Properties

Label 441.2.h.h.373.3
Level $441$
Weight $2$
Character 441.373
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.h (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 373.3
Character \(\chi\) \(=\) 441.373
Dual form 441.2.h.h.214.3

$q$-expansion

\(f(q)\) \(=\) \(q-1.72661 q^{2} +(-1.70981 - 0.276691i) q^{3} +0.981184 q^{4} +(-1.75616 - 3.04175i) q^{5} +(2.95217 + 0.477737i) q^{6} +1.75910 q^{8} +(2.84688 + 0.946176i) q^{9} +O(q^{10})\) \(q-1.72661 q^{2} +(-1.70981 - 0.276691i) q^{3} +0.981184 q^{4} +(-1.75616 - 3.04175i) q^{5} +(2.95217 + 0.477737i) q^{6} +1.75910 q^{8} +(2.84688 + 0.946176i) q^{9} +(3.03220 + 5.25192i) q^{10} +(3.04532 - 5.27465i) q^{11} +(-1.67764 - 0.271484i) q^{12} +(0.560139 - 0.970190i) q^{13} +(2.16106 + 5.68672i) q^{15} -4.99965 q^{16} +(-0.601978 - 1.04266i) q^{17} +(-4.91546 - 1.63368i) q^{18} +(1.10269 - 1.90991i) q^{19} +(-1.72311 - 2.98452i) q^{20} +(-5.25808 + 9.10727i) q^{22} +(0.636695 + 1.10279i) q^{23} +(-3.00772 - 0.486726i) q^{24} +(-3.66817 + 6.35345i) q^{25} +(-0.967143 + 1.67514i) q^{26} +(-4.60583 - 2.40548i) q^{27} +(-3.10262 - 5.37390i) q^{29} +(-3.73132 - 9.81875i) q^{30} -0.188404 q^{31} +5.11425 q^{32} +(-6.66636 + 8.17602i) q^{33} +(1.03938 + 1.80026i) q^{34} +(2.79332 + 0.928373i) q^{36} +(-1.78835 + 3.09752i) q^{37} +(-1.90391 + 3.29767i) q^{38} +(-1.22617 + 1.50385i) q^{39} +(-3.08925 - 5.35074i) q^{40} +(1.68320 - 2.91538i) q^{41} +(-1.90276 - 3.29567i) q^{43} +(2.98802 - 5.17540i) q^{44} +(-2.12154 - 10.3211i) q^{45} +(-1.09932 - 1.90408i) q^{46} -5.72070 q^{47} +(8.54843 + 1.38336i) q^{48} +(6.33349 - 10.9699i) q^{50} +(0.740773 + 1.94930i) q^{51} +(0.549600 - 0.951935i) q^{52} +(4.16913 + 7.22115i) q^{53} +(7.95247 + 4.15334i) q^{54} -21.3922 q^{55} +(-2.41384 + 2.96047i) q^{57} +(5.35702 + 9.27862i) q^{58} -11.2685 q^{59} +(2.12040 + 5.57972i) q^{60} +12.0022 q^{61} +0.325300 q^{62} +1.16898 q^{64} -3.93477 q^{65} +(11.5102 - 14.1168i) q^{66} -7.91303 q^{67} +(-0.590651 - 1.02304i) q^{68} +(-0.783494 - 2.06172i) q^{69} -12.2052 q^{71} +(5.00795 + 1.66442i) q^{72} +(2.65737 + 4.60269i) q^{73} +(3.08779 - 5.34820i) q^{74} +(8.02980 - 9.84823i) q^{75} +(1.08194 - 1.87397i) q^{76} +(2.11712 - 2.59657i) q^{78} +9.21711 q^{79} +(8.78016 + 15.2077i) q^{80} +(7.20950 + 5.38731i) q^{81} +(-2.90623 + 5.03373i) q^{82} +(0.624950 + 1.08245i) q^{83} +(-2.11433 + 3.66213i) q^{85} +(3.28532 + 5.69034i) q^{86} +(3.81798 + 10.0468i) q^{87} +(5.35702 - 9.27862i) q^{88} +(-2.77066 + 4.79892i) q^{89} +(3.66308 + 17.8206i) q^{90} +(0.624715 + 1.08204i) q^{92} +(0.322134 + 0.0521295i) q^{93} +9.87741 q^{94} -7.74596 q^{95} +(-8.74438 - 1.41506i) q^{96} +(8.24277 + 14.2769i) q^{97} +(13.6604 - 12.1349i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 8q^{2} + 24q^{4} - 24q^{8} - 4q^{9} + O(q^{10}) \) \( 24q - 8q^{2} + 24q^{4} - 24q^{8} - 4q^{9} + 20q^{11} + 4q^{15} + 24q^{16} - 32q^{18} + 32q^{23} - 12q^{25} + 16q^{29} - 84q^{30} - 96q^{32} - 4q^{36} - 12q^{37} + 8q^{39} + 56q^{44} + 24q^{46} - 4q^{50} + 64q^{51} + 32q^{53} - 12q^{57} + 32q^{60} + 96q^{64} - 120q^{65} + 24q^{67} - 112q^{71} + 68q^{74} - 60q^{78} - 24q^{79} - 40q^{81} + 12q^{85} + 76q^{86} + 16q^{92} - 32q^{93} - 128q^{95} + 20q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.72661 −1.22090 −0.610449 0.792056i \(-0.709011\pi\)
−0.610449 + 0.792056i \(0.709011\pi\)
\(3\) −1.70981 0.276691i −0.987158 0.159747i
\(4\) 0.981184 0.490592
\(5\) −1.75616 3.04175i −0.785377 1.36031i −0.928774 0.370647i \(-0.879136\pi\)
0.143397 0.989665i \(-0.454197\pi\)
\(6\) 2.95217 + 0.477737i 1.20522 + 0.195035i
\(7\) 0 0
\(8\) 1.75910 0.621935
\(9\) 2.84688 + 0.946176i 0.948962 + 0.315392i
\(10\) 3.03220 + 5.25192i 0.958865 + 1.66080i
\(11\) 3.04532 5.27465i 0.918199 1.59037i 0.116049 0.993244i \(-0.462977\pi\)
0.802150 0.597123i \(-0.203690\pi\)
\(12\) −1.67764 0.271484i −0.484292 0.0783708i
\(13\) 0.560139 0.970190i 0.155355 0.269082i −0.777833 0.628471i \(-0.783681\pi\)
0.933188 + 0.359388i \(0.117015\pi\)
\(14\) 0 0
\(15\) 2.16106 + 5.68672i 0.557984 + 1.46831i
\(16\) −4.99965 −1.24991
\(17\) −0.601978 1.04266i −0.146001 0.252881i 0.783745 0.621083i \(-0.213307\pi\)
−0.929746 + 0.368202i \(0.879974\pi\)
\(18\) −4.91546 1.63368i −1.15859 0.385061i
\(19\) 1.10269 1.90991i 0.252974 0.438163i −0.711370 0.702818i \(-0.751925\pi\)
0.964343 + 0.264655i \(0.0852581\pi\)
\(20\) −1.72311 2.98452i −0.385300 0.667359i
\(21\) 0 0
\(22\) −5.25808 + 9.10727i −1.12103 + 1.94168i
\(23\) 0.636695 + 1.10279i 0.132760 + 0.229947i 0.924740 0.380601i \(-0.124283\pi\)
−0.791980 + 0.610548i \(0.790949\pi\)
\(24\) −3.00772 0.486726i −0.613948 0.0993525i
\(25\) −3.66817 + 6.35345i −0.733633 + 1.27069i
\(26\) −0.967143 + 1.67514i −0.189672 + 0.328522i
\(27\) −4.60583 2.40548i −0.886392 0.462936i
\(28\) 0 0
\(29\) −3.10262 5.37390i −0.576142 0.997907i −0.995917 0.0902789i \(-0.971224\pi\)
0.419774 0.907628i \(-0.362109\pi\)
\(30\) −3.73132 9.81875i −0.681242 1.79265i
\(31\) −0.188404 −0.0338383 −0.0169192 0.999857i \(-0.505386\pi\)
−0.0169192 + 0.999857i \(0.505386\pi\)
\(32\) 5.11425 0.904079
\(33\) −6.66636 + 8.17602i −1.16046 + 1.42326i
\(34\) 1.03938 + 1.80026i 0.178252 + 0.308742i
\(35\) 0 0
\(36\) 2.79332 + 0.928373i 0.465553 + 0.154729i
\(37\) −1.78835 + 3.09752i −0.294003 + 0.509228i −0.974753 0.223288i \(-0.928321\pi\)
0.680749 + 0.732516i \(0.261654\pi\)
\(38\) −1.90391 + 3.29767i −0.308855 + 0.534953i
\(39\) −1.22617 + 1.50385i −0.196345 + 0.240809i
\(40\) −3.08925 5.35074i −0.488453 0.846026i
\(41\) 1.68320 2.91538i 0.262871 0.455307i −0.704132 0.710069i \(-0.748664\pi\)
0.967004 + 0.254762i \(0.0819972\pi\)
\(42\) 0 0
\(43\) −1.90276 3.29567i −0.290168 0.502585i 0.683681 0.729781i \(-0.260378\pi\)
−0.973849 + 0.227195i \(0.927044\pi\)
\(44\) 2.98802 5.17540i 0.450461 0.780221i
\(45\) −2.12154 10.3211i −0.316261 1.53859i
\(46\) −1.09932 1.90408i −0.162086 0.280742i
\(47\) −5.72070 −0.834449 −0.417225 0.908803i \(-0.636997\pi\)
−0.417225 + 0.908803i \(0.636997\pi\)
\(48\) 8.54843 + 1.38336i 1.23386 + 0.199670i
\(49\) 0 0
\(50\) 6.33349 10.9699i 0.895691 1.55138i
\(51\) 0.740773 + 1.94930i 0.103729 + 0.272957i
\(52\) 0.549600 0.951935i 0.0762158 0.132010i
\(53\) 4.16913 + 7.22115i 0.572675 + 0.991901i 0.996290 + 0.0860593i \(0.0274275\pi\)
−0.423615 + 0.905842i \(0.639239\pi\)
\(54\) 7.95247 + 4.15334i 1.08219 + 0.565197i
\(55\) −21.3922 −2.88453
\(56\) 0 0
\(57\) −2.41384 + 2.96047i −0.319720 + 0.392124i
\(58\) 5.35702 + 9.27862i 0.703411 + 1.21834i
\(59\) −11.2685 −1.46704 −0.733519 0.679669i \(-0.762123\pi\)
−0.733519 + 0.679669i \(0.762123\pi\)
\(60\) 2.12040 + 5.57972i 0.273743 + 0.720339i
\(61\) 12.0022 1.53672 0.768361 0.640017i \(-0.221073\pi\)
0.768361 + 0.640017i \(0.221073\pi\)
\(62\) 0.325300 0.0413131
\(63\) 0 0
\(64\) 1.16898 0.146123
\(65\) −3.93477 −0.488048
\(66\) 11.5102 14.1168i 1.41681 1.73766i
\(67\) −7.91303 −0.966731 −0.483366 0.875419i \(-0.660586\pi\)
−0.483366 + 0.875419i \(0.660586\pi\)
\(68\) −0.590651 1.02304i −0.0716270 0.124062i
\(69\) −0.783494 2.06172i −0.0943217 0.248202i
\(70\) 0 0
\(71\) −12.2052 −1.44850 −0.724248 0.689540i \(-0.757813\pi\)
−0.724248 + 0.689540i \(0.757813\pi\)
\(72\) 5.00795 + 1.66442i 0.590192 + 0.196153i
\(73\) 2.65737 + 4.60269i 0.311021 + 0.538704i 0.978584 0.205849i \(-0.0659957\pi\)
−0.667563 + 0.744554i \(0.732662\pi\)
\(74\) 3.08779 5.34820i 0.358948 0.621716i
\(75\) 8.02980 9.84823i 0.927201 1.13718i
\(76\) 1.08194 1.87397i 0.124107 0.214959i
\(77\) 0 0
\(78\) 2.11712 2.59657i 0.239717 0.294003i
\(79\) 9.21711 1.03701 0.518503 0.855076i \(-0.326490\pi\)
0.518503 + 0.855076i \(0.326490\pi\)
\(80\) 8.78016 + 15.2077i 0.981651 + 1.70027i
\(81\) 7.20950 + 5.38731i 0.801056 + 0.598589i
\(82\) −2.90623 + 5.03373i −0.320939 + 0.555883i
\(83\) 0.624950 + 1.08245i 0.0685972 + 0.118814i 0.898284 0.439415i \(-0.144814\pi\)
−0.829687 + 0.558229i \(0.811481\pi\)
\(84\) 0 0
\(85\) −2.11433 + 3.66213i −0.229332 + 0.397214i
\(86\) 3.28532 + 5.69034i 0.354265 + 0.613605i
\(87\) 3.81798 + 10.0468i 0.409330 + 1.07713i
\(88\) 5.35702 9.27862i 0.571060 0.989105i
\(89\) −2.77066 + 4.79892i −0.293689 + 0.508684i −0.974679 0.223608i \(-0.928216\pi\)
0.680990 + 0.732293i \(0.261550\pi\)
\(90\) 3.66308 + 17.8206i 0.386122 + 1.87846i
\(91\) 0 0
\(92\) 0.624715 + 1.08204i 0.0651310 + 0.112810i
\(93\) 0.322134 + 0.0521295i 0.0334038 + 0.00540558i
\(94\) 9.87741 1.01878
\(95\) −7.74596 −0.794718
\(96\) −8.74438 1.41506i −0.892469 0.144424i
\(97\) 8.24277 + 14.2769i 0.836926 + 1.44960i 0.892452 + 0.451142i \(0.148983\pi\)
−0.0555261 + 0.998457i \(0.517684\pi\)
\(98\) 0 0
\(99\) 13.6604 12.1349i 1.37292 1.21960i
\(100\) −3.59915 + 6.23391i −0.359915 + 0.623391i
\(101\) 6.48192 11.2270i 0.644975 1.11713i −0.339332 0.940667i \(-0.610201\pi\)
0.984307 0.176463i \(-0.0564657\pi\)
\(102\) −1.27903 3.36569i −0.126643 0.333253i
\(103\) −1.35091 2.33984i −0.133109 0.230552i 0.791765 0.610826i \(-0.209163\pi\)
−0.924873 + 0.380275i \(0.875829\pi\)
\(104\) 0.985340 1.70666i 0.0966205 0.167352i
\(105\) 0 0
\(106\) −7.19847 12.4681i −0.699177 1.21101i
\(107\) 0.0892402 0.154569i 0.00862718 0.0149427i −0.861680 0.507453i \(-0.830587\pi\)
0.870307 + 0.492510i \(0.163921\pi\)
\(108\) −4.51917 2.36022i −0.434857 0.227113i
\(109\) −4.67927 8.10473i −0.448192 0.776292i 0.550076 0.835115i \(-0.314599\pi\)
−0.998268 + 0.0588226i \(0.981265\pi\)
\(110\) 36.9360 3.52171
\(111\) 3.91479 4.80134i 0.371575 0.455723i
\(112\) 0 0
\(113\) 4.21019 7.29226i 0.396061 0.685998i −0.597175 0.802111i \(-0.703710\pi\)
0.993236 + 0.116113i \(0.0370434\pi\)
\(114\) 4.16775 5.11159i 0.390346 0.478744i
\(115\) 2.23627 3.87333i 0.208533 0.361190i
\(116\) −3.04424 5.27278i −0.282651 0.489565i
\(117\) 2.51262 2.23203i 0.232292 0.206351i
\(118\) 19.4564 1.79110
\(119\) 0 0
\(120\) 3.80152 + 10.0035i 0.347030 + 0.913190i
\(121\) −13.0479 22.5997i −1.18618 2.05452i
\(122\) −20.7231 −1.87618
\(123\) −3.68460 + 4.51902i −0.332230 + 0.407467i
\(124\) −0.184859 −0.0166008
\(125\) 8.20593 0.733960
\(126\) 0 0
\(127\) −9.92438 −0.880647 −0.440323 0.897839i \(-0.645136\pi\)
−0.440323 + 0.897839i \(0.645136\pi\)
\(128\) −12.2469 −1.08248
\(129\) 2.34147 + 6.16144i 0.206155 + 0.542485i
\(130\) 6.79381 0.595857
\(131\) 7.62335 + 13.2040i 0.666055 + 1.15364i 0.978998 + 0.203870i \(0.0653519\pi\)
−0.312943 + 0.949772i \(0.601315\pi\)
\(132\) −6.54093 + 8.02219i −0.569314 + 0.698242i
\(133\) 0 0
\(134\) 13.6627 1.18028
\(135\) 0.771665 + 18.2342i 0.0664144 + 1.56935i
\(136\) −1.05894 1.83413i −0.0908032 0.157276i
\(137\) −3.07350 + 5.32346i −0.262587 + 0.454814i −0.966929 0.255047i \(-0.917909\pi\)
0.704342 + 0.709861i \(0.251242\pi\)
\(138\) 1.35279 + 3.55979i 0.115157 + 0.303030i
\(139\) 0.438687 0.759829i 0.0372090 0.0644478i −0.846821 0.531878i \(-0.821487\pi\)
0.884030 + 0.467430i \(0.154820\pi\)
\(140\) 0 0
\(141\) 9.78129 + 1.58286i 0.823733 + 0.133301i
\(142\) 21.0737 1.76847
\(143\) −3.41161 5.90908i −0.285293 0.494142i
\(144\) −14.2334 4.73054i −1.18612 0.394212i
\(145\) −10.8974 + 18.8748i −0.904977 + 1.56747i
\(146\) −4.58824 7.94706i −0.379725 0.657703i
\(147\) 0 0
\(148\) −1.75470 + 3.03923i −0.144236 + 0.249823i
\(149\) −2.88776 5.00175i −0.236575 0.409760i 0.723154 0.690686i \(-0.242692\pi\)
−0.959729 + 0.280927i \(0.909358\pi\)
\(150\) −13.8643 + 17.0041i −1.13202 + 1.38838i
\(151\) 1.01321 1.75494i 0.0824541 0.142815i −0.821849 0.569705i \(-0.807058\pi\)
0.904304 + 0.426890i \(0.140391\pi\)
\(152\) 1.93973 3.35972i 0.157333 0.272509i
\(153\) −0.727226 3.53790i −0.0587927 0.286022i
\(154\) 0 0
\(155\) 0.330866 + 0.573077i 0.0265758 + 0.0460307i
\(156\) −1.20310 + 1.47556i −0.0963252 + 0.118139i
\(157\) −3.04756 −0.243222 −0.121611 0.992578i \(-0.538806\pi\)
−0.121611 + 0.992578i \(0.538806\pi\)
\(158\) −15.9144 −1.26608
\(159\) −5.13039 13.5003i −0.406867 1.07065i
\(160\) −8.98141 15.5563i −0.710043 1.22983i
\(161\) 0 0
\(162\) −12.4480 9.30178i −0.978008 0.730817i
\(163\) 2.69445 4.66693i 0.211046 0.365542i −0.740996 0.671509i \(-0.765646\pi\)
0.952042 + 0.305967i \(0.0989797\pi\)
\(164\) 1.65153 2.86053i 0.128963 0.223370i
\(165\) 36.5766 + 5.91903i 2.84748 + 0.460796i
\(166\) −1.07905 1.86896i −0.0837502 0.145060i
\(167\) −8.30480 + 14.3843i −0.642645 + 1.11309i 0.342196 + 0.939629i \(0.388829\pi\)
−0.984840 + 0.173464i \(0.944504\pi\)
\(168\) 0 0
\(169\) 5.87249 + 10.1714i 0.451730 + 0.782419i
\(170\) 3.65063 6.32308i 0.279991 0.484958i
\(171\) 4.94633 4.39396i 0.378255 0.336014i
\(172\) −1.86696 3.23366i −0.142354 0.246564i
\(173\) −17.6503 −1.34193 −0.670965 0.741489i \(-0.734120\pi\)
−0.670965 + 0.741489i \(0.734120\pi\)
\(174\) −6.59216 17.3469i −0.499750 1.31507i
\(175\) 0 0
\(176\) −15.2255 + 26.3714i −1.14767 + 1.98782i
\(177\) 19.2670 + 3.11790i 1.44820 + 0.234355i
\(178\) 4.78384 8.28586i 0.358564 0.621051i
\(179\) −1.31422 2.27630i −0.0982294 0.170138i 0.812722 0.582651i \(-0.197985\pi\)
−0.910952 + 0.412513i \(0.864651\pi\)
\(180\) −2.08162 10.1269i −0.155155 0.754818i
\(181\) 3.97391 0.295378 0.147689 0.989034i \(-0.452816\pi\)
0.147689 + 0.989034i \(0.452816\pi\)
\(182\) 0 0
\(183\) −20.5214 3.32089i −1.51699 0.245487i
\(184\) 1.12001 + 1.93991i 0.0825681 + 0.143012i
\(185\) 12.5625 0.923613
\(186\) −0.556200 0.0900074i −0.0407826 0.00659966i
\(187\) −7.33286 −0.536232
\(188\) −5.61306 −0.409374
\(189\) 0 0
\(190\) 13.3743 0.970270
\(191\) −18.2059 −1.31733 −0.658666 0.752435i \(-0.728879\pi\)
−0.658666 + 0.752435i \(0.728879\pi\)
\(192\) −1.99873 0.323446i −0.144246 0.0233427i
\(193\) −0.202385 −0.0145680 −0.00728401 0.999973i \(-0.502319\pi\)
−0.00728401 + 0.999973i \(0.502319\pi\)
\(194\) −14.2321 24.6506i −1.02180 1.76981i
\(195\) 6.72770 + 1.08871i 0.481780 + 0.0779644i
\(196\) 0 0
\(197\) −1.63136 −0.116229 −0.0581147 0.998310i \(-0.518509\pi\)
−0.0581147 + 0.998310i \(0.518509\pi\)
\(198\) −23.5862 + 20.9523i −1.67620 + 1.48901i
\(199\) −3.14605 5.44912i −0.223018 0.386278i 0.732705 0.680546i \(-0.238257\pi\)
−0.955723 + 0.294268i \(0.904924\pi\)
\(200\) −6.45266 + 11.1763i −0.456272 + 0.790287i
\(201\) 13.5298 + 2.18946i 0.954316 + 0.154433i
\(202\) −11.1918 + 19.3847i −0.787449 + 1.36390i
\(203\) 0 0
\(204\) 0.726835 + 1.91263i 0.0508886 + 0.133911i
\(205\) −11.8238 −0.825812
\(206\) 2.33249 + 4.04000i 0.162512 + 0.281480i
\(207\) 0.769166 + 3.74193i 0.0534607 + 0.260082i
\(208\) −2.80050 + 4.85061i −0.194180 + 0.336329i
\(209\) −6.71607 11.6326i −0.464560 0.804642i
\(210\) 0 0
\(211\) 8.14368 14.1053i 0.560634 0.971046i −0.436807 0.899555i \(-0.643891\pi\)
0.997441 0.0714912i \(-0.0227758\pi\)
\(212\) 4.09069 + 7.08528i 0.280950 + 0.486619i
\(213\) 20.8686 + 3.37708i 1.42989 + 0.231393i
\(214\) −0.154083 + 0.266880i −0.0105329 + 0.0182435i
\(215\) −6.68308 + 11.5754i −0.455782 + 0.789438i
\(216\) −8.10210 4.23148i −0.551278 0.287916i
\(217\) 0 0
\(218\) 8.07927 + 13.9937i 0.547197 + 0.947773i
\(219\) −3.27006 8.60499i −0.220970 0.581471i
\(220\) −20.9897 −1.41513
\(221\) −1.34877 −0.0907278
\(222\) −6.75932 + 8.29004i −0.453656 + 0.556391i
\(223\) −9.98472 17.2940i −0.668626 1.15809i −0.978288 0.207248i \(-0.933549\pi\)
0.309662 0.950847i \(-0.399784\pi\)
\(224\) 0 0
\(225\) −16.4543 + 14.6168i −1.09695 + 0.974454i
\(226\) −7.26936 + 12.5909i −0.483551 + 0.837534i
\(227\) −1.80642 + 3.12880i −0.119896 + 0.207666i −0.919726 0.392560i \(-0.871589\pi\)
0.799830 + 0.600226i \(0.204923\pi\)
\(228\) −2.36842 + 2.90477i −0.156852 + 0.192373i
\(229\) −6.85733 11.8772i −0.453145 0.784870i 0.545435 0.838153i \(-0.316365\pi\)
−0.998579 + 0.0532835i \(0.983031\pi\)
\(230\) −3.86117 + 6.68774i −0.254598 + 0.440976i
\(231\) 0 0
\(232\) −5.45781 9.45321i −0.358323 0.620634i
\(233\) 12.6271 21.8707i 0.827227 1.43280i −0.0729776 0.997334i \(-0.523250\pi\)
0.900205 0.435466i \(-0.143417\pi\)
\(234\) −4.33832 + 3.85384i −0.283605 + 0.251934i
\(235\) 10.0464 + 17.4009i 0.655357 + 1.13511i
\(236\) −11.0565 −0.719717
\(237\) −15.7595 2.55029i −1.02369 0.165659i
\(238\) 0 0
\(239\) −4.49495 + 7.78549i −0.290754 + 0.503601i −0.973988 0.226598i \(-0.927240\pi\)
0.683234 + 0.730200i \(0.260573\pi\)
\(240\) −10.8046 28.4316i −0.697431 1.83525i
\(241\) −4.62862 + 8.01701i −0.298156 + 0.516421i −0.975714 0.219048i \(-0.929705\pi\)
0.677558 + 0.735469i \(0.263038\pi\)
\(242\) 22.5287 + 39.0209i 1.44820 + 2.50836i
\(243\) −10.8362 11.2061i −0.695146 0.718869i
\(244\) 11.7763 0.753903
\(245\) 0 0
\(246\) 6.36188 7.80259i 0.405619 0.497475i
\(247\) −1.23532 2.13963i −0.0786013 0.136141i
\(248\) −0.331421 −0.0210452
\(249\) −0.769042 2.02369i −0.0487361 0.128246i
\(250\) −14.1684 −0.896091
\(251\) 20.6517 1.30353 0.651763 0.758422i \(-0.274030\pi\)
0.651763 + 0.758422i \(0.274030\pi\)
\(252\) 0 0
\(253\) 7.75576 0.487600
\(254\) 17.1355 1.07518
\(255\) 4.62838 5.67653i 0.289841 0.355478i
\(256\) 18.8076 1.17548
\(257\) 1.22289 + 2.11811i 0.0762819 + 0.132124i 0.901643 0.432481i \(-0.142362\pi\)
−0.825361 + 0.564605i \(0.809028\pi\)
\(258\) −4.04280 10.6384i −0.251694 0.662318i
\(259\) 0 0
\(260\) −3.86073 −0.239432
\(261\) −3.74815 18.2345i −0.232005 1.12869i
\(262\) −13.1626 22.7982i −0.813186 1.40848i
\(263\) 12.2814 21.2720i 0.757302 1.31169i −0.186919 0.982375i \(-0.559850\pi\)
0.944222 0.329311i \(-0.106816\pi\)
\(264\) −11.7268 + 14.3824i −0.721733 + 0.885177i
\(265\) 14.6433 25.3629i 0.899531 1.55803i
\(266\) 0 0
\(267\) 6.06510 7.43861i 0.371178 0.455236i
\(268\) −7.76415 −0.474271
\(269\) 14.7851 + 25.6086i 0.901466 + 1.56139i 0.825592 + 0.564268i \(0.190842\pi\)
0.0758746 + 0.997117i \(0.475825\pi\)
\(270\) −1.33237 31.4833i −0.0810852 1.91601i
\(271\) 12.3958 21.4701i 0.752989 1.30421i −0.193380 0.981124i \(-0.561945\pi\)
0.946368 0.323090i \(-0.104722\pi\)
\(272\) 3.00968 + 5.21291i 0.182488 + 0.316079i
\(273\) 0 0
\(274\) 5.30674 9.19154i 0.320592 0.555281i
\(275\) 22.3415 + 38.6966i 1.34724 + 2.33349i
\(276\) −0.768752 2.02293i −0.0462735 0.121766i
\(277\) −0.939249 + 1.62683i −0.0564340 + 0.0977466i −0.892862 0.450330i \(-0.851306\pi\)
0.836428 + 0.548076i \(0.184640\pi\)
\(278\) −0.757442 + 1.31193i −0.0454284 + 0.0786842i
\(279\) −0.536364 0.178263i −0.0321113 0.0106723i
\(280\) 0 0
\(281\) 6.03965 + 10.4610i 0.360295 + 0.624049i 0.988009 0.154395i \(-0.0493427\pi\)
−0.627714 + 0.778444i \(0.716009\pi\)
\(282\) −16.8885 2.73299i −1.00569 0.162747i
\(283\) −27.9719 −1.66276 −0.831378 0.555708i \(-0.812447\pi\)
−0.831378 + 0.555708i \(0.812447\pi\)
\(284\) −11.9756 −0.710620
\(285\) 13.2441 + 2.14323i 0.784513 + 0.126954i
\(286\) 5.89052 + 10.2027i 0.348314 + 0.603297i
\(287\) 0 0
\(288\) 14.5597 + 4.83897i 0.857937 + 0.285139i
\(289\) 7.77524 13.4671i 0.457367 0.792183i
\(290\) 18.8155 32.5894i 1.10488 1.91372i
\(291\) −10.1433 26.6914i −0.594609 1.56468i
\(292\) 2.60736 + 4.51609i 0.152584 + 0.264284i
\(293\) −4.41163 + 7.64117i −0.257730 + 0.446402i −0.965634 0.259908i \(-0.916308\pi\)
0.707903 + 0.706309i \(0.249641\pi\)
\(294\) 0 0
\(295\) 19.7893 + 34.2761i 1.15218 + 1.99563i
\(296\) −3.14589 + 5.44883i −0.182851 + 0.316707i
\(297\) −26.7143 + 16.9687i −1.55012 + 0.984621i
\(298\) 4.98604 + 8.63608i 0.288834 + 0.500275i
\(299\) 1.42655 0.0824996
\(300\) 7.87871 9.66293i 0.454878 0.557889i
\(301\) 0 0
\(302\) −1.74942 + 3.03009i −0.100668 + 0.174362i
\(303\) −14.1893 + 17.4026i −0.815151 + 0.999751i
\(304\) −5.51304 + 9.54887i −0.316195 + 0.547665i
\(305\) −21.0777 36.5076i −1.20691 2.09042i
\(306\) 1.25564 + 6.10857i 0.0717799 + 0.349204i
\(307\) 1.05532 0.0602304 0.0301152 0.999546i \(-0.490413\pi\)
0.0301152 + 0.999546i \(0.490413\pi\)
\(308\) 0 0
\(309\) 1.66238 + 4.37446i 0.0945696 + 0.248855i
\(310\) −0.571277 0.989481i −0.0324464 0.0561988i
\(311\) 3.07215 0.174206 0.0871029 0.996199i \(-0.472239\pi\)
0.0871029 + 0.996199i \(0.472239\pi\)
\(312\) −2.15696 + 2.64542i −0.122114 + 0.149768i
\(313\) 28.1621 1.59181 0.795907 0.605419i \(-0.206994\pi\)
0.795907 + 0.605419i \(0.206994\pi\)
\(314\) 5.26196 0.296949
\(315\) 0 0
\(316\) 9.04368 0.508747
\(317\) 12.8465 0.721530 0.360765 0.932657i \(-0.382516\pi\)
0.360765 + 0.932657i \(0.382516\pi\)
\(318\) 8.85819 + 23.3098i 0.496743 + 1.30715i
\(319\) −37.7939 −2.11605
\(320\) −2.05291 3.55575i −0.114761 0.198772i
\(321\) −0.195351 + 0.239591i −0.0109034 + 0.0133726i
\(322\) 0 0
\(323\) −2.65517 −0.147738
\(324\) 7.07385 + 5.28594i 0.392992 + 0.293663i
\(325\) 4.10937 + 7.11763i 0.227947 + 0.394815i
\(326\) −4.65227 + 8.05797i −0.257665 + 0.446290i
\(327\) 5.75814 + 15.1522i 0.318426 + 0.837920i
\(328\) 2.96091 5.12845i 0.163489 0.283171i
\(329\) 0 0
\(330\) −63.1535 10.2199i −3.47649 0.562585i
\(331\) −21.5560 −1.18483 −0.592413 0.805634i \(-0.701825\pi\)
−0.592413 + 0.805634i \(0.701825\pi\)
\(332\) 0.613191 + 1.06208i 0.0336532 + 0.0582891i
\(333\) −8.02202 + 7.12617i −0.439604 + 0.390512i
\(334\) 14.3392 24.8361i 0.784604 1.35897i
\(335\) 13.8965 + 24.0695i 0.759248 + 1.31506i
\(336\) 0 0
\(337\) 6.30340 10.9178i 0.343368 0.594731i −0.641688 0.766966i \(-0.721766\pi\)
0.985056 + 0.172235i \(0.0550989\pi\)
\(338\) −10.1395 17.5621i −0.551516 0.955254i
\(339\) −9.21632 + 11.3034i −0.500562 + 0.613919i
\(340\) −2.07455 + 3.59323i −0.112508 + 0.194870i
\(341\) −0.573750 + 0.993764i −0.0310703 + 0.0538153i
\(342\) −8.54039 + 7.58665i −0.461811 + 0.410239i
\(343\) 0 0
\(344\) −3.34714 5.79741i −0.180466 0.312575i
\(345\) −4.89531 + 6.00390i −0.263554 + 0.323239i
\(346\) 30.4752 1.63836
\(347\) 23.1366 1.24204 0.621020 0.783795i \(-0.286719\pi\)
0.621020 + 0.783795i \(0.286719\pi\)
\(348\) 3.74614 + 9.85776i 0.200814 + 0.528431i
\(349\) 8.24346 + 14.2781i 0.441262 + 0.764289i 0.997783 0.0665448i \(-0.0211975\pi\)
−0.556521 + 0.830833i \(0.687864\pi\)
\(350\) 0 0
\(351\) −4.91368 + 3.12112i −0.262273 + 0.166593i
\(352\) 15.5745 26.9759i 0.830124 1.43782i
\(353\) 12.2438 21.2068i 0.651669 1.12872i −0.331049 0.943614i \(-0.607402\pi\)
0.982718 0.185110i \(-0.0592642\pi\)
\(354\) −33.2666 5.38339i −1.76810 0.286124i
\(355\) 21.4343 + 37.1253i 1.13761 + 1.97041i
\(356\) −2.71852 + 4.70862i −0.144081 + 0.249556i
\(357\) 0 0
\(358\) 2.26915 + 3.93028i 0.119928 + 0.207722i
\(359\) −10.2389 + 17.7342i −0.540386 + 0.935977i 0.458495 + 0.888697i \(0.348389\pi\)
−0.998882 + 0.0472797i \(0.984945\pi\)
\(360\) −3.73200 18.1559i −0.196694 0.956900i
\(361\) 7.06816 + 12.2424i 0.372009 + 0.644338i
\(362\) −6.86139 −0.360627
\(363\) 16.0564 + 42.2514i 0.842740 + 2.21762i
\(364\) 0 0
\(365\) 9.33349 16.1661i 0.488537 0.846172i
\(366\) 35.4325 + 5.73388i 1.85209 + 0.299715i
\(367\) −11.1269 + 19.2724i −0.580821 + 1.00601i 0.414561 + 0.910021i \(0.363935\pi\)
−0.995382 + 0.0959900i \(0.969398\pi\)
\(368\) −3.18325 5.51355i −0.165938 0.287414i
\(369\) 7.55034 6.70716i 0.393055 0.349161i
\(370\) −21.6905 −1.12764
\(371\) 0 0
\(372\) 0.316073 + 0.0511487i 0.0163876 + 0.00265194i
\(373\) 16.2684 + 28.1777i 0.842347 + 1.45899i 0.887905 + 0.460027i \(0.152160\pi\)
−0.0455576 + 0.998962i \(0.514506\pi\)
\(374\) 12.6610 0.654685
\(375\) −14.0306 2.27050i −0.724535 0.117248i
\(376\) −10.0633 −0.518973
\(377\) −6.95160 −0.358026
\(378\) 0 0
\(379\) 1.54440 0.0793306 0.0396653 0.999213i \(-0.487371\pi\)
0.0396653 + 0.999213i \(0.487371\pi\)
\(380\) −7.60021 −0.389883
\(381\) 16.9688 + 2.74598i 0.869337 + 0.140681i
\(382\) 31.4345 1.60833
\(383\) −15.8147 27.3919i −0.808093 1.39966i −0.914183 0.405302i \(-0.867166\pi\)
0.106090 0.994357i \(-0.466167\pi\)
\(384\) 20.9398 + 3.38859i 1.06858 + 0.172923i
\(385\) 0 0
\(386\) 0.349441 0.0177861
\(387\) −2.29865 11.1827i −0.116847 0.568451i
\(388\) 8.08767 + 14.0083i 0.410589 + 0.711162i
\(389\) 2.62313 4.54340i 0.132998 0.230359i −0.791833 0.610738i \(-0.790873\pi\)
0.924831 + 0.380378i \(0.124206\pi\)
\(390\) −11.6161 1.87978i −0.588205 0.0951866i
\(391\) 0.766552 1.32771i 0.0387662 0.0671451i
\(392\) 0 0
\(393\) −9.38103 24.6857i −0.473210 1.24523i
\(394\) 2.81672 0.141904
\(395\) −16.1867 28.0362i −0.814440 1.41065i
\(396\) 13.4034 11.9066i 0.673546 0.598328i
\(397\) −0.0138175 + 0.0239325i −0.000693478 + 0.00120114i −0.866372 0.499399i \(-0.833554\pi\)
0.865678 + 0.500600i \(0.166887\pi\)
\(398\) 5.43201 + 9.40851i 0.272282 + 0.471606i
\(399\) 0 0
\(400\) 18.3395 31.7650i 0.916977 1.58825i
\(401\) −6.06885 10.5115i −0.303064 0.524922i 0.673765 0.738946i \(-0.264676\pi\)
−0.976828 + 0.214024i \(0.931343\pi\)
\(402\) −23.3606 3.78035i −1.16512 0.188547i
\(403\) −0.105532 + 0.182787i −0.00525694 + 0.00910529i
\(404\) 6.35996 11.0158i 0.316420 0.548055i
\(405\) 3.72583 31.3905i 0.185138 1.55980i
\(406\) 0 0
\(407\) 10.8922 + 18.8659i 0.539907 + 0.935146i
\(408\) 1.30309 + 3.42902i 0.0645127 + 0.169762i
\(409\) 31.3453 1.54993 0.774963 0.632007i \(-0.217769\pi\)
0.774963 + 0.632007i \(0.217769\pi\)
\(410\) 20.4152 1.00823
\(411\) 6.72805 8.25168i 0.331870 0.407025i
\(412\) −1.32549 2.29582i −0.0653022 0.113107i
\(413\) 0 0
\(414\) −1.32805 6.46086i −0.0652701 0.317534i
\(415\) 2.19502 3.80189i 0.107749 0.186627i
\(416\) 2.86469 4.96179i 0.140453 0.243272i
\(417\) −0.960308 + 1.17778i −0.0470265 + 0.0576762i
\(418\) 11.5960 + 20.0849i 0.567181 + 0.982385i
\(419\) 7.44319 12.8920i 0.363623 0.629814i −0.624931 0.780680i \(-0.714873\pi\)
0.988554 + 0.150866i \(0.0482061\pi\)
\(420\) 0 0
\(421\) −4.54213 7.86721i −0.221370 0.383424i 0.733854 0.679307i \(-0.237720\pi\)
−0.955224 + 0.295883i \(0.904386\pi\)
\(422\) −14.0610 + 24.3543i −0.684477 + 1.18555i
\(423\) −16.2862 5.41278i −0.791860 0.263179i
\(424\) 7.33392 + 12.7027i 0.356166 + 0.616898i
\(425\) 8.83262 0.428445
\(426\) −36.0320 5.83089i −1.74575 0.282508i
\(427\) 0 0
\(428\) 0.0875611 0.151660i 0.00423243 0.00733078i
\(429\) 4.19821 + 11.0473i 0.202691 + 0.533371i
\(430\) 11.5391 19.9863i 0.556463 0.963823i
\(431\) 8.31776 + 14.4068i 0.400652 + 0.693950i 0.993805 0.111140i \(-0.0354502\pi\)
−0.593152 + 0.805090i \(0.702117\pi\)
\(432\) 23.0275 + 12.0266i 1.10791 + 0.578629i
\(433\) 19.7423 0.948756 0.474378 0.880321i \(-0.342673\pi\)
0.474378 + 0.880321i \(0.342673\pi\)
\(434\) 0 0
\(435\) 23.8549 29.2571i 1.14375 1.40277i
\(436\) −4.59122 7.95223i −0.219880 0.380843i
\(437\) 2.80830 0.134339
\(438\) 5.64612 + 14.8575i 0.269782 + 0.709917i
\(439\) −6.73514 −0.321451 −0.160725 0.986999i \(-0.551383\pi\)
−0.160725 + 0.986999i \(0.551383\pi\)
\(440\) −37.6310 −1.79399
\(441\) 0 0
\(442\) 2.32879 0.110769
\(443\) 28.6403 1.36074 0.680372 0.732867i \(-0.261818\pi\)
0.680372 + 0.732867i \(0.261818\pi\)
\(444\) 3.84113 4.71100i 0.182292 0.223574i
\(445\) 19.4628 0.922626
\(446\) 17.2397 + 29.8601i 0.816324 + 1.41392i
\(447\) 3.55358 + 9.35105i 0.168079 + 0.442290i
\(448\) 0 0
\(449\) −6.66872 −0.314716 −0.157358 0.987542i \(-0.550298\pi\)
−0.157358 + 0.987542i \(0.550298\pi\)
\(450\) 28.4102 25.2375i 1.33927 1.18971i
\(451\) −10.2518 17.7566i −0.482736 0.836124i
\(452\) 4.13097 7.15505i 0.194305 0.336545i
\(453\) −2.21797 + 2.72026i −0.104210 + 0.127809i
\(454\) 3.11898 5.40223i 0.146381 0.253539i
\(455\) 0 0
\(456\) −4.24617 + 5.20776i −0.198845 + 0.243876i
\(457\) −28.6573 −1.34053 −0.670266 0.742121i \(-0.733820\pi\)
−0.670266 + 0.742121i \(0.733820\pi\)
\(458\) 11.8399 + 20.5074i 0.553244 + 0.958246i
\(459\) 0.264513 + 6.25034i 0.0123464 + 0.291741i
\(460\) 2.19419 3.80045i 0.102305 0.177197i
\(461\) −10.0087 17.3355i −0.466150 0.807395i 0.533103 0.846050i \(-0.321026\pi\)
−0.999253 + 0.0386554i \(0.987693\pi\)
\(462\) 0 0
\(463\) −4.95789 + 8.58731i −0.230413 + 0.399086i −0.957930 0.287003i \(-0.907341\pi\)
0.727517 + 0.686090i \(0.240674\pi\)
\(464\) 15.5120 + 26.8676i 0.720127 + 1.24730i
\(465\) −0.407153 1.07140i −0.0188813 0.0496850i
\(466\) −21.8020 + 37.7623i −1.00996 + 1.74930i
\(467\) 8.04035 13.9263i 0.372063 0.644432i −0.617820 0.786320i \(-0.711984\pi\)
0.989883 + 0.141888i \(0.0453172\pi\)
\(468\) 2.46535 2.19003i 0.113961 0.101234i
\(469\) 0 0
\(470\) −17.3463 30.0446i −0.800124 1.38586i
\(471\) 5.21075 + 0.843232i 0.240099 + 0.0388541i
\(472\) −19.8225 −0.912402
\(473\) −23.1780 −1.06573
\(474\) 27.2105 + 4.40335i 1.24982 + 0.202253i
\(475\) 8.08967 + 14.0117i 0.371180 + 0.642902i
\(476\) 0 0
\(477\) 5.03657 + 24.5025i 0.230609 + 1.12189i
\(478\) 7.76103 13.4425i 0.354981 0.614846i
\(479\) −4.10128 + 7.10362i −0.187392 + 0.324573i −0.944380 0.328856i \(-0.893337\pi\)
0.756988 + 0.653429i \(0.226670\pi\)
\(480\) 11.0522 + 29.0833i 0.504462 + 1.32746i
\(481\) 2.00345 + 3.47008i 0.0913496 + 0.158222i
\(482\) 7.99183 13.8423i 0.364018 0.630497i
\(483\) 0 0
\(484\) −12.8024 22.1745i −0.581929 1.00793i
\(485\) 28.9512 50.1449i 1.31460 2.27696i
\(486\) 18.7100 + 19.3485i 0.848702 + 0.877666i
\(487\) −1.36840 2.37014i −0.0620081 0.107401i 0.833355 0.552738i \(-0.186417\pi\)
−0.895363 + 0.445337i \(0.853084\pi\)
\(488\) 21.1130 0.955741
\(489\) −5.89829 + 7.23402i −0.266730 + 0.327134i
\(490\) 0 0
\(491\) 9.85482 17.0690i 0.444742 0.770315i −0.553293 0.832987i \(-0.686629\pi\)
0.998034 + 0.0626719i \(0.0199622\pi\)
\(492\) −3.61528 + 4.43399i −0.162989 + 0.199900i
\(493\) −3.73542 + 6.46993i −0.168235 + 0.291391i
\(494\) 2.13291 + 3.69431i 0.0959642 + 0.166215i
\(495\) −60.9012 20.2408i −2.73731 0.909756i
\(496\) 0.941952 0.0422949
\(497\) 0 0
\(498\) 1.32784 + 3.49413i 0.0595018 + 0.156576i
\(499\) 16.5480 + 28.6619i 0.740789 + 1.28309i 0.952136 + 0.305674i \(0.0988817\pi\)
−0.211347 + 0.977411i \(0.567785\pi\)
\(500\) 8.05153 0.360075
\(501\) 18.1796 22.2966i 0.812205 0.996138i
\(502\) −35.6575 −1.59147
\(503\) −12.1860 −0.543346 −0.271673 0.962390i \(-0.587577\pi\)
−0.271673 + 0.962390i \(0.587577\pi\)
\(504\) 0 0
\(505\) −45.5331 −2.02619
\(506\) −13.3912 −0.595310
\(507\) −7.22648 19.0161i −0.320939 0.844534i
\(508\) −9.73765 −0.432038
\(509\) 6.81965 + 11.8120i 0.302276 + 0.523557i 0.976651 0.214832i \(-0.0689204\pi\)
−0.674375 + 0.738389i \(0.735587\pi\)
\(510\) −7.99142 + 9.80116i −0.353866 + 0.434002i
\(511\) 0 0
\(512\) −7.97968 −0.352656
\(513\) −9.67304 + 6.14422i −0.427075 + 0.271274i
\(514\) −2.11146 3.65715i −0.0931325 0.161310i
\(515\) −4.74481 + 8.21826i −0.209081 + 0.362140i
\(516\) 2.29741 + 6.04551i 0.101138 + 0.266139i
\(517\) −17.4214 + 30.1747i −0.766190 + 1.32708i
\(518\) 0 0
\(519\) 30.1787 + 4.88368i 1.32470 + 0.214370i
\(520\) −6.92164 −0.303534
\(521\) −17.7745 30.7863i −0.778714 1.34877i −0.932683 0.360697i \(-0.882539\pi\)
0.153969 0.988076i \(-0.450794\pi\)
\(522\) 6.47160 + 31.4839i 0.283254 + 1.37801i
\(523\) 13.3593 23.1391i 0.584163 1.01180i −0.410816 0.911718i \(-0.634756\pi\)
0.994979 0.100082i \(-0.0319105\pi\)
\(524\) 7.47991 + 12.9556i 0.326761 + 0.565967i
\(525\) 0 0
\(526\) −21.2052 + 36.7284i −0.924589 + 1.60143i
\(527\) 0.113415 + 0.196440i 0.00494043 + 0.00855708i
\(528\) 33.3294 40.8772i 1.45048 1.77895i
\(529\) 10.6892 18.5143i 0.464750 0.804970i
\(530\) −25.2833 + 43.7919i −1.09824 + 1.90220i
\(531\) −32.0802 10.6620i −1.39216 0.462692i
\(532\) 0 0
\(533\) −1.88565 3.26604i −0.0816766 0.141468i
\(534\) −10.4721 + 12.8436i −0.453171 + 0.555796i
\(535\) −0.626879 −0.0271023
\(536\) −13.9198 −0.601244
\(537\) 1.61723 + 4.25566i 0.0697888 + 0.183645i
\(538\) −25.5282 44.2161i −1.10060 1.90629i
\(539\) 0 0
\(540\) 0.757146 + 17.8911i 0.0325824 + 0.769910i
\(541\) −18.7927 + 32.5500i −0.807963 + 1.39943i 0.106309 + 0.994333i \(0.466097\pi\)
−0.914272 + 0.405100i \(0.867237\pi\)
\(542\) −21.4026 + 37.0705i −0.919322 + 1.59231i
\(543\) −6.79462 1.09954i −0.291585 0.0471859i
\(544\) −3.07866 5.33240i −0.131997 0.228625i
\(545\) −16.4350 + 28.4663i −0.704000 + 1.21936i
\(546\) 0 0
\(547\) −9.13381 15.8202i −0.390533 0.676424i 0.601986 0.798506i \(-0.294376\pi\)
−0.992520 + 0.122082i \(0.961043\pi\)
\(548\) −3.01567 + 5.22329i −0.128823 + 0.223128i
\(549\) 34.1688 + 11.3562i 1.45829 + 0.484669i
\(550\) −38.5750 66.8139i −1.64485 2.84896i
\(551\) −13.6849 −0.582995
\(552\) −1.37824 3.62677i −0.0586619 0.154366i
\(553\) 0 0
\(554\) 1.62172 2.80890i 0.0689002 0.119339i
\(555\) −21.4794 3.47592i −0.911752 0.147545i
\(556\) 0.430433 0.745532i 0.0182544 0.0316176i
\(557\) 1.94636 + 3.37119i 0.0824698 + 0.142842i 0.904310 0.426876i \(-0.140386\pi\)
−0.821840 + 0.569718i \(0.807053\pi\)
\(558\) 0.926091 + 0.307791i 0.0392046 + 0.0130298i
\(559\) −4.26324 −0.180316
\(560\) 0 0
\(561\) 12.5378 + 2.02893i 0.529346 + 0.0856617i
\(562\) −10.4281 18.0620i −0.439884 0.761901i
\(563\) 3.32855 0.140282 0.0701409 0.997537i \(-0.477655\pi\)
0.0701409 + 0.997537i \(0.477655\pi\)
\(564\) 9.59725 + 1.55308i 0.404117 + 0.0653965i
\(565\) −29.5750 −1.24423
\(566\) 48.2965 2.03006
\(567\) 0 0
\(568\) −21.4702 −0.900870
\(569\) −36.6244 −1.53538 −0.767688 0.640824i \(-0.778593\pi\)
−0.767688 + 0.640824i \(0.778593\pi\)
\(570\) −22.8674 3.70053i −0.957810 0.154998i
\(571\) −22.5824 −0.945044 −0.472522 0.881319i \(-0.656656\pi\)
−0.472522 + 0.881319i \(0.656656\pi\)
\(572\) −3.34742 5.79789i −0.139962 0.242422i
\(573\) 31.1286 + 5.03740i 1.30042 + 0.210441i
\(574\) 0 0
\(575\) −9.34201 −0.389589
\(576\) 3.32795 + 1.10606i 0.138665 + 0.0460859i
\(577\) −11.2725 19.5245i −0.469279 0.812815i 0.530104 0.847932i \(-0.322153\pi\)
−0.999383 + 0.0351177i \(0.988819\pi\)
\(578\) −13.4248 + 23.2525i −0.558399 + 0.967175i
\(579\) 0.346040 + 0.0559981i 0.0143809 + 0.00232720i
\(580\) −10.6923 + 18.5197i −0.443975 + 0.768987i
\(581\) 0 0
\(582\) 17.5135 + 46.0857i 0.725957 + 1.91031i
\(583\) 50.7854 2.10332
\(584\) 4.67457 + 8.09659i 0.193435 + 0.335039i
\(585\) −11.2018 3.72298i −0.463139 0.153926i
\(586\) 7.61717 13.1933i 0.314662 0.545011i
\(587\) −12.1198 20.9921i −0.500237 0.866436i −1.00000 0.000273884i \(-0.999913\pi\)
0.499763 0.866162i \(-0.333421\pi\)
\(588\) 0 0
\(589\) −0.207750 + 0.359834i −0.00856020 + 0.0148267i
\(590\) −34.1684 59.1814i −1.40669 2.43646i
\(591\) 2.78931 + 0.451381i 0.114737 + 0.0185673i
\(592\) 8.94112 15.4865i 0.367478 0.636490i
\(593\) 22.8663 39.6056i 0.939007 1.62641i 0.171680 0.985153i \(-0.445081\pi\)
0.767328 0.641255i \(-0.221586\pi\)
\(594\) 46.1252 29.2983i 1.89254 1.20212i
\(595\) 0 0
\(596\) −2.83343 4.90764i −0.116062 0.201025i
\(597\) 3.87142 + 10.1874i 0.158447 + 0.416944i
\(598\) −2.46310 −0.100724
\(599\) −30.1668 −1.23258 −0.616290 0.787519i \(-0.711365\pi\)
−0.616290 + 0.787519i \(0.711365\pi\)
\(600\) 14.1252 17.3240i 0.576659 0.707249i
\(601\) 7.36933 + 12.7641i 0.300601 + 0.520657i 0.976272 0.216547i \(-0.0694794\pi\)
−0.675671 + 0.737203i \(0.736146\pi\)
\(602\) 0 0
\(603\) −22.5275 7.48712i −0.917391 0.304899i
\(604\) 0.994149 1.72192i 0.0404513 0.0700638i
\(605\) −45.8285 + 79.3772i −1.86319 + 3.22714i
\(606\) 24.4993 30.0474i 0.995217 1.22059i
\(607\) 3.03918 + 5.26401i 0.123356 + 0.213660i 0.921089 0.389351i \(-0.127301\pi\)
−0.797733 + 0.603011i \(0.793967\pi\)
\(608\) 5.63941 9.76774i 0.228708 0.396134i
\(609\) 0 0
\(610\) 36.3930 + 63.0345i 1.47351 + 2.55219i
\(611\) −3.20439 + 5.55016i −0.129636 + 0.224535i
\(612\) −0.713543 3.47133i −0.0288432 0.140320i
\(613\) −5.88668 10.1960i −0.237761 0.411814i 0.722311 0.691569i \(-0.243080\pi\)
−0.960071 + 0.279755i \(0.909747\pi\)
\(614\) −1.82213 −0.0735352
\(615\) 20.2165 + 3.27154i 0.815207 + 0.131921i
\(616\) 0 0
\(617\) −16.0319 + 27.7680i −0.645418 + 1.11790i 0.338786 + 0.940863i \(0.389984\pi\)
−0.984205 + 0.177034i \(0.943350\pi\)
\(618\) −2.87029 7.55300i −0.115460 0.303826i
\(619\) 6.27588 10.8701i 0.252249 0.436908i −0.711896 0.702285i \(-0.752163\pi\)
0.964145 + 0.265377i \(0.0854965\pi\)
\(620\) 0.324641 + 0.562294i 0.0130379 + 0.0225823i
\(621\) −0.279767 6.61081i −0.0112267 0.265283i
\(622\) −5.30441 −0.212688
\(623\) 0 0
\(624\) 6.13043 7.51873i 0.245414 0.300990i
\(625\) 3.92995 + 6.80687i 0.157198 + 0.272275i
\(626\) −48.6249 −1.94344
\(627\) 8.26456 + 21.7477i 0.330055 + 0.868521i
\(628\) −2.99022 −0.119323
\(629\) 4.30619 0.171699
\(630\) 0 0
\(631\) 33.4642 1.33219 0.666095 0.745867i \(-0.267964\pi\)
0.666095 + 0.745867i \(0.267964\pi\)
\(632\) 16.2138 0.644950
\(633\) −17.8269 + 21.8640i −0.708556 + 0.869016i
\(634\) −22.1809 −0.880915
\(635\) 17.4288 + 30.1875i 0.691639 + 1.19795i
\(636\) −5.03386 13.2463i −0.199606 0.525251i
\(637\) 0 0
\(638\) 65.2553 2.58348
\(639\) −34.7469 11.5483i −1.37457 0.456844i
\(640\) 21.5074 + 37.2519i 0.850155 + 1.47251i
\(641\) 9.49183 16.4403i 0.374905 0.649354i −0.615408 0.788209i \(-0.711009\pi\)
0.990313 + 0.138855i \(0.0443421\pi\)
\(642\) 0.337296 0.413680i 0.0133120 0.0163266i
\(643\) 4.81347 8.33718i 0.189825 0.328786i −0.755367 0.655302i \(-0.772541\pi\)
0.945192 + 0.326516i \(0.105875\pi\)
\(644\) 0 0
\(645\) 14.6296 17.9426i 0.576039 0.706490i
\(646\) 4.58445 0.180373
\(647\) 3.90607 + 6.76551i 0.153564 + 0.265980i 0.932535 0.361079i \(-0.117592\pi\)
−0.778972 + 0.627059i \(0.784258\pi\)
\(648\) 12.6822 + 9.47680i 0.498205 + 0.372284i
\(649\) −34.3163 + 59.4375i −1.34703 + 2.33313i
\(650\) −7.09528 12.2894i −0.278300 0.482029i
\(651\) 0 0
\(652\) 2.64376 4.57912i 0.103537 0.179332i
\(653\) −15.8714 27.4901i −0.621097 1.07577i −0.989282 0.146019i \(-0.953354\pi\)
0.368185 0.929753i \(-0.379979\pi\)
\(654\) −9.94207 26.1620i −0.388766 1.02302i
\(655\) 26.7756 46.3767i 1.04621 1.81209i
\(656\) −8.41540 + 14.5759i −0.328566 + 0.569093i
\(657\) 3.21026 + 15.6177i 0.125244 + 0.609303i
\(658\) 0 0
\(659\) 3.10685 + 5.38122i 0.121026 + 0.209623i 0.920172 0.391513i \(-0.128048\pi\)
−0.799147 + 0.601136i \(0.794715\pi\)
\(660\) 35.8884 + 5.80766i 1.39695 + 0.226063i
\(661\) 27.5263 1.07065 0.535324 0.844647i \(-0.320190\pi\)
0.535324 + 0.844647i \(0.320190\pi\)
\(662\) 37.2189 1.44655
\(663\) 2.30613 + 0.373191i 0.0895627 + 0.0144935i
\(664\) 1.09935 + 1.90413i 0.0426630 + 0.0738945i
\(665\) 0 0
\(666\) 13.8509 12.3041i 0.536712 0.476775i
\(667\) 3.95084 6.84306i 0.152977 0.264964i
\(668\) −8.14854 + 14.1137i −0.315276 + 0.546075i
\(669\) 12.2868 + 32.3322i 0.475037 + 1.25003i
\(670\) −23.9939 41.5586i −0.926965 1.60555i
\(671\) 36.5505 63.3073i 1.41102 2.44395i
\(672\) 0 0
\(673\) −8.10894 14.0451i −0.312577 0.541399i 0.666343 0.745646i \(-0.267859\pi\)
−0.978919 + 0.204247i \(0.934526\pi\)
\(674\) −10.8835 + 18.8508i −0.419217 + 0.726106i
\(675\) 32.1781 20.4392i 1.23853 0.786704i
\(676\) 5.76199 + 9.98006i 0.221615 + 0.383849i
\(677\) −20.5090 −0.788225 −0.394112 0.919062i \(-0.628948\pi\)
−0.394112 + 0.919062i \(0.628948\pi\)
\(678\) 15.9130 19.5167i 0.611135 0.749532i
\(679\) 0 0
\(680\) −3.71932 + 6.44205i −0.142629 + 0.247041i
\(681\) 3.95433 4.84983i 0.151530 0.185846i
\(682\) 0.990642 1.71584i 0.0379337 0.0657030i
\(683\) 0.0561542 + 0.0972618i 0.00214868 + 0.00372162i 0.867098 0.498138i \(-0.165983\pi\)
−0.864949 + 0.501860i \(0.832649\pi\)
\(684\) 4.85326 4.31128i 0.185569 0.164846i
\(685\) 21.5902 0.824918
\(686\) 0 0
\(687\) 8.43839 + 22.2052i 0.321945 + 0.847179i
\(688\) 9.51311 + 16.4772i 0.362684 + 0.628187i
\(689\) 9.34118 0.355871
\(690\) 8.45229 10.3664i 0.321773 0.394642i
\(691\) 18.8670 0.717735 0.358868 0.933388i \(-0.383163\pi\)
0.358868 + 0.933388i \(0.383163\pi\)
\(692\) −17.3182 −0.658340
\(693\) 0 0
\(694\) −39.9480 −1.51640
\(695\) −3.08161 −0.116892
\(696\) 6.71620 + 17.6733i 0.254577 + 0.669905i
\(697\) −4.05299 −0.153518
\(698\) −14.2332 24.6527i −0.538736 0.933118i
\(699\) −27.6413 + 33.9010i −1.04549 + 1.28225i
\(700\) 0 0
\(701\) −3.16006 −0.119354 −0.0596770 0.998218i \(-0.519007\pi\)
−0.0596770 + 0.998218i \(0.519007\pi\)
\(702\) 8.48402 5.38896i 0.320209 0.203393i
\(703\) 3.94398 + 6.83118i 0.148750 + 0.257643i
\(704\) 3.55992 6.16596i 0.134170 0.232388i
\(705\) −12.3628 32.5320i −0.465610 1.22523i
\(706\) −21.1402 + 36.6159i −0.795622 + 1.37806i
\(707\) 0 0
\(708\) 18.9045 + 3.05923i 0.710475 + 0.114973i
\(709\) −21.5211 −0.808243 −0.404121 0.914705i \(-0.632423\pi\)
−0.404121 + 0.914705i \(0.632423\pi\)
\(710\) −37.0087 64.1009i −1.38891 2.40567i
\(711\) 26.2400 + 8.72100i 0.984079 + 0.327063i
\(712\) −4.87385 + 8.44176i −0.182655 + 0.316368i
\(713\) −0.119956 0.207769i −0.00449237 0.00778102i
\(714\) 0 0
\(715\) −11.9826 + 20.7545i −0.448125 + 0.776175i
\(716\) −1.28949 2.23347i −0.0481906 0.0834685i
\(717\) 9.83968 12.0680i 0.367469 0.450687i
\(718\) 17.6785 30.6201i 0.659757 1.14273i
\(719\) 9.41508 16.3074i 0.351123 0.608163i −0.635323 0.772246i \(-0.719133\pi\)
0.986447 + 0.164083i \(0.0524665\pi\)
\(720\) 10.6070 + 51.6021i 0.395298 + 1.92310i
\(721\) 0 0
\(722\) −12.2040 21.1379i −0.454185 0.786671i
\(723\) 10.1323 12.4268i 0.376824 0.462159i
\(724\) 3.89914 0.144910
\(725\) 45.5237 1.69071
\(726\) −27.7231 72.9517i −1.02890 2.70749i
\(727\) −19.5426 33.8489i −0.724797 1.25538i −0.959058 0.283211i \(-0.908600\pi\)
0.234261 0.972174i \(-0.424733\pi\)
\(728\) 0 0
\(729\) 15.4273 + 22.1585i 0.571381 + 0.820685i
\(730\) −16.1153 + 27.9125i −0.596454 + 1.03309i
\(731\) −2.29084 + 3.96784i −0.0847296 + 0.146756i
\(732\) −20.1353 3.25841i −0.744222 0.120434i
\(733\) −9.29924 16.1068i −0.343475 0.594917i 0.641600 0.767039i \(-0.278271\pi\)
−0.985076 + 0.172123i \(0.944937\pi\)
\(734\) 19.2119 33.2759i 0.709123 1.22824i
\(735\) 0 0
\(736\) 3.25621 + 5.63993i 0.120026 + 0.207890i
\(737\) −24.0977 + 41.7385i −0.887651 + 1.53746i
\(738\) −13.0365 + 11.5807i −0.479880 + 0.426290i
\(739\) −2.75068 4.76432i −0.101185 0.175258i 0.810988 0.585063i \(-0.198930\pi\)
−0.912173 + 0.409805i \(0.865597\pi\)
\(740\) 12.3261 0.453117
\(741\) 1.52014 + 4.00016i 0.0558436 + 0.146949i
\(742\) 0 0
\(743\) 10.2326 17.7234i 0.375399 0.650210i −0.614988 0.788537i \(-0.710839\pi\)
0.990387 + 0.138327i \(0.0441725\pi\)
\(744\) 0.566666 + 0.0917010i 0.0207750 + 0.00336192i
\(745\) −10.1427 + 17.5677i −0.371601 + 0.643631i
\(746\) −28.0892 48.6520i −1.02842 1.78128i
\(747\) 0.754977 + 3.67291i 0.0276232 + 0.134385i
\(748\) −7.19489 −0.263071
\(749\) 0 0
\(750\) 24.2253 + 3.92027i 0.884583 + 0.143148i
\(751\) −19.0230 32.9488i −0.694159 1.20232i −0.970463 0.241248i \(-0.922443\pi\)
0.276305 0.961070i \(-0.410890\pi\)
\(752\) 28.6015 1.04299
\(753\) −35.3105 5.71414i −1.28679 0.208235i
\(754\) 12.0027 0.437113
\(755\) −7.11744 −0.259030
\(756\) 0 0
\(757\) −51.0780 −1.85646 −0.928230 0.372006i \(-0.878670\pi\)
−0.928230 + 0.372006i \(0.878670\pi\)
\(758\) −2.66658 −0.0968546
\(759\) −13.2609 2.14595i −0.481338 0.0778929i
\(760\) −13.6259 −0.494263
\(761\) 20.0375 + 34.7059i 0.726357 + 1.25809i 0.958413 + 0.285385i \(0.0921216\pi\)
−0.232055 + 0.972703i \(0.574545\pi\)
\(762\) −29.2985 4.74124i −1.06137 0.171757i
\(763\) 0 0
\(764\) −17.8633 −0.646273
\(765\) −9.48429 + 8.42514i −0.342905 + 0.304612i
\(766\) 27.3058 + 47.2951i 0.986599 + 1.70884i
\(767\) −6.31195 + 10.9326i −0.227911 + 0.394754i
\(768\) −32.1574 5.20389i −1.16038 0.187779i
\(769\) 22.4828 38.9414i 0.810751 1.40426i −0.101587 0.994827i \(-0.532392\pi\)
0.912339 0.409436i \(-0.134274\pi\)
\(770\) 0 0
\(771\) −1.50485 3.95993i −0.0541958 0.142613i
\(772\) −0.198577 −0.00714695
\(773\) 12.1781 + 21.0930i 0.438014 + 0.758663i 0.997536 0.0701524i \(-0.0223485\pi\)
−0.559522 + 0.828816i \(0.689015\pi\)
\(774\) 3.96887 + 19.3082i 0.142658 + 0.694020i
\(775\) 0.691096 1.19701i 0.0248249 0.0429980i
\(776\) 14.4998 + 25.1145i 0.520514 + 0.901556i
\(777\) 0 0
\(778\) −4.52913 + 7.84468i −0.162377 + 0.281245i
\(779\) −3.71208 6.42951i −0.132999 0.230361i
\(780\) 6.60111 + 1.06823i 0.236358 + 0.0382487i
\(781\) −37.1689 + 64.3784i −1.33001 + 2.30364i
\(782\) −1.32354 + 2.29243i −0.0473296 + 0.0819773i