Properties

Label 441.2.h.h.214.2
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 214.2
Character \(\chi\) \(=\) 441.214
Dual form 441.2.h.h.373.2

$q$-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 −0.632343 0.774688i \(-0.717907\pi\)
0.987071 + 0.160281i \(0.0512400\pi\)
\(6\) −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 0.997746 0.0671096i \(-0.0213777\pi\)
−0.556991 + 0.830518i \(0.688044\pi\)
\(14\) 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 −0.984360 0.176167i \(-0.943630\pi\)
0.644745 + 0.764397i \(0.276963\pi\)
\(18\) 0.717292 8.11375i 0.169067 1.91243i
\(19\) −0.312846 0.541866i −0.0717719 0.124313i 0.827906 0.560867i \(-0.189532\pi\)
−0.899678 + 0.436554i \(0.856199\pi\)
\(20\) 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 \(-0.267476\pi\)
0.667238 + 0.744845i \(0.267476\pi\)
\(32\) −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 \(0.119616\pi\)
−0.147275 + 0.989096i \(0.547050\pi\)
\(42\) 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 \(-0.197819\pi\)
0.813026 + 0.582227i \(0.197819\pi\)
\(48\) 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 \(-0.403752\pi\)
0.297787 + 0.954632i \(0.403752\pi\)
\(60\) 14.4121 3.18822i 1.86060 0.411598i
\(61\) −0.385014 −0.0492960 −0.0246480 0.999696i \(-0.507846\pi\)
−0.0246480 + 0.999696i \(0.507846\pi\)
\(62\) −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 −0.852003 0.523538i \(-0.824612\pi\)
0.879398 + 0.476087i \(0.157945\pi\)
\(74\) 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 \(0.445228\pi\)
−0.938848 + 0.344331i \(0.888106\pi\)
\(84\) 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 0.926403 0.376534i \(-0.122884\pi\)
−0.789289 + 0.614022i \(0.789551\pi\)
\(90\) −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 \(-0.570958\pi\)
0.955136 0.296168i \(-0.0957089\pi\)
\(98\) 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 0.510479 0.859890i \(-0.329468\pi\)
−0.999926 + 0.0121430i \(0.996135\pi\)
\(102\) 12.8593 2.84471i 1.27326 0.281669i
\(103\) −5.52897 + 9.57646i −0.544786 + 0.943597i 0.453834 + 0.891086i \(0.350056\pi\)
−0.998620 + 0.0525110i \(0.983278\pi\)
\(104\) −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 \(-0.658137\pi\)
0.999641 0.0267937i \(-0.00852971\pi\)
\(132\) −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 0.983511 0.180849i \(-0.0578845\pi\)
−0.648375 + 0.761321i \(0.724551\pi\)
\(140\) 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 \(-0.503739\pi\)
−0.0117459 + 0.999931i \(0.503739\pi\)
\(158\) 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 0.921229 0.389020i \(-0.127186\pi\)
−0.797516 + 0.603298i \(0.793853\pi\)
\(168\) 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 \(-0.643177\pi\)
−0.434789 + 0.900533i \(0.643177\pi\)
\(174\) −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 \(-0.462172\pi\)
0.118560 + 0.992947i \(0.462172\pi\)
\(182\) 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 −0.956062 0.293164i \(-0.905292\pi\)
0.731919 + 0.681392i \(0.238625\pi\)
\(200\) −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 \(-0.644213\pi\)
0.997513 0.0704822i \(-0.0224538\pi\)
\(224\) 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 \(-0.974968\pi\)
0.430421 0.902628i \(-0.358365\pi\)
\(228\) 1.75316 5.55150i 0.116106 0.367657i
\(229\) −9.89471 + 17.1381i −0.653861 + 1.13252i 0.328317 + 0.944567i \(0.393518\pi\)
−0.982178 + 0.187953i \(0.939815\pi\)
\(230\) 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 \(-0.774346\pi\)
−0.184256 0.982878i \(-0.558988\pi\)
\(242\) −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 \(-0.755448\pi\)
−0.719106 + 0.694901i \(0.755448\pi\)
\(252\) 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 \(-0.559730\pi\)
0.944097 0.329668i \(-0.106937\pi\)
\(258\) 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 −0.534839 0.844954i \(-0.679628\pi\)
0.999171 + 0.0407073i \(0.0129611\pi\)
\(270\) −2.89109 22.1937i −0.175946 1.35067i
\(271\) 2.33910 + 4.05144i 0.142090 + 0.246108i 0.928284 0.371873i \(-0.121284\pi\)
−0.786193 + 0.617981i \(0.787951\pi\)
\(272\) −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 \(-0.217813\pi\)
0.774874 + 0.632116i \(0.217813\pi\)
\(284\) −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 \(-0.980683\pi\)
0.446556 0.894756i \(-0.352650\pi\)
\(294\) 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 \(-0.711875\pi\)
−0.617551 + 0.786531i \(0.711875\pi\)
\(308\) 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 \(-0.459327\pi\)
0.127429 + 0.991848i \(0.459327\pi\)
\(312\) 15.1774 48.0604i 0.859251 2.72089i
\(313\) 8.60204 0.486216 0.243108 0.969999i \(-0.421833\pi\)
0.243108 + 0.969999i \(0.421833\pi\)
\(314\) 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 −0.910440 0.413642i \(-0.864256\pi\)
0.813444 + 0.581643i \(0.197590\pi\)
\(350\) 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 0.900342 0.435184i \(-0.143317\pi\)
−0.827051 + 0.562127i \(0.809983\pi\)
\(354\) −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 \(0.0480999\pi\)
−0.363934 + 0.931425i \(0.618567\pi\)
\(368\) 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 \(-0.661258\pi\)
0.999856 0.0169915i \(-0.00540883\pi\)
\(384\) −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 0.998512 0.0545313i \(-0.0173665\pi\)
−0.546482 + 0.837471i \(0.684033\pi\)
\(398\) 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 \(-0.586516\pi\)
−0.268465 + 0.963289i \(0.586516\pi\)
\(410\) −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 0.859915 0.510438i \(-0.170517\pi\)
−0.872009 + 0.489489i \(0.837183\pi\)
\(420\) 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 \(-0.797476\pi\)
−0.804330 + 0.594183i \(0.797476\pi\)
\(434\) 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 \(-0.333516\pi\)
0.499502 + 0.866313i \(0.333516\pi\)
\(440\) −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 −0.596058 0.802941i \(-0.703267\pi\)
0.993397 + 0.114731i \(0.0366005\pi\)
\(462\) 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 0.945094 0.326799i \(-0.105970\pi\)
−0.755563 + 0.655076i \(0.772637\pi\)
\(468\) −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 \(0.0317747\pi\)
−0.411205 + 0.911543i \(0.634892\pi\)
\(480\) −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 \(-0.541252\pi\)
−0.129236 + 0.991614i \(0.541252\pi\)
\(504\) 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 \(0.354770\pi\)
−0.997733 + 0.0672931i \(0.978564\pi\)
\(510\) 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 −0.934809 0.355152i \(-0.884429\pi\)
0.774975 + 0.631992i \(0.217763\pi\)
\(522\) −30.3259 21.2755i −1.32733 0.931203i
\(523\) −8.38637 14.5256i −0.366710 0.635161i 0.622339 0.782748i \(-0.286183\pi\)
−0.989049 + 0.147587i \(0.952849\pi\)
\(524\) 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 \(-0.301891\pi\)
0.582970 + 0.812494i \(0.301891\pi\)
\(564\) 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 \(-0.559443\pi\)
0.943799 0.330519i \(-0.107224\pi\)
\(578\) −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 −0.727605 0.685996i \(-0.759367\pi\)
0.957893 + 0.287126i \(0.0927000\pi\)
\(588\) 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 0.587800 0.809006i \(-0.299994\pi\)
−0.994520 + 0.104547i \(0.966661\pi\)
\(594\) 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 \(0.334396\pi\)
−0.999994 + 0.00333942i \(0.998937\pi\)
\(602\) 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 −0.986361 0.164596i \(-0.947368\pi\)
0.635725 + 0.771916i \(0.280701\pi\)
\(608\) 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 \(-0.928922\pi\)
0.295807 0.955248i \(-0.404412\pi\)
\(620\) 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 \(-0.991616\pi\)
0.477017 0.878894i \(-0.341718\pi\)
\(644\) 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 −0.866183 0.499727i \(-0.833434\pi\)
0.865868 + 0.500273i \(0.166767\pi\)
\(648\) 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 \(-0.467092\pi\)
0.103198 + 0.994661i \(0.467092\pi\)
\(662\) 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 \(-0.733041\pi\)
−0.668449 + 0.743758i \(0.733041\pi\)
\(678\) 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 \(-0.540290\pi\)
−0.126237 + 0.992000i \(0.540290\pi\)
\(692\) −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 \(0.142649\pi\)
−0.0753825 + 0.997155i \(0.524018\pi\)
\(720\) 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 \(-0.657826\pi\)
0.999614 0.0277700i \(-0.00884060\pi\)
\(728\) 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 −0.537051 0.843550i \(-0.680462\pi\)
0.999061 + 0.0433249i \(0.0137951\pi\)
\(734\) −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 −0.719683 0.694303i \(-0.755713\pi\)
0.961125 + 0.276113i \(0.0890462\pi\)
\(762\) 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 \(0.280991\pi\)
0.351488 + 0.936192i \(0.385676\pi\)
\(770\) 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 −0.886469 0.462787i \(-0.846849\pi\)
0.844020 + 0.536311i \(0.180183\pi\)
\(774\) 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