Properties

Label 405.2.r.a.152.16
Level $405$
Weight $2$
Character 405.152
Analytic conductor $3.234$
Analytic rank $0$
Dimension $192$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.r (of order \(36\), degree \(12\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.23394128186\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(16\) over \(\Q(\zeta_{36})\)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 152.16
Character \(\chi\) \(=\) 405.152
Dual form 405.2.r.a.8.16

$q$-expansion

\(f(q)\) \(=\) \(q+(2.18018 + 1.52658i) q^{2} +(1.73870 + 4.77703i) q^{4} +(-1.64880 - 1.51045i) q^{5} +(1.30062 + 2.78918i) q^{7} +(-2.12414 + 7.92739i) q^{8} +O(q^{10})\) \(q+(2.18018 + 1.52658i) q^{2} +(1.73870 + 4.77703i) q^{4} +(-1.64880 - 1.51045i) q^{5} +(1.30062 + 2.78918i) q^{7} +(-2.12414 + 7.92739i) q^{8} +(-1.28885 - 5.81007i) q^{10} +(0.426793 + 0.508631i) q^{11} +(-0.269123 - 0.384347i) q^{13} +(-1.42232 + 8.06640i) q^{14} +(-8.94423 + 7.50510i) q^{16} +(-1.20591 - 4.50051i) q^{17} +(4.80938 - 2.77670i) q^{19} +(4.34871 - 10.5026i) q^{20} +(0.154018 + 1.76044i) q^{22} +(0.0602123 + 0.0280775i) q^{23} +(0.437073 + 4.98086i) q^{25} -1.24878i q^{26} +(-11.0626 + 11.0626i) q^{28} +(-0.434735 - 2.46551i) q^{29} +(1.76652 - 0.642961i) q^{31} +(-14.6055 + 1.27781i) q^{32} +(4.24128 - 11.6528i) q^{34} +(2.06847 - 6.56331i) q^{35} +(-2.44933 + 0.656295i) q^{37} +(14.7241 + 1.28820i) q^{38} +(15.4762 - 9.86226i) q^{40} +(-1.62695 - 0.286875i) q^{41} +(0.732214 - 8.36925i) q^{43} +(-1.68769 + 2.92316i) q^{44} +(0.0884111 + 0.153133i) q^{46} +(3.71355 - 1.73166i) q^{47} +(-1.58841 + 1.89299i) q^{49} +(-6.65077 + 11.5264i) q^{50} +(1.36812 - 1.95387i) q^{52} +(-7.52870 - 7.52870i) q^{53} +(0.0645683 - 1.48328i) q^{55} +(-24.8736 + 4.38589i) q^{56} +(2.81598 - 6.03890i) q^{58} +(3.49452 + 2.93225i) q^{59} +(-5.84534 - 2.12753i) q^{61} +(4.83286 + 1.29496i) q^{62} +(-13.5701 - 7.83468i) q^{64} +(-0.136808 + 1.04021i) q^{65} +(-4.48268 + 3.13881i) q^{67} +(19.4024 - 13.5857i) q^{68} +(14.5290 - 11.1515i) q^{70} +(5.33043 + 3.07752i) q^{71} +(13.6146 + 3.64803i) q^{73} +(-6.34185 - 2.30824i) q^{74} +(21.6264 + 18.1467i) q^{76} +(-0.863572 + 1.85194i) q^{77} +(-5.34198 + 0.941936i) q^{79} +(26.0833 + 1.13543i) q^{80} +(-3.10910 - 3.10910i) q^{82} +(-3.25316 + 4.64599i) q^{83} +(-4.80950 + 9.24190i) q^{85} +(14.3727 - 17.1287i) q^{86} +(-4.93869 + 2.30295i) q^{88} +(3.08131 + 5.33699i) q^{89} +(0.721988 - 1.25052i) q^{91} +(-0.0294359 + 0.336454i) q^{92} +(10.7397 + 1.89370i) q^{94} +(-12.1238 - 2.68612i) q^{95} +(-13.5821 - 1.18828i) q^{97} +(-6.35281 + 1.70223i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{17}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.18018 + 1.52658i 1.54162 + 1.07945i 0.964936 + 0.262484i \(0.0845416\pi\)
0.576682 + 0.816969i \(0.304347\pi\)
\(3\) 0 0
\(4\) 1.73870 + 4.77703i 0.869348 + 2.38851i
\(5\) −1.64880 1.51045i −0.737365 0.675494i
\(6\) 0 0
\(7\) 1.30062 + 2.78918i 0.491587 + 1.05421i 0.983054 + 0.183315i \(0.0586829\pi\)
−0.491468 + 0.870896i \(0.663539\pi\)
\(8\) −2.12414 + 7.92739i −0.750996 + 2.80276i
\(9\) 0 0
\(10\) −1.28885 5.81007i −0.407571 1.83731i
\(11\) 0.426793 + 0.508631i 0.128683 + 0.153358i 0.826538 0.562880i \(-0.190307\pi\)
−0.697856 + 0.716238i \(0.745862\pi\)
\(12\) 0 0
\(13\) −0.269123 0.384347i −0.0746412 0.106599i 0.780096 0.625660i \(-0.215170\pi\)
−0.854737 + 0.519062i \(0.826282\pi\)
\(14\) −1.42232 + 8.06640i −0.380132 + 2.15584i
\(15\) 0 0
\(16\) −8.94423 + 7.50510i −2.23606 + 1.87627i
\(17\) −1.20591 4.50051i −0.292476 1.09153i −0.943201 0.332221i \(-0.892202\pi\)
0.650726 0.759313i \(-0.274465\pi\)
\(18\) 0 0
\(19\) 4.80938 2.77670i 1.10335 0.637018i 0.166249 0.986084i \(-0.446834\pi\)
0.937098 + 0.349066i \(0.113501\pi\)
\(20\) 4.34871 10.5026i 0.972401 2.34845i
\(21\) 0 0
\(22\) 0.154018 + 1.76044i 0.0328368 + 0.375327i
\(23\) 0.0602123 + 0.0280775i 0.0125551 + 0.00585456i 0.428886 0.903359i \(-0.358906\pi\)
−0.416331 + 0.909213i \(0.636684\pi\)
\(24\) 0 0
\(25\) 0.437073 + 4.98086i 0.0874146 + 0.996172i
\(26\) 1.24878i 0.244906i
\(27\) 0 0
\(28\) −11.0626 + 11.0626i −2.09064 + 2.09064i
\(29\) −0.434735 2.46551i −0.0807283 0.457833i −0.998197 0.0600247i \(-0.980882\pi\)
0.917469 0.397808i \(-0.130229\pi\)
\(30\) 0 0
\(31\) 1.76652 0.642961i 0.317276 0.115479i −0.178473 0.983945i \(-0.557116\pi\)
0.495749 + 0.868466i \(0.334893\pi\)
\(32\) −14.6055 + 1.27781i −2.58191 + 0.225888i
\(33\) 0 0
\(34\) 4.24128 11.6528i 0.727373 1.99844i
\(35\) 2.06847 6.56331i 0.349635 1.10940i
\(36\) 0 0
\(37\) −2.44933 + 0.656295i −0.402667 + 0.107894i −0.454468 0.890763i \(-0.650170\pi\)
0.0518010 + 0.998657i \(0.483504\pi\)
\(38\) 14.7241 + 1.28820i 2.38857 + 0.208973i
\(39\) 0 0
\(40\) 15.4762 9.86226i 2.44700 1.55936i
\(41\) −1.62695 0.286875i −0.254087 0.0448023i 0.0451539 0.998980i \(-0.485622\pi\)
−0.299241 + 0.954178i \(0.596733\pi\)
\(42\) 0 0
\(43\) 0.732214 8.36925i 0.111662 1.27630i −0.709133 0.705075i \(-0.750913\pi\)
0.820794 0.571224i \(-0.193531\pi\)
\(44\) −1.68769 + 2.92316i −0.254428 + 0.440682i
\(45\) 0 0
\(46\) 0.0884111 + 0.153133i 0.0130355 + 0.0225782i
\(47\) 3.71355 1.73166i 0.541677 0.252588i −0.132468 0.991187i \(-0.542290\pi\)
0.674145 + 0.738599i \(0.264512\pi\)
\(48\) 0 0
\(49\) −1.58841 + 1.89299i −0.226916 + 0.270428i
\(50\) −6.65077 + 11.5264i −0.940561 + 1.63008i
\(51\) 0 0
\(52\) 1.36812 1.95387i 0.189723 0.270953i
\(53\) −7.52870 7.52870i −1.03415 1.03415i −0.999396 0.0347509i \(-0.988936\pi\)
−0.0347509 0.999396i \(-0.511064\pi\)
\(54\) 0 0
\(55\) 0.0645683 1.48328i 0.00870639 0.200005i
\(56\) −24.8736 + 4.38589i −3.32388 + 0.586089i
\(57\) 0 0
\(58\) 2.81598 6.03890i 0.369757 0.792946i
\(59\) 3.49452 + 2.93225i 0.454948 + 0.381747i 0.841268 0.540618i \(-0.181810\pi\)
−0.386320 + 0.922365i \(0.626254\pi\)
\(60\) 0 0
\(61\) −5.84534 2.12753i −0.748419 0.272402i −0.0604785 0.998169i \(-0.519263\pi\)
−0.687940 + 0.725767i \(0.741485\pi\)
\(62\) 4.83286 + 1.29496i 0.613773 + 0.164460i
\(63\) 0 0
\(64\) −13.5701 7.83468i −1.69626 0.979335i
\(65\) −0.136808 + 1.04021i −0.0169690 + 0.129022i
\(66\) 0 0
\(67\) −4.48268 + 3.13881i −0.547646 + 0.383466i −0.814405 0.580297i \(-0.802936\pi\)
0.266758 + 0.963763i \(0.414047\pi\)
\(68\) 19.4024 13.5857i 2.35288 1.64751i
\(69\) 0 0
\(70\) 14.5290 11.1515i 1.73655 1.33286i
\(71\) 5.33043 + 3.07752i 0.632605 + 0.365235i 0.781760 0.623579i \(-0.214322\pi\)
−0.149155 + 0.988814i \(0.547655\pi\)
\(72\) 0 0
\(73\) 13.6146 + 3.64803i 1.59347 + 0.426970i 0.943063 0.332613i \(-0.107930\pi\)
0.650410 + 0.759583i \(0.274597\pi\)
\(74\) −6.34185 2.30824i −0.737225 0.268328i
\(75\) 0 0
\(76\) 21.6264 + 18.1467i 2.48072 + 2.08157i
\(77\) −0.863572 + 1.85194i −0.0984131 + 0.211048i
\(78\) 0 0
\(79\) −5.34198 + 0.941936i −0.601020 + 0.105976i −0.465876 0.884850i \(-0.654261\pi\)
−0.135144 + 0.990826i \(0.543150\pi\)
\(80\) 26.0833 + 1.13543i 2.91620 + 0.126945i
\(81\) 0 0
\(82\) −3.10910 3.10910i −0.343343 0.343343i
\(83\) −3.25316 + 4.64599i −0.357081 + 0.509964i −0.956997 0.290099i \(-0.906312\pi\)
0.599916 + 0.800063i \(0.295201\pi\)
\(84\) 0 0
\(85\) −4.80950 + 9.24190i −0.521664 + 1.00242i
\(86\) 14.3727 17.1287i 1.54984 1.84703i
\(87\) 0 0
\(88\) −4.93869 + 2.30295i −0.526466 + 0.245495i
\(89\) 3.08131 + 5.33699i 0.326619 + 0.565720i 0.981839 0.189718i \(-0.0607574\pi\)
−0.655220 + 0.755438i \(0.727424\pi\)
\(90\) 0 0
\(91\) 0.721988 1.25052i 0.0756849 0.131090i
\(92\) −0.0294359 + 0.336454i −0.00306891 + 0.0350778i
\(93\) 0 0
\(94\) 10.7397 + 1.89370i 1.10772 + 0.195320i
\(95\) −12.1238 2.68612i −1.24387 0.275590i
\(96\) 0 0
\(97\) −13.5821 1.18828i −1.37906 0.120652i −0.626625 0.779321i \(-0.715564\pi\)
−0.752433 + 0.658669i \(0.771120\pi\)
\(98\) −6.35281 + 1.70223i −0.641731 + 0.171951i
\(99\) 0 0
\(100\) −23.0338 + 10.7481i −2.30338 + 1.07481i
\(101\) 0.629841 1.73048i 0.0626716 0.172189i −0.904405 0.426676i \(-0.859684\pi\)
0.967076 + 0.254487i \(0.0819067\pi\)
\(102\) 0 0
\(103\) −16.2704 + 1.42347i −1.60317 + 0.140259i −0.853332 0.521368i \(-0.825422\pi\)
−0.749833 + 0.661627i \(0.769866\pi\)
\(104\) 3.61852 1.31704i 0.354826 0.129146i
\(105\) 0 0
\(106\) −4.92077 27.9071i −0.477947 2.71057i
\(107\) −10.4880 + 10.4880i −1.01391 + 1.01391i −0.0140087 + 0.999902i \(0.504459\pi\)
−0.999902 + 0.0140087i \(0.995541\pi\)
\(108\) 0 0
\(109\) 9.34913i 0.895484i 0.894163 + 0.447742i \(0.147772\pi\)
−0.894163 + 0.447742i \(0.852228\pi\)
\(110\) 2.40511 3.13525i 0.229318 0.298934i
\(111\) 0 0
\(112\) −32.5661 15.1858i −3.07721 1.43492i
\(113\) 1.81095 + 20.6993i 0.170360 + 1.94722i 0.296094 + 0.955159i \(0.404316\pi\)
−0.125734 + 0.992064i \(0.540129\pi\)
\(114\) 0 0
\(115\) −0.0568683 0.137242i −0.00530300 0.0127979i
\(116\) 11.0219 6.36351i 1.02336 0.590837i
\(117\) 0 0
\(118\) 3.14237 + 11.7275i 0.289278 + 1.07960i
\(119\) 10.9843 9.21693i 1.00693 0.844915i
\(120\) 0 0
\(121\) 1.83358 10.3987i 0.166689 0.945339i
\(122\) −9.49604 13.5617i −0.859731 1.22782i
\(123\) 0 0
\(124\) 6.14289 + 7.32081i 0.551648 + 0.657428i
\(125\) 6.80270 8.87261i 0.608452 0.793591i
\(126\) 0 0
\(127\) −1.97054 + 7.35416i −0.174857 + 0.652576i 0.821719 + 0.569893i \(0.193016\pi\)
−0.996576 + 0.0826829i \(0.973651\pi\)
\(128\) −5.23265 11.2214i −0.462505 0.991845i
\(129\) 0 0
\(130\) −1.88622 + 2.05899i −0.165433 + 0.180585i
\(131\) −4.01388 11.0280i −0.350694 0.963524i −0.982148 0.188111i \(-0.939764\pi\)
0.631454 0.775414i \(-0.282459\pi\)
\(132\) 0 0
\(133\) 13.9999 + 9.80281i 1.21394 + 0.850012i
\(134\) −14.5647 −1.25820
\(135\) 0 0
\(136\) 38.2388 3.27895
\(137\) −5.50755 3.85643i −0.470542 0.329477i 0.314139 0.949377i \(-0.398284\pi\)
−0.784681 + 0.619900i \(0.787173\pi\)
\(138\) 0 0
\(139\) −0.519349 1.42690i −0.0440506 0.121028i 0.915717 0.401824i \(-0.131624\pi\)
−0.959767 + 0.280796i \(0.909402\pi\)
\(140\) 34.9496 1.53048i 2.95378 0.129349i
\(141\) 0 0
\(142\) 6.92320 + 14.8468i 0.580982 + 1.24592i
\(143\) 0.0806315 0.300921i 0.00674274 0.0251643i
\(144\) 0 0
\(145\) −3.00724 + 4.72177i −0.249737 + 0.392122i
\(146\) 24.1133 + 28.7372i 1.99563 + 2.37830i
\(147\) 0 0
\(148\) −7.39377 10.5594i −0.607764 0.867978i
\(149\) −3.69731 + 20.9685i −0.302895 + 1.71780i 0.330355 + 0.943857i \(0.392832\pi\)
−0.633250 + 0.773947i \(0.718280\pi\)
\(150\) 0 0
\(151\) 6.08208 5.10347i 0.494952 0.415314i −0.360845 0.932626i \(-0.617512\pi\)
0.855797 + 0.517312i \(0.173067\pi\)
\(152\) 11.7962 + 44.0239i 0.956797 + 3.57081i
\(153\) 0 0
\(154\) −4.70986 + 2.71924i −0.379531 + 0.219123i
\(155\) −3.88380 1.60813i −0.311954 0.129168i
\(156\) 0 0
\(157\) −1.19160 13.6200i −0.0950997 1.08699i −0.882424 0.470455i \(-0.844090\pi\)
0.787324 0.616539i \(-0.211466\pi\)
\(158\) −13.0844 6.10136i −1.04094 0.485398i
\(159\) 0 0
\(160\) 26.0116 + 19.9540i 2.05640 + 1.57750i
\(161\) 0.204461i 0.0161138i
\(162\) 0 0
\(163\) 13.8462 13.8462i 1.08452 1.08452i 0.0884330 0.996082i \(-0.471814\pi\)
0.996082 0.0884330i \(-0.0281859\pi\)
\(164\) −1.45836 8.27077i −0.113879 0.645839i
\(165\) 0 0
\(166\) −14.1849 + 5.16289i −1.10096 + 0.400718i
\(167\) −21.8892 + 1.91506i −1.69384 + 0.148192i −0.892809 0.450435i \(-0.851269\pi\)
−0.801028 + 0.598627i \(0.795713\pi\)
\(168\) 0 0
\(169\) 4.37097 12.0091i 0.336228 0.923779i
\(170\) −24.5940 + 12.8069i −1.88628 + 0.982245i
\(171\) 0 0
\(172\) 41.2533 11.0538i 3.14553 0.842842i
\(173\) −3.73833 0.327061i −0.284220 0.0248660i −0.0558456 0.998439i \(-0.517785\pi\)
−0.228374 + 0.973573i \(0.573341\pi\)
\(174\) 0 0
\(175\) −13.3241 + 7.69726i −1.00720 + 0.581858i
\(176\) −7.63466 1.34620i −0.575484 0.101473i
\(177\) 0 0
\(178\) −1.42952 + 16.3394i −0.107147 + 1.22469i
\(179\) 7.21345 12.4941i 0.539158 0.933850i −0.459791 0.888027i \(-0.652076\pi\)
0.998950 0.0458226i \(-0.0145909\pi\)
\(180\) 0 0
\(181\) −7.06370 12.2347i −0.525041 0.909397i −0.999575 0.0291599i \(-0.990717\pi\)
0.474534 0.880237i \(-0.342617\pi\)
\(182\) 3.48308 1.62419i 0.258183 0.120393i
\(183\) 0 0
\(184\) −0.350480 + 0.417686i −0.0258378 + 0.0307922i
\(185\) 5.02975 + 2.61749i 0.369794 + 0.192442i
\(186\) 0 0
\(187\) 1.77443 2.53415i 0.129759 0.185315i
\(188\) 14.7289 + 14.7289i 1.07422 + 1.07422i
\(189\) 0 0
\(190\) −22.3314 24.3641i −1.62009 1.76756i
\(191\) 2.54718 0.449136i 0.184307 0.0324983i −0.0807326 0.996736i \(-0.525726\pi\)
0.265040 + 0.964237i \(0.414615\pi\)
\(192\) 0 0
\(193\) −6.02445 + 12.9195i −0.433649 + 0.929963i 0.561112 + 0.827740i \(0.310374\pi\)
−0.994761 + 0.102224i \(0.967404\pi\)
\(194\) −27.7975 23.3248i −1.99574 1.67463i
\(195\) 0 0
\(196\) −11.8046 4.29654i −0.843189 0.306896i
\(197\) 8.06170 + 2.16013i 0.574372 + 0.153903i 0.534301 0.845294i \(-0.320575\pi\)
0.0400711 + 0.999197i \(0.487242\pi\)
\(198\) 0 0
\(199\) 3.27312 + 1.88973i 0.232025 + 0.133960i 0.611506 0.791240i \(-0.290564\pi\)
−0.379481 + 0.925200i \(0.623897\pi\)
\(200\) −40.4136 7.11519i −2.85768 0.503120i
\(201\) 0 0
\(202\) 4.01487 2.81124i 0.282485 0.197798i
\(203\) 6.31132 4.41923i 0.442968 0.310169i
\(204\) 0 0
\(205\) 2.24920 + 2.93043i 0.157091 + 0.204670i
\(206\) −37.6453 21.7345i −2.62287 1.51432i
\(207\) 0 0
\(208\) 5.29166 + 1.41790i 0.366911 + 0.0983134i
\(209\) 3.46492 + 1.26113i 0.239674 + 0.0872341i
\(210\) 0 0
\(211\) −13.6392 11.4447i −0.938964 0.787885i 0.0384403 0.999261i \(-0.487761\pi\)
−0.977405 + 0.211376i \(0.932205\pi\)
\(212\) 22.8747 49.0550i 1.57104 3.36911i
\(213\) 0 0
\(214\) −38.8763 + 6.85495i −2.65753 + 0.468594i
\(215\) −13.8486 + 12.6932i −0.944468 + 0.865671i
\(216\) 0 0
\(217\) 4.09090 + 4.09090i 0.277708 + 0.277708i
\(218\) −14.2722 + 20.3828i −0.966633 + 1.38049i
\(219\) 0 0
\(220\) 7.19794 2.27053i 0.485285 0.153079i
\(221\) −1.40522 + 1.67468i −0.0945254 + 0.112651i
\(222\) 0 0
\(223\) −17.3515 + 8.09113i −1.16194 + 0.541822i −0.905337 0.424694i \(-0.860382\pi\)
−0.256605 + 0.966516i \(0.582604\pi\)
\(224\) −22.5602 39.0754i −1.50737 2.61083i
\(225\) 0 0
\(226\) −27.6508 + 47.8926i −1.83930 + 3.18577i
\(227\) 0.0420779 0.480953i 0.00279281 0.0319220i −0.994670 0.103106i \(-0.967122\pi\)
0.997463 + 0.0711836i \(0.0226776\pi\)
\(228\) 0 0
\(229\) 14.7979 + 2.60927i 0.977875 + 0.172426i 0.639672 0.768648i \(-0.279070\pi\)
0.338203 + 0.941073i \(0.390181\pi\)
\(230\) 0.0855272 0.386026i 0.00563950 0.0254538i
\(231\) 0 0
\(232\) 20.4685 + 1.79076i 1.34382 + 0.117569i
\(233\) 0.534587 0.143242i 0.0350220 0.00938411i −0.241266 0.970459i \(-0.577562\pi\)
0.276287 + 0.961075i \(0.410896\pi\)
\(234\) 0 0
\(235\) −8.73847 2.75398i −0.570035 0.179650i
\(236\) −7.93154 + 21.7917i −0.516299 + 1.41852i
\(237\) 0 0
\(238\) 38.0181 3.32615i 2.46435 0.215602i
\(239\) 5.32354 1.93761i 0.344351 0.125334i −0.164054 0.986451i \(-0.552457\pi\)
0.508406 + 0.861118i \(0.330235\pi\)
\(240\) 0 0
\(241\) 0.317967 + 1.80328i 0.0204821 + 0.116160i 0.993335 0.115266i \(-0.0367721\pi\)
−0.972853 + 0.231426i \(0.925661\pi\)
\(242\) 19.8720 19.8720i 1.27742 1.27742i
\(243\) 0 0
\(244\) 31.6225i 2.02442i
\(245\) 5.47824 0.721948i 0.349992 0.0461236i
\(246\) 0 0
\(247\) −2.36153 1.10120i −0.150261 0.0700677i
\(248\) 1.34467 + 15.3696i 0.0853866 + 0.975973i
\(249\) 0 0
\(250\) 28.3758 8.95902i 1.79464 0.566618i
\(251\) 16.8470 9.72663i 1.06337 0.613939i 0.137011 0.990570i \(-0.456251\pi\)
0.926364 + 0.376630i \(0.122917\pi\)
\(252\) 0 0
\(253\) 0.0114171 + 0.0426091i 0.000717786 + 0.00267881i
\(254\) −15.5228 + 13.0252i −0.973988 + 0.817273i
\(255\) 0 0
\(256\) 0.280392 1.59018i 0.0175245 0.0993864i
\(257\) 17.1627 + 24.5109i 1.07058 + 1.52895i 0.829553 + 0.558428i \(0.188595\pi\)
0.241027 + 0.970518i \(0.422516\pi\)
\(258\) 0 0
\(259\) −5.01616 5.97802i −0.311689 0.371456i
\(260\) −5.20697 + 1.15507i −0.322923 + 0.0716343i
\(261\) 0 0
\(262\) 8.08418 30.1706i 0.499442 1.86394i
\(263\) 3.54766 + 7.60797i 0.218758 + 0.469128i 0.984807 0.173655i \(-0.0555577\pi\)
−0.766049 + 0.642782i \(0.777780\pi\)
\(264\) 0 0
\(265\) 1.04157 + 23.7851i 0.0639834 + 1.46110i
\(266\) 15.5574 + 42.7437i 0.953888 + 2.62079i
\(267\) 0 0
\(268\) −22.7882 15.9565i −1.39201 0.974696i
\(269\) 2.21545 0.135079 0.0675393 0.997717i \(-0.478485\pi\)
0.0675393 + 0.997717i \(0.478485\pi\)
\(270\) 0 0
\(271\) −5.87725 −0.357017 −0.178509 0.983938i \(-0.557127\pi\)
−0.178509 + 0.983938i \(0.557127\pi\)
\(272\) 44.5627 + 31.2031i 2.70201 + 1.89197i
\(273\) 0 0
\(274\) −6.12031 16.8154i −0.369741 1.01586i
\(275\) −2.34688 + 2.34810i −0.141522 + 0.141596i
\(276\) 0 0
\(277\) 4.78156 + 10.2541i 0.287296 + 0.616108i 0.995996 0.0894020i \(-0.0284956\pi\)
−0.708700 + 0.705510i \(0.750718\pi\)
\(278\) 1.04600 3.90372i 0.0627348 0.234130i
\(279\) 0 0
\(280\) 47.6362 + 30.3389i 2.84681 + 1.81310i
\(281\) −13.9719 16.6511i −0.833496 0.993322i −0.999974 0.00727642i \(-0.997684\pi\)
0.166478 0.986045i \(-0.446761\pi\)
\(282\) 0 0
\(283\) −7.52820 10.7514i −0.447505 0.639103i 0.530500 0.847685i \(-0.322004\pi\)
−0.978005 + 0.208582i \(0.933115\pi\)
\(284\) −5.43342 + 30.8145i −0.322414 + 1.82850i
\(285\) 0 0
\(286\) 0.635170 0.532971i 0.0375584 0.0315152i
\(287\) −1.31589 4.91097i −0.0776745 0.289885i
\(288\) 0 0
\(289\) −4.07794 + 2.35440i −0.239879 + 0.138494i
\(290\) −13.7645 + 5.70352i −0.808276 + 0.334922i
\(291\) 0 0
\(292\) 6.24497 + 71.3804i 0.365460 + 4.17722i
\(293\) 3.86399 + 1.80181i 0.225736 + 0.105263i 0.532196 0.846621i \(-0.321367\pi\)
−0.306460 + 0.951884i \(0.599145\pi\)
\(294\) 0 0
\(295\) −1.33274 10.1130i −0.0775950 0.588801i
\(296\) 20.8108i 1.20960i
\(297\) 0 0
\(298\) −40.0708 + 40.0708i −2.32124 + 2.32124i
\(299\) −0.00541301 0.0306987i −0.000313043 0.00177535i
\(300\) 0 0
\(301\) 24.2957 8.84290i 1.40038 0.509696i
\(302\) 21.0508 1.84171i 1.21134 0.105978i
\(303\) 0 0
\(304\) −22.1768 + 60.9303i −1.27193 + 3.49459i
\(305\) 6.42425 + 12.3370i 0.367852 + 0.706413i
\(306\) 0 0
\(307\) 17.9955 4.82189i 1.02706 0.275200i 0.294318 0.955707i \(-0.404907\pi\)
0.732741 + 0.680508i \(0.238241\pi\)
\(308\) −10.3482 0.905354i −0.589646 0.0515873i
\(309\) 0 0
\(310\) −6.01243 9.43492i −0.341483 0.535868i
\(311\) 8.07539 + 1.42391i 0.457913 + 0.0807425i 0.397847 0.917452i \(-0.369758\pi\)
0.0600667 + 0.998194i \(0.480869\pi\)
\(312\) 0 0
\(313\) −1.66176 + 18.9940i −0.0939283 + 1.07360i 0.792230 + 0.610222i \(0.208920\pi\)
−0.886158 + 0.463382i \(0.846636\pi\)
\(314\) 18.1941 31.5131i 1.02675 1.77839i
\(315\) 0 0
\(316\) −13.7877 23.8811i −0.775621 1.34342i
\(317\) −15.3899 + 7.17642i −0.864382 + 0.403068i −0.803661 0.595087i \(-0.797118\pi\)
−0.0607206 + 0.998155i \(0.519340\pi\)
\(318\) 0 0
\(319\) 1.06849 1.27338i 0.0598241 0.0712956i
\(320\) 10.5404 + 33.4147i 0.589226 + 1.86794i
\(321\) 0 0
\(322\) −0.312125 + 0.445761i −0.0173941 + 0.0248413i
\(323\) −18.2962 18.2962i −1.01803 1.01803i
\(324\) 0 0
\(325\) 1.79675 1.50845i 0.0996659 0.0836738i
\(326\) 51.3243 9.04986i 2.84259 0.501225i
\(327\) 0 0
\(328\) 5.73003 12.2881i 0.316388 0.678497i
\(329\) 9.65980 + 8.10554i 0.532562 + 0.446873i
\(330\) 0 0
\(331\) 13.3657 + 4.86470i 0.734643 + 0.267388i 0.682129 0.731232i \(-0.261054\pi\)
0.0525142 + 0.998620i \(0.483277\pi\)
\(332\) −27.8503 7.46247i −1.52848 0.409556i
\(333\) 0 0
\(334\) −50.6458 29.2404i −2.77122 1.59996i
\(335\) 12.1320 + 1.59561i 0.662845 + 0.0871775i
\(336\) 0 0
\(337\) 5.58245 3.90887i 0.304095 0.212930i −0.411561 0.911382i \(-0.635016\pi\)
0.715657 + 0.698452i \(0.246128\pi\)
\(338\) 27.8623 19.5094i 1.51551 1.06117i
\(339\) 0 0
\(340\) −52.5111 6.90628i −2.84781 0.374545i
\(341\) 1.08097 + 0.624097i 0.0585377 + 0.0337968i
\(342\) 0 0
\(343\) 13.4628 + 3.60734i 0.726922 + 0.194778i
\(344\) 64.7910 + 23.5820i 3.49330 + 1.27146i
\(345\) 0 0
\(346\) −7.65094 6.41990i −0.411317 0.345136i
\(347\) −5.81216 + 12.4642i −0.312013 + 0.669114i −0.998304 0.0582130i \(-0.981460\pi\)
0.686291 + 0.727327i \(0.259238\pi\)
\(348\) 0 0
\(349\) 26.3484 4.64594i 1.41040 0.248691i 0.583990 0.811761i \(-0.301491\pi\)
0.826409 + 0.563070i \(0.190380\pi\)
\(350\) −40.7993 3.55879i −2.18081 0.190225i
\(351\) 0 0
\(352\) −6.88345 6.88345i −0.366889 0.366889i
\(353\) 0.0271374 0.0387563i 0.00144438 0.00206279i −0.818429 0.574607i \(-0.805155\pi\)
0.819874 + 0.572545i \(0.194044\pi\)
\(354\) 0 0
\(355\) −4.14035 13.1256i −0.219747 0.696633i
\(356\) −20.1375 + 23.9989i −1.06729 + 1.27194i
\(357\) 0 0
\(358\) 34.7997 16.2274i 1.83922 0.857644i
\(359\) 9.42597 + 16.3263i 0.497484 + 0.861667i 0.999996 0.00290290i \(-0.000924023\pi\)
−0.502512 + 0.864570i \(0.667591\pi\)
\(360\) 0 0
\(361\) 5.92010 10.2539i 0.311584 0.539680i
\(362\) 3.27707 37.4571i 0.172239 1.96870i
\(363\) 0 0
\(364\) 7.22909 + 1.27468i 0.378907 + 0.0668116i
\(365\) −16.9376 26.5791i −0.886556 1.39122i
\(366\) 0 0
\(367\) −19.7504 1.72794i −1.03096 0.0901977i −0.440902 0.897555i \(-0.645341\pi\)
−0.590063 + 0.807357i \(0.700897\pi\)
\(368\) −0.749277 + 0.200768i −0.0390588 + 0.0104658i
\(369\) 0 0
\(370\) 6.96994 + 13.3849i 0.362350 + 0.695847i
\(371\) 11.2070 30.7909i 0.581836 1.59858i
\(372\) 0 0
\(373\) 21.1273 1.84840i 1.09393 0.0957063i 0.474120 0.880460i \(-0.342766\pi\)
0.619808 + 0.784754i \(0.287211\pi\)
\(374\) 7.73714 2.81609i 0.400078 0.145616i
\(375\) 0 0
\(376\) 5.83943 + 33.1170i 0.301145 + 1.70788i
\(377\) −0.830613 + 0.830613i −0.0427788 + 0.0427788i
\(378\) 0 0
\(379\) 4.95221i 0.254378i 0.991878 + 0.127189i \(0.0405955\pi\)
−0.991878 + 0.127189i \(0.959405\pi\)
\(380\) −8.24787 62.5860i −0.423107 3.21059i
\(381\) 0 0
\(382\) 6.23894 + 2.90926i 0.319212 + 0.148851i
\(383\) −2.46502 28.1753i −0.125957 1.43969i −0.751620 0.659596i \(-0.770727\pi\)
0.625663 0.780093i \(-0.284828\pi\)
\(384\) 0 0
\(385\) 4.22111 1.74909i 0.215128 0.0891416i
\(386\) −32.8569 + 18.9699i −1.67237 + 0.965545i
\(387\) 0 0
\(388\) −17.9388 66.9484i −0.910703 3.39879i
\(389\) −22.5434 + 18.9162i −1.14300 + 0.959088i −0.999533 0.0305681i \(-0.990268\pi\)
−0.143463 + 0.989656i \(0.545824\pi\)
\(390\) 0 0
\(391\) 0.0537524 0.304845i 0.00271838 0.0154167i
\(392\) −11.6325 16.6129i −0.587530 0.839080i
\(393\) 0 0
\(394\) 14.2783 + 17.0163i 0.719332 + 0.857267i
\(395\) 10.2306 + 6.51574i 0.514757 + 0.327843i
\(396\) 0 0
\(397\) −5.07320 + 18.9334i −0.254616 + 0.950242i 0.713687 + 0.700465i \(0.247024\pi\)
−0.968303 + 0.249777i \(0.919643\pi\)
\(398\) 4.25115 + 9.11662i 0.213091 + 0.456975i
\(399\) 0 0
\(400\) −41.2911 41.2697i −2.06456 2.06348i
\(401\) 0.0115561 + 0.0317502i 0.000577086 + 0.00158553i 0.939981 0.341227i \(-0.110843\pi\)
−0.939404 + 0.342813i \(0.888620\pi\)
\(402\) 0 0
\(403\) −0.722531 0.505922i −0.0359918 0.0252018i
\(404\) 9.36163 0.465759
\(405\) 0 0
\(406\) 20.5061 1.01770
\(407\) −1.37917 0.965702i −0.0683627 0.0478681i
\(408\) 0 0
\(409\) 3.01485 + 8.28322i 0.149075 + 0.409579i 0.991643 0.129010i \(-0.0411799\pi\)
−0.842569 + 0.538589i \(0.818958\pi\)
\(410\) 0.430135 + 9.82242i 0.0212428 + 0.485095i
\(411\) 0 0
\(412\) −35.0892 75.2490i −1.72872 3.70725i
\(413\) −3.63355 + 13.5606i −0.178795 + 0.667272i
\(414\) 0 0
\(415\) 12.3814 2.74657i 0.607777 0.134824i
\(416\) 4.42180 + 5.26969i 0.216796 + 0.258368i
\(417\) 0 0
\(418\) 5.62894 + 8.03896i 0.275320 + 0.393198i
\(419\) 5.75122 32.6168i 0.280966 1.59344i −0.438384 0.898788i \(-0.644449\pi\)
0.719350 0.694648i \(-0.244440\pi\)
\(420\) 0 0
\(421\) 12.7180 10.6716i 0.619835 0.520104i −0.277916 0.960605i \(-0.589644\pi\)
0.897752 + 0.440502i \(0.145199\pi\)
\(422\) −12.2648 45.7728i −0.597040 2.22819i
\(423\) 0 0
\(424\) 75.6750 43.6910i 3.67510 2.12182i
\(425\) 21.8893 7.97351i 1.06179 0.386772i
\(426\) 0 0
\(427\) −1.66848 19.0708i −0.0807433 0.922901i
\(428\) −68.3368 31.8660i −3.30318 1.54030i
\(429\) 0 0
\(430\) −49.5696 + 6.53252i −2.39046 + 0.315026i
\(431\) 14.4385i 0.695480i 0.937591 + 0.347740i \(0.113051\pi\)
−0.937591 + 0.347740i \(0.886949\pi\)
\(432\) 0 0
\(433\) 16.4822 16.4822i 0.792085 0.792085i −0.189748 0.981833i \(-0.560767\pi\)
0.981833 + 0.189748i \(0.0607670\pi\)
\(434\) 2.67381 + 15.1640i 0.128347 + 0.727893i
\(435\) 0 0
\(436\) −44.6611 + 16.2553i −2.13888 + 0.778488i
\(437\) 0.367547 0.0321562i 0.0175821 0.00153824i
\(438\) 0 0
\(439\) −10.9388 + 30.0541i −0.522080 + 1.43440i 0.346121 + 0.938190i \(0.387499\pi\)
−0.868201 + 0.496213i \(0.834723\pi\)
\(440\) 11.6214 + 3.66255i 0.554028 + 0.174605i
\(441\) 0 0
\(442\) −5.62015 + 1.50592i −0.267323 + 0.0716291i
\(443\) −17.8910 1.56526i −0.850027 0.0743677i −0.346188 0.938165i \(-0.612524\pi\)
−0.503839 + 0.863798i \(0.668080\pi\)
\(444\) 0 0
\(445\) 2.98080 13.4538i 0.141304 0.637771i
\(446\) −50.1811 8.84827i −2.37614 0.418978i
\(447\) 0 0
\(448\) 4.20289 48.0392i 0.198568 2.26964i
\(449\) 6.63475 11.4917i 0.313113 0.542328i −0.665921 0.746022i \(-0.731961\pi\)
0.979035 + 0.203694i \(0.0652947\pi\)
\(450\) 0 0
\(451\) −0.548456 0.949953i −0.0258258 0.0447316i
\(452\) −95.7323 + 44.6407i −4.50287 + 2.09972i
\(453\) 0 0
\(454\) 0.825948 0.984327i 0.0387637 0.0461968i
\(455\) −3.07926 + 0.971328i −0.144358 + 0.0455365i
\(456\) 0 0
\(457\) −4.61784 + 6.59496i −0.216013 + 0.308499i −0.912505 0.409066i \(-0.865855\pi\)
0.696491 + 0.717565i \(0.254743\pi\)
\(458\) 28.2789 + 28.2789i 1.32138 + 1.32138i
\(459\) 0 0
\(460\) 0.556732 0.510284i 0.0259578 0.0237921i
\(461\) 14.1578 2.49640i 0.659393 0.116269i 0.166068 0.986114i \(-0.446893\pi\)
0.493324 + 0.869846i \(0.335782\pi\)
\(462\) 0 0
\(463\) 8.79261 18.8558i 0.408627 0.876304i −0.589044 0.808101i \(-0.700496\pi\)
0.997671 0.0682032i \(-0.0217266\pi\)
\(464\) 22.3922 + 18.7893i 1.03953 + 0.872272i
\(465\) 0 0
\(466\) 1.38417 + 0.503795i 0.0641202 + 0.0233378i
\(467\) 23.8222 + 6.38314i 1.10236 + 0.295376i 0.763725 0.645542i \(-0.223368\pi\)
0.338635 + 0.940918i \(0.390035\pi\)
\(468\) 0 0
\(469\) −14.5849 8.42062i −0.673470 0.388828i
\(470\) −14.8473 19.3441i −0.684853 0.892278i
\(471\) 0 0
\(472\) −30.6679 + 21.4739i −1.41161 + 0.988418i
\(473\) 4.56937 3.19951i 0.210100 0.147113i
\(474\) 0 0
\(475\) 15.9324 + 22.7412i 0.731028 + 1.04344i
\(476\) 63.1279 + 36.4469i 2.89346 + 1.67054i
\(477\) 0 0
\(478\) 14.5642 + 3.90246i 0.666150 + 0.178494i
\(479\) −25.2593 9.19362i −1.15412 0.420067i −0.307130 0.951668i \(-0.599368\pi\)
−0.846995 + 0.531601i \(0.821591\pi\)
\(480\) 0 0
\(481\) 0.911414 + 0.764768i 0.0415569 + 0.0348704i
\(482\) −2.05962 + 4.41687i −0.0938132 + 0.201183i
\(483\) 0 0
\(484\) 52.8631 9.32118i 2.40287 0.423690i
\(485\) 20.5994 + 22.4744i 0.935369 + 1.02051i
\(486\) 0 0
\(487\) 1.39406 + 1.39406i 0.0631711 + 0.0631711i 0.737987 0.674815i \(-0.235777\pi\)
−0.674815 + 0.737987i \(0.735777\pi\)
\(488\) 29.2821 41.8191i 1.32554 1.89306i
\(489\) 0 0
\(490\) 13.0456 + 6.78898i 0.589342 + 0.306695i
\(491\) 15.2423 18.1651i 0.687875 0.819777i −0.303222 0.952920i \(-0.598062\pi\)
0.991097 + 0.133143i \(0.0425068\pi\)
\(492\) 0 0
\(493\) −10.5718 + 4.92970i −0.476129 + 0.222023i
\(494\) −3.46749 6.00587i −0.156010 0.270217i
\(495\) 0 0
\(496\) −10.9747 + 19.0087i −0.492778 + 0.853516i
\(497\) −1.65093 + 18.8702i −0.0740542 + 0.846444i
\(498\) 0 0
\(499\) 30.8900 + 5.44673i 1.38282 + 0.243829i 0.815067 0.579366i \(-0.196700\pi\)
0.567758 + 0.823196i \(0.307811\pi\)
\(500\) 54.2126 + 17.0699i 2.42446 + 0.763390i
\(501\) 0 0
\(502\) 51.5779 + 4.51248i 2.30204 + 0.201402i
\(503\) 5.95437 1.59547i 0.265492 0.0711385i −0.123617 0.992330i \(-0.539449\pi\)
0.389109 + 0.921192i \(0.372783\pi\)
\(504\) 0 0
\(505\) −3.65228 + 1.90186i −0.162524 + 0.0846317i
\(506\) −0.0401548 + 0.110325i −0.00178510 + 0.00490452i
\(507\) 0 0
\(508\) −38.5572 + 3.37332i −1.71070 + 0.149667i
\(509\) −18.3832 + 6.69092i −0.814819 + 0.296570i −0.715613 0.698497i \(-0.753853\pi\)
−0.0992061 + 0.995067i \(0.531630\pi\)
\(510\) 0 0
\(511\) 7.53240 + 42.7184i 0.333214 + 1.88975i
\(512\) −14.4712 + 14.4712i −0.639545 + 0.639545i
\(513\) 0 0
\(514\) 79.6382i 3.51269i
\(515\) 28.9766 + 22.2286i 1.27686 + 0.979507i
\(516\) 0 0
\(517\) 2.46569 + 1.14977i 0.108441 + 0.0505668i
\(518\) −1.81020 20.6907i −0.0795357 0.909097i
\(519\) 0 0
\(520\) −7.95554 3.29408i −0.348873 0.144455i
\(521\) −1.02507 + 0.591824i −0.0449091 + 0.0259283i −0.522286 0.852770i \(-0.674921\pi\)
0.477377 + 0.878698i \(0.341587\pi\)
\(522\) 0 0
\(523\) −11.5734 43.1925i −0.506069 1.88868i −0.456106 0.889926i \(-0.650756\pi\)
−0.0499636 0.998751i \(-0.515911\pi\)
\(524\) 45.7023 38.3488i 1.99652 1.67528i
\(525\) 0 0
\(526\) −3.87963 + 22.0025i −0.169160 + 0.959354i
\(527\) −5.02391 7.17489i −0.218845 0.312543i
\(528\) 0 0
\(529\) −14.7813 17.6156i −0.642664 0.765897i
\(530\) −34.0389 + 53.4457i −1.47856 + 2.32153i
\(531\) 0 0
\(532\) −22.4868 + 83.9219i −0.974927 + 3.63848i
\(533\) 0.327589 + 0.702518i 0.0141895 + 0.0304294i
\(534\) 0 0
\(535\) 33.1341 1.45098i 1.43251 0.0627313i
\(536\) −15.3607 42.2032i −0.663482 1.82290i
\(537\) 0 0
\(538\) 4.83008 + 3.38206i 0.208240 + 0.145811i
\(539\) −1.64076 −0.0706724
\(540\) 0 0
\(541\) −0.781277 −0.0335897 −0.0167949 0.999859i \(-0.505346\pi\)
−0.0167949 + 0.999859i \(0.505346\pi\)
\(542\) −12.8134 8.97207i −0.550384 0.385383i
\(543\) 0 0
\(544\) 23.3637 + 64.1912i 1.00171 + 2.75218i
\(545\) 14.1214 15.4148i 0.604895 0.660299i
\(546\) 0 0
\(547\) −4.68743 10.0522i −0.200420 0.429802i 0.780251 0.625467i \(-0.215091\pi\)
−0.980671 + 0.195665i \(0.937314\pi\)
\(548\) 8.84632 33.0149i 0.377896 1.41033i
\(549\) 0 0
\(550\) −8.70118 + 1.53658i −0.371020 + 0.0655202i
\(551\) −8.93677 10.6504i −0.380719 0.453724i
\(552\) 0 0
\(553\) −9.57510 13.6747i −0.407175 0.581505i
\(554\) −5.22900 + 29.6551i −0.222159 + 1.25993i
\(555\) 0 0
\(556\) 5.91335 4.96189i 0.250782 0.210431i
\(557\) −3.48849 13.0192i −0.147812 0.551642i −0.999614 0.0277782i \(-0.991157\pi\)
0.851802 0.523864i \(-0.175510\pi\)
\(558\) 0 0
\(559\) −3.41375 + 1.97093i −0.144386 + 0.0833615i
\(560\) 30.7575 + 74.2278i 1.29974 + 3.13670i
\(561\) 0 0
\(562\) −5.04211 57.6316i −0.212689 2.43104i
\(563\) 34.0720 + 15.8881i 1.43596 + 0.669601i 0.975887 0.218277i \(-0.0700436\pi\)
0.460078 + 0.887878i \(0.347821\pi\)
\(564\) 0 0
\(565\) 28.2793 36.8643i 1.18972 1.55089i
\(566\) 34.9323i 1.46831i
\(567\) 0 0
\(568\) −35.7193 + 35.7193i −1.49875 + 1.49875i
\(569\) −2.09817 11.8993i −0.0879598 0.498845i −0.996679 0.0814360i \(-0.974049\pi\)
0.908719 0.417409i \(-0.137062\pi\)
\(570\) 0 0
\(571\) 0.672547 0.244787i 0.0281452 0.0102440i −0.327909 0.944709i \(-0.606344\pi\)
0.356054 + 0.934465i \(0.384122\pi\)
\(572\) 1.57770 0.138031i 0.0659670 0.00577137i
\(573\) 0 0
\(574\) 4.62809 12.7156i 0.193173 0.530738i
\(575\) −0.113533 + 0.312181i −0.00473464 + 0.0130189i
\(576\) 0 0
\(577\) −36.1045 + 9.67417i −1.50305 + 0.402741i −0.914120 0.405443i \(-0.867117\pi\)
−0.588930 + 0.808184i \(0.700451\pi\)
\(578\) −12.4848 1.09228i −0.519300 0.0454328i
\(579\) 0 0
\(580\) −27.7847 6.15593i −1.15370 0.255611i
\(581\) −17.1896 3.03100i −0.713146 0.125747i
\(582\) 0 0
\(583\) 0.616142 7.04253i 0.0255180 0.291672i
\(584\) −57.8388 + 100.180i −2.39339 + 4.14547i
\(585\) 0 0
\(586\) 5.67358 + 9.82693i 0.234373 + 0.405947i
\(587\) 8.34577 3.89170i 0.344467 0.160628i −0.242683 0.970106i \(-0.578028\pi\)
0.587150 + 0.809478i \(0.300250\pi\)
\(588\) 0 0
\(589\) 6.71056 7.99734i 0.276504 0.329525i
\(590\) 12.5327 24.0826i 0.515961 0.991467i
\(591\) 0 0
\(592\) 16.9818 24.2525i 0.697946 0.996771i
\(593\) −9.96484 9.96484i −0.409207 0.409207i 0.472255 0.881462i \(-0.343440\pi\)
−0.881462 + 0.472255i \(0.843440\pi\)
\(594\) 0 0
\(595\) −32.0326 1.39441i −1.31321 0.0571651i
\(596\) −106.595 + 18.7957i −4.36632 + 0.769900i
\(597\) 0 0
\(598\) 0.0350626 0.0751920i 0.00143382 0.00307483i
\(599\) 5.73610 + 4.81316i 0.234371 + 0.196660i 0.752407 0.658698i \(-0.228893\pi\)
−0.518037 + 0.855358i \(0.673337\pi\)
\(600\) 0 0
\(601\) −20.4882 7.45708i −0.835730 0.304181i −0.111522 0.993762i \(-0.535572\pi\)
−0.724208 + 0.689581i \(0.757795\pi\)
\(602\) 66.4682 + 17.8101i 2.70904 + 0.725886i
\(603\) 0 0
\(604\) 34.9543 + 20.1809i 1.42227 + 0.821148i
\(605\) −18.7300 + 14.3759i −0.761481 + 0.584462i
\(606\) 0 0
\(607\) −18.7469 + 13.1267i −0.760912 + 0.532796i −0.888415 0.459042i \(-0.848193\pi\)
0.127503 + 0.991838i \(0.459304\pi\)
\(608\) −66.6953 + 46.7005i −2.70485 + 1.89396i
\(609\) 0 0
\(610\) −4.82731 + 36.7039i −0.195452 + 1.48610i
\(611\) −1.66496 0.961264i −0.0673570 0.0388886i
\(612\) 0 0
\(613\) −14.4667 3.87633i −0.584303 0.156564i −0.0454549 0.998966i \(-0.514474\pi\)
−0.538848 + 0.842403i \(0.681140\pi\)
\(614\) 46.5944 + 16.9590i 1.88040 + 0.684409i
\(615\) 0 0
\(616\) −12.8467 10.7796i −0.517607 0.434324i
\(617\) −0.200538 + 0.430054i −0.00807334 + 0.0173133i −0.910303 0.413942i \(-0.864152\pi\)
0.902230 + 0.431256i \(0.141929\pi\)
\(618\) 0 0
\(619\) −10.1152 + 1.78359i −0.406565 + 0.0716885i −0.373191 0.927754i \(-0.621736\pi\)
−0.0333743 + 0.999443i \(0.510625\pi\)
\(620\) 0.929342 21.3491i 0.0373233 0.857399i
\(621\) 0 0
\(622\) 15.4321 + 15.4321i 0.618770 + 0.618770i
\(623\) −10.8782 + 15.5357i −0.435827 + 0.622425i
\(624\) 0 0
\(625\) −24.6179 + 4.35400i −0.984717 + 0.174160i
\(626\) −32.6187 + 38.8735i −1.30371 + 1.55370i
\(627\) 0 0
\(628\) 62.9913 29.3733i 2.51363 1.17212i
\(629\) 5.90732 + 10.2318i 0.235540 + 0.407968i
\(630\) 0 0
\(631\) −6.48152 + 11.2263i −0.258025 + 0.446913i −0.965713 0.259613i \(-0.916405\pi\)
0.707688 + 0.706526i \(0.249738\pi\)
\(632\) 3.88002 44.3488i 0.154339 1.76410i
\(633\) 0 0
\(634\) −44.5080 7.84797i −1.76764 0.311683i
\(635\) 14.3571 9.14912i 0.569745 0.363072i
\(636\) 0 0
\(637\) 1.15504 + 0.101053i 0.0457645 + 0.00400388i
\(638\) 4.27341 1.14506i 0.169186 0.0453333i
\(639\) 0 0
\(640\) −8.32187 + 26.4056i −0.328951 + 1.04377i
\(641\) −16.0051 + 43.9737i −0.632164 + 1.73686i 0.0428806 + 0.999080i \(0.486347\pi\)
−0.675045 + 0.737777i \(0.735876\pi\)
\(642\) 0 0
\(643\) −22.0886 + 1.93250i −0.871088 + 0.0762103i −0.513928 0.857833i \(-0.671810\pi\)
−0.357160 + 0.934043i \(0.616255\pi\)
\(644\) −0.976716 + 0.355496i −0.0384880 + 0.0140085i
\(645\) 0 0
\(646\) −11.9584 67.8196i −0.470498 2.66833i
\(647\) 23.9696 23.9696i 0.942341 0.942341i −0.0560849 0.998426i \(-0.517862\pi\)
0.998426 + 0.0560849i \(0.0178617\pi\)
\(648\) 0 0
\(649\) 3.02889i 0.118894i
\(650\) 6.22001 0.545809i 0.243969 0.0214084i
\(651\) 0 0
\(652\) 90.2178 + 42.0693i 3.53320 + 1.64756i
\(653\) 0.846075 + 9.67068i 0.0331095 + 0.378443i 0.994614 + 0.103652i \(0.0330530\pi\)
−0.961504 + 0.274791i \(0.911391\pi\)
\(654\) 0 0
\(655\) −10.0392 + 24.2458i −0.392266 + 0.947361i
\(656\) 16.7048 9.64453i 0.652214 0.376556i
\(657\) 0 0
\(658\) 8.68636 + 32.4179i 0.338629 + 1.26378i
\(659\) 15.9731 13.4030i 0.622224 0.522108i −0.276278 0.961078i \(-0.589101\pi\)
0.898502 + 0.438970i \(0.144657\pi\)
\(660\) 0 0
\(661\) −6.68365 + 37.9049i −0.259964 + 1.47433i 0.523038 + 0.852310i \(0.324799\pi\)
−0.783002 + 0.622020i \(0.786312\pi\)
\(662\) 21.7132 + 31.0096i 0.843906 + 1.20522i
\(663\) 0 0
\(664\) −29.9205 35.6578i −1.16114 1.38379i
\(665\) −8.27629 37.3090i −0.320941 1.44678i
\(666\) 0 0
\(667\) 0.0430488 0.160660i 0.00166685 0.00622079i
\(668\) −47.2070 101.236i −1.82649 3.91693i
\(669\) 0 0
\(670\) 24.0142 + 21.9992i 0.927749 + 0.849904i
\(671\) −1.41262 3.88114i −0.0545335 0.149830i
\(672\) 0 0
\(673\) 16.8631 + 11.8077i 0.650026 + 0.455153i 0.851510 0.524339i \(-0.175687\pi\)
−0.201484 + 0.979492i \(0.564576\pi\)
\(674\) 18.1379 0.698646
\(675\) 0 0
\(676\) 64.9678 2.49876
\(677\) −18.5670 13.0007i −0.713588 0.499659i 0.159515 0.987195i \(-0.449007\pi\)
−0.873103 + 0.487536i \(0.837896\pi\)
\(678\) 0 0
\(679\) −14.3508 39.4285i −0.550734 1.51313i
\(680\) −63.0481 57.7579i −2.41778 2.21491i
\(681\) 0 0
\(682\) 1.40397 + 3.01082i 0.0537608 + 0.115290i
\(683\) −2.12172 + 7.91835i −0.0811852 + 0.302987i −0.994564 0.104122i \(-0.966797\pi\)
0.913379 + 0.407110i \(0.133463\pi\)
\(684\) 0 0
\(685\) 3.25589 + 14.6774i 0.124401 + 0.560793i
\(686\) 23.8444 + 28.4166i 0.910382 + 1.08495i
\(687\) 0 0
\(688\) 56.2630 + 80.3518i 2.14500 + 3.06338i
\(689\) −0.867490 + 4.91978i −0.0330487 + 0.187429i
\(690\) 0 0
\(691\) 2.09562 1.75844i 0.0797212 0.0668941i −0.602056 0.798454i \(-0.705652\pi\)
0.681777 + 0.731560i \(0.261207\pi\)
\(692\) −4.93744 18.4268i −0.187693 0.700481i
\(693\) 0 0
\(694\) −31.6991 + 18.3015i −1.20328 + 0.694715i
\(695\) −1.29896 + 3.13712i −0.0492724 + 0.118998i
\(696\) 0 0
\(697\) 0.670867 + 7.66804i 0.0254109 + 0.290448i
\(698\) 64.5366 + 30.0939i 2.44275 + 1.13907i
\(699\) 0 0
\(700\) −59.9365 50.2662i −2.26539 1.89988i
\(701\) 45.2015i 1.70724i 0.520899 + 0.853618i \(0.325597\pi\)
−0.520899 + 0.853618i \(0.674403\pi\)
\(702\) 0 0
\(703\) −9.95741 + 9.95741i −0.375551 + 0.375551i
\(704\) −1.80664 10.2459i −0.0680901 0.386158i
\(705\) 0 0
\(706\) 0.118329 0.0430682i 0.00445337 0.00162089i
\(707\) 5.64579 0.493942i 0.212332 0.0185766i
\(708\) 0 0
\(709\) −6.90171 + 18.9623i −0.259199 + 0.712144i 0.740018 + 0.672587i \(0.234817\pi\)
−0.999217 + 0.0395569i \(0.987405\pi\)
\(710\) 11.0105 34.9366i 0.413216 1.31115i
\(711\) 0 0
\(712\) −48.8536 + 13.0903i −1.83086 + 0.490579i
\(713\) 0.124419 + 0.0108853i 0.00465953 + 0.000407656i
\(714\) 0 0
\(715\) −0.587471 + 0.374368i −0.0219702 + 0.0140006i
\(716\) 72.2265 + 12.7355i 2.69923 + 0.475947i
\(717\) 0 0
\(718\) −4.37300 + 49.9836i −0.163199 + 1.86537i
\(719\) −18.2157 + 31.5505i −0.679331 + 1.17664i 0.295852 + 0.955234i \(0.404396\pi\)
−0.975183 + 0.221402i \(0.928937\pi\)
\(720\) 0 0
\(721\) −25.1318 43.5295i −0.935957 1.62113i
\(722\) 28.5603 13.3179i 1.06290 0.495640i
\(723\) 0 0
\(724\) 46.1638 55.0159i 1.71566 2.04465i
\(725\) 12.0903 3.24296i 0.449024 0.120441i
\(726\) 0 0
\(727\) −7.67153 + 10.9561i −0.284521 + 0.406338i −0.935817 0.352485i \(-0.885337\pi\)
0.651296 + 0.758824i \(0.274226\pi\)
\(728\) 8.37976 + 8.37976i 0.310575 + 0.310575i
\(729\) 0 0
\(730\) 3.64805 83.8038i 0.135020 3.10172i
\(731\) −38.5489 + 6.79721i −1.42578 + 0.251404i
\(732\) 0 0
\(733\) −17.7462 + 38.0568i −0.655470 + 1.40566i 0.244474 + 0.969656i \(0.421385\pi\)
−0.899944 + 0.436005i \(0.856393\pi\)
\(734\) −40.4216 33.9178i −1.49199 1.25193i
\(735\) 0 0
\(736\) −0.915308 0.333145i −0.0337387 0.0122799i
\(737\) −3.50967 0.940413i −0.129280 0.0346406i
\(738\) 0 0
\(739\) 34.0711 + 19.6709i 1.25332 + 0.723607i 0.971768 0.235938i \(-0.0758162\pi\)
0.281556 + 0.959545i \(0.409150\pi\)
\(740\) −3.75862 + 28.5783i −0.138170 + 1.05056i
\(741\) 0 0
\(742\) 71.4378 50.0213i 2.62256 1.83634i
\(743\) −10.6136 + 7.43173i −0.389376 + 0.272644i −0.751829 0.659358i \(-0.770828\pi\)
0.362453 + 0.932002i \(0.381939\pi\)
\(744\) 0 0
\(745\) 37.7680 28.9882i 1.38371 1.06204i
\(746\) 48.8829 + 28.2225i 1.78973 + 1.03330i
\(747\) 0 0
\(748\) 15.1909 + 4.07039i 0.555434 + 0.148828i
\(749\) −42.8937 15.6120i −1.56730 0.570451i
\(750\) 0 0
\(751\) 30.6700 + 25.7352i 1.11916 + 0.939089i 0.998562 0.0536119i \(-0.0170734\pi\)
0.120601 + 0.992701i \(0.461518\pi\)
\(752\) −20.2186 + 43.3589i −0.737296 + 1.58114i
\(753\) 0 0
\(754\) −3.07888 + 0.542889i −0.112126 + 0.0197709i
\(755\) −17.7367 0.772091i −0.645503 0.0280993i
\(756\) 0 0
\(757\) 0.846964 + 0.846964i 0.0307834 + 0.0307834i 0.722331 0.691548i \(-0.243071\pi\)
−0.691548 + 0.722331i \(0.743071\pi\)
\(758\) −7.55993 + 10.7967i −0.274589 + 0.392154i
\(759\) 0 0
\(760\) 47.0465 90.4042i 1.70656 3.27930i
\(761\) 3.25980 3.88488i 0.118168 0.140827i −0.703718 0.710480i \(-0.748478\pi\)
0.821885 + 0.569653i \(0.192922\pi\)
\(762\) 0 0
\(763\) −26.0764 + 12.1596i −0.944029 + 0.440208i
\(764\) 6.57430 + 11.3870i 0.237850 + 0.411968i
\(765\) 0 0
\(766\) 37.6375 65.1901i 1.35990 2.35542i
\(767\) 0.186547 2.13224i 0.00673583 0.0769909i
\(768\) 0 0
\(769\) 26.0795 + 4.59852i 0.940451 + 0.165827i 0.622800 0.782381i \(-0.285995\pi\)
0.317651 + 0.948208i \(0.397106\pi\)
\(770\) 11.8729 + 2.63054i 0.427869 + 0.0947980i
\(771\) 0 0
\(772\) −72.1914 6.31593i −2.59822 0.227315i
\(773\) 10.4941 2.81189i 0.377447 0.101137i −0.0651074 0.997878i \(-0.520739\pi\)
0.442555 + 0.896742i \(0.354072\pi\)
\(774\) 0 0
\(775\) 3.97460 + 8.51777i 0.142772 + 0.305967i
\(776\) 38.2703 105.147i 1.37383 3.77455i
\(777\) 0 0
\(778\) −78.0256 + 6.82635i −2.79735 + 0.244737i
\(779\) −8.62118 + 3.13785i −0.308886 + 0.112425i
\(780\) 0 0
\(781\) 0.709661 + 4.02469i 0.0253937 + 0.144015i
\(782\) 0.582559 0.582559i 0.0208323 0.0208323i
\(783\) 0 0
\(784\) 28.8525i 1.03045i
\(785\) −18.6076 + 24.2565i −0.664135 + 0.865751i
\(786\) 0 0
\(787\) 7.22332 + 3.36829i 0.257484