Properties

Label 105.3.t.b.11.11
Level 105
Weight 3
Character 105.11
Analytic conductor 2.861
Analytic rank 0
Dimension 36
CM no
Inner twists 4

Related objects

Downloads

Learn more about

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 11.11
Character \(\chi\) \(=\) 105.11
Dual form 105.3.t.b.86.11

$q$-expansion

\(f(q)\) \(=\) \(q+(0.860118 - 0.496589i) q^{2} +(-2.67624 - 1.35563i) q^{3} +(-1.50680 + 2.60985i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-2.97507 + 0.162987i) q^{6} +(-1.66850 + 6.79824i) q^{7} +6.96575i q^{8} +(5.32451 + 7.25600i) q^{9} +O(q^{10})\) \(q+(0.860118 - 0.496589i) q^{2} +(-2.67624 - 1.35563i) 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} +(5.32451 + 7.25600i) q^{9} +(-1.11041 + 1.92328i) q^{10} +(0.568919 + 0.328465i) q^{11} +(7.57056 - 4.94192i) 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} +(8.18296 + 3.59692i) q^{18} +(9.11844 + 15.7936i) q^{19} -6.73861i q^{20} +(13.6812 - 15.9318i) q^{21} +0.652449 q^{22} +(-3.29154 + 1.90037i) q^{23} +(9.44301 - 18.6420i) 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} +(5.57898 - 3.64186i) q^{30} +(26.8895 - 46.5740i) q^{31} +(-28.5478 - 16.4821i) q^{32} +(-1.07728 - 1.65030i) 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} +(27.1970 + 13.7765i) q^{39} +(-7.78795 - 13.4891i) q^{40} +57.3936i q^{41} +(3.85590 - 20.4972i) q^{42} +65.7755 q^{43} +(-1.71449 + 0.989862i) q^{44} +(-18.4233 - 8.09820i) 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} +(31.8805 + 48.8379i) q^{51} +(15.3127 - 26.5224i) q^{52} +(-5.64406 - 3.25860i) q^{53} +(-17.0235 - 20.7193i) 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} +(-9.13508 + 18.0341i) q^{60} +(17.1465 + 29.6986i) q^{61} -53.4122i q^{62} +(-58.2120 + 24.0906i) q^{63} -12.1947 q^{64} +(19.6794 - 11.3619i) q^{65} +(-1.74611 - 0.884483i) 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} +(-50.5435 + 37.0892i) q^{72} +(-19.9202 + 34.5027i) q^{73} +(13.4494 + 7.76500i) q^{74} +(-12.5607 + 8.19937i) 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} +(-24.2991 + 77.2693i) q^{81} +(28.5011 + 49.3653i) q^{82} +75.6992i q^{83} +(20.9649 + 59.7121i) q^{84} +43.4710 q^{85} +(56.5747 - 32.6634i) q^{86} +(68.9865 - 136.190i) 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} +(-135.100 + 88.1909i) q^{93} +(12.8562 - 22.2677i) q^{94} +(-35.3155 - 20.3894i) q^{95} +(54.0570 + 82.8103i) 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 −0.269313 0.963053i \(-0.586797\pi\)
0.699372 + 0.714758i \(0.253463\pi\)
\(3\) −2.67624 1.35563i −0.892080 0.451878i
\(4\) −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
\(9\) 5.32451 + 7.25600i 0.591613 + 0.806222i
\(10\) −1.11041 + 1.92328i −0.111041 + 0.192328i
\(11\) 0.568919 + 0.328465i 0.0517199 + 0.0298605i 0.525637 0.850709i \(-0.323827\pi\)
−0.473917 + 0.880569i \(0.657160\pi\)
\(12\) 7.57056 4.94192i 0.630880 0.411827i
\(13\) −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 −0.0849830 0.996382i \(-0.527084\pi\)
−0.905384 + 0.424594i \(0.860417\pi\)
\(18\) 8.18296 + 3.59692i 0.454609 + 0.199829i
\(19\) 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
\(21\) 13.6812 15.9318i 0.651488 0.758659i
\(22\) 0.652449 0.0296568
\(23\) −3.29154 + 1.90037i −0.143110 + 0.0826248i −0.569846 0.821752i \(-0.692997\pi\)
0.426735 + 0.904377i \(0.359664\pi\)
\(24\) 9.44301 18.6420i 0.393459 0.776751i
\(25\) 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 \(0.340719\pi\)
−0.479774 + 0.877392i \(0.659281\pi\)
\(30\) 5.57898 3.64186i 0.185966 0.121395i
\(31\) 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
\(33\) −1.07728 1.65030i −0.0326450 0.0500090i
\(34\) −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
\(39\) 27.1970 + 13.7765i 0.697360 + 0.353244i
\(40\) −7.78795 13.4891i −0.194699 0.337228i
\(41\) 57.3936i 1.39985i 0.714219 + 0.699923i \(0.246782\pi\)
−0.714219 + 0.699923i \(0.753218\pi\)
\(42\) 3.85590 20.4972i 0.0918072 0.488029i
\(43\) 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
\(45\) −18.4233 8.09820i −0.409407 0.179960i
\(46\) −1.88741 + 3.26909i −0.0410306 + 0.0710671i
\(47\) 22.4206 12.9445i 0.477034 0.275416i −0.242146 0.970240i \(-0.577851\pi\)
0.719180 + 0.694824i \(0.244518\pi\)
\(48\) 0.842874 + 15.3854i 0.0175599 + 0.320529i
\(49\) −43.4322 22.6858i −0.886371 0.462976i
\(50\) 4.96589i 0.0993178i
\(51\) 31.8805 + 48.8379i 0.625108 + 0.957606i
\(52\) 15.3127 26.5224i 0.294475 0.510046i
\(53\) −5.64406 3.25860i −0.106492 0.0614830i 0.445808 0.895129i \(-0.352916\pi\)
−0.552300 + 0.833645i \(0.686250\pi\)
\(54\) −17.0235 20.7193i −0.315249 0.383691i
\(55\) −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 0.650234 0.759734i \(-0.274671\pi\)
−0.332831 + 0.942986i \(0.608004\pi\)
\(60\) −9.13508 + 18.0341i −0.152251 + 0.300569i
\(61\) 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
\(63\) −58.2120 + 24.0906i −0.924000 + 0.382391i
\(64\) −12.1947 −0.190542
\(65\) 19.6794 11.3619i 0.302760 0.174799i
\(66\) −1.74611 0.884483i −0.0264562 0.0134013i
\(67\) −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 \(-0.911392\pi\)
0.961504 0.274789i \(-0.0886082\pi\)
\(72\) −50.5435 + 37.0892i −0.701993 + 0.515128i
\(73\) −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
\(75\) −12.5607 + 8.19937i −0.167476 + 0.109325i
\(76\) −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
\(81\) −24.2991 + 77.2693i −0.299989 + 0.953943i
\(82\) 28.5011 + 49.3653i 0.347574 + 0.602016i
\(83\) 75.6992i 0.912038i 0.889970 + 0.456019i \(0.150725\pi\)
−0.889970 + 0.456019i \(0.849275\pi\)
\(84\) 20.9649 + 59.7121i 0.249582 + 0.710858i
\(85\) 43.4710 0.511423
\(86\) 56.5747 32.6634i 0.657845 0.379807i
\(87\) 68.9865 136.190i 0.792949 1.56541i
\(88\) −2.28801 + 3.96295i −0.0260001 + 0.0450335i
\(89\) −57.0756 + 32.9526i −0.641299 + 0.370254i −0.785115 0.619350i \(-0.787396\pi\)
0.143816 + 0.989604i \(0.454063\pi\)
\(90\) −19.8677 + 2.18342i −0.220752 + 0.0242602i
\(91\) 16.9560 69.0865i 0.186330 0.759193i
\(92\) 11.4539i 0.124499i
\(93\) −135.100 + 88.1909i −1.45269 + 0.948289i
\(94\) 12.8562 22.2677i 0.136769 0.236890i
\(95\) −35.3155 20.3894i −0.371743 0.214626i
\(96\) 54.0570 + 82.8103i 0.563094 + 0.862607i
\(97\) −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 0.967939 0.251184i \(-0.0808198\pi\)
0.266438 + 0.963852i \(0.414153\pi\)
\(102\) 51.6734 + 26.1748i 0.506602 + 0.256616i
\(103\) −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
\(105\) −8.68128 + 46.1480i −0.0826789 + 0.439504i
\(106\) −6.47274 −0.0610636
\(107\) −2.65292 + 1.53166i −0.0247936 + 0.0143146i −0.512346 0.858779i \(-0.671223\pi\)
0.487552 + 0.873094i \(0.337890\pi\)
\(108\) 76.1681 + 28.6187i 0.705260 + 0.264988i
\(109\) 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 \(-0.727806\pi\)
0.656126 0.754652i \(-0.272194\pi\)
\(114\) −29.7022 45.5009i −0.260545 0.399131i
\(115\) 4.24936 7.36011i 0.0369510 0.0640009i
\(116\) −132.812 76.6791i −1.14493 0.661027i
\(117\) −54.1099 73.7385i −0.462478 0.630243i
\(118\) 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
\(123\) 77.8048 153.599i 0.632559 1.24877i
\(124\) 81.0342 + 140.355i 0.653502 + 1.13190i
\(125\) 11.1803i 0.0894427i
\(126\) −38.1060 + 49.6283i −0.302429 + 0.393875i
\(127\) 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
\(129\) −176.031 89.1675i −1.36458 0.691221i
\(130\) 11.2844 19.5452i 0.0868032 0.150348i
\(131\) −36.8200 + 21.2580i −0.281068 + 0.162275i −0.633907 0.773409i \(-0.718550\pi\)
0.352839 + 0.935684i \(0.385216\pi\)
\(132\) 5.93028 0.324885i 0.0449264 0.00246125i
\(133\) −122.583 + 35.6376i −0.921675 + 0.267952i
\(134\) 78.6229i 0.586738i
\(135\) 38.3270 + 46.6480i 0.283904 + 0.345541i
\(136\) 67.7100 117.277i 0.497867 0.862331i
\(137\) 113.230 + 65.3735i 0.826498 + 0.477179i 0.852652 0.522479i \(-0.174993\pi\)
−0.0261540 + 0.999658i \(0.508326\pi\)
\(138\) 9.48284 6.19022i 0.0687162 0.0448567i
\(139\) 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
\(144\) 18.6012 42.3176i 0.129175 0.293872i
\(145\) −56.8954 98.5456i −0.392382 0.679625i
\(146\) 39.5686i 0.271018i
\(147\) 85.4813 + 119.591i 0.581505 + 0.813543i
\(148\) −47.1226 −0.318396
\(149\) 161.380 93.1729i 1.08309 0.625321i 0.151360 0.988479i \(-0.451635\pi\)
0.931728 + 0.363157i \(0.118301\pi\)
\(150\) −6.73193 + 13.2899i −0.0448796 + 0.0885994i
\(151\) 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
\(156\) −76.9351 + 50.2218i −0.493174 + 0.321935i
\(157\) −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
\(159\) 10.6874 + 16.3721i 0.0672163 + 0.102969i
\(160\) 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
\(165\) 3.93124 + 1.99135i 0.0238257 + 0.0120688i
\(166\) 37.5914 + 65.1102i 0.226454 + 0.392230i
\(167\) 296.532i 1.77564i 0.460193 + 0.887819i \(0.347780\pi\)
−0.460193 + 0.887819i \(0.652220\pi\)
\(168\) 110.977 + 95.3002i 0.660579 + 0.567263i
\(169\) −65.7254 −0.388908
\(170\) 37.3902 21.5872i 0.219942 0.126984i
\(171\) −66.0471 + 150.257i −0.386240 + 0.878693i
\(172\) −99.1104 + 171.664i −0.576223 + 0.998048i
\(173\) −35.2279 + 20.3388i −0.203629 + 0.117565i −0.598347 0.801237i \(-0.704176\pi\)
0.394718 + 0.918802i \(0.370842\pi\)
\(174\) −8.29419 151.398i −0.0476677 0.870102i
\(175\) 25.2660 + 24.2204i 0.144377 + 0.138403i
\(176\) 3.37409i 0.0191710i
\(177\) −35.4604 54.3219i −0.200341 0.306904i
\(178\) −32.7278 + 56.6863i −0.183864 + 0.318462i
\(179\) −263.287 152.009i −1.47088 0.849213i −0.471414 0.881912i \(-0.656256\pi\)
−0.999465 + 0.0326995i \(0.989590\pi\)
\(180\) 48.8953 35.8798i 0.271641 0.199332i
\(181\) −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
\(186\) −72.4074 + 142.944i −0.389287 + 0.768515i
\(187\) −6.38563 11.0602i −0.0341478 0.0591457i
\(188\) 78.0192i 0.414996i
\(189\) 188.447 + 14.4419i 0.997076 + 0.0764120i
\(190\) −40.5007 −0.213162
\(191\) 79.3405 45.8073i 0.415395 0.239829i −0.277710 0.960665i \(-0.589575\pi\)
0.693105 + 0.720836i \(0.256242\pi\)
\(192\) 32.6358 + 16.5315i 0.169978 + 0.0861015i
\(193\) −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 \(0.103053\pi\)
−0.948049 + 0.318126i \(0.896947\pi\)
\(198\) 3.47398 + 4.73417i 0.0175453 + 0.0239100i
\(199\) −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
\(201\) 198.868 129.817i 0.989392 0.645857i
\(202\) 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
\(207\) −31.3149 13.7649i −0.151280 0.0664969i
\(208\) 26.0978 + 45.2028i 0.125470 + 0.217321i
\(209\) 11.9804i 0.0573223i
\(210\) 15.4497 + 44.0037i 0.0735698 + 0.209542i
\(211\) 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
\(213\) −52.8970 + 104.427i −0.248343 + 0.490268i
\(214\) −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
\(219\) 100.084 65.3331i 0.457006 0.298325i
\(220\) 2.21340 3.83372i 0.0100609 0.0174260i
\(221\) 171.097 + 98.7828i 0.774193 + 0.446981i
\(222\) −25.4673 39.0134i −0.114717 0.175736i
\(223\) 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 0.828354 0.560206i \(-0.189278\pi\)
−0.0709755 + 0.997478i \(0.522611\pi\)
\(228\) 147.082 + 74.5037i 0.645098 + 0.326771i
\(229\) −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
\(231\) 13.0166 4.57011i 0.0563488 0.0197840i
\(232\) −354.478 −1.52792
\(233\) −277.136 + 160.005i −1.18943 + 0.686715i −0.958176 0.286179i \(-0.907615\pi\)
−0.231250 + 0.972894i \(0.574281\pi\)
\(234\) −83.1586 36.5534i −0.355379 0.156211i
\(235\) −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 \(0.259134\pi\)
−0.686528 + 0.727104i \(0.740866\pi\)
\(240\) −18.8336 28.8513i −0.0784733 0.120214i
\(241\) −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
\(243\) 169.779 173.851i 0.698680 0.715434i
\(244\) −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
\(249\) 102.620 202.589i 0.412130 0.813611i
\(250\) 5.55204 + 9.61641i 0.0222081 + 0.0384656i
\(251\) 46.7632i 0.186307i 0.995652 + 0.0931537i \(0.0296948\pi\)
−0.995652 + 0.0931537i \(0.970305\pi\)
\(252\) 24.8408 188.224i 0.0985745 0.746923i
\(253\) −2.49682 −0.00986887
\(254\) 92.4311 53.3651i 0.363902 0.210099i
\(255\) −116.339 58.9307i −0.456230 0.231101i
\(256\) 83.8534 145.238i 0.327552 0.567337i
\(257\) 293.930 169.701i 1.14370 0.660314i 0.196354 0.980533i \(-0.437090\pi\)
0.947344 + 0.320219i \(0.103757\pi\)
\(258\) −195.687 + 10.7205i −0.758477 + 0.0415524i
\(259\) −105.105 + 30.5565i −0.405811 + 0.117979i
\(260\) 68.4805i 0.263386i
\(261\) −369.249 + 270.958i −1.41475 + 1.03815i
\(262\) −21.1130 + 36.5688i −0.0805840 + 0.139576i
\(263\) −86.0787 49.6976i −0.327296 0.188964i 0.327344 0.944905i \(-0.393846\pi\)
−0.654640 + 0.755941i \(0.727180\pi\)
\(264\) 11.4956 7.50409i 0.0435438 0.0284246i
\(265\) 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 0.0254629 0.999676i \(-0.491894\pi\)
−0.853013 + 0.521889i \(0.825227\pi\)
\(270\) 56.1307 + 21.0900i 0.207891 + 0.0781111i
\(271\) −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
\(273\) −139.034 + 161.906i −0.509284 + 0.593062i
\(274\) 129.855 0.473924
\(275\) 2.84459 1.64233i 0.0103440 0.00597210i
\(276\) −15.5273 + 30.6534i −0.0562583 + 0.111063i
\(277\) 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 \(-0.705301\pi\)
0.601175 0.799117i \(-0.294699\pi\)
\(282\) −64.5932 + 42.1652i −0.229054 + 0.149522i
\(283\) −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
\(285\) 66.8722 + 102.442i 0.234639 + 0.359446i
\(286\) −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
\(291\) 304.577 + 154.282i 1.04666 + 0.530178i
\(292\) −60.0313 103.977i −0.205587 0.356087i
\(293\) 250.565i 0.855171i 0.903975 + 0.427585i \(0.140636\pi\)
−0.903975 + 0.427585i \(0.859364\pi\)
\(294\) 132.911 + 60.4131i 0.452080 + 0.205487i
\(295\) −48.3523 −0.163906
\(296\) −94.3285 + 54.4606i −0.318677 + 0.183988i
\(297\) 6.23855 16.6038i 0.0210052 0.0559051i
\(298\) 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
\(303\) −236.075 361.644i −0.779124 1.19355i
\(304\) 46.8337 81.1183i 0.154058 0.266836i
\(305\) −66.4080 38.3407i −0.217731 0.125707i
\(306\) −102.807 140.100i −0.335970 0.457844i
\(307\) −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 0.891321 0.453372i \(-0.149779\pi\)
0.0530290 + 0.998593i \(0.483112\pi\)
\(312\) −95.9638 + 189.448i −0.307576 + 0.607205i
\(313\) 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
\(315\) 85.7929 111.734i 0.272359 0.354712i
\(316\) −192.419 −0.608921
\(317\) 286.243 165.262i 0.902974 0.521332i 0.0248101 0.999692i \(-0.492102\pi\)
0.878164 + 0.478360i \(0.158769\pi\)
\(318\) 17.3226 + 8.77467i 0.0544736 + 0.0275933i
\(319\) −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
\(324\) −165.048 179.846i −0.509406 0.555082i
\(325\) −25.4060 + 44.0045i −0.0781724 + 0.135399i
\(326\) 74.8376 + 43.2075i 0.229563 + 0.132538i
\(327\) −94.0495 + 61.3938i −0.287613 + 0.187749i
\(328\) −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
\(333\) −56.6302 + 128.833i −0.170061 + 0.386886i
\(334\) 147.254 + 255.052i 0.440881 + 0.763629i
\(335\) 177.014i 0.528399i
\(336\) −106.000 19.9405i −0.315476 0.0593468i
\(337\) 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
\(339\) −231.205 + 456.436i −0.682021 + 1.34642i
\(340\) −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
\(345\) −21.3499 + 13.9368i −0.0618838 + 0.0403966i
\(346\) −20.2001 + 34.9876i −0.0583817 + 0.101120i
\(347\) −425.845 245.862i −1.22722 0.708535i −0.260771 0.965401i \(-0.583977\pi\)
−0.966447 + 0.256866i \(0.917310\pi\)
\(348\) 251.488 + 385.256i 0.722667 + 1.10706i
\(349\) −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 0.921172 0.389155i \(-0.127233\pi\)
0.123568 + 0.992336i \(0.460566\pi\)
\(354\) −57.4758 29.1140i −0.162361 0.0822430i
\(355\) 43.6258 + 75.5621i 0.122890 + 0.212851i
\(356\) 198.612i 0.557898i
\(357\) −385.205 + 135.245i −1.07900 + 0.378837i
\(358\) −301.944 −0.843420
\(359\) 578.750 334.142i 1.61212 0.930756i 0.623239 0.782032i \(-0.285816\pi\)
0.988879 0.148725i \(-0.0475169\pi\)
\(360\) 56.4101 128.332i 0.156695 0.356479i
\(361\) 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
\(366\) −55.8525 85.5608i −0.152602 0.233773i
\(367\) −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
\(369\) −416.448 + 305.593i −1.12859 + 0.828166i
\(370\) −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
\(375\) 15.1564 29.9213i 0.0404172 0.0797900i
\(376\) 90.1685 + 156.176i 0.239810 + 0.415363i
\(377\) 517.152i 1.37176i
\(378\) 169.259 81.1593i 0.447774 0.214707i
\(379\) −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
\(381\) −287.598 145.681i −0.754849 0.382365i
\(382\) 45.4948 78.7993i 0.119096 0.206281i
\(383\) 298.557 172.372i 0.779523 0.450058i −0.0567384 0.998389i \(-0.518070\pi\)
0.836261 + 0.548331i \(0.184737\pi\)
\(384\) −358.697 + 19.6509i −0.934107 + 0.0511742i
\(385\) 2.45094 9.98622i 0.00636607 0.0259382i
\(386\) 74.1858i 0.192191i
\(387\) 350.222 + 477.267i 0.904968 + 1.23325i
\(388\) 171.485 297.021i 0.441973 0.765519i
\(389\) 110.104 + 63.5688i 0.283044 + 0.163416i 0.634801 0.772676i \(-0.281082\pi\)
−0.351756 + 0.936092i \(0.614415\pi\)
\(390\) −56.6959 + 37.0100i −0.145374 + 0.0948975i
\(391\) 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
\(396\) −16.3113 7.16982i −0.0411901 0.0181056i
\(397\) −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
\(399\) 376.373 + 70.8026i 0.943290 + 0.177450i
\(400\) −25.6808 −0.0642019
\(401\) −321.734 + 185.753i −0.802329 + 0.463225i −0.844285 0.535895i \(-0.819974\pi\)
0.0419560 + 0.999119i \(0.486641\pi\)
\(402\) 106.584 210.414i 0.265134 0.523417i
\(403\) −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
\(408\) −340.193 + 222.072i −0.833806 + 0.544293i
\(409\) 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
\(411\) −214.409 328.454i −0.521676 0.799158i
\(412\) 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
\(417\) −158.346 80.2092i −0.379726 0.192348i
\(418\) 5.94932 + 10.3045i 0.0142328 + 0.0246520i
\(419\) 375.735i 0.896743i −0.893847 0.448371i \(-0.852004\pi\)
0.893847 0.448371i \(-0.147996\pi\)
\(420\) −107.358 92.1925i −0.255615 0.219506i
\(421\) 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
\(423\) 213.304 + 93.7606i 0.504266 + 0.221656i
\(424\) 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
\(429\) 10.9478 + 16.7710i 0.0255193 + 0.0390932i
\(430\) −73.0376 + 126.505i −0.169855 + 0.294197i
\(431\) −306.385 176.891i −0.710869 0.410421i 0.100513 0.994936i \(-0.467951\pi\)
−0.811383 + 0.584515i \(0.801285\pi\)
\(432\) −107.148 + 88.0355i −0.248029 + 0.203786i
\(433\) −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
\(438\) 53.6405 105.895i 0.122467 0.241769i
\(439\) −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
\(441\) −66.6470 435.935i −0.151127 0.988514i
\(442\) 196.218 0.443932
\(443\) −87.0998 + 50.2871i −0.196613 + 0.113515i −0.595075 0.803670i \(-0.702878\pi\)
0.398461 + 0.917185i \(0.369544\pi\)
\(444\) 126.111 + 63.8810i 0.284035 + 0.143876i
\(445\) 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 \(0.278804\pi\)
−0.640314 + 0.768113i \(0.721196\pi\)
\(450\) 36.0325 26.4410i 0.0800723 0.0587577i
\(451\) −18.8518 + 32.6523i −0.0418001 + 0.0723998i
\(452\) 445.113 + 256.986i 0.984764 + 0.568554i
\(453\) −384.684 + 251.114i −0.849191 + 0.554336i
\(454\) 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
\(459\) −184.620 + 491.363i −0.402222 + 1.07051i
\(460\) 12.8059 + 22.1804i 0.0278388 + 0.0482182i
\(461\) 151.784i 0.329250i 0.986356 + 0.164625i \(0.0526414\pi\)
−0.986356 + 0.164625i \(0.947359\pi\)
\(462\) 8.92632 10.3947i 0.0193210 0.0224994i
\(463\) −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
\(465\) 163.020 321.827i 0.350580 0.692102i
\(466\) −158.913 + 275.246i −0.341015 + 0.590656i
\(467\) −96.6708 + 55.8129i −0.207004 + 0.119514i −0.599918 0.800061i \(-0.704800\pi\)
0.392914 + 0.919575i \(0.371467\pi\)
\(468\) 273.979 30.1097i 0.585425 0.0643371i
\(469\) −400.026 383.472i −0.852933 0.817638i
\(470\) 57.4949i 0.122329i
\(471\) 555.796 362.814i 1.18003 0.770305i
\(472\) −75.3131 + 130.446i −0.159562 + 0.276369i
\(473\) 37.4209 + 21.6050i 0.0791140 + 0.0456765i
\(474\) −103.992 159.306i −0.219393 0.336089i
\(475\) 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 \(-0.966613\pi\)
−0.587923 0.808917i \(-0.700054\pi\)
\(480\) −197.266 99.9238i −0.410970 0.208175i
\(481\) −79.4531 137.617i −0.165183 0.286106i
\(482\) 163.054i 0.338287i
\(483\) −14.7560 + 78.4397i −0.0305506 + 0.162401i
\(484\) 363.345 0.750712
\(485\) 220.388 127.241i 0.454408 0.262353i
\(486\) 59.6978 233.842i 0.122835 0.481157i
\(487\) 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 \(-0.826928\pi\)
0.855789 0.517325i \(-0.173072\pi\)
\(492\) 283.635 + 434.502i 0.576493 + 0.883134i
\(493\) 494.659 856.775i 1.00337 1.73788i
\(494\) −159.406 92.0332i −0.322684 0.186302i
\(495\) −7.82140 10.6586i −0.0158008 0.0215326i
\(496\) −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
\(501\) 401.988 793.589i 0.802372 1.58401i
\(502\) 23.2221 + 40.2218i 0.0462591 + 0.0801232i
\(503\) 258.341i 0.513601i −0.966464 0.256801i \(-0.917332\pi\)
0.966464 0.256801i \(-0.0826684\pi\)
\(504\) −167.810 405.491i −0.332955 0.804545i
\(505\) −321.902 −0.637430
\(506\) −2.14756 + 1.23990i −0.00424420 + 0.00245039i
\(507\) 175.897 + 89.0996i 0.346937 + 0.175739i
\(508\) −161.926 + 280.463i −0.318751 + 0.552093i
\(509\) 155.758 89.9271i 0.306009 0.176674i −0.339130 0.940739i \(-0.610133\pi\)
0.645139 + 0.764065i \(0.276799\pi\)
\(510\) −129.329 + 7.08519i −0.253587 + 0.0138925i
\(511\) −201.321 192.990i −0.393975 0.377671i
\(512\) 312.417i 0.610190i
\(513\) 380.451 312.587i 0.741620 0.609331i
\(514\) 168.543 291.925i 0.327905 0.567948i
\(515\) 278.090 + 160.555i 0.539981 + 0.311758i
\(516\) 497.957 325.057i 0.965033 0.629956i
\(517\) 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 0.682762 0.730641i \(-0.260779\pi\)
−0.291373 + 0.956610i \(0.594112\pi\)
\(522\) −183.043 + 416.421i −0.350657 + 0.797741i
\(523\) 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
\(525\) −34.7838 99.0711i −0.0662548 0.188707i
\(526\) −98.7171 −0.187675
\(527\) −905.437 + 522.754i −1.71810 + 0.991944i
\(528\) −4.57404 + 9.02989i −0.00866295 + 0.0171021i
\(529\) −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
\(534\) 164.433 107.339i 0.307928 0.201009i
\(535\) 3.42491 5.93211i 0.00640169 0.0110881i
\(536\) −477.552 275.715i −0.890955 0.514393i
\(537\) 498.551 + 763.734i 0.928401 + 1.42222i
\(538\) −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
\(543\) 40.6111 + 20.5713i 0.0747902 + 0.0378846i
\(544\) 320.425 + 554.992i 0.589016 + 1.02021i
\(545\) 83.7141i 0.153604i
\(546\) −39.1853 + 208.301i −0.0717679 + 0.381504i
\(547\) −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
\(549\) −124.196 + 282.545i −0.226223 + 0.514654i
\(550\) 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
\(555\) 57.3376 + 87.8359i 0.103311 + 0.158263i
\(556\) −89.1532 + 154.418i −0.160347 + 0.277730i
\(557\) 542.908 + 313.448i 0.974700 + 0.562743i 0.900666 0.434512i \(-0.143079\pi\)
0.0740343 + 0.997256i \(0.476413\pi\)
\(558\) 387.559 284.394i 0.694550 0.509667i
\(559\) −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 0.926537 0.376203i \(-0.122770\pi\)
0.137468 + 0.990506i \(0.456104\pi\)
\(564\) 105.766 208.798i 0.187528 0.370210i
\(565\) 190.682 + 330.271i 0.337490 + 0.584551i
\(566\) 124.838i 0.220561i
\(567\) −484.753 294.116i −0.854943 0.518722i
\(568\) 271.804 0.478529
\(569\) −763.556 + 440.839i −1.34193 + 0.774761i −0.987090 0.160167i \(-0.948797\pi\)
−0.354836 + 0.934929i \(0.615463\pi\)
\(570\) 108.390 + 54.9041i 0.190157 + 0.0963231i
\(571\) −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
\(576\) −64.9306 88.4845i −0.112727 0.153619i
\(577\) −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
\(579\) 187.645 122.491i 0.324084 0.211556i
\(580\) 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
\(585\) 187.225 + 82.2972i 0.320044 + 0.140679i
\(586\) 124.428 + 215.515i 0.212334 + 0.367774i
\(587\) 496.760i 0.846270i 0.906067 + 0.423135i \(0.139070\pi\)
−0.906067 + 0.423135i \(0.860930\pi\)
\(588\) −440.917 + 42.8942i −0.749859 + 0.0729493i
\(589\) 980.762 1.66513
\(590\) −41.5887 + 24.0113i −0.0704893 + 0.0406970i
\(591\) 169.917 335.444i 0.287508 0.567587i
\(592\) 40.1561 69.5525i 0.0678313 0.117487i
\(593\) 510.563 294.774i 0.860983 0.497089i −0.00335849 0.999994i \(-0.501069\pi\)
0.864341 + 0.502906i \(0.167736\pi\)
\(594\) −2.87938 17.3792i −0.00484744 0.0292579i
\(595\) −72.5315 + 295.526i −0.121902 + 0.496683i
\(596\) 561.571i 0.942233i
\(597\) 365.805 238.791i 0.612739 0.399985i
\(598\) 19.1806 33.2218i 0.0320746 0.0555548i
\(599\) 261.851 + 151.180i 0.437147 + 0.252387i 0.702387 0.711796i \(-0.252118\pi\)
−0.265240 + 0.964182i \(0.585451\pi\)
\(600\) −57.1148 87.4945i −0.0951913 0.145824i
\(601\) −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
\(606\) −382.641 193.824i −0.631420 0.319842i
\(607\) −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
\(609\) 810.751 + 696.222i 1.33128 + 1.14322i
\(610\) −76.1583 −0.124850
\(611\) −227.847 + 131.548i −0.372909 + 0.215299i
\(612\) 482.706 + 212.179i 0.788735 + 0.346698i
\(613\) 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 \(0.0466141\pi\)
−0.989296 + 0.145920i \(0.953386\pi\)
\(618\) 233.888 + 358.294i 0.378459 + 0.579764i
\(619\) 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
\(621\) 65.1462 + 79.2897i 0.104905 + 0.127681i
\(622\) 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
\(627\) 16.2410 32.0623i 0.0259027 0.0511361i
\(628\) −333.371 577.416i −0.530846 0.919452i
\(629\) 303.990i 0.483290i
\(630\) 18.3060 138.709i 0.0290571 0.220172i
\(631\) 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
\(633\) −150.952 76.4641i −0.238471 0.120796i
\(634\) 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
\(639\) 283.130 207.763i 0.443083 0.325138i
\(640\) −133.879 + 231.885i −0.209186 + 0.362321i
\(641\) 821.724 + 474.423i 1.28194 + 0.740129i 0.977203 0.212307i \(-0.0680976\pi\)
0.304738 + 0.952436i \(0.401431\pi\)
\(642\) 7.64299 4.98921i 0.0119050 0.00777135i
\(643\) −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 0.610398 0.792095i \(-0.291009\pi\)
−0.380775 + 0.924668i \(0.624343\pi\)
\(648\) −538.239 169.262i −0.830616 0.261206i
\(649\) 7.10268 + 12.3022i 0.0109440 + 0.0189556i
\(650\) 50.4654i 0.0776391i
\(651\) −374.128 1065.59i −0.574697 1.63685i
\(652\) −262.208 −0.402160
\(653\) −314.093 + 181.342i −0.481000 + 0.277705i −0.720833 0.693109i \(-0.756241\pi\)
0.239833 + 0.970814i \(0.422907\pi\)
\(654\) −50.4062 + 99.5098i −0.0770736 + 0.152156i
\(655\) 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 \(-0.743804\pi\)
0.693209 0.720737i \(-0.256196\pi\)
\(660\) −11.1207 + 7.25939i −0.0168496 + 0.0109991i
\(661\) −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
\(663\) −323.983 496.311i −0.488662 0.748584i
\(664\) −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
\(669\) −1132.13 573.472i −1.69227 0.857208i
\(670\) −87.9031 152.253i −0.131199 0.227243i
\(671\) 22.5281i 0.0335739i
\(672\) −653.159 + 229.323i −0.971962 + 0.341255i
\(673\) 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
\(675\) −126.374 47.4826i −0.187221 0.0703445i
\(676\) 99.0349 171.534i 0.146501 0.253748i
\(677\) 720.753 416.127i 1.06463 0.614663i 0.137919 0.990444i \(-0.455959\pi\)
0.926709 + 0.375780i \(0.122625\pi\)
\(678\) 27.7976 + 507.403i 0.0409994 + 0.748381i
\(679\) 189.889 773.693i 0.279660 1.13946i
\(680\) 302.808i 0.445306i
\(681\) −325.551 498.713i −0.478048 0.732324i
\(682\) 17.5441 30.3872i 0.0257244 0.0445560i
\(683\) 487.430 + 281.418i 0.713660 + 0.412032i 0.812415 0.583080i \(-0.198153\pi\)
−0.0987549 + 0.995112i \(0.531486\pi\)
\(684\) −292.628 398.780i −0.427818 0.583011i
\(685\) −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
\(690\) −11.4426 + 22.5895i −0.0165834 + 0.0327383i
\(691\) 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
\(693\) −41.0309 5.41502i −0.0592076 0.00781387i
\(694\) −488.369 −0.703701
\(695\) −114.577 + 66.1510i −0.164859 + 0.0951814i
\(696\) 948.669 + 480.543i 1.36303 + 0.690436i
\(697\) 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 \(-0.807998\pi\)
0.823528 0.567275i \(-0.192002\pi\)
\(702\) 172.999 + 210.558i 0.246438 + 0.299940i
\(703\) −142.582 + 246.959i −0.202819 + 0.351293i
\(704\) −6.93777 4.00552i −0.00985479 0.00568966i
\(705\) 145.427 94.9319i 0.206279 0.134655i
\(706\) 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
\(711\) −231.242 + 526.073i −0.325235 + 0.739905i
\(712\) −229.540 397.575i −0.322387 0.558391i
\(713\) 204.400i 0.286677i
\(714\) −264.160 + 307.615i −0.369972 + 0.430833i
\(715\) 14.9280 0.0208783
\(716\) 793.442 458.094i 1.10816 0.639796i
\(717\) 471.158 930.142i 0.657124 1.29727i
\(718\) 331.862 574.802i 0.462204 0.800560i
\(719\) 701.360 404.931i 0.975466 0.563186i 0.0745679 0.997216i \(-0.476242\pi\)
0.900898 + 0.434030i \(0.142909\pi\)
\(720\) 11.2914 + 102.744i 0.0156825 + 0.142701i
\(721\) 965.271 280.626i 1.33879 0.389218i
\(722\) 28.2227i 0.0390896i
\(723\) 412.428 269.225i 0.570439 0.372372i
\(724\) 22.8652 39.6037i 0.0315818 0.0547012i
\(725\) 220.355 + 127.222i 0.303938 + 0.175478i
\(726\) 196.368 + 300.818i 0.270480 + 0.414350i
\(727\) 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
\(732\) 276.576 + 140.098i 0.377836 + 0.191391i
\(733\) 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
\(735\) −299.240 136.016i −0.407130 0.185055i
\(736\) 125.288 0.170228
\(737\) −45.0372 + 26.0023i −0.0611089 + 0.0352812i
\(738\) −206.440 + 469.650i −0.279730 + 0.636382i
\(739\) −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 \(0.120619\pi\)
−0.929059 + 0.369931i \(0.879381\pi\)
\(744\) −614.316 941.074i −0.825693 1.26488i
\(745\) −208.341 + 360.857i −0.279652 + 0.484372i
\(746\) 219.572 + 126.770i 0.294332 + 0.169933i
\(747\) −549.273 + 403.061i −0.735306 + 0.539573i
\(748\) 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
\(753\) 63.3937 125.149i 0.0841882 0.166201i
\(754\) −256.812 444.812i −0.340600 0.589936i
\(755\) 342.410i 0.453523i
\(756\) −321.643 + 470.059i −0.425454 + 0.621771i
\(757\) −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
\(759\) 6.68210 + 3.38478i 0.00880382 + 0.00445953i
\(760\) 142.028 245.999i 0.186879 0.323683i
\(761\) −679.478 + 392.297i −0.892875 + 0.515502i −0.874882 0.484337i \(-0.839061\pi\)
−0.0179931 + 0.999838i \(0.505728\pi\)
\(762\) −319.711 + 17.5151i −0.419569 + 0.0229857i
\(763\) 189.182 + 181.353i 0.247945 + 0.237685i
\(764\) 276.089i 0.361373i
\(765\) 231.462 +