Properties

Label 720.2.u.a.179.19
Level $720$
Weight $2$
Character 720.179
Analytic conductor $5.749$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $8$

Related objects

Downloads

Learn more about

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 179.19
Character \(\chi\) \(=\) 720.179
Dual form 720.2.u.a.539.19

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.581659 + 1.28906i) q^{2} +(-1.32335 - 1.49958i) q^{4} +(-2.23581 - 0.0342493i) q^{5} +4.97879i q^{7} +(2.70279 - 0.833625i) q^{8} +O(q^{10})\) \(q+(-0.581659 + 1.28906i) q^{2} +(-1.32335 - 1.49958i) q^{4} +(-2.23581 - 0.0342493i) q^{5} +4.97879i q^{7} +(2.70279 - 0.833625i) q^{8} +(1.34463 - 2.86216i) q^{10} +(-0.299629 + 0.299629i) q^{11} +(3.41391 - 3.41391i) q^{13} +(-6.41795 - 2.89596i) q^{14} +(-0.497509 + 3.96894i) q^{16} -5.22586 q^{17} +(-3.58000 + 3.58000i) q^{19} +(2.90739 + 3.39810i) q^{20} +(-0.211957 - 0.560520i) q^{22} -6.15703 q^{23} +(4.99765 + 0.153150i) q^{25} +(2.41500 + 6.38646i) q^{26} +(7.46612 - 6.58866i) q^{28} +(3.26048 - 3.26048i) q^{29} -7.77031i q^{31} +(-4.82682 - 2.94989i) q^{32} +(3.03966 - 6.73644i) q^{34} +(0.170520 - 11.1316i) q^{35} +(-2.27648 - 2.27648i) q^{37} +(-2.53249 - 6.69716i) q^{38} +(-6.07146 + 1.77126i) q^{40} -7.32246 q^{41} +(-1.76594 + 1.76594i) q^{43} +(0.845831 + 0.0528060i) q^{44} +(3.58129 - 7.93678i) q^{46} +1.69344i q^{47} -17.7884 q^{49} +(-3.10435 + 6.35319i) q^{50} +(-9.63723 - 0.601662i) q^{52} +(2.95155 - 2.95155i) q^{53} +(0.680173 - 0.659649i) q^{55} +(4.15045 + 13.4566i) q^{56} +(2.30646 + 6.09944i) q^{58} +(4.14389 - 4.14389i) q^{59} +(-9.38240 - 9.38240i) q^{61} +(10.0164 + 4.51967i) q^{62} +(6.61014 - 4.50623i) q^{64} +(-7.74976 + 7.51592i) q^{65} +(0.0409648 + 0.0409648i) q^{67} +(6.91562 + 7.83661i) q^{68} +(14.2501 + 6.69461i) q^{70} -4.96779i q^{71} -3.87421 q^{73} +(4.25865 - 1.61038i) q^{74} +(10.1061 + 0.630932i) q^{76} +(-1.49179 - 1.49179i) q^{77} -0.521248i q^{79} +(1.24827 - 8.85674i) q^{80} +(4.25917 - 9.43908i) q^{82} +(-9.49013 + 9.49013i) q^{83} +(11.6840 + 0.178982i) q^{85} +(-1.24923 - 3.30358i) q^{86} +(-0.560055 + 1.05961i) q^{88} -3.52625 q^{89} +(16.9971 + 16.9971i) q^{91} +(8.14788 + 9.23299i) q^{92} +(-2.18294 - 0.985002i) q^{94} +(8.12679 - 7.88156i) q^{95} +3.30729i q^{97} +(10.3467 - 22.9302i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96q + O(q^{10}) \) \( 96q - 8q^{16} - 16q^{19} + 72q^{34} + 8q^{40} + 8q^{46} - 96q^{49} + 64q^{55} - 32q^{61} + 48q^{64} + 24q^{70} + 40q^{76} - 88q^{94} + O(q^{100}) \)

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
\(5\) −2.23581 0.0342493i −0.999883 0.0153168i
\(6\) 0 0
\(7\) 4.97879i 1.88181i 0.338676 + 0.940903i \(0.390021\pi\)
−0.338676 + 0.940903i \(0.609979\pi\)
\(8\) 2.70279 0.833625i 0.955580 0.294731i
\(9\) 0 0
\(10\) 1.34463 2.86216i 0.425208 0.905096i
\(11\) −0.299629 + 0.299629i −0.0903414 + 0.0903414i −0.750833 0.660492i \(-0.770348\pi\)
0.660492 + 0.750833i \(0.270348\pi\)
\(12\) 0 0
\(13\) 3.41391 3.41391i 0.946848 0.946848i −0.0518087 0.998657i \(-0.516499\pi\)
0.998657 + 0.0518087i \(0.0164986\pi\)
\(14\) −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 \(0.447241\pi\)
\(20\) 2.90739 + 3.39810i 0.650111 + 0.759839i
\(21\) 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 −0.336299 0.941755i \(-0.609175\pi\)
0.941755 + 0.336299i \(0.109175\pi\)
\(30\) 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
\(35\) 0.170520 11.1316i 0.0288232 1.88159i
\(36\) 0 0
\(37\) −2.27648 2.27648i −0.374251 0.374251i 0.494772 0.869023i \(-0.335252\pi\)
−0.869023 + 0.494772i \(0.835252\pi\)
\(38\) −2.53249 6.69716i −0.410824 1.08642i
\(39\) 0 0
\(40\) −6.07146 + 1.77126i −0.959982 + 0.280060i
\(41\) −7.32246 −1.14358 −0.571788 0.820401i \(-0.693750\pi\)
−0.571788 + 0.820401i \(0.693750\pi\)
\(42\) 0 0
\(43\) −1.76594 + 1.76594i −0.269304 + 0.269304i −0.828820 0.559516i \(-0.810987\pi\)
0.559516 + 0.828820i \(0.310987\pi\)
\(44\) 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
\(50\) −3.10435 + 6.35319i −0.439021 + 0.898477i
\(51\) 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 −0.383890 0.923379i \(-0.625416\pi\)
0.923379 + 0.383890i \(0.125416\pi\)
\(60\) 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 0.709605 0.704600i \(-0.248874\pi\)
−0.704600 + 0.709605i \(0.748874\pi\)
\(68\) 6.91562 + 7.83661i 0.838642 + 0.950329i
\(69\) 0 0
\(70\) 14.2501 + 6.69461i 1.70321 + 0.800159i
\(71\) 4.96779i 0.589568i −0.955564 0.294784i \(-0.904752\pi\)
0.955564 0.294784i \(-0.0952477\pi\)
\(72\) 0 0
\(73\) −3.87421 −0.453442 −0.226721 0.973960i \(-0.572801\pi\)
−0.226721 + 0.973960i \(0.572801\pi\)
\(74\) 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 \(-0.00933498\pi\)
\(80\) 1.24827 8.85674i 0.139560 0.990214i
\(81\) 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
\(85\) 11.6840 + 0.178982i 1.26731 + 0.0194133i
\(86\) −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 \(-0.559841\pi\)
−0.186891 + 0.982381i \(0.559841\pi\)
\(90\) 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 \(0.0536993\pi\)
−0.985804 + 0.167902i \(0.946301\pi\)
\(98\) 10.3467 22.9302i 1.04518 2.31630i
\(99\) 0 0
\(100\) −6.38397 7.69708i −0.638397 0.769708i
\(101\) 7.55836 + 7.55836i 0.752085 + 0.752085i 0.974868 0.222783i \(-0.0715143\pi\)
−0.222783 + 0.974868i \(0.571514\pi\)
\(102\) 0 0
\(103\) 13.0592i 1.28676i 0.765546 + 0.643381i \(0.222469\pi\)
−0.765546 + 0.643381i \(0.777531\pi\)
\(104\) 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 \(0.675270\pi\)
\(110\) 0.454698 + 1.26047i 0.0433538 + 0.120181i
\(111\) 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
\(115\) 13.7659 + 0.210874i 1.28368 + 0.0196641i
\(116\) −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
\(125\) −11.1685 0.513580i −0.998944 0.0459359i
\(126\) 0 0
\(127\) −9.57690 −0.849813 −0.424906 0.905237i \(-0.639693\pi\)
−0.424906 + 0.905237i \(0.639693\pi\)
\(128\) 1.96395 + 11.1419i 0.173590 + 0.984818i
\(129\) 0 0
\(130\) −5.18074 14.3616i −0.454381 1.25960i
\(131\) 12.5044 + 12.5044i 1.09252 + 1.09252i 0.995259 + 0.0972558i \(0.0310065\pi\)
0.0972558 + 0.995259i \(0.468994\pi\)
\(132\) 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 \(0.763914\pi\)
\(140\) −16.9184 + 14.4753i −1.42987 + 1.22338i
\(141\) 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 0.848582 0.529064i \(-0.177457\pi\)
−0.529064 + 0.848582i \(0.677457\pi\)
\(150\) 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
\(155\) −0.266128 + 17.3729i −0.0213759 + 1.39543i
\(156\) 0 0
\(157\) −6.88372 + 6.88372i −0.549380 + 0.549380i −0.926262 0.376881i \(-0.876997\pi\)
0.376881 + 0.926262i \(0.376997\pi\)
\(158\) 0.671920 + 0.303189i 0.0534551 + 0.0241204i
\(159\) 0 0
\(160\) 10.6908 + 6.76069i 0.845182 + 0.534479i
\(161\) 30.6546i 2.41592i
\(162\) 0 0
\(163\) 0.954196 + 0.954196i 0.0747384 + 0.0747384i 0.743488 0.668749i \(-0.233170\pi\)
−0.668749 + 0.743488i \(0.733170\pi\)
\(164\) 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
\(170\) −7.02682 + 14.9573i −0.538932 + 1.14717i
\(171\) 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 0.277868 0.960619i \(-0.410372\pi\)
−0.960619 + 0.277868i \(0.910372\pi\)
\(180\) 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
\(190\) 5.43278 + 15.0603i 0.394136 + 1.09259i
\(191\) −2.16753 −0.156837 −0.0784183 0.996921i \(-0.524987\pi\)
−0.0784183 + 0.996921i \(0.524987\pi\)
\(192\) 0 0
\(193\) 23.0521i 1.65932i −0.558265 0.829662i \(-0.688533\pi\)
0.558265 0.829662i \(-0.311467\pi\)
\(194\) −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 \(0.535359\pi\)
\(200\) 13.6353 3.75224i 0.964159 0.265323i
\(201\) 0 0
\(202\) −14.1396 + 5.34678i −0.994855 + 0.376198i
\(203\) 16.2332 + 16.2332i 1.13935 + 1.13935i
\(204\) 0 0
\(205\) 16.3716 + 0.250789i 1.14344 + 0.0175159i
\(206\) −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
\(220\) −1.88930 0.147033i −0.127377 0.00991297i
\(221\) −17.8406 + 17.8406i −1.20009 + 1.20009i
\(222\) 0 0
\(223\) −22.8494 −1.53011 −0.765053 0.643967i \(-0.777287\pi\)
−0.765053 + 0.643967i \(0.777287\pi\)
\(224\) 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 \(0.0271199\pi\)
\(230\) −8.27890 + 17.6224i −0.545894 + 1.16199i
\(231\) 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
\(235\) 0.0579991 3.78619i 0.00378344 0.246984i
\(236\) −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 \(-0.236144\pi\)
0.737207 + 0.675667i \(0.236144\pi\)
\(240\) 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
\(245\) 39.7713 + 0.609240i 2.54090 + 0.0389229i
\(246\) 0 0
\(247\) 24.4436i 1.55531i
\(248\) −6.47753 21.0015i −0.411324 1.33360i
\(249\) 0 0
\(250\) 7.15831 14.0982i 0.452731 0.891647i
\(251\) −4.97266 + 4.97266i −0.313872 + 0.313872i −0.846407 0.532536i \(-0.821239\pi\)
0.532536 + 0.846407i \(0.321239\pi\)
\(252\) 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
\(260\) 21.5264 + 1.67527i 1.33501 + 0.103896i
\(261\) 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 −0.647751 0.761852i \(-0.724290\pi\)
0.761852 + 0.647751i \(0.224290\pi\)
\(270\) 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
\(275\) −1.54333 + 1.45155i −0.0930662 + 0.0875319i
\(276\) 0 0
\(277\) −13.2521 13.2521i −0.796239 0.796239i 0.186261 0.982500i \(-0.440363\pi\)
−0.982500 + 0.186261i \(0.940363\pi\)
\(278\) 1.36301 0.515415i 0.0817481 0.0309126i
\(279\) 0 0
\(280\) −8.81871 30.2285i −0.527019 1.80650i
\(281\) −12.2485 −0.730684 −0.365342 0.930873i \(-0.619048\pi\)
−0.365342 + 0.930873i \(0.619048\pi\)
\(282\) 0 0
\(283\) 2.62423 2.62423i 0.155994 0.155994i −0.624795 0.780789i \(-0.714817\pi\)
0.780789 + 0.624795i \(0.214817\pi\)
\(284\) −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
\(290\) −4.94790 13.7161i −0.290551 0.805440i
\(291\) 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 0.526787 0.849997i \(-0.323397\pi\)
−0.849997 + 0.526787i \(0.823397\pi\)
\(308\) −0.262910 + 4.21121i −0.0149807 + 0.239956i
\(309\) 0 0
\(310\) −22.2399 10.4482i −1.26314 0.593416i
\(311\) 29.5732i 1.67694i 0.544947 + 0.838470i \(0.316550\pi\)
−0.544947 + 0.838470i \(0.683450\pi\)
\(312\) 0 0
\(313\) −12.2408 −0.691891 −0.345945 0.938255i \(-0.612442\pi\)
−0.345945 + 0.938255i \(0.612442\pi\)
\(314\) −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
\(320\) −14.9333 + 9.84865i −0.834798 + 0.550556i
\(321\) 0 0
\(322\) 39.5155 + 17.8305i 2.20212 + 0.993655i
\(323\) 18.7085 18.7085i 1.04097 1.04097i
\(324\) 0 0
\(325\) 17.5844 16.5387i 0.975406 0.917402i
\(326\) −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 \(0.0212335\pi\)
−0.997776 + 0.0666574i \(0.978767\pi\)
\(338\) 13.2896 + 5.99665i 0.722861 + 0.326175i
\(339\) 0 0
\(340\) −15.1936 17.7580i −0.823987 0.963063i
\(341\) 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 \(0.995257\pi\)
\(350\) −31.6312 15.4559i −1.69076 0.826152i
\(351\) 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
\(355\) −0.170143 + 11.1070i −0.00903028 + 0.589499i
\(356\) 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 \(-0.996125\pi\)
0.999926 0.0121748i \(-0.00387544\pi\)
\(360\) 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
\(365\) 8.66199 + 0.132689i 0.453389 + 0.00694528i
\(366\) 0 0
\(367\) 20.2030 1.05459 0.527294 0.849683i \(-0.323207\pi\)
0.527294 + 0.849683i \(0.323207\pi\)
\(368\) 3.06318 24.4369i 0.159679 1.27386i
\(369\) 0 0
\(370\) −9.57667 + 3.45465i −0.497867 + 0.179598i
\(371\) 14.6952 + 14.6952i 0.762934 + 0.762934i
\(372\) 0 0
\(373\) 5.66776 + 5.66776i 0.293465 + 0.293465i 0.838448 0.544982i \(-0.183464\pi\)
−0.544982 + 0.838448i \(0.683464\pi\)
\(374\) 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 \(0.677670\pi\)
\(380\) −22.5736 1.75677i −1.15800 0.0901204i
\(381\) 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 0.963949 0.266089i \(-0.0857314\pi\)
−0.266089 + 0.963949i \(0.585731\pi\)
\(390\) 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
\(395\) −0.0178524 + 1.16541i −0.000898253 + 0.0586381i
\(396\) 0 0
\(397\) 16.2544 16.2544i 0.815787 0.815787i −0.169707 0.985495i \(-0.554282\pi\)
0.985495 + 0.169707i \(0.0542822\pi\)
\(398\) 1.81918 4.03162i 0.0911872 0.202087i
\(399\) 0 0
\(400\) −3.09422 + 19.7592i −0.154711 + 0.987960i
\(401\) 10.0348i 0.501116i −0.968102 0.250558i \(-0.919386\pi\)
0.968102 0.250558i \(-0.0806140\pi\)
\(402\) 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 \(0.690870\pi\)
\(410\) −9.84596 + 20.9581i −0.486257 + 1.03505i
\(411\) 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 0.317530 0.948248i \(-0.397147\pi\)
−0.948248 + 0.317530i \(0.897147\pi\)
\(420\) 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
\(430\) 2.67989 + 7.42895i 0.129236 + 0.358256i
\(431\) 23.5531 1.13451 0.567255 0.823542i \(-0.308005\pi\)
0.567255 + 0.823542i \(0.308005\pi\)
\(432\) 0 0
\(433\) 38.5735i 1.85373i 0.375400 + 0.926863i \(0.377505\pi\)
−0.375400 + 0.926863i \(0.622495\pi\)
\(434\) −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 \(0.757862\pi\)
\(440\) 1.28846 2.34990i 0.0614252 0.112027i
\(441\) 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
\(445\) 7.88401 + 0.120772i 0.373738 + 0.00572513i
\(446\) 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 \(0.0768055\pi\)
−0.971030 + 0.238957i \(0.923194\pi\)
\(450\) 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 \(-0.510756\pi\)
−0.0337847 + 0.999429i \(0.510756\pi\)
\(458\) 9.75513 + 25.7974i 0.455827 + 1.20543i
\(459\) 0 0
\(460\) −17.9009 20.9222i −0.834632 0.975504i
\(461\) 26.8623 26.8623i 1.25110 1.25110i 0.295878 0.955226i \(-0.404388\pi\)
0.955226 0.295878i \(-0.0956121\pi\)
\(462\) 0 0
\(463\) −20.2597 −0.941547 −0.470774 0.882254i \(-0.656025\pi\)
−0.470774 + 0.882254i \(0.656025\pi\)
\(464\) 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
\(470\) 4.84689 + 2.27704i 0.223570 + 0.105032i
\(471\) 0 0
\(472\) 7.74561 14.6545i 0.356521 0.674529i
\(473\) 1.05825i 0.0486586i
\(474\) 0 0
\(475\) −18.4399 + 17.3433i −0.846079 + 0.795765i
\(476\) −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 \(-0.533547\pi\)
−0.105196 + 0.994452i \(0.533547\pi\)
\(480\) 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
\(485\) 0.113273 7.39446i 0.00514344 0.335765i
\(486\) 0 0
\(487\) 32.2084i 1.45950i 0.683713 + 0.729751i \(0.260364\pi\)
−0.683713 + 0.729751i \(0.739636\pi\)
\(488\) −33.1801 17.5372i −1.50199 0.793874i
\(489\) 0 0
\(490\) −23.9187 + 50.9132i −1.08054 + 2.30002i
\(491\) −17.4179 + 17.4179i −0.786059 + 0.786059i −0.980846 0.194786i \(-0.937599\pi\)
0.194786 + 0.980846i \(0.437599\pi\)
\(492\) 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 \(0.414396\pi\)
\(500\) 14.0097 + 17.4278i 0.626532 + 0.779395i
\(501\) 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 −0.745489 0.666518i \(-0.767784\pi\)
0.666518 + 0.745489i \(0.267784\pi\)
\(510\) 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
\(515\) 0.447269 29.1979i 0.0197090 1.28661i
\(516\) 0 0
\(517\) −0.507402 0.507402i −0.0223155 0.0223155i
\(518\) 8.01776 + 21.2029i 0.352280 + 0.931603i
\(519\) 0 0
\(520\) −14.6805 + 26.7743i −0.643783 + 1.17413i
\(521\) −6.52761 −0.285980 −0.142990 0.989724i \(-0.545672\pi\)
−0.142990 + 0.989724i \(0.545672\pi\)
\(522\) 0 0
\(523\) 8.63265 8.63265i 0.377479 0.377479i −0.492713 0.870192i \(-0.663995\pi\)
0.870192 + 0.492713i \(0.163995\pi\)
\(524\) 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
\(530\) −4.47909 12.4166i −0.194559 0.539341i
\(531\) 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 0.530783 0.847508i \(-0.321898\pi\)
−0.847508 + 0.530783i \(0.821898\pi\)
\(548\) 4.82055 4.25401i 0.205924 0.181722i
\(549\) 0 0
\(550\) −0.973446 2.83375i −0.0415079 0.120831i
\(551\) 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
\(560\) 44.0958 + 6.21486i 1.86339 + 0.262626i
\(561\) 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
\(565\) 12.1277 + 0.185780i 0.510218 + 0.00781581i
\(566\) 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 \(-0.363509\pi\)
0.415779 + 0.909466i \(0.363509\pi\)
\(570\) 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 \(0.108214\pi\)
−0.942766 + 0.333454i \(0.891786\pi\)
\(578\) −5.99665 + 13.2896i −0.249428 + 0.552776i
\(579\) 0 0
\(580\) 20.5589 + 1.59998i 0.853663 + 0.0664354i
\(581\) −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
\(590\) −6.28852 17.4325i −0.258894 0.717684i
\(591\) 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
\(595\) −0.891115 + 58.1722i −0.0365321 + 2.38483i
\(596\) 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 \(0.299578\pi\)
−0.588857 + 0.808237i \(0.700422\pi\)
\(600\) 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
\(605\) 0.370593 24.1924i 0.0150668 0.983561i
\(606\) 0 0
\(607\) 19.1918 0.778971 0.389485 0.921033i \(-0.372653\pi\)
0.389485 + 0.921033i \(0.372653\pi\)
\(608\) 27.8406 6.71941i 1.12908 0.272508i
\(609\) 0 0
\(610\) −39.4698 + 14.2382i −1.59809 + 0.576486i
\(611\) 5.78124 + 5.78124i 0.233884 + 0.233884i
\(612\) 0 0
\(613\) −3.14030 3.14030i −0.126836 0.126836i 0.640839 0.767675i \(-0.278586\pi\)
−0.767675 + 0.640839i \(0.778586\pi\)
\(614\) 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 \(0.842932\pi\)
\(620\) 26.4043 22.5913i 1.06042 0.907288i
\(621\) 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
\(635\) 21.4121 + 0.328003i 0.849713 + 0.0130164i
\(636\) 0 0
\(637\) −60.7278 + 60.7278i −2.40612 + 2.40612i
\(638\) −2.51865 1.13648i −0.0997142 0.0449938i
\(639\) 0 0
\(640\) −4.00940 24.9785i −0.158485 0.987361i
\(641\) 20.1001i 0.793908i −0.917839 0.396954i \(-0.870067\pi\)
0.917839 0.396954i \(-0.129933\pi\)
\(642\) 0 0
\(643\) 6.20809 + 6.20809i 0.244823 + 0.244823i 0.818842 0.574019i \(-0.194616\pi\)
−0.574019 + 0.818842i \(0.694616\pi\)
\(644\) −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
\(650\) 11.0913 + 32.2872i 0.435035 + 1.26641i
\(651\) 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 \(0.0943737\pi\)
0.292159 + 0.956370i \(0.405626\pi\)
\(660\) 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
\(670\) 0.172330 0.0621657i 0.00665770 0.00240167i
\(671\) 5.62247 0.217053
\(672\) 0 0
\(673\) 4.29764i 0.165662i −0.996564 0.0828309i \(-0.973604\pi\)
0.996564 0.0828309i \(-0.0263961\pi\)
\(674\) −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
\(680\) 31.7286 9.25632i 1.21674 0.354964i
\(681\) 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
\(685\) 0.110098 7.18720i 0.00420661 0.274609i
\(686\) 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
\(700\) 38.3221 31.7844i 1.44844 1.20134i
\(701\) 32.3973 32.3973i 1.22363 1.22363i 0.257298 0.966332i \(-0.417168\pi\)
0.966332 0.257298i \(-0.0828323\pi\)
\(702\) 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 \(0.147281\pi\)
\(710\) −14.2186 6.67981i −0.533615 0.250689i
\(711\) 0 0
\(712\) −9.53071 + 2.93957i −0.357178 + 0.110165i
\(713\) 47.8421i 1.79170i
\(714\) 0 0
\(715\) 0.0700677 4.57403i 0.00262038 0.171059i
\(716\) −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 \(-0.885419\pi\)
−0.935908 + 0.352243i \(0.885419\pi\)
\(720\) 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
\(725\) 16.7941 15.7954i 0.623717 0.586627i
\(726\) 0 0
\(727\) 8.79380i 0.326144i 0.986614 + 0.163072i \(0.0521403\pi\)
−0.986614 + 0.163072i \(0.947860\pi\)
\(728\) 60.1089 + 31.7704i 2.22779 + 1.17749i
\(729\) 0 0
\(730\) −5.20937 + 11.0886i −0.192807 + 0.410409i
\(731\) 9.22857 9.22857i 0.341331 0.341331i
\(732\) 0 0
\(733\) 23.9818 23.9818i 0.885787 0.885787i −0.108328 0.994115i \(-0.534550\pi\)
0.994115 + 0.108328i \(0.0345496\pi\)
\(734\) −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 \(0.287792\pi\)
\(740\) 1.11711 14.3543i 0.0410658 0.527675i
\(741\) 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
\(755\) −5.56257 0.0852107i −0.202443 0.00310113i
\(756\) 0 0
\(757\) −13.2358 13.2358i −0.481064 0.481064i 0.424407 0.905471i \(-0.360482\pi\)
−0.905471 + 0.424407i \(0.860482\pi\)
\(758\) −11.6029 + 4.38756i −0.421436 + 0.159363i
\(759\) 0 0
\(760\) 15.3947 28.0769i 0.558425 1.01846i
\(761\) −3.22651 −0.116961 −0.0584805 0.998289i \(-0.518626\pi\)
−0.0584805 + 0.998289i \(0.518626\pi\)
\(762\) 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 \(0.294444\pi\)
\(770\) −6.27564 + 2.26385i −0.226158 + 0.0815833i
\(771\) 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 0.163531 0.986538i \(-0.447712\pi\)
−0.986538 + 0.163531i \(0.947712\pi\)
\(788\) −4.31251 0.269234i −0.153627 0.00959108i
\(789\) 0 0
\(790\) −1.49190 0.700884i −0.0530794 0.0249363i
\(791\) 27.0066i 0.960244i