Properties

Label 690.2.e.a.551.12
Level $690$
Weight $2$
Character 690.551
Analytic conductor $5.510$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 2 x^{15} + 3 x^{14} - 12 x^{13} + 15 x^{12} - 4 x^{11} + 45 x^{10} - 66 x^{9} - 32 x^{8} - 198 x^{7} + 405 x^{6} - 108 x^{5} + 1215 x^{4} - 2916 x^{3} + 2187 x^{2} - 4374 x + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 551.12
Root \(-1.62589 - 0.597052i\) of defining polynomial
Character \(\chi\) \(=\) 690.551
Dual form 690.2.e.a.551.4

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(-0.597052 + 1.62589i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(-1.62589 - 0.597052i) q^{6} +3.80421i q^{7} -1.00000i q^{8} +(-2.28706 - 1.94149i) q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(-0.597052 + 1.62589i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(-1.62589 - 0.597052i) q^{6} +3.80421i q^{7} -1.00000i q^{8} +(-2.28706 - 1.94149i) q^{9} -1.00000i q^{10} -3.48413 q^{11} +(0.597052 - 1.62589i) q^{12} +3.19916 q^{13} -3.80421 q^{14} +(0.597052 - 1.62589i) q^{15} +1.00000 q^{16} -4.76053 q^{17} +(1.94149 - 2.28706i) q^{18} -1.88297i q^{19} +1.00000 q^{20} +(-6.18523 - 2.27131i) q^{21} -3.48413i q^{22} +(0.785398 + 4.73108i) q^{23} +(1.62589 + 0.597052i) q^{24} +1.00000 q^{25} +3.19916i q^{26} +(4.52214 - 2.55934i) q^{27} -3.80421i q^{28} -7.50582i q^{29} +(1.62589 + 0.597052i) q^{30} -3.72122 q^{31} +1.00000i q^{32} +(2.08021 - 5.66482i) q^{33} -4.76053i q^{34} -3.80421i q^{35} +(2.28706 + 1.94149i) q^{36} -4.88527i q^{37} +1.88297 q^{38} +(-1.91007 + 5.20149i) q^{39} +1.00000i q^{40} +3.99062i q^{41} +(2.27131 - 6.18523i) q^{42} +6.96125i q^{43} +3.48413 q^{44} +(2.28706 + 1.94149i) q^{45} +(-4.73108 + 0.785398i) q^{46} -10.8399i q^{47} +(-0.597052 + 1.62589i) q^{48} -7.47199 q^{49} +1.00000i q^{50} +(2.84229 - 7.74011i) q^{51} -3.19916 q^{52} -7.07396 q^{53} +(2.55934 + 4.52214i) q^{54} +3.48413 q^{55} +3.80421 q^{56} +(3.06151 + 1.12423i) q^{57} +7.50582 q^{58} +7.35646i q^{59} +(-0.597052 + 1.62589i) q^{60} -3.31936i q^{61} -3.72122i q^{62} +(7.38582 - 8.70044i) q^{63} -1.00000 q^{64} -3.19916 q^{65} +(5.66482 + 2.08021i) q^{66} +3.70440i q^{67} +4.76053 q^{68} +(-8.16116 - 1.54773i) q^{69} +3.80421 q^{70} +9.92565i q^{71} +(-1.94149 + 2.28706i) q^{72} +3.18473 q^{73} +4.88527 q^{74} +(-0.597052 + 1.62589i) q^{75} +1.88297i q^{76} -13.2543i q^{77} +(-5.20149 - 1.91007i) q^{78} -10.1264i q^{79} -1.00000 q^{80} +(1.46126 + 8.88058i) q^{81} -3.99062 q^{82} -12.8088 q^{83} +(6.18523 + 2.27131i) q^{84} +4.76053 q^{85} -6.96125 q^{86} +(12.2037 + 4.48137i) q^{87} +3.48413i q^{88} -11.0510 q^{89} +(-1.94149 + 2.28706i) q^{90} +12.1703i q^{91} +(-0.785398 - 4.73108i) q^{92} +(2.22176 - 6.05031i) q^{93} +10.8399 q^{94} +1.88297i q^{95} +(-1.62589 - 0.597052i) q^{96} -2.98155i q^{97} -7.47199i q^{98} +(7.96840 + 6.76439i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 16q^{4} - 16q^{5} + 2q^{6} + 2q^{9} + O(q^{10}) \) \( 16q - 16q^{4} - 16q^{5} + 2q^{6} + 2q^{9} - 12q^{11} - 12q^{14} + 16q^{16} + 8q^{18} + 16q^{20} - 4q^{21} + 4q^{23} - 2q^{24} + 16q^{25} + 24q^{27} - 2q^{30} + 4q^{31} - 28q^{33} - 2q^{36} - 16q^{38} - 8q^{39} + 12q^{44} - 2q^{45} - 4q^{46} - 4q^{49} - 2q^{51} - 8q^{53} - 26q^{54} + 12q^{55} + 12q^{56} + 28q^{57} - 8q^{58} - 16q^{64} + 10q^{66} + 30q^{69} + 12q^{70} - 8q^{72} - 16q^{73} - 24q^{74} - 12q^{78} - 16q^{80} + 22q^{81} - 16q^{82} - 40q^{83} + 4q^{84} - 40q^{86} + 20q^{87} + 80q^{89} - 8q^{90} - 4q^{92} - 4q^{93} - 24q^{94} + 2q^{96} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −0.597052 + 1.62589i −0.344708 + 0.938710i
\(4\) −1.00000 −0.500000
\(5\) −1.00000 −0.447214
\(6\) −1.62589 0.597052i −0.663768 0.243746i
\(7\) 3.80421i 1.43786i 0.695085 + 0.718928i \(0.255367\pi\)
−0.695085 + 0.718928i \(0.744633\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −2.28706 1.94149i −0.762352 0.647162i
\(10\) 1.00000i 0.316228i
\(11\) −3.48413 −1.05050 −0.525252 0.850947i \(-0.676029\pi\)
−0.525252 + 0.850947i \(0.676029\pi\)
\(12\) 0.597052 1.62589i 0.172354 0.469355i
\(13\) 3.19916 0.887287 0.443644 0.896203i \(-0.353686\pi\)
0.443644 + 0.896203i \(0.353686\pi\)
\(14\) −3.80421 −1.01672
\(15\) 0.597052 1.62589i 0.154158 0.419804i
\(16\) 1.00000 0.250000
\(17\) −4.76053 −1.15460 −0.577299 0.816533i \(-0.695893\pi\)
−0.577299 + 0.816533i \(0.695893\pi\)
\(18\) 1.94149 2.28706i 0.457613 0.539064i
\(19\) 1.88297i 0.431984i −0.976395 0.215992i \(-0.930702\pi\)
0.976395 0.215992i \(-0.0692985\pi\)
\(20\) 1.00000 0.223607
\(21\) −6.18523 2.27131i −1.34973 0.495641i
\(22\) 3.48413i 0.742818i
\(23\) 0.785398 + 4.73108i 0.163767 + 0.986499i
\(24\) 1.62589 + 0.597052i 0.331884 + 0.121873i
\(25\) 1.00000 0.200000
\(26\) 3.19916i 0.627407i
\(27\) 4.52214 2.55934i 0.870287 0.492545i
\(28\) 3.80421i 0.718928i
\(29\) 7.50582i 1.39380i −0.717170 0.696898i \(-0.754563\pi\)
0.717170 0.696898i \(-0.245437\pi\)
\(30\) 1.62589 + 0.597052i 0.296846 + 0.109006i
\(31\) −3.72122 −0.668351 −0.334176 0.942511i \(-0.608458\pi\)
−0.334176 + 0.942511i \(0.608458\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 2.08021 5.66482i 0.362117 0.986118i
\(34\) 4.76053i 0.816424i
\(35\) 3.80421i 0.643028i
\(36\) 2.28706 + 1.94149i 0.381176 + 0.323581i
\(37\) 4.88527i 0.803133i −0.915830 0.401567i \(-0.868466\pi\)
0.915830 0.401567i \(-0.131534\pi\)
\(38\) 1.88297 0.305459
\(39\) −1.91007 + 5.20149i −0.305855 + 0.832905i
\(40\) 1.00000i 0.158114i
\(41\) 3.99062i 0.623231i 0.950208 + 0.311615i \(0.100870\pi\)
−0.950208 + 0.311615i \(0.899130\pi\)
\(42\) 2.27131 6.18523i 0.350471 0.954402i
\(43\) 6.96125i 1.06158i 0.847503 + 0.530791i \(0.178105\pi\)
−0.847503 + 0.530791i \(0.821895\pi\)
\(44\) 3.48413 0.525252
\(45\) 2.28706 + 1.94149i 0.340934 + 0.289420i
\(46\) −4.73108 + 0.785398i −0.697560 + 0.115801i
\(47\) 10.8399i 1.58116i −0.612357 0.790581i \(-0.709779\pi\)
0.612357 0.790581i \(-0.290221\pi\)
\(48\) −0.597052 + 1.62589i −0.0861771 + 0.234677i
\(49\) −7.47199 −1.06743
\(50\) 1.00000i 0.141421i
\(51\) 2.84229 7.74011i 0.398000 1.08383i
\(52\) −3.19916 −0.443644
\(53\) −7.07396 −0.971683 −0.485841 0.874047i \(-0.661487\pi\)
−0.485841 + 0.874047i \(0.661487\pi\)
\(54\) 2.55934 + 4.52214i 0.348282 + 0.615386i
\(55\) 3.48413 0.469800
\(56\) 3.80421 0.508359
\(57\) 3.06151 + 1.12423i 0.405507 + 0.148908i
\(58\) 7.50582 0.985562
\(59\) 7.35646i 0.957730i 0.877889 + 0.478865i \(0.158952\pi\)
−0.877889 + 0.478865i \(0.841048\pi\)
\(60\) −0.597052 + 1.62589i −0.0770791 + 0.209902i
\(61\) 3.31936i 0.425000i −0.977161 0.212500i \(-0.931839\pi\)
0.977161 0.212500i \(-0.0681606\pi\)
\(62\) 3.72122i 0.472596i
\(63\) 7.38582 8.70044i 0.930526 1.09615i
\(64\) −1.00000 −0.125000
\(65\) −3.19916 −0.396807
\(66\) 5.66482 + 2.08021i 0.697291 + 0.256056i
\(67\) 3.70440i 0.452564i 0.974062 + 0.226282i \(0.0726571\pi\)
−0.974062 + 0.226282i \(0.927343\pi\)
\(68\) 4.76053 0.577299
\(69\) −8.16116 1.54773i −0.982488 0.186325i
\(70\) 3.80421 0.454690
\(71\) 9.92565i 1.17796i 0.808148 + 0.588979i \(0.200470\pi\)
−0.808148 + 0.588979i \(0.799530\pi\)
\(72\) −1.94149 + 2.28706i −0.228806 + 0.269532i
\(73\) 3.18473 0.372744 0.186372 0.982479i \(-0.440327\pi\)
0.186372 + 0.982479i \(0.440327\pi\)
\(74\) 4.88527 0.567901
\(75\) −0.597052 + 1.62589i −0.0689417 + 0.187742i
\(76\) 1.88297i 0.215992i
\(77\) 13.2543i 1.51047i
\(78\) −5.20149 1.91007i −0.588953 0.216272i
\(79\) 10.1264i 1.13931i −0.821885 0.569653i \(-0.807078\pi\)
0.821885 0.569653i \(-0.192922\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.46126 + 8.88058i 0.162362 + 0.986731i
\(82\) −3.99062 −0.440691
\(83\) −12.8088 −1.40595 −0.702974 0.711215i \(-0.748145\pi\)
−0.702974 + 0.711215i \(0.748145\pi\)
\(84\) 6.18523 + 2.27131i 0.674864 + 0.247820i
\(85\) 4.76053 0.516352
\(86\) −6.96125 −0.750651
\(87\) 12.2037 + 4.48137i 1.30837 + 0.480453i
\(88\) 3.48413i 0.371409i
\(89\) −11.0510 −1.17140 −0.585700 0.810528i \(-0.699180\pi\)
−0.585700 + 0.810528i \(0.699180\pi\)
\(90\) −1.94149 + 2.28706i −0.204651 + 0.241077i
\(91\) 12.1703i 1.27579i
\(92\) −0.785398 4.73108i −0.0818834 0.493250i
\(93\) 2.22176 6.05031i 0.230386 0.627388i
\(94\) 10.8399 1.11805
\(95\) 1.88297i 0.193189i
\(96\) −1.62589 0.597052i −0.165942 0.0609364i
\(97\) 2.98155i 0.302730i −0.988478 0.151365i \(-0.951633\pi\)
0.988478 0.151365i \(-0.0483669\pi\)
\(98\) 7.47199i 0.754785i
\(99\) 7.96840 + 6.76439i 0.800854 + 0.679846i
\(100\) −1.00000 −0.100000
\(101\) 9.15523i 0.910979i 0.890241 + 0.455490i \(0.150536\pi\)
−0.890241 + 0.455490i \(0.849464\pi\)
\(102\) 7.74011 + 2.84229i 0.766385 + 0.281428i
\(103\) 16.0594i 1.58238i 0.611570 + 0.791190i \(0.290538\pi\)
−0.611570 + 0.791190i \(0.709462\pi\)
\(104\) 3.19916i 0.313703i
\(105\) 6.18523 + 2.27131i 0.603617 + 0.221657i
\(106\) 7.07396i 0.687083i
\(107\) 17.6195 1.70334 0.851669 0.524080i \(-0.175591\pi\)
0.851669 + 0.524080i \(0.175591\pi\)
\(108\) −4.52214 + 2.55934i −0.435143 + 0.246273i
\(109\) 12.7316i 1.21947i 0.792607 + 0.609733i \(0.208723\pi\)
−0.792607 + 0.609733i \(0.791277\pi\)
\(110\) 3.48413i 0.332198i
\(111\) 7.94293 + 2.91676i 0.753909 + 0.276847i
\(112\) 3.80421i 0.359464i
\(113\) −9.34208 −0.878829 −0.439414 0.898284i \(-0.644814\pi\)
−0.439414 + 0.898284i \(0.644814\pi\)
\(114\) −1.12423 + 3.06151i −0.105294 + 0.286737i
\(115\) −0.785398 4.73108i −0.0732387 0.441176i
\(116\) 7.50582i 0.696898i
\(117\) −7.31666 6.21113i −0.676426 0.574219i
\(118\) −7.35646 −0.677217
\(119\) 18.1100i 1.66014i
\(120\) −1.62589 0.597052i −0.148423 0.0545032i
\(121\) 1.13914 0.103558
\(122\) 3.31936 0.300520
\(123\) −6.48833 2.38261i −0.585033 0.214833i
\(124\) 3.72122 0.334176
\(125\) −1.00000 −0.0894427
\(126\) 8.70044 + 7.38582i 0.775097 + 0.657981i
\(127\) −15.6846 −1.39178 −0.695892 0.718146i \(-0.744991\pi\)
−0.695892 + 0.718146i \(0.744991\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −11.3183 4.15623i −0.996517 0.365936i
\(130\) 3.19916i 0.280585i
\(131\) 10.5503i 0.921787i 0.887455 + 0.460894i \(0.152471\pi\)
−0.887455 + 0.460894i \(0.847529\pi\)
\(132\) −2.08021 + 5.66482i −0.181059 + 0.493059i
\(133\) 7.16322 0.621130
\(134\) −3.70440 −0.320011
\(135\) −4.52214 + 2.55934i −0.389204 + 0.220273i
\(136\) 4.76053i 0.408212i
\(137\) −16.2614 −1.38930 −0.694652 0.719346i \(-0.744442\pi\)
−0.694652 + 0.719346i \(0.744442\pi\)
\(138\) 1.54773 8.16116i 0.131752 0.694724i
\(139\) −23.3435 −1.97997 −0.989984 0.141180i \(-0.954910\pi\)
−0.989984 + 0.141180i \(0.954910\pi\)
\(140\) 3.80421i 0.321514i
\(141\) 17.6245 + 6.47199i 1.48425 + 0.545040i
\(142\) −9.92565 −0.832942
\(143\) −11.1463 −0.932099
\(144\) −2.28706 1.94149i −0.190588 0.161791i
\(145\) 7.50582i 0.623324i
\(146\) 3.18473i 0.263570i
\(147\) 4.46117 12.1487i 0.367951 1.00200i
\(148\) 4.88527i 0.401567i
\(149\) 7.01303 0.574530 0.287265 0.957851i \(-0.407254\pi\)
0.287265 + 0.957851i \(0.407254\pi\)
\(150\) −1.62589 0.597052i −0.132754 0.0487491i
\(151\) −14.3153 −1.16496 −0.582481 0.812844i \(-0.697918\pi\)
−0.582481 + 0.812844i \(0.697918\pi\)
\(152\) −1.88297 −0.152729
\(153\) 10.8876 + 9.24251i 0.880210 + 0.747212i
\(154\) 13.2543 1.06807
\(155\) 3.72122 0.298896
\(156\) 1.91007 5.20149i 0.152928 0.416453i
\(157\) 16.3884i 1.30794i 0.756521 + 0.653970i \(0.226898\pi\)
−0.756521 + 0.653970i \(0.773102\pi\)
\(158\) 10.1264 0.805611
\(159\) 4.22352 11.5015i 0.334947 0.912128i
\(160\) 1.00000i 0.0790569i
\(161\) −17.9980 + 2.98781i −1.41844 + 0.235473i
\(162\) −8.88058 + 1.46126i −0.697724 + 0.114807i
\(163\) 5.26525 0.412407 0.206203 0.978509i \(-0.433889\pi\)
0.206203 + 0.978509i \(0.433889\pi\)
\(164\) 3.99062i 0.311615i
\(165\) −2.08021 + 5.66482i −0.161944 + 0.441006i
\(166\) 12.8088i 0.994156i
\(167\) 7.87574i 0.609443i 0.952441 + 0.304722i \(0.0985634\pi\)
−0.952441 + 0.304722i \(0.901437\pi\)
\(168\) −2.27131 + 6.18523i −0.175235 + 0.477201i
\(169\) −2.76537 −0.212721
\(170\) 4.76053i 0.365116i
\(171\) −3.65577 + 4.30647i −0.279564 + 0.329324i
\(172\) 6.96125i 0.530791i
\(173\) 2.12595i 0.161633i −0.996729 0.0808165i \(-0.974247\pi\)
0.996729 0.0808165i \(-0.0257528\pi\)
\(174\) −4.48137 + 12.2037i −0.339732 + 0.925157i
\(175\) 3.80421i 0.287571i
\(176\) −3.48413 −0.262626
\(177\) −11.9608 4.39219i −0.899031 0.330138i
\(178\) 11.0510i 0.828305i
\(179\) 12.4614i 0.931409i −0.884940 0.465704i \(-0.845801\pi\)
0.884940 0.465704i \(-0.154199\pi\)
\(180\) −2.28706 1.94149i −0.170467 0.144710i
\(181\) 10.2922i 0.765012i 0.923953 + 0.382506i \(0.124939\pi\)
−0.923953 + 0.382506i \(0.875061\pi\)
\(182\) −12.1703 −0.902120
\(183\) 5.39692 + 1.98183i 0.398952 + 0.146501i
\(184\) 4.73108 0.785398i 0.348780 0.0579003i
\(185\) 4.88527i 0.359172i
\(186\) 6.05031 + 2.22176i 0.443630 + 0.162908i
\(187\) 16.5863 1.21291
\(188\) 10.8399i 0.790581i
\(189\) 9.73626 + 17.2032i 0.708209 + 1.25135i
\(190\) −1.88297 −0.136605
\(191\) 22.5181 1.62935 0.814676 0.579916i \(-0.196915\pi\)
0.814676 + 0.579916i \(0.196915\pi\)
\(192\) 0.597052 1.62589i 0.0430885 0.117339i
\(193\) 12.3106 0.886134 0.443067 0.896489i \(-0.353890\pi\)
0.443067 + 0.896489i \(0.353890\pi\)
\(194\) 2.98155 0.214063
\(195\) 1.91007 5.20149i 0.136783 0.372487i
\(196\) 7.47199 0.533714
\(197\) 0.321151i 0.0228811i 0.999935 + 0.0114405i \(0.00364171\pi\)
−0.999935 + 0.0114405i \(0.996358\pi\)
\(198\) −6.76439 + 7.96840i −0.480724 + 0.566289i
\(199\) 14.6664i 1.03968i −0.854265 0.519838i \(-0.825992\pi\)
0.854265 0.519838i \(-0.174008\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) −6.02295 2.21172i −0.424826 0.156003i
\(202\) −9.15523 −0.644160
\(203\) 28.5537 2.00408
\(204\) −2.84229 + 7.74011i −0.199000 + 0.541916i
\(205\) 3.99062i 0.278717i
\(206\) −16.0594 −1.11891
\(207\) 7.38909 12.3451i 0.513577 0.858043i
\(208\) 3.19916 0.221822
\(209\) 6.56052i 0.453801i
\(210\) −2.27131 + 6.18523i −0.156735 + 0.426822i
\(211\) 12.3848 0.852604 0.426302 0.904581i \(-0.359816\pi\)
0.426302 + 0.904581i \(0.359816\pi\)
\(212\) 7.07396 0.485841
\(213\) −16.1380 5.92613i −1.10576 0.406052i
\(214\) 17.6195i 1.20444i
\(215\) 6.96125i 0.474753i
\(216\) −2.55934 4.52214i −0.174141 0.307693i
\(217\) 14.1563i 0.960992i
\(218\) −12.7316 −0.862292
\(219\) −1.90145 + 5.17803i −0.128488 + 0.349899i
\(220\) −3.48413 −0.234900
\(221\) −15.2297 −1.02446
\(222\) −2.91676 + 7.94293i −0.195760 + 0.533094i
\(223\) 5.19193 0.347677 0.173839 0.984774i \(-0.444383\pi\)
0.173839 + 0.984774i \(0.444383\pi\)
\(224\) −3.80421 −0.254179
\(225\) −2.28706 1.94149i −0.152470 0.129432i
\(226\) 9.34208i 0.621426i
\(227\) 16.7298 1.11040 0.555199 0.831718i \(-0.312642\pi\)
0.555199 + 0.831718i \(0.312642\pi\)
\(228\) −3.06151 1.12423i −0.202754 0.0744542i
\(229\) 18.2985i 1.20920i 0.796530 + 0.604599i \(0.206666\pi\)
−0.796530 + 0.604599i \(0.793334\pi\)
\(230\) 4.73108 0.785398i 0.311958 0.0517876i
\(231\) 21.5501 + 7.91354i 1.41790 + 0.520672i
\(232\) −7.50582 −0.492781
\(233\) 6.92267i 0.453519i 0.973951 + 0.226759i \(0.0728131\pi\)
−0.973951 + 0.226759i \(0.927187\pi\)
\(234\) 6.21113 7.31666i 0.406034 0.478305i
\(235\) 10.8399i 0.707117i
\(236\) 7.35646i 0.478865i
\(237\) 16.4644 + 6.04597i 1.06948 + 0.392728i
\(238\) 18.1100 1.17390
\(239\) 2.10045i 0.135867i 0.997690 + 0.0679335i \(0.0216406\pi\)
−0.997690 + 0.0679335i \(0.978359\pi\)
\(240\) 0.597052 1.62589i 0.0385396 0.104951i
\(241\) 0.0258170i 0.00166302i −1.00000 0.000831511i \(-0.999735\pi\)
1.00000 0.000831511i \(-0.000264678\pi\)
\(242\) 1.13914i 0.0732268i
\(243\) −15.3113 2.92632i −0.982222 0.187724i
\(244\) 3.31936i 0.212500i
\(245\) 7.47199 0.477368
\(246\) 2.38261 6.48833i 0.151910 0.413681i
\(247\) 6.02393i 0.383294i
\(248\) 3.72122i 0.236298i
\(249\) 7.64752 20.8257i 0.484642 1.31978i
\(250\) 1.00000i 0.0632456i
\(251\) 7.11730 0.449240 0.224620 0.974446i \(-0.427886\pi\)
0.224620 + 0.974446i \(0.427886\pi\)
\(252\) −7.38582 + 8.70044i −0.465263 + 0.548076i
\(253\) −2.73642 16.4837i −0.172038 1.03632i
\(254\) 15.6846i 0.984141i
\(255\) −2.84229 + 7.74011i −0.177991 + 0.484705i
\(256\) 1.00000 0.0625000
\(257\) 5.27667i 0.329150i 0.986365 + 0.164575i \(0.0526252\pi\)
−0.986365 + 0.164575i \(0.947375\pi\)
\(258\) 4.15623 11.3183i 0.258756 0.704644i
\(259\) 18.5846 1.15479
\(260\) 3.19916 0.198404
\(261\) −14.5725 + 17.1662i −0.902012 + 1.06256i
\(262\) −10.5503 −0.651802
\(263\) 13.6544 0.841967 0.420984 0.907068i \(-0.361685\pi\)
0.420984 + 0.907068i \(0.361685\pi\)
\(264\) −5.66482 2.08021i −0.348645 0.128028i
\(265\) 7.07396 0.434550
\(266\) 7.16322i 0.439205i
\(267\) 6.59801 17.9677i 0.403792 1.09961i
\(268\) 3.70440i 0.226282i
\(269\) 14.9128i 0.909249i −0.890683 0.454624i \(-0.849774\pi\)
0.890683 0.454624i \(-0.150226\pi\)
\(270\) −2.55934 4.52214i −0.155757 0.275209i
\(271\) −22.4734 −1.36516 −0.682580 0.730811i \(-0.739142\pi\)
−0.682580 + 0.730811i \(0.739142\pi\)
\(272\) −4.76053 −0.288650
\(273\) −19.7876 7.26629i −1.19760 0.439776i
\(274\) 16.2614i 0.982387i
\(275\) −3.48413 −0.210101
\(276\) 8.16116 + 1.54773i 0.491244 + 0.0931625i
\(277\) −25.7920 −1.54969 −0.774846 0.632150i \(-0.782173\pi\)
−0.774846 + 0.632150i \(0.782173\pi\)
\(278\) 23.3435i 1.40005i
\(279\) 8.51065 + 7.22470i 0.509519 + 0.432532i
\(280\) −3.80421 −0.227345
\(281\) 5.19176 0.309714 0.154857 0.987937i \(-0.450508\pi\)
0.154857 + 0.987937i \(0.450508\pi\)
\(282\) −6.47199 + 17.6245i −0.385401 + 1.04953i
\(283\) 6.60335i 0.392528i −0.980551 0.196264i \(-0.937119\pi\)
0.980551 0.196264i \(-0.0628810\pi\)
\(284\) 9.92565i 0.588979i
\(285\) −3.06151 1.12423i −0.181348 0.0665939i
\(286\) 11.1463i 0.659093i
\(287\) −15.1812 −0.896115
\(288\) 1.94149 2.28706i 0.114403 0.134766i
\(289\) 5.66264 0.333097
\(290\) −7.50582 −0.440757
\(291\) 4.84768 + 1.78014i 0.284176 + 0.104354i
\(292\) −3.18473 −0.186372
\(293\) 30.6756 1.79209 0.896044 0.443964i \(-0.146428\pi\)
0.896044 + 0.443964i \(0.146428\pi\)
\(294\) 12.1487 + 4.46117i 0.708524 + 0.260181i
\(295\) 7.35646i 0.428310i
\(296\) −4.88527 −0.283951
\(297\) −15.7557 + 8.91707i −0.914240 + 0.517421i
\(298\) 7.01303i 0.406254i
\(299\) 2.51261 + 15.1355i 0.145308 + 0.875308i
\(300\) 0.597052 1.62589i 0.0344708 0.0938710i
\(301\) −26.4820 −1.52640
\(302\) 14.3153i 0.823753i
\(303\) −14.8854 5.46615i −0.855145 0.314022i
\(304\) 1.88297i 0.107996i
\(305\) 3.31936i 0.190066i
\(306\) −9.24251 + 10.8876i −0.528359 + 0.622403i
\(307\) 19.3975 1.10707 0.553537 0.832825i \(-0.313278\pi\)
0.553537 + 0.832825i \(0.313278\pi\)
\(308\) 13.2543i 0.755236i
\(309\) −26.1109 9.58831i −1.48540 0.545460i
\(310\) 3.72122i 0.211351i
\(311\) 16.8790i 0.957118i −0.878055 0.478559i \(-0.841159\pi\)
0.878055 0.478559i \(-0.158841\pi\)
\(312\) 5.20149 + 1.91007i 0.294477 + 0.108136i
\(313\) 26.7256i 1.51062i −0.655367 0.755310i \(-0.727486\pi\)
0.655367 0.755310i \(-0.272514\pi\)
\(314\) −16.3884 −0.924853
\(315\) −7.38582 + 8.70044i −0.416144 + 0.490214i
\(316\) 10.1264i 0.569653i
\(317\) 7.55156i 0.424138i 0.977255 + 0.212069i \(0.0680201\pi\)
−0.977255 + 0.212069i \(0.931980\pi\)
\(318\) 11.5015 + 4.22352i 0.644972 + 0.236843i
\(319\) 26.1512i 1.46419i
\(320\) 1.00000 0.0559017
\(321\) −10.5197 + 28.6474i −0.587155 + 1.59894i
\(322\) −2.98781 17.9980i −0.166504 1.00299i
\(323\) 8.96395i 0.498768i
\(324\) −1.46126 8.88058i −0.0811810 0.493366i
\(325\) 3.19916 0.177457
\(326\) 5.26525i 0.291615i
\(327\) −20.7002 7.60143i −1.14472 0.420360i
\(328\) 3.99062 0.220345
\(329\) 41.2372 2.27348
\(330\) −5.66482 2.08021i −0.311838 0.114512i
\(331\) 25.3475 1.39323 0.696613 0.717447i \(-0.254690\pi\)
0.696613 + 0.717447i \(0.254690\pi\)
\(332\) 12.8088 0.702974
\(333\) −9.48469 + 11.1729i −0.519758 + 0.612271i
\(334\) −7.87574 −0.430941
\(335\) 3.70440i 0.202393i
\(336\) −6.18523 2.27131i −0.337432 0.123910i
\(337\) 21.0505i 1.14669i −0.819313 0.573346i \(-0.805645\pi\)
0.819313 0.573346i \(-0.194355\pi\)
\(338\) 2.76537i 0.150416i
\(339\) 5.57771 15.1892i 0.302940 0.824965i
\(340\) −4.76053 −0.258176
\(341\) 12.9652 0.702106
\(342\) −4.30647 3.65577i −0.232867 0.197681i
\(343\) 1.79555i 0.0969506i
\(344\) 6.96125 0.375326
\(345\) 8.16116 + 1.54773i 0.439382 + 0.0833271i
\(346\) 2.12595 0.114292
\(347\) 6.08253i 0.326528i 0.986582 + 0.163264i \(0.0522022\pi\)
−0.986582 + 0.163264i \(0.947798\pi\)
\(348\) −12.2037 4.48137i −0.654185 0.240227i
\(349\) 1.98670 0.106345 0.0531727 0.998585i \(-0.483067\pi\)
0.0531727 + 0.998585i \(0.483067\pi\)
\(350\) −3.80421 −0.203343
\(351\) 14.4671 8.18774i 0.772195 0.437029i
\(352\) 3.48413i 0.185705i
\(353\) 8.53950i 0.454512i 0.973835 + 0.227256i \(0.0729754\pi\)
−0.973835 + 0.227256i \(0.927025\pi\)
\(354\) 4.39219 11.9608i 0.233442 0.635711i
\(355\) 9.92565i 0.526799i
\(356\) 11.0510 0.585700
\(357\) 29.4450 + 10.8126i 1.55839 + 0.572266i
\(358\) 12.4614 0.658606
\(359\) −27.5129 −1.45207 −0.726037 0.687656i \(-0.758640\pi\)
−0.726037 + 0.687656i \(0.758640\pi\)
\(360\) 1.94149 2.28706i 0.102325 0.120538i
\(361\) 15.4544 0.813390
\(362\) −10.2922 −0.540945
\(363\) −0.680127 + 1.85212i −0.0356974 + 0.0972112i
\(364\) 12.1703i 0.637895i
\(365\) −3.18473 −0.166696
\(366\) −1.98183 + 5.39692i −0.103592 + 0.282101i
\(367\) 31.2664i 1.63209i 0.577986 + 0.816046i \(0.303839\pi\)
−0.577986 + 0.816046i \(0.696161\pi\)
\(368\) 0.785398 + 4.73108i 0.0409417 + 0.246625i
\(369\) 7.74774 9.12678i 0.403331 0.475121i
\(370\) −4.88527 −0.253973
\(371\) 26.9108i 1.39714i
\(372\) −2.22176 + 6.05031i −0.115193 + 0.313694i
\(373\) 13.5799i 0.703138i −0.936162 0.351569i \(-0.885648\pi\)
0.936162 0.351569i \(-0.114352\pi\)
\(374\) 16.5863i 0.857657i
\(375\) 0.597052 1.62589i 0.0308317 0.0839608i
\(376\) −10.8399 −0.559025
\(377\) 24.0123i 1.23670i
\(378\) −17.2032 + 9.73626i −0.884835 + 0.500779i
\(379\) 31.3374i 1.60970i −0.593482 0.804848i \(-0.702247\pi\)
0.593482 0.804848i \(-0.297753\pi\)
\(380\) 1.88297i 0.0965945i
\(381\) 9.36454 25.5015i 0.479760 1.30648i
\(382\) 22.5181i 1.15213i
\(383\) −11.1675 −0.570632 −0.285316 0.958433i \(-0.592099\pi\)
−0.285316 + 0.958433i \(0.592099\pi\)
\(384\) 1.62589 + 0.597052i 0.0829710 + 0.0304682i
\(385\) 13.2543i 0.675504i
\(386\) 12.3106i 0.626591i
\(387\) 13.5152 15.9208i 0.687015 0.809299i
\(388\) 2.98155i 0.151365i
\(389\) −12.5852 −0.638093 −0.319046 0.947739i \(-0.603363\pi\)
−0.319046 + 0.947739i \(0.603363\pi\)
\(390\) 5.20149 + 1.91007i 0.263388 + 0.0967200i
\(391\) −3.73891 22.5225i −0.189085 1.13901i
\(392\) 7.47199i 0.377393i
\(393\) −17.1537 6.29910i −0.865291 0.317748i
\(394\) −0.321151 −0.0161793
\(395\) 10.1264i 0.509513i
\(396\) −7.96840 6.76439i −0.400427 0.339923i
\(397\) 12.3539 0.620024 0.310012 0.950733i \(-0.399667\pi\)
0.310012 + 0.950733i \(0.399667\pi\)
\(398\) 14.6664 0.735162
\(399\) −4.27682 + 11.6466i −0.214109 + 0.583061i
\(400\) 1.00000 0.0500000
\(401\) 27.2453 1.36057 0.680283 0.732950i \(-0.261857\pi\)
0.680283 + 0.732950i \(0.261857\pi\)
\(402\) 2.21172 6.02295i 0.110311 0.300398i
\(403\) −11.9048 −0.593020
\(404\) 9.15523i 0.455490i
\(405\) −1.46126 8.88058i −0.0726105 0.441280i
\(406\) 28.5537i 1.41710i
\(407\) 17.0209i 0.843695i
\(408\) −7.74011 2.84229i −0.383193 0.140714i
\(409\) −27.3294 −1.35135 −0.675675 0.737200i \(-0.736148\pi\)
−0.675675 + 0.737200i \(0.736148\pi\)
\(410\) 3.99062 0.197083
\(411\) 9.70890 26.4393i 0.478905 1.30415i
\(412\) 16.0594i 0.791190i
\(413\) −27.9855 −1.37708
\(414\) 12.3451 + 7.38909i 0.606728 + 0.363154i
\(415\) 12.8088 0.628759
\(416\) 3.19916i 0.156852i
\(417\) 13.9373 37.9540i 0.682511 1.85862i
\(418\) −6.56052 −0.320885
\(419\) 15.1668 0.740949 0.370474 0.928843i \(-0.379195\pi\)
0.370474 + 0.928843i \(0.379195\pi\)
\(420\) −6.18523 2.27131i −0.301809 0.110829i
\(421\) 34.7728i 1.69472i −0.531018 0.847361i \(-0.678190\pi\)
0.531018 0.847361i \(-0.321810\pi\)
\(422\) 12.3848i 0.602882i
\(423\) −21.0455 + 24.7915i −1.02327 + 1.20540i
\(424\) 7.07396i 0.343542i
\(425\) −4.76053 −0.230920
\(426\) 5.92613 16.1380i 0.287122 0.781891i
\(427\) 12.6275 0.611088
\(428\) −17.6195 −0.851669
\(429\) 6.65491 18.1227i 0.321302 0.874970i
\(430\) 6.96125 0.335701
\(431\) −5.86936 −0.282717 −0.141358 0.989958i \(-0.545147\pi\)
−0.141358 + 0.989958i \(0.545147\pi\)
\(432\) 4.52214 2.55934i 0.217572 0.123136i
\(433\) 30.4782i 1.46469i 0.680935 + 0.732344i \(0.261574\pi\)
−0.680935 + 0.732344i \(0.738426\pi\)
\(434\) 14.1563 0.679524
\(435\) −12.2037 4.48137i −0.585121 0.214865i
\(436\) 12.7316i 0.609733i
\(437\) 8.90850 1.47888i 0.426152 0.0707446i
\(438\) −5.17803 1.90145i −0.247416 0.0908548i
\(439\) 20.8965 0.997334 0.498667 0.866794i \(-0.333823\pi\)
0.498667 + 0.866794i \(0.333823\pi\)
\(440\) 3.48413i 0.166099i
\(441\) 17.0889 + 14.5068i 0.813756 + 0.690799i
\(442\) 15.2297i 0.724403i
\(443\) 38.9828i 1.85213i 0.377365 + 0.926065i \(0.376830\pi\)
−0.377365 + 0.926065i \(0.623170\pi\)
\(444\) −7.94293 2.91676i −0.376955 0.138423i
\(445\) 11.0510 0.523866
\(446\) 5.19193i 0.245845i
\(447\) −4.18714 + 11.4024i −0.198045 + 0.539317i
\(448\) 3.80421i 0.179732i
\(449\) 8.98085i 0.423832i −0.977288 0.211916i \(-0.932030\pi\)
0.977288 0.211916i \(-0.0679704\pi\)
\(450\) 1.94149 2.28706i 0.0915226 0.107813i
\(451\) 13.9038i 0.654706i
\(452\) 9.34208 0.439414
\(453\) 8.54699 23.2752i 0.401572 1.09356i
\(454\) 16.7298i 0.785170i
\(455\) 12.1703i 0.570551i
\(456\) 1.12423 3.06151i 0.0526471 0.143369i
\(457\) 5.68472i 0.265920i −0.991121 0.132960i \(-0.957552\pi\)
0.991121 0.132960i \(-0.0424482\pi\)
\(458\) −18.2985 −0.855031
\(459\) −21.5278 + 12.1838i −1.00483 + 0.568692i
\(460\) 0.785398 + 4.73108i 0.0366194 + 0.220588i
\(461\) 23.4737i 1.09328i 0.837368 + 0.546640i \(0.184093\pi\)
−0.837368 + 0.546640i \(0.815907\pi\)
\(462\) −7.91354 + 21.5501i −0.368171 + 1.00260i
\(463\) −41.4142 −1.92468 −0.962339 0.271851i \(-0.912364\pi\)
−0.962339 + 0.271851i \(0.912364\pi\)
\(464\) 7.50582i 0.348449i
\(465\) −2.22176 + 6.05031i −0.103032 + 0.280576i
\(466\) −6.92267 −0.320686
\(467\) 28.5266 1.32006 0.660028 0.751241i \(-0.270545\pi\)
0.660028 + 0.751241i \(0.270545\pi\)
\(468\) 7.31666 + 6.21113i 0.338213 + 0.287109i
\(469\) −14.0923 −0.650722
\(470\) −10.8399 −0.500007
\(471\) −26.6458 9.78475i −1.22778 0.450858i
\(472\) 7.35646 0.338609
\(473\) 24.2539i 1.11519i
\(474\) −6.04597 + 16.4644i −0.277701 + 0.756235i
\(475\) 1.88297i 0.0863967i
\(476\) 18.1100i 0.830072i
\(477\) 16.1785 + 13.7340i 0.740765 + 0.628836i
\(478\) −2.10045 −0.0960724
\(479\) 3.94290 0.180155 0.0900777 0.995935i \(-0.471288\pi\)
0.0900777 + 0.995935i \(0.471288\pi\)
\(480\) 1.62589 + 0.597052i 0.0742115 + 0.0272516i
\(481\) 15.6288i 0.712610i
\(482\) 0.0258170 0.00117593
\(483\) 5.88789 31.0467i 0.267908 1.41268i
\(484\) −1.13914 −0.0517792
\(485\) 2.98155i 0.135385i
\(486\) 2.92632 15.3113i 0.132741 0.694536i
\(487\) 1.02454 0.0464262 0.0232131 0.999731i \(-0.492610\pi\)
0.0232131 + 0.999731i \(0.492610\pi\)
\(488\) −3.31936 −0.150260
\(489\) −3.14363 + 8.56074i −0.142160 + 0.387130i
\(490\) 7.47199i 0.337550i
\(491\) 12.3413i 0.556954i −0.960443 0.278477i \(-0.910170\pi\)
0.960443 0.278477i \(-0.0898296\pi\)
\(492\) 6.48833 + 2.38261i 0.292516 + 0.107416i
\(493\) 35.7317i 1.60927i
\(494\) 6.02393 0.271030
\(495\) −7.96840 6.76439i −0.358153 0.304037i
\(496\) −3.72122 −0.167088
\(497\) −37.7592 −1.69373
\(498\) 20.8257 + 7.64752i 0.933224 + 0.342694i
\(499\) −29.3987 −1.31607 −0.658033 0.752989i \(-0.728611\pi\)
−0.658033 + 0.752989i \(0.728611\pi\)
\(500\) 1.00000 0.0447214
\(501\) −12.8051 4.70223i −0.572090 0.210080i
\(502\) 7.11730i 0.317661i
\(503\) −27.8709 −1.24270 −0.621350 0.783533i \(-0.713416\pi\)
−0.621350 + 0.783533i \(0.713416\pi\)
\(504\) −8.70044 7.38582i −0.387548 0.328990i
\(505\) 9.15523i 0.407402i
\(506\) 16.4837 2.73642i 0.732790 0.121649i
\(507\) 1.65107 4.49620i 0.0733267 0.199683i
\(508\) 15.6846 0.695892
\(509\) 33.5429i 1.48676i 0.668868 + 0.743381i \(0.266779\pi\)
−0.668868 + 0.743381i \(0.733221\pi\)
\(510\) −7.74011 2.84229i −0.342738 0.125859i
\(511\) 12.1154i 0.535952i
\(512\) 1.00000i 0.0441942i
\(513\) −4.81917 8.51507i −0.212772 0.375950i
\(514\) −5.27667 −0.232744
\(515\) 16.0594i 0.707662i
\(516\) 11.3183 + 4.15623i 0.498258 + 0.182968i
\(517\) 37.7676i 1.66102i
\(518\) 18.5846i 0.816559i
\(519\) 3.45657 + 1.26930i 0.151727 + 0.0557163i
\(520\) 3.19916i 0.140292i
\(521\) 4.78488 0.209629 0.104815 0.994492i \(-0.466575\pi\)
0.104815 + 0.994492i \(0.466575\pi\)
\(522\) −17.1662 14.5725i −0.751346 0.637819i
\(523\) 16.7160i 0.730939i −0.930823 0.365470i \(-0.880908\pi\)
0.930823 0.365470i \(-0.119092\pi\)
\(524\) 10.5503i 0.460894i
\(525\) −6.18523 2.27131i −0.269946 0.0991281i
\(526\) 13.6544i 0.595361i
\(527\) 17.7150 0.771677
\(528\) 2.08021 5.66482i 0.0905294 0.246530i
\(529\) −21.7663 + 7.43156i −0.946361 + 0.323111i
\(530\) 7.07396i 0.307273i
\(531\) 14.2825 16.8247i 0.619807 0.730128i
\(532\) −7.16322 −0.310565
\(533\) 12.7666i 0.552985i
\(534\) 17.9677 + 6.59801i 0.777538 + 0.285524i
\(535\) −17.6195 −0.761756
\(536\) 3.70440 0.160006
\(537\) 20.2609 + 7.44011i 0.874323 + 0.321064i
\(538\) 14.9128 0.642936
\(539\) 26.0334 1.12134
\(540\) 4.52214 2.55934i 0.194602 0.110136i
\(541\) −16.8464 −0.724284 −0.362142 0.932123i \(-0.617954\pi\)
−0.362142 + 0.932123i \(0.617954\pi\)
\(542\) 22.4734i 0.965314i
\(543\) −16.7340 6.14497i −0.718124 0.263706i
\(544\) 4.76053i 0.204106i
\(545\) 12.7316i 0.545361i
\(546\) 7.26629 19.7876i 0.310968 0.846829i
\(547\) 17.5645 0.751005 0.375503 0.926821i \(-0.377470\pi\)
0.375503 + 0.926821i \(0.377470\pi\)
\(548\) 16.2614 0.694652
\(549\) −6.44449 + 7.59156i −0.275044 + 0.324000i
\(550\) 3.48413i 0.148564i
\(551\) −14.1333 −0.602097
\(552\) −1.54773 + 8.16116i −0.0658759 + 0.347362i
\(553\) 38.5228 1.63816
\(554\) 25.7920i 1.09580i
\(555\) −7.94293 2.91676i −0.337158 0.123810i
\(556\) 23.3435 0.989984
\(557\) 6.58788 0.279137 0.139569 0.990212i \(-0.455428\pi\)
0.139569 + 0.990212i \(0.455428\pi\)
\(558\) −7.22470 + 8.51065i −0.305846 + 0.360284i
\(559\) 22.2702i 0.941928i
\(560\) 3.80421i 0.160757i
\(561\) −9.90288 + 26.9675i −0.418100 + 1.13857i
\(562\) 5.19176i 0.219001i
\(563\) 32.6960 1.37797 0.688987 0.724774i \(-0.258056\pi\)
0.688987 + 0.724774i \(0.258056\pi\)
\(564\) −17.6245 6.47199i −0.742126 0.272520i
\(565\) 9.34208 0.393024
\(566\) 6.60335 0.277560
\(567\) −33.7836 + 5.55893i −1.41878 + 0.233453i
\(568\) 9.92565 0.416471
\(569\) 0.358940 0.0150476 0.00752378 0.999972i \(-0.497605\pi\)
0.00752378 + 0.999972i \(0.497605\pi\)
\(570\) 1.12423 3.06151i 0.0470890 0.128233i
\(571\) 32.0526i 1.34136i 0.741747 + 0.670680i \(0.233998\pi\)
−0.741747 + 0.670680i \(0.766002\pi\)
\(572\) 11.1463 0.466049
\(573\) −13.4445 + 36.6120i −0.561651 + 1.52949i
\(574\) 15.1812i 0.633649i
\(575\) 0.785398 + 4.73108i 0.0327533 + 0.197300i
\(576\) 2.28706 + 1.94149i 0.0952940 + 0.0808953i
\(577\) 4.12555 0.171749 0.0858745 0.996306i \(-0.472632\pi\)
0.0858745 + 0.996306i \(0.472632\pi\)
\(578\) 5.66264i 0.235535i
\(579\) −7.35005 + 20.0157i −0.305458 + 0.831822i
\(580\) 7.50582i 0.311662i
\(581\) 48.7273i 2.02155i
\(582\) −1.78014 + 4.84768i −0.0737892 + 0.200943i
\(583\) 24.6466 1.02076
\(584\) 3.18473i 0.131785i
\(585\) 7.31666 + 6.21113i 0.302507 + 0.256799i
\(586\) 30.6756i 1.26720i
\(587\) 41.6293i 1.71822i 0.511787 + 0.859112i \(0.328984\pi\)
−0.511787 + 0.859112i \(0.671016\pi\)
\(588\) −4.46117 + 12.1487i −0.183976 + 0.501002i
\(589\) 7.00696i 0.288717i
\(590\) 7.35646 0.302861
\(591\) −0.522157 0.191744i −0.0214787 0.00788729i
\(592\) 4.88527i 0.200783i
\(593\) 7.96907i 0.327250i −0.986523 0.163625i \(-0.947681\pi\)
0.986523 0.163625i \(-0.0523188\pi\)
\(594\) −8.91707 15.7557i −0.365872 0.646465i
\(595\) 18.1100i 0.742439i
\(596\) −7.01303 −0.287265
\(597\) 23.8461 + 8.75663i 0.975955 + 0.358385i
\(598\) −15.1355 + 2.51261i −0.618936 + 0.102748i
\(599\) 18.0460i 0.737338i 0.929561 + 0.368669i \(0.120186\pi\)
−0.929561 + 0.368669i \(0.879814\pi\)
\(600\) 1.62589 + 0.597052i 0.0663768 + 0.0243746i
\(601\) −14.6307 −0.596800 −0.298400 0.954441i \(-0.596453\pi\)
−0.298400 + 0.954441i \(0.596453\pi\)
\(602\) 26.4820i 1.07933i
\(603\) 7.19204 8.47217i 0.292882 0.345013i
\(604\) 14.3153 0.582481
\(605\) −1.13914 −0.0463127
\(606\) 5.46615 14.8854i 0.222047 0.604679i
\(607\) −6.64798 −0.269833 −0.134917 0.990857i \(-0.543077\pi\)
−0.134917 + 0.990857i \(0.543077\pi\)
\(608\) 1.88297 0.0763647
\(609\) −17.0481 + 46.4253i −0.690822 + 1.88125i
\(610\) −3.31936 −0.134397
\(611\) 34.6786i 1.40295i
\(612\) −10.8876 9.24251i −0.440105 0.373606i
\(613\) 3.79751i 0.153380i 0.997055 + 0.0766899i \(0.0244351\pi\)
−0.997055 + 0.0766899i \(0.975565\pi\)
\(614\) 19.3975i 0.782819i
\(615\) 6.48833 + 2.38261i 0.261635 + 0.0960761i
\(616\) −13.2543 −0.534033
\(617\) 10.0968 0.406483 0.203242 0.979129i \(-0.434852\pi\)
0.203242 + 0.979129i \(0.434852\pi\)
\(618\) 9.58831 26.1109i 0.385698 1.05033i
\(619\) 19.8519i 0.797917i 0.916969 + 0.398959i \(0.130628\pi\)
−0.916969 + 0.398959i \(0.869372\pi\)
\(620\) −3.72122 −0.149448
\(621\) 15.6601 + 19.3845i 0.628420 + 0.777875i
\(622\) 16.8790 0.676785
\(623\) 42.0402i 1.68430i
\(624\) −1.91007 + 5.20149i −0.0764638 + 0.208226i
\(625\) 1.00000 0.0400000
\(626\) 26.7256 1.06817
\(627\) −10.6667 3.91697i −0.425987 0.156429i
\(628\) 16.3884i 0.653970i
\(629\) 23.2565i 0.927296i
\(630\) −8.70044 7.38582i −0.346634 0.294258i
\(631\) 32.8990i 1.30969i 0.755764 + 0.654845i \(0.227266\pi\)
−0.755764 + 0.654845i \(0.772734\pi\)
\(632\) −10.1264 −0.402805
\(633\) −7.39437 + 20.1363i −0.293900 + 0.800348i
\(634\) −7.55156 −0.299911
\(635\) 15.6846 0.622425
\(636\) −4.22352 + 11.5015i −0.167474 + 0.456064i
\(637\) −23.9041 −0.947115
\(638\) −26.1512 −1.03534
\(639\) 19.2705 22.7005i 0.762330 0.898019i
\(640\) 1.00000i 0.0395285i
\(641\) −3.24280 −0.128083 −0.0640415 0.997947i \(-0.520399\pi\)
−0.0640415 + 0.997947i \(0.520399\pi\)
\(642\) −28.6474 10.5197i −1.13062 0.415181i
\(643\) 29.2876i 1.15499i 0.816395 + 0.577494i \(0.195969\pi\)
−0.816395 + 0.577494i \(0.804031\pi\)
\(644\) 17.9980 2.98781i 0.709221 0.117736i
\(645\) 11.3183 + 4.15623i 0.445656 + 0.163651i
\(646\) −8.96395 −0.352682
\(647\) 1.01376i 0.0398551i −0.999801 0.0199276i \(-0.993656\pi\)
0.999801 0.0199276i \(-0.00634356\pi\)
\(648\) 8.88058 1.46126i 0.348862 0.0574037i
\(649\) 25.6309i 1.00610i
\(650\) 3.19916i 0.125481i
\(651\) 23.0166 + 8.45205i 0.902093 + 0.331262i
\(652\) −5.26525 −0.206203
\(653\) 1.94489i 0.0761093i 0.999276 + 0.0380546i \(0.0121161\pi\)
−0.999276 + 0.0380546i \(0.987884\pi\)
\(654\) 7.60143 20.7002i 0.297239 0.809442i
\(655\) 10.5503i 0.412236i
\(656\) 3.99062i 0.155808i
\(657\) −7.28365 6.18311i −0.284162 0.241226i
\(658\) 41.2372i 1.60759i
\(659\) −40.4721 −1.57657 −0.788285 0.615310i \(-0.789031\pi\)
−0.788285 + 0.615310i \(0.789031\pi\)
\(660\) 2.08021 5.66482i 0.0809719 0.220503i
\(661\) 18.3138i 0.712324i 0.934424 + 0.356162i \(0.115915\pi\)
−0.934424 + 0.356162i \(0.884085\pi\)
\(662\) 25.3475i 0.985159i
\(663\) 9.09293 24.7619i 0.353140 0.961671i
\(664\) 12.8088i 0.497078i
\(665\) −7.16322 −0.277778
\(666\) −11.1729 9.48469i −0.432941 0.367524i
\(667\) 35.5107 5.89505i 1.37498 0.228257i
\(668\) 7.87574i 0.304722i
\(669\) −3.09985 + 8.44152i −0.119847 + 0.326368i
\(670\) 3.70440 0.143113
\(671\) 11.5651i 0.446464i
\(672\) 2.27131 6.18523i 0.0876177 0.238601i
\(673\) 31.8250 1.22676 0.613381 0.789787i \(-0.289809\pi\)
0.613381 + 0.789787i \(0.289809\pi\)
\(674\) 21.0505 0.810834
\(675\) 4.52214 2.55934i 0.174057 0.0985091i
\(676\) 2.76537 0.106360
\(677\) 18.5947 0.714654 0.357327 0.933979i \(-0.383688\pi\)
0.357327 + 0.933979i \(0.383688\pi\)
\(678\) 15.1892 + 5.57771i 0.583339 + 0.214211i
\(679\) 11.3424 0.435282
\(680\) 4.76053i 0.182558i
\(681\) −9.98859 + 27.2009i −0.382763 + 1.04234i
\(682\) 12.9652i 0.496464i
\(683\) 12.1437i 0.464667i 0.972636 + 0.232334i \(0.0746361\pi\)
−0.972636 + 0.232334i \(0.925364\pi\)
\(684\) 3.65577 4.30647i 0.139782 0.164662i
\(685\) 16.2614 0.621316
\(686\) 1.79555 0.0685544
\(687\) −29.7514 10.9251i −1.13509 0.416820i
\(688\) 6.96125i 0.265395i
\(689\) −22.6307 −0.862162
\(690\) −1.54773 + 8.16116i −0.0589212 + 0.310690i
\(691\) −33.6060 −1.27843 −0.639217 0.769027i \(-0.720741\pi\)
−0.639217 + 0.769027i \(0.720741\pi\)
\(692\) 2.12595i 0.0808165i
\(693\) −25.7331 + 30.3134i −0.977521 + 1.15151i
\(694\) −6.08253 −0.230890
\(695\) 23.3435 0.885469
\(696\) 4.48137 12.2037i 0.169866 0.462579i
\(697\) 18.9975i 0.719581i
\(698\) 1.98670i 0.0751975i
\(699\) −11.2555 4.13319i −0.425723 0.156332i
\(700\) 3.80421i 0.143786i
\(701\) −36.0032 −1.35982 −0.679911 0.733295i \(-0.737982\pi\)
−0.679911 + 0.733295i \(0.737982\pi\)
\(702\) 8.18774 + 14.4671i 0.309026 + 0.546024i
\(703\) −9.19883 −0.346941
\(704\) 3.48413 0.131313
\(705\) −17.6245 6.47199i −0.663778 0.243749i
\(706\) −8.53950 −0.321388
\(707\) −34.8284 −1.30986
\(708\) 11.9608 + 4.39219i 0.449515 + 0.165069i
\(709\) 37.0502i 1.39145i −0.718308 0.695725i \(-0.755083\pi\)
0.718308 0.695725i \(-0.244917\pi\)
\(710\) 9.92565 0.372503
\(711\) −19.6602 + 23.1596i −0.737316 + 0.868552i
\(712\) 11.0510i 0.414153i
\(713\) −2.92264 17.6054i −0.109454 0.659328i
\(714\) −10.8126 + 29.4450i −0.404653 + 1.10195i
\(715\) 11.1463 0.416847
\(716\) 12.4614i 0.465704i
\(717\) −3.41511 1.25408i −0.127540 0.0468345i
\(718\) 27.5129i 1.02677i
\(719\) 22.1798i 0.827167i 0.910466 + 0.413583i \(0.135723\pi\)
−0.910466 + 0.413583i \(0.864277\pi\)
\(720\) 2.28706 + 1.94149i 0.0852336 + 0.0723549i
\(721\) −61.0933 −2.27523
\(722\) 15.4544i 0.575154i
\(723\) 0.0419757 + 0.0154141i 0.00156109 + 0.000573257i
\(724\) 10.2922i 0.382506i
\(725\) 7.50582i 0.278759i
\(726\) −1.85212 0.680127i −0.0687387 0.0252419i
\(727\) 25.7337i 0.954410i 0.878792 + 0.477205i \(0.158350\pi\)
−0.878792 + 0.477205i \(0.841650\pi\)
\(728\) 12.1703 0.451060
\(729\) 13.8995 23.1474i 0.514798 0.857311i
\(730\) 3.18473i 0.117872i
\(731\) 33.1392i 1.22570i
\(732\) −5.39692 1.98183i −0.199476 0.0732505i
\(733\) 29.9581i 1.10653i 0.833006 + 0.553264i \(0.186618\pi\)
−0.833006 + 0.553264i \(0.813382\pi\)
\(734\) −31.2664 −1.15406
\(735\) −4.46117 + 12.1487i −0.164553 + 0.448110i
\(736\) −4.73108 + 0.785398i −0.174390 + 0.0289501i
\(737\) 12.9066i 0.475420i
\(738\) 9.12678 + 7.74774i 0.335961 + 0.285198i
\(739\) −5.95900 −0.219206 −0.109603 0.993975i \(-0.534958\pi\)
−0.109603 + 0.993975i \(0.534958\pi\)
\(740\) 4.88527i 0.179586i
\(741\) 9.79427 + 3.59660i 0.359802 + 0.132125i
\(742\) 26.9108 0.987926
\(743\) 20.9476 0.768494 0.384247 0.923230i \(-0.374461\pi\)
0.384247 + 0.923230i \(0.374461\pi\)
\(744\) −6.05031 2.22176i −0.221815 0.0814539i
\(745\) −7.01303 −0.256937
\(746\) 13.5799 0.497194
\(747\) 29.2944 + 24.8681i 1.07183 + 0.909877i
\(748\) −16.5863 −0.606455
\(749\) 67.0281i 2.44915i
\(750\) 1.62589 + 0.597052i 0.0593692 + 0.0218013i
\(751\) 30.8923i 1.12727i −0.826022 0.563637i \(-0.809402\pi\)
0.826022 0.563637i \(-0.190598\pi\)
\(752\) 10.8399i 0.395291i
\(753\) −4.24940 + 11.5720i −0.154857 + 0.421706i
\(754\) 24.0123 0.874477
\(755\) 14.3153 0.520987
\(756\) −9.73626 17.2032i −0.354104 0.625673i
\(757\) 15.9263i 0.578851i −0.957200 0.289426i \(-0.906536\pi\)
0.957200 0.289426i \(-0.0934643\pi\)
\(758\) 31.3374 1.13823
\(759\) 28.4345 + 5.39250i 1.03211 + 0.195735i
\(760\) 1.88297 0.0683026
\(761\) 23.2817i 0.843960i −0.906605 0.421980i \(-0.861335\pi\)
0.906605 0.421980i \(-0.138665\pi\)
\(762\) 25.5015 + 9.36454i 0.923822 + 0.339241i
\(763\) −48.4336 −1.75341
\(764\) −22.5181 −0.814676
\(765\) −10.8876 9.24251i −0.393642 0.334163i
\(766\) 11.1675i 0.403498i
\(767\) 23.5345i 0.849782i
\(768\) −0.597052 + 1.62589i −0.0215443 + 0.0586694i
\(769\) 33.0800i 1.19289i −0.802653 0.596447i \(-0.796579\pi\)
0.802653 0.596447i \(-0.203421\pi\)
\(770\) −13.2543 −0.477653
\(771\) −8.57931 3.15045i −0.308976 0.113461i
\(772\) −12.3106 −0.443067
\(773\) 37.7407 1.35744 0.678720 0.734397i \(-0.262535\pi\)
0.678720 + 0.734397i \(0.262535\pi\)
\(774\) 15.9208 + 13.5152i 0.572261 + 0.485793i
\(775\) −3.72122 −0.133670
\(776\) −2.98155 −0.107031
\(777\) −11.0960 + 30.2165i −0.398066 + 1.08401i
\(778\) 12.5852i 0.451200i
\(779\) 7.51424 0.269225
\(780\) −1.91007 + 5.20149i −0.0683913 + 0.186243i
\(781\) 34.5822i 1.23745i
\(782\) 22.5225 3.73891i 0.805402 0.133703i
\(783\) −19.2100 33.9424i −0.686508 1.21300i
\(784\) −7.47199 −0.266857
\(785\)