Properties

Label 441.2.g.h.67.11
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 67.11
Character \(\chi\) \(=\) 441.67
Dual form 441.2.g.h.79.11

$q$-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 \(-0.615427\pi\)
−0.354728 + 0.934969i \(0.615427\pi\)
\(6\) −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 −0.556991 0.830518i \(-0.688044\pi\)
0.997746 + 0.0671096i \(0.0213777\pi\)
\(14\) 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 −0.984360 0.176167i \(-0.943630\pi\)
0.644745 + 0.764397i \(0.276963\pi\)
\(18\) 6.66807 4.67807i 1.57168 1.10263i
\(19\) −0.312846 0.541866i −0.0717719 0.124313i 0.827906 0.560867i \(-0.189532\pi\)
−0.899678 + 0.436554i \(0.856199\pi\)
\(20\) 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 \(-0.934143\pi\)
0.311435 0.950267i \(-0.399190\pi\)
\(32\) 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 \(-0.547050\pi\)
0.930219 0.367004i \(-0.119616\pi\)
\(42\) 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 \(0.468848\pi\)
−0.910737 + 0.412988i \(0.864485\pi\)
\(48\) 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 0.677842 0.735207i \(-0.262915\pi\)
−0.975629 + 0.219425i \(0.929582\pi\)
\(60\) −4.44498 14.0754i −0.573845 1.81712i
\(61\) 0.192507 0.333432i 0.0246480 0.0426916i −0.853438 0.521194i \(-0.825487\pi\)
0.878086 + 0.478502i \(0.158820\pi\)
\(62\) −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 −0.852003 0.523538i \(-0.824612\pi\)
0.879398 + 0.476087i \(0.157945\pi\)
\(74\) −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 \(-0.888106\pi\)
0.171225 0.985232i \(-0.445228\pi\)
\(84\) 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 0.926403 0.376534i \(-0.122884\pi\)
−0.789289 + 0.614022i \(0.789551\pi\)
\(90\) −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 \(0.0957089\pi\)
−0.221079 + 0.975256i \(0.570958\pi\)
\(98\) 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 \(-0.337199\pi\)
0.489447 + 0.872033i \(0.337199\pi\)
\(102\) −3.96607 12.5589i −0.392699 1.24351i
\(103\) 11.0579 1.08957 0.544786 0.838575i \(-0.316611\pi\)
0.544786 + 0.838575i \(0.316611\pi\)
\(104\) −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 \(-0.675196\pi\)
−0.523024 + 0.852318i \(0.675196\pi\)
\(132\) −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 −0.648375 0.761321i \(-0.724551\pi\)
0.983511 + 0.180849i \(0.0578845\pi\)
\(140\) 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 0.871839 0.489793i \(-0.162928\pi\)
−0.860093 + 0.510138i \(0.829594\pi\)
\(158\) −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 −0.797516 0.603298i \(-0.793853\pi\)
0.921229 + 0.389020i \(0.127186\pi\)
\(168\) 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 −0.562490 0.826804i \(-0.690156\pi\)
0.997278 + 0.0737284i \(0.0234898\pi\)
\(174\) −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 \(-0.462172\pi\)
0.118560 + 0.992947i \(0.462172\pi\)
\(182\) 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 −0.956062 0.293164i \(-0.905292\pi\)
0.731919 + 0.681392i \(0.238625\pi\)
\(200\) 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 \(0.0224538\pi\)
−0.437717 + 0.899113i \(0.644213\pi\)
\(224\) 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 \(-0.308302\pi\)
0.566489 + 0.824070i \(0.308302\pi\)
\(228\) 3.93117 4.29403i 0.260348 0.284379i
\(229\) 19.7894 1.30772 0.653861 0.756615i \(-0.273148\pi\)
0.653861 + 0.756615i \(0.273148\pi\)
\(230\) 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 \(-0.107679\pi\)
0.943326 + 0.331869i \(0.107679\pi\)
\(242\) −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 \(-0.755448\pi\)
−0.719106 + 0.694901i \(0.755448\pi\)
\(252\) 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 \(-0.773604\pi\)
−0.757550 + 0.652778i \(0.773604\pi\)
\(258\) 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 −0.534839 0.844954i \(-0.679628\pi\)
0.999171 + 0.0407073i \(0.0129611\pi\)
\(270\) 20.6659 8.59310i 1.25768 0.522959i
\(271\) 2.33910 + 4.05144i 0.142090 + 0.246108i 0.928284 0.371873i \(-0.121284\pi\)
−0.786193 + 0.617981i \(0.787951\pi\)
\(272\) −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 \(-0.884480\pi\)
0.159992 0.987118i \(-0.448853\pi\)
\(284\) 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 \(0.352650\pi\)
−0.998159 + 0.0606487i \(0.980683\pi\)
\(294\) 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 \(-0.711875\pi\)
−0.617551 + 0.786531i \(0.711875\pi\)
\(308\) 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 0.795251 0.606281i \(-0.207339\pi\)
−0.922680 + 0.385567i \(0.874006\pi\)
\(312\) 34.0329 37.1742i 1.92673 2.10458i
\(313\) −4.30102 + 7.44958i −0.243108 + 0.421075i −0.961598 0.274462i \(-0.911500\pi\)
0.718490 + 0.695537i \(0.244834\pi\)
\(314\) 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 0.813444 0.581643i \(-0.197590\pi\)
−0.910440 + 0.413642i \(0.864256\pi\)
\(350\) 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 \(-0.523350\pi\)
−0.0732907 + 0.997311i \(0.523350\pi\)
\(354\) 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 \(-0.714767\pi\)
−0.624670 + 0.780889i \(0.714767\pi\)
\(368\) 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 \(-0.672075\pi\)
−0.514643 + 0.857405i \(0.672075\pi\)
\(384\) −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 0.998512 0.0545313i \(-0.0173665\pi\)
−0.546482 + 0.837471i \(0.684033\pi\)
\(398\) 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 0.968466 0.249147i \(-0.0801502\pi\)
−0.700000 + 0.714142i \(0.746817\pi\)
\(410\) 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 −0.872009 0.489489i \(-0.837183\pi\)
0.859915 + 0.510438i \(0.170517\pi\)
\(420\) 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 \(-0.797476\pi\)
−0.804330 + 0.594183i \(0.797476\pi\)
\(434\) 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 −1.00000 0.000574559i \(-0.999817\pi\)
0.500498 + 0.865738i \(0.333150\pi\)
\(440\) −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 0.993397 0.114731i \(-0.0366005\pi\)
−0.596058 + 0.802941i \(0.703267\pi\)
\(462\) 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 0.945094 0.326799i \(-0.105970\pi\)
−0.755563 + 0.655076i \(0.772637\pi\)
\(468\) −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 \(-0.698441\pi\)
−0.583817 + 0.811885i \(0.698441\pi\)
\(480\) 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 \(-0.541252\pi\)
−0.129236 + 0.991614i \(0.541252\pi\)
\(504\) 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 \(-0.311897\pi\)
0.557144 + 0.830416i \(0.311897\pi\)
\(510\) 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 −0.934809 0.355152i \(-0.884429\pi\)
0.774975 + 0.631992i \(0.217763\pi\)
\(522\) 33.5880 + 15.6252i 1.47011 + 0.683897i
\(523\) −8.38637 14.5256i −0.366710 0.635161i 0.622339 0.782748i \(-0.286183\pi\)
−0.989049 + 0.147587i \(0.952849\pi\)
\(524\) 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 \(-0.968557\pi\)
0.412155 0.911114i \(-0.364776\pi\)
\(564\) −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 \(-0.559443\pi\)
0.943799 0.330519i \(-0.107224\pi\)
\(578\) 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 0.957893 0.287126i \(-0.0927000\pi\)
−0.727605 + 0.685996i \(0.759367\pi\)
\(588\) 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 0.587800 0.809006i \(-0.299994\pi\)
−0.994520 + 0.104547i \(0.966661\pi\)
\(594\) 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 \(-0.998937\pi\)
0.497105 0.867690i \(-0.334396\pi\)
\(602\) 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 \(-0.385965\pi\)
0.350637 + 0.936512i \(0.385965\pi\)
\(608\) 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 \(-0.262255\pi\)
0.679366 + 0.733800i \(0.262255\pi\)
\(620\) 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 \(0.341718\pi\)
−0.999653 + 0.0263376i \(0.991616\pi\)
\(644\) 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 −0.866183 0.499727i \(-0.833434\pi\)
0.865868 + 0.500273i \(0.166767\pi\)
\(648\) −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 0.809802 0.586703i \(-0.199574\pi\)
−0.913001 + 0.407958i \(0.866241\pi\)
\(662\) −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 \(-0.600292\pi\)
0.978338 0.207014i \(-0.0663747\pi\)
\(678\) 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 −0.795979 0.605324i \(-0.793043\pi\)
0.922216 + 0.386676i \(0.126377\pi\)
\(692\) −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 \(0.142649\pi\)
−0.0753825 + 0.997155i \(0.524018\pi\)
\(720\) 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 \(0.00884060\pi\)
−0.475758 + 0.879576i \(0.657826\pi\)
\(728\) 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 \(-0.652872\pi\)
−0.462010 + 0.886875i \(0.652872\pi\)
\(734\) −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 \(-0.577620\pi\)
−0.241442 + 0.970415i \(0.577620\pi\)
\(762\) 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 \(-0.385676\pi\)
0.635022 0.772494i \(-0.280991\pi\)
\(770\) 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 −0.886469 0.462787i \(-0.846849\pi\)
0.844020 + 0.536311i \(0.180183\pi\)
\(774\) −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