Properties

Label 91.2.q.a.36.2
Level $91$
Weight $2$
Character 91.36
Analytic conductor $0.727$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.q (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.726638658394\)
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: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 36.2
Root \(0.759479 - 1.19298i\) of defining polynomial
Character \(\chi\) \(=\) 91.36
Dual form 91.2.q.a.43.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.20027 + 0.692976i) q^{2} +(1.41289 + 2.44719i) q^{3} +(-0.0395678 + 0.0685334i) q^{4} -0.518957i q^{5} +(-3.39169 - 1.95819i) q^{6} +(-0.866025 - 0.500000i) q^{7} -2.88158i q^{8} +(-2.49250 + 4.31714i) q^{9} +O(q^{10})\) \(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} +(-0.866025 - 0.500000i) q^{7} -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} +1.38595 q^{14} +(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} -2.82577i q^{21} +(-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} +(0.0685334 - 0.0395678i) q^{28} +(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} +(-0.259479 + 0.449430i) q^{35} +(-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} +(1.95819 + 3.39169i) q^{42} +(-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} +(0.500000 + 0.866025i) q^{49} +(-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} +(-1.44079 + 2.49552i) q^{56} +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} +(4.31714 - 2.49250i) q^{63} -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} -0.719250i q^{70} +(-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} -1.62416 q^{77} +(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} +(0.193660 + 0.111810i) q^{84} +(-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} +(0.420388 - 3.58096i) q^{91} +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} +(-1.20027 - 0.692976i) q^{98} +8.09643i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 4q^{4} - 18q^{6} - 4q^{9} + O(q^{10}) \) \( 12q + 4q^{4} - 18q^{6} - 4q^{9} + 12q^{10} + 6q^{11} - 4q^{12} + 4q^{13} - 8q^{14} + 6q^{15} - 8q^{16} - 4q^{17} - 12q^{20} + 6q^{22} - 12q^{23} + 12q^{24} - 20q^{25} - 42q^{26} + 12q^{27} + 8q^{29} + 8q^{30} + 36q^{32} - 30q^{33} + 6q^{35} - 10q^{36} - 42q^{37} + 4q^{38} - 4q^{39} + 92q^{40} + 30q^{41} + 4q^{42} + 2q^{43} + 12q^{46} - 2q^{48} + 6q^{49} - 18q^{50} + 52q^{51} + 2q^{52} - 44q^{53} + 12q^{54} - 6q^{55} - 12q^{56} - 12q^{58} + 18q^{59} + 14q^{61} - 4q^{62} + 12q^{63} - 52q^{64} + 60q^{65} - 52q^{66} - 24q^{67} - 8q^{68} + 4q^{69} - 24q^{71} + 60q^{72} + 6q^{74} + 46q^{75} - 18q^{76} + 8q^{77} - 10q^{78} - 56q^{79} - 72q^{80} + 2q^{81} + 14q^{82} + 18q^{84} - 48q^{85} - 2q^{87} - 14q^{88} - 12q^{89} + 24q^{90} + 14q^{91} + 24q^{92} - 18q^{93} + 4q^{94} - 22q^{95} + 6q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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 −0.860218 0.509926i \(-0.829673\pi\)
0.0114993 + 0.999934i \(0.496340\pi\)
\(3\) 1.41289 + 2.44719i 0.815731 + 1.41289i 0.908802 + 0.417228i \(0.136998\pi\)
−0.0930713 + 0.995659i \(0.529668\pi\)
\(4\) −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
\(7\) −0.866025 0.500000i −0.327327 0.188982i
\(8\) 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 −0.272733 0.962090i \(-0.587928\pi\)
0.696828 + 0.717239i \(0.254594\pi\)
\(12\) −0.223619 −0.0645533
\(13\) 1.42641 + 3.31140i 0.395616 + 0.918416i
\(14\) 1.38595 0.370411
\(15\) 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 \(-0.757411\pi\)
0.959638 + 0.281237i \(0.0907448\pi\)
\(18\) 6.90897i 1.62846i
\(19\) 2.15740 + 1.24558i 0.494942 + 0.285755i 0.726622 0.687037i \(-0.241089\pi\)
−0.231680 + 0.972792i \(0.574422\pi\)
\(20\) 0.0355659 + 0.0205340i 0.00795277 + 0.00459154i
\(21\) 2.82577i 0.616634i
\(22\) −1.12550 + 1.94943i −0.239958 + 0.415620i
\(23\) −4.57029 7.91598i −0.952971 1.65059i −0.738943 0.673767i \(-0.764675\pi\)
−0.214028 0.976828i \(-0.568658\pi\)
\(24\) 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
\(28\) 0.0685334 0.0395678i 0.0129516 0.00747761i
\(29\) 2.61498 + 4.52928i 0.485589 + 0.841065i 0.999863 0.0165608i \(-0.00527172\pi\)
−0.514274 + 0.857626i \(0.671938\pi\)
\(30\) −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
\(35\) −0.259479 + 0.449430i −0.0438599 + 0.0759675i
\(36\) −0.197245 0.341639i −0.0328742 0.0569398i
\(37\) −8.85879 + 5.11463i −1.45638 + 0.840840i −0.998831 0.0483462i \(-0.984605\pi\)
−0.457546 + 0.889186i \(0.651272\pi\)
\(38\) −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 \(-0.560066\pi\)
0.756859 + 0.653578i \(0.226733\pi\)
\(42\) 1.95819 + 3.39169i 0.302156 + 0.523349i
\(43\) −0.498655 + 0.863697i −0.0760442 + 0.131712i −0.901540 0.432696i \(-0.857562\pi\)
0.825496 + 0.564408i \(0.190896\pi\)
\(44\) 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
\(49\) 0.500000 + 0.866025i 0.0714286 + 0.123718i
\(50\) −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
\(56\) −1.44079 + 2.49552i −0.192534 + 0.333478i
\(57\) 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 \(-0.465689\pi\)
−0.807207 + 0.590268i \(0.799022\pi\)
\(60\) 0.116049i 0.0149818i
\(61\) 6.73536 11.6660i 0.862375 1.49368i −0.00725571 0.999974i \(-0.502310\pi\)
0.869630 0.493703i \(-0.164357\pi\)
\(62\) 4.01504 + 6.95426i 0.509911 + 0.883191i
\(63\) 4.31714 2.49250i 0.543908 0.314025i
\(64\) −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 −0.872580 0.488470i \(-0.837555\pi\)
−0.0132624 + 0.999912i \(0.504222\pi\)
\(68\) 0.0770880 + 0.133520i 0.00934830 + 0.0161917i
\(69\) 12.9146 22.3688i 1.55474 2.69288i
\(70\) 0.719250i 0.0859668i
\(71\) −4.50168 2.59905i −0.534251 0.308450i 0.208495 0.978023i \(-0.433144\pi\)
−0.742746 + 0.669573i \(0.766477\pi\)
\(72\) 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
\(77\) −1.62416 −0.185090
\(78\) 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 \(0.837191\pi\)
\(84\) 0.193660 + 0.111810i 0.0211300 + 0.0121994i
\(85\) −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 \(-0.886494\pi\)
−0.166233 + 0.986087i \(0.553160\pi\)
\(90\) −3.58546 −0.377941
\(91\) 0.420388 3.58096i 0.0440686 0.375387i
\(92\) 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 \(-0.261256\pi\)
−0.292807 + 0.956172i \(0.594589\pi\)
\(98\) −1.20027 0.692976i −0.121246 0.0700012i
\(99\) 8.09643i 0.813722i
\(100\) −0.187183 + 0.324210i −0.0187183 + 0.0324210i
\(101\) 9.15132 + 15.8506i 0.910591 + 1.57719i 0.813231 + 0.581940i \(0.197706\pi\)
0.0973594 + 0.995249i \(0.468960\pi\)
\(102\) −6.60787 + 3.81506i −0.654277 + 0.377747i
\(103\) −5.02046 −0.494680 −0.247340 0.968929i \(-0.579556\pi\)
−0.247340 + 0.968929i \(0.579556\pi\)
\(104\) 9.54206 4.11033i 0.935676 0.403051i
\(105\) −1.46646 −0.143111
\(106\) 10.6782 6.16507i 1.03716 0.598804i
\(107\) −3.07228 5.32134i −0.297008 0.514434i 0.678442 0.734654i \(-0.262656\pi\)
−0.975450 + 0.220221i \(0.929322\pi\)
\(108\) 0.221942 0.384415i 0.0213564 0.0369903i
\(109\) 11.8962i 1.13945i −0.821834 0.569727i \(-0.807049\pi\)
0.821834 0.569727i \(-0.192951\pi\)
\(110\) 1.01167 + 0.584088i 0.0964590 + 0.0556906i
\(111\) −25.0330 14.4528i −2.37602 1.37180i
\(112\) 3.83547i 0.362418i
\(113\) −1.77806 + 3.07969i −0.167266 + 0.289713i −0.937458 0.348099i \(-0.886827\pi\)
0.770192 + 0.637812i \(0.220161\pi\)
\(114\) −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
\(119\) −1.68724 + 0.974127i −0.154669 + 0.0892980i
\(120\) −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
\(126\) −3.45449 + 5.98335i −0.307750 + 0.533039i
\(127\) −0.711749 1.23279i −0.0631575 0.109392i 0.832718 0.553698i \(-0.186784\pi\)
−0.895875 + 0.444306i \(0.853450\pi\)
\(128\) 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 \(-0.376298\pi\)
0.378914 + 0.925432i \(0.376298\pi\)
\(132\) −0.314535 + 0.181597i −0.0273767 + 0.0158060i
\(133\) −1.24558 2.15740i −0.108005 0.187071i
\(134\) 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 0.780842 0.624729i \(-0.214791\pi\)
−0.150611 + 0.988593i \(0.548124\pi\)
\(138\) 35.7981i 3.04733i
\(139\) 2.51922 4.36342i 0.213677 0.370100i −0.739185 0.673502i \(-0.764789\pi\)
0.952863 + 0.303402i \(0.0981225\pi\)
\(140\) −0.0205340 0.0355659i −0.00173544 0.00300587i
\(141\) 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
\(147\) −1.41289 + 2.44719i −0.116533 + 0.201841i
\(148\) 0.809498i 0.0665403i
\(149\) 2.91409 + 1.68245i 0.238732 + 0.137832i 0.614594 0.788844i \(-0.289320\pi\)
−0.375862 + 0.926676i \(0.622653\pi\)
\(150\) −16.0450 9.26360i −1.31007 0.756370i
\(151\) 12.6566i 1.02998i 0.857196 + 0.514991i \(0.172205\pi\)
−0.857196 + 0.514991i \(0.827795\pi\)
\(152\) 3.58924 6.21674i 0.291125 0.504244i
\(153\) 4.85602 + 8.41087i 0.392586 + 0.679979i
\(154\) 1.94943 1.12550i 0.157090 0.0906957i
\(155\) −3.00679 −0.241511
\(156\) −0.318973 0.740492i −0.0255383 0.0592868i
\(157\) 10.3691 0.827547 0.413773 0.910380i \(-0.364211\pi\)
0.413773 + 0.910380i \(0.364211\pi\)
\(158\) −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
\(161\) 9.14058i 0.720379i
\(162\) 1.07450 + 0.620364i 0.0844209 + 0.0487404i
\(163\) 13.6428 + 7.87669i 1.06859 + 0.616950i 0.927796 0.373089i \(-0.121701\pi\)
0.140794 + 0.990039i \(0.455035\pi\)
\(164\) 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 \(-0.885453\pi\)
−0.163007 + 0.986625i \(0.552119\pi\)
\(168\) −8.14270 −0.628223
\(169\) −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 \(-0.836980\pi\)
0.860241 + 0.509888i \(0.170313\pi\)
\(174\) 20.4825i 1.55278i
\(175\) −4.09689 2.36534i −0.309696 0.178803i
\(176\) 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 0.622234 0.782831i \(-0.286225\pi\)
−0.989069 + 0.147455i \(0.952892\pi\)
\(180\) −0.177296 + 0.102362i −0.0132149 + 0.00762960i
\(181\) 12.4320 0.924062 0.462031 0.886864i \(-0.347121\pi\)
0.462031 + 0.886864i \(0.347121\pi\)
\(182\) 1.97694 + 4.58944i 0.146541 + 0.340192i
\(183\) 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
\(189\) 4.85767 + 2.80458i 0.353344 + 0.204003i
\(190\) 1.79176i 0.129988i
\(191\) 6.12346 10.6061i 0.443078 0.767434i −0.554838 0.831958i \(-0.687220\pi\)
0.997916 + 0.0645248i \(0.0205531\pi\)
\(192\) −11.7142 20.2897i −0.845403 1.46428i
\(193\) −10.0752 + 5.81692i −0.725229 + 0.418711i −0.816674 0.577099i \(-0.804185\pi\)
0.0914452 + 0.995810i \(0.470851\pi\)
\(194\) −6.12908 −0.440042
\(195\) 4.23953 + 3.15955i 0.303599 + 0.226260i
\(196\) −0.0791355 −0.00565254
\(197\) −1.55984 + 0.900572i −0.111134 + 0.0641631i −0.554537 0.832159i \(-0.687104\pi\)
0.443403 + 0.896322i \(0.353771\pi\)
\(198\) −5.61064 9.71791i −0.398731 0.690622i
\(199\) 3.29657 5.70982i 0.233687 0.404759i −0.725203 0.688535i \(-0.758254\pi\)
0.958890 + 0.283777i \(0.0915874\pi\)
\(200\) 13.6319i 0.963918i
\(201\) −20.4895 11.8296i −1.44522 0.834397i
\(202\) −21.9681 12.6833i −1.54567 0.892394i
\(203\) 5.22996i 0.367071i
\(204\) −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
\(210\) 1.76014 1.01622i 0.121461 0.0701258i
\(211\) −5.35996 9.28373i −0.368995 0.639118i 0.620414 0.784275i \(-0.286965\pi\)
−0.989409 + 0.145157i \(0.953631\pi\)
\(212\) 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
\(217\) −2.89695 + 5.01767i −0.196658 + 0.340622i
\(218\) 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 \(-0.808688\pi\)
0.0773480 + 0.997004i \(0.475355\pi\)
\(224\) −0.223696 0.387453i −0.0149463 0.0258878i
\(225\) −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 \(-0.340720\pi\)
−0.519959 + 0.854191i \(0.674053\pi\)
\(228\) −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
\(231\) −2.29475 3.97463i −0.150984 0.261511i
\(232\) 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
\(238\) 1.35009 2.33843i 0.0875135 0.151578i
\(239\) 16.6177i 1.07491i 0.843293 + 0.537454i \(0.180614\pi\)
−0.843293 + 0.537454i \(0.819386\pi\)
\(240\) 4.87099 + 2.81227i 0.314421 + 0.181531i
\(241\) 15.0800 + 8.70643i 0.971387 + 0.560830i 0.899659 0.436594i \(-0.143815\pi\)
0.0717279 + 0.997424i \(0.477149\pi\)
\(242\) 11.5895i 0.745000i
\(243\) −7.14890 + 12.3823i −0.458602 + 0.794322i
\(244\) 0.533007 + 0.923194i 0.0341222 + 0.0591015i
\(245\) 0.449430 0.259479i 0.0287130 0.0165775i
\(246\) −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 \(-0.898583\pi\)
0.746117 + 0.665815i \(0.231916\pi\)
\(252\) 0.394491i 0.0248506i
\(253\) −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 \(-0.203197\pi\)
−0.917585 + 0.397540i \(0.869864\pi\)
\(258\) 3.38257 1.95293i 0.210590 0.121584i
\(259\) 10.2293 0.635615
\(260\) −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 −0.997068 0.0765263i \(-0.975617\pi\)
0.432260 0.901749i \(-0.357716\pi\)
\(264\) 6.61252 11.4532i 0.406973 0.704897i
\(265\) 4.61690i 0.283614i
\(266\) 2.99006 + 1.72631i 0.183332 + 0.105847i
\(267\) −29.4128 16.9815i −1.80003 1.03925i
\(268\) 0.662575i 0.0404732i
\(269\) −13.7715 + 23.8529i −0.839661 + 1.45434i 0.0505171 + 0.998723i \(0.483913\pi\)
−0.890178 + 0.455613i \(0.849420\pi\)
\(270\) −2.01719 3.49388i −0.122762 0.212631i
\(271\) 5.64582 3.25961i 0.342959 0.198007i −0.318621 0.947882i \(-0.603220\pi\)
0.661580 + 0.749875i \(0.269886\pi\)
\(272\) 7.47246 0.453084
\(273\) 9.35726 4.03072i 0.566327 0.243950i
\(274\) −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 −0.772631 0.634855i \(-0.781060\pi\)
0.936116 + 0.351691i \(0.114393\pi\)
\(278\) 6.98304i 0.418815i
\(279\) 25.0131 + 14.4413i 1.49749 + 0.864579i
\(280\) 1.29507 + 0.747709i 0.0773952 + 0.0446842i
\(281\) 3.54237i 0.211320i 0.994402 + 0.105660i \(0.0336955\pi\)
−0.994402 + 0.105660i \(0.966304\pi\)
\(282\) −8.84566 + 15.3211i −0.526752 + 0.912360i
\(283\) −7.06956 12.2448i −0.420242 0.727880i 0.575721 0.817646i \(-0.304721\pi\)
−0.995963 + 0.0897658i \(0.971388\pi\)
\(284\) 0.356243 0.205677i 0.0211391 0.0122047i
\(285\) 3.65317 0.216395
\(286\) −8.06077 0.946296i −0.476643 0.0559556i
\(287\) −4.20903 −0.248451
\(288\) −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 \(-0.411756\pi\)
−0.696113 + 0.717932i \(0.745089\pi\)
\(294\) 3.91639i 0.228408i
\(295\) −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
\(301\) 0.863697 0.498655i 0.0497826 0.0287420i
\(302\) −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 \(-0.0764304\pi\)
\(308\) 0.0642644 0.111309i 0.00366180 0.00634243i
\(309\) −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 \(-0.363926\pi\)
0.414588 + 0.910009i \(0.363926\pi\)
\(312\) 23.5406 + 17.5438i 1.33273 + 0.993224i
\(313\) 17.1328 0.968404 0.484202 0.874956i \(-0.339110\pi\)
0.484202 + 0.874956i \(0.339110\pi\)
\(314\) −12.4458 + 7.18556i −0.702355 + 0.405505i
\(315\) −1.29350 2.24041i −0.0728805 0.126233i
\(316\) −0.0388678 + 0.0673210i −0.00218649 + 0.00378710i
\(317\) 14.0000i 0.786320i 0.919470 + 0.393160i \(0.128618\pi\)
−0.919470 + 0.393160i \(0.871382\pi\)
\(318\) 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
\(322\) −6.33421 10.9712i −0.352991 0.611399i
\(323\) 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
\(329\) −2.25863 + 3.91206i −0.124522 + 0.215679i
\(330\) 3.30100i 0.181714i
\(331\) 5.99286 + 3.45998i 0.329397 + 0.190178i 0.655574 0.755131i \(-0.272427\pi\)
−0.326176 + 0.945309i \(0.605760\pi\)
\(332\) −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
\(336\) 9.38612 5.41908i 0.512055 0.295635i
\(337\) 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
\(343\) 1.00000i 0.0539949i
\(344\) 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 −0.792326 0.610097i \(-0.791130\pi\)
0.924523 + 0.381126i \(0.124464\pi\)
\(348\) −0.584759 1.01283i −0.0313464 0.0542935i
\(349\) 1.31926 0.761675i 0.0706183 0.0407715i −0.464275 0.885691i \(-0.653685\pi\)
0.534893 + 0.844920i \(0.320352\pi\)
\(350\) 6.55650 0.350460
\(351\) −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 \(-0.508352\pi\)
0.852609 + 0.522550i \(0.175019\pi\)
\(354\) 12.1511 + 21.0463i 0.645824 + 1.11860i
\(355\) −1.34879 + 2.33618i −0.0715865 + 0.123991i
\(356\) 0.951129i 0.0504097i
\(357\) −4.76775 2.75266i −0.252336 0.145686i
\(358\) 11.7816 + 6.80213i 0.622679 + 0.359504i
\(359\) 20.0014i 1.05563i −0.849359 0.527816i \(-0.823011\pi\)
0.849359 0.527816i \(-0.176989\pi\)
\(360\) 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
\(364\) 0.228782 + 0.170501i 0.0119914 + 0.00893669i
\(365\) −6.14421 −0.321602
\(366\) −45.6885 + 26.3783i −2.38818 + 1.37882i
\(367\) −13.7078 23.7427i −0.715544 1.23936i −0.962749 0.270395i \(-0.912846\pi\)
0.247206 0.968963i \(-0.420488\pi\)
\(368\) 17.5292 30.3615i 0.913772 1.58270i
\(369\) 20.9820i 1.09228i
\(370\) −6.37169 3.67870i −0.331248 0.191246i
\(371\) 7.70460 + 4.44825i 0.400003 + 0.230942i
\(372\) 1.29563i 0.0671752i
\(373\) 7.94643 13.7636i 0.411451 0.712653i −0.583598 0.812043i \(-0.698356\pi\)
0.995049 + 0.0993893i \(0.0316889\pi\)
\(374\) 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
\(378\) −7.77403 −0.399853
\(379\) 7.60284 4.38950i 0.390532 0.225474i −0.291859 0.956461i \(-0.594274\pi\)
0.682390 + 0.730988i \(0.260940\pi\)
\(380\) 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 \(-0.268125\pi\)
−0.313370 + 0.949631i \(0.601458\pi\)
\(384\) 25.9308 + 14.9712i 1.32328 + 0.763994i
\(385\) 0.842869i 0.0429566i
\(386\) 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
\(392\) 2.49552 1.44079i 0.126043 0.0727710i
\(393\) 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 \(-0.281710\pi\)
−0.353601 + 0.935396i \(0.615043\pi\)
\(398\) 9.13777i 0.458035i
\(399\) 3.51972 6.09633i 0.176206 0.305198i
\(400\) 9.07219 + 15.7135i 0.453609 + 0.785675i
\(401\) −0.462092 + 0.266789i −0.0230758 + 0.0133228i −0.511494 0.859287i \(-0.670908\pi\)
0.488418 + 0.872610i \(0.337574\pi\)
\(402\) 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
\(406\) 3.62424 + 6.27736i 0.179868 + 0.311540i
\(407\) −8.30697 + 14.3881i −0.411761 + 0.713191i
\(408\) 15.8640i 0.785387i
\(409\) −34.4269 19.8764i −1.70230 0.982824i −0.943424 0.331590i \(-0.892415\pi\)
−0.758877 0.651234i \(-0.774252\pi\)
\(410\) 2.62176 + 1.51367i 0.129479 + 0.0747550i
\(411\) 24.0695i 1.18726i
\(412\) 0.198648 0.344069i 0.00978670 0.0169511i
\(413\) 3.10263 + 5.37392i 0.152671 + 0.264433i
\(414\) −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 −0.995268 0.0971665i \(-0.969022\pi\)
0.413485 0.910511i \(-0.364311\pi\)
\(420\) 0.0580244 0.100501i 0.00283130 0.00490395i
\(421\) 23.2419i 1.13274i −0.824151 0.566370i \(-0.808347\pi\)
0.824151 0.566370i \(-0.191653\pi\)
\(422\) 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
\(427\) −11.6660 + 6.73536i −0.564557 + 0.325947i
\(428\) 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 −0.555395 0.831586i \(-0.687433\pi\)
0.442477 + 0.896780i \(0.354100\pi\)
\(432\) −10.7569 18.6314i −0.517540 0.896406i
\(433\) −2.90945 + 5.03932i −0.139819 + 0.242174i −0.927428 0.374002i \(-0.877985\pi\)
0.787609 + 0.616176i \(0.211319\pi\)
\(434\) 8.03008i 0.385456i
\(435\) 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 0.812822 + 0.582513i \(0.197930\pi\)
0.0980599 + 0.995181i \(0.468736\pi\)
\(440\) −2.10340 + 1.21440i −0.100276 + 0.0578942i
\(441\) −4.98500 −0.237381
\(442\) −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
\(448\) 7.18021 + 4.14550i 0.339233 + 0.195856i
\(449\) 27.1975 + 15.7025i 1.28353 + 0.741045i 0.977491 0.210975i \(-0.0676638\pi\)
0.306036 + 0.952020i \(0.400997\pi\)
\(450\) 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
\(455\) −1.85836 0.218163i −0.0871215 0.0102276i
\(456\) 20.2847 0.949920
\(457\) 27.5640 15.9141i 1.28939 0.744429i 0.310844 0.950461i \(-0.399388\pi\)
0.978545 + 0.206032i \(0.0660551\pi\)
\(458\) −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 \(-0.324687\pi\)
−0.476294 + 0.879286i \(0.658020\pi\)
\(462\) 5.50865 + 3.18042i 0.256286 + 0.147967i
\(463\) 20.3441i 0.945469i 0.881205 + 0.472734i \(0.156733\pi\)
−0.881205 + 0.472734i \(0.843267\pi\)
\(464\) −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 \(-0.488439\pi\)
0.0363114 + 0.999341i \(0.488439\pi\)
\(468\) 0.849948 1.14048i 0.0392889 0.0527185i
\(469\) 8.37266 0.386614
\(470\) 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
\(476\) 0.154176i 0.00706665i
\(477\) 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 \(-0.610238\pi\)
0.644887 + 0.764278i \(0.276905\pi\)
\(480\) 0.656080 0.0299458
\(481\) −29.5729 22.0394i −1.34841 1.00491i
\(482\) −24.1334 −1.09925
\(483\) −22.3688 + 12.9146i −1.01781 + 0.587635i
\(484\) −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 0.498504 0.866887i \(-0.333883\pi\)
−0.501494 + 0.865161i \(0.667216\pi\)
\(488\) −33.6165 19.4085i −1.52175 0.878582i
\(489\) 44.5155i 2.01306i
\(490\) −0.359625 + 0.622889i −0.0162462 + 0.0281392i
\(491\) 0.893574 + 1.54772i 0.0403264 + 0.0698474i 0.885484 0.464670i \(-0.153827\pi\)
−0.845158 + 0.534517i \(0.820494\pi\)
\(492\) −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
\(497\) 2.59905 + 4.50168i 0.116583 + 0.201928i
\(498\) 17.4642 30.2488i 0.782589 1.35548i
\(499\) 8.33493i 0.373123i −0.982443 0.186561i \(-0.940266\pi\)
0.982443 0.186561i \(-0.0597343\pi\)
\(500\) 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 \(-0.843557\pi\)
0.849522 + 0.527554i \(0.176891\pi\)
\(504\) −7.18234 12.4402i −0.319927 0.554130i
\(505\) 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 \(-0.560101\pi\)
0.756788 + 0.653660i \(0.226767\pi\)
\(510\) 1.97985 + 3.42920i 0.0876693 + 0.151848i
\(511\) −5.91976 + 10.2533i −0.261875 + 0.453581i
\(512\) 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
\(518\) −12.2779 + 7.08863i −0.539459 + 0.311457i
\(519\) −0.851561 −0.0373794
\(520\) −2.13308 4.95192i −0.0935419 0.217156i
\(521\) −0.334388 −0.0146498 −0.00732489 0.999973i \(-0.502332\pi\)
−0.00732489 + 0.999973i \(0.502332\pi\)
\(522\) 31.2926 18.0668i 1.36964 0.790763i
\(523\) 16.2533 + 28.1515i 0.710705 + 1.23098i 0.964593 + 0.263744i \(0.0849574\pi\)
−0.253887 + 0.967234i \(0.581709\pi\)
\(524\) −0.343201 + 0.594441i −0.0149928 + 0.0259683i
\(525\) 13.3678i 0.583420i
\(526\) 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
\(532\) 0.197139 0.00854706
\(533\) 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
\(539\) 1.40656 + 0.812080i 0.0605850 + 0.0349787i
\(540\) −0.199495 0.115178i −0.00858488 0.00495649i
\(541\) 10.6015i 0.455796i 0.973685 + 0.227898i \(0.0731852\pi\)
−0.973685 + 0.227898i \(0.926815\pi\)
\(542\) −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
\(546\) −8.43804 + 11.3223i −0.361115 + 0.484550i
\(547\) 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
\(553\) −0.850705 0.491155i −0.0361757 0.0208860i
\(554\) 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 0.219359 0.975644i \(-0.429603\pi\)
0.954612 + 0.297851i \(0.0962700\pi\)
\(558\) −40.0300 −1.69460
\(559\) −3.57133 0.419257i −0.151051 0.0177327i
\(560\) −1.99044 −0.0841115
\(561\) 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 \(-0.760311\pi\)
0.957037 + 0.289967i \(0.0936442\pi\)
\(564\) 1.01014i 0.0425348i
\(565\) 1.59823 + 0.922737i 0.0672380 + 0.0388199i
\(566\) 16.9708 + 9.79808i 0.713335 + 0.411844i
\(567\) 0.895217i 0.0375956i
\(568\) −7.48937 + 12.9720i −0.314247 + 0.544292i
\(569\) −12.3007 21.3054i −0.515672 0.893170i −0.999835 0.0181917i \(-0.994209\pi\)
0.484163 0.874978i \(-0.339124\pi\)
\(570\) −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
\(574\) 5.05197 2.91676i 0.210865 0.121743i
\(575\) −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
\(581\) 4.45926 7.72366i 0.185001 0.320431i
\(582\) −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 \(-0.406565\pi\)
0.973652 + 0.228041i \(0.0732320\pi\)
\(588\) −0.111810 0.193660i −0.00461095 0.00798640i
\(589\) 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
\(595\) 0.505530 + 0.875603i 0.0207247 + 0.0358962i
\(596\) −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 \(-0.217619\pi\)
−0.934648 + 0.355574i \(0.884285\pi\)
\(602\) −0.691113 + 1.19704i −0.0281677 + 0.0487878i
\(603\) 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 0.238523 + 0.971137i \(0.423337\pi\)
−0.960291 + 0.279002i \(0.909996\pi\)
\(608\) 0.557261 + 0.965205i 0.0225999 + 0.0391442i
\(609\) 12.7987 7.38934i 0.518630 0.299431i
\(610\) 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 −0.694020 0.719956i \(-0.744162\pi\)
0.276490 + 0.961017i \(0.410829\pi\)
\(614\) 5.77500 + 10.0026i 0.233060 + 0.403672i
\(615\) 3.08618 5.34542i 0.124447 0.215548i
\(616\) 4.68015i 0.188569i
\(617\) −20.4124 11.7851i −0.821772 0.474450i 0.0292550 0.999572i \(-0.490687\pi\)
−0.851027 + 0.525122i \(0.824020\pi\)
\(618\) 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
\(623\) 12.0190 0.481530
\(624\) −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
\(630\) 3.10510 + 1.79273i 0.123710 + 0.0714241i
\(631\) −38.9646 22.4962i −1.55116 0.895561i −0.998048 0.0624526i \(-0.980108\pi\)
−0.553109 0.833109i \(-0.686559\pi\)
\(632\) 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
\(637\) −2.15455 + 2.89101i −0.0853662 + 0.114546i
\(638\) −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 −0.889953 0.456052i \(-0.849263\pi\)
0.839929 + 0.542696i \(0.182596\pi\)
\(642\) 24.0645i 0.949749i
\(643\) 15.9150 + 9.18853i 0.627627 + 0.362360i 0.779832 0.625988i \(-0.215304\pi\)
−0.152206 + 0.988349i \(0.548638\pi\)
\(644\) −0.626435 0.361672i −0.0246850 0.0142519i
\(645\) 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 \(-0.0317081\pi\)
−0.583647 + 0.812008i \(0.698375\pi\)
\(648\) −2.23404 + 1.28982i −0.0877612 + 0.0506690i
\(649\) −10.0783 −0.395609
\(650\) −18.9549 14.1263i −0.743473 0.554079i
\(651\) −16.3723 −0.641680
\(652\) −1.07963 + 0.623326i −0.0422817 + 0.0244113i
\(653\) 24.0580 + 41.6696i 0.941461 + 1.63066i 0.762686 + 0.646769i \(0.223880\pi\)
0.178775 + 0.983890i \(0.442786\pi\)
\(654\) −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
\(658\) 6.26070i 0.244068i
\(659\) 1.10819 1.91944i 0.0431690 0.0747708i −0.843634 0.536919i \(-0.819588\pi\)
0.886803 + 0.462148i \(0.152921\pi\)
\(660\) 0.0942408 + 0.163230i 0.00366832 + 0.00635371i
\(661\) −0.552034 + 0.318717i −0.0214716 + 0.0123966i −0.510697 0.859761i \(-0.670613\pi\)
0.489226 + 0.872157i \(0.337279\pi\)
\(662\) −9.59073 −0.372754
\(663\) 7.85287 + 18.2303i 0.304980 + 0.708006i
\(664\) 25.6994 0.997331
\(665\) −1.11960 + 0.646401i −0.0434162 + 0.0250664i
\(666\) 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
\(672\) 0.632114 1.09485i 0.0243843 0.0422349i
\(673\) 7.70343 + 13.3427i 0.296945 + 0.514324i 0.975436 0.220285i \(-0.0706988\pi\)
−0.678490 + 0.734609i \(0.737365\pi\)
\(674\) −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 \(-0.572066\pi\)
−0.224473 + 0.974480i \(0.572066\pi\)
\(678\) 12.0613 6.96358i 0.463210 0.267435i
\(679\) −2.21114 3.82981i −0.0848559 0.146975i
\(680\) −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 0.829018 0.559221i \(-0.188900\pi\)
−0.0697909 + 0.997562i \(0.522233\pi\)
\(684\) 0.982737i 0.0375759i
\(685\) 2.21020 3.82817i 0.0844473 0.146267i
\(686\) 0.692976 + 1.20027i 0.0264580 + 0.0458265i
\(687\) −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 −0.558458 + 0.829533i \(0.688607\pi\)
−0.997625 + 0.0688729i \(0.978060\pi\)
\(692\) −0.0119239 0.0206529i −0.000453280 0.000785104i
\(693\) 4.04822 7.01172i 0.153779 0.266353i
\(694\) 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
\(700\) 0.324210 0.187183i 0.0122540 0.00707484i
\(701\) 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
\(707\) 18.3026i 0.688342i
\(708\) 1.20171 + 0.693808i 0.0451630 + 0.0260749i
\(709\) −15.4910 8.94374i −0.581777 0.335889i 0.180062 0.983655i \(-0.442370\pi\)
−0.761839 + 0.647766i \(0.775703\pi\)
\(710\) 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
\(714\) 7.63012 0.285550
\(715\) 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 \(-0.778899\pi\)
0.938482 + 0.345329i \(0.112233\pi\)
\(720\) 9.92235i 0.369784i
\(721\) 4.34784 + 2.51023i 0.161922 + 0.0934858i
\(722\) 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 \(-0.285233\pi\)
0.624670 + 0.780889i \(0.285233\pi\)
\(728\) −10.3188 1.21138i −0.382441 0.0448968i
\(729\) −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
\(735\) 1.26999 + 0.733228i 0.0468442 + 0.0270455i
\(736\) 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 −0.529182 0.848508i \(-0.677501\pi\)
0.470238 + 0.882539i \(0.344168\pi\)
\(740\) −0.420095 −0.0154430
\(741\) −23.3104 + 10.0412i −0.856328 + 0.368871i
\(742\) −12.3301 −0.452654
\(743\) 28.7095 16.5755i 1.05325 0.608094i 0.129693 0.991554i \(-0.458601\pi\)
0.923558 + 0.383460i \(0.125268\pi\)
\(744\) −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
\(749\) 6.14456i 0.224517i
\(750\) −9.88850 + 17.1274i −0.361077 + 0.625404i
\(751\) −10.3871 17.9910i −0.379032 0.656503i 0.611890 0.790943i \(-0.290410\pi\)
−0.990922 + 0.134441i \(0.957076\pi\)
\(752\) 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
\(756\) −0.384415 + 0.221942i −0.0139810 + 0.00807195i
\(757\) −21.8075 37.7717i −0.792607 1.37283i −0.924348 0.381551i \(-0.875390\pi\)
0.131741 0.991284i \(-0.457943\pi\)
\(758\) −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 \(-0.261235\pi\)
−0.292743 + 0.956191i \(0.594568\pi\)
\(762\) 5.57497i 0.201960i
\(763\) −5.94812 + 10.3025i −0.215337 + 0.372974i
\(764\) 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 \(-0.698594\pi\)
0.410769 + 0.911740i \(0.365260\pi\)
\(770\) −0.584088 1.01167i −0.0210491 0.0364581i
\(771\) 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 \(-0.0445721\pi\)
0.374235 + 0.927334i \(0.377905\pi\)
\(774\) 5.96726 + 3.44520i 0.214489 + 0.123835i
\(775\) 27.4092i 0.984566i
\(776\)