Properties

Label 432.2.be.c.47.4
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 47.4
Character \(\chi\) \(=\) 432.47
Dual form 432.2.be.c.239.4

$q$-expansion

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

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 −0.757164 0.653225i \(-0.773416\pi\)
0.774781 + 0.632230i \(0.217860\pi\)
\(8\) 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 \(-0.663495\pi\)
0.759601 0.650389i \(-0.225394\pi\)
\(12\) 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 0.946313 0.323252i \(-0.104776\pi\)
0.193212 + 0.981157i \(0.438110\pi\)
\(20\) 0 0
\(21\) −0.0370715 0.120000i −0.00808966 0.0261861i
\(22\) 0 0
\(23\) 3.14687 2.64054i 0.656168 0.550590i −0.252768 0.967527i \(-0.581341\pi\)
0.908935 + 0.416937i \(0.136896\pi\)
\(24\) 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 0.947729 0.319076i \(-0.103373\pi\)
−0.478800 + 0.877924i \(0.658928\pi\)
\(32\) 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 0.163816 0.986491i \(-0.447620\pi\)
−0.183463 + 0.983027i \(0.558731\pi\)
\(44\) 0 0
\(45\) 1.83995 + 2.69373i 0.274283 + 0.401557i
\(46\) 0 0
\(47\) 4.26138 + 3.57572i 0.621586 + 0.521573i 0.898302 0.439379i \(-0.144802\pi\)
−0.276716 + 0.960952i \(0.589246\pi\)
\(48\) 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 \(-0.836901\pi\)
0.651333 0.758792i \(-0.274210\pi\)
\(60\) 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 \(-0.755097\pi\)
0.997463 0.0711921i \(-0.0226803\pi\)
\(68\) 0 0
\(69\) −0.887762 7.05957i −0.106874 0.849873i
\(70\) 0 0
\(71\) −3.47730 6.02286i −0.412680 0.714782i 0.582502 0.812829i \(-0.302074\pi\)
−0.995182 + 0.0980471i \(0.968740\pi\)
\(72\) 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 \(0.181694\pi\)
−0.297294 + 0.954786i \(0.596084\pi\)
\(80\) 0 0
\(81\) −5.94356 + 6.75826i −0.660396 + 0.750918i
\(82\) 0 0
\(83\) 3.77579 1.37428i 0.414447 0.150846i −0.126377 0.991982i \(-0.540335\pi\)
0.540824 + 0.841136i \(0.318113\pi\)
\(84\) 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 −0.128230 0.991744i \(-0.540930\pi\)
0.218700 + 0.975792i \(0.429818\pi\)
\(104\) 0 0
\(105\) 0.0623569 + 0.121503i 0.00608541 + 0.0118575i
\(106\) 0 0
\(107\) 11.2973 1.09215 0.546076 0.837736i \(-0.316121\pi\)
0.546076 + 0.837736i \(0.316121\pi\)
\(108\) 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 0.680141 0.733081i \(-0.261919\pi\)
−0.294797 + 0.955560i \(0.595252\pi\)
\(128\) 0 0
\(129\) −0.154045 + 0.166164i −0.0135629 + 0.0146300i
\(130\) 0 0
\(131\) −1.94960 + 1.63591i −0.170337 + 0.142930i −0.723971 0.689830i \(-0.757685\pi\)
0.553634 + 0.832760i \(0.313241\pi\)
\(132\) 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 0.665747 0.746178i \(-0.268113\pi\)
−0.850447 + 0.526060i \(0.823669\pi\)
\(140\) 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 −0.729128 0.684377i \(-0.760074\pi\)
−0.919227 + 0.393728i \(0.871185\pi\)
\(152\) 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 \(0.158828\pi\)
−0.878074 + 0.478524i \(0.841172\pi\)
\(164\) 0 0
\(165\) 8.10832 + 5.23197i 0.631231 + 0.407308i
\(166\) 0 0
\(167\) −0.673297 3.81846i −0.0521013 0.295481i 0.947612 0.319423i \(-0.103489\pi\)
−0.999713 + 0.0239425i \(0.992378\pi\)
\(168\) 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 0.547535 0.836783i \(-0.315566\pi\)
−0.998443 + 0.0557882i \(0.982233\pi\)
\(180\) 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 0.708786 0.705424i \(-0.249243\pi\)
0.996399 + 0.0847874i \(0.0270211\pi\)
\(192\) 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 0.282157 0.959368i \(-0.408950\pi\)
0.971916 + 0.235329i \(0.0756167\pi\)
\(200\) 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 0.471924 0.881639i \(-0.343559\pi\)
0.745002 + 0.667062i \(0.232448\pi\)
\(212\) 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 −0.772498 0.635018i \(-0.780993\pi\)
0.759513 + 0.650492i \(0.225437\pi\)
\(224\) 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 \(0.293112\pi\)
−0.840943 + 0.541124i \(0.817999\pi\)
\(228\) 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 −0.578355 0.815785i \(-0.696305\pi\)
0.702962 + 0.711228i \(0.251861\pi\)
\(240\) 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 \(0.380363\pi\)
−0.989105 + 0.147212i \(0.952970\pi\)
\(252\) 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 0.857024 0.515277i \(-0.172311\pi\)
−0.358628 + 0.933481i \(0.616755\pi\)
\(264\) 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 \(-0.645018\pi\)
0.439991 0.898002i \(-0.354982\pi\)
\(272\) 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 −0.856485 0.516172i \(-0.827356\pi\)
0.987895 + 0.155127i \(0.0495787\pi\)
\(284\) 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 \(0.695242\pi\)
−0.995973 + 0.0896520i \(0.971425\pi\)
\(308\) 0 0
\(309\) 0.626622 1.48831i 0.0356473 0.0846670i
\(310\) 0 0
\(311\) −13.5550 4.93361i −0.768633 0.279759i −0.0722083 0.997390i \(-0.523005\pi\)
−0.696424 + 0.717630i \(0.745227\pi\)
\(312\) 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 −0.880537 0.473977i \(-0.842818\pi\)
0.619680 + 0.784855i \(0.287262\pi\)
\(332\) 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 −0.893965 0.448137i \(-0.852088\pi\)
0.286093 + 0.958202i \(0.407643\pi\)
\(348\) 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 \(0.398709\pi\)
−0.978983 + 0.203944i \(0.934624\pi\)
\(360\) 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 0.459485 0.888185i \(-0.348034\pi\)
0.127997 + 0.991774i \(0.459145\pi\)
\(368\) 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 \(0.132480\pi\)
−0.914633 + 0.404286i \(0.867520\pi\)
\(380\) 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 \(-0.758981\pi\)
0.448018 0.894024i \(-0.352130\pi\)
\(384\) 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 0.614988 0.788536i \(-0.289161\pi\)
−0.0357528 + 0.999361i \(0.511383\pi\)
\(420\) 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 \(-0.467066\pi\)
0.103282 + 0.994652i \(0.467066\pi\)
\(432\) 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 −0.862920 0.505340i \(-0.831367\pi\)
0.647507 + 0.762059i \(0.275812\pi\)
\(440\) 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 \(-0.688376\pi\)
0.808069 0.589088i \(-0.200513\pi\)
\(444\) 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 0.891366 0.453284i \(-0.149748\pi\)
−0.601181 + 0.799113i \(0.705303\pi\)
\(464\) 0 0
\(465\) −7.30918 + 2.25802i −0.338955 + 0.104713i
\(466\) 0 0
\(467\) −9.87482 + 17.1037i −0.456952 + 0.791464i −0.998798 0.0490137i \(-0.984392\pi\)
0.541846 + 0.840478i \(0.317726\pi\)
\(468\) 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 0.920523 0.390689i \(-0.127763\pi\)
−0.224906 + 0.974380i \(0.572208\pi\)
\(480\) 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 \(0.0241378\pi\)
−0.997126 + 0.0757584i \(0.975862\pi\)
\(488\) 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 \(0.261703\pi\)
−0.389020 + 0.921229i \(0.627186\pi\)
\(492\) 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 \(0.245431\pi\)
−0.997343 + 0.0728472i \(0.976791\pi\)
\(500\) 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 \(-0.818239\pi\)
−0.0474040 0.998876i \(-0.515095\pi\)
\(504\) 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 0.155408 0.987850i \(-0.450331\pi\)
0.933208 + 0.359337i \(0.116997\pi\)
\(524\) 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 −0.543750 0.839247i \(-0.682996\pi\)
0.920919 + 0.389755i \(0.127440\pi\)
\(548\) 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 −0.460736 0.887537i \(-0.652414\pi\)
0.794048 + 0.607856i \(0.207970\pi\)
\(564\) 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 \(0.0579485\pi\)
0.00751760 + 0.999972i \(0.497607\pi\)
\(572\) 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 −0.0724993 0.997368i \(-0.523098\pi\)
−0.994806 + 0.101793i \(0.967542\pi\)
\(588\) 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 \(-0.941718\pi\)
0.861712 0.507398i \(-0.169393\pi\)
\(600\) 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 \(0.351150\pi\)
−0.919087 + 0.394055i \(0.871072\pi\)
\(608\) 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 \(0.0527105\pi\)
−0.649609 + 0.760269i \(0.725067\pi\)
\(620\) 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 −0.294768 0.955569i \(-0.595242\pi\)
0.680163 + 0.733061i \(0.261909\pi\)
\(632\) 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 −0.0193702 0.999812i \(-0.506166\pi\)
0.323754 + 0.946141i \(0.395055\pi\)
\(644\) 0 0
\(645\) 0.133586 0.207026i 0.00525992 0.00815164i
\(646\) 0 0
\(647\) 44.0555 1.73200 0.866000 0.500044i \(-0.166683\pi\)
0.866000 + 0.500044i \(0.166683\pi\)
\(648\) 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 \(-0.884670\pi\)
0.999912 0.0132549i \(-0.00421930\pi\)
\(660\) 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 \(-0.459564\pi\)
0.795701 0.605690i \(-0.207103\pi\)
\(684\) 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 0.558917 0.829224i \(-0.311217\pi\)
0.241599 + 0.970376i \(0.422328\pi\)
\(692\) 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 \(-0.983837\pi\)
0.455401 0.890287i \(-0.349496\pi\)
\(720\) 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 0.980056 0.198720i \(-0.0636786\pi\)
−0.878502 + 0.477739i \(0.841456\pi\)
\(728\) 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 −0.847292 0.531128i \(-0.821768\pi\)
0.0363245 + 0.999340i \(0.488435\pi\)
\(740\) 0 0
\(741\) −55.7634 + 7.01240i −2.04852 + 0.257607i
\(742\) 0 0
\(743\) 2.02834 + 0.738257i 0.0744127 + 0.0270840i 0.378958 0.925414i \(-0.376282\pi\)
−0.304546 + 0.952498i \(0.598505\pi\)
\(744\) 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 −0.232940 0.972491i \(-0.574835\pi\)
0.113719 + 0.993513i \(0.463724\pi\)
\(752\) 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 0.941070 0.338213i \(-0.109822\pi\)
−0.496490 + 0.868043i \(0.665378\pi\)
\(788\) 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