Properties

Label 261.3.s.a.10.2
Level $261$
Weight $3$
Character 261.10
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 10.2
Character \(\chi\) \(=\) 261.10
Dual form 261.3.s.a.235.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.44470 + 0.907767i) q^{2} +(-0.472410 + 0.980970i) q^{4} +(8.15497 + 1.86132i) q^{5} +(7.53715 - 3.62970i) q^{7} +(-0.972146 - 8.62804i) q^{8} +O(q^{10})\) \(q+(-1.44470 + 0.907767i) q^{2} +(-0.472410 + 0.980970i) q^{4} +(8.15497 + 1.86132i) q^{5} +(7.53715 - 3.62970i) q^{7} +(-0.972146 - 8.62804i) q^{8} +(-13.4711 + 4.71376i) q^{10} +(1.08366 - 9.61773i) q^{11} +(8.88076 - 7.08217i) q^{13} +(-7.59401 + 12.0858i) q^{14} +(6.52130 + 8.17745i) q^{16} +(-11.2928 - 11.2928i) q^{17} +(-5.31570 - 15.1914i) q^{19} +(-5.67839 + 7.12047i) q^{20} +(7.16509 + 14.8785i) q^{22} +(2.98784 + 13.0906i) q^{23} +(40.5148 + 19.5109i) q^{25} +(-6.40109 + 18.2933i) q^{26} +9.10842i q^{28} +(25.9185 - 13.0088i) q^{29} +(1.32569 - 0.832985i) q^{31} +(15.9370 + 5.57660i) q^{32} +(26.5659 + 6.06349i) q^{34} +(68.2212 - 15.5711i) q^{35} +(2.36887 + 21.0243i) q^{37} +(21.4699 + 17.1216i) q^{38} +(8.13170 - 72.1709i) q^{40} +(0.193896 - 0.193896i) q^{41} +(-38.8303 + 61.7981i) q^{43} +(8.92277 + 5.60655i) q^{44} +(-16.1997 - 16.1997i) q^{46} +(-42.6067 - 4.80062i) q^{47} +(13.0829 - 16.4054i) q^{49} +(-76.2432 + 8.59054i) q^{50} +(2.75203 + 12.0574i) q^{52} +(-17.1572 + 75.1706i) q^{53} +(26.7389 - 76.4152i) q^{55} +(-38.6444 - 61.5022i) q^{56} +(-25.6356 + 42.3219i) q^{58} +23.4840 q^{59} +(56.8778 + 19.9024i) q^{61} +(-1.15907 + 2.40683i) q^{62} +(-68.8749 + 15.7203i) q^{64} +(85.6045 - 41.2249i) q^{65} +(-48.7873 - 38.9066i) q^{67} +(16.4127 - 5.74304i) q^{68} +(-84.4245 + 84.4245i) q^{70} +(-79.7652 + 63.6106i) q^{71} +(-23.3031 - 14.6423i) q^{73} +(-22.5075 - 28.2235i) q^{74} +(17.4135 + 1.96203i) q^{76} +(-26.7418 - 76.4236i) q^{77} +(11.7798 - 1.32727i) q^{79} +(37.9602 + 78.8251i) q^{80} +(-0.104110 + 0.456135i) q^{82} +(-0.116523 - 0.0561147i) q^{83} +(-71.0727 - 113.112i) q^{85} -124.529i q^{86} -84.0356 q^{88} +(-24.8431 + 15.6099i) q^{89} +(41.2294 - 85.6138i) q^{91} +(-14.2529 - 3.25314i) q^{92} +(65.9118 - 31.7415i) q^{94} +(-15.0734 - 133.780i) q^{95} +(23.5730 - 8.24856i) q^{97} +(-4.00858 + 35.5771i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} + O(q^{10}) \) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} - 20q^{10} + 8q^{11} - 14q^{13} - 26q^{14} + 18q^{16} + 26q^{17} + 2q^{19} - 46q^{20} + 154q^{22} - 56q^{23} - 34q^{25} - 110q^{26} + 170q^{29} - 88q^{31} + 132q^{32} - 224q^{34} + 210q^{35} - 56q^{37} + 294q^{38} - 492q^{40} + 34q^{41} + 176q^{43} - 126q^{44} + 744q^{46} - 208q^{47} + 506q^{49} - 732q^{50} + 690q^{52} + 14q^{53} + 284q^{55} - 332q^{56} - 508q^{58} + 44q^{59} - 30q^{61} + 504q^{62} - 896q^{64} + 554q^{65} - 574q^{67} + 796q^{68} - 1066q^{70} - 224q^{71} - 22q^{73} - 820q^{74} + 514q^{76} - 436q^{77} + 564q^{79} - 1162q^{80} - 18q^{82} + 126q^{83} + 38q^{85} - 384q^{88} + 160q^{89} - 434q^{91} + 1022q^{92} - 2q^{94} + 642q^{95} + 604q^{97} + 102q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(118\) \(146\)
\(\chi(n)\) \(e\left(\frac{23}{28}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.44470 + 0.907767i −0.722351 + 0.453883i −0.842378 0.538887i \(-0.818845\pi\)
0.120027 + 0.992771i \(0.461702\pi\)
\(3\) 0 0
\(4\) −0.472410 + 0.980970i −0.118103 + 0.245242i
\(5\) 8.15497 + 1.86132i 1.63099 + 0.372264i 0.937442 0.348142i \(-0.113187\pi\)
0.693552 + 0.720406i \(0.256045\pi\)
\(6\) 0 0
\(7\) 7.53715 3.62970i 1.07674 0.518528i 0.190464 0.981694i \(-0.439001\pi\)
0.886272 + 0.463166i \(0.153287\pi\)
\(8\) −0.972146 8.62804i −0.121518 1.07850i
\(9\) 0 0
\(10\) −13.4711 + 4.71376i −1.34711 + 0.471376i
\(11\) 1.08366 9.61773i 0.0985143 0.874339i −0.843126 0.537717i \(-0.819287\pi\)
0.941640 0.336622i \(-0.109284\pi\)
\(12\) 0 0
\(13\) 8.88076 7.08217i 0.683135 0.544782i −0.219274 0.975663i \(-0.570369\pi\)
0.902409 + 0.430881i \(0.141797\pi\)
\(14\) −7.59401 + 12.0858i −0.542430 + 0.863272i
\(15\) 0 0
\(16\) 6.52130 + 8.17745i 0.407581 + 0.511091i
\(17\) −11.2928 11.2928i −0.664280 0.664280i 0.292106 0.956386i \(-0.405644\pi\)
−0.956386 + 0.292106i \(0.905644\pi\)
\(18\) 0 0
\(19\) −5.31570 15.1914i −0.279774 0.799548i −0.994929 0.100582i \(-0.967930\pi\)
0.715155 0.698966i \(-0.246356\pi\)
\(20\) −5.67839 + 7.12047i −0.283919 + 0.356024i
\(21\) 0 0
\(22\) 7.16509 + 14.8785i 0.325686 + 0.676294i
\(23\) 2.98784 + 13.0906i 0.129906 + 0.569155i 0.997423 + 0.0717472i \(0.0228575\pi\)
−0.867517 + 0.497408i \(0.834285\pi\)
\(24\) 0 0
\(25\) 40.5148 + 19.5109i 1.62059 + 0.780436i
\(26\) −6.40109 + 18.2933i −0.246196 + 0.703588i
\(27\) 0 0
\(28\) 9.10842i 0.325301i
\(29\) 25.9185 13.0088i 0.893743 0.448580i
\(30\) 0 0
\(31\) 1.32569 0.832985i 0.0427641 0.0268705i −0.510480 0.859889i \(-0.670532\pi\)
0.553244 + 0.833019i \(0.313390\pi\)
\(32\) 15.9370 + 5.57660i 0.498032 + 0.174269i
\(33\) 0 0
\(34\) 26.5659 + 6.06349i 0.781349 + 0.178338i
\(35\) 68.2212 15.5711i 1.94918 0.444887i
\(36\) 0 0
\(37\) 2.36887 + 21.0243i 0.0640236 + 0.568225i 0.984243 + 0.176822i \(0.0565817\pi\)
−0.920219 + 0.391403i \(0.871990\pi\)
\(38\) 21.4699 + 17.1216i 0.564997 + 0.450570i
\(39\) 0 0
\(40\) 8.13170 72.1709i 0.203293 1.80427i
\(41\) 0.193896 0.193896i 0.00472917 0.00472917i −0.704738 0.709467i \(-0.748936\pi\)
0.709467 + 0.704738i \(0.248936\pi\)
\(42\) 0 0
\(43\) −38.8303 + 61.7981i −0.903031 + 1.43717i −0.00365282 + 0.999993i \(0.501163\pi\)
−0.899378 + 0.437172i \(0.855980\pi\)
\(44\) 8.92277 + 5.60655i 0.202790 + 0.127422i
\(45\) 0 0
\(46\) −16.1997 16.1997i −0.352168 0.352168i
\(47\) −42.6067 4.80062i −0.906525 0.102141i −0.353624 0.935388i \(-0.615051\pi\)
−0.552901 + 0.833247i \(0.686479\pi\)
\(48\) 0 0
\(49\) 13.0829 16.4054i 0.266997 0.334804i
\(50\) −76.2432 + 8.59054i −1.52486 + 0.171811i
\(51\) 0 0
\(52\) 2.75203 + 12.0574i 0.0529237 + 0.231874i
\(53\) −17.1572 + 75.1706i −0.323721 + 1.41831i 0.507155 + 0.861855i \(0.330697\pi\)
−0.830875 + 0.556459i \(0.812160\pi\)
\(54\) 0 0
\(55\) 26.7389 76.4152i 0.486161 1.38937i
\(56\) −38.6444 61.5022i −0.690078 1.09825i
\(57\) 0 0
\(58\) −25.6356 + 42.3219i −0.441993 + 0.729687i
\(59\) 23.4840 0.398034 0.199017 0.979996i \(-0.436225\pi\)
0.199017 + 0.979996i \(0.436225\pi\)
\(60\) 0 0
\(61\) 56.8778 + 19.9024i 0.932423 + 0.326269i 0.753390 0.657574i \(-0.228417\pi\)
0.179033 + 0.983843i \(0.442703\pi\)
\(62\) −1.15907 + 2.40683i −0.0186947 + 0.0388199i
\(63\) 0 0
\(64\) −68.8749 + 15.7203i −1.07617 + 0.245629i
\(65\) 85.6045 41.2249i 1.31699 0.634230i
\(66\) 0 0
\(67\) −48.7873 38.9066i −0.728169 0.580696i 0.187674 0.982231i \(-0.439905\pi\)
−0.915843 + 0.401536i \(0.868477\pi\)
\(68\) 16.4127 5.74304i 0.241363 0.0844565i
\(69\) 0 0
\(70\) −84.4245 + 84.4245i −1.20606 + 1.20606i
\(71\) −79.7652 + 63.6106i −1.12345 + 0.895924i −0.995396 0.0958430i \(-0.969445\pi\)
−0.128057 + 0.991767i \(0.540874\pi\)
\(72\) 0 0
\(73\) −23.3031 14.6423i −0.319220 0.200579i 0.362884 0.931834i \(-0.381792\pi\)
−0.682104 + 0.731255i \(0.738935\pi\)
\(74\) −22.5075 28.2235i −0.304156 0.381399i
\(75\) 0 0
\(76\) 17.4135 + 1.96203i 0.229125 + 0.0258162i
\(77\) −26.7418 76.4236i −0.347296 0.992514i
\(78\) 0 0
\(79\) 11.7798 1.32727i 0.149112 0.0168009i −0.0370930 0.999312i \(-0.511810\pi\)
0.186205 + 0.982511i \(0.440381\pi\)
\(80\) 37.9602 + 78.8251i 0.474502 + 0.985313i
\(81\) 0 0
\(82\) −0.104110 + 0.456135i −0.00126963 + 0.00556262i
\(83\) −0.116523 0.0561147i −0.00140390 0.000676081i 0.433182 0.901307i \(-0.357391\pi\)
−0.434586 + 0.900631i \(0.643105\pi\)
\(84\) 0 0
\(85\) −71.0727 113.112i −0.836150 1.33072i
\(86\) 124.529i 1.44801i
\(87\) 0 0
\(88\) −84.0356 −0.954950
\(89\) −24.8431 + 15.6099i −0.279136 + 0.175392i −0.664322 0.747446i \(-0.731280\pi\)
0.385187 + 0.922839i \(0.374137\pi\)
\(90\) 0 0
\(91\) 41.2294 85.6138i 0.453071 0.940811i
\(92\) −14.2529 3.25314i −0.154923 0.0353602i
\(93\) 0 0
\(94\) 65.9118 31.7415i 0.701190 0.337675i
\(95\) −15.0734 133.780i −0.158667 1.40821i
\(96\) 0 0
\(97\) 23.5730 8.24856i 0.243021 0.0850367i −0.206020 0.978548i \(-0.566051\pi\)
0.449041 + 0.893511i \(0.351766\pi\)
\(98\) −4.00858 + 35.5771i −0.0409038 + 0.363032i
\(99\) 0 0
\(100\) −38.2792 + 30.5267i −0.382792 + 0.305267i
\(101\) −83.3997 + 132.730i −0.825740 + 1.31416i 0.121162 + 0.992633i \(0.461338\pi\)
−0.946901 + 0.321524i \(0.895805\pi\)
\(102\) 0 0
\(103\) −74.0720 92.8833i −0.719146 0.901780i 0.279144 0.960249i \(-0.409949\pi\)
−0.998289 + 0.0584693i \(0.981378\pi\)
\(104\) −69.7386 69.7386i −0.670563 0.670563i
\(105\) 0 0
\(106\) −43.4503 124.174i −0.409909 1.17145i
\(107\) 82.4205 103.352i 0.770285 0.965907i −0.229688 0.973264i \(-0.573771\pi\)
0.999973 + 0.00735775i \(0.00234207\pi\)
\(108\) 0 0
\(109\) 90.6920 + 188.324i 0.832037 + 1.72774i 0.671892 + 0.740649i \(0.265482\pi\)
0.160144 + 0.987094i \(0.448804\pi\)
\(110\) 30.7375 + 134.670i 0.279432 + 1.22427i
\(111\) 0 0
\(112\) 78.8337 + 37.9643i 0.703872 + 0.338967i
\(113\) 9.02228 25.7842i 0.0798432 0.228179i −0.897041 0.441947i \(-0.854288\pi\)
0.976884 + 0.213768i \(0.0685737\pi\)
\(114\) 0 0
\(115\) 112.314i 0.976647i
\(116\) 0.517082 + 31.5708i 0.00445760 + 0.272162i
\(117\) 0 0
\(118\) −33.9274 + 21.3180i −0.287521 + 0.180661i
\(119\) −126.105 44.1259i −1.05970 0.370806i
\(120\) 0 0
\(121\) 26.6399 + 6.08039i 0.220165 + 0.0502511i
\(122\) −100.238 + 22.8787i −0.821625 + 0.187531i
\(123\) 0 0
\(124\) 0.190865 + 1.69397i 0.00153923 + 0.0136611i
\(125\) 130.587 + 104.139i 1.04469 + 0.833114i
\(126\) 0 0
\(127\) 3.73540 33.1526i 0.0294126 0.261044i −0.970397 0.241516i \(-0.922355\pi\)
0.999809 0.0195276i \(-0.00621621\pi\)
\(128\) 37.4769 37.4769i 0.292788 0.292788i
\(129\) 0 0
\(130\) −86.2503 + 137.267i −0.663464 + 1.05590i
\(131\) 5.80196 + 3.64561i 0.0442898 + 0.0278291i 0.553995 0.832520i \(-0.313103\pi\)
−0.509705 + 0.860349i \(0.670246\pi\)
\(132\) 0 0
\(133\) −95.2055 95.2055i −0.715831 0.715831i
\(134\) 105.801 + 11.9209i 0.789562 + 0.0889623i
\(135\) 0 0
\(136\) −86.4562 + 108.413i −0.635707 + 0.797152i
\(137\) 66.1910 7.45794i 0.483146 0.0544375i 0.132968 0.991120i \(-0.457549\pi\)
0.350179 + 0.936683i \(0.386121\pi\)
\(138\) 0 0
\(139\) −26.8670 117.712i −0.193287 0.846848i −0.974822 0.222985i \(-0.928420\pi\)
0.781534 0.623862i \(-0.214437\pi\)
\(140\) −16.9537 + 74.2789i −0.121098 + 0.530563i
\(141\) 0 0
\(142\) 57.4933 164.307i 0.404883 1.15709i
\(143\) −58.4906 93.0873i −0.409025 0.650960i
\(144\) 0 0
\(145\) 235.578 57.8439i 1.62468 0.398923i
\(146\) 46.9578 0.321629
\(147\) 0 0
\(148\) −21.7433 7.60832i −0.146914 0.0514076i
\(149\) 35.6122 73.9495i 0.239008 0.496306i −0.746617 0.665255i \(-0.768323\pi\)
0.985625 + 0.168949i \(0.0540373\pi\)
\(150\) 0 0
\(151\) −25.5032 + 5.82094i −0.168895 + 0.0385493i −0.306132 0.951989i \(-0.599035\pi\)
0.137237 + 0.990538i \(0.456178\pi\)
\(152\) −125.904 + 60.6324i −0.828318 + 0.398897i
\(153\) 0 0
\(154\) 108.009 + 86.1340i 0.701355 + 0.559312i
\(155\) 12.3614 4.32544i 0.0797510 0.0279061i
\(156\) 0 0
\(157\) −150.103 + 150.103i −0.956069 + 0.956069i −0.999075 0.0430058i \(-0.986307\pi\)
0.0430058 + 0.999075i \(0.486307\pi\)
\(158\) −15.8135 + 12.6109i −0.100085 + 0.0798155i
\(159\) 0 0
\(160\) 119.586 + 75.1409i 0.747413 + 0.469630i
\(161\) 70.0345 + 87.8205i 0.434997 + 0.545469i
\(162\) 0 0
\(163\) 296.077 + 33.3599i 1.81642 + 0.204662i 0.953648 0.300926i \(-0.0972956\pi\)
0.862775 + 0.505587i \(0.168724\pi\)
\(164\) 0.0986077 + 0.281805i 0.000601267 + 0.00171832i
\(165\) 0 0
\(166\) 0.219281 0.0247070i 0.00132097 0.000148837i
\(167\) 11.8990 + 24.7085i 0.0712514 + 0.147955i 0.933552 0.358441i \(-0.116692\pi\)
−0.862301 + 0.506396i \(0.830977\pi\)
\(168\) 0 0
\(169\) −8.89530 + 38.9729i −0.0526349 + 0.230609i
\(170\) 205.358 + 98.8951i 1.20799 + 0.581736i
\(171\) 0 0
\(172\) −42.2782 67.2854i −0.245804 0.391194i
\(173\) 70.3363i 0.406568i 0.979120 + 0.203284i \(0.0651615\pi\)
−0.979120 + 0.203284i \(0.934838\pi\)
\(174\) 0 0
\(175\) 376.185 2.14963
\(176\) 85.7153 53.8585i 0.487019 0.306014i
\(177\) 0 0
\(178\) 21.7207 45.1034i 0.122026 0.253390i
\(179\) 156.687 + 35.7629i 0.875349 + 0.199793i 0.636512 0.771267i \(-0.280377\pi\)
0.238837 + 0.971060i \(0.423234\pi\)
\(180\) 0 0
\(181\) −227.552 + 109.583i −1.25719 + 0.605432i −0.939431 0.342739i \(-0.888645\pi\)
−0.317761 + 0.948171i \(0.602931\pi\)
\(182\) 18.1531 + 161.113i 0.0997423 + 0.885237i
\(183\) 0 0
\(184\) 110.041 38.5051i 0.598050 0.209267i
\(185\) −19.8149 + 175.862i −0.107108 + 0.950606i
\(186\) 0 0
\(187\) −120.848 + 96.3732i −0.646247 + 0.515365i
\(188\) 24.8371 39.5280i 0.132112 0.210255i
\(189\) 0 0
\(190\) 143.217 + 179.589i 0.753775 + 0.945204i
\(191\) 78.7301 + 78.7301i 0.412199 + 0.412199i 0.882504 0.470305i \(-0.155856\pi\)
−0.470305 + 0.882504i \(0.655856\pi\)
\(192\) 0 0
\(193\) 48.1790 + 137.688i 0.249632 + 0.713408i 0.998703 + 0.0509180i \(0.0162147\pi\)
−0.749070 + 0.662490i \(0.769500\pi\)
\(194\) −26.5683 + 33.3155i −0.136950 + 0.171730i
\(195\) 0 0
\(196\) 9.91272 + 20.5840i 0.0505751 + 0.105020i
\(197\) −45.2414 198.216i −0.229652 1.00617i −0.949924 0.312480i \(-0.898840\pi\)
0.720272 0.693691i \(-0.244017\pi\)
\(198\) 0 0
\(199\) −223.780 107.767i −1.12452 0.541542i −0.223237 0.974764i \(-0.571662\pi\)
−0.901287 + 0.433222i \(0.857377\pi\)
\(200\) 128.954 368.531i 0.644772 1.84265i
\(201\) 0 0
\(202\) 267.463i 1.32407i
\(203\) 148.134 192.126i 0.729723 0.946433i
\(204\) 0 0
\(205\) 1.94212 1.22031i 0.00947375 0.00595275i
\(206\) 191.328 + 66.9487i 0.928779 + 0.324994i
\(207\) 0 0
\(208\) 115.828 + 26.4370i 0.556866 + 0.127101i
\(209\) −151.867 + 34.6627i −0.726638 + 0.165850i
\(210\) 0 0
\(211\) −10.1040 89.6752i −0.0478861 0.425001i −0.994668 0.103126i \(-0.967115\pi\)
0.946782 0.321875i \(-0.104313\pi\)
\(212\) −65.6349 52.3421i −0.309598 0.246897i
\(213\) 0 0
\(214\) −25.2535 + 224.131i −0.118007 + 1.04734i
\(215\) −431.686 + 431.686i −2.00784 + 2.00784i
\(216\) 0 0
\(217\) 6.96842 11.0902i 0.0321125 0.0511068i
\(218\) −301.977 189.745i −1.38522 0.870389i
\(219\) 0 0
\(220\) 62.3293 + 62.3293i 0.283315 + 0.283315i
\(221\) −180.266 20.3110i −0.815681 0.0919052i
\(222\) 0 0
\(223\) 108.671 136.270i 0.487316 0.611075i −0.476000 0.879445i \(-0.657914\pi\)
0.963316 + 0.268371i \(0.0864852\pi\)
\(224\) 140.361 15.8149i 0.626611 0.0706022i
\(225\) 0 0
\(226\) 10.3715 + 45.4406i 0.0458917 + 0.201065i
\(227\) 78.3123 343.109i 0.344988 1.51149i −0.443405 0.896321i \(-0.646230\pi\)
0.788394 0.615171i \(-0.210913\pi\)
\(228\) 0 0
\(229\) 72.4465 207.040i 0.316360 0.904106i −0.670411 0.741990i \(-0.733882\pi\)
0.986772 0.162116i \(-0.0518319\pi\)
\(230\) −101.955 162.261i −0.443284 0.705482i
\(231\) 0 0
\(232\) −137.437 210.980i −0.592402 0.909395i
\(233\) −20.3820 −0.0874763 −0.0437381 0.999043i \(-0.513927\pi\)
−0.0437381 + 0.999043i \(0.513927\pi\)
\(234\) 0 0
\(235\) −338.521 118.454i −1.44051 0.504058i
\(236\) −11.0941 + 23.0371i −0.0470089 + 0.0976149i
\(237\) 0 0
\(238\) 222.240 50.7247i 0.933780 0.213129i
\(239\) −247.461 + 119.171i −1.03540 + 0.498623i −0.872805 0.488070i \(-0.837701\pi\)
−0.162597 + 0.986693i \(0.551987\pi\)
\(240\) 0 0
\(241\) 174.583 + 139.225i 0.724409 + 0.577697i 0.914750 0.404021i \(-0.132388\pi\)
−0.190341 + 0.981718i \(0.560959\pi\)
\(242\) −44.0063 + 15.3985i −0.181844 + 0.0636301i
\(243\) 0 0
\(244\) −46.3933 + 46.3933i −0.190137 + 0.190137i
\(245\) 137.226 109.434i 0.560106 0.446670i
\(246\) 0 0
\(247\) −154.796 97.2645i −0.626703 0.393783i
\(248\) −8.47579 10.6283i −0.0341766 0.0428561i
\(249\) 0 0
\(250\) −283.193 31.9082i −1.13277 0.127633i
\(251\) 93.9755 + 268.567i 0.374404 + 1.06999i 0.964826 + 0.262891i \(0.0846759\pi\)
−0.590421 + 0.807095i \(0.701038\pi\)
\(252\) 0 0
\(253\) 129.139 14.5505i 0.510432 0.0575118i
\(254\) 24.6983 + 51.2865i 0.0972373 + 0.201915i
\(255\) 0 0
\(256\) 42.7584 187.337i 0.167025 0.731784i
\(257\) −258.752 124.608i −1.00682 0.484857i −0.143569 0.989640i \(-0.545858\pi\)
−0.863246 + 0.504784i \(0.831572\pi\)
\(258\) 0 0
\(259\) 94.1666 + 149.865i 0.363577 + 0.578630i
\(260\) 103.450i 0.397886i
\(261\) 0 0
\(262\) −11.6915 −0.0446239
\(263\) −179.053 + 112.507i −0.680810 + 0.427782i −0.827549 0.561394i \(-0.810265\pi\)
0.146738 + 0.989175i \(0.453122\pi\)
\(264\) 0 0
\(265\) −279.833 + 581.079i −1.05597 + 2.19275i
\(266\) 223.968 + 51.1192i 0.841985 + 0.192178i
\(267\) 0 0
\(268\) 61.2138 29.4790i 0.228410 0.109996i
\(269\) −0.714016 6.33707i −0.00265434 0.0235579i 0.992315 0.123736i \(-0.0394875\pi\)
−0.994970 + 0.100178i \(0.968059\pi\)
\(270\) 0 0
\(271\) −249.689 + 87.3701i −0.921363 + 0.322399i −0.748950 0.662626i \(-0.769442\pi\)
−0.172412 + 0.985025i \(0.555156\pi\)
\(272\) 18.7025 165.989i 0.0687593 0.610255i
\(273\) 0 0
\(274\) −88.8563 + 70.8605i −0.324293 + 0.258615i
\(275\) 231.555 368.517i 0.842017 1.34006i
\(276\) 0 0
\(277\) −227.456 285.220i −0.821140 1.02968i −0.998959 0.0456136i \(-0.985476\pi\)
0.177819 0.984063i \(-0.443096\pi\)
\(278\) 145.670 + 145.670i 0.523992 + 0.523992i
\(279\) 0 0
\(280\) −200.669 573.478i −0.716674 2.04814i
\(281\) 34.9750 43.8573i 0.124466 0.156076i −0.715694 0.698414i \(-0.753889\pi\)
0.840160 + 0.542338i \(0.182461\pi\)
\(282\) 0 0
\(283\) 22.9297 + 47.6140i 0.0810237 + 0.168247i 0.937545 0.347865i \(-0.113093\pi\)
−0.856521 + 0.516112i \(0.827379\pi\)
\(284\) −24.7182 108.298i −0.0870359 0.381329i
\(285\) 0 0
\(286\) 169.003 + 81.3876i 0.590920 + 0.284572i
\(287\) 0.757639 2.16521i 0.00263986 0.00754428i
\(288\) 0 0
\(289\) 33.9469i 0.117463i
\(290\) −287.832 + 297.418i −0.992524 + 1.02558i
\(291\) 0 0
\(292\) 25.3723 15.9424i 0.0868913 0.0545974i
\(293\) 26.3205 + 9.20996i 0.0898312 + 0.0314333i 0.374821 0.927097i \(-0.377704\pi\)
−0.284989 + 0.958531i \(0.591990\pi\)
\(294\) 0 0
\(295\) 191.511 + 43.7112i 0.649191 + 0.148174i
\(296\) 179.096 40.8775i 0.605054 0.138100i
\(297\) 0 0
\(298\) 15.6799 + 139.163i 0.0526170 + 0.466989i
\(299\) 119.244 + 95.0937i 0.398809 + 0.318039i
\(300\) 0 0
\(301\) −68.3613 + 606.724i −0.227114 + 2.01569i
\(302\) 31.5605 31.5605i 0.104505 0.104505i
\(303\) 0 0
\(304\) 89.5617 142.537i 0.294611 0.468870i
\(305\) 426.792 + 268.171i 1.39932 + 0.879250i
\(306\) 0 0
\(307\) −317.297 317.297i −1.03354 1.03354i −0.999418 0.0341225i \(-0.989136\pi\)
−0.0341225 0.999418i \(-0.510864\pi\)
\(308\) 87.6023 + 9.87041i 0.284423 + 0.0320468i
\(309\) 0 0
\(310\) −13.9321 + 17.4702i −0.0449421 + 0.0563556i
\(311\) 452.122 50.9419i 1.45377 0.163800i 0.650540 0.759472i \(-0.274543\pi\)
0.803228 + 0.595671i \(0.203114\pi\)
\(312\) 0 0
\(313\) 75.0822 + 328.956i 0.239879 + 1.05098i 0.941125 + 0.338059i \(0.109770\pi\)
−0.701246 + 0.712920i \(0.747372\pi\)
\(314\) 80.5956 353.112i 0.256674 1.12456i
\(315\) 0 0
\(316\) −4.26290 + 12.1827i −0.0134902 + 0.0385528i
\(317\) −33.4800 53.2832i −0.105615 0.168086i 0.789735 0.613448i \(-0.210218\pi\)
−0.895351 + 0.445362i \(0.853075\pi\)
\(318\) 0 0
\(319\) −97.0285 263.375i −0.304165 0.825625i
\(320\) −590.933 −1.84667
\(321\) 0 0
\(322\) −180.900 63.2995i −0.561800 0.196582i
\(323\) −111.524 + 231.582i −0.345276 + 0.716972i
\(324\) 0 0
\(325\) 497.982 113.661i 1.53225 0.349726i
\(326\) −458.026 + 220.574i −1.40499 + 0.676607i
\(327\) 0 0
\(328\) −1.86144 1.48445i −0.00567511 0.00452575i
\(329\) −338.558 + 118.466i −1.02905 + 0.360080i
\(330\) 0 0
\(331\) 286.146 286.146i 0.864490 0.864490i −0.127366 0.991856i \(-0.540652\pi\)
0.991856 + 0.127366i \(0.0406523\pi\)
\(332\) 0.110094 0.0877968i 0.000331607 0.000264448i
\(333\) 0 0
\(334\) −39.6200 24.8949i −0.118623 0.0745357i
\(335\) −325.442 408.091i −0.971468 1.21818i
\(336\) 0 0
\(337\) −264.583 29.8114i −0.785114 0.0884611i −0.289699 0.957118i \(-0.593555\pi\)
−0.495414 + 0.868657i \(0.664984\pi\)
\(338\) −22.5272 64.3790i −0.0666485 0.190471i
\(339\) 0 0
\(340\) 144.535 16.2851i 0.425102 0.0478974i
\(341\) −6.57483 13.6528i −0.0192810 0.0400375i
\(342\) 0 0
\(343\) −52.1537 + 228.500i −0.152052 + 0.666182i
\(344\) 570.945 + 274.953i 1.65972 + 0.799281i
\(345\) 0 0
\(346\) −63.8490 101.615i −0.184535 0.293685i
\(347\) 77.2491i 0.222620i 0.993786 + 0.111310i \(0.0355046\pi\)
−0.993786 + 0.111310i \(0.964495\pi\)
\(348\) 0 0
\(349\) 16.2689 0.0466157 0.0233079 0.999728i \(-0.492580\pi\)
0.0233079 + 0.999728i \(0.492580\pi\)
\(350\) −543.475 + 341.488i −1.55279 + 0.975680i
\(351\) 0 0
\(352\) 70.9045 147.235i 0.201433 0.418280i
\(353\) −64.7164 14.7711i −0.183332 0.0418444i 0.129869 0.991531i \(-0.458544\pi\)
−0.313201 + 0.949687i \(0.601401\pi\)
\(354\) 0 0
\(355\) −768.882 + 370.274i −2.16587 + 1.04303i
\(356\) −3.57676 31.7446i −0.0100471 0.0891702i
\(357\) 0 0
\(358\) −258.831 + 90.5689i −0.722992 + 0.252986i
\(359\) 1.89890 16.8532i 0.00528941 0.0469449i −0.990790 0.135406i \(-0.956766\pi\)
0.996080 + 0.0884608i \(0.0281948\pi\)
\(360\) 0 0
\(361\) 79.7189 63.5737i 0.220828 0.176105i
\(362\) 229.269 364.879i 0.633339 1.00795i
\(363\) 0 0
\(364\) 64.5073 + 80.8896i 0.177218 + 0.222224i
\(365\) −162.782 162.782i −0.445978 0.445978i
\(366\) 0 0
\(367\) −9.38650 26.8251i −0.0255763 0.0730929i 0.930387 0.366578i \(-0.119471\pi\)
−0.955964 + 0.293485i \(0.905185\pi\)
\(368\) −87.5628 + 109.800i −0.237942 + 0.298370i
\(369\) 0 0
\(370\) −131.015 272.056i −0.354095 0.735286i
\(371\) 143.530 + 628.847i 0.386874 + 1.69501i
\(372\) 0 0
\(373\) −208.198 100.263i −0.558171 0.268801i 0.133457 0.991055i \(-0.457392\pi\)
−0.691628 + 0.722254i \(0.743106\pi\)
\(374\) 87.1053 248.933i 0.232902 0.665595i
\(375\) 0 0
\(376\) 372.279i 0.990104i
\(377\) 138.046 299.088i 0.366169 0.793336i
\(378\) 0 0
\(379\) −135.794 + 85.3248i −0.358295 + 0.225131i −0.699135 0.714990i \(-0.746431\pi\)
0.340840 + 0.940121i \(0.389288\pi\)
\(380\) 138.355 + 48.4124i 0.364091 + 0.127401i
\(381\) 0 0
\(382\) −185.210 42.2730i −0.484843 0.110662i
\(383\) 244.516 55.8092i 0.638424 0.145716i 0.108957 0.994047i \(-0.465249\pi\)
0.529467 + 0.848330i \(0.322392\pi\)
\(384\) 0 0
\(385\) −75.8297 673.007i −0.196960 1.74807i
\(386\) −194.593 155.183i −0.504126 0.402027i
\(387\) 0 0
\(388\) −3.04455 + 27.0211i −0.00784678 + 0.0696421i
\(389\) −231.524 + 231.524i −0.595179 + 0.595179i −0.939026 0.343847i \(-0.888270\pi\)
0.343847 + 0.939026i \(0.388270\pi\)
\(390\) 0 0
\(391\) 114.088 181.570i 0.291784 0.464372i
\(392\) −154.265 96.9310i −0.393533 0.247273i
\(393\) 0 0
\(394\) 245.294 + 245.294i 0.622574 + 0.622574i
\(395\) 98.5347 + 11.1022i 0.249455 + 0.0281068i
\(396\) 0 0
\(397\) 174.313 218.581i 0.439075 0.550583i −0.512224 0.858852i \(-0.671178\pi\)
0.951299 + 0.308269i \(0.0997496\pi\)
\(398\) 421.123 47.4492i 1.05810 0.119219i
\(399\) 0 0
\(400\) 104.660 + 458.544i 0.261649 + 1.14636i
\(401\) −11.6128 + 50.8791i −0.0289597 + 0.126881i −0.987341 0.158609i \(-0.949299\pi\)
0.958382 + 0.285490i \(0.0921562\pi\)
\(402\) 0 0
\(403\) 5.87377 16.7863i 0.0145751 0.0416533i
\(404\) −90.8051 144.516i −0.224765 0.357712i
\(405\) 0 0
\(406\) −39.6037 + 412.036i −0.0975459 + 1.01487i
\(407\) 204.773 0.503129
\(408\) 0 0
\(409\) 718.514 + 251.419i 1.75676 + 0.614716i 0.999273 0.0381358i \(-0.0121419\pi\)
0.757485 + 0.652852i \(0.226428\pi\)
\(410\) −1.69802 + 3.52598i −0.00414152 + 0.00859996i
\(411\) 0 0
\(412\) 126.108 28.7834i 0.306088 0.0698625i
\(413\) 177.003 85.2399i 0.428577 0.206392i
\(414\) 0 0
\(415\) −0.845798 0.674501i −0.00203807 0.00162530i
\(416\) 181.027 63.3441i 0.435161 0.152270i
\(417\) 0 0
\(418\) 187.937 187.937i 0.449611 0.449611i
\(419\) −277.644 + 221.413i −0.662634 + 0.528433i −0.896055 0.443943i \(-0.853579\pi\)
0.233421 + 0.972376i \(0.425008\pi\)
\(420\) 0 0
\(421\) 549.468 + 345.254i 1.30515 + 0.820080i 0.991581 0.129486i \(-0.0413327\pi\)
0.313568 + 0.949566i \(0.398476\pi\)
\(422\) 96.0014 + 120.382i 0.227492 + 0.285265i
\(423\) 0 0
\(424\) 665.254 + 74.9561i 1.56900 + 0.176783i
\(425\) −237.192 677.856i −0.558099 1.59496i
\(426\) 0 0
\(427\) 500.936 56.4420i 1.17315 0.132183i
\(428\) 62.4489 + 129.677i 0.145909 + 0.302983i
\(429\) 0 0
\(430\) 231.788 1015.53i 0.539041 2.36169i
\(431\) 267.983 + 129.054i 0.621771 + 0.299429i 0.718121 0.695918i \(-0.245002\pi\)
−0.0963498 + 0.995348i \(0.530717\pi\)
\(432\) 0 0
\(433\) −188.276 299.639i −0.434817 0.692007i 0.555394 0.831587i \(-0.312568\pi\)
−0.990211 + 0.139580i \(0.955425\pi\)
\(434\) 22.3477i 0.0514924i
\(435\) 0 0
\(436\) −227.584 −0.521981
\(437\) 182.982 114.975i 0.418722 0.263101i
\(438\) 0 0
\(439\) −287.672 + 597.356i −0.655289 + 1.36072i 0.262995 + 0.964797i \(0.415290\pi\)
−0.918283 + 0.395923i \(0.870425\pi\)
\(440\) −685.308 156.417i −1.55752 0.355493i
\(441\) 0 0
\(442\) 278.868 134.296i 0.630922 0.303836i
\(443\) 42.8152 + 379.995i 0.0966483 + 0.857777i 0.944716 + 0.327889i \(0.106337\pi\)
−0.848068 + 0.529888i \(0.822234\pi\)
\(444\) 0 0
\(445\) −231.649 + 81.0577i −0.520561 + 0.182152i
\(446\) −33.2968 + 295.517i −0.0746565 + 0.662595i
\(447\) 0 0
\(448\) −462.061 + 368.481i −1.03139 + 0.822503i
\(449\) 154.314 245.590i 0.343685 0.546971i −0.629499 0.777001i \(-0.716740\pi\)
0.973183 + 0.230031i \(0.0738826\pi\)
\(450\) 0 0
\(451\) −1.65472 2.07496i −0.00366901 0.00460079i
\(452\) 21.0313 + 21.0313i 0.0465294 + 0.0465294i
\(453\) 0 0
\(454\) 198.325 + 566.779i 0.436839 + 1.24841i
\(455\) 495.579 621.437i 1.08919 1.36580i
\(456\) 0 0
\(457\) 74.1101 + 153.891i 0.162166 + 0.336742i 0.966180 0.257869i \(-0.0830203\pi\)
−0.804013 + 0.594611i \(0.797306\pi\)
\(458\) 83.2806 + 364.876i 0.181835 + 0.796673i
\(459\) 0 0
\(460\) −110.177 53.0585i −0.239515 0.115345i
\(461\) −223.278 + 638.091i −0.484334 + 1.38415i 0.399667 + 0.916660i \(0.369126\pi\)
−0.884001 + 0.467486i \(0.845160\pi\)
\(462\) 0 0
\(463\) 298.561i 0.644841i 0.946597 + 0.322420i \(0.104496\pi\)
−0.946597 + 0.322420i \(0.895504\pi\)
\(464\) 275.401 + 127.113i 0.593538 + 0.273951i
\(465\) 0 0
\(466\) 29.4459 18.5021i 0.0631886 0.0397040i
\(467\) −601.371 210.429i −1.28773 0.450597i −0.402361 0.915481i \(-0.631810\pi\)
−0.885372 + 0.464884i \(0.846096\pi\)
\(468\) 0 0
\(469\) −508.937 116.161i −1.08515 0.247679i
\(470\) 596.590 136.168i 1.26934 0.289719i
\(471\) 0 0
\(472\) −22.8299 202.621i −0.0483684 0.429282i
\(473\) 552.279 + 440.427i 1.16761 + 0.931136i
\(474\) 0 0
\(475\) 81.0334 719.191i 0.170597 1.51409i
\(476\) 102.859 102.859i 0.216091 0.216091i
\(477\) 0 0
\(478\) 249.328 396.803i 0.521607 0.830132i
\(479\) −640.189 402.257i −1.33651 0.839785i −0.341532 0.939870i \(-0.610946\pi\)
−0.994979 + 0.100085i \(0.968089\pi\)
\(480\) 0 0
\(481\) 169.935 + 169.935i 0.353296 + 0.353296i
\(482\) −378.604 42.6584i −0.785485 0.0885029i
\(483\) 0 0
\(484\) −18.5496 + 23.2605i −0.0383257 + 0.0480589i
\(485\) 207.591 23.3898i 0.428022 0.0482265i
\(486\) 0 0
\(487\) 37.7010 + 165.179i 0.0774148 + 0.339176i 0.998772 0.0495403i \(-0.0157756\pi\)
−0.921357 + 0.388717i \(0.872918\pi\)
\(488\) 116.425 510.092i 0.238576 1.04527i
\(489\) 0 0
\(490\) −98.9102 + 282.669i −0.201857 + 0.576875i
\(491\) −419.070 666.946i −0.853503 1.35834i −0.932388 0.361458i \(-0.882279\pi\)
0.0788859 0.996884i \(-0.474864\pi\)
\(492\) 0 0
\(493\) −439.598 145.786i −0.891679 0.295713i
\(494\) 311.927 0.631431
\(495\) 0 0
\(496\) 15.4569 + 5.40860i 0.0311631 + 0.0109044i
\(497\) −370.314 + 768.966i −0.745099 + 1.54722i
\(498\) 0 0
\(499\) 450.785 102.889i 0.903376 0.206190i 0.254490 0.967075i \(-0.418092\pi\)
0.648886 + 0.760886i \(0.275235\pi\)
\(500\) −163.848 + 78.9050i −0.327696 + 0.157810i
\(501\) 0 0
\(502\) −379.562 302.691i −0.756100 0.602970i
\(503\) 142.888 49.9987i 0.284072 0.0994010i −0.184482 0.982836i \(-0.559061\pi\)
0.468554 + 0.883435i \(0.344775\pi\)
\(504\) 0 0
\(505\) −927.175 + 927.175i −1.83599 + 1.83599i
\(506\) −173.359 + 138.249i −0.342607 + 0.273220i
\(507\) 0 0
\(508\) 30.7570 + 19.3259i 0.0605454 + 0.0380432i
\(509\) 505.672 + 634.093i 0.993462 + 1.24576i 0.969256 + 0.246054i \(0.0791342\pi\)
0.0242055 + 0.999707i \(0.492294\pi\)
\(510\) 0 0
\(511\) −228.786 25.7780i −0.447722 0.0504461i
\(512\) 178.304 + 509.565i 0.348251 + 0.995243i
\(513\) 0 0
\(514\) 486.934 54.8643i 0.947343 0.106740i
\(515\) −431.169 895.333i −0.837222 1.73851i
\(516\) 0 0
\(517\) −92.3421 + 404.577i −0.178611 + 0.782548i
\(518\) −272.085 131.029i −0.525261 0.252952i
\(519\) 0 0
\(520\) −438.910 698.522i −0.844058 1.34331i
\(521\) 17.4200i 0.0334356i 0.999860 + 0.0167178i \(0.00532169\pi\)
−0.999860 + 0.0167178i \(0.994678\pi\)
\(522\) 0 0
\(523\) 347.118 0.663706 0.331853 0.943331i \(-0.392326\pi\)
0.331853 + 0.943331i \(0.392326\pi\)
\(524\) −6.31714 + 3.96932i −0.0120556 + 0.00757504i
\(525\) 0 0
\(526\) 156.549 325.077i 0.297621 0.618017i
\(527\) −24.3774 5.56398i −0.0462569 0.0105578i
\(528\) 0 0
\(529\) 314.177 151.300i 0.593907 0.286011i
\(530\) −123.209 1093.51i −0.232470 2.06323i
\(531\) 0 0
\(532\) 138.370 48.4177i 0.260093 0.0910106i
\(533\) 0.348739 3.09515i 0.000654295 0.00580703i
\(534\) 0 0
\(535\) 864.507 689.422i 1.61590 1.28864i
\(536\) −288.259 + 458.762i −0.537797 + 0.855899i
\(537\) 0 0
\(538\) 6.78412 + 8.50702i 0.0126099 + 0.0158123i
\(539\) −143.605 143.605i −0.266429 0.266429i
\(540\) 0 0
\(541\) 221.641 + 633.412i 0.409687 + 1.17082i 0.945257 + 0.326327i \(0.105811\pi\)
−0.535570 + 0.844491i \(0.679903\pi\)
\(542\) 281.415 352.883i 0.519216 0.651076i
\(543\) 0 0
\(544\) −116.998 242.948i −0.215069 0.446596i
\(545\) 389.060 + 1704.58i 0.713871 + 3.12767i
\(546\) 0 0
\(547\) 149.344 + 71.9205i 0.273025 + 0.131482i 0.565387 0.824826i \(-0.308727\pi\)
−0.292362 + 0.956308i \(0.594441\pi\)
\(548\) −23.9533 + 68.4546i −0.0437104 + 0.124917i
\(549\) 0 0
\(550\) 742.595i 1.35017i
\(551\) −335.398 324.588i −0.608707 0.589089i
\(552\) 0 0
\(553\) 83.9688 52.7611i 0.151842 0.0954088i
\(554\) 587.520 + 205.582i 1.06050 + 0.371087i
\(555\) 0 0
\(556\) 128.164 + 29.2526i 0.230511 + 0.0526126i
\(557\) 170.373 38.8865i 0.305876 0.0698142i −0.0668279 0.997765i \(-0.521288\pi\)
0.372704 + 0.927950i \(0.378431\pi\)
\(558\) 0 0
\(559\) 92.8218 + 823.817i 0.166050 + 1.47373i
\(560\) 572.222 + 456.332i 1.02183 + 0.814879i
\(561\) 0 0
\(562\) −10.7163 + 95.1098i −0.0190682 + 0.169235i
\(563\) 304.717 304.717i 0.541238 0.541238i −0.382654 0.923892i \(-0.624990\pi\)
0.923892 + 0.382654i \(0.124990\pi\)
\(564\) 0 0
\(565\) 121.569 193.476i 0.215166 0.342435i
\(566\) −76.3491 47.9733i −0.134892 0.0847585i
\(567\) 0 0
\(568\) 626.378 + 626.378i 1.10278 + 1.10278i
\(569\) 505.078 + 56.9087i 0.887660 + 0.100015i 0.544006 0.839081i \(-0.316907\pi\)
0.343654 + 0.939097i \(0.388335\pi\)
\(570\) 0 0
\(571\) 368.997 462.708i 0.646229 0.810346i −0.345537 0.938405i \(-0.612303\pi\)
0.991767 + 0.128059i \(0.0408747\pi\)
\(572\) 118.947 13.4022i 0.207950 0.0234303i
\(573\) 0 0
\(574\) 0.870941 + 3.81584i 0.00151732 + 0.00664780i
\(575\) −134.357 + 588.657i −0.233665 + 1.02375i
\(576\) 0 0
\(577\) 72.7651 207.951i 0.126109 0.360400i −0.863468 0.504404i \(-0.831712\pi\)
0.989577 + 0.144004i \(0.0459979\pi\)
\(578\) 30.8159 + 49.0432i 0.0533147 + 0.0848498i
\(579\) 0 0
\(580\) −54.5465 + 258.421i −0.0940457 + 0.445554i
\(581\) −1.08193 −0.00186219
\(582\) 0 0
\(583\) 704.378 + 246.473i 1.20820 + 0.422766i
\(584\) −103.680 + 215.294i −0.177535 + 0.368655i
\(585\) 0 0
\(586\) −46.3858 + 10.5873i −0.0791567 + 0.0180670i
\(587\) 6.27948 3.02404i 0.0106976 0.00515168i −0.428527 0.903529i \(-0.640967\pi\)
0.439225 + 0.898377i \(0.355253\pi\)
\(588\) 0 0
\(589\) −19.7012 15.7112i −0.0334485 0.0266743i
\(590\) −316.357 + 110.698i −0.536198 + 0.187624i
\(591\) 0 0
\(592\) −156.477 + 156.477i −0.264320 + 0.264320i
\(593\) −203.228 + 162.069i −0.342711 + 0.273303i −0.779686 0.626171i \(-0.784621\pi\)
0.436975 + 0.899474i \(0.356050\pi\)
\(594\) 0 0
\(595\) −946.246 594.566i −1.59033 0.999271i
\(596\) 55.7187 + 69.8690i 0.0934877 + 0.117230i
\(597\) 0 0
\(598\) −258.595 29.1366i −0.432433 0.0487234i
\(599\) 139.976 + 400.030i 0.233683 + 0.667829i 0.999688 + 0.0249934i \(0.00795647\pi\)
−0.766004 + 0.642836i \(0.777758\pi\)
\(600\) 0 0
\(601\) 276.392 31.1419i 0.459886 0.0518167i 0.121017 0.992650i \(-0.461384\pi\)
0.338869 + 0.940834i \(0.389956\pi\)
\(602\) −452.002 938.591i −0.750834 1.55912i
\(603\) 0 0
\(604\) 6.33781 27.7677i 0.0104931 0.0459731i
\(605\) 205.930 + 99.1707i 0.340380 + 0.163919i
\(606\) 0 0
\(607\) −550.914 876.775i −0.907602 1.44444i −0.895774 0.444510i \(-0.853378\pi\)
−0.0118280 0.999930i \(-0.503765\pi\)
\(608\) 271.749i 0.446956i
\(609\) 0 0
\(610\) −860.025 −1.40988
\(611\) −412.378 + 259.115i −0.674924 + 0.424083i
\(612\) 0 0
\(613\) 35.6576 74.0438i 0.0581690 0.120789i −0.869858 0.493302i \(-0.835790\pi\)
0.928027 + 0.372513i \(0.121504\pi\)
\(614\) 746.431 + 170.368i 1.21569 + 0.277472i
\(615\) 0 0
\(616\) −633.388 + 305.024i −1.02823 + 0.495168i
\(617\) −118.841 1054.75i −0.192612 1.70947i −0.603147 0.797630i \(-0.706087\pi\)
0.410535 0.911845i \(-0.365342\pi\)
\(618\) 0 0
\(619\) −983.102 + 344.002i −1.58821 + 0.555739i −0.972635 0.232339i \(-0.925362\pi\)
−0.615575 + 0.788078i \(0.711076\pi\)
\(620\) −1.59652 + 14.1695i −0.00257504 + 0.0228541i
\(621\) 0 0
\(622\) −606.938 + 484.017i −0.975785 + 0.778163i
\(623\) −130.586 + 207.827i −0.209609 + 0.333591i
\(624\) 0 0
\(625\) 170.165 + 213.380i 0.272264 + 0.341409i
\(626\) −407.087 407.087i −0.650299 0.650299i
\(627\) 0 0
\(628\) −76.3362 218.156i −0.121555 0.347383i
\(629\) 210.672 264.174i 0.334931 0.419991i
\(630\) 0 0
\(631\) −404.134 839.193i −0.640466 1.32994i −0.928146 0.372215i \(-0.878598\pi\)
0.287680 0.957727i \(-0.407116\pi\)
\(632\) −22.9034 100.347i −0.0362396 0.158776i
\(633\) 0 0
\(634\) 96.7374 + 46.5863i 0.152583 + 0.0734799i
\(635\) 92.1696 263.406i 0.145149 0.414812i
\(636\) 0 0
\(637\) 238.347i 0.374172i
\(638\) 379.260 + 292.419i 0.594451 + 0.458336i
\(639\) 0 0
\(640\) 375.379 235.866i 0.586530 0.368541i
\(641\) 109.871 + 38.4457i 0.171406 + 0.0599777i 0.414618 0.909996i \(-0.363915\pi\)
−0.243212 + 0.969973i \(0.578201\pi\)
\(642\) 0 0
\(643\) −887.185 202.494i −1.37976 0.314921i −0.532648 0.846337i \(-0.678803\pi\)
−0.847111 + 0.531416i \(0.821660\pi\)
\(644\) −119.234 + 27.2145i −0.185146 + 0.0422585i
\(645\) 0 0
\(646\) −49.1034 435.805i −0.0760115 0.674621i
\(647\) 184.679 + 147.277i 0.285439 + 0.227630i 0.755733 0.654880i \(-0.227281\pi\)
−0.470294 + 0.882510i \(0.655852\pi\)
\(648\) 0 0
\(649\) 25.4486 225.863i 0.0392121 0.348017i
\(650\) −616.257 + 616.257i −0.948088 + 0.948088i
\(651\) 0 0
\(652\) −172.595 + 274.683i −0.264716 + 0.421293i
\(653\) −182.035 114.380i −0.278767 0.175161i 0.385391 0.922753i \(-0.374067\pi\)
−0.664157 + 0.747593i \(0.731210\pi\)
\(654\) 0 0
\(655\) 40.5292 + 40.5292i 0.0618766 + 0.0618766i
\(656\) 2.85003 + 0.321121i 0.00434456 + 0.000489514i
\(657\) 0 0
\(658\) 381.575 478.480i 0.579902 0.727174i
\(659\) −729.824 + 82.2314i −1.10747 + 0.124782i −0.646706 0.762739i \(-0.723854\pi\)
−0.460766 + 0.887522i \(0.652425\pi\)
\(660\) 0 0
\(661\) 74.4513 + 326.192i 0.112634 + 0.493483i 0.999505 + 0.0314652i \(0.0100173\pi\)
−0.886871 + 0.462018i \(0.847126\pi\)
\(662\) −153.642 + 673.150i −0.232088 + 1.01684i
\(663\) 0 0
\(664\) −0.370882 + 1.05992i −0.000558557 + 0.00159626i
\(665\) −599.190 953.606i −0.901038 1.43399i
\(666\) 0 0
\(667\) 247.733 + 300.420i 0.371414 + 0.450405i
\(668\) −29.8595 −0.0446998
\(669\) 0 0
\(670\) 840.618 + 294.145i 1.25465 + 0.439022i
\(671\) 253.052 525.468i 0.377127 0.783112i
\(672\) 0 0
\(673\) −487.763 + 111.329i −0.724760 + 0.165422i −0.568958 0.822367i \(-0.692653\pi\)
−0.155802 + 0.987788i \(0.549796\pi\)
\(674\) 409.306 197.111i 0.607279 0.292450i
\(675\) 0 0
\(676\) −34.0290 27.1372i −0.0503387 0.0401438i
\(677\) −846.992 + 296.375i −1.25110 + 0.437777i −0.872878 0.487939i \(-0.837749\pi\)
−0.378218 + 0.925716i \(0.623463\pi\)
\(678\) 0 0
\(679\) 147.734 147.734i 0.217575 0.217575i
\(680\) −906.838 + 723.179i −1.33359 + 1.06350i
\(681\) 0 0
\(682\) 21.8922 + 13.7558i 0.0321000 + 0.0201698i
\(683\) −636.584 798.251i −0.932041 1.16874i −0.985415 0.170168i \(-0.945569\pi\)
0.0533743 0.998575i \(-0.483002\pi\)
\(684\) 0 0
\(685\) 553.668 + 62.3833i 0.808274 + 0.0910706i
\(686\) −132.078 377.458i −0.192534 0.550231i
\(687\) 0 0
\(688\) −758.575 + 85.4709i −1.10258 + 0.124231i
\(689\) 380.002 + 789.082i 0.551527 + 1.14526i
\(690\) 0 0
\(691\) −8.72945 + 38.2462i −0.0126331 + 0.0553491i −0.980852 0.194757i \(-0.937608\pi\)
0.968219 + 0.250106i \(0.0804654\pi\)
\(692\) −68.9978 33.2276i −0.0997078 0.0480167i
\(693\) 0 0
\(694\) −70.1242 111.602i −0.101044 0.160810i
\(695\) 1009.94i 1.45316i
\(696\) 0 0
\(697\) −4.37925 −0.00628299
\(698\) −23.5037 + 14.7684i −0.0336729 + 0.0211581i
\(699\) 0 0
\(700\) −177.713 + 369.026i −0.253876 + 0.527180i
\(701\) −730.823 166.806i −1.04254 0.237954i −0.333229 0.942846i \(-0.608138\pi\)
−0.709314 + 0.704892i \(0.750995\pi\)
\(702\) 0 0
\(703\) 306.797 147.746i 0.436411 0.210165i
\(704\) 76.5563 + 679.456i 0.108745 + 0.965136i
\(705\) 0 0
\(706\) 106.905 37.4075i 0.151423 0.0529852i
\(707\) −146.826 + 1303.12i −0.207675 + 1.84317i
\(708\) 0 0
\(709\) 226.904 180.950i 0.320034 0.255218i −0.450275 0.892890i \(-0.648674\pi\)
0.770308 + 0.637672i \(0.220102\pi\)
\(710\) 774.683 1232.90i 1.09110 1.73648i
\(711\) 0 0
\(712\) 158.834 + 199.172i 0.223082 + 0.279736i
\(713\) 14.8652 + 14.8652i 0.0208488 + 0.0208488i
\(714\) 0 0
\(715\) −303.724 867.994i −0.424789 1.21398i
\(716\) −109.103 + 136.811i −0.152379 + 0.191077i
\(717\) 0 0
\(718\) 12.5554 + 26.0716i 0.0174867 + 0.0363115i
\(719\) −176.737 774.336i −0.245810 1.07696i −0.935630 0.352982i \(-0.885168\pi\)
0.689820 0.723981i \(-0.257689\pi\)
\(720\) 0 0
\(721\) −895.430 431.216i −1.24193 0.598081i
\(722\) −57.4600 + 164.211i −0.0795845 + 0.227440i
\(723\) 0 0
\(724\) 274.989i 0.379820i
\(725\) 1303.90 21.3559i 1.79848 0.0294564i
\(726\) 0 0
\(727\) −1129.81 + 709.908i −1.55407 + 0.976489i −0.565672 + 0.824631i \(0.691383\pi\)
−0.988402 + 0.151859i \(0.951474\pi\)
\(728\) −778.760 272.500i −1.06973 0.374313i
\(729\) 0 0
\(730\) 382.939 + 87.4034i 0.524575 + 0.119731i
\(731\) 1136.37 259.370i 1.55455 0.354815i
\(732\) 0 0
\(733\) 55.6770 + 494.147i 0.0759577 + 0.674143i 0.972777 + 0.231745i \(0.0744435\pi\)
−0.896819 + 0.442398i \(0.854128\pi\)
\(734\) 37.9116 + 30.2335i 0.0516507 + 0.0411901i
\(735\) 0 0
\(736\) −25.3837 + 225.286i −0.0344887 + 0.306096i
\(737\) −427.062 + 427.062i −0.579460 + 0.579460i
\(738\) 0 0
\(739\) 224.344 357.042i 0.303578 0.483142i −0.659744 0.751491i \(-0.729335\pi\)
0.963322 + 0.268349i \(0.0864781\pi\)
\(740\) −163.155 102.517i −0.220479 0.138536i
\(741\) 0 0
\(742\) −778.205 778.205i −1.04879 1.04879i
\(743\) −69.6091 7.84306i −0.0936865 0.0105559i 0.0649967 0.997885i \(-0.479296\pi\)
−0.158683 + 0.987330i \(0.550725\pi\)
\(744\) 0 0
\(745\) 428.060 536.771i 0.574577 0.720497i
\(746\) 391.799 44.1452i 0.525200 0.0591758i
\(747\) 0 0
\(748\) −37.4493 164.076i −0.0500659 0.219353i
\(749\) 246.079 1078.14i 0.328543 1.43944i
\(750\) 0 0
\(751\) 254.301 726.750i 0.338616 0.967710i −0.641124 0.767438i \(-0.721531\pi\)
0.979740 0.200273i \(-0.0641828\pi\)
\(752\) −238.594 379.720i −0.317279 0.504947i
\(753\) 0 0
\(754\) 72.0670 + 557.406i 0.0955796 + 0.739265i
\(755\) −218.812 −0.289818
\(756\) 0 0
\(757\) −1308.76 457.955i −1.72888 0.604960i −0.731811 0.681507i \(-0.761325\pi\)
−0.997066 + 0.0765471i \(0.975610\pi\)
\(758\) 118.726 246.538i 0.156631 0.325248i
\(759\) 0 0
\(760\) −1139.60 + 260.107i −1.49948 + 0.342246i
\(761\) 750.154 361.255i 0.985748 0.474711i 0.129670 0.991557i \(-0.458608\pi\)
0.856078 + 0.516846i \(0.172894\pi\)
\(762\) 0 0
\(763\) 1367.12 + 1090.24i 1.79177 + 1.42889i
\(764\) −114.425 + 40.0389i −0.149771 + 0.0524070i
\(765\) 0 0
\(766\) −302.591 + 302.591i −0.395028 + 0.395028i
\(767\) 208.556 166.318i 0.271911 0.216842i
\(768\) 0 0
\(769\) −338.952 212.978i −0.440770 0.276954i 0.293310 0.956017i \(-0.405243\pi\)
−0.734080 + 0.679063i \(0.762386\pi\)
\(770\) 720.485 + 903.459i 0.935694 + 1.17332i
\(771\) 0 0
\(772\) −157.828 17.7829i −0.204440 0.0230349i
\(773\) 48.0158 + 137.221i 0.0621162 + 0.177518i 0.970759 0.240057i \(-0.0771660\pi\)
−0.908643 + 0.417575i \(0.862880\pi\)
\(774\) 0 0
\(775\) 69.9623 7.88286i 0.0902739 0.0101714i
\(776\) −94.0854 195.370i −0.121244 0.251766i
\(777\) 0 0
\(778\) 124.314 544.654i 0.159786 0.700070i
\(779\) −3.97625 1.91486i −0.00510430 0.00245810i
\(780\) 0 0
\(781\) 525.351 + 836.092i 0.672665 + 1.07054i
\(782\) 365.879i 0.467876i
\(783\) 0 0
\(784\) 219.472 0.279938
\(785\) −1503.47 + 944.695i −1.91525 + 1.20343i
\(786\) 0 0
\(787\) 433.290 899.737i 0.550560 1.14325i −0.421133