Properties

Label 432.2.be.b.239.2
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 239.2
Character \(\chi\) \(=\) 432.239
Dual form 432.2.be.b.47.2

$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

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

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
\(3\) −1.59623 + 0.672336i −0.921586 + 0.388173i
\(4\) 0 0
\(5\) 4.18690 + 0.738263i 1.87244 + 0.330161i 0.990090 0.140435i \(-0.0448502\pi\)
0.882348 + 0.470597i \(0.155961\pi\)
\(6\) 0 0
\(7\) 1.26944 + 1.51285i 0.479801 + 0.571805i 0.950593 0.310439i \(-0.100476\pi\)
−0.470792 + 0.882244i \(0.656032\pi\)
\(8\) 0 0
\(9\) 2.09593 2.14641i 0.698643 0.715470i
\(10\) 0 0
\(11\) −0.313474 1.77780i −0.0945158 0.536026i −0.994895 0.100919i \(-0.967822\pi\)
0.900379 0.435107i \(-0.143289\pi\)
\(12\) 0 0
\(13\) −3.16732 + 1.15281i −0.878456 + 0.319732i −0.741587 0.670857i \(-0.765926\pi\)
−0.136870 + 0.990589i \(0.543704\pi\)
\(14\) 0 0
\(15\) −7.17963 + 1.63656i −1.85377 + 0.422558i
\(16\) 0 0
\(17\) −1.51308 0.873578i −0.366976 0.211874i 0.305160 0.952301i \(-0.401290\pi\)
−0.672137 + 0.740427i \(0.734623\pi\)
\(18\) 0 0
\(19\) 3.62765 2.09442i 0.832240 0.480494i −0.0223793 0.999750i \(-0.507124\pi\)
0.854619 + 0.519256i \(0.173791\pi\)
\(20\) 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 \(-0.0144163\pi\)
0.128883 + 0.991660i \(0.458861\pi\)
\(24\) 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 0.263355 + 0.964699i \(0.415171\pi\)
−0.821838 + 0.569721i \(0.807051\pi\)
\(30\) 0 0
\(31\) 3.17218 3.78046i 0.569741 0.678991i −0.401837 0.915711i \(-0.631628\pi\)
0.971578 + 0.236720i \(0.0760725\pi\)
\(32\) 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 −0.786180 0.617997i \(-0.787944\pi\)
0.928291 + 0.371854i \(0.121278\pi\)
\(38\) 0 0
\(39\) 4.28071 3.96966i 0.685462 0.635654i
\(40\) 0 0
\(41\) −1.58140 4.34487i −0.246974 0.678554i −0.999793 0.0203276i \(-0.993529\pi\)
0.752820 0.658227i \(-0.228693\pi\)
\(42\) 0 0
\(43\) −9.92458 + 1.74997i −1.51348 + 0.266868i −0.867869 0.496794i \(-0.834510\pi\)
−0.645616 + 0.763662i \(0.723399\pi\)
\(44\) 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 \(-0.802873\pi\)
0.430240 + 0.902715i \(0.358429\pi\)
\(48\) 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 \(0.0111918\pi\)
−0.999382 + 0.0351528i \(0.988808\pi\)
\(54\) 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 0.625541 + 0.780191i \(0.284878\pi\)
−0.854657 + 0.519193i \(0.826233\pi\)
\(60\) 0 0
\(61\) 0.752671 0.631566i 0.0963697 0.0808638i −0.593330 0.804959i \(-0.702187\pi\)
0.689700 + 0.724096i \(0.257743\pi\)
\(62\) 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 −0.889514 0.456908i \(-0.848957\pi\)
0.387712 0.921780i \(-0.373265\pi\)
\(68\) 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 \(-0.794204\pi\)
0.920799 + 0.390037i \(0.127538\pi\)
\(72\) 0 0
\(73\) 1.31302 + 2.27422i 0.153678 + 0.266178i 0.932577 0.360972i \(-0.117555\pi\)
−0.778899 + 0.627149i \(0.784222\pi\)
\(74\) 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 0.209133 0.977887i \(-0.432936\pi\)
0.468369 0.883533i \(-0.344842\pi\)
\(80\) 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 \(-0.324142\pi\)
−0.145143 + 0.989411i \(0.546364\pi\)
\(84\) 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 −0.801944 0.597399i \(-0.796201\pi\)
0.116390 + 0.993204i \(0.462868\pi\)
\(90\) 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 0.969427 0.245378i \(-0.0789122\pi\)
−0.994888 + 0.100983i \(0.967801\pi\)
\(98\) 0 0
\(99\) −4.47290 3.05329i −0.449543 0.306868i
\(100\) 0 0
\(101\) −4.74078 5.64984i −0.471725 0.562180i 0.476747 0.879041i \(-0.341816\pi\)
−0.948472 + 0.316860i \(0.897371\pi\)
\(102\) 0 0
\(103\) 12.8583 + 2.26726i 1.26696 + 0.223399i 0.766435 0.642322i \(-0.222029\pi\)
0.500526 + 0.865721i \(0.333140\pi\)
\(104\) 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 −0.134838 0.990868i \(-0.543051\pi\)
−0.465603 + 0.884994i \(0.654163\pi\)
\(114\) 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 \(-0.813236\pi\)
0.0630972 + 0.998007i \(0.479902\pi\)
\(128\) 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 \(-0.445059\pi\)
−0.940351 + 0.340206i \(0.889503\pi\)
\(132\) 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 −0.881608 0.471982i \(-0.843539\pi\)
0.978735 + 0.205128i \(0.0657611\pi\)
\(138\) 0 0
\(139\) 6.27514 7.47842i 0.532251 0.634311i −0.431181 0.902265i \(-0.641903\pi\)
0.963432 + 0.267954i \(0.0863475\pi\)
\(140\) 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 −0.799761 0.600319i \(-0.795040\pi\)
0.226774 0.973947i \(-0.427182\pi\)
\(150\) 0 0
\(151\) −10.4203 + 1.83738i −0.847990 + 0.149524i −0.580725 0.814100i \(-0.697231\pi\)
−0.267265 + 0.963623i \(0.586120\pi\)
\(152\) 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 −0.341686 0.939814i \(-0.610998\pi\)
0.642515 0.766273i \(-0.277891\pi\)
\(158\) 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 −0.829779 0.558092i \(-0.811533\pi\)
0.970616 0.240634i \(-0.0773555\pi\)
\(168\) 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 −0.182752 0.983159i \(-0.558501\pi\)
0.164529 + 0.986372i \(0.447390\pi\)
\(174\) 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 \(-0.842191\pi\)
0.851778 + 0.523904i \(0.175525\pi\)
\(180\) 0 0
\(181\) 8.83351 + 15.3001i 0.656590 + 1.13725i 0.981493 + 0.191500i \(0.0613351\pi\)
−0.324903 + 0.945747i \(0.605332\pi\)
\(182\) 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 \(-0.504214\pi\)
−0.652873 + 0.757468i \(0.726436\pi\)
\(192\) 0 0
\(193\) −6.56436 5.50815i −0.472513 0.396486i 0.375197 0.926945i \(-0.377575\pi\)
−0.847710 + 0.530459i \(0.822019\pi\)
\(194\) 0 0
\(195\) 20.8535 13.4603i 1.49335 0.963909i
\(196\) 0 0
\(197\) 1.15257 0.665435i 0.0821170 0.0474103i −0.458379 0.888757i \(-0.651570\pi\)
0.540496 + 0.841346i \(0.318237\pi\)
\(198\) 0 0
\(199\) −14.2785 8.24368i −1.01217 0.584379i −0.100347 0.994953i \(-0.531995\pi\)
−0.911828 + 0.410573i \(0.865329\pi\)
\(200\) 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 \(-0.579897\pi\)
−0.564701 + 0.825296i \(0.691008\pi\)
\(212\) 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 \(-0.325094\pi\)
−0.930526 + 0.366226i \(0.880650\pi\)
\(224\) 0 0
\(225\) 35.3506 16.9992i 2.35671 1.13328i
\(226\) 0 0
\(227\) 1.39601 + 7.91718i 0.0926565 + 0.525481i 0.995440 + 0.0953866i \(0.0304087\pi\)
−0.902784 + 0.430095i \(0.858480\pi\)
\(228\) 0 0
\(229\) 9.27154 3.37456i 0.612680 0.222997i −0.0169953 0.999856i \(-0.505410\pi\)
0.629676 + 0.776858i \(0.283188\pi\)
\(230\) 0 0
\(231\) −1.82178 + 5.90011i −0.119864 + 0.388199i
\(232\) 0 0
\(233\) 17.5103 + 10.1096i 1.14714 + 0.662302i 0.948189 0.317707i \(-0.102913\pi\)
0.198952 + 0.980009i \(0.436246\pi\)
\(234\) 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 0.976224 + 0.216766i \(0.0695510\pi\)
0.382993 + 0.923751i \(0.374893\pi\)
\(240\) 0 0
\(241\) 7.83906 + 2.85318i 0.504958 + 0.183790i 0.581923 0.813244i \(-0.302301\pi\)
−0.0769646 + 0.997034i \(0.524523\pi\)
\(242\) 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 0.987225 + 0.159335i \(0.0509349\pi\)
−0.355624 + 0.934629i \(0.615732\pi\)
\(252\) 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 0.961342 0.275357i \(-0.0887962\pi\)
−0.913427 + 0.407003i \(0.866574\pi\)
\(258\) 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 \(-0.850539\pi\)
0.290752 + 0.956798i \(0.406094\pi\)
\(264\) 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 \(-0.860332\pi\)
0.905271 0.424834i \(-0.139668\pi\)
\(270\) 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 −0.472670 0.881239i \(-0.656710\pi\)
0.785773 + 0.618515i \(0.212265\pi\)
\(278\) 0 0
\(279\) −1.46575 14.7324i −0.0877521 0.882005i
\(280\) 0 0
\(281\) −3.97579 + 0.701039i −0.237176 + 0.0418205i −0.290972 0.956731i \(-0.593979\pi\)
0.0537967 + 0.998552i \(0.482868\pi\)
\(282\) 0 0
\(283\) 0.187770 + 0.515894i 0.0111618 + 0.0306667i 0.945148 0.326641i \(-0.105917\pi\)
−0.933987 + 0.357308i \(0.883695\pi\)
\(284\) 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 −0.302969 0.953000i \(-0.597978\pi\)
0.991132 + 0.132880i \(0.0424224\pi\)
\(294\) 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 \(-0.203942\pi\)
−0.116836 + 0.993151i \(0.537275\pi\)
\(308\) 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 \(-0.577529\pi\)
0.439074 + 0.898451i \(0.355307\pi\)
\(312\) 0 0
\(313\) 3.96289 + 22.4747i 0.223996 + 1.27034i 0.864595 + 0.502469i \(0.167575\pi\)
−0.640599 + 0.767875i \(0.721314\pi\)
\(314\) 0 0
\(315\) 24.4062 + 6.22935i 1.37514 + 0.350984i
\(316\) 0 0
\(317\) 11.1228 + 13.2557i 0.624720 + 0.744512i 0.981874 0.189533i \(-0.0606975\pi\)
−0.357155 + 0.934045i \(0.616253\pi\)
\(318\) 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 \(-0.285668\pi\)
−0.878152 + 0.478382i \(0.841224\pi\)
\(332\) 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 −0.896830 0.442375i \(-0.854136\pi\)
−0.402659 + 0.915350i \(0.631914\pi\)
\(338\) 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 \(-0.361057\pi\)
−0.819054 + 0.573717i \(0.805501\pi\)
\(348\) 0 0
\(349\) −1.04043 0.378686i −0.0556930 0.0202706i 0.314023 0.949415i \(-0.398323\pi\)
−0.369716 + 0.929145i \(0.620545\pi\)
\(350\) 0 0
\(351\) 0.451552 17.5083i 0.0241021 0.934523i
\(352\) 0 0
\(353\) −10.9418 + 30.0625i −0.582375 + 1.60006i 0.201734 + 0.979440i \(0.435342\pi\)
−0.784109 + 0.620623i \(0.786880\pi\)
\(354\) 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 \(-0.0209300\pi\)
−0.555823 + 0.831301i \(0.687597\pi\)
\(360\) 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 \(-0.593152\pi\)
0.0563897 + 0.998409i \(0.482041\pi\)
\(368\) 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 0.829372 + 0.558698i \(0.188699\pi\)
−0.970440 + 0.241342i \(0.922412\pi\)
\(374\) 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 0.704111 + 0.710090i \(0.251346\pi\)
−0.904513 + 0.426446i \(0.859765\pi\)
\(384\) 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 −0.499423 0.866358i \(-0.666455\pi\)
−0.172992 + 0.984923i \(0.555343\pi\)
\(390\) 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 0.822697 0.568481i \(-0.192469\pi\)
−0.903667 + 0.428236i \(0.859135\pi\)
\(398\) 0 0
\(399\) −14.3108 + 0.710149i −0.716437 + 0.0355519i
\(400\) 0 0
\(401\) 18.1787 21.6646i 0.907803 1.08188i −0.0885090 0.996075i \(-0.528210\pi\)
0.996312 0.0858023i \(-0.0273453\pi\)
\(402\) 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 0.525026 0.851086i \(-0.324056\pi\)
−0.746987 + 0.664839i \(0.768500\pi\)
\(410\) 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 \(-0.527197\pi\)
0.575070 + 0.818105i \(0.304975\pi\)
\(420\) 0 0
\(421\) 3.69487 + 20.9547i 0.180077 + 1.02127i 0.932119 + 0.362153i \(0.117958\pi\)
−0.752042 + 0.659116i \(0.770931\pi\)
\(422\) 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 0.407253 0.913315i \(-0.366487\pi\)
−0.970159 + 0.242470i \(0.922042\pi\)
\(440\) 0 0
\(441\) −5.42419 7.55363i −0.258295 0.359697i
\(442\) 0 0
\(443\) 1.71016 + 9.69879i 0.0812521 + 0.460804i 0.998103 + 0.0615728i \(0.0196116\pi\)
−0.916850 + 0.399231i \(0.869277\pi\)
\(444\) 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 0.150467 0.988615i \(-0.451922\pi\)
−0.780932 + 0.624616i \(0.785255\pi\)
\(450\) 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 −0.132841 0.991137i \(-0.542410\pi\)
−0.738853 + 0.673866i \(0.764632\pi\)
\(458\) 0 0
\(459\) 7.10267 5.65430i 0.331524 0.263920i
\(460\) 0 0
\(461\) 1.17082 3.21680i 0.0545306 0.149822i −0.909437 0.415842i \(-0.863487\pi\)
0.963967 + 0.266021i \(0.0857090\pi\)
\(462\) 0 0
\(463\) −8.06961 + 9.61699i −0.375027 + 0.446939i −0.920238 0.391359i \(-0.872005\pi\)
0.545211 + 0.838299i \(0.316449\pi\)
\(464\) 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 \(-0.322237\pi\)
−0.999392 + 0.0348520i \(0.988904\pi\)
\(468\) 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 \(-0.705126\pi\)
0.682984 + 0.730433i \(0.260682\pi\)
\(480\) 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 0.638623 + 0.769520i \(0.279504\pi\)
−0.863301 + 0.504690i \(0.831607\pi\)
\(492\) 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 −0.907267 0.420554i \(-0.861836\pi\)
0.424680 0.905344i \(-0.360387\pi\)
\(500\) 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 \(-0.962070\pi\)
0.599405 + 0.800446i \(0.295404\pi\)
\(504\) 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 −0.932815 0.360356i \(-0.882655\pi\)
0.516863 + 0.856068i \(0.327100\pi\)
\(510\) 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 −0.984069 0.177790i \(-0.943105\pi\)
−0.338064 + 0.941123i \(0.609772\pi\)
\(522\) 0 0
\(523\) −24.2393 13.9946i −1.05991 0.611940i −0.134504 0.990913i \(-0.542944\pi\)
−0.925408 + 0.378973i \(0.876277\pi\)
\(524\) 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 \(-0.359437\pi\)
−0.964552 + 0.263894i \(0.914993\pi\)
\(548\) 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 0.854156 0.520018i \(-0.174075\pi\)
−0.0232707 + 0.999729i \(0.507408\pi\)
\(558\) 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 0.999984 + 0.00569511i \(0.00181282\pi\)
0.179254 + 0.983803i \(0.442632\pi\)
\(564\) 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 −0.994024 0.109166i \(-0.965182\pi\)
0.831637 + 0.555320i \(0.187404\pi\)
\(570\) 0 0
\(571\) 12.9162 15.3929i 0.540525 0.644172i −0.424781 0.905296i \(-0.639649\pi\)
0.965305 + 0.261124i \(0.0840932\pi\)
\(572\) 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 −0.845073 0.534651i \(-0.820443\pi\)
0.885558 + 0.464529i \(0.153776\pi\)
\(578\) 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 −0.303284 + 0.952900i \(0.598083\pi\)
−0.991088 + 0.133207i \(0.957472\pi\)
\(588\) 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 \(-0.755560\pi\)
0.719349 0.694649i \(-0.244440\pi\)
\(594\) 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 −0.674659 0.738130i \(-0.735709\pi\)
0.886427 0.462868i \(-0.153180\pi\)
\(600\) 0 0
\(601\) 10.6280 8.91796i 0.433525 0.363771i −0.399755 0.916622i \(-0.630905\pi\)
0.833280 + 0.552851i \(0.186460\pi\)
\(602\) 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 0.999407 + 0.0344323i \(0.0109623\pi\)
−0.743458 + 0.668783i \(0.766815\pi\)
\(608\) 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 0.999453 + 0.0330609i \(0.0105255\pi\)
−0.471095 + 0.882082i \(0.656141\pi\)
\(614\) 0 0
\(615\) 18.4645 + 28.6065i 0.744562 + 1.15353i
\(616\) 0 0
\(617\) −12.3160 + 14.6776i −0.495823 + 0.590898i −0.954688 0.297607i \(-0.903811\pi\)
0.458866 + 0.888506i \(0.348256\pi\)
\(618\) 0 0
\(619\) 6.02766 16.5608i 0.242272 0.665637i −0.757644 0.652668i \(-0.773650\pi\)
0.999916 0.0129686i \(-0.00412814\pi\)
\(620\) 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 \(-0.189990\pi\)
−0.0732067 + 0.997317i \(0.523323\pi\)
\(632\) 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 0.905597 0.424138i \(-0.139423\pi\)
−0.574950 + 0.818188i \(0.694979\pi\)
\(642\) 0 0
\(643\) 20.5512 + 3.62373i 0.810461 + 0.142906i 0.563497 0.826118i \(-0.309456\pi\)
0.246964 + 0.969025i \(0.420567\pi\)
\(644\) 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 0.316737 0.948513i \(-0.397413\pi\)
−0.0267752 + 0.999641i \(0.508524\pi\)
\(654\) 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 0.575083 + 0.818095i \(0.304970\pi\)
−0.260597 + 0.965448i \(0.583919\pi\)
\(660\) 0 0
\(661\) 37.5470 13.6660i 1.46041 0.531546i 0.514932 0.857231i \(-0.327817\pi\)
0.945478 + 0.325685i \(0.105595\pi\)
\(662\) 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 −0.160921 0.986967i \(-0.551446\pi\)
−0.757683 + 0.652623i \(0.773669\pi\)
\(674\) 0 0
\(675\) −44.9987 + 50.9022i −1.73200 + 1.95923i
\(676\) 0 0
\(677\) 5.71041 15.6892i 0.219469 0.602986i −0.780279 0.625431i \(-0.784923\pi\)
0.999748 + 0.0224457i \(0.00714528\pi\)
\(678\) 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 \(-0.195846\pi\)
−0.908159 + 0.418625i \(0.862512\pi\)
\(684\) 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 \(-0.198999\pi\)
0.962123 + 0.272614i \(0.0878882\pi\)
\(692\) 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 \(-0.988051\pi\)
0.999295 0.0375308i \(-0.0119492\pi\)
\(702\) 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 −0.204092 + 0.978952i \(0.565424\pi\)
−0.999519 + 0.0309977i \(0.990132\pi\)
\(710\) 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 \(-0.702097\pi\)
0.993812 + 0.111078i \(0.0354303\pi\)
\(720\) 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 \(-0.840629\pi\)
0.980569 + 0.196174i \(0.0628516\pi\)
\(728\) 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 1.00000 9.33087e-5i \(-2.97011e-5\pi\)
0.173556 + 0.984824i \(0.444474\pi\)
\(734\) 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 \(-0.225666\pi\)
−0.184293 + 0.982871i \(0.558999\pi\)
\(740\) 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 \(-0.423803\pi\)
0.806088 + 0.591795i \(0.201581\pi\)
\(744\) 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 \(-0.492228\pi\)
−0.318976 + 0.947763i \(0.603339\pi\)
\(752\) 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 0.726449 0.687220i \(-0.241169\pi\)
0.447596 + 0.894236i \(0.352280\pi\)
\(762\) 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 −0.598035 0.801470i \(-0.704052\pi\)
0.0570536 + 0.998371i \(0.481829\pi\)
\(770\) 0 0
\(771\) −2.64504 2.85230i −0.0952590 0.102723i
\(772\) 0 0
\(773\) −31.6586 18.2781i −1.13868 0.657417i −0.192576 0.981282i \(-0.561684\pi\)
−0.946103 + 0.323865i \(0.895018\pi\)
\(774\) 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 −0.121184 + 0.992630i \(0.538669\pi\)
−0.956506 + 0.291712i \(0.905775\pi\)
\(788\) 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