Properties

Label 105.3.t.b.11.8
Level 105
Weight 3
Character 105.11
Analytic conductor 2.861
Analytic rank 0
Dimension 36
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.t (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 11.8
Character \(\chi\) \(=\) 105.11
Dual form 105.3.t.b.86.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.860118 + 0.496589i) q^{2} +(2.51213 + 1.63987i) q^{3} +(-1.50680 + 2.60985i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-2.97507 - 0.162987i) q^{6} +(-1.66850 + 6.79824i) q^{7} -6.96575i q^{8} +(3.62163 + 8.23916i) q^{9} +O(q^{10})\) \(q+(-0.860118 + 0.496589i) q^{2} +(2.51213 + 1.63987i) q^{3} +(-1.50680 + 2.60985i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-2.97507 - 0.162987i) q^{6} +(-1.66850 + 6.79824i) q^{7} -6.96575i q^{8} +(3.62163 + 8.23916i) q^{9} +(-1.11041 + 1.92328i) q^{10} +(-0.568919 - 0.328465i) q^{11} +(-8.06511 + 4.08533i) q^{12} -10.1624 q^{13} +(-1.94082 - 6.67585i) q^{14} +(6.69816 + 0.366952i) q^{15} +(-2.56808 - 4.44804i) q^{16} +(16.8362 + 9.72041i) q^{17} +(-7.20650 - 5.28819i) q^{18} +(9.11844 + 15.7936i) q^{19} +6.73861i q^{20} +(-15.3398 + 14.3420i) q^{21} +0.652449 q^{22} +(3.29154 - 1.90037i) q^{23} +(11.4230 - 17.4989i) q^{24} +(2.50000 - 4.33013i) q^{25} +(8.74087 - 5.04654i) q^{26} +(-4.41319 + 26.6369i) q^{27} +(-15.2283 - 14.5981i) q^{28} -50.8888i q^{29} +(-5.94343 + 3.01061i) q^{30} +(26.8895 - 46.5740i) q^{31} +(28.5478 + 16.4821i) q^{32} +(-0.890558 - 1.75810i) q^{33} -19.3082 q^{34} +(4.36962 + 15.0302i) q^{35} +(-26.9601 - 2.96285i) q^{36} +(7.81834 + 13.5418i) q^{37} +(-15.6859 - 9.05623i) q^{38} +(-25.5293 - 16.6651i) q^{39} +(-7.78795 - 13.4891i) q^{40} -57.3936i q^{41} +(6.07195 - 19.9533i) q^{42} +65.7755 q^{43} +(1.71449 - 0.989862i) q^{44} +(16.2249 + 11.9060i) q^{45} +(-1.88741 + 3.26909i) q^{46} +(-22.4206 + 12.9445i) q^{47} +(0.842874 - 15.3854i) q^{48} +(-43.4322 - 22.6858i) q^{49} +4.96589i q^{50} +(26.3546 + 52.0283i) q^{51} +(15.3127 - 26.5224i) q^{52} +(5.64406 + 3.25860i) q^{53} +(-9.43173 - 25.1024i) q^{54} -1.46894 q^{55} +(47.3549 + 11.6224i) q^{56} +(-2.99278 + 54.6287i) q^{57} +(25.2708 + 43.7703i) q^{58} +(-18.7268 - 10.8119i) q^{59} +(-11.0505 + 16.9283i) q^{60} +(17.1465 + 29.6986i) q^{61} +53.4122i q^{62} +(-62.0545 + 10.8736i) q^{63} -12.1947 q^{64} +(-19.6794 + 11.3619i) q^{65} +(1.63904 + 1.06993i) q^{66} +(-39.5814 + 68.5571i) q^{67} +(-50.7376 + 29.2934i) q^{68} +(11.3852 + 0.623725i) q^{69} +(-11.2222 - 10.7578i) q^{70} +39.0201i q^{71} +(57.3920 - 25.2274i) q^{72} +(-19.9202 + 34.5027i) q^{73} +(-13.4494 - 7.76500i) q^{74} +(13.3812 - 6.77817i) q^{75} -54.9586 q^{76} +(3.18223 - 3.31960i) q^{77} +(30.2339 + 1.65634i) q^{78} +(31.9251 + 55.2959i) q^{79} +(-9.94611 - 5.74239i) q^{80} +(-54.7677 + 59.6783i) q^{81} +(28.5011 + 49.3653i) q^{82} -75.6992i q^{83} +(-14.3164 - 61.6449i) q^{84} +43.4710 q^{85} +(-56.5747 + 32.6634i) q^{86} +(83.4512 - 127.839i) q^{87} +(-2.28801 + 3.96295i) q^{88} +(57.0756 - 32.9526i) q^{89} +(-19.8677 - 2.18342i) q^{90} +(16.9560 - 69.0865i) q^{91} +11.4539i q^{92} +(143.926 - 72.9047i) q^{93} +(12.8562 - 22.2677i) q^{94} +(35.3155 + 20.3894i) q^{95} +(44.6873 + 88.2199i) q^{96} -113.808 q^{97} +(48.6223 - 2.05549i) q^{98} +(0.645869 - 5.87699i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 4q^{3} + 36q^{4} - 24q^{6} - 58q^{7} - 2q^{9} + O(q^{10}) \) \( 36q + 4q^{3} + 36q^{4} - 24q^{6} - 58q^{7} - 2q^{9} + 20q^{10} - 42q^{12} - 100q^{13} + 20q^{15} - 12q^{16} - 14q^{18} + 50q^{19} - 12q^{21} + 256q^{22} - 140q^{24} + 90q^{25} + 4q^{27} - 48q^{28} + 60q^{30} - 82q^{31} - 76q^{33} - 64q^{34} + 296q^{36} - 26q^{37} - 130q^{39} - 60q^{40} - 98q^{42} - 204q^{43} + 40q^{45} + 28q^{46} + 532q^{48} - 382q^{49} + 208q^{51} + 200q^{52} - 44q^{54} - 160q^{55} + 252q^{57} + 264q^{58} - 130q^{60} - 324q^{61} - 258q^{63} - 24q^{64} - 164q^{66} - 142q^{67} - 112q^{69} + 200q^{70} - 322q^{72} + 386q^{73} - 20q^{75} - 424q^{76} - 440q^{78} + 334q^{79} + 186q^{81} - 68q^{82} + 80q^{84} - 200q^{85} + 342q^{87} + 180q^{88} + 100q^{90} + 46q^{91} - 2q^{93} + 324q^{94} + 732q^{96} + 1616q^{97} + 384q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.860118 + 0.496589i −0.430059 + 0.248295i −0.699372 0.714758i \(-0.746537\pi\)
0.269313 + 0.963053i \(0.413203\pi\)
\(3\) 2.51213 + 1.63987i 0.837378 + 0.546625i
\(4\) −1.50680 + 2.60985i −0.376700 + 0.652463i
\(5\) 1.93649 1.11803i 0.387298 0.223607i
\(6\) −2.97507 0.162987i −0.495846 0.0271644i
\(7\) −1.66850 + 6.79824i −0.238358 + 0.971177i
\(8\) 6.96575i 0.870719i
\(9\) 3.62163 + 8.23916i 0.402403 + 0.915463i
\(10\) −1.11041 + 1.92328i −0.111041 + 0.192328i
\(11\) −0.568919 0.328465i −0.0517199 0.0298605i 0.473917 0.880569i \(-0.342840\pi\)
−0.525637 + 0.850709i \(0.676173\pi\)
\(12\) −8.06511 + 4.08533i −0.672092 + 0.340445i
\(13\) −10.1624 −0.781724 −0.390862 0.920449i \(-0.627823\pi\)
−0.390862 + 0.920449i \(0.627823\pi\)
\(14\) −1.94082 6.67585i −0.138630 0.476846i
\(15\) 6.69816 + 0.366952i 0.446544 + 0.0244635i
\(16\) −2.56808 4.44804i −0.160505 0.278002i
\(17\) 16.8362 + 9.72041i 0.990367 + 0.571789i 0.905384 0.424594i \(-0.139583\pi\)
0.0849830 + 0.996382i \(0.472916\pi\)
\(18\) −7.20650 5.28819i −0.400361 0.293788i
\(19\) 9.11844 + 15.7936i 0.479918 + 0.831242i 0.999735 0.0230359i \(-0.00733320\pi\)
−0.519817 + 0.854278i \(0.674000\pi\)
\(20\) 6.73861i 0.336930i
\(21\) −15.3398 + 14.3420i −0.730465 + 0.682950i
\(22\) 0.652449 0.0296568
\(23\) 3.29154 1.90037i 0.143110 0.0826248i −0.426735 0.904377i \(-0.640336\pi\)
0.569846 + 0.821752i \(0.307003\pi\)
\(24\) 11.4230 17.4989i 0.475957 0.729121i
\(25\) 2.50000 4.33013i 0.100000 0.173205i
\(26\) 8.74087 5.04654i 0.336187 0.194098i
\(27\) −4.41319 + 26.6369i −0.163451 + 0.986551i
\(28\) −15.2283 14.5981i −0.543868 0.521362i
\(29\) 50.8888i 1.75478i −0.479774 0.877392i \(-0.659281\pi\)
0.479774 0.877392i \(-0.340719\pi\)
\(30\) −5.94343 + 3.01061i −0.198114 + 0.100354i
\(31\) 26.8895 46.5740i 0.867404 1.50239i 0.00276405 0.999996i \(-0.499120\pi\)
0.864640 0.502392i \(-0.167546\pi\)
\(32\) 28.5478 + 16.4821i 0.892118 + 0.515064i
\(33\) −0.890558 1.75810i −0.0269866 0.0532759i
\(34\) −19.3082 −0.567888
\(35\) 4.36962 + 15.0302i 0.124846 + 0.429434i
\(36\) −26.9601 2.96285i −0.748890 0.0823015i
\(37\) 7.81834 + 13.5418i 0.211306 + 0.365993i 0.952124 0.305713i \(-0.0988949\pi\)
−0.740817 + 0.671707i \(0.765562\pi\)
\(38\) −15.6859 9.05623i −0.412786 0.238322i
\(39\) −25.5293 16.6651i −0.654598 0.427310i
\(40\) −7.78795 13.4891i −0.194699 0.337228i
\(41\) 57.3936i 1.39985i −0.714219 0.699923i \(-0.753218\pi\)
0.714219 0.699923i \(-0.246782\pi\)
\(42\) 6.07195 19.9533i 0.144570 0.475079i
\(43\) 65.7755 1.52966 0.764831 0.644230i \(-0.222822\pi\)
0.764831 + 0.644230i \(0.222822\pi\)
\(44\) 1.71449 0.989862i 0.0389657 0.0224969i
\(45\) 16.2249 + 11.9060i 0.360554 + 0.264577i
\(46\) −1.88741 + 3.26909i −0.0410306 + 0.0710671i
\(47\) −22.4206 + 12.9445i −0.477034 + 0.275416i −0.719180 0.694824i \(-0.755482\pi\)
0.242146 + 0.970240i \(0.422149\pi\)
\(48\) 0.842874 15.3854i 0.0175599 0.320529i
\(49\) −43.4322 22.6858i −0.886371 0.462976i
\(50\) 4.96589i 0.0993178i
\(51\) 26.3546 + 52.0283i 0.516757 + 1.02016i
\(52\) 15.3127 26.5224i 0.294475 0.510046i
\(53\) 5.64406 + 3.25860i 0.106492 + 0.0614830i 0.552300 0.833645i \(-0.313750\pi\)
−0.445808 + 0.895129i \(0.647084\pi\)
\(54\) −9.43173 25.1024i −0.174662 0.464859i
\(55\) −1.46894 −0.0267080
\(56\) 47.3549 + 11.6224i 0.845623 + 0.207543i
\(57\) −2.99278 + 54.6287i −0.0525049 + 0.958398i
\(58\) 25.2708 + 43.7703i 0.435704 + 0.754661i
\(59\) −18.7268 10.8119i −0.317403 0.183253i 0.332831 0.942986i \(-0.391996\pi\)
−0.650234 + 0.759734i \(0.725329\pi\)
\(60\) −11.0505 + 16.9283i −0.184174 + 0.282138i
\(61\) 17.1465 + 29.6986i 0.281090 + 0.486862i 0.971653 0.236410i \(-0.0759708\pi\)
−0.690564 + 0.723272i \(0.742637\pi\)
\(62\) 53.4122i 0.861487i
\(63\) −62.0545 + 10.8736i −0.984993 + 0.172597i
\(64\) −12.1947 −0.190542
\(65\) −19.6794 + 11.3619i −0.302760 + 0.174799i
\(66\) 1.63904 + 1.06993i 0.0248339 + 0.0162111i
\(67\) −39.5814 + 68.5571i −0.590768 + 1.02324i 0.403361 + 0.915041i \(0.367842\pi\)
−0.994129 + 0.108199i \(0.965492\pi\)
\(68\) −50.7376 + 29.2934i −0.746142 + 0.430785i
\(69\) 11.3852 + 0.623725i 0.165002 + 0.00903949i
\(70\) −11.2222 10.7578i −0.160317 0.153683i
\(71\) 39.0201i 0.549579i 0.961504 + 0.274789i \(0.0886082\pi\)
−0.961504 + 0.274789i \(0.911392\pi\)
\(72\) 57.3920 25.2274i 0.797111 0.350380i
\(73\) −19.9202 + 34.5027i −0.272879 + 0.472640i −0.969598 0.244704i \(-0.921309\pi\)
0.696719 + 0.717344i \(0.254643\pi\)
\(74\) −13.4494 7.76500i −0.181748 0.104932i
\(75\) 13.3812 6.77817i 0.178416 0.0903756i
\(76\) −54.9586 −0.723139
\(77\) 3.18223 3.31960i 0.0413277 0.0431117i
\(78\) 30.2339 + 1.65634i 0.387614 + 0.0212351i
\(79\) 31.9251 + 55.2959i 0.404116 + 0.699949i 0.994218 0.107380i \(-0.0342460\pi\)
−0.590103 + 0.807328i \(0.700913\pi\)
\(80\) −9.94611 5.74239i −0.124326 0.0717799i
\(81\) −54.7677 + 59.6783i −0.676144 + 0.736770i
\(82\) 28.5011 + 49.3653i 0.347574 + 0.602016i
\(83\) 75.6992i 0.912038i −0.889970 0.456019i \(-0.849275\pi\)
0.889970 0.456019i \(-0.150725\pi\)
\(84\) −14.3164 61.6449i −0.170434 0.733868i
\(85\) 43.4710 0.511423
\(86\) −56.5747 + 32.6634i −0.657845 + 0.379807i
\(87\) 83.4512 127.839i 0.959209 1.46942i
\(88\) −2.28801 + 3.96295i −0.0260001 + 0.0450335i
\(89\) 57.0756 32.9526i 0.641299 0.370254i −0.143816 0.989604i \(-0.545937\pi\)
0.785115 + 0.619350i \(0.212604\pi\)
\(90\) −19.8677 2.18342i −0.220752 0.0242602i
\(91\) 16.9560 69.0865i 0.186330 0.759193i
\(92\) 11.4539i 0.124499i
\(93\) 143.926 72.9047i 1.54759 0.783922i
\(94\) 12.8562 22.2677i 0.136769 0.236890i
\(95\) 35.3155 + 20.3894i 0.371743 + 0.214626i
\(96\) 44.6873 + 88.2199i 0.465493 + 0.918957i
\(97\) −113.808 −1.17328 −0.586638 0.809849i \(-0.699549\pi\)
−0.586638 + 0.809849i \(0.699549\pi\)
\(98\) 48.6223 2.05549i 0.496146 0.0209744i
\(99\) 0.645869 5.87699i 0.00652393 0.0593636i
\(100\) 7.53399 + 13.0493i 0.0753399 + 0.130493i
\(101\) −124.672 71.9795i −1.23438 0.712668i −0.266438 0.963852i \(-0.585847\pi\)
−0.967939 + 0.251184i \(0.919180\pi\)
\(102\) −48.5048 31.6630i −0.475537 0.310422i
\(103\) −71.8026 124.366i −0.697112 1.20743i −0.969463 0.245236i \(-0.921135\pi\)
0.272351 0.962198i \(-0.412199\pi\)
\(104\) 70.7888i 0.680662i
\(105\) −13.6705 + 44.9234i −0.130196 + 0.427842i
\(106\) −6.47274 −0.0610636
\(107\) 2.65292 1.53166i 0.0247936 0.0143146i −0.487552 0.873094i \(-0.662110\pi\)
0.512346 + 0.858779i \(0.328777\pi\)
\(108\) −62.8685 51.6542i −0.582116 0.478279i
\(109\) 18.7190 32.4223i 0.171734 0.297453i −0.767292 0.641298i \(-0.778396\pi\)
0.939026 + 0.343845i \(0.111730\pi\)
\(110\) 1.26346 0.729461i 0.0114860 0.00663146i
\(111\) −2.56607 + 46.8398i −0.0231178 + 0.421980i
\(112\) 34.5237 10.0368i 0.308247 0.0896145i
\(113\) 170.551i 1.50930i 0.656126 + 0.754652i \(0.272194\pi\)
−0.656126 + 0.754652i \(0.727806\pi\)
\(114\) −24.5539 48.4733i −0.215385 0.425204i
\(115\) 4.24936 7.36011i 0.0369510 0.0640009i
\(116\) 132.812 + 76.6791i 1.14493 + 0.661027i
\(117\) −36.8044 83.7298i −0.314568 0.715639i
\(118\) 21.4763 0.182003
\(119\) −94.1730 + 98.2383i −0.791370 + 0.825532i
\(120\) 2.55610 46.6577i 0.0213008 0.388814i
\(121\) −60.2842 104.415i −0.498217 0.862937i
\(122\) −29.4960 17.0295i −0.241770 0.139586i
\(123\) 94.1184 144.180i 0.765190 1.17220i
\(124\) 81.0342 + 140.355i 0.653502 + 1.13190i
\(125\) 11.1803i 0.0894427i
\(126\) 47.9745 40.1682i 0.380750 0.318795i
\(127\) 107.463 0.846168 0.423084 0.906091i \(-0.360948\pi\)
0.423084 + 0.906091i \(0.360948\pi\)
\(128\) −103.702 + 59.8725i −0.810174 + 0.467754i
\(129\) 165.237 + 107.864i 1.28091 + 0.836152i
\(130\) 11.2844 19.5452i 0.0868032 0.150348i
\(131\) 36.8200 21.2580i 0.281068 0.162275i −0.352839 0.935684i \(-0.614784\pi\)
0.633907 + 0.773409i \(0.281450\pi\)
\(132\) 5.93028 + 0.324885i 0.0449264 + 0.00246125i
\(133\) −122.583 + 35.6376i −0.921675 + 0.267952i
\(134\) 78.6229i 0.586738i
\(135\) 21.2348 + 56.5162i 0.157295 + 0.418639i
\(136\) 67.7100 117.277i 0.497867 0.862331i
\(137\) −113.230 65.3735i −0.826498 0.477179i 0.0261540 0.999658i \(-0.491674\pi\)
−0.852652 + 0.522479i \(0.825007\pi\)
\(138\) −10.1023 + 5.11727i −0.0732051 + 0.0370817i
\(139\) 59.1673 0.425664 0.212832 0.977089i \(-0.431731\pi\)
0.212832 + 0.977089i \(0.431731\pi\)
\(140\) −45.8107 11.2434i −0.327219 0.0803100i
\(141\) −77.5510 4.24856i −0.550007 0.0301316i
\(142\) −19.3770 33.5619i −0.136458 0.236351i
\(143\) 5.78159 + 3.33800i 0.0404307 + 0.0233427i
\(144\) 27.3475 37.2679i 0.189913 0.258805i
\(145\) −56.8954 98.5456i −0.392382 0.679625i
\(146\) 39.5686i 0.271018i
\(147\) −71.9056 128.213i −0.489154 0.872198i
\(148\) −47.1226 −0.318396
\(149\) −161.380 + 93.1729i −1.08309 + 0.625321i −0.931728 0.363157i \(-0.881699\pi\)
−0.151360 + 0.988479i \(0.548365\pi\)
\(150\) −8.14344 + 12.4750i −0.0542896 + 0.0831665i
\(151\) 76.5651 132.615i 0.507054 0.878243i −0.492913 0.870079i \(-0.664068\pi\)
0.999967 0.00816421i \(-0.00259878\pi\)
\(152\) 110.014 63.5168i 0.723778 0.417873i
\(153\) −19.1135 + 173.920i −0.124925 + 1.13673i
\(154\) −1.08862 + 4.43551i −0.00706893 + 0.0288020i
\(155\) 120.254i 0.775830i
\(156\) 81.9609 41.5168i 0.525390 0.266134i
\(157\) −110.622 + 191.604i −0.704601 + 1.22040i 0.262234 + 0.965004i \(0.415541\pi\)
−0.966835 + 0.255401i \(0.917793\pi\)
\(158\) −54.9187 31.7074i −0.347587 0.200679i
\(159\) 8.83494 + 17.4416i 0.0555657 + 0.109696i
\(160\) 73.7100 0.460688
\(161\) 7.42723 + 25.5475i 0.0461319 + 0.158680i
\(162\) 17.4710 78.5274i 0.107846 0.484737i
\(163\) 43.5042 + 75.3516i 0.266897 + 0.462280i 0.968059 0.250723i \(-0.0806682\pi\)
−0.701162 + 0.713002i \(0.747335\pi\)
\(164\) 149.789 + 86.4806i 0.913347 + 0.527321i
\(165\) −3.69018 2.40888i −0.0223647 0.0145993i
\(166\) 37.5914 + 65.1102i 0.226454 + 0.392230i
\(167\) 296.532i 1.77564i −0.460193 0.887819i \(-0.652220\pi\)
0.460193 0.887819i \(-0.347780\pi\)
\(168\) 99.9025 + 106.853i 0.594658 + 0.636030i
\(169\) −65.7254 −0.388908
\(170\) −37.3902 + 21.5872i −0.219942 + 0.126984i
\(171\) −97.1025 + 132.327i −0.567851 + 0.773841i
\(172\) −99.1104 + 171.664i −0.576223 + 0.998048i
\(173\) 35.2279 20.3388i 0.203629 0.117565i −0.394718 0.918802i \(-0.629158\pi\)
0.598347 + 0.801237i \(0.295824\pi\)
\(174\) −8.29419 + 151.398i −0.0476677 + 0.870102i
\(175\) 25.2660 + 24.2204i 0.144377 + 0.138403i
\(176\) 3.37409i 0.0191710i
\(177\) −29.3140 57.8705i −0.165616 0.326952i
\(178\) −32.7278 + 56.6863i −0.183864 + 0.318462i
\(179\) 263.287 + 152.009i 1.47088 + 0.849213i 0.999465 0.0326995i \(-0.0104104\pi\)
0.471414 + 0.881912i \(0.343744\pi\)
\(180\) −55.5205 + 24.4047i −0.308447 + 0.135582i
\(181\) −15.1747 −0.0838380 −0.0419190 0.999121i \(-0.513347\pi\)
−0.0419190 + 0.999121i \(0.513347\pi\)
\(182\) 19.7234 + 67.8427i 0.108371 + 0.372762i
\(183\) −5.62768 + 102.725i −0.0307524 + 0.561338i
\(184\) −13.2375 22.9281i −0.0719430 0.124609i
\(185\) 30.2803 + 17.4823i 0.163677 + 0.0944991i
\(186\) −87.5893 + 134.179i −0.470910 + 0.721390i
\(187\) −6.38563 11.0602i −0.0341478 0.0591457i
\(188\) 78.0192i 0.414996i
\(189\) −173.721 74.4457i −0.919157 0.393893i
\(190\) −40.5007 −0.213162
\(191\) −79.3405 + 45.8073i −0.415395 + 0.239829i −0.693105 0.720836i \(-0.743758\pi\)
0.277710 + 0.960665i \(0.410425\pi\)
\(192\) −30.6346 19.9977i −0.159555 0.104155i
\(193\) −37.3477 + 64.6880i −0.193511 + 0.335171i −0.946411 0.322963i \(-0.895321\pi\)
0.752900 + 0.658135i \(0.228654\pi\)
\(194\) 97.8881 56.5157i 0.504578 0.291318i
\(195\) −68.0694 3.72912i −0.349074 0.0191237i
\(196\) 124.650 79.1686i 0.635970 0.403921i
\(197\) 125.342i 0.636251i −0.948049 0.318126i \(-0.896947\pi\)
0.948049 0.318126i \(-0.103053\pi\)
\(198\) 2.36293 + 5.37564i 0.0119340 + 0.0271497i
\(199\) −72.8077 + 126.107i −0.365868 + 0.633701i −0.988915 0.148483i \(-0.952561\pi\)
0.623047 + 0.782184i \(0.285894\pi\)
\(200\) −30.1626 17.4144i −0.150813 0.0870719i
\(201\) −211.859 + 107.316i −1.05402 + 0.533910i
\(202\) 142.977 0.707807
\(203\) 345.954 + 84.9081i 1.70421 + 0.418267i
\(204\) −175.497 9.61445i −0.860280 0.0471296i
\(205\) −64.1680 111.142i −0.313015 0.542158i
\(206\) 123.517 + 71.3128i 0.599599 + 0.346178i
\(207\) 27.5782 + 20.2371i 0.133228 + 0.0977638i
\(208\) 26.0978 + 45.2028i 0.125470 + 0.217321i
\(209\) 11.9804i 0.0573223i
\(210\) −10.5502 45.4281i −0.0502392 0.216324i
\(211\) 56.4047 0.267321 0.133660 0.991027i \(-0.457327\pi\)
0.133660 + 0.991027i \(0.457327\pi\)
\(212\) −17.0089 + 9.82011i −0.0802308 + 0.0463213i
\(213\) −63.9881 + 98.0237i −0.300413 + 0.460205i
\(214\) −1.52122 + 2.63482i −0.00710849 + 0.0123123i
\(215\) 127.374 73.5392i 0.592436 0.342043i
\(216\) 185.546 + 30.7412i 0.859009 + 0.142320i
\(217\) 271.756 + 260.511i 1.25233 + 1.20051i
\(218\) 37.1827i 0.170563i
\(219\) −106.622 + 54.0089i −0.486860 + 0.246616i
\(220\) 2.21340 3.83372i 0.0100609 0.0174260i
\(221\) −171.097 98.7828i −0.774193 0.446981i
\(222\) −21.0530 41.5620i −0.0948333 0.187216i
\(223\) 423.029 1.89699 0.948495 0.316791i \(-0.102606\pi\)
0.948495 + 0.316791i \(0.102606\pi\)
\(224\) −159.681 + 166.574i −0.712862 + 0.743635i
\(225\) 44.7307 + 4.91581i 0.198803 + 0.0218481i
\(226\) −84.6939 146.694i −0.374752 0.649089i
\(227\) −171.925 99.2608i −0.757378 0.437272i 0.0709755 0.997478i \(-0.477389\pi\)
−0.828354 + 0.560206i \(0.810722\pi\)
\(228\) −138.063 90.1251i −0.605541 0.395286i
\(229\) −101.058 175.038i −0.441302 0.764357i 0.556485 0.830858i \(-0.312150\pi\)
−0.997786 + 0.0665008i \(0.978817\pi\)
\(230\) 8.44074i 0.0366989i
\(231\) 13.4379 3.12082i 0.0581728 0.0135100i
\(232\) −354.478 −1.52792
\(233\) 277.136 160.005i 1.18943 0.686715i 0.231250 0.972894i \(-0.425719\pi\)
0.958176 + 0.286179i \(0.0923853\pi\)
\(234\) 73.2355 + 53.7408i 0.312972 + 0.229661i
\(235\) −28.9449 + 50.1340i −0.123170 + 0.213336i
\(236\) 56.4350 32.5827i 0.239131 0.138062i
\(237\) −10.4782 + 191.264i −0.0442119 + 0.807021i
\(238\) 32.2158 131.262i 0.135361 0.551520i
\(239\) 347.556i 1.45421i −0.686528 0.727104i \(-0.740866\pi\)
0.686528 0.727104i \(-0.259134\pi\)
\(240\) −15.5692 30.7360i −0.0648715 0.128067i
\(241\) −82.0871 + 142.179i −0.340611 + 0.589955i −0.984546 0.175125i \(-0.943967\pi\)
0.643936 + 0.765080i \(0.277300\pi\)
\(242\) 103.703 + 59.8730i 0.428525 + 0.247409i
\(243\) −235.449 + 60.1079i −0.968924 + 0.247357i
\(244\) −103.345 −0.423545
\(245\) −109.470 + 4.62779i −0.446815 + 0.0188890i
\(246\) −9.35440 + 170.750i −0.0380260 + 0.694107i
\(247\) −92.6653 160.501i −0.375163 0.649802i
\(248\) −324.423 187.306i −1.30816 0.755265i
\(249\) 124.137 190.166i 0.498543 0.763721i
\(250\) 5.55204 + 9.61641i 0.0222081 + 0.0384656i
\(251\) 46.7632i 0.186307i −0.995652 0.0931537i \(-0.970305\pi\)
0.995652 0.0931537i \(-0.0296948\pi\)
\(252\) 65.1252 178.337i 0.258433 0.707688i
\(253\) −2.49682 −0.00986887
\(254\) −92.4311 + 53.3651i −0.363902 + 0.210099i
\(255\) 109.205 + 71.2869i 0.428254 + 0.279557i
\(256\) 83.8534 145.238i 0.327552 0.567337i
\(257\) −293.930 + 169.701i −1.14370 + 0.660314i −0.947344 0.320219i \(-0.896243\pi\)
−0.196354 + 0.980533i \(0.562910\pi\)
\(258\) −195.687 10.7205i −0.758477 0.0415524i
\(259\) −105.105 + 30.5565i −0.405811 + 0.117979i
\(260\) 68.4805i 0.263386i
\(261\) 419.281 184.300i 1.60644 0.706130i
\(262\) −21.1130 + 36.5688i −0.0805840 + 0.139576i
\(263\) 86.0787 + 49.6976i 0.327296 + 0.188964i 0.654640 0.755941i \(-0.272820\pi\)
−0.327344 + 0.944905i \(0.606154\pi\)
\(264\) −12.2465 + 6.20340i −0.0463883 + 0.0234977i
\(265\) 14.5729 0.0549921
\(266\) 87.7384 91.5259i 0.329844 0.344082i
\(267\) 197.420 + 10.8155i 0.739400 + 0.0405073i
\(268\) −119.283 206.603i −0.445084 0.770908i
\(269\) 222.611 + 128.525i 0.827550 + 0.477786i 0.853013 0.521889i \(-0.174773\pi\)
−0.0254629 + 0.999676i \(0.508106\pi\)
\(270\) −46.3298 38.0656i −0.171592 0.140984i
\(271\) −109.254 189.234i −0.403152 0.698280i 0.590952 0.806707i \(-0.298752\pi\)
−0.994104 + 0.108426i \(0.965419\pi\)
\(272\) 99.8509i 0.367099i
\(273\) 155.889 145.749i 0.571022 0.533878i
\(274\) 129.855 0.473924
\(275\) −2.84459 + 1.64233i −0.0103440 + 0.00597210i
\(276\) −18.7830 + 28.7737i −0.0680542 + 0.104253i
\(277\) 192.880 334.078i 0.696317 1.20606i −0.273418 0.961895i \(-0.588154\pi\)
0.969735 0.244161i \(-0.0785125\pi\)
\(278\) −50.8908 + 29.3818i −0.183061 + 0.105690i
\(279\) 481.115 + 52.8735i 1.72443 + 0.189511i
\(280\) 104.697 30.4377i 0.373916 0.108706i
\(281\) 449.104i 1.59823i 0.601175 + 0.799117i \(0.294699\pi\)
−0.601175 + 0.799117i \(0.705301\pi\)
\(282\) 68.8127 34.8567i 0.244017 0.123605i
\(283\) −62.8475 + 108.855i −0.222076 + 0.384647i −0.955438 0.295191i \(-0.904617\pi\)
0.733362 + 0.679838i \(0.237950\pi\)
\(284\) −101.837 58.7954i −0.358580 0.207026i
\(285\) 55.2812 + 109.134i 0.193969 + 0.382926i
\(286\) −6.63046 −0.0231834
\(287\) 390.176 + 95.7616i 1.35950 + 0.333664i
\(288\) −32.4091 + 294.902i −0.112532 + 1.02396i
\(289\) 44.4726 + 77.0288i 0.153884 + 0.266536i
\(290\) 97.8734 + 56.5072i 0.337495 + 0.194853i
\(291\) −285.900 186.630i −0.982475 0.641342i
\(292\) −60.0313 103.977i −0.205587 0.356087i
\(293\) 250.565i 0.855171i −0.903975 0.427585i \(-0.859364\pi\)
0.903975 0.427585i \(-0.140636\pi\)
\(294\) 125.516 + 74.5708i 0.426927 + 0.253642i
\(295\) −48.3523 −0.163906
\(296\) 94.3285 54.4606i 0.318677 0.183988i
\(297\) 11.2600 13.7046i 0.0379126 0.0461436i
\(298\) 92.5373 160.279i 0.310528 0.537850i
\(299\) −33.4500 + 19.3124i −0.111873 + 0.0645898i
\(300\) −2.47275 + 45.1363i −0.00824249 + 0.150454i
\(301\) −109.747 + 447.158i −0.364607 + 1.48557i
\(302\) 152.086i 0.503595i
\(303\) −195.156 385.269i −0.644078 1.27151i
\(304\) 46.8337 81.1183i 0.154058 0.266836i
\(305\) 66.4080 + 38.3407i 0.217731 + 0.125707i
\(306\) −69.9271 159.083i −0.228520 0.519880i
\(307\) −66.2847 −0.215911 −0.107956 0.994156i \(-0.534430\pi\)
−0.107956 + 0.994156i \(0.534430\pi\)
\(308\) 3.86868 + 13.3071i 0.0125607 + 0.0432049i
\(309\) 23.5665 430.170i 0.0762669 1.39214i
\(310\) 59.7167 + 103.432i 0.192634 + 0.333653i
\(311\) −293.693 169.564i −0.944350 0.545221i −0.0530290 0.998593i \(-0.516888\pi\)
−0.891321 + 0.453372i \(0.850221\pi\)
\(312\) −116.085 + 177.831i −0.372067 + 0.569971i
\(313\) 115.937 + 200.808i 0.370404 + 0.641559i 0.989628 0.143656i \(-0.0458858\pi\)
−0.619223 + 0.785215i \(0.712552\pi\)
\(314\) 219.735i 0.699795i
\(315\) −108.011 + 90.4357i −0.342892 + 0.287098i
\(316\) −192.419 −0.608921
\(317\) −286.243 + 165.262i −0.902974 + 0.521332i −0.878164 0.478360i \(-0.841231\pi\)
−0.0248101 + 0.999692i \(0.507898\pi\)
\(318\) −16.2604 10.6145i −0.0511333 0.0333789i
\(319\) −16.7152 + 28.9516i −0.0523987 + 0.0907573i
\(320\) −23.6149 + 13.6340i −0.0737964 + 0.0426064i
\(321\) 9.17623 + 0.502711i 0.0285864 + 0.00156608i
\(322\) −19.0749 18.2855i −0.0592388 0.0567874i
\(323\) 354.540i 1.09765i
\(324\) −73.2278 232.859i −0.226012 0.718700i
\(325\) −25.4060 + 44.0045i −0.0781724 + 0.135399i
\(326\) −74.8376 43.2075i −0.229563 0.132538i
\(327\) 100.193 50.7524i 0.306402 0.155206i
\(328\) −399.790 −1.21887
\(329\) −50.5912 174.019i −0.153773 0.528932i
\(330\) 4.37021 + 0.239418i 0.0132431 + 0.000725509i
\(331\) 156.100 + 270.374i 0.471602 + 0.816839i 0.999472 0.0324860i \(-0.0103424\pi\)
−0.527870 + 0.849325i \(0.677009\pi\)
\(332\) 197.564 + 114.063i 0.595071 + 0.343565i
\(333\) −83.2577 + 113.460i −0.250023 + 0.340720i
\(334\) 147.254 + 255.052i 0.440881 + 0.763629i
\(335\) 177.014i 0.528399i
\(336\) 103.187 + 31.4006i 0.307105 + 0.0934543i
\(337\) 238.189 0.706791 0.353396 0.935474i \(-0.385027\pi\)
0.353396 + 0.935474i \(0.385027\pi\)
\(338\) 56.5316 32.6385i 0.167253 0.0965637i
\(339\) −279.683 + 428.447i −0.825022 + 1.26386i
\(340\) −65.5020 + 113.453i −0.192653 + 0.333685i
\(341\) −30.5959 + 17.6646i −0.0897241 + 0.0518022i
\(342\) 17.8075 162.037i 0.0520687 0.473791i
\(343\) 226.690 257.411i 0.660905 0.750470i
\(344\) 458.176i 1.33191i
\(345\) 22.7446 11.5212i 0.0659264 0.0333946i
\(346\) −20.2001 + 34.9876i −0.0583817 + 0.101120i
\(347\) 425.845 + 245.862i 1.22722 + 0.708535i 0.966447 0.256866i \(-0.0826899\pi\)
0.260771 + 0.965401i \(0.416023\pi\)
\(348\) 207.898 + 410.423i 0.597407 + 1.17938i
\(349\) −147.217 −0.421825 −0.210912 0.977505i \(-0.567643\pi\)
−0.210912 + 0.977505i \(0.567643\pi\)
\(350\) −33.7593 8.28562i −0.0964552 0.0236732i
\(351\) 44.8486 270.695i 0.127774 0.771211i
\(352\) −10.8276 18.7539i −0.0307602 0.0532781i
\(353\) −368.793 212.923i −1.04474 0.603181i −0.123568 0.992336i \(-0.539434\pi\)
−0.921172 + 0.389155i \(0.872767\pi\)
\(354\) 53.9514 + 35.2185i 0.152405 + 0.0994872i
\(355\) 43.6258 + 75.5621i 0.122890 + 0.212851i
\(356\) 198.612i 0.557898i
\(357\) −397.674 + 92.3557i −1.11393 + 0.258699i
\(358\) −301.944 −0.843420
\(359\) −578.750 + 334.142i −1.61212 + 0.930756i −0.623239 + 0.782032i \(0.714184\pi\)
−0.988879 + 0.148725i \(0.952483\pi\)
\(360\) 82.9341 113.019i 0.230372 0.313941i
\(361\) 14.2083 24.6094i 0.0393581 0.0681702i
\(362\) 13.0520 7.53559i 0.0360553 0.0208165i
\(363\) 19.7860 361.164i 0.0545069 0.994941i
\(364\) 154.756 + 148.352i 0.425154 + 0.407561i
\(365\) 89.0857i 0.244070i
\(366\) −46.1716 91.1501i −0.126152 0.249044i
\(367\) −35.3374 + 61.2062i −0.0962873 + 0.166774i −0.910145 0.414290i \(-0.864030\pi\)
0.813858 + 0.581064i \(0.197363\pi\)
\(368\) −16.9058 9.76059i −0.0459398 0.0265234i
\(369\) 472.876 207.858i 1.28151 0.563302i
\(370\) −34.7261 −0.0938545
\(371\) −31.5699 + 32.9327i −0.0850941 + 0.0887674i
\(372\) −26.5964 + 485.477i −0.0714957 + 1.30505i
\(373\) 127.640 + 221.080i 0.342200 + 0.592707i 0.984841 0.173460i \(-0.0554948\pi\)
−0.642641 + 0.766167i \(0.722161\pi\)
\(374\) 10.9848 + 6.34207i 0.0293711 + 0.0169574i
\(375\) 18.3344 28.0865i 0.0488916 0.0748973i
\(376\) 90.1685 + 156.176i 0.239810 + 0.415363i
\(377\) 517.152i 1.37176i
\(378\) 186.389 22.2357i 0.493093 0.0588246i
\(379\) −224.572 −0.592537 −0.296269 0.955105i \(-0.595742\pi\)
−0.296269 + 0.955105i \(0.595742\pi\)
\(380\) −106.427 + 61.4456i −0.280071 + 0.161699i
\(381\) 269.962 + 176.226i 0.708562 + 0.462536i
\(382\) 45.4948 78.7993i 0.119096 0.206281i
\(383\) −298.557 + 172.372i −0.779523 + 0.450058i −0.836261 0.548331i \(-0.815263\pi\)
0.0567384 + 0.998389i \(0.481930\pi\)
\(384\) −358.697 19.6509i −0.934107 0.0511742i
\(385\) 2.45094 9.98622i 0.00636607 0.0259382i
\(386\) 74.1858i 0.192191i
\(387\) 238.214 + 541.935i 0.615541 + 1.40035i
\(388\) 171.485 297.021i 0.441973 0.765519i
\(389\) −110.104 63.5688i −0.283044 0.163416i 0.351756 0.936092i \(-0.385585\pi\)
−0.634801 + 0.772676i \(0.718918\pi\)
\(390\) 60.3996 30.5951i 0.154871 0.0784489i
\(391\) 73.8895 0.188976
\(392\) −158.024 + 302.538i −0.403122 + 0.771780i
\(393\) 127.357 + 6.97714i 0.324064 + 0.0177535i
\(394\) 62.2432 + 107.808i 0.157978 + 0.273626i
\(395\) 123.645 + 71.3868i 0.313027 + 0.180726i
\(396\) 14.3649 + 10.5411i 0.0362750 + 0.0266189i
\(397\) −115.056 199.283i −0.289813 0.501972i 0.683952 0.729527i \(-0.260260\pi\)
−0.973765 + 0.227556i \(0.926927\pi\)
\(398\) 144.622i 0.363372i
\(399\) −366.386 111.494i −0.918260 0.279433i
\(400\) −25.6808 −0.0642019
\(401\) 321.734 185.753i 0.802329 0.463225i −0.0419560 0.999119i \(-0.513359\pi\)
0.844285 + 0.535895i \(0.180026\pi\)
\(402\) 128.932 197.511i 0.320725 0.491321i
\(403\) −273.262 + 473.304i −0.678071 + 1.17445i
\(404\) 375.712 216.917i 0.929979 0.536924i
\(405\) −39.3347 + 176.799i −0.0971227 + 0.436540i
\(406\) −339.726 + 98.7661i −0.836763 + 0.243266i
\(407\) 10.2722i 0.0252388i
\(408\) 362.416 183.580i 0.888275 0.449951i
\(409\) 376.668 652.409i 0.920950 1.59513i 0.123000 0.992407i \(-0.460748\pi\)
0.797949 0.602725i \(-0.205918\pi\)
\(410\) 110.384 + 63.7303i 0.269230 + 0.155440i
\(411\) −177.245 349.910i −0.431253 0.851363i
\(412\) 432.768 1.05041
\(413\) 104.748 109.269i 0.253626 0.264575i
\(414\) −33.7700 3.71126i −0.0815701 0.00896439i
\(415\) −84.6343 146.591i −0.203938 0.353231i
\(416\) −290.114 167.497i −0.697390 0.402638i
\(417\) 148.636 + 97.0269i 0.356442 + 0.232678i
\(418\) 5.94932 + 10.3045i 0.0142328 + 0.0246520i
\(419\) 375.735i 0.896743i 0.893847 + 0.448371i \(0.147996\pi\)
−0.893847 + 0.448371i \(0.852004\pi\)
\(420\) −96.6448 103.369i −0.230107 0.246116i
\(421\) 598.959 1.42271 0.711353 0.702835i \(-0.248083\pi\)
0.711353 + 0.702835i \(0.248083\pi\)
\(422\) −48.5147 + 28.0100i −0.114964 + 0.0663743i
\(423\) −187.851 137.847i −0.444093 0.325879i
\(424\) 22.6986 39.3151i 0.0535344 0.0927244i
\(425\) 84.1812 48.6020i 0.198073 0.114358i
\(426\) 6.35976 116.088i 0.0149290 0.272506i
\(427\) −230.507 + 67.0137i −0.539829 + 0.156941i
\(428\) 9.23164i 0.0215692i
\(429\) 9.05021 + 17.8666i 0.0210961 + 0.0416470i
\(430\) −73.0376 + 126.505i −0.169855 + 0.294197i
\(431\) 306.385 + 176.891i 0.710869 + 0.410421i 0.811383 0.584515i \(-0.198715\pi\)
−0.100513 + 0.994936i \(0.532049\pi\)
\(432\) 129.815 48.7755i 0.300498 0.112906i
\(433\) −97.7768 −0.225812 −0.112906 0.993606i \(-0.536016\pi\)
−0.112906 + 0.993606i \(0.536016\pi\)
\(434\) −363.109 89.1185i −0.836657 0.205342i
\(435\) 18.6737 340.861i 0.0429282 0.783589i
\(436\) 56.4117 + 97.7079i 0.129385 + 0.224101i
\(437\) 60.0274 + 34.6568i 0.137362 + 0.0793062i
\(438\) 64.8875 99.4015i 0.148145 0.226944i
\(439\) −376.075 651.381i −0.856663 1.48378i −0.875094 0.483953i \(-0.839201\pi\)
0.0184316 0.999830i \(-0.494133\pi\)
\(440\) 10.2323i 0.0232552i
\(441\) 29.6169 440.004i 0.0671586 0.997742i
\(442\) 196.218 0.443932
\(443\) 87.0998 50.2871i 0.196613 0.113515i −0.398461 0.917185i \(-0.630456\pi\)
0.595075 + 0.803670i \(0.297122\pi\)
\(444\) −118.378 77.2752i −0.266618 0.174043i
\(445\) 73.6843 127.625i 0.165583 0.286798i
\(446\) −363.855 + 210.072i −0.815818 + 0.471013i
\(447\) −558.200 30.5805i −1.24877 0.0684127i
\(448\) 20.3468 82.9022i 0.0454171 0.185050i
\(449\) 689.765i 1.53623i −0.640314 0.768113i \(-0.721196\pi\)
0.640314 0.768113i \(-0.278804\pi\)
\(450\) −40.9148 + 17.9846i −0.0909218 + 0.0399658i
\(451\) −18.8518 + 32.6523i −0.0418001 + 0.0723998i
\(452\) −445.113 256.986i −0.984764 0.568554i
\(453\) 409.813 207.589i 0.904665 0.458253i
\(454\) 197.167 0.434290
\(455\) −44.4059 152.743i −0.0975953 0.335699i
\(456\) 380.530 + 20.8470i 0.834496 + 0.0457171i
\(457\) −115.297 199.700i −0.252291 0.436981i 0.711865 0.702316i \(-0.247851\pi\)
−0.964156 + 0.265335i \(0.914517\pi\)
\(458\) 173.844 + 100.369i 0.379572 + 0.219146i
\(459\) −333.223 + 405.567i −0.725976 + 0.883588i
\(460\) 12.8059 + 22.1804i 0.0278388 + 0.0482182i
\(461\) 151.784i 0.329250i −0.986356 0.164625i \(-0.947359\pi\)
0.986356 0.164625i \(-0.0526414\pi\)
\(462\) −10.0084 + 9.35740i −0.0216633 + 0.0202541i
\(463\) −195.792 −0.422878 −0.211439 0.977391i \(-0.567815\pi\)
−0.211439 + 0.977391i \(0.567815\pi\)
\(464\) −226.355 + 130.686i −0.487834 + 0.281651i
\(465\) 197.201 302.093i 0.424088 0.649663i
\(466\) −158.913 + 275.246i −0.341015 + 0.590656i
\(467\) 96.6708 55.8129i 0.207004 0.119514i −0.392914 0.919575i \(-0.628533\pi\)
0.599918 + 0.800061i \(0.295200\pi\)
\(468\) 273.979 + 30.1097i 0.585425 + 0.0643371i
\(469\) −400.026 383.472i −0.852933 0.817638i
\(470\) 57.4949i 0.122329i
\(471\) −592.104 + 299.927i −1.25712 + 0.636787i
\(472\) −75.3131 + 130.446i −0.159562 + 0.276369i
\(473\) −37.4209 21.6050i −0.0791140 0.0456765i
\(474\) −85.9671 169.713i −0.181365 0.358044i
\(475\) 91.1844 0.191967
\(476\) −114.488 393.803i −0.240520 0.827317i
\(477\) −6.40747 + 58.3038i −0.0134328 + 0.122230i
\(478\) 172.592 + 298.939i 0.361072 + 0.625395i
\(479\) 757.982 + 437.621i 1.58243 + 0.913615i 0.994504 + 0.104697i \(0.0333874\pi\)
0.587923 + 0.808917i \(0.299946\pi\)
\(480\) 185.169 + 120.875i 0.385770 + 0.251823i
\(481\) −79.4531 137.617i −0.165183 0.286106i
\(482\) 163.054i 0.338287i
\(483\) −23.2364 + 76.3584i −0.0481085 + 0.158092i
\(484\) 363.345 0.750712
\(485\) −220.388 + 127.241i −0.454408 + 0.262353i
\(486\) 172.665 168.621i 0.355277 0.346957i
\(487\) 241.066 417.538i 0.495002 0.857368i −0.504982 0.863130i \(-0.668501\pi\)
0.999983 + 0.00576174i \(0.00183403\pi\)
\(488\) 206.873 119.438i 0.423920 0.244750i
\(489\) −14.2786 + 260.635i −0.0291996 + 0.532995i
\(490\) 91.8586 58.3418i 0.187467 0.119065i
\(491\) 508.013i 1.03465i 0.855789 + 0.517325i \(0.173072\pi\)
−0.855789 + 0.517325i \(0.826928\pi\)
\(492\) 234.472 + 462.886i 0.476570 + 0.940825i
\(493\) 494.659 856.775i 1.00337 1.73788i
\(494\) 159.406 + 92.0332i 0.322684 + 0.186302i
\(495\) −5.31996 12.1029i −0.0107474 0.0244502i
\(496\) −276.217 −0.556890
\(497\) −265.268 65.1052i −0.533739 0.130996i
\(498\) −12.3380 + 225.211i −0.0247750 + 0.452230i
\(499\) 198.591 + 343.969i 0.397977 + 0.689317i 0.993476 0.114039i \(-0.0363789\pi\)
−0.595499 + 0.803356i \(0.703046\pi\)
\(500\) 29.1790 + 16.8465i 0.0583580 + 0.0336930i
\(501\) 486.274 744.927i 0.970607 1.48688i
\(502\) 23.2221 + 40.2218i 0.0462591 + 0.0801232i
\(503\) 258.341i 0.513601i 0.966464 + 0.256801i \(0.0826684\pi\)
−0.966464 + 0.256801i \(0.917332\pi\)
\(504\) 75.7428 + 432.257i 0.150283 + 0.857652i
\(505\) −321.902 −0.637430
\(506\) 2.14756 1.23990i 0.00424420 0.00245039i
\(507\) −165.111 107.781i −0.325663 0.212587i
\(508\) −161.926 + 280.463i −0.318751 + 0.552093i
\(509\) −155.758 + 89.9271i −0.306009 + 0.176674i −0.645139 0.764065i \(-0.723201\pi\)
0.339130 + 0.940739i \(0.389867\pi\)
\(510\) −129.329 7.08519i −0.253587 0.0138925i
\(511\) −201.321 192.990i −0.393975 0.377671i
\(512\) 312.417i 0.610190i
\(513\) −460.934 + 173.187i −0.898506 + 0.337596i
\(514\) 168.543 291.925i 0.327905 0.567948i
\(515\) −278.090 160.555i −0.539981 0.311758i
\(516\) −530.486 + 268.715i −1.02807 + 0.520765i
\(517\) 17.0073 0.0328962
\(518\) 75.2287 78.4762i 0.145229 0.151498i
\(519\) 121.850 + 6.67545i 0.234779 + 0.0128621i
\(520\) 79.1443 + 137.082i 0.152201 + 0.263619i
\(521\) −203.914 117.730i −0.391389 0.225969i 0.291373 0.956610i \(-0.405888\pi\)
−0.682762 + 0.730641i \(0.739221\pi\)
\(522\) −269.109 + 366.730i −0.515535 + 0.702548i
\(523\) 135.925 + 235.428i 0.259894 + 0.450150i 0.966213 0.257743i \(-0.0829790\pi\)
−0.706319 + 0.707894i \(0.749646\pi\)
\(524\) 128.126i 0.244516i
\(525\) 23.7530 + 102.278i 0.0452439 + 0.194815i
\(526\) −98.7171 −0.187675
\(527\) 905.437 522.754i 1.71810 0.991944i
\(528\) −5.53309 + 8.47618i −0.0104793 + 0.0160534i
\(529\) −257.277 + 445.617i −0.486346 + 0.842376i
\(530\) −12.5344 + 7.23675i −0.0236498 + 0.0136542i
\(531\) 21.2597 193.450i 0.0400372 0.364312i
\(532\) 91.6986 373.622i 0.172366 0.702296i
\(533\) 583.258i 1.09429i
\(534\) −175.175 + 88.7339i −0.328043 + 0.166168i
\(535\) 3.42491 5.93211i 0.00640169 0.0110881i
\(536\) 477.552 + 275.715i 0.890955 + 0.514393i
\(537\) 412.137 + 813.625i 0.767481 + 1.51513i
\(538\) −255.296 −0.474527
\(539\) 17.2579 + 27.1723i 0.0320183 + 0.0504125i
\(540\) −179.496 29.7387i −0.332399 0.0550717i
\(541\) 316.920 + 548.921i 0.585804 + 1.01464i 0.994775 + 0.102094i \(0.0325543\pi\)
−0.408971 + 0.912547i \(0.634112\pi\)
\(542\) 187.943 + 108.509i 0.346759 + 0.200201i
\(543\) −38.1208 24.8846i −0.0702041 0.0458279i
\(544\) 320.425 + 554.992i 0.589016 + 1.02021i
\(545\) 83.7141i 0.153604i
\(546\) −61.7056 + 202.774i −0.113014 + 0.371381i
\(547\) −551.602 −1.00841 −0.504207 0.863583i \(-0.668215\pi\)
−0.504207 + 0.863583i \(0.668215\pi\)
\(548\) 341.230 197.009i 0.622683 0.359506i
\(549\) −182.593 + 248.830i −0.332592 + 0.453242i
\(550\) 1.63112 2.82519i 0.00296568 0.00513671i
\(551\) 803.716 464.026i 1.45865 0.842152i
\(552\) 4.34471 79.3062i 0.00787086 0.143671i
\(553\) −429.182 + 124.773i −0.776098 + 0.225630i
\(554\) 383.128i 0.691567i
\(555\) 47.3993 + 93.5738i 0.0854041 + 0.168601i
\(556\) −89.1532 + 154.418i −0.160347 + 0.277730i
\(557\) −542.908 313.448i −0.974700 0.562743i −0.0740343 0.997256i \(-0.523587\pi\)
−0.900666 + 0.434512i \(0.856921\pi\)
\(558\) −440.072 + 193.439i −0.788659 + 0.346665i
\(559\) −668.438 −1.19577
\(560\) 55.6333 58.0349i 0.0993452 0.103634i
\(561\) 2.09584 38.2564i 0.00373591 0.0681933i
\(562\) −223.020 386.282i −0.396833 0.687335i
\(563\) −599.035 345.853i −1.06401 0.614304i −0.137468 0.990506i \(-0.543896\pi\)
−0.926537 + 0.376203i \(0.877230\pi\)
\(564\) 127.942 195.995i 0.226847 0.347508i
\(565\) 190.682 + 330.271i 0.337490 + 0.584551i
\(566\) 124.838i 0.220561i
\(567\) −314.328 471.897i −0.554370 0.832270i
\(568\) 271.804 0.478529
\(569\) 763.556 440.839i 1.34193 0.774761i 0.354836 0.934929i \(-0.384537\pi\)
0.987090 + 0.160167i \(0.0512034\pi\)
\(570\) −101.743 66.4161i −0.178497 0.116519i
\(571\) −421.729 + 730.456i −0.738580 + 1.27926i 0.214555 + 0.976712i \(0.431170\pi\)
−0.953135 + 0.302546i \(0.902163\pi\)
\(572\) −17.4234 + 10.0594i −0.0304604 + 0.0175863i
\(573\) −274.432 15.0345i −0.478939 0.0262382i
\(574\) −383.151 + 111.391i −0.667511 + 0.194061i
\(575\) 19.0037i 0.0330499i
\(576\) −44.1645 100.474i −0.0766745 0.174434i
\(577\) −131.558 + 227.864i −0.228003 + 0.394912i −0.957216 0.289374i \(-0.906553\pi\)
0.729213 + 0.684286i \(0.239886\pi\)
\(578\) −76.5034 44.1692i −0.132359 0.0764174i
\(579\) −199.903 + 101.259i −0.345255 + 0.174887i
\(580\) 342.919 0.591240
\(581\) 514.621 + 126.304i 0.885751 + 0.217392i
\(582\) 338.587 + 18.5491i 0.581764 + 0.0318714i
\(583\) −2.14067 3.70776i −0.00367183 0.00635979i
\(584\) 240.338 + 138.759i 0.411537 + 0.237601i
\(585\) −164.884 120.993i −0.281853 0.206826i
\(586\) 124.428 + 215.515i 0.212334 + 0.367774i
\(587\) 496.760i 0.846270i −0.906067 0.423135i \(-0.860930\pi\)
0.906067 0.423135i \(-0.139070\pi\)
\(588\) 442.964 + 5.52839i 0.753340 + 0.00940202i
\(589\) 980.762 1.66513
\(590\) 41.5887 24.0113i 0.0704893 0.0406970i
\(591\) 205.544 314.875i 0.347791 0.532783i
\(592\) 40.1561 69.5525i 0.0678313 0.117487i
\(593\) −510.563 + 294.774i −0.860983 + 0.497089i −0.864341 0.502906i \(-0.832264\pi\)
0.00335849 + 0.999994i \(0.498931\pi\)
\(594\) −2.87938 + 17.3792i −0.00484744 + 0.0292579i
\(595\) −72.5315 + 295.526i −0.121902 + 0.496683i
\(596\) 561.571i 0.942233i
\(597\) −389.702 + 197.401i −0.652766 + 0.330655i
\(598\) 19.1806 33.2218i 0.0320746 0.0555548i
\(599\) −261.851 151.180i −0.437147 0.252387i 0.265240 0.964182i \(-0.414549\pi\)
−0.702387 + 0.711796i \(0.747882\pi\)
\(600\) −47.2151 93.2101i −0.0786918 0.155350i
\(601\) −546.705 −0.909659 −0.454829 0.890579i \(-0.650300\pi\)
−0.454829 + 0.890579i \(0.650300\pi\)
\(602\) −127.659 439.107i −0.212057 0.729414i
\(603\) −708.202 77.8300i −1.17446 0.129071i
\(604\) 230.736 + 399.647i 0.382014 + 0.661667i
\(605\) −233.480 134.800i −0.385917 0.222809i
\(606\) 359.177 + 234.464i 0.592702 + 0.386905i
\(607\) −11.7287 20.3147i −0.0193224 0.0334674i 0.856203 0.516640i \(-0.172818\pi\)
−0.875525 + 0.483173i \(0.839484\pi\)
\(608\) 601.163i 0.988754i
\(609\) 729.844 + 780.622i 1.19843 + 1.28181i
\(610\) −76.1583 −0.124850
\(611\) 227.847 131.548i 0.372909 0.215299i
\(612\) −425.106 311.946i −0.694617 0.509716i
\(613\) 76.9855 133.343i 0.125588 0.217525i −0.796375 0.604804i \(-0.793252\pi\)
0.921963 + 0.387279i \(0.126585\pi\)
\(614\) 57.0126 32.9163i 0.0928545 0.0536095i
\(615\) 21.0607 384.432i 0.0342451 0.625092i
\(616\) −23.1235 22.1666i −0.0375382 0.0359848i
\(617\) 180.065i 0.291839i −0.989296 0.145920i \(-0.953386\pi\)
0.989296 0.145920i \(-0.0466141\pi\)
\(618\) 193.348 + 381.700i 0.312861 + 0.617638i
\(619\) 262.098 453.967i 0.423421 0.733387i −0.572850 0.819660i \(-0.694162\pi\)
0.996272 + 0.0862727i \(0.0274956\pi\)
\(620\) 313.844 + 181.198i 0.506200 + 0.292255i
\(621\) 36.0938 + 96.0631i 0.0581221 + 0.154691i
\(622\) 336.814 0.541502
\(623\) 128.789 + 442.995i 0.206724 + 0.711068i
\(624\) −8.56563 + 156.353i −0.0137270 + 0.250565i
\(625\) −12.5000 21.6506i −0.0200000 0.0346410i
\(626\) −199.438 115.146i −0.318591 0.183939i
\(627\) 19.6463 30.0963i 0.0313338 0.0480004i
\(628\) −333.371 577.416i −0.530846 0.919452i
\(629\) 303.990i 0.483290i
\(630\) 47.9928 131.422i 0.0761791 0.208607i
\(631\) 52.9592 0.0839290 0.0419645 0.999119i \(-0.486638\pi\)
0.0419645 + 0.999119i \(0.486638\pi\)
\(632\) 385.178 222.383i 0.609459 0.351871i
\(633\) 141.696 + 92.4966i 0.223848 + 0.146124i
\(634\) 164.135 284.290i 0.258888 0.448407i
\(635\) 208.102 120.148i 0.327719 0.189209i
\(636\) −58.8324 3.22308i −0.0925038 0.00506773i
\(637\) 441.376 + 230.542i 0.692897 + 0.361919i
\(638\) 33.2023i 0.0520413i
\(639\) −321.493 + 141.316i −0.503119 + 0.221152i
\(640\) −133.879 + 231.885i −0.209186 + 0.362321i
\(641\) −821.724 474.423i −1.28194 0.740129i −0.304738 0.952436i \(-0.598569\pi\)
−0.977203 + 0.212307i \(0.931902\pi\)
\(642\) −8.14228 + 4.12442i −0.0126827 + 0.00642434i
\(643\) −181.011 −0.281510 −0.140755 0.990044i \(-0.544953\pi\)
−0.140755 + 0.990044i \(0.544953\pi\)
\(644\) −77.8664 19.1109i −0.120911 0.0296753i
\(645\) 440.575 + 24.1365i 0.683062 + 0.0374209i
\(646\) −176.061 304.946i −0.272540 0.472052i
\(647\) −148.566 85.7748i −0.229623 0.132573i 0.380775 0.924668i \(-0.375657\pi\)
−0.610398 + 0.792095i \(0.708991\pi\)
\(648\) 415.705 + 381.498i 0.641519 + 0.588731i
\(649\) 7.10268 + 12.3022i 0.0109440 + 0.0189556i
\(650\) 50.4654i 0.0776391i
\(651\) 255.483 + 1100.08i 0.392447 + 1.68984i
\(652\) −262.208 −0.402160
\(653\) 314.093 181.342i 0.481000 0.277705i −0.239833 0.970814i \(-0.577093\pi\)
0.720833 + 0.693109i \(0.243759\pi\)
\(654\) −60.9750 + 93.4079i −0.0932339 + 0.142826i
\(655\) 47.5344 82.3319i 0.0725715 0.125698i
\(656\) −255.289 + 147.391i −0.389160 + 0.224682i
\(657\) −356.417 39.1695i −0.542492 0.0596187i
\(658\) 129.930 + 124.554i 0.197462 + 0.189291i
\(659\) 949.931i 1.44147i 0.693209 + 0.720737i \(0.256196\pi\)
−0.693209 + 0.720737i \(0.743804\pi\)
\(660\) 11.8472 6.00112i 0.0179503 0.00909260i
\(661\) −188.128 + 325.847i −0.284611 + 0.492961i −0.972515 0.232841i \(-0.925198\pi\)
0.687904 + 0.725802i \(0.258531\pi\)
\(662\) −268.529 155.036i −0.405634 0.234193i
\(663\) −267.827 528.733i −0.403962 0.797485i
\(664\) −527.302 −0.794129
\(665\) −197.537 + 206.064i −0.297047 + 0.309870i
\(666\) 15.2685 138.934i 0.0229257 0.208609i
\(667\) −96.7075 167.502i −0.144989 0.251128i
\(668\) 773.903 + 446.813i 1.15854 + 0.668882i
\(669\) 1062.70 + 693.714i 1.58850 + 1.03694i
\(670\) −87.9031 152.253i −0.131199 0.227243i
\(671\) 22.5281i 0.0335739i
\(672\) −674.301 + 156.600i −1.00342 + 0.233035i
\(673\) 1136.46 1.68864 0.844320 0.535839i \(-0.180005\pi\)
0.844320 + 0.535839i \(0.180005\pi\)
\(674\) −204.870 + 118.282i −0.303962 + 0.175492i
\(675\) 104.308 + 85.7019i 0.154531 + 0.126966i
\(676\) 99.0349 171.534i 0.146501 0.253748i
\(677\) −720.753 + 416.127i −1.06463 + 0.614663i −0.926709 0.375780i \(-0.877375\pi\)
−0.137919 + 0.990444i \(0.544041\pi\)
\(678\) 27.7976 507.403i 0.0409994 0.748381i
\(679\) 189.889 773.693i 0.279660 1.13946i
\(680\) 302.808i 0.445306i
\(681\) −269.123 531.292i −0.395188 0.780164i
\(682\) 17.5441 30.3872i 0.0257244 0.0445560i
\(683\) −487.430 281.418i −0.713660 0.412032i 0.0987549 0.995112i \(-0.468514\pi\)
−0.812415 + 0.583080i \(0.801847\pi\)
\(684\) −199.039 452.813i −0.290993 0.662007i
\(685\) −292.359 −0.426802
\(686\) −67.1528 + 333.976i −0.0978904 + 0.486845i
\(687\) 33.1685 605.441i 0.0482802 0.881282i
\(688\) −168.916 292.572i −0.245518 0.425250i
\(689\) −57.3573 33.1152i −0.0832471 0.0480628i
\(690\) −13.8418 + 21.2043i −0.0200605 + 0.0307308i
\(691\) 226.749 + 392.741i 0.328146 + 0.568366i 0.982144 0.188131i \(-0.0602429\pi\)
−0.653998 + 0.756496i \(0.726910\pi\)
\(692\) 122.586i 0.177147i
\(693\) 38.8756 + 14.1966i 0.0560975 + 0.0204857i
\(694\) −488.369 −0.703701
\(695\) 114.577 66.1510i 0.164859 0.0951814i
\(696\) −890.497 581.300i −1.27945 0.835201i
\(697\) 557.890 966.293i 0.800415 1.38636i
\(698\) 126.624 73.1063i 0.181409 0.104737i
\(699\) 958.590 + 52.5155i 1.37137 + 0.0751294i
\(700\) −101.282 + 29.4451i −0.144689 + 0.0420645i
\(701\) 795.319i 1.13455i 0.823528 + 0.567275i \(0.192002\pi\)
−0.823528 + 0.567275i \(0.807998\pi\)
\(702\) 95.8491 + 255.101i 0.136537 + 0.363392i
\(703\) −142.582 + 246.959i −0.202819 + 0.351293i
\(704\) 6.93777 + 4.00552i 0.00985479 + 0.00568966i
\(705\) −154.927 + 78.4773i −0.219754 + 0.111315i
\(706\) 422.941 0.599067
\(707\) 697.350 727.453i 0.986351 1.02893i
\(708\) 195.204 + 10.6941i 0.275711 + 0.0151046i
\(709\) −259.254 449.041i −0.365661 0.633344i 0.623221 0.782046i \(-0.285824\pi\)
−0.988882 + 0.148702i \(0.952490\pi\)
\(710\) −75.0467 43.3282i −0.105700 0.0610256i
\(711\) −339.972 + 463.298i −0.478160 + 0.651614i
\(712\) −229.540 397.575i −0.322387 0.558391i
\(713\) 204.400i 0.286677i
\(714\) 296.183 276.917i 0.414822 0.387839i
\(715\) 14.9280 0.0208783
\(716\) −793.442 + 458.094i −1.10816 + 0.639796i
\(717\) 569.947 873.106i 0.794906 1.21772i
\(718\) 331.862 574.802i 0.462204 0.800560i
\(719\) −701.360 + 404.931i −0.975466 + 0.563186i −0.900898 0.434030i \(-0.857091\pi\)
−0.0745679 + 0.997216i \(0.523758\pi\)
\(720\) 11.2914 102.744i 0.0156825 0.142701i
\(721\) 965.271 280.626i 1.33879 0.389218i
\(722\) 28.2227i 0.0390896i
\(723\) −439.370 + 222.560i −0.607704 + 0.307829i
\(724\) 22.8652 39.6037i 0.0315818 0.0547012i
\(725\) −220.355 127.222i −0.303938 0.175478i
\(726\) 162.332 + 320.469i 0.223597 + 0.441417i
\(727\) 772.417 1.06247 0.531236 0.847224i \(-0.321728\pi\)
0.531236 + 0.847224i \(0.321728\pi\)
\(728\) −481.240 118.112i −0.661043 0.162241i
\(729\) −690.048 235.107i −0.946567 0.322506i
\(730\) −44.2390 76.6242i −0.0606014 0.104965i
\(731\) 1107.41 + 639.365i 1.51493 + 0.874644i
\(732\) −259.617 169.473i −0.354668 0.231520i
\(733\) 181.568 + 314.485i 0.247705 + 0.429038i 0.962889 0.269898i \(-0.0869901\pi\)
−0.715183 + 0.698937i \(0.753657\pi\)
\(734\) 70.1927i 0.0956304i
\(735\) −282.591 167.891i −0.384478 0.228423i
\(736\) 125.288 0.170228
\(737\) 45.0372 26.0023i 0.0611089 0.0352812i
\(738\) −303.509 + 413.608i −0.411258 + 0.560444i
\(739\) −324.308 + 561.717i −0.438847 + 0.760104i −0.997601 0.0692288i \(-0.977946\pi\)
0.558754 + 0.829333i \(0.311279\pi\)
\(740\) −91.2526 + 52.6847i −0.123314 + 0.0711955i
\(741\) 30.4139 555.159i 0.0410444 0.749203i
\(742\) 10.7998 44.0033i 0.0145550 0.0593036i
\(743\) 549.717i 0.739862i −0.929059 0.369931i \(-0.879381\pi\)
0.929059 0.369931i \(-0.120619\pi\)
\(744\) −507.836 1002.55i −0.682576 1.34751i
\(745\) −208.341 + 360.857i −0.279652 + 0.484372i
\(746\) −219.572 126.770i −0.294332 0.169933i
\(747\) 623.698 274.154i 0.834937 0.367007i
\(748\) 38.4874 0.0514538
\(749\) 5.98621 + 20.5908i 0.00799227 + 0.0274910i
\(750\) −1.82225 + 33.2623i −0.00242966 + 0.0443498i
\(751\) 175.429 + 303.852i 0.233594 + 0.404597i 0.958863 0.283869i \(-0.0916180\pi\)
−0.725269 + 0.688465i \(0.758285\pi\)
\(752\) 115.156 + 66.4851i 0.153132 + 0.0884111i
\(753\) 76.6857 117.475i 0.101840 0.156010i
\(754\) −256.812 444.812i −0.340600 0.589936i
\(755\) 342.410i 0.453523i
\(756\) 456.054 341.210i 0.603246 0.451336i
\(757\) −482.553 −0.637455 −0.318727 0.947846i \(-0.603255\pi\)
−0.318727 + 0.947846i \(0.603255\pi\)
\(758\) 193.158 111.520i 0.254826 0.147124i
\(759\) −6.27236 4.09448i −0.00826397 0.00539457i
\(760\) 142.028 245.999i 0.186879 0.323683i
\(761\) 679.478 392.297i 0.892875 0.515502i 0.0179931 0.999838i \(-0.494272\pi\)
0.874882 + 0.484337i \(0.160939\pi\)
\(762\) −319.711 17.5151i −0.419569 0.0229857i
\(763\) 189.182 + 181.353i 0.247945 + 0.237685i
\(764\) 276.089i 0.361373i
\