Properties

Label 432.2.be.c.239.4
Level $432$
Weight $2$
Character 432.239
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 239.4
Character \(\chi\) \(=\) 432.239
Dual form 432.2.be.c.47.4

$q$-expansion

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

Character values

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

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{11}{18}\right)\)

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 −0.0710149 0.997475i \(-0.522624\pi\)
−0.407889 + 0.913032i \(0.633735\pi\)
\(6\) 0 0
\(7\) 0.0466102 + 0.0555478i 0.0176170 + 0.0209951i 0.774781 0.632230i \(-0.217860\pi\)
−0.757164 + 0.653225i \(0.773416\pi\)
\(8\) 0 0
\(9\) −1.23621 + 2.73346i −0.412071 + 0.911152i
\(10\) 0 0
\(11\) 0.889704 + 5.04576i 0.268256 + 1.52135i 0.759601 + 0.650389i \(0.225394\pi\)
−0.491346 + 0.870965i \(0.663495\pi\)
\(12\) 0 0
\(13\) −5.31632 + 1.93498i −1.47448 + 0.536668i −0.949314 0.314331i \(-0.898220\pi\)
−0.525168 + 0.850998i \(0.675998\pi\)
\(14\) 0 0
\(15\) −0.730832 1.73582i −0.188700 0.448187i
\(16\) 0 0
\(17\) 3.79605 + 2.19165i 0.920678 + 0.531554i 0.883851 0.467768i \(-0.154942\pi\)
0.0368269 + 0.999322i \(0.488275\pi\)
\(18\) 0 0
\(19\) 4.96707 2.86774i 1.13952 0.657905i 0.193212 0.981157i \(-0.438110\pi\)
0.946313 + 0.323252i \(0.104776\pi\)
\(20\) 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 \(-0.136896\pi\)
−0.252768 + 0.967527i \(0.581341\pi\)
\(24\) 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 0.757862 + 0.652415i \(0.226244\pi\)
−0.999920 + 0.0126352i \(0.995978\pi\)
\(30\) 0 0
\(31\) 2.61088 3.11153i 0.468929 0.558847i −0.478800 0.877924i \(-0.658928\pi\)
0.947729 + 0.319076i \(0.103373\pi\)
\(32\) 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 −0.944741 0.327818i \(-0.893687\pi\)
0.756269 + 0.654260i \(0.227020\pi\)
\(38\) 0 0
\(39\) −7.80863 5.92009i −1.25038 0.947974i
\(40\) 0 0
\(41\) −0.494495 1.35861i −0.0772271 0.212180i 0.895071 0.445923i \(-0.147125\pi\)
−0.972298 + 0.233744i \(0.924902\pi\)
\(42\) 0 0
\(43\) −0.128831 + 0.0227164i −0.0196466 + 0.00346422i −0.183463 0.983027i \(-0.558731\pi\)
0.163816 + 0.986491i \(0.447620\pi\)
\(44\) 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 \(-0.589246\pi\)
0.898302 + 0.439379i \(0.144802\pi\)
\(48\) 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 \(-0.744427\pi\)
0.694619 0.719378i \(-0.255573\pi\)
\(54\) 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 0.651333 + 0.758792i \(0.274210\pi\)
−0.871575 + 0.490262i \(0.836901\pi\)
\(60\) 0 0
\(61\) 4.96656 4.16744i 0.635903 0.533586i −0.266854 0.963737i \(-0.585984\pi\)
0.902757 + 0.430151i \(0.141540\pi\)
\(62\) 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 0.997463 + 0.0711921i \(0.0226803\pi\)
−0.718339 + 0.695693i \(0.755097\pi\)
\(68\) 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 \(-0.968740\pi\)
0.582502 + 0.812829i \(0.302074\pi\)
\(72\) 0 0
\(73\) 2.77130 + 4.80004i 0.324356 + 0.561802i 0.981382 0.192067i \(-0.0615190\pi\)
−0.657026 + 0.753868i \(0.728186\pi\)
\(74\) 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 −0.297294 0.954786i \(-0.596084\pi\)
0.841465 0.540312i \(-0.181694\pi\)
\(80\) 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 \(-0.318113\pi\)
−0.126377 + 0.991982i \(0.540335\pi\)
\(84\) 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 0.532932 0.846158i \(-0.321090\pi\)
0.999260 0.0384538i \(-0.0122432\pi\)
\(90\) 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 −0.725608 0.688108i \(-0.758442\pi\)
0.446502 0.894783i \(-0.352670\pi\)
\(98\) 0 0
\(99\) −14.8922 3.80566i −1.49672 0.382483i
\(100\) 0 0
\(101\) 5.40951 + 6.44680i 0.538266 + 0.641481i 0.964798 0.262992i \(-0.0847092\pi\)
−0.426532 + 0.904473i \(0.640265\pi\)
\(102\) 0 0
\(103\) 0.918166 + 0.161897i 0.0904696 + 0.0159522i 0.218700 0.975792i \(-0.429818\pi\)
−0.128230 + 0.991744i \(0.540930\pi\)
\(104\) 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 −0.220782 0.975323i \(-0.570861\pi\)
−0.541048 + 0.840992i \(0.681972\pi\)
\(114\) 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 \(-0.595252\pi\)
0.680141 + 0.733081i \(0.261919\pi\)
\(128\) 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 \(-0.313241\pi\)
−0.723971 + 0.689830i \(0.757685\pi\)
\(132\) 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 0.701048 + 0.713115i \(0.252716\pi\)
−0.995415 + 0.0956528i \(0.969506\pi\)
\(138\) 0 0
\(139\) −2.17758 + 2.59514i −0.184700 + 0.220117i −0.850447 0.526060i \(-0.823669\pi\)
0.665747 + 0.746178i \(0.268113\pi\)
\(140\) 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 −0.774886 0.632101i \(-0.782193\pi\)
0.187290 0.982305i \(-0.440030\pi\)
\(150\) 0 0
\(151\) −20.2553 + 3.57156i −1.64835 + 0.290649i −0.919227 0.393728i \(-0.871185\pi\)
−0.729128 + 0.684377i \(0.760074\pi\)
\(152\) 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 0.00154349 + 0.999999i \(0.499509\pi\)
−0.343470 + 0.939164i \(0.611602\pi\)
\(158\) 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 \(-0.992378\pi\)
0.947612 + 0.319423i \(0.103489\pi\)
\(168\) 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 −0.725330 0.688401i \(-0.758313\pi\)
−0.446141 + 0.894963i \(0.647202\pi\)
\(174\) 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 \(-0.982233\pi\)
0.547535 + 0.836783i \(0.315566\pi\)
\(180\) 0 0
\(181\) 10.1241 + 17.5354i 0.752515 + 1.30339i 0.946600 + 0.322410i \(0.104493\pi\)
−0.194085 + 0.980985i \(0.562174\pi\)
\(182\) 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 \(-0.0270211\pi\)
0.708786 + 0.705424i \(0.249243\pi\)
\(192\) 0 0
\(193\) −11.3801 9.54906i −0.819160 0.687357i 0.133615 0.991033i \(-0.457341\pi\)
−0.952775 + 0.303677i \(0.901786\pi\)
\(194\) 0 0
\(195\) 7.24412 + 7.81404i 0.518762 + 0.559575i
\(196\) 0 0
\(197\) −14.3982 + 8.31282i −1.02583 + 0.592264i −0.915788 0.401663i \(-0.868432\pi\)
−0.110043 + 0.993927i \(0.535099\pi\)
\(198\) 0 0
\(199\) 17.6909 + 10.2138i 1.25407 + 0.724039i 0.971916 0.235329i \(-0.0756167\pi\)
0.282157 + 0.959368i \(0.408950\pi\)
\(200\) 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 \(-0.232448\pi\)
0.471924 + 0.881639i \(0.343559\pi\)
\(212\) 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 \(-0.225437\pi\)
−0.772498 + 0.635018i \(0.780993\pi\)
\(224\) 0 0
\(225\) 8.00382 8.19181i 0.533588 0.546121i
\(226\) 0 0
\(227\) −3.55254 20.1475i −0.235790 1.33723i −0.840943 0.541124i \(-0.817999\pi\)
0.605152 0.796110i \(-0.293112\pi\)
\(228\) 0 0
\(229\) 6.31957 2.30013i 0.417609 0.151997i −0.124665 0.992199i \(-0.539786\pi\)
0.542274 + 0.840202i \(0.317563\pi\)
\(230\) 0 0
\(231\) −0.638472 0.0802897i −0.0420084 0.00528267i
\(232\) 0 0
\(233\) 5.00964 + 2.89232i 0.328193 + 0.189482i 0.655038 0.755596i \(-0.272652\pi\)
−0.326846 + 0.945078i \(0.605986\pi\)
\(234\) 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 \(-0.251861\pi\)
−0.578355 + 0.815785i \(0.696305\pi\)
\(240\) 0 0
\(241\) 0.855851 + 0.311504i 0.0551302 + 0.0200657i 0.369438 0.929255i \(-0.379550\pi\)
−0.314308 + 0.949321i \(0.601772\pi\)
\(242\) 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 −0.989105 0.147212i \(-0.952970\pi\)
0.367064 0.930196i \(-0.380363\pi\)
\(252\) 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 0.999955 + 0.00944810i \(0.00300747\pi\)
−0.759937 + 0.649997i \(0.774770\pi\)
\(258\) 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 \(-0.616755\pi\)
0.857024 + 0.515277i \(0.172311\pi\)
\(264\) 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 \(-0.655589\pi\)
0.469564 0.882898i \(-0.344411\pi\)
\(270\) 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 −0.687966 0.725743i \(-0.741496\pi\)
0.595253 + 0.803538i \(0.297052\pi\)
\(278\) 0 0
\(279\) 5.27763 + 10.9832i 0.315963 + 0.657550i
\(280\) 0 0
\(281\) −4.06067 + 0.716005i −0.242239 + 0.0427133i −0.293449 0.955975i \(-0.594803\pi\)
0.0512103 + 0.998688i \(0.483692\pi\)
\(282\) 0 0
\(283\) 2.21065 + 6.07372i 0.131410 + 0.361045i 0.987895 0.155127i \(-0.0495787\pi\)
−0.856485 + 0.516172i \(0.827356\pi\)
\(284\) 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 −0.246915 + 0.969037i \(0.579417\pi\)
−0.911439 + 0.411435i \(0.865028\pi\)
\(294\) 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 −0.995973 0.0896520i \(-0.971425\pi\)
−0.575628 0.817712i \(-0.695242\pi\)
\(308\) 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 \(-0.745227\pi\)
−0.0722083 + 0.997390i \(0.523005\pi\)
\(312\) 0 0
\(313\) 0.513567 + 2.91258i 0.0290285 + 0.164629i 0.995876 0.0907261i \(-0.0289188\pi\)
−0.966847 + 0.255355i \(0.917808\pi\)
\(314\) 0 0
\(315\) 0.235391 0.0233501i 0.0132628 0.00131563i
\(316\) 0 0
\(317\) −14.9386 17.8031i −0.839035 0.999923i −0.999916 0.0129495i \(-0.995878\pi\)
0.160881 0.986974i \(-0.448567\pi\)
\(318\) 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 \(-0.287262\pi\)
−0.880537 + 0.473977i \(0.842818\pi\)
\(332\) 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 −0.101430 0.994843i \(-0.532342\pi\)
0.561773 + 0.827292i \(0.310119\pi\)
\(338\) 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 \(-0.407643\pi\)
−0.893965 + 0.448137i \(0.852088\pi\)
\(348\) 0 0
\(349\) 6.57893 + 2.39453i 0.352162 + 0.128176i 0.512043 0.858960i \(-0.328889\pi\)
−0.159881 + 0.987136i \(0.551111\pi\)
\(350\) 0 0
\(351\) 25.8354 14.0261i 1.37899 0.748656i
\(352\) 0 0
\(353\) −3.61218 + 9.92437i −0.192257 + 0.528221i −0.997942 0.0641228i \(-0.979575\pi\)
0.805685 + 0.592344i \(0.201797\pi\)
\(354\) 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 −0.978983 0.203944i \(-0.934624\pi\)
0.312871 0.949796i \(-0.398709\pi\)
\(360\) 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 \(-0.459145\pi\)
0.459485 + 0.888185i \(0.348034\pi\)
\(368\) 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 −0.816492 0.577357i \(-0.804084\pi\)
0.964719 0.263282i \(-0.0848048\pi\)
\(374\) 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 0.448018 + 0.894024i \(0.352130\pi\)
−0.726774 + 0.686877i \(0.758981\pi\)
\(384\) 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 0.0966646 0.995317i \(-0.469183\pi\)
0.431253 + 0.902231i \(0.358071\pi\)
\(390\) 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 0.914336 0.404957i \(-0.132714\pi\)
−0.807871 + 0.589359i \(0.799380\pi\)
\(398\) 0 0
\(399\) 0.159991 + 0.702358i 0.00800957 + 0.0351619i
\(400\) 0 0
\(401\) 17.6057 20.9817i 0.879189 1.04778i −0.119302 0.992858i \(-0.538066\pi\)
0.998491 0.0549188i \(-0.0174900\pi\)
\(402\) 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 0.652568 0.757731i \(-0.273692\pi\)
−0.632902 + 0.774232i \(0.718136\pi\)
\(410\) 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 \(-0.511383\pi\)
0.614988 + 0.788536i \(0.289161\pi\)
\(420\) 0 0
\(421\) −2.43676 13.8196i −0.118760 0.673524i −0.984819 0.173582i \(-0.944466\pi\)
0.866059 0.499942i \(-0.166645\pi\)
\(422\) 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 0.647507 0.762059i \(-0.275812\pi\)
−0.862920 + 0.505340i \(0.831367\pi\)
\(440\) 0 0
\(441\) 17.3278 + 11.8357i 0.825134 + 0.563606i
\(442\) 0 0
\(443\) 5.26637 + 29.8670i 0.250213 + 1.41903i 0.808069 + 0.589088i \(0.200513\pi\)
−0.557856 + 0.829938i \(0.688376\pi\)
\(444\) 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 0.953402 0.301703i \(-0.0975552\pi\)
0.215418 + 0.976522i \(0.430889\pi\)
\(450\) 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 0.326144 0.945320i \(-0.394251\pi\)
−0.357799 + 0.933799i \(0.616473\pi\)
\(458\) 0 0
\(459\) −21.1911 8.34846i −0.989117 0.389673i
\(460\) 0 0
\(461\) 0.907267 2.49269i 0.0422556 0.116096i −0.916770 0.399415i \(-0.869213\pi\)
0.959026 + 0.283319i \(0.0914354\pi\)
\(462\) 0 0
\(463\) 6.24403 7.44135i 0.290185 0.345829i −0.601181 0.799113i \(-0.705303\pi\)
0.891366 + 0.453284i \(0.149748\pi\)
\(464\) 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 \(-0.317726\pi\)
−0.998798 + 0.0490137i \(0.984392\pi\)
\(468\) 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 \(-0.572208\pi\)
0.920523 + 0.390689i \(0.127763\pi\)
\(480\) 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 −0.389020 0.921229i \(-0.627186\pi\)
0.680638 0.732620i \(-0.261703\pi\)
\(492\) 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 −0.997343 0.0728472i \(-0.976791\pi\)
0.717184 0.696884i \(-0.245431\pi\)
\(500\) 0 0
\(501\) −6.18956 + 2.60599i −0.276529 + 0.116427i
\(502\) 0 0
\(503\) −19.9327 + 34.5244i −0.888754 + 1.53937i −0.0474040 + 0.998876i \(0.515095\pi\)
−0.841350 + 0.540491i \(0.818239\pi\)
\(504\) 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 −0.760949 0.648812i \(-0.775266\pi\)
0.771092 + 0.636723i \(0.219711\pi\)
\(510\) 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 −0.915179 0.403049i \(-0.867951\pi\)
−0.108539 + 0.994092i \(0.534617\pi\)
\(522\) 0 0
\(523\) 24.8958 + 14.3736i 1.08862 + 0.628513i 0.933208 0.359337i \(-0.116997\pi\)
0.155408 + 0.987850i \(0.450331\pi\)
\(524\) 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 \(-0.127440\pi\)
−0.543750 + 0.839247i \(0.682996\pi\)
\(548\) 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 −0.292046 0.956404i \(-0.594336\pi\)
−0.974293 + 0.225283i \(0.927669\pi\)
\(558\) 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 \(-0.207970\pi\)
−0.460736 + 0.887537i \(0.652414\pi\)
\(564\) 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 −0.508989 0.860773i \(-0.669981\pi\)
0.943202 0.332219i \(-0.107797\pi\)
\(570\) 0 0
\(571\) 23.6804 28.2212i 0.990992 1.18102i 0.00751760 0.999972i \(-0.497607\pi\)
0.983475 0.181047i \(-0.0579485\pi\)
\(572\) 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 −0.729685 0.683784i \(-0.760333\pi\)
0.957016 + 0.290034i \(0.0936665\pi\)
\(578\) 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 \(-0.967542\pi\)
−0.0724993 + 0.997368i \(0.523098\pi\)
\(588\) 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 \(-0.989167\pi\)
0.999421 0.0340265i \(-0.0108330\pi\)
\(594\) 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 0.861712 + 0.507398i \(0.169393\pi\)
−0.983285 + 0.182076i \(0.941718\pi\)
\(600\) 0 0
\(601\) −24.6454 + 20.6799i −1.00531 + 0.843552i −0.987711 0.156294i \(-0.950045\pi\)
−0.0175950 + 0.999845i \(0.505601\pi\)
\(602\) 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 −0.919087 0.394055i \(-0.871072\pi\)
0.450768 0.892641i \(-0.351150\pi\)
\(608\) 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 −0.854904 0.518787i \(-0.826384\pi\)
−0.0218308 0.999762i \(-0.506949\pi\)
\(614\) 0 0
\(615\) −1.99692 + 1.85127i −0.0805235 + 0.0746505i
\(616\) 0 0
\(617\) −4.65341 + 5.54572i −0.187339 + 0.223262i −0.851537 0.524295i \(-0.824329\pi\)
0.664198 + 0.747557i \(0.268773\pi\)
\(618\) 0 0
\(619\) 8.37729 23.0164i 0.336712 0.925108i −0.649609 0.760269i \(-0.725067\pi\)
0.986320 0.164839i \(-0.0527105\pi\)
\(620\) 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 \(-0.261909\pi\)
−0.294768 + 0.955569i \(0.595242\pi\)
\(632\) 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 0.591633 0.806207i \(-0.298483\pi\)
−0.896695 + 0.442649i \(0.854039\pi\)
\(642\) 0 0
\(643\) 7.71839 + 1.36096i 0.304384 + 0.0536711i 0.323754 0.946141i \(-0.395055\pi\)
−0.0193702 + 0.999812i \(0.506166\pi\)
\(644\) 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 0.873721 0.486428i \(-0.161700\pi\)
0.654661 + 0.755923i \(0.272811\pi\)
\(654\) 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 0.999912 + 0.0132549i \(0.00421930\pi\)
−0.935077 + 0.354446i \(0.884670\pi\)
\(660\) 0 0
\(661\) −10.0924 + 3.67332i −0.392547 + 0.142876i −0.530750 0.847528i \(-0.678090\pi\)
0.138203 + 0.990404i \(0.455867\pi\)
\(662\) 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 0.331706 0.943383i \(-0.392376\pi\)
−0.352294 + 0.935890i \(0.614598\pi\)
\(674\) 0 0
\(675\) 19.4384 + 3.95566i 0.748186 + 0.152254i
\(676\) 0 0
\(677\) 2.40412 6.60528i 0.0923980 0.253861i −0.884881 0.465816i \(-0.845761\pi\)
0.977279 + 0.211955i \(0.0679830\pi\)
\(678\) 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 0.795701 + 0.605690i \(0.207103\pi\)
0.126693 + 0.991942i \(0.459564\pi\)
\(684\) 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 \(-0.422328\pi\)
0.558917 + 0.829224i \(0.311217\pi\)
\(692\) 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 \(0.0753347\pi\)
−0.972124 + 0.234468i \(0.924665\pi\)
\(702\) 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 −0.660948 0.750432i \(-0.729845\pi\)
0.624259 + 0.781218i \(0.285401\pi\)
\(710\) 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 0.455401 + 0.890287i \(0.349496\pi\)
−0.998711 + 0.0507546i \(0.983837\pi\)
\(720\) 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 \(-0.841456\pi\)
0.980056 + 0.198720i \(0.0636786\pi\)
\(728\) 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 0.681209 0.732089i \(-0.261455\pi\)
−0.602676 + 0.797986i \(0.705899\pi\)
\(734\) 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 \(-0.488435\pi\)
−0.847292 + 0.531128i \(0.821768\pi\)
\(740\) 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 \(-0.598505\pi\)
0.378958 + 0.925414i \(0.376282\pi\)
\(744\) 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 \(-0.463724\pi\)
−0.232940 + 0.972491i \(0.574835\pi\)
\(752\) 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 0.0532815 0.998580i \(-0.483032\pi\)
−0.291466 + 0.956581i \(0.594143\pi\)
\(762\) 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 0.447487 0.894290i \(-0.352319\pi\)
0.917634 + 0.397427i \(0.130097\pi\)
\(770\) 0 0
\(771\) −11.7723 + 15.5278i −0.423970 + 0.559219i
\(772\) 0 0
\(773\) 15.8074 + 9.12640i 0.568552 + 0.328254i 0.756571 0.653912i \(-0.226873\pi\)
−0.188019 + 0.982165i \(0.560207\pi\)
\(774\) 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 \(-0.665378\pi\)
0.941070 + 0.338213i \(0.109822\pi\)
\(788\) 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