Properties

Label 720.2.u.a.179.20
Level $720$
Weight $2$
Character 720.179
Analytic conductor $5.749$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 720.u (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.74922894553\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(48\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 179.20
Character \(\chi\) \(=\) 720.179
Dual form 720.2.u.a.539.20

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.581659 + 1.28906i) q^{2} +(-1.32335 - 1.49958i) q^{4} +(0.0342493 + 2.23581i) q^{5} -4.97879i q^{7} +(2.70279 - 0.833625i) q^{8} +O(q^{10})\) \(q+(-0.581659 + 1.28906i) q^{2} +(-1.32335 - 1.49958i) q^{4} +(0.0342493 + 2.23581i) q^{5} -4.97879i q^{7} +(2.70279 - 0.833625i) q^{8} +(-2.90201 - 1.25633i) q^{10} +(0.299629 - 0.299629i) q^{11} +(-3.41391 + 3.41391i) q^{13} +(6.41795 + 2.89596i) q^{14} +(-0.497509 + 3.96894i) q^{16} -5.22586 q^{17} +(-3.58000 + 3.58000i) q^{19} +(3.30746 - 3.01011i) q^{20} +(0.211957 + 0.560520i) q^{22} -6.15703 q^{23} +(-4.99765 + 0.153150i) q^{25} +(-2.41500 - 6.38646i) q^{26} +(-7.46612 + 6.58866i) q^{28} +(-3.26048 + 3.26048i) q^{29} -7.77031i q^{31} +(-4.82682 - 2.94989i) q^{32} +(3.03966 - 6.73644i) q^{34} +(11.1316 - 0.170520i) q^{35} +(2.27648 + 2.27648i) q^{37} +(-2.53249 - 6.69716i) q^{38} +(1.95639 + 6.01436i) q^{40} +7.32246 q^{41} +(1.76594 - 1.76594i) q^{43} +(-0.845831 - 0.0528060i) q^{44} +(3.58129 - 7.93678i) q^{46} +1.69344i q^{47} -17.7884 q^{49} +(2.70951 - 6.53135i) q^{50} +(9.63723 + 0.601662i) q^{52} +(2.95155 - 2.95155i) q^{53} +(0.680173 + 0.659649i) q^{55} +(-4.15045 - 13.4566i) q^{56} +(-2.30646 - 6.09944i) q^{58} +(-4.14389 + 4.14389i) q^{59} +(-9.38240 - 9.38240i) q^{61} +(10.0164 + 4.51967i) q^{62} +(6.61014 - 4.50623i) q^{64} +(-7.74976 - 7.51592i) q^{65} +(-0.0409648 - 0.0409648i) q^{67} +(6.91562 + 7.83661i) q^{68} +(-6.25499 + 14.4485i) q^{70} +4.96779i q^{71} +3.87421 q^{73} +(-4.25865 + 1.61038i) q^{74} +(10.1061 + 0.630932i) q^{76} +(-1.49179 - 1.49179i) q^{77} -0.521248i q^{79} +(-8.89082 - 0.976399i) q^{80} +(-4.25917 + 9.43908i) q^{82} +(-9.49013 + 9.49013i) q^{83} +(-0.178982 - 11.6840i) q^{85} +(1.24923 + 3.30358i) q^{86} +(0.560055 - 1.05961i) q^{88} +3.52625 q^{89} +(16.9971 + 16.9971i) q^{91} +(8.14788 + 9.23299i) q^{92} +(-2.18294 - 0.985002i) q^{94} +(-8.12679 - 7.88156i) q^{95} -3.30729i q^{97} +(10.3467 - 22.9302i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96q + O(q^{10}) \) \( 96q - 8q^{16} - 16q^{19} + 72q^{34} + 8q^{40} + 8q^{46} - 96q^{49} + 64q^{55} - 32q^{61} + 48q^{64} + 24q^{70} + 40q^{76} - 88q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(271\) \(577\) \(641\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.581659 + 1.28906i −0.411295 + 0.911502i
\(3\) 0 0
\(4\) −1.32335 1.49958i −0.661673 0.749792i
\(5\) 0.0342493 + 2.23581i 0.0153168 + 0.999883i
\(6\) 0 0
\(7\) 4.97879i 1.88181i −0.338676 0.940903i \(-0.609979\pi\)
0.338676 0.940903i \(-0.390021\pi\)
\(8\) 2.70279 0.833625i 0.955580 0.294731i
\(9\) 0 0
\(10\) −2.90201 1.25633i −0.917695 0.397285i
\(11\) 0.299629 0.299629i 0.0903414 0.0903414i −0.660492 0.750833i \(-0.729652\pi\)
0.750833 + 0.660492i \(0.229652\pi\)
\(12\) 0 0
\(13\) −3.41391 + 3.41391i −0.946848 + 0.946848i −0.998657 0.0518087i \(-0.983501\pi\)
0.0518087 + 0.998657i \(0.483501\pi\)
\(14\) 6.41795 + 2.89596i 1.71527 + 0.773977i
\(15\) 0 0
\(16\) −0.497509 + 3.96894i −0.124377 + 0.992235i
\(17\) −5.22586 −1.26746 −0.633728 0.773556i \(-0.718476\pi\)
−0.633728 + 0.773556i \(0.718476\pi\)
\(18\) 0 0
\(19\) −3.58000 + 3.58000i −0.821307 + 0.821307i −0.986296 0.164988i \(-0.947241\pi\)
0.164988 + 0.986296i \(0.447241\pi\)
\(20\) 3.30746 3.01011i 0.739570 0.673080i
\(21\) 0 0
\(22\) 0.211957 + 0.560520i 0.0451895 + 0.119503i
\(23\) −6.15703 −1.28383 −0.641915 0.766776i \(-0.721860\pi\)
−0.641915 + 0.766776i \(0.721860\pi\)
\(24\) 0 0
\(25\) −4.99765 + 0.153150i −0.999531 + 0.0306300i
\(26\) −2.41500 6.38646i −0.473621 1.25249i
\(27\) 0 0
\(28\) −7.46612 + 6.58866i −1.41096 + 1.24514i
\(29\) −3.26048 + 3.26048i −0.605456 + 0.605456i −0.941755 0.336299i \(-0.890825\pi\)
0.336299 + 0.941755i \(0.390825\pi\)
\(30\) 0 0
\(31\) 7.77031i 1.39559i −0.716298 0.697795i \(-0.754165\pi\)
0.716298 0.697795i \(-0.245835\pi\)
\(32\) −4.82682 2.94989i −0.853269 0.521471i
\(33\) 0 0
\(34\) 3.03966 6.73644i 0.521298 1.15529i
\(35\) 11.1316 0.170520i 1.88159 0.0288232i
\(36\) 0 0
\(37\) 2.27648 + 2.27648i 0.374251 + 0.374251i 0.869023 0.494772i \(-0.164748\pi\)
−0.494772 + 0.869023i \(0.664748\pi\)
\(38\) −2.53249 6.69716i −0.410824 1.08642i
\(39\) 0 0
\(40\) 1.95639 + 6.01436i 0.309333 + 0.950954i
\(41\) 7.32246 1.14358 0.571788 0.820401i \(-0.306250\pi\)
0.571788 + 0.820401i \(0.306250\pi\)
\(42\) 0 0
\(43\) 1.76594 1.76594i 0.269304 0.269304i −0.559516 0.828820i \(-0.689013\pi\)
0.828820 + 0.559516i \(0.189013\pi\)
\(44\) −0.845831 0.0528060i −0.127514 0.00796081i
\(45\) 0 0
\(46\) 3.58129 7.93678i 0.528032 1.17021i
\(47\) 1.69344i 0.247013i 0.992344 + 0.123507i \(0.0394140\pi\)
−0.992344 + 0.123507i \(0.960586\pi\)
\(48\) 0 0
\(49\) −17.7884 −2.54119
\(50\) 2.70951 6.53135i 0.383183 0.923673i
\(51\) 0 0
\(52\) 9.63723 + 0.601662i 1.33644 + 0.0834355i
\(53\) 2.95155 2.95155i 0.405427 0.405427i −0.474714 0.880140i \(-0.657448\pi\)
0.880140 + 0.474714i \(0.157448\pi\)
\(54\) 0 0
\(55\) 0.680173 + 0.659649i 0.0917145 + 0.0889471i
\(56\) −4.15045 13.4566i −0.554627 1.79822i
\(57\) 0 0
\(58\) −2.30646 6.09944i −0.302854 0.800895i
\(59\) −4.14389 + 4.14389i −0.539489 + 0.539489i −0.923379 0.383890i \(-0.874584\pi\)
0.383890 + 0.923379i \(0.374584\pi\)
\(60\) 0 0
\(61\) −9.38240 9.38240i −1.20129 1.20129i −0.973773 0.227520i \(-0.926938\pi\)
−0.227520 0.973773i \(-0.573062\pi\)
\(62\) 10.0164 + 4.51967i 1.27208 + 0.573999i
\(63\) 0 0
\(64\) 6.61014 4.50623i 0.826267 0.563278i
\(65\) −7.74976 7.51592i −0.961240 0.932235i
\(66\) 0 0
\(67\) −0.0409648 0.0409648i −0.00500465 0.00500465i 0.704600 0.709605i \(-0.251126\pi\)
−0.709605 + 0.704600i \(0.751126\pi\)
\(68\) 6.91562 + 7.83661i 0.838642 + 0.950329i
\(69\) 0 0
\(70\) −6.25499 + 14.4485i −0.747614 + 1.72692i
\(71\) 4.96779i 0.589568i 0.955564 + 0.294784i \(0.0952477\pi\)
−0.955564 + 0.294784i \(0.904752\pi\)
\(72\) 0 0
\(73\) 3.87421 0.453442 0.226721 0.973960i \(-0.427199\pi\)
0.226721 + 0.973960i \(0.427199\pi\)
\(74\) −4.25865 + 1.61038i −0.495058 + 0.187203i
\(75\) 0 0
\(76\) 10.1061 + 0.630932i 1.15925 + 0.0723729i
\(77\) −1.49179 1.49179i −0.170005 0.170005i
\(78\) 0 0
\(79\) 0.521248i 0.0586450i −0.999570 0.0293225i \(-0.990665\pi\)
0.999570 0.0293225i \(-0.00933498\pi\)
\(80\) −8.89082 0.976399i −0.994024 0.109165i
\(81\) 0 0
\(82\) −4.25917 + 9.43908i −0.470347 + 1.04237i
\(83\) −9.49013 + 9.49013i −1.04168 + 1.04168i −0.0425846 + 0.999093i \(0.513559\pi\)
−0.999093 + 0.0425846i \(0.986441\pi\)
\(84\) 0 0
\(85\) −0.178982 11.6840i −0.0194133 1.26731i
\(86\) 1.24923 + 3.30358i 0.134708 + 0.356234i
\(87\) 0 0
\(88\) 0.560055 1.05961i 0.0597020 0.112955i
\(89\) 3.52625 0.373782 0.186891 0.982381i \(-0.440159\pi\)
0.186891 + 0.982381i \(0.440159\pi\)
\(90\) 0 0
\(91\) 16.9971 + 16.9971i 1.78178 + 1.78178i
\(92\) 8.14788 + 9.23299i 0.849476 + 0.962606i
\(93\) 0 0
\(94\) −2.18294 0.985002i −0.225153 0.101595i
\(95\) −8.12679 7.88156i −0.833791 0.808631i
\(96\) 0 0
\(97\) 3.30729i 0.335805i −0.985804 0.167902i \(-0.946301\pi\)
0.985804 0.167902i \(-0.0536993\pi\)
\(98\) 10.3467 22.9302i 1.04518 2.31630i
\(99\) 0 0
\(100\) 6.84329 + 7.29174i 0.684329 + 0.729174i
\(101\) −7.55836 7.55836i −0.752085 0.752085i 0.222783 0.974868i \(-0.428486\pi\)
−0.974868 + 0.222783i \(0.928486\pi\)
\(102\) 0 0
\(103\) 13.0592i 1.28676i −0.765546 0.643381i \(-0.777531\pi\)
0.765546 0.643381i \(-0.222469\pi\)
\(104\) −6.38116 + 12.0730i −0.625724 + 1.18386i
\(105\) 0 0
\(106\) 2.08793 + 5.52152i 0.202797 + 0.536297i
\(107\) 7.46283 + 7.46283i 0.721459 + 0.721459i 0.968902 0.247443i \(-0.0795904\pi\)
−0.247443 + 0.968902i \(0.579590\pi\)
\(108\) 0 0
\(109\) 3.43459 + 3.43459i 0.328974 + 0.328974i 0.852196 0.523222i \(-0.175270\pi\)
−0.523222 + 0.852196i \(0.675270\pi\)
\(110\) −1.24596 + 0.493093i −0.118797 + 0.0470146i
\(111\) 0 0
\(112\) 19.7605 + 2.47699i 1.86719 + 0.234054i
\(113\) −5.42433 −0.510278 −0.255139 0.966904i \(-0.582121\pi\)
−0.255139 + 0.966904i \(0.582121\pi\)
\(114\) 0 0
\(115\) −0.210874 13.7659i −0.0196641 1.28368i
\(116\) 9.20411 + 0.574621i 0.854580 + 0.0533523i
\(117\) 0 0
\(118\) −2.93139 7.75205i −0.269856 0.713634i
\(119\) 26.0184i 2.38511i
\(120\) 0 0
\(121\) 10.8204i 0.983677i
\(122\) 17.5518 6.63712i 1.58907 0.600896i
\(123\) 0 0
\(124\) −11.6522 + 10.2828i −1.04640 + 0.923424i
\(125\) −0.513580 11.1685i −0.0459359 0.998944i
\(126\) 0 0
\(127\) 9.57690 0.849813 0.424906 0.905237i \(-0.360307\pi\)
0.424906 + 0.905237i \(0.360307\pi\)
\(128\) 1.96395 + 11.1419i 0.173590 + 0.984818i
\(129\) 0 0
\(130\) 14.1962 5.61821i 1.24509 0.492749i
\(131\) −12.5044 12.5044i −1.09252 1.09252i −0.995259 0.0972558i \(-0.968994\pi\)
−0.0972558 0.995259i \(-0.531006\pi\)
\(132\) 0 0
\(133\) 17.8241 + 17.8241i 1.54554 + 1.54554i
\(134\) 0.0766335 0.0289785i 0.00662013 0.00250336i
\(135\) 0 0
\(136\) −14.1244 + 4.35640i −1.21116 + 0.373559i
\(137\) 3.21459i 0.274641i 0.990527 + 0.137320i \(0.0438490\pi\)
−0.990527 + 0.137320i \(0.956151\pi\)
\(138\) 0 0
\(139\) −0.728605 0.728605i −0.0617994 0.0617994i 0.675532 0.737331i \(-0.263914\pi\)
−0.737331 + 0.675532i \(0.763914\pi\)
\(140\) −14.9867 16.4671i −1.26661 1.39173i
\(141\) 0 0
\(142\) −6.40377 2.88956i −0.537392 0.242486i
\(143\) 2.04581i 0.171079i
\(144\) 0 0
\(145\) −7.40147 7.17813i −0.614658 0.596111i
\(146\) −2.25347 + 4.99409i −0.186498 + 0.413314i
\(147\) 0 0
\(148\) 0.401203 6.42634i 0.0329787 0.528242i
\(149\) −3.90021 3.90021i −0.319518 0.319518i 0.529064 0.848582i \(-0.322543\pi\)
−0.848582 + 0.529064i \(0.822543\pi\)
\(150\) 0 0
\(151\) 2.48795 0.202467 0.101233 0.994863i \(-0.467721\pi\)
0.101233 + 0.994863i \(0.467721\pi\)
\(152\) −6.69160 + 12.6603i −0.542760 + 1.02689i
\(153\) 0 0
\(154\) 2.79071 1.05529i 0.224882 0.0850378i
\(155\) 17.3729 0.266128i 1.39543 0.0213759i
\(156\) 0 0
\(157\) 6.88372 6.88372i 0.549380 0.549380i −0.376881 0.926262i \(-0.623003\pi\)
0.926262 + 0.376881i \(0.123003\pi\)
\(158\) 0.671920 + 0.303189i 0.0534551 + 0.0241204i
\(159\) 0 0
\(160\) 6.43006 10.8929i 0.508341 0.861156i
\(161\) 30.6546i 2.41592i
\(162\) 0 0
\(163\) −0.954196 0.954196i −0.0747384 0.0747384i 0.668749 0.743488i \(-0.266830\pi\)
−0.743488 + 0.668749i \(0.766830\pi\)
\(164\) −9.69015 10.9806i −0.756674 0.857445i
\(165\) 0 0
\(166\) −6.71332 17.7534i −0.521055 1.37793i
\(167\) 9.73397 0.753237 0.376619 0.926368i \(-0.377087\pi\)
0.376619 + 0.926368i \(0.377087\pi\)
\(168\) 0 0
\(169\) 10.3096i 0.793044i
\(170\) 15.1655 + 6.56538i 1.16314 + 0.503542i
\(171\) 0 0
\(172\) −4.98514 0.311227i −0.380113 0.0237308i
\(173\) −7.85395 7.85395i −0.597125 0.597125i 0.342421 0.939546i \(-0.388753\pi\)
−0.939546 + 0.342421i \(0.888753\pi\)
\(174\) 0 0
\(175\) 0.762501 + 24.8823i 0.0576396 + 1.88092i
\(176\) 1.04014 + 1.33828i 0.0784035 + 0.100876i
\(177\) 0 0
\(178\) −2.05107 + 4.54554i −0.153734 + 0.340703i
\(179\) 9.13459 + 9.13459i 0.682751 + 0.682751i 0.960619 0.277868i \(-0.0896278\pi\)
−0.277868 + 0.960619i \(0.589628\pi\)
\(180\) 0 0
\(181\) −15.9005 + 15.9005i −1.18188 + 1.18188i −0.202621 + 0.979257i \(0.564946\pi\)
−0.979257 + 0.202621i \(0.935054\pi\)
\(182\) −31.7969 + 12.0238i −2.35694 + 0.891262i
\(183\) 0 0
\(184\) −16.6412 + 5.13266i −1.22680 + 0.378384i
\(185\) −5.01180 + 5.16773i −0.368475 + 0.379939i
\(186\) 0 0
\(187\) −1.56582 + 1.56582i −0.114504 + 0.114504i
\(188\) 2.53945 2.24100i 0.185209 0.163442i
\(189\) 0 0
\(190\) 14.8868 5.89153i 1.08000 0.427417i
\(191\) 2.16753 0.156837 0.0784183 0.996921i \(-0.475013\pi\)
0.0784183 + 0.996921i \(0.475013\pi\)
\(192\) 0 0
\(193\) 23.0521i 1.65932i 0.558265 + 0.829662i \(0.311467\pi\)
−0.558265 + 0.829662i \(0.688533\pi\)
\(194\) 4.26329 + 1.92371i 0.306087 + 0.138115i
\(195\) 0 0
\(196\) 23.5402 + 26.6751i 1.68144 + 1.90537i
\(197\) 1.52767 1.52767i 0.108842 0.108842i −0.650588 0.759431i \(-0.725478\pi\)
0.759431 + 0.650588i \(0.225478\pi\)
\(198\) 0 0
\(199\) −3.12757 −0.221708 −0.110854 0.993837i \(-0.535359\pi\)
−0.110854 + 0.993837i \(0.535359\pi\)
\(200\) −13.3799 + 4.58010i −0.946104 + 0.323862i
\(201\) 0 0
\(202\) 14.1396 5.34678i 0.994855 0.376198i
\(203\) 16.2332 + 16.2332i 1.13935 + 1.13935i
\(204\) 0 0
\(205\) 0.250789 + 16.3716i 0.0175159 + 1.14344i
\(206\) 16.8341 + 7.59600i 1.17289 + 0.529239i
\(207\) 0 0
\(208\) −11.8512 15.2481i −0.821730 1.05726i
\(209\) 2.14534i 0.148396i
\(210\) 0 0
\(211\) 2.66344 2.66344i 0.183359 0.183359i −0.609459 0.792818i \(-0.708613\pi\)
0.792818 + 0.609459i \(0.208613\pi\)
\(212\) −8.33202 0.520176i −0.572246 0.0357259i
\(213\) 0 0
\(214\) −13.9608 + 5.27921i −0.954344 + 0.360879i
\(215\) 4.00879 + 3.88782i 0.273397 + 0.265147i
\(216\) 0 0
\(217\) −38.6868 −2.62623
\(218\) −6.42515 + 2.42963i −0.435166 + 0.164555i
\(219\) 0 0
\(220\) 0.0890949 1.89292i 0.00600677 0.127621i
\(221\) 17.8406 17.8406i 1.20009 1.20009i
\(222\) 0 0
\(223\) 22.8494 1.53011 0.765053 0.643967i \(-0.222713\pi\)
0.765053 + 0.643967i \(0.222713\pi\)
\(224\) −14.6869 + 24.0317i −0.981307 + 1.60569i
\(225\) 0 0
\(226\) 3.15511 6.99228i 0.209875 0.465119i
\(227\) 2.89777 2.89777i 0.192332 0.192332i −0.604371 0.796703i \(-0.706576\pi\)
0.796703 + 0.604371i \(0.206576\pi\)
\(228\) 0 0
\(229\) 13.7901 13.7901i 0.911276 0.911276i −0.0850965 0.996373i \(-0.527120\pi\)
0.996373 + 0.0850965i \(0.0271199\pi\)
\(230\) 17.8677 + 7.73524i 1.17816 + 0.510047i
\(231\) 0 0
\(232\) −6.09437 + 11.5304i −0.400115 + 0.757008i
\(233\) 27.8531i 1.82472i 0.409388 + 0.912360i \(0.365742\pi\)
−0.409388 + 0.912360i \(0.634258\pi\)
\(234\) 0 0
\(235\) −3.78619 + 0.0579991i −0.246984 + 0.00378344i
\(236\) 11.6979 + 0.730312i 0.761470 + 0.0475393i
\(237\) 0 0
\(238\) −33.5393 15.1339i −2.17403 0.980982i
\(239\) −22.7939 −1.47441 −0.737207 0.675667i \(-0.763856\pi\)
−0.737207 + 0.675667i \(0.763856\pi\)
\(240\) 0 0
\(241\) 4.33189 0.279042 0.139521 0.990219i \(-0.455444\pi\)
0.139521 + 0.990219i \(0.455444\pi\)
\(242\) −13.9482 6.29381i −0.896624 0.404581i
\(243\) 0 0
\(244\) −1.65354 + 26.4859i −0.105857 + 1.69558i
\(245\) −0.609240 39.7713i −0.0389229 2.54090i
\(246\) 0 0
\(247\) 24.4436i 1.55531i
\(248\) −6.47753 21.0015i −0.411324 1.33360i
\(249\) 0 0
\(250\) 14.6956 + 5.83424i 0.929433 + 0.368990i
\(251\) 4.97266 4.97266i 0.313872 0.313872i −0.532536 0.846407i \(-0.678761\pi\)
0.846407 + 0.532536i \(0.178761\pi\)
\(252\) 0 0
\(253\) −1.84482 + 1.84482i −0.115983 + 0.115983i
\(254\) −5.57049 + 12.3452i −0.349524 + 0.774606i
\(255\) 0 0
\(256\) −15.5050 3.94916i −0.969061 0.246823i
\(257\) −8.06975 −0.503377 −0.251689 0.967808i \(-0.580986\pi\)
−0.251689 + 0.967808i \(0.580986\pi\)
\(258\) 0 0
\(259\) 11.3341 11.3341i 0.704267 0.704267i
\(260\) −1.01513 + 21.5676i −0.0629557 + 1.33757i
\(261\) 0 0
\(262\) 23.3922 8.84562i 1.44518 0.546484i
\(263\) −17.5377 −1.08142 −0.540710 0.841209i \(-0.681845\pi\)
−0.540710 + 0.841209i \(0.681845\pi\)
\(264\) 0 0
\(265\) 6.70018 + 6.49800i 0.411589 + 0.399169i
\(266\) −33.3438 + 12.6087i −2.04444 + 0.773091i
\(267\) 0 0
\(268\) −0.00721956 + 0.115641i −0.000441005 + 0.00706388i
\(269\) −1.87139 + 1.87139i −0.114101 + 0.114101i −0.761852 0.647751i \(-0.775710\pi\)
0.647751 + 0.761852i \(0.275710\pi\)
\(270\) 0 0
\(271\) 22.9224i 1.39244i −0.717831 0.696218i \(-0.754865\pi\)
0.717831 0.696218i \(-0.245135\pi\)
\(272\) 2.59991 20.7411i 0.157643 1.25761i
\(273\) 0 0
\(274\) −4.14379 1.86979i −0.250336 0.112958i
\(275\) −1.45155 + 1.54333i −0.0875319 + 0.0930662i
\(276\) 0 0
\(277\) 13.2521 + 13.2521i 0.796239 + 0.796239i 0.982500 0.186261i \(-0.0596372\pi\)
−0.186261 + 0.982500i \(0.559637\pi\)
\(278\) 1.36301 0.515415i 0.0817481 0.0309126i
\(279\) 0 0
\(280\) 29.9442 9.74047i 1.78951 0.582104i
\(281\) 12.2485 0.730684 0.365342 0.930873i \(-0.380952\pi\)
0.365342 + 0.930873i \(0.380952\pi\)
\(282\) 0 0
\(283\) −2.62423 + 2.62423i −0.155994 + 0.155994i −0.780789 0.624795i \(-0.785183\pi\)
0.624795 + 0.780789i \(0.285183\pi\)
\(284\) 7.44962 6.57410i 0.442053 0.390101i
\(285\) 0 0
\(286\) −2.63717 1.18996i −0.155939 0.0703640i
\(287\) 36.4570i 2.15199i
\(288\) 0 0
\(289\) 10.3096 0.606445
\(290\) 13.5582 5.36571i 0.796163 0.315085i
\(291\) 0 0
\(292\) −5.12693 5.80971i −0.300031 0.339988i
\(293\) 3.96865 3.96865i 0.231851 0.231851i −0.581614 0.813465i \(-0.697578\pi\)
0.813465 + 0.581614i \(0.197578\pi\)
\(294\) 0 0
\(295\) −9.40686 9.12301i −0.547689 0.531162i
\(296\) 8.05057 + 4.25511i 0.467930 + 0.247323i
\(297\) 0 0
\(298\) 7.29619 2.75901i 0.422657 0.159825i
\(299\) 21.0196 21.0196i 1.21559 1.21559i
\(300\) 0 0
\(301\) −8.79226 8.79226i −0.506778 0.506778i
\(302\) −1.44714 + 3.20712i −0.0832734 + 0.184549i
\(303\) 0 0
\(304\) −12.4277 15.9899i −0.712778 0.917082i
\(305\) 20.6559 21.2986i 1.18275 1.21955i
\(306\) 0 0
\(307\) 5.66311 + 5.66311i 0.323211 + 0.323211i 0.849997 0.526787i \(-0.176603\pi\)
−0.526787 + 0.849997i \(0.676603\pi\)
\(308\) −0.262910 + 4.21121i −0.0149807 + 0.239956i
\(309\) 0 0
\(310\) −9.76205 + 22.5495i −0.554447 + 1.28073i
\(311\) 29.5732i 1.67694i −0.544947 0.838470i \(-0.683450\pi\)
0.544947 0.838470i \(-0.316550\pi\)
\(312\) 0 0
\(313\) 12.2408 0.691891 0.345945 0.938255i \(-0.387558\pi\)
0.345945 + 0.938255i \(0.387558\pi\)
\(314\) 4.86954 + 12.8775i 0.274804 + 0.726719i
\(315\) 0 0
\(316\) −0.781656 + 0.689792i −0.0439716 + 0.0388038i
\(317\) 12.0077 + 12.0077i 0.674419 + 0.674419i 0.958732 0.284312i \(-0.0917653\pi\)
−0.284312 + 0.958732i \(0.591765\pi\)
\(318\) 0 0
\(319\) 1.95387i 0.109395i
\(320\) 10.3014 + 14.6246i 0.575868 + 0.817543i
\(321\) 0 0
\(322\) −39.5155 17.8305i −2.20212 0.993655i
\(323\) 18.7085 18.7085i 1.04097 1.04097i
\(324\) 0 0
\(325\) 16.5387 17.5844i 0.917402 0.975406i
\(326\) 1.78503 0.674998i 0.0988637 0.0373847i
\(327\) 0 0
\(328\) 19.7911 6.10419i 1.09278 0.337047i
\(329\) 8.43126 0.464831
\(330\) 0 0
\(331\) 6.22467 + 6.22467i 0.342139 + 0.342139i 0.857171 0.515032i \(-0.172220\pi\)
−0.515032 + 0.857171i \(0.672220\pi\)
\(332\) 26.7900 + 1.67253i 1.47029 + 0.0917917i
\(333\) 0 0
\(334\) −5.66185 + 12.5477i −0.309803 + 0.686578i
\(335\) 0.0901863 0.0929923i 0.00492740 0.00508071i
\(336\) 0 0
\(337\) 2.44733i 0.133315i −0.997776 0.0666574i \(-0.978767\pi\)
0.997776 0.0666574i \(-0.0212335\pi\)
\(338\) 13.2896 + 5.99665i 0.722861 + 0.326175i
\(339\) 0 0
\(340\) −17.2843 + 15.7304i −0.937372 + 0.853099i
\(341\) −2.32821 2.32821i −0.126080 0.126080i
\(342\) 0 0
\(343\) 53.7130i 2.90023i
\(344\) 3.30084 6.24511i 0.177969 0.336714i
\(345\) 0 0
\(346\) 14.6925 5.55589i 0.789875 0.298687i
\(347\) −7.80648 7.80648i −0.419074 0.419074i 0.465811 0.884884i \(-0.345763\pi\)
−0.884884 + 0.465811i \(0.845763\pi\)
\(348\) 0 0
\(349\) −18.4011 18.4011i −0.984990 0.984990i 0.0148993 0.999889i \(-0.495257\pi\)
−0.999889 + 0.0148993i \(0.995257\pi\)
\(350\) −32.5182 13.4901i −1.73817 0.721075i
\(351\) 0 0
\(352\) −2.33012 + 0.562382i −0.124196 + 0.0299751i
\(353\) −23.6781 −1.26026 −0.630128 0.776491i \(-0.716998\pi\)
−0.630128 + 0.776491i \(0.716998\pi\)
\(354\) 0 0
\(355\) −11.1070 + 0.170143i −0.589499 + 0.00903028i
\(356\) −4.66645 5.28791i −0.247321 0.280259i
\(357\) 0 0
\(358\) −17.0882 + 6.46181i −0.903141 + 0.341517i
\(359\) 0.461358i 0.0243495i 0.999926 + 0.0121748i \(0.00387544\pi\)
−0.999926 + 0.0121748i \(0.996125\pi\)
\(360\) 0 0
\(361\) 6.63274i 0.349092i
\(362\) −11.2481 29.7454i −0.591185 1.56339i
\(363\) 0 0
\(364\) 2.99555 47.9818i 0.157009 2.51493i
\(365\) 0.132689 + 8.66199i 0.00694528 + 0.453389i
\(366\) 0 0
\(367\) −20.2030 −1.05459 −0.527294 0.849683i \(-0.676793\pi\)
−0.527294 + 0.849683i \(0.676793\pi\)
\(368\) 3.06318 24.4369i 0.159679 1.27386i
\(369\) 0 0
\(370\) −3.74636 9.46636i −0.194764 0.492133i
\(371\) −14.6952 14.6952i −0.762934 0.762934i
\(372\) 0 0
\(373\) −5.66776 5.66776i −0.293465 0.293465i 0.544982 0.838448i \(-0.316536\pi\)
−0.838448 + 0.544982i \(0.816536\pi\)
\(374\) −1.10766 2.92920i −0.0572757 0.151465i
\(375\) 0 0
\(376\) 1.41169 + 4.57700i 0.0728024 + 0.236041i
\(377\) 22.2620i 1.14655i
\(378\) 0 0
\(379\) 6.20237 + 6.20237i 0.318594 + 0.318594i 0.848227 0.529633i \(-0.177670\pi\)
−0.529633 + 0.848227i \(0.677670\pi\)
\(380\) −1.06452 + 22.6168i −0.0546085 + 1.16022i
\(381\) 0 0
\(382\) −1.26076 + 2.79407i −0.0645061 + 0.142957i
\(383\) 4.89671i 0.250210i 0.992143 + 0.125105i \(0.0399268\pi\)
−0.992143 + 0.125105i \(0.960073\pi\)
\(384\) 0 0
\(385\) 3.28425 3.38644i 0.167381 0.172589i
\(386\) −29.7155 13.4084i −1.51248 0.682472i
\(387\) 0 0
\(388\) −4.95956 + 4.37669i −0.251784 + 0.222193i
\(389\) −13.7639 13.7639i −0.697860 0.697860i 0.266089 0.963949i \(-0.414269\pi\)
−0.963949 + 0.266089i \(0.914269\pi\)
\(390\) 0 0
\(391\) 32.1758 1.62720
\(392\) −48.0782 + 14.8288i −2.42831 + 0.748969i
\(393\) 0 0
\(394\) 1.08068 + 2.85784i 0.0544437 + 0.143976i
\(395\) 1.16541 0.0178524i 0.0586381 0.000898253i
\(396\) 0 0
\(397\) −16.2544 + 16.2544i −0.815787 + 0.815787i −0.985495 0.169707i \(-0.945718\pi\)
0.169707 + 0.985495i \(0.445718\pi\)
\(398\) 1.81918 4.03162i 0.0911872 0.202087i
\(399\) 0 0
\(400\) 1.87853 19.9116i 0.0939267 0.995579i
\(401\) 10.0348i 0.501116i 0.968102 + 0.250558i \(0.0806140\pi\)
−0.968102 + 0.250558i \(0.919386\pi\)
\(402\) 0 0
\(403\) 26.5272 + 26.5272i 1.32141 + 1.32141i
\(404\) −1.33207 + 21.3367i −0.0662731 + 1.06154i
\(405\) 0 0
\(406\) −30.3678 + 11.4834i −1.50713 + 0.569912i
\(407\) 1.36420 0.0676207
\(408\) 0 0
\(409\) 33.3911i 1.65108i 0.564341 + 0.825542i \(0.309130\pi\)
−0.564341 + 0.825542i \(0.690870\pi\)
\(410\) −21.2498 9.19940i −1.04945 0.454326i
\(411\) 0 0
\(412\) −19.5834 + 17.2819i −0.964804 + 0.851416i
\(413\) 20.6316 + 20.6316i 1.01521 + 1.01521i
\(414\) 0 0
\(415\) −21.5431 20.8931i −1.05751 1.02560i
\(416\) 26.5490 6.40768i 1.30167 0.314162i
\(417\) 0 0
\(418\) −2.76547 1.24785i −0.135263 0.0610346i
\(419\) 12.9105 + 12.9105i 0.630718 + 0.630718i 0.948248 0.317530i \(-0.102853\pi\)
−0.317530 + 0.948248i \(0.602853\pi\)
\(420\) 0 0
\(421\) 0.923750 0.923750i 0.0450208 0.0450208i −0.684238 0.729259i \(-0.739865\pi\)
0.729259 + 0.684238i \(0.239865\pi\)
\(422\) 1.88412 + 4.98255i 0.0917175 + 0.242547i
\(423\) 0 0
\(424\) 5.51693 10.4379i 0.267926 0.506910i
\(425\) 26.1170 0.800339i 1.26686 0.0388221i
\(426\) 0 0
\(427\) −46.7130 + 46.7130i −2.26060 + 2.26060i
\(428\) 1.31524 21.0671i 0.0635743 1.01831i
\(429\) 0 0
\(430\) −7.34338 + 2.90618i −0.354129 + 0.140148i
\(431\) −23.5531 −1.13451 −0.567255 0.823542i \(-0.691995\pi\)
−0.567255 + 0.823542i \(0.691995\pi\)
\(432\) 0 0
\(433\) 38.5735i 1.85373i −0.375400 0.926863i \(-0.622495\pi\)
0.375400 0.926863i \(-0.377505\pi\)
\(434\) 22.5025 49.8695i 1.08015 2.39381i
\(435\) 0 0
\(436\) 0.605306 9.69561i 0.0289889 0.464336i
\(437\) 22.0421 22.0421i 1.05442 1.05442i
\(438\) 0 0
\(439\) −30.3538 −1.44871 −0.724355 0.689427i \(-0.757862\pi\)
−0.724355 + 0.689427i \(0.757862\pi\)
\(440\) 2.38827 + 1.21588i 0.113856 + 0.0579649i
\(441\) 0 0
\(442\) 12.6204 + 33.3747i 0.600294 + 1.58747i
\(443\) 4.74763 + 4.74763i 0.225567 + 0.225567i 0.810838 0.585271i \(-0.199012\pi\)
−0.585271 + 0.810838i \(0.699012\pi\)
\(444\) 0 0
\(445\) 0.120772 + 7.88401i 0.00572513 + 0.373738i
\(446\) −13.2905 + 29.4542i −0.629325 + 1.39470i
\(447\) 0 0
\(448\) −22.4356 32.9105i −1.05998 1.55487i
\(449\) 10.1268i 0.477914i −0.971030 0.238957i \(-0.923194\pi\)
0.971030 0.238957i \(-0.0768055\pi\)
\(450\) 0 0
\(451\) 2.19402 2.19402i 0.103312 0.103312i
\(452\) 7.17826 + 8.13424i 0.337637 + 0.382602i
\(453\) 0 0
\(454\) 2.04988 + 5.42091i 0.0962058 + 0.254416i
\(455\) −37.4202 + 38.5845i −1.75428 + 1.80887i
\(456\) 0 0
\(457\) 1.44447 0.0675695 0.0337847 0.999429i \(-0.489244\pi\)
0.0337847 + 0.999429i \(0.489244\pi\)
\(458\) 9.75513 + 25.7974i 0.455827 + 1.20543i
\(459\) 0 0
\(460\) −20.3641 + 18.5333i −0.949482 + 0.864120i
\(461\) −26.8623 + 26.8623i −1.25110 + 1.25110i −0.295878 + 0.955226i \(0.595612\pi\)
−0.955226 + 0.295878i \(0.904388\pi\)
\(462\) 0 0
\(463\) 20.2597 0.941547 0.470774 0.882254i \(-0.343975\pi\)
0.470774 + 0.882254i \(0.343975\pi\)
\(464\) −11.3185 14.5628i −0.525450 0.676059i
\(465\) 0 0
\(466\) −35.9044 16.2010i −1.66324 0.750498i
\(467\) −9.09888 + 9.09888i −0.421046 + 0.421046i −0.885564 0.464518i \(-0.846228\pi\)
0.464518 + 0.885564i \(0.346228\pi\)
\(468\) 0 0
\(469\) −0.203955 + 0.203955i −0.00941777 + 0.00941777i
\(470\) 2.12751 4.91436i 0.0981346 0.226683i
\(471\) 0 0
\(472\) −7.74561 + 14.6545i −0.356521 + 0.674529i
\(473\) 1.05825i 0.0486586i
\(474\) 0 0
\(475\) 17.3433 18.4399i 0.795765 0.846079i
\(476\) 39.0169 34.4314i 1.78833 1.57816i
\(477\) 0 0
\(478\) 13.2583 29.3827i 0.606419 1.34393i
\(479\) 4.60465 0.210392 0.105196 0.994452i \(-0.466453\pi\)
0.105196 + 0.994452i \(0.466453\pi\)
\(480\) 0 0
\(481\) −15.5434 −0.708718
\(482\) −2.51968 + 5.58406i −0.114768 + 0.254347i
\(483\) 0 0
\(484\) 16.2262 14.3192i 0.737553 0.650873i
\(485\) 7.39446 0.113273i 0.335765 0.00514344i
\(486\) 0 0
\(487\) 32.2084i 1.45950i −0.683713 0.729751i \(-0.739636\pi\)
0.683713 0.729751i \(-0.260364\pi\)
\(488\) −33.1801 17.5372i −1.50199 0.793874i
\(489\) 0 0
\(490\) 51.6219 + 22.3480i 2.33204 + 1.00958i
\(491\) 17.4179 17.4179i 0.786059 0.786059i −0.194786 0.980846i \(-0.562401\pi\)
0.980846 + 0.194786i \(0.0624014\pi\)
\(492\) 0 0
\(493\) 17.0388 17.0388i 0.767389 0.767389i
\(494\) 31.5092 + 14.2178i 1.41767 + 0.639690i
\(495\) 0 0
\(496\) 30.8399 + 3.86580i 1.38475 + 0.173579i
\(497\) 24.7336 1.10945
\(498\) 0 0
\(499\) −15.6000 + 15.6000i −0.698354 + 0.698354i −0.964055 0.265701i \(-0.914396\pi\)
0.265701 + 0.964055i \(0.414396\pi\)
\(500\) −16.0685 + 15.5500i −0.718606 + 0.695417i
\(501\) 0 0
\(502\) 3.51766 + 9.30245i 0.157001 + 0.415189i
\(503\) 2.39149 0.106631 0.0533157 0.998578i \(-0.483021\pi\)
0.0533157 + 0.998578i \(0.483021\pi\)
\(504\) 0 0
\(505\) 16.6401 17.1579i 0.740477 0.763516i
\(506\) −1.30503 3.45114i −0.0580156 0.153422i
\(507\) 0 0
\(508\) −12.6736 14.3614i −0.562298 0.637183i
\(509\) 1.78164 1.78164i 0.0789700 0.0789700i −0.666518 0.745489i \(-0.732216\pi\)
0.745489 + 0.666518i \(0.232216\pi\)
\(510\) 0 0
\(511\) 19.2889i 0.853291i
\(512\) 14.1093 17.6898i 0.623549 0.781784i
\(513\) 0 0
\(514\) 4.69384 10.4024i 0.207036 0.458829i
\(515\) 29.1979 0.447269i 1.28661 0.0197090i
\(516\) 0 0
\(517\) 0.507402 + 0.507402i 0.0223155 + 0.0223155i
\(518\) 8.01776 + 21.2029i 0.352280 + 0.931603i
\(519\) 0 0
\(520\) −27.2114 13.8535i −1.19330 0.607518i
\(521\) 6.52761 0.285980 0.142990 0.989724i \(-0.454328\pi\)
0.142990 + 0.989724i \(0.454328\pi\)
\(522\) 0 0
\(523\) −8.63265 + 8.63265i −0.377479 + 0.377479i −0.870192 0.492713i \(-0.836005\pi\)
0.492713 + 0.870192i \(0.336005\pi\)
\(524\) −2.20376 + 35.2991i −0.0962715 + 1.54205i
\(525\) 0 0
\(526\) 10.2010 22.6071i 0.444783 0.985718i
\(527\) 40.6065i 1.76885i
\(528\) 0 0
\(529\) 14.9090 0.648219
\(530\) −12.2735 + 4.85731i −0.533128 + 0.210988i
\(531\) 0 0
\(532\) 3.14128 50.3161i 0.136192 2.18148i
\(533\) −24.9982 + 24.9982i −1.08279 + 1.08279i
\(534\) 0 0
\(535\) −16.4298 + 16.9410i −0.710324 + 0.732425i
\(536\) −0.144868 0.0765699i −0.00625736 0.00330732i
\(537\) 0 0
\(538\) −1.32382 3.50085i −0.0570741 0.150932i
\(539\) −5.32990 + 5.32990i −0.229575 + 0.229575i
\(540\) 0 0
\(541\) 28.4777 + 28.4777i 1.22435 + 1.22435i 0.966070 + 0.258280i \(0.0831557\pi\)
0.258280 + 0.966070i \(0.416844\pi\)
\(542\) 29.5483 + 13.3330i 1.26921 + 0.572701i
\(543\) 0 0
\(544\) 25.2243 + 15.4157i 1.08148 + 0.660942i
\(545\) −7.56144 + 7.79671i −0.323897 + 0.333974i
\(546\) 0 0
\(547\) 7.40756 + 7.40756i 0.316724 + 0.316724i 0.847508 0.530783i \(-0.178102\pi\)
−0.530783 + 0.847508i \(0.678102\pi\)
\(548\) 4.82055 4.25401i 0.205924 0.181722i
\(549\) 0 0
\(550\) −1.14513 2.76883i −0.0488286 0.118063i
\(551\) 23.3450i 0.994531i
\(552\) 0 0
\(553\) −2.59519 −0.110359
\(554\) −24.7909 + 9.37451i −1.05326 + 0.398285i
\(555\) 0 0
\(556\) −0.128408 + 2.05680i −0.00544571 + 0.0872278i
\(557\) 1.55719 + 1.55719i 0.0659803 + 0.0659803i 0.739327 0.673347i \(-0.235144\pi\)
−0.673347 + 0.739327i \(0.735144\pi\)
\(558\) 0 0
\(559\) 12.0575i 0.509980i
\(560\) −4.86129 + 44.2655i −0.205427 + 1.87056i
\(561\) 0 0
\(562\) −7.12444 + 15.7890i −0.300526 + 0.666020i
\(563\) −14.0768 + 14.0768i −0.593265 + 0.593265i −0.938512 0.345247i \(-0.887795\pi\)
0.345247 + 0.938512i \(0.387795\pi\)
\(564\) 0 0
\(565\) −0.185780 12.1277i −0.00781581 0.510218i
\(566\) −1.85638 4.90920i −0.0780296 0.206349i
\(567\) 0 0
\(568\) 4.14127 + 13.4269i 0.173764 + 0.563379i
\(569\) −19.8358 −0.831559 −0.415779 0.909466i \(-0.636491\pi\)
−0.415779 + 0.909466i \(0.636491\pi\)
\(570\) 0 0
\(571\) −14.2584 14.2584i −0.596696 0.596696i 0.342736 0.939432i \(-0.388646\pi\)
−0.939432 + 0.342736i \(0.888646\pi\)
\(572\) 3.06787 2.70732i 0.128274 0.113199i
\(573\) 0 0
\(574\) 46.9952 + 21.2055i 1.96154 + 0.885101i
\(575\) 30.7707 0.942948i 1.28323 0.0393236i
\(576\) 0 0
\(577\) 16.0197i 0.666908i −0.942766 0.333454i \(-0.891786\pi\)
0.942766 0.333454i \(-0.108214\pi\)
\(578\) −5.99665 + 13.2896i −0.249428 + 0.552776i
\(579\) 0 0
\(580\) −0.969507 + 20.5983i −0.0402566 + 0.855297i
\(581\) 47.2494 + 47.2494i 1.96023 + 1.96023i
\(582\) 0 0
\(583\) 1.76874i 0.0732536i
\(584\) 10.4712 3.22964i 0.433301 0.133644i
\(585\) 0 0
\(586\) 2.80743 + 7.42423i 0.115974 + 0.306692i
\(587\) −6.80793 6.80793i −0.280993 0.280993i 0.552512 0.833505i \(-0.313669\pi\)
−0.833505 + 0.552512i \(0.813669\pi\)
\(588\) 0 0
\(589\) 27.8177 + 27.8177i 1.14621 + 1.14621i
\(590\) 17.2317 6.81952i 0.709417 0.280755i
\(591\) 0 0
\(592\) −10.1678 + 7.90264i −0.417893 + 0.324797i
\(593\) −27.4172 −1.12589 −0.562944 0.826495i \(-0.690331\pi\)
−0.562944 + 0.826495i \(0.690331\pi\)
\(594\) 0 0
\(595\) −58.1722 + 0.891115i −2.38483 + 0.0365321i
\(596\) −0.687367 + 11.0100i −0.0281556 + 0.450988i
\(597\) 0 0
\(598\) 14.8692 + 39.3216i 0.608048 + 1.60798i
\(599\) 39.5624i 1.61647i −0.588857 0.808237i \(-0.700422\pi\)
0.588857 0.808237i \(-0.299578\pi\)
\(600\) 0 0
\(601\) 20.5453i 0.838061i 0.907972 + 0.419030i \(0.137630\pi\)
−0.907972 + 0.419030i \(0.862370\pi\)
\(602\) 16.4478 6.21965i 0.670364 0.253494i
\(603\) 0 0
\(604\) −3.29242 3.73089i −0.133967 0.151808i
\(605\) −24.1924 + 0.370593i −0.983561 + 0.0150668i
\(606\) 0 0
\(607\) −19.1918 −0.778971 −0.389485 0.921033i \(-0.627347\pi\)
−0.389485 + 0.921033i \(0.627347\pi\)
\(608\) 27.8406 6.71941i 1.12908 0.272508i
\(609\) 0 0
\(610\) 15.4404 + 39.0152i 0.625165 + 1.57968i
\(611\) −5.78124 5.78124i −0.233884 0.233884i
\(612\) 0 0
\(613\) 3.14030 + 3.14030i 0.126836 + 0.126836i 0.767675 0.640839i \(-0.221414\pi\)
−0.640839 + 0.767675i \(0.721414\pi\)
\(614\) −10.5941 + 4.00608i −0.427542 + 0.161672i
\(615\) 0 0
\(616\) −5.27558 2.78840i −0.212559 0.112348i
\(617\) 26.9611i 1.08541i −0.839922 0.542707i \(-0.817399\pi\)
0.839922 0.542707i \(-0.182601\pi\)
\(618\) 0 0
\(619\) −10.1272 10.1272i −0.407046 0.407046i 0.473661 0.880707i \(-0.342932\pi\)
−0.880707 + 0.473661i \(0.842932\pi\)
\(620\) −23.3895 25.7000i −0.939343 1.03214i
\(621\) 0 0
\(622\) 38.1216 + 17.2015i 1.52854 + 0.689717i
\(623\) 17.5565i 0.703385i
\(624\) 0 0
\(625\) 24.9531 1.53078i 0.998124 0.0612312i
\(626\) −7.11997 + 15.7791i −0.284571 + 0.630660i
\(627\) 0 0
\(628\) −19.4323 1.21317i −0.775432 0.0484109i
\(629\) −11.8966 11.8966i −0.474347 0.474347i
\(630\) 0 0
\(631\) −24.9414 −0.992900 −0.496450 0.868065i \(-0.665363\pi\)
−0.496450 + 0.868065i \(0.665363\pi\)
\(632\) −0.434526 1.40882i −0.0172845 0.0560400i
\(633\) 0 0
\(634\) −22.4630 + 8.49425i −0.892120 + 0.337350i
\(635\) 0.328003 + 21.4121i 0.0130164 + 0.849713i
\(636\) 0 0
\(637\) 60.7278 60.7278i 2.40612 2.40612i
\(638\) −2.51865 1.13648i −0.0997142 0.0449938i
\(639\) 0 0
\(640\) −24.8440 + 4.77261i −0.982044 + 0.188654i
\(641\) 20.1001i 0.793908i 0.917839 + 0.396954i \(0.129933\pi\)
−0.917839 + 0.396954i \(0.870067\pi\)
\(642\) 0 0
\(643\) −6.20809 6.20809i −0.244823 0.244823i 0.574019 0.818842i \(-0.305384\pi\)
−0.818842 + 0.574019i \(0.805384\pi\)
\(644\) 45.9691 40.5666i 1.81144 1.59855i
\(645\) 0 0
\(646\) 13.2344 + 34.9984i 0.520702 + 1.37699i
\(647\) 3.57164 0.140416 0.0702078 0.997532i \(-0.477634\pi\)
0.0702078 + 0.997532i \(0.477634\pi\)
\(648\) 0 0
\(649\) 2.48326i 0.0974763i
\(650\) 13.0474 + 31.5475i 0.511762 + 1.23739i
\(651\) 0 0
\(652\) −0.168166 + 2.69363i −0.00658588 + 0.105491i
\(653\) −27.2873 27.2873i −1.06783 1.06783i −0.997525 0.0703096i \(-0.977601\pi\)
−0.0703096 0.997525i \(-0.522399\pi\)
\(654\) 0 0
\(655\) 27.5292 28.3857i 1.07565 1.10912i
\(656\) −3.64299 + 29.0624i −0.142235 + 1.13470i
\(657\) 0 0
\(658\) −4.90412 + 10.8684i −0.191182 + 0.423694i
\(659\) −32.0510 32.0510i −1.24853 1.24853i −0.956370 0.292159i \(-0.905626\pi\)
−0.292159 0.956370i \(-0.594374\pi\)
\(660\) 0 0
\(661\) 11.8765 11.8765i 0.461942 0.461942i −0.437350 0.899291i \(-0.644083\pi\)
0.899291 + 0.437350i \(0.144083\pi\)
\(662\) −11.6446 + 4.40334i −0.452580 + 0.171140i
\(663\) 0 0
\(664\) −17.7386 + 33.5610i −0.688392 + 1.30242i
\(665\) −39.2407 + 40.4616i −1.52169 + 1.56903i
\(666\) 0 0
\(667\) 20.0749 20.0749i 0.777302 0.777302i
\(668\) −12.8814 14.5969i −0.498397 0.564772i
\(669\) 0 0
\(670\) 0.0674150 + 0.170345i 0.00260447 + 0.00658101i
\(671\) −5.62247 −0.217053
\(672\) 0 0
\(673\) 4.29764i 0.165662i 0.996564 + 0.0828309i \(0.0263961\pi\)
−0.996564 + 0.0828309i \(0.973604\pi\)
\(674\) 3.15476 + 1.42351i 0.121517 + 0.0548317i
\(675\) 0 0
\(676\) −15.4601 + 13.6431i −0.594618 + 0.524736i
\(677\) −22.4731 + 22.4731i −0.863711 + 0.863711i −0.991767 0.128056i \(-0.959126\pi\)
0.128056 + 0.991767i \(0.459126\pi\)
\(678\) 0 0
\(679\) −16.4663 −0.631919
\(680\) −10.2238 31.4302i −0.392066 1.20529i
\(681\) 0 0
\(682\) 4.35542 1.64698i 0.166778 0.0630659i
\(683\) −6.83685 6.83685i −0.261605 0.261605i 0.564101 0.825706i \(-0.309223\pi\)
−0.825706 + 0.564101i \(0.809223\pi\)
\(684\) 0 0
\(685\) −7.18720 + 0.110098i −0.274609 + 0.00420661i
\(686\) −69.2392 31.2426i −2.64356 1.19285i
\(687\) 0 0
\(688\) 6.13035 + 7.88750i 0.233717 + 0.300708i
\(689\) 20.1527i 0.767755i
\(690\) 0 0
\(691\) 8.12866 8.12866i 0.309229 0.309229i −0.535381 0.844610i \(-0.679832\pi\)
0.844610 + 0.535381i \(0.179832\pi\)
\(692\) −1.38417 + 22.1712i −0.0526182 + 0.842821i
\(693\) 0 0
\(694\) 14.6037 5.52231i 0.554349 0.209624i
\(695\) 1.60406 1.65397i 0.0608456 0.0627388i
\(696\) 0 0
\(697\) −38.2661 −1.44943
\(698\) 34.4233 13.0170i 1.30294 0.492699i
\(699\) 0 0
\(700\) 36.3040 34.0713i 1.37216 1.28777i
\(701\) −32.3973 + 32.3973i −1.22363 + 1.22363i −0.257298 + 0.966332i \(0.582832\pi\)
−0.966332 + 0.257298i \(0.917168\pi\)
\(702\) 0 0
\(703\) −16.2996 −0.614750
\(704\) 0.630392 3.33078i 0.0237588 0.125533i
\(705\) 0 0
\(706\) 13.7726 30.5224i 0.518337 1.14873i
\(707\) −37.6315 + 37.6315i −1.41528 + 1.41528i
\(708\) 0 0
\(709\) 11.9419 11.9419i 0.448488 0.448488i −0.446364 0.894852i \(-0.647281\pi\)
0.894852 + 0.446364i \(0.147281\pi\)
\(710\) 6.24116 14.4166i 0.234227 0.541044i
\(711\) 0 0
\(712\) 9.53071 2.93957i 0.357178 0.110165i
\(713\) 47.8421i 1.79170i
\(714\) 0 0
\(715\) −4.57403 + 0.0700677i −0.171059 + 0.00262038i
\(716\) 1.60986 25.7863i 0.0601634 0.963680i
\(717\) 0 0
\(718\) −0.594717 0.268353i −0.0221947 0.0100148i
\(719\) 50.1912 1.87182 0.935908 0.352243i \(-0.114581\pi\)
0.935908 + 0.352243i \(0.114581\pi\)
\(720\) 0 0
\(721\) −65.0191 −2.42144
\(722\) 8.55000 + 3.85799i 0.318198 + 0.143580i
\(723\) 0 0
\(724\) 44.8862 + 2.80229i 1.66818 + 0.104146i
\(725\) 15.7954 16.7941i 0.586627 0.623717i
\(726\) 0 0
\(727\) 8.79380i 0.326144i −0.986614 0.163072i \(-0.947860\pi\)
0.986614 0.163072i \(-0.0521403\pi\)
\(728\) 60.1089 + 31.7704i 2.22779 + 1.17749i
\(729\) 0 0
\(730\) −11.2430 4.86728i −0.416122 0.180146i
\(731\) −9.22857 + 9.22857i −0.341331 + 0.341331i
\(732\) 0 0
\(733\) −23.9818 + 23.9818i −0.885787 + 0.885787i −0.994115 0.108328i \(-0.965450\pi\)
0.108328 + 0.994115i \(0.465450\pi\)
\(734\) 11.7513 26.0429i 0.433747 0.961260i
\(735\) 0 0
\(736\) 29.7189 + 18.1625i 1.09545 + 0.669480i
\(737\) −0.0245484 −0.000904253
\(738\) 0 0
\(739\) −4.55372 + 4.55372i −0.167511 + 0.167511i −0.785884 0.618373i \(-0.787792\pi\)
0.618373 + 0.785884i \(0.287792\pi\)
\(740\) 14.3818 + 0.676913i 0.528685 + 0.0248838i
\(741\) 0 0
\(742\) 27.4905 10.3954i 1.00921 0.381626i
\(743\) −5.94900 −0.218248 −0.109124 0.994028i \(-0.534805\pi\)
−0.109124 + 0.994028i \(0.534805\pi\)
\(744\) 0 0
\(745\) 8.58653 8.85369i 0.314586 0.324374i
\(746\) 10.6028 4.00937i 0.388195 0.146794i
\(747\) 0 0
\(748\) 4.42019 + 0.275957i 0.161618 + 0.0100900i
\(749\) 37.1559 37.1559i 1.35765 1.35765i
\(750\) 0 0
\(751\) 40.6618i 1.48377i 0.670528 + 0.741884i \(0.266068\pi\)
−0.670528 + 0.741884i \(0.733932\pi\)
\(752\) −6.72115 0.842499i −0.245095 0.0307228i
\(753\) 0 0
\(754\) 28.6970 + 12.9489i 1.04508 + 0.471570i
\(755\) 0.0852107 + 5.56257i 0.00310113 + 0.202443i
\(756\) 0 0
\(757\) 13.2358 + 13.2358i 0.481064 + 0.481064i 0.905471 0.424407i \(-0.139518\pi\)
−0.424407 + 0.905471i \(0.639518\pi\)
\(758\) −11.6029 + 4.38756i −0.421436 + 0.159363i
\(759\) 0 0
\(760\) −28.5353 14.5275i −1.03508 0.526968i
\(761\) 3.22651 0.116961 0.0584805 0.998289i \(-0.481374\pi\)
0.0584805 + 0.998289i \(0.481374\pi\)
\(762\) 0 0
\(763\) 17.1001 17.1001i 0.619065 0.619065i
\(764\) −2.86839 3.25039i −0.103775 0.117595i
\(765\) 0 0
\(766\) −6.31215 2.84821i −0.228067 0.102910i
\(767\) 28.2937i 1.02163i
\(768\) 0 0
\(769\) 33.3777 1.20363 0.601815 0.798635i \(-0.294444\pi\)
0.601815 + 0.798635i \(0.294444\pi\)
\(770\) 2.45501 + 6.20335i 0.0884723 + 0.223553i
\(771\) 0 0
\(772\) 34.5685 30.5059i 1.24415 1.09793i
\(773\) 22.5192 22.5192i 0.809958 0.809958i −0.174669 0.984627i \(-0.555886\pi\)
0.984627 + 0.174669i \(0.0558857\pi\)
\(774\) 0 0
\(775\) 1.19002 + 38.8333i 0.0427468 + 1.39493i
\(776\) −2.75704 8.93891i −0.0989720 0.320888i
\(777\) 0 0
\(778\) 25.7485 9.73662i 0.923127 0.349075i
\(779\) −26.2144 + 26.2144i −0.939227 + 0.939227i
\(780\) 0 0
\(781\) 1.48849 + 1.48849i 0.0532624 + 0.0532624i
\(782\) −18.7153 + 41.4764i −0.669258 + 1.48319i
\(783\) 0 0
\(784\) 8.84986 70.6009i 0.316066 2.52146i
\(785\) 15.6264 + 15.1549i 0.557731 + 0.540901i
\(786\) 0 0
\(787\) 23.0883 + 23.0883i 0.823007 + 0.823007i 0.986538 0.163531i \(-0.0522883\pi\)
−0.163531 + 0.986538i \(0.552288\pi\)
\(788\) −4.31251 0.269234i −0.153627 0.00959108i
\(789\) 0 0
\(790\) −0.654858 + 1.51267i −0.0232988 + 0.0538183i
\(791\) 27.0066i 0.960244i