Properties

Label 432.2.be.b.47.3
Level $432$
Weight $2$
Character 432.47
Analytic conductor $3.450$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.be (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 47.3
Character \(\chi\) \(=\) 432.47
Dual form 432.2.be.b.239.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.939092 + 1.45537i) q^{3} +(-1.07086 + 0.188822i) q^{5} +(-0.0466102 + 0.0555478i) q^{7} +(-1.23621 - 2.73346i) q^{9} +O(q^{10})\) \(q+(-0.939092 + 1.45537i) q^{3} +(-1.07086 + 0.188822i) q^{5} +(-0.0466102 + 0.0555478i) q^{7} +(-1.23621 - 2.73346i) q^{9} +(-0.889704 + 5.04576i) q^{11} +(-5.31632 - 1.93498i) q^{13} +(0.730832 - 1.73582i) q^{15} +(3.79605 - 2.19165i) q^{17} +(-4.96707 - 2.86774i) q^{19} +(-0.0370715 - 0.120000i) q^{21} +(-3.14687 + 2.64054i) q^{23} +(-3.58737 + 1.30570i) q^{25} +(5.13911 + 0.767820i) q^{27} +(-1.30353 - 3.58141i) q^{29} +(-2.61088 - 3.11153i) q^{31} +(-6.50794 - 6.03328i) q^{33} +(0.0394244 - 0.0682850i) q^{35} +(-1.14643 - 1.98567i) q^{37} +(7.80863 - 5.92009i) q^{39} +(-0.494495 + 1.35861i) q^{41} +(0.128831 + 0.0227164i) q^{43} +(1.83995 + 2.69373i) q^{45} +(-4.26138 - 3.57572i) q^{47} +(1.21462 + 6.88848i) q^{49} +(-0.375176 + 7.58283i) q^{51} +10.4743i q^{53} -5.57130i q^{55} +(8.83817 - 4.53586i) q^{57} +(1.69171 + 9.59417i) q^{59} +(4.96656 + 4.16744i) q^{61} +(0.209458 + 0.0587379i) q^{63} +(6.05841 + 1.06826i) q^{65} +(-2.28472 + 6.27722i) q^{67} +(-0.887762 - 7.05957i) q^{69} +(3.47730 + 6.02286i) q^{71} +(2.77130 - 4.80004i) q^{73} +(1.46860 - 6.44713i) q^{75} +(-0.238812 - 0.284605i) q^{77} +(-4.83670 - 13.2887i) q^{79} +(-5.94356 + 6.75826i) q^{81} +(-3.77579 + 1.37428i) q^{83} +(-3.65122 + 3.06373i) q^{85} +(6.43641 + 1.46616i) q^{87} +(14.4547 + 8.34541i) q^{89} +(0.355279 - 0.205120i) q^{91} +(6.98029 - 0.877792i) q^{93} +(5.86054 + 2.13306i) q^{95} +(-2.74888 + 15.5897i) q^{97} +(14.8922 - 3.80566i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 3q^{5} + 6q^{9} + O(q^{10}) \) \( 36q + 3q^{5} + 6q^{9} - 18q^{11} + 9q^{15} + 18q^{21} - 9q^{25} + 30q^{29} + 27q^{31} + 27q^{33} + 27q^{35} - 45q^{39} + 18q^{41} + 27q^{45} + 45q^{47} - 63q^{51} - 9q^{57} + 54q^{59} - 63q^{63} - 57q^{65} - 63q^{69} + 36q^{71} + 9q^{73} - 45q^{75} - 81q^{77} - 54q^{81} - 27q^{83} - 36q^{85} + 45q^{87} - 63q^{89} + 27q^{91} - 63q^{93} - 72q^{95} + 99q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{7}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.939092 + 1.45537i −0.542185 + 0.840259i
\(4\) 0 0
\(5\) −1.07086 + 0.188822i −0.478904 + 0.0844436i −0.407889 0.913032i \(-0.633735\pi\)
−0.0710149 + 0.997475i \(0.522624\pi\)
\(6\) 0 0
\(7\) −0.0466102 + 0.0555478i −0.0176170 + 0.0209951i −0.774781 0.632230i \(-0.782140\pi\)
0.757164 + 0.653225i \(0.226584\pi\)
\(8\) 0 0
\(9\) −1.23621 2.73346i −0.412071 0.911152i
\(10\) 0 0
\(11\) −0.889704 + 5.04576i −0.268256 + 1.52135i 0.491346 + 0.870965i \(0.336505\pi\)
−0.759601 + 0.650389i \(0.774606\pi\)
\(12\) 0 0
\(13\) −5.31632 1.93498i −1.47448 0.536668i −0.525168 0.850998i \(-0.675998\pi\)
−0.949314 + 0.314331i \(0.898220\pi\)
\(14\) 0 0
\(15\) 0.730832 1.73582i 0.188700 0.448187i
\(16\) 0 0
\(17\) 3.79605 2.19165i 0.920678 0.531554i 0.0368269 0.999322i \(-0.488275\pi\)
0.883851 + 0.467768i \(0.154942\pi\)
\(18\) 0 0
\(19\) −4.96707 2.86774i −1.13952 0.657905i −0.193212 0.981157i \(-0.561890\pi\)
−0.946313 + 0.323252i \(0.895224\pi\)
\(20\) 0 0
\(21\) −0.0370715 0.120000i −0.00808966 0.0261861i
\(22\) 0 0
\(23\) −3.14687 + 2.64054i −0.656168 + 0.550590i −0.908935 0.416937i \(-0.863104\pi\)
0.252768 + 0.967527i \(0.418659\pi\)
\(24\) 0 0
\(25\) −3.58737 + 1.30570i −0.717475 + 0.261139i
\(26\) 0 0
\(27\) 5.13911 + 0.767820i 0.989022 + 0.147767i
\(28\) 0 0
\(29\) −1.30353 3.58141i −0.242059 0.665051i −0.999920 0.0126352i \(-0.995978\pi\)
0.757862 0.652415i \(-0.226244\pi\)
\(30\) 0 0
\(31\) −2.61088 3.11153i −0.468929 0.558847i 0.478800 0.877924i \(-0.341072\pi\)
−0.947729 + 0.319076i \(0.896627\pi\)
\(32\) 0 0
\(33\) −6.50794 6.03328i −1.13289 1.05026i
\(34\) 0 0
\(35\) 0.0394244 0.0682850i 0.00666394 0.0115423i
\(36\) 0 0
\(37\) −1.14643 1.98567i −0.188471 0.326442i 0.756269 0.654260i \(-0.227020\pi\)
−0.944741 + 0.327818i \(0.893687\pi\)
\(38\) 0 0
\(39\) 7.80863 5.92009i 1.25038 0.947974i
\(40\) 0 0
\(41\) −0.494495 + 1.35861i −0.0772271 + 0.212180i −0.972298 0.233744i \(-0.924902\pi\)
0.895071 + 0.445923i \(0.147125\pi\)
\(42\) 0 0
\(43\) 0.128831 + 0.0227164i 0.0196466 + 0.00346422i 0.183463 0.983027i \(-0.441269\pi\)
−0.163816 + 0.986491i \(0.552380\pi\)
\(44\) 0 0
\(45\) 1.83995 + 2.69373i 0.274283 + 0.401557i
\(46\) 0 0
\(47\) −4.26138 3.57572i −0.621586 0.521573i 0.276716 0.960952i \(-0.410754\pi\)
−0.898302 + 0.439379i \(0.855198\pi\)
\(48\) 0 0
\(49\) 1.21462 + 6.88848i 0.173518 + 0.984068i
\(50\) 0 0
\(51\) −0.375176 + 7.58283i −0.0525351 + 1.06181i
\(52\) 0 0
\(53\) 10.4743i 1.43876i 0.694619 + 0.719378i \(0.255573\pi\)
−0.694619 + 0.719378i \(0.744427\pi\)
\(54\) 0 0
\(55\) 5.57130i 0.751234i
\(56\) 0 0
\(57\) 8.83817 4.53586i 1.17064 0.600790i
\(58\) 0 0
\(59\) 1.69171 + 9.59417i 0.220242 + 1.24905i 0.871575 + 0.490262i \(0.163099\pi\)
−0.651333 + 0.758792i \(0.725790\pi\)
\(60\) 0 0
\(61\) 4.96656 + 4.16744i 0.635903 + 0.533586i 0.902757 0.430151i \(-0.141540\pi\)
−0.266854 + 0.963737i \(0.585984\pi\)
\(62\) 0 0
\(63\) 0.209458 + 0.0587379i 0.0263892 + 0.00740029i
\(64\) 0 0
\(65\) 6.05841 + 1.06826i 0.751453 + 0.132501i
\(66\) 0 0
\(67\) −2.28472 + 6.27722i −0.279123 + 0.766885i 0.718339 + 0.695693i \(0.244903\pi\)
−0.997463 + 0.0711921i \(0.977320\pi\)
\(68\) 0 0
\(69\) −0.887762 7.05957i −0.106874 0.849873i
\(70\) 0 0
\(71\) 3.47730 + 6.02286i 0.412680 + 0.714782i 0.995182 0.0980471i \(-0.0312596\pi\)
−0.582502 + 0.812829i \(0.697926\pi\)
\(72\) 0 0
\(73\) 2.77130 4.80004i 0.324356 0.561802i −0.657026 0.753868i \(-0.728186\pi\)
0.981382 + 0.192067i \(0.0615190\pi\)
\(74\) 0 0
\(75\) 1.46860 6.44713i 0.169579 0.744450i
\(76\) 0 0
\(77\) −0.238812 0.284605i −0.0272151 0.0324337i
\(78\) 0 0
\(79\) −4.83670 13.2887i −0.544171 1.49510i −0.841465 0.540312i \(-0.818306\pi\)
0.297294 0.954786i \(-0.403916\pi\)
\(80\) 0 0
\(81\) −5.94356 + 6.75826i −0.660396 + 0.750918i
\(82\) 0 0
\(83\) −3.77579 + 1.37428i −0.414447 + 0.150846i −0.540824 0.841136i \(-0.681887\pi\)
0.126377 + 0.991982i \(0.459665\pi\)
\(84\) 0 0
\(85\) −3.65122 + 3.06373i −0.396030 + 0.332309i
\(86\) 0 0
\(87\) 6.43641 + 1.46616i 0.690055 + 0.157189i
\(88\) 0 0
\(89\) 14.4547 + 8.34541i 1.53219 + 0.884612i 0.999260 + 0.0384538i \(0.0122432\pi\)
0.532932 + 0.846158i \(0.321090\pi\)
\(90\) 0 0
\(91\) 0.355279 0.205120i 0.0372433 0.0215024i
\(92\) 0 0
\(93\) 6.98029 0.877792i 0.723823 0.0910228i
\(94\) 0 0
\(95\) 5.86054 + 2.13306i 0.601278 + 0.218847i
\(96\) 0 0
\(97\) −2.74888 + 15.5897i −0.279106 + 1.58289i 0.446502 + 0.894783i \(0.352670\pi\)
−0.725608 + 0.688108i \(0.758442\pi\)
\(98\) 0 0
\(99\) 14.8922 3.80566i 1.49672 0.382483i
\(100\) 0 0
\(101\) 5.40951 6.44680i 0.538266 0.641481i −0.426532 0.904473i \(-0.640265\pi\)
0.964798 + 0.262992i \(0.0847092\pi\)
\(102\) 0 0
\(103\) −0.918166 + 0.161897i −0.0904696 + 0.0159522i −0.218700 0.975792i \(-0.570182\pi\)
0.128230 + 0.991744i \(0.459070\pi\)
\(104\) 0 0
\(105\) 0.0623569 + 0.121503i 0.00608541 + 0.0118575i
\(106\) 0 0
\(107\) −11.2973 −1.09215 −0.546076 0.837736i \(-0.683879\pi\)
−0.546076 + 0.837736i \(0.683879\pi\)
\(108\) 0 0
\(109\) 7.80915 0.747981 0.373991 0.927433i \(-0.377989\pi\)
0.373991 + 0.927433i \(0.377989\pi\)
\(110\) 0 0
\(111\) 3.96649 + 0.196250i 0.376482 + 0.0186272i
\(112\) 0 0
\(113\) −8.09837 + 1.42796i −0.761830 + 0.134331i −0.541048 0.840992i \(-0.681972\pi\)
−0.220782 + 0.975323i \(0.570861\pi\)
\(114\) 0 0
\(115\) 2.87127 3.42185i 0.267747 0.319089i
\(116\) 0 0
\(117\) 1.28291 + 16.9240i 0.118605 + 1.56462i
\(118\) 0 0
\(119\) −0.0551931 + 0.313016i −0.00505955 + 0.0286941i
\(120\) 0 0
\(121\) −14.3315 5.21624i −1.30286 0.474203i
\(122\) 0 0
\(123\) −1.51291 1.99554i −0.136415 0.179931i
\(124\) 0 0
\(125\) 8.30353 4.79405i 0.742690 0.428793i
\(126\) 0 0
\(127\) −4.34261 2.50721i −0.385344 0.222479i 0.294797 0.955560i \(-0.404748\pi\)
−0.680141 + 0.733081i \(0.738081\pi\)
\(128\) 0 0
\(129\) −0.154045 + 0.166164i −0.0135629 + 0.0146300i
\(130\) 0 0
\(131\) 1.94960 1.63591i 0.170337 0.142930i −0.553634 0.832760i \(-0.686759\pi\)
0.723971 + 0.689830i \(0.242315\pi\)
\(132\) 0 0
\(133\) 0.390813 0.142244i 0.0338878 0.0123341i
\(134\) 0 0
\(135\) −5.64825 + 0.148147i −0.486124 + 0.0127505i
\(136\) 0 0
\(137\) −3.44548 9.46638i −0.294367 0.808767i −0.995415 0.0956528i \(-0.969506\pi\)
0.701048 0.713115i \(-0.252716\pi\)
\(138\) 0 0
\(139\) 2.17758 + 2.59514i 0.184700 + 0.220117i 0.850447 0.526060i \(-0.176331\pi\)
−0.665747 + 0.746178i \(0.731887\pi\)
\(140\) 0 0
\(141\) 9.20583 2.84396i 0.775271 0.239504i
\(142\) 0 0
\(143\) 14.4934 25.1033i 1.21200 2.09924i
\(144\) 0 0
\(145\) 2.07214 + 3.58906i 0.172082 + 0.298055i
\(146\) 0 0
\(147\) −11.1659 4.70118i −0.920951 0.387747i
\(148\) 0 0
\(149\) −7.17252 + 19.7063i −0.587596 + 1.61441i 0.187290 + 0.982305i \(0.440030\pi\)
−0.774886 + 0.632101i \(0.782193\pi\)
\(150\) 0 0
\(151\) 20.2553 + 3.57156i 1.64835 + 0.290649i 0.919227 0.393728i \(-0.128815\pi\)
0.729128 + 0.684377i \(0.239926\pi\)
\(152\) 0 0
\(153\) −10.6835 7.66700i −0.863711 0.619840i
\(154\) 0 0
\(155\) 3.38342 + 2.83903i 0.271763 + 0.228036i
\(156\) 0 0
\(157\) −4.28433 24.2976i −0.341927 1.93916i −0.343470 0.939164i \(-0.611602\pi\)
0.00154349 0.999999i \(-0.499509\pi\)
\(158\) 0 0
\(159\) −15.2440 9.83633i −1.20893 0.780072i
\(160\) 0 0
\(161\) 0.297878i 0.0234761i
\(162\) 0 0
\(163\) 12.2188i 0.957048i −0.878074 0.478524i \(-0.841172\pi\)
0.878074 0.478524i \(-0.158828\pi\)
\(164\) 0 0
\(165\) 8.10832 + 5.23197i 0.631231 + 0.407308i
\(166\) 0 0
\(167\) 0.673297 + 3.81846i 0.0521013 + 0.295481i 0.999713 0.0239425i \(-0.00762187\pi\)
−0.947612 + 0.319423i \(0.896511\pi\)
\(168\) 0 0
\(169\) 14.5605 + 12.2177i 1.12004 + 0.939826i
\(170\) 0 0
\(171\) −1.69849 + 17.1224i −0.129887 + 1.30938i
\(172\) 0 0
\(173\) −15.4083 2.71690i −1.17147 0.206562i −0.446141 0.894963i \(-0.647202\pi\)
−0.725330 + 0.688401i \(0.758313\pi\)
\(174\) 0 0
\(175\) 0.0946794 0.260130i 0.00715709 0.0196639i
\(176\) 0 0
\(177\) −15.5518 6.54774i −1.16894 0.492158i
\(178\) 0 0
\(179\) 6.03273 + 10.4490i 0.450907 + 0.780994i 0.998443 0.0557882i \(-0.0177671\pi\)
−0.547535 + 0.836783i \(0.684434\pi\)
\(180\) 0 0
\(181\) 10.1241 17.5354i 0.752515 1.30339i −0.194085 0.980985i \(-0.562174\pi\)
0.946600 0.322410i \(-0.104493\pi\)
\(182\) 0 0
\(183\) −10.7292 + 3.31458i −0.793127 + 0.245021i
\(184\) 0 0
\(185\) 1.60260 + 1.90991i 0.117826 + 0.140419i
\(186\) 0 0
\(187\) 7.68119 + 21.1039i 0.561704 + 1.54327i
\(188\) 0 0
\(189\) −0.282186 + 0.249678i −0.0205260 + 0.0181614i
\(190\) 0 0
\(191\) −23.5661 + 8.57737i −1.70518 + 0.620636i −0.996399 0.0847874i \(-0.972979\pi\)
−0.708786 + 0.705424i \(0.750757\pi\)
\(192\) 0 0
\(193\) −11.3801 + 9.54906i −0.819160 + 0.687357i −0.952775 0.303677i \(-0.901786\pi\)
0.133615 + 0.991033i \(0.457341\pi\)
\(194\) 0 0
\(195\) −7.24412 + 7.81404i −0.518762 + 0.559575i
\(196\) 0 0
\(197\) −14.3982 8.31282i −1.02583 0.592264i −0.110043 0.993927i \(-0.535099\pi\)
−0.915788 + 0.401663i \(0.868432\pi\)
\(198\) 0 0
\(199\) −17.6909 + 10.2138i −1.25407 + 0.724039i −0.971916 0.235329i \(-0.924383\pi\)
−0.282157 + 0.959368i \(0.591050\pi\)
\(200\) 0 0
\(201\) −6.99013 9.22001i −0.493046 0.650330i
\(202\) 0 0
\(203\) 0.259697 + 0.0945220i 0.0182272 + 0.00663414i
\(204\) 0 0
\(205\) 0.272999 1.54826i 0.0190671 0.108135i
\(206\) 0 0
\(207\) 11.1080 + 5.33757i 0.772059 + 0.370987i
\(208\) 0 0
\(209\) 18.8892 22.5112i 1.30659 1.55713i
\(210\) 0 0
\(211\) −17.6769 + 3.11691i −1.21693 + 0.214577i −0.745002 0.667062i \(-0.767552\pi\)
−0.471924 + 0.881639i \(0.656441\pi\)
\(212\) 0 0
\(213\) −12.0310 0.595258i −0.824351 0.0407864i
\(214\) 0 0
\(215\) −0.142250 −0.00970134
\(216\) 0 0
\(217\) 0.294533 0.0199942
\(218\) 0 0
\(219\) 4.38333 + 8.54095i 0.296198 + 0.577144i
\(220\) 0 0
\(221\) −24.4218 + 4.30623i −1.64279 + 0.289668i
\(222\) 0 0
\(223\) 0.193902 0.231084i 0.0129846 0.0154745i −0.759513 0.650492i \(-0.774563\pi\)
0.772498 + 0.635018i \(0.219007\pi\)
\(224\) 0 0
\(225\) 8.00382 + 8.19181i 0.533588 + 0.546121i
\(226\) 0 0
\(227\) 3.55254 20.1475i 0.235790 1.33723i −0.605152 0.796110i \(-0.706888\pi\)
0.840943 0.541124i \(-0.182001\pi\)
\(228\) 0 0
\(229\) 6.31957 + 2.30013i 0.417609 + 0.151997i 0.542274 0.840202i \(-0.317563\pi\)
−0.124665 + 0.992199i \(0.539786\pi\)
\(230\) 0 0
\(231\) 0.638472 0.0802897i 0.0420084 0.00528267i
\(232\) 0 0
\(233\) 5.00964 2.89232i 0.328193 0.189482i −0.326846 0.945078i \(-0.605986\pi\)
0.655038 + 0.755596i \(0.272652\pi\)
\(234\) 0 0
\(235\) 5.23852 + 3.02446i 0.341723 + 0.197294i
\(236\) 0 0
\(237\) 23.8821 + 5.44014i 1.55131 + 0.353375i
\(238\) 0 0
\(239\) −1.92638 + 1.61642i −0.124607 + 0.104558i −0.702962 0.711228i \(-0.748139\pi\)
0.578355 + 0.815785i \(0.303695\pi\)
\(240\) 0 0
\(241\) 0.855851 0.311504i 0.0551302 0.0200657i −0.314308 0.949321i \(-0.601772\pi\)
0.369438 + 0.929255i \(0.379550\pi\)
\(242\) 0 0
\(243\) −4.25423 14.9967i −0.272909 0.962040i
\(244\) 0 0
\(245\) −2.60139 7.14725i −0.166197 0.456621i
\(246\) 0 0
\(247\) 20.8575 + 24.8570i 1.32713 + 1.58161i
\(248\) 0 0
\(249\) 1.54573 6.78575i 0.0979569 0.430029i
\(250\) 0 0
\(251\) 9.85499 17.0693i 0.622041 1.07741i −0.367064 0.930196i \(-0.619637\pi\)
0.989105 0.147212i \(-0.0470298\pi\)
\(252\) 0 0
\(253\) −10.5237 18.2276i −0.661622 1.14596i
\(254\) 0 0
\(255\) −1.03004 8.19100i −0.0645037 0.512940i
\(256\) 0 0
\(257\) 3.84779 10.5717i 0.240018 0.659445i −0.759937 0.649997i \(-0.774770\pi\)
0.999955 0.00944810i \(-0.00300747\pi\)
\(258\) 0 0
\(259\) 0.163735 + 0.0288709i 0.0101740 + 0.00179395i
\(260\) 0 0
\(261\) −8.17818 + 7.99051i −0.506217 + 0.494600i
\(262\) 0 0
\(263\) −8.08262 6.78213i −0.498396 0.418204i 0.358628 0.933481i \(-0.383245\pi\)
−0.857024 + 0.515277i \(0.827689\pi\)
\(264\) 0 0
\(265\) −1.97778 11.2165i −0.121494 0.689025i
\(266\) 0 0
\(267\) −25.7199 + 13.1998i −1.57404 + 0.807815i
\(268\) 0 0
\(269\) 28.9612i 1.76580i 0.469564 + 0.882898i \(0.344411\pi\)
−0.469564 + 0.882898i \(0.655589\pi\)
\(270\) 0 0
\(271\) 29.5660i 1.79600i 0.439991 + 0.898002i \(0.354982\pi\)
−0.439991 + 0.898002i \(0.645018\pi\)
\(272\) 0 0
\(273\) −0.0351133 + 0.709689i −0.00212515 + 0.0429523i
\(274\) 0 0
\(275\) −3.39653 19.2627i −0.204819 1.16158i
\(276\) 0 0
\(277\) −1.54306 1.29478i −0.0927134 0.0777958i 0.595253 0.803538i \(-0.297052\pi\)
−0.687966 + 0.725743i \(0.741496\pi\)
\(278\) 0 0
\(279\) −5.27763 + 10.9832i −0.315963 + 0.657550i
\(280\) 0 0
\(281\) −4.06067 0.716005i −0.242239 0.0427133i 0.0512103 0.998688i \(-0.483692\pi\)
−0.293449 + 0.955975i \(0.594803\pi\)
\(282\) 0 0
\(283\) −2.21065 + 6.07372i −0.131410 + 0.361045i −0.987895 0.155127i \(-0.950421\pi\)
0.856485 + 0.516172i \(0.172644\pi\)
\(284\) 0 0
\(285\) −8.60798 + 6.52612i −0.509893 + 0.386574i
\(286\) 0 0
\(287\) −0.0524195 0.0907933i −0.00309423 0.00535936i
\(288\) 0 0
\(289\) 1.10668 1.91683i 0.0650990 0.112755i
\(290\) 0 0
\(291\) −20.1073 18.6408i −1.17871 1.09274i
\(292\) 0 0
\(293\) −19.8278 23.6299i −1.15835 1.38047i −0.911439 0.411435i \(-0.865028\pi\)
−0.246915 0.969037i \(-0.579417\pi\)
\(294\) 0 0
\(295\) −3.62318 9.95459i −0.210949 0.579579i
\(296\) 0 0
\(297\) −8.44652 + 25.2476i −0.490117 + 1.46501i
\(298\) 0 0
\(299\) 21.8392 7.94881i 1.26299 0.459691i
\(300\) 0 0
\(301\) −0.00726669 + 0.00609748i −0.000418845 + 0.000351453i
\(302\) 0 0
\(303\) 4.30246 + 13.9270i 0.247170 + 0.800084i
\(304\) 0 0
\(305\) −6.10540 3.52495i −0.349594 0.201838i
\(306\) 0 0
\(307\) 27.5367 15.8983i 1.57160 0.907364i 0.575628 0.817712i \(-0.304758\pi\)
0.995973 0.0896520i \(-0.0285755\pi\)
\(308\) 0 0
\(309\) 0.626622 1.48831i 0.0356473 0.0846670i
\(310\) 0 0
\(311\) 13.5550 + 4.93361i 0.768633 + 0.279759i 0.696424 0.717630i \(-0.254773\pi\)
0.0722083 + 0.997390i \(0.476995\pi\)
\(312\) 0 0
\(313\) 0.513567 2.91258i 0.0290285 0.164629i −0.966847 0.255355i \(-0.917808\pi\)
0.995876 + 0.0907261i \(0.0289188\pi\)
\(314\) 0 0
\(315\) −0.235391 0.0233501i −0.0132628 0.00131563i
\(316\) 0 0
\(317\) −14.9386 + 17.8031i −0.839035 + 0.999923i 0.160881 + 0.986974i \(0.448567\pi\)
−0.999916 + 0.0129495i \(0.995878\pi\)
\(318\) 0 0
\(319\) 19.2307 3.39089i 1.07671 0.189853i
\(320\) 0 0
\(321\) 10.6092 16.4418i 0.592148 0.917690i
\(322\) 0 0
\(323\) −25.1404 −1.39885
\(324\) 0 0
\(325\) 21.5981 1.19805
\(326\) 0 0
\(327\) −7.33351 + 11.3652i −0.405544 + 0.628498i
\(328\) 0 0
\(329\) 0.397247 0.0700454i 0.0219010 0.00386173i
\(330\) 0 0
\(331\) 4.74589 5.65593i 0.260857 0.310878i −0.619680 0.784855i \(-0.712738\pi\)
0.880537 + 0.473977i \(0.157182\pi\)
\(332\) 0 0
\(333\) −4.01051 + 5.58842i −0.219775 + 0.306243i
\(334\) 0 0
\(335\) 1.26134 7.15344i 0.0689146 0.390834i
\(336\) 0 0
\(337\) 8.45078 + 3.07583i 0.460343 + 0.167551i 0.561773 0.827292i \(-0.310119\pi\)
−0.101430 + 0.994843i \(0.532342\pi\)
\(338\) 0 0
\(339\) 5.52690 13.1271i 0.300180 0.712967i
\(340\) 0 0
\(341\) 18.0230 10.4056i 0.975997 0.563492i
\(342\) 0 0
\(343\) −0.878838 0.507397i −0.0474528 0.0273969i
\(344\) 0 0
\(345\) 2.28367 + 7.39219i 0.122949 + 0.397982i
\(346\) 0 0
\(347\) 11.3234 9.50146i 0.607872 0.510065i −0.286093 0.958202i \(-0.592357\pi\)
0.893965 + 0.448137i \(0.147912\pi\)
\(348\) 0 0
\(349\) 6.57893 2.39453i 0.352162 0.128176i −0.159881 0.987136i \(-0.551111\pi\)
0.512043 + 0.858960i \(0.328889\pi\)
\(350\) 0 0
\(351\) −25.8354 14.0261i −1.37899 0.748656i
\(352\) 0 0
\(353\) −3.61218 9.92437i −0.192257 0.528221i 0.805685 0.592344i \(-0.201797\pi\)
−0.997942 + 0.0641228i \(0.979575\pi\)
\(354\) 0 0
\(355\) −4.86095 5.79306i −0.257993 0.307464i
\(356\) 0 0
\(357\) −0.403723 0.374277i −0.0213673 0.0198089i
\(358\) 0 0
\(359\) 12.6210 21.8603i 0.666112 1.15374i −0.312871 0.949796i \(-0.601291\pi\)
0.978983 0.203944i \(-0.0653761\pi\)
\(360\) 0 0
\(361\) 6.94788 + 12.0341i 0.365678 + 0.633373i
\(362\) 0 0
\(363\) 21.0502 15.9591i 1.10485 0.837637i
\(364\) 0 0
\(365\) −2.06133 + 5.66345i −0.107895 + 0.296439i
\(366\) 0 0
\(367\) −11.2545 1.98448i −0.587483 0.103589i −0.127997 0.991774i \(-0.540855\pi\)
−0.459485 + 0.888185i \(0.651966\pi\)
\(368\) 0 0
\(369\) 4.32501 0.327854i 0.225151 0.0170674i
\(370\) 0 0
\(371\) −0.581825 0.488209i −0.0302068 0.0253465i
\(372\) 0 0
\(373\) 2.86274 + 16.2354i 0.148227 + 0.840639i 0.964719 + 0.263282i \(0.0848048\pi\)
−0.816492 + 0.577357i \(0.804084\pi\)
\(374\) 0 0
\(375\) −0.820664 + 16.5868i −0.0423789 + 0.856537i
\(376\) 0 0
\(377\) 21.5622i 1.11051i
\(378\) 0 0
\(379\) 15.7412i 0.808572i −0.914633 0.404286i \(-0.867520\pi\)
0.914633 0.404286i \(-0.132480\pi\)
\(380\) 0 0
\(381\) 7.72703 3.96561i 0.395868 0.203164i
\(382\) 0 0
\(383\) 5.45535 + 30.9388i 0.278756 + 1.58090i 0.726774 + 0.686877i \(0.241019\pi\)
−0.448018 + 0.894024i \(0.647870\pi\)
\(384\) 0 0
\(385\) 0.309474 + 0.259679i 0.0157722 + 0.0132345i
\(386\) 0 0
\(387\) −0.0971683 0.380237i −0.00493934 0.0193285i
\(388\) 0 0
\(389\) 10.4122 + 1.83595i 0.527918 + 0.0930862i 0.431253 0.902231i \(-0.358071\pi\)
0.0966646 + 0.995317i \(0.469183\pi\)
\(390\) 0 0
\(391\) −6.15855 + 16.9205i −0.311451 + 0.855705i
\(392\) 0 0
\(393\) 0.550001 + 4.37366i 0.0277439 + 0.220622i
\(394\) 0 0
\(395\) 7.68863 + 13.3171i 0.386857 + 0.670056i
\(396\) 0 0
\(397\) 2.12129 3.67419i 0.106465 0.184402i −0.807871 0.589359i \(-0.799380\pi\)
0.914336 + 0.404957i \(0.132714\pi\)
\(398\) 0 0
\(399\) −0.159991 + 0.702358i −0.00800957 + 0.0351619i
\(400\) 0 0
\(401\) 17.6057 + 20.9817i 0.879189 + 1.04778i 0.998491 + 0.0549188i \(0.0174900\pi\)
−0.119302 + 0.992858i \(0.538066\pi\)
\(402\) 0 0
\(403\) 7.85954 + 21.5939i 0.391512 + 1.07567i
\(404\) 0 0
\(405\) 5.08862 8.35943i 0.252856 0.415384i
\(406\) 0 0
\(407\) 11.0392 4.01794i 0.547193 0.199162i
\(408\) 0 0
\(409\) 0.397716 0.333723i 0.0196658 0.0165016i −0.632902 0.774232i \(-0.718136\pi\)
0.652568 + 0.757731i \(0.273692\pi\)
\(410\) 0 0
\(411\) 17.0127 + 3.87535i 0.839176 + 0.191157i
\(412\) 0 0
\(413\) −0.611786 0.353215i −0.0301040 0.0173806i
\(414\) 0 0
\(415\) 3.78385 2.18461i 0.185742 0.107238i
\(416\) 0 0
\(417\) −5.82185 + 0.732114i −0.285097 + 0.0358518i
\(418\) 0 0
\(419\) −11.8567 4.31547i −0.579236 0.210825i 0.0357528 0.999361i \(-0.488617\pi\)
−0.614988 + 0.788536i \(0.710839\pi\)
\(420\) 0 0
\(421\) −2.43676 + 13.8196i −0.118760 + 0.673524i 0.866059 + 0.499942i \(0.166645\pi\)
−0.984819 + 0.173582i \(0.944466\pi\)
\(422\) 0 0
\(423\) −4.50611 + 16.0686i −0.219095 + 0.781284i
\(424\) 0 0
\(425\) −10.7562 + 12.8188i −0.521754 + 0.621802i
\(426\) 0 0
\(427\) −0.462984 + 0.0816366i −0.0224054 + 0.00395067i
\(428\) 0 0
\(429\) 22.9240 + 44.6676i 1.10678 + 2.15657i
\(430\) 0 0
\(431\) −4.28837 −0.206564 −0.103282 0.994652i \(-0.532934\pi\)
−0.103282 + 0.994652i \(0.532934\pi\)
\(432\) 0 0
\(433\) 5.60769 0.269488 0.134744 0.990880i \(-0.456979\pi\)
0.134744 + 0.990880i \(0.456979\pi\)
\(434\) 0 0
\(435\) −7.16934 0.354718i −0.343744 0.0170074i
\(436\) 0 0
\(437\) 23.2031 4.09133i 1.10996 0.195715i
\(438\) 0 0
\(439\) 4.51341 5.37887i 0.215413 0.256719i −0.647507 0.762059i \(-0.724188\pi\)
0.862920 + 0.505340i \(0.168633\pi\)
\(440\) 0 0
\(441\) 17.3278 11.8357i 0.825134 0.563606i
\(442\) 0 0
\(443\) −5.26637 + 29.8670i −0.250213 + 1.41903i 0.557856 + 0.829938i \(0.311624\pi\)
−0.808069 + 0.589088i \(0.799487\pi\)
\(444\) 0 0
\(445\) −17.0547 6.20742i −0.808472 0.294260i
\(446\) 0 0
\(447\) −21.9444 28.9447i −1.03793 1.36904i
\(448\) 0 0
\(449\) 24.7669 14.2991i 1.16882 0.674819i 0.215418 0.976522i \(-0.430889\pi\)
0.953402 + 0.301703i \(0.0975552\pi\)
\(450\) 0 0
\(451\) −6.41528 3.70386i −0.302084 0.174408i
\(452\) 0 0
\(453\) −24.2196 + 26.1250i −1.13793 + 1.22746i
\(454\) 0 0
\(455\) −0.341723 + 0.286740i −0.0160202 + 0.0134426i
\(456\) 0 0
\(457\) −0.676715 + 0.246304i −0.0316554 + 0.0115216i −0.357799 0.933799i \(-0.616473\pi\)
0.326144 + 0.945320i \(0.394251\pi\)
\(458\) 0 0
\(459\) 21.1911 8.34846i 0.989117 0.389673i
\(460\) 0 0
\(461\) 0.907267 + 2.49269i 0.0422556 + 0.116096i 0.959026 0.283319i \(-0.0914354\pi\)
−0.916770 + 0.399415i \(0.869213\pi\)
\(462\) 0 0
\(463\) −6.24403 7.44135i −0.290185 0.345829i 0.601181 0.799113i \(-0.294697\pi\)
−0.891366 + 0.453284i \(0.850252\pi\)
\(464\) 0 0
\(465\) −7.30918 + 2.25802i −0.338955 + 0.104713i
\(466\) 0 0
\(467\) 9.87482 17.1037i 0.456952 0.791464i −0.541846 0.840478i \(-0.682274\pi\)
0.998798 + 0.0490137i \(0.0156078\pi\)
\(468\) 0 0
\(469\) −0.242195 0.419494i −0.0111835 0.0193704i
\(470\) 0 0
\(471\) 39.3855 + 16.5824i 1.81479 + 0.764078i
\(472\) 0 0
\(473\) −0.229243 + 0.629840i −0.0105406 + 0.0289601i
\(474\) 0 0
\(475\) 21.5631 + 3.80216i 0.989385 + 0.174455i
\(476\) 0 0
\(477\) 28.6310 12.9485i 1.31093 0.592869i
\(478\) 0 0
\(479\) −15.2243 12.7747i −0.695616 0.583691i 0.224906 0.974380i \(-0.427792\pi\)
−0.920523 + 0.390689i \(0.872237\pi\)
\(480\) 0 0
\(481\) 2.25254 + 12.7748i 0.102707 + 0.582480i
\(482\) 0 0
\(483\) 0.433523 + 0.279735i 0.0197260 + 0.0127284i
\(484\) 0 0
\(485\) 17.2134i 0.781621i
\(486\) 0 0
\(487\) 3.34369i 0.151517i −0.997126 0.0757584i \(-0.975862\pi\)
0.997126 0.0757584i \(-0.0241378\pi\)
\(488\) 0 0
\(489\) 17.7829 + 11.4746i 0.804169 + 0.518897i
\(490\) 0 0
\(491\) −6.46183 36.6468i −0.291618 1.65385i −0.680638 0.732620i \(-0.738297\pi\)
0.389020 0.921229i \(-0.372814\pi\)
\(492\) 0 0
\(493\) −12.7975 10.7383i −0.576368 0.483630i
\(494\) 0 0
\(495\) −15.2289 + 6.88731i −0.684489 + 0.309562i
\(496\) 0 0
\(497\) −0.496634 0.0875700i −0.0222771 0.00392805i
\(498\) 0 0
\(499\) 6.25828 17.1945i 0.280159 0.769731i −0.717184 0.696884i \(-0.754569\pi\)
0.997343 0.0728472i \(-0.0232085\pi\)
\(500\) 0 0
\(501\) −6.18956 2.60599i −0.276529 0.116427i
\(502\) 0 0
\(503\) 19.9327 + 34.5244i 0.888754 + 1.53937i 0.841350 + 0.540491i \(0.181761\pi\)
0.0474040 + 0.998876i \(0.484905\pi\)
\(504\) 0 0
\(505\) −4.57554 + 7.92506i −0.203609 + 0.352661i
\(506\) 0 0
\(507\) −31.4550 + 9.71740i −1.39697 + 0.431565i
\(508\) 0 0
\(509\) 0.228853 + 0.272736i 0.0101437 + 0.0120888i 0.771092 0.636723i \(-0.219711\pi\)
−0.760949 + 0.648812i \(0.775266\pi\)
\(510\) 0 0
\(511\) 0.137461 + 0.377670i 0.00608091 + 0.0167072i
\(512\) 0 0
\(513\) −23.3244 18.5515i −1.02980 0.819067i
\(514\) 0 0
\(515\) 0.952659 0.346739i 0.0419792 0.0152792i
\(516\) 0 0
\(517\) 21.8336 18.3206i 0.960241 0.805738i
\(518\) 0 0
\(519\) 18.4239 19.8734i 0.808720 0.872344i
\(520\) 0 0
\(521\) −23.3668 13.4908i −1.02372 0.591044i −0.108539 0.994092i \(-0.534617\pi\)
−0.915179 + 0.403049i \(0.867951\pi\)
\(522\) 0 0
\(523\) −24.8958 + 14.3736i −1.08862 + 0.628513i −0.933208 0.359337i \(-0.883003\pi\)
−0.155408 + 0.987850i \(0.549669\pi\)
\(524\) 0 0
\(525\) 0.289672 + 0.382079i 0.0126423 + 0.0166753i
\(526\) 0 0
\(527\) −16.7305 6.08939i −0.728790 0.265258i
\(528\) 0 0
\(529\) −1.06356 + 6.03172i −0.0462415 + 0.262249i
\(530\) 0 0
\(531\) 24.1339 16.4846i 1.04732 0.715373i
\(532\) 0 0
\(533\) 5.25778 6.26598i 0.227740 0.271410i
\(534\) 0 0
\(535\) 12.0978 2.13318i 0.523035 0.0922253i
\(536\) 0 0
\(537\) −20.8725 1.03271i −0.900713 0.0445646i
\(538\) 0 0
\(539\) −35.8382 −1.54366
\(540\) 0 0
\(541\) −21.2500 −0.913608 −0.456804 0.889567i \(-0.651006\pi\)
−0.456804 + 0.889567i \(0.651006\pi\)
\(542\) 0 0
\(543\) 16.0131 + 31.2016i 0.687186 + 1.33899i
\(544\) 0 0
\(545\) −8.36252 + 1.47454i −0.358211 + 0.0631622i
\(546\) 0 0
\(547\) −8.82124 + 10.5127i −0.377169 + 0.449492i −0.920919 0.389755i \(-0.872560\pi\)
0.543750 + 0.839247i \(0.317004\pi\)
\(548\) 0 0
\(549\) 5.25179 18.7277i 0.224141 0.799279i
\(550\) 0 0
\(551\) −3.79584 + 21.5273i −0.161708 + 0.917093i
\(552\) 0 0
\(553\) 0.963599 + 0.350721i 0.0409764 + 0.0149142i
\(554\) 0 0
\(555\) −4.28461 + 0.538803i −0.181872 + 0.0228709i
\(556\) 0 0
\(557\) −29.8867 + 17.2551i −1.26634 + 0.731121i −0.974293 0.225283i \(-0.927669\pi\)
−0.292046 + 0.956404i \(0.594336\pi\)
\(558\) 0 0
\(559\) −0.640952 0.370054i −0.0271094 0.0156516i
\(560\) 0 0
\(561\) −37.9274 8.63952i −1.60129 0.364761i
\(562\) 0 0
\(563\) −7.90869 + 6.63618i −0.333312 + 0.279682i −0.794048 0.607856i \(-0.792030\pi\)
0.460736 + 0.887537i \(0.347586\pi\)
\(564\) 0 0
\(565\) 8.40260 3.05830i 0.353500 0.128663i
\(566\) 0 0
\(567\) −0.0983763 0.645156i −0.00413142 0.0270940i
\(568\) 0 0
\(569\) 10.3576 + 28.4573i 0.434214 + 1.19299i 0.943202 + 0.332219i \(0.107797\pi\)
−0.508989 + 0.860773i \(0.669981\pi\)
\(570\) 0 0
\(571\) −23.6804 28.2212i −0.990992 1.18102i −0.983475 0.181047i \(-0.942051\pi\)
−0.00751760 0.999972i \(-0.502393\pi\)
\(572\) 0 0
\(573\) 9.64751 42.3524i 0.403030 1.76930i
\(574\) 0 0
\(575\) 7.84125 13.5815i 0.327003 0.566386i
\(576\) 0 0
\(577\) 5.46070 + 9.45821i 0.227332 + 0.393750i 0.957016 0.290034i \(-0.0936665\pi\)
−0.729685 + 0.683784i \(0.760333\pi\)
\(578\) 0 0
\(579\) −3.21044 25.5298i −0.133421 1.06098i
\(580\) 0 0
\(581\) 0.0996522 0.273792i 0.00413427 0.0113588i
\(582\) 0 0
\(583\) −52.8508 9.31902i −2.18886 0.385954i
\(584\) 0 0
\(585\) −4.56943 17.8810i −0.188923 0.739288i
\(586\) 0 0
\(587\) 25.8588 + 21.6981i 1.06730 + 0.895575i 0.994806 0.101793i \(-0.0324580\pi\)
0.0724993 + 0.997368i \(0.476902\pi\)
\(588\) 0 0
\(589\) 4.04539 + 22.9425i 0.166687 + 0.945331i
\(590\) 0 0
\(591\) 25.6195 13.1483i 1.05385 0.540847i
\(592\) 0 0
\(593\) 1.65720i 0.0680529i 0.999421 + 0.0340265i \(0.0108330\pi\)
−0.999421 + 0.0340265i \(0.989167\pi\)
\(594\) 0 0
\(595\) 0.345618i 0.0141690i
\(596\) 0 0
\(597\) 1.74845 35.3385i 0.0715591 1.44631i
\(598\) 0 0
\(599\) 2.97543 + 16.8745i 0.121573 + 0.689474i 0.983285 + 0.182076i \(0.0582816\pi\)
−0.861712 + 0.507398i \(0.830607\pi\)
\(600\) 0 0
\(601\) −24.6454 20.6799i −1.00531 0.843552i −0.0175950 0.999845i \(-0.505601\pi\)
−0.987711 + 0.156294i \(0.950045\pi\)
\(602\) 0 0
\(603\) 19.9829 1.51479i 0.813767 0.0616870i
\(604\) 0 0
\(605\) 16.3320 + 2.87977i 0.663990 + 0.117079i
\(606\) 0 0
\(607\) 11.5382 31.7008i 0.468319 1.28670i −0.450768 0.892641i \(-0.648850\pi\)
0.919087 0.394055i \(-0.128928\pi\)
\(608\) 0 0
\(609\) −0.381444 + 0.289191i −0.0154569 + 0.0117186i
\(610\) 0 0
\(611\) 15.7359 + 27.2554i 0.636606 + 1.10263i
\(612\) 0 0
\(613\) −21.7069 + 37.5975i −0.876734 + 1.51855i −0.0218308 + 0.999762i \(0.506949\pi\)
−0.854904 + 0.518787i \(0.826384\pi\)
\(614\) 0 0
\(615\) 1.99692 + 1.85127i 0.0805235 + 0.0746505i
\(616\) 0 0
\(617\) −4.65341 5.54572i −0.187339 0.223262i 0.664198 0.747557i \(-0.268773\pi\)
−0.851537 + 0.524295i \(0.824329\pi\)
\(618\) 0 0
\(619\) −8.37729 23.0164i −0.336712 0.925108i −0.986320 0.164839i \(-0.947289\pi\)
0.649609 0.760269i \(-0.274933\pi\)
\(620\) 0 0
\(621\) −18.1996 + 11.1538i −0.730324 + 0.447586i
\(622\) 0 0
\(623\) −1.13730 + 0.413945i −0.0455651 + 0.0165844i
\(624\) 0 0
\(625\) 6.63556 5.56789i 0.265422 0.222716i
\(626\) 0 0
\(627\) 15.0235 + 48.6308i 0.599982 + 1.94213i
\(628\) 0 0
\(629\) −8.70380 5.02514i −0.347043 0.200365i
\(630\) 0 0
\(631\) −9.68103 + 5.58935i −0.385396 + 0.222508i −0.680163 0.733061i \(-0.738091\pi\)
0.294768 + 0.955569i \(0.404758\pi\)
\(632\) 0 0
\(633\) 12.0640 28.6535i 0.479499 1.13887i
\(634\) 0 0
\(635\) 5.12375 + 1.86489i 0.203330 + 0.0740060i
\(636\) 0 0
\(637\) 6.87175 38.9716i 0.272269 1.54411i
\(638\) 0 0
\(639\) 12.1645 16.9506i 0.481222 0.670554i
\(640\) 0 0
\(641\) −7.72355 + 9.20457i −0.305062 + 0.363559i −0.896695 0.442649i \(-0.854039\pi\)
0.591633 + 0.806207i \(0.298483\pi\)
\(642\) 0 0
\(643\) −7.71839 + 1.36096i −0.304384 + 0.0536711i −0.323754 0.946141i \(-0.604945\pi\)
0.0193702 + 0.999812i \(0.493834\pi\)
\(644\) 0 0
\(645\) 0.133586 0.207026i 0.00525992 0.00815164i
\(646\) 0 0
\(647\) −44.0555 −1.73200 −0.866000 0.500044i \(-0.833317\pi\)
−0.866000 + 0.500044i \(0.833317\pi\)
\(648\) 0 0
\(649\) −49.9150 −1.95933
\(650\) 0 0
\(651\) −0.276593 + 0.428654i −0.0108405 + 0.0168003i
\(652\) 0 0
\(653\) 39.0561 6.88664i 1.52838 0.269495i 0.654661 0.755923i \(-0.272811\pi\)
0.873721 + 0.486428i \(0.161700\pi\)
\(654\) 0 0
\(655\) −1.77886 + 2.11996i −0.0695057 + 0.0828336i
\(656\) 0 0
\(657\) −16.5466 1.64137i −0.645544 0.0640360i
\(658\) 0 0
\(659\) −1.66439 + 9.43924i −0.0648355 + 0.367701i 0.935077 + 0.354446i \(0.115330\pi\)
−0.999912 + 0.0132549i \(0.995781\pi\)
\(660\) 0 0
\(661\) −10.0924 3.67332i −0.392547 0.142876i 0.138203 0.990404i \(-0.455867\pi\)
−0.530750 + 0.847528i \(0.678090\pi\)
\(662\) 0 0
\(663\) 16.6672 39.5868i 0.647301 1.53742i
\(664\) 0 0
\(665\) −0.391648 + 0.226118i −0.0151874 + 0.00876847i
\(666\) 0 0
\(667\) 13.5589 + 7.82821i 0.525001 + 0.303110i
\(668\) 0 0
\(669\) 0.154220 + 0.499208i 0.00596250 + 0.0193005i
\(670\) 0 0
\(671\) −25.4467 + 21.3523i −0.982357 + 0.824296i
\(672\) 0 0
\(673\) −0.534095 + 0.194395i −0.0205878 + 0.00749336i −0.352294 0.935890i \(-0.614598\pi\)
0.331706 + 0.943383i \(0.392376\pi\)
\(674\) 0 0
\(675\) −19.4384 + 3.95566i −0.748186 + 0.152254i
\(676\) 0 0
\(677\) 2.40412 + 6.60528i 0.0923980 + 0.253861i 0.977279 0.211955i \(-0.0679830\pi\)
−0.884881 + 0.465816i \(0.845761\pi\)
\(678\) 0 0
\(679\) −0.737846 0.879331i −0.0283159 0.0337456i
\(680\) 0 0
\(681\) 25.9859 + 24.0906i 0.995781 + 0.923153i
\(682\) 0 0
\(683\) −24.1061 + 41.7529i −0.922393 + 1.59763i −0.126693 + 0.991942i \(0.540436\pi\)
−0.795701 + 0.605690i \(0.792897\pi\)
\(684\) 0 0
\(685\) 5.47709 + 9.48660i 0.209269 + 0.362464i
\(686\) 0 0
\(687\) −9.28220 + 7.03728i −0.354138 + 0.268489i
\(688\) 0 0
\(689\) 20.2676 55.6847i 0.772134 2.12142i
\(690\) 0 0
\(691\) −21.0430 3.71046i −0.800515 0.141152i −0.241599 0.970376i \(-0.577672\pi\)
−0.558917 + 0.829224i \(0.688783\pi\)
\(692\) 0 0
\(693\) −0.482733 + 1.00461i −0.0183375 + 0.0381621i
\(694\) 0 0
\(695\) −2.82191 2.36786i −0.107041 0.0898182i
\(696\) 0 0
\(697\) 1.10048 + 6.24113i 0.0416836 + 0.236400i
\(698\) 0 0
\(699\) −0.495119 + 10.0070i −0.0187271 + 0.378501i
\(700\) 0 0
\(701\) 12.4157i 0.468935i −0.972124 0.234468i \(-0.924665\pi\)
0.972124 0.234468i \(-0.0753347\pi\)
\(702\) 0 0
\(703\) 13.1506i 0.495985i
\(704\) 0 0
\(705\) −9.32117 + 4.78375i −0.351056 + 0.180166i
\(706\) 0 0
\(707\) 0.105968 + 0.600973i 0.00398533 + 0.0226019i
\(708\) 0 0
\(709\) −0.976912 0.819726i −0.0366887 0.0307855i 0.624259 0.781218i \(-0.285401\pi\)
−0.660948 + 0.750432i \(0.729845\pi\)
\(710\) 0 0
\(711\) −30.3449 + 29.6486i −1.13802 + 1.11191i
\(712\) 0 0
\(713\) 16.4322 + 2.89745i 0.615392 + 0.108510i
\(714\) 0 0
\(715\) −10.7804 + 29.6188i −0.403163 + 1.10768i
\(716\) 0 0
\(717\) −0.543449 4.32157i −0.0202955 0.161392i
\(718\) 0 0
\(719\) 14.5684 + 25.2332i 0.543310 + 0.941041i 0.998711 + 0.0507546i \(0.0161627\pi\)
−0.455401 + 0.890287i \(0.650504\pi\)
\(720\) 0 0
\(721\) 0.0338028 0.0585482i 0.00125888 0.00218045i
\(722\) 0 0
\(723\) −0.350368 + 1.53811i −0.0130303 + 0.0572030i
\(724\) 0 0
\(725\) 9.35246 + 11.1458i 0.347342 + 0.413946i
\(726\) 0 0
\(727\) −2.73821 7.52317i −0.101555 0.279019i 0.878502 0.477739i \(-0.158544\pi\)
−0.980056 + 0.198720i \(0.936321\pi\)
\(728\) 0 0
\(729\) 25.8209 + 7.89182i 0.956330 + 0.292290i
\(730\) 0 0
\(731\) 0.538836 0.196120i 0.0199296 0.00725378i
\(732\) 0 0
\(733\) 2.12619 1.78409i 0.0785326 0.0658967i −0.602676 0.797986i \(-0.705899\pi\)
0.681209 + 0.732089i \(0.261455\pi\)
\(734\) 0 0
\(735\) 12.8449 + 2.92595i 0.473790 + 0.107925i
\(736\) 0 0
\(737\) −29.6406 17.1130i −1.09183 0.630367i
\(738\) 0 0
\(739\) 22.0458 12.7281i 0.810967 0.468212i −0.0363245 0.999340i \(-0.511565\pi\)
0.847292 + 0.531128i \(0.178232\pi\)
\(740\) 0 0
\(741\) −55.7634 + 7.01240i −2.04852 + 0.257607i
\(742\) 0 0
\(743\) −2.02834 0.738257i −0.0744127 0.0270840i 0.304546 0.952498i \(-0.401495\pi\)
−0.378958 + 0.925414i \(0.623718\pi\)
\(744\) 0 0
\(745\) 3.95979 22.4571i 0.145075 0.822764i
\(746\) 0 0
\(747\) 8.42420 + 8.62206i 0.308225 + 0.315465i
\(748\) 0 0
\(749\) 0.526569 0.627541i 0.0192404 0.0229298i
\(750\) 0 0
\(751\) 3.26718 0.576092i 0.119221 0.0210219i −0.113719 0.993513i \(-0.536276\pi\)
0.232940 + 0.972491i \(0.425165\pi\)
\(752\) 0 0
\(753\) 15.5875 + 30.3724i 0.568040 + 1.10683i
\(754\) 0 0
\(755\) −22.3650 −0.813947
\(756\) 0 0
\(757\) −21.4846 −0.780869 −0.390435 0.920631i \(-0.627675\pi\)
−0.390435 + 0.920631i \(0.627675\pi\)
\(758\) 0 0
\(759\) 36.4108 + 1.80150i 1.32163 + 0.0653901i
\(760\) 0 0
\(761\) −6.57062 + 1.15858i −0.238185 + 0.0419984i −0.291466 0.956581i \(-0.594143\pi\)
0.0532815 + 0.998580i \(0.483032\pi\)
\(762\) 0 0
\(763\) −0.363986 + 0.433781i −0.0131772 + 0.0157039i
\(764\) 0 0
\(765\) 12.8883 + 6.19301i 0.465976 + 0.223909i
\(766\) 0 0
\(767\) 9.57087 54.2791i 0.345584 1.95991i
\(768\) 0 0
\(769\) 37.8560 + 13.7784i 1.36512 + 0.496863i 0.917634 0.397427i \(-0.130097\pi\)
0.447487 + 0.894290i \(0.352319\pi\)
\(770\) 0 0
\(771\) 11.7723 + 15.5278i 0.423970 + 0.559219i
\(772\) 0 0
\(773\) 15.8074 9.12640i 0.568552 0.328254i −0.188019 0.982165i \(-0.560207\pi\)
0.756571 + 0.653912i \(0.226873\pi\)
\(774\) 0 0
\(775\) 13.4289 + 7.75320i 0.482382 + 0.278503i
\(776\) 0 0
\(777\) −0.195780 + 0.211183i −0.00702357 + 0.00757613i
\(778\) 0 0
\(779\) 6.35234 5.33025i 0.227596 0.190976i
\(780\) 0 0
\(781\) −33.4837 + 12.1871i −1.19814 + 0.436087i
\(782\) 0 0
\(783\) −3.94909 19.4061i −0.141129 0.693518i
\(784\) 0 0
\(785\) 9.17584 + 25.2104i 0.327500 + 0.899798i
\(786\) 0 0
\(787\) −12.4720 14.8636i −0.444580 0.529830i 0.496490 0.868043i \(-0.334622\pi\)
−0.941070 + 0.338213i \(0.890178\pi\)
\(788\) 0 0
\(789\) 17.4608 5.39418i 0.621622 0.192038i
\(790\) 0 0
\(791\) 0.298146 0.516404i 0.0106009 0.0183612i
\(792\) 0 0
\(793\) −18.3399 31.7656i −0.651269 1.12803i
\(794\) 0 0
\(795\) 18.1815 + 7.65495i 0.644832 + 0.271493i