Properties

Label 441.2.h.h.214.3
Level $441$
Weight $2$
Character 441.214
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 214.3
Character \(\chi\) \(=\) 441.214
Dual form 441.2.h.h.373.3

$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

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

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 0.143397 + 0.989665i \(0.454197\pi\)
−0.928774 + 0.370647i \(0.879136\pi\)
\(6\) 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 0.802150 + 0.597123i \(0.203690\pi\)
0.116049 + 0.993244i \(0.462977\pi\)
\(12\) −1.67764 + 0.271484i −0.484292 + 0.0783708i
\(13\) 0.560139 + 0.970190i 0.155355 + 0.269082i 0.933188 0.359388i \(-0.117015\pi\)
−0.777833 + 0.628471i \(0.783681\pi\)
\(14\) 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 −0.929746 0.368202i \(-0.879974\pi\)
0.783745 + 0.621083i \(0.213307\pi\)
\(18\) −4.91546 + 1.63368i −1.15859 + 0.385061i
\(19\) 1.10269 + 1.90991i 0.252974 + 0.438163i 0.964343 0.264655i \(-0.0852581\pi\)
−0.711370 + 0.702818i \(0.751925\pi\)
\(20\) −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 −0.791980 0.610548i \(-0.790949\pi\)
0.924740 + 0.380601i \(0.124283\pi\)
\(24\) −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 0.419774 + 0.907628i \(0.362109\pi\)
−0.995917 + 0.0902789i \(0.971224\pi\)
\(30\) −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 0.680749 0.732516i \(-0.261654\pi\)
−0.974753 + 0.223288i \(0.928321\pi\)
\(38\) −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 0.967004 0.254762i \(-0.0819972\pi\)
−0.704132 + 0.710069i \(0.748664\pi\)
\(42\) 0 0
\(43\) −1.90276 + 3.29567i −0.290168 + 0.502585i −0.973849 0.227195i \(-0.927044\pi\)
0.683681 + 0.729781i \(0.260378\pi\)
\(44\) 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 −0.423615 0.905842i \(-0.639239\pi\)
0.996290 0.0860593i \(-0.0274275\pi\)
\(54\) 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 −0.667563 0.744554i \(-0.732662\pi\)
0.978584 + 0.205849i \(0.0659957\pi\)
\(74\) 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 −0.829687 0.558229i \(-0.811481\pi\)
0.898284 + 0.439415i \(0.144814\pi\)
\(84\) 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 0.680990 0.732293i \(-0.261550\pi\)
−0.974679 + 0.223608i \(0.928216\pi\)
\(90\) 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 −0.0555261 0.998457i \(-0.517684\pi\)
0.892452 0.451142i \(-0.148983\pi\)
\(98\) 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 0.984307 + 0.176463i \(0.0564657\pi\)
−0.339332 + 0.940667i \(0.610201\pi\)
\(102\) −1.27903 + 3.36569i −0.126643 + 0.333253i
\(103\) −1.35091 + 2.33984i −0.133109 + 0.230552i −0.924873 0.380275i \(-0.875829\pi\)
0.791765 + 0.610826i \(0.209163\pi\)
\(104\) 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 0.870307 0.492510i \(-0.163921\pi\)
−0.861680 + 0.507453i \(0.830587\pi\)
\(108\) −4.51917 + 2.36022i −0.434857 + 0.227113i
\(109\) −4.67927 + 8.10473i −0.448192 + 0.776292i −0.998268 0.0588226i \(-0.981265\pi\)
0.550076 + 0.835115i \(0.314599\pi\)
\(110\) 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 0.993236 0.116113i \(-0.0370434\pi\)
−0.597175 + 0.802111i \(0.703710\pi\)
\(114\) 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 −0.312943 0.949772i \(-0.601315\pi\)
0.978998 0.203870i \(-0.0653519\pi\)
\(132\) −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 0.704342 0.709861i \(-0.251242\pi\)
−0.966929 + 0.255047i \(0.917909\pi\)
\(138\) 1.35279 3.55979i 0.115157 0.303030i
\(139\) 0.438687 + 0.759829i 0.0372090 + 0.0644478i 0.884030 0.467430i \(-0.154820\pi\)
−0.846821 + 0.531878i \(0.821487\pi\)
\(140\) 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 −0.959729 0.280927i \(-0.909358\pi\)
0.723154 + 0.690686i \(0.242692\pi\)
\(150\) −13.8643 17.0041i −1.13202 1.38838i
\(151\) 1.01321 + 1.75494i 0.0824541 + 0.142815i 0.904304 0.426890i \(-0.140391\pi\)
−0.821849 + 0.569705i \(0.807058\pi\)
\(152\) 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 0.952042 0.305967i \(-0.0989797\pi\)
−0.740996 + 0.671509i \(0.765646\pi\)
\(164\) 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 −0.984840 0.173464i \(-0.944504\pi\)
0.342196 0.939629i \(-0.388829\pi\)
\(168\) 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 −0.910952 0.412513i \(-0.864651\pi\)
0.812722 + 0.582651i \(0.197985\pi\)
\(180\) −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 −0.955723 0.294268i \(-0.904924\pi\)
0.732705 + 0.680546i \(0.238257\pi\)
\(200\) −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 0.997441 + 0.0714912i \(0.0227758\pi\)
−0.436807 + 0.899555i \(0.643891\pi\)
\(212\) 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 0.309662 + 0.950847i \(0.399784\pi\)
−0.978288 + 0.207248i \(0.933549\pi\)
\(224\) 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 0.799830 0.600226i \(-0.204923\pi\)
−0.919726 + 0.392560i \(0.871589\pi\)
\(228\) −2.36842 2.90477i −0.156852 0.192373i
\(229\) −6.85733 + 11.8772i −0.453145 + 0.784870i −0.998579 0.0532835i \(-0.983031\pi\)
0.545435 + 0.838153i \(0.316365\pi\)
\(230\) −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 0.900205 + 0.435466i \(0.143417\pi\)
−0.0729776 + 0.997334i \(0.523250\pi\)
\(234\) −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 0.683234 0.730200i \(-0.260573\pi\)
−0.973988 + 0.226598i \(0.927240\pi\)
\(240\) −10.8046 + 28.4316i −0.697431 + 1.83525i
\(241\) −4.62862 8.01701i −0.298156 0.516421i 0.677558 0.735469i \(-0.263038\pi\)
−0.975714 + 0.219048i \(0.929705\pi\)
\(242\) 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 −0.825361 0.564605i \(-0.809028\pi\)
0.901643 + 0.432481i \(0.142362\pi\)
\(258\) −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 0.944222 + 0.329311i \(0.106816\pi\)
−0.186919 + 0.982375i \(0.559850\pi\)
\(264\) −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 0.0758746 0.997117i \(-0.475825\pi\)
0.825592 0.564268i \(-0.190842\pi\)
\(270\) −1.33237 + 31.4833i −0.0810852 + 1.91601i
\(271\) 12.3958 + 21.4701i 0.752989 + 1.30421i 0.946368 + 0.323090i \(0.104722\pi\)
−0.193380 + 0.981124i \(0.561945\pi\)
\(272\) 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 0.836428 0.548076i \(-0.184640\pi\)
−0.892862 + 0.450330i \(0.851306\pi\)
\(278\) −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 −0.627714 0.778444i \(-0.716009\pi\)
0.988009 + 0.154395i \(0.0493427\pi\)
\(282\) −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 0.707903 0.706309i \(-0.249641\pi\)
−0.965634 + 0.259908i \(0.916308\pi\)
\(294\) 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 0.985056 0.172235i \(-0.0550989\pi\)
−0.641688 + 0.766966i \(0.721766\pi\)
\(338\) −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 −0.556521 0.830833i \(-0.687864\pi\)
0.997783 + 0.0665448i \(0.0211975\pi\)
\(350\) 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 0.982718 + 0.185110i \(0.0592642\pi\)
−0.331049 + 0.943614i \(0.607402\pi\)
\(354\) −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 −0.998882 0.0472797i \(-0.984945\pi\)
0.458495 0.888697i \(-0.348389\pi\)
\(360\) −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 −0.995382 0.0959900i \(-0.969398\pi\)
0.414561 0.910021i \(-0.363935\pi\)
\(368\) −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 −0.0455576 0.998962i \(-0.514506\pi\)
0.887905 0.460027i \(-0.152160\pi\)
\(374\) 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 0.106090 + 0.994357i \(0.466167\pi\)
−0.914183 + 0.405302i \(0.867166\pi\)
\(384\) 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 0.924831 0.380378i \(-0.124206\pi\)
−0.791833 + 0.610738i \(0.790873\pi\)
\(390\) −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 0.865678 0.500600i \(-0.166887\pi\)
−0.866372 + 0.499399i \(0.833554\pi\)
\(398\) 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 −0.976828 0.214024i \(-0.931343\pi\)
0.673765 + 0.738946i \(0.264676\pi\)
\(402\) −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 0.988554 0.150866i \(-0.0482061\pi\)
−0.624931 + 0.780680i \(0.714873\pi\)
\(420\) 0 0
\(421\) −4.54213 + 7.86721i −0.221370 + 0.383424i −0.955224 0.295883i \(-0.904386\pi\)
0.733854 + 0.679307i \(0.237720\pi\)
\(422\) −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 −0.593152 0.805090i \(-0.702117\pi\)
0.993805 + 0.111140i \(0.0354502\pi\)
\(432\) 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 −0.999253 0.0386554i \(-0.987693\pi\)
0.533103 + 0.846050i \(0.321026\pi\)
\(462\) 0 0
\(463\) −4.95789 8.58731i −0.230413 0.399086i 0.727517 0.686090i \(-0.240674\pi\)
−0.957930 + 0.287003i \(0.907341\pi\)
\(464\) 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 0.989883 0.141888i \(-0.0453172\pi\)
−0.617820 + 0.786320i \(0.711984\pi\)
\(468\) 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 0.756988 0.653429i \(-0.226670\pi\)
−0.944380 + 0.328856i \(0.893337\pi\)
\(480\) 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 −0.895363 0.445337i \(-0.853084\pi\)
0.833355 + 0.552738i \(0.186417\pi\)
\(488\) 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 0.998034 0.0626719i \(-0.0199622\pi\)
−0.553293 + 0.832987i \(0.686629\pi\)
\(492\) −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 −0.211347 0.977411i \(-0.567785\pi\)
0.952136 0.305674i \(-0.0988817\pi\)
\(500\) 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 −0.674375 0.738389i \(-0.735587\pi\)
0.976651 + 0.214832i \(0.0689204\pi\)
\(510\) −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 0.153969 + 0.988076i \(0.450794\pi\)
−0.932683 + 0.360697i \(0.882539\pi\)
\(522\) 6.47160 31.4839i 0.283254 1.37801i
\(523\) 13.3593 + 23.1391i 0.584163 + 1.01180i 0.994979 + 0.100082i \(0.0319105\pi\)
−0.410816 + 0.911718i \(0.634756\pi\)
\(524\) 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 −0.914272 0.405100i \(-0.867237\pi\)
0.106309 0.994333i \(-0.466097\pi\)
\(542\) −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 −0.992520 0.122082i \(-0.961043\pi\)
0.601986 + 0.798506i \(0.294376\pi\)
\(548\) −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 −0.821840 0.569718i \(-0.807053\pi\)
0.904310 + 0.426876i \(0.140386\pi\)
\(558\) 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 −0.999383 0.0351177i \(-0.988819\pi\)
0.530104 + 0.847932i \(0.322153\pi\)
\(578\) −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 0.499763 + 0.866162i \(0.333421\pi\)
−1.00000 0.000273884i \(0.999913\pi\)
\(588\) 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 0.767328 + 0.641255i \(0.221586\pi\)
0.171680 + 0.985153i \(0.445081\pi\)
\(594\) 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 −0.675671 0.737203i \(-0.736146\pi\)
0.976272 + 0.216547i \(0.0694794\pi\)
\(602\) 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 −0.797733 0.603011i \(-0.793967\pi\)
0.921089 + 0.389351i \(0.127301\pi\)
\(608\) 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 −0.960071 0.279755i \(-0.909747\pi\)
0.722311 + 0.691569i \(0.243080\pi\)
\(614\) −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 −0.984205 0.177034i \(-0.943350\pi\)
0.338786 0.940863i \(-0.389984\pi\)
\(618\) −2.87029 + 7.55300i −0.115460 + 0.303826i
\(619\) 6.27588 + 10.8701i 0.252249 + 0.436908i 0.964145 0.265377i \(-0.0854965\pi\)
−0.711896 + 0.702285i \(0.752163\pi\)
\(620\) 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 0.990313 0.138855i \(-0.0443421\pi\)
−0.615408 + 0.788209i \(0.711009\pi\)
\(642\) 0.337296 + 0.413680i 0.0133120 + 0.0163266i
\(643\) 4.81347 + 8.33718i 0.189825 + 0.328786i 0.945192 0.326516i \(-0.105875\pi\)
−0.755367 + 0.655302i \(0.772541\pi\)
\(644\) 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 −0.778972 0.627059i \(-0.784258\pi\)
0.932535 + 0.361079i \(0.117592\pi\)
\(648\) 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 0.368185 + 0.929753i \(0.379979\pi\)
−0.989282 + 0.146019i \(0.953354\pi\)
\(654\) −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 −0.799147 0.601136i \(-0.794715\pi\)
0.920172 + 0.391513i \(0.128048\pi\)
\(660\) 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 −0.978919 0.204247i \(-0.934526\pi\)
0.666343 + 0.745646i \(0.267859\pi\)
\(674\) −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 −0.864949 0.501860i \(-0.832649\pi\)
0.867098 + 0.498138i \(0.165983\pi\)
\(684\) 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 0.986447 0.164083i \(-0.0524665\pi\)
−0.635323 + 0.772246i \(0.719133\pi\)
\(720\) 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 0.234261 + 0.972174i \(0.424733\pi\)
−0.959058 + 0.283211i \(0.908600\pi\)
\(728\) 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 −0.985076 0.172123i \(-0.944937\pi\)
0.641600 + 0.767039i \(0.278271\pi\)
\(734\) 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 −0.912173 0.409805i \(-0.865597\pi\)
0.810988 + 0.585063i \(0.198930\pi\)
\(740\) 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 0.990387 0.138327i \(-0.0441725\pi\)
−0.614988 + 0.788537i \(0.710839\pi\)
\(744\) 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 0.276305 + 0.961070i \(0.410890\pi\)
−0.970463 + 0.241248i \(0.922443\pi\)
\(752\) 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 −0.232055 0.972703i \(-0.574545\pi\)
0.958413 0.285385i \(-0.0921216\pi\)
\(762\) −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 0.912339 + 0.409436i \(0.134274\pi\)
−0.101587 + 0.994827i \(0.532392\pi\)
\(770\) 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 −0.559522 0.828816i \(-0.689015\pi\)
0.997536 + 0.0701524i \(0.0223485\pi\)
\(774\) 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