Properties

Label 261.3.s.a.37.4
Level $261$
Weight $3$
Character 261.37
Analytic conductor $7.112$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 261 = 3^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 261.s (of order \(28\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.11173489980\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(4\) over \(\Q(\zeta_{28})\)
Twist minimal: no (minimal twist has level 29)
Sato-Tate group: $\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label 37.4
Character \(\chi\) \(=\) 261.37
Dual form 261.3.s.a.127.4

$q$-expansion

\(f(q)\) \(=\) \(q+(2.32673 + 0.814157i) q^{2} +(1.62348 + 1.29468i) q^{4} +(3.83207 + 7.95737i) q^{5} +(2.23777 + 2.80607i) q^{7} +(-2.52264 - 4.01476i) q^{8} +O(q^{10})\) \(q+(2.32673 + 0.814157i) q^{2} +(1.62348 + 1.29468i) q^{4} +(3.83207 + 7.95737i) q^{5} +(2.23777 + 2.80607i) q^{7} +(-2.52264 - 4.01476i) q^{8} +(2.43763 + 21.6345i) q^{10} +(-4.04453 + 6.43684i) q^{11} +(-7.19807 + 1.64291i) q^{13} +(2.92209 + 8.35085i) q^{14} +(-4.44912 - 19.4929i) q^{16} +(-1.60706 - 1.60706i) q^{17} +(33.1033 - 3.72985i) q^{19} +(-4.08097 + 17.8799i) q^{20} +(-14.6511 + 11.6839i) q^{22} +(20.4388 + 9.84282i) q^{23} +(-33.0478 + 41.4406i) q^{25} +(-18.0855 - 2.03775i) q^{26} +7.45278i q^{28} +(-14.4627 - 25.1362i) q^{29} +(5.30982 + 1.85799i) q^{31} +(3.39483 - 30.1300i) q^{32} +(-2.43079 - 5.04759i) q^{34} +(-13.7537 + 28.5598i) q^{35} +(8.64092 + 13.7519i) q^{37} +(80.0590 + 18.2729i) q^{38} +(22.2800 - 35.4584i) q^{40} +(42.1095 - 42.1095i) q^{41} +(1.74483 + 4.98643i) q^{43} +(-14.8999 + 5.21368i) q^{44} +(39.5419 + 39.5419i) q^{46} +(-60.4551 - 37.9864i) q^{47} +(8.03709 - 35.2128i) q^{49} +(-110.632 + 69.5148i) q^{50} +(-13.8130 - 6.65197i) q^{52} +(78.2991 - 37.7068i) q^{53} +(-66.7192 - 7.51745i) q^{55} +(5.62062 - 16.0628i) q^{56} +(-13.1859 - 70.2600i) q^{58} -67.9548 q^{59} +(5.72557 - 50.8159i) q^{61} +(10.8418 + 8.64605i) q^{62} +(-2.27117 + 4.71614i) q^{64} +(-40.6568 - 50.9820i) q^{65} +(-29.4645 - 6.72508i) q^{67} +(-0.528398 - 4.68966i) q^{68} +(-55.2532 + 55.2532i) q^{70} +(-17.3364 + 3.95693i) q^{71} +(29.8255 - 10.4364i) q^{73} +(8.90881 + 39.0321i) q^{74} +(58.5714 + 36.8029i) q^{76} +(-27.1129 + 3.05489i) q^{77} +(-38.0418 + 23.9032i) q^{79} +(138.063 - 110.101i) q^{80} +(132.261 - 63.6936i) q^{82} +(-3.87179 + 4.85507i) q^{83} +(6.62962 - 18.9464i) q^{85} +13.0226i q^{86} +36.0453 q^{88} +(19.6772 + 6.88537i) q^{89} +(-20.7177 - 16.5218i) q^{91} +(20.4387 + 42.4413i) q^{92} +(-109.735 - 137.604i) q^{94} +(156.534 + 249.122i) q^{95} +(5.86295 + 52.0352i) q^{97} +(47.3689 - 75.3871i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} + O(q^{10}) \) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} - 20q^{10} + 8q^{11} - 14q^{13} - 26q^{14} + 18q^{16} + 26q^{17} + 2q^{19} - 46q^{20} + 154q^{22} - 56q^{23} - 34q^{25} - 110q^{26} + 170q^{29} - 88q^{31} + 132q^{32} - 224q^{34} + 210q^{35} - 56q^{37} + 294q^{38} - 492q^{40} + 34q^{41} + 176q^{43} - 126q^{44} + 744q^{46} - 208q^{47} + 506q^{49} - 732q^{50} + 690q^{52} + 14q^{53} + 284q^{55} - 332q^{56} - 508q^{58} + 44q^{59} - 30q^{61} + 504q^{62} - 896q^{64} + 554q^{65} - 574q^{67} + 796q^{68} - 1066q^{70} - 224q^{71} - 22q^{73} - 820q^{74} + 514q^{76} - 436q^{77} + 564q^{79} - 1162q^{80} - 18q^{82} + 126q^{83} + 38q^{85} - 384q^{88} + 160q^{89} - 434q^{91} + 1022q^{92} - 2q^{94} + 642q^{95} + 604q^{97} + 102q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/261\mathbb{Z}\right)^\times\).

\(n\) \(118\) \(146\)
\(\chi(n)\) \(e\left(\frac{3}{28}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.32673 + 0.814157i 1.16336 + 0.407078i 0.841789 0.539806i \(-0.181502\pi\)
0.321574 + 0.946885i \(0.395788\pi\)
\(3\) 0 0
\(4\) 1.62348 + 1.29468i 0.405869 + 0.323670i
\(5\) 3.83207 + 7.95737i 0.766414 + 1.59147i 0.805755 + 0.592248i \(0.201760\pi\)
−0.0393418 + 0.999226i \(0.512526\pi\)
\(6\) 0 0
\(7\) 2.23777 + 2.80607i 0.319681 + 0.400867i 0.915543 0.402219i \(-0.131761\pi\)
−0.595862 + 0.803087i \(0.703190\pi\)
\(8\) −2.52264 4.01476i −0.315330 0.501845i
\(9\) 0 0
\(10\) 2.43763 + 21.6345i 0.243763 + 2.16345i
\(11\) −4.04453 + 6.43684i −0.367685 + 0.585167i −0.978409 0.206676i \(-0.933735\pi\)
0.610725 + 0.791843i \(0.290878\pi\)
\(12\) 0 0
\(13\) −7.19807 + 1.64291i −0.553698 + 0.126378i −0.490210 0.871605i \(-0.663080\pi\)
−0.0634884 + 0.997983i \(0.520223\pi\)
\(14\) 2.92209 + 8.35085i 0.208721 + 0.596489i
\(15\) 0 0
\(16\) −4.44912 19.4929i −0.278070 1.21830i
\(17\) −1.60706 1.60706i −0.0945331 0.0945331i 0.658259 0.752792i \(-0.271293\pi\)
−0.752792 + 0.658259i \(0.771293\pi\)
\(18\) 0 0
\(19\) 33.1033 3.72985i 1.74228 0.196308i 0.817270 0.576254i \(-0.195486\pi\)
0.925008 + 0.379947i \(0.124058\pi\)
\(20\) −4.08097 + 17.8799i −0.204049 + 0.893996i
\(21\) 0 0
\(22\) −14.6511 + 11.6839i −0.665960 + 0.531085i
\(23\) 20.4388 + 9.84282i 0.888644 + 0.427948i 0.821774 0.569813i \(-0.192984\pi\)
0.0668700 + 0.997762i \(0.478699\pi\)
\(24\) 0 0
\(25\) −33.0478 + 41.4406i −1.32191 + 1.65762i
\(26\) −18.0855 2.03775i −0.695597 0.0783750i
\(27\) 0 0
\(28\) 7.45278i 0.266171i
\(29\) −14.4627 25.1362i −0.498714 0.866766i
\(30\) 0 0
\(31\) 5.30982 + 1.85799i 0.171284 + 0.0599350i 0.414559 0.910022i \(-0.363936\pi\)
−0.243275 + 0.969957i \(0.578222\pi\)
\(32\) 3.39483 30.1300i 0.106089 0.941562i
\(33\) 0 0
\(34\) −2.43079 5.04759i −0.0714939 0.148459i
\(35\) −13.7537 + 28.5598i −0.392962 + 0.815994i
\(36\) 0 0
\(37\) 8.64092 + 13.7519i 0.233538 + 0.371674i 0.942848 0.333223i \(-0.108136\pi\)
−0.709310 + 0.704897i \(0.750993\pi\)
\(38\) 80.0590 + 18.2729i 2.10682 + 0.480867i
\(39\) 0 0
\(40\) 22.2800 35.4584i 0.557000 0.886461i
\(41\) 42.1095 42.1095i 1.02706 1.02706i 0.0274377 0.999624i \(-0.491265\pi\)
0.999624 0.0274377i \(-0.00873478\pi\)
\(42\) 0 0
\(43\) 1.74483 + 4.98643i 0.0405774 + 0.115964i 0.962389 0.271674i \(-0.0875771\pi\)
−0.921812 + 0.387637i \(0.873291\pi\)
\(44\) −14.8999 + 5.21368i −0.338633 + 0.118493i
\(45\) 0 0
\(46\) 39.5419 + 39.5419i 0.859607 + 0.859607i
\(47\) −60.4551 37.9864i −1.28628 0.808222i −0.297086 0.954851i \(-0.596015\pi\)
−0.989192 + 0.146629i \(0.953158\pi\)
\(48\) 0 0
\(49\) 8.03709 35.2128i 0.164022 0.718629i
\(50\) −110.632 + 69.5148i −2.21264 + 1.39030i
\(51\) 0 0
\(52\) −13.8130 6.65197i −0.265634 0.127923i
\(53\) 78.2991 37.7068i 1.47734 0.711450i 0.490246 0.871584i \(-0.336907\pi\)
0.987095 + 0.160134i \(0.0511928\pi\)
\(54\) 0 0
\(55\) −66.7192 7.51745i −1.21308 0.136681i
\(56\) 5.62062 16.0628i 0.100368 0.286836i
\(57\) 0 0
\(58\) −13.1859 70.2600i −0.227344 1.21138i
\(59\) −67.9548 −1.15178 −0.575888 0.817528i \(-0.695344\pi\)
−0.575888 + 0.817528i \(0.695344\pi\)
\(60\) 0 0
\(61\) 5.72557 50.8159i 0.0938619 0.833047i −0.855273 0.518178i \(-0.826611\pi\)
0.949135 0.314870i \(-0.101961\pi\)
\(62\) 10.8418 + 8.64605i 0.174868 + 0.139452i
\(63\) 0 0
\(64\) −2.27117 + 4.71614i −0.0354871 + 0.0736897i
\(65\) −40.6568 50.9820i −0.625489 0.784338i
\(66\) 0 0
\(67\) −29.4645 6.72508i −0.439769 0.100374i −0.00309676 0.999995i \(-0.500986\pi\)
−0.436672 + 0.899621i \(0.643843\pi\)
\(68\) −0.528398 4.68966i −0.00777056 0.0689656i
\(69\) 0 0
\(70\) −55.2532 + 55.2532i −0.789331 + 0.789331i
\(71\) −17.3364 + 3.95693i −0.244175 + 0.0557314i −0.342857 0.939388i \(-0.611395\pi\)
0.0986817 + 0.995119i \(0.468537\pi\)
\(72\) 0 0
\(73\) 29.8255 10.4364i 0.408569 0.142965i −0.118166 0.992994i \(-0.537702\pi\)
0.526735 + 0.850029i \(0.323416\pi\)
\(74\) 8.90881 + 39.0321i 0.120389 + 0.527460i
\(75\) 0 0
\(76\) 58.5714 + 36.8029i 0.770677 + 0.484248i
\(77\) −27.1129 + 3.05489i −0.352116 + 0.0396739i
\(78\) 0 0
\(79\) −38.0418 + 23.9032i −0.481541 + 0.302572i −0.750840 0.660484i \(-0.770351\pi\)
0.269299 + 0.963057i \(0.413208\pi\)
\(80\) 138.063 110.101i 1.72578 1.37627i
\(81\) 0 0
\(82\) 132.261 63.6936i 1.61294 0.776751i
\(83\) −3.87179 + 4.85507i −0.0466480 + 0.0584948i −0.804608 0.593806i \(-0.797625\pi\)
0.757960 + 0.652301i \(0.226196\pi\)
\(84\) 0 0
\(85\) 6.62962 18.9464i 0.0779955 0.222898i
\(86\) 13.0226i 0.151426i
\(87\) 0 0
\(88\) 36.0453 0.409605
\(89\) 19.6772 + 6.88537i 0.221093 + 0.0773637i 0.438552 0.898706i \(-0.355491\pi\)
−0.217460 + 0.976069i \(0.569777\pi\)
\(90\) 0 0
\(91\) −20.7177 16.5218i −0.227667 0.181559i
\(92\) 20.4387 + 42.4413i 0.222159 + 0.461319i
\(93\) 0 0
\(94\) −109.735 137.604i −1.16740 1.46387i
\(95\) 156.534 + 249.122i 1.64772 + 2.62234i
\(96\) 0 0
\(97\) 5.86295 + 52.0352i 0.0604428 + 0.536445i 0.987050 + 0.160414i \(0.0512829\pi\)
−0.926607 + 0.376031i \(0.877289\pi\)
\(98\) 47.3689 75.3871i 0.483356 0.769256i
\(99\) 0 0
\(100\) −107.305 + 24.4916i −1.07305 + 0.244916i
\(101\) 13.5414 + 38.6991i 0.134073 + 0.383159i 0.991273 0.131825i \(-0.0420836\pi\)
−0.857200 + 0.514984i \(0.827798\pi\)
\(102\) 0 0
\(103\) −18.1203 79.3902i −0.175925 0.770779i −0.983485 0.180992i \(-0.942069\pi\)
0.807559 0.589786i \(-0.200788\pi\)
\(104\) 24.7541 + 24.7541i 0.238020 + 0.238020i
\(105\) 0 0
\(106\) 212.880 23.9858i 2.00830 0.226281i
\(107\) −3.47716 + 15.2344i −0.0324968 + 0.142378i −0.988574 0.150738i \(-0.951835\pi\)
0.956077 + 0.293116i \(0.0946921\pi\)
\(108\) 0 0
\(109\) −24.8134 + 19.7880i −0.227646 + 0.181542i −0.730670 0.682731i \(-0.760792\pi\)
0.503024 + 0.864272i \(0.332221\pi\)
\(110\) −149.117 71.8109i −1.35561 0.652827i
\(111\) 0 0
\(112\) 44.7422 56.1050i 0.399484 0.500937i
\(113\) −80.1964 9.03596i −0.709703 0.0799643i −0.250269 0.968176i \(-0.580519\pi\)
−0.459434 + 0.888212i \(0.651948\pi\)
\(114\) 0 0
\(115\) 200.358i 1.74224i
\(116\) 9.06348 59.5327i 0.0781335 0.513213i
\(117\) 0 0
\(118\) −158.112 55.3259i −1.33993 0.468863i
\(119\) 0.913300 8.10576i 0.00767479 0.0681156i
\(120\) 0 0
\(121\) 27.4253 + 56.9493i 0.226655 + 0.470655i
\(122\) 54.6939 113.573i 0.448311 0.930927i
\(123\) 0 0
\(124\) 6.21487 + 9.89091i 0.0501199 + 0.0797654i
\(125\) −241.135 55.0375i −1.92908 0.440300i
\(126\) 0 0
\(127\) −47.5028 + 75.6003i −0.374038 + 0.595278i −0.979706 0.200439i \(-0.935763\pi\)
0.605668 + 0.795717i \(0.292906\pi\)
\(128\) −94.8838 + 94.8838i −0.741279 + 0.741279i
\(129\) 0 0
\(130\) −53.0899 151.722i −0.408384 1.16709i
\(131\) 122.442 42.8444i 0.934674 0.327057i 0.180383 0.983596i \(-0.442266\pi\)
0.754291 + 0.656540i \(0.227981\pi\)
\(132\) 0 0
\(133\) 84.5437 + 84.5437i 0.635667 + 0.635667i
\(134\) −63.0805 39.6361i −0.470750 0.295792i
\(135\) 0 0
\(136\) −2.39793 + 10.5060i −0.0176318 + 0.0772501i
\(137\) 104.753 65.8204i 0.764618 0.480441i −0.0924040 0.995722i \(-0.529455\pi\)
0.857022 + 0.515281i \(0.172312\pi\)
\(138\) 0 0
\(139\) 40.2937 + 19.4044i 0.289883 + 0.139600i 0.573174 0.819434i \(-0.305712\pi\)
−0.283291 + 0.959034i \(0.591426\pi\)
\(140\) −59.3046 + 28.5596i −0.423604 + 0.203997i
\(141\) 0 0
\(142\) −43.5587 4.90789i −0.306751 0.0345626i
\(143\) 18.5377 52.9776i 0.129634 0.370473i
\(144\) 0 0
\(145\) 144.596 211.409i 0.997215 1.45799i
\(146\) 77.8928 0.533512
\(147\) 0 0
\(148\) −3.77603 + 33.5132i −0.0255137 + 0.226440i
\(149\) 92.6321 + 73.8716i 0.621692 + 0.495783i 0.882938 0.469489i \(-0.155562\pi\)
−0.261246 + 0.965272i \(0.584133\pi\)
\(150\) 0 0
\(151\) −79.3234 + 164.717i −0.525320 + 1.09084i 0.454461 + 0.890767i \(0.349832\pi\)
−0.979781 + 0.200072i \(0.935882\pi\)
\(152\) −98.4822 123.493i −0.647909 0.812453i
\(153\) 0 0
\(154\) −65.5715 14.9663i −0.425789 0.0971836i
\(155\) 5.56290 + 49.3721i 0.0358897 + 0.318530i
\(156\) 0 0
\(157\) −78.3608 + 78.3608i −0.499113 + 0.499113i −0.911162 0.412049i \(-0.864813\pi\)
0.412049 + 0.911162i \(0.364813\pi\)
\(158\) −107.974 + 24.6443i −0.683378 + 0.155977i
\(159\) 0 0
\(160\) 252.765 88.4462i 1.57978 0.552789i
\(161\) 18.1177 + 79.3787i 0.112532 + 0.493035i
\(162\) 0 0
\(163\) −12.8408 8.06844i −0.0787782 0.0494996i 0.492067 0.870557i \(-0.336242\pi\)
−0.570845 + 0.821058i \(0.693384\pi\)
\(164\) 122.882 13.8455i 0.749282 0.0844238i
\(165\) 0 0
\(166\) −12.9614 + 8.14417i −0.0780806 + 0.0490613i
\(167\) −205.173 + 163.620i −1.22858 + 0.979760i −0.228600 + 0.973521i \(0.573415\pi\)
−0.999981 + 0.00623948i \(0.998014\pi\)
\(168\) 0 0
\(169\) −103.151 + 49.6747i −0.610359 + 0.293933i
\(170\) 30.8506 38.6854i 0.181474 0.227561i
\(171\) 0 0
\(172\) −3.62315 + 10.3544i −0.0210648 + 0.0601998i
\(173\) 61.9144i 0.357887i 0.983859 + 0.178943i \(0.0572679\pi\)
−0.983859 + 0.178943i \(0.942732\pi\)
\(174\) 0 0
\(175\) −190.238 −1.08708
\(176\) 143.467 + 50.2012i 0.815153 + 0.285234i
\(177\) 0 0
\(178\) 40.1778 + 32.0407i 0.225718 + 0.180004i
\(179\) −139.692 290.074i −0.780403 1.62052i −0.784182 0.620531i \(-0.786917\pi\)
0.00377939 0.999993i \(-0.498797\pi\)
\(180\) 0 0
\(181\) −185.369 232.445i −1.02414 1.28423i −0.958108 0.286408i \(-0.907539\pi\)
−0.0660276 0.997818i \(-0.521033\pi\)
\(182\) −34.7531 55.3093i −0.190951 0.303897i
\(183\) 0 0
\(184\) −12.0433 106.887i −0.0654525 0.580907i
\(185\) −76.3167 + 121.457i −0.412523 + 0.656526i
\(186\) 0 0
\(187\) 16.8442 3.84458i 0.0900760 0.0205593i
\(188\) −48.9672 139.940i −0.260464 0.744362i
\(189\) 0 0
\(190\) 161.387 + 707.082i 0.849405 + 3.72149i
\(191\) 191.734 + 191.734i 1.00384 + 1.00384i 0.999993 + 0.00384775i \(0.00122478\pi\)
0.00384775 + 0.999993i \(0.498775\pi\)
\(192\) 0 0
\(193\) 134.893 15.1987i 0.698925 0.0787500i 0.244650 0.969611i \(-0.421327\pi\)
0.454275 + 0.890861i \(0.349898\pi\)
\(194\) −28.7233 + 125.845i −0.148058 + 0.648685i
\(195\) 0 0
\(196\) 58.6374 46.7617i 0.299170 0.238580i
\(197\) 102.900 + 49.5541i 0.522336 + 0.251544i 0.676423 0.736514i \(-0.263529\pi\)
−0.154087 + 0.988057i \(0.549244\pi\)
\(198\) 0 0
\(199\) −50.0688 + 62.7843i −0.251602 + 0.315499i −0.891553 0.452917i \(-0.850383\pi\)
0.639951 + 0.768416i \(0.278955\pi\)
\(200\) 249.742 + 28.1391i 1.24871 + 0.140696i
\(201\) 0 0
\(202\) 101.067i 0.500332i
\(203\) 38.1698 96.8324i 0.188029 0.477007i
\(204\) 0 0
\(205\) 496.447 + 173.714i 2.42170 + 0.847388i
\(206\) 22.4751 199.472i 0.109102 0.968311i
\(207\) 0 0
\(208\) 64.0501 + 133.001i 0.307933 + 0.639430i
\(209\) −109.879 + 228.166i −0.525737 + 1.09170i
\(210\) 0 0
\(211\) −34.1531 54.3543i −0.161863 0.257604i 0.755939 0.654642i \(-0.227181\pi\)
−0.917802 + 0.397039i \(0.870038\pi\)
\(212\) 175.935 + 40.1560i 0.829883 + 0.189415i
\(213\) 0 0
\(214\) −20.4936 + 32.6154i −0.0957645 + 0.152408i
\(215\) −32.9926 + 32.9926i −0.153454 + 0.153454i
\(216\) 0 0
\(217\) 6.66849 + 19.0575i 0.0307304 + 0.0878224i
\(218\) −73.8446 + 25.8393i −0.338736 + 0.118529i
\(219\) 0 0
\(220\) −98.5845 98.5845i −0.448111 0.448111i
\(221\) 14.2080 + 8.92749i 0.0642897 + 0.0403959i
\(222\) 0 0
\(223\) −47.0630 + 206.196i −0.211045 + 0.924648i 0.752814 + 0.658234i \(0.228696\pi\)
−0.963859 + 0.266414i \(0.914161\pi\)
\(224\) 92.1437 57.8977i 0.411356 0.258472i
\(225\) 0 0
\(226\) −179.238 86.3166i −0.793090 0.381932i
\(227\) −276.625 + 133.216i −1.21861 + 0.586853i −0.928925 0.370268i \(-0.879266\pi\)
−0.289688 + 0.957121i \(0.593552\pi\)
\(228\) 0 0
\(229\) 85.7684 + 9.66378i 0.374535 + 0.0421999i 0.297226 0.954807i \(-0.403939\pi\)
0.0773089 + 0.997007i \(0.475367\pi\)
\(230\) −163.122 + 466.177i −0.709228 + 2.02686i
\(231\) 0 0
\(232\) −64.4317 + 121.474i −0.277723 + 0.523595i
\(233\) 141.899 0.609008 0.304504 0.952511i \(-0.401509\pi\)
0.304504 + 0.952511i \(0.401509\pi\)
\(234\) 0 0
\(235\) 70.6042 626.630i 0.300444 2.66651i
\(236\) −110.323 87.9797i −0.467471 0.372796i
\(237\) 0 0
\(238\) 8.72436 18.1163i 0.0366570 0.0761190i
\(239\) −86.5736 108.560i −0.362233 0.454225i 0.567002 0.823717i \(-0.308103\pi\)
−0.929234 + 0.369491i \(0.879532\pi\)
\(240\) 0 0
\(241\) −178.803 40.8106i −0.741922 0.169339i −0.165178 0.986264i \(-0.552820\pi\)
−0.576744 + 0.816925i \(0.695677\pi\)
\(242\) 17.4456 + 154.834i 0.0720892 + 0.639809i
\(243\) 0 0
\(244\) 75.0857 75.0857i 0.307728 0.307728i
\(245\) 311.000 70.9837i 1.26939 0.289730i
\(246\) 0 0
\(247\) −232.152 + 81.2336i −0.939887 + 0.328881i
\(248\) −5.93540 26.0047i −0.0239331 0.104858i
\(249\) 0 0
\(250\) −516.246 324.379i −2.06498 1.29752i
\(251\) 253.427 28.5543i 1.00967 0.113762i 0.408394 0.912806i \(-0.366089\pi\)
0.601273 + 0.799043i \(0.294660\pi\)
\(252\) 0 0
\(253\) −146.022 + 91.7517i −0.577162 + 0.362655i
\(254\) −172.077 + 137.227i −0.677467 + 0.540262i
\(255\) 0 0
\(256\) −279.154 + 134.434i −1.09045 + 0.525131i
\(257\) 9.57230 12.0033i 0.0372463 0.0467054i −0.762859 0.646564i \(-0.776205\pi\)
0.800106 + 0.599859i \(0.204777\pi\)
\(258\) 0 0
\(259\) −19.2526 + 55.0206i −0.0743342 + 0.212435i
\(260\) 135.406i 0.520791i
\(261\) 0 0
\(262\) 319.772 1.22050
\(263\) −210.667 73.7155i −0.801014 0.280287i −0.101435 0.994842i \(-0.532343\pi\)
−0.699579 + 0.714555i \(0.746629\pi\)
\(264\) 0 0
\(265\) 600.095 + 478.560i 2.26451 + 1.80589i
\(266\) 127.878 + 265.542i 0.480745 + 0.998277i
\(267\) 0 0
\(268\) −39.1281 49.0651i −0.146000 0.183079i
\(269\) −206.896 329.273i −0.769129 1.22406i −0.969680 0.244379i \(-0.921416\pi\)
0.200551 0.979683i \(-0.435727\pi\)
\(270\) 0 0
\(271\) 43.4468 + 385.601i 0.160320 + 1.42288i 0.773929 + 0.633273i \(0.218289\pi\)
−0.613608 + 0.789611i \(0.710283\pi\)
\(272\) −24.1762 + 38.4762i −0.0888831 + 0.141457i
\(273\) 0 0
\(274\) 297.319 67.8611i 1.08511 0.247668i
\(275\) −133.084 380.331i −0.483940 1.38302i
\(276\) 0 0
\(277\) −73.9544 324.015i −0.266983 1.16973i −0.913503 0.406833i \(-0.866633\pi\)
0.646519 0.762897i \(-0.276224\pi\)
\(278\) 77.9542 + 77.9542i 0.280411 + 0.280411i
\(279\) 0 0
\(280\) 149.356 16.8284i 0.533415 0.0601015i
\(281\) 0.644237 2.82259i 0.00229266 0.0100448i −0.973769 0.227540i \(-0.926932\pi\)
0.976061 + 0.217496i \(0.0697888\pi\)
\(282\) 0 0
\(283\) 275.054 219.348i 0.971921 0.775081i −0.00245718 0.999997i \(-0.500782\pi\)
0.974378 + 0.224916i \(0.0722107\pi\)
\(284\) −33.2683 16.0212i −0.117142 0.0564125i
\(285\) 0 0
\(286\) 86.2642 108.172i 0.301623 0.378223i
\(287\) 212.393 + 23.9310i 0.740047 + 0.0833833i
\(288\) 0 0
\(289\) 283.835i 0.982127i
\(290\) 508.556 374.167i 1.75364 1.29023i
\(291\) 0 0
\(292\) 61.9329 + 21.6713i 0.212099 + 0.0742167i
\(293\) 10.4159 92.4441i 0.0355493 0.315509i −0.963336 0.268299i \(-0.913538\pi\)
0.998885 0.0472098i \(-0.0150329\pi\)
\(294\) 0 0
\(295\) −260.407 540.742i −0.882737 1.83302i
\(296\) 33.4128 69.3824i 0.112881 0.234400i
\(297\) 0 0
\(298\) 155.386 + 247.296i 0.521431 + 0.829853i
\(299\) −163.291 37.2701i −0.546124 0.124649i
\(300\) 0 0
\(301\) −10.0878 + 16.0546i −0.0335142 + 0.0533375i
\(302\) −318.669 + 318.669i −1.05520 + 1.05520i
\(303\) 0 0
\(304\) −219.986 628.683i −0.723637 2.06804i
\(305\) 426.302 149.169i 1.39771 0.489080i
\(306\) 0 0
\(307\) −32.6117 32.6117i −0.106227 0.106227i 0.651996 0.758223i \(-0.273932\pi\)
−0.758223 + 0.651996i \(0.773932\pi\)
\(308\) −47.9724 30.1430i −0.155754 0.0978670i
\(309\) 0 0
\(310\) −27.2533 + 119.404i −0.0879138 + 0.385176i
\(311\) −55.7972 + 35.0597i −0.179412 + 0.112732i −0.618744 0.785593i \(-0.712358\pi\)
0.439332 + 0.898325i \(0.355215\pi\)
\(312\) 0 0
\(313\) −145.236 69.9418i −0.464012 0.223456i 0.187246 0.982313i \(-0.440044\pi\)
−0.651257 + 0.758857i \(0.725758\pi\)
\(314\) −246.122 + 118.526i −0.783828 + 0.377472i
\(315\) 0 0
\(316\) −92.7070 10.4456i −0.293377 0.0330556i
\(317\) −92.7815 + 265.154i −0.292686 + 0.836449i 0.699827 + 0.714312i \(0.253260\pi\)
−0.992513 + 0.122137i \(0.961025\pi\)
\(318\) 0 0
\(319\) 220.293 + 8.57016i 0.690573 + 0.0268657i
\(320\) −46.2314 −0.144473
\(321\) 0 0
\(322\) −22.4718 + 199.443i −0.0697883 + 0.619388i
\(323\) −59.1931 47.2050i −0.183261 0.146145i
\(324\) 0 0
\(325\) 169.797 352.587i 0.522452 1.08488i
\(326\) −23.3082 29.2275i −0.0714974 0.0896549i
\(327\) 0 0
\(328\) −275.287 62.8324i −0.839289 0.191562i
\(329\) −28.6917 254.646i −0.0872088 0.774000i
\(330\) 0 0
\(331\) −35.3548 + 35.3548i −0.106812 + 0.106812i −0.758493 0.651681i \(-0.774064\pi\)
0.651681 + 0.758493i \(0.274064\pi\)
\(332\) −12.5715 + 2.86937i −0.0378660 + 0.00864268i
\(333\) 0 0
\(334\) −610.593 + 213.656i −1.82812 + 0.639688i
\(335\) −59.3960 260.231i −0.177301 0.776808i
\(336\) 0 0
\(337\) −233.227 146.546i −0.692069 0.434856i 0.139541 0.990216i \(-0.455437\pi\)
−0.831610 + 0.555361i \(0.812580\pi\)
\(338\) −280.446 + 31.5987i −0.829723 + 0.0934873i
\(339\) 0 0
\(340\) 35.2925 22.1758i 0.103802 0.0652228i
\(341\) −33.4353 + 26.6637i −0.0980506 + 0.0781928i
\(342\) 0 0
\(343\) 275.244 132.551i 0.802462 0.386445i
\(344\) 15.6178 19.5841i 0.0454005 0.0569304i
\(345\) 0 0
\(346\) −50.4080 + 144.058i −0.145688 + 0.416352i
\(347\) 506.789i 1.46049i −0.683186 0.730244i \(-0.739406\pi\)
0.683186 0.730244i \(-0.260594\pi\)
\(348\) 0 0
\(349\) −308.138 −0.882917 −0.441459 0.897282i \(-0.645539\pi\)
−0.441459 + 0.897282i \(0.645539\pi\)
\(350\) −442.633 154.884i −1.26466 0.442525i
\(351\) 0 0
\(352\) 180.211 + 143.714i 0.511964 + 0.408277i
\(353\) −48.7910 101.316i −0.138218 0.287013i 0.820358 0.571851i \(-0.193774\pi\)
−0.958576 + 0.284838i \(0.908060\pi\)
\(354\) 0 0
\(355\) −97.9212 122.789i −0.275834 0.345885i
\(356\) 23.0312 + 36.6540i 0.0646945 + 0.102961i
\(357\) 0 0
\(358\) −88.8599 788.653i −0.248212 2.20294i
\(359\) 38.4941 61.2630i 0.107226 0.170649i −0.788801 0.614648i \(-0.789298\pi\)
0.896027 + 0.443999i \(0.146441\pi\)
\(360\) 0 0
\(361\) 729.968 166.610i 2.02207 0.461525i
\(362\) −242.055 691.754i −0.668661 1.91092i
\(363\) 0 0
\(364\) −12.2443 53.6457i −0.0336381 0.147378i
\(365\) 197.340 + 197.340i 0.540657 + 0.540657i
\(366\) 0 0
\(367\) 39.4991 4.45048i 0.107627 0.0121267i −0.0579866 0.998317i \(-0.518468\pi\)
0.165614 + 0.986191i \(0.447040\pi\)
\(368\) 100.930 442.203i 0.274266 1.20164i
\(369\) 0 0
\(370\) −276.453 + 220.464i −0.747171 + 0.595849i
\(371\) 281.023 + 135.334i 0.757475 + 0.364781i
\(372\) 0 0
\(373\) −312.636 + 392.033i −0.838165 + 1.05103i 0.159793 + 0.987151i \(0.448917\pi\)
−0.997958 + 0.0638753i \(0.979654\pi\)
\(374\) 42.3220 + 4.76854i 0.113160 + 0.0127501i
\(375\) 0 0
\(376\) 338.539i 0.900369i
\(377\) 145.400 + 157.171i 0.385677 + 0.416900i
\(378\) 0 0
\(379\) −296.798 103.854i −0.783109 0.274022i −0.0910346 0.995848i \(-0.529017\pi\)
−0.692075 + 0.721826i \(0.743303\pi\)
\(380\) −68.4044 + 607.106i −0.180012 + 1.59765i
\(381\) 0 0
\(382\) 290.010 + 602.212i 0.759189 + 1.57647i
\(383\) −184.851 + 383.847i −0.482639 + 1.00221i 0.507438 + 0.861688i \(0.330593\pi\)
−0.990077 + 0.140522i \(0.955122\pi\)
\(384\) 0 0
\(385\) −128.208 204.041i −0.333007 0.529977i
\(386\) 326.232 + 74.4604i 0.845161 + 0.192903i
\(387\) 0 0
\(388\) −57.8505 + 92.0686i −0.149099 + 0.237290i
\(389\) −11.1950 + 11.1950i −0.0287790 + 0.0287790i −0.721350 0.692571i \(-0.756478\pi\)
0.692571 + 0.721350i \(0.256478\pi\)
\(390\) 0 0
\(391\) −17.0284 48.6645i −0.0435510 0.124462i
\(392\) −161.646 + 56.5623i −0.412362 + 0.144292i
\(393\) 0 0
\(394\) 199.076 + 199.076i 0.505268 + 0.505268i
\(395\) −335.985 211.114i −0.850596 0.534465i
\(396\) 0 0
\(397\) 56.3270 246.785i 0.141882 0.621624i −0.853116 0.521722i \(-0.825290\pi\)
0.994997 0.0999023i \(-0.0318530\pi\)
\(398\) −167.613 + 105.318i −0.421137 + 0.264618i
\(399\) 0 0
\(400\) 954.829 + 459.821i 2.38707 + 1.14955i
\(401\) 400.299 192.774i 0.998253 0.480733i 0.137908 0.990445i \(-0.455962\pi\)
0.860345 + 0.509712i \(0.170248\pi\)
\(402\) 0 0
\(403\) −41.2730 4.65035i −0.102414 0.0115393i
\(404\) −28.1188 + 80.3589i −0.0696010 + 0.198908i
\(405\) 0 0
\(406\) 167.648 194.226i 0.412925 0.478390i
\(407\) −123.467 −0.303360
\(408\) 0 0
\(409\) −60.3508 + 535.628i −0.147557 + 1.30960i 0.673683 + 0.739021i \(0.264711\pi\)
−0.821240 + 0.570583i \(0.806717\pi\)
\(410\) 1013.67 + 808.372i 2.47236 + 1.97164i
\(411\) 0 0
\(412\) 73.3670 152.348i 0.178075 0.369777i
\(413\) −152.067 190.686i −0.368201 0.461709i
\(414\) 0 0
\(415\) −53.4705 12.2043i −0.128845 0.0294080i
\(416\) 25.0647 + 222.455i 0.0602516 + 0.534748i
\(417\) 0 0
\(418\) −441.421 + 441.421i −1.05603 + 1.05603i
\(419\) 428.228 97.7402i 1.02202 0.233270i 0.321508 0.946907i \(-0.395810\pi\)
0.700516 + 0.713637i \(0.252953\pi\)
\(420\) 0 0
\(421\) 736.985 257.882i 1.75056 0.612547i 0.751664 0.659546i \(-0.229251\pi\)
0.998895 + 0.0469987i \(0.0149657\pi\)
\(422\) −35.2120 154.274i −0.0834407 0.365577i
\(423\) 0 0
\(424\) −348.905 219.231i −0.822888 0.517055i
\(425\) 119.707 13.4878i 0.281664 0.0317360i
\(426\) 0 0
\(427\) 155.405 97.6477i 0.363947 0.228683i
\(428\) −25.3688 + 20.2309i −0.0592729 + 0.0472685i
\(429\) 0 0
\(430\) −103.626 + 49.9036i −0.240990 + 0.116055i
\(431\) −476.007 + 596.893i −1.10442 + 1.38490i −0.189209 + 0.981937i \(0.560592\pi\)
−0.915215 + 0.402967i \(0.867979\pi\)
\(432\) 0 0
\(433\) −91.9842 + 262.876i −0.212435 + 0.607104i −0.999958 0.00918154i \(-0.997077\pi\)
0.787523 + 0.616285i \(0.211363\pi\)
\(434\) 49.7707i 0.114679i
\(435\) 0 0
\(436\) −65.9032 −0.151154
\(437\) 713.304 + 249.596i 1.63228 + 0.571158i
\(438\) 0 0
\(439\) −116.941 93.2577i −0.266382 0.212432i 0.481185 0.876619i \(-0.340207\pi\)
−0.747567 + 0.664187i \(0.768778\pi\)
\(440\) 138.128 + 286.826i 0.313927 + 0.651876i
\(441\) 0 0
\(442\) 25.7898 + 32.3394i 0.0583479 + 0.0731660i
\(443\) 391.882 + 623.676i 0.884609 + 1.40785i 0.912872 + 0.408246i \(0.133859\pi\)
−0.0282635 + 0.999601i \(0.508998\pi\)
\(444\) 0 0
\(445\) 20.6151 + 182.964i 0.0463261 + 0.411156i
\(446\) −277.379 + 441.446i −0.621926 + 0.989790i
\(447\) 0 0
\(448\) −18.3162 + 4.18055i −0.0408843 + 0.00933158i
\(449\) 24.4486 + 69.8700i 0.0544511 + 0.155612i 0.967897 0.251349i \(-0.0808741\pi\)
−0.913445 + 0.406961i \(0.866588\pi\)
\(450\) 0 0
\(451\) 100.739 + 441.365i 0.223367 + 0.978637i
\(452\) −118.498 118.498i −0.262165 0.262165i
\(453\) 0 0
\(454\) −752.089 + 84.7401i −1.65658 + 0.186652i
\(455\) 52.0787 228.172i 0.114459 0.501476i
\(456\) 0 0
\(457\) 617.662 492.569i 1.35156 1.07783i 0.362237 0.932086i \(-0.382013\pi\)
0.989322 0.145746i \(-0.0465582\pi\)
\(458\) 191.692 + 92.3139i 0.418541 + 0.201559i
\(459\) 0 0
\(460\) −259.399 + 325.276i −0.563911 + 0.707122i
\(461\) −444.021 50.0291i −0.963169 0.108523i −0.383647 0.923480i \(-0.625332\pi\)
−0.579522 + 0.814957i \(0.696761\pi\)
\(462\) 0 0
\(463\) 515.055i 1.11243i −0.831039 0.556215i \(-0.812253\pi\)
0.831039 0.556215i \(-0.187747\pi\)
\(464\) −425.630 + 393.754i −0.917307 + 0.848607i
\(465\) 0 0
\(466\) 330.160 + 115.528i 0.708498 + 0.247914i
\(467\) −62.2491 + 552.476i −0.133296 + 1.18303i 0.731834 + 0.681483i \(0.238665\pi\)
−0.865129 + 0.501549i \(0.832764\pi\)
\(468\) 0 0
\(469\) −47.0636 97.7286i −0.100349 0.208376i
\(470\) 674.452 1400.51i 1.43500 2.97982i
\(471\) 0 0
\(472\) 171.426 + 272.822i 0.363190 + 0.578013i
\(473\) −39.1539 8.93661i −0.0827777 0.0188935i
\(474\) 0 0
\(475\) −939.423 + 1495.08i −1.97773 + 3.14754i
\(476\) 11.9771 11.9771i 0.0251619 0.0251619i
\(477\) 0 0
\(478\) −113.048 323.074i −0.236503 0.675886i
\(479\) −47.7444 + 16.7065i −0.0996752 + 0.0348779i −0.379656 0.925128i \(-0.623958\pi\)
0.279981 + 0.960006i \(0.409672\pi\)
\(480\) 0 0
\(481\) −84.7912 84.7912i −0.176281 0.176281i
\(482\) −382.800 240.529i −0.794190 0.499023i
\(483\) 0 0
\(484\) −29.2067 + 127.963i −0.0603444 + 0.264386i
\(485\) −391.596 + 246.056i −0.807414 + 0.507332i
\(486\) 0 0
\(487\) 565.353 + 272.260i 1.16089 + 0.559055i 0.912288 0.409550i \(-0.134314\pi\)
0.248603 + 0.968606i \(0.420029\pi\)
\(488\) −218.457 + 105.203i −0.447658 + 0.215581i
\(489\) 0 0
\(490\) 781.404 + 88.0431i 1.59470 + 0.179680i
\(491\) 213.075 608.934i 0.433962 1.24019i −0.494634 0.869101i \(-0.664698\pi\)
0.928596 0.371091i \(-0.121016\pi\)
\(492\) 0 0
\(493\) −17.1530 + 63.6380i −0.0347931 + 0.129083i
\(494\) −606.291 −1.22731
\(495\) 0 0
\(496\) 12.5934 111.770i 0.0253900 0.225342i
\(497\) −49.8983 39.7926i −0.100399 0.0800655i
\(498\) 0 0
\(499\) 59.2142 122.960i 0.118666 0.246412i −0.833172 0.553014i \(-0.813478\pi\)
0.951838 + 0.306602i \(0.0991920\pi\)
\(500\) −320.221 401.545i −0.640443 0.803090i
\(501\) 0 0
\(502\) 612.902 + 139.891i 1.22092 + 0.278667i
\(503\) −0.982486 8.71980i −0.00195325 0.0173356i 0.992698 0.120628i \(-0.0384908\pi\)
−0.994651 + 0.103292i \(0.967062\pi\)
\(504\) 0 0
\(505\) −256.052 + 256.052i −0.507033 + 0.507033i
\(506\) −414.454 + 94.5963i −0.819078 + 0.186949i
\(507\) 0 0
\(508\) −174.998 + 61.2345i −0.344484 + 0.120540i
\(509\) 29.4818 + 129.168i 0.0579210 + 0.253768i 0.995596 0.0937442i \(-0.0298836\pi\)
−0.937675 + 0.347512i \(0.887026\pi\)
\(510\) 0 0
\(511\) 96.0279 + 60.3383i 0.187922 + 0.118079i
\(512\) −225.597 + 25.4186i −0.440619 + 0.0496458i
\(513\) 0 0
\(514\) 32.0447 20.1350i 0.0623437 0.0391732i
\(515\) 562.299 448.419i 1.09184 0.870716i
\(516\) 0 0
\(517\) 489.025 235.502i 0.945889 0.455516i
\(518\) −89.5908 + 112.343i −0.172955 + 0.216879i
\(519\) 0 0
\(520\) −102.118 + 291.837i −0.196381 + 0.561224i
\(521\) 754.287i 1.44777i −0.689921 0.723884i \(-0.742355\pi\)
0.689921 0.723884i \(-0.257645\pi\)
\(522\) 0 0
\(523\) −645.744 −1.23469 −0.617346 0.786692i \(-0.711792\pi\)
−0.617346 + 0.786692i \(0.711792\pi\)
\(524\) 254.252 + 88.9667i 0.485214 + 0.169784i
\(525\) 0 0
\(526\) −430.148 343.031i −0.817771 0.652151i
\(527\) −5.54731 11.5191i −0.0105262 0.0218579i
\(528\) 0 0
\(529\) −8.96189 11.2379i −0.0169412 0.0212436i
\(530\) 1006.63 + 1602.05i 1.89931 + 3.02273i
\(531\) 0 0
\(532\) 27.7977 + 246.712i 0.0522514 + 0.463744i
\(533\) −233.925 + 372.290i −0.438884 + 0.698480i
\(534\) 0 0
\(535\) −134.551 + 30.7103i −0.251496 + 0.0574024i
\(536\) 47.3288 + 135.258i 0.0883000 + 0.252347i
\(537\) 0 0
\(538\) −213.310 934.573i −0.396487 1.73712i
\(539\) 194.153 + 194.153i 0.360209 + 0.360209i
\(540\) 0 0
\(541\) 447.985 50.4757i 0.828068 0.0933008i 0.312251 0.950000i \(-0.398917\pi\)
0.515817 + 0.856699i \(0.327488\pi\)
\(542\) −212.851 + 932.561i −0.392714 + 1.72059i
\(543\) 0 0
\(544\) −53.8764 + 42.9650i −0.0990376 + 0.0789798i
\(545\) −252.547 121.620i −0.463390 0.223157i
\(546\) 0 0
\(547\) −506.301 + 634.881i −0.925596 + 1.16066i 0.0611077 + 0.998131i \(0.480537\pi\)
−0.986704 + 0.162530i \(0.948035\pi\)
\(548\) 255.280 + 28.7631i 0.465839 + 0.0524875i
\(549\) 0 0
\(550\) 993.277i 1.80596i
\(551\) −572.518 778.148i −1.03905 1.41225i
\(552\) 0 0
\(553\) −152.203 53.2580i −0.275231 0.0963075i
\(554\) 91.7276 814.105i 0.165573 1.46950i
\(555\) 0 0
\(556\) 40.2934 + 83.6702i 0.0724702 + 0.150486i
\(557\) 293.291 609.025i 0.526554 1.09340i −0.452868 0.891578i \(-0.649599\pi\)
0.979422 0.201824i \(-0.0646867\pi\)
\(558\) 0 0
\(559\) −20.7517 33.0261i −0.0371229 0.0590807i
\(560\) 617.903 + 141.032i 1.10340 + 0.251844i
\(561\) 0 0
\(562\) 3.79699 6.04288i 0.00675622 0.0107525i
\(563\) −429.885 + 429.885i −0.763562 + 0.763562i −0.976964 0.213403i \(-0.931545\pi\)
0.213403 + 0.976964i \(0.431545\pi\)
\(564\) 0 0
\(565\) −235.416 672.779i −0.416665 1.19076i
\(566\) 818.558 286.426i 1.44622 0.506053i
\(567\) 0 0
\(568\) 59.6197 + 59.6197i 0.104964 + 0.104964i
\(569\) −630.677 396.281i −1.10840 0.696451i −0.151958 0.988387i \(-0.548558\pi\)
−0.956438 + 0.291936i \(0.905701\pi\)
\(570\) 0 0
\(571\) 30.9764 135.717i 0.0542495 0.237682i −0.940533 0.339703i \(-0.889674\pi\)
0.994782 + 0.102020i \(0.0325307\pi\)
\(572\) 98.6846 62.0076i 0.172526 0.108405i
\(573\) 0 0
\(574\) 474.698 + 228.602i 0.827000 + 0.398262i
\(575\) −1083.35 + 521.714i −1.88409 + 0.907328i
\(576\) 0 0
\(577\) −751.398 84.6622i −1.30225 0.146728i −0.566545 0.824031i \(-0.691720\pi\)
−0.735705 + 0.677302i \(0.763149\pi\)
\(578\) 231.086 660.406i 0.399803 1.14257i
\(579\) 0 0
\(580\) 508.456 156.012i 0.876648 0.268986i
\(581\) −22.2878 −0.0383611
\(582\) 0 0
\(583\) −73.9703 + 656.505i −0.126879 + 1.12608i
\(584\) −117.139 93.4151i −0.200580 0.159957i
\(585\) 0 0
\(586\) 99.4990 206.612i 0.169794 0.352580i
\(587\) 481.461 + 603.732i 0.820205 + 1.02850i 0.999004 + 0.0446193i \(0.0142075\pi\)
−0.178799 + 0.983886i \(0.557221\pi\)
\(588\) 0 0
\(589\) 182.702 + 41.7006i 0.310191 + 0.0707990i
\(590\) −165.648 1470.17i −0.280760 2.49181i
\(591\) 0 0
\(592\) 229.620 229.620i 0.387872 0.387872i
\(593\) 636.417 145.258i 1.07322 0.244954i 0.350826 0.936441i \(-0.385901\pi\)
0.722390 + 0.691486i \(0.243044\pi\)
\(594\) 0 0
\(595\) 68.0004 23.7944i 0.114286 0.0399905i
\(596\) 54.7460 + 239.858i 0.0918557 + 0.402446i
\(597\) 0 0
\(598\) −349.590 219.662i −0.584598 0.367327i
\(599\) 106.941 12.0494i 0.178533 0.0201158i −0.0222453 0.999753i \(-0.507081\pi\)
0.200778 + 0.979637i \(0.435653\pi\)
\(600\) 0 0
\(601\) 561.034 352.521i 0.933500 0.586557i 0.0228515 0.999739i \(-0.492726\pi\)
0.910649 + 0.413182i \(0.135583\pi\)
\(602\) −36.5424 + 29.1416i −0.0607017 + 0.0484080i
\(603\) 0 0
\(604\) −342.035 + 164.715i −0.566283 + 0.272708i
\(605\) −348.071 + 436.467i −0.575323 + 0.721433i
\(606\) 0 0
\(607\) −170.406 + 486.993i −0.280735 + 0.802294i 0.714031 + 0.700114i \(0.246868\pi\)
−0.994766 + 0.102180i \(0.967418\pi\)
\(608\) 1010.06i 1.66129i
\(609\) 0 0
\(610\) 1113.33 1.82514
\(611\) 497.568 + 174.107i 0.814351 + 0.284954i
\(612\) 0 0
\(613\) 437.145 + 348.611i 0.713124 + 0.568697i 0.911436 0.411442i \(-0.134975\pi\)
−0.198313 + 0.980139i \(0.563546\pi\)
\(614\) −49.3275 102.430i −0.0803380 0.166824i
\(615\) 0 0
\(616\) 80.6609 + 101.146i 0.130943 + 0.164197i
\(617\) −365.703 582.013i −0.592711 0.943295i −0.999556 0.0297975i \(-0.990514\pi\)
0.406844 0.913497i \(-0.366629\pi\)
\(618\) 0 0
\(619\) −113.508 1007.42i −0.183374 1.62749i −0.662024 0.749483i \(-0.730302\pi\)
0.478650 0.878006i \(-0.341126\pi\)
\(620\) −54.8898 + 87.3567i −0.0885320 + 0.140898i
\(621\) 0 0
\(622\) −158.369 + 36.1467i −0.254612 + 0.0581136i
\(623\) 24.7123 + 70.6236i 0.0396665 + 0.113360i
\(624\) 0 0
\(625\) −191.227 837.819i −0.305963 1.34051i
\(626\) −280.980 280.980i −0.448850 0.448850i
\(627\) 0 0
\(628\) −228.669 + 25.7648i −0.364123 + 0.0410268i
\(629\) 8.21373 35.9867i 0.0130584 0.0572126i
\(630\) 0 0
\(631\) −402.770 + 321.198i −0.638304 + 0.509030i −0.888328 0.459209i \(-0.848133\pi\)
0.250025 + 0.968240i \(0.419561\pi\)
\(632\) 191.931 + 92.4293i 0.303689 + 0.146249i
\(633\) 0 0
\(634\) −431.754 + 541.403i −0.681001 + 0.853948i
\(635\) −783.614 88.2921i −1.23404 0.139043i
\(636\) 0 0
\(637\) 266.669i 0.418632i
\(638\) 505.583 + 199.293i 0.792450 + 0.312372i
\(639\) 0 0
\(640\) −1118.63 391.424i −1.74785 0.611600i
\(641\) −44.9011 + 398.508i −0.0700485 + 0.621698i 0.908817 + 0.417194i \(0.136987\pi\)
−0.978866 + 0.204504i \(0.934442\pi\)
\(642\) 0 0
\(643\) −470.130 976.234i −0.731150 1.51825i −0.850833 0.525437i \(-0.823902\pi\)
0.119683 0.992812i \(-0.461812\pi\)
\(644\) −73.3564 + 152.326i −0.113907 + 0.236531i
\(645\) 0 0
\(646\) −99.2940 158.026i −0.153706 0.244622i
\(647\) 625.852 + 142.847i 0.967313 + 0.220783i 0.676865 0.736108i \(-0.263338\pi\)
0.290449 + 0.956891i \(0.406195\pi\)
\(648\) 0 0
\(649\) 274.845 437.414i 0.423491 0.673981i
\(650\) 682.132 682.132i 1.04943 1.04943i
\(651\) 0 0
\(652\) −10.4008 29.7237i −0.0159521 0.0455885i
\(653\) 459.623 160.829i 0.703863 0.246292i 0.0454690 0.998966i \(-0.485522\pi\)
0.658394 + 0.752673i \(0.271236\pi\)
\(654\) 0 0
\(655\) 810.136 + 810.136i 1.23685 + 1.23685i
\(656\) −1008.18 633.484i −1.53687 0.965677i
\(657\) 0 0
\(658\) 140.564 615.851i 0.213623 0.935943i
\(659\) −782.367 + 491.594i −1.18720 + 0.745969i −0.972997 0.230820i \(-0.925859\pi\)
−0.214206 + 0.976788i \(0.568716\pi\)
\(660\) 0 0
\(661\) −504.495 242.952i −0.763229 0.367552i 0.0114268 0.999935i \(-0.496363\pi\)
−0.774656 + 0.632383i \(0.782077\pi\)
\(662\) −111.045 + 53.4767i −0.167742 + 0.0807805i
\(663\) 0 0
\(664\) 29.2591 + 3.29671i 0.0440649 + 0.00496492i
\(665\) −348.768 + 996.722i −0.524463 + 1.49883i
\(666\) 0 0
\(667\) −48.1895 656.109i −0.0722482 0.983671i
\(668\) −544.929 −0.815762
\(669\) 0 0
\(670\) 73.6705 653.844i 0.109956 0.975886i
\(671\) 303.936 + 242.381i 0.452960 + 0.361224i
\(672\) 0 0
\(673\) −326.415 + 677.808i −0.485015 + 1.00714i 0.504594 + 0.863357i \(0.331642\pi\)
−0.989609 + 0.143787i \(0.954072\pi\)
\(674\) −423.344 530.857i −0.628107 0.787621i
\(675\) 0 0
\(676\) −231.776 52.9013i −0.342863 0.0782563i
\(677\) −34.5918 307.011i −0.0510957 0.453487i −0.993045 0.117733i \(-0.962437\pi\)
0.941950 0.335754i \(-0.108991\pi\)
\(678\) 0 0
\(679\) −132.894 + 132.894i −0.195721 + 0.195721i
\(680\) −92.7893 + 21.1785i −0.136455 + 0.0311449i
\(681\) 0 0
\(682\) −99.5032 + 34.8177i −0.145899 + 0.0510523i
\(683\) 39.2932 + 172.155i 0.0575304 + 0.252057i 0.995513 0.0946254i \(-0.0301653\pi\)
−0.937983 + 0.346682i \(0.887308\pi\)
\(684\) 0 0
\(685\) 925.177 + 581.327i 1.35062 + 0.848653i
\(686\) 748.335 84.3171i 1.09087 0.122911i
\(687\) 0 0
\(688\) 89.4368 56.1969i 0.129995 0.0816815i
\(689\) −501.653 + 400.055i −0.728089 + 0.580632i
\(690\) 0 0
\(691\) −1218.08 + 586.597i −1.76278 + 0.848910i −0.791430 + 0.611260i \(0.790663\pi\)
−0.971351 + 0.237651i \(0.923623\pi\)
\(692\) −80.1593 + 100.517i −0.115837 + 0.145255i
\(693\) 0 0
\(694\) 412.606 1179.16i 0.594533 1.69908i
\(695\) 394.991i 0.568333i
\(696\) 0 0
\(697\) −135.345 −0.194182
\(698\) −716.953 250.873i −1.02715 0.359417i
\(699\) 0 0
\(700\) −308.848 246.298i −0.441211 0.351854i
\(701\) 358.817 + 745.091i 0.511865 + 1.06290i 0.983467 + 0.181087i \(0.0579615\pi\)
−0.471602 + 0.881811i \(0.656324\pi\)
\(702\) 0 0
\(703\) 337.335 + 423.005i 0.479851 + 0.601714i
\(704\) −21.1712 33.6938i −0.0300727 0.0478605i
\(705\) 0 0
\(706\) −31.0366 275.457i −0.0439611 0.390166i
\(707\) −78.2899 + 124.598i −0.110735 + 0.176234i
\(708\) 0 0
\(709\) −149.080 + 34.0265i −0.210268 + 0.0479923i −0.326357 0.945246i \(-0.605821\pi\)
0.116089 + 0.993239i \(0.462964\pi\)
\(710\) −127.866 365.420i −0.180093 0.514676i
\(711\) 0 0
\(712\) −21.9955 96.3688i −0.0308926 0.135349i
\(713\) 90.2386 + 90.2386i 0.126562 + 0.126562i
\(714\) 0 0
\(715\) 492.600 55.5027i 0.688952 0.0776262i
\(716\) 148.766 651.785i 0.207773 0.910314i
\(717\) 0 0
\(718\) 139.443 111.202i 0.194210 0.154877i
\(719\) −188.055 90.5627i −0.261551 0.125957i 0.298513 0.954406i \(-0.403509\pi\)
−0.560064 + 0.828449i \(0.689224\pi\)
\(720\) 0 0
\(721\) 182.226 228.504i 0.252740 0.316926i
\(722\) 1834.08 + 206.651i 2.54028 + 0.286221i
\(723\) 0 0
\(724\) 617.362i 0.852710i
\(725\) 1519.62 + 231.353i 2.09603 + 0.319107i
\(726\) 0 0
\(727\) 1244.50 + 435.470i 1.71183 + 0.598996i 0.995147 0.0984004i \(-0.0313726\pi\)
0.716686 + 0.697396i \(0.245658\pi\)
\(728\) −14.0678 + 124.855i −0.0193239 + 0.171505i
\(729\) 0 0
\(730\) 298.490 + 619.822i 0.408891 + 0.849071i
\(731\) 5.20946 10.8176i 0.00712648 0.0147983i
\(732\) 0 0
\(733\) 63.1015 + 100.425i 0.0860866 + 0.137006i 0.886992 0.461785i \(-0.152791\pi\)
−0.800905 + 0.598791i \(0.795648\pi\)
\(734\) 95.5271 + 21.8034i 0.130146 + 0.0297050i
\(735\) 0 0
\(736\) 365.950 582.406i 0.497215 0.791313i
\(737\) 162.458 162.458i 0.220432 0.220432i
\(738\) 0 0
\(739\) 235.151 + 672.023i 0.318202 + 0.909369i 0.986251 + 0.165252i \(0.0528437\pi\)
−0.668050 + 0.744117i \(0.732871\pi\)
\(740\) −281.147 + 98.3776i −0.379928 + 0.132943i
\(741\) 0 0
\(742\) 543.681 + 543.681i 0.732724 + 0.732724i
\(743\) 1147.96 + 721.309i 1.54503 + 0.970806i 0.990326 + 0.138757i \(0.0443107\pi\)
0.554702 + 0.832049i \(0.312832\pi\)
\(744\) 0 0
\(745\) −232.852 + 1020.19i −0.312552 + 1.36938i
\(746\) −1046.59 + 657.618i −1.40294 + 0.881526i
\(747\) 0 0
\(748\) 32.3237 + 15.5663i 0.0432135 + 0.0208105i
\(749\) −50.5299 + 24.3339i −0.0674632 + 0.0324885i
\(750\) 0 0
\(751\) 601.896 + 67.8174i 0.801460 + 0.0903028i 0.503187 0.864178i \(-0.332161\pi\)
0.298273 + 0.954481i \(0.403589\pi\)
\(752\) −471.492 + 1347.45i −0.626984 + 1.79182i
\(753\) 0 0
\(754\) 210.345 + 484.074i 0.278972 + 0.642007i
\(755\) −1614.68 −2.13866
\(756\) 0 0
\(757\) −84.2696 + 747.913i −0.111320 + 0.987997i 0.806563 + 0.591148i \(0.201325\pi\)
−0.917884 + 0.396849i \(0.870104\pi\)
\(758\) −606.015 483.281i −0.799492 0.637574i
\(759\) 0 0
\(760\) 605.287 1256.89i 0.796431 1.65381i
\(761\) 315.470 + 395.587i 0.414547 + 0.519825i 0.944638 0.328116i \(-0.106414\pi\)
−0.530091 + 0.847941i \(0.677842\pi\)
\(762\) 0 0
\(763\) −111.053 25.3472i −0.145548 0.0332204i
\(764\) 63.0415 + 559.509i 0.0825150 + 0.732341i
\(765\) 0 0
\(766\) −742.608 + 742.608i −0.969463 + 0.969463i
\(767\) 489.144 111.644i 0.637736 0.145559i
\(768\) 0 0
\(769\) −331.756 + 116.087i −0.431413 + 0.150958i −0.537245 0.843426i \(-0.680535\pi\)
0.105832 + 0.994384i \(0.466249\pi\)
\(770\) −132.182 579.129i −0.171665 0.752115i
\(771\) 0 0
\(772\) 238.673 + 149.968i 0.309161 + 0.194259i
\(773\) 440.543 49.6373i 0.569914 0.0642139i 0.177695 0.984086i \(-0.443136\pi\)
0.392219 + 0.919872i \(0.371707\pi\)
\(774\) 0 0
\(775\) −252.474 + 158.640i −0.325772 + 0.204696i
\(776\) 194.119 154.804i 0.250153 0.199490i
\(777\) 0 0
\(778\) −35.1623 + 16.9332i −0.0451957 + 0.0217651i
\(779\) 1236.90 1551.03i 1.58781 1.99105i
\(780\) 0 0
\(781\) 44.6477 127.596i 0.0571673 0.163375i
\(782\) 127.093i 0.162523i
\(783\) 0 0
\(784\) −722.156 −0.921117
\(785\) −923.830 323.262i −1.17685 0.411799i
\(786\) 0 0
\(787\) −201.707 160.856i −0.256298 0.204391i 0.486908 0.873453i \(-0.338125\pi\)