Properties

Label 1110.2.o.a.487.2
Level $1110$
Weight $2$
Character 1110.487
Analytic conductor $8.863$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.o (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 487.2
Character \(\chi\) \(=\) 1110.487
Dual form 1110.2.o.a.253.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-2.22064 + 0.262217i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-2.69527 - 2.69527i) q^{7} -1.00000 q^{8} +1.00000i q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-2.22064 + 0.262217i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-2.69527 - 2.69527i) q^{7} -1.00000 q^{8} +1.00000i q^{9} +(2.22064 - 0.262217i) q^{10} -3.85429i q^{11} +(-0.707107 - 0.707107i) q^{12} +1.07171 q^{13} +(2.69527 + 2.69527i) q^{14} +(1.75564 + 1.38481i) q^{15} +1.00000 q^{16} -3.12620i q^{17} -1.00000i q^{18} +(4.87828 - 4.87828i) q^{19} +(-2.22064 + 0.262217i) q^{20} +3.81169i q^{21} +3.85429i q^{22} -6.72404 q^{23} +(0.707107 + 0.707107i) q^{24} +(4.86248 - 1.16458i) q^{25} -1.07171 q^{26} +(0.707107 - 0.707107i) q^{27} +(-2.69527 - 2.69527i) q^{28} +(-0.240261 - 0.240261i) q^{29} +(-1.75564 - 1.38481i) q^{30} +(-7.29610 + 7.29610i) q^{31} -1.00000 q^{32} +(-2.72539 + 2.72539i) q^{33} +3.12620i q^{34} +(6.69198 + 5.27849i) q^{35} +1.00000i q^{36} +(6.03268 + 0.778980i) q^{37} +(-4.87828 + 4.87828i) q^{38} +(-0.757816 - 0.757816i) q^{39} +(2.22064 - 0.262217i) q^{40} +9.24361i q^{41} -3.81169i q^{42} -8.98058 q^{43} -3.85429i q^{44} +(-0.262217 - 2.22064i) q^{45} +6.72404 q^{46} +(-3.13731 - 3.13731i) q^{47} +(-0.707107 - 0.707107i) q^{48} +7.52901i q^{49} +(-4.86248 + 1.16458i) q^{50} +(-2.21056 + 2.21056i) q^{51} +1.07171 q^{52} +(-6.75117 + 6.75117i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(1.01066 + 8.55899i) q^{55} +(2.69527 + 2.69527i) q^{56} -6.89894 q^{57} +(0.240261 + 0.240261i) q^{58} +(1.03632 - 1.03632i) q^{59} +(1.75564 + 1.38481i) q^{60} +(9.33589 - 9.33589i) q^{61} +(7.29610 - 7.29610i) q^{62} +(2.69527 - 2.69527i) q^{63} +1.00000 q^{64} +(-2.37989 + 0.281021i) q^{65} +(2.72539 - 2.72539i) q^{66} +(0.0813396 - 0.0813396i) q^{67} -3.12620i q^{68} +(4.75461 + 4.75461i) q^{69} +(-6.69198 - 5.27849i) q^{70} -9.73699 q^{71} -1.00000i q^{72} +(3.77094 + 3.77094i) q^{73} +(-6.03268 - 0.778980i) q^{74} +(-4.26178 - 2.61482i) q^{75} +(4.87828 - 4.87828i) q^{76} +(-10.3884 + 10.3884i) q^{77} +(0.757816 + 0.757816i) q^{78} +(4.33967 - 4.33967i) q^{79} +(-2.22064 + 0.262217i) q^{80} -1.00000 q^{81} -9.24361i q^{82} +(-5.06491 + 5.06491i) q^{83} +3.81169i q^{84} +(0.819742 + 6.94217i) q^{85} +8.98058 q^{86} +0.339781i q^{87} +3.85429i q^{88} +(4.92656 + 4.92656i) q^{89} +(0.262217 + 2.22064i) q^{90} +(-2.88856 - 2.88856i) q^{91} -6.72404 q^{92} +10.3182 q^{93} +(3.13731 + 3.13731i) q^{94} +(-9.55375 + 12.1121i) q^{95} +(0.707107 + 0.707107i) q^{96} -2.13394i q^{97} -7.52901i q^{98} +3.85429 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 36q^{2} + 36q^{4} + 4q^{5} + 4q^{7} - 36q^{8} + O(q^{10}) \) \( 36q - 36q^{2} + 36q^{4} + 4q^{5} + 4q^{7} - 36q^{8} - 4q^{10} - 8q^{13} - 4q^{14} + 36q^{16} - 4q^{19} + 4q^{20} + 4q^{25} + 8q^{26} + 4q^{28} - 36q^{29} - 4q^{31} - 36q^{32} + 4q^{33} + 28q^{35} + 28q^{37} + 4q^{38} - 4q^{39} - 4q^{40} - 32q^{43} + 16q^{47} - 4q^{50} - 8q^{52} - 8q^{53} - 8q^{55} - 4q^{56} - 8q^{57} + 36q^{58} + 4q^{59} - 4q^{61} + 4q^{62} - 4q^{63} + 36q^{64} - 52q^{65} - 4q^{66} - 16q^{67} + 8q^{69} - 28q^{70} - 8q^{71} + 4q^{73} - 28q^{74} + 16q^{75} - 4q^{76} - 8q^{77} + 4q^{78} + 12q^{79} + 4q^{80} - 36q^{81} + 8q^{83} - 8q^{85} + 32q^{86} + 24q^{89} + 56q^{91} - 8q^{93} - 16q^{94} + 20q^{95} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −0.707107 0.707107i −0.408248 0.408248i
\(4\) 1.00000 0.500000
\(5\) −2.22064 + 0.262217i −0.993100 + 0.117267i
\(6\) 0.707107 + 0.707107i 0.288675 + 0.288675i
\(7\) −2.69527 2.69527i −1.01872 1.01872i −0.999821 0.0188964i \(-0.993985\pi\)
−0.0188964 0.999821i \(-0.506015\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000i 0.333333i
\(10\) 2.22064 0.262217i 0.702228 0.0829202i
\(11\) 3.85429i 1.16211i −0.813864 0.581056i \(-0.802640\pi\)
0.813864 0.581056i \(-0.197360\pi\)
\(12\) −0.707107 0.707107i −0.204124 0.204124i
\(13\) 1.07171 0.297240 0.148620 0.988894i \(-0.452517\pi\)
0.148620 + 0.988894i \(0.452517\pi\)
\(14\) 2.69527 + 2.69527i 0.720342 + 0.720342i
\(15\) 1.75564 + 1.38481i 0.453306 + 0.357558i
\(16\) 1.00000 0.250000
\(17\) 3.12620i 0.758216i −0.925353 0.379108i \(-0.876231\pi\)
0.925353 0.379108i \(-0.123769\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 4.87828 4.87828i 1.11916 1.11916i 0.127289 0.991866i \(-0.459372\pi\)
0.991866 0.127289i \(-0.0406277\pi\)
\(20\) −2.22064 + 0.262217i −0.496550 + 0.0586334i
\(21\) 3.81169i 0.831780i
\(22\) 3.85429i 0.821737i
\(23\) −6.72404 −1.40206 −0.701029 0.713133i \(-0.747276\pi\)
−0.701029 + 0.713133i \(0.747276\pi\)
\(24\) 0.707107 + 0.707107i 0.144338 + 0.144338i
\(25\) 4.86248 1.16458i 0.972497 0.232916i
\(26\) −1.07171 −0.210180
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) −2.69527 2.69527i −0.509359 0.509359i
\(29\) −0.240261 0.240261i −0.0446154 0.0446154i 0.684447 0.729063i \(-0.260044\pi\)
−0.729063 + 0.684447i \(0.760044\pi\)
\(30\) −1.75564 1.38481i −0.320535 0.252831i
\(31\) −7.29610 + 7.29610i −1.31042 + 1.31042i −0.389312 + 0.921106i \(0.627287\pi\)
−0.921106 + 0.389312i \(0.872713\pi\)
\(32\) −1.00000 −0.176777
\(33\) −2.72539 + 2.72539i −0.474430 + 0.474430i
\(34\) 3.12620i 0.536139i
\(35\) 6.69198 + 5.27849i 1.13115 + 0.892227i
\(36\) 1.00000i 0.166667i
\(37\) 6.03268 + 0.778980i 0.991766 + 0.128063i
\(38\) −4.87828 + 4.87828i −0.791362 + 0.791362i
\(39\) −0.757816 0.757816i −0.121348 0.121348i
\(40\) 2.22064 0.262217i 0.351114 0.0414601i
\(41\) 9.24361i 1.44361i 0.692097 + 0.721805i \(0.256687\pi\)
−0.692097 + 0.721805i \(0.743313\pi\)
\(42\) 3.81169i 0.588157i
\(43\) −8.98058 −1.36952 −0.684762 0.728766i \(-0.740094\pi\)
−0.684762 + 0.728766i \(0.740094\pi\)
\(44\) 3.85429i 0.581056i
\(45\) −0.262217 2.22064i −0.0390890 0.331033i
\(46\) 6.72404 0.991405
\(47\) −3.13731 3.13731i −0.457623 0.457623i 0.440252 0.897874i \(-0.354889\pi\)
−0.897874 + 0.440252i \(0.854889\pi\)
\(48\) −0.707107 0.707107i −0.102062 0.102062i
\(49\) 7.52901i 1.07557i
\(50\) −4.86248 + 1.16458i −0.687659 + 0.164696i
\(51\) −2.21056 + 2.21056i −0.309540 + 0.309540i
\(52\) 1.07171 0.148620
\(53\) −6.75117 + 6.75117i −0.927345 + 0.927345i −0.997534 0.0701888i \(-0.977640\pi\)
0.0701888 + 0.997534i \(0.477640\pi\)
\(54\) −0.707107 + 0.707107i −0.0962250 + 0.0962250i
\(55\) 1.01066 + 8.55899i 0.136277 + 1.15409i
\(56\) 2.69527 + 2.69527i 0.360171 + 0.360171i
\(57\) −6.89894 −0.913786
\(58\) 0.240261 + 0.240261i 0.0315478 + 0.0315478i
\(59\) 1.03632 1.03632i 0.134918 0.134918i −0.636423 0.771341i \(-0.719587\pi\)
0.771341 + 0.636423i \(0.219587\pi\)
\(60\) 1.75564 + 1.38481i 0.226653 + 0.178779i
\(61\) 9.33589 9.33589i 1.19534 1.19534i 0.219791 0.975547i \(-0.429463\pi\)
0.975547 0.219791i \(-0.0705375\pi\)
\(62\) 7.29610 7.29610i 0.926605 0.926605i
\(63\) 2.69527 2.69527i 0.339573 0.339573i
\(64\) 1.00000 0.125000
\(65\) −2.37989 + 0.281021i −0.295189 + 0.0348564i
\(66\) 2.72539 2.72539i 0.335473 0.335473i
\(67\) 0.0813396 0.0813396i 0.00993722 0.00993722i −0.702121 0.712058i \(-0.747763\pi\)
0.712058 + 0.702121i \(0.247763\pi\)
\(68\) 3.12620i 0.379108i
\(69\) 4.75461 + 4.75461i 0.572388 + 0.572388i
\(70\) −6.69198 5.27849i −0.799845 0.630900i
\(71\) −9.73699 −1.15557 −0.577784 0.816190i \(-0.696082\pi\)
−0.577784 + 0.816190i \(0.696082\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 3.77094 + 3.77094i 0.441355 + 0.441355i 0.892467 0.451112i \(-0.148973\pi\)
−0.451112 + 0.892467i \(0.648973\pi\)
\(74\) −6.03268 0.778980i −0.701284 0.0905546i
\(75\) −4.26178 2.61482i −0.492108 0.301933i
\(76\) 4.87828 4.87828i 0.559578 0.559578i
\(77\) −10.3884 + 10.3884i −1.18386 + 1.18386i
\(78\) 0.757816 + 0.757816i 0.0858058 + 0.0858058i
\(79\) 4.33967 4.33967i 0.488251 0.488251i −0.419503 0.907754i \(-0.637796\pi\)
0.907754 + 0.419503i \(0.137796\pi\)
\(80\) −2.22064 + 0.262217i −0.248275 + 0.0293167i
\(81\) −1.00000 −0.111111
\(82\) 9.24361i 1.02079i
\(83\) −5.06491 + 5.06491i −0.555946 + 0.555946i −0.928151 0.372205i \(-0.878602\pi\)
0.372205 + 0.928151i \(0.378602\pi\)
\(84\) 3.81169i 0.415890i
\(85\) 0.819742 + 6.94217i 0.0889136 + 0.752984i
\(86\) 8.98058 0.968400
\(87\) 0.339781i 0.0364283i
\(88\) 3.85429i 0.410869i
\(89\) 4.92656 + 4.92656i 0.522215 + 0.522215i 0.918240 0.396025i \(-0.129611\pi\)
−0.396025 + 0.918240i \(0.629611\pi\)
\(90\) 0.262217 + 2.22064i 0.0276401 + 0.234076i
\(91\) −2.88856 2.88856i −0.302804 0.302804i
\(92\) −6.72404 −0.701029
\(93\) 10.3182 1.06995
\(94\) 3.13731 + 3.13731i 0.323588 + 0.323588i
\(95\) −9.55375 + 12.1121i −0.980194 + 1.24267i
\(96\) 0.707107 + 0.707107i 0.0721688 + 0.0721688i
\(97\) 2.13394i 0.216668i −0.994115 0.108334i \(-0.965448\pi\)
0.994115 0.108334i \(-0.0345517\pi\)
\(98\) 7.52901i 0.760544i
\(99\) 3.85429 0.387371
\(100\) 4.86248 1.16458i 0.486248 0.116458i
\(101\) 15.9490i 1.58699i 0.608578 + 0.793494i \(0.291740\pi\)
−0.608578 + 0.793494i \(0.708260\pi\)
\(102\) 2.21056 2.21056i 0.218878 0.218878i
\(103\) 7.78216i 0.766799i 0.923583 + 0.383399i \(0.125247\pi\)
−0.923583 + 0.383399i \(0.874753\pi\)
\(104\) −1.07171 −0.105090
\(105\) −0.999489 8.46440i −0.0975402 0.826041i
\(106\) 6.75117 6.75117i 0.655732 0.655732i
\(107\) 6.27687 + 6.27687i 0.606808 + 0.606808i 0.942111 0.335302i \(-0.108838\pi\)
−0.335302 + 0.942111i \(0.608838\pi\)
\(108\) 0.707107 0.707107i 0.0680414 0.0680414i
\(109\) −8.01624 + 8.01624i −0.767817 + 0.767817i −0.977722 0.209905i \(-0.932685\pi\)
0.209905 + 0.977722i \(0.432685\pi\)
\(110\) −1.01066 8.55899i −0.0963625 0.816067i
\(111\) −3.71492 4.81657i −0.352605 0.457168i
\(112\) −2.69527 2.69527i −0.254679 0.254679i
\(113\) 19.1057i 1.79732i −0.438650 0.898658i \(-0.644543\pi\)
0.438650 0.898658i \(-0.355457\pi\)
\(114\) 6.89894 0.646144
\(115\) 14.9317 1.76315i 1.39238 0.164415i
\(116\) −0.240261 0.240261i −0.0223077 0.0223077i
\(117\) 1.07171i 0.0990800i
\(118\) −1.03632 + 1.03632i −0.0954014 + 0.0954014i
\(119\) −8.42597 + 8.42597i −0.772408 + 0.772408i
\(120\) −1.75564 1.38481i −0.160268 0.126416i
\(121\) −3.85554 −0.350504
\(122\) −9.33589 + 9.33589i −0.845231 + 0.845231i
\(123\) 6.53622 6.53622i 0.589351 0.589351i
\(124\) −7.29610 + 7.29610i −0.655209 + 0.655209i
\(125\) −10.4925 + 3.86113i −0.938474 + 0.345350i
\(126\) −2.69527 + 2.69527i −0.240114 + 0.240114i
\(127\) 4.73530 + 4.73530i 0.420190 + 0.420190i 0.885269 0.465079i \(-0.153974\pi\)
−0.465079 + 0.885269i \(0.653974\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 6.35023 + 6.35023i 0.559106 + 0.559106i
\(130\) 2.37989 0.281021i 0.208730 0.0246472i
\(131\) 10.1880 10.1880i 0.890127 0.890127i −0.104408 0.994535i \(-0.533295\pi\)
0.994535 + 0.104408i \(0.0332947\pi\)
\(132\) −2.72539 + 2.72539i −0.237215 + 0.237215i
\(133\) −26.2966 −2.28021
\(134\) −0.0813396 + 0.0813396i −0.00702667 + 0.00702667i
\(135\) −1.38481 + 1.75564i −0.119186 + 0.151102i
\(136\) 3.12620i 0.268070i
\(137\) 7.57254 + 7.57254i 0.646965 + 0.646965i 0.952258 0.305293i \(-0.0987544\pi\)
−0.305293 + 0.952258i \(0.598754\pi\)
\(138\) −4.75461 4.75461i −0.404739 0.404739i
\(139\) −12.3073 −1.04390 −0.521948 0.852977i \(-0.674794\pi\)
−0.521948 + 0.852977i \(0.674794\pi\)
\(140\) 6.69198 + 5.27849i 0.565575 + 0.446114i
\(141\) 4.43682i 0.373648i
\(142\) 9.73699 0.817110
\(143\) 4.13069i 0.345426i
\(144\) 1.00000i 0.0833333i
\(145\) 0.596534 + 0.470533i 0.0495395 + 0.0390756i
\(146\) −3.77094 3.77094i −0.312085 0.312085i
\(147\) 5.32381 5.32381i 0.439100 0.439100i
\(148\) 6.03268 + 0.778980i 0.495883 + 0.0640317i
\(149\) 18.0558i 1.47919i 0.673052 + 0.739596i \(0.264983\pi\)
−0.673052 + 0.739596i \(0.735017\pi\)
\(150\) 4.26178 + 2.61482i 0.347973 + 0.213499i
\(151\) 0.527274i 0.0429089i −0.999770 0.0214545i \(-0.993170\pi\)
0.999770 0.0214545i \(-0.00682969\pi\)
\(152\) −4.87828 + 4.87828i −0.395681 + 0.395681i
\(153\) 3.12620 0.252739
\(154\) 10.3884 10.3884i 0.837118 0.837118i
\(155\) 14.2888 18.1152i 1.14771 1.45504i
\(156\) −0.757816 0.757816i −0.0606738 0.0606738i
\(157\) −7.56393 7.56393i −0.603668 0.603668i 0.337616 0.941284i \(-0.390379\pi\)
−0.941284 + 0.337616i \(0.890379\pi\)
\(158\) −4.33967 + 4.33967i −0.345245 + 0.345245i
\(159\) 9.54760 0.757174
\(160\) 2.22064 0.262217i 0.175557 0.0207300i
\(161\) 18.1231 + 18.1231i 1.42830 + 1.42830i
\(162\) 1.00000 0.0785674
\(163\) 16.8338i 1.31852i 0.751914 + 0.659262i \(0.229131\pi\)
−0.751914 + 0.659262i \(0.770869\pi\)
\(164\) 9.24361i 0.721805i
\(165\) 5.33747 6.76676i 0.415522 0.526792i
\(166\) 5.06491 5.06491i 0.393113 0.393113i
\(167\) 19.7919i 1.53154i −0.643112 0.765772i \(-0.722357\pi\)
0.643112 0.765772i \(-0.277643\pi\)
\(168\) 3.81169i 0.294079i
\(169\) −11.8514 −0.911648
\(170\) −0.819742 6.94217i −0.0628714 0.532440i
\(171\) 4.87828 + 4.87828i 0.373052 + 0.373052i
\(172\) −8.98058 −0.684762
\(173\) −11.9282 11.9282i −0.906886 0.906886i 0.0891340 0.996020i \(-0.471590\pi\)
−0.996020 + 0.0891340i \(0.971590\pi\)
\(174\) 0.339781i 0.0257587i
\(175\) −16.2446 9.96687i −1.22798 0.753425i
\(176\) 3.85429i 0.290528i
\(177\) −1.46558 −0.110160
\(178\) −4.92656 4.92656i −0.369262 0.369262i
\(179\) −6.14221 6.14221i −0.459090 0.459090i 0.439266 0.898357i \(-0.355238\pi\)
−0.898357 + 0.439266i \(0.855238\pi\)
\(180\) −0.262217 2.22064i −0.0195445 0.165517i
\(181\) −11.3224 −0.841587 −0.420793 0.907157i \(-0.638248\pi\)
−0.420793 + 0.907157i \(0.638248\pi\)
\(182\) 2.88856 + 2.88856i 0.214114 + 0.214114i
\(183\) −13.2029 −0.975989
\(184\) 6.72404 0.495702
\(185\) −13.6007 0.147965i −0.999941 0.0108786i
\(186\) −10.3182 −0.756570
\(187\) −12.0493 −0.881131
\(188\) −3.13731 3.13731i −0.228811 0.228811i
\(189\) −3.81169 −0.277260
\(190\) 9.55375 12.1121i 0.693102 0.878703i
\(191\) 11.4031 + 11.4031i 0.825101 + 0.825101i 0.986834 0.161734i \(-0.0517086\pi\)
−0.161734 + 0.986834i \(0.551709\pi\)
\(192\) −0.707107 0.707107i −0.0510310 0.0510310i
\(193\) 25.7217 1.85149 0.925744 0.378150i \(-0.123440\pi\)
0.925744 + 0.378150i \(0.123440\pi\)
\(194\) 2.13394i 0.153208i
\(195\) 1.88155 + 1.48412i 0.134740 + 0.106280i
\(196\) 7.52901i 0.537786i
\(197\) 0.296894 + 0.296894i 0.0211528 + 0.0211528i 0.717604 0.696451i \(-0.245239\pi\)
−0.696451 + 0.717604i \(0.745239\pi\)
\(198\) −3.85429 −0.273912
\(199\) −5.41052 5.41052i −0.383541 0.383541i 0.488835 0.872376i \(-0.337422\pi\)
−0.872376 + 0.488835i \(0.837422\pi\)
\(200\) −4.86248 + 1.16458i −0.343830 + 0.0823481i
\(201\) −0.115032 −0.00811370
\(202\) 15.9490i 1.12217i
\(203\) 1.29514i 0.0909010i
\(204\) −2.21056 + 2.21056i −0.154770 + 0.154770i
\(205\) −2.42383 20.5267i −0.169287 1.43365i
\(206\) 7.78216i 0.542209i
\(207\) 6.72404i 0.467353i
\(208\) 1.07171 0.0743100
\(209\) −18.8023 18.8023i −1.30058 1.30058i
\(210\) 0.999489 + 8.46440i 0.0689713 + 0.584099i
\(211\) 14.5704 1.00306 0.501532 0.865139i \(-0.332770\pi\)
0.501532 + 0.865139i \(0.332770\pi\)
\(212\) −6.75117 + 6.75117i −0.463672 + 0.463672i
\(213\) 6.88509 + 6.88509i 0.471759 + 0.471759i
\(214\) −6.27687 6.27687i −0.429078 0.429078i
\(215\) 19.9426 2.35486i 1.36008 0.160600i
\(216\) −0.707107 + 0.707107i −0.0481125 + 0.0481125i
\(217\) 39.3300 2.66989
\(218\) 8.01624 8.01624i 0.542929 0.542929i
\(219\) 5.33291i 0.360365i
\(220\) 1.01066 + 8.55899i 0.0681386 + 0.577047i
\(221\) 3.35039i 0.225372i
\(222\) 3.71492 + 4.81657i 0.249329 + 0.323267i
\(223\) 7.68371 7.68371i 0.514540 0.514540i −0.401374 0.915914i \(-0.631467\pi\)
0.915914 + 0.401374i \(0.131467\pi\)
\(224\) 2.69527 + 2.69527i 0.180086 + 0.180086i
\(225\) 1.16458 + 4.86248i 0.0776385 + 0.324166i
\(226\) 19.1057i 1.27089i
\(227\) 16.0147i 1.06293i 0.847080 + 0.531465i \(0.178358\pi\)
−0.847080 + 0.531465i \(0.821642\pi\)
\(228\) −6.89894 −0.456893
\(229\) 9.95500i 0.657845i 0.944357 + 0.328923i \(0.106686\pi\)
−0.944357 + 0.328923i \(0.893314\pi\)
\(230\) −14.9317 + 1.76315i −0.984565 + 0.116259i
\(231\) 14.6914 0.966621
\(232\) 0.240261 + 0.240261i 0.0157739 + 0.0157739i
\(233\) −16.4078 16.4078i −1.07491 1.07491i −0.996957 0.0779551i \(-0.975161\pi\)
−0.0779551 0.996957i \(-0.524839\pi\)
\(234\) 1.07171i 0.0700601i
\(235\) 7.78948 + 6.14417i 0.508130 + 0.400802i
\(236\) 1.03632 1.03632i 0.0674590 0.0674590i
\(237\) −6.13722 −0.398655
\(238\) 8.42597 8.42597i 0.546175 0.546175i
\(239\) 16.5390 16.5390i 1.06982 1.06982i 0.0724452 0.997372i \(-0.476920\pi\)
0.997372 0.0724452i \(-0.0230802\pi\)
\(240\) 1.75564 + 1.38481i 0.113326 + 0.0893894i
\(241\) −9.38903 9.38903i −0.604801 0.604801i 0.336782 0.941583i \(-0.390662\pi\)
−0.941583 + 0.336782i \(0.890662\pi\)
\(242\) 3.85554 0.247844
\(243\) 0.707107 + 0.707107i 0.0453609 + 0.0453609i
\(244\) 9.33589 9.33589i 0.597669 0.597669i
\(245\) −1.97423 16.7192i −0.126129 1.06815i
\(246\) −6.53622 + 6.53622i −0.416734 + 0.416734i
\(247\) 5.22812 5.22812i 0.332658 0.332658i
\(248\) 7.29610 7.29610i 0.463303 0.463303i
\(249\) 7.16286 0.453928
\(250\) 10.4925 3.86113i 0.663601 0.244199i
\(251\) −5.58629 + 5.58629i −0.352603 + 0.352603i −0.861077 0.508474i \(-0.830210\pi\)
0.508474 + 0.861077i \(0.330210\pi\)
\(252\) 2.69527 2.69527i 0.169786 0.169786i
\(253\) 25.9164i 1.62935i
\(254\) −4.73530 4.73530i −0.297119 0.297119i
\(255\) 4.32921 5.48850i 0.271106 0.343703i
\(256\) 1.00000 0.0625000
\(257\) 10.1055i 0.630365i −0.949031 0.315183i \(-0.897934\pi\)
0.949031 0.315183i \(-0.102066\pi\)
\(258\) −6.35023 6.35023i −0.395348 0.395348i
\(259\) −14.1602 18.3593i −0.879869 1.14079i
\(260\) −2.37989 + 0.281021i −0.147595 + 0.0174282i
\(261\) 0.240261 0.240261i 0.0148718 0.0148718i
\(262\) −10.1880 + 10.1880i −0.629415 + 0.629415i
\(263\) 12.6819 + 12.6819i 0.781998 + 0.781998i 0.980168 0.198170i \(-0.0634998\pi\)
−0.198170 + 0.980168i \(0.563500\pi\)
\(264\) 2.72539 2.72539i 0.167736 0.167736i
\(265\) 13.2217 16.7622i 0.812200 1.02969i
\(266\) 26.2966 1.61235
\(267\) 6.96721i 0.426387i
\(268\) 0.0813396 0.0813396i 0.00496861 0.00496861i
\(269\) 26.5570i 1.61921i −0.586978 0.809603i \(-0.699682\pi\)
0.586978 0.809603i \(-0.300318\pi\)
\(270\) 1.38481 1.75564i 0.0842771 0.106845i
\(271\) −16.3151 −0.991073 −0.495536 0.868587i \(-0.665028\pi\)
−0.495536 + 0.868587i \(0.665028\pi\)
\(272\) 3.12620i 0.189554i
\(273\) 4.08504i 0.247238i
\(274\) −7.57254 7.57254i −0.457474 0.457474i
\(275\) −4.48862 18.7414i −0.270674 1.13015i
\(276\) 4.75461 + 4.75461i 0.286194 + 0.286194i
\(277\) 1.82943 0.109920 0.0549600 0.998489i \(-0.482497\pi\)
0.0549600 + 0.998489i \(0.482497\pi\)
\(278\) 12.3073 0.738146
\(279\) −7.29610 7.29610i −0.436806 0.436806i
\(280\) −6.69198 5.27849i −0.399922 0.315450i
\(281\) −8.49578 8.49578i −0.506816 0.506816i 0.406732 0.913548i \(-0.366668\pi\)
−0.913548 + 0.406732i \(0.866668\pi\)
\(282\) 4.43682i 0.264209i
\(283\) 4.60113i 0.273509i −0.990605 0.136754i \(-0.956333\pi\)
0.990605 0.136754i \(-0.0436671\pi\)
\(284\) −9.73699 −0.577784
\(285\) 15.3201 1.80902i 0.907482 0.107157i
\(286\) 4.13069i 0.244253i
\(287\) 24.9141 24.9141i 1.47063 1.47063i
\(288\) 1.00000i 0.0589256i
\(289\) 7.22686 0.425109
\(290\) −0.596534 0.470533i −0.0350297 0.0276307i
\(291\) −1.50892 + 1.50892i −0.0884545 + 0.0884545i
\(292\) 3.77094 + 3.77094i 0.220677 + 0.220677i
\(293\) −6.31819 + 6.31819i −0.369113 + 0.369113i −0.867154 0.498041i \(-0.834053\pi\)
0.498041 + 0.867154i \(0.334053\pi\)
\(294\) −5.32381 + 5.32381i −0.310491 + 0.310491i
\(295\) −2.02956 + 2.57304i −0.118166 + 0.149808i
\(296\) −6.03268 0.778980i −0.350642 0.0452773i
\(297\) −2.72539 2.72539i −0.158143 0.158143i
\(298\) 18.0558i 1.04595i
\(299\) −7.20624 −0.416748
\(300\) −4.26178 2.61482i −0.246054 0.150966i
\(301\) 24.2051 + 24.2051i 1.39516 + 1.39516i
\(302\) 0.527274i 0.0303412i
\(303\) 11.2777 11.2777i 0.647885 0.647885i
\(304\) 4.87828 4.87828i 0.279789 0.279789i
\(305\) −18.2836 + 23.1797i −1.04692 + 1.32726i
\(306\) −3.12620 −0.178713
\(307\) −18.6155 + 18.6155i −1.06244 + 1.06244i −0.0645243 + 0.997916i \(0.520553\pi\)
−0.997916 + 0.0645243i \(0.979447\pi\)
\(308\) −10.3884 + 10.3884i −0.591932 + 0.591932i
\(309\) 5.50282 5.50282i 0.313044 0.313044i
\(310\) −14.2888 + 18.1152i −0.811552 + 1.02887i
\(311\) 1.28712 1.28712i 0.0729856 0.0729856i −0.669672 0.742657i \(-0.733565\pi\)
0.742657 + 0.669672i \(0.233565\pi\)
\(312\) 0.757816 + 0.757816i 0.0429029 + 0.0429029i
\(313\) −32.0767 −1.81308 −0.906540 0.422120i \(-0.861286\pi\)
−0.906540 + 0.422120i \(0.861286\pi\)
\(314\) 7.56393 + 7.56393i 0.426857 + 0.426857i
\(315\) −5.27849 + 6.69198i −0.297409 + 0.377050i
\(316\) 4.33967 4.33967i 0.244125 0.244125i
\(317\) 5.14557 5.14557i 0.289004 0.289004i −0.547682 0.836686i \(-0.684490\pi\)
0.836686 + 0.547682i \(0.184490\pi\)
\(318\) −9.54760 −0.535403
\(319\) −0.926036 + 0.926036i −0.0518481 + 0.0518481i
\(320\) −2.22064 + 0.262217i −0.124138 + 0.0146584i
\(321\) 8.87684i 0.495457i
\(322\) −18.1231 18.1231i −1.00996 1.00996i
\(323\) −15.2505 15.2505i −0.848561 0.848561i
\(324\) −1.00000 −0.0555556
\(325\) 5.21119 1.24809i 0.289065 0.0692318i
\(326\) 16.8338i 0.932337i
\(327\) 11.3367 0.626920
\(328\) 9.24361i 0.510393i
\(329\) 16.9118i 0.932377i
\(330\) −5.33747 + 6.76676i −0.293818 + 0.372498i
\(331\) −8.41827 8.41827i −0.462710 0.462710i 0.436833 0.899543i \(-0.356100\pi\)
−0.899543 + 0.436833i \(0.856100\pi\)
\(332\) −5.06491 + 5.06491i −0.277973 + 0.277973i
\(333\) −0.778980 + 6.03268i −0.0426878 + 0.330589i
\(334\) 19.7919i 1.08297i
\(335\) −0.159297 + 0.201955i −0.00870335 + 0.0110340i
\(336\) 3.81169i 0.207945i
\(337\) 5.24126 5.24126i 0.285510 0.285510i −0.549792 0.835302i \(-0.685293\pi\)
0.835302 + 0.549792i \(0.185293\pi\)
\(338\) 11.8514 0.644633
\(339\) −13.5098 + 13.5098i −0.733751 + 0.733751i
\(340\) 0.819742 + 6.94217i 0.0444568 + 0.376492i
\(341\) 28.1213 + 28.1213i 1.52285 + 1.52285i
\(342\) −4.87828 4.87828i −0.263787 0.263787i
\(343\) 1.42581 1.42581i 0.0769867 0.0769867i
\(344\) 8.98058 0.484200
\(345\) −11.8050 9.31154i −0.635561 0.501317i
\(346\) 11.9282 + 11.9282i 0.641265 + 0.641265i
\(347\) 27.4976 1.47615 0.738074 0.674720i \(-0.235735\pi\)
0.738074 + 0.674720i \(0.235735\pi\)
\(348\) 0.339781i 0.0182142i
\(349\) 5.28646i 0.282978i 0.989940 + 0.141489i \(0.0451890\pi\)
−0.989940 + 0.141489i \(0.954811\pi\)
\(350\) 16.2446 + 9.96687i 0.868310 + 0.532752i
\(351\) 0.757816 0.757816i 0.0404492 0.0404492i
\(352\) 3.85429i 0.205434i
\(353\) 2.70748i 0.144105i 0.997401 + 0.0720523i \(0.0229548\pi\)
−0.997401 + 0.0720523i \(0.977045\pi\)
\(354\) 1.46558 0.0778949
\(355\) 21.6224 2.55320i 1.14760 0.135510i
\(356\) 4.92656 + 4.92656i 0.261107 + 0.261107i
\(357\) 11.9161 0.630668
\(358\) 6.14221 + 6.14221i 0.324626 + 0.324626i
\(359\) 20.4504i 1.07933i −0.841880 0.539665i \(-0.818551\pi\)
0.841880 0.539665i \(-0.181449\pi\)
\(360\) 0.262217 + 2.22064i 0.0138200 + 0.117038i
\(361\) 28.5953i 1.50502i
\(362\) 11.3224 0.595092
\(363\) 2.72628 + 2.72628i 0.143093 + 0.143093i
\(364\) −2.88856 2.88856i −0.151402 0.151402i
\(365\) −9.36269 7.38509i −0.490066 0.386553i
\(366\) 13.2029 0.690129
\(367\) −0.867537 0.867537i −0.0452851 0.0452851i 0.684102 0.729387i \(-0.260194\pi\)
−0.729387 + 0.684102i \(0.760194\pi\)
\(368\) −6.72404 −0.350515
\(369\) −9.24361 −0.481203
\(370\) 13.6007 + 0.147965i 0.707065 + 0.00769235i
\(371\) 36.3925 1.88941
\(372\) 10.3182 0.534976
\(373\) 20.6119 + 20.6119i 1.06725 + 1.06725i 0.997570 + 0.0696765i \(0.0221967\pi\)
0.0696765 + 0.997570i \(0.477803\pi\)
\(374\) 12.0493 0.623054
\(375\) 10.1495 + 4.68905i 0.524119 + 0.242142i
\(376\) 3.13731 + 3.13731i 0.161794 + 0.161794i
\(377\) −0.257491 0.257491i −0.0132615 0.0132615i
\(378\) 3.81169 0.196052
\(379\) 9.54382i 0.490233i 0.969494 + 0.245117i \(0.0788263\pi\)
−0.969494 + 0.245117i \(0.921174\pi\)
\(380\) −9.55375 + 12.1121i −0.490097 + 0.621337i
\(381\) 6.69672i 0.343083i
\(382\) −11.4031 11.4031i −0.583434 0.583434i
\(383\) 5.14097 0.262691 0.131346 0.991337i \(-0.458070\pi\)
0.131346 + 0.991337i \(0.458070\pi\)
\(384\) 0.707107 + 0.707107i 0.0360844 + 0.0360844i
\(385\) 20.3448 25.7928i 1.03687 1.31452i
\(386\) −25.7217 −1.30920
\(387\) 8.98058i 0.456508i
\(388\) 2.13394i 0.108334i
\(389\) −13.7109 + 13.7109i −0.695168 + 0.695168i −0.963364 0.268196i \(-0.913572\pi\)
0.268196 + 0.963364i \(0.413572\pi\)
\(390\) −1.88155 1.48412i −0.0952759 0.0751516i
\(391\) 21.0207i 1.06306i
\(392\) 7.52901i 0.380272i
\(393\) −14.4080 −0.726786
\(394\) −0.296894 0.296894i −0.0149573 0.0149573i
\(395\) −8.49891 + 10.7748i −0.427626 + 0.542138i
\(396\) 3.85429 0.193685
\(397\) −22.3090 + 22.3090i −1.11966 + 1.11966i −0.127864 + 0.991792i \(0.540812\pi\)
−0.991792 + 0.127864i \(0.959188\pi\)
\(398\) 5.41052 + 5.41052i 0.271205 + 0.271205i
\(399\) 18.5945 + 18.5945i 0.930890 + 0.930890i
\(400\) 4.86248 1.16458i 0.243124 0.0582289i
\(401\) 6.05401 6.05401i 0.302323 0.302323i −0.539599 0.841922i \(-0.681424\pi\)
0.841922 + 0.539599i \(0.181424\pi\)
\(402\) 0.115032 0.00573725
\(403\) −7.81933 + 7.81933i −0.389508 + 0.389508i
\(404\) 15.9490i 0.793494i
\(405\) 2.22064 0.262217i 0.110344 0.0130297i
\(406\) 1.29514i 0.0642767i
\(407\) 3.00241 23.2517i 0.148824 1.15254i
\(408\) 2.21056 2.21056i 0.109439 0.109439i
\(409\) −6.83746 6.83746i −0.338091 0.338091i 0.517558 0.855648i \(-0.326841\pi\)
−0.855648 + 0.517558i \(0.826841\pi\)
\(410\) 2.42383 + 20.5267i 0.119704 + 1.01374i
\(411\) 10.7092i 0.528245i
\(412\) 7.78216i 0.383399i
\(413\) −5.58636 −0.274887
\(414\) 6.72404i 0.330468i
\(415\) 9.91924 12.5754i 0.486916 0.617304i
\(416\) −1.07171 −0.0525451
\(417\) 8.70261 + 8.70261i 0.426169 + 0.426169i
\(418\) 18.8023 + 18.8023i 0.919651 + 0.919651i
\(419\) 12.4992i 0.610627i 0.952252 + 0.305314i \(0.0987613\pi\)
−0.952252 + 0.305314i \(0.901239\pi\)
\(420\) −0.999489 8.46440i −0.0487701 0.413020i
\(421\) 1.21803 1.21803i 0.0593634 0.0593634i −0.676802 0.736165i \(-0.736635\pi\)
0.736165 + 0.676802i \(0.236635\pi\)
\(422\) −14.5704 −0.709274
\(423\) 3.13731 3.13731i 0.152541 0.152541i
\(424\) 6.75117 6.75117i 0.327866 0.327866i
\(425\) −3.64071 15.2011i −0.176600 0.737362i
\(426\) −6.88509 6.88509i −0.333584 0.333584i
\(427\) −50.3255 −2.43542
\(428\) 6.27687 + 6.27687i 0.303404 + 0.303404i
\(429\) −2.92084 + 2.92084i −0.141020 + 0.141020i
\(430\) −19.9426 + 2.35486i −0.961719 + 0.113561i
\(431\) −12.0202 + 12.0202i −0.578993 + 0.578993i −0.934626 0.355633i \(-0.884265\pi\)
0.355633 + 0.934626i \(0.384265\pi\)
\(432\) 0.707107 0.707107i 0.0340207 0.0340207i
\(433\) −15.2027 + 15.2027i −0.730596 + 0.730596i −0.970738 0.240142i \(-0.922806\pi\)
0.240142 + 0.970738i \(0.422806\pi\)
\(434\) −39.3300 −1.88790
\(435\) −0.0890961 0.754530i −0.00427183 0.0361770i
\(436\) −8.01624 + 8.01624i −0.383908 + 0.383908i
\(437\) −32.8018 + 32.8018i −1.56912 + 1.56912i
\(438\) 5.33291i 0.254816i
\(439\) −3.20813 3.20813i −0.153116 0.153116i 0.626392 0.779508i \(-0.284531\pi\)
−0.779508 + 0.626392i \(0.784531\pi\)
\(440\) −1.01066 8.55899i −0.0481813 0.408034i
\(441\) −7.52901 −0.358524
\(442\) 3.35039i 0.159362i
\(443\) 7.74996 + 7.74996i 0.368211 + 0.368211i 0.866825 0.498613i \(-0.166157\pi\)
−0.498613 + 0.866825i \(0.666157\pi\)
\(444\) −3.71492 4.81657i −0.176303 0.228584i
\(445\) −12.2320 9.64830i −0.579850 0.457373i
\(446\) −7.68371 + 7.68371i −0.363834 + 0.363834i
\(447\) 12.7674 12.7674i 0.603877 0.603877i
\(448\) −2.69527 2.69527i −0.127340 0.127340i
\(449\) −10.4682 + 10.4682i −0.494024 + 0.494024i −0.909571 0.415548i \(-0.863590\pi\)
0.415548 + 0.909571i \(0.363590\pi\)
\(450\) −1.16458 4.86248i −0.0548987 0.229220i
\(451\) 35.6275 1.67764
\(452\) 19.1057i 0.898658i
\(453\) −0.372839 + 0.372839i −0.0175175 + 0.0175175i
\(454\) 16.0147i 0.751606i
\(455\) 7.17189 + 5.65703i 0.336223 + 0.265206i
\(456\) 6.89894 0.323072
\(457\) 1.41085i 0.0659970i −0.999455 0.0329985i \(-0.989494\pi\)
0.999455 0.0329985i \(-0.0105057\pi\)
\(458\) 9.95500i 0.465167i
\(459\) −2.21056 2.21056i −0.103180 0.103180i
\(460\) 14.9317 1.76315i 0.696192 0.0822075i
\(461\) −17.2878 17.2878i −0.805173 0.805173i 0.178726 0.983899i \(-0.442802\pi\)
−0.983899 + 0.178726i \(0.942802\pi\)
\(462\) −14.6914 −0.683504
\(463\) −27.9587 −1.29935 −0.649675 0.760212i \(-0.725095\pi\)
−0.649675 + 0.760212i \(0.725095\pi\)
\(464\) −0.240261 0.240261i −0.0111538 0.0111538i
\(465\) −22.9131 + 2.70561i −1.06257 + 0.125470i
\(466\) 16.4078 + 16.4078i 0.760078 + 0.760078i
\(467\) 25.1108i 1.16199i −0.813907 0.580995i \(-0.802664\pi\)
0.813907 0.580995i \(-0.197336\pi\)
\(468\) 1.07171i 0.0495400i
\(469\) −0.438465 −0.0202464
\(470\) −7.78948 6.14417i −0.359302 0.283410i
\(471\) 10.6970i 0.492893i
\(472\) −1.03632 + 1.03632i −0.0477007 + 0.0477007i
\(473\) 34.6137i 1.59154i
\(474\) 6.13722 0.281892
\(475\) 18.0394 29.4017i 0.827706 1.34904i
\(476\) −8.42597 + 8.42597i −0.386204 + 0.386204i
\(477\) −6.75117 6.75117i −0.309115 0.309115i
\(478\) −16.5390 + 16.5390i −0.756475 + 0.756475i
\(479\) −9.67259 + 9.67259i −0.441952 + 0.441952i −0.892668 0.450716i \(-0.851169\pi\)
0.450716 + 0.892668i \(0.351169\pi\)
\(480\) −1.75564 1.38481i −0.0801339 0.0632078i
\(481\) 6.46530 + 0.834843i 0.294792 + 0.0380656i
\(482\) 9.38903 + 9.38903i 0.427659 + 0.427659i
\(483\) 25.6300i 1.16620i
\(484\) −3.85554 −0.175252
\(485\) 0.559554 + 4.73871i 0.0254080 + 0.215174i
\(486\) −0.707107 0.707107i −0.0320750 0.0320750i
\(487\) 28.7468i 1.30264i −0.758803 0.651321i \(-0.774215\pi\)
0.758803 0.651321i \(-0.225785\pi\)
\(488\) −9.33589 + 9.33589i −0.422616 + 0.422616i
\(489\) 11.9033 11.9033i 0.538285 0.538285i
\(490\) 1.97423 + 16.7192i 0.0891866 + 0.755297i
\(491\) −17.9127 −0.808391 −0.404195 0.914673i \(-0.632448\pi\)
−0.404195 + 0.914673i \(0.632448\pi\)
\(492\) 6.53622 6.53622i 0.294675 0.294675i
\(493\) −0.751105 + 0.751105i −0.0338281 + 0.0338281i
\(494\) −5.22812 + 5.22812i −0.235224 + 0.235224i
\(495\) −8.55899 + 1.01066i −0.384698 + 0.0454257i
\(496\) −7.29610 + 7.29610i −0.327604 + 0.327604i
\(497\) 26.2439 + 26.2439i 1.17720 + 1.17720i
\(498\) −7.16286 −0.320976
\(499\) −6.22662 6.22662i −0.278742 0.278742i 0.553865 0.832607i \(-0.313152\pi\)
−0.832607 + 0.553865i \(0.813152\pi\)
\(500\) −10.4925 + 3.86113i −0.469237 + 0.172675i
\(501\) −13.9950 + 13.9950i −0.625251 + 0.625251i
\(502\) 5.58629 5.58629i 0.249328 0.249328i
\(503\) −2.20186 −0.0981761 −0.0490880 0.998794i \(-0.515631\pi\)
−0.0490880 + 0.998794i \(0.515631\pi\)
\(504\) −2.69527 + 2.69527i −0.120057 + 0.120057i
\(505\) −4.18210 35.4171i −0.186101 1.57604i
\(506\) 25.9164i 1.15212i
\(507\) 8.38023 + 8.38023i 0.372179 + 0.372179i
\(508\) 4.73530 + 4.73530i 0.210095 + 0.210095i
\(509\) 4.45209 0.197335 0.0986677 0.995120i \(-0.468542\pi\)
0.0986677 + 0.995120i \(0.468542\pi\)
\(510\) −4.32921 + 5.48850i −0.191701 + 0.243035i
\(511\) 20.3274i 0.899232i
\(512\) −1.00000 −0.0441942
\(513\) 6.89894i 0.304595i
\(514\) 10.1055i 0.445735i
\(515\) −2.04061 17.2814i −0.0899201 0.761508i
\(516\) 6.35023 + 6.35023i 0.279553 + 0.279553i
\(517\) −12.0921 + 12.0921i −0.531809 + 0.531809i
\(518\) 14.1602 + 18.3593i 0.622161 + 0.806661i
\(519\) 16.8690i 0.740469i
\(520\) 2.37989 0.281021i 0.104365 0.0123236i
\(521\) 3.61089i 0.158196i 0.996867 + 0.0790979i \(0.0252040\pi\)
−0.996867 + 0.0790979i \(0.974796\pi\)
\(522\) −0.240261 + 0.240261i −0.0105159 + 0.0105159i
\(523\) −30.6225 −1.33903 −0.669514 0.742799i \(-0.733498\pi\)
−0.669514 + 0.742799i \(0.733498\pi\)
\(524\) 10.1880 10.1880i 0.445063 0.445063i
\(525\) 4.43901 + 18.5343i 0.193734 + 0.808903i
\(526\) −12.6819 12.6819i −0.552956 0.552956i
\(527\) 22.8091 + 22.8091i 0.993579 + 0.993579i
\(528\) −2.72539 + 2.72539i −0.118608 + 0.118608i
\(529\) 22.2127 0.965768
\(530\) −13.2217 + 16.7622i −0.574312 + 0.728103i
\(531\) 1.03632 + 1.03632i 0.0449726 + 0.0449726i
\(532\) −26.2966 −1.14010
\(533\) 9.90650i 0.429098i
\(534\) 6.96721i 0.301501i
\(535\) −15.5846 12.2928i −0.673780 0.531463i
\(536\) −0.0813396 + 0.0813396i −0.00351334 + 0.00351334i
\(537\) 8.68640i 0.374846i
\(538\) 26.5570i 1.14495i
\(539\) 29.0190 1.24994
\(540\) −1.38481 + 1.75564i −0.0595929 + 0.0755509i
\(541\) −28.0745 28.0745i −1.20702 1.20702i −0.971989 0.235027i \(-0.924482\pi\)
−0.235027 0.971989i \(-0.575518\pi\)
\(542\) 16.3151 0.700794
\(543\) 8.00614 + 8.00614i 0.343576 + 0.343576i
\(544\) 3.12620i 0.134035i
\(545\) 15.6992 19.9032i 0.672480 0.852559i
\(546\) 4.08504i 0.174824i
\(547\) −20.4389 −0.873904 −0.436952 0.899485i \(-0.643942\pi\)
−0.436952 + 0.899485i \(0.643942\pi\)
\(548\) 7.57254 + 7.57254i 0.323483 + 0.323483i
\(549\) 9.33589 + 9.33589i 0.398446 + 0.398446i
\(550\) 4.48862 + 18.7414i 0.191395 + 0.799137i
\(551\) −2.34412 −0.0998631
\(552\) −4.75461 4.75461i −0.202370 0.202370i
\(553\) −23.3932 −0.994780
\(554\) −1.82943 −0.0777252
\(555\) 9.51250 + 9.72175i 0.403783 + 0.412665i
\(556\) −12.3073 −0.521948
\(557\) 39.1876 1.66043 0.830215 0.557443i \(-0.188217\pi\)
0.830215 + 0.557443i \(0.188217\pi\)
\(558\) 7.29610 + 7.29610i 0.308868 + 0.308868i
\(559\) −9.62461 −0.407077
\(560\) 6.69198 + 5.27849i 0.282788 + 0.223057i
\(561\) 8.52013 + 8.52013i 0.359720 + 0.359720i
\(562\) 8.49578 + 8.49578i 0.358373 + 0.358373i
\(563\) −15.3734 −0.647910 −0.323955 0.946073i \(-0.605013\pi\)
−0.323955 + 0.946073i \(0.605013\pi\)
\(564\) 4.43682i 0.186824i
\(565\) 5.00984 + 42.4270i 0.210766 + 1.78492i
\(566\) 4.60113i 0.193400i
\(567\) 2.69527 + 2.69527i 0.113191 + 0.113191i
\(568\) 9.73699 0.408555
\(569\) 11.9446 + 11.9446i 0.500743 + 0.500743i 0.911669 0.410925i \(-0.134794\pi\)
−0.410925 + 0.911669i \(0.634794\pi\)
\(570\) −15.3201 + 1.80902i −0.641686 + 0.0757713i
\(571\) −19.6843 −0.823762 −0.411881 0.911238i \(-0.635128\pi\)
−0.411881 + 0.911238i \(0.635128\pi\)
\(572\) 4.13069i 0.172713i
\(573\) 16.1264i 0.673692i
\(574\) −24.9141 + 24.9141i −1.03989 + 1.03989i
\(575\) −32.6955 + 7.83066i −1.36350 + 0.326561i
\(576\) 1.00000i 0.0416667i
\(577\) 43.0027i 1.79022i 0.445841 + 0.895112i \(0.352905\pi\)
−0.445841 + 0.895112i \(0.647095\pi\)
\(578\) −7.22686 −0.300598
\(579\) −18.1880 18.1880i −0.755867 0.755867i
\(580\) 0.596534 + 0.470533i 0.0247697 + 0.0195378i
\(581\) 27.3026 1.13270
\(582\) 1.50892 1.50892i 0.0625468 0.0625468i
\(583\) 26.0210 + 26.0210i 1.07768 + 1.07768i
\(584\) −3.77094 3.77094i −0.156042 0.156042i
\(585\) −0.281021 2.37989i −0.0116188 0.0983964i
\(586\) 6.31819 6.31819i 0.261002 0.261002i
\(587\) 2.93901 0.121306 0.0606530 0.998159i \(-0.480682\pi\)
0.0606530 + 0.998159i \(0.480682\pi\)
\(588\) 5.32381 5.32381i 0.219550 0.219550i
\(589\) 71.1849i 2.93312i
\(590\) 2.02956 2.57304i 0.0835557 0.105931i
\(591\) 0.419872i 0.0172712i
\(592\) 6.03268 + 0.778980i 0.247941 + 0.0320159i
\(593\) −31.5947 + 31.5947i −1.29744 + 1.29744i −0.367359 + 0.930079i \(0.619738\pi\)
−0.930079 + 0.367359i \(0.880262\pi\)
\(594\) 2.72539 + 2.72539i 0.111824 + 0.111824i
\(595\) 16.5016 20.9205i 0.676501 0.857656i
\(596\) 18.0558i 0.739596i
\(597\) 7.65163i 0.313160i
\(598\) 7.20624 0.294685
\(599\) 37.7290i 1.54156i −0.637099 0.770782i \(-0.719866\pi\)
0.637099 0.770782i \(-0.280134\pi\)
\(600\) 4.26178 + 2.61482i 0.173986 + 0.106749i
\(601\) −20.0120 −0.816305 −0.408152 0.912914i \(-0.633827\pi\)
−0.408152 + 0.912914i \(0.633827\pi\)
\(602\) −24.2051 24.2051i −0.986527 0.986527i
\(603\) 0.0813396 + 0.0813396i 0.00331241 + 0.00331241i
\(604\) 0.527274i 0.0214545i
\(605\) 8.56177 1.01099i 0.348085 0.0411025i
\(606\) −11.2777 + 11.2777i −0.458124 + 0.458124i
\(607\) 4.73701 0.192269 0.0961347 0.995368i \(-0.469352\pi\)
0.0961347 + 0.995368i \(0.469352\pi\)
\(608\) −4.87828 + 4.87828i −0.197841 + 0.197841i
\(609\) 0.915802 0.915802i 0.0371102 0.0371102i
\(610\) 18.2836 23.1797i 0.740282 0.938517i
\(611\) −3.36229 3.36229i −0.136024 0.136024i
\(612\) 3.12620 0.126369
\(613\) 7.31952 + 7.31952i 0.295633 + 0.295633i 0.839301 0.543668i \(-0.182965\pi\)
−0.543668 + 0.839301i \(0.682965\pi\)
\(614\) 18.6155 18.6155i 0.751259 0.751259i
\(615\) −12.8007 + 16.2285i −0.516173 + 0.654396i
\(616\) 10.3884 10.3884i 0.418559 0.418559i
\(617\) −9.15306 + 9.15306i −0.368488 + 0.368488i −0.866926 0.498437i \(-0.833907\pi\)
0.498437 + 0.866926i \(0.333907\pi\)
\(618\) −5.50282 + 5.50282i −0.221356 + 0.221356i
\(619\) 19.9520 0.801939 0.400970 0.916091i \(-0.368673\pi\)
0.400970 + 0.916091i \(0.368673\pi\)
\(620\) 14.2888 18.1152i 0.573854 0.727522i
\(621\) −4.75461 + 4.75461i −0.190796 + 0.190796i
\(622\) −1.28712 + 1.28712i −0.0516086 + 0.0516086i
\(623\) 26.5569i 1.06398i
\(624\) −0.757816 0.757816i −0.0303369 0.0303369i
\(625\) 22.2875 11.3255i 0.891501 0.453019i
\(626\) 32.0767 1.28204
\(627\) 26.5905i 1.06192i
\(628\) −7.56393 7.56393i −0.301834 0.301834i
\(629\) 2.43525 18.8594i 0.0970997 0.751972i
\(630\) 5.27849 6.69198i 0.210300 0.266615i
\(631\) −8.03580 + 8.03580i −0.319900 + 0.319900i −0.848729 0.528828i \(-0.822631\pi\)
0.528828 + 0.848729i \(0.322631\pi\)
\(632\) −4.33967 + 4.33967i −0.172623 + 0.172623i
\(633\) −10.3028 10.3028i −0.409499 0.409499i
\(634\) −5.14557 + 5.14557i −0.204357 + 0.204357i
\(635\) −11.7571 9.27372i −0.466565 0.368016i
\(636\) 9.54760 0.378587
\(637\) 8.06894i 0.319703i
\(638\) 0.926036 0.926036i 0.0366621 0.0366621i
\(639\) 9.73699i 0.385189i
\(640\) 2.22064 0.262217i 0.0877785 0.0103650i
\(641\) −6.64909 −0.262623 −0.131312 0.991341i \(-0.541919\pi\)
−0.131312 + 0.991341i \(0.541919\pi\)
\(642\) 8.87684i 0.350341i
\(643\) 18.3325i 0.722963i 0.932379 + 0.361481i \(0.117729\pi\)
−0.932379 + 0.361481i \(0.882271\pi\)
\(644\) 18.1231 + 18.1231i 0.714151 + 0.714151i
\(645\) −15.7667 12.4364i −0.620813 0.489684i
\(646\) 15.2505 + 15.2505i 0.600023 + 0.600023i
\(647\) 31.8700 1.25294 0.626470 0.779445i \(-0.284499\pi\)
0.626470 + 0.779445i \(0.284499\pi\)
\(648\) 1.00000 0.0392837
\(649\) −3.99429 3.99429i −0.156790 0.156790i
\(650\) −5.21119 + 1.24809i −0.204400 + 0.0489543i
\(651\) −27.8105 27.8105i −1.08998 1.08998i
\(652\) 16.8338i 0.659262i
\(653\) 6.13141i 0.239941i 0.992777 + 0.119970i \(0.0382800\pi\)
−0.992777 + 0.119970i \(0.961720\pi\)
\(654\) −11.3367 −0.443299
\(655\) −19.9524 + 25.2953i −0.779603 + 0.988368i
\(656\) 9.24361i 0.360902i
\(657\) −3.77094 + 3.77094i −0.147118 + 0.147118i
\(658\) 16.9118i 0.659290i
\(659\) 9.15530 0.356640 0.178320 0.983973i \(-0.442934\pi\)
0.178320 + 0.983973i \(0.442934\pi\)
\(660\) 5.33747 6.76676i 0.207761 0.263396i
\(661\) −6.95018 + 6.95018i −0.270331 + 0.270331i −0.829233 0.558903i \(-0.811223\pi\)
0.558903 + 0.829233i \(0.311223\pi\)
\(662\) 8.41827 + 8.41827i 0.327185 + 0.327185i
\(663\) −2.36909 + 2.36909i −0.0920077 + 0.0920077i
\(664\) 5.06491 5.06491i 0.196557 0.196557i
\(665\) 58.3953 6.89541i 2.26447 0.267393i
\(666\) 0.778980 6.03268i 0.0301849 0.233761i
\(667\) 1.61552 + 1.61552i 0.0625534 + 0.0625534i
\(668\) 19.7919i 0.765772i
\(669\) −10.8664 −0.420120
\(670\) 0.159297 0.201955i 0.00615420 0.00780219i
\(671\) −35.9832 35.9832i −1.38912 1.38912i
\(672\) 3.81169i 0.147039i
\(673\) 10.9734 10.9734i 0.422993 0.422993i −0.463240 0.886233i \(-0.653313\pi\)
0.886233 + 0.463240i \(0.153313\pi\)
\(674\) −5.24126 + 5.24126i −0.201886 + 0.201886i
\(675\) 2.61482 4.26178i 0.100644 0.164036i
\(676\) −11.8514 −0.455824
\(677\) 0.690751 0.690751i 0.0265477 0.0265477i −0.693708 0.720256i \(-0.744024\pi\)
0.720256 + 0.693708i \(0.244024\pi\)
\(678\) 13.5098 13.5098i 0.518841 0.518841i
\(679\) −5.75155 + 5.75155i −0.220724 + 0.220724i
\(680\) −0.819742 6.94217i −0.0314357 0.266220i
\(681\) 11.3241 11.3241i 0.433940 0.433940i
\(682\) −28.1213 28.1213i −1.07682 1.07682i
\(683\) −1.42429 −0.0544990 −0.0272495 0.999629i \(-0.508675\pi\)
−0.0272495 + 0.999629i \(0.508675\pi\)
\(684\) 4.87828 + 4.87828i 0.186526 + 0.186526i
\(685\) −18.8015 14.8302i −0.718369 0.566634i
\(686\) −1.42581 + 1.42581i −0.0544378 + 0.0544378i
\(687\) 7.03925 7.03925i 0.268564 0.268564i
\(688\) −8.98058 −0.342381
\(689\) −7.23532 + 7.23532i −0.275644 + 0.275644i
\(690\) 11.8050 + 9.31154i 0.449409 + 0.354484i
\(691\) 20.8427i 0.792894i −0.918058 0.396447i \(-0.870243\pi\)
0.918058 0.396447i \(-0.129757\pi\)
\(692\) −11.9282 11.9282i −0.453443 0.453443i
\(693\) −10.3884 10.3884i −0.394621 0.394621i
\(694\) −27.4976 −1.04379
\(695\) 27.3302 3.22719i 1.03669 0.122414i
\(696\) 0.339781i 0.0128794i
\(697\) 28.8974 1.09457
\(698\) 5.28646i 0.200096i
\(699\) 23.2042i 0.877662i
\(700\) −16.2446 9.96687i −0.613988 0.376712i
\(701\) 12.5457 + 12.5457i 0.473846 + 0.473846i 0.903157 0.429311i \(-0.141244\pi\)
−0.429311 + 0.903157i \(0.641244\pi\)
\(702\) −0.757816 + 0.757816i −0.0286019 + 0.0286019i
\(703\) 33.2292 25.6290i 1.25326 0.966617i
\(704\) 3.85429i 0.145264i
\(705\) −1.16341 9.85258i −0.0438165 0.371070i
\(706\) 2.70748i 0.101897i
\(707\) 42.9870 42.9870i 1.61669 1.61669i
\(708\) −1.46558 −0.0550800
\(709\) −31.0687 + 31.0687i −1.16681 + 1.16681i −0.183856 + 0.982953i \(0.558858\pi\)
−0.982953 + 0.183856i \(0.941142\pi\)
\(710\) −21.6224 + 2.55320i −0.811472 + 0.0958199i
\(711\) 4.33967 + 4.33967i 0.162750 + 0.162750i
\(712\) −4.92656 4.92656i −0.184631 0.184631i
\(713\) 49.0592 49.0592i 1.83728 1.83728i
\(714\) −11.9161 −0.445950
\(715\) 1.08314 + 9.17278i 0.0405070 + 0.343043i
\(716\) −6.14221 6.14221i −0.229545 0.229545i
\(717\) −23.3896 −0.873502
\(718\) 20.4504i 0.763202i
\(719\) 4.08903i 0.152495i −0.997089 0.0762475i \(-0.975706\pi\)
0.997089 0.0762475i \(-0.0242939\pi\)
\(720\) −0.262217 2.22064i −0.00977224 0.0827584i
\(721\) 20.9750 20.9750i 0.781151 0.781151i
\(722\) 28.5953i 1.06421i
\(723\) 13.2781i 0.493818i
\(724\) −11.3224 −0.420793
\(725\) −1.44807 0.888464i −0.0537799 0.0329967i
\(726\) −2.72628 2.72628i −0.101182 0.101182i
\(727\) 4.10966 0.152419 0.0762094 0.997092i \(-0.475718\pi\)
0.0762094 + 0.997092i \(0.475718\pi\)
\(728\) 2.88856 + 2.88856i 0.107057 + 0.107057i
\(729\) 1.00000i 0.0370370i
\(730\) 9.36269 + 7.38509i 0.346529 + 0.273334i
\(731\) 28.0751i 1.03840i
\(732\) −13.2029 −0.487995
\(733\) 18.6280 + 18.6280i 0.688042 + 0.688042i 0.961799 0.273757i \(-0.0882663\pi\)
−0.273757 + 0.961799i \(0.588266\pi\)
\(734\) 0.867537 + 0.867537i 0.0320214 + 0.0320214i
\(735\) −10.4263 + 13.2183i −0.384579 + 0.487563i
\(736\) 6.72404 0.247851
\(737\) −0.313506 0.313506i −0.0115482 0.0115482i
\(738\) 9.24361 0.340262
\(739\) 14.2761 0.525154 0.262577 0.964911i \(-0.415428\pi\)
0.262577 + 0.964911i \(0.415428\pi\)
\(740\) −13.6007 0.147965i −0.499970 0.00543932i
\(741\) −7.39368 −0.271614
\(742\) −36.3925 −1.33601
\(743\) 16.7892 + 16.7892i 0.615937 + 0.615937i 0.944487 0.328550i \(-0.106560\pi\)
−0.328550 + 0.944487i \(0.606560\pi\)
\(744\) −10.3182 −0.378285
\(745\) −4.73454 40.0955i −0.173460 1.46899i
\(746\) −20.6119 20.6119i −0.754657 0.754657i
\(747\) −5.06491 5.06491i −0.185315 0.185315i
\(748\) −12.0493 −0.440566
\(749\) 33.8358i 1.23633i
\(750\) −10.1495 4.68905i −0.370608 0.171220i
\(751\) 29.4388i 1.07424i 0.843506 + 0.537119i \(0.180487\pi\)
−0.843506 + 0.537119i \(0.819513\pi\)
\(752\) −3.13731 3.13731i −0.114406 0.114406i
\(753\) 7.90020 0.287899
\(754\) 0.257491 + 0.257491i 0.00937728 + 0.00937728i
\(755\) 0.138260 + 1.17089i 0.00503180 + 0.0426129i
\(756\) −3.81169 −0.138630
\(757\) 9.76824i 0.355033i −0.984118 0.177516i \(-0.943194\pi\)
0.984118 0.177516i \(-0.0568063\pi\)
\(758\) 9.54382i 0.346647i
\(759\) 18.3256 18.3256i 0.665179 0.665179i
\(760\) 9.55375 12.1121i 0.346551 0.439351i
\(761\) 15.7759i 0.571875i −0.958248 0.285938i \(-0.907695\pi\)
0.958248 0.285938i \(-0.0923051\pi\)
\(762\) 6.69672i 0.242597i
\(763\) 43.2120 1.56438
\(764\) 11.4031 + 11.4031i 0.412550 + 0.412550i
\(765\) −6.94217 + 0.819742i −0.250995 + 0.0296379i
\(766\) −5.14097 −0.185751
\(767\) 1.11064 1.11064i 0.0401030 0.0401030i
\(768\) −0.707107 0.707107i −0.0255155 0.0255155i
\(769\) −28.2128 28.2128i −1.01738 1.01738i −0.999846 0.0175316i \(-0.994419\pi\)
−0.0175316 0.999846i \(-0.505581\pi\)
\(770\) −20.3448 + 25.7928i −0.733176 + 0.929509i
\(771\) −7.14568 + 7.14568i −0.257345 + 0.257345i
\(772\) 25.7217 0.925744
\(773\) 26.4095 26.4095i 0.949882 0.949882i −0.0489203 0.998803i \(-0.515578\pi\)
0.998803 + 0.0489203i \(0.0155780\pi\)
\(774\) 8.98058i 0.322800i
\(775\) −26.9803 + 43.9740i −0.969161 + 1.57959i
\(776\) 2.13394i 0.0766039i
\(777\) −2.96923 + 22.9947i −0.106521 + 0.824931i
\(778\) 13.7109 13.7109i 0.491558 0.491558i
\(779\) 45.0929 + 45.0929i 1.61562 + 1.61562i