Properties

Label 756.2.ck.a.5.7
Level 756
Weight 2
Character 756.5
Analytic conductor 6.037
Analytic rank 0
Dimension 144
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 756.ck (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{18})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.7
Character \(\chi\) = 756.5
Dual form 756.2.ck.a.605.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.33105 - 1.10829i) q^{3} +(0.180656 - 1.02455i) q^{5} +(-1.77393 - 1.96295i) q^{7} +(0.543390 + 2.95038i) q^{9} +O(q^{10})\) \(q+(-1.33105 - 1.10829i) q^{3} +(0.180656 - 1.02455i) q^{5} +(-1.77393 - 1.96295i) q^{7} +(0.543390 + 2.95038i) q^{9} +(-3.15289 + 0.555939i) q^{11} +(-3.61991 + 4.31404i) q^{13} +(-1.37596 + 1.16351i) q^{15} +4.20835 q^{17} -4.25097i q^{19} +(0.185685 + 4.57881i) q^{21} +(-4.31087 + 5.13749i) q^{23} +(3.68139 + 1.33992i) q^{25} +(2.54659 - 4.52933i) q^{27} +(-2.19872 - 2.62033i) q^{29} +(2.78840 + 7.66106i) q^{31} +(4.81279 + 2.75433i) q^{33} +(-2.33161 + 1.46287i) q^{35} +(3.98796 + 6.90735i) q^{37} +(9.59948 - 1.73030i) q^{39} +(-5.69481 - 4.77851i) q^{41} +(-3.83125 - 1.39446i) q^{43} +(3.12098 - 0.0237272i) q^{45} +(6.45334 + 2.34882i) q^{47} +(-0.706311 + 6.96427i) q^{49} +(-5.60152 - 4.66407i) q^{51} +(-10.0687 + 5.81318i) q^{53} +3.33073i q^{55} +(-4.71130 + 5.65825i) q^{57} +(1.63882 + 1.37513i) q^{59} +(-2.63335 + 7.23508i) q^{61} +(4.82749 - 6.30042i) q^{63} +(3.76600 + 4.48814i) q^{65} +(-1.85427 + 10.5161i) q^{67} +(11.4318 - 2.06057i) q^{69} +(-14.4695 - 8.35397i) q^{71} +(-5.08376 - 2.93511i) q^{73} +(-3.41510 - 5.86355i) q^{75} +(6.68430 + 5.20275i) q^{77} +(-0.736951 - 4.17946i) q^{79} +(-8.40946 + 3.20641i) q^{81} +(-0.806976 + 0.677133i) q^{83} +(0.760264 - 4.31167i) q^{85} +(0.0225205 + 5.92461i) q^{87} -3.70603 q^{89} +(14.8897 - 0.547140i) q^{91} +(4.77918 - 13.2876i) q^{93} +(-4.35534 - 0.767963i) q^{95} +(1.71054 - 4.69967i) q^{97} +(-3.35348 - 9.00012i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144q + 6q^{9} + O(q^{10}) \) \( 144q + 6q^{9} - 6q^{11} + 12q^{15} + 33q^{21} + 21q^{23} - 6q^{29} + 27q^{35} + 39q^{39} - 54q^{47} + 18q^{49} - 9q^{51} - 45q^{53} + 3q^{57} + 45q^{59} + 39q^{63} + 24q^{65} - 36q^{69} + 36q^{71} + 45q^{75} + 21q^{77} - 18q^{79} + 18q^{81} + 36q^{85} - 45q^{87} + 9q^{91} - 48q^{93} - 66q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.33105 1.10829i −0.768482 0.639871i
\(4\) 0 0
\(5\) 0.180656 1.02455i 0.0807919 0.458194i −0.917394 0.397981i \(-0.869711\pi\)
0.998186 0.0602126i \(-0.0191779\pi\)
\(6\) 0 0
\(7\) −1.77393 1.96295i −0.670484 0.741924i
\(8\) 0 0
\(9\) 0.543390 + 2.95038i 0.181130 + 0.983459i
\(10\) 0 0
\(11\) −3.15289 + 0.555939i −0.950632 + 0.167622i −0.627399 0.778698i \(-0.715881\pi\)
−0.323232 + 0.946320i \(0.604769\pi\)
\(12\) 0 0
\(13\) −3.61991 + 4.31404i −1.00398 + 1.19650i −0.0235337 + 0.999723i \(0.507492\pi\)
−0.980448 + 0.196776i \(0.936953\pi\)
\(14\) 0 0
\(15\) −1.37596 + 1.16351i −0.355272 + 0.300417i
\(16\) 0 0
\(17\) 4.20835 1.02067 0.510337 0.859975i \(-0.329521\pi\)
0.510337 + 0.859975i \(0.329521\pi\)
\(18\) 0 0
\(19\) 4.25097i 0.975238i −0.873056 0.487619i \(-0.837865\pi\)
0.873056 0.487619i \(-0.162135\pi\)
\(20\) 0 0
\(21\) 0.185685 + 4.57881i 0.0405197 + 0.999179i
\(22\) 0 0
\(23\) −4.31087 + 5.13749i −0.898878 + 1.07124i 0.0982241 + 0.995164i \(0.468684\pi\)
−0.997102 + 0.0760766i \(0.975761\pi\)
\(24\) 0 0
\(25\) 3.68139 + 1.33992i 0.736279 + 0.267983i
\(26\) 0 0
\(27\) 2.54659 4.52933i 0.490092 0.871671i
\(28\) 0 0
\(29\) −2.19872 2.62033i −0.408292 0.486583i 0.522238 0.852800i \(-0.325097\pi\)
−0.930530 + 0.366217i \(0.880653\pi\)
\(30\) 0 0
\(31\) 2.78840 + 7.66106i 0.500811 + 1.37597i 0.890484 + 0.455014i \(0.150366\pi\)
−0.389673 + 0.920953i \(0.627412\pi\)
\(32\) 0 0
\(33\) 4.81279 + 2.75433i 0.837800 + 0.479467i
\(34\) 0 0
\(35\) −2.33161 + 1.46287i −0.394114 + 0.247270i
\(36\) 0 0
\(37\) 3.98796 + 6.90735i 0.655617 + 1.13556i 0.981739 + 0.190234i \(0.0609245\pi\)
−0.326122 + 0.945328i \(0.605742\pi\)
\(38\) 0 0
\(39\) 9.59948 1.73030i 1.53715 0.277069i
\(40\) 0 0
\(41\) −5.69481 4.77851i −0.889379 0.746278i 0.0787062 0.996898i \(-0.474921\pi\)
−0.968086 + 0.250620i \(0.919366\pi\)
\(42\) 0 0
\(43\) −3.83125 1.39446i −0.584260 0.212653i 0.0329429 0.999457i \(-0.489512\pi\)
−0.617203 + 0.786804i \(0.711734\pi\)
\(44\) 0 0
\(45\) 3.12098 0.0237272i 0.465249 0.00353705i
\(46\) 0 0
\(47\) 6.45334 + 2.34882i 0.941317 + 0.342611i 0.766686 0.642023i \(-0.221905\pi\)
0.174631 + 0.984634i \(0.444127\pi\)
\(48\) 0 0
\(49\) −0.706311 + 6.96427i −0.100902 + 0.994896i
\(50\) 0 0
\(51\) −5.60152 4.66407i −0.784370 0.653100i
\(52\) 0 0
\(53\) −10.0687 + 5.81318i −1.38305 + 0.798502i −0.992519 0.122089i \(-0.961041\pi\)
−0.390527 + 0.920591i \(0.627707\pi\)
\(54\) 0 0
\(55\) 3.33073i 0.449116i
\(56\) 0 0
\(57\) −4.71130 + 5.65825i −0.624027 + 0.749453i
\(58\) 0 0
\(59\) 1.63882 + 1.37513i 0.213356 + 0.179027i 0.743202 0.669067i \(-0.233306\pi\)
−0.529846 + 0.848094i \(0.677750\pi\)
\(60\) 0 0
\(61\) −2.63335 + 7.23508i −0.337166 + 0.926357i 0.649028 + 0.760765i \(0.275176\pi\)
−0.986194 + 0.165593i \(0.947046\pi\)
\(62\) 0 0
\(63\) 4.82749 6.30042i 0.608207 0.793779i
\(64\) 0 0
\(65\) 3.76600 + 4.48814i 0.467115 + 0.556686i
\(66\) 0 0
\(67\) −1.85427 + 10.5161i −0.226535 + 1.28475i 0.633193 + 0.773994i \(0.281744\pi\)
−0.859728 + 0.510752i \(0.829367\pi\)
\(68\) 0 0
\(69\) 11.4318 2.06057i 1.37623 0.248064i
\(70\) 0 0
\(71\) −14.4695 8.35397i −1.71721 0.991434i −0.923911 0.382607i \(-0.875026\pi\)
−0.793303 0.608827i \(-0.791640\pi\)
\(72\) 0 0
\(73\) −5.08376 2.93511i −0.595009 0.343529i 0.172066 0.985085i \(-0.444956\pi\)
−0.767076 + 0.641557i \(0.778289\pi\)
\(74\) 0 0
\(75\) −3.41510 5.86355i −0.394342 0.677064i
\(76\) 0 0
\(77\) 6.68430 + 5.20275i 0.761746 + 0.592908i
\(78\) 0 0
\(79\) −0.736951 4.17946i −0.0829135 0.470226i −0.997787 0.0664859i \(-0.978821\pi\)
0.914874 0.403740i \(-0.132290\pi\)
\(80\) 0 0
\(81\) −8.40946 + 3.20641i −0.934384 + 0.356268i
\(82\) 0 0
\(83\) −0.806976 + 0.677133i −0.0885771 + 0.0743251i −0.686001 0.727601i \(-0.740635\pi\)
0.597424 + 0.801926i \(0.296191\pi\)
\(84\) 0 0
\(85\) 0.760264 4.31167i 0.0824622 0.467666i
\(86\) 0 0
\(87\) 0.0225205 + 5.92461i 0.00241446 + 0.635184i
\(88\) 0 0
\(89\) −3.70603 −0.392839 −0.196419 0.980520i \(-0.562931\pi\)
−0.196419 + 0.980520i \(0.562931\pi\)
\(90\) 0 0
\(91\) 14.8897 0.547140i 1.56087 0.0573559i
\(92\) 0 0
\(93\) 4.77918 13.2876i 0.495577 1.37786i
\(94\) 0 0
\(95\) −4.35534 0.767963i −0.446848 0.0787914i
\(96\) 0 0
\(97\) 1.71054 4.69967i 0.173679 0.477179i −0.822059 0.569402i \(-0.807175\pi\)
0.995738 + 0.0922225i \(0.0293971\pi\)
\(98\) 0 0
\(99\) −3.35348 9.00012i −0.337037 0.904546i
\(100\) 0 0
\(101\) 5.71563 4.79598i 0.568726 0.477218i −0.312497 0.949919i \(-0.601165\pi\)
0.881223 + 0.472701i \(0.156721\pi\)
\(102\) 0 0
\(103\) 17.0739 + 3.01059i 1.68234 + 0.296643i 0.931474 0.363808i \(-0.118523\pi\)
0.750870 + 0.660450i \(0.229635\pi\)
\(104\) 0 0
\(105\) 4.72478 + 0.636947i 0.461091 + 0.0621597i
\(106\) 0 0
\(107\) −11.6596 6.73167i −1.12718 0.650775i −0.183952 0.982935i \(-0.558889\pi\)
−0.943223 + 0.332160i \(0.892223\pi\)
\(108\) 0 0
\(109\) 3.21351 + 5.56596i 0.307798 + 0.533122i 0.977880 0.209165i \(-0.0670746\pi\)
−0.670082 + 0.742287i \(0.733741\pi\)
\(110\) 0 0
\(111\) 2.34717 13.6138i 0.222783 1.29217i
\(112\) 0 0
\(113\) 4.24375 + 11.6596i 0.399218 + 1.09684i 0.962666 + 0.270691i \(0.0872522\pi\)
−0.563448 + 0.826151i \(0.690526\pi\)
\(114\) 0 0
\(115\) 4.48484 + 5.34483i 0.418214 + 0.498408i
\(116\) 0 0
\(117\) −14.6951 8.33589i −1.35856 0.770654i
\(118\) 0 0
\(119\) −7.46533 8.26076i −0.684346 0.757262i
\(120\) 0 0
\(121\) −0.704983 + 0.256593i −0.0640894 + 0.0233266i
\(122\) 0 0
\(123\) 2.28410 + 12.6719i 0.205951 + 1.14259i
\(124\) 0 0
\(125\) 4.63877 8.03459i 0.414905 0.718636i
\(126\) 0 0
\(127\) 0.751871 + 1.30228i 0.0667178 + 0.115559i 0.897455 0.441107i \(-0.145414\pi\)
−0.830737 + 0.556665i \(0.812081\pi\)
\(128\) 0 0
\(129\) 3.55412 + 6.10223i 0.312923 + 0.537271i
\(130\) 0 0
\(131\) −11.0025 9.23223i −0.961297 0.806624i 0.0198667 0.999803i \(-0.493676\pi\)
−0.981164 + 0.193179i \(0.938120\pi\)
\(132\) 0 0
\(133\) −8.34441 + 7.54094i −0.723553 + 0.653882i
\(134\) 0 0
\(135\) −4.18048 3.42737i −0.359798 0.294981i
\(136\) 0 0
\(137\) −0.192260 + 0.528231i −0.0164259 + 0.0451298i −0.947635 0.319357i \(-0.896533\pi\)
0.931209 + 0.364486i \(0.118755\pi\)
\(138\) 0 0
\(139\) −19.7935 3.49013i −1.67886 0.296029i −0.748627 0.662991i \(-0.769287\pi\)
−0.930236 + 0.366962i \(0.880398\pi\)
\(140\) 0 0
\(141\) −5.98655 10.2786i −0.504158 0.865612i
\(142\) 0 0
\(143\) 9.01482 15.6141i 0.753858 1.30572i
\(144\) 0 0
\(145\) −3.08188 + 1.77932i −0.255936 + 0.147765i
\(146\) 0 0
\(147\) 8.65857 8.48700i 0.714147 0.699996i
\(148\) 0 0
\(149\) −6.70021 18.4087i −0.548903 1.50810i −0.835194 0.549956i \(-0.814645\pi\)
0.286291 0.958143i \(-0.407578\pi\)
\(150\) 0 0
\(151\) 0.856796 + 4.85913i 0.0697250 + 0.395430i 0.999619 + 0.0276026i \(0.00878728\pi\)
−0.929894 + 0.367828i \(0.880102\pi\)
\(152\) 0 0
\(153\) 2.28677 + 12.4162i 0.184875 + 1.00379i
\(154\) 0 0
\(155\) 8.35290 1.47284i 0.670921 0.118301i
\(156\) 0 0
\(157\) 8.43876 10.0569i 0.673487 0.802630i −0.315768 0.948837i \(-0.602262\pi\)
0.989254 + 0.146207i \(0.0467064\pi\)
\(158\) 0 0
\(159\) 19.8447 + 3.42143i 1.57379 + 0.271337i
\(160\) 0 0
\(161\) 17.7318 0.651576i 1.39746 0.0513514i
\(162\) 0 0
\(163\) −2.70825 + 4.69083i −0.212127 + 0.367414i −0.952380 0.304914i \(-0.901372\pi\)
0.740253 + 0.672328i \(0.234706\pi\)
\(164\) 0 0
\(165\) 3.69141 4.43337i 0.287376 0.345138i
\(166\) 0 0
\(167\) −17.6448 + 6.42219i −1.36540 + 0.496964i −0.917719 0.397231i \(-0.869971\pi\)
−0.447678 + 0.894195i \(0.647749\pi\)
\(168\) 0 0
\(169\) −3.24977 18.4304i −0.249982 1.41772i
\(170\) 0 0
\(171\) 12.5420 2.30993i 0.959107 0.176645i
\(172\) 0 0
\(173\) −0.770078 + 0.646172i −0.0585479 + 0.0491276i −0.671592 0.740921i \(-0.734389\pi\)
0.613044 + 0.790049i \(0.289945\pi\)
\(174\) 0 0
\(175\) −3.90037 9.60330i −0.294840 0.725941i
\(176\) 0 0
\(177\) −0.657306 3.64666i −0.0494062 0.274100i
\(178\) 0 0
\(179\) 26.0886i 1.94995i −0.222307 0.974977i \(-0.571359\pi\)
0.222307 0.974977i \(-0.428641\pi\)
\(180\) 0 0
\(181\) 0.793323 0.458026i 0.0589673 0.0340448i −0.470227 0.882546i \(-0.655828\pi\)
0.529194 + 0.848501i \(0.322494\pi\)
\(182\) 0 0
\(183\) 11.5237 6.71174i 0.851856 0.496146i
\(184\) 0 0
\(185\) 7.79739 2.83802i 0.573275 0.208655i
\(186\) 0 0
\(187\) −13.2684 + 2.33959i −0.970285 + 0.171087i
\(188\) 0 0
\(189\) −13.4083 + 3.03592i −0.975312 + 0.220831i
\(190\) 0 0
\(191\) −6.34061 + 1.11802i −0.458790 + 0.0808971i −0.398267 0.917270i \(-0.630388\pi\)
−0.0605236 + 0.998167i \(0.519277\pi\)
\(192\) 0 0
\(193\) −9.14158 + 3.32726i −0.658026 + 0.239502i −0.649384 0.760461i \(-0.724973\pi\)
−0.00864188 + 0.999963i \(0.502751\pi\)
\(194\) 0 0
\(195\) −0.0385735 10.1478i −0.00276231 0.726696i
\(196\) 0 0
\(197\) −8.98992 + 5.19033i −0.640505 + 0.369796i −0.784809 0.619738i \(-0.787239\pi\)
0.144304 + 0.989533i \(0.453906\pi\)
\(198\) 0 0
\(199\) 2.58419i 0.183188i −0.995796 0.0915941i \(-0.970804\pi\)
0.995796 0.0915941i \(-0.0291962\pi\)
\(200\) 0 0
\(201\) 14.1230 11.9424i 0.996160 0.842351i
\(202\) 0 0
\(203\) −1.24318 + 8.96426i −0.0872544 + 0.629168i
\(204\) 0 0
\(205\) −5.92463 + 4.97136i −0.413794 + 0.347215i
\(206\) 0 0
\(207\) −17.5000 9.92702i −1.21634 0.689976i
\(208\) 0 0
\(209\) 2.36328 + 13.4028i 0.163471 + 0.927092i
\(210\) 0 0
\(211\) −13.6574 + 4.97088i −0.940213 + 0.342210i −0.766250 0.642542i \(-0.777880\pi\)
−0.173963 + 0.984752i \(0.555657\pi\)
\(212\) 0 0
\(213\) 10.0010 + 27.1560i 0.685259 + 1.86070i
\(214\) 0 0
\(215\) −2.12084 + 3.67340i −0.144640 + 0.250524i
\(216\) 0 0
\(217\) 10.0918 19.0637i 0.685077 1.29413i
\(218\) 0 0
\(219\) 3.51379 + 9.54106i 0.237440 + 0.644725i
\(220\) 0 0
\(221\) −15.2338 + 18.1550i −1.02474 + 1.22124i
\(222\) 0 0
\(223\) 10.4953 1.85061i 0.702818 0.123926i 0.189192 0.981940i \(-0.439413\pi\)
0.513626 + 0.858014i \(0.328302\pi\)
\(224\) 0 0
\(225\) −1.95283 + 11.5896i −0.130189 + 0.772640i
\(226\) 0 0
\(227\) 3.60603 + 20.4508i 0.239341 + 1.35737i 0.833276 + 0.552857i \(0.186462\pi\)
−0.593936 + 0.804513i \(0.702427\pi\)
\(228\) 0 0
\(229\) 4.57450 + 12.5683i 0.302291 + 0.830539i 0.994101 + 0.108459i \(0.0345916\pi\)
−0.691810 + 0.722080i \(0.743186\pi\)
\(230\) 0 0
\(231\) −3.13098 14.3333i −0.206004 0.943059i
\(232\) 0 0
\(233\) 13.0930 7.55926i 0.857752 0.495223i −0.00550680 0.999985i \(-0.501753\pi\)
0.863259 + 0.504761i \(0.168420\pi\)
\(234\) 0 0
\(235\) 3.57233 6.18745i 0.233033 0.403625i
\(236\) 0 0
\(237\) −3.65113 + 6.37982i −0.237166 + 0.414414i
\(238\) 0 0
\(239\) 10.9911 + 1.93803i 0.710955 + 0.125361i 0.517418 0.855733i \(-0.326893\pi\)
0.193536 + 0.981093i \(0.438004\pi\)
\(240\) 0 0
\(241\) 1.42884 3.92570i 0.0920396 0.252877i −0.885128 0.465348i \(-0.845929\pi\)
0.977167 + 0.212472i \(0.0681513\pi\)
\(242\) 0 0
\(243\) 14.7470 + 5.05222i 0.946023 + 0.324100i
\(244\) 0 0
\(245\) 7.00766 + 1.98179i 0.447703 + 0.126612i
\(246\) 0 0
\(247\) 18.3388 + 15.3881i 1.16687 + 0.979122i
\(248\) 0 0
\(249\) 1.82459 0.00693559i 0.115628 0.000439525i
\(250\) 0 0
\(251\) −5.12996 8.88536i −0.323800 0.560839i 0.657468 0.753482i \(-0.271627\pi\)
−0.981269 + 0.192643i \(0.938294\pi\)
\(252\) 0 0
\(253\) 10.7355 18.5945i 0.674938 1.16903i
\(254\) 0 0
\(255\) −5.79053 + 4.89646i −0.362617 + 0.306628i
\(256\) 0 0
\(257\) −19.1202 + 6.95920i −1.19269 + 0.434103i −0.860667 0.509169i \(-0.829953\pi\)
−0.332022 + 0.943272i \(0.607731\pi\)
\(258\) 0 0
\(259\) 6.48437 20.0813i 0.402919 1.24779i
\(260\) 0 0
\(261\) 6.53620 7.91091i 0.404581 0.489673i
\(262\) 0 0
\(263\) 14.8895 + 17.7446i 0.918123 + 1.09418i 0.995269 + 0.0971568i \(0.0309748\pi\)
−0.0771459 + 0.997020i \(0.524581\pi\)
\(264\) 0 0
\(265\) 4.13693 + 11.3661i 0.254130 + 0.698216i
\(266\) 0 0
\(267\) 4.93292 + 4.10736i 0.301890 + 0.251366i
\(268\) 0 0
\(269\) 6.90423 + 11.9585i 0.420958 + 0.729121i 0.996033 0.0889793i \(-0.0283605\pi\)
−0.575075 + 0.818101i \(0.695027\pi\)
\(270\) 0 0
\(271\) 17.5834 + 10.1518i 1.06812 + 0.616678i 0.927667 0.373410i \(-0.121811\pi\)
0.140451 + 0.990088i \(0.455145\pi\)
\(272\) 0 0
\(273\) −20.4253 15.7738i −1.23620 0.954676i
\(274\) 0 0
\(275\) −12.3519 2.17798i −0.744850 0.131337i
\(276\) 0 0
\(277\) −12.1880 + 10.2270i −0.732308 + 0.614479i −0.930760 0.365631i \(-0.880853\pi\)
0.198452 + 0.980111i \(0.436409\pi\)
\(278\) 0 0
\(279\) −21.0878 + 12.3898i −1.26250 + 0.741756i
\(280\) 0 0
\(281\) 7.50502 20.6199i 0.447712 1.23008i −0.486601 0.873625i \(-0.661763\pi\)
0.934313 0.356454i \(-0.116015\pi\)
\(282\) 0 0
\(283\) 0.867207 + 0.152912i 0.0515501 + 0.00908967i 0.199364 0.979926i \(-0.436112\pi\)
−0.147814 + 0.989015i \(0.547224\pi\)
\(284\) 0 0
\(285\) 4.94605 + 5.84917i 0.292978 + 0.346475i
\(286\) 0 0
\(287\) 0.722259 + 19.6554i 0.0426336 + 1.16022i
\(288\) 0 0
\(289\) 0.710180 0.0417753
\(290\) 0 0
\(291\) −7.48541 + 4.35973i −0.438803 + 0.255572i
\(292\) 0 0
\(293\) 2.51485 14.2624i 0.146919 0.833221i −0.818887 0.573955i \(-0.805408\pi\)
0.965806 0.259266i \(-0.0834805\pi\)
\(294\) 0 0
\(295\) 1.70496 1.43063i 0.0992665 0.0832945i
\(296\) 0 0
\(297\) −5.51109 + 15.6962i −0.319786 + 0.910788i
\(298\) 0 0
\(299\) −6.55839 37.1945i −0.379282 2.15101i
\(300\) 0 0
\(301\) 4.05914 + 9.99422i 0.233965 + 0.576057i
\(302\) 0 0
\(303\) −12.9231 + 0.0491232i −0.742414 + 0.00282206i
\(304\) 0 0
\(305\) 6.93699 + 4.00507i 0.397211 + 0.229330i
\(306\) 0 0
\(307\) 9.66111 + 5.57784i 0.551388 + 0.318344i 0.749682 0.661798i \(-0.230207\pi\)
−0.198293 + 0.980143i \(0.563540\pi\)
\(308\) 0 0
\(309\) −19.3896 22.9301i −1.10304 1.30445i
\(310\) 0 0
\(311\) −2.01607 + 11.4337i −0.114321 + 0.648347i 0.872763 + 0.488144i \(0.162326\pi\)
−0.987084 + 0.160203i \(0.948785\pi\)
\(312\) 0 0
\(313\) −10.2513 12.2170i −0.579435 0.690544i 0.394104 0.919066i \(-0.371055\pi\)
−0.973539 + 0.228522i \(0.926611\pi\)
\(314\) 0 0
\(315\) −5.58299 6.08423i −0.314566 0.342807i
\(316\) 0 0
\(317\) −8.44013 + 23.1891i −0.474045 + 1.30243i 0.440431 + 0.897787i \(0.354826\pi\)
−0.914476 + 0.404641i \(0.867396\pi\)
\(318\) 0 0
\(319\) 8.38906 + 7.03925i 0.469697 + 0.394123i
\(320\) 0 0
\(321\) 8.05887 + 21.8824i 0.449802 + 1.22136i
\(322\) 0 0
\(323\) 17.8895i 0.995400i
\(324\) 0 0
\(325\) −19.1068 + 11.0313i −1.05985 + 0.611906i
\(326\) 0 0
\(327\) 1.89135 10.9701i 0.104592 0.606646i
\(328\) 0 0
\(329\) −6.83719 16.8342i −0.376947 0.928101i
\(330\) 0 0
\(331\) 6.47121 + 2.35533i 0.355690 + 0.129460i 0.513684 0.857980i \(-0.328280\pi\)
−0.157994 + 0.987440i \(0.550503\pi\)
\(332\) 0 0
\(333\) −18.2123 + 15.5194i −0.998026 + 0.850456i
\(334\) 0 0
\(335\) 10.4393 + 3.79960i 0.570360 + 0.207594i
\(336\) 0 0
\(337\) 2.78612 + 2.33783i 0.151770 + 0.127350i 0.715511 0.698602i \(-0.246194\pi\)
−0.563741 + 0.825951i \(0.690638\pi\)
\(338\) 0 0
\(339\) 7.27357 20.2228i 0.395046 1.09835i
\(340\) 0 0
\(341\) −13.0506 22.6043i −0.706729 1.22409i
\(342\) 0 0
\(343\) 14.9234 10.9677i 0.805790 0.592201i
\(344\) 0 0
\(345\) −0.0459364 12.0847i −0.00247313 0.650620i
\(346\) 0 0
\(347\) 6.90040 + 18.9587i 0.370433 + 1.01776i 0.975195 + 0.221349i \(0.0710461\pi\)
−0.604762 + 0.796406i \(0.706732\pi\)
\(348\) 0 0
\(349\) −16.9430 20.1919i −0.906938 1.08085i −0.996393 0.0848561i \(-0.972957\pi\)
0.0894549 0.995991i \(-0.471487\pi\)
\(350\) 0 0
\(351\) 10.3213 + 27.3819i 0.550910 + 1.46154i
\(352\) 0 0
\(353\) 2.39086 + 0.870202i 0.127253 + 0.0463162i 0.404862 0.914378i \(-0.367320\pi\)
−0.277609 + 0.960694i \(0.589542\pi\)
\(354\) 0 0
\(355\) −11.1731 + 13.3156i −0.593006 + 0.706717i
\(356\) 0 0
\(357\) 0.781426 + 19.2692i 0.0413574 + 1.01984i
\(358\) 0 0
\(359\) 24.1573i 1.27497i 0.770462 + 0.637486i \(0.220026\pi\)
−0.770462 + 0.637486i \(0.779974\pi\)
\(360\) 0 0
\(361\) 0.929290 0.0489100
\(362\) 0 0
\(363\) 1.22275 + 0.439787i 0.0641776 + 0.0230828i
\(364\) 0 0
\(365\) −3.92559 + 4.67833i −0.205475 + 0.244875i
\(366\) 0 0
\(367\) −18.2957 + 3.22602i −0.955027 + 0.168397i −0.629383 0.777095i \(-0.716692\pi\)
−0.325644 + 0.945492i \(0.605581\pi\)
\(368\) 0 0
\(369\) 11.0039 19.3984i 0.572841 1.00984i
\(370\) 0 0
\(371\) 29.2722 + 9.45216i 1.51974 + 0.490732i
\(372\) 0 0
\(373\) 3.27355 18.5652i 0.169498 0.961271i −0.774807 0.632198i \(-0.782153\pi\)
0.944305 0.329073i \(-0.106736\pi\)
\(374\) 0 0
\(375\) −15.0791 + 5.55334i −0.778681 + 0.286773i
\(376\) 0 0
\(377\) 19.2634 0.992114
\(378\) 0 0
\(379\) −22.5186 −1.15670 −0.578352 0.815788i \(-0.696304\pi\)
−0.578352 + 0.815788i \(0.696304\pi\)
\(380\) 0 0
\(381\) 0.442524 2.56669i 0.0226712 0.131495i
\(382\) 0 0
\(383\) 0.178794 1.01399i 0.00913594 0.0518125i −0.979899 0.199494i \(-0.936070\pi\)
0.989035 + 0.147682i \(0.0471812\pi\)
\(384\) 0 0
\(385\) 6.53805 5.90850i 0.333210 0.301125i
\(386\) 0 0
\(387\) 2.03232 12.0614i 0.103309 0.613114i
\(388\) 0 0
\(389\) −5.57571 + 0.983148i −0.282700 + 0.0498476i −0.313200 0.949687i \(-0.601401\pi\)
0.0305004 + 0.999535i \(0.490290\pi\)
\(390\) 0 0
\(391\) −18.1416 + 21.6203i −0.917461 + 1.09339i
\(392\) 0 0
\(393\) 4.41296 + 24.4826i 0.222604 + 1.23498i
\(394\) 0 0
\(395\) −4.41521 −0.222153
\(396\) 0 0
\(397\) 15.0350i 0.754586i −0.926094 0.377293i \(-0.876855\pi\)
0.926094 0.377293i \(-0.123145\pi\)
\(398\) 0 0
\(399\) 19.4644 0.789339i 0.974438 0.0395164i
\(400\) 0 0
\(401\) −16.1931 + 19.2982i −0.808646 + 0.963707i −0.999841 0.0178453i \(-0.994319\pi\)
0.191195 + 0.981552i \(0.438764\pi\)
\(402\) 0 0
\(403\) −43.1439 15.7031i −2.14915 0.782227i
\(404\) 0 0
\(405\) 1.76591 + 9.19518i 0.0877490 + 0.456912i
\(406\) 0 0
\(407\) −16.4137 19.5610i −0.813595 0.969605i
\(408\) 0 0
\(409\) −7.38281 20.2841i −0.365056 1.00298i −0.977215 0.212250i \(-0.931921\pi\)
0.612159 0.790735i \(-0.290301\pi\)
\(410\) 0 0
\(411\) 0.841341 0.490022i 0.0415003 0.0241710i
\(412\) 0 0
\(413\) −0.207848 5.65631i −0.0102275 0.278329i
\(414\) 0 0
\(415\) 0.547973 + 0.949117i 0.0268989 + 0.0465903i
\(416\) 0 0
\(417\) 22.4781 + 26.5825i 1.10076 + 1.30175i
\(418\) 0 0
\(419\) 15.5980 + 13.0883i 0.762012 + 0.639404i 0.938650 0.344872i \(-0.112078\pi\)
−0.176638 + 0.984276i \(0.556522\pi\)
\(420\) 0 0
\(421\) 19.3992 + 7.06073i 0.945459 + 0.344119i 0.768319 0.640067i \(-0.221093\pi\)
0.177140 + 0.984186i \(0.443316\pi\)
\(422\) 0 0
\(423\) −3.42324 + 20.3161i −0.166444 + 0.987804i
\(424\) 0 0
\(425\) 15.4926 + 5.63884i 0.751500 + 0.273524i
\(426\) 0 0
\(427\) 18.8735 7.66543i 0.913351 0.370956i
\(428\) 0 0
\(429\) −29.3042 + 10.7922i −1.41482 + 0.521051i
\(430\) 0 0
\(431\) 4.87013 2.81177i 0.234586 0.135438i −0.378100 0.925765i \(-0.623422\pi\)
0.612686 + 0.790327i \(0.290089\pi\)
\(432\) 0 0
\(433\) 21.1008i 1.01404i 0.861934 + 0.507020i \(0.169253\pi\)
−0.861934 + 0.507020i \(0.830747\pi\)
\(434\) 0 0
\(435\) 6.07414 + 1.04724i 0.291232 + 0.0502115i
\(436\) 0 0
\(437\) 21.8393 + 18.3253i 1.04472 + 0.876620i
\(438\) 0 0
\(439\) −7.62477 + 20.9489i −0.363910 + 0.999836i 0.613723 + 0.789521i \(0.289671\pi\)
−0.977634 + 0.210315i \(0.932551\pi\)
\(440\) 0 0
\(441\) −20.9310 + 1.70043i −0.996716 + 0.0809729i
\(442\) 0 0
\(443\) 9.81811 + 11.7008i 0.466473 + 0.555920i 0.947073 0.321020i \(-0.104026\pi\)
−0.480600 + 0.876940i \(0.659581\pi\)
\(444\) 0 0
\(445\) −0.669518 + 3.79703i −0.0317382 + 0.179996i
\(446\) 0 0
\(447\) −11.4838 + 31.9287i −0.543166 + 1.51017i
\(448\) 0 0
\(449\) 19.7219 + 11.3864i 0.930734 + 0.537359i 0.887044 0.461686i \(-0.152755\pi\)
0.0436902 + 0.999045i \(0.486089\pi\)
\(450\) 0 0
\(451\) 20.6116 + 11.9001i 0.970565 + 0.560356i
\(452\) 0 0
\(453\) 4.24488 7.41732i 0.199442 0.348496i
\(454\) 0 0
\(455\) 2.12934 15.3541i 0.0998252 0.719812i
\(456\) 0 0
\(457\) 2.64733 + 15.0137i 0.123837 + 0.702313i 0.981992 + 0.188923i \(0.0604995\pi\)
−0.858155 + 0.513390i \(0.828389\pi\)
\(458\) 0 0
\(459\) 10.7169 19.0610i 0.500224 0.889692i
\(460\) 0 0
\(461\) 8.45610 7.09551i 0.393840 0.330471i −0.424267 0.905537i \(-0.639468\pi\)
0.818107 + 0.575066i \(0.195024\pi\)
\(462\) 0 0
\(463\) 2.82578 16.0258i 0.131325 0.744781i −0.846024 0.533145i \(-0.821010\pi\)
0.977349 0.211636i \(-0.0678791\pi\)
\(464\) 0 0
\(465\) −12.7505 7.29700i −0.591289 0.338390i
\(466\) 0 0
\(467\) −24.4283 −1.13041 −0.565203 0.824952i \(-0.691202\pi\)
−0.565203 + 0.824952i \(0.691202\pi\)
\(468\) 0 0
\(469\) 23.9319 15.0150i 1.10507 0.693330i
\(470\) 0 0
\(471\) −22.3784 + 4.03368i −1.03114 + 0.185862i
\(472\) 0 0
\(473\) 12.8547 + 2.26664i 0.591061 + 0.104220i
\(474\) 0 0
\(475\) 5.69594 15.6495i 0.261348 0.718047i
\(476\) 0 0
\(477\) −22.6223 26.5477i −1.03581 1.21554i
\(478\) 0 0
\(479\) 14.3565 12.0465i 0.655964 0.550419i −0.252910 0.967490i \(-0.581388\pi\)
0.908874 + 0.417071i \(0.136943\pi\)
\(480\) 0 0
\(481\) −44.2346 7.79976i −2.01693 0.355638i
\(482\) 0 0
\(483\) −24.3241 18.7847i −1.10678 0.854733i
\(484\) 0 0
\(485\) −4.50604 2.60156i −0.204609 0.118131i
\(486\) 0 0
\(487\) −5.53657 9.58961i −0.250886 0.434547i 0.712884 0.701282i \(-0.247389\pi\)
−0.963770 + 0.266735i \(0.914055\pi\)
\(488\) 0 0
\(489\) 8.80362 3.24221i 0.398113 0.146618i
\(490\) 0 0
\(491\) 5.05302 + 13.8831i 0.228040 + 0.626534i 0.999958 0.00918816i \(-0.00292472\pi\)
−0.771918 + 0.635722i \(0.780703\pi\)
\(492\) 0 0
\(493\) −9.25297 11.0273i −0.416733 0.496643i
\(494\) 0 0
\(495\) −9.82692 + 1.80989i −0.441687 + 0.0813483i
\(496\) 0 0
\(497\) 9.26956 + 43.2223i 0.415797 + 1.93878i
\(498\) 0 0
\(499\) 10.0211 3.64739i 0.448607 0.163280i −0.107830 0.994169i \(-0.534390\pi\)
0.556437 + 0.830890i \(0.312168\pi\)
\(500\) 0 0
\(501\) 30.6038 + 11.0073i 1.36728 + 0.491770i
\(502\) 0 0
\(503\) −10.1407 + 17.5643i −0.452154 + 0.783153i −0.998520 0.0543935i \(-0.982677\pi\)
0.546366 + 0.837547i \(0.316011\pi\)
\(504\) 0 0
\(505\) −3.88117 6.72238i −0.172710 0.299142i
\(506\) 0 0
\(507\) −16.1006 + 28.1334i −0.715051 + 1.24945i
\(508\) 0 0
\(509\) 8.85975 + 7.43421i 0.392701 + 0.329516i 0.817664 0.575695i \(-0.195268\pi\)
−0.424963 + 0.905211i \(0.639713\pi\)
\(510\) 0 0
\(511\) 3.25680 + 15.1858i 0.144072 + 0.671782i
\(512\) 0 0
\(513\) −19.2540 10.8255i −0.850087 0.477957i
\(514\) 0 0
\(515\) 6.16902 16.9492i 0.271840 0.746873i
\(516\) 0 0
\(517\) −21.6525 3.81791i −0.952274 0.167912i
\(518\) 0 0
\(519\) 1.74116 0.00661847i 0.0764284 0.000290519i
\(520\) 0 0
\(521\) 9.61790 16.6587i 0.421368 0.729830i −0.574706 0.818360i \(-0.694884\pi\)
0.996074 + 0.0885297i \(0.0282168\pi\)
\(522\) 0 0
\(523\) −12.5265 + 7.23220i −0.547747 + 0.316242i −0.748213 0.663459i \(-0.769088\pi\)
0.200466 + 0.979701i \(0.435755\pi\)
\(524\) 0 0
\(525\) −5.45165 + 17.1052i −0.237930 + 0.746533i
\(526\) 0 0
\(527\) 11.7346 + 32.2404i 0.511165 + 1.40441i
\(528\) 0 0
\(529\) −3.81633 21.6435i −0.165928 0.941022i
\(530\) 0 0
\(531\) −3.16664 + 5.58237i −0.137421 + 0.242254i
\(532\) 0 0
\(533\) 41.2294 7.26985i 1.78584 0.314892i
\(534\) 0 0
\(535\) −9.00332 + 10.7297i −0.389248 + 0.463887i
\(536\) 0 0
\(537\) −28.9137 + 34.7252i −1.24772 + 1.49850i
\(538\) 0 0
\(539\) −1.64479 22.3502i −0.0708463 0.962693i
\(540\) 0 0
\(541\) 20.7842 35.9992i 0.893581 1.54773i 0.0580304 0.998315i \(-0.481518\pi\)
0.835551 0.549413i \(-0.185149\pi\)
\(542\) 0 0
\(543\) −1.56358 0.269577i −0.0670996 0.0115687i
\(544\) 0 0
\(545\) 6.28315 2.28688i 0.269141 0.0979592i
\(546\) 0 0
\(547\) −0.705826 4.00294i −0.0301789 0.171153i 0.965993 0.258568i \(-0.0832506\pi\)
−0.996172 + 0.0874147i \(0.972139\pi\)
\(548\) 0 0
\(549\) −22.7772 3.83792i −0.972106 0.163798i
\(550\) 0 0
\(551\) −11.1389 + 9.34667i −0.474534 + 0.398182i
\(552\) 0 0
\(553\) −6.89674 + 8.86068i −0.293279 + 0.376794i
\(554\) 0 0
\(555\) −13.5241 4.86422i −0.574064 0.206475i
\(556\) 0 0
\(557\) 34.5593i 1.46432i −0.681131 0.732162i \(-0.738511\pi\)
0.681131 0.732162i \(-0.261489\pi\)
\(558\) 0 0
\(559\) 19.8845 11.4803i 0.841026 0.485567i
\(560\) 0 0
\(561\) 20.2539 + 11.5912i 0.855121 + 0.489380i
\(562\) 0 0
\(563\) −5.25710 + 1.91343i −0.221560 + 0.0806414i −0.450415 0.892819i \(-0.648724\pi\)
0.228855 + 0.973461i \(0.426502\pi\)
\(564\) 0 0
\(565\) 12.7125 2.24156i 0.534820 0.0943032i
\(566\) 0 0
\(567\) 21.2118 + 10.8193i 0.890813 + 0.454370i
\(568\) 0 0
\(569\) −6.12310 + 1.07967i −0.256694 + 0.0452620i −0.300514 0.953777i \(-0.597158\pi\)
0.0438203 + 0.999039i \(0.486047\pi\)
\(570\) 0 0
\(571\) 7.26870 2.64559i 0.304185 0.110714i −0.185418 0.982660i \(-0.559364\pi\)
0.489603 + 0.871945i \(0.337142\pi\)
\(572\) 0 0
\(573\) 9.67876 + 5.53909i 0.404336 + 0.231399i
\(574\) 0 0
\(575\) −22.7538 + 13.1369i −0.948899 + 0.547847i
\(576\) 0 0
\(577\) 27.4212i 1.14156i −0.821103 0.570781i \(-0.806641\pi\)
0.821103 0.570781i \(-0.193359\pi\)
\(578\) 0 0
\(579\) 15.8555 + 5.70276i 0.658931 + 0.236999i
\(580\) 0 0
\(581\) 2.76070 + 0.382860i 0.114533 + 0.0158837i
\(582\) 0 0
\(583\) 28.5138 23.9259i 1.18092 0.990910i
\(584\) 0 0
\(585\) −11.1953 + 13.5499i −0.462869 + 0.560221i
\(586\) 0 0
\(587\) −6.31806 35.8315i −0.260774 1.47892i −0.780804 0.624776i \(-0.785190\pi\)
0.520030 0.854148i \(-0.325921\pi\)
\(588\) 0 0
\(589\) 32.5669 11.8534i 1.34190 0.488410i
\(590\) 0 0
\(591\) 17.7184 + 3.05484i 0.728838 + 0.125659i
\(592\) 0 0
\(593\) 20.9240 36.2414i 0.859245 1.48826i −0.0134060 0.999910i \(-0.504267\pi\)
0.872651 0.488345i \(-0.162399\pi\)
\(594\) 0 0
\(595\) −9.81223 + 6.15626i −0.402262 + 0.252382i
\(596\) 0 0
\(597\) −2.86403 + 3.43968i −0.117217 + 0.140777i
\(598\) 0 0
\(599\) 7.62840 9.09117i 0.311688 0.371455i −0.587345 0.809337i \(-0.699827\pi\)
0.899033 + 0.437882i \(0.144271\pi\)
\(600\) 0 0
\(601\) −0.550033 + 0.0969857i −0.0224363 + 0.00395613i −0.184855 0.982766i \(-0.559182\pi\)
0.162419 + 0.986722i \(0.448070\pi\)
\(602\) 0 0
\(603\) −32.0340 + 0.243538i −1.30453 + 0.00991765i
\(604\) 0 0
\(605\) 0.135533 + 0.768647i 0.00551021 + 0.0312499i
\(606\) 0 0
\(607\) 6.51556 + 17.9014i 0.264459 + 0.726594i 0.998854 + 0.0478715i \(0.0152438\pi\)
−0.734395 + 0.678722i \(0.762534\pi\)
\(608\) 0 0
\(609\) 11.5897 10.5541i 0.469640 0.427673i
\(610\) 0 0
\(611\) −33.4934 + 19.3374i −1.35500 + 0.782309i
\(612\) 0 0
\(613\) −11.4442 + 19.8220i −0.462227 + 0.800601i −0.999072 0.0430801i \(-0.986283\pi\)
0.536844 + 0.843681i \(0.319616\pi\)
\(614\) 0 0
\(615\) 13.3957 0.0509195i 0.540166 0.00205327i
\(616\) 0 0
\(617\) 8.14188 + 1.43563i 0.327780 + 0.0577964i 0.335117 0.942177i \(-0.391224\pi\)
−0.00733686 + 0.999973i \(0.502335\pi\)
\(618\) 0 0
\(619\) 8.59529 23.6154i 0.345474 0.949182i −0.638303 0.769785i \(-0.720363\pi\)
0.983777 0.179396i \(-0.0574145\pi\)
\(620\) 0 0
\(621\) 12.2914 + 32.6085i 0.493237 + 1.30853i
\(622\) 0 0
\(623\) 6.57426 + 7.27474i 0.263392 + 0.291456i
\(624\) 0 0
\(625\) 7.61166 + 6.38694i 0.304466 + 0.255478i
\(626\) 0 0
\(627\) 11.7086 20.4590i 0.467595 0.817055i
\(628\) 0 0
\(629\) 16.7827 + 29.0685i 0.669171 + 1.15904i
\(630\) 0 0
\(631\) −22.4808 + 38.9380i −0.894948 + 1.55010i −0.0610790 + 0.998133i \(0.519454\pi\)
−0.833869 + 0.551962i \(0.813879\pi\)
\(632\) 0 0
\(633\) 23.6878 + 8.51984i 0.941507 + 0.338633i
\(634\) 0 0
\(635\) 1.47008 0.535066i 0.0583385 0.0212335i
\(636\) 0 0
\(637\) −27.4874 28.2571i −1.08909 1.11959i
\(638\) 0 0
\(639\) 16.7848 47.2300i 0.663996 1.86839i
\(640\) 0 0
\(641\) 17.5145 + 20.8730i 0.691781 + 0.824433i 0.991570 0.129573i \(-0.0413606\pi\)
−0.299789 + 0.954006i \(0.596916\pi\)
\(642\) 0 0
\(643\) 2.60698 + 7.16261i 0.102809 + 0.282466i 0.980423 0.196902i \(-0.0630881\pi\)
−0.877614 + 0.479368i \(0.840866\pi\)
\(644\) 0 0
\(645\) 6.89413 2.53898i 0.271456 0.0999721i
\(646\) 0 0
\(647\) 19.9589 + 34.5698i 0.784665 + 1.35908i 0.929199 + 0.369580i \(0.120498\pi\)
−0.144534 + 0.989500i \(0.546168\pi\)
\(648\) 0 0
\(649\) −5.93151 3.42456i −0.232832 0.134426i
\(650\) 0 0
\(651\) −34.5608 + 14.1901i −1.35454 + 0.556154i
\(652\) 0 0
\(653\) −9.27688 1.63576i −0.363032 0.0640124i −0.0108431 0.999941i \(-0.503452\pi\)
−0.352189 + 0.935929i \(0.614563\pi\)
\(654\) 0 0
\(655\) −11.4466 + 9.60482i −0.447255 + 0.375291i
\(656\) 0 0
\(657\) 5.89722 16.5939i 0.230073 0.647391i
\(658\) 0 0
\(659\) −8.23740 + 22.6321i −0.320883 + 0.881620i 0.669443 + 0.742863i \(0.266533\pi\)
−0.990327 + 0.138757i \(0.955689\pi\)
\(660\) 0 0
\(661\) 11.6789 + 2.05930i 0.454256 + 0.0800975i 0.396095 0.918210i \(-0.370365\pi\)
0.0581609 + 0.998307i \(0.481476\pi\)
\(662\) 0 0
\(663\) 40.3980 7.28169i 1.56893 0.282797i
\(664\) 0 0
\(665\) 6.21861 + 9.91160i 0.241147 + 0.384355i
\(666\) 0 0
\(667\) 22.9403 0.888252
\(668\) 0 0
\(669\) −16.0208 9.16859i −0.619399 0.354478i
\(670\) 0 0
\(671\) 4.28041 24.2754i 0.165243 0.937141i
\(672\) 0 0
\(673\) −8.05026 + 6.75497i −0.310315 + 0.260385i −0.784622 0.619974i \(-0.787143\pi\)
0.474307 + 0.880359i \(0.342699\pi\)
\(674\) 0 0
\(675\) 15.4439 13.2620i 0.594438 0.510456i
\(676\) 0 0
\(677\) −6.82193 38.6891i −0.262188 1.48694i −0.776924 0.629594i \(-0.783221\pi\)
0.514736 0.857349i \(-0.327890\pi\)
\(678\) 0 0
\(679\) −12.2596 + 4.97921i −0.470480 + 0.191085i
\(680\) 0 0
\(681\) 17.8656 31.2176i 0.684612 1.19626i
\(682\) 0 0
\(683\) −29.6515 17.1193i −1.13458 0.655051i −0.189498 0.981881i \(-0.560686\pi\)
−0.945083 + 0.326830i \(0.894019\pi\)
\(684\) 0 0
\(685\) 0.506467 + 0.292409i 0.0193511 + 0.0111724i
\(686\) 0 0
\(687\) 7.84046 21.7990i 0.299132 0.831682i
\(688\) 0 0
\(689\) 11.3696 64.4801i 0.433147 2.45650i
\(690\) 0 0
\(691\) 4.32267 + 5.15156i 0.164442 + 0.195975i 0.841973 0.539520i \(-0.181394\pi\)
−0.677531 + 0.735495i \(0.736950\pi\)
\(692\) 0 0
\(693\) −11.7179 + 22.5483i −0.445126 + 0.856540i
\(694\) 0 0
\(695\) −7.15164 + 19.6490i −0.271277 + 0.745328i
\(696\) 0 0
\(697\) −23.9657 20.1096i −0.907766 0.761706i
\(698\) 0 0
\(699\) −25.8053 4.44910i −0.976046 0.168280i
\(700\) 0 0
\(701\) 6.11612i 0.231003i 0.993307 + 0.115501i \(0.0368475\pi\)
−0.993307 + 0.115501i \(0.963153\pi\)
\(702\) 0 0
\(703\) 29.3629 16.9527i 1.10744 0.639382i
\(704\) 0 0
\(705\) −11.6124 + 4.27664i −0.437350 + 0.161068i
\(706\) 0 0
\(707\) −19.5534 2.71171i −0.735382 0.101984i
\(708\) 0 0
\(709\) 22.4892 + 8.18540i 0.844600 + 0.307409i 0.727837 0.685751i \(-0.240526\pi\)
0.116763 + 0.993160i \(0.462748\pi\)
\(710\) 0 0
\(711\) 11.9305 4.44536i 0.447430 0.166714i
\(712\) 0 0
\(713\) −51.3791 18.7005i −1.92416 0.700337i
\(714\) 0 0
\(715\) −14.3689 12.0569i −0.537367 0.450904i
\(716\) 0 0
\(717\) −12.4818 14.7609i −0.466142 0.551257i
\(718\) 0 0
\(719\) 2.89246 + 5.00989i 0.107871 + 0.186837i 0.914907 0.403664i \(-0.132263\pi\)
−0.807037 + 0.590501i \(0.798930\pi\)
\(720\) 0 0
\(721\) −24.3784 38.8558i −0.907899 1.44707i
\(722\) 0 0
\(723\) −6.25267 + 3.64174i −0.232539 + 0.135438i
\(724\) 0 0
\(725\) −4.58332 12.5926i −0.170220 0.467676i
\(726\) 0 0
\(727\) −27.9583 33.3194i −1.03691 1.23575i −0.971289 0.237903i \(-0.923540\pi\)
−0.0656260 0.997844i \(-0.520904\pi\)
\(728\) 0 0
\(729\) −14.0297 23.0687i −0.519620 0.854398i
\(730\) 0 0
\(731\) −16.1232 5.86837i −0.596339 0.217050i
\(732\) 0 0
\(733\) 1.57436 1.87625i 0.0581504 0.0693010i −0.736185 0.676780i \(-0.763375\pi\)
0.794336 + 0.607479i \(0.207819\pi\)
\(734\) 0 0
\(735\) −7.13115 10.4044i −0.263037 0.383771i
\(736\) 0 0
\(737\) 34.1869i 1.25929i
\(738\) 0 0
\(739\) 35.8434 1.31852 0.659260 0.751915i \(-0.270870\pi\)
0.659260 + 0.751915i \(0.270870\pi\)
\(740\) 0 0
\(741\) −7.35543 40.8071i −0.270209 1.49909i
\(742\) 0 0
\(743\) 13.1744 15.7006i 0.483320 0.575999i −0.468185 0.883630i \(-0.655092\pi\)
0.951506 + 0.307632i \(0.0995364\pi\)
\(744\) 0 0
\(745\) −20.0711 + 3.53907i −0.735348 + 0.129662i
\(746\) 0 0
\(747\) −2.43630 2.01294i −0.0891396 0.0736495i
\(748\) 0 0
\(749\) 7.46946 + 34.8287i 0.272928 + 1.27261i
\(750\) 0 0
\(751\) −5.66199 + 32.1108i −0.206609 + 1.17174i 0.688278 + 0.725447i \(0.258367\pi\)
−0.894887 + 0.446292i \(0.852744\pi\)
\(752\) 0 0
\(753\) −3.01931 + 17.5123i −0.110030 + 0.638185i
\(754\) 0 0
\(755\) 5.13322 0.186817
\(756\) 0 0
\(757\) −16.2169 −0.589415 −0.294707 0.955588i \(-0.595222\pi\)
−0.294707 + 0.955588i \(0.595222\pi\)
\(758\) 0 0
\(759\) −34.8977 + 12.8521i −1.26670 + 0.466503i
\(760\) 0 0
\(761\) −0.184575 + 1.04678i −0.00669084 + 0.0379456i −0.987970 0.154643i \(-0.950577\pi\)
0.981280 + 0.192589i \(0.0616883\pi\)
\(762\) 0 0
\(763\) 5.22512 16.1816i 0.189162 0.585812i
\(764\) 0 0
\(765\) 13.1342 0.0998524i 0.474867 0.00361017i
\(766\) 0 0
\(767\) −11.8648 + 2.09208i −0.428412 + 0.0755405i
\(768\) 0 0
\(769\) 18.2576 21.7586i 0.658386 0.784634i −0.328767 0.944411i \(-0.606633\pi\)
0.987153 + 0.159777i \(0.0510775\pi\)
\(770\) 0 0
\(771\) 33.1628 + 11.9277i 1.19433 + 0.429566i
\(772\) 0 0
\(773\) 10.6270 0.382226 0.191113 0.981568i \(-0.438790\pi\)
0.191113 + 0.981568i \(0.438790\pi\)
\(774\) 0 0
\(775\) 31.9396i 1.14730i
\(776\) 0 0
\(777\) −30.8870 + 19.5427i −1.10806 + 0.701091i
\(778\)