674 q^{94} -0.992595 q^{95} +(23.4039 + 25.5642i) q^{96} +(-7.22962 + 12.5221i) q^{97} +(-3.66871 + 1.70669i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 8q^{2} + 24q^{4} - 24q^{8} - 4q^{9} + O(q^{10}) \) \( 24q - 8q^{2} + 24q^{4} - 24q^{8} - 4q^{9} + 20q^{11} + 4q^{15} + 24q^{16} - 32q^{18} + 32q^{23} - 12q^{25} + 16q^{29} - 84q^{30} - 96q^{32} - 4q^{36} - 12q^{37} + 8q^{39} + 56q^{44} + 24q^{46} - 4q^{50} + 64q^{51} + 32q^{53} - 12q^{57} + 32q^{60} + 96q^{64} - 120q^{65} + 24q^{67} - 112q^{71} + 68q^{74} - 60q^{78} - 24q^{79} - 40q^{81} + 12q^{85} + 76q^{86} + 16q^{92} - 32q^{93} - 128q^{95} + 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.71513 −1.91989 −0.959944 0.280191i \(-0.909602\pi\)
−0.959944 + 0.280191i \(0.909602\pi\)
\(3\) −1.16958 1.27753i −0.675255 0.737584i
\(4\) 5.37195 2.68597
\(5\) −0.793197 + 1.37386i −0.354728 + 0.614407i −0.987071 0.160281i \(-0.948760\pi\)
0.632343 + 0.774688i \(0.282093\pi\)
\(6\) 3.17555 + 3.46867i 1.29641 + 1.41608i
\(7\) 0 0
\(8\) −9.15528 −3.23688
\(9\) −0.264183 + 2.98835i −0.0880610 + 0.996115i
\(10\) 2.15363 3.73020i 0.681039 1.17959i
\(11\) 0.674376 + 1.16805i 0.203332 + 0.352181i 0.949600 0.313464i \(-0.101490\pi\)
−0.746268 + 0.665646i \(0.768156\pi\)
\(12\) −6.28290 6.86284i −1.81372 1.98113i
\(13\) −1.58916 2.75251i −0.440754 0.763409i 0.556991 0.830518i \(-0.311956\pi\)
−0.997746 + 0.0671096i \(0.978622\pi\)
\(14\) 0 0
\(15\) 2.68285 0.593495i 0.692709 0.153240i
\(16\) 14.1139 3.52848
\(17\) 1.40027 2.42534i 0.339615 0.588230i −0.644745 0.764397i \(-0.723037\pi\)
0.984360 + 0.176167i \(0.0563699\pi\)
\(18\) 0.717292 8.11375i 0.169067 1.91243i
\(19\) 0.312846 + 0.541866i 0.0717719 + 0.124313i 0.899678 0.436554i \(-0.143801\pi\)
−0.827906 + 0.560867i \(0.810468\pi\)
\(20\) −4.26101 + 7.38028i −0.952791 + 1.65028i
\(21\) 0 0
\(22\) −1.83102 3.17142i −0.390375 0.676149i
\(23\) 0.142434 0.246702i 0.0296995 0.0514410i −0.850794 0.525500i \(-0.823878\pi\)
0.880493 + 0.474059i \(0.157212\pi\)
\(24\) 10.7078 + 11.6962i 2.18572 + 2.38747i
\(25\) 1.24168 + 2.15065i 0.248336 + 0.430130i
\(26\) 4.31479 + 7.47343i 0.846199 + 1.46566i
\(27\) 4.12669 3.15760i 0.794182 0.607679i
\(28\) 0 0
\(29\) 2.27396 3.93861i 0.422264 0.731382i −0.573897 0.818928i \(-0.694569\pi\)
0.996161 + 0.0875454i \(0.0279023\pi\)
\(30\) −7.28430 + 1.61142i −1.32992 + 0.294203i
\(31\) −7.43005 −1.33448 −0.667238 0.744845i \(-0.732524\pi\)
−0.667238 + 0.744845i \(0.732524\pi\)
\(32\) −20.0106 −3.53741
\(33\) 0.703493 2.22767i 0.122462 0.387787i
\(34\) −3.80191 + 6.58511i −0.652023 + 1.12934i
\(35\) 0 0
\(36\) −1.41918 + 16.0532i −0.236529 + 2.67554i
\(37\) −4.01126 6.94770i −0.659447 1.14220i −0.980759 0.195222i \(-0.937457\pi\)
0.321312 0.946973i \(-0.395876\pi\)
\(38\) −0.849420 1.47124i −0.137794 0.238666i
\(39\) −1.65778 + 5.24948i −0.265457 + 0.840589i
\(40\) 7.26194 12.5780i 1.14821 1.98876i
\(41\) −5.01329 8.68327i −0.782944 1.35610i −0.930219 0.367004i \(-0.880384\pi\)
0.147275 0.989096i \(-0.452950\pi\)
\(42\) 0 0
\(43\) −3.12937 + 5.42022i −0.477224 + 0.826576i −0.999659 0.0261027i \(-0.991690\pi\)
0.522435 + 0.852679i \(0.325024\pi\)
\(44\) 3.62271 + 6.27472i 0.546144 + 0.945950i
\(45\) −3.89601 2.73329i −0.580783 0.407455i
\(46\) −0.386726 + 0.669829i −0.0570197 + 0.0987609i
\(47\) −11.1477 −1.62605 −0.813026 0.582227i \(-0.802181\pi\)
−0.813026 + 0.582227i \(0.802181\pi\)
\(48\) −16.5073 18.0310i −2.38262 2.60255i
\(49\) 0 0
\(50\) −3.37132 5.83930i −0.476777 0.825802i
\(51\) −4.73617 + 1.04773i −0.663196 + 0.146711i
\(52\) −8.53689 14.7863i −1.18385 2.05049i
\(53\) −1.39349 + 2.41359i −0.191410 + 0.331532i −0.945718 0.324989i \(-0.894639\pi\)
0.754308 + 0.656521i \(0.227973\pi\)
\(54\) −11.2045 + 8.57329i −1.52474 + 1.16668i
\(55\) −2.13965 −0.288510
\(56\) 0 0
\(57\) 0.326354 1.03343i 0.0432266 0.136881i
\(58\) −6.17410 + 10.6939i −0.810699 + 1.40417i
\(59\) −4.57469 −0.595574 −0.297787 0.954632i \(-0.596248\pi\)
−0.297787 + 0.954632i \(0.596248\pi\)
\(60\) 14.4121 3.18822i 1.86060 0.411598i
\(61\) 0.385014 0.0492960 0.0246480 0.999696i \(-0.492154\pi\)
0.0246480 + 0.999696i \(0.492154\pi\)
\(62\) 20.1736 2.56205
\(63\) 0 0
\(64\) 26.1036 3.26295
\(65\) 5.04207 0.625392
\(66\) −1.91008 + 6.04841i −0.235114 + 0.744508i
\(67\) −2.53916 −0.310208 −0.155104 0.987898i \(-0.549571\pi\)
−0.155104 + 0.987898i \(0.549571\pi\)
\(68\) 7.52217 13.0288i 0.912197 1.57997i
\(69\) −0.481757 + 0.106573i −0.0579968 + 0.0128299i
\(70\) 0 0
\(71\) −1.45208 −0.172330 −0.0861651 0.996281i \(-0.527461\pi\)
−0.0861651 + 0.996281i \(0.527461\pi\)
\(72\) 2.41867 27.3591i 0.285043 3.22431i
\(73\) −0.234067 + 0.405416i −0.0273955 + 0.0474503i −0.879398 0.476087i \(-0.842055\pi\)
0.852003 + 0.523538i \(0.175388\pi\)
\(74\) 10.8911 + 18.8639i 1.26606 + 2.19289i
\(75\) 1.29529 4.10164i 0.149567 0.473616i
\(76\) 1.68059 + 2.91087i 0.192777 + 0.333900i
\(77\) 0 0
\(78\) 4.50108 14.2530i 0.509647 1.61384i
\(79\) −15.7124 −1.76778 −0.883892 0.467691i \(-0.845086\pi\)
−0.883892 + 0.467691i \(0.845086\pi\)
\(80\) −11.1951 + 19.3905i −1.25165 + 2.16792i
\(81\) −8.86041 1.57894i −0.984491 0.175438i
\(82\) 13.6117 + 23.5762i 1.50317 + 2.60356i
\(83\) 6.99338 12.1129i 0.767623 1.32956i −0.171225 0.985232i \(-0.554772\pi\)
0.938848 0.344331i \(-0.111894\pi\)
\(84\) 0 0
\(85\) 2.22138 + 3.84754i 0.240942 + 0.417324i
\(86\) 8.49665 14.7166i 0.916217 1.58693i
\(87\) −7.69128 + 1.70145i −0.824592 + 0.182415i
\(88\) −6.17410 10.6939i −0.658162 1.13997i
\(89\) −1.29353 2.24046i −0.137114 0.237488i 0.789289 0.614022i \(-0.210449\pi\)
−0.926403 + 0.376534i \(0.877116\pi\)
\(90\) 10.5782 + 7.42126i 1.11504 + 0.782269i
\(91\) 0 0
\(92\) 0.765146 1.32527i 0.0797719 0.138169i
\(93\) 8.69001 + 9.49213i 0.901112 + 0.984288i
\(94\) 30.2674 3.12184
\(95\) −0.992595 −0.101838
\(96\) 23.4039 + 25.5642i 2.38865 + 2.60913i
\(97\) −7.22962 + 12.5221i −0.734057 + 1.27142i 0.221079 + 0.975256i \(0.429042\pi\)
−0.955136 + 0.296168i \(0.904291\pi\)
\(98\) 0 0
\(99\) −3.66871 + 1.70669i −0.368719 + 0.171529i
\(100\) 6.67023 + 11.5532i 0.667023 + 1.15532i
\(101\) 4.91888 + 8.51975i 0.489447 + 0.847747i 0.999926 0.0121430i \(-0.00386534\pi\)
−0.510479 + 0.859890i \(0.670532\pi\)
\(102\) 12.8593 2.84471i 1.27326 0.281669i
\(103\) 5.52897 9.57646i 0.544786 0.943597i −0.453834 0.891086i \(-0.649944\pi\)
0.998620 0.0525110i \(-0.0167225\pi\)
\(104\) 14.5492 + 25.2000i 1.42667 + 2.47106i
\(105\) 0 0
\(106\) 3.78350 6.55322i 0.367486 0.636505i
\(107\) 0.962153 + 1.66650i 0.0930149 + 0.161106i 0.908778 0.417279i \(-0.137016\pi\)
−0.815764 + 0.578386i \(0.803683\pi\)
\(108\) 22.1684 16.9624i 2.13315 1.63221i
\(109\) 9.30341 16.1140i 0.891105 1.54344i 0.0525523 0.998618i \(-0.483264\pi\)
0.838553 0.544821i \(-0.183402\pi\)
\(110\) 5.80944 0.553908
\(111\) −4.18445 + 13.2504i −0.397170 + 1.25767i
\(112\) 0 0
\(113\) 1.59338 + 2.75982i 0.149893 + 0.259622i 0.931188 0.364540i \(-0.118774\pi\)
−0.781295 + 0.624162i \(0.785440\pi\)
\(114\) −0.886094 + 2.80589i −0.0829903 + 0.262795i
\(115\) 0.225956 + 0.391367i 0.0210705 + 0.0364951i
\(116\) 12.2156 21.1580i 1.13419 1.96447i
\(117\) 8.64528 4.02180i 0.799256 0.371815i
\(118\) 12.4209 1.14344
\(119\) 0 0
\(120\) −24.5623 + 5.43361i −2.24222 + 0.496019i
\(121\) 4.59043 7.95086i 0.417312 0.722806i
\(122\) −1.04536 −0.0946428
\(123\) −5.22975 + 16.5604i −0.471550 + 1.49320i
\(124\) −39.9138 −3.58437
\(125\) −11.8715 −1.06182
\(126\) 0 0
\(127\) −8.37387 −0.743061 −0.371530 0.928421i \(-0.621167\pi\)
−0.371530 + 0.928421i \(0.621167\pi\)
\(128\) −30.8535 −2.72709
\(129\) 10.5845 2.34149i 0.931918 0.206157i
\(130\) −13.6899 −1.20068
\(131\) −5.98629 + 10.3686i −0.523024 + 0.905905i 0.476616 + 0.879111i \(0.341863\pi\)
−0.999641 + 0.0267937i \(0.991470\pi\)
\(132\) 3.77913 11.9669i 0.328931 1.04158i
\(133\) 0 0
\(134\) 6.89415 0.595564
\(135\) 1.06480 + 8.17408i 0.0916438 + 0.703513i
\(136\) −12.8199 + 22.2046i −1.09929 + 1.90403i
\(137\) −8.27525 14.3332i −0.707003 1.22456i −0.965964 0.258677i \(-0.916714\pi\)
0.258961 0.965888i \(-0.416620\pi\)
\(138\) 1.30803 0.289361i 0.111347 0.0246320i
\(139\) −3.95119 6.84367i −0.335136 0.580472i 0.648375 0.761321i \(-0.275449\pi\)
−0.983511 + 0.180849i \(0.942116\pi\)
\(140\) 0 0
\(141\) 13.0380 + 14.2415i 1.09800 + 1.19935i
\(142\) 3.94259 0.330855
\(143\) 2.14339 3.71245i 0.179239 0.310451i
\(144\) −3.72865 + 42.1772i −0.310721 + 3.51477i
\(145\) 3.60739 + 6.24819i 0.299578 + 0.518884i
\(146\) 0.635523 1.10076i 0.0525962 0.0910994i
\(147\) 0 0
\(148\) −21.5483 37.3227i −1.77126 3.06791i
\(149\) 6.83427 11.8373i 0.559885 0.969749i −0.437620 0.899160i \(-0.644179\pi\)
0.997505 0.0705895i \(-0.0224881\pi\)
\(150\) −3.51688 + 11.1365i −0.287152 + 0.909290i
\(151\) −1.94982 3.37718i −0.158674 0.274831i 0.775717 0.631081i \(-0.217389\pi\)
−0.934391 + 0.356250i \(0.884055\pi\)
\(152\) −2.86420 4.96093i −0.232317 0.402385i
\(153\) 6.87781 + 4.82522i 0.556038 + 0.390096i
\(154\) 0 0
\(155\) 5.89349 10.2078i 0.473376 0.819912i
\(156\) −8.90548 + 28.1999i −0.713009 + 2.25780i
\(157\) 0.294352 0.0234919 0.0117459 0.999931i \(-0.496261\pi\)
0.0117459 + 0.999931i \(0.496261\pi\)
\(158\) 42.6613 3.39395
\(159\) 4.71323 1.04265i 0.373784 0.0826877i
\(160\) 15.8723 27.4917i 1.25482 2.17341i
\(161\) 0 0
\(162\) 24.0572 + 4.28703i 1.89011 + 0.336821i
\(163\) −5.35455 9.27436i −0.419401 0.726424i 0.576478 0.817112i \(-0.304427\pi\)
−0.995879 + 0.0906886i \(0.971093\pi\)
\(164\) −26.9311 46.6461i −2.10297 3.64245i
\(165\) 2.50249 + 2.73348i 0.194818 + 0.212801i
\(166\) −18.9880 + 32.8881i −1.47375 + 2.55261i
\(167\) −1.59872 2.76907i −0.123713 0.214277i 0.797516 0.603298i \(-0.206147\pi\)
−0.921229 + 0.389020i \(0.872814\pi\)
\(168\) 0 0
\(169\) 1.44913 2.50997i 0.111472 0.193074i
\(170\) −6.03133 10.4466i −0.462582 0.801215i
\(171\) −1.70193 + 0.791741i −0.130150 + 0.0605460i
\(172\) −16.8108 + 29.1171i −1.28181 + 2.22016i
\(173\) 11.4375 0.869577 0.434789 0.900533i \(-0.356823\pi\)
0.434789 + 0.900533i \(0.356823\pi\)
\(174\) 20.8828 4.61966i 1.58312 0.350216i
\(175\) 0 0
\(176\) 9.51809 + 16.4858i 0.717453 + 1.24266i
\(177\) 5.35045 + 5.84432i 0.402164 + 0.439286i
\(178\) 3.51210 + 6.08314i 0.263243 + 0.455951i
\(179\) −0.549275 + 0.951372i −0.0410547 + 0.0711089i −0.885823 0.464024i \(-0.846405\pi\)
0.844768 + 0.535133i \(0.179738\pi\)
\(180\) −20.9292 14.6831i −1.55997 1.09441i
\(181\) −3.19013 −0.237120 −0.118560 0.992947i \(-0.537828\pi\)
−0.118560 + 0.992947i \(0.537828\pi\)
\(182\) 0 0
\(183\) −0.450303 0.491868i −0.0332874 0.0363599i
\(184\) −1.30402 + 2.25863i −0.0961336 + 0.166508i
\(185\) 12.7269 0.935698
\(186\) −23.5945 25.7724i −1.73003 1.88972i
\(187\) 3.77723 0.276218
\(188\) −59.8846 −4.36753
\(189\) 0 0
\(190\) 2.69503 0.195518
\(191\) 3.86815 0.279889 0.139945 0.990159i \(-0.455308\pi\)
0.139945 + 0.990159i \(0.455308\pi\)
\(192\) −30.5301 33.3482i −2.20332 2.40670i
\(193\) −4.13585 −0.297705 −0.148853 0.988859i \(-0.547558\pi\)
−0.148853 + 0.988859i \(0.547558\pi\)
\(194\) 19.6294 33.9991i 1.40931 2.44099i
\(195\) −5.89709 6.44141i −0.422299 0.461279i
\(196\) 0 0
\(197\) −0.889267 −0.0633576 −0.0316788 0.999498i \(-0.510085\pi\)
−0.0316788 + 0.999498i \(0.510085\pi\)
\(198\) 9.96102 4.63389i 0.707899 0.329316i
\(199\) 3.16193 5.47663i 0.224143 0.388228i −0.731919 0.681392i \(-0.761375\pi\)
0.956062 + 0.293164i \(0.0947083\pi\)
\(200\) −11.3679 19.6898i −0.803833 1.39228i
\(201\) 2.96974 + 3.24386i 0.209469 + 0.228804i
\(202\) −13.3554 23.1323i −0.939684 1.62758i
\(203\) 0 0
\(204\) −25.4424 + 5.62833i −1.78133 + 0.394062i
\(205\) 15.9061 1.11093
\(206\) −15.0119 + 26.0014i −1.04593 + 1.81160i
\(207\) 0.699603 + 0.490815i 0.0486258 + 0.0341140i
\(208\) −22.4293 38.8487i −1.55519 2.69367i
\(209\) −0.421952 + 0.730843i −0.0291870 + 0.0505535i
\(210\) 0 0
\(211\) 5.71291 + 9.89505i 0.393293 + 0.681204i 0.992882 0.119105i \(-0.0380025\pi\)
−0.599589 + 0.800308i \(0.704669\pi\)
\(212\) −7.48574 + 12.9657i −0.514123 + 0.890487i
\(213\) 1.69832 + 1.85508i 0.116367 + 0.127108i
\(214\) −2.61237 4.52476i −0.178578 0.309307i
\(215\) −4.96441 8.59860i −0.338570 0.586420i
\(216\) −37.7810 + 28.9087i −2.57067 + 1.96699i
\(217\) 0 0
\(218\) −25.2600 + 43.7516i −1.71082 + 2.96323i
\(219\) 0.791691 0.175136i 0.0534975 0.0118346i
\(220\) −11.4941 −0.774931
\(221\) −8.90101 −0.598747
\(222\) 11.3613 35.9766i 0.762523 2.41459i
\(223\) −8.35953 + 14.4791i −0.559796 + 0.969595i 0.437717 + 0.899113i \(0.355787\pi\)
−0.997513 + 0.0704822i \(0.977546\pi\)
\(224\) 0 0
\(225\) −6.75492 + 3.14240i −0.450328 + 0.209493i
\(226\) −4.32625 7.49328i −0.287778 0.498446i
\(227\) 8.53501 + 14.7831i 0.566489 + 0.981187i 0.996909 + 0.0785588i \(0.0250318\pi\)
−0.430421 + 0.902628i \(0.641635\pi\)
\(228\) 1.75316 5.55150i 0.116106 0.367657i
\(229\) 9.89471 17.1381i 0.653861 1.13252i −0.328317 0.944567i \(-0.606482\pi\)
0.982178 0.187953i \(-0.0601851\pi\)
\(230\) −0.613500 1.06261i −0.0404530 0.0700666i
\(231\) 0 0
\(232\) −20.8187 + 36.0591i −1.36682 + 2.36740i
\(233\) −2.96579 5.13691i −0.194296 0.336530i 0.752374 0.658736i \(-0.228909\pi\)
−0.946669 + 0.322207i \(0.895575\pi\)
\(234\) −23.4731 + 10.9197i −1.53448 + 0.713844i
\(235\) 8.84228 15.3153i 0.576807 0.999058i
\(236\) −24.5750 −1.59969
\(237\) 18.3769 + 20.0731i 1.19371 + 1.30389i
\(238\) 0 0
\(239\) −10.0277 17.3685i −0.648637 1.12347i −0.983449 0.181187i \(-0.942006\pi\)
0.334812 0.942285i \(-0.391327\pi\)
\(240\) 37.8655 8.37654i 2.44421 0.540703i
\(241\) 14.6444 + 25.3648i 0.943326 + 1.63389i 0.759069 + 0.651010i \(0.225654\pi\)
0.184256 + 0.982878i \(0.441012\pi\)
\(242\) −12.4636 + 21.5877i −0.801193 + 1.38771i
\(243\) 8.34578 + 13.1662i 0.535382 + 0.844610i
\(244\) 2.06827 0.132408
\(245\) 0 0
\(246\) 14.1995 44.9637i 0.905324 2.86678i
\(247\) 0.994327 1.72223i 0.0632675 0.109583i
\(248\) 68.0242 4.31954
\(249\) −23.6539 + 5.23267i −1.49901 + 0.331607i
\(250\) 32.2328 2.03858
\(251\) 22.7856 1.43821 0.719106 0.694901i \(-0.244552\pi\)
0.719106 + 0.694901i \(0.244552\pi\)
\(252\) 0 0
\(253\) 0.384215 0.0241554
\(254\) 22.7362 1.42659
\(255\) 2.31729 7.33787i 0.145114 0.459515i
\(256\) 31.5642 1.97276
\(257\) −12.1444 + 21.0348i −0.757550 + 1.31211i 0.186547 + 0.982446i \(0.440270\pi\)
−0.944097 + 0.329668i \(0.893063\pi\)
\(258\) −28.7385 + 6.35747i −1.78918 + 0.395798i
\(259\) 0 0
\(260\) 27.0857 1.67979
\(261\) 11.1692 + 7.83589i 0.691356 + 0.485030i
\(262\) 16.2536 28.1520i 1.00415 1.73924i
\(263\) 4.30578 + 7.45782i 0.265506 + 0.459869i 0.967696 0.252120i \(-0.0811278\pi\)
−0.702190 + 0.711989i \(0.747794\pi\)
\(264\) −6.44068 + 20.3949i −0.396396 + 1.25522i
\(265\) −2.21062 3.82890i −0.135797 0.235208i
\(266\) 0 0
\(267\) −1.34938 + 4.27291i −0.0825807 + 0.261498i
\(268\) −13.6402 −0.833209
\(269\) −7.61561 + 13.1906i −0.464332 + 0.804247i −0.999171 0.0407073i \(-0.987039\pi\)
0.534839 + 0.844954i \(0.320372\pi\)
\(270\) −2.89109 22.1937i −0.175946 1.35067i
\(271\) −2.33910 4.05144i −0.142090 0.246108i 0.786193 0.617981i \(-0.212049\pi\)
−0.928284 + 0.371873i \(0.878716\pi\)
\(272\) 19.7633 34.2310i 1.19832 2.07556i
\(273\) 0 0
\(274\) 22.4684 + 38.9164i 1.35737 + 2.35103i
\(275\) −1.67472 + 2.90069i −0.100989 + 0.174918i
\(276\) −2.58797 + 0.572507i −0.155778 + 0.0344608i
\(277\) 8.19537 + 14.1948i 0.492412 + 0.852883i 0.999962 0.00873986i \(-0.00278202\pi\)
−0.507550 + 0.861622i \(0.669449\pi\)
\(278\) 10.7280 + 18.5815i 0.643423 + 1.11444i
\(279\) 1.96289 22.2035i 0.117515 1.32929i
\(280\) 0 0
\(281\) 1.75702 3.04325i 0.104815 0.181545i −0.808848 0.588018i \(-0.799908\pi\)
0.913663 + 0.406473i \(0.133242\pi\)
\(282\) −35.4000 38.6676i −2.10804 2.30262i
\(283\) −26.0708 −1.54975 −0.774874 0.632116i \(-0.782187\pi\)
−0.774874 + 0.632116i \(0.782187\pi\)
\(284\) −7.80050 −0.462874
\(285\) 1.16092 + 1.26807i 0.0687667 + 0.0751142i
\(286\) −5.81958 + 10.0798i −0.344119 + 0.596031i
\(287\) 0 0
\(288\) 5.28645 59.7985i 0.311507 3.52366i
\(289\) 4.57850 + 7.93019i 0.269323 + 0.466482i
\(290\) −9.79455 16.9647i −0.575156 0.996199i
\(291\) 24.4530 5.40944i 1.43346 0.317107i
\(292\) −1.25740 + 2.17787i −0.0735835 + 0.127450i
\(293\) 9.44192 + 16.3539i 0.551603 + 0.955404i 0.998159 + 0.0606487i \(0.0193169\pi\)
−0.446556 + 0.894756i \(0.647350\pi\)
\(294\) 0 0
\(295\) 3.62863 6.28497i 0.211267 0.365925i
\(296\) 36.7242 + 63.6082i 2.13455 + 3.69715i
\(297\) 6.47118 + 2.69079i 0.375496 + 0.156136i
\(298\) −18.5559 + 32.1398i −1.07492 + 1.86181i
\(299\) −0.905400 −0.0523606
\(300\) 6.95823 22.0338i 0.401733 1.27212i
\(301\) 0 0
\(302\) 5.29401 + 9.16950i 0.304636 + 0.527645i
\(303\) 5.13126 16.2485i 0.294783 0.933454i
\(304\) 4.41549 + 7.64785i 0.253246 + 0.438634i
\(305\) −0.305392 + 0.528954i −0.0174867 + 0.0302878i
\(306\) −18.6742 13.1011i −1.06753 0.748940i
\(307\) 21.6407 1.23510 0.617551 0.786531i \(-0.288125\pi\)
0.617551 + 0.786531i \(0.288125\pi\)
\(308\) 0 0
\(309\) −18.7008 + 4.13696i −1.06385 + 0.235343i
\(310\) −16.0016 + 27.7156i −0.908830 + 1.57414i
\(311\) −4.49448 −0.254859 −0.127429 0.991848i \(-0.540673\pi\)
−0.127429 + 0.991848i \(0.540673\pi\)
\(312\) 15.1774 48.0604i 0.859251 2.72089i
\(313\) −8.60204 −0.486216 −0.243108 0.969999i \(-0.578167\pi\)
−0.243108 + 0.969999i \(0.578167\pi\)
\(314\) −0.799206 −0.0451018
\(315\) 0 0
\(316\) −84.4062 −4.74822
\(317\) −8.06255 −0.452838 −0.226419 0.974030i \(-0.572702\pi\)
−0.226419 + 0.974030i \(0.572702\pi\)
\(318\) −12.7971 + 2.83094i −0.717623 + 0.158751i
\(319\) 6.13402 0.343439
\(320\) −20.7053 + 35.8626i −1.15746 + 2.00478i
\(321\) 1.00370 3.17828i 0.0560208 0.177394i
\(322\) 0 0
\(323\) 1.75228 0.0974992
\(324\) −47.5977 8.48198i −2.64432 0.471221i
\(325\) 3.94646 6.83546i 0.218910 0.379163i
\(326\) 14.5383 + 25.1811i 0.805203 + 1.39465i
\(327\) −31.4672 + 6.96111i −1.74014 + 0.384950i
\(328\) 45.8981 + 79.4978i 2.53430 + 4.38953i
\(329\) 0 0
\(330\) −6.79458 7.42175i −0.374029 0.408554i
\(331\) −22.9026 −1.25884 −0.629419 0.777066i \(-0.716707\pi\)
−0.629419 + 0.777066i \(0.716707\pi\)
\(332\) 37.5681 65.0698i 2.06182 3.57117i
\(333\) 21.8218 10.1516i 1.19583 0.556302i
\(334\) 4.34075 + 7.51840i 0.237515 + 0.411388i
\(335\) 2.01405 3.48844i 0.110039 0.190594i
\(336\) 0 0
\(337\) −6.81891 11.8107i −0.371450 0.643369i 0.618339 0.785911i \(-0.287806\pi\)
−0.989789 + 0.142542i \(0.954472\pi\)
\(338\) −3.93458 + 6.81489i −0.214013 + 0.370681i
\(339\) 1.66218 5.26342i 0.0902772 0.285870i
\(340\) 11.9331 + 20.6688i 0.647164 + 1.12092i
\(341\) −5.01065 8.67869i −0.271342 0.469978i
\(342\) 4.62097 2.14968i 0.249873 0.116242i
\(343\) 0 0
\(344\) 28.6502 49.6237i 1.54472 2.67553i
\(345\) 0.235712 0.746399i 0.0126903 0.0401848i
\(346\) −31.0543 −1.66949
\(347\) −2.82563 −0.151688 −0.0758440 0.997120i \(-0.524165\pi\)
−0.0758440 + 0.997120i \(0.524165\pi\)
\(348\) −41.3171 + 9.14010i −2.21483 + 0.489961i
\(349\) 1.81202 3.13851i 0.0969951 0.168000i −0.813444 0.581643i \(-0.802410\pi\)
0.910440 + 0.413642i \(0.135744\pi\)
\(350\) 0 0
\(351\) −15.2493 6.34083i −0.813947 0.338448i
\(352\) −13.4947 23.3734i −0.719268 1.24581i
\(353\) −1.37701 2.38504i −0.0732907 0.126943i 0.827051 0.562127i \(-0.190017\pi\)
−0.900342 + 0.435184i \(0.856683\pi\)
\(354\) −14.5272 15.8681i −0.772110 0.843380i
\(355\) 1.15179 1.99495i 0.0611304 0.105881i
\(356\) −6.94877 12.0356i −0.368284 0.637887i
\(357\) 0 0
\(358\) 1.49135 2.58310i 0.0788205 0.136521i
\(359\) 8.40076 + 14.5505i 0.443375 + 0.767948i 0.997937 0.0641941i \(-0.0204477\pi\)
−0.554562 + 0.832142i \(0.687114\pi\)
\(360\) 35.6691 + 25.0241i 1.87992 + 1.31888i
\(361\) 9.30425 16.1154i 0.489698 0.848181i
\(362\) 8.66163 0.455245
\(363\) −15.5264 + 3.43471i −0.814922 + 0.180276i
\(364\) 0 0
\(365\) −0.371322 0.643149i −0.0194359 0.0336640i
\(366\) 1.22263 + 1.33549i 0.0639080 + 0.0698070i
\(367\) −11.9670 20.7274i −0.624670 1.08196i −0.988605 0.150536i \(-0.951900\pi\)
0.363934 0.931425i \(-0.381433\pi\)
\(368\) 2.01030 3.48193i 0.104794 0.181508i
\(369\) 27.2730 12.6875i 1.41978 0.660483i
\(370\) −34.5551 −1.79644
\(371\) 0 0
\(372\) 46.6822 + 50.9912i 2.42036 + 2.64377i
\(373\) 9.58030 16.5936i 0.496049 0.859182i −0.503941 0.863738i \(-0.668117\pi\)
0.999990 + 0.00455622i \(0.00145030\pi\)
\(374\) −10.2557 −0.530309
\(375\) 13.8847 + 15.1663i 0.717002 + 0.783184i
\(376\) 102.060 5.26334
\(377\) −14.4548 −0.744458
\(378\) 0 0
\(379\) 10.0770 0.517622 0.258811 0.965928i \(-0.416669\pi\)
0.258811 + 0.965928i \(0.416669\pi\)
\(380\) −5.33217 −0.273534
\(381\) 9.79388 + 10.6979i 0.501756 + 0.548070i
\(382\) −10.5025 −0.537357
\(383\) −10.0718 + 17.4448i −0.514643 + 0.891388i 0.485213 + 0.874396i \(0.338742\pi\)
−0.999856 + 0.0169915i \(0.994591\pi\)
\(384\) 36.0855 + 39.4164i 1.84148 + 2.01146i
\(385\) 0 0
\(386\) 11.2294 0.571561
\(387\) −15.3708 10.7836i −0.781340 0.548159i
\(388\) −38.8372 + 67.2679i −1.97166 + 3.41501i
\(389\) −6.69736 11.6002i −0.339570 0.588152i 0.644782 0.764366i \(-0.276948\pi\)
−0.984352 + 0.176215i \(0.943615\pi\)
\(390\) 16.0114 + 17.4893i 0.810767 + 0.885605i
\(391\) −0.398891 0.690899i −0.0201728 0.0349402i
\(392\) 0 0
\(393\) 20.2476 4.47913i 1.02136 0.225942i
\(394\) 2.41448 0.121640
\(395\) 12.4630 21.5866i 0.627083 1.08614i
\(396\) −19.7081 + 9.16824i −0.990369 + 0.460721i
\(397\) −9.00664 15.6000i −0.452031 0.782940i 0.546482 0.837471i \(-0.315967\pi\)
−0.998512 + 0.0545313i \(0.982634\pi\)
\(398\) −8.58506 + 14.8698i −0.430330 + 0.745354i
\(399\) 0 0
\(400\) 17.5249 + 30.3541i 0.876247 + 1.51770i
\(401\) −14.4337 + 25.0000i −0.720787 + 1.24844i 0.239898 + 0.970798i \(0.422886\pi\)
−0.960685 + 0.277642i \(0.910447\pi\)
\(402\) −8.06324 8.80751i −0.402158 0.439279i
\(403\) 11.8075 + 20.4513i 0.588176 + 1.01875i
\(404\) 26.4240 + 45.7676i 1.31464 + 2.27703i
\(405\) 9.19729 10.9205i 0.457017 0.542646i
\(406\) 0 0
\(407\) 5.41019 9.37073i 0.268173 0.464490i
\(408\) 43.3610 9.59222i 2.14669 0.474886i
\(409\) 10.8587 0.536931 0.268465 0.963289i \(-0.413484\pi\)
0.268465 + 0.963289i \(0.413484\pi\)
\(410\) −43.1872 −2.13286
\(411\) −8.63255 + 27.3356i −0.425812 + 1.34837i
\(412\) 29.7014 51.4443i 1.46328 2.53448i
\(413\) 0 0
\(414\) −1.89951 1.33263i −0.0933561 0.0654951i
\(415\) 11.0943 + 19.2158i 0.544595 + 0.943267i
\(416\) 31.8001 + 55.0793i 1.55913 + 2.70049i
\(417\) −4.12179 + 13.0520i −0.201845 + 0.639158i
\(418\) 1.14566 1.98434i 0.0560359 0.0970570i
\(419\) 0.247572 + 0.428807i 0.0120947 + 0.0209486i 0.872009 0.489489i \(-0.162817\pi\)
−0.859915 + 0.510438i \(0.829483\pi\)
\(420\) 0 0
\(421\) 9.50320 16.4600i 0.463158 0.802212i −0.535959 0.844244i \(-0.680050\pi\)
0.999116 + 0.0420318i \(0.0133831\pi\)
\(422\) −15.5113 26.8664i −0.755079 1.30784i
\(423\) 2.94502 33.3130i 0.143192 1.61974i
\(424\) 12.7578 22.0971i 0.619572 1.07313i
\(425\) 6.95473 0.337354
\(426\) −4.61116 5.03679i −0.223411 0.244033i
\(427\) 0 0
\(428\) 5.16864 + 8.95234i 0.249835 + 0.432728i
\(429\) −7.24963 + 1.60375i −0.350016 + 0.0774298i
\(430\) 13.4790 + 23.3464i 0.650016 + 1.12586i
\(431\) 8.46073 14.6544i 0.407539 0.705878i −0.587074 0.809533i \(-0.699720\pi\)
0.994613 + 0.103655i \(0.0330538\pi\)
\(432\) 58.2438 44.5660i 2.80226 2.14418i
\(433\) 33.4740 1.60866 0.804330 0.594183i \(-0.202524\pi\)
0.804330 + 0.594183i \(0.202524\pi\)
\(434\) 0 0
\(435\) 3.76315 11.9163i 0.180429 0.571343i
\(436\) 49.9774 86.5634i 2.39348 4.14564i
\(437\) 0.178239 0.00852634
\(438\) −2.14955 + 0.475519i −0.102709 + 0.0227212i
\(439\) −20.9315 −0.999005 −0.499502 0.866313i \(-0.666484\pi\)
−0.499502 + 0.866313i \(0.666484\pi\)
\(440\) 19.5891 0.933874
\(441\) 0 0
\(442\) 24.1674 1.14953
\(443\) −30.8580 −1.46611 −0.733054 0.680170i \(-0.761906\pi\)
−0.733054 + 0.680170i \(0.761906\pi\)
\(444\) −22.4786 + 71.1804i −1.06679 + 3.37807i
\(445\) 4.10409 0.194553
\(446\) 22.6972 39.3128i 1.07475 1.86151i
\(447\) −23.1157 + 5.11362i −1.09334 + 0.241866i
\(448\) 0 0
\(449\) −33.2789 −1.57053 −0.785263 0.619162i \(-0.787472\pi\)
−0.785263 + 0.619162i \(0.787472\pi\)
\(450\) 18.3405 8.53203i 0.864579 0.402204i
\(451\) 6.76168 11.7116i 0.318395 0.551477i
\(452\) 8.55957 + 14.8256i 0.402608 + 0.697338i
\(453\) −2.03400 + 6.44083i −0.0955658 + 0.302617i
\(454\) −23.1737 40.1380i −1.08760 1.88377i
\(455\) 0 0
\(456\) −2.98786 + 9.46130i −0.139919 + 0.443066i
\(457\) 23.7904 1.11287 0.556434 0.830892i \(-0.312169\pi\)
0.556434 + 0.830892i \(0.312169\pi\)
\(458\) −26.8654 + 46.5323i −1.25534 + 2.17431i
\(459\) −1.87975 14.4301i −0.0877393 0.673539i
\(460\) 1.21382 + 2.10240i 0.0565947 + 0.0980249i
\(461\) −8.53122 + 14.7765i −0.397339 + 0.688211i −0.993397 0.114731i \(-0.963400\pi\)
0.596058 + 0.802941i \(0.296733\pi\)
\(462\) 0 0
\(463\) 18.1243 + 31.3922i 0.842306 + 1.45892i 0.887940 + 0.459959i \(0.152136\pi\)
−0.0456338 + 0.998958i \(0.514531\pi\)
\(464\) 32.0945 55.5893i 1.48995 2.58067i
\(465\) −19.9337 + 4.40970i −0.924404 + 0.204495i
\(466\) 8.05253 + 13.9474i 0.373026 + 0.646100i
\(467\) −4.09580 7.09413i −0.189531 0.328277i 0.755563 0.655076i \(-0.227363\pi\)
−0.945094 + 0.326799i \(0.894030\pi\)
\(468\) 46.4420 21.6049i 2.14678 0.998686i
\(469\) 0 0
\(470\) −24.0080 + 41.5830i −1.10740 + 1.91808i
\(471\) −0.344268 0.376045i −0.0158630 0.0173272i
\(472\) 41.8826 1.92780
\(473\) −8.44148 −0.388140
\(474\) −49.8956 54.5012i −2.29178 2.50332i
\(475\) −0.776909 + 1.34565i −0.0356470 + 0.0617425i
\(476\) 0 0
\(477\) −6.84451 4.80185i −0.313389 0.219862i
\(478\) 27.2265 + 47.1577i 1.24531 + 2.15694i
\(479\) −12.7775 22.1312i −0.583817 1.01120i −0.995022 0.0996574i \(-0.968225\pi\)
0.411205 0.911543i \(-0.365108\pi\)
\(480\) −53.6854 + 11.8762i −2.45039 + 0.542071i
\(481\) −12.7491 + 22.0820i −0.581308 + 1.00685i
\(482\) −39.7614 68.8687i −1.81108 3.13688i
\(483\) 0 0
\(484\) 24.6596 42.7116i 1.12089 1.94144i
\(485\) −11.4690 19.8649i −0.520782 0.902020i
\(486\) −22.6599 35.7479i −1.02787 1.62156i
\(487\) 3.46140 5.99533i 0.156851 0.271674i −0.776880 0.629648i \(-0.783199\pi\)
0.933732 + 0.357974i \(0.116532\pi\)
\(488\) −3.52491 −0.159565
\(489\) −5.58574 + 17.6877i −0.252596 + 0.799865i
\(490\) 0 0
\(491\) 18.7262 + 32.4348i 0.845103 + 1.46376i 0.885532 + 0.464578i \(0.153794\pi\)
−0.0404294 + 0.999182i \(0.512873\pi\)
\(492\) −28.0939 + 88.9615i −1.26657 + 4.01070i
\(493\) −6.36831 11.0302i −0.286814 0.496777i
\(494\) −2.69973 + 4.67607i −0.121467 + 0.210386i
\(495\) 0.565259 6.39402i 0.0254065 0.287390i
\(496\) −104.867 −4.70867
\(497\) 0 0
\(498\) 64.2235 14.2074i 2.87793 0.636649i
\(499\) −12.8125 + 22.1919i −0.573566 + 0.993446i 0.422630 + 0.906302i \(0.361107\pi\)
−0.996196 + 0.0871432i \(0.972226\pi\)
\(500\) −63.7733 −2.85203
\(501\) −1.66775 + 5.28106i −0.0745096 + 0.235941i
\(502\) −61.8658 −2.76121
\(503\) 5.79692 0.258472 0.129236 0.991614i \(-0.458748\pi\)
0.129236 + 0.991614i \(0.458748\pi\)
\(504\) 0 0
\(505\) −15.6066 −0.694483
\(506\) −1.04320 −0.0463757
\(507\) −4.90143 + 1.08429i −0.217680 + 0.0481548i
\(508\) −44.9840 −1.99584
\(509\) 12.5697 21.7714i 0.557144 0.965002i −0.440589 0.897709i \(-0.645230\pi\)
0.997733 0.0672931i \(-0.0214363\pi\)
\(510\) −6.29174 + 19.9233i −0.278603 + 0.882218i
\(511\) 0 0
\(512\) −23.9940 −1.06039
\(513\) 3.00201 + 1.24827i 0.132542 + 0.0551125i
\(514\) 32.9738 57.1123i 1.45441 2.51911i
\(515\) 8.77113 + 15.1920i 0.386502 + 0.669441i
\(516\) 56.8596 12.5784i 2.50311 0.553732i
\(517\) −7.51771 13.0211i −0.330629 0.572665i
\(518\) 0 0
\(519\) −13.3770 14.6118i −0.587186 0.641386i
\(520\) −46.1616 −2.02432
\(521\) 3.64828 6.31900i 0.159834 0.276841i −0.774975 0.631992i \(-0.782237\pi\)
0.934809 + 0.355152i \(0.115571\pi\)
\(522\) −30.3259 21.2755i −1.32733 0.931203i
\(523\) 8.38637 + 14.5256i 0.366710 + 0.635161i 0.989049 0.147587i \(-0.0471506\pi\)
−0.622339 + 0.782748i \(0.713817\pi\)
\(524\) −32.1580 + 55.6993i −1.40483 + 2.43324i
\(525\) 0 0
\(526\) −11.6908 20.2490i −0.509741 0.882898i
\(527\) −10.4041 + 18.0204i −0.453208 + 0.784979i
\(528\) 9.92904 31.4411i 0.432106 1.36830i
\(529\) 11.4594 + 19.8483i 0.498236 + 0.862970i
\(530\) 6.00212 + 10.3960i 0.260716 + 0.451573i
\(531\) 1.20855 13.6707i 0.0524468 0.593260i
\(532\) 0 0
\(533\) −15.9339 + 27.5982i −0.690172 + 1.19541i
\(534\) 3.66374 11.6015i 0.158546 0.502047i
\(535\) −3.05271 −0.131980
\(536\) 23.2467 1.00411
\(537\) 1.85783 0.410985i 0.0801712 0.0177353i
\(538\) 20.6774 35.8143i 0.891466 1.54406i
\(539\) 0 0
\(540\) 5.72007 + 43.9107i 0.246153 + 1.88962i
\(541\) 2.64908 + 4.58834i 0.113893 + 0.197268i 0.917337 0.398112i \(-0.130335\pi\)
−0.803444 + 0.595381i \(0.797001\pi\)
\(542\) 6.35097 + 11.0002i 0.272798 + 0.472499i
\(543\) 3.73110 + 4.07550i 0.160117 + 0.174896i
\(544\) −28.0202 + 48.5324i −1.20136 + 2.08081i
\(545\) 14.7589 + 25.5631i 0.632200 + 1.09500i
\(546\) 0 0
\(547\) 16.4325 28.4619i 0.702603 1.21694i −0.264947 0.964263i \(-0.585354\pi\)
0.967550 0.252681i \(-0.0813123\pi\)
\(548\) −44.4542 76.9970i −1.89899 3.28915i
\(549\) −0.101714 + 1.15055i −0.00434105 + 0.0491045i
\(550\) 4.54708 7.87577i 0.193888 0.335824i
\(551\) 2.84560 0.121227
\(552\) 4.41062 0.975709i 0.187729 0.0415290i
\(553\) 0 0
\(554\) −22.2515 38.5408i −0.945376 1.63744i
\(555\) −14.8850 16.2590i −0.631835 0.690156i
\(556\) −21.2256 36.7638i −0.900166 1.55913i
\(557\) 9.40798 16.2951i 0.398629 0.690446i −0.594928 0.803779i \(-0.702819\pi\)
0.993557 + 0.113333i \(0.0361527\pi\)
\(558\) −5.32951 + 60.2856i −0.225616 + 2.55209i
\(559\) 19.8923 0.841354
\(560\) 0 0
\(561\) −4.41776 4.82554i −0.186518 0.203734i
\(562\) −4.77054 + 8.26282i −0.201233 + 0.348546i
\(563\) −27.6650 −1.16594 −0.582970 0.812494i \(-0.698109\pi\)
−0.582970 + 0.812494i \(0.698109\pi\)
\(564\) 70.0396 + 76.5046i 2.94920 + 3.22142i
\(565\) −5.05547 −0.212685
\(566\) 70.7856 2.97534
\(567\) 0 0
\(568\) 13.2942 0.557812
\(569\) −40.1831 −1.68456 −0.842282 0.539037i \(-0.818788\pi\)
−0.842282 + 0.539037i \(0.818788\pi\)
\(570\) −3.15204 3.44299i −0.132024 0.144211i
\(571\) −6.81129 −0.285044 −0.142522 0.989792i \(-0.545521\pi\)
−0.142522 + 0.989792i \(0.545521\pi\)
\(572\) 11.5142 19.9431i 0.481431 0.833863i
\(573\) −4.52409 4.94169i −0.188997 0.206442i
\(574\) 0 0
\(575\) 0.707427 0.0295017
\(576\) −6.89612 + 78.0065i −0.287338 + 3.25027i
\(577\) −18.2111 + 31.5425i −0.758138 + 1.31313i 0.185661 + 0.982614i \(0.440557\pi\)
−0.943799 + 0.330519i \(0.892776\pi\)
\(578\) −12.4312 21.5315i −0.517071 0.895593i
\(579\) 4.83720 + 5.28369i 0.201027 + 0.219583i
\(580\) 19.3787 + 33.5649i 0.804658 + 1.39371i
\(581\) 0 0
\(582\) −66.3930 + 14.6873i −2.75208 + 0.608810i
\(583\) −3.75894 −0.155679
\(584\) 2.14295 3.71170i 0.0886759 0.153591i
\(585\) −1.33203 + 15.0674i −0.0550726 + 0.622962i
\(586\) −25.6361 44.4030i −1.05902 1.83427i
\(587\) −5.57943 + 9.66385i −0.230288 + 0.398870i −0.957893 0.287126i \(-0.907300\pi\)
0.727605 + 0.685996i \(0.240633\pi\)
\(588\) 0 0
\(589\) −2.32446 4.02609i −0.0957779 0.165892i
\(590\) −9.85220 + 17.0645i −0.405609 + 0.702535i
\(591\) 1.04007 + 1.13607i 0.0427826 + 0.0467316i
\(592\) −56.6145 98.0593i −2.32684 4.03021i
\(593\) 9.90427 + 17.1547i 0.406720 + 0.704459i 0.994520 0.104547i \(-0.0333392\pi\)
−0.587800 + 0.809006i \(0.700006\pi\)
\(594\) −17.5701 7.30586i −0.720911 0.299763i
\(595\) 0 0
\(596\) 36.7133 63.5893i 1.50384 2.60472i
\(597\) −10.6947 + 2.36586i −0.437705 + 0.0968281i
\(598\) 2.45828 0.100527
\(599\) −18.1320 −0.740853 −0.370427 0.928862i \(-0.620789\pi\)
−0.370427 + 0.928862i \(0.620789\pi\)
\(600\) −11.8587 + 37.5516i −0.484131 + 1.53304i
\(601\) 12.3285 21.3536i 0.502889 0.871030i −0.497105 0.867690i \(-0.665604\pi\)
0.999994 0.00333942i \(-0.00106297\pi\)
\(602\) 0 0
\(603\) 0.670802 7.58788i 0.0273172 0.309003i
\(604\) −10.4743 18.1420i −0.426194 0.738189i
\(605\) 7.28223 + 12.6132i 0.296065 + 0.512799i
\(606\) −13.9321 + 44.1169i −0.565951 + 1.79213i
\(607\) 8.63876 14.9628i 0.350637 0.607320i −0.635725 0.771916i \(-0.719299\pi\)
0.986361 + 0.164596i \(0.0526319\pi\)
\(608\) −6.26024 10.8431i −0.253886 0.439744i
\(609\) 0 0
\(610\) 0.829179 1.43618i 0.0335725 0.0581492i
\(611\) 17.7154 + 30.6840i 0.716689 + 1.24134i
\(612\) 36.9472 + 25.9208i 1.49350 + 1.04779i
\(613\) −9.77828 + 16.9365i −0.394941 + 0.684058i −0.993094 0.117324i \(-0.962568\pi\)
0.598153 + 0.801382i \(0.295902\pi\)
\(614\) −58.7575 −2.37126
\(615\) −18.6034 20.3206i −0.750161 0.819404i
\(616\) 0 0
\(617\) 10.8723 + 18.8314i 0.437702 + 0.758122i 0.997512 0.0704988i \(-0.0224591\pi\)
−0.559810 + 0.828621i \(0.689126\pi\)
\(618\) 50.7752 11.2324i 2.04248 0.451833i
\(619\) 16.9024 + 29.2758i 0.679366 + 1.17670i 0.975172 + 0.221448i \(0.0710782\pi\)
−0.295807 + 0.955248i \(0.595588\pi\)
\(620\) 31.6595 54.8359i 1.27148 2.20226i
\(621\) −0.191206 1.46781i −0.00767284 0.0589013i
\(622\) 12.2031 0.489300
\(623\) 0 0
\(624\) −23.3977 + 74.0906i −0.936658 + 2.96600i
\(625\) 3.20808 5.55655i 0.128323 0.222262i
\(626\) 23.3557 0.933481
\(627\) 1.42718 0.315718i 0.0569961 0.0126086i
\(628\) 1.58125 0.0630986
\(629\) −22.4674 −0.895832
\(630\) 0 0
\(631\) −23.6410 −0.941134 −0.470567 0.882364i \(-0.655951\pi\)
−0.470567 + 0.882364i \(0.655951\pi\)
\(632\) 143.852 5.72211
\(633\) 5.95957 18.8715i 0.236872 0.750073i
\(634\) 21.8909 0.869399
\(635\) 6.64213 11.5045i 0.263585 0.456542i
\(636\) 25.3192 5.60107i 1.00397 0.222097i
\(637\) 0 0
\(638\) −16.6547 −0.659365
\(639\) 0.383615 4.33932i 0.0151756 0.171661i
\(640\) 24.4729 42.3883i 0.967375 1.67554i
\(641\) −7.95901 13.7854i −0.314362 0.544491i 0.664940 0.746897i \(-0.268457\pi\)
−0.979302 + 0.202406i \(0.935124\pi\)
\(642\) −2.72517 + 8.62945i −0.107554 + 0.340577i
\(643\) 13.2527 + 22.9544i 0.522636 + 0.905231i 0.999653 + 0.0263376i \(0.00838450\pi\)
−0.477017 + 0.878894i \(0.658282\pi\)
\(644\) 0 0
\(645\) −5.17875 + 16.3989i −0.203913 + 0.645707i
\(646\) −4.75766 −0.187188
\(647\) 0.00801958 0.0138903i 0.000315282 0.000546085i −0.865868 0.500273i \(-0.833233\pi\)
0.866183 + 0.499727i \(0.166566\pi\)
\(648\) 81.1196 + 14.4556i 3.18668 + 0.567871i
\(649\) −3.08506 5.34348i −0.121099 0.209750i
\(650\) −10.7152 + 18.5592i −0.420283 + 0.727951i
\(651\) 0 0
\(652\) −28.7644 49.8214i −1.12650 1.95115i
\(653\) 16.6440 28.8282i 0.651328 1.12813i −0.331473 0.943465i \(-0.607545\pi\)
0.982801 0.184669i \(-0.0591212\pi\)
\(654\) 85.4376 18.9003i 3.34087 0.739062i
\(655\) −9.49661 16.4486i −0.371063 0.642700i
\(656\) −70.7571 122.555i −2.76260 4.78497i
\(657\) −1.14969 0.806577i −0.0448535 0.0314676i
\(658\) 0 0
\(659\) 19.4156 33.6288i 0.756324 1.30999i −0.188389 0.982094i \(-0.560327\pi\)
0.944713 0.327897i \(-0.106340\pi\)
\(660\) 13.4432 + 14.6841i 0.523276 + 0.571577i
\(661\) −5.30644 −0.206397 −0.103198 0.994661i \(-0.532908\pi\)
−0.103198 + 0.994661i \(0.532908\pi\)
\(662\) 62.1835 2.41683
\(663\) 10.4104 + 11.3713i 0.404307 + 0.441626i
\(664\) −64.0264 + 110.897i −2.48471 + 4.30364i
\(665\) 0 0
\(666\) −59.2492 + 27.5628i −2.29586 + 1.06804i
\(667\) −0.647777 1.12198i −0.0250820 0.0434433i
\(668\) −8.58826 14.8753i −0.332290 0.575543i
\(669\) 28.2747 6.25487i 1.09316 0.241827i
\(670\) −5.46842 + 9.47158i −0.211263 + 0.365919i
\(671\) 0.259644 + 0.449717i 0.0100235 + 0.0173611i
\(672\) 0 0
\(673\) −3.03565 + 5.25789i −0.117016 + 0.202677i −0.918584 0.395227i \(-0.870666\pi\)
0.801568 + 0.597903i \(0.203999\pi\)
\(674\) 18.5142 + 32.0676i 0.713142 + 1.23520i
\(675\) 11.9149 + 4.95435i 0.458605 + 0.190693i
\(676\) 7.78465 13.4834i 0.299410 0.518593i
\(677\) 34.7850 1.33690 0.668449 0.743758i \(-0.266959\pi\)
0.668449 + 0.743758i \(0.266959\pi\)
\(678\) −4.51304 + 14.2909i −0.173322 + 0.548838i
\(679\) 0 0
\(680\) −20.3373 35.2253i −0.779901 1.35083i
\(681\) 8.90352 28.1937i 0.341184 1.08038i
\(682\) 13.6046 + 23.5638i 0.520946 + 0.902305i
\(683\) −9.71206 + 16.8218i −0.371622 + 0.643667i −0.989815 0.142358i \(-0.954531\pi\)
0.618194 + 0.786026i \(0.287865\pi\)
\(684\) −9.14268 + 4.25319i −0.349579 + 0.162625i
\(685\) 26.2556 1.00318
\(686\) 0 0
\(687\) −33.4672 + 7.40354i −1.27685 + 0.282463i
\(688\) −44.1676 + 76.5006i −1.68387 + 2.91656i
\(689\) 8.85791 0.337459
\(690\) −0.639988 + 2.02657i −0.0243639 + 0.0771503i
\(691\) 6.63675 0.252474 0.126237 0.992000i \(-0.459710\pi\)
0.126237 + 0.992000i \(0.459710\pi\)
\(692\) 61.4416 2.33566
\(693\) 0 0
\(694\) 7.67197 0.291224
\(695\) 12.5363 0.475529
\(696\) 70.4158 15.5773i 2.66911 0.590454i
\(697\) −28.0798 −1.06360
\(698\) −4.91987 + 8.52147i −0.186220 + 0.322542i
\(699\) −3.09385 + 9.79690i −0.117020 + 0.370553i
\(700\) 0 0
\(701\) −13.9153 −0.525574 −0.262787 0.964854i \(-0.584642\pi\)
−0.262787 + 0.964854i \(0.584642\pi\)
\(702\) 41.4038 + 17.2162i 1.56269 + 0.649783i
\(703\) 2.50982 4.34713i 0.0946595 0.163955i
\(704\) 17.6036 + 30.4904i 0.663462 + 1.14915i
\(705\) −29.9075 + 6.61608i −1.12638 + 0.249176i
\(706\) 3.73876 + 6.47571i 0.140710 + 0.243717i
\(707\) 0 0
\(708\) 28.7423 + 31.3954i 1.08020 + 1.17991i
\(709\) 34.1556 1.28274 0.641370 0.767231i \(-0.278366\pi\)
0.641370 + 0.767231i \(0.278366\pi\)
\(710\) −3.12725 + 5.41655i −0.117364 + 0.203280i
\(711\) 4.15095 46.9541i 0.155673 1.76092i
\(712\) 11.8426 + 20.5120i 0.443821 + 0.768721i
\(713\) −1.05829 + 1.83301i −0.0396332 + 0.0686467i
\(714\) 0 0
\(715\) 3.40025 + 5.88941i 0.127162 + 0.220251i
\(716\) −2.95068 + 5.11072i −0.110272 + 0.190997i
\(717\) −10.4606 + 33.1244i −0.390660 + 1.23705i
\(718\) −22.8092 39.5066i −0.851231 1.47437i
\(719\) −22.1450 38.3563i −0.825870 1.43045i −0.901253 0.433294i \(-0.857351\pi\)
0.0753825 0.997155i \(-0.475982\pi\)
\(720\) −54.9879 38.5775i −2.04928 1.43770i
\(721\) 0 0
\(722\) −25.2623 + 43.7556i −0.940165 + 1.62841i
\(723\) 15.2766 48.3747i 0.568144 1.79907i
\(724\) −17.1372 −0.636899
\(725\) 11.2941 0.419453
\(726\) 42.1561 9.32569i 1.56456 0.346109i
\(727\) −14.1247 + 24.4647i −0.523857 + 0.907346i 0.475758 + 0.879576i \(0.342174\pi\)
−0.999614 + 0.0277700i \(0.991159\pi\)
\(728\) 0 0
\(729\) 7.05919 26.0608i 0.261451 0.965217i
\(730\) 1.00819 + 1.74623i 0.0373147 + 0.0646310i
\(731\) 8.76391 + 15.1795i 0.324145 + 0.561435i
\(732\) −2.41900 2.64229i −0.0894090 0.0976618i
\(733\) −12.5084 + 21.6653i −0.462010 + 0.800225i −0.999061 0.0433249i \(-0.986205\pi\)
0.537051 + 0.843550i \(0.319538\pi\)
\(734\) 32.4919 + 56.2776i 1.19930 + 2.07724i
\(735\) 0 0
\(736\) −2.85018 + 4.93666i −0.105059 + 0.181968i
\(737\) −1.71235 2.96587i −0.0630752 0.109249i
\(738\) −74.0499 + 34.4482i −2.72582 + 1.26805i
\(739\) −16.0115 + 27.7327i −0.588992 + 1.02016i 0.405373 + 0.914151i \(0.367142\pi\)
−0.994365 + 0.106013i \(0.966192\pi\)
\(740\) 68.3680 2.51326
\(741\) −3.36314 + 0.743987i −0.123548 + 0.0273311i
\(742\) 0 0
\(743\) 19.4031 + 33.6072i 0.711833 + 1.23293i 0.964169 + 0.265290i \(0.0854678\pi\)
−0.252336 + 0.967640i \(0.581199\pi\)
\(744\) −79.5595 86.9032i −2.91679 3.18602i
\(745\) 10.8418 + 18.7786i 0.397214 + 0.687995i
\(746\) −26.0118 + 45.0537i −0.952359 + 1.64953i
\(747\) 34.3500 + 24.0987i 1.25680 + 0.881724i
\(748\) 20.2911 0.741915
\(749\) 0 0
\(750\) −37.6987 41.1785i −1.37656 1.50363i
\(751\) −10.8495 + 18.7920i −0.395905 + 0.685728i −0.993216 0.116282i \(-0.962903\pi\)
0.597311 + 0.802010i \(0.296236\pi\)
\(752\) −157.337 −5.73749
\(753\) −26.6494 29.1093i −0.971160 1.06080i
\(754\) 39.2466 1.42928
\(755\) 6.18635 0.225144
\(756\) 0 0
\(757\) 33.5242 1.21846 0.609229 0.792995i \(-0.291479\pi\)
0.609229 + 0.792995i \(0.291479\pi\)
\(758\) −27.3605 −0.993778
\(759\) −0.449369 0.490848i −0.0163111 0.0178166i
\(760\) 9.08748 0.329638
\(761\) −6.66048 + 11.5363i −0.241442 + 0.418190i −0.961125 0.276113i \(-0.910954\pi\)
0.719683 + 0.694303i \(0.244287\pi\)
\(762\) −26.5917 29.0462i −0.963315 1.05223i
\(763\) 0 0
\(764\) 20.7795 0.751775
\(765\) −12.0846 + 5.62179i −0.436920 + 0.203256i
\(766\) 27.3462 47.3649i 0.988057 1.71137i
\(767\) 7.26992 + 12.5919i 0.262502 + 0.454666i
\(768\) −36.9167 40.3243i −1.33212 1.45508i
\(769\) −27.3568 47.3833i −0.986510 1.70869i −0.635022 0.772494i \(-0.719009\pi\)
−0.351488 0.936192i \(-0.614324\pi\)
\(770\) 0 0
\(771\) 41.0765 9.08686i 1.47933 0.327255i
\(772\) −22.2176 −0.799628
\(773\) 1.18021 2.04418i 0.0424491 0.0735240i −0.844020 0.536311i \(-0.819817\pi\)
0.886469 + 0.462787i \(0.153151\pi\)
\(774\) 41.7337 + 29.2788i 1.50009 + 1.05240i
\(775\) −9.22573 15.9794i −0.331398 0.573998i
\(776\) 66.1892 114.643i 2.37606 4.11545i
\(777\) 0 0
\(778\) 18.1842 + 31.4960i 0.651936 + 1.12919i
\(779\) 3.13678 5.43306i 0.112387 0.194660i
\(780\) −31.6788 34.6029i −1.13428 1.23898i
\(781\) −0.979248 1.69611i −0.0350403 0.0606915i
\(782\) 1.08304 + 1.87588i 0.0387295 + 0.0670814i