Properties

Label 1386.2.r.d.1277.4
Level $1386$
Weight $2$
Character 1386.1277
Analytic conductor $11.067$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.r (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1277.4
Character \(\chi\) \(=\) 1386.1277
Dual form 1386.2.r.d.89.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.171460 - 0.296977i) q^{5} +(-2.33970 + 1.23523i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.171460 - 0.296977i) q^{5} +(-2.33970 + 1.23523i) q^{7} +1.00000i q^{8} +(0.296977 + 0.171460i) q^{10} +(0.866025 + 0.500000i) q^{11} +4.10525i q^{13} +(1.40862 - 2.23959i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.61291 - 4.52569i) q^{17} +(-6.70061 + 3.86860i) q^{19} -0.342920 q^{20} -1.00000 q^{22} +(1.74222 - 1.00587i) q^{23} +(2.44120 - 4.22829i) q^{25} +(-2.05263 - 3.55525i) q^{26} +(-0.100107 + 2.64386i) q^{28} -0.958744i q^{29} +(-1.01394 - 0.585401i) q^{31} +(0.866025 + 0.500000i) q^{32} +5.22582i q^{34} +(0.768001 + 0.483045i) q^{35} +(0.314796 + 0.545243i) q^{37} +(3.86860 - 6.70061i) q^{38} +(0.296977 - 0.171460i) q^{40} -4.34939 q^{41} -6.93485 q^{43} +(0.866025 - 0.500000i) q^{44} +(-1.00587 + 1.74222i) q^{46} +(-5.28715 - 9.15761i) q^{47} +(3.94840 - 5.78015i) q^{49} +4.88241i q^{50} +(3.55525 + 2.05263i) q^{52} +(-6.37383 - 3.67993i) q^{53} -0.342920i q^{55} +(-1.23523 - 2.33970i) q^{56} +(0.479372 + 0.830296i) q^{58} +(-5.67216 + 9.82447i) q^{59} +(-8.21529 + 4.74310i) q^{61} +1.17080 q^{62} -1.00000 q^{64} +(1.21917 - 0.703886i) q^{65} +(-6.84977 + 11.8641i) q^{67} +(-2.61291 - 4.52569i) q^{68} +(-0.906631 - 0.0343286i) q^{70} -7.47863i q^{71} +(-7.35478 - 4.24628i) q^{73} +(-0.545243 - 0.314796i) q^{74} +7.73720i q^{76} +(-2.64386 - 0.100107i) q^{77} +(-1.37587 - 2.38308i) q^{79} +(-0.171460 + 0.296977i) q^{80} +(3.76668 - 2.17469i) q^{82} +6.08907 q^{83} -1.79204 q^{85} +(6.00576 - 3.46743i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(0.164386 + 0.284725i) q^{89} +(-5.07095 - 9.60506i) q^{91} -2.01175i q^{92} +(9.15761 + 5.28715i) q^{94} +(2.29777 + 1.32662i) q^{95} +5.22968i q^{97} +(-0.529335 + 6.97996i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 12 q^{4} + 8 q^{7} + O(q^{10}) \) \( 24 q + 12 q^{4} + 8 q^{7} - 12 q^{16} + 12 q^{19} - 24 q^{22} + 4 q^{25} + 4 q^{28} + 20 q^{37} + 24 q^{43} + 12 q^{46} + 40 q^{49} - 28 q^{58} - 120 q^{61} - 24 q^{64} - 32 q^{67} + 48 q^{70} - 48 q^{73} - 64 q^{79} - 48 q^{82} + 32 q^{85} - 12 q^{88} + 56 q^{91} + 60 q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −0.171460 0.296977i −0.0766792 0.132812i 0.825136 0.564934i \(-0.191098\pi\)
−0.901815 + 0.432122i \(0.857765\pi\)
\(6\) 0 0
\(7\) −2.33970 + 1.23523i −0.884324 + 0.466874i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0.296977 + 0.171460i 0.0939125 + 0.0542204i
\(11\) 0.866025 + 0.500000i 0.261116 + 0.150756i
\(12\) 0 0
\(13\) 4.10525i 1.13859i 0.822133 + 0.569296i \(0.192784\pi\)
−0.822133 + 0.569296i \(0.807216\pi\)
\(14\) 1.40862 2.23959i 0.376470 0.598557i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.61291 4.52569i 0.633724 1.09764i −0.353060 0.935601i \(-0.614859\pi\)
0.986784 0.162041i \(-0.0518077\pi\)
\(18\) 0 0
\(19\) −6.70061 + 3.86860i −1.53723 + 0.887518i −0.538227 + 0.842800i \(0.680906\pi\)
−0.999000 + 0.0447180i \(0.985761\pi\)
\(20\) −0.342920 −0.0766792
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) 1.74222 1.00587i 0.363279 0.209739i −0.307239 0.951632i \(-0.599405\pi\)
0.670518 + 0.741893i \(0.266072\pi\)
\(24\) 0 0
\(25\) 2.44120 4.22829i 0.488241 0.845658i
\(26\) −2.05263 3.55525i −0.402553 0.697243i
\(27\) 0 0
\(28\) −0.100107 + 2.64386i −0.0189184 + 0.499642i
\(29\) 0.958744i 0.178034i −0.996030 0.0890171i \(-0.971627\pi\)
0.996030 0.0890171i \(-0.0283726\pi\)
\(30\) 0 0
\(31\) −1.01394 0.585401i −0.182110 0.105141i 0.406174 0.913796i \(-0.366863\pi\)
−0.588284 + 0.808655i \(0.700196\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 5.22582i 0.896221i
\(35\) 0.768001 + 0.483045i 0.129816 + 0.0816495i
\(36\) 0 0
\(37\) 0.314796 + 0.545243i 0.0517522 + 0.0896374i 0.890741 0.454511i \(-0.150186\pi\)
−0.838989 + 0.544149i \(0.816853\pi\)
\(38\) 3.86860 6.70061i 0.627570 1.08698i
\(39\) 0 0
\(40\) 0.296977 0.171460i 0.0469562 0.0271102i
\(41\) −4.34939 −0.679260 −0.339630 0.940559i \(-0.610302\pi\)
−0.339630 + 0.940559i \(0.610302\pi\)
\(42\) 0 0
\(43\) −6.93485 −1.05756 −0.528778 0.848760i \(-0.677349\pi\)
−0.528778 + 0.848760i \(0.677349\pi\)
\(44\) 0.866025 0.500000i 0.130558 0.0753778i
\(45\) 0 0
\(46\) −1.00587 + 1.74222i −0.148308 + 0.256877i
\(47\) −5.28715 9.15761i −0.771210 1.33578i −0.936900 0.349597i \(-0.886318\pi\)
0.165690 0.986178i \(-0.447015\pi\)
\(48\) 0 0
\(49\) 3.94840 5.78015i 0.564057 0.825736i
\(50\) 4.88241i 0.690476i
\(51\) 0 0
\(52\) 3.55525 + 2.05263i 0.493025 + 0.284648i
\(53\) −6.37383 3.67993i −0.875513 0.505478i −0.00633669 0.999980i \(-0.502017\pi\)
−0.869176 + 0.494502i \(0.835350\pi\)
\(54\) 0 0
\(55\) 0.342920i 0.0462393i
\(56\) −1.23523 2.33970i −0.165065 0.312656i
\(57\) 0 0
\(58\) 0.479372 + 0.830296i 0.0629446 + 0.109023i
\(59\) −5.67216 + 9.82447i −0.738452 + 1.27904i 0.214740 + 0.976671i \(0.431110\pi\)
−0.953192 + 0.302365i \(0.902224\pi\)
\(60\) 0 0
\(61\) −8.21529 + 4.74310i −1.05186 + 0.607292i −0.923170 0.384393i \(-0.874411\pi\)
−0.128691 + 0.991685i \(0.541077\pi\)
\(62\) 1.17080 0.148692
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 1.21917 0.703886i 0.151219 0.0873064i
\(66\) 0 0
\(67\) −6.84977 + 11.8641i −0.836833 + 1.44944i 0.0556971 + 0.998448i \(0.482262\pi\)
−0.892530 + 0.450989i \(0.851071\pi\)
\(68\) −2.61291 4.52569i −0.316862 0.548821i
\(69\) 0 0
\(70\) −0.906631 0.0343286i −0.108363 0.00410305i
\(71\) 7.47863i 0.887550i −0.896138 0.443775i \(-0.853639\pi\)
0.896138 0.443775i \(-0.146361\pi\)
\(72\) 0 0
\(73\) −7.35478 4.24628i −0.860812 0.496990i 0.00347222 0.999994i \(-0.498895\pi\)
−0.864284 + 0.503004i \(0.832228\pi\)
\(74\) −0.545243 0.314796i −0.0633832 0.0365943i
\(75\) 0 0
\(76\) 7.73720i 0.887518i
\(77\) −2.64386 0.100107i −0.301295 0.0114082i
\(78\) 0 0
\(79\) −1.37587 2.38308i −0.154797 0.268117i 0.778188 0.628032i \(-0.216139\pi\)
−0.932985 + 0.359915i \(0.882806\pi\)
\(80\) −0.171460 + 0.296977i −0.0191698 + 0.0332031i
\(81\) 0 0
\(82\) 3.76668 2.17469i 0.415960 0.240155i
\(83\) 6.08907 0.668362 0.334181 0.942509i \(-0.391540\pi\)
0.334181 + 0.942509i \(0.391540\pi\)
\(84\) 0 0
\(85\) −1.79204 −0.194374
\(86\) 6.00576 3.46743i 0.647618 0.373902i
\(87\) 0 0
\(88\) −0.500000 + 0.866025i −0.0533002 + 0.0923186i
\(89\) 0.164386 + 0.284725i 0.0174249 + 0.0301808i 0.874606 0.484834i \(-0.161120\pi\)
−0.857181 + 0.515014i \(0.827787\pi\)
\(90\) 0 0
\(91\) −5.07095 9.60506i −0.531580 1.00688i
\(92\) 2.01175i 0.209739i
\(93\) 0 0
\(94\) 9.15761 + 5.28715i 0.944536 + 0.545328i
\(95\) 2.29777 + 1.32662i 0.235747 + 0.136108i
\(96\) 0 0
\(97\) 5.22968i 0.530994i 0.964112 + 0.265497i \(0.0855360\pi\)
−0.964112 + 0.265497i \(0.914464\pi\)
\(98\) −0.529335 + 6.97996i −0.0534709 + 0.705082i
\(99\) 0 0
\(100\) −2.44120 4.22829i −0.244120 0.422829i
\(101\) −1.69189 + 2.93044i −0.168350 + 0.291590i −0.937840 0.347069i \(-0.887177\pi\)
0.769490 + 0.638659i \(0.220510\pi\)
\(102\) 0 0
\(103\) 6.85976 3.96048i 0.675912 0.390238i −0.122401 0.992481i \(-0.539059\pi\)
0.798313 + 0.602243i \(0.205726\pi\)
\(104\) −4.10525 −0.402553
\(105\) 0 0
\(106\) 7.35987 0.714853
\(107\) −9.90128 + 5.71650i −0.957192 + 0.552635i −0.895308 0.445448i \(-0.853044\pi\)
−0.0618846 + 0.998083i \(0.519711\pi\)
\(108\) 0 0
\(109\) 1.49772 2.59413i 0.143456 0.248473i −0.785340 0.619065i \(-0.787512\pi\)
0.928796 + 0.370592i \(0.120845\pi\)
\(110\) 0.171460 + 0.296977i 0.0163481 + 0.0283157i
\(111\) 0 0
\(112\) 2.23959 + 1.40862i 0.211622 + 0.133102i
\(113\) 5.21758i 0.490829i 0.969418 + 0.245414i \(0.0789240\pi\)
−0.969418 + 0.245414i \(0.921076\pi\)
\(114\) 0 0
\(115\) −0.597443 0.344934i −0.0557119 0.0321653i
\(116\) −0.830296 0.479372i −0.0770911 0.0445086i
\(117\) 0 0
\(118\) 11.3443i 1.04433i
\(119\) −0.523139 + 13.8163i −0.0479561 + 1.26654i
\(120\) 0 0
\(121\) 0.500000 + 0.866025i 0.0454545 + 0.0787296i
\(122\) 4.74310 8.21529i 0.429420 0.743778i
\(123\) 0 0
\(124\) −1.01394 + 0.585401i −0.0910548 + 0.0525705i
\(125\) −3.38887 −0.303110
\(126\) 0 0
\(127\) −17.5835 −1.56029 −0.780143 0.625602i \(-0.784853\pi\)
−0.780143 + 0.625602i \(0.784853\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) −0.703886 + 1.21917i −0.0617349 + 0.106928i
\(131\) −2.66440 4.61488i −0.232790 0.403204i 0.725838 0.687866i \(-0.241452\pi\)
−0.958628 + 0.284661i \(0.908119\pi\)
\(132\) 0 0
\(133\) 10.8988 17.3282i 0.945046 1.50254i
\(134\) 13.6995i 1.18346i
\(135\) 0 0
\(136\) 4.52569 + 2.61291i 0.388075 + 0.224055i
\(137\) −18.4177 10.6335i −1.57353 0.908480i −0.995731 0.0923027i \(-0.970577\pi\)
−0.577802 0.816177i \(-0.696089\pi\)
\(138\) 0 0
\(139\) 14.4632i 1.22675i 0.789792 + 0.613375i \(0.210188\pi\)
−0.789792 + 0.613375i \(0.789812\pi\)
\(140\) 0.802330 0.423586i 0.0678092 0.0357996i
\(141\) 0 0
\(142\) 3.73932 + 6.47668i 0.313796 + 0.543511i
\(143\) −2.05263 + 3.55525i −0.171649 + 0.297305i
\(144\) 0 0
\(145\) −0.284725 + 0.164386i −0.0236451 + 0.0136515i
\(146\) 8.49257 0.702850
\(147\) 0 0
\(148\) 0.629592 0.0517522
\(149\) 9.48082 5.47375i 0.776699 0.448427i −0.0585602 0.998284i \(-0.518651\pi\)
0.835259 + 0.549857i \(0.185318\pi\)
\(150\) 0 0
\(151\) 12.2096 21.1476i 0.993599 1.72096i 0.398972 0.916963i \(-0.369367\pi\)
0.594627 0.804001i \(-0.297300\pi\)
\(152\) −3.86860 6.70061i −0.313785 0.543492i
\(153\) 0 0
\(154\) 2.33970 1.23523i 0.188538 0.0995380i
\(155\) 0.401491i 0.0322485i
\(156\) 0 0
\(157\) −4.12533 2.38176i −0.329237 0.190085i 0.326265 0.945278i \(-0.394210\pi\)
−0.655502 + 0.755193i \(0.727543\pi\)
\(158\) 2.38308 + 1.37587i 0.189587 + 0.109458i
\(159\) 0 0
\(160\) 0.342920i 0.0271102i
\(161\) −2.83379 + 4.50550i −0.223334 + 0.355083i
\(162\) 0 0
\(163\) −10.9446 18.9566i −0.857248 1.48480i −0.874544 0.484946i \(-0.838839\pi\)
0.0172964 0.999850i \(-0.494494\pi\)
\(164\) −2.17469 + 3.76668i −0.169815 + 0.294128i
\(165\) 0 0
\(166\) −5.27329 + 3.04454i −0.409287 + 0.236302i
\(167\) −3.63316 −0.281143 −0.140571 0.990071i \(-0.544894\pi\)
−0.140571 + 0.990071i \(0.544894\pi\)
\(168\) 0 0
\(169\) −3.85310 −0.296393
\(170\) 1.55195 0.896018i 0.119029 0.0687215i
\(171\) 0 0
\(172\) −3.46743 + 6.00576i −0.264389 + 0.457935i
\(173\) −10.9866 19.0293i −0.835293 1.44677i −0.893792 0.448482i \(-0.851965\pi\)
0.0584987 0.998287i \(-0.481369\pi\)
\(174\) 0 0
\(175\) −0.488761 + 12.9084i −0.0369469 + 0.975782i
\(176\) 1.00000i 0.0753778i
\(177\) 0 0
\(178\) −0.284725 0.164386i −0.0213410 0.0123213i
\(179\) 7.78611 + 4.49531i 0.581961 + 0.335996i 0.761913 0.647680i \(-0.224261\pi\)
−0.179951 + 0.983676i \(0.557594\pi\)
\(180\) 0 0
\(181\) 4.34535i 0.322987i −0.986874 0.161494i \(-0.948369\pi\)
0.986874 0.161494i \(-0.0516312\pi\)
\(182\) 9.19410 + 5.78276i 0.681512 + 0.428646i
\(183\) 0 0
\(184\) 1.00587 + 1.74222i 0.0741540 + 0.128439i
\(185\) 0.107950 0.186975i 0.00793663 0.0137466i
\(186\) 0 0
\(187\) 4.52569 2.61291i 0.330951 0.191075i
\(188\) −10.5743 −0.771210
\(189\) 0 0
\(190\) −2.65324 −0.192486
\(191\) 15.9257 9.19472i 1.15235 0.665307i 0.202888 0.979202i \(-0.434967\pi\)
0.949458 + 0.313895i \(0.101634\pi\)
\(192\) 0 0
\(193\) −3.24347 + 5.61785i −0.233470 + 0.404382i −0.958827 0.283991i \(-0.908341\pi\)
0.725357 + 0.688373i \(0.241675\pi\)
\(194\) −2.61484 4.52904i −0.187735 0.325166i
\(195\) 0 0
\(196\) −3.03156 6.30949i −0.216540 0.450678i
\(197\) 14.8328i 1.05680i 0.848997 + 0.528398i \(0.177207\pi\)
−0.848997 + 0.528398i \(0.822793\pi\)
\(198\) 0 0
\(199\) −8.33957 4.81486i −0.591177 0.341316i 0.174386 0.984677i \(-0.444206\pi\)
−0.765563 + 0.643361i \(0.777539\pi\)
\(200\) 4.22829 + 2.44120i 0.298985 + 0.172619i
\(201\) 0 0
\(202\) 3.38379i 0.238082i
\(203\) 1.18427 + 2.24317i 0.0831196 + 0.157440i
\(204\) 0 0
\(205\) 0.745746 + 1.29167i 0.0520852 + 0.0902141i
\(206\) −3.96048 + 6.85976i −0.275940 + 0.477942i
\(207\) 0 0
\(208\) 3.55525 2.05263i 0.246512 0.142324i
\(209\) −7.73720 −0.535194
\(210\) 0 0
\(211\) 6.76858 0.465968 0.232984 0.972481i \(-0.425151\pi\)
0.232984 + 0.972481i \(0.425151\pi\)
\(212\) −6.37383 + 3.67993i −0.437757 + 0.252739i
\(213\) 0 0
\(214\) 5.71650 9.90128i 0.390772 0.676837i
\(215\) 1.18905 + 2.05949i 0.0810925 + 0.140456i
\(216\) 0 0
\(217\) 3.09543 + 0.117205i 0.210132 + 0.00795640i
\(218\) 2.99545i 0.202877i
\(219\) 0 0
\(220\) −0.296977 0.171460i −0.0200222 0.0115598i
\(221\) 18.5791 + 10.7267i 1.24977 + 0.721553i
\(222\) 0 0
\(223\) 17.7015i 1.18538i 0.805430 + 0.592692i \(0.201935\pi\)
−0.805430 + 0.592692i \(0.798065\pi\)
\(224\) −2.64386 0.100107i −0.176650 0.00668866i
\(225\) 0 0
\(226\) −2.60879 4.51856i −0.173534 0.300570i
\(227\) −7.57961 + 13.1283i −0.503077 + 0.871354i 0.496917 + 0.867798i \(0.334465\pi\)
−0.999994 + 0.00355619i \(0.998868\pi\)
\(228\) 0 0
\(229\) 13.8726 8.00935i 0.916727 0.529273i 0.0341378 0.999417i \(-0.489131\pi\)
0.882590 + 0.470144i \(0.155798\pi\)
\(230\) 0.689868 0.0454886
\(231\) 0 0
\(232\) 0.958744 0.0629446
\(233\) 25.7401 14.8610i 1.68629 0.973579i 0.728969 0.684547i \(-0.240000\pi\)
0.957319 0.289032i \(-0.0933334\pi\)
\(234\) 0 0
\(235\) −1.81307 + 3.14033i −0.118272 + 0.204852i
\(236\) 5.67216 + 9.82447i 0.369226 + 0.639518i
\(237\) 0 0
\(238\) −6.45511 12.2269i −0.418422 0.792549i
\(239\) 23.3896i 1.51295i 0.654023 + 0.756474i \(0.273080\pi\)
−0.654023 + 0.756474i \(0.726920\pi\)
\(240\) 0 0
\(241\) 24.9509 + 14.4054i 1.60723 + 0.927934i 0.989987 + 0.141160i \(0.0450833\pi\)
0.617242 + 0.786774i \(0.288250\pi\)
\(242\) −0.866025 0.500000i −0.0556702 0.0321412i
\(243\) 0 0
\(244\) 9.48620i 0.607292i
\(245\) −2.39357 0.181520i −0.152919 0.0115969i
\(246\) 0 0
\(247\) −15.8816 27.5077i −1.01052 1.75027i
\(248\) 0.585401 1.01394i 0.0371730 0.0643855i
\(249\) 0 0
\(250\) 2.93485 1.69444i 0.185616 0.107166i
\(251\) 0.000629331 0 3.97230e−5 0 1.98615e−5 1.00000i \(-0.499994\pi\)
1.98615e−5 1.00000i \(0.499994\pi\)
\(252\) 0 0
\(253\) 2.01175 0.126478
\(254\) 15.2278 8.79176i 0.955476 0.551644i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 4.66866 + 8.08636i 0.291223 + 0.504413i 0.974099 0.226121i \(-0.0726045\pi\)
−0.682876 + 0.730534i \(0.739271\pi\)
\(258\) 0 0
\(259\) −1.41003 0.886858i −0.0876150 0.0551067i
\(260\) 1.40777i 0.0873064i
\(261\) 0 0
\(262\) 4.61488 + 2.66440i 0.285108 + 0.164607i
\(263\) −10.2387 5.91129i −0.631343 0.364506i 0.149929 0.988697i \(-0.452095\pi\)
−0.781272 + 0.624191i \(0.785429\pi\)
\(264\) 0 0
\(265\) 2.52384i 0.155039i
\(266\) −0.774546 + 20.4561i −0.0474904 + 1.25424i
\(267\) 0 0
\(268\) 6.84977 + 11.8641i 0.418416 + 0.724718i
\(269\) 7.03957 12.1929i 0.429210 0.743414i −0.567593 0.823309i \(-0.692125\pi\)
0.996803 + 0.0798953i \(0.0254586\pi\)
\(270\) 0 0
\(271\) 0.920811 0.531631i 0.0559353 0.0322943i −0.471772 0.881721i \(-0.656385\pi\)
0.527707 + 0.849427i \(0.323052\pi\)
\(272\) −5.22582 −0.316862
\(273\) 0 0
\(274\) 21.2670 1.28478
\(275\) 4.22829 2.44120i 0.254975 0.147210i
\(276\) 0 0
\(277\) 5.35251 9.27082i 0.321601 0.557029i −0.659217 0.751952i \(-0.729112\pi\)
0.980819 + 0.194923i \(0.0624457\pi\)
\(278\) −7.23158 12.5255i −0.433721 0.751227i
\(279\) 0 0
\(280\) −0.483045 + 0.768001i −0.0288675 + 0.0458968i
\(281\) 14.1624i 0.844856i 0.906397 + 0.422428i \(0.138822\pi\)
−0.906397 + 0.422428i \(0.861178\pi\)
\(282\) 0 0
\(283\) −5.38593 3.10957i −0.320161 0.184845i 0.331304 0.943524i \(-0.392512\pi\)
−0.651464 + 0.758679i \(0.725845\pi\)
\(284\) −6.47668 3.73932i −0.384321 0.221888i
\(285\) 0 0
\(286\) 4.10525i 0.242749i
\(287\) 10.1763 5.37251i 0.600686 0.317129i
\(288\) 0 0
\(289\) −5.15459 8.92801i −0.303211 0.525177i
\(290\) 0.164386 0.284725i 0.00965308 0.0167196i
\(291\) 0 0
\(292\) −7.35478 + 4.24628i −0.430406 + 0.248495i
\(293\) 2.59450 0.151572 0.0757862 0.997124i \(-0.475853\pi\)
0.0757862 + 0.997124i \(0.475853\pi\)
\(294\) 0 0
\(295\) 3.89019 0.226496
\(296\) −0.545243 + 0.314796i −0.0316916 + 0.0182972i
\(297\) 0 0
\(298\) −5.47375 + 9.48082i −0.317086 + 0.549209i
\(299\) 4.12937 + 7.15227i 0.238807 + 0.413627i
\(300\) 0 0
\(301\) 16.2255 8.56616i 0.935221 0.493745i
\(302\) 24.4191i 1.40516i
\(303\) 0 0
\(304\) 6.70061 + 3.86860i 0.384307 + 0.221880i
\(305\) 2.81719 + 1.62650i 0.161312 + 0.0931333i
\(306\) 0 0
\(307\) 25.0546i 1.42994i 0.699155 + 0.714970i \(0.253560\pi\)
−0.699155 + 0.714970i \(0.746440\pi\)
\(308\) −1.40862 + 2.23959i −0.0802638 + 0.127613i
\(309\) 0 0
\(310\) −0.200746 0.347701i −0.0114016 0.0197481i
\(311\) −10.7158 + 18.5603i −0.607636 + 1.05246i 0.383993 + 0.923336i \(0.374549\pi\)
−0.991629 + 0.129121i \(0.958785\pi\)
\(312\) 0 0
\(313\) −13.2979 + 7.67756i −0.751643 + 0.433961i −0.826287 0.563249i \(-0.809551\pi\)
0.0746444 + 0.997210i \(0.476218\pi\)
\(314\) 4.76352 0.268821
\(315\) 0 0
\(316\) −2.75174 −0.154797
\(317\) −25.1894 + 14.5431i −1.41478 + 0.816823i −0.995834 0.0911886i \(-0.970933\pi\)
−0.418945 + 0.908012i \(0.637600\pi\)
\(318\) 0 0
\(319\) 0.479372 0.830296i 0.0268397 0.0464877i
\(320\) 0.171460 + 0.296977i 0.00958490 + 0.0166015i
\(321\) 0 0
\(322\) 0.201389 5.31877i 0.0112230 0.296404i
\(323\) 40.4332i 2.24976i
\(324\) 0 0
\(325\) 17.3582 + 10.0218i 0.962859 + 0.555907i
\(326\) 18.9566 + 10.9446i 1.04991 + 0.606166i
\(327\) 0 0
\(328\) 4.34939i 0.240155i
\(329\) 23.6821 + 14.8952i 1.30564 + 0.821199i
\(330\) 0 0
\(331\) 14.0602 + 24.3529i 0.772817 + 1.33856i 0.936013 + 0.351965i \(0.114486\pi\)
−0.163196 + 0.986594i \(0.552180\pi\)
\(332\) 3.04454 5.27329i 0.167091 0.289409i
\(333\) 0 0
\(334\) 3.14641 1.81658i 0.172164 0.0993990i
\(335\) 4.69784 0.256671
\(336\) 0 0
\(337\) 5.48292 0.298674 0.149337 0.988786i \(-0.452286\pi\)
0.149337 + 0.988786i \(0.452286\pi\)
\(338\) 3.33689 1.92655i 0.181503 0.104791i
\(339\) 0 0
\(340\) −0.896018 + 1.55195i −0.0485934 + 0.0841663i
\(341\) −0.585401 1.01394i −0.0317012 0.0549081i
\(342\) 0 0
\(343\) −2.09823 + 18.4010i −0.113294 + 0.993562i
\(344\) 6.93485i 0.373902i
\(345\) 0 0
\(346\) 19.0293 + 10.9866i 1.02302 + 0.590641i
\(347\) 3.34986 + 1.93404i 0.179830 + 0.103825i 0.587213 0.809433i \(-0.300225\pi\)
−0.407383 + 0.913258i \(0.633558\pi\)
\(348\) 0 0
\(349\) 14.7716i 0.790704i −0.918530 0.395352i \(-0.870623\pi\)
0.918530 0.395352i \(-0.129377\pi\)
\(350\) −6.03091 11.4234i −0.322366 0.610605i
\(351\) 0 0
\(352\) 0.500000 + 0.866025i 0.0266501 + 0.0461593i
\(353\) −14.0267 + 24.2949i −0.746565 + 1.29309i 0.202895 + 0.979200i \(0.434965\pi\)
−0.949460 + 0.313888i \(0.898368\pi\)
\(354\) 0 0
\(355\) −2.22098 + 1.28229i −0.117878 + 0.0680566i
\(356\) 0.328772 0.0174249
\(357\) 0 0
\(358\) −8.99063 −0.475170
\(359\) 0.862655 0.498054i 0.0455292 0.0262863i −0.477063 0.878869i \(-0.658299\pi\)
0.522592 + 0.852583i \(0.324965\pi\)
\(360\) 0 0
\(361\) 20.4322 35.3895i 1.07538 1.86261i
\(362\) 2.17268 + 3.76318i 0.114193 + 0.197789i
\(363\) 0 0
\(364\) −10.8537 0.410963i −0.568889 0.0215403i
\(365\) 2.91227i 0.152435i
\(366\) 0 0
\(367\) 24.1175 + 13.9243i 1.25892 + 0.726840i 0.972865 0.231372i \(-0.0743214\pi\)
0.286059 + 0.958212i \(0.407655\pi\)
\(368\) −1.74222 1.00587i −0.0908197 0.0524348i
\(369\) 0 0
\(370\) 0.215900i 0.0112241i
\(371\) 19.4584 + 0.736772i 1.01023 + 0.0382513i
\(372\) 0 0
\(373\) 6.25226 + 10.8292i 0.323730 + 0.560717i 0.981255 0.192716i \(-0.0617297\pi\)
−0.657525 + 0.753433i \(0.728396\pi\)
\(374\) −2.61291 + 4.52569i −0.135110 + 0.234018i
\(375\) 0 0
\(376\) 9.15761 5.28715i 0.472268 0.272664i
\(377\) 3.93589 0.202708
\(378\) 0 0
\(379\) −19.4258 −0.997837 −0.498919 0.866649i \(-0.666269\pi\)
−0.498919 + 0.866649i \(0.666269\pi\)
\(380\) 2.29777 1.32662i 0.117873 0.0680542i
\(381\) 0 0
\(382\) −9.19472 + 15.9257i −0.470443 + 0.814831i
\(383\) −7.17025 12.4192i −0.366383 0.634593i 0.622614 0.782529i \(-0.286071\pi\)
−0.988997 + 0.147935i \(0.952737\pi\)
\(384\) 0 0
\(385\) 0.423586 + 0.802330i 0.0215879 + 0.0408905i
\(386\) 6.48694i 0.330176i
\(387\) 0 0
\(388\) 4.52904 + 2.61484i 0.229927 + 0.132749i
\(389\) −30.8956 17.8376i −1.56647 0.904400i −0.996576 0.0826796i \(-0.973652\pi\)
−0.569891 0.821721i \(-0.693014\pi\)
\(390\) 0 0
\(391\) 10.5130i 0.531667i
\(392\) 5.78015 + 3.94840i 0.291942 + 0.199424i
\(393\) 0 0
\(394\) −7.41642 12.8456i −0.373634 0.647153i
\(395\) −0.471813 + 0.817204i −0.0237395 + 0.0411180i
\(396\) 0 0
\(397\) −17.7667 + 10.2576i −0.891684 + 0.514814i −0.874493 0.485038i \(-0.838806\pi\)
−0.0171910 + 0.999852i \(0.505472\pi\)
\(398\) 9.62971 0.482694
\(399\) 0 0
\(400\) −4.88241 −0.244120
\(401\) 28.9810 16.7322i 1.44724 0.835566i 0.448926 0.893569i \(-0.351807\pi\)
0.998316 + 0.0580032i \(0.0184733\pi\)
\(402\) 0 0
\(403\) 2.40322 4.16250i 0.119713 0.207349i
\(404\) 1.69189 + 2.93044i 0.0841748 + 0.145795i
\(405\) 0 0
\(406\) −2.14720 1.35051i −0.106564 0.0670246i
\(407\) 0.629592i 0.0312077i
\(408\) 0 0
\(409\) 0.652343 + 0.376630i 0.0322563 + 0.0186232i 0.516041 0.856564i \(-0.327405\pi\)
−0.483785 + 0.875187i \(0.660738\pi\)
\(410\) −1.29167 0.745746i −0.0637910 0.0368298i
\(411\) 0 0
\(412\) 7.92096i 0.390238i
\(413\) 1.13564 29.9927i 0.0558813 1.47585i
\(414\) 0 0
\(415\) −1.04403 1.80832i −0.0512495 0.0887667i
\(416\) −2.05263 + 3.55525i −0.100638 + 0.174311i
\(417\) 0 0
\(418\) 6.70061 3.86860i 0.327738 0.189219i
\(419\) 35.3035 1.72469 0.862344 0.506324i \(-0.168996\pi\)
0.862344 + 0.506324i \(0.168996\pi\)
\(420\) 0 0
\(421\) 5.07369 0.247276 0.123638 0.992327i \(-0.460544\pi\)
0.123638 + 0.992327i \(0.460544\pi\)
\(422\) −5.86176 + 3.38429i −0.285346 + 0.164745i
\(423\) 0 0
\(424\) 3.67993 6.37383i 0.178713 0.309541i
\(425\) −12.7573 22.0963i −0.618819 1.07183i
\(426\) 0 0
\(427\) 13.3625 21.2452i 0.646656 1.02813i
\(428\) 11.4330i 0.552635i
\(429\) 0 0
\(430\) −2.05949 1.18905i −0.0993176 0.0573411i
\(431\) 2.69425 + 1.55553i 0.129777 + 0.0749270i 0.563483 0.826128i \(-0.309461\pi\)
−0.433706 + 0.901055i \(0.642794\pi\)
\(432\) 0 0
\(433\) 9.26126i 0.445068i 0.974925 + 0.222534i \(0.0714328\pi\)
−0.974925 + 0.222534i \(0.928567\pi\)
\(434\) −2.73932 + 1.44621i −0.131492 + 0.0694205i
\(435\) 0 0
\(436\) −1.49772 2.59413i −0.0717279 0.124236i
\(437\) −7.78265 + 13.4799i −0.372295 + 0.644833i
\(438\) 0 0
\(439\) −30.4323 + 17.5701i −1.45245 + 0.838574i −0.998620 0.0525123i \(-0.983277\pi\)
−0.453833 + 0.891087i \(0.649944\pi\)
\(440\) 0.342920 0.0163481
\(441\) 0 0
\(442\) −21.4533 −1.02043
\(443\) 35.0430 20.2321i 1.66494 0.961255i 0.694642 0.719356i \(-0.255563\pi\)
0.970301 0.241900i \(-0.0777705\pi\)
\(444\) 0 0
\(445\) 0.0563713 0.0976379i 0.00267225 0.00462848i
\(446\) −8.85077 15.3300i −0.419096 0.725896i
\(447\) 0 0
\(448\) 2.33970 1.23523i 0.110540 0.0583593i
\(449\) 6.15757i 0.290594i −0.989388 0.145297i \(-0.953586\pi\)
0.989388 0.145297i \(-0.0464137\pi\)
\(450\) 0 0
\(451\) −3.76668 2.17469i −0.177366 0.102402i
\(452\) 4.51856 + 2.60879i 0.212535 + 0.122707i
\(453\) 0 0
\(454\) 15.1592i 0.711458i
\(455\) −1.98302 + 3.15284i −0.0929655 + 0.147807i
\(456\) 0 0
\(457\) 6.47557 + 11.2160i 0.302914 + 0.524663i 0.976795 0.214177i \(-0.0687071\pi\)
−0.673880 + 0.738840i \(0.735374\pi\)
\(458\) −8.00935 + 13.8726i −0.374252 + 0.648224i
\(459\) 0 0
\(460\) −0.597443 + 0.344934i −0.0278559 + 0.0160826i
\(461\) 17.4323 0.811903 0.405951 0.913895i \(-0.366940\pi\)
0.405951 + 0.913895i \(0.366940\pi\)
\(462\) 0 0
\(463\) 12.1519 0.564745 0.282373 0.959305i \(-0.408879\pi\)
0.282373 + 0.959305i \(0.408879\pi\)
\(464\) −0.830296 + 0.479372i −0.0385455 + 0.0222543i
\(465\) 0 0
\(466\) −14.8610 + 25.7401i −0.688424 + 1.19239i
\(467\) −17.4259 30.1826i −0.806377 1.39669i −0.915358 0.402642i \(-0.868092\pi\)
0.108981 0.994044i \(-0.465241\pi\)
\(468\) 0 0
\(469\) 1.37142 36.2196i 0.0633261 1.67247i
\(470\) 3.62614i 0.167261i
\(471\) 0 0
\(472\) −9.82447 5.67216i −0.452208 0.261082i
\(473\) −6.00576 3.46743i −0.276145 0.159432i
\(474\) 0 0
\(475\) 37.7762i 1.73329i
\(476\) 11.7037 + 7.36121i 0.536439 + 0.337401i
\(477\) 0 0
\(478\) −11.6948 20.2560i −0.534908 0.926488i
\(479\) −2.95464 + 5.11758i −0.135001 + 0.233828i −0.925598 0.378509i \(-0.876437\pi\)
0.790597 + 0.612337i \(0.209770\pi\)
\(480\) 0 0
\(481\) −2.23836 + 1.29232i −0.102060 + 0.0589246i
\(482\) −28.8108 −1.31230
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 1.55310 0.896681i 0.0705225 0.0407162i
\(486\) 0 0
\(487\) −4.93015 + 8.53927i −0.223407 + 0.386951i −0.955840 0.293887i \(-0.905051\pi\)
0.732434 + 0.680838i \(0.238384\pi\)
\(488\) −4.74310 8.21529i −0.214710 0.371889i
\(489\) 0 0
\(490\) 2.16365 1.03958i 0.0977437 0.0469635i
\(491\) 18.1217i 0.817820i −0.912575 0.408910i \(-0.865909\pi\)
0.912575 0.408910i \(-0.134091\pi\)
\(492\) 0 0
\(493\) −4.33898 2.50511i −0.195418 0.112824i
\(494\) 27.5077 + 15.8816i 1.23763 + 0.714546i
\(495\) 0 0
\(496\) 1.17080i 0.0525705i
\(497\) 9.23786 + 17.4978i 0.414374 + 0.784882i
\(498\) 0 0
\(499\) 7.02722 + 12.1715i 0.314582 + 0.544872i 0.979348 0.202179i \(-0.0648024\pi\)
−0.664767 + 0.747051i \(0.731469\pi\)
\(500\) −1.69444 + 2.93485i −0.0757775 + 0.131250i
\(501\) 0 0
\(502\) −0.000545017 0 0.000314665i −2.43253e−5 0 1.40442e-5i
\(503\) −21.2369 −0.946907 −0.473454 0.880819i \(-0.656993\pi\)
−0.473454 + 0.880819i \(0.656993\pi\)
\(504\) 0 0
\(505\) 1.16037 0.0516357
\(506\) −1.74222 + 1.00587i −0.0774513 + 0.0447166i
\(507\) 0 0
\(508\) −8.79176 + 15.2278i −0.390071 + 0.675623i
\(509\) 4.71027 + 8.15842i 0.208779 + 0.361616i 0.951330 0.308174i \(-0.0997177\pi\)
−0.742551 + 0.669789i \(0.766384\pi\)
\(510\) 0 0
\(511\) 22.4531 + 0.850163i 0.993268 + 0.0376090i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −8.08636 4.66866i −0.356674 0.205926i
\(515\) −2.35235 1.35813i −0.103657 0.0598463i
\(516\) 0 0
\(517\) 10.5743i 0.465057i
\(518\) 1.66455 + 0.0630264i 0.0731362 + 0.00276922i
\(519\) 0 0
\(520\) 0.703886 + 1.21917i 0.0308675 + 0.0534640i
\(521\) −5.44022 + 9.42274i −0.238340 + 0.412818i −0.960238 0.279182i \(-0.909937\pi\)
0.721898 + 0.692000i \(0.243270\pi\)
\(522\) 0 0
\(523\) −0.772444 + 0.445971i −0.0337766 + 0.0195010i −0.516793 0.856110i \(-0.672874\pi\)
0.483017 + 0.875611i \(0.339541\pi\)
\(524\) −5.32881 −0.232790
\(525\) 0 0
\(526\) 11.8226 0.515489
\(527\) −5.29869 + 3.05920i −0.230814 + 0.133261i
\(528\) 0 0
\(529\) −9.47644 + 16.4137i −0.412019 + 0.713638i
\(530\) −1.26192 2.18571i −0.0548144 0.0949413i
\(531\) 0 0
\(532\) −9.55725 18.1027i −0.414359 0.784853i
\(533\) 17.8553i 0.773401i
\(534\) 0 0
\(535\) 3.39534 + 1.96030i 0.146794 + 0.0847513i
\(536\) −11.8641 6.84977i −0.512453 0.295865i
\(537\) 0 0
\(538\) 14.0791i 0.606995i
\(539\) 6.30949 3.03156i 0.271769 0.130579i
\(540\) 0 0
\(541\) −2.66539 4.61658i −0.114594 0.198482i 0.803023 0.595947i \(-0.203223\pi\)
−0.917617 + 0.397465i \(0.869890\pi\)
\(542\) −0.531631 + 0.920811i −0.0228355 + 0.0395522i
\(543\) 0 0
\(544\) 4.52569 2.61291i 0.194037 0.112028i
\(545\) −1.02720 −0.0440003
\(546\) 0 0
\(547\) 30.2188 1.29206 0.646032 0.763311i \(-0.276427\pi\)
0.646032 + 0.763311i \(0.276427\pi\)
\(548\) −18.4177 + 10.6335i −0.786767 + 0.454240i
\(549\) 0 0
\(550\) −2.44120 + 4.22829i −0.104093 + 0.180295i
\(551\) 3.70900 + 6.42417i 0.158009 + 0.273679i
\(552\) 0 0
\(553\) 6.16278 + 3.87617i 0.262068 + 0.164831i
\(554\) 10.7050i 0.454813i
\(555\) 0 0
\(556\) 12.5255 + 7.23158i 0.531198 + 0.306687i
\(557\) −25.3468 14.6340i −1.07398 0.620062i −0.144713 0.989474i \(-0.546226\pi\)
−0.929266 + 0.369412i \(0.879559\pi\)
\(558\) 0 0
\(559\) 28.4693i 1.20412i
\(560\) 0.0343286 0.906631i 0.00145065 0.0383121i
\(561\) 0 0
\(562\) −7.08118 12.2650i −0.298702 0.517366i
\(563\) −2.81618 + 4.87776i −0.118688 + 0.205573i −0.919248 0.393679i \(-0.871202\pi\)
0.800560 + 0.599252i \(0.204535\pi\)
\(564\) 0 0
\(565\) 1.54950 0.894606i 0.0651881 0.0376364i
\(566\) 6.21914 0.261410
\(567\) 0 0
\(568\) 7.47863 0.313796
\(569\) −12.9650 + 7.48535i −0.543522 + 0.313802i −0.746505 0.665380i \(-0.768270\pi\)
0.202983 + 0.979182i \(0.434936\pi\)
\(570\) 0 0
\(571\) −16.4658 + 28.5197i −0.689074 + 1.19351i 0.283064 + 0.959101i \(0.408649\pi\)
−0.972138 + 0.234410i \(0.924684\pi\)
\(572\) 2.05263 + 3.55525i 0.0858246 + 0.148653i
\(573\) 0 0
\(574\) −6.12665 + 9.74086i −0.255721 + 0.406576i
\(575\) 9.82217i 0.409613i
\(576\) 0 0
\(577\) −20.7012 11.9519i −0.861803 0.497562i 0.00281285 0.999996i \(-0.499105\pi\)
−0.864616 + 0.502434i \(0.832438\pi\)
\(578\) 8.92801 + 5.15459i 0.371356 + 0.214403i
\(579\) 0 0
\(580\) 0.328772i 0.0136515i
\(581\) −14.2466 + 7.52142i −0.591049 + 0.312041i
\(582\) 0 0
\(583\) −3.67993 6.37383i −0.152407 0.263977i
\(584\) 4.24628 7.35478i 0.175712 0.304343i
\(585\) 0 0
\(586\) −2.24690 + 1.29725i −0.0928188 + 0.0535889i
\(587\) 2.77837 0.114676 0.0573378 0.998355i \(-0.481739\pi\)
0.0573378 + 0.998355i \(0.481739\pi\)
\(588\) 0 0
\(589\) 9.05873 0.373258
\(590\) −3.36900 + 1.94510i −0.138700 + 0.0800783i
\(591\) 0 0
\(592\) 0.314796 0.545243i 0.0129380 0.0224093i
\(593\) 7.35007 + 12.7307i 0.301831 + 0.522787i 0.976551 0.215287i \(-0.0690688\pi\)
−0.674720 + 0.738074i \(0.735735\pi\)
\(594\) 0 0
\(595\) 4.19283 2.21358i 0.171889 0.0907481i
\(596\) 10.9475i 0.448427i
\(597\) 0 0
\(598\) −7.15227 4.12937i −0.292478 0.168862i
\(599\) −4.77123 2.75467i −0.194947 0.112553i 0.399349 0.916799i \(-0.369236\pi\)
−0.594296 + 0.804246i \(0.702569\pi\)
\(600\) 0 0
\(601\) 32.9981i 1.34602i 0.739634 + 0.673009i \(0.234999\pi\)
−0.739634 + 0.673009i \(0.765001\pi\)
\(602\) −9.76860 + 15.5313i −0.398138 + 0.633007i
\(603\) 0 0
\(604\) −12.2096 21.1476i −0.496800 0.860482i
\(605\) 0.171460 0.296977i 0.00697084 0.0120738i
\(606\) 0 0
\(607\) −8.53044 + 4.92505i −0.346240 + 0.199902i −0.663028 0.748595i \(-0.730729\pi\)
0.316788 + 0.948496i \(0.397396\pi\)
\(608\) −7.73720 −0.313785
\(609\) 0 0
\(610\) −3.25301 −0.131710
\(611\) 37.5943 21.7051i 1.52090 0.878094i
\(612\) 0 0
\(613\) 16.5829 28.7224i 0.669776 1.16009i −0.308190 0.951325i \(-0.599723\pi\)
0.977967 0.208762i \(-0.0669434\pi\)
\(614\) −12.5273 21.6979i −0.505560 0.875656i
\(615\) 0 0
\(616\) 0.100107 2.64386i 0.00403341 0.106524i
\(617\) 48.4917i 1.95220i −0.217317 0.976101i \(-0.569731\pi\)
0.217317 0.976101i \(-0.430269\pi\)
\(618\) 0 0
\(619\) −25.8202 14.9073i −1.03780 0.599174i −0.118591 0.992943i \(-0.537838\pi\)
−0.919210 + 0.393769i \(0.871171\pi\)
\(620\) 0.347701 + 0.200746i 0.0139640 + 0.00806213i
\(621\) 0 0
\(622\) 21.4316i 0.859327i
\(623\) −0.736316 0.463116i −0.0294999 0.0185544i
\(624\) 0 0
\(625\) −11.6250 20.1350i −0.464998 0.805401i
\(626\) 7.67756 13.2979i 0.306857 0.531492i
\(627\) 0 0
\(628\) −4.12533 + 2.38176i −0.164619 + 0.0950426i
\(629\) 3.29013 0.131186
\(630\) 0 0
\(631\) −39.7713 −1.58327 −0.791636 0.610993i \(-0.790770\pi\)
−0.791636 + 0.610993i \(0.790770\pi\)
\(632\) 2.38308 1.37587i 0.0947937 0.0547292i
\(633\) 0 0
\(634\) 14.5431 25.1894i 0.577581 1.00040i
\(635\) 3.01487 + 5.22191i 0.119641 + 0.207225i
\(636\) 0 0
\(637\) 23.7290 + 16.2092i 0.940177 + 0.642231i
\(638\) 0.958744i 0.0379570i
\(639\) 0 0
\(640\) −0.296977 0.171460i −0.0117391 0.00677755i
\(641\) −16.6615 9.61950i −0.658088 0.379947i 0.133460 0.991054i \(-0.457391\pi\)
−0.791548 + 0.611107i \(0.790725\pi\)
\(642\) 0 0
\(643\) 1.83592i 0.0724017i 0.999345 + 0.0362009i \(0.0115256\pi\)
−0.999345 + 0.0362009i \(0.988474\pi\)
\(644\) 2.48498 + 4.70689i 0.0979219 + 0.185477i
\(645\) 0 0
\(646\) −20.2166 35.0162i −0.795412 1.37769i
\(647\) −11.6142 + 20.1163i −0.456599 + 0.790853i −0.998779 0.0494095i \(-0.984266\pi\)
0.542179 + 0.840263i \(0.317599\pi\)
\(648\) 0 0
\(649\) −9.82447 + 5.67216i −0.385644 + 0.222652i
\(650\) −20.0435 −0.786171
\(651\) 0 0
\(652\) −21.8892 −0.857248
\(653\) 16.7558 9.67399i 0.655707 0.378573i −0.134932 0.990855i \(-0.543082\pi\)
0.790639 + 0.612282i \(0.209748\pi\)
\(654\) 0 0
\(655\) −0.913677 + 1.58254i −0.0357003 + 0.0618348i
\(656\) 2.17469 + 3.76668i 0.0849076 + 0.147064i
\(657\) 0 0
\(658\) −27.9569 1.05856i −1.08987 0.0412669i
\(659\) 0.487412i 0.0189869i −0.999955 0.00949345i \(-0.996978\pi\)
0.999955 0.00949345i \(-0.00302190\pi\)
\(660\) 0 0
\(661\) 41.9237 + 24.2047i 1.63064 + 0.941452i 0.983895 + 0.178749i \(0.0572051\pi\)
0.646749 + 0.762703i \(0.276128\pi\)
\(662\) −24.3529 14.0602i −0.946504 0.546464i
\(663\) 0 0
\(664\) 6.08907i 0.236302i
\(665\) −7.01479 0.265607i −0.272022 0.0102998i
\(666\) 0 0
\(667\) −0.964375 1.67035i −0.0373408 0.0646761i
\(668\) −1.81658 + 3.14641i −0.0702857 + 0.121738i
\(669\) 0 0
\(670\) −4.06845 + 2.34892i −0.157178 + 0.0907468i
\(671\) −9.48620 −0.366211
\(672\) 0 0
\(673\) 47.0899 1.81518 0.907591 0.419855i \(-0.137919\pi\)
0.907591 + 0.419855i \(0.137919\pi\)
\(674\) −4.74835 + 2.74146i −0.182899 + 0.105597i
\(675\) 0 0
\(676\) −1.92655 + 3.33689i −0.0740981 + 0.128342i
\(677\) −22.3275 38.6723i −0.858115 1.48630i −0.873725 0.486421i \(-0.838302\pi\)
0.0156095 0.999878i \(-0.495031\pi\)
\(678\) 0 0
\(679\) −6.45988 12.2359i −0.247908 0.469571i
\(680\) 1.79204i 0.0687215i
\(681\) 0 0
\(682\) 1.01394 + 0.585401i 0.0388259 + 0.0224162i
\(683\) −4.02722 2.32512i −0.154097 0.0889681i 0.420969 0.907075i \(-0.361690\pi\)
−0.575066 + 0.818107i \(0.695024\pi\)
\(684\) 0 0
\(685\) 7.29286i 0.278646i
\(686\) −7.38339 16.9849i −0.281899 0.648485i
\(687\) 0 0
\(688\) 3.46743 + 6.00576i 0.132194 + 0.228967i
\(689\) 15.1071 26.1662i 0.575533 0.996852i
\(690\) 0 0
\(691\) −3.15984 + 1.82433i −0.120206 + 0.0694009i −0.558897 0.829237i \(-0.688775\pi\)
0.438691 + 0.898638i \(0.355442\pi\)
\(692\) −21.9731 −0.835293
\(693\) 0 0
\(694\) −3.86809 −0.146831
\(695\) 4.29523 2.47985i 0.162927 0.0940661i
\(696\) 0 0
\(697\) −11.3646 + 19.6840i −0.430463 + 0.745584i
\(698\) 7.38578 + 12.7926i 0.279556 + 0.484205i
\(699\) 0 0
\(700\) 10.9346 + 6.87747i 0.413289 + 0.259944i
\(701\) 26.2563i 0.991687i −0.868412 0.495844i \(-0.834859\pi\)
0.868412 0.495844i \(-0.165141\pi\)
\(702\) 0 0
\(703\) −4.21865 2.43564i −0.159110 0.0918619i
\(704\) −0.866025 0.500000i −0.0326396 0.0188445i
\(705\) 0 0
\(706\) 28.0534i 1.05580i
\(707\) 0.338739 8.94624i 0.0127396 0.336458i
\(708\) 0 0
\(709\) 2.84243 + 4.92324i 0.106750 + 0.184896i 0.914452 0.404695i \(-0.132622\pi\)
−0.807702 + 0.589591i \(0.799289\pi\)
\(710\) 1.28229 2.22098i 0.0481233 0.0833520i
\(711\) 0 0
\(712\) −0.284725 + 0.164386i −0.0106705 + 0.00616063i
\(713\) −2.35536 −0.0882088
\(714\) 0 0
\(715\) 1.40777 0.0526477
\(716\) 7.78611 4.49531i 0.290981 0.167998i
\(717\) 0 0
\(718\) −0.498054 + 0.862655i −0.0185872 + 0.0321940i
\(719\) 18.0907 + 31.3340i 0.674670 + 1.16856i 0.976565 + 0.215222i \(0.0690474\pi\)
−0.301895 + 0.953341i \(0.597619\pi\)
\(720\) 0 0
\(721\) −11.1577 + 17.7397i −0.415533 + 0.660662i
\(722\) 40.8643i 1.52081i
\(723\) 0 0
\(724\) −3.76318 2.17268i −0.139858 0.0807469i
\(725\) −4.05384 2.34049i −0.150556 0.0869235i
\(726\) 0 0
\(727\) 1.70442i 0.0632135i −0.999500 0.0316067i \(-0.989938\pi\)
0.999500 0.0316067i \(-0.0100624\pi\)
\(728\) 9.60506 5.07095i 0.355987 0.187942i
\(729\) 0 0
\(730\) −1.45614 2.52210i −0.0538940 0.0933471i
\(731\) −18.1201 + 31.3850i −0.670198 + 1.16082i
\(732\) 0 0
\(733\) −13.5609 + 7.82937i −0.500882 + 0.289185i −0.729078 0.684431i \(-0.760051\pi\)
0.228196 + 0.973615i \(0.426717\pi\)
\(734\) −27.8485 −1.02791
\(735\) 0 0
\(736\) 2.01175 0.0741540
\(737\) −11.8641 + 6.84977i −0.437022 + 0.252315i
\(738\) 0 0
\(739\) −4.43514 + 7.68189i −0.163149 + 0.282583i −0.935996 0.352009i \(-0.885499\pi\)
0.772847 + 0.634592i \(0.218832\pi\)
\(740\) −0.107950 0.186975i −0.00396831 0.00687332i
\(741\) 0 0
\(742\) −17.2199 + 9.09115i −0.632162 + 0.333747i
\(743\) 20.0508i 0.735592i 0.929906 + 0.367796i \(0.119888\pi\)
−0.929906 + 0.367796i \(0.880112\pi\)
\(744\) 0 0
\(745\) −3.25116 1.87706i −0.119113 0.0687701i
\(746\) −10.8292 6.25226i −0.396487 0.228912i
\(747\) 0 0
\(748\) 5.22582i 0.191075i
\(749\) 16.1048 25.6053i 0.588457 0.935597i
\(750\) 0 0
\(751\) 10.2892 + 17.8214i 0.375457 + 0.650311i 0.990395 0.138264i \(-0.0441523\pi\)
−0.614938 + 0.788575i \(0.710819\pi\)
\(752\) −5.28715 + 9.15761i −0.192803 + 0.333944i
\(753\) 0 0
\(754\) −3.40858 + 1.96794i −0.124133 + 0.0716682i
\(755\) −8.37380 −0.304754
\(756\) 0 0
\(757\) −1.02449 −0.0372359 −0.0186179 0.999827i \(-0.505927\pi\)
−0.0186179 + 0.999827i \(0.505927\pi\)
\(758\) 16.8233 9.71291i 0.611048 0.352789i
\(759\) 0 0
\(760\) −1.32662 + 2.29777i −0.0481216 + 0.0833490i
\(761\) −12.6630 21.9330i −0.459035 0.795072i 0.539875 0.841745i \(-0.318471\pi\)
−0.998910 + 0.0466734i \(0.985138\pi\)
\(762\) 0 0
\(763\) −0.299864 + 7.91953i −0.0108558 + 0.286706i
\(764\) 18.3894i 0.665307i
\(765\) 0 0
\(766\) 12.4192 + 7.17025i 0.448725 + 0.259072i
\(767\) −40.3319 23.2856i −1.45630 0.840796i
\(768\) 0 0
\(769\) 24.2686i 0.875147i 0.899183 + 0.437573i \(0.144162\pi\)
−0.899183 + 0.437573i \(0.855838\pi\)
\(770\) −0.768001 0.483045i −0.0276768 0.0174077i
\(771\) 0 0
\(772\) 3.24347 + 5.61785i 0.116735 + 0.202191i
\(773\) 18.4903 32.0261i 0.665050 1.15190i −0.314222 0.949350i \(-0.601744\pi\)
0.979272 0.202551i \(-0.0649231\pi\)
\(774\) 0 0
\(775\) −4.95049 + 2.85816i −0.177827 + 0.102668i
\(776\) −5.22968 −0.187735
\(777\) 0 0
\(778\) 35.6751 1.27901
\(779\) 29.1436 16.8261i 1.04418 0.602856i
\(780\) 0 0
\(781\) 3.73932 6.47668i 0.133803 0.231754i
\(782\) 5.25651 + 9.10455i 0.187973 + 0.325578i
\(783\) 0 0
\(784\) −6.97996 0.529335i −0.249284 0.0189048i
\(785\) 1.63351i 0.0583023i
\(786\) 0 0
\(787\) −8.74398 5.04834i −0.311689 0.179954i 0.335993 0.941864i \(-0.390928\pi\)
−0.647682 + 0.761911i \(0.724261\pi\)
\(788\) 12.8456 + 7.41642i 0.457606 + 0.264199i
\(789\) 0 0
\(790\) 0.943626i 0.0335727i