Properties

Label 441.2.g.h.67.12
Level $441$
Weight $2$
Character 441.67
Analytic conductor $3.521$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.12
Character \(\chi\) \(=\) 441.67
Dual form 441.2.g.h.79.12

$q$-expansion

\(f(q)\) \(=\) \(q+(1.35757 - 2.35137i) q^{2} +(1.69116 + 0.374116i) q^{3} +(-2.68597 - 4.65224i) q^{4} +1.58639 q^{5} +(3.17555 - 3.46867i) q^{6} -9.15528 q^{8} +(2.72007 + 1.26538i) q^{9} +O(q^{10})\) \(q+(1.35757 - 2.35137i) q^{2} +(1.69116 + 0.374116i) q^{3} +(-2.68597 - 4.65224i) q^{4} +1.58639 q^{5} +(3.17555 - 3.46867i) q^{6} -9.15528 q^{8} +(2.72007 + 1.26538i) q^{9} +(2.15363 - 3.73020i) q^{10} -1.34875 q^{11} +(-2.80194 - 8.87257i) q^{12} +(-1.58916 + 2.75251i) q^{13} +(2.68285 + 0.593495i) q^{15} +(-7.05696 + 12.2230i) q^{16} +(1.40027 - 2.42534i) q^{17} +(6.66807 - 4.67807i) q^{18} +(0.312846 + 0.541866i) q^{19} +(-4.26101 - 7.38028i) q^{20} +(-1.83102 + 3.17142i) q^{22} -0.284867 q^{23} +(-15.4831 - 3.42514i) q^{24} -2.48336 q^{25} +(4.31479 + 7.47343i) q^{26} +(4.12669 + 3.15760i) q^{27} +(2.27396 + 3.93861i) q^{29} +(5.03768 - 5.50268i) q^{30} +(3.71502 + 6.43461i) q^{31} +(10.0053 + 17.3297i) q^{32} +(-2.28096 - 0.504590i) q^{33} +(-3.80191 - 6.58511i) q^{34} +(-1.41918 - 16.0532i) q^{36} +(-4.01126 - 6.94770i) q^{37} +1.69884 q^{38} +(-3.71729 + 4.06041i) q^{39} -14.5239 q^{40} +(-5.01329 + 8.68327i) q^{41} +(-3.12937 - 5.42022i) q^{43} +(3.62271 + 6.27472i) q^{44} +(4.31511 + 2.00740i) q^{45} +(-0.386726 + 0.669829i) q^{46} +(5.57383 - 9.65415i) q^{47} +(-16.5073 + 18.0310i) q^{48} +(-3.37132 + 5.83930i) q^{50} +(3.27544 - 3.57778i) q^{51} +17.0738 q^{52} +(-1.39349 + 2.41359i) q^{53} +(13.0269 - 5.41675i) q^{54} -2.13965 q^{55} +(0.326354 + 1.03343i) q^{57} +12.3482 q^{58} +(2.28734 + 3.96180i) q^{59} +(-4.44498 - 14.0754i) q^{60} +(-0.192507 + 0.333432i) q^{61} +20.1736 q^{62} +26.1036 q^{64} +(-2.52104 + 4.36656i) q^{65} +(-4.28304 + 4.67838i) q^{66} +(1.26958 + 2.19898i) q^{67} -15.0443 q^{68} +(-0.481757 - 0.106573i) q^{69} -1.45208 q^{71} +(-24.9030 - 11.5849i) q^{72} +(-0.234067 + 0.405416i) q^{73} -21.7822 q^{74} +(-4.19977 - 0.929064i) q^{75} +(1.68059 - 2.91087i) q^{76} +(4.50108 + 14.2530i) q^{78} +(7.85620 - 13.6073i) q^{79} +(-11.1951 + 19.3905i) q^{80} +(5.79761 + 6.88387i) q^{81} +(13.6117 + 23.5762i) q^{82} +(6.99338 + 12.1129i) q^{83} +(2.22138 - 3.84754i) q^{85} -16.9933 q^{86} +(2.37214 + 7.51157i) q^{87} +12.3482 q^{88} +(-1.29353 - 2.24046i) q^{89} +(10.5782 - 7.42126i) q^{90} +(0.765146 + 1.32527i) q^{92} +(3.87543 + 12.2718i) q^{93} +(-15.1337 - 26.2123i) q^{94} +(0.496297 + 0.859612i) q^{95} +(10.4373 + 33.0505i) q^{96} +(-7.22962 - 12.5221i) q^{97} +(-3.66871 - 1.70669i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 4q^{2} - 12q^{4} - 24q^{8} - 4q^{9} + O(q^{10}) \) \( 24q + 4q^{2} - 12q^{4} - 24q^{8} - 4q^{9} - 40q^{11} + 4q^{15} - 12q^{16} + 28q^{18} - 64q^{23} + 24q^{25} + 16q^{29} + 84q^{30} + 48q^{32} - 4q^{36} - 12q^{37} - 40q^{39} + 56q^{44} + 24q^{46} - 4q^{50} - 8q^{51} + 32q^{53} - 12q^{57} + 56q^{60} + 96q^{64} + 60q^{65} - 12q^{67} - 112q^{71} - 168q^{72} - 136q^{74} - 60q^{78} + 12q^{79} - 40q^{81} + 12q^{85} - 152q^{86} + 16q^{92} + 112q^{93} + 64q^{95} + 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.35757 2.35137i 0.959944 1.66267i 0.237320 0.971432i \(-0.423731\pi\)
0.722624 0.691241i \(-0.242936\pi\)
\(3\) 1.69116 + 0.374116i 0.976394 + 0.215996i
\(4\) −2.68597 4.65224i −1.34299 2.32612i
\(5\) 1.58639 0.709457 0.354728 0.934969i \(-0.384573\pi\)
0.354728 + 0.934969i \(0.384573\pi\)
\(6\) 3.17555 3.46867i 1.29641 1.41608i
\(7\) 0 0
\(8\) −9.15528 −3.23688
\(9\) 2.72007 + 1.26538i 0.906691 + 0.421795i
\(10\) 2.15363 3.73020i 0.681039 1.17959i
\(11\) −1.34875 −0.406664 −0.203332 0.979110i \(-0.565177\pi\)
−0.203332 + 0.979110i \(0.565177\pi\)
\(12\) −2.80194 8.87257i −0.808851 2.56129i
\(13\) −1.58916 + 2.75251i −0.440754 + 0.763409i −0.997746 0.0671096i \(-0.978622\pi\)
0.556991 + 0.830518i \(0.311956\pi\)
\(14\) 0 0
\(15\) 2.68285 + 0.593495i 0.692709 + 0.153240i
\(16\) −7.05696 + 12.2230i −1.76424 + 3.05575i
\(17\) 1.40027 2.42534i 0.339615 0.588230i −0.644745 0.764397i \(-0.723037\pi\)
0.984360 + 0.176167i \(0.0563699\pi\)
\(18\) 6.66807 4.67807i 1.57168 1.10263i
\(19\) 0.312846 + 0.541866i 0.0717719 + 0.124313i 0.899678 0.436554i \(-0.143801\pi\)
−0.827906 + 0.560867i \(0.810468\pi\)
\(20\) −4.26101 7.38028i −0.952791 1.65028i
\(21\) 0 0
\(22\) −1.83102 + 3.17142i −0.390375 + 0.676149i
\(23\) −0.284867 −0.0593989 −0.0296995 0.999559i \(-0.509455\pi\)
−0.0296995 + 0.999559i \(0.509455\pi\)
\(24\) −15.4831 3.42514i −3.16047 0.699153i
\(25\) −2.48336 −0.496671
\(26\) 4.31479 + 7.47343i 0.846199 + 1.46566i
\(27\) 4.12669 + 3.15760i 0.794182 + 0.607679i
\(28\) 0 0
\(29\) 2.27396 + 3.93861i 0.422264 + 0.731382i 0.996161 0.0875454i \(-0.0279023\pi\)
−0.573897 + 0.818928i \(0.694569\pi\)
\(30\) 5.03768 5.50268i 0.919750 1.00465i
\(31\) 3.71502 + 6.43461i 0.667238 + 1.15569i 0.978673 + 0.205423i \(0.0658569\pi\)
−0.311435 + 0.950267i \(0.600810\pi\)
\(32\) 10.0053 + 17.3297i 1.76870 + 3.06348i
\(33\) −2.28096 0.504590i −0.397064 0.0878378i
\(34\) −3.80191 6.58511i −0.652023 1.12934i
\(35\) 0 0
\(36\) −1.41918 16.0532i −0.236529 2.67554i
\(37\) −4.01126 6.94770i −0.659447 1.14220i −0.980759 0.195222i \(-0.937457\pi\)
0.321312 0.946973i \(-0.395876\pi\)
\(38\) 1.69884 0.275588
\(39\) −3.71729 + 4.06041i −0.595243 + 0.650187i
\(40\) −14.5239 −2.29643
\(41\) −5.01329 + 8.68327i −0.782944 + 1.35610i 0.147275 + 0.989096i \(0.452950\pi\)
−0.930219 + 0.367004i \(0.880384\pi\)
\(42\) 0 0
\(43\) −3.12937 5.42022i −0.477224 0.826576i 0.522435 0.852679i \(-0.325024\pi\)
−0.999659 + 0.0261027i \(0.991690\pi\)
\(44\) 3.62271 + 6.27472i 0.546144 + 0.945950i
\(45\) 4.31511 + 2.00740i 0.643258 + 0.299245i
\(46\) −0.386726 + 0.669829i −0.0570197 + 0.0987609i
\(47\) 5.57383 9.65415i 0.813026 1.40820i −0.0977106 0.995215i \(-0.531152\pi\)
0.910737 0.412988i \(-0.135515\pi\)
\(48\) −16.5073 + 18.0310i −2.38262 + 2.60255i
\(49\) 0 0
\(50\) −3.37132 + 5.83930i −0.476777 + 0.825802i
\(51\) 3.27544 3.57778i 0.458653 0.500989i
\(52\) 17.0738 2.36771
\(53\) −1.39349 + 2.41359i −0.191410 + 0.331532i −0.945718 0.324989i \(-0.894639\pi\)
0.754308 + 0.656521i \(0.227973\pi\)
\(54\) 13.0269 5.41675i 1.77274 0.737127i
\(55\) −2.13965 −0.288510
\(56\) 0 0
\(57\) 0.326354 + 1.03343i 0.0432266 + 0.136881i
\(58\) 12.3482 1.62140
\(59\) 2.28734 + 3.96180i 0.297787 + 0.515782i 0.975629 0.219425i \(-0.0704182\pi\)
−0.677842 + 0.735207i \(0.737085\pi\)
\(60\) −4.44498 14.0754i −0.573845 1.81712i
\(61\) −0.192507 + 0.333432i −0.0246480 + 0.0426916i −0.878086 0.478502i \(-0.841180\pi\)
0.853438 + 0.521194i \(0.174513\pi\)
\(62\) 20.1736 2.56205
\(63\) 0 0
\(64\) 26.1036 3.26295
\(65\) −2.52104 + 4.36656i −0.312696 + 0.541605i
\(66\) −4.28304 + 4.67838i −0.527205 + 0.575869i
\(67\) 1.26958 + 2.19898i 0.155104 + 0.268648i 0.933097 0.359625i \(-0.117095\pi\)
−0.777993 + 0.628273i \(0.783762\pi\)
\(68\) −15.0443 −1.82439
\(69\) −0.481757 0.106573i −0.0579968 0.0128299i
\(70\) 0 0
\(71\) −1.45208 −0.172330 −0.0861651 0.996281i \(-0.527461\pi\)
−0.0861651 + 0.996281i \(0.527461\pi\)
\(72\) −24.9030 11.5849i −2.93485 1.36530i
\(73\) −0.234067 + 0.405416i −0.0273955 + 0.0474503i −0.879398 0.476087i \(-0.842055\pi\)
0.852003 + 0.523538i \(0.175388\pi\)
\(74\) −21.7822 −2.53213
\(75\) −4.19977 0.929064i −0.484947 0.107279i
\(76\) 1.68059 2.91087i 0.192777 0.333900i
\(77\) 0 0
\(78\) 4.50108 + 14.2530i 0.509647 + 1.61384i
\(79\) 7.85620 13.6073i 0.883892 1.53095i 0.0369135 0.999318i \(-0.488247\pi\)
0.846978 0.531627i \(-0.178419\pi\)
\(80\) −11.1951 + 19.3905i −1.25165 + 2.16792i
\(81\) 5.79761 + 6.88387i 0.644179 + 0.764875i
\(82\) 13.6117 + 23.5762i 1.50317 + 2.60356i
\(83\) 6.99338 + 12.1129i 0.767623 + 1.32956i 0.938848 + 0.344331i \(0.111894\pi\)
−0.171225 + 0.985232i \(0.554772\pi\)
\(84\) 0 0
\(85\) 2.22138 3.84754i 0.240942 0.417324i
\(86\) −16.9933 −1.83243
\(87\) 2.37214 + 7.51157i 0.254320 + 0.805325i
\(88\) 12.3482 1.31632
\(89\) −1.29353 2.24046i −0.137114 0.237488i 0.789289 0.614022i \(-0.210449\pi\)
−0.926403 + 0.376534i \(0.877116\pi\)
\(90\) 10.5782 7.42126i 1.11504 0.782269i
\(91\) 0 0
\(92\) 0.765146 + 1.32527i 0.0797719 + 0.138169i
\(93\) 3.87543 + 12.2718i 0.401863 + 1.27253i
\(94\) −15.1337 26.2123i −1.56092 2.70359i
\(95\) 0.496297 + 0.859612i 0.0509190 + 0.0881944i
\(96\) 10.4373 + 33.0505i 1.06525 + 3.37320i
\(97\) −7.22962 12.5221i −0.734057 1.27142i −0.955136 0.296168i \(-0.904291\pi\)
0.221079 0.975256i \(-0.429042\pi\)
\(98\) 0 0
\(99\) −3.66871 1.70669i −0.368719 0.171529i
\(100\) 6.67023 + 11.5532i 0.667023 + 1.15532i
\(101\) −9.83776 −0.978894 −0.489447 0.872033i \(-0.662801\pi\)
−0.489447 + 0.872033i \(0.662801\pi\)
\(102\) −3.96607 12.5589i −0.392699 1.24351i
\(103\) −11.0579 −1.08957 −0.544786 0.838575i \(-0.683389\pi\)
−0.544786 + 0.838575i \(0.683389\pi\)
\(104\) 14.5492 25.2000i 1.42667 2.47106i
\(105\) 0 0
\(106\) 3.78350 + 6.55322i 0.367486 + 0.636505i
\(107\) 0.962153 + 1.66650i 0.0930149 + 0.161106i 0.908778 0.417279i \(-0.137016\pi\)
−0.815764 + 0.578386i \(0.803683\pi\)
\(108\) 3.60571 27.6796i 0.346960 2.66347i
\(109\) 9.30341 16.1140i 0.891105 1.54344i 0.0525523 0.998618i \(-0.483264\pi\)
0.838553 0.544821i \(-0.183402\pi\)
\(110\) −2.90472 + 5.03112i −0.276954 + 0.479698i
\(111\) −4.18445 13.2504i −0.397170 1.25767i
\(112\) 0 0
\(113\) 1.59338 2.75982i 0.149893 0.259622i −0.781295 0.624162i \(-0.785440\pi\)
0.931188 + 0.364540i \(0.118774\pi\)
\(114\) 2.87302 + 0.635563i 0.269083 + 0.0595259i
\(115\) −0.451911 −0.0421410
\(116\) 12.2156 21.1580i 1.13419 1.96447i
\(117\) −7.80562 + 5.47613i −0.721630 + 0.506268i
\(118\) 12.4209 1.14344
\(119\) 0 0
\(120\) −24.5623 5.43361i −2.24222 0.496019i
\(121\) −9.18087 −0.834624
\(122\) 0.522682 + 0.905312i 0.0473214 + 0.0819631i
\(123\) −11.7268 + 12.8093i −1.05737 + 1.15497i
\(124\) 19.9569 34.5664i 1.79218 3.10415i
\(125\) −11.8715 −1.06182
\(126\) 0 0
\(127\) −8.37387 −0.743061 −0.371530 0.928421i \(-0.621167\pi\)
−0.371530 + 0.928421i \(0.621167\pi\)
\(128\) 15.4267 26.7199i 1.36354 2.36173i
\(129\) −3.26448 10.3372i −0.287422 0.910143i
\(130\) 6.84495 + 11.8558i 0.600341 + 1.03982i
\(131\) 11.9726 1.04605 0.523024 0.852318i \(-0.324804\pi\)
0.523024 + 0.852318i \(0.324804\pi\)
\(132\) 3.77913 + 11.9669i 0.328931 + 1.04158i
\(133\) 0 0
\(134\) 6.89415 0.595564
\(135\) 6.54656 + 5.00919i 0.563438 + 0.431122i
\(136\) −12.8199 + 22.2046i −1.09929 + 1.90403i
\(137\) 16.5505 1.41401 0.707003 0.707211i \(-0.250047\pi\)
0.707003 + 0.707211i \(0.250047\pi\)
\(138\) −0.904611 + 0.988111i −0.0770056 + 0.0841136i
\(139\) −3.95119 + 6.84367i −0.335136 + 0.580472i −0.983511 0.180849i \(-0.942116\pi\)
0.648375 + 0.761321i \(0.275449\pi\)
\(140\) 0 0
\(141\) 13.0380 14.2415i 1.09800 1.19935i
\(142\) −1.97130 + 3.41438i −0.165427 + 0.286529i
\(143\) 2.14339 3.71245i 0.179239 0.310451i
\(144\) −34.6622 + 24.3177i −2.88852 + 2.02648i
\(145\) 3.60739 + 6.24819i 0.299578 + 0.518884i
\(146\) 0.635523 + 1.10076i 0.0525962 + 0.0910994i
\(147\) 0 0
\(148\) −21.5483 + 37.3227i −1.77126 + 3.06791i
\(149\) −13.6685 −1.11977 −0.559885 0.828570i \(-0.689155\pi\)
−0.559885 + 0.828570i \(0.689155\pi\)
\(150\) −7.88604 + 8.61395i −0.643892 + 0.703326i
\(151\) 3.89963 0.317348 0.158674 0.987331i \(-0.449278\pi\)
0.158674 + 0.987331i \(0.449278\pi\)
\(152\) −2.86420 4.96093i −0.232317 0.402385i
\(153\) 6.87781 4.82522i 0.556038 0.390096i
\(154\) 0 0
\(155\) 5.89349 + 10.2078i 0.473376 + 0.819912i
\(156\) 28.8746 + 6.38758i 2.31182 + 0.511415i
\(157\) −0.147176 0.254917i −0.0117459 0.0203446i 0.860093 0.510138i \(-0.170406\pi\)
−0.871839 + 0.489793i \(0.837072\pi\)
\(158\) −21.3306 36.9457i −1.69697 2.93925i
\(159\) −3.25958 + 3.56045i −0.258502 + 0.282362i
\(160\) 15.8723 + 27.4917i 1.25482 + 2.17341i
\(161\) 0 0
\(162\) 24.0572 4.28703i 1.89011 0.336821i
\(163\) −5.35455 9.27436i −0.419401 0.726424i 0.576478 0.817112i \(-0.304427\pi\)
−0.995879 + 0.0906886i \(0.971093\pi\)
\(164\) 53.8622 4.20593
\(165\) −3.61850 0.800478i −0.281700 0.0623171i
\(166\) 37.9759 2.94750
\(167\) −1.59872 + 2.76907i −0.123713 + 0.214277i −0.921229 0.389020i \(-0.872814\pi\)
0.797516 + 0.603298i \(0.206147\pi\)
\(168\) 0 0
\(169\) 1.44913 + 2.50997i 0.111472 + 0.193074i
\(170\) −6.03133 10.4466i −0.462582 0.801215i
\(171\) 0.165297 + 1.86979i 0.0126406 + 0.142986i
\(172\) −16.8108 + 29.1171i −1.28181 + 2.22016i
\(173\) −5.71875 + 9.90517i −0.434789 + 0.753076i −0.997278 0.0737284i \(-0.976510\pi\)
0.562490 + 0.826804i \(0.309844\pi\)
\(174\) 20.8828 + 4.61966i 1.58312 + 0.350216i
\(175\) 0 0
\(176\) 9.51809 16.4858i 0.717453 1.24266i
\(177\) 2.38610 + 7.55578i 0.179351 + 0.567927i
\(178\) −7.02421 −0.526487
\(179\) −0.549275 + 0.951372i −0.0410547 + 0.0711089i −0.885823 0.464024i \(-0.846405\pi\)
0.844768 + 0.535133i \(0.179738\pi\)
\(180\) −2.25137 25.4667i −0.167807 1.89818i
\(181\) −3.19013 −0.237120 −0.118560 0.992947i \(-0.537828\pi\)
−0.118560 + 0.992947i \(0.537828\pi\)
\(182\) 0 0
\(183\) −0.450303 + 0.491868i −0.0332874 + 0.0363599i
\(184\) 2.60804 0.192267
\(185\) −6.36343 11.0218i −0.467849 0.810338i
\(186\) 34.1168 + 7.54725i 2.50157 + 0.553392i
\(187\) −1.88861 + 3.27118i −0.138109 + 0.239212i
\(188\) −59.8846 −4.36753
\(189\) 0 0
\(190\) 2.69503 0.195518
\(191\) −1.93407 + 3.34992i −0.139945 + 0.242391i −0.927475 0.373884i \(-0.878026\pi\)
0.787531 + 0.616275i \(0.211359\pi\)
\(192\) 44.1454 + 9.76576i 3.18592 + 0.704783i
\(193\) 2.06793 + 3.58175i 0.148853 + 0.257820i 0.930804 0.365520i \(-0.119109\pi\)
−0.781951 + 0.623340i \(0.785775\pi\)
\(194\) −39.2588 −2.81862
\(195\) −5.89709 + 6.44141i −0.422299 + 0.461279i
\(196\) 0 0
\(197\) −0.889267 −0.0633576 −0.0316788 0.999498i \(-0.510085\pi\)
−0.0316788 + 0.999498i \(0.510085\pi\)
\(198\) −8.99358 + 6.30956i −0.639146 + 0.448401i
\(199\) 3.16193 5.47663i 0.224143 0.388228i −0.731919 0.681392i \(-0.761375\pi\)
0.956062 + 0.293164i \(0.0947083\pi\)
\(200\) 22.7358 1.60767
\(201\) 1.32440 + 4.19380i 0.0934157 + 0.295808i
\(202\) −13.3554 + 23.1323i −0.939684 + 1.62758i
\(203\) 0 0
\(204\) −25.4424 5.62833i −1.78133 0.394062i
\(205\) −7.95305 + 13.7751i −0.555465 + 0.962093i
\(206\) −15.0119 + 26.0014i −1.04593 + 1.81160i
\(207\) −0.774860 0.360466i −0.0538565 0.0250541i
\(208\) −22.4293 38.8487i −1.55519 2.69367i
\(209\) −0.421952 0.730843i −0.0291870 0.0505535i
\(210\) 0 0
\(211\) 5.71291 9.89505i 0.393293 0.681204i −0.599589 0.800308i \(-0.704669\pi\)
0.992882 + 0.119105i \(0.0380025\pi\)
\(212\) 14.9715 1.02825
\(213\) −2.45571 0.543247i −0.168262 0.0372226i
\(214\) 5.22475 0.357156
\(215\) −4.96441 8.59860i −0.338570 0.586420i
\(216\) −37.7810 28.9087i −2.57067 1.96699i
\(217\) 0 0
\(218\) −25.2600 43.7516i −1.71082 2.96323i
\(219\) −0.547518 + 0.598057i −0.0369979 + 0.0404129i
\(220\) 5.74705 + 9.95417i 0.387466 + 0.671110i
\(221\) 4.45051 + 7.70850i 0.299373 + 0.518530i
\(222\) −36.8373 8.14907i −2.47236 0.546930i
\(223\) −8.35953 14.4791i −0.559796 0.969595i −0.997513 0.0704822i \(-0.977546\pi\)
0.437717 0.899113i \(-0.355787\pi\)
\(224\) 0 0
\(225\) −6.75492 3.14240i −0.450328 0.209493i
\(226\) −4.32625 7.49328i −0.287778 0.498446i
\(227\) −17.0700 −1.13298 −0.566489 0.824070i \(-0.691698\pi\)
−0.566489 + 0.824070i \(0.691698\pi\)
\(228\) 3.93117 4.29403i 0.260348 0.284379i
\(229\) −19.7894 −1.30772 −0.653861 0.756615i \(-0.726852\pi\)
−0.653861 + 0.756615i \(0.726852\pi\)
\(230\) −0.613500 + 1.06261i −0.0404530 + 0.0700666i
\(231\) 0 0
\(232\) −20.8187 36.0591i −1.36682 2.36740i
\(233\) −2.96579 5.13691i −0.194296 0.336530i 0.752374 0.658736i \(-0.228909\pi\)
−0.946669 + 0.322207i \(0.895575\pi\)
\(234\) 2.27978 + 25.7881i 0.149034 + 1.68582i
\(235\) 8.84228 15.3153i 0.576807 0.999058i
\(236\) 12.2875 21.2826i 0.799847 1.38538i
\(237\) 18.3769 20.0731i 1.19371 1.30389i
\(238\) 0 0
\(239\) −10.0277 + 17.3685i −0.648637 + 1.12347i 0.334812 + 0.942285i \(0.391327\pi\)
−0.983449 + 0.181187i \(0.942006\pi\)
\(240\) −26.1871 + 28.6042i −1.69037 + 1.84640i
\(241\) −29.2887 −1.88665 −0.943326 0.331869i \(-0.892321\pi\)
−0.943326 + 0.331869i \(0.892321\pi\)
\(242\) −12.4636 + 21.5877i −0.801193 + 1.38771i
\(243\) 7.22934 + 13.8107i 0.463763 + 0.885960i
\(244\) 2.06827 0.132408
\(245\) 0 0
\(246\) 14.1995 + 44.9637i 0.905324 + 2.86678i
\(247\) −1.98865 −0.126535
\(248\) −34.0121 58.9107i −2.15977 3.74083i
\(249\) 7.29533 + 23.1012i 0.462323 + 1.46398i
\(250\) −16.1164 + 27.9144i −1.01929 + 1.76546i
\(251\) 22.7856 1.43821 0.719106 0.694901i \(-0.244552\pi\)
0.719106 + 0.694901i \(0.244552\pi\)
\(252\) 0 0
\(253\) 0.384215 0.0241554
\(254\) −11.3681 + 19.6901i −0.713297 + 1.23547i
\(255\) 5.19614 5.67576i 0.325395 0.355430i
\(256\) −15.7821 27.3354i −0.986381 1.70846i
\(257\) 24.2889 1.51510 0.757550 0.652778i \(-0.226396\pi\)
0.757550 + 0.652778i \(0.226396\pi\)
\(258\) −28.7385 6.35747i −1.78918 0.395798i
\(259\) 0 0
\(260\) 27.0857 1.67979
\(261\) 1.20148 + 13.5908i 0.0743699 + 0.841247i
\(262\) 16.2536 28.1520i 1.00415 1.73924i
\(263\) −8.61155 −0.531011 −0.265506 0.964109i \(-0.585539\pi\)
−0.265506 + 0.964109i \(0.585539\pi\)
\(264\) 20.8828 + 4.61966i 1.28525 + 0.284321i
\(265\) −2.21062 + 3.82890i −0.135797 + 0.235208i
\(266\) 0 0
\(267\) −1.34938 4.27291i −0.0825807 0.261498i
\(268\) 6.82011 11.8128i 0.416605 0.721581i
\(269\) −7.61561 + 13.1906i −0.464332 + 0.804247i −0.999171 0.0407073i \(-0.987039\pi\)
0.534839 + 0.844954i \(0.320372\pi\)
\(270\) 20.6659 8.59310i 1.25768 0.522959i
\(271\) −2.33910 4.05144i −0.142090 0.246108i 0.786193 0.617981i \(-0.212049\pi\)
−0.928284 + 0.371873i \(0.878716\pi\)
\(272\) 19.7633 + 34.2310i 1.19832 + 2.07556i
\(273\) 0 0
\(274\) 22.4684 38.9164i 1.35737 2.35103i
\(275\) 3.34943 0.201978
\(276\) 0.798182 + 2.52750i 0.0480449 + 0.152138i
\(277\) −16.3907 −0.984824 −0.492412 0.870362i \(-0.663885\pi\)
−0.492412 + 0.870362i \(0.663885\pi\)
\(278\) 10.7280 + 18.5815i 0.643423 + 1.11444i
\(279\) 1.96289 + 22.2035i 0.117515 + 1.32929i
\(280\) 0 0
\(281\) 1.75702 + 3.04325i 0.104815 + 0.181545i 0.913663 0.406473i \(-0.133242\pi\)
−0.808848 + 0.588018i \(0.799908\pi\)
\(282\) −15.7871 49.9911i −0.940108 2.97692i
\(283\) 13.0354 + 22.5780i 0.774874 + 1.34212i 0.934865 + 0.355002i \(0.115520\pi\)
−0.159992 + 0.987118i \(0.551147\pi\)
\(284\) 3.90025 + 6.75543i 0.231437 + 0.400861i
\(285\) 0.517726 + 1.63942i 0.0306674 + 0.0971108i
\(286\) −5.81958 10.0798i −0.344119 0.596031i
\(287\) 0 0
\(288\) 5.28645 + 59.7985i 0.311507 + 3.52366i
\(289\) 4.57850 + 7.93019i 0.269323 + 0.466482i
\(290\) 19.5891 1.15031
\(291\) −7.54177 23.8816i −0.442107 1.39996i
\(292\) 2.51479 0.147167
\(293\) 9.44192 16.3539i 0.551603 0.955404i −0.446556 0.894756i \(-0.647350\pi\)
0.998159 0.0606487i \(-0.0193169\pi\)
\(294\) 0 0
\(295\) 3.62863 + 6.28497i 0.211267 + 0.365925i
\(296\) 36.7242 + 63.6082i 2.13455 + 3.69715i
\(297\) −5.56589 4.25881i −0.322965 0.247121i
\(298\) −18.5559 + 32.1398i −1.07492 + 1.86181i
\(299\) 0.452700 0.784099i 0.0261803 0.0453456i
\(300\) 6.95823 + 22.0338i 0.401733 + 1.27212i
\(301\) 0 0
\(302\) 5.29401 9.16950i 0.304636 0.527645i
\(303\) −16.6373 3.68046i −0.955786 0.211437i
\(304\) −8.83097 −0.506491
\(305\) −0.305392 + 0.528954i −0.0174867 + 0.0302878i
\(306\) −2.00880 22.7229i −0.114836 1.29898i
\(307\) 21.6407 1.23510 0.617551 0.786531i \(-0.288125\pi\)
0.617551 + 0.786531i \(0.288125\pi\)
\(308\) 0 0
\(309\) −18.7008 4.13696i −1.06385 0.235343i
\(310\) 32.0032 1.81766
\(311\) 2.24724 + 3.89234i 0.127429 + 0.220714i 0.922680 0.385567i \(-0.125994\pi\)
−0.795251 + 0.606281i \(0.792661\pi\)
\(312\) 34.0329 37.1742i 1.92673 2.10458i
\(313\) 4.30102 7.44958i 0.243108 0.421075i −0.718490 0.695537i \(-0.755166\pi\)
0.961598 + 0.274462i \(0.0884997\pi\)
\(314\) −0.799206 −0.0451018
\(315\) 0 0
\(316\) −84.4062 −4.74822
\(317\) 4.03128 6.98237i 0.226419 0.392169i −0.730325 0.683100i \(-0.760631\pi\)
0.956744 + 0.290930i \(0.0939648\pi\)
\(318\) 3.94686 + 12.4980i 0.221329 + 0.700856i
\(319\) −3.06701 5.31221i −0.171719 0.297427i
\(320\) 41.4105 2.31492
\(321\) 1.00370 + 3.17828i 0.0560208 + 0.177394i
\(322\) 0 0
\(323\) 1.75228 0.0974992
\(324\) 16.4532 45.4618i 0.914068 2.52565i
\(325\) 3.94646 6.83546i 0.218910 0.379163i
\(326\) −29.0766 −1.61041
\(327\) 21.7621 23.7708i 1.20345 1.31453i
\(328\) 45.8981 79.4978i 2.53430 4.38953i
\(329\) 0 0
\(330\) −6.79458 + 7.42175i −0.374029 + 0.408554i
\(331\) 11.4513 19.8342i 0.629419 1.09019i −0.358249 0.933626i \(-0.616626\pi\)
0.987668 0.156560i \(-0.0500405\pi\)
\(332\) 37.5681 65.0698i 2.06182 3.57117i
\(333\) −2.11941 23.9740i −0.116143 1.31377i
\(334\) 4.34075 + 7.51840i 0.237515 + 0.411388i
\(335\) 2.01405 + 3.48844i 0.110039 + 0.190594i
\(336\) 0 0
\(337\) −6.81891 + 11.8107i −0.371450 + 0.643369i −0.989789 0.142542i \(-0.954472\pi\)
0.618339 + 0.785911i \(0.287806\pi\)
\(338\) 7.86916 0.428026
\(339\) 3.72717 4.07120i 0.202432 0.221117i
\(340\) −23.8662 −1.29433
\(341\) −5.01065 8.67869i −0.271342 0.469978i
\(342\) 4.62097 + 2.14968i 0.249873 + 0.116242i
\(343\) 0 0
\(344\) 28.6502 + 49.6237i 1.54472 + 2.67553i
\(345\) −0.764256 0.169067i −0.0411462 0.00910228i
\(346\) 15.5272 + 26.8938i 0.834746 + 1.44582i
\(347\) 1.41282 + 2.44707i 0.0758440 + 0.131366i 0.901453 0.432877i \(-0.142502\pi\)
−0.825609 + 0.564243i \(0.809168\pi\)
\(348\) 28.5741 31.2116i 1.53173 1.67312i
\(349\) 1.81202 + 3.13851i 0.0969951 + 0.168000i 0.910440 0.413642i \(-0.135744\pi\)
−0.813444 + 0.581643i \(0.802410\pi\)
\(350\) 0 0
\(351\) −15.2493 + 6.34083i −0.813947 + 0.338448i
\(352\) −13.4947 23.3734i −0.719268 1.24581i
\(353\) 2.75401 0.146581 0.0732907 0.997311i \(-0.476650\pi\)
0.0732907 + 0.997311i \(0.476650\pi\)
\(354\) 21.0058 + 4.64685i 1.11644 + 0.246977i
\(355\) −2.30357 −0.122261
\(356\) −6.94877 + 12.0356i −0.368284 + 0.637887i
\(357\) 0 0
\(358\) 1.49135 + 2.58310i 0.0788205 + 0.136521i
\(359\) 8.40076 + 14.5505i 0.443375 + 0.767948i 0.997937 0.0641941i \(-0.0204477\pi\)
−0.554562 + 0.832142i \(0.687114\pi\)
\(360\) −39.5060 18.3783i −2.08215 0.968620i
\(361\) 9.30425 16.1154i 0.489698 0.848181i
\(362\) −4.33081 + 7.50119i −0.227622 + 0.394254i
\(363\) −15.5264 3.43471i −0.814922 0.180276i
\(364\) 0 0
\(365\) −0.371322 + 0.643149i −0.0194359 + 0.0336640i
\(366\) 0.545250 + 1.72657i 0.0285007 + 0.0902495i
\(367\) 23.9339 1.24934 0.624670 0.780889i \(-0.285233\pi\)
0.624670 + 0.780889i \(0.285233\pi\)
\(368\) 2.01030 3.48193i 0.104794 0.181508i
\(369\) −24.6242 + 17.2754i −1.28188 + 0.899322i
\(370\) −34.5551 −1.79644
\(371\) 0 0
\(372\) 46.6822 50.9912i 2.42036 2.64377i
\(373\) −19.1606 −0.992098 −0.496049 0.868295i \(-0.665216\pi\)
−0.496049 + 0.868295i \(0.665216\pi\)
\(374\) 5.12784 + 8.88168i 0.265154 + 0.459261i
\(375\) −20.0767 4.44134i −1.03676 0.229350i
\(376\) −51.0299 + 88.3865i −2.63167 + 4.55818i
\(377\) −14.4548 −0.744458
\(378\) 0 0
\(379\) 10.0770 0.517622 0.258811 0.965928i \(-0.416669\pi\)
0.258811 + 0.965928i \(0.416669\pi\)
\(380\) 2.66608 4.61779i 0.136767 0.236888i
\(381\) −14.1616 3.13280i −0.725520 0.160498i
\(382\) 5.25127 + 9.09546i 0.268678 + 0.465364i
\(383\) 20.1435 1.02929 0.514643 0.857405i \(-0.327925\pi\)
0.514643 + 0.857405i \(0.327925\pi\)
\(384\) 36.0855 39.4164i 1.84148 2.01146i
\(385\) 0 0
\(386\) 11.2294 0.571561
\(387\) −1.65345 18.7033i −0.0840496 0.950740i
\(388\) −38.8372 + 67.2679i −1.97166 + 3.41501i
\(389\) 13.3947 0.679139 0.339570 0.940581i \(-0.389719\pi\)
0.339570 + 0.940581i \(0.389719\pi\)
\(390\) 7.14049 + 22.6109i 0.361573 + 1.14495i
\(391\) −0.398891 + 0.690899i −0.0201728 + 0.0349402i
\(392\) 0 0
\(393\) 20.2476 + 4.47913i 1.02136 + 0.225942i
\(394\) −1.20724 + 2.09100i −0.0608198 + 0.105343i
\(395\) 12.4630 21.5866i 0.627083 1.08614i
\(396\) 1.91412 + 21.6518i 0.0961880 + 1.08805i
\(397\) −9.00664 15.6000i −0.452031 0.782940i 0.546482 0.837471i \(-0.315967\pi\)
−0.998512 + 0.0545313i \(0.982634\pi\)
\(398\) −8.58506 14.8698i −0.430330 0.745354i
\(399\) 0 0
\(400\) 17.5249 30.3541i 0.876247 1.51770i
\(401\) 28.8675 1.44157 0.720787 0.693157i \(-0.243781\pi\)
0.720787 + 0.693157i \(0.243781\pi\)
\(402\) 11.6591 + 2.57921i 0.581505 + 0.128639i
\(403\) −23.6151 −1.17635
\(404\) 26.4240 + 45.7676i 1.31464 + 2.27703i
\(405\) 9.19729 + 10.9205i 0.457017 + 0.542646i
\(406\) 0 0
\(407\) 5.41019 + 9.37073i 0.268173 + 0.464490i
\(408\) −29.9876 + 32.7556i −1.48461 + 1.62164i
\(409\) −5.42937 9.40395i −0.268465 0.464995i 0.700000 0.714142i \(-0.253183\pi\)
−0.968466 + 0.249147i \(0.919850\pi\)
\(410\) 21.5936 + 37.4012i 1.06643 + 1.84711i
\(411\) 27.9896 + 6.19181i 1.38063 + 0.305419i
\(412\) 29.7014 + 51.4443i 1.46328 + 2.53448i
\(413\) 0 0
\(414\) −1.89951 + 1.33263i −0.0933561 + 0.0654951i
\(415\) 11.0943 + 19.2158i 0.544595 + 0.943267i
\(416\) −63.6001 −3.11825
\(417\) −9.24244 + 10.0956i −0.452604 + 0.494382i
\(418\) −2.29131 −0.112072
\(419\) 0.247572 0.428807i 0.0120947 0.0209486i −0.859915 0.510438i \(-0.829483\pi\)
0.872009 + 0.489489i \(0.162817\pi\)
\(420\) 0 0
\(421\) 9.50320 + 16.4600i 0.463158 + 0.802212i 0.999116 0.0420318i \(-0.0133831\pi\)
−0.535959 + 0.844244i \(0.680050\pi\)
\(422\) −15.5113 26.8664i −0.755079 1.30784i
\(423\) 27.3774 19.2070i 1.33114 0.933875i
\(424\) 12.7578 22.0971i 0.619572 1.07313i
\(425\) −3.47737 + 6.02298i −0.168677 + 0.292157i
\(426\) −4.61116 + 5.03679i −0.223411 + 0.244033i
\(427\) 0 0
\(428\) 5.16864 8.95234i 0.249835 0.432728i
\(429\) 5.01371 5.47649i 0.242064 0.264408i
\(430\) −26.9580 −1.30003
\(431\) 8.46073 14.6544i 0.407539 0.705878i −0.587074 0.809533i \(-0.699720\pi\)
0.994613 + 0.103655i \(0.0330538\pi\)
\(432\) −67.7172 + 28.1576i −3.25805 + 1.35473i
\(433\) 33.4740 1.60866 0.804330 0.594183i \(-0.202524\pi\)
0.804330 + 0.594183i \(0.202524\pi\)
\(434\) 0 0
\(435\) 3.76315 + 11.9163i 0.180429 + 0.571343i
\(436\) −99.9548 −4.78697
\(437\) −0.0891197 0.154360i −0.00426317 0.00738403i
\(438\) 0.662962 + 2.09932i 0.0316776 + 0.100309i
\(439\) 10.4657 18.1272i 0.499502 0.865163i −0.500498 0.865738i \(-0.666850\pi\)
1.00000 0.000574559i \(0.000182888\pi\)
\(440\) 19.5891 0.933874
\(441\) 0 0
\(442\) 24.1674 1.14953
\(443\) 15.4290 26.7238i 0.733054 1.26969i −0.222517 0.974929i \(-0.571427\pi\)
0.955572 0.294759i \(-0.0952393\pi\)
\(444\) −50.4047 + 55.0572i −2.39210 + 2.61290i
\(445\) −2.05205 3.55425i −0.0972763 0.168487i
\(446\) −45.3945 −2.14949
\(447\) −23.1157 5.11362i −1.09334 0.241866i
\(448\) 0 0
\(449\) −33.2789 −1.57053 −0.785263 0.619162i \(-0.787472\pi\)
−0.785263 + 0.619162i \(0.787472\pi\)
\(450\) −16.5592 + 11.6173i −0.780608 + 0.547646i
\(451\) 6.76168 11.7116i 0.318395 0.551477i
\(452\) −17.1191 −0.805217
\(453\) 6.59492 + 1.45892i 0.309857 + 0.0685458i
\(454\) −23.1737 + 40.1380i −1.08760 + 1.88377i
\(455\) 0 0
\(456\) −2.98786 9.46130i −0.139919 0.443066i
\(457\) −11.8952 + 20.6031i −0.556434 + 0.963772i 0.441356 + 0.897332i \(0.354498\pi\)
−0.997790 + 0.0664402i \(0.978836\pi\)
\(458\) −26.8654 + 46.5323i −1.25534 + 2.17431i
\(459\) 13.4367 5.58714i 0.627172 0.260785i
\(460\) 1.21382 + 2.10240i 0.0565947 + 0.0980249i
\(461\) −8.53122 14.7765i −0.397339 0.688211i 0.596058 0.802941i \(-0.296733\pi\)
−0.993397 + 0.114731i \(0.963400\pi\)
\(462\) 0 0
\(463\) 18.1243 31.3922i 0.842306 1.45892i −0.0456338 0.998958i \(-0.514531\pi\)
0.887940 0.459959i \(-0.152136\pi\)
\(464\) −64.1889 −2.97990
\(465\) 6.14795 + 19.4680i 0.285104 + 0.902805i
\(466\) −16.1051 −0.746052
\(467\) −4.09580 7.09413i −0.189531 0.328277i 0.755563 0.655076i \(-0.227363\pi\)
−0.945094 + 0.326799i \(0.894030\pi\)
\(468\) 46.4420 + 21.6049i 2.14678 + 0.998686i
\(469\) 0 0
\(470\) −24.0080 41.5830i −1.10740 1.91808i
\(471\) −0.153531 0.486167i −0.00707432 0.0224014i
\(472\) −20.9413 36.2714i −0.963900 1.66952i
\(473\) 4.22074 + 7.31054i 0.194070 + 0.336139i
\(474\) −22.2516 70.4615i −1.02205 3.23640i
\(475\) −0.776909 1.34565i −0.0356470 0.0617425i
\(476\) 0 0
\(477\) −6.84451 + 4.80185i −0.313389 + 0.219862i
\(478\) 27.2265 + 47.1577i 1.24531 + 2.15694i
\(479\) 25.5549 1.16763 0.583817 0.811885i \(-0.301559\pi\)
0.583817 + 0.811885i \(0.301559\pi\)
\(480\) 16.5576 + 52.4310i 0.755749 + 2.39314i
\(481\) 25.4982 1.16262
\(482\) −39.7614 + 68.8687i −1.81108 + 3.13688i
\(483\) 0 0
\(484\) 24.6596 + 42.7116i 1.12089 + 1.94144i
\(485\) −11.4690 19.8649i −0.520782 0.902020i
\(486\) 42.2885 + 1.75011i 1.91825 + 0.0793868i
\(487\) 3.46140 5.99533i 0.156851 0.271674i −0.776880 0.629648i \(-0.783199\pi\)
0.933732 + 0.357974i \(0.116532\pi\)
\(488\) 1.76246 3.05266i 0.0797826 0.138188i
\(489\) −5.58574 17.6877i −0.252596 0.799865i
\(490\) 0 0
\(491\) 18.7262 32.4348i 0.845103 1.46376i −0.0404294 0.999182i \(-0.512873\pi\)
0.885532 0.464578i \(-0.153794\pi\)
\(492\) 91.0899 + 20.1507i 4.10665 + 0.908465i
\(493\) 12.7366 0.573628
\(494\) −2.69973 + 4.67607i −0.121467 + 0.210386i
\(495\) −5.82001 2.70748i −0.261590 0.121692i
\(496\) −104.867 −4.70867
\(497\) 0 0
\(498\) 64.2235 + 14.2074i 2.87793 + 0.636649i
\(499\) 25.6250 1.14713 0.573566 0.819159i \(-0.305560\pi\)
0.573566 + 0.819159i \(0.305560\pi\)
\(500\) 31.8867 + 55.2293i 1.42601 + 2.46993i
\(501\) −3.73966 + 4.08485i −0.167076 + 0.182497i
\(502\) 30.9329 53.5774i 1.38060 2.39127i
\(503\) 5.79692 0.258472 0.129236 0.991614i \(-0.458748\pi\)
0.129236 + 0.991614i \(0.458748\pi\)
\(504\) 0 0
\(505\) −15.6066 −0.694483
\(506\) 0.521598 0.903434i 0.0231878 0.0401625i
\(507\) 1.51170 + 4.78691i 0.0671369 + 0.212594i
\(508\) 22.4920 + 38.9573i 0.997921 + 1.72845i
\(509\) −25.1395 −1.11429 −0.557144 0.830416i \(-0.688103\pi\)
−0.557144 + 0.830416i \(0.688103\pi\)
\(510\) −6.29174 19.9233i −0.278603 0.882218i
\(511\) 0 0
\(512\) −23.9940 −1.06039
\(513\) −0.419972 + 3.22396i −0.0185422 + 0.142341i
\(514\) 32.9738 57.1123i 1.45441 2.51911i
\(515\) −17.5423 −0.773004
\(516\) −39.3230 + 42.9527i −1.73110 + 1.89089i
\(517\) −7.51771 + 13.0211i −0.330629 + 0.572665i
\(518\) 0 0
\(519\) −13.3770 + 14.6118i −0.587186 + 0.641386i
\(520\) 23.0808 39.9771i 1.01216 1.75311i
\(521\) 3.64828 6.31900i 0.159834 0.276841i −0.774975 0.631992i \(-0.782237\pi\)
0.934809 + 0.355152i \(0.115571\pi\)
\(522\) 33.5880 + 15.6252i 1.47011 + 0.683897i
\(523\) 8.38637 + 14.5256i 0.366710 + 0.635161i 0.989049 0.147587i \(-0.0471506\pi\)
−0.622339 + 0.782748i \(0.713817\pi\)
\(524\) −32.1580 55.6993i −1.40483 2.43324i
\(525\) 0 0
\(526\) −11.6908 + 20.2490i −0.509741 + 0.882898i
\(527\) 20.8081 0.906416
\(528\) 22.2643 24.3193i 0.968927 1.05836i
\(529\) −22.9189 −0.996472
\(530\) 6.00212 + 10.3960i 0.260716 + 0.451573i
\(531\) 1.20855 + 13.6707i 0.0524468 + 0.593260i
\(532\) 0 0
\(533\) −15.9339 27.5982i −0.690172 1.19541i
\(534\) −11.8791 2.62787i −0.514058 0.113719i
\(535\) 1.52635 + 2.64372i 0.0659900 + 0.114298i
\(536\) −11.6234 20.1322i −0.502053 0.869581i
\(537\) −1.28484 + 1.40343i −0.0554449 + 0.0605627i
\(538\) 20.6774 + 35.8143i 0.891466 + 1.54406i
\(539\) 0 0
\(540\) 5.72007 43.9107i 0.246153 1.88962i
\(541\) 2.64908 + 4.58834i 0.113893 + 0.197268i 0.917337 0.398112i \(-0.130335\pi\)
−0.803444 + 0.595381i \(0.797001\pi\)
\(542\) −12.7019 −0.545595
\(543\) −5.39503 1.19348i −0.231523 0.0512171i
\(544\) 56.0404 2.40271
\(545\) 14.7589 25.5631i 0.632200 1.09500i
\(546\) 0 0
\(547\) 16.4325 + 28.4619i 0.702603 + 1.21694i 0.967550 + 0.252681i \(0.0813123\pi\)
−0.264947 + 0.964263i \(0.585354\pi\)
\(548\) −44.4542 76.9970i −1.89899 3.28915i
\(549\) −0.945552 + 0.663364i −0.0403552 + 0.0283117i
\(550\) 4.54708 7.87577i 0.193888 0.335824i
\(551\) −1.42280 + 2.46436i −0.0606133 + 0.104985i
\(552\) 4.41062 + 0.975709i 0.187729 + 0.0415290i
\(553\) 0 0
\(554\) −22.2515 + 38.5408i −0.945376 + 1.63744i
\(555\) −6.63818 21.0203i −0.281775 0.892263i
\(556\) 42.4512 1.80033
\(557\) 9.40798 16.2951i 0.398629 0.690446i −0.594928 0.803779i \(-0.702819\pi\)
0.993557 + 0.113333i \(0.0361527\pi\)
\(558\) 54.8736 + 25.5273i 2.32298 + 1.08066i
\(559\) 19.8923 0.841354
\(560\) 0 0
\(561\) −4.41776 + 4.82554i −0.186518 + 0.203734i
\(562\) 9.54108 0.402466
\(563\) 13.8325 + 23.9586i 0.582970 + 1.00973i 0.995125 + 0.0986197i \(0.0314427\pi\)
−0.412155 + 0.911114i \(0.635224\pi\)
\(564\) −101.275 22.4038i −4.26443 0.943370i
\(565\) 2.52773 4.37816i 0.106343 0.184191i
\(566\) 70.7856 2.97534
\(567\) 0 0
\(568\) 13.2942 0.557812
\(569\) 20.0916 34.7996i 0.842282 1.45888i −0.0456782 0.998956i \(-0.514545\pi\)
0.887961 0.459920i \(-0.152122\pi\)
\(570\) 4.55773 + 1.00825i 0.190902 + 0.0422311i
\(571\) 3.40565 + 5.89875i 0.142522 + 0.246855i 0.928446 0.371468i \(-0.121146\pi\)
−0.785924 + 0.618323i \(0.787812\pi\)
\(572\) −23.0283 −0.962862
\(573\) −4.52409 + 4.94169i −0.188997 + 0.206442i
\(574\) 0 0
\(575\) 0.707427 0.0295017
\(576\) 71.0036 + 33.0310i 2.95849 + 1.37629i
\(577\) −18.2111 + 31.5425i −0.758138 + 1.31313i 0.185661 + 0.982614i \(0.440557\pi\)
−0.943799 + 0.330519i \(0.892776\pi\)
\(578\) 24.8625 1.03414
\(579\) 2.15721 + 6.83098i 0.0896507 + 0.283886i
\(580\) 19.3787 33.5649i 0.804658 1.39371i
\(581\) 0 0
\(582\) −66.3930 14.6873i −2.75208 0.608810i
\(583\) 1.87947 3.25534i 0.0778397 0.134822i
\(584\) 2.14295 3.71170i 0.0886759 0.153591i
\(585\) −12.3828 + 8.68729i −0.511965 + 0.359175i
\(586\) −25.6361 44.4030i −1.05902 1.83427i
\(587\) −5.57943 9.66385i −0.230288 0.398870i 0.727605 0.685996i \(-0.240633\pi\)
−0.957893 + 0.287126i \(0.907300\pi\)
\(588\) 0 0
\(589\) −2.32446 + 4.02609i −0.0957779 + 0.165892i
\(590\) 19.7044 0.811218
\(591\) −1.50390 0.332689i −0.0618620 0.0136850i
\(592\) 113.229 4.65369
\(593\) 9.90427 + 17.1547i 0.406720 + 0.704459i 0.994520 0.104547i \(-0.0333392\pi\)
−0.587800 + 0.809006i \(0.700006\pi\)
\(594\) −17.5701 + 7.30586i −0.720911 + 0.299763i
\(595\) 0 0
\(596\) 36.7133 + 63.5893i 1.50384 + 2.60472i
\(597\) 7.39624 8.07895i 0.302708 0.330649i
\(598\) −1.22914 2.12893i −0.0502633 0.0870586i
\(599\) 9.06600 + 15.7028i 0.370427 + 0.641598i 0.989631 0.143632i \(-0.0458781\pi\)
−0.619204 + 0.785230i \(0.712545\pi\)
\(600\) 38.4500 + 8.50584i 1.56972 + 0.347249i
\(601\) 12.3285 + 21.3536i 0.502889 + 0.871030i 0.999994 + 0.00333942i \(0.00106297\pi\)
−0.497105 + 0.867690i \(0.665604\pi\)
\(602\) 0 0
\(603\) 0.670802 + 7.58788i 0.0273172 + 0.309003i
\(604\) −10.4743 18.1420i −0.426194 0.738189i
\(605\) −14.5645 −0.592130
\(606\) −31.2404 + 34.1240i −1.26905 + 1.38619i
\(607\) −17.2775 −0.701273 −0.350637 0.936512i \(-0.614035\pi\)
−0.350637 + 0.936512i \(0.614035\pi\)
\(608\) −6.26024 + 10.8431i −0.253886 + 0.439744i
\(609\) 0 0
\(610\) 0.829179 + 1.43618i 0.0335725 + 0.0581492i
\(611\) 17.7154 + 30.6840i 0.716689 + 1.24134i
\(612\) −40.9217 19.0368i −1.65416 0.769519i
\(613\) −9.77828 + 16.9365i −0.394941 + 0.684058i −0.993094 0.117324i \(-0.962568\pi\)
0.598153 + 0.801382i \(0.295902\pi\)
\(614\) 29.3787 50.8855i 1.18563 2.05357i
\(615\) −18.6034 + 20.3206i −0.750161 + 0.819404i
\(616\) 0 0
\(617\) 10.8723 18.8314i 0.437702 0.758122i −0.559810 0.828621i \(-0.689126\pi\)
0.997512 + 0.0704988i \(0.0224591\pi\)
\(618\) −35.1151 + 38.3564i −1.41254 + 1.54292i
\(619\) −33.8048 −1.35873 −0.679366 0.733800i \(-0.737745\pi\)
−0.679366 + 0.733800i \(0.737745\pi\)
\(620\) 31.6595 54.8359i 1.27148 2.20226i
\(621\) −1.17556 0.899495i −0.0471736 0.0360955i
\(622\) 12.2031 0.489300
\(623\) 0 0
\(624\) −23.3977 74.0906i −0.936658 2.96600i
\(625\) −6.41615 −0.256646
\(626\) −11.6778 20.2266i −0.466740 0.808418i
\(627\) −0.440171 1.39383i −0.0175787 0.0556644i
\(628\) −0.790623 + 1.36940i −0.0315493 + 0.0546450i
\(629\) −22.4674 −0.895832
\(630\) 0 0
\(631\) −23.6410 −0.941134 −0.470567 0.882364i \(-0.655951\pi\)
−0.470567 + 0.882364i \(0.655951\pi\)
\(632\) −71.9258 + 124.579i −2.86105 + 4.95549i
\(633\) 13.3634 14.5969i 0.531146 0.580173i
\(634\) −10.9454 18.9581i −0.434699 0.752921i
\(635\) −13.2843 −0.527169
\(636\) 25.3192 + 5.60107i 1.00397 + 0.222097i
\(637\) 0 0
\(638\) −16.6547 −0.659365
\(639\) −3.94977 1.83744i −0.156250 0.0726879i
\(640\) 24.4729 42.3883i 0.967375 1.67554i
\(641\) 15.9180 0.628724 0.314362 0.949303i \(-0.398209\pi\)
0.314362 + 0.949303i \(0.398209\pi\)
\(642\) 8.83591 + 1.95466i 0.348725 + 0.0771444i
\(643\) 13.2527 22.9544i 0.522636 0.905231i −0.477017 0.878894i \(-0.658282\pi\)
0.999653 0.0263376i \(-0.00838450\pi\)
\(644\) 0 0
\(645\) −5.17875 16.3989i −0.203913 0.645707i
\(646\) 2.37883 4.12026i 0.0935938 0.162109i
\(647\) 0.00801958 0.0138903i 0.000315282 0.000546085i −0.865868 0.500273i \(-0.833233\pi\)
0.866183 + 0.499727i \(0.166566\pi\)
\(648\) −53.0787 63.0238i −2.08513 2.47581i
\(649\) −3.08506 5.34348i −0.121099 0.209750i
\(650\) −10.7152 18.5592i −0.420283 0.727951i
\(651\) 0 0
\(652\) −28.7644 + 49.8214i −1.12650 + 1.95115i
\(653\) −33.2879 −1.30266 −0.651328 0.758796i \(-0.725788\pi\)
−0.651328 + 0.758796i \(0.725788\pi\)
\(654\) −26.3506 83.4413i −1.03039 3.26281i
\(655\) 18.9932 0.742126
\(656\) −70.7571 122.555i −2.76260 4.78497i
\(657\) −1.14969 + 0.806577i −0.0448535 + 0.0314676i
\(658\) 0 0
\(659\) 19.4156 + 33.6288i 0.756324 + 1.30999i 0.944713 + 0.327897i \(0.106340\pi\)
−0.188389 + 0.982094i \(0.560327\pi\)
\(660\) 5.99518 + 18.9842i 0.233362 + 0.738959i
\(661\) 2.65322 + 4.59551i 0.103198 + 0.178745i 0.913001 0.407958i \(-0.133759\pi\)
−0.809802 + 0.586703i \(0.800426\pi\)
\(662\) −31.0917 53.8525i −1.20842 2.09304i
\(663\) 4.64266 + 14.7013i 0.180306 + 0.570953i
\(664\) −64.0264 110.897i −2.48471 4.30364i
\(665\) 0 0
\(666\) −59.2492 27.5628i −2.29586 1.06804i
\(667\) −0.647777 1.12198i −0.0250820 0.0434433i
\(668\) 17.1765 0.664579
\(669\) −8.72047 27.6140i −0.337153 1.06762i
\(670\) 10.9368 0.422527
\(671\) 0.259644 0.449717i 0.0100235 0.0173611i
\(672\) 0 0
\(673\) −3.03565 5.25789i −0.117016 0.202677i 0.801568 0.597903i \(-0.203999\pi\)
−0.918584 + 0.395227i \(0.870666\pi\)
\(674\) 18.5142 + 32.0676i 0.713142 + 1.23520i
\(675\) −10.2481 7.84144i −0.394448 0.301817i
\(676\) 7.78465 13.4834i 0.299410 0.518593i
\(677\) −17.3925 + 30.1247i −0.668449 + 1.15779i 0.309889 + 0.950773i \(0.399708\pi\)
−0.978338 + 0.207014i \(0.933625\pi\)
\(678\) −4.51304 14.2909i −0.173322 0.548838i
\(679\) 0 0
\(680\) −20.3373 + 35.2253i −0.779901 + 1.35083i
\(681\) −28.8682 6.38617i −1.10623 0.244719i
\(682\) −27.2091 −1.04189
\(683\) −9.71206 + 16.8218i −0.371622 + 0.643667i −0.989815 0.142358i \(-0.954531\pi\)
0.618194 + 0.786026i \(0.287865\pi\)
\(684\) 8.25471 5.79120i 0.315627 0.221432i
\(685\) 26.2556 1.00318
\(686\) 0 0
\(687\) −33.4672 7.40354i −1.27685 0.282463i
\(688\) 88.3352 3.36775
\(689\) −4.42895 7.67117i −0.168730 0.292248i
\(690\) −1.43507 + 1.56753i −0.0546322 + 0.0596749i
\(691\) −3.31837 + 5.74759i −0.126237 + 0.218649i −0.922216 0.386676i \(-0.873623\pi\)
0.795979 + 0.605324i \(0.206957\pi\)
\(692\) 61.4416 2.33566
\(693\) 0 0
\(694\) 7.67197 0.291224
\(695\) −6.26814 + 10.8567i −0.237764 + 0.411820i
\(696\) −21.7176 68.7705i −0.823204 2.60674i
\(697\) 14.0399 + 24.3178i 0.531799 + 0.921103i
\(698\) 9.83974 0.372440
\(699\) −3.09385 9.79690i −0.117020 0.370553i
\(700\) 0 0
\(701\) −13.9153 −0.525574 −0.262787 0.964854i \(-0.584642\pi\)
−0.262787 + 0.964854i \(0.584642\pi\)
\(702\) −5.79226 + 44.4649i −0.218615 + 1.67822i
\(703\) 2.50982 4.34713i 0.0946595 0.163955i
\(704\) −35.2072 −1.32692
\(705\) 20.6834 22.5926i 0.778983 0.850887i
\(706\) 3.73876 6.47571i 0.140710 0.243717i
\(707\) 0 0
\(708\) 28.7423 31.3954i 1.08020 1.17991i
\(709\) −17.0778 + 29.5796i −0.641370 + 1.11089i 0.343757 + 0.939059i \(0.388300\pi\)
−0.985127 + 0.171827i \(0.945033\pi\)
\(710\) −3.12725 + 5.41655i −0.117364 + 0.203280i
\(711\) 38.5880 27.0719i 1.44716 1.01527i
\(712\) 11.8426 + 20.5120i 0.443821 + 0.768721i
\(713\) −1.05829 1.83301i −0.0396332 0.0686467i
\(714\) 0 0
\(715\) 3.40025 5.88941i 0.127162 0.220251i
\(716\) 5.90135 0.220544
\(717\) −23.4563 + 25.6214i −0.875991 + 0.956849i
\(718\) 45.6183 1.70246
\(719\) −22.1450 38.3563i −0.825870 1.43045i −0.901253 0.433294i \(-0.857351\pi\)
0.0753825 0.997155i \(-0.475982\pi\)
\(720\) −54.9879 + 38.5775i −2.04928 + 1.43770i
\(721\) 0 0
\(722\) −25.2623 43.7556i −0.940165 1.62841i
\(723\) −49.5320 10.9574i −1.84212 0.407509i
\(724\) 8.56860 + 14.8413i 0.318450 + 0.551571i
\(725\) −5.64705 9.78099i −0.209726 0.363257i
\(726\) −29.1543 + 31.8454i −1.08202 + 1.18189i
\(727\) −14.1247 24.4647i −0.523857 0.907346i −0.999614 0.0277700i \(-0.991159\pi\)
0.475758 0.879576i \(-0.342174\pi\)
\(728\) 0 0
\(729\) 7.05919 + 26.0608i 0.261451 + 0.965217i
\(730\) 1.00819 + 1.74623i 0.0373147 + 0.0646310i
\(731\) −17.5278 −0.648290
\(732\) 3.49779 + 0.773775i 0.129282 + 0.0285995i
\(733\) 25.0169 0.924020 0.462010 0.886875i \(-0.347128\pi\)
0.462010 + 0.886875i \(0.347128\pi\)
\(734\) 32.4919 56.2776i 1.19930 2.07724i
\(735\) 0 0
\(736\) −2.85018 4.93666i −0.105059 0.181968i
\(737\) −1.71235 2.96587i −0.0630752 0.109249i
\(738\) 7.19198 + 81.3532i 0.264740 + 2.99465i
\(739\) −16.0115 + 27.7327i −0.588992 + 1.02016i 0.405373 + 0.914151i \(0.367142\pi\)
−0.994365 + 0.106013i \(0.966192\pi\)
\(740\) −34.1840 + 59.2084i −1.25663 + 2.17655i
\(741\) −3.36314 0.743987i −0.123548 0.0273311i
\(742\) 0 0
\(743\) 19.4031 33.6072i 0.711833 1.23293i −0.252336 0.967640i \(-0.581199\pi\)
0.964169 0.265290i \(-0.0854678\pi\)
\(744\) −35.4806 112.352i −1.30078 4.11903i
\(745\) −21.6837 −0.794428
\(746\) −26.0118 + 45.0537i −0.952359 + 1.64953i
\(747\) 3.69506 + 41.7973i 0.135195 + 1.52928i
\(748\) 20.2911 0.741915
\(749\) 0 0
\(750\) −37.6987 + 41.1785i −1.37656 + 1.50363i
\(751\) 21.6991 0.791811 0.395905 0.918291i \(-0.370431\pi\)
0.395905 + 0.918291i \(0.370431\pi\)
\(752\) 78.6685 + 136.258i 2.86874 + 4.96881i
\(753\) 38.5341 + 8.52444i 1.40426 + 0.310648i
\(754\) −19.6233 + 33.9885i −0.714638 + 1.23779i
\(755\) 6.18635 0.225144
\(756\) 0 0
\(757\) 33.5242 1.21846 0.609229 0.792995i \(-0.291479\pi\)
0.609229 + 0.792995i \(0.291479\pi\)
\(758\) 13.6802 23.6949i 0.496889 0.860637i
\(759\) 0.649771 + 0.143741i 0.0235852 + 0.00521747i
\(760\) −4.54374 7.86999i −0.164819 0.285475i
\(761\) 13.3210 0.482884 0.241442 0.970415i \(-0.422380\pi\)
0.241442 + 0.970415i \(0.422380\pi\)
\(762\) −26.5917 + 29.0462i −0.963315 + 1.05223i
\(763\) 0 0
\(764\) 20.7795 0.751775
\(765\) 10.9109 7.65469i 0.394485 0.276756i
\(766\) 27.3462 47.3649i 0.988057 1.71137i
\(767\) −14.5398 −0.525003
\(768\) −16.4635 52.1330i −0.594075 1.88119i
\(769\) −27.3568 + 47.3833i −0.986510 + 1.70869i −0.351488 + 0.936192i \(0.614324\pi\)
−0.635022 + 0.772494i \(0.719009\pi\)
\(770\) 0 0
\(771\) 41.0765 + 9.08686i 1.47933 + 0.327255i
\(772\) 11.1088 19.2410i 0.399814 0.692498i
\(773\) 1.18021 2.04418i 0.0424491 0.0735240i −0.844020 0.536311i \(-0.819817\pi\)
0.886469 + 0.462787i \(0.153151\pi\)
\(774\) −46.2230 21.5030i −1.66145 0.772911i
\(775\) −9.22573 15.9794i −0.331398 0.573998i
\(776\) 66.1892 + 114.643i 2.37606 + 4.11545i
\(777\) 0 0
\(778\) 18.1842 31.4960i 0.651936 1.12919i
\(779\) −6.27356 −0.224774
\(780\) 45.8064 + 10.1332i 1.64013 + 0.362827i
\(781\) 1.95850 0.0700805
\(782\) 1.08304 + 1.87588i 0.0387295 + 0.0670814i
\(783\) −3.05261 + 23.4337i −0.109092 + 0.837452i