Properties

Label 432.2.be.c.47.5
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 47.5
Character \(\chi\) \(=\) 432.47
Dual form 432.2.be.c.239.5

$q$-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 −0.950593 0.310439i \(-0.899524\pi\)
0.470792 + 0.882244i \(0.343968\pi\)
\(8\) 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 \(-0.856711\pi\)
0.994895 0.100919i \(-0.0321783\pi\)
\(12\) 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 0.0223793 0.999750i \(-0.492876\pi\)
−0.854619 + 0.519256i \(0.826209\pi\)
\(20\) 0 0
\(21\) −3.04346 + 1.56138i −0.664138 + 0.340722i
\(22\) 0 0
\(23\) −5.40902 + 4.53870i −1.12786 + 0.946385i −0.998975 0.0452747i \(-0.985584\pi\)
−0.128883 + 0.991660i \(0.541139\pi\)
\(24\) 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 0.401837 0.915711i \(-0.368372\pi\)
−0.971578 + 0.236720i \(0.923928\pi\)
\(32\) 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 0.867869 0.496794i \(-0.165490\pi\)
0.645616 + 0.763662i \(0.276601\pi\)
\(44\) 0 0
\(45\) 10.3601 + 7.43946i 1.54439 + 1.10901i
\(46\) 0 0
\(47\) 2.63291 + 2.20928i 0.384050 + 0.322256i 0.814290 0.580458i \(-0.197127\pi\)
−0.430240 + 0.902715i \(0.641571\pi\)
\(48\) 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 \(0.173767\pi\)
−0.625541 + 0.780191i \(0.715122\pi\)
\(60\) 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 \(-0.626735\pi\)
0.889514 0.456908i \(-0.151043\pi\)
\(68\) 0 0
\(69\) −11.6856 + 3.60816i −1.40678 + 0.434372i
\(70\) 0 0
\(71\) −1.03319 1.78955i −0.122618 0.212380i 0.798182 0.602417i \(-0.205796\pi\)
−0.920799 + 0.390037i \(0.872462\pi\)
\(72\) 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 \(-0.655158\pi\)
−0.209133 0.977887i \(-0.567064\pi\)
\(80\) 0 0
\(81\) −0.214158 + 8.99745i −0.0237953 + 0.999717i
\(82\) 0 0
\(83\) −3.45879 + 1.25890i −0.379652 + 0.138182i −0.524795 0.851229i \(-0.675858\pi\)
0.145143 + 0.989411i \(0.453636\pi\)
\(84\) 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 −0.766435 0.642322i \(-0.777971\pi\)
−0.500526 + 0.865721i \(0.666860\pi\)
\(104\) 0 0
\(105\) −11.5900 + 8.78423i −1.13106 + 0.857253i
\(106\) 0 0
\(107\) 9.16482 0.885997 0.442998 0.896522i \(-0.353915\pi\)
0.442998 + 0.896522i \(0.353915\pi\)
\(108\) 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 0.832751 0.553647i \(-0.186764\pi\)
−0.0630972 + 0.998007i \(0.520098\pi\)
\(128\) 0 0
\(129\) 14.6654 + 9.46602i 1.29122 + 0.833436i
\(130\) 0 0
\(131\) 8.79708 7.38162i 0.768604 0.644936i −0.171747 0.985141i \(-0.554941\pi\)
0.940351 + 0.340206i \(0.110497\pi\)
\(132\) 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 0.431181 0.902265i \(-0.358097\pi\)
−0.963432 + 0.267954i \(0.913653\pi\)
\(140\) 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 0.580725 0.814100i \(-0.302769\pi\)
0.267265 + 0.963623i \(0.413880\pi\)
\(152\) 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 \(0.0137444\pi\)
−0.999068 + 0.0431658i \(0.986256\pi\)
\(164\) 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 \(-0.922645\pi\)
0.829779 0.558092i \(-0.188467\pi\)
\(168\) 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 0.879603 0.475709i \(-0.157809\pi\)
−0.851778 + 0.523904i \(0.824475\pi\)
\(180\) 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 0.0132384 0.999912i \(-0.495786\pi\)
0.652873 + 0.757468i \(0.273564\pi\)
\(192\) 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 0.100347 0.994953i \(-0.468005\pi\)
0.911828 + 0.410573i \(0.134671\pi\)
\(200\) 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 0.248377 0.968663i \(-0.420103\pi\)
0.564701 + 0.825296i \(0.308992\pi\)
\(212\) 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 −0.522246 0.852795i \(-0.674906\pi\)
0.930526 + 0.366226i \(0.119350\pi\)
\(224\) 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 \(0.141520\pi\)
−0.995440 + 0.0953866i \(0.969591\pi\)
\(228\) 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 \(0.625107\pi\)
−0.976224 + 0.216766i \(0.930449\pi\)
\(240\) 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 \(0.384268\pi\)
−0.987225 + 0.159335i \(0.949065\pi\)
\(252\) 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 0.891774 0.452481i \(-0.149461\pi\)
−0.290752 + 0.956798i \(0.593906\pi\)
\(264\) 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 \(0.0128506\pi\)
−0.999185 + 0.0403604i \(0.987149\pi\)
\(272\) 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 −0.945148 0.326641i \(-0.894083\pi\)
0.933987 + 0.357308i \(0.116305\pi\)
\(284\) 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 −0.801676 0.597758i \(-0.796058\pi\)
0.116836 + 0.993151i \(0.462725\pi\)
\(308\) 0 0
\(309\) −22.0491 5.02599i −1.25433 0.285918i
\(310\) 0 0
\(311\) −3.49020 1.27033i −0.197911 0.0720338i 0.241163 0.970485i \(-0.422471\pi\)
−0.439074 + 0.898451i \(0.644693\pi\)
\(312\) 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 −0.623603 0.781741i \(-0.714332\pi\)
0.878152 + 0.478382i \(0.158776\pi\)
\(332\) 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 −0.422773 0.906235i \(-0.638943\pi\)
0.819054 + 0.573717i \(0.194499\pi\)
\(348\) 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 −0.997839 0.0657061i \(-0.979070\pi\)
0.555823 + 0.831301i \(0.312403\pi\)
\(360\) 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 0.288487 0.957484i \(-0.406848\pi\)
−0.0563897 + 0.998409i \(0.517959\pi\)
\(368\) 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 \(0.129339\pi\)
−0.918577 + 0.395242i \(0.870661\pi\)
\(380\) 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 \(0.140235\pi\)
−0.704111 + 0.710090i \(0.748654\pi\)
\(384\) 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 0.0853386 0.996352i \(-0.472803\pi\)
−0.575070 + 0.818105i \(0.695025\pi\)
\(420\) 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 \(-0.371309\pi\)
0.393372 + 0.919379i \(0.371309\pi\)
\(432\) 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 −0.407253 0.913315i \(-0.633513\pi\)
0.970159 + 0.242470i \(0.0779577\pi\)
\(440\) 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 \(0.130723\pi\)
−0.998103 + 0.0615728i \(0.980388\pi\)
\(444\) 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 0.920238 0.391359i \(-0.127995\pi\)
−0.545211 + 0.838299i \(0.683551\pi\)
\(464\) 0 0
\(465\) −16.5882 32.3338i −0.769258 1.49944i
\(466\) 0 0
\(467\) 10.1463 17.5739i 0.469514 0.813221i −0.529879 0.848073i \(-0.677763\pi\)
0.999392 + 0.0348520i \(0.0110960\pi\)
\(468\) 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 0.600737 0.799446i \(-0.294874\pi\)
−0.682984 + 0.730433i \(0.739318\pi\)
\(480\) 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 \(-0.951661\pi\)
0.988491 0.151278i \(-0.0483388\pi\)
\(488\) 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 \(0.168393\pi\)
−0.638623 + 0.769520i \(0.720496\pi\)
\(492\) 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 \(-0.639613\pi\)
0.907267 0.420554i \(-0.138164\pi\)
\(500\) 0 0
\(501\) 4.03456 17.6997i 0.180251 0.790765i
\(502\) 0 0
\(503\) 8.82536 + 15.2860i 0.393504 + 0.681568i 0.992909 0.118878i \(-0.0379296\pi\)
−0.599405 + 0.800446i \(0.704596\pi\)
\(504\) 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 0.134504 0.990913i \(-0.457056\pi\)
0.925408 + 0.378973i \(0.123723\pi\)
\(524\) 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 −0.427378 0.904073i \(-0.640563\pi\)
0.964552 + 0.263894i \(0.0850071\pi\)
\(548\) 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 \(0.557368\pi\)
−0.999984 + 0.00569511i \(0.998187\pi\)
\(564\) 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 0.424781 0.905296i \(-0.360351\pi\)
−0.965305 + 0.261124i \(0.915907\pi\)
\(572\) 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 \(0.0425276\pi\)
0.303284 + 0.952900i \(0.401917\pi\)
\(588\) 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 \(-0.846820\pi\)
0.674659 0.738130i \(-0.264291\pi\)
\(600\) 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 \(0.233185\pi\)
−0.999407 + 0.0344323i \(0.989038\pi\)
\(608\) 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 \(-0.995872\pi\)
0.757644 0.652668i \(-0.226350\pi\)
\(620\) 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 −0.827098 0.562057i \(-0.810010\pi\)
0.0732067 + 0.997317i \(0.476677\pi\)
\(632\) 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 −0.563497 0.826118i \(-0.690544\pi\)
−0.246964 + 0.969025i \(0.579433\pi\)
\(644\) 0 0
\(645\) 68.3909 + 28.8063i 2.69289 + 1.13425i
\(646\) 0 0
\(647\) −20.0883 −0.789751 −0.394875 0.918735i \(-0.629212\pi\)
−0.394875 + 0.918735i \(0.629212\pi\)
\(648\) 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 \(0.416081\pi\)
−0.575083 + 0.818095i \(0.695030\pi\)
\(660\) 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 −0.816619 0.577176i \(-0.804154\pi\)
0.908159 + 0.418625i \(0.137488\pi\)
\(684\) 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 −0.810861 0.585239i \(-0.801001\pi\)
−0.962123 + 0.272614i \(0.912112\pi\)
\(692\) 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 0.593102 0.805127i \(-0.297903\pi\)
−0.993812 + 0.111078i \(0.964570\pi\)
\(720\) 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 0.877258 0.480020i \(-0.159371\pi\)
−0.980569 + 0.196174i \(0.937148\pi\)
\(728\) 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 −0.759045 0.651038i \(-0.774334\pi\)
0.184293 + 0.982871i \(0.441001\pi\)
\(740\) 0 0
\(741\) 7.21476 + 23.3661i 0.265041 + 0.858376i
\(742\) 0 0
\(743\) −28.4353 10.3496i −1.04319 0.379690i −0.237101 0.971485i \(-0.576197\pi\)
−0.806088 + 0.591795i \(0.798419\pi\)
\(744\) 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 −0.0244149 0.999702i \(-0.507772\pi\)
0.318976 + 0.947763i \(0.396661\pi\)
\(752\) 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 \(0.0942248\pi\)
0.121184 + 0.992630i \(0.461331\pi\)
\(788\) 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
\(796\) 0