Properties

Label 1110.2.o.a.253.6
Level $1110$
Weight $2$
Character 1110.253
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 253.6
Character \(\chi\) \(=\) 1110.253
Dual form 1110.2.o.a.487.6

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(1.69741 - 1.45560i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-0.764053 + 0.764053i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(1.69741 - 1.45560i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-0.764053 + 0.764053i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +(-1.69741 + 1.45560i) q^{10} +4.86540i q^{11} +(-0.707107 + 0.707107i) q^{12} -4.63243 q^{13} +(0.764053 - 0.764053i) q^{14} +(-0.170986 + 2.22952i) q^{15} +1.00000 q^{16} -5.18001i q^{17} +1.00000i q^{18} +(-1.84375 - 1.84375i) q^{19} +(1.69741 - 1.45560i) q^{20} -1.08053i q^{21} -4.86540i q^{22} -4.72007 q^{23} +(0.707107 - 0.707107i) q^{24} +(0.762435 - 4.94153i) q^{25} +4.63243 q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.764053 + 0.764053i) q^{28} +(-6.46705 + 6.46705i) q^{29} +(0.170986 - 2.22952i) q^{30} +(1.27858 + 1.27858i) q^{31} -1.00000 q^{32} +(-3.44036 - 3.44036i) q^{33} +5.18001i q^{34} +(-0.184756 + 2.40907i) q^{35} -1.00000i q^{36} +(0.720368 - 6.03996i) q^{37} +(1.84375 + 1.84375i) q^{38} +(3.27562 - 3.27562i) q^{39} +(-1.69741 + 1.45560i) q^{40} +3.55371i q^{41} +1.08053i q^{42} +7.49989 q^{43} +4.86540i q^{44} +(-1.45560 - 1.69741i) q^{45} +4.72007 q^{46} +(-8.00838 + 8.00838i) q^{47} +(-0.707107 + 0.707107i) q^{48} +5.83245i q^{49} +(-0.762435 + 4.94153i) q^{50} +(3.66282 + 3.66282i) q^{51} -4.63243 q^{52} +(-5.64274 - 5.64274i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(7.08210 + 8.25861i) q^{55} +(0.764053 - 0.764053i) q^{56} +2.60746 q^{57} +(6.46705 - 6.46705i) q^{58} +(-0.790336 - 0.790336i) q^{59} +(-0.170986 + 2.22952i) q^{60} +(-5.24494 - 5.24494i) q^{61} +(-1.27858 - 1.27858i) q^{62} +(0.764053 + 0.764053i) q^{63} +1.00000 q^{64} +(-7.86316 + 6.74298i) q^{65} +(3.44036 + 3.44036i) q^{66} +(-0.777747 - 0.777747i) q^{67} -5.18001i q^{68} +(3.33760 - 3.33760i) q^{69} +(0.184756 - 2.40907i) q^{70} +0.599197 q^{71} +1.00000i q^{72} +(-1.07198 + 1.07198i) q^{73} +(-0.720368 + 6.03996i) q^{74} +(2.95506 + 4.03331i) q^{75} +(-1.84375 - 1.84375i) q^{76} +(-3.71743 - 3.71743i) q^{77} +(-3.27562 + 3.27562i) q^{78} +(-9.56948 - 9.56948i) q^{79} +(1.69741 - 1.45560i) q^{80} -1.00000 q^{81} -3.55371i q^{82} +(-11.2549 - 11.2549i) q^{83} -1.08053i q^{84} +(-7.54004 - 8.79263i) q^{85} -7.49989 q^{86} -9.14579i q^{87} -4.86540i q^{88} +(-1.70075 + 1.70075i) q^{89} +(1.45560 + 1.69741i) q^{90} +(3.53942 - 3.53942i) q^{91} -4.72007 q^{92} -1.80819 q^{93} +(8.00838 - 8.00838i) q^{94} +(-5.81338 - 0.445840i) q^{95} +(0.707107 - 0.707107i) q^{96} -6.03720i q^{97} -5.83245i q^{98} +4.86540 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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

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

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
\(5\) 1.69741 1.45560i 0.759107 0.650966i
\(6\) 0.707107 0.707107i 0.288675 0.288675i
\(7\) −0.764053 + 0.764053i −0.288785 + 0.288785i −0.836600 0.547815i \(-0.815460\pi\)
0.547815 + 0.836600i \(0.315460\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000i 0.333333i
\(10\) −1.69741 + 1.45560i −0.536770 + 0.460302i
\(11\) 4.86540i 1.46697i 0.679703 + 0.733487i \(0.262109\pi\)
−0.679703 + 0.733487i \(0.737891\pi\)
\(12\) −0.707107 + 0.707107i −0.204124 + 0.204124i
\(13\) −4.63243 −1.28481 −0.642403 0.766367i \(-0.722062\pi\)
−0.642403 + 0.766367i \(0.722062\pi\)
\(14\) 0.764053 0.764053i 0.204202 0.204202i
\(15\) −0.170986 + 2.22952i −0.0441484 + 0.575660i
\(16\) 1.00000 0.250000
\(17\) 5.18001i 1.25634i −0.778077 0.628169i \(-0.783805\pi\)
0.778077 0.628169i \(-0.216195\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −1.84375 1.84375i −0.422986 0.422986i 0.463245 0.886230i \(-0.346685\pi\)
−0.886230 + 0.463245i \(0.846685\pi\)
\(20\) 1.69741 1.45560i 0.379554 0.325483i
\(21\) 1.08053i 0.235792i
\(22\) 4.86540i 1.03731i
\(23\) −4.72007 −0.984203 −0.492102 0.870538i \(-0.663771\pi\)
−0.492102 + 0.870538i \(0.663771\pi\)
\(24\) 0.707107 0.707107i 0.144338 0.144338i
\(25\) 0.762435 4.94153i 0.152487 0.988305i
\(26\) 4.63243 0.908494
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) −0.764053 + 0.764053i −0.144392 + 0.144392i
\(29\) −6.46705 + 6.46705i −1.20090 + 1.20090i −0.227008 + 0.973893i \(0.572894\pi\)
−0.973893 + 0.227008i \(0.927106\pi\)
\(30\) 0.170986 2.22952i 0.0312177 0.407053i
\(31\) 1.27858 + 1.27858i 0.229640 + 0.229640i 0.812542 0.582902i \(-0.198083\pi\)
−0.582902 + 0.812542i \(0.698083\pi\)
\(32\) −1.00000 −0.176777
\(33\) −3.44036 3.44036i −0.598890 0.598890i
\(34\) 5.18001i 0.888364i
\(35\) −0.184756 + 2.40907i −0.0312295 + 0.407208i
\(36\) 1.00000i 0.166667i
\(37\) 0.720368 6.03996i 0.118428 0.992963i
\(38\) 1.84375 + 1.84375i 0.299096 + 0.299096i
\(39\) 3.27562 3.27562i 0.524519 0.524519i
\(40\) −1.69741 + 1.45560i −0.268385 + 0.230151i
\(41\) 3.55371i 0.554997i 0.960726 + 0.277498i \(0.0895053\pi\)
−0.960726 + 0.277498i \(0.910495\pi\)
\(42\) 1.08053i 0.166730i
\(43\) 7.49989 1.14372 0.571861 0.820350i \(-0.306221\pi\)
0.571861 + 0.820350i \(0.306221\pi\)
\(44\) 4.86540i 0.733487i
\(45\) −1.45560 1.69741i −0.216989 0.253036i
\(46\) 4.72007 0.695937
\(47\) −8.00838 + 8.00838i −1.16814 + 1.16814i −0.185498 + 0.982645i \(0.559390\pi\)
−0.982645 + 0.185498i \(0.940610\pi\)
\(48\) −0.707107 + 0.707107i −0.102062 + 0.102062i
\(49\) 5.83245i 0.833207i
\(50\) −0.762435 + 4.94153i −0.107825 + 0.698838i
\(51\) 3.66282 + 3.66282i 0.512897 + 0.512897i
\(52\) −4.63243 −0.642403
\(53\) −5.64274 5.64274i −0.775090 0.775090i 0.203902 0.978991i \(-0.434638\pi\)
−0.978991 + 0.203902i \(0.934638\pi\)
\(54\) −0.707107 0.707107i −0.0962250 0.0962250i
\(55\) 7.08210 + 8.25861i 0.954950 + 1.11359i
\(56\) 0.764053 0.764053i 0.102101 0.102101i
\(57\) 2.60746 0.345366
\(58\) 6.46705 6.46705i 0.849165 0.849165i
\(59\) −0.790336 0.790336i −0.102893 0.102893i 0.653786 0.756679i \(-0.273180\pi\)
−0.756679 + 0.653786i \(0.773180\pi\)
\(60\) −0.170986 + 2.22952i −0.0220742 + 0.287830i
\(61\) −5.24494 5.24494i −0.671545 0.671545i 0.286527 0.958072i \(-0.407499\pi\)
−0.958072 + 0.286527i \(0.907499\pi\)
\(62\) −1.27858 1.27858i −0.162380 0.162380i
\(63\) 0.764053 + 0.764053i 0.0962616 + 0.0962616i
\(64\) 1.00000 0.125000
\(65\) −7.86316 + 6.74298i −0.975304 + 0.836364i
\(66\) 3.44036 + 3.44036i 0.423479 + 0.423479i
\(67\) −0.777747 0.777747i −0.0950169 0.0950169i 0.658001 0.753017i \(-0.271402\pi\)
−0.753017 + 0.658001i \(0.771402\pi\)
\(68\) 5.18001i 0.628169i
\(69\) 3.33760 3.33760i 0.401799 0.401799i
\(70\) 0.184756 2.40907i 0.0220826 0.287939i
\(71\) 0.599197 0.0711117 0.0355558 0.999368i \(-0.488680\pi\)
0.0355558 + 0.999368i \(0.488680\pi\)
\(72\) 1.00000i 0.117851i
\(73\) −1.07198 + 1.07198i −0.125466 + 0.125466i −0.767051 0.641586i \(-0.778277\pi\)
0.641586 + 0.767051i \(0.278277\pi\)
\(74\) −0.720368 + 6.03996i −0.0837411 + 0.702131i
\(75\) 2.95506 + 4.03331i 0.341221 + 0.465727i
\(76\) −1.84375 1.84375i −0.211493 0.211493i
\(77\) −3.71743 3.71743i −0.423640 0.423640i
\(78\) −3.27562 + 3.27562i −0.370891 + 0.370891i
\(79\) −9.56948 9.56948i −1.07665 1.07665i −0.996807 0.0798429i \(-0.974558\pi\)
−0.0798429 0.996807i \(-0.525442\pi\)
\(80\) 1.69741 1.45560i 0.189777 0.162741i
\(81\) −1.00000 −0.111111
\(82\) 3.55371i 0.392442i
\(83\) −11.2549 11.2549i −1.23538 1.23538i −0.961868 0.273513i \(-0.911814\pi\)
−0.273513 0.961868i \(-0.588186\pi\)
\(84\) 1.08053i 0.117896i
\(85\) −7.54004 8.79263i −0.817833 0.953694i
\(86\) −7.49989 −0.808734
\(87\) 9.14579i 0.980531i
\(88\) 4.86540i 0.518654i
\(89\) −1.70075 + 1.70075i −0.180279 + 0.180279i −0.791477 0.611199i \(-0.790688\pi\)
0.611199 + 0.791477i \(0.290688\pi\)
\(90\) 1.45560 + 1.69741i 0.153434 + 0.178923i
\(91\) 3.53942 3.53942i 0.371032 0.371032i
\(92\) −4.72007 −0.492102
\(93\) −1.80819 −0.187500
\(94\) 8.00838 8.00838i 0.826002 0.826002i
\(95\) −5.81338 0.445840i −0.596441 0.0457422i
\(96\) 0.707107 0.707107i 0.0721688 0.0721688i
\(97\) 6.03720i 0.612985i −0.951873 0.306492i \(-0.900845\pi\)
0.951873 0.306492i \(-0.0991554\pi\)
\(98\) 5.83245i 0.589166i
\(99\) 4.86540 0.488991
\(100\) 0.762435 4.94153i 0.0762435 0.494153i
\(101\) 5.63152i 0.560357i 0.959948 + 0.280178i \(0.0903936\pi\)
−0.959948 + 0.280178i \(0.909606\pi\)
\(102\) −3.66282 3.66282i −0.362673 0.362673i
\(103\) 15.8811i 1.56481i 0.622767 + 0.782407i \(0.286008\pi\)
−0.622767 + 0.782407i \(0.713992\pi\)
\(104\) 4.63243 0.454247
\(105\) −1.57283 1.83411i −0.153492 0.178991i
\(106\) 5.64274 + 5.64274i 0.548071 + 0.548071i
\(107\) −7.21271 + 7.21271i −0.697279 + 0.697279i −0.963823 0.266544i \(-0.914118\pi\)
0.266544 + 0.963823i \(0.414118\pi\)
\(108\) 0.707107 + 0.707107i 0.0680414 + 0.0680414i
\(109\) −7.52179 7.52179i −0.720457 0.720457i 0.248241 0.968698i \(-0.420147\pi\)
−0.968698 + 0.248241i \(0.920147\pi\)
\(110\) −7.08210 8.25861i −0.675252 0.787427i
\(111\) 3.76152 + 4.78027i 0.357027 + 0.453723i
\(112\) −0.764053 + 0.764053i −0.0721962 + 0.0721962i
\(113\) 4.80474i 0.451991i 0.974128 + 0.225996i \(0.0725635\pi\)
−0.974128 + 0.225996i \(0.927436\pi\)
\(114\) −2.60746 −0.244211
\(115\) −8.01192 + 6.87056i −0.747115 + 0.640683i
\(116\) −6.46705 + 6.46705i −0.600450 + 0.600450i
\(117\) 4.63243i 0.428268i
\(118\) 0.790336 + 0.790336i 0.0727563 + 0.0727563i
\(119\) 3.95780 + 3.95780i 0.362811 + 0.362811i
\(120\) 0.170986 2.22952i 0.0156088 0.203526i
\(121\) −12.6722 −1.15201
\(122\) 5.24494 + 5.24494i 0.474854 + 0.474854i
\(123\) −2.51285 2.51285i −0.226576 0.226576i
\(124\) 1.27858 + 1.27858i 0.114820 + 0.114820i
\(125\) −5.89874 9.49763i −0.527599 0.849493i
\(126\) −0.764053 0.764053i −0.0680672 0.0680672i
\(127\) 4.71555 4.71555i 0.418437 0.418437i −0.466227 0.884665i \(-0.654387\pi\)
0.884665 + 0.466227i \(0.154387\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −5.30322 + 5.30322i −0.466923 + 0.466923i
\(130\) 7.86316 6.74298i 0.689644 0.591399i
\(131\) −1.70970 1.70970i −0.149377 0.149377i 0.628463 0.777840i \(-0.283684\pi\)
−0.777840 + 0.628463i \(0.783684\pi\)
\(132\) −3.44036 3.44036i −0.299445 0.299445i
\(133\) 2.81745 0.244304
\(134\) 0.777747 + 0.777747i 0.0671871 + 0.0671871i
\(135\) 2.22952 + 0.170986i 0.191887 + 0.0147161i
\(136\) 5.18001i 0.444182i
\(137\) −3.74548 + 3.74548i −0.319998 + 0.319998i −0.848766 0.528768i \(-0.822654\pi\)
0.528768 + 0.848766i \(0.322654\pi\)
\(138\) −3.33760 + 3.33760i −0.284115 + 0.284115i
\(139\) 11.5750 0.981782 0.490891 0.871221i \(-0.336671\pi\)
0.490891 + 0.871221i \(0.336671\pi\)
\(140\) −0.184756 + 2.40907i −0.0156148 + 0.203604i
\(141\) 11.3256i 0.953785i
\(142\) −0.599197 −0.0502835
\(143\) 22.5386i 1.88478i
\(144\) 1.00000i 0.0833333i
\(145\) −1.56380 + 20.3907i −0.129867 + 1.69336i
\(146\) 1.07198 1.07198i 0.0887178 0.0887178i
\(147\) −4.12416 4.12416i −0.340155 0.340155i
\(148\) 0.720368 6.03996i 0.0592139 0.496481i
\(149\) 4.52394i 0.370616i 0.982681 + 0.185308i \(0.0593282\pi\)
−0.982681 + 0.185308i \(0.940672\pi\)
\(150\) −2.95506 4.03331i −0.241280 0.329318i
\(151\) 6.86682i 0.558814i 0.960173 + 0.279407i \(0.0901378\pi\)
−0.960173 + 0.279407i \(0.909862\pi\)
\(152\) 1.84375 + 1.84375i 0.149548 + 0.149548i
\(153\) −5.18001 −0.418779
\(154\) 3.71743 + 3.71743i 0.299559 + 0.299559i
\(155\) 4.03139 + 0.309175i 0.323809 + 0.0248336i
\(156\) 3.27562 3.27562i 0.262260 0.262260i
\(157\) −9.23383 + 9.23383i −0.736940 + 0.736940i −0.971985 0.235044i \(-0.924476\pi\)
0.235044 + 0.971985i \(0.424476\pi\)
\(158\) 9.56948 + 9.56948i 0.761307 + 0.761307i
\(159\) 7.98004 0.632858
\(160\) −1.69741 + 1.45560i −0.134192 + 0.115076i
\(161\) 3.60638 3.60638i 0.284223 0.284223i
\(162\) 1.00000 0.0785674
\(163\) 23.9624i 1.87688i −0.345446 0.938439i \(-0.612272\pi\)
0.345446 0.938439i \(-0.387728\pi\)
\(164\) 3.55371i 0.277498i
\(165\) −10.8475 0.831917i −0.844478 0.0647646i
\(166\) 11.2549 + 11.2549i 0.873547 + 0.873547i
\(167\) 15.1621i 1.17328i 0.809849 + 0.586638i \(0.199549\pi\)
−0.809849 + 0.586638i \(0.800451\pi\)
\(168\) 1.08053i 0.0833650i
\(169\) 8.45941 0.650724
\(170\) 7.54004 + 8.79263i 0.578295 + 0.674364i
\(171\) −1.84375 + 1.84375i −0.140995 + 0.140995i
\(172\) 7.49989 0.571861
\(173\) −4.54073 + 4.54073i −0.345225 + 0.345225i −0.858327 0.513102i \(-0.828496\pi\)
0.513102 + 0.858327i \(0.328496\pi\)
\(174\) 9.14579i 0.693340i
\(175\) 3.19305 + 4.35813i 0.241372 + 0.329444i
\(176\) 4.86540i 0.366744i
\(177\) 1.11770 0.0840117
\(178\) 1.70075 1.70075i 0.127476 0.127476i
\(179\) 3.90880 3.90880i 0.292157 0.292157i −0.545775 0.837932i \(-0.683765\pi\)
0.837932 + 0.545775i \(0.183765\pi\)
\(180\) −1.45560 1.69741i −0.108494 0.126518i
\(181\) 16.2780 1.20993 0.604967 0.796251i \(-0.293186\pi\)
0.604967 + 0.796251i \(0.293186\pi\)
\(182\) −3.53942 + 3.53942i −0.262359 + 0.262359i
\(183\) 7.41746 0.548314
\(184\) 4.72007 0.347968
\(185\) −7.56902 11.3009i −0.556485 0.830857i
\(186\) 1.80819 0.132583
\(187\) 25.2028 1.84301
\(188\) −8.00838 + 8.00838i −0.584071 + 0.584071i
\(189\) −1.08053 −0.0785973
\(190\) 5.81338 + 0.445840i 0.421747 + 0.0323446i
\(191\) 6.72993 6.72993i 0.486961 0.486961i −0.420385 0.907346i \(-0.638105\pi\)
0.907346 + 0.420385i \(0.138105\pi\)
\(192\) −0.707107 + 0.707107i −0.0510310 + 0.0510310i
\(193\) −11.3986 −0.820490 −0.410245 0.911975i \(-0.634557\pi\)
−0.410245 + 0.911975i \(0.634557\pi\)
\(194\) 6.03720i 0.433446i
\(195\) 0.792082 10.3281i 0.0567221 0.739611i
\(196\) 5.83245i 0.416603i
\(197\) −10.5213 + 10.5213i −0.749610 + 0.749610i −0.974406 0.224796i \(-0.927828\pi\)
0.224796 + 0.974406i \(0.427828\pi\)
\(198\) −4.86540 −0.345769
\(199\) −5.10780 + 5.10780i −0.362082 + 0.362082i −0.864579 0.502497i \(-0.832415\pi\)
0.502497 + 0.864579i \(0.332415\pi\)
\(200\) −0.762435 + 4.94153i −0.0539123 + 0.349419i
\(201\) 1.09990 0.0775810
\(202\) 5.63152i 0.396232i
\(203\) 9.88233i 0.693604i
\(204\) 3.66282 + 3.66282i 0.256449 + 0.256449i
\(205\) 5.17280 + 6.03212i 0.361284 + 0.421302i
\(206\) 15.8811i 1.10649i
\(207\) 4.72007i 0.328068i
\(208\) −4.63243 −0.321201
\(209\) 8.97060 8.97060i 0.620509 0.620509i
\(210\) 1.57283 + 1.83411i 0.108536 + 0.126566i
\(211\) −3.92055 −0.269902 −0.134951 0.990852i \(-0.543088\pi\)
−0.134951 + 0.990852i \(0.543088\pi\)
\(212\) −5.64274 5.64274i −0.387545 0.387545i
\(213\) −0.423697 + 0.423697i −0.0290312 + 0.0290312i
\(214\) 7.21271 7.21271i 0.493051 0.493051i
\(215\) 12.7304 10.9169i 0.868208 0.744525i
\(216\) −0.707107 0.707107i −0.0481125 0.0481125i
\(217\) −1.95381 −0.132633
\(218\) 7.52179 + 7.52179i 0.509440 + 0.509440i
\(219\) 1.51601i 0.102442i
\(220\) 7.08210 + 8.25861i 0.477475 + 0.556795i
\(221\) 23.9960i 1.61415i
\(222\) −3.76152 4.78027i −0.252456 0.320831i
\(223\) 13.0140 + 13.0140i 0.871480 + 0.871480i 0.992634 0.121153i \(-0.0386593\pi\)
−0.121153 + 0.992634i \(0.538659\pi\)
\(224\) 0.764053 0.764053i 0.0510504 0.0510504i
\(225\) −4.94153 0.762435i −0.329435 0.0508290i
\(226\) 4.80474i 0.319606i
\(227\) 10.4498i 0.693577i 0.937943 + 0.346788i \(0.112728\pi\)
−0.937943 + 0.346788i \(0.887272\pi\)
\(228\) 2.60746 0.172683
\(229\) 12.6086i 0.833197i −0.909091 0.416598i \(-0.863222\pi\)
0.909091 0.416598i \(-0.136778\pi\)
\(230\) 8.01192 6.87056i 0.528290 0.453031i
\(231\) 5.25723 0.345901
\(232\) 6.46705 6.46705i 0.424583 0.424583i
\(233\) 16.9357 16.9357i 1.10950 1.10950i 0.116278 0.993217i \(-0.462904\pi\)
0.993217 0.116278i \(-0.0370965\pi\)
\(234\) 4.63243i 0.302831i
\(235\) −1.93652 + 25.2506i −0.126324 + 1.64717i
\(236\) −0.790336 0.790336i −0.0514465 0.0514465i
\(237\) 13.5333 0.879081
\(238\) −3.95780 3.95780i −0.256546 0.256546i
\(239\) −2.61342 2.61342i −0.169048 0.169048i 0.617513 0.786561i \(-0.288140\pi\)
−0.786561 + 0.617513i \(0.788140\pi\)
\(240\) −0.170986 + 2.22952i −0.0110371 + 0.143915i
\(241\) 14.3186 14.3186i 0.922340 0.922340i −0.0748547 0.997194i \(-0.523849\pi\)
0.997194 + 0.0748547i \(0.0238493\pi\)
\(242\) 12.6722 0.814597
\(243\) 0.707107 0.707107i 0.0453609 0.0453609i
\(244\) −5.24494 5.24494i −0.335773 0.335773i
\(245\) 8.48973 + 9.90008i 0.542389 + 0.632493i
\(246\) 2.51285 + 2.51285i 0.160214 + 0.160214i
\(247\) 8.54105 + 8.54105i 0.543454 + 0.543454i
\(248\) −1.27858 1.27858i −0.0811901 0.0811901i
\(249\) 15.9168 1.00868
\(250\) 5.89874 + 9.49763i 0.373069 + 0.600683i
\(251\) 5.64176 + 5.64176i 0.356105 + 0.356105i 0.862375 0.506270i \(-0.168976\pi\)
−0.506270 + 0.862375i \(0.668976\pi\)
\(252\) 0.764053 + 0.764053i 0.0481308 + 0.0481308i
\(253\) 22.9651i 1.44380i
\(254\) −4.71555 + 4.71555i −0.295880 + 0.295880i
\(255\) 11.5489 + 0.885710i 0.723223 + 0.0554653i
\(256\) 1.00000 0.0625000
\(257\) 23.3521i 1.45666i 0.685226 + 0.728331i \(0.259704\pi\)
−0.685226 + 0.728331i \(0.740296\pi\)
\(258\) 5.30322 5.30322i 0.330164 0.330164i
\(259\) 4.06445 + 5.16525i 0.252552 + 0.320953i
\(260\) −7.86316 + 6.74298i −0.487652 + 0.418182i
\(261\) 6.46705 + 6.46705i 0.400300 + 0.400300i
\(262\) 1.70970 + 1.70970i 0.105625 + 0.105625i
\(263\) −9.20714 + 9.20714i −0.567737 + 0.567737i −0.931494 0.363757i \(-0.881494\pi\)
0.363757 + 0.931494i \(0.381494\pi\)
\(264\) 3.44036 + 3.44036i 0.211740 + 0.211740i
\(265\) −17.7917 1.36448i −1.09293 0.0838191i
\(266\) −2.81745 −0.172749
\(267\) 2.40522i 0.147197i
\(268\) −0.777747 0.777747i −0.0475084 0.0475084i
\(269\) 19.2094i 1.17122i −0.810593 0.585610i \(-0.800855\pi\)
0.810593 0.585610i \(-0.199145\pi\)
\(270\) −2.22952 0.170986i −0.135684 0.0104059i
\(271\) 14.4883 0.880103 0.440052 0.897972i \(-0.354960\pi\)
0.440052 + 0.897972i \(0.354960\pi\)
\(272\) 5.18001i 0.314084i
\(273\) 5.00550i 0.302947i
\(274\) 3.74548 3.74548i 0.226272 0.226272i
\(275\) 24.0425 + 3.70955i 1.44982 + 0.223694i
\(276\) 3.33760 3.33760i 0.200900 0.200900i
\(277\) −29.6974 −1.78434 −0.892172 0.451696i \(-0.850819\pi\)
−0.892172 + 0.451696i \(0.850819\pi\)
\(278\) −11.5750 −0.694225
\(279\) 1.27858 1.27858i 0.0765467 0.0765467i
\(280\) 0.184756 2.40907i 0.0110413 0.143970i
\(281\) 3.49186 3.49186i 0.208307 0.208307i −0.595240 0.803548i \(-0.702943\pi\)
0.803548 + 0.595240i \(0.202943\pi\)
\(282\) 11.3256i 0.674428i
\(283\) 14.7733i 0.878182i −0.898442 0.439091i \(-0.855300\pi\)
0.898442 0.439091i \(-0.144700\pi\)
\(284\) 0.599197 0.0355558
\(285\) 4.42594 3.79543i 0.262170 0.224822i
\(286\) 22.5386i 1.33274i
\(287\) −2.71522 2.71522i −0.160275 0.160275i
\(288\) 1.00000i 0.0589256i
\(289\) −9.83251 −0.578383
\(290\) 1.56380 20.3907i 0.0918297 1.19738i
\(291\) 4.26895 + 4.26895i 0.250250 + 0.250250i
\(292\) −1.07198 + 1.07198i −0.0627329 + 0.0627329i
\(293\) 23.9405 + 23.9405i 1.39862 + 1.39862i 0.804034 + 0.594583i \(0.202683\pi\)
0.594583 + 0.804034i \(0.297317\pi\)
\(294\) 4.12416 + 4.12416i 0.240526 + 0.240526i
\(295\) −2.49194 0.191112i −0.145087 0.0111270i
\(296\) −0.720368 + 6.03996i −0.0418705 + 0.351065i
\(297\) −3.44036 + 3.44036i −0.199630 + 0.199630i
\(298\) 4.52394i 0.262065i
\(299\) 21.8654 1.26451
\(300\) 2.95506 + 4.03331i 0.170611 + 0.232863i
\(301\) −5.73031 + 5.73031i −0.330290 + 0.330290i
\(302\) 6.86682i 0.395141i
\(303\) −3.98208 3.98208i −0.228765 0.228765i
\(304\) −1.84375 1.84375i −0.105746 0.105746i
\(305\) −16.5374 1.26828i −0.946928 0.0726217i
\(306\) 5.18001 0.296121
\(307\) −23.3965 23.3965i −1.33531 1.33531i −0.900543 0.434767i \(-0.856831\pi\)
−0.434767 0.900543i \(-0.643169\pi\)
\(308\) −3.71743 3.71743i −0.211820 0.211820i
\(309\) −11.2297 11.2297i −0.638833 0.638833i
\(310\) −4.03139 0.309175i −0.228968 0.0175600i
\(311\) 18.7483 + 18.7483i 1.06312 + 1.06312i 0.997869 + 0.0652489i \(0.0207841\pi\)
0.0652489 + 0.997869i \(0.479216\pi\)
\(312\) −3.27562 + 3.27562i −0.185446 + 0.185446i
\(313\) 26.7290 1.51081 0.755407 0.655255i \(-0.227439\pi\)
0.755407 + 0.655255i \(0.227439\pi\)
\(314\) 9.23383 9.23383i 0.521095 0.521095i
\(315\) 2.40907 + 0.184756i 0.135736 + 0.0104098i
\(316\) −9.56948 9.56948i −0.538325 0.538325i
\(317\) 18.5839 + 18.5839i 1.04378 + 1.04378i 0.998997 + 0.0447783i \(0.0142581\pi\)
0.0447783 + 0.998997i \(0.485742\pi\)
\(318\) −7.98004 −0.447498
\(319\) −31.4648 31.4648i −1.76169 1.76169i
\(320\) 1.69741 1.45560i 0.0948884 0.0813707i
\(321\) 10.2003i 0.569326i
\(322\) −3.60638 + 3.60638i −0.200976 + 0.200976i
\(323\) −9.55065 + 9.55065i −0.531413 + 0.531413i
\(324\) −1.00000 −0.0555556
\(325\) −3.53193 + 22.8913i −0.195916 + 1.26978i
\(326\) 23.9624i 1.32715i
\(327\) 10.6374 0.588251
\(328\) 3.55371i 0.196221i
\(329\) 12.2377i 0.674684i
\(330\) 10.8475 + 0.831917i 0.597136 + 0.0457955i
\(331\) −4.72692 + 4.72692i −0.259815 + 0.259815i −0.824979 0.565164i \(-0.808813\pi\)
0.565164 + 0.824979i \(0.308813\pi\)
\(332\) −11.2549 11.2549i −0.617691 0.617691i
\(333\) −6.03996 0.720368i −0.330988 0.0394759i
\(334\) 15.1621i 0.829631i
\(335\) −2.45225 0.188068i −0.133981 0.0102752i
\(336\) 1.08053i 0.0589480i
\(337\) 13.9016 + 13.9016i 0.757270 + 0.757270i 0.975825 0.218555i \(-0.0701343\pi\)
−0.218555 + 0.975825i \(0.570134\pi\)
\(338\) −8.45941 −0.460131
\(339\) −3.39746 3.39746i −0.184525 0.184525i
\(340\) −7.54004 8.79263i −0.408916 0.476847i
\(341\) −6.22082 + 6.22082i −0.336876 + 0.336876i
\(342\) 1.84375 1.84375i 0.0996987 0.0996987i
\(343\) −9.80467 9.80467i −0.529402 0.529402i
\(344\) −7.49989 −0.404367
\(345\) 0.807067 10.5235i 0.0434510 0.566566i
\(346\) 4.54073 4.54073i 0.244111 0.244111i
\(347\) 0.651438 0.0349710 0.0174855 0.999847i \(-0.494434\pi\)
0.0174855 + 0.999847i \(0.494434\pi\)
\(348\) 9.14579i 0.490266i
\(349\) 25.5234i 1.36624i 0.730308 + 0.683118i \(0.239376\pi\)
−0.730308 + 0.683118i \(0.760624\pi\)
\(350\) −3.19305 4.35813i −0.170676 0.232952i
\(351\) −3.27562 3.27562i −0.174840 0.174840i
\(352\) 4.86540i 0.259327i
\(353\) 34.3501i 1.82827i −0.405408 0.914136i \(-0.632870\pi\)
0.405408 0.914136i \(-0.367130\pi\)
\(354\) −1.11770 −0.0594053
\(355\) 1.01709 0.872194i 0.0539814 0.0462913i
\(356\) −1.70075 + 1.70075i −0.0901394 + 0.0901394i
\(357\) −5.59718 −0.296234
\(358\) −3.90880 + 3.90880i −0.206586 + 0.206586i
\(359\) 17.0122i 0.897868i −0.893565 0.448934i \(-0.851804\pi\)
0.893565 0.448934i \(-0.148196\pi\)
\(360\) 1.45560 + 1.69741i 0.0767171 + 0.0894616i
\(361\) 12.2012i 0.642166i
\(362\) −16.2780 −0.855552
\(363\) 8.96057 8.96057i 0.470308 0.470308i
\(364\) 3.53942 3.53942i 0.185516 0.185516i
\(365\) −0.259217 + 3.37998i −0.0135680 + 0.176916i
\(366\) −7.41746 −0.387717
\(367\) −10.2747 + 10.2747i −0.536335 + 0.536335i −0.922451 0.386115i \(-0.873817\pi\)
0.386115 + 0.922451i \(0.373817\pi\)
\(368\) −4.72007 −0.246051
\(369\) 3.55371 0.184999
\(370\) 7.56902 + 11.3009i 0.393495 + 0.587505i
\(371\) 8.62270 0.447668
\(372\) −1.80819 −0.0937502
\(373\) 6.19992 6.19992i 0.321020 0.321020i −0.528139 0.849158i \(-0.677110\pi\)
0.849158 + 0.528139i \(0.177110\pi\)
\(374\) −25.2028 −1.30321
\(375\) 10.8869 + 2.54480i 0.562196 + 0.131413i
\(376\) 8.00838 8.00838i 0.413001 0.413001i
\(377\) 29.9582 29.9582i 1.54292 1.54292i
\(378\) 1.08053 0.0555767
\(379\) 31.3961i 1.61271i 0.591433 + 0.806354i \(0.298562\pi\)
−0.591433 + 0.806354i \(0.701438\pi\)
\(380\) −5.81338 0.445840i −0.298220 0.0228711i
\(381\) 6.66879i 0.341653i
\(382\) −6.72993 + 6.72993i −0.344333 + 0.344333i
\(383\) 17.9026 0.914778 0.457389 0.889267i \(-0.348785\pi\)
0.457389 + 0.889267i \(0.348785\pi\)
\(384\) 0.707107 0.707107i 0.0360844 0.0360844i
\(385\) −11.7211 0.898915i −0.597363 0.0458129i
\(386\) 11.3986 0.580174
\(387\) 7.49989i 0.381241i
\(388\) 6.03720i 0.306492i
\(389\) 7.54313 + 7.54313i 0.382452 + 0.382452i 0.871985 0.489533i \(-0.162833\pi\)
−0.489533 + 0.871985i \(0.662833\pi\)
\(390\) −0.792082 + 10.3281i −0.0401086 + 0.522984i
\(391\) 24.4500i 1.23649i
\(392\) 5.83245i 0.294583i
\(393\) 2.41788 0.121966
\(394\) 10.5213 10.5213i 0.530054 0.530054i
\(395\) −30.1727 2.31401i −1.51816 0.116430i
\(396\) 4.86540 0.244496
\(397\) 11.1198 + 11.1198i 0.558087 + 0.558087i 0.928762 0.370676i \(-0.120874\pi\)
−0.370676 + 0.928762i \(0.620874\pi\)
\(398\) 5.10780 5.10780i 0.256031 0.256031i
\(399\) −1.99224 + 1.99224i −0.0997366 + 0.0997366i
\(400\) 0.762435 4.94153i 0.0381217 0.247076i
\(401\) −22.3136 22.3136i −1.11429 1.11429i −0.992564 0.121725i \(-0.961157\pi\)
−0.121725 0.992564i \(-0.538843\pi\)
\(402\) −1.09990 −0.0548580
\(403\) −5.92294 5.92294i −0.295043 0.295043i
\(404\) 5.63152i 0.280178i
\(405\) −1.69741 + 1.45560i −0.0843452 + 0.0723295i
\(406\) 9.88233i 0.490452i
\(407\) 29.3868 + 3.50488i 1.45665 + 0.173731i
\(408\) −3.66282 3.66282i −0.181337 0.181337i
\(409\) 16.7999 16.7999i 0.830701 0.830701i −0.156912 0.987613i \(-0.550154\pi\)
0.987613 + 0.156912i \(0.0501538\pi\)
\(410\) −5.17280 6.03212i −0.255466 0.297905i
\(411\) 5.29690i 0.261277i
\(412\) 15.8811i 0.782407i
\(413\) 1.20772 0.0594279
\(414\) 4.72007i 0.231979i
\(415\) −35.4868 2.72155i −1.74198 0.133596i
\(416\) 4.63243 0.227124
\(417\) −8.18479 + 8.18479i −0.400811 + 0.400811i
\(418\) −8.97060 + 8.97060i −0.438766 + 0.438766i
\(419\) 3.07947i 0.150442i 0.997167 + 0.0752210i \(0.0239662\pi\)
−0.997167 + 0.0752210i \(0.976034\pi\)
\(420\) −1.57283 1.83411i −0.0767462 0.0894956i
\(421\) −2.58223 2.58223i −0.125850 0.125850i 0.641376 0.767227i \(-0.278364\pi\)
−0.767227 + 0.641376i \(0.778364\pi\)
\(422\) 3.92055 0.190849
\(423\) 8.00838 + 8.00838i 0.389381 + 0.389381i
\(424\) 5.64274 + 5.64274i 0.274036 + 0.274036i
\(425\) −25.5972 3.94942i −1.24164 0.191575i
\(426\) 0.423697 0.423697i 0.0205282 0.0205282i
\(427\) 8.01482 0.387864
\(428\) −7.21271 + 7.21271i −0.348639 + 0.348639i
\(429\) 15.9372 + 15.9372i 0.769457 + 0.769457i
\(430\) −12.7304 + 10.9169i −0.613916 + 0.526458i
\(431\) −9.94058 9.94058i −0.478821 0.478821i 0.425934 0.904754i \(-0.359946\pi\)
−0.904754 + 0.425934i \(0.859946\pi\)
\(432\) 0.707107 + 0.707107i 0.0340207 + 0.0340207i
\(433\) 13.7642 + 13.7642i 0.661465 + 0.661465i 0.955725 0.294260i \(-0.0950732\pi\)
−0.294260 + 0.955725i \(0.595073\pi\)
\(434\) 1.95381 0.0937859
\(435\) −13.3126 15.5242i −0.638292 0.744328i
\(436\) −7.52179 7.52179i −0.360228 0.360228i
\(437\) 8.70264 + 8.70264i 0.416304 + 0.416304i
\(438\) 1.51601i 0.0724377i
\(439\) −21.9903 + 21.9903i −1.04954 + 1.04954i −0.0508336 + 0.998707i \(0.516188\pi\)
−0.998707 + 0.0508336i \(0.983812\pi\)
\(440\) −7.08210 8.25861i −0.337626 0.393714i
\(441\) 5.83245 0.277736
\(442\) 23.9960i 1.14138i
\(443\) 17.2453 17.2453i 0.819348 0.819348i −0.166665 0.986014i \(-0.553300\pi\)
0.986014 + 0.166665i \(0.0533000\pi\)
\(444\) 3.76152 + 4.78027i 0.178514 + 0.226862i
\(445\) −0.411259 + 5.36248i −0.0194956 + 0.254206i
\(446\) −13.0140 13.0140i −0.616230 0.616230i
\(447\) −3.19891 3.19891i −0.151303 0.151303i
\(448\) −0.764053 + 0.764053i −0.0360981 + 0.0360981i
\(449\) −0.574002 0.574002i −0.0270888 0.0270888i 0.693433 0.720521i \(-0.256098\pi\)
−0.720521 + 0.693433i \(0.756098\pi\)
\(450\) 4.94153 + 0.762435i 0.232946 + 0.0359415i
\(451\) −17.2902 −0.814166
\(452\) 4.80474i 0.225996i
\(453\) −4.85557 4.85557i −0.228135 0.228135i
\(454\) 10.4498i 0.490433i
\(455\) 0.855871 11.1599i 0.0401239 0.523182i
\(456\) −2.60746 −0.122105
\(457\) 12.9457i 0.605574i −0.953058 0.302787i \(-0.902083\pi\)
0.953058 0.302787i \(-0.0979171\pi\)
\(458\) 12.6086i 0.589159i
\(459\) 3.66282 3.66282i 0.170966 0.170966i
\(460\) −8.01192 + 6.87056i −0.373558 + 0.320341i
\(461\) 21.0318 21.0318i 0.979548 0.979548i −0.0202466 0.999795i \(-0.506445\pi\)
0.999795 + 0.0202466i \(0.00644514\pi\)
\(462\) −5.25723 −0.244589
\(463\) 14.6765 0.682076 0.341038 0.940050i \(-0.389222\pi\)
0.341038 + 0.940050i \(0.389222\pi\)
\(464\) −6.46705 + 6.46705i −0.300225 + 0.300225i
\(465\) −3.06925 + 2.63201i −0.142333 + 0.122056i
\(466\) −16.9357 + 16.9357i −0.784531 + 0.784531i
\(467\) 12.6925i 0.587341i 0.955907 + 0.293670i \(0.0948768\pi\)
−0.955907 + 0.293670i \(0.905123\pi\)
\(468\) 4.63243i 0.214134i
\(469\) 1.18848 0.0548789
\(470\) 1.93652 25.2506i 0.0893248 1.16472i
\(471\) 13.0586i 0.601709i
\(472\) 0.790336 + 0.790336i 0.0363782 + 0.0363782i
\(473\) 36.4900i 1.67781i
\(474\) −13.5333 −0.621604
\(475\) −10.5167 + 7.70521i −0.482539 + 0.353539i
\(476\) 3.95780 + 3.95780i 0.181406 + 0.181406i
\(477\) −5.64274 + 5.64274i −0.258363 + 0.258363i
\(478\) 2.61342 + 2.61342i 0.119535 + 0.119535i
\(479\) 17.3000 + 17.3000i 0.790459 + 0.790459i 0.981569 0.191110i \(-0.0612086\pi\)
−0.191110 + 0.981569i \(0.561209\pi\)
\(480\) 0.170986 2.22952i 0.00780442 0.101763i
\(481\) −3.33706 + 27.9797i −0.152157 + 1.27576i
\(482\) −14.3186 + 14.3186i −0.652193 + 0.652193i
\(483\) 5.10020i 0.232067i
\(484\) −12.6722 −0.576007
\(485\) −8.78777 10.2476i −0.399032 0.465321i
\(486\) −0.707107 + 0.707107i −0.0320750 + 0.0320750i
\(487\) 25.7666i 1.16760i 0.811899 + 0.583798i \(0.198434\pi\)
−0.811899 + 0.583798i \(0.801566\pi\)
\(488\) 5.24494 + 5.24494i 0.237427 + 0.237427i
\(489\) 16.9440 + 16.9440i 0.766232 + 0.766232i
\(490\) −8.48973 9.90008i −0.383527 0.447240i
\(491\) −4.97935 −0.224715 −0.112358 0.993668i \(-0.535840\pi\)
−0.112358 + 0.993668i \(0.535840\pi\)
\(492\) −2.51285 2.51285i −0.113288 0.113288i
\(493\) 33.4994 + 33.4994i 1.50874 + 1.50874i
\(494\) −8.54105 8.54105i −0.384280 0.384280i
\(495\) 8.25861 7.08210i 0.371197 0.318317i
\(496\) 1.27858 + 1.27858i 0.0574101 + 0.0574101i
\(497\) −0.457819 + 0.457819i −0.0205360 + 0.0205360i
\(498\) −15.9168 −0.713248
\(499\) 19.1310 19.1310i 0.856423 0.856423i −0.134492 0.990915i \(-0.542940\pi\)
0.990915 + 0.134492i \(0.0429403\pi\)
\(500\) −5.89874 9.49763i −0.263800 0.424747i
\(501\) −10.7212 10.7212i −0.478988 0.478988i
\(502\) −5.64176 5.64176i −0.251804 0.251804i
\(503\) 12.4777 0.556353 0.278177 0.960530i \(-0.410270\pi\)
0.278177 + 0.960530i \(0.410270\pi\)
\(504\) −0.764053 0.764053i −0.0340336 0.0340336i
\(505\) 8.19726 + 9.55902i 0.364773 + 0.425371i
\(506\) 22.9651i 1.02092i
\(507\) −5.98171 + 5.98171i −0.265657 + 0.265657i
\(508\) 4.71555 4.71555i 0.209219 0.209219i
\(509\) −31.1191 −1.37933 −0.689665 0.724129i \(-0.742242\pi\)
−0.689665 + 0.724129i \(0.742242\pi\)
\(510\) −11.5489 0.885710i −0.511396 0.0392199i
\(511\) 1.63810i 0.0724653i
\(512\) −1.00000 −0.0441942
\(513\) 2.60746i 0.115122i
\(514\) 23.3521i 1.03002i
\(515\) 23.1166 + 26.9569i 1.01864 + 1.18786i
\(516\) −5.30322 + 5.30322i −0.233461 + 0.233461i
\(517\) −38.9640 38.9640i −1.71364 1.71364i
\(518\) −4.06445 5.16525i −0.178582 0.226948i
\(519\) 6.42156i 0.281875i
\(520\) 7.86316 6.74298i 0.344822 0.295699i
\(521\) 11.3207i 0.495967i 0.968764 + 0.247983i \(0.0797679\pi\)
−0.968764 + 0.247983i \(0.920232\pi\)
\(522\) −6.46705 6.46705i −0.283055 0.283055i
\(523\) 2.09242 0.0914952 0.0457476 0.998953i \(-0.485433\pi\)
0.0457476 + 0.998953i \(0.485433\pi\)
\(524\) −1.70970 1.70970i −0.0746884 0.0746884i
\(525\) −5.33949 0.823837i −0.233034 0.0359552i
\(526\) 9.20714 9.20714i 0.401450 0.401450i
\(527\) 6.62307 6.62307i 0.288506 0.288506i
\(528\) −3.44036 3.44036i −0.149722 0.149722i
\(529\) −0.720919 −0.0313443
\(530\) 17.7917 + 1.36448i 0.772821 + 0.0592691i
\(531\) −0.790336 + 0.790336i −0.0342977 + 0.0342977i
\(532\) 2.81745 0.122152
\(533\) 16.4623i 0.713062i
\(534\) 2.40522i 0.104084i
\(535\) −1.74411 + 22.7418i −0.0754045 + 0.983214i
\(536\) 0.777747 + 0.777747i 0.0335935 + 0.0335935i
\(537\) 5.52788i 0.238545i
\(538\) 19.2094i 0.828178i
\(539\) −28.3772 −1.22229
\(540\) 2.22952 + 0.170986i 0.0959433 + 0.00735807i
\(541\) −6.92733 + 6.92733i −0.297829 + 0.297829i −0.840163 0.542334i \(-0.817541\pi\)
0.542334 + 0.840163i \(0.317541\pi\)
\(542\) −14.4883 −0.622327
\(543\) −11.5103 + 11.5103i −0.493953 + 0.493953i
\(544\) 5.18001i 0.222091i
\(545\) −23.7163 1.81885i −1.01590 0.0779110i
\(546\) 5.00550i 0.214216i
\(547\) 4.89932 0.209480 0.104740 0.994500i \(-0.466599\pi\)
0.104740 + 0.994500i \(0.466599\pi\)
\(548\) −3.74548 + 3.74548i −0.159999 + 0.159999i
\(549\) −5.24494 + 5.24494i −0.223848 + 0.223848i
\(550\) −24.0425 3.70955i −1.02518 0.158176i
\(551\) 23.8473 1.01593
\(552\) −3.33760 + 3.33760i −0.142057 + 0.142057i
\(553\) 14.6232 0.621841
\(554\) 29.6974 1.26172
\(555\) 13.3430 + 2.63883i 0.566380 + 0.112012i
\(556\) 11.5750 0.490891
\(557\) −31.8866 −1.35108 −0.675539 0.737324i \(-0.736089\pi\)
−0.675539 + 0.737324i \(0.736089\pi\)
\(558\) −1.27858 + 1.27858i −0.0541267 + 0.0541267i
\(559\) −34.7427 −1.46946
\(560\) −0.184756 + 2.40907i −0.00780738 + 0.101802i
\(561\) −17.8211 + 17.8211i −0.752407 + 0.752407i
\(562\) −3.49186 + 3.49186i −0.147295 + 0.147295i
\(563\) −43.4484 −1.83113 −0.915565 0.402170i \(-0.868256\pi\)
−0.915565 + 0.402170i \(0.868256\pi\)
\(564\) 11.3256i 0.476892i
\(565\) 6.99379 + 8.15563i 0.294231 + 0.343110i
\(566\) 14.7733i 0.620969i
\(567\) 0.764053 0.764053i 0.0320872 0.0320872i
\(568\) −0.599197 −0.0251418
\(569\) −19.9460 + 19.9460i −0.836180 + 0.836180i −0.988354 0.152174i \(-0.951373\pi\)
0.152174 + 0.988354i \(0.451373\pi\)
\(570\) −4.42594 + 3.79543i −0.185382 + 0.158973i
\(571\) 7.76992 0.325161 0.162581 0.986695i \(-0.448018\pi\)
0.162581 + 0.986695i \(0.448018\pi\)
\(572\) 22.5386i 0.942388i
\(573\) 9.51756i 0.397602i
\(574\) 2.71522 + 2.71522i 0.113331 + 0.113331i
\(575\) −3.59875 + 23.3244i −0.150078 + 0.972693i
\(576\) 1.00000i 0.0416667i
\(577\) 10.9161i 0.454442i −0.973843 0.227221i \(-0.927036\pi\)
0.973843 0.227221i \(-0.0729640\pi\)
\(578\) 9.83251 0.408978
\(579\) 8.06003 8.06003i 0.334964 0.334964i
\(580\) −1.56380 + 20.3907i −0.0649334 + 0.846679i
\(581\) 17.1986 0.713519
\(582\) −4.26895 4.26895i −0.176954 0.176954i
\(583\) 27.4542 27.4542i 1.13704 1.13704i
\(584\) 1.07198 1.07198i 0.0443589 0.0443589i
\(585\) 6.74298 + 7.86316i 0.278788 + 0.325101i
\(586\) −23.9405 23.9405i −0.988972 0.988972i
\(587\) 22.1879 0.915793 0.457897 0.889005i \(-0.348603\pi\)
0.457897 + 0.889005i \(0.348603\pi\)
\(588\) −4.12416 4.12416i −0.170078 0.170078i
\(589\) 4.71478i 0.194269i
\(590\) 2.49194 + 0.191112i 0.102592 + 0.00786795i
\(591\) 14.8793i 0.612054i
\(592\) 0.720368 6.03996i 0.0296069 0.248241i
\(593\) −24.0835 24.0835i −0.988991 0.988991i 0.0109487 0.999940i \(-0.496515\pi\)
−0.999940 + 0.0109487i \(0.996515\pi\)
\(594\) 3.44036 3.44036i 0.141160 0.141160i
\(595\) 12.4790 + 0.957040i 0.511590 + 0.0392348i
\(596\) 4.52394i 0.185308i
\(597\) 7.22351i 0.295639i
\(598\) −21.8654 −0.894143
\(599\) 43.9186i 1.79446i −0.441560 0.897232i \(-0.645575\pi\)
0.441560 0.897232i \(-0.354425\pi\)
\(600\) −2.95506 4.03331i −0.120640 0.164659i
\(601\) −32.0175 −1.30602 −0.653010 0.757349i \(-0.726494\pi\)
−0.653010 + 0.757349i \(0.726494\pi\)
\(602\) 5.73031 5.73031i 0.233550 0.233550i
\(603\) −0.777747 + 0.777747i −0.0316723 + 0.0316723i
\(604\) 6.86682i 0.279407i
\(605\) −21.5099 + 18.4456i −0.874502 + 0.749922i
\(606\) 3.98208 + 3.98208i 0.161761 + 0.161761i
\(607\) −44.7940 −1.81813 −0.909067 0.416651i \(-0.863204\pi\)
−0.909067 + 0.416651i \(0.863204\pi\)
\(608\) 1.84375 + 1.84375i 0.0747740 + 0.0747740i
\(609\) 6.98787 + 6.98787i 0.283163 + 0.283163i
\(610\) 16.5374 + 1.26828i 0.669579 + 0.0513513i
\(611\) 37.0983 37.0983i 1.50084 1.50084i
\(612\) −5.18001 −0.209390
\(613\) 30.3408 30.3408i 1.22545 1.22545i 0.259787 0.965666i \(-0.416348\pi\)
0.965666 0.259787i \(-0.0836524\pi\)
\(614\) 23.3965 + 23.3965i 0.944207 + 0.944207i
\(615\) −7.92308 0.607636i −0.319489 0.0245022i
\(616\) 3.71743 + 3.71743i 0.149779 + 0.149779i
\(617\) −24.4682 24.4682i −0.985053 0.985053i 0.0148372 0.999890i \(-0.495277\pi\)
−0.999890 + 0.0148372i \(0.995277\pi\)
\(618\) 11.2297 + 11.2297i 0.451723 + 0.451723i
\(619\) 18.8165 0.756299 0.378150 0.925745i \(-0.376561\pi\)
0.378150 + 0.925745i \(0.376561\pi\)
\(620\) 4.03139 + 0.309175i 0.161905 + 0.0124168i
\(621\) −3.33760 3.33760i −0.133933 0.133933i
\(622\) −18.7483 18.7483i −0.751738 0.751738i
\(623\) 2.59892i 0.104124i
\(624\) 3.27562 3.27562i 0.131130 0.131130i
\(625\) −23.8374 7.53518i −0.953495 0.301407i
\(626\) −26.7290 −1.06831
\(627\) 12.6863i 0.506644i
\(628\) −9.23383 + 9.23383i −0.368470 + 0.368470i
\(629\) −31.2870 3.73151i −1.24750 0.148785i
\(630\) −2.40907 0.184756i −0.0959798 0.00736087i
\(631\) −5.74618 5.74618i −0.228752 0.228752i 0.583419 0.812171i \(-0.301714\pi\)
−0.812171 + 0.583419i \(0.801714\pi\)
\(632\) 9.56948 + 9.56948i 0.380653 + 0.380653i
\(633\) 2.77225 2.77225i 0.110187 0.110187i
\(634\) −18.5839 18.5839i −0.738061 0.738061i
\(635\) 1.14027 14.8682i 0.0452503 0.590027i
\(636\) 7.98004 0.316429
\(637\) 27.0184i 1.07051i
\(638\) 31.4648 + 31.4648i 1.24570 + 1.24570i
\(639\) 0.599197i 0.0237039i
\(640\) −1.69741 + 1.45560i −0.0670962 + 0.0575378i
\(641\) 9.84764 0.388958 0.194479 0.980907i \(-0.437698\pi\)
0.194479 + 0.980907i \(0.437698\pi\)
\(642\) 10.2003i 0.402574i
\(643\) 45.3302i 1.78765i 0.448417 + 0.893825i \(0.351988\pi\)
−0.448417 + 0.893825i \(0.648012\pi\)
\(644\) 3.60638 3.60638i 0.142111 0.142111i
\(645\) −1.28238 + 16.7212i −0.0504936 + 0.658395i
\(646\) 9.55065 9.55065i 0.375765 0.375765i
\(647\) 48.2835 1.89822 0.949111 0.314942i \(-0.101985\pi\)
0.949111 + 0.314942i \(0.101985\pi\)
\(648\) 1.00000 0.0392837
\(649\) 3.84530 3.84530i 0.150941 0.150941i
\(650\) 3.53193 22.8913i 0.138534 0.897870i
\(651\) 1.38155 1.38155i 0.0541473 0.0541473i
\(652\) 23.9624i 0.938439i
\(653\) 23.4562i 0.917912i −0.888459 0.458956i \(-0.848224\pi\)
0.888459 0.458956i \(-0.151776\pi\)
\(654\) −10.6374 −0.415956
\(655\) −5.39071 0.413423i −0.210632 0.0161538i
\(656\) 3.55371i 0.138749i
\(657\) 1.07198 + 1.07198i 0.0418219 + 0.0418219i
\(658\) 12.2377i 0.477074i
\(659\) −42.8689 −1.66993 −0.834967 0.550300i \(-0.814513\pi\)
−0.834967 + 0.550300i \(0.814513\pi\)
\(660\) −10.8475 0.831917i −0.422239 0.0323823i
\(661\) −11.0362 11.0362i −0.429259 0.429259i 0.459117 0.888376i \(-0.348166\pi\)
−0.888376 + 0.459117i \(0.848166\pi\)
\(662\) 4.72692 4.72692i 0.183717 0.183717i
\(663\) −16.9678 16.9678i −0.658973 0.658973i
\(664\) 11.2549 + 11.2549i 0.436773 + 0.436773i
\(665\) 4.78238 4.10109i 0.185453 0.159033i
\(666\) 6.03996 + 0.720368i 0.234044 + 0.0279137i
\(667\) 30.5249 30.5249i 1.18193 1.18193i
\(668\) 15.1621i 0.586638i
\(669\) −18.4045 −0.711561
\(670\) 2.45225 + 0.188068i 0.0947387 + 0.00726569i
\(671\) 25.5187 25.5187i 0.985140 0.985140i
\(672\) 1.08053i 0.0416825i
\(673\) 17.9122 + 17.9122i 0.690463 + 0.690463i 0.962334 0.271870i \(-0.0876422\pi\)
−0.271870 + 0.962334i \(0.587642\pi\)
\(674\) −13.9016 13.9016i −0.535470 0.535470i
\(675\) 4.03331 2.95506i 0.155242 0.113740i
\(676\) 8.45941 0.325362
\(677\) −11.1599 11.1599i −0.428909 0.428909i 0.459347 0.888257i \(-0.348083\pi\)
−0.888257 + 0.459347i \(0.848083\pi\)
\(678\) 3.39746 + 3.39746i 0.130479 + 0.130479i
\(679\) 4.61274 + 4.61274i 0.177021 + 0.177021i
\(680\) 7.54004 + 8.79263i 0.289147 + 0.337182i
\(681\) −7.38911 7.38911i −0.283151 0.283151i
\(682\) 6.22082 6.22082i 0.238208 0.238208i
\(683\) −28.1871 −1.07855 −0.539274 0.842130i \(-0.681301\pi\)
−0.539274 + 0.842130i \(0.681301\pi\)
\(684\) −1.84375 + 1.84375i −0.0704976 + 0.0704976i
\(685\) −0.905697 + 11.8096i −0.0346049 + 0.451220i
\(686\) 9.80467 + 9.80467i 0.374344 + 0.374344i
\(687\) 8.91559 + 8.91559i 0.340151 + 0.340151i
\(688\) 7.49989 0.285931
\(689\) 26.1396 + 26.1396i 0.995839 + 0.995839i
\(690\) −0.807067 + 10.5235i −0.0307245 + 0.400623i
\(691\) 13.7497i 0.523063i −0.965195 0.261531i \(-0.915773\pi\)
0.965195 0.261531i \(-0.0842275\pi\)
\(692\) −4.54073 + 4.54073i −0.172612 + 0.172612i
\(693\) −3.71743 + 3.71743i −0.141213 + 0.141213i
\(694\) −0.651438 −0.0247282
\(695\) 19.6476 16.8487i 0.745278 0.639107i
\(696\) 9.14579i 0.346670i
\(697\) 18.4083 0.697263
\(698\) 25.5234i 0.966074i
\(699\) 23.9507i 0.905899i
\(700\) 3.19305 + 4.35813i 0.120686 + 0.164722i
\(701\) 7.09322 7.09322i 0.267907 0.267907i −0.560349 0.828257i \(-0.689333\pi\)
0.828257 + 0.560349i \(0.189333\pi\)
\(702\) 3.27562 + 3.27562i 0.123630 + 0.123630i
\(703\) −12.4644 + 9.80800i −0.470102 + 0.369916i
\(704\) 4.86540i 0.183372i
\(705\) −16.4855 19.2242i −0.620881 0.724025i
\(706\) 34.3501i 1.29278i
\(707\) −4.30278 4.30278i −0.161823 0.161823i
\(708\) 1.11770 0.0420059
\(709\) −30.9530 30.9530i −1.16247 1.16247i −0.983934 0.178531i \(-0.942865\pi\)
−0.178531 0.983934i \(-0.557135\pi\)
\(710\) −1.01709 + 0.872194i −0.0381706 + 0.0327329i
\(711\) −9.56948 + 9.56948i −0.358883 + 0.358883i
\(712\) 1.70075 1.70075i 0.0637382 0.0637382i
\(713\) −6.03500 6.03500i −0.226013 0.226013i
\(714\) 5.59718 0.209469
\(715\) −32.8073 38.2574i −1.22692 1.43075i
\(716\) 3.90880 3.90880i 0.146079 0.146079i
\(717\) 3.69593 0.138027
\(718\) 17.0122i 0.634889i
\(719\) 16.8010i 0.626571i 0.949659 + 0.313285i \(0.101430\pi\)
−0.949659 + 0.313285i \(0.898570\pi\)
\(720\) −1.45560 1.69741i −0.0542472 0.0632589i
\(721\) −12.1340 12.1340i −0.451895 0.451895i
\(722\) 12.2012i 0.454080i
\(723\) 20.2495i 0.753087i
\(724\) 16.2780 0.604967
\(725\) 27.0264 + 36.8878i 1.00374 + 1.36998i
\(726\) −8.96057 + 8.96057i −0.332558 + 0.332558i
\(727\) 21.2760 0.789085 0.394542 0.918878i \(-0.370903\pi\)
0.394542 + 0.918878i \(0.370903\pi\)
\(728\) −3.53942 + 3.53942i −0.131180 + 0.131180i
\(729\) 1.00000i 0.0370370i
\(730\) 0.259217 3.37998i 0.00959404 0.125098i
\(731\) 38.8495i 1.43690i
\(732\) 7.41746 0.274157
\(733\) −36.8126 + 36.8126i −1.35970 + 1.35970i −0.485428 + 0.874277i \(0.661336\pi\)
−0.874277 + 0.485428i \(0.838664\pi\)
\(734\) 10.2747 10.2747i 0.379246 0.379246i
\(735\) −13.0036 0.997268i −0.479644 0.0367848i
\(736\) 4.72007 0.173984
\(737\) 3.78405 3.78405i 0.139387 0.139387i
\(738\) −3.55371 −0.130814
\(739\) −9.01878 −0.331761 −0.165881 0.986146i \(-0.553047\pi\)
−0.165881 + 0.986146i \(0.553047\pi\)
\(740\) −7.56902 11.3009i −0.278243 0.415429i
\(741\) −12.0789 −0.443728
\(742\) −8.62270 −0.316549
\(743\) −35.3819 + 35.3819i −1.29803 + 1.29803i −0.368345 + 0.929689i \(0.620076\pi\)
−0.929689 + 0.368345i \(0.879924\pi\)
\(744\) 1.80819 0.0662914
\(745\) 6.58507 + 7.67901i 0.241258 + 0.281337i
\(746\) −6.19992 + 6.19992i −0.226995 + 0.226995i
\(747\) −11.2549 + 11.2549i −0.411794 + 0.411794i
\(748\) 25.2028 0.921507
\(749\) 11.0218i 0.402727i
\(750\) −10.8869 2.54480i −0.397532 0.0929228i
\(751\) 20.1864i 0.736613i 0.929704 + 0.368307i \(0.120062\pi\)
−0.929704 + 0.368307i \(0.879938\pi\)
\(752\) −8.00838 + 8.00838i −0.292036 + 0.292036i
\(753\) −7.97866 −0.290759
\(754\) −29.9582 + 29.9582i −1.09101 + 1.09101i
\(755\) 9.99537 + 11.6558i 0.363769 + 0.424199i
\(756\) −1.08053 −0.0392986
\(757\) 23.3149i 0.847394i 0.905804 + 0.423697i \(0.139268\pi\)
−0.905804 + 0.423697i \(0.860732\pi\)
\(758\) 31.3961i 1.14036i
\(759\) 16.2387 + 16.2387i 0.589429 + 0.589429i
\(760\) 5.81338 + 0.445840i 0.210874 + 0.0161723i
\(761\) 14.6952i 0.532702i 0.963876 + 0.266351i \(0.0858180\pi\)
−0.963876 + 0.266351i \(0.914182\pi\)
\(762\) 6.66879i 0.241585i
\(763\) 11.4941 0.416114
\(764\) 6.72993 6.72993i 0.243480 0.243480i
\(765\) −8.79263 + 7.54004i −0.317898 + 0.272611i
\(766\) −17.9026 −0.646846
\(767\) 3.66118 + 3.66118i 0.132197 + 0.132197i
\(768\) −0.707107 + 0.707107i −0.0255155 + 0.0255155i
\(769\) 18.5881 18.5881i 0.670304 0.670304i −0.287482 0.957786i \(-0.592818\pi\)
0.957786 + 0.287482i \(0.0928181\pi\)
\(770\) 11.7211 + 0.898915i 0.422400 + 0.0323946i
\(771\) −16.5124 16.5124i −0.594680 0.594680i
\(772\) −11.3986 −0.410245
\(773\) −21.3379 21.3379i −0.767471 0.767471i 0.210190 0.977661i \(-0.432592\pi\)
−0.977661 + 0.210190i \(0.932592\pi\)
\(774\) 7.49989i 0.269578i
\(775\) 7.29299 5.34332i 0.261972 0.191938i
\(776\) 6.03720i 0.216723i
\(777\) −6.52638 0.778382i −0.234133 0.0279243i
\(778\) −7.54313 7.54313i −0.270434 0.270434i
\(779\) 6.55216 6.55216i 0.234756 0.234756i
\(780\) 0.792082