Properties

Label 432.2.be.b.47.2
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 47.2
Character \(\chi\) \(=\) 432.47
Dual form 432.2.be.b.239.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.59623 - 0.672336i) q^{3} +(4.18690 - 0.738263i) q^{5} +(1.26944 - 1.51285i) q^{7} +(2.09593 + 2.14641i) q^{9} +O(q^{10})\) \(q+(-1.59623 - 0.672336i) q^{3} +(4.18690 - 0.738263i) q^{5} +(1.26944 - 1.51285i) q^{7} +(2.09593 + 2.14641i) q^{9} +(-0.313474 + 1.77780i) q^{11} +(-3.16732 - 1.15281i) q^{13} +(-7.17963 - 1.63656i) q^{15} +(-1.51308 + 0.873578i) q^{17} +(3.62765 + 2.09442i) q^{19} +(-3.04346 + 1.56138i) q^{21} +(5.40902 - 4.53870i) q^{23} +(12.2866 - 4.47197i) q^{25} +(-1.90249 - 4.83534i) q^{27} +(-3.00752 - 8.26311i) q^{29} +(3.17218 + 3.78046i) q^{31} +(1.69565 - 2.62702i) q^{33} +(4.19811 - 7.27134i) q^{35} +(0.864428 + 1.49723i) q^{37} +(4.28071 + 3.96966i) q^{39} +(-1.58140 + 4.34487i) q^{41} +(-9.92458 - 1.74997i) q^{43} +(10.3601 + 7.43946i) q^{45} +(-2.63291 - 2.20928i) q^{47} +(0.538276 + 3.05271i) q^{49} +(3.00257 - 0.377137i) q^{51} -0.511832i q^{53} +7.67488i q^{55} +(-4.38242 - 5.78219i) q^{57} +(-1.75988 - 9.98076i) q^{59} +(0.752671 + 0.631566i) q^{61} +(5.90785 - 0.446106i) q^{63} +(-14.1123 - 2.48838i) q^{65} +(-4.10742 + 11.2851i) q^{67} +(-11.6856 + 3.60816i) q^{69} +(1.03319 + 1.78955i) q^{71} +(1.31302 - 2.27422i) q^{73} +(-22.6190 - 1.12243i) q^{75} +(2.29161 + 2.73104i) q^{77} +(6.02177 + 16.5447i) q^{79} +(-0.214158 + 8.99745i) q^{81} +(3.45879 - 1.25890i) q^{83} +(-5.69019 + 4.77464i) q^{85} +(-0.754866 + 15.2119i) q^{87} +(-6.46750 - 3.73401i) q^{89} +(-5.76474 + 3.32827i) q^{91} +(-2.52181 - 8.16728i) q^{93} +(16.7348 + 6.09098i) q^{95} +(-0.250759 + 1.42213i) q^{97} +(-4.47290 + 3.05329i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 3q^{5} + 6q^{9} + O(q^{10}) \) \( 36q + 3q^{5} + 6q^{9} - 18q^{11} + 9q^{15} + 18q^{21} - 9q^{25} + 30q^{29} + 27q^{31} + 27q^{33} + 27q^{35} - 45q^{39} + 18q^{41} + 27q^{45} + 45q^{47} - 63q^{51} - 9q^{57} + 54q^{59} - 63q^{63} - 57q^{65} - 63q^{69} + 36q^{71} + 9q^{73} - 45q^{75} - 81q^{77} - 54q^{81} - 27q^{83} - 36q^{85} + 45q^{87} - 63q^{89} + 27q^{91} - 63q^{93} - 72q^{95} + 99q^{99} + O(q^{100}) \)

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
\(3\) −1.59623 0.672336i −0.921586 0.388173i
\(4\) 0 0
\(5\) 4.18690 0.738263i 1.87244 0.330161i 0.882348 0.470597i \(-0.155961\pi\)
0.990090 + 0.140435i \(0.0448502\pi\)
\(6\) 0 0
\(7\) 1.26944 1.51285i 0.479801 0.571805i −0.470792 0.882244i \(-0.656032\pi\)
0.950593 + 0.310439i \(0.100476\pi\)
\(8\) 0 0
\(9\) 2.09593 + 2.14641i 0.698643 + 0.715470i
\(10\) 0 0
\(11\) −0.313474 + 1.77780i −0.0945158 + 0.536026i 0.900379 + 0.435107i \(0.143289\pi\)
−0.994895 + 0.100919i \(0.967822\pi\)
\(12\) 0 0
\(13\) −3.16732 1.15281i −0.878456 0.319732i −0.136870 0.990589i \(-0.543704\pi\)
−0.741587 + 0.670857i \(0.765926\pi\)
\(14\) 0 0
\(15\) −7.17963 1.63656i −1.85377 0.422558i
\(16\) 0 0
\(17\) −1.51308 + 0.873578i −0.366976 + 0.211874i −0.672137 0.740427i \(-0.734623\pi\)
0.305160 + 0.952301i \(0.401290\pi\)
\(18\) 0 0
\(19\) 3.62765 + 2.09442i 0.832240 + 0.480494i 0.854619 0.519256i \(-0.173791\pi\)
−0.0223793 + 0.999750i \(0.507124\pi\)
\(20\) 0 0
\(21\) −3.04346 + 1.56138i −0.664138 + 0.340722i
\(22\) 0 0
\(23\) 5.40902 4.53870i 1.12786 0.946385i 0.128883 0.991660i \(-0.458861\pi\)
0.998975 + 0.0452747i \(0.0144163\pi\)
\(24\) 0 0
\(25\) 12.2866 4.47197i 2.45733 0.894393i
\(26\) 0 0
\(27\) −1.90249 4.83534i −0.366134 0.930562i
\(28\) 0 0
\(29\) −3.00752 8.26311i −0.558483 1.53442i −0.821838 0.569721i \(-0.807051\pi\)
0.263355 0.964699i \(-0.415171\pi\)
\(30\) 0 0
\(31\) 3.17218 + 3.78046i 0.569741 + 0.678991i 0.971578 0.236720i \(-0.0760725\pi\)
−0.401837 + 0.915711i \(0.631628\pi\)
\(32\) 0 0
\(33\) 1.69565 2.62702i 0.295175 0.457306i
\(34\) 0 0
\(35\) 4.19811 7.27134i 0.709611 1.22908i
\(36\) 0 0
\(37\) 0.864428 + 1.49723i 0.142111 + 0.246144i 0.928291 0.371854i \(-0.121278\pi\)
−0.786180 + 0.617997i \(0.787944\pi\)
\(38\) 0 0
\(39\) 4.28071 + 3.96966i 0.685462 + 0.635654i
\(40\) 0 0
\(41\) −1.58140 + 4.34487i −0.246974 + 0.678554i 0.752820 + 0.658227i \(0.228693\pi\)
−0.999793 + 0.0203276i \(0.993529\pi\)
\(42\) 0 0
\(43\) −9.92458 1.74997i −1.51348 0.266868i −0.645616 0.763662i \(-0.723399\pi\)
−0.867869 + 0.496794i \(0.834510\pi\)
\(44\) 0 0
\(45\) 10.3601 + 7.43946i 1.54439 + 1.10901i
\(46\) 0 0
\(47\) −2.63291 2.20928i −0.384050 0.322256i 0.430240 0.902715i \(-0.358429\pi\)
−0.814290 + 0.580458i \(0.802873\pi\)
\(48\) 0 0
\(49\) 0.538276 + 3.05271i 0.0768965 + 0.436102i
\(50\) 0 0
\(51\) 3.00257 0.377137i 0.420444 0.0528097i
\(52\) 0 0
\(53\) 0.511832i 0.0703056i −0.999382 0.0351528i \(-0.988808\pi\)
0.999382 0.0351528i \(-0.0111918\pi\)
\(54\) 0 0
\(55\) 7.67488i 1.03488i
\(56\) 0 0
\(57\) −4.38242 5.78219i −0.580466 0.765870i
\(58\) 0 0
\(59\) −1.75988 9.98076i −0.229116 1.29938i −0.854657 0.519193i \(-0.826233\pi\)
0.625541 0.780191i \(-0.284878\pi\)
\(60\) 0 0
\(61\) 0.752671 + 0.631566i 0.0963697 + 0.0808638i 0.689700 0.724096i \(-0.257743\pi\)
−0.593330 + 0.804959i \(0.702187\pi\)
\(62\) 0 0
\(63\) 5.90785 0.446106i 0.744320 0.0562041i
\(64\) 0 0
\(65\) −14.1123 2.48838i −1.75042 0.308646i
\(66\) 0 0
\(67\) −4.10742 + 11.2851i −0.501802 + 1.37869i 0.387712 + 0.921780i \(0.373265\pi\)
−0.889514 + 0.456908i \(0.848957\pi\)
\(68\) 0 0
\(69\) −11.6856 + 3.60816i −1.40678 + 0.434372i
\(70\) 0 0
\(71\) 1.03319 + 1.78955i 0.122618 + 0.212380i 0.920799 0.390037i \(-0.127538\pi\)
−0.798182 + 0.602417i \(0.794204\pi\)
\(72\) 0 0
\(73\) 1.31302 2.27422i 0.153678 0.266178i −0.778899 0.627149i \(-0.784222\pi\)
0.932577 + 0.360972i \(0.117555\pi\)
\(74\) 0 0
\(75\) −22.6190 1.12243i −2.61182 0.129607i
\(76\) 0 0
\(77\) 2.29161 + 2.73104i 0.261154 + 0.311231i
\(78\) 0 0
\(79\) 6.02177 + 16.5447i 0.677502 + 1.86142i 0.468369 + 0.883533i \(0.344842\pi\)
0.209133 + 0.977887i \(0.432936\pi\)
\(80\) 0 0
\(81\) −0.214158 + 8.99745i −0.0237953 + 0.999717i
\(82\) 0 0
\(83\) 3.45879 1.25890i 0.379652 0.138182i −0.145143 0.989411i \(-0.546364\pi\)
0.524795 + 0.851229i \(0.324142\pi\)
\(84\) 0 0
\(85\) −5.69019 + 4.77464i −0.617188 + 0.517882i
\(86\) 0 0
\(87\) −0.754866 + 15.2119i −0.0809301 + 1.63089i
\(88\) 0 0
\(89\) −6.46750 3.73401i −0.685554 0.395805i 0.116390 0.993204i \(-0.462868\pi\)
−0.801944 + 0.597399i \(0.796201\pi\)
\(90\) 0 0
\(91\) −5.76474 + 3.32827i −0.604309 + 0.348898i
\(92\) 0 0
\(93\) −2.52181 8.16728i −0.261500 0.846907i
\(94\) 0 0
\(95\) 16.7348 + 6.09098i 1.71696 + 0.624922i
\(96\) 0 0
\(97\) −0.250759 + 1.42213i −0.0254607 + 0.144395i −0.994888 0.100983i \(-0.967801\pi\)
0.969427 + 0.245378i \(0.0789122\pi\)
\(98\) 0 0
\(99\) −4.47290 + 3.05329i −0.449543 + 0.306868i
\(100\) 0 0
\(101\) −4.74078 + 5.64984i −0.471725 + 0.562180i −0.948472 0.316860i \(-0.897371\pi\)
0.476747 + 0.879041i \(0.341816\pi\)
\(102\) 0 0
\(103\) 12.8583 2.26726i 1.26696 0.223399i 0.500526 0.865721i \(-0.333140\pi\)
0.766435 + 0.642322i \(0.222029\pi\)
\(104\) 0 0
\(105\) −11.5900 + 8.78423i −1.13106 + 0.857253i
\(106\) 0 0
\(107\) −9.16482 −0.885997 −0.442998 0.896522i \(-0.646085\pi\)
−0.442998 + 0.896522i \(0.646085\pi\)
\(108\) 0 0
\(109\) −12.4898 −1.19630 −0.598151 0.801383i \(-0.704098\pi\)
−0.598151 + 0.801383i \(0.704098\pi\)
\(110\) 0 0
\(111\) −0.373187 2.97112i −0.0354213 0.282006i
\(112\) 0 0
\(113\) −6.38278 + 1.12546i −0.600441 + 0.105874i −0.465603 0.884994i \(-0.654163\pi\)
−0.134838 + 0.990868i \(0.543051\pi\)
\(114\) 0 0
\(115\) 19.2962 22.9964i 1.79938 2.14442i
\(116\) 0 0
\(117\) −4.16407 9.21457i −0.384969 0.851888i
\(118\) 0 0
\(119\) −0.599163 + 3.39802i −0.0549252 + 0.311496i
\(120\) 0 0
\(121\) 7.27432 + 2.64764i 0.661302 + 0.240694i
\(122\) 0 0
\(123\) 5.44550 5.87219i 0.491004 0.529478i
\(124\) 0 0
\(125\) 29.7319 17.1657i 2.65930 1.53535i
\(126\) 0 0
\(127\) −8.67356 5.00768i −0.769654 0.444360i 0.0630972 0.998007i \(-0.479902\pi\)
−0.832751 + 0.553647i \(0.813236\pi\)
\(128\) 0 0
\(129\) 14.6654 + 9.46602i 1.29122 + 0.833436i
\(130\) 0 0
\(131\) −8.79708 + 7.38162i −0.768604 + 0.644936i −0.940351 0.340206i \(-0.889503\pi\)
0.171747 + 0.985141i \(0.445059\pi\)
\(132\) 0 0
\(133\) 7.77362 2.82937i 0.674059 0.245337i
\(134\) 0 0
\(135\) −11.5353 18.8406i −0.992799 1.62154i
\(136\) 0 0
\(137\) 1.13684 + 3.12344i 0.0971268 + 0.266854i 0.978735 0.205128i \(-0.0657611\pi\)
−0.881608 + 0.471982i \(0.843539\pi\)
\(138\) 0 0
\(139\) 6.27514 + 7.47842i 0.532251 + 0.634311i 0.963432 0.267954i \(-0.0863475\pi\)
−0.431181 + 0.902265i \(0.641903\pi\)
\(140\) 0 0
\(141\) 2.71737 + 5.29673i 0.228844 + 0.446065i
\(142\) 0 0
\(143\) 3.04233 5.26947i 0.254413 0.440656i
\(144\) 0 0
\(145\) −18.6926 32.3764i −1.55233 2.68872i
\(146\) 0 0
\(147\) 1.19323 5.23475i 0.0984163 0.431755i
\(148\) 0 0
\(149\) −6.99419 + 19.2164i −0.572986 + 1.57427i 0.226774 + 0.973947i \(0.427182\pi\)
−0.799761 + 0.600319i \(0.795040\pi\)
\(150\) 0 0
\(151\) −10.4203 1.83738i −0.847990 0.149524i −0.267265 0.963623i \(-0.586120\pi\)
−0.580725 + 0.814100i \(0.697231\pi\)
\(152\) 0 0
\(153\) −5.04637 1.41674i −0.407975 0.114536i
\(154\) 0 0
\(155\) 16.0726 + 13.4865i 1.29098 + 1.08326i
\(156\) 0 0
\(157\) 3.76938 + 21.3772i 0.300829 + 1.70609i 0.642515 + 0.766273i \(0.277891\pi\)
−0.341686 + 0.939814i \(0.610998\pi\)
\(158\) 0 0
\(159\) −0.344123 + 0.817005i −0.0272907 + 0.0647927i
\(160\) 0 0
\(161\) 13.9446i 1.09899i
\(162\) 0 0
\(163\) 1.10221i 0.0863315i −0.999068 0.0431658i \(-0.986256\pi\)
0.999068 0.0431658i \(-0.0137444\pi\)
\(164\) 0 0
\(165\) 5.16010 12.2509i 0.401713 0.953732i
\(166\) 0 0
\(167\) 1.82002 + 10.3218i 0.140837 + 0.798727i 0.970616 + 0.240634i \(0.0773555\pi\)
−0.829779 + 0.558092i \(0.811533\pi\)
\(168\) 0 0
\(169\) −1.25564 1.05361i −0.0965879 0.0810468i
\(170\) 0 0
\(171\) 3.10780 + 12.1762i 0.237660 + 0.931136i
\(172\) 0 0
\(173\) −0.239692 0.0422642i −0.0182235 0.00321329i 0.164529 0.986372i \(-0.447390\pi\)
−0.182752 + 0.983159i \(0.558501\pi\)
\(174\) 0 0
\(175\) 8.83165 24.2648i 0.667610 1.83424i
\(176\) 0 0
\(177\) −3.90124 + 17.1149i −0.293235 + 1.28643i
\(178\) 0 0
\(179\) −0.372275 0.644799i −0.0278251 0.0481946i 0.851778 0.523904i \(-0.175525\pi\)
−0.879603 + 0.475709i \(0.842191\pi\)
\(180\) 0 0
\(181\) 8.83351 15.3001i 0.656590 1.13725i −0.324903 0.945747i \(-0.605332\pi\)
0.981493 0.191500i \(-0.0613351\pi\)
\(182\) 0 0
\(183\) −0.776815 1.51418i −0.0574239 0.111931i
\(184\) 0 0
\(185\) 4.72463 + 5.63059i 0.347361 + 0.413969i
\(186\) 0 0
\(187\) −1.07873 2.96380i −0.0788848 0.216734i
\(188\) 0 0
\(189\) −9.73025 3.25997i −0.707772 0.237128i
\(190\) 0 0
\(191\) −9.20584 + 3.35065i −0.666111 + 0.242445i −0.652873 0.757468i \(-0.726436\pi\)
−0.0132384 + 0.999912i \(0.504214\pi\)
\(192\) 0 0
\(193\) −6.56436 + 5.50815i −0.472513 + 0.396486i −0.847710 0.530459i \(-0.822019\pi\)
0.375197 + 0.926945i \(0.377575\pi\)
\(194\) 0 0
\(195\) 20.8535 + 13.4603i 1.49335 + 0.963909i
\(196\) 0 0
\(197\) 1.15257 + 0.665435i 0.0821170 + 0.0474103i 0.540496 0.841346i \(-0.318237\pi\)
−0.458379 + 0.888757i \(0.651570\pi\)
\(198\) 0 0
\(199\) −14.2785 + 8.24368i −1.01217 + 0.584379i −0.911828 0.410573i \(-0.865329\pi\)
−0.100347 + 0.994953i \(0.531995\pi\)
\(200\) 0 0
\(201\) 14.1438 15.2520i 0.997623 1.07579i
\(202\) 0 0
\(203\) −16.3187 5.93953i −1.14535 0.416873i
\(204\) 0 0
\(205\) −3.41352 + 19.3590i −0.238410 + 1.35209i
\(206\) 0 0
\(207\) 21.0788 + 2.09717i 1.46508 + 0.145763i
\(208\) 0 0
\(209\) −4.86063 + 5.79268i −0.336217 + 0.400688i
\(210\) 0 0
\(211\) −11.8106 + 2.08253i −0.813078 + 0.143368i −0.564701 0.825296i \(-0.691008\pi\)
−0.248377 + 0.968663i \(0.579897\pi\)
\(212\) 0 0
\(213\) −0.446046 3.55119i −0.0305626 0.243323i
\(214\) 0 0
\(215\) −42.8452 −2.92202
\(216\) 0 0
\(217\) 9.74617 0.661613
\(218\) 0 0
\(219\) −3.62493 + 2.74740i −0.244950 + 0.185652i
\(220\) 0 0
\(221\) 5.79948 1.02260i 0.390115 0.0687878i
\(222\) 0 0
\(223\) −6.09692 + 7.26603i −0.408280 + 0.486569i −0.930526 0.366226i \(-0.880650\pi\)
0.522246 + 0.852795i \(0.325094\pi\)
\(224\) 0 0
\(225\) 35.3506 + 16.9992i 2.35671 + 1.13328i
\(226\) 0 0
\(227\) 1.39601 7.91718i 0.0926565 0.525481i −0.902784 0.430095i \(-0.858480\pi\)
0.995440 0.0953866i \(-0.0304087\pi\)
\(228\) 0 0
\(229\) 9.27154 + 3.37456i 0.612680 + 0.222997i 0.629676 0.776858i \(-0.283188\pi\)
−0.0169953 + 0.999856i \(0.505410\pi\)
\(230\) 0 0
\(231\) −1.82178 5.90011i −0.119864 0.388199i
\(232\) 0 0
\(233\) 17.5103 10.1096i 1.14714 0.662302i 0.198952 0.980009i \(-0.436246\pi\)
0.948189 + 0.317707i \(0.102913\pi\)
\(234\) 0 0
\(235\) −12.6548 7.30624i −0.825507 0.476606i
\(236\) 0 0
\(237\) 1.51142 30.4578i 0.0981771 1.97845i
\(238\) 0 0
\(239\) 21.0130 17.6320i 1.35922 1.14052i 0.382993 0.923751i \(-0.374893\pi\)
0.976224 0.216766i \(-0.0695510\pi\)
\(240\) 0 0
\(241\) 7.83906 2.85318i 0.504958 0.183790i −0.0769646 0.997034i \(-0.524523\pi\)
0.581923 + 0.813244i \(0.302301\pi\)
\(242\) 0 0
\(243\) 6.39115 14.2181i 0.409993 0.912089i
\(244\) 0 0
\(245\) 4.50741 + 12.3840i 0.287968 + 0.791186i
\(246\) 0 0
\(247\) −9.07545 10.8157i −0.577457 0.688186i
\(248\) 0 0
\(249\) −6.36744 0.315973i −0.403520 0.0200240i
\(250\) 0 0
\(251\) 10.0064 17.3316i 0.631600 1.09396i −0.355624 0.934629i \(-0.615732\pi\)
0.987225 0.159335i \(-0.0509349\pi\)
\(252\) 0 0
\(253\) 6.37331 + 11.0389i 0.400687 + 0.694009i
\(254\) 0 0
\(255\) 12.2930 3.79572i 0.769820 0.237697i
\(256\) 0 0
\(257\) 0.768135 2.11043i 0.0479150 0.131645i −0.913427 0.407003i \(-0.866574\pi\)
0.961342 + 0.275357i \(0.0887962\pi\)
\(258\) 0 0
\(259\) 3.36243 + 0.592887i 0.208931 + 0.0368402i
\(260\) 0 0
\(261\) 11.4325 23.7743i 0.707651 1.47159i
\(262\) 0 0
\(263\) −9.74693 8.17865i −0.601022 0.504317i 0.290752 0.956798i \(-0.406094\pi\)
−0.891774 + 0.452481i \(0.850539\pi\)
\(264\) 0 0
\(265\) −0.377867 2.14299i −0.0232122 0.131643i
\(266\) 0 0
\(267\) 7.81314 + 10.3087i 0.478156 + 0.630882i
\(268\) 0 0
\(269\) 13.9356i 0.849668i 0.905271 + 0.424834i \(0.139668\pi\)
−0.905271 + 0.424834i \(0.860332\pi\)
\(270\) 0 0
\(271\) 1.32883i 0.0807208i −0.999185 0.0403604i \(-0.987149\pi\)
0.999185 0.0403604i \(-0.0128506\pi\)
\(272\) 0 0
\(273\) 11.4396 1.43687i 0.692356 0.0869631i
\(274\) 0 0
\(275\) 4.09872 + 23.2450i 0.247162 + 1.40172i
\(276\) 0 0
\(277\) 5.21107 + 4.37261i 0.313103 + 0.262724i 0.785773 0.618515i \(-0.212265\pi\)
−0.472670 + 0.881239i \(0.656710\pi\)
\(278\) 0 0
\(279\) −1.46575 + 14.7324i −0.0877521 + 0.882005i
\(280\) 0 0
\(281\) −3.97579 0.701039i −0.237176 0.0418205i 0.0537967 0.998552i \(-0.482868\pi\)
−0.290972 + 0.956731i \(0.593979\pi\)
\(282\) 0 0
\(283\) 0.187770 0.515894i 0.0111618 0.0306667i −0.933987 0.357308i \(-0.883695\pi\)
0.945148 + 0.326641i \(0.105917\pi\)
\(284\) 0 0
\(285\) −22.6175 20.9741i −1.33975 1.24240i
\(286\) 0 0
\(287\) 4.56566 + 7.90796i 0.269502 + 0.466792i
\(288\) 0 0
\(289\) −6.97372 + 12.0788i −0.410219 + 0.710520i
\(290\) 0 0
\(291\) 1.35642 2.10145i 0.0795146 0.123189i
\(292\) 0 0
\(293\) 11.7794 + 14.0382i 0.688163 + 0.820121i 0.991132 0.132880i \(-0.0424224\pi\)
−0.302969 + 0.953000i \(0.597978\pi\)
\(294\) 0 0
\(295\) −14.7369 40.4892i −0.858013 2.35737i
\(296\) 0 0
\(297\) 9.19264 1.86648i 0.533411 0.108304i
\(298\) 0 0
\(299\) −22.3643 + 8.13995i −1.29336 + 0.470746i
\(300\) 0 0
\(301\) −15.2461 + 12.7930i −0.878769 + 0.737374i
\(302\) 0 0
\(303\) 11.3660 5.83108i 0.652959 0.334987i
\(304\) 0 0
\(305\) 3.61762 + 2.08863i 0.207144 + 0.119595i
\(306\) 0 0
\(307\) 11.9994 6.92784i 0.684841 0.395393i −0.116836 0.993151i \(-0.537275\pi\)
0.801676 + 0.597758i \(0.203942\pi\)
\(308\) 0 0
\(309\) −22.0491 5.02599i −1.25433 0.285918i
\(310\) 0 0
\(311\) 3.49020 + 1.27033i 0.197911 + 0.0720338i 0.439074 0.898451i \(-0.355307\pi\)
−0.241163 + 0.970485i \(0.577529\pi\)
\(312\) 0 0
\(313\) 3.96289 22.4747i 0.223996 1.27034i −0.640599 0.767875i \(-0.721314\pi\)
0.864595 0.502469i \(-0.167575\pi\)
\(314\) 0 0
\(315\) 24.4062 6.22935i 1.37514 0.350984i
\(316\) 0 0
\(317\) 11.1228 13.2557i 0.624720 0.744512i −0.357155 0.934045i \(-0.616253\pi\)
0.981874 + 0.189533i \(0.0606975\pi\)
\(318\) 0 0
\(319\) 15.6329 2.75650i 0.875275 0.154335i
\(320\) 0 0
\(321\) 14.6292 + 6.16184i 0.816523 + 0.343920i
\(322\) 0 0
\(323\) −7.31857 −0.407216
\(324\) 0 0
\(325\) −44.0710 −2.44462
\(326\) 0 0
\(327\) 19.9366 + 8.39731i 1.10250 + 0.464372i
\(328\) 0 0
\(329\) −6.68463 + 1.17868i −0.368536 + 0.0649828i
\(330\) 0 0
\(331\) −4.63111 + 5.51914i −0.254549 + 0.303359i −0.878152 0.478382i \(-0.841224\pi\)
0.623603 + 0.781741i \(0.285668\pi\)
\(332\) 0 0
\(333\) −1.40190 + 4.99351i −0.0768235 + 0.273643i
\(334\) 0 0
\(335\) −8.86603 + 50.2817i −0.484403 + 2.74718i
\(336\) 0 0
\(337\) −23.8554 8.68267i −1.29949 0.472975i −0.402659 0.915350i \(-0.631914\pi\)
−0.896830 + 0.442375i \(0.854136\pi\)
\(338\) 0 0
\(339\) 10.9451 + 2.49488i 0.594456 + 0.135503i
\(340\) 0 0
\(341\) −7.71529 + 4.45443i −0.417806 + 0.241221i
\(342\) 0 0
\(343\) 17.2738 + 9.97301i 0.932695 + 0.538492i
\(344\) 0 0
\(345\) −46.2626 + 23.7341i −2.49070 + 1.27780i
\(346\) 0 0
\(347\) −7.38189 + 6.19414i −0.396281 + 0.332519i −0.819054 0.573717i \(-0.805501\pi\)
0.422773 + 0.906235i \(0.361057\pi\)
\(348\) 0 0
\(349\) −1.04043 + 0.378686i −0.0556930 + 0.0202706i −0.369716 0.929145i \(-0.620545\pi\)
0.314023 + 0.949415i \(0.398323\pi\)
\(350\) 0 0
\(351\) 0.451552 + 17.5083i 0.0241021 + 0.934523i
\(352\) 0 0
\(353\) −10.9418 30.0625i −0.582375 1.60006i −0.784109 0.620623i \(-0.786880\pi\)
0.201734 0.979440i \(-0.435342\pi\)
\(354\) 0 0
\(355\) 5.64704 + 6.72988i 0.299714 + 0.357185i
\(356\) 0 0
\(357\) 3.24102 5.02120i 0.171533 0.265750i
\(358\) 0 0
\(359\) 8.37501 14.5059i 0.442016 0.765595i −0.555823 0.831301i \(-0.687597\pi\)
0.997839 + 0.0657061i \(0.0209300\pi\)
\(360\) 0 0
\(361\) −0.726778 1.25882i −0.0382515 0.0662535i
\(362\) 0 0
\(363\) −9.83142 9.11704i −0.516016 0.478520i
\(364\) 0 0
\(365\) 3.81852 10.4913i 0.199870 0.549140i
\(366\) 0 0
\(367\) −4.44634 0.784010i −0.232097 0.0409250i 0.0563897 0.998409i \(-0.482041\pi\)
−0.288487 + 0.957484i \(0.593152\pi\)
\(368\) 0 0
\(369\) −12.6404 + 5.71220i −0.658032 + 0.297365i
\(370\) 0 0
\(371\) −0.774328 0.649738i −0.0402011 0.0337327i
\(372\) 0 0
\(373\) −2.72449 15.4513i −0.141069 0.800040i −0.970440 0.241342i \(-0.922412\pi\)
0.829372 0.558698i \(-0.188699\pi\)
\(374\) 0 0
\(375\) −59.0002 + 7.41070i −3.04676 + 0.382687i
\(376\) 0 0
\(377\) 29.6390i 1.52649i
\(378\) 0 0
\(379\) 15.3891i 0.790485i −0.918577 0.395242i \(-0.870661\pi\)
0.918577 0.395242i \(-0.129339\pi\)
\(380\) 0 0
\(381\) 10.4782 + 13.8250i 0.536814 + 0.708275i
\(382\) 0 0
\(383\) −3.92194 22.2424i −0.200402 1.13654i −0.904513 0.426446i \(-0.859765\pi\)
0.704111 0.710090i \(-0.251346\pi\)
\(384\) 0 0
\(385\) 11.6110 + 9.74277i 0.591750 + 0.496537i
\(386\) 0 0
\(387\) −17.0451 24.9700i −0.866450 1.26930i
\(388\) 0 0
\(389\) −13.2621 2.33846i −0.672414 0.118565i −0.172992 0.984923i \(-0.555343\pi\)
−0.499423 + 0.866358i \(0.666455\pi\)
\(390\) 0 0
\(391\) −4.21937 + 11.5926i −0.213383 + 0.586264i
\(392\) 0 0
\(393\) 19.0051 5.86822i 0.958682 0.296012i
\(394\) 0 0
\(395\) 37.4268 + 64.8252i 1.88315 + 3.26171i
\(396\) 0 0
\(397\) −1.61332 + 2.79436i −0.0809704 + 0.140245i −0.903667 0.428236i \(-0.859135\pi\)
0.822697 + 0.568481i \(0.192469\pi\)
\(398\) 0 0
\(399\) −14.3108 0.710149i −0.716437 0.0355519i
\(400\) 0 0
\(401\) 18.1787 + 21.6646i 0.907803 + 1.08188i 0.996312 + 0.0858023i \(0.0273453\pi\)
−0.0885090 + 0.996075i \(0.528210\pi\)
\(402\) 0 0
\(403\) −5.68917 15.6309i −0.283398 0.778628i
\(404\) 0 0
\(405\) 5.74583 + 37.8295i 0.285513 + 1.87976i
\(406\) 0 0
\(407\) −2.93275 + 1.06743i −0.145371 + 0.0529108i
\(408\) 0 0
\(409\) −4.48887 + 3.76661i −0.221961 + 0.186247i −0.746987 0.664839i \(-0.768500\pi\)
0.525026 + 0.851086i \(0.324056\pi\)
\(410\) 0 0
\(411\) 0.285338 5.75009i 0.0140747 0.283631i
\(412\) 0 0
\(413\) −17.3335 10.0075i −0.852925 0.492436i
\(414\) 0 0
\(415\) 13.5522 7.82437i 0.665252 0.384083i
\(416\) 0 0
\(417\) −4.98859 16.1563i −0.244292 0.791178i
\(418\) 0 0
\(419\) 10.0245 + 3.64864i 0.489731 + 0.178248i 0.575070 0.818105i \(-0.304975\pi\)
−0.0853386 + 0.996352i \(0.527197\pi\)
\(420\) 0 0
\(421\) 3.69487 20.9547i 0.180077 1.02127i −0.752042 0.659116i \(-0.770931\pi\)
0.932119 0.362153i \(-0.117958\pi\)
\(422\) 0 0
\(423\) −0.776387 10.2818i −0.0377492 0.499919i
\(424\) 0 0
\(425\) −14.6841 + 17.4998i −0.712282 + 0.848864i
\(426\) 0 0
\(427\) 1.91093 0.336949i 0.0924766 0.0163061i
\(428\) 0 0
\(429\) −8.39913 + 6.36585i −0.405514 + 0.307346i
\(430\) 0 0
\(431\) −16.3332 −0.786744 −0.393372 0.919379i \(-0.628691\pi\)
−0.393372 + 0.919379i \(0.628691\pi\)
\(432\) 0 0
\(433\) 36.2969 1.74432 0.872159 0.489222i \(-0.162719\pi\)
0.872159 + 0.489222i \(0.162719\pi\)
\(434\) 0 0
\(435\) 8.06986 + 64.2481i 0.386920 + 3.08046i
\(436\) 0 0
\(437\) 29.1280 5.13605i 1.39338 0.245691i
\(438\) 0 0
\(439\) −11.7942 + 14.0558i −0.562906 + 0.670845i −0.970159 0.242470i \(-0.922042\pi\)
0.407253 + 0.913315i \(0.366487\pi\)
\(440\) 0 0
\(441\) −5.42419 + 7.55363i −0.258295 + 0.359697i
\(442\) 0 0
\(443\) 1.71016 9.69879i 0.0812521 0.460804i −0.916850 0.399231i \(-0.869277\pi\)
0.998103 0.0615728i \(-0.0196116\pi\)
\(444\) 0 0
\(445\) −29.8355 10.8592i −1.41434 0.514776i
\(446\) 0 0
\(447\) 24.0842 25.9714i 1.13914 1.22840i
\(448\) 0 0
\(449\) −13.3593 + 7.71300i −0.630465 + 0.363999i −0.780932 0.624616i \(-0.785255\pi\)
0.150467 + 0.988615i \(0.451922\pi\)
\(450\) 0 0
\(451\) −7.22856 4.17341i −0.340380 0.196518i
\(452\) 0 0
\(453\) 15.3979 + 9.93881i 0.723455 + 0.466966i
\(454\) 0 0
\(455\) −21.6792 + 18.1910i −1.01634 + 0.852809i
\(456\) 0 0
\(457\) −18.6347 + 6.78248i −0.871695 + 0.317271i −0.738853 0.673866i \(-0.764632\pi\)
−0.132841 + 0.991137i \(0.542410\pi\)
\(458\) 0 0
\(459\) 7.10267 + 5.65430i 0.331524 + 0.263920i
\(460\) 0 0
\(461\) 1.17082 + 3.21680i 0.0545306 + 0.149822i 0.963967 0.266021i \(-0.0857090\pi\)
−0.909437 + 0.415842i \(0.863487\pi\)
\(462\) 0 0
\(463\) −8.06961 9.61699i −0.375027 0.446939i 0.545211 0.838299i \(-0.316449\pi\)
−0.920238 + 0.391359i \(0.872005\pi\)
\(464\) 0 0
\(465\) −16.5882 32.3338i −0.769258 1.49944i
\(466\) 0 0
\(467\) −10.1463 + 17.5739i −0.469514 + 0.813221i −0.999392 0.0348520i \(-0.988904\pi\)
0.529879 + 0.848073i \(0.322237\pi\)
\(468\) 0 0
\(469\) 11.8585 + 20.5396i 0.547576 + 0.948429i
\(470\) 0 0
\(471\) 8.35585 36.6573i 0.385017 1.68908i
\(472\) 0 0
\(473\) 6.22219 17.0953i 0.286097 0.786044i
\(474\) 0 0
\(475\) 53.9378 + 9.51068i 2.47483 + 0.436380i
\(476\) 0 0
\(477\) 1.09860 1.07276i 0.0503016 0.0491185i
\(478\) 0 0
\(479\) 1.80006 + 1.51043i 0.0822467 + 0.0690131i 0.682984 0.730433i \(-0.260682\pi\)
−0.600737 + 0.799446i \(0.705126\pi\)
\(480\) 0 0
\(481\) −1.01189 5.73874i −0.0461384 0.261664i
\(482\) 0 0
\(483\) −9.37548 + 22.2589i −0.426599 + 1.01282i
\(484\) 0 0
\(485\) 6.13943i 0.278777i
\(486\) 0 0
\(487\) 6.67682i 0.302555i 0.988491 + 0.151278i \(0.0483388\pi\)
−0.988491 + 0.151278i \(0.951661\pi\)
\(488\) 0 0
\(489\) −0.741053 + 1.75938i −0.0335116 + 0.0795620i
\(490\) 0 0
\(491\) −4.97852 28.2346i −0.224677 1.27421i −0.863301 0.504690i \(-0.831607\pi\)
0.638623 0.769520i \(-0.279504\pi\)
\(492\) 0 0
\(493\) 11.7691 + 9.87545i 0.530053 + 0.444768i
\(494\) 0 0
\(495\) −16.4735 + 16.0860i −0.740427 + 0.723013i
\(496\) 0 0
\(497\) 4.01890 + 0.708640i 0.180272 + 0.0317868i
\(498\) 0 0
\(499\) −10.7802 + 29.6183i −0.482587 + 1.32590i 0.424680 + 0.905344i \(0.360387\pi\)
−0.907267 + 0.420554i \(0.861836\pi\)
\(500\) 0 0
\(501\) 4.03456 17.6997i 0.180251 0.790765i
\(502\) 0 0
\(503\) −8.82536 15.2860i −0.393504 0.681568i 0.599405 0.800446i \(-0.295404\pi\)
−0.992909 + 0.118878i \(0.962070\pi\)
\(504\) 0 0
\(505\) −15.6781 + 27.1553i −0.697666 + 1.20839i
\(506\) 0 0
\(507\) 1.29592 + 2.52602i 0.0575539 + 0.112184i
\(508\) 0 0
\(509\) −9.38432 11.1838i −0.415953 0.495713i 0.516863 0.856068i \(-0.327100\pi\)
−0.932815 + 0.360356i \(0.882655\pi\)
\(510\) 0 0
\(511\) −1.77377 4.87339i −0.0784669 0.215586i
\(512\) 0 0
\(513\) 3.22570 21.5255i 0.142418 0.950376i
\(514\) 0 0
\(515\) 52.1624 18.9856i 2.29855 0.836603i
\(516\) 0 0
\(517\) 4.75300 3.98824i 0.209037 0.175402i
\(518\) 0 0
\(519\) 0.354189 + 0.228617i 0.0155472 + 0.0100352i
\(520\) 0 0
\(521\) −30.1782 17.4234i −1.32213 0.763334i −0.338064 0.941123i \(-0.609772\pi\)
−0.984069 + 0.177790i \(0.943105\pi\)
\(522\) 0 0
\(523\) −24.2393 + 13.9946i −1.05991 + 0.611940i −0.925408 0.378973i \(-0.876277\pi\)
−0.134504 + 0.990913i \(0.542944\pi\)
\(524\) 0 0
\(525\) −30.4114 + 32.7944i −1.32726 + 1.43127i
\(526\) 0 0
\(527\) −8.10230 2.94900i −0.352942 0.128460i
\(528\) 0 0
\(529\) 4.66372 26.4493i 0.202770 1.14997i
\(530\) 0 0
\(531\) 17.7342 24.6964i 0.769600 1.07173i
\(532\) 0 0
\(533\) 10.0176 11.9385i 0.433911 0.517115i
\(534\) 0 0
\(535\) −38.3722 + 6.76605i −1.65897 + 0.292522i
\(536\) 0 0
\(537\) 0.160717 + 1.27954i 0.00693544 + 0.0552164i
\(538\) 0 0
\(539\) −5.59584 −0.241030
\(540\) 0 0
\(541\) 8.19075 0.352148 0.176074 0.984377i \(-0.443660\pi\)
0.176074 + 0.984377i \(0.443660\pi\)
\(542\) 0 0
\(543\) −24.3872 + 18.4835i −1.04655 + 0.793201i
\(544\) 0 0
\(545\) −52.2934 + 9.22073i −2.24000 + 0.394973i
\(546\) 0 0
\(547\) −12.5634 + 14.9725i −0.537174 + 0.640179i −0.964552 0.263894i \(-0.914993\pi\)
0.427378 + 0.904073i \(0.359437\pi\)
\(548\) 0 0
\(549\) 0.221946 + 2.93926i 0.00947241 + 0.125445i
\(550\) 0 0
\(551\) 6.39620 36.2747i 0.272487 1.54535i
\(552\) 0 0
\(553\) 32.6739 + 11.8923i 1.38944 + 0.505713i
\(554\) 0 0
\(555\) −3.75596 12.1643i −0.159432 0.516345i
\(556\) 0 0
\(557\) 19.6096 11.3216i 0.830885 0.479712i −0.0232707 0.999729i \(-0.507408\pi\)
0.854156 + 0.520018i \(0.174075\pi\)
\(558\) 0 0
\(559\) 29.4169 + 16.9839i 1.24420 + 0.718341i
\(560\) 0 0
\(561\) −0.270754 + 5.45618i −0.0114312 + 0.230360i
\(562\) 0 0
\(563\) 27.9805 23.4784i 1.17924 0.989498i 0.179254 0.983803i \(-0.442632\pi\)
0.999984 0.00569511i \(-0.00181282\pi\)
\(564\) 0 0
\(565\) −25.8932 + 9.42434i −1.08933 + 0.396485i
\(566\) 0 0
\(567\) 13.3400 + 11.7457i 0.560226 + 0.493272i
\(568\) 0 0
\(569\) −3.87353 10.6424i −0.162387 0.446155i 0.831637 0.555320i \(-0.187404\pi\)
−0.994024 + 0.109166i \(0.965182\pi\)
\(570\) 0 0
\(571\) 12.9162 + 15.3929i 0.540525 + 0.644172i 0.965305 0.261124i \(-0.0840932\pi\)
−0.424781 + 0.905296i \(0.639649\pi\)
\(572\) 0 0
\(573\) 16.9474 + 0.840987i 0.707989 + 0.0351328i
\(574\) 0 0
\(575\) 46.1616 79.9543i 1.92507 3.33433i
\(576\) 0 0
\(577\) 0.972478 + 1.68438i 0.0404848 + 0.0701217i 0.885558 0.464529i \(-0.153776\pi\)
−0.845073 + 0.534651i \(0.820443\pi\)
\(578\) 0 0
\(579\) 14.1816 4.37885i 0.589367 0.181979i
\(580\) 0 0
\(581\) 2.48618 6.83073i 0.103144 0.283387i
\(582\) 0 0
\(583\) 0.909934 + 0.160446i 0.0376856 + 0.00664499i
\(584\) 0 0
\(585\) −24.2373 35.5063i −1.00209 1.46801i
\(586\) 0 0
\(587\) −31.3602 26.3143i −1.29437 1.08611i −0.991088 0.133207i \(-0.957472\pi\)
−0.303284 0.952900i \(-0.598083\pi\)
\(588\) 0 0
\(589\) 3.58968 + 20.3581i 0.147910 + 0.838840i
\(590\) 0 0
\(591\) −1.39237 1.83710i −0.0572745 0.0755683i
\(592\) 0 0
\(593\) 33.8316i 1.38930i 0.719349 + 0.694649i \(0.244440\pi\)
−0.719349 + 0.694649i \(0.755560\pi\)
\(594\) 0 0
\(595\) 14.6695i 0.601392i
\(596\) 0 0
\(597\) 28.3343 3.55892i 1.15965 0.145657i
\(598\) 0 0
\(599\) 5.18292 + 29.3938i 0.211768 + 1.20100i 0.886427 + 0.462868i \(0.153180\pi\)
−0.674659 + 0.738130i \(0.735709\pi\)
\(600\) 0 0
\(601\) 10.6280 + 8.91796i 0.433525 + 0.363771i 0.833280 0.552851i \(-0.186460\pi\)
−0.399755 + 0.916622i \(0.630905\pi\)
\(602\) 0 0
\(603\) −32.8312 + 14.8365i −1.33699 + 0.604187i
\(604\) 0 0
\(605\) 32.4115 + 5.71502i 1.31772 + 0.232349i
\(606\) 0 0
\(607\) 6.30592 17.3254i 0.255949 0.703215i −0.743458 0.668783i \(-0.766815\pi\)
0.999407 0.0344323i \(-0.0109623\pi\)
\(608\) 0 0
\(609\) 22.0552 + 20.4526i 0.893720 + 0.828779i
\(610\) 0 0
\(611\) 5.79240 + 10.0327i 0.234336 + 0.405881i
\(612\) 0 0
\(613\) 13.0815 22.6579i 0.528358 0.915143i −0.471095 0.882082i \(-0.656141\pi\)
0.999453 0.0330609i \(-0.0105255\pi\)
\(614\) 0 0
\(615\) 18.4645 28.6065i 0.744562 1.15353i
\(616\) 0 0
\(617\) −12.3160 14.6776i −0.495823 0.590898i 0.458866 0.888506i \(-0.348256\pi\)
−0.954688 + 0.297607i \(0.903811\pi\)
\(618\) 0 0
\(619\) 6.02766 + 16.5608i 0.242272 + 0.665637i 0.999916 + 0.0129686i \(0.00412814\pi\)
−0.757644 + 0.652668i \(0.773650\pi\)
\(620\) 0 0
\(621\) −32.2368 17.5196i −1.29362 0.703038i
\(622\) 0 0
\(623\) −13.8591 + 5.04430i −0.555253 + 0.202096i
\(624\) 0 0
\(625\) 61.7309 51.7984i 2.46924 2.07194i
\(626\) 0 0
\(627\) 11.6533 5.97849i 0.465389 0.238758i
\(628\) 0 0
\(629\) −2.61590 1.51029i −0.104303 0.0602192i
\(630\) 0 0
\(631\) 18.9375 10.9336i 0.753892 0.435260i −0.0732067 0.997317i \(-0.523323\pi\)
0.827098 + 0.562057i \(0.189990\pi\)
\(632\) 0 0
\(633\) 20.2527 + 4.61650i 0.804973 + 0.183489i
\(634\) 0 0
\(635\) −40.0123 14.5633i −1.58784 0.577926i
\(636\) 0 0
\(637\) 1.81431 10.2894i 0.0718855 0.407683i
\(638\) 0 0
\(639\) −1.67560 + 5.96842i −0.0662856 + 0.236107i
\(640\) 0 0
\(641\) 8.37132 9.97655i 0.330647 0.394050i −0.574950 0.818188i \(-0.694979\pi\)
0.905597 + 0.424138i \(0.139423\pi\)
\(642\) 0 0
\(643\) 20.5512 3.62373i 0.810461 0.142906i 0.246964 0.969025i \(-0.420567\pi\)
0.563497 + 0.826118i \(0.309456\pi\)
\(644\) 0 0
\(645\) 68.3909 + 28.8063i 2.69289 + 1.13425i
\(646\) 0 0
\(647\) 20.0883 0.789751 0.394875 0.918735i \(-0.370788\pi\)
0.394875 + 0.918735i \(0.370788\pi\)
\(648\) 0 0
\(649\) 18.2954 0.718159
\(650\) 0 0
\(651\) −15.5572 6.55270i −0.609734 0.256820i
\(652\) 0 0
\(653\) 7.40965 1.30652i 0.289962 0.0511281i −0.0267752 0.999641i \(-0.508524\pi\)
0.316737 + 0.948513i \(0.397413\pi\)
\(654\) 0 0
\(655\) −31.3829 + 37.4007i −1.22623 + 1.46137i
\(656\) 0 0
\(657\) 7.63342 1.94832i 0.297808 0.0760113i
\(658\) 0 0
\(659\) 8.07319 45.7853i 0.314487 1.78354i −0.260597 0.965448i \(-0.583919\pi\)
0.575083 0.818095i \(-0.304970\pi\)
\(660\) 0 0
\(661\) 37.5470 + 13.6660i 1.46041 + 0.531546i 0.945478 0.325685i \(-0.105595\pi\)
0.514932 + 0.857231i \(0.327817\pi\)
\(662\) 0 0
\(663\) −9.94486 2.26688i −0.386227 0.0880383i
\(664\) 0 0
\(665\) 30.4586 17.5853i 1.18113 0.681927i
\(666\) 0 0
\(667\) −53.7715 31.0450i −2.08204 1.20207i
\(668\) 0 0
\(669\) 14.6173 7.49911i 0.565138 0.289932i
\(670\) 0 0
\(671\) −1.35874 + 1.14012i −0.0524535 + 0.0440137i
\(672\) 0 0
\(673\) −23.8306 + 8.67365i −0.918604 + 0.334345i −0.757683 0.652623i \(-0.773669\pi\)
−0.160921 + 0.986967i \(0.551446\pi\)
\(674\) 0 0
\(675\) −44.9987 50.9022i −1.73200 1.95923i
\(676\) 0 0
\(677\) 5.71041 + 15.6892i 0.219469 + 0.602986i 0.999748 0.0224457i \(-0.00714528\pi\)
−0.780279 + 0.625431i \(0.784923\pi\)
\(678\) 0 0
\(679\) 1.83315 + 2.18466i 0.0703497 + 0.0838395i
\(680\) 0 0
\(681\) −7.55136 + 11.6991i −0.289369 + 0.448310i
\(682\) 0 0
\(683\) −2.39233 + 4.14363i −0.0915398 + 0.158552i −0.908159 0.418625i \(-0.862512\pi\)
0.816619 + 0.577176i \(0.195846\pi\)
\(684\) 0 0
\(685\) 7.06576 + 12.2383i 0.269969 + 0.467600i
\(686\) 0 0
\(687\) −12.5307 11.6202i −0.478076 0.443337i
\(688\) 0 0
\(689\) −0.590045 + 1.62114i −0.0224789 + 0.0617604i
\(690\) 0 0
\(691\) 46.6062 + 8.21794i 1.77298 + 0.312625i 0.962123 0.272614i \(-0.0878882\pi\)
0.810861 + 0.585239i \(0.198999\pi\)
\(692\) 0 0
\(693\) −1.05887 + 10.6428i −0.0402231 + 0.404287i
\(694\) 0 0
\(695\) 31.7944 + 26.6787i 1.20603 + 1.01198i
\(696\) 0 0
\(697\) −1.40279 7.95562i −0.0531345 0.301340i
\(698\) 0 0
\(699\) −34.7477 + 4.36447i −1.31428 + 0.165079i
\(700\) 0 0
\(701\) 1.98736i 0.0750617i 0.999295 + 0.0375308i \(0.0119492\pi\)
−0.999295 + 0.0375308i \(0.988051\pi\)
\(702\) 0 0
\(703\) 7.24191i 0.273134i
\(704\) 0 0
\(705\) 15.2877 + 20.1707i 0.575770 + 0.759674i
\(706\) 0 0
\(707\) 2.52927 + 14.3442i 0.0951231 + 0.539470i
\(708\) 0 0
\(709\) −32.0486 26.8920i −1.20361 1.00995i −0.999519 0.0309977i \(-0.990132\pi\)
−0.204092 0.978952i \(-0.565424\pi\)
\(710\) 0 0
\(711\) −22.8904 + 47.6016i −0.858459 + 1.78520i
\(712\) 0 0
\(713\) 34.3168 + 6.05098i 1.28517 + 0.226611i
\(714\) 0 0
\(715\) 8.84768 24.3088i 0.330884 0.909097i
\(716\) 0 0
\(717\) −45.3962 + 14.0170i −1.69535 + 0.523475i
\(718\) 0 0
\(719\) 10.7447 + 18.6104i 0.400710 + 0.694049i 0.993812 0.111078i \(-0.0354303\pi\)
−0.593102 + 0.805127i \(0.702097\pi\)
\(720\) 0 0
\(721\) 12.8927 22.3308i 0.480149 0.831642i
\(722\) 0 0
\(723\) −14.4313 0.716127i −0.536705 0.0266330i
\(724\) 0 0
\(725\) −73.9047 88.0762i −2.74475 3.27107i
\(726\) 0 0
\(727\) 2.78558 + 7.65333i 0.103312 + 0.283846i 0.980569 0.196174i \(-0.0628516\pi\)
−0.877258 + 0.480020i \(0.840629\pi\)
\(728\) 0 0
\(729\) −19.7611 + 18.3984i −0.731892 + 0.681421i
\(730\) 0 0
\(731\) 16.5454 6.02205i 0.611955 0.222733i
\(732\) 0 0
\(733\) 31.7728 26.6606i 1.17356 0.984731i 0.173556 0.984824i \(-0.444474\pi\)
1.00000 9.33087e-5i \(2.97011e-5\pi\)
\(734\) 0 0
\(735\) 1.13133 22.7983i 0.0417296 0.840928i
\(736\) 0 0
\(737\) −18.7750 10.8397i −0.691585 0.399287i
\(738\) 0 0
\(739\) 15.6244 9.02075i 0.574753 0.331834i −0.184293 0.982871i \(-0.558999\pi\)
0.759045 + 0.651038i \(0.225666\pi\)
\(740\) 0 0
\(741\) 7.21476 + 23.3661i 0.265041 + 0.858376i
\(742\) 0 0
\(743\) 28.4353 + 10.3496i 1.04319 + 0.379690i 0.806088 0.591795i \(-0.201581\pi\)
0.237101 + 0.971485i \(0.423803\pi\)
\(744\) 0 0
\(745\) −15.0972 + 85.6206i −0.553119 + 3.13689i
\(746\) 0 0
\(747\) 9.95149 + 4.78543i 0.364106 + 0.175090i
\(748\) 0 0
\(749\) −11.6341 + 13.8650i −0.425102 + 0.506617i
\(750\) 0 0
\(751\) −8.07225 + 1.42336i −0.294561 + 0.0519390i −0.318976 0.947763i \(-0.603339\pi\)
0.0244149 + 0.999702i \(0.492228\pi\)
\(752\) 0 0
\(753\) −27.6253 + 20.9377i −1.00672 + 0.763012i
\(754\) 0 0
\(755\) −44.9851 −1.63718
\(756\) 0 0
\(757\) 12.4321 0.451852 0.225926 0.974144i \(-0.427459\pi\)
0.225926 + 0.974144i \(0.427459\pi\)
\(758\) 0 0
\(759\) −2.75145 21.9057i −0.0998715 0.795126i
\(760\) 0 0
\(761\) 32.3875 5.71079i 1.17405 0.207016i 0.447596 0.894236i \(-0.352280\pi\)
0.726449 + 0.687220i \(0.241169\pi\)
\(762\) 0 0
\(763\) −15.8549 + 18.8952i −0.573987 + 0.684051i
\(764\) 0 0
\(765\) −22.1746 2.20618i −0.801723 0.0797647i
\(766\) 0 0
\(767\) −5.93182 + 33.6410i −0.214186 + 1.21471i
\(768\) 0 0
\(769\) −15.0019 5.46024i −0.540981 0.196901i 0.0570536 0.998371i \(-0.481829\pi\)
−0.598035 + 0.801470i \(0.704052\pi\)
\(770\) 0 0
\(771\) −2.64504 + 2.85230i −0.0952590 + 0.102723i
\(772\) 0 0
\(773\) −31.6586 + 18.2781i −1.13868 + 0.657417i −0.946103 0.323865i \(-0.895018\pi\)
−0.192576 + 0.981282i \(0.561684\pi\)
\(774\) 0 0
\(775\) 55.8816 + 32.2632i 2.00733 + 1.15893i
\(776\) 0 0
\(777\) −4.96861 3.20707i −0.178248 0.115053i
\(778\) 0 0
\(779\) −14.8368 + 12.4495i −0.531582 + 0.446050i
\(780\) 0 0
\(781\) −3.50533 + 1.27584i −0.125431 + 0.0456530i
\(782\) 0 0
\(783\) −34.2332 + 30.2629i −1.22339 + 1.08151i
\(784\) 0 0
\(785\) 31.5640 + 86.7215i 1.12657 + 3.09522i
\(786\) 0 0
\(787\) −30.2330 36.0303i −1.07769 1.28434i −0.956506 0.291712i \(-0.905775\pi\)
−0.121184 0.992630i \(-0.538669\pi\)
\(788\) 0 0
\(789\) 10.0596 + 19.6082i 0.358131 + 0.698072i
\(790\) 0 0
\(791\) −6.39987 + 11.0849i −0.227553 + 0.394134i
\(792\) 0 0
\(793\) −1.65587 2.86806i −0.0588018 0.101848i
\(794\) 0 0
\(795\) −0.837644 + 3.67477i −0.0297082 + 0.130331i
\(796\) </