Properties

Label 637.2.q.h.589.2
Level $637$
Weight $2$
Character 637.589
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.q (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.58891012706304.1
Defining polynomial: \(x^{12} - 5 x^{10} - 2 x^{9} + 15 x^{8} + 2 x^{7} - 30 x^{6} + 4 x^{5} + 60 x^{4} - 16 x^{3} - 80 x^{2} + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 589.2
Root \(0.759479 + 1.19298i\) of defining polynomial
Character \(\chi\) \(=\) 637.589
Dual form 637.2.q.h.491.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.20027 - 0.692976i) q^{2} +(-1.41289 + 2.44719i) q^{3} +(-0.0395678 - 0.0685334i) q^{4} -0.518957i q^{5} +(3.39169 - 1.95819i) q^{6} +2.88158i q^{8} +(-2.49250 - 4.31714i) q^{9} +O(q^{10})\) \(q+(-1.20027 - 0.692976i) q^{2} +(-1.41289 + 2.44719i) q^{3} +(-0.0395678 - 0.0685334i) q^{4} -0.518957i q^{5} +(3.39169 - 1.95819i) q^{6} +2.88158i q^{8} +(-2.49250 - 4.31714i) q^{9} +(-0.359625 + 0.622889i) q^{10} +(1.40656 + 0.812080i) q^{11} +0.223619 q^{12} +(-1.42641 + 3.31140i) q^{13} +(1.26999 + 0.733228i) q^{15} +(1.91773 - 3.32161i) q^{16} +(-0.974127 - 1.68724i) q^{17} +6.90897i q^{18} +(-2.15740 + 1.24558i) q^{19} +(-0.0355659 + 0.0205340i) q^{20} +(-1.12550 - 1.94943i) q^{22} +(-4.57029 + 7.91598i) q^{23} +(-7.05179 - 4.07135i) q^{24} +4.73068 q^{25} +(4.00680 - 2.98610i) q^{26} +5.60916 q^{27} +(2.61498 - 4.52928i) q^{29} +(-1.01622 - 1.76014i) q^{30} -5.79391i q^{31} +(0.387453 - 0.223696i) q^{32} +(-3.97463 + 2.29475i) q^{33} +2.70019i q^{34} +(-0.197245 + 0.341639i) q^{36} +(-8.85879 - 5.11463i) q^{37} +3.45262 q^{38} +(-6.08826 - 8.16934i) q^{39} +1.49542 q^{40} +(-3.64513 - 2.10452i) q^{41} +(-0.498655 - 0.863697i) q^{43} -0.128529i q^{44} +(-2.24041 + 1.29350i) q^{45} +(10.9712 - 6.33421i) q^{46} -4.51725i q^{47} +(5.41908 + 9.38612i) q^{48} +(-5.67810 - 3.27825i) q^{50} +5.50532 q^{51} +(0.283381 - 0.0332676i) q^{52} -8.89651 q^{53} +(-6.73251 - 3.88701i) q^{54} +(0.421434 - 0.729946i) q^{55} -7.03944i q^{57} +(-6.27736 + 3.62424i) q^{58} +(5.37392 - 3.10263i) q^{59} -0.116049i q^{60} +(-6.73536 - 11.6660i) q^{61} +(-4.01504 + 6.95426i) q^{62} -8.29100 q^{64} +(1.71847 + 0.740247i) q^{65} +6.36084 q^{66} +(-7.25094 - 4.18633i) q^{67} +(-0.0770880 + 0.133520i) q^{68} +(-12.9146 - 22.3688i) q^{69} +(-4.50168 + 2.59905i) q^{71} +(12.4402 - 7.18234i) q^{72} -11.8395i q^{73} +(7.08863 + 12.2779i) q^{74} +(-6.68392 + 11.5769i) q^{75} +(0.170727 + 0.0985694i) q^{76} +(1.64640 + 14.0244i) q^{78} +0.982310 q^{79} +(-1.72377 - 0.995221i) q^{80} +(-0.447609 + 0.775281i) q^{81} +(2.91676 + 5.05197i) q^{82} +8.91851i q^{83} +(-0.875603 + 0.505530i) q^{85} +1.38223i q^{86} +(7.38934 + 12.7987i) q^{87} +(-2.34008 + 4.05313i) q^{88} +(10.4087 + 6.00949i) q^{89} +3.58546 q^{90} +0.723345 q^{92} +(14.1788 + 8.18614i) q^{93} +(-3.13035 + 5.42193i) q^{94} +(0.646401 + 1.11960i) q^{95} +1.26423i q^{96} +(-3.82981 + 2.21114i) q^{97} -8.09643i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9} + O(q^{10}) \) \( 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9} - 12 q^{10} + 6 q^{11} + 4 q^{12} - 4 q^{13} + 6 q^{15} - 8 q^{16} + 4 q^{17} + 12 q^{20} + 6 q^{22} - 12 q^{23} - 12 q^{24} - 20 q^{25} + 42 q^{26} - 12 q^{27} + 8 q^{29} + 8 q^{30} + 36 q^{32} + 30 q^{33} - 10 q^{36} - 42 q^{37} - 4 q^{38} - 4 q^{39} - 92 q^{40} - 30 q^{41} + 2 q^{43} + 12 q^{46} + 2 q^{48} - 18 q^{50} + 52 q^{51} - 2 q^{52} - 44 q^{53} - 12 q^{54} + 6 q^{55} - 12 q^{58} - 18 q^{59} - 14 q^{61} + 4 q^{62} - 52 q^{64} + 60 q^{65} + 52 q^{66} - 24 q^{67} + 8 q^{68} - 4 q^{69} - 24 q^{71} + 60 q^{72} + 6 q^{74} - 46 q^{75} + 18 q^{76} - 10 q^{78} - 56 q^{79} + 72 q^{80} + 2 q^{81} - 14 q^{82} - 48 q^{85} + 2 q^{87} - 14 q^{88} + 12 q^{89} - 24 q^{90} + 24 q^{92} - 18 q^{93} - 4 q^{94} - 22 q^{95} - 6 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.20027 0.692976i −0.848719 0.490008i 0.0114993 0.999934i \(-0.496340\pi\)
−0.860218 + 0.509926i \(0.829673\pi\)
\(3\) −1.41289 + 2.44719i −0.815731 + 1.41289i 0.0930713 + 0.995659i \(0.470332\pi\)
−0.908802 + 0.417228i \(0.863002\pi\)
\(4\) −0.0395678 0.0685334i −0.0197839 0.0342667i
\(5\) 0.518957i 0.232085i −0.993244 0.116042i \(-0.962979\pi\)
0.993244 0.116042i \(-0.0370208\pi\)
\(6\) 3.39169 1.95819i 1.38465 0.799429i
\(7\) 0 0
\(8\) 2.88158i 1.01879i
\(9\) −2.49250 4.31714i −0.830833 1.43905i
\(10\) −0.359625 + 0.622889i −0.113723 + 0.196975i
\(11\) 1.40656 + 0.812080i 0.424095 + 0.244851i 0.696828 0.717239i \(-0.254594\pi\)
−0.272733 + 0.962090i \(0.587928\pi\)
\(12\) 0.223619 0.0645533
\(13\) −1.42641 + 3.31140i −0.395616 + 0.918416i
\(14\) 0 0
\(15\) 1.26999 + 0.733228i 0.327909 + 0.189319i
\(16\) 1.91773 3.32161i 0.479433 0.830403i
\(17\) −0.974127 1.68724i −0.236260 0.409215i 0.723378 0.690452i \(-0.242589\pi\)
−0.959638 + 0.281237i \(0.909255\pi\)
\(18\) 6.90897i 1.62846i
\(19\) −2.15740 + 1.24558i −0.494942 + 0.285755i −0.726622 0.687037i \(-0.758911\pi\)
0.231680 + 0.972792i \(0.425578\pi\)
\(20\) −0.0355659 + 0.0205340i −0.00795277 + 0.00459154i
\(21\) 0 0
\(22\) −1.12550 1.94943i −0.239958 0.415620i
\(23\) −4.57029 + 7.91598i −0.952971 + 1.65059i −0.214028 + 0.976828i \(0.568658\pi\)
−0.738943 + 0.673767i \(0.764675\pi\)
\(24\) −7.05179 4.07135i −1.43944 0.831061i
\(25\) 4.73068 0.946137
\(26\) 4.00680 2.98610i 0.785798 0.585622i
\(27\) 5.60916 1.07948
\(28\) 0 0
\(29\) 2.61498 4.52928i 0.485589 0.841065i −0.514274 0.857626i \(-0.671938\pi\)
0.999863 + 0.0165608i \(0.00527172\pi\)
\(30\) −1.01622 1.76014i −0.185535 0.321357i
\(31\) 5.79391i 1.04062i −0.853978 0.520308i \(-0.825817\pi\)
0.853978 0.520308i \(-0.174183\pi\)
\(32\) 0.387453 0.223696i 0.0684926 0.0395442i
\(33\) −3.97463 + 2.29475i −0.691894 + 0.399465i
\(34\) 2.70019i 0.463078i
\(35\) 0 0
\(36\) −0.197245 + 0.341639i −0.0328742 + 0.0569398i
\(37\) −8.85879 5.11463i −1.45638 0.840840i −0.457546 0.889186i \(-0.651272\pi\)
−0.998831 + 0.0483462i \(0.984605\pi\)
\(38\) 3.45262 0.560089
\(39\) −6.08826 8.16934i −0.974902 1.30814i
\(40\) 1.49542 0.236446
\(41\) −3.64513 2.10452i −0.569273 0.328670i 0.187586 0.982248i \(-0.439934\pi\)
−0.756859 + 0.653578i \(0.773267\pi\)
\(42\) 0 0
\(43\) −0.498655 0.863697i −0.0760442 0.131712i 0.825496 0.564408i \(-0.190896\pi\)
−0.901540 + 0.432696i \(0.857562\pi\)
\(44\) 0.128529i 0.0193764i
\(45\) −2.24041 + 1.29350i −0.333980 + 0.192824i
\(46\) 10.9712 6.33421i 1.61761 0.933928i
\(47\) 4.51725i 0.658909i −0.944171 0.329455i \(-0.893135\pi\)
0.944171 0.329455i \(-0.106865\pi\)
\(48\) 5.41908 + 9.38612i 0.782177 + 1.35477i
\(49\) 0 0
\(50\) −5.67810 3.27825i −0.803004 0.463615i
\(51\) 5.50532 0.770899
\(52\) 0.283381 0.0332676i 0.0392979 0.00461339i
\(53\) −8.89651 −1.22203 −0.611015 0.791619i \(-0.709238\pi\)
−0.611015 + 0.791619i \(0.709238\pi\)
\(54\) −6.73251 3.88701i −0.916178 0.528956i
\(55\) 0.421434 0.729946i 0.0568262 0.0984259i
\(56\) 0 0
\(57\) 7.03944i 0.932397i
\(58\) −6.27736 + 3.62424i −0.824258 + 0.475886i
\(59\) 5.37392 3.10263i 0.699624 0.403928i −0.107583 0.994196i \(-0.534311\pi\)
0.807207 + 0.590268i \(0.200978\pi\)
\(60\) 0.116049i 0.0149818i
\(61\) −6.73536 11.6660i −0.862375 1.49368i −0.869630 0.493703i \(-0.835643\pi\)
0.00725571 0.999974i \(-0.497690\pi\)
\(62\) −4.01504 + 6.95426i −0.509911 + 0.883191i
\(63\) 0 0
\(64\) −8.29100 −1.03637
\(65\) 1.71847 + 0.740247i 0.213150 + 0.0918164i
\(66\) 6.36084 0.782965
\(67\) −7.25094 4.18633i −0.885843 0.511442i −0.0132624 0.999912i \(-0.504222\pi\)
−0.872580 + 0.488470i \(0.837555\pi\)
\(68\) −0.0770880 + 0.133520i −0.00934830 + 0.0161917i
\(69\) −12.9146 22.3688i −1.55474 2.69288i
\(70\) 0 0
\(71\) −4.50168 + 2.59905i −0.534251 + 0.308450i −0.742746 0.669573i \(-0.766477\pi\)
0.208495 + 0.978023i \(0.433144\pi\)
\(72\) 12.4402 7.18234i 1.46609 0.846447i
\(73\) 11.8395i 1.38571i −0.721076 0.692856i \(-0.756352\pi\)
0.721076 0.692856i \(-0.243648\pi\)
\(74\) 7.08863 + 12.2779i 0.824037 + 1.42727i
\(75\) −6.68392 + 11.5769i −0.771793 + 1.33678i
\(76\) 0.170727 + 0.0985694i 0.0195838 + 0.0113067i
\(77\) 0 0
\(78\) 1.64640 + 14.0244i 0.186418 + 1.58795i
\(79\) 0.982310 0.110518 0.0552592 0.998472i \(-0.482401\pi\)
0.0552592 + 0.998472i \(0.482401\pi\)
\(80\) −1.72377 0.995221i −0.192724 0.111269i
\(81\) −0.447609 + 0.775281i −0.0497343 + 0.0861423i
\(82\) 2.91676 + 5.05197i 0.322102 + 0.557897i
\(83\) 8.91851i 0.978934i 0.872022 + 0.489467i \(0.162809\pi\)
−0.872022 + 0.489467i \(0.837191\pi\)
\(84\) 0 0
\(85\) −0.875603 + 0.505530i −0.0949725 + 0.0548324i
\(86\) 1.38223i 0.149049i
\(87\) 7.38934 + 12.7987i 0.792220 + 1.37217i
\(88\) −2.34008 + 4.05313i −0.249453 + 0.432065i
\(89\) 10.4087 + 6.00949i 1.10332 + 0.637005i 0.937092 0.349082i \(-0.113506\pi\)
0.166233 + 0.986087i \(0.446840\pi\)
\(90\) 3.58546 0.377941
\(91\) 0 0
\(92\) 0.723345 0.0754139
\(93\) 14.1788 + 8.18614i 1.47027 + 0.848863i
\(94\) −3.13035 + 5.42193i −0.322871 + 0.559229i
\(95\) 0.646401 + 1.11960i 0.0663194 + 0.114869i
\(96\) 1.26423i 0.129030i
\(97\) −3.82981 + 2.21114i −0.388858 + 0.224507i −0.681665 0.731664i \(-0.738744\pi\)
0.292807 + 0.956172i \(0.405411\pi\)
\(98\) 0 0
\(99\) 8.09643i 0.813722i
\(100\) −0.187183 0.324210i −0.0187183 0.0324210i
\(101\) −9.15132 + 15.8506i −0.910591 + 1.57719i −0.0973594 + 0.995249i \(0.531040\pi\)
−0.813231 + 0.581940i \(0.802294\pi\)
\(102\) −6.60787 3.81506i −0.654277 0.377747i
\(103\) 5.02046 0.494680 0.247340 0.968929i \(-0.420444\pi\)
0.247340 + 0.968929i \(0.420444\pi\)
\(104\) −9.54206 4.11033i −0.935676 0.403051i
\(105\) 0 0
\(106\) 10.6782 + 6.16507i 1.03716 + 0.598804i
\(107\) −3.07228 + 5.32134i −0.297008 + 0.514434i −0.975450 0.220221i \(-0.929322\pi\)
0.678442 + 0.734654i \(0.262656\pi\)
\(108\) −0.221942 0.384415i −0.0213564 0.0369903i
\(109\) 11.8962i 1.13945i 0.821834 + 0.569727i \(0.192951\pi\)
−0.821834 + 0.569727i \(0.807049\pi\)
\(110\) −1.01167 + 0.584088i −0.0964590 + 0.0556906i
\(111\) 25.0330 14.4528i 2.37602 1.37180i
\(112\) 0 0
\(113\) −1.77806 3.07969i −0.167266 0.289713i 0.770192 0.637812i \(-0.220161\pi\)
−0.937458 + 0.348099i \(0.886827\pi\)
\(114\) −4.87817 + 8.44923i −0.456882 + 0.791343i
\(115\) 4.10805 + 2.37178i 0.383078 + 0.221170i
\(116\) −0.413875 −0.0384274
\(117\) 17.8511 2.09563i 1.65033 0.193741i
\(118\) −8.60020 −0.791713
\(119\) 0 0
\(120\) −2.11286 + 3.65957i −0.192877 + 0.334072i
\(121\) −4.18105 7.24180i −0.380096 0.658345i
\(122\) 18.6698i 1.69028i
\(123\) 10.3003 5.94689i 0.928748 0.536213i
\(124\) −0.397076 + 0.229252i −0.0356585 + 0.0205874i
\(125\) 5.04981i 0.451668i
\(126\) 0 0
\(127\) −0.711749 + 1.23279i −0.0631575 + 0.109392i −0.895875 0.444306i \(-0.853450\pi\)
0.832718 + 0.553698i \(0.186784\pi\)
\(128\) 9.17653 + 5.29807i 0.811098 + 0.468288i
\(129\) 2.81818 0.248127
\(130\) −1.54966 2.07936i −0.135914 0.182372i
\(131\) −8.67374 −0.757828 −0.378914 0.925432i \(-0.623702\pi\)
−0.378914 + 0.925432i \(0.623702\pi\)
\(132\) 0.314535 + 0.181597i 0.0273767 + 0.0158060i
\(133\) 0 0
\(134\) 5.80205 + 10.0495i 0.501221 + 0.868141i
\(135\) 2.91091i 0.250531i
\(136\) 4.86191 2.80703i 0.416906 0.240701i
\(137\) 7.37667 4.25892i 0.630231 0.363864i −0.150611 0.988593i \(-0.548124\pi\)
0.780842 + 0.624729i \(0.214791\pi\)
\(138\) 35.7981i 3.04733i
\(139\) −2.51922 4.36342i −0.213677 0.370100i 0.739185 0.673502i \(-0.235211\pi\)
−0.952863 + 0.303402i \(0.901877\pi\)
\(140\) 0 0
\(141\) 11.0546 + 6.38237i 0.930964 + 0.537493i
\(142\) 7.20431 0.604572
\(143\) −4.69546 + 3.49933i −0.392654 + 0.292628i
\(144\) −19.1198 −1.59332
\(145\) −2.35050 1.35706i −0.195198 0.112698i
\(146\) −8.20451 + 14.2106i −0.679010 + 1.17608i
\(147\) 0 0
\(148\) 0.809498i 0.0665403i
\(149\) 2.91409 1.68245i 0.238732 0.137832i −0.375862 0.926676i \(-0.622653\pi\)
0.614594 + 0.788844i \(0.289320\pi\)
\(150\) 16.0450 9.26360i 1.31007 0.756370i
\(151\) 12.6566i 1.02998i −0.857196 0.514991i \(-0.827795\pi\)
0.857196 0.514991i \(-0.172205\pi\)
\(152\) −3.58924 6.21674i −0.291125 0.504244i
\(153\) −4.85602 + 8.41087i −0.392586 + 0.679979i
\(154\) 0 0
\(155\) −3.00679 −0.241511
\(156\) −0.318973 + 0.740492i −0.0255383 + 0.0592868i
\(157\) −10.3691 −0.827547 −0.413773 0.910380i \(-0.635789\pi\)
−0.413773 + 0.910380i \(0.635789\pi\)
\(158\) −1.17904 0.680717i −0.0937992 0.0541550i
\(159\) 12.5698 21.7715i 0.996847 1.72659i
\(160\) −0.116089 0.201071i −0.00917761 0.0158961i
\(161\) 0 0
\(162\) 1.07450 0.620364i 0.0844209 0.0487404i
\(163\) 13.6428 7.87669i 1.06859 0.616950i 0.140794 0.990039i \(-0.455035\pi\)
0.927796 + 0.373089i \(0.121701\pi\)
\(164\) 0.333084i 0.0260095i
\(165\) 1.19088 + 2.06266i 0.0927098 + 0.160578i
\(166\) 6.18032 10.7046i 0.479686 0.830840i
\(167\) 14.2016 + 8.19930i 1.09895 + 0.634481i 0.935946 0.352144i \(-0.114547\pi\)
0.163007 + 0.986625i \(0.447881\pi\)
\(168\) 0 0
\(169\) −8.93069 9.44684i −0.686976 0.726680i
\(170\) 1.40128 0.107473
\(171\) 10.7547 + 6.20920i 0.822429 + 0.474830i
\(172\) −0.0394614 + 0.0683491i −0.00300890 + 0.00521157i
\(173\) 0.150677 + 0.260981i 0.0114558 + 0.0198420i 0.871696 0.490046i \(-0.163020\pi\)
−0.860241 + 0.509888i \(0.829687\pi\)
\(174\) 20.4825i 1.55278i
\(175\) 0 0
\(176\) 5.39483 3.11470i 0.406650 0.234780i
\(177\) 17.5347i 1.31799i
\(178\) −8.32887 14.4260i −0.624275 1.08128i
\(179\) −4.90791 + 8.50075i −0.366834 + 0.635376i −0.989069 0.147455i \(-0.952892\pi\)
0.622234 + 0.782831i \(0.286225\pi\)
\(180\) 0.177296 + 0.102362i 0.0132149 + 0.00762960i
\(181\) −12.4320 −0.924062 −0.462031 0.886864i \(-0.652879\pi\)
−0.462031 + 0.886864i \(0.652879\pi\)
\(182\) 0 0
\(183\) 38.0652 2.81386
\(184\) −22.8105 13.1697i −1.68162 0.970881i
\(185\) −2.65427 + 4.59733i −0.195146 + 0.338003i
\(186\) −11.3456 19.6512i −0.831900 1.44089i
\(187\) 3.16427i 0.231395i
\(188\) −0.309583 + 0.178738i −0.0225786 + 0.0130358i
\(189\) 0 0
\(190\) 1.79176i 0.129988i
\(191\) 6.12346 + 10.6061i 0.443078 + 0.767434i 0.997916 0.0645248i \(-0.0205531\pi\)
−0.554838 + 0.831958i \(0.687220\pi\)
\(192\) 11.7142 20.2897i 0.845403 1.46428i
\(193\) −10.0752 5.81692i −0.725229 0.418711i 0.0914452 0.995810i \(-0.470851\pi\)
−0.816674 + 0.577099i \(0.804185\pi\)
\(194\) 6.12908 0.440042
\(195\) −4.23953 + 3.15955i −0.303599 + 0.226260i
\(196\) 0 0
\(197\) −1.55984 0.900572i −0.111134 0.0641631i 0.443403 0.896322i \(-0.353771\pi\)
−0.554537 + 0.832159i \(0.687104\pi\)
\(198\) −5.61064 + 9.71791i −0.398731 + 0.690622i
\(199\) −3.29657 5.70982i −0.233687 0.404759i 0.725203 0.688535i \(-0.241746\pi\)
−0.958890 + 0.283777i \(0.908413\pi\)
\(200\) 13.6319i 0.963918i
\(201\) 20.4895 11.8296i 1.44522 0.834397i
\(202\) 21.9681 12.6833i 1.54567 0.892394i
\(203\) 0 0
\(204\) −0.217833 0.377298i −0.0152514 0.0264162i
\(205\) −1.09215 + 1.89166i −0.0762793 + 0.132120i
\(206\) −6.02590 3.47906i −0.419845 0.242397i
\(207\) 45.5658 3.16704
\(208\) 8.26369 + 11.0884i 0.572984 + 0.768840i
\(209\) −4.04603 −0.279870
\(210\) 0 0
\(211\) −5.35996 + 9.28373i −0.368995 + 0.639118i −0.989409 0.145157i \(-0.953631\pi\)
0.620414 + 0.784275i \(0.286965\pi\)
\(212\) 0.352015 + 0.609708i 0.0241765 + 0.0418749i
\(213\) 14.6886i 1.00645i
\(214\) 7.37513 4.25803i 0.504154 0.291073i
\(215\) −0.448221 + 0.258781i −0.0305684 + 0.0176487i
\(216\) 16.1633i 1.09977i
\(217\) 0 0
\(218\) 8.24382 14.2787i 0.558342 0.967076i
\(219\) 28.9736 + 16.7279i 1.95785 + 1.13037i
\(220\) −0.0667009 −0.00449697
\(221\) 6.97662 0.819021i 0.469298 0.0550933i
\(222\) −40.0617 −2.68877
\(223\) 11.1612 + 6.44392i 0.747409 + 0.431517i 0.824757 0.565487i \(-0.191312\pi\)
−0.0773480 + 0.997004i \(0.524645\pi\)
\(224\) 0 0
\(225\) −11.7912 20.4230i −0.786082 1.36153i
\(226\) 4.92862i 0.327847i
\(227\) 0.605486 0.349577i 0.0401875 0.0232023i −0.479772 0.877393i \(-0.659280\pi\)
0.519959 + 0.854191i \(0.325947\pi\)
\(228\) −0.482437 + 0.278535i −0.0319502 + 0.0184464i
\(229\) 18.2868i 1.20843i 0.796822 + 0.604214i \(0.206513\pi\)
−0.796822 + 0.604214i \(0.793487\pi\)
\(230\) −3.28718 5.69356i −0.216750 0.375422i
\(231\) 0 0
\(232\) 13.0515 + 7.53528i 0.856872 + 0.494715i
\(233\) −26.7796 −1.75439 −0.877194 0.480137i \(-0.840587\pi\)
−0.877194 + 0.480137i \(0.840587\pi\)
\(234\) −22.8783 9.85505i −1.49560 0.644245i
\(235\) −2.34426 −0.152923
\(236\) −0.425268 0.245528i −0.0276826 0.0159825i
\(237\) −1.38789 + 2.40390i −0.0901533 + 0.156150i
\(238\) 0 0
\(239\) 16.6177i 1.07491i −0.843293 0.537454i \(-0.819386\pi\)
0.843293 0.537454i \(-0.180614\pi\)
\(240\) 4.87099 2.81227i 0.314421 0.181531i
\(241\) −15.0800 + 8.70643i −0.971387 + 0.560830i −0.899659 0.436594i \(-0.856185\pi\)
−0.0717279 + 0.997424i \(0.522851\pi\)
\(242\) 11.5895i 0.745000i
\(243\) 7.14890 + 12.3823i 0.458602 + 0.794322i
\(244\) −0.533007 + 0.923194i −0.0341222 + 0.0591015i
\(245\) 0 0
\(246\) −16.4842 −1.05099
\(247\) −1.04725 8.92073i −0.0666350 0.567612i
\(248\) 16.6956 1.06017
\(249\) −21.8253 12.6008i −1.38312 0.798546i
\(250\) −3.49940 + 6.06113i −0.221321 + 0.383340i
\(251\) 3.22491 + 5.58571i 0.203554 + 0.352567i 0.949671 0.313249i \(-0.101417\pi\)
−0.746117 + 0.665815i \(0.768084\pi\)
\(252\) 0 0
\(253\) −12.8568 + 7.42288i −0.808300 + 0.466672i
\(254\) 1.70858 0.986451i 0.107206 0.0618954i
\(255\) 2.85703i 0.178914i
\(256\) 0.948120 + 1.64219i 0.0592575 + 0.102637i
\(257\) 1.83578 3.17966i 0.114513 0.198342i −0.803072 0.595882i \(-0.796803\pi\)
0.917585 + 0.397540i \(0.130136\pi\)
\(258\) −3.38257 1.95293i −0.210590 0.121584i
\(259\) 0 0
\(260\) −0.0172645 0.147063i −0.00107070 0.00912044i
\(261\) −26.0713 −1.61377
\(262\) 10.4108 + 6.01070i 0.643183 + 0.371342i
\(263\) −9.15964 + 15.8650i −0.564807 + 0.978275i 0.432260 + 0.901749i \(0.357716\pi\)
−0.997068 + 0.0765263i \(0.975617\pi\)
\(264\) −6.61252 11.4532i −0.406973 0.704897i
\(265\) 4.61690i 0.283614i
\(266\) 0 0
\(267\) −29.4128 + 16.9815i −1.80003 + 1.03925i
\(268\) 0.662575i 0.0404732i
\(269\) 13.7715 + 23.8529i 0.839661 + 1.45434i 0.890178 + 0.455613i \(0.150580\pi\)
−0.0505171 + 0.998723i \(0.516087\pi\)
\(270\) −2.01719 + 3.49388i −0.122762 + 0.212631i
\(271\) −5.64582 3.25961i −0.342959 0.198007i 0.318621 0.947882i \(-0.396780\pi\)
−0.661580 + 0.749875i \(0.730114\pi\)
\(272\) −7.47246 −0.453084
\(273\) 0 0
\(274\) −11.8053 −0.713186
\(275\) 6.65401 + 3.84169i 0.401252 + 0.231663i
\(276\) −1.02200 + 1.77016i −0.0615174 + 0.106551i
\(277\) 2.72093 + 4.71279i 0.163485 + 0.283164i 0.936116 0.351691i \(-0.114393\pi\)
−0.772631 + 0.634855i \(0.781060\pi\)
\(278\) 6.98304i 0.418815i
\(279\) −25.0131 + 14.4413i −1.49749 + 0.864579i
\(280\) 0 0
\(281\) 3.54237i 0.211320i −0.994402 0.105660i \(-0.966304\pi\)
0.994402 0.105660i \(-0.0336955\pi\)
\(282\) −8.84566 15.3211i −0.526752 0.912360i
\(283\) 7.06956 12.2448i 0.420242 0.727880i −0.575721 0.817646i \(-0.695279\pi\)
0.995963 + 0.0897658i \(0.0286119\pi\)
\(284\) 0.356243 + 0.205677i 0.0211391 + 0.0122047i
\(285\) −3.65317 −0.216395
\(286\) 8.06077 0.946296i 0.476643 0.0559556i
\(287\) 0 0
\(288\) −1.93145 1.11512i −0.113812 0.0657093i
\(289\) 6.60215 11.4353i 0.388362 0.672663i
\(290\) 1.88082 + 3.25768i 0.110446 + 0.191298i
\(291\) 12.4964i 0.732551i
\(292\) −0.811403 + 0.468464i −0.0474838 + 0.0274148i
\(293\) 7.23071 4.17465i 0.422423 0.243886i −0.273691 0.961818i \(-0.588244\pi\)
0.696113 + 0.717932i \(0.254911\pi\)
\(294\) 0 0
\(295\) −1.61013 2.78883i −0.0937455 0.162372i
\(296\) 14.7382 25.5274i 0.856642 1.48375i
\(297\) 7.88964 + 4.55508i 0.457803 + 0.264313i
\(298\) −4.66359 −0.270155
\(299\) −19.6938 26.4255i −1.13892 1.52823i
\(300\) 1.05787 0.0610762
\(301\) 0 0
\(302\) −8.77074 + 15.1914i −0.504699 + 0.874165i
\(303\) −25.8596 44.7901i −1.48559 2.57312i
\(304\) 9.55474i 0.548002i
\(305\) −6.05415 + 3.49536i −0.346659 + 0.200144i
\(306\) 11.6571 6.73021i 0.666390 0.384741i
\(307\) 8.33362i 0.475625i −0.971311 0.237813i \(-0.923570\pi\)
0.971311 0.237813i \(-0.0764304\pi\)
\(308\) 0 0
\(309\) −7.09334 + 12.2860i −0.403526 + 0.698927i
\(310\) 3.60896 + 2.08363i 0.204975 + 0.118342i
\(311\) −14.6227 −0.829176 −0.414588 0.910009i \(-0.636074\pi\)
−0.414588 + 0.910009i \(0.636074\pi\)
\(312\) 23.5406 17.5438i 1.33273 0.993224i
\(313\) −17.1328 −0.968404 −0.484202 0.874956i \(-0.660890\pi\)
−0.484202 + 0.874956i \(0.660890\pi\)
\(314\) 12.4458 + 7.18556i 0.702355 + 0.405505i
\(315\) 0 0
\(316\) −0.0388678 0.0673210i −0.00218649 0.00378710i
\(317\) 14.0000i 0.786320i −0.919470 0.393160i \(-0.871382\pi\)
0.919470 0.393160i \(-0.128618\pi\)
\(318\) −30.1742 + 17.4211i −1.69209 + 0.976926i
\(319\) 7.35627 4.24714i 0.411872 0.237794i
\(320\) 4.30267i 0.240527i
\(321\) −8.68157 15.0369i −0.484558 0.839279i
\(322\) 0 0
\(323\) 4.20317 + 2.42670i 0.233871 + 0.135025i
\(324\) 0.0708435 0.00393575
\(325\) −6.74791 + 15.6652i −0.374307 + 0.868947i
\(326\) −21.8334 −1.20924
\(327\) −29.1124 16.8081i −1.60992 0.929487i
\(328\) 6.06434 10.5037i 0.334847 0.579972i
\(329\) 0 0
\(330\) 3.30100i 0.181714i
\(331\) 5.99286 3.45998i 0.329397 0.190178i −0.326176 0.945309i \(-0.605760\pi\)
0.655574 + 0.755131i \(0.272427\pi\)
\(332\) 0.611216 0.352886i 0.0335448 0.0193671i
\(333\) 50.9928i 2.79439i
\(334\) −11.3638 19.6827i −0.621801 1.07699i
\(335\) −2.17253 + 3.76292i −0.118698 + 0.205591i
\(336\) 0 0
\(337\) 11.1559 0.607703 0.303852 0.952719i \(-0.401727\pi\)
0.303852 + 0.952719i \(0.401727\pi\)
\(338\) 4.17280 + 17.5275i 0.226970 + 0.953371i
\(339\) 10.0488 0.545776
\(340\) 0.0692913 + 0.0400054i 0.00375785 + 0.00216960i
\(341\) 4.70512 8.14950i 0.254796 0.441320i
\(342\) −8.60566 14.9054i −0.465341 0.805994i
\(343\) 0 0
\(344\) 2.48881 1.43692i 0.134188 0.0774734i
\(345\) −11.6084 + 6.70213i −0.624977 + 0.360830i
\(346\) 0.417663i 0.0224537i
\(347\) 2.46255 + 4.26527i 0.132197 + 0.228971i 0.924523 0.381126i \(-0.124464\pi\)
−0.792326 + 0.610097i \(0.791130\pi\)
\(348\) 0.584759 1.01283i 0.0313464 0.0542935i
\(349\) −1.31926 0.761675i −0.0706183 0.0407715i 0.464275 0.885691i \(-0.346315\pi\)
−0.534893 + 0.844920i \(0.679648\pi\)
\(350\) 0 0
\(351\) −8.00098 + 18.5741i −0.427061 + 0.991415i
\(352\) 0.726636 0.0387298
\(353\) −15.5261 8.96401i −0.826372 0.477106i 0.0262367 0.999656i \(-0.491648\pi\)
−0.852609 + 0.522550i \(0.824981\pi\)
\(354\) 12.1511 21.0463i 0.645824 1.11860i
\(355\) 1.34879 + 2.33618i 0.0715865 + 0.123991i
\(356\) 0.951129i 0.0504097i
\(357\) 0 0
\(358\) 11.7816 6.80213i 0.622679 0.359504i
\(359\) 20.0014i 1.05563i 0.849359 + 0.527816i \(0.176989\pi\)
−0.849359 + 0.527816i \(0.823011\pi\)
\(360\) −3.72733 6.45592i −0.196447 0.340257i
\(361\) −6.39707 + 11.0801i −0.336688 + 0.583161i
\(362\) 14.9217 + 8.61507i 0.784269 + 0.452798i
\(363\) 23.6294 1.24022
\(364\) 0 0
\(365\) −6.14421 −0.321602
\(366\) −45.6885 26.3783i −2.38818 1.37882i
\(367\) 13.7078 23.7427i 0.715544 1.23936i −0.247206 0.968963i \(-0.579512\pi\)
0.962749 0.270395i \(-0.0871543\pi\)
\(368\) 17.5292 + 30.3615i 0.913772 + 1.58270i
\(369\) 20.9820i 1.09228i
\(370\) 6.37169 3.67870i 0.331248 0.191246i
\(371\) 0 0
\(372\) 1.29563i 0.0671752i
\(373\) 7.94643 + 13.7636i 0.411451 + 0.712653i 0.995049 0.0993893i \(-0.0316889\pi\)
−0.583598 + 0.812043i \(0.698356\pi\)
\(374\) −2.19277 + 3.79798i −0.113385 + 0.196389i
\(375\) 12.3578 + 7.13481i 0.638156 + 0.368440i
\(376\) 13.0168 0.671292
\(377\) 11.2682 + 15.1199i 0.580341 + 0.778712i
\(378\) 0 0
\(379\) 7.60284 + 4.38950i 0.390532 + 0.225474i 0.682390 0.730988i \(-0.260940\pi\)
−0.291859 + 0.956461i \(0.594274\pi\)
\(380\) 0.0511533 0.0886001i 0.00262411 0.00454509i
\(381\) −2.01124 3.48357i −0.103039 0.178469i
\(382\) 16.9736i 0.868447i
\(383\) −6.89562 + 3.98119i −0.352349 + 0.203429i −0.665720 0.746202i \(-0.731875\pi\)
0.313370 + 0.949631i \(0.398542\pi\)
\(384\) −25.9308 + 14.9712i −1.32328 + 0.763994i
\(385\) 0 0
\(386\) 8.06198 + 13.9638i 0.410344 + 0.710736i
\(387\) −2.48580 + 4.30553i −0.126360 + 0.218862i
\(388\) 0.303074 + 0.174980i 0.0153863 + 0.00888326i
\(389\) −32.0434 −1.62467 −0.812333 0.583194i \(-0.801803\pi\)
−0.812333 + 0.583194i \(0.801803\pi\)
\(390\) 7.27808 0.854411i 0.368540 0.0432648i
\(391\) 17.8082 0.900598
\(392\) 0 0
\(393\) 12.2550 21.2263i 0.618184 1.07073i
\(394\) 1.24815 + 2.16186i 0.0628809 + 0.108913i
\(395\) 0.509777i 0.0256496i
\(396\) −0.554876 + 0.320358i −0.0278836 + 0.0160986i
\(397\) −5.57251 + 3.21729i −0.279676 + 0.161471i −0.633277 0.773925i \(-0.718290\pi\)
0.353601 + 0.935396i \(0.384957\pi\)
\(398\) 9.13777i 0.458035i
\(399\) 0 0
\(400\) 9.07219 15.7135i 0.453609 0.785675i
\(401\) −0.462092 0.266789i −0.0230758 0.0133228i 0.488418 0.872610i \(-0.337574\pi\)
−0.511494 + 0.859287i \(0.670908\pi\)
\(402\) −32.7906 −1.63545
\(403\) 19.1859 + 8.26451i 0.955719 + 0.411685i
\(404\) 1.44839 0.0720601
\(405\) 0.402337 + 0.232290i 0.0199923 + 0.0115426i
\(406\) 0 0
\(407\) −8.30697 14.3881i −0.411761 0.713191i
\(408\) 15.8640i 0.785387i
\(409\) 34.4269 19.8764i 1.70230 0.982824i 0.758877 0.651234i \(-0.225748\pi\)
0.943424 0.331590i \(-0.107585\pi\)
\(410\) 2.62176 1.51367i 0.129479 0.0747550i
\(411\) 24.0695i 1.18726i
\(412\) −0.198648 0.344069i −0.00978670 0.0169511i
\(413\) 0 0
\(414\) −54.6913 31.5760i −2.68793 1.55188i
\(415\) 4.62832 0.227195
\(416\) 0.188078 + 1.60209i 0.00922128 + 0.0785490i
\(417\) 14.2375 0.697213
\(418\) 4.85633 + 2.80380i 0.237531 + 0.137139i
\(419\) 11.9088 20.6266i 0.581783 1.00768i −0.413485 0.910511i \(-0.635689\pi\)
0.995268 0.0971665i \(-0.0309779\pi\)
\(420\) 0 0
\(421\) 23.2419i 1.13274i 0.824151 + 0.566370i \(0.191653\pi\)
−0.824151 + 0.566370i \(0.808347\pi\)
\(422\) 12.8668 7.42865i 0.626346 0.361621i
\(423\) −19.5016 + 11.2593i −0.948200 + 0.547444i
\(424\) 25.6360i 1.24500i
\(425\) −4.60828 7.98178i −0.223535 0.387173i
\(426\) −10.1789 + 17.6303i −0.493168 + 0.854192i
\(427\) 0 0
\(428\) 0.486253 0.0235039
\(429\) −1.92937 16.4348i −0.0931510 0.793482i
\(430\) 0.717316 0.0345920
\(431\) −2.34424 1.35345i −0.112918 0.0651932i 0.442477 0.896780i \(-0.354100\pi\)
−0.555395 + 0.831586i \(0.687433\pi\)
\(432\) 10.7569 18.6314i 0.517540 0.896406i
\(433\) 2.90945 + 5.03932i 0.139819 + 0.242174i 0.927428 0.374002i \(-0.122015\pi\)
−0.787609 + 0.616176i \(0.788681\pi\)
\(434\) 0 0
\(435\) 6.64198 3.83475i 0.318459 0.183862i
\(436\) 0.815290 0.470708i 0.0390453 0.0225428i
\(437\) 22.7706i 1.08927i
\(438\) −23.1841 40.1560i −1.10778 1.91873i
\(439\) −19.0851 + 33.0563i −0.910882 + 1.57769i −0.0980599 + 0.995181i \(0.531264\pi\)
−0.812822 + 0.582513i \(0.802070\pi\)
\(440\) 2.10340 + 1.21440i 0.100276 + 0.0578942i
\(441\) 0 0
\(442\) −8.94139 3.85158i −0.425298 0.183201i
\(443\) −31.6740 −1.50488 −0.752440 0.658661i \(-0.771123\pi\)
−0.752440 + 0.658661i \(0.771123\pi\)
\(444\) −1.98100 1.14373i −0.0940139 0.0542790i
\(445\) 3.11867 5.40169i 0.147839 0.256065i
\(446\) −8.93097 15.4689i −0.422894 0.732473i
\(447\) 9.50845i 0.449734i
\(448\) 0 0
\(449\) 27.1975 15.7025i 1.28353 0.741045i 0.306036 0.952020i \(-0.400997\pi\)
0.977491 + 0.210975i \(0.0676638\pi\)
\(450\) 32.6842i 1.54075i
\(451\) −3.41807 5.92027i −0.160951 0.278775i
\(452\) −0.140708 + 0.243713i −0.00661834 + 0.0114633i
\(453\) 30.9732 + 17.8824i 1.45525 + 0.840187i
\(454\) −0.968995 −0.0454772
\(455\) 0 0
\(456\) 20.2847 0.949920
\(457\) 27.5640 + 15.9141i 1.28939 + 0.744429i 0.978545 0.206032i \(-0.0660551\pi\)
0.310844 + 0.950461i \(0.399388\pi\)
\(458\) 12.6723 21.9491i 0.592140 1.02562i
\(459\) −5.46403 9.46398i −0.255039 0.441741i
\(460\) 0.375385i 0.0175024i
\(461\) −1.01005 + 0.583153i −0.0470427 + 0.0271601i −0.523337 0.852126i \(-0.675313\pi\)
0.476294 + 0.879286i \(0.341980\pi\)
\(462\) 0 0
\(463\) 20.3441i 0.945469i −0.881205 0.472734i \(-0.843267\pi\)
0.881205 0.472734i \(-0.156733\pi\)
\(464\) −10.0297 17.3719i −0.465615 0.806470i
\(465\) 4.24825 7.35819i 0.197008 0.341228i
\(466\) 32.1427 + 18.5576i 1.48898 + 0.859664i
\(467\) −1.56939 −0.0726229 −0.0363114 0.999341i \(-0.511561\pi\)
−0.0363114 + 0.999341i \(0.511561\pi\)
\(468\) −0.849948 1.14048i −0.0392889 0.0527185i
\(469\) 0 0
\(470\) 2.81375 + 1.62452i 0.129788 + 0.0749334i
\(471\) 14.6504 25.3753i 0.675055 1.16923i
\(472\) 8.94049 + 15.4854i 0.411519 + 0.712773i
\(473\) 1.61979i 0.0744781i
\(474\) 3.33169 1.92355i 0.153030 0.0883517i
\(475\) −10.2060 + 5.89243i −0.468283 + 0.270363i
\(476\) 0 0
\(477\) 22.1745 + 38.4074i 1.01530 + 1.75856i
\(478\) −11.5157 + 19.9457i −0.526714 + 0.912295i
\(479\) −6.68501 3.85959i −0.305446 0.176349i 0.339441 0.940627i \(-0.389762\pi\)
−0.644887 + 0.764278i \(0.723095\pi\)
\(480\) 0.656080 0.0299458
\(481\) 29.5729 22.0394i 1.34841 1.00491i
\(482\) 24.1334 1.09925
\(483\) 0 0
\(484\) −0.330870 + 0.573083i −0.0150395 + 0.0260492i
\(485\) 1.14749 + 1.98751i 0.0521047 + 0.0902481i
\(486\) 19.8161i 0.898875i
\(487\) −0.0659739 + 0.0380900i −0.00298956 + 0.00172602i −0.501494 0.865161i \(-0.667216\pi\)
0.498504 + 0.866887i \(0.333883\pi\)
\(488\) 33.6165 19.4085i 1.52175 0.878582i
\(489\) 44.5155i 2.01306i
\(490\) 0 0
\(491\) 0.893574 1.54772i 0.0403264 0.0698474i −0.845158 0.534517i \(-0.820494\pi\)
0.885484 + 0.464670i \(0.153827\pi\)
\(492\) −0.815121 0.470610i −0.0367485 0.0212167i
\(493\) −10.1893 −0.458902
\(494\) −4.92487 + 11.4330i −0.221580 + 0.514395i
\(495\) −4.20170 −0.188852
\(496\) −19.2451 11.1112i −0.864131 0.498906i
\(497\) 0 0
\(498\) 17.4642 + 30.2488i 0.782589 + 1.35548i
\(499\) 8.33493i 0.373123i 0.982443 + 0.186561i \(0.0597343\pi\)
−0.982443 + 0.186561i \(0.940266\pi\)
\(500\) −0.346080 + 0.199810i −0.0154772 + 0.00893576i
\(501\) −40.1305 + 23.1694i −1.79290 + 1.03513i
\(502\) 8.93914i 0.398973i
\(503\) 0.720238 + 1.24749i 0.0321138 + 0.0556228i 0.881636 0.471931i \(-0.156443\pi\)
−0.849522 + 0.527554i \(0.823109\pi\)
\(504\) 0 0
\(505\) 8.22576 + 4.74914i 0.366041 + 0.211334i
\(506\) 20.5755 0.914693
\(507\) 35.7363 8.50779i 1.58710 0.377844i
\(508\) 0.112649 0.00499801
\(509\) −12.8394 7.41282i −0.569096 0.328568i 0.187692 0.982228i \(-0.439899\pi\)
−0.756788 + 0.653660i \(0.773233\pi\)
\(510\) −1.97985 + 3.42920i −0.0876693 + 0.151848i
\(511\) 0 0
\(512\) 23.8204i 1.05272i
\(513\) −12.1012 + 6.98664i −0.534282 + 0.308468i
\(514\) −4.40686 + 2.54430i −0.194378 + 0.112224i
\(515\) 2.60540i 0.114808i
\(516\) −0.111509 0.193139i −0.00490891 0.00850248i
\(517\) 3.66837 6.35380i 0.161335 0.279440i
\(518\) 0 0
\(519\) −0.851561 −0.0373794
\(520\) −2.13308 + 4.95192i −0.0935419 + 0.217156i
\(521\) 0.334388 0.0146498 0.00732489 0.999973i \(-0.497668\pi\)
0.00732489 + 0.999973i \(0.497668\pi\)
\(522\) 31.2926 + 18.0668i 1.36964 + 0.790763i
\(523\) −16.2533 + 28.1515i −0.710705 + 1.23098i 0.253887 + 0.967234i \(0.418291\pi\)
−0.964593 + 0.263744i \(0.915043\pi\)
\(524\) 0.343201 + 0.594441i 0.0149928 + 0.0259683i
\(525\) 0 0
\(526\) 21.9881 12.6948i 0.958726 0.553521i
\(527\) −9.77570 + 5.64400i −0.425836 + 0.245857i
\(528\) 17.6029i 0.766068i
\(529\) −30.2751 52.4380i −1.31631 2.27991i
\(530\) 3.19941 5.54153i 0.138973 0.240709i
\(531\) −26.7890 15.4666i −1.16254 0.671194i
\(532\) 0 0
\(533\) 12.1683 9.06855i 0.527070 0.392803i
\(534\) 47.0710 2.03696
\(535\) 2.76155 + 1.59438i 0.119392 + 0.0689311i
\(536\) 12.0633 20.8942i 0.521053 0.902491i
\(537\) −13.8686 24.0212i −0.598476 1.03659i
\(538\) 38.1732i 1.64576i
\(539\) 0 0
\(540\) −0.199495 + 0.115178i −0.00858488 + 0.00495649i
\(541\) 10.6015i 0.455796i −0.973685 0.227898i \(-0.926815\pi\)
0.973685 0.227898i \(-0.0731852\pi\)
\(542\) 4.51767 + 7.82483i 0.194051 + 0.336105i
\(543\) 17.5650 30.4235i 0.753786 1.30560i
\(544\) −0.754856 0.435816i −0.0323642 0.0186855i
\(545\) 6.17364 0.264450
\(546\) 0 0
\(547\) 10.2327 0.437519 0.218760 0.975779i \(-0.429799\pi\)
0.218760 + 0.975779i \(0.429799\pi\)
\(548\) −0.583756 0.337032i −0.0249368 0.0143973i
\(549\) −33.5758 + 58.1549i −1.43298 + 2.48199i
\(550\) −5.32440 9.22214i −0.227033 0.393233i
\(551\) 13.0286i 0.555038i
\(552\) 64.4574 37.2145i 2.74349 1.58396i
\(553\) 0 0
\(554\) 7.54216i 0.320436i
\(555\) −7.50037 12.9910i −0.318373 0.551438i
\(556\) −0.199360 + 0.345301i −0.00845474 + 0.0146440i
\(557\) 27.7067 + 15.9965i 1.17397 + 0.677793i 0.954612 0.297851i \(-0.0962700\pi\)
0.219359 + 0.975644i \(0.429603\pi\)
\(558\) 40.0300 1.69460
\(559\) 3.57133 0.419257i 0.151051 0.0177327i
\(560\) 0 0
\(561\) 7.74359 + 4.47076i 0.326934 + 0.188756i
\(562\) −2.45478 + 4.25180i −0.103549 + 0.179351i
\(563\) −5.39566 9.34556i −0.227400 0.393868i 0.729637 0.683835i \(-0.239689\pi\)
−0.957037 + 0.289967i \(0.906356\pi\)
\(564\) 1.01014i 0.0425348i
\(565\) −1.59823 + 0.922737i −0.0672380 + 0.0388199i
\(566\) −16.9708 + 9.79808i −0.713335 + 0.411844i
\(567\) 0 0
\(568\) −7.48937 12.9720i −0.314247 0.544292i
\(569\) −12.3007 + 21.3054i −0.515672 + 0.893170i 0.484163 + 0.874978i \(0.339124\pi\)
−0.999835 + 0.0181917i \(0.994209\pi\)
\(570\) 4.38479 + 2.53156i 0.183659 + 0.106035i
\(571\) −16.5724 −0.693534 −0.346767 0.937951i \(-0.612721\pi\)
−0.346767 + 0.937951i \(0.612721\pi\)
\(572\) 0.425610 + 0.183335i 0.0177956 + 0.00766563i
\(573\) −34.6070 −1.44573
\(574\) 0 0
\(575\) −21.6206 + 37.4480i −0.901641 + 1.56169i
\(576\) 20.6653 + 35.7934i 0.861054 + 1.49139i
\(577\) 14.6611i 0.610348i −0.952297 0.305174i \(-0.901285\pi\)
0.952297 0.305174i \(-0.0987147\pi\)
\(578\) −15.8487 + 9.15027i −0.659221 + 0.380601i
\(579\) 28.4702 16.4373i 1.18318 0.683111i
\(580\) 0.214784i 0.00891840i
\(581\) 0 0
\(582\) −8.65969 + 14.9990i −0.358956 + 0.621730i
\(583\) −12.5135 7.22467i −0.518256 0.299215i
\(584\) 34.1166 1.41175
\(585\) −1.08754 9.26394i −0.0449644 0.383017i
\(586\) −11.5717 −0.478024
\(587\) −30.5998 17.6668i −1.26299 0.729186i −0.289336 0.957227i \(-0.593435\pi\)
−0.973652 + 0.228041i \(0.926768\pi\)
\(588\) 0 0
\(589\) 7.21676 + 12.4998i 0.297362 + 0.515045i
\(590\) 4.46313i 0.183744i
\(591\) 4.40775 2.54481i 0.181310 0.104680i
\(592\) −33.9776 + 19.6170i −1.39647 + 0.806253i
\(593\) 16.4294i 0.674675i 0.941384 + 0.337338i \(0.109526\pi\)
−0.941384 + 0.337338i \(0.890474\pi\)
\(594\) −6.31313 10.9347i −0.259031 0.448655i
\(595\) 0 0
\(596\) −0.230608 0.133142i −0.00944608 0.00545370i
\(597\) 18.6307 0.762504
\(598\) 5.32564 + 45.3651i 0.217782 + 1.85512i
\(599\) 12.0819 0.493653 0.246826 0.969060i \(-0.420612\pi\)
0.246826 + 0.969060i \(0.420612\pi\)
\(600\) −33.3598 19.2603i −1.36191 0.786297i
\(601\) 3.90743 6.76787i 0.159387 0.276067i −0.775261 0.631642i \(-0.782381\pi\)
0.934648 + 0.355574i \(0.115715\pi\)
\(602\) 0 0
\(603\) 41.7377i 1.69969i
\(604\) −0.867401 + 0.500794i −0.0352941 + 0.0203770i
\(605\) −3.75818 + 2.16979i −0.152792 + 0.0882144i
\(606\) 71.6803i 2.91181i
\(607\) 17.7825 + 30.8001i 0.721768 + 1.25014i 0.960291 + 0.279002i \(0.0900035\pi\)
−0.238523 + 0.971137i \(0.576663\pi\)
\(608\) −0.557261 + 0.965205i −0.0225999 + 0.0391442i
\(609\) 0 0
\(610\) 9.68882 0.392289
\(611\) 14.9584 + 6.44347i 0.605153 + 0.260675i
\(612\) 0.768568 0.0310675
\(613\) −10.3376 5.96839i −0.417530 0.241061i 0.276490 0.961017i \(-0.410829\pi\)
−0.694020 + 0.719956i \(0.744162\pi\)
\(614\) −5.77500 + 10.0026i −0.233060 + 0.403672i
\(615\) −3.08618 5.34542i −0.124447 0.215548i
\(616\) 0 0
\(617\) −20.4124 + 11.7851i −0.821772 + 0.474450i −0.851027 0.525122i \(-0.824020\pi\)
0.0292550 + 0.999572i \(0.490687\pi\)
\(618\) 17.0278 9.83103i 0.684960 0.395462i
\(619\) 28.5571i 1.14781i 0.818923 + 0.573904i \(0.194572\pi\)
−0.818923 + 0.573904i \(0.805428\pi\)
\(620\) 0.118972 + 0.206066i 0.00477803 + 0.00827579i
\(621\) −25.6355 + 44.4020i −1.02872 + 1.78179i
\(622\) 17.5512 + 10.1332i 0.703738 + 0.406303i
\(623\) 0 0
\(624\) −38.8110 + 4.55623i −1.55368 + 0.182395i
\(625\) 21.0328 0.841311
\(626\) 20.5640 + 11.8726i 0.821903 + 0.474526i
\(627\) 5.71659 9.90142i 0.228298 0.395425i
\(628\) 0.410283 + 0.710632i 0.0163721 + 0.0283573i
\(629\) 19.9292i 0.794628i
\(630\) 0 0
\(631\) −38.9646 + 22.4962i −1.55116 + 0.895561i −0.553109 + 0.833109i \(0.686559\pi\)
−0.998048 + 0.0624526i \(0.980108\pi\)
\(632\) 2.83061i 0.112596i
\(633\) −15.1460 26.2337i −0.602001 1.04270i
\(634\) −9.70169 + 16.8038i −0.385303 + 0.667365i
\(635\) 0.639763 + 0.369367i 0.0253882 + 0.0146579i
\(636\) −1.98943 −0.0788860
\(637\) 0 0
\(638\) −11.7727 −0.466085
\(639\) 22.4409 + 12.9562i 0.887747 + 0.512541i
\(640\) 2.74947 4.76222i 0.108682 0.188243i
\(641\) −1.26650 2.19364i −0.0500238 0.0866437i 0.839929 0.542696i \(-0.182596\pi\)
−0.889953 + 0.456052i \(0.849263\pi\)
\(642\) 24.0645i 0.949749i
\(643\) −15.9150 + 9.18853i −0.627627 + 0.362360i −0.779832 0.625988i \(-0.784696\pi\)
0.152206 + 0.988349i \(0.451362\pi\)
\(644\) 0 0
\(645\) 1.46251i 0.0575863i
\(646\) −3.36329 5.82539i −0.132327 0.229197i
\(647\) −10.4643 + 18.1248i −0.411396 + 0.712558i −0.995043 0.0994494i \(-0.968292\pi\)
0.583647 + 0.812008i \(0.301625\pi\)
\(648\) −2.23404 1.28982i −0.0877612 0.0506690i
\(649\) 10.0783 0.395609
\(650\) 18.9549 14.1263i 0.743473 0.554079i
\(651\) 0 0
\(652\) −1.07963 0.623326i −0.0422817 0.0244113i
\(653\) 24.0580 41.6696i 0.941461 1.63066i 0.178775 0.983890i \(-0.442786\pi\)
0.762686 0.646769i \(-0.223880\pi\)
\(654\) 23.2952 + 40.3484i 0.910913 + 1.57775i
\(655\) 4.50130i 0.175880i
\(656\) −13.9808 + 8.07180i −0.545857 + 0.315151i
\(657\) −51.1129 + 29.5100i −1.99410 + 1.15130i
\(658\) 0 0
\(659\) 1.10819 + 1.91944i 0.0431690 + 0.0747708i 0.886803 0.462148i \(-0.152921\pi\)
−0.843634 + 0.536919i \(0.819588\pi\)
\(660\) 0.0942408 0.163230i 0.00366832 0.00635371i
\(661\) 0.552034 + 0.318717i 0.0214716 + 0.0123966i 0.510697 0.859761i \(-0.329387\pi\)
−0.489226 + 0.872157i \(0.662721\pi\)
\(662\) −9.59073 −0.372754
\(663\) −7.85287 + 18.2303i −0.304980 + 0.708006i
\(664\) −25.6994 −0.997331
\(665\) 0 0
\(666\) 35.3368 61.2052i 1.36927 2.37165i
\(667\) 23.9024 + 41.4002i 0.925506 + 1.60302i
\(668\) 1.29771i 0.0502100i
\(669\) −31.5390 + 18.2091i −1.21937 + 0.704003i
\(670\) 5.21523 3.01102i 0.201482 0.116326i
\(671\) 21.8786i 0.844614i
\(672\) 0 0
\(673\) 7.70343 13.3427i 0.296945 0.514324i −0.678490 0.734609i \(-0.737365\pi\)
0.975436 + 0.220285i \(0.0706988\pi\)
\(674\) −13.3901 7.73081i −0.515769 0.297780i
\(675\) 26.5352 1.02134
\(676\) −0.294057 + 0.985841i −0.0113099 + 0.0379170i
\(677\) 11.6812 0.448945 0.224473 0.974480i \(-0.427934\pi\)
0.224473 + 0.974480i \(0.427934\pi\)
\(678\) −12.0613 6.96358i −0.463210 0.267435i
\(679\) 0 0
\(680\) −1.45673 2.52312i −0.0558629 0.0967574i
\(681\) 1.97565i 0.0757072i
\(682\) −11.2948 + 6.52107i −0.432501 + 0.249705i
\(683\) 19.8419 11.4557i 0.759227 0.438340i −0.0697909 0.997562i \(-0.522233\pi\)
0.829018 + 0.559221i \(0.188900\pi\)
\(684\) 0.982737i 0.0375759i
\(685\) −2.21020 3.82817i −0.0844473 0.146267i
\(686\) 0 0
\(687\) −44.7514 25.8372i −1.70737 0.985752i
\(688\) −3.82515 −0.145833
\(689\) 12.6901 29.4599i 0.483454 1.12233i
\(690\) 18.5777 0.707239
\(691\) 40.9046 + 23.6163i 1.55608 + 0.898405i 0.997625 + 0.0688729i \(0.0219403\pi\)
0.558458 + 0.829533i \(0.311393\pi\)
\(692\) 0.0119239 0.0206529i 0.000453280 0.000785104i
\(693\) 0 0
\(694\) 6.82596i 0.259110i
\(695\) −2.26443 + 1.30737i −0.0858946 + 0.0495913i
\(696\) −36.8805 + 21.2930i −1.39795 + 0.807109i
\(697\) 8.20026i 0.310607i
\(698\) 1.05565 + 1.82843i 0.0399568 + 0.0692071i
\(699\) 37.8365 65.5347i 1.43111 2.47875i
\(700\) 0 0
\(701\) 12.2098 0.461158 0.230579 0.973054i \(-0.425938\pi\)
0.230579 + 0.973054i \(0.425938\pi\)
\(702\) 22.4748 16.7495i 0.848256 0.632169i
\(703\) 25.4827 0.961097
\(704\) −11.6618 6.73295i −0.439521 0.253758i
\(705\) 3.31218 5.73686i 0.124744 0.216063i
\(706\) 12.4237 + 21.5185i 0.467572 + 0.809858i
\(707\) 0 0
\(708\) 1.20171 0.693808i 0.0451630 0.0260749i
\(709\) −15.4910 + 8.94374i −0.581777 + 0.335889i −0.761839 0.647766i \(-0.775703\pi\)
0.180062 + 0.983655i \(0.442370\pi\)
\(710\) 3.73873i 0.140312i
\(711\) −2.44841 4.24076i −0.0918224 0.159041i
\(712\) −17.3169 + 29.9937i −0.648977 + 1.12406i
\(713\) 45.8644 + 26.4798i 1.71764 + 0.991678i
\(714\) 0 0
\(715\) 1.81600 + 2.43674i 0.0679146 + 0.0911290i
\(716\) 0.776780 0.0290296
\(717\) 40.6667 + 23.4789i 1.51872 + 0.876836i
\(718\) 13.8605 24.0070i 0.517268 0.895935i
\(719\) −4.56317 7.90364i −0.170178 0.294756i 0.768304 0.640085i \(-0.221101\pi\)
−0.938482 + 0.345329i \(0.887767\pi\)
\(720\) 9.92235i 0.369784i
\(721\) 0 0
\(722\) 15.3564 8.86604i 0.571507 0.329960i
\(723\) 49.2048i 1.82995i
\(724\) 0.491906 + 0.852006i 0.0182815 + 0.0316646i
\(725\) 12.3706 21.4266i 0.459434 0.795763i
\(726\) −28.3617 16.3746i −1.05260 0.607719i
\(727\) −33.6859 −1.24934 −0.624670 0.780889i \(-0.714767\pi\)
−0.624670 + 0.780889i \(0.714767\pi\)
\(728\) 0 0
\(729\) −43.0880 −1.59585
\(730\) 7.37471 + 4.25779i 0.272950 + 0.157588i
\(731\) −0.971507 + 1.68270i −0.0359325 + 0.0622369i
\(732\) −1.50616 2.60874i −0.0556691 0.0964218i
\(733\) 46.4344i 1.71509i −0.514406 0.857547i \(-0.671987\pi\)
0.514406 0.857547i \(-0.328013\pi\)
\(734\) −32.9062 + 18.9984i −1.21459 + 0.701245i
\(735\) 0 0
\(736\) 4.08942i 0.150738i
\(737\) −6.79927 11.7767i −0.250454 0.433799i
\(738\) 14.5400 25.1841i 0.535226 0.927039i
\(739\) −1.60237 0.925127i −0.0589440 0.0340314i 0.470238 0.882539i \(-0.344168\pi\)
−0.529182 + 0.848508i \(0.677501\pi\)
\(740\) 0.420095 0.0154430
\(741\) 23.3104 + 10.0412i 0.856328 + 0.368871i
\(742\) 0 0
\(743\) 28.7095 + 16.5755i 1.05325 + 0.608094i 0.923558 0.383460i \(-0.125268\pi\)
0.129693 + 0.991554i \(0.458601\pi\)
\(744\) −23.5890 + 40.8574i −0.864816 + 1.49791i
\(745\) −0.873120 1.51229i −0.0319886 0.0554059i
\(746\) 22.0268i 0.806457i
\(747\) 38.5024 22.2294i 1.40873 0.813331i
\(748\) −0.216858 + 0.125203i −0.00792913 + 0.00457788i
\(749\) 0 0
\(750\) −9.88850 17.1274i −0.361077 0.625404i
\(751\) −10.3871 + 17.9910i −0.379032 + 0.656503i −0.990922 0.134441i \(-0.957076\pi\)
0.611890 + 0.790943i \(0.290410\pi\)
\(752\) −15.0046 8.66289i −0.547160 0.315903i
\(753\) −18.2257 −0.664182
\(754\) −3.04717 25.9565i −0.110971 0.945280i
\(755\) −6.56824 −0.239043
\(756\) 0 0
\(757\) −21.8075 + 37.7717i −0.792607 + 1.37283i 0.131741 + 0.991284i \(0.457943\pi\)
−0.924348 + 0.381551i \(0.875390\pi\)
\(758\) −6.08364 10.5372i −0.220968 0.382727i
\(759\) 41.9508i 1.52272i
\(760\) −3.22622 + 1.86266i −0.117027 + 0.0675657i
\(761\) −10.7302 + 6.19511i −0.388971 + 0.224573i −0.681714 0.731619i \(-0.738765\pi\)
0.292743 + 0.956191i \(0.405432\pi\)
\(762\) 5.57497i 0.201960i
\(763\) 0 0
\(764\) 0.484583 0.839323i 0.0175316 0.0303656i
\(765\) 4.36488 + 2.52007i 0.157813 + 0.0911132i
\(766\) 11.0355 0.398728
\(767\) 2.60862 + 22.2208i 0.0941917 + 0.802347i
\(768\) −5.35835 −0.193353
\(769\) 4.80955 + 2.77680i 0.173437 + 0.100134i 0.584205 0.811606i \(-0.301406\pi\)
−0.410769 + 0.911740i \(0.634740\pi\)
\(770\) 0 0
\(771\) 5.18750 + 8.98501i 0.186823 + 0.323587i
\(772\) 0.920651i 0.0331349i
\(773\) −37.9355 + 21.9021i −1.36445 + 0.787764i −0.990212 0.139570i \(-0.955428\pi\)
−0.374235 + 0.927334i \(0.622095\pi\)
\(774\) 5.96726 3.44520i 0.214489 0.123835i
\(775\) 27.4092i 0.984566i
\(776\) −6.37159 11.0359i −0.228727 0.396166i
\(777\) 0 0
\(778\) 38.4608 + 22.2053i 1.37889 + 0.796100i
\(779\) 10.4853 0.375677
\(780\) 0.384283 + 0.165534i 0.0137596 + 0.00592705i